id	sid	tid	token	lemma	pos
iajs-871	1	1	2011	2011	NUM
iajs-871	1	2	)	)	PUNCT
iajs-871	1	3	1	1	NUM
iajs-871	1	4	(	(	PUNCT
iajs-871	1	5	24المجلد	24المجلد	NUM
iajs-871	1	6	بیقیةالھیثم	بیقیةالھیثم	VERB
iajs-871	1	7	للعلوم	للعلوم	PROPN
iajs-871	1	8	الصرفة	الصرفة	PROPN
iajs-871	1	9	والتط	والتط	PROPN
iajs-871	1	10	بنا	بنا	VERB
iajs-871	1	11	مجلة	مجلة	VERB
iajs-871	2	1	-l	-l	PUNCT
iajs-871	2	2	فضاءات	فضاءات	NOUN
iajs-871	2	3	الرص	الرص	NOUN
iajs-871	2	4	من	من	PROPN
iajs-871	2	5	النوع	النوع	PROPN
iajs-871	2	6	سعاد	سعاد	ADP
iajs-871	2	7	جدعان	جدعان	ADJ
iajs-871	2	8	جامعة	جامعة	PROPN
iajs-871	2	9	بغداد	بغداد	PROPN
iajs-871	2	10	،	،	PROPN
iajs-871	2	11	ابن	ابن	PROPN
iajs-871	2	12	الهیثم	الهیثم	PROPN
iajs-871	2	13	-كلیة	-كلیة	PROPN
iajs-871	2	14	التربیة	التربیة	NOUN
iajs-871	2	15	،	،	NOUN
iajs-871	2	16	قسم	قسم	PROPN
iajs-871	3	1	الریاضیات	الریاضیات	NOUN
iajs-871	3	2	2010	2010	NUM
iajs-871	3	3	ایار	ایار	ADJ
iajs-871	3	4	25	25	NUM
iajs-871	3	5	في	في	NOUN
iajs-871	3	6	البحث	البحث	PROPN
iajs-871	3	7	استلم	استلم	PROPN
iajs-871	3	8	2010	2010	NUM
iajs-871	3	9	ایلول	ایلول	NOUN
iajs-871	3	10	27	27	NUM
iajs-871	3	11	في	في	ADP
iajs-871	3	12	البحث	البحث	ADV
iajs-871	3	13	قبل	قبل	PROPN
iajs-871	3	14	الخالصة	الخالصة	PROPN
iajs-871	3	15	ـة	ـة	AUX
iajs-871	3	16	أنــواع	أنــواع	PROPN
iajs-871	3	17	جدیــدة	جدیــدة	PROPN
iajs-871	3	18	مــن	مــن	PROPN
iajs-871	3	19	التــراص	التــراص	VERB
iajs-871	3	20	فــي	فــي	ADJ
iajs-871	3	21	الفضــاءات	الفضــاءات	PROPN
iajs-871	3	22	التبلوجیــه	التبلوجیــه	PROPN
iajs-871	3	23	الثنائیــة	الثنائیــة	PROPN
iajs-871	3	24	ســنقدم	ســنقدم	PROPN
iajs-871	3	25	التــراص	التــراص	VERB
iajs-871	3	26	مـــن	مـــن	PROPN
iajs-871	3	27	أذ	أذ	PROPN
iajs-871	3	28	،	،	PROPN
iajs-871	3	29	الغــرض	الغــرض	ADJ
iajs-871	3	30	مــن	مــن	PROPN
iajs-871	3	31	هــذا	هــذا	PROPN
iajs-871	3	32	البحــث	البحــث	PROPN
iajs-871	3	33	دراسـ	دراسـ	PROPN
iajs-871	3	34	ال	ال	ADP
iajs-871	3	35	-النوع	-النوع	PROPN
iajs-871	3	36	ibn	ibn	PROPN
iajs-871	3	37	alhaitham	alhaitham	NOUN
iajs-871	3	38	j.	j.	PROPN
iajs-871	4	1	fo	fo	ADP
iajs-871	4	2	r	r	NOUN
iajs-871	4	3	pure	pure	ADJ
iajs-871	4	4	&	&	CCONJ
iajs-871	4	5	appl	appl	PROPN
iajs-871	4	6	.	.	PUNCT
iajs-871	5	1	sc	sc	PROPN
iajs-871	5	2	i.	i.	PROPN
iajs-871	5	3	vo	vo	PROPN
iajs-871	5	4	l.24	l.24	PROPN
iajs-871	5	5	(	(	PUNCT
iajs-871	5	6	1	1	NUM
iajs-871	5	7	)	)	PUNCT
iajs-871	5	8	2011	2011	NUM
iajs-871	5	9	lcompact	lcompact	NOUN
iajs-871	5	10	spaces	space	NOUN
iajs-871	5	11	s.	s.	PROPN
iajs-871	5	12	gedaan	gedaan	PROPN
iajs-871	5	13	department	department	PROPN
iajs-871	5	14	of	of	ADP
iajs-871	5	15	mathematics	mathematics	PROPN
iajs-871	5	16	,	,	PUNCT
iajs-871	5	17	ibn	ibn	PROPN
iajs-871	5	18	-	-	PUNCT
iajs-871	5	19	al	al	PROPN
iajs-871	5	20	-	-	PUNCT
iajs-871	5	21	haitham	haitham	PROPN
iajs-871	5	22	college	college	PROPN
iajs-871	5	23	of	of	ADP
iajs-871	5	24	education	education	NOUN
iajs-871	5	25	,	,	PUNCT
iajs-871	5	26	university	university	PROPN
iajs-871	5	27	of	of	ADP
iajs-871	5	28	baghdad	baghdad	PROPN
iajs-871	5	29	received	receive	VERB
iajs-871	5	30	in	in	ADP
iajs-871	5	31	may,25,2010	may,25,2010	PROPN
iajs-871	5	32	accepted	accept	VERB
iajs-871	5	33	in	in	ADP
iajs-871	5	34	s	s	VERB
iajs-871	5	35	ept,27,2010	ept,27,2010	PROPN
iajs-871	5	36	abstract	abstract	ADJ
iajs-871	5	37	the	the	DET
iajs-871	5	38	purpose	purpose	NOUN
iajs-871	5	39	of	of	ADP
iajs-871	5	40	this	this	DET
iajs-871	5	41	paper	paper	NOUN
iajs-871	5	42	is	be	AUX
iajs-871	5	43	to	to	PART
iajs-871	5	44	study	study	VERB
iajs-871	5	45	a	a	DET
iajs-871	5	46	new	new	ADJ
iajs-871	5	47	types	type	NOUN
iajs-871	5	48	of	of	ADP
iajs-871	5	49	compactness	compactness	NOUN
iajs-871	5	50	in	in	ADP
iajs-871	5	51	bitopological	bitopological	ADJ
iajs-871	5	52	spaces	space	NOUN
iajs-871	5	53	.	.	PUNCT
iajs-871	6	1	we	we	PRON
iajs-871	6	2	shall	shall	AUX
iajs-871	6	3	introduce	introduce	VERB
iajs-871	6	4	the	the	DET
iajs-871	6	5	concepts	concept	NOUN
iajs-871	6	6	of	of	ADP
iajs-871	6	7	lcompactness	lcompactness	NOUN
iajs-871	6	8	.	.	PUNCT
iajs-871	7	1	introduction	introduction	NOUN
iajs-871	7	2	the	the	DET
iajs-871	7	3	concept	concept	NOUN
iajs-871	7	4	of	of	ADP
iajs-871	7	5	bitopological	bitopological	ADJ
iajs-871	7	6	space	space	NOUN
iajs-871	7	7	was	be	AUX
iajs-871	7	8	initiated	initiate	VERB
iajs-871	7	9	by	by	ADP
iajs-871	7	10	kelly[1].a	kelly[1].a	NOUN
iajs-871	7	11	set	set	NOUN
iajs-871	7	12	x	x	NUM
iajs-871	7	13	equipped	equip	VERB
iajs-871	7	14	with	with	ADP
iajs-871	7	15	two	two	NUM
iajs-871	7	16	topologies	topology	NOUN
iajs-871	7	17	and	and	PROPN
iajs-871	7	18	2	2	NUM
iajs-871	7	19	is	be	AUX
iajs-871	7	20	called	call	VERB
iajs-871	7	21	a	a	DET
iajs-871	7	22	bitopological	bitopological	ADJ
iajs-871	7	23	space	space	NOUN
iajs-871	7	24	denoted	denote	VERB
iajs-871	7	25	by	by	ADP
iajs-871	7	26	.	.	PUNCT
iajs-871	8	1	by	by	ADP
iajs-871	8	2	a	a	DET
iajs-871	8	3	directed	direct	VERB
iajs-871	8	4	set	set	NOUN
iajs-871	8	5	we	we	PRON
iajs-871	8	6	mean	mean	VERB
iajs-871	8	7	a	a	DET
iajs-871	8	8	pair	pair	NOUN
iajs-871	8	9	(	(	PUNCT
iajs-871	8	10	a	a	PRON
iajs-871	8	11	,	,	PUNCT
iajs-871	8	12			NUM
iajs-871	8	13	)	)	PUNCT
iajs-871	8	14	consisting	consist	VERB
iajs-871	8	15	of	of	ADP
iajs-871	8	16	a	a	DET
iajs-871	8	17	non	non	ADJ
iajs-871	8	18	-	-	ADJ
iajs-871	8	19	empty	empty	ADJ
iajs-871	8	20	set	set	NOUN
iajs-871	8	21	a	a	PRON
iajs-871	8	22	and	and	CCONJ
iajs-871	8	23	a	a	DET
iajs-871	8	24	binary	binary	ADJ
iajs-871	8	25	relation	relation	NOUN
iajs-871	8	26			NUM
iajs-871	8	27	defined	define	VERB
iajs-871	8	28	on	on	ADP
iajs-871	8	29	a	a	PRON
iajs-871	8	30	and	and	CCONJ
iajs-871	8	31	satisfies	satisfy	VERB
iajs-871	8	32	the	the	DET
iajs-871	8	33	following	follow	VERB
iajs-871	8	34	conditions	condition	NOUN
iajs-871	8	35	:	:	PUNCT
iajs-871	8	36	(	(	PUNCT
iajs-871	8	37	1	1	X
iajs-871	8	38	)	)	PUNCT
iajs-871	8	39	a	a	DET
iajs-871	8	40			NUM
iajs-871	8	41	a	a	DET
iajs-871	8	42	for	for	ADP
iajs-871	8	43	each	each	PRON
iajs-871	8	44	a	a	DET
iajs-871	8	45			PROPN
iajs-871	8	46	a.	a.	NOUN
iajs-871	8	47	(	(	PUNCT
iajs-871	8	48	2	2	NUM
iajs-871	8	49	)	)	PUNCT
iajs-871	8	50	if	if	SCONJ
iajs-871	8	51	a	a	DET
iajs-871	8	52			NUM
iajs-871	8	53	b	b	NOUN
iajs-871	8	54	and	and	CCONJ
iajs-871	8	55	b	b	NOUN
iajs-871	8	56			NUM
iajs-871	8	57	c	c	PROPN
iajs-871	8	58	,	,	PUNCT
iajs-871	8	59	then	then	ADV
iajs-871	8	60	a	a	DET
iajs-871	8	61			NUM
iajs-871	8	62	c	c	NOUN
iajs-871	8	63	for	for	ADP
iajs-871	8	64	each	each	DET
iajs-871	8	65	a	a	DET
iajs-871	8	66	,	,	PUNCT
iajs-871	8	67	b	b	NOUN
iajs-871	8	68	,	,	PUNCT
iajs-871	8	69	and	and	CCONJ
iajs-871	8	70	c	c	X
iajs-871	8	71	in	in	ADP
iajs-871	8	72	a.	a.	NOUN
iajs-871	8	73	(	(	PUNCT
iajs-871	8	74	3	3	NUM
iajs-871	8	75	)	)	PUNCT
iajs-871	8	76	for	for	ADP
iajs-871	8	77	each	each	DET
iajs-871	8	78	two	two	NUM
iajs-871	8	79	members	member	NOUN
iajs-871	8	80	a	a	PRON
iajs-871	8	81	and	and	CCONJ
iajs-871	8	82	b	b	NOUN
iajs-871	8	83	of	of	ADP
iajs-871	8	84	a	a	PRON
iajs-871	8	85	,	,	PUNCT
iajs-871	8	86	there	there	PRON
iajs-871	8	87	exists	exist	VERB
iajs-871	8	88	a	a	DET
iajs-871	8	89	member	member	NOUN
iajs-871	8	90	c	c	PROPN
iajs-871	8	91			PROPN
iajs-871	8	92	a	a	DET
iajs-871	8	93	such	such	ADJ
iajs-871	8	94	that	that	SCONJ
iajs-871	8	95	c	c	PROPN
iajs-871	8	96			NUM
iajs-871	8	97	a	a	PRON
iajs-871	8	98	and	and	CCONJ
iajs-871	8	99	c	c	NOUN
iajs-871	8	100	b	b	NOUN
iajs-871	8	101	.	.	PUNCT
iajs-871	9	1	if	if	SCONJ
iajs-871	9	2	(	(	PUNCT
iajs-871	9	3	a	a	DET
iajs-871	9	4	,	,	PUNCT
iajs-871	9	5			NUM
iajs-871	9	6	)	)	PUNCT
iajs-871	9	7	is	be	AUX
iajs-871	9	8	a	a	DET
iajs-871	9	9	directed	direct	VERB
iajs-871	9	10	set	set	NOUN
iajs-871	9	11	and	and	CCONJ
iajs-871	9	12	f	f	PROPN
iajs-871	9	13	is	be	AUX
iajs-871	9	14	a	a	DET
iajs-871	9	15	function	function	NOUN
iajs-871	9	16	of	of	ADP
iajs-871	9	17	a	a	PRON
iajs-871	9	18	into	into	ADP
iajs-871	9	19	a	a	DET
iajs-871	9	20	non	non	ADJ
iajs-871	9	21	-	-	ADJ
iajs-871	9	22	empty	empty	ADJ
iajs-871	9	23	set	set	NOUN
iajs-871	9	24	x	x	NOUN
iajs-871	9	25	,	,	PUNCT
iajs-871	9	26	then	then	ADV
iajs-871	9	27	f	f	PROPN
iajs-871	9	28	is	be	AUX
iajs-871	9	29	called	call	VERB
iajs-871	9	30	a	a	DET
iajs-871	9	31	"	"	PUNCT
iajs-871	9	32	net	net	NOUN
iajs-871	9	33	"	"	PUNCT
iajs-871	9	34	in	in	ADP
iajs-871	9	35	x	x	PUNCT
iajs-871	9	36	and	and	CCONJ
iajs-871	9	37	is	be	AUX
iajs-871	9	38	denoted	denote	VERB
iajs-871	9	39	by	by	ADP
iajs-871	9	40	(	(	PUNCT
iajs-871	9	41	f	f	X
iajs-871	9	42	,	,	PUNCT
iajs-871	9	43	x	x	X
iajs-871	9	44	,	,	PUNCT
iajs-871	9	45	a	a	PRON
iajs-871	9	46	,	,	PUNCT
iajs-871	9	47			NUM
iajs-871	9	48	)	)	PUNCT
iajs-871	9	49	.	.	PUNCT
iajs-871	10	1	the	the	DET
iajs-871	10	2	image	image	NOUN
iajs-871	10	3	of	of	ADP
iajs-871	10	4	a	a	DET
iajs-871	10	5			NOUN
iajs-871	10	6	a	a	PRON
iajs-871	10	7	under	under	PROPN
iajs-871	10	8	f	f	PROPN
iajs-871	10	9	is	be	AUX
iajs-871	10	10	denoted	denote	VERB
iajs-871	10	11	by	by	ADP
iajs-871	10	12	fa	fa	PROPN
iajs-871	10	13	and	and	CCONJ
iajs-871	10	14	a	a	DET
iajs-871	10	15	net	net	NOUN
iajs-871	10	16	in	in	ADP
iajs-871	10	17	x	x	X
iajs-871	10	18	will	will	AUX
iajs-871	10	19	be	be	AUX
iajs-871	10	20	sometimes	sometimes	ADV
iajs-871	10	21	denoted	denote	VERB
iajs-871	10	22	by	by	ADP
iajs-871	10	23	{	{	PUNCT
iajs-871	10	24	fa	fa	NOUN
iajs-871	10	25	:	:	PUNCT
iajs-871	10	26	a	a	DET
iajs-871	10	27			NOUN
iajs-871	10	28	a}.[2	a}.[2	NOUN
iajs-871	10	29	]	]	PUNCT
iajs-871	10	30	a	a	DET
iajs-871	10	31	"	"	PUNCT
iajs-871	10	32	filter	filter	NOUN
iajs-871	10	33	"	"	PUNCT
iajs-871	10	34	on	on	ADP
iajs-871	10	35	a	a	DET
iajs-871	10	36	non	non	ADJ
iajs-871	10	37	-	-	ADJ
iajs-871	10	38	empty	empty	ADJ
iajs-871	10	39	set	set	NOUN
iajs-871	10	40	x	x	PUNCT
iajs-871	10	41	is	be	AUX
iajs-871	10	42	a	a	DET
iajs-871	10	43	non	non	ADJ
iajs-871	10	44	-	-	ADJ
iajs-871	10	45	empty	empty	ADJ
iajs-871	10	46	family	family	NOUN
iajs-871	10	47	f	f	PROPN
iajs-871	10	48	of	of	ADP
iajs-871	10	49	subsets	subset	NOUN
iajs-871	10	50	of	of	ADP
iajs-871	10	51	x	x	PUNCT
iajs-871	10	52	with	with	ADP
iajs-871	10	53	the	the	DET
iajs-871	10	54	following	follow	VERB
iajs-871	10	55	properties	property	NOUN
iajs-871	10	56	:	:	PUNCT
iajs-871	10	57	(	(	PUNCT
iajs-871	10	58	1	1	X
iajs-871	10	59	)	)	PUNCT
iajs-871	10	60			PROPN
iajs-871	10	61			PROPN
iajs-871	10	62	f.	f.	PROPN
iajs-871	10	63	(	(	PUNCT
iajs-871	10	64	2	2	NUM
iajs-871	10	65	)	)	PUNCT
iajs-871	10	66	if	if	SCONJ
iajs-871	10	67	f	f	PROPN
iajs-871	10	68			PROPN
