id	sid	tid	token	lemma	pos
ejpam-300	1	1	3_300_hussain.dvi	3_300_hussain.dvi	NUM
ejpam-300	1	2	european	european	ADJ
ejpam-300	1	3	journal	journal	NOUN
ejpam-300	1	4	of	of	ADP
ejpam-300	1	5	pure	pure	ADJ
ejpam-300	1	6	and	and	CCONJ
ejpam-300	1	7	applied	apply	VERB
ejpam-300	1	8	mathematics	mathematic	NOUN
ejpam-300	1	9	vol	vol	NOUN
ejpam-300	1	10	.	.	PROPN
ejpam-300	2	1	2	2	NUM
ejpam-300	2	2	,	,	PUNCT
ejpam-300	2	3	no	no	INTJ
ejpam-300	2	4	.	.	NOUN
ejpam-300	2	5	3	3	NUM
ejpam-300	2	6	,	,	PUNCT
ejpam-300	2	7	2009	2009	NUM
ejpam-300	2	8	,	,	PUNCT
ejpam-300	2	9	(	(	PUNCT
ejpam-300	2	10	338	338	NUM
ejpam-300	2	11	-	-	SYM
ejpam-300	2	12	351	351	NUM
ejpam-300	2	13	)	)	PUNCT
ejpam-300	2	14	issn	issn	PROPN
ejpam-300	2	15	1307	1307	NUM
ejpam-300	2	16	-	-	SYM
ejpam-300	2	17	5543	5543	NUM
ejpam-300	2	18	–	–	PUNCT
ejpam-300	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-300	2	20	on	on	ADP
ejpam-300	2	21	minimal	minimal	ADJ
ejpam-300	2	22	γ	γ	X
ejpam-300	2	23	-	-	ADJ
ejpam-300	2	24	open	open	ADJ
ejpam-300	2	25	sets	set	NOUN
ejpam-300	2	26	sabir	sabir	PROPN
ejpam-300	2	27	hussain1∗	hussain1∗	PROPN
ejpam-300	2	28	and	and	CCONJ
ejpam-300	2	29	bashir	bashir	PROPN
ejpam-300	2	30	ahmad2	ahmad2	PROPN
ejpam-300	2	31	1	1	NUM
ejpam-300	2	32	department	department	NOUN
ejpam-300	2	33	of	of	ADP
ejpam-300	2	34	mathematics	mathematics	PROPN
ejpam-300	2	35	,	,	PUNCT
ejpam-300	2	36	islamia	islamia	PROPN
ejpam-300	2	37	university	university	PROPN
ejpam-300	2	38	,	,	PUNCT
ejpam-300	2	39	bahawalpur	bahawalpur	PROPN
ejpam-300	2	40	,	,	PUNCT
ejpam-300	2	41	pakistan	pakistan	PROPN
ejpam-300	2	42	.	.	PUNCT
ejpam-300	3	1	present	present	ADJ
ejpam-300	3	2	address	address	NOUN
ejpam-300	3	3	:	:	PUNCT
ejpam-300	3	4	department	department	NOUN
ejpam-300	3	5	of	of	ADP
ejpam-300	3	6	mathematics	mathematics	PROPN
ejpam-300	3	7	,	,	PUNCT
ejpam-300	3	8	yanbu	yanbu	ADJ
ejpam-300	3	9	university	university	NOUN
ejpam-300	3	10	,	,	PUNCT
ejpam-300	3	11	p.	p.	PROPN
ejpam-300	3	12	o.	o.	PROPN
ejpam-300	3	13	box	box	PROPN
ejpam-300	3	14	31387	31387	NUM
ejpam-300	3	15	,	,	PUNCT
ejpam-300	3	16	yanbu	yanbu	ADJ
ejpam-300	3	17	alsinaiyah	alsinaiyah	NOUN
ejpam-300	3	18	,	,	PUNCT
ejpam-300	3	19	saudi	saudi	PROPN
ejpam-300	3	20	arabia	arabia	PROPN
ejpam-300	3	21	.	.	PUNCT
ejpam-300	4	1	2	2	NUM
ejpam-300	4	2	centre	centre	NOUN
ejpam-300	4	3	for	for	ADP
ejpam-300	4	4	advanced	advanced	ADJ
ejpam-300	4	5	studies	study	NOUN
ejpam-300	4	6	in	in	ADP
ejpam-300	4	7	pure	pure	ADJ
ejpam-300	4	8	and	and	CCONJ
ejpam-300	4	9	applied	applied	ADJ
ejpam-300	4	10	mathematics	mathematic	NOUN
ejpam-300	4	11	,	,	PUNCT
ejpam-300	4	12	bahauddin	bahauddin	PROPN
ejpam-300	4	13	zakariya	zakariya	PROPN
ejpam-300	4	14	university	university	PROPN
ejpam-300	4	15	,	,	PUNCT
ejpam-300	4	16	multan	multan	PROPN
ejpam-300	4	17	,	,	PUNCT
ejpam-300	4	18	pakistan	pakistan	PROPN
ejpam-300	4	19	.	.	PUNCT
ejpam-300	5	1	present	present	ADJ
ejpam-300	5	2	address	address	NOUN
ejpam-300	5	3	:	:	PUNCT
ejpam-300	5	4	department	department	NOUN
ejpam-300	5	5	of	of	ADP
ejpam-300	5	6	mathematics	mathematics	PROPN
ejpam-300	5	7	,	,	PUNCT
ejpam-300	5	8	king	king	NOUN
ejpam-300	5	9	abdul	abdul	PROPN
ejpam-300	5	10	aziz	aziz	PROPN
ejpam-300	5	11	university	university	PROPN
ejpam-300	5	12	p.	p.	PROPN
ejpam-300	5	13	o.	o.	PROPN
ejpam-300	5	14	box	box	PROPN
ejpam-300	5	15	80203	80203	NUM
ejpam-300	5	16	,	,	PUNCT
ejpam-300	5	17	jeddah	jeddah	PROPN
ejpam-300	5	18	21589	21589	NUM
ejpam-300	5	19	,	,	PUNCT
ejpam-300	5	20	saudi	saudi	PROPN
ejpam-300	5	21	arabia	arabia	PROPN
ejpam-300	5	22	.	.	PUNCT
ejpam-300	6	1	abstract	abstract	ADJ
ejpam-300	6	2	.	.	PUNCT
ejpam-300	7	1	in	in	ADP
ejpam-300	7	2	this	this	DET
ejpam-300	7	3	paper	paper	NOUN
ejpam-300	7	4	,	,	PUNCT
ejpam-300	7	5	we	we	PRON
ejpam-300	7	6	introduce	introduce	VERB
ejpam-300	7	7	and	and	CCONJ
ejpam-300	7	8	discuss	discuss	VERB
ejpam-300	7	9	minimal	minimal	ADJ
ejpam-300	7	10	γ	γ	X
ejpam-300	7	11	-	-	ADJ
ejpam-300	7	12	open	open	ADJ
ejpam-300	7	13	sets	set	NOUN
ejpam-300	7	14	in	in	ADP
ejpam-300	7	15	topological	topological	ADJ
ejpam-300	7	16	spaces	space	NOUN
ejpam-300	7	17	.	.	PUNCT
ejpam-300	8	1	we	we	PRON
ejpam-300	8	2	establish	establish	VERB
ejpam-300	8	3	some	some	DET
ejpam-300	8	4	basic	basic	ADJ
ejpam-300	8	5	properties	property	NOUN
ejpam-300	8	6	of	of	ADP
ejpam-300	8	7	minimal	minimal	ADJ
ejpam-300	8	8	γ	γ	X
ejpam-300	8	9	-	-	ADJ
ejpam-300	8	10	open	open	ADJ
ejpam-300	8	11	sets	set	NOUN
ejpam-300	8	12	and	and	CCONJ
ejpam-300	8	13	provide	provide	VERB
ejpam-300	8	14	an	an	DET
ejpam-300	8	15	example	example	NOUN
ejpam-300	8	16	to	to	PART
ejpam-300	8	17	illustrate	illustrate	VERB
ejpam-300	8	18	that	that	PRON
ejpam-300	8	19	minimal	minimal	ADJ
ejpam-300	8	20	γ	γ	X
ejpam-300	8	21	-	-	ADJ
ejpam-300	8	22	open	open	ADJ
ejpam-300	8	23	sets	set	NOUN
ejpam-300	8	24	are	be	AUX
ejpam-300	8	25	independent	independent	ADJ
ejpam-300	8	26	of	of	ADP
ejpam-300	8	27	minimal	minimal	ADJ
ejpam-300	8	28	open	open	ADJ
ejpam-300	8	29	sets	set	NOUN
ejpam-300	8	30	introduced	introduce	VERB
ejpam-300	8	31	and	and	CCONJ
ejpam-300	8	32	discussed	discuss	VERB
ejpam-300	8	33	in	in	ADP
ejpam-300	8	34	[	[	X
ejpam-300	8	35	3	3	NUM
ejpam-300	8	36	]	]	PUNCT
ejpam-300	8	37	.	.	PUNCT
ejpam-300	9	1	we	we	PRON
ejpam-300	9	2	obtain	obtain	VERB
ejpam-300	9	3	some	some	DET
ejpam-300	9	4	properties	property	NOUN
ejpam-300	9	5	of	of	ADP
ejpam-300	9	6	pre	pre	VERB
ejpam-300	9	7	γ	γ	X
ejpam-300	9	8	-	-	ADJ
ejpam-300	9	9	open	open	ADJ
ejpam-300	9	10	sets	set	NOUN
ejpam-300	9	11	using	use	VERB
ejpam-300	9	12	properties	property	NOUN
ejpam-300	9	13	of	of	ADP
ejpam-300	9	14	minimal	minimal	ADJ
ejpam-300	9	15	γ	γ	X
ejpam-300	9	16	-	-	ADJ
ejpam-300	9	17	open	open	ADJ
ejpam-300	9	18	sets	set	NOUN
ejpam-300	9	19	.	.	PUNCT
ejpam-300	10	1	as	as	ADP
ejpam-300	10	2	an	an	DET
ejpam-300	10	3	application	application	NOUN
ejpam-300	10	4	of	of	ADP
ejpam-300	10	5	a	a	DET
ejpam-300	10	6	theory	theory	NOUN
ejpam-300	10	7	of	of	ADP
ejpam-300	10	8	minimal	minimal	ADJ
ejpam-300	10	9	γ	γ	X
ejpam-300	10	10	-	-	ADJ
ejpam-300	10	11	open	open	ADJ
ejpam-300	10	12	sets	set	NOUN
ejpam-300	10	13	,	,	PUNCT
ejpam-300	10	14	we	we	PRON
ejpam-300	10	15	obtain	obtain	VERB
ejpam-300	10	16	a	a	DET
ejpam-300	10	17	sufficient	sufficient	ADJ
ejpam-300	10	18	condition	condition	NOUN
ejpam-300	10	19	for	for	ADP
ejpam-300	10	20	a	a	DET
ejpam-300	10	21	γ	γ	X
ejpam-300	10	22	-	-	ADJ
ejpam-300	10	23	locally	locally	ADV
ejpam-300	10	24	finite	finite	ADJ
ejpam-300	10	25	space	space	NOUN
ejpam-300	10	26	to	to	PART
ejpam-300	10	27	be	be	AUX
ejpam-300	10	28	a	a	DET
ejpam-300	10	29	pre	pre	ADJ
ejpam-300	10	30	γ	γ	PROPN
ejpam-300	10	31	-	-	ADJ
ejpam-300	10	32	t2	t2	ADJ
ejpam-300	10	33	space	space	NOUN
ejpam-300	10	34	.	.	PUNCT
ejpam-300	11	1	2000	2000	NUM
ejpam-300	11	2	mathematics	mathematic	NOUN
ejpam-300	11	3	subject	subject	NOUN
ejpam-300	11	4	classifications	classification	NOUN
ejpam-300	11	5	:	:	PUNCT
ejpam-300	11	6	54a05	54a05	NUM
ejpam-300	11	7	,	,	PUNCT
ejpam-300	11	8	54a10	54a10	NUM
ejpam-300	11	9	,	,	PUNCT
ejpam-300	11	10	54d10	54d10	NUM
ejpam-300	11	11	,	,	PUNCT
ejpam-300	11	12	54d99	54d99	NUM
ejpam-300	11	13	.	.	PUNCT
ejpam-300	12	1	key	key	ADJ
ejpam-300	12	2	words	word	NOUN
ejpam-300	12	3	and	and	CCONJ
ejpam-300	12	4	phrases	phrase	NOUN
ejpam-300	12	5	:	:	PUNCT
ejpam-300	12	6	γ	γ	X
ejpam-300	12	7	-	-	ADJ
ejpam-300	12	8	closed	closed	ADJ
ejpam-300	12	9	(	(	PUNCT
ejpam-300	12	10	open	open	ADJ
ejpam-300	12	11	)	)	PUNCT
ejpam-300	12	12	,	,	PUNCT
ejpam-300	12	13	γ	γ	NOUN
ejpam-300	12	14	-	-	NOUN
ejpam-300	12	15	closure	closure	NOUN
ejpam-300	12	16	,	,	PUNCT
ejpam-300	12	17	minimal	minimal	ADJ
ejpam-300	12	18	γ	γ	X
ejpam-300	12	19	-	-	ADJ
ejpam-300	12	20	open	open	ADJ
ejpam-300	12	21	,	,	PUNCT
ejpam-300	12	22	pre	pre	VERB
ejpam-300	12	23	γ	γ	X
ejpam-300	12	24	-	-	ADJ
ejpam-300	12	25	open	open	ADJ
ejpam-300	12	26	,	,	PUNCT
ejpam-300	12	27	finite	finite	VERB
ejpam-300	12	28	γ	γ	X
ejpam-300	12	29	-	-	ADJ
ejpam-300	12	30	open	open	ADJ
ejpam-300	12	31	,	,	PUNCT
ejpam-300	12	32	γ	γ	X
ejpam-300	12	33	-	-	ADJ
ejpam-300	12	34	locally	locally	ADV
ejpam-300	12	35	finite	finite	NOUN
ejpam-300	12	36	,	,	PUNCT
ejpam-300	12	37	pre	pre	VERB
ejpam-300	12	38	γ	γ	PROPN
ejpam-300	12	39	-	-	ADJ
ejpam-300	12	40	t2	t2	ADJ
ejpam-300	12	41	space	space	NOUN
ejpam-300	12	42	.	.	PUNCT
ejpam-300	13	1	∗corresponding	∗corresponde	VERB
ejpam-300	13	2	author	author	NOUN
ejpam-300	13	3	.	.	PUNCT
ejpam-300	14	1	email	email	NOUN
ejpam-300	14	2	addresses	address	NOUN
ejpam-300	14	3	:	:	PUNCT
ejpam-300	14	4	sabiriub	sabiriub	PROPN
ejpam-300	14	5	�	�	PROPN
ejpam-300	14	6	yahoo	yahoo	PROPN
ejpam-300	14	7	.	.	PUNCT
ejpam-300	14	8	om	om	PROPN
ejpam-300	14	9	(	(	PUNCT
ejpam-300	14	10	s.	s.	PROPN
ejpam-300	14	11	hussain	hussain	PROPN
ejpam-300	14	12	)	)	PUNCT
ejpam-300	14	13	,	,	PUNCT
ejpam-300	14	14	drbashir9	drbashir9	PROPN
ejpam-300	14	15	�	�	NOUN
ejpam-300	14	16	gmail	gmail	NOUN
ejpam-300	14	17	.	.	PUNCT
ejpam-300	15	1	om	om	PROPN
ejpam-300	15	2	(	(	PUNCT
ejpam-300	15	3	b.	b.	PROPN
ejpam-300	15	4	ahmad	ahmad	PROPN
ejpam-300	15	5	)	)	PUNCT
ejpam-300	15	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-300	16	1	338	338	NUM
ejpam-300	16	2	c	c	AUX
ejpam-300	16	3	©	©	PROPN
ejpam-300	16	4	2009	2009	NUM
ejpam-300	16	5	ejpam	ejpam	NOUN
ejpam-300	16	6	all	all	DET
ejpam-300	16	7	rights	right	NOUN
ejpam-300	16	8	reserved	reserve	VERB
ejpam-300	16	9	.	.	PUNCT
ejpam-300	17	1	s.	s.	PROPN
ejpam-300	17	2	hussain	hussain	PROPN
ejpam-300	17	3	and	and	CCONJ
ejpam-300	17	4	b.	b.	PROPN
ejpam-300	17	5	ahmad	ahmad	PROPN
ejpam-300	17	6	/	/	SYM
ejpam-300	17	7	eur	eur	PROPN
ejpam-300	17	8	.	.	PUNCT
ejpam-300	18	1	j.	j.	PROPN
ejpam-300	18	2	pure	pure	PROPN
ejpam-300	18	3	appl	appl	PROPN
ejpam-300	18	4	.	.	PROPN
ejpam-300	18	5	math	math	PROPN
ejpam-300	18	6	,	,	PUNCT
ejpam-300	18	7	2	2	NUM
ejpam-300	18	8	(	(	PUNCT
ejpam-300	18	9	2009	2009	NUM
ejpam-300	18	10	)	)	PUNCT
ejpam-300	18	11	,	,	PUNCT
ejpam-300	18	12	(	(	PUNCT
ejpam-300	18	13	338	338	NUM
ejpam-300	18	14	-	-	SYM
ejpam-300	18	15	351	351	NUM
ejpam-300	18	16	)	)	PUNCT
ejpam-300	18	17	339	339	NUM
ejpam-300	18	18	1	1	NUM
ejpam-300	18	19	.	.	PUNCT
ejpam-300	19	1	introduction	introduction	NOUN
ejpam-300	19	2	several	several	ADJ
ejpam-300	19	3	known	know	VERB
ejpam-300	19	4	characterizations	characterization	NOUN
ejpam-300	19	5	of	of	ADP
ejpam-300	19	6	compact	compact	ADJ
ejpam-300	19	7	spaces	space	NOUN
ejpam-300	19	8	,	,	PUNCT
ejpam-300	19	9	nearly	nearly	ADV
ejpam-300	19	10	compact	compact	ADJ
ejpam-300	19	11	spaces	space	NOUN
ejpam-300	19	12	and	and	CCONJ
ejpam-300	19	13	hclosed	hclosed	ADJ
ejpam-300	19	14	spaces	space	NOUN
ejpam-300	19	15	are	be	AUX
ejpam-300	19	16	unified	unify	VERB
ejpam-300	19	17	by	by	ADP
ejpam-300	19	18	generalizing	generalize	VERB
ejpam-300	19	19	the	the	DET
ejpam-300	19	20	notion	notion	NOUN
ejpam-300	19	21	of	of	ADP
ejpam-300	19	22	compactness	compactness	NOUN
ejpam-300	19	23	with	with	ADP
ejpam-300	19	24	the	the	DET
ejpam-300	19	25	help	help	NOUN
ejpam-300	19	26	of	of	ADP
ejpam-300	19	27	a	a	DET
ejpam-300	19	28	certain	certain	ADJ
ejpam-300	19	29	operation	operation	NOUN
ejpam-300	19	30	γ	γ	NOUN
ejpam-300	19	31	of	of	ADP
ejpam-300	19	32	a	a	DET
ejpam-300	19	33	topology	topology	NOUN
ejpam-300	19	34	τ	τ	X
ejpam-300	19	35	into	into	ADP
ejpam-300	19	36	the	the	DET
ejpam-300	19	37	power	power	NOUN
ejpam-300	19	38	set	set	NOUN
ejpam-300	19	39	p(x	p(x	NOUN
ejpam-300	19	40	)	)	PUNCT
ejpam-300	19	41	of	of	ADP
ejpam-300	19	42	a	a	DET
ejpam-300	19	43	space	space	NOUN
ejpam-300	19	44	x	x	PUNCT
ejpam-300	19	45	introduced	introduce	VERB
ejpam-300	19	46	and	and	CCONJ
ejpam-300	19	47	discussed	discuss	VERB
ejpam-300	19	48	by	by	ADP
ejpam-300	19	49	s.	s.	PROPN
ejpam-300	19	50	kasahara	kasahara	PROPN
ejpam-300	20	1	[	[	X
ejpam-300	20	2	2	2	NUM
ejpam-300	20	3	]	]	PUNCT
ejpam-300	20	4	.	.	PUNCT
ejpam-300	21	1	by	by	ADP
ejpam-300	21	2	using	use	VERB
ejpam-300	21	3	operation	operation	NOUN
ejpam-300	21	4	γ	γ	PROPN
ejpam-300	21	5	,	,	PUNCT
ejpam-300	21	6	h.	h.	PROPN
ejpam-300	21	7	ogata	ogata	PROPN
ejpam-300	22	1	[	[	X
ejpam-300	22	2	4	4	NUM
ejpam-300	22	3	]	]	PUNCT
ejpam-300	22	4	,	,	PUNCT
ejpam-300	22	5	introduced	introduce	VERB
ejpam-300	22	6	the	the	DET
ejpam-300	22	7	concept	concept	NOUN
ejpam-300	22	8	of	of	ADP
ejpam-300	22	9	γ	γ	NOUN
ejpam-300	22	10	-	-	ADJ
ejpam-300	22	11	open	open	ADJ
ejpam-300	22	12	sets	set	NOUN
ejpam-300	22	13	and	and	CCONJ
ejpam-300	22	14	investigated	investigate	VERB
ejpam-300	22	15	the	the	DET
ejpam-300	22	16	related	related	ADJ
ejpam-300	22	17	topological	topological	ADJ
ejpam-300	22	18	properties	property	NOUN
ejpam-300	22	19	of	of	ADP
ejpam-300	22	20	the	the	DET
ejpam-300	22	21	associated	associated	ADJ
ejpam-300	22	22	topology	topology	NOUN
ejpam-300	22	23	τγ	τγ	PUNCT
ejpam-300	22	24	and	and	CCONJ
ejpam-300	22	25	τ	τ	PROPN
ejpam-300	22	26	.	.	PUNCT
ejpam-300	23	1	he	he	PRON
ejpam-300	23	2	introduced	introduce	VERB
ejpam-300	23	3	the	the	DET
ejpam-300	23	4	notions	notion	NOUN
ejpam-300	23	5	of	of	ADP
ejpam-300	23	6	γ	γ	X
ejpam-300	23	7	-	-	PUNCT
ejpam-300	23	8	ti	ti	NOUN
ejpam-300	23	9	(	(	PUNCT
ejpam-300	23	10	i	i	NOUN
ejpam-300	23	11	=	=	NOUN
ejpam-300	23	12	0	0	NUM
ejpam-300	23	13	,	,	PUNCT
ejpam-300	23	14	1/2	1/2	NUM
ejpam-300	23	15	,	,	PUNCT
ejpam-300	23	16	1	1	NUM
ejpam-300	23	17	,	,	PUNCT
ejpam-300	23	18	2	2	NUM
ejpam-300	23	19	)	)	PUNCT
ejpam-300	23	20	spaces	space	NOUN
ejpam-300	23	21	which	which	PRON
ejpam-300	23	22	generalize	generalize	VERB
ejpam-300	23	23	ti	ti	NOUN
ejpam-300	23	24	spaces	space	NOUN
ejpam-300	23	25	(	(	PUNCT
ejpam-300	23	26	i	i	NOUN
ejpam-300	23	27	=	=	NOUN
ejpam-300	23	28	0	0	NUM
ejpam-300	23	29	,	,	PUNCT
ejpam-300	23	30	1/2	1/2	NUM
ejpam-300	23	31	,	,	PUNCT
ejpam-300	23	32	1	1	NUM
ejpam-300	23	33	,	,	PUNCT
ejpam-300	23	34	2	2	NUM
ejpam-300	23	35	)	)	PUNCT
ejpam-300	23	36	respectively	respectively	ADV
ejpam-300	23	37	.	.	PUNCT
ejpam-300	24	1	moreover	moreover	ADV
ejpam-300	24	2	,	,	PUNCT
ejpam-300	24	3	he	he	PRON
ejpam-300	24	4	investigated	investigate	VERB
ejpam-300	24	5	general	general	ADJ
ejpam-300	24	6	operator	operator	NOUN
ejpam-300	24	7	approaches	approach	NOUN
ejpam-300	24	8	of	of	ADP
ejpam-300	24	9	the	the	DET
ejpam-300	24	10	closed	closed	ADJ
ejpam-300	24	11	graph	graph	NOUN
ejpam-300	24	12	mappings	mapping	NOUN
ejpam-300	24	13	.	.	PUNCT
ejpam-300	25	1	in	in	ADP
ejpam-300	25	2	2003	2003	NUM
ejpam-300	25	3	,	,	PUNCT
ejpam-300	25	4	b.	b.	PROPN
ejpam-300	25	5	ahmad	ahmad	PROPN
ejpam-300	25	6	and	and	CCONJ
ejpam-300	25	7	s.	s.	PROPN
ejpam-300	25	8	hussain	hussain	PROPN
ejpam-300	26	1	[	[	X
ejpam-300	26	2	1	1	NUM
ejpam-300	26	3	]	]	PUNCT
ejpam-300	26	4	continued	continue	VERB
ejpam-300	26	5	studying	study	VERB
ejpam-300	26	6	the	the	DET
ejpam-300	26	7	properties	property	NOUN
ejpam-300	26	8	of	of	ADP
ejpam-300	26	9	γoperations	γoperation	NOUN
ejpam-300	26	10	on	on	ADP
ejpam-300	26	11	topological	topological	ADJ
ejpam-300	26	12	spaces	space	NOUN
ejpam-300	26	13	and	and	CCONJ
ejpam-300	26	14	investigated	investigate	VERB
ejpam-300	26	15	many	many	ADJ
ejpam-300	26	16	interesting	interesting	ADJ
ejpam-300	26	17	results	result	NOUN
ejpam-300	26	18	.	.	PUNCT
ejpam-300	27	1	in	in	ADP
ejpam-300	27	2	this	this	DET
ejpam-300	27	3	paper	paper	NOUN
ejpam-300	27	4	,	,	PUNCT
ejpam-300	27	5	we	we	PRON
ejpam-300	27	6	introduce	introduce	VERB
ejpam-300	27	7	and	and	CCONJ
ejpam-300	27	8	discuss	discuss	VERB
ejpam-300	27	9	minimal	minimal	ADJ
ejpam-300	27	10	γ	γ	X
ejpam-300	27	11	-	-	ADJ
ejpam-300	27	12	open	open	ADJ
ejpam-300	27	13	sets	set	NOUN
ejpam-300	27	14	in	in	ADP
ejpam-300	27	15	topological	topological	ADJ
ejpam-300	27	16	spaces	space	NOUN
ejpam-300	27	17	.	.	PUNCT
ejpam-300	28	1	we	we	PRON
ejpam-300	28	2	establish	establish	VERB
ejpam-300	28	3	some	some	DET
ejpam-300	28	4	basic	basic	ADJ
ejpam-300	28	5	properties	property	NOUN
ejpam-300	28	6	of	of	ADP
ejpam-300	28	7	minimal	minimal	ADJ
ejpam-300	28	8	γ	γ	X
ejpam-300	28	9	-	-	ADJ
ejpam-300	28	10	open	open	ADJ
ejpam-300	28	11	sets	set	NOUN
ejpam-300	28	12	and	and	CCONJ
ejpam-300	28	13	provide	provide	VERB
ejpam-300	28	14	an	an	DET
ejpam-300	28	15	example	example	NOUN
ejpam-300	28	16	to	to	PART
ejpam-300	28	17	illustrate	illustrate	VERB
ejpam-300	28	18	that	that	PRON
ejpam-300	28	19	minimal	minimal	ADJ
ejpam-300	28	20	γ	γ	X
ejpam-300	28	21	-	-	ADJ
ejpam-300	28	22	open	open	ADJ
ejpam-300	28	23	sets	set	NOUN
ejpam-300	28	24	are	be	AUX
ejpam-300	28	25	independent	independent	ADJ
ejpam-300	28	26	of	of	ADP
ejpam-300	28	27	minimal	minimal	ADJ
ejpam-300	28	28	open	open	ADJ
ejpam-300	28	29	sets	set	NOUN
ejpam-300	28	30	introduced	introduce	VERB
ejpam-300	28	31	and	and	CCONJ
ejpam-300	28	32	investigated	investigate	VERB
ejpam-300	28	33	in	in	ADP
ejpam-300	28	34	[	[	X
ejpam-300	28	35	3	3	NUM
ejpam-300	28	36	]	]	PUNCT
ejpam-300	28	37	.	.	PUNCT
ejpam-300	29	1	we	we	PRON
ejpam-300	29	2	obtain	obtain	VERB
ejpam-300	29	3	some	some	DET
ejpam-300	29	4	properties	property	NOUN
ejpam-300	29	5	of	of	ADP
ejpam-300	29	6	pre	pre	VERB
ejpam-300	29	7	γ	γ	X
ejpam-300	29	8	-	-	ADJ
ejpam-300	29	9	open	open	ADJ
ejpam-300	29	10	sets	set	NOUN
ejpam-300	29	11	using	use	VERB
ejpam-300	29	12	properties	property	NOUN
ejpam-300	29	13	of	of	ADP
ejpam-300	29	14	minimal	minimal	ADJ
ejpam-300	29	15	γ	γ	X
ejpam-300	29	16	-	-	ADJ
ejpam-300	29	17	open	open	ADJ
ejpam-300	29	18	sets	set	NOUN
ejpam-300	29	19	.	.	PUNCT
ejpam-300	30	1	as	as	ADP
ejpam-300	30	2	an	an	DET
ejpam-300	30	3	application	application	NOUN
ejpam-300	30	4	of	of	ADP
ejpam-300	30	5	a	a	DET
ejpam-300	30	6	theory	theory	NOUN
ejpam-300	30	7	of	of	ADP
ejpam-300	30	8	minimal	minimal	ADJ
ejpam-300	30	9	γ	γ	X
ejpam-300	30	10	-	-	ADJ
ejpam-300	30	11	open	open	ADJ
ejpam-300	30	12	sets	set	NOUN
ejpam-300	30	13	,	,	PUNCT
ejpam-300	30	14	we	we	PRON
ejpam-300	30	15	obtain	obtain	VERB
ejpam-300	30	16	a	a	DET
ejpam-300	30	17	sufficient	sufficient	ADJ
ejpam-300	30	18	condition	condition	NOUN
ejpam-300	30	19	for	for	ADP
ejpam-300	30	20	a	a	DET
ejpam-300	30	21	γ	γ	X
ejpam-300	30	22	-	-	ADJ
ejpam-300	30	23	locally	locally	ADV
ejpam-300	30	24	finite	finite	ADJ
ejpam-300	30	25	space	space	NOUN
ejpam-300	30	26	to	to	PART
ejpam-300	30	27	be	be	AUX
ejpam-300	30	28	a	a	DET
ejpam-300	30	29	pre	pre	ADJ
ejpam-300	30	30	γ	γ	PROPN
ejpam-300	30	31	-	-	ADJ
ejpam-300	30	32	t2	t2	ADJ
ejpam-300	30	33	space	space	NOUN
ejpam-300	30	34	.	.	PUNCT
ejpam-300	31	1	first	first	ADV
ejpam-300	31	2	,	,	PUNCT
ejpam-300	31	3	we	we	PRON
ejpam-300	31	4	recall	recall	VERB
ejpam-300	31	5	some	some	DET
ejpam-300	31	6	definitions	definition	NOUN
ejpam-300	31	7	and	and	CCONJ
ejpam-300	31	8	results	result	NOUN
ejpam-300	31	9	used	use	VERB
ejpam-300	31	10	in	in	ADP
ejpam-300	31	11	this	this	DET
ejpam-300	31	12	paper	paper	NOUN
ejpam-300	31	13	.	.	PUNCT
ejpam-300	32	1	hereafter	hereafter	ADV
ejpam-300	32	2	,	,	PUNCT
ejpam-300	32	3	we	we	PRON
ejpam-300	32	4	shall	shall	AUX
ejpam-300	32	5	write	write	VERB
ejpam-300	32	6	a	a	DET
ejpam-300	32	7	space	space	NOUN
ejpam-300	32	8	in	in	ADP
ejpam-300	32	9	place	place	NOUN
ejpam-300	32	10	of	of	ADP
ejpam-300	32	11	a	a	DET
ejpam-300	32	12	topological	topological	ADJ
ejpam-300	32	13	space	space	NOUN
ejpam-300	32	14	.	.	PUNCT
ejpam-300	33	1	2	2	X
ejpam-300	33	2	.	.	X
ejpam-300	33	3	preliminaries	preliminary	NOUN
ejpam-300	33	4	definition	definition	NOUN
ejpam-300	33	5	2.1	2.1	NUM
ejpam-300	33	6	.	.	PUNCT
ejpam-300	34	1	[	[	X
ejpam-300	34	2	2	2	NUM
ejpam-300	34	3	]	]	X
ejpam-300	34	4	let	let	VERB
ejpam-300	34	5	(	(	PUNCT
ejpam-300	34	6	x	x	X
ejpam-300	34	7	,	,	PUNCT
ejpam-300	34	8	τ	τ	X
ejpam-300	34	9	)	)	PUNCT
ejpam-300	34	10	be	be	AUX
ejpam-300	34	11	a	a	DET
ejpam-300	34	12	space	space	NOUN
ejpam-300	34	13	.	.	PUNCT
ejpam-300	35	1	an	an	DET
ejpam-300	35	2	operation	operation	NOUN
ejpam-300	35	3	γ	γ	X
ejpam-300	35	4	:	:	PUNCT
ejpam-300	35	5	τ→	τ→	PUNCT
ejpam-300	35	6	p(x	p(x	PROPN
ejpam-300	35	7	)	)	PUNCT
ejpam-300	35	8	is	be	AUX
ejpam-300	35	9	a	a	DET
ejpam-300	35	10	function	function	NOUN
ejpam-300	35	11	from	from	ADP
ejpam-300	35	12	τ	τ	PROPN
ejpam-300	35	13	to	to	ADP
ejpam-300	35	14	the	the	DET
ejpam-300	35	15	power	power	NOUN
ejpam-300	35	16	set	set	NOUN
ejpam-300	35	17	of	of	ADP
ejpam-300	35	18	x	x	PUNCT
ejpam-300	35	19	such	such	ADJ
ejpam-300	35	20	that	that	PRON
ejpam-300	35	21	v	v	ADP
ejpam-300	35	22	⊆	⊆	NUM
ejpam-300	35	23	v	v	ADP
ejpam-300	35	24	γ	γ	X
ejpam-300	35	25	,	,	PUNCT
ejpam-300	35	26	for	for	ADP
ejpam-300	35	27	each	each	DET
ejpam-300	35	28	v	v	NOUN
ejpam-300	35	29	∈	∈	PROPN
ejpam-300	35	30	τ	τ	NOUN
ejpam-300	35	31	,	,	PUNCT
ejpam-300	35	32	where	where	SCONJ
ejpam-300	35	33	v	v	NOUN
ejpam-300	35	34	γ	γ	PROPN
ejpam-300	35	35	denotes	denote	VERB
ejpam-300	35	36	the	the	DET
ejpam-300	35	37	value	value	NOUN
ejpam-300	35	38	of	of	ADP
ejpam-300	35	39	γ	γ	NOUN
ejpam-300	35	40	at	at	ADP
ejpam-300	35	41	v.	v.	ADP
ejpam-300	35	42	the	the	DET
ejpam-300	35	43	operations	operation	NOUN
ejpam-300	35	44	defined	define	VERB
ejpam-300	35	45	by	by	ADP
ejpam-300	35	46	γ(g	γ(g	PROPN
ejpam-300	35	47	)	)	PUNCT
ejpam-300	35	48	=	=	SYM
ejpam-300	35	49	g	g	PROPN
ejpam-300	35	50	,	,	PUNCT
ejpam-300	35	51	γ(g	γ(g	PROPN
ejpam-300	35	52	)	)	PUNCT
ejpam-300	35	53	=	=	SYM
ejpam-300	35	54	cl(g	cl(g	X
ejpam-300	35	55	)	)	PUNCT
ejpam-300	35	56	and	and	CCONJ
ejpam-300	35	57	γ(g	γ(g	PROPN
ejpam-300	35	58	)	)	PUNCT
ejpam-300	36	1	=	=	SYM
ejpam-300	36	2	intcl(g	intcl(g	NOUN
ejpam-300	36	3	)	)	PUNCT
ejpam-300	36	4	are	be	AUX
ejpam-300	36	5	examples	example	NOUN
ejpam-300	36	6	of	of	ADP
ejpam-300	36	7	operation	operation	NOUN
ejpam-300	36	8	γ	γ	PROPN
ejpam-300	36	9	.	.	PROPN
ejpam-300	36	10	s.	s.	PROPN
ejpam-300	36	11	hussain	hussain	PROPN
ejpam-300	36	12	and	and	CCONJ
ejpam-300	36	13	b.	b.	PROPN
ejpam-300	36	14	ahmad	ahmad	PROPN
ejpam-300	36	15	/	/	SYM
ejpam-300	36	16	eur	eur	PROPN
ejpam-300	36	17	.	.	PUNCT
ejpam-300	37	1	j.	j.	PROPN
ejpam-300	37	2	pure	pure	PROPN
ejpam-300	37	3	appl	appl	PROPN
ejpam-300	37	4	.	.	PROPN
ejpam-300	37	5	math	math	PROPN
ejpam-300	37	6	,	,	PUNCT
ejpam-300	37	7	2	2	NUM
ejpam-300	37	8	(	(	PUNCT
ejpam-300	37	9	2009	2009	NUM
ejpam-300	37	10	)	)	PUNCT
ejpam-300	37	11	,	,	PUNCT
ejpam-300	37	12	(	(	PUNCT
ejpam-300	37	13	338	338	NUM
ejpam-300	37	14	-	-	SYM
ejpam-300	37	15	351	351	NUM
ejpam-300	37	16	)	)	PUNCT
ejpam-300	37	17	340	340	NUM
ejpam-300	37	18	definition	definition	NOUN
ejpam-300	37	19	2.2	2.2	NUM
ejpam-300	37	20	.	.	PUNCT
ejpam-300	38	1	[	[	X
ejpam-300	38	2	4	4	X
ejpam-300	38	3	]	]	PUNCT
