id	sid	tid	token	lemma	pos
ejpam-2494	1	1	compile	compile	VERB
ejpam-2494	1	2	/	/	SYM
ejpam-2494	1	3	output.dvi	output.dvi	NOUN
ejpam-2494	1	4	new	new	ADJ
ejpam-2494	1	5	generalized	generalized	ADJ
ejpam-2494	1	6	classes	class	NOUN
ejpam-2494	1	7	of	of	ADP
ejpam-2494	1	8	τω	τω	DET
ejpam-2494	1	9	otchana	otchana	PROPN
ejpam-2494	1	10	thevar	thevar	NOUN
ejpam-2494	1	11	ravi1,∗	ravi1,∗	NOUN
ejpam-2494	1	12	,	,	PUNCT
ejpam-2494	1	13	ilangovan	ilangovan	PROPN
ejpam-2494	1	14	rajasekaran1	rajasekaran1	PROPN
ejpam-2494	1	15	,	,	PUNCT
ejpam-2494	1	16	soundararajan	soundararajan	PROPN
ejpam-2494	1	17	satheesh	satheesh	PROPN
ejpam-2494	1	18	kanna2	kanna2	PROPN
ejpam-2494	1	19	and	and	CCONJ
ejpam-2494	1	20	malliharjunaiah	malliharjunaiah	NOUN
ejpam-2494	1	21	paranjothi3	paranjothi3	NOUN
ejpam-2494	1	22	1	1	NUM
ejpam-2494	1	23	department	department	NOUN
ejpam-2494	1	24	of	of	ADP
ejpam-2494	1	25	mathematics	mathematic	NOUN
ejpam-2494	1	26	,	,	PUNCT
ejpam-2494	1	27	p.	p.	NOUN
ejpam-2494	1	28	m.	m.	NOUN
ejpam-2494	1	29	thevar	thevar	PROPN
ejpam-2494	1	30	college	college	PROPN
ejpam-2494	1	31	,	,	PUNCT
ejpam-2494	1	32	usilampatti	usilampatti	PROPN
ejpam-2494	1	33	,	,	PUNCT
ejpam-2494	1	34	madurai	madurai	PROPN
ejpam-2494	1	35	district	district	NOUN
ejpam-2494	1	36	,	,	PUNCT
ejpam-2494	1	37	tamil	tamil	PROPN
ejpam-2494	1	38	nadu	nadu	PROPN
ejpam-2494	1	39	,	,	PUNCT
ejpam-2494	1	40	india	india	PROPN
ejpam-2494	1	41	.	.	PROPN
ejpam-2494	1	42	2	2	NUM
ejpam-2494	1	43	department	department	NOUN
ejpam-2494	1	44	of	of	ADP
ejpam-2494	1	45	mathematics	mathematic	NOUN
ejpam-2494	1	46	,	,	PUNCT
ejpam-2494	1	47	research	research	NOUN
ejpam-2494	1	48	scholar	scholar	NOUN
ejpam-2494	1	49	,	,	PUNCT
ejpam-2494	1	50	bharathidasan	bharathidasan	ADJ
ejpam-2494	1	51	university	university	NOUN
ejpam-2494	1	52	,	,	PUNCT
ejpam-2494	1	53	tiruchirapalli	tiruchirapalli	PROPN
ejpam-2494	1	54	,	,	PUNCT
ejpam-2494	1	55	tamil	tamil	PROPN
ejpam-2494	1	56	nadu	nadu	PROPN
ejpam-2494	1	57	,	,	PUNCT
ejpam-2494	1	58	india	india	PROPN
ejpam-2494	1	59	.	.	PROPN
ejpam-2494	1	60	3	3	NUM
ejpam-2494	1	61	department	department	NOUN
ejpam-2494	1	62	of	of	ADP
ejpam-2494	1	63	mathematics	mathematics	PROPN
ejpam-2494	1	64	,	,	PUNCT
ejpam-2494	1	65	sree	sree	PROPN
ejpam-2494	1	66	sowdambiga	sowdambiga	PROPN
ejpam-2494	1	67	college	college	PROPN
ejpam-2494	1	68	of	of	ADP
ejpam-2494	1	69	engineering	engineering	NOUN
ejpam-2494	1	70	,	,	PUNCT
ejpam-2494	1	71	aruppukottai	aruppukottai	NOUN
ejpam-2494	1	72	,	,	PUNCT
ejpam-2494	1	73	virudhunagar	virudhunagar	NOUN
ejpam-2494	1	74	district	district	NOUN
ejpam-2494	1	75	,	,	PUNCT
ejpam-2494	1	76	tamil	tamil	PROPN
ejpam-2494	1	77	nadu	nadu	PROPN
ejpam-2494	1	78	,	,	PUNCT
ejpam-2494	1	79	india	india	PROPN
ejpam-2494	1	80	.	.	PUNCT
ejpam-2494	2	1	abstract	abstract	PROPN
ejpam-2494	2	2	.	.	PUNCT
ejpam-2494	3	1	the	the	DET
ejpam-2494	3	2	purpose	purpose	NOUN
ejpam-2494	3	3	of	of	ADP
ejpam-2494	3	4	this	this	DET
ejpam-2494	3	5	paper	paper	NOUN
ejpam-2494	3	6	is	be	AUX
ejpam-2494	3	7	to	to	PART
ejpam-2494	3	8	introduce	introduce	VERB
ejpam-2494	3	9	a	a	DET
ejpam-2494	3	10	new	new	ADJ
ejpam-2494	3	11	class	class	NOUN
ejpam-2494	3	12	of	of	ADP
ejpam-2494	3	13	sets	set	NOUN
ejpam-2494	3	14	called	call	VERB
ejpam-2494	3	15	semi	semi	ADJ
ejpam-2494	3	16	-	-	ADJ
ejpam-2494	3	17	ω	ω	VERB
ejpam-2494	3	18	-	-	NOUN
ejpam-2494	3	19	open	open	NOUN
ejpam-2494	3	20	which	which	PRON
ejpam-2494	3	21	lies	lie	VERB
ejpam-2494	3	22	between	between	ADP
ejpam-2494	3	23	the	the	DET
ejpam-2494	3	24	class	class	NOUN
ejpam-2494	3	25	of	of	ADP
ejpam-2494	3	26	α	α	PROPN
ejpam-2494	3	27	−	−	PROPN
ejpam-2494	3	28	ω	ω	VERB
ejpam-2494	3	29	-	-	ADJ
ejpam-2494	3	30	open	open	ADJ
ejpam-2494	3	31	sets	set	NOUN
ejpam-2494	3	32	and	and	CCONJ
ejpam-2494	3	33	the	the	DET
ejpam-2494	3	34	class	class	NOUN
ejpam-2494	3	35	of	of	ADP
ejpam-2494	3	36	β	β	PROPN
ejpam-2494	3	37	−	−	PROPN
ejpam-2494	3	38	ω	ω	VERB
ejpam-2494	3	39	-	-	ADJ
ejpam-2494	3	40	open	open	ADJ
ejpam-2494	3	41	sets	set	NOUN
ejpam-2494	3	42	and	and	CCONJ
ejpam-2494	3	43	to	to	PART
ejpam-2494	3	44	investigate	investigate	VERB
ejpam-2494	3	45	the	the	DET
ejpam-2494	3	46	basic	basic	ADJ
ejpam-2494	3	47	properties	property	NOUN
ejpam-2494	3	48	of	of	ADP
ejpam-2494	3	49	such	such	ADJ
ejpam-2494	3	50	sets	set	NOUN
ejpam-2494	3	51	.	.	PUNCT
ejpam-2494	4	1	this	this	PRON
ejpam-2494	4	2	apart	apart	ADV
ejpam-2494	4	3	,	,	PUNCT
ejpam-2494	4	4	some	some	DET
ejpam-2494	4	5	new	new	ADJ
ejpam-2494	4	6	generalized	generalized	ADJ
ejpam-2494	4	7	classes	class	NOUN
ejpam-2494	4	8	of	of	ADP
ejpam-2494	4	9	τω	τω	NOUN
ejpam-2494	4	10	are	be	AUX
ejpam-2494	4	11	introduced	introduce	VERB
ejpam-2494	4	12	and	and	CCONJ
ejpam-2494	4	13	investigated	investigate	VERB
ejpam-2494	4	14	on	on	ADP
ejpam-2494	4	15	the	the	DET
ejpam-2494	4	16	line	line	NOUN
ejpam-2494	4	17	of	of	ADP
ejpam-2494	4	18	research	research	NOUN
ejpam-2494	4	19	.	.	PUNCT
ejpam-2494	5	1	2010	2010	NUM
ejpam-2494	5	2	mathematics	mathematic	NOUN
ejpam-2494	5	3	subject	subject	NOUN
ejpam-2494	5	4	classifications	classification	NOUN
ejpam-2494	5	5	:	:	PUNCT
ejpam-2494	5	6	54c05	54c05	NUM
ejpam-2494	5	7	,	,	PUNCT
ejpam-2494	5	8	54c08	54c08	NUM
ejpam-2494	5	9	,	,	PUNCT
ejpam-2494	5	10	54c10	54c10	NUM
ejpam-2494	5	11	key	key	ADJ
ejpam-2494	5	12	words	word	NOUN
ejpam-2494	5	13	and	and	CCONJ
ejpam-2494	5	14	phrases	phrase	NOUN
ejpam-2494	5	15	:	:	PUNCT
ejpam-2494	5	16	ω	ω	NUM
ejpam-2494	5	17	-	-	ADJ
ejpam-2494	5	18	open	open	ADJ
ejpam-2494	5	19	set	set	NOUN
ejpam-2494	5	20	,	,	PUNCT
ejpam-2494	5	21	α−ω	α−ω	NOUN
ejpam-2494	5	22	-	-	PUNCT
ejpam-2494	5	23	open	open	ADJ
ejpam-2494	5	24	set	set	NOUN
ejpam-2494	5	25	,	,	PUNCT
ejpam-2494	5	26	pre	pre	ADJ
ejpam-2494	5	27	-	-	ADJ
ejpam-2494	5	28	ω	ω	ADJ
ejpam-2494	5	29	-	-	ADJ
ejpam-2494	5	30	open	open	ADJ
ejpam-2494	5	31	set	set	NOUN
ejpam-2494	5	32	,	,	PUNCT
ejpam-2494	5	33	β	β	X
ejpam-2494	5	34	−ω	−ω	ADJ
ejpam-2494	5	35	-	-	ADJ
ejpam-2494	5	36	open	open	ADJ
ejpam-2494	5	37	set	set	NOUN
ejpam-2494	5	38	,	,	PUNCT
ejpam-2494	5	39	b−ω	b−ω	NOUN
ejpam-2494	5	40	-	-	PUNCT
ejpam-2494	5	41	open	open	ADJ
ejpam-2494	5	42	set	set	NOUN
ejpam-2494	5	43	,	,	PUNCT
ejpam-2494	5	44	ω−	ω−	PROPN
ejpam-2494	5	45	t	t	NOUN
ejpam-2494	5	46	-	-	PUNCT
ejpam-2494	5	47	set	set	VERB
ejpam-2494	5	48	,	,	PUNCT
ejpam-2494	5	49	δ−ω	δ−ω	NOUN
ejpam-2494	5	50	-	-	PUNCT
ejpam-2494	5	51	open	open	ADJ
ejpam-2494	5	52	set	set	NOUN
ejpam-2494	5	53	,	,	PUNCT
ejpam-2494	5	54	semi⋆	semi⋆	PROPN
ejpam-2494	5	55	−ω	−ω	ADJ
ejpam-2494	5	56	-	-	PUNCT
ejpam-2494	5	57	closed	closed	ADJ
ejpam-2494	5	58	set	set	NOUN
ejpam-2494	5	59	.	.	PUNCT
ejpam-2494	6	1	1	1	X
ejpam-2494	6	2	.	.	X
ejpam-2494	6	3	introduction	introduction	NOUN
ejpam-2494	6	4	in	in	ADP
ejpam-2494	6	5	1982	1982	NUM
ejpam-2494	6	6	,	,	PUNCT
ejpam-2494	6	7	the	the	DET
ejpam-2494	6	8	notions	notion	NOUN
ejpam-2494	6	9	of	of	ADP
ejpam-2494	6	10	ω	ω	VERB
ejpam-2494	6	11	-	-	PUNCT
ejpam-2494	6	12	closed	closed	ADJ
ejpam-2494	6	13	sets	set	NOUN
ejpam-2494	6	14	and	and	CCONJ
ejpam-2494	6	15	ω	ω	VERB
ejpam-2494	6	16	-	-	ADJ
ejpam-2494	6	17	open	open	ADJ
ejpam-2494	6	18	sets	set	NOUN
ejpam-2494	6	19	were	be	AUX
ejpam-2494	6	20	introduced	introduce	VERB
ejpam-2494	6	21	and	and	CCONJ
ejpam-2494	6	22	studied	study	VERB
ejpam-2494	6	23	by	by	ADP
ejpam-2494	6	24	hdeib	hdeib	PROPN
ejpam-2494	6	25	[	[	X
ejpam-2494	6	26	7	7	NUM
ejpam-2494	6	27	]	]	PUNCT
ejpam-2494	6	28	.	.	PUNCT
ejpam-2494	7	1	in	in	ADP
ejpam-2494	7	2	2009	2009	NUM
ejpam-2494	7	3	,	,	PUNCT
ejpam-2494	7	4	noiri	noiri	ADV
ejpam-2494	7	5	et	et	PROPN
ejpam-2494	7	6	al	al	PROPN
ejpam-2494	7	7	.	.	PUNCT
ejpam-2494	8	1	[	[	X
ejpam-2494	8	2	10	10	NUM
ejpam-2494	8	3	]	]	PUNCT
ejpam-2494	8	4	introduced	introduce	VERB
ejpam-2494	8	5	some	some	DET
ejpam-2494	8	6	generalizations	generalization	NOUN
ejpam-2494	8	7	of	of	ADP
ejpam-2494	8	8	ω	ω	VERB
ejpam-2494	8	9	-	-	ADJ
ejpam-2494	8	10	open	open	ADJ
ejpam-2494	8	11	sets	set	NOUN
ejpam-2494	8	12	and	and	CCONJ
ejpam-2494	8	13	investigated	investigate	VERB
ejpam-2494	8	14	some	some	DET
ejpam-2494	8	15	properties	property	NOUN
ejpam-2494	8	16	of	of	ADP
ejpam-2494	8	17	the	the	DET
ejpam-2494	8	18	sets	set	NOUN
ejpam-2494	8	19	.	.	PUNCT
ejpam-2494	9	1	moreover	moreover	ADV
ejpam-2494	9	2	,	,	PUNCT
ejpam-2494	9	3	they	they	PRON
ejpam-2494	9	4	used	use	VERB
ejpam-2494	9	5	them	they	PRON
ejpam-2494	9	6	to	to	PART
ejpam-2494	9	7	obtain	obtain	VERB
ejpam-2494	9	8	decompositions	decomposition	NOUN
ejpam-2494	9	9	of	of	ADP
ejpam-2494	9	10	continuity	continuity	NOUN
ejpam-2494	9	11	.	.	PUNCT
ejpam-2494	10	1	in	in	ADP
ejpam-2494	10	2	this	this	DET
ejpam-2494	10	3	paper	paper	NOUN
ejpam-2494	10	4	,	,	PUNCT
ejpam-2494	10	5	we	we	PRON
ejpam-2494	10	6	introduce	introduce	VERB
ejpam-2494	10	7	and	and	CCONJ
ejpam-2494	10	8	investigate	investigate	VERB
ejpam-2494	10	9	the	the	DET
ejpam-2494	10	10	new	new	ADJ
ejpam-2494	10	11	notion	notion	NOUN
ejpam-2494	10	12	called	call	VERB
ejpam-2494	10	13	semi	semi	ADJ
ejpam-2494	10	14	-	-	ADJ
ejpam-2494	10	15	ω	ω	ADJ
ejpam-2494	10	16	-	-	ADJ
ejpam-2494	10	17	open	open	ADJ
ejpam-2494	10	18	sets	set	NOUN
ejpam-2494	10	19	which	which	PRON
ejpam-2494	10	20	is	be	AUX
ejpam-2494	10	21	weaker	weak	ADJ
ejpam-2494	10	22	than	than	ADP
ejpam-2494	10	23	α	α	DET
ejpam-2494	10	24	−ω	−ω	ADJ
ejpam-2494	10	25	-	-	ADJ
ejpam-2494	10	26	open	open	ADJ
ejpam-2494	10	27	sets	set	NOUN
ejpam-2494	10	28	and	and	CCONJ
ejpam-2494	10	29	stronger	strong	ADJ
ejpam-2494	10	30	than	than	ADP
ejpam-2494	10	31	β	β	NOUN
ejpam-2494	10	32	−ω	−ω	ADJ
ejpam-2494	10	33	-	-	ADJ
ejpam-2494	10	34	open	open	ADJ
ejpam-2494	10	35	sets	set	NOUN
ejpam-2494	10	36	.	.	PUNCT
ejpam-2494	11	1	also	also	ADV
ejpam-2494	11	2	we	we	PRON
ejpam-2494	11	3	introduce	introduce	VERB
ejpam-2494	11	4	and	and	CCONJ
ejpam-2494	11	5	investigate	investigate	VERB
ejpam-2494	11	6	some	some	DET
ejpam-2494	11	7	new	new	ADJ
ejpam-2494	11	8	generalized	generalized	ADJ
ejpam-2494	11	9	classes	class	NOUN
ejpam-2494	11	10	of	of	ADP
ejpam-2494	11	11	τω	τω	PROPN
ejpam-2494	11	12	.	.	PUNCT
ejpam-2494	11	13	∗corresponding	∗corresponde	VERB
ejpam-2494	11	14	author	author	NOUN
ejpam-2494	11	15	.	.	PUNCT
ejpam-2494	12	1	email	email	NOUN
ejpam-2494	12	2	addresses	address	NOUN
ejpam-2494	12	3	:	:	PUNCT
ejpam-2494	12	4	siingam@yahoo.com	siingam@yahoo.com	X
ejpam-2494	13	1	(	(	PUNCT
ejpam-2494	13	2	o.	o.	PROPN
ejpam-2494	13	3	ravi	ravi	PROPN
ejpam-2494	13	4	)	)	PUNCT
ejpam-2494	13	5	,	,	PUNCT
ejpam-2494	13	6	rajasekarani@yahoo.com	rajasekarani@yahoo.com	X
ejpam-2494	13	7	(	(	PUNCT
ejpam-2494	13	8	i.	i.	NOUN
ejpam-2494	13	9	rajasekaran	rajasekaran	PROPN
ejpam-2494	13	10	)	)	PUNCT
ejpam-2494	13	11	,	,	PUNCT
ejpam-2494	13	12	satheesh−kanna@yahoo.co.in	satheesh−kanna@yahoo.co.in	PROPN
ejpam-2494	13	13	(	(	PUNCT
ejpam-2494	13	14	s.	s.	PROPN
ejpam-2494	13	15	kanna	kanna	PROPN
ejpam-2494	13	16	)	)	PUNCT
ejpam-2494	13	17	and	and	CCONJ
ejpam-2494	13	18	jothimp123@gmail.com	jothimp123@gmail.com	NUM
ejpam-2494	13	19	(	(	PUNCT
ejpam-2494	13	20	m.	m.	NOUN
ejpam-2494	13	21	paranjothi	paranjothi	PROPN
ejpam-2494	13	22	)	)	PUNCT
ejpam-2494	13	23	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2494	14	1	152	152	NUM
ejpam-2494	14	2	c	c	X
ejpam-2494	14	3	©	©	PROPN
ejpam-2494	14	4	2016	2016	NUM
ejpam-2494	14	5	ejpam	ejpam	VERB
ejpam-2494	14	6	all	all	DET
ejpam-2494	14	7	rights	right	NOUN
ejpam-2494	14	8	reserved	reserve	VERB
ejpam-2494	14	9	.	.	PUNCT
ejpam-2494	15	1	european	european	ADJ
ejpam-2494	15	2	journal	journal	PROPN
ejpam-2494	15	3	of	of	ADP
ejpam-2494	15	4	pure	pure	ADJ
ejpam-2494	15	5	and	and	CCONJ
ejpam-2494	15	6	applied	apply	VERB
ejpam-2494	15	7	mathematics	mathematic	NOUN
ejpam-2494	15	8	vol	vol	NOUN
ejpam-2494	15	9	.	.	PROPN
ejpam-2494	16	1	9	9	NUM
ejpam-2494	16	2	,	,	PUNCT
ejpam-2494	16	3	no	no	INTJ
ejpam-2494	16	4	.	.	NOUN
ejpam-2494	16	5	2	2	NUM
ejpam-2494	16	6	,	,	PUNCT
ejpam-2494	16	7	2016	2016	NUM
ejpam-2494	16	8	,	,	PUNCT
ejpam-2494	16	9	152	152	NUM
ejpam-2494	16	10	-	-	SYM
ejpam-2494	16	11	164	164	NUM
ejpam-2494	16	12	issn	issn	PROPN
ejpam-2494	16	13	1307	1307	NUM
ejpam-2494	16	14	-	-	SYM
ejpam-2494	16	15	5543	5543	NUM
ejpam-2494	16	16	–	–	PUNCT
ejpam-2494	16	17	www.ejpam.com	www.ejpam.com	X
ejpam-2494	16	18	o.	o.	PROPN
ejpam-2494	16	19	ravi	ravi	PROPN
ejpam-2494	16	20	,	,	PUNCT
ejpam-2494	16	21	i.	i.	NOUN
ejpam-2494	16	22	rajasekaran	rajasekaran	PROPN
ejpam-2494	16	23	,	,	PUNCT
ejpam-2494	16	24	s.	s.	PROPN
ejpam-2494	16	25	kanna	kanna	PROPN
ejpam-2494	16	26	and	and	CCONJ
ejpam-2494	16	27	m.	m.	NOUN
ejpam-2494	16	28	paranjothi	paranjothi	PROPN
ejpam-2494	16	29	/	/	SYM
ejpam-2494	16	30	eur	eur	PROPN
ejpam-2494	16	31	.	.	PUNCT
ejpam-2494	17	1	j.	j.	PROPN
ejpam-2494	17	2	pure	pure	PROPN
ejpam-2494	17	3	appl	appl	PROPN
ejpam-2494	17	4	.	.	PROPN
ejpam-2494	17	5	math	math	PROPN
ejpam-2494	17	6	,	,	PUNCT
ejpam-2494	17	7	9	9	NUM
ejpam-2494	17	8	(	(	PUNCT
ejpam-2494	17	9	2016	2016	NUM
ejpam-2494	17	10	)	)	PUNCT
ejpam-2494	17	11	,	,	PUNCT
ejpam-2494	17	12	152	152	NUM
ejpam-2494	17	13	-	-	SYM
ejpam-2494	17	14	164	164	NUM
ejpam-2494	17	15	153	153	NUM
ejpam-2494	17	16	2	2	NUM
ejpam-2494	17	17	.	.	PUNCT
ejpam-2494	17	18	preliminaries	preliminary	NOUN
ejpam-2494	17	19	throughout	throughout	ADP
ejpam-2494	17	20	this	this	DET
ejpam-2494	17	21	paper	paper	NOUN
ejpam-2494	17	22	,	,	PUNCT
ejpam-2494	17	23	r	r	NOUN
ejpam-2494	17	24	(	(	PUNCT
ejpam-2494	17	25	resp	resp	NOUN
ejpam-2494	17	26	.	.	PUNCT
ejpam-2494	18	1	q	q	X
ejpam-2494	18	2	,	,	PUNCT
ejpam-2494	18	3	q⋆	q⋆	NOUN
ejpam-2494	18	4	)	)	PUNCT
ejpam-2494	18	5	denotes	denote	VERB
ejpam-2494	18	6	the	the	DET
ejpam-2494	18	7	set	set	NOUN
ejpam-2494	18	8	of	of	ADP
ejpam-2494	18	9	all	all	DET
ejpam-2494	18	10	real	real	ADJ
ejpam-2494	18	11	numbers	number	NOUN
ejpam-2494	18	12	(	(	PUNCT
ejpam-2494	18	13	resp	resp	NOUN
ejpam-2494	18	14	.	.	PUNCT
ejpam-2494	19	1	the	the	DET
ejpam-2494	19	2	set	set	NOUN
ejpam-2494	19	3	of	of	ADP
ejpam-2494	19	4	all	all	DET
ejpam-2494	19	5	rational	rational	ADJ
ejpam-2494	19	6	numbers	number	NOUN
ejpam-2494	19	7	,	,	PUNCT
ejpam-2494	19	8	the	the	DET
ejpam-2494	19	9	set	set	NOUN
ejpam-2494	19	10	of	of	ADP
ejpam-2494	19	11	all	all	DET
ejpam-2494	19	12	irrational	irrational	ADJ
ejpam-2494	19	13	numbers	number	NOUN
ejpam-2494	19	14	)	)	PUNCT
ejpam-2494	19	15	.	.	PUNCT
ejpam-2494	20	1	by	by	ADP
ejpam-2494	20	2	a	a	DET
ejpam-2494	20	3	space	space	NOUN
ejpam-2494	20	4	(	(	PUNCT
ejpam-2494	20	5	x	x	X
ejpam-2494	20	6	,	,	PUNCT
ejpam-2494	20	7	τ	τ	PROPN
ejpam-2494	20	8	)	)	PUNCT
ejpam-2494	20	9	,	,	PUNCT
ejpam-2494	20	10	we	we	PRON
ejpam-2494	20	11	always	always	ADV
ejpam-2494	20	12	mean	mean	VERB
ejpam-2494	20	13	a	a	DET
ejpam-2494	20	14	topological	topological	ADJ
ejpam-2494	20	15	space	space	NOUN
ejpam-2494	20	16	(	(	PUNCT
ejpam-2494	20	17	x	x	NOUN
ejpam-2494	20	18	,	,	PUNCT
ejpam-2494	20	19	τ)with	τ)with	PUNCT
ejpam-2494	20	20	no	no	DET
ejpam-2494	20	21	separation	separation	NOUN
ejpam-2494	20	22	properties	property	NOUN
ejpam-2494	20	23	assumed	assume	VERB
ejpam-2494	20	24	.	.	PUNCT
ejpam-2494	21	1	if	if	SCONJ
ejpam-2494	21	2	h	h	PROPN
ejpam-2494	21	3	⊂	⊂	PROPN
ejpam-2494	21	4	x	x	X
ejpam-2494	21	5	,	,	PUNCT
ejpam-2494	21	6	cl(h	cl(h	NUM
ejpam-2494	21	7	)	)	PUNCT
ejpam-2494	21	8	and	and	CCONJ
ejpam-2494	21	9	int(h	int(h	X
ejpam-2494	21	10	)	)	PUNCT
ejpam-2494	21	11	will	will	AUX
ejpam-2494	21	12	,	,	PUNCT
ejpam-2494	21	13	respectively	respectively	ADV
ejpam-2494	21	14	,	,	PUNCT
ejpam-2494	21	15	denote	denote	VERB
ejpam-2494	21	16	the	the	DET
ejpam-2494	21	17	closure	closure	NOUN
ejpam-2494	21	18	and	and	CCONJ
ejpam-2494	21	19	interior	interior	NOUN
ejpam-2494	21	20	of	of	ADP
ejpam-2494	21	21	h	h	NOUN
ejpam-2494	21	22	in	in	ADP
ejpam-2494	21	23	(	(	PUNCT
ejpam-2494	21	24	x	x	INTJ
ejpam-2494	21	25	,	,	PUNCT
ejpam-2494	21	26	τ	τ	PROPN
ejpam-2494	21	27	)	)	PUNCT
ejpam-2494	21	28	.	.	PUNCT
ejpam-2494	22	1	τh	τh	ADP
ejpam-2494	22	2	denotes	denote	VERB
ejpam-2494	22	3	the	the	DET
ejpam-2494	22	4	relative	relative	ADJ
ejpam-2494	22	5	topology	topology	NOUN
ejpam-2494	22	6	on	on	ADP
ejpam-2494	22	7	h	h	NOUN
ejpam-2494	22	8	and	and	CCONJ
ejpam-2494	22	9	τu	τu	ADP
ejpam-2494	22	10	denotes	denote	VERB
ejpam-2494	22	11	the	the	DET
ejpam-2494	22	12	usual	usual	ADJ
ejpam-2494	22	13	topology	topology	NOUN
ejpam-2494	22	14	on	on	ADP
ejpam-2494	22	15	r.	r.	PROPN
ejpam-2494	22	16	definition	definition	NOUN
ejpam-2494	22	17	1	1	NUM
ejpam-2494	22	18	.	.	PUNCT
ejpam-2494	22	19	a	a	DET
ejpam-2494	22	20	subset	subset	ADJ
ejpam-2494	22	21	h	h	NOUN
ejpam-2494	22	22	of	of	ADP
ejpam-2494	22	23	a	a	DET
ejpam-2494	22	24	space	space	NOUN
ejpam-2494	22	25	(	(	PUNCT
ejpam-2494	22	26	x	x	X
ejpam-2494	22	27	,	,	PUNCT
ejpam-2494	22	28	τ	τ	X
ejpam-2494	22	29	)	)	PUNCT
ejpam-2494	22	30	is	be	AUX
ejpam-2494	22	31	said	say	VERB
ejpam-2494	22	32	to	to	PART
ejpam-2494	22	33	be	be	AUX
ejpam-2494	22	34	semi	semi	ADJ
ejpam-2494	22	35	-	-	ADJ
ejpam-2494	22	36	open	open	ADJ
ejpam-2494	22	37	[	[	X
ejpam-2494	22	38	9	9	NUM
ejpam-2494	22	39	]	]	PUNCT
ejpam-2494	22	40	if	if	SCONJ
ejpam-2494	22	41	h	h	PROPN
ejpam-2494	22	42	⊂	⊂	PROPN
ejpam-2494	22	43	cl(int(h	cl(int(h	PROPN
ejpam-2494	22	44	)	)	PUNCT
ejpam-2494	22	45	)	)	PUNCT
ejpam-2494	22	46	.	.	PUNCT
ejpam-2494	23	1	definition	definition	NOUN
ejpam-2494	23	2	2	2	NUM
ejpam-2494	23	3	(	(	PUNCT
ejpam-2494	23	4	[	[	X
ejpam-2494	23	5	11	11	NUM
ejpam-2494	23	6	]	]	NUM
ejpam-2494	23	7	)	)	PUNCT
ejpam-2494	23	8	.	.	PUNCT
ejpam-2494	24	1	let	let	VERB
ejpam-2494	24	2	h	h	PRON
ejpam-2494	24	3	be	be	AUX
ejpam-2494	24	4	a	a	DET
ejpam-2494	24	5	subset	subset	NOUN
ejpam-2494	24	6	of	of	ADP
ejpam-2494	24	7	a	a	DET
ejpam-2494	24	8	space	space	NOUN
ejpam-2494	24	9	(	(	PUNCT
ejpam-2494	24	10	x	x	X
ejpam-2494	24	11	,	,	PUNCT
ejpam-2494	24	12	τ	τ	PROPN
ejpam-2494	24	13	)	)	PUNCT
ejpam-2494	24	14	,	,	PUNCT
ejpam-2494	24	15	a	a	DET
ejpam-2494	24	16	point	point	NOUN
ejpam-2494	24	17	p	p	NOUN
ejpam-2494	24	18	in	in	ADP
ejpam-2494	24	19	x	x	PROPN
ejpam-2494	24	20	is	be	AUX
ejpam-2494	24	21	called	call	VERB
ejpam-2494	24	22	a	a	DET
ejpam-2494	24	23	condensation	condensation	NOUN
ejpam-2494	24	24	point	point	NOUN
ejpam-2494	24	25	of	of	ADP
ejpam-2494	24	26	h	h	NOUN
ejpam-2494	24	27	if	if	SCONJ
ejpam-2494	24	28	for	for	ADP
ejpam-2494	24	29	each	each	DET
ejpam-2494	24	30	open	open	ADJ
ejpam-2494	24	31	set	set	VERB
ejpam-2494	24	32	u	u	NOUN
ejpam-2494	24	33	containing	contain	VERB
ejpam-2494	24	34	p	p	PRON
ejpam-2494	24	35	,	,	PUNCT
ejpam-2494	24	36	u	u	PROPN
ejpam-2494	24	37	∩	∩	ADJ
ejpam-2494	24	38	h	h	NOUN
ejpam-2494	24	39	is	be	AUX
ejpam-2494	24	40	uncountable	uncountable	ADJ
ejpam-2494	24	41	.	.	PUNCT
ejpam-2494	25	1	definition	definition	NOUN
ejpam-2494	25	2	3	3	NUM
ejpam-2494	25	3	(	(	PUNCT
ejpam-2494	25	4	[	[	X
ejpam-2494	25	5	7	7	NUM
ejpam-2494	25	6	]	]	NUM
ejpam-2494	25	7	)	)	PUNCT
ejpam-2494	25	8	.	.	PUNCT
ejpam-2494	26	1	a	a	DET
ejpam-2494	26	2	subset	subset	ADJ
ejpam-2494	26	3	h	h	NOUN
ejpam-2494	26	4	of	of	ADP
ejpam-2494	26	5	a	a	DET
ejpam-2494	26	6	space	space	NOUN
ejpam-2494	26	7	(	(	PUNCT
ejpam-2494	26	8	x	x	X
ejpam-2494	26	9	,	,	PUNCT
ejpam-2494	26	10	τ	τ	X
ejpam-2494	26	11	)	)	PUNCT
ejpam-2494	26	12	is	be	AUX
ejpam-2494	26	13	calledω	calledω	NOUN
ejpam-2494	26	14	-	-	PUNCT
ejpam-2494	26	15	closed	closed	ADJ
ejpam-2494	26	16	if	if	SCONJ
ejpam-2494	26	17	it	it	PRON
ejpam-2494	26	18	contains	contain	VERB
ejpam-2494	26	19	all	all	DET
ejpam-2494	26	20	its	its	PRON
ejpam-2494	26	21	condensation	condensation	NOUN
ejpam-2494	26	22	points	point	NOUN
ejpam-2494	26	23	.	.	PUNCT
ejpam-2494	27	1	the	the	DET
ejpam-2494	27	2	complement	complement	NOUN
ejpam-2494	27	3	of	of	ADP
ejpam-2494	27	4	an	an	DET
ejpam-2494	27	5	ω	ω	ADV
ejpam-2494	27	6	-	-	PUNCT
ejpam-2494	27	7	closed	closed	ADJ
ejpam-2494	27	8	set	set	NOUN
ejpam-2494	27	9	is	be	AUX
ejpam-2494	27	10	called	call	VERB
ejpam-2494	27	11	ω	ω	NOUN
ejpam-2494	27	12	-	-	NOUN
ejpam-2494	27	13	open	open	ADJ
ejpam-2494	27	14	.	.	PUNCT
ejpam-2494	28	1	it	it	PRON
ejpam-2494	28	2	is	be	AUX
ejpam-2494	28	3	well	well	ADV
ejpam-2494	28	4	known	know	VERB
ejpam-2494	28	5	that	that	SCONJ
ejpam-2494	28	6	a	a	DET
ejpam-2494	28	7	subset	subset	NOUN
ejpam-2494	28	8	w	w	NOUN
ejpam-2494	28	9	of	of	ADP
ejpam-2494	28	10	a	a	DET
ejpam-2494	28	11	space	space	NOUN
ejpam-2494	28	12	(	(	PUNCT
ejpam-2494	28	13	x	x	X
ejpam-2494	28	14	,	,	PUNCT
ejpam-2494	28	15	τ	τ	X
ejpam-2494	28	16	)	)	PUNCT
ejpam-2494	28	17	is	be	AUX
ejpam-2494	28	18	ω	ω	NOUN
ejpam-2494	28	19	-	-	NOUN
ejpam-2494	28	20	open	open	ADJ
ejpam-2494	28	21	if	if	SCONJ
ejpam-2494	28	22	and	and	CCONJ
ejpam-2494	28	23	only	only	ADV
ejpam-2494	28	24	if	if	SCONJ
ejpam-2494	28	25	for	for	ADP
ejpam-2494	28	26	each	each	DET
ejpam-2494	28	27	x	x	PUNCT
ejpam-2494	28	28	∈w	∈w	NOUN
ejpam-2494	28	29	,	,	PUNCT
ejpam-2494	28	30	there	there	PRON
ejpam-2494	28	31	exists	exist	VERB
ejpam-2494	28	32	u	u	PROPN
ejpam-2494	28	33	∈	∈	PROPN
ejpam-2494	28	34	τ	τ	X
ejpam-2494	28	35	such	such	ADJ
ejpam-2494	28	36	that	that	SCONJ
ejpam-2494	28	37	x	x	SYM
ejpam-2494	28	38	∈	∈	PROPN
ejpam-2494	28	39	u	u	NOUN
ejpam-2494	28	40	and	and	CCONJ
ejpam-2494	28	41	u	u	PRON
ejpam-2494	28	42	−w	−w	ADV
ejpam-2494	28	43	is	be	AUX
ejpam-2494	28	44	countable	countable	ADJ
ejpam-2494	28	45	.	.	PUNCT
ejpam-2494	29	1	the	the	DET
ejpam-2494	29	2	family	family	NOUN
ejpam-2494	29	3	of	of	ADP
ejpam-2494	29	4	all	all	DET
ejpam-2494	29	5	ω	ω	ADJ
ejpam-2494	29	6	-	-	ADJ
ejpam-2494	29	7	open	open	ADJ
ejpam-2494	29	8	sets	set	NOUN
ejpam-2494	29	9	,	,	PUNCT
ejpam-2494	29	10	denoted	denote	VERB
ejpam-2494	29	11	by	by	ADP
ejpam-2494	29	12	τω	τω	INTJ
ejpam-2494	29	13	,	,	PUNCT
ejpam-2494	29	14	is	be	AUX
ejpam-2494	29	15	a	a	DET
ejpam-2494	29	16	topology	topology	NOUN
ejpam-2494	29	17	on	on	ADP
ejpam-2494	29	18	x	x	SYM
ejpam-2494	29	19	,	,	PUNCT
ejpam-2494	29	20	which	which	PRON
ejpam-2494	29	21	is	be	AUX
ejpam-2494	29	22	finer	fine	ADJ
ejpam-2494	29	23	than	than	ADP
ejpam-2494	29	24	τ	τ	PROPN
ejpam-2494	29	25	.	.	PUNCT
ejpam-2494	30	1	the	the	DET
ejpam-2494	30	2	interior	interior	ADJ
ejpam-2494	30	3	and	and	CCONJ
ejpam-2494	30	4	closure	closure	NOUN
ejpam-2494	30	5	operator	operator	NOUN
ejpam-2494	30	6	in	in	ADP
ejpam-2494	30	7	(	(	PUNCT
ejpam-2494	30	8	x	x	INTJ
ejpam-2494	30	9	,	,	PUNCT
ejpam-2494	30	10	τω	τω	INTJ
ejpam-2494	30	11	)	)	PUNCT
ejpam-2494	30	12	are	be	AUX
ejpam-2494	30	13	denoted	denote	VERB
ejpam-2494	30	14	by	by	ADP
ejpam-2494	30	15	intω	intω	NOUN
ejpam-2494	30	16	and	and	CCONJ
ejpam-2494	30	17	clω	clω	PROPN
ejpam-2494	30	18	respectively	respectively	ADV
ejpam-2494	30	19	.	.	PUNCT
ejpam-2494	31	1	lemma	lemma	PROPN
ejpam-2494	31	2	1	1	NUM
ejpam-2494	31	3	(	(	PUNCT
ejpam-2494	31	4	[	[	X
ejpam-2494	31	5	7	7	NUM
ejpam-2494	31	6	]	]	NUM
ejpam-2494	31	7	)	)	PUNCT
ejpam-2494	31	8	.	.	PUNCT
ejpam-2494	32	1	let	let	VERB
ejpam-2494	32	2	h	h	PRON
ejpam-2494	32	3	be	be	AUX
ejpam-2494	32	4	a	a	DET
ejpam-2494	32	5	subset	subset	NOUN
ejpam-2494	32	6	of	of	ADP
ejpam-2494	32	7	a	a	DET
ejpam-2494	32	8	space	space	NOUN
ejpam-2494	32	9	(	(	PUNCT
ejpam-2494	32	10	x	x	X
ejpam-2494	32	11	,	,	PUNCT
ejpam-2494	32	12	τ	τ	PROPN
ejpam-2494	32	13	)	)	PUNCT
ejpam-2494	32	14	.	.	PUNCT
ejpam-2494	33	1	then	then	ADV
ejpam-2494	33	2	(	(	PUNCT
ejpam-2494	33	3	i	i	NOUN
ejpam-2494	33	4	)	)	PUNCT
ejpam-2494	33	5	h	h	PROPN
ejpam-2494	33	6	is	be	AUX
ejpam-2494	33	7	ω	ω	NOUN
ejpam-2494	33	8	-	-	ADJ
ejpam-2494	33	9	closed	closed	ADJ
ejpam-2494	33	10	in	in	ADP
ejpam-2494	33	11	x	x	PUNCT
ejpam-2494	33	12	if	if	SCONJ
ejpam-2494	34	1	and	and	CCONJ
ejpam-2494	34	2	only	only	ADV
ejpam-2494	34	3	if	if	SCONJ
ejpam-2494	34	4	h	h	NOUN
ejpam-2494	34	5	=	=	SYM
ejpam-2494	34	6	clω(h	clω(h	PROPN
ejpam-2494	34	7	)	)	PUNCT
ejpam-2494	34	8	.	.	PUNCT
ejpam-2494	35	1	(	(	PUNCT
ejpam-2494	35	2	ii	ii	X
ejpam-2494	35	3	)	)	PUNCT
ejpam-2494	35	4	clω(x\h	clω(x\h	PROPN
ejpam-2494	35	5	)	)	PUNCT
ejpam-2494	35	6	=	=	PUNCT
ejpam-2494	36	1	x\intω(h	x\intω(h	PROPN
ejpam-2494	36	2	)	)	PUNCT
ejpam-2494	36	3	.	.	PUNCT
ejpam-2494	37	1	(	(	PUNCT
ejpam-2494	37	2	iii	iii	X
ejpam-2494	37	3	)	)	PUNCT
ejpam-2494	37	4	clω(h	clω(h	NOUN
ejpam-2494	37	5	)	)	PUNCT
ejpam-2494	37	6	is	be	AUX
ejpam-2494	37	7	ω	ω	NOUN
ejpam-2494	37	8	-	-	ADJ
ejpam-2494	37	9	closed	closed	ADJ
ejpam-2494	37	10	in	in	ADP
ejpam-2494	37	11	x	x	X
ejpam-2494	37	12	.	.	PUNCT
ejpam-2494	38	1	(	(	PUNCT
ejpam-2494	38	2	iv	iv	X
ejpam-2494	38	3	)	)	PUNCT
ejpam-2494	38	4	x	x	SYM
ejpam-2494	38	5	∈	∈	PROPN
ejpam-2494	38	6	clω(h	clω(h	NOUN
ejpam-2494	38	7	)	)	PUNCT
ejpam-2494	38	8	if	if	SCONJ
ejpam-2494	38	9	and	and	CCONJ
ejpam-2494	38	10	only	only	ADV
ejpam-2494	38	11	if	if	SCONJ
ejpam-2494	38	12	h	h	NOUN
ejpam-2494	38	13	∩	∩	PROPN
ejpam-2494	38	14	g	g	PROPN
ejpam-2494	38	15	6=	6=	PROPN
ejpam-2494	38	16	φ	φ	PROPN
ejpam-2494	38	17	for	for	ADP
ejpam-2494	38	18	each	each	DET
ejpam-2494	38	19	ω	ω	NOUN
ejpam-2494	38	20	-	-	ADJ
ejpam-2494	38	21	open	open	ADJ
ejpam-2494	38	22	set	set	NOUN
ejpam-2494	38	23	g	g	NOUN
ejpam-2494	38	24	containing	contain	VERB
ejpam-2494	38	25	x.	x.	NOUN
ejpam-2494	38	26	(	(	PUNCT
ejpam-2494	38	27	v	v	NOUN
ejpam-2494	38	28	)	)	PUNCT
ejpam-2494	38	29	clω(h	clω(h	PROPN
ejpam-2494	38	30	)	)	PUNCT
ejpam-2494	39	1	⊂	⊂	PROPN
ejpam-2494	39	2	cl(h	cl(h	X
ejpam-2494	39	3	)	)	PUNCT
ejpam-2494	39	4	.	.	PUNCT
ejpam-2494	40	1	(	(	PUNCT
ejpam-2494	40	2	vi	vi	X
ejpam-2494	40	3	)	)	PUNCT
ejpam-2494	40	4	int(h	int(h	NOUN
ejpam-2494	40	5	)	)	PUNCT
ejpam-2494	41	1	⊂	⊂	PROPN
ejpam-2494	41	2	intω(h	intω(h	NOUN
ejpam-2494	41	3	)	)	PUNCT
ejpam-2494	41	4	.	.	PUNCT
ejpam-2494	42	1	remark	remark	PROPN
ejpam-2494	42	2	1	1	NUM
ejpam-2494	42	3	.	.	PUNCT
ejpam-2494	43	1	for	for	ADP
ejpam-2494	43	2	a	a	DET
ejpam-2494	43	3	subset	subset	NOUN
ejpam-2494	43	4	of	of	ADP
ejpam-2494	43	5	a	a	DET
ejpam-2494	43	6	space	space	NOUN
ejpam-2494	43	7	(	(	PUNCT
ejpam-2494	43	8	x	x	X
ejpam-2494	43	9	,	,	PUNCT
ejpam-2494	43	10	τ	τ	PROPN
ejpam-2494	43	11	)	)	PUNCT
ejpam-2494	43	12	,	,	PUNCT
ejpam-2494	43	13	the	the	DET
ejpam-2494	43	14	following	follow	VERB
ejpam-2494	43	15	property	property	NOUN
ejpam-2494	43	16	holds	hold	VERB
ejpam-2494	43	17	:	:	PUNCT
ejpam-2494	43	18	every	every	DET
ejpam-2494	43	19	closed	closed	ADJ
ejpam-2494	43	20	set	set	NOUN
ejpam-2494	43	21	is	be	AUX
ejpam-2494	43	22	ω	ω	NOUN
ejpam-2494	43	23	-	-	ADJ
ejpam-2494	43	24	closed	closed	ADJ
ejpam-2494	43	25	but	but	CCONJ
ejpam-2494	43	26	not	not	PART
ejpam-2494	43	27	conversely	conversely	ADV
ejpam-2494	43	28	[	[	X
ejpam-2494	43	29	2	2	NUM
ejpam-2494	43	30	,	,	PUNCT
ejpam-2494	43	31	7	7	NUM
ejpam-2494	43	32	]	]	PUNCT
ejpam-2494	43	33	.	.	PUNCT
ejpam-2494	44	1	definition	definition	NOUN
ejpam-2494	44	2	4	4	NUM
ejpam-2494	44	3	.	.	PUNCT
ejpam-2494	45	1	[	[	X
ejpam-2494	45	2	1	1	X
ejpam-2494	45	3	]	]	PUNCT
ejpam-2494	45	4	a	a	DET
ejpam-2494	45	5	space	space	NOUN
ejpam-2494	45	6	(	(	PUNCT
ejpam-2494	45	7	x	x	X
ejpam-2494	45	8	,	,	PUNCT
ejpam-2494	45	9	τ	τ	X
ejpam-2494	45	10	)	)	PUNCT
ejpam-2494	45	11	is	be	AUX
ejpam-2494	45	12	called	call	VERB
ejpam-2494	45	13	anti	anti	ADJ
ejpam-2494	45	14	-	-	ADJ
ejpam-2494	45	15	locally	locally	ADV
ejpam-2494	45	16	countable	countable	ADJ
ejpam-2494	45	17	if	if	SCONJ
ejpam-2494	45	18	each	each	DET
ejpam-2494	45	19	non	non	ADJ
ejpam-2494	45	20	-	-	ADJ
ejpam-2494	45	21	empty	empty	ADJ
ejpam-2494	45	22	open	open	ADJ
ejpam-2494	45	23	set	set	NOUN
ejpam-2494	45	24	is	be	AUX
ejpam-2494	45	25	uncountable	uncountable	ADJ
ejpam-2494	45	26	.	.	PUNCT
ejpam-2494	46	1	lemma	lemma	PROPN
ejpam-2494	46	2	2	2	NUM
ejpam-2494	46	3	(	(	PUNCT
ejpam-2494	46	4	[	[	X
ejpam-2494	46	5	8	8	NUM
ejpam-2494	46	6	]	]	PUNCT
ejpam-2494	46	7	)	)	PUNCT
ejpam-2494	46	8	.	.	PUNCT
ejpam-2494	47	1	let	let	AUX
ejpam-2494	47	2	(	(	PUNCT
ejpam-2494	47	3	h	h	NOUN
ejpam-2494	47	4	,	,	PUNCT
ejpam-2494	47	5	τh	τh	ADP
ejpam-2494	47	6	)	)	PUNCT
ejpam-2494	47	7	be	be	AUX
ejpam-2494	47	8	an	an	DET
ejpam-2494	47	9	anti	anti	ADJ
ejpam-2494	47	10	-	-	ADJ
ejpam-2494	47	11	locally	locally	ADV
ejpam-2494	47	12	countable	countable	ADJ
ejpam-2494	47	13	subspace	subspace	NOUN
ejpam-2494	47	14	of	of	ADP
ejpam-2494	47	15	a	a	DET
ejpam-2494	47	16	space	space	NOUN
ejpam-2494	47	17	(	(	PUNCT
ejpam-2494	47	18	x	x	X
ejpam-2494	47	19	,	,	PUNCT
ejpam-2494	47	20	τ	τ	PROPN
ejpam-2494	47	21	)	)	PUNCT
ejpam-2494	47	22	.	.	PUNCT
ejpam-2494	48	1	then	then	ADV
ejpam-2494	48	2	cl(h	cl(h	VERB
ejpam-2494	48	3	)	)	PUNCT
ejpam-2494	48	4	=	=	SYM
ejpam-2494	48	5	clω(h	clω(h	PROPN
ejpam-2494	48	6	)	)	PUNCT
ejpam-2494	48	7	.	.	PUNCT
ejpam-2494	49	1	lemma	lemma	PROPN
ejpam-2494	49	2	3	3	NUM
ejpam-2494	49	3	(	(	PUNCT
ejpam-2494	49	4	[	[	X
ejpam-2494	49	5	6	6	NUM
ejpam-2494	49	6	]	]	PUNCT
ejpam-2494	49	7	)	)	PUNCT
ejpam-2494	49	8	.	.	PUNCT
ejpam-2494	50	1	if	if	SCONJ
