id	sid	tid	token	lemma	pos
iajs-153	1	1	microsoft	microsoft	PROPN
iajs-153	1	2	word	word	NOUN
iajs-153	1	3	204	204	NUM
iajs-153	1	4	-	-	SYM
iajs-153	1	5	213	213	NUM
iajs-153	1	6	204	204	NUM
iajs-153	1	7	|	|	NOUN
iajs-153	1	8	mathematics	mathematic	NOUN
iajs-153	1	9	2015	2015	NUM
iajs-153	1	10	)	)	PUNCT
iajs-153	1	11	عام	عام	ADP
iajs-153	1	12	3العدد	3العدد	NUM
iajs-153	1	13	(	(	PUNCT
iajs-153	1	14	28الھيثم	28الھيثم	NUM
iajs-153	1	15	للعلوم	للعلوم	PROPN
iajs-153	1	16	الصرفة	الصرفة	NOUN
iajs-153	1	17	و	و	PRON
iajs-153	1	18	التطبيقية	التطبيقية	ADV
iajs-153	1	19	المجلد	المجلد	ADV
iajs-153	1	20	مجلة	مجلة	VERB
iajs-153	1	21	إبن	إبن	VERB
iajs-153	1	22	ibn	ibn	PROPN
iajs-153	1	23	al	al	PROPN
iajs-153	1	24	-	-	PUNCT
iajs-153	1	25	haitham	haitham	PROPN
iajs-153	1	26	jour	jour	X
iajs-153	1	27	.	.	PROPN
iajs-153	1	28	for	for	ADP
iajs-153	1	29	pure	pure	ADJ
iajs-153	1	30	&	&	CCONJ
iajs-153	1	31	appl	appl	PROPN
iajs-153	1	32	.	.	PUNCT
iajs-153	2	1	sci	sci	PROPN
iajs-153	2	2	.	.	PUNCT
iajs-153	2	3	vol	vol	NOUN
iajs-153	2	4	.	.	PROPN
iajs-153	3	1	28	28	NUM
iajs-153	3	2	(	(	PUNCT
iajs-153	3	3	3	3	NUM
iajs-153	3	4	)	)	PUNCT
iajs-153	3	5	2015	2015	NUM
iajs-153	3	6	on	on	ADP
iajs-153	3	7	generalized	generalized	ADJ
iajs-153	3	8	b*-closed	b*-close	VERB
iajs-153	3	9	sets	set	NOUN
iajs-153	3	10	in	in	ADP
iajs-153	3	11	topological	topological	ADJ
iajs-153	3	12	spaces	space	NOUN
iajs-153	3	13	zinah	zinah	PROPN
iajs-153	3	14	t.	t.	PROPN
iajs-153	3	15	alhawez	alhawez	PROPN
iajs-153	3	16	dept	dept	PROPN
iajs-153	3	17	.	.	PROPN
iajs-153	4	1	of	of	ADP
iajs-153	4	2	mathematics	mathematics	PROPN
iajs-153	4	3	/	/	SYM
iajs-153	4	4	college	college	NOUN
iajs-153	4	5	of	of	ADP
iajs-153	4	6	education	education	NOUN
iajs-153	4	7	for	for	ADP
iajs-153	4	8	woman	woman	NOUN
iajs-153	4	9	/	/	SYM
iajs-153	4	10	university	university	NOUN
iajs-153	4	11	of	of	ADP
iajs-153	4	12	tikrit	tikrit	NOUN
iajs-153	4	13	received	receive	VERB
iajs-153	4	14	in:22	in:22	PROPN
iajs-153	4	15	/	/	SYM
iajs-153	4	16	december/2014	december/2014	PROPN
iajs-153	4	17	,	,	PUNCT
iajs-153	4	18	accepted	accept	VERB
iajs-153	4	19	in:20	in:20	PROPN
iajs-153	4	20	/	/	SYM
iajs-153	4	21	september/2015	september/2015	NOUN
iajs-153	4	22	abstract	abstract	NOUN
iajs-153	4	23	in	in	ADP
iajs-153	4	24	this	this	DET
iajs-153	4	25	paper	paper	NOUN
iajs-153	4	26	,	,	PUNCT
iajs-153	4	27	we	we	PRON
iajs-153	4	28	introduce	introduce	VERB
iajs-153	4	29	and	and	CCONJ
iajs-153	4	30	study	study	VERB
iajs-153	4	31	the	the	DET
iajs-153	4	32	concept	concept	NOUN
iajs-153	4	33	of	of	ADP
iajs-153	4	34	a	a	DET
iajs-153	4	35	new	new	ADJ
iajs-153	4	36	class	class	NOUN
iajs-153	4	37	of	of	ADP
iajs-153	4	38	generalized	generalize	VERB
iajs-153	4	39	closed	close	VERB
iajs-153	4	40	set	set	NOUN
iajs-153	4	41	which	which	PRON
iajs-153	4	42	is	be	AUX
iajs-153	4	43	called	call	VERB
iajs-153	4	44	generalized	generalized	ADJ
iajs-153	4	45	b*-closed	b*-close	VERB
iajs-153	4	46	set	set	NOUN
iajs-153	4	47	in	in	ADP
iajs-153	4	48	topological	topological	ADJ
iajs-153	4	49	spaces	space	NOUN
iajs-153	4	50	(	(	PUNCT
iajs-153	4	51	briefly	briefly	NOUN
iajs-153	4	52	.g	.g	PROPN
iajs-153	4	53	b*-closed	b*-close	VERB
iajs-153	4	54	)	)	PUNCT
iajs-153	4	55	we	we	PRON
iajs-153	4	56	study	study	VERB
iajs-153	4	57	also	also	ADV
iajs-153	4	58	.	.	PUNCT
iajs-153	5	1	some	some	PRON
iajs-153	5	2	of	of	ADP
iajs-153	5	3	its	its	PRON
iajs-153	5	4	basic	basic	ADJ
iajs-153	5	5	properties	property	NOUN
iajs-153	5	6	and	and	CCONJ
iajs-153	5	7	investigate	investigate	VERB
iajs-153	5	8	the	the	DET
iajs-153	5	9	relations	relation	NOUN
iajs-153	5	10	between	between	ADP
iajs-153	5	11	the	the	DET
iajs-153	5	12	associated	associated	ADJ
iajs-153	5	13	topology	topology	NOUN
iajs-153	5	14	.	.	PUNCT
iajs-153	6	1	keywords	keyword	NOUN
iajs-153	6	2	:	:	PUNCT
iajs-153	6	3	gb	gb	ADP
iajs-153	6	4	*	*	PUNCT
iajs-153	6	5	-closed	-close	VERB
iajs-153	6	6	set	set	NOUN
iajs-153	6	7	,	,	PUNCT
iajs-153	6	8	gb	gb	ADP
iajs-153	6	9	-closed	-close	VERB
iajs-153	6	10	set	set	NOUN
iajs-153	6	11	,	,	PUNCT
iajs-153	6	12	g	g	NOUN
iajs-153	6	13	-	-	PUNCT
iajs-153	6	14	closed	close	VERB
iajs-153	6	15	set	set	NOUN
iajs-153	6	16	.	.	PUNCT
iajs-153	7	1	205	205	NUM
iajs-153	8	1	|	|	ADV
iajs-153	8	2	mathematics	mathematic	NOUN
iajs-153	8	3	2015	2015	NUM
iajs-153	8	4	)	)	PUNCT
iajs-153	8	5	عام	عام	ADP
iajs-153	8	6	3العدد	3العدد	NUM
iajs-153	8	7	(	(	PUNCT
iajs-153	8	8	28الھيثم	28الھيثم	NUM
iajs-153	8	9	للعلوم	للعلوم	PROPN
iajs-153	8	10	الصرفة	الصرفة	NOUN
iajs-153	8	11	و	و	PRON
iajs-153	8	12	التطبيقية	التطبيقية	ADV
iajs-153	8	13	المجلد	المجلد	ADV
iajs-153	8	14	مجلة	مجلة	VERB
iajs-153	8	15	إبن	إبن	VERB
iajs-153	8	16	ibn	ibn	PROPN
iajs-153	8	17	al	al	PROPN
iajs-153	8	18	-	-	PUNCT
iajs-153	8	19	haitham	haitham	PROPN
iajs-153	8	20	jour	jour	X
iajs-153	8	21	.	.	PROPN
iajs-153	8	22	for	for	ADP
iajs-153	8	23	pure	pure	ADJ
iajs-153	8	24	&	&	CCONJ
iajs-153	8	25	appl	appl	PROPN
iajs-153	8	26	.	.	PUNCT
iajs-153	9	1	sci	sci	PROPN
iajs-153	9	2	.	.	PUNCT
iajs-153	9	3	vol	vol	NOUN
iajs-153	9	4	.	.	PROPN
iajs-153	10	1	28	28	NUM
iajs-153	10	2	(	(	PUNCT
iajs-153	10	3	3	3	NUM
iajs-153	10	4	)	)	PUNCT
iajs-153	10	5	2015	2015	NUM
iajs-153	10	6	introduction	introduction	NOUN
iajs-153	10	7	1	1	NUM
iajs-153	10	8	.	.	PUNCT
iajs-153	11	1	levine[9	levine[9	PROPN
iajs-153	11	2	]	]	PUNCT
iajs-153	11	3	introduced	introduce	VERB
iajs-153	11	4	the	the	DET
iajs-153	11	5	concept	concept	NOUN
iajs-153	11	6	of	of	ADP
iajs-153	11	7	generalized	generalized	ADJ
iajs-153	11	8	closed	closed	ADJ
iajs-153	11	9	sets	set	NOUN
iajs-153	11	10	(	(	PUNCT
iajs-153	11	11	briefly	briefly	ADV
iajs-153	11	12	,	,	PUNCT
iajs-153	11	13	g	g	NOUN
iajs-153	11	14	-	-	PUNCT
iajs-153	11	15	closed	close	VERB
iajs-153	11	16	)	)	PUNCT
iajs-153	11	17	and	and	CCONJ
iajs-153	11	18	studied	study	VERB
iajs-153	11	19	their	their	PRON
iajs-153	11	20	most	most	ADV
iajs-153	11	21	fundamental	fundamental	ADJ
iajs-153	11	22	properties	property	NOUN
iajs-153	11	23	in	in	ADP
iajs-153	11	24	topological	topological	ADJ
iajs-153	11	25	spaces	space	NOUN
iajs-153	11	26	.	.	PUNCT
iajs-153	12	1	arya	arya	PROPN
iajs-153	12	2	and	and	CCONJ
iajs-153	12	3	nour[6	nour[6	PROPN
iajs-153	12	4	]	]	X
iajs-153	12	5	,	,	PUNCT
iajs-153	12	6	bhattacharya	bhattacharya	NOUN
iajs-153	12	7	and	and	CCONJ
iajs-153	12	8	lahiri[7	lahiri[7	ADV
iajs-153	12	9	]	]	PUNCT
iajs-153	12	10	,	,	PUNCT
iajs-153	12	11	levine[10	levine[10	X
iajs-153	12	12	]	]	PUNCT
iajs-153	12	13	,	,	PUNCT
iajs-153	12	14	mashhour[11	mashhour[11	ADV
iajs-153	12	15	]	]	X
iajs-153	12	16	,	,	PUNCT
iajs-153	12	17	njastad[13]and	njastad[13]and	PROPN
iajs-153	12	18	andrijevic[3,4	andrijevic[3,4	NUM
iajs-153	12	19	]	]	PUNCT
iajs-153	12	20	introduced	introduce	VERB
iajs-153	12	21	and	and	CCONJ
iajs-153	12	22	investigated	investigate	VERB
iajs-153	12	23	generalized	generalized	ADJ
iajs-153	12	24	semi	semi	ADJ
iajs-153	12	25	-	-	ADJ
iajs-153	12	26	open	open	ADJ
iajs-153	12	27	sets	set	NOUN
iajs-153	12	28	,	,	PUNCT
iajs-153	12	29	semi	semi	ADV
iajs-153	12	30	generalized	generalized	ADJ
iajs-153	12	31	open	open	ADJ
iajs-153	12	32	sets	set	NOUN
iajs-153	12	33	,	,	PUNCT
iajs-153	12	34	generalized	generalize	VERB
iajs-153	12	35	open	open	ADJ
iajs-153	12	36	sets	set	NOUN
iajs-153	12	37	,	,	PUNCT
iajs-153	12	38	semi	semi	ADJ
iajs-153	12	39	-	-	ADJ
iajs-153	12	40	open	open	ADJ
iajs-153	12	41	sets	set	NOUN
iajs-153	12	42	,	,	PUNCT
iajs-153	12	43	pre	pre	ADJ