iajs-871	10	69	f	f	PROPN
iajs-871	10	70	and	and	CCONJ
iajs-871	10	71	f	f	PROPN
iajs-871	10	72			PROPN
iajs-871	10	73	h	h	PROPN
iajs-871	10	74	,	,	PUNCT
iajs-871	10	75	then	then	ADV
iajs-871	10	76	h	h	PROPN
iajs-871	10	77			PROPN
iajs-871	10	78	f.	f.	PROPN
iajs-871	10	79	(	(	PUNCT
iajs-871	10	80	3	3	NUM
iajs-871	10	81	)	)	PUNCT
iajs-871	10	82	if	if	SCONJ
iajs-871	10	83	f	f	PROPN
iajs-871	10	84			PROPN
iajs-871	10	85	f	f	PROPN
iajs-871	10	86	and	and	CCONJ
iajs-871	10	87	h	h	PROPN
iajs-871	11	1			NOUN
iajs-871	11	2	f	f	X
iajs-871	11	3	,	,	PUNCT
iajs-871	11	4	then	then	ADV
iajs-871	11	5	f	f	PROPN
iajs-871	11	6			PUNCT
iajs-871	11	7	h	h	PROPN
iajs-871	11	8			PROPN
iajs-871	11	9	f.	f.	PROPN
iajs-871	12	1	a	a	DET
iajs-871	12	2	filter	filter	NOUN
iajs-871	12	3	on	on	ADP
iajs-871	12	4	a	a	DET
iajs-871	12	5	non	non	ADJ
iajs-871	12	6	-	-	ADJ
iajs-871	12	7	empty	empty	ADJ
iajs-871	12	8	set	set	NOUN
iajs-871	12	9	is	be	AUX
iajs-871	12	10	said	say	VERB
iajs-871	12	11	to	to	PART
iajs-871	12	12	be	be	AUX
iajs-871	12	13	an	an	DET
iajs-871	12	14	ultrafilter	ultrafilter	NOUN
iajs-871	12	15	if	if	NOUN
iajs-871	12	16	and	and	CCONJ
iajs-871	12	17	only	only	ADV
iajs-871	12	18	if	if	SCONJ
iajs-871	12	19	it	it	PRON
iajs-871	12	20	is	be	AUX
iajs-871	12	21	not	not	PART
iajs-871	12	22	properly	properly	ADV
iajs-871	12	23	contained	contain	VERB
iajs-871	12	24	in	in	ADP
iajs-871	12	25	any	any	DET
iajs-871	12	26	other	other	ADJ
iajs-871	12	27	filter	filter	NOUN
iajs-871	12	28	on	on	ADP
iajs-871	12	29	this	this	DET
iajs-871	12	30	set.[2	set.[2	NOUN
iajs-871	12	31	]	]	X
iajs-871	12	32	ibn	ibn	NOUN
iajs-871	12	33	alhaitham	alhaitham	NOUN
iajs-871	13	1	j.	j.	PROPN
iajs-871	14	1	fo	fo	ADP
iajs-871	14	2	r	r	NOUN
iajs-871	14	3	pure	pure	ADJ
iajs-871	14	4	&	&	CCONJ
iajs-871	14	5	appl	appl	PROPN
iajs-871	14	6	.	.	PUNCT
iajs-871	15	1	sc	sc	PROPN
iajs-871	15	2	i.	i.	PROPN
iajs-871	15	3	vo	vo	PROPN
iajs-871	16	1	l.24	l.24	PROPN
iajs-871	16	2	(	(	PUNCT
iajs-871	16	3	1	1	NUM
iajs-871	16	4	)	)	PUNCT
iajs-871	16	5	2011	2011	NUM
iajs-871	16	6	l	l	NOUN
iajs-871	16	7	-	-	ADJ
iajs-871	16	8	open	open	ADJ
iajs-871	16	9	set	set	NOUN
iajs-871	16	10	was	be	AUX
iajs-871	16	11	studied	study	VERB
iajs-871	16	12	by	by	ADP
iajs-871	16	13	al	al	PROPN
iajs-871	16	14	-	-	PUNCT
iajs-871	16	15	swid[2	swid[2	PROPN
iajs-871	16	16	]	]	PUNCT
iajs-871	16	17	,	,	PUNCT
iajs-871	16	18	asubset	asubset	VERB
iajs-871	16	19	g	g	NOUN
iajs-871	16	20	of	of	ADP
iajs-871	16	21	a	a	DET
iajs-871	16	22	bitopological	bitopological	ADJ
iajs-871	16	23	space	space	NOUN
iajs-871	16	24	is	be	AUX
iajs-871	16	25	said	say	VERB
iajs-871	16	26	to	to	PART
iajs-871	16	27	be	be	AUX
iajs-871	16	28	“	"	PUNCT
iajs-871	16	29	l	l	NOUN
iajs-871	16	30	–	–	PUNCT
iajs-871	16	31	open	open	ADJ
iajs-871	16	32	”	"	PUNCT
iajs-871	16	33	set	set	VERB
iajs-871	16	34	if	if	SCONJ
iajs-871	16	35	and	and	CCONJ
iajs-871	16	36	only	only	ADV
iajs-871	16	37	if	if	SCONJ
iajs-871	16	38	there	there	PRON
iajs-871	16	39	exists	exist	VERB
iajs-871	16	40	a	a	DET
iajs-871	16	41	-open	-open	ADJ
iajs-871	16	42	set	set	VERB
iajs-871	16	43	u	u	NOUN
iajs-871	16	44	such	such	ADJ
iajs-871	16	45	that	that	SCONJ
iajs-871	16	46			PROPN
iajs-871	16	47	uclgu	uclgu	PROPN
iajs-871	16	48	2	2	NUM
iajs-871	16	49	,	,	PUNCT
iajs-871	16	50	the	the	DET
iajs-871	16	51	family	family	NOUN
iajs-871	16	52	of	of	ADP
iajs-871	16	53	all	all	DET
iajs-871	16	54	l	l	ADJ
iajs-871	16	55	-	-	ADJ
iajs-871	16	56	open	open	ADJ
iajs-871	16	57	subsets	subset	NOUN
iajs-871	16	58	of	of	ADP
iajs-871	16	59	x	x	PROPN
iajs-871	16	60	is	be	AUX
iajs-871	16	61	denoted	denote	VERB
iajs-871	16	62	by	by	ADP
iajs-871	16	63	l	l	NOUN
iajs-871	16	64	-	-	ADJ
iajs-871	16	65	o(x).the	o(x).the	PRON
iajs-871	16	66	complement	complement	NOUN
iajs-871	16	67	of	of	ADP
iajs-871	16	68	an	an	DET
iajs-871	16	69	l	l	NOUN
iajs-871	16	70	-	-	ADJ
iajs-871	16	71	open	open	ADJ
iajs-871	16	72	set	set	NOUN
iajs-871	16	73	is	be	AUX
iajs-871	16	74	called	call	VERB
iajs-871	16	75	“	"	PUNCT
iajs-871	16	76	l	l	NOUN
iajs-871	16	77	-	-	ADJ
iajs-871	16	78	closed	closed	ADJ
iajs-871	16	79	”	"	PUNCT
iajs-871	16	80	set	set	NOUN
iajs-871	16	81	,	,	PUNCT
iajs-871	16	82	the	the	DET
iajs-871	16	83	family	family	NOUN
iajs-871	16	84	of	of	ADP
iajs-871	16	85	all	all	DET
iajs-871	16	86	l	l	ADJ
iajs-871	16	87	-	-	ADJ
iajs-871	16	88	closed	closed	ADJ
iajs-871	16	89	subsets	subset	NOUN
iajs-871	16	90	of	of	ADP
iajs-871	16	91	x	x	PROPN
iajs-871	16	92	is	be	AUX
iajs-871	16	93	denoted	denote	VERB
iajs-871	16	94	by	by	ADP
iajs-871	16	95	l	l	NOUN
iajs-871	16	96	-	-	VERB
iajs-871	16	97	c(x).in	c(x).in	VERB
iajs-871	16	98	a	a	DET
iajs-871	16	99	bitopological	bitopological	ADJ
iajs-871	16	100	space	space	NOUN
iajs-871	16	101	every	every	DET
iajs-871	16	102	-open	-open	NOUN
iajs-871	16	103	set	set	NOUN
iajs-871	16	104	is	be	AUX
iajs-871	16	105	an	an	DET
iajs-871	16	106	l	l	NOUN
iajs-871	16	107	-	-	ADJ
iajs-871	16	108	open	open	ADJ
iajs-871	16	109	set[3].the	set[3].the	PROPN
iajs-871	16	110	union	union	NOUN
iajs-871	16	111	of	of	ADP
iajs-871	16	112	any	any	DET
iajs-871	16	113	family	family	NOUN
iajs-871	16	114	of	of	ADP
iajs-871	16	115	l	l	ADJ
iajs-871	16	116	-	-	ADJ
iajs-871	16	117	open	open	ADJ
iajs-871	16	118	subsets	subset	NOUN
iajs-871	16	119	of	of	ADP
iajs-871	16	120	x	x	X
iajs-871	16	121	is	be	AUX
iajs-871	16	122	an	an	DET
iajs-871	16	123	l	l	NOUN
iajs-871	16	124	-	-	ADJ
iajs-871	16	125	open	open	ADJ
iajs-871	16	126	set	set	NOUN
iajs-871	16	127	,	,	PUNCT
iajs-871	16	128	but	but	CCONJ
iajs-871	16	129	the	the	DET
iajs-871	16	130	intersection	intersection	NOUN
iajs-871	16	131	of	of	ADP
iajs-871	16	132	any	any	DET
iajs-871	16	133	two	two	NUM
iajs-871	16	134	l	l	ADJ
iajs-871	16	135	-	-	ADJ
iajs-871	16	136	open	open	ADJ
iajs-871	16	137	subsets	subset	NOUN
iajs-871	16	138	of	of	ADP
iajs-871	16	139	x	x	PUNCT
iajs-871	16	140	need	need	AUX
iajs-871	16	141	not	not	PART
iajs-871	16	142	be	be	AUX
iajs-871	16	143	l	l	NOUN
iajs-871	16	144	-	-	ADJ
iajs-871	16	145	open	open	ADJ
iajs-871	16	146	set[2].al	set[2].al	PROPN
iajs-871	16	147	-	-	PUNCT
iajs-871	16	148	talkahny	talkahny	NOUN
iajs-871	17	1	[	[	X
iajs-871	17	2	3],introduced	3],introduce	VERB
iajs-871	17	3	two	two	NUM
iajs-871	17	4	new	new	ADJ
iajs-871	17	5	concepts	concept	NOUN
iajs-871	17	6	“	"	PUNCT
iajs-871	17	7	l2	l2	VERB
iajs-871	17	8	t	t	NOUN
iajs-871	17	9	-spaces	-space	NOUN
iajs-871	17	10	”	"	PUNCT
iajs-871	17	11	and	and	CCONJ
iajs-871	17	12	“	"	PUNCT
iajs-871	17	13	l	l	ADJ
iajs-871	17	14	-	-	ADJ
iajs-871	17	15	continuous	continuous	ADJ
iajs-871	17	16	functions	function	NOUN
iajs-871	17	17	”	"	PUNCT
iajs-871	17	18	.	.	PUNCT
iajs-871	18	1	a	a	DET
iajs-871	18	2	bitopological	bitopological	ADJ
iajs-871	18	3	space	space	NOUN
iajs-871	18	4	is	be	AUX
iajs-871	18	5	said	say	VERB
iajs-871	18	6	to	to	PART
iajs-871	18	7	be	be	AUX
iajs-871	18	8	“	"	PUNCT
iajs-871	18	9	l2	l2	NOUN
iajs-871	18	10	t	t	NOUN
iajs-871	18	11	-space	-space	NOUN
iajs-871	18	12	”	"	PUNCT
iajs-871	18	13	if	if	SCONJ
iajs-871	18	14	and	and	CCONJ
iajs-871	18	15	only	only	ADV
iajs-871	18	16	if	if	SCONJ
iajs-871	18	17	for	for	ADP
iajs-871	18	18	each	each	DET
iajs-871	18	19	pair	pair	NOUN
iajs-871	18	20	of	of	ADP
iajs-871	18	21	distinct	distinct	ADJ
iajs-871	18	22	points	point	NOUN
iajs-871	18	23	x	x	PUNCT
iajs-871	18	24	and	and	CCONJ
iajs-871	18	25	y	y	PROPN
iajs-871	18	26	in	in	ADP
iajs-871	18	27	x	x	SYM
iajs-871	18	28	,	,	PUNCT
iajs-871	18	29	there	there	PRON
iajs-871	18	30	exist	exist	VERB
iajs-871	18	31	two	two	NUM
iajs-871	18	32	disjoint	disjoint	NOUN
iajs-871	18	33	l	l	ADJ
iajs-871	18	34	-	-	ADJ
iajs-871	18	35	open	open	ADJ
iajs-871	18	36	subset	subset	NOUN
iajs-871	18	37	g	g	NOUN
iajs-871	18	38	and	and	CCONJ
iajs-871	18	39	h	h	NOUN
iajs-871	18	40	of	of	ADP
iajs-871	18	41	x	x	INTJ
iajs-871	18	42	such	such	ADJ
iajs-871	18	43	that	that	SCONJ
iajs-871	18	44	gx	gx	VERB
iajs-871	18	45	and	and	CCONJ
iajs-871	18	46	hy	hy	NOUN
iajs-871	18	47	.let	.let	PUNCT
iajs-871	19	1			NOUN
iajs-871	19	2			NOUN
iajs-871	19	3	21	21	NUM
iajs-871	19	4	,	,	PUNCT
iajs-871	19	5	,	,	PUNCT
iajs-871	19	6	x	x	SYM
iajs-871	19	7	,	,	PUNCT
iajs-871	19	8			PROPN
iajs-871	19	9			NOUN
iajs-871	19	10			PRON
iajs-871	19	11			PROPN
iajs-871	19	12			PROPN
iajs-871	19	13			NOUN
iajs-871	19	14			PROPN
iajs-871	19	15			NOUN
iajs-871	19	16	21	21	NUM
iajs-871	19	17	,	,	PUNCT
iajs-871	19	18	,	,	PUNCT
iajs-871	19	19	y	y	PROPN
iajs-871	19	20	be	be	VERB
iajs-871	19	21	any	any	DET
iajs-871	19	22	bitopological	bitopological	ADJ
iajs-871	19	23	spaces	space	NOUN
iajs-871	19	24	and	and	CCONJ
iajs-871	19	25	let	let	VERB
iajs-871	19	26	yxf	yxf	PRON
iajs-871	19	27			NOUN
iajs-871	19	28	:	:	PUNCT
iajs-871	19	29	be	be	AUX
iajs-871	19	30	any	any	DET
iajs-871	19	31	function	function	NOUN
iajs-871	19	32	,	,	PUNCT
iajs-871	19	33	then	then	ADV
iajs-871	19	34	f	f	PROPN
iajs-871	19	35	is	be	AUX
iajs-871	19	36	said	say	VERB
iajs-871	19	37	to	to	PART
iajs-871	19	38	be	be	AUX
iajs-871	19	39	“	"	PUNCT
iajs-871	19	40	l	l	ADJ
iajs-871	19	41	-	-	ADJ
iajs-871	19	42	continuous	continuous	ADJ
iajs-871	19	43	”	"	PUNCT
iajs-871	19	44	function	function	NOUN
iajs-871	19	45	if	if	SCONJ
iajs-871	19	46	and	and	CCONJ
iajs-871	19	47	only	only	ADV
iajs-871	19	48	if	if	SCONJ
iajs-871	19	49	the	the	DET
iajs-871	19	50	inverse	inverse	ADJ
iajs-871	19	51	image	image	NOUN
iajs-871	19	52	of	of	ADP
iajs-871	19	53	any	any	DET
iajs-871	19	54	l	l	NOUN
iajs-871	19	55	-	-	ADJ
iajs-871	19	56	open	open	ADJ
iajs-871	19	57	subset	subset	NOUN
iajs-871	19	58	of	of	ADP
iajs-871	19	59	y	y	PROPN
iajs-871	19	60	is	be	AUX
iajs-871	19	61	an	an	DET
iajs-871	19	62	l	l	NOUN
iajs-871	19	63	-	-	ADJ
iajs-871	19	64	open	open	ADJ
iajs-871	19	65	subset	subset	NOUN
iajs-871	19	66	of	of	ADP
iajs-871	19	67	x.	x.	NOUN
iajs-871	19	68	2l	2l	NUM
iajs-871	19	69	-	-	PUNCT
iajs-871	19	70	compactness	compactness	NOUN
iajs-871	19	71	definition(2.1	definition(2.1	NOUN
iajs-871	19	72	)	)	PUNCT
iajs-871	19	73	let	let	AUX
iajs-871	19	74	be	be	AUX
iajs-871	19	75	a	a	DET
iajs-871	19	76	bitopological	bitopological	ADJ
iajs-871	19	77	space	space	NOUN
iajs-871	19	78	and	and	CCONJ
iajs-871	19	79	let	let	VERB
iajs-871	19	80	a	a	PRON
iajs-871	19	81	be	be	AUX
iajs-871	19	82	a	a	DET
iajs-871	19	83	subset	subset	NOUN
iajs-871	19	84	of	of	ADP
iajs-871	19	85	x.	x.	NOUN
iajs-871	19	86	by	by	ADP
iajs-871	19	87	an	an	DET
iajs-871	19	88	“	"	PUNCT
iajs-871	19	89	l	l	ADJ
iajs-871	19	90	-	-	ADJ
iajs-871	19	91	open	open	ADJ
