id	sid	tid	token	lemma	pos
iajs-807	1	1	ibn	ibn	PROPN
iajs-807	1	2	alhaitham	alhaitham	NOUN
iajs-807	1	3	j.	j.	PROPN
iajs-807	1	4	for	for	ADP
iajs-807	1	5	pure	pure	ADJ
iajs-807	1	6	&	&	CCONJ
iajs-807	1	7	appl	appl	PROPN
iajs-807	1	8	.	.	PUNCT
iajs-807	2	1	sci	sci	PROPN
iajs-807	2	2	.	.	PUNCT
iajs-807	2	3	vol.24	vol.24	NOUN
iajs-807	2	4	(	(	PUNCT
iajs-807	2	5	3	3	NUM
iajs-807	2	6	)	)	PUNCT
iajs-807	2	7	2011	2011	NUM
iajs-807	2	8			PROPN
iajs-807	2	9	-generalized	-generalized	ADJ
iajs-807	2	10	bclosed	bclose	VERB
iajs-807	2	11	sets	set	NOUN
iajs-807	2	12	in	in	ADP
iajs-807	2	13	topological	topological	ADJ
iajs-807	2	14	spaces	space	NOUN
iajs-807	2	15	a.	a.	PROPN
iajs-807	2	16	k.	k.	PROPN
iajs-807	2	17	al	al	PROPN
iajs-807	2	18	-	-	PUNCT
iajs-807	2	19	obiadi	obiadi	PROPN
iajs-807	2	20	department	department	NOUN
iajs-807	2	21	of	of	ADP
iajs-807	2	22	mathematics	mathematics	PROPN
iajs-807	2	23	,	,	PUNCT
iajs-807	2	24	college	college	NOUN
iajs-807	2	25	of	of	ADP
iajs-807	2	26	basic	basic	ADJ
iajs-807	2	27	education	education	NOUN
iajs-807	2	28	university	university	PROPN
iajs-807	2	29	of	of	ADP
iajs-807	2	30	almustansiryah	almustansiryah	PROPN
iajs-807	2	31	received	receive	VERB
iajs-807	2	32	in	in	ADP
iajs-807	2	33	:	:	PUNCT
iajs-807	2	34	10	10	NUM
iajs-807	2	35	may	may	PROPN
iajs-807	2	36	2011	2011	NUM
iajs-807	2	37	accepted	accept	VERB
iajs-807	2	38	in	in	ADP
iajs-807	2	39	:	:	PUNCT
iajs-807	2	40	16	16	NUM
iajs-807	2	41	june	june	PROPN
iajs-807	2	42	2011	2011	NUM
iajs-807	2	43	abstract	abstract	ADV
iajs-807	2	44	in	in	ADP
iajs-807	2	45	this	this	DET
iajs-807	2	46	paper	paper	NOUN
iajs-807	2	47	we	we	PRON
iajs-807	2	48	introduce	introduce	VERB
iajs-807	2	49	a	a	DET
iajs-807	2	50	new	new	ADJ
iajs-807	2	51	class	class	NOUN
iajs-807	2	52	of	of	ADP
iajs-807	2	53	sets	set	NOUN
iajs-807	2	54	called	call	VERB
iajs-807	2	55			PROPN
iajs-807	3	1	generalized	generalize	VERB
iajs-807	3	2	bclosed	bclose	VERB
iajs-807	3	3	(	(	PUNCT
iajs-807	3	4	briefly	briefly	ADV
iajs-807	3	5			ADJ
iajs-807	3	6	gb	gb	NOUN
iajs-807	3	7	closed	closed	ADJ
iajs-807	3	8	)	)	PUNCT
iajs-807	3	9	sets	set	NOUN
iajs-807	3	10	.	.	PUNCT
iajs-807	4	1	we	we	PRON
iajs-807	4	2	study	study	VERB
iajs-807	4	3	some	some	PRON
iajs-807	4	4	of	of	ADP
iajs-807	4	5	its	its	PRON
iajs-807	4	6	basic	basic	ADJ
iajs-807	4	7	properties	property	NOUN
iajs-807	4	8	.	.	PUNCT
iajs-807	5	1	this	this	DET
iajs-807	5	2	class	class	NOUN
iajs-807	5	3	of	of	ADP
iajs-807	5	4	sets	set	NOUN
iajs-807	5	5	is	be	AUX
iajs-807	5	6	strictly	strictly	ADV
iajs-807	5	7	placed	place	VERB
iajs-807	5	8	between	between	ADP
iajs-807	5	9	the	the	DET
iajs-807	5	10	class	class	NOUN
iajs-807	5	11	of	of	ADP
iajs-807	5	12			ADJ
iajs-807	5	13	gpclosed	gpclose	VERB
iajs-807	5	14	sets	set	NOUN
iajs-807	5	15	and	and	CCONJ
iajs-807	5	16	the	the	DET
iajs-807	5	17	class	class	NOUN
iajs-807	5	18	of	of	ADP
iajs-807	5	19			ADJ
iajs-807	5	20	gspclosed	gspclosed	ADJ
iajs-807	5	21	sets	set	NOUN
iajs-807	5	22	.	.	PUNCT
iajs-807	6	1	further	far	ADV
iajs-807	6	2	the	the	DET
iajs-807	6	3	notion	notion	NOUN
iajs-807	6	4	of	of	ADP
iajs-807	6	5			PROPN
iajs-807	6	6	b	b	NOUN
iajs-807	6	7	2	2	NUM
iajs-807	6	8	1	1	NUM
iajs-807	6	9	t	t	NOUN
iajs-807	6	10	space	space	NOUN
iajs-807	6	11	is	be	AUX
iajs-807	6	12	introduced	introduce	VERB
iajs-807	6	13	and	and	CCONJ
iajs-807	6	14	studied	study	VERB
iajs-807	6	15	.	.	PUNCT
iajs-807	7	1	2000	2000	NUM
iajs-807	7	2	mathematics	mathematic	NOUN
iajs-807	7	3	subject	subject	ADJ
iajs-807	7	4	classification	classification	NOUN
iajs-807	7	5	:	:	PUNCT
iajs-807	7	6	54a05	54a05	NUM
iajs-807	7	7	keywords	keyword	NOUN
iajs-807	7	8	:	:	PUNCT
iajs-807	7	9	bopen	bopen	VERB
iajs-807	7	10	set	set	VERB
iajs-807	7	11	,	,	PUNCT
iajs-807	7	12	regular	regular	ADJ
iajs-807	7	13	open	open	ADJ
iajs-807	7	14	set	set	NOUN
iajs-807	7	15	,	,	PUNCT
iajs-807	7	16			PROPN
iajs-807	7	17	-generalized	-generalized	ADJ
iajs-807	7	18	bclosed	bclose	VERB
iajs-807	7	19	set	set	NOUN
iajs-807	7	20	.	.	PUNCT
iajs-807	8	1	1	1	X
iajs-807	8	2	.	.	X
iajs-807	8	3	introduction	introduction	NOUN
iajs-807	8	4	and	and	CCONJ
iajs-807	8	5	prelimimnaries	prelimimnarie	NOUN
iajs-807	8	6	.	.	PUNCT
iajs-807	9	1	park[1	park[1	NOUN
iajs-807	9	2	]	]	PUNCT
iajs-807	9	3	introduced	introduce	VERB
iajs-807	9	4	the	the	DET
iajs-807	9	5	class	class	NOUN
iajs-807	9	6	of	of	ADP
iajs-807	9	7			PROPN
iajs-807	9	8	-generalized	-generalized	ADJ
iajs-807	9	9	pre	pre	NOUN
iajs-807	9	10	-	-	ADJ
iajs-807	9	11	closed(briefly	closed(briefly	ADJ
iajs-807	9	12			ADJ
iajs-807	9	13	gp	gp	NOUN
iajs-807	9	14	closed	close	VERB
iajs-807	9	15	)	)	PUNCT
iajs-807	9	16	sets	set	NOUN
iajs-807	9	17	and	and	CCONJ
iajs-807	9	18	the	the	DET
iajs-807	9	19	class	class	NOUN
iajs-807	9	20	of	of	ADP
iajs-807	9	21			PROPN
iajs-807	9	22	-generalized	-generalized	ADJ
iajs-807	9	23	semipreopen	semipreopen	NOUN
iajs-807	9	24	closed	close	VERB
iajs-807	9	25	(	(	PUNCT
iajs-807	9	26	briefly	briefly	NOUN
iajs-807	9	27			PROPN
iajs-807	9	28	gsp	gsp	NOUN
iajs-807	9	29	closed	close	VERB
iajs-807	9	30	)	)	PUNCT
iajs-807	9	31	sets	set	NOUN
iajs-807	9	32	was	be	AUX
iajs-807	9	33	introduced	introduce	VERB
iajs-807	9	34	by	by	ADP
iajs-807	9	35	sarsak	sarsak	NOUN
iajs-807	10	1	[	[	X
iajs-807	10	2	2	2	NUM
iajs-807	10	3	]	]	PUNCT
iajs-807	10	4	as	as	ADP
iajs-807	10	5	a	a	DET
iajs-807	10	6	generalization	generalization	NOUN
iajs-807	10	7	of	of	ADP
iajs-807	10	8	closed	closed	ADJ
iajs-807	10	9	sets	set	NOUN
iajs-807	10	10	.	.	PUNCT
iajs-807	11	1	in	in	ADP
iajs-807	11	2	this	this	DET
iajs-807	11	3	paper	paper	NOUN
iajs-807	11	4	we	we	PRON
iajs-807	11	5	define	define	VERB
iajs-807	11	6	and	and	CCONJ
iajs-807	11	7	study	study	VERB
iajs-807	11	8	a	a	DET
iajs-807	11	9	new	new	ADJ
iajs-807	11	10	class	class	NOUN
iajs-807	11	11	of	of	ADP
iajs-807	11	12			ADJ
iajs-807	11	13	generalized	generalize	VERB
iajs-807	11	14	closed	closed	ADJ
iajs-807	11	15	sets	set	NOUN
iajs-807	11	16	,	,	PUNCT
iajs-807	11	17	we	we	PRON
iajs-807	11	18	denote	denote	VERB
iajs-807	11	19	by	by	ADP
iajs-807	11	20			PROPN
iajs-807	11	21	-generalized	-generalized	ADJ
iajs-807	11	22	bclosed	bclose	VERB
iajs-807	11	23	(	(	PUNCT
iajs-807	11	24	briefly	briefly	NOUN
iajs-807	11	25			ADJ
iajs-807	11	26	gbclosed	gbclosed	ADJ
iajs-807	11	27	)	)	PUNCT
iajs-807	11	28	sets	set	NOUN
iajs-807	11	29	,	,	PUNCT
iajs-807	11	30	which	which	PRON
iajs-807	11	31	is	be	AUX
iajs-807	11	32	strictly	strictly	ADV
iajs-807	11	33	placed	place	VERB
iajs-807	11	34	between	between	ADP
iajs-807	11	35	the	the	DET
iajs-807	11	36	class	class	NOUN
iajs-807	11	37	of	of	ADP
iajs-807	11	38			PROPN
iajs-807	11	39	gpclosed	gpclose	VERB
iajs-807	11	40	set	set	NOUN
iajs-807	11	41	and	and	CCONJ
iajs-807	11	42			ADJ
iajs-807	11	43	gspclosed	gspclosed	ADJ
iajs-807	11	44	sets	set	NOUN
iajs-807	11	45	.	.	PUNCT
iajs-807	12	1	moreover	moreover	ADV
iajs-807	12	2	,	,	PUNCT
iajs-807	12	3	we	we	PRON
iajs-807	12	4	define	define	VERB
iajs-807	12	5			PROPN
iajs-807	12	6	b2	b2	NOUN
iajs-807	12	7	1	1	NUM
iajs-807	12	8	t	t	NOUN
iajs-807	12	9	space	space	NOUN
iajs-807	12	10	as	as	ADP
iajs-807	12	11	the	the	DET
iajs-807	12	12	space	space	NOUN
iajs-807	12	13	in	in	ADP
iajs-807	12	14	which	which	PRON
iajs-807	12	15	every	every	DET
iajs-807	12	16			NOUN
iajs-807	12	17	gbclosed	gbclose	VERB
iajs-807	12	18	set	set	NOUN
iajs-807	12	19	is	be	AUX
iajs-807	12	20	bclosed	bclose	VERB
iajs-807	12	21	.	.	PUNCT
iajs-807	13	1	throughout	throughout	ADP
iajs-807	13	2	this	this	DET
iajs-807	13	3	paper	paper	NOUN
iajs-807	13	4	)	)	PUNCT
iajs-807	13	5	,	,	PUNCT
iajs-807	13	6	(	(	PUNCT
iajs-807	13	7	x	x	PROPN
iajs-807	13	8	and	and	CCONJ
iajs-807	13	9	)	)	PUNCT
iajs-807	13	10	,	,	PUNCT
iajs-807	13	11	(	(	PUNCT
iajs-807	13	12	y	y	PROPN
iajs-807	13	13	represent	represent	VERB
iajs-807	13	14	nonempty	nonempty	ADJ
iajs-807	13	15	topological	topological	ADJ
iajs-807	13	16	spaces	space	NOUN
iajs-807	13	17	on	on	ADP
iajs-807	13	18	which	which	PRON
iajs-807	13	19	no	no	DET
iajs-807	13	20	separation	separation	NOUN
iajs-807	13	21	axioms	axiom	NOUN
iajs-807	13	22	are	be	AUX
iajs-807	13	23	assumed	assume	VERB
iajs-807	13	24	unless	unless	SCONJ
iajs-807	13	25	otherwise	otherwise	ADV
iajs-807	13	26	mentioned	mention	VERB
iajs-807	13	27	.	.	PUNCT
iajs-807	14	1	for	for	ADP
iajs-807	14	2	a	a	DET
iajs-807	14	3	subset	subset	NOUN
iajs-807	14	4	a	a	PRON
iajs-807	14	5	of	of	ADP
iajs-807	14	6	a	a	DET
iajs-807	14	7	space	space	NOUN
iajs-807	14	8	)	)	PUNCT
iajs-807	14	9	,	,	PUNCT
iajs-807	14	10	(	(	PUNCT
iajs-807	14	11	x	x	PROPN
iajs-807	14	12	,	,	PUNCT
iajs-807	14	13	cl(a	cl(a	NUM
iajs-807	14	14	)	)	PUNCT
iajs-807	14	15	,	,	PUNCT
iajs-807	14	16	int(a	int(a	PROPN
iajs-807	14	17	)	)	PUNCT
iajs-807	14	18	and	and	CCONJ
iajs-807	14	19	p(x	p(x	PROPN
iajs-807	14	20	)	)	PUNCT
iajs-807	14	21	denote	denote	VERB
iajs-807	14	22	the	the	DET
iajs-807	14	23	closure	closure	NOUN
iajs-807	14	24	,	,	PUNCT
iajs-807	14	25	the	the	DET
iajs-807	14	26	interior	interior	ADJ
iajs-807	14	27	and	and	CCONJ
iajs-807	14	28	power	power	NOUN
iajs-807	14	29	set	set	NOUN
iajs-807	14	30	of	of	ADP
iajs-807	14	31	a	a	DET
iajs-807	14	32	respectively	respectively	ADV
iajs-807	14	33	.	.	PUNCT
iajs-807	14	34	)	)	PUNCT
iajs-807	15	1	,	,	PUNCT
iajs-807	15	2	(	(	PUNCT
iajs-807	15	3	x	x	PROPN
iajs-807	15	4	will	will	AUX
iajs-807	15	5	be	be	AUX
iajs-807	15	6	replaced	replace	VERB
iajs-807	15	7	by	by	ADP
iajs-807	15	8	x	x	PUNCT
iajs-807	15	9	if	if	SCONJ
iajs-807	15	10	there	there	PRON
iajs-807	15	11	is	be	VERB
iajs-807	15	12	no	no	DET
iajs-807	15	13	confusion	confusion	NOUN
iajs-807	15	14	.	.	PUNCT
iajs-807	16	1	let	let	VERB
iajs-807	16	2	us	we	PRON
iajs-807	16	3	recall	recall	VERB
iajs-807	16	4	the	the	DET
iajs-807	16	5	following	follow	VERB
iajs-807	16	6	definitions	definition	NOUN
iajs-807	16	7	which	which	PRON
iajs-807	16	8	are	be	AUX
iajs-807	16	9	useful	useful	ADJ
iajs-807	16	10	in	in	ADP
iajs-807	16	11	the	the	DET
iajs-807	16	12	sequel	sequel	NOUN
iajs-807	16	13	.	.	PUNCT
iajs-807	17	1	definition	definition	NOUN
iajs-807	17	2	1.1	1.1	NUM
iajs-807	17	3	.	.	PUNCT
iajs-807	18	1	a	a	DET
iajs-807	18	2	subset	subset	NOUN
iajs-807	18	3	a	a	PRON
iajs-807	18	4	of	of	ADP
iajs-807	18	5	a	a	DET
iajs-807	18	6	space	space	NOUN
iajs-807	18	7	x	x	PUNCT
iajs-807	18	8	is	be	AUX
iajs-807	18	9	called	call	VERB
iajs-807	18	10	:	:	PUNCT
iajs-807	18	11	(	(	PUNCT
iajs-807	18	12	1	1	X
iajs-807	18	13	)	)	PUNCT
iajs-807	18	14	semiopen	semiopen	VERB
iajs-807	18	15	if	if	SCONJ
iajs-807	18	16	)	)	PUNCT
iajs-807	18	17	)	)	PUNCT
iajs-807	19	1	(	(	PUNCT
iajs-807	19	2	int(acla	int(acla	PRON
iajs-807	19	3			PROPN
iajs-807	19	4	and	and	CCONJ
iajs-807	19	5	semiclosed	semiclose	VERB
iajs-807	19	6	if	if	SCONJ
iajs-807	19	7	aacl	aacl	PROPN
iajs-807	19	8	))(int	))(int	PROPN
iajs-807	19	9	(	(	PUNCT
iajs-807	19	10	.[3	.[3	NOUN
iajs-807	19	11	]	]	X
iajs-807	19	12	(	(	PUNCT
iajs-807	19	13	2	2	X
iajs-807	19	14	)	)	PUNCT
iajs-807	19	15			NOUN
iajs-807	19	16	open	open	VERB
iajs-807	19	17	if	if	SCONJ
iajs-807	19	18	)	)	PUNCT
iajs-807	19	19	)	)	PUNCT
iajs-807	19	20	)	)	PUNCT
iajs-807	19	21	(	(	PUNCT
iajs-807	19	22	int(int	int(int	NOUN
iajs-807	19	23	(	(	PUNCT
iajs-807	19	24	acla	acla	VERB
iajs-807	19	25			PROPN
iajs-807	19	26	and	and	CCONJ
iajs-807	19	27			NOUN
iajs-807	19	28	closed	close	VERB
iajs-807	19	29	if	if	SCONJ
iajs-807	19	30	aaclcl	aaclcl	VERB
iajs-807	19	31	)))((int	)))((int	NOUN
iajs-807	19	32	(	(	PUNCT
iajs-807	19	33	.[4	.[4	NOUN
iajs-807	19	34	]	]	PUNCT
iajs-807	19	35	.	.	PUNCT
iajs-807	20	1	ibn	ibn	PROPN
iajs-807	20	2	alhaitham	alhaitham	PROPN
iajs-807	20	3	j.	j.	PROPN
iajs-807	20	4	for	for	ADP
iajs-807	20	5	pure	pure	ADJ
iajs-807	20	6	&	&	CCONJ
iajs-807	20	7	appl	appl	PROPN
iajs-807	20	8	.	.	PUNCT
iajs-807	21	1	sci	sci	PROPN
iajs-807	21	2	.	.	PUNCT
iajs-807	21	3	vol.24	vol.24	NOUN
iajs-807	21	4	(	(	PUNCT
iajs-807	21	5	3	3	NUM
iajs-807	21	6	)	)	PUNCT
iajs-807	21	7	2011	2011	NUM
iajs-807	21	8	(	(	PUNCT
iajs-807	21	9	3	3	X
iajs-807	21	10	)	)	PUNCT
iajs-807	21	11	preopenif	preopenif	NOUN
iajs-807	21	12	)	)	PUNCT
iajs-807	21	13	)	)	PUNCT
iajs-807	22	1	(	(	PUNCT
iajs-807	22	2	int	int	NOUN
iajs-807	22	3	(	(	PUNCT
iajs-807	22	4	acla	acla	VERB
iajs-807	22	5			PROPN
iajs-807	22	6	and	and	CCONJ
iajs-807	22	7	preclosed	preclose	VERB
iajs-807	22	8	set	set	VERB
iajs-807	22	9	if	if	SCONJ
iajs-807	22	10	aacl	aacl	PROPN
iajs-807	22	11	))(int	))(int	PROPN
iajs-807	22	12	(	(	PUNCT
iajs-807	22	13	.[5	.[5	ADV
iajs-807	22	14	]	]	X
iajs-807	22	15	(	(	PUNCT
iajs-807	22	16	4	4	X
iajs-807	22	17	)	)	PUNCT
iajs-807	22	18	semipreopenif	semipreopenif	NOUN
iajs-807	22	19	)	)	PUNCT
iajs-807	22	20	)	)	PUNCT
iajs-807	22	21	)	)	PUNCT
iajs-807	22	22	(	(	PUNCT
iajs-807	22	23	(	(	PUNCT
iajs-807	22	24	int	int	NOUN
iajs-807	22	25	(	(	PUNCT
iajs-807	22	26	aclcla	aclcla	NOUN
iajs-807	22	27			PROPN
iajs-807	22	28	and	and	CCONJ
iajs-807	22	29	a	a	DET
iajs-807	22	30	semipreclosed	semipreclose	VERB
iajs-807	22	31	if	if	SCONJ
iajs-807	22	32	.)))(int(int	.)))(int(int	PROPN
iajs-807	22	33	(	(	PUNCT
iajs-807	22	34	aacl	aacl	PROPN
iajs-807	22	35			PROPN
iajs-807	23	1	[	[	X
iajs-807	23	2	6	6	NUM
iajs-807	23	3	]	]	PUNCT
iajs-807	23	4	(	(	PUNCT
iajs-807	23	5	5	5	NUM
iajs-807	23	6	)	)	PUNCT
iajs-807	23	7	regular	regular	ADJ
iajs-807	23	8	openif	openif	NOUN
iajs-807	23	9	)	)	PUNCT
iajs-807	23	10	)	)	PUNCT
iajs-807	24	1	(	(	PUNCT