iajs-153	12	44	-	-	ADJ
iajs-153	12	45	open	open	ADJ
iajs-153	12	46	sets	set	NOUN
iajs-153	12	47	and	and	CCONJ
iajs-153	12	48	α	α	DET
iajs-153	12	49	open	open	ADJ
iajs-153	12	50	sets	set	NOUN
iajs-153	12	51	,	,	PUNCT
iajs-153	12	52	semi	semi	ADV
iajs-153	12	53	pre	pre	ADJ
iajs-153	12	54	-	-	ADJ
iajs-153	12	55	open	open	ADJ
iajs-153	12	56	sets	set	NOUN
iajs-153	12	57	and	and	CCONJ
iajs-153	12	58	b	b	X
iajs-153	12	59	-	-	PUNCT
iajs-153	12	60	open	open	ADJ
iajs-153	12	61	sets	set	NOUN
iajs-153	12	62	which	which	PRON
iajs-153	12	63	are	be	AUX
iajs-153	12	64	some	some	PRON
iajs-153	12	65	of	of	ADP
iajs-153	12	66	the	the	DET
iajs-153	12	67	weak	weak	ADJ
iajs-153	12	68	forms	form	NOUN
iajs-153	12	69	of	of	ADP
iajs-153	12	70	open	open	ADJ
iajs-153	12	71	sets	set	NOUN
iajs-153	12	72	and	and	CCONJ
iajs-153	12	73	the	the	DET
iajs-153	12	74	complements	complement	NOUN
iajs-153	12	75	of	of	ADP
iajs-153	12	76	these	these	DET
iajs-153	12	77	sets	set	NOUN
iajs-153	12	78	are	be	AUX
iajs-153	12	79	called	call	VERB
iajs-153	12	80	the	the	DET
iajs-153	12	81	same	same	ADJ
iajs-153	12	82	types	type	NOUN
iajs-153	12	83	of	of	ADP
iajs-153	12	84	closed	closed	ADJ
iajs-153	12	85	sets	set	NOUN
iajs-153	12	86	.	.	PUNCT
iajs-153	13	1	a.a.omari	a.a.omari	PROPN
iajs-153	13	2	and	and	CCONJ
iajs-153	13	3	m.s.m.noorani[14	m.s.m.noorani[14	PROPN
iajs-153	13	4	]	]	PUNCT
iajs-153	13	5	introduced	introduce	VERB
iajs-153	13	6	and	and	CCONJ
iajs-153	13	7	studied	study	VERB
iajs-153	13	8	the	the	DET
iajs-153	13	9	concept	concept	NOUN
iajs-153	13	10	of	of	ADP
iajs-153	13	11	generalized	generalized	ADJ
iajs-153	13	12	b	b	NOUN
iajs-153	13	13	-	-	PUNCT
iajs-153	13	14	closed	close	VERB
iajs-153	13	15	sets(briey	sets(briey	NOUN
iajs-153	13	16	gb	gb	ADV
iajs-153	13	17	-	-	PUNCT
iajs-153	13	18	closed	closed	ADJ
iajs-153	13	19	)	)	PUNCT
iajs-153	13	20	in	in	ADP
iajs-153	13	21	topological	topological	ADJ
iajs-153	13	22	spaces	space	NOUN
iajs-153	13	23	.	.	PUNCT
iajs-153	14	1	recently	recently	ADV
iajs-153	14	2	sundaram	sundaram	PROPN
iajs-153	14	3	and	and	CCONJ
iajs-153	14	4	sheik	sheik	PROPN
iajs-153	14	5	john	john	PROPN
iajs-153	15	1	[	[	X
iajs-153	15	2	15	15	NUM
iajs-153	15	3	]	]	PUNCT
iajs-153	15	4	introduced	introduce	VERB
iajs-153	15	5	and	and	CCONJ
iajs-153	15	6	studied	study	VERB
iajs-153	15	7	w	w	ADJ
iajs-153	15	8	-	-	PUNCT
iajs-153	15	9	closed	closed	ADJ
iajs-153	15	10	sets	set	NOUN
iajs-153	15	11	.	.	PUNCT
iajs-153	16	1	s.muthuvel	s.muthuvel	VERB
iajs-153	16	2	and	and	CCONJ
iajs-153	16	3	r.parimelazhagan	r.parimelazhagan	VERB
iajs-153	17	1	[	[	X
iajs-153	17	2	12	12	NUM
iajs-153	17	3	]	]	PUNCT
iajs-153	17	4	introduced	introduce	VERB
iajs-153	17	5	and	and	CCONJ
iajs-153	17	6	studied	study	VERB
iajs-153	17	7	b*closed	b*closed	ADJ
iajs-153	17	8	sets	set	NOUN
iajs-153	17	9	,	,	PUNCT
iajs-153	17	10	a.poongothai	a.poongothai	ADJ
iajs-153	17	11	and	and	CCONJ
iajs-153	17	12	r.parimelazhagan	r.parimelazhagan	X
iajs-153	18	1	[	[	X
iajs-153	18	2	5	5	NUM
iajs-153	18	3	]	]	PUNCT
iajs-153	18	4	introduced	introduce	VERB
iajs-153	18	5	and	and	CCONJ
iajs-153	18	6	studied	study	VERB
iajs-153	18	7	strongly	strongly	ADV
iajs-153	18	8	b*-closed	b*-close	VERB
iajs-153	18	9	set	set	NOUN
iajs-153	18	10	in	in	ADP
iajs-153	18	11	topological	topological	ADJ
iajs-153	18	12	spaces	space	NOUN
iajs-153	18	13	.	.	PUNCT
iajs-153	19	1	in	in	ADP
iajs-153	19	2	this	this	DET
iajs-153	19	3	paper	paper	NOUN
iajs-153	19	4	,	,	PUNCT
iajs-153	19	5	we	we	PRON
iajs-153	19	6	introduce	introduce	VERB
iajs-153	19	7	a	a	DET
iajs-153	19	8	new	new	ADJ
iajs-153	19	9	class	class	NOUN
iajs-153	19	10	of	of	ADP
iajs-153	19	11	sets	set	NOUN
iajs-153	19	12	,	,	PUNCT
iajs-153	19	13	namely	namely	ADV
iajs-153	19	14	gb*closed	gb*close	VERB
iajs-153	19	15	sets	set	NOUN
iajs-153	19	16	for	for	ADP
iajs-153	19	17	topological	topological	ADJ
iajs-153	19	18	spaces	space	NOUN
iajs-153	19	19	.	.	PUNCT
iajs-153	20	1	this	this	DET
iajs-153	20	2	class	class	NOUN
iajs-153	20	3	lies	lie	VERB
iajs-153	20	4	between	between	ADP
iajs-153	20	5	the	the	DET
iajs-153	20	6	class	class	NOUN
iajs-153	20	7	b*-closed	b*-close	VERB
iajs-153	20	8	set	set	NOUN
iajs-153	20	9	and	and	CCONJ
iajs-153	20	10	strongly	strongly	ADV
iajs-153	20	11	b*-closed	b*-close	VERB
iajs-153	20	12	set	set	NOUN
iajs-153	20	13	.	.	PUNCT
iajs-153	21	1	2.preliminaries	2.preliminarie	NOUN
iajs-153	21	2	let	let	VERB
iajs-153	21	3	(	(	PUNCT
iajs-153	21	4	x	x	X
iajs-153	21	5	,	,	PUNCT
iajs-153	21	6	t	t	PROPN
iajs-153	21	7	)	)	PUNCT
iajs-153	21	8	be	be	AUX
iajs-153	21	9	topological	topological	ADJ
iajs-153	21	10	spaces	space	NOUN
iajs-153	21	11	and	and	CCONJ
iajs-153	21	12	a	a	DET
iajs-153	21	13	be	be	AUX
iajs-153	21	14	a	a	DET
iajs-153	21	15	subset	subset	NOUN
iajs-153	21	16	of	of	ADP
iajs-153	21	17	x	x	SYM
iajs-153	21	18	.the	.the	DET
iajs-153	21	19	closure	closure	NOUN
iajs-153	21	20	of	of	ADP
iajs-153	21	21	a	a	PRON
iajs-153	21	22	and	and	CCONJ
iajs-153	21	23	interior	interior	ADJ
iajs-153	21	24	of	of	ADP
iajs-153	21	25	a	a	PRON
iajs-153	21	26	are	be	AUX
iajs-153	21	27	denoted	denote	VERB
iajs-153	21	28	by	by	ADP
iajs-153	21	29	cl(a	cl(a	NOUN
iajs-153	21	30	)	)	PUNCT
iajs-153	21	31	and	and	CCONJ
iajs-153	21	32	int(a	int(a	PROPN
iajs-153	21	33	)	)	PUNCT
iajs-153	21	34	respectively	respectively	ADV
iajs-153	21	35	,	,	PUNCT
iajs-153	21	36	union	union	NOUN
iajs-153	21	37	of	of	ADP
iajs-153	21	38	all	all	DET
iajs-153	21	39	b	b	NOUN
iajs-153	21	40	-	-	PUNCT
iajs-153	21	41	open	open	ADJ
iajs-153	21	42	(	(	PUNCT
iajs-153	21	43	semi	semi	ADJ
iajs-153	21	44	-	-	ADJ
iajs-153	21	45	open	open	ADJ
iajs-153	21	46	,	,	PUNCT
iajs-153	21	47	pre	pre	ADJ
iajs-153	21	48	-	-	ADJ
iajs-153	21	49	open	open	ADJ
iajs-153	21	50	,	,	PUNCT
iajs-153	21	51	α	α	NOUN
iajs-153	21	52	–	–	PUNCT
iajs-153	21	53	open	open	ADJ
iajs-153	21	54	)	)	PUNCT
iajs-153	21	55	sets	set	NOUN
iajs-153	21	56	x	x	PRON
iajs-153	21	57	contained	contain	VERB
iajs-153	21	58	in	in	ADP
iajs-153	21	59	a	a	PRON
iajs-153	21	60	is	be	AUX
iajs-153	21	61	called	call	VERB
iajs-153	21	62	binterior	binterior	ADJ
iajs-153	21	63	(	(	PUNCT
iajs-153	21	64	semiinterior	semiinterior	NOUN
iajs-153	21	65	,	,	PUNCT
iajs-153	21	66	pre	pre	ADJ
iajs-153	21	67	-	-	NOUN
iajs-153	21	68	interior	interior	ADJ
iajs-153	21	69	,	,	PUNCT
iajs-153	21	70	α	α	NOUN
iajs-153	21	71	–	–	PUNCT
iajs-153	21	72	interior	interior	NOUN
iajs-153	21	73	,	,	PUNCT
iajs-153	21	74	respectively	respectively	ADV
iajs-153	21	75	)	)	PUNCT
iajs-153	21	76	of	of	ADP
iajs-153	21	77	a	a	PRON
iajs-153	21	78	,	,	PUNCT
iajs-153	21	79	it	it	PRON
iajs-153	21	80	is	be	AUX
iajs-153	21	81	denoted	denote	VERB
iajs-153	21	82	by	by	ADP
iajs-153	21	83	b	b	NOUN
iajs-153	21	84	-	-	PUNCT
iajs-153	21	85	int	int	NOUN
iajs-153	21	86	(	(	PUNCT
iajs-153	21	87	a)(s	a)(s	ADV
iajs-153	21	88	-	-	PUNCT
iajs-153	21	89	int(a),p	int(a),p	NOUN
iajs-153	21	90	-	-	PUNCT
iajs-153	21	91	int(a	int(a	NOUN
iajs-153	21	92	)	)	PUNCT
iajs-153	21	93	,	,	PUNCT
iajs-153	21	94	α	α	X
iajs-153	21	95	-	-	PUNCT
iajs-153	21	96	int(a	int(a	NOUN
iajs-153	21	97	)	)	PUNCT
iajs-153	21	98	,	,	PUNCT
iajs-153	21	99	respectively),the	respectively),the	PROPN
iajs-153	21	100	intersection	intersection	NOUN
iajs-153	21	101	of	of	ADP
iajs-153	21	102	all	all	PRON
iajs-153	21	103	b	b	NOUN
iajs-153	21	104	-	-	PUNCT
iajs-153	21	105	closed	closed	ADJ
iajs-153	21	106	(	(	PUNCT
iajs-153	21	107	semiclosed	semiclose	VERB
iajs-153	21	108	,	,	PUNCT
iajs-153	21	109	preclosed	preclose	VERB
