id	sid	tid	token	lemma	pos
iajs-1170	1	1	2009	2009	NUM
iajs-1170	1	2	)	)	PUNCT
iajs-1170	1	3	3	3	NUM
iajs-1170	1	4	(	(	PUNCT
iajs-1170	1	5	22مجلة	22مجلة	NUM
iajs-1170	1	6	ابن	ابن	VERB
iajs-1170	1	7	الهیثم	الهیثم	PROPN
iajs-1170	1	8	للعلوم	للعلوم	PROPN
iajs-1170	1	9	الصرفة	الصرفة	PROPN
iajs-1170	1	10	والتطبیقیة	والتطبیقیة	PROPN
iajs-1170	1	11	المجلد	المجلد	PROPN
iajs-1170	1	12	--cالتراص	--cالتراص	PROPN
iajs-1170	2	1	من	من	ADP
iajs-1170	2	2	نوع	نوع	PROPN
iajs-1170	2	3	رنا	رنا	PROPN
iajs-1170	2	4	بهجت	بهجت	PROPN
iajs-1170	2	5	اسماعیل	اسماعیل	PROPN
iajs-1170	2	6	جامعة	جامعة	PROPN
iajs-1170	2	7	بغداد	بغداد	PROPN
iajs-1170	2	8	-ابن	-ابن	PUNCT
iajs-1170	2	9	الهیثم	الهیثم	VERB
iajs-1170	2	10	كلیة	كلیة	PROPN
iajs-1170	2	11	التربیة	التربیة	NOUN
iajs-1170	2	12	-قسم	-قسم	PUNCT
iajs-1170	2	13	الریاضیات	الریاضیات	PROPN
iajs-1170	2	14	الخالصة	الخالصة	PROPN
iajs-1170	2	15	ـمیناه	ـمیناه	NOUN
iajs-1170	2	16	ة	ة	DET
iajs-1170	2	17	بعــض	بعــض	PROPN
iajs-1170	2	18	"	"	PUNCT
iajs-1170	2	19	-cالتـراص	-cالتـراص	PROPN
iajs-1170	2	20	مـن	مـن	NOUN
iajs-1170	2	21	نــوع	نــوع	NOUN
iajs-1170	2	22	"	"	PUNCT
iajs-1170	2	23	قمنـا	قمنـا	PROPN
iajs-1170	2	24	فـي	فـي	NOUN
iajs-1170	3	1	هــذا	هــذا	NOUN
iajs-1170	3	2	البحـث	البحـث	PROPN
iajs-1170	3	3	بتعریــف	بتعریــف	PROPN
iajs-1170	3	4	نـوع	نـوع	PROPN
iajs-1170	3	5	جدیـد	جدیـد	PROPN
iajs-1170	3	6	مــن	مــن	PROPN
iajs-1170	3	7	التـراص	التـراص	PROPN
iajs-1170	3	8	اسـ	اسـ	PROPN
iajs-1170	3	9	كـذلك	كـذلك	PROPN
iajs-1170	3	10	قمنــا	قمنــا	SCONJ
iajs-1170	3	11	بدراسـ	بدراسـ	PROPN
iajs-1170	3	12	.-cوالتراص	.-cوالتراص	PROPN
iajs-1170	3	13	من	من	ADP
iajs-1170	3	14	نوع	نوع	PROPN
iajs-1170	3	15	-خواصه	-خواصه	PART
iajs-1170	3	16	والعالقة	والعالقة	PROPN
iajs-1170	3	17	بینه	بینه	PROPN
iajs-1170	3	18	وبین	وبین	PROPN
iajs-1170	3	19	التراص	التراص	PROPN
iajs-1170	3	20	والتراص	والتراص	NOUN
iajs-1170	3	21	من	من	ADP
iajs-1170	3	22	نوع	نوع	PROPN
iajs-1170	3	23	ibn	ibn	PROPN
iajs-1170	3	24	alhaitham	alhaitham	NOUN
iajs-1170	4	1	j.	j.	PROPN
iajs-1170	5	1	fo	fo	ADP
iajs-1170	5	2	r	r	NOUN
iajs-1170	5	3	pure	pure	ADJ
iajs-1170	5	4	&	&	CCONJ
iajs-1170	5	5	appl	appl	PROPN
iajs-1170	5	6	.	.	PUNCT
iajs-1170	6	1	sc	sc	PROPN
iajs-1170	7	1	i	i	PRON
iajs-1170	7	2	vo	vo	INTJ
iajs-1170	7	3	l.22	l.22	X
iajs-1170	7	4	(	(	PUNCT
iajs-1170	7	5	3	3	NUM
iajs-1170	7	6	)	)	PUNCT
iajs-1170	7	7	2009	2009	NUM
iajs-1170	7	8			NOUN
iajs-1170	7	9	c	c	NOUN
iajs-1170	7	10	-	-	PUNCT
iajs-1170	7	11	compactness	compactness	NOUN
iajs-1170	7	12	r.	r.	PROPN
iajs-1170	7	13	b.	b.	PROPN
iajs-1170	7	14	esmaeel	esmaeel	PROPN
iajs-1170	7	15	department	department	PROPN
iajs-1170	7	16	of	of	ADP
iajs-1170	7	17	mathematics	mathematics	PROPN
iajs-1170	7	18	,	,	PUNCT
iajs-1170	7	19	college	college	NOUN
iajs-1170	7	20	of	of	ADP
iajs-1170	7	21	education	education	PROPN
iajs-1170	7	22	ibn	ibn	PROPN
iajs-1170	7	23	-	-	PUNCT
iajs-1170	7	24	al	al	PROPN
iajs-1170	7	25	-	-	PUNCT
iajs-1170	7	26	haitham	haitham	PROPN
iajs-1170	7	27	,	,	PUNCT
iajs-1170	7	28	university	university	PROPN
iajs-1170	7	29	of	of	ADP
iajs-1170	7	30	baghdad	baghdad	PROPN
iajs-1170	7	31	abstract	abstract	ADV
iajs-1170	7	32	in	in	ADP
iajs-1170	7	33	this	this	DET
iajs-1170	7	34	paper	paper	NOUN
iajs-1170	7	35	,	,	PUNCT
iajs-1170	7	36	we	we	PRON
iajs-1170	7	37	introduce	introduce	VERB
iajs-1170	7	38	a	a	DET
iajs-1170	7	39	new	new	ADJ
iajs-1170	7	40	type	type	NOUN
iajs-1170	7	41	of	of	ADP
iajs-1170	7	42	compactness	compactness	NOUN
iajs-1170	7	43	which	which	PRON
iajs-1170	7	44	is	be	AUX
iajs-1170	7	45	called	call	VERB
iajs-1170	7	46	"	"	PUNCT
iajs-1170	7	47	-ccompactness	-ccompactness	PROPN
iajs-1170	7	48	"	"	PUNCT
iajs-1170	7	49	.	.	PUNCT
iajs-1170	8	1	also	also	ADV
iajs-1170	8	2	,	,	PUNCT
iajs-1170	8	3	we	we	PRON
iajs-1170	8	4	study	study	VERB
iajs-1170	8	5	some	some	DET
iajs-1170	8	6	properties	property	NOUN
iajs-1170	8	7	of	of	ADP
iajs-1170	8	8	this	this	DET
iajs-1170	8	9	type	type	NOUN
iajs-1170	8	10	of	of	ADP
iajs-1170	8	11	compactness	compactness	NOUN
iajs-1170	8	12	and	and	CCONJ
iajs-1170	8	13	the	the	DET
iajs-1170	8	14	relationships	relationship	NOUN
iajs-1170	8	15	among	among	ADP
iajs-1170	8	16	it	it	PRON
iajs-1170	8	17	and	and	CCONJ
iajs-1170	8	18	compactness	compactness	NOUN
iajs-1170	8	19	,	,	PUNCT
iajs-1170	8	20	-compactness	-compactness	PROPN
iajs-1170	8	21	and	and	CCONJ
iajs-1170	8	22	c	c	NOUN
iajs-1170	8	23	-	-	PUNCT
iajs-1170	8	24	compactness	compactness	NOUN
iajs-1170	8	25	.	.	PUNCT
iajs-1170	9	1	1	1	X
iajs-1170	9	2	.	.	X
iajs-1170	9	3	introduction	introduction	NOUN
iajs-1170	9	4	and	and	CCONJ
iajs-1170	9	5	preliminaries	preliminary	NOUN
iajs-1170	9	6	a	a	DET
iajs-1170	9	7	topological	topological	ADJ
iajs-1170	9	8	space	space	NOUN
iajs-1170	9	9	(	(	PUNCT
iajs-1170	9	10	x,	x,	X
iajs-1170	9	11	)	)	PUNCT
iajs-1170	9	12	is	be	AUX
iajs-1170	9	13	said	say	VERB
iajs-1170	9	14	to	to	PART
iajs-1170	9	15	be	be	AUX
iajs-1170	9	16	c	c	ADJ
iajs-1170	9	17	-	-	ADJ
iajs-1170	9	18	compact	compact	ADJ
iajs-1170	9	19	space	space	NOUN
iajs-1170	9	20	if	if	SCONJ
iajs-1170	9	21	for	for	ADP
iajs-1170	9	22	each	each	DET
iajs-1170	9	23	closed	close	VERB
iajs-1170	9	24	set	set	VERB
iajs-1170	9	25	a	a	DET
iajs-1170	9	26			PROPN
iajs-1170	9	27	x	x	NOUN
iajs-1170	9	28	,	,	PUNCT
iajs-1170	9	29	each	each	DET
iajs-1170	9	30	open	open	ADJ
iajs-1170	9	31	cover	cover	NOUN
iajs-1170	9	32	of	of	ADP
iajs-1170	9	33	a	a	DET
iajs-1170	9	34	contains	contain	VERB
iajs-1170	9	35	a	a	DET
iajs-1170	9	36	finite	finite	NOUN
iajs-1170	9	37	subfamily	subfamily	ADV
iajs-1170	9	38	w	w	ADP
iajs-1170	9	39	such	such	ADJ
iajs-1170	9	40	that	that	SCONJ
iajs-1170	9	41	{	{	PUNCT
iajs-1170	9	42	cl	cl	NOUN
iajs-1170	9	43	v	v	NOUN
iajs-1170	9	44	:	:	PUNCT
iajs-1170	9	45	v	v	ADP
iajs-1170	9	46			NOUN
iajs-1170	9	47	w	w	NOUN
iajs-1170	9	48	}	}	PUNCT
iajs-1170	9	49	covers	cover	VERB
iajs-1170	9	50	a	a	DET
iajs-1170	9	51	,	,	PUNCT
iajs-1170	9	52	[	[	X
iajs-1170	9	53	1	1	NUM
iajs-1170	9	54	]	]	PUNCT
iajs-1170	9	55	.	.	PUNCT
iajs-1170	10	1	in	in	ADP
iajs-1170	10	2	1965	1965	NUM
iajs-1170	10	3	,	,	PUNCT
iajs-1170	10	4	o.njasted	o.njaste	VERB
iajs-1170	10	5	[	[	X
iajs-1170	10	6	2	2	NUM
iajs-1170	10	7	]	]	PUNCT
iajs-1170	10	8	introduced	introduce	VERB
iajs-1170	10	9	"	"	PUNCT
iajs-1170	10	10	-open	-open	PROPN
iajs-1170	10	11	set	set	NOUN
iajs-1170	10	12	"	"	PUNCT
iajs-1170	10	13	in	in	ADP
iajs-1170	10	14	topology	topology	NOUN
iajs-1170	10	15	[	[	X
iajs-1170	10	16	a	a	DET
iajs-1170	10	17	subset	subset	NOUN
iajs-1170	10	18	a	a	PRON
iajs-1170	10	19	of	of	ADP
iajs-1170	10	20	a	a	DET
iajs-1170	10	21	topological	topological	ADJ
iajs-1170	10	22	space	space	NOUN
iajs-1170	10	23	x	x	PRON
iajs-1170	10	24	is	be	AUX
iajs-1170	10	25	said	say	VERB
iajs-1170	10	26	to	to	PART
iajs-1170	10	27	be	be	AUX
iajs-1170	10	28	"	"	PUNCT
iajs-1170	10	29	-open	-open	PROPN
iajs-1170	10	30	set	set	VERB
iajs-1170	10	31	if	if	SCONJ
iajs-1170	10	32	a	a	DET
iajs-1170	10	33			PROPN
iajs-1170	10	34	int	int	NOUN
iajs-1170	10	35	(	(	PUNCT
iajs-1170	10	36	cl(int(a	cl(int(a	PROPN
iajs-1170	10	37	)	)	PUNCT
iajs-1170	10	38	)	)	PUNCT
iajs-1170	10	39	)	)	PUNCT
iajs-1170	11	1	]	]	PUNCT
iajs-1170	11	2	,	,	PUNCT
iajs-1170	11	3	and	and	CCONJ
iajs-1170	11	4	he	he	PRON
iajs-1170	11	5	proved	prove	VERB
iajs-1170	11	6	that	that	SCONJ
iajs-1170	11	7	the	the	DET
iajs-1170	11	8	family	family	NOUN
iajs-1170	11	9	of	of	ADP
iajs-1170	11	10	all	all	DET
iajs-1170	11	11	"	"	PUNCT
iajs-1170	11	12	-open	-open	PROPN
iajs-1170	11	13	sets	set	VERB
iajs-1170	11	14	in	in	ADP
iajs-1170	11	15	a	a	DET
iajs-1170	11	16	space	space	NOUN
iajs-1170	11	17	(	(	PUNCT
iajs-1170	11	18	x,	x,	X
iajs-1170	11	19	)	)	PUNCT
iajs-1170	11	20	is	be	AUX
iajs-1170	11	21	a	a	DET
iajs-1170	11	22	topology	topology	NOUN
iajs-1170	11	23	on	on	ADP
iajs-1170	11	24	x	x	NOUN
iajs-1170	11	25	,	,	PUNCT
iajs-1170	11	26	which	which	PRON
iajs-1170	11	27	is	be	AUX
iajs-1170	11	28	finer	fine	ADJ
iajs-1170	11	29	than	than	ADP
iajs-1170	11	30			NOUN
iajs-1170	11	31	and	and	CCONJ
iajs-1170	11	32	denoted	denote	VERB
iajs-1170	11	33	by	by	ADP
iajs-1170	11	34	.	.	ADJ
iajs-1170	11	35	-open	-open	PROPN
iajs-1170	11	36	sets	set	NOUN
iajs-1170	11	37	are	be	AUX
iajs-1170	11	38	discussed	discuss	VERB
iajs-1170	11	39	in	in	ADP
iajs-1170	11	40	[	[	X
iajs-1170	11	41	3	3	NUM
iajs-1170	11	42	]	]	PUNCT
iajs-1170	11	43	,	,	PUNCT
iajs-1170	11	44	[	[	X
iajs-1170	11	45	4	4	NUM
iajs-1170	11	46	]	]	PUNCT
iajs-1170	11	47	,	,	PUNCT
iajs-1170	11	48	[	[	X
iajs-1170	11	49	5	5	NUM
iajs-1170	11	50	]	]	PUNCT
iajs-1170	11	51	,	,	PUNCT
iajs-1170	11	52	some	some	DET
iajs-1170	11	53	concepts	concept	NOUN
iajs-1170	11	54	were	be	AUX
iajs-1170	11	55	studied	study	VERB
iajs-1170	11	56	as	as	SCONJ
iajs-1170	11	57	follows	follow	VERB
iajs-1170	11	58	:	:	PUNCT
iajs-1170	11	59	i.	i.	NOUN
iajs-1170	11	60	the	the	DET
iajs-1170	11	61	complement	complement	NOUN
iajs-1170	11	62	of	of	ADP
iajs-1170	11	63	an	an	DET
iajs-1170	11	64	-open	-open	PROPN
iajs-1170	11	65	set	set	NOUN
iajs-1170	11	66	is	be	AUX
iajs-1170	11	67	called	call	VERB
iajs-1170	11	68	-closed	-closed	ADJ
iajs-1170	11	69	set	set	NOUN
iajs-1170	11	70	and	and	CCONJ
iajs-1170	11	71	the	the	DET
iajs-1170	11	72	intersection	intersection	NOUN
iajs-1170	11	73	of	of	ADP
iajs-1170	11	74	all	all	DET
iajs-1170	11	75	-closed	-closed	ADJ
iajs-1170	11	76	sets	set	NOUN
iajs-1170	11	77	contains	contain	VERB
iajs-1170	11	78	a	a	DET
iajs-1170	11	79	set	set	NOUN
iajs-1170	11	80	a	a	PRON
iajs-1170	11	81	which	which	PRON
iajs-1170	11	82	is	be	AUX
iajs-1170	11	83	called	call	VERB
iajs-1170	11	84	the	the	DET
iajs-1170	11	85	-closure	-closure	PROPN
iajs-1170	11	86	of	of	ADP
iajs-1170	11	87	a	a	PRON
iajs-1170	11	88	and	and	CCONJ
iajs-1170	11	89	denoted	denote	VERB
iajs-1170	11	90	by	by	ADP
iajs-1170	11	91	-cla	-cla	NOUN
iajs-1170	11	92	.	.	PUNCT
iajs-1170	12	1	so	so	ADV
iajs-1170	12	2	,	,	PUNCT
iajs-1170	12	3	-cla	-cla	PRON
iajs-1170	12	4	is	be	AUX
iajs-1170	12	5	an	an	DET
iajs-1170	12	6	-closed	-closed	ADJ
iajs-1170	12	7	set	set	NOUN
iajs-1170	12	8	and	and	CCONJ
iajs-1170	12	9	proved	prove	VERB
iajs-1170	12	10	(	(	PUNCT
iajs-1170	12	11	-cla	-cla	X
iajs-1170	12	12	=	=	PUNCT
iajs-1170	12	13	a	a	DET
iajs-1170	12	14	iff	iff	PROPN
iajs-1170	12	15	a	a	PRON
iajs-1170	12	16	is	be	AUX
iajs-1170	12	17	-closed	-close	VERB
iajs-1170	12	18	set	set	NOUN
iajs-1170	12	19	)	)	PUNCT
iajs-1170	12	20	.	.	PUNCT
iajs-1170	13	1	ii	ii	PROPN
iajs-1170	13	2	.	.	PUNCT
iajs-1170	14	1	if	if	SCONJ
iajs-1170	14	2	a	a	PRON
iajs-1170	14	3	be	be	AUX
iajs-1170	14	4	a	a	DET
iajs-1170	14	5	subset	subset	NOUN
iajs-1170	14	6	of	of	ADP
iajs-1170	14	7	a	a	DET
iajs-1170	14	8	topological	topological	ADJ
iajs-1170	14	9	space	space	NOUN
iajs-1170	14	10	x	x	PUNCT
iajs-1170	14	11	the	the	DET
iajs-1170	14	12	-derived	-derived	PROPN
iajs-1170	14	13	of	of	ADP
iajs-1170	14	14	a	a	PRON
iajs-1170	14	15	is	be	AUX
iajs-1170	14	16	the	the	DET
iajs-1170	14	17	set	set	NOUN
iajs-1170	14	18	of	of	ADP
iajs-1170	14	19	all	all	DET
iajs-1170	14	20	elements	element	NOUN
iajs-1170	14	21	x	x	PUNCT
iajs-1170	14	22	satisfies	satisfy	VERB
iajs-1170	14	23	the	the	DET
iajs-1170	14	24	condition	condition	NOUN
iajs-1170	14	25	,	,	PUNCT
iajs-1170	14	26	that	that	SCONJ
iajs-1170	14	27	for	for	SCONJ
iajs-1170	14	28	every	every	DET
iajs-1170	14	29	-open	-open	PROPN
iajs-1170	14	30	set	set	VERB
iajs-1170	14	31	v	v	NOUN
iajs-1170	14	32	contains	contain	VERB
iajs-1170	14	33	x	x	X
iajs-1170	14	34	,	,	PUNCT
iajs-1170	14	35	implies	imply	VERB
iajs-1170	14	36	v\{x}a	v\{x}a	ADJ
iajs-1170	14	37			PROPN
iajs-1170	14	38	.	.	PUNCT
iajs-1170	15	1	in	in	ADP
iajs-1170	15	2	1985	1985	NUM
iajs-1170	15	3	,	,	PUNCT
iajs-1170	15	4	the	the	DET
iajs-1170	15	5	term	term	NOUN
iajs-1170	15	6	of	of	ADP
iajs-1170	15	7	"	"	PUNCT
iajs-1170	15	8	-compactness	-compactness	PROPN
iajs-1170	15	9	"	"	PUNCT
iajs-1170	15	10	was	be	AUX
iajs-1170	15	11	used	use	VERB
iajs-1170	15	12	for	for	ADP
iajs-1170	15	13	the	the	DET
iajs-1170	15	14	first	first	ADJ
iajs-1170	15	15	time	time	NOUN
iajs-1170	15	16	by	by	ADP
iajs-1170	15	17	s.n.m	s.n.m	NOUN
iajs-1170	15	18	aheshwari	aheshwari	PROPN
iajs-1170	15	19	and	and	CCONJ
iajs-1170	15	20	thakur	thakur	NOUN
iajs-1170	16	1	[	[	X
iajs-1170	16	2	6	6	NUM
iajs-1170	16	3	]	]	PUNCT
iajs-1170	16	4	.	.	PUNCT
iajs-1170	17	1	a	a	DET
iajs-1170	17	2	space	space	NOUN
iajs-1170	17	3	x	x	PUNCT
iajs-1170	17	4	is	be	AUX
iajs-1170	17	5	called	call	VERB
iajs-1170	17	6	-compact	-compact	ADJ
iajs-1170	17	7	space	space	NOUN
iajs-1170	17	8	if	if	SCONJ
iajs-1170	17	9	every	every	DET
iajs-1170	17	10	-open	-open	PROPN
iajs-1170	17	11	cover	cover	VERB
iajs-1170	17	12	for	for	ADP
iajs-1170	17	13	x	x	PUNCT
iajs-1170	17	14	has	have	VERB
iajs-1170	17	15	a	a	DET
iajs-1170	17	16	finite	finite	ADJ
iajs-1170	17	17	subcover	subcover	PROPN
iajs-1170	17	18	.	.	PUNCT
iajs-1170	18	1	in	in	ADP
iajs-1170	18	2	this	this	DET
iajs-1170	18	3	paper	paper	NOUN
iajs-1170	18	4	we	we	PRON
iajs-1170	18	5	shall	shall	AUX
iajs-1170	18	6	introduce	introduce	VERB