iajs-807	24	2	int	int	NOUN
iajs-807	24	3	(	(	PUNCT
iajs-807	24	4	acla	acla	VERB
iajs-807	24	5			NOUN
iajs-807	24	6	and	and	CCONJ
iajs-807	24	7	a	a	DET
iajs-807	24	8	regular	regular	ADJ
iajs-807	24	9	closed	closed	ADJ
iajs-807	24	10	set	set	NOUN
iajs-807	24	11	if	if	SCONJ
iajs-807	24	12	)	)	PUNCT
iajs-807	24	13	)	)	PUNCT
iajs-807	24	14	(	(	PUNCT
iajs-807	24	15	int(acla	int(acla	PRON
iajs-807	24	16			VERB
iajs-807	24	17	.[7	.[7	NOUN
iajs-807	24	18	]	]	X
iajs-807	24	19	(	(	PUNCT
iajs-807	24	20	6	6	X
iajs-807	24	21	)	)	PUNCT
iajs-807	24	22	bopen	bopen	VERB
iajs-807	24	23	if	if	SCONJ
iajs-807	24	24	)	)	PUNCT
iajs-807	24	25	)	)	PUNCT
iajs-807	24	26	(	(	PUNCT
iajs-807	24	27	int())(int	int())(int	NOUN
iajs-807	24	28	(	(	PUNCT
iajs-807	24	29	aclacla	aclacla	ADJ
iajs-807	24	30			NOUN
iajs-807	24	31	and	and	CCONJ
iajs-807	24	32	bclosed	bclose	VERB
iajs-807	24	33	if	if	SCONJ
iajs-807	24	34	.))(int())(int	.))(int())(int	PROPN
iajs-807	24	35	(	(	PUNCT
iajs-807	24	36	aaclacl	aaclacl	PROPN
iajs-807	24	37			NOUN
iajs-807	24	38	[	[	X
iajs-807	24	39	8	8	NUM
iajs-807	24	40	]	]	SYM
iajs-807	24	41	(	(	PUNCT
iajs-807	24	42	7	7	NUM
iajs-807	24	43	)	)	PUNCT
iajs-807	24	44			NOUN
iajs-807	24	45	open	open	ADJ
iajs-807	24	46	if	if	SCONJ
iajs-807	24	47	a	a	PRON
iajs-807	24	48	is	be	AUX
iajs-807	24	49	the	the	DET
iajs-807	24	50	union	union	NOUN
iajs-807	24	51	of	of	ADP
iajs-807	24	52	regular	regular	ADJ
iajs-807	24	53	open	open	ADJ
iajs-807	24	54	sets	set	NOUN
iajs-807	24	55	,	,	PUNCT
iajs-807	24	56	and	and	CCONJ
iajs-807	24	57			PROPN
iajs-807	24	58	-closed	-close	VERB
iajs-807	24	59	if	if	SCONJ
iajs-807	24	60	a	a	PRON
iajs-807	24	61	is	be	AUX
iajs-807	24	62	the	the	DET
iajs-807	24	63	intersection	intersection	NOUN
iajs-807	24	64	of	of	ADP
iajs-807	24	65	regular	regular	ADJ
iajs-807	24	66	closed	closed	ADJ
iajs-807	24	67	sets	set	NOUN
iajs-807	24	68	.	.	PUNCT
iajs-807	25	1	[	[	X
iajs-807	25	2	9	9	NUM
iajs-807	25	3	]	]	PUNCT
iajs-807	25	4	the	the	DET
iajs-807	25	5	binterior	binterior	ADJ
iajs-807	25	6	(	(	PUNCT
iajs-807	25	7	briefly	briefly	NOUN
iajs-807	25	8	bint	bint	NOUN
iajs-807	25	9	)	)	PUNCT
iajs-807	25	10	of	of	ADP
iajs-807	25	11	a	a	DET
iajs-807	25	12	subset	subset	NOUN
iajs-807	25	13	a	a	PRON
iajs-807	25	14	of	of	ADP
iajs-807	25	15	x	x	SYM
iajs-807	25	16	is	be	AUX
iajs-807	25	17	the	the	DET
iajs-807	25	18	union	union	NOUN
iajs-807	25	19	of	of	ADP
iajs-807	25	20	all	all	DET
iajs-807	25	21	bopen	bopen	NOUN
iajs-807	25	22	sets	set	NOUN
iajs-807	25	23	contained	contain	VERB
iajs-807	25	24	in	in	ADP
iajs-807	25	25	a.	a.	NOUN
iajs-807	25	26	the	the	DET
iajs-807	25	27	bclosure	bclosure	NOUN
iajs-807	25	28	(	(	PUNCT
iajs-807	25	29	resp	resp	NOUN
iajs-807	25	30	.	.	PUNCT
iajs-807	26	1	pre	pre	ADJ
iajs-807	26	2	-	-	ADJ
iajs-807	26	3	closure	closure	ADJ
iajs-807	26	4	,	,	PUNCT
iajs-807	26	5	semipreclosure	semipreclosure	NOUN
iajs-807	26	6	)	)	PUNCT
iajs-807	26	7	of	of	ADP
iajs-807	26	8	a	a	PRON
iajs-807	26	9	is	be	AUX
iajs-807	26	10	the	the	DET
iajs-807	26	11	intersection	intersection	NOUN
iajs-807	26	12	of	of	ADP
iajs-807	26	13	all	all	DET
iajs-807	26	14	b	b	NOUN
iajs-807	26	15	-	-	PUNCT
iajs-807	26	16	closed	closed	ADJ
iajs-807	26	17	(	(	PUNCT
iajs-807	26	18	resp	resp	NOUN
iajs-807	26	19	.	.	PUNCT
iajs-807	27	1	preclosed	preclose	VERB
iajs-807	27	2	,	,	PUNCT
iajs-807	27	3	semipreclosed	semipreclose	VERB
iajs-807	27	4	)	)	PUNCT
iajs-807	27	5	sets	set	NOUN
iajs-807	27	6	containing	contain	VERB
iajs-807	27	7	a	a	PRON
iajs-807	27	8	,	,	PUNCT
iajs-807	27	9	and	and	CCONJ
iajs-807	27	10	is	be	AUX
iajs-807	27	11	denoted	denote	VERB
iajs-807	27	12	by	by	ADP
iajs-807	27	13	bcl(a	bcl(a	PROPN
iajs-807	27	14	)	)	PUNCT
iajs-807	27	15	(	(	PUNCT
iajs-807	27	16	resp.pcl(a	resp.pcl(a	NOUN
iajs-807	27	17	)	)	PUNCT
iajs-807	27	18	,	,	PUNCT
iajs-807	27	19	spcl(a	spcl(a	NUM
iajs-807	27	20	)	)	PUNCT
iajs-807	27	21	)	)	PUNCT
iajs-807	27	22	.	.	PUNCT
iajs-807	28	1	the	the	DET
iajs-807	28	2	collection	collection	NOUN
iajs-807	28	3	of	of	ADP
iajs-807	28	4	all	all	PRON
iajs-807	28	5	bopen	bopen	NOUN
iajs-807	28	6	(	(	PUNCT
iajs-807	28	7	resp	resp	NOUN
iajs-807	28	8	.	.	PUNCT
iajs-807	28	9	bclosed	bclose	VERB
iajs-807	28	10	)	)	PUNCT
iajs-807	28	11	sets	set	NOUN
iajs-807	28	12	is	be	AUX
iajs-807	28	13	denoted	denote	VERB
iajs-807	28	14	by	by	ADP
iajs-807	28	15	bo(x	bo(x	NUM
iajs-807	28	16	)	)	PUNCT
iajs-807	28	17	(	(	PUNCT
iajs-807	28	18	resp	resp	NOUN
iajs-807	28	19	.	.	PUNCT
iajs-807	29	1	bc(x)).[8	bc(x)).[8	NOUN
iajs-807	29	2	]	]	X
iajs-807	30	1	it	it	PRON
iajs-807	30	2	is	be	AUX
iajs-807	30	3	well	well	ADV
iajs-807	30	4	known	know	VERB
iajs-807	30	5	that	that	SCONJ
iajs-807	30	6	:	:	PUNCT
iajs-807	30	7	(	(	PUNCT
iajs-807	30	8	1	1	X
iajs-807	30	9	)	)	PUNCT
iajs-807	30	10			NOUN
iajs-807	30	11	open	open	VERB
iajs-807	30	12	set	set	ADJ
iajs-807	30	13	preopen	preopen	ADJ
iajs-807	30	14	set	set	ADJ
iajs-807	30	15	bopen	bopen	NOUN
iajs-807	30	16	set	set	VERB
iajs-807	30	17			NOUN
iajs-807	30	18	semipreopen.[8	semipreopen.[8	NOUN
iajs-807	30	19	]	]	X
iajs-807	30	20	(	(	PUNCT
iajs-807	30	21	2	2	X
iajs-807	30	22	)	)	PUNCT
iajs-807	30	23	the	the	DET
iajs-807	30	24	intersection	intersection	NOUN
iajs-807	30	25	of	of	ADP
iajs-807	30	26	a	a	DET
iajs-807	30	27	bopen	bopen	NOUN
iajs-807	30	28	set	set	VERB
iajs-807	30	29	with	with	ADP
iajs-807	30	30			NOUN
iajs-807	30	31	open	open	ADJ
iajs-807	30	32	set	set	NOUN
iajs-807	30	33	is	be	AUX
iajs-807	30	34	bopen.[8	bopen.[8	NUM
iajs-807	30	35	]	]	PUNCT
iajs-807	30	36	definition	definition	NOUN
iajs-807	30	37	1.2	1.2	NUM
iajs-807	30	38	.	.	PUNCT
iajs-807	31	1	a	a	DET
iajs-807	31	2	subset	subset	NOUN
iajs-807	31	3	a	a	PRON
iajs-807	31	4	of	of	ADP
iajs-807	31	5	a	a	DET
iajs-807	31	6	space	space	NOUN
iajs-807	31	7	x	x	PUNCT
iajs-807	31	8	is	be	AUX
iajs-807	31	9	called	call	VERB
iajs-807	31	10	:	:	PUNCT
iajs-807	31	11	(	(	PUNCT
iajs-807	31	12	1	1	X
iajs-807	31	13	)	)	PUNCT
iajs-807	31	14	generalized	generalize	VERB
iajs-807	31	15	closed	close	VERB
iajs-807	31	16	(	(	PUNCT
iajs-807	31	17	briefly	briefly	ADV
iajs-807	31	18	gclosed	gclose	VERB
iajs-807	31	19	)	)	PUNCT
iajs-807	31	20	if	if	SCONJ
iajs-807	31	21	uacl	uacl	PROPN
iajs-807	31	22			PROPN
iajs-807	31	23	)	)	PUNCT
iajs-807	31	24	(	(	PUNCT
iajs-807	31	25	whenever	whenever	SCONJ
iajs-807	31	26	ua	ua	PROPN
iajs-807	31	27			PROPN
iajs-807	31	28	and	and	CCONJ
iajs-807	31	29	u	u	NOUN
iajs-807	31	30	is	be	AUX
iajs-807	31	31	open	open	ADJ
iajs-807	31	32	in	in	ADP
iajs-807	31	33	x.[10	x.[10	PROPN
iajs-807	31	34	]	]	X
iajs-807	31	35	(	(	PUNCT
iajs-807	31	36	2	2	NUM
iajs-807	31	37	)	)	PUNCT
iajs-807	31	38			ADJ
iajs-807	32	1	generalized	generalize	VERB
iajs-807	32	2	closed	close	VERB
iajs-807	32	3	(	(	PUNCT
iajs-807	32	4	briefly	briefly	NOUN
iajs-807	32	5			NOUN
iajs-807	32	6	gclosed	gclosed	ADJ
iajs-807	32	7	)	)	PUNCT
iajs-807	32	8	if	if	SCONJ
iajs-807	32	9	uacl	uacl	PROPN
iajs-807	32	10			PROPN
iajs-807	32	11	)	)	PUNCT
iajs-807	32	12	(	(	PUNCT
iajs-807	32	13	whenever	whenever	SCONJ
iajs-807	32	14	ua	ua	PROPN
iajs-807	32	15			PROPN
iajs-807	32	16	and	and	CCONJ
iajs-807	32	17	u	u	NOUN
iajs-807	32	18	is	be	AUX
iajs-807	32	19			ADJ
iajs-807	32	20	-open.[11	-open.[11	NOUN
iajs-807	32	21	]	]	X
iajs-807	32	22	(	(	PUNCT
iajs-807	32	23	3	3	X
iajs-807	32	24	)	)	PUNCT
iajs-807	32	25			NOUN
iajs-807	32	26	generalized	generalize	VERB
iajs-807	32	27	pre	pre	NOUN
iajs-807	32	28	cosed	cosed	ADJ
iajs-807	32	29	(	(	PUNCT
iajs-807	32	30	briefly	briefly	ADV
iajs-807	32	31			NOUN
iajs-807	32	32	gpclosed	gpclose	VERB
iajs-807	32	33	)	)	PUNCT
iajs-807	32	34	if	if	SCONJ
iajs-807	32	35	uapcl	uapcl	PROPN
iajs-807	32	36			PROPN
iajs-807	32	37	)	)	PUNCT
iajs-807	32	38	(	(	PUNCT
iajs-807	32	39	whenever	whenever	SCONJ
iajs-807	32	40	ua	ua	PROPN
iajs-807	32	41			PROPN
iajs-807	32	42	and	and	CCONJ
iajs-807	32	43	u	u	NOUN
iajs-807	32	44	is	be	AUX
iajs-807	32	45			ADJ
iajs-807	32	46	open.[1	open.[1	NOUN
iajs-807	32	47	]	]	PUNCT
iajs-807	32	48	(	(	PUNCT
iajs-807	32	49	4	4	X
iajs-807	32	50	)	)	PUNCT
iajs-807	32	51			PROPN
iajs-807	32	52	-generalized	-generalized	ADJ
iajs-807	32	53	semipreclosed	semipreclose	VERB
iajs-807	32	54	(	(	PUNCT
iajs-807	32	55	briefly	briefly	NOUN
iajs-807	32	56			NOUN
iajs-807	32	57	gspclosed	gspclosed	ADJ
iajs-807	32	58	)	)	PUNCT
iajs-807	32	59	if	if	SCONJ
iajs-807	32	60	uaspcl	uaspcl	NOUN
iajs-807	32	61			PROPN
iajs-807	32	62	)	)	PUNCT
iajs-807	32	63	(	(	PUNCT
iajs-807	32	64	whenever	whenever	SCONJ
iajs-807	32	65	ua	ua	PROPN
iajs-807	32	66			PROPN
iajs-807	32	67	and	and	CCONJ
iajs-807	32	68	u	u	NOUN
iajs-807	32	69	is	be	AUX
iajs-807	32	70			ADJ
iajs-807	32	71	open.[2	open.[2	X
iajs-807	32	72	]	]	X
iajs-807	32	73	lemma	lemma	PROPN
iajs-807	32	74	1.3	1.3	NUM
iajs-807	32	75	.	.	PUNCT
iajs-807	33	1	[	[	X
iajs-807	33	2	12	12	NUM
iajs-807	33	3	]	]	PUNCT
iajs-807	33	4	let	let	VERB
iajs-807	33	5	ax	ax	PRON
iajs-807	33	6	then	then	ADV
iajs-807	33	7	,	,	PUNCT
iajs-807	33	8	(	(	PUNCT
iajs-807	33	9	1	1	X
iajs-807	33	10	)	)	PUNCT
iajs-807	33	11	ab	ab	NOUN
iajs-807	33	12	bcl	bcl	PROPN
iajs-807	33	13	(	(	PUNCT
iajs-807	33	14	a	a	PRON
iajs-807	33	15	)	)	PUNCT
iajs-807	33	16	bcl(b	bcl(b	NOUN
iajs-807	33	17	)	)	PUNCT
iajs-807	33	18	.	.	PUNCT
iajs-807	34	1	(	(	PUNCT
iajs-807	34	2	2	2	X
iajs-807	34	3	)	)	PUNCT
iajs-807	34	4	a	a	PRON
iajs-807	34	5	is	be	AUX
iajs-807	34	6	bclosed	bclosed	ADP
iajs-807	34	7	bcl	bcl	NOUN
iajs-807	34	8	(	(	PUNCT
iajs-807	34	9	a	a	X
iajs-807	34	10	)	)	PUNCT
iajs-807	35	1	=	=	NOUN
iajs-807	35	2	a.	a.	NOUN
iajs-807	35	3	(	(	PUNCT
iajs-807	35	4	3	3	X
iajs-807	35	5	)	)	PUNCT
iajs-807	35	6	let	let	VERB
iajs-807	35	7	xx	xx	PROPN
iajs-807	35	8	,	,	PUNCT
iajs-807	35	9	then	then	ADV
iajs-807	35	10	xbcl	xbcl	X
iajs-807	35	11	(	(	PUNCT
iajs-807	35	12	a	a	X
iajs-807	35	13	)	)	PUNCT
iajs-807	35	14	if	if	SCONJ
iajs-807	35	15	and	and	CCONJ
iajs-807	35	16	only	only	ADV
iajs-807	35	17	if	if	SCONJ
iajs-807	35	18	every	every	DET
iajs-807	35	19	ubo(x	ubo(x	NOUN
iajs-807	35	20	)	)	PUNCT
iajs-807	35	21	such	such	ADJ
iajs-807	35	22	that	that	SCONJ
iajs-807	35	23	xu	xu	PROPN
iajs-807	35	24	,	,	PUNCT
iajs-807	35	25	u	u	NOUN
iajs-807	35	26	a	a	NOUN
iajs-807	35	27			PROPN
iajs-807	35	28	.	.	PUNCT
iajs-807	36	1	2	2	X
iajs-807	36	2	.	.	X
iajs-807	36	3			ADJ
iajs-807	36	4	generalized	generalize	VERB
iajs-807	36	5	bclosed	bclose	VERB
iajs-807	36	6	sets	set	NOUN
iajs-807	36	7	.	.	PUNCT
iajs-807	37	1	definition	definition	NOUN
iajs-807	37	2	2.1	2.1	NUM
iajs-807	37	3	.	.	PUNCT
iajs-807	38	1	a	a	DET
iajs-807	38	2	subset	subset	NOUN
iajs-807	38	3	a	a	PRON
iajs-807	38	4	of	of	ADP
iajs-807	38	5	a	a	DET
iajs-807	38	6	space	space	NOUN
iajs-807	38	7	x	x	PUNCT
iajs-807	38	8	is	be	AUX
iajs-807	38	9	called	call	VERB
iajs-807	38	10			PROPN
iajs-807	38	11	generalized	generalize	VERB
iajs-807	38	12	bclosed	bclose	VERB
iajs-807	38	13	(	(	PUNCT
iajs-807	38	14	breifly	breifly	NOUN
iajs-807	38	15			PROPN
iajs-807	38	16	gb	gb	NOUN
iajs-807	38	17	closed	close	VERB
iajs-807	38	18	)	)	PUNCT
iajs-807	38	19	if	if	SCONJ
iajs-807	38	20	bcl(a)	bcl(a)	PROPN
iajs-807	38	21	u	u	PRON
iajs-807	38	22	whenever	whenever	SCONJ
iajs-807	38	23	a	a	DET
iajs-807	38	24	u	u	NOUN
iajs-807	38	25	and	and	CCONJ
iajs-807	38	26	u	u	NOUN
iajs-807	38	27	is	be	AUX
iajs-807	38	28			ADJ
iajs-807	38	29	open	open	NOUN
iajs-807	38	30	.	.	PUNCT
iajs-807	39	1	the	the	DET
iajs-807	39	2	complement	complement	NOUN
iajs-807	39	3	of	of	ADP
iajs-807	39	4			ADJ
iajs-807	39	5	gbclosed	gbclose	VERB
iajs-807	39	6	set	set	NOUN
iajs-807	39	7	is	be	AUX
iajs-807	39	8	called	call	VERB
iajs-807	39	9			ADJ
iajs-807	39	10	gbopen	gbopen	NOUN
iajs-807	39	11	.	.	PUNCT
iajs-807	40	1	the	the	DET
iajs-807	40	2	family	family	NOUN
iajs-807	40	3	of	of	ADP
iajs-807	40	4	all	all	DET
iajs-807	40	5			NOUN
iajs-807	40	6	gbclosed	gbclose	VERB
iajs-807	40	7	(	(	PUNCT
iajs-807	40	8	resp	resp	NOUN
iajs-807	40	9	.	.	PUNCT
iajs-807	41	1			ADJ
iajs-807	41	2	gbopen	gbopen	NOUN
iajs-807	41	3	)	)	PUNCT
iajs-807	41	4	subsets	subset	NOUN
iajs-807	41	5	of	of	ADP
iajs-807	41	6	the	the	DET
iajs-807	41	7	space	space	NOUN
iajs-807	41	8	x	x	PUNCT
iajs-807	41	9	is	be	AUX
iajs-807	41	10	denoted	denote	VERB
iajs-807	41	11	by	by	ADP
iajs-807	41	12			ADJ
iajs-807	41	13	gbc(x	gbc(x	NOUN
iajs-807	41	14	)	)	PUNCT
iajs-807	41	15	(	(	PUNCT
iajs-807	41	16	resp	resp	NOUN
iajs-807	41	17	.	.	PUNCT
iajs-807	42	1			PROPN
iajs-807	42	2	gbo(x	gbo(x	NOUN
iajs-807	42	3	)	)	PUNCT
iajs-807	42	4	)	)	PUNCT
iajs-807	42	5	.	.	PUNCT
iajs-807	43	1	definition	definition	NOUN
iajs-807	43	2	2.2	2.2	NUM
iajs-807	43	3	.	.	PUNCT
iajs-807	44	1	the	the	DET
iajs-807	44	2			PROPN
iajs-807	44	3	kernel	kernel	NOUN
iajs-807	44	4	(	(	PUNCT
iajs-807	44	5			PROPN
iajs-807	44	6	ker	ker	NOUN
iajs-807	44	7	(	(	PUNCT
iajs-807	44	8	a	a	NOUN
iajs-807	44	9	)	)	PUNCT
iajs-807	44	10	)	)	PUNCT
iajs-807	44	11	of	of	ADP
iajs-807	44	12	a	a	PRON
iajs-807	44	13	is	be	AUX
iajs-807	44	14	the	the	DET
iajs-807	44	15	intersection	intersection	NOUN
iajs-807	44	16	of	of	ADP
iajs-807	44	17	all	all	DET
iajs-807	44	18			ADJ
iajs-807	44	19	open	open	ADJ
iajs-807	44	20	sets	set	NOUN
iajs-807	44	21	containing	contain	VERB
iajs-807	44	22	a.	a.	NOUN
iajs-807	44	23	.	.	PUNCT
iajs-807	45	1	ibn	ibn	PROPN
iajs-807	45	2	alhaitham	alhaitham	PROPN
iajs-807	45	3	j.	j.	PROPN
iajs-807	45	4	for	for	ADP
iajs-807	45	5	pure	pure	ADJ
iajs-807	45	6	&	&	CCONJ
iajs-807	45	7	appl	appl	PROPN