iajs-153	21	110	,	,	PUNCT
iajs-153	21	111	α	α	PRON
iajs-153	21	112	–	–	PUNCT
iajs-153	21	113	closed	closed	ADJ
iajs-153	21	114	)	)	PUNCT
iajs-153	21	115	sets	set	VERB
iajs-153	21	116	x	x	PUNCT
iajs-153	21	117	containing	contain	VERB
iajs-153	21	118	a	a	PRON
iajs-153	21	119	is	be	AUX
iajs-153	21	120	called	call	VERB
iajs-153	21	121	bclosure	bclosure	NOUN
iajs-153	21	122	(	(	PUNCT
iajs-153	21	123	semiclosure	semiclosure	NOUN
iajs-153	21	124	,	,	PUNCT
iajs-153	21	125	preclosure	preclosure	ADJ
iajs-153	21	126	,	,	PUNCT
iajs-153	21	127	α	α	NOUN
iajs-153	21	128	–	–	PUNCT
iajs-153	21	129	closure	closure	NOUN
iajs-153	21	130	,	,	PUNCT
iajs-153	21	131	respectively	respectively	ADV
iajs-153	21	132	)	)	PUNCT
iajs-153	21	133	of	of	ADP
iajs-153	21	134	a	a	PRON
iajs-153	21	135	and	and	CCONJ
iajs-153	21	136	it	it	PRON
iajs-153	21	137	is	be	AUX
iajs-153	21	138	denoted	denote	VERB
iajs-153	21	139	by	by	ADP
iajs-153	21	140	bcl(a	bcl(a	PROPN
iajs-153	21	141	)	)	PUNCT
iajs-153	21	142	(	(	PUNCT
iajs-153	21	143	scl(a	scl(a	PROPN
iajs-153	21	144	)	)	PUNCT
iajs-153	21	145	,	,	PUNCT
iajs-153	21	146	pcl(a	pcl(a	PROPN
iajs-153	21	147	)	)	PUNCT
iajs-153	21	148	,	,	PUNCT
iajs-153	21	149	αcl(a	αcl(a	PROPN
iajs-153	21	150	)	)	PUNCT
iajs-153	21	151	,	,	PUNCT
iajs-153	21	152	respectively).in	respectively).in	CCONJ
iajs-153	21	153	this	this	DET
iajs-153	21	154	section	section	NOUN
iajs-153	21	155	,	,	PUNCT
iajs-153	21	156	we	we	PRON
iajs-153	21	157	recall	recall	VERB
iajs-153	21	158	some	some	DET
iajs-153	21	159	definitions	definition	NOUN
iajs-153	21	160	of	of	ADP
iajs-153	21	161	open	open	ADJ
iajs-153	21	162	sets	set	NOUN
iajs-153	21	163	in	in	ADP
iajs-153	21	164	topological	topological	ADJ
iajs-153	21	165	spaces	space	NOUN
iajs-153	21	166	.	.	PUNCT
iajs-153	22	1	definition	definition	NOUN
iajs-153	22	2	2	2	NUM
iajs-153	22	3	-	-	SYM
iajs-153	22	4	1[15	1[15	NUM
iajs-153	22	5	]	]	PUNCT
iajs-153	22	6	:	:	PUNCT
iajs-153	22	7	a	a	DET
iajs-153	22	8	subset	subset	NOUN
iajs-153	22	9	a	a	PRON
iajs-153	22	10	of	of	ADP
iajs-153	22	11	a	a	DET
iajs-153	22	12	topological	topological	ADJ
iajs-153	22	13	space	space	NOUN
iajs-153	22	14	(	(	PUNCT
iajs-153	22	15	x	x	X
iajs-153	22	16	,	,	PUNCT
iajs-153	22	17	t	t	PROPN
iajs-153	22	18	)	)	PUNCT
iajs-153	22	19	is	be	AUX
iajs-153	22	20	called	call	VERB
iajs-153	22	21	a	a	DET
iajs-153	22	22	pre	pre	ADJ
iajs-153	22	23	–	–	PUNCT
iajs-153	22	24	open	open	ADJ
iajs-153	22	25	set	set	NOUN
iajs-153	22	26	if	if	SCONJ
iajs-153	22	27	a	a	DET
iajs-153	22	28	⊆	⊆	NUM
iajs-153	22	29	int	int	NOUN
iajs-153	22	30	cl	cl	NOUN
iajs-153	22	31	a	a	PRON
iajs-153	22	32	and	and	CCONJ
iajs-153	22	33	pre	pre	ADJ
iajs-153	22	34	-	-	ADJ
iajs-153	22	35	closed	closed	ADJ
iajs-153	22	36	set	set	NOUN
iajs-153	22	37	if	if	SCONJ
iajs-153	22	38	cl	cl	NOUN
iajs-153	22	39	int	int	NOUN
iajs-153	22	40	a	a	DET
iajs-153	22	41	⊆	⊆	NUM
iajs-153	22	42	a.	a.	NOUN
iajs-153	22	43	definition	definition	NOUN
iajs-153	22	44	2	2	NUM
iajs-153	22	45	-	-	SYM
iajs-153	22	46	2[10]:a	2[10]:a	NUM
iajs-153	22	47	subset	subset	VERB
iajs-153	22	48	a	a	PRON
iajs-153	22	49	of	of	ADP
iajs-153	22	50	a	a	DET
iajs-153	22	51	topological	topological	ADJ
iajs-153	22	52	space	space	NOUN
iajs-153	22	53	(	(	PUNCT
iajs-153	22	54	x	x	X
iajs-153	22	55	,	,	PUNCT
iajs-153	22	56	t	t	PROPN
iajs-153	22	57	)	)	PUNCT
iajs-153	22	58	is	be	AUX
iajs-153	22	59	called	call	VERB
iajs-153	22	60	a	a	DET
iajs-153	22	61	semi	semi	ADJ
iajs-153	22	62	–	–	PUNCT
iajs-153	22	63	open	open	ADJ
iajs-153	22	64	set	set	NOUN
iajs-153	22	65	if	if	SCONJ
iajs-153	22	66	a	a	DET
iajs-153	22	67	⊆	⊆	NUM
iajs-153	22	68	cl	cl	NOUN
iajs-153	22	69	int	int	NOUN
iajs-153	22	70	a	a	DET
iajs-153	22	71	and	and	CCONJ
iajs-153	22	72	semi	semi	ADJ
iajs-153	22	73	-	-	ADJ
iajs-153	22	74	closed	closed	ADJ
iajs-153	22	75	set	set	NOUN
iajs-153	22	76	if	if	SCONJ
iajs-153	22	77	int	int	NOUN
iajs-153	22	78	cl	cl	NOUN
iajs-153	22	79	a	a	DET
iajs-153	22	80	⊆	⊆	NUM
iajs-153	22	81	a.	a.	NOUN
iajs-153	22	82	definition	definition	NOUN
iajs-153	22	83	2	2	NUM
iajs-153	22	84	-	-	SYM
iajs-153	22	85	3[3	3[3	NUM
iajs-153	22	86	]	]	NOUN
iajs-153	22	87	:	:	PUNCT
iajs-153	22	88	a	a	DET
iajs-153	22	89	subset	subset	NOUN
iajs-153	22	90	a	a	PRON
iajs-153	22	91	of	of	ADP
iajs-153	22	92	a	a	DET
iajs-153	22	93	topological	topological	ADJ
iajs-153	22	94	space	space	NOUN
iajs-153	22	95	(	(	PUNCT
iajs-153	22	96	x	x	X
iajs-153	22	97	,	,	PUNCT
iajs-153	22	98	t	t	PROPN
iajs-153	22	99	)	)	PUNCT
iajs-153	22	100	is	be	AUX
iajs-153	22	101	called	call	VERB
iajs-153	22	102	a	a	DET
iajs-153	22	103	α	α	NOUN
iajs-153	22	104	–	–	PUNCT
iajs-153	22	105	open	open	ADJ
iajs-153	22	106	set	set	NOUN
iajs-153	22	107	if	if	SCONJ
iajs-153	22	108	a	a	DET
iajs-153	22	109	⊆	⊆	NUM
iajs-153	22	110	int	int	NOUN
iajs-153	22	111	cl	cl	NOUN
iajs-153	22	112	int	int	NOUN
iajs-153	22	113	a	a	PRON
iajs-153	22	114	and	and	CCONJ
iajs-153	22	115	α	α	NOUN
iajs-153	22	116	-closed	-close	VERB
iajs-153	22	117	set	set	NOUN
iajs-153	22	118	if	if	SCONJ
iajs-153	22	119	cl	cl	NOUN
iajs-153	22	120	int	int	NOUN
iajs-153	22	121	cl	cl	NOUN
iajs-153	22	122	a	a	DET
iajs-153	22	123	⊆	⊆	NUM
iajs-153	22	124	a.	a.	NOUN
iajs-153	22	125	definition	definition	NOUN
iajs-153	22	126	2	2	NUM
iajs-153	22	127	-	-	SYM
iajs-153	22	128	4[8]:a	4[8]:a	NUM
iajs-153	22	129	subset	subset	VERB
iajs-153	22	130	a	a	PRON
iajs-153	22	131	of	of	ADP
iajs-153	22	132	a	a	DET
iajs-153	22	133	topological	topological	ADJ
iajs-153	22	134	space	space	NOUN
iajs-153	22	135	(	(	PUNCT
iajs-153	22	136	x	x	X
iajs-153	22	137	,	,	PUNCT
iajs-153	22	138	t	t	PROPN
iajs-153	22	139	)	)	PUNCT
iajs-153	22	140	is	be	AUX
iajs-153	22	141	called	call	VERB
iajs-153	22	142	a	a	DET
iajs-153	22	143	β	β	NOUN
iajs-153	22	144	–	–	PUNCT
iajs-153	22	145	open	open	ADJ
iajs-153	22	146	set	set	NOUN
iajs-153	22	147	if	if	SCONJ
iajs-153	22	148	a	a	DET
iajs-153	22	149	⊆	⊆	NUM
iajs-153	22	150	cl	cl	NOUN
iajs-153	22	151	int	int	NOUN
iajs-153	22	152	cl	cl	NOUN
iajs-153	22	153	a	a	PRON
iajs-153	22	154	and	and	CCONJ
iajs-153	22	155	β	β	X
iajs-153	22	156	-	-	ADJ
iajs-153	22	157	closed	closed	ADJ
iajs-153	22	158	set	set	NOUN
iajs-153	22	159	if	if	SCONJ
iajs-153	22	160	int	int	NOUN
iajs-153	22	161	cl	cl	NOUN
iajs-153	22	162	int	int	NOUN
iajs-153	22	163	a	a	DET
iajs-153	22	164	⊆	⊆	NUM
iajs-153	22	165	a.	a.	NOUN
iajs-153	22	166	definition	definition	NOUN
iajs-153	22	167	2	2	NUM
iajs-153	22	168	-	-	SYM
iajs-153	22	169	5[1]:a	5[1]:a	NUM
iajs-153	22	170	subset	subset	VERB
iajs-153	22	171	a	a	PRON
iajs-153	22	172	of	of	ADP
iajs-153	22	173	a	a	DET
iajs-153	22	174	topological	topological	ADJ
iajs-153	22	175	space	space	NOUN
iajs-153	22	176	(	(	PUNCT
iajs-153	22	177	x	x	X
iajs-153	22	178	,	,	PUNCT
iajs-153	22	179	t	t	PROPN
iajs-153	22	180	)	)	PUNCT
iajs-153	22	181	is	be	AUX
iajs-153	22	182	called	call	VERB
iajs-153	22	183	a	a	DET
iajs-153	22	184	b	b	NOUN
iajs-153	22	185	–	–	PUNCT
iajs-153	22	186	open	open	ADJ
iajs-153	22	187	set	set	NOUN
iajs-153	22	188	if	if	SCONJ
iajs-153	22	189	a	a	DET
iajs-153	22	190	⊆	⊆	NUM
iajs-153	22	191	cl	cl	NOUN
iajs-153	22	192	int	int	NOUN
iajs-153	22	193	a	a	DET
iajs-153	22	194	∪	∪	ADJ
iajs-153	22	195	int	int	NOUN
iajs-153	22	196	cl	cl	NOUN
iajs-153	22	197	a	a	DET
iajs-153	22	198	and	and	CCONJ
iajs-153	22	199	b	b	X
iajs-153	22	200	-	-	PUNCT
iajs-153	22	201	closed	closed	ADJ
iajs-153	22	202	set	set	NOUN
iajs-153	22	203	if	if	SCONJ
iajs-153	22	204	int	int	NOUN
iajs-153	22	205	cl	cl	NOUN
