id	sid	tid	token	lemma	pos
iajs-1000	1	1	ibn	ibn	PROPN
iajs-1000	1	2	alhaitham	alhaitham	NOUN
iajs-1000	1	3	j.	j.	PROPN
iajs-1000	1	4	for	for	ADP
iajs-1000	1	5	pure	pure	ADJ
iajs-1000	1	6	&	&	CCONJ
iajs-1000	1	7	appl	appl	PROPN
iajs-1000	1	8	.	.	PUNCT
iajs-1000	2	1	sci	sci	PROPN
iajs-1000	2	2	.	.	PUNCT
iajs-1000	3	1	vol.23	vol.23	PROPN
iajs-1000	3	2	(	(	PUNCT
iajs-1000	3	3	1	1	NUM
iajs-1000	3	4	)	)	PUNCT
iajs-1000	3	5	2010	2010	NUM
iajs-1000	4	1	some	some	DET
iajs-1000	4	2	types	type	NOUN
iajs-1000	4	3	of	of	ADP
iajs-1000	4	4	compactness	compactness	NOUN
iajs-1000	4	5	in	in	ADP
iajs-1000	4	6	bitopological	bitopological	ADJ
iajs-1000	4	7	spaces	space	NOUN
iajs-1000	4	8	*	*	PUNCT
iajs-1000	4	9	n	n	PRON
iajs-1000	4	10	.a	.a	NOUN
iajs-1000	4	11	.	.	PUNCT
iajs-1000	5	1	jabbar	jabbar	PROPN
iajs-1000	5	2	.	.	PUNCT
iajs-1000	5	3	a.	a.	PROPN
iajs-1000	5	4	i.	i.	PROPN
iajs-1000	5	5	nasir	nasir	PROPN
iajs-1000	5	6	.	.	PUNCT
iajs-1000	6	1	department	department	PROPN
iajs-1000	6	2	of	of	ADP
iajs-1000	6	3	mathematics	mathematic	NOUN
iajs-1000	6	4	,	,	PUNCT
iajs-1000	6	5	ibn	ibn	PROPN
iajs-1000	6	6	al	al	PROPN
iajs-1000	6	7	-	-	PUNCT
iajs-1000	6	8	haitham	haitham	PROPN
iajs-1000	6	9	,	,	PUNCT
iajs-1000	6	10	college	college	NOUN
iajs-1000	6	11	of	of	ADP
iajs-1000	6	12	education	education	NOUN
iajs-1000	6	13	,	,	PUNCT
iajs-1000	6	14	university	university	NOUN
iajs-1000	6	15	of	of	ADP
iajs-1000	6	16	baghdad	baghdad	PROPN
iajs-1000	6	17	abstract	abstract	ADV
iajs-1000	6	18	in	in	ADP
iajs-1000	6	19	this	this	DET
iajs-1000	6	20	paper	paper	NOUN
iajs-1000	6	21	,	,	PUNCT
iajs-1000	6	22	we	we	PRON
iajs-1000	6	23	give	give	VERB
iajs-1000	6	24	the	the	DET
iajs-1000	6	25	concept	concept	NOUN
iajs-1000	6	26	of	of	ADP
iajs-1000	6	27	n	n	CCONJ
iajs-1000	6	28	-	-	PUNCT
iajs-1000	6	29	open	open	ADJ
iajs-1000	6	30	set	set	NOUN
iajs-1000	6	31	in	in	ADP
iajs-1000	6	32	bitopological	bitopological	ADJ
iajs-1000	6	33	spaces	space	NOUN
iajs-1000	6	34	,	,	PUNCT
iajs-1000	6	35	where	where	SCONJ
iajs-1000	6	36	n	n	X
iajs-1000	6	37	is	be	AUX
iajs-1000	6	38	the	the	DET
iajs-1000	6	39	first	first	ADJ
iajs-1000	6	40	letter	letter	NOUN
iajs-1000	6	41	of	of	ADP
iajs-1000	6	42	the	the	DET
iajs-1000	6	43	name	name	NOUN
iajs-1000	6	44	of	of	ADP
iajs-1000	6	45	one	one	NUM
iajs-1000	6	46	of	of	ADP
iajs-1000	6	47	the	the	DET
iajs-1000	6	48	authors	author	NOUN
iajs-1000	6	49	,	,	PUNCT
iajs-1000	6	50	then	then	ADV
iajs-1000	6	51	we	we	PRON
iajs-1000	6	52	used	use	VERB
iajs-1000	6	53	this	this	DET
iajs-1000	6	54	concept	concept	NOUN
iajs-1000	6	55	to	to	PART
iajs-1000	6	56	define	define	VERB
iajs-1000	6	57	a	a	DET
iajs-1000	6	58	new	new	ADJ
iajs-1000	6	59	kind	kind	NOUN
iajs-1000	6	60	of	of	ADP
iajs-1000	6	61	compactness	compactness	NOUN
iajs-1000	6	62	,	,	PUNCT
iajs-1000	6	63	namely	namely	ADV
iajs-1000	6	64	n	n	CCONJ
iajs-1000	6	65	-	-	PUNCT
iajs-1000	6	66	compactness	compactness	NOUN
iajs-1000	6	67	and	and	CCONJ
iajs-1000	6	68	we	we	PRON
iajs-1000	6	69	define	define	VERB
iajs-1000	6	70	the	the	DET
iajs-1000	6	71	n	n	ADV
iajs-1000	6	72	-	-	PUNCT
iajs-1000	6	73	continuous	continuous	ADJ
iajs-1000	6	74	function	function	NOUN
iajs-1000	6	75	in	in	ADP
iajs-1000	6	76	bitopological	bitopological	ADJ
iajs-1000	6	77	spaces	space	NOUN
iajs-1000	6	78	.	.	PUNCT
iajs-1000	7	1	we	we	PRON
iajs-1000	7	2	study	study	VERB
iajs-1000	7	3	some	some	DET
iajs-1000	7	4	properties	property	NOUN
iajs-1000	7	5	of	of	ADP
iajs-1000	7	6	n	n	CCONJ
iajs-1000	7	7	-	-	PUNCT
iajs-1000	7	8	compact	compact	ADJ
iajs-1000	7	9	spaces	space	NOUN
iajs-1000	7	10	,	,	PUNCT
iajs-1000	7	11	and	and	CCONJ
iajs-1000	7	12	the	the	DET
iajs-1000	7	13	relationships	relationship	NOUN
iajs-1000	7	14	between	between	ADP
iajs-1000	7	15	this	this	DET
iajs-1000	7	16	kind	kind	NOUN
iajs-1000	7	17	and	and	CCONJ
iajs-1000	7	18	two	two	NUM
iajs-1000	7	19	other	other	ADJ
iajs-1000	7	20	known	know	VERB
iajs-1000	7	21	kinds	kind	NOUN
iajs-1000	7	22	which	which	PRON
iajs-1000	7	23	are	be	AUX
iajs-1000	7	24	s	s	NOUN
iajs-1000	7	25	-	-	PUNCT
iajs-1000	7	26	compactness	compactness	NOUN
iajs-1000	7	27	and	and	CCONJ
iajs-1000	7	28	pair	pair	NOUN
iajs-1000	7	29	-	-	PUNCT
iajs-1000	7	30	wise	wise	ADJ
iajs-1000	7	31	compactness	compactness	NOUN
iajs-1000	7	32	.	.	PUNCT
iajs-1000	8	1	1introduction	1introduction	NUM
iajs-1000	8	2	in	in	ADP
iajs-1000	8	3	1963	1963	NUM
iajs-1000	8	4	,	,	PUNCT
iajs-1000	8	5	the	the	DET
iajs-1000	8	6	concept	concept	NOUN
iajs-1000	8	7	of	of	ADP
iajs-1000	8	8	"	"	PUNCT
iajs-1000	8	9	bitopological	bitopological	ADJ
iajs-1000	8	10	space	space	NOUN
iajs-1000	8	11	"	"	PUNCT
iajs-1000	8	12	was	be	AUX
iajs-1000	8	13	introduced	introduce	VERB
iajs-1000	8	14	by	by	ADP
iajs-1000	8	15	kelly[1	kelly[1	PROPN
iajs-1000	8	16	]	]	PUNCT
iajs-1000	8	17	.	.	PUNCT
iajs-1000	9	1	a	a	DET
iajs-1000	9	2	set	set	NOUN
iajs-1000	9	3	equipped	equip	VERB
iajs-1000	9	4	with	with	ADP
iajs-1000	9	5	two	two	NUM
iajs-1000	9	6	topologies	topology	NOUN
iajs-1000	9	7	is	be	AUX
iajs-1000	9	8	called	call	VERB
iajs-1000	9	9	a	a	DET
iajs-1000	9	10	'	'	PUNCT
iajs-1000	9	11	bitopological	bitopological	ADJ
iajs-1000	9	12	space	space	NOUN
iajs-1000	9	13	"	"	PUNCT
iajs-1000	9	14	and	and	CCONJ
iajs-1000	9	15	denoted	denote	VERB
iajs-1000	9	16	by	by	ADP
iajs-1000	9	17	(	(	PUNCT
iajs-1000	9	18	x	x	X
iajs-1000	9	19	,	,	PUNCT
iajs-1000	9	20	τ	τ	PROPN
iajs-1000	9	21	,	,	PUNCT
iajs-1000	9	22	τ	τ	NOUN
iajs-1000	9	23	)	)	PUNCT
iajs-1000	9	24	,	,	PUNCT
iajs-1000	9	25	where	where	SCONJ
iajs-1000	9	26	(	(	PUNCT
iajs-1000	9	27	x	x	X
iajs-1000	9	28	,	,	PUNCT
iajs-1000	9	29	τ	τ	PROPN
iajs-1000	9	30	)	)	PUNCT
iajs-1000	9	31	,	,	PUNCT
iajs-1000	9	32	(	(	PUNCT
iajs-1000	9	33	(	(	PUNCT
iajs-1000	9	34	x	x	NOUN
iajs-1000	9	35	,	,	PUNCT
iajs-1000	9	36	τ	τ	NOUN
iajs-1000	9	37	)	)	PUNCT
iajs-1000	9	38	are	be	AUX
iajs-1000	9	39	two	two	NUM
iajs-1000	9	40	topological	topological	ADJ
iajs-1000	9	41	spaces	space	NOUN
iajs-1000	9	42	.	.	PUNCT
iajs-1000	10	1	from	from	ADP
iajs-1000	10	2	that	that	DET
iajs-1000	10	3	time	time	NOUN
iajs-1000	10	4	many	many	ADJ
iajs-1000	10	5	authors	author	NOUN
iajs-1000	10	6	used	use	VERB
iajs-1000	10	7	the	the	DET
iajs-1000	10	8	concept	concept	NOUN
iajs-1000	10	9	of	of	ADP
iajs-1000	10	10	bitopological	bitopological	ADJ
iajs-1000	10	11	space	space	NOUN
iajs-1000	10	12	to	to	PART
iajs-1000	10	13	define	define	VERB
iajs-1000	10	14	new	new	ADJ
iajs-1000	10	15	concepts	concept	NOUN
iajs-1000	10	16	like	like	ADP
iajs-1000	10	17	seperation	seperation	NOUN
iajs-1000	10	18	axioms	axiom	NOUN
iajs-1000	10	19	,	,	PUNCT
iajs-1000	10	20	some	some	DET
iajs-1000	10	21	types	type	NOUN
iajs-1000	10	22	of	of	ADP
iajs-1000	10	23	connectedness	connectedness	NOUN
iajs-1000	10	24	and	and	CCONJ
iajs-1000	10	25	covering	cover	VERB
iajs-1000	10	26	properties	property	NOUN
iajs-1000	10	27	,	,	PUNCT
iajs-1000	10	28	for	for	ADP
iajs-1000	10	29	more	more	ADJ
iajs-1000	10	30	details	detail	NOUN
iajs-1000	10	31	see	see	VERB
iajs-1000	10	32	[	[	X
iajs-1000	10	33	2	2	X
iajs-1000	10	34	]	]	PUNCT
iajs-1000	10	35	and	and	CCONJ
iajs-1000	10	36	[	[	X
iajs-1000	10	37	3	3	NUM
iajs-1000	10	38	]	]	PUNCT
iajs-1000	10	39	.	.	PUNCT
iajs-1000	11	1	in	in	ADP
iajs-1000	11	2	this	this	DET
iajs-1000	11	3	paper	paper	NOUN
iajs-1000	11	4	,	,	PUNCT
iajs-1000	11	5	we	we	PRON
iajs-1000	11	6	introduce	introduce	VERB
iajs-1000	11	7	the	the	DET
iajs-1000	11	8	concept	concept	NOUN
iajs-1000	11	9	of	of	ADP
iajs-1000	11	10	n	n	CCONJ
iajs-1000	11	11	-	-	PUNCT
iajs-1000	11	12	compactness	compactness	NOUN
iajs-1000	11	13	,	,	PUNCT
iajs-1000	11	14	we	we	PRON
iajs-1000	11	15	study	study	VERB
iajs-1000	11	16	some	some	DET
iajs-1000	11	17	properties	property	NOUN
iajs-1000	11	18	of	of	ADP
iajs-1000	11	19	this	this	DET
iajs-1000	11	20	kind	kind	NOUN
iajs-1000	11	21	with	with	ADP
iajs-1000	11	22	many	many	ADJ
iajs-1000	11	23	examples	example	NOUN
iajs-1000	11	24	,	,	PUNCT
iajs-1000	11	25	we	we	PRON
iajs-1000	11	26	also	also	ADV
iajs-1000	11	27	give	give	VERB
iajs-1000	11	28	some	some	DET
iajs-1000	11	29	new	new	ADJ
iajs-1000	11	30	properties	property	NOUN
iajs-1000	11	31	about	about	ADP
iajs-1000	11	32	the	the	DET
iajs-1000	11	33	s	s	NOUN
iajs-1000	11	34	-	-	PUNCT
iajs-1000	11	35	compactness	compactness	NOUN
iajs-1000	11	36	and	and	CCONJ
iajs-1000	11	37	pair	pair	NOUN
iajs-1000	11	38	-	-	PUNCT
iajs-1000	11	39	wise	wise	ADJ
iajs-1000	11	40	compactness	compactness	NOUN
iajs-1000	11	41	which	which	PRON
iajs-1000	11	42	was	be	AUX
iajs-1000	11	43	introduced	introduce	VERB
iajs-1000	11	44	by	by	ADP
iajs-1000	11	45	mrsevic	mrsevic	ADJ
iajs-1000	11	46	and	and	CCONJ
iajs-1000	11	47	reilly	reilly	ADV
iajs-1000	12	1	[	[	X
iajs-1000	12	2	4	4	NUM
iajs-1000	12	3	]	]	PUNCT
iajs-1000	12	4	,	,	PUNCT
iajs-1000	12	5	where	where	SCONJ
iajs-1000	12	6	we	we	PRON
iajs-1000	12	7	give	give	VERB
iajs-1000	12	8	for	for	ADP
iajs-1000	12	9	example	example	NOUN
iajs-1000	12	10	propositions	proposition	NOUN
iajs-1000	12	11	2.21	2.21	NUM
iajs-1000	12	12	,	,	PUNCT
iajs-1000	12	13	2.23	2.23	NUM
iajs-1000	12	14	,	,	PUNCT
iajs-1000	12	15	2.24	2.24	NUM
iajs-1000	12	16	,	,	PUNCT
iajs-1000	12	17	2.27	2.27	NUM
iajs-1000	12	18	,	,	PUNCT
iajs-1000	12	19	2.28	2.28	NUM
iajs-1000	12	20	,	,	PUNCT
iajs-1000	12	21	2.40	2.40	NUM
iajs-1000	12	22	and	and	CCONJ
iajs-1000	12	23	theorem	theorem	VERB
iajs-1000	12	24	2.41	2.41	NUM
iajs-1000	12	25	.	.	PUNCT
iajs-1000	13	1	we	we	PRON
iajs-1000	13	2	also	also	ADV
iajs-1000	13	3	study	study	VERB
iajs-1000	13	4	the	the	DET
iajs-1000	13	5	relationships	relationship	NOUN
iajs-1000	13	6	between	between	ADP
iajs-1000	13	7	the	the	DET
iajs-1000	13	8	three	three	NUM
iajs-1000	13	9	kinds	kind	NOUN
iajs-1000	13	10	of	of	ADP
iajs-1000	13	11	compactness	compactness	NOUN
iajs-1000	13	12	,	,	PUNCT
iajs-1000	13	13	where	where	SCONJ
iajs-1000	13	14	we	we	PRON
iajs-1000	13	15	proved	prove	VERB
iajs-1000	13	16	the	the	DET
iajs-1000	13	17	valid	valid	ADJ
iajs-1000	13	18	directions	direction	NOUN
iajs-1000	13	19	and	and	CCONJ
iajs-1000	13	20	give	give	VERB
iajs-1000	13	21	counter	counter	ADJ
iajs-1000	13	22	examples	example	NOUN
iajs-1000	13	23	for	for	ADP
iajs-1000	13	24	the	the	DET
iajs-1000	13	25	invalid	invalid	ADJ
iajs-1000	13	26	ones	one	NOUN
iajs-1000	13	27	,	,	PUNCT
iajs-1000	13	28	and	and	CCONJ
iajs-1000	13	29	we	we	PRON
iajs-1000	13	30	put	put	VERB
iajs-1000	13	31	certain	certain	ADJ
iajs-1000	13	32	conditions	condition	NOUN
iajs-1000	13	33	to	to	PART
iajs-1000	13	34	make	make	VERB
iajs-1000	13	35	the	the	DET
iajs-1000	13	36	invalid	invalid	ADJ
iajs-1000	13	37	direction	direction	NOUN
iajs-1000	13	38	true	true	ADJ
iajs-1000	13	39	.	.	PUNCT
iajs-1000	14	1	*	*	PUNCT
iajs-1000	14	2	this	this	DET
iajs-1000	14	3	paper	paper	NOUN
iajs-1000	14	4	is	be	AUX
iajs-1000	14	5	a	a	DET
iajs-1000	14	6	part	part	NOUN
iajs-1000	14	7	of	of	ADP
iajs-1000	14	8	an	an	DET
iajs-1000	14	9	m.sc	m.sc	PROPN
iajs-1000	14	10	.	.	PUNCT
iajs-1000	15	1	thesis	thesis	NOUN
iajs-1000	15	2	by	by	ADP
iajs-1000	15	3	the	the	DET
iajs-1000	15	4	second	second	ADJ
iajs-1000	15	5	author	author	NOUN
iajs-1000	15	6	and	and	CCONJ
iajs-1000	15	7	is	be	AUX
iajs-1000	15	8	supervised	supervise	VERB
iajs-1000	15	9	by	by	ADP
iajs-1000	15	10	the	the	DET
iajs-1000	15	11	first	first	ADJ
iajs-1000	15	12	author	author	NOUN
iajs-1000	15	13	.	.	PUNCT
iajs-1000	16	1	ibn	ibn	PROPN
iajs-1000	16	2	alhaitham	alhaitham	PROPN
iajs-1000	16	3	j.	j.	PROPN
iajs-1000	16	4	for	for	ADP
iajs-1000	16	5	pure	pure	ADJ
iajs-1000	16	6	&	&	CCONJ
iajs-1000	16	7	appl	appl	PROPN
iajs-1000	16	8	.	.	PUNCT
iajs-1000	17	1	sci	sci	PROPN
iajs-1000	17	2	.	.	PUNCT
iajs-1000	18	1	vol.23	vol.23	PROPN
iajs-1000	18	2	(	(	PUNCT
iajs-1000	18	3	1	1	NUM
iajs-1000	18	4	)	)	PUNCT
iajs-1000	18	5	2010	2010	NUM
iajs-1000	18	6	2.2	2.2	NUM
iajs-1000	18	7	definition	definition	NOUN
iajs-1000	18	8	a	a	DET
iajs-1000	18	9	subset	subset	NOUN
iajs-1000	18	10	a	a	PRON
iajs-1000	18	11	of	of	ADP
iajs-1000	18	12	a	a	DET
iajs-1000	18	13	bitopological	bitopological	ADJ
iajs-1000	18	14	space	space	NOUN
iajs-1000	18	15	(	(	PUNCT
iajs-1000	18	16	x	x	X
iajs-1000	18	17	,	,	PUNCT
iajs-1000	18	18	τ	τ	PROPN
iajs-1000	18	19	,	,	PUNCT
iajs-1000	18	20	τ	τ	NOUN
iajs-1000	18	21	)	)	PUNCT
iajs-1000	18	22	is	be	AUX
iajs-1000	18	23	called	call	VERB
iajs-1000	18	24	an	an	DET
iajs-1000	18	25	"	"	PUNCT
iajs-1000	18	26	n	n	CCONJ
iajs-1000	18	27	-	-	PUNCT
iajs-1000	18	28	open	open	VERB
iajs-1000	18	29	set"if	set"if	NOUN
iajs-1000	18	30	and	and	CCONJ
iajs-1000	18	31	only	only	ADV
iajs-1000	18	32	if	if	SCONJ
iajs-1000	18	33	it	it	PRON
iajs-1000	18	34	is	be	AUX
iajs-1000	18	35	open	open	ADJ
iajs-1000	18	36	in	in	ADP
iajs-1000	18	37	the	the	DET
iajs-1000	18	38	space	space	NOUN
iajs-1000	18	39	(	(	PUNCT
iajs-1000	18	40	x	x	X
iajs-1000	18	41	,	,	PUNCT
iajs-1000	18	42	ττ	ττ	NOUN
iajs-1000	18	43	)	)	PUNCT
iajs-1000	18	44	,	,	PUNCT
iajs-1000	18	45	where	where	SCONJ
iajs-1000	18	46	ττ	ττ	PROPN
iajs-1000	18	47	is	be	AUX
iajs-1000	18	48	the	the	DET
iajs-1000	18	49	supremum	supremum	ADJ
iajs-1000	18	50	topology	topology	NOUN
iajs-1000	18	51	on	on	ADP
iajs-1000	18	52	x	x	PUNCT
iajs-1000	18	53	contains	contain	VERB
iajs-1000	18	54	τ	τ	PROPN
iajs-1000	18	55	and	and	CCONJ
iajs-1000	18	56	τ.	τ.	SCONJ
iajs-1000	18	57	2.3	2.3	NUM
iajs-1000	18	58	definition	definition	NOUN
iajs-1000	18	59	the	the	DET
iajs-1000	18	60	complement	complement	NOUN
iajs-1000	18	61	of	of	ADP
iajs-1000	18	62	an	an	DET
iajs-1000	18	63	n	n	ADV
iajs-1000	18	64	-	-	PUNCT
iajs-1000	18	65	open	open	ADJ
iajs-1000	18	66	set	set	NOUN
iajs-1000	18	67	in	in	ADP
iajs-1000	18	68	a	a	DET
iajs-1000	18	69	bitopological	bitopological	ADJ
iajs-1000	18	70	space	space	NOUN
iajs-1000	18	71	(	(	PUNCT
iajs-1000	18	72	x	x	X
iajs-1000	18	73	,	,	PUNCT
iajs-1000	18	74	τ	τ	PROPN
iajs-1000	18	75	,	,	PUNCT
iajs-1000	18	76	τ	τ	NOUN
iajs-1000	18	77	)	)	PUNCT
iajs-1000	18	78	is	be	AUX
iajs-1000	18	79	called	call	VERB
iajs-1000	18	80	"	"	PUNCT
iajs-1000	18	81	n	n	CCONJ
iajs-1000	18	82	-	-	PUNCT
iajs-1000	18	83	closed	closed	ADJ
iajs-1000	18	84	set	set	NOUN
iajs-1000	18	85	"	"	PUNCT
iajs-1000	18	86	.	.	PUNCT
iajs-1000	19	1	2.4	2.4	NUM
iajs-1000	19	2	remark	remark	NOUN
iajs-1000	19	3	let	let	VERB
iajs-1000	19	4	(	(	PUNCT
iajs-1000	19	5	x	x	NOUN
iajs-1000	19	6	,	,	PUNCT
iajs-1000	19	7	τ	τ	PROPN
iajs-1000	19	8	,	,	PUNCT
iajs-1000	19	9	τ	τ	NOUN
iajs-1000	19	10	)	)	PUNCT
iajs-1000	19	11	be	be	AUX
iajs-1000	19	12	a	a	DET
iajs-1000	19	13	bitopological	bitopological	ADJ
iajs-1000	19	14	space	space	NOUN
iajs-1000	19	15	,	,	PUNCT
iajs-1000	19	16	then	then	ADV
iajs-1000	19	17	:	:	PUNCT
iajs-1000	19	18	(	(	PUNCT
iajs-1000	19	19	i	i	NOUN
iajs-1000	19	20	)	)	PUNCT
iajs-1000	19	21	every	every	DET
iajs-1000	19	22	open	open	ADJ
iajs-1000	19	23	set	set	NOUN
iajs-1000	19	24	in	in	ADP
iajs-1000	19	25	(	(	PUNCT
iajs-1000	19	26	x	x	NOUN
iajs-1000	19	27	,	,	PUNCT
iajs-1000	19	28	τ	τ	X
iajs-1000	19	29	)	)	PUNCT
iajs-1000	19	30	or	or	CCONJ
iajs-1000	19	31	in	in	ADP
iajs-1000	19	32	(	(	PUNCT
