id	sid	tid	token	lemma	pos
ejpam-164	1	1	4_noiri.dvi	4_noiri.dvi	PROPN
ejpam-164	1	2	european	european	PROPN
ejpam-164	1	3	journal	journal	PROPN
ejpam-164	1	4	of	of	ADP
ejpam-164	1	5	pure	pure	ADJ
ejpam-164	1	6	and	and	CCONJ
ejpam-164	1	7	applied	apply	VERB
ejpam-164	1	8	mathematics	mathematic	NOUN
ejpam-164	1	9	vol	vol	NOUN
ejpam-164	1	10	.	.	PROPN
ejpam-164	2	1	2	2	NUM
ejpam-164	2	2	,	,	PUNCT
ejpam-164	2	3	no	no	INTJ
ejpam-164	2	4	.	.	NOUN
ejpam-164	2	5	1	1	NUM
ejpam-164	2	6	,	,	PUNCT
ejpam-164	2	7	2009	2009	NUM
ejpam-164	2	8	,	,	PUNCT
ejpam-164	2	9	(	(	PUNCT
ejpam-164	2	10	73	73	NUM
ejpam-164	2	11	-	-	SYM
ejpam-164	2	12	84	84	NUM
ejpam-164	2	13	)	)	PUNCT
ejpam-164	2	14	issn	issn	PROPN
ejpam-164	2	15	1307	1307	NUM
ejpam-164	2	16	-	-	SYM
ejpam-164	2	17	5543	5543	NUM
ejpam-164	2	18	–	–	PUNCT
ejpam-164	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-164	2	20	weak	weak	ADJ
ejpam-164	2	21	forms	form	NOUN
ejpam-164	2	22	of	of	ADP
ejpam-164	2	23	ω	ω	VERB
ejpam-164	2	24	-	-	ADJ
ejpam-164	2	25	open	open	ADJ
ejpam-164	2	26	sets	set	NOUN
ejpam-164	2	27	and	and	CCONJ
ejpam-164	2	28	decompositions	decomposition	NOUN
ejpam-164	2	29	of	of	ADP
ejpam-164	2	30	continuity	continuity	NOUN
ejpam-164	2	31	takashi	takashi	PROPN
ejpam-164	2	32	noiri1	noiri1	PROPN
ejpam-164	2	33	,	,	PUNCT
ejpam-164	2	34	ahmad	ahmad	PROPN
ejpam-164	2	35	al	al	PROPN
ejpam-164	2	36	-	-	PUNCT
ejpam-164	2	37	omari2∗	omari2∗	PROPN
ejpam-164	2	38	and	and	CCONJ
ejpam-164	2	39	mohd	mohd	PROPN
ejpam-164	2	40	.	.	PUNCT
ejpam-164	3	1	salmi	salmi	PROPN
ejpam-164	3	2	md	md	PROPN
ejpam-164	3	3	.	.	PUNCT
ejpam-164	4	1	noorani3	noorani3	PROPN
ejpam-164	4	2	1	1	NUM
ejpam-164	4	3	2949	2949	NUM
ejpam-164	4	4	-	-	SYM
ejpam-164	4	5	1	1	NUM
ejpam-164	4	6	shiokita	shiokita	NOUN
ejpam-164	4	7	-	-	PUNCT
ejpam-164	4	8	cho	cho	ADJ
ejpam-164	4	9	,	,	PUNCT
ejpam-164	4	10	hinagu	hinagu	ADJ
ejpam-164	4	11	,	,	PUNCT
ejpam-164	4	12	yatsushiro	yatsushiro	PROPN
ejpam-164	4	13	-	-	PUNCT
ejpam-164	4	14	shi	shi	PROPN
ejpam-164	4	15	,	,	PUNCT
ejpam-164	4	16	kumamoto	kumamoto	PROPN
ejpam-164	4	17	-	-	PUNCT
ejpam-164	4	18	ken	ken	PROPN
ejpam-164	4	19	,	,	PUNCT
ejpam-164	4	20	869	869	NUM
ejpam-164	4	21	-	-	SYM
ejpam-164	4	22	5142	5142	NUM
ejpam-164	4	23	japan	japan	PROPN
ejpam-164	4	24	2department	2department	NUM
ejpam-164	4	25	of	of	ADP
ejpam-164	4	26	mathematics	mathematic	NOUN
ejpam-164	4	27	,	,	PUNCT
ejpam-164	4	28	faculty	faculty	NOUN
ejpam-164	4	29	of	of	ADP
ejpam-164	4	30	science	science	NOUN
ejpam-164	4	31	,	,	PUNCT
ejpam-164	4	32	mu’tah	mu’tah	PROPN
ejpam-164	4	33	university	university	NOUN
ejpam-164	4	34	,	,	PUNCT
ejpam-164	4	35	p.o.box	p.o.box	PROPN
ejpam-164	4	36	7	7	NUM
ejpam-164	4	37	,	,	PUNCT
ejpam-164	4	38	karak	karak	PROPN
ejpam-164	4	39	-	-	PUNCT
ejpam-164	4	40	jordan	jordan	PROPN
ejpam-164	4	41	3school	3school	PROPN
ejpam-164	4	42	of	of	ADP
ejpam-164	4	43	mathematical	mathematical	ADJ
ejpam-164	4	44	sciences	science	NOUN
ejpam-164	4	45	,	,	PUNCT
ejpam-164	4	46	faculty	faculty	NOUN
ejpam-164	4	47	of	of	ADP
ejpam-164	4	48	science	science	NOUN
ejpam-164	4	49	and	and	CCONJ
ejpam-164	4	50	technology	technology	NOUN
ejpam-164	4	51	,	,	PUNCT
ejpam-164	4	52	universiti	universiti	PROPN
ejpam-164	4	53	kebangsaan	kebangsaan	PROPN
ejpam-164	4	54	malaysia	malaysia	PROPN
ejpam-164	4	55	,	,	PUNCT
ejpam-164	4	56	43600	43600	NUM
ejpam-164	4	57	ukm	ukm	PROPN
ejpam-164	4	58	bangi	bangi	PROPN
ejpam-164	4	59	,	,	PUNCT
ejpam-164	4	60	selangor	selangor	PROPN
ejpam-164	4	61	,	,	PUNCT
ejpam-164	4	62	malaysia	malaysia	PROPN
ejpam-164	4	63	abstract	abstract	NOUN
ejpam-164	4	64	.	.	PUNCT
ejpam-164	5	1	in	in	ADP
ejpam-164	5	2	this	this	DET
ejpam-164	5	3	paper	paper	NOUN
ejpam-164	5	4	,	,	PUNCT
ejpam-164	5	5	we	we	PRON
ejpam-164	5	6	introduce	introduce	VERB
ejpam-164	5	7	some	some	DET
ejpam-164	5	8	generalizations	generalization	NOUN
ejpam-164	5	9	of	of	ADP
ejpam-164	5	10	ω	ω	VERB
ejpam-164	5	11	-	-	ADJ
ejpam-164	5	12	open	open	ADJ
ejpam-164	5	13	sets	set	NOUN
ejpam-164	5	14	and	and	CCONJ
ejpam-164	5	15	investigate	investigate	VERB
ejpam-164	5	16	some	some	DET
ejpam-164	5	17	properties	property	NOUN
ejpam-164	5	18	of	of	ADP
ejpam-164	5	19	the	the	DET
ejpam-164	5	20	sets	set	NOUN
ejpam-164	5	21	.	.	PUNCT
ejpam-164	6	1	moreover	moreover	ADV
ejpam-164	6	2	,	,	PUNCT
ejpam-164	6	3	we	we	PRON
ejpam-164	6	4	use	use	VERB
ejpam-164	6	5	them	they	PRON
ejpam-164	6	6	to	to	PART
ejpam-164	6	7	obtain	obtain	VERB
ejpam-164	6	8	decompositions	decomposition	NOUN
ejpam-164	6	9	of	of	ADP
ejpam-164	6	10	continuity	continuity	NOUN
ejpam-164	6	11	.	.	PUNCT
ejpam-164	7	1	ams	am	NOUN
ejpam-164	7	2	subject	subject	ADJ
ejpam-164	7	3	classifications	classification	NOUN
ejpam-164	7	4	:	:	PUNCT
ejpam-164	7	5	54c05	54c05	NUM
ejpam-164	7	6	,	,	PUNCT
ejpam-164	7	7	54c08	54c08	NUM
ejpam-164	7	8	,	,	PUNCT
ejpam-164	7	9	54c10	54c10	NUM
ejpam-164	7	10	key	key	ADJ
ejpam-164	7	11	words	word	NOUN
ejpam-164	7	12	:	:	PUNCT
ejpam-164	7	13	b	b	X
ejpam-164	7	14	-	-	PUNCT
ejpam-164	7	15	open	open	ADJ
ejpam-164	7	16	,	,	PUNCT
ejpam-164	7	17	ω	ω	NOUN
ejpam-164	7	18	-	-	NOUN
ejpam-164	7	19	open	open	ADJ
ejpam-164	7	20	,	,	PUNCT
ejpam-164	7	21	pre	pre	ADJ
ejpam-164	7	22	-	-	ADJ
ejpam-164	7	23	ω	ω	VERB
ejpam-164	7	24	-	-	ADJ
ejpam-164	7	25	open	open	ADJ
ejpam-164	7	26	,	,	PUNCT
ejpam-164	7	27	α	α	NOUN
ejpam-164	7	28	-	-	PUNCT
ejpam-164	7	29	ω	ω	NOUN
ejpam-164	7	30	-	-	ADJ
ejpam-164	7	31	open	open	ADJ
ejpam-164	7	32	,	,	PUNCT
ejpam-164	7	33	decomposition	decomposition	NOUN
ejpam-164	7	34	of	of	ADP
ejpam-164	7	35	continuity	continuity	NOUN
ejpam-164	7	36	.	.	PUNCT
ejpam-164	8	1	1	1	X
ejpam-164	8	2	.	.	X
ejpam-164	8	3	introduction	introduction	NOUN
ejpam-164	8	4	throughout	throughout	ADP
ejpam-164	8	5	this	this	DET
ejpam-164	8	6	paper	paper	NOUN
ejpam-164	8	7	,	,	PUNCT
ejpam-164	8	8	(	(	PUNCT
ejpam-164	8	9	x	x	X
ejpam-164	8	10	,	,	PUNCT
ejpam-164	8	11	τ	τ	PROPN
ejpam-164	8	12	)	)	PUNCT
ejpam-164	8	13	and	and	CCONJ
ejpam-164	8	14	(	(	PUNCT
ejpam-164	8	15	y	y	PROPN
ejpam-164	8	16	,	,	PUNCT
ejpam-164	8	17	σ	σ	PROPN
ejpam-164	8	18	)	)	PUNCT
ejpam-164	8	19	stand	stand	NOUN
ejpam-164	8	20	for	for	ADP
ejpam-164	8	21	topological	topological	ADJ
ejpam-164	8	22	spaces	space	NOUN
ejpam-164	8	23	with	with	ADP
ejpam-164	8	24	no	no	DET
ejpam-164	8	25	separation	separation	NOUN
ejpam-164	8	26	axioms	axiom	NOUN
ejpam-164	8	27	assumed	assume	VERB
ejpam-164	8	28	unless	unless	SCONJ
ejpam-164	8	29	otherwise	otherwise	ADV
ejpam-164	8	30	stated	state	VERB
ejpam-164	8	31	.	.	PUNCT
ejpam-164	9	1	for	for	ADP
ejpam-164	9	2	a	a	DET
ejpam-164	9	3	subset	subset	NOUN
ejpam-164	9	4	a	a	PRON
ejpam-164	9	5	of	of	ADP
ejpam-164	9	6	x	x	PRON
ejpam-164	9	7	,	,	PUNCT
ejpam-164	9	8	the	the	DET
ejpam-164	9	9	closure	closure	NOUN
ejpam-164	9	10	of	of	ADP
ejpam-164	9	11	a	a	PRON
ejpam-164	9	12	and	and	CCONJ
ejpam-164	9	13	the	the	DET
ejpam-164	9	14	interior	interior	NOUN
ejpam-164	9	15	of	of	ADP
ejpam-164	9	16	a	a	PRON
ejpam-164	9	17	will	will	AUX
ejpam-164	9	18	be	be	AUX
ejpam-164	9	19	denoted	denote	VERB
ejpam-164	9	20	by	by	ADP
ejpam-164	9	21	cl(a	cl(a	NOUN
ejpam-164	9	22	)	)	PUNCT
ejpam-164	9	23	and	and	CCONJ
ejpam-164	9	24	int(a	int(a	PROPN
ejpam-164	9	25	)	)	PUNCT
ejpam-164	9	26	,	,	PUNCT
ejpam-164	9	27	respectively	respectively	ADV
ejpam-164	9	28	.	.	PUNCT
ejpam-164	10	1	let	let	AUX
ejpam-164	10	2	(	(	PUNCT
ejpam-164	10	3	x	x	X
ejpam-164	10	4	,	,	PUNCT
ejpam-164	10	5	τ	τ	X
ejpam-164	10	6	)	)	PUNCT
ejpam-164	10	7	be	be	VERB
ejpam-164	10	8	a	a	DET
ejpam-164	10	9	space	space	NOUN
ejpam-164	10	10	and	and	CCONJ
ejpam-164	10	11	a	a	DET
ejpam-164	10	12	a	a	DET
ejpam-164	10	13	subset	subset	NOUN
ejpam-164	10	14	of	of	ADP
ejpam-164	10	15	x	x	X
ejpam-164	10	16	.	.	PUNCT
ejpam-164	11	1	a	a	DET
ejpam-164	11	2	point	point	NOUN
ejpam-164	11	3	x	x	X
ejpam-164	11	4	∈	∈	NOUN
ejpam-164	11	5	x	x	PUNCT
ejpam-164	11	6	is	be	AUX
ejpam-164	11	7	called	call	VERB
ejpam-164	11	8	a	a	DET
ejpam-164	11	9	condensation	condensation	NOUN
ejpam-164	11	10	point	point	NOUN
ejpam-164	11	11	of	of	ADP
ejpam-164	11	12	a	a	DET
ejpam-164	11	13	if	if	NOUN
ejpam-164	11	14	for	for	ADP
ejpam-164	11	15	each	each	DET
ejpam-164	11	16	u	u	NOUN
ejpam-164	11	17	∈	∈	PROPN
ejpam-164	11	18	τ	τ	X
ejpam-164	11	19	with	with	ADP
ejpam-164	11	20	x	x	PROPN
ejpam-164	11	21	∈	∈	PROPN
ejpam-164	11	22	u	u	NOUN
ejpam-164	11	23	,	,	PUNCT
ejpam-164	11	24	the	the	DET
ejpam-164	11	25	set	set	ADJ
ejpam-164	11	26	u	u	NOUN
ejpam-164	11	27	∩	∩	NOUN
ejpam-164	11	28	a	a	PRON
ejpam-164	11	29	is	be	AUX
ejpam-164	11	30	uncountable	uncountable	ADJ
ejpam-164	11	31	.	.	PUNCT
ejpam-164	12	1	a	a	PRON
ejpam-164	12	2	is	be	AUX
ejpam-164	12	3	said	say	VERB
ejpam-164	12	4	to	to	PART
ejpam-164	12	5	be	be	AUX
ejpam-164	12	6	ω	ω	NOUN
ejpam-164	12	7	-	-	ADJ
ejpam-164	12	8	closed	closed	ADJ
ejpam-164	12	9	[	[	X
ejpam-164	12	10	8	8	NUM
ejpam-164	12	11	]	]	X
ejpam-164	12	12	if	if	SCONJ
ejpam-164	12	13	it	it	PRON
ejpam-164	12	14	contains	contain	VERB
ejpam-164	12	15	all	all	DET
ejpam-164	12	16	its	its	PRON
ejpam-164	12	17	condensation	condensation	NOUN
ejpam-164	12	18	points	point	NOUN
ejpam-164	12	19	.	.	PUNCT
ejpam-164	13	1	the	the	DET
ejpam-164	13	2	complement	complement	NOUN
ejpam-164	13	3	of	of	ADP
ejpam-164	13	4	an	an	DET
ejpam-164	13	5	ω	ω	ADV
ejpam-164	13	6	-	-	PUNCT
ejpam-164	13	7	closed	closed	ADJ
ejpam-164	13	8	set	set	NOUN
ejpam-164	13	9	is	be	AUX
ejpam-164	13	10	said	say	VERB
ejpam-164	13	11	to	to	PART
ejpam-164	13	12	be	be	AUX
ejpam-164	13	13	ω	ω	NOUN
ejpam-164	13	14	-	-	NOUN
ejpam-164	13	15	open	open	ADJ
ejpam-164	13	16	.	.	PUNCT
ejpam-164	14	1	it	it	PRON
ejpam-164	14	2	is	be	AUX
ejpam-164	14	3	well	well	ADV
ejpam-164	14	4	known	know	VERB
ejpam-164	14	5	that	that	SCONJ
ejpam-164	14	6	a	a	DET
ejpam-164	14	7	subset	subset	NOUN
ejpam-164	14	8	w	w	NOUN
ejpam-164	14	9	of	of	ADP
ejpam-164	14	10	a	a	DET
ejpam-164	14	11	space	space	NOUN
ejpam-164	14	12	(	(	PUNCT
ejpam-164	14	13	x	x	X
ejpam-164	14	14	,	,	PUNCT
ejpam-164	14	15	τ	τ	X
ejpam-164	14	16	)	)	PUNCT
ejpam-164	14	17	is	be	AUX
ejpam-164	14	18	ω	ω	NOUN
ejpam-164	14	19	-	-	NOUN
ejpam-164	14	20	open	open	ADJ
ejpam-164	14	21	if	if	SCONJ
ejpam-164	14	22	and	and	CCONJ
ejpam-164	14	23	only	only	ADV
ejpam-164	14	24	if	if	SCONJ
ejpam-164	14	25	for	for	ADP
ejpam-164	14	26	each	each	DET
ejpam-164	14	27	x	x	PUNCT
ejpam-164	14	28	∈w	∈w	NOUN
ejpam-164	14	29	,	,	PUNCT
ejpam-164	14	30	there	there	PRON
ejpam-164	14	31	exists	exist	VERB
ejpam-164	14	32	u	u	PROPN
ejpam-164	14	33	∈	∈	PROPN
ejpam-164	14	34	τ	τ	X
ejpam-164	14	35	such	such	ADJ
ejpam-164	14	36	that	that	SCONJ
ejpam-164	14	37	x	x	SYM
ejpam-164	14	38	∈	∈	PROPN
ejpam-164	14	39	u	u	NOUN
ejpam-164	14	40	and	and	CCONJ
ejpam-164	14	41	u	u	PRON
ejpam-164	14	42	−w	−w	ADV
ejpam-164	14	43	is	be	AUX
ejpam-164	14	44	countable	countable	ADJ
ejpam-164	14	45	.	.	PUNCT
ejpam-164	15	1	the	the	DET
ejpam-164	15	2	family	family	NOUN
ejpam-164	15	3	of	of	ADP
ejpam-164	15	4	all	all	DET
ejpam-164	15	5	ω	ω	ADJ
ejpam-164	15	6	-	-	ADJ
ejpam-164	15	7	open	open	ADJ
ejpam-164	15	8	sets	set	NOUN
ejpam-164	15	9	of	of	ADP
ejpam-164	15	10	a	a	DET
ejpam-164	15	11	space	space	NOUN
ejpam-164	15	12	(	(	PUNCT
ejpam-164	15	13	x	x	X
ejpam-164	15	14	,	,	PUNCT
ejpam-164	15	15	τ	τ	PROPN
ejpam-164	15	16	)	)	PUNCT
ejpam-164	15	17	,	,	PUNCT
ejpam-164	15	18	denoted	denote	VERB
ejpam-164	15	19	by	by	ADP
ejpam-164	15	20	τω	τω	PRON
ejpam-164	15	21	or	or	CCONJ
ejpam-164	15	22	ωo(x	ωo(x	NUM
ejpam-164	15	23	)	)	PUNCT
ejpam-164	15	24	,	,	PUNCT
ejpam-164	15	25	forms	form	VERB
ejpam-164	15	26	a	a	DET
ejpam-164	15	27	topology	topology	NOUN
ejpam-164	15	28	on	on	ADP
ejpam-164	15	29	x	x	SYM
ejpam-164	15	30	finer	fine	ADJ
ejpam-164	15	31	than	than	ADP
ejpam-164	15	32	τ	τ	PROPN
ejpam-164	15	33	.	.	PUNCT
ejpam-164	15	34	theω	theω	ADJ
ejpam-164	15	35	-	-	PUNCT
ejpam-164	15	36	closure	closure	NOUN
ejpam-164	15	37	andω	andω	ADJ
ejpam-164	15	38	-	-	PUNCT
ejpam-164	15	39	interior	interior	NOUN
ejpam-164	15	40	,	,	PUNCT
ejpam-164	15	41	that	that	PRON
ejpam-164	15	42	can	can	AUX
ejpam-164	15	43	be	be	AUX
ejpam-164	15	44	defined	define	VERB
ejpam-164	15	45	∗corresponding	∗corresponde	VERB
ejpam-164	15	46	author	author	NOUN
ejpam-164	15	47	.	.	PUNCT
ejpam-164	16	1	email	email	NOUN
ejpam-164	16	2	addresses	address	NOUN
ejpam-164	16	3	:	:	PUNCT
ejpam-164	16	4	t.noiri	t.noiri	X
ejpam-164	16	5	�	�	NOUN
ejpam-164	16	6	nifty	nifty	ADJ
ejpam-164	16	7	.	.	PUNCT
ejpam-164	17	1	om	om	PROPN
ejpam-164	17	2	(	(	PUNCT
ejpam-164	17	3	t.	t.	PROPN
ejpam-164	17	4	noiri	noiri	PROPN
ejpam-164	17	5	)	)	PUNCT
ejpam-164	17	6	,	,	PUNCT
ejpam-164	17	7	omarimutah1	omarimutah1	PROPN
ejpam-164	17	8	�	�	PROPN
ejpam-164	17	9	yahoo	yahoo	PROPN
ejpam-164	17	10	.	.	PUNCT
ejpam-164	17	11	om	om	PROPN
ejpam-164	17	12	(	(	PUNCT
ejpam-164	17	13	a.	a.	NOUN
ejpam-164	17	14	alomari	alomari	PROPN
ejpam-164	17	15	)	)	PUNCT
ejpam-164	17	16	,	,	PUNCT
ejpam-164	17	17	msn�ukm.my	msn�ukm.my	PROPN
ejpam-164	17	18	(	(	PUNCT
ejpam-164	17	19	m.	m.	NOUN
ejpam-164	17	20	noorani	noorani	PROPN
ejpam-164	17	21	)	)	PUNCT
ejpam-164	17	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-164	18	1	73	73	NUM
ejpam-164	19	1	c	c	NOUN
ejpam-164	19	2	©	©	PROPN
ejpam-164	19	3	2009	2009	NUM
ejpam-164	19	4	ejpam	ejpam	NOUN
ejpam-164	19	5	all	all	DET
ejpam-164	19	6	rights	right	NOUN
ejpam-164	19	7	reserved	reserve	VERB
ejpam-164	19	8	.	.	PUNCT
ejpam-164	20	1	t.	t.	PROPN
ejpam-164	20	2	noiri	noiri	PROPN
ejpam-164	20	3	,	,	PUNCT
ejpam-164	20	4	a.	a.	PROPN
ejpam-164	20	5	al	al	PROPN
ejpam-164	20	6	-	-	PUNCT
ejpam-164	20	7	omari	omari	PROPN
ejpam-164	20	8	,	,	PUNCT
ejpam-164	20	9	and	and	CCONJ
ejpam-164	20	10	m.	m.	NOUN
ejpam-164	20	11	noorani	noorani	PROPN
ejpam-164	20	12	/	/	SYM
ejpam-164	20	13	eur	eur	PROPN
ejpam-164	20	14	.	.	PUNCT
ejpam-164	21	1	j.	j.	PROPN
ejpam-164	21	2	pure	pure	PROPN
ejpam-164	21	3	appl	appl	PROPN
ejpam-164	21	4	.	.	PROPN
ejpam-164	21	5	math	math	PROPN
ejpam-164	21	6	,	,	PUNCT
ejpam-164	21	7	2	2	NUM
ejpam-164	21	8	(	(	PUNCT
ejpam-164	21	9	2009	2009	NUM
ejpam-164	21	10	)	)	PUNCT
ejpam-164	21	11	,	,	PUNCT
ejpam-164	21	12	(	(	PUNCT
ejpam-164	21	13	73	73	NUM
ejpam-164	21	14	-	-	SYM
ejpam-164	21	15	84	84	NUM
ejpam-164	21	16	)	)	PUNCT
ejpam-164	21	17	74	74	NUM
ejpam-164	21	18	in	in	ADP
ejpam-164	21	19	the	the	DET
ejpam-164	21	20	same	same	ADJ
ejpam-164	21	21	way	way	NOUN
ejpam-164	21	22	as	as	ADP
ejpam-164	21	23	cl(a	cl(a	NUM
ejpam-164	21	24	)	)	PUNCT
ejpam-164	21	25	and	and	CCONJ
ejpam-164	21	26	int(a	int(a	PROPN
ejpam-164	21	27	)	)	PUNCT
ejpam-164	21	28	,	,	PUNCT
ejpam-164	21	29	respectively	respectively	ADV
ejpam-164	21	30	,	,	PUNCT
ejpam-164	21	31	will	will	AUX
ejpam-164	21	32	be	be	AUX
ejpam-164	21	33	denoted	denote	VERB
ejpam-164	21	34	by	by	ADP
ejpam-164	21	35	clω(a	clω(a	PROPN
ejpam-164	21	36	)	)	PUNCT
ejpam-164	21	37	and	and	CCONJ
ejpam-164	21	38	intω(a	intω(a	PROPN
ejpam-164	21	39	)	)	PUNCT
ejpam-164	21	40	,	,	PUNCT
ejpam-164	21	41	respectively	respectively	ADV
ejpam-164	21	42	.	.	PUNCT
ejpam-164	22	1	several	several	ADJ
ejpam-164	22	2	characterizations	characterization	NOUN
ejpam-164	22	3	of	of	ADP
ejpam-164	22	4	ω	ω	VERB
ejpam-164	22	5	-	-	PUNCT
ejpam-164	22	6	closed	closed	ADJ
ejpam-164	22	7	sets	set	NOUN
ejpam-164	22	8	were	be	AUX
ejpam-164	22	9	provided	provide	VERB
ejpam-164	22	10	in	in	ADP
ejpam-164	22	11	[	[	X
ejpam-164	22	12	2,3,8,9,13	2,3,8,9,13	PROPN
ejpam-164	22	13	]	]	PUNCT
ejpam-164	22	14	.	.	PUNCT
ejpam-164	23	1	definition	definition	NOUN
ejpam-164	23	2	1.1	1.1	NUM
ejpam-164	23	3	.	.	PUNCT
ejpam-164	24	1	a	a	DET
ejpam-164	24	2	subset	subset	NOUN
ejpam-164	24	3	a	a	PRON
ejpam-164	24	4	of	of	ADP
ejpam-164	24	5	a	a	DET
ejpam-164	24	6	space	space	NOUN
ejpam-164	24	7	x	x	PUNCT
ejpam-164	24	8	is	be	AUX
ejpam-164	24	9	said	say	VERB
ejpam-164	24	10	to	to	PART
ejpam-164	24	11	be	be	AUX
ejpam-164	24	12	1	1	NUM
ejpam-164	24	13	.	.	PUNCT
ejpam-164	25	1	α	α	X
ejpam-164	25	2	-	-	ADJ
ejpam-164	25	3	open	open	ADJ
ejpam-164	25	4	[	[	X
ejpam-164	25	5	12	12	NUM
ejpam-164	25	6	]	]	X
ejpam-164	25	7	if	if	SCONJ
ejpam-164	25	8	a⊆	a⊆	ADP
ejpam-164	25	9	int(cl(int(a	int(cl(int(a	PROPN
ejpam-164	25	10	)	)	PUNCT
ejpam-164	25	11	)	)	PUNCT
ejpam-164	25	12	)	)	PUNCT
ejpam-164	26	1	;	;	PUNCT
ejpam-164	26	2	2	2	X
ejpam-164	26	3	.	.	X
ejpam-164	26	4	semi	semi	ADJ
ejpam-164	26	5	-	-	ADJ
ejpam-164	26	6	open	open	ADJ
ejpam-164	26	7	[	[	X
ejpam-164	26	8	10	10	NUM
ejpam-164	26	9	]	]	X
ejpam-164	26	10	if	if	SCONJ
ejpam-164	26	11	a⊆	a⊆	PROPN
ejpam-164	26	12	cl(int(a	cl(int(a	NOUN
ejpam-164	26	13	)	)	PUNCT
ejpam-164	26	14	)	)	PUNCT
ejpam-164	26	15	;	;	PUNCT
ejpam-164	26	16	3	3	X
ejpam-164	26	17	.	.	X
ejpam-164	26	18	pre	pre	VERB
ejpam-164	26	19	-	-	ADJ
ejpam-164	26	20	open	open	ADJ
ejpam-164	26	21	[	[	X
ejpam-164	26	22	11	11	NUM
ejpam-164	26	23	]	]	X
ejpam-164	26	24	if	if	SCONJ
ejpam-164	26	25	a⊆	a⊆	ADP
ejpam-164	26	26	int(cl(a	int(cl(a	PROPN
ejpam-164	26	27	)	)	PUNCT
ejpam-164	26	28	)	)	PUNCT
ejpam-164	26	29	;	;	PUNCT
ejpam-164	26	30	4	4	X
ejpam-164	26	31	.	.	X
ejpam-164	26	32	β	β	X
ejpam-164	26	33	-open	-open	NOUN
ejpam-164	27	1	[	[	X
ejpam-164	27	2	1	1	NUM
ejpam-164	27	3	]	]	X
ejpam-164	27	4	if	if	SCONJ
ejpam-164	27	5	a⊆	a⊆	NOUN
ejpam-164	27	6	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-164	27	7	)	)	PUNCT
ejpam-164	27	8	)	)	PUNCT
ejpam-164	27	9	)	)	PUNCT
ejpam-164	27	10	;	;	PUNCT
ejpam-164	28	1	5	5	X
ejpam-164	28	2	.	.	X
ejpam-164	28	3	b	b	X
ejpam-164	28	4	-	-	PUNCT
ejpam-164	28	5	open	open	ADJ
ejpam-164	28	6	[	[	X
ejpam-164	28	7	5	5	NUM
ejpam-164	28	8	]	]	X
ejpam-164	28	9	if	if	SCONJ
ejpam-164	28	10	a⊆	a⊆	PROPN
ejpam-164	28	11	cl(int(a))∪	cl(int(a))∪	VERB
ejpam-164	28	12	int(cl(a	int(cl(a	PROPN
ejpam-164	28	13	)	)	PUNCT
ejpam-164	28	14	)	)	PUNCT
ejpam-164	28	15	.	.	PUNCT
ejpam-164	29	1	in	in	ADP
ejpam-164	29	2	this	this	DET
ejpam-164	29	3	paper	paper	NOUN
ejpam-164	29	4	we	we	PRON
ejpam-164	29	5	introduce	introduce	VERB
ejpam-164	29	6	and	and	CCONJ