ejpam-300	38	4	let	let	VERB
ejpam-300	38	5	a⊆	a⊆	NOUN
ejpam-300	38	6	x.	x.	NOUN
ejpam-300	38	7	a	a	DET
ejpam-300	38	8	point	point	NOUN
ejpam-300	38	9	x∈	x∈	NOUN
ejpam-300	38	10	a	a	PRON
ejpam-300	38	11	is	be	AUX
ejpam-300	38	12	said	say	VERB
ejpam-300	38	13	to	to	PART
ejpam-300	38	14	be	be	AUX
ejpam-300	38	15	γ	γ	ADJ
ejpam-300	38	16	-	-	ADJ
ejpam-300	38	17	interior	interior	ADJ
ejpam-300	38	18	point	point	NOUN
ejpam-300	38	19	of	of	ADP
ejpam-300	38	20	a	a	PRON
ejpam-300	38	21	if	if	SCONJ
ejpam-300	38	22	there	there	PRON
ejpam-300	38	23	exists	exist	VERB
ejpam-300	38	24	an	an	DET
ejpam-300	38	25	open	open	ADJ
ejpam-300	38	26	nbd	nbd	PROPN
ejpam-300	38	27	n	n	PROPN
ejpam-300	38	28	of	of	ADP
ejpam-300	38	29	x	x	PUNCT
ejpam-300	38	30	such	such	ADJ
ejpam-300	38	31	that	that	DET
ejpam-300	38	32	nγ	nγ	NOUN
ejpam-300	38	33	⊆	⊆	NUM
ejpam-300	38	34	a	a	PRON
ejpam-300	39	1	and	and	CCONJ
ejpam-300	39	2	we	we	PRON
ejpam-300	39	3	denote	denote	VERB
ejpam-300	39	4	the	the	DET
ejpam-300	39	5	set	set	NOUN
ejpam-300	39	6	of	of	ADP
ejpam-300	39	7	all	all	DET
ejpam-300	39	8	such	such	ADJ
ejpam-300	39	9	points	point	NOUN
ejpam-300	39	10	by	by	ADP
ejpam-300	39	11	intγ(a	intγ(a	NOUN
ejpam-300	39	12	)	)	PUNCT
ejpam-300	39	13	.	.	PUNCT
ejpam-300	40	1	thus	thus	ADV
ejpam-300	40	2	intγ	intγ	ADJ
ejpam-300	40	3	(	(	PUNCT
ejpam-300	40	4	a	a	X
ejpam-300	40	5	)	)	PUNCT
ejpam-300	40	6	=	=	SYM
ejpam-300	40	7	{	{	PUNCT
ejpam-300	40	8	x	x	PUNCT
ejpam-300	40	9	∈	∈	PROPN
ejpam-300	40	10	a	a	DET
ejpam-300	40	11	:	:	PUNCT
ejpam-300	40	12	x	x	SYM
ejpam-300	40	13	∈	∈	PROPN
ejpam-300	40	14	n	n	PRON
ejpam-300	40	15	∈	∈	NOUN
ejpam-300	40	16	τ	τ	X
ejpam-300	40	17	and	and	CCONJ
ejpam-300	40	18	nγ	nγ	VERB
ejpam-300	40	19	⊆	⊆	NUM
ejpam-300	40	20	a	a	DET
ejpam-300	40	21	}	}	PUNCT
ejpam-300	40	22	⊆	⊆	NUM
ejpam-300	40	23	a.	a.	NOUN
ejpam-300	40	24	note	note	NOUN
ejpam-300	40	25	that	that	SCONJ
ejpam-300	40	26	a	a	PRON
ejpam-300	40	27	is	be	AUX
ejpam-300	40	28	γ	γ	X
ejpam-300	40	29	-	-	ADJ
ejpam-300	40	30	open	open	ADJ
ejpam-300	40	31	[	[	X
ejpam-300	40	32	1	1	NUM
ejpam-300	40	33	]	]	X
ejpam-300	40	34	iff	iff	VERB
ejpam-300	40	35	a	a	DET
ejpam-300	40	36	=	=	SYM
ejpam-300	40	37	intγ(a	intγ(a	PROPN
ejpam-300	40	38	)	)	PUNCT
ejpam-300	40	39	.	.	PUNCT
ejpam-300	41	1	a	a	DET
ejpam-300	41	2	set	set	NOUN
ejpam-300	41	3	a	a	PRON
ejpam-300	41	4	is	be	AUX
ejpam-300	41	5	called	call	VERB
ejpam-300	41	6	γclosed	γclose	VERB
ejpam-300	41	7	[	[	X
ejpam-300	41	8	1	1	X
ejpam-300	41	9	]	]	X
ejpam-300	41	10	iff	iff	PROPN
ejpam-300	41	11	x	x	PUNCT
ejpam-300	41	12	-	-	PUNCT
ejpam-300	41	13	a	a	PRON
ejpam-300	41	14	is	be	AUX
ejpam-300	41	15	γ	γ	X
ejpam-300	41	16	-	-	ADJ
ejpam-300	41	17	open	open	ADJ
ejpam-300	41	18	.	.	PUNCT
ejpam-300	42	1	definition	definition	NOUN
ejpam-300	42	2	2.3	2.3	NUM
ejpam-300	42	3	.	.	PUNCT
ejpam-300	43	1	[	[	X
ejpam-300	43	2	4	4	X
ejpam-300	43	3	]	]	PUNCT
ejpam-300	43	4	a	a	DET
ejpam-300	43	5	point	point	NOUN
ejpam-300	43	6	x∈	x∈	NOUN
ejpam-300	43	7	x	x	VERB
ejpam-300	43	8	is	be	AUX
ejpam-300	43	9	called	call	VERB
ejpam-300	43	10	a	a	DET
ejpam-300	43	11	γ	γ	NOUN
ejpam-300	43	12	-	-	PUNCT
ejpam-300	43	13	closure	closure	NOUN
ejpam-300	43	14	point	point	NOUN
ejpam-300	43	15	of	of	ADP
ejpam-300	43	16	a⊆	a⊆	PROPN
ejpam-300	43	17	x	x	X
ejpam-300	43	18	,	,	PUNCT
ejpam-300	43	19	if	if	SCONJ
ejpam-300	43	20	uγ	uγ	ADP
ejpam-300	43	21	∩	∩	NOUN
ejpam-300	43	22	a	a	DET
ejpam-300	43	23	6=	6=	NUM
ejpam-300	43	24	φ	φ	NUM
ejpam-300	43	25	,	,	PUNCT
ejpam-300	43	26	for	for	ADP
ejpam-300	43	27	each	each	DET
ejpam-300	43	28	open	open	ADJ
ejpam-300	43	29	nbd	nbd	PROPN
ejpam-300	43	30	u	u	PROPN
ejpam-300	43	31	of	of	ADP
ejpam-300	43	32	x.	x.	NOUN
ejpam-300	43	33	the	the	DET
ejpam-300	43	34	set	set	NOUN
ejpam-300	43	35	of	of	ADP
ejpam-300	43	36	all	all	DET
ejpam-300	43	37	γ	γ	NOUN
ejpam-300	43	38	-	-	PUNCT
ejpam-300	43	39	closure	closure	NOUN
ejpam-300	43	40	points	point	NOUN
ejpam-300	43	41	of	of	ADP
ejpam-300	43	42	a	a	PRON
ejpam-300	43	43	is	be	AUX
ejpam-300	43	44	called	call	VERB
ejpam-300	43	45	γ	γ	NOUN
ejpam-300	43	46	-	-	NOUN
ejpam-300	43	47	closure	closure	NOUN
ejpam-300	43	48	of	of	ADP
ejpam-300	43	49	a	a	PRON
ejpam-300	43	50	and	and	CCONJ
ejpam-300	43	51	is	be	AUX
ejpam-300	43	52	denoted	denote	VERB
ejpam-300	43	53	by	by	ADP
ejpam-300	43	54	clγ(a	clγ(a	PROPN
ejpam-300	43	55	)	)	PUNCT
ejpam-300	43	56	.	.	PUNCT
ejpam-300	44	1	a	a	DET
ejpam-300	44	2	subset	subset	NOUN
ejpam-300	44	3	a	a	PRON
ejpam-300	44	4	of	of	ADP
ejpam-300	44	5	x	x	PRON
ejpam-300	44	6	is	be	AUX
ejpam-300	44	7	called	call	VERB
ejpam-300	44	8	γ	γ	NOUN
ejpam-300	44	9	-	-	VERB
ejpam-300	44	10	closed	closed	ADJ
ejpam-300	44	11	,	,	PUNCT
ejpam-300	44	12	if	if	SCONJ
ejpam-300	44	13	clγ(a	clγ(a	PROPN
ejpam-300	44	14	)	)	PUNCT
ejpam-300	44	15	⊆	⊆	NUM
ejpam-300	44	16	a.	a.	NOUN
ejpam-300	44	17	note	note	NOUN
ejpam-300	44	18	that	that	SCONJ
ejpam-300	44	19	clγ(a	clγ(a	PROPN
ejpam-300	44	20	)	)	PUNCT
ejpam-300	44	21	is	be	AUX
ejpam-300	44	22	contained	contain	VERB
ejpam-300	44	23	in	in	ADP
ejpam-300	44	24	every	every	DET
ejpam-300	44	25	γ	γ	PROPN
ejpam-300	44	26	-	-	ADJ
ejpam-300	44	27	closed	closed	ADJ
ejpam-300	44	28	superset	superset	NOUN
ejpam-300	44	29	of	of	ADP
ejpam-300	44	30	a.	a.	NOUN
ejpam-300	44	31	definition	definition	NOUN
ejpam-300	44	32	2.4	2.4	NUM
ejpam-300	44	33	.	.	PUNCT
ejpam-300	45	1	[	[	X
ejpam-300	45	2	4	4	X
ejpam-300	45	3	]	]	X
ejpam-300	45	4	an	an	DET
ejpam-300	45	5	operation	operation	NOUN
ejpam-300	45	6	γ	γ	NOUN
ejpam-300	45	7	on	on	ADP
ejpam-300	45	8	τ	τ	PROPN
ejpam-300	45	9	is	be	AUX
ejpam-300	45	10	said	say	VERB
ejpam-300	45	11	be	be	AUX
ejpam-300	45	12	regular	regular	ADJ
ejpam-300	45	13	,	,	PUNCT
ejpam-300	45	14	if	if	SCONJ
ejpam-300	45	15	for	for	ADP
ejpam-300	45	16	any	any	DET
ejpam-300	45	17	open	open	ADJ
ejpam-300	45	18	nbds	nbds	NOUN
ejpam-300	45	19	u	u	NOUN
ejpam-300	45	20	,	,	PUNCT
ejpam-300	45	21	v	v	NOUN
ejpam-300	45	22	of	of	ADP
ejpam-300	45	23	x	x	PUNCT
ejpam-300	45	24	∈	∈	PROPN
ejpam-300	45	25	x	x	NOUN
ejpam-300	45	26	,	,	PUNCT
ejpam-300	45	27	there	there	PRON
ejpam-300	45	28	exists	exist	VERB
ejpam-300	45	29	an	an	DET
ejpam-300	45	30	open	open	ADJ
ejpam-300	45	31	nbd	nbd	PROPN
ejpam-300	45	32	w	w	PROPN
ejpam-300	45	33	of	of	ADP
ejpam-300	45	34	x	x	SYM
ejpam-300	45	35	such	such	ADJ
ejpam-300	45	36	that	that	SCONJ
ejpam-300	45	37	uγ	uγ	ADJ
ejpam-300	45	38	∩	∩	NOUN
ejpam-300	45	39	v	v	ADP
ejpam-300	45	40	γ	γ	NOUN
ejpam-300	45	41	⊇w	⊇w	ADP
ejpam-300	45	42	γ	γ	PROPN
ejpam-300	45	43	.	.	PROPN
ejpam-300	45	44	definition	definition	NOUN
ejpam-300	45	45	2.5	2.5	NUM
ejpam-300	45	46	.	.	PUNCT
ejpam-300	46	1	[	[	X
ejpam-300	46	2	4	4	X
ejpam-300	46	3	]	]	X
ejpam-300	46	4	an	an	DET
ejpam-300	46	5	operation	operation	NOUN
ejpam-300	46	6	γ	γ	NOUN
ejpam-300	46	7	on	on	ADP
ejpam-300	46	8	τ	τ	PROPN
ejpam-300	46	9	is	be	AUX
ejpam-300	46	10	said	say	VERB
ejpam-300	46	11	to	to	PART
ejpam-300	46	12	be	be	AUX
ejpam-300	46	13	open	open	ADJ
ejpam-300	46	14	,	,	PUNCT
ejpam-300	46	15	if	if	SCONJ
ejpam-300	46	16	for	for	ADP
ejpam-300	46	17	any	any	DET
ejpam-300	46	18	open	open	ADJ
ejpam-300	46	19	nbd	nbd	PROPN
ejpam-300	46	20	u	u	PROPN
ejpam-300	46	21	of	of	ADP
ejpam-300	46	22	each	each	DET
ejpam-300	46	23	x	x	SYM
ejpam-300	46	24	∈	∈	PROPN
ejpam-300	46	25	x	x	X
ejpam-300	46	26	,	,	PUNCT
ejpam-300	46	27	there	there	PRON
ejpam-300	46	28	exists	exist	VERB
ejpam-300	46	29	γ	γ	ADJ
ejpam-300	46	30	-	-	ADJ
ejpam-300	46	31	open	open	ADJ
ejpam-300	46	32	set	set	NOUN
ejpam-300	46	33	b	b	NOUN
ejpam-300	46	34	such	such	ADJ
ejpam-300	46	35	that	that	SCONJ
ejpam-300	46	36	x	x	SYM
ejpam-300	46	37	∈	∈	PROPN
ejpam-300	46	38	b	b	PROPN
ejpam-300	46	39	and	and	CCONJ
ejpam-300	46	40	uγ	uγ	PROPN
ejpam-300	46	41	⊇	⊇	PROPN
ejpam-300	46	42	b.	b.	PROPN
ejpam-300	47	1	3	3	X
ejpam-300	47	2	.	.	PUNCT
ejpam-300	47	3	minimal	minimal	ADJ
ejpam-300	47	4	γ	γ	X
ejpam-300	47	5	-	-	ADJ
ejpam-300	47	6	open	open	ADJ
ejpam-300	47	7	sets	set	NOUN
ejpam-300	47	8	in	in	ADP
ejpam-300	47	9	view	view	NOUN
ejpam-300	47	10	of	of	ADP
ejpam-300	47	11	the	the	DET
ejpam-300	47	12	definition	definition	NOUN
ejpam-300	47	13	of	of	ADP
ejpam-300	47	14	minimal	minimal	ADJ
ejpam-300	47	15	open	open	ADJ
ejpam-300	47	16	sets	set	NOUN
ejpam-300	47	17	[	[	X
ejpam-300	47	18	3	3	NUM
ejpam-300	47	19	]	]	PUNCT
ejpam-300	47	20	,	,	PUNCT
ejpam-300	47	21	we	we	PRON
ejpam-300	47	22	define	define	VERB
ejpam-300	47	23	minimal	minimal	ADJ
ejpam-300	47	24	γ	γ	X
ejpam-300	47	25	-	-	ADJ
ejpam-300	47	26	open	open	ADJ
ejpam-300	47	27	sets	set	NOUN
ejpam-300	47	28	as	as	ADP
ejpam-300	47	29	:	:	PUNCT
ejpam-300	47	30	definition	definition	NOUN
ejpam-300	47	31	3.1	3.1	NUM
ejpam-300	47	32	.	.	PUNCT
ejpam-300	48	1	let	let	VERB
ejpam-300	48	2	x	x	PRON
ejpam-300	48	3	be	be	AUX
ejpam-300	48	4	a	a	DET
ejpam-300	48	5	space	space	NOUN
ejpam-300	48	6	and	and	CCONJ
ejpam-300	48	7	a	a	DET
ejpam-300	48	8	⊆	⊆	NUM
ejpam-300	48	9	x	x	SYM
ejpam-300	48	10	a	a	DET
ejpam-300	48	11	γ	γ	X
ejpam-300	48	12	-	-	ADJ
ejpam-300	48	13	open	open	ADJ
ejpam-300	48	14	set	set	NOUN
ejpam-300	48	15	.	.	PUNCT
ejpam-300	49	1	then	then	ADV
ejpam-300	49	2	a	a	PRON
ejpam-300	49	3	is	be	AUX
ejpam-300	49	4	called	call	VERB
ejpam-300	49	5	a	a	DET
ejpam-300	49	6	minimal	minimal	ADJ
ejpam-300	49	7	γ	γ	X
ejpam-300	49	8	-	-	ADJ
ejpam-300	49	9	open	open	ADJ
ejpam-300	49	10	set	set	NOUN
ejpam-300	49	11	if	if	SCONJ
ejpam-300	49	12	φ	φ	PROPN
ejpam-300	49	13	and	and	CCONJ
ejpam-300	49	14	a	a	PRON
ejpam-300	49	15	are	be	AUX
ejpam-300	49	16	the	the	DET
ejpam-300	49	17	only	only	ADV
ejpam-300	49	18	γ	γ	ADJ
ejpam-300	49	19	-	-	ADJ
ejpam-300	49	20	open	open	ADJ
ejpam-300	49	21	subsets	subset	NOUN
ejpam-300	49	22	of	of	ADP
ejpam-300	49	23	a.	a.	NOUN
ejpam-300	49	24	the	the	DET
ejpam-300	49	25	following	follow	VERB
ejpam-300	49	26	example	example	NOUN
ejpam-300	49	27	shows	show	VERB
ejpam-300	49	28	that	that	SCONJ
ejpam-300	49	29	minimal	minimal	ADJ
ejpam-300	49	30	γ	γ	ADJ
ejpam-300	49	31	-	-	ADJ
ejpam-300	49	32	open	open	ADJ
ejpam-300	49	33	sets	set	NOUN
ejpam-300	49	34	and	and	CCONJ
ejpam-300	49	35	minimal	minimal	ADJ
ejpam-300	49	36	open	open	ADJ
ejpam-300	49	37	sets	set	NOUN
ejpam-300	49	38	are	be	AUX
ejpam-300	49	39	independent	independent	ADJ
ejpam-300	49	40	of	of	ADP
ejpam-300	49	41	each	each	DET
ejpam-300	49	42	other	other	ADJ
ejpam-300	49	43	.	.	PUNCT
ejpam-300	49	44	example	example	NOUN
ejpam-300	50	1	3.1	3.1	NUM
ejpam-300	50	2	.	.	PUNCT
ejpam-300	51	1	let	let	VERB
ejpam-300	51	2	x=	x=	PUNCT
ejpam-300	52	1	{	{	PUNCT
ejpam-300	52	2	a	a	DET
ejpam-300	52	3	,	,	PUNCT
ejpam-300	52	4	b	b	NOUN
ejpam-300	52	5	,	,	PUNCT
ejpam-300	52	6	c	c	NOUN
ejpam-300	52	7	}	}	PUNCT
ejpam-300	52	8	,	,	PUNCT
ejpam-300	52	9	τ	τ	X
ejpam-300	52	10	=	=	PUNCT
ejpam-300	52	11	{	{	PUNCT
ejpam-300	52	12	φ	φ	PROPN
ejpam-300	52	13	,	,	PUNCT
ejpam-300	52	14	x	x	INTJ
ejpam-300	52	15	,	,	PUNCT
ejpam-300	52	16	{	{	PUNCT
ejpam-300	52	17	a	a	NOUN
ejpam-300	52	18	}	}	PUNCT
ejpam-300	52	19	,	,	PUNCT
ejpam-300	52	20	{	{	PUNCT
ejpam-300	52	21	b	b	NOUN
ejpam-300	52	22	}	}	PUNCT
ejpam-300	52	23	,	,	PUNCT
ejpam-300	52	24	{	{	PUNCT
ejpam-300	52	25	a	a	DET
ejpam-300	52	26	,	,	PUNCT
ejpam-300	52	27	b	b	NOUN
ejpam-300	52	28	}	}	PUNCT
ejpam-300	52	29	,	,	PUNCT
ejpam-300	52	30	{	{	PUNCT
ejpam-300	52	31	a	a	PRON
ejpam-300	52	32	,	,	PUNCT
ejpam-300	52	33	c	c	NOUN
ejpam-300	52	34	}	}	PUNCT
ejpam-300	52	35	}	}	PUNCT
ejpam-300	52	36	.	.	PUNCT
ejpam-300	53	1	for	for	ADP
ejpam-300	53	2	b	b	PROPN
ejpam-300	53	3	∈	∈	PROPN
ejpam-300	53	4	x	x	PUNCT
ejpam-300	53	5	,	,	PUNCT
ejpam-300	53	6	define	define	VERB
ejpam-300	53	7	an	an	DET
ejpam-300	53	8	operation	operation	NOUN
ejpam-300	53	9	γ	γ	X
ejpam-300	53	10	:	:	PUNCT
ejpam-300	53	11	τ→	τ→	PUNCT
ejpam-300	53	12	p(x	p(x	PROPN
ejpam-300	53	13	)	)	PUNCT
ejpam-300	53	14	by	by	ADP
ejpam-300	53	15	s.	s.	PROPN
ejpam-300	53	16	hussain	hussain	PROPN
ejpam-300	53	17	and	and	CCONJ
ejpam-300	53	18	b.	b.	PROPN
ejpam-300	53	19	ahmad	ahmad	PROPN
ejpam-300	53	20	/	/	SYM
ejpam-300	53	21	eur	eur	PROPN
ejpam-300	53	22	.	.	PUNCT
ejpam-300	54	1	j.	j.	PROPN
ejpam-300	54	2	pure	pure	PROPN
ejpam-300	54	3	appl	appl	PROPN
ejpam-300	54	4	.	.	PROPN
ejpam-300	54	5	math	math	PROPN
ejpam-300	54	6	,	,	PUNCT
ejpam-300	54	7	2	2	NUM
ejpam-300	54	8	(	(	PUNCT
ejpam-300	54	9	2009	2009	NUM
ejpam-300	54	10	)	)	PUNCT
ejpam-300	54	11	,	,	PUNCT
ejpam-300	54	12	(	(	PUNCT
ejpam-300	54	13	338	338	NUM
ejpam-300	54	14	-	-	SYM
ejpam-300	54	15	351	351	NUM
ejpam-300	54	16	)	)	PUNCT
ejpam-300	54	17	341	341	NUM
ejpam-300	54	18	γ(a	γ(a	NOUN
ejpam-300	54	19	)	)	PUNCT
ejpam-300	55	1	=	=	SYM
ejpam-300	55	2	aγ	aγ	NOUN
ejpam-300	55	3	=	=	PUNCT
ejpam-300	55	4			PROPN
ejpam-300	55	5			NOUN
ejpam-300	55	6			PROPN
ejpam-300	55	7	a	a	X
ejpam-300	55	8	,	,	PUNCT
ejpam-300	55	9	if	if	SCONJ
ejpam-300	55	10	b	b	PROPN
ejpam-300	55	11	∈	∈	PROPN
ejpam-300	55	12	a	a	DET
ejpam-300	55	13	cl(a	cl(a	NUM
ejpam-300	55	14	)	)	PUNCT
ejpam-300	55	15	,	,	PUNCT
ejpam-300	55	16	if	if	SCONJ
ejpam-300	55	17	b	b	PROPN
ejpam-300	55	18	6∈	6∈	PROPN
ejpam-300	55	19	a.	a.	NOUN
ejpam-300	55	20	the	the	DET
ejpam-300	55	21	γ	γ	X
ejpam-300	55	22	-	-	ADJ
ejpam-300	55	23	open	open	ADJ
ejpam-300	55	24	sets	set	NOUN
ejpam-300	55	25	are	be	AUX
ejpam-300	55	26	φ	φ	NUM
ejpam-300	55	27	,	,	PUNCT
ejpam-300	55	28	x	x	PRON
ejpam-300	55	29	,	,	PUNCT
ejpam-300	55	30	{	{	PUNCT
ejpam-300	55	31	b},{a	b},{a	ADV
ejpam-300	55	32	,	,	PUNCT
ejpam-300	55	33	b	b	NOUN
ejpam-300	55	34	}	}	PUNCT
ejpam-300	55	35	,	,	PUNCT
ejpam-300	55	36	{	{	PUNCT
ejpam-300	55	37	a	a	PRON
ejpam-300	55	38	,	,	PUNCT
ejpam-300	55	39	c	c	NOUN
ejpam-300	55	40	}	}	PUNCT
ejpam-300	55	41	[	[	X
ejpam-300	55	42	4	4	NUM
ejpam-300	55	43	]	]	PUNCT
ejpam-300	55	44	.	.	PUNCT
ejpam-300	56	1	here	here	ADV
ejpam-300	56	2	{	{	PUNCT
ejpam-300	56	3	a	a	PRON
ejpam-300	56	4	}	}	PUNCT
ejpam-300	56	5	is	be	AUX
ejpam-300	56	6	a	a	DET
ejpam-300	56	7	minimal	minimal	ADJ
ejpam-300	56	8	open	open	ADJ
ejpam-300	56	9	set	set	NOUN
ejpam-300	56	10	which	which	PRON
ejpam-300	56	11	is	be	AUX
ejpam-300	56	12	not	not	PART
ejpam-300	56	13	minimal	minimal	ADJ
ejpam-300	56	14	γ	γ	X
ejpam-300	56	15	-	-	ADJ
ejpam-300	56	16	open	open	ADJ
ejpam-300	56	17	.	.	PUNCT
ejpam-300	57	1	also	also	ADV
ejpam-300	57	2	{	{	PUNCT
ejpam-300	57	3	a	a	PRON
ejpam-300	57	4	,	,	PUNCT
ejpam-300	57	5	c	c	NOUN
ejpam-300	57	6	}	}	PUNCT
ejpam-300	57	7	is	be	AUX
ejpam-300	57	8	minimal	minimal	ADJ
ejpam-300	57	9	γ	γ	X
ejpam-300	57	10	-	-	ADJ
ejpam-300	57	11	open	open	ADJ
ejpam-300	57	12	set	set	NOUN
ejpam-300	57	13	which	which	PRON
ejpam-300	57	14	is	be	AUX
ejpam-300	57	15	not	not	PART
ejpam-300	57	16	minimal	minimal	ADJ
ejpam-300	57	17	open	open	ADJ
ejpam-300	57	18	.	.	PUNCT
ejpam-300	58	1	the	the	DET
ejpam-300	58	2	following	follow	VERB
ejpam-300	58	3	is	be	AUX
ejpam-300	58	4	immediate	immediate	ADJ
ejpam-300	58	5	:	:	PUNCT
ejpam-300	58	6	proposition	proposition	NOUN
ejpam-300	58	7	3.1	3.1	NUM
ejpam-300	58	8	.	.	PUNCT
ejpam-300	59	1	let	let	VERB
ejpam-300	59	2	x	x	PRON
ejpam-300	59	3	is	be	AUX
ejpam-300	59	4	a	a	DET
ejpam-300	59	5	space	space	NOUN
ejpam-300	59	6	.	.	PUNCT
ejpam-300	60	1	then	then	ADV
ejpam-300	60	2	(	(	PUNCT
ejpam-300	60	3	1	1	X
ejpam-300	60	4	)	)	PUNCT
ejpam-300	60	5	let	let	VERB
ejpam-300	60	6	a	a	PRON
ejpam-300	60	7	be	be	AUX
ejpam-300	60	8	a	a	DET
ejpam-300	60	9	minimal	minimal	ADJ
ejpam-300	60	10	γ	γ	X
ejpam-300	60	11	-	-	ADJ
ejpam-300	60	12	open	open	ADJ
ejpam-300	60	13	set	set	NOUN
ejpam-300	60	14	and	and	CCONJ
ejpam-300	60	15	b	b	NOUN
ejpam-300	60	16	a	a	DET
ejpam-300	60	17	γ	γ	X
ejpam-300	60	18	-	-	ADJ
ejpam-300	60	19	open	open	ADJ
ejpam-300	60	20	set	set	NOUN
ejpam-300	60	21	.	.	PUNCT
ejpam-300	61	1	then	then	ADV
ejpam-300	61	2	a∩	a∩	PROPN
ejpam-300	61	3	b	b	PROPN
ejpam-300	61	4	=	=	SYM
ejpam-300	61	5	φ	φ	PROPN
ejpam-300	61	6	or	or	CCONJ
ejpam-300	61	7	a⊆	a⊆	PROPN
ejpam-300	61	8	b	b	NOUN
ejpam-300	61	9	,	,	PUNCT
ejpam-300	61	10	where	where	SCONJ
ejpam-300	61	11	γ	γ	NOUN
ejpam-300	61	12	is	be	AUX
ejpam-300	61	13	regular	regular	ADJ
ejpam-300	61	14	.	.	PUNCT
ejpam-300	62	1	(	(	PUNCT
ejpam-300	62	2	2	2	X
ejpam-300	62	3	)	)	PUNCT
ejpam-300	62	4	let	let	VERB
ejpam-300	62	5	b	b	NOUN
ejpam-300	62	6	and	and	CCONJ
ejpam-300	62	7	c	c	AUX
ejpam-300	62	8	be	be	AUX
ejpam-300	62	9	minimal	minimal	ADJ
ejpam-300	62	10	γ	γ	X
ejpam-300	62	11	-	-	ADJ
ejpam-300	62	12	open	open	ADJ
ejpam-300	62	13	sets	set	NOUN
ejpam-300	62	14	.	.	PUNCT
ejpam-300	63	1	then	then	ADV
ejpam-300	63	2	b	b	X
ejpam-300	63	3	∩	∩	NOUN
ejpam-300	63	4	c	c	NOUN
ejpam-300	63	5	=	=	SYM
ejpam-300	63	6	φ	φ	PROPN
ejpam-300	63	7	or	or	CCONJ
ejpam-300	63	8	b	b	X
ejpam-300	63	9	=	=	SYM
ejpam-300	63	10	c	c	PROPN
ejpam-300	63	11	,	,	PUNCT
ejpam-300	63	12	where	where	SCONJ
ejpam-300	63	13	γ	γ	NOUN
ejpam-300	63	14	is	be	AUX
ejpam-300	63	15	regular	regular	ADJ
ejpam-300	63	16	.	.	PUNCT
ejpam-300	64	1	proposition	proposition	NOUN
ejpam-300	64	2	3.2	3.2	NUM
ejpam-300	64	3	.	.	PUNCT
ejpam-300	65	1	let	let	VERB
ejpam-300	65	2	x	x	PRON
ejpam-300	65	3	be	be	AUX
ejpam-300	65	4	a	a	DET
ejpam-300	65	5	space	space	NOUN
ejpam-300	65	6	and	and	CCONJ
ejpam-300	65	7	a	a	DET
ejpam-300	65	8	a	a	DET
ejpam-300	65	9	minimal	minimal	ADJ
ejpam-300	65	10	γ	γ	X
ejpam-300	65	11	-	-	ADJ
ejpam-300	65	12	open	open	ADJ
ejpam-300	65	13	set	set	NOUN
ejpam-300	65	14	.	.	PUNCT
ejpam-300	66	1	if	if	SCONJ
ejpam-300	66	2	a	a	DET
ejpam-300	66	3	∈	∈	PROPN
ejpam-300	66	4	a	a	PRON
ejpam-300	66	5	,	,	PUNCT
ejpam-300	66	6	then	then	ADV
ejpam-300	66	7	for	for	ADP
ejpam-300	66	8	any	any	DET
ejpam-300	66	9	γ	γ	X
ejpam-300	66	10	-	-	ADJ
ejpam-300	66	11	open	open	ADJ
ejpam-300	66	12	nbd	nbd	PROPN
ejpam-300	66	13	b	b	PROPN
ejpam-300	66	14	of	of	ADP
ejpam-300	66	15	a	a	DET
ejpam-300	66	16	,	,	PUNCT
ejpam-300	66	17	a⊆	a⊆	PROPN
ejpam-300	66	18	b	b	NOUN
ejpam-300	66	19	,	,	PUNCT
ejpam-300	66	20	where	where	SCONJ
ejpam-300	66	21	γ	γ	NOUN
ejpam-300	66	22	is	be	AUX
ejpam-300	66	23	regular	regular	ADJ
ejpam-300	66	24	.	.	PUNCT
ejpam-300	67	1	proof	proof	NOUN
ejpam-300	67	2	.	.	PUNCT
ejpam-300	68	1	suppose	suppose	VERB
ejpam-300	68	2	on	on	ADP
ejpam-300	68	3	the	the	DET
ejpam-300	68	4	contrary	contrary	NOUN
ejpam-300	68	5	that	that	SCONJ
ejpam-300	68	6	b	b	PROPN
ejpam-300	68	7	is	be	AUX
ejpam-300	68	8	a	a	DET
ejpam-300	68	9	γ	γ	NOUN
ejpam-300	68	10	-	-	ADJ
ejpam-300	68	11	open	open	ADJ
ejpam-300	68	12	nbd	nbd	PROPN
ejpam-300	68	13	b	b	PROPN
ejpam-300	68	14	of	of	ADP
ejpam-300	68	15	a	a	DET
ejpam-300	68	16	∈	∈	PROPN
ejpam-300	68	17	a	a	DET
ejpam-300	68	18	such	such	ADJ
ejpam-300	68	19	that	that	SCONJ
ejpam-300	68	20	a	a	DET
ejpam-300	68	21	*	*	PROPN
ejpam-300	68	22	b	b	PROPN
ejpam-300	68	23	.	.	PUNCT
ejpam-300	69	1	since	since	SCONJ
ejpam-300	69	2	γ	γ	PROPN
ejpam-300	69	3	is	be	AUX
ejpam-300	69	4	a	a	DET
ejpam-300	69	5	regular	regular	ADJ
ejpam-300	69	6	operation	operation	NOUN
ejpam-300	69	7	,	,	PUNCT
ejpam-300	69	8	therefore	therefore	ADV
ejpam-300	69	9	a∩	a∩	PROPN
ejpam-300	69	10	b	b	PROPN
ejpam-300	69	11	is	be	AUX
ejpam-300	69	12	a	a	DET
ejpam-300	69	13	γ	γ	NOUN
ejpam-300	69	14	-	-	ADJ
ejpam-300	69	15	open	open	ADJ
ejpam-300	69	16	set	set	NOUN
ejpam-300	69	17	[	[	X
ejpam-300	69	18	4	4	NUM
ejpam-300	69	19	]	]	PUNCT
ejpam-300	69	20	with	with	ADP
ejpam-300	69	21	a∩	a∩	PROPN
ejpam-300	69	22	b	b	PROPN
ejpam-300	69	23	⊆	⊆	NUM
ejpam-300	69	24	a	a	PRON
ejpam-300	69	25	and	and	CCONJ
ejpam-300	69	26	a∩	a∩	PROPN
ejpam-300	69	27	b	b	PROPN
ejpam-300	69	28	6=	6=	NUM
ejpam-300	69	29	φ	φ	PROPN
ejpam-300	69	30	.	.	PUNCT
ejpam-300	70	1	this	this	PRON
ejpam-300	70	2	is	be	AUX
ejpam-300	70	3	a	a	DET
ejpam-300	70	4	contradiction	contradiction	NOUN
ejpam-300	70	5	to	to	ADP
ejpam-300	70	6	our	our	PRON
ejpam-300	70	7	supposition	supposition	NOUN
ejpam-300	70	8	that	that	SCONJ
ejpam-300	70	9	a	a	PRON
ejpam-300	70	10	is	be	AUX
ejpam-300	70	11	a	a	DET
ejpam-300	70	12	minimal	minimal	ADJ
ejpam-300	70	13	γ	γ	X
ejpam-300	70	14	-	-	ADJ
ejpam-300	70	15	open	open	ADJ
ejpam-300	70	16	set	set	NOUN
ejpam-300	70	17	.	.	PUNCT
ejpam-300	71	1	hence	hence	ADV
ejpam-300	71	2	the	the	DET
ejpam-300	71	3	proof	proof	NOUN
ejpam-300	71	4	.	.	PUNCT
ejpam-300	72	1	the	the	DET
ejpam-300	72	2	following	follow	VERB
ejpam-300	72	3	example	example	NOUN
ejpam-300	72	4	shows	show	VERB
ejpam-300	72	5	that	that	SCONJ
ejpam-300	72	6	the	the	DET
ejpam-300	72	7	condition	condition	NOUN
ejpam-300	72	8	that	that	SCONJ
ejpam-300	72	9	γ	γ	NOUN
ejpam-300	72	10	is	be	AUX
ejpam-300	72	11	regular	regular	ADJ
ejpam-300	72	12	is	be	AUX
ejpam-300	72	13	necessary	necessary	ADJ
ejpam-300	72	14	for	for	ADP
ejpam-300	72	15	the	the	DET
ejpam-300	72	16	above	above	ADJ
ejpam-300	72	17	proposition	proposition	NOUN
ejpam-300	72	18	.	.	PUNCT
ejpam-300	73	1	example	example	NOUN
ejpam-300	73	2	3.2	3.2	NUM
ejpam-300	73	3	.	.	PUNCT
ejpam-300	74	1	let	let	VERB
ejpam-300	74	2	x=	x=	PUNCT
ejpam-300	75	1	{	{	PUNCT
ejpam-300	75	2	a	a	DET
ejpam-300	75	3	,	,	PUNCT
ejpam-300	75	4	b	b	NOUN
ejpam-300	75	5	,	,	PUNCT
ejpam-300	75	6	c	c	NOUN
ejpam-300	75	7	}	}	PUNCT
ejpam-300	75	8	,	,	PUNCT
ejpam-300	75	9	τ	τ	X
ejpam-300	75	10	=	=	PUNCT
ejpam-300	75	11	{	{	PUNCT
ejpam-300	75	12	φ	φ	PROPN
ejpam-300	75	13	,	,	PUNCT
ejpam-300	75	14	x	x	INTJ
ejpam-300	75	15	,	,	PUNCT
ejpam-300	75	16	{	{	PUNCT
ejpam-300	75	17	a	a	NOUN
ejpam-300	75	18	}	}	PUNCT
ejpam-300	75	19	,	,	PUNCT
ejpam-300	75	20	{	{	PUNCT
ejpam-300	75	21	b	b	NOUN
ejpam-300	75	22	}	}	PUNCT
ejpam-300	75	23	,	,	PUNCT
ejpam-300	75	24	{	{	PUNCT
ejpam-300	75	25	a	a	DET
ejpam-300	75	26	,	,	PUNCT
ejpam-300	75	27	b	b	NOUN
ejpam-300	75	28	}	}	PUNCT
ejpam-300	75	29	,	,	PUNCT
ejpam-300	75	30	{	{	PUNCT
ejpam-300	75	31	a	a	PRON
ejpam-300	75	32	,	,	PUNCT
ejpam-300	75	33	c	c	NOUN
ejpam-300	75	34	}	}	PUNCT
ejpam-300	75	35	}	}	PUNCT
ejpam-300	75	36	.	.	PUNCT
ejpam-300	76	1	for	for	ADP
ejpam-300	76	2	b	b	PROPN
ejpam-300	76	3	∈	∈	PROPN
ejpam-300	76	4	x	x	PUNCT
ejpam-300	76	5	,	,	PUNCT
ejpam-300	76	6	define	define	VERB
ejpam-300	76	7	an	an	DET
ejpam-300	76	8	operation	operation	NOUN
ejpam-300	76	9	γ	γ	X
ejpam-300	76	10	:	:	PUNCT
ejpam-300	76	11	τ→	τ→	PUNCT
ejpam-300	76	12	p(x	p(x	PROPN
ejpam-300	76	13	)	)	PUNCT
ejpam-300	76	14	by	by	ADP
ejpam-300	76	15	γ(a	γ(a	NOUN
ejpam-300	76	16	)	)	PUNCT
ejpam-300	76	17	=	=	PUNCT
ejpam-300	76	18	aγ	aγ	NOUN
ejpam-300	76	19	=	=	PUNCT
ejpam-300	76	20			PROPN
ejpam-300	76	21			NOUN
ejpam-300	76	22			PROPN
ejpam-300	76	23	a	a	X
ejpam-300	76	24	,	,	PUNCT
ejpam-300	76	25	if	if	SCONJ
ejpam-300	76	26	b	b	PROPN
ejpam-300	76	27	∈	∈	PROPN
ejpam-300	76	28	a	a	DET
ejpam-300	76	29	cl(a	cl(a	NUM
ejpam-300	76	30	)	)	PUNCT