iajs-1000	19	33	x	x	NOUN
iajs-1000	19	34	,	,	PUNCT
iajs-1000	19	35	τ	τ	NOUN
iajs-1000	19	36	)	)	PUNCT
iajs-1000	19	37	is	be	AUX
iajs-1000	19	38	an	an	DET
iajs-1000	19	39	n	n	ADV
iajs-1000	19	40	-	-	PUNCT
iajs-1000	19	41	open	open	ADJ
iajs-1000	19	42	set	set	NOUN
iajs-1000	19	43	in	in	ADP
iajs-1000	19	44	(	(	PUNCT
iajs-1000	19	45	x	x	NOUN
iajs-1000	19	46	,	,	PUNCT
iajs-1000	19	47	τ	τ	PROPN
iajs-1000	19	48	,	,	PUNCT
iajs-1000	19	49	τ	τ	NOUN
iajs-1000	19	50	)	)	PUNCT
iajs-1000	19	51	.	.	PUNCT
iajs-1000	20	1	(	(	PUNCT
iajs-1000	20	2	ii	ii	NOUN
iajs-1000	20	3	)	)	PUNCT
iajs-1000	20	4	every	every	DET
iajs-1000	20	5	closed	close	VERB
iajs-1000	20	6	set	set	VERB
iajs-1000	20	7	in	in	ADP
iajs-1000	20	8	(	(	PUNCT
iajs-1000	20	9	x	x	NOUN
iajs-1000	20	10	,	,	PUNCT
iajs-1000	20	11	τ	τ	X
iajs-1000	20	12	)	)	PUNCT
iajs-1000	20	13	or	or	CCONJ
iajs-1000	20	14	in	in	ADP
iajs-1000	20	15	(	(	PUNCT
iajs-1000	20	16	x	x	NOUN
iajs-1000	20	17	,	,	PUNCT
iajs-1000	20	18	τ	τ	NOUN
iajs-1000	20	19	)	)	PUNCT
iajs-1000	20	20	is	be	AUX
iajs-1000	20	21	an	an	DET
iajs-1000	20	22	n	n	ADV
iajs-1000	20	23	-	-	PUNCT
iajs-1000	20	24	closed	close	VERB
iajs-1000	20	25	set	set	NOUN
iajs-1000	20	26	in	in	ADP
iajs-1000	20	27	(	(	PUNCT
iajs-1000	20	28	x	x	NOUN
iajs-1000	20	29	,	,	PUNCT
iajs-1000	20	30	τ	τ	PROPN
iajs-1000	20	31	,	,	PUNCT
iajs-1000	20	32	τ	τ	NOUN
iajs-1000	20	33	)	)	PUNCT
iajs-1000	20	34	.	.	PUNCT
iajs-1000	21	1	2.5	2.5	NUM
iajs-1000	21	2	note	note	VERB
iajs-1000	21	3	the	the	DET
iajs-1000	21	4	opposite	opposite	ADJ
iajs-1000	21	5	direction	direction	NOUN
iajs-1000	21	6	of	of	ADP
iajs-1000	21	7	this	this	DET
iajs-1000	21	8	remark	remark	NOUN
iajs-1000	21	9	2.4	2.4	NUM
iajs-1000	21	10	may	may	AUX
iajs-1000	21	11	be	be	AUX
iajs-1000	21	12	untrue	untrue	ADJ
iajs-1000	21	13	as	as	SCONJ
iajs-1000	21	14	the	the	DET
iajs-1000	21	15	following	follow	VERB
iajs-1000	21	16	example	example	NOUN
iajs-1000	21	17	shows	show	VERB
iajs-1000	21	18	:	:	PUNCT
iajs-1000	21	19	example	example	NOUN
iajs-1000	21	20	let	let	VERB
iajs-1000	21	21	x={1,2,3	x={1,2,3	NUM
iajs-1000	21	22	}	}	PUNCT
iajs-1000	21	23	,	,	PUNCT
iajs-1000	21	24	τ={,{1},x	τ={,{1},x	VERB
iajs-1000	21	25	}	}	PUNCT
iajs-1000	21	26	and	and	CCONJ
iajs-1000	21	27	τ={,{2},x	τ={,{2},x	NUM
iajs-1000	21	28	}	}	PUNCT
iajs-1000	21	29	then	then	ADV
iajs-1000	21	30	ττ={,{1},{2},{1,2},x	ττ={,{1},{2},{1,2},x	VERB
iajs-1000	21	31	}	}	PUNCT
iajs-1000	21	32	is	be	AUX
iajs-1000	21	33	the	the	DET
iajs-1000	21	34	family	family	NOUN
iajs-1000	21	35	of	of	ADP
iajs-1000	21	36	all	all	DET
iajs-1000	21	37	n	n	CCONJ
iajs-1000	21	38	-	-	PUNCT
iajs-1000	21	39	open	open	ADJ
iajs-1000	21	40	subsets	subset	NOUN
iajs-1000	21	41	of	of	ADP
iajs-1000	21	42	(	(	PUNCT
iajs-1000	21	43	x	x	X
iajs-1000	21	44	,	,	PUNCT
iajs-1000	21	45	τ	τ	PROPN
iajs-1000	21	46	,	,	PUNCT
iajs-1000	21	47	τ	τ	NOUN
iajs-1000	21	48	)	)	PUNCT
iajs-1000	21	49	.	.	PUNCT
iajs-1000	22	1	{	{	PUNCT
iajs-1000	22	2	1,2	1,2	NUM
iajs-1000	22	3	}	}	PUNCT
iajs-1000	22	4	is	be	AUX
iajs-1000	22	5	an	an	DET
iajs-1000	22	6	n	n	ADV
iajs-1000	22	7	-	-	PUNCT
iajs-1000	22	8	open	open	ADJ
iajs-1000	22	9	set	set	NOUN
iajs-1000	22	10	in	in	ADP
iajs-1000	22	11	(	(	PUNCT
iajs-1000	22	12	x	x	NOUN
iajs-1000	22	13	,	,	PUNCT
iajs-1000	22	14	τ	τ	PROPN
iajs-1000	22	15	,	,	PUNCT
iajs-1000	22	16	τ	τ	NOUN
iajs-1000	22	17	)	)	PUNCT
iajs-1000	23	1	but	but	CCONJ
iajs-1000	23	2	it	it	PRON
iajs-1000	23	3	is	be	AUX
iajs-1000	23	4	not	not	PART
iajs-1000	23	5	open	open	ADJ
iajs-1000	23	6	in	in	ADP
iajs-1000	23	7	both	both	DET
iajs-1000	23	8	(	(	PUNCT
iajs-1000	23	9	x	x	X
iajs-1000	23	10	,	,	PUNCT
iajs-1000	23	11	τ	τ	X
iajs-1000	23	12	)	)	PUNCT
iajs-1000	23	13	and	and	CCONJ
iajs-1000	23	14	(	(	PUNCT
iajs-1000	23	15	x	x	NOUN
iajs-1000	23	16	,	,	PUNCT
iajs-1000	23	17	τ	τ	NOUN
iajs-1000	23	18	)	)	PUNCT
iajs-1000	23	19	.	.	PUNCT
iajs-1000	24	1	so	so	ADV
iajs-1000	24	2	{	{	PUNCT
iajs-1000	24	3	3	3	NUM
iajs-1000	24	4	}	}	PUNCT
iajs-1000	24	5	is	be	AUX
iajs-1000	24	6	an	an	DET
iajs-1000	24	7	n	n	ADV
iajs-1000	24	8	-	-	PUNCT
iajs-1000	24	9	closed	close	VERB
iajs-1000	24	10	set	set	NOUN
iajs-1000	24	11	in	in	ADP
iajs-1000	24	12	(	(	PUNCT
iajs-1000	24	13	x	x	NOUN
iajs-1000	24	14	,	,	PUNCT
iajs-1000	24	15	τ	τ	PROPN
iajs-1000	24	16	,	,	PUNCT
iajs-1000	24	17	τ	τ	NOUN
iajs-1000	24	18	)	)	PUNCT
iajs-1000	24	19	which	which	PRON
iajs-1000	24	20	is	be	AUX
iajs-1000	24	21	not	not	PART
iajs-1000	24	22	closed	close	VERB
iajs-1000	24	23	in	in	ADP
iajs-1000	24	24	both	both	DET
iajs-1000	24	25	(	(	PUNCT
iajs-1000	24	26	x	x	X
iajs-1000	24	27	,	,	PUNCT
iajs-1000	24	28	τ	τ	X
iajs-1000	24	29	)	)	PUNCT
iajs-1000	24	30	and	and	CCONJ
iajs-1000	24	31	(	(	PUNCT
iajs-1000	24	32	x	x	NOUN
iajs-1000	24	33	,	,	PUNCT
iajs-1000	24	34	τ	τ	NOUN
iajs-1000	24	35	)	)	PUNCT
iajs-1000	24	36	.	.	PUNCT
iajs-1000	25	1	2.6	2.6	NUM
iajs-1000	25	2	definition	definition	NOUN
iajs-1000	25	3	let	let	VERB
iajs-1000	25	4	(	(	PUNCT
iajs-1000	25	5	x	x	NOUN
iajs-1000	25	6	,	,	PUNCT
iajs-1000	25	7	τ	τ	PROPN
iajs-1000	25	8	,	,	PUNCT
iajs-1000	25	9	τ	τ	NOUN
iajs-1000	25	10	)	)	PUNCT
iajs-1000	25	11	be	be	AUX
iajs-1000	25	12	a	a	DET
iajs-1000	25	13	bitopological	bitopological	ADJ
iajs-1000	25	14	space	space	NOUN
iajs-1000	25	15	,	,	PUNCT
iajs-1000	25	16	let	let	VERB
iajs-1000	25	17	a	a	PRON
iajs-1000	25	18	be	be	AUX
iajs-1000	25	19	a	a	DET
iajs-1000	25	20	subset	subset	NOUN
iajs-1000	25	21	of	of	ADP
iajs-1000	25	22	x.	x.	PROPN
iajs-1000	25	23	a	a	DET
iajs-1000	25	24	subcollection	subcollection	NOUN
iajs-1000	25	25	of	of	ADP
iajs-1000	25	26	the	the	DET
iajs-1000	25	27	family	family	NOUN
iajs-1000	25	28	ττ	ττ	PROPN
iajs-1000	25	29	is	be	AUX
iajs-1000	25	30	called	call	VERB
iajs-1000	25	31	an	an	DET
iajs-1000	25	32	"	"	PUNCT
iajs-1000	25	33	n	n	CCONJ
iajs-1000	25	34	-	-	PUNCT
iajs-1000	25	35	open	open	ADJ
iajs-1000	25	36	cover	cover	NOUN
iajs-1000	25	37	of	of	ADP
iajs-1000	25	38	a	a	PRON
iajs-1000	25	39	"	"	PUNCT
iajs-1000	25	40	if	if	SCONJ
iajs-1000	25	41	the	the	DET
iajs-1000	25	42	union	union	NOUN
iajs-1000	25	43	of	of	ADP
iajs-1000	25	44	members	member	NOUN
iajs-1000	25	45	of	of	ADP
iajs-1000	25	46	this	this	DET
iajs-1000	25	47	collection	collection	NOUN
iajs-1000	25	48	contains	contain	VERB
iajs-1000	25	49	a.	a.	NOUN
iajs-1000	25	50	2.7	2.7	NUM
iajs-1000	25	51	definition	definition	NOUN
iajs-1000	25	52	a	a	DET
iajs-1000	25	53	bitopological	bitopological	ADJ
iajs-1000	25	54	space	space	NOUN
iajs-1000	25	55	(	(	PUNCT
iajs-1000	25	56	x	x	X
iajs-1000	25	57	,	,	PUNCT
iajs-1000	25	58	τ	τ	PROPN
iajs-1000	25	59	,	,	PUNCT
iajs-1000	25	60	τ	τ	NOUN
iajs-1000	25	61	)	)	PUNCT
iajs-1000	25	62	is	be	AUX
iajs-1000	25	63	said	say	VERB
iajs-1000	25	64	to	to	PART
iajs-1000	25	65	be	be	AUX
iajs-1000	25	66	an	an	DET
iajs-1000	25	67	"	"	PUNCT
iajs-1000	25	68	n	n	CCONJ
iajs-1000	25	69	-	-	PUNCT
iajs-1000	25	70	compact	compact	ADJ
iajs-1000	25	71	space	space	NOUN
iajs-1000	25	72	"	"	PUNCT
iajs-1000	25	73	if	if	SCONJ
iajs-1000	25	74	and	and	CCONJ
iajs-1000	25	75	only	only	ADV
iajs-1000	25	76	if	if	SCONJ
iajs-1000	25	77	every	every	DET
iajs-1000	25	78	nopen	nopen	ADJ
iajs-1000	25	79	cover	cover	NOUN
iajs-1000	25	80	of	of	ADP
iajs-1000	25	81	x	x	PUNCT
iajs-1000	25	82	has	have	VERB
iajs-1000	25	83	a	a	DET
iajs-1000	25	84	finite	finite	ADJ
iajs-1000	25	85	subcover	subcover	PROPN
iajs-1000	25	86	.	.	PUNCT
iajs-1000	26	1	2.8	2.8	NUM
iajs-1000	26	2	proposition	proposition	NOUN
iajs-1000	26	3	if	if	SCONJ
iajs-1000	26	4	(	(	PUNCT
iajs-1000	26	5	x	x	NOUN
iajs-1000	26	6	,	,	PUNCT
iajs-1000	26	7	τ	τ	PROPN
iajs-1000	26	8	,	,	PUNCT
iajs-1000	26	9	τ	τ	NOUN
iajs-1000	26	10	)	)	PUNCT
iajs-1000	26	11	is	be	AUX
iajs-1000	26	12	an	an	DET
iajs-1000	26	13	n	n	CCONJ
iajs-1000	26	14	-	-	PUNCT
iajs-1000	26	15	compact	compact	ADJ
iajs-1000	26	16	space	space	NOUN
iajs-1000	26	17	,	,	PUNCT
iajs-1000	26	18	then	then	ADV
iajs-1000	26	19	both	both	PRON
iajs-1000	26	20	(	(	PUNCT
iajs-1000	26	21	x	x	X
iajs-1000	26	22	,	,	PUNCT
iajs-1000	26	23	τ	τ	X
iajs-1000	26	24	)	)	PUNCT
iajs-1000	26	25	and	and	CCONJ
iajs-1000	26	26	(	(	PUNCT
iajs-1000	26	27	x	x	NOUN
iajs-1000	26	28	,	,	PUNCT
iajs-1000	26	29	τ	τ	NOUN
iajs-1000	26	30	)	)	PUNCT
iajs-1000	26	31	are	be	AUX
iajs-1000	26	32	compact	compact	ADJ
iajs-1000	26	33	spaces	space	NOUN
iajs-1000	26	34	.	.	PUNCT
iajs-1000	27	1	proof	proof	NOUN
iajs-1000	27	2	:	:	PUNCT
iajs-1000	27	3	follows	follow	VERB
iajs-1000	27	4	from	from	ADP
iajs-1000	27	5	remark	remark	NOUN
iajs-1000	27	6	(	(	PUNCT
iajs-1000	27	7	2.4	2.4	NUM
iajs-1000	27	8	)	)	PUNCT
iajs-1000	27	9	.	.	PUNCT
iajs-1000	28	1			NUM
iajs-1000	28	2	2.9	2.9	NUM
iajs-1000	28	3	note	note	VERB
iajs-1000	28	4	the	the	DET
iajs-1000	28	5	implication	implication	NOUN
iajs-1000	28	6	in	in	ADP
iajs-1000	28	7	proposition	proposition	NOUN
iajs-1000	28	8	(	(	PUNCT
iajs-1000	28	9	2.8	2.8	NUM
iajs-1000	28	10	)	)	PUNCT
iajs-1000	28	11	is	be	AUX
iajs-1000	28	12	not	not	PART
iajs-1000	28	13	reversible	reversible	ADJ
iajs-1000	28	14	,	,	PUNCT
iajs-1000	28	15	as	as	SCONJ
iajs-1000	28	16	the	the	DET
iajs-1000	28	17	following	follow	VERB
iajs-1000	28	18	example	example	NOUN
iajs-1000	28	19	shows	show	VERB
iajs-1000	28	20	:	:	PUNCT
iajs-1000	28	21	example	example	NOUN
iajs-1000	28	22	let	let	VERB
iajs-1000	28	23	�	�	PROPN
iajs-1000	28	24	be	be	AUX
iajs-1000	28	25	the	the	DET
iajs-1000	28	26	set	set	NOUN
iajs-1000	28	27	of	of	ADP
iajs-1000	28	28	all	all	DET
iajs-1000	28	29	natural	natural	ADJ
iajs-1000	28	30	numbers	number	NOUN
iajs-1000	28	31	,	,	PUNCT
iajs-1000	28	32	τ=	τ=	X
iajs-1000	28	33	{	{	PUNCT
iajs-1000	28	34	�	�	PROPN
iajs-1000	28	35	}	}	PUNCT
iajs-1000	28	36			NOUN
iajs-1000	28	37	p(o	p(o	NOUN
iajs-1000	28	38	+	+	CCONJ
iajs-1000	28	39	)	)	PUNCT
iajs-1000	28	40	and	and	CCONJ
iajs-1000	28	41	τ=	τ=	PRON
iajs-1000	28	42	{	{	PUNCT
iajs-1000	28	43	�	�	PROPN
iajs-1000	28	44	}	}	PUNCT
iajs-1000	28	45			NOUN
iajs-1000	28	46	p(e	p(e	PROPN
iajs-1000	28	47	+	+	CCONJ
iajs-1000	28	48	)	)	PUNCT
iajs-1000	28	49	.	.	PUNCT
iajs-1000	29	1	then	then	ADV
iajs-1000	29	2	ττ	ττ	PROPN
iajs-1000	29	3	is	be	AUX
iajs-1000	29	4	the	the	DET
iajs-1000	29	5	discrete	discrete	ADJ
iajs-1000	29	6	topology	topology	NOUN
iajs-1000	29	7	on	on	ADP
iajs-1000	29	8	n	n	CCONJ
iajs-1000	29	9	,	,	PUNCT
iajs-1000	29	10	where	where	SCONJ
iajs-1000	29	11	p(o	p(o	NOUN
iajs-1000	29	12	+	+	NOUN
iajs-1000	29	13	)	)	PUNCT
iajs-1000	29	14	and	and	CCONJ
iajs-1000	29	15	p(e+	p(e+	NOUN
iajs-1000	29	16	)	)	PUNCT
iajs-1000	29	17	are	be	AUX
iajs-1000	29	18	the	the	DET
iajs-1000	29	19	power	power	NOUN
iajs-1000	29	20	sets	set	NOUN
iajs-1000	29	21	of	of	ADP
iajs-1000	29	22	o+	o+	PROPN
iajs-1000	29	23	and	and	CCONJ
iajs-1000	29	24	e+	e+	VERB
iajs-1000	29	25	respectively	respectively	ADV
iajs-1000	29	26	.	.	PUNCT
iajs-1000	30	1	now	now	ADV
iajs-1000	30	2	,	,	PUNCT
iajs-1000	30	3	both	both	PRON
iajs-1000	30	4	(	(	PUNCT
iajs-1000	30	5	�	�	PROPN
iajs-1000	30	6	,	,	PUNCT
iajs-1000	30	7	τ	τ	PROPN
iajs-1000	30	8	)	)	PUNCT
iajs-1000	30	9	and	and	CCONJ
iajs-1000	30	10	(	(	PUNCT
iajs-1000	30	11	�	�	PROPN
iajs-1000	30	12	,	,	PUNCT
iajs-1000	30	13	τ	τ	PROPN
iajs-1000	30	14	)	)	PUNCT
iajs-1000	30	15	are	be	AUX
iajs-1000	30	16	compact	compact	ADJ
iajs-1000	30	17	spaces	space	NOUN
iajs-1000	30	18	,	,	PUNCT
iajs-1000	30	19	but	but	CCONJ
iajs-1000	30	20	(	(	PUNCT
iajs-1000	30	21	�	�	PROPN
iajs-1000	30	22	,	,	PUNCT
iajs-1000	30	23	τ	τ	PROPN
iajs-1000	30	24	,	,	PUNCT
iajs-1000	30	25	τ	τ	NOUN
iajs-1000	30	26	)	)	PUNCT
iajs-1000	30	27	is	be	AUX
iajs-1000	30	28	not	not	PART
iajs-1000	30	29	n	n	ADV
iajs-1000	30	30	-	-	PUNCT
iajs-1000	30	31	compact	compact	ADJ
iajs-1000	30	32	.	.	PUNCT
iajs-1000	31	1	since	since	SCONJ
iajs-1000	31	2	the	the	DET
iajs-1000	31	3	n	n	ADV
iajs-1000	31	4	-	-	PUNCT
iajs-1000	31	5	open	open	ADJ
iajs-1000	31	6	cover	cover	NOUN
iajs-1000	31	7	{	{	PUNCT
iajs-1000	31	8	{	{	PUNCT
iajs-1000	31	9	n}n	n}n	NOUN
iajs-1000	31	10	�	�	PROPN
iajs-1000	31	11	}	}	PUNCT
iajs-1000	31	12	of	of	ADP
iajs-1000	31	13	�	�	PROPN
iajs-1000	31	14	has	have	VERB
iajs-1000	31	15	no	no	DET
iajs-1000	31	16	finite	finite	PROPN
iajs-1000	31	17	subcover	subcover	PROPN
iajs-1000	31	18	.	.	PUNCT
iajs-1000	32	1	the	the	DET
iajs-1000	32	2	opposite	opposite	ADJ
iajs-1000	32	3	direction	direction	NOUN
iajs-1000	32	4	of	of	ADP
iajs-1000	32	5	proposition	proposition	NOUN
iajs-1000	32	6	(	(	PUNCT
iajs-1000	32	7	2.8	2.8	NUM
iajs-1000	32	8	)	)	PUNCT
iajs-1000	32	9	becomes	become	VERB
iajs-1000	32	10	valid	valid	ADJ
iajs-1000	32	11	in	in	ADP
iajs-1000	32	12	a	a	DET
iajs-1000	32	13	special	special	ADJ
iajs-1000	32	14	case	case	NOUN
iajs-1000	32	15	,	,	PUNCT
iajs-1000	32	16	when	when	SCONJ
iajs-1000	32	17	τ	τ	PROPN
iajs-1000	32	18	is	be	AUX
iajs-1000	32	19	a	a	DET
iajs-1000	32	20	subfamily	subfamily	NOUN
iajs-1000	32	21	of	of	ADP
iajs-1000	32	22	τ	τ	NOUN
iajs-1000	32	23	,	,	PUNCT
iajs-1000	32	24	as	as	SCONJ
iajs-1000	32	25	the	the	DET
iajs-1000	32	26	following	follow	VERB
iajs-1000	32	27	proposition	proposition	NOUN
iajs-1000	32	28	shows	show	VERB
iajs-1000	32	29	:	:	PUNCT
iajs-1000	32	30	2.10	2.10	NUM
iajs-1000	32	31	proposition	proposition	NOUN
iajs-1000	32	32	if	if	SCONJ
iajs-1000	32	33	τ	τ	PROPN
iajs-1000	32	34	is	be	AUX
iajs-1000	32	35	a	a	DET
iajs-1000	32	36	subfamily	subfamily	NOUN
iajs-1000	32	37	of	of	ADP
iajs-1000	32	38	τ	τ	NOUN
iajs-1000	32	39	,	,	PUNCT
iajs-1000	32	40	then	then	ADV
iajs-1000	32	41	(	(	PUNCT
iajs-1000	32	42	x	x	X
iajs-1000	32	43	,	,	PUNCT
iajs-1000	32	44	τ	τ	PROPN
iajs-1000	32	45	,	,	PUNCT
iajs-1000	32	46	τ	τ	NOUN
iajs-1000	32	47	)	)	PUNCT
iajs-1000	32	48	is	be	AUX
iajs-1000	32	49	an	an	DET
iajs-1000	32	50	n	n	CCONJ
iajs-1000	32	51	-	-	PUNCT
iajs-1000	32	52	compact	compact	ADJ
iajs-1000	32	53	space	space	NOUN
iajs-1000	33	1	if	if	SCONJ
iajs-1000	33	2	and	and	CCONJ
iajs-1000	33	3	only	only	ADV
iajs-1000	33	4	if	if	SCONJ
iajs-1000	33	5	(	(	PUNCT
iajs-1000	33	6	x	x	NOUN
iajs-1000	33	7	,	,	PUNCT
iajs-1000	33	8	τ	τ	NOUN
iajs-1000	33	9	)	)	PUNCT
iajs-1000	33	10	and	and	CCONJ
iajs-1000	33	11	(	(	PUNCT
iajs-1000	33	12	x	x	X
iajs-1000	33	13	,	,	PUNCT
iajs-1000	33	14	τ	τ	X
iajs-1000	33	15	)	)	PUNCT
iajs-1000	33	16	are	be	AUX
iajs-1000	33	17	compact	compact	ADJ
iajs-1000	33	18	.	.	PUNCT
iajs-1000	34	1	proof	proof	NOUN
iajs-1000	34	2	:	:	PUNCT
iajs-1000	35	1			ADJ
iajs-1000	35	2			NOUN
iajs-1000	35	3			PUNCT
iajs-1000	36	1			NOUN
iajs-1000	36	2	ibn	ibn	PROPN
iajs-1000	36	3	alhaitham	alhaitham	NOUN
iajs-1000	36	4	j.	j.	PROPN
iajs-1000	36	5	for	for	ADP
iajs-1000	36	6	pure	pure	ADJ
iajs-1000	36	7	&	&	CCONJ
iajs-1000	36	8	appl	appl	PROPN
iajs-1000	36	9	.	.	PUNCT
iajs-1000	37	1	sci	sci	PROPN
iajs-1000	37	2	.	.	PUNCT
iajs-1000	38	1	vol.23	vol.23	PROPN
iajs-1000	38	2	(	(	PUNCT
iajs-1000	38	3	1	1	NUM
iajs-1000	38	4	)	)	PUNCT
iajs-1000	38	5	2010	2010	NUM
iajs-1000	38	6	necessity	necessity	NOUN
iajs-1000	38	7	,	,	PUNCT
iajs-1000	38	8	follows	follow	VERB
iajs-1000	38	9	from	from	ADP
iajs-1000	38	10	proposition	proposition	NOUN
iajs-1000	38	11	(	(	PUNCT
iajs-1000	38	12	2.8	2.8	NUM