iajs-871	19	92	cover	cover	NOUN
iajs-871	19	93	of	of	ADP
iajs-871	19	94	a	a	PRON
iajs-871	19	95	”	"	PUNCT
iajs-871	19	96	we	we	PRON
iajs-871	19	97	mean	mean	VERB
iajs-871	19	98	a	a	DET
iajs-871	19	99	subcollection	subcollection	NOUN
iajs-871	19	100	of	of	ADP
iajs-871	19	101	the	the	DET
iajs-871	19	102	family	family	NOUN
iajs-871	19	103	l	l	PROPN
iajs-871	19	104	-	-	PROPN
iajs-871	19	105	o(x	o(x	PROPN
iajs-871	19	106	)	)	PUNCT
iajs-871	19	107	which	which	PRON
iajs-871	19	108	covers	cover	VERB
iajs-871	19	109	a.	a.	NOUN
iajs-871	19	110	remark(2.2	remark(2.2	NOUN
iajs-871	19	111	):	):	PUNCT
iajs-871	19	112	every	every	DET
iajs-871	19	113	-open	-open	ADJ
iajs-871	19	114	cover	cover	NOUN
iajs-871	19	115	in	in	ADP
iajs-871	19	116	a	a	DET
iajs-871	19	117	bitopological	bitopological	ADJ
iajs-871	19	118	space	space	NOUN
iajs-871	19	119	is	be	AUX
iajs-871	19	120	an	an	DET
iajs-871	19	121	l	l	NOUN
iajs-871	19	122	-	-	ADJ
iajs-871	19	123	open	open	ADJ
iajs-871	19	124	cover	cover	NOUN
iajs-871	19	125	.	.	PUNCT
iajs-871	20	1	the	the	DET
iajs-871	20	2	converse	converse	NOUN
iajs-871	20	3	of	of	ADP
iajs-871	20	4	remark	remark	NOUN
iajs-871	20	5	(	(	PUNCT
iajs-871	20	6	2.2	2.2	NUM
iajs-871	20	7	)	)	PUNCT
iajs-871	20	8	is	be	AUX
iajs-871	20	9	not	not	PART
iajs-871	20	10	true	true	ADJ
iajs-871	20	11	in	in	ADP
iajs-871	20	12	general	general	ADJ
iajs-871	20	13	as	as	SCONJ
iajs-871	20	14	the	the	DET
iajs-871	20	15	following	follow	VERB
iajs-871	20	16	example	example	NOUN
iajs-871	20	17	shows	show	VERB
iajs-871	20	18	:	:	PUNCT
iajs-871	20	19	example	example	NOUN
iajs-871	20	20	(	(	PUNCT
iajs-871	20	21	2.3	2.3	NUM
iajs-871	20	22	)	)	PUNCT
iajs-871	20	23			PROPN
iajs-871	21	1			PROPN
iajs-871	22	1			PROPN
iajs-871	22	2			PROPN
iajs-871	22	3			PROPN
iajs-871	22	4			PROPN
iajs-871	22	5			NOUN
iajs-871	22	6			PROPN
iajs-871	22	7			NOUN
iajs-871	22	8			PROPN
iajs-871	22	9			PROPN
iajs-871	22	10			ADV
iajs-871	22	11	4,3,2,,f	4,3,2,,f	PROPN
iajs-871	22	12	1	1	NUM
iajs-871	22	13	,	,	PUNCT
iajs-871	22	14	,	,	PUNCT
iajs-871	22	15	3,2,1,3,2,1	3,2,1,3,2,1	NUM
iajs-871	22	16	,	,	PUNCT
iajs-871	22	17	,	,	PUNCT
iajs-871	22	18	4,3,2,1	4,3,2,1	NUM
iajs-871	22	19	2	2	NUM
iajs-871	22	20	2	2	NUM
iajs-871	22	21	1	1	NUM
iajs-871	22	22			NOUN
iajs-871	22	23			NOUN
iajs-871	22	24			NOUN
iajs-871	22	25			NOUN
iajs-871	22	26			NOUN
iajs-871	22	27	x	x	NOUN
iajs-871	22	28	x	x	PUNCT
iajs-871	22	29	x	x	PUNCT
iajs-871	22	30	x	x	PUNCT
iajs-871	22	31			NOUN
iajs-871	22	32			NUM
iajs-871	22	33			NUM
iajs-871	22	34			ADJ
iajs-871	22	35			NOUN
iajs-871	23	1			PUNCT
iajs-871	24	1			PROPN
iajs-871	25	1			PROPN
iajs-871	25	2			PROPN
iajs-871	25	3			PROPN
iajs-871	25	4			PROPN
iajs-871	25	5			PROPN
iajs-871	25	6			PROPN
iajs-871	25	7			PROPN
iajs-871	25	8			PROPN
iajs-871	25	9			PROPN
iajs-871	25	10			PROPN
iajs-871	25	11			PROPN
iajs-871	25	12			PROPN
iajs-871	25	13			PROPN
iajs-871	25	14			PROPN
iajs-871	25	15			PROPN
iajs-871	25	16			PROPN
iajs-871	26	1			NOUN
iajs-871	26	2	4,3,2,3,1,4,3,1,2,1,4,1,4,2,1,3,2,1,3,2,1,,xxol	4,3,2,3,1,4,3,1,2,1,4,1,4,2,1,3,2,1,3,2,1,,xxol	NOUN
iajs-871	26	3			PROPN
iajs-871	26	4	l	l	X
iajs-871	26	5	et	et	NOUN
iajs-871	26	6			PROPN
iajs-871	26	7			PROPN
iajs-871	26	8			PROPN
iajs-871	26	9			NOUN
iajs-871	26	10	4,3,2,1c	4,3,2,1c	NOUN
iajs-871	26	11	,	,	PUNCT
iajs-871	26	12	note	note	VERB
iajs-871	26	13	that	that	SCONJ
iajs-871	26	14	c	c	PROPN
iajs-871	26	15	is	be	AUX
iajs-871	26	16	an	an	DET
iajs-871	26	17	l	l	NOUN
iajs-871	26	18	-	-	ADJ
iajs-871	26	19	open	open	ADJ
iajs-871	26	20	cover	cover	NOUN
iajs-871	26	21	of	of	ADP
iajs-871	26	22	x	x	PRON
iajs-871	26	23	,	,	PUNCT
iajs-871	26	24	but	but	CCONJ
iajs-871	26	25	it	it	PRON
iajs-871	26	26	is	be	AUX
iajs-871	26	27	not	not	PART
iajs-871	26	28	-open	-open	ADJ
iajs-871	26	29	cover	cover	NOUN
iajs-871	26	30	.	.	PUNCT
iajs-871	27	1	definition(2.4	definition(2.4	NOUN
iajs-871	27	2	)	)	PUNCT
iajs-871	27	3	a	a	DET
iajs-871	27	4	bitopological	bitopological	ADJ
iajs-871	27	5	space	space	NOUN
iajs-871	27	6	is	be	AUX
iajs-871	27	7	said	say	VERB
iajs-871	27	8	to	to	PART
iajs-871	27	9	be	be	AUX
iajs-871	27	10	“	"	PUNCT
iajs-871	27	11	l	l	ADJ
iajs-871	27	12	-	-	ADJ
iajs-871	27	13	compact	compact	ADJ
iajs-871	27	14	space	space	NOUN
iajs-871	27	15	”	"	PUNCT
iajs-871	27	16	if	if	SCONJ
iajs-871	27	17	and	and	CCONJ
iajs-871	27	18	only	only	ADV
iajs-871	27	19	if	if	SCONJ
iajs-871	27	20	every	every	DET
iajs-871	27	21	lopen	lopen	ADJ
iajs-871	27	22	cover	cover	NOUN
iajs-871	27	23	of	of	ADP
iajs-871	27	24	x	x	PUNCT
iajs-871	27	25	has	have	VERB
iajs-871	27	26	a	a	DET
iajs-871	27	27	finit	finit	PROPN
iajs-871	27	28	subcover	subcover	PROPN
iajs-871	27	29	.	.	PUNCT
iajs-871	28	1	proposition	proposition	NOUN
iajs-871	28	2	(	(	PUNCT
iajs-871	28	3	2.5	2.5	NUM
iajs-871	28	4	)	)	PUNCT
iajs-871	28	5	ibn	ibn	PROPN
iajs-871	28	6	alhaitham	alhaitham	NOUN
iajs-871	28	7	j.	j.	PROPN
iajs-871	29	1	fo	fo	ADP
iajs-871	29	2	r	r	NOUN
iajs-871	29	3	pure	pure	ADJ
iajs-871	29	4	&	&	CCONJ
iajs-871	29	5	appl	appl	PROPN
iajs-871	29	6	.	.	PUNCT
iajs-871	30	1	sc	sc	PROPN
iajs-871	30	2	i.	i.	PROPN
iajs-871	30	3	vo	vo	PROPN
iajs-871	30	4	l.24	l.24	PROPN
iajs-871	30	5	(	(	PUNCT
iajs-871	30	6	1	1	NUM
iajs-871	30	7	)	)	PUNCT
iajs-871	30	8	2011	2011	NUM
iajs-871	30	9	if	if	SCONJ
iajs-871	30	10	a	a	DET
iajs-871	30	11	bitopological	bitopological	ADJ
iajs-871	30	12	space	space	NOUN
iajs-871	30	13	is	be	AUX
iajs-871	30	14	an	an	DET
iajs-871	30	15	l	l	ADJ
iajs-871	30	16	-	-	ADJ
iajs-871	30	17	compact	compact	ADJ
iajs-871	30	18	space	space	NOUN
iajs-871	30	19	,	,	PUNCT
iajs-871	30	20	then	then	ADV
iajs-871	30	21			PROPN
iajs-871	30	22			ADP
iajs-871	30	23	1	1	NUM
iajs-871	30	24	,	,	PUNCT
iajs-871	30	25	x	x	X
iajs-871	30	26	is	be	AUX
iajs-871	30	27	a	a	DET
iajs-871	30	28	compact	compact	ADJ
iajs-871	30	29	space	space	NOUN
iajs-871	30	30	.	.	PUNCT
iajs-871	31	1	proof	proof	NOUN
iajs-871	31	2	:	:	PUNCT
iajs-871	31	3	follows	follow	VERB
iajs-871	31	4	from	from	ADP
iajs-871	31	5	remark	remark	NOUN
iajs-871	31	6	(	(	PUNCT
iajs-871	31	7	2.2	2.2	NUM
iajs-871	31	8	)	)	PUNCT
iajs-871	31	9	.	.	PUNCT
iajs-871	32	1	remark	remark	NOUN
iajs-871	32	2	(	(	PUNCT
iajs-871	32	3	2.6	2.6	NUM
iajs-871	32	4	)	)	PUNCT
iajs-871	32	5	the	the	DET
iajs-871	32	6	opposite	opposite	ADJ
iajs-871	32	7	direction	direction	NOUN
iajs-871	32	8	of	of	ADP
iajs-871	32	9	proposition	proposition	NOUN
iajs-871	32	10	(	(	PUNCT
iajs-871	32	11	2.5	2.5	NUM
iajs-871	32	12	)	)	PUNCT
iajs-871	32	13	is	be	AUX
iajs-871	32	14	not	not	PART
iajs-871	32	15	true	true	ADJ
iajs-871	32	16	in	in	ADP
iajs-871	32	17	general	general	ADJ
iajs-871	32	18	,	,	PUNCT
iajs-871	32	19	as	as	SCONJ
iajs-871	32	20	the	the	DET
iajs-871	32	21	following	follow	VERB
iajs-871	32	22	example	example	NOUN
iajs-871	32	23	shows	show	VERB
iajs-871	32	24	:	:	PUNCT
iajs-871	32	25	let	let	VERB
iajs-871	32	26	x	x	NOUN
iajs-871	32	27	and	and	CCONJ
iajs-871	32	28	let	let	VERB
iajs-871	32	29	ox	ox	NOUN
iajs-871	32	30			PROPN
iajs-871	32	31			NOUN
iajs-871	32	32	ox,,1	ox,,1	PROPN
iajs-871	32	33			PROPN
iajs-871	32	34			X
iajs-871	32	35	i2	i2	NUM
iajs-871	33	1	=	=	NOUN
iajs-871	33	2	the	the	DET
iajs-871	33	3	indiscrete	indiscrete	ADJ
iajs-871	33	4	topology	topology	NOUN
iajs-871	33	5			NOUN
iajs-871	33	6			PROPN
iajs-871	33	7			PROPN
iajs-871	33	8			ADJ
iajs-871	33	9	uoruxuxol	uoruxuxol	ADJ
iajs-871	33	10	o	o	NOUN
iajs-871	33	11	;	;	PUNCT
iajs-871	33	12	note	note	VERB
iajs-871	33	13	that	that	SCONJ
iajs-871	33	14			NOUN
iajs-871	33	15	1	1	NOUN
iajs-871	33	16	,	,	PUNCT
iajs-871	33	17			PROPN
iajs-871	33	18	is	be	AUX
iajs-871	33	19	compact	compact	ADJ
iajs-871	33	20	but	but	CCONJ
iajs-871	33	21			PROPN
iajs-871	33	22	21	21	PUNCT
iajs-871	33	23	,	,	PUNCT
iajs-871	33	24	,	,	PUNCT
iajs-871	33	25			PROPN
iajs-871	33	26	is	be	AUX
iajs-871	33	27	not	not	PART
iajs-871	33	28	l	l	NOUN
iajs-871	33	29	-	-	ADJ
iajs-871	33	30	compact	compact	ADJ
iajs-871	33	31	.	.	PUNCT
iajs-871	34	1	proposition	proposition	NOUN
iajs-871	34	2	(	(	PUNCT
iajs-871	34	3	2.7	2.7	NUM
iajs-871	34	4	)	)	PUNCT
iajs-871	34	5	an	an	DET
iajs-871	34	6	l	l	NOUN
iajs-871	34	7	-	-	ADJ
iajs-871	34	8	closed	closed	ADJ
iajs-871	34	9	subset	subset	NOUN
iajs-871	34	10	of	of	ADP
iajs-871	34	11	an	an	DET
iajs-871	34	12	l	l	ADJ
iajs-871	34	13	-	-	ADJ
iajs-871	34	14	compact	compact	ADJ
iajs-871	34	15	space	space	NOUN
iajs-871	34	16	is	be	AUX
iajs-871	34	17	l	l	NOUN
iajs-871	34	18	-	-	ADJ
iajs-871	34	19	compact	compact	ADJ
iajs-871	34	20	.	.	PUNCT
iajs-871	35	1	proof	proof	NOUN
iajs-871	35	2	:	:	PUNCT
iajs-871	35	3	let	let	VERB
iajs-871	35	4	a	a	PRON
iajs-871	35	5	be	be	AUX
iajs-871	35	6	an	an	DET
iajs-871	35	7	l	l	NOUN
iajs-871	35	8	-	-	ADJ
iajs-871	35	9	closed	closed	ADJ
iajs-871	35	10	subset	subset	NOUN
iajs-871	35	11	of	of	ADP
iajs-871	35	12	an	an	DET
iajs-871	35	13	l	l	ADJ
iajs-871	35	14	-	-	ADJ
iajs-871	35	15	compact	compact	ADJ
iajs-871	35	16	space	space	NOUN
iajs-871	35	17	and	and	CCONJ
iajs-871	35	18	let	let	VERB
iajs-871	35	19			PRON
iajs-871	35	20			VERB
iajs-871	35	21			NOUN
iajs-871	35	22	:	:	PUNCT
iajs-871	35	23	g	g	NOUN
iajs-871	35	24	be	be	AUX
iajs-871	35	25	an	an	DET
iajs-871	35	26	l	l	NOUN
iajs-871	35	27	-	-	ADJ
iajs-871	35	28	open	open	ADJ
iajs-871	35	29	cover	cover	NOUN
iajs-871	35	30	of	of	ADP
iajs-871	35	31	a	a	PRON
iajs-871	35	32	.then	.then	PUNCT
iajs-871	36	1			PROPN
iajs-871	36	2			PROPN
iajs-871	36	3	cag	cag	PROPN
iajs-871	36	4			PROPN
iajs-871	36	5			NOUN
iajs-871	36	6	:	:	PUNCT
iajs-871	36	7	forms	form	VERB
iajs-871	36	8	an	an	DET
iajs-871	36	9	l	l	NOUN
iajs-871	36	10	-	-	ADJ
iajs-871	36	11	open	open	ADJ
iajs-871	36	12	cover	cover	NOUN
iajs-871	36	13	of	of	ADP
iajs-871	36	14	x	x	PUNCT
iajs-871	36	15	which	which	PRON
iajs-871	36	16	is	be	AUX
iajs-871	36	17	lcompact	lcompact	ADJ
iajs-871	36	18	space	space	NOUN
iajs-871	36	19	.	.	PUNCT
iajs-871	37	1	so	so	ADV
iajs-871	37	2	there	there	PRON
iajs-871	37	3	are	be	VERB
iajs-871	37	4	finitely	finitely	ADV
iajs-871	37	5	many	many	ADJ
iajs-871	37	6	elements	element	NOUN
iajs-871	37	7	n	n	NOUN
iajs-871	37	8	,	,	PUNCT
iajs-871	37	9	,	,	PUNCT
iajs-871	37	10	,	,	PUNCT
iajs-871	37	11	21	21	NUM
iajs-871	37	12			NUM
iajs-871	37	13	such	such	ADJ
iajs-871	37	14	that	that	SCONJ
iajs-871	38	1	c	c	PROPN
iajs-871	39	1	n	n	NOUN
iajs-871	40	1	i	i	PRON
iajs-871	40	2	agx	agx	VERB
iajs-871	40	3	i	i	PRON
iajs-871	40	4			PROPN
iajs-871	40	5	1	1	NUM
iajs-871	41	1			NUM
iajs-871	41	2			NOUN