ejpam-300	76	31	,	,	PUNCT
ejpam-300	76	32	if	if	SCONJ
ejpam-300	76	33	b	b	PROPN
ejpam-300	76	34	6∈	6∈	NOUN
ejpam-300	76	35	a	a	X
ejpam-300	76	36	.	.	PUNCT
ejpam-300	77	1	then	then	ADV
ejpam-300	77	2	calculations	calculation	NOUN
ejpam-300	77	3	show	show	VERB
ejpam-300	77	4	that	that	SCONJ
ejpam-300	77	5	the	the	DET
ejpam-300	77	6	operation	operation	NOUN
ejpam-300	77	7	γ	γ	NOUN
ejpam-300	77	8	is	be	AUX
ejpam-300	77	9	not	not	PART
ejpam-300	77	10	regular	regular	ADJ
ejpam-300	77	11	[	[	X
ejpam-300	77	12	4	4	NUM
ejpam-300	77	13	]	]	PUNCT
ejpam-300	77	14	.	.	PUNCT
ejpam-300	78	1	the	the	DET
ejpam-300	78	2	γ	γ	NOUN
ejpam-300	78	3	-	-	ADJ
ejpam-300	78	4	open	open	ADJ
ejpam-300	78	5	sets	set	NOUN
ejpam-300	78	6	are	be	AUX
ejpam-300	78	7	φ	φ	NOUN
ejpam-300	78	8	,	,	PUNCT
ejpam-300	78	9	x	x	PRON
ejpam-300	78	10	,	,	PUNCT
ejpam-300	78	11	{	{	PUNCT
ejpam-300	78	12	b	b	NOUN
ejpam-300	78	13	}	}	PUNCT
ejpam-300	78	14	,	,	PUNCT
ejpam-300	78	15	{	{	PUNCT
ejpam-300	78	16	a	a	DET
ejpam-300	78	17	,	,	PUNCT
ejpam-300	78	18	b	b	NOUN
ejpam-300	78	19	}	}	PUNCT
ejpam-300	78	20	,	,	PUNCT
ejpam-300	78	21	{	{	PUNCT
ejpam-300	78	22	a	a	PRON
ejpam-300	78	23	,	,	PUNCT
ejpam-300	78	24	c}[4	c}[4	PROPN
ejpam-300	78	25	]	]	PUNCT
ejpam-300	78	26	.	.	PUNCT
ejpam-300	79	1	clearly	clearly	ADV
ejpam-300	79	2	a	a	PRON
ejpam-300	79	3	=	=	X
ejpam-300	79	4	{	{	PUNCT
ejpam-300	79	5	a	a	NOUN
ejpam-300	79	6	,	,	PUNCT
ejpam-300	79	7	c	c	NOUN
ejpam-300	79	8	}	}	PUNCT
ejpam-300	79	9	is	be	AUX
ejpam-300	79	10	a	a	DET
ejpam-300	79	11	minimal	minimal	ADJ
ejpam-300	79	12	γ	γ	X
ejpam-300	79	13	-	-	ADJ
ejpam-300	79	14	open	open	ADJ
ejpam-300	79	15	set	set	NOUN
ejpam-300	79	16	.	.	PUNCT
ejpam-300	80	1	thus	thus	ADV
ejpam-300	80	2	for	for	ADP
ejpam-300	80	3	a	a	DET
ejpam-300	80	4	∈	∈	PROPN
ejpam-300	80	5	a	a	PRON
ejpam-300	80	6	,	,	PUNCT
ejpam-300	80	7	there	there	PRON
ejpam-300	80	8	does	do	AUX
ejpam-300	80	9	not	not	PART
ejpam-300	80	10	exist	exist	VERB
ejpam-300	80	11	γ	γ	NOUN
ejpam-300	80	12	-	-	ADJ
ejpam-300	80	13	open	open	ADJ
ejpam-300	80	14	nbd	nbd	PROPN
ejpam-300	80	15	b	b	PROPN
ejpam-300	80	16	of	of	ADP
ejpam-300	80	17	a	a	DET
ejpam-300	80	18	such	such	ADJ
ejpam-300	80	19	that	that	PRON
ejpam-300	80	20	a⊆	a⊆	PROPN
ejpam-300	80	21	b.	b.	PROPN
ejpam-300	80	22	s.	s.	PROPN
ejpam-300	80	23	hussain	hussain	PROPN
ejpam-300	80	24	and	and	CCONJ
ejpam-300	80	25	b.	b.	PROPN
ejpam-300	80	26	ahmad	ahmad	PROPN
ejpam-300	80	27	/	/	SYM
ejpam-300	80	28	eur	eur	PROPN
ejpam-300	80	29	.	.	PUNCT
ejpam-300	81	1	j.	j.	PROPN
ejpam-300	81	2	pure	pure	PROPN
ejpam-300	81	3	appl	appl	PROPN
ejpam-300	81	4	.	.	PROPN
ejpam-300	81	5	math	math	PROPN
ejpam-300	81	6	,	,	PUNCT
ejpam-300	81	7	2	2	NUM
ejpam-300	81	8	(	(	PUNCT
ejpam-300	81	9	2009	2009	NUM
ejpam-300	81	10	)	)	PUNCT
ejpam-300	81	11	,	,	PUNCT
ejpam-300	81	12	(	(	PUNCT
ejpam-300	81	13	338	338	NUM
ejpam-300	81	14	-	-	SYM
ejpam-300	81	15	351	351	NUM
ejpam-300	81	16	)	)	PUNCT
ejpam-300	81	17	342	342	NUM
ejpam-300	81	18	the	the	DET
ejpam-300	81	19	following	follow	VERB
ejpam-300	81	20	proposition	proposition	NOUN
ejpam-300	81	21	easily	easily	ADV
ejpam-300	81	22	follows	follow	VERB
ejpam-300	81	23	from	from	ADP
ejpam-300	81	24	proposition	proposition	NOUN
ejpam-300	81	25	3.1	3.1	NUM
ejpam-300	81	26	.	.	PUNCT
ejpam-300	82	1	proposition	proposition	NOUN
ejpam-300	82	2	3.3	3.3	NUM
ejpam-300	82	3	.	.	PUNCT
ejpam-300	83	1	let	let	VERB
ejpam-300	83	2	x	x	PRON
ejpam-300	83	3	be	be	AUX
ejpam-300	83	4	a	a	DET
ejpam-300	83	5	space	space	NOUN
ejpam-300	83	6	and	and	CCONJ
ejpam-300	83	7	a	a	DET
ejpam-300	83	8	a	a	DET
ejpam-300	83	9	minimal	minimal	ADJ
ejpam-300	83	10	γ	γ	X
ejpam-300	83	11	-	-	ADJ
ejpam-300	83	12	open	open	ADJ
ejpam-300	83	13	set	set	NOUN
ejpam-300	83	14	.	.	PUNCT
ejpam-300	84	1	then	then	ADV
ejpam-300	84	2	for	for	ADP
ejpam-300	84	3	any	any	DET
ejpam-300	84	4	y	y	PROPN
ejpam-300	84	5	∈	∈	PROPN
ejpam-300	84	6	a	a	PRON
ejpam-300	84	7	,	,	PUNCT
ejpam-300	84	8	a=	a=	ADJ
ejpam-300	84	9	∩{b	∩{b	X
ejpam-300	85	1	:	:	PUNCT
ejpam-300	85	2	b	b	X
ejpam-300	85	3	is	be	AUX
ejpam-300	85	4	γ	γ	X
ejpam-300	85	5	-	-	ADJ
ejpam-300	85	6	open	open	ADJ
ejpam-300	85	7	nbd	nbd	PROPN
ejpam-300	85	8	of	of	ADP
ejpam-300	85	9	y	y	PROPN
ejpam-300	85	10	}	}	PUNCT
ejpam-300	85	11	,	,	PUNCT
ejpam-300	85	12	where	where	SCONJ
ejpam-300	85	13	γ	γ	PROPN
ejpam-300	85	14	is	be	AUX
ejpam-300	85	15	regular	regular	ADJ
ejpam-300	85	16	.	.	PUNCT
ejpam-300	86	1	similarly	similarly	ADV
ejpam-300	86	2	we	we	PRON
ejpam-300	86	3	have	have	AUX
ejpam-300	86	4	:	:	PUNCT
ejpam-300	86	5	proposition	proposition	NOUN
ejpam-300	86	6	3.4	3.4	NUM
ejpam-300	86	7	.	.	PUNCT
ejpam-300	87	1	let	let	VERB
ejpam-300	87	2	a	a	PRON
ejpam-300	87	3	be	be	AUX
ejpam-300	87	4	a	a	DET
ejpam-300	87	5	minimal	minimal	ADJ
ejpam-300	87	6	γ	γ	X
ejpam-300	87	7	-	-	ADJ
ejpam-300	87	8	open	open	ADJ
ejpam-300	87	9	set	set	NOUN
ejpam-300	87	10	in	in	ADP
ejpam-300	87	11	x	x	PUNCT
ejpam-300	87	12	and	and	CCONJ
ejpam-300	87	13	x	x	SYM
ejpam-300	87	14	∈	∈	PROPN
ejpam-300	87	15	x	x	PUNCT
ejpam-300	87	16	such	such	ADJ
ejpam-300	87	17	that	that	PRON
ejpam-300	87	18	x	x	PROPN
ejpam-300	87	19	/∈	/∈	PUNCT
ejpam-300	88	1	a	a	INTJ
ejpam-300	88	2	.	.	PUNCT
ejpam-300	89	1	then	then	ADV
ejpam-300	89	2	for	for	ADP
ejpam-300	89	3	any	any	DET
ejpam-300	89	4	γ	γ	X
ejpam-300	89	5	-	-	ADJ
ejpam-300	89	6	open	open	ADJ
ejpam-300	89	7	nbd	nbd	PROPN
ejpam-300	89	8	c	c	PROPN
ejpam-300	89	9	of	of	ADP
ejpam-300	89	10	x	x	PROPN
ejpam-300	89	11	,	,	PUNCT
ejpam-300	89	12	c	c	PROPN
ejpam-300	89	13	∩	∩	PROPN
ejpam-300	89	14	a=	a=	PROPN
ejpam-300	89	15	φ	φ	PROPN
ejpam-300	89	16	or	or	CCONJ
ejpam-300	89	17	a⊆	a⊆	PROPN
ejpam-300	89	18	c.	c.	PROPN
ejpam-300	89	19	corollary	corollary	NOUN
ejpam-300	89	20	3.1	3.1	NUM
ejpam-300	89	21	.	.	PUNCT
ejpam-300	90	1	let	let	VERB
ejpam-300	90	2	a	a	PRON
ejpam-300	90	3	be	be	AUX
ejpam-300	90	4	a	a	DET
ejpam-300	90	5	minimal	minimal	ADJ
ejpam-300	90	6	γ	γ	X
ejpam-300	90	7	-	-	ADJ
ejpam-300	90	8	open	open	ADJ
ejpam-300	90	9	set	set	NOUN
ejpam-300	90	10	in	in	ADP
ejpam-300	90	11	x	x	PUNCT
ejpam-300	90	12	and	and	CCONJ
ejpam-300	90	13	x	x	SYM
ejpam-300	90	14	∈	∈	PROPN
ejpam-300	90	15	x	x	PUNCT
ejpam-300	90	16	such	such	ADJ
ejpam-300	90	17	that	that	PRON
ejpam-300	90	18	x	x	PROPN
ejpam-300	90	19	/∈	/∈	PUNCT
ejpam-300	91	1	a	a	INTJ
ejpam-300	91	2	.	.	PUNCT
ejpam-300	92	1	if	if	SCONJ
ejpam-300	92	2	ax	ax	NOUN
ejpam-300	92	3	=	=	PUNCT
ejpam-300	92	4	{	{	PUNCT
ejpam-300	92	5	b	b	NOUN
ejpam-300	92	6	:	:	PUNCT
ejpam-300	92	7	b	b	NOUN
ejpam-300	92	8	is	be	AUX
ejpam-300	92	9	a	a	DET
ejpam-300	92	10	γ	γ	NOUN
ejpam-300	92	11	-	-	ADJ
ejpam-300	92	12	open	open	ADJ
ejpam-300	92	13	nbd	nbd	PROPN
ejpam-300	92	14	of	of	ADP
ejpam-300	92	15	x	x	X
ejpam-300	92	16	}	}	PUNCT
ejpam-300	92	17	.	.	PUNCT
ejpam-300	93	1	then	then	ADV
ejpam-300	93	2	ax	ax	NOUN
ejpam-300	93	3	∩	∩	X
ejpam-300	93	4	a=	a=	VERB
ejpam-300	93	5	φ	φ	PROPN
ejpam-300	93	6	or	or	CCONJ
ejpam-300	93	7	a⊆	a⊆	PROPN
ejpam-300	93	8	ax	ax	NOUN
ejpam-300	93	9	.	.	PUNCT
ejpam-300	94	1	if	if	SCONJ
ejpam-300	94	2	γ(x	γ(x	NOUN
ejpam-300	94	3	)	)	PUNCT
ejpam-300	94	4	denotes	denote	VERB
ejpam-300	94	5	the	the	DET
ejpam-300	94	6	class	class	NOUN
ejpam-300	94	7	of	of	ADP
ejpam-300	94	8	monotone	monotone	ADJ
ejpam-300	94	9	operators	operator	NOUN
ejpam-300	94	10	,	,	PUNCT
ejpam-300	94	11	then	then	ADV
ejpam-300	94	12	we	we	PRON
ejpam-300	94	13	have	have	VERB
ejpam-300	94	14	:	:	PUNCT
ejpam-300	94	15	corollary	corollary	ADJ
ejpam-300	94	16	3.2	3.2	NUM
ejpam-300	94	17	.	.	PUNCT
ejpam-300	95	1	let	let	VERB
ejpam-300	95	2	x	x	PRON
ejpam-300	95	3	be	be	AUX
ejpam-300	95	4	a	a	DET
ejpam-300	95	5	space	space	NOUN
ejpam-300	95	6	and	and	CCONJ
ejpam-300	95	7	γ	γ	NOUN
ejpam-300	95	8	∈	∈	PROPN
ejpam-300	95	9	γ(x	γ(x	PROPN
ejpam-300	95	10	)	)	PUNCT
ejpam-300	95	11	.	.	PUNCT
ejpam-300	96	1	if	if	SCONJ
ejpam-300	96	2	a	a	PRON
ejpam-300	96	3	is	be	AUX
ejpam-300	96	4	a	a	DET
ejpam-300	96	5	nonempty	nonempty	ADJ
ejpam-300	96	6	minimal	minimal	ADJ
ejpam-300	96	7	γ	γ	X
ejpam-300	96	8	-	-	ADJ
ejpam-300	96	9	open	open	ADJ
ejpam-300	96	10	set	set	NOUN
ejpam-300	96	11	of	of	ADP
ejpam-300	96	12	x	x	NOUN
ejpam-300	96	13	,	,	PUNCT
ejpam-300	96	14	then	then	ADV
ejpam-300	96	15	for	for	ADP
ejpam-300	96	16	a	a	DET
ejpam-300	96	17	nonempty	nonempty	NOUN
ejpam-300	96	18	subset	subset	VERB
ejpam-300	96	19	c	c	NOUN
ejpam-300	96	20	of	of	ADP
ejpam-300	96	21	a	a	PRON
ejpam-300	96	22	,	,	PUNCT
ejpam-300	96	23	a⊆	a⊆	PROPN
ejpam-300	96	24	clγ(c	clγ(c	NOUN
ejpam-300	96	25	)	)	PUNCT
ejpam-300	96	26	,	,	PUNCT
ejpam-300	96	27	where	where	SCONJ
ejpam-300	96	28	γ	γ	NOUN
ejpam-300	96	29	is	be	AUX
ejpam-300	96	30	regular	regular	ADJ
ejpam-300	96	31	.	.	PUNCT
ejpam-300	97	1	proof	proof	NOUN
ejpam-300	97	2	.	.	PUNCT
ejpam-300	98	1	let	let	VERB
ejpam-300	98	2	c	c	PRON
ejpam-300	98	3	be	be	AUX
ejpam-300	98	4	any	any	DET
ejpam-300	98	5	nonempty	nonempty	NOUN
ejpam-300	98	6	subset	subset	NOUN
ejpam-300	98	7	of	of	ADP
ejpam-300	98	8	a.	a.	NOUN
ejpam-300	98	9	let	let	VERB
ejpam-300	98	10	y	y	PROPN
ejpam-300	98	11	∈	∈	PROPN
ejpam-300	98	12	a	a	PRON
ejpam-300	98	13	and	and	CCONJ
ejpam-300	98	14	b	b	NOUN
ejpam-300	98	15	be	be	AUX
ejpam-300	98	16	any	any	DET
ejpam-300	98	17	γ	γ	X
ejpam-300	98	18	-	-	ADJ
ejpam-300	98	19	open	open	ADJ
ejpam-300	98	20	nbd	nbd	PROPN
ejpam-300	98	21	b	b	PROPN
ejpam-300	98	22	of	of	ADP
ejpam-300	98	23	y.	y.	NOUN
ejpam-300	98	24	by	by	ADP
ejpam-300	98	25	proposition	proposition	NOUN
ejpam-300	98	26	3.3	3.3	NUM
ejpam-300	98	27	,	,	PUNCT
ejpam-300	98	28	we	we	PRON
ejpam-300	98	29	have	have	VERB
ejpam-300	98	30	a⊆	a⊆	PROPN
ejpam-300	98	31	b.	b.	PROPN
ejpam-300	99	1	also	also	ADV
ejpam-300	99	2	since	since	SCONJ
ejpam-300	99	3	γ	γ	PROPN
ejpam-300	99	4	is	be	AUX
ejpam-300	99	5	monotone	monotone	ADJ
ejpam-300	99	6	,	,	PUNCT
ejpam-300	99	7	c	c	NOUN
ejpam-300	99	8	=	=	SYM
ejpam-300	99	9	aγ	aγ	NOUN
ejpam-300	99	10	∩	∩	NOUN
ejpam-300	99	11	c	c	PROPN
ejpam-300	99	12	⊆	⊆	NUM
ejpam-300	99	13	bγ	bγ	PROPN
ejpam-300	99	14	∩	∩	ADJ
ejpam-300	99	15	c	c	NOUN
ejpam-300	99	16	.	.	PUNCT
ejpam-300	100	1	thus	thus	ADV
ejpam-300	100	2	we	we	PRON
ejpam-300	100	3	have	have	VERB
ejpam-300	100	4	bγ∩c	bγ∩c	NOUN
ejpam-300	100	5	6=	6=	NUM
ejpam-300	100	6	φ	φ	NOUN
ejpam-300	100	7	and	and	CCONJ
ejpam-300	100	8	hence	hence	ADV
ejpam-300	100	9	y	y	PROPN
ejpam-300	100	10	∈	∈	PROPN
ejpam-300	100	11	clγ(c)[4	clγ(c)[4	PROPN
ejpam-300	100	12	]	]	PUNCT
ejpam-300	100	13	.	.	PUNCT
ejpam-300	101	1	this	this	PRON
ejpam-300	101	2	implies	imply	VERB
ejpam-300	101	3	that	that	PRON
ejpam-300	101	4	a⊆	a⊆	VERB
ejpam-300	101	5	clγ(c	clγ(c	PROPN
ejpam-300	101	6	)	)	PUNCT
ejpam-300	101	7	.	.	PUNCT
ejpam-300	102	1	this	this	PRON
ejpam-300	102	2	completes	complete	VERB
ejpam-300	102	3	the	the	DET
ejpam-300	102	4	proof	proof	NOUN
ejpam-300	102	5	.	.	PUNCT
ejpam-300	103	1	proposition	proposition	NOUN
ejpam-300	103	2	3.5	3.5	NUM
ejpam-300	103	3	.	.	PUNCT
ejpam-300	104	1	let	let	VERB
ejpam-300	104	2	a	a	PRON
ejpam-300	104	3	be	be	AUX
ejpam-300	104	4	a	a	DET
ejpam-300	104	5	nonempty	nonempty	ADV
ejpam-300	104	6	γ	γ	ADJ
ejpam-300	104	7	-	-	ADJ
ejpam-300	104	8	open	open	ADJ
ejpam-300	104	9	subset	subset	NOUN
ejpam-300	104	10	of	of	ADP
ejpam-300	104	11	a	a	DET
ejpam-300	104	12	space	space	NOUN
ejpam-300	104	13	x	x	X
ejpam-300	104	14	.	.	PUNCT
ejpam-300	105	1	if	if	SCONJ
ejpam-300	105	2	a⊆	a⊆	VERB
ejpam-300	105	3	clγ(c	clγ(c	PROPN
ejpam-300	105	4	)	)	PUNCT
ejpam-300	105	5	,	,	PUNCT
ejpam-300	105	6	then	then	ADV
ejpam-300	105	7	clγ(a	clγ(a	PROPN
ejpam-300	105	8	)	)	PUNCT
ejpam-300	105	9	=	=	SYM
ejpam-300	105	10	clγ(c	clγ(c	PROPN
ejpam-300	105	11	)	)	PUNCT
ejpam-300	105	12	,	,	PUNCT
ejpam-300	105	13	for	for	ADP
ejpam-300	105	14	any	any	DET
ejpam-300	105	15	nonempty	nonempty	NOUN
ejpam-300	105	16	subset	subset	VERB
ejpam-300	105	17	c	c	NOUN
ejpam-300	105	18	of	of	ADP
ejpam-300	105	19	a	a	PRON
ejpam-300	105	20	,	,	PUNCT
ejpam-300	105	21	where	where	SCONJ
ejpam-300	105	22	γ	γ	NOUN
ejpam-300	105	23	is	be	AUX
ejpam-300	105	24	open	open	ADJ
ejpam-300	105	25	.	.	PUNCT
ejpam-300	106	1	proof	proof	NOUN
ejpam-300	106	2	.	.	PUNCT
ejpam-300	107	1	since	since	SCONJ
ejpam-300	107	2	for	for	ADP
ejpam-300	107	3	any	any	DET
ejpam-300	107	4	nonempty	nonempty	ADJ
ejpam-300	107	5	c	c	NOUN
ejpam-300	107	6	such	such	ADJ
ejpam-300	107	7	that	that	SCONJ
ejpam-300	107	8	c	c	PROPN
ejpam-300	107	9	⊆	⊆	NUM
ejpam-300	107	10	a	a	DET
ejpam-300	107	11	implies	implie	NOUN
ejpam-300	107	12	clγ(c	clγ(c	PROPN
ejpam-300	107	13	)	)	PUNCT
ejpam-300	107	14	⊆	⊆	NUM
ejpam-300	107	15	clγ(a	clγ(a	PROPN
ejpam-300	107	16	)	)	PUNCT
ejpam-300	107	17	.	.	PUNCT
ejpam-300	108	1	on	on	ADP
ejpam-300	108	2	the	the	DET
ejpam-300	108	3	other	other	ADJ
ejpam-300	108	4	hand	hand	NOUN
ejpam-300	108	5	,	,	PUNCT
ejpam-300	108	6	by	by	ADP
ejpam-300	108	7	supposition	supposition	NOUN
ejpam-300	108	8	we	we	PRON
ejpam-300	108	9	have	have	AUX
ejpam-300	108	10	a⊆	a⊆	VERB
ejpam-300	108	11	clγ(c	clγ(c	PROPN
ejpam-300	108	12	)	)	PUNCT
ejpam-300	108	13	.	.	PUNCT
ejpam-300	109	1	since	since	SCONJ
ejpam-300	109	2	γ	γ	X
ejpam-300	109	3	is	be	AUX
ejpam-300	109	4	open	open	ADJ
ejpam-300	109	5	,	,	PUNCT
ejpam-300	109	6	clγ(a)⊆	clγ(a)⊆	PROPN
ejpam-300	109	7	clγ(clγ(c	clγ(clγ(c	NOUN
ejpam-300	109	8	)	)	PUNCT
ejpam-300	109	9	)	)	PUNCT
ejpam-300	110	1	=	=	PUNCT
ejpam-300	110	2	clγ(c)[4	clγ(c)[4	PROPN
ejpam-300	110	3	]	]	PUNCT
ejpam-300	110	4	implies	imply	VERB
ejpam-300	110	5	clγ(a	clγ(a	PROPN
ejpam-300	110	6	)	)	PUNCT
ejpam-300	110	7	⊆	⊆	NUM
ejpam-300	110	8	clγ(c	clγ(c	NUM
ejpam-300	110	9	)	)	PUNCT
ejpam-300	110	10	.	.	PUNCT
ejpam-300	111	1	hence	hence	ADV
ejpam-300	111	2	the	the	DET
ejpam-300	111	3	proof	proof	NOUN
ejpam-300	111	4	.	.	PUNCT
ejpam-300	112	1	the	the	DET
ejpam-300	112	2	following	follow	VERB
ejpam-300	112	3	example	example	NOUN
ejpam-300	112	4	shows	show	VERB
ejpam-300	112	5	that	that	SCONJ
ejpam-300	112	6	the	the	DET
ejpam-300	112	7	condition	condition	NOUN
ejpam-300	112	8	that	that	SCONJ
ejpam-300	112	9	γ	γ	NOUN
ejpam-300	112	10	is	be	AUX
ejpam-300	112	11	open	open	ADJ
ejpam-300	112	12	is	be	AUX
ejpam-300	112	13	necessary	necessary	ADJ
ejpam-300	112	14	for	for	ADP
ejpam-300	112	15	the	the	DET
ejpam-300	112	16	above	above	ADJ
ejpam-300	112	17	proposition	proposition	NOUN
ejpam-300	112	18	.	.	PUNCT
ejpam-300	113	1	example	example	NOUN
ejpam-300	113	2	3.3	3.3	NUM
ejpam-300	113	3	.	.	PUNCT
ejpam-300	114	1	let	let	VERB
ejpam-300	114	2	x=	x=	PUNCT
ejpam-300	115	1	{	{	PUNCT
ejpam-300	115	2	a	a	DET
ejpam-300	115	3	,	,	PUNCT
ejpam-300	115	4	b	b	NOUN
ejpam-300	115	5	,	,	PUNCT
ejpam-300	115	6	c	c	NOUN
ejpam-300	115	7	}	}	PUNCT
ejpam-300	115	8	,	,	PUNCT
ejpam-300	115	9	τ	τ	X
ejpam-300	115	10	=	=	PUNCT
ejpam-300	115	11	{	{	PUNCT
ejpam-300	115	12	φ	φ	PROPN
ejpam-300	115	13	,	,	PUNCT
ejpam-300	115	14	x	x	INTJ
ejpam-300	115	15	,	,	PUNCT
ejpam-300	115	16	{	{	PUNCT
ejpam-300	115	17	a	a	NOUN
ejpam-300	115	18	}	}	PUNCT
ejpam-300	115	19	,	,	PUNCT
ejpam-300	115	20	{	{	PUNCT
ejpam-300	115	21	b	b	NOUN
ejpam-300	115	22	}	}	PUNCT
ejpam-300	115	23	,	,	PUNCT
ejpam-300	115	24	{	{	PUNCT
ejpam-300	115	25	a	a	DET
ejpam-300	115	26	,	,	PUNCT
ejpam-300	115	27	b	b	NOUN
ejpam-300	115	28	}	}	PUNCT
ejpam-300	115	29	,	,	PUNCT
ejpam-300	115	30	{	{	PUNCT
ejpam-300	115	31	a	a	PRON
ejpam-300	115	32	,	,	PUNCT
ejpam-300	115	33	c	c	NOUN
ejpam-300	115	34	}	}	PUNCT
ejpam-300	115	35	}	}	PUNCT
ejpam-300	115	36	.	.	PUNCT
ejpam-300	116	1	for	for	ADP
ejpam-300	116	2	b	b	PROPN
ejpam-300	116	3	∈	∈	PROPN
ejpam-300	116	4	x	x	PUNCT
ejpam-300	116	5	,	,	PUNCT
ejpam-300	116	6	define	define	VERB
ejpam-300	116	7	an	an	DET
ejpam-300	116	8	operation	operation	NOUN
ejpam-300	116	9	γ	γ	X
ejpam-300	116	10	:	:	PUNCT
ejpam-300	116	11	τ→	τ→	PUNCT
ejpam-300	116	12	p(x	p(x	PROPN
ejpam-300	116	13	)	)	PUNCT
ejpam-300	116	14	by	by	ADP
ejpam-300	116	15	s.	s.	PROPN
ejpam-300	116	16	hussain	hussain	PROPN
ejpam-300	116	17	and	and	CCONJ
ejpam-300	116	18	b.	b.	PROPN
ejpam-300	116	19	ahmad	ahmad	PROPN
ejpam-300	116	20	/	/	SYM
ejpam-300	116	21	eur	eur	PROPN
ejpam-300	116	22	.	.	PUNCT
ejpam-300	117	1	j.	j.	PROPN
ejpam-300	117	2	pure	pure	PROPN
ejpam-300	117	3	appl	appl	PROPN
ejpam-300	117	4	.	.	PROPN
ejpam-300	117	5	math	math	PROPN
ejpam-300	117	6	,	,	PUNCT
ejpam-300	117	7	2	2	NUM
ejpam-300	117	8	(	(	PUNCT
ejpam-300	117	9	2009	2009	NUM
ejpam-300	117	10	)	)	PUNCT
ejpam-300	117	11	,	,	PUNCT
ejpam-300	117	12	(	(	PUNCT
ejpam-300	117	13	338	338	NUM
ejpam-300	117	14	-	-	SYM
ejpam-300	117	15	351	351	NUM
ejpam-300	117	16	)	)	PUNCT
ejpam-300	117	17	343	343	NUM
ejpam-300	117	18	γ(a	γ(a	NOUN
ejpam-300	117	19	)	)	PUNCT
ejpam-300	118	1	=	=	PUNCT
ejpam-300	118	2	aγ	aγ	NOUN
ejpam-300	118	3	=	=	PUNCT
ejpam-300	118	4			PROPN
ejpam-300	118	5			ADJ
ejpam-300	118	6			NOUN
ejpam-300	118	7	cl(a	cl(a	PUNCT
ejpam-300	118	8	)	)	PUNCT
ejpam-300	118	9	,	,	PUNCT
ejpam-300	118	10	if	if	SCONJ
ejpam-300	118	11	b	b	PROPN
ejpam-300	118	12	∈	∈	PROPN
ejpam-300	118	13	a	a	DET
ejpam-300	118	14	int(cl(a	int(cl(a	PROPN
ejpam-300	118	15	)	)	PUNCT
ejpam-300	118	16	)	)	PUNCT
ejpam-300	118	17	,	,	PUNCT
ejpam-300	118	18	if	if	SCONJ
ejpam-300	118	19	b	b	PROPN
ejpam-300	118	20	6∈	6∈	NOUN
ejpam-300	118	21	a.	a.	NOUN
ejpam-300	118	22	then	then	ADV
ejpam-300	118	23	the	the	DET
ejpam-300	118	24	operation	operation	NOUN
ejpam-300	118	25	γ	γ	NOUN
ejpam-300	118	26	is	be	AUX
ejpam-300	118	27	not	not	PART
ejpam-300	118	28	open	open	ADJ
ejpam-300	118	29	.	.	PUNCT
ejpam-300	119	1	the	the	DET
ejpam-300	119	2	γ	γ	NOUN
ejpam-300	119	3	-	-	ADJ
ejpam-300	119	4	open	open	ADJ
ejpam-300	119	5	sets	set	NOUN
ejpam-300	119	6	are	be	AUX
ejpam-300	119	7	φ	φ	NUM
ejpam-300	119	8	,	,	PUNCT
ejpam-300	119	9	x	x	PRON
ejpam-300	119	10	,	,	PUNCT
ejpam-300	119	11	{	{	PUNCT
ejpam-300	119	12	b	b	NOUN
ejpam-300	119	13	}	}	PUNCT
ejpam-300	119	14	,	,	PUNCT
ejpam-300	119	15	{	{	PUNCT
ejpam-300	119	16	a	a	X
ejpam-300	119	17	,	,	PUNCT
ejpam-300	119	18	c	c	NOUN
ejpam-300	119	19	}	}	PUNCT
ejpam-300	119	20	.	.	PUNCT
ejpam-300	120	1	let	let	VERB
ejpam-300	120	2	a=	a=	VERB
ejpam-300	120	3	{	{	PUNCT
ejpam-300	120	4	b	b	NOUN
ejpam-300	120	5	}	}	PUNCT
ejpam-300	120	6	and	and	CCONJ
ejpam-300	120	7	c	c	X
ejpam-300	120	8	=	=	PUNCT
ejpam-300	120	9	{	{	PUNCT
ejpam-300	120	10	a	a	DET
ejpam-300	120	11	,	,	PUNCT
ejpam-300	120	12	b	b	NOUN
ejpam-300	120	13	}	}	PUNCT
ejpam-300	120	14	,	,	PUNCT
ejpam-300	120	15	then	then	ADV
ejpam-300	120	16	clγ(a	clγ(a	PROPN
ejpam-300	120	17	)	)	PUNCT
ejpam-300	120	18	=	=	PRON
ejpam-300	120	19	{	{	PUNCT
ejpam-300	120	20	b	b	NOUN
ejpam-300	120	21	}	}	PUNCT
ejpam-300	120	22	6=	6=	NOUN
ejpam-300	120	23	x	x	SYM
ejpam-300	120	24	=	=	SYM
ejpam-300	120	25	clγ(c	clγ(c	PROPN
ejpam-300	120	26	)	)	PUNCT
ejpam-300	120	27	.	.	PUNCT
ejpam-300	121	1	proposition	proposition	NOUN
ejpam-300	121	2	3.6	3.6	NUM
ejpam-300	121	3	.	.	PUNCT
ejpam-300	122	1	let	let	VERB
ejpam-300	122	2	a	a	PRON
ejpam-300	122	3	be	be	AUX
ejpam-300	122	4	a	a	DET
ejpam-300	122	5	nonempty	nonempty	ADV
ejpam-300	122	6	γ	γ	ADJ
ejpam-300	122	7	-	-	ADJ
ejpam-300	122	8	open	open	ADJ
ejpam-300	122	9	subset	subset	NOUN
ejpam-300	122	10	of	of	ADP
ejpam-300	122	11	a	a	DET
ejpam-300	122	12	space	space	NOUN
ejpam-300	122	13	x.	x.	NOUN
ejpam-300	123	1	if	if	SCONJ
ejpam-300	123	2	clγ(a	clγ(a	PROPN
ejpam-300	123	3	)	)	PUNCT
ejpam-300	123	4	=	=	SYM
ejpam-300	123	5	clγ(c	clγ(c	PROPN
ejpam-300	123	6	)	)	PUNCT
ejpam-300	123	7	,	,	PUNCT
ejpam-300	123	8	for	for	ADP
ejpam-300	123	9	any	any	DET
ejpam-300	123	10	nonempty	nonempty	NOUN
ejpam-300	123	11	subset	subset	VERB
ejpam-300	123	12	c	c	NOUN
ejpam-300	123	13	of	of	ADP
ejpam-300	123	14	a	a	PRON
ejpam-300	123	15	,	,	PUNCT
ejpam-300	123	16	then	then	ADV
ejpam-300	123	17	a	a	PRON
ejpam-300	123	18	is	be	AUX
ejpam-300	123	19	a	a	DET
ejpam-300	123	20	minimal	minimal	ADJ
ejpam-300	123	21	γ	γ	X
ejpam-300	123	22	-	-	ADJ
ejpam-300	123	23	open	open	ADJ
ejpam-300	123	24	set	set	NOUN
ejpam-300	123	25	.	.	PUNCT
ejpam-300	124	1	proof	proof	NOUN
ejpam-300	124	2	.	.	PUNCT
ejpam-300	125	1	we	we	PRON
ejpam-300	125	2	suppose	suppose	VERB
ejpam-300	125	3	on	on	ADP
ejpam-300	125	4	the	the	DET
ejpam-300	125	5	contrary	contrary	NOUN
ejpam-300	125	6	that	that	SCONJ
ejpam-300	125	7	a	a	PRON
ejpam-300	125	8	is	be	AUX
ejpam-300	125	9	not	not	PART
ejpam-300	125	10	a	a	DET
ejpam-300	125	11	minimal	minimal	ADJ
ejpam-300	125	12	γ	γ	X
ejpam-300	125	13	-	-	ADJ
ejpam-300	125	14	open	open	ADJ
ejpam-300	125	15	set	set	NOUN
ejpam-300	125	16	.	.	PUNCT
ejpam-300	126	1	then	then	ADV
ejpam-300	126	2	there	there	PRON
ejpam-300	126	3	exists	exist	VERB
ejpam-300	126	4	a	a	DET
ejpam-300	126	5	nonempty	nonempty	ADV
ejpam-300	126	6	γ	γ	X
ejpam-300	126	7	-	-	ADJ
ejpam-300	126	8	open	open	ADJ
ejpam-300	126	9	set	set	NOUN
ejpam-300	126	10	d	d	ADP
ejpam-300	126	11	such	such	ADJ
ejpam-300	126	12	that	that	SCONJ
ejpam-300	126	13	d	d	PROPN
ejpam-300	126	14	⊆	⊆	SYM
ejpam-300	126	15	a	a	PRON
ejpam-300	126	16	and	and	CCONJ
ejpam-300	126	17	hence	hence	ADV
ejpam-300	126	18	there	there	PRON
ejpam-300	126	19	exists	exist	VERB
ejpam-300	126	20	an	an	DET
ejpam-300	126	21	element	element	NOUN
ejpam-300	126	22	x	x	SYM
ejpam-300	126	23	∈	∈	PROPN
ejpam-300	126	24	a	a	DET
ejpam-300	126	25	such	such	ADJ
ejpam-300	126	26	that	that	PRON
ejpam-300	126	27	x	x	X
ejpam-300	126	28	/∈	/∈	PROPN
ejpam-300	126	29	d.	d.	PROPN
ejpam-300	127	1	then	then	ADV
ejpam-300	127	2	we	we	PRON
ejpam-300	127	3	have	have	VERB
ejpam-300	127	4	clγ({x	clγ({x	NOUN
ejpam-300	127	5	}	}	PUNCT
ejpam-300	127	6	)	)	PUNCT
ejpam-300	128	1	⊆	⊆	NUM
ejpam-300	128	2	dγ	dγ	NOUN
ejpam-300	128	3	implies	imply	VERB
ejpam-300	128	4	that	that	SCONJ
ejpam-300	128	5	clγ({x	clγ({x	NOUN
ejpam-300	128	6	}	}	PUNCT
ejpam-300	128	7	)	)	PUNCT
ejpam-300	128	8	6=	6=	ADP
ejpam-300	128	9	clγ(a	clγ(a	PROPN
ejpam-300	128	10	)	)	PUNCT
ejpam-300	128	11	.	.	PUNCT
ejpam-300	129	1	this	this	DET
ejpam-300	129	2	contradiction	contradiction	NOUN
ejpam-300	129	3	proves	prove	VERB
ejpam-300	129	4	the	the	DET
ejpam-300	129	5	proposition	proposition	NOUN
ejpam-300	129	6	.	.	PUNCT
ejpam-300	130	1	combining	combine	VERB
ejpam-300	130	2	propositions	proposition	NOUN
ejpam-300	130	3	3.4	3.4	NUM
ejpam-300	130	4	,	,	PUNCT
ejpam-300	130	5	3.5	3.5	NUM
ejpam-300	130	6	and	and	CCONJ
ejpam-300	130	7	3.6	3.6	NUM
ejpam-300	130	8	,	,	PUNCT
ejpam-300	130	9	we	we	PRON
ejpam-300	130	10	have	have	AUX
ejpam-300	130	11	:	:	PUNCT
ejpam-300	130	12	theorem	theorem	VERB
ejpam-300	130	13	3.1	3.1	NUM
ejpam-300	130	14	.	.	PUNCT
ejpam-300	131	1	let	let	VERB
ejpam-300	131	2	a	a	PRON
ejpam-300	131	3	be	be	AUX
ejpam-300	131	4	a	a	DET