iajs-807	45	8	.	.	PUNCT
iajs-807	46	1	sci	sci	PROPN
iajs-807	46	2	.	.	PUNCT
iajs-807	46	3	vol.24	vol.24	NOUN
iajs-807	46	4	(	(	PUNCT
iajs-807	46	5	3	3	NUM
iajs-807	46	6	)	)	PUNCT
iajs-807	46	7	2011	2011	NUM
iajs-807	46	8	remark	remark	VERB
iajs-807	46	9	2.3	2.3	NUM
iajs-807	46	10	.	.	PUNCT
iajs-807	47	1	a	a	DET
iajs-807	47	2	subset	subset	NOUN
iajs-807	47	3	a	a	PRON
iajs-807	47	4	of	of	ADP
iajs-807	47	5	a	a	DET
iajs-807	47	6	space	space	NOUN
iajs-807	47	7	x	x	PUNCT
iajs-807	47	8	is	be	AUX
iajs-807	47	9			NOUN
iajs-807	47	10	gbclosed	gbclose	VERB
iajs-807	47	11	if	if	SCONJ
iajs-807	47	12	and	and	CCONJ
iajs-807	47	13	only	only	ADV
iajs-807	47	14	if	if	SCONJ
iajs-807	47	15	bcl(a	bcl(a	PROPN
iajs-807	47	16	)	)	PUNCT
iajs-807	47	17			PROPN
iajs-807	47	18			PROPN
iajs-807	47	19	ker(a	ker(a	PROPN
iajs-807	47	20	)	)	PUNCT
iajs-807	47	21	.	.	PUNCT
iajs-807	48	1	remark	remark	PROPN
iajs-807	48	2	2.4	2.4	NUM
iajs-807	48	3	.	.	PUNCT
iajs-807	49	1	every	every	DET
iajs-807	49	2	bclosed	bclose	VERB
iajs-807	49	3	set	set	NOUN
iajs-807	49	4	is	be	AUX
iajs-807	49	5			NOUN
iajs-807	49	6	gbclosed	gbclose	VERB
iajs-807	49	7	.	.	PUNCT
iajs-807	50	1	proposition	proposition	NOUN
iajs-807	50	2	2.5	2.5	NUM
iajs-807	50	3	.	.	PUNCT
iajs-807	51	1	every	every	DET
iajs-807	51	2			PROPN
iajs-807	51	3	gpclosed	gpclose	VERB
iajs-807	51	4	set	set	NOUN
iajs-807	51	5	is	be	AUX
iajs-807	51	6			NOUN
iajs-807	51	7	gbclosed	gbclose	VERB
iajs-807	51	8	.	.	PUNCT
iajs-807	52	1	proof	proof	NOUN
iajs-807	52	2	.	.	PUNCT
iajs-807	53	1	let	let	VERB
iajs-807	53	2	a	a	DET
iajs-807	53	3	be	be	AUX
iajs-807	53	4			ADJ
iajs-807	53	5	gpclosed	gpclose	VERB
iajs-807	53	6	subset	subset	NOUN
iajs-807	53	7	of	of	ADP
iajs-807	53	8	x	x	PUNCT
iajs-807	53	9	and	and	CCONJ
iajs-807	53	10	u	u	NOUN
iajs-807	53	11	be	be	VERB
iajs-807	53	12			ADJ
iajs-807	53	13	open	open	ADJ
iajs-807	53	14	such	such	ADJ
iajs-807	53	15	that	that	DET
iajs-807	53	16	au	au	PROPN
iajs-807	53	17	.	.	PROPN
iajs-807	53	18	then	then	ADV
iajs-807	53	19	pcl	pcl	PROPN
iajs-807	53	20	(	(	PUNCT
iajs-807	53	21	a)u	a)u	PROPN
iajs-807	53	22	.	.	PUNCT
iajs-807	54	1	since	since	SCONJ
iajs-807	54	2	every	every	DET
iajs-807	54	3	preclosed	preclose	VERB
iajs-807	54	4	set	set	NOUN
iajs-807	54	5	is	be	AUX
iajs-807	54	6	b	b	NOUN
iajs-807	54	7	-	-	PUNCT
iajs-807	54	8	closed	closed	ADJ
iajs-807	54	9	.	.	PUNCT
iajs-807	55	1	therefore	therefore	ADV
iajs-807	55	2	bcl(a)pcl	bcl(a)pcl	VERB
iajs-807	55	3	(	(	PUNCT
iajs-807	55	4	a	a	NOUN
iajs-807	55	5	)	)	PUNCT
iajs-807	55	6	.	.	PUNCT
iajs-807	56	1	hence	hence	ADV
iajs-807	56	2	a	a	PRON
iajs-807	56	3	is	be	AUX
iajs-807	56	4			NOUN
iajs-807	56	5	gbclosed	gbclose	VERB
iajs-807	56	6	.	.	PUNCT
iajs-807	57	1	proposition	proposition	NOUN
iajs-807	57	2	2.6	2.6	NUM
iajs-807	57	3	.	.	PUNCT
iajs-807	58	1	every	every	DET
iajs-807	58	2			ADJ
iajs-807	58	3	gbclosed	gbclose	VERB
iajs-807	58	4	set	set	NOUN
iajs-807	58	5	is	be	AUX
iajs-807	58	6			ADJ
iajs-807	58	7	gspclosed	gspclosed	ADJ
iajs-807	58	8	.	.	PUNCT
iajs-807	59	1	proof	proof	NOUN
iajs-807	59	2	.	.	PUNCT
iajs-807	60	1	let	let	VERB
iajs-807	60	2	a	a	DET
iajs-807	60	3	be	be	AUX
iajs-807	60	4			ADJ
iajs-807	60	5	gbcosed	gbcose	VERB
iajs-807	60	6	and	and	CCONJ
iajs-807	60	7	u	u	PRON
iajs-807	60	8	be	be	VERB
iajs-807	60	9			ADJ
iajs-807	60	10	open	open	ADJ
iajs-807	60	11	such	such	ADJ
iajs-807	60	12	that	that	DET
iajs-807	60	13	au	au	PROPN
iajs-807	60	14	,	,	PUNCT
iajs-807	60	15	then	then	ADV
iajs-807	60	16	bcl(a	bcl(a	VERB
iajs-807	60	17	)	)	PUNCT
iajs-807	60	18	u	u	NOUN
iajs-807	60	19	.	.	PUNCT
iajs-807	61	1	since	since	SCONJ
iajs-807	61	2	every	every	DET
iajs-807	61	3	b	b	NOUN
iajs-807	61	4	-	-	PUNCT
iajs-807	61	5	closed	closed	ADJ
iajs-807	61	6	set	set	NOUN
iajs-807	61	7	is	be	AUX
iajs-807	61	8			ADJ
iajs-807	61	9	gsp	gsp	NOUN
iajs-807	61	10	-	-	PUNCT
iajs-807	61	11	closed	closed	ADJ
iajs-807	61	12	.	.	PUNCT
iajs-807	62	1	therefore	therefore	ADV
iajs-807	62	2	spcl(a	spcl(a	NUM
iajs-807	62	3	)	)	PUNCT
iajs-807	62	4	bcl(a	bcl(a	NUM
iajs-807	62	5	)	)	PUNCT
iajs-807	62	6	.	.	PUNCT
iajs-807	63	1	hence	hence	ADV
iajs-807	63	2	,	,	PUNCT
iajs-807	63	3	a	a	PRON
iajs-807	63	4	is	be	AUX
iajs-807	63	5			NOUN
iajs-807	63	6	gspclosed	gspclosed	ADJ
iajs-807	63	7	.	.	PUNCT
iajs-807	64	1	the	the	DET
iajs-807	64	2	following	follow	VERB
iajs-807	64	3	diagram	diagram	NOUN
iajs-807	64	4	summarizes	summarize	VERB
iajs-807	64	5	the	the	DET
iajs-807	64	6	implications	implication	NOUN
iajs-807	64	7	among	among	ADP
iajs-807	64	8	the	the	DET
iajs-807	64	9	introduced	introduce	VERB
iajs-807	64	10	concept	concept	NOUN
iajs-807	64	11	and	and	CCONJ
iajs-807	64	12	other	other	ADJ
iajs-807	64	13	related	related	ADJ
iajs-807	64	14	concepts	concept	NOUN
iajs-807	64	15	.	.	PUNCT
iajs-807	65	1			ADJ
iajs-807	65	2	gclosed	gclosed	ADJ
iajs-807	65	3			ADV
iajs-807	65	4	gpclosed	gpclose	VERB
iajs-807	65	5			NOUN
iajs-807	65	6	bclosed	bclose	VERB
iajs-807	65	7			ADV
iajs-807	65	8	gbclosed	gbclose	VERB
iajs-807	65	9			NOUN
iajs-807	65	10			ADP
iajs-807	65	11	gspclosed	gspclosed	ADJ
iajs-807	65	12	diagram	diagram	NOUN
iajs-807	65	13	(	(	PUNCT
iajs-807	65	14	1	1	X
iajs-807	65	15	)	)	PUNCT
iajs-807	65	16	the	the	DET
iajs-807	65	17	following	follow	VERB
iajs-807	65	18	three	three	NUM
iajs-807	65	19	examples	example	NOUN
iajs-807	65	20	show	show	VERB
iajs-807	65	21	that	that	SCONJ
iajs-807	65	22	the	the	DET
iajs-807	65	23	converses	converse	NOUN
iajs-807	65	24	of	of	ADP
iajs-807	65	25	remarks	remark	NOUN
iajs-807	65	26	2.4	2.4	NUM
iajs-807	65	27	and	and	CCONJ
iajs-807	65	28	proposition	proposition	NOUN
iajs-807	65	29	2.5	2.5	NUM
iajs-807	65	30	are	be	AUX
iajs-807	65	31	not	not	PART
iajs-807	65	32	true	true	ADJ
iajs-807	65	33	in	in	ADP
iajs-807	65	34	general	general	ADJ
iajs-807	65	35	.	.	PUNCT
iajs-807	66	1	example	example	NOUN
iajs-807	66	2	2.7	2.7	NUM
iajs-807	66	3	.	.	PUNCT
iajs-807	67	1	let	let	VERB
iajs-807	67	2	x=	x=	PUNCT
iajs-807	68	1	{	{	PUNCT
iajs-807	68	2	a	a	DET
iajs-807	68	3	,	,	PUNCT
iajs-807	68	4	b	b	NOUN
iajs-807	68	5	,	,	PUNCT
iajs-807	68	6	c	c	NOUN
iajs-807	68	7	}	}	PUNCT
iajs-807	68	8	,	,	PUNCT
iajs-807	68	9			NOUN
iajs-807	68	10	=	=	SYM
iajs-807	68	11	{	{	PUNCT
iajs-807	68	12	x,	x,	PROPN
iajs-807	68	13	,	,	PUNCT
iajs-807	68	14	{	{	PUNCT
iajs-807	68	15	a}}and	a}}and	VERB
iajs-807	68	16	a	a	X
iajs-807	68	17	=	=	X
iajs-807	68	18	{	{	PUNCT
iajs-807	68	19	a	a	PROPN
iajs-807	68	20	,	,	PUNCT
iajs-807	68	21	b	b	NOUN
iajs-807	68	22	}	}	PUNCT
iajs-807	68	23	.	.	PUNCT
iajs-807	69	1	then	then	ADV
iajs-807	69	2	x	x	X
iajs-807	69	3	is	be	AUX
iajs-807	69	4	the	the	DET
iajs-807	69	5	only	only	ADJ
iajs-807	69	6	regular	regular	ADJ
iajs-807	69	7	open	open	ADJ
iajs-807	69	8	(	(	PUNCT
iajs-807	69	9			ADJ
iajs-807	69	10	open	open	ADJ
iajs-807	69	11	)	)	PUNCT
iajs-807	69	12	set	set	NOUN
iajs-807	69	13	containing	contain	VERB
iajs-807	69	14	a.	a.	NOUN
iajs-807	69	15	hence	hence	ADV
iajs-807	69	16	a	a	PRON
iajs-807	69	17	is	be	AUX
iajs-807	69	18			NOUN
iajs-807	69	19	gbclosed	gbclose	VERB
iajs-807	69	20	,	,	PUNCT
iajs-807	69	21	but	but	CCONJ
iajs-807	69	22	a	a	PRON
iajs-807	69	23	is	be	AUX
iajs-807	69	24	not	not	PART
iajs-807	69	25	bclosed	bclose	VERB
iajs-807	69	26	,	,	PUNCT
iajs-807	69	27	since	since	SCONJ
iajs-807	69	28	bcl	bcl	NOUN
iajs-807	69	29	(	(	PUNCT
iajs-807	69	30	a	a	NOUN
iajs-807	69	31	)	)	PUNCT
iajs-807	69	32	=	=	SYM
iajs-807	69	33	x.	x.	NOUN
iajs-807	69	34	example	example	NOUN
iajs-807	70	1	2.8	2.8	NUM
iajs-807	70	2	.	.	PUNCT
iajs-807	71	1	let	let	VERB
iajs-807	71	2	x=	x=	PUNCT
iajs-807	72	1	{	{	PUNCT
iajs-807	72	2	a	a	DET
iajs-807	72	3	,	,	PUNCT
iajs-807	72	4	b	b	NOUN
iajs-807	72	5	,	,	PUNCT
iajs-807	72	6	c	c	NOUN
iajs-807	72	7	}	}	PUNCT
iajs-807	72	8	,	,	PUNCT
iajs-807	72	9			NOUN
iajs-807	72	10	=	=	SYM
iajs-807	72	11	{	{	PUNCT
iajs-807	72	12	x,	x,	PROPN
iajs-807	72	13	,	,	PUNCT
iajs-807	72	14	{	{	PUNCT
iajs-807	72	15	a	a	NOUN
iajs-807	72	16	}	}	PUNCT
iajs-807	72	17	,	,	PUNCT
iajs-807	72	18	{	{	PUNCT
iajs-807	72	19	b	b	NOUN
iajs-807	72	20	}	}	PUNCT
iajs-807	72	21	,	,	PUNCT
iajs-807	72	22	{	{	PUNCT
iajs-807	72	23	a	a	DET
iajs-807	72	24	,	,	PUNCT
iajs-807	72	25	b	b	NOUN
iajs-807	72	26	}	}	PUNCT
iajs-807	72	27	}	}	PUNCT
iajs-807	72	28	.	.	PUNCT
iajs-807	73	1	let	let	VERB
iajs-807	73	2	a=	a=	VERB
iajs-807	73	3	{	{	PUNCT
iajs-807	73	4	a	a	NOUN
iajs-807	73	5	}	}	PUNCT
iajs-807	73	6	.	.	PUNCT
iajs-807	74	1	then	then	ADV
iajs-807	74	2	a	a	PRON
iajs-807	74	3	is	be	AUX
iajs-807	74	4	bclosed	bclose	VERB
iajs-807	74	5	.	.	PUNCT
iajs-807	75	1	hence	hence	ADV
iajs-807	75	2	a	a	PRON
iajs-807	75	3	is	be	AUX
iajs-807	75	4			NOUN
iajs-807	75	5	gbclosed	gbclose	VERB
iajs-807	75	6	,	,	PUNCT
iajs-807	75	7	but	but	CCONJ
iajs-807	75	8	a	a	PRON
iajs-807	75	9	is	be	AUX
iajs-807	75	10	not	not	PART
iajs-807	75	11			NOUN
iajs-807	75	12	gpclosed	gpclose	VERB
iajs-807	75	13	,	,	PUNCT
iajs-807	75	14	since	since	SCONJ
iajs-807	75	15	a	a	PRON
iajs-807	75	16	is	be	AUX
iajs-807	75	17	regular	regular	ADJ
iajs-807	75	18	open	open	ADJ
iajs-807	75	19	(	(	PUNCT
iajs-807	75	20			ADJ
iajs-807	75	21	open	open	NOUN
iajs-807	75	22	)	)	PUNCT
iajs-807	75	23	and	and	CCONJ
iajs-807	75	24	pcl(a)=	pcl(a)=	PROPN
iajs-807	75	25	{	{	PUNCT
iajs-807	75	26	a	a	DET
iajs-807	75	27	,	,	PUNCT
iajs-807	75	28	c}a	c}a	NOUN
iajs-807	75	29	.	.	NOUN
iajs-807	75	30	3	3	NUM
iajs-807	75	31	.	.	X
iajs-807	76	1	some	some	DET
iajs-807	76	2	properties	property	NOUN
iajs-807	76	3	of	of	ADP
iajs-807	76	4			ADJ
iajs-807	76	5	gbclosed	gbclose	VERB
iajs-807	76	6	sets	set	NOUN
iajs-807	76	7	.	.	PUNCT
iajs-807	77	1	proposition	proposition	NOUN
iajs-807	77	2	3.1	3.1	NUM
iajs-807	77	3	.	.	PUNCT
iajs-807	78	1	if	if	SCONJ
iajs-807	78	2	a	a	PRON
iajs-807	78	3	is	be	AUX
iajs-807	78	4			ADJ
iajs-807	78	5	open	open	ADJ
iajs-807	78	6	and	and	CCONJ
iajs-807	78	7			ADJ
iajs-807	78	8	gbclosed	gbclose	VERB
iajs-807	78	9	,	,	PUNCT
iajs-807	78	10	then	then	ADV
iajs-807	78	11	a	a	PRON
iajs-807	78	12	is	be	AUX
iajs-807	78	13	bclosed	bclose	VERB
iajs-807	78	14	and	and	CCONJ
iajs-807	78	15	hence	hence	ADV
iajs-807	78	16	gbclosed	gbclose	VERB
iajs-807	78	17	.	.	PUNCT
iajs-807	79	1	proof	proof	NOUN
iajs-807	79	2	.	.	PUNCT
iajs-807	80	1	since	since	SCONJ
iajs-807	80	2	a	a	PRON
iajs-807	80	3	is	be	AUX
iajs-807	80	4			ADJ
iajs-807	80	5	open	open	ADJ
iajs-807	80	6	and	and	CCONJ
iajs-807	80	7			ADJ
iajs-807	80	8	gbclosed	gbclose	VERB
iajs-807	80	9	.	.	PUNCT
iajs-807	81	1	so	so	ADV
iajs-807	81	2	bcl(a	bcl(a	PROPN
iajs-807	81	3	)	)	PUNCT
iajs-807	81	4	a	a	NOUN
iajs-807	81	5	.	.	PUNCT
iajs-807	81	6	but	but	CCONJ
iajs-807	81	7	abcl(a	abcl(a	NUM
iajs-807	81	8	)	)	PUNCT
iajs-807	81	9	.	.	PUNCT
iajs-807	82	1	so	so	ADV
iajs-807	82	2	a=	a=	ADV
iajs-807	82	3	bcl(a	bcl(a	VERB
iajs-807	82	4	)	)	PUNCT
iajs-807	82	5	.	.	PUNCT
iajs-807	83	1	hence	hence	ADV
iajs-807	83	2	a	a	PRON
iajs-807	83	3	is	be	AUX
iajs-807	83	4	bclosed	bclose	VERB
iajs-807	83	5	.	.	PUNCT
iajs-807	84	1	hence	hence	ADV
iajs-807	84	2	gbclosed	gbclose	VERB
iajs-807	84	3	.	.	PUNCT
iajs-807	85	1	proposition	proposition	NOUN
iajs-807	85	2	3.2	3.2	NUM
iajs-807	85	3	.	.	PUNCT
iajs-807	86	1	let	let	VERB
iajs-807	86	2	a	a	DET
iajs-807	86	3	be	be	AUX
iajs-807	86	4	a	a	DET
iajs-807	86	5			NOUN
iajs-807	86	6	gbclosed	gbclose	VERB
iajs-807	86	7	in	in	ADP
iajs-807	86	8	x.	x.	NOUN
iajs-807	86	9	then	then	ADV
iajs-807	86	10	bcl(a)\	bcl(a)\	X
iajs-807	86	11	a	a	PRON
iajs-807	86	12	does	do	AUX
iajs-807	86	13	not	not	PART
iajs-807	86	14	contain	contain	VERB
iajs-807	86	15	any	any	DET
iajs-807	86	16	nonempty	nonempty	ADJ
iajs-807	86	17			ADJ
iajs-807	86	18	closed	close	VERB
iajs-807	86	19	set	set	NOUN
iajs-807	86	20	.	.	PUNCT
iajs-807	86	21	.	.	PUNCT
iajs-807	87	1	ibn	ibn	PROPN
iajs-807	87	2	alhaitham	alhaitham	PROPN
iajs-807	87	3	j.	j.	PROPN
iajs-807	87	4	for	for	ADP
iajs-807	87	5	pure	pure	ADJ
iajs-807	87	6	&	&	CCONJ
iajs-807	87	7	appl	appl	PROPN
iajs-807	87	8	.	.	PUNCT
iajs-807	88	1	sci	sci	PROPN
iajs-807	88	2	.	.	PUNCT
iajs-807	88	3	vol.24	vol.24	NOUN
iajs-807	88	4	(	(	PUNCT
iajs-807	88	5	3	3	NUM
iajs-807	88	6	)	)	PUNCT
iajs-807	88	7	2011	2011	NUM
iajs-807	88	8	proof	proof	NOUN
iajs-807	88	9	.	.	PUNCT
iajs-807	89	1	let	let	VERB
iajs-807	89	2	f	f	PRON
iajs-807	89	3	be	be	AUX
iajs-807	89	4	a	a	DET
iajs-807	89	5			ADJ
iajs-807	89	6	closed	closed	ADJ
iajs-807	89	7	set	set	NOUN
iajs-807	89	8	such	such	ADJ
iajs-807	89	9	that	that	SCONJ
iajs-807	89	10	f	f	PROPN
iajs-807	89	11	bcl(a)\	bcl(a)\	X
iajs-807	89	12	a	a	PRON
iajs-807	89	13	,	,	PUNCT
iajs-807	89	14	so	so	PROPN
iajs-807	89	15	f	f	PROPN
iajs-807	89	16	x\a	x\a	PROPN
iajs-807	89	17	.	.	PUNCT
iajs-807	90	1	hence	hence	ADV
iajs-807	90	2	a	a	DET
iajs-807	90	3	x\f	x\f	PROPN
iajs-807	90	4	.	.	PUNCT
iajs-807	91	1	since	since	SCONJ
iajs-807	91	2	a	a	PRON
iajs-807	91	3	is	be	AUX
iajs-807	91	4			ADJ
iajs-807	91	5	gb	gb	NOUN
iajs-807	91	6	closed	closed	ADJ
iajs-807	91	7	and	and	CCONJ
iajs-807	91	8	x\	x\	PROPN
iajs-807	91	9	f	f	PROPN
iajs-807	91	10	is	be	AUX
iajs-807	91	11			ADJ
iajs-807	91	12	open	open	NOUN
iajs-807	91	13	.	.	PUNCT
iajs-807	92	1	so	so	ADV
iajs-807	92	2	bcl(a	bcl(a	VERB
iajs-807	92	3	)	)	PUNCT
iajs-807	92	4	x\	x\	NOUN
iajs-807	92	5	f.	f.	PROPN
iajs-807	92	6	that	that	PRON
iajs-807	92	7	is	be	AUX
iajs-807	92	8	fx\	fx\	ADJ
iajs-807	92	9	bcl(a	bcl(a	PROPN
iajs-807	92	10	)	)	PUNCT
iajs-807	92	11	.	.	PUNCT
iajs-807	93	1	therefore	therefore	ADV