ejpam-2494	50	2	u	u	NOUN
ejpam-2494	50	3	is	be	AUX
ejpam-2494	50	4	an	an	DET
ejpam-2494	50	5	open	open	ADJ
ejpam-2494	50	6	set	set	NOUN
ejpam-2494	50	7	,	,	PUNCT
ejpam-2494	50	8	then	then	ADV
ejpam-2494	50	9	cl(u	cl(u	PUNCT
ejpam-2494	50	10	∩	∩	ADJ
ejpam-2494	50	11	h	h	NOUN
ejpam-2494	50	12	)	)	PUNCT
ejpam-2494	50	13	=	=	NOUN
ejpam-2494	50	14	cl(u	cl(u	NOUN
ejpam-2494	50	15	∩	∩	NOUN
ejpam-2494	50	16	cl(h	cl(h	NOUN
ejpam-2494	50	17	)	)	PUNCT
ejpam-2494	50	18	)	)	PUNCT
ejpam-2494	50	19	and	and	CCONJ
ejpam-2494	50	20	hence	hence	ADV
ejpam-2494	50	21	u	u	NOUN
ejpam-2494	50	22	∩	∩	NOUN
ejpam-2494	50	23	cl(h	cl(h	X
ejpam-2494	50	24	)	)	PUNCT
ejpam-2494	50	25	⊂	⊂	PROPN
ejpam-2494	50	26	cl(u	cl(u	NOUN
ejpam-2494	50	27	∩	∩	ADJ
ejpam-2494	50	28	h	h	NOUN
ejpam-2494	50	29	)	)	PUNCT
ejpam-2494	50	30	for	for	ADP
ejpam-2494	50	31	any	any	DET
ejpam-2494	50	32	subset	subset	NOUN
ejpam-2494	50	33	h.	h.	PROPN
ejpam-2494	50	34	lemma	lemma	PROPN
ejpam-2494	50	35	4	4	NUM
ejpam-2494	50	36	(	(	PUNCT
ejpam-2494	50	37	[	[	X
ejpam-2494	50	38	1	1	NUM
ejpam-2494	50	39	,	,	PUNCT
ejpam-2494	50	40	4	4	NUM
ejpam-2494	50	41	]	]	NUM
ejpam-2494	50	42	)	)	PUNCT
ejpam-2494	50	43	.	.	PUNCT
ejpam-2494	51	1	if	if	SCONJ
ejpam-2494	51	2	(	(	PUNCT
ejpam-2494	51	3	x	x	X
ejpam-2494	51	4	,	,	PUNCT
ejpam-2494	51	5	τ	τ	X
ejpam-2494	51	6	)	)	PUNCT
ejpam-2494	51	7	is	be	AUX
ejpam-2494	51	8	an	an	DET
ejpam-2494	51	9	anti	anti	ADJ
ejpam-2494	51	10	-	-	ADJ
ejpam-2494	51	11	locally	locally	ADV
ejpam-2494	51	12	countable	countable	ADJ
ejpam-2494	51	13	space	space	NOUN
ejpam-2494	51	14	,	,	PUNCT
ejpam-2494	51	15	then	then	ADV
ejpam-2494	51	16	intω(h	intω(h	NUM
ejpam-2494	51	17	)	)	PUNCT
ejpam-2494	51	18	=	=	SYM
ejpam-2494	51	19	int(h	int(h	X
ejpam-2494	51	20	)	)	PUNCT
ejpam-2494	51	21	for	for	ADP
ejpam-2494	51	22	every	every	DET
ejpam-2494	51	23	ω	ω	VERB
ejpam-2494	51	24	-	-	PUNCT
ejpam-2494	51	25	closed	closed	ADJ
ejpam-2494	51	26	set	set	ADJ
ejpam-2494	51	27	h	h	NOUN
ejpam-2494	51	28	of	of	ADP
ejpam-2494	51	29	x	x	X
ejpam-2494	51	30	and	and	CCONJ
ejpam-2494	51	31	clω(h	clω(h	NOUN
ejpam-2494	51	32	)	)	PUNCT
ejpam-2494	51	33	=	=	PRON
ejpam-2494	51	34	cl(h	cl(h	X
ejpam-2494	51	35	)	)	PUNCT
ejpam-2494	51	36	for	for	ADP
ejpam-2494	51	37	every	every	DET
ejpam-2494	51	38	ω	ω	ADJ
ejpam-2494	51	39	-	-	ADJ
ejpam-2494	51	40	open	open	ADJ
ejpam-2494	51	41	set	set	ADJ
ejpam-2494	51	42	h	h	NOUN
ejpam-2494	51	43	of	of	ADP
ejpam-2494	51	44	x.	x.	PROPN
ejpam-2494	51	45	o.	o.	PROPN
ejpam-2494	51	46	ravi	ravi	PROPN
ejpam-2494	51	47	,	,	PUNCT
ejpam-2494	51	48	i.	i.	NOUN
ejpam-2494	51	49	rajasekaran	rajasekaran	PROPN
ejpam-2494	51	50	,	,	PUNCT
ejpam-2494	51	51	s.	s.	PROPN
ejpam-2494	51	52	kanna	kanna	PROPN
ejpam-2494	51	53	and	and	CCONJ
ejpam-2494	51	54	m.	m.	NOUN
ejpam-2494	51	55	paranjothi	paranjothi	PROPN
ejpam-2494	51	56	/	/	SYM
ejpam-2494	51	57	eur	eur	PROPN
ejpam-2494	51	58	.	.	PUNCT
ejpam-2494	52	1	j.	j.	PROPN
ejpam-2494	52	2	pure	pure	PROPN
ejpam-2494	52	3	appl	appl	PROPN
ejpam-2494	52	4	.	.	PROPN
ejpam-2494	52	5	math	math	PROPN
ejpam-2494	52	6	,	,	PUNCT
ejpam-2494	52	7	9	9	NUM
ejpam-2494	52	8	(	(	PUNCT
ejpam-2494	52	9	2016	2016	NUM
ejpam-2494	52	10	)	)	PUNCT
ejpam-2494	52	11	,	,	PUNCT
ejpam-2494	52	12	152	152	NUM
ejpam-2494	52	13	-	-	SYM
ejpam-2494	52	14	164	164	NUM
ejpam-2494	52	15	154	154	NUM
ejpam-2494	52	16	definition	definition	NOUN
ejpam-2494	52	17	5	5	NUM
ejpam-2494	52	18	(	(	PUNCT
ejpam-2494	52	19	[	[	X
ejpam-2494	52	20	10	10	NUM
ejpam-2494	52	21	]	]	NUM
ejpam-2494	52	22	)	)	PUNCT
ejpam-2494	52	23	.	.	PUNCT
ejpam-2494	53	1	a	a	DET
ejpam-2494	53	2	subset	subset	ADJ
ejpam-2494	53	3	h	h	NOUN
ejpam-2494	53	4	of	of	ADP
ejpam-2494	53	5	a	a	DET
ejpam-2494	53	6	space	space	NOUN
ejpam-2494	53	7	(	(	PUNCT
ejpam-2494	53	8	x	x	X
ejpam-2494	53	9	,	,	PUNCT
ejpam-2494	53	10	τ	τ	X
ejpam-2494	53	11	)	)	PUNCT
ejpam-2494	53	12	is	be	AUX
ejpam-2494	53	13	called	call	VERB
ejpam-2494	53	14	(	(	PUNCT
ejpam-2494	53	15	i	i	NOUN
ejpam-2494	53	16	)	)	PUNCT
ejpam-2494	53	17	α−ω	α−ω	PROPN
ejpam-2494	53	18	-	-	PUNCT
ejpam-2494	53	19	open	open	ADJ
ejpam-2494	53	20	if	if	SCONJ
ejpam-2494	53	21	h	h	PROPN
ejpam-2494	53	22	⊂	⊂	PROPN
ejpam-2494	53	23	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	53	24	)	)	PUNCT
ejpam-2494	53	25	)	)	PUNCT
ejpam-2494	53	26	)	)	PUNCT
ejpam-2494	53	27	;	;	PUNCT
ejpam-2494	53	28	(	(	PUNCT
ejpam-2494	53	29	ii	ii	NOUN
ejpam-2494	53	30	)	)	PUNCT
ejpam-2494	53	31	pre	pre	ADJ
ejpam-2494	53	32	-	-	ADJ
ejpam-2494	53	33	ω	ω	VERB
ejpam-2494	53	34	-	-	NOUN
ejpam-2494	53	35	open	open	ADJ
ejpam-2494	53	36	if	if	SCONJ
ejpam-2494	53	37	h	h	PROPN
ejpam-2494	53	38	⊂	⊂	X
ejpam-2494	53	39	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	53	40	)	)	PUNCT
ejpam-2494	53	41	)	)	PUNCT
ejpam-2494	53	42	;	;	PUNCT
ejpam-2494	53	43	(	(	PUNCT
ejpam-2494	53	44	iii	iii	X
ejpam-2494	53	45	)	)	PUNCT
ejpam-2494	53	46	β	β	NOUN
ejpam-2494	53	47	−ω	−ω	ADJ
ejpam-2494	53	48	-	-	PUNCT
ejpam-2494	53	49	open	open	ADJ
ejpam-2494	53	50	if	if	SCONJ
ejpam-2494	53	51	h	h	PROPN
ejpam-2494	53	52	⊂	⊂	PROPN
ejpam-2494	53	53	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	53	54	)	)	PUNCT
ejpam-2494	53	55	)	)	PUNCT
ejpam-2494	53	56	)	)	PUNCT
ejpam-2494	53	57	;	;	PUNCT
ejpam-2494	53	58	(	(	PUNCT
ejpam-2494	53	59	iv	iv	X
ejpam-2494	53	60	)	)	PUNCT
ejpam-2494	53	61	b−ω	b−ω	NOUN
ejpam-2494	53	62	-	-	PUNCT
ejpam-2494	53	63	open	open	ADJ
ejpam-2494	53	64	if	if	SCONJ
ejpam-2494	53	65	h	h	PROPN
ejpam-2494	53	66	⊂	⊂	PROPN
ejpam-2494	53	67	intω(cl(h))∪	intω(cl(h))∪	PROPN
ejpam-2494	53	68	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	53	69	)	)	PUNCT
ejpam-2494	53	70	)	)	PUNCT
ejpam-2494	53	71	.	.	PUNCT
ejpam-2494	54	1	definition	definition	NOUN
ejpam-2494	54	2	6	6	NUM
ejpam-2494	54	3	(	(	PUNCT
ejpam-2494	54	4	[	[	X
ejpam-2494	54	5	10	10	NUM
ejpam-2494	54	6	]	]	NUM
ejpam-2494	54	7	)	)	PUNCT
ejpam-2494	54	8	.	.	PUNCT
ejpam-2494	55	1	a	a	DET
ejpam-2494	55	2	subset	subset	ADJ
ejpam-2494	55	3	h	h	NOUN
ejpam-2494	55	4	of	of	ADP
ejpam-2494	55	5	a	a	DET
ejpam-2494	55	6	space	space	NOUN
ejpam-2494	55	7	(	(	PUNCT
ejpam-2494	55	8	x	x	X
ejpam-2494	55	9	,	,	PUNCT
ejpam-2494	55	10	τ	τ	X
ejpam-2494	55	11	)	)	PUNCT
ejpam-2494	55	12	is	be	AUX
ejpam-2494	55	13	called	call	VERB
ejpam-2494	55	14	an	an	DET
ejpam-2494	55	15	ω−	ω−	PROPN
ejpam-2494	55	16	t	t	NOUN
ejpam-2494	55	17	-	-	PUNCT
ejpam-2494	55	18	set	set	VERB
ejpam-2494	55	19	if	if	SCONJ
ejpam-2494	55	20	int(h	int(h	NOUN
ejpam-2494	55	21	)	)	PUNCT
ejpam-2494	55	22	=	=	SYM
ejpam-2494	55	23	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	55	24	)	)	PUNCT
ejpam-2494	55	25	)	)	PUNCT
ejpam-2494	55	26	.	.	PUNCT
ejpam-2494	56	1	definition	definition	NOUN
ejpam-2494	56	2	7	7	NUM
ejpam-2494	56	3	.	.	PUNCT
ejpam-2494	57	1	a	a	DET
ejpam-2494	57	2	space	space	NOUN
ejpam-2494	57	3	(	(	PUNCT
ejpam-2494	57	4	x	x	X
ejpam-2494	57	5	,	,	PUNCT
ejpam-2494	57	6	τ	τ	X
ejpam-2494	57	7	)	)	PUNCT
ejpam-2494	57	8	is	be	AUX
ejpam-2494	57	9	called	call	VERB
ejpam-2494	57	10	submaximal	submaximal	ADJ
ejpam-2494	57	11	[	[	X
ejpam-2494	57	12	5	5	NUM
ejpam-2494	57	13	]	]	PUNCT
ejpam-2494	57	14	if	if	SCONJ
ejpam-2494	57	15	every	every	DET
ejpam-2494	57	16	dense	dense	ADJ
ejpam-2494	57	17	subset	subset	NOUN
ejpam-2494	57	18	is	be	AUX
ejpam-2494	57	19	open	open	ADJ
ejpam-2494	57	20	.	.	PUNCT
ejpam-2494	58	1	definition	definition	NOUN
ejpam-2494	58	2	8	8	NUM
ejpam-2494	58	3	.	.	PUNCT
ejpam-2494	59	1	a	a	DET
ejpam-2494	59	2	subset	subset	ADJ
ejpam-2494	59	3	h	h	NOUN
ejpam-2494	59	4	of	of	ADP
ejpam-2494	59	5	a	a	DET
ejpam-2494	59	6	space	space	NOUN
ejpam-2494	59	7	(	(	PUNCT
ejpam-2494	59	8	x	x	X
ejpam-2494	59	9	,	,	PUNCT
ejpam-2494	59	10	τ	τ	X
ejpam-2494	59	11	)	)	PUNCT
ejpam-2494	59	12	is	be	AUX
ejpam-2494	59	13	called	call	VERB
ejpam-2494	59	14	ω	ω	NOUN
ejpam-2494	59	15	-	-	ADJ
ejpam-2494	59	16	dense	dense	ADJ
ejpam-2494	59	17	[	[	X
ejpam-2494	59	18	3	3	NUM
ejpam-2494	59	19	]	]	PUNCT
ejpam-2494	59	20	if	if	SCONJ
ejpam-2494	59	21	clω(h	clω(h	PROPN
ejpam-2494	59	22	)	)	PUNCT
ejpam-2494	59	23	=	=	SYM
ejpam-2494	60	1	x	x	X
ejpam-2494	60	2	.	.	PUNCT
ejpam-2494	61	1	3	3	X
ejpam-2494	61	2	.	.	X
ejpam-2494	61	3	properties	property	NOUN
ejpam-2494	61	4	of	of	ADP
ejpam-2494	61	5	semi	semi	ADJ
ejpam-2494	61	6	-	-	ADJ
ejpam-2494	61	7	ω	ω	ADJ
ejpam-2494	61	8	-	-	ADJ
ejpam-2494	61	9	open	open	ADJ
ejpam-2494	61	10	sets	set	NOUN
ejpam-2494	61	11	definition	definition	NOUN
ejpam-2494	61	12	9	9	NUM
ejpam-2494	61	13	.	.	PUNCT
ejpam-2494	62	1	a	a	DET
ejpam-2494	62	2	subset	subset	ADJ
ejpam-2494	62	3	h	h	NOUN
ejpam-2494	62	4	of	of	ADP
ejpam-2494	62	5	a	a	DET
ejpam-2494	62	6	space	space	NOUN
ejpam-2494	62	7	(	(	PUNCT
ejpam-2494	62	8	x	x	X
ejpam-2494	62	9	,	,	PUNCT
ejpam-2494	62	10	τ	τ	X
ejpam-2494	62	11	)	)	PUNCT
ejpam-2494	62	12	is	be	AUX
ejpam-2494	62	13	said	say	VERB
ejpam-2494	62	14	to	to	PART
ejpam-2494	62	15	be	be	AUX
ejpam-2494	62	16	(	(	PUNCT
ejpam-2494	62	17	i	i	NOUN
ejpam-2494	62	18	)	)	PUNCT
ejpam-2494	62	19	semi	semi	ADJ
ejpam-2494	62	20	-	-	ADJ
ejpam-2494	62	21	ω	ω	ADV
ejpam-2494	62	22	-	-	NOUN
ejpam-2494	62	23	open	open	ADJ
ejpam-2494	62	24	if	if	SCONJ
ejpam-2494	62	25	h	h	PROPN
ejpam-2494	62	26	⊂	⊂	X
ejpam-2494	62	27	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	62	28	)	)	PUNCT
ejpam-2494	62	29	)	)	PUNCT
ejpam-2494	62	30	.	.	PUNCT
ejpam-2494	63	1	(	(	PUNCT
ejpam-2494	63	2	ii	ii	NOUN
ejpam-2494	63	3	)	)	PUNCT
ejpam-2494	63	4	semi	semi	ADJ
ejpam-2494	63	5	-	-	ADJ
ejpam-2494	63	6	ω	ω	ADV
ejpam-2494	63	7	-	-	PUNCT
ejpam-2494	63	8	closed	closed	ADJ
ejpam-2494	63	9	if	if	SCONJ
ejpam-2494	63	10	int(clω(h	int(clω(h	PROPN
ejpam-2494	63	11	)	)	PUNCT
ejpam-2494	63	12	)	)	PUNCT
ejpam-2494	64	1	⊂	⊂	PROPN
ejpam-2494	64	2	h.	h.	PROPN
ejpam-2494	65	1	the	the	DET
ejpam-2494	65	2	complement	complement	NOUN
ejpam-2494	65	3	of	of	ADP
ejpam-2494	65	4	semi	semi	ADJ
ejpam-2494	65	5	-	-	ADJ
ejpam-2494	65	6	ω	ω	ADJ
ejpam-2494	65	7	-	-	ADJ
ejpam-2494	65	8	open	open	ADJ
ejpam-2494	65	9	set	set	NOUN
ejpam-2494	65	10	is	be	AUX
ejpam-2494	65	11	called	call	VERB
ejpam-2494	65	12	semi	semi	ADJ
ejpam-2494	65	13	-	-	ADJ
ejpam-2494	65	14	ω	ω	ADJ
ejpam-2494	65	15	-	-	PUNCT
ejpam-2494	65	16	closed	closed	ADJ
ejpam-2494	65	17	.	.	PUNCT
ejpam-2494	66	1	example	example	NOUN
ejpam-2494	67	1	1	1	NUM
ejpam-2494	67	2	.	.	PUNCT
ejpam-2494	67	3	let	let	VERB
ejpam-2494	67	4	x	x	PUNCT
ejpam-2494	67	5	=	=	PRON
ejpam-2494	67	6	{	{	PUNCT
ejpam-2494	67	7	a	a	PRON
ejpam-2494	67	8	,	,	PUNCT
ejpam-2494	67	9	b	b	NOUN
ejpam-2494	67	10	,	,	PUNCT
ejpam-2494	67	11	c	c	NOUN
ejpam-2494	67	12	}	}	PUNCT
ejpam-2494	67	13	with	with	ADP
ejpam-2494	67	14	the	the	DET
ejpam-2494	67	15	topology	topology	NOUN
ejpam-2494	67	16	τ=	τ=	PRON
ejpam-2494	67	17	{	{	PUNCT
ejpam-2494	67	18	φ	φ	PROPN
ejpam-2494	67	19	,	,	PUNCT
ejpam-2494	67	20	x	x	INTJ
ejpam-2494	67	21	,	,	PUNCT
ejpam-2494	67	22	{	{	PUNCT
ejpam-2494	67	23	a	a	NOUN
ejpam-2494	67	24	}	}	PUNCT
ejpam-2494	67	25	,	,	PUNCT
ejpam-2494	67	26	{	{	PUNCT
ejpam-2494	67	27	a	a	DET
ejpam-2494	67	28	,	,	PUNCT
ejpam-2494	67	29	b	b	NOUN
ejpam-2494	67	30	}	}	PUNCT
ejpam-2494	67	31	}	}	PUNCT
ejpam-2494	67	32	.	.	PUNCT
ejpam-2494	68	1	then	then	ADV
ejpam-2494	68	2	{	{	PUNCT
ejpam-2494	68	3	a	a	PRON
ejpam-2494	68	4	}	}	PUNCT
ejpam-2494	68	5	is	be	AUX
ejpam-2494	68	6	semi	semi	ADJ
ejpam-2494	68	7	-	-	ADJ
ejpam-2494	68	8	ω	ω	ADJ
ejpam-2494	68	9	-	-	ADJ
ejpam-2494	68	10	open	open	ADJ
ejpam-2494	68	11	.	.	PUNCT
ejpam-2494	69	1	example	example	NOUN
ejpam-2494	70	1	2	2	NUM
ejpam-2494	70	2	.	.	PUNCT
ejpam-2494	70	3	let	let	VERB
ejpam-2494	70	4	x	x	PUNCT
ejpam-2494	70	5	=	=	PRON
ejpam-2494	70	6	rwith	rwith	ADP
ejpam-2494	70	7	the	the	DET
ejpam-2494	70	8	usual	usual	ADJ
ejpam-2494	70	9	topology	topology	NOUN
ejpam-2494	70	10	τu	τu	PROPN
ejpam-2494	70	11	.	.	PUNCT
ejpam-2494	71	1	let	let	VERB
ejpam-2494	71	2	h	h	NOUN
ejpam-2494	71	3	=	=	PUNCT
ejpam-2494	71	4	(	(	PUNCT
ejpam-2494	71	5	0,1)∩q	0,1)∩q	NUM
ejpam-2494	71	6	.	.	PUNCT
ejpam-2494	72	1	then	then	ADV
ejpam-2494	72	2	h	h	PROPN
ejpam-2494	72	3	is	be	AUX
ejpam-2494	72	4	not	not	PART
ejpam-2494	72	5	semi	semi	ADJ
ejpam-2494	72	6	-	-	ADJ
ejpam-2494	72	7	ω	ω	ADJ
ejpam-2494	72	8	-	-	ADJ
ejpam-2494	72	9	open	open	ADJ
ejpam-2494	72	10	,	,	PUNCT
ejpam-2494	72	11	since	since	SCONJ
ejpam-2494	72	12	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	72	13	)	)	PUNCT
ejpam-2494	72	14	)	)	PUNCT
ejpam-2494	73	1	=	=	PRON
ejpam-2494	73	2	cl(φ	cl(φ	X
ejpam-2494	73	3	)	)	PUNCT
ejpam-2494	73	4	=	=	SYM
ejpam-2494	74	1	φ	φ	X
ejpam-2494	74	2	.	.	PUNCT
ejpam-2494	74	3	proposition	proposition	NOUN
ejpam-2494	74	4	1	1	NUM
ejpam-2494	74	5	.	.	PUNCT
ejpam-2494	75	1	in	in	ADP
ejpam-2494	75	2	a	a	DET
ejpam-2494	75	3	space	space	NOUN
ejpam-2494	75	4	(	(	PUNCT
ejpam-2494	75	5	x	x	X
ejpam-2494	75	6	,	,	PUNCT
ejpam-2494	75	7	τ	τ	PROPN
ejpam-2494	75	8	)	)	PUNCT
ejpam-2494	75	9	,	,	PUNCT
ejpam-2494	75	10	every	every	DET
ejpam-2494	75	11	semi	semi	ADJ
ejpam-2494	75	12	-	-	ADJ
ejpam-2494	75	13	open	open	ADJ
ejpam-2494	75	14	subset	subset	NOUN
ejpam-2494	75	15	is	be	AUX
ejpam-2494	75	16	semi	semi	ADJ
ejpam-2494	75	17	-	-	ADJ
ejpam-2494	75	18	ω	ω	ADJ
ejpam-2494	75	19	-	-	ADJ
ejpam-2494	75	20	open	open	ADJ
ejpam-2494	75	21	.	.	PUNCT
ejpam-2494	76	1	proof	proof	NOUN
ejpam-2494	76	2	.	.	PUNCT
ejpam-2494	77	1	let	let	VERB
ejpam-2494	77	2	h	h	PRON
ejpam-2494	77	3	be	be	AUX
ejpam-2494	77	4	semi	semi	ADJ
ejpam-2494	77	5	-	-	ADJ
ejpam-2494	77	6	open	open	ADJ
ejpam-2494	77	7	in	in	ADP
ejpam-2494	77	8	(	(	PUNCT
ejpam-2494	77	9	x	x	INTJ
ejpam-2494	77	10	,	,	PUNCT
ejpam-2494	77	11	τ	τ	PROPN
ejpam-2494	77	12	)	)	PUNCT
ejpam-2494	77	13	.	.	PUNCT
ejpam-2494	78	1	then	then	ADV
ejpam-2494	78	2	h	h	PROPN
ejpam-2494	78	3	⊂	⊂	PROPN
ejpam-2494	78	4	cl(int(h	cl(int(h	PROPN
ejpam-2494	78	5	)	)	PUNCT
ejpam-2494	78	6	)	)	PUNCT
ejpam-2494	79	1	⊂	⊂	PROPN
ejpam-2494	79	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	79	3	)	)	PUNCT
ejpam-2494	79	4	)	)	PUNCT
ejpam-2494	79	5	.	.	PUNCT
ejpam-2494	80	1	this	this	PRON
ejpam-2494	80	2	proves	prove	VERB
ejpam-2494	80	3	that	that	SCONJ
ejpam-2494	80	4	h	h	NOUN
ejpam-2494	80	5	is	be	AUX
ejpam-2494	80	6	semi	semi	ADJ
ejpam-2494	80	7	-	-	ADJ
ejpam-2494	80	8	ω	ω	ADJ
ejpam-2494	80	9	-	-	ADJ
ejpam-2494	80	10	open	open	ADJ
ejpam-2494	80	11	.	.	PUNCT
ejpam-2494	81	1	remark	remark	NOUN
ejpam-2494	81	2	2	2	NUM
ejpam-2494	81	3	.	.	PUNCT
ejpam-2494	82	1	the	the	DET
ejpam-2494	82	2	converse	converse	NOUN
ejpam-2494	82	3	of	of	ADP
ejpam-2494	82	4	proposition	proposition	NOUN
ejpam-2494	82	5	1	1	NUM
ejpam-2494	82	6	is	be	AUX
ejpam-2494	82	7	not	not	PART
ejpam-2494	82	8	true	true	ADJ
ejpam-2494	82	9	.	.	PUNCT
ejpam-2494	82	10	example	example	NOUN
ejpam-2494	83	1	3	3	X
ejpam-2494	83	2	.	.	PUNCT
ejpam-2494	83	3	let	let	VERB
ejpam-2494	83	4	x	x	PUNCT
ejpam-2494	83	5	=	=	PUNCT
ejpam-2494	83	6	r	r	NOUN
ejpam-2494	83	7	with	with	ADP
ejpam-2494	83	8	the	the	DET
ejpam-2494	83	9	usual	usual	ADJ
ejpam-2494	83	10	topology	topology	NOUN
ejpam-2494	83	11	τu	τu	PROPN
ejpam-2494	83	12	.	.	PUNCT
ejpam-2494	84	1	then	then	ADV
ejpam-2494	84	2	h	h	NOUN
ejpam-2494	84	3	=	=	NOUN
ejpam-2494	84	4	q⋆	q⋆	NOUN
ejpam-2494	84	5	is	be	AUX
ejpam-2494	84	6	semi	semi	ADJ
ejpam-2494	84	7	-	-	ADJ
ejpam-2494	84	8	ω	ω	ADJ
ejpam-2494	84	9	-	-	NOUN
ejpam-2494	84	10	open	open	ADJ
ejpam-2494	84	11	for	for	ADP
ejpam-2494	84	12	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	84	13	)	)	PUNCT
ejpam-2494	84	14	)	)	PUNCT
ejpam-2494	85	1	=	=	SYM
ejpam-2494	85	2	cl(h	cl(h	X
ejpam-2494	85	3	)	)	PUNCT
ejpam-2494	85	4	=	=	SYM
ejpam-2494	85	5	r	r	NOUN
ejpam-2494	85	6	and	and	CCONJ
ejpam-2494	85	7	h	h	NOUN
ejpam-2494	85	8	⊂	⊂	PROPN
ejpam-2494	85	9	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	85	10	)	)	PUNCT
ejpam-2494	85	11	)	)	PUNCT
ejpam-2494	85	12	.	.	PUNCT
ejpam-2494	86	1	but	but	CCONJ
ejpam-2494	86	2	h	h	NOUN
ejpam-2494	86	3	is	be	AUX
ejpam-2494	86	4	not	not	PART
ejpam-2494	86	5	semi	semi	ADJ
ejpam-2494	86	6	-	-	ADJ
ejpam-2494	86	7	open	open	ADJ
ejpam-2494	86	8	for	for	ADP
ejpam-2494	86	9	cl(int(h	cl(int(h	NOUN
ejpam-2494	86	10	)	)	PUNCT
ejpam-2494	86	11	)	)	PUNCT
ejpam-2494	87	1	=	=	PRON
ejpam-2494	87	2	cl(φ	cl(φ	X
ejpam-2494	87	3	)	)	PUNCT
ejpam-2494	87	4	=	=	SYM
ejpam-2494	87	5	φ	φ	PROPN
ejpam-2494	87	6	and	and	CCONJ
ejpam-2494	87	7	h	h	PROPN
ejpam-2494	87	8	6⊆	6⊆	PROPN
ejpam-2494	87	9	cl(int(h	cl(int(h	PROPN
ejpam-2494	87	10	)	)	PUNCT
ejpam-2494	87	11	)	)	PUNCT
ejpam-2494	87	12	.	.	PUNCT
ejpam-2494	88	1	from	from	ADP
ejpam-2494	88	2	the	the	DET
ejpam-2494	88	3	above	above	ADJ
ejpam-2494	88	4	example	example	NOUN
ejpam-2494	88	5	,	,	PUNCT
ejpam-2494	88	6	we	we	PRON
ejpam-2494	88	7	observe	observe	VERB
ejpam-2494	88	8	that	that	SCONJ
ejpam-2494	88	9	the	the	DET
ejpam-2494	88	10	converse	converse	NOUN
ejpam-2494	88	11	fails	fail	VERB
ejpam-2494	88	12	in	in	ADP
ejpam-2494	88	13	an	an	DET
ejpam-2494	88	14	anti	anti	ADJ
ejpam-2494	88	15	-	-	ADJ
ejpam-2494	88	16	locally	locally	ADV
ejpam-2494	88	17	countable	countable	ADJ
ejpam-2494	88	18	space	space	NOUN
ejpam-2494	88	19	also	also	ADV
ejpam-2494	88	20	.	.	PUNCT
ejpam-2494	89	1	theorem	theorem	ADJ
ejpam-2494	89	2	1	1	NUM
ejpam-2494	89	3	.	.	PUNCT
ejpam-2494	90	1	in	in	ADP
ejpam-2494	90	2	an	an	DET
ejpam-2494	90	3	anti	anti	ADJ
ejpam-2494	90	4	-	-	ADJ
ejpam-2494	90	5	locally	locally	ADV
ejpam-2494	90	6	countable	countable	ADJ
ejpam-2494	90	7	space	space	NOUN
ejpam-2494	90	8	,	,	PUNCT
ejpam-2494	90	9	an	an	DET
ejpam-2494	90	10	ω	ω	NOUN
ejpam-2494	90	11	-	-	PUNCT
ejpam-2494	90	12	closed	closed	ADJ
ejpam-2494	90	13	and	and	CCONJ
ejpam-2494	90	14	a	a	DET
ejpam-2494	90	15	semi	semi	ADJ
ejpam-2494	90	16	-	-	ADJ
ejpam-2494	90	17	ω	ω	ADJ
ejpam-2494	90	18	-	-	ADJ
ejpam-2494	90	19	open	open	ADJ
ejpam-2494	90	20	subset	subset	NOUN
ejpam-2494	90	21	is	be	AUX
ejpam-2494	90	22	semiopen	semiopen	ADJ
ejpam-2494	90	23	.	.	PUNCT
ejpam-2494	91	1	o.	o.	PROPN
ejpam-2494	91	2	ravi	ravi	PROPN
ejpam-2494	91	3	,	,	PUNCT
ejpam-2494	91	4	i.	i.	NOUN
ejpam-2494	91	5	rajasekaran	rajasekaran	PROPN
ejpam-2494	91	6	,	,	PUNCT
ejpam-2494	91	7	s.	s.	PROPN
ejpam-2494	91	8	kanna	kanna	PROPN
ejpam-2494	91	9	and	and	CCONJ
ejpam-2494	91	10	m.	m.	NOUN
ejpam-2494	91	11	paranjothi	paranjothi	PROPN
ejpam-2494	91	12	/	/	SYM
ejpam-2494	91	13	eur	eur	PROPN
ejpam-2494	91	14	.	.	PUNCT
ejpam-2494	92	1	j.	j.	PROPN
ejpam-2494	92	2	pure	pure	PROPN
ejpam-2494	92	3	appl	appl	PROPN
ejpam-2494	92	4	.	.	PROPN
ejpam-2494	92	5	math	math	PROPN
ejpam-2494	92	6	,	,	PUNCT
ejpam-2494	92	7	9	9	NUM
ejpam-2494	92	8	(	(	PUNCT
ejpam-2494	92	9	2016	2016	NUM
ejpam-2494	92	10	)	)	PUNCT
ejpam-2494	92	11	,	,	PUNCT
ejpam-2494	92	12	152	152	NUM
ejpam-2494	92	13	-	-	SYM
ejpam-2494	92	14	164	164	NUM
ejpam-2494	92	15	155	155	NUM
ejpam-2494	92	16	proof	proof	NOUN
ejpam-2494	92	17	.	.	PUNCT
ejpam-2494	93	1	let	let	AUX
ejpam-2494	93	2	(	(	PUNCT
ejpam-2494	93	3	x	x	X
ejpam-2494	93	4	,	,	PUNCT
ejpam-2494	93	5	τ	τ	X
ejpam-2494	93	6	)	)	PUNCT
ejpam-2494	93	7	be	be	AUX
ejpam-2494	93	8	an	an	DET
ejpam-2494	93	9	anti	anti	ADJ
ejpam-2494	93	10	-	-	ADJ
ejpam-2494	93	11	locally	locally	ADV
ejpam-2494	93	12	countable	countable	ADJ
ejpam-2494	93	13	space	space	NOUN
ejpam-2494	93	14	and	and	CCONJ
ejpam-2494	93	15	h	h	NOUN
ejpam-2494	93	16	be	be	AUX
ejpam-2494	93	17	an	an	DET
ejpam-2494	93	18	ω	ω	NOUN
ejpam-2494	93	19	-	-	PUNCT
ejpam-2494	93	20	closed	closed	ADJ
ejpam-2494	93	21	and	and	CCONJ
ejpam-2494	93	22	a	a	DET
ejpam-2494	93	23	semi	semi	ADJ
ejpam-2494	93	24	-	-	ADJ
ejpam-2494	93	25	ωopen	ωopen	ADJ
ejpam-2494	93	26	subset	subset	NOUN
ejpam-2494	93	27	.	.	PUNCT
ejpam-2494	94	1	since	since	SCONJ
ejpam-2494	94	2	h	h	PROPN
ejpam-2494	94	3	is	be	AUX
ejpam-2494	94	4	semi	semi	ADJ
ejpam-2494	94	5	-	-	ADJ
ejpam-2494	94	6	ω	ω	ADJ
ejpam-2494	94	7	-	-	ADJ
ejpam-2494	94	8	open	open	ADJ
ejpam-2494	94	9	,	,	PUNCT
ejpam-2494	94	10	h	h	NOUN
ejpam-2494	94	11	⊂	⊂	PROPN
ejpam-2494	94	12	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	94	13	)	)	PUNCT
ejpam-2494	94	14	)	)	PUNCT
ejpam-2494	94	15	.	.	PUNCT
ejpam-2494	95	1	since	since	SCONJ
ejpam-2494	95	2	(	(	PUNCT
ejpam-2494	95	3	x	x	X
ejpam-2494	95	4	,	,	PUNCT
ejpam-2494	95	5	τ	τ	X
ejpam-2494	95	6	)	)	PUNCT
ejpam-2494	95	7	is	be	AUX
ejpam-2494	95	8	anti	anti	ADJ
ejpam-2494	95	9	-	-	ADJ
ejpam-2494	95	10	locally	locally	ADV
ejpam-2494	95	11	countable	countable	ADJ
ejpam-2494	95	12	and	and	CCONJ
ejpam-2494	95	13	h	h	NOUN
ejpam-2494	95	14	is	be	AUX
ejpam-2494	95	15	ω	ω	NOUN
ejpam-2494	95	16	-	-	ADJ
ejpam-2494	95	17	closed	closed	ADJ
ejpam-2494	95	18	,	,	PUNCT
ejpam-2494	95	19	intω(h	intω(h	NOUN
ejpam-2494	95	20	)	)	PUNCT
ejpam-2494	95	21	=	=	SYM
ejpam-2494	96	1	int(h	int(h	X
ejpam-2494	96	2	)	)	PUNCT
ejpam-2494	96	3	by	by	ADP
ejpam-2494	96	4	lemma	lemma	PROPN
ejpam-2494	96	5	4	4	NUM
ejpam-2494	96	6	.	.	PUNCT
ejpam-2494	97	1	hence	hence	ADV
ejpam-2494	97	2	h	h	NOUN
ejpam-2494	97	3	⊂	⊂	PROPN
ejpam-2494	97	4	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	97	5	)	)	PUNCT
ejpam-2494	97	6	)	)	PUNCT
ejpam-2494	98	1	=	=	SYM
ejpam-2494	98	2	cl(int(h	cl(int(h	NOUN
ejpam-2494	98	3	)	)	PUNCT
ejpam-2494	98	4	)	)	PUNCT
ejpam-2494	98	5	and	and	CCONJ
ejpam-2494	98	6	thus	thus	ADV
ejpam-2494	98	7	h	h	NOUN
ejpam-2494	98	8	is	be	AUX
ejpam-2494	98	9	semi	semi	ADJ
ejpam-2494	98	10	-	-	ADJ
ejpam-2494	98	11	open	open	ADJ
ejpam-2494	98	12	.	.	PUNCT
ejpam-2494	99	1	theorem	theorem	NOUN
ejpam-2494	99	2	2	2	NUM
ejpam-2494	99	3	.	.	X
ejpam-2494	99	4	for	for	ADP
ejpam-2494	99	5	a	a	DET
ejpam-2494	99	6	subset	subset	NOUN
ejpam-2494	99	7	of	of	ADP
ejpam-2494	99	8	space	space	NOUN
ejpam-2494	99	9	(	(	PUNCT
ejpam-2494	99	10	x	x	X
ejpam-2494	99	11	,	,	PUNCT
ejpam-2494	99	12	τ	τ	PROPN
ejpam-2494	99	13	)	)	PUNCT
ejpam-2494	99	14	,	,	PUNCT
ejpam-2494	99	15	the	the	DET
ejpam-2494	99	16	following	follow	VERB
ejpam-2494	99	17	properties	property	NOUN
ejpam-2494	99	18	hold	hold	VERB
ejpam-2494	99	19	:	:	PUNCT
ejpam-2494	99	20	(	(	PUNCT
ejpam-2494	99	21	i	i	NOUN
ejpam-2494	99	22	)	)	PUNCT
ejpam-2494	99	23	every	every	DET
ejpam-2494	99	24	ω	ω	NOUN
ejpam-2494	99	25	-	-	ADJ
ejpam-2494	99	26	open	open	ADJ
ejpam-2494	99	27	set	set	NOUN
ejpam-2494	99	28	is	be	AUX
ejpam-2494	99	29	semi	semi	ADJ
ejpam-2494	99	30	-	-	ADJ
ejpam-2494	99	31	ω	ω	ADJ
ejpam-2494	99	32	-	-	ADJ
ejpam-2494	99	33	open	open	ADJ
ejpam-2494	99	34	.	.	PUNCT
ejpam-2494	100	1	(	(	PUNCT
ejpam-2494	100	2	ii	ii	NOUN
ejpam-2494	100	3	)	)	PUNCT
ejpam-2494	100	4	every	every	DET
ejpam-2494	100	5	α−ω	α−ω	PROPN
ejpam-2494	100	6	-	-	PUNCT
ejpam-2494	100	7	open	open	ADJ
ejpam-2494	100	8	set	set	NOUN
ejpam-2494	100	9	is	be	AUX
ejpam-2494	100	10	semi	semi	ADJ
ejpam-2494	100	11	-	-	ADJ
ejpam-2494	100	12	ω	ω	ADJ
ejpam-2494	100	13	-	-	ADJ
ejpam-2494	100	14	open	open	ADJ
ejpam-2494	100	15	.	.	PUNCT
ejpam-2494	101	1	(	(	PUNCT
ejpam-2494	101	2	iii	iii	NOUN
ejpam-2494	101	3	)	)	PUNCT
ejpam-2494	101	4	every	every	DET
ejpam-2494	101	5	semi	semi	ADJ
ejpam-2494	101	6	-	-	ADJ
ejpam-2494	101	7	ω	ω	ADJ
ejpam-2494	101	8	-	-	ADJ
ejpam-2494	101	9	open	open	ADJ
ejpam-2494	101	10	set	set	NOUN
ejpam-2494	101	11	is	be	AUX
ejpam-2494	101	12	β	β	NOUN
ejpam-2494	101	13	−ω	−ω	ADJ
ejpam-2494	101	14	-	-	ADJ
ejpam-2494	101	15	open	open	ADJ
ejpam-2494	101	16	.	.	PUNCT
ejpam-2494	102	1	(	(	PUNCT
ejpam-2494	102	2	iv	iv	X
ejpam-2494	102	3	)	)	PUNCT
ejpam-2494	102	4	every	every	DET
ejpam-2494	102	5	semi	semi	ADJ
ejpam-2494	102	6	-	-	ADJ
ejpam-2494	102	7	ω	ω	ADJ
ejpam-2494	102	8	-	-	ADJ
ejpam-2494	102	9	open	open	ADJ
ejpam-2494	102	10	set	set	NOUN
ejpam-2494	102	11	is	be	AUX
ejpam-2494	102	12	b−ω	b−ω	NOUN
ejpam-2494	102	13	-	-	PUNCT
ejpam-2494	102	14	open	open	ADJ
ejpam-2494	102	15	.	.	PUNCT
ejpam-2494	103	1	proof	proof	NOUN
ejpam-2494	103	2	.	.	PUNCT
ejpam-2494	104	1	(	(	PUNCT
ejpam-2494	104	2	i	i	NOUN
ejpam-2494	104	3	)	)	PUNCT
ejpam-2494	104	4	.	.	PUNCT
ejpam-2494	105	1	if	if	SCONJ
ejpam-2494	105	2	h	h	NOUN
ejpam-2494	105	3	is	be	AUX
ejpam-2494	105	4	an	an	DET
ejpam-2494	105	5	ω	ω	ADJ
ejpam-2494	105	6	-	-	ADJ
ejpam-2494	105	7	open	open	ADJ
ejpam-2494	105	8	set	set	NOUN
ejpam-2494	105	9	,	,	PUNCT
ejpam-2494	105	10	then	then	ADV
ejpam-2494	105	11	h	h	NOUN
ejpam-2494	105	12	=	=	SYM
ejpam-2494	105	13	intω(h	intω(h	PROPN
ejpam-2494	105	14	)	)	PUNCT
ejpam-2494	105	15	⊂	⊂	PROPN
ejpam-2494	105	16	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	105	17	)	)	PUNCT
ejpam-2494	105	18	)	)	PUNCT
ejpam-2494	105	19	.	.	PUNCT
ejpam-2494	106	1	therefore	therefore	ADV
ejpam-2494	106	2	h	h	PROPN
ejpam-2494	106	3	is	be	AUX
ejpam-2494	106	4	semiω	semiω	NOUN
ejpam-2494	106	5	-	-	PUNCT
ejpam-2494	106	6	open	open	ADJ
ejpam-2494	106	7	.	.	PUNCT
ejpam-2494	107	1	(	(	PUNCT
ejpam-2494	107	2	ii	ii	NOUN
ejpam-2494	107	3	)	)	PUNCT
ejpam-2494	107	4	.	.	PUNCT
ejpam-2494	108	1	if	if	SCONJ
ejpam-2494	108	2	h	h	NOUN
ejpam-2494	108	3	is	be	AUX
ejpam-2494	108	4	an	an	DET
ejpam-2494	108	5	α−ω	α−ω	NOUN
ejpam-2494	108	6	-	-	PUNCT
ejpam-2494	108	7	open	open	ADJ
ejpam-2494	108	8	set	set	NOUN
ejpam-2494	108	9	,	,	PUNCT
ejpam-2494	108	10	then	then	ADV
ejpam-2494	108	11	h	h	PROPN
ejpam-2494	108	12	⊂	⊂	PROPN
ejpam-2494	108	13	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	108	14	)	)	PUNCT
ejpam-2494	108	15	)	)	PUNCT
ejpam-2494	108	16	)	)	PUNCT
ejpam-2494	109	1	⊂	⊂	PROPN
ejpam-2494	109	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	109	3	)	)	PUNCT
ejpam-2494	109	4	)	)	PUNCT
ejpam-2494	109	5	.	.	PUNCT
ejpam-2494	110	1	therefore	therefore	ADV
ejpam-2494	110	2	h	h	PROPN
ejpam-2494	110	3	is	be	AUX
ejpam-2494	110	4	semi	semi	ADJ
ejpam-2494	110	5	-	-	ADJ
ejpam-2494	110	6	ω	ω	ADJ
ejpam-2494	110	7	-	-	ADJ
ejpam-2494	110	8	open	open	ADJ
ejpam-2494	110	9	.	.	PUNCT
ejpam-2494	111	1	(	(	PUNCT
ejpam-2494	111	2	iii	iii	NOUN
ejpam-2494	111	3	)	)	PUNCT
ejpam-2494	111	4	.	.	PUNCT
ejpam-2494	112	1	if	if	SCONJ
ejpam-2494	112	2	h	h	NOUN
ejpam-2494	112	3	is	be	AUX
ejpam-2494	112	4	an	an	DET
ejpam-2494	112	5	semi	semi	ADJ
ejpam-2494	112	6	-	-	ADJ
ejpam-2494	112	7	ω	ω	ADJ
ejpam-2494	112	8	-	-	ADJ
ejpam-2494	112	9	open	open	ADJ
ejpam-2494	112	10	set	set	NOUN
ejpam-2494	112	11	,	,	PUNCT
ejpam-2494	112	12	then	then	ADV
ejpam-2494	112	13	h	h	PROPN
ejpam-2494	112	14	⊂	⊂	PROPN
ejpam-2494	112	15	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	112	16	)	)	PUNCT
ejpam-2494	112	17	)	)	PUNCT
ejpam-2494	113	1	⊂	⊂	PROPN
ejpam-2494	113	2	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	113	3	)	)	PUNCT
ejpam-2494	113	4	)	)	PUNCT
ejpam-2494	113	5	)	)	PUNCT
ejpam-2494	113	6	.	.	PUNCT
ejpam-2494	114	1	therefore	therefore	ADV
ejpam-2494	114	2	h	h	PROPN
ejpam-2494	114	3	is	be	AUX
ejpam-2494	114	4	β	β	X
ejpam-2494	114	5	−ω	−ω	ADJ
ejpam-2494	114	6	-	-	ADJ
ejpam-2494	114	7	open	open	ADJ
ejpam-2494	114	8	.	.	PUNCT
ejpam-2494	115	1	(	(	PUNCT
ejpam-2494	115	2	iv	iv	X
ejpam-2494	115	3	)	)	PUNCT
ejpam-2494	115	4	.	.	PUNCT
ejpam-2494	116	1	if	if	SCONJ
ejpam-2494	116	2	h	h	NOUN
ejpam-2494	116	3	is	be	AUX
ejpam-2494	116	4	an	an	DET
ejpam-2494	116	5	semi	semi	ADJ
ejpam-2494	116	6	-	-	ADJ
ejpam-2494	116	7	ω	ω	ADJ
ejpam-2494	116	8	-	-	ADJ
ejpam-2494	116	9	open	open	ADJ
ejpam-2494	116	10	set	set	NOUN
ejpam-2494	116	11	,	,	PUNCT
ejpam-2494	116	12	then	then	ADV
ejpam-2494	116	13	h	h	PROPN
ejpam-2494	116	14	⊂	⊂	PROPN
ejpam-2494	116	15	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	116	16	)	)	PUNCT
ejpam-2494	116	17	)	)	PUNCT
ejpam-2494	117	1	⊂	⊂	PROPN
ejpam-2494	117	2	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	117	3	)	)	PUNCT
ejpam-2494	117	4	)	)	PUNCT
ejpam-2494	118	1	∪	∪	ADP
ejpam-2494	118	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	118	3	)	)	PUNCT
ejpam-2494	118	4	)	)	PUNCT
ejpam-2494	118	5	.	.	PUNCT
ejpam-2494	119	1	therefore	therefore	ADV
ejpam-2494	119	2	h	h	PROPN
ejpam-2494	119	3	is	be	AUX
ejpam-2494	119	4	b−ω	b−ω	NOUN
ejpam-2494	119	5	-	-	PUNCT
ejpam-2494	119	6	open	open	ADJ
ejpam-2494	119	7	.	.	PUNCT
ejpam-2494	120	1	the	the	DET
ejpam-2494	120	2	following	follow	VERB
ejpam-2494	120	3	examples	example	NOUN
ejpam-2494	120	4	support	support	VERB
ejpam-2494	120	5	that	that	SCONJ
ejpam-2494	120	6	the	the	DET
ejpam-2494	120	7	separate	separate	ADJ
ejpam-2494	120	8	converses	converse	NOUN
ejpam-2494	120	9	of	of	ADP
ejpam-2494	120	10	theorem	theorem	ADJ
ejpam-2494	120	11	2	2	NUM
ejpam-2494	120	12	are	be	AUX
ejpam-2494	120	13	not	not	PART
ejpam-2494	120	14	true	true	ADJ
ejpam-2494	120	15	in	in	ADP
ejpam-2494	120	16	general	general	ADJ
ejpam-2494	120	17	.	.	PUNCT
ejpam-2494	121	1	example	example	NOUN
ejpam-2494	122	1	4	4	X
ejpam-2494	122	2	.	.	PUNCT
ejpam-2494	122	3	let	let	VERB
ejpam-2494	122	4	x	x	PUNCT
ejpam-2494	122	5	=	=	PUNCT
ejpam-2494	122	6	r	r	NOUN
ejpam-2494	122	7	with	with	ADP
ejpam-2494	122	8	the	the	DET
ejpam-2494	122	9	usual	usual	ADJ
ejpam-2494	122	10	topology	topology	NOUN
ejpam-2494	122	11	τu	τu	PROPN