ejpam-164	29	7	investigate	investigate	VERB
ejpam-164	29	8	the	the	DET
ejpam-164	29	9	new	new	ADJ
ejpam-164	29	10	notions	notion	NOUN
ejpam-164	29	11	called	call	VERB
ejpam-164	29	12	b	b	PROPN
ejpam-164	29	13	-	-	PUNCT
ejpam-164	29	14	ω	ω	VERB
ejpam-164	29	15	-	-	ADJ
ejpam-164	29	16	open	open	ADJ
ejpam-164	29	17	sets	set	NOUN
ejpam-164	29	18	,	,	PUNCT
ejpam-164	29	19	pre	pre	ADJ
ejpam-164	29	20	-	-	ADJ
ejpam-164	29	21	ωopen	ωopen	ADJ
ejpam-164	29	22	sets	set	NOUN
ejpam-164	29	23	and	and	CCONJ
ejpam-164	29	24	α	α	NOUN
ejpam-164	29	25	-	-	PUNCT
ejpam-164	29	26	ω	ω	VERB
ejpam-164	29	27	-	-	ADJ
ejpam-164	29	28	open	open	ADJ
ejpam-164	29	29	sets	set	NOUN
ejpam-164	29	30	which	which	PRON
ejpam-164	29	31	are	be	AUX
ejpam-164	29	32	weaker	weak	ADJ
ejpam-164	29	33	than	than	ADP
ejpam-164	29	34	ω	ω	NOUN
ejpam-164	29	35	-	-	NOUN
ejpam-164	29	36	open	open	ADJ
ejpam-164	29	37	.	.	PUNCT
ejpam-164	30	1	moreover	moreover	ADV
ejpam-164	30	2	,	,	PUNCT
ejpam-164	30	3	we	we	PRON
ejpam-164	30	4	use	use	VERB
ejpam-164	30	5	these	these	DET
ejpam-164	30	6	notions	notion	NOUN
ejpam-164	30	7	to	to	PART
ejpam-164	30	8	obtain	obtain	VERB
ejpam-164	30	9	decompositions	decomposition	NOUN
ejpam-164	30	10	of	of	ADP
ejpam-164	30	11	continuity	continuity	NOUN
ejpam-164	30	12	.	.	PUNCT
ejpam-164	31	1	2	2	X
ejpam-164	31	2	.	.	X
ejpam-164	31	3	weak	weak	ADJ
ejpam-164	31	4	forms	form	NOUN
ejpam-164	31	5	of	of	ADP
ejpam-164	31	6	ω	ω	VERB
ejpam-164	31	7	-	-	ADJ
ejpam-164	31	8	open	open	ADJ
ejpam-164	31	9	sets	set	NOUN
ejpam-164	31	10	in	in	ADP
ejpam-164	31	11	this	this	DET
ejpam-164	31	12	section	section	NOUN
ejpam-164	31	13	we	we	PRON
ejpam-164	31	14	introduce	introduce	VERB
ejpam-164	31	15	the	the	DET
ejpam-164	31	16	following	follow	VERB
ejpam-164	31	17	notions	notion	NOUN
ejpam-164	31	18	.	.	PUNCT
ejpam-164	32	1	definition	definition	NOUN
ejpam-164	32	2	2.1	2.1	NUM
ejpam-164	32	3	.	.	PUNCT
ejpam-164	33	1	a	a	DET
ejpam-164	33	2	subset	subset	NOUN
ejpam-164	33	3	a	a	PRON
ejpam-164	33	4	of	of	ADP
ejpam-164	33	5	a	a	DET
ejpam-164	33	6	space	space	NOUN
ejpam-164	33	7	x	x	PUNCT
ejpam-164	33	8	is	be	AUX
ejpam-164	33	9	said	say	VERB
ejpam-164	33	10	to	to	PART
ejpam-164	33	11	be	be	AUX
ejpam-164	33	12	1	1	NUM
ejpam-164	33	13	.	.	PUNCT
ejpam-164	34	1	α	α	X
ejpam-164	34	2	-	-	PUNCT
ejpam-164	34	3	ω	ω	NOUN
ejpam-164	34	4	-	-	NOUN
ejpam-164	34	5	open	open	ADJ
ejpam-164	34	6	if	if	SCONJ
ejpam-164	34	7	a⊆	a⊆	NOUN
ejpam-164	34	8	intω(cl(intω(a	intω(cl(intω(a	NOUN
ejpam-164	34	9	)	)	PUNCT
ejpam-164	34	10	)	)	PUNCT
ejpam-164	35	1	)	)	PUNCT
ejpam-164	36	1	;	;	PUNCT
ejpam-164	37	1	2	2	X
ejpam-164	37	2	.	.	X
ejpam-164	37	3	pre	pre	ADJ
ejpam-164	37	4	-	-	ADJ
ejpam-164	37	5	ω	ω	VERB
ejpam-164	37	6	-	-	NOUN
ejpam-164	37	7	open	open	ADJ
ejpam-164	37	8	if	if	SCONJ
ejpam-164	37	9	a⊆	a⊆	NOUN
ejpam-164	37	10	intω(cl(a	intω(cl(a	ADJ
ejpam-164	37	11	)	)	PUNCT
ejpam-164	37	12	)	)	PUNCT
ejpam-164	37	13	;	;	PUNCT
ejpam-164	37	14	3	3	X
ejpam-164	37	15	.	.	X
ejpam-164	37	16	β	β	X
ejpam-164	37	17	-ω	-ω	PUNCT
ejpam-164	37	18	-	-	VERB
ejpam-164	37	19	open	open	ADJ
ejpam-164	37	20	if	if	SCONJ
ejpam-164	37	21	a⊆	a⊆	NOUN
ejpam-164	37	22	cl(intω(cl(a	cl(intω(cl(a	NOUN
ejpam-164	37	23	)	)	PUNCT
ejpam-164	37	24	)	)	PUNCT
ejpam-164	37	25	)	)	PUNCT
ejpam-164	37	26	;	;	PUNCT
ejpam-164	37	27	4	4	X
ejpam-164	37	28	.	.	X
ejpam-164	37	29	b	b	X
ejpam-164	37	30	-	-	PUNCT
ejpam-164	37	31	ω	ω	NOUN
ejpam-164	37	32	-	-	NOUN
ejpam-164	37	33	open	open	ADJ
ejpam-164	37	34	if	if	SCONJ
ejpam-164	37	35	a⊆	a⊆	PROPN
ejpam-164	37	36	intω(cl(a))∪	intω(cl(a))∪	PROPN
ejpam-164	37	37	cl(intω(a	cl(intω(a	NOUN
ejpam-164	37	38	)	)	PUNCT
ejpam-164	37	39	)	)	PUNCT
ejpam-164	37	40	.	.	PUNCT
ejpam-164	38	1	lemma	lemma	PROPN
ejpam-164	38	2	2.2	2.2	NUM
ejpam-164	38	3	.	.	PUNCT
ejpam-164	39	1	let	let	AUX
ejpam-164	39	2	(	(	PUNCT
ejpam-164	39	3	x	x	X
ejpam-164	39	4	,	,	PUNCT
ejpam-164	39	5	τ	τ	X
ejpam-164	39	6	)	)	PUNCT
ejpam-164	39	7	be	be	VERB
ejpam-164	39	8	a	a	DET
ejpam-164	39	9	topological	topological	ADJ
ejpam-164	39	10	space	space	NOUN
ejpam-164	39	11	,	,	PUNCT
ejpam-164	39	12	then	then	ADV
ejpam-164	39	13	the	the	DET
ejpam-164	39	14	following	follow	VERB
ejpam-164	39	15	properties	property	NOUN
ejpam-164	39	16	hold	hold	VERB
ejpam-164	39	17	:	:	PUNCT
ejpam-164	40	1	1	1	X
ejpam-164	40	2	.	.	X
ejpam-164	40	3	every	every	DET
ejpam-164	40	4	ω	ω	VERB
ejpam-164	40	5	-	-	ADJ
ejpam-164	40	6	open	open	ADJ
ejpam-164	40	7	set	set	NOUN
ejpam-164	40	8	is	be	AUX
ejpam-164	40	9	α	α	NOUN
ejpam-164	40	10	-	-	PUNCT
ejpam-164	40	11	ω	ω	NOUN
ejpam-164	40	12	-	-	NOUN
ejpam-164	40	13	open	open	ADJ
ejpam-164	40	14	.	.	PUNCT
ejpam-164	41	1	2	2	X
ejpam-164	41	2	.	.	X
ejpam-164	41	3	every	every	DET
ejpam-164	41	4	α	α	PROPN
ejpam-164	41	5	-	-	PUNCT
ejpam-164	41	6	ω	ω	VERB
ejpam-164	41	7	-	-	PUNCT
ejpam-164	41	8	open	open	ADJ
ejpam-164	41	9	set	set	NOUN
ejpam-164	41	10	is	be	AUX
ejpam-164	41	11	pre	pre	ADJ
ejpam-164	41	12	-	-	ADJ
ejpam-164	41	13	ω	ω	VERB
ejpam-164	41	14	-	-	NOUN
ejpam-164	41	15	open	open	ADJ
ejpam-164	41	16	.	.	PUNCT
ejpam-164	42	1	t.	t.	PROPN
ejpam-164	42	2	noiri	noiri	PROPN
ejpam-164	42	3	,	,	PUNCT
ejpam-164	42	4	a.	a.	PROPN
ejpam-164	42	5	al	al	PROPN
ejpam-164	42	6	-	-	PUNCT
ejpam-164	42	7	omari	omari	PROPN
ejpam-164	42	8	,	,	PUNCT
ejpam-164	42	9	and	and	CCONJ
ejpam-164	42	10	m.	m.	NOUN
ejpam-164	42	11	noorani	noorani	PROPN
ejpam-164	42	12	/	/	SYM
ejpam-164	42	13	eur	eur	PROPN
ejpam-164	42	14	.	.	PUNCT
ejpam-164	43	1	j.	j.	PROPN
ejpam-164	43	2	pure	pure	PROPN
ejpam-164	43	3	appl	appl	PROPN
ejpam-164	43	4	.	.	PROPN
ejpam-164	43	5	math	math	PROPN
ejpam-164	43	6	,	,	PUNCT
ejpam-164	43	7	2	2	NUM
ejpam-164	43	8	(	(	PUNCT
ejpam-164	43	9	2009	2009	NUM
ejpam-164	43	10	)	)	PUNCT
ejpam-164	43	11	,	,	PUNCT
ejpam-164	43	12	(	(	PUNCT
ejpam-164	43	13	73	73	NUM
ejpam-164	43	14	-	-	SYM
ejpam-164	43	15	84	84	NUM
ejpam-164	43	16	)	)	PUNCT
ejpam-164	43	17	75	75	NUM
ejpam-164	43	18	3	3	NUM
ejpam-164	43	19	.	.	PUNCT
ejpam-164	44	1	every	every	DET
ejpam-164	44	2	pre	pre	ADJ
ejpam-164	44	3	-	-	ADJ
ejpam-164	44	4	ω	ω	ADJ
ejpam-164	44	5	-	-	ADJ
ejpam-164	44	6	open	open	ADJ
ejpam-164	44	7	set	set	NOUN
ejpam-164	44	8	is	be	AUX
ejpam-164	44	9	b	b	NOUN
ejpam-164	44	10	-	-	PUNCT
ejpam-164	44	11	ω	ω	NOUN
ejpam-164	44	12	-	-	NOUN
ejpam-164	44	13	open	open	ADJ
ejpam-164	44	14	.	.	PUNCT
ejpam-164	45	1	4	4	X
ejpam-164	45	2	.	.	X
ejpam-164	45	3	every	every	DET
ejpam-164	45	4	b	b	X
ejpam-164	45	5	-	-	PUNCT
ejpam-164	45	6	ω	ω	VERB
ejpam-164	45	7	-	-	ADJ
ejpam-164	45	8	open	open	ADJ
ejpam-164	45	9	set	set	NOUN
ejpam-164	45	10	is	be	AUX
ejpam-164	45	11	β	β	NOUN
ejpam-164	45	12	-ω	-ω	X
ejpam-164	45	13	-	-	ADJ
ejpam-164	45	14	open	open	ADJ
ejpam-164	45	15	.	.	PUNCT
ejpam-164	46	1	proof	proof	NOUN
ejpam-164	46	2	.	.	PUNCT
ejpam-164	47	1	(	(	PUNCT
ejpam-164	47	2	1	1	X
ejpam-164	47	3	)	)	PUNCT
ejpam-164	47	4	if	if	SCONJ
ejpam-164	47	5	a	a	PRON
ejpam-164	47	6	is	be	AUX
ejpam-164	47	7	an	an	DET
ejpam-164	47	8	ω	ω	ADJ
ejpam-164	47	9	-	-	ADJ
ejpam-164	47	10	open	open	ADJ
ejpam-164	47	11	set	set	NOUN
ejpam-164	47	12	,	,	PUNCT
ejpam-164	47	13	then	then	ADV
ejpam-164	47	14	a=	a=	PROPN
ejpam-164	47	15	intω(a	intω(a	PROPN
ejpam-164	47	16	)	)	PUNCT
ejpam-164	47	17	.	.	PUNCT
ejpam-164	48	1	since	since	SCONJ
ejpam-164	48	2	a⊆	a⊆	NOUN
ejpam-164	48	3	cl(a	cl(a	NUM
ejpam-164	48	4	)	)	PUNCT
ejpam-164	48	5	,	,	PUNCT
ejpam-164	48	6	then	then	ADV
ejpam-164	48	7	a⊆	a⊆	VERB
ejpam-164	48	8	cl(intω(a	cl(intω(a	NOUN
ejpam-164	48	9	)	)	PUNCT
ejpam-164	48	10	)	)	PUNCT
ejpam-164	48	11	and	and	CCONJ
ejpam-164	48	12	a⊆	a⊆	VERB
ejpam-164	48	13	intω(cl(intω(a	intω(cl(intω(a	NOUN
ejpam-164	48	14	)	)	PUNCT
ejpam-164	48	15	)	)	PUNCT
ejpam-164	48	16	)	)	PUNCT
ejpam-164	48	17	.	.	PUNCT
ejpam-164	49	1	therefore	therefore	ADV
ejpam-164	49	2	a	a	PRON
ejpam-164	49	3	is	be	AUX
ejpam-164	49	4	α	α	NOUN
ejpam-164	49	5	-	-	PUNCT
ejpam-164	49	6	ω	ω	NOUN
ejpam-164	49	7	-	-	NOUN
ejpam-164	49	8	open	open	ADJ
ejpam-164	49	9	.	.	PUNCT
ejpam-164	50	1	(	(	PUNCT
ejpam-164	50	2	2	2	X
ejpam-164	50	3	)	)	PUNCT
ejpam-164	50	4	if	if	SCONJ
ejpam-164	50	5	a	a	PRON
ejpam-164	50	6	is	be	AUX
ejpam-164	50	7	an	an	DET
ejpam-164	50	8	α	α	PROPN
ejpam-164	50	9	-	-	PUNCT
ejpam-164	50	10	ω	ω	VERB
ejpam-164	50	11	-	-	PUNCT
ejpam-164	50	12	open	open	ADJ
ejpam-164	50	13	set	set	NOUN
ejpam-164	50	14	,	,	PUNCT
ejpam-164	50	15	then	then	ADV
ejpam-164	50	16	a	a	DET
ejpam-164	50	17	⊆	⊆	NUM
ejpam-164	50	18	intω(cl(intω(a	intω(cl(intω(a	NOUN
ejpam-164	50	19	)	)	PUNCT
ejpam-164	50	20	)	)	PUNCT
ejpam-164	50	21	)	)	PUNCT
ejpam-164	51	1	⊆	⊆	NUM
ejpam-164	51	2	intω(cl(a	intω(cl(a	NOUN
ejpam-164	51	3	)	)	PUNCT
ejpam-164	51	4	)	)	PUNCT
ejpam-164	51	5	.	.	PUNCT
ejpam-164	52	1	therefore	therefore	ADV
ejpam-164	52	2	a	a	PRON
ejpam-164	52	3	is	be	AUX
ejpam-164	52	4	preω	preω	NOUN
ejpam-164	52	5	-	-	PUNCT
ejpam-164	52	6	open	open	ADJ
ejpam-164	52	7	.	.	PUNCT
ejpam-164	53	1	(	(	PUNCT
ejpam-164	53	2	3	3	X
ejpam-164	53	3	)	)	PUNCT
ejpam-164	53	4	if	if	SCONJ
ejpam-164	53	5	a	a	PRON
ejpam-164	53	6	is	be	AUX
ejpam-164	53	7	pre	pre	ADJ
ejpam-164	53	8	-	-	ADJ
ejpam-164	53	9	ω	ω	VERB
ejpam-164	53	10	-	-	ADJ
ejpam-164	53	11	open	open	ADJ
ejpam-164	53	12	,	,	PUNCT
ejpam-164	53	13	then	then	ADV
ejpam-164	53	14	a	a	DET
ejpam-164	53	15	⊆	⊆	NUM
ejpam-164	53	16	intω(cl(a	intω(cl(a	NOUN
ejpam-164	53	17	)	)	PUNCT
ejpam-164	53	18	)	)	PUNCT
ejpam-164	54	1	⊆	⊆	NUM
ejpam-164	54	2	intω(cl(a	intω(cl(a	X
ejpam-164	54	3	)	)	PUNCT
ejpam-164	54	4	)	)	PUNCT
ejpam-164	54	5	∪	∪	ADP
ejpam-164	54	6	cl(intω(a	cl(intω(a	NOUN
ejpam-164	54	7	)	)	PUNCT
ejpam-164	54	8	)	)	PUNCT
ejpam-164	54	9	.	.	PUNCT
ejpam-164	55	1	therefore	therefore	ADV
ejpam-164	55	2	,	,	PUNCT
ejpam-164	55	3	a	a	PRON
ejpam-164	55	4	is	be	AUX
ejpam-164	55	5	b	b	NOUN
ejpam-164	55	6	-	-	PUNCT
ejpam-164	55	7	ω	ω	NOUN
ejpam-164	55	8	-	-	NOUN
ejpam-164	55	9	open	open	ADJ
ejpam-164	55	10	.	.	PUNCT
ejpam-164	56	1	(	(	PUNCT
ejpam-164	56	2	4	4	X
ejpam-164	56	3	)	)	PUNCT
ejpam-164	56	4	if	if	SCONJ
ejpam-164	56	5	a	a	PRON
ejpam-164	56	6	is	be	AUX
ejpam-164	56	7	b	b	NOUN
ejpam-164	56	8	-	-	PUNCT
ejpam-164	56	9	ω	ω	NOUN
ejpam-164	56	10	-	-	NOUN
ejpam-164	56	11	open	open	ADJ
ejpam-164	56	12	,	,	PUNCT
ejpam-164	56	13	then	then	ADV
ejpam-164	56	14	a⊆	a⊆	VERB
ejpam-164	56	15	intω(cl(a))∪cl(intω(a))⊆	intω(cl(a))∪cl(intω(a))⊆	NOUN
ejpam-164	56	16	cl(intω(cl(a)))∪cl(intω(a))⊆	cl(intω(cl(a)))∪cl(intω(a))⊆	NOUN
ejpam-164	56	17	cl(intω(cl(a	cl(intω(cl(a	NUM
ejpam-164	56	18	)	)	PUNCT
ejpam-164	56	19	)	)	PUNCT
ejpam-164	56	20	)	)	PUNCT
ejpam-164	56	21	.	.	PUNCT
ejpam-164	57	1	therefore	therefore	ADV
ejpam-164	57	2	a	a	PRON
ejpam-164	57	3	is	be	AUX
ejpam-164	57	4	β	β	NOUN
ejpam-164	57	5	-ω	-ω	VERB
ejpam-164	57	6	-	-	VERB
ejpam-164	57	7	open	open	ADJ
ejpam-164	57	8	.	.	PUNCT
ejpam-164	58	1	since	since	SCONJ
ejpam-164	58	2	every	every	DET
ejpam-164	58	3	open	open	ADJ
ejpam-164	58	4	set	set	NOUN
ejpam-164	58	5	is	be	AUX
ejpam-164	58	6	ω	ω	NOUN
ejpam-164	58	7	-	-	NOUN
ejpam-164	58	8	open	open	ADJ
ejpam-164	58	9	,	,	PUNCT
ejpam-164	58	10	then	then	ADV
ejpam-164	58	11	we	we	PRON
ejpam-164	58	12	have	have	VERB
ejpam-164	58	13	the	the	DET
ejpam-164	58	14	following	follow	VERB
ejpam-164	58	15	diagram	diagram	NOUN
ejpam-164	58	16	for	for	ADP
ejpam-164	58	17	properties	property	NOUN
ejpam-164	58	18	of	of	ADP
ejpam-164	58	19	subsets	subset	NOUN
ejpam-164	58	20	.	.	PUNCT
ejpam-164	59	1	open	open	ADJ
ejpam-164	59	2	//	//	SYM
ejpam-164	59	3	�	�	PROPN
ejpam-164	59	4	�	�	PROPN
ejpam-164	59	5	α	α	NOUN
ejpam-164	59	6	-	-	ADJ
ejpam-164	59	7	open	open	ADJ
ejpam-164	59	8	//	//	SYM
ejpam-164	59	9	�	�	PROPN
ejpam-164	59	10	�	�	PROPN
ejpam-164	59	11	preopen	preopen	PROPN
ejpam-164	59	12	//	//	NUM
ejpam-164	59	13	�	�	PROPN
ejpam-164	59	14	�	�	PROPN
ejpam-164	59	15	b	b	PROPN
ejpam-164	59	16	-	-	PUNCT
ejpam-164	59	17	open	open	ADJ
ejpam-164	59	18	//	//	SYM
ejpam-164	59	19	�	�	PROPN
ejpam-164	59	20	�	�	PROPN
ejpam-164	59	21	β	β	X
ejpam-164	59	22	-open	-open	PROPN
ejpam-164	59	23	�	�	PROPN
ejpam-164	59	24	�	�	PROPN
ejpam-164	59	25	ω	ω	PROPN
ejpam-164	59	26	-	-	NOUN
ejpam-164	59	27	open	open	ADJ
ejpam-164	59	28	//	//	PUNCT
ejpam-164	59	29	α	α	X
ejpam-164	59	30	-	-	PUNCT
ejpam-164	59	31	ω	ω	VERB
ejpam-164	59	32	-	-	PUNCT
ejpam-164	59	33	open	open	ADJ
ejpam-164	59	34	//	//	SYM
ejpam-164	59	35	pre	pre	X
ejpam-164	59	36	ω	ω	VERB
ejpam-164	59	37	-	-	ADJ
ejpam-164	59	38	open	open	ADJ
ejpam-164	59	39	//	//	SYM
ejpam-164	59	40	b	b	X
ejpam-164	59	41	-	-	PUNCT
ejpam-164	59	42	ω	ω	NOUN
ejpam-164	59	43	-	-	NOUN
ejpam-164	59	44	open	open	ADJ
ejpam-164	59	45	//	//	X
ejpam-164	59	46	β	β	X
ejpam-164	59	47	-ω	-ω	PUNCT
ejpam-164	59	48	-	-	VERB
ejpam-164	59	49	open	open	ADJ
ejpam-164	59	50	the	the	DET
ejpam-164	59	51	converses	converse	NOUN
ejpam-164	59	52	need	need	AUX
ejpam-164	59	53	not	not	PART
ejpam-164	59	54	be	be	AUX
ejpam-164	59	55	true	true	ADJ
ejpam-164	59	56	as	as	SCONJ
ejpam-164	59	57	shown	show	VERB
ejpam-164	59	58	by	by	ADP
ejpam-164	59	59	the	the	DET
ejpam-164	59	60	following	follow	VERB
ejpam-164	59	61	examples	example	NOUN
ejpam-164	59	62	.	.	PUNCT
ejpam-164	60	1	example	example	NOUN
ejpam-164	60	2	2.3	2.3	NUM
ejpam-164	60	3	.	.	PUNCT
ejpam-164	61	1	let	let	VERB
ejpam-164	61	2	x	x	PUNCT
ejpam-164	61	3	=	=	PRON
ejpam-164	61	4	{	{	PUNCT
ejpam-164	61	5	a	a	PRON
ejpam-164	61	6	,	,	PUNCT
ejpam-164	61	7	b	b	NOUN
ejpam-164	61	8	,	,	PUNCT
ejpam-164	61	9	c	c	NOUN
ejpam-164	61	10	}	}	PUNCT
ejpam-164	61	11	and	and	CCONJ
ejpam-164	61	12	τ	τ	PROPN
ejpam-164	61	13	=	=	SYM
ejpam-164	61	14	{	{	PUNCT
ejpam-164	61	15	x	x	PROPN
ejpam-164	61	16	,	,	PUNCT
ejpam-164	61	17	φ	φ	PROPN
ejpam-164	61	18	,	,	PUNCT
ejpam-164	61	19	{	{	PUNCT
ejpam-164	61	20	a	a	X
ejpam-164	61	21	}	}	PUNCT
ejpam-164	61	22	,	,	PUNCT
ejpam-164	61	23	{	{	PUNCT
ejpam-164	61	24	b	b	NOUN
ejpam-164	61	25	}	}	PUNCT
ejpam-164	61	26	,	,	PUNCT
ejpam-164	61	27	{	{	PUNCT
ejpam-164	61	28	a	a	PRON
ejpam-164	61	29	,	,	PUNCT
ejpam-164	61	30	b	b	NOUN
ejpam-164	61	31	}	}	PUNCT
ejpam-164	61	32	}	}	PUNCT
ejpam-164	61	33	.	.	PUNCT
ejpam-164	62	1	then	then	ADV
ejpam-164	62	2	{	{	PUNCT
ejpam-164	62	3	c	c	X
ejpam-164	62	4	}	}	PUNCT
ejpam-164	62	5	is	be	AUX
ejpam-164	62	6	an	an	DET
ejpam-164	62	7	ω	ω	NOUN
ejpam-164	62	8	-	-	ADJ
ejpam-164	62	9	open	open	ADJ
ejpam-164	62	10	(	(	PUNCT
ejpam-164	62	11	since	since	SCONJ
ejpam-164	62	12	x	x	PRON
ejpam-164	62	13	is	be	AUX
ejpam-164	62	14	a	a	DET
ejpam-164	62	15	countable	countable	ADJ
ejpam-164	62	16	set	set	NOUN
ejpam-164	62	17	)	)	PUNCT
ejpam-164	62	18	set	set	NOUN
ejpam-164	63	1	but	but	CCONJ
ejpam-164	63	2	it	it	PRON
ejpam-164	63	3	is	be	AUX
ejpam-164	63	4	not	not	PART
ejpam-164	63	5	β	β	PART
ejpam-164	63	6	-open	-open	PROPN
ejpam-164	63	7	.	.	PUNCT
ejpam-164	63	8	example	example	NOUN
ejpam-164	63	9	2.4	2.4	NUM
ejpam-164	63	10	.	.	PUNCT
ejpam-164	64	1	let	let	VERB
ejpam-164	64	2	x	x	PUNCT
ejpam-164	64	3	=	=	PUNCT
ejpam-164	64	4	r	r	NOUN
ejpam-164	64	5	with	with	ADP
ejpam-164	64	6	the	the	DET
ejpam-164	64	7	usual	usual	ADJ
ejpam-164	64	8	topology	topology	NOUN
ejpam-164	64	9	τ	τ	PROPN
ejpam-164	64	10	.	.	PUNCT
ejpam-164	65	1	let	let	VERB
ejpam-164	65	2	a=	a=	VERB
ejpam-164	65	3	q∩	q∩	NOUN
ejpam-164	66	1	[	[	X
ejpam-164	66	2	0,1	0,1	NUM
ejpam-164	66	3	]	]	PUNCT
ejpam-164	66	4	.	.	PUNCT
ejpam-164	67	1	then	then	ADV
ejpam-164	67	2	a	a	PRON
ejpam-164	67	3	is	be	AUX
ejpam-164	67	4	a	a	DET
ejpam-164	67	5	β	β	X
ejpam-164	67	6	-open	-open	NOUN
ejpam-164	67	7	set	set	NOUN
ejpam-164	67	8	which	which	PRON
ejpam-164	67	9	is	be	AUX
ejpam-164	67	10	not	not	PART
ejpam-164	67	11	b	b	PROPN
ejpam-164	67	12	-	-	PUNCT
ejpam-164	67	13	ω	ω	NOUN
ejpam-164	67	14	-	-	NOUN
ejpam-164	67	15	open	open	ADJ
ejpam-164	67	16	.	.	PUNCT
ejpam-164	68	1	example	example	NOUN
ejpam-164	68	2	2.5	2.5	NUM
ejpam-164	68	3	.	.	PUNCT
ejpam-164	69	1	let	let	VERB
ejpam-164	69	2	x	x	PUNCT
ejpam-164	69	3	=	=	PUNCT
ejpam-164	69	4	r	r	NOUN
ejpam-164	69	5	with	with	ADP
ejpam-164	69	6	the	the	DET
ejpam-164	69	7	usual	usual	ADJ
ejpam-164	69	8	topology	topology	NOUN
ejpam-164	69	9	τ	τ	PROPN
ejpam-164	69	10	.	.	PUNCT
ejpam-164	70	1	let	let	VERB
ejpam-164	70	2	a=	a=	VERB
ejpam-164	70	3	(	(	PUNCT
ejpam-164	70	4	0,1	0,1	NUM
ejpam-164	70	5	]	]	PUNCT
ejpam-164	70	6	.	.	PUNCT
ejpam-164	71	1	then	then	ADV
ejpam-164	71	2	a	a	PRON
ejpam-164	71	3	is	be	AUX
ejpam-164	71	4	a	a	DET
ejpam-164	71	5	b	b	NOUN
ejpam-164	71	6	-	-	PUNCT
ejpam-164	71	7	open	open	ADJ
ejpam-164	71	8	set	set	NOUN
ejpam-164	71	9	which	which	PRON
ejpam-164	71	10	is	be	AUX
ejpam-164	71	11	not	not	PART
ejpam-164	71	12	pre	pre	ADJ
ejpam-164	71	13	-	-	ADJ
ejpam-164	71	14	ω	ω	ADV
ejpam-164	71	15	-	-	ADJ
ejpam-164	71	16	open	open	ADJ
ejpam-164	71	17	.	.	PUNCT
ejpam-164	72	1	example	example	NOUN
ejpam-164	72	2	2.6	2.6	NUM
ejpam-164	72	3	.	.	PUNCT
ejpam-164	73	1	let	let	VERB
ejpam-164	73	2	x	x	PUNCT
ejpam-164	73	3	=	=	PUNCT
ejpam-164	73	4	r	r	NOUN
ejpam-164	73	5	with	with	ADP
ejpam-164	73	6	the	the	DET
ejpam-164	73	7	usual	usual	ADJ
ejpam-164	73	8	topology	topology	NOUN
ejpam-164	73	9	τ	τ	PROPN
ejpam-164	73	10	.	.	PUNCT
ejpam-164	74	1	let	let	AUX
ejpam-164	74	2	a=	a=	ADV
ejpam-164	74	3	q	q	PUNCT
ejpam-164	74	4	be	be	AUX
ejpam-164	74	5	the	the	DET
ejpam-164	74	6	set	set	NOUN
ejpam-164	74	7	of	of	ADP
ejpam-164	74	8	all	all	DET
ejpam-164	74	9	rational	rational	ADJ
ejpam-164	74	10	numbers	number	NOUN
ejpam-164	74	11	.	.	PUNCT
ejpam-164	75	1	then	then	ADV
ejpam-164	75	2	a	a	PRON
ejpam-164	75	3	is	be	AUX
ejpam-164	75	4	a	a	DET
ejpam-164	75	5	preopen	preopen	ADJ
ejpam-164	75	6	set	set	NOUN
ejpam-164	75	7	which	which	PRON
ejpam-164	75	8	is	be	AUX
ejpam-164	75	9	not	not	PART
ejpam-164	75	10	α	α	PROPN
ejpam-164	75	11	-	-	PUNCT
ejpam-164	75	12	ω	ω	NOUN
ejpam-164	75	13	-	-	NOUN
ejpam-164	75	14	open	open	ADJ
ejpam-164	75	15	.	.	PUNCT
ejpam-164	76	1	example	example	NOUN
ejpam-164	76	2	2.7	2.7	NUM
ejpam-164	76	3	.	.	PUNCT
ejpam-164	77	1	let	let	VERB
ejpam-164	77	2	x	x	PRON
ejpam-164	77	3	be	be	AUX