iajs-807	93	2	fbcl(a	fbcl(a	NUM
iajs-807	93	3	)	)	PUNCT
iajs-807	93	4			PROPN
iajs-807	93	5	(	(	PUNCT
iajs-807	93	6	x\	x\	PROPN
iajs-807	93	7	bcl(a	bcl(a	PROPN
iajs-807	93	8	)	)	PUNCT
iajs-807	93	9	)	)	PUNCT
iajs-807	94	1	=	=	NOUN
iajs-807	94	2			NOUN
iajs-807	94	3	.	.	PUNCT
iajs-807	95	1	thus	thus	ADV
iajs-807	95	2	f	f	X
iajs-807	95	3	=	=	NOUN
iajs-807	95	4			NOUN
iajs-807	95	5	.	.	PUNCT
iajs-807	96	1	corollary	corollary	ADJ
iajs-807	96	2	3.3	3.3	NUM
iajs-807	96	3	.	.	PUNCT
iajs-807	97	1	let	let	VERB
iajs-807	97	2	a	a	DET
iajs-807	97	3	be	be	AUX
iajs-807	97	4			ADJ
iajs-807	97	5	gbclosed	gbclose	VERB
iajs-807	97	6	set	set	NOUN
iajs-807	97	7	in	in	ADP
iajs-807	97	8	x.	x.	NOUN
iajs-807	97	9	then	then	ADV
iajs-807	97	10	a	a	PRON
iajs-807	97	11	is	be	AUX
iajs-807	97	12	bclosed	bclose	VERB
iajs-807	97	13	if	if	SCONJ
iajs-807	97	14	and	and	CCONJ
iajs-807	97	15	only	only	ADV
iajs-807	97	16	if	if	SCONJ
iajs-807	97	17	bcl(a)a	bcl(a)a	NOUN
iajs-807	97	18	is	be	AUX
iajs-807	97	19			ADJ
iajs-807	97	20	closed	closed	ADJ
iajs-807	97	21	.	.	PUNCT
iajs-807	98	1	proof	proof	NOUN
iajs-807	98	2	.	.	PUNCT
iajs-807	99	1	let	let	VERB
iajs-807	99	2	a	a	DET
iajs-807	99	3	be	be	AUX
iajs-807	99	4			NOUN
iajs-807	99	5	gbclosed	gbclose	VERB
iajs-807	99	6	.	.	PUNCT
iajs-807	100	1	by	by	ADP
iajs-807	100	2	hypothesis	hypothesis	NOUN
iajs-807	100	3	bcl(a)=	bcl(a)=	PUNCT
iajs-807	100	4	a	a	PRON
iajs-807	100	5	and	and	CCONJ
iajs-807	100	6	so	so	ADV
iajs-807	100	7	bcl(a)\a=	bcl(a)\a=	NOUN
iajs-807	100	8	,	,	PUNCT
iajs-807	100	9	which	which	PRON
iajs-807	100	10	is	be	AUX
iajs-807	100	11			PROPN
iajs-807	100	12	closed	closed	ADJ
iajs-807	100	13	.	.	PUNCT
iajs-807	101	1	conversely	conversely	ADV
iajs-807	101	2	,	,	PUNCT
iajs-807	101	3	suppose	suppose	VERB
iajs-807	101	4	that	that	SCONJ
iajs-807	101	5	bcl(a)\a	bcl(a)\a	VERB
iajs-807	101	6	is	be	AUX
iajs-807	101	7			NOUN
iajs-807	101	8	closed	closed	ADJ
iajs-807	101	9	.	.	PUNCT
iajs-807	102	1	then	then	ADV
iajs-807	102	2	by	by	ADP
iajs-807	102	3	theorem	theorem	NOUN
iajs-807	102	4	3.2	3.2	NUM
iajs-807	102	5	,	,	PUNCT
iajs-807	102	6	bcl(a)\a=	bcl(a)\a=	PROPN
iajs-807	102	7			NOUN
iajs-807	102	8	,	,	PUNCT
iajs-807	102	9	that	that	PRON
iajs-807	102	10	is	is	ADV
iajs-807	102	11	bcl(a)=	bcl(a)=	ADJ
iajs-807	102	12	a.	a.	NOUN
iajs-807	102	13	hence	hence	ADV
iajs-807	102	14	a	a	PRON
iajs-807	102	15	is	be	AUX
iajs-807	102	16	bclosed	bclose	VERB
iajs-807	102	17	.	.	PUNCT
iajs-807	103	1	proposition	proposition	NOUN
iajs-807	103	2	3.4	3.4	NUM
iajs-807	103	3	.	.	PUNCT
iajs-807	104	1	if	if	SCONJ
iajs-807	104	2	a	a	PRON
iajs-807	104	3	is	be	AUX
iajs-807	104	4			NOUN
iajs-807	104	5	gbclosed	gbclose	VERB
iajs-807	104	6	and	and	CCONJ
iajs-807	104	7	abbcl(a	abbcl(a	PROPN
iajs-807	104	8	)	)	PUNCT
iajs-807	104	9	.	.	PUNCT
iajs-807	105	1	then	then	ADV
iajs-807	105	2	b	b	X
iajs-807	105	3	is	be	AUX
iajs-807	105	4			NOUN
iajs-807	105	5	gbclosed	gbclose	VERB
iajs-807	105	6	.	.	PUNCT
iajs-807	106	1	proof	proof	NOUN
iajs-807	106	2	.	.	PUNCT
iajs-807	107	1	let	let	VERB
iajs-807	107	2	bu	bu	PROPN
iajs-807	107	3	,	,	PUNCT
iajs-807	107	4	where	where	SCONJ
iajs-807	107	5	u	u	NOUN
iajs-807	107	6	is	be	AUX
iajs-807	107	7			ADJ
iajs-807	107	8	open	open	NOUN
iajs-807	107	9	.	.	PUNCT
iajs-807	108	1	then	then	ADV
iajs-807	108	2	ab	ab	X
iajs-807	108	3	implies	imply	VERB
iajs-807	108	4	a	a	DET
iajs-807	108	5	u	u	NOUN
iajs-807	108	6	.	.	NOUN
iajs-807	109	1	since	since	SCONJ
iajs-807	109	2	a	a	PRON
iajs-807	109	3	is	be	AUX
iajs-807	109	4			NOUN
iajs-807	109	5	gbclosed	gbclose	VERB
iajs-807	109	6	,	,	PUNCT
iajs-807	109	7	so	so	ADV
iajs-807	109	8	bcl(a	bcl(a	PROPN
iajs-807	109	9	)	)	PUNCT
iajs-807	109	10	u	u	NOUN
iajs-807	109	11	and	and	CCONJ
iajs-807	109	12	since	since	SCONJ
iajs-807	109	13	bbcl(a	bbcl(a	NUM
iajs-807	109	14	)	)	PUNCT
iajs-807	109	15	,	,	PUNCT
iajs-807	109	16	then	then	ADV
iajs-807	109	17	bcl(b	bcl(b	PROPN
iajs-807	109	18	)	)	PUNCT
iajs-807	109	19	bcl(bcl(a))=	bcl(bcl(a))=	PROPN
iajs-807	109	20	bcl(a	bcl(a	NUM
iajs-807	109	21	)	)	PUNCT
iajs-807	109	22	.	.	PUNCT
iajs-807	110	1	therefore	therefore	ADV
iajs-807	110	2	bcl(b	bcl(b	PROPN
iajs-807	110	3	)	)	PUNCT
iajs-807	110	4	u	u	NOUN
iajs-807	110	5	.	.	PUNCT
iajs-807	110	6	hence	hence	ADV
iajs-807	110	7	b	b	PROPN
iajs-807	110	8	is	be	AUX
iajs-807	110	9			ADJ
iajs-807	110	10	gbclosed	gbclose	VERB
iajs-807	110	11	.	.	PUNCT
iajs-807	111	1	definition	definition	NOUN
iajs-807	111	2	3.5.[13	3.5.[13	NUM
iajs-807	111	3	]	]	PUNCT
iajs-807	111	4	let	let	VERB
iajs-807	111	5	(	(	PUNCT
iajs-807	111	6	x,	x,	PROPN
iajs-807	111	7	)	)	PUNCT
iajs-807	111	8	be	be	AUX
iajs-807	111	9	a	a	DET
iajs-807	111	10	topological	topological	ADJ
iajs-807	111	11	space	space	NOUN
iajs-807	111	12	,	,	PUNCT
iajs-807	111	13	a	a	DET
iajs-807	111	14	x	x	ADJ
iajs-807	111	15	and	and	CCONJ
iajs-807	111	16	xx	xx	PROPN
iajs-807	111	17	.	.	PUNCT
iajs-807	112	1	then	then	ADV
iajs-807	112	2	x	x	X
iajs-807	112	3	is	be	AUX
iajs-807	112	4	said	say	VERB
iajs-807	112	5	to	to	PART
iajs-807	112	6	be	be	AUX
iajs-807	112	7	a	a	DET
iajs-807	112	8	blimit	blimit	NOUN
iajs-807	112	9	point	point	NOUN
iajs-807	112	10	of	of	ADP
iajs-807	112	11	a	a	PRON
iajs-807	112	12	and	and	CCONJ
iajs-807	112	13	only	only	ADV
iajs-807	112	14	if	if	SCONJ
iajs-807	112	15	every	every	DET
iajs-807	112	16	bopen	bopen	NOUN
iajs-807	112	17	set	set	NOUN
iajs-807	112	18	containing	contain	VERB
iajs-807	112	19	x	x	PUNCT
iajs-807	112	20	contains	contain	VERB
iajs-807	112	21	a	a	DET
iajs-807	112	22	point	point	NOUN
iajs-807	112	23	of	of	ADP
iajs-807	112	24	a	a	DET
iajs-807	112	25	different	different	ADJ
iajs-807	112	26	from	from	ADP
iajs-807	112	27	x	x	PRON
iajs-807	112	28	,	,	PUNCT
iajs-807	112	29	and	and	CCONJ
iajs-807	112	30	the	the	DET
iajs-807	112	31	set	set	NOUN
iajs-807	112	32	of	of	ADP
iajs-807	112	33	all	all	DET
iajs-807	112	34	blimit	blimit	NOUN
iajs-807	112	35	points	point	NOUN
iajs-807	112	36	of	of	ADP
iajs-807	112	37	a	a	PRON
iajs-807	112	38	is	be	AUX
iajs-807	112	39	said	say	VERB
iajs-807	112	40	to	to	PART
iajs-807	112	41	be	be	AUX
iajs-807	112	42	the	the	DET
iajs-807	112	43	bderived	bderived	ADJ
iajs-807	112	44	set	set	NOUN
iajs-807	112	45	of	of	ADP
iajs-807	112	46	a	a	PRON
iajs-807	112	47	and	and	CCONJ
iajs-807	112	48	is	be	AUX
iajs-807	112	49	denoted	denote	VERB
iajs-807	112	50	by	by	ADP
iajs-807	112	51	bd	bd	PROPN
iajs-807	112	52	(	(	PUNCT
iajs-807	112	53	a	a	NOUN
iajs-807	112	54	)	)	PUNCT
iajs-807	112	55	.	.	PUNCT
iajs-807	113	1	usual	usual	ADJ
iajs-807	113	2	derived	derive	VERB
iajs-807	113	3	set	set	NOUN
iajs-807	113	4	of	of	ADP
iajs-807	113	5	a	a	PRON
iajs-807	113	6	is	be	AUX
iajs-807	113	7	denoted	denote	VERB
iajs-807	113	8	by	by	ADP
iajs-807	113	9	d	d	PROPN
iajs-807	113	10	(	(	PUNCT
iajs-807	113	11	a	a	NOUN
iajs-807	113	12	)	)	PUNCT
iajs-807	113	13	.	.	PUNCT
iajs-807	114	1	the	the	DET
iajs-807	114	2	proof	proof	NOUN
iajs-807	114	3	of	of	ADP
iajs-807	114	4	the	the	DET
iajs-807	114	5	following	following	ADJ
iajs-807	114	6	result	result	NOUN
iajs-807	114	7	is	be	AUX
iajs-807	114	8	analogous	analogous	ADJ
iajs-807	114	9	to	to	ADP
iajs-807	114	10	the	the	DET
iajs-807	114	11	well	well	ADV
iajs-807	114	12	known	know	VERB
iajs-807	114	13	ones	one	NOUN
iajs-807	114	14	.	.	PUNCT
iajs-807	115	1	lemma	lemma	PROPN
iajs-807	115	2	3.6	3.6	NUM
iajs-807	115	3	.	.	PUNCT
iajs-807	116	1	let	let	VERB
iajs-807	116	2	(	(	PUNCT
iajs-807	116	3	x,	x,	PROPN
iajs-807	116	4	)	)	PUNCT
iajs-807	116	5	be	be	AUX
iajs-807	116	6	a	a	DET
iajs-807	116	7	topological	topological	ADJ
iajs-807	116	8	space	space	NOUN
iajs-807	116	9	and	and	CCONJ
iajs-807	116	10	a	a	DET
iajs-807	116	11	x	x	NOUN
iajs-807	116	12	.	.	PUNCT
iajs-807	117	1	then	then	ADV
iajs-807	117	2	bcl(a	bcl(a	VERB
iajs-807	117	3	)	)	PUNCT
iajs-807	117	4	=	=	PRON
iajs-807	117	5	a	a	NOUN
iajs-807	117	6	bd	bd	PROPN
iajs-807	117	7	(	(	PUNCT
iajs-807	117	8	a	a	NOUN
iajs-807	117	9	)	)	PUNCT
iajs-807	117	10	.	.	PUNCT
iajs-807	118	1	remark	remark	PROPN
iajs-807	118	2	3.7	3.7	NUM
iajs-807	118	3	.	.	PUNCT
iajs-807	119	1	the	the	DET
iajs-807	119	2	union	union	NOUN
iajs-807	119	3	of	of	ADP
iajs-807	119	4	two	two	NUM
iajs-807	119	5			ADJ
iajs-807	119	6	gbclosed	gbclose	VERB
iajs-807	119	7	sets	set	NOUN
iajs-807	119	8	is	be	AUX
iajs-807	119	9	not	not	PART
iajs-807	119	10	necessarily	necessarily	ADV
iajs-807	119	11	a	a	DET
iajs-807	119	12			ADJ
iajs-807	119	13	gbclosed	gbclose	VERB
iajs-807	119	14	set	set	NOUN
iajs-807	119	15	as	as	ADP
iajs-807	119	16	the	the	DET
iajs-807	119	17	following	follow	VERB
iajs-807	119	18	example	example	NOUN
iajs-807	119	19	shows	show	NOUN
iajs-807	119	20	.	.	PUNCT
iajs-807	120	1	example	example	NOUN
iajs-807	120	2	3.8	3.8	NUM
iajs-807	120	3	.	.	PUNCT
iajs-807	121	1	consider	consider	VERB
iajs-807	121	2	the	the	DET
iajs-807	121	3	space	space	NOUN
iajs-807	121	4	(	(	PUNCT
iajs-807	121	5	x,	x,	PROPN
iajs-807	121	6	)	)	PUNCT
iajs-807	121	7	in	in	ADP
iajs-807	121	8	example	example	NOUN
iajs-807	121	9	2.8	2.8	NUM
iajs-807	121	10	,	,	PUNCT
iajs-807	121	11	the	the	DET
iajs-807	121	12	sets	set	NOUN
iajs-807	121	13	a=	a=	VERB
iajs-807	121	14	{	{	PUNCT
iajs-807	121	15	a	a	NOUN
iajs-807	121	16	}	}	PUNCT
iajs-807	121	17	and	and	CCONJ
iajs-807	121	18	b=	b=	NOUN
iajs-807	121	19	{	{	PUNCT
iajs-807	121	20	b	b	NOUN
iajs-807	121	21	}	}	PUNCT
iajs-807	121	22	are	be	AUX
iajs-807	121	23			ADJ
iajs-807	121	24	gbclosed	gbclose	VERB
iajs-807	121	25	.	.	PUNCT
iajs-807	122	1	but	but	CCONJ
iajs-807	122	2	a	a	DET
iajs-807	122	3	b=	b=	PROPN
iajs-807	122	4	{	{	PUNCT
iajs-807	122	5	a	a	DET
iajs-807	122	6	,	,	PUNCT
iajs-807	122	7	b	b	NOUN
iajs-807	122	8	}	}	PUNCT
iajs-807	122	9	is	be	AUX
iajs-807	122	10	not	not	PART
iajs-807	122	11			NOUN
iajs-807	122	12	gbclosed	gbclose	VERB
iajs-807	122	13	.	.	PUNCT
iajs-807	123	1	proposition	proposition	NOUN
iajs-807	123	2	3.9	3.9	NUM
iajs-807	123	3	.	.	PUNCT
iajs-807	124	1	let	let	VERB
iajs-807	124	2	a	a	PRON
iajs-807	124	3	and	and	CCONJ
iajs-807	124	4	b	b	NOUN
iajs-807	124	5	be	be	AUX
iajs-807	124	6			ADJ
iajs-807	124	7	gbclosed	gbclose	VERB
iajs-807	124	8	sets	set	NOUN
iajs-807	124	9	in	in	ADP
iajs-807	124	10	(	(	PUNCT
iajs-807	124	11	x,	x,	PROPN
iajs-807	124	12	)	)	PUNCT
iajs-807	124	13	such	such	ADJ
iajs-807	124	14	that	that	SCONJ
iajs-807	124	15	cl(a)=	cl(a)=	PROPN
iajs-807	124	16	bcl(a	bcl(a	PROPN
iajs-807	124	17	)	)	PUNCT
iajs-807	124	18	and	and	CCONJ
iajs-807	124	19	cl(b)=	cl(b)=	VERB
iajs-807	124	20	bcl(b	bcl(b	PROPN
iajs-807	124	21	)	)	PUNCT
iajs-807	124	22	.	.	PUNCT
iajs-807	125	1	then	then	ADV
iajs-807	125	2	a	a	DET
iajs-807	125	3	b	b	NOUN
iajs-807	125	4	is	be	AUX
iajs-807	125	5			ADJ
iajs-807	125	6	gb	gb	ADV
iajs-807	125	7	-	-	PUNCT
iajs-807	125	8	closed	closed	ADJ
iajs-807	125	9	.	.	PUNCT
iajs-807	126	1	proof	proof	NOUN
iajs-807	126	2	.	.	PUNCT
iajs-807	127	1	let	let	VERB
iajs-807	127	2	(	(	PUNCT
iajs-807	127	3	a	a	DET
iajs-807	127	4	b	b	NOUN
iajs-807	127	5	)	)	PUNCT
iajs-807	127	6	u	u	NOUN
iajs-807	127	7	and	and	CCONJ
iajs-807	127	8	u	u	NOUN
iajs-807	127	9	is	be	AUX
iajs-807	127	10			ADJ
iajs-807	127	11	open	open	ADJ
iajs-807	127	12	in	in	ADP
iajs-807	127	13	(	(	PUNCT
iajs-807	127	14	x,	x,	PROPN
iajs-807	127	15	)	)	PUNCT
iajs-807	127	16	.	.	PUNCT
iajs-807	128	1	then	then	ADV
iajs-807	128	2	bcl	bcl	NOUN
iajs-807	128	3	(	(	PUNCT
iajs-807	128	4	a	a	X
iajs-807	128	5	)	)	PUNCT
iajs-807	128	6	u	u	NOUN
iajs-807	128	7	and	and	CCONJ
iajs-807	128	8	bcl(b	bcl(b	PROPN
iajs-807	128	9	)	)	PUNCT
iajs-807	128	10	u	u	NOUN
iajs-807	128	11	.	.	PUNCT
iajs-807	129	1	now	now	ADV
iajs-807	129	2	,	,	PUNCT
iajs-807	129	3	cl	cl	INTJ
iajs-807	129	4	(	(	PUNCT
iajs-807	129	5	a	a	DET
iajs-807	129	6	b	b	NOUN
iajs-807	129	7	)	)	PUNCT
iajs-807	130	1	=	=	SYM
iajs-807	130	2	cl	cl	INTJ
iajs-807	130	3	(	(	PUNCT
iajs-807	130	4	a	a	NOUN
iajs-807	130	5	)	)	PUNCT
iajs-807	130	6			ADJ
iajs-807	130	7	cl	cl	NOUN
iajs-807	130	8	(	(	PUNCT
iajs-807	130	9	b	b	NOUN
iajs-807	130	10	)	)	PUNCT
iajs-807	130	11	=	=	SYM
iajs-807	130	12	bcl	bcl	NOUN
iajs-807	130	13	(	(	PUNCT
iajs-807	130	14	a	a	NOUN
iajs-807	130	15	)	)	PUNCT
iajs-807	130	16			PROPN
iajs-807	130	17	bcl(b	bcl(b	PROPN
iajs-807	130	18	)	)	PUNCT
iajs-807	130	19	u	u	NOUN
iajs-807	130	20	.	.	PROPN
iajs-807	131	1	but	but	CCONJ
iajs-807	131	2	bcl	bcl	NOUN
iajs-807	131	3	(	(	PUNCT
iajs-807	131	4	a	a	DET
iajs-807	131	5	b	b	NOUN
iajs-807	131	6	)	)	PUNCT
iajs-807	132	1			PROPN
iajs-807	132	2	cl	cl	NOUN
iajs-807	132	3	(	(	PUNCT
iajs-807	132	4	a	a	DET
iajs-807	132	5	b	b	NOUN
iajs-807	132	6	)	)	PUNCT
iajs-807	132	7	.	.	PUNCT
iajs-807	133	1	so	so	ADV
iajs-807	133	2	,	,	PUNCT
iajs-807	133	3	bcl	bcl	NOUN
iajs-807	133	4	(	(	PUNCT
iajs-807	133	5	a	a	DET
iajs-807	133	6	b	b	NOUN
iajs-807	133	7	)	)	PUNCT
iajs-807	133	8	u	u	NOUN
iajs-807	133	9	and	and	CCONJ
iajs-807	133	10	hence	hence	ADV
iajs-807	133	11	a	a	DET
iajs-807	133	12	b	b	NOUN
iajs-807	133	13	is	be	AUX
iajs-807	133	14			NOUN
iajs-807	133	15	gbclosed	gbclose	VERB
iajs-807	133	16	.	.	PUNCT
iajs-807	134	1	from	from	ADP
iajs-807	134	2	the	the	DET
iajs-807	134	3	fact	fact	NOUN
iajs-807	134	4	that	that	SCONJ
iajs-807	134	5	bd	bd	PROPN
iajs-807	134	6	(	(	PUNCT
iajs-807	134	7	a	a	X
iajs-807	134	8	)	)	PUNCT
iajs-807	134	9			PROPN
iajs-807	134	10	d	d	PROPN
iajs-807	134	11	(	(	PUNCT
iajs-807	134	12	a	a	NOUN
iajs-807	134	13	)	)	PUNCT
iajs-807	134	14	and	and	CCONJ
iajs-807	134	15	lemma	lemma	PROPN
iajs-807	134	16	3.6	3.6	NUM