iajs-1000	38	13	)	)	PUNCT
iajs-1000	38	14	.	.	PUNCT
iajs-1000	39	1	sufficiency	sufficiency	PROPN
iajs-1000	39	2	,	,	PUNCT
iajs-1000	39	3	in	in	ADP
iajs-1000	39	4	view	view	NOUN
iajs-1000	39	5	of	of	ADP
iajs-1000	39	6	τ	τ	PROPN
iajs-1000	39	7	is	be	AUX
iajs-1000	39	8	a	a	DET
iajs-1000	39	9	subfamily	subfamily	NOUN
iajs-1000	39	10	of	of	ADP
iajs-1000	39	11	τ	τ	NOUN
iajs-1000	39	12	,	,	PUNCT
iajs-1000	39	13	then	then	ADV
iajs-1000	39	14	ττ	ττ	PUNCT
iajs-1000	40	1	=	=	SYM
iajs-1000	40	2	τ.	τ.	SCONJ
iajs-1000	40	3	so	so	ADV
iajs-1000	40	4	(	(	PUNCT
iajs-1000	40	5	x	x	X
iajs-1000	40	6	,	,	PUNCT
iajs-1000	40	7	τ	τ	PROPN
iajs-1000	40	8	,	,	PUNCT
iajs-1000	40	9	τ	τ	NOUN
iajs-1000	40	10	)	)	PUNCT
iajs-1000	40	11	is	be	AUX
iajs-1000	40	12	ncompact	ncompact	ADJ
iajs-1000	40	13	.	.	PUNCT
iajs-1000	41	1			NUM
iajs-1000	41	2	2.11	2.11	NUM
iajs-1000	41	3	proposition	proposition	NOUN
iajs-1000	41	4	the	the	DET
iajs-1000	41	5	n	n	ADV
iajs-1000	41	6	-	-	PUNCT
iajs-1000	41	7	closed	closed	ADJ
iajs-1000	41	8	subset	subset	NOUN
iajs-1000	41	9	of	of	ADP
iajs-1000	41	10	an	an	DET
iajs-1000	41	11	n	n	CCONJ
iajs-1000	41	12	-	-	PUNCT
iajs-1000	41	13	compact	compact	ADJ
iajs-1000	41	14	space	space	NOUN
iajs-1000	41	15	is	be	AUX
iajs-1000	41	16	n	n	ADV
iajs-1000	41	17	-	-	PUNCT
iajs-1000	41	18	compact	compact	ADJ
iajs-1000	41	19	.	.	PUNCT
iajs-1000	42	1	proof	proof	NOUN
iajs-1000	42	2	:	:	PUNCT
iajs-1000	42	3	let	let	VERB
iajs-1000	42	4	(	(	PUNCT
iajs-1000	42	5	x	x	X
iajs-1000	42	6	,	,	PUNCT
iajs-1000	42	7	τ	τ	PROPN
iajs-1000	42	8	,	,	PUNCT
iajs-1000	42	9	τ	τ	NOUN
iajs-1000	42	10	)	)	PUNCT
iajs-1000	42	11	be	be	VERB
iajs-1000	42	12	an	an	DET
iajs-1000	42	13	n	n	CCONJ
iajs-1000	42	14	-	-	PUNCT
iajs-1000	42	15	compact	compact	ADJ
iajs-1000	42	16	space	space	NOUN
iajs-1000	42	17	and	and	CCONJ
iajs-1000	42	18	let	let	VERB
iajs-1000	42	19	a	a	PRON
iajs-1000	42	20	be	be	AUX
iajs-1000	42	21	an	an	DET
iajs-1000	42	22	n	n	ADV
iajs-1000	42	23	-	-	PUNCT
iajs-1000	42	24	closed	closed	ADJ
iajs-1000	42	25	subset	subset	NOUN
iajs-1000	42	26	of	of	ADP
iajs-1000	42	27	x	x	PRON
iajs-1000	42	28	to	to	PART
iajs-1000	42	29	show	show	VERB
iajs-1000	42	30	that	that	SCONJ
iajs-1000	42	31	a	a	PRON
iajs-1000	42	32	is	be	AUX
iajs-1000	42	33	an	an	DET
iajs-1000	42	34	n	n	ADV
iajs-1000	42	35	-	-	PUNCT
iajs-1000	42	36	compact	compact	ADJ
iajs-1000	42	37	set	set	NOUN
iajs-1000	42	38	.	.	PUNCT
iajs-1000	43	1	let	let	AUX
iajs-1000	43	2	{	{	PUNCT
iajs-1000	43	3	ui	ui	NOUN
iajs-1000	43	4	:	:	PUNCT
iajs-1000	43	5	i	i	PRON
iajs-1000	43	6			NOUN
iajs-1000	43	7			NOUN
iajs-1000	43	8	}	}	PUNCT
iajs-1000	43	9	be	be	VERB
iajs-1000	43	10	an	an	DET
iajs-1000	43	11	n	n	ADV
iajs-1000	43	12	-	-	PUNCT
iajs-1000	43	13	open	open	ADJ
iajs-1000	43	14	cover	cover	NOUN
iajs-1000	43	15	of	of	ADP
iajs-1000	43	16	a.	a.	NOUN
iajs-1000	43	17	since	since	SCONJ
iajs-1000	43	18	a	a	DET
iajs-1000	43	19	is	be	AUX
iajs-1000	43	20	n	n	PRON
iajs-1000	43	21	-	-	PUNCT
iajs-1000	43	22	closed	closed	ADJ
iajs-1000	43	23	subset	subset	NOUN
iajs-1000	43	24	of	of	ADP
iajs-1000	43	25	x	x	X
iajs-1000	43	26	,	,	PUNCT
iajs-1000	43	27	then	then	ADV
iajs-1000	43	28	x	x	X
iajs-1000	43	29	–	–	PUNCT
iajs-1000	43	30	a	a	PRON
iajs-1000	43	31	is	be	AUX
iajs-1000	43	32	n	n	PRON
iajs-1000	43	33	-	-	PUNCT
iajs-1000	43	34	open	open	ADJ
iajs-1000	43	35	subset	subset	NOUN
iajs-1000	43	36	of	of	ADP
iajs-1000	43	37	x	x	PRON
iajs-1000	43	38	,	,	PUNCT
iajs-1000	43	39	so	so	CCONJ
iajs-1000	43	40	{	{	PUNCT
iajs-1000	43	41	x	x	NOUN
iajs-1000	43	42	–	–	PUNCT
iajs-1000	43	43	a	a	PRON
iajs-1000	43	44	}	}	PUNCT
iajs-1000	43	45			NOUN
iajs-1000	43	46	{	{	PUNCT
iajs-1000	43	47	ui	ui	NOUN
iajs-1000	43	48	:	:	PUNCT
iajs-1000	43	49	i	i	PRON
iajs-1000	43	50			NOUN
iajs-1000	43	51			NOUN
iajs-1000	43	52	}	}	PUNCT
iajs-1000	43	53	is	be	AUX
iajs-1000	43	54	an	an	DET
iajs-1000	43	55	n	n	ADV
iajs-1000	43	56	-	-	PUNCT
iajs-1000	43	57	open	open	ADJ
iajs-1000	43	58	cover	cover	NOUN
iajs-1000	43	59	of	of	ADP
iajs-1000	43	60	x	x	X
iajs-1000	43	61	,	,	PUNCT
iajs-1000	43	62	which	which	PRON
iajs-1000	43	63	is	be	AUX
iajs-1000	43	64	an	an	DET
iajs-1000	43	65	n	n	CCONJ
iajs-1000	43	66	-	-	PUNCT
iajs-1000	43	67	compact	compact	ADJ
iajs-1000	43	68	space	space	NOUN
iajs-1000	43	69	.	.	PUNCT
iajs-1000	44	1	therefore	therefore	ADV
iajs-1000	44	2	,	,	PUNCT
iajs-1000	44	3	there	there	PRON
iajs-1000	44	4	exists	exist	VERB
iajs-1000	44	5	i1	i1	PROPN
iajs-1000	44	6	,	,	PUNCT
iajs-1000	44	7	i2,,in	i2,,in	VERB
iajs-1000	44	8			NOUN
iajs-1000	44	9			NOUN
iajs-1000	44	10	,	,	PUNCT
iajs-1000	44	11	such	such	ADJ
iajs-1000	44	12	that	that	SCONJ
iajs-1000	44	13	{	{	PUNCT
iajs-1000	44	14	x	x	NOUN
iajs-1000	44	15	–	–	PUNCT
iajs-1000	44	16	a	a	PRON
iajs-1000	44	17	,	,	PUNCT
iajs-1000	44	18	i1	i1	PROPN
iajs-1000	44	19	u	u	PROPN
iajs-1000	44	20	,	,	PUNCT
iajs-1000	44	21	i2	i2	PROPN
iajs-1000	44	22	u	u	PROPN
iajs-1000	44	23	,	,	PUNCT
iajs-1000	44	24			PROPN
iajs-1000	44	25	,	,	PUNCT
iajs-1000	44	26	in	in	ADP
iajs-1000	44	27	u	u	NOUN
iajs-1000	44	28	}	}	PUNCT
iajs-1000	44	29	is	be	AUX
iajs-1000	44	30	a	a	DET
iajs-1000	44	31	finite	finite	ADJ
iajs-1000	44	32	subcover	subcover	NOUN
iajs-1000	44	33	of	of	ADP
iajs-1000	44	34	x.	x.	PROPN
iajs-1000	44	35	as	as	ADP
iajs-1000	44	36	a	a	DET
iajs-1000	44	37			PROPN
iajs-1000	44	38	x	x	X
iajs-1000	44	39	and	and	CCONJ
iajs-1000	44	40	x	x	X
iajs-1000	44	41	–	–	PUNCT
iajs-1000	44	42	a	a	DET
iajs-1000	44	43	covers	cover	VERB
iajs-1000	44	44	no	no	DET
iajs-1000	44	45	part	part	NOUN
iajs-1000	44	46	of	of	ADP
iajs-1000	44	47	a	a	PRON
iajs-1000	44	48	,	,	PUNCT
iajs-1000	44	49	then	then	ADV
iajs-1000	44	50	{	{	PUNCT
iajs-1000	44	51	i1	i1	PROPN
iajs-1000	44	52	u	u	PROPN
iajs-1000	44	53	,	,	PUNCT
iajs-1000	44	54	i2	i2	PROPN
iajs-1000	44	55	u	u	PROPN
iajs-1000	44	56	,	,	PUNCT
iajs-1000	44	57			PROPN
iajs-1000	44	58	,	,	PUNCT
iajs-1000	44	59	in	in	ADP
iajs-1000	44	60	u	u	NOUN
iajs-1000	44	61	}	}	PUNCT
iajs-1000	44	62	is	be	AUX
iajs-1000	44	63	a	a	DET
iajs-1000	44	64	finite	finite	ADJ
iajs-1000	44	65	subcover	subcover	NOUN
iajs-1000	44	66	of	of	ADP
iajs-1000	44	67	a.	a.	PROPN
iajs-1000	45	1	so	so	ADV
iajs-1000	45	2	a	a	PRON
iajs-1000	45	3	is	be	AUX
iajs-1000	45	4	n	n	PRON
iajs-1000	45	5	-	-	PUNCT
iajs-1000	45	6	compact	compact	ADJ
iajs-1000	45	7	set	set	NOUN
iajs-1000	45	8	.	.	PUNCT
iajs-1000	46	1			NUM
iajs-1000	46	2	2.12	2.12	NUM
iajs-1000	46	3	definition	definition	NOUN
iajs-1000	46	4	a	a	DET
iajs-1000	46	5	function	function	NOUN
iajs-1000	47	1	f	f	X
iajs-1000	47	2	:	:	PUNCT
iajs-1000	47	3	(	(	PUNCT
iajs-1000	47	4	x	x	X
iajs-1000	47	5	,	,	PUNCT
iajs-1000	47	6	τ	τ	PROPN
iajs-1000	47	7	,	,	PUNCT
iajs-1000	47	8	τ	τ	NOUN
iajs-1000	47	9	)	)	PUNCT
iajs-1000	47	10			PROPN
iajs-1000	47	11	(	(	PUNCT
iajs-1000	47	12	y	y	PROPN
iajs-1000	47	13	,	,	PUNCT
iajs-1000	47	14	t	t	PROPN
iajs-1000	47	15	,	,	PUNCT
iajs-1000	47	16	t	t	NUM
iajs-1000	47	17	)	)	PUNCT
iajs-1000	47	18	is	be	AUX
iajs-1000	47	19	said	say	VERB
iajs-1000	47	20	to	to	PART
iajs-1000	47	21	be	be	AUX
iajs-1000	47	22	an	an	DET
iajs-1000	47	23	"	"	PUNCT
iajs-1000	47	24	n	n	CCONJ
iajs-1000	47	25	-	-	PUNCT
iajs-1000	47	26	continuous	continuous	ADJ
iajs-1000	47	27	function	function	NOUN
iajs-1000	47	28	"	"	PUNCT
iajs-1000	47	29	if	if	SCONJ
iajs-1000	47	30	and	and	CCONJ
iajs-1000	47	31	only	only	ADV
iajs-1000	47	32	if	if	SCONJ
iajs-1000	47	33	the	the	DET
iajs-1000	47	34	inverse	inverse	ADJ
iajs-1000	47	35	image	image	NOUN
iajs-1000	47	36	of	of	ADP
iajs-1000	47	37	each	each	DET
iajs-1000	47	38	n	n	ADV
iajs-1000	47	39	-	-	PUNCT
iajs-1000	47	40	open	open	ADJ
iajs-1000	47	41	subset	subset	NOUN
iajs-1000	47	42	of	of	ADP
iajs-1000	47	43	y	y	PROPN
iajs-1000	47	44	is	be	AUX
iajs-1000	47	45	an	an	DET
iajs-1000	47	46	n	n	ADV
iajs-1000	47	47	-	-	PUNCT
iajs-1000	47	48	open	open	ADJ
iajs-1000	47	49	subset	subset	NOUN
iajs-1000	47	50	of	of	ADP
iajs-1000	47	51	x.	x.	PROPN
iajs-1000	47	52	2.13	2.13	NUM
iajs-1000	47	53	proposition	proposition	NOUN
iajs-1000	47	54	the	the	DET
iajs-1000	47	55	n	n	ADV
iajs-1000	47	56	-	-	PUNCT
iajs-1000	47	57	continuous	continuous	ADJ
iajs-1000	47	58	image	image	NOUN
iajs-1000	47	59	of	of	ADP
iajs-1000	47	60	an	an	DET
iajs-1000	47	61	n	n	CCONJ
iajs-1000	47	62	-	-	PUNCT
iajs-1000	47	63	compact	compact	ADJ
iajs-1000	47	64	space	space	NOUN
iajs-1000	47	65	is	be	AUX
iajs-1000	47	66	an	an	DET
iajs-1000	47	67	n	n	CCONJ
iajs-1000	47	68	-	-	PUNCT
iajs-1000	47	69	compact	compact	ADJ
iajs-1000	47	70	space	space	NOUN
iajs-1000	47	71	.	.	PUNCT
iajs-1000	48	1	proof	proof	NOUN
iajs-1000	48	2	:	:	PUNCT
iajs-1000	48	3	let	let	VERB
iajs-1000	48	4	(	(	PUNCT
iajs-1000	48	5	x	x	X
iajs-1000	48	6	,	,	PUNCT
iajs-1000	48	7	τ	τ	PROPN
iajs-1000	48	8	,	,	PUNCT
iajs-1000	48	9	τ	τ	NOUN
iajs-1000	48	10	)	)	PUNCT
iajs-1000	48	11	be	be	VERB
iajs-1000	48	12	an	an	DET
iajs-1000	48	13	n	n	CCONJ
iajs-1000	48	14	-	-	PUNCT
iajs-1000	48	15	compact	compact	ADJ
iajs-1000	48	16	space	space	NOUN
iajs-1000	48	17	,	,	PUNCT
iajs-1000	48	18	and	and	CCONJ
iajs-1000	48	19	let	let	VERB
iajs-1000	48	20	f	f	X
iajs-1000	48	21	:	:	PUNCT
iajs-1000	48	22	(	(	PUNCT
iajs-1000	48	23	x	x	X
iajs-1000	48	24	,	,	PUNCT
iajs-1000	48	25	τ	τ	PROPN
iajs-1000	48	26	,	,	PUNCT
iajs-1000	48	27	τ	τ	NOUN
iajs-1000	48	28	)	)	PUNCT
iajs-1000	48	29			PROPN
iajs-1000	49	1	(	(	PUNCT
iajs-1000	49	2	y	y	PROPN
iajs-1000	49	3	,	,	PUNCT
iajs-1000	49	4	t	t	PROPN
iajs-1000	49	5	,	,	PUNCT
iajs-1000	49	6	t	t	NUM
iajs-1000	49	7	)	)	PUNCT
iajs-1000	49	8	be	be	AUX
iajs-1000	49	9	an	an	DET
iajs-1000	49	10	ncontinuous	ncontinuous	ADJ
iajs-1000	49	11	,	,	PUNCT
iajs-1000	49	12	onto	onto	ADP
iajs-1000	49	13	function	function	NOUN
iajs-1000	49	14	.	.	PUNCT
iajs-1000	50	1	to	to	PART
iajs-1000	50	2	show	show	VERB
iajs-1000	50	3	that	that	SCONJ
iajs-1000	50	4	(	(	PUNCT
iajs-1000	50	5	y	y	PROPN
iajs-1000	50	6	,	,	PUNCT
iajs-1000	50	7	t	t	PROPN
iajs-1000	50	8	,	,	PUNCT
iajs-1000	50	9	t	t	PROPN
iajs-1000	50	10			ADJ
iajs-1000	50	11	)	)	PUNCT
iajs-1000	50	12	is	be	AUX
iajs-1000	50	13	an	an	DET
iajs-1000	50	14	n	n	CCONJ
iajs-1000	50	15	-	-	PUNCT
iajs-1000	50	16	compact	compact	ADJ
iajs-1000	50	17	space	space	NOUN
iajs-1000	50	18	.	.	PUNCT
iajs-1000	51	1	let	let	VERB
iajs-1000	51	2	{	{	PUNCT
iajs-1000	51	3	ui	ui	NOUN
iajs-1000	51	4	:	:	PUNCT
iajs-1000	51	5	i	i	PRON
iajs-1000	51	6			NOUN
iajs-1000	51	7			NOUN
iajs-1000	51	8	}	}	PUNCT
iajs-1000	51	9	be	be	VERB
iajs-1000	51	10	an	an	DET
iajs-1000	51	11	n	n	ADV
iajs-1000	51	12	-	-	PUNCT
iajs-1000	51	13	open	open	ADJ
iajs-1000	51	14	cover	cover	NOUN
iajs-1000	51	15	of	of	ADP
iajs-1000	51	16	y	y	PROPN
iajs-1000	51	17	,	,	PUNCT
iajs-1000	51	18	then	then	ADV
iajs-1000	51	19	{	{	PUNCT
iajs-1000	51	20	f	f	PROPN
iajs-1000	51	21	–	–	PUNCT
iajs-1000	51	22	1	1	NUM
iajs-1000	51	23	(	(	PUNCT
iajs-1000	51	24	ui	ui	NOUN
iajs-1000	51	25	):	):	PUNCT
iajs-1000	51	26	i	i	PRON
iajs-1000	51	27			NOUN
iajs-1000	51	28			NOUN
iajs-1000	51	29	}	}	PUNCT
iajs-1000	51	30	is	be	AUX
iajs-1000	51	31	an	an	DET
iajs-1000	51	32	n	n	ADV
iajs-1000	51	33	-	-	PUNCT
iajs-1000	51	34	open	open	ADJ
iajs-1000	51	35	cover	cover	NOUN
iajs-1000	51	36	of	of	ADP
iajs-1000	51	37	x	x	X
iajs-1000	51	38	,	,	PUNCT
iajs-1000	51	39	which	which	PRON
iajs-1000	51	40	is	be	AUX
iajs-1000	51	41	n	n	CCONJ
iajs-1000	51	42	-	-	PUNCT
iajs-1000	51	43	compact	compact	ADJ
iajs-1000	51	44	space	space	NOUN
iajs-1000	51	45	.	.	PUNCT
iajs-1000	52	1	so	so	ADV
iajs-1000	52	2	,	,	PUNCT
iajs-1000	52	3	there	there	PRON
iajs-1000	52	4	exists	exist	VERB
iajs-1000	52	5	i1	i1	PROPN
iajs-1000	52	6	,	,	PUNCT
iajs-1000	52	7	i2,,in	i2,,in	VERB
iajs-1000	52	8			NOUN
iajs-1000	52	9			NOUN
iajs-1000	52	10	,	,	PUNCT
iajs-1000	52	11	such	such	ADJ
iajs-1000	52	12	that	that	SCONJ
iajs-1000	52	13	the	the	DET
iajs-1000	52	14	family	family	NOUN
iajs-1000	52	15	{	{	PUNCT
iajs-1000	52	16	f	f	PROPN
iajs-1000	52	17	–	–	PUNCT
iajs-1000	52	18	1(uij	1(uij	NUM
iajs-1000	52	19	):	):	PUNCT
iajs-1000	52	20	j=1	j=1	PROPN
iajs-1000	52	21	,	,	PUNCT
iajs-1000	52	22	2	2	NUM
iajs-1000	52	23	,	,	PUNCT
iajs-1000	52	24	…	…	PUNCT
iajs-1000	52	25	,	,	PUNCT
iajs-1000	52	26	n	n	CCONJ
iajs-1000	52	27	}	}	PUNCT
iajs-1000	52	28	covers	cover	VERB
iajs-1000	52	29	x	x	PUNCT
iajs-1000	52	30	and	and	CCONJ
iajs-1000	52	31	since	since	SCONJ
iajs-1000	52	32	f	f	PROPN
iajs-1000	52	33	is	be	AUX
iajs-1000	52	34	onto	onto	ADP
iajs-1000	52	35	,	,	PUNCT
iajs-1000	52	36	then	then	ADV
iajs-1000	52	37	{	{	PUNCT
iajs-1000	52	38	uij	uij	PROPN
iajs-1000	52	39	:	:	PUNCT
iajs-1000	52	40	j=1	j=1	NOUN
iajs-1000	52	41	,	,	PUNCT
iajs-1000	52	42	2	2	NUM
iajs-1000	52	43	,	,	PUNCT
iajs-1000	52	44	…	…	PUNCT
iajs-1000	52	45	,	,	PUNCT
iajs-1000	52	46	n	n	CCONJ
iajs-1000	52	47	}	}	PUNCT
iajs-1000	52	48	is	be	AUX
iajs-1000	52	49	a	a	DET
iajs-1000	52	50	finite	finite	ADJ
iajs-1000	52	51	subcover	subcover	NOUN
iajs-1000	52	52	of	of	ADP
iajs-1000	52	53	y.	y.	PROPN
iajs-1000	52	54			NUM
iajs-1000	52	55	2.14	2.14	NUM
iajs-1000	52	56	proposition	proposition	NOUN
iajs-1000	52	57	if	if	SCONJ
iajs-1000	52	58	a	a	PRON
iajs-1000	52	59	and	and	CCONJ
iajs-1000	52	60	b	b	NOUN
iajs-1000	52	61	are	be	AUX
iajs-1000	52	62	two	two	NUM
iajs-1000	52	63	n	n	CCONJ
iajs-1000	52	64	-	-	PUNCT
iajs-1000	52	65	compact	compact	ADJ
iajs-1000	52	66	subsets	subset	NOUN
iajs-1000	52	67	of	of	ADP
iajs-1000	52	68	a	a	DET
iajs-1000	52	69	bitopological	bitopological	ADJ
iajs-1000	52	70	space	space	NOUN
iajs-1000	52	71	(	(	PUNCT
iajs-1000	52	72	x	x	X
iajs-1000	52	73	,	,	PUNCT
iajs-1000	52	74	τ	τ	PROPN
iajs-1000	52	75	,	,	PUNCT
iajs-1000	52	76	τ	τ	NOUN
iajs-1000	52	77	)	)	PUNCT
iajs-1000	52	78	,	,	PUNCT
iajs-1000	52	79	then	then	ADV
iajs-1000	52	80	ab	ab	NOUN
iajs-1000	52	81	is	be	AUX
iajs-1000	52	82	an	an	DET
iajs-1000	52	83	n	n	ADV
iajs-1000	52	84	-	-	PUNCT
iajs-1000	52	85	compact	compact	ADJ
iajs-1000	52	86	subset	subset	NOUN
iajs-1000	52	87	of	of	ADP
iajs-1000	52	88	x.	x.	NOUN
iajs-1000	52	89	proof	proof	PROPN
iajs-1000	52	90	:	:	PUNCT
iajs-1000	52	91	clear	clear	ADJ
iajs-1000	52	92	.	.	PUNCT
iajs-1000	53	1			NUM
iajs-1000	53	2	2.15	2.15	NUM
iajs-1000	53	3	remark	remark	NOUN
iajs-1000	53	4	if	if	SCONJ
iajs-1000	53	5	a	a	PRON
iajs-1000	53	6	and	and	CCONJ
iajs-1000	53	7	b	b	NOUN
iajs-1000	53	8	are	be	AUX
iajs-1000	53	9	two	two	NUM
iajs-1000	53	10	n	n	CCONJ
iajs-1000	53	11	-	-	PUNCT
iajs-1000	53	12	compact	compact	ADJ
iajs-1000	53	13	subsets	subset	NOUN
iajs-1000	53	14	of	of	ADP
iajs-1000	53	15	a	a	DET
iajs-1000	53	16	bitopology	bitopology	NOUN
iajs-1000	53	17	space	space	NOUN
iajs-1000	53	18	(	(	PUNCT
iajs-1000	53	19	x	x	X
iajs-1000	53	20	,	,	PUNCT
iajs-1000	53	21	τ	τ	PROPN
iajs-1000	53	22	,	,	PUNCT
iajs-1000	53	23	τ	τ	NOUN
iajs-1000	53	24	)	)	PUNCT
iajs-1000	53	25	,	,	PUNCT
iajs-1000	53	26	then	then	ADV
iajs-1000	53	27	a	a	DET
iajs-1000	53	28			NOUN
iajs-1000	53	29	b	b	NOUN
iajs-1000	53	30	need	need	AUX
iajs-1000	53	31	not	not	PART
iajs-1000	53	32	be	be	AUX
iajs-1000	53	33	n	n	ADV
iajs-1000	53	34	-	-	PUNCT
iajs-1000	53	35	compact	compact	ADJ
iajs-1000	53	36	.	.	PUNCT