iajs-871	41	3	,	,	PUNCT
iajs-871	41	4	it	it	PRON
iajs-871	41	5	follows	follow	VERB
iajs-871	41	6	that	that	SCONJ
iajs-871	41	7			VERB
iajs-871	41	8	n	n	VERB
iajs-871	42	1	i	i	PRON
iajs-871	43	1	i	i	PRON
iajs-871	43	2	ga	ga	PROPN
iajs-871	43	3	1	1	NUM
iajs-871	43	4			PROPN
iajs-871	43	5			X
iajs-871	43	6	.hence	.hence	ADP
iajs-871	43	7	a	a	PRON
iajs-871	43	8	is	be	AUX
iajs-871	43	9	an	an	DET
iajs-871	43	10	l	l	NOUN
iajs-871	43	11	-	-	ADJ
iajs-871	43	12	compact	compact	ADJ
iajs-871	43	13	.	.	PUNCT
iajs-871	44	1	corollary	corollary	ADJ
iajs-871	44	2	(	(	PUNCT
iajs-871	44	3	2.8	2.8	NUM
iajs-871	44	4	)	)	PUNCT
iajs-871	44	5	an	an	DET
iajs-871	44	6	l	l	NOUN
iajs-871	44	7	-	-	ADJ
iajs-871	44	8	closed	closed	ADJ
iajs-871	44	9	subset	subset	NOUN
iajs-871	44	10	of	of	ADP
iajs-871	44	11	an	an	DET
iajs-871	44	12	l	l	ADJ
iajs-871	44	13	-	-	ADJ
iajs-871	44	14	compact	compact	ADJ
iajs-871	44	15	space	space	NOUN
iajs-871	44	16	is	be	AUX
iajs-871	44	17	-compact	-compact	ADJ
iajs-871	44	18	.	.	PUNCT
iajs-871	45	1	proof	proof	NOUN
iajs-871	45	2	:	:	PUNCT
iajs-871	45	3	follows	follow	VERB
iajs-871	45	4	from	from	ADP
iajs-871	45	5	proposition	proposition	NOUN
iajs-871	45	6	(	(	PUNCT
iajs-871	45	7	2.7	2.7	NUM
iajs-871	45	8	)	)	PUNCT
iajs-871	45	9	and	and	CCONJ
iajs-871	45	10	(	(	PUNCT
iajs-871	45	11	2.5	2.5	NUM
iajs-871	45	12	)	)	PUNCT
iajs-871	45	13	.	.	PUNCT
iajs-871	46	1	corollary	corollary	ADJ
iajs-871	46	2	(	(	PUNCT
iajs-871	46	3	2.9	2.9	NUM
iajs-871	46	4	)	)	PUNCT
iajs-871	46	5	a	a	DET
iajs-871	46	6	-closed	-close	VERB
iajs-871	46	7	subset	subset	NOUN
iajs-871	46	8	of	of	ADP
iajs-871	46	9	an	an	DET
iajs-871	46	10	l	l	ADJ
iajs-871	46	11	-	-	ADJ
iajs-871	46	12	compact	compact	ADJ
iajs-871	46	13	space	space	NOUN
iajs-871	46	14	is	be	AUX
iajs-871	46	15	l	l	NOUN
iajs-871	46	16	-	-	ADJ
iajs-871	46	17	compact	compact	ADJ
iajs-871	46	18	.	.	PUNCT
iajs-871	47	1	proof	proof	NOUN
iajs-871	47	2	:	:	PUNCT
iajs-871	47	3	since	since	SCONJ
iajs-871	47	4	every	every	DET
iajs-871	47	5	-closed	-close	VERB
iajs-871	47	6	set	set	NOUN
iajs-871	47	7	is	be	AUX
iajs-871	47	8	an	an	DET
iajs-871	47	9	l	l	NOUN
iajs-871	47	10	-	-	ADJ
iajs-871	47	11	closed	closed	ADJ
iajs-871	47	12	set	set	NOUN
iajs-871	47	13	and	and	CCONJ
iajs-871	47	14	by	by	ADP
iajs-871	47	15	proposition	proposition	NOUN
iajs-871	47	16	(	(	PUNCT
iajs-871	47	17	2.7	2.7	NUM
iajs-871	47	18	)	)	PUNCT
iajs-871	47	19	.	.	PUNCT
iajs-871	48	1	corollary	corollary	ADJ
iajs-871	48	2	(	(	PUNCT
iajs-871	48	3	2.10	2.10	NUM
iajs-871	48	4	)	)	PUNCT
iajs-871	48	5	a	a	DET
iajs-871	48	6	-closed	-close	VERB
iajs-871	48	7	subset	subset	NOUN
iajs-871	48	8	of	of	ADP
iajs-871	48	9	an	an	DET
iajs-871	48	10	l	l	ADJ
iajs-871	48	11	-	-	ADJ
iajs-871	48	12	compact	compact	ADJ
iajs-871	48	13	space	space	NOUN
iajs-871	48	14	is	be	AUX
iajs-871	48	15	-compact	-compact	ADJ
iajs-871	48	16	.	.	PUNCT
iajs-871	49	1	ibn	ibn	PROPN
iajs-871	49	2	alhaitham	alhaitham	PROPN
iajs-871	50	1	j.	j.	PROPN
iajs-871	51	1	fo	fo	ADP
iajs-871	51	2	r	r	NOUN
iajs-871	51	3	pure	pure	ADJ
iajs-871	51	4	&	&	CCONJ
iajs-871	51	5	appl	appl	PROPN
iajs-871	51	6	.	.	PUNCT
iajs-871	52	1	sc	sc	PROPN
iajs-871	52	2	i.	i.	PROPN
iajs-871	52	3	vo	vo	PROPN
iajs-871	52	4	l.24	l.24	PROPN
iajs-871	52	5	(	(	PUNCT
iajs-871	52	6	1	1	NUM
iajs-871	52	7	)	)	PUNCT
iajs-871	52	8	2011	2011	NUM
iajs-871	52	9	proof	proof	NOUN
iajs-871	52	10	:	:	PUNCT
iajs-871	52	11	follows	follow	VERB
iajs-871	52	12	from	from	ADP
iajs-871	52	13	corollary(2.9	corollary(2.9	NOUN
iajs-871	52	14	)	)	PUNCT
iajs-871	52	15	and	and	CCONJ
iajs-871	52	16	proposition	proposition	NOUN
iajs-871	52	17	(	(	PUNCT
iajs-871	52	18	2.5	2.5	NUM
iajs-871	52	19	)	)	PUNCT
iajs-871	52	20	.	.	PUNCT
iajs-871	53	1	proposition(2.11	proposition(2.11	X
iajs-871	53	2	)	)	PUNCT
iajs-871	53	3	the	the	DET
iajs-871	53	4	l	l	ADJ
iajs-871	53	5	-	-	ADJ
iajs-871	53	6	continuous	continuous	ADJ
iajs-871	53	7	image	image	NOUN
iajs-871	53	8	of	of	ADP
iajs-871	53	9	an	an	DET
iajs-871	53	10	l	l	ADJ
iajs-871	53	11	-	-	ADJ
iajs-871	53	12	compact	compact	ADJ
iajs-871	53	13	space	space	NOUN
iajs-871	53	14	is	be	AUX
iajs-871	53	15	an	an	DET
iajs-871	53	16	l	l	NOUN
iajs-871	53	17	-	-	ADJ
iajs-871	53	18	compact	compact	ADJ
iajs-871	53	19	.	.	PUNCT
iajs-871	54	1	proof	proof	NOUN
iajs-871	54	2	:	:	PUNCT
iajs-871	54	3	suppose	suppose	VERB
iajs-871	54	4	that	that	PRON
iajs-871	54	5	is	be	AUX
iajs-871	54	6	an	an	DET
iajs-871	54	7	l	l	NOUN
iajs-871	54	8	-	-	ADJ
iajs-871	54	9	continuous	continuous	ADJ
iajs-871	54	10	and	and	CCONJ
iajs-871	54	11	onto	onto	ADP
iajs-871	54	12	function	function	NOUN
iajs-871	54	13	and	and	CCONJ
iajs-871	54	14	is	be	AUX
iajs-871	54	15	an	an	DET
iajs-871	54	16	l	l	ADJ
iajs-871	54	17	-	-	ADJ
iajs-871	54	18	compact	compact	ADJ
iajs-871	54	19	space	space	NOUN
iajs-871	54	20	.	.	PUNCT
iajs-871	55	1	let	let	AUX
iajs-871	55	2	be	be	AUX
iajs-871	55	3	an	an	DET
iajs-871	55	4	l	l	NOUN
iajs-871	55	5	-	-	ADJ
iajs-871	55	6	open	open	ADJ
iajs-871	55	7	cover	cover	NOUN
iajs-871	55	8	of	of	ADP
iajs-871	55	9	,	,	PUNCT
iajs-871	55	10	it	it	PRON
iajs-871	55	11	follows	follow	VERB
iajs-871	55	12	that	that	PRON
iajs-871	55	13	is	be	AUX
iajs-871	55	14	an	an	DET
iajs-871	55	15	l	l	NOUN
iajs-871	55	16	-	-	ADJ
iajs-871	55	17	open	open	ADJ
iajs-871	55	18	cover	cover	NOUN
iajs-871	55	19	of	of	ADP
iajs-871	55	20	which	which	PRON
iajs-871	55	21	is	be	AUX
iajs-871	55	22	l-compact.so	l-compact.so	PROPN
iajs-871	55	23	there	there	PRON
iajs-871	55	24	are	be	VERB
iajs-871	55	25	finitely	finitely	ADV
iajs-871	55	26	many	many	ADJ
iajs-871	55	27	elements	element	NOUN
iajs-871	55	28	such	such	ADJ
iajs-871	55	29	that	that	PRON
iajs-871	55	30	.therefore	.therefore	NOUN
iajs-871	55	31	,	,	PUNCT
iajs-871	55	32	hence	hence	ADV
iajs-871	55	33	is	be	AUX
iajs-871	55	34	an	an	DET
iajs-871	55	35	l	l	NOUN
iajs-871	55	36	-	-	ADJ
iajs-871	55	37	compact	compact	ADJ
iajs-871	55	38	.	.	PUNCT
iajs-871	56	1	corollary	corollary	ADJ
iajs-871	56	2	(	(	PUNCT
iajs-871	56	3	2.12	2.12	NUM
iajs-871	56	4	)	)	PUNCT
iajs-871	56	5	let	let	AUX
iajs-871	56	6	be	be	AUX
iajs-871	56	7	an	an	DET
iajs-871	56	8	l	l	ADJ
iajs-871	56	9	-	-	ADJ
iajs-871	56	10	continuous	continuous	ADJ
iajs-871	56	11	function	function	NOUN
iajs-871	56	12	,	,	PUNCT
iajs-871	56	13	then	then	ADV
iajs-871	56	14	is	be	AUX
iajs-871	56	15	a	a	DET
iajs-871	56	16	compact	compact	ADJ
iajs-871	56	17	subset	subset	NOUN
iajs-871	56	18	of	of	ADP
iajs-871	56	19	for	for	ADP
iajs-871	56	20	each	each	DET
iajs-871	56	21	l	l	ADJ
iajs-871	56	22	-	-	ADJ
iajs-871	56	23	compact	compact	ADJ
iajs-871	56	24	subset	subset	NOUN
iajs-871	56	25	of	of	ADP
iajs-871	56	26	.	.	PUNCT
iajs-871	57	1	proof	proof	NOUN
iajs-871	57	2	:	:	PUNCT
iajs-871	57	3	follows	follow	VERB
iajs-871	57	4	from	from	ADP
iajs-871	57	5	propositions	proposition	NOUN
iajs-871	57	6	(	(	PUNCT
iajs-871	57	7	2.11	2.11	NUM
iajs-871	57	8	)	)	PUNCT
iajs-871	57	9	and	and	CCONJ
iajs-871	57	10	(	(	PUNCT
iajs-871	57	11	2.5	2.5	NUM
iajs-871	57	12	)	)	PUNCT
iajs-871	57	13	.	.	PUNCT
iajs-871	58	1	it	it	PRON
iajs-871	58	2	is	be	AUX
iajs-871	58	3	known	know	VERB
iajs-871	58	4	that	that	SCONJ
iajs-871	58	5	every	every	DET
iajs-871	58	6	compact	compact	ADJ
iajs-871	58	7	subset	subset	NOUN
iajs-871	58	8	of	of	ADP
iajs-871	58	9	any	any	DET
iajs-871	58	10	2	2	NUM
iajs-871	58	11	t	t	NOUN
iajs-871	58	12	-space	-space	NOUN
iajs-871	58	13	is	be	AUX
iajs-871	58	14	closed	closed	ADJ
iajs-871	58	15	.	.	PUNCT
iajs-871	59	1	if	if	SCONJ
iajs-871	59	2	we	we	PRON
iajs-871	59	3	change	change	VERB
iajs-871	59	4	the	the	DET
iajs-871	59	5	concepts	concept	NOUN
iajs-871	59	6	of	of	ADP
iajs-871	59	7	compact	compact	ADJ
iajs-871	59	8	,	,	PUNCT
iajs-871	59	9	2	2	NUM
iajs-871	59	10	t	t	NOUN
iajs-871	59	11	and	and	CCONJ
iajs-871	59	12	closed	close	VERB
iajs-871	59	13	by	by	ADP
iajs-871	59	14	the	the	DET
iajs-871	59	15	concepts	concept	NOUN
iajs-871	59	16	l	l	PROPN
iajs-871	59	17	-	-	NOUN
iajs-871	59	18	compact2	compact2	ADJ
iajs-871	59	19	t	t	PROPN
iajs-871	59	20	and	and	CCONJ
iajs-871	59	21	l	l	NOUN
iajs-871	59	22	-	-	ADJ
iajs-871	59	23	closed	closed	ADJ
iajs-871	59	24	,	,	PUNCT
iajs-871	59	25	then	then	ADV
iajs-871	59	26	this	this	DET
iajs-871	59	27	fact	fact	NOUN
iajs-871	59	28	being	be	AUX
iajs-871	59	29	invalid	invalid	ADJ
iajs-871	59	30	in	in	ADP
iajs-871	59	31	general	general	ADJ
iajs-871	59	32	,	,	PUNCT
iajs-871	59	33	as	as	SCONJ
iajs-871	59	34	the	the	DET
iajs-871	59	35	following	follow	VERB
iajs-871	59	36	example	example	NOUN
iajs-871	59	37	shows	show	VERB
iajs-871	59	38	:	:	PUNCT
iajs-871	59	39	example	example	NOUN
iajs-871	59	40	(	(	PUNCT
iajs-871	59	41	2.13	2.13	NUM
iajs-871	59	42	)	)	PUNCT
iajs-871	59	43			NOUN
iajs-871	60	1			PROPN
iajs-871	60	2			PROPN
iajs-871	60	3			PROPN
iajs-871	60	4			PROPN
iajs-871	60	5			PROPN
iajs-871	60	6			PROPN
iajs-871	60	7			NOUN
iajs-871	60	8			PROPN
iajs-871	61	1	i	i	NOUN
iajs-871	61	2	x	x	PUNCT
iajs-871	61	3	x	x	X
iajs-871	62	1			NOUN
iajs-871	62	2			NUM
iajs-871	62	3			NOUN
iajs-871	62	4			NOUN
iajs-871	62	5			NOUN
iajs-871	62	6			NOUN
iajs-871	62	7	2	2	NUM
iajs-871	62	8	1	1	NUM
iajs-871	62	9	2,1,2,1	2,1,2,1	NUM
iajs-871	62	10	,	,	PUNCT
iajs-871	62	11	,	,	PUNCT
iajs-871	62	12	3,2,1	3,2,1	NUM
iajs-871	62	13			NOUN
iajs-871	62	14			PUNCT
iajs-871	63	1			PROPN
iajs-871	63	2			PROPN
iajs-871	63	3			PROPN
iajs-871	63	4			PROPN
iajs-871	63	5			PROPN
iajs-871	63	6			PROPN
iajs-871	63	7			PROPN
iajs-871	63	8			PROPN
iajs-871	63	9			PROPN
iajs-871	63	10			ADV
iajs-871	63	11	3,2,3,1,2,1,2,1,,xxol	3,2,3,1,2,1,2,1,,xxol	DET
iajs-871	63	12			NOUN
iajs-871	63	13			NOUN
iajs-871	63	14			PUNCT
iajs-871	64	1			PROPN
iajs-871	64	2			PROPN
iajs-871	64	3			PROPN
iajs-871	64	4			PROPN
iajs-871	64	5			PROPN
iajs-871	64	6			PROPN
iajs-871	64	7			PROPN
iajs-871	64	8			PROPN
iajs-871	64	9			PROPN
iajs-871	64	10			NOUN
iajs-871	64	11	1,2,3,3,1,3,2,,xxcl	1,2,3,3,1,3,2,,xxcl	NOUN
iajs-871	64	12			PROPN
iajs-871	64	13	.	.	PUNCT
iajs-871	65	1	clear	clear	ADJ
iajs-871	65	2	that	that	SCONJ
iajs-871	65	3	x	x	PRON
iajs-871	65	4	is	be	AUX
iajs-871	65	5	an	an	DET
iajs-871	65	6	l2	l2	NOUN
iajs-871	65	7	t	t	NOUN
iajs-871	65	8	-space	-space	NOUN
iajs-871	65	9	.	.	PUNCT
iajs-871	66	1	if	if	SCONJ
iajs-871	66	2			PROPN
iajs-871	66	3	2,1a	2,1a	VERB
iajs-871	66	4	,	,	PUNCT
iajs-871	66	5	then	then	ADV
iajs-871	66	6	a	a	PRON
iajs-871	66	7	is	be	AUX
iajs-871	66	8	an	an	DET
iajs-871	66	9	l	l	ADJ
iajs-871	66	10	-	-	ADJ
iajs-871	66	11	compact	compact	ADJ