iajs-153	22	206	a	a	DET
iajs-153	22	207	∩	∩	ADJ
iajs-153	22	208	cl	cl	NOUN
iajs-153	22	209	int	int	NOUN
iajs-153	22	210	a	a	DET
iajs-153	22	211	⊆	⊆	NUM
iajs-153	22	212	a.	a.	NOUN
iajs-153	22	213	definition	definition	NOUN
iajs-153	22	214	2	2	NUM
iajs-153	22	215	-	-	SYM
iajs-153	22	216	6[9]:a	6[9]:a	NUM
iajs-153	22	217	subset	subset	VERB
iajs-153	22	218	a	a	PRON
iajs-153	22	219	of	of	ADP
iajs-153	22	220	a	a	DET
iajs-153	22	221	topological	topological	ADJ
iajs-153	22	222	space	space	NOUN
iajs-153	22	223	(	(	PUNCT
iajs-153	22	224	x	x	X
iajs-153	22	225	,	,	PUNCT
iajs-153	22	226	t	t	PROPN
iajs-153	22	227	)	)	PUNCT
iajs-153	22	228	is	be	AUX
iajs-153	22	229	called	call	VERB
iajs-153	22	230	a	a	DET
iajs-153	22	231	generalized	generalized	ADJ
iajs-153	22	232	–	–	PUNCT
iajs-153	22	233	closed	closed	ADJ
iajs-153	22	234	set	set	NOUN
iajs-153	22	235	(	(	PUNCT
iajs-153	22	236	briefly	briefly	ADV
iajs-153	22	237	,	,	PUNCT
iajs-153	22	238	g	g	NOUN
iajs-153	22	239	-	-	PUNCT
iajs-153	22	240	closed	closed	ADJ
iajs-153	22	241	)	)	PUNCT
iajs-153	22	242	if	if	SCONJ
iajs-153	22	243	cl	cl	VERB
iajs-153	22	244	a	a	DET
iajs-153	22	245	⊆	⊆	NUM
iajs-153	22	246	u	u	NOUN
iajs-153	22	247	,	,	PUNCT
iajs-153	22	248	whenever	whenever	SCONJ
iajs-153	22	249	a	a	DET
iajs-153	22	250	⊆	⊆	NUM
iajs-153	22	251	u	u	NOUN
iajs-153	22	252	and	and	CCONJ
iajs-153	22	253	u	u	NOUN
iajs-153	22	254	is	be	AUX
iajs-153	22	255	open	open	ADJ
iajs-153	22	256	set	set	VERB
iajs-153	22	257	.	.	PUNCT
iajs-153	23	1	definition	definition	NOUN
iajs-153	23	2	2	2	NUM
iajs-153	23	3	-	-	SYM
iajs-153	23	4	7[7]:a	7[7]:a	NUM
iajs-153	23	5	subset	subset	VERB
iajs-153	23	6	a	a	PRON
iajs-153	23	7	of	of	ADP
iajs-153	23	8	a	a	DET
iajs-153	23	9	topological	topological	ADJ
iajs-153	23	10	space	space	NOUN
iajs-153	23	11	(	(	PUNCT
iajs-153	23	12	x	x	X
iajs-153	23	13	,	,	PUNCT
iajs-153	23	14	t	t	PROPN
iajs-153	23	15	)	)	PUNCT
iajs-153	23	16	is	be	AUX
iajs-153	23	17	called	call	VERB
iajs-153	23	18	a	a	DET
iajs-153	23	19	semi	semi	ADV
iajs-153	23	20	generalized	generalize	VERB
iajs-153	23	21	closed	closed	ADJ
iajs-153	23	22	set	set	NOUN
iajs-153	23	23	(	(	PUNCT
iajs-153	23	24	briefly	briefly	ADV
iajs-153	23	25	,	,	PUNCT
iajs-153	23	26	sg	sg	ADV
iajs-153	23	27	-	-	PUNCT
iajs-153	23	28	closed	closed	ADJ
iajs-153	23	29	)	)	PUNCT
iajs-153	23	30	if	if	SCONJ
iajs-153	23	31	scl	scl	PROPN
iajs-153	23	32	a	a	DET
iajs-153	23	33	⊆	⊆	NUM
iajs-153	23	34	u	u	NOUN
iajs-153	23	35	,	,	PUNCT
iajs-153	23	36	whenever	whenever	SCONJ
iajs-153	23	37	a	a	DET
iajs-153	23	38	⊆	⊆	NUM
iajs-153	23	39	u	u	NOUN
iajs-153	23	40	and	and	CCONJ
iajs-153	23	41	u	u	NOUN
iajs-153	23	42	is	be	AUX
iajs-153	23	43	semiopen	semiopen	ADJ
iajs-153	23	44	set	set	VERB
iajs-153	23	45	.	.	PUNCT
iajs-153	24	1	206	206	NUM
iajs-153	25	1	|	|	ADV
iajs-153	25	2	mathematics	mathematic	NOUN
iajs-153	25	3	2015	2015	NUM
iajs-153	25	4	)	)	PUNCT
iajs-153	25	5	عام	عام	ADP
iajs-153	25	6	3العدد	3العدد	NUM
iajs-153	25	7	(	(	PUNCT
iajs-153	25	8	28الھيثم	28الھيثم	NUM
iajs-153	25	9	للعلوم	للعلوم	PROPN
iajs-153	25	10	الصرفة	الصرفة	NOUN
iajs-153	25	11	و	و	PRON
iajs-153	25	12	التطبيقية	التطبيقية	ADV
iajs-153	25	13	المجلد	المجلد	ADV
iajs-153	25	14	مجلة	مجلة	VERB
iajs-153	25	15	إبن	إبن	VERB
iajs-153	25	16	ibn	ibn	PROPN
iajs-153	25	17	al	al	PROPN
iajs-153	25	18	-	-	PUNCT
iajs-153	25	19	haitham	haitham	PROPN
iajs-153	25	20	jour	jour	X
iajs-153	25	21	.	.	PROPN
iajs-153	26	1	for	for	ADP
iajs-153	26	2	pure	pure	ADJ
iajs-153	26	3	&	&	CCONJ
iajs-153	26	4	appl	appl	PROPN
iajs-153	26	5	.	.	PUNCT
iajs-153	27	1	sci	sci	PROPN
iajs-153	27	2	.	.	PUNCT
iajs-153	27	3	vol	vol	NOUN
iajs-153	27	4	.	.	PROPN
iajs-153	28	1	28	28	NUM
iajs-153	28	2	(	(	PUNCT
iajs-153	28	3	3	3	NUM
iajs-153	28	4	)	)	PUNCT
iajs-153	28	5	2015	2015	NUM
iajs-153	28	6	definition	definition	NOUN
iajs-153	28	7	2	2	NUM
iajs-153	28	8	-	-	SYM
iajs-153	28	9	8[8]:a	8[8]:a	NUM
iajs-153	28	10	subset	subset	VERB
iajs-153	28	11	a	a	PRON
iajs-153	28	12	of	of	ADP
iajs-153	28	13	a	a	DET
iajs-153	28	14	topological	topological	ADJ
iajs-153	28	15	space	space	NOUN
iajs-153	28	16	(	(	PUNCT
iajs-153	28	17	x	x	X
iajs-153	28	18	,	,	PUNCT
iajs-153	28	19	t	t	PROPN
iajs-153	28	20	)	)	PUNCT
iajs-153	28	21	is	be	AUX
iajs-153	28	22	called	call	VERB
iajs-153	28	23	a	a	DET
iajs-153	28	24	generalized	generalize	VERB
iajs-153	28	25	αclosed	αclose	VERB
iajs-153	28	26	set	set	NOUN
iajs-153	28	27	(	(	PUNCT
iajs-153	28	28	briefly	briefly	ADV
iajs-153	28	29	gα	gα	NOUN
iajs-153	28	30	-	-	PUNCT
iajs-153	28	31	closed	closed	ADJ
iajs-153	28	32	)	)	PUNCT
iajs-153	28	33	if	if	SCONJ
iajs-153	28	34	αcl	αcl	PRON
iajs-153	28	35	a	a	DET
iajs-153	28	36	⊆	⊆	NUM
iajs-153	28	37	u	u	NOUN
iajs-153	28	38	,	,	PUNCT
iajs-153	28	39	whenever	whenever	SCONJ
iajs-153	28	40	a	a	DET
iajs-153	28	41	⊆	⊆	NUM
iajs-153	28	42	u	u	NOUN
iajs-153	28	43	and	and	CCONJ
iajs-153	28	44	u	u	NOUN
iajs-153	28	45	is	be	AUX
iajs-153	28	46	αopen	αopen	ADJ
iajs-153	28	47	set	set	VERB
iajs-153	28	48	.	.	PUNCT
iajs-153	29	1	definition	definition	NOUN
iajs-153	29	2	2	2	NUM
iajs-153	29	3	-	-	SYM
iajs-153	29	4	9[2]:a	9[2]:a	NUM
iajs-153	29	5	subset	subset	VERB
iajs-153	29	6	a	a	PRON
iajs-153	29	7	of	of	ADP
iajs-153	29	8	a	a	DET
iajs-153	29	9	topological	topological	ADJ
iajs-153	29	10	space	space	NOUN
iajs-153	29	11	(	(	PUNCT
iajs-153	29	12	x	x	X
iajs-153	29	13	,	,	PUNCT
iajs-153	29	14	t	t	PROPN
iajs-153	29	15	)	)	PUNCT
iajs-153	29	16	is	be	AUX
iajs-153	29	17	called	call	VERB
iajs-153	29	18	a	a	DET
iajs-153	29	19	generalized	generalize	VERB
iajs-153	29	20	bclosed	bclose	VERB
iajs-153	29	21	set	set	NOUN
iajs-153	29	22	(	(	PUNCT
iajs-153	29	23	briefly	briefly	ADV
iajs-153	29	24	gb	gb	ADP
iajs-153	29	25	-closed	-close	VERB
iajs-153	29	26	)	)	PUNCT
iajs-153	29	27	if	if	SCONJ
iajs-153	29	28	bcl	bcl	NOUN
iajs-153	29	29	a	a	DET
iajs-153	29	30	⊆	⊆	NUM
iajs-153	29	31	u	u	NOUN
iajs-153	29	32	,	,	PUNCT
iajs-153	29	33	whenever	whenever	SCONJ
iajs-153	29	34	a	a	DET
iajs-153	29	35	⊆	⊆	NUM
iajs-153	29	36	u	u	NOUN
iajs-153	29	37	and	and	CCONJ
iajs-153	29	38	u	u	NOUN
iajs-153	29	39	is	be	AUX
iajs-153	29	40	open	open	ADJ
iajs-153	29	41	set	set	VERB
iajs-153	29	42	.	.	PUNCT
iajs-153	30	1	definition	definition	NOUN
iajs-153	30	2	2	2	NUM
iajs-153	30	3	-	-	SYM
iajs-153	30	4	10[8]:a	10[8]:a	NUM
iajs-153	30	5	subset	subset	VERB
iajs-153	30	6	a	a	PRON
iajs-153	30	7	of	of	ADP
iajs-153	30	8	a	a	DET
iajs-153	30	9	topological	topological	ADJ
iajs-153	30	10	space	space	NOUN
iajs-153	30	11	(	(	PUNCT
iajs-153	30	12	x	x	X
iajs-153	30	13	,	,	PUNCT
iajs-153	30	14	t	t	PROPN
iajs-153	30	15	)	)	PUNCT
iajs-153	30	16	is	be	AUX
iajs-153	30	17	called	call	VERB
iajs-153	30	18	a	a	DET
iajs-153	30	19	generalized	generalize	VERB
iajs-153	30	20	βclosed	βclose	VERB
iajs-153	30	21	set	set	NOUN
iajs-153	30	22	(	(	PUNCT
iajs-153	30	23	briefly	briefly	ADV
iajs-153	30	24	gβ	gβ	NOUN
iajs-153	30	25	-	-	PUNCT
iajs-153	30	26	closed	closed	ADJ
iajs-153	30	27	)	)	PUNCT
iajs-153	30	28	if	if	SCONJ
iajs-153	30	29	βcl	βcl	ADJ
iajs-153	30	30	a	a	DET
iajs-153	30	31	⊆	⊆	NUM
iajs-153	30	32	u	u	NOUN
iajs-153	30	33	,	,	PUNCT
iajs-153	30	34	whenever	whenever	SCONJ
iajs-153	30	35	a	a	DET
iajs-153	30	36	⊆	⊆	NUM
iajs-153	30	37	u	u	NOUN
iajs-153	30	38	and	and	CCONJ
iajs-153	30	39	u	u	NOUN
iajs-153	30	40	is	be	AUX
iajs-153	30	41	open	open	ADJ
iajs-153	30	42	set	set	VERB
iajs-153	30	43	.	.	PUNCT
iajs-153	31	1	definition	definition	NOUN
iajs-153	31	2	2	2	NUM
iajs-153	31	3	-	-	SYM
iajs-153	31	4	11[5]:a	11[5]:a	NUM