iajs-1000	54	1	for	for	ADP
iajs-1000	54	2	example	example	NOUN
iajs-1000	54	3	,	,	PUNCT
iajs-1000	54	4	let	let	VERB
iajs-1000	54	5	x=	x=	PROPN
iajs-1000	54	6	�	�	PROPN
iajs-1000	54	7			PROPN
iajs-1000	54	8	{	{	PUNCT
iajs-1000	54	9	0,-1	0,-1	NUM
iajs-1000	54	10	}	}	PUNCT
iajs-1000	54	11	and	and	CCONJ
iajs-1000	54	12	let	let	VERB
iajs-1000	54	13	=p	=p	PROPN
iajs-1000	54	14	(	(	PUNCT
iajs-1000	54	15	�	�	PROPN
iajs-1000	54	16	)	)	PUNCT
iajs-1000	54	17	{hx-1,0h(x	{hx-1,0h(x	PROPN
iajs-1000	54	18	–	–	PUNCT
iajs-1000	54	19	h	h	NOUN
iajs-1000	54	20	)	)	PUNCT
iajs-1000	54	21	is	be	AUX
iajs-1000	54	22	finite	finite	ADJ
iajs-1000	54	23	}	}	PUNCT
iajs-1000	54	24	.	.	PUNCT
iajs-1000	55	1	let	let	VERB
iajs-1000	55	2	=	=	PROPN
iajs-1000	55	3			NOUN
iajs-1000	55	4	{	{	PUNCT
iajs-1000	55	5	hx(-1h	hx(-1h	ADJ
iajs-1000	55	6	or	or	CCONJ
iajs-1000	55	7	0	0	NUM
iajs-1000	55	8	h)(x	h)(x	ADJ
iajs-1000	55	9	–	–	PUNCT
iajs-1000	55	10	h	h	NOUN
iajs-1000	55	11	)	)	PUNCT
iajs-1000	55	12	finite	finite	NOUN
iajs-1000	55	13	}	}	PUNCT
iajs-1000	55	14	.	.	PUNCT
iajs-1000	56	1	now	now	ADV
iajs-1000	56	2	,	,	PUNCT
iajs-1000	56	3	let	let	VERB
iajs-1000	56	4	a	a	DET
iajs-1000	56	5	=	=	X
iajs-1000	56	6	�	�	PROPN
iajs-1000	56	7			PROPN
iajs-1000	56	8	{	{	PUNCT
iajs-1000	56	9	0	0	NUM
iajs-1000	56	10	}	}	PUNCT
iajs-1000	56	11	and	and	CCONJ
iajs-1000	56	12	b	b	X
iajs-1000	56	13	=	=	SYM
iajs-1000	56	14	�	�	PROPN
iajs-1000	56	15			PROPN
iajs-1000	56	16	{	{	PUNCT
iajs-1000	56	17	-1	-1	NOUN
iajs-1000	56	18	}	}	PUNCT
iajs-1000	56	19	,	,	PUNCT
iajs-1000	56	20	then	then	ADV
iajs-1000	56	21	both	both	CCONJ
iajs-1000	56	22	a	a	PRON
iajs-1000	56	23	and	and	CCONJ
iajs-1000	56	24	b	b	NOUN
iajs-1000	56	25	are	be	AUX
iajs-1000	56	26	n	n	CCONJ
iajs-1000	56	27	-	-	PUNCT
iajs-1000	56	28	compact	compact	ADJ
iajs-1000	56	29	subsets	subset	NOUN
iajs-1000	56	30	of	of	ADP
iajs-1000	56	31	the	the	DET
iajs-1000	56	32	bitopologycal	bitopologycal	ADJ
iajs-1000	56	33	space	space	NOUN
iajs-1000	56	34	(	(	PUNCT
iajs-1000	56	35	x	x	X
iajs-1000	56	36	,	,	PUNCT
iajs-1000	56	37	τ	τ	PROPN
iajs-1000	56	38	,	,	PUNCT
iajs-1000	56	39	τ	τ	NOUN
iajs-1000	56	40	)	)	PUNCT
iajs-1000	56	41	,	,	PUNCT
iajs-1000	56	42	but	but	CCONJ
iajs-1000	56	43	a	a	DET
iajs-1000	56	44			NOUN
iajs-1000	56	45	b	b	NOUN
iajs-1000	56	46	=	=	SYM
iajs-1000	56	47	�	�	PROPN
iajs-1000	56	48	is	be	AUX
iajs-1000	56	49	not	not	PART
iajs-1000	56	50	n	n	CCONJ
iajs-1000	56	51	-	-	PUNCT
iajs-1000	56	52	compact	compact	ADJ
iajs-1000	56	53	set	set	NOUN
iajs-1000	56	54	.	.	PUNCT
iajs-1000	57	1	in	in	ADP
iajs-1000	57	2	the	the	DET
iajs-1000	57	3	following	follow	VERB
iajs-1000	57	4	definition	definition	NOUN
iajs-1000	57	5	,	,	PUNCT
iajs-1000	57	6	we	we	PRON
iajs-1000	57	7	study	study	VERB
iajs-1000	57	8	another	another	DET
iajs-1000	57	9	kind	kind	NOUN
iajs-1000	57	10	of	of	ADP
iajs-1000	57	11	open	open	ADJ
iajs-1000	57	12	sets	set	NOUN
iajs-1000	57	13	in	in	ADP
iajs-1000	57	14	bitopological	bitopological	ADJ
iajs-1000	57	15	spaces	space	NOUN
iajs-1000	57	16	,	,	PUNCT
iajs-1000	57	17	namely	namely	ADV
iajs-1000	57	18	"	"	PUNCT
iajs-1000	57	19	s	s	X
iajs-1000	57	20	-	-	ADJ
iajs-1000	57	21	open	open	ADJ
iajs-1000	57	22	set	set	NOUN
iajs-1000	57	23	"	"	PUNCT
iajs-1000	57	24	.	.	PUNCT
iajs-1000	58	1	2.16	2.16	NUM
iajs-1000	58	2	definition	definition	NOUN
iajs-1000	58	3	[	[	X
iajs-1000	58	4	4	4	X
iajs-1000	58	5	]	]	X
iajs-1000	58	6	a	a	DET
iajs-1000	58	7	subset	subset	NOUN
iajs-1000	58	8	a	a	PRON
iajs-1000	58	9	of	of	ADP
iajs-1000	58	10	a	a	DET
iajs-1000	58	11	topological	topological	ADJ
iajs-1000	58	12	space	space	NOUN
iajs-1000	58	13	(	(	PUNCT
iajs-1000	58	14	x	x	X
iajs-1000	58	15	,	,	PUNCT
iajs-1000	58	16	τ	τ	PROPN
iajs-1000	58	17	,	,	PUNCT
iajs-1000	58	18	τ	τ	NOUN
iajs-1000	58	19	)	)	PUNCT
iajs-1000	58	20	is	be	AUX
iajs-1000	58	21	said	say	VERB
iajs-1000	58	22	to	to	PART
iajs-1000	58	23	be	be	AUX
iajs-1000	58	24	"	"	PUNCT
iajs-1000	58	25	s	s	NOUN
iajs-1000	58	26	-	-	PUNCT
iajs-1000	58	27	open	open	ADJ
iajs-1000	58	28	set	set	NOUN
iajs-1000	58	29	"	"	PUNCT
iajs-1000	58	30	if	if	SCONJ
iajs-1000	58	31	it	it	PRON
iajs-1000	58	32	is	be	AUX
iajs-1000	58	33	-open	-open	ADJ
iajs-1000	58	34	or	or	CCONJ
iajs-1000	58	35	-open	-open	VERB
iajs-1000	58	36	.	.	PUNCT
iajs-1000	59	1	the	the	DET
iajs-1000	59	2	complement	complement	NOUN
iajs-1000	59	3	of	of	ADP
iajs-1000	59	4	the	the	DET
iajs-1000	59	5	s	s	NOUN
iajs-1000	59	6	-	-	ADJ
iajs-1000	59	7	open	open	ADJ
iajs-1000	59	8	set	set	NOUN
iajs-1000	59	9	is	be	AUX
iajs-1000	59	10	called	call	VERB
iajs-1000	59	11	"	"	PUNCT
iajs-1000	59	12	s	s	NOUN
iajs-1000	59	13	-	-	PUNCT
iajs-1000	59	14	closed	closed	ADJ
iajs-1000	59	15	set	set	NOUN
iajs-1000	59	16	"	"	PUNCT
iajs-1000	59	17	.	.	PUNCT
iajs-1000	60	1	ibn	ibn	PROPN
iajs-1000	60	2	alhaitham	alhaitham	PROPN
iajs-1000	60	3	j.	j.	PROPN
iajs-1000	60	4	for	for	ADP
iajs-1000	60	5	pure	pure	ADJ
iajs-1000	60	6	&	&	CCONJ
iajs-1000	60	7	appl	appl	PROPN
iajs-1000	60	8	.	.	PUNCT
iajs-1000	61	1	sci	sci	PROPN
iajs-1000	61	2	.	.	PUNCT
iajs-1000	62	1	vol.23	vol.23	PROPN
iajs-1000	62	2	(	(	PUNCT
iajs-1000	62	3	1	1	NUM
iajs-1000	62	4	)	)	PUNCT
iajs-1000	62	5	2010	2010	NUM
iajs-1000	62	6	2.17	2.17	NUM
iajs-1000	62	7	remark	remark	NOUN
iajs-1000	62	8	(	(	PUNCT
iajs-1000	62	9	i	i	NOUN
iajs-1000	62	10	)	)	PUNCT
iajs-1000	62	11	every	every	DET
iajs-1000	62	12	s	s	NOUN
iajs-1000	62	13	-	-	ADJ
iajs-1000	62	14	open	open	ADJ
iajs-1000	62	15	set	set	NOUN
iajs-1000	62	16	in	in	ADP
iajs-1000	62	17	a	a	DET
iajs-1000	62	18	bitopological	bitopological	ADJ
iajs-1000	62	19	space	space	NOUN
iajs-1000	62	20	(	(	PUNCT
iajs-1000	62	21	x	x	X
iajs-1000	62	22	,	,	PUNCT
iajs-1000	62	23	τ	τ	PROPN
iajs-1000	62	24	,	,	PUNCT
iajs-1000	62	25	τ	τ	NOUN
iajs-1000	62	26	)	)	PUNCT
iajs-1000	62	27	is	be	AUX
iajs-1000	62	28	an	an	DET
iajs-1000	62	29	n	n	ADV
iajs-1000	62	30	-	-	PUNCT
iajs-1000	62	31	open	open	ADJ
iajs-1000	62	32	set	set	NOUN
iajs-1000	62	33	.	.	PUNCT
iajs-1000	63	1	(	(	PUNCT
iajs-1000	63	2	ii	ii	NOUN
iajs-1000	63	3	)	)	PUNCT
iajs-1000	63	4	every	every	DET
iajs-1000	63	5	s	s	NOUN
iajs-1000	63	6	-	-	PUNCT
iajs-1000	63	7	closed	closed	ADJ
iajs-1000	63	8	set	set	NOUN
iajs-1000	63	9	in	in	ADP
iajs-1000	63	10	a	a	DET
iajs-1000	63	11	bitopological	bitopological	ADJ
iajs-1000	63	12	space	space	NOUN
iajs-1000	63	13	(	(	PUNCT
iajs-1000	63	14	x	x	X
iajs-1000	63	15	,	,	PUNCT
iajs-1000	63	16	τ	τ	PROPN
iajs-1000	63	17	,	,	PUNCT
iajs-1000	63	18	τ	τ	NOUN
iajs-1000	63	19	)	)	PUNCT
iajs-1000	63	20	is	be	AUX
iajs-1000	63	21	an	an	DET
iajs-1000	63	22	n	n	ADV
iajs-1000	63	23	-	-	PUNCT
iajs-1000	63	24	closed	close	VERB
iajs-1000	63	25	set	set	NOUN
iajs-1000	63	26	.	.	PUNCT
iajs-1000	64	1	2.18	2.18	NUM
iajs-1000	64	2	note	note	VERB
iajs-1000	64	3	the	the	DET
iajs-1000	64	4	implication	implication	NOUN
iajs-1000	64	5	in	in	ADP
iajs-1000	64	6	remark	remark	NOUN
iajs-1000	64	7	(	(	PUNCT
iajs-1000	64	8	2.17	2.17	NUM
iajs-1000	64	9	)	)	PUNCT
iajs-1000	64	10	is	be	AUX
iajs-1000	64	11	not	not	PART
iajs-1000	64	12	reversible	reversible	ADJ
iajs-1000	64	13	.	.	PUNCT
iajs-1000	65	1	see	see	VERB
iajs-1000	65	2	the	the	DET
iajs-1000	65	3	example	example	NOUN
iajs-1000	65	4	of	of	ADP
iajs-1000	65	5	note	note	NOUN
iajs-1000	65	6	(	(	PUNCT
iajs-1000	65	7	2.5	2.5	NUM
iajs-1000	65	8	)	)	PUNCT
iajs-1000	65	9	,	,	PUNCT
iajs-1000	65	10	where	where	SCONJ
iajs-1000	65	11	the	the	DET
iajs-1000	65	12	set	set	NOUN
iajs-1000	65	13	{	{	PUNCT
iajs-1000	65	14	1,2	1,2	NUM
iajs-1000	65	15	}	}	PUNCT
iajs-1000	65	16	is	be	AUX
iajs-1000	65	17	n	n	ADV
iajs-1000	65	18	-	-	PUNCT
iajs-1000	65	19	open	open	ADJ
iajs-1000	65	20	set	set	NOUN
iajs-1000	65	21	which	which	PRON
iajs-1000	65	22	is	be	AUX
iajs-1000	65	23	not	not	PART
iajs-1000	65	24	s	s	NOUN
iajs-1000	65	25	-	-	ADJ
iajs-1000	65	26	open	open	ADJ
iajs-1000	65	27	set	set	NOUN
iajs-1000	65	28	.	.	PUNCT
iajs-1000	66	1	so	so	ADV
iajs-1000	66	2	the	the	DET
iajs-1000	66	3	set	set	NOUN
iajs-1000	66	4	{	{	PUNCT
iajs-1000	66	5	3	3	NUM
iajs-1000	66	6	}	}	PUNCT
iajs-1000	66	7	is	be	AUX
iajs-1000	66	8	n	n	ADV
iajs-1000	66	9	-	-	PUNCT
iajs-1000	66	10	closed	close	VERB
iajs-1000	66	11	set	set	NOUN
iajs-1000	66	12	which	which	PRON
iajs-1000	66	13	is	be	AUX
iajs-1000	66	14	not	not	PART
iajs-1000	66	15	s	s	NOUN
iajs-1000	66	16	-	-	PUNCT
iajs-1000	66	17	closed	closed	ADJ
iajs-1000	66	18	set	set	NOUN
iajs-1000	66	19	.	.	PUNCT
iajs-1000	67	1	2.19	2.19	NUM
iajs-1000	67	2	definition	definition	NOUN
iajs-1000	67	3	[	[	X
iajs-1000	67	4	4	4	X
iajs-1000	67	5	]	]	X
iajs-1000	67	6	let	let	VERB
iajs-1000	67	7	(	(	PUNCT
iajs-1000	67	8	x	x	NOUN
iajs-1000	67	9	,	,	PUNCT
iajs-1000	67	10	τ	τ	PROPN
iajs-1000	67	11	,	,	PUNCT
iajs-1000	67	12	τ	τ	NOUN
iajs-1000	67	13	)	)	PUNCT
iajs-1000	67	14	be	be	AUX
iajs-1000	67	15	a	a	DET
iajs-1000	67	16	bitopological	bitopological	ADJ
iajs-1000	67	17	space	space	NOUN
iajs-1000	67	18	,	,	PUNCT
iajs-1000	67	19	let	let	VERB
iajs-1000	67	20	a	a	PRON
iajs-1000	67	21	be	be	AUX
iajs-1000	67	22	a	a	DET
iajs-1000	67	23	subset	subset	NOUN
iajs-1000	67	24	of	of	ADP
iajs-1000	67	25	x.	x.	PROPN
iajs-1000	67	26	a	a	DET
iajs-1000	67	27	subcollection	subcollection	NOUN
iajs-1000	67	28	of	of	ADP
iajs-1000	67	29	the	the	DET
iajs-1000	67	30	family	family	NOUN
iajs-1000	67	31			PROPN
iajs-1000	67	32	is	be	AUX
iajs-1000	67	33	called	call	VERB
iajs-1000	67	34	an	an	DET
iajs-1000	67	35	"	"	PUNCT
iajs-1000	67	36	s	s	NOUN
iajs-1000	67	37	-	-	PUNCT
iajs-1000	67	38	open	open	ADJ
iajs-1000	67	39	cover	cover	NOUN
iajs-1000	67	40	"	"	PUNCT
iajs-1000	67	41	of	of	ADP
iajs-1000	67	42	a	a	PRON
iajs-1000	67	43	if	if	SCONJ
iajs-1000	67	44	the	the	DET
iajs-1000	67	45	union	union	NOUN
iajs-1000	67	46	of	of	ADP
iajs-1000	67	47	members	member	NOUN
iajs-1000	67	48	of	of	ADP
iajs-1000	67	49	this	this	DET
iajs-1000	67	50	collection	collection	NOUN
iajs-1000	67	51	contains	contain	VERB
iajs-1000	67	52	a.	a.	NOUN
iajs-1000	67	53	in	in	ADP
iajs-1000	67	54	the	the	DET
iajs-1000	67	55	definitions	definition	NOUN
iajs-1000	67	56	(	(	PUNCT
iajs-1000	67	57	2.16	2.16	NUM
iajs-1000	67	58	)	)	PUNCT
iajs-1000	67	59	and	and	CCONJ
iajs-1000	67	60	(	(	PUNCT
iajs-1000	67	61	2.19	2.19	NUM
iajs-1000	67	62	)	)	PUNCT
iajs-1000	67	63	,	,	PUNCT
iajs-1000	67	64	we	we	PRON
iajs-1000	67	65	use	use	VERB
iajs-1000	67	66	the	the	DET
iajs-1000	67	67	concept	concept	NOUN
iajs-1000	67	68	of	of	ADP
iajs-1000	67	69	s	s	NOUN
iajs-1000	67	70	-	-	ADJ
iajs-1000	67	71	open	open	ADJ
iajs-1000	67	72	sets	set	NOUN
iajs-1000	67	73	in	in	ADP
iajs-1000	67	74	bitopological	bitopological	ADJ
iajs-1000	67	75	spaces	space	NOUN
iajs-1000	67	76	inorder	inorder	VERB
iajs-1000	67	77	to	to	PART
iajs-1000	67	78	expose	expose	VERB
iajs-1000	67	79	another	another	DET
iajs-1000	67	80	type	type	NOUN
iajs-1000	67	81	of	of	ADP
iajs-1000	67	82	compactness	compactness	NOUN
iajs-1000	67	83	in	in	ADP
iajs-1000	67	84	bitopological	bitopological	ADJ
iajs-1000	67	85	spaces	space	NOUN
iajs-1000	67	86	,	,	PUNCT
iajs-1000	67	87	called	call	VERB
iajs-1000	67	88	scompactness	scompactness	NOUN
iajs-1000	67	89	,	,	PUNCT
iajs-1000	67	90	which	which	PRON
iajs-1000	67	91	was	be	AUX
iajs-1000	67	92	introduced	introduce	VERB
iajs-1000	67	93	in	in	ADP
iajs-1000	67	94	the	the	DET
iajs-1000	67	95	first	first	ADJ
iajs-1000	67	96	time	time	NOUN
iajs-1000	67	97	by	by	ADP
iajs-1000	67	98	mrsevic	mrsevic	ADJ
iajs-1000	67	99	and	and	CCONJ
iajs-1000	67	100	reilly	reilly	ADJ
iajs-1000	67	101	,	,	PUNCT
iajs-1000	67	102	(	(	PUNCT
iajs-1000	67	103	4	4	NUM
iajs-1000	67	104	)	)	PUNCT
iajs-1000	67	105	.	.	PUNCT
iajs-1000	68	1	2.20	2.20	NUM
iajs-1000	68	2	definition	definition	NOUN
iajs-1000	68	3	[	[	X
iajs-1000	68	4	4	4	X
iajs-1000	68	5	]	]	PUNCT
iajs-1000	68	6	a	a	DET
iajs-1000	68	7	bitopological	bitopological	ADJ
iajs-1000	68	8	space	space	NOUN
iajs-1000	68	9	(	(	PUNCT
iajs-1000	68	10	x	x	X
iajs-1000	68	11	,	,	PUNCT
iajs-1000	68	12	τ	τ	PROPN
iajs-1000	68	13	,	,	PUNCT
iajs-1000	68	14	τ	τ	NOUN
iajs-1000	68	15	)	)	PUNCT
iajs-1000	68	16	is	be	AUX
iajs-1000	68	17	called	call	VERB
iajs-1000	68	18	an	an	DET
iajs-1000	68	19	"	"	PUNCT
iajs-1000	68	20	s	s	ADJ
iajs-1000	68	21	-	-	ADJ
iajs-1000	68	22	compact	compact	ADJ
iajs-1000	68	23	space	space	NOUN
iajs-1000	68	24	"	"	PUNCT
iajs-1000	68	25	if	if	SCONJ
iajs-1000	68	26	and	and	CCONJ
iajs-1000	68	27	only	only	ADV
iajs-1000	68	28	if	if	SCONJ
iajs-1000	68	29	every	every	PRON
iajs-1000	68	30	s	s	NOUN
iajs-1000	68	31	-	-	ADJ
iajs-1000	68	32	open	open	ADJ
iajs-1000	68	33	cover	cover	NOUN
iajs-1000	68	34	of	of	ADP
iajs-1000	68	35	x	x	PUNCT
iajs-1000	68	36	has	have	VERB
iajs-1000	68	37	a	a	DET
iajs-1000	68	38	finite	finite	ADJ
iajs-1000	68	39	subcover	subcover	PROPN
iajs-1000	68	40	.	.	PUNCT
iajs-1000	69	1	2.21	2.21	NUM
iajs-1000	69	2	proposition	proposition	NOUN
iajs-1000	69	3	if	if	SCONJ
iajs-1000	69	4	(	(	PUNCT
iajs-1000	69	5	x	x	NOUN
iajs-1000	69	6	,	,	PUNCT
iajs-1000	69	7	τ	τ	PROPN
iajs-1000	69	8	,	,	PUNCT
iajs-1000	69	9	τ	τ	NOUN
iajs-1000	69	10	)	)	PUNCT
iajs-1000	69	11	is	be	AUX
iajs-1000	69	12	an	an	DET
iajs-1000	69	13	s	s	ADJ
iajs-1000	69	14	-	-	ADJ
iajs-1000	69	15	compact	compact	ADJ
iajs-1000	69	16	space	space	NOUN
iajs-1000	69	17	,	,	PUNCT
iajs-1000	69	18	then	then	ADV
iajs-1000	69	19	both	both	PRON
iajs-1000	69	20	(	(	PUNCT
iajs-1000	69	21	x	x	X
iajs-1000	69	22	,	,	PUNCT
iajs-1000	69	23	τ	τ	X
iajs-1000	69	24	)	)	PUNCT
iajs-1000	69	25	and	and	CCONJ
iajs-1000	69	26	(	(	PUNCT
iajs-1000	69	27	x	x	NOUN
iajs-1000	69	28	,	,	PUNCT
iajs-1000	69	29	τ	τ	NOUN
iajs-1000	69	30	)	)	PUNCT
iajs-1000	69	31	are	be	AUX
iajs-1000	69	32	compact	compact	ADJ
iajs-1000	69	33	.	.	PUNCT
iajs-1000	70	1	proof	proof	NOUN
iajs-1000	70	2	:	:	PUNCT
iajs-1000	70	3	clear	clear	ADJ
iajs-1000	70	4	.	.	PUNCT
iajs-1000	71	1			NUM
iajs-1000	71	2	2.22	2.22	NUM
iajs-1000	71	3	note	note	NOUN
iajs-1000	71	4	the	the	DET
iajs-1000	71	5	opposite	opposite	ADJ
iajs-1000	71	6	direction	direction	NOUN
iajs-1000	71	7	of	of	ADP
iajs-1000	71	8	proposition	proposition	NOUN
iajs-1000	71	9	(	(	PUNCT
iajs-1000	71	10	2.21	2.21	NUM
iajs-1000	71	11	)	)	PUNCT
iajs-1000	71	12	may	may	AUX
iajs-1000	71	13	be	be	AUX
iajs-1000	71	14	false	false	ADJ
iajs-1000	71	15	.	.	PUNCT
iajs-1000	72	1	for	for	ADP
iajs-1000	72	2	example	example	NOUN
iajs-1000	72	3	:	:	PUNCT
iajs-1000	72	4	let	let	VERB
iajs-1000	72	5	x	x	PROPN
iajs-1000	72	6	=[	=[	NOUN
iajs-1000	72	7	0,1	0,1	NUM
iajs-1000	72	8	]	]	PUNCT
iajs-1000	72	9	and	and	CCONJ
iajs-1000	72	10	let	let	VERB
iajs-1000	72	11			NOUN
iajs-1000	72	12	=	=	SYM
iajs-1000	72	13	{	{	PUNCT
iajs-1000	72	14	,x,{0	,x,{0	PROPN
iajs-1000	72	15	}	}	PUNCT
iajs-1000	72	16	}	}	PUNCT
iajs-1000	72	17	and	and	CCONJ
iajs-1000	72	18	={,x,(0,1]}	={,x,(0,1]}	NUM
iajs-1000	72	19	1	1	NUM
iajs-1000	72	20	{	{	PUNCT
iajs-1000	72	21	(	(	PUNCT
iajs-1000	72	22	,	,	PUNCT
iajs-1000	72	23	1	1	X
iajs-1000	72	24	]	]	SYM
iajs-1000	72	25	n	n	CCONJ
iajs-1000	72	26	}	}	PUNCT
iajs-1000	72	27	n	n	CCONJ
iajs-1000	72	28			PROPN
iajs-1000	72	29	�	�	PROPN
iajs-1000	72	30	.	.	PUNCT