iajs-807	134	17	we	we	PRON
iajs-807	134	18	have	have	AUX
iajs-807	134	19	the	the	DET
iajs-807	134	20	following	following	NOUN
iajs-807	134	21	,	,	PUNCT
iajs-807	134	22	.	.	PUNCT
iajs-807	135	1	ibn	ibn	PROPN
iajs-807	135	2	alhaitham	alhaitham	PROPN
iajs-807	135	3	j.	j.	PROPN
iajs-807	135	4	for	for	ADP
iajs-807	135	5	pure	pure	ADJ
iajs-807	135	6	&	&	CCONJ
iajs-807	135	7	appl	appl	PROPN
iajs-807	135	8	.	.	PUNCT
iajs-807	136	1	sci	sci	PROPN
iajs-807	136	2	.	.	PUNCT
iajs-807	136	3	vol.24	vol.24	NOUN
iajs-807	136	4	(	(	PUNCT
iajs-807	136	5	3	3	NUM
iajs-807	136	6	)	)	PUNCT
iajs-807	136	7	2011	2011	NUM
iajs-807	136	8	remark	remark	VERB
iajs-807	136	9	3.10	3.10	NUM
iajs-807	136	10	.	.	PUNCT
iajs-807	137	1	for	for	ADP
iajs-807	137	2	any	any	DET
iajs-807	137	3	subset	subset	NOUN
iajs-807	137	4	a	a	PRON
iajs-807	137	5	of	of	ADP
iajs-807	137	6	x	x	SYM
iajs-807	137	7	such	such	ADJ
iajs-807	137	8	that	that	SCONJ
iajs-807	137	9	d	d	X
iajs-807	137	10	(	(	PUNCT
iajs-807	137	11	a	a	X
iajs-807	137	12	)	)	PUNCT
iajs-807	137	13			PROPN
iajs-807	137	14	bd	bd	PROPN
iajs-807	137	15	(	(	PUNCT
iajs-807	137	16	a	a	NOUN
iajs-807	137	17	)	)	PUNCT
iajs-807	137	18	.	.	PUNCT
iajs-807	138	1	then	then	ADV
iajs-807	138	2	cl(a)=	cl(a)=	PROPN
iajs-807	138	3	bcl(a	bcl(a	PROPN
iajs-807	138	4	)	)	PUNCT
iajs-807	138	5	.	.	PUNCT
iajs-807	139	1	we	we	PRON
iajs-807	139	2	get	get	VERB
iajs-807	139	3	the	the	DET
iajs-807	139	4	following	follow	VERB
iajs-807	139	5	,	,	PUNCT
iajs-807	139	6	corollary	corollary	NOUN
iajs-807	139	7	3.11	3.11	NUM
iajs-807	139	8	.	.	PUNCT
iajs-807	140	1	let	let	VERB
iajs-807	140	2	a	a	PRON
iajs-807	140	3	and	and	CCONJ
iajs-807	140	4	b	b	NOUN
iajs-807	140	5	be	be	AUX
iajs-807	140	6			ADJ
iajs-807	140	7	gbclosed	gbclose	VERB
iajs-807	140	8	sets	set	NOUN
iajs-807	140	9	in	in	ADP
iajs-807	140	10	(	(	PUNCT
iajs-807	140	11	x	x	NOUN
iajs-807	140	12	,	,	PUNCT
iajs-807	140	13			NOUN
iajs-807	140	14	)	)	PUNCT
iajs-807	141	1	such	such	ADJ
iajs-807	141	2	that	that	SCONJ
iajs-807	141	3	d	d	X
iajs-807	141	4	(	(	PUNCT
iajs-807	141	5	a	a	X
iajs-807	141	6	)	)	PUNCT
iajs-807	141	7			PROPN
iajs-807	141	8	bd	bd	PROPN
iajs-807	141	9	(	(	PUNCT
iajs-807	141	10	a	a	NOUN
iajs-807	141	11	)	)	PUNCT
iajs-807	141	12	and	and	CCONJ
iajs-807	141	13	d	d	X
iajs-807	141	14	(	(	PUNCT
iajs-807	141	15	b	b	X
iajs-807	141	16	)	)	PUNCT
iajs-807	141	17			PROPN
iajs-807	141	18	bd	bd	PROPN
iajs-807	141	19	(	(	PUNCT
iajs-807	141	20	b	b	NOUN
iajs-807	141	21	)	)	PUNCT
iajs-807	141	22	.	.	PUNCT
iajs-807	142	1	then	then	ADV
iajs-807	142	2	ab	ab	PROPN
iajs-807	142	3	is	be	AUX
iajs-807	142	4			ADJ
iajs-807	142	5	gbclosed	gbclose	VERB
iajs-807	142	6	.	.	PUNCT
iajs-807	143	1	proposition	proposition	NOUN
iajs-807	143	2	3.12	3.12	NUM
iajs-807	143	3	.	.	PUNCT
iajs-807	144	1	for	for	ADP
iajs-807	144	2	every	every	PRON
iajs-807	144	3	xx	xx	PROPN
iajs-807	145	1	its	its	PRON
iajs-807	145	2	complement	complement	NOUN
iajs-807	145	3	x\{x	x\{x	PRON
iajs-807	145	4	}	}	PUNCT
iajs-807	145	5	is	be	AUX
iajs-807	145	6			ADJ
iajs-807	145	7	gbclosed	gbclosed	ADJ
iajs-807	145	8	or	or	CCONJ
iajs-807	145	9			ADJ
iajs-807	145	10	-open	-open	NOUN
iajs-807	145	11	in	in	ADP
iajs-807	145	12	(	(	PUNCT
iajs-807	145	13	x,	x,	PROPN
iajs-807	145	14	)	)	PUNCT
iajs-807	145	15	.	.	PUNCT
iajs-807	146	1	proof	proof	NOUN
iajs-807	146	2	.	.	PUNCT
iajs-807	147	1	suppose	suppose	VERB
iajs-807	147	2	x\{x	x\{x	PRON
iajs-807	147	3	}	}	PUNCT
iajs-807	147	4	is	be	AUX
iajs-807	147	5	not	not	PART
iajs-807	147	6			ADJ
iajs-807	147	7	open	open	NOUN
iajs-807	147	8	.	.	PUNCT
iajs-807	148	1	then	then	ADV
iajs-807	148	2	x	x	X
iajs-807	148	3	is	be	AUX
iajs-807	148	4	the	the	DET
iajs-807	148	5	only	only	ADJ
iajs-807	148	6			ADJ
iajs-807	148	7	open	open	ADJ
iajs-807	148	8	set	set	NOUN
iajs-807	148	9	containing	contain	VERB
iajs-807	148	10	x\{x	x\{x	PROPN
iajs-807	148	11	}	}	PUNCT
iajs-807	148	12	.	.	PUNCT
iajs-807	149	1	this	this	PRON
iajs-807	149	2	implies	imply	VERB
iajs-807	149	3	bcl	bcl	NOUN
iajs-807	149	4	(	(	PUNCT
iajs-807	149	5	x\{x	x\{x	NOUN
iajs-807	149	6	}	}	PUNCT
iajs-807	149	7	)	)	PUNCT
iajs-807	149	8	x	x	NOUN
iajs-807	149	9	.	.	PUNCT
iajs-807	150	1	hence	hence	ADV
iajs-807	150	2	x\{x	x\{x	PROPN
iajs-807	150	3	}	}	PUNCT
iajs-807	150	4	is	be	AUX
iajs-807	150	5			NOUN
iajs-807	150	6	gbclosed	gbclose	VERB
iajs-807	150	7	.	.	PUNCT
iajs-807	151	1	4	4	X
iajs-807	151	2	.	.	X
iajs-807	151	3			ADJ
iajs-807	151	4	gbopen	gbopen	ADJ
iajs-807	151	5	sets	set	NOUN
iajs-807	151	6	.	.	PUNCT
iajs-807	152	1	the	the	DET
iajs-807	152	2	following	following	ADJ
iajs-807	152	3	result	result	NOUN
iajs-807	152	4	is	be	AUX
iajs-807	152	5	analogous	analogous	ADJ
iajs-807	152	6	to	to	ADP
iajs-807	152	7	well	well	ADV
iajs-807	152	8	known	know	VERB
iajs-807	152	9	corresponding	corresponding	ADJ
iajs-807	152	10	ones	one	NOUN
iajs-807	152	11	.	.	PUNCT
iajs-807	153	1	lemma	lemma	PROPN
iajs-807	153	2	4.1	4.1	NUM
iajs-807	153	3	.	.	PUNCT
iajs-807	153	4	bcl(x\	bcl(x\	PROPN
iajs-807	154	1	a)=	a)=	PROPN
iajs-807	155	1	x\	x\	PROPN
iajs-807	156	1	bint(a	bint(a	PROPN
iajs-807	156	2	)	)	PUNCT
iajs-807	156	3	.	.	PUNCT
iajs-807	157	1	by	by	ADP
iajs-807	157	2	lemma	lemma	PROPN
iajs-807	157	3	4.1	4.1	NUM
iajs-807	157	4	and	and	CCONJ
iajs-807	157	5	definition	definition	NOUN
iajs-807	157	6	2.1	2.1	NUM
iajs-807	157	7	we	we	PRON
iajs-807	157	8	get	get	VERB
iajs-807	157	9	the	the	DET
iajs-807	157	10	following	following	NOUN
iajs-807	157	11	which	which	PRON
iajs-807	157	12	is	be	AUX
iajs-807	157	13	similar	similar	ADJ
iajs-807	157	14	to	to	PART
iajs-807	157	15	corollary	corollary	VERB
iajs-807	157	16	4.1	4.1	NUM
iajs-807	157	17	of	of	ADP
iajs-807	157	18	[	[	X
iajs-807	157	19	2	2	NUM
iajs-807	157	20	]	]	PUNCT
iajs-807	157	21	.	.	PUNCT
iajs-807	158	1	corollary	corollary	ADJ
iajs-807	158	2	4.2	4.2	NUM
iajs-807	158	3	.	.	PUNCT
iajs-807	159	1	a	a	DET
iajs-807	159	2	subset	subset	NOUN
iajs-807	159	3	a	a	PRON
iajs-807	159	4	of	of	ADP
iajs-807	159	5	x	x	NOUN
iajs-807	159	6	is	be	AUX
iajs-807	159	7			ADJ
iajs-807	159	8	gbopen	gbopen	NOUN
iajs-807	159	9	if	if	SCONJ
iajs-807	160	1	and	and	CCONJ
iajs-807	160	2	only	only	ADV
iajs-807	160	3	if	if	SCONJ
iajs-807	160	4	fbint(a	fbint(a	NOUN
iajs-807	160	5	)	)	PUNCT
iajs-807	160	6	whenever	whenever	SCONJ
iajs-807	160	7	f	f	PROPN
iajs-807	160	8	is	be	AUX
iajs-807	160	9			NOUN
iajs-807	160	10	-closed	-closed	ADJ
iajs-807	160	11	in	in	ADP
iajs-807	160	12	x	x	X
iajs-807	160	13	and	and	CCONJ
iajs-807	160	14	fa	fa	NOUN
iajs-807	160	15	.	.	NOUN
iajs-807	160	16	proposition	proposition	NOUN
iajs-807	160	17	4.3	4.3	NUM
iajs-807	160	18	.	.	PUNCT
iajs-807	161	1	if	if	SCONJ
iajs-807	161	2	bint(a	bint(a	NUM
iajs-807	161	3	)	)	PUNCT
iajs-807	161	4	ba	ba	NOUN
iajs-807	161	5	and	and	CCONJ
iajs-807	161	6	a	a	DET
iajs-807	161	7	is	be	AUX
iajs-807	161	8			ADJ
iajs-807	161	9	gbopen	gbopen	NOUN
iajs-807	161	10	,	,	PUNCT
iajs-807	161	11	then	then	ADV
iajs-807	161	12	b	b	PROPN
iajs-807	161	13	is	be	AUX
iajs-807	161	14			ADJ
iajs-807	161	15	gbopen	gbopen	NOUN
iajs-807	161	16	.	.	PUNCT
iajs-807	162	1	proof	proof	NOUN
iajs-807	162	2	.	.	PUNCT
iajs-807	163	1	since	since	SCONJ
iajs-807	163	2	bint(a	bint(a	NUM
iajs-807	163	3	)	)	PUNCT
iajs-807	163	4	ba	ba	NOUN
iajs-807	163	5	.	.	PUNCT
iajs-807	164	1	hence	hence	ADV
iajs-807	164	2	x\	x\	VERB
iajs-807	164	3	a	a	DET
iajs-807	164	4	x\	x\	NOUN
iajs-807	164	5	bbcl(x\	bbcl(x\	NUM
iajs-807	164	6	a	a	PRON
iajs-807	164	7	)	)	PUNCT
iajs-807	164	8	,	,	PUNCT
iajs-807	164	9	by	by	ADP
iajs-807	164	10	lemma	lemma	PROPN
iajs-807	164	11	4.1	4.1	NUM
iajs-807	164	12	.	.	PUNCT
iajs-807	165	1	since	since	SCONJ
iajs-807	165	2	x\	x\	PROPN
iajs-807	165	3	a	a	PRON
iajs-807	165	4	is	be	AUX
iajs-807	165	5			ADJ
iajs-807	165	6	gb	gb	NOUN
iajs-807	165	7	closed	closed	ADJ
iajs-807	165	8	,	,	PUNCT
iajs-807	165	9	so	so	ADV
iajs-807	165	10	by	by	ADP
iajs-807	165	11	theorem	theorem	NOUN
iajs-807	165	12	3.4	3.4	NUM
iajs-807	165	13	,	,	PUNCT
iajs-807	165	14	x\	x\	PROPN
iajs-807	165	15	b	b	PROPN
iajs-807	165	16	is	be	AUX
iajs-807	165	17			NOUN
iajs-807	165	18	gbclosed	gbclose	VERB
iajs-807	165	19	.	.	PUNCT
iajs-807	166	1	thus	thus	ADV
iajs-807	166	2	b	b	X
iajs-807	166	3	is	be	AUX
iajs-807	166	4			ADJ
iajs-807	166	5	gbopen	gbopen	NOUN
iajs-807	166	6	.	.	PUNCT
iajs-807	167	1	proposition	proposition	NOUN
iajs-807	167	2	4.4	4.4	NUM
iajs-807	167	3	.	.	PUNCT
iajs-807	168	1	let	let	VERB
iajs-807	168	2	a	a	DET
iajs-807	168	3	be	be	AUX
iajs-807	168	4			ADJ
iajs-807	168	5	gbopen	gbopen	NOUN
iajs-807	168	6	in	in	ADP
iajs-807	168	7	x	x	PUNCT
iajs-807	168	8	and	and	CCONJ
iajs-807	168	9	let	let	VERB
iajs-807	168	10	b	b	X
iajs-807	168	11	be	be	AUX
iajs-807	168	12			NOUN
iajs-807	168	13	open	open	ADJ
iajs-807	168	14	.	.	PUNCT
iajs-807	169	1	then	then	ADV
iajs-807	169	2	ab	ab	PROPN
iajs-807	169	3	is	be	AUX
iajs-807	169	4			ADJ
iajs-807	169	5	gbopen	gbopen	NOUN
iajs-807	169	6	in	in	ADP
iajs-807	169	7	x.	x.	NOUN
iajs-807	169	8	proof	proof	NOUN
iajs-807	169	9	.	.	PUNCT
iajs-807	170	1	let	let	VERB
iajs-807	170	2	f	f	PRON
iajs-807	170	3	be	be	AUX
iajs-807	170	4	any	any	DET
iajs-807	170	5			ADJ
iajs-807	170	6	closed	closed	ADJ
iajs-807	170	7	subset	subset	NOUN
iajs-807	170	8	of	of	ADP
iajs-807	170	9	x	x	SYM
iajs-807	170	10	such	such	ADJ
iajs-807	170	11	that	that	SCONJ
iajs-807	170	12	f	f	PROPN
iajs-807	170	13	a	a	DET
iajs-807	170	14	b	b	NOUN
iajs-807	170	15	.	.	PUNCT
iajs-807	171	1	hence	hence	ADV
iajs-807	171	2	f	f	PROPN
iajs-807	171	3	a	a	NOUN
iajs-807	171	4	and	and	CCONJ
iajs-807	171	5	by	by	ADP
iajs-807	171	6	theorem	theorem	NOUN
iajs-807	171	7	4.2	4.2	NUM
iajs-807	171	8	,	,	PUNCT
iajs-807	171	9	fbint(a)=	fbint(a)=	ADJ
iajs-807	171	10			NOUN
iajs-807	171	11	{	{	PUNCT
iajs-807	171	12	u	u	NOUN
iajs-807	171	13	:	:	PUNCT
iajs-807	171	14	u	u	NOUN
iajs-807	171	15	is	be	AUX
iajs-807	171	16	bopen	bopen	ADJ
iajs-807	171	17	and	and	CCONJ
iajs-807	171	18	ua	ua	ADP
iajs-807	171	19	}	}	PUNCT
iajs-807	171	20	.	.	PUNCT
iajs-807	172	1	then	then	ADV
iajs-807	172	2	f	f	PROPN
iajs-807	172	3			PROPN
iajs-807	172	4	(	(	PUNCT
iajs-807	172	5	u	u	NOUN
iajs-807	172	6	b	b	ADJ
iajs-807	172	7	)	)	PUNCT
iajs-807	172	8	,	,	PUNCT
iajs-807	172	9	where	where	SCONJ
iajs-807	172	10	u	u	NOUN
iajs-807	172	11	is	be	AUX
iajs-807	172	12	a	a	DET
iajs-807	172	13	bopen	bopen	ADJ
iajs-807	172	14	set	set	NOUN
iajs-807	172	15	contained	contain	VERB
iajs-807	172	16	in	in	ADP
iajs-807	172	17	a.	a.	NOUN
iajs-807	172	18	since	since	SCONJ
iajs-807	172	19	u	u	PROPN
iajs-807	172	20	b	b	ADJ
iajs-807	172	21	is	be	AUX
iajs-807	172	22	a	a	DET
iajs-807	172	23	bopen	bopen	ADJ
iajs-807	172	24	set	set	NOUN
iajs-807	172	25	contained	contain	VERB
iajs-807	172	26	in	in	ADP
iajs-807	172	27	a	a	DET
iajs-807	172	28	b	b	NOUN
iajs-807	172	29	for	for	SCONJ
iajs-807	172	30	each	each	DET
iajs-807	172	31	bopen	bopen	NOUN
iajs-807	172	32	set	set	VERB
iajs-807	172	33	u	u	NOUN
iajs-807	172	34	contained	contain	VERB
iajs-807	172	35	in	in	ADP
iajs-807	172	36	a	a	DET
iajs-807	172	37	,	,	PUNCT
iajs-807	172	38	fbint(ab	fbint(ab	PROPN
iajs-807	172	39	)	)	PUNCT
iajs-807	172	40	,	,	PUNCT
iajs-807	172	41	and	and	CCONJ
iajs-807	172	42	by	by	ADP
iajs-807	172	43	theorem	theorem	NOUN
iajs-807	172	44	4.2	4.2	NUM
iajs-807	172	45	,	,	PUNCT
iajs-807	172	46	ab	ab	PROPN
iajs-807	172	47	is	be	AUX
iajs-807	172	48			ADJ
iajs-807	172	49	gbopen	gbopen	NOUN
iajs-807	172	50	in	in	ADP
iajs-807	172	51	x.	x.	PROPN
iajs-807	172	52	lemma	lemma	PROPN
iajs-807	172	53	4.5	4.5	NUM
iajs-807	172	54	.	.	PUNCT
iajs-807	173	1	for	for	ADP
iajs-807	173	2	any	any	DET
iajs-807	173	3	ax	ax	PROPN
iajs-807	173	4	,	,	PUNCT
iajs-807	173	5	bint(bcl(a)\	bint(bcl(a)\	ADP
iajs-807	173	6	a)=	a)=	PROPN
iajs-807	173	7			NOUN
iajs-807	173	8	.	.	PUNCT
iajs-807	174	1	proof	proof	NOUN
iajs-807	174	2	.	.	PUNCT
iajs-807	175	1	if	if	SCONJ
iajs-807	175	2	bint	bint	PROPN
iajs-807	175	3	(	(	PUNCT
iajs-807	175	4	bcl(a)\	bcl(a)\	X
iajs-807	175	5	a	a	PRON
iajs-807	175	6	)	)	PUNCT
iajs-807	175	7			NOUN
iajs-807	175	8			NOUN
iajs-807	175	9	.	.	PUNCT
iajs-807	176	1	then	then	ADV
iajs-807	176	2	there	there	PRON
iajs-807	176	3	is	be	VERB
iajs-807	176	4	an	an	DET
iajs-807	176	5	element	element	NOUN
iajs-807	176	6	xbint	xbint	PUNCT
iajs-807	176	7	(	(	PUNCT
iajs-807	176	8	bcl(a)-a	bcl(a)-a	NUM
iajs-807	176	9	)	)	PUNCT
iajs-807	176	10	,	,	PUNCT
iajs-807	176	11	so	so	CCONJ
iajs-807	176	12	there	there	PRON
iajs-807	176	13	is	be	VERB
iajs-807	176	14	ubo(x	ubo(x	NOUN
iajs-807	176	15	)	)	PUNCT
iajs-807	176	16	such	such	ADJ
iajs-807	176	17	that	that	SCONJ
iajs-807	176	18	xubcl(a)-a	xubcl(a)-a	PROPN
iajs-807	176	19	.	.	PUNCT
iajs-807	177	1	therefore	therefore	ADV
iajs-807	177	2	ubcl	ubcl	NOUN
iajs-807	177	3	(	(	PUNCT
iajs-807	177	4	a	a	X
iajs-807	177	5	)	)	PUNCT
iajs-807	177	6	and	and	CCONJ
iajs-807	177	7	ua	ua	NOUN
iajs-807	177	8	.	.	PUNCT
iajs-807	178	1	thus	thus	ADV
iajs-807	178	2	u	u	X
iajs-807	178	3			PROPN
iajs-807	178	4	bcl(a	bcl(a	PROPN
iajs-807	178	5	)	)	PUNCT
iajs-807	178	6	and	and	CCONJ
iajs-807	178	7	ux	ux	PROPN
iajs-807	178	8	-	-	NOUN
iajs-807	178	9	a.	a.	NOUN
iajs-807	178	10	hence	hence	ADV
iajs-807	178	11	there	there	PRON
iajs-807	178	12	is	be	VERB
iajs-807	178	13	ubo(x	ubo(x	NOUN
iajs-807	178	14	)	)	PUNCT
iajs-807	178	15	,	,	PUNCT
iajs-807	178	16	ua=	ua=	INTJ
iajs-807	178	17	,	,	PUNCT
iajs-807	178	18	a	a	DET
iajs-807	178	19	contradiction	contradiction	NOUN
iajs-807	178	20	,	,	PUNCT