iajs-1170	18	7	a	a	DET
iajs-1170	18	8	new	new	ADJ
iajs-1170	18	9	concept	concept	NOUN
iajs-1170	18	10	of	of	ADP
iajs-1170	18	11	compactness	compactness	NOUN
iajs-1170	18	12	,	,	PUNCT
iajs-1170	18	13	which	which	PRON
iajs-1170	18	14	is	be	AUX
iajs-1170	18	15	called	call	VERB
iajs-1170	18	16	an	an	DET
iajs-1170	18	17	"	"	PUNCT
iajs-1170	18	18	-ccompactness	-ccompactness	PROPN
iajs-1170	18	19	"	"	PUNCT
iajs-1170	18	20	where	where	SCONJ
iajs-1170	18	21	[	[	X
iajs-1170	18	22	a	a	DET
iajs-1170	18	23	topological	topological	ADJ
iajs-1170	18	24	space	space	NOUN
iajs-1170	18	25	x	x	PRON
iajs-1170	18	26	is	be	AUX
iajs-1170	18	27	said	say	VERB
iajs-1170	18	28	to	to	PART
iajs-1170	18	29	be	be	AUX
iajs-1170	18	30	-c	-c	ADV
iajs-1170	18	31	-	-	PUNCT
iajs-1170	18	32	compact	compact	ADJ
iajs-1170	18	33	space	space	NOUN
iajs-1170	18	34	if	if	SCONJ
iajs-1170	18	35	for	for	ADP
iajs-1170	18	36	every	every	DET
iajs-1170	18	37	closed	close	VERB
iajs-1170	18	38	set	set	NOUN
iajs-1170	18	39	a	a	DET
iajs-1170	18	40			PROPN
iajs-1170	18	41	x	x	NOUN
iajs-1170	18	42	,	,	PUNCT
iajs-1170	18	43	each	each	DET
iajs-1170	18	44	family	family	NOUN
iajs-1170	18	45	of	of	ADP
iajs-1170	18	46	-open	-open	PROPN
iajs-1170	18	47	sets	set	VERB
iajs-1170	18	48	in	in	ADP
iajs-1170	18	49	x	x	PUNCT
iajs-1170	18	50	which	which	PRON
iajs-1170	18	51	covers	cover	VERB
iajs-1170	18	52	a	a	PRON
iajs-1170	18	53	,	,	PUNCT
iajs-1170	18	54	there	there	PRON
iajs-1170	18	55	is	be	VERB
iajs-1170	18	56	a	a	DET
iajs-1170	18	57	finite	finite	NOUN
iajs-1170	18	58	subfamily	subfamily	ADV
iajs-1170	18	59	w	w	ADP
iajs-1170	18	60	such	such	ADJ
iajs-1170	18	61	that	that	SCONJ
iajs-1170	18	62	{	{	PUNCT
iajs-1170	18	63	-cl	-cl	NOUN
iajs-1170	18	64	u	u	NOUN
iajs-1170	18	65	:	:	PUNCT
iajs-1170	18	66	u	u	PROPN
iajs-1170	18	67			PROPN
iajs-1170	18	68	w	w	PROPN
iajs-1170	18	69	}	}	PUNCT
iajs-1170	18	70	covers	cover	VERB
iajs-1170	18	71	a	a	DET
iajs-1170	18	72	]	]	X
iajs-1170	18	73	.	.	PUNCT
iajs-1170	19	1	we	we	PRON
iajs-1170	19	2	discuss	discuss	VERB
iajs-1170	19	3	some	some	DET
iajs-1170	19	4	properties	property	NOUN
iajs-1170	19	5	of	of	ADP
iajs-1170	19	6	this	this	DET
iajs-1170	19	7	kind	kind	NOUN
iajs-1170	19	8	of	of	ADP
iajs-1170	19	9	compactness	compactness	NOUN
iajs-1170	19	10	and	and	CCONJ
iajs-1170	19	11	give	give	VERB
iajs-1170	19	12	some	some	DET
iajs-1170	19	13	propositions	proposition	NOUN
iajs-1170	19	14	,	,	PUNCT
iajs-1170	19	15	corollaries	corollary	NOUN
iajs-1170	19	16	and	and	CCONJ
iajs-1170	19	17	examples	example	NOUN
iajs-1170	19	18	after	after	ADP
iajs-1170	19	19	investigating	investigate	VERB
iajs-1170	19	20	the	the	DET
iajs-1170	19	21	relationships	relationship	NOUN
iajs-1170	19	22	among	among	ADP
iajs-1170	19	23	compact	compact	ADJ
iajs-1170	19	24	spaces	space	NOUN
iajs-1170	19	25	,	,	PUNCT
iajs-1170	19	26	ccompact	ccompact	NOUN
iajs-1170	19	27	spaces	space	NOUN
iajs-1170	19	28	,	,	PUNCT
iajs-1170	19	29	-compact	-compact	PROPN
iajs-1170	19	30	spaces	space	NOUN
iajs-1170	19	31	and	and	CCONJ
iajs-1170	19	32	-c	-c	ADV
iajs-1170	19	33	-	-	PUNCT
iajs-1170	19	34	compact	compact	ADJ
iajs-1170	19	35	spaces	space	NOUN
iajs-1170	19	36	are	be	AUX
iajs-1170	19	37	considered	consider	VERB
iajs-1170	19	38	.	.	PUNCT
iajs-1170	20	1	1.1	1.1	NUM
iajs-1170	20	2	definition	definition	NOUN
iajs-1170	20	3	[	[	X
iajs-1170	20	4	1	1	X
iajs-1170	20	5	]	]	PUNCT
iajs-1170	20	6	a	a	DET
iajs-1170	20	7	topological	topological	ADJ
iajs-1170	20	8	space	space	NOUN
iajs-1170	20	9	(	(	PUNCT
iajs-1170	20	10	x,	x,	X
iajs-1170	20	11	)	)	PUNCT
iajs-1170	20	12	is	be	AUX
iajs-1170	20	13	said	say	VERB
iajs-1170	20	14	to	to	PART
iajs-1170	20	15	be	be	AUX
iajs-1170	20	16	c	c	NOUN
iajs-1170	20	17	-	-	ADJ
iajs-1170	20	18	compact	compact	ADJ
iajs-1170	20	19	if	if	SCONJ
iajs-1170	20	20	for	for	ADP
iajs-1170	20	21	each	each	DET
iajs-1170	20	22	closed	close	VERB
iajs-1170	20	23	set	set	VERB
iajs-1170	20	24	a	a	DET
iajs-1170	20	25			PROPN
iajs-1170	20	26	x	x	NOUN
iajs-1170	20	27	,	,	PUNCT
iajs-1170	20	28	each	each	DET
iajs-1170	20	29	open	open	ADJ
iajs-1170	20	30	cover	cover	NOUN
iajs-1170	20	31	of	of	ADP
iajs-1170	20	32	a	a	DET
iajs-1170	20	33	contains	contain	VERB
iajs-1170	20	34	a	a	DET
iajs-1170	20	35	finite	finite	NOUN
iajs-1170	20	36	subfamily	subfamily	ADV
iajs-1170	20	37	w	w	ADP
iajs-1170	20	38	such	such	ADJ
iajs-1170	20	39	that	that	SCONJ
iajs-1170	20	40	{	{	PUNCT
iajs-1170	20	41	cl	cl	NOUN
iajs-1170	20	42	v	v	NOUN
iajs-1170	20	43	:	:	PUNCT
iajs-1170	20	44	v	v	ADP
iajs-1170	20	45			NOUN
iajs-1170	20	46	w	w	NOUN
iajs-1170	20	47	}	}	PUNCT
iajs-1170	20	48	covers	cover	VERB
iajs-1170	20	49	a.	a.	NOUN
iajs-1170	20	50	1.2	1.2	NUM
iajs-1170	20	51	proposition	proposition	NOUN
iajs-1170	20	52	[	[	X
iajs-1170	20	53	1	1	NUM
iajs-1170	20	54	]	]	PUNCT
iajs-1170	20	55	every	every	DET
iajs-1170	20	56	compact	compact	ADJ
iajs-1170	20	57	space	space	NOUN
iajs-1170	20	58	is	be	AUX
iajs-1170	20	59	c	c	NOUN
iajs-1170	20	60	-	-	ADJ
iajs-1170	20	61	compact	compact	ADJ
iajs-1170	20	62	.	.	PUNCT
iajs-1170	21	1	1.3	1.3	NUM
iajs-1170	21	2	remark	remark	NOUN
iajs-1170	21	3	the	the	DET
iajs-1170	21	4	implication	implication	NOUN
iajs-1170	21	5	in	in	ADP
iajs-1170	21	6	proposition	proposition	NOUN
iajs-1170	21	7	(	(	PUNCT
iajs-1170	21	8	1.2	1.2	NUM
iajs-1170	21	9	)	)	PUNCT
iajs-1170	21	10	is	be	AUX
iajs-1170	21	11	not	not	PART
iajs-1170	21	12	reversible	reversible	ADJ
iajs-1170	21	13	,	,	PUNCT
iajs-1170	21	14	for	for	ADP
iajs-1170	21	15	example	example	NOUN
iajs-1170	21	16	:	:	PUNCT
iajs-1170	21	17	a	a	DET
iajs-1170	21	18	space	space	NOUN
iajs-1170	21	19	(	(	PUNCT
iajs-1170	21	20	n,	n,	NOUN
iajs-1170	21	21	)	)	PUNCT
iajs-1170	21	22	where	where	SCONJ
iajs-1170	21	23	,	,	PUNCT
iajs-1170	21	24			PROPN
iajs-1170	21	25	=	=	SYM
iajs-1170	21	26	{	{	PUNCT
iajs-1170	21	27	un	un	PROPN
iajs-1170	21	28	=	=	PROPN
iajs-1170	21	29	{	{	PUNCT
iajs-1170	21	30	1,2,	1,2,	NUM
iajs-1170	21	31	…	…	SYM
iajs-1170	21	32	,n}n	,n}n	PUNCT
iajs-1170	21	33			NOUN
iajs-1170	21	34	n	n	CCONJ
iajs-1170	21	35	}	}	PUNCT
iajs-1170	21	36			NOUN
iajs-1170	21	37	{	{	PUNCT
iajs-1170	21	38	n,	n,	VERB
iajs-1170	21	39	}	}	PUNCT
iajs-1170	21	40	is	be	AUX
iajs-1170	21	41	c	c	NOUN
iajs-1170	21	42	-	-	ADJ
iajs-1170	21	43	compact	compact	ADJ
iajs-1170	21	44	which	which	PRON
iajs-1170	21	45	is	be	AUX
iajs-1170	21	46	not	not	PART
iajs-1170	21	47	compact	compact	ADJ
iajs-1170	21	48	.	.	PUNCT
iajs-1170	22	1	1.4	1.4	NUM
iajs-1170	22	2	proposition	proposition	NOUN
iajs-1170	22	3	[	[	X
iajs-1170	22	4	1	1	X
iajs-1170	22	5	]	]	PUNCT
iajs-1170	22	6	a	a	DET
iajs-1170	22	7	t3	t3	PROPN
iajs-1170	22	8	-	-	PUNCT
iajs-1170	22	9	c	c	NOUN
iajs-1170	22	10	-	-	ADJ
iajs-1170	22	11	compact	compact	ADJ
iajs-1170	22	12	space	space	NOUN
iajs-1170	22	13	is	be	AUX
iajs-1170	22	14	compact	compact	ADJ
iajs-1170	22	15	.	.	PUNCT
iajs-1170	23	1	1.5	1.5	NUM
iajs-1170	23	2	definition	definition	NOUN
iajs-1170	23	3	[	[	X
iajs-1170	23	4	6	6	NUM
iajs-1170	23	5	]	]	X
iajs-1170	23	6	ibn	ibn	PROPN
iajs-1170	23	7	alhaitham	alhaitham	NOUN
iajs-1170	24	1	j.	j.	PROPN
iajs-1170	25	1	fo	fo	ADP
iajs-1170	25	2	r	r	NOUN
iajs-1170	25	3	pure	pure	ADJ
iajs-1170	25	4	&	&	CCONJ
iajs-1170	25	5	appl	appl	PROPN
iajs-1170	25	6	.	.	PUNCT
iajs-1170	26	1	sc	sc	PROPN
iajs-1170	27	1	i	i	PRON
iajs-1170	27	2	vo	vo	INTJ
iajs-1170	27	3	l.22	l.22	X
iajs-1170	27	4	(	(	PUNCT
iajs-1170	27	5	3	3	NUM
iajs-1170	27	6	)	)	PUNCT
iajs-1170	27	7	2009	2009	NUM
iajs-1170	27	8	a	a	DET
iajs-1170	27	9	space	space	NOUN
iajs-1170	27	10	x	x	PUNCT
iajs-1170	27	11	is	be	AUX
iajs-1170	27	12	said	say	VERB
iajs-1170	27	13	to	to	PART
iajs-1170	27	14	be	be	AUX
iajs-1170	27	15	-compact	-compact	ADJ
iajs-1170	27	16	space	space	NOUN
iajs-1170	27	17	if	if	SCONJ
iajs-1170	27	18	every	every	DET
iajs-1170	27	19	-open	-open	PROPN
iajs-1170	27	20	cover	cover	NOUN
iajs-1170	27	21	of	of	ADP
iajs-1170	27	22	x	x	PUNCT
iajs-1170	27	23	has	have	VERB
iajs-1170	27	24	a	a	DET
iajs-1170	27	25	finite	finite	ADJ
iajs-1170	27	26	subcover	subcover	PROPN
iajs-1170	27	27	.	.	PUNCT
iajs-1170	28	1	1.6	1.6	NUM
iajs-1170	28	2	proposition	proposition	NOUN
iajs-1170	28	3	[	[	X
iajs-1170	28	4	6	6	NUM
iajs-1170	28	5	]	]	PUNCT
iajs-1170	28	6	every	every	DET
iajs-1170	28	7	-compact	-compact	PROPN
iajs-1170	28	8	space	space	NOUN
iajs-1170	28	9	is	be	AUX
iajs-1170	28	10	compact	compact	ADJ
iajs-1170	28	11	.	.	PUNCT
iajs-1170	29	1	1.7	1.7	NUM
iajs-1170	29	2	remark	remark	NOUN
iajs-1170	29	3	the	the	DET
iajs-1170	29	4	opposite	opposite	ADJ
iajs-1170	29	5	direction	direction	NOUN
iajs-1170	29	6	of	of	ADP
iajs-1170	29	7	proposition	proposition	NOUN
iajs-1170	29	8	(	(	PUNCT
iajs-1170	29	9	1.6	1.6	NUM
iajs-1170	29	10	)	)	PUNCT
iajs-1170	29	11	may	may	AUX
iajs-1170	29	12	be	be	AUX
iajs-1170	29	13	false	false	ADJ
iajs-1170	29	14	,	,	PUNCT
iajs-1170	29	15	for	for	ADP
iajs-1170	29	16	example	example	NOUN
iajs-1170	29	17	:	:	PUNCT
iajs-1170	29	18	let	let	VERB
iajs-1170	29	19	x	x	PUNCT
iajs-1170	29	20	=	=	PRON
iajs-1170	29	21	{	{	PUNCT
iajs-1170	29	22	0	0	NUM
iajs-1170	29	23	}	}	PUNCT
iajs-1170	29	24			NOUN
iajs-1170	29	25	n	n	NOUN
iajs-1170	29	26	and	and	CCONJ
iajs-1170	29	27			NOUN
iajs-1170	29	28	=	=	X
iajs-1170	29	29	{	{	PUNCT
iajs-1170	29	30			PROPN
iajs-1170	29	31	,	,	PUNCT
iajs-1170	29	32	{	{	PUNCT
iajs-1170	29	33	0},x	0},x	PROPN
iajs-1170	29	34	}	}	PUNCT
iajs-1170	29	35	be	be	VERB
iajs-1170	29	36	a	a	DET
iajs-1170	29	37	topology	topology	NOUN
iajs-1170	29	38	on	on	ADP
iajs-1170	29	39	x.	x.	NOUN
iajs-1170	29	40	evidently	evidently	ADV
iajs-1170	29	41	,	,	PUNCT
iajs-1170	29	42	x	x	X
iajs-1170	29	43	is	be	AUX
iajs-1170	29	44	a	a	DET
iajs-1170	29	45	compact	compact	ADJ
iajs-1170	29	46	space	space	NOUN
iajs-1170	29	47	.	.	PUNCT
iajs-1170	30	1	however	however	ADV
iajs-1170	30	2	,	,	PUNCT
iajs-1170	30	3	it	it	PRON
iajs-1170	30	4	is	be	AUX
iajs-1170	30	5	not	not	PART
iajs-1170	30	6	-compact	-compact	ADJ
iajs-1170	30	7	space	space	NOUN
iajs-1170	30	8	.	.	PUNCT
iajs-1170	31	1	1.8	1.8	NUM
iajs-1170	31	2	proposition	proposition	NOUN
iajs-1170	31	3	[	[	X
iajs-1170	31	4	6	6	NUM
iajs-1170	31	5	]	]	PUNCT
iajs-1170	31	6	,	,	PUNCT
iajs-1170	31	7	[	[	X
iajs-1170	31	8	7	7	X
iajs-1170	31	9	]	]	X
iajs-1170	31	10	if	if	SCONJ
iajs-1170	31	11	all	all	DET
iajs-1170	31	12	nowhere	nowhere	ADV
iajs-1170	31	13	dense	dense	ADJ
iajs-1170	31	14	subsets	subset	NOUN
iajs-1170	31	15	of	of	ADP
iajs-1170	31	16	a	a	DET
iajs-1170	31	17	topological	topological	ADJ
iajs-1170	31	18	space	space	NOUN
iajs-1170	31	19	x	x	PRON
iajs-1170	31	20	are	be	AUX
iajs-1170	31	21	finite	finite	ADJ
iajs-1170	31	22	,	,	PUNCT
iajs-1170	31	23	then	then	ADV
iajs-1170	31	24	the	the	DET
iajs-1170	31	25	concepts	concept	NOUN
iajs-1170	31	26	of	of	ADP
iajs-1170	31	27	compactness	compactness	NOUN
iajs-1170	31	28	and	and	CCONJ
iajs-1170	31	29	-compactness	-compactness	PROPN
iajs-1170	31	30	are	be	AUX
iajs-1170	31	31	concident	concident	ADJ
iajs-1170	31	32	.	.	PUNCT
iajs-1170	32	1	in	in	ADP
iajs-1170	32	2	propositions	proposition	NOUN
iajs-1170	32	3	(	(	PUNCT
iajs-1170	32	4	1.9	1.9	NUM
iajs-1170	32	5	)	)	PUNCT
iajs-1170	32	6	and	and	CCONJ
iajs-1170	32	7	(	(	PUNCT
iajs-1170	32	8	1.11	1.11	NUM
iajs-1170	32	9	)	)	PUNCT
iajs-1170	32	10	we	we	PRON
iajs-1170	32	11	shall	shall	AUX
iajs-1170	32	12	discuss	discuss	VERB
iajs-1170	32	13	the	the	DET
iajs-1170	32	14	relationships	relationship	NOUN
iajs-1170	32	15	between	between	ADP
iajs-1170	32	16	-compatness	-compatness	PROPN
iajs-1170	32	17	and	and	CCONJ
iajs-1170	32	18	c	c	NOUN
iajs-1170	32	19	-	-	PUNCT
iajs-1170	32	20	compactness	compactness	NOUN
iajs-1170	32	21	.	.	PUNCT
iajs-1170	33	1	1.9	1.9	NUM
iajs-1170	33	2	proposition	proposition	NOUN
iajs-1170	33	3	every	every	DET
iajs-1170	33	4	-compact	-compact	PROPN
iajs-1170	33	5	space	space	NOUN
iajs-1170	33	6	is	be	AUX
iajs-1170	33	7	c	c	NOUN
iajs-1170	33	8	-	-	ADJ
iajs-1170	33	9	compact	compact	ADJ
iajs-1170	33	10	.	.	PUNCT
iajs-1170	34	1	proof	proof	NOUN
iajs-1170	34	2	:	:	PUNCT
iajs-1170	34	3	follows	follow	VERB
iajs-1170	34	4	directly	directly	ADV
iajs-1170	34	5	from	from	ADP
iajs-1170	34	6	propositions	proposition	NOUN
iajs-1170	34	7	(	(	PUNCT
iajs-1170	34	8	1.6	1.6	NUM
iajs-1170	34	9	)	)	PUNCT
iajs-1170	34	10	and	and	CCONJ
iajs-1170	34	11	(	(	PUNCT
iajs-1170	34	12	1.2	1.2	NUM
iajs-1170	34	13	)	)	PUNCT
iajs-1170	34	14	.	.	PUNCT
iajs-1170	35	1	1.10	1.10	NUM
iajs-1170	35	2	remark	remark	NOUN
iajs-1170	35	3	the	the	DET
iajs-1170	35	4	opposite	opposite	ADJ
iajs-1170	35	5	direction	direction	NOUN
iajs-1170	35	6	of	of	ADP
iajs-1170	35	7	proposition	proposition	NOUN
iajs-1170	35	8	(	(	PUNCT
iajs-1170	35	9	1.9	1.9	NUM
iajs-1170	35	10	)	)	PUNCT
iajs-1170	35	11	may	may	AUX
iajs-1170	35	12	be	be	AUX
iajs-1170	35	13	false	false	ADJ
iajs-1170	35	14	,	,	PUNCT
iajs-1170	35	15	see	see	VERB
iajs-1170	35	16	the	the	DET
iajs-1170	35	17	example	example	NOUN
iajs-1170	35	18	in	in	ADP
iajs-1170	35	19	remark	remark	NOUN
iajs-1170	35	20	(	(	PUNCT