iajs-153	31	5	subset	subset	VERB
iajs-153	31	6	a	a	PRON
iajs-153	31	7	of	of	ADP
iajs-153	31	8	a	a	DET
iajs-153	31	9	topological	topological	ADJ
iajs-153	31	10	space	space	NOUN
iajs-153	31	11	(	(	PUNCT
iajs-153	31	12	x	x	X
iajs-153	31	13	,	,	PUNCT
iajs-153	31	14	t	t	PROPN
iajs-153	31	15	)	)	PUNCT
iajs-153	31	16	is	be	AUX
iajs-153	31	17	called	call	VERB
iajs-153	31	18	weakly	weakly	ADV
iajs-153	31	19	generalized	generalize	VERB
iajs-153	31	20	closed	close	VERB
iajs-153	31	21	set	set	NOUN
iajs-153	31	22	(	(	PUNCT
iajs-153	31	23	briefly	briefly	ADV
iajs-153	31	24	wg	wg	NOUN
iajs-153	31	25	-	-	PUNCT
iajs-153	31	26	closed	closed	ADJ
iajs-153	31	27	)	)	PUNCT
iajs-153	31	28	if	if	SCONJ
iajs-153	31	29	cl	cl	NOUN
iajs-153	31	30	int	int	VERB
iajs-153	31	31	a	a	DET
iajs-153	31	32	⊆	⊆	NUM
iajs-153	31	33	u	u	NOUN
iajs-153	31	34	,	,	PUNCT
iajs-153	31	35	whenever	whenever	SCONJ
iajs-153	31	36	a	a	DET
iajs-153	31	37	⊆	⊆	NUM
iajs-153	31	38	u	u	NOUN
iajs-153	31	39	and	and	CCONJ
iajs-153	31	40	u	u	NOUN
iajs-153	31	41	is	be	AUX
iajs-153	31	42	open	open	ADJ
iajs-153	31	43	set	set	VERB
iajs-153	31	44	.	.	PUNCT
iajs-153	32	1	definition	definition	NOUN
iajs-153	32	2	2	2	NUM
iajs-153	32	3	-	-	SYM
iajs-153	32	4	12[15]:a	12[15]:a	NUM
iajs-153	32	5	subset	subset	VERB
iajs-153	32	6	a	a	PRON
iajs-153	32	7	of	of	ADP
iajs-153	32	8	a	a	DET
iajs-153	32	9	topological	topological	ADJ
iajs-153	32	10	space	space	NOUN
iajs-153	32	11	(	(	PUNCT
iajs-153	32	12	x	x	X
iajs-153	32	13	,	,	PUNCT
iajs-153	32	14	t	t	PROPN
iajs-153	32	15	)	)	PUNCT
iajs-153	32	16	is	be	AUX
iajs-153	32	17	called	call	VERB
iajs-153	32	18	wekly	wekly	ADV
iajs-153	32	19	-	-	PUNCT
iajs-153	32	20	closed	close	VERB
iajs-153	32	21	set	set	NOUN
iajs-153	32	22	(	(	PUNCT
iajs-153	32	23	briefly	briefly	NOUN
iajs-153	32	24	w	w	NOUN
iajs-153	32	25	-	-	PUNCT
iajs-153	32	26	closed	closed	ADJ
iajs-153	32	27	)	)	PUNCT
iajs-153	32	28	if	if	SCONJ
iajs-153	32	29	cl	cl	VERB
iajs-153	32	30	a	a	DET
iajs-153	32	31	⊆	⊆	NUM
iajs-153	32	32	u	u	NOUN
iajs-153	32	33	,	,	PUNCT
iajs-153	32	34	whenever	whenever	SCONJ
iajs-153	32	35	a	a	DET
iajs-153	32	36	⊆	⊆	NUM
iajs-153	32	37	u	u	NOUN
iajs-153	32	38	and	and	CCONJ
iajs-153	32	39	u	u	NOUN
iajs-153	32	40	is	be	AUX
iajs-153	32	41	semiopen	semiopen	ADJ
iajs-153	32	42	set	set	VERB
iajs-153	32	43	.	.	PUNCT
iajs-153	33	1	definition	definition	NOUN
iajs-153	33	2	2	2	NUM
iajs-153	33	3	-	-	SYM
iajs-153	33	4	13[12]:a	13[12]:a	NUM
iajs-153	33	5	subset	subset	VERB
iajs-153	33	6	a	a	PRON
iajs-153	33	7	of	of	ADP
iajs-153	33	8	a	a	DET
iajs-153	33	9	topological	topological	ADJ
iajs-153	33	10	space	space	NOUN
iajs-153	33	11	(	(	PUNCT
iajs-153	33	12	x	x	X
iajs-153	33	13	,	,	PUNCT
iajs-153	33	14	t	t	PROPN
iajs-153	33	15	)	)	PUNCT
iajs-153	33	16	is	be	AUX
iajs-153	33	17	called	call	VERB
iajs-153	33	18	b*-closed	b*-closed	ADJ
iajs-153	33	19	set	set	NOUN
iajs-153	33	20	if	if	SCONJ
iajs-153	33	21	int	int	NOUN
iajs-153	33	22	cl	cl	NOUN
iajs-153	33	23	a	a	DET
iajs-153	33	24	⊆	⊆	NUM
iajs-153	33	25	u	u	NOUN
iajs-153	33	26	,	,	PUNCT
iajs-153	33	27	whenever	whenever	SCONJ
iajs-153	33	28	a	a	DET
iajs-153	33	29	⊆	⊆	NUM
iajs-153	33	30	u	u	NOUN
iajs-153	33	31	and	and	CCONJ
iajs-153	33	32	u	u	NOUN
iajs-153	33	33	is	be	AUX
iajs-153	33	34	bopen	bopen	ADJ
iajs-153	33	35	set	set	VERB
iajs-153	33	36	.	.	PUNCT
iajs-153	34	1	definition	definition	NOUN
iajs-153	34	2	2	2	NUM
iajs-153	34	3	-	-	SYM
iajs-153	34	4	14[5]:a	14[5]:a	NUM
iajs-153	34	5	subset	subset	VERB
iajs-153	34	6	a	a	PRON
iajs-153	34	7	of	of	ADP
iajs-153	34	8	a	a	DET
iajs-153	34	9	topological	topological	ADJ
iajs-153	34	10	space	space	NOUN
iajs-153	34	11	(	(	PUNCT
iajs-153	34	12	x	x	X
iajs-153	34	13	,	,	PUNCT
iajs-153	34	14	t	t	PROPN
iajs-153	34	15	)	)	PUNCT
iajs-153	34	16	is	be	AUX
iajs-153	34	17	called	call	VERB
iajs-153	34	18	g	g	PROPN
iajs-153	34	19	*	*	PUNCT
iajs-153	34	20	-closed	-close	VERB
iajs-153	34	21	set	set	NOUN
iajs-153	34	22	if	if	SCONJ
iajs-153	34	23	cl	cl	NOUN
iajs-153	34	24	a	a	DET
iajs-153	34	25	⊆	⊆	NUM
iajs-153	34	26	u	u	NOUN
iajs-153	34	27	,	,	PUNCT
iajs-153	34	28	whenever	whenever	SCONJ
iajs-153	34	29	a	a	DET
iajs-153	34	30	⊆	⊆	NUM
iajs-153	34	31	u	u	NOUN
iajs-153	34	32	and	and	CCONJ
iajs-153	34	33	u	u	NOUN
iajs-153	34	34	is	be	AUX
iajs-153	34	35	gopen	gopen	NOUN
iajs-153	34	36	set	set	VERB
iajs-153	34	37	.	.	PUNCT
iajs-153	35	1	definition	definition	NOUN
iajs-153	35	2	2	2	NUM
iajs-153	35	3	-	-	SYM
iajs-153	35	4	15[5]:a	15[5]:a	NUM
iajs-153	35	5	subset	subset	VERB
iajs-153	35	6	a	a	PRON
iajs-153	35	7	of	of	ADP
iajs-153	35	8	a	a	DET
iajs-153	35	9	topological	topological	ADJ
iajs-153	35	10	space	space	NOUN
iajs-153	35	11	(	(	PUNCT
iajs-153	35	12	x	x	X
iajs-153	35	13	,	,	PUNCT
iajs-153	35	14	t	t	PROPN
iajs-153	35	15	)	)	PUNCT
iajs-153	35	16	is	be	AUX
iajs-153	35	17	called	call	VERB
iajs-153	35	18	a	a	DET
iajs-153	35	19	g*b	g*b	NOUN
iajs-153	35	20	-closed	-close	VERB
iajs-153	35	21	set	set	NOUN
iajs-153	35	22	if	if	SCONJ
iajs-153	35	23	bcl	bcl	NOUN
iajs-153	35	24	a	a	DET
iajs-153	35	25	⊆	⊆	NUM
iajs-153	35	26	u	u	NOUN
iajs-153	35	27	,	,	PUNCT
iajs-153	35	28	whenever	whenever	SCONJ
iajs-153	35	29	a	a	DET
iajs-153	35	30	⊆	⊆	NUM
iajs-153	35	31	u	u	NOUN
iajs-153	35	32	and	and	CCONJ
iajs-153	35	33	u	u	NOUN
iajs-153	35	34	is	be	AUX
iajs-153	35	35	gopen	gopen	NOUN
iajs-153	35	36	set	set	VERB
iajs-153	35	37	.	.	PUNCT
iajs-153	36	1	definition	definition	NOUN
iajs-153	36	2	2	2	NUM
iajs-153	36	3	-	-	SYM
iajs-153	36	4	16[5	16[5	NUM
iajs-153	36	5	]	]	PUNCT
iajs-153	36	6	:	:	PUNCT
iajs-153	36	7	a	a	DET
iajs-153	36	8	subset	subset	NOUN
iajs-153	36	9	a	a	PRON
iajs-153	36	10	of	of	ADP
iajs-153	36	11	a	a	DET
iajs-153	36	12	topological	topological	ADJ
iajs-153	36	13	space	space	NOUN
iajs-153	36	14	(	(	PUNCT
iajs-153	36	15	x	x	X
iajs-153	36	16	,	,	PUNCT
iajs-153	36	17	t	t	PROPN
iajs-153	36	18	)	)	PUNCT
iajs-153	36	19	is	be	AUX
iajs-153	36	20	called	call	VERB
iajs-153	36	21	strongly	strongly	ADV
iajs-153	36	22	b*-closed	b*-close	VERB
iajs-153	36	23	set	set	NOUN
iajs-153	36	24	(	(	PUNCT
iajs-153	36	25	briefly	briefly	ADV
iajs-153	36	26	,	,	PUNCT
iajs-153	36	27	sb*-closed	sb*-close	VERB
iajs-153	36	28	)	)	PUNCT
iajs-153	36	29	if	if	SCONJ
iajs-153	36	30	cl	cl	NOUN
iajs-153	36	31	int	int	VERB
iajs-153	36	32	a	a	DET
iajs-153	36	33	⊆	⊆	NUM
iajs-153	36	34	u	u	NOUN
iajs-153	36	35	,	,	PUNCT
iajs-153	36	36	whenever	whenever	SCONJ
iajs-153	36	37	a	a	DET
iajs-153	36	38	⊆	⊆	NUM
iajs-153	36	39	u	u	NOUN
iajs-153	36	40	and	and	CCONJ
iajs-153	36	41	u	u	NOUN
iajs-153	36	42	is	be	AUX
iajs-153	36	43	bopen	bopen	ADJ
iajs-153	36	44	set	set	VERB
iajs-153	36	45	.	.	PUNCT
iajs-153	37	1	definition	definition	NOUN
iajs-153	37	2	2	2	NUM
iajs-153	37	3	-	-	SYM
iajs-153	37	4	17[5	17[5	NUM
iajs-153	37	5	]	]	X
iajs-153	37	6	:	:	PUNCT
iajs-153	37	7	a	a	DET
iajs-153	37	8	subset	subset	NOUN
iajs-153	37	9	a	a	PRON
iajs-153	37	10	of	of	ADP
iajs-153	37	11	a	a	DET
iajs-153	37	12	topological	topological	ADJ
iajs-153	37	13	space	space	NOUN
iajs-153	37	14	(	(	PUNCT
iajs-153	37	15	x	x	X
iajs-153	37	16	,	,	PUNCT
iajs-153	37	17	t	t	PROPN
iajs-153	37	18	)	)	PUNCT
iajs-153	37	19	is	be	AUX
iajs-153	37	20	called	call	VERB
iajs-153	37	21	b**-open	b**-open	NOUN
iajs-153	37	22	set	set	VERB
iajs-153	37	23	if	if	SCONJ
iajs-153	37	24	a⊆int(cl(int(a)))∪cl(int(cl(a	a⊆int(cl(int(a)))∪cl(int(cl(a	PROPN
iajs-153	37	25	)	)	PUNCT
iajs-153	37	26	)	)	PUNCT
iajs-153	37	27	)	)	PUNCT
iajs-153	37	28	and	and	CCONJ