iajs-807	178	21	since	since	SCONJ
iajs-807	178	22	xbcl(a	xbcl(a	NUM
iajs-807	178	23	)	)	PUNCT
iajs-807	178	24	.	.	PUNCT
iajs-807	178	25	.	.	PUNCT
iajs-807	179	1	ibn	ibn	PROPN
iajs-807	179	2	alhaitham	alhaitham	PROPN
iajs-807	179	3	j.	j.	PROPN
iajs-807	179	4	for	for	ADP
iajs-807	179	5	pure	pure	ADJ
iajs-807	179	6	&	&	CCONJ
iajs-807	179	7	appl	appl	PROPN
iajs-807	179	8	.	.	PUNCT
iajs-807	180	1	sci	sci	PROPN
iajs-807	180	2	.	.	PUNCT
iajs-807	180	3	vol.24	vol.24	NOUN
iajs-807	180	4	(	(	PUNCT
iajs-807	180	5	3	3	NUM
iajs-807	180	6	)	)	PUNCT
iajs-807	180	7	2011	2011	NUM
iajs-807	180	8	proposition	proposition	NOUN
iajs-807	180	9	4.6	4.6	NUM
iajs-807	180	10	.	.	PUNCT
iajs-807	181	1	let	let	VERB
iajs-807	181	2	abx	abx	PUNCT
iajs-807	181	3	and	and	CCONJ
iajs-807	181	4	let	let	VERB
iajs-807	181	5	bcl(a)\a	bcl(a)\a	VERB
iajs-807	181	6	be	be	AUX
iajs-807	181	7			ADJ
iajs-807	181	8	gbclosed	gbclose	VERB
iajs-807	181	9	set	set	NOUN
iajs-807	181	10	.	.	PUNCT
iajs-807	182	1	then	then	ADV
iajs-807	182	2	bcl(a)\b	bcl(a)\b	PROPN
iajs-807	182	3	is	be	AUX
iajs-807	182	4	also	also	ADV
iajs-807	182	5			ADJ
iajs-807	182	6	gbopen	gbopen	NOUN
iajs-807	182	7	.	.	PUNCT
iajs-807	183	1	proof	proof	NOUN
iajs-807	183	2	.	.	PUNCT
iajs-807	184	1	suppose	suppose	VERB
iajs-807	184	2	bcl(a)\a	bcl(a)\a	NOUN
iajs-807	184	3	is	be	AUX
iajs-807	184	4			ADJ
iajs-807	184	5	gbopen	gbopen	NOUN
iajs-807	184	6	and	and	CCONJ
iajs-807	184	7	let	let	VERB
iajs-807	184	8	f	f	PRON
iajs-807	184	9	be	be	AUX
iajs-807	184	10	a	a	DET
iajs-807	184	11			ADJ
iajs-807	184	12	closed	closed	ADJ
iajs-807	184	13	subset	subset	NOUN
iajs-807	184	14	of	of	ADP
iajs-807	184	15	x	x	PUNCT
iajs-807	184	16	with	with	ADP
iajs-807	184	17	fbcl(a)\b	fbcl(a)\b	PROPN
iajs-807	184	18	.	.	PUNCT
iajs-807	185	1	then	then	ADV
iajs-807	185	2	fbcl(a)\a	fbcl(a)\a	PROPN
iajs-807	185	3	.	.	PROPN
iajs-807	185	4	by	by	ADP
iajs-807	185	5	theorem	theorem	ADJ
iajs-807	185	6	2.4	2.4	NUM
iajs-807	185	7	and	and	CCONJ
iajs-807	185	8	lemma	lemma	PROPN
iajs-807	185	9	4.5	4.5	NUM
iajs-807	185	10	,	,	PUNCT
iajs-807	185	11	f	f	PROPN
iajs-807	185	12	bint(bcl(a)\a)=	bint(bcl(a)\a)=	PROPN
iajs-807	185	13			NOUN
iajs-807	185	14	.	.	PUNCT
iajs-807	186	1	so	so	ADV
iajs-807	186	2	,	,	PUNCT
iajs-807	186	3	f=	f=	NUM
iajs-807	186	4	.consequently	.consequently	ADV
iajs-807	186	5	,	,	PUNCT
iajs-807	186	6	fbint(bcl(a)\b	fbint(bcl(a)\b	PROPN
iajs-807	186	7	)	)	PUNCT
iajs-807	186	8	.	.	PUNCT
iajs-807	187	1	proposition	proposition	NOUN
iajs-807	187	2	4.7	4.7	NUM
iajs-807	187	3	.	.	PUNCT
iajs-807	188	1	let	let	VERB
iajs-807	188	2	ax	ax	PRON
iajs-807	188	3	be	be	AUX
iajs-807	188	4	a	a	DET
iajs-807	188	5			ADJ
iajs-807	188	6	gb	gb	ADV
iajs-807	188	7	-	-	PUNCT
iajs-807	188	8	closed	closed	ADJ
iajs-807	188	9	.	.	PUNCT
iajs-807	189	1	then	then	ADV
iajs-807	189	2	bcl(a)\	bcl(a)\	X
iajs-807	189	3	a	a	PRON
iajs-807	189	4	is	be	AUX
iajs-807	189	5			ADJ
iajs-807	189	6	gbopen	gbopen	NOUN
iajs-807	189	7	.	.	PUNCT
iajs-807	190	1	proof	proof	NOUN
iajs-807	190	2	.	.	PUNCT
iajs-807	191	1	let	let	VERB
iajs-807	191	2	f	f	PRON
iajs-807	191	3	be	be	AUX
iajs-807	191	4	a	a	DET
iajs-807	191	5			NOUN
iajs-807	191	6	closed	close	VERB
iajs-807	191	7	such	such	ADJ
iajs-807	191	8	that	that	DET
iajs-807	191	9	fbcl(a)a	fbcl(a)a	NOUN
iajs-807	191	10	.	.	PUNCT
iajs-807	192	1	then	then	ADV
iajs-807	192	2	by	by	ADP
iajs-807	192	3	theorem	theorem	NOUN
iajs-807	192	4	3.2	3.2	NUM
iajs-807	192	5	,	,	PUNCT
iajs-807	192	6	f=	f=	NUM
iajs-807	192	7	.	.	PUNCT
iajs-807	193	1	so	so	ADV
iajs-807	193	2	f	f	PROPN
iajs-807	193	3	bint	bint	PROPN
iajs-807	193	4	(	(	PUNCT
iajs-807	193	5	bcl(a)\a	bcl(a)\a	PROPN
iajs-807	193	6	)	)	PUNCT
iajs-807	193	7	.	.	PUNCT
iajs-807	194	1	therefore	therefore	ADV
iajs-807	194	2	bcl(a)-a	bcl(a)-a	PROPN
iajs-807	194	3	is	be	AUX
iajs-807	194	4			ADJ
iajs-807	194	5	gbopen	gbopen	NOUN
iajs-807	194	6	,	,	PUNCT
iajs-807	194	7	by	by	ADP
iajs-807	194	8	theorem	theorem	NOUN
iajs-807	194	9	4.2	4.2	NUM
iajs-807	194	10	.	.	PUNCT
iajs-807	195	1	5	5	NUM
iajs-807	195	2	.	.	PUNCT
iajs-807	195	3			PROPN
iajs-807	195	4	b	b	NOUN
iajs-807	195	5	2	2	NUM
iajs-807	195	6	1	1	NUM
iajs-807	195	7	t	t	NOUN
iajs-807	195	8	spaces	space	NOUN
iajs-807	195	9	in	in	ADP
iajs-807	195	10	this	this	DET
iajs-807	195	11	section	section	NOUN
iajs-807	195	12	we	we	PRON
iajs-807	195	13	define	define	VERB
iajs-807	195	14	a	a	DET
iajs-807	195	15	new	new	ADJ
iajs-807	195	16	class	class	NOUN
iajs-807	195	17	of	of	ADP
iajs-807	195	18	spaces	space	NOUN
iajs-807	195	19	,	,	PUNCT
iajs-807	195	20	named	name	VERB
iajs-807	195	21			PROPN
iajs-807	195	22	b	b	NOUN
iajs-807	195	23	2	2	NUM
iajs-807	195	24	1	1	NUM
iajs-807	195	25	t	t	NOUN
iajs-807	195	26	space	space	NOUN
iajs-807	195	27	which	which	PRON
iajs-807	195	28	is	be	AUX
iajs-807	195	29	a	a	DET
iajs-807	195	30	generalization	generalization	NOUN
iajs-807	195	31	of	of	ADP
iajs-807	195	32	2	2	NUM
iajs-807	195	33	1	1	NUM
iajs-807	195	34	t	t	NOUN
iajs-807	195	35	[	[	X
iajs-807	195	36	14	14	NUM
iajs-807	195	37	]	]	PUNCT
iajs-807	195	38	.	.	PUNCT
iajs-807	196	1	definition	definition	NOUN
iajs-807	196	2	5.1	5.1	NUM
iajs-807	196	3	.	.	PUNCT
iajs-807	197	1	a	a	DET
iajs-807	197	2	space	space	NOUN
iajs-807	197	3	(	(	PUNCT
iajs-807	197	4	x,	x,	PROPN
iajs-807	197	5	)	)	PUNCT
iajs-807	197	6	is	be	AUX
iajs-807	197	7	called	call	VERB
iajs-807	197	8	a	a	DET
iajs-807	197	9			PROPN
iajs-807	197	10	b	b	NOUN
iajs-807	197	11	2	2	NUM
iajs-807	197	12	1	1	NUM
iajs-807	197	13	t	t	NOUN
iajs-807	197	14	space	space	NOUN
iajs-807	197	15	if	if	SCONJ
iajs-807	197	16	every	every	DET
iajs-807	197	17			ADJ
iajs-807	197	18	gbclosed	gbclose	VERB
iajs-807	197	19	set	set	NOUN
iajs-807	197	20	is	be	AUX
iajs-807	197	21	bclosed	bclose	VERB
iajs-807	197	22	.	.	PUNCT
iajs-807	197	23	example	example	NOUN
iajs-807	198	1	5.2	5.2	NUM
iajs-807	198	2	.	.	PUNCT
iajs-807	199	1	if	if	SCONJ
iajs-807	199	2	x	x	PROPN
iajs-807	199	3			NOUN
iajs-807	199	4			NOUN
iajs-807	199	5	be	be	VERB
iajs-807	199	6	any	any	DET
iajs-807	199	7	set	set	NOUN
iajs-807	199	8	.	.	PUNCT
iajs-807	200	1	then	then	ADV
iajs-807	200	2	(	(	PUNCT
iajs-807	200	3	x	x	X
iajs-807	200	4	,	,	PUNCT
iajs-807	200	5	.ind	.ind	PUNCT
iajs-807	200	6	)	)	PUNCT
iajs-807	200	7	is	be	AUX
iajs-807	200	8			PROPN
iajs-807	200	9	b	b	NOUN
iajs-807	200	10	2	2	NUM
iajs-807	200	11	1	1	NUM
iajs-807	200	12	t	t	NOUN
iajs-807	200	13	space	space	NOUN
iajs-807	200	14	.	.	PUNCT
iajs-807	201	1	recall	recall	VERB
iajs-807	201	2	that	that	PRON
iajs-807	201	3	x	x	PRON
iajs-807	201	4	is	be	AUX
iajs-807	201	5	2	2	NUM
iajs-807	201	6	1	1	NUM
iajs-807	201	7	t	t	NOUN
iajs-807	201	8	space	space	NOUN
iajs-807	201	9	if	if	SCONJ
iajs-807	201	10	every	every	DET
iajs-807	201	11	gclosed	gclose	VERB
iajs-807	201	12	set	set	NOUN
iajs-807	201	13	is	be	AUX
iajs-807	201	14	closed	close	VERB
iajs-807	201	15	or	or	CCONJ
iajs-807	201	16	equivalently	equivalently	ADV
iajs-807	201	17	if	if	SCONJ
iajs-807	201	18	every	every	DET
iajs-807	201	19	singleton	singleton	NOUN
iajs-807	201	20	is	be	AUX
iajs-807	201	21	open	open	ADJ
iajs-807	201	22	or	or	CCONJ
iajs-807	201	23	closed	closed	ADJ
iajs-807	201	24	.	.	PUNCT
iajs-807	202	1	the	the	DET
iajs-807	202	2	notions	notion	NOUN
iajs-807	202	3	of	of	ADP
iajs-807	202	4			ADJ
iajs-807	202	5	b2	b2	NOUN
iajs-807	202	6	1	1	NUM
iajs-807	202	7	t	t	NOUN
iajs-807	202	8	and	and	CCONJ
iajs-807	202	9	2	2	NUM
iajs-807	202	10	1	1	NUM
iajs-807	202	11	t	t	NOUN
iajs-807	202	12	are	be	AUX
iajs-807	202	13	independent	independent	ADJ
iajs-807	202	14	as	as	SCONJ
iajs-807	202	15	it	it	PRON
iajs-807	202	16	can	can	AUX
iajs-807	202	17	be	be	AUX
iajs-807	202	18	seen	see	VERB
iajs-807	202	19	through	through	ADP
iajs-807	202	20	the	the	DET
iajs-807	202	21	following	follow	VERB
iajs-807	202	22	examples	example	NOUN
iajs-807	202	23	.	.	PUNCT
iajs-807	203	1	example	example	NOUN
iajs-807	203	2	5.3	5.3	NUM
iajs-807	203	3	.	.	PUNCT
iajs-807	204	1	let	let	VERB
iajs-807	204	2	x=	x=	PUNCT
iajs-807	205	1	{	{	PUNCT
iajs-807	205	2	a	a	DET
iajs-807	205	3	,	,	PUNCT
iajs-807	205	4	b	b	NOUN
iajs-807	205	5	,	,	PUNCT
iajs-807	205	6	c	c	NOUN
iajs-807	205	7	}	}	PUNCT
iajs-807	205	8	,	,	PUNCT
iajs-807	205	9			NOUN
iajs-807	205	10	=	=	SYM
iajs-807	205	11	{	{	PUNCT
iajs-807	205	12	x,	x,	PROPN
iajs-807	205	13	,	,	PUNCT
iajs-807	205	14	{	{	PUNCT
iajs-807	205	15	c	c	NOUN
iajs-807	205	16	}	}	PUNCT
iajs-807	205	17	,	,	PUNCT
iajs-807	205	18	{	{	PUNCT
iajs-807	205	19	a	a	DET
iajs-807	205	20	,	,	PUNCT
iajs-807	205	21	b	b	NOUN
iajs-807	205	22	}	}	PUNCT
iajs-807	205	23	}	}	PUNCT
iajs-807	205	24	.	.	PUNCT
iajs-807	206	1	then	then	ADV
iajs-807	206	2	ro(x	ro(x	PUNCT
iajs-807	206	3	)	)	PUNCT
iajs-807	207	1	=	=	NOUN
iajs-807	207	2			NOUN
iajs-807	207	3	,	,	PUNCT
iajs-807	207	4	bo(x	bo(x	NUM
iajs-807	207	5	)	)	PUNCT
iajs-807	207	6	=	=	SYM
iajs-807	207	7	p(x	p(x	PROPN
iajs-807	207	8	)	)	PUNCT
iajs-807	207	9	=	=	SYM
iajs-807	207	10	bc(x	bc(x	NOUN
iajs-807	207	11	)	)	PUNCT
iajs-807	207	12	=	=	SYM
iajs-807	207	13			PROPN
iajs-807	207	14	gbc(x	gbc(x	NOUN
iajs-807	207	15	)	)	PUNCT
iajs-807	207	16	.	.	PUNCT
iajs-807	208	1	then	then	ADV
iajs-807	208	2	x	x	PRON
iajs-807	208	3	is	be	AUX
iajs-807	208	4			PROPN
iajs-807	208	5	b2	b2	NOUN
iajs-807	208	6	1	1	NUM
iajs-807	208	7	t	t	NOUN
iajs-807	208	8	but	but	CCONJ
iajs-807	208	9	not	not	PART
iajs-807	208	10	2	2	NUM
iajs-807	208	11	1	1	NUM
iajs-807	208	12	t	t	NOUN
iajs-807	208	13	.	.	PUNCT
iajs-807	209	1	example	example	NOUN
iajs-807	209	2	5.4	5.4	NUM
iajs-807	209	3	.	.	PUNCT
iajs-807	210	1	consider	consider	VERB
iajs-807	210	2	(	(	PUNCT
iajs-807	210	3	n,	n,	NOUN
iajs-807	210	4	)	)	PUNCT
iajs-807	210	5	where	where	SCONJ
iajs-807	210	6	n	n	PRON
iajs-807	210	7	is	be	AUX
iajs-807	210	8	the	the	DET
iajs-807	210	9	set	set	NOUN
iajs-807	210	10	of	of	ADP
iajs-807	210	11	natural	natural	ADJ
iajs-807	210	12	numbers	number	NOUN
iajs-807	210	13	and	and	CCONJ
iajs-807	210	14			NOUN
iajs-807	210	15	=	=	X
iajs-807	210	16	{	{	PUNCT
iajs-807	210	17	un	un	ADV
iajs-807	210	18	:	:	PUNCT
iajs-807	210	19	1u}	1u}	NUM
iajs-807	210	20	{	{	PUNCT
iajs-807	210	21			NOUN
iajs-807	210	22	}	}	PUNCT
iajs-807	210	23	,	,	PUNCT
iajs-807	210	24	then	then	ADV
iajs-807	210	25			PROPN
iajs-807	210	26	is	be	AUX
iajs-807	210	27	a	a	DET
iajs-807	210	28	topology	topology	NOUN
iajs-807	210	29	on	on	ADP
iajs-807	210	30	n	n	CCONJ
iajs-807	210	31	,	,	PUNCT
iajs-807	210	32	and	and	CCONJ
iajs-807	210	33	(	(	PUNCT
iajs-807	210	34	n,	n,	PROPN
iajs-807	210	35	)	)	PUNCT
iajs-807	210	36	is	be	AUX
iajs-807	210	37	2	2	NUM
iajs-807	210	38	1	1	NUM
iajs-807	210	39	t	t	NOUN
iajs-807	210	40	but	but	CCONJ
iajs-807	210	41	not	not	PART
iajs-807	210	42			NOUN
iajs-807	210	43	b2	b2	NOUN
iajs-807	210	44	1	1	NUM
iajs-807	210	45	t	t	NOUN
iajs-807	210	46	.	.	PUNCT
iajs-807	211	1	next	next	ADV
iajs-807	211	2	,	,	PUNCT
iajs-807	211	3	we	we	PRON
iajs-807	211	4	recall	recall	VERB
iajs-807	211	5	the	the	DET
iajs-807	211	6	following	following	NOUN
iajs-807	211	7	,	,	PUNCT
iajs-807	211	8	definition	definition	NOUN
iajs-807	211	9	5.5	5.5	NUM
iajs-807	211	10	.	.	PUNCT
iajs-807	212	1	a	a	DET
iajs-807	212	2	space	space	NOUN
iajs-807	212	3	x	x	PUNCT
iajs-807	212	4	is	be	AUX
iajs-807	212	5			ADJ
iajs-807	212	6	gsp	gsp	NOUN
iajs-807	212	7	2	2	NUM
iajs-807	212	8	1	1	NUM
iajs-807	212	9	t	t	NOUN
iajs-807	212	10	(	(	PUNCT
iajs-807	212	11	or	or	CCONJ
iajs-807	212	12			NOUN
iajs-807	212	13	gsp	gsp	NOUN
iajs-807	212	14	in	in	ADP
iajs-807	212	15	[	[	X
iajs-807	212	16	2	2	NUM
iajs-807	212	17	]	]	PUNCT
iajs-807	212	18	)	)	PUNCT
iajs-807	212	19	if	if	SCONJ
iajs-807	212	20	every	every	DET
iajs-807	212	21			ADJ
iajs-807	212	22	gspclosed	gspclosed	ADJ
iajs-807	212	23	subset	subset	NOUN
iajs-807	212	24	of	of	ADP
iajs-807	212	25	x	x	PROPN
iajs-807	212	26	is	be	AUX
iajs-807	212	27	semipreclosed	semipreclose	VERB
iajs-807	212	28	.	.	PUNCT
iajs-807	212	29	.	.	PUNCT
iajs-807	213	1	ibn	ibn	PROPN
iajs-807	213	2	alhaitham	alhaitham	PROPN
iajs-807	213	3	j.	j.	PROPN
iajs-807	213	4	for	for	ADP
iajs-807	213	5	pure	pure	ADJ
iajs-807	213	6	&	&	CCONJ
iajs-807	213	7	appl	appl	PROPN
iajs-807	213	8	.	.	PUNCT
iajs-807	214	1	sci	sci	PROPN
iajs-807	214	2	.	.	PUNCT
iajs-807	214	3	vol.24	vol.24	NOUN
iajs-807	214	4	(	(	PUNCT
iajs-807	214	5	3	3	NUM
iajs-807	214	6	)	)	PUNCT
iajs-807	214	7	2011	2011	NUM
iajs-807	214	8	remark	remark	VERB
iajs-807	214	9	5.6	5.6	NUM
iajs-807	214	10	.	.	PUNCT
iajs-807	215	1	it	it	PRON
iajs-807	215	2	seems	seem	VERB
iajs-807	215	3	that	that	SCONJ
iajs-807	215	4	the	the	DET
iajs-807	215	5	notions	notion	NOUN
iajs-807	215	6	of	of	ADP
iajs-807	215	7			PROPN
iajs-807	215	8	gsp	gsp	NOUN
iajs-807	215	9	2	2	NUM
iajs-807	215	10	1	1	NUM
iajs-807	215	11	t	t	NOUN
iajs-807	215	12	and	and	CCONJ
iajs-807	215	13			PROPN
iajs-807	215	14	b	b	NOUN
iajs-807	215	15	2	2	NUM
iajs-807	215	16	1	1	NUM
iajs-807	215	17	t	t	NOUN
iajs-807	215	18	are	be	AUX
iajs-807	215	19	independent	independent	ADJ
iajs-807	215	20	of	of	ADP
iajs-807	215	21	each	each	DET
iajs-807	215	22	other	other	ADJ
iajs-807	215	23	,	,	PUNCT
iajs-807	215	24	but	but	CCONJ
iajs-807	215	25	we	we	PRON
iajs-807	215	26	could	could	AUX
iajs-807	215	27	not	not	PART
iajs-807	215	28	disprove	disprove	VERB
iajs-807	215	29	it	it	PRON
iajs-807	215	30	.	.	PUNCT
iajs-807	216	1	the	the	DET
iajs-807	216	2	following	following	ADJ
iajs-807	216	3	result	result	NOUN
iajs-807	216	4	is	be	AUX
iajs-807	216	5	analogous	analogous	ADJ