ejpam-164	77	4	an	an	DET
ejpam-164	77	5	uncountable	uncountable	ADJ
ejpam-164	77	6	set	set	NOUN
ejpam-164	77	7	and	and	CCONJ
ejpam-164	77	8	let	let	VERB
ejpam-164	77	9	a	a	DET
ejpam-164	77	10	,	,	PUNCT
ejpam-164	77	11	b	b	NOUN
ejpam-164	77	12	,	,	PUNCT
ejpam-164	77	13	c	c	PROPN
ejpam-164	77	14	and	and	CCONJ
ejpam-164	77	15	d	d	PROPN
ejpam-164	77	16	be	be	VERB
ejpam-164	77	17	subsets	subset	NOUN
ejpam-164	77	18	of	of	ADP
ejpam-164	77	19	x	x	SYM
ejpam-164	77	20	such	such	ADJ
ejpam-164	77	21	that	that	SCONJ
ejpam-164	77	22	each	each	PRON
ejpam-164	77	23	of	of	ADP
ejpam-164	77	24	them	they	PRON
ejpam-164	77	25	is	be	AUX
ejpam-164	77	26	uncountable	uncountable	ADJ
ejpam-164	77	27	and	and	CCONJ
ejpam-164	77	28	the	the	DET
ejpam-164	77	29	family	family	NOUN
ejpam-164	77	30	{	{	PUNCT
ejpam-164	77	31	a	a	PROPN
ejpam-164	77	32	,	,	PUNCT
ejpam-164	77	33	b	b	NOUN
ejpam-164	77	34	,	,	PUNCT
ejpam-164	77	35	c	c	NOUN
ejpam-164	77	36	,	,	PUNCT
ejpam-164	77	37	d	d	X
ejpam-164	77	38	}	}	PUNCT
ejpam-164	77	39	is	be	AUX
ejpam-164	77	40	a	a	DET
ejpam-164	77	41	partition	partition	NOUN
ejpam-164	77	42	of	of	ADP
ejpam-164	77	43	x	x	X
ejpam-164	77	44	.	.	PUNCT
ejpam-164	78	1	we	we	PRON
ejpam-164	78	2	defined	define	VERB
ejpam-164	78	3	the	the	DET
ejpam-164	78	4	topology	topology	NOUN
ejpam-164	78	5	t.	t.	PROPN
ejpam-164	78	6	noiri	noiri	PROPN
ejpam-164	78	7	,	,	PUNCT
ejpam-164	78	8	a.	a.	PROPN
ejpam-164	78	9	al	al	PROPN
ejpam-164	78	10	-	-	PUNCT
ejpam-164	78	11	omari	omari	PROPN
ejpam-164	78	12	,	,	PUNCT
ejpam-164	78	13	and	and	CCONJ
ejpam-164	78	14	m.	m.	NOUN
ejpam-164	78	15	noorani	noorani	PROPN
ejpam-164	78	16	/	/	SYM
ejpam-164	78	17	eur	eur	PROPN
ejpam-164	78	18	.	.	PUNCT
ejpam-164	79	1	j.	j.	PROPN
ejpam-164	79	2	pure	pure	PROPN
ejpam-164	79	3	appl	appl	PROPN
ejpam-164	79	4	.	.	PROPN
ejpam-164	79	5	math	math	PROPN
ejpam-164	79	6	,	,	PUNCT
ejpam-164	79	7	2	2	NUM
ejpam-164	79	8	(	(	PUNCT
ejpam-164	79	9	2009	2009	NUM
ejpam-164	79	10	)	)	PUNCT
ejpam-164	79	11	,	,	PUNCT
ejpam-164	79	12	(	(	PUNCT
ejpam-164	79	13	73	73	NUM
ejpam-164	79	14	-	-	SYM
ejpam-164	79	15	84	84	NUM
ejpam-164	79	16	)	)	PUNCT
ejpam-164	79	17	76	76	NUM
ejpam-164	79	18	τ={φ	τ={φ	NOUN
ejpam-164	79	19	,	,	PUNCT
ejpam-164	79	20	x	x	INTJ
ejpam-164	79	21	,	,	PUNCT
ejpam-164	79	22	{	{	PUNCT
ejpam-164	79	23	a	a	NOUN
ejpam-164	79	24	}	}	PUNCT
ejpam-164	79	25	,	,	PUNCT
ejpam-164	79	26	{	{	PUNCT
ejpam-164	79	27	b	b	NOUN
ejpam-164	79	28	}	}	PUNCT
ejpam-164	79	29	,	,	PUNCT
ejpam-164	79	30	{	{	PUNCT
ejpam-164	79	31	a	a	DET
ejpam-164	79	32	,	,	PUNCT
ejpam-164	79	33	b	b	NOUN
ejpam-164	79	34	}	}	PUNCT
ejpam-164	79	35	,	,	PUNCT
ejpam-164	79	36	{	{	PUNCT
ejpam-164	79	37	a	a	PRON
ejpam-164	79	38	,	,	PUNCT
ejpam-164	79	39	b	b	NOUN
ejpam-164	79	40	,	,	PUNCT
ejpam-164	79	41	c	c	NOUN
ejpam-164	79	42	}	}	PUNCT
ejpam-164	79	43	}	}	PUNCT
ejpam-164	79	44	.	.	PUNCT
ejpam-164	80	1	then	then	ADV
ejpam-164	80	2	{	{	PUNCT
ejpam-164	80	3	a	a	PRON
ejpam-164	80	4	,	,	PUNCT
ejpam-164	80	5	b	b	NOUN
ejpam-164	80	6	,	,	PUNCT
ejpam-164	80	7	d	d	NOUN
ejpam-164	80	8	}	}	PUNCT
ejpam-164	80	9	is	be	AUX
ejpam-164	80	10	an	an	DET
ejpam-164	80	11	α	α	NOUN
ejpam-164	80	12	-	-	ADJ
ejpam-164	80	13	open	open	ADJ
ejpam-164	80	14	set	set	NOUN
ejpam-164	80	15	which	which	PRON
ejpam-164	80	16	is	be	AUX
ejpam-164	80	17	not	not	PART
ejpam-164	80	18	ω	ω	NOUN
ejpam-164	80	19	-	-	NOUN
ejpam-164	80	20	open	open	ADJ
ejpam-164	80	21	.	.	PUNCT
ejpam-164	81	1	lemma	lemma	PROPN
ejpam-164	81	2	2.8	2.8	NUM
ejpam-164	81	3	.	.	PUNCT
ejpam-164	82	1	[	[	X
ejpam-164	82	2	7	7	X
ejpam-164	82	3	]	]	X
ejpam-164	82	4	if	if	SCONJ
ejpam-164	82	5	u	u	NOUN
ejpam-164	82	6	is	be	AUX
ejpam-164	82	7	an	an	DET
ejpam-164	82	8	open	open	ADJ
ejpam-164	82	9	set	set	NOUN
ejpam-164	82	10	,	,	PUNCT
ejpam-164	82	11	then	then	ADV
ejpam-164	82	12	cl(u	cl(u	VERB
ejpam-164	82	13	∩	∩	NOUN
ejpam-164	82	14	a	a	X
ejpam-164	82	15	)	)	PUNCT
ejpam-164	82	16	=	=	SYM
ejpam-164	82	17	cl(u	cl(u	NOUN
ejpam-164	82	18	∩	∩	NOUN
ejpam-164	82	19	cl(a	cl(a	NUM
ejpam-164	82	20	)	)	PUNCT
ejpam-164	82	21	)	)	PUNCT
ejpam-164	82	22	and	and	CCONJ
ejpam-164	82	23	hence	hence	ADV
ejpam-164	82	24	u	u	NOUN
ejpam-164	82	25	∩	∩	NOUN
ejpam-164	82	26	cl(a	cl(a	X
ejpam-164	82	27	)	)	PUNCT
ejpam-164	82	28	⊆	⊆	NUM
ejpam-164	82	29	cl(u	cl(u	NOUN
ejpam-164	82	30	∩	∩	NOUN
ejpam-164	82	31	a	a	X
ejpam-164	82	32	)	)	PUNCT
ejpam-164	82	33	for	for	SCONJ
ejpam-164	82	34	any	any	DET
ejpam-164	82	35	subset	subset	NOUN
ejpam-164	82	36	a.	a.	NOUN
ejpam-164	82	37	theorem	theorem	VERB
ejpam-164	82	38	2.9	2.9	NUM
ejpam-164	82	39	.	.	PUNCT
ejpam-164	83	1	if	if	SCONJ
ejpam-164	83	2	a	a	PRON
ejpam-164	83	3	is	be	AUX
ejpam-164	83	4	a	a	DET
ejpam-164	83	5	pre	pre	ADJ
ejpam-164	83	6	-	-	ADJ
ejpam-164	83	7	ω	ω	ADJ
ejpam-164	83	8	-	-	ADJ
ejpam-164	83	9	open	open	ADJ
ejpam-164	83	10	subset	subset	NOUN
ejpam-164	83	11	of	of	ADP
ejpam-164	83	12	a	a	DET
ejpam-164	83	13	space	space	NOUN
ejpam-164	83	14	(	(	PUNCT
ejpam-164	83	15	x	x	X
ejpam-164	83	16	,	,	PUNCT
ejpam-164	83	17	τ	τ	X
ejpam-164	83	18	)	)	PUNCT
ejpam-164	83	19	such	such	ADJ
ejpam-164	83	20	that	that	SCONJ
ejpam-164	83	21	u	u	PROPN
ejpam-164	83	22	⊆	⊆	NUM
ejpam-164	83	23	a⊆	a⊆	NOUN
ejpam-164	83	24	cl(u	cl(u	NOUN
ejpam-164	83	25	)	)	PUNCT
ejpam-164	83	26	for	for	ADP
ejpam-164	83	27	a	a	DET
ejpam-164	83	28	subset	subset	ADJ
ejpam-164	83	29	u	u	NOUN
ejpam-164	83	30	of	of	ADP
ejpam-164	83	31	x	x	SYM
ejpam-164	83	32	,	,	PUNCT
ejpam-164	83	33	then	then	ADV
ejpam-164	83	34	u	u	NOUN
ejpam-164	83	35	is	be	AUX
ejpam-164	83	36	a	a	DET
ejpam-164	83	37	pre	pre	ADJ
ejpam-164	83	38	-	-	ADJ
ejpam-164	83	39	ω	ω	ADJ
ejpam-164	83	40	-	-	ADJ
ejpam-164	83	41	open	open	ADJ
ejpam-164	83	42	set	set	NOUN
ejpam-164	83	43	.	.	PUNCT
ejpam-164	84	1	proof	proof	NOUN
ejpam-164	84	2	.	.	PUNCT
ejpam-164	85	1	since	since	SCONJ
ejpam-164	85	2	a	a	DET
ejpam-164	85	3	⊆	⊆	NUM
ejpam-164	85	4	intω(cl(a	intω(cl(a	NOUN
ejpam-164	85	5	)	)	PUNCT
ejpam-164	85	6	)	)	PUNCT
ejpam-164	85	7	,	,	PUNCT
ejpam-164	85	8	u	u	NOUN
ejpam-164	85	9	⊆	⊆	NUM
ejpam-164	85	10	intω(cl(a	intω(cl(a	NUM
ejpam-164	85	11	)	)	PUNCT
ejpam-164	85	12	)	)	PUNCT
ejpam-164	85	13	.	.	PUNCT
ejpam-164	85	14	also	also	ADV
ejpam-164	85	15	cl(a	cl(a	PUNCT
ejpam-164	85	16	)	)	PUNCT
ejpam-164	85	17	⊆	⊆	NUM
ejpam-164	85	18	cl(u	cl(u	NUM
ejpam-164	85	19	)	)	PUNCT
ejpam-164	85	20	implies	imply	VERB
ejpam-164	85	21	that	that	SCONJ
ejpam-164	85	22	intω(cl(a))⊆	intω(cl(a))⊆	NOUN
ejpam-164	85	23	intω(cl(u	intω(cl(u	PRON
ejpam-164	85	24	)	)	PUNCT
ejpam-164	85	25	)	)	PUNCT
ejpam-164	85	26	.	.	PUNCT
ejpam-164	86	1	thus	thus	ADV
ejpam-164	86	2	u	u	X
ejpam-164	86	3	⊆	⊆	NUM
ejpam-164	86	4	intω(cl(a	intω(cl(a	NOUN
ejpam-164	86	5	)	)	PUNCT
ejpam-164	86	6	)	)	PUNCT
ejpam-164	87	1	⊆	⊆	NUM
ejpam-164	87	2	intω(cl(u	intω(cl(u	NOUN
ejpam-164	87	3	)	)	PUNCT
ejpam-164	87	4	)	)	PUNCT
ejpam-164	88	1	and	and	CCONJ
ejpam-164	88	2	hence	hence	ADV
ejpam-164	88	3	u	u	PROPN
ejpam-164	88	4	ia	ia	PROPN
ejpam-164	88	5	a	a	DET
ejpam-164	88	6	pre	pre	ADJ
ejpam-164	88	7	-	-	ADJ
ejpam-164	88	8	ω	ω	ADJ
ejpam-164	88	9	-	-	PUNCT
ejpam-164	88	10	open	open	ADJ
ejpam-164	88	11	set	set	NOUN
ejpam-164	88	12	.	.	PUNCT
ejpam-164	89	1	theorem	theorem	VERB
ejpam-164	89	2	2.10	2.10	NUM
ejpam-164	89	3	.	.	PUNCT
ejpam-164	90	1	a	a	DET
ejpam-164	90	2	subset	subset	NOUN
ejpam-164	90	3	a	a	PRON
ejpam-164	90	4	of	of	ADP
ejpam-164	90	5	a	a	DET
ejpam-164	90	6	space	space	NOUN
ejpam-164	90	7	(	(	PUNCT
ejpam-164	90	8	x	x	X
ejpam-164	90	9	,	,	PUNCT
ejpam-164	90	10	τ	τ	X
ejpam-164	90	11	)	)	PUNCT
ejpam-164	90	12	is	be	AUX
ejpam-164	90	13	semi	semi	ADJ
ejpam-164	90	14	-	-	ADJ
ejpam-164	90	15	open	open	ADJ
ejpam-164	90	16	if	if	SCONJ
ejpam-164	91	1	and	and	CCONJ
ejpam-164	91	2	only	only	ADV
ejpam-164	91	3	if	if	SCONJ
ejpam-164	91	4	a	a	PRON
ejpam-164	91	5	is	be	AUX
ejpam-164	91	6	β	β	NOUN
ejpam-164	91	7	-ω	-ω	VERB
ejpam-164	91	8	-	-	ADJ
ejpam-164	91	9	open	open	ADJ
ejpam-164	91	10	and	and	CCONJ
ejpam-164	91	11	intω(cl(a))⊆	intω(cl(a))⊆	VERB
ejpam-164	91	12	cl(int(a	cl(int(a	NOUN
ejpam-164	91	13	)	)	PUNCT
ejpam-164	91	14	)	)	PUNCT
ejpam-164	91	15	.	.	PUNCT
ejpam-164	92	1	proof	proof	NOUN
ejpam-164	92	2	.	.	PUNCT
ejpam-164	93	1	let	let	VERB
ejpam-164	93	2	a	a	PRON
ejpam-164	93	3	be	be	AUX
ejpam-164	93	4	semi	semi	ADJ
ejpam-164	93	5	-	-	ADJ
ejpam-164	93	6	open	open	ADJ
ejpam-164	93	7	.	.	PUNCT
ejpam-164	94	1	then	then	ADV
ejpam-164	94	2	a	a	DET
ejpam-164	94	3	⊆	⊆	NUM
ejpam-164	94	4	cl(int(a	cl(int(a	NOUN
ejpam-164	94	5	)	)	PUNCT
ejpam-164	94	6	)	)	PUNCT
ejpam-164	95	1	⊆	⊆	NUM
ejpam-164	95	2	cl(intω(cl(a	cl(intω(cl(a	NUM
ejpam-164	95	3	)	)	PUNCT
ejpam-164	95	4	)	)	PUNCT
ejpam-164	95	5	)	)	PUNCT
ejpam-164	95	6	and	and	CCONJ
ejpam-164	95	7	hence	hence	ADV
ejpam-164	95	8	a	a	PRON
ejpam-164	95	9	is	be	AUX
ejpam-164	95	10	β	β	X
ejpam-164	95	11	-ωopen	-ωopen	ADJ
ejpam-164	95	12	.	.	PUNCT
ejpam-164	96	1	in	in	ADP
ejpam-164	96	2	addition	addition	NOUN
ejpam-164	96	3	cl(a)⊆	cl(a)⊆	PROPN
ejpam-164	96	4	cl(int(a	cl(int(a	PROPN
ejpam-164	96	5	)	)	PUNCT
ejpam-164	96	6	)	)	PUNCT
ejpam-164	97	1	and	and	CCONJ
ejpam-164	97	2	hence	hence	ADV
ejpam-164	97	3	intω(cl(a))⊆	intω(cl(a))⊆	VERB
ejpam-164	97	4	cl(int(a	cl(int(a	NOUN
ejpam-164	97	5	)	)	PUNCT
ejpam-164	97	6	)	)	PUNCT
ejpam-164	97	7	.	.	PUNCT
ejpam-164	98	1	conversely	conversely	ADV
ejpam-164	98	2	let	let	VERB
ejpam-164	98	3	a	a	PRON
ejpam-164	98	4	be	be	AUX
ejpam-164	98	5	β	β	X
ejpam-164	98	6	-ω	-ω	X
ejpam-164	98	7	-	-	ADJ
ejpam-164	98	8	open	open	ADJ
ejpam-164	98	9	and	and	CCONJ
ejpam-164	98	10	intω(cl(a	intω(cl(a	ADJ
ejpam-164	98	11	)	)	PUNCT
ejpam-164	98	12	)	)	PUNCT
ejpam-164	99	1	⊆	⊆	NUM
ejpam-164	99	2	cl(int(a	cl(int(a	NOUN
ejpam-164	99	3	)	)	PUNCT
ejpam-164	99	4	)	)	PUNCT
ejpam-164	99	5	.	.	PUNCT
ejpam-164	100	1	then	then	ADV
ejpam-164	100	2	a	a	DET
ejpam-164	100	3	⊆	⊆	NUM
ejpam-164	100	4	cl(intω(cl(a	cl(intω(cl(a	NUM
ejpam-164	100	5	)	)	PUNCT
ejpam-164	100	6	)	)	PUNCT
ejpam-164	100	7	)	)	PUNCT
ejpam-164	101	1	⊆	⊆	NUM
ejpam-164	101	2	cl(cl(int(a	cl(cl(int(a	NOUN
ejpam-164	101	3	)	)	PUNCT
ejpam-164	101	4	)	)	PUNCT
ejpam-164	101	5	)	)	PUNCT
ejpam-164	102	1	=	=	SYM
ejpam-164	102	2	cl(int(a	cl(int(a	PROPN
ejpam-164	102	3	)	)	PUNCT
ejpam-164	102	4	)	)	PUNCT
ejpam-164	102	5	.	.	PUNCT
ejpam-164	103	1	and	and	CCONJ
ejpam-164	103	2	hence	hence	ADV
ejpam-164	103	3	a	a	PRON
ejpam-164	103	4	is	be	AUX
ejpam-164	103	5	semi	semi	ADJ
ejpam-164	103	6	-	-	ADJ
ejpam-164	103	7	open	open	ADJ
ejpam-164	103	8	.	.	PUNCT
ejpam-164	104	1	proposition	proposition	NOUN
ejpam-164	104	2	2.11	2.11	NUM
ejpam-164	104	3	.	.	PUNCT
ejpam-164	105	1	the	the	DET
ejpam-164	105	2	intersection	intersection	NOUN
ejpam-164	105	3	of	of	ADP
ejpam-164	105	4	a	a	DET
ejpam-164	105	5	pre	pre	ADJ
ejpam-164	105	6	-	-	ADJ
ejpam-164	105	7	ω	ω	ADJ
ejpam-164	105	8	-	-	ADJ
ejpam-164	105	9	open	open	ADJ
ejpam-164	105	10	set	set	NOUN
ejpam-164	105	11	and	and	CCONJ
ejpam-164	105	12	an	an	DET
ejpam-164	105	13	open	open	ADJ
ejpam-164	105	14	set	set	NOUN
ejpam-164	105	15	is	be	AUX
ejpam-164	105	16	pre	pre	ADJ
ejpam-164	105	17	-	-	ADJ
ejpam-164	105	18	ω	ω	ADV
ejpam-164	105	19	-	-	ADJ
ejpam-164	105	20	open	open	ADJ
ejpam-164	105	21	.	.	PUNCT
ejpam-164	106	1	proof	proof	NOUN
ejpam-164	106	2	.	.	PUNCT
ejpam-164	107	1	let	let	VERB
ejpam-164	107	2	a	a	PRON
ejpam-164	107	3	be	be	AUX
ejpam-164	107	4	a	a	DET
ejpam-164	107	5	pre	pre	ADJ
ejpam-164	107	6	-	-	ADJ
ejpam-164	107	7	ω	ω	ADJ
ejpam-164	107	8	-	-	ADJ
ejpam-164	107	9	open	open	ADJ
ejpam-164	107	10	set	set	NOUN
ejpam-164	107	11	and	and	CCONJ
ejpam-164	107	12	u	u	NOUN
ejpam-164	107	13	be	be	VERB
ejpam-164	107	14	an	an	DET
ejpam-164	107	15	open	open	ADJ
ejpam-164	107	16	set	set	NOUN
ejpam-164	107	17	in	in	ADP
ejpam-164	107	18	x	x	X
ejpam-164	107	19	.	.	PUNCT
ejpam-164	108	1	then	then	ADV
ejpam-164	108	2	a	a	DET
ejpam-164	108	3	⊆	⊆	NUM
ejpam-164	108	4	intω(cl(a	intω(cl(a	NOUN
ejpam-164	108	5	)	)	PUNCT
ejpam-164	108	6	)	)	PUNCT
ejpam-164	108	7	and	and	CCONJ
ejpam-164	108	8	intω(u	intω(u	PROPN
ejpam-164	108	9	)	)	PUNCT
ejpam-164	108	10	=	=	SYM
ejpam-164	108	11	u	u	NOUN
ejpam-164	108	12	,	,	PUNCT
ejpam-164	108	13	by	by	ADP
ejpam-164	108	14	lemma	lemma	PROPN
ejpam-164	108	15	2.8	2.8	NUM
ejpam-164	108	16	,	,	PUNCT
ejpam-164	108	17	we	we	PRON
ejpam-164	108	18	have	have	VERB
ejpam-164	108	19	u	u	NOUN
ejpam-164	108	20	∩	∩	NOUN
ejpam-164	108	21	a⊆	a⊆	NUM
ejpam-164	108	22	intω(u	intω(u	PROPN
ejpam-164	108	23	)	)	PUNCT
ejpam-164	108	24	∩	∩	NOUN
ejpam-164	108	25	intω(cl(a	intω(cl(a	ADJ
ejpam-164	108	26	)	)	PUNCT
ejpam-164	108	27	)	)	PUNCT
ejpam-164	109	1	⊆	⊆	NUM
ejpam-164	109	2	intω(u	intω(u	NOUN
ejpam-164	109	3	∩	∩	NOUN
ejpam-164	109	4	cl(a	cl(a	NUM
ejpam-164	109	5	)	)	PUNCT
ejpam-164	109	6	)	)	PUNCT
ejpam-164	110	1	⊆	⊆	NUM
ejpam-164	110	2	intω(cl(u	intω(cl(u	NOUN
ejpam-164	110	3	∩	∩	PROPN
ejpam-164	110	4	a	a	X
ejpam-164	110	5	)	)	PUNCT
ejpam-164	110	6	)	)	PUNCT
ejpam-164	110	7	.	.	PUNCT
ejpam-164	111	1	therefore	therefore	ADV
ejpam-164	111	2	,	,	PUNCT
ejpam-164	111	3	a∩	a∩	PROPN
ejpam-164	111	4	u	u	PROPN
ejpam-164	111	5	is	be	AUX
ejpam-164	111	6	pre	pre	ADJ
ejpam-164	111	7	-	-	ADJ
ejpam-164	111	8	ω	ω	ADJ
ejpam-164	111	9	-	-	ADJ
ejpam-164	111	10	open	open	ADJ
ejpam-164	111	11	.	.	PUNCT
ejpam-164	112	1	proposition	proposition	NOUN
ejpam-164	112	2	2.12	2.12	NUM
ejpam-164	112	3	.	.	PUNCT
ejpam-164	113	1	the	the	DET
ejpam-164	113	2	intersection	intersection	NOUN
ejpam-164	113	3	of	of	ADP
ejpam-164	113	4	a	a	DET
ejpam-164	113	5	β	β	X
ejpam-164	113	6	-ω	-ω	VERB
ejpam-164	113	7	-	-	ADJ
ejpam-164	113	8	open	open	ADJ
ejpam-164	113	9	set	set	NOUN
ejpam-164	113	10	and	and	CCONJ
ejpam-164	113	11	an	an	DET
ejpam-164	113	12	open	open	ADJ
ejpam-164	113	13	set	set	NOUN
ejpam-164	113	14	is	be	AUX
ejpam-164	113	15	β	β	NOUN
ejpam-164	113	16	-ω	-ω	X
ejpam-164	113	17	-	-	ADJ
ejpam-164	113	18	open	open	ADJ
ejpam-164	113	19	.	.	PUNCT
ejpam-164	114	1	proof	proof	NOUN
ejpam-164	114	2	.	.	PUNCT
ejpam-164	115	1	let	let	VERB
ejpam-164	115	2	u	u	PRON
ejpam-164	115	3	be	be	AUX
ejpam-164	115	4	an	an	DET
ejpam-164	115	5	open	open	ADJ
ejpam-164	115	6	set	set	NOUN
ejpam-164	115	7	and	and	CCONJ
ejpam-164	115	8	a	a	DET
ejpam-164	115	9	a	a	DET
ejpam-164	115	10	β	β	X
ejpam-164	115	11	-ω	-ω	VERB
ejpam-164	115	12	-	-	ADJ
ejpam-164	115	13	open	open	ADJ
ejpam-164	115	14	set	set	NOUN
ejpam-164	115	15	.	.	PUNCT
ejpam-164	116	1	since	since	SCONJ
ejpam-164	116	2	every	every	DET
ejpam-164	116	3	open	open	ADJ
ejpam-164	116	4	set	set	NOUN
ejpam-164	116	5	is	be	AUX
ejpam-164	116	6	ω	ω	NOUN
ejpam-164	116	7	-	-	ADJ
ejpam-164	116	8	open	open	ADJ
ejpam-164	116	9	,	,	PUNCT
ejpam-164	116	10	by	by	ADP
ejpam-164	116	11	t.	t.	PROPN
ejpam-164	116	12	noiri	noiri	PROPN
ejpam-164	116	13	,	,	PUNCT
ejpam-164	116	14	a.	a.	PROPN
ejpam-164	116	15	al	al	PROPN
ejpam-164	116	16	-	-	PUNCT
ejpam-164	116	17	omari	omari	PROPN
ejpam-164	116	18	,	,	PUNCT
ejpam-164	116	19	and	and	CCONJ
ejpam-164	116	20	m.	m.	NOUN
ejpam-164	116	21	noorani	noorani	PROPN
ejpam-164	116	22	/	/	SYM
ejpam-164	116	23	eur	eur	PROPN
ejpam-164	116	24	.	.	PUNCT
ejpam-164	117	1	j.	j.	PROPN
ejpam-164	117	2	pure	pure	PROPN
ejpam-164	117	3	appl	appl	PROPN
ejpam-164	117	4	.	.	PROPN
ejpam-164	117	5	math	math	PROPN
ejpam-164	117	6	,	,	PUNCT
ejpam-164	117	7	2	2	NUM
ejpam-164	117	8	(	(	PUNCT
ejpam-164	117	9	2009	2009	NUM
ejpam-164	117	10	)	)	PUNCT
ejpam-164	117	11	,	,	PUNCT
ejpam-164	117	12	(	(	PUNCT
ejpam-164	117	13	73	73	NUM
ejpam-164	117	14	-	-	SYM
ejpam-164	117	15	84	84	NUM
ejpam-164	117	16	)	)	PUNCT
ejpam-164	117	17	77	77	NUM
ejpam-164	117	18	lemma	lemma	PROPN
ejpam-164	117	19	2.8	2.8	NUM
ejpam-164	117	20	,	,	PUNCT
ejpam-164	117	21	we	we	PRON
ejpam-164	117	22	have	have	AUX
ejpam-164	117	23	u	u	NOUN
ejpam-164	117	24	∩	∩	NOUN
ejpam-164	117	25	a⊆	a⊆	NOUN
ejpam-164	117	26	u	u	NOUN
ejpam-164	117	27	∩	∩	NOUN
ejpam-164	117	28	cl(intω(cl(a	cl(intω(cl(a	NUM
ejpam-164	117	29	)	)	PUNCT
ejpam-164	117	30	)	)	PUNCT
ejpam-164	117	31	)	)	PUNCT
ejpam-164	118	1	⊆	⊆	NUM
ejpam-164	118	2	cl(u	cl(u	NOUN
ejpam-164	118	3	∩	∩	NOUN
ejpam-164	118	4	intω(cl(a	intω(cl(a	NOUN
ejpam-164	118	5	)	)	PUNCT
ejpam-164	118	6	)	)	PUNCT
ejpam-164	118	7	)	)	PUNCT
ejpam-164	119	1	=	=	PRON
ejpam-164	119	2	cl(intω(u)∩	cl(intω(u)∩	PROPN
ejpam-164	119	3	intω(cl(a	intω(cl(a	PROPN
ejpam-164	119	4	)	)	PUNCT
ejpam-164	119	5	)	)	PUNCT
ejpam-164	119	6	)	)	PUNCT
ejpam-164	120	1	=	=	SYM
ejpam-164	120	2	cl(intω(u	cl(intω(u	NOUN
ejpam-164	120	3	∩	∩	NOUN
ejpam-164	120	4	cl(a	cl(a	NUM
ejpam-164	120	5	)	)	PUNCT
ejpam-164	120	6	)	)	PUNCT
ejpam-164	120	7	)	)	PUNCT
ejpam-164	121	1	⊆	⊆	NUM
ejpam-164	121	2	cl(intω(cl(u	cl(intω(cl(u	PROPN
ejpam-164	121	3	∩	∩	NOUN
ejpam-164	121	4	a	a	X
ejpam-164	121	5	)	)	PUNCT
ejpam-164	121	6	)	)	PUNCT
ejpam-164	121	7	)	)	PUNCT
ejpam-164	121	8	.	.	PUNCT
ejpam-164	122	1	this	this	PRON
ejpam-164	122	2	shows	show	VERB
ejpam-164	122	3	that	that	SCONJ
ejpam-164	122	4	u	u	PROPN
ejpam-164	122	5	∩	∩	NOUN
ejpam-164	122	6	a	a	PRON
ejpam-164	122	7	is	be	AUX
ejpam-164	122	8	β	β	NOUN
ejpam-164	122	9	-ω	-ω	X
ejpam-164	122	10	-	-	ADJ
ejpam-164	122	11	open	open	ADJ
ejpam-164	122	12	.	.	PUNCT
ejpam-164	123	1	we	we	PRON
ejpam-164	123	2	note	note	VERB
ejpam-164	123	3	that	that	SCONJ
ejpam-164	123	4	the	the	DET
ejpam-164	123	5	intersection	intersection	NOUN
ejpam-164	123	6	of	of	ADP
ejpam-164	123	7	two	two	NUM
ejpam-164	123	8	pre	pre	ADJ
ejpam-164	123	9	-	-	ADJ
ejpam-164	123	10	ω	ω	VERB
ejpam-164	123	11	-	-	ADJ
ejpam-164	123	12	open	open	ADJ
ejpam-164	123	13	(	(	PUNCT
ejpam-164	123	14	resp	resp	NOUN
ejpam-164	123	15	.	.	PUNCT
ejpam-164	124	1	b	b	X
ejpam-164	124	2	-	-	PUNCT
ejpam-164	124	3	ω	ω	NOUN
ejpam-164	124	4	-	-	NOUN
ejpam-164	124	5	open	open	ADJ
ejpam-164	124	6	,	,	PUNCT
ejpam-164	124	7	β	β	X
ejpam-164	124	8	-ω	-ω	ADJ
ejpam-164	124	9	-	-	ADJ
ejpam-164	124	10	open	open	ADJ
ejpam-164	124	11	)	)	PUNCT
ejpam-164	124	12	sets	set	NOUN
ejpam-164	124	13	need	need	AUX
ejpam-164	124	14	not	not	PART
ejpam-164	124	15	be	be	AUX