iajs-153	37	29	b**-closed	b**-close	VERB
iajs-153	37	30	set	set	VERB
iajs-153	37	31	if	if	SCONJ
iajs-153	37	32	cl(int(cl(a))∩int(cl(int(a	cl(int(cl(a))∩int(cl(int(a	NOUN
iajs-153	37	33	)	)	PUNCT
iajs-153	37	34	)	)	PUNCT
iajs-153	38	1	⊆	⊆	NUM
iajs-153	38	2	)	)	PUNCT
iajs-153	38	3	.	.	PUNCT
iajs-153	39	1	3	3	X
iajs-153	39	2	.	.	NUM
iajs-153	39	3	generalized	generalize	VERB
iajs-153	39	4	b*-closed	b*-close	VERB
iajs-153	39	5	sets	set	NOUN
iajs-153	39	6	.	.	PUNCT
iajs-153	40	1	in	in	ADP
iajs-153	40	2	this	this	DET
iajs-153	40	3	section	section	NOUN
iajs-153	40	4	,	,	PUNCT
iajs-153	40	5	we	we	PRON
iajs-153	40	6	introduce	introduce	VERB
iajs-153	40	7	and	and	CCONJ
iajs-153	40	8	study	study	VERB
iajs-153	40	9	the	the	DET
iajs-153	40	10	concept	concept	NOUN
iajs-153	40	11	of	of	ADP
iajs-153	40	12	generalized	generalized	ADJ
iajs-153	40	13	b*-closed	b*-close	VERB
iajs-153	40	14	set	set	NOUN
iajs-153	40	15	in	in	ADP
iajs-153	40	16	topological	topological	ADJ
iajs-153	40	17	spaces	space	NOUN
iajs-153	40	18	.	.	PUNCT
iajs-153	41	1	also	also	ADV
iajs-153	41	2	we	we	PRON
iajs-153	41	3	study	study	VERB
iajs-153	41	4	the	the	DET
iajs-153	41	5	relationship	relationship	NOUN
iajs-153	41	6	between	between	ADP
iajs-153	41	7	this	this	DET
iajs-153	41	8	set	set	NOUN
iajs-153	41	9	and	and	CCONJ
iajs-153	41	10	the	the	DET
iajs-153	41	11	other	other	ADJ
iajs-153	41	12	types	type	NOUN
iajs-153	41	13	of	of	ADP
iajs-153	41	14	sets	set	NOUN
iajs-153	41	15	.	.	PUNCT
iajs-153	42	1	definition	definition	NOUN
iajs-153	42	2	3	3	NUM
iajs-153	42	3	-	-	SYM
iajs-153	42	4	1	1	NUM
iajs-153	42	5	:	:	PUNCT
iajs-153	42	6	a	a	DET
iajs-153	42	7	subset	subset	NOUN
iajs-153	42	8	a	a	PRON
iajs-153	42	9	of	of	ADP
iajs-153	42	10	a	a	DET
iajs-153	42	11	topological	topological	ADJ
iajs-153	42	12	space	space	NOUN
iajs-153	42	13	(	(	PUNCT
iajs-153	42	14	x	x	X
iajs-153	42	15	,	,	PUNCT
iajs-153	42	16	t	t	PROPN
iajs-153	42	17	)	)	PUNCT
iajs-153	42	18	is	be	AUX
iajs-153	42	19	called	call	VERB
iajs-153	42	20	generalized	generalized	ADJ
iajs-153	42	21	b	b	PROPN
iajs-153	42	22	*	*	ADJ
iajs-153	42	23	closed	closed	ADJ
iajs-153	42	24	set	set	NOUN
iajs-153	42	25	(	(	PUNCT
iajs-153	42	26	briefly	briefly	ADV
iajs-153	42	27	,	,	PUNCT
iajs-153	42	28	gb*-closed	gb*-close	VERB
iajs-153	42	29	)	)	PUNCT
iajs-153	42	30	if	if	SCONJ
iajs-153	42	31	int	int	NOUN
iajs-153	42	32	cl	cl	NOUN
iajs-153	42	33	a	a	DET
iajs-153	42	34	⊆	⊆	NUM
iajs-153	42	35	u	u	NOUN
iajs-153	42	36	,	,	PUNCT
iajs-153	42	37	whenever	whenever	SCONJ
iajs-153	42	38	a	a	DET
iajs-153	42	39	⊆	⊆	NUM
iajs-153	42	40	u	u	NOUN
iajs-153	42	41	and	and	CCONJ
iajs-153	42	42	u	u	NOUN
iajs-153	42	43	is	be	AUX
iajs-153	42	44	gbopen	gbopen	ADJ
iajs-153	42	45	set	set	VERB
iajs-153	42	46	.	.	PUNCT
iajs-153	43	1	theorem	theorem	VERB
iajs-153	43	2	3	3	NUM
iajs-153	43	3	-	-	SYM
iajs-153	43	4	2	2	NUM
iajs-153	43	5	:	:	PUNCT
iajs-153	43	6	every	every	DET
iajs-153	43	7	closed	closed	ADJ
iajs-153	43	8	set	set	NOUN
iajs-153	43	9	is	be	AUX
iajs-153	43	10	gb	gb	ADP
iajs-153	43	11	*	*	PUNCT
iajs-153	43	12	-closed	-close	VERB
iajs-153	43	13	set	set	NOUN
iajs-153	43	14	.	.	PUNCT
iajs-153	44	1	proof	proof	NOUN
iajs-153	44	2	:	:	PUNCT
iajs-153	44	3	assume	assume	VERB
iajs-153	44	4	that	that	SCONJ
iajs-153	44	5	a	a	PRON
iajs-153	44	6	is	be	AUX
iajs-153	44	7	a	a	DET
iajs-153	44	8	closed	closed	ADJ
iajs-153	44	9	set	set	NOUN
iajs-153	44	10	in	in	ADP
iajs-153	44	11	x	x	PUNCT
iajs-153	44	12	then	then	ADV
iajs-153	44	13	cl	cl	INTJ
iajs-153	44	14	(	(	PUNCT
iajs-153	44	15	a)=a	a)=a	X
iajs-153	44	16	,	,	PUNCT
iajs-153	44	17	and	and	CCONJ
iajs-153	44	18	u	u	PRON
iajs-153	44	19	be	be	VERB
iajs-153	44	20	any	any	DET
iajs-153	44	21	gb	gb	ADV
iajs-153	44	22	-	-	PUNCT
iajs-153	44	23	open	open	NOUN
iajs-153	44	24	set	set	NOUN
iajs-153	44	25	where	where	SCONJ
iajs-153	44	26	a	a	DET
iajs-153	44	27	⊆	⊆	NUM
iajs-153	44	28	u	u	NOUN
iajs-153	44	29	.	.	PUNCT
iajs-153	45	1	since	since	SCONJ
iajs-153	45	2	int	int	PROPN
iajs-153	45	3	a	a	DET
iajs-153	45	4	⊆	⊆	NUM
iajs-153	45	5	a	a	PRON
iajs-153	45	6	.	.	PUNCT
iajs-153	45	7	implies	imply	VERB
iajs-153	45	8	that	that	DET
iajs-153	45	9	int	int	NOUN
iajs-153	45	10	cl	cl	NOUN
iajs-153	45	11	a	a	DET
iajs-153	45	12	⊆	⊆	NUM
iajs-153	45	13	u	u	NOUN
iajs-153	45	14	.hence	.hence	NOUN
iajs-153	45	15	a	a	DET
iajs-153	45	16	is	be	AUX
iajs-153	45	17	gb	gb	ADP
iajs-153	45	18	*	*	PUNCT
iajs-153	45	19	-closed	-closed	ADJ
iajs-153	45	20	set	set	NOUN
iajs-153	45	21	in	in	ADP
iajs-153	45	22	x.	x.	PROPN
iajs-153	45	23	207	207	NUM
iajs-153	45	24	|	|	ADV
iajs-153	45	25	mathematics	mathematic	NOUN
iajs-153	45	26	2015	2015	NUM
iajs-153	45	27	)	)	PUNCT
iajs-153	45	28	عام	عام	ADP
iajs-153	45	29	3العدد	3العدد	NUM
iajs-153	45	30	(	(	PUNCT
iajs-153	45	31	28الھيثم	28الھيثم	NUM
iajs-153	45	32	للعلوم	للعلوم	PROPN
iajs-153	45	33	الصرفة	الصرفة	NOUN
iajs-153	45	34	و	و	PRON
iajs-153	45	35	التطبيقية	التطبيقية	ADV
iajs-153	45	36	المجلد	المجلد	ADV
iajs-153	45	37	مجلة	مجلة	VERB
iajs-153	45	38	إبن	إبن	VERB
iajs-153	45	39	ibn	ibn	PROPN
iajs-153	45	40	al	al	PROPN
iajs-153	45	41	-	-	PUNCT
iajs-153	45	42	haitham	haitham	PROPN
iajs-153	45	43	jour	jour	X
iajs-153	45	44	.	.	PROPN
iajs-153	46	1	for	for	ADP
iajs-153	46	2	pure	pure	ADJ
iajs-153	46	3	&	&	CCONJ
iajs-153	46	4	appl	appl	PROPN
iajs-153	46	5	.	.	PUNCT
iajs-153	47	1	sci	sci	PROPN
iajs-153	47	2	.	.	PUNCT
iajs-153	47	3	vol	vol	NOUN
iajs-153	47	4	.	.	PROPN
iajs-153	48	1	28	28	NUM
iajs-153	48	2	(	(	PUNCT
iajs-153	48	3	3	3	NUM
iajs-153	48	4	)	)	PUNCT
iajs-153	48	5	2015	2015	NUM
iajs-153	48	6	remark	remark	NOUN
iajs-153	48	7	3	3	NUM
iajs-153	48	8	-	-	SYM
iajs-153	48	9	3	3	NUM
iajs-153	48	10	:	:	PUNCT
iajs-153	48	11	the	the	DET
iajs-153	48	12	converse	converse	NOUN
iajs-153	48	13	of	of	ADP
iajs-153	48	14	the	the	DET
iajs-153	48	15	theorem	theorem	NOUN
iajs-153	48	16	[	[	X
iajs-153	48	17	32	32	NUM
iajs-153	48	18	]	]	PUNCT
iajs-153	48	19	need	need	AUX
iajs-153	48	20	not	not	PART
iajs-153	48	21	be	be	AUX
iajs-153	48	22	true	true	ADJ
iajs-153	48	23	as	as	SCONJ
iajs-153	48	24	seen	see	VERB
iajs-153	48	25	by	by	ADP
iajs-153	48	26	the	the	DET
iajs-153	48	27	following	follow	VERB
iajs-153	48	28	example	example	NOUN
iajs-153	48	29	.	.	PUNCT
iajs-153	49	1	example3	example3	PROPN
iajs-153	49	2	-	-	PUNCT
iajs-153	49	3	4	4	NUM
iajs-153	49	4	:	:	PUNCT
iajs-153	49	5	let	let	VERB
iajs-153	49	6	x=	x=	ADJ
iajs-153	49	7	{	{	PUNCT
iajs-153	49	8	a	a	DET
iajs-153	49	9	,	,	PUNCT
iajs-153	49	10	b	b	NOUN
iajs-153	49	11	,	,	PUNCT
iajs-153	49	12	c	c	NOUN
iajs-153	49	13	}	}	PUNCT
iajs-153	49	14	with	with	ADP
iajs-153	49	15	t={x	t={x	ADJ
iajs-153	49	16	,	,	PUNCT
iajs-153	49	17			ADJ
iajs-153	49	18	,	,	PUNCT
iajs-153	49	19	{	{	PUNCT
iajs-153	49	20	a	a	X
iajs-153	49	21	}	}	PUNCT
iajs-153	49	22	}	}	PUNCT
iajs-153	49	23	.in	.in	PUNCT
iajs-153	49	24	this	this	DET
iajs-153	49	25	topological	topological	ADJ
iajs-153	49	26	space	space	NOUN
iajs-153	49	27	,	,	PUNCT
iajs-153	49	28	the	the	DET
iajs-153	49	29	sub	sub	NOUN
iajs-153	49	30	set	set	VERB
iajs-153	49	31	a={b	a={b	ADV
iajs-153	49	32	}	}	PUNCT
iajs-153	49	33	is	be	AUX
iajs-153	49	34	gb*closed	gb*close	VERB
iajs-153	49	35	set	set	VERB
iajs-153	49	36	but	but	CCONJ
iajs-153	49	37	not	not	PART
iajs-153	49	38	closed	close	VERB
iajs-153	49	39	set	set	VERB
iajs-153	49	40	.	.	PUNCT
iajs-153	50	1	theorem	theorem	VERB
iajs-153	50	2	3	3	NUM
iajs-153	50	3	-	-	SYM
iajs-153	50	4	5	5	NUM
iajs-153	50	5	:	:	PUNCT
iajs-153	50	6	a	a	DET