iajs-871	66	12	subset	subset	NOUN
iajs-871	66	13	of	of	ADP
iajs-871	66	14	x	x	PRON
iajs-871	66	15	,	,	PUNCT
iajs-871	66	16	but	but	CCONJ
iajs-871	66	17	it	it	PRON
iajs-871	66	18	is	be	AUX
iajs-871	66	19	not	not	PART
iajs-871	66	20	l	l	NOUN
iajs-871	66	21	-	-	ADJ
iajs-871	66	22	closed	closed	ADJ
iajs-871	66	23	.	.	PUNCT
iajs-871	67	1	definition	definition	NOUN
iajs-871	67	2	(	(	PUNCT
iajs-871	67	3	2.14	2.14	NUM
iajs-871	67	4	):	):	PUNCT
iajs-871	67	5	[	[	X
iajs-871	67	6	3	3	NUM
iajs-871	67	7	]	]	PUNCT
iajs-871	67	8	let	let	AUX
iajs-871	67	9	be	be	AUX
iajs-871	67	10	a	a	DET
iajs-871	67	11	bitopological	bitopological	ADJ
iajs-871	67	12	space	space	NOUN
iajs-871	67	13	and	and	CCONJ
iajs-871	67	14	let	let	VERB
iajs-871	67	15	a	a	PRON
iajs-871	67	16	be	be	AUX
iajs-871	67	17	a	a	DET
iajs-871	67	18	subset	subset	NOUN
iajs-871	67	19	of	of	ADP
iajs-871	67	20	x	x	PRON
iajs-871	67	21	,	,	PUNCT
iajs-871	67	22	xx	xx	PROPN
iajs-871	67	23	.then	.then	AUX
iajs-871	68	1	a	a	PRON
iajs-871	68	2	is	be	AUX
iajs-871	68	3	called	call	VERB
iajs-871	68	4	an	an	DET
iajs-871	68	5	ibn	ibn	PROPN
iajs-871	68	6	alhaitham	alhaitham	NOUN
iajs-871	68	7	j.	j.	PROPN
iajs-871	69	1	fo	fo	ADP
iajs-871	69	2	r	r	NOUN
iajs-871	69	3	pure	pure	ADJ
iajs-871	69	4	&	&	CCONJ
iajs-871	69	5	appl	appl	PROPN
iajs-871	69	6	.	.	PUNCT
iajs-871	70	1	sc	sc	PROPN
iajs-871	70	2	i.	i.	PROPN
iajs-871	70	3	vo	vo	PROPN
iajs-871	71	1	l.24	l.24	PROPN
iajs-871	71	2	(	(	PUNCT
iajs-871	71	3	1	1	NUM
iajs-871	71	4	)	)	PUNCT
iajs-871	71	5	2011	2011	NUM
iajs-871	71	6	l	l	NOUN
iajs-871	71	7	-	-	NOUN
iajs-871	71	8	neighborhood	neighborhood	NOUN
iajs-871	71	9	of	of	ADP
iajs-871	71	10	x	x	PART
iajs-871	71	11	if	if	SCONJ
iajs-871	71	12	and	and	CCONJ
iajs-871	71	13	only	only	ADV
iajs-871	71	14	if	if	SCONJ
iajs-871	71	15	there	there	PRON
iajs-871	71	16	is	be	VERB
iajs-871	71	17	an	an	DET
iajs-871	71	18	l	l	NOUN
iajs-871	71	19	-	-	ADJ
iajs-871	71	20	open	open	ADJ
iajs-871	71	21	set	set	VERB
iajs-871	71	22	g	g	NOUN
iajs-871	71	23	in	in	ADP
iajs-871	71	24	x	x	PUNCT
iajs-871	71	25	such	such	ADJ
iajs-871	71	26	that	that	SCONJ
iajs-871	71	27	agx	agx	PROPN
iajs-871	71	28			PROPN
iajs-871	71	29	.	.	PUNCT
iajs-871	72	1	definition	definition	NOUN
iajs-871	72	2	(	(	PUNCT
iajs-871	72	3	2.15	2.15	NUM
iajs-871	72	4	)	)	PUNCT
iajs-871	73	1	[	[	X
iajs-871	73	2	3	3	X
iajs-871	73	3	]	]	PUNCT
iajs-871	73	4	let	let	AUX
iajs-871	73	5	be	be	AUX
iajs-871	73	6	a	a	DET
iajs-871	73	7	bitopological	bitopological	ADJ
iajs-871	73	8	space	space	NOUN
iajs-871	73	9	and	and	CCONJ
iajs-871	73	10	let	let	VERB
iajs-871	73	11	a	a	PRON
iajs-871	73	12	be	be	AUX
iajs-871	73	13	a	a	DET
iajs-871	73	14	subset	subset	NOUN
iajs-871	73	15	of	of	ADP
iajs-871	73	16	x.the	x.the	DET
iajs-871	73	17	intersection	intersection	NOUN
iajs-871	73	18	of	of	ADP
iajs-871	73	19	all	all	DET
iajs-871	73	20	l	l	NOUN
iajs-871	73	21	-	-	ADJ
iajs-871	73	22	closed	closed	ADJ
iajs-871	73	23	set	set	NOUN
iajs-871	73	24	containing	contain	VERB
iajs-871	73	25	a	a	PRON
iajs-871	73	26	is	be	AUX
iajs-871	73	27	called	call	VERB
iajs-871	73	28	“	"	PUNCT
iajs-871	73	29	l	l	NOUN
iajs-871	73	30	-	-	NOUN
iajs-871	73	31	closure	closure	NOUN
iajs-871	73	32	of	of	ADP
iajs-871	73	33	a”denoted	a”denote	VERB
iajs-871	73	34	by	by	ADP
iajs-871	73	35	l	l	NOUN
iajs-871	73	36	-	-	NOUN
iajs-871	73	37	cl(a	cl(a	NUM
iajs-871	73	38	)	)	PUNCT
iajs-871	73	39	.	.	PUNCT
iajs-871	74	1	theorem	theorem	NOUN
iajs-871	74	2	(	(	PUNCT
iajs-871	74	3	2.16	2.16	NUM
iajs-871	74	4	)	)	PUNCT
iajs-871	75	1	[	[	X
iajs-871	75	2	4	4	X
iajs-871	75	3	]	]	X
iajs-871	75	4	l	l	NOUN
iajs-871	75	5	et	et	NOUN
iajs-871	75	6	be	be	AUX
iajs-871	75	7	a	a	DET
iajs-871	75	8	bitopological	bitopological	ADJ
iajs-871	75	9	space	space	NOUN
iajs-871	75	10	and	and	CCONJ
iajs-871	75	11	let	let	VERB
iajs-871	75	12	a	a	PRON
iajs-871	75	13	be	be	AUX
iajs-871	75	14	a	a	DET
iajs-871	75	15	subset	subset	NOUN
iajs-871	75	16	of	of	ADP
iajs-871	75	17	x.	x.	NOUN
iajs-871	75	18	a	a	DET
iajs-871	75	19	point	point	NOUN
iajs-871	75	20	x	x	INTJ
iajs-871	75	21	in	in	ADP
iajs-871	75	22	x	x	PROPN
iajs-871	75	23	is	be	AUX
iajs-871	75	24	an	an	DET
iajs-871	75	25	l	l	NOUN
iajs-871	75	26	-	-	ADJ
iajs-871	75	27	closure	closure	NOUN
iajs-871	75	28	point	point	NOUN
iajs-871	75	29	of	of	ADP
iajs-871	75	30	a	a	DET
iajs-871	75	31	if	if	NOUN
iajs-871	75	32	and	and	CCONJ
iajs-871	75	33	only	only	ADV
iajs-871	75	34	if	if	SCONJ
iajs-871	75	35	every	every	DET
iajs-871	75	36	l	l	NOUN
iajs-871	75	37	-	-	ADJ
iajs-871	75	38	open	open	ADJ
iajs-871	75	39	neighborhood	neighborhood	NOUN
iajs-871	75	40	of	of	ADP
iajs-871	75	41	x	x	NOUN
iajs-871	75	42	intersects	intersects	NOUN
iajs-871	75	43	a.	a.	NOUN
iajs-871	75	44	definition	definition	NOUN
iajs-871	75	45	(	(	PUNCT
iajs-871	75	46	2.17	2.17	NUM
iajs-871	75	47	)	)	PUNCT
iajs-871	76	1	[	[	X
iajs-871	76	2	4	4	X
iajs-871	76	3	]	]	PUNCT
iajs-871	76	4	let	let	AUX
iajs-871	76	5	be	be	AUX
iajs-871	76	6	a	a	DET
iajs-871	76	7	bitopological	bitopological	ADJ
iajs-871	76	8	space	space	NOUN
iajs-871	76	9	and	and	CCONJ
iajs-871	76	10	let	let	VERB
iajs-871	76	11			NOUN
iajs-871	76	12			PROPN
iajs-871	76	13	,	,	PUNCT
iajs-871	76	14	,	,	PUNCT
iajs-871	76	15	,	,	PUNCT
iajs-871	76	16	axf	axf	ADV
iajs-871	76	17	be	be	AUX
iajs-871	76	18	a	a	DET
iajs-871	76	19	net	net	NOUN
iajs-871	76	20	in	in	ADP
iajs-871	76	21	x	x	PRON
iajs-871	76	22	,	,	PUNCT
iajs-871	76	23	then	then	ADV
iajs-871	76	24	f	f	PROPN
iajs-871	76	25	is	be	AUX
iajs-871	76	26	said	say	VERB
iajs-871	76	27	to	to	PART
iajs-871	76	28	be	be	AUX
iajs-871	76	29	“	"	PUNCT
iajs-871	76	30	l	l	NOUN
iajs-871	76	31	-	-	NOUN
iajs-871	76	32	convergent	convergent	NOUN
iajs-871	76	33	”	"	PUNCT
iajs-871	76	34	to	to	ADP
iajs-871	76	35	a	a	DET
iajs-871	76	36	point	point	NOUN
iajs-871	76	37	ox	ox	NOUN
iajs-871	76	38	in	in	ADP
iajs-871	76	39	x	x	SYM
iajs-871	76	40	if	if	SCONJ
iajs-871	76	41	and	and	CCONJ
iajs-871	76	42	only	only	ADV
iajs-871	76	43	if	if	SCONJ
iajs-871	76	44	for	for	ADP
iajs-871	76	45	each	each	DET
iajs-871	76	46	l	l	ADJ
iajs-871	76	47	-	-	ADJ
iajs-871	76	48	open	open	ADJ
iajs-871	76	49	neighborhood	neighborhood	NOUN
iajs-871	76	50	n	n	NOUN
iajs-871	76	51	of	of	ADP
iajs-871	76	52	ox	ox	NOUN
iajs-871	76	53	,	,	PUNCT
iajs-871	76	54	there	there	PRON
iajs-871	76	55	exists	exist	VERB
iajs-871	76	56	an	an	DET
iajs-871	76	57	element	element	NOUN
iajs-871	76	58	aao	aao	NOUN
iajs-871	76	59	such	such	ADJ
iajs-871	76	60	that	that	SCONJ
iajs-871	76	61	nfa	nfa	PROPN
iajs-871	76	62			PROPN
iajs-871	76	63	for	for	ADP
iajs-871	76	64	each	each	DET
iajs-871	76	65	oaa	oaa	PROPN
iajs-871	76	66			PROPN
iajs-871	76	67	.	.	PUNCT
iajs-871	77	1	definition	definition	NOUN
iajs-871	77	2	(	(	PUNCT
iajs-871	77	3	2.18	2.18	NUM
iajs-871	77	4	)	)	PUNCT
iajs-871	78	1	[	[	X
iajs-871	78	2	4	4	X
iajs-871	78	3	]	]	PUNCT
iajs-871	78	4	let	let	AUX
iajs-871	78	5	be	be	AUX
iajs-871	78	6	a	a	DET
iajs-871	78	7	bitopological	bitopological	ADJ
iajs-871	78	8	space	space	NOUN
iajs-871	78	9	and	and	CCONJ
iajs-871	78	10	let	let	VERB
iajs-871	78	11			NOUN
iajs-871	78	12			PROPN
iajs-871	78	13	,	,	PUNCT
iajs-871	78	14	,	,	PUNCT
iajs-871	78	15	,	,	PUNCT
iajs-871	78	16	axf	axf	ADV
iajs-871	78	17	be	be	AUX
iajs-871	78	18	a	a	DET
iajs-871	78	19	net	net	NOUN
iajs-871	78	20	in	in	ADP
iajs-871	78	21	x.	x.	PROPN
iajs-871	78	22	a	a	DET
iajs-871	78	23	point	point	NOUN
iajs-871	78	24	ox	ox	NOUN
iajs-871	78	25	in	in	ADP
iajs-871	78	26	x	x	PROPN
iajs-871	78	27	is	be	AUX
iajs-871	78	28	called	call	VERB
iajs-871	78	29	an	an	DET
iajs-871	78	30	“	"	PUNCT
iajs-871	78	31	l	l	NOUN
iajs-871	78	32	-	-	NOUN
iajs-871	78	33	cluster	cluster	NOUN
iajs-871	78	34	point	point	NOUN
iajs-871	78	35	of	of	ADP
iajs-871	78	36	f	f	NOUN
iajs-871	78	37	”	"	PUNCT
iajs-871	78	38	if	if	SCONJ
iajs-871	78	39	and	and	CCONJ
iajs-871	78	40	only	only	ADV
iajs-871	78	41	if	if	SCONJ
iajs-871	78	42	for	for	ADP
iajs-871	78	43	each	each	DET
iajs-871	78	44	aa	aa	NOUN
iajs-871	78	45	and	and	CCONJ
iajs-871	78	46	for	for	ADP
iajs-871	78	47	each	each	DET
iajs-871	78	48	l	l	ADJ
iajs-871	78	49	-	-	ADJ
iajs-871	78	50	open	open	ADJ
iajs-871	78	51	neighborhood	neighborhood	NOUN
iajs-871	78	52	n	n	NOUN
iajs-871	78	53	of	of	ADP
iajs-871	78	54	ox	ox	NOUN
iajs-871	78	55	,	,	PUNCT
iajs-871	78	56	there	there	PRON
iajs-871	78	57	exists	exist	VERB
iajs-871	78	58	an	an	DET
iajs-871	78	59	element	element	NOUN
iajs-871	78	60	ab	ab	PROPN
iajs-871	78	61			NUM
iajs-871	78	62	in	in	ADP
iajs-871	78	63	a	a	DET
iajs-871	78	64	such	such	ADJ
iajs-871	78	65	that	that	SCONJ
iajs-871	78	66	nfb	nfb	PROPN
iajs-871	78	67	.	.	PUNCT
iajs-871	79	1	theorem	theorem	PROPN
iajs-871	79	2	(	(	PUNCT
iajs-871	79	3	2.19	2.19	NUM
iajs-871	79	4	)	)	PUNCT
iajs-871	80	1	[	[	X
iajs-871	80	2	4	4	X
iajs-871	80	3	]	]	PUNCT
iajs-871	80	4	let	let	AUX
iajs-871	80	5	be	be	AUX
iajs-871	80	6	a	a	DET
iajs-871	80	7	bitopological	bitopological	ADJ
iajs-871	80	8	space	space	NOUN
iajs-871	80	9	and	and	CCONJ
iajs-871	80	10	let	let	VERB
iajs-871	80	11			NOUN
iajs-871	80	12			PROPN
iajs-871	80	13	,	,	PUNCT
iajs-871	80	14	,	,	PUNCT
iajs-871	80	15	,	,	PUNCT
iajs-871	80	16	axf	axf	ADV
iajs-871	80	17	be	be	AUX
iajs-871	80	18	a	a	DET
iajs-871	80	19	net	net	NOUN
iajs-871	80	20	in	in	ADP
iajs-871	80	21	x.	x.	NOUN
iajs-871	80	22	for	for	ADP
iajs-871	80	23	each	each	DET
iajs-871	80	24	aa	aa	NOUN
iajs-871	80	25	let	let	VERB
iajs-871	80	26			NOUN
iajs-871	80	27			ADJ
iajs-871	80	28	ainaxxfm	ainaxxfm	PROPN
iajs-871	80	29			ADJ
iajs-871	80	30	:	:	PUNCT
iajs-871	80	31			X
iajs-871	80	32	,	,	PUNCT
iajs-871	80	33	then	then	ADV
iajs-871	80	34	a	a	DET
iajs-871	80	35	point	point	NOUN
iajs-871	80	36	p	p	NOUN
iajs-871	80	37	of	of	ADP
iajs-871	80	38	x	x	PUNCT
iajs-871	80	39	is	be	AUX
iajs-871	80	40	an	an	DET
iajs-871	80	41	l	l	NOUN
iajs-871	80	42	-	-	ADJ
iajs-871	80	43	cluster	cluster	NOUN
iajs-871	80	44	point	point	NOUN
iajs-871	80	45	of	of	ADP
iajs-871	80	46	f	f	PROPN
iajs-871	81	1	if	if	SCONJ
iajs-871	81	2	and	and	CCONJ
iajs-871	81	3	only	only	ADV
iajs-871	81	4	if	if	SCONJ
iajs-871	81	5			PROPN
iajs-871	81	6	mcllp	mcllp	X
iajs-871	81	7			NOUN
iajs-871	81	8	for	for	ADP
iajs-871	81	9	each	each	DET
iajs-871	81	10	aa	aa	NOUN
iajs-871	81	11	.	.	PUNCT
iajs-871	82	1	definition	definition	NOUN
iajs-871	82	2	(	(	PUNCT
iajs-871	82	3	2.20	2.20	NUM
iajs-871	82	4	)	)	PUNCT
iajs-871	82	5	let	let	AUX
iajs-871	82	6	be	be	AUX
iajs-871	82	7	a	a	DET
iajs-871	82	8	bitopological	bitopological	ADJ