iajs-1170	35	21	1.3	1.3	NUM
iajs-1170	35	22	)	)	PUNCT
iajs-1170	35	23	,	,	PUNCT
iajs-1170	35	24	(	(	PUNCT
iajs-1170	35	25	n,	n,	X
iajs-1170	35	26	)	)	PUNCT
iajs-1170	35	27	is	be	AUX
iajs-1170	35	28	c	c	ADJ
iajs-1170	35	29	-	-	ADJ
iajs-1170	35	30	compact	compact	ADJ
iajs-1170	35	31	space	space	NOUN
iajs-1170	35	32	which	which	PRON
iajs-1170	35	33	is	be	AUX
iajs-1170	35	34	not	not	PART
iajs-1170	35	35	-compact	-compact	ADJ
iajs-1170	35	36	,	,	PUNCT
iajs-1170	35	37	since	since	SCONJ
iajs-1170	35	38	{	{	PUNCT
iajs-1170	35	39	{	{	PUNCT
iajs-1170	35	40	1,n}	1,n}	PROPN
iajs-1170	35	41	n	n	PRON
iajs-1170	35	42			NOUN
iajs-1170	35	43	n	n	CCONJ
iajs-1170	35	44	}	}	PUNCT
iajs-1170	35	45	is	be	AUX
iajs-1170	35	46	-open	-open	PROPN
iajs-1170	35	47	cover	cover	NOUN
iajs-1170	35	48	for	for	ADP
iajs-1170	35	49	n	n	PRON
iajs-1170	35	50	which	which	PRON
iajs-1170	35	51	has	have	VERB
iajs-1170	35	52	no	no	DET
iajs-1170	35	53	finite	finite	PROPN
iajs-1170	35	54	subcover	subcover	PROPN
iajs-1170	35	55	.	.	PUNCT
iajs-1170	36	1	1.11	1.11	NUM
iajs-1170	36	2	proposition	proposition	NOUN
iajs-1170	36	3	if	if	SCONJ
iajs-1170	36	4	all	all	DET
iajs-1170	36	5	nowhere	nowhere	ADV
iajs-1170	36	6	dense	dense	ADJ
iajs-1170	36	7	subsets	subset	NOUN
iajs-1170	36	8	of	of	ADP
iajs-1170	36	9	a	a	DET
iajs-1170	36	10	t3space	t3space	NOUN
iajs-1170	36	11	x	x	PART
iajs-1170	36	12	are	be	AUX
iajs-1170	36	13	finite	finite	ADJ
iajs-1170	36	14	,	,	PUNCT
iajs-1170	36	15	then	then	ADV
iajs-1170	36	16	x	x	PUNCT
iajs-1170	36	17	is	be	AUX
iajs-1170	36	18	-compact	-compact	ADJ
iajs-1170	36	19	space	space	NOUN
iajs-1170	36	20	,	,	PUNCT
iajs-1170	36	21	whenever	whenever	SCONJ
iajs-1170	36	22	it	it	PRON
iajs-1170	36	23	is	be	AUX
iajs-1170	36	24	c	c	NOUN
iajs-1170	36	25	-	-	ADJ
iajs-1170	36	26	compact	compact	ADJ
iajs-1170	36	27	..	..	PUNCT
iajs-1170	37	1	proof	proof	NOUN
iajs-1170	37	2	:	:	PUNCT
iajs-1170	37	3	follows	follow	VERB
iajs-1170	37	4	from	from	ADP
iajs-1170	37	5	propositions	proposition	NOUN
iajs-1170	37	6	(	(	PUNCT
iajs-1170	37	7	1.4	1.4	NUM
iajs-1170	37	8	)	)	PUNCT
iajs-1170	37	9	and	and	CCONJ
iajs-1170	37	10	(	(	PUNCT
iajs-1170	37	11	1.8	1.8	NUM
iajs-1170	37	12	)	)	PUNCT
iajs-1170	37	13	.	.	PUNCT
iajs-1170	38	1	2	2	X
iajs-1170	38	2	.	.	X
iajs-1170	38	3	-c	-c	NOUN
iajs-1170	38	4	-	-	PUNCT
iajs-1170	38	5	compactness	compactness	NOUN
iajs-1170	38	6	2.0	2.0	NUM
iajs-1170	38	7	introduction	introduction	NOUN
iajs-1170	38	8	in	in	ADP
iajs-1170	38	9	this	this	DET
iajs-1170	38	10	section	section	NOUN
iajs-1170	38	11	we	we	PRON
iajs-1170	38	12	shall	shall	AUX
iajs-1170	38	13	introduce	introduce	VERB
iajs-1170	38	14	a	a	DET
iajs-1170	38	15	new	new	ADJ
iajs-1170	38	16	type	type	NOUN
iajs-1170	38	17	of	of	ADP
iajs-1170	38	18	compactness	compactness	NOUN
iajs-1170	38	19	which	which	PRON
iajs-1170	38	20	is	be	AUX
iajs-1170	38	21	termed	term	VERB
iajs-1170	38	22	"	"	PUNCT
iajs-1170	38	23	-ccompactness	-ccompactness	PROPN
iajs-1170	38	24	"	"	PUNCT
iajs-1170	38	25	,	,	PUNCT
iajs-1170	38	26	we	we	PRON
iajs-1170	38	27	shall	shall	AUX
iajs-1170	38	28	study	study	VERB
iajs-1170	38	29	further	further	ADJ
iajs-1170	38	30	properties	property	NOUN
iajs-1170	38	31	of	of	ADP
iajs-1170	38	32	this	this	DET
iajs-1170	38	33	type	type	NOUN
iajs-1170	38	34	of	of	ADP
iajs-1170	38	35	compactness	compactness	NOUN
iajs-1170	38	36	.	.	PUNCT
iajs-1170	39	1	examples	example	NOUN
iajs-1170	39	2	were	be	AUX
iajs-1170	39	3	constructed	construct	VERB
iajs-1170	39	4	to	to	PART
iajs-1170	39	5	show	show	VERB
iajs-1170	39	6	the	the	DET
iajs-1170	39	7	relationships	relationship	NOUN
iajs-1170	39	8	among	among	ADP
iajs-1170	39	9	"	"	PUNCT
iajs-1170	39	10	compact	compact	ADJ
iajs-1170	39	11	,	,	PUNCT
iajs-1170	39	12	c	c	NOUN
iajs-1170	39	13	-	-	ADJ
iajs-1170	39	14	compact	compact	ADJ
iajs-1170	39	15	,	,	PUNCT
iajs-1170	39	16	-compact	-compact	PROPN
iajs-1170	39	17	and	and	CCONJ
iajs-1170	39	18	-ccompact	-ccompact	PROPN
iajs-1170	39	19	space	space	NOUN
iajs-1170	39	20	"	"	PUNCT
iajs-1170	39	21	.	.	PUNCT
iajs-1170	40	1	several	several	ADJ
iajs-1170	40	2	propositions	proposition	NOUN
iajs-1170	40	3	of	of	ADP
iajs-1170	40	4	these	these	DET
iajs-1170	40	5	spaces	space	NOUN
iajs-1170	40	6	are	be	AUX
iajs-1170	40	7	given	give	VERB
iajs-1170	40	8	also	also	ADV
iajs-1170	40	9	2.1	2.1	NUM
iajs-1170	40	10	definition	definition	NOUN
iajs-1170	40	11	a	a	DET
iajs-1170	40	12	topological	topological	ADJ
iajs-1170	40	13	space	space	NOUN
iajs-1170	40	14	(	(	PUNCT
iajs-1170	40	15	x,	x,	X
iajs-1170	40	16	)	)	PUNCT
iajs-1170	40	17	is	be	AUX
iajs-1170	40	18	said	say	VERB
iajs-1170	40	19	to	to	PART
iajs-1170	40	20	be	be	AUX
iajs-1170	40	21	-c	-c	ADV
iajs-1170	40	22	-	-	PUNCT
iajs-1170	40	23	compact	compact	ADJ
iajs-1170	40	24	space	space	NOUN
iajs-1170	40	25	if	if	SCONJ
iajs-1170	40	26	for	for	SCONJ
iajs-1170	40	27	each	each	DET
iajs-1170	40	28	-closed	-close	VERB
iajs-1170	40	29	set	set	VERB
iajs-1170	40	30	a	a	DET
iajs-1170	40	31			PROPN
iajs-1170	40	32	x	x	NOUN
iajs-1170	40	33	,	,	PUNCT
iajs-1170	40	34	each	each	DET
iajs-1170	40	35	family	family	NOUN
iajs-1170	40	36	of	of	ADP
iajs-1170	40	37	-open	-open	PROPN
iajs-1170	40	38	subset	subset	VERB
iajs-1170	40	39	of	of	ADP
iajs-1170	40	40	x	x	PRON
iajs-1170	40	41	which	which	PRON
iajs-1170	40	42	covers	cover	VERB
iajs-1170	40	43	a	a	PRON
iajs-1170	40	44	has	have	VERB
iajs-1170	40	45	a	a	DET
iajs-1170	40	46	finite	finite	NOUN
iajs-1170	40	47	subfamily	subfamily	ADV
iajs-1170	40	48	whose	whose	DET
iajs-1170	40	49	-closures	-closures	PROPN
iajs-1170	40	50	in	in	ADP
iajs-1170	40	51	x	x	PUNCT
iajs-1170	40	52	covers	cover	VERB
iajs-1170	40	53	a.	a.	NOUN
iajs-1170	40	54	2.2	2.2	NUM
iajs-1170	40	55	proposition	proposition	NOUN
iajs-1170	40	56	an	an	DET
iajs-1170	40	57	-compact	-compact	PROPN
iajs-1170	40	58	space	space	NOUN
iajs-1170	40	59	is	be	AUX
iajs-1170	40	60	-c	-c	ADV
iajs-1170	40	61	-	-	PUNCT
iajs-1170	40	62	compact	compact	ADJ
iajs-1170	40	63	.	.	PUNCT
iajs-1170	41	1	proof	proof	NOUN
iajs-1170	41	2	:	:	PUNCT
iajs-1170	41	3	let	let	VERB
iajs-1170	41	4	a	a	PRON
iajs-1170	41	5	be	be	AUX
iajs-1170	41	6	an	an	DET
iajs-1170	41	7	-closed	-closed	ADJ
iajs-1170	41	8	subset	subset	NOUN
iajs-1170	41	9	of	of	ADP
iajs-1170	41	10	an	an	DET
iajs-1170	41	11	-compact	-compact	PROPN
iajs-1170	41	12	space	space	NOUN
iajs-1170	41	13	x	x	PUNCT
iajs-1170	41	14	and	and	CCONJ
iajs-1170	41	15	{	{	PUNCT
iajs-1170	41	16	u:	u:	PROPN
iajs-1170	41	17			NOUN
iajs-1170	41	18	}	}	PUNCT
iajs-1170	41	19	be	be	VERB
iajs-1170	41	20	a	a	DET
iajs-1170	41	21	family	family	NOUN
iajs-1170	41	22	of	of	ADP
iajs-1170	41	23	-open	-open	PROPN
iajs-1170	41	24	sets	set	VERB
iajs-1170	41	25	in	in	ADP
iajs-1170	41	26	x	x	PUNCT
iajs-1170	41	27	which	which	PRON
iajs-1170	41	28	covers	cover	VERB
iajs-1170	41	29	a	a	PRON
iajs-1170	41	30	,	,	PUNCT
iajs-1170	41	31	implies	imply	VERB
iajs-1170	41	32	,	,	PUNCT
iajs-1170	41	33	{	{	PUNCT
iajs-1170	41	34	u:	u:	PROPN
iajs-1170	41	35			PROPN
iajs-1170	41	36	}	}	PUNCT
iajs-1170	41	37			NOUN
iajs-1170	41	38	{	{	PUNCT
iajs-1170	41	39	x	x	PROPN
iajs-1170	41	40	–	–	PUNCT
iajs-1170	41	41	a	a	PRON
iajs-1170	41	42	}	}	PUNCT
iajs-1170	41	43	is	be	AUX
iajs-1170	41	44	an	an	DET
iajs-1170	41	45	-open	-open	PROPN
iajs-1170	41	46	cover	cover	NOUN
iajs-1170	41	47	of	of	ADP
iajs-1170	41	48	x	x	PUNCT
iajs-1170	41	49	which	which	PRON
iajs-1170	41	50	is	be	AUX
iajs-1170	41	51	compact	compact	ADJ
iajs-1170	41	52	space	space	NOUN
iajs-1170	41	53	,	,	PUNCT
iajs-1170	41	54	then	then	ADV
iajs-1170	41	55	there	there	PRON
iajs-1170	41	56	is	be	VERB
iajs-1170	41	57	a	a	DET
iajs-1170	41	58	finite	finite	ADJ
iajs-1170	41	59	family	family	NOUN
iajs-1170	41	60	{	{	PUNCT
iajs-1170	41	61	u	u	NOUN
iajs-1170	41	62	i	i	PROPN
iajs-1170	41	63	:	:	PUNCT
iajs-1170	41	64	i	i	PRON
iajs-1170	41	65	=	=	SYM
iajs-1170	41	66	1,2,	1,2,	NUM
iajs-1170	41	67	…	…	SYM
iajs-1170	41	68	,n	,n	NOUN
iajs-1170	41	69	}	}	PUNCT
iajs-1170	41	70			NOUN
iajs-1170	41	71	{	{	PUNCT
iajs-1170	41	72	x	x	INTJ
iajs-1170	41	73	–	–	PUNCT
iajs-1170	41	74	a	a	PRON
iajs-1170	41	75	}	}	PUNCT
iajs-1170	41	76	covers	cover	VERB
iajs-1170	41	77	x.	x.	NOUN
iajs-1170	42	1	but	but	CCONJ
iajs-1170	42	2	(	(	PUNCT
iajs-1170	42	3	x	x	X
iajs-1170	42	4	–	–	PUNCT
iajs-1170	42	5	a	a	X
iajs-1170	42	6	)	)	PUNCT
iajs-1170	42	7	covers	cover	VERB
iajs-1170	42	8	no	no	DET
iajs-1170	42	9	part	part	NOUN
iajs-1170	42	10	from	from	ADP
iajs-1170	42	11	a	a	PRON
iajs-1170	42	12	,	,	PUNCT
iajs-1170	42	13	implies	imply	VERB
iajs-1170	42	14	,	,	PUNCT
iajs-1170	42	15	{	{	PUNCT
iajs-1170	42	16	u	u	NOUN
iajs-1170	42	17	i	i	PROPN
iajs-1170	42	18	:	:	PUNCT
iajs-1170	43	1	i	i	PRON
iajs-1170	43	2	=	=	SYM
iajs-1170	43	3	1,2,	1,2,	NUM
iajs-1170	43	4	…	…	SYM
iajs-1170	43	5	,n	,n	NOUN
iajs-1170	43	6	}	}	PUNCT
iajs-1170	43	7	covers	cover	VERB
iajs-1170	43	8	a.	a.	NOUN
iajs-1170	44	1	so	so	ADV
iajs-1170	44	2	{	{	PUNCT
iajs-1170	44	3	-closur	-closur	PROPN
iajs-1170	44	4	u	u	NOUN
iajs-1170	45	1	i	i	PROPN
iajs-1170	45	2	:	:	PUNCT
iajs-1170	46	1	i	i	PRON
iajs-1170	46	2	=	=	NOUN
iajs-1170	46	3	1,2,	1,2,	NUM
iajs-1170	46	4	…	…	SYM
iajs-1170	46	5	,n	,n	NOUN
iajs-1170	46	6	}	}	PUNCT
iajs-1170	46	7	covers	cover	VERB
iajs-1170	46	8	a.	a.	NOUN
iajs-1170	46	9	hence	hence	ADV
iajs-1170	46	10	,	,	PUNCT
iajs-1170	46	11	x	x	PUNCT
iajs-1170	46	12	is	be	AUX
iajs-1170	46	13	-c	-c	ADV
iajs-1170	46	14	-	-	PUNCT
iajs-1170	46	15	compact	compact	ADJ
iajs-1170	46	16	space	space	NOUN
iajs-1170	46	17	.	.	PUNCT
iajs-1170	47	1	2.3	2.3	NUM
iajs-1170	47	2	corollary	corollary	NOUN
iajs-1170	47	3	if	if	SCONJ
iajs-1170	47	4	every	every	DET
iajs-1170	47	5	nowhere	nowhere	ADV
iajs-1170	47	6	dense	dense	ADJ
iajs-1170	47	7	subset	subset	NOUN
iajs-1170	47	8	of	of	ADP
iajs-1170	47	9	a	a	DET
iajs-1170	47	10	topological	topological	ADJ
iajs-1170	47	11	space	space	NOUN
iajs-1170	47	12	(	(	PUNCT
iajs-1170	47	13	x,	x,	X
iajs-1170	47	14	)	)	PUNCT
iajs-1170	47	15	is	be	AUX
iajs-1170	47	16	finite	finite	ADJ
iajs-1170	47	17	,	,	PUNCT
iajs-1170	47	18	then	then	ADV
iajs-1170	47	19	x	x	PUNCT
iajs-1170	47	20	is	be	AUX
iajs-1170	47	21	-ccompact	-ccompact	PROPN
iajs-1170	47	22	space	space	NOUN
iajs-1170	47	23	whenever	whenever	SCONJ
iajs-1170	47	24	it	it	PRON
iajs-1170	47	25	is	be	AUX
iajs-1170	47	26	compact	compact	ADJ
iajs-1170	47	27	.	.	PUNCT
iajs-1170	48	1	ibn	ibn	PROPN
iajs-1170	48	2	alhaitham	alhaitham	NOUN
iajs-1170	49	1	j.	j.	PROPN
iajs-1170	50	1	fo	fo	ADP
iajs-1170	50	2	r	r	NOUN
iajs-1170	50	3	pure	pure	ADJ
iajs-1170	50	4	&	&	CCONJ
iajs-1170	50	5	appl	appl	PROPN
iajs-1170	50	6	.	.	PUNCT
iajs-1170	51	1	sc	sc	PROPN
iajs-1170	52	1	i	i	PRON
iajs-1170	52	2	vo	vo	INTJ
iajs-1170	52	3	l.22	l.22	X
iajs-1170	52	4	(	(	PUNCT
iajs-1170	52	5	3	3	NUM
iajs-1170	52	6	)	)	PUNCT
iajs-1170	52	7	2009	2009	NUM
iajs-1170	52	8	proof	proof	NOUN
iajs-1170	52	9	:	:	PUNCT
iajs-1170	52	10	follows	follow	VERB
iajs-1170	52	11	from	from	ADP
iajs-1170	52	12	propositions	proposition	NOUN
iajs-1170	52	13	(	(	PUNCT
iajs-1170	52	14	1.8	1.8	NUM
iajs-1170	52	15	)	)	PUNCT
iajs-1170	52	16	and	and	CCONJ
iajs-1170	52	17	(	(	PUNCT
iajs-1170	52	18	2.2	2.2	NUM
iajs-1170	52	19	)	)	PUNCT
iajs-1170	52	20	.	.	PUNCT
iajs-1170	53	1	2.4	2.4	NUM
iajs-1170	53	2	corollary	corollary	NOUN
iajs-1170	53	3	if	if	SCONJ
iajs-1170	53	4	every	every	DET
iajs-1170	53	5	nowhere	nowhere	ADV
iajs-1170	53	6	dense	dense	ADJ
iajs-1170	53	7	set	set	NOUN
iajs-1170	53	8	is	be	AUX
iajs-1170	53	9	finite	finite	ADJ
iajs-1170	53	10	in	in	ADP
iajs-1170	53	11	a	a	DET
iajs-1170	53	12	t3	t3	PROPN
iajs-1170	53	13	-	-	PUNCT
iajs-1170	53	14	c	c	NOUN
iajs-1170	53	15	-	-	ADJ
iajs-1170	53	16	compact	compact	ADJ
iajs-1170	53	17	space	space	NOUN
iajs-1170	53	18	(	(	PUNCT
iajs-1170	53	19	x,	x,	PROPN
iajs-1170	53	20	)	)	PUNCT
iajs-1170	53	21	,	,	PUNCT
iajs-1170	53	22	then	then	ADV
iajs-1170	53	23	it	it	PRON
iajs-1170	53	24	is	be	AUX
iajs-1170	53	25	-c	-c	ADV
iajs-1170	53	26	-	-	PUNCT
iajs-1170	53	27	compact	compact	ADJ
iajs-1170	53	28	space	space	NOUN
iajs-1170	53	29	.	.	PUNCT
iajs-1170	54	1	proof	proof	NOUN
iajs-1170	54	2	:	:	PUNCT
iajs-1170	54	3	follows	follow	VERB
iajs-1170	54	4	from	from	ADP
iajs-1170	54	5	propositions	proposition	NOUN
iajs-1170	54	6	(	(	PUNCT
iajs-1170	54	7	1.4	1.4	NUM
iajs-1170	54	8	)	)	PUNCT
iajs-1170	54	9	and	and	CCONJ
iajs-1170	54	10	corollary	corollary	ADJ
iajs-1170	54	11	(	(	PUNCT
iajs-1170	54	12	2.3	2.3	NUM
iajs-1170	54	13	)	)	PUNCT
iajs-1170	54	14	.	.	PUNCT
iajs-1170	55	1	2.5	2.5	NUM
iajs-1170	55	2	remark	remark	VERB
iajs-1170	55	3	the	the	DET
iajs-1170	55	4	opposite	opposite	ADJ
iajs-1170	55	5	direction	direction	NOUN
iajs-1170	55	6	of	of	ADP
iajs-1170	55	7	proposition	proposition	NOUN
iajs-1170	55	8	(	(	PUNCT
iajs-1170	55	9	2.2	2.2	NUM
iajs-1170	55	10	)	)	PUNCT
iajs-1170	55	11	may	may	AUX
iajs-1170	55	12	be	be	AUX
iajs-1170	55	13	untrue	untrue	ADJ
iajs-1170	55	14	.	.	PUNCT
iajs-1170	56	1	for	for	ADP
iajs-1170	56	2	example	example	NOUN
iajs-1170	56	3	:	:	PUNCT