ejpam-2494	122	12	.	.	PUNCT
ejpam-2494	123	1	(	(	PUNCT
ejpam-2494	123	2	i	i	NOUN
ejpam-2494	123	3	)	)	PUNCT
ejpam-2494	123	4	let	let	VERB
ejpam-2494	123	5	h	h	NOUN
ejpam-2494	123	6	=	=	PUNCT
ejpam-2494	123	7	(	(	PUNCT
ejpam-2494	123	8	0,1	0,1	NUM
ejpam-2494	123	9	]	]	PUNCT
ejpam-2494	123	10	.	.	PUNCT
ejpam-2494	124	1	then	then	ADV
ejpam-2494	124	2	h	h	PROPN
ejpam-2494	124	3	is	be	AUX
ejpam-2494	124	4	semi	semi	ADJ
ejpam-2494	124	5	-	-	ADJ
ejpam-2494	124	6	ω	ω	ADJ
ejpam-2494	124	7	-	-	ADJ
ejpam-2494	124	8	open	open	ADJ
ejpam-2494	124	9	set	set	NOUN
ejpam-2494	124	10	but	but	CCONJ
ejpam-2494	124	11	not	not	PART
ejpam-2494	124	12	ω	ω	VERB
ejpam-2494	124	13	-	-	NOUN
ejpam-2494	124	14	open	open	ADJ
ejpam-2494	124	15	,	,	PUNCT
ejpam-2494	124	16	since	since	SCONJ
ejpam-2494	124	17	h	h	NOUN
ejpam-2494	124	18	=	=	SYM
ejpam-2494	124	19	(	(	PUNCT
ejpam-2494	124	20	0,1	0,1	NUM
ejpam-2494	124	21	]	]	PUNCT
ejpam-2494	124	22	6=	6=	NUM
ejpam-2494	124	23	(	(	PUNCT
ejpam-2494	124	24	0,1	0,1	NUM
ejpam-2494	124	25	)	)	PUNCT
ejpam-2494	124	26	=	=	SYM
ejpam-2494	124	27	intω(h	intω(h	NOUN
ejpam-2494	124	28	)	)	PUNCT
ejpam-2494	124	29	.	.	PUNCT
ejpam-2494	125	1	(	(	PUNCT
ejpam-2494	125	2	ii	ii	NOUN
ejpam-2494	125	3	)	)	PUNCT
ejpam-2494	125	4	let	let	VERB
ejpam-2494	125	5	h	h	NOUN
ejpam-2494	125	6	=	=	PUNCT
ejpam-2494	125	7	(	(	PUNCT
ejpam-2494	125	8	0,1	0,1	NUM
ejpam-2494	125	9	]	]	PUNCT
ejpam-2494	125	10	.	.	PUNCT
ejpam-2494	126	1	then	then	ADV
ejpam-2494	126	2	h	h	PROPN
ejpam-2494	126	3	is	be	AUX
ejpam-2494	126	4	semi	semi	ADJ
ejpam-2494	126	5	-	-	ADJ
ejpam-2494	126	6	ω	ω	ADJ
ejpam-2494	126	7	-	-	ADJ
ejpam-2494	126	8	open	open	ADJ
ejpam-2494	126	9	set	set	NOUN
ejpam-2494	126	10	but	but	CCONJ
ejpam-2494	126	11	not	not	PART
ejpam-2494	126	12	α−ω	α−ω	NOUN
ejpam-2494	126	13	-	-	VERB
ejpam-2494	126	14	open	open	ADJ
ejpam-2494	126	15	,	,	PUNCT
ejpam-2494	126	16	since	since	SCONJ
ejpam-2494	126	17	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	126	18	)	)	PUNCT
ejpam-2494	126	19	)	)	PUNCT
ejpam-2494	126	20	)	)	PUNCT
ejpam-2494	127	1	=	=	PUNCT
ejpam-2494	127	2	intω(cl(0,1	intω(cl(0,1	NOUN
ejpam-2494	127	3	)	)	PUNCT
ejpam-2494	127	4	)	)	PUNCT
ejpam-2494	128	1	=	=	PUNCT
ejpam-2494	128	2	intω([0,1	intω([0,1	NOUN
ejpam-2494	128	3	]	]	PUNCT
ejpam-2494	128	4	)	)	PUNCT
ejpam-2494	128	5	=	=	SYM
ejpam-2494	128	6	(	(	PUNCT
ejpam-2494	128	7	0,1	0,1	NUM
ejpam-2494	128	8	)	)	PUNCT
ejpam-2494	128	9	.	.	PUNCT
ejpam-2494	129	1	(	(	PUNCT
ejpam-2494	129	2	iii	iii	X
ejpam-2494	129	3	)	)	PUNCT
ejpam-2494	129	4	let	let	VERB
ejpam-2494	129	5	h	h	NOUN
ejpam-2494	129	6	=	=	PUNCT
ejpam-2494	130	1	[	[	X
ejpam-2494	130	2	0,1]∩q	0,1]∩q	NUM
ejpam-2494	130	3	.	.	PUNCT
ejpam-2494	131	1	then	then	ADV
ejpam-2494	131	2	h	h	PROPN
ejpam-2494	131	3	is	be	AUX
ejpam-2494	131	4	β	β	X
ejpam-2494	131	5	−ω	−ω	ADJ
ejpam-2494	131	6	-	-	ADJ
ejpam-2494	131	7	open	open	ADJ
ejpam-2494	131	8	set	set	NOUN
ejpam-2494	131	9	but	but	CCONJ
ejpam-2494	131	10	not	not	PART
ejpam-2494	131	11	semi	semi	ADJ
ejpam-2494	131	12	-	-	ADJ
ejpam-2494	131	13	ω	ω	VERB
ejpam-2494	131	14	-	-	ADJ
ejpam-2494	131	15	open	open	ADJ
ejpam-2494	131	16	,	,	PUNCT
ejpam-2494	131	17	since	since	SCONJ
ejpam-2494	131	18	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	131	19	)	)	PUNCT
ejpam-2494	131	20	)	)	PUNCT
ejpam-2494	132	1	=	=	PRON
ejpam-2494	132	2	cl(φ	cl(φ	X
ejpam-2494	132	3	)	)	PUNCT
ejpam-2494	132	4	=	=	SYM
ejpam-2494	133	1	φ	φ	PROPN
ejpam-2494	133	2	.	.	PUNCT
ejpam-2494	133	3	(	(	PUNCT
ejpam-2494	133	4	iv	iv	X
ejpam-2494	133	5	)	)	PUNCT
ejpam-2494	133	6	let	let	VERB
ejpam-2494	133	7	h	h	NOUN
ejpam-2494	134	1	=	=	PUNCT
ejpam-2494	134	2	q.	q.	PROPN
ejpam-2494	134	3	then	then	ADV
ejpam-2494	134	4	h	h	PROPN
ejpam-2494	134	5	is	be	AUX
ejpam-2494	134	6	b−ω	b−ω	NOUN
ejpam-2494	134	7	-	-	PUNCT
ejpam-2494	134	8	open	open	ADJ
ejpam-2494	134	9	set	set	NOUN
ejpam-2494	134	10	but	but	CCONJ
ejpam-2494	134	11	not	not	PART
ejpam-2494	134	12	semi	semi	ADJ
ejpam-2494	134	13	-	-	ADJ
ejpam-2494	134	14	ω	ω	VERB
ejpam-2494	134	15	-	-	ADJ
ejpam-2494	134	16	open	open	ADJ
ejpam-2494	134	17	,	,	PUNCT
ejpam-2494	134	18	since	since	SCONJ
ejpam-2494	134	19	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	134	20	)	)	PUNCT
ejpam-2494	134	21	)	)	PUNCT
ejpam-2494	135	1	=	=	PRON
ejpam-2494	135	2	cl(φ	cl(φ	X
ejpam-2494	135	3	)	)	PUNCT
ejpam-2494	135	4	=	=	SYM
ejpam-2494	135	5	φ	φ	X
ejpam-2494	135	6	.	.	PUNCT
ejpam-2494	135	7	theorem	theorem	NOUN
ejpam-2494	135	8	3	3	X
ejpam-2494	135	9	.	.	PUNCT
ejpam-2494	136	1	let	let	VERB
ejpam-2494	136	2	h	h	PRON
ejpam-2494	136	3	be	be	AUX
ejpam-2494	136	4	a	a	DET
ejpam-2494	136	5	subset	subset	NOUN
ejpam-2494	136	6	of	of	ADP
ejpam-2494	136	7	a	a	DET
ejpam-2494	136	8	space	space	NOUN
ejpam-2494	136	9	(	(	PUNCT
ejpam-2494	136	10	x	x	X
ejpam-2494	136	11	,	,	PUNCT
ejpam-2494	136	12	τ	τ	PROPN
ejpam-2494	136	13	)	)	PUNCT
ejpam-2494	136	14	.	.	PUNCT
ejpam-2494	137	1	then	then	ADV
ejpam-2494	137	2	h	h	PROPN
ejpam-2494	137	3	is	be	AUX
ejpam-2494	137	4	α−ω	α−ω	NOUN
ejpam-2494	137	5	-	-	PUNCT
ejpam-2494	137	6	open	open	ADJ
ejpam-2494	137	7	if	if	SCONJ
ejpam-2494	137	8	and	and	CCONJ
ejpam-2494	137	9	only	only	ADV
ejpam-2494	137	10	if	if	SCONJ
ejpam-2494	137	11	it	it	PRON
ejpam-2494	137	12	is	be	AUX
ejpam-2494	137	13	semi	semi	ADJ
ejpam-2494	137	14	-	-	ADJ
ejpam-2494	137	15	ωopen	ωopen	ADJ
ejpam-2494	137	16	and	and	CCONJ
ejpam-2494	137	17	pre	pre	ADJ
ejpam-2494	137	18	-	-	ADJ
ejpam-2494	137	19	ω	ω	VERB
ejpam-2494	137	20	-	-	ADJ
ejpam-2494	137	21	open	open	ADJ
ejpam-2494	137	22	.	.	PUNCT
ejpam-2494	138	1	proof	proof	NOUN
ejpam-2494	138	2	.	.	PUNCT
ejpam-2494	139	1	let	let	VERB
ejpam-2494	139	2	h	h	PRON
ejpam-2494	139	3	be	be	AUX
ejpam-2494	139	4	an	an	DET
ejpam-2494	139	5	α−ω	α−ω	NOUN
ejpam-2494	139	6	-	-	NOUN
ejpam-2494	139	7	open	open	ADJ
ejpam-2494	139	8	.	.	PUNCT
ejpam-2494	140	1	then	then	ADV
ejpam-2494	140	2	h	h	PROPN
ejpam-2494	140	3	⊂	⊂	PROPN
ejpam-2494	140	4	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	140	5	)	)	PUNCT
ejpam-2494	140	6	)	)	PUNCT
ejpam-2494	140	7	)	)	PUNCT
ejpam-2494	140	8	.	.	PUNCT
ejpam-2494	141	1	it	it	PRON
ejpam-2494	141	2	implies	imply	VERB
ejpam-2494	141	3	that	that	SCONJ
ejpam-2494	141	4	h	h	PROPN
ejpam-2494	141	5	⊂	⊂	PROPN
ejpam-2494	141	6	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	141	7	)	)	PUNCT
ejpam-2494	141	8	)	)	PUNCT
ejpam-2494	141	9	)	)	PUNCT
ejpam-2494	142	1	⊂	⊂	PROPN
ejpam-2494	142	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	142	3	)	)	PUNCT
ejpam-2494	142	4	)	)	PUNCT
ejpam-2494	143	1	and	and	CCONJ
ejpam-2494	143	2	h	h	PROPN
ejpam-2494	143	3	⊂	⊂	PROPN
ejpam-2494	143	4	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	143	5	)	)	PUNCT
ejpam-2494	143	6	)	)	PUNCT
ejpam-2494	143	7	)	)	PUNCT
ejpam-2494	144	1	⊂	⊂	PROPN
ejpam-2494	144	2	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	144	3	)	)	PUNCT
ejpam-2494	144	4	)	)	PUNCT
ejpam-2494	144	5	.	.	PUNCT
ejpam-2494	145	1	thus	thus	ADV
ejpam-2494	145	2	h	h	NOUN
ejpam-2494	145	3	is	be	AUX
ejpam-2494	145	4	semi	semi	ADJ
ejpam-2494	145	5	-	-	ADJ
ejpam-2494	145	6	ω	ω	ADJ
ejpam-2494	145	7	-	-	ADJ
ejpam-2494	145	8	open	open	ADJ
ejpam-2494	145	9	and	and	CCONJ
ejpam-2494	145	10	pre	pre	ADJ
ejpam-2494	145	11	-	-	ADJ
ejpam-2494	145	12	ω	ω	VERB
ejpam-2494	145	13	-	-	NOUN
ejpam-2494	145	14	open	open	ADJ
ejpam-2494	145	15	.	.	PUNCT
ejpam-2494	146	1	conversely	conversely	ADV
ejpam-2494	146	2	,	,	PUNCT
ejpam-2494	146	3	let	let	VERB
ejpam-2494	146	4	h	h	PRON
ejpam-2494	146	5	be	be	AUX
ejpam-2494	146	6	semi	semi	ADJ
ejpam-2494	146	7	-	-	ADJ
ejpam-2494	146	8	ω	ω	ADJ
ejpam-2494	146	9	-	-	ADJ
ejpam-2494	146	10	open	open	ADJ
ejpam-2494	146	11	and	and	CCONJ
ejpam-2494	146	12	pre	pre	ADJ
ejpam-2494	146	13	-	-	ADJ
ejpam-2494	146	14	ω	ω	VERB
ejpam-2494	146	15	-	-	NOUN
ejpam-2494	146	16	open	open	ADJ
ejpam-2494	146	17	.	.	PUNCT
ejpam-2494	147	1	then	then	ADV
ejpam-2494	147	2	we	we	PRON
ejpam-2494	147	3	have	have	VERB
ejpam-2494	147	4	h	h	NOUN
ejpam-2494	147	5	⊂	⊂	PROPN
ejpam-2494	147	6	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	147	7	)	)	PUNCT
ejpam-2494	147	8	)	)	PUNCT
ejpam-2494	148	1	and	and	CCONJ
ejpam-2494	148	2	h	h	PROPN
ejpam-2494	148	3	⊂	⊂	PROPN
ejpam-2494	148	4	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	148	5	)	)	PUNCT
ejpam-2494	148	6	)	)	PUNCT
ejpam-2494	148	7	.	.	PUNCT
ejpam-2494	149	1	hence	hence	ADV
ejpam-2494	149	2	h	h	PROPN
ejpam-2494	149	3	⊂	⊂	PROPN
ejpam-2494	149	4	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	149	5	)	)	PUNCT
ejpam-2494	149	6	)	)	PUNCT
ejpam-2494	150	1	⊂	⊂	PROPN
ejpam-2494	150	2	intω(cl(intω(h)))which	intω(cl(intω(h)))which	PROPN
ejpam-2494	150	3	implies	imply	VERB
ejpam-2494	150	4	that	that	SCONJ
ejpam-2494	150	5	h	h	NOUN
ejpam-2494	150	6	is	be	AUX
ejpam-2494	150	7	α−ωopen	α−ωopen	NOUN
ejpam-2494	150	8	.	.	PUNCT
ejpam-2494	151	1	o.	o.	PROPN
ejpam-2494	151	2	ravi	ravi	PROPN
ejpam-2494	151	3	,	,	PUNCT
ejpam-2494	151	4	i.	i.	NOUN
ejpam-2494	151	5	rajasekaran	rajasekaran	PROPN
ejpam-2494	151	6	,	,	PUNCT
ejpam-2494	151	7	s.	s.	PROPN
ejpam-2494	151	8	kanna	kanna	PROPN
ejpam-2494	151	9	and	and	CCONJ
ejpam-2494	151	10	m.	m.	NOUN
ejpam-2494	151	11	paranjothi	paranjothi	PROPN
ejpam-2494	151	12	/	/	SYM
ejpam-2494	151	13	eur	eur	PROPN
ejpam-2494	151	14	.	.	PUNCT
ejpam-2494	152	1	j.	j.	PROPN
ejpam-2494	152	2	pure	pure	PROPN
ejpam-2494	152	3	appl	appl	PROPN
ejpam-2494	152	4	.	.	PROPN
ejpam-2494	152	5	math	math	PROPN
ejpam-2494	152	6	,	,	PUNCT
ejpam-2494	152	7	9	9	NUM
ejpam-2494	152	8	(	(	PUNCT
ejpam-2494	152	9	2016	2016	NUM
ejpam-2494	152	10	)	)	PUNCT
ejpam-2494	152	11	,	,	PUNCT
ejpam-2494	152	12	152	152	NUM
ejpam-2494	152	13	-	-	SYM
ejpam-2494	152	14	164	164	NUM
ejpam-2494	152	15	156	156	NUM
ejpam-2494	152	16	remark	remark	NOUN
ejpam-2494	152	17	3	3	NUM
ejpam-2494	152	18	.	.	PUNCT
ejpam-2494	153	1	the	the	DET
ejpam-2494	153	2	concepts	concept	NOUN
ejpam-2494	153	3	of	of	ADP
ejpam-2494	153	4	semi	semi	ADJ
ejpam-2494	153	5	-	-	ADJ
ejpam-2494	153	6	ω	ω	ADJ
ejpam-2494	153	7	-	-	PUNCT
ejpam-2494	153	8	openness	openness	NOUN
ejpam-2494	153	9	and	and	CCONJ
ejpam-2494	153	10	pre	pre	ADJ
ejpam-2494	153	11	-	-	ADJ
ejpam-2494	153	12	ω	ω	ADJ
ejpam-2494	153	13	-	-	PUNCT
ejpam-2494	153	14	openness	openness	NOUN
ejpam-2494	153	15	are	be	AUX
ejpam-2494	153	16	independent	independent	ADJ
ejpam-2494	153	17	.	.	PUNCT
ejpam-2494	153	18	example	example	NOUN
ejpam-2494	154	1	5	5	NUM
ejpam-2494	154	2	.	.	PUNCT
ejpam-2494	154	3	let	let	VERB
ejpam-2494	154	4	x	x	PUNCT
ejpam-2494	154	5	=	=	PUNCT
ejpam-2494	154	6	r	r	NOUN
ejpam-2494	154	7	with	with	ADP
ejpam-2494	154	8	the	the	DET
ejpam-2494	154	9	usual	usual	ADJ
ejpam-2494	154	10	topology	topology	NOUN
ejpam-2494	154	11	τu	τu	PROPN
ejpam-2494	154	12	.	.	PUNCT
ejpam-2494	155	1	the	the	DET
ejpam-2494	155	2	interval	interval	NOUN
ejpam-2494	155	3	h	h	NOUN
ejpam-2494	155	4	=	=	PUNCT
ejpam-2494	155	5	(	(	PUNCT
ejpam-2494	155	6	0,1	0,1	NUM
ejpam-2494	155	7	]	]	PUNCT
ejpam-2494	155	8	is	be	AUX
ejpam-2494	155	9	semi	semi	ADJ
ejpam-2494	155	10	-	-	ADJ
ejpam-2494	155	11	ω	ω	ADJ
ejpam-2494	155	12	-	-	ADJ
ejpam-2494	155	13	open	open	ADJ
ejpam-2494	155	14	but	but	CCONJ
ejpam-2494	155	15	not	not	PART
ejpam-2494	155	16	pre	pre	ADJ
ejpam-2494	155	17	-	-	ADJ
ejpam-2494	155	18	ω	ω	VERB
ejpam-2494	155	19	-	-	ADJ
ejpam-2494	155	20	open	open	ADJ
ejpam-2494	155	21	,	,	PUNCT
ejpam-2494	155	22	since	since	SCONJ
ejpam-2494	155	23	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	155	24	)	)	PUNCT
ejpam-2494	155	25	)	)	PUNCT
ejpam-2494	156	1	=	=	PUNCT
ejpam-2494	156	2	intω([0,1	intω([0,1	NOUN
ejpam-2494	156	3	]	]	PUNCT
ejpam-2494	156	4	)	)	PUNCT
ejpam-2494	156	5	=	=	SYM
ejpam-2494	156	6	(	(	PUNCT
ejpam-2494	156	7	0,1	0,1	NUM
ejpam-2494	156	8	)	)	PUNCT
ejpam-2494	156	9	.	.	PUNCT
ejpam-2494	157	1	example	example	NOUN
ejpam-2494	158	1	6	6	NUM
ejpam-2494	158	2	.	.	PUNCT
ejpam-2494	159	1	let	let	VERB
ejpam-2494	159	2	x	x	PUNCT
ejpam-2494	159	3	=	=	PUNCT
ejpam-2494	159	4	r	r	NOUN
ejpam-2494	159	5	with	with	ADP
ejpam-2494	159	6	the	the	DET
ejpam-2494	159	7	usual	usual	ADJ
ejpam-2494	159	8	topology	topology	NOUN
ejpam-2494	159	9	τu	τu	PROPN
ejpam-2494	159	10	.	.	PUNCT
ejpam-2494	160	1	let	let	VERB
ejpam-2494	160	2	h	h	NOUN
ejpam-2494	161	1	=	=	PUNCT
ejpam-2494	161	2	q.	q.	PROPN
ejpam-2494	161	3	then	then	ADV
ejpam-2494	161	4	h	h	PROPN
ejpam-2494	161	5	is	be	AUX
ejpam-2494	161	6	pre	pre	ADJ
ejpam-2494	161	7	-	-	ADJ
ejpam-2494	161	8	ω	ω	ADV
ejpam-2494	161	9	-	-	ADJ
ejpam-2494	161	10	open	open	ADJ
ejpam-2494	161	11	but	but	CCONJ
ejpam-2494	161	12	not	not	PART
ejpam-2494	161	13	semi	semi	ADJ
ejpam-2494	161	14	-	-	ADJ
ejpam-2494	161	15	ω	ω	VERB
ejpam-2494	161	16	-	-	ADJ
ejpam-2494	161	17	open	open	ADJ
ejpam-2494	161	18	,	,	PUNCT
ejpam-2494	161	19	since	since	SCONJ
ejpam-2494	161	20	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	161	21	)	)	PUNCT
ejpam-2494	161	22	)	)	PUNCT
ejpam-2494	162	1	=	=	PRON
ejpam-2494	162	2	cl(φ	cl(φ	X
ejpam-2494	162	3	)	)	PUNCT
ejpam-2494	162	4	=	=	SYM
ejpam-2494	163	1	φ	φ	X
ejpam-2494	163	2	.	.	PUNCT
ejpam-2494	163	3	proposition	proposition	NOUN
ejpam-2494	163	4	2	2	NUM
ejpam-2494	163	5	.	.	PUNCT
ejpam-2494	164	1	the	the	DET
ejpam-2494	164	2	intersection	intersection	NOUN
ejpam-2494	164	3	of	of	ADP
ejpam-2494	164	4	a	a	DET
ejpam-2494	164	5	semi	semi	ADJ
ejpam-2494	164	6	-	-	ADJ
ejpam-2494	164	7	ω	ω	ADJ
ejpam-2494	164	8	-	-	ADJ
ejpam-2494	164	9	open	open	ADJ
ejpam-2494	164	10	set	set	NOUN
ejpam-2494	164	11	and	and	CCONJ
ejpam-2494	164	12	an	an	DET
ejpam-2494	164	13	open	open	ADJ
ejpam-2494	164	14	set	set	NOUN
ejpam-2494	164	15	is	be	AUX
ejpam-2494	164	16	semi	semi	ADJ
ejpam-2494	164	17	-	-	ADJ
ejpam-2494	164	18	ω	ω	ADJ
ejpam-2494	164	19	-	-	ADJ
ejpam-2494	164	20	open	open	ADJ
ejpam-2494	164	21	.	.	PUNCT
ejpam-2494	165	1	proof	proof	NOUN
ejpam-2494	165	2	.	.	PUNCT
ejpam-2494	166	1	let	let	VERB
ejpam-2494	166	2	h	h	PRON
ejpam-2494	166	3	be	be	AUX
ejpam-2494	166	4	a	a	DET
ejpam-2494	166	5	semi	semi	ADJ
ejpam-2494	166	6	-	-	ADJ
ejpam-2494	166	7	ω	ω	ADJ
ejpam-2494	166	8	-	-	ADJ
ejpam-2494	166	9	open	open	ADJ
ejpam-2494	166	10	and	and	CCONJ
ejpam-2494	166	11	u	u	NOUN
ejpam-2494	166	12	be	be	VERB
ejpam-2494	166	13	an	an	DET
ejpam-2494	166	14	open	open	ADJ
ejpam-2494	166	15	set	set	NOUN
ejpam-2494	166	16	in	in	ADP
ejpam-2494	166	17	x.	x.	NOUN
ejpam-2494	167	1	then	then	ADV
ejpam-2494	167	2	h	h	PROPN
ejpam-2494	167	3	⊂	⊂	PROPN
ejpam-2494	167	4	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	167	5	)	)	PUNCT
ejpam-2494	167	6	)	)	PUNCT
ejpam-2494	167	7	and	and	CCONJ
ejpam-2494	167	8	int(u	int(u	ADV
ejpam-2494	167	9	)	)	PUNCT
ejpam-2494	167	10	=	=	SYM
ejpam-2494	167	11	u	u	NOUN
ejpam-2494	167	12	.	.	PUNCT
ejpam-2494	168	1	by	by	ADP
ejpam-2494	168	2	lemma	lemma	PROPN
ejpam-2494	168	3	3	3	NUM
ejpam-2494	168	4	,	,	PUNCT
ejpam-2494	168	5	we	we	PRON
ejpam-2494	168	6	have	have	VERB
ejpam-2494	168	7	u	u	NOUN
ejpam-2494	168	8	∩	∩	ADJ
ejpam-2494	168	9	h	h	NOUN
ejpam-2494	168	10	⊂u	⊂u	PROPN
ejpam-2494	168	11	∩	∩	X
ejpam-2494	168	12	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	168	13	)	)	PUNCT
ejpam-2494	168	14	)	)	PUNCT
ejpam-2494	169	1	⊂	⊂	PRON
ejpam-2494	169	2	cl(u	cl(u	PUNCT
ejpam-2494	169	3	∩	∩	ADJ
ejpam-2494	169	4	intω(h	intω(h	NOUN
ejpam-2494	169	5	)	)	PUNCT
ejpam-2494	169	6	)	)	PUNCT
ejpam-2494	170	1	=	=	X
ejpam-2494	170	2	cl(int(u)∩	cl(int(u)∩	PROPN
ejpam-2494	170	3	intω(h	intω(h	NUM
ejpam-2494	170	4	)	)	PUNCT
ejpam-2494	170	5	)	)	PUNCT
ejpam-2494	171	1	⊂	⊂	PROPN
ejpam-2494	171	2	cl(intω(u)∩	cl(intω(u)∩	PROPN
ejpam-2494	171	3	intω(h	intω(h	NOUN
ejpam-2494	171	4	)	)	PUNCT
ejpam-2494	171	5	)	)	PUNCT
ejpam-2494	172	1	=	=	SYM
ejpam-2494	172	2	cl(intω(u	cl(intω(u	NOUN
ejpam-2494	172	3	∩	∩	ADJ
ejpam-2494	172	4	h	h	NOUN
ejpam-2494	172	5	)	)	PUNCT
ejpam-2494	172	6	)	)	PUNCT
ejpam-2494	172	7	.	.	PUNCT
ejpam-2494	173	1	therefore	therefore	ADV
ejpam-2494	173	2	u	u	PROPN
ejpam-2494	173	3	∩	∩	ADJ
ejpam-2494	173	4	h	h	NOUN
ejpam-2494	173	5	is	be	AUX
ejpam-2494	173	6	semi	semi	ADJ
ejpam-2494	173	7	-	-	ADJ
ejpam-2494	173	8	ω	ω	ADJ
ejpam-2494	173	9	-	-	ADJ
ejpam-2494	173	10	open	open	ADJ
ejpam-2494	173	11	.	.	PUNCT
ejpam-2494	174	1	remark	remark	NOUN
ejpam-2494	174	2	4	4	NUM
ejpam-2494	174	3	.	.	PUNCT
ejpam-2494	175	1	the	the	DET
ejpam-2494	175	2	intersection	intersection	NOUN
ejpam-2494	175	3	of	of	ADP
ejpam-2494	175	4	two	two	NUM
ejpam-2494	175	5	semi	semi	ADJ
ejpam-2494	175	6	-	-	ADJ
ejpam-2494	175	7	ω	ω	ADJ
ejpam-2494	175	8	-	-	ADJ
ejpam-2494	175	9	open	open	ADJ
ejpam-2494	175	10	sets	set	NOUN
ejpam-2494	175	11	need	need	AUX
ejpam-2494	175	12	not	not	PART
ejpam-2494	175	13	be	be	AUX
ejpam-2494	175	14	semi	semi	ADJ
ejpam-2494	175	15	-	-	ADJ
ejpam-2494	175	16	ω	ω	VERB
ejpam-2494	175	17	-	-	NOUN
ejpam-2494	175	18	open	open	ADJ
ejpam-2494	175	19	.	.	PUNCT
ejpam-2494	176	1	this	this	PRON
ejpam-2494	176	2	can	can	AUX
ejpam-2494	176	3	be	be	AUX
ejpam-2494	176	4	seen	see	VERB
ejpam-2494	176	5	from	from	ADP
ejpam-2494	176	6	the	the	DET
ejpam-2494	176	7	following	follow	VERB
ejpam-2494	176	8	example	example	NOUN
ejpam-2494	176	9	.	.	PUNCT
ejpam-2494	177	1	example	example	NOUN
ejpam-2494	178	1	7	7	NUM
ejpam-2494	178	2	.	.	PUNCT
ejpam-2494	179	1	let	let	VERB
ejpam-2494	179	2	x	x	PUNCT
ejpam-2494	179	3	=	=	PUNCT
ejpam-2494	179	4	r	r	NOUN
ejpam-2494	179	5	with	with	ADP
ejpam-2494	179	6	the	the	DET
ejpam-2494	179	7	usual	usual	ADJ
ejpam-2494	179	8	topology	topology	NOUN
ejpam-2494	179	9	τu	τu	PROPN
ejpam-2494	179	10	.	.	PUNCT
ejpam-2494	180	1	let	let	VERB
ejpam-2494	180	2	a=	a=	VERB
ejpam-2494	180	3	(	(	PUNCT
ejpam-2494	180	4	0,1	0,1	NUM
ejpam-2494	180	5	]	]	PUNCT
ejpam-2494	180	6	and	and	CCONJ
ejpam-2494	180	7	b	b	X
ejpam-2494	180	8	=	=	SYM
ejpam-2494	181	1	[	[	X
ejpam-2494	181	2	1,2	1,2	NUM
ejpam-2494	181	3	)	)	PUNCT
ejpam-2494	181	4	,	,	PUNCT
ejpam-2494	181	5	then	then	ADV
ejpam-2494	181	6	a	a	PRON
ejpam-2494	181	7	and	and	CCONJ
ejpam-2494	181	8	b	b	NOUN
ejpam-2494	181	9	are	be	AUX
ejpam-2494	181	10	semi	semi	ADJ
ejpam-2494	181	11	-	-	ADJ
ejpam-2494	181	12	ω	ω	ADJ
ejpam-2494	181	13	-	-	ADJ
ejpam-2494	181	14	open	open	ADJ
ejpam-2494	181	15	,	,	PUNCT
ejpam-2494	181	16	but	but	CCONJ
ejpam-2494	181	17	a∩	a∩	PROPN
ejpam-2494	181	18	b	b	X
ejpam-2494	181	19	=	=	PUNCT
ejpam-2494	181	20	{	{	PUNCT
ejpam-2494	181	21	1	1	NUM
ejpam-2494	181	22	}	}	PUNCT
ejpam-2494	181	23	which	which	PRON
ejpam-2494	181	24	is	be	AUX
ejpam-2494	181	25	not	not	PART
ejpam-2494	181	26	semi	semi	ADJ
ejpam-2494	181	27	-	-	ADJ
ejpam-2494	181	28	ω	ω	ADJ
ejpam-2494	181	29	-	-	ADJ
ejpam-2494	181	30	open	open	ADJ
ejpam-2494	181	31	,	,	PUNCT
ejpam-2494	181	32	since	since	SCONJ
ejpam-2494	181	33	cl(intω(a∩	cl(intω(a∩	PROPN
ejpam-2494	181	34	b	b	NOUN
ejpam-2494	181	35	)	)	PUNCT
ejpam-2494	181	36	)	)	PUNCT
ejpam-2494	182	1	=	=	PRON
ejpam-2494	182	2	cl(φ	cl(φ	X
ejpam-2494	182	3	)	)	PUNCT
ejpam-2494	182	4	=	=	SYM
ejpam-2494	182	5	φ	φ	X
ejpam-2494	182	6	.	.	PUNCT
ejpam-2494	182	7	theorem	theorem	NOUN
ejpam-2494	182	8	4	4	NUM
ejpam-2494	182	9	.	.	PUNCT
ejpam-2494	183	1	let	let	VERB
ejpam-2494	183	2	h	h	PRON
ejpam-2494	183	3	be	be	AUX
ejpam-2494	183	4	a	a	DET
ejpam-2494	183	5	subset	subset	NOUN
ejpam-2494	183	6	of	of	ADP
ejpam-2494	183	7	a	a	DET
ejpam-2494	183	8	space	space	NOUN
ejpam-2494	183	9	(	(	PUNCT
ejpam-2494	183	10	x	x	X
ejpam-2494	183	11	,	,	PUNCT
ejpam-2494	183	12	τ	τ	PROPN
ejpam-2494	183	13	)	)	PUNCT
ejpam-2494	183	14	.	.	PUNCT
ejpam-2494	184	1	if	if	SCONJ
ejpam-2494	184	2	h	h	NOUN
ejpam-2494	184	3	is	be	AUX
ejpam-2494	184	4	both	both	PRON
ejpam-2494	184	5	closed	closed	ADJ
ejpam-2494	184	6	and	and	CCONJ
ejpam-2494	184	7	β	β	X
ejpam-2494	184	8	−ω	−ω	ADJ
ejpam-2494	184	9	-	-	ADJ
ejpam-2494	184	10	open	open	ADJ
ejpam-2494	184	11	,	,	PUNCT
ejpam-2494	184	12	then	then	ADV
ejpam-2494	184	13	h	h	NOUN
ejpam-2494	184	14	is	be	AUX
ejpam-2494	184	15	semi	semi	ADJ
ejpam-2494	184	16	-	-	ADJ
ejpam-2494	184	17	ω	ω	ADJ
ejpam-2494	184	18	-	-	ADJ
ejpam-2494	184	19	open	open	ADJ
ejpam-2494	184	20	.	.	PUNCT
ejpam-2494	185	1	proof	proof	NOUN
ejpam-2494	185	2	.	.	PUNCT
ejpam-2494	186	1	since	since	SCONJ
ejpam-2494	186	2	h	h	NOUN
ejpam-2494	186	3	is	be	AUX
ejpam-2494	186	4	a	a	DET
ejpam-2494	186	5	β	β	X
ejpam-2494	186	6	−ω	−ω	ADJ
ejpam-2494	186	7	-	-	ADJ
ejpam-2494	186	8	open	open	ADJ
ejpam-2494	186	9	set	set	NOUN
ejpam-2494	186	10	,	,	PUNCT
ejpam-2494	186	11	h	h	PROPN
ejpam-2494	186	12	⊂	⊂	PROPN
ejpam-2494	186	13	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	186	14	)	)	PUNCT
ejpam-2494	186	15	)	)	PUNCT
ejpam-2494	186	16	)	)	PUNCT
ejpam-2494	187	1	=	=	PUNCT
ejpam-2494	187	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	187	3	)	)	PUNCT
ejpam-2494	187	4	)	)	PUNCT
ejpam-2494	187	5	,	,	PUNCT
ejpam-2494	187	6	h	h	NOUN
ejpam-2494	187	7	being	be	AUX
ejpam-2494	187	8	closed	close	VERB
ejpam-2494	187	9	.	.	PUNCT
ejpam-2494	188	1	therefore	therefore	ADV
ejpam-2494	188	2	h	h	PROPN
ejpam-2494	188	3	is	be	AUX
ejpam-2494	188	4	semi	semi	ADJ
ejpam-2494	188	5	-	-	ADJ
ejpam-2494	188	6	ω	ω	ADJ
ejpam-2494	188	7	-	-	ADJ
ejpam-2494	188	8	open	open	ADJ
ejpam-2494	188	9	.	.	PUNCT
ejpam-2494	189	1	theorem	theorem	NOUN
ejpam-2494	189	2	5	5	NUM
ejpam-2494	189	3	.	.	PUNCT
ejpam-2494	190	1	let	let	VERB
ejpam-2494	190	2	h	h	PRON
ejpam-2494	190	3	be	be	AUX
ejpam-2494	190	4	a	a	DET
ejpam-2494	190	5	subset	subset	NOUN
ejpam-2494	190	6	of	of	ADP
ejpam-2494	190	7	a	a	DET
ejpam-2494	190	8	space	space	NOUN
ejpam-2494	190	9	(	(	PUNCT
ejpam-2494	190	10	x	x	X
ejpam-2494	190	11	,	,	PUNCT
ejpam-2494	190	12	τ	τ	PROPN
ejpam-2494	190	13	)	)	PUNCT
ejpam-2494	190	14	.	.	PUNCT
ejpam-2494	191	1	if	if	SCONJ
ejpam-2494	191	2	h	h	NOUN
ejpam-2494	191	3	is	be	AUX
ejpam-2494	191	4	both	both	PRON
ejpam-2494	191	5	β	β	X
ejpam-2494	191	6	−ω	−ω	ADJ
ejpam-2494	191	7	-	-	ADJ
ejpam-2494	191	8	open	open	ADJ
ejpam-2494	191	9	and	and	CCONJ
ejpam-2494	191	10	ω−	ω−	ADJ
ejpam-2494	191	11	t	t	PROPN
ejpam-2494	191	12	-	-	PUNCT
ejpam-2494	191	13	set	set	NOUN
ejpam-2494	191	14	,	,	PUNCT
ejpam-2494	191	15	then	then	ADV
ejpam-2494	191	16	h	h	NOUN
ejpam-2494	191	17	is	be	AUX
ejpam-2494	191	18	semi	semi	ADJ
ejpam-2494	191	19	-	-	ADJ
ejpam-2494	191	20	ω	ω	ADJ
ejpam-2494	191	21	-	-	ADJ
ejpam-2494	191	22	open	open	ADJ
ejpam-2494	191	23	.	.	PUNCT
ejpam-2494	192	1	proof	proof	NOUN
ejpam-2494	192	2	.	.	PUNCT
ejpam-2494	193	1	since	since	SCONJ
ejpam-2494	193	2	h	h	NOUN
ejpam-2494	193	3	is	be	AUX
ejpam-2494	193	4	a	a	DET
ejpam-2494	193	5	ω−	ω−	PROPN
ejpam-2494	193	6	t	t	NOUN
ejpam-2494	193	7	-	-	PUNCT
ejpam-2494	193	8	set	set	VERB
ejpam-2494	193	9	,	,	PUNCT
ejpam-2494	193	10	int(h	int(h	NOUN
ejpam-2494	193	11	)	)	PUNCT
ejpam-2494	193	12	=	=	SYM
ejpam-2494	193	13	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	193	14	)	)	PUNCT
ejpam-2494	193	15	)	)	PUNCT
ejpam-2494	193	16	.	.	PUNCT
ejpam-2494	194	1	since	since	SCONJ
ejpam-2494	194	2	h	h	PROPN
ejpam-2494	194	3	is	be	AUX
ejpam-2494	194	4	β	β	X
ejpam-2494	194	5	−ω	−ω	ADJ
ejpam-2494	194	6	-	-	ADJ
ejpam-2494	194	7	open	open	ADJ
ejpam-2494	194	8	also	also	ADV
ejpam-2494	194	9	,	,	PUNCT
ejpam-2494	194	10	h	h	PROPN
ejpam-2494	194	11	⊂	⊂	PROPN
ejpam-2494	194	12	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	194	13	)	)	PUNCT
ejpam-2494	194	14	)	)	PUNCT
ejpam-2494	194	15	)	)	PUNCT
ejpam-2494	195	1	⊂	⊂	PROPN
ejpam-2494	195	2	cl(int(h	cl(int(h	NOUN
ejpam-2494	195	3	)	)	PUNCT
ejpam-2494	195	4	)	)	PUNCT
ejpam-2494	196	1	⊂	⊂	PROPN
ejpam-2494	196	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	196	3	)	)	PUNCT
ejpam-2494	196	4	)	)	PUNCT
ejpam-2494	196	5	.	.	PUNCT
ejpam-2494	197	1	therefore	therefore	ADV
ejpam-2494	197	2	h	h	PROPN
ejpam-2494	197	3	is	be	AUX
ejpam-2494	197	4	semi	semi	ADJ
ejpam-2494	197	5	-	-	ADJ
ejpam-2494	197	6	ω	ω	ADJ
ejpam-2494	197	7	-	-	ADJ
ejpam-2494	197	8	open	open	ADJ
ejpam-2494	197	9	.	.	PUNCT
ejpam-2494	198	1	theorem	theorem	NOUN
ejpam-2494	198	2	6	6	NUM
ejpam-2494	198	3	.	.	PUNCT
ejpam-2494	199	1	let	let	VERB
ejpam-2494	199	2	h	h	PRON
ejpam-2494	199	3	be	be	AUX
ejpam-2494	199	4	a	a	DET
ejpam-2494	199	5	subset	subset	NOUN
ejpam-2494	199	6	of	of	ADP
ejpam-2494	199	7	a	a	DET
ejpam-2494	199	8	space	space	NOUN
ejpam-2494	199	9	(	(	PUNCT
ejpam-2494	199	10	x	x	X
ejpam-2494	199	11	,	,	PUNCT
ejpam-2494	199	12	τ	τ	PROPN
ejpam-2494	199	13	)	)	PUNCT
ejpam-2494	199	14	.	.	PUNCT
ejpam-2494	200	1	if	if	SCONJ
ejpam-2494	200	2	h	h	NOUN
ejpam-2494	200	3	is	be	AUX
ejpam-2494	200	4	both	both	DET
ejpam-2494	200	5	b−ω	b−ω	NOUN
ejpam-2494	200	6	-	-	PUNCT
ejpam-2494	200	7	open	open	ADJ
ejpam-2494	200	8	and	and	CCONJ
ejpam-2494	200	9	ω−	ω−	ADJ
ejpam-2494	200	10	t	t	PROPN
ejpam-2494	200	11	-	-	PUNCT
ejpam-2494	200	12	set	set	NOUN
ejpam-2494	200	13	,	,	PUNCT
ejpam-2494	200	14	then	then	ADV
ejpam-2494	200	15	h	h	NOUN
ejpam-2494	200	16	is	be	AUX
ejpam-2494	200	17	semi	semi	ADJ
ejpam-2494	200	18	-	-	ADJ
ejpam-2494	200	19	ω	ω	ADJ
ejpam-2494	200	20	-	-	ADJ
ejpam-2494	200	21	open	open	ADJ
ejpam-2494	200	22	.	.	PUNCT
ejpam-2494	201	1	proof	proof	NOUN
ejpam-2494	201	2	.	.	PUNCT
ejpam-2494	202	1	since	since	SCONJ
ejpam-2494	202	2	h	h	PROPN
ejpam-2494	202	3	is	be	AUX
ejpam-2494	202	4	ω	ω	NUM
ejpam-2494	202	5	−	−	PROPN
ejpam-2494	202	6	t	t	PROPN
ejpam-2494	202	7	-	-	PUNCT
ejpam-2494	202	8	set	set	VERB
ejpam-2494	202	9	,	,	PUNCT
ejpam-2494	202	10	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	202	11	)	)	PUNCT
ejpam-2494	202	12	)	)	PUNCT
ejpam-2494	203	1	=	=	PUNCT
ejpam-2494	203	2	int(h	int(h	X
ejpam-2494	203	3	)	)	PUNCT
ejpam-2494	203	4	⊂	⊂	PROPN
ejpam-2494	203	5	intω(h	intω(h	NOUN
ejpam-2494	203	6	)	)	PUNCT
ejpam-2494	203	7	.	.	PUNCT
ejpam-2494	204	1	since	since	SCONJ
ejpam-2494	204	2	h	h	NOUN
ejpam-2494	204	3	is	be	AUX
ejpam-2494	204	4	b	b	PROPN
ejpam-2494	204	5	−	−	PROPN
ejpam-2494	204	6	ω	ω	NUM
ejpam-2494	204	7	-	-	NOUN
ejpam-2494	204	8	open	open	ADJ
ejpam-2494	204	9	also	also	ADV
ejpam-2494	204	10	,	,	PUNCT
ejpam-2494	204	11	h	h	PROPN
ejpam-2494	204	12	⊂	⊂	PROPN
ejpam-2494	204	13	intω(cl(h))∪	intω(cl(h))∪	PROPN
ejpam-2494	204	14	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	204	15	)	)	PUNCT
ejpam-2494	204	16	)	)	PUNCT
ejpam-2494	205	1	⊂	⊂	PROPN
ejpam-2494	205	2	intω(h)∪	intω(h)∪	PROPN
ejpam-2494	205	3	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	205	4	)	)	PUNCT
ejpam-2494	205	5	)	)	PUNCT
ejpam-2494	206	1	=	=	PUNCT
ejpam-2494	206	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	206	3	)	)	PUNCT
ejpam-2494	206	4	)	)	PUNCT
ejpam-2494	206	5	.	.	PUNCT
ejpam-2494	207	1	therefore	therefore	ADV
ejpam-2494	207	2	h	h	PROPN
ejpam-2494	207	3	is	be	AUX
ejpam-2494	207	4	semi	semi	ADJ
ejpam-2494	207	5	-	-	ADJ
ejpam-2494	207	6	ω	ω	ADJ
ejpam-2494	207	7	-	-	ADJ
ejpam-2494	207	8	open	open	ADJ
ejpam-2494	207	9	.	.	PUNCT
ejpam-2494	208	1	o.	o.	PROPN
ejpam-2494	208	2	ravi	ravi	PROPN
ejpam-2494	208	3	,	,	PUNCT
ejpam-2494	208	4	i.	i.	NOUN
ejpam-2494	208	5	rajasekaran	rajasekaran	PROPN
ejpam-2494	208	6	,	,	PUNCT
ejpam-2494	208	7	s.	s.	PROPN
ejpam-2494	208	8	kanna	kanna	PROPN
ejpam-2494	208	9	and	and	CCONJ
ejpam-2494	208	10	m.	m.	NOUN
ejpam-2494	208	11	paranjothi	paranjothi	PROPN
ejpam-2494	208	12	/	/	SYM
ejpam-2494	208	13	eur	eur	PROPN
ejpam-2494	208	14	.	.	PUNCT
ejpam-2494	209	1	j.	j.	PROPN
ejpam-2494	209	2	pure	pure	PROPN
ejpam-2494	209	3	appl	appl	PROPN
ejpam-2494	209	4	.	.	PROPN
ejpam-2494	209	5	math	math	PROPN
ejpam-2494	209	6	,	,	PUNCT
ejpam-2494	209	7	9	9	NUM
ejpam-2494	209	8	(	(	PUNCT
ejpam-2494	209	9	2016	2016	NUM
ejpam-2494	209	10	)	)	PUNCT
ejpam-2494	209	11	,	,	PUNCT
ejpam-2494	209	12	152	152	NUM
ejpam-2494	209	13	-	-	SYM
ejpam-2494	209	14	164	164	NUM
ejpam-2494	209	15	157	157	NUM
ejpam-2494	209	16	proposition	proposition	NOUN
ejpam-2494	209	17	3	3	NUM
ejpam-2494	209	18	.	.	PUNCT
ejpam-2494	210	1	let	let	VERB
ejpam-2494	210	2	h	h	PRON
ejpam-2494	210	3	be	be	AUX
ejpam-2494	210	4	a	a	DET
ejpam-2494	210	5	subset	subset	NOUN
ejpam-2494	210	6	of	of	ADP
ejpam-2494	210	7	a	a	DET
ejpam-2494	210	8	space	space	NOUN
ejpam-2494	210	9	(	(	PUNCT
ejpam-2494	210	10	x	x	X
ejpam-2494	210	11	,	,	PUNCT
ejpam-2494	210	12	τ	τ	PROPN
ejpam-2494	210	13	)	)	PUNCT
ejpam-2494	210	14	.	.	PUNCT
ejpam-2494	211	1	then	then	ADV
ejpam-2494	211	2	h	h	PROPN
ejpam-2494	211	3	is	be	AUX
ejpam-2494	211	4	semi	semi	ADJ
ejpam-2494	211	5	-	-	ADJ
ejpam-2494	211	6	ω	ω	ADJ
ejpam-2494	211	7	-	-	NOUN
ejpam-2494	211	8	open	open	ADJ
ejpam-2494	211	9	if	if	SCONJ
ejpam-2494	211	10	and	and	CCONJ
ejpam-2494	211	11	only	only	ADV
ejpam-2494	211	12	if	if	SCONJ
ejpam-2494	211	13	cl(h	cl(h	NUM
ejpam-2494	211	14	)	)	PUNCT
ejpam-2494	211	15	=	=	PUNCT
ejpam-2494	211	16	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	211	17	)	)	PUNCT
ejpam-2494	211	18	)	)	PUNCT
ejpam-2494	211	19	.	.	PUNCT
ejpam-2494	212	1	proof	proof	NOUN
ejpam-2494	212	2	.	.	PUNCT
ejpam-2494	213	1	let	let	VERB
ejpam-2494	213	2	h	h	PRON