ejpam-164	124	16	pre	pre	ADJ
ejpam-164	124	17	-	-	ADJ
ejpam-164	124	18	ω	ω	VERB
ejpam-164	124	19	-	-	ADJ
ejpam-164	124	20	open	open	ADJ
ejpam-164	124	21	(	(	PUNCT
ejpam-164	124	22	resp	resp	NOUN
ejpam-164	124	23	.	.	PUNCT
ejpam-164	125	1	b	b	X
ejpam-164	125	2	-	-	PUNCT
ejpam-164	125	3	ω	ω	NOUN
ejpam-164	125	4	-	-	NOUN
ejpam-164	125	5	open	open	ADJ
ejpam-164	125	6	,	,	PUNCT
ejpam-164	125	7	β	β	X
ejpam-164	125	8	-ω	-ω	ADJ
ejpam-164	125	9	-	-	ADJ
ejpam-164	125	10	open	open	ADJ
ejpam-164	125	11	)	)	PUNCT
ejpam-164	125	12	as	as	SCONJ
ejpam-164	125	13	can	can	AUX
ejpam-164	125	14	be	be	AUX
ejpam-164	125	15	seen	see	VERB
ejpam-164	125	16	from	from	ADP
ejpam-164	125	17	the	the	DET
ejpam-164	125	18	following	follow	VERB
ejpam-164	125	19	example	example	NOUN
ejpam-164	125	20	:	:	PUNCT
ejpam-164	125	21	example	example	NOUN
ejpam-164	125	22	2.13	2.13	NUM
ejpam-164	125	23	.	.	PUNCT
ejpam-164	126	1	let	let	VERB
ejpam-164	126	2	x	x	PUNCT
ejpam-164	126	3	=	=	PUNCT
ejpam-164	126	4	r	r	NOUN
ejpam-164	126	5	with	with	ADP
ejpam-164	126	6	the	the	DET
ejpam-164	126	7	usual	usual	ADJ
ejpam-164	126	8	topology	topology	NOUN
ejpam-164	126	9	τ	τ	PROPN
ejpam-164	126	10	.	.	PUNCT
ejpam-164	127	1	let	let	VERB
ejpam-164	127	2	a	a	DET
ejpam-164	127	3	=	=	X
ejpam-164	127	4	q	q	NOUN
ejpam-164	127	5	and	and	CCONJ
ejpam-164	127	6	b	b	X
ejpam-164	127	7	=	=	SYM
ejpam-164	127	8	(	(	PUNCT
ejpam-164	127	9	r\q	r\q	NOUN
ejpam-164	127	10	)	)	PUNCT
ejpam-164	127	11	∪	∪	X
ejpam-164	127	12	{	{	PUNCT
ejpam-164	127	13	1	1	NUM
ejpam-164	127	14	}	}	PUNCT
ejpam-164	127	15	,	,	PUNCT
ejpam-164	127	16	then	then	ADV
ejpam-164	127	17	a	a	PRON
ejpam-164	127	18	and	and	CCONJ
ejpam-164	127	19	b	b	NOUN
ejpam-164	127	20	are	be	AUX
ejpam-164	127	21	pre	pre	ADJ
ejpam-164	127	22	-	-	ADJ
ejpam-164	127	23	ω	ω	VERB
ejpam-164	127	24	-	-	ADJ
ejpam-164	127	25	open	open	ADJ
ejpam-164	127	26	,	,	PUNCT
ejpam-164	127	27	but	but	CCONJ
ejpam-164	128	1	a∩	a∩	PROPN
ejpam-164	128	2	b	b	X
ejpam-164	128	3	=	=	PUNCT
ejpam-164	128	4	{	{	PUNCT
ejpam-164	128	5	1	1	NUM
ejpam-164	128	6	}	}	PUNCT
ejpam-164	128	7	which	which	PRON
ejpam-164	128	8	is	be	AUX
ejpam-164	128	9	not	not	PART
ejpam-164	128	10	β	β	NOUN
ejpam-164	128	11	-ω	-ω	VERB
ejpam-164	128	12	-	-	VERB
ejpam-164	128	13	open	open	ADJ
ejpam-164	128	14	since	since	SCONJ
ejpam-164	128	15	cl(intω(cl({1	cl(intω(cl({1	NOUN
ejpam-164	128	16	}	}	PUNCT
ejpam-164	128	17	)	)	PUNCT
ejpam-164	128	18	)	)	PUNCT
ejpam-164	128	19	)	)	PUNCT
ejpam-164	129	1	=	=	PUNCT
ejpam-164	129	2	cl(intω({1	cl(intω({1	PROPN
ejpam-164	129	3	}	}	PUNCT
ejpam-164	129	4	)	)	PUNCT
ejpam-164	129	5	=	=	SYM
ejpam-164	129	6	cl({φ	cl({φ	NOUN
ejpam-164	129	7	}	}	PUNCT
ejpam-164	129	8	)	)	PUNCT
ejpam-164	129	9	=	=	SYM
ejpam-164	130	1	φ	φ	PROPN
ejpam-164	130	2	.	.	PUNCT
ejpam-164	130	3	proposition	proposition	NOUN
ejpam-164	130	4	2.14	2.14	NUM
ejpam-164	130	5	.	.	PUNCT
ejpam-164	131	1	the	the	DET
ejpam-164	131	2	intersection	intersection	NOUN
ejpam-164	131	3	of	of	ADP
ejpam-164	131	4	a	a	DET
ejpam-164	131	5	b	b	PROPN
ejpam-164	131	6	-	-	PUNCT
ejpam-164	131	7	ω	ω	VERB
ejpam-164	131	8	-	-	ADJ
ejpam-164	131	9	open	open	ADJ
ejpam-164	131	10	set	set	NOUN
ejpam-164	131	11	and	and	CCONJ
ejpam-164	131	12	an	an	DET
ejpam-164	131	13	open	open	ADJ
ejpam-164	131	14	set	set	NOUN
ejpam-164	131	15	is	be	AUX
ejpam-164	131	16	b	b	NOUN
ejpam-164	131	17	-	-	PUNCT
ejpam-164	131	18	ω	ω	NOUN
ejpam-164	131	19	-	-	NOUN
ejpam-164	131	20	open	open	ADJ
ejpam-164	131	21	.	.	PUNCT
ejpam-164	132	1	proof	proof	NOUN
ejpam-164	132	2	.	.	PUNCT
ejpam-164	133	1	let	let	VERB
ejpam-164	133	2	a	a	DET
ejpam-164	133	3	be	be	AUX
ejpam-164	133	4	b	b	NUM
ejpam-164	133	5	-	-	PUNCT
ejpam-164	133	6	ω	ω	NOUN
ejpam-164	133	7	-	-	NOUN
ejpam-164	133	8	open	open	ADJ
ejpam-164	133	9	and	and	CCONJ
ejpam-164	133	10	u	u	NOUN
ejpam-164	133	11	be	be	VERB
ejpam-164	133	12	open	open	ADJ
ejpam-164	133	13	,	,	PUNCT
ejpam-164	133	14	then	then	ADV
ejpam-164	133	15	a	a	DET
ejpam-164	133	16	⊆	⊆	NUM
ejpam-164	133	17	intω(cl(a	intω(cl(a	NOUN
ejpam-164	133	18	)	)	PUNCT
ejpam-164	133	19	)	)	PUNCT
ejpam-164	133	20	∪	∪	ADP
ejpam-164	133	21	cl(intω(a	cl(intω(a	NOUN
ejpam-164	133	22	)	)	PUNCT
ejpam-164	133	23	)	)	PUNCT
ejpam-164	133	24	and	and	CCONJ
ejpam-164	133	25	u	u	X
ejpam-164	133	26	=	=	PROPN
ejpam-164	133	27	intω(u	intω(u	PROPN
ejpam-164	133	28	)	)	PUNCT
ejpam-164	133	29	.	.	PUNCT
ejpam-164	134	1	then	then	ADV
ejpam-164	134	2	we	we	PRON
ejpam-164	134	3	have	have	VERB
ejpam-164	134	4	u	u	NOUN
ejpam-164	134	5	∩	∩	NOUN
ejpam-164	134	6	a⊆	a⊆	NOUN
ejpam-164	134	7	u	u	NOUN
ejpam-164	134	8	∩	∩	NOUN
ejpam-164	134	9	[	[	X
ejpam-164	134	10	intω(cl(a))∪	intω(cl(a))∪	PROPN
ejpam-164	134	11	cl(intω(a	cl(intω(a	NOUN
ejpam-164	134	12	)	)	PUNCT
ejpam-164	134	13	)	)	PUNCT
ejpam-164	134	14	]	]	PUNCT
ejpam-164	135	1	=	=	PUNCT
ejpam-164	136	1	[	[	X
ejpam-164	136	2	u	u	NOUN
ejpam-164	136	3	∩	∩	NOUN
ejpam-164	136	4	intω(cl(a))]∪	intω(cl(a))]∪	NOUN
ejpam-164	136	5	[	[	X
ejpam-164	136	6	u	u	X
ejpam-164	136	7	∩	∩	NOUN
ejpam-164	136	8	cl(intω(a	cl(intω(a	NOUN
ejpam-164	136	9	)	)	PUNCT
ejpam-164	136	10	)	)	PUNCT
ejpam-164	136	11	]	]	PUNCT
ejpam-164	137	1	=	=	PUNCT
ejpam-164	138	1	[	[	X
ejpam-164	138	2	intω(u)∩	intω(u)∩	PROPN
ejpam-164	138	3	intω(cl(a))]∪	intω(cl(a))]∪	PROPN
ejpam-164	138	4	[	[	X
ejpam-164	138	5	u	u	X
ejpam-164	138	6	∩	∩	ADJ
ejpam-164	138	7	cl(intω(a	cl(intω(a	NOUN
ejpam-164	138	8	)	)	PUNCT
ejpam-164	138	9	)	)	PUNCT
ejpam-164	138	10	]	]	PUNCT
ejpam-164	139	1	⊆	⊆	NUM
ejpam-164	140	1	[	[	X
ejpam-164	140	2	intω(u	intω(u	NOUN
ejpam-164	140	3	∩	∩	NOUN
ejpam-164	140	4	cl(a))]∪	cl(a))]∪	X
ejpam-164	140	5	[	[	X
ejpam-164	140	6	cl(u	cl(u	X
ejpam-164	140	7	∩	∩	ADJ
ejpam-164	140	8	intω(a	intω(a	NOUN
ejpam-164	140	9	)	)	PUNCT
ejpam-164	140	10	)	)	PUNCT
ejpam-164	140	11	]	]	PUNCT
ejpam-164	141	1	⊆	⊆	NUM
ejpam-164	141	2	[	[	X
ejpam-164	141	3	intω(cl(u	intω(cl(u	NOUN
ejpam-164	141	4	∩	∩	NOUN
ejpam-164	141	5	a))]∪	a))]∪	VERB
ejpam-164	142	1	[	[	X
ejpam-164	142	2	cl(intω(u	cl(intω(u	X
ejpam-164	142	3	∩	∩	ADJ
ejpam-164	142	4	a	a	X
ejpam-164	142	5	)	)	PUNCT
ejpam-164	142	6	)	)	PUNCT
ejpam-164	142	7	]	]	PUNCT
ejpam-164	142	8	.	.	PUNCT
ejpam-164	143	1	this	this	PRON
ejpam-164	143	2	shows	show	VERB
ejpam-164	143	3	that	that	SCONJ
ejpam-164	143	4	u	u	PROPN
ejpam-164	143	5	∩	∩	NOUN
ejpam-164	143	6	a	a	PRON
ejpam-164	143	7	is	be	AUX
ejpam-164	143	8	b	b	NOUN
ejpam-164	143	9	-	-	PUNCT
ejpam-164	143	10	ω	ω	NOUN
ejpam-164	143	11	-	-	NOUN
ejpam-164	143	12	open	open	ADJ
ejpam-164	143	13	.	.	PUNCT
ejpam-164	144	1	proposition	proposition	NOUN
ejpam-164	144	2	2.15	2.15	NUM
ejpam-164	144	3	.	.	PUNCT
ejpam-164	145	1	the	the	DET
ejpam-164	145	2	intersection	intersection	NOUN
ejpam-164	145	3	of	of	ADP
ejpam-164	145	4	an	an	DET
ejpam-164	145	5	α	α	PROPN
ejpam-164	145	6	-	-	PUNCT
ejpam-164	145	7	ω	ω	VERB
ejpam-164	145	8	-	-	ADJ
ejpam-164	145	9	open	open	ADJ
ejpam-164	145	10	set	set	NOUN
ejpam-164	145	11	and	and	CCONJ
ejpam-164	145	12	an	an	DET
ejpam-164	145	13	open	open	ADJ
ejpam-164	145	14	set	set	NOUN
ejpam-164	145	15	is	be	AUX
ejpam-164	145	16	α	α	NOUN
ejpam-164	145	17	-	-	PUNCT
ejpam-164	145	18	ω	ω	VERB
ejpam-164	145	19	-	-	ADJ
ejpam-164	145	20	open	open	ADJ
ejpam-164	145	21	.	.	PUNCT
ejpam-164	146	1	theorem	theorem	VERB
ejpam-164	146	2	2.16	2.16	NUM
ejpam-164	146	3	.	.	PUNCT
ejpam-164	147	1	if	if	SCONJ
ejpam-164	147	2	{	{	PUNCT
ejpam-164	147	3	aα	aα	NOUN
ejpam-164	147	4	:	:	PUNCT
ejpam-164	147	5	α	α	PRON
ejpam-164	147	6	∈∆	∈∆	NOUN
ejpam-164	147	7	}	}	PUNCT
ejpam-164	147	8	is	be	AUX
ejpam-164	147	9	a	a	DET
ejpam-164	147	10	collection	collection	NOUN
ejpam-164	147	11	of	of	ADP
ejpam-164	147	12	b	b	PROPN
ejpam-164	147	13	-	-	PUNCT
ejpam-164	147	14	ω	ω	NOUN
ejpam-164	147	15	-	-	NOUN
ejpam-164	147	16	open	open	ADJ
ejpam-164	147	17	(	(	PUNCT
ejpam-164	147	18	resp	resp	NOUN
ejpam-164	147	19	.	.	PUNCT
ejpam-164	148	1	pre	pre	ADJ
ejpam-164	148	2	-	-	ADJ
ejpam-164	148	3	ω	ω	VERB
ejpam-164	148	4	-	-	ADJ
ejpam-164	148	5	open	open	ADJ
ejpam-164	148	6	,	,	PUNCT
ejpam-164	148	7	β	β	X
ejpam-164	148	8	-ω	-ω	ADJ
ejpam-164	148	9	-	-	ADJ
ejpam-164	148	10	open	open	ADJ
ejpam-164	148	11	)	)	PUNCT
ejpam-164	148	12	sets	set	NOUN
ejpam-164	148	13	of	of	ADP
ejpam-164	148	14	a	a	DET
ejpam-164	148	15	space	space	NOUN
ejpam-164	148	16	(	(	PUNCT
ejpam-164	148	17	x	x	X
ejpam-164	148	18	,	,	PUNCT
ejpam-164	148	19	τ	τ	PROPN
ejpam-164	148	20	)	)	PUNCT
ejpam-164	148	21	,	,	PUNCT
ejpam-164	148	22	then	then	ADV
ejpam-164	148	23	∪α∈∆aα	∪α∈∆aα	PROPN
ejpam-164	148	24	is	be	AUX
ejpam-164	148	25	b	b	PROPN
ejpam-164	148	26	-	-	PUNCT
ejpam-164	148	27	ω	ω	NOUN
ejpam-164	148	28	-	-	NOUN
ejpam-164	148	29	open	open	ADJ
ejpam-164	148	30	(	(	PUNCT
ejpam-164	148	31	resp	resp	NOUN
ejpam-164	148	32	.	.	PUNCT
ejpam-164	149	1	pre	pre	ADJ
ejpam-164	149	2	-	-	ADJ
ejpam-164	149	3	ω	ω	VERB
ejpam-164	149	4	-	-	ADJ
ejpam-164	149	5	open	open	ADJ
ejpam-164	149	6	,	,	PUNCT
ejpam-164	149	7	β	β	X
ejpam-164	149	8	-ω	-ω	ADJ
ejpam-164	149	9	-	-	ADJ
ejpam-164	149	10	open	open	ADJ
ejpam-164	149	11	)	)	PUNCT
ejpam-164	149	12	.	.	PUNCT
ejpam-164	150	1	t.	t.	PROPN
ejpam-164	150	2	noiri	noiri	PROPN
ejpam-164	150	3	,	,	PUNCT
ejpam-164	150	4	a.	a.	PROPN
ejpam-164	150	5	al	al	PROPN
ejpam-164	150	6	-	-	PUNCT
ejpam-164	150	7	omari	omari	PROPN
ejpam-164	150	8	,	,	PUNCT
ejpam-164	150	9	and	and	CCONJ
ejpam-164	150	10	m.	m.	NOUN
ejpam-164	150	11	noorani	noorani	PROPN
ejpam-164	150	12	/	/	SYM
ejpam-164	150	13	eur	eur	PROPN
ejpam-164	150	14	.	.	PUNCT
ejpam-164	151	1	j.	j.	PROPN
ejpam-164	151	2	pure	pure	PROPN
ejpam-164	151	3	appl	appl	PROPN
ejpam-164	151	4	.	.	PROPN
ejpam-164	151	5	math	math	PROPN
ejpam-164	151	6	,	,	PUNCT
ejpam-164	151	7	2	2	NUM
ejpam-164	151	8	(	(	PUNCT
ejpam-164	151	9	2009	2009	NUM
ejpam-164	151	10	)	)	PUNCT
ejpam-164	151	11	,	,	PUNCT
ejpam-164	151	12	(	(	PUNCT
ejpam-164	151	13	73	73	NUM
ejpam-164	151	14	-	-	SYM
ejpam-164	151	15	84	84	NUM
ejpam-164	151	16	)	)	PUNCT
ejpam-164	151	17	78	78	NUM
ejpam-164	151	18	proof	proof	NOUN
ejpam-164	151	19	.	.	PUNCT
ejpam-164	152	1	we	we	PRON
ejpam-164	152	2	prove	prove	VERB
ejpam-164	152	3	only	only	ADV
ejpam-164	152	4	the	the	DET
ejpam-164	152	5	first	first	ADJ
ejpam-164	152	6	case	case	NOUN
ejpam-164	152	7	since	since	SCONJ
ejpam-164	152	8	the	the	DET
ejpam-164	152	9	other	other	ADJ
ejpam-164	152	10	cases	case	NOUN
ejpam-164	152	11	are	be	AUX
ejpam-164	152	12	similarly	similarly	ADV
ejpam-164	152	13	shown	show	VERB
ejpam-164	152	14	.	.	PUNCT
ejpam-164	153	1	since	since	SCONJ
ejpam-164	153	2	aα	aα	NOUN
ejpam-164	153	3	⊆	⊆	NUM
ejpam-164	153	4	intω(cl(aα))∪	intω(cl(aα))∪	PROPN
ejpam-164	153	5	cl(intω(aα	cl(intω(aα	NOUN
ejpam-164	153	6	)	)	PUNCT
ejpam-164	153	7	)	)	PUNCT
ejpam-164	153	8	for	for	SCONJ
ejpam-164	153	9	every	every	DET
ejpam-164	153	10	α	α	NOUN
ejpam-164	153	11	∈∆	∈∆	NOUN
ejpam-164	153	12	,	,	PUNCT
ejpam-164	153	13	we	we	PRON
ejpam-164	153	14	have	have	VERB
ejpam-164	153	15	∪α∈∆aα	∪α∈∆aα	NOUN
ejpam-164	153	16	⊆	⊆	NUM
ejpam-164	153	17	∪α∈∆[intω(cl(aα))∪	∪α∈∆[intω(cl(aα))∪	ADJ
ejpam-164	153	18	cl(intω(aα	cl(intω(aα	NOUN
ejpam-164	153	19	)	)	PUNCT
ejpam-164	153	20	)	)	PUNCT
ejpam-164	153	21	]	]	PUNCT
ejpam-164	154	1	⊆	⊆	NUM
ejpam-164	154	2	[	[	X
ejpam-164	154	3	∪α∈∆	∪α∈∆	NOUN
ejpam-164	154	4	intω(cl(aα))]∪	intω(cl(aα))]∪	PRON
ejpam-164	154	5	[	[	X
ejpam-164	154	6	∪α∈∆cl(intω(aα	∪α∈∆cl(intω(aα	NOUN
ejpam-164	154	7	)	)	PUNCT
ejpam-164	154	8	)	)	PUNCT
ejpam-164	154	9	]	]	PUNCT
ejpam-164	155	1	⊆	⊆	NUM
ejpam-164	155	2	[	[	X
ejpam-164	155	3	intω(∪α∈∆cl(aα))]∪	intω(∪α∈∆cl(aα))]∪	X
ejpam-164	156	1	[	[	X
ejpam-164	156	2	cl(∪α∈∆	cl(∪α∈∆	NOUN
ejpam-164	156	3	intω(aα	intω(aα	ADJ
ejpam-164	156	4	)	)	PUNCT
ejpam-164	156	5	)	)	PUNCT
ejpam-164	156	6	]	]	PUNCT
ejpam-164	157	1	⊆	⊆	NUM
ejpam-164	157	2	[	[	X
ejpam-164	157	3	intω(cl(∪α∈∆aα))]∪	intω(cl(∪α∈∆aα))]∪	NOUN
ejpam-164	157	4	[	[	X
ejpam-164	157	5	cl(intω(∪α∈∆aα	cl(intω(∪α∈∆aα	NOUN
ejpam-164	157	6	)	)	PUNCT
ejpam-164	157	7	)	)	PUNCT
ejpam-164	157	8	]	]	PUNCT
ejpam-164	157	9	.	.	PUNCT
ejpam-164	158	1	therefore	therefore	ADV
ejpam-164	158	2	,	,	PUNCT
ejpam-164	158	3	∪α∈∆aα	∪α∈∆aα	PROPN
ejpam-164	158	4	is	be	AUX
ejpam-164	158	5	b	b	PROPN
ejpam-164	158	6	-	-	PUNCT
ejpam-164	158	7	ω	ω	NOUN
ejpam-164	158	8	-	-	NOUN
ejpam-164	158	9	open	open	ADJ
ejpam-164	158	10	.	.	PUNCT
ejpam-164	159	1	proposition	proposition	NOUN
ejpam-164	159	2	2.17	2.17	NUM
ejpam-164	159	3	.	.	PUNCT
ejpam-164	160	1	let	let	VERB
ejpam-164	160	2	a	a	PRON
ejpam-164	160	3	be	be	AUX
ejpam-164	160	4	a	a	DET
ejpam-164	160	5	b	b	PROPN
ejpam-164	160	6	-	-	PUNCT
ejpam-164	160	7	ω	ω	VERB
ejpam-164	160	8	-	-	NOUN
ejpam-164	160	9	open	open	NOUN
ejpam-164	160	10	set	set	NOUN
ejpam-164	160	11	such	such	ADJ
ejpam-164	160	12	that	that	DET
ejpam-164	160	13	intω(a	intω(a	PROPN
ejpam-164	160	14	)	)	PUNCT
ejpam-164	160	15	=	=	SYM
ejpam-164	161	1	φ	φ	PROPN
ejpam-164	161	2	.	.	PUNCT
ejpam-164	162	1	then	then	ADV
ejpam-164	162	2	a	a	PRON
ejpam-164	162	3	is	be	AUX
ejpam-164	162	4	pre	pre	ADJ
ejpam-164	162	5	-	-	ADJ
ejpam-164	162	6	ω	ω	VERB
ejpam-164	162	7	-	-	NOUN
ejpam-164	162	8	open	open	ADJ
ejpam-164	162	9	.	.	PUNCT
ejpam-164	163	1	a	a	DET
ejpam-164	163	2	space	space	NOUN
ejpam-164	163	3	(	(	PUNCT
ejpam-164	163	4	x	x	X
ejpam-164	163	5	,	,	PUNCT
ejpam-164	163	6	τ	τ	X
ejpam-164	163	7	)	)	PUNCT
ejpam-164	163	8	is	be	AUX
ejpam-164	163	9	called	call	VERB
ejpam-164	163	10	a	a	DET
ejpam-164	163	11	door	door	NOUN
ejpam-164	163	12	space	space	NOUN
ejpam-164	163	13	if	if	SCONJ
ejpam-164	163	14	every	every	DET
ejpam-164	163	15	subset	subset	NOUN
ejpam-164	163	16	of	of	ADP
ejpam-164	163	17	x	x	PUNCT
ejpam-164	163	18	is	be	AUX
ejpam-164	163	19	open	open	ADJ
ejpam-164	163	20	or	or	CCONJ
ejpam-164	163	21	closed	closed	ADJ
ejpam-164	163	22	.	.	PUNCT
ejpam-164	164	1	proposition	proposition	NOUN
ejpam-164	164	2	2.18	2.18	NUM
ejpam-164	164	3	.	.	PUNCT
ejpam-164	165	1	if	if	SCONJ
ejpam-164	165	2	(	(	PUNCT
ejpam-164	165	3	x	x	X
ejpam-164	165	4	,	,	PUNCT
ejpam-164	165	5	τ	τ	X
ejpam-164	165	6	)	)	PUNCT
ejpam-164	165	7	is	be	AUX
ejpam-164	165	8	a	a	DET
ejpam-164	165	9	door	door	NOUN
ejpam-164	165	10	space	space	NOUN
ejpam-164	165	11	,	,	PUNCT
ejpam-164	165	12	then	then	ADV
ejpam-164	165	13	every	every	DET
ejpam-164	165	14	pre	pre	ADJ
ejpam-164	165	15	-	-	ADJ
ejpam-164	165	16	ω	ω	ADJ
ejpam-164	165	17	-	-	ADJ
ejpam-164	165	18	open	open	ADJ
ejpam-164	165	19	set	set	NOUN
ejpam-164	165	20	is	be	AUX
ejpam-164	165	21	ω	ω	NOUN
ejpam-164	165	22	-	-	ADJ
ejpam-164	165	23	open	open	ADJ
ejpam-164	165	24	.	.	PUNCT
ejpam-164	166	1	proof	proof	NOUN
ejpam-164	166	2	.	.	PUNCT
ejpam-164	167	1	let	let	VERB
ejpam-164	167	2	a	a	PRON
ejpam-164	167	3	be	be	AUX
ejpam-164	167	4	a	a	DET
ejpam-164	167	5	pre	pre	ADJ
ejpam-164	167	6	-	-	ADJ
ejpam-164	167	7	ω	ω	ADJ
ejpam-164	167	8	-	-	ADJ
ejpam-164	167	9	open	open	ADJ
ejpam-164	167	10	set	set	NOUN
ejpam-164	167	11	.	.	PUNCT
ejpam-164	168	1	if	if	SCONJ
ejpam-164	168	2	a	a	PRON
ejpam-164	168	3	is	be	AUX
ejpam-164	168	4	open	open	ADJ
ejpam-164	168	5	,	,	PUNCT
ejpam-164	168	6	then	then	ADV
ejpam-164	168	7	a	a	PRON
ejpam-164	168	8	is	be	AUX
ejpam-164	168	9	ω	ω	NOUN
ejpam-164	168	10	-	-	NOUN
ejpam-164	168	11	open	open	ADJ
ejpam-164	168	12	.	.	PUNCT
ejpam-164	169	1	otherwise	otherwise	ADV
ejpam-164	169	2	,	,	PUNCT
ejpam-164	169	3	a	a	PRON
ejpam-164	169	4	is	be	AUX
ejpam-164	169	5	closed	close	VERB
ejpam-164	169	6	and	and	CCONJ
ejpam-164	169	7	hence	hence	ADV
ejpam-164	169	8	a⊆	a⊆	VERB
ejpam-164	169	9	intω(cl(a	intω(cl(a	ADJ
ejpam-164	169	10	)	)	PUNCT
ejpam-164	169	11	)	)	PUNCT
ejpam-164	170	1	=	=	PRON
ejpam-164	171	1	intω(a)⊆	intω(a)⊆	NOUN
ejpam-164	171	2	a.	a.	NOUN
ejpam-164	171	3	therefore	therefore	ADV
ejpam-164	171	4	,	,	PUNCT
ejpam-164	171	5	a=	a=	PROPN
ejpam-164	171	6	intω(a	intω(a	ADP
ejpam-164	171	7	)	)	PUNCT
ejpam-164	171	8	and	and	CCONJ
ejpam-164	171	9	thus	thus	ADV
ejpam-164	171	10	a	a	PRON
ejpam-164	171	11	is	be	AUX
ejpam-164	171	12	an	an	DET
ejpam-164	171	13	ω	ω	ADJ
ejpam-164	171	14	-	-	ADJ
ejpam-164	171	15	open	open	ADJ
ejpam-164	171	16	set	set	NOUN
ejpam-164	171	17	.	.	PUNCT
ejpam-164	172	1	a	a	DET
ejpam-164	172	2	topological	topological	ADJ
ejpam-164	172	3	space	space	NOUN
ejpam-164	172	4	x	x	PRON
ejpam-164	172	5	is	be	AUX
ejpam-164	172	6	said	say	VERB
ejpam-164	172	7	to	to	PART
ejpam-164	172	8	be	be	AUX
ejpam-164	172	9	anti	anti	ADJ
ejpam-164	172	10	-	-	ADJ
ejpam-164	172	11	locally	locally	ADV
ejpam-164	172	12	countable	countable	ADJ
ejpam-164	172	13	[	[	X
ejpam-164	172	14	4	4	NUM
ejpam-164	172	15	]	]	X
ejpam-164	172	16	if	if	SCONJ
ejpam-164	172	17	every	every	DET
ejpam-164	172	18	non	non	ADJ
ejpam-164	172	19	-	-	ADJ
ejpam-164	172	20	empty	empty	ADJ
ejpam-164	172	21	open	open	ADJ
ejpam-164	172	22	set	set	NOUN
ejpam-164	172	23	is	be	AUX
ejpam-164	172	24	uncountable	uncountable	ADJ
ejpam-164	172	25	.	.	PUNCT
ejpam-164	173	1	lemma	lemma	PROPN
ejpam-164	173	2	2.19	2.19	NUM
ejpam-164	173	3	.	.	PUNCT
ejpam-164	174	1	[	[	X
ejpam-164	174	2	4	4	X
ejpam-164	174	3	]	]	X
ejpam-164	174	4	if	if	SCONJ
ejpam-164	174	5	(	(	PUNCT
ejpam-164	174	6	x	x	X
ejpam-164	174	7	,	,	PUNCT
ejpam-164	174	8	τ	τ	X
ejpam-164	174	9	)	)	PUNCT
ejpam-164	174	10	is	be	AUX
ejpam-164	174	11	an	an	DET
ejpam-164	174	12	anti	anti	ADJ
ejpam-164	174	13	-	-	ADJ
ejpam-164	174	14	locally	locally	ADV
ejpam-164	174	15	countable	countable	ADJ
ejpam-164	174	16	space	space	NOUN
ejpam-164	174	17	,	,	PUNCT
ejpam-164	174	18	then	then	ADV
ejpam-164	174	19	intω(a	intω(a	ADP
ejpam-164	174	20	)	)	PUNCT
ejpam-164	175	1	=	=	SYM
ejpam-164	175	2	int(a	int(a	PROPN
ejpam-164	175	3	)	)	PUNCT
ejpam-164	175	4	for	for	ADP
ejpam-164	175	5	every	every	DET
ejpam-164	175	6	ω	ω	NOUN
ejpam-164	175	7	-	-	PUNCT
ejpam-164	175	8	closed	closed	ADJ
ejpam-164	175	9	set	set	NOUN
ejpam-164	175	10	a	a	PRON
ejpam-164	175	11	of	of	ADP
ejpam-164	175	12	x	x	X
ejpam-164	175	13	and	and	CCONJ
ejpam-164	175	14	clω(a	clω(a	NOUN
ejpam-164	175	15	)	)	PUNCT
ejpam-164	175	16	=	=	SYM
ejpam-164	175	17	cl(a	cl(a	X