iajs-871	82	9	space	space	NOUN
iajs-871	82	10	and	and	CCONJ
iajs-871	82	11	let	let	VERB
iajs-871	82	12	ғ	ғ	PART
iajs-871	82	13	be	be	AUX
iajs-871	82	14	a	a	DET
iajs-871	82	15	filter	filter	NOUN
iajs-871	82	16	on	on	ADP
iajs-871	82	17	x	x	X
iajs-871	82	18	.	.	PUNCT
iajs-871	83	1	a	a	DET
iajs-871	83	2	point	point	NOUN
iajs-871	83	3	x	x	INTJ
iajs-871	83	4	in	in	ADP
iajs-871	83	5	x	x	PROPN
iajs-871	83	6	is	be	AUX
iajs-871	83	7	called	call	VERB
iajs-871	83	8	an	an	DET
iajs-871	83	9	“	"	PUNCT
iajs-871	83	10	l	l	NOUN
iajs-871	83	11	-	-	NOUN
iajs-871	83	12	cluster	cluster	NOUN
iajs-871	83	13	point	point	NOUN
iajs-871	83	14	of	of	ADP
iajs-871	83	15	ғ	ғ	PROPN
iajs-871	83	16	”	"	PUNCT
iajs-871	83	17	if	if	SCONJ
iajs-871	83	18	and	and	CCONJ
iajs-871	83	19	only	only	ADV
iajs-871	83	20	if	if	SCONJ
iajs-871	83	21	each	each	DET
iajs-871	83	22	l	l	ADJ
iajs-871	83	23	-	-	ADJ
iajs-871	83	24	open	open	ADJ
iajs-871	83	25	neighborhood	neighborhood	NOUN
iajs-871	83	26	of	of	ADP
iajs-871	83	27	x	x	NOUN
iajs-871	83	28	intersects	intersect	VERB
iajs-871	83	29	every	every	DET
iajs-871	83	30	member	member	NOUN
iajs-871	83	31	of	of	ADP
iajs-871	83	32	ғ.	ғ.	PROPN
iajs-871	83	33	theorem	theorem	PROPN
iajs-871	83	34	(	(	PUNCT
iajs-871	83	35	2.21	2.21	NUM
iajs-871	83	36	)	)	PUNCT
iajs-871	83	37	let	let	AUX
iajs-871	83	38	be	be	AUX
iajs-871	83	39	a	a	DET
iajs-871	83	40	bitopological	bitopological	ADJ
iajs-871	83	41	space	space	NOUN
iajs-871	83	42	and	and	CCONJ
iajs-871	83	43	let	let	VERB
iajs-871	83	44	ғ	ғ	PART
iajs-871	83	45	be	be	AUX
iajs-871	83	46	a	a	DET
iajs-871	83	47	filter	filter	NOUN
iajs-871	83	48	on	on	ADP
iajs-871	83	49	x	x	X
iajs-871	83	50	.	.	PUNCT
iajs-871	84	1	a	a	DET
iajs-871	84	2	point	point	NOUN
iajs-871	84	3	p	p	NOUN
iajs-871	84	4	in	in	ADP
iajs-871	84	5	x	x	PROPN
iajs-871	84	6	is	be	AUX
iajs-871	84	7	an	an	DET
iajs-871	84	8	lcluster	lcluster	NOUN
iajs-871	84	9	point	point	NOUN
iajs-871	84	10	of	of	ADP
iajs-871	84	11	ғ	ғ	PRON
iajs-871	84	12	if	if	SCONJ
iajs-871	85	1	and	and	CCONJ
iajs-871	85	2	only	only	ADV
iajs-871	85	3	if	if	SCONJ
iajs-871	85	4			PROPN
iajs-871	85	5	fcllp	fcllp	PUNCT
iajs-871	85	6			NOUN
iajs-871	85	7	for	for	ADP
iajs-871	85	8	each	each	DET
iajs-871	85	9	f	f	NOUN
iajs-871	85	10	ғ.	ғ.	PUNCT
iajs-871	86	1	proof	proof	NOUN
iajs-871	86	2	:	:	PUNCT
iajs-871	86	3	the	the	DET
iajs-871	86	4	“	"	PUNCT
iajs-871	86	5	first	first	ADJ
iajs-871	86	6	direction	direction	NOUN
iajs-871	86	7	”	"	PUNCT
iajs-871	86	8	suppose	suppose	VERB
iajs-871	86	9	that	that	SCONJ
iajs-871	86	10	p	p	PROPN
iajs-871	86	11	is	be	AUX
iajs-871	86	12	an	an	DET
iajs-871	86	13	l	l	NOUN
iajs-871	86	14	-	-	ADJ
iajs-871	86	15	cluster	cluster	NOUN
iajs-871	86	16	point	point	NOUN
iajs-871	86	17	of	of	ADP
iajs-871	86	18	ғ.	ғ.	NOUN
iajs-871	86	19	then	then	ADV
iajs-871	86	20	for	for	ADP
iajs-871	86	21	each	each	DET
iajs-871	86	22	l	l	ADJ
iajs-871	86	23	-	-	ADJ
iajs-871	86	24	open	open	ADJ
iajs-871	86	25	neighborhood	neighborhood	NOUN
iajs-871	86	26	g	g	NOUN
iajs-871	86	27	of	of	ADP
iajs-871	86	28	p	p	PROPN
iajs-871	86	29	,	,	PUNCT
iajs-871	86	30	fg	fg	PROPN
iajs-871	86	31	for	for	ADP
iajs-871	86	32	each	each	DET
iajs-871	86	33	f	f	NUM
iajs-871	86	34	ғ	ғ	PUNCT
iajs-871	86	35	,	,	PUNCT
iajs-871	86	36	it	it	PRON
iajs-871	86	37	follows	follow	VERB
iajs-871	86	38	by	by	ADP
iajs-871	86	39	theorem	theorem	NOUN
iajs-871	86	40	(	(	PUNCT
iajs-871	86	41	2.16	2.16	NUM
iajs-871	86	42	)	)	PUNCT
iajs-871	87	1	that	that	PRON
iajs-871	87	2			NOUN
iajs-871	87	3	fcllp	fcllp	PUNCT
iajs-871	87	4			NOUN
iajs-871	87	5	for	for	ADP
iajs-871	87	6	each	each	DET
iajs-871	87	7	f	f	NOUN
iajs-871	87	8	ғ.	ғ.	PUNCT
iajs-871	88	1	ibn	ibn	PROPN
iajs-871	88	2	alhaitham	alhaitham	NOUN
iajs-871	88	3	j.	j.	PROPN
iajs-871	89	1	fo	fo	ADP
iajs-871	89	2	r	r	NOUN
iajs-871	89	3	pure	pure	ADJ
iajs-871	89	4	&	&	CCONJ
iajs-871	89	5	appl	appl	PROPN
iajs-871	89	6	.	.	PUNCT
iajs-871	90	1	sc	sc	PROPN
iajs-871	90	2	i.	i.	PROPN
iajs-871	90	3	vo	vo	PROPN
iajs-871	91	1	l.24	l.24	PROPN
iajs-871	91	2	(	(	PUNCT
iajs-871	91	3	1	1	NUM
iajs-871	91	4	)	)	PUNCT
iajs-871	91	5	2011	2011	NUM
iajs-871	91	6	the	the	DET
iajs-871	91	7	“	"	PUNCT
iajs-871	91	8	second	second	ADJ
iajs-871	91	9	direction	direction	NOUN
iajs-871	91	10	”	"	PUNCT
iajs-871	91	11	assume	assume	VERB
iajs-871	91	12	that	that	SCONJ
iajs-871	91	13			NOUN
iajs-871	92	1	fcllp	fcllp	X
iajs-871	92	2			NOUN
iajs-871	92	3	for	for	ADP
iajs-871	92	4	each	each	DET
iajs-871	92	5	f	f	NUM
iajs-871	92	6	ғ	ғ	ADP
iajs-871	92	7	,	,	PUNCT
iajs-871	92	8	then	then	ADV
iajs-871	92	9	by	by	ADP
iajs-871	92	10	theorem	theorem	NOUN
iajs-871	92	11	(	(	PUNCT
iajs-871	92	12	2.16	2.16	NUM
iajs-871	92	13	)	)	PUNCT
iajs-871	92	14	every	every	DET
iajs-871	92	15	l	l	NOUN
iajs-871	92	16	-	-	ADJ
iajs-871	92	17	open	open	ADJ
iajs-871	92	18	neighborhood	neighborhood	NOUN
iajs-871	92	19	of	of	ADP
iajs-871	92	20	p	p	NOUN
iajs-871	92	21	intersects	intersect	NOUN
iajs-871	92	22	f	f	NOUN
iajs-871	92	23	for	for	ADP
iajs-871	92	24	each	each	DET
iajs-871	92	25	f	f	NOUN
iajs-871	92	26	ғ.	ғ.	VERB
iajs-871	93	1	hence	hence	ADV
iajs-871	93	2	p	p	PROPN
iajs-871	93	3	is	be	AUX
iajs-871	93	4	an	an	DET
iajs-871	93	5	l	l	NOUN
iajs-871	93	6	-	-	ADJ
iajs-871	93	7	cluster	cluster	NOUN
iajs-871	93	8	point	point	NOUN
iajs-871	93	9	of	of	ADP
iajs-871	93	10	ғ	ғ	DET
iajs-871	93	11	definition	definition	NOUN
iajs-871	93	12	(	(	PUNCT
iajs-871	93	13	2.22	2.22	NUM
iajs-871	93	14	)	)	PUNCT
iajs-871	94	1	[	[	X
iajs-871	94	2	2	2	X
iajs-871	94	3	]	]	PUNCT
iajs-871	94	4	a	a	DET
iajs-871	94	5	collection	collection	NOUN
iajs-871	94	6	of	of	ADP
iajs-871	94	7	sets	set	NOUN
iajs-871	94	8	is	be	AUX
iajs-871	94	9	said	say	VERB
iajs-871	94	10	to	to	PART
iajs-871	94	11	have	have	VERB
iajs-871	94	12	the	the	DET
iajs-871	94	13	finite	finite	ADJ
iajs-871	94	14	intersection	intersection	NOUN
iajs-871	94	15	property	property	NOUN
iajs-871	94	16	(	(	PUNCT
iajs-871	94	17	fip	fip	PROPN
iajs-871	94	18	)	)	PUNCT
iajs-871	95	1	if	if	SCONJ
iajs-871	95	2	and	and	CCONJ
iajs-871	95	3	only	only	ADV
iajs-871	95	4	if	if	SCONJ
iajs-871	95	5	the	the	DET
iajs-871	95	6	intersection	intersection	NOUN
iajs-871	95	7	of	of	ADP
iajs-871	95	8	each	each	DET
iajs-871	95	9	finite	finite	ADJ
iajs-871	95	10	subcollection	subcollection	NOUN
iajs-871	95	11	of	of	ADP
iajs-871	95	12	it	it	PRON
iajs-871	95	13	is	be	AUX
iajs-871	95	14	non	non	X
iajs-871	95	15	empty	empty	ADJ
iajs-871	95	16	.	.	PUNCT
iajs-871	96	1	remark	remark	NOUN
iajs-871	96	2	(	(	PUNCT
iajs-871	96	3	2.23	2.23	NUM
iajs-871	96	4	)	)	PUNCT
iajs-871	97	1	[	[	X
iajs-871	97	2	2	2	X
iajs-871	97	3	]	]	PUNCT
iajs-871	97	4	every	every	DET
iajs-871	97	5	filter	filter	NOUN
iajs-871	97	6	in	in	ADP
iajs-871	97	7	a	a	DET
iajs-871	97	8	nonempty	nonempty	ADV
iajs-871	97	9	set	set	VERB
iajs-871	97	10	x	x	PUNCT
iajs-871	97	11	has	have	VERB
iajs-871	97	12	the	the	DET
iajs-871	97	13	fip	fip	PROPN
iajs-871	97	14	.	.	PROPN
iajs-871	97	15	theorem	theorem	PROPN
iajs-871	97	16	(	(	PUNCT
iajs-871	97	17	2.24	2.24	NUM
iajs-871	97	18	)	)	PUNCT
iajs-871	98	1	[	[	X
iajs-871	98	2	3	3	X
iajs-871	98	3	]	]	PUNCT
iajs-871	98	4	let	let	VERB
iajs-871	98	5	a	a	PRON
iajs-871	98	6	be	be	AUX
iajs-871	98	7	a	a	DET
iajs-871	98	8	non	non	X
iajs-871	98	9	empty	empty	ADJ
iajs-871	98	10	collection	collection	NOUN
iajs-871	98	11	of	of	ADP
iajs-871	98	12	subsets	subset	NOUN
iajs-871	98	13	of	of	ADP
iajs-871	98	14	a	a	DET
iajs-871	98	15	set	set	NOUN
iajs-871	98	16	x	x	PUNCT
iajs-871	98	17	such	such	ADJ
iajs-871	98	18	that	that	SCONJ
iajs-871	98	19	a	a	PRON
iajs-871	98	20	has	have	VERB
iajs-871	98	21	the	the	DET
iajs-871	98	22	fip	fip	PROPN
iajs-871	98	23	.	.	PUNCT
iajs-871	99	1	then	then	ADV
iajs-871	99	2	there	there	PRON
iajs-871	99	3	exists	exist	VERB
iajs-871	99	4	an	an	DET
iajs-871	99	5	ultra	ultra	ADJ
iajs-871	99	6	filter	filter	NOUN
iajs-871	99	7	ғ	ғ	ADP
iajs-871	99	8	containing	contain	VERB
iajs-871	99	9	a	a	PRON
iajs-871	99	10	.	.	PUNCT
iajs-871	100	1	proposition	proposition	NOUN
iajs-871	100	2	(	(	PUNCT
iajs-871	100	3	2.25	2.25	NUM
iajs-871	100	4	)	)	PUNCT
iajs-871	101	1	[	[	X
iajs-871	101	2	4	4	X
iajs-871	101	3	]	]	PUNCT
iajs-871	101	4	let	let	VERB
iajs-871	101	5	a	a	PRON
iajs-871	101	6	be	be	AUX
iajs-871	101	7	a	a	DET
iajs-871	101	8	subset	subset	NOUN
iajs-871	101	9	of	of	ADP
iajs-871	101	10	a	a	DET
iajs-871	101	11	bitopological	bitopological	ADJ
iajs-871	101	12	space	space	NOUN
iajs-871	101	13	.	.	PUNCT
iajs-871	102	1	then	then	ADV
iajs-871	102	2	a	a	PRON
iajs-871	102	3	is	be	AUX
iajs-871	102	4	an	an	DET
iajs-871	102	5	l	l	NOUN
iajs-871	102	6	-	-	ADJ
iajs-871	102	7	closed	closed	ADJ
iajs-871	102	8	set	set	NOUN
iajs-871	102	9	if	if	SCONJ
iajs-871	102	10	and	and	CCONJ
iajs-871	102	11	only	only	ADV
iajs-871	102	12	if	if	SCONJ
iajs-871	102	13			NOUN
iajs-871	102	14	aclla	aclla	SYM
iajs-871	102	15			PROPN
iajs-871	102	16	.	.	PUNCT
iajs-871	103	1	theorem	theorem	NOUN
iajs-871	103	2	(	(	PUNCT
iajs-871	103	3	2.26	2.26	NUM
iajs-871	103	4	)	)	PUNCT
iajs-871	103	5	let	let	AUX
iajs-871	103	6	be	be	AUX
iajs-871	103	7	a	a	DET
iajs-871	103	8	bitopological	bitopological	ADJ
iajs-871	103	9	space	space	NOUN
iajs-871	103	10	.	.	PUNCT
iajs-871	104	1	then	then	ADV
iajs-871	104	2	the	the	DET
iajs-871	104	3	following	follow	VERB
iajs-871	104	4	statements	statement	NOUN
iajs-871	104	5	are	be	AUX
iajs-871	104	6	equivalent	equivalent	ADJ
iajs-871	104	7	:	:	PUNCT
iajs-871	104	8	1x	1x	NUM
iajs-871	104	9	is	be	AUX
iajs-871	104	10	an	an	DET
iajs-871	104	11	l	l	ADJ
iajs-871	104	12	-	-	ADJ
iajs-871	104	13	compact	compact	ADJ
iajs-871	104	14	space	space	NOUN
iajs-871	104	15	,	,	PUNCT
iajs-871	104	16	2every	2every	ADJ
iajs-871	104	17	collection	collection	NOUN
iajs-871	104	18	of	of	ADP
iajs-871	104	19	l	l	NOUN
iajs-871	104	20	-	-	ADJ
iajs-871	104	21	closed	closed	ADJ
iajs-871	104	22	subsets	subset	NOUN
iajs-871	104	23	of	of	ADP
iajs-871	104	24	x	x	PUNCT
iajs-871	104	25	with	with	SCONJ
iajs-871	104	26	the	the	DET
iajs-871	104	27	fip	fip	PROPN
iajs-871	104	28	has	have	VERB
iajs-871	104	29	anon	anon	X
iajs-871	104	30	empty	empty	ADJ
iajs-871	104	31	intersection	intersection	NOUN
iajs-871	104	32	,	,	PUNCT
iajs-871	104	33	and	and	CCONJ
iajs-871	104	34	3every	3every	NUM
iajs-871	104	35	filter	filter	NOUN
iajs-871	104	36	on	on	ADP
iajs-871	104	37	x	x	PUNCT
iajs-871	104	38	has	have	VERB
iajs-871	104	39	an	an	DET
iajs-871	104	40	l	l	ADJ
iajs-871	104	41	-	-	PUNCT
iajs-871	104	42	cluster	cluster	NOUN
iajs-871	104	43	point	point	NOUN