ejpam-300	131	5	nonempty	nonempty	ADV
ejpam-300	131	6	γ	γ	ADJ
ejpam-300	131	7	-	-	ADJ
ejpam-300	131	8	open	open	ADJ
ejpam-300	131	9	subset	subset	NOUN
ejpam-300	131	10	of	of	ADP
ejpam-300	131	11	space	space	NOUN
ejpam-300	131	12	x	x	X
ejpam-300	131	13	and	and	CCONJ
ejpam-300	131	14	γ	γ	PROPN
ejpam-300	131	15	∈	∈	PROPN
ejpam-300	131	16	γ(x	γ(x	PROPN
ejpam-300	131	17	)	)	PUNCT
ejpam-300	131	18	.	.	PUNCT
ejpam-300	132	1	then	then	ADV
ejpam-300	132	2	the	the	DET
ejpam-300	132	3	following	follow	VERB
ejpam-300	132	4	are	be	AUX
ejpam-300	132	5	equivalent	equivalent	ADJ
ejpam-300	132	6	:	:	PUNCT
ejpam-300	132	7	(	(	PUNCT
ejpam-300	132	8	1	1	X
ejpam-300	132	9	)	)	PUNCT
ejpam-300	132	10	a	a	PRON
ejpam-300	132	11	is	be	AUX
ejpam-300	132	12	minimal	minimal	ADJ
ejpam-300	132	13	γ	γ	X
ejpam-300	132	14	-	-	ADJ
ejpam-300	132	15	open	open	ADJ
ejpam-300	132	16	set	set	NOUN
ejpam-300	132	17	,	,	PUNCT
ejpam-300	132	18	where	where	SCONJ
ejpam-300	132	19	γ	γ	PROPN
ejpam-300	132	20	is	be	AUX
ejpam-300	132	21	regular	regular	ADJ
ejpam-300	132	22	.	.	PUNCT
ejpam-300	133	1	(	(	PUNCT
ejpam-300	133	2	2	2	X
ejpam-300	133	3	)	)	PUNCT
ejpam-300	133	4	for	for	ADP
ejpam-300	133	5	any	any	DET
ejpam-300	133	6	nonempty	nonempty	NOUN
ejpam-300	133	7	subset	subset	VERB
ejpam-300	133	8	c	c	NOUN
ejpam-300	133	9	of	of	ADP
ejpam-300	133	10	a	a	DET
ejpam-300	133	11	,	,	PUNCT
ejpam-300	133	12	a⊆	a⊆	PROPN
ejpam-300	133	13	clγ(a	clγ(a	PROPN
ejpam-300	133	14	)	)	PUNCT
ejpam-300	133	15	,	,	PUNCT
ejpam-300	133	16	where	where	SCONJ
ejpam-300	133	17	γ	γ	NOUN
ejpam-300	133	18	is	be	AUX
ejpam-300	133	19	open	open	ADJ
ejpam-300	133	20	.	.	PUNCT
ejpam-300	134	1	(	(	PUNCT
ejpam-300	134	2	3	3	X
ejpam-300	134	3	)	)	PUNCT
ejpam-300	134	4	for	for	ADP
ejpam-300	134	5	any	any	DET
ejpam-300	134	6	nonempty	nonempty	NOUN
ejpam-300	134	7	subset	subset	VERB
ejpam-300	134	8	c	c	NOUN
ejpam-300	134	9	of	of	ADP
ejpam-300	134	10	a	a	DET
ejpam-300	134	11	,	,	PUNCT
ejpam-300	134	12	clγ(a	clγ(a	PROPN
ejpam-300	134	13	)	)	PUNCT
ejpam-300	134	14	=	=	SYM
ejpam-300	134	15	clγ(c	clγ(c	PROPN
ejpam-300	134	16	)	)	PUNCT
ejpam-300	134	17	.	.	PUNCT
ejpam-300	135	1	definition	definition	NOUN
ejpam-300	135	2	3.2	3.2	NUM
ejpam-300	135	3	.	.	PUNCT
ejpam-300	136	1	let	let	VERB
ejpam-300	136	2	x	x	PRON
ejpam-300	136	3	be	be	AUX
ejpam-300	136	4	a	a	DET
ejpam-300	136	5	space	space	NOUN
ejpam-300	136	6	and	and	CCONJ
ejpam-300	136	7	a	a	DET
ejpam-300	136	8	⊆	⊆	NUM
ejpam-300	136	9	x	x	SYM
ejpam-300	136	10	.	.	PUNCT
ejpam-300	137	1	then	then	ADV
ejpam-300	137	2	a	a	PRON
ejpam-300	137	3	is	be	AUX
ejpam-300	137	4	called	call	VERB
ejpam-300	137	5	a	a	DET
ejpam-300	137	6	pre	pre	ADJ
ejpam-300	137	7	-	-	ADJ
ejpam-300	137	8	γ	γ	ADJ
ejpam-300	137	9	-	-	ADJ
ejpam-300	137	10	open	open	ADJ
ejpam-300	137	11	set	set	NOUN
ejpam-300	137	12	,	,	PUNCT
ejpam-300	137	13	if	if	SCONJ
ejpam-300	137	14	a⊆	a⊆	VERB
ejpam-300	137	15	intγ(clγ(a	intγ(clγ(a	NOUN
ejpam-300	137	16	)	)	PUNCT
ejpam-300	137	17	)	)	PUNCT
ejpam-300	137	18	.	.	PUNCT
ejpam-300	138	1	the	the	DET
ejpam-300	138	2	family	family	NOUN
ejpam-300	138	3	of	of	ADP
ejpam-300	138	4	all	all	DET
ejpam-300	138	5	pre	pre	ADJ
ejpam-300	138	6	-	-	ADJ
ejpam-300	138	7	γ	γ	ADJ
ejpam-300	138	8	-	-	ADJ
ejpam-300	138	9	open	open	ADJ
ejpam-300	138	10	sets	set	NOUN
ejpam-300	138	11	of	of	ADP
ejpam-300	138	12	x	x	PUNCT
ejpam-300	138	13	will	will	AUX
ejpam-300	138	14	be	be	AUX
ejpam-300	138	15	denoted	denote	VERB
ejpam-300	138	16	by	by	ADP
ejpam-300	138	17	poγ(x	poγ(x	PROPN
ejpam-300	138	18	)	)	PUNCT
ejpam-300	138	19	.	.	PUNCT
ejpam-300	139	1	in	in	ADP
ejpam-300	139	2	view	view	NOUN
ejpam-300	139	3	of	of	ADP
ejpam-300	139	4	the	the	DET
ejpam-300	139	5	definition	definition	NOUN
ejpam-300	139	6	of	of	ADP
ejpam-300	139	7	a	a	DET
ejpam-300	139	8	pre	pre	ADJ
ejpam-300	139	9	-	-	ADJ
ejpam-300	139	10	hausdorff	hausdorff	ADJ
ejpam-300	139	11	space	space	NOUN
ejpam-300	139	12	[	[	X
ejpam-300	139	13	3	3	NUM
ejpam-300	139	14	]	]	PUNCT
ejpam-300	139	15	,	,	PUNCT
ejpam-300	139	16	we	we	PRON
ejpam-300	139	17	define	define	VERB
ejpam-300	139	18	a	a	DET
ejpam-300	139	19	γ	γ	NOUN
ejpam-300	139	20	-	-	ADJ
ejpam-300	139	21	t2	t2	ADJ
ejpam-300	139	22	space	space	NOUN
ejpam-300	139	23	as	as	ADP
ejpam-300	139	24	:	:	PUNCT
ejpam-300	139	25	definition	definition	NOUN
ejpam-300	139	26	3.3	3.3	NUM
ejpam-300	139	27	.	.	PUNCT
ejpam-300	140	1	a	a	DET
ejpam-300	140	2	space	space	NOUN
ejpam-300	140	3	x	x	PUNCT
ejpam-300	140	4	is	be	AUX
ejpam-300	140	5	called	call	VERB
ejpam-300	140	6	a	a	DET
ejpam-300	140	7	pre	pre	ADJ
ejpam-300	140	8	γ	γ	PROPN
ejpam-300	140	9	-	-	ADJ
ejpam-300	140	10	t2	t2	ADJ
ejpam-300	140	11	space	space	NOUN
ejpam-300	140	12	,	,	PUNCT
ejpam-300	140	13	if	if	SCONJ
ejpam-300	140	14	for	for	ADP
ejpam-300	140	15	any	any	DET
ejpam-300	140	16	x	x	NOUN
ejpam-300	140	17	,	,	PUNCT
ejpam-300	140	18	y	y	PROPN
ejpam-300	140	19	∈	∈	PROPN
ejpam-300	140	20	x	x	X
ejpam-300	140	21	,	,	PUNCT
ejpam-300	140	22	x	x	PROPN
ejpam-300	140	23	6=	6=	PROPN
ejpam-300	140	24	y	y	PROPN
ejpam-300	140	25	,	,	PUNCT
ejpam-300	140	26	there	there	PRON
ejpam-300	140	27	exist	exist	VERB
ejpam-300	140	28	subsets	subset	NOUN
ejpam-300	140	29	u	u	NOUN
ejpam-300	140	30	and	and	CCONJ
ejpam-300	140	31	v	v	NOUN
ejpam-300	140	32	of	of	ADP
ejpam-300	140	33	poγ(x	poγ(x	NOUN
ejpam-300	140	34	)	)	PUNCT
ejpam-300	140	35	such	such	ADJ
ejpam-300	140	36	that	that	SCONJ
ejpam-300	140	37	x	x	SYM
ejpam-300	140	38	∈	∈	PROPN
ejpam-300	140	39	u	u	NOUN
ejpam-300	140	40	,	,	PUNCT
ejpam-300	140	41	y	y	PROPN
ejpam-300	140	42	∈	∈	PROPN
ejpam-300	140	43	v	v	NOUN
ejpam-300	140	44	and	and	CCONJ
ejpam-300	140	45	u	u	NOUN
ejpam-300	140	46	∩	∩	NOUN
ejpam-300	140	47	v	v	NOUN
ejpam-300	140	48	=	=	SYM
ejpam-300	140	49	φ	φ	PROPN
ejpam-300	140	50	.	.	PUNCT
ejpam-300	141	1	proposition	proposition	NOUN
ejpam-300	141	2	3.7	3.7	NUM
ejpam-300	141	3	.	.	PUNCT
ejpam-300	142	1	let	let	VERB
ejpam-300	142	2	x	x	PRON
ejpam-300	142	3	be	be	AUX
ejpam-300	142	4	a	a	DET
ejpam-300	142	5	space	space	NOUN
ejpam-300	142	6	and	and	CCONJ
ejpam-300	142	7	γ	γ	NOUN
ejpam-300	142	8	∈	∈	PROPN
ejpam-300	142	9	γ(x	γ(x	PROPN
ejpam-300	142	10	)	)	PUNCT
ejpam-300	142	11	.	.	PUNCT
ejpam-300	143	1	if	if	SCONJ
ejpam-300	143	2	a⊆	a⊆	NOUN
ejpam-300	143	3	x	x	VERB
ejpam-300	143	4	is	be	AUX
ejpam-300	143	5	a	a	DET
ejpam-300	143	6	minimal	minimal	ADJ
ejpam-300	143	7	γ	γ	X
ejpam-300	143	8	-	-	ADJ
ejpam-300	143	9	open	open	ADJ
ejpam-300	143	10	set	set	NOUN
ejpam-300	143	11	,	,	PUNCT
ejpam-300	143	12	then	then	ADV
ejpam-300	143	13	φ	φ	PROPN
ejpam-300	143	14	6=	6=	PROPN
ejpam-300	143	15	c	c	PROPN
ejpam-300	143	16	⊆	⊆	NUM
ejpam-300	143	17	a	a	PRON
ejpam-300	143	18	is	be	AUX
ejpam-300	143	19	a	a	DET
ejpam-300	143	20	pre	pre	ADJ
ejpam-300	143	21	-	-	ADJ
ejpam-300	143	22	γ	γ	ADJ
ejpam-300	143	23	-	-	ADJ
ejpam-300	143	24	open	open	ADJ
ejpam-300	143	25	set	set	NOUN
ejpam-300	143	26	,	,	PUNCT
ejpam-300	143	27	where	where	SCONJ
ejpam-300	143	28	γ	γ	PROPN
ejpam-300	143	29	is	be	AUX
ejpam-300	143	30	regular	regular	ADJ
ejpam-300	143	31	.	.	PUNCT
ejpam-300	144	1	s.	s.	PROPN
ejpam-300	144	2	hussain	hussain	PROPN
ejpam-300	144	3	and	and	CCONJ
ejpam-300	144	4	b.	b.	PROPN
ejpam-300	144	5	ahmad	ahmad	PROPN
ejpam-300	144	6	/	/	SYM
ejpam-300	144	7	eur	eur	PROPN
ejpam-300	144	8	.	.	PUNCT
ejpam-300	145	1	j.	j.	PROPN
ejpam-300	145	2	pure	pure	PROPN
ejpam-300	145	3	appl	appl	PROPN
ejpam-300	145	4	.	.	PROPN
ejpam-300	145	5	math	math	PROPN
ejpam-300	145	6	,	,	PUNCT
ejpam-300	145	7	2	2	NUM
ejpam-300	145	8	(	(	PUNCT
ejpam-300	145	9	2009	2009	NUM
ejpam-300	145	10	)	)	PUNCT
ejpam-300	145	11	,	,	PUNCT
ejpam-300	145	12	(	(	PUNCT
ejpam-300	145	13	338	338	NUM
ejpam-300	145	14	-	-	SYM
ejpam-300	145	15	351	351	NUM
ejpam-300	145	16	)	)	PUNCT
ejpam-300	145	17	344	344	NUM
ejpam-300	145	18	proof	proof	NOUN
ejpam-300	145	19	.	.	PUNCT
ejpam-300	146	1	let	let	VERB
ejpam-300	146	2	a	a	PRON
ejpam-300	146	3	be	be	AUX
ejpam-300	146	4	a	a	DET
ejpam-300	146	5	minimal	minimal	ADJ
ejpam-300	146	6	γ	γ	X
ejpam-300	146	7	-	-	ADJ
ejpam-300	146	8	open	open	ADJ
ejpam-300	146	9	set	set	NOUN
ejpam-300	146	10	and	and	CCONJ
ejpam-300	146	11	φ	φ	PROPN
ejpam-300	146	12	6=	6=	PROPN
ejpam-300	146	13	c	c	PROPN
ejpam-300	146	14	⊆	⊆	NUM
ejpam-300	146	15	a.	a.	NOUN
ejpam-300	146	16	by	by	ADP
ejpam-300	146	17	proposition	proposition	NOUN
ejpam-300	146	18	3.6	3.6	NUM
ejpam-300	146	19	,	,	PUNCT
ejpam-300	146	20	we	we	PRON
ejpam-300	146	21	have	have	VERB
ejpam-300	146	22	a	a	DET
ejpam-300	146	23	⊆	⊆	NUM
ejpam-300	146	24	clγ(c	clγ(c	NUM
ejpam-300	146	25	)	)	PUNCT
ejpam-300	146	26	implies	imply	VERB
ejpam-300	146	27	intγ(a	intγ(a	PROPN
ejpam-300	146	28	)	)	PUNCT
ejpam-300	146	29	⊆	⊆	NUM
ejpam-300	146	30	intγ(clγ(c	intγ(clγ(c	NOUN
ejpam-300	146	31	)	)	PUNCT
ejpam-300	146	32	)	)	PUNCT
ejpam-300	146	33	.	.	PUNCT
ejpam-300	147	1	since	since	SCONJ
ejpam-300	147	2	a	a	PRON
ejpam-300	147	3	is	be	AUX
ejpam-300	147	4	a	a	DET
ejpam-300	147	5	γ	γ	NOUN
ejpam-300	147	6	-	-	ADJ
ejpam-300	147	7	open	open	ADJ
ejpam-300	147	8	set	set	NOUN
ejpam-300	147	9	,	,	PUNCT
ejpam-300	147	10	therefore	therefore	ADV
ejpam-300	147	11	c	c	PROPN
ejpam-300	147	12	⊆	⊆	NUM
ejpam-300	147	13	a	a	DET
ejpam-300	147	14	=	=	SYM
ejpam-300	147	15	intγ(a	intγ(a	NOUN
ejpam-300	147	16	)	)	PUNCT
ejpam-300	147	17	⊆	⊆	NUM
ejpam-300	147	18	intγ(clγ(c	intγ(clγ(c	NOUN
ejpam-300	147	19	)	)	PUNCT
ejpam-300	147	20	)	)	PUNCT
ejpam-300	147	21	or	or	CCONJ
ejpam-300	147	22	c	c	PROPN
ejpam-300	147	23	⊆	⊆	NUM
ejpam-300	147	24	intγ(clγ(c	intγ(clγ(c	NOUN
ejpam-300	147	25	)	)	PUNCT
ejpam-300	147	26	)	)	PUNCT
ejpam-300	147	27	,	,	PUNCT
ejpam-300	147	28	that	that	ADV
ejpam-300	147	29	is	is	ADV
ejpam-300	147	30	,	,	PUNCT
ejpam-300	147	31	c	c	PROPN
ejpam-300	147	32	is	be	AUX
ejpam-300	147	33	pre	pre	ADJ
ejpam-300	147	34	-	-	ADJ
ejpam-300	147	35	γ	γ	ADV
ejpam-300	147	36	-	-	ADJ
ejpam-300	147	37	open	open	ADJ
ejpam-300	147	38	.	.	PUNCT
ejpam-300	148	1	hence	hence	ADV
ejpam-300	148	2	the	the	DET
ejpam-300	148	3	proof	proof	NOUN
ejpam-300	148	4	.	.	PUNCT
ejpam-300	149	1	we	we	PRON
ejpam-300	149	2	use	use	VERB
ejpam-300	149	3	theorem	theorem	NOUN
ejpam-300	149	4	3.1(3	3.1(3	NUM
ejpam-300	149	5	)	)	PUNCT
ejpam-300	149	6	and	and	CCONJ
ejpam-300	149	7	prove	prove	VERB
ejpam-300	149	8	the	the	DET
ejpam-300	149	9	following	following	NOUN
ejpam-300	149	10	:	:	PUNCT
ejpam-300	149	11	theorem	theorem	NOUN
ejpam-300	149	12	3.2	3.2	NUM
ejpam-300	149	13	.	.	PUNCT
ejpam-300	150	1	let	let	VERB
ejpam-300	150	2	b	b	X
ejpam-300	150	3	be	be	AUX
ejpam-300	150	4	a	a	DET
ejpam-300	150	5	nonempty	nonempty	ADJ
ejpam-300	150	6	subset	subset	NOUN
ejpam-300	150	7	of	of	ADP
ejpam-300	150	8	a	a	DET
ejpam-300	150	9	space	space	NOUN
ejpam-300	151	1	x.	x.	NOUN
ejpam-300	151	2	let	let	VERB
ejpam-300	151	3	a	a	PRON
ejpam-300	151	4	be	be	AUX
ejpam-300	151	5	a	a	DET
ejpam-300	151	6	minimal	minimal	ADJ
ejpam-300	151	7	γ	γ	X
ejpam-300	151	8	-	-	ADJ
ejpam-300	151	9	open	open	ADJ
ejpam-300	151	10	set	set	NOUN
ejpam-300	151	11	in	in	ADP
ejpam-300	151	12	x	x	PUNCT
ejpam-300	151	13	and	and	CCONJ
ejpam-300	151	14	γ	γ	PROPN
ejpam-300	151	15	∈	∈	PROPN
ejpam-300	151	16	γ(x	γ(x	PROPN
ejpam-300	151	17	)	)	PUNCT
ejpam-300	151	18	.	.	PUNCT
ejpam-300	152	1	if	if	SCONJ
ejpam-300	152	2	there	there	PRON
ejpam-300	152	3	exists	exist	VERB
ejpam-300	152	4	a	a	DET
ejpam-300	152	5	γ	γ	X
ejpam-300	152	6	-	-	ADJ
ejpam-300	152	7	open	open	ADJ
ejpam-300	152	8	set	set	NOUN
ejpam-300	152	9	c	c	NOUN
ejpam-300	152	10	containing	contain	VERB
ejpam-300	152	11	b	b	PROPN
ejpam-300	152	12	such	such	ADJ
ejpam-300	152	13	that	that	SCONJ
ejpam-300	152	14	c	c	PROPN
ejpam-300	152	15	⊆	⊆	NUM
ejpam-300	152	16	clγ(b	clγ(b	X
ejpam-300	152	17	∪	∪	NOUN
ejpam-300	152	18	a	a	PRON
ejpam-300	152	19	)	)	PUNCT
ejpam-300	152	20	,	,	PUNCT
ejpam-300	152	21	then	then	ADV
ejpam-300	152	22	for	for	ADP
ejpam-300	152	23	any	any	DET
ejpam-300	152	24	nonempty	nonempty	NOUN
ejpam-300	152	25	subset	subset	VERB
ejpam-300	152	26	d	d	NOUN
ejpam-300	152	27	of	of	ADP
ejpam-300	152	28	a	a	PRON
ejpam-300	152	29	,	,	PUNCT
ejpam-300	152	30	b	b	NOUN
ejpam-300	152	31	∪	∪	NOUN
ejpam-300	152	32	d	d	X
ejpam-300	152	33	is	be	AUX
ejpam-300	152	34	a	a	DET
ejpam-300	152	35	pre	pre	ADJ
ejpam-300	152	36	-	-	ADJ
ejpam-300	152	37	γ	γ	ADJ
ejpam-300	152	38	-	-	ADJ
ejpam-300	152	39	open	open	ADJ
ejpam-300	152	40	set	set	NOUN
ejpam-300	152	41	,	,	PUNCT
ejpam-300	152	42	where	where	SCONJ
ejpam-300	152	43	γ	γ	PROPN
ejpam-300	152	44	is	be	AUX
ejpam-300	152	45	regular	regular	ADJ
ejpam-300	152	46	and	and	CCONJ
ejpam-300	152	47	open	open	ADJ
ejpam-300	152	48	.	.	PUNCT
ejpam-300	153	1	proof	proof	NOUN
ejpam-300	153	2	.	.	PUNCT
ejpam-300	154	1	suppose	suppose	VERB
ejpam-300	154	2	a	a	PRON
ejpam-300	154	3	is	be	AUX
ejpam-300	154	4	a	a	DET
ejpam-300	154	5	minimal	minimal	ADJ
ejpam-300	154	6	γ	γ	X
ejpam-300	154	7	-	-	ADJ
ejpam-300	154	8	open	open	ADJ
ejpam-300	154	9	set	set	NOUN
ejpam-300	154	10	in	in	ADP
ejpam-300	154	11	x.	x.	NOUN
ejpam-300	154	12	since	since	SCONJ
ejpam-300	154	13	γ	γ	PROPN
ejpam-300	154	14	is	be	AUX
ejpam-300	154	15	regular	regular	ADJ
ejpam-300	154	16	,	,	PUNCT
ejpam-300	154	17	therefore	therefore	ADV
ejpam-300	154	18	for	for	ADP
ejpam-300	154	19	any	any	DET
ejpam-300	154	20	nonempty	nonempty	NOUN
ejpam-300	154	21	subset	subset	VERB
ejpam-300	155	1	d	d	NOUN
ejpam-300	155	2	of	of	ADP
ejpam-300	155	3	a	a	PRON
ejpam-300	155	4	,	,	PUNCT
ejpam-300	155	5	we	we	PRON
ejpam-300	155	6	have	have	VERB
ejpam-300	155	7	clγ(b	clγ(b	PROPN
ejpam-300	155	8	∪	∪	NOUN
ejpam-300	155	9	d	d	NOUN
ejpam-300	155	10	)	)	PUNCT
ejpam-300	155	11	=	=	SYM
ejpam-300	155	12	clγ(b)∪	clγ(b)∪	PROPN
ejpam-300	155	13	clγ(d	clγ(d	PROPN
ejpam-300	155	14	)	)	PUNCT
ejpam-300	155	15	=	=	PUNCT
ejpam-300	156	1	clγ(b)∪	clγ(b)∪	PROPN
ejpam-300	156	2	clγ(a	clγ(a	PROPN
ejpam-300	156	3	)	)	PUNCT
ejpam-300	157	1	=	=	PUNCT
ejpam-300	157	2	clγ(b	clγ(b	X
ejpam-300	157	3	∪	∪	VERB
ejpam-300	157	4	a	a	PRON
ejpam-300	157	5	)	)	PUNCT
ejpam-300	157	6	.	.	PUNCT
ejpam-300	158	1	by	by	ADP
ejpam-300	158	2	supposition	supposition	NOUN
ejpam-300	158	3	,	,	PUNCT
ejpam-300	158	4	we	we	PRON
ejpam-300	158	5	have	have	VERB
ejpam-300	158	6	c	c	NOUN
ejpam-300	158	7	⊆	⊆	NUM
ejpam-300	158	8	clγ(b∪a	clγ(b∪a	NOUN
ejpam-300	158	9	)	)	PUNCT
ejpam-300	158	10	=	=	SYM
ejpam-300	158	11	clγ(b∪d	clγ(b∪d	X
ejpam-300	158	12	)	)	PUNCT
ejpam-300	158	13	implies	imply	VERB
ejpam-300	158	14	intγ(c	intγ(c	NOUN
ejpam-300	158	15	)	)	PUNCT
ejpam-300	158	16	⊆	⊆	NUM
ejpam-300	158	17	intγ(clγ(b∪d	intγ(clγ(b∪d	NUM
ejpam-300	158	18	)	)	PUNCT
ejpam-300	158	19	)	)	PUNCT
ejpam-300	158	20	,	,	PUNCT
ejpam-300	159	1	c	c	X
ejpam-300	159	2	being	be	AUX
ejpam-300	159	3	γ	γ	X
ejpam-300	159	4	-	-	ADJ
ejpam-300	159	5	open	open	ADJ
ejpam-300	159	6	set	set	NOUN
ejpam-300	159	7	such	such	ADJ
ejpam-300	159	8	that	that	DET
ejpam-300	159	9	b	b	NOUN
ejpam-300	159	10	⊆	⊆	NUM
ejpam-300	159	11	c	c	NOUN
ejpam-300	159	12	.	.	PUNCT
ejpam-300	160	1	it	it	PRON
ejpam-300	160	2	follows	follow	VERB
ejpam-300	160	3	that	that	PRON
ejpam-300	160	4	b	b	NOUN
ejpam-300	160	5	⊆	⊆	NUM
ejpam-300	160	6	c	c	NOUN
ejpam-300	160	7	=	=	PUNCT
ejpam-300	160	8	intγ(c)⊆	intγ(c)⊆	NOUN
ejpam-300	160	9	intγ(clγ(b	intγ(clγ(b	CCONJ
ejpam-300	160	10	∪	∪	ADJ
ejpam-300	160	11	d	d	NOUN
ejpam-300	160	12	)	)	PUNCT
ejpam-300	160	13	)	)	PUNCT
ejpam-300	160	14	or	or	CCONJ
ejpam-300	160	15	b	b	NOUN
ejpam-300	160	16	⊆	⊆	NUM
ejpam-300	160	17	intγ(clγ(b	intγ(clγ(b	CCONJ
ejpam-300	160	18	∪	∪	ADJ
ejpam-300	160	19	d	d	NOUN
ejpam-300	160	20	)	)	PUNCT
ejpam-300	160	21	)	)	PUNCT
ejpam-300	160	22	.....	.....	PUNCT
ejpam-300	161	1	(	(	PUNCT
ejpam-300	161	2	1	1	NUM
ejpam-300	161	3	)	)	PUNCT
ejpam-300	161	4	and	and	CCONJ
ejpam-300	161	5	intγ(a	intγ(a	NOUN
ejpam-300	161	6	)	)	PUNCT
ejpam-300	161	7	=	=	PUNCT
ejpam-300	161	8	a⊆	a⊆	PROPN
ejpam-300	161	9	clγ(a	clγ(a	PROPN
ejpam-300	161	10	)	)	PUNCT
ejpam-300	162	1	⊆	⊆	NUM
ejpam-300	162	2	clγ(b)∪	clγ(b)∪	PROPN
ejpam-300	162	3	clγ(a	clγ(a	PROPN
ejpam-300	162	4	)	)	PUNCT
ejpam-300	162	5	=	=	PUNCT
ejpam-300	163	1	clγ(b	clγ(b	NOUN
ejpam-300	163	2	∪	∪	VERB
ejpam-300	163	3	a	a	PRON
ejpam-300	163	4	)	)	PUNCT
ejpam-300	163	5	implies	imply	VERB
ejpam-300	163	6	intγ(a	intγ(a	NOUN
ejpam-300	163	7	)	)	PUNCT
ejpam-300	163	8	⊆	⊆	NUM
ejpam-300	163	9	intγ(clγ(b	intγ(clγ(b	ADP
ejpam-300	163	10	∪	∪	ADP
ejpam-300	163	11	a	a	PRON
ejpam-300	163	12	)	)	PUNCT
ejpam-300	163	13	)	)	PUNCT
ejpam-300	163	14	.....	.....	PUNCT
ejpam-300	164	1	(	(	PUNCT
ejpam-300	164	2	2	2	NUM
ejpam-300	164	3	)	)	PUNCT
ejpam-300	164	4	since	since	SCONJ
ejpam-300	164	5	a	a	PRON
ejpam-300	164	6	is	be	AUX
ejpam-300	164	7	a	a	DET
ejpam-300	164	8	γ	γ	NOUN
ejpam-300	164	9	-	-	ADJ
ejpam-300	164	10	open	open	ADJ
ejpam-300	164	11	set	set	NOUN
ejpam-300	164	12	,	,	PUNCT
ejpam-300	164	13	therefore	therefore	ADV
ejpam-300	164	14	d	d	X
ejpam-300	164	15	⊆	⊆	NUM
ejpam-300	164	16	a=	a=	ADJ
ejpam-300	164	17	intγ(a)⊆	intγ(a)⊆	X
ejpam-300	164	18	intγ(clγ(b	intγ(clγ(b	X
ejpam-300	164	19	∪	∪	VERB
ejpam-300	164	20	a	a	PRON
ejpam-300	164	21	)	)	PUNCT
ejpam-300	164	22	)	)	PUNCT
ejpam-300	165	1	=	=	SYM
ejpam-300	165	2	⊆	⊆	NUM
ejpam-300	165	3	intγ(clγ(b	intγ(clγ(b	CCONJ
ejpam-300	165	4	∪	∪	ADJ
ejpam-300	165	5	d	d	NOUN
ejpam-300	165	6	)	)	PUNCT
ejpam-300	165	7	)	)	PUNCT
ejpam-300	165	8	.....	.....	PUNCT
ejpam-300	166	1	(	(	PUNCT
ejpam-300	166	2	3	3	X
ejpam-300	166	3	)	)	PUNCT
ejpam-300	166	4	from	from	ADP
ejpam-300	166	5	(	(	PUNCT
ejpam-300	166	6	1	1	NUM
ejpam-300	166	7	)	)	PUNCT
ejpam-300	166	8	and	and	CCONJ
ejpam-300	166	9	(	(	PUNCT
ejpam-300	166	10	3	3	NUM
ejpam-300	166	11	)	)	PUNCT
ejpam-300	166	12	,	,	PUNCT
ejpam-300	166	13	b	b	PROPN
ejpam-300	166	14	∪	∪	ADJ
ejpam-300	166	15	d	d	NUM
ejpam-300	166	16	⊆	⊆	NUM
ejpam-300	166	17	intγ(clγ(b	intγ(clγ(b	CCONJ
ejpam-300	166	18	∪	∪	ADJ
ejpam-300	166	19	d	d	NOUN
ejpam-300	166	20	)	)	PUNCT
ejpam-300	166	21	)	)	PUNCT
ejpam-300	166	22	implies	imply	VERB
ejpam-300	166	23	b	b	NOUN
ejpam-300	166	24	∪	∪	NOUN
ejpam-300	166	25	d	d	X
ejpam-300	166	26	is	be	AUX
ejpam-300	166	27	a	a	DET
ejpam-300	166	28	pre	pre	ADJ
ejpam-300	166	29	-	-	ADJ
ejpam-300	166	30	γ	γ	ADJ
ejpam-300	166	31	-	-	ADJ
ejpam-300	166	32	open	open	ADJ
ejpam-300	166	33	set	set	NOUN
ejpam-300	166	34	.	.	PUNCT
ejpam-300	167	1	this	this	PRON
ejpam-300	167	2	completes	complete	VERB
ejpam-300	167	3	the	the	DET
ejpam-300	167	4	proof	proof	NOUN
ejpam-300	167	5	.	.	PUNCT
ejpam-300	168	1	corollary	corollary	ADJ
ejpam-300	168	2	3.3	3.3	NUM
ejpam-300	168	3	.	.	PUNCT
ejpam-300	169	1	let	let	VERB
ejpam-300	169	2	x	x	PRON
ejpam-300	169	3	be	be	AUX
ejpam-300	169	4	a	a	DET
ejpam-300	169	5	space	space	NOUN
ejpam-300	169	6	,	,	PUNCT
ejpam-300	169	7	φ	φ	PROPN
ejpam-300	169	8	6=	6=	PROPN
ejpam-300	169	9	b	b	PROPN
ejpam-300	169	10	⊆	⊆	NUM
ejpam-300	169	11	x	x	SYM
ejpam-300	169	12	,	,	PUNCT
ejpam-300	169	13	a	a	DET
ejpam-300	169	14	a	a	DET
ejpam-300	169	15	minimal	minimal	ADJ
ejpam-300	169	16	γ	γ	X
ejpam-300	169	17	-	-	ADJ
ejpam-300	169	18	open	open	ADJ
ejpam-300	169	19	set	set	NOUN
ejpam-300	169	20	of	of	ADP
ejpam-300	169	21	a	a	DET
ejpam-300	169	22	space	space	NOUN
ejpam-300	169	23	x	x	NOUN
ejpam-300	169	24	and	and	CCONJ
ejpam-300	169	25	γ	γ	PROPN
ejpam-300	169	26	∈	∈	PROPN
ejpam-300	169	27	γ(x	γ(x	PROPN
ejpam-300	169	28	)	)	PUNCT
ejpam-300	169	29	.	.	PUNCT
ejpam-300	170	1	if	if	SCONJ
ejpam-300	170	2	there	there	PRON
ejpam-300	170	3	exists	exist	VERB
ejpam-300	170	4	a	a	DET
ejpam-300	170	5	γ	γ	X
ejpam-300	170	6	-	-	ADJ
ejpam-300	170	7	open	open	ADJ
ejpam-300	170	8	set	set	NOUN
ejpam-300	170	9	c	c	NOUN
ejpam-300	170	10	containing	contain	VERB
ejpam-300	170	11	b	b	PROPN
ejpam-300	170	12	such	such	ADJ
ejpam-300	171	1	that	that	PRON
ejpam-300	171	2	c	c	PROPN
ejpam-300	171	3	⊆	⊆	NUM
ejpam-300	171	4	clγ(a	clγ(a	PROPN
ejpam-300	171	5	)	)	PUNCT
ejpam-300	171	6	,	,	PUNCT
ejpam-300	171	7	then	then	ADV
ejpam-300	171	8	for	for	ADP
ejpam-300	171	9	any	any	DET
ejpam-300	171	10	nonempty	nonempty	NOUN
ejpam-300	171	11	subset	subset	VERB
ejpam-300	171	12	d	d	NOUN
ejpam-300	171	13	of	of	ADP
ejpam-300	171	14	a	a	PRON
ejpam-300	171	15	,	,	PUNCT
ejpam-300	171	16	b	b	NOUN
ejpam-300	171	17	∪	∪	NOUN
ejpam-300	171	18	d	d	X
ejpam-300	171	19	is	be	AUX
ejpam-300	171	20	a	a	DET
ejpam-300	171	21	pre	pre	ADJ
ejpam-300	171	22	γ	γ	X
ejpam-300	171	23	-	-	ADJ
ejpam-300	171	24	open	open	ADJ
ejpam-300	171	25	set	set	NOUN
ejpam-300	171	26	,	,	PUNCT
ejpam-300	171	27	where	where	SCONJ
ejpam-300	171	28	γ	γ	PROPN
ejpam-300	171	29	is	be	AUX
ejpam-300	171	30	regular	regular	ADJ
ejpam-300	171	31	and	and	CCONJ
ejpam-300	171	32	open	open	ADJ
ejpam-300	171	33	.	.	PUNCT
ejpam-300	172	1	s.	s.	PROPN
ejpam-300	172	2	hussain	hussain	PROPN
ejpam-300	172	3	and	and	CCONJ
ejpam-300	172	4	b.	b.	PROPN
ejpam-300	172	5	ahmad	ahmad	PROPN
ejpam-300	172	6	/	/	SYM
ejpam-300	172	7	eur	eur	PROPN
ejpam-300	172	8	.	.	PUNCT
ejpam-300	173	1	j.	j.	PROPN
ejpam-300	173	2	pure	pure	PROPN
ejpam-300	173	3	appl	appl	PROPN
ejpam-300	173	4	.	.	PROPN
ejpam-300	173	5	math	math	PROPN
ejpam-300	173	6	,	,	PUNCT
ejpam-300	173	7	2	2	NUM
ejpam-300	173	8	(	(	PUNCT
ejpam-300	173	9	2009	2009	NUM
ejpam-300	173	10	)	)	PUNCT
ejpam-300	173	11	,	,	PUNCT
ejpam-300	173	12	(	(	PUNCT
ejpam-300	173	13	338	338	NUM
ejpam-300	173	14	-	-	SYM
ejpam-300	173	15	351	351	NUM
ejpam-300	173	16	)	)	PUNCT
ejpam-300	173	17	345	345	NUM
ejpam-300	173	18	proof	proof	NOUN
ejpam-300	173	19	.	.	PUNCT
ejpam-300	174	1	let	let	VERB
ejpam-300	174	2	a	a	PRON
ejpam-300	174	3	be	be	AUX
ejpam-300	174	4	a	a	DET
ejpam-300	174	5	minimal	minimal	ADJ
ejpam-300	174	6	γ	γ	X
ejpam-300	174	7	-	-	ADJ
ejpam-300	174	8	open	open	ADJ
ejpam-300	174	9	set	set	NOUN
ejpam-300	174	10	and	and	CCONJ
ejpam-300	174	11	b	b	NOUN
ejpam-300	174	12	⊆	⊆	NUM
ejpam-300	174	13	x	x	X
ejpam-300	174	14	.	.	PUNCT
ejpam-300	175	1	suppose	suppose	VERB
ejpam-300	175	2	there	there	PRON
ejpam-300	175	3	exists	exist	VERB
ejpam-300	175	4	a	a	DET
ejpam-300	175	5	γ	γ	X
ejpam-300	175	6	-	-	ADJ
ejpam-300	175	7	open	open	ADJ
ejpam-300	175	8	set	set	NOUN
ejpam-300	175	9	c	c	NOUN
ejpam-300	175	10	containing	contain	VERB
ejpam-300	175	11	b	b	PROPN
ejpam-300	175	12	such	such	ADJ
ejpam-300	175	13	that	that	DET
ejpam-300	175	14	c	c	PROPN
ejpam-300	175	15	⊆	⊆	NUM
ejpam-300	175	16	clγ(a	clγ(a	PROPN
ejpam-300	175	17	)	)	PUNCT
ejpam-300	175	18	.	.	PUNCT
ejpam-300	176	1	then	then	ADV
ejpam-300	176	2	we	we	PRON
ejpam-300	176	3	have	have	VERB
ejpam-300	176	4	c	c	NOUN
ejpam-300	176	5	⊆	⊆	NUM
ejpam-300	176	6	clγ(b)∪clγ(a	clγ(b)∪clγ(a	PROPN
ejpam-300	176	7	)	)	PUNCT
ejpam-300	176	8	=	=	PUNCT
ejpam-300	176	9	clγ(a∪b)[4	clγ(a∪b)[4	X
ejpam-300	176	10	]	]	PUNCT