ejpam-2494	213	3	be	be	AUX
ejpam-2494	213	4	semi	semi	ADJ
ejpam-2494	213	5	-	-	ADJ
ejpam-2494	213	6	ω	ω	ADJ
ejpam-2494	213	7	-	-	NOUN
ejpam-2494	213	8	open	open	ADJ
ejpam-2494	213	9	.	.	PUNCT
ejpam-2494	214	1	then	then	ADV
ejpam-2494	214	2	h	h	PROPN
ejpam-2494	214	3	⊂	⊂	PROPN
ejpam-2494	214	4	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	214	5	)	)	PUNCT
ejpam-2494	214	6	)	)	PUNCT
ejpam-2494	214	7	and	and	CCONJ
ejpam-2494	214	8	cl(h	cl(h	NUM
ejpam-2494	214	9	)	)	PUNCT
ejpam-2494	214	10	⊂	⊂	PROPN
ejpam-2494	214	11	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	214	12	)	)	PUNCT
ejpam-2494	214	13	)	)	PUNCT
ejpam-2494	214	14	.	.	PUNCT
ejpam-2494	215	1	but	but	CCONJ
ejpam-2494	215	2	always	always	ADV
ejpam-2494	215	3	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	215	4	)	)	PUNCT
ejpam-2494	215	5	)	)	PUNCT
ejpam-2494	216	1	⊂	⊂	PROPN
ejpam-2494	216	2	cl(h	cl(h	X
ejpam-2494	216	3	)	)	PUNCT
ejpam-2494	216	4	.	.	PUNCT
ejpam-2494	217	1	thus	thus	ADV
ejpam-2494	217	2	,	,	PUNCT
ejpam-2494	217	3	we	we	PRON
ejpam-2494	217	4	obtain	obtain	VERB
ejpam-2494	217	5	that	that	PRON
ejpam-2494	217	6	cl(h	cl(h	NOUN
ejpam-2494	217	7	)	)	PUNCT
ejpam-2494	217	8	=	=	PUNCT
ejpam-2494	217	9	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	217	10	)	)	PUNCT
ejpam-2494	217	11	)	)	PUNCT
ejpam-2494	217	12	.	.	PUNCT
ejpam-2494	218	1	conversely	conversely	ADV
ejpam-2494	218	2	,	,	PUNCT
ejpam-2494	218	3	let	let	VERB
ejpam-2494	218	4	the	the	DET
ejpam-2494	218	5	condition	condition	NOUN
ejpam-2494	218	6	hold	hold	VERB
ejpam-2494	218	7	.	.	PUNCT
ejpam-2494	219	1	we	we	PRON
ejpam-2494	219	2	have	have	VERB
ejpam-2494	219	3	h	h	PROPN
ejpam-2494	219	4	⊂	⊂	PROPN
ejpam-2494	219	5	cl(h	cl(h	X
ejpam-2494	219	6	)	)	PUNCT
ejpam-2494	219	7	=	=	PUNCT
ejpam-2494	219	8	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	219	9	)	)	PUNCT
ejpam-2494	219	10	)	)	PUNCT
ejpam-2494	219	11	,	,	PUNCT
ejpam-2494	219	12	by	by	ADP
ejpam-2494	219	13	the	the	DET
ejpam-2494	219	14	given	give	VERB
ejpam-2494	219	15	condition	condition	NOUN
ejpam-2494	219	16	.	.	PUNCT
ejpam-2494	220	1	thus	thus	ADV
ejpam-2494	220	2	h	h	X
ejpam-2494	220	3	⊂	⊂	PROPN
ejpam-2494	220	4	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	220	5	)	)	PUNCT
ejpam-2494	220	6	)	)	PUNCT
ejpam-2494	220	7	and	and	CCONJ
ejpam-2494	220	8	hence	hence	ADV
ejpam-2494	220	9	h	h	NOUN
ejpam-2494	220	10	is	be	AUX
ejpam-2494	220	11	semi	semi	ADJ
ejpam-2494	220	12	-	-	ADJ
ejpam-2494	220	13	ω	ω	ADJ
ejpam-2494	220	14	-	-	ADJ
ejpam-2494	220	15	open	open	ADJ
ejpam-2494	220	16	.	.	PUNCT
ejpam-2494	221	1	proposition	proposition	NOUN
ejpam-2494	221	2	4	4	NUM
ejpam-2494	221	3	.	.	PUNCT
ejpam-2494	222	1	let	let	AUX
ejpam-2494	222	2	h	h	PRON
ejpam-2494	222	3	⊂	⊂	PROPN
ejpam-2494	222	4	(	(	PUNCT
ejpam-2494	222	5	x	x	X
ejpam-2494	222	6	,	,	PUNCT
ejpam-2494	222	7	τ	τ	X
ejpam-2494	222	8	)	)	PUNCT
ejpam-2494	222	9	be	be	VERB
ejpam-2494	222	10	a	a	DET
ejpam-2494	222	11	b−ω	b−ω	NOUN
ejpam-2494	222	12	-	-	PUNCT
ejpam-2494	222	13	open	open	NOUN
ejpam-2494	222	14	set	set	NOUN
ejpam-2494	222	15	such	such	ADJ
ejpam-2494	222	16	that	that	PRON
ejpam-2494	222	17	cl(h	cl(h	NOUN
ejpam-2494	222	18	)	)	PUNCT
ejpam-2494	223	1	=	=	SYM
ejpam-2494	223	2	φ	φ	PROPN
ejpam-2494	223	3	.	.	PUNCT
ejpam-2494	224	1	then	then	ADV
ejpam-2494	224	2	h	h	PROPN
ejpam-2494	224	3	is	be	AUX
ejpam-2494	224	4	semi	semi	ADJ
ejpam-2494	224	5	-	-	ADJ
ejpam-2494	224	6	ω	ω	ADJ
ejpam-2494	224	7	-	-	ADJ
ejpam-2494	224	8	open	open	ADJ
ejpam-2494	224	9	.	.	PUNCT
ejpam-2494	225	1	theorem	theorem	VERB
ejpam-2494	225	2	7	7	NUM
ejpam-2494	225	3	.	.	X
ejpam-2494	225	4	for	for	ADP
ejpam-2494	225	5	a	a	DET
ejpam-2494	225	6	subset	subset	ADJ
ejpam-2494	225	7	h	h	NOUN
ejpam-2494	225	8	of	of	ADP
ejpam-2494	225	9	a	a	DET
ejpam-2494	225	10	submaximal	submaximal	ADJ
ejpam-2494	225	11	space	space	NOUN
ejpam-2494	225	12	(	(	PUNCT
ejpam-2494	225	13	x	x	X
ejpam-2494	225	14	,	,	PUNCT
ejpam-2494	225	15	τ	τ	PROPN
ejpam-2494	225	16	)	)	PUNCT
ejpam-2494	225	17	,	,	PUNCT
ejpam-2494	225	18	the	the	DET
ejpam-2494	225	19	following	follow	VERB
ejpam-2494	225	20	properties	property	NOUN
ejpam-2494	225	21	are	be	AUX
ejpam-2494	225	22	equivalent	equivalent	ADJ
ejpam-2494	225	23	.	.	PUNCT
ejpam-2494	226	1	(	(	PUNCT
ejpam-2494	226	2	i	i	NOUN
ejpam-2494	226	3	)	)	PUNCT
ejpam-2494	226	4	h	h	PROPN
ejpam-2494	226	5	is	be	AUX
ejpam-2494	226	6	semi	semi	ADJ
ejpam-2494	226	7	-	-	ADJ
ejpam-2494	226	8	ω	ω	ADJ
ejpam-2494	226	9	-	-	ADJ
ejpam-2494	226	10	open	open	ADJ
ejpam-2494	226	11	,	,	PUNCT
ejpam-2494	226	12	(	(	PUNCT
ejpam-2494	226	13	ii	ii	NOUN
ejpam-2494	226	14	)	)	PUNCT
ejpam-2494	226	15	h	h	PROPN
ejpam-2494	226	16	is	be	AUX
ejpam-2494	226	17	β	β	X
ejpam-2494	226	18	−ω	−ω	ADJ
ejpam-2494	226	19	-	-	ADJ
ejpam-2494	226	20	open	open	ADJ
ejpam-2494	226	21	.	.	PUNCT
ejpam-2494	227	1	proof	proof	NOUN
ejpam-2494	227	2	.	.	PUNCT
ejpam-2494	228	1	(	(	PUNCT
ejpam-2494	228	2	i)⇒	i)⇒	PROPN
ejpam-2494	228	3	(	(	PUNCT
ejpam-2494	228	4	ii	ii	PROPN
ejpam-2494	228	5	):	):	PUNCT
ejpam-2494	228	6	it	it	PRON
ejpam-2494	228	7	follows	follow	VERB
ejpam-2494	228	8	from	from	ADP
ejpam-2494	228	9	the	the	DET
ejpam-2494	228	10	fact	fact	NOUN
ejpam-2494	228	11	that	that	SCONJ
ejpam-2494	228	12	every	every	DET
ejpam-2494	228	13	semi	semi	ADJ
ejpam-2494	228	14	-	-	ADJ
ejpam-2494	228	15	ω	ω	ADJ
ejpam-2494	228	16	-	-	ADJ
ejpam-2494	228	17	open	open	ADJ
ejpam-2494	228	18	set	set	NOUN
ejpam-2494	228	19	is	be	AUX
ejpam-2494	228	20	β	β	NOUN
ejpam-2494	228	21	−ω	−ω	ADJ
ejpam-2494	228	22	-	-	ADJ
ejpam-2494	228	23	open	open	ADJ
ejpam-2494	228	24	.	.	PUNCT
ejpam-2494	229	1	(	(	PUNCT
ejpam-2494	229	2	ii)⇒	ii)⇒	PROPN
ejpam-2494	229	3	(	(	PUNCT
ejpam-2494	229	4	i	i	NOUN
ejpam-2494	229	5	):	):	PUNCT
ejpam-2494	229	6	let	let	VERB
ejpam-2494	229	7	h	h	PRON
ejpam-2494	229	8	be	be	AUX
ejpam-2494	229	9	a	a	DET
ejpam-2494	229	10	β	β	X
ejpam-2494	229	11	−ω	−ω	ADJ
ejpam-2494	229	12	-	-	ADJ
ejpam-2494	229	13	open	open	ADJ
ejpam-2494	229	14	set	set	NOUN
ejpam-2494	229	15	in	in	ADP
ejpam-2494	229	16	x.	x.	NOUN
ejpam-2494	230	1	then	then	ADV
ejpam-2494	230	2	h	h	PROPN
ejpam-2494	230	3	⊂	⊂	PROPN
ejpam-2494	230	4	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	230	5	)	)	PUNCT
ejpam-2494	230	6	)	)	PUNCT
ejpam-2494	230	7	)	)	PUNCT
ejpam-2494	231	1	and	and	CCONJ
ejpam-2494	231	2	cl(h	cl(h	NUM
ejpam-2494	231	3	)	)	PUNCT
ejpam-2494	231	4	⊂	⊂	PROPN
ejpam-2494	231	5	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	231	6	)	)	PUNCT
ejpam-2494	231	7	)	)	PUNCT
ejpam-2494	231	8	)	)	PUNCT
ejpam-2494	231	9	.	.	PUNCT
ejpam-2494	232	1	thus	thus	ADV
ejpam-2494	232	2	,	,	PUNCT
ejpam-2494	232	3	cl(h	cl(h	CCONJ
ejpam-2494	232	4	)	)	PUNCT
ejpam-2494	232	5	is	be	AUX
ejpam-2494	232	6	semi	semi	ADJ
ejpam-2494	232	7	-	-	ADJ
ejpam-2494	232	8	ω	ω	ADJ
ejpam-2494	232	9	-	-	ADJ
ejpam-2494	232	10	open	open	ADJ
ejpam-2494	232	11	.	.	PUNCT
ejpam-2494	233	1	put	put	VERB
ejpam-2494	233	2	a=	a=	ADV
ejpam-2494	233	3	cl(h	cl(h	NUM
ejpam-2494	233	4	)	)	PUNCT
ejpam-2494	234	1	and	and	CCONJ
ejpam-2494	234	2	k	k	X
ejpam-2494	234	3	=	=	NOUN
ejpam-2494	234	4	h	h	NOUN
ejpam-2494	234	5	∪	∪	ADV
ejpam-2494	234	6	(	(	PUNCT
ejpam-2494	234	7	x\cl(h	x\cl(h	NUM
ejpam-2494	234	8	)	)	PUNCT
ejpam-2494	234	9	)	)	PUNCT
ejpam-2494	234	10	.	.	PUNCT
ejpam-2494	235	1	we	we	PRON
ejpam-2494	235	2	have	have	VERB
ejpam-2494	235	3	h	h	NOUN
ejpam-2494	235	4	=	=	PUNCT
ejpam-2494	235	5	cl(h	cl(h	X
ejpam-2494	235	6	)	)	PUNCT
ejpam-2494	235	7	∩	∩	PROPN
ejpam-2494	235	8	k	k	PROPN
ejpam-2494	235	9	and	and	CCONJ
ejpam-2494	235	10	cl(k	cl(k	NOUN
ejpam-2494	235	11	)	)	PUNCT
ejpam-2494	236	1	=	=	SYM
ejpam-2494	237	1	x	x	X
ejpam-2494	237	2	.	.	PUNCT
ejpam-2494	238	1	this	this	PRON
ejpam-2494	238	2	implies	imply	VERB
ejpam-2494	238	3	that	that	SCONJ
ejpam-2494	238	4	h	h	NOUN
ejpam-2494	238	5	=	=	PUNCT
ejpam-2494	238	6	a∩	a∩	PROPN
ejpam-2494	239	1	k	k	NOUN
ejpam-2494	239	2	,	,	PUNCT
ejpam-2494	239	3	where	where	SCONJ
ejpam-2494	239	4	a	a	PRON
ejpam-2494	239	5	is	be	AUX
ejpam-2494	239	6	semi	semi	ADJ
ejpam-2494	239	7	-	-	ADJ
ejpam-2494	239	8	ωopen	ωopen	ADJ
ejpam-2494	239	9	and	and	CCONJ
ejpam-2494	239	10	k	k	PROPN
ejpam-2494	239	11	is	be	AUX
ejpam-2494	239	12	dense	dense	ADJ
ejpam-2494	239	13	.	.	PUNCT
ejpam-2494	240	1	since	since	SCONJ
ejpam-2494	240	2	x	x	PRON
ejpam-2494	240	3	is	be	AUX
ejpam-2494	240	4	submaximal	submaximal	ADJ
ejpam-2494	240	5	,	,	PUNCT
ejpam-2494	240	6	then	then	ADV
ejpam-2494	240	7	k	k	PROPN
ejpam-2494	240	8	is	be	AUX
ejpam-2494	240	9	open	open	ADJ
ejpam-2494	240	10	.	.	PUNCT
ejpam-2494	241	1	by	by	ADP
ejpam-2494	241	2	proposition	proposition	NOUN
ejpam-2494	241	3	2	2	NUM
ejpam-2494	241	4	,	,	PUNCT
ejpam-2494	241	5	h	h	NOUN
ejpam-2494	241	6	=	=	PUNCT
ejpam-2494	241	7	a∩	a∩	PROPN
ejpam-2494	242	1	k	k	PROPN
ejpam-2494	242	2	is	be	AUX
ejpam-2494	242	3	semi	semi	ADJ
ejpam-2494	242	4	-	-	ADJ
ejpam-2494	242	5	ω	ω	ADJ
ejpam-2494	242	6	-	-	ADJ
ejpam-2494	242	7	open	open	ADJ
ejpam-2494	242	8	.	.	PUNCT
ejpam-2494	243	1	theorem	theorem	VERB
ejpam-2494	243	2	8	8	NUM
ejpam-2494	243	3	.	.	PUNCT
ejpam-2494	244	1	a	a	DET
ejpam-2494	244	2	subset	subset	ADJ
ejpam-2494	244	3	h	h	NOUN
ejpam-2494	244	4	of	of	ADP
ejpam-2494	244	5	a	a	DET
ejpam-2494	244	6	space	space	NOUN
ejpam-2494	244	7	(	(	PUNCT
ejpam-2494	244	8	x	x	X
ejpam-2494	244	9	,	,	PUNCT
ejpam-2494	244	10	τ	τ	X
ejpam-2494	244	11	)	)	PUNCT
ejpam-2494	244	12	is	be	AUX
ejpam-2494	244	13	semi	semi	ADJ
ejpam-2494	244	14	-	-	ADJ
ejpam-2494	244	15	ω	ω	ADJ
ejpam-2494	244	16	-	-	NOUN
ejpam-2494	244	17	open	open	ADJ
ejpam-2494	244	18	if	if	SCONJ
ejpam-2494	244	19	and	and	CCONJ
ejpam-2494	244	20	only	only	ADV
ejpam-2494	244	21	if	if	SCONJ
ejpam-2494	244	22	there	there	PRON
ejpam-2494	244	23	exists	exist	VERB
ejpam-2494	244	24	u	u	NOUN
ejpam-2494	244	25	∈	∈	PROPN
ejpam-2494	244	26	τω	τω	SCONJ
ejpam-2494	244	27	such	such	ADJ
ejpam-2494	244	28	that	that	SCONJ
ejpam-2494	244	29	u	u	PROPN
ejpam-2494	244	30	⊂	⊂	PROPN
ejpam-2494	244	31	h	h	PROPN
ejpam-2494	244	32	⊂	⊂	PROPN
ejpam-2494	244	33	cl(u	cl(u	PROPN
ejpam-2494	244	34	)	)	PUNCT
ejpam-2494	244	35	.	.	PUNCT
ejpam-2494	245	1	proof	proof	NOUN
ejpam-2494	245	2	.	.	PUNCT
ejpam-2494	246	1	let	let	VERB
ejpam-2494	246	2	h	h	PRON
ejpam-2494	246	3	be	be	AUX
ejpam-2494	246	4	semi	semi	ADJ
ejpam-2494	246	5	-	-	ADJ
ejpam-2494	246	6	ω	ω	ADJ
ejpam-2494	246	7	-	-	NOUN
ejpam-2494	246	8	open	open	ADJ
ejpam-2494	246	9	.	.	PUNCT
ejpam-2494	247	1	then	then	ADV
ejpam-2494	247	2	h	h	PROPN
ejpam-2494	247	3	⊂	⊂	PROPN
ejpam-2494	247	4	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	247	5	)	)	PUNCT
ejpam-2494	247	6	)	)	PUNCT
ejpam-2494	247	7	.	.	PUNCT
ejpam-2494	248	1	take	take	VERB
ejpam-2494	248	2	intω(h	intω(h	NOUN
ejpam-2494	248	3	)	)	PUNCT
ejpam-2494	249	1	=	=	SYM
ejpam-2494	249	2	u	u	PROPN
ejpam-2494	249	3	.	.	PUNCT
ejpam-2494	250	1	then	then	ADV
ejpam-2494	250	2	,	,	PUNCT
ejpam-2494	250	3	we	we	PRON
ejpam-2494	250	4	have	have	VERB
ejpam-2494	250	5	u	u	PROPN
ejpam-2494	250	6	⊂	⊂	PROPN
ejpam-2494	250	7	h	h	NOUN
ejpam-2494	250	8	⊂	⊂	PROPN
ejpam-2494	250	9	cl(u	cl(u	PROPN
ejpam-2494	250	10	)	)	PUNCT
ejpam-2494	250	11	.	.	PUNCT
ejpam-2494	251	1	conversely	conversely	ADV
ejpam-2494	251	2	,	,	PUNCT
ejpam-2494	251	3	let	let	VERB
ejpam-2494	251	4	u	u	PRON
ejpam-2494	251	5	⊂	⊂	PROPN
ejpam-2494	251	6	h	h	PROPN
ejpam-2494	251	7	⊂	⊂	PROPN
ejpam-2494	251	8	cl(u	cl(u	PROPN
ejpam-2494	251	9	)	)	PUNCT
ejpam-2494	251	10	for	for	ADP
ejpam-2494	251	11	some	some	DET
ejpam-2494	251	12	u	u	NOUN
ejpam-2494	251	13	∈	∈	PROPN
ejpam-2494	251	14	τω	τω	INTJ
ejpam-2494	251	15	.	.	PUNCT
ejpam-2494	252	1	since	since	SCONJ
ejpam-2494	252	2	u	u	PROPN
ejpam-2494	252	3	⊂	⊂	PROPN
ejpam-2494	252	4	h	h	NOUN
ejpam-2494	252	5	,	,	PUNCT
ejpam-2494	252	6	we	we	PRON
ejpam-2494	252	7	have	have	VERB
ejpam-2494	252	8	u	u	NOUN
ejpam-2494	252	9	⊂	⊂	NOUN
ejpam-2494	252	10	intω(h	intω(h	NOUN
ejpam-2494	252	11	)	)	PUNCT
ejpam-2494	252	12	and	and	CCONJ
ejpam-2494	252	13	hence	hence	ADV
ejpam-2494	252	14	cl(u	cl(u	NUM
ejpam-2494	252	15	)	)	PUNCT
ejpam-2494	252	16	⊂	⊂	PROPN
ejpam-2494	252	17	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	252	18	)	)	PUNCT
ejpam-2494	252	19	)	)	PUNCT
ejpam-2494	252	20	.	.	PUNCT
ejpam-2494	253	1	thus	thus	ADV
ejpam-2494	253	2	we	we	PRON
ejpam-2494	253	3	obtain	obtain	VERB
ejpam-2494	253	4	h	h	NOUN
ejpam-2494	253	5	⊂	⊂	PROPN
ejpam-2494	253	6	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	253	7	)	)	PUNCT
ejpam-2494	253	8	)	)	PUNCT
ejpam-2494	254	1	and	and	CCONJ
ejpam-2494	254	2	h	h	NOUN
ejpam-2494	254	3	is	be	AUX
ejpam-2494	254	4	semi	semi	ADJ
ejpam-2494	254	5	-	-	ADJ
ejpam-2494	254	6	ω	ω	ADJ
ejpam-2494	254	7	-	-	ADJ
ejpam-2494	254	8	open	open	ADJ
ejpam-2494	254	9	.	.	PUNCT
ejpam-2494	255	1	corollary	corollary	ADJ
ejpam-2494	255	2	1	1	NUM
ejpam-2494	255	3	.	.	PUNCT
ejpam-2494	256	1	if	if	SCONJ
ejpam-2494	256	2	a	a	PRON
ejpam-2494	256	3	is	be	AUX
ejpam-2494	256	4	a	a	DET
ejpam-2494	256	5	semi	semi	ADJ
ejpam-2494	256	6	-	-	ADJ
ejpam-2494	256	7	ω	ω	ADJ
ejpam-2494	256	8	-	-	ADJ
ejpam-2494	256	9	open	open	ADJ
ejpam-2494	256	10	set	set	NOUN
ejpam-2494	256	11	in	in	ADP
ejpam-2494	256	12	a	a	DET
ejpam-2494	256	13	space	space	NOUN
ejpam-2494	256	14	(	(	PUNCT
ejpam-2494	256	15	x	x	X
ejpam-2494	256	16	,	,	PUNCT
ejpam-2494	256	17	τ	τ	PROPN
ejpam-2494	256	18	)	)	PUNCT
ejpam-2494	256	19	and	and	CCONJ
ejpam-2494	256	20	a⊂	a⊂	AUX
ejpam-2494	256	21	b	b	PROPN
ejpam-2494	256	22	⊂	⊂	X
ejpam-2494	256	23	cl(a	cl(a	X
ejpam-2494	256	24	)	)	PUNCT
ejpam-2494	256	25	,	,	PUNCT
ejpam-2494	256	26	then	then	ADV
ejpam-2494	256	27	b	b	PROPN
ejpam-2494	256	28	is	be	AUX
ejpam-2494	256	29	semi	semi	ADJ
ejpam-2494	256	30	-	-	ADJ
ejpam-2494	256	31	ω	ω	VERB
ejpam-2494	256	32	-	-	NOUN
ejpam-2494	256	33	open	open	ADJ
ejpam-2494	256	34	in	in	ADP
ejpam-2494	256	35	x.	x.	NOUN
ejpam-2494	256	36	proof	proof	NOUN
ejpam-2494	256	37	.	.	PUNCT
ejpam-2494	257	1	since	since	SCONJ
ejpam-2494	257	2	a	a	PRON
ejpam-2494	257	3	is	be	AUX
ejpam-2494	257	4	semi	semi	ADJ
ejpam-2494	257	5	-	-	ADJ
ejpam-2494	257	6	ω	ω	ADJ
ejpam-2494	257	7	-	-	ADJ
ejpam-2494	257	8	open	open	ADJ
ejpam-2494	257	9	,	,	PUNCT
ejpam-2494	257	10	a⊂	a⊂	PRON
ejpam-2494	257	11	cl(intω(a	cl(intω(a	NOUN
ejpam-2494	257	12	)	)	PUNCT
ejpam-2494	257	13	)	)	PUNCT
ejpam-2494	258	1	⊂	⊂	PROPN
ejpam-2494	258	2	cl(intω(b	cl(intω(b	PROPN
ejpam-2494	258	3	)	)	PUNCT
ejpam-2494	258	4	)	)	PUNCT
ejpam-2494	259	1	for	for	ADP
ejpam-2494	259	2	a⊂	a⊂	DET
ejpam-2494	259	3	b.	b.	NOUN
ejpam-2494	259	4	so	so	ADV
ejpam-2494	259	5	cl(a	cl(a	NUM
ejpam-2494	259	6	)	)	PUNCT
ejpam-2494	259	7	⊂	⊂	X
ejpam-2494	259	8	cl(intω(b	cl(intω(b	PROPN
ejpam-2494	259	9	)	)	PUNCT
ejpam-2494	259	10	)	)	PUNCT
ejpam-2494	259	11	.	.	PUNCT
ejpam-2494	260	1	since	since	SCONJ
ejpam-2494	260	2	b	b	PROPN
ejpam-2494	260	3	⊂	⊂	PROPN
ejpam-2494	260	4	cl(a	cl(a	X
ejpam-2494	260	5	)	)	PUNCT
ejpam-2494	260	6	,	,	PUNCT
ejpam-2494	260	7	b	b	X
ejpam-2494	260	8	⊂	⊂	ADJ
ejpam-2494	260	9	cl(intω(b	cl(intω(b	PROPN
ejpam-2494	260	10	)	)	PUNCT
ejpam-2494	260	11	)	)	PUNCT
ejpam-2494	260	12	.	.	PUNCT
ejpam-2494	261	1	thus	thus	ADV
ejpam-2494	261	2	b	b	X
ejpam-2494	261	3	is	be	AUX
ejpam-2494	261	4	semi	semi	ADJ
ejpam-2494	261	5	-	-	ADJ
ejpam-2494	261	6	ω	ω	ADJ
ejpam-2494	261	7	-	-	NOUN
ejpam-2494	261	8	open	open	ADJ
ejpam-2494	261	9	.	.	PUNCT
ejpam-2494	262	1	4	4	X
ejpam-2494	262	2	.	.	X
ejpam-2494	262	3	properties	property	NOUN
ejpam-2494	262	4	of	of	ADP
ejpam-2494	262	5	δ−ω	δ−ω	NOUN
ejpam-2494	262	6	-	-	PUNCT
ejpam-2494	262	7	open	open	ADJ
ejpam-2494	262	8	sets	set	NOUN
ejpam-2494	262	9	definition	definition	NOUN
ejpam-2494	262	10	10	10	NUM
ejpam-2494	262	11	.	.	PUNCT
ejpam-2494	263	1	a	a	DET
ejpam-2494	263	2	subset	subset	ADJ
ejpam-2494	263	3	h	h	NOUN
ejpam-2494	263	4	of	of	ADP
ejpam-2494	263	5	a	a	DET
ejpam-2494	263	6	space	space	NOUN
ejpam-2494	263	7	(	(	PUNCT
ejpam-2494	263	8	x	x	X
ejpam-2494	263	9	,	,	PUNCT
ejpam-2494	263	10	τ	τ	X
ejpam-2494	263	11	)	)	PUNCT
ejpam-2494	263	12	is	be	AUX
ejpam-2494	263	13	said	say	VERB
ejpam-2494	263	14	to	to	PART
ejpam-2494	263	15	be	be	AUX
ejpam-2494	263	16	(	(	PUNCT
ejpam-2494	263	17	i	i	NOUN
ejpam-2494	263	18	)	)	PUNCT
ejpam-2494	263	19	δ−ω	δ−ω	NOUN
ejpam-2494	263	20	-	-	PUNCT
ejpam-2494	263	21	open	open	ADJ
ejpam-2494	263	22	if	if	SCONJ
ejpam-2494	263	23	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	263	24	)	)	PUNCT
ejpam-2494	263	25	)	)	PUNCT
ejpam-2494	264	1	⊂	⊂	PROPN
ejpam-2494	264	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	264	3	)	)	PUNCT
ejpam-2494	264	4	)	)	PUNCT
ejpam-2494	264	5	.	.	PUNCT
ejpam-2494	265	1	(	(	PUNCT
ejpam-2494	265	2	ii	ii	NOUN
ejpam-2494	265	3	)	)	PUNCT
ejpam-2494	265	4	δ−ω	δ−ω	NOUN
ejpam-2494	265	5	-	-	PUNCT
ejpam-2494	265	6	closed	closed	ADJ
ejpam-2494	265	7	if	if	SCONJ
ejpam-2494	265	8	int(clω(h	int(clω(h	PROPN
ejpam-2494	265	9	)	)	PUNCT
ejpam-2494	265	10	)	)	PUNCT
ejpam-2494	266	1	⊂	⊂	PROPN
ejpam-2494	266	2	clω(int(h	clω(int(h	NOUN
ejpam-2494	266	3	)	)	PUNCT
ejpam-2494	266	4	)	)	PUNCT
ejpam-2494	266	5	.	.	PUNCT
ejpam-2494	267	1	the	the	DET
ejpam-2494	267	2	complement	complement	NOUN
ejpam-2494	267	3	of	of	ADP
ejpam-2494	267	4	δ−ω	δ−ω	NOUN
ejpam-2494	267	5	-	-	PUNCT
ejpam-2494	267	6	open	open	ADJ
ejpam-2494	267	7	set	set	NOUN
ejpam-2494	267	8	is	be	AUX
ejpam-2494	267	9	called	call	VERB
ejpam-2494	267	10	δ−ω	δ−ω	NOUN
ejpam-2494	267	11	-	-	PUNCT
ejpam-2494	267	12	closed	closed	ADJ
ejpam-2494	267	13	.	.	PUNCT
ejpam-2494	268	1	o.	o.	PROPN
ejpam-2494	268	2	ravi	ravi	PROPN
ejpam-2494	268	3	,	,	PUNCT
ejpam-2494	268	4	i.	i.	NOUN
ejpam-2494	268	5	rajasekaran	rajasekaran	PROPN
ejpam-2494	268	6	,	,	PUNCT
ejpam-2494	268	7	s.	s.	PROPN
ejpam-2494	268	8	kanna	kanna	PROPN
ejpam-2494	268	9	and	and	CCONJ
ejpam-2494	268	10	m.	m.	NOUN
ejpam-2494	268	11	paranjothi	paranjothi	PROPN
ejpam-2494	268	12	/	/	SYM
ejpam-2494	268	13	eur	eur	PROPN
ejpam-2494	268	14	.	.	PUNCT
ejpam-2494	269	1	j.	j.	PROPN
ejpam-2494	269	2	pure	pure	PROPN
ejpam-2494	269	3	appl	appl	PROPN
ejpam-2494	269	4	.	.	PROPN
ejpam-2494	269	5	math	math	PROPN
ejpam-2494	269	6	,	,	PUNCT
ejpam-2494	269	7	9	9	NUM
ejpam-2494	269	8	(	(	PUNCT
ejpam-2494	269	9	2016	2016	NUM
ejpam-2494	269	10	)	)	PUNCT
ejpam-2494	269	11	,	,	PUNCT
ejpam-2494	269	12	152	152	NUM
ejpam-2494	269	13	-	-	SYM
ejpam-2494	269	14	164	164	NUM
ejpam-2494	269	15	158	158	NUM
ejpam-2494	269	16	example	example	NOUN
ejpam-2494	269	17	8	8	NUM
ejpam-2494	269	18	.	.	PUNCT
ejpam-2494	270	1	let	let	VERB
ejpam-2494	270	2	x	x	PUNCT
ejpam-2494	270	3	=	=	PUNCT
ejpam-2494	270	4	r	r	NOUN
ejpam-2494	270	5	with	with	ADP
ejpam-2494	270	6	the	the	DET
ejpam-2494	270	7	usual	usual	ADJ
ejpam-2494	270	8	topology	topology	NOUN
ejpam-2494	270	9	τu	τu	PROPN
ejpam-2494	270	10	.	.	PUNCT
ejpam-2494	271	1	let	let	VERB
ejpam-2494	271	2	h	h	NOUN
ejpam-2494	272	1	=	=	PUNCT
ejpam-2494	272	2	q.	q.	PROPN
ejpam-2494	272	3	then	then	ADV
ejpam-2494	272	4	h	h	PROPN
ejpam-2494	272	5	is	be	AUX
ejpam-2494	272	6	not	not	PART
ejpam-2494	272	7	δ−ω	δ−ω	NOUN
ejpam-2494	272	8	-	-	PUNCT
ejpam-2494	272	9	open	open	ADJ
ejpam-2494	272	10	,	,	PUNCT
ejpam-2494	272	11	since	since	SCONJ
ejpam-2494	272	12	intω(cl(q	intω(cl(q	NOUN
ejpam-2494	272	13	)	)	PUNCT
ejpam-2494	272	14	)	)	PUNCT
ejpam-2494	273	1	=	=	SYM
ejpam-2494	273	2	intω(r	intω(r	NOUN
ejpam-2494	273	3	)	)	PUNCT
ejpam-2494	273	4	=	=	SYM
ejpam-2494	273	5	r	r	NOUN
ejpam-2494	273	6	and	and	CCONJ
ejpam-2494	273	7	cl(intω(q	cl(intω(q	NOUN
ejpam-2494	273	8	)	)	PUNCT
ejpam-2494	273	9	)	)	PUNCT
ejpam-2494	274	1	=	=	PRON
ejpam-2494	274	2	cl(φ	cl(φ	X
ejpam-2494	274	3	)	)	PUNCT
ejpam-2494	274	4	=	=	SYM
ejpam-2494	274	5	φ	φ	PROPN
ejpam-2494	274	6	.	.	PROPN
ejpam-2494	274	7	example	example	NOUN
ejpam-2494	274	8	9	9	NUM
ejpam-2494	274	9	.	.	PUNCT
ejpam-2494	275	1	let	let	VERB
ejpam-2494	275	2	x	x	PUNCT
ejpam-2494	275	3	=	=	PUNCT
ejpam-2494	275	4	r	r	NOUN
ejpam-2494	275	5	with	with	ADP
ejpam-2494	275	6	the	the	DET
ejpam-2494	275	7	usual	usual	ADJ
ejpam-2494	275	8	topology	topology	NOUN
ejpam-2494	275	9	τu	τu	PROPN
ejpam-2494	275	10	.	.	PUNCT
ejpam-2494	276	1	let	let	VERB
ejpam-2494	276	2	h	h	NOUN
ejpam-2494	276	3	=	=	PUNCT
ejpam-2494	276	4	(	(	PUNCT
ejpam-2494	276	5	0,1	0,1	NUM
ejpam-2494	276	6	]	]	PUNCT
ejpam-2494	276	7	.	.	PUNCT
ejpam-2494	277	1	then	then	ADV
ejpam-2494	277	2	h	h	PROPN
ejpam-2494	277	3	is	be	AUX
ejpam-2494	277	4	δ−ω	δ−ω	NOUN
ejpam-2494	277	5	-	-	PUNCT
ejpam-2494	277	6	open	open	ADJ
ejpam-2494	277	7	,	,	PUNCT
ejpam-2494	277	8	since	since	SCONJ
ejpam-2494	277	9	intω(cl((0,1	intω(cl((0,1	NOUN
ejpam-2494	277	10	]	]	PUNCT
ejpam-2494	277	11	)	)	PUNCT
ejpam-2494	277	12	)	)	PUNCT
ejpam-2494	278	1	=	=	PUNCT
ejpam-2494	278	2	intω([0,1	intω([0,1	NOUN
ejpam-2494	278	3	]	]	PUNCT
ejpam-2494	278	4	)	)	PUNCT
ejpam-2494	278	5	=	=	SYM
ejpam-2494	278	6	(	(	PUNCT
ejpam-2494	278	7	0,1	0,1	NUM
ejpam-2494	278	8	)	)	PUNCT
ejpam-2494	278	9	and	and	CCONJ
ejpam-2494	278	10	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	278	11	)	)	PUNCT
ejpam-2494	278	12	)	)	PUNCT
ejpam-2494	279	1	=	=	SYM
ejpam-2494	279	2	cl(0,1	cl(0,1	NOUN
ejpam-2494	279	3	)	)	PUNCT
ejpam-2494	279	4	=	=	PUNCT
ejpam-2494	280	1	[	[	X
ejpam-2494	280	2	0,1	0,1	NUM
ejpam-2494	280	3	]	]	PUNCT
ejpam-2494	280	4	.	.	PUNCT
ejpam-2494	281	1	proposition	proposition	NOUN
ejpam-2494	281	2	5	5	NUM
ejpam-2494	281	3	.	.	PUNCT
ejpam-2494	281	4	for	for	ADP
ejpam-2494	281	5	a	a	DET
ejpam-2494	281	6	subset	subset	NOUN
ejpam-2494	281	7	of	of	ADP
ejpam-2494	281	8	a	a	DET
ejpam-2494	281	9	space	space	NOUN
ejpam-2494	281	10	(	(	PUNCT
ejpam-2494	281	11	x	x	X
ejpam-2494	281	12	,	,	PUNCT
ejpam-2494	281	13	τ	τ	PROPN
ejpam-2494	281	14	)	)	PUNCT
ejpam-2494	281	15	,	,	PUNCT
ejpam-2494	281	16	the	the	DET
ejpam-2494	281	17	following	follow	VERB
ejpam-2494	281	18	properties	property	NOUN
ejpam-2494	281	19	hold	hold	VERB
ejpam-2494	281	20	:	:	PUNCT
ejpam-2494	281	21	(	(	PUNCT
ejpam-2494	281	22	i	i	NOUN
ejpam-2494	281	23	)	)	PUNCT
ejpam-2494	281	24	every	every	DET
ejpam-2494	281	25	α−ω	α−ω	PROPN
ejpam-2494	281	26	-	-	PUNCT
ejpam-2494	281	27	open	open	ADJ
ejpam-2494	281	28	set	set	NOUN
ejpam-2494	281	29	is	be	AUX
ejpam-2494	281	30	δ−ω	δ−ω	NOUN
ejpam-2494	281	31	-	-	PUNCT
ejpam-2494	281	32	open	open	ADJ
ejpam-2494	281	33	.	.	PUNCT
ejpam-2494	282	1	(	(	PUNCT
ejpam-2494	282	2	ii	ii	NOUN
ejpam-2494	282	3	)	)	PUNCT
ejpam-2494	282	4	every	every	DET
ejpam-2494	282	5	ω−	ω−	PROPN
ejpam-2494	282	6	t	t	PROPN
ejpam-2494	282	7	-	-	PUNCT
ejpam-2494	282	8	set	set	NOUN
ejpam-2494	282	9	is	be	AUX
ejpam-2494	282	10	δ−ω	δ−ω	NOUN
ejpam-2494	282	11	-	-	PUNCT
ejpam-2494	282	12	open	open	ADJ
ejpam-2494	282	13	.	.	PUNCT
ejpam-2494	283	1	proof	proof	NOUN
ejpam-2494	283	2	.	.	PUNCT
ejpam-2494	284	1	(	(	PUNCT
ejpam-2494	284	2	i	i	NOUN
ejpam-2494	284	3	)	)	PUNCT
ejpam-2494	284	4	since	since	SCONJ
ejpam-2494	284	5	h	h	NOUN
ejpam-2494	284	6	is	be	AUX
ejpam-2494	284	7	an	an	DET
ejpam-2494	284	8	α−ω	α−ω	NOUN
ejpam-2494	284	9	-	-	PUNCT
ejpam-2494	284	10	open	open	ADJ
ejpam-2494	284	11	set	set	NOUN
ejpam-2494	284	12	,	,	PUNCT
ejpam-2494	284	13	h	h	PROPN
ejpam-2494	284	14	⊂	⊂	PROPN
ejpam-2494	284	15	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	284	16	)	)	PUNCT
ejpam-2494	284	17	)	)	PUNCT
ejpam-2494	284	18	)	)	PUNCT
ejpam-2494	285	1	⊂	⊂	PROPN
ejpam-2494	285	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	285	3	)	)	PUNCT
ejpam-2494	285	4	)	)	PUNCT
ejpam-2494	285	5	.	.	PUNCT
ejpam-2494	286	1	then	then	ADV
ejpam-2494	286	2	we	we	PRON
ejpam-2494	286	3	obtain	obtain	VERB
ejpam-2494	286	4	cl(h	cl(h	PUNCT
ejpam-2494	286	5	)	)	PUNCT
ejpam-2494	286	6	⊂	⊂	PROPN
ejpam-2494	286	7	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	286	8	)	)	PUNCT
ejpam-2494	286	9	)	)	PUNCT
ejpam-2494	286	10	and	and	CCONJ
ejpam-2494	286	11	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	286	12	)	)	PUNCT
ejpam-2494	286	13	)	)	PUNCT
ejpam-2494	287	1	⊂	⊂	PROPN
ejpam-2494	287	2	cl(h	cl(h	X
ejpam-2494	287	3	)	)	PUNCT
ejpam-2494	288	1	⊂	⊂	PROPN
ejpam-2494	288	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	288	3	)	)	PUNCT
ejpam-2494	288	4	)	)	PUNCT
ejpam-2494	288	5	.	.	PUNCT
ejpam-2494	289	1	therefore	therefore	ADV
ejpam-2494	289	2	h	h	PROPN
ejpam-2494	289	3	is	be	AUX
ejpam-2494	289	4	δ	δ	PROPN
ejpam-2494	289	5	−ωopen	−ωopen	PROPN
ejpam-2494	289	6	.	.	PUNCT
ejpam-2494	290	1	(	(	PUNCT
ejpam-2494	290	2	ii	ii	NOUN
ejpam-2494	290	3	)	)	PUNCT
ejpam-2494	290	4	since	since	SCONJ
ejpam-2494	290	5	h	h	NOUN
ejpam-2494	290	6	is	be	AUX
ejpam-2494	290	7	an	an	DET
ejpam-2494	290	8	ω−	ω−	PROPN
ejpam-2494	290	9	t	t	NOUN
ejpam-2494	290	10	-	-	PUNCT
ejpam-2494	290	11	set	set	VERB
ejpam-2494	290	12	,	,	PUNCT
ejpam-2494	290	13	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	290	14	)	)	PUNCT
ejpam-2494	290	15	)	)	PUNCT
ejpam-2494	291	1	=	=	PUNCT
ejpam-2494	291	2	int(h	int(h	X
ejpam-2494	291	3	)	)	PUNCT
ejpam-2494	292	1	⊂	⊂	PROPN
ejpam-2494	292	2	h.	h.	PROPN
ejpam-2494	292	3	then	then	ADV
ejpam-2494	292	4	we	we	PRON
ejpam-2494	292	5	obtain	obtain	VERB
ejpam-2494	292	6	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	292	7	)	)	PUNCT
ejpam-2494	292	8	)	)	PUNCT
ejpam-2494	293	1	⊂	⊂	PROPN
ejpam-2494	293	2	intω(h	intω(h	PROPN
ejpam-2494	293	3	)	)	PUNCT
ejpam-2494	293	4	⊂	⊂	PROPN
ejpam-2494	293	5	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	293	6	)	)	PUNCT
ejpam-2494	293	7	)	)	PUNCT
ejpam-2494	293	8	.	.	PUNCT
ejpam-2494	294	1	therefore	therefore	ADV
ejpam-2494	294	2	h	h	PROPN
ejpam-2494	294	3	is	be	AUX
ejpam-2494	294	4	δ−ω	δ−ω	NOUN
ejpam-2494	294	5	-	-	PUNCT
ejpam-2494	294	6	open	open	ADJ
ejpam-2494	294	7	.	.	PUNCT
ejpam-2494	294	8	example	example	NOUN
ejpam-2494	295	1	10	10	NUM
ejpam-2494	295	2	.	.	PUNCT
ejpam-2494	296	1	let	let	VERB
ejpam-2494	296	2	x	x	PUNCT
ejpam-2494	296	3	=	=	PUNCT
ejpam-2494	296	4	r	r	NOUN
ejpam-2494	296	5	with	with	ADP
ejpam-2494	296	6	the	the	DET
ejpam-2494	296	7	usual	usual	ADJ
ejpam-2494	296	8	topology	topology	NOUN
ejpam-2494	296	9	τu	τu	PROPN
ejpam-2494	296	10	.	.	PUNCT
ejpam-2494	297	1	(	(	PUNCT
ejpam-2494	297	2	i	i	NOUN
ejpam-2494	297	3	)	)	PUNCT
ejpam-2494	297	4	let	let	VERB
ejpam-2494	297	5	h	h	NOUN
ejpam-2494	297	6	=	=	PUNCT
ejpam-2494	297	7	(	(	PUNCT
ejpam-2494	297	8	0,1	0,1	NUM
ejpam-2494	297	9	]	]	PUNCT
ejpam-2494	297	10	.	.	PUNCT
ejpam-2494	298	1	then	then	ADV
ejpam-2494	298	2	h	h	PROPN
ejpam-2494	298	3	is	be	AUX
ejpam-2494	298	4	δ−ω	δ−ω	NOUN
ejpam-2494	298	5	-	-	PUNCT
ejpam-2494	298	6	open	open	ADJ
ejpam-2494	298	7	but	but	CCONJ
ejpam-2494	298	8	not	not	PART
ejpam-2494	298	9	α−ω	α−ω	NOUN
ejpam-2494	298	10	-	-	VERB
ejpam-2494	298	11	open	open	ADJ
ejpam-2494	298	12	,	,	PUNCT
ejpam-2494	298	13	since	since	SCONJ
ejpam-2494	298	14	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	298	15	)	)	PUNCT
ejpam-2494	298	16	)	)	PUNCT
ejpam-2494	299	1	=	=	PUNCT
ejpam-2494	299	2	(	(	PUNCT
ejpam-2494	299	3	0,1	0,1	NUM
ejpam-2494	299	4	)	)	PUNCT
ejpam-2494	299	5	and	and	CCONJ
ejpam-2494	299	6	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	299	7	)	)	PUNCT
ejpam-2494	299	8	)	)	PUNCT
ejpam-2494	300	1	=	=	PUNCT
ejpam-2494	301	1	[	[	X
ejpam-2494	301	2	0,1	0,1	NUM
ejpam-2494	301	3	]	]	PUNCT
ejpam-2494	301	4	.	.	PUNCT
ejpam-2494	302	1	(	(	PUNCT
ejpam-2494	302	2	ii	ii	NOUN
ejpam-2494	302	3	)	)	PUNCT
ejpam-2494	302	4	let	let	VERB
ejpam-2494	302	5	h	h	NOUN
ejpam-2494	302	6	=	=	PRON
ejpam-2494	302	7	q⋆.	q⋆.	VERB
ejpam-2494	302	8	then	then	ADV
ejpam-2494	302	9	h	h	PROPN
ejpam-2494	302	10	is	be	AUX
ejpam-2494	302	11	δ−ω	δ−ω	NOUN
ejpam-2494	302	12	-	-	PUNCT
ejpam-2494	302	13	open	open	ADJ
ejpam-2494	302	14	but	but	CCONJ
ejpam-2494	302	15	notω−	notω−	NOUN
ejpam-2494	302	16	t	t	PROPN
ejpam-2494	302	17	-	-	PUNCT
ejpam-2494	302	18	set	set	NOUN
ejpam-2494	302	19	,	,	PUNCT
ejpam-2494	302	20	since	since	SCONJ
ejpam-2494	302	21	int(q⋆	int(q⋆	NOUN
ejpam-2494	302	22	)	)	PUNCT
ejpam-2494	302	23	=	=	SYM
ejpam-2494	302	24	φ	φ	NUM
ejpam-2494	302	25	,	,	PUNCT
ejpam-2494	302	26	intω(cl(q⋆	intω(cl(q⋆	NOUN
ejpam-2494	302	27	)	)	PUNCT
ejpam-2494	302	28	)	)	PUNCT
ejpam-2494	303	1	=	=	SYM
ejpam-2494	303	2	r	r	NOUN
ejpam-2494	303	3	and	and	CCONJ
ejpam-2494	303	4	cl(intω(q	cl(intω(q	PROPN
ejpam-2494	303	5	⋆	⋆	NOUN
ejpam-2494	303	6	)	)	PUNCT
ejpam-2494	303	7	)	)	PUNCT
ejpam-2494	304	1	=	=	PUNCT
ejpam-2494	304	2	cl(q⋆	cl(q⋆	X
ejpam-2494	304	3	)	)	PUNCT
ejpam-2494	305	1	=	=	SYM
ejpam-2494	305	2	r.	r.	NOUN
ejpam-2494	305	3	definition	definition	NOUN
ejpam-2494	305	4	11	11	NUM
ejpam-2494	305	5	.	.	PUNCT
ejpam-2494	306	1	a	a	DET
ejpam-2494	306	2	subset	subset	ADJ
ejpam-2494	306	3	h	h	NOUN
ejpam-2494	306	4	of	of	ADP
ejpam-2494	306	5	a	a	DET
ejpam-2494	306	6	space	space	NOUN
ejpam-2494	306	7	(	(	PUNCT
ejpam-2494	306	8	x	x	X
ejpam-2494	306	9	,	,	PUNCT
ejpam-2494	306	10	τ	τ	X
ejpam-2494	306	11	)	)	PUNCT
ejpam-2494	306	12	is	be	AUX