iajs-871	104	44	.	.	PUNCT
iajs-871	105	1	proof	proof	NOUN
iajs-871	105	2	:	:	PUNCT
iajs-871	105	3	1→2	1→2	ADV
iajs-871	105	4	let	let	VERB
iajs-871	105	5			PRON
iajs-871	105	6			VERB
iajs-871	105	7			NOUN
iajs-871	105	8	:	:	PUNCT
iajs-871	105	9	f	f	X
iajs-871	105	10	be	be	AUX
iajs-871	105	11	a	a	DET
iajs-871	105	12	collection	collection	NOUN
iajs-871	105	13	of	of	ADP
iajs-871	105	14	l	l	NOUN
iajs-871	105	15	-	-	ADJ
iajs-871	105	16	closed	closed	ADJ
iajs-871	105	17	subset	subset	NOUN
iajs-871	105	18	of	of	ADP
iajs-871	105	19	x	x	PUNCT
iajs-871	105	20	with	with	ADP
iajs-871	105	21	the	the	DET
iajs-871	105	22	fip	fip	PROPN
iajs-871	105	23	.	.	PROPN
iajs-871	105	24	suppose	suppose	VERB
iajs-871	105	25	that	that	SCONJ
iajs-871	105	26			NOUN
iajs-871	105	27			X
iajs-871	105	28			X
iajs-871	105	29			PROPN
iajs-871	105	30			PROPN
iajs-871	105	31	f	f	NOUN
iajs-871	105	32	,	,	PUNCT
iajs-871	105	33	it	it	PRON
iajs-871	105	34	follows	follow	VERB
iajs-871	105	35	by	by	ADP
iajs-871	105	36	de	de	PROPN
iajs-871	105	37	-	-	PROPN
iajs-871	105	38	morgan	morgan	ADJ
iajs-871	105	39	laws	law	NOUN
iajs-871	105	40	that	that	PRON
iajs-871	105	41	xf	xf	PROPN
iajs-871	105	42	c	c	PROPN
iajs-871	105	43			NOUN
iajs-871	105	44			ADJ
iajs-871	105	45			ADJ
iajs-871	105	46			NOUN
iajs-871	105	47			X
iajs-871	105	48	therefore	therefore	ADV
iajs-871	105	49			PROPN
iajs-871	106	1			PROPN
iajs-871	106	2			PROPN
iajs-871	107	1			INTJ
iajs-871	107	2			NUM
iajs-871	107	3			ADP
iajs-871	107	4			X
iajs-871	107	5			NOUN
iajs-871	107	6	:	:	PUNCT
iajs-871	107	7	cf	cf	NOUN
iajs-871	107	8	forms	form	VERB
iajs-871	107	9	an	an	DET
iajs-871	107	10	l	l	NOUN
iajs-871	107	11	-	-	ADJ
iajs-871	107	12	open	open	ADJ
iajs-871	107	13	cover	cover	NOUN
iajs-871	107	14	for	for	ADP
iajs-871	107	15	x	x	SYM
iajs-871	107	16	which	which	PRON
iajs-871	107	17	is	be	AUX
iajs-871	107	18	an	an	DET
iajs-871	107	19	l	l	ADJ
iajs-871	107	20	-	-	ADJ
iajs-871	107	21	compact	compact	ADJ
iajs-871	107	22	space	space	NOUN
iajs-871	107	23	,	,	PUNCT
iajs-871	107	24	then	then	ADV
iajs-871	107	25	there	there	PRON
iajs-871	107	26	exists	exist	VERB
iajs-871	107	27	finitely	finitely	ADV
iajs-871	107	28	many	many	ADJ
iajs-871	107	29	elements	element	NOUN
iajs-871	107	30	n	n	NOUN
iajs-871	107	31	,	,	PUNCT
iajs-871	107	32	,	,	PUNCT
iajs-871	107	33	,	,	PUNCT
iajs-871	107	34	21	21	NUM
iajs-871	107	35			NUM
iajs-871	107	36	such	such	ADJ
iajs-871	107	37	that	that	SCONJ
iajs-871	107	38	xf	xf	PROPN
iajs-871	107	39	n	n	PROPN
iajs-871	108	1	i	i	PRON
iajs-871	108	2	c	c	VERB
iajs-871	109	1	i	i	PRON
iajs-871	109	2			VERB
iajs-871	109	3			VERB
iajs-871	109	4			ADJ
iajs-871	109	5	1	1	NUM
iajs-871	109	6			NOUN
iajs-871	109	7	.	.	PUNCT
iajs-871	110	1	again	again	ADV
iajs-871	110	2	by	by	ADP
iajs-871	110	3	de	de	PROPN
iajs-871	110	4	-	-	PROPN
iajs-871	110	5	morgan	morgan	ADJ
iajs-871	110	6	laws	law	NOUN
iajs-871	110	7	we	we	PRON
iajs-871	110	8	have	have	VERB
iajs-871	111	1	that	that	DET
iajs-871	111	2			VERB
iajs-871	112	1			PRON
iajs-871	112	2			PROPN
iajs-871	112	3			PROPN
iajs-871	113	1	n	n	INTJ
iajs-871	113	2	i	i	PRON
iajs-871	114	1	i	i	PRON
iajs-871	114	2	f	f	PROPN
iajs-871	114	3	1	1	NUM
iajs-871	114	4	which	which	PRON
iajs-871	114	5	is	be	AUX
iajs-871	114	6	a	a	DET
iajs-871	114	7	contradiction	contradiction	NOUN
iajs-871	114	8	since	since	SCONJ
iajs-871	114	9			PROPN
iajs-871	114	10			NOUN
iajs-871	114	11			X
iajs-871	114	12	:	:	PUNCT
iajs-871	114	13	f	f	PROPN
iajs-871	114	14	has	have	VERB
iajs-871	114	15	the	the	DET
iajs-871	114	16	fip	fip	PROPN
iajs-871	114	17	.	.	PROPN
iajs-871	115	1	hence	hence	ADV
iajs-871	115	2			NOUN
iajs-871	115	3			X
iajs-871	115	4			X
iajs-871	115	5			PROPN
iajs-871	115	6			PROPN
iajs-871	115	7	f	f	VERB
iajs-871	115	8	ibn	ibn	PROPN
iajs-871	115	9	alhaitham	alhaitham	NOUN
iajs-871	115	10	j.	j.	PROPN
iajs-871	116	1	fo	fo	ADP
iajs-871	116	2	r	r	NOUN
iajs-871	116	3	pure	pure	ADJ
iajs-871	116	4	&	&	CCONJ
iajs-871	116	5	appl	appl	PROPN
iajs-871	116	6	.	.	PUNCT
iajs-871	117	1	sc	sc	PROPN
iajs-871	117	2	i.	i.	PROPN
iajs-871	117	3	vo	vo	PROPN
iajs-871	118	1	l.24	l.24	PROPN
iajs-871	118	2	(	(	PUNCT
iajs-871	118	3	1	1	NUM
iajs-871	118	4	)	)	PUNCT
iajs-871	118	5	2011	2011	NUM
iajs-871	118	6	2→3	2→3	NOUN
iajs-871	118	7	let	let	VERB
iajs-871	118	8	ғ	ғ	PUNCT
iajs-871	118	9	be	be	AUX
iajs-871	118	10	a	a	DET
iajs-871	118	11	filter	filter	NOUN
iajs-871	118	12	on	on	ADP
iajs-871	118	13	x	x	NOUN
iajs-871	118	14	,	,	PUNCT
iajs-871	118	15	then	then	ADV
iajs-871	118	16	by	by	ADP
iajs-871	118	17	remark	remark	NOUN
iajs-871	118	18	(	(	PUNCT
iajs-871	118	19	2.23	2.23	NUM
iajs-871	118	20	)	)	PUNCT
iajs-871	118	21	ғ	ғ	PRON
iajs-871	118	22	has	have	VERB
iajs-871	118	23	the	the	DET
iajs-871	118	24	fip	fip	NOUN
iajs-871	118	25	,	,	PUNCT
iajs-871	118	26	it	it	PRON
iajs-871	118	27	follows	follow	VERB
iajs-871	118	28	that	that	SCONJ
iajs-871	118	29	the	the	DET
iajs-871	118	30	collection	collection	NOUN
iajs-871	118	31			PROPN
iajs-871	118	32			NOUN
iajs-871	118	33			NUM
iajs-871	118	34	ffcll	ffcll	NOUN
iajs-871	118	35	:	:	PUNCT
iajs-871	118	36	ғ	ғ	SYM
iajs-871	118	37	}	}	PUNCT
iajs-871	118	38	of	of	ADP
iajs-871	118	39	l	l	NOUN
iajs-871	118	40	-	-	ADJ
iajs-871	118	41	closed	closed	ADJ
iajs-871	118	42	subsets	subset	NOUN
iajs-871	118	43	of	of	ADP
iajs-871	118	44	x	x	PRON
iajs-871	118	45	also	also	ADV
iajs-871	118	46	has	have	VERB
iajs-871	118	47	the	the	DET
iajs-871	118	48	fip	fip	NOUN
iajs-871	118	49	,	,	PUNCT
iajs-871	118	50	so	so	ADV
iajs-871	118	51	by	by	ADP
iajs-871	118	52	(	(	PUNCT
iajs-871	118	53	2	2	X
iajs-871	118	54	)	)	PUNCT
iajs-871	118	55	there	there	PRON
iajs-871	118	56	exists	exist	VERB
iajs-871	118	57	at	at	ADP
iajs-871	118	58	least	least	ADV
iajs-871	118	59	one	one	NUM
iajs-871	118	60	point	point	NOUN
iajs-871	118	61			NOUN
iajs-871	118	62			NOUN
iajs-871	118	63	:	:	PUNCT
iajs-871	118	64			PROPN
iajs-871	118	65	ffcllx	ffcllx	PROPN
iajs-871	118	66			PROPN
iajs-871	118	67	ғ	ғ	PROPN
iajs-871	118	68	}	}	PUNCT
iajs-871	118	69	then	then	ADV
iajs-871	118	70	by	by	ADP
iajs-871	118	71	theorem	theorem	NOUN
iajs-871	118	72	(	(	PUNCT
iajs-871	118	73	2.21	2.21	NUM
iajs-871	118	74	)	)	PUNCT
iajs-871	118	75	x	x	X
iajs-871	118	76	is	be	AUX
iajs-871	118	77	an	an	DET
iajs-871	118	78	l	l	NOUN
iajs-871	118	79	-	-	ADJ
iajs-871	118	80	cluster	cluster	NOUN
iajs-871	118	81	point	point	NOUN
iajs-871	118	82	of	of	ADP
iajs-871	118	83	ғ	ғ	PRON
iajs-871	118	84	.	.	PUNCT
iajs-871	119	1	thus	thus	ADV
iajs-871	119	2	every	every	DET
iajs-871	119	3	filter	filter	NOUN
iajs-871	119	4	on	on	ADP
iajs-871	119	5	x	x	PUNCT
iajs-871	119	6	has	have	VERB
iajs-871	119	7	an	an	DET
iajs-871	119	8	l	l	ADJ
iajs-871	119	9	-	-	PUNCT
iajs-871	119	10	cluster	cluster	NOUN
iajs-871	119	11	point	point	NOUN
iajs-871	119	12	.	.	PUNCT
iajs-871	120	1	3→1	3→1	NOUN
iajs-871	120	2	assume	assume	VERB
iajs-871	120	3	that	that	SCONJ
iajs-871	120	4	every	every	DET
iajs-871	120	5	filter	filter	NOUN
iajs-871	120	6	on	on	ADP
iajs-871	120	7	x	x	PUNCT
iajs-871	120	8	has	have	VERB
iajs-871	120	9	an	an	DET
iajs-871	120	10	l	l	ADJ
iajs-871	120	11	-	-	NOUN
iajs-871	120	12	cluster	cluster	NOUN
iajs-871	120	13	point	point	NOUN
iajs-871	120	14	and	and	CCONJ
iajs-871	120	15	let	let	VERB
iajs-871	120	16			NOUN
iajs-871	120	17	be	be	AUX
iajs-871	120	18	an	an	DET
iajs-871	120	19	l	l	NOUN
iajs-871	120	20	-	-	ADJ
iajs-871	120	21	open	open	ADJ
iajs-871	120	22	cover	cover	NOUN
iajs-871	120	23	of	of	ADP
iajs-871	120	24	x.	x.	NOUN
iajs-871	120	25	suppose	suppose	VERB
iajs-871	120	26	,	,	PUNCT
iajs-871	120	27	if	if	SCONJ
iajs-871	120	28	possible	possible	ADJ
iajs-871	120	29	,	,	PUNCT
iajs-871	120	30	has	has	INTJ
iajs-871	120	31	no	no	DET
iajs-871	120	32	finite	finite	ADJ
iajs-871	120	33	sub	sub	NOUN
iajs-871	120	34	cover	cover	VERB
iajs-871	120	35	the	the	DET
iajs-871	120	36	collection	collection	NOUN
iajs-871	120	37			PROPN
iajs-871	120	38			PROPN
iajs-871	120	39	:	:	PUNCT
iajs-871	120	40			NUM
iajs-871	120	41	ggx	ggx	PROPN
iajs-871	120	42	has	have	VERB
iajs-871	120	43	the	the	DET
iajs-871	120	44	fip	fip	NOUN
iajs-871	120	45	,	,	PUNCT
iajs-871	120	46	for	for	SCONJ
iajs-871	120	47	if	if	SCONJ
iajs-871	120	48	there	there	PRON
iajs-871	120	49	is	be	VERB
iajs-871	120	50	a	a	DET
iajs-871	120	51	finite	finite	ADJ
iajs-871	120	52	sub	sub	NOUN
iajs-871	120	53	collection	collection	NOUN
iajs-871	120	54			PROPN
iajs-871	120	55			PROPN
iajs-871	120	56	1	1	NUM
iajs-871	120	57	:	:	PUNCT
iajs-871	120	58	nigx	nigx	PROPN
iajs-871	120	59	i	i	PRON
iajs-871	120	60			PROPN
iajs-871	120	61	of	of	ADP
iajs-871	120	62	such	such	ADJ
iajs-871	120	63	that	that	SCONJ
iajs-871	120	64			PROPN
iajs-871	120	65			X
iajs-871	120	66			NUM
iajs-871	120	67	1	1	NUM
iajs-871	120	68	:	:	PUNCT
iajs-871	120	69	nigx	nigx	PROPN
iajs-871	120	70	i	i	PROPN
iajs-871	120	71	this	this	PRON
iajs-871	120	72	implies	imply	VERB
iajs-871	120	73	that	that	SCONJ
iajs-871	120	74			PROPN
iajs-871	120	75			PROPN
iajs-871	120	76	xnigi	xnigi	PROPN
iajs-871	120	77			ADJ
iajs-871	120	78	1:	1:	NUM
iajs-871	120	79	which	which	PRON
iajs-871	120	80	contradicts	contradict	VERB
iajs-871	120	81	our	our	PRON
iajs-871	120	82	supposition	supposition	NOUN
iajs-871	120	83	that	that	SCONJ
iajs-871	120	84	has	has	NOUN
iajs-871	120	85	no	no	DET
iajs-871	120	86	finite	finite	ADJ
iajs-871	120	87	sub	sub	NOUN
iajs-871	120	88	cover	cover	NOUN
iajs-871	120	89	,	,	PUNCT
iajs-871	120	90	thus	thus	ADV
iajs-871	120	91	must	must	AUX
iajs-871	120	92	have	have	AUX
iajs-871	120	93	the	the	DET
iajs-871	120	94	fip	fip	NOUN
iajs-871	120	95	,	,	PUNCT
iajs-871	120	96	it	it	PRON
iajs-871	120	97	follows	follow	VERB
iajs-871	120	98	by	by	ADP
iajs-871	120	99	theorem	theorem	NOUN
iajs-871	120	100	(	(	PUNCT
iajs-871	120	101	2.24)that	2.24)that	NUM
iajs-871	120	102	there	there	PRON
iajs-871	120	103	exists	exist	VERB
iajs-871	120	104	an	an	DET
iajs-871	120	105	ultra	ultra	ADJ
iajs-871	120	106	filter	filter	NOUN
iajs-871	120	107	ғ	ғ	NOUN
iajs-871	120	108	on	on	ADP
iajs-871	120	109	x	x	PUNCT
iajs-871	120	110	containing	contain	VERB
iajs-871	120	111	.by	.by	PROPN
iajs-871	120	112	(	(	PUNCT
iajs-871	120	113	3	3	NUM
iajs-871	120	114	)	)	PUNCT
iajs-871	120	115	ғ	ғ	PRON
iajs-871	120	116	has	have	VERB
iajs-871	120	117	an	an	DET
iajs-871	120	118	l	l	NOUN
iajs-871	120	119	-	-	NOUN
iajs-871	120	120	cluster	cluster	NOUN
iajs-871	120	121	point	point	NOUN
iajs-871	120	122	xx	xx	PROPN
iajs-871	120	123	,	,	PUNCT
iajs-871	120	124	then	then	ADV