iajs-1170	56	4	let	let	VERB
iajs-1170	56	5	n	n	PRON
iajs-1170	56	6	be	be	AUX
iajs-1170	56	7	the	the	DET
iajs-1170	56	8	set	set	NOUN
iajs-1170	56	9	of	of	ADP
iajs-1170	56	10	all	all	DET
iajs-1170	56	11	natural	natural	ADJ
iajs-1170	56	12	numbers	number	NOUN
iajs-1170	56	13	,	,	PUNCT
iajs-1170	56	14	and	and	CCONJ
iajs-1170	56	15	let	let	VERB
iajs-1170	56	16			NOUN
iajs-1170	56	17	=	=	PRON
iajs-1170	56	18	{	{	PUNCT
iajs-1170	56	19			PROPN
iajs-1170	56	20	,	,	PUNCT
iajs-1170	56	21	{	{	PUNCT
iajs-1170	56	22	1},n	1},n	X
iajs-1170	56	23	}	}	PUNCT
iajs-1170	56	24	be	be	VERB
iajs-1170	56	25	a	a	DET
iajs-1170	56	26	topology	topology	NOUN
iajs-1170	56	27	on	on	ADP
iajs-1170	56	28	n.	n.	PROPN
iajs-1170	56	29	then	then	ADV
iajs-1170	56	30	{	{	PUNCT
iajs-1170	56	31	{	{	PUNCT
iajs-1170	56	32	1,n}	1,n}	PROPN
iajs-1170	56	33	n	n	PRON
iajs-1170	56	34			NOUN
iajs-1170	56	35	n	n	CCONJ
iajs-1170	56	36	}	}	PUNCT
iajs-1170	56	37	is	be	AUX
iajs-1170	56	38	an	an	DET
iajs-1170	56	39	-open	-open	PROPN
iajs-1170	56	40	cover	cover	NOUN
iajs-1170	56	41	for	for	ADP
iajs-1170	56	42	n	n	PRON
iajs-1170	56	43	which	which	PRON
iajs-1170	56	44	has	have	VERB
iajs-1170	56	45	no	no	DET
iajs-1170	56	46	finite	finite	PROPN
iajs-1170	56	47	subcover	subcover	PROPN
iajs-1170	56	48	.	.	PUNCT
iajs-1170	57	1	so	so	ADV
iajs-1170	57	2	n	n	ADV
iajs-1170	57	3	is	be	AUX
iajs-1170	57	4	not	not	PART
iajs-1170	57	5	compact	compact	ADJ
iajs-1170	57	6	space	space	NOUN
iajs-1170	57	7	.	.	PUNCT
iajs-1170	58	1	but	but	CCONJ
iajs-1170	58	2	n	n	PRON
iajs-1170	58	3	is	be	AUX
iajs-1170	58	4	-c	-c	ADV
iajs-1170	58	5	-	-	PUNCT
iajs-1170	58	6	compact	compact	ADJ
iajs-1170	58	7	,	,	PUNCT
iajs-1170	58	8	since	since	SCONJ
iajs-1170	58	9	n	n	ADV
iajs-1170	58	10	is	be	AUX
iajs-1170	58	11	the	the	DET
iajs-1170	58	12	unique	unique	ADJ
iajs-1170	58	13	-closed	-closed	ADJ
iajs-1170	58	14	set	set	NOUN
iajs-1170	58	15	contains	contain	VERB
iajs-1170	58	16	1	1	NUM
iajs-1170	58	17	.	.	PUNCT
iajs-1170	59	1	in	in	ADP
iajs-1170	59	2	the	the	DET
iajs-1170	59	3	following	follow	VERB
iajs-1170	59	4	proposition	proposition	NOUN
iajs-1170	59	5	we	we	PRON
iajs-1170	59	6	put	put	VERB
iajs-1170	59	7	some	some	DET
iajs-1170	59	8	condition	condition	NOUN
iajs-1170	59	9	to	to	PART
iajs-1170	59	10	make	make	VERB
iajs-1170	59	11	the	the	DET
iajs-1170	59	12	-c	-c	ADV
iajs-1170	59	13	-	-	PUNCT
iajs-1170	59	14	compact	compact	ADJ
iajs-1170	59	15	space	space	NOUN
iajs-1170	59	16	an	an	DET
iajs-1170	59	17	compact	compact	ADJ
iajs-1170	59	18	space	space	NOUN
iajs-1170	59	19	.	.	PUNCT
iajs-1170	60	1	2.6	2.6	NUM
iajs-1170	60	2	proposition	proposition	NOUN
iajs-1170	60	3	a	a	DET
iajs-1170	60	4	t3--c	t3--c	PROPN
iajs-1170	60	5	-	-	PUNCT
iajs-1170	60	6	compact	compact	ADJ
iajs-1170	60	7	space	space	NOUN
iajs-1170	60	8	is	be	AUX
iajs-1170	60	9	-compact	-compact	ADJ
iajs-1170	60	10	.	.	PUNCT
iajs-1170	61	1	proof	proof	NOUN
iajs-1170	61	2	:	:	PUNCT
iajs-1170	61	3	let	let	VERB
iajs-1170	61	4	x	x	PRON
iajs-1170	61	5	be	be	AUX
iajs-1170	61	6	a	a	DET
iajs-1170	61	7	t3--c	t3--c	ADJ
iajs-1170	61	8	-	-	PUNCT
iajs-1170	61	9	compact	compact	ADJ
iajs-1170	61	10	space	space	NOUN
iajs-1170	61	11	,	,	PUNCT
iajs-1170	61	12	if	if	SCONJ
iajs-1170	61	13	it	it	PRON
iajs-1170	61	14	is	be	AUX
iajs-1170	61	15	not	not	PART
iajs-1170	61	16	-compact	-compact	ADJ
iajs-1170	61	17	,	,	PUNCT
iajs-1170	61	18	then	then	ADV
iajs-1170	61	19	there	there	PRON
iajs-1170	61	20	is	be	VERB
iajs-1170	61	21	an	an	DET
iajs-1170	61	22	-open	-open	PROPN
iajs-1170	61	23	cover	cover	NOUN
iajs-1170	61	24	for	for	ADP
iajs-1170	61	25	x	x	PRON
iajs-1170	61	26	say	say	VERB
iajs-1170	61	27	{	{	PUNCT
iajs-1170	61	28	u:	u:	PROPN
iajs-1170	61	29			NOUN
iajs-1170	61	30	}	}	PUNCT
iajs-1170	61	31	which	which	PRON
iajs-1170	61	32	has	have	VERB
iajs-1170	61	33	no	no	DET
iajs-1170	61	34	finite	finite	PROPN
iajs-1170	61	35	subcover	subcover	PROPN
iajs-1170	61	36	.	.	PUNCT
iajs-1170	62	1	since	since	SCONJ
iajs-1170	62	2	x	x	PRON
iajs-1170	62	3	is	be	AUX
iajs-1170	62	4	-c	-c	ADV
iajs-1170	62	5	-	-	PUNCT
iajs-1170	62	6	compact	compact	ADJ
iajs-1170	62	7	space	space	NOUN
iajs-1170	62	8	,	,	PUNCT
iajs-1170	62	9	then	then	ADV
iajs-1170	62	10	there	there	PRON
iajs-1170	62	11	is	be	VERB
iajs-1170	62	12	a	a	DET
iajs-1170	62	13	finite	finite	NOUN
iajs-1170	62	14	subfamily	subfamily	ADV
iajs-1170	62	15	{	{	PUNCT
iajs-1170	62	16	u	u	NOUN
iajs-1170	62	17	i	i	PROPN
iajs-1170	62	18	:	:	PUNCT
iajs-1170	63	1	i	i	PRON
iajs-1170	63	2	=	=	NOUN
iajs-1170	63	3	1,2,	1,2,	NUM
iajs-1170	63	4	…	…	SYM
iajs-1170	63	5	,n	,n	NOUN
iajs-1170	63	6	}	}	PUNCT
iajs-1170	63	7	such	such	ADJ
iajs-1170	63	8	that	that	SCONJ
iajs-1170	63	9	{	{	PUNCT
iajs-1170	63	10	-closure	-closure	PROPN
iajs-1170	63	11	u	u	NOUN
iajs-1170	63	12	i	i	NOUN
iajs-1170	63	13	:	:	PUNCT
iajs-1170	64	1	i	i	PRON
iajs-1170	64	2	=	=	NOUN
iajs-1170	64	3	1,2,	1,2,	NUM
iajs-1170	64	4	…	…	SYM
iajs-1170	64	5	,n	,n	NOUN
iajs-1170	64	6	}	}	PUNCT
iajs-1170	64	7	covers	cover	VERB
iajs-1170	64	8	x.	x.	NOUN
iajs-1170	65	1	this	this	PRON
iajs-1170	65	2	means	mean	VERB
iajs-1170	65	3	,	,	PUNCT
iajs-1170	65	4	there	there	PRON
iajs-1170	65	5	exists	exist	VERB
iajs-1170	65	6	x	x	X
iajs-1170	65	7			NOUN
iajs-1170	65	8	x	x	PUNCT
iajs-1170	65	9	such	such	ADJ
iajs-1170	65	10	that	that	SCONJ
iajs-1170	65	11	x	x	SYM
iajs-1170	65	12			NOUN
iajs-1170	65	13	-cl	-cl	PROPN
iajs-1170	65	14	u	u	SYM
iajs-1170	65	15	i	i	PROPN
iajs-1170	65	16	and	and	CCONJ
iajs-1170	65	17	x	x	ADJ
iajs-1170	65	18			NUM
iajs-1170	65	19	u	u	X
iajs-1170	65	20	i	i	PROPN
iajs-1170	65	21	for	for	ADP
iajs-1170	65	22	some	some	DET
iajs-1170	65	23	i	i	NOUN
iajs-1170	65	24	=	=	SYM
iajs-1170	65	25	1,2,	1,2,	NUM
iajs-1170	65	26	…	…	PUNCT
iajs-1170	65	27	,n	,n	NOUN
iajs-1170	65	28	.	.	PUNCT
iajs-1170	65	29	implies	imply	VERB
iajs-1170	65	30	x	x	PUNCT
iajs-1170	65	31			PROPN
iajs-1170	65	32	-derived	-derive	VERB
iajs-1170	65	33	u	u	NOUN
iajs-1170	65	34	i	i	NOUN
iajs-1170	65	35	for	for	ADP
iajs-1170	65	36	some	some	DET
iajs-1170	65	37	i	i	NOUN
iajs-1170	65	38	=	=	SYM
iajs-1170	65	39	1,2,	1,2,	NUM
iajs-1170	65	40	…	…	SYM
iajs-1170	65	41	,n	,n	NOUN
iajs-1170	65	42	.	.	PUNCT
iajs-1170	66	1	now	now	ADV
iajs-1170	66	2	,	,	PUNCT
iajs-1170	66	3	since	since	SCONJ
iajs-1170	66	4	x	x	PRON
iajs-1170	66	5	is	be	AUX
iajs-1170	66	6	t1	t1	NOUN
iajs-1170	66	7	-	-	PUNCT
iajs-1170	66	8	space	space	NOUN
iajs-1170	66	9	,	,	PUNCT
iajs-1170	66	10	then	then	ADV
iajs-1170	66	11	{	{	PUNCT
iajs-1170	66	12	x	x	X
iajs-1170	66	13	}	}	PUNCT
iajs-1170	66	14	is	be	AUX
iajs-1170	66	15	closed	close	VERB
iajs-1170	66	16	set	set	VERB
iajs-1170	66	17	and	and	CCONJ
iajs-1170	66	18	since	since	SCONJ
iajs-1170	66	19	x	x	SYM
iajs-1170	66	20			NUM
iajs-1170	66	21	u	u	NOUN
iajs-1170	66	22	i	i	PROPN
iajs-1170	66	23	,	,	PUNCT
iajs-1170	66	24	then	then	ADV
iajs-1170	66	25	y	y	PROPN
iajs-1170	66	26			PROPN
iajs-1170	66	27	{	{	PUNCT
iajs-1170	66	28	x	x	X
iajs-1170	66	29	}	}	PUNCT
iajs-1170	66	30	for	for	ADP
iajs-1170	66	31	each	each	DET
iajs-1170	66	32	y	y	PROPN
iajs-1170	66	33			PROPN
iajs-1170	66	34	u	u	NOUN
iajs-1170	66	35	i	i	PROPN
iajs-1170	66	36	and	and	CCONJ
iajs-1170	66	37	x	x	X
iajs-1170	66	38	is	be	AUX
iajs-1170	66	39	regular	regular	ADJ
iajs-1170	66	40	space	space	NOUN
iajs-1170	66	41	,	,	PUNCT
iajs-1170	66	42	implies	imply	VERB
iajs-1170	66	43	for	for	ADP
iajs-1170	66	44	each	each	DET
iajs-1170	66	45	y	y	PROPN
iajs-1170	66	46			PROPN
iajs-1170	66	47	u	u	X
iajs-1170	66	48	i	i	PROPN
iajs-1170	66	49	,	,	PUNCT
iajs-1170	66	50	there	there	PRON
iajs-1170	66	51	are	be	VERB
iajs-1170	66	52	two	two	NUM
iajs-1170	66	53	open	open	ADJ
iajs-1170	66	54	sets	set	NOUN
iajs-1170	66	55	vy	vy	NOUN
iajs-1170	66	56	and	and	CCONJ
iajs-1170	66	57	vy	vy	VERB
iajs-1170	66	58	such	such	ADJ
iajs-1170	66	59	that	that	SCONJ
iajs-1170	66	60	y	y	PROPN
iajs-1170	66	61			PROPN
iajs-1170	66	62	vy	vy	PROPN
iajs-1170	66	63	and	and	CCONJ
iajs-1170	66	64	{	{	PUNCT
iajs-1170	66	65	x	x	ADJ
iajs-1170	66	66	}	}	PUNCT
iajs-1170	66	67			ADJ
iajs-1170	66	68	vy	vy	NOUN
iajs-1170	66	69	and	and	CCONJ
iajs-1170	66	70	vy	vy	NOUN
iajs-1170	66	71	,	,	PUNCT
iajs-1170	66	72			X
iajs-1170	66	73	vy	vy	NOUN
iajs-1170	66	74	=	=	PUNCT
iajs-1170	66	75			ADJ
iajs-1170	66	76	.	.	PUNCT
iajs-1170	67	1	implies	imply	VERB
iajs-1170	67	2	,	,	PUNCT
iajs-1170	67	3	{	{	PUNCT
iajs-1170	67	4	x	x	ADJ
iajs-1170	67	5	}	}	PUNCT
iajs-1170	67	6			PROPN
iajs-1170	67	7			PROPN
iajs-1170	67	8	{	{	PUNCT
iajs-1170	67	9	vy	vy	NOUN
iajs-1170	67	10	:	:	PUNCT
iajs-1170	67	11	y	y	PROPN
iajs-1170	67	12			PROPN
iajs-1170	67	13	u	u	NOUN
iajs-1170	67	14	i	i	PROPN
iajs-1170	67	15	}	}	PUNCT
iajs-1170	67	16	and	and	CCONJ
iajs-1170	67	17	u	u	X
iajs-1170	67	18	i	i	PROPN
iajs-1170	67	19			PROPN
iajs-1170	67	20	{vy	{vy	PROPN
iajs-1170	67	21	:	:	PUNCT
iajs-1170	67	22	y	y	PROPN
iajs-1170	67	23			PROPN
iajs-1170	67	24	u	u	NOUN
iajs-1170	67	25	i	i	PROPN
iajs-1170	67	26	}	}	PUNCT
iajs-1170	67	27	.	.	PUNCT
iajs-1170	68	1	but	but	CCONJ
iajs-1170	68	2	{	{	PUNCT
iajs-1170	68	3	x	x	X
iajs-1170	68	4	}	}	PUNCT
iajs-1170	68	5	is	be	AUX
iajs-1170	68	6	compact	compact	ADJ
iajs-1170	68	7	set	set	NOUN
iajs-1170	68	8	,	,	PUNCT
iajs-1170	68	9	then	then	ADV
iajs-1170	68	10	there	there	PRON
iajs-1170	68	11	is	be	VERB
iajs-1170	68	12	a	a	DET
iajs-1170	68	13	finite	finite	NOUN
iajs-1170	68	14	subset	subset	NOUN
iajs-1170	68	15	of	of	ADP
iajs-1170	68	16	u	u	PROPN
iajs-1170	68	17	i	i	PROPN
iajs-1170	68	18	say	say	VERB
iajs-1170	68	19	{	{	PUNCT
iajs-1170	68	20	y1	y1	NOUN
iajs-1170	68	21	,	,	PUNCT
iajs-1170	68	22	y2	y2	PROPN
iajs-1170	68	23	,	,	PUNCT
iajs-1170	68	24	…	…	PUNCT
iajs-1170	68	25	,	,	PUNCT
iajs-1170	68	26	yn	yn	INTJ
iajs-1170	68	27	}	}	PUNCT
iajs-1170	68	28	such	such	ADJ
iajs-1170	68	29	that	that	SCONJ
iajs-1170	68	30	{	{	PUNCT
iajs-1170	68	31	x	x	ADJ
iajs-1170	68	32	}	}	PUNCT
iajs-1170	68	33			PROPN
iajs-1170	68	34			PROPN
iajs-1170	68	35	{	{	PUNCT
iajs-1170	68	36	v	v	NUM
iajs-1170	68	37	jy	jy	PROPN
iajs-1170	68	38			PROPN
iajs-1170	68	39	:	:	PUNCT
iajs-1170	68	40	j	j	PROPN
iajs-1170	68	41	=	=	SYM
iajs-1170	68	42	1,2,	1,2,	NUM
iajs-1170	68	43	…	…	PUNCT
iajs-1170	68	44	,n	,n	NOUN
iajs-1170	68	45	}	}	PUNCT
iajs-1170	68	46	.	.	PUNCT
iajs-1170	69	1	now	now	ADV
iajs-1170	69	2	,	,	PUNCT
iajs-1170	69	3	let	let	VERB
iajs-1170	69	4	v	v	NOUN
iajs-1170	69	5	=	=	PUNCT
iajs-1170	70	1			X
iajs-1170	70	2	{	{	PUNCT
iajs-1170	70	3	v	v	NUM
iajs-1170	70	4	jy	jy	PROPN
iajs-1170	70	5			PROPN
iajs-1170	70	6	:	:	PUNCT
iajs-1170	70	7	j	j	PROPN
iajs-1170	70	8	=	=	SYM
iajs-1170	70	9	1,2,	1,2,	NUM
iajs-1170	70	10	…	…	PUNCT
iajs-1170	70	11	,n	,n	NOUN
iajs-1170	70	12	}	}	PUNCT
iajs-1170	70	13	,	,	PUNCT
iajs-1170	70	14	then	then	ADV
iajs-1170	70	15	v	v	NOUN
iajs-1170	70	16	is	be	AUX
iajs-1170	70	17	an	an	DET
iajs-1170	70	18	open	open	ADJ
iajs-1170	70	19	set	set	NOUN
iajs-1170	70	20	contains	contain	VERB
iajs-1170	70	21	x.	x.	NOUN
iajs-1170	70	22	on	on	ADP
iajs-1170	70	23	the	the	DET
iajs-1170	70	24	other	other	ADJ
iajs-1170	70	25	side	side	NOUN
iajs-1170	70	26	,	,	PUNCT
iajs-1170	70	27	let	let	VERB
iajs-1170	70	28	v	v	NOUN
iajs-1170	70	29	=	=	SYM
iajs-1170	70	30			NOUN
iajs-1170	70	31	{	{	PUNCT
iajs-1170	70	32	vy	vy	NOUN
iajs-1170	70	33	:	:	PUNCT
iajs-1170	70	34	y	y	PROPN
iajs-1170	70	35			PROPN
iajs-1170	70	36	u	u	X
iajs-1170	70	37	i	i	PROPN
iajs-1170	70	38	}	}	PUNCT
iajs-1170	70	39	implies	imply	VERB
iajs-1170	70	40	v	v	NOUN
iajs-1170	70	41	is	be	AUX
iajs-1170	70	42	an	an	DET
iajs-1170	70	43	open	open	ADJ
iajs-1170	70	44	set	set	NOUN
iajs-1170	70	45	contains	contain	VERB
iajs-1170	70	46	u	u	NOUN
iajs-1170	70	47	i	i	PROPN
iajs-1170	70	48	.	.	PUNCT
iajs-1170	71	1	so	so	ADV
iajs-1170	71	2	v	v	ADP
iajs-1170	71	3			X
iajs-1170	71	4	v	v	NOUN
iajs-1170	71	5	=	=	PUNCT
iajs-1170	71	6			NOUN
iajs-1170	71	7	.	.	PUNCT
iajs-1170	72	1	in	in	ADP
iajs-1170	72	2	view	view	NOUN
iajs-1170	72	3	of	of	ADP
iajs-1170	72	4	,	,	PUNCT
iajs-1170	72	5	every	every	DET
iajs-1170	72	6	open	open	ADJ
iajs-1170	72	7	set	set	NOUN
iajs-1170	72	8	is	be	AUX
iajs-1170	72	9	-open	-open	PROPN
iajs-1170	72	10	,	,	PUNCT
iajs-1170	72	11	hence	hence	ADV
iajs-1170	72	12	,	,	PUNCT
iajs-1170	72	13	x	x	PROPN
iajs-1170	72	14			X
iajs-1170	72	15	-derived	-derive	VERB
iajs-1170	72	16	u	u	NOUN
iajs-1170	72	17	i	i	NOUN
iajs-1170	72	18	which	which	PRON
iajs-1170	72	19	is	be	AUX
iajs-1170	72	20	a	a	DET
iajs-1170	72	21	contradiction	contradiction	NOUN
iajs-1170	72	22	.	.	PUNCT
iajs-1170	73	1	thereupon	thereupon	ADV
iajs-1170	73	2	,	,	PUNCT
iajs-1170	73	3	x	x	PRON
iajs-1170	73	4	is	be	AUX
iajs-1170	73	5	-compact	-compact	ADJ
iajs-1170	73	6	space	space	NOUN
iajs-1170	73	7	.	.	PUNCT
iajs-1170	74	1	2.7	2.7	NUM
iajs-1170	74	2	corollary	corollary	ADJ
iajs-1170	74	3	a	a	DET
iajs-1170	74	4	t3--c	t3--c	PROPN
iajs-1170	74	5	-	-	PUNCT
iajs-1170	74	6	compact	compact	ADJ
iajs-1170	74	7	space	space	NOUN
iajs-1170	74	8	is	be	AUX
iajs-1170	74	9	compact	compact	ADJ
iajs-1170	74	10	.	.	PUNCT