ejpam-300	176	11	.	.	PUNCT
ejpam-300	177	1	by	by	ADP
ejpam-300	177	2	theorem	theorem	NOUN
ejpam-300	177	3	3.2	3.2	NUM
ejpam-300	177	4	,	,	PUNCT
ejpam-300	177	5	it	it	PRON
ejpam-300	177	6	follows	follow	VERB
ejpam-300	177	7	that	that	SCONJ
ejpam-300	177	8	for	for	ADP
ejpam-300	177	9	any	any	DET
ejpam-300	177	10	nonempty	nonempty	NOUN
ejpam-300	177	11	subset	subset	VERB
ejpam-300	177	12	d	d	NOUN
ejpam-300	177	13	of	of	ADP
ejpam-300	177	14	a	a	PRON
ejpam-300	177	15	,	,	PUNCT
ejpam-300	177	16	b∪	b∪	PROPN
ejpam-300	177	17	d	d	NOUN
ejpam-300	177	18	is	be	AUX
ejpam-300	177	19	a	a	DET
ejpam-300	177	20	pre	pre	ADJ
ejpam-300	177	21	γ	γ	X
ejpam-300	177	22	-	-	ADJ
ejpam-300	177	23	open	open	ADJ
ejpam-300	177	24	set	set	NOUN
ejpam-300	177	25	.	.	PUNCT
ejpam-300	178	1	this	this	PRON
ejpam-300	178	2	completes	complete	VERB
ejpam-300	178	3	the	the	DET
ejpam-300	178	4	proof	proof	NOUN
ejpam-300	178	5	.	.	PUNCT
ejpam-300	179	1	4	4	X
ejpam-300	179	2	.	.	X
ejpam-300	179	3	finite	finite	VERB
ejpam-300	179	4	γ	γ	X
ejpam-300	179	5	-	-	ADJ
ejpam-300	179	6	open	open	ADJ
ejpam-300	179	7	sets	set	NOUN
ejpam-300	179	8	proposition	proposition	NOUN
ejpam-300	179	9	4.1	4.1	NUM
ejpam-300	179	10	.	.	PUNCT
ejpam-300	180	1	let	let	VERB
ejpam-300	180	2	x	x	PRON
ejpam-300	180	3	be	be	AUX
ejpam-300	180	4	a	a	DET
ejpam-300	180	5	space	space	NOUN
ejpam-300	180	6	and	and	CCONJ
ejpam-300	180	7	φ	φ	PROPN
ejpam-300	181	1	6=	6=	PROPN
ejpam-300	181	2	b	b	PROPN
ejpam-300	181	3	a	a	DET
ejpam-300	181	4	finite	finite	ADJ
ejpam-300	181	5	γ	γ	X
ejpam-300	181	6	-	-	ADJ
ejpam-300	181	7	open	open	ADJ
ejpam-300	181	8	set	set	NOUN
ejpam-300	181	9	in	in	ADP
ejpam-300	181	10	x.	x.	NOUN
ejpam-300	181	11	then	then	ADV
ejpam-300	181	12	there	there	PRON
ejpam-300	181	13	exists	exist	VERB
ejpam-300	181	14	at	at	ADP
ejpam-300	181	15	least	least	ADJ
ejpam-300	181	16	one	one	NUM
ejpam-300	181	17	(	(	PUNCT
ejpam-300	181	18	finite	finite	PROPN
ejpam-300	181	19	)	)	PUNCT
ejpam-300	181	20	minimal	minimal	ADJ
ejpam-300	181	21	γ	γ	X
ejpam-300	181	22	-	-	ADJ
ejpam-300	181	23	open	open	ADJ
ejpam-300	181	24	set	set	VERB
ejpam-300	181	25	a	a	DET
ejpam-300	181	26	such	such	ADJ
ejpam-300	181	27	that	that	PRON
ejpam-300	181	28	a⊆	a⊆	PROPN
ejpam-300	181	29	b.	b.	PROPN
ejpam-300	181	30	proof	proof	NOUN
ejpam-300	181	31	.	.	PUNCT
ejpam-300	182	1	suppose	suppose	VERB
ejpam-300	182	2	that	that	SCONJ
ejpam-300	182	3	b	b	PROPN
ejpam-300	182	4	is	be	AUX
ejpam-300	182	5	a	a	DET
ejpam-300	182	6	finite	finite	NOUN
ejpam-300	182	7	γ	γ	X
ejpam-300	182	8	-	-	ADJ
ejpam-300	182	9	open	open	ADJ
ejpam-300	182	10	set	set	NOUN
ejpam-300	182	11	in	in	ADP
ejpam-300	182	12	x.	x.	NOUN
ejpam-300	182	13	then	then	ADV
ejpam-300	182	14	we	we	PRON
ejpam-300	182	15	have	have	VERB
ejpam-300	182	16	the	the	DET
ejpam-300	182	17	following	follow	VERB
ejpam-300	182	18	two	two	NUM
ejpam-300	182	19	possibilities	possibility	NOUN
ejpam-300	182	20	:	:	PUNCT
ejpam-300	182	21	(	(	PUNCT
ejpam-300	182	22	1	1	X
ejpam-300	182	23	)	)	PUNCT
ejpam-300	182	24	b	b	NOUN
ejpam-300	182	25	is	be	AUX
ejpam-300	182	26	a	a	DET
ejpam-300	182	27	minimal	minimal	ADJ
ejpam-300	182	28	γ	γ	X
ejpam-300	182	29	-	-	ADJ
ejpam-300	182	30	open	open	ADJ
ejpam-300	182	31	set	set	NOUN
ejpam-300	182	32	.	.	PUNCT
ejpam-300	183	1	(	(	PUNCT
ejpam-300	183	2	2	2	X
ejpam-300	183	3	)	)	PUNCT
ejpam-300	183	4	b	b	NOUN
ejpam-300	183	5	is	be	AUX
ejpam-300	183	6	not	not	PART
ejpam-300	183	7	a	a	DET
ejpam-300	183	8	minimal	minimal	ADJ
ejpam-300	183	9	γ	γ	X
ejpam-300	183	10	-	-	ADJ
ejpam-300	183	11	open	open	ADJ
ejpam-300	183	12	set	set	NOUN
ejpam-300	183	13	.	.	PUNCT
ejpam-300	184	1	in	in	ADP
ejpam-300	184	2	case	case	NOUN
ejpam-300	184	3	(	(	PUNCT
ejpam-300	184	4	1	1	NUM
ejpam-300	184	5	)	)	PUNCT
ejpam-300	184	6	,	,	PUNCT
ejpam-300	184	7	if	if	SCONJ
ejpam-300	184	8	we	we	PRON
ejpam-300	184	9	choose	choose	VERB
ejpam-300	184	10	b	b	NOUN
ejpam-300	184	11	=	=	SYM
ejpam-300	184	12	a	a	PROPN
ejpam-300	184	13	,	,	PUNCT
ejpam-300	184	14	then	then	ADV
ejpam-300	184	15	the	the	DET
ejpam-300	184	16	theorem	theorem	NOUN
ejpam-300	184	17	is	be	AUX
ejpam-300	184	18	proved	prove	VERB
ejpam-300	184	19	.	.	PUNCT
ejpam-300	185	1	if	if	SCONJ
ejpam-300	185	2	the	the	DET
ejpam-300	185	3	case	case	NOUN
ejpam-300	185	4	(	(	PUNCT
ejpam-300	185	5	2	2	X
ejpam-300	185	6	)	)	PUNCT
ejpam-300	185	7	is	be	AUX
ejpam-300	185	8	true	true	ADJ
ejpam-300	185	9	,	,	PUNCT
ejpam-300	185	10	then	then	ADV
ejpam-300	185	11	there	there	PRON
ejpam-300	185	12	exists	exist	VERB
ejpam-300	185	13	a	a	DET
ejpam-300	185	14	nonempty	nonempty	ADJ
ejpam-300	185	15	(	(	PUNCT
ejpam-300	185	16	finite	finite	NOUN
ejpam-300	185	17	)	)	PUNCT
ejpam-300	185	18	γ	γ	PROPN
ejpam-300	185	19	-	-	ADJ
ejpam-300	185	20	open	open	ADJ
ejpam-300	185	21	set	set	VERB
ejpam-300	185	22	b1	b1	NOUN
ejpam-300	185	23	which	which	PRON
ejpam-300	185	24	is	be	AUX
ejpam-300	185	25	properly	properly	ADV
ejpam-300	185	26	contained	contain	VERB
ejpam-300	185	27	in	in	ADP
ejpam-300	185	28	b.	b.	PROPN
ejpam-300	185	29	if	if	SCONJ
ejpam-300	185	30	b1	b1	NOUN
ejpam-300	185	31	is	be	AUX
ejpam-300	185	32	minimal	minimal	ADJ
ejpam-300	185	33	γ	γ	X
ejpam-300	185	34	-	-	ADJ
ejpam-300	185	35	open	open	ADJ
ejpam-300	185	36	,	,	PUNCT
ejpam-300	185	37	we	we	PRON
ejpam-300	185	38	take	take	VERB
ejpam-300	185	39	a=	a=	ADV
ejpam-300	185	40	b1	b1	NOUN
ejpam-300	185	41	.	.	PUNCT
ejpam-300	186	1	if	if	SCONJ
ejpam-300	186	2	b1	b1	NOUN
ejpam-300	186	3	is	be	AUX
ejpam-300	186	4	not	not	PART
ejpam-300	186	5	a	a	DET
ejpam-300	186	6	minimal	minimal	ADJ
ejpam-300	186	7	γ	γ	X
ejpam-300	186	8	-	-	ADJ
ejpam-300	186	9	open	open	ADJ
ejpam-300	186	10	set	set	NOUN
ejpam-300	186	11	,	,	PUNCT
ejpam-300	186	12	then	then	ADV
ejpam-300	186	13	there	there	PRON
ejpam-300	186	14	exists	exist	VERB
ejpam-300	186	15	a	a	DET
ejpam-300	186	16	nonempty	nonempty	ADJ
ejpam-300	186	17	(	(	PUNCT
ejpam-300	186	18	finite	finite	NOUN
ejpam-300	186	19	)	)	PUNCT
ejpam-300	186	20	γ	γ	PROPN
ejpam-300	186	21	-	-	ADJ
ejpam-300	186	22	open	open	ADJ
ejpam-300	186	23	set	set	VERB
ejpam-300	186	24	b2	b2	NOUN
ejpam-300	186	25	such	such	ADJ
ejpam-300	186	26	that	that	DET
ejpam-300	186	27	b2	b2	NOUN
ejpam-300	186	28	⊂	⊂	PROPN
ejpam-300	186	29	b1	b1	PROPN
ejpam-300	186	30	⊂	⊂	PROPN
ejpam-300	186	31	b.	b.	PROPN
ejpam-300	187	1	we	we	PRON
ejpam-300	187	2	continue	continue	VERB
ejpam-300	187	3	this	this	DET
ejpam-300	187	4	process	process	NOUN
ejpam-300	187	5	and	and	CCONJ
ejpam-300	187	6	have	have	VERB
ejpam-300	187	7	a	a	DET
ejpam-300	187	8	sequence	sequence	NOUN
ejpam-300	187	9	of	of	ADP
ejpam-300	187	10	γ	γ	X
ejpam-300	187	11	-	-	ADJ
ejpam-300	187	12	open	open	ADJ
ejpam-300	187	13	sets	set	NOUN
ejpam-300	187	14	...	...	PUNCT
ejpam-300	188	1	⊂	⊂	PROPN
ejpam-300	188	2	bm	bm	PROPN
ejpam-300	188	3	⊂	⊂	PROPN
ejpam-300	188	4	...	...	PUNCT
ejpam-300	189	1	⊂	⊂	PROPN
ejpam-300	189	2	b2	b2	PROPN
ejpam-300	189	3	⊂	⊂	PROPN
ejpam-300	189	4	b1	b1	PROPN
ejpam-300	189	5	⊂	⊂	PROPN
ejpam-300	189	6	b.	b.	PROPN
ejpam-300	190	1	since	since	SCONJ
ejpam-300	190	2	b	b	PROPN
ejpam-300	190	3	is	be	AUX
ejpam-300	190	4	a	a	DET
ejpam-300	190	5	finite	finite	NOUN
ejpam-300	190	6	,	,	PUNCT
ejpam-300	190	7	this	this	DET
ejpam-300	190	8	process	process	NOUN
ejpam-300	190	9	will	will	AUX
ejpam-300	190	10	end	end	VERB
ejpam-300	190	11	in	in	ADP
ejpam-300	190	12	a	a	DET
ejpam-300	190	13	finite	finite	ADJ
ejpam-300	190	14	number	number	NOUN
ejpam-300	190	15	of	of	ADP
ejpam-300	190	16	steps	step	NOUN
ejpam-300	190	17	.	.	PUNCT
ejpam-300	191	1	that	that	PRON
ejpam-300	191	2	is	be	AUX
ejpam-300	191	3	,	,	PUNCT
ejpam-300	191	4	for	for	ADP
ejpam-300	191	5	some	some	DET
ejpam-300	191	6	natural	natural	ADJ
ejpam-300	191	7	number	number	NOUN
ejpam-300	191	8	k	k	NOUN
ejpam-300	191	9	,	,	PUNCT
ejpam-300	191	10	we	we	PRON
ejpam-300	191	11	have	have	VERB
ejpam-300	191	12	a	a	DET
ejpam-300	191	13	minimal	minimal	ADJ
ejpam-300	191	14	γ	γ	X
ejpam-300	191	15	-	-	ADJ
ejpam-300	191	16	open	open	ADJ
ejpam-300	191	17	set	set	NOUN
ejpam-300	191	18	bk	bk	ADP
ejpam-300	191	19	such	such	ADJ
ejpam-300	191	20	that	that	SCONJ
ejpam-300	191	21	bk	bk	X
ejpam-300	191	22	=	=	PUNCT
ejpam-300	191	23	a.	a.	NOUN
ejpam-300	191	24	this	this	PRON
ejpam-300	191	25	completes	complete	VERB
ejpam-300	191	26	the	the	DET
ejpam-300	191	27	proof	proof	NOUN
ejpam-300	191	28	.	.	PUNCT
ejpam-300	192	1	in	in	ADP
ejpam-300	192	2	view	view	NOUN
ejpam-300	192	3	of	of	ADP
ejpam-300	192	4	the	the	DET
ejpam-300	192	5	definition	definition	NOUN
ejpam-300	192	6	of	of	ADP
ejpam-300	192	7	locally	locally	ADV
ejpam-300	192	8	finite	finite	ADJ
ejpam-300	192	9	space	space	NOUN
ejpam-300	192	10	[	[	X
ejpam-300	192	11	3	3	NUM
ejpam-300	192	12	]	]	PUNCT
ejpam-300	192	13	,	,	PUNCT
ejpam-300	192	14	we	we	PRON
ejpam-300	192	15	define	define	VERB
ejpam-300	192	16	γ	γ	NOUN
ejpam-300	192	17	-	-	ADJ
ejpam-300	192	18	locally	locally	ADV
ejpam-300	192	19	finite	finite	ADJ
ejpam-300	192	20	space	space	NOUN
ejpam-300	192	21	as	as	ADP
ejpam-300	192	22	:	:	PUNCT
ejpam-300	192	23	definition	definition	NOUN
ejpam-300	192	24	4.1	4.1	NUM
ejpam-300	192	25	.	.	PUNCT
ejpam-300	193	1	a	a	DET
ejpam-300	193	2	space	space	NOUN
ejpam-300	193	3	x	x	PUNCT
ejpam-300	193	4	is	be	AUX
ejpam-300	193	5	said	say	VERB
ejpam-300	193	6	to	to	PART
ejpam-300	193	7	be	be	AUX
ejpam-300	193	8	a	a	DET
ejpam-300	193	9	γ	γ	X
ejpam-300	193	10	-	-	ADJ
ejpam-300	193	11	locally	locally	ADV
ejpam-300	193	12	finite	finite	ADJ
ejpam-300	193	13	space	space	NOUN
ejpam-300	193	14	,	,	PUNCT
ejpam-300	193	15	if	if	SCONJ
ejpam-300	193	16	for	for	ADP
ejpam-300	193	17	each	each	DET
ejpam-300	193	18	x	x	SYM
ejpam-300	193	19	∈	∈	PROPN
ejpam-300	193	20	x	x	PUNCT
ejpam-300	193	21	there	there	PRON
ejpam-300	193	22	exists	exist	VERB
ejpam-300	193	23	a	a	DET
ejpam-300	193	24	finite	finite	NOUN
ejpam-300	193	25	γ	γ	X
ejpam-300	193	26	-	-	ADJ
ejpam-300	193	27	open	open	ADJ
ejpam-300	193	28	set	set	VERB
ejpam-300	193	29	a	a	PRON
ejpam-300	193	30	in	in	ADP
ejpam-300	193	31	x	x	PUNCT
ejpam-300	193	32	such	such	ADJ
ejpam-300	193	33	that	that	SCONJ
ejpam-300	193	34	x	x	SYM
ejpam-300	193	35	∈	∈	PROPN
ejpam-300	193	36	a.	a.	NOUN
ejpam-300	193	37	s.	s.	PROPN
ejpam-300	193	38	hussain	hussain	PROPN
ejpam-300	193	39	and	and	CCONJ
ejpam-300	193	40	b.	b.	PROPN
ejpam-300	193	41	ahmad	ahmad	PROPN
ejpam-300	193	42	/	/	SYM
ejpam-300	193	43	eur	eur	PROPN
ejpam-300	193	44	.	.	PUNCT
ejpam-300	194	1	j.	j.	PROPN
ejpam-300	194	2	pure	pure	PROPN
ejpam-300	194	3	appl	appl	PROPN
ejpam-300	194	4	.	.	PROPN
ejpam-300	194	5	math	math	PROPN
ejpam-300	194	6	,	,	PUNCT
ejpam-300	194	7	2	2	NUM
ejpam-300	194	8	(	(	PUNCT
ejpam-300	194	9	2009	2009	NUM
ejpam-300	194	10	)	)	PUNCT
ejpam-300	194	11	,	,	PUNCT
ejpam-300	194	12	(	(	PUNCT
ejpam-300	194	13	338	338	NUM
ejpam-300	194	14	-	-	SYM
ejpam-300	194	15	351	351	NUM
ejpam-300	194	16	)	)	PUNCT
ejpam-300	194	17	346	346	NUM
ejpam-300	194	18	example	example	NOUN
ejpam-300	194	19	4.1	4.1	NUM
ejpam-300	194	20	.	.	PUNCT
ejpam-300	195	1	let	let	VERB
ejpam-300	195	2	x=	x=	PUNCT
ejpam-300	196	1	{	{	PUNCT
ejpam-300	196	2	a	a	DET
ejpam-300	196	3	,	,	PUNCT
ejpam-300	196	4	b	b	NOUN
ejpam-300	196	5	,	,	PUNCT
ejpam-300	196	6	c	c	NOUN
ejpam-300	196	7	}	}	PUNCT
ejpam-300	196	8	,	,	PUNCT
ejpam-300	196	9	τ=	τ=	X
ejpam-300	196	10	{	{	PUNCT
ejpam-300	196	11	φ	φ	PROPN
ejpam-300	196	12	,	,	PUNCT
ejpam-300	196	13	x	x	INTJ
ejpam-300	196	14	,	,	PUNCT
ejpam-300	196	15	{	{	PUNCT
ejpam-300	196	16	a	a	NOUN
ejpam-300	196	17	}	}	PUNCT
ejpam-300	196	18	,	,	PUNCT
ejpam-300	196	19	{	{	PUNCT
ejpam-300	196	20	b	b	NOUN
ejpam-300	196	21	}	}	PUNCT
ejpam-300	196	22	,	,	PUNCT
ejpam-300	196	23	{	{	PUNCT
ejpam-300	196	24	a	a	DET
ejpam-300	196	25	,	,	PUNCT
ejpam-300	196	26	b	b	NOUN
ejpam-300	196	27	}	}	PUNCT
ejpam-300	196	28	,	,	PUNCT
ejpam-300	196	29	{	{	PUNCT
ejpam-300	196	30	a	a	PRON
ejpam-300	196	31	,	,	PUNCT
ejpam-300	196	32	c	c	NOUN
ejpam-300	196	33	}	}	PUNCT
ejpam-300	196	34	}	}	PUNCT
ejpam-300	197	1	[	[	X
ejpam-300	197	2	4	4	NUM
ejpam-300	197	3	]	]	PUNCT
ejpam-300	197	4	.	.	PUNCT
ejpam-300	198	1	for	for	ADP
ejpam-300	198	2	b	b	PROPN
ejpam-300	198	3	∈	∈	PROPN
ejpam-300	198	4	x	x	PUNCT
ejpam-300	198	5	,	,	PUNCT
ejpam-300	198	6	define	define	VERB
ejpam-300	198	7	an	an	DET
ejpam-300	198	8	operation	operation	NOUN
ejpam-300	198	9	γ	γ	X
ejpam-300	198	10	:	:	PUNCT
ejpam-300	198	11	τ→	τ→	PUNCT
ejpam-300	198	12	p(x	p(x	PROPN
ejpam-300	198	13	)	)	PUNCT
ejpam-300	198	14	by	by	ADP
ejpam-300	198	15	γ(a	γ(a	NOUN
ejpam-300	198	16	)	)	PUNCT
ejpam-300	199	1	=	=	PUNCT
ejpam-300	199	2	aγ	aγ	NOUN
ejpam-300	199	3	=	=	PUNCT
ejpam-300	199	4			PROPN
ejpam-300	199	5			NOUN
ejpam-300	199	6			PROPN
ejpam-300	199	7	a	a	X
ejpam-300	199	8	,	,	PUNCT
ejpam-300	199	9	if	if	SCONJ
ejpam-300	199	10	b	b	PROPN
ejpam-300	199	11	∈	∈	PROPN
ejpam-300	199	12	a	a	DET
ejpam-300	199	13	cl(a	cl(a	NUM
ejpam-300	199	14	)	)	PUNCT
ejpam-300	199	15	,	,	PUNCT
ejpam-300	199	16	if	if	SCONJ
ejpam-300	199	17	b	b	PROPN
ejpam-300	199	18	6∈	6∈	PROPN
ejpam-300	199	19	a.	a.	NOUN
ejpam-300	199	20	then	then	ADV
ejpam-300	199	21	calculations	calculation	NOUN
ejpam-300	199	22	show	show	VERB
ejpam-300	199	23	that	that	SCONJ
ejpam-300	199	24	the	the	DET
ejpam-300	199	25	γ	γ	X
ejpam-300	199	26	-	-	ADJ
ejpam-300	199	27	open	open	ADJ
ejpam-300	199	28	sets	set	NOUN
ejpam-300	199	29	are	be	AUX
ejpam-300	199	30	φ	φ	NOUN
ejpam-300	199	31	,	,	PUNCT
ejpam-300	199	32	x	x	PRON
ejpam-300	199	33	,	,	PUNCT
ejpam-300	199	34	{	{	PUNCT
ejpam-300	199	35	b	b	NOUN
ejpam-300	199	36	}	}	PUNCT
ejpam-300	199	37	,	,	PUNCT
ejpam-300	199	38	{	{	PUNCT
ejpam-300	199	39	a	a	DET
ejpam-300	199	40	,	,	PUNCT
ejpam-300	199	41	b	b	NOUN
ejpam-300	199	42	}	}	PUNCT
ejpam-300	199	43	,	,	PUNCT
ejpam-300	199	44	{	{	PUNCT
ejpam-300	199	45	a	a	PRON
ejpam-300	199	46	,	,	PUNCT
ejpam-300	199	47	c}[4	c}[4	PROPN
ejpam-300	199	48	]	]	PUNCT
ejpam-300	199	49	.	.	PUNCT
ejpam-300	200	1	clearly	clearly	ADV
ejpam-300	200	2	x	x	PUNCT
ejpam-300	200	3	is	be	AUX
ejpam-300	200	4	γ	γ	X
ejpam-300	200	5	-	-	ADJ
ejpam-300	200	6	locally	locally	ADV
ejpam-300	200	7	finite	finite	ADJ
ejpam-300	200	8	space	space	NOUN
ejpam-300	200	9	.	.	PUNCT
ejpam-300	201	1	proposition	proposition	NOUN
ejpam-300	201	2	4.2	4.2	NUM
ejpam-300	201	3	.	.	PUNCT
ejpam-300	202	1	letφ	letφ	PROPN
ejpam-300	203	1	6=	6=	PROPN
ejpam-300	204	1	b	b	X
ejpam-300	204	2	be	be	AUX
ejpam-300	204	3	a	a	DET
ejpam-300	204	4	γ	γ	NOUN
ejpam-300	204	5	-	-	ADJ
ejpam-300	204	6	open	open	ADJ
ejpam-300	204	7	set	set	NOUN
ejpam-300	204	8	in	in	ADP
ejpam-300	204	9	a	a	DET
ejpam-300	204	10	γ	γ	X
ejpam-300	204	11	-	-	ADJ
ejpam-300	204	12	locally	locally	ADV
ejpam-300	204	13	finite	finite	ADJ
ejpam-300	204	14	space	space	NOUN
ejpam-300	204	15	x.	x.	NOUN
ejpam-300	205	1	then	then	ADV
ejpam-300	205	2	there	there	PRON
ejpam-300	205	3	exists	exist	VERB
ejpam-300	205	4	at	at	ADP
ejpam-300	205	5	least	least	ADJ
ejpam-300	205	6	one	one	NUM
ejpam-300	205	7	(	(	PUNCT
ejpam-300	205	8	finite	finite	PROPN
ejpam-300	205	9	)	)	PUNCT
ejpam-300	205	10	minimal	minimal	ADJ
ejpam-300	205	11	γ	γ	X
ejpam-300	205	12	-	-	ADJ
ejpam-300	205	13	open	open	ADJ
ejpam-300	205	14	set	set	NOUN
ejpam-300	205	15	a	a	PRON
ejpam-300	205	16	which	which	PRON
ejpam-300	205	17	is	be	AUX
ejpam-300	205	18	contained	contain	VERB
ejpam-300	205	19	in	in	ADP
ejpam-300	205	20	b	b	NOUN
ejpam-300	205	21	,	,	PUNCT
ejpam-300	205	22	where	where	SCONJ
ejpam-300	205	23	γ	γ	NOUN
ejpam-300	205	24	is	be	AUX
ejpam-300	205	25	regular	regular	ADJ
ejpam-300	205	26	.	.	PUNCT
ejpam-300	206	1	proof	proof	NOUN
ejpam-300	206	2	.	.	PUNCT
ejpam-300	207	1	let	let	VERB
ejpam-300	207	2	y	y	PROPN
ejpam-300	207	3	∈	∈	PROPN
ejpam-300	207	4	b.	b.	PROPN
ejpam-300	207	5	since	since	SCONJ
ejpam-300	207	6	x	x	PRON
ejpam-300	207	7	is	be	AUX
ejpam-300	207	8	a	a	DET
ejpam-300	207	9	γ	γ	X
ejpam-300	207	10	-	-	ADJ
ejpam-300	207	11	locally	locally	ADV
ejpam-300	207	12	finite	finite	ADJ
ejpam-300	207	13	space	space	NOUN
ejpam-300	207	14	,	,	PUNCT
ejpam-300	207	15	then	then	ADV
ejpam-300	207	16	there	there	PRON
ejpam-300	207	17	exists	exist	VERB
ejpam-300	207	18	a	a	DET
ejpam-300	207	19	finite	finite	NOUN
ejpam-300	207	20	γ	γ	X
ejpam-300	207	21	-	-	ADJ
ejpam-300	207	22	open	open	ADJ
ejpam-300	207	23	set	set	VERB
ejpam-300	207	24	by	by	ADP
ejpam-300	207	25	such	such	ADJ
ejpam-300	207	26	that	that	SCONJ
ejpam-300	207	27	y	y	PROPN
ejpam-300	207	28	∈	∈	PROPN
ejpam-300	207	29	by	by	ADP
ejpam-300	207	30	.	.	PUNCT
ejpam-300	208	1	since	since	SCONJ
ejpam-300	208	2	b	b	NOUN
ejpam-300	208	3	∩	∩	NOUN
ejpam-300	208	4	by	by	ADP
ejpam-300	208	5	is	be	AUX
ejpam-300	208	6	a	a	DET
ejpam-300	208	7	finite	finite	NOUN
ejpam-300	208	8	γ	γ	X
ejpam-300	208	9	-	-	ADJ
ejpam-300	208	10	open	open	ADJ
ejpam-300	208	11	set	set	NOUN
ejpam-300	208	12	[	[	X
ejpam-300	208	13	4	4	NUM
ejpam-300	208	14	]	]	PUNCT
ejpam-300	208	15	,	,	PUNCT
ejpam-300	208	16	therefore	therefore	ADV
ejpam-300	208	17	by	by	ADP
ejpam-300	208	18	proposition	proposition	NOUN
ejpam-300	208	19	4.1	4.1	NUM
ejpam-300	208	20	there	there	ADV
ejpam-300	208	21	exists	exist	VERB
ejpam-300	208	22	a	a	DET
ejpam-300	208	23	minimal	minimal	ADJ
ejpam-300	208	24	γ	γ	NOUN
ejpam-300	208	25	-	-	ADJ
ejpam-300	208	26	open	open	ADJ
ejpam-300	208	27	set	set	VERB
ejpam-300	208	28	a	a	DET
ejpam-300	208	29	such	such	ADJ
ejpam-300	208	30	that	that	SCONJ
ejpam-300	208	31	a	a	DET
ejpam-300	208	32	⊆	⊆	NUM
ejpam-300	208	33	b	b	NOUN
ejpam-300	208	34	∩	∩	NOUN
ejpam-300	208	35	by	by	ADP
ejpam-300	208	36	⊆	⊆	NUM
ejpam-300	208	37	b.	b.	PROPN
ejpam-300	208	38	this	this	PRON
ejpam-300	208	39	completes	complete	VERB
ejpam-300	208	40	the	the	DET
ejpam-300	208	41	proof	proof	NOUN
ejpam-300	208	42	.	.	PUNCT
ejpam-300	209	1	proposition	proposition	NOUN
ejpam-300	209	2	4.3	4.3	NUM
ejpam-300	209	3	.	.	PUNCT
ejpam-300	210	1	let	let	VERB
ejpam-300	210	2	x	x	PRON
ejpam-300	210	3	be	be	AUX
ejpam-300	210	4	a	a	DET
ejpam-300	210	5	γ	γ	X
ejpam-300	210	6	-	-	ADJ
ejpam-300	210	7	locally	locally	ADV
ejpam-300	210	8	finite	finite	ADJ
ejpam-300	210	9	space	space	NOUN
ejpam-300	210	10	and	and	CCONJ
ejpam-300	210	11	for	for	ADP
ejpam-300	210	12	any	any	DET
ejpam-300	210	13	α	α	NOUN
ejpam-300	210	14	∈	∈	NOUN
ejpam-300	210	15	i	i	PRON
ejpam-300	210	16	,	,	PUNCT
ejpam-300	210	17	bα	bα	VERB
ejpam-300	210	18	a	a	DET
ejpam-300	210	19	γ	γ	X
ejpam-300	210	20	-	-	ADJ
ejpam-300	210	21	open	open	ADJ
ejpam-300	210	22	set	set	NOUN
ejpam-300	210	23	and	and	CCONJ
ejpam-300	210	24	φ	φ	PROPN
ejpam-300	210	25	6=	6=	PROPN
ejpam-300	210	26	a	a	DET
ejpam-300	210	27	a	a	DET
ejpam-300	210	28	finite	finite	NOUN
ejpam-300	210	29	γ	γ	X
ejpam-300	210	30	-	-	ADJ
ejpam-300	210	31	open	open	ADJ
ejpam-300	210	32	set	set	NOUN
ejpam-300	210	33	.	.	PUNCT
ejpam-300	211	1	then	then	ADV
ejpam-300	211	2	a∩	a∩	PROPN
ejpam-300	211	3	(	(	PUNCT
ejpam-300	211	4	⋂	⋂	PROPN
ejpam-300	211	5	α∈i	α∈i	ADJ
ejpam-300	211	6	bα	bα	NOUN
ejpam-300	211	7	)	)	PUNCT
ejpam-300	211	8	is	be	AUX
ejpam-300	211	9	a	a	DET
ejpam-300	211	10	finite	finite	NOUN
ejpam-300	211	11	γ	γ	X
ejpam-300	211	12	-	-	ADJ
ejpam-300	211	13	open	open	ADJ
ejpam-300	211	14	set	set	NOUN
ejpam-300	211	15	,	,	PUNCT
ejpam-300	211	16	where	where	SCONJ
ejpam-300	211	17	γ	γ	PROPN
ejpam-300	211	18	is	be	AUX
ejpam-300	211	19	regular	regular	ADJ
ejpam-300	211	20	.	.	PUNCT
ejpam-300	212	1	proof	proof	NOUN
ejpam-300	212	2	.	.	PUNCT
ejpam-300	213	1	since	since	SCONJ
ejpam-300	213	2	x	x	PRON
ejpam-300	213	3	is	be	AUX
ejpam-300	213	4	a	a	DET
ejpam-300	213	5	γ	γ	X
ejpam-300	213	6	-	-	ADJ
ejpam-300	213	7	locally	locally	ADV
ejpam-300	213	8	finite	finite	ADJ
ejpam-300	213	9	space	space	NOUN
ejpam-300	213	10	,	,	PUNCT
ejpam-300	213	11	then	then	ADV
ejpam-300	213	12	there	there	PRON
ejpam-300	213	13	exists	exist	VERB
ejpam-300	213	14	an	an	DET
ejpam-300	213	15	integer	integer	NOUN
ejpam-300	213	16	k	k	PROPN
ejpam-300	213	17	such	such	ADJ
ejpam-300	213	18	that	that	SCONJ
ejpam-300	213	19	a∩	a∩	PROPN
ejpam-300	213	20	(	(	PUNCT
ejpam-300	213	21	⋂	⋂	PROPN
ejpam-300	213	22	α∈i	α∈i	ADJ
ejpam-300	213	23	bα	bα	NOUN
ejpam-300	213	24	)	)	PUNCT
ejpam-300	213	25	=	=	SYM
ejpam-300	213	26	a∩	a∩	PROPN
ejpam-300	213	27	(	(	PUNCT
ejpam-300	213	28	⋂k	⋂k	PROPN
ejpam-300	213	29	i=1	i=1	PROPN
ejpam-300	213	30	bi	bi	PROPN
ejpam-300	213	31	)	)	PUNCT
ejpam-300	213	32	.	.	PUNCT
ejpam-300	214	1	since	since	SCONJ
ejpam-300	214	2	γ	γ	X
ejpam-300	214	3	is	be	AUX
ejpam-300	214	4	regular	regular	ADJ
ejpam-300	214	5	[	[	X
ejpam-300	214	6	4	4	NUM
ejpam-300	214	7	]	]	PUNCT
ejpam-300	214	8	,	,	PUNCT
ejpam-300	214	9	a∩	a∩	PROPN
ejpam-300	214	10	(	(	PUNCT
ejpam-300	214	11	⋂	⋂	PROPN
ejpam-300	214	12	α∈i	α∈i	ADJ
ejpam-300	214	13	bα	bα	NOUN
ejpam-300	214	14	)	)	PUNCT
ejpam-300	214	15	is	be	AUX
ejpam-300	214	16	a	a	DET
ejpam-300	214	17	finite	finite	NOUN
ejpam-300	214	18	γ	γ	X
ejpam-300	214	19	-	-	ADJ
ejpam-300	214	20	open	open	ADJ
ejpam-300	214	21	set	set	NOUN
ejpam-300	214	22	.	.	PUNCT
ejpam-300	215	1	this	this	PRON
ejpam-300	215	2	completes	complete	VERB
ejpam-300	215	3	the	the	DET
ejpam-300	215	4	proof	proof	NOUN
ejpam-300	215	5	.	.	PUNCT
ejpam-300	216	1	using	use	VERB
ejpam-300	216	2	proposition	proposition	NOUN
ejpam-300	216	3	4.3	4.3	NUM
ejpam-300	216	4	,	,	PUNCT
ejpam-300	216	5	we	we	PRON
ejpam-300	216	6	can	can	AUX
ejpam-300	216	7	prove	prove	VERB
ejpam-300	216	8	the	the	DET
ejpam-300	216	9	following	following	NOUN
ejpam-300	216	10	:	:	PUNCT
ejpam-300	216	11	theorem	theorem	VERB
ejpam-300	216	12	4.1	4.1	NUM
ejpam-300	216	13	.	.	PUNCT
ejpam-300	217	1	let	let	VERB
ejpam-300	217	2	x	x	PRON
ejpam-300	217	3	be	be	AUX
ejpam-300	217	4	a	a	DET
ejpam-300	217	5	space	space	NOUN
ejpam-300	217	6	and	and	CCONJ
ejpam-300	217	7	for	for	ADP
ejpam-300	217	8	any	any	DET
ejpam-300	217	9	α	α	NOUN
ejpam-300	217	10	∈	∈	NOUN
ejpam-300	217	11	i	i	PRON
ejpam-300	217	12	,	,	PUNCT
ejpam-300	217	13	bα	bα	VERB
ejpam-300	217	14	a	a	DET
ejpam-300	217	15	γ	γ	X
ejpam-300	217	16	-	-	ADJ
ejpam-300	217	17	open	open	ADJ
ejpam-300	217	18	set	set	NOUN
ejpam-300	217	19	and	and	CCONJ
ejpam-300	217	20	for	for	ADP
ejpam-300	217	21	any	any	DET
ejpam-300	217	22	β	β	X
ejpam-300	217	23	∈	∈	PROPN
ejpam-300	217	24	j	j	PROPN
ejpam-300	217	25	,	,	PUNCT
ejpam-300	217	26	aβ	aβ	ADP
ejpam-300	217	27	a	a	DET
ejpam-300	217	28	nonempty	nonempty	ADJ
ejpam-300	217	29	finite	finite	VERB
ejpam-300	217	30	γ	γ	X
ejpam-300	217	31	-	-	ADJ
ejpam-300	217	32	open	open	ADJ
ejpam-300	217	33	set	set	NOUN
ejpam-300	217	34	.	.	PUNCT
ejpam-300	218	1	then	then	ADV
ejpam-300	218	2	(	(	PUNCT
ejpam-300	218	3	⋃	⋃	ADP
ejpam-300	218	4	β∈j	β∈j	ADJ
ejpam-300	218	5	aβ)∩	aβ)∩	X