iajs-1000	73	1	then	then	ADV
iajs-1000	73	2	both	both	PRON
iajs-1000	73	3	(	(	PUNCT
iajs-1000	73	4	x	x	X
iajs-1000	73	5	,	,	PUNCT
iajs-1000	73	6	τ	τ	X
iajs-1000	73	7	)	)	PUNCT
iajs-1000	73	8	and	and	CCONJ
iajs-1000	73	9	(	(	PUNCT
iajs-1000	73	10	x	x	NOUN
iajs-1000	73	11	,	,	PUNCT
iajs-1000	73	12	τ	τ	NOUN
iajs-1000	73	13	)	)	PUNCT
iajs-1000	73	14	are	be	AUX
iajs-1000	73	15	compact	compact	ADJ
iajs-1000	73	16	spaces	space	NOUN
iajs-1000	73	17	,	,	PUNCT
iajs-1000	73	18	but	but	CCONJ
iajs-1000	73	19	(	(	PUNCT
iajs-1000	73	20	x	x	X
iajs-1000	73	21	,	,	PUNCT
iajs-1000	73	22	τ	τ	PROPN
iajs-1000	73	23	,	,	PUNCT
iajs-1000	73	24	τ	τ	NOUN
iajs-1000	73	25	)	)	PUNCT
iajs-1000	73	26	is	be	AUX
iajs-1000	73	27	not	not	PART
iajs-1000	73	28	s	s	NOUN
iajs-1000	73	29	-	-	NOUN
iajs-1000	73	30	compact	compact	ADJ
iajs-1000	73	31	,	,	PUNCT
iajs-1000	73	32	since	since	SCONJ
iajs-1000	73	33	the	the	DET
iajs-1000	73	34	s	s	NOUN
iajs-1000	73	35	-	-	ADJ
iajs-1000	73	36	open	open	ADJ
iajs-1000	73	37	cover	cover	NOUN
iajs-1000	73	38	{	{	PUNCT
iajs-1000	73	39	{	{	PUNCT
iajs-1000	73	40	0	0	NUM
iajs-1000	73	41	}	}	PUNCT
iajs-1000	73	42	}	}	PUNCT
iajs-1000	73	43			NOUN
iajs-1000	73	44	1	1	NUM
iajs-1000	73	45	{	{	PUNCT
iajs-1000	73	46	(	(	PUNCT
iajs-1000	73	47	,	,	PUNCT
iajs-1000	73	48	1	1	X
iajs-1000	73	49	]	]	SYM
iajs-1000	73	50	n	n	CCONJ
iajs-1000	73	51	}	}	PUNCT
iajs-1000	73	52	n	n	CCONJ
iajs-1000	73	53			NOUN
iajs-1000	73	54	�	�	PROPN
iajs-1000	73	55	of	of	ADP
iajs-1000	73	56	x	x	PROPN
iajs-1000	73	57	has	have	VERB
iajs-1000	73	58	no	no	DET
iajs-1000	73	59	finite	finite	PROPN
iajs-1000	73	60	subcover	subcover	PROPN
iajs-1000	73	61	.	.	PUNCT
iajs-1000	74	1	the	the	DET
iajs-1000	74	2	opposite	opposite	ADJ
iajs-1000	74	3	direction	direction	NOUN
iajs-1000	74	4	of	of	ADP
iajs-1000	74	5	proposition	proposition	NOUN
iajs-1000	74	6	(	(	PUNCT
iajs-1000	74	7	2.21	2.21	NUM
iajs-1000	74	8	)	)	PUNCT
iajs-1000	74	9	becomes	become	VERB
iajs-1000	74	10	valid	valid	ADJ
iajs-1000	74	11	in	in	ADP
iajs-1000	74	12	a	a	DET
iajs-1000	74	13	special	special	ADJ
iajs-1000	74	14	case	case	NOUN
iajs-1000	74	15	,	,	PUNCT
iajs-1000	74	16	where	where	SCONJ
iajs-1000	74	17			NOUN
iajs-1000	74	18	is	be	AUX
iajs-1000	74	19	a	a	DET
iajs-1000	74	20	subfamily	subfamily	NOUN
iajs-1000	74	21	of	of	ADP
iajs-1000	74	22			PROPN
iajs-1000	74	23	,	,	PUNCT
iajs-1000	74	24	as	as	SCONJ
iajs-1000	74	25	the	the	DET
iajs-1000	74	26	following	follow	VERB
iajs-1000	74	27	proposition	proposition	NOUN
iajs-1000	74	28	shows	show	VERB
iajs-1000	74	29	:	:	PUNCT
iajs-1000	74	30	2.23	2.23	NUM
iajs-1000	74	31	proposition	proposition	NOUN
iajs-1000	74	32	if	if	SCONJ
iajs-1000	74	33	τ	τ	PROPN
iajs-1000	74	34	is	be	AUX
iajs-1000	74	35	a	a	DET
iajs-1000	74	36	subfamily	subfamily	NOUN
iajs-1000	74	37	of	of	ADP
iajs-1000	74	38	τ	τ	NOUN
iajs-1000	74	39	,	,	PUNCT
iajs-1000	74	40	then	then	ADV
iajs-1000	74	41	(	(	PUNCT
iajs-1000	74	42	x	x	X
iajs-1000	74	43	,	,	PUNCT
iajs-1000	74	44	τ	τ	PROPN
iajs-1000	74	45	,	,	PUNCT
iajs-1000	74	46	τ	τ	NOUN
iajs-1000	74	47	)	)	PUNCT
iajs-1000	74	48	is	be	AUX
iajs-1000	74	49	an	an	DET
iajs-1000	74	50	s	s	ADJ
iajs-1000	74	51	-	-	ADJ
iajs-1000	74	52	compact	compact	ADJ
iajs-1000	74	53	space	space	NOUN
iajs-1000	74	54	if	if	SCONJ
iajs-1000	74	55	and	and	CCONJ
iajs-1000	74	56	only	only	ADV
iajs-1000	74	57	if	if	SCONJ
iajs-1000	74	58	(	(	PUNCT
iajs-1000	74	59	x	x	NOUN
iajs-1000	74	60	,	,	PUNCT
iajs-1000	74	61	τ	τ	NOUN
iajs-1000	74	62	)	)	PUNCT
iajs-1000	74	63	and	and	CCONJ
iajs-1000	74	64	(	(	PUNCT
iajs-1000	74	65	x	x	X
iajs-1000	74	66	,	,	PUNCT
iajs-1000	74	67	τ	τ	X
iajs-1000	74	68	)	)	PUNCT
iajs-1000	74	69	are	be	AUX
iajs-1000	74	70	compact	compact	ADJ
iajs-1000	74	71	spaces	space	NOUN
iajs-1000	74	72	.	.	PUNCT
iajs-1000	75	1	proof	proof	NOUN
iajs-1000	75	2	:	:	PUNCT
iajs-1000	75	3	clear	clear	ADJ
iajs-1000	75	4	.	.	PUNCT
iajs-1000	76	1			NUM
iajs-1000	76	2	2.24	2.24	NUM
iajs-1000	76	3	proposition	proposition	NOUN
iajs-1000	76	4	an	an	DET
iajs-1000	76	5	s	s	NOUN
iajs-1000	76	6	-	-	PUNCT
iajs-1000	76	7	closed	closed	ADJ
iajs-1000	76	8	subset	subset	NOUN
iajs-1000	76	9	of	of	ADP
iajs-1000	76	10	an	an	DET
iajs-1000	76	11	s	s	ADJ
iajs-1000	76	12	-	-	ADJ
iajs-1000	76	13	compact	compact	ADJ
iajs-1000	76	14	space	space	NOUN
iajs-1000	76	15	is	be	AUX
iajs-1000	76	16	s	s	NOUN
iajs-1000	76	17	-	-	ADJ
iajs-1000	76	18	compact	compact	ADJ
iajs-1000	76	19	.	.	PUNCT
iajs-1000	77	1	proof	proof	NOUN
iajs-1000	77	2	:	:	PUNCT
iajs-1000	77	3	let	let	VERB
iajs-1000	77	4	(	(	PUNCT
iajs-1000	77	5	x	x	X
iajs-1000	77	6	,	,	PUNCT
iajs-1000	77	7	τ	τ	PROPN
iajs-1000	77	8	,	,	PUNCT
iajs-1000	77	9	τ	τ	NOUN
iajs-1000	77	10	)	)	PUNCT
iajs-1000	77	11	be	be	AUX
iajs-1000	77	12	an	an	DET
iajs-1000	77	13	s	s	ADJ
iajs-1000	77	14	-	-	ADJ
iajs-1000	77	15	compact	compact	ADJ
iajs-1000	77	16	space	space	NOUN
iajs-1000	77	17	,	,	PUNCT
iajs-1000	77	18	let	let	VERB
iajs-1000	77	19	a	a	PRON
iajs-1000	77	20	be	be	AUX
iajs-1000	77	21	an	an	DET
iajs-1000	77	22	s	s	NOUN
iajs-1000	77	23	-	-	PUNCT
iajs-1000	77	24	closed	closed	ADJ
iajs-1000	77	25	subset	subset	NOUN
iajs-1000	77	26	of	of	ADP
iajs-1000	77	27	x.	x.	NOUN
iajs-1000	77	28	to	to	PART
iajs-1000	77	29	show	show	VERB
iajs-1000	77	30	that	that	SCONJ
iajs-1000	77	31	a	a	PRON
iajs-1000	77	32	is	be	AUX
iajs-1000	77	33	an	an	DET
iajs-1000	77	34	s	s	ADJ
iajs-1000	77	35	-	-	ADJ
iajs-1000	77	36	compact	compact	ADJ
iajs-1000	77	37	set	set	NOUN
iajs-1000	77	38	.	.	PUNCT
iajs-1000	78	1	ibn	ibn	PROPN
iajs-1000	78	2	alhaitham	alhaitham	PROPN
iajs-1000	78	3	j.	j.	PROPN
iajs-1000	78	4	for	for	ADP
iajs-1000	78	5	pure	pure	ADJ
iajs-1000	78	6	&	&	CCONJ
iajs-1000	78	7	appl	appl	PROPN
iajs-1000	78	8	.	.	PUNCT
iajs-1000	79	1	sci	sci	PROPN
iajs-1000	79	2	.	.	PUNCT
iajs-1000	80	1	vol.23	vol.23	PROPN
iajs-1000	80	2	(	(	PUNCT
iajs-1000	80	3	1	1	NUM
iajs-1000	80	4	)	)	PUNCT
iajs-1000	80	5	2010	2010	NUM
iajs-1000	80	6	let	let	VERB
iajs-1000	80	7	{	{	PUNCT
iajs-1000	80	8	ui	ui	NOUN
iajs-1000	80	9	:	:	PUNCT
iajs-1000	80	10	i	i	PRON
iajs-1000	80	11			NOUN
iajs-1000	80	12			NOUN
iajs-1000	80	13	}	}	PUNCT
iajs-1000	80	14	be	be	VERB
iajs-1000	80	15	an	an	DET
iajs-1000	80	16	s	s	NOUN
iajs-1000	80	17	-	-	ADJ
iajs-1000	80	18	open	open	ADJ
iajs-1000	80	19	cover	cover	NOUN
iajs-1000	80	20	of	of	ADP
iajs-1000	80	21	a.	a.	NOUN
iajs-1000	80	22	since	since	SCONJ
iajs-1000	80	23	a	a	PRON
iajs-1000	80	24	is	be	AUX
iajs-1000	80	25	an	an	DET
iajs-1000	80	26	s	s	NOUN
iajs-1000	80	27	-	-	PUNCT
iajs-1000	80	28	closed	closed	ADJ
iajs-1000	80	29	subset	subset	NOUN
iajs-1000	80	30	of	of	ADP
iajs-1000	80	31	x	x	X
iajs-1000	80	32	,	,	PUNCT
iajs-1000	80	33	then	then	ADV
iajs-1000	80	34	x	x	X
iajs-1000	80	35	–	–	PUNCT
iajs-1000	80	36	a	a	PRON
iajs-1000	80	37	is	be	AUX
iajs-1000	80	38	an	an	DET
iajs-1000	80	39	s	s	NOUN
iajs-1000	80	40	-	-	ADJ
iajs-1000	80	41	open	open	ADJ
iajs-1000	80	42	subset	subset	NOUN
iajs-1000	80	43	of	of	ADP
iajs-1000	80	44	x.	x.	NOUN
iajs-1000	80	45	then	then	ADV
iajs-1000	80	46	{	{	PUNCT
iajs-1000	80	47	ui	ui	NOUN
iajs-1000	80	48	:	:	PUNCT
iajs-1000	80	49	i	i	PRON
iajs-1000	80	50			NOUN
iajs-1000	80	51	}{x	}{x	PUNCT
iajs-1000	80	52	–	–	PUNCT
iajs-1000	80	53	a	a	PRON
iajs-1000	80	54	}	}	PUNCT
iajs-1000	80	55	is	be	AUX
iajs-1000	80	56	an	an	DET
iajs-1000	80	57	s	s	NOUN
iajs-1000	80	58	-	-	ADJ
iajs-1000	80	59	open	open	ADJ
iajs-1000	80	60	cover	cover	NOUN
iajs-1000	80	61	of	of	ADP
iajs-1000	80	62	x	x	X
iajs-1000	80	63	,	,	PUNCT
iajs-1000	80	64	which	which	PRON
iajs-1000	80	65	is	be	AUX
iajs-1000	80	66	scompact	scompact	ADJ
iajs-1000	80	67	space	space	NOUN
iajs-1000	80	68	.	.	PUNCT
iajs-1000	81	1	therefore	therefore	ADV
iajs-1000	81	2	,	,	PUNCT
iajs-1000	81	3	there	there	PRON
iajs-1000	81	4	exists	exist	VERB
iajs-1000	81	5	i1	i1	PROPN
iajs-1000	81	6	,	,	PUNCT
iajs-1000	81	7	i2,,in	i2,,in	VERB
iajs-1000	81	8			NOUN
iajs-1000	81	9			NOUN
iajs-1000	81	10	,	,	PUNCT
iajs-1000	81	11	such	such	ADJ
iajs-1000	81	12	that	that	SCONJ
iajs-1000	81	13	{	{	PUNCT
iajs-1000	81	14	uij	uij	PRON
iajs-1000	81	15	:	:	PUNCT
iajs-1000	81	16	j=1	j=1	NOUN
iajs-1000	81	17	,	,	PUNCT
iajs-1000	81	18	2	2	NUM
iajs-1000	81	19	,	,	PUNCT
iajs-1000	81	20	…	…	NUM
iajs-1000	81	21	,	,	PUNCT
iajs-1000	81	22	n}{x	n}{x	PROPN
iajs-1000	81	23	–	–	PUNCT
iajs-1000	81	24	a	a	PRON
iajs-1000	81	25	}	}	PUNCT
iajs-1000	81	26	is	be	AUX
iajs-1000	81	27	a	a	DET
iajs-1000	81	28	finite	finite	ADJ
iajs-1000	81	29	subcover	subcover	NOUN
iajs-1000	81	30	of	of	ADP
iajs-1000	81	31	x.	x.	PROPN
iajs-1000	81	32	since	since	SCONJ
iajs-1000	81	33	ax	ax	PROPN
iajs-1000	81	34	and	and	CCONJ
iajs-1000	81	35	x	x	NOUN
iajs-1000	81	36	–	–	PUNCT
iajs-1000	81	37	a	a	DET
iajs-1000	81	38	covers	cover	VERB
iajs-1000	81	39	no	no	DET
iajs-1000	81	40	part	part	NOUN
iajs-1000	81	41	of	of	ADP
iajs-1000	81	42	a	a	PRON
iajs-1000	81	43	,	,	PUNCT
iajs-1000	81	44	then	then	ADV
iajs-1000	81	45	{	{	PUNCT
iajs-1000	81	46	uij	uij	PROPN
iajs-1000	81	47	:	:	PUNCT
iajs-1000	81	48	j=1	j=1	NOUN
iajs-1000	81	49	,	,	PUNCT
iajs-1000	81	50	2	2	NUM
iajs-1000	81	51	,	,	PUNCT
iajs-1000	81	52	…	…	PUNCT
iajs-1000	81	53	,	,	PUNCT
iajs-1000	81	54	n	n	CCONJ
iajs-1000	81	55	}	}	PUNCT
iajs-1000	81	56	is	be	AUX
iajs-1000	81	57	a	a	DET
iajs-1000	81	58	finite	finite	ADJ
iajs-1000	81	59	subcover	subcover	NOUN
iajs-1000	81	60	of	of	ADP
iajs-1000	81	61	a.	a.	PROPN
iajs-1000	82	1	so	so	ADV
iajs-1000	82	2	a	a	PRON
iajs-1000	82	3	is	be	AUX
iajs-1000	82	4	an	an	DET
iajs-1000	82	5	s	s	NOUN
iajs-1000	82	6	-	-	NOUN
iajs-1000	82	7	compact	compact	ADJ
iajs-1000	82	8	.	.	PUNCT
iajs-1000	83	1			NUM
iajs-1000	83	2	2.25	2.25	NUM
iajs-1000	83	3	definition	definition	NOUN
iajs-1000	83	4	[	[	X
iajs-1000	83	5	5	5	NUM
iajs-1000	83	6	]	]	PUNCT
iajs-1000	83	7	let	let	VERB
iajs-1000	83	8	f	f	X
iajs-1000	83	9	:	:	PUNCT
iajs-1000	83	10	(	(	PUNCT
iajs-1000	83	11	x	x	X
iajs-1000	83	12	,	,	PUNCT
iajs-1000	83	13	τ	τ	PROPN
iajs-1000	83	14	,	,	PUNCT
iajs-1000	83	15	τ	τ	NOUN
iajs-1000	83	16	)	)	PUNCT
iajs-1000	83	17			PROPN
iajs-1000	83	18	(	(	PUNCT
iajs-1000	83	19	y	y	PROPN
iajs-1000	83	20	,	,	PUNCT
iajs-1000	83	21	t	t	PROPN
iajs-1000	83	22	,	,	PUNCT
iajs-1000	83	23	t	t	NUM
iajs-1000	83	24	)	)	PUNCT
iajs-1000	83	25	be	be	AUX
iajs-1000	83	26	a	a	DET
iajs-1000	83	27	function	function	NOUN
iajs-1000	83	28	,	,	PUNCT
iajs-1000	83	29	then	then	ADV
iajs-1000	83	30	f	f	PROPN
iajs-1000	83	31	is	be	AUX
iajs-1000	83	32	said	say	VERB
iajs-1000	83	33	to	to	PART
iajs-1000	83	34	be	be	AUX
iajs-1000	83	35	a	a	DET
iajs-1000	83	36	"	"	PUNCT
iajs-1000	83	37	bicontinuous	bicontinuous	ADJ
iajs-1000	83	38	function	function	NOUN
iajs-1000	83	39	"	"	PUNCT
iajs-1000	83	40	if	if	SCONJ
iajs-1000	83	41	and	and	CCONJ
iajs-1000	83	42	only	only	ADV
iajs-1000	83	43	if	if	SCONJ
iajs-1000	83	44	f	f	X
iajs-1000	83	45	–	–	PUNCT
iajs-1000	83	46	1(u	1(u	NUM
iajs-1000	83	47	)	)	PUNCT
iajs-1000	83	48			NOUN
iajs-1000	83	49	τ	τ	NOUN
iajs-1000	83	50	,	,	PUNCT
iajs-1000	83	51	for	for	ADP
iajs-1000	83	52	each	each	DET
iajs-1000	83	53	ut	ut	NOUN
iajs-1000	83	54	,	,	PUNCT
iajs-1000	83	55	and	and	CCONJ
iajs-1000	83	56	f	f	PROPN
iajs-1000	83	57	–	–	PUNCT
iajs-1000	83	58	1(v	1(v	NUM
iajs-1000	83	59	)	)	PUNCT
iajs-1000	83	60			NOUN
iajs-1000	83	61	τ	τ	NOUN
iajs-1000	83	62	,	,	PUNCT
iajs-1000	83	63	for	for	ADP
iajs-1000	83	64	each	each	DET
iajs-1000	83	65	v	v	ADJ
iajs-1000	83	66			PROPN
iajs-1000	83	67	t.	t.	NOUN
iajs-1000	83	68	2.26	2.26	NUM
iajs-1000	83	69	example	example	NOUN
iajs-1000	83	70	let	let	VERB
iajs-1000	83	71	x={1,2,3	x={1,2,3	NUM
iajs-1000	83	72	}	}	PUNCT
iajs-1000	83	73	,	,	PUNCT
iajs-1000	83	74	τ={,x,{1},{2},{1,2	τ={,x,{1},{2},{1,2	NUM
iajs-1000	83	75	}	}	PUNCT
iajs-1000	83	76	}	}	PUNCT
iajs-1000	83	77	and	and	CCONJ
iajs-1000	83	78	τ	τ	PUNCT
iajs-1000	83	79	=	=	SYM
iajs-1000	83	80	τd	τd	NOUN
iajs-1000	83	81	.	.	PUNCT
iajs-1000	84	1	and	and	CCONJ
iajs-1000	84	2	let	let	VERB
iajs-1000	84	3	y={a	y={a	PROPN
iajs-1000	84	4	,	,	PUNCT
iajs-1000	84	5	b	b	NOUN
iajs-1000	84	6	,	,	PUNCT
iajs-1000	84	7	c	c	NOUN
iajs-1000	84	8	}	}	PUNCT
iajs-1000	84	9	,	,	PUNCT
iajs-1000	84	10	t={,y,{a	t={,y,{a	ADV
iajs-1000	84	11	}	}	PUNCT
iajs-1000	84	12	}	}	PUNCT
iajs-1000	84	13	and	and	CCONJ
iajs-1000	84	14	t=	t=	AUX
iajs-1000	84	15	τi	τi	NOUN
iajs-1000	84	16	.	.	PUNCT
iajs-1000	85	1	define	define	VERB
iajs-1000	85	2	f	f	X
iajs-1000	85	3	:	:	PUNCT
iajs-1000	85	4	(	(	PUNCT
iajs-1000	85	5	x	x	X
iajs-1000	85	6	,	,	PUNCT
iajs-1000	85	7	τ	τ	PROPN
iajs-1000	85	8	,	,	PUNCT
iajs-1000	85	9	τ	τ	NOUN
iajs-1000	85	10	)	)	PUNCT
iajs-1000	85	11			PROPN
iajs-1000	85	12	(	(	PUNCT
iajs-1000	85	13	y	y	PROPN
iajs-1000	85	14	,	,	PUNCT
iajs-1000	85	15	t	t	PROPN
iajs-1000	85	16	,	,	PUNCT
iajs-1000	85	17	t	t	NUM
iajs-1000	85	18	)	)	PUNCT
iajs-1000	85	19	,	,	PUNCT
iajs-1000	86	1	such	such	ADJ
iajs-1000	86	2	that	that	DET
iajs-1000	86	3	f(1	f(1	PROPN
iajs-1000	86	4	)	)	PUNCT
iajs-1000	86	5	=	=	SYM
iajs-1000	87	1	a	a	PRON
iajs-1000	87	2	,	,	PUNCT
iajs-1000	87	3	f(2	f(2	PROPN
iajs-1000	87	4	)	)	PUNCT
iajs-1000	87	5	=	=	SYM
iajs-1000	87	6	b	b	PROPN
iajs-1000	87	7	and	and	CCONJ
iajs-1000	87	8	f(3	f(3	PROPN
iajs-1000	87	9	)	)	PUNCT
iajs-1000	87	10	=	=	SYM
iajs-1000	88	1	c.	c.	NOUN
iajs-1000	88	2	then	then	ADV
iajs-1000	88	3	f	f	PROPN
iajs-1000	88	4	is	be	AUX
iajs-1000	88	5	bicontinuous	bicontinuous	ADJ
iajs-1000	88	6	function	function	NOUN
iajs-1000	88	7	.	.	PUNCT
iajs-1000	89	1	where	where	SCONJ
iajs-1000	89	2	τd	τd	ADV
iajs-1000	89	3	and	and	CCONJ
iajs-1000	89	4	τi	τi	ADP
iajs-1000	89	5	are	be	AUX
iajs-1000	89	6	the	the	DET
iajs-1000	89	7	discrete	discrete	ADJ
iajs-1000	89	8	and	and	CCONJ
iajs-1000	89	9	indiscrete	indiscrete	ADJ
iajs-1000	89	10	topologies	topology	NOUN
iajs-1000	89	11	on	on	ADP
iajs-1000	89	12	x	x	PUNCT
iajs-1000	89	13	and	and	CCONJ
iajs-1000	89	14	y	y	PROPN
iajs-1000	89	15	respectively	respectively	ADV
iajs-1000	89	16	.	.	PUNCT
iajs-1000	90	1	2.27	2.27	NUM
iajs-1000	90	2	proposition	proposition	NOUN
iajs-1000	90	3	a	a	DET
iajs-1000	90	4	bicontinuous	bicontinuous	ADJ
iajs-1000	90	5	image	image	NOUN
iajs-1000	90	6	of	of	ADP
iajs-1000	90	7	an	an	DET
iajs-1000	90	8	s	s	ADJ
iajs-1000	90	9	-	-	ADJ
iajs-1000	90	10	compact	compact	ADJ
iajs-1000	90	11	space	space	NOUN
iajs-1000	90	12	is	be	AUX
iajs-1000	90	13	an	an	DET
iajs-1000	90	14	s	s	ADJ
iajs-1000	90	15	-	-	ADJ
iajs-1000	90	16	compact	compact	ADJ
iajs-1000	90	17	space	space	NOUN
iajs-1000	90	18	.	.	PUNCT
iajs-1000	91	1	proof	proof	NOUN
iajs-1000	91	2	:	:	PUNCT
iajs-1000	91	3	let	let	VERB
iajs-1000	91	4	f	f	X
iajs-1000	91	5	:	:	PUNCT
iajs-1000	91	6	(	(	PUNCT
iajs-1000	91	7	x	x	X
iajs-1000	91	8	,	,	PUNCT
iajs-1000	91	9	τ	τ	PROPN
iajs-1000	91	10	,	,	PUNCT
iajs-1000	91	11	τ	τ	NOUN
iajs-1000	91	12	)	)	PUNCT
iajs-1000	91	13			PROPN
iajs-1000	92	1	(	(	PUNCT
iajs-1000	92	2	y	y	PROPN
iajs-1000	92	3	,	,	PUNCT
iajs-1000	92	4	t	t	PROPN
iajs-1000	92	5	,	,	PUNCT
iajs-1000	92	6	t	t	NUM
iajs-1000	92	7	)	)	PUNCT
iajs-1000	92	8	be	be	AUX
iajs-1000	92	9	a	a	DET
iajs-1000	92	10	bicontinuous	bicontinuous	NOUN