iajs-1170	75	1	proof	proof	NOUN
iajs-1170	75	2	:	:	PUNCT
iajs-1170	75	3	in	in	ADP
iajs-1170	75	4	view	view	NOUN
iajs-1170	75	5	of	of	ADP
iajs-1170	75	6	,	,	PUNCT
iajs-1170	75	7	every	every	DET
iajs-1170	75	8	-compact	-compact	ADJ
iajs-1170	75	9	space	space	NOUN
iajs-1170	75	10	is	be	AUX
iajs-1170	75	11	compact	compact	ADJ
iajs-1170	75	12	,	,	PUNCT
iajs-1170	75	13	then	then	ADV
iajs-1170	75	14	proposition	proposition	NOUN
iajs-1170	75	15	(	(	PUNCT
iajs-1170	75	16	2.6	2.6	NUM
iajs-1170	75	17	)	)	PUNCT
iajs-1170	75	18	is	be	AUX
iajs-1170	75	19	applicable	applicable	ADJ
iajs-1170	75	20	.	.	PUNCT
iajs-1170	76	1			NUM
iajs-1170	76	2	2.8	2.8	NUM
iajs-1170	76	3	remark	remark	NOUN
iajs-1170	76	4	in	in	ADP
iajs-1170	76	5	general	general	ADJ
iajs-1170	76	6	,	,	PUNCT
iajs-1170	76	7	-c	-c	ADV
iajs-1170	76	8	-	-	PUNCT
iajs-1170	76	9	compact	compact	ADJ
iajs-1170	76	10	space	space	NOUN
iajs-1170	76	11	need	need	AUX
iajs-1170	76	12	not	not	PART
iajs-1170	76	13	be	be	AUX
iajs-1170	76	14	compact	compact	ADJ
iajs-1170	76	15	as	as	SCONJ
iajs-1170	76	16	the	the	DET
iajs-1170	76	17	following	follow	VERB
iajs-1170	76	18	example	example	NOUN
iajs-1170	76	19	shows	show	VERB
iajs-1170	76	20	:	:	PUNCT
iajs-1170	76	21	let	let	VERB
iajs-1170	76	22	n	n	PRON
iajs-1170	76	23	be	be	AUX
iajs-1170	76	24	the	the	DET
iajs-1170	76	25	set	set	NOUN
iajs-1170	76	26	of	of	ADP
iajs-1170	76	27	all	all	DET
iajs-1170	76	28	natural	natural	ADJ
iajs-1170	76	29	numbers	number	NOUN
iajs-1170	76	30	and	and	CCONJ
iajs-1170	76	31	let	let	VERB
iajs-1170	76	32			NOUN
iajs-1170	76	33	=	=	SYM
iajs-1170	76	34	{	{	PUNCT
iajs-1170	76	35	un	un	PROPN
iajs-1170	76	36	un	un	PROPN
iajs-1170	76	37	=	=	PUNCT
iajs-1170	76	38	{	{	PUNCT
iajs-1170	76	39	1,2,	1,2,	NUM
iajs-1170	76	40	…	…	PUNCT
iajs-1170	76	41	,n	,n	NOUN
iajs-1170	76	42	}	}	PUNCT
iajs-1170	76	43	;	;	PUNCT
iajs-1170	76	44	n	n	CCONJ
iajs-1170	76	45			NOUN
iajs-1170	76	46	n	n	CCONJ
iajs-1170	76	47	}	}	PUNCT
iajs-1170	76	48			NOUN
iajs-1170	76	49	{	{	PUNCT
iajs-1170	76	50			PROPN
iajs-1170	76	51	,	,	PUNCT
iajs-1170	76	52	n	n	CCONJ
iajs-1170	76	53	}	}	PUNCT
iajs-1170	76	54	.	.	PUNCT
iajs-1170	77	1	then	then	ADV
iajs-1170	77	2	(	(	PUNCT
iajs-1170	77	3	n,	n,	X
iajs-1170	77	4	)	)	PUNCT
iajs-1170	77	5	is	be	AUX
iajs-1170	77	6	-c	-c	ADV
iajs-1170	77	7	-	-	PUNCT
iajs-1170	77	8	compact	compact	ADJ
iajs-1170	77	9	space	space	NOUN
iajs-1170	77	10	,	,	PUNCT
iajs-1170	77	11	since	since	SCONJ
iajs-1170	77	12	n	n	ADV
iajs-1170	77	13	is	be	AUX
iajs-1170	77	14	the	the	DET
iajs-1170	77	15	unique	unique	ADJ
iajs-1170	77	16	-closed	-closed	ADJ
iajs-1170	77	17	set	set	NOUN
iajs-1170	77	18	contains	contain	VERB
iajs-1170	77	19	1	1	NUM
iajs-1170	77	20	.	.	PUNCT
iajs-1170	78	1	but	but	CCONJ
iajs-1170	78	2	n	n	PRON
iajs-1170	78	3	is	be	AUX
iajs-1170	78	4	not	not	PART
iajs-1170	78	5	compact	compact	ADJ
iajs-1170	78	6	space	space	NOUN
iajs-1170	78	7	.	.	PUNCT
iajs-1170	79	1	in	in	ADP
iajs-1170	79	2	corollary	corollary	ADJ
iajs-1170	79	3	(	(	PUNCT
iajs-1170	79	4	2.4	2.4	NUM
iajs-1170	79	5	)	)	PUNCT
iajs-1170	79	6	,	,	PUNCT
iajs-1170	79	7	we	we	PRON
iajs-1170	79	8	discussed	discuss	VERB
iajs-1170	79	9	the	the	DET
iajs-1170	79	10	relationship	relationship	NOUN
iajs-1170	79	11	between	between	ADP
iajs-1170	79	12	,	,	PUNCT
iajs-1170	79	13	c	c	NOUN
iajs-1170	79	14	-	-	ADJ
iajs-1170	79	15	compact	compact	ADJ
iajs-1170	79	16	and	and	CCONJ
iajs-1170	79	17	-c	-c	ADV
iajs-1170	79	18	-	-	PUNCT
iajs-1170	79	19	compact	compact	ADJ
iajs-1170	79	20	space	space	NOUN
iajs-1170	79	21	,	,	PUNCT
iajs-1170	79	22	in	in	ADP
iajs-1170	79	23	one	one	NUM
iajs-1170	79	24	side	side	NOUN
iajs-1170	79	25	,	,	PUNCT
iajs-1170	79	26	the	the	DET
iajs-1170	79	27	other	other	ADJ
iajs-1170	79	28	side	side	NOUN
iajs-1170	79	29	of	of	ADP
iajs-1170	79	30	this	this	DET
iajs-1170	79	31	relation	relation	NOUN
iajs-1170	79	32	we	we	PRON
iajs-1170	79	33	shall	shall	AUX
iajs-1170	79	34	descry	descry	VERB
iajs-1170	79	35	in	in	ADP
iajs-1170	79	36	the	the	DET
iajs-1170	79	37	following	follow	VERB
iajs-1170	79	38	proposition	proposition	NOUN
iajs-1170	79	39	.	.	PUNCT
iajs-1170	80	1	2.9	2.9	NUM
iajs-1170	80	2	proposition	proposition	VERB
iajs-1170	80	3	an	an	DET
iajs-1170	80	4	-c	-c	ADV
iajs-1170	80	5	-	-	PUNCT
iajs-1170	80	6	compact	compact	ADJ
iajs-1170	80	7	space	space	NOUN
iajs-1170	80	8	is	be	AUX
iajs-1170	80	9	c	c	NOUN
iajs-1170	80	10	-	-	ADJ
iajs-1170	80	11	compact	compact	ADJ
iajs-1170	80	12	.	.	PUNCT
iajs-1170	81	1	proof	proof	NOUN
iajs-1170	81	2	:	:	PUNCT
iajs-1170	81	3	ibn	ibn	PROPN
iajs-1170	81	4	alhaitham	alhaitham	NOUN
iajs-1170	82	1	j.	j.	PROPN
iajs-1170	83	1	fo	fo	ADP
iajs-1170	83	2	r	r	NOUN
iajs-1170	83	3	pure	pure	ADJ
iajs-1170	83	4	&	&	CCONJ
iajs-1170	83	5	appl	appl	PROPN
iajs-1170	83	6	.	.	PUNCT
iajs-1170	84	1	sc	sc	PROPN
iajs-1170	85	1	i	i	PRON
iajs-1170	85	2	vo	vo	INTJ
iajs-1170	85	3	l.22	l.22	X
iajs-1170	85	4	(	(	PUNCT
iajs-1170	85	5	3	3	NUM
iajs-1170	85	6	)	)	PUNCT
iajs-1170	85	7	2009	2009	NUM
iajs-1170	85	8	let	let	VERB
iajs-1170	85	9	x	x	PRON
iajs-1170	85	10	be	be	AUX
iajs-1170	85	11	an	an	DET
iajs-1170	85	12	-c	-c	ADV
iajs-1170	85	13	-	-	PUNCT
iajs-1170	85	14	compact	compact	ADJ
iajs-1170	85	15	space	space	NOUN
iajs-1170	85	16	.	.	PUNCT
iajs-1170	86	1	if	if	SCONJ
iajs-1170	86	2	it	it	PRON
iajs-1170	86	3	is	be	AUX
iajs-1170	86	4	not	not	PART
iajs-1170	86	5	c	c	NOUN
iajs-1170	86	6	-	-	ADJ
iajs-1170	86	7	compact	compact	ADJ
iajs-1170	86	8	space	space	NOUN
iajs-1170	86	9	,	,	PUNCT
iajs-1170	86	10	then	then	ADV
iajs-1170	86	11	there	there	PRON
iajs-1170	86	12	is	be	VERB
iajs-1170	86	13	a	a	DET
iajs-1170	86	14	closed	closed	ADJ
iajs-1170	86	15	set	set	NOUN
iajs-1170	86	16	a	a	DET
iajs-1170	86	17			PROPN
iajs-1170	86	18	x	x	NOUN
iajs-1170	86	19	,	,	PUNCT
iajs-1170	86	20	and	and	CCONJ
iajs-1170	86	21	a	a	DET
iajs-1170	86	22	family	family	NOUN
iajs-1170	86	23	of	of	ADP
iajs-1170	86	24	open	open	ADJ
iajs-1170	86	25	sets	set	NOUN
iajs-1170	86	26	in	in	ADP
iajs-1170	86	27	x	x	PART
iajs-1170	86	28	say	say	VERB
iajs-1170	86	29	{	{	PUNCT
iajs-1170	86	30	u:	u:	NOUN
iajs-1170	86	31	}	}	PUNCT
iajs-1170	86	32	covers	cover	VERB
iajs-1170	86	33	a.	a.	NOUN
iajs-1170	86	34	but	but	CCONJ
iajs-1170	86	35	for	for	ADP
iajs-1170	86	36	each	each	DET
iajs-1170	86	37	n	n	ADJ
iajs-1170	86	38			NOUN
iajs-1170	86	39	n	n	CCONJ
iajs-1170	86	40	,	,	PUNCT
iajs-1170	86	41	implies	imply	VERB
iajs-1170	86	42	a	a	DET
iajs-1170	86	43			PROPN
iajs-1170	86	44			NOUN
iajs-1170	86	45	{	{	PUNCT
iajs-1170	86	46	cl	cl	NOUN
iajs-1170	86	47	u	u	NOUN
iajs-1170	86	48	i	i	PROPN
iajs-1170	86	49	,	,	PUNCT
iajs-1170	86	50	i	i	PRON
iajs-1170	86	51	=	=	NOUN
iajs-1170	86	52	1,2,	1,2,	NUM
iajs-1170	86	53	…	…	PUNCT
iajs-1170	86	54	,n	,n	NOUN
iajs-1170	86	55	}	}	PUNCT
iajs-1170	86	56	.	.	PUNCT
iajs-1170	87	1	on	on	ADP
iajs-1170	87	2	the	the	DET
iajs-1170	87	3	other	other	ADJ
iajs-1170	87	4	side	side	NOUN
iajs-1170	87	5	,	,	PUNCT
iajs-1170	87	6	clearly	clearly	ADV
iajs-1170	87	7	a	a	DET
iajs-1170	87	8	is	be	AUX
iajs-1170	87	9	-closed	-close	VERB
iajs-1170	87	10	subset	subset	NOUN
iajs-1170	87	11	of	of	ADP
iajs-1170	87	12	an	an	DET
iajs-1170	87	13	-c	-c	ADV
iajs-1170	87	14	-	-	PUNCT
iajs-1170	87	15	compact	compact	ADJ
iajs-1170	87	16	space	space	NOUN
iajs-1170	87	17	x	x	PUNCT
iajs-1170	87	18	and	and	CCONJ
iajs-1170	87	19	{	{	PUNCT
iajs-1170	87	20	u:	u:	X
iajs-1170	87	21	}	}	PUNCT
iajs-1170	87	22	is	be	AUX
iajs-1170	87	23	an	an	DET
iajs-1170	87	24	-open	-open	PROPN
iajs-1170	87	25	cover	cover	NOUN
iajs-1170	87	26	for	for	ADP
iajs-1170	87	27	a	a	DET
iajs-1170	87	28	in	in	ADP
iajs-1170	87	29	x	x	NOUN
iajs-1170	87	30	,	,	PUNCT
iajs-1170	87	31	then	then	ADV
iajs-1170	87	32	there	there	PRON
iajs-1170	87	33	exists	exist	VERB
iajs-1170	87	34	n	n	PRON
iajs-1170	87	35			NOUN
iajs-1170	87	36	n	n	CCONJ
iajs-1170	87	37	such	such	ADJ
iajs-1170	87	38	that	that	SCONJ
iajs-1170	87	39	a	a	DET
iajs-1170	87	40			PROPN
iajs-1170	87	41	{-cl	{-cl	PROPN
iajs-1170	87	42	u	u	NOUN
iajs-1170	87	43	i	i	NOUN
iajs-1170	87	44	:	:	PUNCT
iajs-1170	87	45	i	i	PRON
iajs-1170	87	46	=	=	NOUN
iajs-1170	87	47	1,2,	1,2,	NUM
iajs-1170	87	48	…	…	PUNCT
iajs-1170	87	49	,n	,n	NOUN
iajs-1170	87	50	}	}	PUNCT
iajs-1170	87	51	.	.	PUNCT
iajs-1170	88	1	this	this	PRON
iajs-1170	88	2	means	mean	VERB
iajs-1170	88	3	,	,	PUNCT
iajs-1170	88	4	there	there	PRON
iajs-1170	88	5	exists	exist	VERB
iajs-1170	88	6	x	x	PUNCT
iajs-1170	88	7			NOUN
iajs-1170	88	8	a	a	DET
iajs-1170	88	9	such	such	ADJ
iajs-1170	88	10	that	that	SCONJ
iajs-1170	88	11	x	x	SYM
iajs-1170	88	12			NOUN
iajs-1170	88	13	-cl	-cl	PROPN
iajs-1170	88	14	u	u	SYM
iajs-1170	88	15	i	i	PROPN
iajs-1170	88	16	and	and	CCONJ
iajs-1170	88	17	x	x	NOUN
iajs-1170	88	18			NOUN
iajs-1170	88	19	cl	cl	NOUN
iajs-1170	88	20	u	u	NOUN
iajs-1170	88	21	i	i	PROPN
iajs-1170	88	22	for	for	ADP
iajs-1170	88	23	some	some	DET
iajs-1170	88	24	i	i	NOUN
iajs-1170	88	25	=	=	SYM
iajs-1170	88	26	1,2,	1,2,	NUM
iajs-1170	88	27	…	…	PUNCT
iajs-1170	88	28	,n	,n	NOUN
iajs-1170	88	29	.	.	PUNCT
iajs-1170	89	1	since	since	SCONJ
iajs-1170	89	2	x	x	PRON
iajs-1170	89	3			NUM
iajs-1170	89	4	cl	cl	NOUN
iajs-1170	89	5	u	u	NOUN
iajs-1170	89	6	i	i	PROPN
iajs-1170	89	7	,	,	PUNCT
iajs-1170	89	8	implies	imply	VERB
iajs-1170	89	9	xu	xu	PROPN
iajs-1170	89	10	i	i	PROPN
iajs-1170	89	11	and	and	CCONJ
iajs-1170	89	12	x	x	NOUN
iajs-1170	89	13			VERB
iajs-1170	89	14	derived	derive	VERB
iajs-1170	89	15	u	u	NOUN
iajs-1170	89	16	i	i	PROPN
iajs-1170	89	17	.	.	PUNCT
iajs-1170	90	1	but	but	CCONJ
iajs-1170	90	2	x	x	X
iajs-1170	90	3			NOUN
iajs-1170	90	4	-cl	-cl	PROPN
iajs-1170	90	5	u	u	SYM
iajs-1170	90	6	i	i	PROPN
iajs-1170	90	7	,	,	PUNCT
iajs-1170	90	8	then	then	ADV
iajs-1170	90	9	x	x	SYM
iajs-1170	90	10			PROPN
iajs-1170	90	11	-derived	-derive	VERB
iajs-1170	90	12	u	u	NOUN
iajs-1170	90	13	i	i	PROPN
iajs-1170	90	14	.	.	PUNCT
iajs-1170	91	1	since	since	SCONJ
iajs-1170	91	2	x	x	PRON
iajs-1170	91	3			NUM
iajs-1170	91	4	derived	derive	VERB
iajs-1170	91	5	u	u	NOUN
iajs-1170	91	6	i	i	PROPN
iajs-1170	91	7	then	then	ADV
iajs-1170	91	8	there	there	PRON
iajs-1170	91	9	exists	exist	VERB
iajs-1170	91	10	an	an	DET
iajs-1170	91	11	open	open	ADJ
iajs-1170	91	12	set	set	NOUN
iajs-1170	91	13	say	say	VERB
iajs-1170	91	14	v	v	ADP
iajs-1170	91	15	such	such	ADJ
iajs-1170	91	16	that	that	SCONJ
iajs-1170	91	17	x	x	X
iajs-1170	91	18	v	v	X
iajs-1170	91	19	and	and	CCONJ
iajs-1170	91	20	v	v	ADP
iajs-1170	91	21	\{x}u	\{x}u	NOUN
iajs-1170	91	22	i	i	NOUN
iajs-1170	91	23	=	=	PUNCT
iajs-1170	91	24			X
iajs-1170	91	25	.	.	PUNCT
iajs-1170	92	1	in	in	ADP
iajs-1170	92	2	view	view	NOUN
iajs-1170	92	3	of	of	ADP
iajs-1170	92	4	,	,	PUNCT
iajs-1170	92	5	every	every	DET
iajs-1170	92	6	open	open	ADJ
iajs-1170	92	7	set	set	NOUN
iajs-1170	92	8	is	be	AUX
iajs-1170	92	9	-open	-open	PROPN
iajs-1170	92	10	then	then	ADV
iajs-1170	92	11	v	v	NOUN
iajs-1170	92	12	is	be	AUX
iajs-1170	92	13	-open	-open	PROPN
iajs-1170	92	14	set	set	NOUN
iajs-1170	92	15	implies	imply	VERB
iajs-1170	92	16	x	x	PUNCT
iajs-1170	92	17			PUNCT
iajs-1170	92	18	-derived	-derive	VERB
iajs-1170	92	19	u	u	NOUN
iajs-1170	92	20	i	i	NOUN
iajs-1170	92	21	which	which	PRON
iajs-1170	92	22	is	be	AUX
iajs-1170	92	23	a	a	DET
iajs-1170	92	24	contradiction	contradiction	NOUN
iajs-1170	92	25	.	.	PUNCT
iajs-1170	93	1	therefore	therefore	ADV
iajs-1170	93	2	,	,	PUNCT
iajs-1170	93	3	x	x	X
iajs-1170	93	4	is	be	AUX
iajs-1170	93	5	c	c	ADJ
iajs-1170	93	6	-	-	ADJ
iajs-1170	93	7	compact	compact	ADJ
iajs-1170	93	8	space	space	NOUN
iajs-1170	93	9	whenever	whenever	SCONJ
iajs-1170	93	10	it	it	PRON
iajs-1170	93	11	is	be	AUX
iajs-1170	93	12	-c	-c	ADV
iajs-1170	93	13	-	-	PUNCT
iajs-1170	93	14	compact	compact	ADJ
iajs-1170	93	15	.	.	PUNCT
iajs-1170	94	1	the	the	DET
iajs-1170	94	2	following	follow	VERB
iajs-1170	94	3	diagram	diagram	NOUN
iajs-1170	94	4	shows	show	VERB
iajs-1170	94	5	the	the	DET
iajs-1170	94	6	relationships	relationship	NOUN
iajs-1170	94	7	among	among	ADP
iajs-1170	94	8	the	the	DET
iajs-1170	94	9	different	different	ADJ
iajs-1170	94	10	types	type	NOUN
iajs-1170	94	11	of	of	ADP
iajs-1170	94	12	compactness	compactness	NOUN
iajs-1170	94	13	that	that	PRON
iajs-1170	94	14	we	we	PRON
iajs-1170	94	15	studied	study	VERB
iajs-1170	94	16	in	in	ADP
iajs-1170	94	17	this	this	DET
iajs-1170	94	18	paper	paper	NOUN
iajs-1170	94	19	.	.	PUNCT
iajs-1170	95	1	3	3	X
iajs-1170	95	2	.	.	X
iajs-1170	95	3	certain	certain	ADJ
iajs-1170	95	4	fundamental	fundamental	ADJ
iajs-1170	95	5	properties	property	NOUN
iajs-1170	95	6	of	of	ADP
iajs-1170	95	7			NOUN
iajs-1170	95	8	-c	-c	ADJ
iajs-1170	95	9	-	-	ADJ
iajs-1170	95	10	compact	compact	ADJ
iajs-1170	95	11	spaces	space	NOUN
iajs-1170	95	12	in	in	ADP
iajs-1170	95	13	this	this	DET
iajs-1170	95	14	section	section	NOUN
iajs-1170	95	15	,	,	PUNCT
iajs-1170	95	16	we	we	PRON
iajs-1170	95	17	shall	shall	AUX
iajs-1170	95	18	discuss	discuss	VERB
iajs-1170	95	19	some	some	DET
iajs-1170	95	20	properties	property	NOUN
iajs-1170	95	21	of	of	ADP