ejpam-300	218	6	(	(	PUNCT
ejpam-300	218	7	⋂	⋂	PROPN
ejpam-300	218	8	α∈i	α∈i	ADJ
ejpam-300	218	9	bα	bα	NOUN
ejpam-300	218	10	)	)	PUNCT
ejpam-300	218	11	is	be	AUX
ejpam-300	218	12	a	a	DET
ejpam-300	218	13	γ	γ	NOUN
ejpam-300	218	14	-	-	ADJ
ejpam-300	218	15	open	open	ADJ
ejpam-300	218	16	set	set	NOUN
ejpam-300	218	17	,	,	PUNCT
ejpam-300	218	18	where	where	SCONJ
ejpam-300	218	19	γ	γ	PROPN
ejpam-300	218	20	is	be	AUX
ejpam-300	218	21	regular	regular	ADJ
ejpam-300	218	22	.	.	PUNCT
ejpam-300	219	1	s.	s.	PROPN
ejpam-300	219	2	hussain	hussain	PROPN
ejpam-300	219	3	and	and	CCONJ
ejpam-300	219	4	b.	b.	PROPN
ejpam-300	219	5	ahmad	ahmad	PROPN
ejpam-300	219	6	/	/	SYM
ejpam-300	219	7	eur	eur	PROPN
ejpam-300	219	8	.	.	PUNCT
ejpam-300	220	1	j.	j.	PROPN
ejpam-300	220	2	pure	pure	PROPN
ejpam-300	220	3	appl	appl	PROPN
ejpam-300	220	4	.	.	PROPN
ejpam-300	220	5	math	math	PROPN
ejpam-300	220	6	,	,	PUNCT
ejpam-300	220	7	2	2	NUM
ejpam-300	220	8	(	(	PUNCT
ejpam-300	220	9	2009	2009	NUM
ejpam-300	220	10	)	)	PUNCT
ejpam-300	220	11	,	,	PUNCT
ejpam-300	220	12	(	(	PUNCT
ejpam-300	220	13	338	338	NUM
ejpam-300	220	14	-	-	SYM
ejpam-300	220	15	351	351	NUM
ejpam-300	220	16	)	)	PUNCT
ejpam-300	220	17	347	347	NUM
ejpam-300	220	18	5	5	NUM
ejpam-300	220	19	.	.	PUNCT
ejpam-300	221	1	applications	application	NOUN
ejpam-300	221	2	let	let	VERB
ejpam-300	221	3	a	a	PRON
ejpam-300	221	4	be	be	AUX
ejpam-300	221	5	a	a	DET
ejpam-300	221	6	nonempty	nonempty	ADJ
ejpam-300	221	7	finite	finite	ADJ
ejpam-300	221	8	γ	γ	X
ejpam-300	221	9	-	-	ADJ
ejpam-300	221	10	open	open	ADJ
ejpam-300	221	11	set	set	NOUN
ejpam-300	221	12	.	.	PUNCT
ejpam-300	222	1	it	it	PRON
ejpam-300	222	2	is	be	AUX
ejpam-300	222	3	clear	clear	ADJ
ejpam-300	222	4	,	,	PUNCT
ejpam-300	222	5	by	by	ADP
ejpam-300	222	6	proposition	proposition	NOUN
ejpam-300	222	7	3.1	3.1	NUM
ejpam-300	222	8	and	and	CCONJ
ejpam-300	222	9	proposition	proposition	NOUN
ejpam-300	222	10	4.3	4.3	NUM
ejpam-300	222	11	,	,	PUNCT
ejpam-300	222	12	that	that	SCONJ
ejpam-300	222	13	if	if	SCONJ
ejpam-300	222	14	γ	γ	NOUN
ejpam-300	222	15	is	be	AUX
ejpam-300	222	16	regular	regular	ADJ
ejpam-300	222	17	,	,	PUNCT
ejpam-300	222	18	then	then	ADV
ejpam-300	222	19	there	there	PRON
ejpam-300	222	20	exists	exist	VERB
ejpam-300	222	21	a	a	DET
ejpam-300	222	22	natural	natural	ADJ
ejpam-300	222	23	number	number	NOUN
ejpam-300	222	24	m	m	NOUN
ejpam-300	222	25	such	such	ADJ
ejpam-300	222	26	that	that	SCONJ
ejpam-300	222	27	{	{	PUNCT
ejpam-300	222	28	a1	a1	PROPN
ejpam-300	222	29	,	,	PUNCT
ejpam-300	222	30	a2	a2	PROPN
ejpam-300	222	31	,	,	PUNCT
ejpam-300	222	32	...	...	PUNCT
ejpam-300	222	33	,	,	PUNCT
ejpam-300	222	34	am	be	AUX
ejpam-300	222	35	}	}	PUNCT
ejpam-300	222	36	is	be	AUX
ejpam-300	222	37	the	the	DET
ejpam-300	222	38	class	class	NOUN
ejpam-300	222	39	of	of	ADP
ejpam-300	222	40	all	all	DET
ejpam-300	222	41	minimal	minimal	ADJ
ejpam-300	222	42	γ	γ	ADJ
ejpam-300	222	43	-	-	ADJ
ejpam-300	222	44	open	open	ADJ
ejpam-300	222	45	sets	set	NOUN
ejpam-300	222	46	in	in	ADP
ejpam-300	222	47	a	a	DET
ejpam-300	222	48	satisfying	satisfying	NOUN
ejpam-300	222	49	the	the	DET
ejpam-300	222	50	following	follow	VERB
ejpam-300	222	51	two	two	NUM
ejpam-300	222	52	conditions	condition	NOUN
ejpam-300	222	53	:	:	PUNCT
ejpam-300	222	54	(	(	PUNCT
ejpam-300	222	55	1	1	X
ejpam-300	222	56	)	)	PUNCT
ejpam-300	222	57	for	for	ADP
ejpam-300	222	58	any	any	DET
ejpam-300	222	59	l	l	NOUN
ejpam-300	222	60	,	,	PUNCT
ejpam-300	222	61	n	n	X
ejpam-300	222	62	with	with	ADP
ejpam-300	222	63	1≤	1≤	NUM
ejpam-300	222	64	l	l	NOUN
ejpam-300	222	65	,	,	PUNCT
ejpam-300	222	66	n	n	PROPN
ejpam-300	222	67	≤	≤	NOUN
ejpam-300	222	68	m	m	PROPN
ejpam-300	222	69	and	and	CCONJ
ejpam-300	222	70	l	l	PROPN
ejpam-300	222	71	6=	6=	PROPN
ejpam-300	222	72	n	n	CCONJ
ejpam-300	222	73	,	,	PUNCT
ejpam-300	222	74	al	al	PROPN
ejpam-300	222	75	∩	∩	PROPN
ejpam-300	222	76	an	an	DET
ejpam-300	222	77	=	=	SYM
ejpam-300	222	78	φ	φ	PROPN
ejpam-300	222	79	.	.	PUNCT
ejpam-300	223	1	(	(	PUNCT
ejpam-300	223	2	2	2	X
ejpam-300	223	3	)	)	PUNCT
ejpam-300	223	4	if	if	SCONJ
ejpam-300	223	5	c	c	PROPN
ejpam-300	223	6	is	be	AUX
ejpam-300	223	7	a	a	DET
ejpam-300	223	8	minimal	minimal	ADJ
ejpam-300	223	9	γ	γ	X
ejpam-300	223	10	-	-	ADJ
ejpam-300	223	11	open	open	ADJ
ejpam-300	223	12	set	set	NOUN
ejpam-300	223	13	in	in	ADP
ejpam-300	223	14	a	a	PRON
ejpam-300	223	15	,	,	PUNCT
ejpam-300	223	16	then	then	ADV
ejpam-300	223	17	there	there	PRON
ejpam-300	223	18	exists	exist	VERB
ejpam-300	223	19	l	l	NOUN
ejpam-300	223	20	with	with	ADP
ejpam-300	223	21	1	1	NUM
ejpam-300	223	22	≤	≤	NUM
ejpam-300	223	23	l	l	NOUN
ejpam-300	223	24	≤	≤	NUM
ejpam-300	223	25	m	m	VERB
ejpam-300	223	26	such	such	ADJ
ejpam-300	223	27	that	that	SCONJ
ejpam-300	223	28	c	c	PROPN
ejpam-300	223	29	=	=	SYM
ejpam-300	223	30	al	al	PROPN
ejpam-300	223	31	.	.	PUNCT
ejpam-300	224	1	theorem	theorem	VERB
ejpam-300	224	2	5.1	5.1	NUM
ejpam-300	224	3	.	.	PUNCT
ejpam-300	225	1	let	let	VERB
ejpam-300	225	2	x	x	PRON
ejpam-300	225	3	be	be	AUX
ejpam-300	225	4	a	a	DET
ejpam-300	225	5	space	space	NOUN
ejpam-300	225	6	and	and	CCONJ
ejpam-300	225	7	φ	φ	PROPN
ejpam-300	225	8	6=	6=	PROPN
ejpam-300	225	9	a	a	DET
ejpam-300	225	10	a	a	DET
ejpam-300	225	11	finite	finite	NOUN
ejpam-300	225	12	γ	γ	X
ejpam-300	225	13	-	-	ADJ
ejpam-300	225	14	open	open	ADJ
ejpam-300	225	15	set	set	NOUN
ejpam-300	225	16	such	such	ADJ
ejpam-300	225	17	that	that	SCONJ
ejpam-300	225	18	a	a	PRON
ejpam-300	225	19	is	be	AUX
ejpam-300	225	20	not	not	PART
ejpam-300	225	21	a	a	DET
ejpam-300	225	22	minimal	minimal	ADJ
ejpam-300	225	23	γ	γ	X
ejpam-300	225	24	-	-	ADJ
ejpam-300	225	25	open	open	ADJ
ejpam-300	225	26	set	set	NOUN
ejpam-300	225	27	.	.	PUNCT
ejpam-300	226	1	let	let	VERB
ejpam-300	226	2	{	{	PUNCT
ejpam-300	226	3	a1	a1	PROPN
ejpam-300	226	4	,	,	PUNCT
ejpam-300	226	5	a2	a2	PROPN
ejpam-300	226	6	,	,	PUNCT
ejpam-300	226	7	...	...	PUNCT
ejpam-300	226	8	,	,	PUNCT
ejpam-300	226	9	am	be	AUX
ejpam-300	226	10	}	}	PUNCT
ejpam-300	226	11	be	be	AUX
ejpam-300	226	12	a	a	DET
ejpam-300	226	13	class	class	NOUN
ejpam-300	226	14	of	of	ADP
ejpam-300	226	15	all	all	DET
ejpam-300	226	16	minimal	minimal	ADJ
ejpam-300	226	17	γ	γ	ADJ
ejpam-300	226	18	-	-	ADJ
ejpam-300	226	19	open	open	ADJ
ejpam-300	226	20	sets	set	NOUN
ejpam-300	226	21	in	in	ADP
ejpam-300	226	22	a	a	PRON
ejpam-300	226	23	and	and	CCONJ
ejpam-300	226	24	y	y	PROPN
ejpam-300	226	25	∈	∈	PROPN
ejpam-300	226	26	a−	a−	PROPN
ejpam-300	226	27	(	(	PUNCT
ejpam-300	226	28	a1	a1	PROPN
ejpam-300	226	29	∪	∪	NOUN
ejpam-300	226	30	a2	a2	PROPN
ejpam-300	226	31	∪	∪	ADJ
ejpam-300	226	32	...	...	PUNCT
ejpam-300	226	33	∪	∪	X
ejpam-300	226	34	am	am	NOUN
ejpam-300	226	35	)	)	PUNCT
ejpam-300	226	36	.	.	PUNCT
ejpam-300	227	1	if	if	SCONJ
ejpam-300	227	2	ay	ay	PROPN
ejpam-300	227	3	=	=	SYM
ejpam-300	227	4	∩{b	∩{b	NOUN
ejpam-300	227	5	:	:	PUNCT
ejpam-300	227	6	b	b	X
ejpam-300	227	7	is	be	AUX
ejpam-300	227	8	a	a	DET
ejpam-300	227	9	γ	γ	NOUN
ejpam-300	227	10	-	-	ADJ
ejpam-300	227	11	open	open	ADJ
ejpam-300	227	12	nbd	nbd	PROPN
ejpam-300	227	13	of	of	ADP
ejpam-300	227	14	y	y	PROPN
ejpam-300	227	15	}	}	PUNCT
ejpam-300	227	16	.	.	PUNCT
ejpam-300	228	1	then	then	ADV
ejpam-300	228	2	there	there	PRON
ejpam-300	228	3	exists	exist	VERB
ejpam-300	228	4	a	a	DET
ejpam-300	228	5	natural	natural	ADJ
ejpam-300	228	6	number	number	NOUN
ejpam-300	228	7	k	k	PROPN
ejpam-300	228	8	∈	∈	PROPN
ejpam-300	228	9	{	{	PUNCT
ejpam-300	228	10	1	1	NUM
ejpam-300	228	11	,	,	PUNCT
ejpam-300	228	12	2	2	NUM
ejpam-300	228	13	,	,	PUNCT
ejpam-300	228	14	...	...	PUNCT
ejpam-300	228	15	,	,	PUNCT
ejpam-300	228	16	m	m	VERB
ejpam-300	228	17	}	}	PUNCT
ejpam-300	228	18	such	such	ADJ
ejpam-300	228	19	that	that	SCONJ
ejpam-300	228	20	ak	ak	PROPN
ejpam-300	228	21	is	be	AUX
ejpam-300	228	22	contained	contain	VERB
ejpam-300	228	23	in	in	ADP
ejpam-300	228	24	ay	ay	NOUN
ejpam-300	228	25	,	,	PUNCT
ejpam-300	228	26	where	where	SCONJ
ejpam-300	228	27	γ	γ	NOUN
ejpam-300	228	28	is	be	AUX
ejpam-300	228	29	regular	regular	ADJ
ejpam-300	228	30	.	.	PUNCT
ejpam-300	229	1	proof	proof	NOUN
ejpam-300	229	2	.	.	PUNCT
ejpam-300	230	1	suppose	suppose	VERB
ejpam-300	230	2	on	on	ADP
ejpam-300	230	3	the	the	DET
ejpam-300	230	4	contrary	contrary	NOUN
ejpam-300	230	5	that	that	SCONJ
ejpam-300	230	6	for	for	ADP
ejpam-300	230	7	any	any	DET
ejpam-300	230	8	natural	natural	ADJ
ejpam-300	230	9	number	number	NOUN
ejpam-300	230	10	k	k	PROPN
ejpam-300	230	11	∈	∈	PROPN
ejpam-300	230	12	{	{	PUNCT
ejpam-300	230	13	1	1	NUM
ejpam-300	230	14	,	,	PUNCT
ejpam-300	230	15	2	2	NUM
ejpam-300	230	16	,	,	PUNCT
ejpam-300	230	17	...	...	PUNCT
ejpam-300	230	18	,	,	PUNCT
ejpam-300	230	19	m	m	VERB
ejpam-300	230	20	}	}	PUNCT
ejpam-300	230	21	,	,	PUNCT
ejpam-300	230	22	ak	ak	PROPN
ejpam-300	230	23	is	be	AUX
ejpam-300	230	24	not	not	PART
ejpam-300	230	25	contained	contain	VERB
ejpam-300	230	26	in	in	ADP
ejpam-300	230	27	ay	ay	PROPN
ejpam-300	230	28	.	.	PUNCT
ejpam-300	231	1	by	by	ADP
ejpam-300	231	2	corollary	corollary	ADJ
ejpam-300	231	3	3.1	3.1	NUM
ejpam-300	231	4	,	,	PUNCT
ejpam-300	231	5	for	for	ADP
ejpam-300	231	6	any	any	DET
ejpam-300	231	7	minimal	minimal	ADJ
ejpam-300	231	8	γ	γ	NOUN
ejpam-300	231	9	-	-	ADJ
ejpam-300	231	10	open	open	ADJ
ejpam-300	231	11	set	set	VERB
ejpam-300	231	12	ak	ak	PROPN
ejpam-300	231	13	in	in	ADP
ejpam-300	231	14	a	a	PRON
ejpam-300	231	15	,	,	PUNCT
ejpam-300	231	16	ak∩ay	ak∩ay	PROPN
ejpam-300	231	17	=	=	PROPN
ejpam-300	231	18	φ	φ	PROPN
ejpam-300	231	19	.	.	PUNCT
ejpam-300	232	1	by	by	ADP
ejpam-300	232	2	proposition	proposition	NOUN
ejpam-300	232	3	4.3	4.3	NUM
ejpam-300	232	4	,	,	PUNCT
ejpam-300	232	5	φ	φ	PROPN
ejpam-300	232	6	6=	6=	PROPN
ejpam-300	233	1	ay	ay	PROPN
ejpam-300	233	2	is	be	AUX
ejpam-300	233	3	a	a	DET
ejpam-300	233	4	finite	finite	NOUN
ejpam-300	233	5	γ	γ	X
ejpam-300	233	6	-	-	ADJ
ejpam-300	233	7	open	open	ADJ
ejpam-300	233	8	set	set	NOUN
ejpam-300	233	9	.	.	PUNCT
ejpam-300	234	1	therefore	therefore	ADV
ejpam-300	234	2	by	by	ADP
ejpam-300	234	3	proposition	proposition	NOUN
ejpam-300	234	4	4.1	4.1	NUM
ejpam-300	234	5	,	,	PUNCT
ejpam-300	234	6	there	there	PRON
ejpam-300	234	7	exists	exist	VERB
ejpam-300	234	8	a	a	DET
ejpam-300	234	9	minimal	minimal	ADJ
ejpam-300	234	10	γ	γ	X
ejpam-300	234	11	-	-	ADJ
ejpam-300	234	12	open	open	ADJ
ejpam-300	234	13	set	set	NOUN
ejpam-300	234	14	c	c	PROPN
ejpam-300	234	15	such	such	ADJ
ejpam-300	234	16	that	that	PRON
ejpam-300	234	17	c	c	PROPN
ejpam-300	234	18	⊆	⊆	NUM
ejpam-300	234	19	ay	ay	NOUN
ejpam-300	234	20	.	.	PUNCT
ejpam-300	235	1	since	since	SCONJ
ejpam-300	235	2	c	c	PROPN
ejpam-300	235	3	⊆	⊆	NUM
ejpam-300	235	4	ay	ay	NOUN
ejpam-300	235	5	⊆	⊆	NUM
ejpam-300	235	6	a	a	PRON
ejpam-300	235	7	,	,	PUNCT
ejpam-300	235	8	then	then	ADV
ejpam-300	235	9	c	c	PROPN
ejpam-300	235	10	is	be	AUX
ejpam-300	235	11	a	a	DET
ejpam-300	235	12	minimal	minimal	ADJ
ejpam-300	235	13	γ	γ	X
ejpam-300	235	14	-	-	ADJ
ejpam-300	235	15	open	open	ADJ
ejpam-300	235	16	set	set	NOUN
ejpam-300	235	17	in	in	ADP
ejpam-300	235	18	a.	a.	NOUN
ejpam-300	235	19	by	by	ADP
ejpam-300	235	20	supposition	supposition	NOUN
ejpam-300	235	21	,	,	PUNCT
ejpam-300	235	22	for	for	ADP
ejpam-300	235	23	any	any	DET
ejpam-300	235	24	minimal	minimal	ADJ
ejpam-300	235	25	γ	γ	NOUN
ejpam-300	235	26	-	-	ADJ
ejpam-300	235	27	open	open	ADJ
ejpam-300	235	28	set	set	ADJ
ejpam-300	235	29	ak	ak	PROPN
ejpam-300	235	30	,	,	PUNCT
ejpam-300	235	31	we	we	PRON
ejpam-300	235	32	have	have	VERB
ejpam-300	235	33	ak	ak	PROPN
ejpam-300	235	34	∩	∩	NOUN
ejpam-300	235	35	c	c	PROPN
ejpam-300	235	36	⊆	⊆	NUM
ejpam-300	235	37	ak	ak	PROPN
ejpam-300	235	38	∩	∩	PROPN
ejpam-300	235	39	ay	ay	PROPN
ejpam-300	235	40	=	=	SYM
ejpam-300	235	41	φ	φ	PROPN
ejpam-300	235	42	.	.	PUNCT
ejpam-300	236	1	therefore	therefore	ADV
ejpam-300	236	2	for	for	ADP
ejpam-300	236	3	any	any	DET
ejpam-300	236	4	natural	natural	ADJ
ejpam-300	236	5	number	number	NOUN
ejpam-300	236	6	k	k	PROPN
ejpam-300	236	7	∈	∈	PROPN
ejpam-300	236	8	{	{	PUNCT
ejpam-300	236	9	1	1	NUM
ejpam-300	236	10	,	,	PUNCT
ejpam-300	236	11	2	2	NUM
ejpam-300	236	12	,	,	PUNCT
ejpam-300	236	13	...	...	PUNCT
ejpam-300	236	14	,	,	PUNCT
ejpam-300	236	15	m	m	VERB
ejpam-300	236	16	}	}	PUNCT
ejpam-300	236	17	,	,	PUNCT
ejpam-300	236	18	c	c	PROPN
ejpam-300	236	19	6=	6=	PROPN
ejpam-300	236	20	ak	ak	PROPN
ejpam-300	236	21	.	.	PROPN
ejpam-300	237	1	this	this	PRON
ejpam-300	237	2	is	be	AUX
ejpam-300	237	3	a	a	DET
ejpam-300	237	4	contradiction	contradiction	NOUN
ejpam-300	237	5	to	to	ADP
ejpam-300	237	6	our	our	PRON
ejpam-300	237	7	supposition	supposition	NOUN
ejpam-300	237	8	.	.	PUNCT
ejpam-300	238	1	hence	hence	ADV
ejpam-300	238	2	the	the	DET
ejpam-300	238	3	proof	proof	NOUN
ejpam-300	238	4	.	.	PUNCT
ejpam-300	239	1	proposition	proposition	NOUN
ejpam-300	239	2	5.1	5.1	NUM
ejpam-300	239	3	.	.	PUNCT
ejpam-300	240	1	let	let	VERB
ejpam-300	240	2	x	x	PRON
ejpam-300	240	3	be	be	AUX
ejpam-300	240	4	a	a	DET
ejpam-300	240	5	space	space	NOUN
ejpam-300	240	6	and	and	CCONJ
ejpam-300	240	7	φ	φ	PROPN
ejpam-300	240	8	6=	6=	PROPN
ejpam-300	240	9	a	a	DET
ejpam-300	240	10	be	be	AUX
ejpam-300	240	11	a	a	DET
ejpam-300	240	12	finite	finite	NOUN
ejpam-300	240	13	γ	γ	X
ejpam-300	240	14	-	-	ADJ
ejpam-300	240	15	open	open	ADJ
ejpam-300	240	16	set	set	NOUN
ejpam-300	240	17	which	which	PRON
ejpam-300	240	18	is	be	AUX
ejpam-300	240	19	not	not	PART
ejpam-300	240	20	a	a	DET
ejpam-300	240	21	minimal	minimal	ADJ
ejpam-300	240	22	γ	γ	X
ejpam-300	240	23	-	-	ADJ
ejpam-300	240	24	open	open	ADJ
ejpam-300	240	25	set	set	NOUN
ejpam-300	240	26	.	.	PUNCT
ejpam-300	241	1	let	let	VERB
ejpam-300	241	2	{	{	PUNCT
ejpam-300	241	3	a1	a1	PROPN
ejpam-300	241	4	,	,	PUNCT
ejpam-300	241	5	a2	a2	PROPN
ejpam-300	241	6	,	,	PUNCT
ejpam-300	241	7	...	...	PUNCT
ejpam-300	241	8	,	,	PUNCT
ejpam-300	241	9	am	be	AUX
ejpam-300	241	10	}	}	PUNCT
ejpam-300	241	11	be	be	AUX
ejpam-300	241	12	a	a	DET
ejpam-300	241	13	class	class	NOUN
ejpam-300	241	14	of	of	ADP
ejpam-300	241	15	all	all	DET
ejpam-300	241	16	minimal	minimal	ADJ
ejpam-300	241	17	γ	γ	ADJ
ejpam-300	241	18	-	-	ADJ
ejpam-300	241	19	open	open	ADJ
ejpam-300	241	20	sets	set	NOUN
ejpam-300	241	21	in	in	ADP
ejpam-300	241	22	a	a	PRON
ejpam-300	241	23	and	and	CCONJ
ejpam-300	241	24	y	y	PROPN
ejpam-300	241	25	∈	∈	PROPN
ejpam-300	241	26	a−	a−	PROPN
ejpam-300	241	27	(	(	PUNCT
ejpam-300	241	28	a1	a1	PROPN
ejpam-300	241	29	∪	∪	NOUN
ejpam-300	241	30	a2	a2	PROPN
ejpam-300	241	31	∪	∪	ADJ
ejpam-300	241	32	...	...	PUNCT
ejpam-300	241	33	∪	∪	ADP
ejpam-300	241	34	am	am	NOUN
ejpam-300	241	35	)	)	PUNCT
ejpam-300	241	36	.	.	PUNCT
ejpam-300	242	1	then	then	ADV
ejpam-300	242	2	there	there	PRON
ejpam-300	242	3	exists	exist	VERB
ejpam-300	242	4	a	a	DET
ejpam-300	242	5	natural	natural	ADJ
ejpam-300	242	6	number	number	NOUN
ejpam-300	242	7	k	k	PROPN
ejpam-300	242	8	∈	∈	PROPN
ejpam-300	242	9	{	{	PUNCT
ejpam-300	242	10	1	1	NUM
ejpam-300	242	11	,	,	PUNCT
ejpam-300	242	12	2	2	NUM
ejpam-300	242	13	,	,	PUNCT
ejpam-300	242	14	...	...	PUNCT
ejpam-300	242	15	,	,	PUNCT
ejpam-300	242	16	m	m	VERB
ejpam-300	242	17	}	}	PUNCT
ejpam-300	242	18	such	such	ADJ
ejpam-300	242	19	that	that	PRON
ejpam-300	242	20	for	for	ADP
ejpam-300	242	21	any	any	DET
ejpam-300	242	22	γ	γ	X
ejpam-300	242	23	-	-	ADJ
ejpam-300	242	24	open	open	ADJ
ejpam-300	242	25	nbd	nbd	PROPN
ejpam-300	242	26	by	by	ADP
ejpam-300	242	27	of	of	ADP
ejpam-300	242	28	y	y	PROPN
ejpam-300	242	29	,	,	PUNCT
ejpam-300	242	30	ak	ak	PROPN
ejpam-300	242	31	is	be	AUX
ejpam-300	242	32	contained	contain	VERB
ejpam-300	242	33	in	in	ADP
ejpam-300	242	34	by	by	ADP
ejpam-300	242	35	,	,	PUNCT
ejpam-300	242	36	where	where	SCONJ
ejpam-300	242	37	γ	γ	PROPN
ejpam-300	242	38	is	be	AUX
ejpam-300	242	39	regular	regular	ADJ
ejpam-300	242	40	.	.	PUNCT
ejpam-300	243	1	proof	proof	NOUN
ejpam-300	243	2	.	.	PUNCT
ejpam-300	244	1	this	this	PRON
ejpam-300	244	2	follows	follow	VERB
ejpam-300	244	3	from	from	ADP
ejpam-300	244	4	theorem	theorem	ADJ
ejpam-300	244	5	5.1	5.1	NUM
ejpam-300	244	6	as	as	ADP
ejpam-300	244	7	∩{b	∩{b	NUM
ejpam-300	244	8	:	:	PUNCT
ejpam-300	244	9	b	b	X
ejpam-300	244	10	is	be	AUX
ejpam-300	244	11	a	a	DET
ejpam-300	244	12	γ	γ	NOUN
ejpam-300	244	13	-	-	ADJ
ejpam-300	244	14	open	open	ADJ
ejpam-300	244	15	nbd	nbd	PROPN
ejpam-300	244	16	of	of	ADP
ejpam-300	244	17	y	y	PROPN
ejpam-300	244	18	}	}	PUNCT
ejpam-300	244	19	⊆	⊆	NUM
ejpam-300	244	20	by	by	ADP
ejpam-300	244	21	.	.	PUNCT
ejpam-300	245	1	hence	hence	ADV
ejpam-300	245	2	the	the	DET
ejpam-300	245	3	proof	proof	NOUN
ejpam-300	245	4	.	.	PUNCT
ejpam-300	246	1	s.	s.	PROPN
ejpam-300	246	2	hussain	hussain	PROPN
ejpam-300	246	3	and	and	CCONJ
ejpam-300	246	4	b.	b.	PROPN
ejpam-300	246	5	ahmad	ahmad	PROPN
ejpam-300	246	6	/	/	SYM
ejpam-300	246	7	eur	eur	PROPN
ejpam-300	246	8	.	.	PUNCT
ejpam-300	247	1	j.	j.	PROPN
ejpam-300	247	2	pure	pure	PROPN
ejpam-300	247	3	appl	appl	PROPN
ejpam-300	247	4	.	.	PROPN
ejpam-300	247	5	math	math	PROPN
ejpam-300	247	6	,	,	PUNCT
ejpam-300	247	7	2	2	NUM
ejpam-300	247	8	(	(	PUNCT
ejpam-300	247	9	2009	2009	NUM
ejpam-300	247	10	)	)	PUNCT
ejpam-300	247	11	,	,	PUNCT
ejpam-300	247	12	(	(	PUNCT
ejpam-300	247	13	338	338	NUM
ejpam-300	247	14	-	-	SYM
ejpam-300	247	15	351	351	NUM
ejpam-300	247	16	)	)	PUNCT
ejpam-300	247	17	348	348	NUM
ejpam-300	247	18	theorem	theorem	VERB
ejpam-300	247	19	5.2	5.2	NUM
ejpam-300	247	20	.	.	PUNCT
ejpam-300	248	1	let	let	VERB
ejpam-300	248	2	x	x	PRON
ejpam-300	248	3	be	be	AUX
ejpam-300	248	4	a	a	DET
ejpam-300	248	5	space	space	NOUN
ejpam-300	248	6	and	and	CCONJ
ejpam-300	248	7	φ	φ	PROPN
ejpam-300	248	8	6=	6=	PROPN
ejpam-300	248	9	a	a	DET
ejpam-300	248	10	be	be	AUX
ejpam-300	248	11	a	a	DET
ejpam-300	248	12	finite	finite	NOUN
ejpam-300	248	13	γ	γ	X
ejpam-300	248	14	-	-	ADJ
ejpam-300	248	15	open	open	ADJ
ejpam-300	248	16	set	set	NOUN
ejpam-300	248	17	which	which	PRON
ejpam-300	248	18	is	be	AUX
ejpam-300	248	19	not	not	PART
ejpam-300	248	20	a	a	DET
ejpam-300	248	21	minimal	minimal	ADJ
ejpam-300	248	22	γ	γ	X
ejpam-300	248	23	-	-	ADJ
ejpam-300	248	24	open	open	ADJ
ejpam-300	248	25	set	set	NOUN
ejpam-300	248	26	.	.	PUNCT
ejpam-300	249	1	let	let	VERB
ejpam-300	249	2	{	{	PUNCT
ejpam-300	249	3	a1	a1	PROPN
ejpam-300	249	4	,	,	PUNCT
ejpam-300	249	5	a2	a2	PROPN
ejpam-300	249	6	,	,	PUNCT
ejpam-300	249	7	...	...	PUNCT
ejpam-300	249	8	,	,	PUNCT
ejpam-300	249	9	am	be	AUX
ejpam-300	249	10	}	}	PUNCT
ejpam-300	249	11	be	be	AUX
ejpam-300	249	12	the	the	DET
ejpam-300	249	13	class	class	NOUN
ejpam-300	249	14	of	of	ADP
ejpam-300	249	15	all	all	DET
ejpam-300	249	16	minimal	minimal	ADJ
ejpam-300	249	17	γ	γ	ADJ
ejpam-300	249	18	-	-	ADJ
ejpam-300	249	19	open	open	ADJ
ejpam-300	249	20	sets	set	NOUN
ejpam-300	249	21	in	in	ADP
ejpam-300	249	22	a	a	PRON
ejpam-300	249	23	and	and	CCONJ
ejpam-300	249	24	y	y	PROPN
ejpam-300	249	25	∈	∈	PROPN
ejpam-300	249	26	a−	a−	PROPN
ejpam-300	249	27	(	(	PUNCT
ejpam-300	249	28	a1	a1	PROPN
ejpam-300	249	29	∪	∪	NOUN
ejpam-300	249	30	a2	a2	PROPN
ejpam-300	249	31	∪	∪	ADJ
ejpam-300	249	32	...	...	PUNCT
ejpam-300	249	33	∪	∪	ADP
ejpam-300	249	34	am	am	NOUN
ejpam-300	249	35	)	)	PUNCT
ejpam-300	249	36	.	.	PUNCT
ejpam-300	250	1	then	then	ADV
ejpam-300	250	2	there	there	PRON
ejpam-300	250	3	exists	exist	VERB
ejpam-300	250	4	a	a	DET
ejpam-300	250	5	natural	natural	ADJ
ejpam-300	250	6	number	number	NOUN
ejpam-300	250	7	k	k	PROPN
ejpam-300	250	8	∈	∈	PROPN
ejpam-300	250	9	{	{	PUNCT
ejpam-300	250	10	1	1	NUM
ejpam-300	250	11	,	,	PUNCT
ejpam-300	250	12	2	2	NUM
ejpam-300	250	13	,	,	PUNCT
ejpam-300	250	14	...	...	PUNCT
ejpam-300	250	15	,	,	PUNCT
ejpam-300	250	16	m	m	VERB
ejpam-300	250	17	}	}	PUNCT
ejpam-300	250	18	such	such	ADJ
ejpam-300	250	19	that	that	SCONJ
ejpam-300	250	20	y	y	PROPN
ejpam-300	250	21	∈	∈	PROPN
ejpam-300	250	22	clγ(ak	clγ(ak	PROPN
ejpam-300	250	23	)	)	PUNCT
ejpam-300	250	24	,	,	PUNCT
ejpam-300	250	25	where	where	SCONJ
ejpam-300	250	26	γ	γ	NOUN
ejpam-300	250	27	is	be	AUX
ejpam-300	250	28	regular	regular	ADJ
ejpam-300	250	29	.	.	PUNCT
ejpam-300	251	1	proof	proof	NOUN
ejpam-300	251	2	.	.	PUNCT
ejpam-300	252	1	it	it	PRON
ejpam-300	252	2	follows	follow	VERB
ejpam-300	252	3	from	from	ADP
ejpam-300	252	4	proposition	proposition	NOUN
ejpam-300	252	5	5.1	5.1	NUM
ejpam-300	252	6	that	that	SCONJ
ejpam-300	252	7	there	there	PRON
ejpam-300	252	8	exists	exist	VERB
ejpam-300	252	9	a	a	DET
ejpam-300	252	10	natural	natural	ADJ
ejpam-300	252	11	number	number	NOUN
ejpam-300	252	12	k	k	PROPN
ejpam-300	252	13	∈	∈	PROPN
ejpam-300	252	14	{	{	PUNCT
ejpam-300	252	15	1	1	NUM
ejpam-300	252	16	,	,	PUNCT
ejpam-300	252	17	2	2	NUM
ejpam-300	252	18	,	,	PUNCT
ejpam-300	252	19	...	...	PUNCT
ejpam-300	252	20	,	,	PUNCT
ejpam-300	252	21	m	m	VERB
ejpam-300	252	22	}	}	PUNCT
ejpam-300	252	23	such	such	ADJ
ejpam-300	252	24	that	that	SCONJ
ejpam-300	252	25	ak	ak	PROPN
ejpam-300	252	26	⊆	⊆	NUM
ejpam-300	252	27	b	b	PROPN
ejpam-300	252	28	for	for	ADP
ejpam-300	252	29	γ	γ	X
ejpam-300	252	30	-	-	ADJ
ejpam-300	252	31	open	open	ADJ
ejpam-300	252	32	nbd	nbd	PROPN
ejpam-300	252	33	b	b	PROPN
ejpam-300	252	34	of	of	ADP
ejpam-300	252	35	x.	x.	PROPN
ejpam-300	252	36	therefore	therefore	PROPN
ejpam-300	252	37	φ	φ	PROPN
ejpam-300	252	38	6=	6=	PROPN
ejpam-300	252	39	ak	ak	PROPN
ejpam-300	252	40	∩ak	∩ak	ADV
ejpam-300	253	1	⊆	⊆	NUM
ejpam-300	253	2	ak∩b	ak∩b	NUM
ejpam-300	253	3	⊆	⊆	NUM
ejpam-300	253	4	ak	ak	PROPN
ejpam-300	253	5	∩	∩	NOUN
ejpam-300	253	6	bγ	bγ	PROPN
ejpam-300	253	7	implies	imply	VERB
ejpam-300	253	8	y	y	PROPN
ejpam-300	253	9	∈	∈	PROPN
ejpam-300	253	10	clγ(ak	clγ(ak	NOUN
ejpam-300	253	11	)	)	PUNCT
ejpam-300	253	12	.	.	PUNCT
ejpam-300	254	1	this	this	PRON
ejpam-300	254	2	completes	complete	VERB
ejpam-300	254	3	the	the	DET
ejpam-300	254	4	proof	proof	NOUN
ejpam-300	254	5	.	.	PUNCT
ejpam-300	255	1	proposition	proposition	NOUN
ejpam-300	255	2	5.2	5.2	NUM
ejpam-300	255	3	.	.	PUNCT
ejpam-300	256	1	let	let	VERB
ejpam-300	256	2	φ	φ	PROPN
ejpam-300	256	3	6=	6=	ADP
ejpam-300	256	4	a	a	DET
ejpam-300	256	5	be	be	AUX
ejpam-300	256	6	a	a	DET
ejpam-300	256	7	finite	finite	NOUN
ejpam-300	256	8	γ	γ	X
ejpam-300	256	9	-	-	ADJ
ejpam-300	256	10	open	open	ADJ
ejpam-300	256	11	set	set	NOUN
ejpam-300	256	12	in	in	ADP
ejpam-300	256	13	a	a	DET
ejpam-300	256	14	space	space	NOUN
ejpam-300	256	15	x	x	NOUN
ejpam-300	256	16	,	,	PUNCT
ejpam-300	256	17	γ	γ	PROPN
ejpam-300	256	18	∈	∈	PROPN
ejpam-300	256	19	γ(x	γ(x	PROPN
ejpam-300	256	20	)	)	PUNCT
ejpam-300	256	21	and	and	CCONJ
ejpam-300	256	22	for	for	ADP
ejpam-300	256	23	each	each	DET
ejpam-300	256	24	k	k	PROPN
ejpam-300	256	25	∈	∈	PROPN
ejpam-300	256	26	{	{	PUNCT
ejpam-300	256	27	1	1	NUM
ejpam-300	256	28	,	,	PUNCT