ejpam-164	175	18	)	)	PUNCT
ejpam-164	175	19	for	for	ADP
ejpam-164	175	20	every	every	DET
ejpam-164	175	21	ω	ω	NOUN
ejpam-164	175	22	-	-	ADJ
ejpam-164	175	23	open	open	ADJ
ejpam-164	175	24	set	set	VERB
ejpam-164	175	25	a	a	PRON
ejpam-164	175	26	of	of	ADP
ejpam-164	175	27	x	x	SYM
ejpam-164	175	28	.	.	PUNCT
ejpam-164	176	1	theorem	theorem	VERB
ejpam-164	176	2	2.20	2.20	NUM
ejpam-164	176	3	.	.	PUNCT
ejpam-164	177	1	let	let	AUX
ejpam-164	177	2	(	(	PUNCT
ejpam-164	177	3	x	x	X
ejpam-164	177	4	,	,	PUNCT
ejpam-164	177	5	τ	τ	X
ejpam-164	177	6	)	)	PUNCT
ejpam-164	177	7	be	be	AUX
ejpam-164	177	8	an	an	DET
ejpam-164	177	9	anti	anti	ADJ
ejpam-164	177	10	-	-	ADJ
ejpam-164	177	11	locally	locally	ADV
ejpam-164	177	12	countable	countable	ADJ
ejpam-164	177	13	space	space	NOUN
ejpam-164	177	14	and	and	CCONJ
ejpam-164	177	15	a	a	DET
ejpam-164	177	16	a	a	DET
ejpam-164	177	17	subset	subset	NOUN
ejpam-164	177	18	of	of	ADP
ejpam-164	177	19	x	x	X
ejpam-164	177	20	.	.	PUNCT
ejpam-164	178	1	then	then	ADV
ejpam-164	178	2	,	,	PUNCT
ejpam-164	178	3	the	the	DET
ejpam-164	178	4	following	follow	VERB
ejpam-164	178	5	properties	property	NOUN
ejpam-164	178	6	hold	hold	VERB
ejpam-164	178	7	:	:	PUNCT
ejpam-164	179	1	1	1	X
ejpam-164	179	2	.	.	X
ejpam-164	179	3	if	if	SCONJ
ejpam-164	179	4	a	a	PRON
ejpam-164	179	5	is	be	AUX
ejpam-164	179	6	pre	pre	ADJ
ejpam-164	179	7	-	-	ADJ
ejpam-164	179	8	ω	ω	VERB
ejpam-164	179	9	-	-	ADJ
ejpam-164	179	10	open	open	ADJ
ejpam-164	179	11	,	,	PUNCT
ejpam-164	179	12	then	then	ADV
ejpam-164	179	13	it	it	PRON
ejpam-164	179	14	is	be	AUX
ejpam-164	179	15	pre	pre	ADJ
ejpam-164	179	16	-	-	ADJ
ejpam-164	179	17	open	open	ADJ
ejpam-164	179	18	.	.	PUNCT
ejpam-164	180	1	2	2	X
ejpam-164	180	2	.	.	X
ejpam-164	180	3	if	if	SCONJ
ejpam-164	180	4	a	a	PRON
ejpam-164	180	5	is	be	AUX
ejpam-164	180	6	b	b	NOUN
ejpam-164	180	7	-	-	PUNCT
ejpam-164	180	8	ω	ω	NOUN
ejpam-164	180	9	-	-	NOUN
ejpam-164	180	10	open	open	ADJ
ejpam-164	180	11	and	and	CCONJ
ejpam-164	180	12	ω	ω	VERB
ejpam-164	180	13	-	-	VERB
ejpam-164	180	14	closed	closed	ADJ
ejpam-164	180	15	,	,	PUNCT
ejpam-164	180	16	then	then	ADV
ejpam-164	180	17	it	it	PRON
ejpam-164	180	18	is	be	AUX
ejpam-164	180	19	b	b	NOUN
ejpam-164	180	20	-	-	ADV
ejpam-164	180	21	open	open	ADJ
ejpam-164	180	22	.	.	PUNCT
ejpam-164	181	1	3	3	X
ejpam-164	181	2	.	.	X
ejpam-164	181	3	if	if	SCONJ
ejpam-164	181	4	a	a	PRON
ejpam-164	181	5	is	be	AUX
ejpam-164	181	6	β	β	NOUN
ejpam-164	181	7	-ω	-ω	VERB
ejpam-164	181	8	-	-	ADJ
ejpam-164	181	9	open	open	ADJ
ejpam-164	181	10	,	,	PUNCT
ejpam-164	181	11	then	then	ADV
ejpam-164	181	12	it	it	PRON
ejpam-164	181	13	is	be	AUX
ejpam-164	181	14	β	β	NOUN
ejpam-164	181	15	-open	-open	NOUN
ejpam-164	181	16	.	.	PUNCT
ejpam-164	182	1	proof	proof	NOUN
ejpam-164	182	2	.	.	PUNCT
ejpam-164	183	1	(	(	PUNCT
ejpam-164	183	2	1	1	X
ejpam-164	183	3	)	)	PUNCT
ejpam-164	183	4	let	let	VERB
ejpam-164	183	5	a	a	PRON
ejpam-164	183	6	be	be	AUX
ejpam-164	183	7	a	a	DET
ejpam-164	183	8	pre	pre	ADJ
ejpam-164	183	9	-	-	ADJ
ejpam-164	183	10	ω	ω	ADJ
ejpam-164	183	11	-	-	PUNCT
ejpam-164	183	12	open	open	ADJ
ejpam-164	183	13	set	set	NOUN
ejpam-164	183	14	.	.	PUNCT
ejpam-164	184	1	then	then	ADV
ejpam-164	184	2	by	by	ADP
ejpam-164	184	3	lemma	lemma	PROPN
ejpam-164	184	4	2.19	2.19	NUM
ejpam-164	184	5	a⊆	a⊆	NOUN
ejpam-164	184	6	intω(cl(a	intω(cl(a	NOUN
ejpam-164	184	7	)	)	PUNCT
ejpam-164	184	8	)	)	PUNCT
ejpam-164	184	9	=	=	SYM
ejpam-164	184	10	int(cl(a	int(cl(a	PROPN
ejpam-164	184	11	)	)	PUNCT
ejpam-164	184	12	)	)	PUNCT
ejpam-164	184	13	since	since	SCONJ
ejpam-164	184	14	every	every	DET
ejpam-164	184	15	closed	closed	ADJ
ejpam-164	184	16	set	set	NOUN
ejpam-164	184	17	is	be	AUX
ejpam-164	184	18	ω	ω	NOUN
ejpam-164	184	19	-	-	ADJ
ejpam-164	184	20	closed	closed	ADJ
ejpam-164	184	21	.	.	PUNCT
ejpam-164	185	1	t.	t.	PROPN
ejpam-164	185	2	noiri	noiri	PROPN
ejpam-164	185	3	,	,	PUNCT
ejpam-164	185	4	a.	a.	PROPN
ejpam-164	185	5	al	al	PROPN
ejpam-164	185	6	-	-	PUNCT
ejpam-164	185	7	omari	omari	PROPN
ejpam-164	185	8	,	,	PUNCT
ejpam-164	185	9	and	and	CCONJ
ejpam-164	185	10	m.	m.	NOUN
ejpam-164	185	11	noorani	noorani	PROPN
ejpam-164	185	12	/	/	SYM
ejpam-164	185	13	eur	eur	PROPN
ejpam-164	185	14	.	.	PUNCT
ejpam-164	186	1	j.	j.	PROPN
ejpam-164	186	2	pure	pure	PROPN
ejpam-164	186	3	appl	appl	PROPN
ejpam-164	186	4	.	.	PROPN
ejpam-164	186	5	math	math	PROPN
ejpam-164	186	6	,	,	PUNCT
ejpam-164	186	7	2	2	NUM
ejpam-164	186	8	(	(	PUNCT
ejpam-164	186	9	2009	2009	NUM
ejpam-164	186	10	)	)	PUNCT
ejpam-164	186	11	,	,	PUNCT
ejpam-164	186	12	(	(	PUNCT
ejpam-164	186	13	73	73	NUM
ejpam-164	186	14	-	-	SYM
ejpam-164	186	15	84	84	NUM
ejpam-164	186	16	)	)	PUNCT
ejpam-164	186	17	79	79	NUM
ejpam-164	186	18	(	(	PUNCT
ejpam-164	186	19	2	2	X
ejpam-164	186	20	)	)	PUNCT
ejpam-164	186	21	let	let	VERB
ejpam-164	186	22	a	a	PRON
ejpam-164	186	23	be	be	AUX
ejpam-164	186	24	a	a	DET
ejpam-164	186	25	b	b	PROPN
ejpam-164	186	26	-	-	PUNCT
ejpam-164	186	27	ω	ω	VERB
ejpam-164	186	28	-	-	ADJ
ejpam-164	186	29	open	open	ADJ
ejpam-164	186	30	andω	andω	ADJ
ejpam-164	186	31	-	-	PUNCT
ejpam-164	186	32	closed	close	VERB
ejpam-164	186	33	set	set	NOUN
ejpam-164	186	34	.	.	PUNCT
ejpam-164	187	1	by	by	ADP
ejpam-164	187	2	lemma	lemma	PROPN
ejpam-164	187	3	2.19	2.19	NUM
ejpam-164	187	4	,	,	PUNCT
ejpam-164	187	5	we	we	PRON
ejpam-164	187	6	have	have	VERB
ejpam-164	187	7	intω(cl(a	intω(cl(a	VERB
ejpam-164	187	8	)	)	PUNCT
ejpam-164	187	9	)	)	PUNCT
ejpam-164	188	1	=	=	SYM
ejpam-164	188	2	int(cl(a	int(cl(a	PROPN
ejpam-164	188	3	)	)	PUNCT
ejpam-164	188	4	)	)	PUNCT
ejpam-164	188	5	,	,	PUNCT
ejpam-164	188	6	cl(intω(a	cl(intω(a	NOUN
ejpam-164	188	7	)	)	PUNCT
ejpam-164	188	8	)	)	PUNCT
ejpam-164	189	1	=	=	SYM
ejpam-164	189	2	cl(int(a	cl(int(a	PROPN
ejpam-164	189	3	)	)	PUNCT
ejpam-164	189	4	)	)	PUNCT
ejpam-164	190	1	and	and	CCONJ
ejpam-164	190	2	hence	hence	ADV
ejpam-164	190	3	a⊆	a⊆	VERB
ejpam-164	190	4	intω(cl(a))∪cl(intω(a	intω(cl(a))∪cl(intω(a	NOUN
ejpam-164	190	5	)	)	PUNCT
ejpam-164	190	6	)	)	PUNCT
ejpam-164	191	1	=	=	SYM
ejpam-164	191	2	int(cl(a))∪cl(int(a	int(cl(a))∪cl(int(a	NUM
ejpam-164	191	3	)	)	PUNCT
ejpam-164	191	4	)	)	PUNCT
ejpam-164	191	5	.	.	PUNCT
ejpam-164	192	1	this	this	PRON
ejpam-164	192	2	shows	show	VERB
ejpam-164	192	3	that	that	SCONJ
ejpam-164	192	4	a	a	PRON
ejpam-164	192	5	is	be	AUX
ejpam-164	192	6	b	b	NOUN
ejpam-164	192	7	-	-	ADJ
ejpam-164	192	8	open	open	ADJ
ejpam-164	192	9	.	.	PUNCT
ejpam-164	193	1	(	(	PUNCT
ejpam-164	193	2	3	3	X
ejpam-164	193	3	)	)	PUNCT
ejpam-164	193	4	let	let	VERB
ejpam-164	193	5	a	a	PRON
ejpam-164	193	6	be	be	AUX
ejpam-164	193	7	a	a	DET
ejpam-164	193	8	β	β	NOUN
ejpam-164	193	9	-ω	-ω	VERB
ejpam-164	193	10	-	-	ADJ
ejpam-164	193	11	open	open	ADJ
ejpam-164	193	12	set	set	NOUN
ejpam-164	193	13	.	.	PUNCT
ejpam-164	194	1	then	then	ADV
ejpam-164	194	2	,	,	PUNCT
ejpam-164	194	3	by	by	ADP
ejpam-164	194	4	lemma	lemma	PROPN
ejpam-164	194	5	2.19	2.19	NUM
ejpam-164	194	6	,	,	PUNCT
ejpam-164	194	7	we	we	PRON
ejpam-164	194	8	have	have	VERB
ejpam-164	194	9	a	a	DET
ejpam-164	194	10	⊆	⊆	NUM
ejpam-164	194	11	cl(intω(cl(a	cl(intω(cl(a	NUM
ejpam-164	194	12	)	)	PUNCT
ejpam-164	194	13	)	)	PUNCT
ejpam-164	194	14	)	)	PUNCT
ejpam-164	195	1	=	=	SYM
ejpam-164	195	2	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-164	195	3	)	)	PUNCT
ejpam-164	195	4	)	)	PUNCT
ejpam-164	195	5	)	)	PUNCT
ejpam-164	196	1	and	and	CCONJ
ejpam-164	196	2	hence	hence	ADV
ejpam-164	196	3	a	a	PRON
ejpam-164	196	4	is	be	AUX
ejpam-164	196	5	β	β	NOUN
ejpam-164	196	6	-open	-open	NOUN
ejpam-164	196	7	.	.	PUNCT
ejpam-164	197	1	3	3	X
ejpam-164	197	2	.	.	X
ejpam-164	197	3	decompositions	decomposition	NOUN
ejpam-164	197	4	of	of	ADP
ejpam-164	197	5	continuity	continuity	NOUN
ejpam-164	197	6	definition	definition	NOUN
ejpam-164	197	7	3.1	3.1	NUM
ejpam-164	197	8	.	.	PUNCT
ejpam-164	198	1	a	a	DET
ejpam-164	198	2	subset	subset	NOUN
ejpam-164	198	3	a	a	PRON
ejpam-164	198	4	of	of	ADP
ejpam-164	198	5	a	a	DET
ejpam-164	198	6	space	space	NOUN
ejpam-164	198	7	x	x	PUNCT
ejpam-164	198	8	is	be	AUX
ejpam-164	198	9	called	call	VERB
ejpam-164	198	10	1	1	NUM
ejpam-164	198	11	.	.	PUNCT
ejpam-164	199	1	an	an	DET
ejpam-164	199	2	ω	ω	PROPN
ejpam-164	199	3	-	-	PUNCT
ejpam-164	199	4	t	t	NOUN
ejpam-164	199	5	-	-	PUNCT
ejpam-164	199	6	set	set	VERB
ejpam-164	199	7	if	if	SCONJ
ejpam-164	199	8	int(a	int(a	PROPN
ejpam-164	199	9	)	)	PUNCT
ejpam-164	199	10	=	=	SYM
ejpam-164	199	11	intω(cl(a	intω(cl(a	X
ejpam-164	199	12	)	)	PUNCT
ejpam-164	199	13	)	)	PUNCT
ejpam-164	199	14	;	;	PUNCT
ejpam-164	199	15	2	2	X
ejpam-164	199	16	.	.	X
ejpam-164	199	17	an	an	DET
ejpam-164	199	18	ω	ω	PROPN
ejpam-164	199	19	-	-	PUNCT
ejpam-164	199	20	b	b	NOUN
ejpam-164	199	21	-	-	PUNCT
ejpam-164	199	22	set	set	VERB
ejpam-164	199	23	if	if	SCONJ
ejpam-164	199	24	a=	a=	VERB
ejpam-164	199	25	u	u	NOUN
ejpam-164	199	26	∩	∩	NOUN
ejpam-164	199	27	v	v	NOUN
ejpam-164	199	28	,	,	PUNCT
ejpam-164	199	29	where	where	SCONJ
ejpam-164	199	30	u	u	PROPN
ejpam-164	199	31	∈	∈	PROPN
ejpam-164	199	32	τ	τ	X
ejpam-164	199	33	and	and	CCONJ
ejpam-164	199	34	v	v	NOUN
ejpam-164	199	35	is	be	AUX
ejpam-164	199	36	an	an	DET
ejpam-164	199	37	ω	ω	PROPN
ejpam-164	199	38	-	-	PUNCT
ejpam-164	199	39	t	t	NOUN
ejpam-164	199	40	-	-	PUNCT
ejpam-164	199	41	set	set	NOUN
ejpam-164	199	42	.	.	PUNCT
ejpam-164	200	1	proposition	proposition	NOUN
ejpam-164	200	2	3.2	3.2	NUM
ejpam-164	200	3	.	.	PUNCT
ejpam-164	201	1	let	let	VERB
ejpam-164	201	2	a	a	PRON
ejpam-164	201	3	and	and	CCONJ
ejpam-164	201	4	b	b	NOUN
ejpam-164	201	5	be	be	AUX
ejpam-164	201	6	subsets	subset	NOUN
ejpam-164	201	7	of	of	ADP
ejpam-164	201	8	a	a	DET
ejpam-164	201	9	space	space	NOUN
ejpam-164	201	10	(	(	PUNCT
ejpam-164	201	11	x	x	X
ejpam-164	201	12	,	,	PUNCT
ejpam-164	201	13	τ	τ	PROPN
ejpam-164	201	14	)	)	PUNCT
ejpam-164	201	15	.	.	PUNCT
ejpam-164	202	1	if	if	SCONJ
ejpam-164	202	2	a	a	PRON
ejpam-164	202	3	and	and	CCONJ
ejpam-164	202	4	b	b	NOUN
ejpam-164	202	5	are	be	AUX
ejpam-164	202	6	ω	ω	NUM
ejpam-164	202	7	-	-	PUNCT
ejpam-164	202	8	t	t	NOUN
ejpam-164	202	9	-	-	PUNCT
ejpam-164	202	10	sets	set	NOUN
ejpam-164	202	11	,	,	PUNCT
ejpam-164	202	12	then	then	ADV
ejpam-164	202	13	a∩	a∩	PROPN
ejpam-164	202	14	b	b	PROPN
ejpam-164	202	15	is	be	AUX
ejpam-164	202	16	an	an	DET
ejpam-164	202	17	ω	ω	PROPN
ejpam-164	202	18	-	-	PUNCT
ejpam-164	202	19	t	t	NOUN
ejpam-164	202	20	-	-	PUNCT
ejpam-164	202	21	set	set	NOUN
ejpam-164	202	22	.	.	PUNCT
ejpam-164	203	1	proof	proof	NOUN
ejpam-164	203	2	.	.	PUNCT
ejpam-164	204	1	let	let	VERB
ejpam-164	204	2	a	a	PRON
ejpam-164	204	3	and	and	CCONJ
ejpam-164	204	4	b	b	NOUN
ejpam-164	204	5	be	be	AUX
ejpam-164	204	6	ω	ω	PROPN
ejpam-164	204	7	-	-	PUNCT
ejpam-164	204	8	t	t	NOUN
ejpam-164	204	9	-	-	PUNCT
ejpam-164	204	10	sets	set	NOUN
ejpam-164	204	11	.	.	PUNCT
ejpam-164	205	1	then	then	ADV
ejpam-164	205	2	we	we	PRON
ejpam-164	205	3	have	have	VERB
ejpam-164	205	4	int(a∩	int(a∩	PROPN
ejpam-164	205	5	b	b	NOUN
ejpam-164	205	6	)	)	PUNCT
ejpam-164	205	7	⊆	⊆	NUM
ejpam-164	205	8	intω(cl(a∩	intω(cl(a∩	PROPN
ejpam-164	205	9	b	b	NOUN
ejpam-164	205	10	)	)	PUNCT
ejpam-164	205	11	)	)	PUNCT
ejpam-164	206	1	⊆	⊆	X
ejpam-164	206	2	(	(	PUNCT
ejpam-164	206	3	intω(cl(a))∩	intω(cl(a))∩	PROPN
ejpam-164	206	4	(	(	PUNCT
ejpam-164	206	5	cl(b	cl(b	NOUN
ejpam-164	206	6	)	)	PUNCT
ejpam-164	206	7	)	)	PUNCT
ejpam-164	206	8	)	)	PUNCT
ejpam-164	207	1	=	=	PUNCT
ejpam-164	207	2	intω(cl(a)∩	intω(cl(a)∩	PROPN
ejpam-164	207	3	intω(cl(b	intω(cl(b	NOUN
ejpam-164	207	4	)	)	PUNCT
ejpam-164	207	5	)	)	PUNCT
ejpam-164	208	1	=	=	SYM
ejpam-164	208	2	int(a)∩	int(a)∩	X
ejpam-164	208	3	int(b	int(b	X
ejpam-164	208	4	)	)	PUNCT
ejpam-164	208	5	=	=	PROPN
ejpam-164	208	6	int(a∩	int(a∩	PROPN
ejpam-164	208	7	b	b	NOUN
ejpam-164	208	8	)	)	PUNCT
ejpam-164	208	9	.	.	PUNCT
ejpam-164	209	1	then	then	ADV
ejpam-164	209	2	int(a∩	int(a∩	PROPN
ejpam-164	209	3	b	b	NOUN
ejpam-164	209	4	)	)	PUNCT
ejpam-164	209	5	=	=	SYM
ejpam-164	210	1	intω(cl(a∩	intω(cl(a∩	PROPN
ejpam-164	210	2	b	b	NOUN
ejpam-164	210	3	)	)	PUNCT
ejpam-164	210	4	)	)	PUNCT
ejpam-164	211	1	and	and	CCONJ
ejpam-164	211	2	hence	hence	ADV
ejpam-164	211	3	a∩	a∩	PROPN
ejpam-164	211	4	b	b	PROPN
ejpam-164	211	5	is	be	AUX
ejpam-164	211	6	an	an	DET
ejpam-164	211	7	ω	ω	PROPN
ejpam-164	211	8	-	-	PUNCT
ejpam-164	211	9	t	t	NOUN
ejpam-164	211	10	-	-	PUNCT
ejpam-164	211	11	set	set	NOUN
ejpam-164	211	12	.	.	PUNCT
ejpam-164	212	1	from	from	ADP
ejpam-164	212	2	the	the	DET
ejpam-164	212	3	following	follow	VERB
ejpam-164	212	4	examples	example	NOUN
ejpam-164	212	5	one	one	PRON
ejpam-164	212	6	can	can	AUX
ejpam-164	212	7	deduce	deduce	VERB
ejpam-164	212	8	that	that	SCONJ
ejpam-164	212	9	a	a	DET
ejpam-164	212	10	pre	pre	ADJ
ejpam-164	212	11	-	-	ADJ
ejpam-164	212	12	ω	ω	ADJ
ejpam-164	212	13	-	-	ADJ
ejpam-164	212	14	open	open	ADJ
ejpam-164	212	15	set	set	NOUN
ejpam-164	212	16	and	and	CCONJ
ejpam-164	212	17	an	an	DET
ejpam-164	212	18	ω	ω	PROPN
ejpam-164	212	19	-	-	PUNCT
ejpam-164	212	20	b	b	NOUN
ejpam-164	212	21	-	-	PUNCT
ejpam-164	212	22	set	set	NOUN
ejpam-164	212	23	are	be	AUX
ejpam-164	212	24	independent	independent	ADJ
ejpam-164	212	25	.	.	PUNCT
ejpam-164	212	26	example	example	NOUN
ejpam-164	212	27	3.3	3.3	NUM
ejpam-164	212	28	.	.	PUNCT
ejpam-164	213	1	let	let	VERB
ejpam-164	213	2	x	x	PUNCT
ejpam-164	213	3	=	=	PUNCT
ejpam-164	213	4	r	r	NOUN
ejpam-164	213	5	with	with	ADP
ejpam-164	213	6	the	the	DET
ejpam-164	213	7	usual	usual	ADJ
ejpam-164	213	8	topology	topology	NOUN
ejpam-164	213	9	τ	τ	PROPN
ejpam-164	213	10	.	.	PUNCT
ejpam-164	214	1	then	then	ADV
ejpam-164	214	2	r\q	r\q	PROPN
ejpam-164	214	3	is	be	AUX
ejpam-164	214	4	pre	pre	ADJ
ejpam-164	214	5	-	-	ADJ
ejpam-164	214	6	ω	ω	ADV
ejpam-164	214	7	-	-	NOUN
ejpam-164	214	8	open	open	ADJ
ejpam-164	214	9	but	but	CCONJ
ejpam-164	214	10	it	it	PRON
ejpam-164	214	11	is	be	AUX
ejpam-164	214	12	not	not	PART
ejpam-164	214	13	an	an	DET
ejpam-164	214	14	ω	ω	PROPN
ejpam-164	214	15	-	-	PUNCT
ejpam-164	214	16	b	b	NOUN
ejpam-164	214	17	-	-	PUNCT
ejpam-164	214	18	set	set	VERB
ejpam-164	214	19	and	and	CCONJ
ejpam-164	214	20	(	(	PUNCT
ejpam-164	214	21	0,1	0,1	NUM
ejpam-164	214	22	]	]	PUNCT
ejpam-164	214	23	is	be	AUX
ejpam-164	214	24	an	an	DET
ejpam-164	214	25	ω	ω	PROPN
ejpam-164	214	26	-	-	PUNCT
ejpam-164	214	27	b	b	NOUN
ejpam-164	214	28	-	-	PUNCT
ejpam-164	214	29	set	set	NOUN
ejpam-164	214	30	which	which	PRON
ejpam-164	214	31	is	be	AUX
ejpam-164	214	32	not	not	PART
ejpam-164	214	33	pre	pre	ADJ
ejpam-164	214	34	-	-	ADJ
ejpam-164	214	35	ω	ω	VERB
ejpam-164	214	36	-	-	ADJ
ejpam-164	214	37	open	open	ADJ
ejpam-164	214	38	.	.	PUNCT
ejpam-164	215	1	proposition	proposition	NOUN
ejpam-164	215	2	3.4	3.4	NUM
ejpam-164	215	3	.	.	PUNCT
ejpam-164	216	1	for	for	ADP
ejpam-164	216	2	a	a	DET
ejpam-164	216	3	subset	subset	NOUN
ejpam-164	216	4	a	a	PRON
ejpam-164	216	5	of	of	ADP
ejpam-164	216	6	a	a	DET
ejpam-164	216	7	space	space	NOUN
ejpam-164	216	8	(	(	PUNCT
ejpam-164	216	9	x	x	X
ejpam-164	216	10	,	,	PUNCT
ejpam-164	216	11	τ	τ	PROPN
ejpam-164	216	12	)	)	PUNCT
ejpam-164	216	13	,	,	PUNCT
ejpam-164	216	14	the	the	DET
ejpam-164	216	15	following	follow	VERB
ejpam-164	216	16	properties	property	NOUN
ejpam-164	216	17	are	be	AUX
ejpam-164	216	18	equivalent	equivalent	ADJ
ejpam-164	216	19	:	:	PUNCT
ejpam-164	216	20	t.	t.	PROPN
ejpam-164	216	21	noiri	noiri	PROPN
ejpam-164	216	22	,	,	PUNCT
ejpam-164	216	23	a.	a.	PROPN
ejpam-164	216	24	al	al	PROPN
ejpam-164	216	25	-	-	PUNCT
ejpam-164	216	26	omari	omari	PROPN
ejpam-164	216	27	,	,	PUNCT
ejpam-164	216	28	and	and	CCONJ
ejpam-164	216	29	m.	m.	NOUN
ejpam-164	216	30	noorani	noorani	PROPN
ejpam-164	216	31	/	/	SYM
ejpam-164	216	32	eur	eur	PROPN
ejpam-164	216	33	.	.	PUNCT
ejpam-164	217	1	j.	j.	PROPN
ejpam-164	217	2	pure	pure	PROPN
ejpam-164	217	3	appl	appl	PROPN
ejpam-164	217	4	.	.	PROPN
ejpam-164	217	5	math	math	PROPN
ejpam-164	217	6	,	,	PUNCT
ejpam-164	217	7	2	2	NUM
ejpam-164	217	8	(	(	PUNCT
ejpam-164	217	9	2009	2009	NUM
ejpam-164	217	10	)	)	PUNCT
ejpam-164	217	11	,	,	PUNCT
ejpam-164	217	12	(	(	PUNCT
ejpam-164	217	13	73	73	NUM
ejpam-164	217	14	-	-	SYM
ejpam-164	217	15	84	84	NUM
ejpam-164	217	16	)	)	PUNCT
ejpam-164	217	17	80	80	NUM
ejpam-164	217	18	1	1	NUM
ejpam-164	217	19	.	.	PUNCT
ejpam-164	218	1	a	a	PRON
ejpam-164	218	2	is	be	AUX
ejpam-164	218	3	open	open	ADJ
ejpam-164	218	4	;	;	PUNCT
ejpam-164	218	5	2	2	X
ejpam-164	218	6	.	.	X
ejpam-164	218	7	a	a	PRON
ejpam-164	218	8	is	be	AUX
ejpam-164	218	9	pre	pre	ADJ
ejpam-164	218	10	-	-	ADJ
ejpam-164	218	11	ω	ω	ADJ
ejpam-164	218	12	-	-	ADJ
ejpam-164	218	13	open	open	ADJ
ejpam-164	218	14	and	and	CCONJ
ejpam-164	218	15	an	an	DET
ejpam-164	218	16	ω	ω	PROPN
ejpam-164	218	17	-	-	PUNCT
ejpam-164	218	18	b	b	NOUN
ejpam-164	218	19	-	-	PUNCT
ejpam-164	218	20	set	set	NOUN
ejpam-164	218	21	.	.	PUNCT
ejpam-164	219	1	proof	proof	NOUN
ejpam-164	219	2	.	.	PUNCT
ejpam-164	220	1	(	(	PUNCT
ejpam-164	220	2	1	1	X
ejpam-164	220	3	)	)	PUNCT
ejpam-164	220	4	⇒	⇒	NOUN
ejpam-164	220	5	(	(	PUNCT
ejpam-164	220	6	2	2	NUM
ejpam-164	220	7	):	):	PUNCT
ejpam-164	220	8	let	let	VERB
ejpam-164	220	9	a	a	PRON
ejpam-164	220	10	be	be	AUX
ejpam-164	220	11	open	open	ADJ
ejpam-164	220	12	.	.	PUNCT
ejpam-164	221	1	then	then	ADV
ejpam-164	221	2	a	a	DET
ejpam-164	221	3	=	=	SYM
ejpam-164	221	4	int(a	int(a	PROPN
ejpam-164	221	5	)	)	PUNCT
ejpam-164	221	6	⊆	⊆	NUM
ejpam-164	221	7	intω(cl(a	intω(cl(a	NOUN
ejpam-164	221	8	)	)	PUNCT
ejpam-164	221	9	)	)	PUNCT
ejpam-164	221	10	and	and	CCONJ
ejpam-164	221	11	a	a	PRON
ejpam-164	221	12	is	be	AUX
ejpam-164	221	13	pre	pre	ADJ
ejpam-164	221	14	-	-	ADJ
ejpam-164	221	15	ω	ω	ADJ
ejpam-164	221	16	-	-	NOUN
ejpam-164	221	17	open	open	ADJ
ejpam-164	221	18	.	.	PUNCT
ejpam-164	222	1	also	also	ADV
ejpam-164	222	2	a=	a=	VERB
ejpam-164	222	3	a∩	a∩	PROPN
ejpam-164	222	4	x	x	X
ejpam-164	222	5	and	and	CCONJ
ejpam-164	222	6	hence	hence	ADV
ejpam-164	222	7	a	a	PRON
ejpam-164	222	8	is	be	AUX
ejpam-164	222	9	an	an	DET
ejpam-164	222	10	ω	ω	PROPN
ejpam-164	222	11	-	-	PUNCT