iajs-1170	95	22	the	the	DET
iajs-1170	95	23	new	new	ADJ
iajs-1170	95	24	kind	kind	NOUN
iajs-1170	95	25	of	of	ADP
iajs-1170	95	26	compactness	compactness	NOUN
iajs-1170	95	27	which	which	PRON
iajs-1170	95	28	we	we	PRON
iajs-1170	95	29	introduced	introduce	VERB
iajs-1170	95	30	in	in	ADP
iajs-1170	95	31	this	this	DET
iajs-1170	95	32	paper	paper	NOUN
iajs-1170	95	33	.	.	PUNCT
iajs-1170	96	1	+	+	CCONJ
iajs-1170	96	2	c	c	X
iajs-1170	96	3	-	-	ADJ
iajs-1170	96	4	compact	compact	ADJ
iajs-1170	96	5	-ccompact	-ccompact	PROPN
iajs-1170	96	6	+	+	CCONJ
iajs-1170	96	7	+	+	NUM
iajs-1170	96	8	t3	t3	PROPN
iajs-1170	96	9	compact	compact	NOUN
iajs-1170	96	10	every	every	DET
iajs-1170	96	11	nowhere	nowhere	ADV
iajs-1170	96	12	dense	dense	ADJ
iajs-1170	96	13	set	set	NOUN
iajs-1170	96	14	is	be	AUX
iajs-1170	96	15	finite	finite	ADJ
iajs-1170	96	16	t3	t3	PROPN
iajs-1170	96	17	compact	compact	PROPN
iajs-1170	96	18	ibn	ibn	PROPN
iajs-1170	96	19	alhaitham	alhaitham	NOUN
iajs-1170	96	20	j.	j.	PROPN
iajs-1170	97	1	fo	fo	ADP
iajs-1170	97	2	r	r	NOUN
iajs-1170	97	3	pure	pure	ADJ
iajs-1170	97	4	&	&	CCONJ
iajs-1170	97	5	appl	appl	PROPN
iajs-1170	97	6	.	.	PUNCT
iajs-1170	98	1	sc	sc	PROPN
iajs-1170	99	1	i	i	PRON
iajs-1170	99	2	vo	vo	INTJ
iajs-1170	99	3	l.22	l.22	X
iajs-1170	99	4	(	(	PUNCT
iajs-1170	99	5	3	3	NUM
iajs-1170	99	6	)	)	PUNCT
iajs-1170	99	7	2009	2009	NUM
iajs-1170	99	8	in	in	ADP
iajs-1170	99	9	remark	remark	NOUN
iajs-1170	99	10	(	(	PUNCT
iajs-1170	99	11	3.1	3.1	NUM
iajs-1170	99	12	)	)	PUNCT
iajs-1170	99	13	and	and	CCONJ
iajs-1170	99	14	proposition	proposition	NOUN
iajs-1170	99	15	(	(	PUNCT
iajs-1170	99	16	3.3	3.3	NUM
iajs-1170	99	17	)	)	PUNCT
iajs-1170	99	18	we	we	PRON
iajs-1170	99	19	shall	shall	AUX
iajs-1170	99	20	discuss	discuss	VERB
iajs-1170	99	21	the	the	DET
iajs-1170	99	22	heredity	heredity	NOUN
iajs-1170	99	23	property	property	NOUN
iajs-1170	99	24	in	in	ADP
iajs-1170	99	25	-c	-c	ADV
iajs-1170	99	26	-	-	PUNCT
iajs-1170	99	27	compact	compact	ADJ
iajs-1170	99	28	spaces	space	NOUN
iajs-1170	99	29	.	.	PUNCT
iajs-1170	100	1	3.1	3.1	NUM
iajs-1170	100	2	remark	remark	NOUN
iajs-1170	100	3	-c	-c	NOUN
iajs-1170	100	4	-	-	PUNCT
iajs-1170	100	5	compactness	compactness	NOUN
iajs-1170	100	6	is	be	AUX
iajs-1170	100	7	not	not	PART
iajs-1170	100	8	a	a	DET
iajs-1170	100	9	hereditary	hereditary	ADJ
iajs-1170	100	10	property	property	NOUN
iajs-1170	100	11	.	.	PUNCT
iajs-1170	101	1	for	for	ADP
iajs-1170	101	2	example	example	NOUN
iajs-1170	101	3	:	:	PUNCT
iajs-1170	101	4	let	let	VERB
iajs-1170	101	5	x	x	SYM
iajs-1170	101	6	=	=	SYM
iajs-1170	101	7	n	n	X
iajs-1170	101	8	{	{	PUNCT
iajs-1170	101	9	-1,0	-1,0	NOUN
iajs-1170	101	10	}	}	PUNCT
iajs-1170	101	11	and	and	CCONJ
iajs-1170	101	12			NOUN
iajs-1170	101	13	=	=	SYM
iajs-1170	101	14	p(n	p(n	PROPN
iajs-1170	101	15	)	)	PUNCT
iajs-1170	101	16			NOUN
iajs-1170	101	17	{	{	PUNCT
iajs-1170	101	18	hx-1,0hx	hx-1,0hx	NOUN
iajs-1170	101	19	–	–	PUNCT
iajs-1170	101	20	h	h	NOUN
iajs-1170	101	21	is	be	AUX
iajs-1170	101	22	finite	finite	ADJ
iajs-1170	101	23	}	}	PUNCT
iajs-1170	101	24	.	.	PUNCT
iajs-1170	102	1	clearly	clearly	ADV
iajs-1170	102	2	:	:	PUNCT
iajs-1170	102	3	(	(	PUNCT
iajs-1170	102	4	x,	x,	X
iajs-1170	102	5	)	)	PUNCT
iajs-1170	102	6	is	be	AUX
iajs-1170	102	7	-c	-c	ADV
iajs-1170	102	8	-	-	PUNCT
iajs-1170	102	9	compact	compact	ADJ
iajs-1170	102	10	space	space	NOUN
iajs-1170	102	11	,	,	PUNCT
iajs-1170	102	12	since	since	SCONJ
iajs-1170	102	13	the	the	DET
iajs-1170	102	14	complement	complement	NOUN
iajs-1170	102	15	of	of	ADP
iajs-1170	102	16	each	each	DET
iajs-1170	102	17	-closed	-close	VERB
iajs-1170	102	18	set	set	NOUN
iajs-1170	102	19	which	which	PRON
iajs-1170	102	20	contains	contain	VERB
iajs-1170	102	21	(	(	PUNCT
iajs-1170	102	22	-1	-1	INTJ
iajs-1170	102	23	)	)	PUNCT
iajs-1170	102	24	or	or	CCONJ
iajs-1170	102	25	(	(	PUNCT
iajs-1170	102	26	0	0	X
iajs-1170	102	27	)	)	PUNCT
iajs-1170	102	28	is	be	AUX
iajs-1170	102	29	finite	finite	NOUN
iajs-1170	102	30	set	set	NOUN
iajs-1170	102	31	.	.	PUNCT
iajs-1170	103	1	now	now	ADV
iajs-1170	103	2	,	,	PUNCT
iajs-1170	103	3	take	take	VERB
iajs-1170	103	4	n	n	PRON
iajs-1170	103	5	as	as	ADP
iajs-1170	103	6	a	a	DET
iajs-1170	103	7	subspace	subspace	NOUN
iajs-1170	103	8	of	of	ADP
iajs-1170	103	9	(	(	PUNCT
iajs-1170	103	10	x,	x,	PROPN
iajs-1170	103	11	)	)	PUNCT
iajs-1170	103	12	.	.	PUNCT
iajs-1170	104	1	it	it	PRON
iajs-1170	104	2	is	be	AUX
iajs-1170	104	3	clear	clear	ADJ
iajs-1170	104	4	that	that	SCONJ
iajs-1170	104	5	the	the	DET
iajs-1170	104	6	induced	induced	ADJ
iajs-1170	104	7	topology	topology	NOUN
iajs-1170	104	8	on	on	ADP
iajs-1170	104	9	n	n	PRON
iajs-1170	104	10	is	be	AUX
iajs-1170	104	11	the	the	DET
iajs-1170	104	12	discrete	discrete	ADJ
iajs-1170	104	13	topology	topology	NOUN
iajs-1170	104	14	on	on	ADP
iajs-1170	104	15	n	n	PRON
iajs-1170	104	16	hence	hence	ADV
iajs-1170	104	17	,	,	PUNCT
iajs-1170	104	18	n	n	PRON
iajs-1170	104	19	is	be	AUX
iajs-1170	104	20	not	not	PART
iajs-1170	104	21	-c	-c	ADV
iajs-1170	104	22	-	-	PUNCT
iajs-1170	104	23	compact	compact	ADJ
iajs-1170	104	24	space	space	NOUN
iajs-1170	104	25	.	.	PUNCT
iajs-1170	105	1	the	the	DET
iajs-1170	105	2	above	above	ADJ
iajs-1170	105	3	example	example	NOUN
iajs-1170	105	4	shows	show	VERB
iajs-1170	105	5	that	that	SCONJ
iajs-1170	105	6	if	if	SCONJ
iajs-1170	105	7	y	y	PROPN
iajs-1170	105	8	is	be	AUX
iajs-1170	105	9	an	an	DET
iajs-1170	105	10	open	open	ADJ
iajs-1170	105	11	subspace	subspace	NOUN
iajs-1170	105	12	of	of	ADP
iajs-1170	105	13	an	an	DET
iajs-1170	105	14	-c	-c	ADV
iajs-1170	105	15	-	-	PUNCT
iajs-1170	105	16	compact	compact	ADJ
iajs-1170	105	17	space	space	NOUN
iajs-1170	105	18	(	(	PUNCT
iajs-1170	105	19	x,	x,	PROPN
iajs-1170	105	20	)	)	PUNCT
iajs-1170	105	21	,	,	PUNCT
iajs-1170	105	22	then	then	ADV
iajs-1170	105	23	y	y	PROPN
iajs-1170	105	24	need	need	AUX
iajs-1170	105	25	not	not	PART
iajs-1170	105	26	be	be	AUX
iajs-1170	105	27	-c	-c	ADV
iajs-1170	105	28	-	-	PUNCT
iajs-1170	105	29	compact	compact	ADJ
iajs-1170	105	30	.	.	PUNCT
iajs-1170	106	1	3.2	3.2	NUM
iajs-1170	106	2	remark	remark	NOUN
iajs-1170	106	3	[	[	X
iajs-1170	106	4	4	4	NUM
iajs-1170	106	5	]	]	PUNCT
iajs-1170	106	6	,	,	PUNCT
iajs-1170	106	7	[	[	X
iajs-1170	106	8	6	6	NUM
iajs-1170	106	9	]	]	X
iajs-1170	106	10	i.	i.	NOUN
iajs-1170	106	11	if	if	SCONJ
iajs-1170	106	12	y	y	PROPN
iajs-1170	106	13	is	be	AUX
iajs-1170	106	14	an	an	DET
iajs-1170	106	15	open	open	ADJ
iajs-1170	106	16	subset	subset	NOUN
iajs-1170	106	17	of	of	ADP
iajs-1170	106	18	a	a	DET
iajs-1170	106	19	topological	topological	ADJ
iajs-1170	106	20	space	space	NOUN
iajs-1170	106	21	x	x	NOUN
iajs-1170	106	22	,	,	PUNCT
iajs-1170	106	23	then	then	ADV
iajs-1170	106	24	every	every	DET
iajs-1170	106	25	-open	-open	PROPN
iajs-1170	106	26	set	set	VERB
iajs-1170	106	27	in	in	ADP
iajs-1170	106	28	y	y	PROPN
iajs-1170	106	29	is	be	AUX
iajs-1170	106	30	an	an	DET
iajs-1170	106	31	-open	-open	PROPN
iajs-1170	106	32	set	set	VERB
iajs-1170	106	33	in	in	ADP
iajs-1170	106	34	x.	x.	PROPN
iajs-1170	106	35	ii	ii	PROPN
iajs-1170	106	36	.	.	PUNCT
iajs-1170	107	1	if	if	SCONJ
iajs-1170	107	2	y	y	PROPN
iajs-1170	107	3	is	be	AUX
iajs-1170	107	4	an	an	DET
iajs-1170	107	5	open	open	ADJ
iajs-1170	107	6	,	,	PUNCT
iajs-1170	107	7	-closed	-closed	ADJ
iajs-1170	107	8	subspace	subspace	NOUN
iajs-1170	107	9	of	of	ADP
iajs-1170	107	10	an	an	DET
iajs-1170	107	11	-compact	-compact	PROPN
iajs-1170	107	12	space	space	NOUN
iajs-1170	107	13	x	x	NOUN
iajs-1170	107	14	,	,	PUNCT
iajs-1170	107	15	then	then	ADV
iajs-1170	107	16	y	y	PROPN
iajs-1170	107	17	is	be	AUX
iajs-1170	107	18	-compact	-compact	PROPN
iajs-1170	107	19	.	.	PUNCT
iajs-1170	108	1	3.3	3.3	NUM
iajs-1170	108	2	proposition	proposition	NOUN
iajs-1170	108	3	if	if	SCONJ
iajs-1170	108	4	y	y	PROPN
iajs-1170	108	5	is	be	AUX
iajs-1170	108	6	an	an	DET
iajs-1170	108	7	open	open	ADJ
iajs-1170	108	8	and	and	CCONJ
iajs-1170	108	9	-closed	-closed	ADJ
iajs-1170	108	10	subspace	subspace	NOUN
iajs-1170	108	11	of	of	ADP
iajs-1170	108	12	an	an	DET
iajs-1170	108	13	-c	-c	ADV
iajs-1170	108	14	-	-	PUNCT
iajs-1170	108	15	compact	compact	ADJ
iajs-1170	108	16	space	space	NOUN
iajs-1170	108	17	x	x	NOUN
iajs-1170	108	18	,	,	PUNCT
iajs-1170	108	19	then	then	ADV
iajs-1170	108	20	y	y	PROPN
iajs-1170	108	21	is	be	AUX
iajs-1170	108	22	-ccompact	-ccompact	PROPN
iajs-1170	108	23	.	.	PUNCT
iajs-1170	109	1	the	the	DET
iajs-1170	109	2	proof	proof	NOUN
iajs-1170	109	3	of	of	ADP
iajs-1170	109	4	this	this	DET
iajs-1170	109	5	proposition	proposition	NOUN
iajs-1170	109	6	will	will	AUX
iajs-1170	109	7	take	take	VERB
iajs-1170	109	8	effect	effect	NOUN
iajs-1170	109	9	in	in	ADP
iajs-1170	109	10	virtue	virtue	NOUN
iajs-1170	109	11	of	of	ADP
iajs-1170	109	12	remark	remark	NOUN
iajs-1170	109	13	(	(	PUNCT
iajs-1170	109	14	3.2	3.2	NUM
iajs-1170	109	15	)	)	PUNCT
iajs-1170	109	16	.	.	PUNCT
iajs-1170	110	1			NUM
iajs-1170	110	2	3.4	3.4	NUM
iajs-1170	110	3	definition	definition	NOUN
iajs-1170	110	4	[	[	X
iajs-1170	110	5	8	8	NUM
iajs-1170	110	6	]	]	PUNCT
iajs-1170	110	7	,	,	PUNCT
iajs-1170	110	8	[	[	X
iajs-1170	110	9	9	9	NUM
iajs-1170	110	10	]	]	PUNCT
iajs-1170	110	11	a	a	DET
iajs-1170	110	12	function	function	NOUN
iajs-1170	110	13	f	f	PROPN
iajs-1170	110	14	:(	:(	PROPN
iajs-1170	110	15	x,	x,	PROPN
iajs-1170	110	16	)	)	PUNCT
iajs-1170	110	17			PROPN
iajs-1170	110	18	(	(	PUNCT
iajs-1170	110	19	y,	y,	PROPN
iajs-1170	110	20	)	)	PUNCT
iajs-1170	110	21	is	be	AUX
iajs-1170	110	22	said	say	VERB
iajs-1170	110	23	to	to	PART
iajs-1170	110	24	be	be	AUX
iajs-1170	110	25	"	"	PUNCT
iajs-1170	110	26	*-continuous	*-continuous	ADJ
iajs-1170	110	27	"	"	PUNCT
iajs-1170	110	28	,	,	PUNCT
iajs-1170	110	29	if	if	SCONJ
iajs-1170	110	30	and	and	CCONJ
iajs-1170	110	31	only	only	ADV
iajs-1170	110	32	if	if	SCONJ
iajs-1170	110	33	the	the	DET
iajs-1170	110	34	inverse	inverse	ADJ
iajs-1170	110	35	image	image	NOUN
iajs-1170	110	36	of	of	ADP
iajs-1170	110	37	every	every	DET
iajs-1170	110	38	-open	-open	PROPN
iajs-1170	110	39	subset	subset	NOUN
iajs-1170	110	40	of	of	ADP
iajs-1170	110	41	y	y	PROPN
iajs-1170	110	42	is	be	AUX
iajs-1170	110	43	an	an	DET
iajs-1170	110	44	-open	-open	PROPN
iajs-1170	110	45	subset	subset	NOUN
iajs-1170	110	46	of	of	ADP
iajs-1170	110	47	x.	x.	PROPN
iajs-1170	110	48	3.5	3.5	NUM
iajs-1170	110	49	remark	remark	NOUN
iajs-1170	110	50	[	[	X
iajs-1170	110	51	10	10	NUM
iajs-1170	110	52	]	]	X
iajs-1170	110	53	a	a	DET
iajs-1170	110	54	function	function	NOUN
iajs-1170	110	55	f	f	PROPN
iajs-1170	110	56	:(	:(	PROPN
iajs-1170	110	57	x,	x,	PROPN
iajs-1170	110	58	)	)	PUNCT
iajs-1170	110	59			PROPN
iajs-1170	110	60	(	(	PUNCT
iajs-1170	110	61	y,	y,	PROPN
iajs-1170	110	62	)	)	PUNCT
iajs-1170	110	63	is	be	AUX
iajs-1170	110	64	said	say	VERB
iajs-1170	110	65	to	to	PART
iajs-1170	110	66	be	be	AUX
iajs-1170	110	67	"	"	PUNCT
iajs-1170	110	68	*-continuous	*-continuous	ADJ
iajs-1170	110	69	"	"	PUNCT
iajs-1170	110	70	,	,	PUNCT
iajs-1170	110	71	if	if	SCONJ
iajs-1170	110	72	and	and	CCONJ
iajs-1170	110	73	only	only	ADV
iajs-1170	110	74	if	if	SCONJ
iajs-1170	110	75	the	the	DET
iajs-1170	110	76	inverse	inverse	ADJ
iajs-1170	110	77	image	image	NOUN
iajs-1170	110	78	of	of	ADP
iajs-1170	110	79	every	every	DET
iajs-1170	110	80	-closed	-closed	ADJ
iajs-1170	110	81	subset	subset	NOUN
iajs-1170	110	82	of	of	ADP
iajs-1170	110	83	y	y	PROPN
iajs-1170	110	84	is	be	AUX
iajs-1170	110	85	an	an	DET
iajs-1170	110	86	-closed	-closed	ADJ
iajs-1170	110	87	subset	subset	NOUN
iajs-1170	110	88	of	of	ADP
iajs-1170	110	89	x.	x.	PROPN
iajs-1170	110	90	3.6	3.6	NUM
iajs-1170	110	91	lemma	lemma	PROPN
iajs-1170	110	92	a	a	DET
iajs-1170	110	93	function	function	NOUN
iajs-1170	110	94	f	f	PROPN
iajs-1170	110	95	:(	:(	PROPN
iajs-1170	110	96	x,	x,	PROPN
iajs-1170	110	97	)	)	PUNCT
iajs-1170	110	98			PROPN
iajs-1170	110	99	(	(	PUNCT
iajs-1170	110	100	y,	y,	PROPN
iajs-1170	110	101	)	)	PUNCT
iajs-1170	110	102	is	be	AUX
iajs-1170	110	103	*-continuous	*-continuous	ADJ
iajs-1170	110	104	if	if	SCONJ
iajs-1170	110	105	and	and	CCONJ
iajs-1170	110	106	only	only	ADV
iajs-1170	110	107	if	if	SCONJ
iajs-1170	110	108	-closure	-closure	PROPN
iajs-1170	110	109	(	(	PUNCT
iajs-1170	110	110	f	f	PROPN
iajs-1170	110	111	-1(b	-1(b	PROPN
iajs-1170	110	112	)	)	PUNCT
iajs-1170	110	113	)	)	PUNCT
iajs-1170	111	1			PROPN
iajs-1170	111	2	f	f	PROPN
iajs-1170	111	3	-1(closure((b	-1(closure((b	PROPN
iajs-1170	111	4	)	)	PUNCT
iajs-1170	111	5	)	)	PUNCT
iajs-1170	111	6	for	for	ADP
iajs-1170	111	7	each	each	DET
iajs-1170	111	8	b	b	PROPN
iajs-1170	111	9			PROPN
iajs-1170	111	10	y.	y.	PROPN
iajs-1170	111	11	proof	proof	NOUN
iajs-1170	111	12	:	:	PUNCT
iajs-1170	111	13	necessity	necessity	NOUN
iajs-1170	111	14	,	,	PUNCT
iajs-1170	111	15	let	let	VERB
iajs-1170	111	16	f	f	PROPN
iajs-1170	111	17	:(	:(	PROPN
iajs-1170	111	18	x,	x,	PROPN
iajs-1170	111	19	)	)	PUNCT
iajs-1170	111	20			PROPN
iajs-1170	111	21	(	(	PUNCT
iajs-1170	111	22	y,	y,	PROPN
iajs-1170	111	23	)	)	PUNCT
iajs-1170	111	24	be	be	VERB