iajs-153	50	7	set	set	NOUN
iajs-153	50	8	a	a	PRON
iajs-153	50	9	is	be	AUX
iajs-153	50	10	gb*-closed	gb*-close	VERB
iajs-153	50	11	set	set	VERB
iajs-153	50	12	iff	iff	PROPN
iajs-153	50	13	int	int	PROPN
iajs-153	50	14	cl(a)-a	cl(a)-a	PROPN
iajs-153	50	15	contains	contain	VERB
iajs-153	50	16	no	no	DET
iajs-153	50	17	non	non	ADJ
iajs-153	50	18	-	-	ADJ
iajs-153	50	19	empty	empty	ADJ
iajs-153	50	20	gb	gb	ADV
iajs-153	50	21	-	-	PUNCT
iajs-153	50	22	closed	close	VERB
iajs-153	50	23	set	set	NOUN
iajs-153	50	24	.	.	PUNCT
iajs-153	51	1	proof	proof	NOUN
iajs-153	51	2	:	:	PUNCT
iajs-153	51	3	necessity	necessity	NOUN
iajs-153	51	4	:	:	PUNCT
iajs-153	51	5	suppose	suppose	VERB
iajs-153	51	6	that	that	SCONJ
iajs-153	51	7	f	f	PROPN
iajs-153	51	8	is	be	AUX
iajs-153	51	9	a	a	DET
iajs-153	51	10	non	non	ADJ
iajs-153	51	11	-	-	ADJ
iajs-153	51	12	empty	empty	ADJ
iajs-153	51	13	gb	gb	ADV
iajs-153	51	14	-	-	PUNCT
iajs-153	51	15	closed	close	VERB
iajs-153	51	16	subset	subset	NOUN
iajs-153	51	17	of	of	ADP
iajs-153	51	18	int(cl(a	int(cl(a	PROPN
iajs-153	51	19	)	)	PUNCT
iajs-153	51	20	)	)	PUNCT
iajs-153	52	1	such	such	ADJ
iajs-153	52	2	that	that	SCONJ
iajs-153	52	3	f	f	PROPN
iajs-153	52	4	⊆	⊆	NUM
iajs-153	52	5	int	int	NOUN
iajs-153	52	6	cl	cl	NOUN
iajs-153	52	7	a	a	DET
iajs-153	52	8	a	a	NOUN
iajs-153	52	9	.	.	PUNCT
iajs-153	53	1	then	then	ADV
iajs-153	53	2	f	f	PROPN
iajs-153	53	3	⊆	⊆	NUM
iajs-153	53	4	int	int	NOUN
iajs-153	53	5	cl	cl	NOUN
iajs-153	53	6	a	a	DET
iajs-153	53	7	∩	∩	NOUN
iajs-153	53	8	a	a	DET
iajs-153	53	9	.therefore	.therefore	NOUN
iajs-153	53	10	f	f	PROPN
iajs-153	53	11	⊆	⊆	NUM
iajs-153	53	12	int	int	NOUN
iajs-153	53	13	cl	cl	NOUN
iajs-153	53	14	a	a	PRON
iajs-153	53	15	and	and	CCONJ
iajs-153	53	16	f	f	PROPN
iajs-153	53	17	⊆	⊆	NUM
iajs-153	53	18	a	a	PRON
iajs-153	53	19	.	.	PUNCT
iajs-153	54	1	since	since	SCONJ
iajs-153	54	2	f	f	PROPN
iajs-153	54	3	is	be	AUX
iajs-153	54	4	gb	gb	ADV
iajs-153	54	5	-	-	PUNCT
iajs-153	54	6	closed	close	VERB
iajs-153	54	7	set	set	NOUN
iajs-153	54	8	and	and	CCONJ
iajs-153	54	9	a	a	PRON
iajs-153	54	10	is	be	AUX
iajs-153	54	11	gb*-closed	gb*-close	VERB
iajs-153	54	12	set	set	VERB
iajs-153	54	13	,	,	PUNCT
iajs-153	54	14	int	int	NOUN
iajs-153	54	15	cl	cl	NOUN
iajs-153	54	16	a	a	DET
iajs-153	54	17	⊆	⊆	NUM
iajs-153	54	18	f	f	NOUN
iajs-153	54	19	.	.	PUNCT
iajs-153	55	1	thus	thus	ADV
iajs-153	55	2	f	f	PROPN
iajs-153	55	3	⊆	⊆	NUM
iajs-153	55	4	int	int	NOUN
iajs-153	55	5	cl	cl	NOUN
iajs-153	55	6	a	a	PRON
iajs-153	55	7	.	.	PUNCT
iajs-153	56	1	therefore	therefore	ADV
iajs-153	56	2	f	f	PROPN
iajs-153	56	3	⊆	⊆	NUM
iajs-153	56	4	int	int	NOUN
iajs-153	56	5	cl	cl	NOUN
iajs-153	56	6	a	a	DET
iajs-153	56	7	∩	∩	ADJ
iajs-153	56	8	int	int	NOUN
iajs-153	56	9	cl	cl	NOUN
iajs-153	56	10	a	a	DET
iajs-153	56	11			NOUN
iajs-153	56	12	.therefore	.therefore	ADP
iajs-153	56	13	f=	f=	ADJ
iajs-153	56	14			NOUN
iajs-153	56	15	and	and	CCONJ
iajs-153	56	16	this	this	PRON
iajs-153	56	17	implies	imply	VERB
iajs-153	56	18	that	that	SCONJ
iajs-153	56	19	int(cl(a))-a	int(cl(a))-a	NOUN
iajs-153	56	20	contains	contain	VERB
iajs-153	56	21	no	no	DET
iajs-153	56	22	non	non	ADJ
iajs-153	56	23	-	-	ADJ
iajs-153	56	24	empty	empty	ADJ
iajs-153	56	25	gb	gb	ADV
iajs-153	56	26	-	-	PUNCT
iajs-153	56	27	closed	close	VERB
iajs-153	56	28	set	set	NOUN
iajs-153	56	29	.	.	PUNCT
iajs-153	57	1	sufficiency	sufficiency	NOUN
iajs-153	57	2	:	:	PUNCT
iajs-153	57	3	assume	assume	VERB
iajs-153	57	4	that	that	SCONJ
iajs-153	57	5	int(cl(a))-a	int(cl(a))-a	NOUN
iajs-153	57	6	contains	contain	VERB
iajs-153	57	7	no	no	DET
iajs-153	57	8	non	non	ADJ
iajs-153	57	9	-	-	ADJ
iajs-153	57	10	empty	empty	ADJ
iajs-153	57	11	gb	gb	ADV
iajs-153	57	12	-	-	PUNCT
iajs-153	57	13	closed	closed	ADJ
iajs-153	57	14	.	.	PUNCT
iajs-153	58	1	let	let	VERB
iajs-153	58	2	a	a	DET
iajs-153	58	3	⊆	⊆	NUM
iajs-153	58	4	u	u	NOUN
iajs-153	58	5	,	,	PUNCT
iajs-153	58	6	u	u	PROPN
iajs-153	58	7	is	be	AUX
iajs-153	58	8	gb	gb	ADV
iajs-153	58	9	-	-	PUNCT
iajs-153	58	10	open	open	ADJ
iajs-153	58	11	set	set	NOUN
iajs-153	58	12	.suppose	.suppose	PUNCT
iajs-153	58	13	that	that	SCONJ
iajs-153	58	14	int(cl(a	int(cl(a	PROPN
iajs-153	58	15	)	)	PUNCT
iajs-153	58	16	)	)	PUNCT
iajs-153	58	17	is	be	AUX
iajs-153	58	18	not	not	PART
iajs-153	58	19	contained	contain	VERB
iajs-153	58	20	in	in	ADP
iajs-153	58	21	u	u	NOUN
iajs-153	58	22	,	,	PUNCT
iajs-153	58	23	then	then	ADV
iajs-153	58	24	int	int	VERB
iajs-153	58	25	cl	cl	NOUN
iajs-153	58	26	a	a	DET
iajs-153	58	27	∩	∩	ADJ
iajs-153	58	28	u	u	NOUN
iajs-153	58	29	is	be	AUX
iajs-153	58	30	a	a	DET
iajs-153	58	31	nonempty	nonempty	ADJ
iajs-153	58	32	gb	gb	ADV
iajs-153	58	33	-	-	PUNCT
iajs-153	58	34	closed	close	VERB
iajs-153	58	35	set	set	NOUN
iajs-153	58	36	of	of	ADP
iajs-153	58	37	int(cl(a))-a	int(cl(a))-a	NOUN
iajs-153	58	38	which	which	PRON
iajs-153	58	39	is	be	AUX
iajs-153	58	40	a	a	DET
iajs-153	58	41	contradiction	contradiction	NOUN
iajs-153	58	42	.	.	PUNCT
iajs-153	59	1	therefore	therefore	ADV
iajs-153	59	2	int	int	VERB
iajs-153	59	3	cl	cl	NOUN
iajs-153	59	4	a	a	DET
iajs-153	59	5	⊆	⊆	NUM
iajs-153	59	6	and	and	CCONJ
iajs-153	59	7	hence	hence	ADV
iajs-153	59	8	a	a	PRON
iajs-153	59	9	is	be	AUX
iajs-153	59	10	gb*-closed	gb*-close	VERB
iajs-153	59	11	set	set	NOUN
iajs-153	59	12	.	.	PUNCT
iajs-153	60	1	theorem	theorem	VERB
iajs-153	60	2	3	3	NUM
iajs-153	60	3	-	-	SYM
iajs-153	60	4	6	6	NUM
iajs-153	60	5	:	:	PUNCT
iajs-153	60	6	let	let	VERB
iajs-153	60	7	b	b	NOUN
iajs-153	60	8	⊆	⊆	NUM
iajs-153	60	9	y	y	PROPN
iajs-153	60	10	⊆	⊆	NUM
iajs-153	60	11	x	x	X
iajs-153	60	12	,	,	PUNCT
iajs-153	60	13	if	if	SCONJ
iajs-153	60	14	b	b	NOUN
iajs-153	60	15	is	be	AUX
iajs-153	60	16	gb*-closed	gb*-close	VERB
iajs-153	60	17	set	set	VERB
iajs-153	60	18	relative	relative	ADJ
iajs-153	60	19	to	to	ADP
iajs-153	60	20	y	y	PROPN
iajs-153	60	21	and	and	CCONJ
iajs-153	60	22	that	that	SCONJ
iajs-153	60	23	y	y	PROPN
iajs-153	60	24	is	be	AUX
iajs-153	60	25	both	both	PRON
iajs-153	60	26	gb	gb	ADV
iajs-153	60	27	-	-	PUNCT
iajs-153	60	28	open	open	ADJ
iajs-153	60	29	and	and	CCONJ
iajs-153	60	30	gb*‐closed	gb*‐close	VERB
iajs-153	60	31	set	set	VERB
iajs-153	60	32	in	in	ADP
iajs-153	60	33	x	x	PROPN
iajs-153	60	34	,	,	PUNCT
iajs-153	60	35	t	t	PROPN
iajs-153	60	36	then	then	ADV
iajs-153	60	37	b	b	PROPN
iajs-153	60	38	is	be	AUX
iajs-153	60	39	gb*‐closed	gb*‐close	VERB
iajs-153	60	40	set	set	VERB
iajs-153	60	41	in	in	ADP
iajs-153	60	42	x	x	PROPN
iajs-153	60	43	,	,	PUNCT
iajs-153	60	44	t	t	PROPN
iajs-153	60	45	.	.	PUNCT
iajs-153	61	1	proof	proof	NOUN
iajs-153	61	2	:	:	PUNCT
iajs-153	61	3	let	let	VERB
iajs-153	61	4	u	u	PRON
iajs-153	61	5	⊆	⊆	NUM
iajs-153	61	6	b	b	NOUN
iajs-153	61	7	and	and	CCONJ
iajs-153	61	8	u	u	NOUN
iajs-153	61	9	be	be	VERB
iajs-153	61	10	a	a	DET
iajs-153	61	11	gb	gb	ADV
iajs-153	61	12	-	-	PUNCT
iajs-153	61	13	open	open	ADJ
iajs-153	61	14	set	set	NOUN
iajs-153	61	15	in	in	ADP
iajs-153	61	16	(	(	PUNCT
iajs-153	61	17	x	x	NOUN
iajs-153	61	18	,	,	PUNCT
iajs-153	61	19	t).but	t).but	NOUN
iajs-153	61	20	given	give	VERB
iajs-153	61	21	that	that	PRON
iajs-153	61	22	b	b	PROPN
iajs-153	61	23	⊆	⊆	NUM
iajs-153	61	24	y	y	PROPN
iajs-153	61	25	⊆	⊆	NUM
iajs-153	61	26	x	x	X
iajs-153	61	27	.	.	PUNCT
iajs-153	62	1	therefore	therefore	ADV
iajs-153	62	2	b	b	PROPN
iajs-153	62	3	⊆	⊆	NUM
iajs-153	62	4	y	y	PROPN
iajs-153	62	5	and	and	CCONJ
iajs-153	62	6	u	u	NOUN
iajs-153	62	7	⊆	⊆	NUM
iajs-153	62	8	b	b	NOUN
iajs-153	62	9	.	.	PUNCT
iajs-153	63	1	this	this	PRON