iajs-1000	92	11	,	,	PUNCT
iajs-1000	92	12	onto	onto	ADP
iajs-1000	92	13	function	function	NOUN
iajs-1000	92	14	and	and	CCONJ
iajs-1000	92	15	let	let	VERB
iajs-1000	92	16	(	(	PUNCT
iajs-1000	92	17	x	x	NOUN
iajs-1000	92	18	,	,	PUNCT
iajs-1000	92	19	τ	τ	PROPN
iajs-1000	92	20	,	,	PUNCT
iajs-1000	92	21	τ	τ	NOUN
iajs-1000	92	22	)	)	PUNCT
iajs-1000	92	23	be	be	VERB
iajs-1000	92	24	an	an	DET
iajs-1000	92	25	scompact	scompact	ADJ
iajs-1000	92	26	space	space	NOUN
iajs-1000	92	27	.	.	PUNCT
iajs-1000	93	1	to	to	PART
iajs-1000	93	2	prove	prove	VERB
iajs-1000	93	3	that	that	SCONJ
iajs-1000	93	4	(	(	PUNCT
iajs-1000	93	5	y	y	PROPN
iajs-1000	93	6	,	,	PUNCT
iajs-1000	93	7	t	t	PROPN
iajs-1000	93	8	,	,	PUNCT
iajs-1000	93	9	t	t	NUM
iajs-1000	93	10	)	)	PUNCT
iajs-1000	93	11	is	be	AUX
iajs-1000	93	12	an	an	DET
iajs-1000	93	13	s	s	NOUN
iajs-1000	93	14	-	-	ADJ
iajs-1000	93	15	compact	compact	ADJ
iajs-1000	93	16	.	.	PUNCT
iajs-1000	94	1	let	let	VERB
iajs-1000	94	2	{	{	PUNCT
iajs-1000	94	3	ui	ui	NOUN
iajs-1000	94	4	:	:	PUNCT
iajs-1000	94	5	i	i	PRON
iajs-1000	94	6			NOUN
iajs-1000	94	7			NOUN
iajs-1000	94	8	}	}	PUNCT
iajs-1000	94	9	be	be	VERB
iajs-1000	94	10	an	an	DET
iajs-1000	94	11	s	s	NOUN
iajs-1000	94	12	-	-	ADJ
iajs-1000	94	13	open	open	ADJ
iajs-1000	94	14	cover	cover	NOUN
iajs-1000	94	15	of	of	ADP
iajs-1000	94	16	y	y	PROPN
iajs-1000	94	17	,	,	PUNCT
iajs-1000	94	18	then	then	ADV
iajs-1000	94	19	{	{	PUNCT
iajs-1000	94	20	f	f	PROPN
iajs-1000	94	21	–	–	PUNCT
iajs-1000	94	22	1(ui	1(ui	NUM
iajs-1000	94	23	)	)	PUNCT
iajs-1000	94	24	:	:	PUNCT
iajs-1000	95	1	i	i	PRON
iajs-1000	95	2			NOUN
iajs-1000	95	3			NOUN
iajs-1000	95	4	}	}	PUNCT
iajs-1000	95	5	is	be	AUX
iajs-1000	95	6	an	an	DET
iajs-1000	95	7	s	s	NOUN
iajs-1000	95	8	-	-	ADJ
iajs-1000	95	9	open	open	ADJ
iajs-1000	95	10	cover	cover	NOUN
iajs-1000	95	11	of	of	ADP
iajs-1000	95	12	x	x	X
iajs-1000	95	13	,	,	PUNCT
iajs-1000	95	14	which	which	PRON
iajs-1000	95	15	is	be	AUX
iajs-1000	95	16	an	an	DET
iajs-1000	95	17	s	s	ADJ
iajs-1000	95	18	-	-	ADJ
iajs-1000	95	19	compact	compact	ADJ
iajs-1000	95	20	space	space	NOUN
iajs-1000	95	21	.	.	PUNCT
iajs-1000	96	1	therefore	therefore	ADV
iajs-1000	96	2	,	,	PUNCT
iajs-1000	96	3	there	there	PRON
iajs-1000	96	4	exists	exist	VERB
iajs-1000	96	5	i1	i1	PROPN
iajs-1000	96	6	,	,	PUNCT
iajs-1000	96	7	i2,,in	i2,,in	VERB
iajs-1000	96	8			NOUN
iajs-1000	96	9			NOUN
iajs-1000	96	10	,	,	PUNCT
iajs-1000	96	11	such	such	ADJ
iajs-1000	96	12	that	that	SCONJ
iajs-1000	96	13	{	{	PUNCT
iajs-1000	96	14	f	f	X
iajs-1000	96	15	–	–	PUNCT
iajs-1000	96	16	1(uij	1(uij	NUM
iajs-1000	96	17	):	):	PUNCT
iajs-1000	97	1	j=1	j=1	PROPN
iajs-1000	97	2	,	,	PUNCT
iajs-1000	97	3	2	2	NUM
iajs-1000	97	4	,	,	PUNCT
iajs-1000	97	5	…	…	PUNCT
iajs-1000	97	6	,	,	PUNCT
iajs-1000	97	7	n	n	CCONJ
iajs-1000	97	8	}	}	PUNCT
iajs-1000	97	9	is	be	AUX
iajs-1000	97	10	a	a	DET
iajs-1000	97	11	finite	finite	ADJ
iajs-1000	97	12	subcover	subcover	NOUN
iajs-1000	97	13	of	of	ADP
iajs-1000	97	14	x	x	PROPN
iajs-1000	97	15	and	and	CCONJ
iajs-1000	97	16	since	since	SCONJ
iajs-1000	97	17	f	f	PROPN
iajs-1000	97	18	is	be	AUX
iajs-1000	97	19	onto	onto	ADP
iajs-1000	97	20	,	,	PUNCT
iajs-1000	97	21	then	then	ADV
iajs-1000	97	22	we	we	PRON
iajs-1000	97	23	get	get	VERB
iajs-1000	97	24	{	{	PUNCT
iajs-1000	97	25	uij	uij	PRON
iajs-1000	97	26	:	:	PUNCT
iajs-1000	97	27	j=1	j=1	NOUN
iajs-1000	97	28	,	,	PUNCT
iajs-1000	97	29	2	2	NUM
iajs-1000	97	30	,	,	PUNCT
iajs-1000	97	31	…	…	PUNCT
iajs-1000	97	32	,	,	PUNCT
iajs-1000	97	33	n	n	CCONJ
iajs-1000	97	34	}	}	PUNCT
iajs-1000	97	35	is	be	AUX
iajs-1000	97	36	a	a	DET
iajs-1000	97	37	finite	finite	ADJ
iajs-1000	97	38	subcover	subcover	NOUN
iajs-1000	97	39	of	of	ADP
iajs-1000	97	40	y.	y.	PROPN
iajs-1000	98	1	so	so	PROPN
iajs-1000	98	2	y	y	PROPN
iajs-1000	98	3	is	be	AUX
iajs-1000	98	4	an	an	DET
iajs-1000	98	5	s	s	ADJ
iajs-1000	98	6	-	-	ADJ
iajs-1000	98	7	compact	compact	ADJ
iajs-1000	98	8	space	space	NOUN
iajs-1000	98	9	.	.	PUNCT
iajs-1000	99	1			NUM
iajs-1000	99	2	2.28	2.28	NUM
iajs-1000	99	3	proposition	proposition	NOUN
iajs-1000	99	4	if	if	SCONJ
iajs-1000	99	5	a	a	PRON
iajs-1000	99	6	and	and	CCONJ
iajs-1000	99	7	b	b	NOUN
iajs-1000	99	8	are	be	AUX
iajs-1000	99	9	two	two	NUM
iajs-1000	99	10	s	s	ADJ
iajs-1000	99	11	-	-	ADJ
iajs-1000	99	12	compact	compact	ADJ
iajs-1000	99	13	subsets	subset	NOUN
iajs-1000	99	14	of	of	ADP
iajs-1000	99	15	a	a	DET
iajs-1000	99	16	topological	topological	ADJ
iajs-1000	99	17	space	space	NOUN
iajs-1000	99	18	(	(	PUNCT
iajs-1000	99	19	x	x	X
iajs-1000	99	20	,	,	PUNCT
iajs-1000	99	21	τ	τ	PROPN
iajs-1000	99	22	,	,	PUNCT
iajs-1000	99	23	τ	τ	NOUN
iajs-1000	99	24	)	)	PUNCT
iajs-1000	99	25	,	,	PUNCT
iajs-1000	99	26	then	then	ADV
iajs-1000	99	27	ab	ab	NOUN
iajs-1000	99	28	is	be	AUX
iajs-1000	99	29	an	an	DET
iajs-1000	99	30	scompact	scompact	NOUN
iajs-1000	99	31	subset	subset	NOUN
iajs-1000	99	32	of	of	ADP
iajs-1000	99	33	x.	x.	NOUN
iajs-1000	99	34	proof	proof	PROPN
iajs-1000	99	35	:	:	PUNCT
iajs-1000	99	36	clear	clear	ADJ
iajs-1000	99	37	.	.	PUNCT
iajs-1000	100	1			NUM
iajs-1000	100	2	2.29	2.29	NUM
iajs-1000	100	3	remark	remark	NOUN
iajs-1000	100	4	if	if	SCONJ
iajs-1000	100	5	a	a	PRON
iajs-1000	100	6	and	and	CCONJ
iajs-1000	100	7	b	b	NOUN
iajs-1000	100	8	are	be	AUX
iajs-1000	100	9	two	two	NUM
iajs-1000	100	10	s	s	ADJ
iajs-1000	100	11	-	-	ADJ
iajs-1000	100	12	compact	compact	ADJ
iajs-1000	100	13	subsets	subset	NOUN
iajs-1000	100	14	of	of	ADP
iajs-1000	100	15	a	a	DET
iajs-1000	100	16	bitopological	bitopological	ADJ
iajs-1000	100	17	space	space	NOUN
iajs-1000	100	18	(	(	PUNCT
iajs-1000	100	19	x	x	X
iajs-1000	100	20	,	,	PUNCT
iajs-1000	100	21	τ	τ	PROPN
iajs-1000	100	22	,	,	PUNCT
iajs-1000	100	23	τ	τ	NOUN
iajs-1000	100	24	)	)	PUNCT
iajs-1000	100	25	,	,	PUNCT
iajs-1000	100	26	then	then	ADV
iajs-1000	100	27	ab	ab	NOUN
iajs-1000	100	28	need	need	AUX
iajs-1000	100	29	not	not	PART
iajs-1000	100	30	be	be	AUX
iajs-1000	100	31	s	s	ADJ
iajs-1000	100	32	-	-	ADJ
iajs-1000	100	33	compact	compact	ADJ
iajs-1000	100	34	set	set	NOUN
iajs-1000	100	35	.	.	PUNCT
iajs-1000	101	1	for	for	ADP
iajs-1000	101	2	example	example	NOUN
iajs-1000	101	3	:	:	PUNCT
iajs-1000	101	4	see	see	VERB
iajs-1000	101	5	the	the	DET
iajs-1000	101	6	example	example	NOUN
iajs-1000	101	7	of	of	ADP
iajs-1000	101	8	remark	remark	NOUN
iajs-1000	101	9	(	(	PUNCT
iajs-1000	101	10	2.15	2.15	NUM
iajs-1000	101	11	)	)	PUNCT
iajs-1000	101	12	,	,	PUNCT
iajs-1000	101	13	both	both	PRON
iajs-1000	101	14	a	a	PRON
iajs-1000	101	15	and	and	CCONJ
iajs-1000	101	16	b	b	NOUN
iajs-1000	101	17	are	be	AUX
iajs-1000	101	18	s	s	ADJ
iajs-1000	101	19	-	-	ADJ
iajs-1000	101	20	compact	compact	ADJ
iajs-1000	101	21	subsets	subset	NOUN
iajs-1000	101	22	of	of	ADP
iajs-1000	101	23	the	the	DET
iajs-1000	101	24	bitopological	bitopological	ADJ
iajs-1000	101	25	space	space	NOUN
iajs-1000	101	26	(	(	PUNCT
iajs-1000	101	27	x	x	X
iajs-1000	101	28	,	,	PUNCT
iajs-1000	101	29	τ	τ	PROPN
iajs-1000	101	30	,	,	PUNCT
iajs-1000	101	31	τ	τ	NOUN
iajs-1000	101	32	)	)	PUNCT
iajs-1000	101	33	,	,	PUNCT
iajs-1000	101	34	a	a	DET
iajs-1000	101	35			PROPN
iajs-1000	101	36	b	b	NOUN
iajs-1000	101	37	=	=	SYM
iajs-1000	101	38	�	�	PROPN
iajs-1000	101	39	is	be	AUX
iajs-1000	101	40	not	not	PART
iajs-1000	101	41	s	s	ADJ
iajs-1000	101	42	-	-	ADJ
iajs-1000	101	43	compact	compact	ADJ
iajs-1000	101	44	set	set	NOUN
iajs-1000	101	45	.	.	PUNCT
iajs-1000	102	1	2.30	2.30	NUM
iajs-1000	102	2	proposition	proposition	NOUN
iajs-1000	102	3	every	every	DET
iajs-1000	102	4	n	n	CCONJ
iajs-1000	102	5	-	-	PUNCT
iajs-1000	102	6	compact	compact	ADJ
iajs-1000	102	7	space	space	NOUN
iajs-1000	102	8	is	be	AUX
iajs-1000	102	9	an	an	DET
iajs-1000	102	10	s	s	NOUN
iajs-1000	102	11	-	-	ADJ
iajs-1000	102	12	compact	compact	ADJ
iajs-1000	102	13	.	.	PUNCT
iajs-1000	103	1	proof	proof	NOUN
iajs-1000	103	2	:	:	PUNCT
iajs-1000	103	3	follows	follow	VERB
iajs-1000	103	4	from	from	ADP
iajs-1000	103	5	remark	remark	NOUN
iajs-1000	103	6	(	(	PUNCT
iajs-1000	103	7	2.17	2.17	NUM
iajs-1000	103	8	)	)	PUNCT
iajs-1000	103	9	.	.	PUNCT
iajs-1000	104	1			NUM
iajs-1000	104	2	2.31	2.31	NUM
iajs-1000	104	3	proposition	proposition	NOUN
iajs-1000	104	4	let	let	VERB
iajs-1000	104	5	(	(	PUNCT
iajs-1000	104	6	x	x	NOUN
iajs-1000	104	7	,	,	PUNCT
iajs-1000	104	8	τ	τ	PROPN
iajs-1000	104	9	,	,	PUNCT
iajs-1000	104	10	τ	τ	NOUN
iajs-1000	104	11	)	)	PUNCT
iajs-1000	104	12	be	be	AUX
iajs-1000	104	13	a	a	DET
iajs-1000	104	14	topological	topological	ADJ
iajs-1000	104	15	space	space	NOUN
iajs-1000	104	16	.	.	PUNCT
iajs-1000	105	1	if	if	SCONJ
iajs-1000	105	2	τ	τ	PROPN
iajs-1000	105	3	is	be	AUX
iajs-1000	105	4	a	a	DET
iajs-1000	105	5	subfamily	subfamily	NOUN
iajs-1000	105	6	of	of	ADP
iajs-1000	105	7	τ	τ	NOUN
iajs-1000	105	8	,	,	PUNCT
iajs-1000	105	9	then	then	ADV
iajs-1000	105	10	the	the	DET
iajs-1000	105	11	concepts	concept	NOUN
iajs-1000	105	12	of	of	ADP
iajs-1000	105	13	scompactness	scompactness	NOUN
iajs-1000	105	14	and	and	CCONJ
iajs-1000	105	15	n	n	CCONJ
iajs-1000	105	16	-	-	PUNCT
iajs-1000	105	17	compactness	compactness	NOUN
iajs-1000	105	18	are	be	AUX
iajs-1000	105	19	coincident	coincident	ADJ
iajs-1000	105	20	.	.	PUNCT
iajs-1000	106	1	proof	proof	NOUN
iajs-1000	106	2	:	:	PUNCT
iajs-1000	106	3	follows	follow	VERB
iajs-1000	106	4	from	from	ADP
iajs-1000	106	5	propositions	proposition	NOUN
iajs-1000	106	6	(	(	PUNCT
iajs-1000	106	7	2.10	2.10	NUM
iajs-1000	106	8	)	)	PUNCT
iajs-1000	106	9	and	and	CCONJ
iajs-1000	106	10	(	(	PUNCT
iajs-1000	106	11	2.23	2.23	NUM
iajs-1000	106	12	)	)	PUNCT
iajs-1000	106	13	.	.	PUNCT
iajs-1000	107	1			NUM
iajs-1000	107	2	ibn	ibn	PROPN
iajs-1000	107	3	alhaitham	alhaitham	PROPN
iajs-1000	107	4	j.	j.	PROPN
iajs-1000	107	5	for	for	ADP
iajs-1000	107	6	pure	pure	ADJ
iajs-1000	107	7	&	&	CCONJ
iajs-1000	107	8	appl	appl	PROPN
iajs-1000	107	9	.	.	PUNCT
iajs-1000	108	1	sci	sci	PROPN
iajs-1000	108	2	.	.	PUNCT
iajs-1000	109	1	vol.23	vol.23	PROPN
iajs-1000	109	2	(	(	PUNCT
iajs-1000	109	3	1	1	NUM
iajs-1000	109	4	)	)	PUNCT
iajs-1000	109	5	2010	2010	NUM
iajs-1000	110	1	the	the	DET
iajs-1000	110	2	following	follow	VERB
iajs-1000	110	3	diagram	diagram	NOUN
iajs-1000	110	4	shows	show	VERB
iajs-1000	110	5	the	the	DET
iajs-1000	110	6	relationships	relationship	NOUN
iajs-1000	110	7	between	between	ADP
iajs-1000	110	8	n	n	NOUN
iajs-1000	110	9	-	-	PUNCT
iajs-1000	110	10	compact	compact	ADJ
iajs-1000	110	11	and	and	CCONJ
iajs-1000	110	12	s	s	NOUN
iajs-1000	110	13	-	-	ADJ
iajs-1000	110	14	compact	compact	ADJ
iajs-1000	110	15	spaces	space	NOUN
iajs-1000	110	16	:	:	PUNCT
iajs-1000	110	17	now	now	ADV
iajs-1000	110	18	,	,	PUNCT
iajs-1000	110	19	we	we	PRON
iajs-1000	110	20	shall	shall	AUX
iajs-1000	110	21	recall	recall	VERB
iajs-1000	110	22	another	another	DET
iajs-1000	110	23	kind	kind	NOUN
iajs-1000	110	24	of	of	ADP
iajs-1000	110	25	compactness	compactness	NOUN
iajs-1000	110	26	on	on	ADP
iajs-1000	110	27	bitopological	bitopological	ADJ
iajs-1000	110	28	spaces	space	NOUN
iajs-1000	110	29	called	call	VERB
iajs-1000	110	30	"	"	PUNCT
iajs-1000	110	31	pairwise	pairwise	NOUN
iajs-1000	110	32	compact	compact	NOUN
iajs-1000	110	33	"	"	PUNCT
iajs-1000	110	34	to	to	PART
iajs-1000	110	35	study	study	VERB
iajs-1000	110	36	this	this	DET
iajs-1000	110	37	kind	kind	NOUN
iajs-1000	110	38	and	and	CCONJ
iajs-1000	110	39	compare	compare	VERB
iajs-1000	110	40	it	it	PRON
iajs-1000	110	41	with	with	ADP
iajs-1000	110	42	the	the	DET
iajs-1000	110	43	two	two	NUM
iajs-1000	110	44	above	above	ADJ
iajs-1000	110	45	kinds	kind	NOUN
iajs-1000	110	46	of	of	ADP
iajs-1000	110	47	compactness	compactness	NOUN
iajs-1000	110	48	in	in	ADP
iajs-1000	110	49	bitopological	bitopological	ADJ
iajs-1000	110	50	spaces	space	NOUN
iajs-1000	110	51	.	.	PUNCT
iajs-1000	111	1	2.32	2.32	NUM
iajs-1000	111	2	definition	definition	NOUN
iajs-1000	111	3	[	[	X
iajs-1000	111	4	4	4	X
iajs-1000	111	5	]	]	X
iajs-1000	111	6	let	let	VERB
iajs-1000	111	7	(	(	PUNCT
iajs-1000	111	8	x	x	NOUN
iajs-1000	111	9	,	,	PUNCT
iajs-1000	111	10	τ	τ	PROPN
iajs-1000	111	11	,	,	PUNCT
iajs-1000	111	12	τ	τ	NOUN
iajs-1000	111	13	)	)	PUNCT
iajs-1000	111	14	be	be	AUX
iajs-1000	111	15	a	a	DET
iajs-1000	111	16	bitopological	bitopological	ADJ
iajs-1000	111	17	space	space	NOUN
iajs-1000	111	18	,	,	PUNCT
iajs-1000	111	19	a	a	DET
iajs-1000	111	20			PROPN
iajs-1000	111	21	x	x	PROPN
iajs-1000	111	22	,	,	PUNCT
iajs-1000	111	23	an	an	DET
iajs-1000	111	24	s	s	NOUN
iajs-1000	111	25	-	-	ADJ
iajs-1000	111	26	open	open	ADJ
iajs-1000	111	27	cover	cover	NOUN
iajs-1000	111	28	of	of	ADP
iajs-1000	111	29	a	a	PRON
iajs-1000	111	30	is	be	AUX
iajs-1000	111	31	called	call	VERB
iajs-1000	111	32	a	a	DET
iajs-1000	111	33	"	"	PUNCT
iajs-1000	111	34	pair	pair	NOUN
iajs-1000	111	35	-	-	PUNCT
iajs-1000	111	36	wise	wise	ADJ
iajs-1000	111	37	open	open	ADJ
iajs-1000	111	38	cover	cover	NOUN
iajs-1000	111	39	"	"	PUNCT
iajs-1000	111	40	if	if	SCONJ
iajs-1000	111	41	it	it	PRON
iajs-1000	111	42	contains	contain	VERB
iajs-1000	111	43	at	at	ADV
iajs-1000	111	44	least	least	ADV
iajs-1000	111	45	one	one	NUM
iajs-1000	111	46	non	non	ADJ
iajs-1000	111	47	-	-	ADJ
iajs-1000	111	48	empty	empty	ADJ
iajs-1000	111	49	element	element	NOUN
iajs-1000	111	50	from	from	ADP
iajs-1000	111	51	τ	τ	PROPN
iajs-1000	111	52	,	,	PUNCT
iajs-1000	111	53	and	and	CCONJ
iajs-1000	111	54	at	at	ADV
iajs-1000	111	55	least	least	ADJ
iajs-1000	111	56	one	one	NUM
iajs-1000	111	57	non	non	ADJ
iajs-1000	111	58	-	-	ADJ
iajs-1000	111	59	empty	empty	ADJ
iajs-1000	111	60	element	element	NOUN
iajs-1000	111	61	from	from	ADP
iajs-1000	111	62	τ.	τ.	ADP
iajs-1000	111	63	2.33	2.33	NUM
iajs-1000	111	64	example	example	NOUN
iajs-1000	111	65	let	let	VERB
iajs-1000	111	66	x	x	PUNCT
iajs-1000	111	67	=	=	PUNCT
iajs-1000	111	68	{	{	PUNCT
iajs-1000	111	69	1,2,3	1,2,3	NUM
iajs-1000	111	70	}	}	PUNCT
iajs-1000	111	71	,	,	PUNCT
iajs-1000	111	72	τ	τ	X
iajs-1000	111	73	=	=	PUNCT
iajs-1000	111	74	{	{	PUNCT
iajs-1000	111	75			PROPN
iajs-1000	111	76	,	,	PUNCT
iajs-1000	111	77	x,{1	x,{1	PROPN
iajs-1000	111	78	}	}	PUNCT
iajs-1000	111	79	}	}	PUNCT
iajs-1000	111	80	and	and	CCONJ
iajs-1000	111	81	τ	τ	PUNCT
iajs-1000	111	82	=	=	SYM
iajs-1000	111	83	{	{	PUNCT
iajs-1000	111	84			PROPN
iajs-1000	111	85	,	,	PUNCT
iajs-1000	111	86	x,{2},{3},{2,3	x,{2},{3},{2,3	PROPN
iajs-1000	111	87	}	}	PUNCT
iajs-1000	111	88	}	}	PUNCT
iajs-1000	111	89	.	.	PUNCT
iajs-1000	112	1	then	then	ADV
iajs-1000	112	2	the	the	DET
iajs-1000	112	3	cover	cover	NOUN
iajs-1000	112	4	c	c	NOUN
iajs-1000	112	5	=	=	PRON
iajs-1000	112	6	{	{	PUNCT
iajs-1000	112	7	{	{	PUNCT
iajs-1000	112	8	1},{2},{3	1},{2},{3	NUM
iajs-1000	112	9	}	}	PUNCT
iajs-1000	112	10	}	}	PUNCT
iajs-1000	112	11	is	be	AUX
iajs-1000	112	12	a	a	DET
iajs-1000	112	13	pair	pair	NOUN
iajs-1000	112	14	-	-	PUNCT
iajs-1000	112	15	wise	wise	ADJ
iajs-1000	112	16	open	open	ADJ
iajs-1000	112	17	cover	cover	NOUN
iajs-1000	112	18	of	of	ADP
iajs-1000	112	19	x.	x.	NOUN
iajs-1000	112	20	2.34	2.34	NUM
iajs-1000	112	21	remark	remark	NOUN
iajs-1000	112	22	every	every	DET