iajs-1170	111	25	an	an	DET
iajs-1170	111	26	*-continuous	*-continuous	ADJ
iajs-1170	111	27	function	function	NOUN
iajs-1170	111	28	,	,	PUNCT
iajs-1170	111	29	let	let	VERB
iajs-1170	111	30	b	b	NOUN
iajs-1170	111	31			PROPN
iajs-1170	111	32	y.	y.	PROPN
iajs-1170	111	33	now	now	ADV
iajs-1170	111	34	,	,	PUNCT
iajs-1170	111	35	since	since	SCONJ
iajs-1170	111	36	,	,	PUNCT
iajs-1170	111	37	b	b	PROPN
iajs-1170	111	38			PROPN
iajs-1170	111	39	-cl	-cl	PROPN
iajs-1170	111	40	b	b	PROPN
iajs-1170	111	41	,	,	PUNCT
iajs-1170	111	42	then	then	ADV
iajs-1170	111	43	(	(	PUNCT
iajs-1170	111	44	f	f	PROPN
iajs-1170	111	45	-1(b	-1(b	PROPN
iajs-1170	111	46	)	)	PUNCT
iajs-1170	111	47	)	)	PUNCT
iajs-1170	112	1			PROPN
iajs-1170	112	2	f	f	PROPN
iajs-1170	112	3	-1	-1	X
iajs-1170	112	4	(	(	PUNCT
iajs-1170	112	5	-cl	-cl	PROPN
iajs-1170	112	6	b	b	PROPN
iajs-1170	112	7	)	)	PUNCT
iajs-1170	112	8	,	,	PUNCT
iajs-1170	112	9	implies	imply	VERB
iajs-1170	112	10	,	,	PUNCT
iajs-1170	112	11	-cl(f	-cl(f	NOUN
iajs-1170	112	12	-1	-1	PUNCT
iajs-1170	112	13	(	(	PUNCT
iajs-1170	112	14	b	b	NOUN
iajs-1170	112	15	)	)	PUNCT
iajs-1170	112	16	)	)	PUNCT
iajs-1170	112	17			PROPN
iajs-1170	112	18	-cl	-cl	PROPN
iajs-1170	112	19	(	(	PUNCT
iajs-1170	112	20	f	f	NOUN
iajs-1170	112	21	-1	-1	X
iajs-1170	112	22	(	(	PUNCT
iajs-1170	112	23	-cl	-cl	PROPN
iajs-1170	112	24	b	b	NOUN
iajs-1170	112	25	)	)	PUNCT
iajs-1170	112	26	)	)	PUNCT
iajs-1170	112	27	.	.	PUNCT
iajs-1170	113	1	in	in	ADP
iajs-1170	113	2	virtue	virtue	NOUN
iajs-1170	113	3	of	of	ADP
iajs-1170	113	4	remark	remark	NOUN
iajs-1170	113	5	(	(	PUNCT
iajs-1170	113	6	3.5	3.5	NUM
iajs-1170	113	7	)	)	PUNCT
iajs-1170	113	8	,	,	PUNCT
iajs-1170	113	9	f	f	PROPN
iajs-1170	113	10	-1	-1	PUNCT
iajs-1170	113	11	(	(	PUNCT
iajs-1170	113	12	-cl	-cl	PROPN
iajs-1170	113	13	b	b	X
iajs-1170	113	14	)	)	PUNCT
iajs-1170	113	15	is	be	AUX
iajs-1170	113	16	an	an	DET
iajs-1170	113	17	-closed	-closed	ADJ
iajs-1170	113	18	set	set	NOUN
iajs-1170	113	19	in	in	ADP
iajs-1170	113	20	x.	x.	PROPN
iajs-1170	114	1	so	so	ADV
iajs-1170	114	2	-cl	-cl	PROPN
iajs-1170	114	3	(	(	PUNCT
iajs-1170	114	4	f	f	NOUN
iajs-1170	114	5	-1	-1	PROPN
iajs-1170	114	6	(	(	PUNCT
iajs-1170	114	7	-cl	-cl	PROPN
iajs-1170	114	8	b	b	NOUN
iajs-1170	114	9	)	)	PUNCT
iajs-1170	114	10	)	)	PUNCT
iajs-1170	115	1	=	=	SYM
iajs-1170	115	2	f	f	X
iajs-1170	115	3	-1	-1	X
iajs-1170	115	4	(	(	PUNCT
iajs-1170	115	5	-cl	-cl	PROPN
iajs-1170	115	6	b	b	NOUN
iajs-1170	115	7	)	)	PUNCT
iajs-1170	115	8	.	.	PUNCT
iajs-1170	116	1	therefore	therefore	ADV
iajs-1170	116	2	-cl(f	-cl(f	NOUN
iajs-1170	116	3	-1(b	-1(b	NOUN
iajs-1170	116	4	)	)	PUNCT
iajs-1170	116	5	)	)	PUNCT
iajs-1170	117	1			PROPN
iajs-1170	117	2	f	f	PROPN
iajs-1170	117	3	-1(-cl	-1(-cl	NUM
iajs-1170	117	4	b	b	PROPN
iajs-1170	117	5	)	)	PUNCT
iajs-1170	117	6	.	.	PUNCT
iajs-1170	118	1	sufficiency	sufficiency	PROPN
iajs-1170	118	2	,	,	PUNCT
iajs-1170	118	3	suppose	suppose	VERB
iajs-1170	118	4	-cl(f	-cl(f	NOUN
iajs-1170	118	5	-1(b	-1(b	NOUN
iajs-1170	118	6	)	)	PUNCT
iajs-1170	118	7	)	)	PUNCT
iajs-1170	119	1			PROPN
iajs-1170	119	2	f	f	PROPN
iajs-1170	119	3	-1(-cl	-1(-cl	NUM
iajs-1170	119	4	b	b	NOUN
iajs-1170	119	5	)	)	PUNCT
iajs-1170	119	6	for	for	SCONJ
iajs-1170	119	7	each	each	DET
iajs-1170	119	8	b	b	PROPN
iajs-1170	119	9			PROPN
iajs-1170	119	10	y.	y.	PROPN
iajs-1170	119	11	to	to	PART
iajs-1170	119	12	prove	prove	VERB
iajs-1170	119	13	f	f	PROPN
iajs-1170	119	14	is	be	AUX
iajs-1170	119	15	*continuous	*continuous	ADJ
iajs-1170	119	16	function	function	NOUN
iajs-1170	119	17	.	.	PUNCT
iajs-1170	120	1	we	we	PRON
iajs-1170	120	2	must	must	AUX
iajs-1170	120	3	prove	prove	VERB
iajs-1170	120	4	if	if	SCONJ
iajs-1170	120	5	a	a	DET
iajs-1170	120	6	ia	ia	NOUN
iajs-1170	120	7	an	an	DET
iajs-1170	120	8	-closed	-closed	ADJ
iajs-1170	120	9	set	set	NOUN
iajs-1170	120	10	in	in	ADP
iajs-1170	120	11	y	y	PROPN
iajs-1170	120	12	,	,	PUNCT
iajs-1170	120	13	then	then	ADV
iajs-1170	120	14	f	f	PROPN
iajs-1170	120	15	1(a	1(a	NUM
iajs-1170	120	16	)	)	PUNCT
iajs-1170	120	17	is	be	AUX
iajs-1170	120	18	an	an	DET
iajs-1170	120	19	-closed	-closed	ADJ
iajs-1170	120	20	set	set	NOUN
iajs-1170	120	21	in	in	ADP
iajs-1170	120	22	x.	x.	NOUN
iajs-1170	120	23	it	it	PRON
iajs-1170	120	24	is	be	AUX
iajs-1170	120	25	enough	enough	ADJ
iajs-1170	120	26	to	to	PART
iajs-1170	120	27	prove	prove	VERB
iajs-1170	120	28	that	that	DET
iajs-1170	120	29	-cl(f	-cl(f	NOUN
iajs-1170	120	30	-1(a	-1(a	NOUN
iajs-1170	120	31	)	)	PUNCT
iajs-1170	120	32	)	)	PUNCT
iajs-1170	121	1			PROPN
iajs-1170	121	2	f	f	PROPN
iajs-1170	121	3	-1(a	-1(a	PROPN
iajs-1170	121	4	)	)	PUNCT
iajs-1170	121	5	.	.	PUNCT
iajs-1170	122	1	since	since	SCONJ
iajs-1170	122	2	a	a	PRON
iajs-1170	122	3	is	be	AUX
iajs-1170	122	4	-closed	-close	VERB
iajs-1170	122	5	set	set	VERB
iajs-1170	122	6	in	in	ADP
iajs-1170	122	7	y	y	PROPN
iajs-1170	122	8	,	,	PUNCT
iajs-1170	122	9	then	then	ADV
iajs-1170	122	10	-cl(a	-cl(a	NOUN
iajs-1170	122	11	)	)	PUNCT
iajs-1170	123	1	=	=	SYM
iajs-1170	124	1	a	a	DET
iajs-1170	124	2	and	and	CCONJ
iajs-1170	124	3	by	by	ADP
iajs-1170	124	4	hypothesis	hypothesis	NOUN
iajs-1170	124	5	,	,	PUNCT
iajs-1170	124	6	-cl(f	-cl(f	NOUN
iajs-1170	124	7	-1(a	-1(a	NOUN
iajs-1170	124	8	)	)	PUNCT
iajs-1170	124	9	)	)	PUNCT
iajs-1170	125	1			PROPN
iajs-1170	125	2	f	f	PROPN
iajs-1170	125	3	-1(-cl	-1(-cl	NUM
iajs-1170	125	4	(	(	PUNCT
iajs-1170	125	5	a	a	NOUN
iajs-1170	125	6	)	)	PUNCT
iajs-1170	125	7	)	)	PUNCT
iajs-1170	125	8	implies,-cl(f	implies,-cl(f	PROPN
iajs-1170	125	9	-1(a	-1(a	PROPN
iajs-1170	125	10	)	)	PUNCT
iajs-1170	125	11	)	)	PUNCT
iajs-1170	126	1			PROPN
iajs-1170	126	2	f	f	PROPN
iajs-1170	126	3	-1	-1	X
iajs-1170	126	4	(	(	PUNCT
iajs-1170	126	5	a	a	NOUN
iajs-1170	126	6	)	)	PUNCT
iajs-1170	126	7	.	.	PUNCT
iajs-1170	127	1	so	so	ADV
iajs-1170	127	2	f	f	PROPN
iajs-1170	127	3	-1(a	-1(a	PROPN
iajs-1170	127	4	)	)	PUNCT
iajs-1170	127	5	is	be	AUX
iajs-1170	127	6	an	an	DET
iajs-1170	127	7	-closed	-closed	ADJ
iajs-1170	127	8	set	set	NOUN
iajs-1170	127	9	in	in	ADP
iajs-1170	127	10	x	x	PUNCT
iajs-1170	127	11	and	and	CCONJ
iajs-1170	127	12	f	f	PROPN
iajs-1170	127	13	is	be	AUX
iajs-1170	127	14	*-continuous	*-continuous	ADJ
iajs-1170	127	15	function	function	NOUN
iajs-1170	127	16	.	.	PUNCT
iajs-1170	128	1	3.7	3.7	NUM
iajs-1170	128	2	prposition	prposition	NOUN
iajs-1170	128	3	the	the	DET
iajs-1170	128	4	*-continuous	*-continuous	ADJ
iajs-1170	128	5	image	image	NOUN
iajs-1170	128	6	of	of	ADP
iajs-1170	128	7	an	an	DET
iajs-1170	128	8	-c	-c	ADV
iajs-1170	128	9	-	-	PUNCT
iajs-1170	128	10	compact	compact	ADJ
iajs-1170	128	11	space	space	NOUN
iajs-1170	128	12	is	be	AUX
iajs-1170	128	13	-c	-c	ADV
iajs-1170	128	14	-	-	PUNCT
iajs-1170	128	15	compact	compact	ADJ
iajs-1170	128	16	.	.	PUNCT
iajs-1170	129	1	proof	proof	NOUN
iajs-1170	129	2	:	:	PUNCT
iajs-1170	129	3	let	let	VERB
iajs-1170	129	4	(	(	PUNCT
iajs-1170	129	5	x,	x,	X
iajs-1170	129	6	)	)	PUNCT
iajs-1170	129	7	be	be	VERB
iajs-1170	129	8	an	an	DET
iajs-1170	129	9	-c	-c	ADV
iajs-1170	129	10	-	-	PUNCT
iajs-1170	129	11	compact	compact	ADJ
iajs-1170	129	12	space	space	NOUN
iajs-1170	129	13	,	,	PUNCT
iajs-1170	129	14	and	and	CCONJ
iajs-1170	129	15	f	f	PROPN
iajs-1170	129	16	:(	:(	PROPN
iajs-1170	129	17	x,	x,	PROPN
iajs-1170	129	18	)	)	PUNCT
iajs-1170	129	19			PROPN
iajs-1170	129	20	(	(	PUNCT
iajs-1170	129	21	y,	y,	PROPN
iajs-1170	129	22	)	)	PUNCT
iajs-1170	129	23	be	be	VERB
iajs-1170	129	24	an	an	DET
iajs-1170	129	25	*-continuous	*-continuous	ADJ
iajs-1170	129	26	onto	onto	ADP
iajs-1170	129	27	function	function	NOUN
iajs-1170	129	28	.	.	PUNCT
iajs-1170	130	1	to	to	PART
iajs-1170	130	2	prove	prove	VERB
iajs-1170	130	3	(	(	PUNCT
iajs-1170	130	4	y,	y,	NOUN
iajs-1170	130	5	)	)	PUNCT
iajs-1170	130	6	is	be	AUX
iajs-1170	130	7	-c	-c	ADV
iajs-1170	130	8	-	-	PUNCT
iajs-1170	130	9	compact	compact	ADJ
iajs-1170	130	10	space	space	NOUN
iajs-1170	130	11	.	.	PUNCT
iajs-1170	131	1	let	let	VERB
iajs-1170	131	2	a	a	DET
iajs-1170	131	3	be	be	AUX
iajs-1170	131	4	an	an	DET
iajs-1170	131	5	-closed	-closed	ADJ
iajs-1170	131	6	subset	subset	NOUN
iajs-1170	131	7	of	of	ADP
iajs-1170	131	8	y	y	PROPN
iajs-1170	131	9	,	,	PUNCT
iajs-1170	131	10	and	and	CCONJ
iajs-1170	131	11	{	{	PUNCT
iajs-1170	131	12	u	u	NOUN
iajs-1170	131	13	:	:	PUNCT
iajs-1170	131	14			NOUN
iajs-1170	131	15	}	}	PUNCT
iajs-1170	131	16	be	be	VERB
iajs-1170	131	17	an	an	DET
iajs-1170	131	18	-open	-open	PROPN
iajs-1170	131	19	cover	cover	NOUN
iajs-1170	131	20	in	in	ADP
iajs-1170	131	21	y	y	PROPN
iajs-1170	131	22	for	for	ADP
iajs-1170	131	23	a.	a.	NOUN
iajs-1170	131	24	since	since	SCONJ
iajs-1170	131	25	f	f	PROPN
iajs-1170	131	26	is	be	AUX
iajs-1170	131	27	*-continuous	*-continuous	ADJ
iajs-1170	131	28	,	,	PUNCT
iajs-1170	131	29	then	then	ADV
iajs-1170	131	30	f	f	PROPN
iajs-1170	131	31	-1(a	-1(a	PROPN
iajs-1170	131	32	)	)	PUNCT
iajs-1170	131	33	is	be	AUX
iajs-1170	131	34	an	an	DET
iajs-1170	131	35	-closed	-closed	ADJ
iajs-1170	131	36	set	set	NOUN
iajs-1170	131	37	in	in	ADP
iajs-1170	131	38	x	x	PUNCT
iajs-1170	131	39	and	and	CCONJ
iajs-1170	131	40	{	{	PUNCT
iajs-1170	131	41	f	f	PROPN
iajs-1170	131	42	-1(u):	-1(u):	PROPN
iajs-1170	131	43	}	}	PUNCT
iajs-1170	131	44	is	be	AUX
iajs-1170	131	45	a	a	DET
iajs-1170	131	46	family	family	NOUN
iajs-1170	131	47	of	of	ADP
iajs-1170	131	48	-open	-open	PROPN
iajs-1170	131	49	sets	set	VERB
iajs-1170	131	50	in	in	ADP
iajs-1170	131	51	x	x	PUNCT
iajs-1170	131	52	covering	cover	VERB
iajs-1170	131	53	f	f	PROPN
iajs-1170	131	54	-1(a	-1(a	PROPN
iajs-1170	131	55	)	)	PUNCT
iajs-1170	131	56	and	and	CCONJ
iajs-1170	131	57	x	x	ADJ
iajs-1170	131	58	is	be	AUX
iajs-1170	131	59	-ccompact	-ccompact	PROPN
iajs-1170	131	60	space	space	NOUN
iajs-1170	131	61	,	,	PUNCT
iajs-1170	131	62	then	then	ADV
iajs-1170	131	63	there	there	PRON
iajs-1170	131	64	is	be	VERB
iajs-1170	131	65	1	1	NUM
iajs-1170	131	66	,	,	PUNCT
iajs-1170	131	67	2,	2,	NOUN
iajs-1170	131	68	…	…	PUNCT
iajs-1170	131	69	,n	,n	NOUN
iajs-1170	131	70	such	such	ADJ
iajs-1170	131	71	that	that	SCONJ
iajs-1170	131	72	{	{	PUNCT
iajs-1170	131	73	-cl(f	-cl(f	NOUN
iajs-1170	131	74	-1	-1	NOUN
iajs-1170	131	75	(	(	PUNCT
iajs-1170	131	76	u	u	NOUN
iajs-1170	131	77	i	i	PROPN
iajs-1170	131	78	)	)	PUNCT
iajs-1170	131	79	):	):	PUNCT
iajs-1170	131	80	i	i	PRON
iajs-1170	131	81	=	=	SYM
iajs-1170	131	82	1,2,	1,2,	NUM
iajs-1170	131	83	…	…	SYM
iajs-1170	131	84	,n	,n	NOUN
iajs-1170	131	85	}	}	PUNCT
iajs-1170	131	86	covers	cover	VERB
iajs-1170	131	87	f	f	PROPN
iajs-1170	131	88	-1(a	-1(a	PROPN
iajs-1170	131	89	)	)	PUNCT
iajs-1170	131	90	,	,	PUNCT
iajs-1170	131	91	implies	imply	VERB
iajs-1170	131	92	{	{	PUNCT
iajs-1170	131	93	f	f	X
iajs-1170	131	94	(	(	PUNCT
iajs-1170	131	95	-cl(f	-cl(f	NOUN
iajs-1170	131	96	-1	-1	NOUN
iajs-1170	131	97	(	(	PUNCT
iajs-1170	131	98	u	u	NOUN
iajs-1170	131	99	i	i	PROPN
iajs-1170	131	100	)	)	PUNCT
iajs-1170	131	101	)	)	PUNCT
iajs-1170	131	102	):	):	PUNCT
iajs-1170	132	1	i	i	PRON
iajs-1170	132	2	=	=	SYM
iajs-1170	132	3	1,2,	1,2,	NUM
iajs-1170	132	4	…	…	SYM
iajs-1170	132	5	,n	,n	NOUN
iajs-1170	132	6	}	}	PUNCT
iajs-1170	132	7	covers	cover	VERB
iajs-1170	132	8	a.	a.	NOUN
iajs-1170	132	9	in	in	ADP
iajs-1170	132	10	virtue	virtue	NOUN
iajs-1170	132	11	of	of	ADP
iajs-1170	132	12	lemma	lemma	PROPN
iajs-1170	132	13	(	(	PUNCT
iajs-1170	132	14	3.6	3.6	NUM
iajs-1170	132	15	)	)	PUNCT
iajs-1170	132	16	,	,	PUNCT
iajs-1170	132	17	{	{	PUNCT
iajs-1170	132	18	f	f	X
iajs-1170	132	19	(	(	PUNCT
iajs-1170	132	20	f	f	PROPN
iajs-1170	132	21	1	1	NUM
iajs-1170	132	22	(	(	PUNCT
iajs-1170	132	23			X
iajs-1170	132	24	ibn	ibn	PROPN
iajs-1170	132	25	alhaitham	alhaitham	NOUN
iajs-1170	132	26	j.	j.	PROPN
iajs-1170	133	1	fo	fo	ADP
iajs-1170	133	2	r	r	NOUN
iajs-1170	133	3	pure	pure	ADJ
iajs-1170	133	4	&	&	CCONJ
iajs-1170	133	5	appl	appl	PROPN
iajs-1170	133	6	.	.	PUNCT
iajs-1170	134	1	sc	sc	PROPN
iajs-1170	135	1	i	i	PRON
iajs-1170	135	2	vo	vo	INTJ
iajs-1170	135	3	l.22	l.22	X
iajs-1170	135	4	(	(	PUNCT
iajs-1170	135	5	3	3	NUM
iajs-1170	135	6	)	)	PUNCT
iajs-1170	135	7	2009	2009	NUM
iajs-1170	135	8	cl	cl	NOUN
iajs-1170	135	9	(	(	PUNCT
iajs-1170	135	10	u	u	NOUN
iajs-1170	135	11	i	i	PROPN
iajs-1170	135	12	)	)	PUNCT
iajs-1170	135	13	)	)	PUNCT
iajs-1170	135	14	):	):	PUNCT
iajs-1170	136	1	i	i	PRON
iajs-1170	136	2	=	=	SYM
iajs-1170	136	3	1,2,	1,2,	NUM
iajs-1170	136	4	…	…	SYM
iajs-1170	136	5	,n	,n	NOUN
iajs-1170	136	6	}	}	PUNCT
iajs-1170	136	7	covers	cover	VERB
iajs-1170	136	8	a.	a.	NOUN
iajs-1170	136	9	since	since	SCONJ
iajs-1170	136	10	f	f	PROPN
iajs-1170	136	11	is	be	AUX
iajs-1170	136	12	onto	onto	ADP
iajs-1170	136	13	function,{-cl	function,{-cl	PROPN
iajs-1170	136	14	(	(	PUNCT
iajs-1170	136	15	u	u	NOUN
iajs-1170	136	16	i	i	PROPN
iajs-1170	136	17	):	):	PUNCT
iajs-1170	136	18	i	i	NOUN
iajs-1170	136	19	=	=	SYM
iajs-1170	136	20	1,2,	1,2,	NUM
iajs-1170	136	21	…	…	SYM
iajs-1170	136	22	,n	,n	NOUN
iajs-1170	136	23	}	}	PUNCT
iajs-1170	136	24	covers	cover	VERB
iajs-1170	136	25	a.	a.	NOUN