ejpam-164	222	12	b	b	NOUN
ejpam-164	222	13	-	-	PUNCT
ejpam-164	222	14	set	set	NOUN
ejpam-164	222	15	.	.	PUNCT
ejpam-164	223	1	(	(	PUNCT
ejpam-164	223	2	2	2	X
ejpam-164	223	3	)	)	PUNCT
ejpam-164	223	4	⇒	⇒	NOUN
ejpam-164	223	5	(	(	PUNCT
ejpam-164	223	6	1	1	NUM
ejpam-164	223	7	):	):	PUNCT
ejpam-164	223	8	since	since	SCONJ
ejpam-164	223	9	a	a	PRON
ejpam-164	223	10	is	be	AUX
ejpam-164	223	11	an	an	DET
ejpam-164	223	12	ω	ω	PROPN
ejpam-164	223	13	-	-	PUNCT
ejpam-164	223	14	b	b	NOUN
ejpam-164	223	15	-	-	PUNCT
ejpam-164	223	16	set	set	NOUN
ejpam-164	223	17	,	,	PUNCT
ejpam-164	223	18	we	we	PRON
ejpam-164	223	19	have	have	AUX
ejpam-164	223	20	a=	a=	VERB
ejpam-164	223	21	u	u	NOUN
ejpam-164	223	22	∩	∩	NOUN
ejpam-164	223	23	v	v	NOUN
ejpam-164	223	24	,	,	PUNCT
ejpam-164	223	25	where	where	SCONJ
ejpam-164	223	26	u	u	NOUN
ejpam-164	223	27	is	be	AUX
ejpam-164	223	28	an	an	DET
ejpam-164	223	29	open	open	ADJ
ejpam-164	223	30	set	set	NOUN
ejpam-164	223	31	and	and	CCONJ
ejpam-164	223	32	int(v	int(v	NOUN
ejpam-164	223	33	)	)	PUNCT
ejpam-164	223	34	=	=	SYM
ejpam-164	223	35	intω(cl(v	intω(cl(v	PRON
ejpam-164	223	36	)	)	PUNCT
ejpam-164	223	37	)	)	PUNCT
ejpam-164	223	38	.	.	PUNCT
ejpam-164	224	1	by	by	ADP
ejpam-164	224	2	the	the	DET
ejpam-164	224	3	hypothesis	hypothesis	NOUN
ejpam-164	224	4	,	,	PUNCT
ejpam-164	224	5	a	a	PRON
ejpam-164	224	6	is	be	AUX
ejpam-164	224	7	also	also	ADV
ejpam-164	224	8	pre	pre	ADJ
ejpam-164	224	9	-	-	ADJ
ejpam-164	224	10	ω	ω	ADV
ejpam-164	224	11	-	-	NOUN
ejpam-164	224	12	open	open	ADJ
ejpam-164	225	1	and	and	CCONJ
ejpam-164	225	2	we	we	PRON
ejpam-164	225	3	have	have	AUX
ejpam-164	225	4	a⊆	a⊆	VERB
ejpam-164	225	5	intω(cl(a	intω(cl(a	NOUN
ejpam-164	225	6	)	)	PUNCT
ejpam-164	225	7	)	)	PUNCT
ejpam-164	226	1	=	=	SYM
ejpam-164	226	2	intω(cl(u	intω(cl(u	NOUN
ejpam-164	226	3	∩	∩	NOUN
ejpam-164	226	4	v	v	NOUN
ejpam-164	226	5	)	)	PUNCT
ejpam-164	226	6	)	)	PUNCT
ejpam-164	227	1	⊆	⊆	NUM
ejpam-164	227	2	intω(cl(u)∩	intω(cl(u)∩	X
ejpam-164	227	3	cl(v	cl(v	NOUN
ejpam-164	227	4	)	)	PUNCT
ejpam-164	227	5	)	)	PUNCT
ejpam-164	228	1	=	=	PUNCT
ejpam-164	228	2	intω(cl(u))∩	intω(cl(u))∩	NOUN
ejpam-164	228	3	intω(cl(v	intω(cl(v	PRON
ejpam-164	228	4	)	)	PUNCT
ejpam-164	228	5	)	)	PUNCT
ejpam-164	229	1	=	=	PUNCT
ejpam-164	229	2	intω(cl(u))∩	intω(cl(u))∩	NOUN
ejpam-164	229	3	int(v	int(v	PROPN
ejpam-164	229	4	)	)	PUNCT
ejpam-164	229	5	.	.	PUNCT
ejpam-164	230	1	hence	hence	ADV
ejpam-164	230	2	a=	a=	VERB
ejpam-164	230	3	u	u	NOUN
ejpam-164	230	4	∩	∩	ADJ
ejpam-164	230	5	v	v	ADP
ejpam-164	230	6	=(	=(	NOUN
ejpam-164	230	7	u	u	PROPN
ejpam-164	230	8	∩	∩	ADJ
ejpam-164	230	9	v	v	NOUN
ejpam-164	230	10	)	)	PUNCT
ejpam-164	230	11	∩	∩	NOUN
ejpam-164	230	12	u	u	NOUN
ejpam-164	230	13	⊆	⊆	NUM
ejpam-164	230	14	(	(	PUNCT
ejpam-164	230	15	intω(cl(u))∩	intω(cl(u))∩	NOUN
ejpam-164	230	16	int(v	int(v	NOUN
ejpam-164	230	17	)	)	PUNCT
ejpam-164	230	18	)	)	PUNCT
ejpam-164	230	19	∩	∩	NOUN
ejpam-164	230	20	u	u	NOUN
ejpam-164	230	21	=	=	PUNCT
ejpam-164	230	22	(	(	PUNCT
ejpam-164	230	23	intω(cl(u))∩	intω(cl(u))∩	NOUN
ejpam-164	230	24	u)∩	u)∩	PROPN
ejpam-164	230	25	int(v	int(v	PROPN
ejpam-164	230	26	)	)	PUNCT
ejpam-164	230	27	=	=	SYM
ejpam-164	230	28	u	u	NOUN
ejpam-164	230	29	∩	∩	NOUN
ejpam-164	230	30	int(v	int(v	NOUN
ejpam-164	230	31	)	)	PUNCT
ejpam-164	230	32	.	.	PUNCT
ejpam-164	231	1	therefore	therefore	ADV
ejpam-164	231	2	,	,	PUNCT
ejpam-164	231	3	a=	a=	X
ejpam-164	231	4	(	(	PUNCT
ejpam-164	231	5	u	u	NOUN
ejpam-164	231	6	∩	∩	NOUN
ejpam-164	231	7	v	v	NOUN
ejpam-164	231	8	)	)	PUNCT
ejpam-164	231	9	=	=	SYM
ejpam-164	231	10	(	(	PUNCT
ejpam-164	231	11	u	u	X
ejpam-164	231	12	∩	∩	X
ejpam-164	231	13	int(v	int(v	NOUN
ejpam-164	231	14	)	)	PUNCT
ejpam-164	231	15	)	)	PUNCT
ejpam-164	231	16	and	and	CCONJ
ejpam-164	231	17	a	a	PRON
ejpam-164	231	18	is	be	AUX
ejpam-164	231	19	open	open	ADJ
ejpam-164	231	20	.	.	PUNCT
ejpam-164	232	1	definition	definition	NOUN
ejpam-164	232	2	3.5	3.5	NUM
ejpam-164	232	3	.	.	PUNCT
ejpam-164	233	1	a	a	DET
ejpam-164	233	2	subset	subset	NOUN
ejpam-164	233	3	a	a	PRON
ejpam-164	233	4	of	of	ADP
ejpam-164	233	5	a	a	DET
ejpam-164	233	6	space	space	NOUN
ejpam-164	233	7	x	x	PUNCT
ejpam-164	233	8	is	be	AUX
ejpam-164	233	9	called	call	VERB
ejpam-164	233	10	1	1	NUM
ejpam-164	233	11	.	.	PUNCT
ejpam-164	234	1	an	an	DET
ejpam-164	234	2	ω	ω	NUM
ejpam-164	234	3	-	-	PUNCT
ejpam-164	234	4	tα	tα	ADV
ejpam-164	234	5	-	-	PUNCT
ejpam-164	234	6	set	set	NOUN
ejpam-164	234	7	if	if	SCONJ
ejpam-164	234	8	int(a	int(a	PROPN
ejpam-164	234	9	)	)	PUNCT
ejpam-164	234	10	=	=	SYM
ejpam-164	234	11	intω(cl(intω(a	intω(cl(intω(a	NOUN
ejpam-164	234	12	)	)	PUNCT
ejpam-164	234	13	)	)	PUNCT
ejpam-164	234	14	)	)	PUNCT
ejpam-164	234	15	;	;	PUNCT
ejpam-164	235	1	2	2	X
ejpam-164	235	2	.	.	X
ejpam-164	235	3	an	an	DET
ejpam-164	235	4	ω	ω	NUM
ejpam-164	235	5	-	-	PUNCT
ejpam-164	235	6	bα	bα	NOUN
ejpam-164	235	7	-	-	PUNCT
ejpam-164	235	8	set	set	VERB
ejpam-164	235	9	if	if	SCONJ
ejpam-164	235	10	a=	a=	VERB
ejpam-164	235	11	u	u	NOUN
ejpam-164	235	12	∩	∩	NOUN
ejpam-164	235	13	v	v	NOUN
ejpam-164	235	14	,	,	PUNCT
ejpam-164	235	15	where	where	SCONJ
ejpam-164	235	16	u	u	PROPN
ejpam-164	235	17	∈	∈	PROPN
ejpam-164	235	18	τ	τ	X
ejpam-164	235	19	and	and	CCONJ
ejpam-164	235	20	v	v	NOUN
ejpam-164	235	21	is	be	AUX
ejpam-164	235	22	an	an	DET
ejpam-164	235	23	ω	ω	PROPN
ejpam-164	235	24	-	-	PUNCT
ejpam-164	235	25	tα	tα	ADV
ejpam-164	235	26	-	-	PUNCT
ejpam-164	235	27	set	set	NOUN
ejpam-164	235	28	.	.	PUNCT
ejpam-164	236	1	proposition	proposition	NOUN
ejpam-164	236	2	3.6	3.6	NUM
ejpam-164	236	3	.	.	PUNCT
ejpam-164	237	1	let	let	VERB
ejpam-164	237	2	a	a	PRON
ejpam-164	237	3	and	and	CCONJ
ejpam-164	237	4	b	b	NOUN
ejpam-164	237	5	be	be	AUX
ejpam-164	237	6	subsets	subset	NOUN
ejpam-164	237	7	of	of	ADP
ejpam-164	237	8	a	a	DET
ejpam-164	237	9	space	space	NOUN
ejpam-164	237	10	(	(	PUNCT
ejpam-164	237	11	x	x	X
ejpam-164	237	12	,	,	PUNCT
ejpam-164	237	13	τ	τ	PROPN
ejpam-164	237	14	)	)	PUNCT
ejpam-164	237	15	.	.	PUNCT
ejpam-164	238	1	if	if	SCONJ
ejpam-164	238	2	a	a	PRON
ejpam-164	238	3	and	and	CCONJ
ejpam-164	238	4	b	b	NOUN
ejpam-164	238	5	are	be	AUX
ejpam-164	238	6	ω	ω	NUM
ejpam-164	238	7	-	-	PUNCT
ejpam-164	238	8	tα	tα	NOUN
ejpam-164	238	9	-	-	PUNCT
ejpam-164	238	10	sets	set	NOUN
ejpam-164	238	11	,	,	PUNCT
ejpam-164	238	12	then	then	ADV
ejpam-164	238	13	a∩	a∩	PROPN
ejpam-164	238	14	b	b	PROPN
ejpam-164	238	15	is	be	AUX
ejpam-164	238	16	an	an	DET
ejpam-164	238	17	ω	ω	PROPN
ejpam-164	238	18	-	-	PUNCT
ejpam-164	238	19	tα	tα	NOUN
ejpam-164	238	20	-	-	PUNCT
ejpam-164	238	21	set	set	NOUN
ejpam-164	238	22	.	.	PUNCT
ejpam-164	239	1	t.	t.	PROPN
ejpam-164	239	2	noiri	noiri	PROPN
ejpam-164	239	3	,	,	PUNCT
ejpam-164	239	4	a.	a.	PROPN
ejpam-164	239	5	al	al	PROPN
ejpam-164	239	6	-	-	PUNCT
ejpam-164	239	7	omari	omari	PROPN
ejpam-164	239	8	,	,	PUNCT
ejpam-164	239	9	and	and	CCONJ
ejpam-164	239	10	m.	m.	NOUN
ejpam-164	239	11	noorani	noorani	PROPN
ejpam-164	239	12	/	/	SYM
ejpam-164	239	13	eur	eur	PROPN
ejpam-164	239	14	.	.	PUNCT
ejpam-164	240	1	j.	j.	PROPN
ejpam-164	240	2	pure	pure	PROPN
ejpam-164	240	3	appl	appl	PROPN
ejpam-164	240	4	.	.	PROPN
ejpam-164	240	5	math	math	PROPN
ejpam-164	240	6	,	,	PUNCT
ejpam-164	240	7	2	2	NUM
ejpam-164	240	8	(	(	PUNCT
ejpam-164	240	9	2009	2009	NUM
ejpam-164	240	10	)	)	PUNCT
ejpam-164	240	11	,	,	PUNCT
ejpam-164	240	12	(	(	PUNCT
ejpam-164	240	13	73	73	NUM
ejpam-164	240	14	-	-	SYM
ejpam-164	240	15	84	84	NUM
ejpam-164	240	16	)	)	PUNCT
ejpam-164	240	17	81	81	NUM
ejpam-164	240	18	proof	proof	NOUN
ejpam-164	240	19	.	.	PUNCT
ejpam-164	241	1	let	let	VERB
ejpam-164	241	2	a	a	PRON
ejpam-164	241	3	and	and	CCONJ
ejpam-164	241	4	b	b	NOUN
ejpam-164	241	5	be	be	AUX
ejpam-164	241	6	ω	ω	NUM
ejpam-164	241	7	-	-	PUNCT
ejpam-164	241	8	tα	tα	ADP
ejpam-164	241	9	-	-	PUNCT
ejpam-164	241	10	sets	set	NOUN
ejpam-164	241	11	.	.	PUNCT
ejpam-164	242	1	then	then	ADV
ejpam-164	242	2	we	we	PRON
ejpam-164	242	3	have	have	VERB
ejpam-164	242	4	int(a∩	int(a∩	PROPN
ejpam-164	242	5	b	b	NOUN
ejpam-164	242	6	)	)	PUNCT
ejpam-164	242	7	⊆	⊆	PROPN
ejpam-164	242	8	intω(cl(intω(a∩	intω(cl(intω(a∩	PROPN
ejpam-164	242	9	b	b	PROPN
ejpam-164	242	10	)	)	PUNCT
ejpam-164	242	11	)	)	PUNCT
ejpam-164	242	12	)	)	PUNCT
ejpam-164	243	1	⊆	⊆	X
ejpam-164	243	2	(	(	PUNCT
ejpam-164	243	3	intω(cl(intω(a)))∩	intω(cl(intω(a)))∩	X
ejpam-164	243	4	(	(	PUNCT
ejpam-164	243	5	cl(intω(b	cl(intω(b	PROPN
ejpam-164	243	6	)	)	PUNCT
ejpam-164	243	7	)	)	PUNCT
ejpam-164	243	8	)	)	PUNCT
ejpam-164	243	9	)	)	PUNCT
ejpam-164	244	1	=	=	SYM
ejpam-164	244	2	intω(cl(intω(a))∩	intω(cl(intω(a))∩	NOUN
ejpam-164	244	3	intω(cl(intω(b	intω(cl(intω(b	NOUN
ejpam-164	244	4	)	)	PUNCT
ejpam-164	244	5	)	)	PUNCT
ejpam-164	244	6	)	)	PUNCT
ejpam-164	245	1	=	=	SYM
ejpam-164	245	2	int(a)∩	int(a)∩	X
ejpam-164	245	3	int(b	int(b	X
ejpam-164	245	4	)	)	PUNCT
ejpam-164	245	5	=	=	PROPN
ejpam-164	246	1	int(a∩	int(a∩	PROPN
ejpam-164	246	2	b	b	NOUN
ejpam-164	246	3	)	)	PUNCT
ejpam-164	246	4	.	.	PUNCT
ejpam-164	247	1	then	then	ADV
ejpam-164	247	2	int(a∩	int(a∩	PROPN
ejpam-164	247	3	b	b	NOUN
ejpam-164	247	4	)	)	PUNCT
ejpam-164	247	5	=	=	PUNCT
ejpam-164	248	1	intω(cl(intω(a∩	intω(cl(intω(a∩	PROPN
ejpam-164	248	2	b	b	NOUN
ejpam-164	248	3	)	)	PUNCT
ejpam-164	248	4	)	)	PUNCT
ejpam-164	248	5	)	)	PUNCT
ejpam-164	249	1	and	and	CCONJ
ejpam-164	249	2	hence	hence	ADV
ejpam-164	249	3	a∩	a∩	PROPN
ejpam-164	249	4	b	b	PROPN
ejpam-164	249	5	is	be	AUX
ejpam-164	249	6	an	an	DET
ejpam-164	249	7	ω	ω	PROPN
ejpam-164	249	8	-	-	PUNCT
ejpam-164	249	9	tα	tα	NOUN
ejpam-164	249	10	-	-	PUNCT
ejpam-164	249	11	set	set	NOUN
ejpam-164	249	12	.	.	PUNCT
ejpam-164	250	1	from	from	ADP
ejpam-164	250	2	the	the	DET
ejpam-164	250	3	following	follow	VERB
ejpam-164	250	4	examples	example	NOUN
ejpam-164	250	5	one	one	PRON
ejpam-164	250	6	can	can	AUX
ejpam-164	250	7	deduce	deduce	VERB
ejpam-164	250	8	that	that	SCONJ
ejpam-164	250	9	an	an	DET
ejpam-164	250	10	α	α	PROPN
ejpam-164	250	11	-	-	PUNCT
ejpam-164	250	12	ω	ω	VERB
ejpam-164	250	13	-	-	ADJ
ejpam-164	250	14	open	open	ADJ
ejpam-164	250	15	set	set	NOUN
ejpam-164	250	16	and	and	CCONJ
ejpam-164	250	17	an	an	DET
ejpam-164	250	18	ω	ω	ADJ
ejpam-164	250	19	-	-	PUNCT
ejpam-164	250	20	bα	bα	NOUN
ejpam-164	250	21	-	-	PUNCT
ejpam-164	250	22	set	set	NOUN
ejpam-164	250	23	are	be	AUX
ejpam-164	250	24	independent	independent	ADJ
ejpam-164	250	25	.	.	PUNCT
ejpam-164	251	1	example	example	NOUN
ejpam-164	251	2	3.7	3.7	NUM
ejpam-164	251	3	.	.	PUNCT
ejpam-164	252	1	let	let	VERB
ejpam-164	252	2	x	x	PUNCT
ejpam-164	252	3	=	=	PUNCT
ejpam-164	252	4	r	r	NOUN
ejpam-164	252	5	with	with	ADP
ejpam-164	252	6	the	the	DET
ejpam-164	252	7	usual	usual	ADJ
ejpam-164	252	8	topology	topology	NOUN
ejpam-164	252	9	τ	τ	PROPN
ejpam-164	252	10	.	.	PUNCT
ejpam-164	253	1	then	then	ADV
ejpam-164	253	2	r\q	r\q	PROPN
ejpam-164	253	3	is	be	AUX
ejpam-164	253	4	α	α	PROPN
ejpam-164	253	5	-	-	PUNCT
ejpam-164	253	6	ω	ω	NOUN
ejpam-164	253	7	-	-	NOUN
ejpam-164	253	8	open	open	ADJ
ejpam-164	253	9	but	but	CCONJ
ejpam-164	253	10	it	it	PRON
ejpam-164	253	11	is	be	AUX
ejpam-164	253	12	not	not	PART
ejpam-164	253	13	an	an	DET
ejpam-164	253	14	ω	ω	NUM
ejpam-164	253	15	-	-	PUNCT
ejpam-164	253	16	bα	bα	NOUN
ejpam-164	253	17	-	-	PUNCT
ejpam-164	253	18	set	set	VERB
ejpam-164	253	19	and	and	CCONJ
ejpam-164	253	20	(	(	PUNCT
ejpam-164	253	21	0,1	0,1	NUM
ejpam-164	253	22	]	]	PUNCT
ejpam-164	253	23	is	be	AUX
ejpam-164	253	24	an	an	DET
ejpam-164	253	25	ω	ω	ADJ
ejpam-164	253	26	-	-	PUNCT
ejpam-164	253	27	bα	bα	NOUN
ejpam-164	253	28	-	-	PUNCT
ejpam-164	253	29	set	set	NOUN
ejpam-164	253	30	which	which	PRON
ejpam-164	253	31	is	be	AUX
ejpam-164	253	32	not	not	PART
ejpam-164	253	33	α	α	PROPN
ejpam-164	253	34	-	-	PUNCT
ejpam-164	253	35	ω	ω	VERB
ejpam-164	253	36	-	-	NOUN
ejpam-164	253	37	open	open	ADJ
ejpam-164	253	38	.	.	PUNCT
ejpam-164	254	1	proposition	proposition	NOUN
ejpam-164	254	2	3.8	3.8	NUM
ejpam-164	254	3	.	.	PUNCT
ejpam-164	255	1	for	for	ADP
ejpam-164	255	2	a	a	DET
ejpam-164	255	3	subset	subset	NOUN
ejpam-164	255	4	a	a	PRON
ejpam-164	255	5	of	of	ADP
ejpam-164	255	6	a	a	DET
ejpam-164	255	7	space	space	NOUN
ejpam-164	255	8	(	(	PUNCT
ejpam-164	255	9	x	x	X
ejpam-164	255	10	,	,	PUNCT
ejpam-164	255	11	τ	τ	PROPN
ejpam-164	255	12	)	)	PUNCT
ejpam-164	255	13	,	,	PUNCT
ejpam-164	255	14	the	the	DET
ejpam-164	255	15	following	follow	VERB
ejpam-164	255	16	properties	property	NOUN
ejpam-164	255	17	are	be	AUX
ejpam-164	255	18	equivalent	equivalent	ADJ
ejpam-164	255	19	:	:	PUNCT
ejpam-164	256	1	1	1	X
ejpam-164	256	2	.	.	X
ejpam-164	257	1	a	a	PRON
ejpam-164	257	2	is	be	AUX
ejpam-164	257	3	open	open	ADJ
ejpam-164	257	4	;	;	PUNCT
ejpam-164	257	5	2	2	X
ejpam-164	257	6	.	.	X
ejpam-164	257	7	a	a	PRON
ejpam-164	257	8	is	be	AUX
ejpam-164	257	9	α	α	NOUN
ejpam-164	257	10	-	-	PUNCT
ejpam-164	257	11	ω	ω	NOUN
ejpam-164	257	12	-	-	NOUN
ejpam-164	257	13	open	open	ADJ
ejpam-164	257	14	and	and	CCONJ
ejpam-164	257	15	an	an	DET
ejpam-164	257	16	ω	ω	ADJ
ejpam-164	257	17	-	-	PUNCT
ejpam-164	257	18	bα	bα	NOUN
ejpam-164	257	19	-	-	PUNCT
ejpam-164	257	20	set	set	NOUN
ejpam-164	257	21	.	.	PUNCT
ejpam-164	258	1	proof	proof	NOUN
ejpam-164	258	2	.	.	PUNCT
ejpam-164	259	1	(	(	PUNCT
ejpam-164	259	2	1	1	X
ejpam-164	259	3	)	)	PUNCT
ejpam-164	259	4	⇒	⇒	NOUN
ejpam-164	259	5	(	(	PUNCT
ejpam-164	259	6	2	2	NUM
ejpam-164	259	7	):	):	PUNCT
ejpam-164	259	8	let	let	VERB
ejpam-164	259	9	a	a	PRON
ejpam-164	259	10	be	be	AUX
ejpam-164	259	11	open	open	ADJ
ejpam-164	259	12	.	.	PUNCT
ejpam-164	260	1	then	then	ADV
ejpam-164	260	2	a	a	DET
ejpam-164	260	3	=	=	SYM
ejpam-164	260	4	intω(a	intω(a	PROPN
ejpam-164	260	5	)	)	PUNCT
ejpam-164	260	6	⊆	⊆	NUM
ejpam-164	260	7	cl(intω(a	cl(intω(a	NOUN
ejpam-164	260	8	)	)	PUNCT
ejpam-164	260	9	)	)	PUNCT
ejpam-164	260	10	and	and	CCONJ
ejpam-164	260	11	a	a	DET
ejpam-164	260	12	=	=	SYM
ejpam-164	260	13	intω(a	intω(a	PROPN
ejpam-164	260	14	)	)	PUNCT
ejpam-164	260	15	⊆	⊆	NUM
ejpam-164	260	16	intω(cl(intω(a	intω(cl(intω(a	NOUN
ejpam-164	260	17	)	)	PUNCT
ejpam-164	260	18	)	)	PUNCT
ejpam-164	260	19	.	.	PUNCT
ejpam-164	261	1	therefore	therefore	ADV
ejpam-164	261	2	a	a	PRON
ejpam-164	261	3	is	be	AUX
ejpam-164	261	4	α	α	NOUN
ejpam-164	261	5	-	-	PUNCT
ejpam-164	261	6	ω	ω	NOUN
ejpam-164	261	7	-	-	NOUN
ejpam-164	261	8	open	open	ADJ
ejpam-164	261	9	.	.	PUNCT
ejpam-164	262	1	also	also	ADV
ejpam-164	262	2	a=	a=	VERB
ejpam-164	262	3	a∩	a∩	PROPN
ejpam-164	262	4	x	x	X
ejpam-164	262	5	and	and	CCONJ
ejpam-164	262	6	hence	hence	ADV
ejpam-164	262	7	a	a	PRON
ejpam-164	262	8	is	be	AUX
ejpam-164	262	9	an	an	DET
ejpam-164	262	10	ω	ω	NUM
ejpam-164	262	11	-	-	PUNCT
ejpam-164	262	12	bα	bα	NOUN
ejpam-164	262	13	-	-	PUNCT
ejpam-164	262	14	set	set	NOUN
ejpam-164	262	15	.	.	PUNCT
ejpam-164	263	1	(	(	PUNCT
ejpam-164	263	2	2)⇒	2)⇒	NUM
ejpam-164	263	3	(	(	PUNCT
ejpam-164	263	4	1	1	NUM
ejpam-164	263	5	):	):	PUNCT
ejpam-164	263	6	since	since	SCONJ
ejpam-164	263	7	a	a	PRON
ejpam-164	263	8	is	be	AUX
ejpam-164	263	9	an	an	DET
ejpam-164	263	10	ω	ω	ADJ
ejpam-164	263	11	-	-	PUNCT
ejpam-164	263	12	bα	bα	NOUN
ejpam-164	263	13	-	-	PUNCT
ejpam-164	263	14	set	set	NOUN
ejpam-164	263	15	,	,	PUNCT
ejpam-164	263	16	we	we	PRON
ejpam-164	263	17	have	have	AUX
ejpam-164	263	18	a=	a=	VERB
ejpam-164	263	19	u	u	NOUN
ejpam-164	263	20	∩	∩	NOUN
ejpam-164	263	21	v	v	NOUN
ejpam-164	263	22	,	,	PUNCT
ejpam-164	263	23	where	where	SCONJ
ejpam-164	263	24	u	u	NOUN
ejpam-164	263	25	is	be	AUX
ejpam-164	263	26	an	an	DET
ejpam-164	263	27	open	open	ADJ
ejpam-164	263	28	set	set	NOUN
ejpam-164	263	29	and	and	CCONJ
ejpam-164	263	30	int(v	int(v	NOUN
ejpam-164	263	31	)	)	PUNCT
ejpam-164	264	1	=	=	PUNCT
ejpam-164	264	2	intω(cl(intω(v	intω(cl(intω(v	NOUN
ejpam-164	264	3	)	)	PUNCT
ejpam-164	264	4	)	)	PUNCT
ejpam-164	264	5	.	.	PUNCT
ejpam-164	265	1	by	by	ADP
ejpam-164	265	2	the	the	DET
ejpam-164	265	3	hypothesis	hypothesis	NOUN
ejpam-164	265	4	,	,	PUNCT
ejpam-164	265	5	a	a	PRON
ejpam-164	265	6	is	be	AUX
ejpam-164	265	7	also	also	ADV
ejpam-164	265	8	α	α	PROPN
ejpam-164	265	9	-	-	PUNCT
ejpam-164	265	10	ω	ω	NOUN
ejpam-164	265	11	-	-	NOUN
ejpam-164	265	12	open	open	ADJ
ejpam-164	265	13	,	,	PUNCT
ejpam-164	265	14	and	and	CCONJ
ejpam-164	265	15	we	we	PRON
ejpam-164	265	16	have	have	VERB
ejpam-164	265	17	a⊆	a⊆	VERB
ejpam-164	265	18	intω(cl(intω(a	intω(cl(intω(a	NOUN
ejpam-164	265	19	)	)	PUNCT
ejpam-164	265	20	)	)	PUNCT
ejpam-164	265	21	)	)	PUNCT
ejpam-164	266	1	=	=	PUNCT
ejpam-164	266	2	intω(cl(intω(u	intω(cl(intω(u	NOUN
ejpam-164	266	3	∩	∩	NOUN
ejpam-164	266	4	v	v	NOUN
ejpam-164	266	5	)	)	PUNCT
ejpam-164	266	6	)	)	PUNCT
ejpam-164	267	1	⊆	⊆	NUM
ejpam-164	267	2	intω(cl(intω(u)∩	intω(cl(intω(u)∩	PROPN
ejpam-164	267	3	cl(intω(v	cl(intω(v	PROPN
ejpam-164	267	4	)	)	PUNCT
ejpam-164	267	5	)	)	PUNCT
ejpam-164	267	6	)	)	PUNCT
ejpam-164	267	7	)	)	PUNCT
ejpam-164	268	1	=	=	PUNCT
ejpam-164	268	2	intω(cl(u))∩	intω(cl(u))∩	NOUN
ejpam-164	268	3	intω(cl(intω(v	intω(cl(intω(v	VERB
ejpam-164	268	4	)	)	PUNCT
ejpam-164	268	5	)	)	PUNCT
ejpam-164	268	6	)	)	PUNCT
ejpam-164	269	1	=	=	PUNCT
ejpam-164	269	2	intω(cl(u))∩	intω(cl(u))∩	NOUN
ejpam-164	269	3	int(v	int(v	PROPN
ejpam-164	269	4	)	)	PUNCT
ejpam-164	269	5	.	.	PUNCT
ejpam-164	270	1	t.	t.	PROPN
ejpam-164	270	2	noiri	noiri	PROPN
ejpam-164	270	3	,	,	PUNCT
ejpam-164	270	4	a.	a.	PROPN
ejpam-164	270	5	al	al	PROPN
ejpam-164	270	6	-	-	PUNCT
ejpam-164	270	7	omari	omari	PROPN
ejpam-164	270	8	,	,	PUNCT
ejpam-164	270	9	and	and	CCONJ
ejpam-164	270	10	m.	m.	NOUN
ejpam-164	270	11	noorani	noorani	PROPN
ejpam-164	270	12	/	/	SYM
ejpam-164	270	13	eur	eur	PROPN
ejpam-164	270	14	.	.	PUNCT
ejpam-164	271	1	j.	j.	PROPN
ejpam-164	271	2	pure	pure	PROPN
ejpam-164	271	3	appl	appl	PROPN
ejpam-164	271	4	.	.	PROPN
ejpam-164	271	5	math	math	PROPN
ejpam-164	271	6	,	,	PUNCT
ejpam-164	271	7	2	2	NUM
ejpam-164	271	8	(	(	PUNCT
ejpam-164	271	9	2009	2009	NUM
ejpam-164	271	10	)	)	PUNCT
ejpam-164	271	11	,	,	PUNCT
ejpam-164	271	12	(	(	PUNCT
ejpam-164	271	13	73	73	NUM
ejpam-164	271	14	-	-	SYM