ejpam-300	256	29	2	2	NUM
ejpam-300	256	30	,	,	PUNCT
ejpam-300	256	31	...	...	PUNCT
ejpam-300	256	32	,	,	PUNCT
ejpam-300	256	33	m	m	VERB
ejpam-300	256	34	}	}	PUNCT
ejpam-300	256	35	,	,	PUNCT
ejpam-300	256	36	ak	ak	PROPN
ejpam-300	256	37	a	a	DET
ejpam-300	256	38	minimal	minimal	ADJ
ejpam-300	256	39	γ	γ	X
ejpam-300	256	40	-	-	ADJ
ejpam-300	256	41	open	open	ADJ
ejpam-300	256	42	set	set	NOUN
ejpam-300	256	43	in	in	ADP
ejpam-300	256	44	a.	a.	NOUN
ejpam-300	256	45	if	if	SCONJ
ejpam-300	256	46	the	the	DET
ejpam-300	256	47	class	class	NOUN
ejpam-300	256	48	{	{	PUNCT
ejpam-300	256	49	a1	a1	PROPN
ejpam-300	256	50	,	,	PUNCT
ejpam-300	256	51	a2	a2	PROPN
ejpam-300	256	52	,	,	PUNCT
ejpam-300	256	53	...	...	PUNCT
ejpam-300	256	54	,	,	PUNCT
ejpam-300	256	55	am	be	AUX
ejpam-300	256	56	}	}	PUNCT
ejpam-300	256	57	contains	contain	VERB
ejpam-300	256	58	all	all	DET
ejpam-300	256	59	minimal	minimal	ADJ
ejpam-300	256	60	γ	γ	ADJ
ejpam-300	256	61	-	-	ADJ
ejpam-300	256	62	open	open	ADJ
ejpam-300	256	63	sets	set	NOUN
ejpam-300	256	64	in	in	ADP
ejpam-300	256	65	a	a	PRON
ejpam-300	256	66	,	,	PUNCT
ejpam-300	256	67	then	then	ADV
ejpam-300	256	68	for	for	ADP
ejpam-300	256	69	any	any	DET
ejpam-300	256	70	φ	φ	NOUN
ejpam-300	256	71	6=	6=	ADP
ejpam-300	256	72	bk	bk	PROPN
ejpam-300	256	73	⊆	⊆	NUM
ejpam-300	256	74	ak	ak	PROPN
ejpam-300	256	75	,	,	PUNCT
ejpam-300	256	76	a⊆	a⊆	VERB
ejpam-300	257	1	clγ(b1	clγ(b1	NOUN
ejpam-300	257	2	∪	∪	NOUN
ejpam-300	257	3	b2	b2	NOUN
ejpam-300	257	4	∪	∪	NOUN
ejpam-300	257	5	...	...	PUNCT
ejpam-300	257	6	∪	∪	X
ejpam-300	257	7	bm	bm	PROPN
ejpam-300	257	8	)	)	PUNCT
ejpam-300	257	9	,	,	PUNCT
ejpam-300	257	10	where	where	SCONJ
ejpam-300	257	11	γ	γ	PROPN
ejpam-300	257	12	is	be	AUX
ejpam-300	257	13	regular	regular	ADJ
ejpam-300	257	14	and	and	CCONJ
ejpam-300	257	15	open	open	ADJ
ejpam-300	257	16	.	.	PUNCT
ejpam-300	258	1	proof	proof	NOUN
ejpam-300	258	2	.	.	PUNCT
ejpam-300	259	1	let	let	VERB
ejpam-300	259	2	φ	φ	PROPN
ejpam-300	259	3	6=	6=	ADP
ejpam-300	259	4	a	a	DET
ejpam-300	259	5	be	be	AUX
ejpam-300	259	6	a	a	DET
ejpam-300	259	7	finite	finite	NOUN
ejpam-300	259	8	γ	γ	X
ejpam-300	259	9	-	-	ADJ
ejpam-300	259	10	open	open	ADJ
ejpam-300	259	11	set	set	NOUN
ejpam-300	259	12	.	.	PUNCT
ejpam-300	260	1	we	we	PRON
ejpam-300	260	2	consider	consider	VERB
ejpam-300	260	3	the	the	DET
ejpam-300	260	4	following	follow	VERB
ejpam-300	260	5	two	two	NUM
ejpam-300	260	6	cases	case	NOUN
ejpam-300	260	7	:	:	PUNCT
ejpam-300	260	8	case	case	NOUN
ejpam-300	260	9	1	1	NUM
ejpam-300	260	10	.	.	PUNCT
ejpam-300	261	1	if	if	SCONJ
ejpam-300	261	2	a	a	PRON
ejpam-300	261	3	is	be	AUX
ejpam-300	261	4	a	a	DET
ejpam-300	261	5	minimal	minimal	ADJ
ejpam-300	261	6	γ	γ	X
ejpam-300	261	7	-	-	ADJ
ejpam-300	261	8	open	open	ADJ
ejpam-300	261	9	set	set	NOUN
ejpam-300	261	10	,	,	PUNCT
ejpam-300	261	11	then	then	ADV
ejpam-300	261	12	this	this	PRON
ejpam-300	261	13	follows	follow	VERB
ejpam-300	261	14	directly	directly	ADV
ejpam-300	261	15	from	from	ADP
ejpam-300	261	16	proposition	proposition	NOUN
ejpam-300	261	17	3.6	3.6	NUM
ejpam-300	261	18	.	.	PUNCT
ejpam-300	262	1	case	case	NOUN
ejpam-300	262	2	2	2	NUM
ejpam-300	262	3	.	.	PUNCT
ejpam-300	263	1	if	if	SCONJ
ejpam-300	263	2	a	a	PRON
ejpam-300	263	3	is	be	AUX
ejpam-300	263	4	not	not	PART
ejpam-300	263	5	a	a	DET
ejpam-300	263	6	minimal	minimal	ADJ
ejpam-300	263	7	γ	γ	X
ejpam-300	263	8	-	-	ADJ
ejpam-300	263	9	open	open	ADJ
ejpam-300	263	10	set	set	NOUN
ejpam-300	263	11	.	.	PUNCT
ejpam-300	264	1	y	y	PROPN
ejpam-300	264	2	∈	∈	PROPN
ejpam-300	264	3	a−(a1∪a2∪	a−(a1∪a2∪	NUM
ejpam-300	264	4	...	...	PUNCT
ejpam-300	264	5	∪am	∪am	X
ejpam-300	264	6	)	)	PUNCT
ejpam-300	264	7	.	.	PUNCT
ejpam-300	265	1	then	then	ADV
ejpam-300	265	2	by	by	ADP
ejpam-300	265	3	theorem	theorem	NOUN
ejpam-300	265	4	5.2	5.2	NUM
ejpam-300	265	5	,	,	PUNCT
ejpam-300	265	6	it	it	PRON
ejpam-300	265	7	follows	follow	VERB
ejpam-300	265	8	that	that	SCONJ
ejpam-300	265	9	y	y	PROPN
ejpam-300	265	10	∈	∈	PROPN
ejpam-300	266	1	clγ(a1)∪	clγ(a1)∪	ADP
ejpam-300	266	2	clγ(a2)∪	clγ(a2)∪	NOUN
ejpam-300	266	3	...	...	SYM
ejpam-300	266	4	∪	∪	ADJ
ejpam-300	266	5	clγ(am	clγ(am	NOUN
ejpam-300	266	6	)	)	PUNCT
ejpam-300	266	7	.	.	PUNCT
ejpam-300	267	1	therefore	therefore	ADV
ejpam-300	267	2	by	by	ADP
ejpam-300	267	3	proposition	proposition	NOUN
ejpam-300	267	4	3.6	3.6	NUM
ejpam-300	267	5	,	,	PUNCT
ejpam-300	267	6	we	we	PRON
ejpam-300	267	7	have	have	VERB
ejpam-300	267	8	a⊆	a⊆	VERB
ejpam-300	267	9	clγ(a1)∪clγ(a2)∪	clγ(a1)∪clγ(a2)∪	NOUN
ejpam-300	267	10	...	...	PUNCT
ejpam-300	267	11	∪clγ(am	∪clγ(am	PROPN
ejpam-300	267	12	)	)	PUNCT
ejpam-300	268	1	=	=	SYM
ejpam-300	268	2	clγ(b1)∪clγ(b2)∪	clγ(b1)∪clγ(b2)∪	NOUN
ejpam-300	268	3	...	...	PUNCT
ejpam-300	268	4	∪clγ(bm	∪clγ(bm	PROPN
ejpam-300	268	5	)	)	PUNCT
ejpam-300	268	6	=	=	SYM
ejpam-300	268	7	clγ(b1∪b2∪	clγ(b1∪b2∪	PROPN
ejpam-300	268	8	...	...	PUNCT
ejpam-300	268	9	∪bm	∪bm	ADJ
ejpam-300	268	10	)	)	PUNCT
ejpam-300	268	11	.	.	PUNCT
ejpam-300	269	1	this	this	PRON
ejpam-300	269	2	completes	complete	VERB
ejpam-300	269	3	the	the	DET
ejpam-300	269	4	proof	proof	NOUN
ejpam-300	269	5	.	.	PUNCT
ejpam-300	270	1	proposition	proposition	NOUN
ejpam-300	270	2	5.3	5.3	NUM
ejpam-300	270	3	.	.	PUNCT
ejpam-300	271	1	let	let	VERB
ejpam-300	271	2	x	x	PRON
ejpam-300	271	3	be	be	AUX
ejpam-300	271	4	a	a	DET
ejpam-300	271	5	space	space	NOUN
ejpam-300	271	6	and	and	CCONJ
ejpam-300	271	7	φ	φ	PROPN
ejpam-300	271	8	6=	6=	PROPN
ejpam-300	271	9	a	a	DET
ejpam-300	271	10	a	a	DET
ejpam-300	271	11	finite	finite	NOUN
ejpam-300	271	12	γ	γ	X
ejpam-300	271	13	-	-	ADJ
ejpam-300	271	14	open	open	ADJ
ejpam-300	271	15	set	set	NOUN
ejpam-300	271	16	and	and	CCONJ
ejpam-300	271	17	ak	ak	PROPN
ejpam-300	271	18	a	a	DET
ejpam-300	271	19	minimal	minimal	ADJ
ejpam-300	271	20	γopen	γopen	NOUN
ejpam-300	271	21	set	set	NOUN
ejpam-300	271	22	in	in	ADP
ejpam-300	271	23	a	a	PRON
ejpam-300	271	24	,	,	PUNCT
ejpam-300	271	25	for	for	ADP
ejpam-300	271	26	each	each	DET
ejpam-300	271	27	k	k	PROPN
ejpam-300	271	28	∈	∈	PROPN
ejpam-300	271	29	{	{	PUNCT
ejpam-300	271	30	1	1	NUM
ejpam-300	271	31	,	,	PUNCT
ejpam-300	271	32	2	2	NUM
ejpam-300	271	33	,	,	PUNCT
ejpam-300	271	34	...	...	PUNCT
ejpam-300	271	35	,	,	PUNCT
ejpam-300	271	36	m	m	VERB
ejpam-300	271	37	}	}	PUNCT
ejpam-300	271	38	.	.	PUNCT
ejpam-300	272	1	if	if	SCONJ
ejpam-300	272	2	for	for	ADP
ejpam-300	272	3	any	any	DET
ejpam-300	272	4	φ	φ	NOUN
ejpam-300	272	5	6=	6=	ADP
ejpam-300	272	6	bk	bk	PROPN
ejpam-300	272	7	⊆	⊆	NUM
ejpam-300	272	8	ak	ak	PROPN
ejpam-300	272	9	,	,	PUNCT
ejpam-300	272	10	a⊆	a⊆	PROPN
ejpam-300	272	11	clγ(b1∪b2∪	clγ(b1∪b2∪	PROPN
ejpam-300	272	12	...	...	PUNCT
ejpam-300	272	13	∪bm	∪bm	PROPN
ejpam-300	272	14	)	)	PUNCT
ejpam-300	272	15	then	then	ADV
ejpam-300	272	16	clγ(a	clγ(a	PROPN
ejpam-300	272	17	)	)	PUNCT
ejpam-300	273	1	=	=	PUNCT
ejpam-300	273	2	clγ(b1	clγ(b1	AUX
ejpam-300	273	3	∪	∪	VERB
ejpam-300	273	4	b2	b2	NOUN
ejpam-300	273	5	∪	∪	ADJ
ejpam-300	273	6	...	...	PUNCT
ejpam-300	273	7	∪	∪	X
ejpam-300	273	8	bm	bm	PROPN
ejpam-300	273	9	)	)	PUNCT
ejpam-300	273	10	,	,	PUNCT
ejpam-300	273	11	where	where	SCONJ
ejpam-300	273	12	γ	γ	NOUN
ejpam-300	273	13	is	be	AUX
ejpam-300	273	14	open	open	ADJ
ejpam-300	273	15	.	.	PUNCT
ejpam-300	274	1	proof	proof	NOUN
ejpam-300	274	2	.	.	PUNCT
ejpam-300	275	1	for	for	ADP
ejpam-300	275	2	anyφ	anyφ	NOUN
ejpam-300	275	3	6=	6=	NUM
ejpam-300	275	4	bk	bk	PROPN
ejpam-300	275	5	⊆	⊆	NUM
ejpam-300	275	6	ak	ak	PROPN
ejpam-300	275	7	,	,	PUNCT
ejpam-300	275	8	k	k	PROPN
ejpam-300	275	9	∈	∈	PROPN
ejpam-300	275	10	{	{	PUNCT
ejpam-300	275	11	1	1	NUM
ejpam-300	275	12	,	,	PUNCT
ejpam-300	275	13	2	2	NUM
ejpam-300	275	14	,	,	PUNCT
ejpam-300	275	15	...	...	PUNCT
ejpam-300	275	16	,	,	PUNCT
ejpam-300	275	17	m	m	VERB
ejpam-300	275	18	}	}	PUNCT
ejpam-300	275	19	,	,	PUNCT
ejpam-300	275	20	we	we	PRON
ejpam-300	275	21	have	have	VERB
ejpam-300	275	22	clγ(b1∪b2∪	clγ(b1∪b2∪	NOUN
ejpam-300	275	23	...	...	PUNCT
ejpam-300	275	24	∪bm)⊆	∪bm)⊆	PROPN
ejpam-300	275	25	clγ(a	clγ(a	PROPN
ejpam-300	275	26	)	)	PUNCT
ejpam-300	275	27	.	.	PUNCT
ejpam-300	276	1	also	also	ADV
ejpam-300	276	2	,	,	PUNCT
ejpam-300	276	3	we	we	PRON
ejpam-300	276	4	have	have	VERB
ejpam-300	276	5	clγ(a)⊆	clγ(a)⊆	PROPN
ejpam-300	276	6	clγ(clγ(b1	clγ(clγ(b1	NOUN
ejpam-300	276	7	∪	∪	VERB
ejpam-300	276	8	b2	b2	PROPN
ejpam-300	276	9	∪	∪	NOUN
ejpam-300	276	10	...	...	PUNCT
ejpam-300	276	11	∪	∪	X
ejpam-300	276	12	bm	bm	PROPN
ejpam-300	276	13	)	)	PUNCT
ejpam-300	276	14	)	)	PUNCT
ejpam-300	277	1	=	=	PUNCT
ejpam-300	277	2	clγ(b1	clγ(b1	AUX
ejpam-300	277	3	∪	∪	VERB
ejpam-300	277	4	b2	b2	NOUN
ejpam-300	277	5	∪	∪	ADJ
ejpam-300	277	6	...	...	PUNCT
ejpam-300	277	7	∪	∪	X
ejpam-300	277	8	bm	bm	PROPN
ejpam-300	277	9	)	)	PUNCT
ejpam-300	277	10	.	.	PUNCT
ejpam-300	278	1	this	this	PRON
ejpam-300	278	2	implies	imply	VERB
ejpam-300	278	3	that	that	SCONJ
ejpam-300	278	4	for	for	ADP
ejpam-300	278	5	any	any	DET
ejpam-300	278	6	φ	φ	NOUN
ejpam-300	278	7	6=	6=	ADP
ejpam-300	278	8	bk	bk	PROPN
ejpam-300	278	9	⊆	⊆	PROPN
ejpam-300	278	10	ak	ak	PROPN
ejpam-300	278	11	,	,	PUNCT
ejpam-300	278	12	clγ(a	clγ(a	PROPN
ejpam-300	278	13	)	)	PUNCT
ejpam-300	278	14	=	=	SYM
ejpam-300	278	15	clγ(b1∪b2∪	clγ(b1∪b2∪	PROPN
ejpam-300	278	16	...	...	PUNCT
ejpam-300	278	17	∪bm	∪bm	ADJ
ejpam-300	278	18	)	)	PUNCT
ejpam-300	278	19	.	.	PUNCT
ejpam-300	279	1	hence	hence	ADV
ejpam-300	279	2	the	the	DET
ejpam-300	279	3	proof	proof	NOUN
ejpam-300	279	4	.	.	PUNCT
ejpam-300	280	1	s.	s.	PROPN
ejpam-300	280	2	hussain	hussain	PROPN
ejpam-300	280	3	and	and	CCONJ
ejpam-300	280	4	b.	b.	PROPN
ejpam-300	280	5	ahmad	ahmad	PROPN
ejpam-300	280	6	/	/	SYM
ejpam-300	280	7	eur	eur	PROPN
ejpam-300	280	8	.	.	PUNCT
ejpam-300	281	1	j.	j.	PROPN
ejpam-300	281	2	pure	pure	PROPN
ejpam-300	281	3	appl	appl	PROPN
ejpam-300	281	4	.	.	PROPN
ejpam-300	281	5	math	math	PROPN
ejpam-300	281	6	,	,	PUNCT
ejpam-300	281	7	2	2	NUM
ejpam-300	281	8	(	(	PUNCT
ejpam-300	281	9	2009	2009	NUM
ejpam-300	281	10	)	)	PUNCT
ejpam-300	281	11	,	,	PUNCT
ejpam-300	281	12	(	(	PUNCT
ejpam-300	281	13	338	338	NUM
ejpam-300	281	14	-	-	SYM
ejpam-300	281	15	351	351	NUM
ejpam-300	281	16	)	)	PUNCT
ejpam-300	281	17	349	349	NUM
ejpam-300	281	18	proposition	proposition	NOUN
ejpam-300	281	19	5.4	5.4	NUM
ejpam-300	281	20	.	.	PUNCT
ejpam-300	282	1	let	let	VERB
ejpam-300	282	2	x	x	PRON
ejpam-300	282	3	be	be	AUX
ejpam-300	282	4	a	a	DET
ejpam-300	282	5	space	space	NOUN
ejpam-300	282	6	and	and	CCONJ
ejpam-300	282	7	φ	φ	PROPN
ejpam-300	282	8	6=	6=	PROPN
ejpam-300	282	9	a	a	DET
ejpam-300	282	10	be	be	AUX
ejpam-300	282	11	a	a	DET
ejpam-300	282	12	finite	finite	NOUN
ejpam-300	282	13	γ	γ	X
ejpam-300	282	14	-	-	ADJ
ejpam-300	282	15	open	open	ADJ
ejpam-300	282	16	set	set	NOUN
ejpam-300	282	17	and	and	CCONJ
ejpam-300	282	18	for	for	ADP
ejpam-300	282	19	each	each	DET
ejpam-300	282	20	k	k	PROPN
ejpam-300	282	21	∈	∈	PROPN
ejpam-300	282	22	{	{	PUNCT
ejpam-300	282	23	1	1	NUM
ejpam-300	282	24	,	,	PUNCT
ejpam-300	282	25	2	2	NUM
ejpam-300	282	26	,	,	PUNCT
ejpam-300	282	27	...	...	PUNCT
ejpam-300	282	28	,	,	PUNCT
ejpam-300	282	29	m	m	VERB
ejpam-300	282	30	}	}	PUNCT
ejpam-300	282	31	,	,	PUNCT
ejpam-300	282	32	ak	ak	PROPN
ejpam-300	282	33	a	a	DET
ejpam-300	282	34	minimal	minimal	ADJ
ejpam-300	282	35	γ	γ	X
ejpam-300	282	36	-	-	ADJ
ejpam-300	282	37	open	open	ADJ
ejpam-300	282	38	set	set	NOUN
ejpam-300	282	39	in	in	ADP
ejpam-300	282	40	a.	a.	NOUN
ejpam-300	282	41	if	if	SCONJ
ejpam-300	282	42	for	for	ADP
ejpam-300	282	43	any	any	DET
ejpam-300	282	44	φ	φ	NOUN
ejpam-300	282	45	6=	6=	ADP
ejpam-300	282	46	bk	bk	PROPN
ejpam-300	282	47	⊆	⊆	PROPN
ejpam-300	282	48	ak	ak	PROPN
ejpam-300	282	49	,	,	PUNCT
ejpam-300	282	50	clγ(a	clγ(a	PROPN
ejpam-300	282	51	)	)	PUNCT
ejpam-300	282	52	=	=	PUNCT
ejpam-300	283	1	clγ(b1	clγ(b1	AUX
ejpam-300	283	2	∪	∪	VERB
ejpam-300	283	3	b2	b2	NOUN
ejpam-300	283	4	∪	∪	ADJ
ejpam-300	283	5	...	...	PUNCT
ejpam-300	283	6	∪	∪	X
ejpam-300	283	7	bm	bm	PROPN
ejpam-300	283	8	)	)	PUNCT
ejpam-300	283	9	,	,	PUNCT
ejpam-300	283	10	then	then	ADV
ejpam-300	283	11	the	the	DET
ejpam-300	283	12	class	class	NOUN
ejpam-300	283	13	{	{	PUNCT
ejpam-300	283	14	a1	a1	PROPN
ejpam-300	283	15	,	,	PUNCT
ejpam-300	283	16	a2	a2	PROPN
ejpam-300	283	17	,	,	PUNCT
ejpam-300	283	18	...	...	PUNCT
ejpam-300	283	19	,	,	PUNCT
ejpam-300	283	20	am	be	AUX
ejpam-300	283	21	}	}	PUNCT
ejpam-300	283	22	contains	contain	VERB
ejpam-300	283	23	all	all	DET
ejpam-300	283	24	minimal	minimal	ADJ
ejpam-300	283	25	γ	γ	ADJ
ejpam-300	283	26	-	-	ADJ
ejpam-300	283	27	open	open	ADJ
ejpam-300	283	28	sets	set	NOUN
ejpam-300	283	29	in	in	ADP
ejpam-300	283	30	a.	a.	NOUN
ejpam-300	283	31	proof	proof	NOUN
ejpam-300	283	32	.	.	PUNCT
ejpam-300	284	1	suppose	suppose	VERB
ejpam-300	284	2	on	on	ADP
ejpam-300	284	3	the	the	DET
ejpam-300	284	4	contrary	contrary	NOUN
ejpam-300	284	5	that	that	SCONJ
ejpam-300	284	6	c	c	PROPN
ejpam-300	284	7	is	be	AUX
ejpam-300	284	8	a	a	DET
ejpam-300	284	9	minimal	minimal	ADJ
ejpam-300	284	10	γ	γ	X
ejpam-300	284	11	-	-	ADJ
ejpam-300	284	12	open	open	ADJ
ejpam-300	284	13	set	set	NOUN
ejpam-300	284	14	in	in	ADP
ejpam-300	284	15	a	a	PRON
ejpam-300	284	16	and	and	CCONJ
ejpam-300	284	17	for	for	ADP
ejpam-300	284	18	k	k	PROPN
ejpam-300	284	19	∈	∈	PROPN
ejpam-300	284	20	{	{	PUNCT
ejpam-300	284	21	1	1	NUM
ejpam-300	284	22	,	,	PUNCT
ejpam-300	284	23	2	2	NUM
ejpam-300	284	24	,	,	PUNCT
ejpam-300	284	25	...	...	PUNCT
ejpam-300	284	26	,	,	PUNCT
ejpam-300	284	27	m	m	VERB
ejpam-300	284	28	}	}	PUNCT
ejpam-300	284	29	,	,	PUNCT
ejpam-300	284	30	c	c	AUX
ejpam-300	284	31	6=	6=	NUM
ejpam-300	284	32	ai	ai	VERB
ejpam-300	284	33	.	.	PUNCT
ejpam-300	285	1	therefore	therefore	ADV
ejpam-300	285	2	,	,	PUNCT
ejpam-300	285	3	for	for	ADP
ejpam-300	285	4	each	each	DET
ejpam-300	285	5	k	k	PROPN
ejpam-300	285	6	∈	∈	PROPN
ejpam-300	285	7	{	{	PUNCT
ejpam-300	285	8	1	1	NUM
ejpam-300	285	9	,	,	PUNCT
ejpam-300	285	10	2	2	NUM
ejpam-300	285	11	,	,	PUNCT
ejpam-300	285	12	...	...	PUNCT
ejpam-300	285	13	,	,	PUNCT
ejpam-300	285	14	m	m	VERB
ejpam-300	285	15	}	}	PUNCT
ejpam-300	285	16	,	,	PUNCT
ejpam-300	285	17	c	c	PROPN
ejpam-300	285	18	∩	∩	X
ejpam-300	285	19	clγ(ak	clγ(ak	NOUN
ejpam-300	285	20	)	)	PUNCT
ejpam-300	285	21	=	=	SYM
ejpam-300	286	1	φ	φ	PROPN
ejpam-300	286	2	.	.	PUNCT
ejpam-300	287	1	this	this	PRON
ejpam-300	287	2	implies	imply	VERB
ejpam-300	287	3	that	that	SCONJ
ejpam-300	287	4	any	any	DET
ejpam-300	287	5	element	element	NOUN
ejpam-300	287	6	of	of	ADP
ejpam-300	287	7	c	c	PROPN
ejpam-300	287	8	is	be	AUX
ejpam-300	287	9	not	not	PART
ejpam-300	287	10	contained	contain	VERB
ejpam-300	287	11	in	in	ADP
ejpam-300	287	12	clγ(a1∪a2∪	clγ(a1∪a2∪	PROPN
ejpam-300	287	13	...	...	PUNCT
ejpam-300	287	14	∪am	∪am	X
ejpam-300	287	15	)	)	PUNCT
ejpam-300	287	16	.	.	PUNCT
ejpam-300	288	1	this	this	PRON
ejpam-300	288	2	is	be	AUX
ejpam-300	288	3	a	a	DET
ejpam-300	288	4	contradiction	contradiction	NOUN
ejpam-300	288	5	to	to	ADP
ejpam-300	288	6	the	the	DET
ejpam-300	288	7	fact	fact	NOUN
ejpam-300	288	8	that	that	SCONJ
ejpam-300	288	9	c	c	PROPN
ejpam-300	288	10	⊆	⊆	NUM
ejpam-300	288	11	a⊆	a⊆	ADP
ejpam-300	288	12	clγ(a	clγ(a	PROPN
ejpam-300	288	13	)	)	PUNCT
ejpam-300	288	14	=	=	SYM
ejpam-300	288	15	clγ(b1∪b2∪	clγ(b1∪b2∪	PROPN
ejpam-300	288	16	...	...	PUNCT
ejpam-300	288	17	∪bm	∪bm	ADJ
ejpam-300	288	18	)	)	PUNCT
ejpam-300	288	19	.	.	PUNCT
ejpam-300	289	1	this	this	PRON
ejpam-300	289	2	completes	complete	VERB
ejpam-300	289	3	the	the	DET
ejpam-300	289	4	proof	proof	NOUN
ejpam-300	289	5	.	.	PUNCT
ejpam-300	290	1	combining	combine	VERB
ejpam-300	290	2	propositions	proposition	NOUN
ejpam-300	290	3	5.2	5.2	NUM
ejpam-300	290	4	,	,	PUNCT
ejpam-300	290	5	5.3	5.3	NUM
ejpam-300	290	6	and	and	CCONJ
ejpam-300	290	7	5.4	5.4	NUM
ejpam-300	290	8	,	,	PUNCT
ejpam-300	290	9	we	we	PRON
ejpam-300	290	10	have	have	VERB
ejpam-300	290	11	the	the	DET
ejpam-300	290	12	following	follow	VERB
ejpam-300	290	13	theorem	theorem	NOUN
ejpam-300	290	14	:	:	PUNCT
ejpam-300	290	15	theorem	theorem	VERB
ejpam-300	290	16	5.3	5.3	NUM
ejpam-300	290	17	.	.	PUNCT
ejpam-300	291	1	let	let	VERB
ejpam-300	291	2	x	x	PRON
ejpam-300	291	3	be	be	AUX
ejpam-300	291	4	a	a	DET
ejpam-300	291	5	space	space	NOUN
ejpam-300	291	6	and	and	CCONJ
ejpam-300	291	7	φ	φ	PROPN
ejpam-300	291	8	6=	6=	PROPN
ejpam-300	291	9	a	a	DET
ejpam-300	291	10	be	be	AUX
ejpam-300	291	11	a	a	DET
ejpam-300	291	12	finite	finite	NOUN
ejpam-300	291	13	γ	γ	X
ejpam-300	291	14	-	-	ADJ
ejpam-300	291	15	open	open	ADJ
ejpam-300	291	16	set	set	NOUN
ejpam-300	291	17	and	and	CCONJ
ejpam-300	291	18	for	for	ADP
ejpam-300	291	19	each	each	DET
ejpam-300	291	20	k	k	PROPN
ejpam-300	291	21	∈	∈	PROPN
ejpam-300	291	22	{	{	PUNCT
ejpam-300	291	23	1	1	NUM
ejpam-300	291	24	,	,	PUNCT
ejpam-300	291	25	2	2	NUM
ejpam-300	291	26	,	,	PUNCT
ejpam-300	291	27	...	...	PUNCT
ejpam-300	291	28	,	,	PUNCT
ejpam-300	291	29	m	m	VERB
ejpam-300	291	30	}	}	PUNCT
ejpam-300	291	31	,	,	PUNCT
ejpam-300	291	32	ak	ak	PROPN
ejpam-300	291	33	a	a	DET
ejpam-300	291	34	minimal	minimal	ADJ
ejpam-300	291	35	γ	γ	X
ejpam-300	291	36	-	-	ADJ
ejpam-300	291	37	open	open	ADJ
ejpam-300	291	38	set	set	NOUN
ejpam-300	291	39	in	in	ADP
ejpam-300	291	40	a.	a.	NOUN
ejpam-300	291	41	then	then	ADV
ejpam-300	291	42	the	the	DET
ejpam-300	291	43	following	follow	VERB
ejpam-300	291	44	three	three	NUM
ejpam-300	291	45	conditions	condition	NOUN
ejpam-300	291	46	are	be	AUX
ejpam-300	291	47	equivalent	equivalent	ADJ
ejpam-300	291	48	:	:	PUNCT
ejpam-300	291	49	(	(	PUNCT
ejpam-300	291	50	1	1	X
ejpam-300	291	51	)	)	PUNCT
ejpam-300	291	52	the	the	DET
ejpam-300	291	53	class	class	NOUN
ejpam-300	291	54	{	{	PUNCT
ejpam-300	291	55	a1	a1	PROPN
ejpam-300	291	56	,	,	PUNCT
ejpam-300	291	57	a2	a2	PROPN
ejpam-300	291	58	,	,	PUNCT
ejpam-300	291	59	...	...	PUNCT
ejpam-300	291	60	,	,	PUNCT
ejpam-300	291	61	am	be	AUX
ejpam-300	291	62	}	}	PUNCT
ejpam-300	291	63	contains	contain	VERB
ejpam-300	291	64	all	all	DET
ejpam-300	291	65	minimal	minimal	ADJ
ejpam-300	291	66	γ	γ	ADJ
ejpam-300	291	67	-	-	ADJ
ejpam-300	291	68	open	open	ADJ
ejpam-300	291	69	sets	set	NOUN
ejpam-300	291	70	in	in	ADP
ejpam-300	291	71	a.	a.	NOUN
ejpam-300	291	72	(	(	PUNCT
ejpam-300	291	73	2	2	NUM
ejpam-300	291	74	)	)	PUNCT
ejpam-300	291	75	for	for	ADP
ejpam-300	291	76	any	any	DET
ejpam-300	291	77	φ	φ	PROPN
ejpam-300	291	78	6=	6=	ADP
ejpam-300	291	79	bk	bk	PROPN
ejpam-300	291	80	⊆	⊆	NUM
ejpam-300	291	81	ak	ak	PROPN
ejpam-300	291	82	,	,	PUNCT
ejpam-300	291	83	clγ(a)⊆	clγ(a)⊆	PROPN
ejpam-300	291	84	clγ(b1	clγ(b1	NOUN
ejpam-300	291	85	∪	∪	VERB
ejpam-300	291	86	b2	b2	NOUN
ejpam-300	291	87	∪	∪	NOUN
ejpam-300	291	88	...	...	PUNCT
ejpam-300	291	89	∪	∪	X
ejpam-300	291	90	bm	bm	PROPN
ejpam-300	291	91	)	)	PUNCT
ejpam-300	291	92	.	.	PUNCT
ejpam-300	292	1	(	(	PUNCT
ejpam-300	292	2	3	3	X
ejpam-300	292	3	)	)	PUNCT
ejpam-300	292	4	for	for	ADP
ejpam-300	292	5	any	any	DET
ejpam-300	292	6	φ	φ	PROPN
ejpam-300	292	7	6=	6=	ADP
ejpam-300	292	8	bk	bk	PROPN
ejpam-300	292	9	⊆	⊆	PROPN
ejpam-300	292	10	ak	ak	PROPN
ejpam-300	292	11	,	,	PUNCT
ejpam-300	292	12	clγ(a	clγ(a	PROPN
ejpam-300	292	13	)	)	PUNCT
ejpam-300	292	14	=	=	PUNCT
ejpam-300	293	1	clγ(b1	clγ(b1	AUX
ejpam-300	293	2	∪	∪	VERB
ejpam-300	293	3	b2	b2	NOUN
ejpam-300	293	4	∪	∪	ADJ
ejpam-300	293	5	...	...	PUNCT
ejpam-300	293	6	∪	∪	X
ejpam-300	293	7	bm	bm	PROPN
ejpam-300	293	8	)	)	PUNCT
ejpam-300	293	9	,	,	PUNCT
ejpam-300	293	10	where	where	SCONJ
ejpam-300	293	11	γ	γ	PROPN
ejpam-300	293	12	is	be	AUX
ejpam-300	293	13	regular	regular	ADJ
ejpam-300	293	14	and	and	CCONJ
ejpam-300	293	15	open	open	ADJ
ejpam-300	293	16	.	.	PUNCT
ejpam-300	294	1	remark	remark	VERB
ejpam-300	294	2	5.1	5.1	NUM
ejpam-300	294	3	.	.	PUNCT
ejpam-300	295	1	suppose	suppose	VERB
ejpam-300	295	2	that	that	SCONJ
ejpam-300	295	3	φ	φ	PROPN
ejpam-300	295	4	6=	6=	PROPN
ejpam-300	295	5	a	a	PRON
ejpam-300	295	6	is	be	AUX
ejpam-300	295	7	a	a	DET
ejpam-300	295	8	finite	finite	NOUN
ejpam-300	295	9	γ	γ	X
ejpam-300	295	10	-	-	ADJ
ejpam-300	295	11	open	open	ADJ
ejpam-300	295	12	set	set	NOUN
ejpam-300	295	13	and	and	CCONJ
ejpam-300	295	14	{	{	PUNCT
ejpam-300	295	15	a1	a1	PROPN
ejpam-300	295	16	,	,	PUNCT
ejpam-300	295	17	a2	a2	PROPN
ejpam-300	295	18	,	,	PUNCT
ejpam-300	295	19	...	...	PUNCT
ejpam-300	295	20	,	,	PUNCT
ejpam-300	295	21	am	be	AUX
ejpam-300	295	22	}	}	PUNCT
ejpam-300	295	23	is	be	AUX
ejpam-300	295	24	a	a	DET
ejpam-300	295	25	class	class	NOUN
ejpam-300	295	26	of	of	ADP
ejpam-300	295	27	all	all	DET
ejpam-300	295	28	minimal	minimal	ADJ
ejpam-300	295	29	γ	γ	ADJ
ejpam-300	295	30	-	-	ADJ
ejpam-300	295	31	open	open	ADJ
ejpam-300	295	32	sets	set	NOUN
ejpam-300	295	33	in	in	ADP
ejpam-300	295	34	a	a	DET
ejpam-300	295	35	such	such	ADJ
ejpam-300	295	36	that	that	PRON
ejpam-300	295	37	for	for	ADP
ejpam-300	295	38	each	each	DET
ejpam-300	295	39	k	k	PROPN
ejpam-300	295	40	∈	∈	PROPN
ejpam-300	295	41	{	{	PUNCT
ejpam-300	295	42	1	1	NUM
ejpam-300	295	43	,	,	PUNCT
ejpam-300	295	44	2	2	NUM
ejpam-300	295	45	,	,	PUNCT
ejpam-300	295	46	...	...	PUNCT
ejpam-300	295	47	,	,	PUNCT
ejpam-300	295	48	m	m	VERB
ejpam-300	295	49	}	}	PUNCT
ejpam-300	295	50	,	,	PUNCT
ejpam-300	296	1	yk	yk	PROPN
ejpam-300	296	2	∈	∈	PROPN
ejpam-300	296	3	ak	ak	PROPN
ejpam-300	296	4	.	.	PROPN
ejpam-300	296	5	then	then	ADV
ejpam-300	296	6	by	by	ADP
ejpam-300	296	7	theorem	theorem	NOUN
ejpam-300	296	8	5.3	5.3	NUM
ejpam-300	296	9	,	,	PUNCT
ejpam-300	296	10	it	it	PRON
ejpam-300	296	11	is	be	AUX
ejpam-300	296	12	clear	clear	ADJ
ejpam-300	296	13	that	that	SCONJ
ejpam-300	296	14	{	{	PUNCT
ejpam-300	296	15	y1	y1	NOUN
ejpam-300	296	16	,	,	PUNCT
ejpam-300	296	17	y2	y2	PROPN
ejpam-300	296	18	,	,	PUNCT
ejpam-300	296	19	...	...	PUNCT
ejpam-300	296	20	,	,	PUNCT
ejpam-300	296	21	ym	ym	PRON
ejpam-300	296	22	}	}	PUNCT
ejpam-300	296	23	is	be	AUX
ejpam-300	296	24	a	a	DET
ejpam-300	296	25	pre	pre	ADJ
ejpam-300	296	26	-	-	ADJ
ejpam-300	296	27	γ	γ	ADJ
ejpam-300	296	28	-	-	ADJ
ejpam-300	296	29	open	open	ADJ
ejpam-300	296	30	set	set	NOUN
ejpam-300	296	31	.	.	PUNCT
ejpam-300	297	1	theorem	theorem	VERB
ejpam-300	297	2	5.4	5.4	NUM
ejpam-300	297	3	.	.	PUNCT
ejpam-300	298	1	let	let	VERB
ejpam-300	298	2	x	x	PRON
ejpam-300	298	3	be	be	AUX
ejpam-300	298	4	a	a	DET
ejpam-300	298	5	space	space	NOUN
ejpam-300	298	6	.	.	PUNCT
ejpam-300	299	1	suppose	suppose	VERB
ejpam-300	299	2	thatφ	thatφ	NOUN
ejpam-300	299	3	6=	6=	PRON
ejpam-300	299	4	a	a	PRON
ejpam-300	299	5	is	be	AUX
ejpam-300	299	6	a	a	DET
ejpam-300	299	7	finite	finite	NOUN
ejpam-300	299	8	γ	γ	X
ejpam-300	299	9	-	-	ADJ
ejpam-300	299	10	open	open	ADJ
ejpam-300	299	11	set	set	NOUN
ejpam-300	299	12	and	and	CCONJ