iajs-807	216	6	to	to	PART
iajs-807	216	7	proposition	proposition	VERB
iajs-807	216	8	3.7	3.7	NUM
iajs-807	216	9	in	in	ADP
iajs-807	216	10	[	[	X
iajs-807	216	11	2	2	NUM
iajs-807	216	12	]	]	PUNCT
iajs-807	216	13	.	.	PUNCT
iajs-807	217	1	proposition	proposition	NOUN
iajs-807	217	2	5.7	5.7	NUM
iajs-807	217	3	.	.	PUNCT
iajs-807	218	1	a	a	DET
iajs-807	218	2	space	space	NOUN
iajs-807	218	3	x	x	PUNCT
iajs-807	218	4	is	be	AUX
iajs-807	218	5			ADJ
iajs-807	218	6	b	b	NOUN
iajs-807	218	7	2	2	NUM
iajs-807	218	8	1	1	NUM
iajs-807	218	9	t	t	NOUN
iajs-807	218	10	if	if	SCONJ
iajs-807	219	1	and	and	CCONJ
iajs-807	219	2	only	only	ADV
iajs-807	219	3	if	if	SCONJ
iajs-807	219	4	every	every	DET
iajs-807	219	5	singleton	singleton	NOUN
iajs-807	219	6	of	of	ADP
iajs-807	219	7	x	x	SYM
iajs-807	219	8	is	be	AUX
iajs-807	219	9	either	either	CCONJ
iajs-807	219	10			ADJ
iajs-807	219	11	closed	closed	ADJ
iajs-807	219	12	or	or	CCONJ
iajs-807	219	13	bopen	bopen	VERB
iajs-807	219	14	.	.	PUNCT
iajs-807	220	1	proof	proof	NOUN
iajs-807	220	2	.	.	PUNCT
iajs-807	221	1	necessity	necessity	NOUN
iajs-807	221	2	:	:	PUNCT
iajs-807	221	3	let	let	VERB
iajs-807	221	4	x	x	PROPN
iajs-807	221	5	x	x	PUNCT
iajs-807	221	6	and	and	CCONJ
iajs-807	221	7	assume	assume	VERB
iajs-807	221	8	that	that	SCONJ
iajs-807	221	9	{	{	PUNCT
iajs-807	221	10	x	x	X
iajs-807	221	11	}	}	PUNCT
iajs-807	221	12	is	be	AUX
iajs-807	221	13	not	not	PART
iajs-807	221	14			NOUN
iajs-807	221	15	closed	closed	ADJ
iajs-807	221	16	,	,	PUNCT
iajs-807	221	17	then	then	ADV
iajs-807	221	18	x\	x\	PROPN
iajs-807	221	19	{	{	PUNCT
iajs-807	221	20	x	x	X
iajs-807	221	21	}	}	PUNCT
iajs-807	221	22	is	be	AUX
iajs-807	221	23	not	not	PART
iajs-807	221	24			ADJ
iajs-807	221	25	open	open	ADJ
iajs-807	221	26	,	,	PUNCT
iajs-807	221	27	so	so	CCONJ
iajs-807	221	28	the	the	DET
iajs-807	221	29	only	only	ADJ
iajs-807	221	30			ADJ
iajs-807	221	31	open	open	ADJ
iajs-807	221	32	set	set	NOUN
iajs-807	221	33	containing	contain	VERB
iajs-807	221	34	x\	x\	NOUN
iajs-807	221	35	{	{	PUNCT
iajs-807	221	36	x	x	NOUN
iajs-807	221	37	}	}	PUNCT
iajs-807	221	38	is	be	AUX
iajs-807	221	39	x	x	NOUN
iajs-807	221	40	,	,	PUNCT
iajs-807	221	41	hence	hence	ADV
iajs-807	221	42	x\	x\	NOUN
iajs-807	221	43	{	{	PUNCT
iajs-807	221	44	x	x	X
iajs-807	221	45	}	}	PUNCT
iajs-807	221	46	is	be	AUX
iajs-807	221	47			NOUN
iajs-807	221	48	gbclosed	gbclose	VERB
iajs-807	221	49	.	.	PUNCT
iajs-807	222	1	by	by	ADP
iajs-807	222	2	assumption	assumption	NOUN
iajs-807	222	3	x\	x\	NOUN
iajs-807	222	4	{	{	PUNCT
iajs-807	222	5	x	x	X
iajs-807	222	6	}	}	PUNCT
iajs-807	222	7	is	be	AUX
iajs-807	222	8	bclosed	bclose	VERB
iajs-807	222	9	.	.	PUNCT
iajs-807	223	1	thus	thus	ADV
iajs-807	223	2	{	{	PUNCT
iajs-807	223	3	x	x	X
iajs-807	223	4	}	}	PUNCT
iajs-807	223	5	is	be	AUX
iajs-807	223	6	bopen	bopen	ADJ
iajs-807	223	7	.	.	PUNCT
iajs-807	224	1	sufficiency	sufficiency	NOUN
iajs-807	224	2	:	:	PUNCT
iajs-807	224	3	let	let	VERB
iajs-807	224	4	a	a	PRON
iajs-807	224	5	be	be	AUX
iajs-807	224	6	a	a	DET
iajs-807	224	7			ADJ
iajs-807	224	8	gbclosed	gbclose	VERB
iajs-807	224	9	subset	subset	NOUN
iajs-807	224	10	of	of	ADP
iajs-807	224	11	x	x	X
iajs-807	224	12	and	and	CCONJ
iajs-807	224	13	xbcl(a	xbcl(a	NUM
iajs-807	224	14	)	)	PUNCT
iajs-807	224	15	.	.	PUNCT
iajs-807	225	1	by	by	ADP
iajs-807	225	2	assumption	assumption	NOUN
iajs-807	225	3	,	,	PUNCT
iajs-807	225	4	we	we	PRON
iajs-807	225	5	have	have	VERB
iajs-807	225	6	the	the	DET
iajs-807	225	7	following	follow	VERB
iajs-807	225	8	two	two	NUM
iajs-807	225	9	cases	case	NOUN
iajs-807	225	10	:	:	PUNCT
iajs-807	225	11	(	(	PUNCT
iajs-807	225	12	i	i	NOUN
iajs-807	225	13	)	)	PUNCT
iajs-807	225	14	{	{	PUNCT
iajs-807	225	15	x	x	X
iajs-807	225	16	}	}	PUNCT
iajs-807	225	17	is	be	AUX
iajs-807	225	18	bopen	bopen	ADJ
iajs-807	225	19	.	.	PUNCT
iajs-807	226	1	since	since	SCONJ
iajs-807	226	2	xbcl	xbcl	X
iajs-807	226	3	(	(	PUNCT
iajs-807	226	4	a	a	NOUN
iajs-807	226	5	)	)	PUNCT
iajs-807	226	6	,	,	PUNCT
iajs-807	226	7	so	so	CCONJ
iajs-807	226	8	{	{	PUNCT
iajs-807	226	9	x	x	NOUN
iajs-807	226	10	}	}	PUNCT
iajs-807	226	11	a	a	PROPN
iajs-807	226	12			NOUN
iajs-807	226	13			NOUN
iajs-807	226	14	.	.	PUNCT
iajs-807	227	1	thus	thus	ADV
iajs-807	227	2	xa	xa	PUNCT
iajs-807	227	3	.	.	PUNCT
iajs-807	228	1	(	(	PUNCT
iajs-807	228	2	ii	ii	NOUN
iajs-807	228	3	)	)	PUNCT
iajs-807	228	4	{	{	PUNCT
iajs-807	228	5	x	x	X
iajs-807	228	6	}	}	PUNCT
iajs-807	228	7	is	be	AUX
iajs-807	228	8			NOUN
iajs-807	228	9	closed	closed	ADJ
iajs-807	228	10	.	.	PUNCT
iajs-807	229	1	then	then	ADV
iajs-807	229	2	by	by	ADP
iajs-807	229	3	theorem	theorem	NOUN
iajs-807	229	4	3.2	3.2	NUM
iajs-807	229	5	,	,	PUNCT
iajs-807	229	6	x	x	X
iajs-807	229	7			VERB
iajs-807	229	8	(	(	PUNCT
iajs-807	229	9	bcl(a)a	bcl(a)a	NOUN
iajs-807	229	10	)	)	PUNCT
iajs-807	229	11	.	.	PUNCT
iajs-807	230	1	but	but	CCONJ
iajs-807	230	2	xbcl(a	xbcl(a	NUM
iajs-807	230	3	)	)	PUNCT
iajs-807	230	4	,	,	PUNCT
iajs-807	230	5	so	so	ADV
iajs-807	230	6	xa	xa	PROPN
iajs-807	230	7	.	.	PUNCT
iajs-807	231	1	therefore	therefore	ADV
iajs-807	231	2	in	in	ADP
iajs-807	231	3	both	both	DET
iajs-807	231	4	cases	case	NOUN
iajs-807	231	5	xa	xa	PUNCT
iajs-807	231	6	.	.	PUNCT
iajs-807	232	1	this	this	PRON
iajs-807	232	2	shows	show	VERB
iajs-807	232	3	that	that	SCONJ
iajs-807	232	4	bcl(a	bcl(a	PROPN
iajs-807	232	5	)	)	PUNCT
iajs-807	232	6	a	a	NUM
iajs-807	232	7	or	or	CCONJ
iajs-807	232	8	equivalently	equivalently	ADV
iajs-807	232	9	a	a	PRON
iajs-807	232	10	is	be	AUX
iajs-807	232	11	b	b	NOUN
iajs-807	232	12	-	-	PUNCT
iajs-807	232	13	closed	closed	ADJ
iajs-807	232	14	.	.	PUNCT
iajs-807	233	1	proposition	proposition	NOUN
iajs-807	233	2	5.8	5.8	NUM
iajs-807	233	3	.	.	PUNCT
iajs-807	234	1	(	(	PUNCT
iajs-807	234	2	i	i	NOUN
iajs-807	234	3	)	)	PUNCT
iajs-807	235	1	bo(x)	bo(x)	PROPN
iajs-807	235	2			PROPN
iajs-807	235	3	gbo(x	gbo(x	PROPN
iajs-807	235	4	)	)	PUNCT
iajs-807	235	5	.	.	PUNCT
iajs-807	236	1	(	(	PUNCT
iajs-807	236	2	ii	ii	NOUN
iajs-807	236	3	)	)	PUNCT
iajs-807	236	4	a	a	DET
iajs-807	236	5	space	space	NOUN
iajs-807	236	6	x	x	PUNCT
iajs-807	236	7	is	be	AUX
iajs-807	236	8			ADJ
iajs-807	236	9	b	b	NOUN
iajs-807	236	10	2	2	NUM
iajs-807	236	11	1	1	NUM
iajs-807	236	12	t	t	NOUN
iajs-807	236	13	if	if	SCONJ
iajs-807	236	14	and	and	CCONJ
iajs-807	236	15	only	only	ADV
iajs-807	236	16	if	if	SCONJ
iajs-807	236	17	bo(x	bo(x	NUM
iajs-807	236	18	)	)	PUNCT
iajs-807	236	19	=	=	SYM
iajs-807	236	20			PROPN
iajs-807	236	21	gbo(x	gbo(x	PROPN
iajs-807	236	22	)	)	PUNCT
iajs-807	236	23	.	.	PUNCT
iajs-807	237	1	proof	proof	NOUN
iajs-807	237	2	.	.	PUNCT
iajs-807	238	1	(	(	PUNCT
iajs-807	238	2	i	i	NOUN
iajs-807	238	3	)	)	PUNCT
iajs-807	238	4	let	let	VERB
iajs-807	238	5	a	a	PRON
iajs-807	238	6	be	be	AUX
iajs-807	238	7	a	a	DET
iajs-807	238	8	bopen	bopen	NOUN
iajs-807	238	9	.	.	PUNCT
iajs-807	239	1	then	then	ADV
iajs-807	239	2	xa	xa	PROPN
iajs-807	239	3	is	be	AUX
iajs-807	239	4	bclosed	bclose	VERB
iajs-807	239	5	and	and	CCONJ
iajs-807	239	6	so	so	ADV
iajs-807	239	7			PROPN
iajs-807	239	8	gbclosed	gbclose	VERB
iajs-807	239	9	.	.	PUNCT
iajs-807	240	1	thus	thus	ADV
iajs-807	240	2	a	a	DET
iajs-807	240	3	is	be	AUX
iajs-807	240	4			ADJ
iajs-807	240	5	gbopen	gbopen	NOUN
iajs-807	240	6	.	.	PUNCT
iajs-807	241	1	therefore	therefore	ADV
iajs-807	241	2	bo(x)	bo(x)	CCONJ
iajs-807	241	3			PROPN
iajs-807	241	4	gbo(x	gbo(x	PROPN
iajs-807	241	5	)	)	PUNCT
iajs-807	241	6	.	.	PUNCT
iajs-807	242	1	(	(	PUNCT
iajs-807	242	2	ii	ii	NOUN
iajs-807	242	3	)	)	PUNCT
iajs-807	242	4	necessity	necessity	NOUN
iajs-807	242	5	:	:	PUNCT
iajs-807	242	6	let	let	VERB
iajs-807	242	7	x	x	PART
iajs-807	242	8	be	be	AUX
iajs-807	242	9			ADJ
iajs-807	242	10	b2	b2	NOUN
iajs-807	242	11	1	1	NUM
iajs-807	242	12	t	t	NOUN
iajs-807	242	13	.	.	PUNCT
iajs-807	243	1	let	let	VERB
iajs-807	243	2	agbo(x	agbo(x	NOUN
iajs-807	243	3	)	)	PUNCT
iajs-807	243	4	.	.	PUNCT
iajs-807	244	1	then	then	ADV
iajs-807	244	2	x	x	X
iajs-807	244	3	-	-	PUNCT
iajs-807	244	4	a	a	PRON
iajs-807	244	5	is	be	AUX
iajs-807	244	6			ADJ
iajs-807	244	7	gb	gb	NOUN
iajs-807	244	8	closed	closed	ADJ
iajs-807	244	9	.	.	PUNCT
iajs-807	245	1	by	by	ADP
iajs-807	245	2	hypothesis	hypothesis	NOUN
iajs-807	245	3	,	,	PUNCT
iajs-807	245	4	x	x	NOUN
iajs-807	245	5	-	-	PUNCT
iajs-807	245	6	a	a	PRON
iajs-807	245	7	is	be	AUX
iajs-807	245	8	b	b	NOUN
iajs-807	245	9	-	-	PUNCT
iajs-807	245	10	closed	closed	ADJ
iajs-807	245	11	.	.	PUNCT
iajs-807	246	1	thus	thus	ADV
iajs-807	246	2	abo(x	abo(x	NUM
iajs-807	246	3	)	)	PUNCT
iajs-807	246	4	.	.	PUNCT
iajs-807	247	1	hence	hence	ADV
iajs-807	247	2			PROPN
iajs-807	247	3	gbo(x	gbo(x	PROPN
iajs-807	247	4	)	)	PUNCT
iajs-807	247	5	=	=	PUNCT
iajs-807	247	6	bo(x	bo(x	NUM
iajs-807	247	7	)	)	PUNCT
iajs-807	247	8	.	.	PUNCT
iajs-807	248	1	suficiency	suficiency	NOUN
iajs-807	248	2	:	:	PUNCT
iajs-807	248	3	let	let	VERB
iajs-807	248	4	bo(x	bo(x	PUNCT
iajs-807	248	5	)	)	PUNCT
iajs-807	248	6	=	=	SYM
iajs-807	249	1			PROPN
iajs-807	249	2	gbo(x	gbo(x	PROPN
iajs-807	249	3	)	)	PUNCT
iajs-807	249	4	and	and	CCONJ
iajs-807	249	5	a	a	DET
iajs-807	249	6	be	be	NOUN
iajs-807	249	7			NOUN
iajs-807	249	8	gbclosed	gbclose	VERB
iajs-807	249	9	.	.	PUNCT
iajs-807	250	1	then	then	ADV
iajs-807	250	2	x	x	X
iajs-807	250	3	-	-	PUNCT
iajs-807	250	4	a	a	PRON
iajs-807	250	5	is	be	AUX
iajs-807	250	6			ADJ
iajs-807	250	7	gbopen	gbopen	NOUN
iajs-807	250	8	.	.	PUNCT
iajs-807	251	1	hence	hence	ADV
iajs-807	251	2	x	x	ADJ
iajs-807	251	3	-	-	PUNCT
iajs-807	251	4	a	a	PROPN
iajs-807	251	5	bo(x	bo(x	NUM
iajs-807	251	6	)	)	PUNCT
iajs-807	251	7	.	.	PUNCT
iajs-807	252	1	thus	thus	ADV
iajs-807	252	2	a	a	PRON
iajs-807	252	3	is	be	AUX
iajs-807	252	4	bclosed	bclose	VERB
iajs-807	252	5	.	.	PUNCT
iajs-807	253	1	therefore	therefore	ADV
iajs-807	253	2	x	x	X
iajs-807	253	3	is	be	AUX
iajs-807	253	4			PROPN
iajs-807	253	5	b2	b2	NOUN
iajs-807	253	6	1	1	NUM
iajs-807	253	7	t	t	NOUN
iajs-807	253	8	.	.	PUNCT
iajs-807	254	1	acknowledgment	acknowledgment	NOUN
iajs-807	254	2	.	.	PUNCT
iajs-807	255	1	the	the	DET
iajs-807	255	2	author	author	NOUN
iajs-807	255	3	is	be	AUX
iajs-807	255	4	grateful	grateful	ADJ
iajs-807	255	5	to	to	ADP
iajs-807	255	6	the	the	DET
iajs-807	255	7	referees	referee	NOUN
iajs-807	255	8	for	for	ADP
iajs-807	255	9	their	their	PRON
iajs-807	255	10	help	help	NOUN
iajs-807	255	11	in	in	ADP
iajs-807	255	12	improving	improve	VERB
iajs-807	255	13	the	the	DET
iajs-807	255	14	quality	quality	NOUN
iajs-807	255	15	of	of	ADP
iajs-807	255	16	this	this	DET
iajs-807	255	17	paper	paper	NOUN
iajs-807	255	18	.	.	PUNCT
iajs-807	256	1	references	reference	NOUN
iajs-807	256	2	1	1	NUM
iajs-807	256	3	park	park	NOUN
iajs-807	256	4	,	,	PUNCT
iajs-807	256	5	j.	j.	PROPN
iajs-807	256	6	h.	h.	PROPN
iajs-807	256	7	,	,	PUNCT
iajs-807	256	8	(	(	PUNCT
iajs-807	256	9	2006	2006	NUM
iajs-807	256	10	)	)	PUNCT
iajs-807	256	11	“	"	PUNCT
iajs-807	256	12	on	on	ADP
iajs-807	256	13			ADJ
iajs-807	256	14	gpclosed	gpclose	VERB
iajs-807	256	15	sets	set	NOUN
iajs-807	256	16	in	in	ADP
iajs-807	256	17	topological	topological	ADJ
iajs-807	256	18	spaces	space	NOUN
iajs-807	256	19	”	"	PUNCT
iajs-807	256	20	indian	indian	PROPN
iajs-807	256	21	j.	j.	PROPN
iajs-807	256	22	pure	pure	PROPN
iajs-807	256	23	appl	appl	PROPN
iajs-807	256	24	.	.	PUNCT
iajs-807	256	25	math	math	PROPN
iajs-807	256	26	.	.	PUNCT
iajs-807	256	27	,	,	PUNCT
iajs-807	256	28	acta	acta	PROPN
iajs-807	256	29	mathematica	mathematica	PROPN
iajs-807	256	30	hungarica	hungarica	PROPN
iajs-807	256	31	112,(4	112,(4	NUM
iajs-807	256	32	)	)	PUNCT
iajs-807	256	33	,	,	PUNCT
iajs-807	256	34	257283	257283	NUM
iajs-807	256	35	.	.	PUNCT
iajs-807	257	1	2	2	NUM
iajs-807	257	2	-sarsak	-sarsak	NOUN
iajs-807	257	3	,	,	PUNCT
iajs-807	257	4	m.	m.	NOUN
iajs-807	257	5	s.	s.	PROPN
iajs-807	257	6	(	(	PUNCT
iajs-807	257	7	2010	2010	NUM
iajs-807	257	8	)	)	PUNCT
iajs-807	257	9	“	"	PUNCT
iajs-807	257	10			ADJ
iajs-807	257	11	generalied	generalie	VERB
iajs-807	257	12	semipreclosed	semipreclose	VERB
iajs-807	257	13	sets	set	NOUN
iajs-807	257	14	”	"	PUNCT
iajs-807	257	15	int	int	NOUN
iajs-807	257	16	.	.	PUNCT
iajs-807	258	1	math	math	NOUN
iajs-807	258	2	.	.	PUNCT
iajs-807	259	1	foram	foram	PROPN
iajs-807	259	2	,	,	PUNCT
iajs-807	259	3	5	5	NUM
iajs-807	259	4	,	,	PUNCT
iajs-807	259	5	no	no	INTJ
iajs-807	259	6	.	.	NOUN
iajs-807	259	7	12	12	NUM
iajs-807	259	8	,	,	PUNCT
iajs-807	259	9	573578	573578	NUM
iajs-807	259	10	.	.	PUNCT
iajs-807	260	1	3	3	NUM
iajs-807	260	2	levine	levine	PROPN
iajs-807	260	3	n.	n.	PROPN
iajs-807	260	4	,	,	PUNCT
iajs-807	260	5	(	(	PUNCT
iajs-807	260	6	1963	1963	NUM
iajs-807	260	7	)	)	PUNCT
iajs-807	260	8	"	"	PUNCT
iajs-807	260	9	someopen	someopen	ADJ
iajs-807	260	10	sets	set	NOUN
iajs-807	260	11	and	and	CCONJ
iajs-807	260	12	semi	semi	ADJ
iajs-807	260	13	continuity	continuity	NOUN
iajs-807	260	14	in	in	ADP
iajs-807	260	15	topological	topological	ADJ
iajs-807	260	16	spaces	space	NOUN
iajs-807	260	17	"	"	PUNCT
iajs-807	260	18	,	,	PUNCT
iajs-807	260	19	math	math	NOUN
iajs-807	260	20	.	.	PUNCT
iajs-807	261	1	monthly	monthly	ADJ
iajs-807	261	2	70	70	NUM
iajs-807	261	3	,	,	PUNCT
iajs-807	261	4	36	36	NUM
iajs-807	261	5	-	-	SYM
iajs-807	261	6	41	41	NUM
iajs-807	261	7	.	.	PUNCT
iajs-807	261	8	.	.	PUNCT
iajs-807	262	1	ibn	ibn	PROPN
iajs-807	262	2	alhaitham	alhaitham	PROPN
iajs-807	262	3	j.	j.	PROPN
iajs-807	262	4	for	for	ADP
iajs-807	262	5	pure	pure	ADJ
iajs-807	262	6	&	&	CCONJ