ejpam-164	271	15	84	84	NUM
ejpam-164	271	16	)	)	PUNCT
ejpam-164	271	17	82	82	NUM
ejpam-164	271	18	hence	hence	ADV
ejpam-164	271	19	,	,	PUNCT
ejpam-164	271	20	a=	a=	VERB
ejpam-164	271	21	u	u	NOUN
ejpam-164	271	22	∩	∩	X
ejpam-164	271	23	v	v	ADP
ejpam-164	271	24	=(	=(	NOUN
ejpam-164	271	25	u	u	PROPN
ejpam-164	271	26	∩	∩	ADJ
ejpam-164	271	27	v	v	NOUN
ejpam-164	271	28	)	)	PUNCT
ejpam-164	271	29	∩	∩	NOUN
ejpam-164	271	30	u	u	NOUN
ejpam-164	271	31	⊆	⊆	NUM
ejpam-164	271	32	(	(	PUNCT
ejpam-164	271	33	intω(cl(u))∩	intω(cl(u))∩	NOUN
ejpam-164	271	34	int(v	int(v	NOUN
ejpam-164	271	35	)	)	PUNCT
ejpam-164	271	36	)	)	PUNCT
ejpam-164	271	37	∩	∩	NOUN
ejpam-164	271	38	u	u	NOUN
ejpam-164	271	39	=	=	PUNCT
ejpam-164	271	40	(	(	PUNCT
ejpam-164	271	41	intω(cl(u))∩	intω(cl(u))∩	NOUN
ejpam-164	271	42	u)∩	u)∩	PROPN
ejpam-164	271	43	int(v	int(v	PROPN
ejpam-164	271	44	)	)	PUNCT
ejpam-164	271	45	=	=	SYM
ejpam-164	271	46	u	u	NOUN
ejpam-164	271	47	∩	∩	NOUN
ejpam-164	271	48	int(v	int(v	NOUN
ejpam-164	271	49	)	)	PUNCT
ejpam-164	271	50	.	.	PUNCT
ejpam-164	272	1	therefore	therefore	ADV
ejpam-164	272	2	,	,	PUNCT
ejpam-164	272	3	a=	a=	X
ejpam-164	272	4	(	(	PUNCT
ejpam-164	272	5	u	u	NOUN
ejpam-164	272	6	∩	∩	NOUN
ejpam-164	272	7	v	v	NOUN
ejpam-164	272	8	)	)	PUNCT
ejpam-164	272	9	=	=	SYM
ejpam-164	272	10	(	(	PUNCT
ejpam-164	272	11	u	u	X
ejpam-164	272	12	∩	∩	X
ejpam-164	272	13	int(v	int(v	NOUN
ejpam-164	272	14	)	)	PUNCT
ejpam-164	272	15	)	)	PUNCT
ejpam-164	272	16	and	and	CCONJ
ejpam-164	272	17	a	a	PRON
ejpam-164	272	18	is	be	AUX
ejpam-164	272	19	open	open	ADJ
ejpam-164	272	20	.	.	PUNCT
ejpam-164	273	1	definition	definition	NOUN
ejpam-164	273	2	3.9	3.9	NUM
ejpam-164	273	3	.	.	PUNCT
ejpam-164	274	1	a	a	DET
ejpam-164	274	2	subset	subset	NOUN
ejpam-164	274	3	a	a	PRON
ejpam-164	274	4	of	of	ADP
ejpam-164	274	5	a	a	DET
ejpam-164	274	6	space	space	NOUN
ejpam-164	274	7	x	x	PUNCT
ejpam-164	274	8	is	be	AUX
ejpam-164	274	9	called	call	VERB
ejpam-164	274	10	an	an	DET
ejpam-164	274	11	ω	ω	NOUN
ejpam-164	274	12	-	-	PUNCT
ejpam-164	274	13	set	set	VERB
ejpam-164	274	14	if	if	SCONJ
ejpam-164	274	15	a	a	DET
ejpam-164	274	16	=	=	X
ejpam-164	274	17	u	u	NOUN
ejpam-164	274	18	∩	∩	NOUN
ejpam-164	274	19	v	v	NOUN
ejpam-164	274	20	,	,	PUNCT
ejpam-164	274	21	where	where	SCONJ
ejpam-164	274	22	u	u	PROPN
ejpam-164	274	23	∈	∈	PROPN
ejpam-164	274	24	τ	τ	X
ejpam-164	274	25	and	and	CCONJ
ejpam-164	274	26	int(v	int(v	PROPN
ejpam-164	274	27	)	)	PUNCT
ejpam-164	274	28	=	=	SYM
ejpam-164	274	29	intω(v	intω(v	PROPN
ejpam-164	274	30	)	)	PUNCT
ejpam-164	274	31	.	.	PUNCT
ejpam-164	275	1	from	from	ADP
ejpam-164	275	2	the	the	DET
ejpam-164	275	3	following	follow	VERB
ejpam-164	275	4	examples	example	NOUN
ejpam-164	275	5	one	one	PRON
ejpam-164	275	6	can	can	AUX
ejpam-164	275	7	deduce	deduce	VERB
ejpam-164	275	8	that	that	SCONJ
ejpam-164	275	9	an	an	DET
ejpam-164	275	10	ω	ω	ADV
ejpam-164	275	11	-	-	ADJ
ejpam-164	275	12	open	open	ADJ
ejpam-164	275	13	set	set	NOUN
ejpam-164	275	14	and	and	CCONJ
ejpam-164	275	15	an	an	DET
ejpam-164	275	16	ω	ω	NOUN
ejpam-164	275	17	-	-	PUNCT
ejpam-164	275	18	set	set	NOUN
ejpam-164	275	19	are	be	AUX
ejpam-164	275	20	independent	independent	ADJ
ejpam-164	275	21	.	.	PUNCT
ejpam-164	275	22	example	example	NOUN
ejpam-164	276	1	3.10	3.10	NUM
ejpam-164	276	2	.	.	PUNCT
ejpam-164	277	1	let	let	VERB
ejpam-164	277	2	x	x	PUNCT
ejpam-164	277	3	=	=	PUNCT
ejpam-164	277	4	r	r	NOUN
ejpam-164	277	5	with	with	ADP
ejpam-164	277	6	the	the	DET
ejpam-164	277	7	usual	usual	ADJ
ejpam-164	277	8	topology	topology	NOUN
ejpam-164	277	9	τ	τ	PROPN
ejpam-164	277	10	.	.	PUNCT
ejpam-164	278	1	then	then	ADV
ejpam-164	278	2	r\q	r\q	PROPN
ejpam-164	278	3	is	be	AUX
ejpam-164	278	4	ω	ω	NOUN
ejpam-164	278	5	-	-	ADJ
ejpam-164	278	6	open	open	ADJ
ejpam-164	278	7	but	but	CCONJ
ejpam-164	278	8	it	it	PRON
ejpam-164	278	9	is	be	AUX
ejpam-164	278	10	not	not	PART
ejpam-164	278	11	an	an	DET
ejpam-164	278	12	ω	ω	ADV
ejpam-164	278	13	-	-	PUNCT
ejpam-164	278	14	set	set	VERB
ejpam-164	278	15	and	and	CCONJ
ejpam-164	278	16	a=	a=	VERB
ejpam-164	278	17	(	(	PUNCT
ejpam-164	278	18	0,1)∩q	0,1)∩q	NUM
ejpam-164	278	19	is	be	AUX
ejpam-164	278	20	an	an	DET
ejpam-164	278	21	ω	ω	NOUN
ejpam-164	278	22	–	–	PUNCT
ejpam-164	278	23	set	set	NOUN
ejpam-164	278	24	which	which	PRON
ejpam-164	278	25	is	be	AUX
ejpam-164	278	26	not	not	PART
ejpam-164	278	27	ω	ω	NOUN
ejpam-164	278	28	-	-	NOUN
ejpam-164	278	29	open	open	ADJ
ejpam-164	278	30	.	.	PUNCT
ejpam-164	279	1	proposition	proposition	NOUN
ejpam-164	279	2	3.11	3.11	NUM
ejpam-164	279	3	.	.	PUNCT
ejpam-164	280	1	for	for	ADP
ejpam-164	280	2	a	a	DET
ejpam-164	280	3	subset	subset	NOUN
ejpam-164	280	4	a	a	PRON
ejpam-164	280	5	of	of	ADP
ejpam-164	280	6	a	a	DET
ejpam-164	280	7	space	space	NOUN
ejpam-164	280	8	(	(	PUNCT
ejpam-164	280	9	x	x	X
ejpam-164	280	10	,	,	PUNCT
ejpam-164	280	11	τ	τ	PROPN
ejpam-164	280	12	)	)	PUNCT
ejpam-164	280	13	,	,	PUNCT
ejpam-164	280	14	the	the	DET
ejpam-164	280	15	following	follow	VERB
ejpam-164	280	16	properties	property	NOUN
ejpam-164	280	17	are	be	AUX
ejpam-164	280	18	equivalent	equivalent	ADJ
ejpam-164	280	19	:	:	PUNCT
ejpam-164	281	1	1	1	X
ejpam-164	281	2	.	.	X
ejpam-164	282	1	a	a	PRON
ejpam-164	282	2	is	be	AUX
ejpam-164	282	3	open	open	ADJ
ejpam-164	282	4	;	;	PUNCT
ejpam-164	282	5	2	2	X
ejpam-164	282	6	.	.	X
ejpam-164	282	7	a	a	PRON
ejpam-164	282	8	is	be	AUX
ejpam-164	282	9	ω	ω	NOUN
ejpam-164	282	10	-	-	ADJ
ejpam-164	282	11	open	open	ADJ
ejpam-164	282	12	and	and	CCONJ
ejpam-164	282	13	an	an	DET
ejpam-164	282	14	ω	ω	NOUN
ejpam-164	282	15	-	-	PUNCT
ejpam-164	282	16	set	set	NOUN
ejpam-164	282	17	.	.	PUNCT
ejpam-164	283	1	proof	proof	NOUN
ejpam-164	283	2	.	.	PUNCT
ejpam-164	284	1	(	(	PUNCT
ejpam-164	284	2	1)⇒	1)⇒	NUM
ejpam-164	284	3	(	(	PUNCT
ejpam-164	284	4	2	2	NUM
ejpam-164	284	5	):	):	PUNCT
ejpam-164	284	6	this	this	PRON
ejpam-164	284	7	is	be	AUX
ejpam-164	284	8	obvious	obvious	ADJ
ejpam-164	284	9	.	.	PUNCT
ejpam-164	285	1	(	(	PUNCT
ejpam-164	285	2	2	2	X
ejpam-164	285	3	)	)	PUNCT
ejpam-164	285	4	⇒	⇒	NOUN
ejpam-164	285	5	(	(	PUNCT
ejpam-164	285	6	1	1	NUM
ejpam-164	285	7	):	):	PUNCT
ejpam-164	285	8	since	since	SCONJ
ejpam-164	285	9	a	a	PRON
ejpam-164	285	10	is	be	AUX
ejpam-164	285	11	an	an	DET
ejpam-164	285	12	ω	ω	NOUN
ejpam-164	285	13	-	-	PUNCT
ejpam-164	285	14	set	set	NOUN
ejpam-164	285	15	,	,	PUNCT
ejpam-164	285	16	we	we	PRON
ejpam-164	285	17	have	have	VERB
ejpam-164	285	18	a	a	DET
ejpam-164	285	19	=	=	X
ejpam-164	285	20	u	u	NOUN
ejpam-164	285	21	∩	∩	NOUN
ejpam-164	285	22	v	v	NOUN
ejpam-164	285	23	,	,	PUNCT
ejpam-164	285	24	where	where	SCONJ
ejpam-164	285	25	u	u	NOUN
ejpam-164	285	26	is	be	AUX
ejpam-164	285	27	an	an	DET
ejpam-164	285	28	open	open	ADJ
ejpam-164	285	29	set	set	NOUN
ejpam-164	285	30	and	and	CCONJ
ejpam-164	285	31	int(v	int(v	NOUN
ejpam-164	285	32	)	)	PUNCT
ejpam-164	285	33	=	=	SYM
ejpam-164	285	34	intω(v	intω(v	PROPN
ejpam-164	285	35	)	)	PUNCT
ejpam-164	285	36	.	.	PUNCT
ejpam-164	286	1	by	by	ADP
ejpam-164	286	2	the	the	DET
ejpam-164	286	3	hypothesis	hypothesis	NOUN
ejpam-164	286	4	,	,	PUNCT
ejpam-164	286	5	a	a	PRON
ejpam-164	286	6	is	be	AUX
ejpam-164	286	7	also	also	ADV
ejpam-164	286	8	ω	ω	NOUN
ejpam-164	286	9	-	-	ADJ
ejpam-164	286	10	open	open	ADJ
ejpam-164	286	11	and	and	CCONJ
ejpam-164	286	12	we	we	PRON
ejpam-164	286	13	have	have	VERB
ejpam-164	286	14	a	a	DET
ejpam-164	286	15	=	=	SYM
ejpam-164	286	16	intω(a	intω(a	PROPN
ejpam-164	286	17	)	)	PUNCT
ejpam-164	287	1	=	=	SYM
ejpam-164	287	2	intω(u	intω(u	PROPN
ejpam-164	287	3	∩	∩	NOUN
ejpam-164	287	4	v	v	X
ejpam-164	287	5	)	)	PUNCT
ejpam-164	287	6	=	=	PUNCT
ejpam-164	288	1	intω(u)∩	intω(u)∩	PROPN
ejpam-164	288	2	intω(v	intω(v	PROPN
ejpam-164	288	3	)	)	PUNCT
ejpam-164	288	4	=	=	SYM
ejpam-164	288	5	u	u	PROPN
ejpam-164	288	6	∩	∩	X
ejpam-164	288	7	int(v	int(v	NOUN
ejpam-164	288	8	)	)	PUNCT
ejpam-164	288	9	.	.	PUNCT
ejpam-164	289	1	therefore	therefore	ADV
ejpam-164	289	2	,	,	PUNCT
ejpam-164	289	3	a	a	PRON
ejpam-164	289	4	is	be	AUX
ejpam-164	289	5	open	open	ADJ
ejpam-164	289	6	.	.	PUNCT
ejpam-164	290	1	definition	definition	NOUN
ejpam-164	290	2	3.12	3.12	NUM
ejpam-164	290	3	.	.	PUNCT
ejpam-164	291	1	a	a	DET
ejpam-164	291	2	function	function	NOUN
ejpam-164	291	3	f	f	NOUN
ejpam-164	291	4	:	:	PUNCT
ejpam-164	291	5	x	x	X
ejpam-164	291	6	→	→	SYM
ejpam-164	291	7	y	y	PROPN
ejpam-164	291	8	is	be	AUX
ejpam-164	291	9	said	say	VERB
ejpam-164	291	10	to	to	PART
ejpam-164	291	11	be	be	AUX
ejpam-164	291	12	ω	ω	NOUN
ejpam-164	291	13	-	-	ADJ
ejpam-164	291	14	continuous	continuous	ADJ
ejpam-164	291	15	[	[	X
ejpam-164	291	16	9	9	NUM
ejpam-164	291	17	]	]	PUNCT
ejpam-164	291	18	(	(	PUNCT
ejpam-164	291	19	resp	resp	NOUN
ejpam-164	291	20	.	.	PUNCT
ejpam-164	292	1	pre	pre	ADJ
ejpam-164	292	2	-	-	ADJ
ejpam-164	292	3	ωcontinuous	ωcontinuous	ADJ
ejpam-164	292	4	,	,	PUNCT
ejpam-164	292	5	ω	ω	PROPN
ejpam-164	292	6	-	-	PUNCT
ejpam-164	292	7	b	b	NOUN
ejpam-164	292	8	-	-	PUNCT
ejpam-164	292	9	continuous	continuous	ADJ
ejpam-164	292	10	,	,	PUNCT
ejpam-164	292	11	α	α	PROPN
ejpam-164	292	12	-	-	PUNCT
ejpam-164	292	13	ω	ω	NOUN
ejpam-164	292	14	-	-	ADJ
ejpam-164	292	15	continuous	continuous	ADJ
ejpam-164	292	16	,	,	PUNCT
ejpam-164	292	17	ω	ω	ADJ
ejpam-164	292	18	-	-	PUNCT
ejpam-164	292	19	bα	bα	NOUN
ejpam-164	292	20	-	-	PUNCT
ejpam-164	292	21	continuous	continuous	ADJ
ejpam-164	292	22	,	,	PUNCT
ejpam-164	292	23	ω∗-continuous	ω∗-continuous	ADJ
ejpam-164	292	24	)	)	PUNCT
ejpam-164	292	25	if	if	SCONJ
ejpam-164	292	26	f	f	PROPN
ejpam-164	292	27	−1(v	−1(v	PROPN
ejpam-164	292	28	)	)	PUNCT
ejpam-164	292	29	is	be	AUX
ejpam-164	292	30	ω	ω	NOUN
ejpam-164	292	31	-	-	ADJ
ejpam-164	292	32	open	open	ADJ
ejpam-164	292	33	(	(	PUNCT
ejpam-164	292	34	resp	resp	NOUN
ejpam-164	292	35	.	.	PUNCT
ejpam-164	293	1	pre	pre	ADJ
ejpam-164	293	2	-	-	ADJ
ejpam-164	293	3	ω	ω	VERB
ejpam-164	293	4	-	-	ADJ
ejpam-164	293	5	open	open	ADJ
ejpam-164	293	6	,	,	PUNCT
ejpam-164	293	7	an	an	DET
ejpam-164	293	8	ω	ω	PROPN
ejpam-164	293	9	-	-	PUNCT
ejpam-164	293	10	b	b	NOUN
ejpam-164	293	11	-	-	PUNCT
ejpam-164	293	12	set	set	NOUN
ejpam-164	293	13	,	,	PUNCT
ejpam-164	293	14	α	α	PROPN
ejpam-164	293	15	-	-	PUNCT
ejpam-164	293	16	ω	ω	NOUN
ejpam-164	293	17	-	-	NOUN
ejpam-164	293	18	open	open	ADJ
ejpam-164	293	19	,	,	PUNCT
ejpam-164	293	20	an	an	DET
ejpam-164	293	21	ω	ω	ADJ
ejpam-164	293	22	-	-	PUNCT
ejpam-164	293	23	bα	bα	NOUN
ejpam-164	293	24	-	-	PUNCT
ejpam-164	293	25	set	set	NOUN
ejpam-164	293	26	,	,	PUNCT
ejpam-164	293	27	an	an	DET
ejpam-164	293	28	ω	ω	NOUN
ejpam-164	293	29	-	-	PUNCT
ejpam-164	293	30	set	set	NOUN
ejpam-164	293	31	)	)	PUNCT
ejpam-164	293	32	for	for	SCONJ
ejpam-164	293	33	each	each	DET
ejpam-164	293	34	open	open	ADJ
ejpam-164	293	35	set	set	VERB
ejpam-164	293	36	v	v	NOUN
ejpam-164	293	37	in	in	ADP
ejpam-164	293	38	y	y	PROPN
ejpam-164	293	39	.	.	PUNCT
ejpam-164	294	1	t.	t.	PROPN
ejpam-164	294	2	noiri	noiri	PROPN
ejpam-164	294	3	,	,	PUNCT
ejpam-164	294	4	a.	a.	PROPN
ejpam-164	294	5	al	al	PROPN
ejpam-164	294	6	-	-	PUNCT
ejpam-164	294	7	omari	omari	PROPN
ejpam-164	294	8	,	,	PUNCT
ejpam-164	294	9	and	and	CCONJ
ejpam-164	294	10	m.	m.	NOUN
ejpam-164	294	11	noorani	noorani	PROPN
ejpam-164	294	12	/	/	SYM
ejpam-164	294	13	eur	eur	PROPN
ejpam-164	294	14	.	.	PUNCT
ejpam-164	295	1	j.	j.	PROPN
ejpam-164	295	2	pure	pure	PROPN
ejpam-164	295	3	appl	appl	PROPN
ejpam-164	295	4	.	.	PROPN
ejpam-164	295	5	math	math	PROPN
ejpam-164	295	6	,	,	PUNCT
ejpam-164	295	7	2	2	NUM
ejpam-164	295	8	(	(	PUNCT
ejpam-164	295	9	2009	2009	NUM
ejpam-164	295	10	)	)	PUNCT
ejpam-164	295	11	,	,	PUNCT
ejpam-164	295	12	(	(	PUNCT
ejpam-164	295	13	73	73	NUM
ejpam-164	295	14	-	-	SYM
ejpam-164	295	15	84	84	NUM
ejpam-164	295	16	)	)	PUNCT
ejpam-164	295	17	83	83	NUM
ejpam-164	295	18	by	by	ADP
ejpam-164	295	19	propositions	proposition	NOUN
ejpam-164	295	20	3.4	3.4	NUM
ejpam-164	295	21	,	,	PUNCT
ejpam-164	295	22	3.8	3.8	NUM
ejpam-164	295	23	and	and	CCONJ
ejpam-164	295	24	3.11	3.11	NUM
ejpam-164	295	25	we	we	PRON
ejpam-164	295	26	have	have	VERB
ejpam-164	295	27	an	an	DET
ejpam-164	295	28	immediate	immediate	ADJ
ejpam-164	295	29	result	result	NOUN
ejpam-164	295	30	.	.	PUNCT
ejpam-164	296	1	theorem	theorem	VERB
ejpam-164	296	2	3.13	3.13	NUM
ejpam-164	296	3	.	.	PUNCT
ejpam-164	297	1	for	for	ADP
ejpam-164	297	2	a	a	DET
ejpam-164	297	3	function	function	NOUN
ejpam-164	297	4	f	f	NOUN
ejpam-164	297	5	:	:	PUNCT
ejpam-164	297	6	x	x	X
ejpam-164	297	7	→	→	SYM
ejpam-164	297	8	y	y	PROPN
ejpam-164	297	9	,	,	PUNCT
ejpam-164	297	10	the	the	DET
ejpam-164	297	11	following	follow	VERB
ejpam-164	297	12	properties	property	NOUN
ejpam-164	297	13	are	be	AUX
ejpam-164	297	14	equivalent	equivalent	ADJ
ejpam-164	297	15	:	:	PUNCT
ejpam-164	297	16	1	1	X
ejpam-164	297	17	.	.	X
ejpam-164	297	18	f	f	PROPN
ejpam-164	297	19	is	be	AUX
ejpam-164	297	20	continuous	continuous	ADJ
ejpam-164	297	21	;	;	PUNCT
ejpam-164	297	22	2	2	X
ejpam-164	297	23	.	.	X
ejpam-164	297	24	f	f	PROPN
ejpam-164	297	25	is	be	AUX
ejpam-164	297	26	pre	pre	ADJ
ejpam-164	297	27	-	-	ADJ
ejpam-164	297	28	ω	ω	ADJ
ejpam-164	297	29	-	-	ADJ
ejpam-164	297	30	continuous	continuous	ADJ
ejpam-164	297	31	and	and	CCONJ
ejpam-164	297	32	ω	ω	NUM
ejpam-164	297	33	-	-	PUNCT
ejpam-164	297	34	b	b	NOUN
ejpam-164	297	35	-	-	PUNCT
ejpam-164	297	36	continuous	continuous	ADJ
ejpam-164	297	37	;	;	PUNCT
ejpam-164	297	38	3	3	X
ejpam-164	297	39	.	.	X
ejpam-164	297	40	f	f	PROPN
ejpam-164	297	41	is	be	AUX
ejpam-164	297	42	α	α	PROPN
ejpam-164	297	43	-	-	PUNCT
ejpam-164	297	44	ω	ω	NOUN
ejpam-164	297	45	-	-	ADJ
ejpam-164	297	46	continuous	continuous	ADJ
ejpam-164	297	47	and	and	CCONJ
ejpam-164	297	48	ω	ω	VERB
ejpam-164	297	49	-	-	PUNCT
ejpam-164	297	50	bα	bα	NOUN
ejpam-164	297	51	-	-	PUNCT
ejpam-164	297	52	continuous	continuous	ADJ
ejpam-164	297	53	;	;	PUNCT
ejpam-164	297	54	4	4	NUM
ejpam-164	297	55	.	.	X
ejpam-164	297	56	f	f	PROPN
ejpam-164	297	57	is	be	AUX
ejpam-164	297	58	ω	ω	NOUN
ejpam-164	297	59	-	-	ADJ
ejpam-164	297	60	continuous	continuous	ADJ
ejpam-164	297	61	and	and	CCONJ
ejpam-164	297	62	ω∗-continuous	ω∗-continuous	ADJ
ejpam-164	297	63	.	.	PUNCT
ejpam-164	297	64	proposition	proposition	NOUN
ejpam-164	297	65	3.14	3.14	NUM
ejpam-164	297	66	.	.	PUNCT
ejpam-164	298	1	for	for	ADP
ejpam-164	298	2	a	a	DET
ejpam-164	298	3	subset	subset	NOUN
ejpam-164	298	4	a	a	PRON
ejpam-164	298	5	of	of	ADP
ejpam-164	298	6	an	an	DET
ejpam-164	298	7	anti	anti	ADJ
ejpam-164	298	8	-	-	ADJ
ejpam-164	298	9	locally	locally	ADV
ejpam-164	298	10	countable	countable	ADJ
ejpam-164	298	11	space	space	NOUN
ejpam-164	298	12	(	(	PUNCT
ejpam-164	298	13	x	x	X
ejpam-164	298	14	,	,	PUNCT
ejpam-164	298	15	τ	τ	PROPN
ejpam-164	298	16	)	)	PUNCT
ejpam-164	298	17	,	,	PUNCT
ejpam-164	298	18	the	the	DET
ejpam-164	298	19	following	follow	VERB
ejpam-164	298	20	properties	property	NOUN
ejpam-164	298	21	are	be	AUX
ejpam-164	298	22	equivalent	equivalent	ADJ
ejpam-164	298	23	:	:	PUNCT
ejpam-164	299	1	1	1	X
ejpam-164	299	2	.	.	X
ejpam-164	300	1	a	a	PRON
ejpam-164	300	2	is	be	AUX
ejpam-164	300	3	regular	regular	ADJ
ejpam-164	300	4	open	open	ADJ
ejpam-164	300	5	;	;	PUNCT
ejpam-164	300	6	2	2	X
ejpam-164	300	7	.	.	PUNCT
ejpam-164	300	8	a=	a=	ADJ
ejpam-164	300	9	intω(cl(a	intω(cl(a	X
ejpam-164	300	10	)	)	PUNCT
ejpam-164	300	11	)	)	PUNCT
ejpam-164	301	1	;	;	PUNCT
ejpam-164	301	2	3	3	X
ejpam-164	301	3	.	.	X
ejpam-164	301	4	a	a	PRON
ejpam-164	301	5	is	be	AUX
ejpam-164	301	6	pre	pre	ADJ
ejpam-164	301	7	-	-	ADJ
ejpam-164	301	8	ω	ω	ADJ
ejpam-164	301	9	-	-	ADJ
ejpam-164	301	10	open	open	ADJ
ejpam-164	301	11	and	and	CCONJ
ejpam-164	301	12	an	an	DET
ejpam-164	301	13	ω	ω	PROPN
ejpam-164	301	14	-	-	PUNCT
ejpam-164	301	15	t	t	NOUN
ejpam-164	301	16	-	-	PUNCT
ejpam-164	301	17	set	set	NOUN
ejpam-164	301	18	.	.	PUNCT
ejpam-164	302	1	proof	proof	NOUN
ejpam-164	302	2	.	.	PUNCT
ejpam-164	303	1	(	(	PUNCT
ejpam-164	303	2	1	1	X
ejpam-164	303	3	)	)	PUNCT
ejpam-164	303	4	⇒	⇒	NOUN
ejpam-164	303	5	(	(	PUNCT
ejpam-164	303	6	2	2	NUM
ejpam-164	303	7	):	):	PUNCT
ejpam-164	303	8	let	let	VERB
ejpam-164	303	9	a	a	PRON
ejpam-164	303	10	be	be	AUX
ejpam-164	303	11	regular	regular	ADJ
ejpam-164	303	12	open	open	ADJ
ejpam-164	303	13	.	.	PUNCT
ejpam-164	304	1	then	then	ADV
ejpam-164	304	2	by	by	ADP
ejpam-164	304	3	lemma	lemma	PROPN
ejpam-164	304	4	2.19	2.19	NUM
ejpam-164	304	5	,	,	PUNCT
ejpam-164	304	6	we	we	PRON
ejpam-164	304	7	have	have	VERB
ejpam-164	304	8	intω(cl(a	intω(cl(a	VERB
ejpam-164	304	9	)	)	PUNCT
ejpam-164	304	10	)	)	PUNCT
ejpam-164	305	1	=	=	SYM
ejpam-164	305	2	int(cl(a	int(cl(a	PROPN
ejpam-164	305	3	)	)	PUNCT
ejpam-164	305	4	)	)	PUNCT
ejpam-164	306	1	=	=	PUNCT
ejpam-164	306	2	a.	a.	NOUN
ejpam-164	306	3	(	(	PUNCT
ejpam-164	306	4	2)⇒	2)⇒	NUM
ejpam-164	306	5	(	(	PUNCT
ejpam-164	306	6	3	3	NUM
ejpam-164	306	7	):	):	PUNCT
ejpam-164	306	8	the	the	DET
ejpam-164	306	9	proof	proof	NOUN
ejpam-164	306	10	is	be	AUX
ejpam-164	306	11	obvious	obvious	ADJ
ejpam-164	306	12	.	.	PUNCT
ejpam-164	307	1	(	(	PUNCT
ejpam-164	307	2	3)⇒	3)⇒	NUM
ejpam-164	307	3	(	(	PUNCT
ejpam-164	307	4	1	1	NUM
ejpam-164	307	5	):	):	PUNCT
ejpam-164	307	6	let	let	VERB
ejpam-164	307	7	a	a	PRON
ejpam-164	307	8	be	be	AUX
ejpam-164	307	9	pre	pre	ADJ
ejpam-164	307	10	-	-	ADJ
ejpam-164	307	11	ω	ω	ADJ
ejpam-164	307	12	-	-	ADJ
ejpam-164	307	13	open	open	ADJ
ejpam-164	307	14	and	and	CCONJ
ejpam-164	307	15	an	an	DET
ejpam-164	307	16	ω	ω	PROPN
ejpam-164	307	17	-	-	PUNCT
ejpam-164	307	18	t	t	NOUN
ejpam-164	307	19	-	-	PUNCT
ejpam-164	307	20	set	set	NOUN
ejpam-164	307	21	.	.	PUNCT
ejpam-164	308	1	then	then	ADV
ejpam-164	308	2	a	a	DET
ejpam-164	308	3	⊆	⊆	NUM
ejpam-164	308	4	intω(cl(a	intω(cl(a	NOUN
ejpam-164	308	5	)	)	PUNCT
ejpam-164	308	6	)	)	PUNCT
ejpam-164	309	1	=	=	PUNCT
ejpam-164	309	2	int(a	int(a	NOUN
ejpam-164	309	3	)	)	PUNCT
ejpam-164	309	4	⊆	⊆	PROPN
ejpam-164	309	5	a	a	PRON
ejpam-164	309	6	and	and	CCONJ
ejpam-164	309	7	hence	hence	ADV
ejpam-164	309	8	a=	a=	ADV
ejpam-164	309	9	intω(cl(a	intω(cl(a	X
ejpam-164	309	10	)	)	PUNCT