ejpam-300	299	13	{	{	PUNCT
ejpam-300	299	14	a1	a1	PROPN
ejpam-300	299	15	,	,	PUNCT
ejpam-300	299	16	a2	a2	PROPN
ejpam-300	299	17	,	,	PUNCT
ejpam-300	299	18	...	...	PUNCT
ejpam-300	299	19	,	,	PUNCT
ejpam-300	299	20	am	be	AUX
ejpam-300	299	21	}	}	PUNCT
ejpam-300	299	22	is	be	AUX
ejpam-300	299	23	a	a	DET
ejpam-300	299	24	class	class	NOUN
ejpam-300	299	25	of	of	ADP
ejpam-300	299	26	all	all	DET
ejpam-300	299	27	minimal	minimal	ADJ
ejpam-300	299	28	γ	γ	ADJ
ejpam-300	299	29	-	-	ADJ
ejpam-300	299	30	open	open	ADJ
ejpam-300	299	31	sets	set	NOUN
ejpam-300	299	32	in	in	ADP
ejpam-300	299	33	a.	a.	NOUN
ejpam-300	299	34	if	if	SCONJ
ejpam-300	299	35	for	for	ADP
ejpam-300	299	36	any	any	DET
ejpam-300	299	37	b	b	NOUN
ejpam-300	299	38	⊆	⊆	NUM
ejpam-300	299	39	a−{a1	a−{a1	ADJ
ejpam-300	299	40	,	,	PUNCT
ejpam-300	299	41	a2	a2	PROPN
ejpam-300	299	42	,	,	PUNCT
ejpam-300	299	43	...	...	PUNCT
ejpam-300	299	44	,	,	PUNCT
ejpam-300	299	45	am}and	am}and	CCONJ
ejpam-300	299	46	φ	φ	PROPN
ejpam-300	299	47	6=	6=	PROPN
ejpam-300	299	48	bk	bk	PROPN
ejpam-300	299	49	⊆	⊆	NUM
ejpam-300	299	50	ak	ak	PROPN
ejpam-300	299	51	,	,	PUNCT
ejpam-300	299	52	for	for	ADP
ejpam-300	299	53	each	each	DET
ejpam-300	299	54	k	k	PROPN
ejpam-300	299	55	∈	∈	PROPN
ejpam-300	299	56	{	{	PUNCT
ejpam-300	299	57	1	1	NUM
ejpam-300	299	58	,	,	PUNCT
ejpam-300	299	59	2	2	NUM
ejpam-300	299	60	,	,	PUNCT
ejpam-300	299	61	...	...	PUNCT
ejpam-300	299	62	,	,	PUNCT
ejpam-300	299	63	m	m	VERB
ejpam-300	299	64	}	}	PUNCT
ejpam-300	299	65	,	,	PUNCT
ejpam-300	299	66	then	then	ADV
ejpam-300	299	67	b	b	X
ejpam-300	299	68	∪	∪	ADP
ejpam-300	299	69	b1	b1	NOUN
ejpam-300	299	70	∪	∪	NOUN
ejpam-300	299	71	b2	b2	NOUN
ejpam-300	299	72	∪	∪	NOUN
ejpam-300	299	73	...	...	PUNCT
ejpam-300	299	74	∪	∪	X
ejpam-300	299	75	bm	bm	PROPN
ejpam-300	299	76	is	be	AUX
ejpam-300	299	77	a	a	DET
ejpam-300	299	78	pre	pre	ADJ
ejpam-300	299	79	-	-	ADJ
ejpam-300	299	80	γ	γ	ADJ
ejpam-300	299	81	-	-	ADJ
ejpam-300	299	82	open	open	ADJ
ejpam-300	299	83	set	set	NOUN
ejpam-300	299	84	,	,	PUNCT
ejpam-300	299	85	where	where	SCONJ
ejpam-300	299	86	γ	γ	PROPN
ejpam-300	299	87	is	be	AUX
ejpam-300	299	88	regular	regular	ADJ
ejpam-300	299	89	and	and	CCONJ
ejpam-300	299	90	open	open	ADJ
ejpam-300	299	91	.	.	PUNCT
ejpam-300	300	1	proof	proof	NOUN
ejpam-300	300	2	.	.	PUNCT
ejpam-300	301	1	suppose	suppose	VERB
ejpam-300	301	2	that	that	SCONJ
ejpam-300	301	3	φ	φ	PROPN
ejpam-300	301	4	6=	6=	PROPN
ejpam-300	301	5	a	a	PRON
ejpam-300	301	6	is	be	AUX
ejpam-300	301	7	a	a	DET
ejpam-300	301	8	finite	finite	NOUN
ejpam-300	301	9	γ	γ	X
ejpam-300	301	10	-	-	ADJ
ejpam-300	301	11	open	open	ADJ
ejpam-300	301	12	set	set	NOUN
ejpam-300	301	13	and	and	CCONJ
ejpam-300	301	14	{	{	PUNCT
ejpam-300	301	15	a1	a1	PROPN
ejpam-300	301	16	,	,	PUNCT
ejpam-300	301	17	a2	a2	PROPN
ejpam-300	301	18	,	,	PUNCT
ejpam-300	301	19	...	...	PUNCT
ejpam-300	301	20	,	,	PUNCT
ejpam-300	301	21	am	be	AUX
ejpam-300	301	22	}	}	PUNCT
ejpam-300	301	23	is	be	AUX
ejpam-300	301	24	a	a	DET
ejpam-300	301	25	class	class	NOUN
ejpam-300	301	26	of	of	ADP
ejpam-300	301	27	all	all	DET
ejpam-300	301	28	minimal	minimal	ADJ
ejpam-300	301	29	γ	γ	ADJ
ejpam-300	301	30	-	-	ADJ
ejpam-300	301	31	open	open	ADJ
ejpam-300	301	32	sets	set	NOUN
ejpam-300	301	33	in	in	ADP
ejpam-300	301	34	a.	a.	NOUN
ejpam-300	301	35	then	then	ADV
ejpam-300	301	36	by	by	ADP
ejpam-300	301	37	proposition	proposition	NOUN
ejpam-300	301	38	5.2	5.2	NUM
ejpam-300	301	39	a⊆	a⊆	NOUN
ejpam-300	301	40	clγ(b1	clγ(b1	AUX
ejpam-300	301	41	∪	∪	VERB
ejpam-300	301	42	b2	b2	NOUN
ejpam-300	301	43	∪	∪	ADJ
ejpam-300	301	44	...	...	PUNCT
ejpam-300	301	45	∪	∪	VERB
ejpam-300	301	46	bm)⊆	bm)⊆	NOUN
ejpam-300	301	47	clγ(b	clγ(b	PRON
ejpam-300	301	48	∪	∪	ADP
ejpam-300	301	49	b1	b1	NOUN
ejpam-300	301	50	∪	∪	NOUN
ejpam-300	301	51	b2	b2	NOUN
ejpam-300	301	52	∪	∪	NOUN
ejpam-300	301	53	...	...	PUNCT
ejpam-300	301	54	∪	∪	X
ejpam-300	301	55	bm	bm	PROPN
ejpam-300	301	56	)	)	PUNCT
ejpam-300	301	57	.	.	PUNCT
ejpam-300	302	1	references	reference	NOUN
ejpam-300	302	2	350	350	NUM
ejpam-300	302	3	also	also	ADV
ejpam-300	302	4	,	,	PUNCT
ejpam-300	302	5	a	a	PRON
ejpam-300	302	6	is	be	AUX
ejpam-300	302	7	γ	γ	X
ejpam-300	302	8	-	-	ADJ
ejpam-300	302	9	open	open	ADJ
ejpam-300	302	10	implies	imply	VERB
ejpam-300	302	11	b	b	PROPN
ejpam-300	302	12	∪	∪	ADJ
ejpam-300	302	13	b1	b1	NOUN
ejpam-300	302	14	∪	∪	NOUN
ejpam-300	302	15	b2	b2	NOUN
ejpam-300	302	16	∪	∪	NOUN
ejpam-300	302	17	...	...	PUNCT
ejpam-300	302	18	∪	∪	ADP
ejpam-300	302	19	bm	bm	PROPN
ejpam-300	302	20	⊆	⊆	NUM
ejpam-300	302	21	a=	a=	ADJ
ejpam-300	302	22	intγ(a)⊆	intγ(a)⊆	X
ejpam-300	302	23	intγ(clγ(b	intγ(clγ(b	CCONJ
ejpam-300	302	24	∪	∪	VERB
ejpam-300	302	25	b1	b1	NOUN
ejpam-300	302	26	∪	∪	NOUN
ejpam-300	302	27	b2	b2	NOUN
ejpam-300	302	28	∪	∪	NOUN
ejpam-300	302	29	...	...	PUNCT
ejpam-300	302	30	∪	∪	X
ejpam-300	302	31	bm	bm	PROPN
ejpam-300	302	32	)	)	PUNCT
ejpam-300	302	33	)	)	PUNCT
ejpam-300	302	34	.	.	PUNCT
ejpam-300	303	1	this	this	PRON
ejpam-300	303	2	follows	follow	VERB
ejpam-300	303	3	that	that	SCONJ
ejpam-300	303	4	b	b	PROPN
ejpam-300	303	5	∪	∪	ADP
ejpam-300	303	6	b1	b1	NOUN
ejpam-300	303	7	∪	∪	NOUN
ejpam-300	303	8	b2	b2	NOUN
ejpam-300	303	9	∪	∪	NOUN
ejpam-300	303	10	...	...	PUNCT
ejpam-300	303	11	∪	∪	X
ejpam-300	303	12	bm	bm	PROPN
ejpam-300	303	13	is	be	AUX
ejpam-300	303	14	a	a	DET
ejpam-300	303	15	pre	pre	ADJ
ejpam-300	303	16	-	-	ADJ
ejpam-300	303	17	γ	γ	ADJ
ejpam-300	303	18	-	-	ADJ
ejpam-300	303	19	open	open	ADJ
ejpam-300	303	20	set	set	NOUN
ejpam-300	303	21	.	.	PUNCT
ejpam-300	304	1	this	this	PRON
ejpam-300	304	2	completes	complete	VERB
ejpam-300	304	3	the	the	DET
ejpam-300	304	4	proof	proof	NOUN
ejpam-300	304	5	.	.	PUNCT
ejpam-300	305	1	theorem	theorem	VERB
ejpam-300	305	2	5.5	5.5	NUM
ejpam-300	305	3	.	.	PUNCT
ejpam-300	306	1	let	let	VERB
ejpam-300	306	2	x	x	PRON
ejpam-300	306	3	be	be	AUX
ejpam-300	306	4	a	a	DET
ejpam-300	306	5	γ	γ	X
ejpam-300	306	6	-	-	ADJ
ejpam-300	306	7	locally	locally	ADV
ejpam-300	306	8	finite	finite	ADJ
ejpam-300	306	9	space	space	NOUN
ejpam-300	306	10	and	and	CCONJ
ejpam-300	306	11	γ	γ	NOUN
ejpam-300	306	12	∈	∈	PROPN
ejpam-300	306	13	γ(x	γ(x	PROPN
ejpam-300	306	14	)	)	PUNCT
ejpam-300	306	15	.	.	PUNCT
ejpam-300	307	1	if	if	SCONJ
ejpam-300	307	2	a	a	DET
ejpam-300	307	3	minimal	minimal	ADJ
ejpam-300	307	4	γ	γ	NOUN
ejpam-300	307	5	-	-	ADJ
ejpam-300	307	6	open	open	ADJ
ejpam-300	307	7	set	set	VERB
ejpam-300	307	8	a	a	DET
ejpam-300	307	9	⊆	⊆	NUM
ejpam-300	307	10	x	x	PUNCT
ejpam-300	307	11	has	have	VERB
ejpam-300	307	12	more	more	ADJ
ejpam-300	307	13	than	than	ADP
ejpam-300	307	14	one	one	NUM
ejpam-300	307	15	element	element	NOUN
ejpam-300	307	16	,	,	PUNCT
ejpam-300	307	17	then	then	ADV
ejpam-300	307	18	x	x	PUNCT
ejpam-300	307	19	is	be	AUX
ejpam-300	307	20	a	a	DET
ejpam-300	307	21	pre	pre	ADJ
ejpam-300	307	22	γ	γ	PROPN
ejpam-300	307	23	-	-	ADJ
ejpam-300	307	24	t2	t2	ADJ
ejpam-300	307	25	space	space	NOUN
ejpam-300	307	26	,	,	PUNCT
ejpam-300	307	27	where	where	SCONJ
ejpam-300	307	28	γ	γ	PROPN
ejpam-300	307	29	is	be	AUX
ejpam-300	307	30	regular	regular	ADJ
ejpam-300	307	31	and	and	CCONJ
ejpam-300	307	32	open	open	ADJ
ejpam-300	307	33	.	.	PUNCT
ejpam-300	308	1	proof	proof	NOUN
ejpam-300	308	2	.	.	PUNCT
ejpam-300	309	1	let	let	VERB
ejpam-300	309	2	a	a	DET
ejpam-300	309	3	,	,	PUNCT
ejpam-300	309	4	b	b	X
ejpam-300	309	5	∈	∈	PROPN
ejpam-300	309	6	x	x	PUNCT
ejpam-300	309	7	such	such	ADJ
ejpam-300	309	8	that	that	SCONJ
ejpam-300	309	9	a	a	DET
ejpam-300	309	10	6=	6=	ADP
ejpam-300	309	11	b.	b.	PROPN
ejpam-300	309	12	since	since	SCONJ
ejpam-300	309	13	x	x	PROPN
ejpam-300	309	14	is	be	AUX
ejpam-300	309	15	γ	γ	X
ejpam-300	309	16	-	-	ADJ
ejpam-300	309	17	locally	locally	ADV
ejpam-300	309	18	finite	finite	NOUN
ejpam-300	309	19	,	,	PUNCT
ejpam-300	309	20	therefore	therefore	ADV
ejpam-300	309	21	there	there	PRON
ejpam-300	309	22	exist	exist	VERB
ejpam-300	309	23	finite	finite	ADJ
ejpam-300	309	24	γ	γ	X
ejpam-300	309	25	-	-	ADJ
ejpam-300	309	26	open	open	ADJ
ejpam-300	309	27	sets	set	NOUN
ejpam-300	309	28	v	v	ADP
ejpam-300	309	29	and	and	CCONJ
ejpam-300	309	30	w	w	NOUN
ejpam-300	309	31	containing	contain	VERB
ejpam-300	309	32	a	a	PRON
ejpam-300	309	33	and	and	CCONJ
ejpam-300	309	34	b	b	NOUN
ejpam-300	309	35	respectively	respectively	ADV
ejpam-300	309	36	.	.	PUNCT
ejpam-300	310	1	proposition	proposition	NOUN
ejpam-300	310	2	4.1	4.1	NUM
ejpam-300	310	3	implies	imply	VERB
ejpam-300	310	4	that	that	SCONJ
ejpam-300	310	5	there	there	PRON
ejpam-300	310	6	exist	exist	VERB
ejpam-300	310	7	a	a	DET
ejpam-300	310	8	class	class	NOUN
ejpam-300	310	9	{	{	PUNCT
ejpam-300	310	10	v1	v1	NOUN
ejpam-300	310	11	,	,	PUNCT
ejpam-300	310	12	v2	v2	PROPN
ejpam-300	310	13	,	,	PUNCT
ejpam-300	310	14	...	...	PUNCT
ejpam-300	310	15	,	,	PUNCT
ejpam-300	310	16	vm	vm	NOUN
ejpam-300	310	17	}	}	PUNCT
ejpam-300	310	18	of	of	ADP
ejpam-300	310	19	all	all	DET
ejpam-300	310	20	minimal	minimal	ADJ
ejpam-300	310	21	γ	γ	ADJ
ejpam-300	310	22	-	-	ADJ
ejpam-300	310	23	open	open	ADJ
ejpam-300	310	24	sets	set	NOUN
ejpam-300	310	25	in	in	ADP
ejpam-300	310	26	v	v	NOUN
ejpam-300	310	27	and	and	CCONJ
ejpam-300	310	28	a	a	DET
ejpam-300	310	29	class	class	NOUN
ejpam-300	310	30	{	{	PUNCT
ejpam-300	310	31	w1	w1	NOUN
ejpam-300	310	32	,	,	PUNCT
ejpam-300	310	33	w2	w2	NOUN
ejpam-300	310	34	,	,	PUNCT
ejpam-300	310	35	...	...	PUNCT
ejpam-300	310	36	,	,	PUNCT
ejpam-300	310	37	wl	wl	PROPN
ejpam-300	310	38	}	}	PUNCT
ejpam-300	310	39	of	of	ADP
ejpam-300	310	40	all	all	DET
ejpam-300	310	41	minimal	minimal	ADJ
ejpam-300	310	42	γ	γ	ADJ
ejpam-300	310	43	-	-	ADJ
ejpam-300	310	44	open	open	ADJ
ejpam-300	310	45	sets	set	NOUN
ejpam-300	310	46	in	in	ADP
ejpam-300	310	47	w.	w.	NOUN
ejpam-300	310	48	we	we	PRON
ejpam-300	310	49	consider	consider	VERB
ejpam-300	310	50	three	three	NUM
ejpam-300	310	51	possibilities	possibility	NOUN
ejpam-300	310	52	:	:	PUNCT
ejpam-300	310	53	1	1	X
ejpam-300	310	54	.	.	PUNCT
ejpam-300	310	55	suppose	suppose	VERB
ejpam-300	310	56	there	there	PRON
ejpam-300	310	57	exist	exist	VERB
ejpam-300	310	58	k	k	PROPN
ejpam-300	310	59	∈	∈	PROPN
ejpam-300	310	60	{	{	PUNCT
ejpam-300	310	61	1	1	NUM
ejpam-300	310	62	,	,	PUNCT
ejpam-300	310	63	2	2	NUM
ejpam-300	310	64	,	,	PUNCT
ejpam-300	310	65	...	...	PUNCT
ejpam-300	310	66	,	,	PUNCT
ejpam-300	310	67	m	m	VERB
ejpam-300	310	68	}	}	PUNCT
ejpam-300	310	69	and	and	CCONJ
ejpam-300	310	70	i	i	PRON
ejpam-300	310	71	∈	∈	PROPN
ejpam-300	310	72	{	{	PUNCT
ejpam-300	310	73	1	1	NUM
ejpam-300	310	74	,	,	PUNCT
ejpam-300	310	75	2	2	NUM
ejpam-300	310	76	,	,	PUNCT
ejpam-300	310	77	...	...	PUNCT
ejpam-300	310	78	,	,	PUNCT
ejpam-300	310	79	l	l	NOUN
ejpam-300	310	80	}	}	PUNCT
ejpam-300	310	81	such	such	ADJ
ejpam-300	310	82	that	that	SCONJ
ejpam-300	310	83	a	a	DET
ejpam-300	310	84	∈	∈	PROPN
ejpam-300	310	85	vk	vk	NOUN
ejpam-300	310	86	and	and	CCONJ
ejpam-300	310	87	b	b	PROPN
ejpam-300	310	88	∈	∈	PROPN
ejpam-300	310	89	wi	wi	PROPN
ejpam-300	310	90	.	.	PUNCT
ejpam-300	311	1	then	then	ADV
ejpam-300	311	2	proposition	proposition	VERB
ejpam-300	311	3	3.7	3.7	NUM
ejpam-300	311	4	implies	imply	VERB
ejpam-300	311	5	that	that	SCONJ
ejpam-300	311	6	{	{	PUNCT
ejpam-300	311	7	a	a	NOUN
ejpam-300	311	8	}	}	PUNCT
ejpam-300	311	9	and	and	CCONJ
ejpam-300	311	10	{	{	PUNCT
ejpam-300	311	11	b	b	NOUN
ejpam-300	311	12	}	}	PUNCT
ejpam-300	311	13	are	be	AUX
ejpam-300	311	14	pre	pre	ADJ
ejpam-300	311	15	-	-	ADJ
ejpam-300	311	16	γ	γ	ADJ
ejpam-300	311	17	-	-	ADJ
ejpam-300	311	18	open	open	ADJ
ejpam-300	311	19	sets	set	NOUN
ejpam-300	311	20	such	such	ADJ
ejpam-300	311	21	that	that	SCONJ
ejpam-300	311	22	a	a	DET
ejpam-300	311	23	∈	∈	PROPN
ejpam-300	311	24	{	{	PUNCT
ejpam-300	311	25	a	a	NOUN
ejpam-300	311	26	}	}	PUNCT
ejpam-300	311	27	,	,	PUNCT
ejpam-300	311	28	b	b	X
ejpam-300	311	29	∈	∈	PROPN
ejpam-300	311	30	{	{	PUNCT
ejpam-300	311	31	b	b	NOUN
ejpam-300	311	32	}	}	PUNCT
ejpam-300	311	33	and	and	CCONJ
ejpam-300	311	34	{	{	PUNCT
ejpam-300	311	35	a	a	PRON
ejpam-300	311	36	}	}	PUNCT
ejpam-300	311	37	∩	∩	ADJ
ejpam-300	311	38	{	{	PUNCT
ejpam-300	311	39	b	b	NOUN
ejpam-300	311	40	}	}	PUNCT
ejpam-300	311	41	=	=	SYM
ejpam-300	311	42	φ	φ	X
ejpam-300	311	43	.	.	PUNCT
ejpam-300	312	1	2	2	X
ejpam-300	312	2	.	.	X
ejpam-300	312	3	suppose	suppose	VERB
ejpam-300	312	4	there	there	PRON
ejpam-300	312	5	exist	exist	VERB
ejpam-300	312	6	k	k	PROPN
ejpam-300	312	7	∈	∈	PROPN
ejpam-300	312	8	{	{	PUNCT
ejpam-300	312	9	1	1	NUM
ejpam-300	312	10	,	,	PUNCT
ejpam-300	312	11	2	2	NUM
ejpam-300	312	12	,	,	PUNCT
ejpam-300	312	13	...	...	PUNCT
ejpam-300	312	14	,	,	PUNCT
ejpam-300	312	15	m	m	VERB
ejpam-300	312	16	}	}	PUNCT
ejpam-300	312	17	and	and	CCONJ
ejpam-300	312	18	i	i	PRON
ejpam-300	312	19	∈	∈	PROPN
ejpam-300	312	20	{	{	PUNCT
ejpam-300	312	21	1	1	NUM
ejpam-300	312	22	,	,	PUNCT
ejpam-300	312	23	2	2	NUM
ejpam-300	312	24	,	,	PUNCT
ejpam-300	312	25	...	...	PUNCT
ejpam-300	312	26	,	,	PUNCT
ejpam-300	312	27	l	l	NOUN
ejpam-300	312	28	}	}	PUNCT
ejpam-300	312	29	such	such	ADJ
ejpam-300	312	30	that	that	SCONJ
ejpam-300	312	31	a	a	DET
ejpam-300	312	32	∈	∈	PROPN
ejpam-300	312	33	vk	vk	NOUN
ejpam-300	312	34	and	and	CCONJ
ejpam-300	312	35	b	b	PROPN
ejpam-300	312	36	/∈	/∈	PROPN
ejpam-300	312	37	wi	wi	PROPN
ejpam-300	312	38	.	.	PUNCT
ejpam-300	313	1	then	then	ADV
ejpam-300	313	2	by	by	ADP
ejpam-300	313	3	supposition	supposition	NOUN
ejpam-300	313	4	,	,	PUNCT
ejpam-300	313	5	proposition	proposition	NOUN
ejpam-300	313	6	3.7	3.7	NUM
ejpam-300	313	7	and	and	CCONJ
ejpam-300	313	8	theorem	theorem	VERB
ejpam-300	313	9	5.4	5.4	NUM
ejpam-300	313	10	,	,	PUNCT
ejpam-300	313	11	we	we	PRON
ejpam-300	313	12	can	can	AUX
ejpam-300	313	13	find	find	VERB
ejpam-300	313	14	for	for	ADP
ejpam-300	313	15	each	each	DET
ejpam-300	313	16	i	i	PRON
ejpam-300	313	17	,	,	PUNCT
ejpam-300	313	18	bi	bi	PROPN
ejpam-300	313	19	∈	∈	PROPN
ejpam-300	313	20	wi	wi	PROPN
ejpam-300	313	21	such	such	ADJ
ejpam-300	313	22	that	that	SCONJ
ejpam-300	313	23	{	{	PUNCT
ejpam-300	313	24	a	a	NOUN
ejpam-300	313	25	}	}	PUNCT
ejpam-300	313	26	and	and	CCONJ
ejpam-300	313	27	{	{	PUNCT
ejpam-300	313	28	b	b	PROPN
ejpam-300	313	29	,	,	PUNCT
ejpam-300	313	30	b1	b1	NOUN
ejpam-300	313	31	,	,	PUNCT
ejpam-300	313	32	b2	b2	NOUN
ejpam-300	313	33	,	,	PUNCT
ejpam-300	313	34	...	...	PUNCT
ejpam-300	313	35	,	,	PUNCT
ejpam-300	313	36	bl	bl	AUX
ejpam-300	313	37	}	}	PUNCT
ejpam-300	313	38	are	be	AUX
ejpam-300	313	39	pre	pre	ADJ
ejpam-300	313	40	-	-	ADJ
ejpam-300	313	41	γ	γ	ADJ
ejpam-300	313	42	-	-	ADJ
ejpam-300	313	43	open	open	ADJ
ejpam-300	313	44	sets	set	NOUN
ejpam-300	313	45	and	and	CCONJ
ejpam-300	313	46	{	{	PUNCT
ejpam-300	313	47	a	a	PRON
ejpam-300	313	48	}	}	PUNCT
ejpam-300	313	49	∩	∩	ADJ
ejpam-300	313	50	{	{	PUNCT
ejpam-300	313	51	b	b	PROPN
ejpam-300	313	52	,	,	PUNCT
ejpam-300	313	53	b1	b1	NOUN
ejpam-300	313	54	,	,	PUNCT
ejpam-300	313	55	b2	b2	NOUN
ejpam-300	313	56	,	,	PUNCT
ejpam-300	313	57	...	...	PUNCT
ejpam-300	313	58	,	,	PUNCT
ejpam-300	313	59	bl}=	bl}=	VERB
ejpam-300	313	60	φ	φ	PROPN
ejpam-300	313	61	.	.	PROPN
ejpam-300	314	1	3	3	NUM
ejpam-300	314	2	.	.	PUNCT
ejpam-300	314	3	suppose	suppose	VERB
ejpam-300	314	4	that	that	SCONJ
ejpam-300	314	5	there	there	PRON
ejpam-300	314	6	exist	exist	VERB
ejpam-300	314	7	k	k	PROPN
ejpam-300	314	8	∈	∈	PROPN
ejpam-300	314	9	{	{	PUNCT
ejpam-300	314	10	1	1	NUM
ejpam-300	314	11	,	,	PUNCT
ejpam-300	314	12	2	2	NUM
ejpam-300	314	13	,	,	PUNCT
ejpam-300	314	14	...	...	PUNCT
ejpam-300	314	15	,	,	PUNCT
ejpam-300	314	16	m	m	VERB
ejpam-300	314	17	}	}	PUNCT
ejpam-300	314	18	and	and	CCONJ
ejpam-300	314	19	i	i	PRON
ejpam-300	314	20	∈	∈	PROPN
ejpam-300	314	21	{	{	PUNCT
ejpam-300	314	22	1	1	NUM
ejpam-300	314	23	,	,	PUNCT
ejpam-300	314	24	2	2	NUM
ejpam-300	314	25	,	,	PUNCT
ejpam-300	314	26	...	...	PUNCT
ejpam-300	314	27	,	,	PUNCT
ejpam-300	314	28	l	l	NOUN
ejpam-300	314	29	}	}	PUNCT
ejpam-300	314	30	such	such	ADJ
ejpam-300	314	31	that	that	SCONJ
ejpam-300	314	32	a	a	DET
ejpam-300	314	33	/∈	/∈	INTJ
ejpam-300	314	34	vk	vk	NOUN
ejpam-300	314	35	and	and	CCONJ
ejpam-300	314	36	b	b	PROPN
ejpam-300	314	37	/∈wi	/∈wi	PROPN
ejpam-300	314	38	.	.	PUNCT
ejpam-300	315	1	then	then	ADV
ejpam-300	315	2	by	by	ADP
ejpam-300	315	3	supposition	supposition	NOUN
ejpam-300	315	4	and	and	CCONJ
ejpam-300	315	5	theorem	theorem	VERB
ejpam-300	315	6	5.4	5.4	NUM
ejpam-300	315	7	,	,	PUNCT
ejpam-300	315	8	for	for	ADP
ejpam-300	315	9	each	each	DET
ejpam-300	315	10	k	k	PROPN
ejpam-300	315	11	and	and	CCONJ
ejpam-300	315	12	i	i	PRON
ejpam-300	315	13	,	,	PUNCT
ejpam-300	315	14	we	we	PRON
ejpam-300	315	15	can	can	AUX
ejpam-300	315	16	find	find	VERB
ejpam-300	315	17	elements	element	NOUN
ejpam-300	315	18	ak	ak	PROPN
ejpam-300	315	19	∈	∈	PROPN
ejpam-300	315	20	vk	vk	PROPN
ejpam-300	315	21	and	and	CCONJ
ejpam-300	315	22	bi	bi	PROPN
ejpam-300	315	23	∈	∈	PROPN
ejpam-300	315	24	wi	wi	PROPN
ejpam-300	316	1	such	such	ADJ
ejpam-300	316	2	that	that	SCONJ
ejpam-300	316	3	{	{	PUNCT
ejpam-300	316	4	a	a	PRON
ejpam-300	316	5	,	,	PUNCT
ejpam-300	316	6	a1	a1	NOUN
ejpam-300	316	7	,	,	PUNCT
ejpam-300	316	8	a2	a2	PROPN
ejpam-300	316	9	,	,	PUNCT
ejpam-300	316	10	...	...	PUNCT
ejpam-300	316	11	,	,	PUNCT
ejpam-300	316	12	am	be	AUX
ejpam-300	316	13	}	}	PUNCT
ejpam-300	316	14	and	and	CCONJ
ejpam-300	316	15	{	{	PUNCT
ejpam-300	316	16	b	b	NOUN
ejpam-300	316	17	,	,	PUNCT
ejpam-300	316	18	b1	b1	NOUN
ejpam-300	316	19	,	,	PUNCT
ejpam-300	316	20	b2	b2	NOUN
ejpam-300	316	21	,	,	PUNCT
ejpam-300	316	22	...	...	PUNCT
ejpam-300	316	23	,	,	PUNCT
ejpam-300	316	24	bl	bl	AUX
ejpam-300	316	25	}	}	PUNCT
ejpam-300	316	26	are	be	AUX
ejpam-300	316	27	pre	pre	ADJ
ejpam-300	316	28	-	-	ADJ
ejpam-300	316	29	γ	γ	ADJ
ejpam-300	316	30	-	-	ADJ
ejpam-300	316	31	open	open	ADJ
ejpam-300	316	32	sets	set	NOUN
ejpam-300	316	33	and	and	CCONJ
ejpam-300	316	34	{	{	PUNCT
ejpam-300	316	35	a	a	PRON
ejpam-300	316	36	,	,	PUNCT
ejpam-300	316	37	a1	a1	NOUN
ejpam-300	316	38	,	,	PUNCT
ejpam-300	316	39	a2	a2	PROPN
ejpam-300	316	40	,	,	PUNCT
ejpam-300	316	41	...	...	PUNCT
ejpam-300	316	42	,	,	PUNCT
ejpam-300	316	43	am	be	AUX
ejpam-300	316	44	}	}	PUNCT
ejpam-300	316	45	∩	∩	ADJ
ejpam-300	316	46	{	{	PUNCT
ejpam-300	316	47	b	b	PROPN
ejpam-300	316	48	,	,	PUNCT
ejpam-300	316	49	b1	b1	NOUN
ejpam-300	316	50	,	,	PUNCT
ejpam-300	316	51	b2	b2	NOUN
ejpam-300	316	52	,	,	PUNCT
ejpam-300	316	53	...	...	PUNCT
ejpam-300	316	54	,	,	PUNCT
ejpam-300	316	55	bl	bl	ADP
ejpam-300	316	56	}	}	PUNCT
ejpam-300	316	57	=	=	SYM
ejpam-300	316	58	φ	φ	PROPN
ejpam-300	316	59	.	.	PUNCT
ejpam-300	317	1	hence	hence	ADV
ejpam-300	317	2	x	x	PRON
ejpam-300	317	3	is	be	AUX
ejpam-300	317	4	a	a	DET
ejpam-300	317	5	pre	pre	ADJ
ejpam-300	317	6	γ	γ	PROPN
ejpam-300	317	7	-	-	ADJ
ejpam-300	317	8	t2	t2	ADJ
ejpam-300	317	9	space	space	NOUN
ejpam-300	317	10	.	.	PUNCT
ejpam-300	318	1	this	this	PRON
ejpam-300	318	2	completes	complete	VERB
ejpam-300	318	3	the	the	DET
ejpam-300	318	4	proof	proof	NOUN
ejpam-300	318	5	.	.	PUNCT
ejpam-300	319	1	references	reference	NOUN
ejpam-300	319	2	[	[	X
ejpam-300	319	3	1	1	NUM
ejpam-300	319	4	]	]	PUNCT
ejpam-300	319	5	b.	b.	PROPN
ejpam-300	319	6	ahmad	ahmad	PROPN
ejpam-300	319	7	and	and	CCONJ
ejpam-300	319	8	s.	s.	PROPN
ejpam-300	319	9	hussain	hussain	PROPN
ejpam-300	319	10	:	:	PUNCT
ejpam-300	319	11	properties	property	NOUN
ejpam-300	319	12	of	of	ADP
ejpam-300	319	13	γ	γ	NOUN
ejpam-300	319	14	-	-	NOUN
ejpam-300	319	15	operations	operation	NOUN
ejpam-300	319	16	on	on	ADP
ejpam-300	319	17	topological	topological	ADJ
ejpam-300	319	18	spaces	space	NOUN
ejpam-300	319	19	,	,	PUNCT
ejpam-300	319	20	aligarh	aligarh	PROPN
ejpam-300	319	21	bull	bull	PROPN
ejpam-300	319	22	.	.	PUNCT
ejpam-300	320	1	math	math	NOUN
ejpam-300	320	2	.	.	PUNCT
ejpam-300	321	1	22(1	22(1	NUM
ejpam-300	321	2	)	)	PUNCT
ejpam-300	322	1	(	(	PUNCT
ejpam-300	322	2	2003	2003	NUM
ejpam-300	322	3	)	)	PUNCT
ejpam-300	322	4	,	,	PUNCT
ejpam-300	322	5	45	45	NUM
ejpam-300	322	6	-	-	SYM
ejpam-300	322	7	51	51	NUM
ejpam-300	322	8	.	.	PUNCT
ejpam-300	322	9	references	reference	NOUN
ejpam-300	323	1	351	351	NUM
ejpam-300	324	1	[	[	X
ejpam-300	324	2	2	2	NUM
ejpam-300	324	3	]	]	PUNCT
ejpam-300	324	4	s.	s.	PROPN
ejpam-300	324	5	kasahara	kasahara	PROPN
ejpam-300	324	6	:	:	PUNCT
ejpam-300	324	7	operation	operation	NOUN
ejpam-300	324	8	-	-	PUNCT
ejpam-300	324	9	compact	compact	ADJ
ejpam-300	324	10	spaces	space	NOUN
ejpam-300	324	11	,	,	PUNCT
ejpam-300	324	12	math	math	NOUN
ejpam-300	324	13	.	.	PUNCT
ejpam-300	325	1	japon	japon	PROPN
ejpam-300	325	2	.	.	PROPN
ejpam-300	325	3	,	,	PUNCT
ejpam-300	325	4	24(1979	24(1979	NUM
ejpam-300	325	5	)	)	PUNCT
ejpam-300	325	6	,	,	PUNCT
ejpam-300	325	7	97	97	NUM
ejpam-300	325	8	-	-	SYM
ejpam-300	325	9	105	105	NUM
ejpam-300	325	10	.	.	PUNCT
ejpam-300	326	1	[	[	X
ejpam-300	326	2	3	3	X
ejpam-300	326	3	]	]	X
ejpam-300	326	4	f.	f.	PROPN
ejpam-300	326	5	nakaoka	nakaoka	PROPN
ejpam-300	326	6	and	and	CCONJ
ejpam-300	326	7	n.	n.	PROPN
ejpam-300	326	8	oda	oda	PROPN
ejpam-300	326	9	:	:	PUNCT
ejpam-300	326	10	some	some	DET
ejpam-300	326	11	applications	application	NOUN
ejpam-300	326	12	of	of	ADP
ejpam-300	326	13	minimal	minimal	ADJ
ejpam-300	326	14	open	open	ADJ
ejpam-300	326	15	sets	set	NOUN
ejpam-300	326	16	,	,	PUNCT
ejpam-300	326	17	internat	internat	NOUN
ejpam-300	326	18	.	.	PUNCT
ejpam-300	327	1	jr	jr	PROPN
ejpam-300	327	2	.	.	PROPN
ejpam-300	327	3	math	math	PROPN
ejpam-300	327	4	.	.	PUNCT
ejpam-300	328	1	math	math	NOUN
ejpam-300	328	2	.	.	PUNCT
ejpam-300	329	1	sci	sci	PROPN
ejpam-300	329	2	.	.	PROPN
ejpam-300	329	3	,	,	PUNCT
ejpam-300	329	4	27(2001	27(2001	NUM
ejpam-300	329	5	)	)	PUNCT
ejpam-300	329	6	,	,	PUNCT
ejpam-300	329	7	no	no	INTJ
ejpam-300	329	8	.	.	NOUN
ejpam-300	329	9	8	8	NUM
ejpam-300	329	10	,	,	PUNCT
ejpam-300	329	11	471	471	NUM
ejpam-300	329	12	-	-	SYM
ejpam-300	329	13	476	476	NUM
ejpam-300	329	14	.	.	PUNCT
ejpam-300	330	1	[	[	X
ejpam-300	330	2	4	4	X
ejpam-300	330	3	]	]	PUNCT
ejpam-300	330	4	h.	h.	PROPN
ejpam-300	330	5	ogata	ogata	PROPN
ejpam-300	330	6	:	:	PUNCT
ejpam-300	330	7	operations	operation	NOUN
ejpam-300	330	8	on	on	ADP
ejpam-300	330	9	topological	topological	ADJ
ejpam-300	330	10	spaces	space	NOUN
ejpam-300	330	11	and	and	CCONJ
ejpam-300	330	12	associated	associate	VERB
ejpam-300	330	13	topogy	topogy	NOUN
ejpam-300	330	14	,	,	PUNCT
ejpam-300	330	15	math	math	NOUN
ejpam-300	330	16	.	.	PUNCT
ejpam-300	331	1	japon	japon	PROPN
ejpam-300	331	2	.	.	PROPN
ejpam-300	331	3	,	,	PUNCT
ejpam-300	331	4	36(1)(1991	36(1)(1991	NUM
ejpam-300	331	5	)	)	PUNCT
ejpam-300	331	6	,	,	PUNCT
ejpam-300	331	7	175	175	NUM
ejpam-300	331	8	-	-	SYM
ejpam-300	331	9	184	184	NUM
ejpam-300	331	10	.	.	PUNCT