iajs-807	262	7	appl	appl	PROPN
iajs-807	262	8	.	.	PUNCT
iajs-807	263	1	sci	sci	PROPN
iajs-807	263	2	.	.	PUNCT
iajs-807	263	3	vol.24	vol.24	NOUN
iajs-807	263	4	(	(	PUNCT
iajs-807	263	5	3	3	NUM
iajs-807	263	6	)	)	PUNCT
iajs-807	263	7	2011	2011	NUM
iajs-807	263	8	4njasted	4njasted	NUM
iajs-807	263	9	,	,	PUNCT
iajs-807	263	10	o.	o.	PROPN
iajs-807	263	11	,(1965	,(1965	PROPN
iajs-807	263	12	)	)	PUNCT
iajs-807	263	13	,	,	PUNCT
iajs-807	263	14	“	"	PUNCT
iajs-807	263	15	on	on	ADP
iajs-807	263	16	some	some	DET
iajs-807	263	17	classes	class	NOUN
iajs-807	263	18	of	of	ADP
iajs-807	263	19	nearly	nearly	ADV
iajs-807	263	20	open	open	ADJ
iajs-807	263	21	sets	set	NOUN
iajs-807	263	22	”	"	PUNCT
iajs-807	263	23	pacific	pacific	PROPN
iajs-807	263	24	j.	j.	PROPN
iajs-807	263	25	math	math	PROPN
iajs-807	263	26	.	.	PUNCT
iajs-807	263	27	,	,	PUNCT
iajs-807	263	28	15	15	NUM
iajs-807	263	29	,	,	PUNCT
iajs-807	263	30	961970	961970	NUM
iajs-807	263	31	.	.	PUNCT
iajs-807	264	1	5mashhour	5mashhour	NUM
iajs-807	264	2	,	,	PUNCT
iajs-807	264	3	a.	a.	PROPN
iajs-807	264	4	s.	s.	PROPN
iajs-807	264	5	abd	abd	PROPN
iajs-807	264	6	elmonsef	elmonsef	PROPN
iajs-807	264	7	m.	m.	PROPN
iajs-807	264	8	e.	e.	PROPN
iajs-807	264	9	and	and	CCONJ
iajs-807	264	10	el	el	PROPN
iajs-807	264	11	.	.	PROPN
iajs-807	264	12	deep	deep	ADJ
iajs-807	264	13	,	,	PUNCT
iajs-807	264	14	s.	s.	PROPN
iajs-807	264	15	n.	n.	PROPN
iajs-807	264	16	,	,	PUNCT
iajs-807	264	17	(	(	PUNCT
iajs-807	264	18	1982	1982	NUM
iajs-807	264	19	)	)	PUNCT
iajs-807	264	20	,	,	PUNCT
iajs-807	264	21	(	(	PUNCT
iajs-807	264	22	1983	1983	NUM
iajs-807	264	23	)	)	PUNCT
iajs-807	264	24	,	,	PUNCT
iajs-807	264	25	"	"	PUNCT
iajs-807	264	26	on	on	ADP
iajs-807	264	27	p	p	X
iajs-807	264	28	recontinuous	recontinuous	ADJ
iajs-807	264	29	and	and	CCONJ
iajs-807	264	30	weak	weak	ADJ
iajs-807	264	31	precontinuous	precontinuous	ADJ
iajs-807	264	32	mappings	mapping	NOUN
iajs-807	264	33	,	,	PUNCT
iajs-807	264	34	proc	proc	NOUN
iajs-807	264	35	,	,	PUNCT
iajs-807	264	36	phis	phis	PROPN
iajs-807	264	37	.	.	PUNCT
iajs-807	264	38	soc	soc	PROPN
iajs-807	264	39	.	.	PUNCT
iajs-807	265	1	egypt	egypt	PROPN
iajs-807	265	2	no	no	INTJ
iajs-807	265	3	.	.	PROPN
iajs-807	265	4	52	52	NUM
iajs-807	265	5	,	,	PUNCT
iajs-807	265	6	4753	4753	NUM
iajs-807	265	7	6	6	NUM
iajs-807	265	8	andrijevic	andrijevic	VERB
iajs-807	265	9	d	d	NOUN
iajs-807	265	10	,	,	PUNCT
iajs-807	265	11	(	(	PUNCT
iajs-807	265	12	1986	1986	NUM
iajs-807	265	13	)	)	PUNCT
iajs-807	265	14	,	,	PUNCT
iajs-807	265	15	"	"	PUNCT
iajs-807	265	16	semipreopen	semipreopen	ADJ
iajs-807	265	17	sets	set	NOUN
iajs-807	265	18	"	"	PUNCT
iajs-807	265	19	math	math	NOUN
iajs-807	265	20	.	.	PUNCT
iajs-807	266	1	vesnik	vesnik	PROPN
iajs-807	266	2	38	38	NUM
iajs-807	266	3	no.1	no.1	NOUN
iajs-807	266	4	,	,	PUNCT
iajs-807	266	5	2432	2432	NUM
iajs-807	266	6	.	.	PUNCT
iajs-807	267	1	7	7	NUM
iajs-807	267	2	stone	stone	NOUN
iajs-807	267	3	,	,	PUNCT
iajs-807	267	4	m.	m.	NOUN
iajs-807	267	5	(	(	PUNCT
iajs-807	267	6	1937	1937	NUM
iajs-807	267	7	)	)	PUNCT
iajs-807	267	8	,	,	PUNCT
iajs-807	267	9	"	"	PUNCT
iajs-807	267	10	application	application	NOUN
iajs-807	267	11	of	of	ADP
iajs-807	267	12	theory	theory	NOUN
iajs-807	267	13	of	of	ADP
iajs-807	267	14	boolean	boolean	ADJ
iajs-807	267	15	rings	ring	NOUN
iajs-807	267	16	to	to	ADP
iajs-807	267	17	general	general	ADJ
iajs-807	267	18	topology	topology	NOUN
iajs-807	267	19	"	"	PUNCT
iajs-807	267	20	,	,	PUNCT
iajs-807	267	21	trans	trans	PROPN
iajs-807	267	22	.	.	PROPN
iajs-807	268	1	amer	amer	PROPN
iajs-807	268	2	.	.	PUNCT
iajs-807	268	3	math	math	PROPN
iajs-807	268	4	.	.	PUNCT
iajs-807	269	1	soc	soc	PROPN
iajs-807	269	2	.	.	PUNCT
iajs-807	270	1	41	41	NUM
iajs-807	270	2	,	,	PUNCT
iajs-807	270	3	374481	374481	NUM
iajs-807	270	4	.	.	PUNCT
iajs-807	271	1	8	8	NUM
iajs-807	271	2	andrijevic	andrijevic	ADJ
iajs-807	271	3	,	,	PUNCT
iajs-807	271	4	d.	d.	PROPN
iajs-807	271	5	,	,	PUNCT
iajs-807	271	6	(	(	PUNCT
iajs-807	271	7	1996	1996	NUM
iajs-807	271	8	)	)	PUNCT
iajs-807	271	9	,	,	PUNCT
iajs-807	271	10	"	"	PUNCT
iajs-807	271	11	on	on	ADP
iajs-807	271	12	bopen	bopen	NOUN
iajs-807	271	13	sets	set	NOUN
iajs-807	271	14	,	,	PUNCT
iajs-807	271	15	math.vesnik	math.vesnik	X
iajs-807	271	16	48no	48no	NOUN
iajs-807	271	17	.	.	PUNCT
iajs-807	272	1	1	1	NUM
iajs-807	272	2	-	-	SYM
iajs-807	272	3	2	2	NUM
iajs-807	272	4	,	,	PUNCT
iajs-807	272	5	5964	5964	NUM
iajs-807	272	6	.	.	PUNCT
iajs-807	273	1	9	9	NUM
iajs-807	273	2	zaitsav	zaitsav	NOUN
iajs-807	273	3	v.	v.	PROPN
iajs-807	273	4	,	,	PUNCT
iajs-807	273	5	(	(	PUNCT
iajs-807	273	6	1968	1968	NUM
iajs-807	273	7	)	)	PUNCT
iajs-807	273	8	,	,	PUNCT
iajs-807	273	9	“	"	PUNCT
iajs-807	273	10	on	on	ADP
iajs-807	273	11	certain	certain	ADJ
iajs-807	273	12	classes	class	NOUN
iajs-807	273	13	of	of	ADP
iajs-807	273	14	topological	topological	ADJ
iajs-807	273	15	spaces	space	NOUN
iajs-807	273	16	and	and	CCONJ
iajs-807	273	17	their	their	PRON
iajs-807	273	18	bicompactifications	bicompactification	NOUN
iajs-807	273	19	”	"	PUNCT
iajs-807	273	20	dokl	dokl	NOUN
iajs-807	273	21	akad	akad	NOUN
iajs-807	273	22	sssr	sssr	NOUN
iajs-807	273	23	178	178	NUM
iajs-807	273	24	,	,	PUNCT
iajs-807	273	25	778779	778779	NUM
iajs-807	273	26	.	.	PUNCT
iajs-807	273	27	10	10	NUM
iajs-807	273	28	-	-	PUNCT
iajs-807	273	29	levine	levine	NOUN
iajs-807	273	30	,	,	PUNCT
iajs-807	273	31	n.	n.	NOUN
iajs-807	273	32	,	,	PUNCT
iajs-807	273	33	(	(	PUNCT
iajs-807	273	34	1970	1970	NUM
iajs-807	273	35	)	)	PUNCT
iajs-807	273	36	,	,	PUNCT
iajs-807	273	37	"	"	PUNCT
iajs-807	273	38	generalized	generalize	VERB
iajs-807	273	39	closed	closed	ADJ
iajs-807	273	40	sets	set	NOUN
iajs-807	273	41	in	in	ADP
iajs-807	273	42	topology	topology	NOUN
iajs-807	273	43	,	,	PUNCT
iajs-807	273	44	rend	rend	VERB
iajs-807	273	45	.	.	PUNCT
iajs-807	274	1	gen	gen	PROPN
iajs-807	274	2	.	.	PROPN
iajs-807	274	3	math	math	PROPN
iajs-807	274	4	.	.	PUNCT
iajs-807	275	1	palermo	palermo	NOUN
iajs-807	275	2	(	(	PUNCT
iajs-807	275	3	2	2	NUM
iajs-807	275	4	)	)	PUNCT
iajs-807	275	5	19	19	NUM
iajs-807	275	6	,	,	PUNCT
iajs-807	275	7	8996	8996	NUM
iajs-807	275	8	.	.	PUNCT
iajs-807	276	1	11	11	NUM
iajs-807	276	2	dontchev	dontchev	NOUN
iajs-807	276	3	,	,	PUNCT
iajs-807	276	4	z.	z.	PROPN
iajs-807	276	5	and	and	CCONJ
iajs-807	276	6	noiri	noiri	PROPN
iajs-807	276	7	,	,	PUNCT
iajs-807	276	8	t.	t.	PROPN
iajs-807	276	9	,	,	PUNCT
iajs-807	276	10	(	(	PUNCT
iajs-807	276	11	2000	2000	NUM
iajs-807	276	12	)	)	PUNCT
iajs-807	276	13	,	,	PUNCT
iajs-807	276	14	“	"	PUNCT
iajs-807	276	15	quasinormal	quasinormal	ADJ
iajs-807	276	16	spaces	space	NOUN
iajs-807	276	17	and	and	CCONJ
iajs-807	276	18			ADP
iajs-807	276	19	g	g	NOUN
iajs-807	276	20	closed	closed	ADJ
iajs-807	276	21	sets	set	NOUN
iajs-807	276	22	"	"	PUNCT
iajs-807	276	23	,	,	PUNCT
iajs-807	276	24	acta	acta	PROPN
iajs-807	276	25	math.hungar	math.hungar	PROPN
iajs-807	276	26	,	,	PUNCT
iajs-807	276	27	89	89	NUM
iajs-807	276	28	,	,	PUNCT
iajs-807	276	29	(	(	PUNCT
iajs-807	276	30	3	3	NUM
iajs-807	276	31	)	)	PUNCT
iajs-807	276	32	,	,	PUNCT
iajs-807	276	33	211219	211219	NUM
iajs-807	276	34	.	.	PUNCT
iajs-807	277	1	12adea	12adea	NUM
iajs-807	277	2	,	,	PUNCT
iajs-807	277	3	k.	k.	PROPN
iajs-807	277	4	,2009	,2009	PUNCT
iajs-807	277	5	“	"	PUNCT
iajs-807	277	6	on	on	ADP
iajs-807	277	7	bcompactness	bcompactness	NOUN
iajs-807	277	8	and	and	CCONJ
iajs-807	277	9	b*compactness	b*compactness	PROPN
iajs-807	277	10	in	in	ADP
iajs-807	277	11	topological	topological	NOUN
iajs-807	277	12	spaces”.accepted	spaces”.accepte	VERB
iajs-807	277	13	in	in	ADP
iajs-807	277	14	journal	journal	NOUN
iajs-807	277	15	of	of	ADP
iajs-807	277	16	basic	basic	ADJ
iajs-807	277	17	education	education	NOUN
iajs-807	277	18	,	,	PUNCT
iajs-807	277	19	12(2007	12(2007	NUM
iajs-807	277	20	)	)	PUNCT
iajs-807	277	21	.	.	PUNCT
iajs-807	278	1	13alomeri	13alomeri	NUM
iajs-807	278	2	,	,	PUNCT
iajs-807	278	3	a.	a.	NOUN
iajs-807	278	4	,	,	PUNCT
iajs-807	278	5	and	and	CCONJ
iajs-807	278	6	noorani	noorani	PROPN
iajs-807	278	7	,	,	PUNCT
iajs-807	278	8	md	md	PROPN
iajs-807	278	9	.	.	PROPN
iajs-807	278	10	m.	m.	PROPN
iajs-807	278	11	s.	s.	PROPN
iajs-807	278	12	,(2009	,(2009	PUNCT
iajs-807	278	13	)	)	PUNCT
iajs-807	278	14	,	,	PUNCT
iajs-807	278	15	"	"	PUNCT
iajs-807	278	16	on	on	ADP
iajs-807	278	17	generalized	generalized	ADJ
iajs-807	278	18	b0	b0	NOUN
iajs-807	278	19	closed	close	VERB
iajs-807	278	20	sets	set	NOUN
iajs-807	278	21	"	"	PUNCT
iajs-807	278	22	bull	bull	NOUN
iajs-807	278	23	.	.	PUNCT
iajs-807	279	1	math	math	NOUN
iajs-807	279	2	.	.	PUNCT
iajs-807	280	1	sci	sci	PROPN
iajs-807	280	2	.	.	PUNCT
iajs-807	281	1	(	(	PUNCT
iajs-807	281	2	2	2	NUM
iajs-807	281	3	)	)	PUNCT
iajs-807	281	4	,	,	PUNCT
iajs-807	281	5	1930	1930	NUM
iajs-807	281	6	.	.	PUNCT
iajs-807	282	1	14levine	14levine	NUM
iajs-807	282	2	,	,	PUNCT
iajs-807	282	3	n.	n.	NOUN
iajs-807	282	4	,	,	PUNCT
iajs-807	282	5	(	(	PUNCT
iajs-807	282	6	1970	1970	NUM
iajs-807	282	7	)	)	PUNCT
iajs-807	282	8	,	,	PUNCT
iajs-807	282	9	"	"	PUNCT
iajs-807	282	10	generalized	generalize	VERB
iajs-807	282	11	closed	closed	ADJ
iajs-807	282	12	sets	set	NOUN
iajs-807	282	13	in	in	ADP
iajs-807	282	14	topology	topology	NOUN
iajs-807	282	15	"	"	PUNCT
iajs-807	282	16	rend	rend	VERB
iajs-807	282	17	.	.	PUNCT
iajs-807	283	1	gen	gen	PROPN
iajs-807	283	2	.	.	PROPN
iajs-807	283	3	math	math	PROPN
iajs-807	283	4	.	.	PUNCT
iajs-807	284	1	palermo	palermo	NOUN
iajs-807	284	2	(	(	PUNCT
iajs-807	284	3	2	2	NUM
iajs-807	284	4	)	)	PUNCT
iajs-807	284	5	19	19	NUM
iajs-807	284	6	8996	8996	NUM
iajs-807	284	7	.	.	PUNCT
iajs-807	284	8	.	.	PUNCT
iajs-807	285	1	2011	2011	NUM
iajs-807	285	2	)	)	PUNCT
iajs-807	285	3	3	3	NUM
iajs-807	285	4	(	(	PUNCT
iajs-807	285	5	24المجلد	24المجلد	NUM
iajs-807	285	6	مجلة	مجلة	VERB
iajs-807	285	7	ابن	ابن	PROPN
iajs-807	285	8	الهیثم	الهیثم	PROPN
iajs-807	285	9	للعلوم	للعلوم	PROPN
iajs-807	285	10	الصرفة	الصرفة	PROPN
iajs-807	285	11	والتطبیقیة	والتطبیقیة	PROPN
iajs-807	285	12	gbمن	gbمن	PROPN
iajs-807	285	13	النمط	النمط	PROPN
iajs-807	285	14	المجموعات	المجموعات	PROPN
iajs-807	285	15	المغلقة	المغلقة	PROPN
iajs-807	285	16	العبیديعذیة	العبیديعذیة	PROPN
iajs-807	285	17	خلیفة	خلیفة	VERB
iajs-807	285	18	الجامعة	الجامعة	PROPN
iajs-807	285	19	المستنصریة	المستنصریة	PROPN
iajs-807	285	20	،	،	PROPN
iajs-807	285	21	كلیة	كلیة	PROPN
iajs-807	285	22	التربیة	التربیة	PROPN
iajs-807	285	23	االساسیة	االساسیة	PROPN
iajs-807	285	24	،	،	PROPN
iajs-807	286	1	قسم	قسم	PROPN
iajs-807	286	2	الریاضیات	الریاضیات	PROPN
iajs-807	286	3	2011	2011	NUM
iajs-807	286	4	یارآ	یارآ	NOUN
iajs-807	286	5	10	10	NUM
iajs-807	286	6	:	:	PUNCT
iajs-807	286	7	استلم	استلم	PROPN
iajs-807	286	8	البحث	البحث	VERB
iajs-807	286	9	في	في	ADP
iajs-807	286	10	2011	2011	NUM
iajs-807	286	11	حزیران	حزیران	NOUN
iajs-807	286	12	16	16	NUM
iajs-807	286	13	:	:	PUNCT
iajs-807	286	14	قبل	قبل	PROPN
iajs-807	286	15	البحث	البحث	VERB
iajs-807	286	16	في	في	ADP
iajs-807	286	17	المقدمة	المقدمة	PROPN
iajs-807	286	18	gb(المجموعات	gb(المجموعات	VERB
iajs-807	286	19	المغلقة	المغلقة	NOUN
iajs-807	286	20	من	من	DET
iajs-807	286	21	النمط	النمط	NOUN
iajs-807	286	22	في	في	SCONJ
iajs-807	286	23	هذا	هذا	NOUN
iajs-807	286	24	البحث	البحث	PROPN
iajs-807	286	25	قدمنا	قدمنا	PROPN
iajs-807	286	26	صنفا	صنفا	PROPN
iajs-807	286	27	جدیدا	جدیدا	VERB
iajs-807	286	28	من	من	DET
iajs-807	286	29	المجموعات	المجموعات	NOUN
iajs-807	286	30	اسمیناها	اسمیناها	NOUN
iajs-807	286	31			PROPN
iajs-807	286	32	ودرسنا	ودرسنا	NOUN
iajs-807	286	33	بعض	بعض	NOUN
iajs-807	286	34	)	)	PUNCT
iajs-807	287	1	gp	gp	NOUN
iajs-807	287	2	(	(	PUNCT
iajs-807	287	3	هما	هما	INTJ
iajs-807	287	4	المجموعات	المجموعات	PROPN
iajs-807	287	5	المغلقة	المغلقة	PROPN
iajs-807	287	6	من	من	DET
iajs-807	287	7	النمط	النمط	NOUN
iajs-807	288	1	ان	ان	ADP
iajs-807	288	2	هذا	هذا	NOUN
iajs-807	288	3	النوع	النوع	PROPN
iajs-807	288	4	یقع	یقع	PROPN
iajs-807	288	5	بین	بین	AUX
iajs-807	288	6	صنفین	صنفین	PROPN
iajs-807	288	7	من	من	PROPN
iajs-807	288	8	المجموعات	المجموعات	PROPN
iajs-807	288	9	إذ.الخواص	إذ.الخواص	PROPN
iajs-807	289	1	االساسیة	االساسیة	PROPN
iajs-807	289	2	لها	لها	PROPN
iajs-807	289	3			PROPN
iajs-807	289	4	(	(	PUNCT
iajs-807	289	5	gsp	gsp	PROPN
iajs-807	289	6	(	(	PUNCT
iajs-807	289	7	والمجموعات	والمجموعات	ADJ
iajs-807	289	8	المغلقة	المغلقة	PROPN
iajs-807	289	9	من	من	PRON
iajs-807	289	10	النمط	النمط	NOUN
iajs-807	289	11	فضاء	فضاء	NOUN
iajs-807	289	12	.	.	PUNCT
iajs-807	289	13	)	)	PUNCT
iajs-807	290	1	كما	كما	PROPN
iajs-807	290	2	عرفنا	عرفنا	PROPN
iajs-807	290	3	ودرسنا	ودرسنا	PROPN
iajs-807	290	4	نوعا	نوعا	PROPN
iajs-807	290	5	من	من	DET
iajs-807	290	6	الفضاءات	الفضاءات	NOUN
iajs-807	290	7	اسمیناه	اسمیناه	ADV
iajs-807	290	8	ال	ال	ADP
iajs-807	290	9	b	b	NOUN
iajs-807	290	10	2	2	NUM
iajs-807	290	11	1	1	NUM
iajs-807	290	12	t.	t.	NOUN
iajs-807	290	13	gb	gb	NOUN
iajs-807	290	14	المجموعة	المجموعة	PROPN
iajs-807	290	15	المغلقة	المغلقة	PROPN
iajs-807	290	16	من	من	PRON
iajs-807	290	17	النمط	النمط	PROPN
iajs-807	290	18	،	،	PROPN
iajs-807	290	19	المجموعة	المجموعة	PROPN
iajs-807	290	20	المفتوحة	المفتوحة	PROPN
iajs-807	290	21	المنتظمة	المنتظمة	PROPN
iajs-807	290	22	،	،	PROPN
iajs-807	290	23	bلمجموعة	bلمجموعة	PROPN
iajs-807	290	24	المفتوحة	المفتوحة	PROPN
iajs-807	290	25	من	من	PRON
iajs-807	290	26	النمط	النمط	PROPN
iajs-807	290	27	ا	ا	NOUN
iajs-807	290	28	:	:	PUNCT
iajs-807	290	29	الكلمات	الكلمات	VERB
iajs-807	290	30	المفتاحیة	المفتاحیة	ADV
iajs-807	290	31	.	.	NUM