ejpam-164	309	11	)	)	PUNCT
ejpam-164	310	1	=	=	SYM
ejpam-164	310	2	int(cl(a	int(cl(a	PROPN
ejpam-164	310	3	)	)	PUNCT
ejpam-164	310	4	)	)	PUNCT
ejpam-164	310	5	.	.	PUNCT
ejpam-164	311	1	definition	definition	NOUN
ejpam-164	311	2	3.15	3.15	NUM
ejpam-164	311	3	.	.	PUNCT
ejpam-164	312	1	a	a	DET
ejpam-164	312	2	function	function	NOUN
ejpam-164	312	3	f	f	NOUN
ejpam-164	312	4	:	:	PUNCT
ejpam-164	312	5	x	x	X
ejpam-164	312	6	→	→	SYM
ejpam-164	312	7	y	y	PROPN
ejpam-164	312	8	is	be	AUX
ejpam-164	312	9	said	say	VERB
ejpam-164	312	10	to	to	PART
ejpam-164	312	11	be	be	AUX
ejpam-164	312	12	completely	completely	ADV
ejpam-164	312	13	continuous	continuous	ADJ
ejpam-164	312	14	[	[	X
ejpam-164	312	15	6	6	NUM
ejpam-164	312	16	]	]	PUNCT
ejpam-164	312	17	(	(	PUNCT
ejpam-164	312	18	resp	resp	NOUN
ejpam-164	312	19	.	.	PUNCT
ejpam-164	313	1	ω	ω	X
ejpam-164	313	2	-	-	ADJ
ejpam-164	313	3	tcontinuous	tcontinuous	ADJ
ejpam-164	313	4	)	)	PUNCT
ejpam-164	313	5	if	if	SCONJ
ejpam-164	313	6	f	f	PROPN
ejpam-164	313	7	−1(v	−1(v	PROPN
ejpam-164	313	8	)	)	PUNCT
ejpam-164	313	9	is	be	AUX
ejpam-164	313	10	regular	regular	ADJ
ejpam-164	313	11	open	open	ADJ
ejpam-164	313	12	(	(	PUNCT
ejpam-164	313	13	resp	resp	NOUN
ejpam-164	313	14	.	.	PUNCT
ejpam-164	314	1	an	an	DET
ejpam-164	314	2	ω	ω	PROPN
ejpam-164	314	3	-	-	PUNCT
ejpam-164	314	4	t	t	NOUN
ejpam-164	314	5	-	-	PUNCT
ejpam-164	314	6	set	set	NOUN
ejpam-164	314	7	)	)	PUNCT
ejpam-164	314	8	in	in	ADP
ejpam-164	314	9	x	x	PUNCT
ejpam-164	314	10	for	for	SCONJ
ejpam-164	314	11	each	each	DET
ejpam-164	314	12	open	open	ADJ
ejpam-164	314	13	set	set	VERB
ejpam-164	314	14	v	v	NOUN
ejpam-164	314	15	of	of	ADP
ejpam-164	314	16	y	y	PROPN
ejpam-164	314	17	.	.	PUNCT
ejpam-164	315	1	theorem	theorem	VERB
ejpam-164	315	2	3.16	3.16	NUM
ejpam-164	315	3	.	.	PUNCT
ejpam-164	316	1	let	let	AUX
ejpam-164	316	2	(	(	PUNCT
ejpam-164	316	3	x	x	X
ejpam-164	316	4	,	,	PUNCT
ejpam-164	316	5	τ	τ	X
ejpam-164	316	6	)	)	PUNCT
ejpam-164	316	7	be	be	AUX
ejpam-164	316	8	an	an	DET
ejpam-164	316	9	anti	anti	ADJ
ejpam-164	316	10	-	-	ADJ
ejpam-164	316	11	locally	locally	ADV
ejpam-164	316	12	countable	countable	ADJ
ejpam-164	316	13	space	space	NOUN
ejpam-164	316	14	.	.	PUNCT
ejpam-164	317	1	a	a	DET
ejpam-164	317	2	function	function	NOUN
ejpam-164	317	3	f	f	NOUN
ejpam-164	317	4	:	:	PUNCT
ejpam-164	317	5	x	x	X
ejpam-164	317	6	→	→	SYM
ejpam-164	317	7	y	y	PROPN
ejpam-164	317	8	is	be	AUX
ejpam-164	317	9	completely	completely	ADV
ejpam-164	317	10	continuous	continuous	ADJ
ejpam-164	317	11	if	if	SCONJ
ejpam-164	317	12	and	and	CCONJ
ejpam-164	317	13	only	only	ADV
ejpam-164	317	14	if	if	SCONJ
ejpam-164	317	15	f	f	PROPN
ejpam-164	317	16	is	be	AUX
ejpam-164	317	17	pre	pre	ADJ
ejpam-164	317	18	-	-	ADJ
ejpam-164	317	19	ω	ω	ADJ
ejpam-164	317	20	-	-	ADJ
ejpam-164	317	21	continuous	continuous	ADJ
ejpam-164	317	22	and	and	CCONJ
ejpam-164	317	23	ω	ω	NUM
ejpam-164	317	24	-	-	PUNCT
ejpam-164	317	25	t	t	NOUN
ejpam-164	317	26	-	-	PUNCT
ejpam-164	317	27	continuous	continuous	ADJ
ejpam-164	317	28	.	.	PUNCT
ejpam-164	318	1	proof	proof	NOUN
ejpam-164	318	2	.	.	PUNCT
ejpam-164	319	1	this	this	PRON
ejpam-164	319	2	is	be	AUX
ejpam-164	319	3	an	an	DET
ejpam-164	319	4	immediate	immediate	ADJ
ejpam-164	319	5	consequence	consequence	NOUN
ejpam-164	319	6	of	of	ADP
ejpam-164	319	7	proposition	proposition	NOUN
ejpam-164	319	8	3.14	3.14	NUM
ejpam-164	319	9	.	.	PUNCT
ejpam-164	320	1	acknowledgements	acknowledgement	NOUN
ejpam-164	320	2	.	.	PUNCT
ejpam-164	321	1	this	this	DET
ejpam-164	321	2	work	work	NOUN
ejpam-164	321	3	is	be	AUX
ejpam-164	321	4	financially	financially	ADV
ejpam-164	321	5	supported	support	VERB
ejpam-164	321	6	by	by	ADP
ejpam-164	321	7	the	the	DET
ejpam-164	321	8	ministry	ministry	PROPN
ejpam-164	321	9	of	of	ADP
ejpam-164	321	10	higher	high	ADJ
ejpam-164	321	11	education	education	NOUN
ejpam-164	321	12	,	,	PUNCT
ejpam-164	321	13	malaysia	malaysia	PROPN
ejpam-164	321	14	under	under	ADP
ejpam-164	321	15	frgs	frgs	PROPN
ejpam-164	321	16	grant	grant	VERB
ejpam-164	321	17	no	no	PRON
ejpam-164	321	18	:	:	PUNCT
ejpam-164	321	19	ukm	ukm	VERB
ejpam-164	321	20	-	-	PUNCT
ejpam-164	321	21	st-06	st-06	NOUN
ejpam-164	321	22	-	-	PUNCT
ejpam-164	321	23	frgs0008	frgs0008	NOUN
ejpam-164	321	24	-	-	PUNCT
ejpam-164	321	25	2008	2008	NUM
ejpam-164	321	26	.	.	PUNCT
ejpam-164	322	1	references	reference	NOUN
ejpam-164	322	2	84	84	NUM
ejpam-164	322	3	references	reference	NOUN
ejpam-164	322	4	[	[	X
ejpam-164	322	5	1	1	NUM
ejpam-164	322	6	]	]	PUNCT
ejpam-164	322	7	m.	m.	NOUN
ejpam-164	322	8	e.	e.	PROPN
ejpam-164	322	9	abd	abd	PROPN
ejpam-164	322	10	el	el	PROPN
ejpam-164	322	11	-	-	PROPN
ejpam-164	322	12	monsef	monsef	PROPN
ejpam-164	322	13	,	,	PUNCT
ejpam-164	322	14	s.	s.	PROPN
ejpam-164	322	15	n.	n.	PROPN
ejpam-164	322	16	el	el	PROPN
ejpam-164	322	17	-	-	PUNCT
ejpam-164	322	18	deeb	deeb	PROPN
ejpam-164	322	19	and	and	CCONJ
ejpam-164	322	20	r.	r.	PROPN
ejpam-164	322	21	a.	a.	PROPN
ejpam-164	322	22	mahmoud	mahmoud	PROPN
ejpam-164	322	23	,	,	PUNCT
ejpam-164	322	24	"	"	PUNCT
ejpam-164	322	25	β	β	X
ejpam-164	322	26	-open	-open	NOUN
ejpam-164	322	27	sets	set	NOUN
ejpam-164	322	28	and	and	CCONJ
ejpam-164	322	29	β	β	PRON
ejpam-164	322	30	-continuous	-continuous	ADJ
ejpam-164	322	31	mappings	mapping	NOUN
ejpam-164	322	32	"	"	PUNCT
ejpam-164	322	33	,	,	PUNCT
ejpam-164	322	34	bull	bull	NOUN
ejpam-164	322	35	.	.	PUNCT
ejpam-164	323	1	fac	fac	PROPN
ejpam-164	323	2	.	.	PUNCT
ejpam-164	324	1	sci	sci	PROPN
ejpam-164	324	2	.	.	PUNCT
ejpam-164	324	3	assuit	assuit	PROPN
ejpam-164	324	4	univ	univ	PROPN
ejpam-164	324	5	.	.	PUNCT
ejpam-164	325	1	12	12	NUM
ejpam-164	325	2	:	:	PUNCT
ejpam-164	325	3	77	77	NUM
ejpam-164	325	4	-	-	SYM
ejpam-164	325	5	90	90	NUM
ejpam-164	325	6	(	(	PUNCT
ejpam-164	325	7	1983	1983	NUM
ejpam-164	325	8	)	)	PUNCT
ejpam-164	325	9	.	.	PUNCT
ejpam-164	326	1	[	[	X
ejpam-164	326	2	2	2	NUM
ejpam-164	326	3	]	]	PUNCT
ejpam-164	326	4	a.	a.	PROPN
ejpam-164	326	5	al	al	PROPN
ejpam-164	326	6	-	-	PUNCT
ejpam-164	326	7	omari	omari	PROPN
ejpam-164	326	8	and	and	CCONJ
ejpam-164	326	9	m.	m.	PROPN
ejpam-164	326	10	s.	s.	PROPN
ejpam-164	326	11	m.	m.	PROPN
ejpam-164	326	12	noorani	noorani	PROPN
ejpam-164	326	13	,	,	PUNCT
ejpam-164	326	14	"	"	PUNCT
ejpam-164	326	15	regular	regular	ADJ
ejpam-164	326	16	generalized	generalize	VERB
ejpam-164	326	17	ω	ω	VERB
ejpam-164	326	18	-	-	PUNCT
ejpam-164	326	19	closed	closed	ADJ
ejpam-164	326	20	sets	set	NOUN
ejpam-164	326	21	"	"	PUNCT
ejpam-164	326	22	,	,	PUNCT
ejpam-164	326	23	internat	internat	PROPN
ejpam-164	326	24	.	.	PUNCT
ejpam-164	327	1	j.	j.	PROPN
ejpam-164	327	2	math	math	PROPN
ejpam-164	327	3	.	.	PUNCT
ejpam-164	328	1	math	math	NOUN
ejpam-164	328	2	.	.	PUNCT
ejpam-164	329	1	sci	sci	PROPN
ejpam-164	329	2	.	.	PROPN
ejpam-164	329	3	,	,	PUNCT
ejpam-164	329	4	volume	volume	NOUN
ejpam-164	329	5	2007	2007	NUM
ejpam-164	329	6	.	.	PUNCT
ejpam-164	330	1	article	article	NOUN
ejpam-164	330	2	i	i	PROPN
ejpam-164	330	3	d	d	PROPN
ejpam-164	330	4	16292	16292	NUM
ejpam-164	330	5	,	,	PUNCT
ejpam-164	330	6	11	11	NUM
ejpam-164	330	7	pages	page	NOUN
ejpam-164	330	8	,	,	PUNCT
ejpam-164	330	9	doi	doi	NOUN
ejpam-164	330	10	:	:	PUNCT
ejpam-164	330	11	10.1155/2007/16292	10.1155/2007/16292	NUM
ejpam-164	330	12	.	.	PUNCT
ejpam-164	331	1	[	[	X
ejpam-164	331	2	3	3	NUM
ejpam-164	331	3	]	]	PUNCT
ejpam-164	331	4	a.	a.	PROPN
ejpam-164	331	5	al	al	PROPN
ejpam-164	331	6	-	-	PUNCT
ejpam-164	331	7	omari	omari	PROPN
ejpam-164	331	8	and	and	CCONJ
ejpam-164	331	9	m.	m.	PROPN
ejpam-164	331	10	s.	s.	PROPN
ejpam-164	331	11	m.	m.	PROPN
ejpam-164	331	12	noorani	noorani	PROPN
ejpam-164	331	13	,	,	PUNCT
ejpam-164	331	14	"	"	PUNCT
ejpam-164	331	15	contra	contra	PROPN
ejpam-164	331	16	-	-	PUNCT
ejpam-164	331	17	ω	ω	NOUN
ejpam-164	331	18	-	-	ADJ
ejpam-164	331	19	continuous	continuous	ADJ
ejpam-164	331	20	and	and	CCONJ
ejpam-164	331	21	almost	almost	ADV
ejpam-164	331	22	contra	contra	PROPN
ejpam-164	331	23	-	-	PUNCT
ejpam-164	331	24	ω	ω	VERB
ejpam-164	331	25	-	-	ADJ
ejpam-164	331	26	continuous	continuous	ADJ
ejpam-164	331	27	"	"	PUNCT
ejpam-164	331	28	,	,	PUNCT
ejpam-164	331	29	internat	internat	PROPN
ejpam-164	331	30	.	.	PUNCT
ejpam-164	332	1	j.	j.	PROPN
ejpam-164	332	2	math	math	PROPN
ejpam-164	332	3	.	.	PUNCT
ejpam-164	333	1	math	math	NOUN
ejpam-164	333	2	.	.	PUNCT
ejpam-164	334	1	sci	sci	PROPN
ejpam-164	334	2	.	.	PROPN
ejpam-164	334	3	,	,	PUNCT
ejpam-164	334	4	volume	volume	NOUN
ejpam-164	334	5	2007	2007	NUM
ejpam-164	334	6	.	.	PUNCT
ejpam-164	335	1	article	article	NOUN
ejpam-164	335	2	i	i	PROPN
ejpam-164	335	3	d	d	PROPN
ejpam-164	335	4	40469	40469	NUM
ejpam-164	335	5	,	,	PUNCT
ejpam-164	335	6	13	13	NUM
ejpam-164	335	7	pages	page	NOUN
ejpam-164	335	8	.	.	PUNCT
ejpam-164	336	1	doi:10.1155/2007/40469	doi:10.1155/2007/40469	NOUN
ejpam-164	337	1	[	[	X
ejpam-164	337	2	4	4	NUM
ejpam-164	337	3	]	]	PUNCT
ejpam-164	337	4	k.	k.	PROPN
ejpam-164	338	1	al	al	PROPN
ejpam-164	338	2	-	-	PROPN
ejpam-164	338	3	zoubi	zoubi	PROPN
ejpam-164	338	4	and	and	CCONJ
ejpam-164	338	5	b.	b.	PROPN
ejpam-164	338	6	al	al	PROPN
ejpam-164	338	7	-	-	PUNCT
ejpam-164	338	8	nashef	nashef	PROPN
ejpam-164	338	9	,	,	PUNCT
ejpam-164	338	10	"	"	PUNCT
ejpam-164	338	11	the	the	DET
ejpam-164	338	12	topology	topology	NOUN
ejpam-164	338	13	of	of	ADP
ejpam-164	338	14	ω	ω	VERB
ejpam-164	338	15	-	-	ADJ
ejpam-164	338	16	open	open	ADJ
ejpam-164	338	17	subsets	subset	NOUN
ejpam-164	338	18	"	"	PUNCT
ejpam-164	338	19	,	,	PUNCT
ejpam-164	338	20	al	al	PROPN
ejpam-164	338	21	-	-	PUNCT
ejpam-164	338	22	manareh	manareh	NOUN
ejpam-164	338	23	9	9	NUM
ejpam-164	338	24	(	(	PUNCT
ejpam-164	338	25	2	2	NUM
ejpam-164	338	26	):	):	PUNCT
ejpam-164	338	27	169	169	NUM
ejpam-164	338	28	-	-	SYM
ejpam-164	338	29	179	179	NUM
ejpam-164	338	30	(	(	PUNCT
ejpam-164	338	31	2003	2003	NUM
ejpam-164	338	32	)	)	PUNCT
ejpam-164	338	33	.	.	PUNCT
ejpam-164	339	1	[	[	X
ejpam-164	339	2	5	5	X
ejpam-164	339	3	]	]	X
ejpam-164	339	4	d.	d.	PROPN
ejpam-164	339	5	andrijević	andrijević	PROPN
ejpam-164	339	6	,	,	PUNCT
ejpam-164	339	7	"	"	PUNCT
ejpam-164	339	8	on	on	ADP
ejpam-164	339	9	b	b	X
ejpam-164	339	10	-	-	PUNCT
ejpam-164	339	11	open	open	ADJ
ejpam-164	339	12	sets	set	NOUN
ejpam-164	339	13	"	"	PUNCT
ejpam-164	339	14	,	,	PUNCT
ejpam-164	339	15	mat	mat	PROPN
ejpam-164	339	16	.	.	PROPN
ejpam-164	339	17	vesnik	vesnik	PROPN
ejpam-164	339	18	48	48	NUM
ejpam-164	339	19	:	:	PUNCT
ejpam-164	339	20	59	59	NUM
ejpam-164	339	21	-	-	SYM
ejpam-164	339	22	64	64	NUM
ejpam-164	339	23	(	(	PUNCT
ejpam-164	339	24	1996	1996	NUM
ejpam-164	339	25	)	)	PUNCT
ejpam-164	339	26	.	.	PUNCT
ejpam-164	340	1	[	[	X
ejpam-164	340	2	6	6	NUM
ejpam-164	340	3	]	]	PUNCT
ejpam-164	340	4	s.	s.	PROPN
ejpam-164	340	5	p.	p.	PROPN
ejpam-164	340	6	arya	arya	PROPN
ejpam-164	340	7	and	and	CCONJ
ejpam-164	340	8	r.	r.	PROPN
ejpam-164	340	9	gupta	gupta	PROPN
ejpam-164	340	10	,	,	PUNCT
ejpam-164	340	11	"	"	PUNCT
ejpam-164	340	12	on	on	ADP
ejpam-164	340	13	strongly	strongly	ADV
ejpam-164	340	14	continuous	continuous	ADJ
ejpam-164	340	15	mappings	mapping	NOUN
ejpam-164	340	16	"	"	PUNCT
ejpam-164	340	17	,	,	PUNCT
ejpam-164	340	18	kyungpook	kyungpook	PROPN
ejpam-164	340	19	math	math	NOUN
ejpam-164	340	20	.	.	PUNCT
ejpam-164	341	1	j.	j.	PROPN
ejpam-164	341	2	14	14	NUM
ejpam-164	341	3	:	:	PUNCT
ejpam-164	341	4	131	131	NUM
ejpam-164	341	5	-	-	SYM
ejpam-164	341	6	143	143	NUM
ejpam-164	341	7	(	(	PUNCT
ejpam-164	341	8	1974	1974	NUM
ejpam-164	341	9	)	)	PUNCT
ejpam-164	341	10	.	.	PUNCT
ejpam-164	342	1	[	[	X
ejpam-164	342	2	7	7	X
ejpam-164	342	3	]	]	X
ejpam-164	342	4	r.	r.	PROPN
ejpam-164	342	5	engelking	engelking	NOUN
ejpam-164	342	6	,	,	PUNCT
ejpam-164	342	7	general	general	ADJ
ejpam-164	342	8	topology	topology	NOUN
ejpam-164	342	9	,	,	PUNCT
ejpam-164	342	10	heldermann	heldermann	PROPN
ejpam-164	342	11	veriag	veriag	PROPN
ejpam-164	342	12	berlin	berlin	PROPN
ejpam-164	342	13	,	,	PUNCT
ejpam-164	342	14	2nd	2nd	PROPN
ejpam-164	342	15	edition	edition	NOUN
ejpam-164	342	16	,	,	PUNCT
ejpam-164	342	17	1989	1989	NUM
ejpam-164	342	18	.	.	PUNCT
ejpam-164	343	1	[	[	X
ejpam-164	343	2	8	8	X
ejpam-164	343	3	]	]	PUNCT
ejpam-164	343	4	h.	h.	PROPN
ejpam-164	343	5	z.	z.	PROPN
ejpam-164	343	6	hdeib	hdeib	PROPN
ejpam-164	343	7	,	,	PUNCT
ejpam-164	343	8	"	"	PUNCT
ejpam-164	343	9	ω	ω	VERB
ejpam-164	343	10	-	-	PUNCT
ejpam-164	343	11	closed	close	VERB
ejpam-164	343	12	mappings	mapping	NOUN
ejpam-164	343	13	"	"	PUNCT
ejpam-164	343	14	,	,	PUNCT
ejpam-164	343	15	rev	rev	PROPN
ejpam-164	343	16	.	.	PROPN
ejpam-164	343	17	colomb	colomb	PROPN
ejpam-164	343	18	.	.	PUNCT
ejpam-164	344	1	mat	mat	PROPN
ejpam-164	344	2	.	.	PROPN
ejpam-164	345	1	16	16	NUM
ejpam-164	345	2	(	(	PUNCT
ejpam-164	345	3	3	3	NUM
ejpam-164	345	4	-	-	SYM
ejpam-164	345	5	4	4	NUM
ejpam-164	345	6	):	):	PUNCT
ejpam-164	345	7	65	65	NUM
ejpam-164	345	8	-	-	SYM
ejpam-164	345	9	78	78	NUM
ejpam-164	345	10	(	(	PUNCT
ejpam-164	345	11	1982	1982	NUM
ejpam-164	345	12	)	)	PUNCT
ejpam-164	345	13	.	.	PUNCT
ejpam-164	346	1	[	[	X
ejpam-164	346	2	9	9	NUM
ejpam-164	346	3	]	]	PUNCT
ejpam-164	346	4	h.	h.	PROPN
ejpam-164	346	5	z.	z.	PROPN
ejpam-164	346	6	hdeib	hdeib	PROPN
ejpam-164	346	7	,	,	PUNCT
ejpam-164	346	8	"	"	PUNCT
ejpam-164	346	9	ω	ω	ADJ
ejpam-164	346	10	-	-	ADJ
ejpam-164	346	11	continuous	continuous	ADJ
ejpam-164	346	12	functions	function	NOUN
ejpam-164	346	13	"	"	PUNCT
ejpam-164	346	14	,	,	PUNCT
ejpam-164	346	15	dirasat	dirasat	VERB
ejpam-164	346	16	16	16	NUM
ejpam-164	346	17	,	,	PUNCT
ejpam-164	346	18	(	(	PUNCT
ejpam-164	346	19	2	2	NUM
ejpam-164	346	20	):	):	PUNCT
ejpam-164	346	21	136	136	NUM
ejpam-164	346	22	-	-	SYM
ejpam-164	346	23	142	142	NUM
ejpam-164	346	24	(	(	PUNCT
ejpam-164	346	25	1989	1989	NUM
ejpam-164	346	26	)	)	PUNCT
ejpam-164	346	27	.	.	PUNCT
ejpam-164	347	1	[	[	X
ejpam-164	347	2	10	10	NUM
ejpam-164	347	3	]	]	X
ejpam-164	347	4	n.	n.	PROPN
ejpam-164	347	5	levine	levine	PROPN
ejpam-164	347	6	,	,	PUNCT
ejpam-164	347	7	"	"	PUNCT
ejpam-164	347	8	semi	semi	ADJ
ejpam-164	347	9	-	-	ADJ
ejpam-164	347	10	open	open	ADJ
ejpam-164	347	11	sets	set	NOUN
ejpam-164	347	12	and	and	CCONJ
ejpam-164	347	13	semi	semi	ADJ
ejpam-164	347	14	-	-	NOUN
ejpam-164	347	15	continuity	continuity	NOUN
ejpam-164	347	16	in	in	ADP
ejpam-164	347	17	topological	topological	ADJ
ejpam-164	347	18	spaces	space	NOUN
ejpam-164	347	19	"	"	PUNCT
ejpam-164	347	20	,	,	PUNCT
ejpam-164	347	21	amer	amer	PROPN
ejpam-164	347	22	.	.	PROPN
ejpam-164	347	23	math	math	PROPN
ejpam-164	347	24	.	.	PUNCT
ejpam-164	348	1	monthly	monthly	ADJ
ejpam-164	348	2	70	70	NUM
ejpam-164	348	3	:	:	PUNCT
ejpam-164	348	4	36	36	NUM
ejpam-164	348	5	-	-	SYM
ejpam-164	348	6	41	41	NUM
ejpam-164	348	7	(	(	PUNCT
ejpam-164	348	8	1963	1963	NUM
ejpam-164	348	9	)	)	PUNCT
ejpam-164	348	10	.	.	PUNCT
ejpam-164	349	1	[	[	X
ejpam-164	349	2	11	11	NUM
ejpam-164	349	3	]	]	PUNCT
ejpam-164	349	4	a.	a.	NOUN
ejpam-164	349	5	s.	s.	PROPN
ejpam-164	349	6	mashhour	mashhour	PROPN
ejpam-164	349	7	,	,	PUNCT
ejpam-164	349	8	m.	m.	PROPN
ejpam-164	349	9	e.	e.	PROPN
ejpam-164	349	10	abd	abd	PROPN
ejpam-164	349	11	el	el	PROPN
ejpam-164	349	12	-	-	PROPN
ejpam-164	349	13	monsef	monsef	PROPN
ejpam-164	349	14	and	and	CCONJ
ejpam-164	349	15	s.	s.	PROPN
ejpam-164	349	16	n.	n.	PROPN
ejpam-164	349	17	el	el	PROPN
ejpam-164	349	18	-	-	PROPN
ejpam-164	349	19	deeb	deeb	PROPN
ejpam-164	349	20	,	,	PUNCT
ejpam-164	349	21	"	"	PUNCT
ejpam-164	349	22	on	on	ADP
ejpam-164	349	23	precontinuous	precontinuous	ADJ
ejpam-164	349	24	and	and	CCONJ
ejpam-164	349	25	weak	weak	ADJ
ejpam-164	349	26	precontinuous	precontinuous	ADJ
ejpam-164	349	27	functions	function	NOUN
ejpam-164	349	28	"	"	PUNCT
ejpam-164	349	29	,	,	PUNCT
ejpam-164	349	30	proc	proc	PROPN
ejpam-164	349	31	.	.	PUNCT
ejpam-164	350	1	math	math	NOUN
ejpam-164	350	2	.	.	PUNCT
ejpam-164	351	1	phys	phy	NOUN
ejpam-164	351	2	.	.	PUNCT
ejpam-164	352	1	soc	soc	PROPN
ejpam-164	352	2	.	.	PUNCT
ejpam-164	353	1	egypt	egypt	PROPN
ejpam-164	353	2	51	51	NUM
ejpam-164	353	3	:	:	PUNCT
ejpam-164	353	4	47	47	NUM
ejpam-164	353	5	-	-	SYM
ejpam-164	353	6	53	53	NUM
ejpam-164	353	7	(	(	PUNCT
ejpam-164	353	8	1982	1982	NUM
ejpam-164	353	9	)	)	PUNCT
ejpam-164	353	10	.	.	PUNCT
ejpam-164	354	1	[	[	X
ejpam-164	354	2	12	12	NUM
ejpam-164	354	3	]	]	X
ejpam-164	354	4	o.	o.	NOUN
ejpam-164	354	5	njåstad	njåstad	PROPN
ejpam-164	354	6	,	,	PUNCT
ejpam-164	354	7	"	"	PUNCT
ejpam-164	354	8	on	on	ADP
ejpam-164	354	9	some	some	DET
ejpam-164	354	10	classes	class	NOUN
ejpam-164	354	11	of	of	ADP
ejpam-164	354	12	nearly	nearly	ADV
ejpam-164	354	13	open	open	ADJ
ejpam-164	354	14	sets	set	NOUN
ejpam-164	354	15	"	"	PUNCT
ejpam-164	354	16	,	,	PUNCT
ejpam-164	354	17	pacific	pacific	PROPN
ejpam-164	354	18	j.	j.	PROPN
ejpam-164	354	19	math	math	PROPN
ejpam-164	354	20	.	.	PUNCT
ejpam-164	355	1	15	15	NUM
ejpam-164	355	2	:	:	PUNCT
ejpam-164	355	3	961	961	NUM
ejpam-164	355	4	-	-	SYM
ejpam-164	355	5	970	970	NUM
ejpam-164	355	6	(	(	PUNCT
ejpam-164	355	7	1965	1965	NUM
ejpam-164	355	8	.	.	PUNCT
ejpam-164	356	1	[	[	X
ejpam-164	356	2	13	13	NUM
ejpam-164	356	3	]	]	PUNCT
ejpam-164	356	4	t.	t.	PROPN
ejpam-164	356	5	noiri	noiri	PROPN
ejpam-164	356	6	,	,	PUNCT
ejpam-164	356	7	a.	a.	PROPN
ejpam-164	356	8	al	al	PROPN
ejpam-164	356	9	-	-	PUNCT
ejpam-164	356	10	omari	omari	PROPN
ejpam-164	356	11	and	and	CCONJ
ejpam-164	356	12	m.s.m	m.s.m	PROPN
ejpam-164	356	13	.	.	PROPN
ejpam-164	356	14	noorani	noorani	ADJ
ejpam-164	356	15	"	"	PUNCT
ejpam-164	356	16	slightlyω	slightlyω	NOUN
ejpam-164	356	17	-	-	PUNCT
ejpam-164	356	18	continuous	continuous	ADJ
ejpam-164	356	19	functions	function	NOUN
ejpam-164	356	20	"	"	PUNCT
ejpam-164	356	21	fasciculi	fasciculi	PROPN
ejpam-164	356	22	mathematica	mathematica	PROPN
ejpam-164	356	23	41	41	NUM
ejpam-164	356	24	:	:	PUNCT
ejpam-164	356	25	97	97	NUM
ejpam-164	356	26	-	-	SYM
ejpam-164	356	27	106	106	NUM
ejpam-164	356	28	(	(	PUNCT
ejpam-164	356	29	2009	2009	NUM
ejpam-164	356	30	)	)	PUNCT
ejpam-164	356	31	.	.	PUNCT