iajs-871	120	125	by	by	ADP
iajs-871	120	126	theorem	theorem	NOUN
iajs-871	120	127	(	(	PUNCT
iajs-871	120	128	2.21	2.21	NUM
iajs-871	120	129	)	)	PUNCT
iajs-871	120	130			NOUN
iajs-871	120	131	fcllx	fcllx	PUNCT
iajs-871	120	132			PROPN
iajs-871	120	133	for	for	ADP
iajs-871	120	134	each	each	DET
iajs-871	120	135	f	f	NUM
iajs-871	120	136	ғ	ғ	ADP
iajs-871	120	137	,	,	PUNCT
iajs-871	120	138	in	in	ADP
iajs-871	120	139	particular	particular	ADJ
iajs-871	120	140			NOUN
iajs-871	120	141	gxcllx	gxcllx	PUNCT
iajs-871	121	1			VERB
iajs-871	121	2	for	for	ADP
iajs-871	121	3	each	each	DET
iajs-871	121	4	g	g	NUM
iajs-871	121	5	.	.	NOUN
iajs-871	122	1	but	but	CCONJ
iajs-871	122	2	x	x	NOUN
iajs-871	122	3	-	-	PUNCT
iajs-871	122	4	g	g	PROPN
iajs-871	122	5	is	be	AUX
iajs-871	122	6	an	an	DET
iajs-871	122	7	l	l	NOUN
iajs-871	122	8	-	-	ADJ
iajs-871	122	9	closed	closed	ADJ
iajs-871	122	10	subset	subset	NOUN
iajs-871	122	11	of	of	ADP
iajs-871	122	12	x	x	PUNCT
iajs-871	122	13	for	for	ADP
iajs-871	122	14	each	each	DET
iajs-871	122	15	g	g	NOUN
iajs-871	122	16			NOUN
iajs-871	122	17	,	,	PUNCT
iajs-871	122	18	therefore	therefore	ADV
iajs-871	122	19	by	by	ADP
iajs-871	122	20	propostion	propostion	NOUN
iajs-871	122	21	(	(	PUNCT
iajs-871	122	22	2.25	2.25	NUM
iajs-871	122	23	)	)	PUNCT
iajs-871	122	24			NOUN
iajs-871	122	25			PROPN
iajs-871	122	26	gxgxcll	gxgxcll	NOUN
iajs-871	122	27			PROPN
iajs-871	122	28	for	for	ADP
iajs-871	122	29	every	every	DET
iajs-871	122	30	g	g	NOUN
iajs-871	122	31	.	.	NOUN
iajs-871	122	32	this	this	PRON
iajs-871	122	33	implies	imply	VERB
iajs-871	122	34			PROPN
iajs-871	122	35			PROPN
iajs-871	122	36	ggxx	ggxx	NOUN
iajs-871	122	37	:	:	PUNCT
iajs-871	122	38			ADP
iajs-871	122	39			NOUN
iajs-871	122	40	}	}	PUNCT
iajs-871	122	41	,	,	PUNCT
iajs-871	122	42	so	so	ADV
iajs-871	122	43	by	by	ADP
iajs-871	122	44	de	de	PROPN
iajs-871	122	45	-	-	NOUN
iajs-871	122	46	morgen	morgen	X
iajs-871	122	47	laws	law	NOUN
iajs-871	122	48			PROPN
iajs-871	122	49			PROPN
iajs-871	122	50	ggxx	ggxx	NOUN
iajs-871	122	51	:	:	PUNCT
iajs-871	122	52			ADJ
iajs-871	122	53	},that	},that	NOUN
iajs-871	122	54	is	be	AUX
iajs-871	122	55	,	,	PUNCT
iajs-871	122	56			PROPN
iajs-871	122	57			VERB
iajs-871	122	58	ggx	ggx	NOUN
iajs-871	122	59	:	:	PUNCT
iajs-871	122	60			ADJ
iajs-871	122	61	},which	},which	PROPN
iajs-871	122	62	is	be	AUX
iajs-871	122	63	a	a	DET
iajs-871	122	64	contradiction	contradiction	NOUN
iajs-871	122	65	with	with	ADP
iajs-871	122	66	the	the	DET
iajs-871	122	67	fact	fact	NOUN
iajs-871	122	68	that	that	SCONJ
iajs-871	122	69			NOUN
iajs-871	122	70	is	be	AUX
iajs-871	122	71	an	an	DET
iajs-871	122	72	l	l	NOUN
iajs-871	122	73	-	-	ADJ
iajs-871	122	74	open	open	ADJ
iajs-871	122	75	cover	cover	NOUN
iajs-871	122	76	of	of	ADP
iajs-871	122	77	x	x	PRON
iajs-871	122	78	,	,	PUNCT
iajs-871	122	79	hence	hence	ADV
iajs-871	122	80			NOUN
iajs-871	122	81	must	must	AUX
iajs-871	122	82	have	have	VERB
iajs-871	122	83	a	a	DET
iajs-871	122	84	finite	finite	ADJ
iajs-871	122	85	sub	sub	NOUN
iajs-871	122	86	cover	cover	NOUN
iajs-871	122	87	and	and	CCONJ
iajs-871	122	88	consequently	consequently	ADV
iajs-871	122	89	x	x	PRON
iajs-871	122	90	is	be	AUX
iajs-871	122	91	an	an	DET
iajs-871	122	92	l	l	ADJ
iajs-871	122	93	-	-	ADJ
iajs-871	122	94	compact	compact	ADJ
iajs-871	122	95	space	space	NOUN
iajs-871	122	96	.	.	PUNCT
iajs-871	123	1	proposition	proposition	NOUN
iajs-871	123	2	(	(	PUNCT
iajs-871	123	3	2.27	2.27	NUM
iajs-871	123	4	):	):	PUNCT
iajs-871	123	5	let	let	AUX
iajs-871	123	6	be	be	AUX
iajs-871	123	7	a	a	DET
iajs-871	123	8	bitopological	bitopological	ADJ
iajs-871	123	9	space	space	NOUN
iajs-871	123	10	.	.	PUNCT
iajs-871	124	1	if	if	SCONJ
iajs-871	124	2	x	x	PRON
iajs-871	124	3	is	be	AUX
iajs-871	124	4	an	an	DET
iajs-871	124	5	l	l	ADJ
iajs-871	124	6	-	-	ADJ
iajs-871	124	7	compact	compact	ADJ
iajs-871	124	8	space	space	NOUN
iajs-871	124	9	,	,	PUNCT
iajs-871	124	10	then	then	ADV
iajs-871	124	11	every	every	DET
iajs-871	124	12	net	net	NOUN
iajs-871	124	13	in	in	ADP
iajs-871	124	14	x	x	PROPN
iajs-871	124	15	has	have	VERB
iajs-871	124	16	an	an	DET
iajs-871	124	17	l	l	ADJ
iajs-871	124	18	-	-	PUNCT
iajs-871	124	19	cluster	cluster	NOUN
iajs-871	124	20	point	point	NOUN
iajs-871	124	21	.	.	PUNCT
iajs-871	125	1	proof	proof	NOUN
iajs-871	125	2	:	:	PUNCT
iajs-871	125	3	let	let	VERB
iajs-871	125	4			PROPN
iajs-871	125	5			ADP
iajs-871	125	6	,	,	PUNCT
iajs-871	125	7	,	,	PUNCT
iajs-871	125	8	,	,	PUNCT
iajs-871	125	9	axf	axf	ADV
iajs-871	125	10	be	be	AUX
iajs-871	125	11	a	a	DET
iajs-871	125	12	net	net	NOUN
iajs-871	125	13	in	in	ADP
iajs-871	125	14	x	x	X
iajs-871	125	15	.	.	PUNCT
iajs-871	126	1	for	for	ADP
iajs-871	126	2	each	each	DET
iajs-871	126	3	aa	aa	NOUN
iajs-871	126	4	let	let	VERB
iajs-871	126	5			NOUN
iajs-871	127	1	ainaxk	ainaxk	NOUN
iajs-871	127	2	f	f	PROPN
iajs-871	127	3	xa	xa	PROPN
iajs-871	127	4			ADJ
iajs-871	127	5	:	:	PUNCT
iajs-871	127	6	.	.	PUNCT
iajs-871	128	1	since	since	SCONJ
iajs-871	128	2	a	a	PRON
iajs-871	128	3	is	be	AUX
iajs-871	128	4	directed	direct	VERB
iajs-871	128	5	by	by	ADP
iajs-871	128	6			NUM
iajs-871	128	7	,	,	PUNCT
iajs-871	128	8	so	so	CCONJ
iajs-871	128	9	the	the	DET
iajs-871	128	10	collection	collection	NOUN
iajs-871	128	11			PROPN
iajs-871	128	12	aaka	aaka	PROPN
iajs-871	128	13			NOUN
iajs-871	128	14	:	:	PUNCT
iajs-871	128	15	has	have	VERB
iajs-871	128	16	the	the	DET
iajs-871	128	17	fip	fip	PROPN
iajs-871	128	18	.	.	PROPN
iajs-871	128	19	hence	hence	ADV
iajs-871	128	20			PROPN
iajs-871	128	21			NOUN
iajs-871	128	22	aakcll	aakcll	PROPN
iajs-871	128	23	a	a	DET
iajs-871	128	24			PRON
iajs-871	128	25	:	:	PUNCT
iajs-871	128	26	also	also	ADV
iajs-871	128	27	has	have	VERB
iajs-871	128	28	the	the	DET
iajs-871	128	29	fip	fip	NOUN
iajs-871	128	30	,	,	PUNCT
iajs-871	128	31	it	it	PRON
iajs-871	128	32	follows	follow	VERB
iajs-871	128	33	by	by	ADP
iajs-871	128	34	theorem	theorem	NOUN
iajs-871	128	35	(	(	PUNCT
iajs-871	128	36	2.26	2.26	NUM
iajs-871	128	37	)	)	PUNCT
iajs-871	128	38			NOUN
iajs-871	128	39			PROPN
iajs-871	128	40			VERB
iajs-871	128	41			PROPN
iajs-871	128	42			ADP
iajs-871	128	43	aa	aa	PROPN
iajs-871	128	44	akcll	akcll	PROPN
iajs-871	128	45	let	let	VERB
iajs-871	128	46			NOUN
iajs-871	128	47			PUNCT
iajs-871	128	48	aa	aa	PROPN
iajs-871	128	49	akcllp	akcllp	PROPN
iajs-871	128	50			PROPN
iajs-871	128	51			PROPN
iajs-871	128	52	,	,	PUNCT
iajs-871	128	53	then	then	ADV
iajs-871	128	54			PROPN
iajs-871	129	1	akcllp	akcllp	PROPN
iajs-871	129	2			PRON
iajs-871	129	3	for	for	ADP
iajs-871	129	4	each	each	DET
iajs-871	129	5	aa	aa	NOUN
iajs-871	129	6	,	,	PUNCT
iajs-871	129	7	so	so	ADV
iajs-871	129	8	by	by	ADP
iajs-871	129	9	theorem	theorem	NOUN
iajs-871	129	10	(	(	PUNCT
iajs-871	129	11	2.19	2.19	NUM
iajs-871	129	12	)	)	PUNCT
iajs-871	129	13	p	p	NOUN
iajs-871	129	14	is	be	AUX
iajs-871	129	15	an	an	DET
iajs-871	129	16	l	l	NOUN
iajs-871	129	17	-	-	ADJ
iajs-871	129	18	cluster	cluster	NOUN
iajs-871	129	19	point	point	NOUN
iajs-871	129	20	of	of	ADP
iajs-871	129	21	f.	f.	PROPN
iajs-871	129	22	refrences	refrence	VERB
iajs-871	129	23	1	1	NUM
iajs-871	129	24	.	.	PUNCT
iajs-871	130	1	kelly	kelly	PROPN
iajs-871	130	2	,	,	PUNCT
iajs-871	130	3	j.	j.	PROPN
iajs-871	130	4	c.	c.	PROPN
iajs-871	130	5	(	(	PUNCT
iajs-871	130	6	1963	1963	NUM
iajs-871	130	7	)	)	PUNCT
iajs-871	130	8	”	"	PUNCT
iajs-871	130	9	bitopological	bitopological	ADJ
iajs-871	130	10	spaces	space	NOUN
iajs-871	130	11	”	"	PUNCT
iajs-871	130	12	,	,	PUNCT
iajs-871	130	13	proc.london	proc.london	PROPN
iajs-871	130	14	math.soc.13	math.soc.13	NOUN
iajs-871	130	15	,	,	PUNCT
iajs-871	130	16	p.p.71	p.p.71	NOUN
iajs-871	130	17	-	-	PUNCT
iajs-871	130	18	89	89	NUM
iajs-871	130	19	.	.	PUNCT
iajs-871	130	20	2	2	NUM
iajs-871	130	21	.	.	X
iajs-871	130	22	sharma	sharma	PROPN
iajs-871	130	23	,	,	PUNCT
iajs-871	130	24	l.j.n	l.j.n	NOUN
iajs-871	130	25	.	.	PUNCT
iajs-871	131	1	(	(	PUNCT
iajs-871	131	2	2000)”topology”,krishna	2000)”topology”,krishna	NUM
iajs-871	131	3	prakashan	prakashan	NOUN
iajs-871	131	4	media	medium	NOUN
iajs-871	131	5	(	(	PUNCT
iajs-871	131	6	p	p	NOUN
iajs-871	131	7	)	)	PUNCT
iajs-871	131	8	ltd	ltd	PROPN
iajs-871	131	9	,	,	PUNCT
iajs-871	131	10	india	india	PROPN
iajs-871	131	11	,	,	PUNCT
iajs-871	131	12	twenty	twenty	NUM
iajs-871	131	13	fifth	fifth	ADJ
iajs-871	131	14	edition	edition	NOUN
iajs-871	131	15	.	.	PUNCT
iajs-871	132	1	3	3	X
iajs-871	132	2	.	.	X
iajs-871	132	3	al	al	PROPN
iajs-871	132	4	-	-	PUNCT
iajs-871	132	5	talkhany	talkhany	NOUN
iajs-871	132	6	,	,	PUNCT
iajs-871	132	7	y.k	y.k	PROPN
iajs-871	132	8	.	.	PROPN
iajs-871	133	1	(	(	PUNCT
iajs-871	133	2	2001)”separation	2001)”separation	NUM
iajs-871	133	3	axioms	axiom	VERB
iajs-871	133	4	in	in	ADP
iajs-871	133	5	bitopological	bitopological	ADJ
iajs-871	133	6	spaces	space	NOUN
iajs-871	133	7	”	"	PUNCT
iajs-871	133	8	,	,	PUNCT
iajs-871	133	9	research	research	NOUN
iajs-871	133	10	submitted	submit	VERB
iajs-871	133	11	to	to	ADP
iajs-871	133	12	college	college	NOUN
iajs-871	133	13	of	of	ADP
iajs-871	133	14	education	education	PROPN
iajs-871	133	15	babylon	babylon	PROPN
iajs-871	133	16	university	university	PROPN
iajs-871	133	17	as	as	ADP
iajs-871	133	18	apartial	apartial	ADJ
iajs-871	133	19	fulfillment	fulfillment	NOUN
iajs-871	133	20	of	of	ADP
iajs-871	133	21	the	the	DET
iajs-871	133	22	requirement	requirement	NOUN
iajs-871	133	23	for	for	ADP
iajs-871	133	24	degree	degree	NOUN
iajs-871	133	25	of	of	ADP
iajs-871	133	26	master	master	NOUN
iajs-871	133	27	of	of	ADP
iajs-871	133	28	science	science	NOUN
iajs-871	133	29	in	in	ADP
iajs-871	133	30	math	math	NOUN
iajs-871	133	31	.	.	PUNCT
iajs-871	134	1	,	,	PUNCT
iajs-871	134	2	.	.	PUNCT
iajs-871	135	1	4	4	X
iajs-871	135	2	.	.	X
iajs-871	135	3	al	al	PROPN
iajs-871	135	4	-	-	PUNCT
iajs-871	135	5	khafaji	khafaji	PROPN
iajs-871	135	6	,	,	PUNCT
iajs-871	135	7	a.h	a.h	PROPN
iajs-871	135	8	.	.	PROPN
iajs-871	135	9	(	(	PUNCT
iajs-871	135	10	2005	2005	NUM
iajs-871	135	11	)	)	PUNCT
iajs-871	135	12	“	"	PUNCT
iajs-871	135	13	on	on	ADP
iajs-871	135	14	l	l	ADJ
iajs-871	135	15	-	-	ADJ
iajs-871	135	16	proper	proper	ADJ
iajs-871	135	17	actions	action	NOUN
iajs-871	135	18	”	"	PUNCT
iajs-871	135	19	,	,	PUNCT
iajs-871	135	20	m.sc	m.sc	PROPN
iajs-871	135	21	.	.	PUNCT
iajs-871	136	1	thesis	thesis	NOUN
iajs-871	136	2	,	,	PUNCT
iajs-871	136	3	university	university	NOUN
iajs-871	136	4	of	of	ADP
iajs-871	136	5	almustansiriyah	almustansiriyah	NOUN
iajs-871	136	6	.	.	PUNCT