iajs-1170	136	26	hence	hence	ADV
iajs-1170	136	27	,	,	PUNCT
iajs-1170	136	28	y	y	PROPN
iajs-1170	136	29	is	be	AUX
iajs-1170	136	30	-c	-c	ADV
iajs-1170	136	31	-	-	PUNCT
iajs-1170	136	32	compact	compact	ADJ
iajs-1170	136	33	space	space	NOUN
iajs-1170	136	34	.	.	PUNCT
iajs-1170	137	1	3.8	3.8	NUM
iajs-1170	137	2	proposition	proposition	NOUN
iajs-1170	137	3	[	[	X
iajs-1170	137	4	9	9	NUM
iajs-1170	137	5	]	]	PUNCT
iajs-1170	137	6	,	,	PUNCT
iajs-1170	137	7	[	[	X
iajs-1170	137	8	10	10	NUM
iajs-1170	137	9	]	]	X
iajs-1170	137	10	every	every	DET
iajs-1170	137	11	continuous	continuous	ADJ
iajs-1170	137	12	,	,	PUNCT
iajs-1170	137	13	onto	onto	ADP
iajs-1170	137	14	,	,	PUNCT
iajs-1170	137	15	open	open	ADJ
iajs-1170	137	16	function	function	NOUN
iajs-1170	137	17	is	be	AUX
iajs-1170	137	18	*-continuous	*-continuous	ADJ
iajs-1170	137	19	.	.	PUNCT
iajs-1170	138	1	3.9	3.9	NUM
iajs-1170	138	2	corollary	corollary	NOUN
iajs-1170	138	3	an	an	DET
iajs-1170	138	4	-c	-c	ADV
iajs-1170	138	5	-	-	PUNCT
iajs-1170	138	6	compactness	compactness	NOUN
iajs-1170	138	7	is	be	AUX
iajs-1170	138	8	a	a	DET
iajs-1170	138	9	topological	topological	ADJ
iajs-1170	138	10	property	property	NOUN
iajs-1170	138	11	.	.	PUNCT
iajs-1170	139	1	proof	proof	NOUN
iajs-1170	139	2	:	:	PUNCT
iajs-1170	139	3	follows	follow	VERB
iajs-1170	139	4	from	from	ADP
iajs-1170	139	5	propositions	proposition	NOUN
iajs-1170	139	6	(	(	PUNCT
iajs-1170	139	7	3.8	3.8	NUM
iajs-1170	139	8	)	)	PUNCT
iajs-1170	139	9	and	and	CCONJ
iajs-1170	139	10	(	(	PUNCT
iajs-1170	139	11	3.7	3.7	NUM
iajs-1170	139	12	)	)	PUNCT
iajs-1170	139	13	.	.	PUNCT
iajs-1170	140	1	4	4	X
iajs-1170	140	2	.	.	X
iajs-1170	140	3	conclusion	conclusion	NOUN
iajs-1170	140	4	and	and	CCONJ
iajs-1170	140	5	recommandation	recommandation	NOUN
iajs-1170	140	6	we	we	PRON
iajs-1170	140	7	introduced	introduce	VERB
iajs-1170	140	8	a	a	DET
iajs-1170	140	9	new	new	ADJ
iajs-1170	140	10	type	type	NOUN
iajs-1170	140	11	of	of	ADP
iajs-1170	140	12	compactness	compactness	NOUN
iajs-1170	140	13	which	which	PRON
iajs-1170	140	14	is	be	AUX
iajs-1170	140	15	called	call	VERB
iajs-1170	140	16	-c	-c	ADV
iajs-1170	140	17	-	-	PUNCT
iajs-1170	140	18	compact	compact	ADJ
iajs-1170	140	19	and	and	CCONJ
iajs-1170	140	20	discussed	discuss	VERB
iajs-1170	140	21	the	the	DET
iajs-1170	140	22	relationships	relationship	NOUN
iajs-1170	140	23	among	among	ADP
iajs-1170	140	24	this	this	DET
iajs-1170	140	25	type	type	NOUN
iajs-1170	140	26	and	and	CCONJ
iajs-1170	140	27	some	some	DET
iajs-1170	140	28	types	type	NOUN
iajs-1170	140	29	of	of	ADP
iajs-1170	140	30	compactness	compactness	NOUN
iajs-1170	140	31	like	like	ADP
iajs-1170	140	32	,	,	PUNCT
iajs-1170	140	33	compact	compact	ADJ
iajs-1170	140	34	,	,	PUNCT
iajs-1170	140	35	-compact	-compact	PROPN
iajs-1170	140	36	and	and	CCONJ
iajs-1170	140	37	c	c	NOUN
iajs-1170	140	38	-	-	ADJ
iajs-1170	140	39	compact	compact	ADJ
iajs-1170	140	40	.	.	PUNCT
iajs-1170	141	1	also	also	ADV
iajs-1170	141	2	,	,	PUNCT
iajs-1170	141	3	we	we	PRON
iajs-1170	141	4	some	some	DET
iajs-1170	141	5	examples	example	NOUN
iajs-1170	141	6	to	to	PART
iajs-1170	141	7	explain	explain	VERB
iajs-1170	141	8	the	the	DET
iajs-1170	141	9	direction	direction	NOUN
iajs-1170	141	10	that	that	PRON
iajs-1170	141	11	not	not	PART
iajs-1170	141	12	hold	hold	VERB
iajs-1170	141	13	and	and	CCONJ
iajs-1170	141	14	we	we	PRON
iajs-1170	141	15	put	put	VERB
iajs-1170	141	16	some	some	DET
iajs-1170	141	17	condition	condition	NOUN
iajs-1170	141	18	to	to	PART
iajs-1170	141	19	make	make	VERB
iajs-1170	141	20	that	that	DET
iajs-1170	141	21	false	false	ADJ
iajs-1170	141	22	direction	direction	NOUN
iajs-1170	141	23	valid	valid	ADJ
iajs-1170	141	24	.	.	PUNCT
iajs-1170	142	1	in	in	ADP
iajs-1170	142	2	future	future	NOUN
iajs-1170	142	3	,	,	PUNCT
iajs-1170	142	4	we	we	PRON
iajs-1170	142	5	shall	shall	AUX
iajs-1170	142	6	study	study	VERB
iajs-1170	142	7	strongly	strongly	ADV
iajs-1170	142	8	c	c	NOUN
iajs-1170	142	9	-	-	ADJ
iajs-1170	142	10	compact	compact	ADJ
iajs-1170	142	11	,	,	PUNCT
iajs-1170	142	12	semi--c	semi--c	NOUN
iajs-1170	142	13	-	-	PUNCT
iajs-1170	142	14	compact	compact	ADJ
iajs-1170	142	15	,	,	PUNCT
iajs-1170	142	16	semi	semi	ADJ
iajs-1170	142	17	-	-	ADJ
iajs-1170	142	18	p	p	ADJ
iajs-1170	142	19	-	-	PUNCT
iajs-1170	142	20	compact	compact	ADJ
iajs-1170	142	21	and	and	CCONJ
iajs-1170	142	22	semi	semi	ADJ
iajs-1170	142	23	-	-	ADJ
iajs-1170	142	24	p	p	ADJ
iajs-1170	142	25	-	-	PUNCT
iajs-1170	142	26	c	c	NOUN
iajs-1170	142	27	-	-	ADJ
iajs-1170	142	28	compact	compact	ADJ
iajs-1170	142	29	.	.	PUNCT
iajs-1170	143	1	references	reference	NOUN
iajs-1170	143	2	1	1	NUM
iajs-1170	143	3	.	.	PUNCT
iajs-1170	143	4	viglion	viglion	NOUN
iajs-1170	143	5	,	,	PUNCT
iajs-1170	143	6	g.	g.	PROPN
iajs-1170	143	7	(	(	PUNCT
iajs-1170	143	8	1969	1969	NUM
iajs-1170	143	9	)	)	PUNCT
iajs-1170	143	10	,	,	PUNCT
iajs-1170	143	11	"	"	PUNCT
iajs-1170	143	12	c	c	X
iajs-1170	143	13	-	-	ADJ
iajs-1170	143	14	compact	compact	ADJ
iajs-1170	143	15	spaces	space	NOUN
iajs-1170	143	16	"	"	PUNCT
iajs-1170	143	17	,	,	PUNCT
iajs-1170	143	18	duke	duke	PROPN
iajs-1170	143	19	math	math	PROPN
iajs-1170	143	20	.	.	PUNCT
iajs-1170	144	1	j.	j.	PROPN
iajs-1170	144	2	,36:761	,36:761	PROPN
iajs-1170	144	3	-	-	PUNCT
iajs-1170	144	4	764	764	NUM
iajs-1170	144	5	.	.	PUNCT
iajs-1170	145	1	2	2	X
iajs-1170	145	2	.	.	X
iajs-1170	145	3	njastad	njastad	NOUN
iajs-1170	145	4	,	,	PUNCT
iajs-1170	145	5	o.	o.	PROPN
iajs-1170	145	6	(	(	PUNCT
iajs-1170	145	7	1965	1965	NUM
iajs-1170	145	8	)	)	PUNCT
iajs-1170	145	9	,	,	PUNCT
iajs-1170	145	10	"	"	PUNCT
iajs-1170	145	11	on	on	ADP
iajs-1170	145	12	some	some	DET
iajs-1170	145	13	classes	class	NOUN
iajs-1170	145	14	of	of	ADP
iajs-1170	145	15	nearly	nearly	ADV
iajs-1170	145	16	open	open	ADJ
iajs-1170	145	17	sets	set	NOUN
iajs-1170	145	18	"	"	PUNCT
iajs-1170	145	19	,	,	PUNCT
iajs-1170	145	20	pacific	pacific	PROPN
iajs-1170	145	21	j.m	j.m	PROPN
iajs-1170	145	22	ath	ath	NOUN
iajs-1170	145	23	.	.	PUNCT
iajs-1170	145	24	,15:961	,15:961	PUNCT
iajs-1170	145	25	-	-	PUNCT
iajs-1170	145	26	970	970	NUM
iajs-1170	145	27	.	.	PUNCT
iajs-1170	146	1	3	3	X
iajs-1170	146	2	.	.	X
iajs-1170	146	3	caldas	caldas	PROPN
iajs-1170	146	4	,	,	PUNCT
iajs-1170	146	5	m.	m.	NOUN
iajs-1170	146	6	and	and	CCONJ
iajs-1170	146	7	jafari	jafari	PROPN
iajs-1170	146	8	,	,	PUNCT
iajs-1170	146	9	s.	s.	PROPN
iajs-1170	146	10	(	(	PUNCT
iajs-1170	146	11	2001	2001	NUM
iajs-1170	146	12	)	)	PUNCT
iajs-1170	146	13	,	,	PUNCT
iajs-1170	146	14	"	"	PUNCT
iajs-1170	146	15	some	some	DET
iajs-1170	146	16	properties	property	NOUN
iajs-1170	146	17	of	of	ADP
iajs-1170	146	18	contra--continuous	contra--continuous	ADJ
iajs-1170	146	19	functions	function	NOUN
iajs-1170	146	20	"	"	PUNCT
iajs-1170	146	21	,	,	PUNCT
iajs-1170	146	22	mem	mem	X
iajs-1170	146	23	.	.	PUNCT
iajs-1170	147	1	fac.sci	fac.sci	NUM
iajs-1170	147	2	.	.	PUNCT
iajs-1170	148	1	kochi	kochi	PROPN
iajs-1170	148	2	univ	univ	PROPN
iajs-1170	148	3	.	.	PUNCT
iajs-1170	149	1	(	(	PUNCT
iajs-1170	149	2	math	math	NOUN
iajs-1170	149	3	.	.	PUNCT
iajs-1170	149	4	)	)	PUNCT
iajs-1170	149	5	,	,	PUNCT
iajs-1170	149	6	22:19	22:19	NUM
iajs-1170	149	7	-	-	SYM
iajs-1170	149	8	28	28	NUM
iajs-1170	149	9	.	.	PUNCT
iajs-1170	150	1	4	4	NUM
iajs-1170	150	2	.	.	X
iajs-1170	150	3	maheshwari	maheshwari	PROPN
iajs-1170	150	4	,	,	PUNCT
iajs-1170	150	5	s.n	s.n	PROPN
iajs-1170	150	6	.	.	PROPN
iajs-1170	150	7	and	and	CCONJ
iajs-1170	150	8	thakur	thakur	PROPN
iajs-1170	150	9	,	,	PUNCT
iajs-1170	150	10	s.s	s.s	PROPN
iajs-1170	150	11	.	.	PROPN
iajs-1170	150	12	(	(	PUNCT
iajs-1170	150	13	1980),"on	1980),"on	PROPN
iajs-1170	150	14	-sets	-sets	PROPN
iajs-1170	150	15	"	"	PUNCT
iajs-1170	150	16	,	,	PUNCT
iajs-1170	150	17	joffnabha	joffnabha	PROPN
iajs-1170	150	18	j.math	j.math	PROPN
iajs-1170	150	19	.	.	PUNCT
iajs-1170	150	20	,11:209	,11:209	PUNCT
iajs-1170	150	21	-	-	PUNCT
iajs-1170	150	22	214	214	NUM
iajs-1170	150	23	.	.	PUNCT
iajs-1170	151	1	5	5	NUM
iajs-1170	151	2	.	.	X
iajs-1170	151	3	kumar	kumar	PROPN
iajs-1170	151	4	,	,	PUNCT
iajs-1170	151	5	m.veera	m.veera	NOUN
iajs-1170	151	6	,	,	PUNCT
iajs-1170	151	7	(	(	PUNCT
iajs-1170	151	8	2002),"pre	2002),"pre	NUM
iajs-1170	151	9	-	-	PUNCT
iajs-1170	151	10	semi	semi	ADJ
iajs-1170	151	11	-	-	ADJ
iajs-1170	151	12	clsed	clsed	ADJ
iajs-1170	151	13	sets	set	NOUN
iajs-1170	151	14	'	'	PART
iajs-1170	151	15	,	,	PUNCT
iajs-1170	151	16	indian	indian	PROPN
iajs-1170	151	17	journal	journal	NOUN
iajs-1170	151	18	of	of	ADP
iajs-1170	151	19	mathematics	mathematic	NOUN
iajs-1170	151	20	,	,	PUNCT
iajs-1170	151	21	4492:165181	4492:165181	NUM
iajs-1170	151	22	.	.	NOUN
iajs-1170	152	1	6	6	NUM
iajs-1170	152	2	.	.	X
iajs-1170	152	3	maheshwari	maheshwari	PROPN
iajs-1170	152	4	,	,	PUNCT
iajs-1170	152	5	s.n	s.n	PROPN
iajs-1170	152	6	.	.	PROPN
iajs-1170	152	7	and	and	CCONJ
iajs-1170	152	8	thakur	thakur	PROPN
iajs-1170	152	9	,	,	PUNCT
iajs-1170	152	10	s.s	s.s	PROPN
iajs-1170	152	11	.	.	PROPN
iajs-1170	152	12	(	(	PUNCT
iajs-1170	152	13	1985	1985	NUM
iajs-1170	152	14	)	)	PUNCT
iajs-1170	152	15	,	,	PUNCT
iajs-1170	152	16	"	"	PUNCT
iajs-1170	152	17	on	on	ADP
iajs-1170	152	18	-compact	-compact	PROPN
iajs-1170	152	19	spaces	space	NOUN
iajs-1170	152	20	"	"	PUNCT
iajs-1170	152	21	,	,	PUNCT
iajs-1170	152	22	bulletin	bulletin	NOUN
iajs-1170	152	23	of	of	ADP
iajs-1170	152	24	the	the	DET
iajs-1170	152	25	institute	institute	NOUN
iajs-1170	152	26	of	of	ADP
iajs-1170	152	27	mathematics	mathematics	PROPN
iajs-1170	152	28	,	,	PUNCT
iajs-1170	152	29	academic	academic	PROPN
iajs-1170	152	30	sinica	sinica	PROPN
iajs-1170	152	31	,	,	PUNCT
iajs-1170	152	32	13(4	13(4	NUM
iajs-1170	152	33	):	):	PUNCT
iajs-1170	152	34	341	341	NUM
iajs-1170	152	35	-	-	SYM
iajs-1170	152	36	347	347	NUM
iajs-1170	152	37	.	.	PUNCT
iajs-1170	152	38	7	7	X
iajs-1170	152	39	.	.	X
iajs-1170	152	40	noiri	noiri	PROPN
iajs-1170	152	41	,	,	PUNCT
iajs-1170	152	42	t.	t.	PROPN
iajs-1170	152	43	and	and	CCONJ
iajs-1170	152	44	maio	maio	PROPN
iajs-1170	152	45	,	,	PUNCT
iajs-1170	152	46	g.di	g.di	PROPN
iajs-1170	152	47	.	.	PUNCT
iajs-1170	152	48	(	(	PUNCT
iajs-1170	152	49	1988	1988	NUM
iajs-1170	152	50	)	)	PUNCT
iajs-1170	152	51	,	,	PUNCT
iajs-1170	152	52	"	"	PUNCT
iajs-1170	152	53	properties	property	NOUN
iajs-1170	152	54	of	of	ADP
iajs-1170	152	55	-c	-c	ADV
iajs-1170	152	56	-	-	PUNCT
iajs-1170	152	57	compact	compact	ADJ
iajs-1170	152	58	spaces	space	NOUN
iajs-1170	152	59	'	'	PART
iajs-1170	152	60	,	,	PUNCT
iajs-1170	152	61	rendiconti	rendiconti	ADJ
iajs-1170	152	62	circ	circ	NOUN
iajs-1170	152	63	.	.	PUNCT
iajs-1170	153	1	math	math	NOUN
iajs-1170	153	2	.	.	PUNCT
iajs-1170	154	1	palermo	palermo	PROPN
iajs-1170	154	2	.	.	PUNCT
iajs-1170	154	3	ser	ser	PROPN
iajs-1170	154	4	ii	ii	PROPN
iajs-1170	154	5	,	,	PUNCT
iajs-1170	154	6	18:359	18:359	NUM
iajs-1170	154	7	-	-	SYM
iajs-1170	154	8	69	69	NUM
iajs-1170	154	9	.	.	NOUN
iajs-1170	155	1	8	8	NUM
iajs-1170	155	2	.	.	X
iajs-1170	155	3	navalagi	navalagi	ADJ
iajs-1170	155	4	,	,	PUNCT
iajs-1170	155	5	g.b	g.b	PROPN
iajs-1170	155	6	.	.	PROPN
iajs-1170	155	7	(	(	PUNCT
iajs-1170	155	8	1991	1991	NUM
iajs-1170	155	9	)	)	PUNCT
iajs-1170	155	10	,	,	PUNCT
iajs-1170	155	11	"	"	PUNCT
iajs-1170	155	12	definition	definition	NOUN
iajs-1170	155	13	bank	bank	NOUN
iajs-1170	155	14	in	in	ADP
iajs-1170	155	15	general	general	ADJ
iajs-1170	155	16	topology	topology	NOUN
iajs-1170	155	17	"	"	PUNCT
iajs-1170	155	18	,	,	PUNCT
iajs-1170	155	19	45	45	NUM
iajs-1170	155	20	g.	g.	NOUN
iajs-1170	155	21	9	9	NUM
iajs-1170	155	22	.	.	PUNCT
iajs-1170	156	1	rielly	rielly	PROPN
iajs-1170	156	2	,	,	PUNCT
iajs-1170	156	3	i.l	i.l	PROPN
iajs-1170	156	4	.	.	PROPN
iajs-1170	157	1	and	and	CCONJ
iajs-1170	157	2	m.k	m.k	INTJ
iajs-1170	157	3	.	.	PROPN
iajs-1170	157	4	,	,	PUNCT
iajs-1170	157	5	(	(	PUNCT
iajs-1170	157	6	1985	1985	NUM
iajs-1170	157	7	)	)	PUNCT
iajs-1170	157	8	,	,	PUNCT
iajs-1170	157	9	"	"	PUNCT
iajs-1170	157	10	on	on	ADP
iajs-1170	157	11	-continuity	-continuity	PROPN
iajs-1170	157	12	in	in	ADP
iajs-1170	157	13	topological	topological	ADJ
iajs-1170	157	14	saces	sace	NOUN
iajs-1170	157	15	"	"	PUNCT
iajs-1170	157	16	,	,	PUNCT
iajs-1170	157	17	acta	acta	PROPN
iajs-1170	157	18	mathematics	mathematics	PROPN
iajs-1170	157	19	hungarica,45	hungarica,45	NOUN
iajs-1170	157	20	.	.	PUNCT
iajs-1170	158	1	10	10	NUM
iajs-1170	158	2	.	.	X
iajs-1170	158	3	ali	ali	PROPN
iajs-1170	158	4	,	,	PUNCT
iajs-1170	158	5	n.m	n.m	PROPN
iajs-1170	158	6	.	.	PUNCT
iajs-1170	158	7	(	(	PUNCT
iajs-1170	158	8	2004),"on	2004),"on	PROPN
iajs-1170	158	9	new	new	ADJ
iajs-1170	158	10	types	type	NOUN
iajs-1170	158	11	of	of	ADP
iajs-1170	158	12	weakly	weakly	ADJ
iajs-1170	158	13	open	open	ADJ
iajs-1170	158	14	sets	set	NOUN
iajs-1170	158	15	"	"	PUNCT
iajs-1170	158	16	,	,	PUNCT
iajs-1170	158	17	m.sc.thesis	m.sc.thesis	NOUN
iajs-1170	158	18	,	,	PUNCT
iajs-1170	158	19	university	university	NOUN
iajs-1170	158	20	of	of	ADP
iajs-1170	158	21	baghdad	baghdad	PROPN
iajs-1170	158	22	.	.	PUNCT