iajs-1000	112	23	pair	pair	NOUN
iajs-1000	112	24	-	-	PUNCT
iajs-1000	112	25	wise	wise	ADJ
iajs-1000	112	26	open	open	ADJ
iajs-1000	112	27	cover	cover	NOUN
iajs-1000	112	28	of	of	ADP
iajs-1000	112	29	the	the	DET
iajs-1000	112	30	bitopological	bitopological	ADJ
iajs-1000	112	31	space	space	NOUN
iajs-1000	112	32	(	(	PUNCT
iajs-1000	112	33	x	x	X
iajs-1000	112	34	,	,	PUNCT
iajs-1000	112	35	τ	τ	PROPN
iajs-1000	112	36	,	,	PUNCT
iajs-1000	112	37	τ	τ	NOUN
iajs-1000	112	38	)	)	PUNCT
iajs-1000	112	39	is	be	AUX
iajs-1000	112	40	an	an	DET
iajs-1000	112	41	s	s	NOUN
iajs-1000	112	42	-	-	PUNCT
iajs-1000	112	43	open	open	ADJ
iajs-1000	112	44	cover	cover	NOUN
iajs-1000	112	45	.	.	PUNCT
iajs-1000	113	1	2.35	2.35	NUM
iajs-1000	113	2	note	note	NOUN
iajs-1000	113	3	the	the	DET
iajs-1000	113	4	implication	implication	NOUN
iajs-1000	113	5	in	in	ADP
iajs-1000	113	6	remark	remark	NOUN
iajs-1000	113	7	2.34	2.34	NUM
iajs-1000	113	8	is	be	AUX
iajs-1000	113	9	not	not	PART
iajs-1000	113	10	reversible	reversible	ADJ
iajs-1000	113	11	.	.	PUNCT
iajs-1000	114	1	for	for	ADP
iajs-1000	114	2	example	example	NOUN
iajs-1000	114	3	:	:	PUNCT
iajs-1000	114	4	let	let	VERB
iajs-1000	114	5	x	x	PUNCT
iajs-1000	114	6	=	=	PUNCT
iajs-1000	114	7	{	{	PUNCT
iajs-1000	114	8	1,2,3	1,2,3	NUM
iajs-1000	114	9	}	}	PUNCT
iajs-1000	114	10	,	,	PUNCT
iajs-1000	114	11	τ	τ	X
iajs-1000	114	12	=	=	PUNCT
iajs-1000	114	13	{	{	PUNCT
iajs-1000	114	14			PROPN
iajs-1000	114	15	,	,	PUNCT
iajs-1000	114	16	{	{	PUNCT
iajs-1000	114	17	1},x	1},x	NOUN
iajs-1000	114	18	}	}	PUNCT
iajs-1000	114	19	and	and	CCONJ
iajs-1000	114	20	τ	τ	PUNCT
iajs-1000	114	21	=	=	SYM
iajs-1000	114	22	{	{	PUNCT
iajs-1000	114	23			PROPN
iajs-1000	114	24	,	,	PUNCT
iajs-1000	114	25	{	{	PUNCT
iajs-1000	114	26	2},{3},{2,3},{1,2},x	2},{3},{2,3},{1,2},x	NOUN
iajs-1000	114	27	}	}	PUNCT
iajs-1000	114	28	.	.	PUNCT
iajs-1000	115	1	then	then	ADV
iajs-1000	115	2	the	the	DET
iajs-1000	115	3	cover	cover	NOUN
iajs-1000	115	4	c	c	NOUN
iajs-1000	115	5	=	=	PRON
iajs-1000	115	6	{	{	PUNCT
iajs-1000	115	7	{	{	PUNCT
iajs-1000	115	8	1,2},{3	1,2},{3	NUM
iajs-1000	115	9	}	}	PUNCT
iajs-1000	115	10	}	}	PUNCT
iajs-1000	115	11	is	be	AUX
iajs-1000	115	12	an	an	DET
iajs-1000	115	13	s	s	NOUN
iajs-1000	115	14	-	-	ADJ
iajs-1000	115	15	open	open	ADJ
iajs-1000	115	16	cover	cover	NOUN
iajs-1000	115	17	of	of	ADP
iajs-1000	115	18	x	x	PRON
iajs-1000	115	19	,	,	PUNCT
iajs-1000	115	20	but	but	CCONJ
iajs-1000	115	21	it	it	PRON
iajs-1000	115	22	is	be	AUX
iajs-1000	115	23	not	not	PART
iajs-1000	115	24	pair	pair	NOUN
iajs-1000	115	25	-	-	PUNCT
iajs-1000	115	26	wise	wise	ADJ
iajs-1000	115	27	open	open	ADJ
iajs-1000	115	28	cover	cover	NOUN
iajs-1000	115	29	..	..	PUNCT
iajs-1000	115	30	2.36	2.36	NUM
iajs-1000	115	31	definition	definition	NOUN
iajs-1000	115	32	[	[	X
iajs-1000	115	33	4	4	X
iajs-1000	115	34	]	]	PUNCT
iajs-1000	115	35	a	a	DET
iajs-1000	115	36	bitopological	bitopological	ADJ
iajs-1000	115	37	space	space	NOUN
iajs-1000	115	38	(	(	PUNCT
iajs-1000	115	39	x	x	X
iajs-1000	115	40	,	,	PUNCT
iajs-1000	115	41	τ	τ	PROPN
iajs-1000	115	42	,	,	PUNCT
iajs-1000	115	43	τ	τ	NOUN
iajs-1000	115	44	)	)	PUNCT
iajs-1000	115	45	is	be	AUX
iajs-1000	115	46	called	call	VERB
iajs-1000	115	47	a	a	DET
iajs-1000	115	48	"	"	PUNCT
iajs-1000	115	49	pair	pair	NOUN
iajs-1000	115	50	-	-	PUNCT
iajs-1000	115	51	wise	wise	ADJ
iajs-1000	115	52	compact	compact	ADJ
iajs-1000	115	53	space	space	NOUN
iajs-1000	115	54	"	"	PUNCT
iajs-1000	115	55	if	if	SCONJ
iajs-1000	115	56	every	every	DET
iajs-1000	115	57	pair	pair	NOUN
iajs-1000	115	58	-	-	PUNCT
iajs-1000	115	59	wise	wise	ADJ
iajs-1000	115	60	open	open	ADJ
iajs-1000	115	61	cover	cover	NOUN
iajs-1000	115	62	of	of	ADP
iajs-1000	115	63	x	x	PUNCT
iajs-1000	115	64	has	have	VERB
iajs-1000	115	65	a	a	DET
iajs-1000	115	66	finite	finite	ADJ
iajs-1000	115	67	subcover	subcover	PROPN
iajs-1000	115	68	.	.	PUNCT
iajs-1000	116	1	2.37	2.37	NUM
iajs-1000	116	2	remark	remark	NOUN
iajs-1000	116	3	let	let	VERB
iajs-1000	116	4	(	(	PUNCT
iajs-1000	116	5	x	x	NOUN
iajs-1000	116	6	,	,	PUNCT
iajs-1000	116	7	τ	τ	PROPN
iajs-1000	116	8	,	,	PUNCT
iajs-1000	116	9	τ	τ	NOUN
iajs-1000	116	10	)	)	PUNCT
iajs-1000	116	11	be	be	AUX
iajs-1000	116	12	a	a	DET
iajs-1000	116	13	bitopological	bitopological	ADJ
iajs-1000	116	14	space	space	NOUN
iajs-1000	116	15	.	.	PUNCT
iajs-1000	117	1	if	if	SCONJ
iajs-1000	117	2	τ	τ	PROPN
iajs-1000	117	3	=	=	SYM
iajs-1000	117	4	τi	τi	NOUN
iajs-1000	117	5	or	or	CCONJ
iajs-1000	117	6	τ	τ	X
iajs-1000	117	7	=	=	SYM
iajs-1000	117	8	τi	τi	PROPN
iajs-1000	117	9	,	,	PUNCT
iajs-1000	117	10	then	then	ADV
iajs-1000	117	11	x	x	PUNCT
iajs-1000	117	12	is	be	AUX
iajs-1000	117	13	a	a	DET
iajs-1000	117	14	pair	pair	NOUN
iajs-1000	117	15	-	-	PUNCT
iajs-1000	117	16	wise	wise	ADJ
iajs-1000	117	17	compact	compact	ADJ
iajs-1000	117	18	space	space	NOUN
iajs-1000	117	19	.	.	PUNCT
iajs-1000	118	1	2.38	2.38	NUM
iajs-1000	118	2	proposition	proposition	NOUN
iajs-1000	118	3	every	every	DET
iajs-1000	118	4	s	s	ADJ
iajs-1000	118	5	-	-	ADJ
iajs-1000	118	6	compact	compact	ADJ
iajs-1000	118	7	space	space	NOUN
iajs-1000	118	8	isa	isa	NOUN
iajs-1000	118	9	pair	pair	NOUN
iajs-1000	118	10	-	-	PUNCT
iajs-1000	118	11	wise	wise	ADJ
iajs-1000	118	12	compact	compact	ADJ
iajs-1000	118	13	space	space	NOUN
iajs-1000	118	14	.	.	PUNCT
iajs-1000	119	1	proof	proof	NOUN
iajs-1000	119	2	:	:	PUNCT
iajs-1000	119	3	follows	follow	VERB
iajs-1000	119	4	from	from	ADP
iajs-1000	119	5	remark	remark	NOUN
iajs-1000	119	6	2.34	2.34	NUM
iajs-1000	119	7	.	.	PUNCT
iajs-1000	120	1	2.39	2.39	NUM
iajs-1000	120	2	note	note	VERB
iajs-1000	120	3	the	the	DET
iajs-1000	120	4	converse	converse	NOUN
iajs-1000	120	5	of	of	ADP
iajs-1000	120	6	proposition	proposition	NOUN
iajs-1000	120	7	2.38	2.38	NUM
iajs-1000	120	8	may	may	AUX
iajs-1000	120	9	be	be	AUX
iajs-1000	120	10	false	false	ADJ
iajs-1000	120	11	.	.	PUNCT
iajs-1000	121	1	for	for	ADP
iajs-1000	121	2	example	example	NOUN
iajs-1000	121	3	:	:	PUNCT
iajs-1000	121	4	(	(	PUNCT
iajs-1000	121	5	�	�	PROPN
iajs-1000	121	6	,	,	PUNCT
iajs-1000	121	7	τu	τu	ADV
iajs-1000	121	8	,	,	PUNCT
iajs-1000	121	9	τi	τi	PROPN
iajs-1000	121	10	)	)	PUNCT
iajs-1000	121	11	is	be	AUX
iajs-1000	121	12	pair	pair	NOUN
iajs-1000	121	13	-	-	PUNCT
iajs-1000	121	14	wise	wise	ADJ
iajs-1000	121	15	compact	compact	ADJ
iajs-1000	121	16	space	space	NOUN
iajs-1000	121	17	,	,	PUNCT
iajs-1000	121	18	but	but	CCONJ
iajs-1000	121	19	not	not	PART
iajs-1000	121	20	s	s	NOUN
iajs-1000	121	21	-	-	NOUN
iajs-1000	121	22	compact	compact	ADJ
iajs-1000	121	23	.	.	PUNCT
iajs-1000	122	1	n	n	CCONJ
iajs-1000	122	2	-	-	PUNCT
iajs-1000	122	3	compact	compact	ADJ
iajs-1000	122	4	s	s	ADJ
iajs-1000	122	5	-	-	ADJ
iajs-1000	122	6	compact	compact	ADJ
iajs-1000	122	7			ADJ
iajs-1000	122	8	–	–	NOUN
iajs-1000	122	9	τ	τ	X
iajs-1000	122	10	is	be	AUX
iajs-1000	122	11	a	a	DET
iajs-1000	122	12	subfamily	subfamily	NOUN
iajs-1000	122	13	of	of	ADP
iajs-1000	122	14	τ	τ	NOUN
iajs-1000	122	15			PROPN
iajs-1000	122	16			PROPN
iajs-1000	122	17	ibn	ibn	PROPN
iajs-1000	122	18	alhaitham	alhaitham	NOUN
iajs-1000	122	19	j.	j.	PROPN
iajs-1000	122	20	for	for	ADP
iajs-1000	122	21	pure	pure	ADJ
iajs-1000	122	22	&	&	CCONJ
iajs-1000	122	23	appl	appl	PROPN
iajs-1000	122	24	.	.	PUNCT
iajs-1000	123	1	sci	sci	PROPN
iajs-1000	123	2	.	.	PUNCT
iajs-1000	124	1	vol.23	vol.23	PROPN
iajs-1000	124	2	(	(	PUNCT
iajs-1000	124	3	1	1	NUM
iajs-1000	124	4	)	)	PUNCT
iajs-1000	124	5	2010	2010	NUM
iajs-1000	124	6	the	the	DET
iajs-1000	124	7	example	example	NOUN
iajs-1000	124	8	of	of	ADP
iajs-1000	124	9	note	note	NOUN
iajs-1000	124	10	2.39	2.39	NUM
iajs-1000	124	11	shows	show	VERB
iajs-1000	124	12	that	that	SCONJ
iajs-1000	124	13	,	,	PUNCT
iajs-1000	124	14	if	if	SCONJ
iajs-1000	124	15	(	(	PUNCT
iajs-1000	124	16	x	x	NOUN
iajs-1000	124	17	,	,	PUNCT
iajs-1000	124	18	τ	τ	PROPN
iajs-1000	124	19	,	,	PUNCT
iajs-1000	124	20	τ	τ	NOUN
iajs-1000	124	21	)	)	PUNCT
iajs-1000	124	22	is	be	AUX
iajs-1000	124	23	a	a	DET
iajs-1000	124	24	pair	pair	NOUN
iajs-1000	124	25	-	-	PUNCT
iajs-1000	124	26	wise	wise	ADJ
iajs-1000	124	27	compact	compact	ADJ
iajs-1000	124	28	space	space	NOUN
iajs-1000	124	29	,	,	PUNCT
iajs-1000	124	30	then	then	ADV
iajs-1000	124	31	(	(	PUNCT
iajs-1000	124	32	x	x	NOUN
iajs-1000	124	33	,	,	PUNCT
iajs-1000	124	34	τ	τ	NOUN
iajs-1000	124	35	)	)	PUNCT
iajs-1000	124	36	need	need	VERB
iajs-1000	124	37	not	not	PART
iajs-1000	124	38	to	to	PART
iajs-1000	124	39	be	be	AUX
iajs-1000	124	40	compact	compact	ADJ
iajs-1000	124	41	and	and	CCONJ
iajs-1000	124	42	the	the	DET
iajs-1000	124	43	example	example	NOUN
iajs-1000	124	44	of	of	ADP
iajs-1000	124	45	note	note	NOUN
iajs-1000	124	46	2.9	2.9	NUM
iajs-1000	124	47	shows	show	VERB
iajs-1000	124	48	that	that	SCONJ
iajs-1000	124	49	,	,	PUNCT
iajs-1000	124	50	if	if	SCONJ
iajs-1000	124	51	(	(	PUNCT
iajs-1000	124	52	x	x	X
iajs-1000	124	53	,	,	PUNCT
iajs-1000	124	54	τ	τ	X
iajs-1000	124	55	)	)	PUNCT
iajs-1000	124	56	and	and	CCONJ
iajs-1000	124	57	(	(	PUNCT
iajs-1000	124	58	x	x	NOUN
iajs-1000	124	59	,	,	PUNCT
iajs-1000	124	60	τ	τ	NOUN
iajs-1000	124	61	)	)	PUNCT
iajs-1000	124	62	are	be	AUX
iajs-1000	124	63	compact	compact	ADJ
iajs-1000	124	64	space	space	NOUN
iajs-1000	124	65	,	,	PUNCT
iajs-1000	124	66	then	then	ADV
iajs-1000	124	67	(	(	PUNCT
iajs-1000	124	68	x	x	X
iajs-1000	124	69	,	,	PUNCT
iajs-1000	124	70	τ	τ	PROPN
iajs-1000	124	71	,	,	PUNCT
iajs-1000	124	72	τ	τ	NOUN
iajs-1000	124	73	)	)	PUNCT
iajs-1000	124	74	need	need	VERB
iajs-1000	124	75	not	not	PART
iajs-1000	124	76	to	to	PART
iajs-1000	124	77	bea	bea	VERB
iajs-1000	124	78	pair	pair	NOUN
iajs-1000	124	79	-	-	PUNCT
iajs-1000	124	80	wise	wise	ADJ
iajs-1000	124	81	compact	compact	ADJ
iajs-1000	124	82	.	.	PUNCT
iajs-1000	125	1	2.40	2.40	NUM
iajs-1000	125	2	proposition	proposition	NOUN
iajs-1000	125	3	if	if	SCONJ
iajs-1000	125	4	τ	τ	PROPN
iajs-1000	125	5	is	be	AUX
iajs-1000	125	6	a	a	DET
iajs-1000	125	7	subfamily	subfamily	NOUN
iajs-1000	125	8	of	of	ADP
iajs-1000	125	9	τ	τ	NOUN
iajs-1000	125	10	and	and	CCONJ
iajs-1000	125	11	(	(	PUNCT
iajs-1000	125	12	x	x	NOUN
iajs-1000	125	13	,	,	PUNCT
iajs-1000	125	14	τ	τ	NOUN
iajs-1000	125	15	)	)	PUNCT
iajs-1000	125	16	isa	isa	NOUN
iajs-1000	125	17	compact	compact	ADJ
iajs-1000	125	18	space	space	NOUN
iajs-1000	125	19	,	,	PUNCT
iajs-1000	125	20	then	then	ADV
iajs-1000	125	21	(	(	PUNCT
iajs-1000	125	22	x	x	X
iajs-1000	125	23	,	,	PUNCT
iajs-1000	125	24	τ	τ	PROPN
iajs-1000	125	25	,	,	PUNCT
iajs-1000	125	26	τ	τ	NOUN
iajs-1000	125	27	)	)	PUNCT
iajs-1000	125	28	is	be	AUX
iajs-1000	125	29	a	a	DET
iajs-1000	125	30	pair	pair	NOUN
iajs-1000	125	31	-	-	PUNCT
iajs-1000	125	32	wise	wise	ADJ
iajs-1000	125	33	compact	compact	ADJ
iajs-1000	125	34	space	space	NOUN
iajs-1000	125	35	.	.	PUNCT
iajs-1000	126	1	proof	proof	NOUN
iajs-1000	126	2	:	:	PUNCT
iajs-1000	126	3	follows	follow	VERB
iajs-1000	126	4	from	from	ADP
iajs-1000	126	5	proposition	proposition	NOUN
iajs-1000	126	6	2.10	2.10	NUM
iajs-1000	126	7	and	and	CCONJ
iajs-1000	126	8	proposition	proposition	NOUN
iajs-1000	126	9	2.38	2.38	NUM
iajs-1000	126	10	.	.	PUNCT
iajs-1000	127	1	2.41	2.41	NUM
iajs-1000	127	2	theorem	theorem	VERB
iajs-1000	127	3	if	if	SCONJ
iajs-1000	127	4	(	(	PUNCT
iajs-1000	127	5	x	x	X
iajs-1000	127	6	,	,	PUNCT
iajs-1000	127	7	τ	τ	X
iajs-1000	127	8	)	)	PUNCT
iajs-1000	127	9	and	and	CCONJ
iajs-1000	127	10	(	(	PUNCT
iajs-1000	127	11	x	x	NOUN
iajs-1000	127	12	,	,	PUNCT
iajs-1000	127	13	τ	τ	NOUN
iajs-1000	127	14	)	)	PUNCT
iajs-1000	127	15	are	be	AUX
iajs-1000	127	16	compact	compact	ADJ
iajs-1000	127	17	spaces	space	NOUN
iajs-1000	127	18	,	,	PUNCT
iajs-1000	127	19	then	then	ADV
iajs-1000	127	20	(	(	PUNCT
iajs-1000	127	21	x	x	X
iajs-1000	127	22	,	,	PUNCT
iajs-1000	127	23	τ	τ	PROPN
iajs-1000	127	24	,	,	PUNCT
iajs-1000	127	25	τ	τ	NOUN
iajs-1000	127	26	)	)	PUNCT
iajs-1000	127	27	is	be	AUX
iajs-1000	127	28	s	s	NOUN
iajs-1000	127	29	-	-	ADJ
iajs-1000	127	30	compact	compact	ADJ
iajs-1000	127	31	if	if	SCONJ
iajs-1000	127	32	and	and	CCONJ
iajs-1000	127	33	only	only	ADV
iajs-1000	127	34	if	if	SCONJ
iajs-1000	127	35	it	it	PRON
iajs-1000	127	36	is	be	AUX
iajs-1000	127	37	a	a	DET
iajs-1000	127	38	pair	pair	NOUN
iajs-1000	127	39	-	-	PUNCT
iajs-1000	127	40	wise	wise	ADJ
iajs-1000	127	41	compact	compact	ADJ
iajs-1000	127	42	.	.	PUNCT
iajs-1000	128	1	proof	proof	NOUN
iajs-1000	128	2	:	:	PUNCT
iajs-1000	128	3	necessity	necessity	NOUN
iajs-1000	128	4	,	,	PUNCT
iajs-1000	128	5	follows	follow	VERB
iajs-1000	128	6	from	from	ADP
iajs-1000	128	7	proposition	proposition	NOUN
iajs-1000	128	8	2.38	2.38	NUM
iajs-1000	128	9	.	.	PUNCT
iajs-1000	129	1	sufficiency	sufficiency	PROPN
iajs-1000	129	2	,	,	PUNCT
iajs-1000	129	3	suppose	suppose	VERB
iajs-1000	129	4	(	(	PUNCT
iajs-1000	129	5	x	x	X
iajs-1000	129	6	,	,	PUNCT
iajs-1000	129	7	τ	τ	PROPN
iajs-1000	129	8	,	,	PUNCT
iajs-1000	129	9	τ	τ	NOUN
iajs-1000	129	10	)	)	PUNCT
iajs-1000	129	11	is	be	AUX
iajs-1000	129	12	a	a	DET
iajs-1000	129	13	pair	pair	NOUN
iajs-1000	129	14	-	-	PUNCT
iajs-1000	129	15	wise	wise	ADJ
iajs-1000	129	16	compact	compact	ADJ
iajs-1000	129	17	space	space	NOUN
iajs-1000	129	18	,	,	PUNCT
iajs-1000	129	19	to	to	PART
iajs-1000	129	20	prove	prove	VERB
iajs-1000	129	21	it	it	PRON
iajs-1000	129	22	,	,	PUNCT
iajs-1000	129	23	is	be	AUX
iajs-1000	129	24	an	an	DET
iajs-1000	129	25	s	s	ADJ
iajs-1000	129	26	-	-	ADJ
iajs-1000	129	27	compact	compact	ADJ
iajs-1000	129	28	space	space	NOUN
iajs-1000	129	29	.	.	PUNCT
iajs-1000	130	1	let	let	VERB
iajs-1000	130	2	w	w	NOUN
iajs-1000	130	3	be	be	AUX
iajs-1000	130	4	an	an	DET
iajs-1000	130	5	s	s	NOUN
iajs-1000	130	6	-	-	ADJ
iajs-1000	130	7	open	open	ADJ
iajs-1000	130	8	cover	cover	NOUN
iajs-1000	130	9	of	of	ADP
iajs-1000	130	10	x	x	PRON
iajs-1000	130	11	,	,	PUNCT
iajs-1000	130	12	then	then	ADV
iajs-1000	130	13	there	there	PRON
iajs-1000	130	14	are	be	VERB
iajs-1000	130	15	three	three	NUM
iajs-1000	130	16	probabilities	probability	NOUN
iajs-1000	130	17	i	i	PRON
iajs-1000	130	18	)	)	PUNCT
iajs-1000	130	19	if	if	SCONJ
iajs-1000	130	20	w	w	NOUN
iajs-1000	130	21	is	be	AUX
iajs-1000	130	22	a	a	DET
iajs-1000	130	23	τ	τ	NOUN
iajs-1000	130	24	-	-	ADJ
iajs-1000	130	25	open	open	ADJ
iajs-1000	130	26	cover	cover	NOUN
iajs-1000	130	27	,	,	PUNCT
iajs-1000	130	28	since	since	SCONJ
iajs-1000	130	29	(	(	PUNCT
iajs-1000	130	30	x	x	X
iajs-1000	130	31	,	,	PUNCT
iajs-1000	130	32	τ	τ	X
iajs-1000	130	33	)	)	PUNCT
iajs-1000	130	34	is	be	AUX
iajs-1000	130	35	compact	compact	ADJ
iajs-1000	130	36	,	,	PUNCT
iajs-1000	130	37	then	then	ADV
iajs-1000	130	38	w	w	PROPN
iajs-1000	130	39	has	have	VERB
iajs-1000	130	40	a	a	DET
iajs-1000	130	41	finite	finite	ADJ
iajs-1000	130	42	subcover	subcover	NOUN
iajs-1000	130	43	of	of	ADP
iajs-1000	130	44	x	x	PROPN
iajs-1000	130	45	,	,	PUNCT
iajs-1000	130	46	so	so	ADV
iajs-1000	130	47	the	the	DET
iajs-1000	130	48	proof	proof	NOUN
iajs-1000	130	49	is	be	AUX
iajs-1000	130	50	over	over	ADP
iajs-1000	130	51	.	.	PUNCT
iajs-1000	131	1	ii	ii	X
iajs-1000	131	2	)	)	PUNCT
iajs-1000	131	3	if	if	SCONJ