ejpam-2494	306	13	said	say	VERB
ejpam-2494	306	14	to	to	PART
ejpam-2494	306	15	be	be	AUX
ejpam-2494	306	16	β	β	X
ejpam-2494	306	17	−ω	−ω	ADJ
ejpam-2494	306	18	-	-	ADJ
ejpam-2494	306	19	closed	closed	ADJ
ejpam-2494	306	20	if	if	SCONJ
ejpam-2494	306	21	int(clω(int(h	int(clω(int(h	ADJ
ejpam-2494	306	22	)	)	PUNCT
ejpam-2494	306	23	)	)	PUNCT
ejpam-2494	306	24	)	)	PUNCT
ejpam-2494	307	1	⊂	⊂	PROPN
ejpam-2494	307	2	h.	h.	PROPN
ejpam-2494	308	1	the	the	DET
ejpam-2494	308	2	complement	complement	NOUN
ejpam-2494	308	3	of	of	ADP
ejpam-2494	308	4	β	β	X
ejpam-2494	308	5	−ω	−ω	ADJ
ejpam-2494	308	6	-	-	ADJ
ejpam-2494	308	7	open	open	ADJ
ejpam-2494	308	8	set	set	NOUN
ejpam-2494	308	9	is	be	AUX
ejpam-2494	308	10	called	call	VERB
ejpam-2494	308	11	β	β	PUNCT
ejpam-2494	308	12	−ω	−ω	ADJ
ejpam-2494	308	13	-	-	VERB
ejpam-2494	308	14	closed	closed	ADJ
ejpam-2494	308	15	.	.	PUNCT
ejpam-2494	309	1	proposition	proposition	NOUN
ejpam-2494	309	2	6	6	NUM
ejpam-2494	309	3	.	.	PUNCT
ejpam-2494	310	1	let	let	VERB
ejpam-2494	310	2	h	h	PRON
ejpam-2494	310	3	be	be	AUX
ejpam-2494	310	4	a	a	DET
ejpam-2494	310	5	subset	subset	NOUN
ejpam-2494	310	6	of	of	ADP
ejpam-2494	310	7	a	a	DET
ejpam-2494	310	8	space	space	NOUN
ejpam-2494	310	9	(	(	PUNCT
ejpam-2494	310	10	x	x	X
ejpam-2494	310	11	,	,	PUNCT
ejpam-2494	310	12	τ	τ	PROPN
ejpam-2494	310	13	)	)	PUNCT
ejpam-2494	310	14	.	.	PUNCT
ejpam-2494	311	1	then	then	ADV
ejpam-2494	311	2	h	h	PROPN
ejpam-2494	311	3	is	be	AUX
ejpam-2494	311	4	β	β	PROPN
ejpam-2494	311	5	−ω	−ω	ADJ
ejpam-2494	311	6	-	-	ADJ
ejpam-2494	311	7	closed	closed	ADJ
ejpam-2494	311	8	if	if	SCONJ
ejpam-2494	311	9	and	and	CCONJ
ejpam-2494	311	10	only	only	ADV
ejpam-2494	311	11	if	if	SCONJ
ejpam-2494	311	12	int(clω(int(h	int(clω(int(h	ADJ
ejpam-2494	311	13	)	)	PUNCT
ejpam-2494	311	14	)	)	PUNCT
ejpam-2494	311	15	)	)	PUNCT
ejpam-2494	312	1	=	=	PUNCT
ejpam-2494	312	2	int(h	int(h	X
ejpam-2494	312	3	)	)	PUNCT
ejpam-2494	312	4	.	.	PUNCT
ejpam-2494	313	1	proof	proof	NOUN
ejpam-2494	313	2	.	.	PUNCT
ejpam-2494	314	1	since	since	SCONJ
ejpam-2494	314	2	h	h	PROPN
ejpam-2494	314	3	is	be	AUX
ejpam-2494	314	4	β	β	PROPN
ejpam-2494	314	5	−ω	−ω	ADJ
ejpam-2494	314	6	-	-	ADJ
ejpam-2494	314	7	closed	closed	ADJ
ejpam-2494	314	8	set	set	NOUN
ejpam-2494	314	9	,	,	PUNCT
ejpam-2494	314	10	int(clω(int(h	int(clω(int(h	ADJ
ejpam-2494	314	11	)	)	PUNCT
ejpam-2494	314	12	)	)	PUNCT
ejpam-2494	314	13	)	)	PUNCT
ejpam-2494	315	1	⊂	⊂	PROPN
ejpam-2494	315	2	h	h	NOUN
ejpam-2494	316	1	and	and	CCONJ
ejpam-2494	316	2	then	then	ADV
ejpam-2494	316	3	we	we	PRON
ejpam-2494	316	4	obtain	obtain	VERB
ejpam-2494	316	5	int(clω(int(h	int(clω(int(h	ADJ
ejpam-2494	316	6	)	)	PUNCT
ejpam-2494	316	7	)	)	PUNCT
ejpam-2494	316	8	)	)	PUNCT
ejpam-2494	317	1	⊂	⊂	PROPN
ejpam-2494	317	2	int(h	int(h	PROPN
ejpam-2494	317	3	)	)	PUNCT
ejpam-2494	317	4	.	.	PUNCT
ejpam-2494	318	1	but	but	CCONJ
ejpam-2494	318	2	int(h	int(h	X
ejpam-2494	318	3	)	)	PUNCT
ejpam-2494	318	4	⊂	⊂	X
ejpam-2494	318	5	int(clω(int(h	int(clω(int(h	ADJ
ejpam-2494	318	6	)	)	PUNCT
ejpam-2494	318	7	)	)	PUNCT
ejpam-2494	318	8	)	)	PUNCT
ejpam-2494	318	9	.	.	PUNCT
ejpam-2494	319	1	thus	thus	ADV
ejpam-2494	319	2	we	we	PRON
ejpam-2494	319	3	have	have	VERB
ejpam-2494	319	4	int(h	int(h	ADV
ejpam-2494	319	5	)	)	PUNCT
ejpam-2494	319	6	=	=	SYM
ejpam-2494	319	7	int(clω(int(h	int(clω(int(h	NOUN
ejpam-2494	319	8	)	)	PUNCT
ejpam-2494	319	9	)	)	PUNCT
ejpam-2494	319	10	)	)	PUNCT
ejpam-2494	319	11	.	.	PUNCT
ejpam-2494	320	1	conversely	conversely	ADV
ejpam-2494	320	2	,	,	PUNCT
ejpam-2494	320	3	let	let	VERB
ejpam-2494	320	4	the	the	DET
ejpam-2494	320	5	condition	condition	NOUN
ejpam-2494	320	6	hold	hold	VERB
ejpam-2494	320	7	.	.	PUNCT
ejpam-2494	321	1	we	we	PRON
ejpam-2494	321	2	have	have	VERB
ejpam-2494	321	3	int(clω(int(h	int(clω(int(h	ADJ
ejpam-2494	321	4	)	)	PUNCT
ejpam-2494	321	5	)	)	PUNCT
ejpam-2494	321	6	)	)	PUNCT
ejpam-2494	322	1	=	=	PUNCT
ejpam-2494	322	2	int(h	int(h	X
ejpam-2494	322	3	)	)	PUNCT
ejpam-2494	322	4	⊂	⊂	PROPN
ejpam-2494	323	1	h.	h.	PROPN
ejpam-2494	323	2	therefore	therefore	ADV
ejpam-2494	323	3	h	h	PROPN
ejpam-2494	323	4	is	be	AUX
ejpam-2494	323	5	β	β	PROPN
ejpam-2494	323	6	−ω	−ω	ADJ
ejpam-2494	323	7	-	-	ADJ
ejpam-2494	323	8	closed	closed	ADJ
ejpam-2494	323	9	.	.	PUNCT
ejpam-2494	324	1	theorem	theorem	VERB
ejpam-2494	324	2	9	9	NUM
ejpam-2494	324	3	.	.	X
ejpam-2494	325	1	for	for	ADP
ejpam-2494	325	2	a	a	DET
ejpam-2494	325	3	subset	subset	ADJ
ejpam-2494	325	4	h	h	NOUN
ejpam-2494	325	5	of	of	ADP
ejpam-2494	325	6	a	a	DET
ejpam-2494	325	7	space	space	NOUN
ejpam-2494	325	8	(	(	PUNCT
ejpam-2494	325	9	x	x	X
ejpam-2494	325	10	,	,	PUNCT
ejpam-2494	325	11	τ	τ	PROPN
ejpam-2494	325	12	)	)	PUNCT
ejpam-2494	325	13	,	,	PUNCT
ejpam-2494	325	14	the	the	DET
ejpam-2494	325	15	following	follow	VERB
ejpam-2494	325	16	properties	property	NOUN
ejpam-2494	325	17	are	be	AUX
ejpam-2494	325	18	equivalent	equivalent	ADJ
ejpam-2494	325	19	:	:	PUNCT
ejpam-2494	325	20	(	(	PUNCT
ejpam-2494	325	21	i	i	NOUN
ejpam-2494	325	22	)	)	PUNCT
ejpam-2494	325	23	h	h	PROPN
ejpam-2494	325	24	is	be	AUX
ejpam-2494	325	25	semi	semi	ADJ
ejpam-2494	325	26	-	-	ADJ
ejpam-2494	325	27	ω	ω	ADV
ejpam-2494	325	28	-	-	PUNCT
ejpam-2494	325	29	closed	closed	ADJ
ejpam-2494	325	30	.	.	PUNCT
ejpam-2494	326	1	(	(	PUNCT
ejpam-2494	326	2	ii	ii	NOUN
ejpam-2494	326	3	)	)	PUNCT
ejpam-2494	326	4	h	h	PROPN
ejpam-2494	326	5	is	be	AUX
ejpam-2494	326	6	β	β	PROPN
ejpam-2494	326	7	−ω	−ω	ADJ
ejpam-2494	326	8	-	-	ADJ
ejpam-2494	326	9	closed	closed	ADJ
ejpam-2494	326	10	and	and	CCONJ
ejpam-2494	326	11	δ−ω	δ−ω	NOUN
ejpam-2494	326	12	-	-	PUNCT
ejpam-2494	326	13	closed	closed	ADJ
ejpam-2494	326	14	.	.	PUNCT
ejpam-2494	327	1	o.	o.	PROPN
ejpam-2494	327	2	ravi	ravi	PROPN
ejpam-2494	327	3	,	,	PUNCT
ejpam-2494	327	4	i.	i.	NOUN
ejpam-2494	327	5	rajasekaran	rajasekaran	PROPN
ejpam-2494	327	6	,	,	PUNCT
ejpam-2494	327	7	s.	s.	PROPN
ejpam-2494	327	8	kanna	kanna	PROPN
ejpam-2494	327	9	and	and	CCONJ
ejpam-2494	327	10	m.	m.	NOUN
ejpam-2494	327	11	paranjothi	paranjothi	PROPN
ejpam-2494	327	12	/	/	SYM
ejpam-2494	327	13	eur	eur	PROPN
ejpam-2494	327	14	.	.	PUNCT
ejpam-2494	328	1	j.	j.	PROPN
ejpam-2494	328	2	pure	pure	PROPN
ejpam-2494	328	3	appl	appl	PROPN
ejpam-2494	328	4	.	.	PROPN
ejpam-2494	328	5	math	math	PROPN
ejpam-2494	328	6	,	,	PUNCT
ejpam-2494	328	7	9	9	NUM
ejpam-2494	328	8	(	(	PUNCT
ejpam-2494	328	9	2016	2016	NUM
ejpam-2494	328	10	)	)	PUNCT
ejpam-2494	328	11	,	,	PUNCT
ejpam-2494	328	12	152	152	NUM
ejpam-2494	328	13	-	-	SYM
ejpam-2494	328	14	164	164	NUM
ejpam-2494	328	15	159	159	NUM
ejpam-2494	328	16	proof	proof	NOUN
ejpam-2494	328	17	.	.	PUNCT
ejpam-2494	329	1	(	(	PUNCT
ejpam-2494	329	2	i)⇒	i)⇒	PROPN
ejpam-2494	329	3	(	(	PUNCT
ejpam-2494	329	4	ii	ii	NOUN
ejpam-2494	329	5	):	):	PUNCT
ejpam-2494	329	6	let	let	VERB
ejpam-2494	329	7	h	h	PRON
ejpam-2494	329	8	be	be	AUX
ejpam-2494	329	9	semi	semi	ADJ
ejpam-2494	329	10	-	-	ADJ
ejpam-2494	329	11	ω	ω	ADV
ejpam-2494	329	12	-	-	PUNCT
ejpam-2494	329	13	closed	closed	ADJ
ejpam-2494	329	14	.	.	PUNCT
ejpam-2494	330	1	by	by	ADP
ejpam-2494	330	2	theorem	theorem	ADJ
ejpam-2494	330	3	2(iii	2(iii	NUM
ejpam-2494	330	4	)	)	PUNCT
ejpam-2494	330	5	,	,	PUNCT
ejpam-2494	330	6	h	h	PROPN
ejpam-2494	330	7	is	be	AUX
ejpam-2494	330	8	β	β	PROPN
ejpam-2494	330	9	−ω	−ω	ADJ
ejpam-2494	330	10	-	-	ADJ
ejpam-2494	330	11	closed	closed	ADJ
ejpam-2494	330	12	.	.	PUNCT
ejpam-2494	331	1	since	since	SCONJ
ejpam-2494	331	2	h	h	PROPN
ejpam-2494	331	3	is	be	AUX
ejpam-2494	331	4	semi	semi	ADJ
ejpam-2494	331	5	-	-	ADJ
ejpam-2494	331	6	ω	ω	ADJ
ejpam-2494	331	7	-	-	PUNCT
ejpam-2494	331	8	closed	closed	ADJ
ejpam-2494	331	9	,	,	PUNCT
ejpam-2494	331	10	int(clω(h	int(clω(h	PROPN
ejpam-2494	331	11	)	)	PUNCT
ejpam-2494	331	12	)	)	PUNCT
ejpam-2494	332	1	⊂	⊂	PROPN
ejpam-2494	332	2	h	h	PROPN
ejpam-2494	332	3	and	and	CCONJ
ejpam-2494	332	4	int(clω(h	int(clω(h	PROPN
ejpam-2494	332	5	)	)	PUNCT
ejpam-2494	332	6	)	)	PUNCT
ejpam-2494	333	1	⊂	⊂	PROPN
ejpam-2494	333	2	int(h	int(h	PROPN
ejpam-2494	333	3	)	)	PUNCT
ejpam-2494	333	4	.	.	PUNCT
ejpam-2494	334	1	it	it	PRON
ejpam-2494	334	2	gives	give	VERB
ejpam-2494	334	3	that	that	DET
ejpam-2494	334	4	clω(int(clω(h	clω(int(clω(h	NOUN
ejpam-2494	334	5	)	)	PUNCT
ejpam-2494	334	6	)	)	PUNCT
ejpam-2494	334	7	)	)	PUNCT
ejpam-2494	335	1	⊂	⊂	PROPN
ejpam-2494	335	2	clω(int(h	clω(int(h	NOUN
ejpam-2494	335	3	)	)	PUNCT
ejpam-2494	335	4	)	)	PUNCT
ejpam-2494	335	5	.	.	PUNCT
ejpam-2494	336	1	thus	thus	ADV
ejpam-2494	336	2	int(clω(h	int(clω(h	NUM
ejpam-2494	336	3	)	)	PUNCT
ejpam-2494	336	4	)	)	PUNCT
ejpam-2494	337	1	⊂	⊂	PROPN
ejpam-2494	337	2	clω(int(clω(h	clω(int(clω(h	NOUN
ejpam-2494	337	3	)	)	PUNCT
ejpam-2494	337	4	)	)	PUNCT
ejpam-2494	337	5	)	)	PUNCT
ejpam-2494	338	1	⊂	⊂	PROPN
ejpam-2494	338	2	clω(int(h	clω(int(h	NOUN
ejpam-2494	338	3	)	)	PUNCT
ejpam-2494	338	4	)	)	PUNCT
ejpam-2494	339	1	and	and	CCONJ
ejpam-2494	339	2	so	so	ADV
ejpam-2494	339	3	h	h	NOUN
ejpam-2494	339	4	is	be	AUX
ejpam-2494	339	5	δ−ω	δ−ω	NOUN
ejpam-2494	339	6	-	-	PUNCT
ejpam-2494	339	7	closed	closed	ADJ
ejpam-2494	339	8	.	.	PUNCT
ejpam-2494	340	1	(	(	PUNCT
ejpam-2494	340	2	ii)⇒	ii)⇒	PROPN
ejpam-2494	340	3	(	(	PUNCT
ejpam-2494	340	4	i	i	NOUN
ejpam-2494	340	5	):	):	PUNCT
ejpam-2494	340	6	since	since	SCONJ
ejpam-2494	340	7	h	h	NOUN
ejpam-2494	340	8	is	be	AUX
ejpam-2494	340	9	δ−ω	δ−ω	NOUN
ejpam-2494	340	10	-	-	PUNCT
ejpam-2494	340	11	closed	closed	ADJ
ejpam-2494	340	12	,	,	PUNCT
ejpam-2494	340	13	int(clω(h	int(clω(h	PROPN
ejpam-2494	340	14	)	)	PUNCT
ejpam-2494	340	15	)	)	PUNCT
ejpam-2494	341	1	⊂	⊂	PROPN
ejpam-2494	341	2	clω(int(h	clω(int(h	NOUN
ejpam-2494	341	3	)	)	PUNCT
ejpam-2494	341	4	)	)	PUNCT
ejpam-2494	341	5	and	and	CCONJ
ejpam-2494	341	6	int(clω(h	int(clω(h	NUM
ejpam-2494	341	7	)	)	PUNCT
ejpam-2494	341	8	)	)	PUNCT
ejpam-2494	342	1	⊂	⊂	PROPN
ejpam-2494	342	2	int(clω(int(h	int(clω(int(h	ADJ
ejpam-2494	342	3	)	)	PUNCT
ejpam-2494	342	4	)	)	PUNCT
ejpam-2494	342	5	)	)	PUNCT
ejpam-2494	342	6	.	.	PUNCT
ejpam-2494	343	1	since	since	SCONJ
ejpam-2494	343	2	h	h	PROPN
ejpam-2494	343	3	is	be	AUX
ejpam-2494	343	4	β	β	X
ejpam-2494	343	5	−	−	PROPN
ejpam-2494	343	6	ω	ω	PROPN
ejpam-2494	343	7	-	-	PUNCT
ejpam-2494	343	8	closed	closed	ADJ
ejpam-2494	343	9	,	,	PUNCT
ejpam-2494	343	10	int(clω(int(h	int(clω(int(h	ADJ
ejpam-2494	343	11	)	)	PUNCT
ejpam-2494	343	12	)	)	PUNCT
ejpam-2494	343	13	)	)	PUNCT
ejpam-2494	344	1	⊂	⊂	PROPN
ejpam-2494	344	2	h.	h.	PROPN
ejpam-2494	344	3	then	then	ADV
ejpam-2494	344	4	int(clω(h	int(clω(h	PROPN
ejpam-2494	344	5	)	)	PUNCT
ejpam-2494	344	6	)	)	PUNCT
ejpam-2494	345	1	⊂	⊂	PROPN
ejpam-2494	345	2	h	h	NOUN
ejpam-2494	346	1	and	and	CCONJ
ejpam-2494	346	2	so	so	ADV
ejpam-2494	346	3	h	h	NOUN
ejpam-2494	346	4	is	be	AUX
ejpam-2494	346	5	semi	semi	ADJ
ejpam-2494	346	6	-	-	ADJ
ejpam-2494	346	7	ω	ω	ADV
ejpam-2494	346	8	-	-	PUNCT
ejpam-2494	346	9	closed	closed	ADJ
ejpam-2494	346	10	.	.	PUNCT
ejpam-2494	347	1	remark	remark	NOUN
ejpam-2494	347	2	5	5	NUM
ejpam-2494	347	3	.	.	PUNCT
ejpam-2494	348	1	the	the	DET
ejpam-2494	348	2	concepts	concept	NOUN
ejpam-2494	348	3	of	of	ADP
ejpam-2494	348	4	β	β	PROPN
ejpam-2494	348	5	−ω	−ω	ADJ
ejpam-2494	348	6	-	-	PUNCT
ejpam-2494	348	7	closedness	closedness	ADJ
ejpam-2494	348	8	and	and	CCONJ
ejpam-2494	348	9	δ−ω	δ−ω	NOUN
ejpam-2494	348	10	-	-	PUNCT
ejpam-2494	348	11	closedness	closedness	NOUN
ejpam-2494	348	12	are	be	AUX
ejpam-2494	348	13	independent	independent	ADJ
ejpam-2494	348	14	.	.	PUNCT
ejpam-2494	348	15	example	example	NOUN
ejpam-2494	349	1	11	11	NUM
ejpam-2494	349	2	.	.	PUNCT
ejpam-2494	350	1	(	(	PUNCT
ejpam-2494	350	2	i	i	NOUN
ejpam-2494	350	3	)	)	PUNCT
ejpam-2494	350	4	let	let	VERB
ejpam-2494	350	5	x	x	PUNCT
ejpam-2494	350	6	=	=	PUNCT
ejpam-2494	350	7	r	r	NOUN
ejpam-2494	350	8	with	with	ADP
ejpam-2494	350	9	the	the	DET
ejpam-2494	350	10	topology	topology	NOUN
ejpam-2494	350	11	τ	τ	X
ejpam-2494	350	12	=	=	SYM
ejpam-2494	350	13	{	{	PUNCT
ejpam-2494	350	14	φ	φ	PROPN
ejpam-2494	350	15	,	,	PUNCT
ejpam-2494	350	16	x	x	INTJ
ejpam-2494	350	17	,	,	PUNCT
ejpam-2494	350	18	q⋆	q⋆	NOUN
ejpam-2494	350	19	}	}	PUNCT
ejpam-2494	350	20	.	.	PUNCT
ejpam-2494	351	1	let	let	VERB
ejpam-2494	351	2	h	h	NOUN
ejpam-2494	351	3	=	=	PRON
ejpam-2494	351	4	q⋆.	q⋆.	VERB
ejpam-2494	351	5	then	then	ADV
ejpam-2494	351	6	h	h	PROPN
ejpam-2494	351	7	is	be	AUX
ejpam-2494	351	8	δ−ω	δ−ω	NOUN
ejpam-2494	351	9	-	-	PUNCT
ejpam-2494	351	10	closed	closed	ADJ
ejpam-2494	351	11	but	but	CCONJ
ejpam-2494	351	12	not	not	PART
ejpam-2494	351	13	β	β	X
ejpam-2494	351	14	−ω	−ω	ADJ
ejpam-2494	351	15	-	-	VERB
ejpam-2494	351	16	closed	closed	ADJ
ejpam-2494	351	17	,	,	PUNCT
ejpam-2494	351	18	since	since	SCONJ
ejpam-2494	351	19	q	q	NOUN
ejpam-2494	351	20	is	be	AUX
ejpam-2494	351	21	not	not	PART
ejpam-2494	351	22	β	β	X
ejpam-2494	351	23	−ω	−ω	ADJ
ejpam-2494	351	24	-	-	ADJ
ejpam-2494	351	25	open	open	ADJ
ejpam-2494	351	26	.	.	PUNCT
ejpam-2494	352	1	(	(	PUNCT
ejpam-2494	352	2	ii	ii	NOUN
ejpam-2494	352	3	)	)	PUNCT
ejpam-2494	352	4	let	let	VERB
ejpam-2494	352	5	x	x	PUNCT
ejpam-2494	352	6	=	=	PUNCT
ejpam-2494	352	7	r	r	NOUN
ejpam-2494	352	8	with	with	ADP
ejpam-2494	352	9	the	the	DET
ejpam-2494	352	10	usual	usual	ADJ
ejpam-2494	352	11	topology	topology	NOUN
ejpam-2494	352	12	τu	τu	PROPN
ejpam-2494	352	13	.	.	PUNCT
ejpam-2494	353	1	let	let	VERB
ejpam-2494	353	2	h	h	NOUN
ejpam-2494	353	3	=	=	PRON
ejpam-2494	353	4	q⋆.	q⋆.	VERB
ejpam-2494	354	1	then	then	ADV
ejpam-2494	354	2	h	h	PROPN
ejpam-2494	354	3	is	be	AUX
ejpam-2494	354	4	β	β	PROPN
ejpam-2494	354	5	−	−	PROPN
ejpam-2494	354	6	ω	ω	PROPN
ejpam-2494	354	7	-	-	PUNCT
ejpam-2494	354	8	closed	closed	ADJ
ejpam-2494	354	9	but	but	CCONJ
ejpam-2494	354	10	not	not	PART
ejpam-2494	354	11	δ−ω	δ−ω	NOUN
ejpam-2494	354	12	-	-	PUNCT
ejpam-2494	354	13	closed	closed	ADJ
ejpam-2494	354	14	,	,	PUNCT
ejpam-2494	354	15	since	since	SCONJ
ejpam-2494	354	16	q	q	NOUN
ejpam-2494	354	17	is	be	AUX
ejpam-2494	354	18	not	not	PART
ejpam-2494	354	19	δ−ω	δ−ω	NOUN
ejpam-2494	354	20	-	-	PUNCT
ejpam-2494	354	21	open	open	ADJ
ejpam-2494	354	22	.	.	PUNCT
ejpam-2494	355	1	theorem	theorem	ADJ
ejpam-2494	355	2	10	10	NUM
ejpam-2494	355	3	.	.	PUNCT
ejpam-2494	356	1	let	let	AUX
ejpam-2494	356	2	(	(	PUNCT
ejpam-2494	356	3	x	x	X
ejpam-2494	356	4	,	,	PUNCT
ejpam-2494	356	5	τ	τ	X
ejpam-2494	356	6	)	)	PUNCT
ejpam-2494	356	7	be	be	AUX
ejpam-2494	356	8	a	a	DET
ejpam-2494	356	9	space	space	NOUN
ejpam-2494	356	10	.	.	PUNCT
ejpam-2494	357	1	then	then	ADV
ejpam-2494	357	2	a	a	DET
ejpam-2494	357	3	subset	subset	NOUN
ejpam-2494	357	4	of	of	ADP
ejpam-2494	357	5	x	x	PROPN
ejpam-2494	357	6	is	be	AUX
ejpam-2494	357	7	α	α	PRON
ejpam-2494	357	8	−ω	−ω	NOUN
ejpam-2494	357	9	-	-	ADJ
ejpam-2494	357	10	open	open	ADJ
ejpam-2494	357	11	if	if	SCONJ
ejpam-2494	357	12	and	and	CCONJ
ejpam-2494	357	13	only	only	ADV
ejpam-2494	357	14	if	if	SCONJ
ejpam-2494	357	15	it	it	PRON
ejpam-2494	357	16	is	be	AUX
ejpam-2494	357	17	both	both	DET
ejpam-2494	357	18	δ−ω	δ−ω	NOUN
ejpam-2494	357	19	-	-	PUNCT
ejpam-2494	357	20	open	open	ADJ
ejpam-2494	357	21	and	and	CCONJ
ejpam-2494	357	22	pre	pre	ADJ
ejpam-2494	357	23	-	-	ADJ
ejpam-2494	357	24	ω	ω	VERB
ejpam-2494	357	25	-	-	ADJ
ejpam-2494	357	26	open	open	ADJ
ejpam-2494	357	27	.	.	PUNCT
ejpam-2494	358	1	proof	proof	NOUN
ejpam-2494	358	2	.	.	PUNCT
ejpam-2494	359	1	necessity	necessity	NOUN
ejpam-2494	359	2	:	:	PUNCT
ejpam-2494	359	3	let	let	VERB
ejpam-2494	359	4	h	h	NOUN
ejpam-2494	359	5	be	be	AUX
ejpam-2494	359	6	an	an	DET
ejpam-2494	359	7	α	α	NOUN
ejpam-2494	359	8	−ω	−ω	ADJ
ejpam-2494	359	9	-	-	ADJ
ejpam-2494	359	10	open	open	ADJ
ejpam-2494	359	11	set	set	NOUN
ejpam-2494	359	12	.	.	PUNCT
ejpam-2494	360	1	then	then	ADV
ejpam-2494	360	2	h	h	PROPN
ejpam-2494	360	3	⊂	⊂	PROPN
ejpam-2494	360	4	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	360	5	)	)	PUNCT
ejpam-2494	360	6	)	)	PUNCT
ejpam-2494	360	7	)	)	PUNCT
ejpam-2494	360	8	.	.	PUNCT
ejpam-2494	361	1	it	it	PRON
ejpam-2494	361	2	implies	imply	VERB
ejpam-2494	361	3	that	that	PRON
ejpam-2494	361	4	cl(h	cl(h	CCONJ
ejpam-2494	361	5	)	)	PUNCT
ejpam-2494	361	6	⊂	⊂	PROPN
ejpam-2494	361	7	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	361	8	)	)	PUNCT
ejpam-2494	361	9	)	)	PUNCT
ejpam-2494	361	10	and	and	CCONJ
ejpam-2494	361	11	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	361	12	)	)	PUNCT
ejpam-2494	361	13	)	)	PUNCT
ejpam-2494	362	1	⊂	⊂	PROPN
ejpam-2494	362	2	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	362	3	)	)	PUNCT
ejpam-2494	362	4	)	)	PUNCT
ejpam-2494	362	5	)	)	PUNCT
ejpam-2494	363	1	⊂	⊂	PROPN
ejpam-2494	363	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	363	3	)	)	PUNCT
ejpam-2494	363	4	)	)	PUNCT
ejpam-2494	363	5	.	.	PUNCT
ejpam-2494	364	1	hence	hence	ADV
ejpam-2494	364	2	,	,	PUNCT
ejpam-2494	364	3	h	h	PROPN
ejpam-2494	364	4	is	be	AUX
ejpam-2494	364	5	a	a	DET
ejpam-2494	364	6	δ−ω	δ−ω	NOUN
ejpam-2494	364	7	-	-	PUNCT
ejpam-2494	364	8	open	open	ADJ
ejpam-2494	364	9	set	set	NOUN
ejpam-2494	364	10	.	.	PUNCT
ejpam-2494	365	1	on	on	ADP
ejpam-2494	365	2	the	the	DET
ejpam-2494	365	3	other	other	ADJ
ejpam-2494	365	4	hand	hand	NOUN
ejpam-2494	365	5	,	,	PUNCT
ejpam-2494	365	6	since	since	SCONJ
ejpam-2494	365	7	h	h	NOUN
ejpam-2494	365	8	is	be	AUX
ejpam-2494	365	9	an	an	DET
ejpam-2494	365	10	α−ω	α−ω	NOUN
ejpam-2494	365	11	-	-	PUNCT
ejpam-2494	365	12	open	open	ADJ
ejpam-2494	365	13	set	set	NOUN
ejpam-2494	365	14	,	,	PUNCT
ejpam-2494	365	15	h	h	PROPN
ejpam-2494	365	16	is	be	AUX
ejpam-2494	365	17	a	a	DET
ejpam-2494	365	18	pre	pre	ADJ
ejpam-2494	365	19	-	-	ADJ
ejpam-2494	365	20	ω	ω	ADJ
ejpam-2494	365	21	-	-	PUNCT
ejpam-2494	365	22	open	open	ADJ
ejpam-2494	365	23	set	set	NOUN
ejpam-2494	365	24	.	.	PUNCT
ejpam-2494	366	1	sufficiency	sufficiency	NOUN
ejpam-2494	366	2	:	:	PUNCT
ejpam-2494	366	3	let	let	VERB
ejpam-2494	366	4	h	h	NOUN
ejpam-2494	366	5	be	be	AUX
ejpam-2494	366	6	both	both	DET
ejpam-2494	366	7	δ−ω	δ−ω	NOUN
ejpam-2494	366	8	-	-	PUNCT
ejpam-2494	366	9	open	open	ADJ
ejpam-2494	366	10	and	and	CCONJ
ejpam-2494	366	11	pre	pre	ADJ
ejpam-2494	366	12	-	-	ADJ
ejpam-2494	366	13	ω	ω	VERB
ejpam-2494	366	14	-	-	NOUN
ejpam-2494	366	15	open	open	ADJ
ejpam-2494	366	16	.	.	PUNCT
ejpam-2494	367	1	since	since	SCONJ
ejpam-2494	367	2	h	h	NOUN
ejpam-2494	367	3	is	be	AUX
ejpam-2494	367	4	δ−ω	δ−ω	NOUN
ejpam-2494	367	5	-	-	PUNCT
ejpam-2494	367	6	open	open	ADJ
ejpam-2494	367	7	,	,	PUNCT
ejpam-2494	367	8	we	we	PRON
ejpam-2494	367	9	have	have	VERB
ejpam-2494	367	10	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	367	11	)	)	PUNCT
ejpam-2494	367	12	)	)	PUNCT
ejpam-2494	368	1	⊂	⊂	PROPN
ejpam-2494	368	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	368	3	)	)	PUNCT
ejpam-2494	368	4	)	)	PUNCT
ejpam-2494	368	5	and	and	CCONJ
ejpam-2494	368	6	hence	hence	ADV
ejpam-2494	368	7	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	368	8	)	)	PUNCT
ejpam-2494	368	9	)	)	PUNCT
ejpam-2494	369	1	⊂	⊂	PROPN
ejpam-2494	369	2	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	369	3	)	)	PUNCT
ejpam-2494	369	4	)	)	PUNCT
ejpam-2494	369	5	)	)	PUNCT
ejpam-2494	369	6	.	.	PUNCT
ejpam-2494	370	1	since	since	SCONJ
ejpam-2494	370	2	h	h	PROPN
ejpam-2494	370	3	is	be	AUX
ejpam-2494	370	4	pre	pre	ADJ
ejpam-2494	370	5	-	-	ADJ
ejpam-2494	370	6	ωopen	ωopen	ADJ
ejpam-2494	370	7	,	,	PUNCT
ejpam-2494	370	8	we	we	PRON
ejpam-2494	370	9	have	have	VERB
ejpam-2494	370	10	h	h	PROPN
ejpam-2494	370	11	⊂	⊂	PROPN
ejpam-2494	370	12	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	370	13	)	)	PUNCT
ejpam-2494	370	14	)	)	PUNCT
ejpam-2494	370	15	.	.	PUNCT
ejpam-2494	371	1	therefore	therefore	ADV
ejpam-2494	371	2	we	we	PRON
ejpam-2494	371	3	obtain	obtain	VERB
ejpam-2494	371	4	that	that	SCONJ
ejpam-2494	371	5	h	h	PROPN
ejpam-2494	371	6	⊂	⊂	PROPN
ejpam-2494	371	7	intω(cl(intω(h	intω(cl(intω(h	NOUN
ejpam-2494	371	8	)	)	PUNCT
ejpam-2494	371	9	)	)	PUNCT
ejpam-2494	371	10	)	)	PUNCT
ejpam-2494	371	11	which	which	PRON
ejpam-2494	371	12	proves	prove	VERB
ejpam-2494	371	13	that	that	SCONJ
ejpam-2494	371	14	h	h	NOUN
ejpam-2494	371	15	is	be	AUX
ejpam-2494	371	16	an	an	DET
ejpam-2494	371	17	α−ω	α−ω	NOUN
ejpam-2494	371	18	-	-	PUNCT
ejpam-2494	371	19	open	open	ADJ
ejpam-2494	371	20	set	set	NOUN
ejpam-2494	371	21	.	.	PUNCT
ejpam-2494	372	1	remark	remark	PROPN
ejpam-2494	372	2	6	6	NUM
ejpam-2494	372	3	.	.	PUNCT
ejpam-2494	373	1	the	the	DET
ejpam-2494	373	2	concepts	concept	NOUN
ejpam-2494	373	3	of	of	ADP
ejpam-2494	373	4	δ−ω	δ−ω	NOUN
ejpam-2494	373	5	-	-	PUNCT
ejpam-2494	373	6	openness	openness	NOUN
ejpam-2494	373	7	and	and	CCONJ
ejpam-2494	373	8	pre	pre	ADJ
ejpam-2494	373	9	-	-	ADJ
ejpam-2494	373	10	ω	ω	ADJ
ejpam-2494	373	11	-	-	PUNCT
ejpam-2494	373	12	openness	openness	NOUN
ejpam-2494	373	13	are	be	AUX
ejpam-2494	373	14	independent	independent	ADJ
ejpam-2494	373	15	.	.	PUNCT
ejpam-2494	373	16	example	example	NOUN
ejpam-2494	374	1	12	12	NUM
ejpam-2494	374	2	.	.	PUNCT
ejpam-2494	375	1	let	let	VERB
ejpam-2494	375	2	x	x	PUNCT
ejpam-2494	375	3	=	=	PUNCT
ejpam-2494	375	4	r	r	NOUN
ejpam-2494	375	5	with	with	ADP
ejpam-2494	375	6	the	the	DET
ejpam-2494	375	7	usual	usual	ADJ
ejpam-2494	375	8	topology	topology	NOUN
ejpam-2494	375	9	τu	τu	PROPN
ejpam-2494	375	10	.	.	PUNCT
ejpam-2494	376	1	(	(	PUNCT
ejpam-2494	376	2	i	i	NOUN
ejpam-2494	376	3	)	)	PUNCT
ejpam-2494	376	4	h	h	NOUN
ejpam-2494	376	5	=	=	SYM
ejpam-2494	376	6	(	(	PUNCT
ejpam-2494	376	7	0,1	0,1	NUM
ejpam-2494	376	8	]	]	PUNCT
ejpam-2494	376	9	is	be	AUX
ejpam-2494	376	10	δ−ω	δ−ω	NOUN
ejpam-2494	376	11	-	-	PUNCT
ejpam-2494	376	12	open	open	ADJ
ejpam-2494	376	13	but	but	CCONJ
ejpam-2494	376	14	not	not	PART
ejpam-2494	376	15	pre	pre	ADJ
ejpam-2494	376	16	-	-	ADJ
ejpam-2494	376	17	ω	ω	ADV
ejpam-2494	376	18	-	-	NOUN
ejpam-2494	376	19	open	open	ADJ
ejpam-2494	376	20	.	.	PUNCT
ejpam-2494	377	1	(	(	PUNCT
ejpam-2494	377	2	ii	ii	NOUN
ejpam-2494	377	3	)	)	PUNCT
ejpam-2494	377	4	h	h	NOUN
ejpam-2494	378	1	=	=	PUNCT
ejpam-2494	378	2	q	q	PROPN
ejpam-2494	378	3	is	be	AUX
ejpam-2494	378	4	pre	pre	ADJ
ejpam-2494	378	5	-	-	ADJ
ejpam-2494	378	6	ω	ω	ADV
ejpam-2494	378	7	-	-	ADJ
ejpam-2494	378	8	open	open	ADJ
ejpam-2494	378	9	but	but	CCONJ
ejpam-2494	378	10	not	not	PART
ejpam-2494	378	11	δ−ω	δ−ω	NOUN
ejpam-2494	378	12	-	-	PUNCT
ejpam-2494	378	13	open	open	ADJ
ejpam-2494	378	14	.	.	PUNCT
ejpam-2494	379	1	proposition	proposition	NOUN
ejpam-2494	379	2	7	7	NUM
ejpam-2494	379	3	.	.	PUNCT
ejpam-2494	380	1	let	let	VERB
ejpam-2494	380	2	a	a	PRON
ejpam-2494	380	3	and	and	CCONJ
ejpam-2494	380	4	b	b	NOUN
ejpam-2494	380	5	be	be	AUX
ejpam-2494	380	6	subsets	subset	NOUN
ejpam-2494	380	7	of	of	ADP
ejpam-2494	380	8	a	a	DET
ejpam-2494	380	9	space	space	NOUN
ejpam-2494	380	10	(	(	PUNCT
ejpam-2494	380	11	x	x	X
ejpam-2494	380	12	,	,	PUNCT
ejpam-2494	380	13	τ	τ	PROPN
ejpam-2494	380	14	)	)	PUNCT
ejpam-2494	380	15	.	.	PUNCT
ejpam-2494	381	1	if	if	SCONJ
ejpam-2494	381	2	a⊂	a⊂	PRON
ejpam-2494	381	3	b	b	X
ejpam-2494	381	4	⊂	⊂	X
ejpam-2494	381	5	cl(a	cl(a	X
ejpam-2494	381	6	)	)	PUNCT
ejpam-2494	381	7	and	and	CCONJ
ejpam-2494	381	8	a	a	PRON
ejpam-2494	381	9	is	be	AUX
ejpam-2494	381	10	δ−ω	δ−ω	NOUN
ejpam-2494	381	11	-	-	PUNCT
ejpam-2494	381	12	open	open	ADJ
ejpam-2494	381	13	in	in	ADP
ejpam-2494	381	14	x	x	NOUN
ejpam-2494	381	15	,	,	PUNCT
ejpam-2494	381	16	then	then	ADV
ejpam-2494	381	17	b	b	NOUN
ejpam-2494	381	18	is	be	AUX
ejpam-2494	381	19	δ−ω	δ−ω	NOUN
ejpam-2494	381	20	-	-	PUNCT
ejpam-2494	381	21	open	open	ADJ
ejpam-2494	381	22	in	in	ADP
ejpam-2494	381	23	x.	x.	NOUN
ejpam-2494	381	24	proof	proof	NOUN
ejpam-2494	381	25	.	.	PUNCT
ejpam-2494	382	1	suppose	suppose	VERB
ejpam-2494	382	2	that	that	SCONJ
ejpam-2494	382	3	a⊂	a⊂	NOUN
ejpam-2494	382	4	b	b	PROPN
ejpam-2494	382	5	⊂	⊂	X
ejpam-2494	382	6	cl(a	cl(a	X
ejpam-2494	382	7	)	)	PUNCT
ejpam-2494	382	8	and	and	CCONJ
ejpam-2494	382	9	a	a	PRON
ejpam-2494	382	10	is	be	AUX
ejpam-2494	382	11	δ−ω	δ−ω	NOUN
ejpam-2494	382	12	-	-	PUNCT
ejpam-2494	382	13	open	open	ADJ
ejpam-2494	382	14	in	in	ADP
ejpam-2494	382	15	x.	x.	NOUN
ejpam-2494	382	16	then	then	ADV
ejpam-2494	382	17	,	,	PUNCT
ejpam-2494	382	18	we	we	PRON
ejpam-2494	382	19	have	have	VERB
ejpam-2494	382	20	intω(cl(a	intω(cl(a	VERB
ejpam-2494	382	21	)	)	PUNCT
ejpam-2494	382	22	)	)	PUNCT
ejpam-2494	383	1	⊂	⊂	PROPN
ejpam-2494	383	2	cl(intω(a	cl(intω(a	NOUN
ejpam-2494	383	3	)	)	PUNCT
ejpam-2494	383	4	)	)	PUNCT
ejpam-2494	383	5	.	.	PUNCT
ejpam-2494	384	1	since	since	SCONJ
ejpam-2494	384	2	a⊂	a⊂	NOUN
ejpam-2494	384	3	b	b	NOUN
ejpam-2494	384	4	,	,	PUNCT
ejpam-2494	384	5	cl(intω(a	cl(intω(a	NOUN
ejpam-2494	384	6	)	)	PUNCT
ejpam-2494	384	7	)	)	PUNCT
ejpam-2494	384	8	⊂	⊂	PROPN
ejpam-2494	384	9	cl(intω(b	cl(intω(b	PROPN
ejpam-2494	384	10	)	)	PUNCT
ejpam-2494	384	11	)	)	PUNCT
ejpam-2494	384	12	and	and	CCONJ
ejpam-2494	384	13	intω(cl(a	intω(cl(a	NOUN
ejpam-2494	384	14	)	)	PUNCT
ejpam-2494	384	15	)	)	PUNCT
ejpam-2494	384	16	⊂	⊂	PROPN
ejpam-2494	384	17	cl(intω(b	cl(intω(b	PROPN
ejpam-2494	384	18	)	)	PUNCT
ejpam-2494	384	19	)	)	PUNCT
ejpam-2494	384	20	.	.	PUNCT
ejpam-2494	385	1	since	since	SCONJ
ejpam-2494	385	2	b	b	PROPN
ejpam-2494	385	3	⊂	⊂	PROPN
ejpam-2494	385	4	cl(a	cl(a	X
ejpam-2494	385	5	)	)	PUNCT
ejpam-2494	385	6	,	,	PUNCT
ejpam-2494	385	7	we	we	PRON
ejpam-2494	385	8	have	have	VERB
ejpam-2494	385	9	cl(b	cl(b	NOUN
ejpam-2494	385	10	)	)	PUNCT
ejpam-2494	386	1	⊂	⊂	PROPN
ejpam-2494	386	2	cl(cl(a	cl(cl(a	PROPN
ejpam-2494	386	3	)	)	PUNCT
ejpam-2494	386	4	)	)	PUNCT
ejpam-2494	387	1	=	=	SYM
ejpam-2494	387	2	cl(a	cl(a	X
ejpam-2494	387	3	)	)	PUNCT
ejpam-2494	387	4	and	and	CCONJ
ejpam-2494	387	5	intω(cl(b	intω(cl(b	NOUN
ejpam-2494	387	6	)	)	PUNCT
ejpam-2494	387	7	)	)	PUNCT
ejpam-2494	388	1	⊂	⊂	PROPN
ejpam-2494	388	2	intω(cl(a	intω(cl(a	X
ejpam-2494	388	3	)	)	PUNCT
ejpam-2494	388	4	)	)	PUNCT
ejpam-2494	388	5	.	.	PUNCT
ejpam-2494	389	1	therefore	therefore	ADV
ejpam-2494	389	2	we	we	PRON
ejpam-2494	389	3	obtain	obtain	VERB
ejpam-2494	389	4	that	that	DET
ejpam-2494	389	5	intω(cl(b	intω(cl(b	NOUN
ejpam-2494	389	6	)	)	PUNCT
ejpam-2494	389	7	)	)	PUNCT
ejpam-2494	390	1	⊂	⊂	PROPN
ejpam-2494	390	2	cl(intω(b	cl(intω(b	PROPN
ejpam-2494	390	3	)	)	PUNCT
ejpam-2494	390	4	)	)	PUNCT
ejpam-2494	390	5	.	.	PUNCT
ejpam-2494	391	1	this	this	PRON
ejpam-2494	391	2	shows	show	VERB
ejpam-2494	391	3	that	that	SCONJ
ejpam-2494	391	4	b	b	NOUN
ejpam-2494	391	5	is	be	AUX
ejpam-2494	391	6	a	a	DET
ejpam-2494	391	7	δ−ω	δ−ω	NOUN
ejpam-2494	391	8	-	-	PUNCT
ejpam-2494	391	9	open	open	ADJ
ejpam-2494	391	10	set	set	NOUN
ejpam-2494	391	11	.	.	PUNCT
ejpam-2494	392	1	corollary	corollary	ADJ
ejpam-2494	392	2	2	2	NUM
ejpam-2494	392	3	.	.	PUNCT
ejpam-2494	393	1	let	let	AUX
ejpam-2494	393	2	(	(	PUNCT
ejpam-2494	393	3	x	x	X
ejpam-2494	393	4	,	,	PUNCT
ejpam-2494	393	5	τ	τ	X
ejpam-2494	393	6	)	)	PUNCT
ejpam-2494	393	7	be	be	AUX
ejpam-2494	393	8	a	a	DET
ejpam-2494	393	9	space	space	NOUN
ejpam-2494	393	10	.	.	PUNCT
ejpam-2494	394	1	if	if	SCONJ
ejpam-2494	394	2	a⊂	a⊂	PRON
ejpam-2494	394	3	x	x	VERB
ejpam-2494	394	4	is	be	AUX
ejpam-2494	394	5	δ−ω	δ−ω	NOUN
ejpam-2494	394	6	-	-	PUNCT
ejpam-2494	394	7	open	open	ADJ
ejpam-2494	394	8	and	and	CCONJ
ejpam-2494	394	9	dense	dense	ADJ
ejpam-2494	394	10	in	in	ADP
ejpam-2494	394	11	(	(	PUNCT
ejpam-2494	394	12	x	x	INTJ
ejpam-2494	394	13	,	,	PUNCT
ejpam-2494	394	14	τ	τ	PROPN
ejpam-2494	394	15	)	)	PUNCT
ejpam-2494	394	16	,	,	PUNCT
ejpam-2494	394	17	then	then	ADV
ejpam-2494	394	18	every	every	DET
ejpam-2494	394	19	subset	subset	NOUN
ejpam-2494	394	20	of	of	ADP
ejpam-2494	394	21	x	x	PUNCT
ejpam-2494	394	22	containing	contain	VERB
ejpam-2494	394	23	a	a	PRON
ejpam-2494	394	24	is	be	AUX
ejpam-2494	394	25	δ−ω	δ−ω	NOUN
ejpam-2494	394	26	-	-	PUNCT
ejpam-2494	394	27	open	open	ADJ
ejpam-2494	394	28	.	.	PUNCT
ejpam-2494	395	1	proof	proof	NOUN
ejpam-2494	395	2	.	.	PUNCT
ejpam-2494	396	1	it	it	PRON
ejpam-2494	396	2	is	be	AUX
ejpam-2494	396	3	obvious	obvious	ADJ
ejpam-2494	396	4	by	by	ADP
ejpam-2494	396	5	proposition	proposition	NOUN
ejpam-2494	396	6	7	7	NUM
ejpam-2494	396	7	.	.	PUNCT
ejpam-2494	397	1	o.	o.	PROPN
ejpam-2494	397	2	ravi	ravi	PROPN
ejpam-2494	397	3	,	,	PUNCT
ejpam-2494	397	4	i.	i.	NOUN
ejpam-2494	397	5	rajasekaran	rajasekaran	PROPN
ejpam-2494	397	6	,	,	PUNCT
ejpam-2494	397	7	s.	s.	PROPN
ejpam-2494	397	8	kanna	kanna	PROPN
ejpam-2494	397	9	and	and	CCONJ
ejpam-2494	397	10	m.	m.	NOUN
ejpam-2494	397	11	paranjothi	paranjothi	PROPN
ejpam-2494	397	12	/	/	SYM
ejpam-2494	397	13	eur	eur	PROPN
ejpam-2494	397	14	.	.	PUNCT
ejpam-2494	398	1	j.	j.	PROPN
ejpam-2494	398	2	pure	pure	PROPN
ejpam-2494	398	3	appl	appl	PROPN
ejpam-2494	398	4	.	.	PROPN
ejpam-2494	398	5	math	math	PROPN
ejpam-2494	398	6	,	,	PUNCT
ejpam-2494	398	7	9	9	NUM
ejpam-2494	398	8	(	(	PUNCT
ejpam-2494	398	9	2016	2016	NUM
ejpam-2494	398	10	)	)	PUNCT
ejpam-2494	398	11	,	,	PUNCT
ejpam-2494	398	12	152	152	NUM
ejpam-2494	398	13	-	-	SYM
ejpam-2494	398	14	164	164	NUM
ejpam-2494	398	15	160	160	NUM
ejpam-2494	398	16	5	5	NUM
ejpam-2494	398	17	.	.	PUNCT
ejpam-2494	399	1	properties	property	NOUN
ejpam-2494	399	2	of	of	ADP
ejpam-2494	399	3	semi	semi	ADJ
ejpam-2494	399	4	⋆	⋆	PUNCT
ejpam-2494	399	5	−ω	−ω	ADJ
ejpam-2494	399	6	-	-	ADJ
ejpam-2494	399	7	open	open	ADJ
ejpam-2494	399	8	sets	set	NOUN
ejpam-2494	399	9	definition	definition	NOUN
ejpam-2494	399	10	12	12	NUM
ejpam-2494	399	11	.	.	PUNCT
ejpam-2494	400	1	a	a	DET
ejpam-2494	400	2	subset	subset	ADJ
ejpam-2494	400	3	h	h	NOUN
ejpam-2494	400	4	of	of	ADP
ejpam-2494	400	5	a	a	DET
ejpam-2494	400	6	space	space	NOUN
ejpam-2494	400	7	(	(	PUNCT
ejpam-2494	400	8	x	x	X
ejpam-2494	400	9	,	,	PUNCT
ejpam-2494	400	10	τ	τ	X
ejpam-2494	400	11	)	)	PUNCT
ejpam-2494	400	12	is	be	AUX
ejpam-2494	400	13	said	say	VERB
ejpam-2494	400	14	to	to	PART
ejpam-2494	400	15	be	be	AUX
ejpam-2494	400	16	(	(	PUNCT
ejpam-2494	400	17	i	i	NOUN
ejpam-2494	400	18	)	)	PUNCT
ejpam-2494	400	19	semi⋆	semi⋆	PROPN
ejpam-2494	400	20	−ω	−ω	NOUN
ejpam-2494	400	21	-	-	NOUN
ejpam-2494	400	22	open	open	ADJ
ejpam-2494	400	23	if	if	SCONJ
ejpam-2494	400	24	h	h	PROPN
ejpam-2494	400	25	⊂	⊂	PROPN
ejpam-2494	400	26	clω(int(h	clω(int(h	PROPN
ejpam-2494	400	27	)	)	PUNCT
ejpam-2494	400	28	)	)	PUNCT
ejpam-2494	400	29	.	.	PUNCT
ejpam-2494	401	1	(	(	PUNCT
ejpam-2494	401	2	ii	ii	X
ejpam-2494	401	3	)	)	PUNCT
ejpam-2494	401	4	semi⋆	semi⋆	PROPN
ejpam-2494	401	5	−ω	−ω	ADJ
ejpam-2494	401	6	-	-	PUNCT
ejpam-2494	401	7	closed	closed	ADJ
ejpam-2494	401	8	if	if	SCONJ
ejpam-2494	401	9	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	401	10	)	)	PUNCT
ejpam-2494	401	11	)	)	PUNCT
ejpam-2494	402	1	⊂	⊂	PROPN
ejpam-2494	402	2	h.	h.	PROPN
ejpam-2494	403	1	the	the	DET
ejpam-2494	403	2	complement	complement	NOUN
ejpam-2494	403	3	of	of	ADP
ejpam-2494	403	4	a	a	DET
ejpam-2494	403	5	semi⋆	semi⋆	NOUN
ejpam-2494	403	6	−ω	−ω	ADJ
ejpam-2494	403	7	-	-	ADJ
ejpam-2494	403	8	open	open	ADJ
ejpam-2494	403	9	set	set	NOUN
ejpam-2494	403	10	is	be	AUX
ejpam-2494	403	11	called	call	VERB
ejpam-2494	403	12	semi⋆	semi⋆	PROPN
ejpam-2494	403	13	−ω	−ω	NOUN
ejpam-2494	403	14	-	-	PUNCT
ejpam-2494	403	15	closed	closed	ADJ
ejpam-2494	403	16	.	.	PUNCT
ejpam-2494	403	17	example	example	NOUN
ejpam-2494	404	1	13	13	NUM
ejpam-2494	404	2	.	.	PUNCT
ejpam-2494	405	1	let	let	VERB
ejpam-2494	405	2	x	x	PUNCT
ejpam-2494	405	3	=	=	PRON
ejpam-2494	405	4	{	{	PUNCT
ejpam-2494	405	5	a	a	PRON
ejpam-2494	405	6	,	,	PUNCT
ejpam-2494	405	7	b	b	NOUN
ejpam-2494	405	8	,	,	PUNCT
ejpam-2494	405	9	c	c	NOUN
ejpam-2494	405	10	}	}	PUNCT
ejpam-2494	405	11	with	with	ADP
ejpam-2494	405	12	the	the	DET
ejpam-2494	405	13	topology	topology	NOUN
ejpam-2494	405	14	τ=	τ=	PRON
ejpam-2494	405	15	{	{	PUNCT
ejpam-2494	405	16	φ	φ	PROPN
ejpam-2494	405	17	,	,	PUNCT
ejpam-2494	405	18	x	x	INTJ
ejpam-2494	405	19	,	,	PUNCT
ejpam-2494	405	20	{	{	PUNCT
ejpam-2494	405	21	a	a	NOUN
ejpam-2494	405	22	}	}	PUNCT
ejpam-2494	405	23	,	,	PUNCT
ejpam-2494	405	24	{	{	PUNCT
ejpam-2494	405	25	a	a	PRON
ejpam-2494	405	26	,	,	PUNCT
ejpam-2494	405	27	b	b	NOUN
ejpam-2494	405	28	}	}	PUNCT
ejpam-2494	405	29	}	}	PUNCT
ejpam-2494	405	30	.	.	PUNCT
ejpam-2494	406	1	(	(	PUNCT
ejpam-2494	406	2	i	i	NOUN
ejpam-2494	406	3	)	)	PUNCT
ejpam-2494	406	4	let	let	VERB
ejpam-2494	406	5	h	h	NOUN
ejpam-2494	406	6	=	=	PRON
ejpam-2494	406	7	{	{	PUNCT
ejpam-2494	406	8	a	a	NOUN
ejpam-2494	406	9	}	}	PUNCT
ejpam-2494	406	10	.	.	PUNCT
ejpam-2494	407	1	then	then	ADV
ejpam-2494	407	2	h	h	PROPN
ejpam-2494	407	3	is	be	AUX
ejpam-2494	407	4	semi⋆	semi⋆	NOUN
ejpam-2494	407	5	−ω	−ω	ADJ
ejpam-2494	407	6	-	-	ADJ
ejpam-2494	407	7	open	open	ADJ
ejpam-2494	407	8	,	,	PUNCT
ejpam-2494	407	9	since	since	SCONJ
ejpam-2494	407	10	int(h	int(h	ADV
ejpam-2494	407	11	)	)	PUNCT
ejpam-2494	407	12	=	=	PRON
ejpam-2494	408	1	{	{	PUNCT
ejpam-2494	408	2	a	a	NOUN
ejpam-2494	408	3	}	}	PUNCT
ejpam-2494	408	4	and	and	CCONJ
ejpam-2494	408	5	clω(int(h	clω(int(h	NOUN
ejpam-2494	408	6	)	)	PUNCT
ejpam-2494	408	7	)	)	PUNCT
ejpam-2494	409	1	=	=	PRON
ejpam-2494	409	2	{	{	PUNCT
ejpam-2494	409	3	a	a	X
ejpam-2494	409	4	}	}	PUNCT
ejpam-2494	409	5	.	.	PUNCT
ejpam-2494	410	1	(	(	PUNCT
ejpam-2494	410	2	ii	ii	NOUN
ejpam-2494	410	3	)	)	PUNCT
ejpam-2494	410	4	let	let	VERB
ejpam-2494	410	5	h	h	NOUN
ejpam-2494	410	6	=	=	PRON
ejpam-2494	410	7	{	{	PUNCT
ejpam-2494	410	8	c	c	NOUN
ejpam-2494	410	9	}	}	PUNCT
ejpam-2494	410	10	.	.	PUNCT
ejpam-2494	411	1	then	then	ADV
ejpam-2494	411	2	h	h	NOUN
ejpam-2494	411	3	is	be	AUX
ejpam-2494	411	4	not	not	PART
ejpam-2494	411	5	semi⋆	semi⋆	NOUN
ejpam-2494	411	6	−ω	−ω	NOUN
ejpam-2494	411	7	-	-	ADJ
ejpam-2494	411	8	open	open	ADJ
ejpam-2494	411	9	,	,	PUNCT
ejpam-2494	411	10	since	since	SCONJ
ejpam-2494	411	11	int(h	int(h	ADV
ejpam-2494	411	12	)	)	PUNCT
ejpam-2494	411	13	=	=	SYM
ejpam-2494	411	14	φ	φ	PROPN
ejpam-2494	411	15	and	and	CCONJ
ejpam-2494	411	16	clω(int(h	clω(int(h	NOUN
ejpam-2494	411	17	)	)	PUNCT
ejpam-2494	411	18	)	)	PUNCT
ejpam-2494	412	1	=	=	SYM
ejpam-2494	412	2	φ	φ	X
ejpam-2494	412	3	.	.	PUNCT
ejpam-2494	412	4	proposition	proposition	NOUN
ejpam-2494	412	5	8	8	NUM
ejpam-2494	412	6	.	.	PUNCT
ejpam-2494	413	1	for	for	ADP
ejpam-2494	413	2	a	a	DET
ejpam-2494	413	3	subset	subset	NOUN
ejpam-2494	413	4	of	of	ADP
ejpam-2494	413	5	a	a	DET
ejpam-2494	413	6	space	space	NOUN
ejpam-2494	413	7	(	(	PUNCT
ejpam-2494	413	8	x	x	X
ejpam-2494	413	9	,	,	PUNCT
ejpam-2494	413	10	τ	τ	PROPN
ejpam-2494	413	11	)	)	PUNCT
ejpam-2494	413	12	,	,	PUNCT
ejpam-2494	413	13	every	every	DET
ejpam-2494	413	14	semi⋆	semi⋆	NOUN
ejpam-2494	413	15	−ω	−ω	ADJ
ejpam-2494	413	16	-	-	ADJ
ejpam-2494	413	17	open	open	ADJ
ejpam-2494	413	18	set	set	NOUN
ejpam-2494	413	19	is	be	AUX
ejpam-2494	413	20	semi	semi	ADJ
ejpam-2494	413	21	-	-	ADJ
ejpam-2494	413	22	ω	ω	ADJ
ejpam-2494	413	23	-	-	ADJ
ejpam-2494	413	24	open	open	ADJ
ejpam-2494	413	25	.	.	PUNCT
ejpam-2494	414	1	proof	proof	NOUN
ejpam-2494	414	2	.	.	PUNCT
ejpam-2494	415	1	if	if	SCONJ
ejpam-2494	415	2	h	h	NOUN
ejpam-2494	415	3	is	be	AUX
ejpam-2494	415	4	semi⋆	semi⋆	PROPN
ejpam-2494	415	5	−ω	−ω	ADJ
ejpam-2494	415	6	-	-	ADJ
ejpam-2494	415	7	open	open	ADJ
ejpam-2494	415	8	set	set	NOUN
ejpam-2494	415	9	,	,	PUNCT
ejpam-2494	415	10	then	then	ADV
ejpam-2494	415	11	h	h	PROPN
ejpam-2494	415	12	⊂	⊂	PROPN
ejpam-2494	415	13	clω(int(h	clω(int(h	PROPN
ejpam-2494	415	14	)	)	PUNCT
ejpam-2494	415	15	)	)	PUNCT
ejpam-2494	416	1	⊂	⊂	PROPN
ejpam-2494	416	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	416	3	)	)	PUNCT
ejpam-2494	416	4	)	)	PUNCT
ejpam-2494	416	5	.	.	PUNCT
ejpam-2494	417	1	therefore	therefore	ADV
ejpam-2494	417	2	h	h	PROPN
ejpam-2494	417	3	is	be	AUX
ejpam-2494	417	4	semi	semi	ADJ
ejpam-2494	417	5	-	-	ADJ
ejpam-2494	417	6	ω	ω	ADJ
ejpam-2494	417	7	-	-	ADJ
ejpam-2494	417	8	open	open	ADJ
ejpam-2494	417	9	.	.	PUNCT
ejpam-2494	417	10	example	example	NOUN
ejpam-2494	418	1	14	14	NUM
ejpam-2494	418	2	.	.	PUNCT
ejpam-2494	419	1	let	let	VERB
ejpam-2494	419	2	x	x	PUNCT
ejpam-2494	419	3	=	=	PUNCT
ejpam-2494	419	4	r	r	NOUN
ejpam-2494	419	5	with	with	ADP
ejpam-2494	419	6	the	the	DET
ejpam-2494	419	7	usual	usual	ADJ
ejpam-2494	419	8	topology	topology	NOUN
ejpam-2494	419	9	τu	τu	PROPN
ejpam-2494	419	10	.	.	PUNCT
ejpam-2494	420	1	let	let	VERB
ejpam-2494	420	2	h	h	NOUN
ejpam-2494	420	3	=	=	PRON
ejpam-2494	420	4	q⋆.	q⋆.	VERB
ejpam-2494	420	5	then	then	ADV
ejpam-2494	420	6	h	h	PROPN
ejpam-2494	420	7	is	be	AUX
ejpam-2494	420	8	semi	semi	ADJ
ejpam-2494	420	9	-	-	ADJ
ejpam-2494	420	10	ω	ω	ADV
ejpam-2494	420	11	-	-	ADJ
ejpam-2494	420	12	open	open	ADJ
ejpam-2494	420	13	but	but	CCONJ
ejpam-2494	420	14	not	not	PART
ejpam-2494	420	15	semi⋆	semi⋆	NOUN
ejpam-2494	420	16	−ω	−ω	NOUN
ejpam-2494	420	17	-	-	ADJ
ejpam-2494	420	18	open	open	ADJ
ejpam-2494	420	19	,	,	PUNCT
ejpam-2494	420	20	since	since	SCONJ
ejpam-2494	420	21	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	420	22	)	)	PUNCT
ejpam-2494	420	23	)	)	PUNCT
ejpam-2494	421	1	=	=	PUNCT
ejpam-2494	421	2	cl(q⋆	cl(q⋆	X
ejpam-2494	421	3	)	)	PUNCT
ejpam-2494	422	1	=	=	SYM
ejpam-2494	422	2	r	r	NOUN
ejpam-2494	422	3	and	and	CCONJ
ejpam-2494	422	4	clω(int(h	clω(int(h	NOUN
ejpam-2494	422	5	)	)	PUNCT
ejpam-2494	422	6	)	)	PUNCT
ejpam-2494	423	1	=	=	PUNCT
ejpam-2494	423	2	clω(φ	clω(φ	PROPN
ejpam-2494	423	3	)	)	PUNCT
ejpam-2494	423	4	=	=	SYM
ejpam-2494	424	1	φ	φ	PROPN
ejpam-2494	424	2	.	.	PUNCT
ejpam-2494	424	3	proposition	proposition	NOUN
ejpam-2494	424	4	9	9	NUM
ejpam-2494	424	5	.	.	PUNCT
ejpam-2494	425	1	a	a	DET
ejpam-2494	425	2	subset	subset	ADJ
ejpam-2494	425	3	h	h	NOUN
ejpam-2494	425	4	of	of	ADP
ejpam-2494	425	5	a	a	DET
ejpam-2494	425	6	space	space	NOUN
ejpam-2494	425	7	(	(	PUNCT
ejpam-2494	425	8	x	x	X
ejpam-2494	425	9	,	,	PUNCT
ejpam-2494	425	10	τ	τ	X
ejpam-2494	425	11	)	)	PUNCT
ejpam-2494	425	12	is	be	AUX
ejpam-2494	425	13	semi⋆−ω	semi⋆−ω	NOUN
ejpam-2494	425	14	-	-	PUNCT
ejpam-2494	425	15	open	open	ADJ
ejpam-2494	425	16	if	if	SCONJ
ejpam-2494	425	17	and	and	CCONJ
ejpam-2494	425	18	only	only	ADV
ejpam-2494	425	19	if	if	SCONJ
ejpam-2494	425	20	clω(h	clω(h	PROPN
ejpam-2494	425	21	)	)	PUNCT
ejpam-2494	425	22	=	=	SYM
ejpam-2494	425	23	clω(int(h	clω(int(h	NOUN
ejpam-2494	425	24	)	)	PUNCT
ejpam-2494	425	25	)	)	PUNCT
ejpam-2494	425	26	.	.	PUNCT
ejpam-2494	426	1	proof	proof	NOUN
ejpam-2494	426	2	.	.	PUNCT
ejpam-2494	427	1	if	if	SCONJ
ejpam-2494	427	2	h	h	NOUN
ejpam-2494	427	3	is	be	AUX
ejpam-2494	427	4	semi⋆	semi⋆	PROPN
ejpam-2494	427	5	−ω	−ω	ADJ
ejpam-2494	427	6	-	-	ADJ
ejpam-2494	427	7	open	open	ADJ
ejpam-2494	427	8	set	set	NOUN
ejpam-2494	427	9	,	,	PUNCT
ejpam-2494	427	10	then	then	ADV
ejpam-2494	427	11	h	h	PROPN
ejpam-2494	427	12	⊂	⊂	PROPN
ejpam-2494	427	13	clω(int(h	clω(int(h	PROPN
ejpam-2494	427	14	)	)	PUNCT
ejpam-2494	427	15	)	)	PUNCT
ejpam-2494	427	16	and	and	CCONJ
ejpam-2494	427	17	clω(h	clω(h	X
ejpam-2494	427	18	)	)	PUNCT
ejpam-2494	427	19	⊂	⊂	PROPN
ejpam-2494	427	20	clω(int(h	clω(int(h	NOUN
ejpam-2494	427	21	)	)	PUNCT
ejpam-2494	427	22	)	)	PUNCT
ejpam-2494	427	23	.	.	PUNCT
ejpam-2494	428	1	but	but	CCONJ
ejpam-2494	428	2	clω(int(h	clω(int(h	NOUN
ejpam-2494	428	3	)	)	PUNCT
ejpam-2494	428	4	)	)	PUNCT
ejpam-2494	429	1	⊂	⊂	PROPN
ejpam-2494	429	2	clω(h	clω(h	PROPN
ejpam-2494	429	3	)	)	PUNCT
ejpam-2494	429	4	.	.	PUNCT
ejpam-2494	430	1	hence	hence	ADV
ejpam-2494	430	2	clω(h	clω(h	PROPN
ejpam-2494	430	3	)	)	PUNCT
ejpam-2494	430	4	=	=	SYM
ejpam-2494	430	5	clω(int(h	clω(int(h	NOUN
ejpam-2494	430	6	)	)	PUNCT
ejpam-2494	430	7	)	)	PUNCT
ejpam-2494	430	8	.	.	PUNCT
ejpam-2494	431	1	conversely	conversely	ADV
ejpam-2494	431	2	,	,	PUNCT
ejpam-2494	431	3	let	let	VERB
ejpam-2494	431	4	the	the	DET
ejpam-2494	431	5	condition	condition	NOUN
ejpam-2494	431	6	hold	hold	VERB
ejpam-2494	431	7	.	.	PUNCT
ejpam-2494	432	1	we	we	PRON
ejpam-2494	432	2	have	have	VERB
ejpam-2494	432	3	h	h	PROPN
ejpam-2494	432	4	⊂	⊂	PROPN
ejpam-2494	432	5	clω(h	clω(h	PROPN
ejpam-2494	432	6	)	)	PUNCT
ejpam-2494	432	7	and	and	CCONJ
ejpam-2494	432	8	clω(h	clω(h	X
ejpam-2494	432	9	)	)	PUNCT
ejpam-2494	432	10	=	=	SYM
ejpam-2494	432	11	clω(int(h	clω(int(h	NOUN
ejpam-2494	432	12	)	)	PUNCT
ejpam-2494	432	13	)	)	PUNCT
ejpam-2494	432	14	.	.	PUNCT
ejpam-2494	433	1	therefore	therefore	ADV
ejpam-2494	433	2	h	h	PROPN
ejpam-2494	433	3	is	be	AUX
ejpam-2494	433	4	semi⋆	semi⋆	NOUN
ejpam-2494	433	5	−ω	−ω	ADJ
ejpam-2494	433	6	-	-	ADJ
ejpam-2494	433	7	open	open	ADJ
ejpam-2494	433	8	.	.	PUNCT
ejpam-2494	434	1	definition	definition	NOUN
ejpam-2494	434	2	13	13	NUM
ejpam-2494	434	3	.	.	PUNCT
ejpam-2494	435	1	a	a	DET
ejpam-2494	435	2	subset	subset	ADJ
ejpam-2494	435	3	h	h	NOUN
ejpam-2494	435	4	of	of	ADP
ejpam-2494	435	5	a	a	DET
ejpam-2494	435	6	space	space	NOUN
ejpam-2494	435	7	(	(	PUNCT
ejpam-2494	435	8	x	x	X
ejpam-2494	435	9	,	,	PUNCT
ejpam-2494	435	10	τ	τ	X
ejpam-2494	435	11	)	)	PUNCT
ejpam-2494	435	12	is	be	AUX
ejpam-2494	435	13	said	say	VERB
ejpam-2494	435	14	to	to	PART
ejpam-2494	435	15	be	be	AUX
ejpam-2494	435	16	ω⋆	ω⋆	NUM
ejpam-2494	435	17	−	−	PRON
ejpam-2494	435	18	t	t	NOUN
ejpam-2494	435	19	-	-	PUNCT
ejpam-2494	435	20	set	set	VERB
ejpam-2494	435	21	if	if	SCONJ
ejpam-2494	435	22	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	435	23	)	)	PUNCT
ejpam-2494	435	24	)	)	PUNCT
ejpam-2494	436	1	=	=	SYM
ejpam-2494	436	2	intω(h	intω(h	NOUN
ejpam-2494	436	3	)	)	PUNCT
ejpam-2494	436	4	.	.	PUNCT
ejpam-2494	437	1	example	example	NOUN
ejpam-2494	438	1	15	15	NUM
ejpam-2494	438	2	.	.	PUNCT
ejpam-2494	439	1	let	let	VERB
ejpam-2494	439	2	x	x	PUNCT
ejpam-2494	439	3	=	=	PUNCT
ejpam-2494	439	4	r	r	NOUN
ejpam-2494	439	5	with	with	ADP
ejpam-2494	439	6	the	the	DET
ejpam-2494	439	7	usual	usual	ADJ
ejpam-2494	439	8	topology	topology	NOUN
ejpam-2494	439	9	τu	τu	PROPN
ejpam-2494	439	10	.	.	PUNCT
ejpam-2494	440	1	(	(	PUNCT
ejpam-2494	440	2	i	i	NOUN
ejpam-2494	440	3	)	)	PUNCT
ejpam-2494	440	4	let	let	VERB
ejpam-2494	440	5	h	h	NOUN
ejpam-2494	440	6	=	=	PUNCT
ejpam-2494	440	7	(	(	PUNCT
ejpam-2494	440	8	0,1	0,1	NUM
ejpam-2494	440	9	]	]	PUNCT
ejpam-2494	440	10	.	.	PUNCT
ejpam-2494	441	1	then	then	ADV
ejpam-2494	441	2	h	h	PROPN
ejpam-2494	441	3	is	be	AUX
ejpam-2494	441	4	a	a	DET
ejpam-2494	441	5	ω⋆	ω⋆	NUM
ejpam-2494	441	6	−	−	PRON
ejpam-2494	441	7	t	t	NOUN
ejpam-2494	441	8	-	-	PUNCT
ejpam-2494	441	9	set	set	NOUN
ejpam-2494	441	10	.	.	PUNCT
ejpam-2494	442	1	(	(	PUNCT
ejpam-2494	442	2	ii	ii	NOUN
ejpam-2494	442	3	)	)	PUNCT
ejpam-2494	442	4	let	let	VERB
ejpam-2494	442	5	h	h	NOUN
ejpam-2494	442	6	=	=	PRON
ejpam-2494	442	7	q⋆.	q⋆.	VERB
ejpam-2494	442	8	then	then	ADV
ejpam-2494	442	9	h	h	PROPN
ejpam-2494	442	10	is	be	AUX
ejpam-2494	442	11	not	not	PART
ejpam-2494	442	12	a	a	DET
ejpam-2494	442	13	ω⋆	ω⋆	NUM
ejpam-2494	442	14	−	−	PRON
ejpam-2494	442	15	t	t	NOUN
ejpam-2494	442	16	-	-	PUNCT
ejpam-2494	442	17	set	set	NOUN
ejpam-2494	442	18	.	.	PUNCT
ejpam-2494	443	1	proposition	proposition	NOUN
ejpam-2494	443	2	10	10	NUM
ejpam-2494	443	3	.	.	PUNCT
ejpam-2494	444	1	in	in	ADP
ejpam-2494	444	2	a	a	DET
ejpam-2494	444	3	space	space	NOUN
ejpam-2494	444	4	(	(	PUNCT
ejpam-2494	444	5	x	x	X
ejpam-2494	444	6	,	,	PUNCT
ejpam-2494	444	7	τ	τ	PROPN
ejpam-2494	444	8	)	)	PUNCT
ejpam-2494	444	9	,	,	PUNCT
ejpam-2494	444	10	every	every	DET
ejpam-2494	444	11	closed	closed	ADJ
ejpam-2494	444	12	set	set	NOUN
ejpam-2494	444	13	is	be	AUX
ejpam-2494	444	14	a	a	DET
ejpam-2494	444	15	ω⋆	ω⋆	NUM
ejpam-2494	444	16	−	−	PRON
ejpam-2494	444	17	t	t	NOUN
ejpam-2494	444	18	-	-	PUNCT
ejpam-2494	444	19	set	set	NOUN
ejpam-2494	444	20	.	.	PUNCT
ejpam-2494	445	1	proof	proof	NOUN
ejpam-2494	445	2	.	.	PUNCT
ejpam-2494	446	1	let	let	VERB
ejpam-2494	446	2	h	h	PRON
ejpam-2494	446	3	be	be	AUX
ejpam-2494	446	4	a	a	DET
ejpam-2494	446	5	closed	closed	ADJ
ejpam-2494	446	6	set	set	NOUN
ejpam-2494	446	7	.	.	PUNCT
ejpam-2494	447	1	then	then	ADV
ejpam-2494	447	2	h	h	NOUN
ejpam-2494	447	3	=	=	PUNCT
ejpam-2494	447	4	cl(h	cl(h	X
ejpam-2494	447	5	)	)	PUNCT
ejpam-2494	447	6	and	and	CCONJ
ejpam-2494	447	7	we	we	PRON
ejpam-2494	447	8	have	have	VERB
ejpam-2494	447	9	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	447	10	)	)	PUNCT
ejpam-2494	447	11	)	)	PUNCT
ejpam-2494	448	1	=	=	SYM
ejpam-2494	448	2	intω(h	intω(h	NOUN
ejpam-2494	448	3	)	)	PUNCT
ejpam-2494	448	4	which	which	PRON
ejpam-2494	448	5	proves	prove	VERB
ejpam-2494	448	6	that	that	SCONJ
ejpam-2494	448	7	h	h	NOUN
ejpam-2494	448	8	is	be	AUX
ejpam-2494	448	9	a	a	DET
ejpam-2494	448	10	ω⋆	ω⋆	NUM
ejpam-2494	448	11	−	−	PRON
ejpam-2494	448	12	t	t	NOUN
ejpam-2494	448	13	-	-	PUNCT
ejpam-2494	448	14	set	set	NOUN
ejpam-2494	448	15	.	.	PUNCT
ejpam-2494	449	1	the	the	DET
ejpam-2494	449	2	converse	converse	NOUN
ejpam-2494	449	3	of	of	ADP
ejpam-2494	449	4	proposition	proposition	NOUN
ejpam-2494	449	5	10	10	NUM
ejpam-2494	449	6	is	be	AUX
ejpam-2494	449	7	not	not	PART
ejpam-2494	449	8	true	true	ADJ
ejpam-2494	449	9	as	as	SCONJ
ejpam-2494	449	10	can	can	AUX
ejpam-2494	449	11	be	be	AUX
ejpam-2494	449	12	seen	see	VERB
ejpam-2494	449	13	from	from	ADP
ejpam-2494	449	14	the	the	DET
ejpam-2494	449	15	following	follow	VERB
ejpam-2494	449	16	example	example	NOUN
ejpam-2494	449	17	.	.	PUNCT
ejpam-2494	450	1	example	example	NOUN
ejpam-2494	451	1	16	16	NUM
ejpam-2494	451	2	.	.	PUNCT
ejpam-2494	452	1	let	let	VERB
ejpam-2494	452	2	x	x	PUNCT
ejpam-2494	452	3	=	=	PUNCT
ejpam-2494	452	4	r	r	NOUN
ejpam-2494	452	5	with	with	ADP
ejpam-2494	452	6	the	the	DET
ejpam-2494	452	7	usual	usual	ADJ
ejpam-2494	452	8	topology	topology	NOUN
ejpam-2494	452	9	τu	τu	PROPN
ejpam-2494	452	10	.	.	PUNCT
ejpam-2494	453	1	let	let	VERB
ejpam-2494	453	2	h	h	NOUN
ejpam-2494	453	3	=	=	PUNCT
ejpam-2494	453	4	(	(	PUNCT
ejpam-2494	453	5	0,1	0,1	NUM
ejpam-2494	453	6	]	]	PUNCT
ejpam-2494	453	7	.	.	PUNCT
ejpam-2494	454	1	then	then	ADV
ejpam-2494	454	2	h	h	PROPN
ejpam-2494	454	3	isω⋆−	isω⋆−	PROPN
ejpam-2494	454	4	t	t	NOUN
ejpam-2494	454	5	-	-	PUNCT
ejpam-2494	454	6	set	set	VERB
ejpam-2494	454	7	but	but	CCONJ
ejpam-2494	454	8	not	not	PART
ejpam-2494	454	9	closed	closed	ADJ
ejpam-2494	454	10	.	.	PUNCT
ejpam-2494	455	1	proposition	proposition	NOUN
ejpam-2494	455	2	11	11	NUM
ejpam-2494	455	3	.	.	PUNCT
ejpam-2494	456	1	in	in	ADP
ejpam-2494	456	2	a	a	DET
ejpam-2494	456	3	space	space	NOUN
ejpam-2494	456	4	(	(	PUNCT
ejpam-2494	456	5	x	x	X
ejpam-2494	456	6	,	,	PUNCT
ejpam-2494	456	7	τ	τ	PROPN
ejpam-2494	456	8	)	)	PUNCT
ejpam-2494	456	9	,	,	PUNCT
ejpam-2494	456	10	every	every	DET
ejpam-2494	456	11	ω−	ω−	PROPN
ejpam-2494	456	12	t	t	PROPN
ejpam-2494	456	13	-	-	PUNCT
ejpam-2494	456	14	set	set	NOUN
ejpam-2494	456	15	is	be	AUX
ejpam-2494	456	16	a	a	DET
ejpam-2494	456	17	ω⋆	ω⋆	NUM
ejpam-2494	456	18	−	−	PRON
ejpam-2494	456	19	t	t	NOUN
ejpam-2494	456	20	-	-	PUNCT
ejpam-2494	456	21	set	set	NOUN
ejpam-2494	456	22	.	.	PUNCT
ejpam-2494	457	1	o.	o.	PROPN
ejpam-2494	457	2	ravi	ravi	PROPN
ejpam-2494	457	3	,	,	PUNCT
ejpam-2494	457	4	i.	i.	NOUN
ejpam-2494	457	5	rajasekaran	rajasekaran	PROPN
ejpam-2494	457	6	,	,	PUNCT
ejpam-2494	457	7	s.	s.	PROPN
ejpam-2494	457	8	kanna	kanna	PROPN
ejpam-2494	457	9	and	and	CCONJ
ejpam-2494	457	10	m.	m.	NOUN
ejpam-2494	457	11	paranjothi	paranjothi	PROPN
ejpam-2494	457	12	/	/	SYM
ejpam-2494	457	13	eur	eur	PROPN
ejpam-2494	457	14	.	.	PUNCT
ejpam-2494	458	1	j.	j.	PROPN
ejpam-2494	458	2	pure	pure	PROPN
ejpam-2494	458	3	appl	appl	PROPN
ejpam-2494	458	4	.	.	PROPN
ejpam-2494	458	5	math	math	PROPN
ejpam-2494	458	6	,	,	PUNCT
ejpam-2494	458	7	9	9	NUM
ejpam-2494	458	8	(	(	PUNCT
ejpam-2494	458	9	2016	2016	NUM
ejpam-2494	458	10	)	)	PUNCT
ejpam-2494	458	11	,	,	PUNCT
ejpam-2494	458	12	152	152	NUM
ejpam-2494	458	13	-	-	SYM
ejpam-2494	458	14	164	164	NUM
ejpam-2494	458	15	161	161	NUM
ejpam-2494	458	16	proof	proof	NOUN
ejpam-2494	458	17	.	.	PUNCT
ejpam-2494	459	1	if	if	SCONJ
ejpam-2494	459	2	h	h	NOUN
ejpam-2494	459	3	is	be	AUX
ejpam-2494	459	4	a	a	DET
ejpam-2494	459	5	ω−	ω−	PROPN
ejpam-2494	459	6	t	t	NOUN
ejpam-2494	459	7	-	-	PUNCT
ejpam-2494	459	8	set	set	NOUN
ejpam-2494	459	9	,	,	PUNCT
ejpam-2494	459	10	then	then	ADV
ejpam-2494	459	11	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	459	12	)	)	PUNCT
ejpam-2494	459	13	)	)	PUNCT
ejpam-2494	460	1	=	=	PUNCT
ejpam-2494	460	2	int(h	int(h	X
ejpam-2494	460	3	)	)	PUNCT
ejpam-2494	460	4	⊂	⊂	PROPN
ejpam-2494	460	5	intω(h	intω(h	PROPN
ejpam-2494	460	6	)	)	PUNCT
ejpam-2494	460	7	⊂	⊂	PROPN
ejpam-2494	460	8	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	460	9	)	)	PUNCT
ejpam-2494	460	10	)	)	PUNCT
ejpam-2494	460	11	.	.	PUNCT
ejpam-2494	461	1	thus	thus	ADV
ejpam-2494	461	2	we	we	PRON
ejpam-2494	461	3	have	have	VERB
ejpam-2494	461	4	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	461	5	)	)	PUNCT
ejpam-2494	461	6	)	)	PUNCT
ejpam-2494	462	1	=	=	SYM
ejpam-2494	462	2	intω(h	intω(h	NOUN
ejpam-2494	462	3	)	)	PUNCT
ejpam-2494	462	4	and	and	CCONJ
ejpam-2494	462	5	hence	hence	ADV
ejpam-2494	462	6	h	h	NOUN
ejpam-2494	462	7	is	be	AUX
ejpam-2494	462	8	a	a	DET
ejpam-2494	462	9	ω⋆	ω⋆	NUM
ejpam-2494	462	10	−	−	PRON
ejpam-2494	462	11	t	t	NOUN
ejpam-2494	462	12	-	-	PUNCT
ejpam-2494	462	13	set	set	NOUN
ejpam-2494	462	14	.	.	PUNCT
ejpam-2494	463	1	example	example	NOUN
ejpam-2494	463	2	17	17	NUM
ejpam-2494	463	3	.	.	PUNCT
ejpam-2494	464	1	let	let	VERB
ejpam-2494	464	2	x	x	PUNCT
ejpam-2494	464	3	=	=	PRON
ejpam-2494	464	4	{	{	PUNCT
ejpam-2494	464	5	a	a	PRON
ejpam-2494	464	6	,	,	PUNCT
ejpam-2494	464	7	b	b	NOUN
ejpam-2494	464	8	,	,	PUNCT
ejpam-2494	464	9	c	c	NOUN
ejpam-2494	464	10	}	}	PUNCT
ejpam-2494	464	11	with	with	ADP
ejpam-2494	464	12	the	the	DET
ejpam-2494	464	13	topology	topology	NOUN
ejpam-2494	464	14	τ	τ	X
ejpam-2494	464	15	=	=	SYM
ejpam-2494	464	16	{	{	PUNCT
ejpam-2494	464	17	φ	φ	PROPN
ejpam-2494	464	18	,	,	PUNCT
ejpam-2494	464	19	x	x	INTJ
ejpam-2494	464	20	,	,	PUNCT
ejpam-2494	464	21	{	{	PUNCT
ejpam-2494	464	22	a	a	NOUN
ejpam-2494	464	23	}	}	PUNCT
ejpam-2494	464	24	,	,	PUNCT
ejpam-2494	464	25	{	{	PUNCT
ejpam-2494	464	26	a	a	DET
ejpam-2494	464	27	,	,	PUNCT
ejpam-2494	464	28	b	b	NOUN
ejpam-2494	464	29	}	}	PUNCT
ejpam-2494	464	30	}	}	PUNCT
ejpam-2494	464	31	.	.	PUNCT
ejpam-2494	465	1	then	then	ADV
ejpam-2494	465	2	h	h	NOUN
ejpam-2494	465	3	=	=	PRON
ejpam-2494	465	4	{	{	PUNCT
ejpam-2494	465	5	c	c	X
ejpam-2494	465	6	}	}	PUNCT
ejpam-2494	465	7	is	be	AUX
ejpam-2494	465	8	a	a	DET
ejpam-2494	465	9	ω⋆−	ω⋆−	NUM
ejpam-2494	465	10	t	t	NOUN
ejpam-2494	465	11	-	-	PUNCT
ejpam-2494	465	12	set	set	VERB
ejpam-2494	465	13	but	but	CCONJ
ejpam-2494	465	14	not	not	PART
ejpam-2494	465	15	aω−	aω−	NUM
ejpam-2494	465	16	t	t	PROPN
ejpam-2494	465	17	-	-	PUNCT
ejpam-2494	465	18	set	set	NOUN
ejpam-2494	465	19	.	.	PUNCT
ejpam-2494	466	1	since	since	SCONJ
ejpam-2494	466	2	intω(h	intω(h	NUM
ejpam-2494	466	3	)	)	PUNCT
ejpam-2494	466	4	=	=	SYM
ejpam-2494	466	5	h	h	NOUN
ejpam-2494	466	6	,	,	PUNCT
ejpam-2494	466	7	int(h	int(h	NOUN
ejpam-2494	466	8	)	)	PUNCT
ejpam-2494	466	9	=	=	SYM
ejpam-2494	466	10	φ	φ	PROPN
ejpam-2494	466	11	and	and	CCONJ
ejpam-2494	466	12	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	466	13	)	)	PUNCT
ejpam-2494	466	14	)	)	PUNCT
ejpam-2494	467	1	=	=	SYM
ejpam-2494	467	2	intω(h	intω(h	NOUN
ejpam-2494	467	3	)	)	PUNCT
ejpam-2494	468	1	=	=	SYM
ejpam-2494	468	2	h	h	NOUN
ejpam-2494	468	3	,	,	PUNCT
ejpam-2494	468	4	we	we	PRON
ejpam-2494	468	5	have	have	VERB
ejpam-2494	468	6	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	468	7	)	)	PUNCT
ejpam-2494	468	8	)	)	PUNCT
ejpam-2494	469	1	=	=	SYM
ejpam-2494	469	2	intω(h	intω(h	NOUN
ejpam-2494	469	3	)	)	PUNCT
ejpam-2494	469	4	and	and	CCONJ
ejpam-2494	469	5	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	469	6	)	)	PUNCT
ejpam-2494	469	7	)	)	PUNCT
ejpam-2494	470	1	6=	6=	X
ejpam-2494	470	2	int(h	int(h	ADJ
ejpam-2494	470	3	)	)	PUNCT
ejpam-2494	470	4	.	.	PUNCT
ejpam-2494	471	1	this	this	PRON
ejpam-2494	471	2	proves	prove	VERB
ejpam-2494	471	3	that	that	SCONJ
ejpam-2494	471	4	h	h	NOUN
ejpam-2494	471	5	is	be	AUX
ejpam-2494	471	6	a	a	DET
ejpam-2494	471	7	ω⋆	ω⋆	NUM
ejpam-2494	471	8	−	−	PRON
ejpam-2494	471	9	t	t	NOUN
ejpam-2494	471	10	-	-	PUNCT
ejpam-2494	471	11	set	set	VERB
ejpam-2494	471	12	but	but	CCONJ
ejpam-2494	471	13	not	not	PART
ejpam-2494	471	14	a	a	DET
ejpam-2494	471	15	ω−	ω−	ADJ
ejpam-2494	471	16	t	t	NOUN
ejpam-2494	471	17	-	-	PUNCT
ejpam-2494	471	18	set	set	NOUN
ejpam-2494	471	19	.	.	PUNCT
ejpam-2494	472	1	theorem	theorem	VERB
ejpam-2494	472	2	11	11	NUM
ejpam-2494	472	3	.	.	PUNCT
ejpam-2494	473	1	a	a	DET
ejpam-2494	473	2	subset	subset	ADJ
ejpam-2494	473	3	h	h	NOUN
ejpam-2494	473	4	of	of	ADP
ejpam-2494	473	5	a	a	DET
ejpam-2494	473	6	space	space	NOUN
ejpam-2494	473	7	(	(	PUNCT
ejpam-2494	473	8	x	x	X
ejpam-2494	473	9	,	,	PUNCT
ejpam-2494	473	10	τ	τ	X
ejpam-2494	473	11	)	)	PUNCT
ejpam-2494	473	12	is	be	AUX
ejpam-2494	473	13	semi⋆	semi⋆	NOUN
ejpam-2494	473	14	−ω	−ω	ADJ
ejpam-2494	473	15	-	-	PUNCT
ejpam-2494	473	16	closed	closed	ADJ
ejpam-2494	473	17	if	if	SCONJ
ejpam-2494	474	1	and	and	CCONJ
ejpam-2494	474	2	only	only	ADV
ejpam-2494	474	3	if	if	SCONJ
ejpam-2494	474	4	h	h	NOUN
ejpam-2494	474	5	is	be	AUX
ejpam-2494	474	6	a	a	DET
ejpam-2494	474	7	ω⋆	ω⋆	NUM
ejpam-2494	474	8	−	−	PRON
ejpam-2494	474	9	t	t	NOUN
ejpam-2494	474	10	-	-	PUNCT
ejpam-2494	474	11	set	set	NOUN
ejpam-2494	474	12	.	.	PUNCT
ejpam-2494	475	1	proof	proof	NOUN
ejpam-2494	475	2	.	.	PUNCT
ejpam-2494	476	1	let	let	VERB
ejpam-2494	476	2	h	h	PRON
ejpam-2494	476	3	be	be	AUX
ejpam-2494	476	4	a	a	DET
ejpam-2494	476	5	semi⋆−ω	semi⋆−ω	NOUN
ejpam-2494	476	6	-	-	PUNCT
ejpam-2494	476	7	closed	close	VERB
ejpam-2494	476	8	set	set	NOUN
ejpam-2494	476	9	in	in	ADP
ejpam-2494	476	10	x.	x.	NOUN
ejpam-2494	476	11	then	then	ADV
ejpam-2494	476	12	x\h	x\h	PROPN
ejpam-2494	476	13	is	be	AUX
ejpam-2494	476	14	semi⋆−ω	semi⋆−ω	NOUN
ejpam-2494	476	15	-	-	PUNCT
ejpam-2494	476	16	open	open	ADJ
ejpam-2494	476	17	.	.	PUNCT
ejpam-2494	477	1	by	by	ADP
ejpam-2494	477	2	proposition	proposition	NOUN
ejpam-2494	477	3	9	9	NUM
ejpam-2494	477	4	,	,	PUNCT
ejpam-2494	477	5	we	we	PRON
ejpam-2494	477	6	have	have	VERB
ejpam-2494	477	7	clω(x\h	clω(x\h	PROPN
ejpam-2494	477	8	)	)	PUNCT
ejpam-2494	478	1	=	=	SYM
ejpam-2494	478	2	clω(int(x\h	clω(int(x\h	NUM
ejpam-2494	478	3	)	)	PUNCT
ejpam-2494	478	4	)	)	PUNCT
ejpam-2494	478	5	.	.	PUNCT
ejpam-2494	479	1	it	it	PRON
ejpam-2494	479	2	follows	follow	VERB
ejpam-2494	479	3	that	that	PRON
ejpam-2494	479	4	x\intω(h	x\intω(h	PUNCT
ejpam-2494	479	5	)	)	PUNCT
ejpam-2494	480	1	=	=	SYM
ejpam-2494	480	2	clω(x\cl(h	clω(x\cl(h	PROPN
ejpam-2494	480	3	)	)	PUNCT
ejpam-2494	480	4	)	)	PUNCT
ejpam-2494	481	1	=	=	SYM
ejpam-2494	481	2	x\intω(cl(h	x\intω(cl(h	PROPN
ejpam-2494	481	3	)	)	PUNCT
ejpam-2494	481	4	)	)	PUNCT
ejpam-2494	481	5	.	.	PUNCT
ejpam-2494	482	1	thus	thus	ADV
ejpam-2494	482	2	,	,	PUNCT
ejpam-2494	482	3	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	482	4	)	)	PUNCT
ejpam-2494	482	5	)	)	PUNCT
ejpam-2494	483	1	=	=	SYM
ejpam-2494	483	2	intω(h	intω(h	NOUN
ejpam-2494	483	3	)	)	PUNCT
ejpam-2494	483	4	and	and	CCONJ
ejpam-2494	483	5	hence	hence	ADV
ejpam-2494	483	6	h	h	NOUN
ejpam-2494	483	7	is	be	AUX
ejpam-2494	483	8	a	a	DET
ejpam-2494	483	9	ω⋆	ω⋆	NUM
ejpam-2494	483	10	−	−	PRON
ejpam-2494	483	11	t	t	NOUN
ejpam-2494	483	12	-	-	PUNCT
ejpam-2494	483	13	set	set	NOUN
ejpam-2494	483	14	in	in	ADP
ejpam-2494	483	15	x.	x.	NOUN
ejpam-2494	483	16	conversely	conversely	ADV
ejpam-2494	483	17	,	,	PUNCT
ejpam-2494	483	18	let	let	VERB
ejpam-2494	483	19	h	h	PRON
ejpam-2494	483	20	be	be	AUX
ejpam-2494	483	21	a	a	DET
ejpam-2494	483	22	ω⋆	ω⋆	NUM
ejpam-2494	483	23	−	−	PRON
ejpam-2494	483	24	t	t	NOUN
ejpam-2494	483	25	-	-	PUNCT
ejpam-2494	483	26	set	set	NOUN
ejpam-2494	483	27	.	.	PUNCT
ejpam-2494	484	1	then	then	ADV
ejpam-2494	484	2	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	484	3	)	)	PUNCT
ejpam-2494	484	4	)	)	PUNCT
ejpam-2494	485	1	=	=	SYM
ejpam-2494	485	2	intω(h	intω(h	X
ejpam-2494	485	3	)	)	PUNCT
ejpam-2494	485	4	⊂	⊂	PROPN
ejpam-2494	485	5	h.	h.	PROPN
ejpam-2494	485	6	therefore	therefore	ADV
ejpam-2494	485	7	h	h	PROPN
ejpam-2494	485	8	is	be	AUX
ejpam-2494	485	9	semi⋆	semi⋆	PROPN
ejpam-2494	485	10	−ω	−ω	ADJ
ejpam-2494	485	11	-	-	PUNCT
ejpam-2494	485	12	closed	closed	ADJ
ejpam-2494	485	13	.	.	PUNCT
ejpam-2494	486	1	proposition	proposition	NOUN
ejpam-2494	486	2	12	12	NUM
ejpam-2494	486	3	.	.	PUNCT
ejpam-2494	487	1	if	if	SCONJ
ejpam-2494	487	2	a	a	PRON
ejpam-2494	487	3	and	and	CCONJ
ejpam-2494	487	4	b	b	NOUN
ejpam-2494	487	5	are	be	AUX
ejpam-2494	487	6	ω⋆	ω⋆	NUM
ejpam-2494	487	7	−	−	PRON
ejpam-2494	487	8	t	t	NOUN
ejpam-2494	487	9	-	-	PUNCT
ejpam-2494	487	10	sets	set	NOUN
ejpam-2494	487	11	of	of	ADP
ejpam-2494	487	12	a	a	DET
ejpam-2494	487	13	space	space	NOUN
ejpam-2494	487	14	(	(	PUNCT
ejpam-2494	487	15	x	x	X
ejpam-2494	487	16	,	,	PUNCT
ejpam-2494	487	17	τ	τ	PROPN
ejpam-2494	487	18	)	)	PUNCT
ejpam-2494	487	19	,	,	PUNCT
ejpam-2494	487	20	then	then	ADV
ejpam-2494	487	21	a∩	a∩	PROPN
ejpam-2494	487	22	b	b	PROPN
ejpam-2494	487	23	is	be	AUX
ejpam-2494	487	24	a	a	DET
ejpam-2494	487	25	ω⋆	ω⋆	NUM
ejpam-2494	487	26	−	−	PRON
ejpam-2494	487	27	t	t	NOUN
ejpam-2494	487	28	-	-	PUNCT
ejpam-2494	487	29	set	set	NOUN
ejpam-2494	487	30	.	.	PUNCT
ejpam-2494	488	1	proof	proof	NOUN
ejpam-2494	488	2	.	.	PUNCT
ejpam-2494	489	1	let	let	VERB
ejpam-2494	489	2	a	a	PRON
ejpam-2494	489	3	and	and	CCONJ
ejpam-2494	489	4	b	b	NOUN
ejpam-2494	489	5	be	be	AUX
ejpam-2494	489	6	ω⋆	ω⋆	NUM
ejpam-2494	489	7	−	−	PRON
ejpam-2494	489	8	t	t	NOUN
ejpam-2494	489	9	-	-	PUNCT
ejpam-2494	489	10	sets	set	NOUN
ejpam-2494	489	11	.	.	PUNCT
ejpam-2494	490	1	then	then	ADV
ejpam-2494	490	2	we	we	PRON
ejpam-2494	490	3	have	have	VERB
ejpam-2494	490	4	intω(a∩	intω(a∩	PROPN
ejpam-2494	490	5	b	b	X
ejpam-2494	490	6	)	)	PUNCT
ejpam-2494	491	1	⊂intω(cl(a∩	⊂intω(cl(a∩	PROPN
ejpam-2494	491	2	b	b	NOUN
ejpam-2494	491	3	)	)	PUNCT
ejpam-2494	491	4	)	)	PUNCT
ejpam-2494	492	1	⊂	⊂	PROPN
ejpam-2494	492	2	intω(cl(a)∩	intω(cl(a)∩	PROPN
ejpam-2494	492	3	cl(b	cl(b	NOUN
ejpam-2494	492	4	)	)	PUNCT
ejpam-2494	492	5	)	)	PUNCT