iajs-1000	131	4	w	w	NOUN
iajs-1000	131	5	is	be	AUX
iajs-1000	131	6	a	a	DET
iajs-1000	131	7	τ-open	τ-open	ADJ
iajs-1000	131	8	cover	cover	NOUN
iajs-1000	131	9	,	,	PUNCT
iajs-1000	131	10	since	since	SCONJ
iajs-1000	131	11	(	(	PUNCT
iajs-1000	131	12	x	x	NOUN
iajs-1000	131	13	,	,	PUNCT
iajs-1000	131	14	τ	τ	NOUN
iajs-1000	131	15	)	)	PUNCT
iajs-1000	131	16	is	be	AUX
iajs-1000	131	17	compact	compact	ADJ
iajs-1000	131	18	space	space	NOUN
iajs-1000	131	19	,	,	PUNCT
iajs-1000	131	20	then	then	ADV
iajs-1000	131	21	w	w	PROPN
iajs-1000	131	22	has	have	VERB
iajs-1000	131	23	a	a	DET
iajs-1000	131	24	finite	finite	ADJ
iajs-1000	131	25	subcover	subcover	NOUN
iajs-1000	131	26	of	of	ADP
iajs-1000	131	27	x	x	PROPN
iajs-1000	131	28	,	,	PUNCT
iajs-1000	131	29	so	so	ADV
iajs-1000	131	30	the	the	DET
iajs-1000	131	31	proof	proof	NOUN
iajs-1000	131	32	is	be	AUX
iajs-1000	131	33	over	over	ADP
iajs-1000	131	34	.	.	PUNCT
iajs-1000	132	1	iii	iii	X
iajs-1000	132	2	)	)	PUNCT
iajs-1000	132	3	if	if	SCONJ
iajs-1000	132	4	w	w	NOUN
iajs-1000	132	5	is	be	AUX
iajs-1000	132	6	a	a	DET
iajs-1000	132	7	pair	pair	NOUN
iajs-1000	132	8	-	-	PUNCT
iajs-1000	132	9	wise	wise	ADJ
iajs-1000	132	10	open	open	ADJ
iajs-1000	132	11	cover	cover	NOUN
iajs-1000	132	12	,	,	PUNCT
iajs-1000	132	13	since	since	SCONJ
iajs-1000	132	14	(	(	PUNCT
iajs-1000	132	15	x	x	X
iajs-1000	132	16	,	,	PUNCT
iajs-1000	132	17	τ	τ	PROPN
iajs-1000	132	18	,	,	PUNCT
iajs-1000	132	19	τ	τ	NOUN
iajs-1000	132	20	)	)	PUNCT
iajs-1000	132	21	isa	isa	VERB
iajs-1000	132	22	pair	pair	NOUN
iajs-1000	132	23	-	-	PUNCT
iajs-1000	132	24	wise	wise	ADJ
iajs-1000	132	25	compact	compact	ADJ
iajs-1000	132	26	space	space	NOUN
iajs-1000	132	27	,	,	PUNCT
iajs-1000	132	28	then	then	ADV
iajs-1000	132	29	w	w	PROPN
iajs-1000	132	30	has	have	VERB
iajs-1000	132	31	a	a	DET
iajs-1000	132	32	finite	finite	ADJ
iajs-1000	132	33	subcover	subcover	PROPN
iajs-1000	132	34	.	.	PUNCT
iajs-1000	133	1	iv	iv	X
iajs-1000	133	2	)	)	PUNCT
iajs-1000	133	3	therefore	therefore	ADV
iajs-1000	133	4	,	,	PUNCT
iajs-1000	133	5	(	(	PUNCT
iajs-1000	133	6	x	x	X
iajs-1000	133	7	,	,	PUNCT
iajs-1000	133	8	τ	τ	PROPN
iajs-1000	133	9	,	,	PUNCT
iajs-1000	133	10	τ	τ	NOUN
iajs-1000	133	11	)	)	PUNCT
iajs-1000	133	12	isan	isan	ADJ
iajs-1000	133	13	s	s	NOUN
iajs-1000	133	14	-	-	ADJ
iajs-1000	133	15	compact	compact	ADJ
iajs-1000	133	16	space	space	NOUN
iajs-1000	133	17	.	.	PUNCT
iajs-1000	134	1	from	from	ADP
iajs-1000	134	2	proposition	proposition	NOUN
iajs-1000	134	3	2.38	2.38	NUM
iajs-1000	134	4	and	and	CCONJ
iajs-1000	134	5	theorem	theorem	VERB
iajs-1000	134	6	2.41	2.41	NUM
iajs-1000	134	7	,	,	PUNCT
iajs-1000	134	8	we	we	PRON
iajs-1000	134	9	get	get	VERB
iajs-1000	134	10	the	the	DET
iajs-1000	134	11	following	follow	VERB
iajs-1000	134	12	diagram	diagram	NOUN
iajs-1000	134	13	:	:	PUNCT
iajs-1000	134	14	:	:	PUNCT
iajs-1000	134	15	2.42	2.42	NUM
iajs-1000	134	16	corollary	corollary	NOUN
iajs-1000	134	17	if	if	SCONJ
iajs-1000	134	18	τ	τ	PROPN
iajs-1000	134	19	is	be	AUX
iajs-1000	134	20	a	a	DET
iajs-1000	134	21	subfamily	subfamily	NOUN
iajs-1000	134	22	of	of	ADP
iajs-1000	134	23	τ	τ	NOUN
iajs-1000	134	24	,	,	PUNCT
iajs-1000	134	25	and	and	CCONJ
iajs-1000	134	26	(	(	PUNCT
iajs-1000	134	27	x	x	NOUN
iajs-1000	134	28	,	,	PUNCT
iajs-1000	134	29	τ	τ	NOUN
iajs-1000	134	30	)	)	PUNCT
iajs-1000	134	31	is	be	AUX
iajs-1000	134	32	a	a	DET
iajs-1000	134	33	compact	compact	ADJ
iajs-1000	134	34	space	space	NOUN
iajs-1000	134	35	,	,	PUNCT
iajs-1000	134	36	then	then	ADV
iajs-1000	134	37	(	(	PUNCT
iajs-1000	134	38	x	x	X
iajs-1000	134	39	,	,	PUNCT
iajs-1000	134	40	τ	τ	PROPN
iajs-1000	134	41	,	,	PUNCT
iajs-1000	134	42	τ	τ	NOUN
iajs-1000	134	43	)	)	PUNCT
iajs-1000	134	44	is	be	AUX
iajs-1000	134	45	a	a	DET
iajs-1000	134	46	pair	pair	NOUN
iajs-1000	134	47	-	-	PUNCT
iajs-1000	134	48	wise	wise	ADJ
iajs-1000	134	49	compact	compact	ADJ
iajs-1000	134	50	if	if	SCONJ
iajs-1000	135	1	and	and	CCONJ
iajs-1000	135	2	only	only	ADV
iajs-1000	135	3	if	if	SCONJ
iajs-1000	135	4	it	it	PRON
iajs-1000	135	5	is	be	AUX
iajs-1000	135	6	an	an	DET
iajs-1000	135	7	s	s	ADJ
iajs-1000	135	8	-	-	ADJ
iajs-1000	135	9	compact	compact	ADJ
iajs-1000	135	10	space	space	NOUN
iajs-1000	135	11	.	.	PUNCT
iajs-1000	136	1	2.43	2.43	NUM
iajs-1000	136	2	remark	remark	VERB
iajs-1000	136	3	the	the	DET
iajs-1000	136	4	following	follow	VERB
iajs-1000	136	5	diagram	diagram	NOUN
iajs-1000	136	6	shows	show	VERB
iajs-1000	136	7	the	the	DET
iajs-1000	136	8	relations	relation	NOUN
iajs-1000	136	9	among	among	ADP
iajs-1000	136	10	the	the	DET
iajs-1000	136	11	different	different	ADJ
iajs-1000	136	12	types	type	NOUN
iajs-1000	136	13	of	of	ADP
iajs-1000	136	14	compactness	compactness	NOUN
iajs-1000	136	15	that	that	PRON
iajs-1000	136	16	are	be	AUX
iajs-1000	136	17	studied	study	VERB
iajs-1000	136	18	in	in	ADP
iajs-1000	136	19	this	this	DET
iajs-1000	136	20	section	section	NOUN
iajs-1000	136	21	:	:	PUNCT
iajs-1000	136	22	in	in	ADP
iajs-1000	136	23	a	a	DET
iajs-1000	136	24	bitopological	bitopological	ADJ
iajs-1000	136	25	space	space	NOUN
iajs-1000	136	26	(	(	PUNCT
iajs-1000	136	27	x	x	X
iajs-1000	136	28	,	,	PUNCT
iajs-1000	136	29	τ	τ	PROPN
iajs-1000	136	30	,	,	PUNCT
iajs-1000	136	31	τ	τ	NOUN
iajs-1000	136	32	)	)	PUNCT
iajs-1000	136	33	refrences	refrence	VERB
iajs-1000	136	34	1	1	NUM
iajs-1000	136	35	.	.	PUNCT
iajs-1000	137	1	j.c.kelly	j.c.kelly	ADV
iajs-1000	137	2	,	,	PUNCT
iajs-1000	137	3	(	(	PUNCT
iajs-1000	137	4	1963	1963	NUM
iajs-1000	137	5	)	)	PUNCT
iajs-1000	137	6	,	,	PUNCT
iajs-1000	137	7	proc	proc	NOUN
iajs-1000	137	8	.	.	PUNCT
iajs-1000	138	1	london	london	PROPN
iajs-1000	138	2	math	math	PROPN
iajs-1000	138	3	.	.	PUNCT
iajs-1000	139	1	soc	soc	PROPN
iajs-1000	139	2	.	.	PUNCT
iajs-1000	140	1	13	13	NUM
iajs-1000	140	2	,	,	PUNCT
iajs-1000	140	3	71	71	NUM
iajs-1000	140	4	-	-	SYM
iajs-1000	140	5	89	89	NUM
iajs-1000	140	6	.	.	NOUN
iajs-1000	141	1	2	2	NUM
iajs-1000	141	2	.	.	X
iajs-1000	141	3	b.dvalishvili	b.dvalishvili	NOUN
iajs-1000	141	4	,	,	PUNCT
iajs-1000	141	5	(	(	PUNCT
iajs-1000	141	6	2003	2003	NUM
iajs-1000	141	7	)	)	PUNCT
iajs-1000	141	8	,	,	PUNCT
iajs-1000	141	9	matemat	matemat	PROPN
iajs-1000	141	10	.	.	PUNCT
iajs-1000	142	1	bech	bech	PROPN
iajs-1000	142	2	.	.	PROPN
iajs-1000	142	3	,	,	PUNCT
iajs-1000	142	4	55	55	NUM
iajs-1000	142	5	,	,	PUNCT
iajs-1000	142	6	37	37	NUM
iajs-1000	142	7	-	-	SYM
iajs-1000	142	8	52	52	NUM
iajs-1000	142	9	3	3	NUM
iajs-1000	142	10	.	.	PUNCT
iajs-1000	143	1	ivan	ivan	PROPN
iajs-1000	143	2	l.reilly	l.reilly	ADV
iajs-1000	143	3	,	,	PUNCT
iajs-1000	143	4	(	(	PUNCT
iajs-1000	143	5	2005	2005	NUM
iajs-1000	143	6	)	)	PUNCT
iajs-1000	143	7	,	,	PUNCT
iajs-1000	143	8	hacettepe	hacettepe	ADJ
iajs-1000	143	9	journal	journal	NOUN
iajs-1000	143	10	of	of	ADP
iajs-1000	143	11	mathematics	mathematic	NOUN
iajs-1000	143	12	and	and	CCONJ
iajs-1000	143	13	statistics	statistic	NOUN
iajs-1000	143	14	,	,	PUNCT
iajs-1000	143	15	345	345	NUM
iajs-1000	143	16	,	,	PUNCT
iajs-1000	143	17	27	27	NUM
iajs-1000	143	18	-	-	SYM
iajs-1000	143	19	34	34	NUM
iajs-1000	143	20	.	.	NOUN
iajs-1000	143	21	4	4	NUM
iajs-1000	143	22	.	.	NOUN
iajs-1000	143	23	mrsevic	mrsevic	ADJ
iajs-1000	143	24	and	and	CCONJ
iajs-1000	143	25	i.l.reilly	i.l.reilly	ADV
iajs-1000	143	26	,	,	PUNCT
iajs-1000	143	27	(	(	PUNCT
iajs-1000	143	28	1996	1996	NUM
iajs-1000	143	29	)	)	PUNCT
iajs-1000	143	30	,	,	PUNCT
iajs-1000	143	31	indian	indian	ADJ
iajs-1000	143	32	j.pure	j.pure	NOUN
iajs-1000	143	33	appl	appl	PROPN
iajs-1000	143	34	.	.	PROPN
iajs-1000	143	35	math	math	PROPN
iajs-1000	143	36	.	.	PUNCT
iajs-1000	144	1	,	,	PUNCT
iajs-1000	144	2	27	27	NUM
iajs-1000	144	3	(	(	PUNCT
iajs-1000	144	4	10	10	NUM
iajs-1000	144	5	)	)	PUNCT
iajs-1000	144	6	,	,	PUNCT
iajs-1000	144	7	995	995	NUM
iajs-1000	144	8	-	-	SYM
iajs-1000	144	9	1004	1004	NUM
iajs-1000	144	10	,	,	PUNCT
iajs-1000	144	11	oct	oct	PROPN
iajs-1000	144	12	5	5	NUM
iajs-1000	144	13	.	.	PUNCT
iajs-1000	144	14	s.n.m	s.n.m	NOUN
iajs-1000	144	15	aheshwari	aheshwari	PROPN
iajs-1000	144	16	and	and	CCONJ
iajs-1000	144	17	s.s	s.s	PROPN
iajs-1000	144	18	.	.	PROPN
iajs-1000	144	19	thakur	thakur	PROPN
iajs-1000	144	20	,	,	PUNCT
iajs-1000	144	21	(	(	PUNCT
iajs-1000	144	22	1985	1985	NUM
iajs-1000	144	23	)	)	PUNCT
iajs-1000	144	24	,	,	PUNCT
iajs-1000	144	25	bulletin	bulletin	NOUN
iajs-1000	144	26	of	of	ADP
iajs-1000	144	27	the	the	DET
iajs-1000	144	28	institute	institute	PROPN
iajs-1000	144	29	of	of	ADP
iajs-1000	144	30	mathematics	mathematics	PROPN
iajs-1000	144	31	academia	academia	PROPN
iajs-1000	144	32	sinica	sinica	PROPN
iajs-1000	144	33	,	,	PUNCT
iajs-1000	144	34	vol	vol	NOUN
iajs-1000	144	35	.	.	PROPN
iajs-1000	144	36	13	13	NUM
iajs-1000	144	37	,	,	PUNCT
iajs-1000	144	38	no.4	no.4	PROPN
iajs-1000	144	39	,	,	PUNCT
iajs-1000	144	40	dece	dece	PROPN
iajs-1000	144	41	.	.	PROPN
iajs-1000	144	42	,	,	PUNCT
iajs-1000	144	43	341	341	NUM
iajs-1000	144	44	-	-	SYM
iajs-1000	144	45	347	347	NUM
iajs-1000	144	46	.	.	PUNCT
iajs-1000	145	1	s	s	X
iajs-1000	145	2	-	-	ADJ
iajs-1000	145	3	compact	compact	ADJ
iajs-1000	145	4	pair	pair	NOUN
iajs-1000	145	5	-	-	PUNCT
iajs-1000	145	6	wise	wise	ADJ
iajs-1000	145	7	compact	compact	ADJ
iajs-1000	145	8			ADJ
iajs-1000	145	9	–	–	NOUN
iajs-1000	145	10	both	both	PRON
iajs-1000	145	11	(	(	PUNCT
iajs-1000	145	12	x	x	X
iajs-1000	145	13	,	,	PUNCT
iajs-1000	145	14	τ	τ	X
iajs-1000	145	15	)	)	PUNCT
iajs-1000	145	16	and	and	CCONJ
iajs-1000	145	17	(	(	PUNCT
iajs-1000	145	18	x	x	NOUN
iajs-1000	145	19	,	,	PUNCT
iajs-1000	145	20	τ	τ	NOUN
iajs-1000	145	21	)	)	PUNCT
iajs-1000	145	22	are	be	AUX
iajs-1000	145	23	compact	compact	ADJ
iajs-1000	145	24	space	space	NOUN
iajs-1000	145	25	+	+	CCONJ
iajs-1000	145	26			PROPN
iajs-1000	145	27			ADJ
iajs-1000	145	28	n	n	CCONJ
iajs-1000	145	29	-	-	PUNCT
iajs-1000	145	30	compact	compact	ADJ
iajs-1000	145	31			PROPN
iajs-1000	145	32	s	s	NOUN
iajs-1000	145	33	-	-	ADJ
iajs-1000	145	34	compact	compact	ADJ
iajs-1000	145	35			ADJ
iajs-1000	145	36	pair	pair	NOUN
iajs-1000	145	37	-	-	PUNCT
iajs-1000	145	38	wise	wise	ADJ
iajs-1000	145	39	compact	compact	ADJ
iajs-1000	145	40			PROPN
iajs-1000	145	41			PROPN
iajs-1000	145	42	–	–	ADP
iajs-1000	145	43	–	–	PROPN
iajs-1000	145	44			PROPN
iajs-1000	145	45			VERB
iajs-1000	145	46	both	both	DET
iajs-1000	145	47	(	(	PUNCT
iajs-1000	145	48	x	x	X
iajs-1000	145	49	,	,	PUNCT
iajs-1000	145	50	τ	τ	X
iajs-1000	145	51	)	)	PUNCT
iajs-1000	145	52	and	and	CCONJ
iajs-1000	145	53	(	(	PUNCT
iajs-1000	145	54	x	x	NOUN
iajs-1000	145	55	,	,	PUNCT
iajs-1000	145	56	τ	τ	NOUN
iajs-1000	145	57	)	)	PUNCT
iajs-1000	145	58	are	be	AUX
iajs-1000	145	59	compact	compact	ADJ
iajs-1000	145	60	space+	space+	ADJ
iajs-1000	145	61	τ	τ	X
iajs-1000	145	62	is	be	AUX
iajs-1000	145	63	a	a	DET
iajs-1000	145	64	subfamily	subfamily	NOUN
iajs-1000	145	65	of	of	ADP
iajs-1000	145	66	τ+	τ+	NOUN
iajs-1000	145	67	للعلوم	للعلوم	PROPN
iajs-1000	145	68	الصرفة	الصرفة	PROPN
iajs-1000	145	69	والتطبیقیة	والتطبیقیة	PROPN
iajs-1000	145	70	2010	2010	NUM
iajs-1000	145	71	)	)	PUNCT
iajs-1000	145	72	1	1	NUM
iajs-1000	145	73	(	(	PUNCT
iajs-1000	145	74	23المجلد	23المجلد	NUM
iajs-1000	145	75	مجلة	مجلة	VERB
iajs-1000	145	76	ابن	ابن	PROPN
iajs-1000	145	77	الھیثم	الھیثم	PROPN
iajs-1000	145	78	انواع	انواع	PROPN
iajs-1000	145	79	الفضاءات	الفضاءات	PROPN
iajs-1000	145	80	ثنائیة	ثنائیة	PROPN
iajs-1000	145	81	الرص	الرص	NOUN
iajs-1000	145	82	بعض	بعض	NOUN
iajs-1000	145	83	أحمد	أحمد	ADJ
iajs-1000	145	84	إبراهیم	إبراهیم	ADJ
iajs-1000	145	85	ناصرنرجس	ناصرنرجس	NOUN
iajs-1000	145	86	عبد	عبد	PROPN
iajs-1000	145	87	الجبار	الجبار	NOUN
iajs-1000	145	88	،	،	PROPN
iajs-1000	146	1	قسم	قسم	PROPN
iajs-1000	147	1	الریاضیات	الریاضیات	PROPN
iajs-1000	147	2	،	،	PROPN
iajs-1000	147	3	كلیة	كلیة	PROPN
iajs-1000	147	4	التربیة	التربیة	PROPN
iajs-1000	147	5	،	،	PROPN
iajs-1000	147	6	ابن	ابن	PROPN
iajs-1000	147	7	الهیثم	الهیثم	PROPN
iajs-1000	147	8	،	،	PROPN
iajs-1000	147	9	جامعة	جامعة	PROPN
iajs-1000	147	10	بغداد	بغداد	PROPN
iajs-1000	147	11	الخالصة	الخالصة	PROPN
iajs-1000	147	12	میناها	میناها	PROPN
iajs-1000	147	13	ــات	ــات	PROPN
iajs-1000	147	14	المفتوحــة	المفتوحــة	PROPN
iajs-1000	147	15	فـــي	فـــي	PROPN
iajs-1000	147	16	الفضــاءات	الفضــاءات	PROPN
iajs-1000	147	17	التبولوجیـــة	التبولوجیـــة	PROPN
iajs-1000	147	18	الثنائیــة	الثنائیــة	PROPN
iajs-1000	147	19	اســـ	اســـ	PROPN
iajs-1000	147	20	ـا	ـا	PROPN
iajs-1000	147	21	فــي	فــي	ADJ
iajs-1000	147	22	هـــذا	هـــذا	NOUN
iajs-1000	147	23	البحــث	البحــث	PROPN
iajs-1000	147	24	بتعریـــف	بتعریـــف	PROPN
iajs-1000	147	25	نــوع	نــوع	PROPN
iajs-1000	147	26	جدیـــد	جدیـــد	NOUN
iajs-1000	147	27	مــن	مــن	PROPN
iajs-1000	147	28	المجموعـ	المجموعـ	PROPN
iajs-1000	147	29	قمنـ	قمنـ	PROPN
iajs-1000	148	1	هــذا	هــذا	PROPN
iajs-1000	148	2	المفهــوم	المفهــوم	PROPN
iajs-1000	148	3	فـــي	فـــي	PROPN
iajs-1000	148	4	مــن	مــن	PROPN
iajs-1000	148	5	ثــم	ثــم	PROPN
iajs-1000	148	6	أســتعملنا	أســتعملنا	PROPN
iajs-1000	148	7	هــو	هــو	PROPN
iajs-1000	148	8	الحــرف	الحــرف	NOUN
iajs-1000	148	9	االول	االول	PROPN
iajs-1000	148	10	الســم	الســم	ADJ
iajs-1000	148	11	أحــد	أحــد	NOUN
iajs-1000	148	12	البــاحثین	البــاحثین	NOUN
iajs-1000	148	13	و	و	PROPN
iajs-1000	148	14	nان	nان	NOUN
iajs-1000	148	15	إذ	إذ	NOUN
iajs-1000	148	16	n	n	PROPN
iajs-1000	148	17	–	–	PUNCT
iajs-1000	148	18	ن	ن	PRON
iajs-1000	148	19	نــوع	نــوع	PROPN
iajs-1000	148	20	المجموعــات	المجموعــات	PROPN
iajs-1000	148	21	المفتوحــة	المفتوحــة	PROPN
iajs-1000	148	22	مــ	مــ	NOUN
iajs-1000	148	23	.في	.في	PUNCT
iajs-1000	149	1	الفضاءات	الفضاءات	PROPN
iajs-1000	149	2	الثنائیة	الثنائیة	ADV
iajs-1000	149	3	n	n	CCONJ
iajs-1000	149	4	–	–	PUNCT
iajs-1000	149	5	وكذلك	وكذلك	NOUN
iajs-1000	149	6	عرفنا	عرفنا	NOUN
iajs-1000	149	7	الدالة	الدالة	PROPN
iajs-1000	149	8	المستمرة	المستمرة	PROPN
iajs-1000	149	9	من	من	PROPN
iajs-1000	149	10	نوع	نوع	PROPN
iajs-1000	149	11	n	n	CCONJ
iajs-1000	149	12	–	–	PUNCT
iajs-1000	149	13	تعریف	تعریف	NOUN
iajs-1000	149	14	نوع	نوع	X
iajs-1000	149	15	جدید	جدید	PROPN
iajs-1000	149	16	من	من	PROPN
iajs-1000	149	17	التراص	التراص	PROPN
iajs-1000	149	18	وهو	وهو	PROPN
iajs-1000	149	19	التراص	التراص	PROPN
iajs-1000	149	20	من	من	PROPN
iajs-1000	149	21	نوع	نوع	PROPN
iajs-1000	149	22	ذا	ذا	PROPN
iajs-1000	149	23	النـوع	النـوع	PROPN
iajs-1000	149	24	بنـوعین	بنـوعین	PROPN
iajs-1000	149	25	آخـرین	آخـرین	PROPN
iajs-1000	149	26	معـروفین	معـروفین	PROPN
iajs-1000	149	27	همـا	همـا	PROPN
iajs-1000	149	28	التـراص	التـراص	PROPN
iajs-1000	149	29	كما	كما	PROPN
iajs-1000	149	30	درسنا	درسنا	ADV
iajs-1000	149	31	عالقـة	عالقـة	ADV
iajs-1000	149	32	هـ	هـ	ADP
iajs-1000	149	33	n	n	PROPN
iajs-1000	149	34	–	–	PUNCT
iajs-1000	149	35	ولقد	ولقد	NOUN
iajs-1000	149	36	درسنا	درسنا	ADJ
iajs-1000	149	37	بعض	بعض	NOUN
iajs-1000	149	38	الخواص	الخواص	PROPN
iajs-1000	149	39	للتراص	للتراص	NOUN
iajs-1000	149	40	من	من	PRON
iajs-1000	149	41	نوع	نوع	PROPN
iajs-1000	149	42	.والتراص	.والتراص	INTJ
iajs-1000	149	43	الثنائي	الثنائي	NOUN
iajs-1000	149	44	s	s	PART
iajs-1000	149	45	–	–	PUNCT
iajs-1000	149	46	من	من	DET
iajs-1000	149	47	نوع	نوع	NOUN