ejpam-2494	493	1	=	=	NOUN
ejpam-2494	493	2	intω(cl(a))∩	intω(cl(a))∩	NOUN
ejpam-2494	493	3	intω(cl(b	intω(cl(b	NOUN
ejpam-2494	493	4	)	)	PUNCT
ejpam-2494	493	5	)	)	PUNCT
ejpam-2494	494	1	=	=	SYM
ejpam-2494	494	2	intω(a)∩	intω(a)∩	PROPN
ejpam-2494	494	3	intω(b	intω(b	PROPN
ejpam-2494	494	4	)	)	PUNCT
ejpam-2494	494	5	=	=	PUNCT
ejpam-2494	494	6	intω(a∩	intω(a∩	PROPN
ejpam-2494	494	7	b	b	NOUN
ejpam-2494	494	8	)	)	PUNCT
ejpam-2494	494	9	.	.	PUNCT
ejpam-2494	495	1	then	then	ADV
ejpam-2494	495	2	intω(a∩	intω(a∩	PROPN
ejpam-2494	495	3	b	b	X
ejpam-2494	495	4	)	)	PUNCT
ejpam-2494	495	5	=	=	SYM
ejpam-2494	495	6	intω(cl(a∩	intω(cl(a∩	PROPN
ejpam-2494	495	7	b	b	NOUN
ejpam-2494	495	8	)	)	PUNCT
ejpam-2494	495	9	)	)	PUNCT
ejpam-2494	495	10	and	and	CCONJ
ejpam-2494	495	11	hence	hence	ADV
ejpam-2494	495	12	a∩	a∩	PROPN
ejpam-2494	495	13	b	b	PROPN
ejpam-2494	495	14	is	be	AUX
ejpam-2494	495	15	an	an	DET
ejpam-2494	495	16	ω⋆	ω⋆	NUM
ejpam-2494	495	17	−	−	PRON
ejpam-2494	495	18	t	t	NOUN
ejpam-2494	495	19	-	-	PUNCT
ejpam-2494	495	20	set	set	NOUN
ejpam-2494	495	21	.	.	PUNCT
ejpam-2494	496	1	definition	definition	NOUN
ejpam-2494	496	2	14	14	NUM
ejpam-2494	496	3	.	.	PUNCT
ejpam-2494	497	1	a	a	DET
ejpam-2494	497	2	subset	subset	ADJ
ejpam-2494	497	3	h	h	NOUN
ejpam-2494	497	4	of	of	ADP
ejpam-2494	497	5	a	a	DET
ejpam-2494	497	6	space	space	NOUN
ejpam-2494	497	7	(	(	PUNCT
ejpam-2494	497	8	x	x	X
ejpam-2494	497	9	,	,	PUNCT
ejpam-2494	497	10	τ	τ	X
ejpam-2494	497	11	)	)	PUNCT
ejpam-2494	497	12	is	be	AUX
ejpam-2494	497	13	said	say	VERB
ejpam-2494	497	14	to	to	PART
ejpam-2494	497	15	be	be	AUX
ejpam-2494	497	16	semi	semi	ADJ
ejpam-2494	497	17	-	-	ADJ
ejpam-2494	497	18	ω	ω	ADJ
ejpam-2494	497	19	-	-	ADJ
ejpam-2494	497	20	regular	regular	ADJ
ejpam-2494	497	21	if	if	SCONJ
ejpam-2494	497	22	h	h	NOUN
ejpam-2494	497	23	is	be	AUX
ejpam-2494	497	24	semi	semi	ADJ
ejpam-2494	497	25	-	-	ADJ
ejpam-2494	497	26	ω	ω	ADJ
ejpam-2494	497	27	-	-	ADJ
ejpam-2494	497	28	open	open	ADJ
ejpam-2494	497	29	and	and	CCONJ
ejpam-2494	497	30	a	a	DET
ejpam-2494	497	31	ω⋆	ω⋆	NUM
ejpam-2494	497	32	−	−	PRON
ejpam-2494	497	33	t	t	NOUN
ejpam-2494	497	34	-	-	PUNCT
ejpam-2494	497	35	set	set	NOUN
ejpam-2494	497	36	.	.	PUNCT
ejpam-2494	498	1	example	example	NOUN
ejpam-2494	498	2	18	18	NUM
ejpam-2494	498	3	.	.	PUNCT
ejpam-2494	499	1	let	let	VERB
ejpam-2494	499	2	x	x	PUNCT
ejpam-2494	499	3	=	=	PUNCT
ejpam-2494	499	4	r	r	NOUN
ejpam-2494	499	5	with	with	ADP
ejpam-2494	499	6	the	the	DET
ejpam-2494	499	7	usual	usual	ADJ
ejpam-2494	499	8	topology	topology	NOUN
ejpam-2494	499	9	τu	τu	PROPN
ejpam-2494	499	10	.	.	PUNCT
ejpam-2494	500	1	(	(	PUNCT
ejpam-2494	500	2	i	i	NOUN
ejpam-2494	500	3	)	)	PUNCT
ejpam-2494	500	4	let	let	VERB
ejpam-2494	500	5	h	h	NOUN
ejpam-2494	500	6	=	=	PUNCT
ejpam-2494	500	7	(	(	PUNCT
ejpam-2494	500	8	0,1	0,1	NUM
ejpam-2494	500	9	]	]	PUNCT
ejpam-2494	500	10	.	.	PUNCT
ejpam-2494	501	1	then	then	ADV
ejpam-2494	501	2	h	h	PROPN
ejpam-2494	501	3	is	be	AUX
ejpam-2494	501	4	semi	semi	ADJ
ejpam-2494	501	5	-	-	ADJ
ejpam-2494	501	6	ω	ω	ADJ
ejpam-2494	501	7	-	-	NOUN
ejpam-2494	501	8	regular	regular	NOUN
ejpam-2494	501	9	.	.	PUNCT
ejpam-2494	502	1	(	(	PUNCT
ejpam-2494	502	2	ii	ii	NOUN
ejpam-2494	502	3	)	)	PUNCT
ejpam-2494	502	4	let	let	VERB
ejpam-2494	502	5	h	h	NOUN
ejpam-2494	502	6	=	=	SYM
ejpam-2494	502	7	r\q	r\q	PROPN
ejpam-2494	502	8	.	.	PUNCT
ejpam-2494	503	1	then	then	ADV
ejpam-2494	503	2	h	h	PROPN
ejpam-2494	503	3	is	be	AUX
ejpam-2494	503	4	not	not	PART
ejpam-2494	503	5	semi	semi	ADJ
ejpam-2494	503	6	-	-	ADJ
ejpam-2494	503	7	ω	ω	ADJ
ejpam-2494	503	8	-	-	NOUN
ejpam-2494	503	9	regular	regular	ADJ
ejpam-2494	503	10	,	,	PUNCT
ejpam-2494	503	11	since	since	SCONJ
ejpam-2494	503	12	h	h	NOUN
ejpam-2494	503	13	is	be	AUX
ejpam-2494	503	14	not	not	PART
ejpam-2494	503	15	ω⋆	ω⋆	NUM
ejpam-2494	503	16	−	−	PRON
ejpam-2494	503	17	t	t	NOUN
ejpam-2494	503	18	-	-	PUNCT
ejpam-2494	503	19	set	set	NOUN
ejpam-2494	503	20	.	.	PUNCT
ejpam-2494	504	1	theorem	theorem	NOUN
ejpam-2494	504	2	12	12	NUM
ejpam-2494	504	3	.	.	PUNCT
ejpam-2494	505	1	let	let	VERB
ejpam-2494	505	2	h	h	PRON
ejpam-2494	505	3	be	be	AUX
ejpam-2494	505	4	a	a	DET
ejpam-2494	505	5	subset	subset	NOUN
ejpam-2494	505	6	of	of	ADP
ejpam-2494	505	7	a	a	DET
ejpam-2494	505	8	space	space	NOUN
ejpam-2494	505	9	(	(	PUNCT
ejpam-2494	505	10	x	x	X
ejpam-2494	505	11	,	,	PUNCT
ejpam-2494	505	12	τ	τ	PROPN
ejpam-2494	505	13	)	)	PUNCT
ejpam-2494	505	14	.	.	PUNCT
ejpam-2494	506	1	then	then	ADV
ejpam-2494	506	2	h	h	PROPN
ejpam-2494	506	3	is	be	AUX
ejpam-2494	506	4	semi	semi	ADJ
ejpam-2494	506	5	-	-	ADJ
ejpam-2494	506	6	ω	ω	ADJ
ejpam-2494	506	7	-	-	ADJ
ejpam-2494	506	8	regular	regular	ADJ
ejpam-2494	506	9	if	if	SCONJ
ejpam-2494	507	1	and	and	CCONJ
ejpam-2494	507	2	only	only	ADV
ejpam-2494	507	3	if	if	SCONJ
ejpam-2494	507	4	h	h	NOUN
ejpam-2494	507	5	is	be	AUX
ejpam-2494	507	6	both	both	PRON
ejpam-2494	507	7	β	β	X
ejpam-2494	507	8	−ω	−ω	ADJ
ejpam-2494	507	9	-	-	ADJ
ejpam-2494	507	10	open	open	ADJ
ejpam-2494	507	11	and	and	CCONJ
ejpam-2494	507	12	semi⋆	semi⋆	NOUN
ejpam-2494	507	13	−ω	−ω	ADJ
ejpam-2494	507	14	-	-	PUNCT
ejpam-2494	507	15	closed	closed	ADJ
ejpam-2494	507	16	.	.	PUNCT
ejpam-2494	508	1	proof	proof	NOUN
ejpam-2494	508	2	.	.	PUNCT
ejpam-2494	509	1	if	if	SCONJ
ejpam-2494	509	2	h	h	NOUN
ejpam-2494	509	3	is	be	AUX
ejpam-2494	509	4	semi	semi	ADJ
ejpam-2494	509	5	-	-	ADJ
ejpam-2494	509	6	ω	ω	ADJ
ejpam-2494	509	7	-	-	NOUN
ejpam-2494	509	8	regular	regular	ADJ
ejpam-2494	509	9	,	,	PUNCT
ejpam-2494	509	10	then	then	ADV
ejpam-2494	509	11	h	h	PROPN
ejpam-2494	509	12	is	be	AUX
ejpam-2494	509	13	both	both	PRON
ejpam-2494	509	14	semi	semi	ADJ
ejpam-2494	509	15	-	-	ADJ
ejpam-2494	509	16	ω	ω	ADJ
ejpam-2494	509	17	-	-	ADJ
ejpam-2494	509	18	open	open	ADJ
ejpam-2494	509	19	and	and	CCONJ
ejpam-2494	509	20	a	a	DET
ejpam-2494	509	21	ω⋆	ω⋆	NUM
ejpam-2494	509	22	−	−	PRON
ejpam-2494	509	23	t	t	NOUN
ejpam-2494	509	24	-	-	PUNCT
ejpam-2494	509	25	set	set	NOUN
ejpam-2494	509	26	.	.	PUNCT
ejpam-2494	510	1	since	since	SCONJ
ejpam-2494	510	2	every	every	DET
ejpam-2494	510	3	semi	semi	ADJ
ejpam-2494	510	4	-	-	ADJ
ejpam-2494	510	5	ω	ω	ADJ
ejpam-2494	510	6	-	-	ADJ
ejpam-2494	510	7	open	open	ADJ
ejpam-2494	510	8	set	set	NOUN
ejpam-2494	510	9	is	be	AUX
ejpam-2494	510	10	β	β	NOUN
ejpam-2494	510	11	−ω	−ω	ADJ
ejpam-2494	510	12	-	-	ADJ
ejpam-2494	510	13	open	open	ADJ
ejpam-2494	510	14	,	,	PUNCT
ejpam-2494	510	15	h	h	NOUN
ejpam-2494	510	16	is	be	AUX
ejpam-2494	510	17	both	both	PRON
ejpam-2494	510	18	β	β	X
ejpam-2494	510	19	−ω	−ω	ADJ
ejpam-2494	510	20	-	-	ADJ
ejpam-2494	510	21	open	open	ADJ
ejpam-2494	510	22	and	and	CCONJ
ejpam-2494	510	23	a	a	DET
ejpam-2494	510	24	ω⋆	ω⋆	NUM
ejpam-2494	510	25	−	−	PRON
ejpam-2494	510	26	t	t	NOUN
ejpam-2494	510	27	-	-	PUNCT
ejpam-2494	510	28	set	set	NOUN
ejpam-2494	510	29	.	.	PUNCT
ejpam-2494	511	1	by	by	ADP
ejpam-2494	511	2	theorem	theorem	NOUN
ejpam-2494	511	3	11	11	NUM
ejpam-2494	511	4	,	,	PUNCT
ejpam-2494	511	5	we	we	PRON
ejpam-2494	511	6	obtain	obtain	VERB
ejpam-2494	511	7	the	the	DET
ejpam-2494	511	8	result	result	NOUN
ejpam-2494	511	9	.	.	PUNCT
ejpam-2494	512	1	conversely	conversely	ADV
ejpam-2494	512	2	,	,	PUNCT
ejpam-2494	512	3	let	let	VERB
ejpam-2494	512	4	h	h	PRON
ejpam-2494	512	5	be	be	AUX
ejpam-2494	512	6	semi⋆	semi⋆	NOUN
ejpam-2494	512	7	−ω	−ω	ADJ
ejpam-2494	512	8	-	-	PUNCT
ejpam-2494	512	9	closed	closed	ADJ
ejpam-2494	512	10	and	and	CCONJ
ejpam-2494	512	11	β	β	NOUN
ejpam-2494	512	12	−ω	−ω	ADJ
ejpam-2494	512	13	-	-	ADJ
ejpam-2494	512	14	open	open	ADJ
ejpam-2494	512	15	.	.	PUNCT
ejpam-2494	513	1	since	since	SCONJ
ejpam-2494	513	2	h	h	NOUN
ejpam-2494	513	3	is	be	AUX
ejpam-2494	513	4	a	a	DET
ejpam-2494	513	5	semi⋆	semi⋆	PROPN
ejpam-2494	513	6	−ω	−ω	NOUN
ejpam-2494	513	7	-	-	PUNCT
ejpam-2494	513	8	closed	closed	ADJ
ejpam-2494	513	9	,	,	PUNCT
ejpam-2494	513	10	by	by	ADP
ejpam-2494	513	11	theorem	theorem	VERB
ejpam-2494	513	12	11	11	NUM
ejpam-2494	513	13	h	h	NOUN
ejpam-2494	513	14	is	be	AUX
ejpam-2494	513	15	a	a	DET
ejpam-2494	513	16	ω⋆	ω⋆	NUM
ejpam-2494	513	17	−	−	PRON
ejpam-2494	513	18	t	t	NOUN
ejpam-2494	513	19	-	-	PUNCT
ejpam-2494	513	20	set	set	NOUN
ejpam-2494	513	21	.	.	PUNCT
ejpam-2494	514	1	since	since	SCONJ
ejpam-2494	514	2	h	h	PROPN
ejpam-2494	514	3	is	be	AUX
ejpam-2494	514	4	β	β	X
ejpam-2494	514	5	−ω	−ω	ADJ
ejpam-2494	514	6	-	-	ADJ
ejpam-2494	514	7	open	open	ADJ
ejpam-2494	514	8	,	,	PUNCT
ejpam-2494	514	9	h	h	PROPN
ejpam-2494	514	10	⊂	⊂	PROPN
ejpam-2494	514	11	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	514	12	)	)	PUNCT
ejpam-2494	514	13	)	)	PUNCT
ejpam-2494	514	14	)	)	PUNCT
ejpam-2494	515	1	=	=	PUNCT
ejpam-2494	515	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	515	3	)	)	PUNCT
ejpam-2494	515	4	)	)	PUNCT
ejpam-2494	515	5	.	.	PUNCT
ejpam-2494	516	1	therefore	therefore	ADV
ejpam-2494	516	2	h	h	PROPN
ejpam-2494	516	3	is	be	AUX
ejpam-2494	516	4	semi	semi	ADJ
ejpam-2494	516	5	-	-	ADJ
ejpam-2494	516	6	ω	ω	ADJ
ejpam-2494	516	7	-	-	NOUN
ejpam-2494	516	8	open	open	ADJ
ejpam-2494	516	9	.	.	PUNCT
ejpam-2494	517	1	since	since	SCONJ
ejpam-2494	517	2	h	h	PROPN
ejpam-2494	517	3	is	be	AUX
ejpam-2494	517	4	both	both	PRON
ejpam-2494	517	5	semi	semi	ADJ
ejpam-2494	517	6	-	-	ADJ
ejpam-2494	517	7	ω	ω	ADJ
ejpam-2494	517	8	-	-	ADJ
ejpam-2494	517	9	open	open	ADJ
ejpam-2494	517	10	and	and	CCONJ
ejpam-2494	517	11	a	a	DET
ejpam-2494	517	12	ω⋆	ω⋆	NUM
ejpam-2494	517	13	−	−	PRON
ejpam-2494	517	14	t	t	NOUN
ejpam-2494	517	15	-	-	PUNCT
ejpam-2494	517	16	set	set	NOUN
ejpam-2494	517	17	,	,	PUNCT
ejpam-2494	517	18	h	h	NOUN
ejpam-2494	517	19	is	be	AUX
ejpam-2494	517	20	semi	semi	ADJ
ejpam-2494	517	21	-	-	ADJ
ejpam-2494	517	22	ωregular	ωregular	ADJ
ejpam-2494	517	23	.	.	PUNCT
ejpam-2494	518	1	o.	o.	PROPN
ejpam-2494	518	2	ravi	ravi	PROPN
ejpam-2494	518	3	,	,	PUNCT
ejpam-2494	518	4	i.	i.	NOUN
ejpam-2494	518	5	rajasekaran	rajasekaran	PROPN
ejpam-2494	518	6	,	,	PUNCT
ejpam-2494	518	7	s.	s.	PROPN
ejpam-2494	518	8	kanna	kanna	PROPN
ejpam-2494	518	9	and	and	CCONJ
ejpam-2494	518	10	m.	m.	NOUN
ejpam-2494	518	11	paranjothi	paranjothi	PROPN
ejpam-2494	518	12	/	/	SYM
ejpam-2494	518	13	eur	eur	PROPN
ejpam-2494	518	14	.	.	PUNCT
ejpam-2494	519	1	j.	j.	PROPN
ejpam-2494	519	2	pure	pure	PROPN
ejpam-2494	519	3	appl	appl	PROPN
ejpam-2494	519	4	.	.	PROPN
ejpam-2494	519	5	math	math	PROPN
ejpam-2494	519	6	,	,	PUNCT
ejpam-2494	519	7	9	9	NUM
ejpam-2494	519	8	(	(	PUNCT
ejpam-2494	519	9	2016	2016	NUM
ejpam-2494	519	10	)	)	PUNCT
ejpam-2494	519	11	,	,	PUNCT
ejpam-2494	519	12	152	152	NUM
ejpam-2494	519	13	-	-	SYM
ejpam-2494	519	14	164	164	NUM
ejpam-2494	519	15	162	162	NUM
ejpam-2494	519	16	remark	remark	NOUN
ejpam-2494	519	17	7	7	NUM
ejpam-2494	519	18	.	.	PUNCT
ejpam-2494	520	1	the	the	DET
ejpam-2494	520	2	concepts	concept	NOUN
ejpam-2494	520	3	of	of	ADP
ejpam-2494	520	4	β	β	PROPN
ejpam-2494	520	5	−ω	−ω	ADJ
ejpam-2494	520	6	-	-	NOUN
ejpam-2494	520	7	openness	openness	NOUN
ejpam-2494	520	8	and	and	CCONJ
ejpam-2494	520	9	semi⋆	semi⋆	NOUN
ejpam-2494	520	10	−ω	−ω	NOUN
ejpam-2494	520	11	-	-	PUNCT
ejpam-2494	520	12	closedness	closedness	NOUN
ejpam-2494	520	13	are	be	AUX
ejpam-2494	520	14	independent	independent	ADJ
ejpam-2494	520	15	.	.	PUNCT
ejpam-2494	520	16	example	example	NOUN
ejpam-2494	521	1	19	19	NUM
ejpam-2494	521	2	.	.	PUNCT
ejpam-2494	522	1	(	(	PUNCT
ejpam-2494	522	2	i	i	NOUN
ejpam-2494	522	3	)	)	PUNCT
ejpam-2494	522	4	let	let	VERB
ejpam-2494	522	5	x	x	PUNCT
ejpam-2494	522	6	=	=	PRON
ejpam-2494	522	7	rwith	rwith	ADP
ejpam-2494	522	8	the	the	DET
ejpam-2494	522	9	topology	topology	NOUN
ejpam-2494	522	10	τ=	τ=	PRON
ejpam-2494	522	11	{	{	PUNCT
ejpam-2494	522	12	φ	φ	PROPN
ejpam-2494	522	13	,	,	PUNCT
ejpam-2494	522	14	x	x	X
ejpam-2494	522	15	,	,	PUNCT
ejpam-2494	522	16	q⋆	q⋆	NOUN
ejpam-2494	522	17	}	}	PUNCT
ejpam-2494	522	18	.	.	PUNCT
ejpam-2494	523	1	then	then	ADV
ejpam-2494	523	2	h	h	NOUN
ejpam-2494	524	1	=	=	PUNCT
ejpam-2494	524	2	q	q	PROPN
ejpam-2494	524	3	is	be	AUX
ejpam-2494	524	4	semi⋆−ω	semi⋆−ω	NOUN
ejpam-2494	524	5	-	-	PUNCT
ejpam-2494	524	6	closed	closed	ADJ
ejpam-2494	524	7	but	but	CCONJ
ejpam-2494	524	8	not	not	PART
ejpam-2494	524	9	β	β	X
ejpam-2494	524	10	−ω	−ω	ADJ
ejpam-2494	524	11	-	-	ADJ
ejpam-2494	524	12	open	open	ADJ
ejpam-2494	524	13	.	.	PUNCT
ejpam-2494	525	1	since	since	SCONJ
ejpam-2494	525	2	intω(cl(h	intω(cl(h	PROPN
ejpam-2494	525	3	)	)	PUNCT
ejpam-2494	525	4	)	)	PUNCT
ejpam-2494	526	1	=	=	SYM
ejpam-2494	526	2	intω(h	intω(h	NOUN
ejpam-2494	526	3	)	)	PUNCT
ejpam-2494	526	4	=	=	PUNCT
ejpam-2494	527	1	φ	φ	PROPN
ejpam-2494	527	2	⊂	⊂	PROPN
ejpam-2494	528	1	h	h	PROPN
ejpam-2494	528	2	,	,	PUNCT
ejpam-2494	528	3	h	h	PROPN
ejpam-2494	528	4	is	be	AUX
ejpam-2494	528	5	semi⋆−ω	semi⋆−ω	NOUN
ejpam-2494	528	6	-	-	PUNCT
ejpam-2494	528	7	closed	closed	ADJ
ejpam-2494	528	8	.	.	PUNCT
ejpam-2494	529	1	again	again	ADV
ejpam-2494	529	2	since	since	SCONJ
ejpam-2494	529	3	h	h	PROPN
ejpam-2494	529	4	6⊆	6⊆	NUM
ejpam-2494	529	5	cl(intω(cl(h	cl(intω(cl(h	NUM
ejpam-2494	529	6	)	)	PUNCT
ejpam-2494	529	7	)	)	PUNCT
ejpam-2494	529	8	)	)	PUNCT
ejpam-2494	530	1	=	=	SYM
ejpam-2494	530	2	φ	φ	PROPN
ejpam-2494	530	3	,	,	PUNCT
ejpam-2494	530	4	h	h	PROPN
ejpam-2494	530	5	is	be	AUX
ejpam-2494	530	6	not	not	PART
ejpam-2494	530	7	β	β	X
ejpam-2494	530	8	−ω	−ω	ADJ
ejpam-2494	530	9	-	-	ADJ
ejpam-2494	530	10	open	open	ADJ
ejpam-2494	530	11	.	.	PUNCT
ejpam-2494	531	1	(	(	PUNCT
ejpam-2494	531	2	ii	ii	NOUN
ejpam-2494	531	3	)	)	PUNCT
ejpam-2494	531	4	let	let	VERB
ejpam-2494	531	5	x	x	PUNCT
ejpam-2494	531	6	=	=	PUNCT
ejpam-2494	531	7	r	r	NOUN
ejpam-2494	531	8	with	with	ADP
ejpam-2494	531	9	the	the	DET
ejpam-2494	531	10	usual	usual	ADJ
ejpam-2494	531	11	topology	topology	NOUN
ejpam-2494	531	12	τu	τu	PROPN
ejpam-2494	531	13	.	.	PUNCT
ejpam-2494	532	1	let	let	VERB
ejpam-2494	532	2	h	h	NOUN
ejpam-2494	533	1	=	=	PUNCT
ejpam-2494	533	2	q.	q.	PROPN
ejpam-2494	533	3	then	then	ADV
ejpam-2494	533	4	h	h	PROPN
ejpam-2494	533	5	is	be	AUX
ejpam-2494	533	6	β−ω	β−ω	NOUN
ejpam-2494	533	7	-	-	ADJ
ejpam-2494	533	8	open	open	ADJ
ejpam-2494	533	9	but	but	CCONJ
ejpam-2494	533	10	not	not	PART
ejpam-2494	533	11	semi⋆−ωclosed	semi⋆−ωclose	VERB
ejpam-2494	533	12	,	,	PUNCT
ejpam-2494	533	13	since	since	SCONJ
ejpam-2494	533	14	intω(cl(h	intω(cl(h	NOUN
ejpam-2494	533	15	)	)	PUNCT
ejpam-2494	533	16	)	)	PUNCT
ejpam-2494	534	1	=	=	SYM
ejpam-2494	534	2	intω(r	intω(r	NOUN
ejpam-2494	534	3	)	)	PUNCT
ejpam-2494	534	4	=	=	PUNCT
ejpam-2494	535	1	r.	r.	PROPN
ejpam-2494	535	2	6	6	NUM
ejpam-2494	535	3	.	.	PUNCT
ejpam-2494	536	1	properties	property	NOUN
ejpam-2494	536	2	of	of	ADP
ejpam-2494	536	3	ω−r	ω−r	ADJ
ejpam-2494	536	4	-	-	PUNCT
ejpam-2494	536	5	closed	closed	ADJ
ejpam-2494	536	6	sets	set	NOUN
ejpam-2494	536	7	definition	definition	NOUN
ejpam-2494	536	8	15	15	NUM
ejpam-2494	536	9	.	.	PUNCT
ejpam-2494	537	1	a	a	DET
ejpam-2494	537	2	subset	subset	ADJ
ejpam-2494	537	3	h	h	NOUN
ejpam-2494	537	4	of	of	ADP
ejpam-2494	537	5	a	a	DET
ejpam-2494	537	6	space	space	NOUN
ejpam-2494	537	7	(	(	PUNCT
ejpam-2494	537	8	x	x	X
ejpam-2494	537	9	,	,	PUNCT
ejpam-2494	537	10	τ	τ	X
ejpam-2494	537	11	)	)	PUNCT
ejpam-2494	537	12	is	be	AUX
ejpam-2494	537	13	called	call	VERB
ejpam-2494	537	14	ω−r	ω−r	ADJ
ejpam-2494	537	15	-	-	PUNCT
ejpam-2494	537	16	closed	closed	ADJ
ejpam-2494	537	17	if	if	SCONJ
ejpam-2494	537	18	h	h	NOUN
ejpam-2494	537	19	=	=	SYM
ejpam-2494	537	20	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	537	21	)	)	PUNCT
ejpam-2494	537	22	)	)	PUNCT
ejpam-2494	537	23	.	.	PUNCT
ejpam-2494	538	1	theorem	theorem	VERB
ejpam-2494	538	2	13	13	NUM
ejpam-2494	538	3	.	.	PUNCT
ejpam-2494	539	1	let	let	AUX
ejpam-2494	539	2	(	(	PUNCT
ejpam-2494	539	3	x	x	X
ejpam-2494	539	4	,	,	PUNCT
ejpam-2494	539	5	τ	τ	X
ejpam-2494	539	6	)	)	PUNCT
ejpam-2494	539	7	be	be	VERB
ejpam-2494	539	8	a	a	DET
ejpam-2494	539	9	space	space	NOUN
ejpam-2494	539	10	and	and	CCONJ
ejpam-2494	539	11	h	h	NOUN
ejpam-2494	539	12	a	a	DET
ejpam-2494	539	13	subset	subset	NOUN
ejpam-2494	539	14	of	of	ADP
ejpam-2494	539	15	x.	x.	NOUN
ejpam-2494	539	16	then	then	ADV
ejpam-2494	539	17	the	the	DET
ejpam-2494	539	18	following	follow	VERB
ejpam-2494	539	19	properties	property	NOUN
ejpam-2494	539	20	are	be	AUX
ejpam-2494	539	21	equivalent	equivalent	ADJ
ejpam-2494	539	22	.	.	PUNCT
ejpam-2494	540	1	(	(	PUNCT
ejpam-2494	540	2	i	i	NOUN
ejpam-2494	540	3	)	)	PUNCT
ejpam-2494	540	4	h	h	PROPN
ejpam-2494	541	1	6=	6=	PROPN
ejpam-2494	541	2	φ	φ	PROPN
ejpam-2494	541	3	is	be	AUX
ejpam-2494	541	4	ω−r	ω−r	ADV
ejpam-2494	541	5	-	-	PUNCT
ejpam-2494	541	6	closed	closed	ADJ
ejpam-2494	541	7	.	.	PUNCT
ejpam-2494	542	1	(	(	PUNCT
ejpam-2494	542	2	ii	ii	NOUN
ejpam-2494	542	3	)	)	PUNCT
ejpam-2494	542	4	there	there	PRON
ejpam-2494	542	5	exists	exist	VERB
ejpam-2494	542	6	a	a	DET
ejpam-2494	542	7	non	non	ADJ
ejpam-2494	542	8	-	-	ADJ
ejpam-2494	542	9	empty	empty	ADJ
ejpam-2494	542	10	ω	ω	ADJ
ejpam-2494	542	11	-	-	ADJ
ejpam-2494	542	12	open	open	ADJ
ejpam-2494	542	13	set	set	NOUN
ejpam-2494	542	14	g	g	PROPN
ejpam-2494	542	15	such	such	ADJ
ejpam-2494	542	16	that	that	SCONJ
ejpam-2494	542	17	g	g	PROPN
ejpam-2494	542	18	⊂	⊂	PROPN
ejpam-2494	542	19	h	h	NOUN
ejpam-2494	542	20	=	=	PUNCT
ejpam-2494	542	21	cl(g	cl(g	X
ejpam-2494	542	22	)	)	PUNCT
ejpam-2494	542	23	.	.	PUNCT
ejpam-2494	543	1	(	(	PUNCT
ejpam-2494	543	2	iii	iii	X
ejpam-2494	543	3	)	)	PUNCT
ejpam-2494	543	4	there	there	PRON
ejpam-2494	543	5	exists	exist	VERB
ejpam-2494	543	6	a	a	DET
ejpam-2494	543	7	non	non	ADJ
ejpam-2494	543	8	-	-	ADJ
ejpam-2494	543	9	empty	empty	ADJ
ejpam-2494	543	10	ω	ω	ADJ
ejpam-2494	543	11	-	-	ADJ
ejpam-2494	543	12	open	open	ADJ
ejpam-2494	543	13	set	set	NOUN
ejpam-2494	543	14	g	g	PROPN
ejpam-2494	543	15	such	such	ADJ
ejpam-2494	543	16	that	that	DET
ejpam-2494	543	17	h	h	NOUN
ejpam-2494	543	18	=	=	NOUN
ejpam-2494	543	19	g	g	NOUN
ejpam-2494	543	20	∪	∪	ADV
ejpam-2494	543	21	(	(	PUNCT
ejpam-2494	543	22	cl(g)−	cl(g)−	ADJ
ejpam-2494	543	23	g	g	NOUN
ejpam-2494	543	24	)	)	PUNCT
ejpam-2494	543	25	.	.	PUNCT
ejpam-2494	544	1	proof	proof	NOUN
ejpam-2494	544	2	.	.	PUNCT
ejpam-2494	545	1	(	(	PUNCT
ejpam-2494	545	2	i)⇒	i)⇒	PROPN
ejpam-2494	545	3	(	(	PUNCT
ejpam-2494	545	4	ii	ii	PROPN
ejpam-2494	545	5	):	):	PUNCT
ejpam-2494	545	6	suppose	suppose	VERB
ejpam-2494	545	7	h	h	PROPN
ejpam-2494	545	8	6=	6=	PROPN
ejpam-2494	545	9	φ	φ	PROPN
ejpam-2494	545	10	is	be	AUX
ejpam-2494	545	11	an	an	DET
ejpam-2494	545	12	ω−r	ω−r	ADJ
ejpam-2494	545	13	-	-	PUNCT
ejpam-2494	545	14	closed	closed	ADJ
ejpam-2494	545	15	set	set	NOUN
ejpam-2494	545	16	.	.	PUNCT
ejpam-2494	546	1	then	then	ADV
ejpam-2494	546	2	h	h	NOUN
ejpam-2494	546	3	=	=	PUNCT
ejpam-2494	546	4	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	546	5	)	)	PUNCT
ejpam-2494	546	6	)	)	PUNCT
ejpam-2494	546	7	.	.	PUNCT
ejpam-2494	547	1	let	let	VERB
ejpam-2494	547	2	g	g	NOUN
ejpam-2494	547	3	=	=	SYM
ejpam-2494	547	4	intω(h	intω(h	PROPN
ejpam-2494	547	5	)	)	PUNCT
ejpam-2494	547	6	.	.	PUNCT
ejpam-2494	548	1	g	g	PROPN
ejpam-2494	548	2	is	be	AUX
ejpam-2494	548	3	the	the	DET
ejpam-2494	548	4	required	require	VERB
ejpam-2494	548	5	ω	ω	VERB
ejpam-2494	548	6	-	-	ADJ
ejpam-2494	548	7	open	open	ADJ
ejpam-2494	548	8	set	set	NOUN
ejpam-2494	548	9	such	such	ADJ
ejpam-2494	548	10	that	that	SCONJ
ejpam-2494	548	11	g	g	PROPN
ejpam-2494	548	12	⊂	⊂	PROPN
ejpam-2494	548	13	h	h	NOUN
ejpam-2494	548	14	=	=	PUNCT
ejpam-2494	548	15	cl(g	cl(g	X
ejpam-2494	548	16	)	)	PUNCT
ejpam-2494	548	17	.	.	PUNCT
ejpam-2494	549	1	(	(	PUNCT
ejpam-2494	549	2	ii)⇒	ii)⇒	X
ejpam-2494	549	3	(	(	PUNCT
ejpam-2494	549	4	iii	iii	NOUN
ejpam-2494	549	5	):	):	PUNCT
ejpam-2494	549	6	since	since	SCONJ
ejpam-2494	549	7	h	h	NOUN
ejpam-2494	549	8	=	=	SYM
ejpam-2494	549	9	cl(g	cl(g	X
ejpam-2494	549	10	)	)	PUNCT
ejpam-2494	549	11	=	=	SYM
ejpam-2494	549	12	g	g	NOUN
ejpam-2494	549	13	∪	∪	VERB
ejpam-2494	549	14	(	(	PUNCT
ejpam-2494	549	15	cl(g)−	cl(g)−	ADJ
ejpam-2494	549	16	g	g	NOUN
ejpam-2494	549	17	)	)	PUNCT
ejpam-2494	549	18	where	where	SCONJ
ejpam-2494	549	19	g	g	PROPN
ejpam-2494	549	20	is	be	AUX
ejpam-2494	549	21	a	a	DET
ejpam-2494	549	22	nonempty	nonempty	ADJ
ejpam-2494	549	23	ω	ω	VERB
ejpam-2494	549	24	-	-	ADJ
ejpam-2494	549	25	open	open	ADJ
ejpam-2494	549	26	set	set	NOUN
ejpam-2494	549	27	,	,	PUNCT
ejpam-2494	549	28	(	(	PUNCT
ejpam-2494	549	29	iii	iii	NOUN
ejpam-2494	549	30	)	)	PUNCT
ejpam-2494	549	31	follows	follow	VERB
ejpam-2494	549	32	.	.	PUNCT
ejpam-2494	550	1	(	(	PUNCT
ejpam-2494	550	2	iii)⇒	iii)⇒	PROPN
ejpam-2494	550	3	(	(	PUNCT
ejpam-2494	550	4	i	i	NOUN
ejpam-2494	550	5	):	):	PUNCT
ejpam-2494	550	6	h	h	PROPN
ejpam-2494	550	7	=	=	PUNCT
ejpam-2494	550	8	g∪(cl(g)−g	g∪(cl(g)−g	PROPN
ejpam-2494	550	9	)	)	PUNCT
ejpam-2494	550	10	implies	imply	VERB
ejpam-2494	550	11	that	that	SCONJ
ejpam-2494	550	12	h	h	NOUN
ejpam-2494	550	13	=	=	NOUN
ejpam-2494	550	14	cl(g	cl(g	X
ejpam-2494	550	15	)	)	PUNCT
ejpam-2494	550	16	=	=	SYM
ejpam-2494	550	17	cl(intω(g	cl(intω(g	NOUN
ejpam-2494	550	18	)	)	PUNCT
ejpam-2494	550	19	)	)	PUNCT
ejpam-2494	551	1	⊂	⊂	PROPN
ejpam-2494	551	2	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	551	3	)	)	PUNCT
ejpam-2494	551	4	)	)	PUNCT
ejpam-2494	551	5	,	,	PUNCT
ejpam-2494	551	6	since	since	SCONJ
ejpam-2494	551	7	g	g	PROPN
ejpam-2494	551	8	is	be	AUX
ejpam-2494	551	9	ω	ω	NOUN
ejpam-2494	551	10	-	-	ADJ
ejpam-2494	551	11	open	open	ADJ
ejpam-2494	551	12	and	and	CCONJ
ejpam-2494	551	13	g	g	PROPN
ejpam-2494	551	14	⊂	⊂	PROPN
ejpam-2494	551	15	h.	h.	PROPN
ejpam-2494	551	16	again	again	ADV
ejpam-2494	551	17	intω(h	intω(h	NUM
ejpam-2494	551	18	)	)	PUNCT
ejpam-2494	552	1	⊂	⊂	PROPN
ejpam-2494	552	2	h	h	PROPN
ejpam-2494	552	3	implies	imply	VERB
ejpam-2494	552	4	that	that	PRON
ejpam-2494	552	5	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	552	6	)	)	PUNCT
ejpam-2494	552	7	)	)	PUNCT
ejpam-2494	553	1	⊂	⊂	PROPN
ejpam-2494	553	2	cl(h	cl(h	X
ejpam-2494	553	3	)	)	PUNCT
ejpam-2494	553	4	=	=	SYM
ejpam-2494	553	5	cl(g	cl(g	X
ejpam-2494	553	6	)	)	PUNCT
ejpam-2494	553	7	=	=	SYM
ejpam-2494	554	1	h.	h.	PROPN
ejpam-2494	554	2	therefore	therefore	ADV
ejpam-2494	554	3	h	h	PROPN
ejpam-2494	554	4	=	=	PUNCT
ejpam-2494	554	5	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	554	6	)	)	PUNCT
ejpam-2494	554	7	)	)	PUNCT
ejpam-2494	554	8	which	which	PRON
ejpam-2494	554	9	implies	imply	VERB
ejpam-2494	554	10	that	that	SCONJ
ejpam-2494	554	11	h	h	NOUN
ejpam-2494	554	12	is	be	AUX
ejpam-2494	554	13	ω−r	ω−r	ADV
ejpam-2494	554	14	-	-	PUNCT
ejpam-2494	554	15	closed	closed	ADJ
ejpam-2494	554	16	.	.	PUNCT
ejpam-2494	555	1	theorem	theorem	VERB
ejpam-2494	555	2	14	14	NUM
ejpam-2494	555	3	.	.	PUNCT
ejpam-2494	556	1	let	let	VERB
ejpam-2494	556	2	h	h	PRON
ejpam-2494	556	3	be	be	AUX
ejpam-2494	556	4	a	a	DET
ejpam-2494	556	5	subset	subset	NOUN
ejpam-2494	556	6	of	of	ADP
ejpam-2494	556	7	a	a	DET
ejpam-2494	556	8	space	space	NOUN
ejpam-2494	556	9	(	(	PUNCT
ejpam-2494	556	10	x	x	X
ejpam-2494	556	11	,	,	PUNCT
ejpam-2494	556	12	τ	τ	PROPN
ejpam-2494	556	13	)	)	PUNCT
ejpam-2494	556	14	.	.	PUNCT
ejpam-2494	557	1	if	if	SCONJ
ejpam-2494	557	2	h	h	NOUN
ejpam-2494	557	3	is	be	AUX
ejpam-2494	557	4	β	β	X
ejpam-2494	557	5	−ω	−ω	ADJ
ejpam-2494	557	6	-	-	ADJ
ejpam-2494	557	7	open	open	ADJ
ejpam-2494	557	8	,	,	PUNCT
ejpam-2494	557	9	then	then	ADV
ejpam-2494	557	10	cl(h	cl(h	AUX
ejpam-2494	557	11	)	)	PUNCT
ejpam-2494	557	12	is	be	AUX
ejpam-2494	557	13	ω−r	ω−r	ADV
ejpam-2494	557	14	-	-	PUNCT
ejpam-2494	557	15	closed	closed	ADJ
ejpam-2494	557	16	.	.	PUNCT
ejpam-2494	558	1	proof	proof	NOUN
ejpam-2494	558	2	.	.	PUNCT
ejpam-2494	559	1	suppose	suppose	VERB
ejpam-2494	559	2	h	h	NOUN
ejpam-2494	559	3	is	be	AUX
ejpam-2494	559	4	β	β	X
ejpam-2494	559	5	−ω	−ω	ADJ
ejpam-2494	559	6	-	-	ADJ
ejpam-2494	559	7	open	open	ADJ
ejpam-2494	559	8	.	.	PUNCT
ejpam-2494	560	1	then	then	ADV
ejpam-2494	560	2	h	h	PROPN
ejpam-2494	560	3	⊂	⊂	PROPN
ejpam-2494	560	4	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	560	5	)	)	PUNCT
ejpam-2494	560	6	)	)	PUNCT
ejpam-2494	560	7	)	)	PUNCT
ejpam-2494	561	1	and	and	CCONJ
ejpam-2494	561	2	so	so	ADV
ejpam-2494	561	3	cl(h	cl(h	PUNCT
ejpam-2494	561	4	)	)	PUNCT
ejpam-2494	562	1	⊂	⊂	PROPN
ejpam-2494	562	2	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	562	3	)	)	PUNCT
ejpam-2494	562	4	)	)	PUNCT
ejpam-2494	562	5	)	)	PUNCT
ejpam-2494	563	1	⊂	⊂	PROPN
ejpam-2494	563	2	cl(h)which	cl(h)which	X
ejpam-2494	563	3	implies	imply	VERB
ejpam-2494	563	4	that	that	PRON
ejpam-2494	563	5	cl(h	cl(h	VERB
ejpam-2494	563	6	)	)	PUNCT
ejpam-2494	563	7	=	=	SYM
ejpam-2494	563	8	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	563	9	)	)	PUNCT
ejpam-2494	563	10	)	)	PUNCT
ejpam-2494	563	11	)	)	PUNCT
ejpam-2494	563	12	.	.	PUNCT
ejpam-2494	564	1	therefore	therefore	ADV
ejpam-2494	564	2	cl(h	cl(h	CCONJ
ejpam-2494	564	3	)	)	PUNCT
ejpam-2494	564	4	is	be	AUX
ejpam-2494	564	5	ω−r	ω−r	ADV
ejpam-2494	564	6	-	-	PUNCT
ejpam-2494	564	7	closed	closed	ADJ
ejpam-2494	564	8	.	.	PUNCT
ejpam-2494	565	1	theorem	theorem	NOUN
ejpam-2494	565	2	15	15	NUM
ejpam-2494	565	3	.	.	PUNCT
ejpam-2494	566	1	let	let	VERB
ejpam-2494	566	2	h	h	PRON
ejpam-2494	566	3	be	be	AUX
ejpam-2494	566	4	a	a	DET
ejpam-2494	566	5	subset	subset	NOUN
ejpam-2494	566	6	of	of	ADP
ejpam-2494	566	7	a	a	DET
ejpam-2494	566	8	space	space	NOUN
ejpam-2494	566	9	(	(	PUNCT
ejpam-2494	566	10	x	x	X
ejpam-2494	566	11	,	,	PUNCT
ejpam-2494	566	12	τ	τ	PROPN
ejpam-2494	566	13	)	)	PUNCT
ejpam-2494	566	14	.	.	PUNCT
ejpam-2494	567	1	then	then	ADV
ejpam-2494	567	2	the	the	DET
ejpam-2494	567	3	following	follow	VERB
ejpam-2494	567	4	properties	property	NOUN
ejpam-2494	567	5	are	be	AUX
ejpam-2494	567	6	equivalent	equivalent	ADJ
ejpam-2494	567	7	.	.	PUNCT
ejpam-2494	568	1	(	(	PUNCT
ejpam-2494	568	2	i	i	NOUN
ejpam-2494	568	3	)	)	PUNCT
ejpam-2494	568	4	h	h	PROPN
ejpam-2494	568	5	is	be	AUX
ejpam-2494	568	6	ω−r	ω−r	ADV
ejpam-2494	568	7	-	-	PUNCT
ejpam-2494	568	8	closed	closed	ADJ
ejpam-2494	568	9	.	.	PUNCT
ejpam-2494	569	1	(	(	PUNCT
ejpam-2494	569	2	ii	ii	NOUN
ejpam-2494	569	3	)	)	PUNCT
ejpam-2494	569	4	h	h	NOUN
ejpam-2494	569	5	is	be	AUX
ejpam-2494	569	6	semi	semi	ADJ
ejpam-2494	569	7	-	-	ADJ
ejpam-2494	569	8	ω	ω	ADJ
ejpam-2494	569	9	-	-	ADJ
ejpam-2494	569	10	open	open	ADJ
ejpam-2494	569	11	and	and	CCONJ
ejpam-2494	569	12	closed	closed	ADJ
ejpam-2494	569	13	.	.	PUNCT
ejpam-2494	570	1	(	(	PUNCT
ejpam-2494	570	2	iii	iii	X
ejpam-2494	570	3	)	)	PUNCT
ejpam-2494	570	4	h	h	NOUN
ejpam-2494	570	5	is	be	AUX
ejpam-2494	570	6	β	β	X
ejpam-2494	570	7	−ω	−ω	ADJ
ejpam-2494	570	8	-	-	ADJ
ejpam-2494	570	9	open	open	ADJ
ejpam-2494	570	10	and	and	CCONJ
ejpam-2494	570	11	closed	closed	ADJ
ejpam-2494	570	12	.	.	PUNCT
ejpam-2494	571	1	o.	o.	PROPN
ejpam-2494	571	2	ravi	ravi	PROPN
ejpam-2494	571	3	,	,	PUNCT
ejpam-2494	571	4	i.	i.	NOUN
ejpam-2494	571	5	rajasekaran	rajasekaran	PROPN
ejpam-2494	571	6	,	,	PUNCT
ejpam-2494	571	7	s.	s.	PROPN
ejpam-2494	571	8	kanna	kanna	PROPN
ejpam-2494	571	9	and	and	CCONJ
ejpam-2494	571	10	m.	m.	NOUN
ejpam-2494	571	11	paranjothi	paranjothi	PROPN
ejpam-2494	571	12	/	/	SYM
ejpam-2494	571	13	eur	eur	PROPN
ejpam-2494	571	14	.	.	PUNCT
ejpam-2494	572	1	j.	j.	PROPN
ejpam-2494	572	2	pure	pure	PROPN
ejpam-2494	572	3	appl	appl	PROPN
ejpam-2494	572	4	.	.	PROPN
ejpam-2494	572	5	math	math	PROPN
ejpam-2494	572	6	,	,	PUNCT
ejpam-2494	572	7	9	9	NUM
ejpam-2494	572	8	(	(	PUNCT
ejpam-2494	572	9	2016	2016	NUM
ejpam-2494	572	10	)	)	PUNCT
ejpam-2494	572	11	,	,	PUNCT
ejpam-2494	572	12	152	152	NUM
ejpam-2494	572	13	-	-	SYM
ejpam-2494	572	14	164	164	NUM
ejpam-2494	572	15	163	163	NUM
ejpam-2494	572	16	proof	proof	NOUN
ejpam-2494	572	17	.	.	PUNCT
ejpam-2494	573	1	(	(	PUNCT
ejpam-2494	573	2	i)⇒	i)⇒	PROPN
ejpam-2494	573	3	(	(	PUNCT
ejpam-2494	573	4	ii	ii	NOUN
ejpam-2494	573	5	):	):	PUNCT
ejpam-2494	573	6	if	if	SCONJ
ejpam-2494	573	7	h	h	NOUN
ejpam-2494	573	8	is	be	AUX
ejpam-2494	573	9	ω−r	ω−r	ADV
ejpam-2494	573	10	-	-	PUNCT
ejpam-2494	573	11	closed	closed	ADJ
ejpam-2494	573	12	,	,	PUNCT
ejpam-2494	573	13	then	then	ADV
ejpam-2494	573	14	h	h	NOUN
ejpam-2494	573	15	=	=	PUNCT
ejpam-2494	573	16	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	573	17	)	)	PUNCT
ejpam-2494	573	18	)	)	PUNCT
ejpam-2494	573	19	and	and	CCONJ
ejpam-2494	573	20	cl(h	cl(h	NUM
ejpam-2494	573	21	)	)	PUNCT
ejpam-2494	573	22	=	=	PUNCT
ejpam-2494	573	23	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	573	24	)	)	PUNCT
ejpam-2494	573	25	)	)	PUNCT
ejpam-2494	573	26	.	.	PUNCT
ejpam-2494	574	1	since	since	SCONJ
ejpam-2494	574	2	h	h	PROPN
ejpam-2494	574	3	⊂	⊂	PROPN
ejpam-2494	574	4	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	574	5	)	)	PUNCT
ejpam-2494	574	6	)	)	PUNCT
ejpam-2494	574	7	,	,	PUNCT
ejpam-2494	574	8	h	h	NOUN
ejpam-2494	574	9	is	be	AUX
ejpam-2494	574	10	semi	semi	ADJ
ejpam-2494	574	11	-	-	ADJ
ejpam-2494	574	12	ω	ω	ADJ
ejpam-2494	574	13	-	-	NOUN
ejpam-2494	574	14	open	open	ADJ
ejpam-2494	574	15	.	.	PUNCT
ejpam-2494	575	1	also	also	ADV
ejpam-2494	575	2	,	,	PUNCT
ejpam-2494	575	3	h	h	NOUN
ejpam-2494	575	4	=	=	PUNCT
ejpam-2494	575	5	cl(h	cl(h	X
ejpam-2494	575	6	)	)	PUNCT
ejpam-2494	575	7	and	and	CCONJ
ejpam-2494	575	8	so	so	ADV
ejpam-2494	575	9	h	h	NOUN
ejpam-2494	575	10	is	be	AUX
ejpam-2494	575	11	closed	closed	ADJ
ejpam-2494	575	12	.	.	PUNCT
ejpam-2494	576	1	(	(	PUNCT
ejpam-2494	576	2	ii)⇒	ii)⇒	X
ejpam-2494	576	3	(	(	PUNCT
ejpam-2494	576	4	iii	iii	NUM
ejpam-2494	576	5	):	):	PUNCT
ejpam-2494	576	6	it	it	PRON
ejpam-2494	576	7	follows	follow	VERB
ejpam-2494	576	8	from	from	ADP
ejpam-2494	576	9	the	the	DET
ejpam-2494	576	10	fact	fact	NOUN
ejpam-2494	576	11	that	that	SCONJ
ejpam-2494	576	12	every	every	DET
ejpam-2494	576	13	semi	semi	ADJ
ejpam-2494	576	14	-	-	ADJ
ejpam-2494	576	15	ω	ω	ADJ
ejpam-2494	576	16	-	-	ADJ
ejpam-2494	576	17	open	open	ADJ
ejpam-2494	576	18	set	set	NOUN
ejpam-2494	576	19	is	be	AUX
ejpam-2494	576	20	a	a	DET
ejpam-2494	576	21	β	β	X
ejpam-2494	576	22	−ω	−ω	NOUN
ejpam-2494	576	23	-	-	NOUN
ejpam-2494	576	24	open	open	ADJ
ejpam-2494	576	25	.	.	PUNCT
ejpam-2494	577	1	(	(	PUNCT
ejpam-2494	577	2	iii	iii	X
ejpam-2494	577	3	)	)	PUNCT
ejpam-2494	577	4	⇒	⇒	NOUN
ejpam-2494	577	5	(	(	PUNCT
ejpam-2494	577	6	i	i	NOUN
ejpam-2494	577	7	):	):	PUNCT
ejpam-2494	577	8	suppose	suppose	VERB
ejpam-2494	577	9	h	h	NOUN
ejpam-2494	577	10	is	be	AUX
ejpam-2494	577	11	β	β	X
ejpam-2494	577	12	−ω	−ω	ADJ
ejpam-2494	577	13	-	-	ADJ
ejpam-2494	577	14	open	open	ADJ
ejpam-2494	577	15	and	and	CCONJ
ejpam-2494	577	16	closed	closed	ADJ
ejpam-2494	577	17	.	.	PUNCT
ejpam-2494	578	1	then	then	ADV
ejpam-2494	578	2	h	h	PROPN
ejpam-2494	578	3	⊂	⊂	PROPN
ejpam-2494	578	4	cl(intω(cl(h	cl(intω(cl(h	PROPN
ejpam-2494	578	5	)	)	PUNCT
ejpam-2494	578	6	)	)	PUNCT
ejpam-2494	578	7	)	)	PUNCT
ejpam-2494	579	1	and	and	CCONJ
ejpam-2494	579	2	h	h	NOUN
ejpam-2494	579	3	=	=	NOUN
ejpam-2494	579	4	cl(h	cl(h	NUM
ejpam-2494	579	5	)	)	PUNCT
ejpam-2494	579	6	.	.	PUNCT
ejpam-2494	580	1	now	now	ADV
ejpam-2494	580	2	cl(intω(h	cl(intω(h	X
ejpam-2494	580	3	)	)	PUNCT
ejpam-2494	580	4	)	)	PUNCT
ejpam-2494	581	1	⊂	⊂	PROPN
ejpam-2494	581	2	cl(h	cl(h	X
ejpam-2494	581	3	)	)	PUNCT
ejpam-2494	582	1	=	=	SYM
ejpam-2494	582	2	h.	h.	PROPN
ejpam-2494	582	3	also	also	ADV
ejpam-2494	582	4	,	,	PUNCT
ejpam-2494	582	5	h	h	PROPN
ejpam-2494	582	6	⊂	⊂	PROPN
ejpam-2494	582	7	cl(intω(h	cl(intω(h	PROPN
ejpam-2494	582	8	)	)	PUNCT
ejpam-2494	582	9	)	)	PUNCT
ejpam-2494	582	10	.	.	PUNCT
ejpam-2494	583	1	therefore	therefore	ADV
ejpam-2494	583	2	h	h	NOUN
ejpam-2494	583	3	=	=	PUNCT
ejpam-2494	583	4	cl(intω(h	cl(intω(h	NOUN
ejpam-2494	583	5	)	)	PUNCT
ejpam-2494	583	6	)	)	PUNCT
ejpam-2494	583	7	which	which	PRON
ejpam-2494	583	8	implies	imply	VERB
ejpam-2494	583	9	that	that	SCONJ
ejpam-2494	583	10	h	h	NOUN
ejpam-2494	583	11	is	be	AUX
ejpam-2494	583	12	ω−r	ω−r	ADV
ejpam-2494	583	13	-	-	PUNCT
ejpam-2494	583	14	closed	closed	ADJ
ejpam-2494	583	15	.	.	PUNCT
ejpam-2494	584	1	remark	remark	PROPN
ejpam-2494	584	2	8	8	NUM
ejpam-2494	584	3	.	.	PUNCT
ejpam-2494	585	1	(	(	PUNCT
ejpam-2494	585	2	i	i	NOUN
ejpam-2494	585	3	)	)	PUNCT
ejpam-2494	585	4	the	the	DET
ejpam-2494	585	5	concepts	concept	NOUN
ejpam-2494	585	6	of	of	ADP
ejpam-2494	585	7	semi	semi	ADJ
ejpam-2494	585	8	-	-	ADJ
ejpam-2494	585	9	ω	ω	ADJ
ejpam-2494	585	10	-	-	PUNCT
ejpam-2494	585	11	openness	openness	NOUN
ejpam-2494	585	12	and	and	CCONJ
ejpam-2494	585	13	closedness	closedness	NOUN
ejpam-2494	585	14	are	be	AUX
ejpam-2494	585	15	independent	independent	ADJ
ejpam-2494	585	16	.	.	PUNCT
ejpam-2494	586	1	(	(	PUNCT
ejpam-2494	586	2	ii	ii	X
ejpam-2494	586	3	)	)	PUNCT
ejpam-2494	586	4	the	the	DET
ejpam-2494	586	5	concepts	concept	NOUN
ejpam-2494	586	6	of	of	ADP
ejpam-2494	586	7	β	β	PROPN
ejpam-2494	586	8	−ω	−ω	ADJ
ejpam-2494	586	9	-	-	NOUN
ejpam-2494	586	10	openness	openness	NOUN
ejpam-2494	586	11	and	and	CCONJ
ejpam-2494	586	12	closedness	closedness	NOUN
ejpam-2494	586	13	are	be	AUX
ejpam-2494	586	14	independent	independent	ADJ
ejpam-2494	586	15	.	.	PUNCT
ejpam-2494	586	16	example	example	NOUN
ejpam-2494	587	1	20	20	NUM
ejpam-2494	587	2	.	.	PUNCT
ejpam-2494	588	1	(	(	PUNCT
ejpam-2494	588	2	i	i	NOUN
ejpam-2494	588	3	)	)	PUNCT
ejpam-2494	588	4	let	let	VERB
ejpam-2494	588	5	x	x	PUNCT
ejpam-2494	588	6	=	=	PUNCT
ejpam-2494	588	7	r	r	NOUN
ejpam-2494	588	8	with	with	ADP
ejpam-2494	588	9	the	the	DET
ejpam-2494	588	10	usual	usual	ADJ
ejpam-2494	588	11	topology	topology	NOUN
ejpam-2494	588	12	τ	τ	PROPN
ejpam-2494	588	13	.	.	PUNCT
ejpam-2494	589	1	let	let	VERB
ejpam-2494	589	2	h	h	NOUN
ejpam-2494	589	3	=	=	PUNCT
ejpam-2494	589	4	(	(	PUNCT
ejpam-2494	589	5	0,1	0,1	NUM
ejpam-2494	589	6	]	]	PUNCT
ejpam-2494	589	7	.	.	PUNCT
ejpam-2494	590	1	then	then	ADV
ejpam-2494	590	2	h	h	PROPN
ejpam-2494	590	3	is	be	AUX
ejpam-2494	590	4	semi	semi	ADJ
ejpam-2494	590	5	-	-	ADJ
ejpam-2494	590	6	ω	ω	ADV
ejpam-2494	590	7	-	-	ADJ
ejpam-2494	590	8	open	open	ADJ
ejpam-2494	590	9	but	but	CCONJ
ejpam-2494	590	10	not	not	PART
ejpam-2494	590	11	closed	closed	ADJ
ejpam-2494	590	12	.	.	PUNCT
ejpam-2494	591	1	(	(	PUNCT
ejpam-2494	591	2	ii	ii	NOUN
ejpam-2494	591	3	)	)	PUNCT
ejpam-2494	591	4	let	let	VERB
ejpam-2494	591	5	x	x	PUNCT
ejpam-2494	591	6	=	=	PUNCT
ejpam-2494	591	7	r	r	NOUN
ejpam-2494	591	8	with	with	ADP
ejpam-2494	591	9	the	the	DET
ejpam-2494	591	10	topology	topology	NOUN
ejpam-2494	591	11	τ	τ	X
ejpam-2494	591	12	=	=	SYM
ejpam-2494	591	13	{	{	PUNCT
ejpam-2494	591	14	φ	φ	NOUN
ejpam-2494	591	15	,	,	PUNCT
ejpam-2494	591	16	r	r	NOUN
ejpam-2494	591	17	,	,	PUNCT
ejpam-2494	591	18	q⋆	q⋆	NOUN
ejpam-2494	591	19	}	}	PUNCT
ejpam-2494	591	20	.	.	PUNCT
ejpam-2494	592	1	let	let	VERB
ejpam-2494	592	2	h	h	NOUN
ejpam-2494	592	3	=	=	PUNCT
ejpam-2494	592	4	q.	q.	PROPN
ejpam-2494	593	1	then	then	ADV
ejpam-2494	593	2	h	h	PROPN
ejpam-2494	593	3	is	be	AUX
ejpam-2494	593	4	closed	closed	ADJ
ejpam-2494	593	5	but	but	CCONJ
ejpam-2494	593	6	not	not	PART
ejpam-2494	593	7	semi	semi	ADV
ejpam-2494	593	8	-	-	ADJ
ejpam-2494	593	9	ωopen	ωopen	ADJ
ejpam-2494	593	10	.	.	PUNCT
ejpam-2494	593	11	example	example	NOUN
ejpam-2494	594	1	21	21	NUM
ejpam-2494	594	2	.	.	PUNCT
ejpam-2494	595	1	(	(	PUNCT
ejpam-2494	595	2	i	i	NOUN
ejpam-2494	595	3	)	)	PUNCT
ejpam-2494	595	4	let	let	VERB
ejpam-2494	595	5	x	x	PUNCT
ejpam-2494	595	6	=	=	PUNCT
ejpam-2494	595	7	r	r	NOUN
ejpam-2494	595	8	with	with	ADP
ejpam-2494	595	9	the	the	DET
ejpam-2494	595	10	usual	usual	ADJ
ejpam-2494	595	11	topology	topology	NOUN
ejpam-2494	595	12	τu	τu	PROPN
ejpam-2494	595	13	.	.	PUNCT
ejpam-2494	596	1	let	let	VERB
ejpam-2494	596	2	h	h	NOUN
ejpam-2494	596	3	=	=	PUNCT
ejpam-2494	596	4	(	(	PUNCT
ejpam-2494	596	5	0,1	0,1	NUM
ejpam-2494	596	6	]	]	PUNCT
ejpam-2494	596	7	.	.	PUNCT
ejpam-2494	597	1	then	then	ADV
ejpam-2494	597	2	h	h	PROPN
ejpam-2494	597	3	is	be	AUX
ejpam-2494	597	4	β−ω	β−ω	NOUN
ejpam-2494	597	5	-	-	ADJ
ejpam-2494	597	6	open	open	ADJ
ejpam-2494	597	7	but	but	CCONJ
ejpam-2494	597	8	not	not	PART
ejpam-2494	597	9	closed	closed	ADJ
ejpam-2494	597	10	.	.	PUNCT
ejpam-2494	598	1	(	(	PUNCT
ejpam-2494	598	2	ii	ii	NOUN
ejpam-2494	598	3	)	)	PUNCT
ejpam-2494	598	4	let	let	VERB
ejpam-2494	598	5	x	x	PUNCT
ejpam-2494	598	6	=	=	PUNCT
ejpam-2494	598	7	r	r	NOUN
ejpam-2494	598	8	with	with	ADP
ejpam-2494	598	9	the	the	DET
ejpam-2494	598	10	topology	topology	NOUN
ejpam-2494	598	11	τu	τu	ADP
ejpam-2494	598	12	=	=	SYM
ejpam-2494	598	13	{	{	PUNCT
ejpam-2494	598	14	φ	φ	NOUN
ejpam-2494	598	15	,	,	PUNCT
ejpam-2494	598	16	r	r	NOUN
ejpam-2494	598	17	,	,	PUNCT
ejpam-2494	598	18	q⋆	q⋆	NOUN
ejpam-2494	598	19	}	}	PUNCT
ejpam-2494	598	20	.	.	PUNCT
ejpam-2494	599	1	let	let	VERB
ejpam-2494	599	2	h	h	NOUN
ejpam-2494	599	3	=	=	PUNCT
ejpam-2494	599	4	q.	q.	PROPN
ejpam-2494	600	1	then	then	ADV
ejpam-2494	600	2	h	h	PROPN
ejpam-2494	600	3	is	be	AUX
ejpam-2494	600	4	closed	closed	ADJ
ejpam-2494	600	5	but	but	CCONJ
ejpam-2494	600	6	not	not	PART
ejpam-2494	600	7	β	β	X
ejpam-2494	600	8	−ω	−ω	ADJ
ejpam-2494	600	9	-	-	ADJ
ejpam-2494	600	10	open	open	ADJ
ejpam-2494	600	11	.	.	PUNCT
ejpam-2494	601	1	7	7	X
ejpam-2494	601	2	.	.	X
ejpam-2494	601	3	further	further	ADJ
ejpam-2494	601	4	properties	property	NOUN
ejpam-2494	601	5	definition	definition	NOUN
ejpam-2494	601	6	16	16	NUM
ejpam-2494	601	7	.	.	PUNCT
ejpam-2494	602	1	a	a	DET
ejpam-2494	602	2	space	space	NOUN
ejpam-2494	602	3	(	(	PUNCT
ejpam-2494	602	4	x	x	X
ejpam-2494	602	5	,	,	PUNCT
ejpam-2494	602	6	τ	τ	X
ejpam-2494	602	7	)	)	PUNCT
ejpam-2494	602	8	is	be	AUX
ejpam-2494	602	9	called	call	VERB
ejpam-2494	602	10	ω	ω	NOUN
ejpam-2494	602	11	-	-	NOUN
ejpam-2494	602	12	submaximal	submaximal	ADJ
ejpam-2494	602	13	if	if	SCONJ
ejpam-2494	602	14	every	every	DET
ejpam-2494	602	15	ω	ω	ADJ
ejpam-2494	602	16	-	-	ADJ
ejpam-2494	602	17	dense	dense	ADJ
ejpam-2494	602	18	subset	subset	NOUN
ejpam-2494	602	19	of	of	ADP
ejpam-2494	602	20	x	x	PROPN
ejpam-2494	602	21	is	be	AUX
ejpam-2494	602	22	ω	ω	NOUN
ejpam-2494	602	23	-	-	ADJ
ejpam-2494	602	24	open	open	ADJ
ejpam-2494	602	25	.	.	PUNCT
ejpam-2494	603	1	proposition	proposition	NOUN
ejpam-2494	603	2	13	13	NUM
ejpam-2494	603	3	.	.	PUNCT
ejpam-2494	604	1	every	every	DET
ejpam-2494	604	2	submaximal	submaximal	ADJ
ejpam-2494	604	3	space	space	NOUN
ejpam-2494	604	4	is	be	AUX
ejpam-2494	604	5	ω	ω	NOUN
ejpam-2494	604	6	-	-	NOUN
ejpam-2494	604	7	submaximal	submaximal	ADJ
ejpam-2494	604	8	.	.	PUNCT
ejpam-2494	605	1	proof	proof	NOUN
ejpam-2494	605	2	.	.	PUNCT
ejpam-2494	606	1	let	let	VERB
ejpam-2494	606	2	h	h	PRON
ejpam-2494	606	3	⊂	⊂	PROPN
ejpam-2494	606	4	x	x	PUNCT
ejpam-2494	606	5	beω	beω	ADJ
ejpam-2494	606	6	-	-	ADJ
ejpam-2494	606	7	dense	dense	ADJ
ejpam-2494	606	8	.	.	PUNCT
ejpam-2494	607	1	then	then	ADV
ejpam-2494	607	2	x	x	X
ejpam-2494	607	3	=	=	SYM
ejpam-2494	607	4	clω(h	clω(h	PROPN
ejpam-2494	607	5	)	)	PUNCT
ejpam-2494	607	6	⊂	⊂	PROPN
ejpam-2494	607	7	cl(h	cl(h	CCONJ
ejpam-2494	607	8	)	)	PUNCT
ejpam-2494	608	1	and	and	CCONJ
ejpam-2494	608	2	x	x	X
ejpam-2494	608	3	=	=	PRON
ejpam-2494	608	4	cl(h	cl(h	NUM
ejpam-2494	608	5	)	)	PUNCT
ejpam-2494	608	6	.	.	PUNCT
ejpam-2494	609	1	thus	thus	ADV
ejpam-2494	609	2	h	h	NOUN
ejpam-2494	609	3	is	be	AUX
ejpam-2494	609	4	dense	dense	ADJ
ejpam-2494	609	5	in	in	ADP
ejpam-2494	609	6	x.	x.	NOUN
ejpam-2494	609	7	since	since	SCONJ
ejpam-2494	609	8	x	x	PRON
ejpam-2494	609	9	is	be	AUX
ejpam-2494	609	10	submaximal	submaximal	ADJ
ejpam-2494	609	11	,	,	PUNCT
ejpam-2494	609	12	h	h	NOUN
ejpam-2494	609	13	is	be	AUX
ejpam-2494	609	14	open	open	ADJ
ejpam-2494	609	15	and	and	CCONJ
ejpam-2494	609	16	henceω	henceω	VERB
ejpam-2494	609	17	-	-	PUNCT
ejpam-2494	609	18	open	open	ADJ
ejpam-2494	609	19	in	in	ADP
ejpam-2494	609	20	x.	x.	NOUN
ejpam-2494	609	21	therefore	therefore	ADV
ejpam-2494	609	22	,	,	PUNCT
ejpam-2494	609	23	x	x	PUNCT
ejpam-2494	609	24	isω	isω	ADV
ejpam-2494	609	25	-	-	PUNCT
ejpam-2494	609	26	submaximal	submaximal	ADJ
ejpam-2494	609	27	.	.	PUNCT
ejpam-2494	609	28	example	example	NOUN
ejpam-2494	610	1	22	22	NUM
ejpam-2494	610	2	.	.	PUNCT
ejpam-2494	611	1	let	let	VERB
ejpam-2494	611	2	x	x	PUNCT
ejpam-2494	611	3	=	=	PRON
ejpam-2494	611	4	{	{	PUNCT
ejpam-2494	611	5	a	a	PRON
ejpam-2494	611	6	,	,	PUNCT
ejpam-2494	611	7	b	b	NOUN
ejpam-2494	611	8	,	,	PUNCT
ejpam-2494	611	9	c	c	NOUN
ejpam-2494	611	10	}	}	PUNCT
ejpam-2494	611	11	with	with	ADP
ejpam-2494	611	12	the	the	DET
ejpam-2494	611	13	topology	topology	NOUN
ejpam-2494	611	14	τ	τ	X
ejpam-2494	611	15	=	=	SYM
ejpam-2494	611	16	{	{	PUNCT
ejpam-2494	611	17	φ	φ	PROPN
ejpam-2494	611	18	,	,	PUNCT
ejpam-2494	611	19	x	x	INTJ
ejpam-2494	611	20	,	,	PUNCT
ejpam-2494	611	21	{	{	PUNCT
ejpam-2494	611	22	c	c	NOUN
ejpam-2494	611	23	}	}	PUNCT
ejpam-2494	611	24	,	,	PUNCT
ejpam-2494	611	25	{	{	PUNCT
ejpam-2494	611	26	b	b	X
ejpam-2494	611	27	,	,	PUNCT
ejpam-2494	611	28	c	c	NOUN
ejpam-2494	611	29	}	}	PUNCT
ejpam-2494	611	30	}	}	PUNCT
ejpam-2494	611	31	.	.	PUNCT
ejpam-2494	612	1	set	set	VERB
ejpam-2494	612	2	h	h	NOUN
ejpam-2494	613	1	=	=	PUNCT
ejpam-2494	613	2	{	{	PUNCT
ejpam-2494	613	3	a	a	X
ejpam-2494	613	4	,	,	PUNCT
ejpam-2494	613	5	c	c	NOUN
ejpam-2494	613	6	}	}	PUNCT
ejpam-2494	613	7	.	.	PUNCT
ejpam-2494	614	1	then	then	ADV
ejpam-2494	614	2	cl(h	cl(h	VERB
ejpam-2494	614	3	)	)	PUNCT
ejpam-2494	614	4	=	=	PUNCT
ejpam-2494	615	1	x	x	PUNCT
ejpam-2494	615	2	and	and	CCONJ
ejpam-2494	615	3	h	h	NOUN
ejpam-2494	615	4	/∈	/∈	PUNCT
ejpam-2494	616	1	τ	τ	PROPN
ejpam-2494	616	2	.	.	PUNCT
ejpam-2494	617	1	hence	hence	ADV
ejpam-2494	617	2	x	x	VERB
ejpam-2494	617	3	is	be	AUX
ejpam-2494	617	4	not	not	PART
ejpam-2494	617	5	submaximal	submaximal	ADJ
ejpam-2494	617	6	but	but	CCONJ
ejpam-2494	617	7	it	it	PRON
ejpam-2494	617	8	isω	isω	ADV
ejpam-2494	617	9	-	-	PUNCT
ejpam-2494	617	10	submaximal	submaximal	ADJ
ejpam-2494	617	11	,	,	PUNCT
ejpam-2494	617	12	since	since	SCONJ
ejpam-2494	617	13	the	the	DET
ejpam-2494	617	14	onlyω	onlyω	NOUN
ejpam-2494	617	15	-	-	PUNCT
ejpam-2494	617	16	dense	dense	ADJ
ejpam-2494	617	17	set	set	NOUN
ejpam-2494	617	18	is	be	AUX
ejpam-2494	617	19	x.	x.	NOUN
ejpam-2494	617	20	definition	definition	NOUN
ejpam-2494	617	21	17	17	NUM
ejpam-2494	617	22	.	.	PUNCT
ejpam-2494	618	1	a	a	DET
ejpam-2494	618	2	subset	subset	ADJ
ejpam-2494	618	3	h	h	NOUN
ejpam-2494	618	4	of	of	ADP
ejpam-2494	618	5	a	a	DET
ejpam-2494	618	6	space	space	NOUN
ejpam-2494	618	7	(	(	PUNCT
ejpam-2494	618	8	x	x	X
ejpam-2494	618	9	,	,	PUNCT
ejpam-2494	618	10	τ	τ	X
ejpam-2494	618	11	)	)	PUNCT
ejpam-2494	618	12	is	be	AUX
ejpam-2494	618	13	called	call	VERB
ejpam-2494	618	14	ω	ω	NOUN
ejpam-2494	618	15	-	-	NOUN
ejpam-2494	618	16	codense	codense	NOUN
ejpam-2494	618	17	if	if	SCONJ
ejpam-2494	618	18	x\h	x\h	PROPN
ejpam-2494	618	19	is	be	AUX
ejpam-2494	618	20	ω	ω	NOUN
ejpam-2494	618	21	-	-	PUNCT
ejpam-2494	618	22	dense	dense	ADJ
ejpam-2494	618	23	.	.	PUNCT
ejpam-2494	619	1	theorem	theorem	VERB
ejpam-2494	619	2	16	16	NUM
ejpam-2494	619	3	.	.	PUNCT
ejpam-2494	620	1	for	for	ADP
ejpam-2494	620	2	a	a	DET
ejpam-2494	620	3	space	space	NOUN
ejpam-2494	620	4	(	(	PUNCT
ejpam-2494	620	5	x	x	X
ejpam-2494	620	6	,	,	PUNCT
ejpam-2494	620	7	τ	τ	PROPN
ejpam-2494	620	8	)	)	PUNCT
ejpam-2494	620	9	,	,	PUNCT
ejpam-2494	620	10	the	the	DET
ejpam-2494	620	11	following	follow	VERB
ejpam-2494	620	12	are	be	AUX
ejpam-2494	620	13	equivalent	equivalent	ADJ
ejpam-2494	620	14	.	.	PUNCT
ejpam-2494	621	1	(	(	PUNCT
ejpam-2494	621	2	i	i	NOUN
ejpam-2494	621	3	)	)	PUNCT
ejpam-2494	621	4	x	x	X
ejpam-2494	621	5	is	be	AUX
ejpam-2494	621	6	ω	ω	NOUN
ejpam-2494	621	7	-	-	NOUN
ejpam-2494	621	8	submaximal	submaximal	ADJ
ejpam-2494	621	9	,	,	PUNCT
ejpam-2494	621	10	(	(	PUNCT
ejpam-2494	621	11	ii	ii	NOUN
ejpam-2494	621	12	)	)	PUNCT
ejpam-2494	621	13	every	every	DET
ejpam-2494	621	14	ω	ω	VERB
ejpam-2494	621	15	-	-	PUNCT
ejpam-2494	621	16	codense	codense	NOUN
ejpam-2494	621	17	subset	subset	NOUN
ejpam-2494	621	18	h	h	NOUN
ejpam-2494	621	19	of	of	ADP
ejpam-2494	621	20	x	x	PROPN
ejpam-2494	621	21	is	be	AUX
ejpam-2494	621	22	ω	ω	NOUN
ejpam-2494	621	23	-	-	PUNCT
ejpam-2494	621	24	closed	closed	ADJ
ejpam-2494	621	25	.	.	PUNCT
ejpam-2494	622	1	proof	proof	NOUN
ejpam-2494	622	2	.	.	PUNCT
ejpam-2494	623	1	(	(	PUNCT
ejpam-2494	623	2	i)⇒	i)⇒	PROPN
ejpam-2494	623	3	(	(	PUNCT
ejpam-2494	623	4	ii	ii	NOUN
ejpam-2494	623	5	):	):	PUNCT
ejpam-2494	623	6	let	let	VERB
ejpam-2494	623	7	h	h	PRON
ejpam-2494	623	8	be	be	AUX
ejpam-2494	623	9	a	a	DET
ejpam-2494	623	10	ω	ω	ADJ
ejpam-2494	623	11	-	-	PUNCT
ejpam-2494	623	12	codense	codense	NOUN
ejpam-2494	623	13	subset	subset	NOUN
ejpam-2494	623	14	of	of	ADP
ejpam-2494	623	15	x.	x.	NOUN
ejpam-2494	623	16	then	then	ADV
ejpam-2494	623	17	x\h	x\h	PROPN
ejpam-2494	623	18	is	be	AUX
ejpam-2494	623	19	ω	ω	NOUN
ejpam-2494	623	20	-	-	PUNCT
ejpam-2494	623	21	dense	dense	ADJ
ejpam-2494	623	22	and	and	CCONJ
ejpam-2494	623	23	therefore	therefore	ADV
ejpam-2494	623	24	x\h	x\h	PROPN
ejpam-2494	623	25	is	be	AUX
ejpam-2494	623	26	ω	ω	NOUN
ejpam-2494	623	27	-	-	NOUN
ejpam-2494	623	28	open	open	ADJ
ejpam-2494	623	29	,	,	PUNCT
ejpam-2494	623	30	x	x	PUNCT
ejpam-2494	623	31	being	be	AUX
ejpam-2494	623	32	ω	ω	NOUN
ejpam-2494	623	33	-	-	PUNCT
ejpam-2494	623	34	submaximal	submaximal	ADJ
ejpam-2494	623	35	by	by	ADP
ejpam-2494	623	36	assumption	assumption	NOUN
ejpam-2494	623	37	.	.	PUNCT
ejpam-2494	624	1	thus	thus	ADV
ejpam-2494	624	2	h	h	PROPN
ejpam-2494	624	3	is	be	AUX
ejpam-2494	624	4	ω	ω	NOUN
ejpam-2494	624	5	-	-	ADJ
ejpam-2494	624	6	closed	closed	ADJ
ejpam-2494	624	7	.	.	PUNCT
ejpam-2494	625	1	(	(	PUNCT
ejpam-2494	625	2	ii)⇒	ii)⇒	PROPN
ejpam-2494	625	3	(	(	PUNCT
ejpam-2494	625	4	i	i	NOUN
ejpam-2494	625	5	):	):	PUNCT
ejpam-2494	625	6	let	let	VERB
ejpam-2494	625	7	h	h	PRON
ejpam-2494	625	8	be	be	AUX
ejpam-2494	625	9	aω	aω	NOUN
ejpam-2494	625	10	-	-	PUNCT
ejpam-2494	625	11	dense	dense	ADJ
ejpam-2494	625	12	subset	subset	NOUN
ejpam-2494	625	13	of	of	ADP
ejpam-2494	625	14	x.	x.	NOUN
ejpam-2494	625	15	then	then	ADV
ejpam-2494	625	16	x\h	x\h	PROPN
ejpam-2494	625	17	isω	isω	VERB
ejpam-2494	625	18	-	-	PUNCT
ejpam-2494	625	19	codense	codense	NOUN
ejpam-2494	625	20	in	in	ADP
ejpam-2494	625	21	x	x	PUNCT
ejpam-2494	625	22	and	and	CCONJ
ejpam-2494	625	23	by	by	ADP
ejpam-2494	625	24	assumption	assumption	NOUN
ejpam-2494	625	25	x\h	x\h	PROPN
ejpam-2494	625	26	is	be	AUX
ejpam-2494	625	27	ω	ω	ADV
ejpam-2494	625	28	-	-	PUNCT
ejpam-2494	625	29	closed	closed	ADJ
ejpam-2494	625	30	.	.	PUNCT
ejpam-2494	626	1	hence	hence	ADV
ejpam-2494	626	2	h	h	PROPN
ejpam-2494	626	3	is	be	AUX
ejpam-2494	626	4	ω	ω	NOUN
ejpam-2494	626	5	-	-	ADJ
ejpam-2494	626	6	open	open	ADJ
ejpam-2494	626	7	and	and	CCONJ
ejpam-2494	626	8	thus	thus	ADV
ejpam-2494	626	9	x	x	PRON
ejpam-2494	626	10	is	be	AUX
ejpam-2494	626	11	ω	ω	NOUN
ejpam-2494	626	12	-	-	NOUN
ejpam-2494	626	13	submaximal	submaximal	ADJ
ejpam-2494	626	14	.	.	PUNCT
ejpam-2494	627	1	references	reference	NOUN
ejpam-2494	627	2	164	164	NUM
ejpam-2494	627	3	acknowledgements	acknowledgement	NOUN
ejpam-2494	627	4	the	the	DET
ejpam-2494	627	5	authors	author	NOUN
ejpam-2494	627	6	thank	thank	VERB
ejpam-2494	627	7	the	the	DET
ejpam-2494	627	8	referee(s	referee(s	NOUN
ejpam-2494	627	9	)	)	PUNCT
ejpam-2494	627	10	for	for	ADP
ejpam-2494	627	11	his	his	PRON
ejpam-2494	627	12	/	/	SYM
ejpam-2494	627	13	her	her	PRON
ejpam-2494	627	14	/	/	PUNCT
ejpam-2494	627	15	their	their	PRON
ejpam-2494	627	16	suggestions	suggestion	NOUN
ejpam-2494	627	17	.	.	PUNCT
ejpam-2494	628	1	references	reference	NOUN
ejpam-2494	628	2	[	[	X
ejpam-2494	628	3	1	1	X
ejpam-2494	628	4	]	]	PUNCT
ejpam-2494	628	5	s.	s.	PROPN
ejpam-2494	628	6	al	al	PROPN
ejpam-2494	628	7	-	-	PROPN
ejpam-2494	628	8	ghour	ghour	PROPN
ejpam-2494	628	9	.	.	PUNCT
ejpam-2494	629	1	certain	certain	ADJ
ejpam-2494	629	2	covering	covering	NOUN
ejpam-2494	629	3	properties	property	NOUN
ejpam-2494	629	4	related	relate	VERB
ejpam-2494	629	5	to	to	ADP
ejpam-2494	629	6	paracompactness	paracompactness	NOUN
ejpam-2494	629	7	,	,	PUNCT
ejpam-2494	629	8	ph.d	ph.d	PROPN
ejpam-2494	629	9	thesis	thesis	NOUN
ejpam-2494	629	10	,	,	PUNCT
ejpam-2494	629	11	university	university	PROPN
ejpam-2494	629	12	of	of	ADP
ejpam-2494	629	13	jordan	jordan	PROPN
ejpam-2494	629	14	,	,	PUNCT
ejpam-2494	629	15	amman	amman	PROPN
ejpam-2494	629	16	,	,	PUNCT
ejpam-2494	629	17	1999	1999	NUM
ejpam-2494	629	18	.	.	PUNCT
ejpam-2494	630	1	[	[	X
ejpam-2494	630	2	2	2	NUM
ejpam-2494	630	3	]	]	PUNCT
ejpam-2494	630	4	a.	a.	PROPN
ejpam-2494	630	5	al	al	PROPN
ejpam-2494	630	6	-	-	PUNCT
ejpam-2494	630	7	omari	omari	PROPN
ejpam-2494	630	8	and	and	CCONJ
ejpam-2494	630	9	m.	m.	PROPN
ejpam-2494	630	10	s.	s.	PROPN
ejpam-2494	630	11	m.	m.	PROPN
ejpam-2494	630	12	noorani	noorani	PROPN
ejpam-2494	630	13	.	.	PUNCT
ejpam-2494	631	1	regular	regular	ADJ
ejpam-2494	631	2	generalized	generalize	VERB
ejpam-2494	631	3	ω	ω	VERB
ejpam-2494	631	4	-	-	PUNCT
ejpam-2494	631	5	closed	closed	ADJ
ejpam-2494	631	6	sets	set	NOUN
ejpam-2494	631	7	,	,	PUNCT
ejpam-2494	631	8	international	international	ADJ
ejpam-2494	631	9	journal	journal	NOUN
ejpam-2494	631	10	of	of	ADP
ejpam-2494	631	11	mathematics	mathematics	PROPN
ejpam-2494	631	12	and	and	CCONJ
ejpam-2494	631	13	mathematical	mathematical	ADJ
ejpam-2494	631	14	sciences	science	NOUN
ejpam-2494	631	15	,	,	PUNCT
ejpam-2494	631	16	article	article	NOUN
ejpam-2494	631	17	i	i	PROPN
ejpam-2494	631	18	d	d	PROPN
ejpam-2494	631	19	16292	16292	NUM
ejpam-2494	631	20	,	,	PUNCT
ejpam-2494	631	21	11	11	NUM
ejpam-2494	631	22	pages	page	NOUN
ejpam-2494	631	23	.	.	PUNCT
ejpam-2494	631	24	2007	2007	NUM
ejpam-2494	631	25	.	.	PUNCT
ejpam-2494	632	1	doi:10.1155/2007/1629	doi:10.1155/2007/1629	NOUN
ejpam-2494	633	1	[	[	X
ejpam-2494	633	2	3	3	NUM
ejpam-2494	633	3	]	]	PUNCT
ejpam-2494	633	4	a.	a.	PROPN
ejpam-2494	633	5	al	al	PROPN
ejpam-2494	633	6	-	-	PUNCT
ejpam-2494	633	7	omari	omari	PROPN
ejpam-2494	633	8	and	and	CCONJ
ejpam-2494	633	9	m.s.m	m.s.m	PROPN
ejpam-2494	633	10	.	.	PUNCT
ejpam-2494	633	11	noorani	noorani	PROPN
ejpam-2494	633	12	.	.	PUNCT
ejpam-2494	634	1	contraωcontinuous	contraωcontinuous	ADJ
ejpam-2494	634	2	and	and	CCONJ
ejpam-2494	634	3	almost	almost	ADV
ejpam-2494	634	4	contraωcontinuous	contraωcontinuous	ADJ
ejpam-2494	634	5	,	,	PUNCT
ejpam-2494	634	6	international	international	ADJ
ejpam-2494	634	7	journal	journal	NOUN
ejpam-2494	634	8	of	of	ADP
ejpam-2494	634	9	mathematics	mathematics	PROPN
ejpam-2494	634	10	and	and	CCONJ
ejpam-2494	634	11	mathematical	mathematical	ADJ
ejpam-2494	634	12	sciences	science	NOUN
ejpam-2494	634	13	,	,	PUNCT
ejpam-2494	634	14	article	article	NOUN
ejpam-2494	634	15	i	i	PROPN
ejpam-2494	634	16	d	d	PROPN
ejpam-2494	634	17	40469	40469	NUM
ejpam-2494	634	18	,	,	PUNCT
ejpam-2494	634	19	13	13	NUM
ejpam-2494	634	20	pages	page	NOUN
ejpam-2494	634	21	.	.	PUNCT
ejpam-2494	635	1	2007	2007	NUM
ejpam-2494	635	2	.	.	PUNCT
ejpam-2494	636	1	doi:10.1155/2007/40469	doi:10.1155/2007/40469	X
ejpam-2494	637	1	[	[	X
ejpam-2494	637	2	4	4	NUM
ejpam-2494	637	3	]	]	PUNCT
ejpam-2494	637	4	k.	k.	PROPN
ejpam-2494	637	5	al	al	PROPN
ejpam-2494	637	6	-	-	PROPN
ejpam-2494	637	7	zoubi	zoubi	PROPN
ejpam-2494	637	8	and	and	CCONJ
ejpam-2494	637	9	b.	b.	PROPN
ejpam-2494	637	10	al	al	PROPN
ejpam-2494	637	11	-	-	PUNCT
ejpam-2494	637	12	nashef	nashef	PROPN
ejpam-2494	637	13	.	.	PUNCT
ejpam-2494	638	1	the	the	DET
ejpam-2494	638	2	topology	topology	NOUN
ejpam-2494	638	3	of	of	ADP
ejpam-2494	638	4	ω	ω	VERB
ejpam-2494	638	5	-	-	ADJ
ejpam-2494	638	6	open	open	ADJ
ejpam-2494	638	7	sets	set	NOUN
ejpam-2494	638	8	,	,	PUNCT
ejpam-2494	638	9	al	al	PROPN
ejpam-2494	638	10	-	-	PUNCT
ejpam-2494	638	11	manarch	manarch	PROPN
ejpam-2494	638	12	,	,	PUNCT
ejpam-2494	638	13	9(2	9(2	NUM
ejpam-2494	638	14	)	)	PUNCT
ejpam-2494	638	15	,	,	PUNCT
ejpam-2494	638	16	169	169	NUM
ejpam-2494	638	17	179	179	NUM
ejpam-2494	638	18	.	.	PUNCT
ejpam-2494	638	19	2003	2003	NUM
ejpam-2494	638	20	.	.	PUNCT
ejpam-2494	639	1	[	[	X
ejpam-2494	639	2	5	5	X
ejpam-2494	639	3	]	]	PUNCT
ejpam-2494	639	4	j.	j.	PROPN
ejpam-2494	639	5	dontchev	dontchev	PROPN
ejpam-2494	639	6	.	.	PUNCT
ejpam-2494	640	1	on	on	ADP
ejpam-2494	640	2	submaximal	submaximal	ADJ
ejpam-2494	640	3	spaces	space	NOUN
ejpam-2494	640	4	,	,	PUNCT
ejpam-2494	640	5	tamkang	tamkang	PROPN
ejpam-2494	640	6	journal	journal	PROPN
ejpam-2494	640	7	of	of	ADP
ejpam-2494	640	8	mathematics	mathematic	NOUN
ejpam-2494	640	9	,	,	PUNCT
ejpam-2494	640	10	26	26	NUM
ejpam-2494	640	11	,	,	PUNCT
ejpam-2494	640	12	253	253	NUM
ejpam-2494	640	13	260	260	NUM
ejpam-2494	640	14	.	.	PUNCT
ejpam-2494	640	15	1995	1995	NUM
ejpam-2494	640	16	.	.	PUNCT
ejpam-2494	641	1	[	[	X
ejpam-2494	641	2	6	6	NUM
ejpam-2494	641	3	]	]	PUNCT
ejpam-2494	641	4	r.	r.	PROPN
ejpam-2494	641	5	engelking	engelke	VERB
ejpam-2494	641	6	.	.	PUNCT
ejpam-2494	642	1	general	general	ADJ
ejpam-2494	642	2	topology	topology	NOUN
ejpam-2494	642	3	,	,	PUNCT
ejpam-2494	642	4	heldermann	heldermann	PROPN
ejpam-2494	642	5	veriag	veriag	PROPN
ejpam-2494	642	6	berlin	berlin	PROPN
ejpam-2494	642	7	,	,	PUNCT
ejpam-2494	642	8	2nd	2nd	PROPN
ejpam-2494	642	9	edition	edition	NOUN
ejpam-2494	642	10	,	,	PUNCT
ejpam-2494	642	11	1989	1989	NUM
ejpam-2494	642	12	.	.	PUNCT
ejpam-2494	643	1	[	[	X
ejpam-2494	643	2	7	7	X
ejpam-2494	643	3	]	]	PUNCT
ejpam-2494	643	4	h.	h.	PROPN
ejpam-2494	643	5	z.	z.	PROPN
ejpam-2494	643	6	hdeib	hdeib	PROPN
ejpam-2494	643	7	.	.	PUNCT
ejpam-2494	644	1	ω	ω	VERB
ejpam-2494	644	2	-	-	PUNCT
ejpam-2494	644	3	closed	close	VERB
ejpam-2494	644	4	mappings	mapping	NOUN
ejpam-2494	644	5	,	,	PUNCT
ejpam-2494	644	6	revista	revista	PROPN
ejpam-2494	644	7	colombiana	colombiana	PROPN
ejpam-2494	644	8	de	de	PROPN
ejpam-2494	644	9	mathematics	mathematics	PROPN
ejpam-2494	644	10	,	,	PUNCT
ejpam-2494	644	11	16	16	NUM
ejpam-2494	644	12	,	,	PUNCT
ejpam-2494	644	13	65	65	NUM
ejpam-2494	644	14	78	78	NUM
ejpam-2494	644	15	.	.	PUNCT
ejpam-2494	644	16	1982	1982	NUM
ejpam-2494	644	17	.	.	PUNCT
ejpam-2494	645	1	[	[	X
ejpam-2494	645	2	8	8	X
ejpam-2494	645	3	]	]	X
ejpam-2494	645	4	khalid	khalid	PROPN
ejpam-2494	645	5	y.	y.	PROPN
ejpam-2494	645	6	al	al	PROPN
ejpam-2494	645	7	-	-	PROPN
ejpam-2494	645	8	zoubi	zoubi	PROPN
ejpam-2494	645	9	.	.	PUNCT
ejpam-2494	646	1	on	on	ADP
ejpam-2494	646	2	generalized	generalized	ADJ
ejpam-2494	646	3	ω	ω	VERB
ejpam-2494	646	4	-	-	PUNCT
ejpam-2494	646	5	closed	closed	ADJ
ejpam-2494	646	6	sets	set	NOUN
ejpam-2494	646	7	,	,	PUNCT
ejpam-2494	646	8	international	international	ADJ
ejpam-2494	646	9	journal	journal	NOUN
ejpam-2494	646	10	of	of	ADP
ejpam-2494	646	11	mathematics	mathematics	PROPN
ejpam-2494	646	12	and	and	CCONJ
ejpam-2494	646	13	mathematical	mathematical	ADJ
ejpam-2494	646	14	sciences	science	NOUN
ejpam-2494	646	15	,	,	PUNCT
ejpam-2494	646	16	13	13	NUM
ejpam-2494	646	17	,	,	PUNCT
ejpam-2494	646	18	2011	2011	NUM
ejpam-2494	646	19	2021	2021	NUM
ejpam-2494	646	20	.	.	PUNCT
ejpam-2494	647	1	2005	2005	NUM
ejpam-2494	647	2	.	.	PUNCT
ejpam-2494	648	1	[	[	X
ejpam-2494	648	2	9	9	NUM
ejpam-2494	648	3	]	]	X
ejpam-2494	648	4	n.	n.	PROPN
ejpam-2494	648	5	levine	levine	PROPN
ejpam-2494	648	6	.	.	PUNCT
ejpam-2494	649	1	semi	semi	ADJ
ejpam-2494	649	2	-	-	ADJ
ejpam-2494	649	3	open	open	ADJ
ejpam-2494	649	4	sets	set	NOUN
ejpam-2494	649	5	and	and	CCONJ
ejpam-2494	649	6	semi	semi	ADJ
ejpam-2494	649	7	-	-	NOUN
ejpam-2494	649	8	continuity	continuity	NOUN
ejpam-2494	649	9	in	in	ADP
ejpam-2494	649	10	topological	topological	ADJ
ejpam-2494	649	11	spaces	space	NOUN
ejpam-2494	649	12	,	,	PUNCT
ejpam-2494	649	13	american	american	PROPN
ejpam-2494	649	14	mathematical	mathematical	PROPN
ejpam-2494	649	15	monthly	monthly	ADV
ejpam-2494	649	16	,	,	PUNCT
ejpam-2494	649	17	70	70	NUM
ejpam-2494	649	18	,	,	PUNCT
ejpam-2494	649	19	36	36	NUM
ejpam-2494	649	20	41	41	NUM
ejpam-2494	649	21	.	.	PUNCT
ejpam-2494	649	22	1963	1963	NUM
ejpam-2494	649	23	.	.	PUNCT
ejpam-2494	650	1	[	[	X
ejpam-2494	650	2	10	10	NUM
ejpam-2494	650	3	]	]	PUNCT
ejpam-2494	650	4	t.	t.	PROPN
ejpam-2494	650	5	noiri	noiri	PROPN
ejpam-2494	650	6	,	,	PUNCT
ejpam-2494	650	7	a.	a.	PROPN
ejpam-2494	650	8	al	al	PROPN
ejpam-2494	650	9	-	-	PUNCT
ejpam-2494	650	10	omari	omari	PROPN
ejpam-2494	650	11	,	,	PUNCT
ejpam-2494	650	12	and	and	CCONJ
ejpam-2494	650	13	m.	m.	PROPN
ejpam-2494	650	14	s.	s.	PROPN
ejpam-2494	650	15	m.	m.	PROPN
ejpam-2494	650	16	noorani	noorani	PROPN
ejpam-2494	650	17	.	.	PUNCT
ejpam-2494	651	1	weak	weak	ADJ
ejpam-2494	651	2	forms	form	NOUN
ejpam-2494	651	3	ofω	ofω	VERB
ejpam-2494	651	4	-	-	PUNCT
ejpam-2494	651	5	open	open	ADJ
ejpam-2494	651	6	sets	set	NOUN
ejpam-2494	651	7	and	and	CCONJ
ejpam-2494	651	8	decompositions	decomposition	NOUN
ejpam-2494	651	9	of	of	ADP
ejpam-2494	651	10	continuity	continuity	NOUN
ejpam-2494	651	11	,	,	PUNCT
ejpam-2494	651	12	european	european	ADJ
ejpam-2494	651	13	journal	journal	NOUN
ejpam-2494	651	14	of	of	ADP
ejpam-2494	651	15	pure	pure	ADJ
ejpam-2494	651	16	and	and	CCONJ
ejpam-2494	651	17	applied	applied	ADJ
ejpam-2494	651	18	mathematics	mathematic	NOUN
ejpam-2494	651	19	,	,	PUNCT
ejpam-2494	651	20	2	2	NUM
ejpam-2494	651	21	,	,	PUNCT
ejpam-2494	651	22	73	73	NUM
ejpam-2494	651	23	84	84	NUM
ejpam-2494	651	24	.	.	PUNCT
ejpam-2494	651	25	2009	2009	NUM
ejpam-2494	651	26	.	.	PUNCT
ejpam-2494	652	1	[	[	X
ejpam-2494	652	2	11	11	NUM
ejpam-2494	652	3	]	]	PUNCT
ejpam-2494	652	4	s.	s.	PROPN
ejpam-2494	652	5	willard	willard	PROPN
ejpam-2494	652	6	.	.	PUNCT
ejpam-2494	652	7	general	general	ADJ
ejpam-2494	652	8	topology	topology	PROPN
ejpam-2494	652	9	,	,	PUNCT
ejpam-2494	652	10	addison	addison	PROPN
ejpam-2494	652	11	-	-	PUNCT
ejpam-2494	652	12	wesley	wesley	PROPN
ejpam-2494	652	13	,	,	PUNCT
ejpam-2494	652	14	reading	reading	NOUN
ejpam-2494	652	15	,	,	PUNCT
ejpam-2494	652	16	mass	mass	PROPN
ejpam-2494	652	17	,	,	PUNCT
ejpam-2494	652	18	usa	usa	PROPN
ejpam-2494	652	19	,	,	PUNCT
ejpam-2494	652	20	1970	1970	NUM
ejpam-2494	652	21	.	.	PUNCT