iajs-153	63	2	implies	imply	VERB
iajs-153	63	3	that	that	SCONJ
iajs-153	63	4	y	y	PROPN
iajs-153	63	5	∩	∩	NOUN
iajs-153	63	6	u	u	PROPN
iajs-153	63	7	⊆	⊆	PROPN
iajs-153	63	8	b.	b.	NOUN
iajs-153	63	9	since	since	SCONJ
iajs-153	63	10	b	b	PROPN
iajs-153	63	11	is	be	AUX
iajs-153	63	12	gb*-closed	gb*-close	VERB
iajs-153	63	13	set	set	VERB
iajs-153	63	14	relative	relative	ADJ
iajs-153	63	15	to	to	ADP
iajs-153	63	16	y	y	PROPN
iajs-153	63	17	,	,	PUNCT
iajs-153	63	18	then	then	ADV
iajs-153	63	19	y	y	PROPN
iajs-153	63	20	∩	∩	NOUN
iajs-153	63	21	u	u	NOUN
iajs-153	63	22	⊆	⊆	NUM
iajs-153	63	23	int	int	NOUN
iajs-153	63	24	cl	cl	NOUN
iajs-153	63	25	y	y	PROPN
iajs-153	63	26	.(i.e	.(i.e	PUNCT
iajs-153	63	27	)	)	PUNCT
iajs-153	64	1	y	y	PROPN
iajs-153	64	2	∩	∩	NOUN
iajs-153	64	3	u	u	PROPN
iajs-153	64	4	⊆	⊆	NUM
iajs-153	64	5	y	y	PROPN
iajs-153	64	6	∩	∩	ADJ
iajs-153	64	7	int	int	NOUN
iajs-153	64	8	cl	cl	NOUN
iajs-153	64	9	y	y	NOUN
iajs-153	64	10	.implies	.implie	NOUN
iajs-153	64	11	that	that	SCONJ
iajs-153	64	12	u	u	PROPN
iajs-153	64	13	⊆	⊆	NUM
iajs-153	64	14	y	y	PROPN
iajs-153	64	15	∩	∩	ADJ
iajs-153	64	16	int	int	NOUN
iajs-153	64	17	cl	cl	NOUN
iajs-153	64	18	y	y	NOUN
iajs-153	64	19	.	.	PUNCT
iajs-153	65	1	thus	thus	ADV
iajs-153	65	2	u	u	PRON
iajs-153	65	3	∪	∪	ADJ
iajs-153	65	4	int	int	PROPN
iajs-153	65	5	cl	cl	NOUN
iajs-153	65	6	b	b	NOUN
iajs-153	65	7	⊆	⊆	NUM
iajs-153	65	8	y	y	PROPN
iajs-153	65	9	∩	∩	ADJ
iajs-153	65	10	int	int	NOUN
iajs-153	65	11	cl	cl	NOUN
iajs-153	65	12	b	b	X
iajs-153	65	13	∪	∪	ADJ
iajs-153	65	14	int	int	NOUN
iajs-153	65	15	cl	cl	NOUN
iajs-153	65	16	b	b	NOUN
iajs-153	65	17	.	.	PUNCT
iajs-153	66	1	this	this	PRON
iajs-153	66	2	implies	imply	VERB
iajs-153	66	3	that	that	SCONJ
iajs-153	66	4	u	u	PROPN
iajs-153	66	5	∪	∪	VERB
iajs-153	66	6	int	int	PROPN
iajs-153	66	7	cl	cl	NOUN
iajs-153	66	8	b	b	NOUN
iajs-153	66	9	⊆	⊆	NUM
iajs-153	66	10	int	int	NOUN
iajs-153	66	11	cl	cl	NOUN
iajs-153	66	12	y	y	PROPN
iajs-153	66	13	⊆	⊆	NUM
iajs-153	66	14	int	int	NOUN
iajs-153	66	15	cl	cl	NOUN
iajs-153	66	16	b	b	NOUN
iajs-153	66	17	.	.	PUNCT
iajs-153	67	1	therefore	therefore	ADV
iajs-153	67	2	u	u	NOUN
iajs-153	67	3	⊆	⊆	NUM
iajs-153	67	4	int	int	NOUN
iajs-153	67	5	cl	cl	NOUN
iajs-153	67	6	b	b	NOUN
iajs-153	67	7	.	.	PUNCT
iajs-153	68	1	since	since	SCONJ
iajs-153	68	2	int(cl(b	int(cl(b	PROPN
iajs-153	68	3	)	)	PUNCT
iajs-153	68	4	)	)	PUNCT
iajs-153	68	5	is	be	AUX
iajs-153	68	6	not	not	PART
iajs-153	68	7	contained	contain	VERB
iajs-153	68	8	in	in	ADP
iajs-153	68	9	int	int	NOUN
iajs-153	68	10	cl	cl	NOUN
iajs-153	68	11	b	b	PROPN
iajs-153	68	12	.	.	PUNCT
iajs-153	69	1	thus	thus	ADV
iajs-153	69	2	b	b	NOUN
iajs-153	69	3	is	be	AUX
iajs-153	69	4	gb*-closed	gb*-close	VERB
iajs-153	69	5	set	set	VERB
iajs-153	69	6	relative	relative	ADJ
iajs-153	69	7	to	to	ADP
iajs-153	69	8	x.	x.	NOUN
iajs-153	69	9	theorem	theorem	VERB
iajs-153	69	10	3	3	NUM
iajs-153	69	11	-	-	SYM
iajs-153	69	12	7	7	NUM
iajs-153	69	13	:	:	PUNCT
iajs-153	69	14	let	let	VERB
iajs-153	69	15	a	a	DET
iajs-153	69	16	⊆	⊆	NUM
iajs-153	69	17	y	y	SYM
iajs-153	69	18	⊆	⊆	NUM
iajs-153	69	19	x	x	PUNCT
iajs-153	69	20	and	and	CCONJ
iajs-153	69	21	suppose	suppose	VERB
iajs-153	69	22	that	that	SCONJ
iajs-153	69	23	a	a	PRON
iajs-153	69	24	is	be	AUX
iajs-153	69	25	gb	gb	ADP
iajs-153	69	26	*	*	PUNCT
iajs-153	69	27	-closed	-closed	ADJ
iajs-153	69	28	set	set	NOUN
iajs-153	69	29	in	in	ADP
iajs-153	69	30	x	x	SYM
iajs-153	69	31	then	then	ADV
iajs-153	69	32	a	a	PRON
iajs-153	69	33	is	be	AUX
iajs-153	69	34	gb	gb	ADP
iajs-153	69	35	*	*	PUNCT
iajs-153	69	36	closed	closed	ADJ
iajs-153	69	37	set	set	VERB
iajs-153	69	38	relative	relative	ADJ
iajs-153	69	39	to	to	ADP
iajs-153	69	40	y.	y.	NOUN
iajs-153	69	41	proof	proof	NOUN
iajs-153	69	42	:	:	PUNCT
iajs-153	69	43	assume	assume	VERB
iajs-153	69	44	that	that	SCONJ
iajs-153	69	45	a	a	DET
iajs-153	69	46	⊆	⊆	NUM
iajs-153	69	47	y	y	SYM
iajs-153	69	48	⊆	⊆	NUM
iajs-153	69	49	x	x	PUNCT
iajs-153	69	50	and	and	CCONJ
iajs-153	69	51	a	a	PRON
iajs-153	69	52	is	be	AUX
iajs-153	69	53	gb	gb	ADP
iajs-153	69	54	*	*	PUNCT
iajs-153	69	55	-closed	-closed	ADJ
iajs-153	69	56	set	set	NOUN
iajs-153	69	57	in	in	ADP
iajs-153	69	58	x	x	X
iajs-153	69	59	.	.	PUNCT
iajs-153	70	1	to	to	PART
iajs-153	70	2	show	show	VERB
iajs-153	70	3	that	that	SCONJ
iajs-153	70	4	a	a	PRON
iajs-153	70	5	is	be	AUX
iajs-153	70	6	gb	gb	ADP
iajs-153	70	7	*	*	PUNCT
iajs-153	70	8	closed	closed	ADJ
iajs-153	70	9	set	set	VERB
iajs-153	70	10	relative	relative	ADJ
iajs-153	70	11	to	to	ADP
iajs-153	70	12	y	y	PROPN
iajs-153	70	13	,	,	PUNCT
iajs-153	70	14	let	let	VERB
iajs-153	70	15	a	a	DET
iajs-153	70	16	⊆	⊆	NUM
iajs-153	70	17	y	y	PROPN
iajs-153	70	18	∩	∩	ADJ
iajs-153	70	19	u	u	NOUN
iajs-153	70	20	where	where	SCONJ
iajs-153	70	21	u	u	NOUN
iajs-153	70	22	is	be	AUX
iajs-153	70	23	gb	gb	ADV
iajs-153	70	24	-	-	PUNCT
iajs-153	70	25	open	open	ADJ
iajs-153	70	26	in	in	ADP
iajs-153	70	27	x	x	X
iajs-153	70	28	.	.	PUNCT
iajs-153	71	1	since	since	SCONJ
iajs-153	71	2	a	a	PRON
iajs-153	71	3	is	be	AUX
iajs-153	71	4	gb	gb	ADP
iajs-153	71	5	*	*	PUNCT
iajs-153	71	6	-closed	-closed	ADJ
iajs-153	71	7	set	set	NOUN
iajs-153	71	8	in	in	ADP
iajs-153	71	9	x	x	SYM
iajs-153	71	10	,	,	PUNCT
iajs-153	71	11	a	a	DET
iajs-153	71	12	⊆	⊆	NUM
iajs-153	71	13	u	u	NOUN
iajs-153	71	14	implies	imply	VERB
iajs-153	71	15	that	that	DET
iajs-153	71	16	int	int	NOUN
iajs-153	71	17	cl	cl	NOUN
iajs-153	71	18	a	a	DET
iajs-153	71	19	⊆	⊆	NUM
iajs-153	71	20	u	u	NOUN
iajs-153	71	21	,	,	PUNCT
iajs-153	71	22	i.e	i.e	PROPN
iajs-153	71	23	)	)	PUNCT
iajs-153	71	24	y	y	PROPN
iajs-153	71	25	∩	∩	ADJ
iajs-153	71	26	int	int	NOUN
iajs-153	71	27	cl	cl	NOUN
iajs-153	71	28	a	a	DET
iajs-153	71	29	⊆	⊆	NUM
iajs-153	71	30	y	y	PROPN
iajs-153	71	31	∩	∩	NOUN
iajs-153	71	32	u.	u.	VERB
iajs-153	71	33	where	where	SCONJ
iajs-153	71	34	y	y	PROPN
iajs-153	71	35	∩	∩	ADJ
iajs-153	71	36	int	int	NOUN
iajs-153	71	37	cl	cl	NOUN
iajs-153	71	38	a	a	PRON
iajs-153	71	39	is	be	AUX
iajs-153	71	40	interior	interior	ADJ
iajs-153	71	41	of	of	ADP
iajs-153	71	42	closure	closure	NOUN
iajs-153	71	43	of	of	ADP
iajs-153	71	44	a	a	PRON
iajs-153	71	45	in	in	ADP
iajs-153	71	46	y	y	PROPN
iajs-153	71	47	.	.	PUNCT
iajs-153	72	1	thus	thus	ADV
iajs-153	72	2	a	a	DET
iajs-153	72	3	is	be	AUX
iajs-153	72	4	gb	gb	ADP
iajs-153	72	5	*	*	PUNCT
iajs-153	72	6	-closed	-closed	ADJ
iajs-153	72	7	set	set	NOUN
iajs-153	72	8	relative	relative	ADJ
iajs-153	72	9	to	to	ADP
iajs-153	72	10	y.	y.	PROPN
iajs-153	72	11	theorem	theorem	VERB
iajs-153	72	12	3	3	NUM
iajs-153	72	13	-	-	SYM
iajs-153	72	14	8	8	NUM
iajs-153	72	15	:	:	PUNCT
iajs-153	72	16	if	if	SCONJ
iajs-153	72	17	a	a	PRON
iajs-153	72	18	is	be	AUX
iajs-153	72	19	a	a	DET
iajs-153	72	20	gb	gb	ADV
iajs-153	72	21	*	*	PUNCT
iajs-153	72	22	-closed	-closed	ADJ
iajs-153	72	23	set	set	NOUN
iajs-153	72	24	and	and	CCONJ
iajs-153	72	25	a	a	DET
iajs-153	72	26	⊆	⊆	NUM
iajs-153	72	27	b	b	SYM
iajs-153	72	28	⊆	⊆	NUM
iajs-153	72	29	int	int	NOUN
iajs-153	72	30	cl	cl	NOUN
iajs-153	72	31	a	a	DET
iajs-153	72	32	then	then	ADV
iajs-153	72	33	b	b	NOUN
iajs-153	72	34	is	be	AUX
iajs-153	72	35	a	a	DET
iajs-153	72	36	gb	gb	ADV
iajs-153	72	37	*	*	PUNCT
iajs-153	72	38	-closed	-close	VERB
iajs-153	72	39	set	set	NOUN
iajs-153	72	40	.	.	PUNCT
iajs-153	73	1	208	208	NUM
iajs-153	73	2	|	|	ADV
iajs-153	73	3	mathematics	mathematic	NOUN
iajs-153	73	4	2015	2015	NUM
iajs-153	73	5	)	)	PUNCT
iajs-153	73	6	عام	عام	ADP
iajs-153	73	7	3العدد	3العدد	NUM
iajs-153	73	8	(	(	PUNCT
iajs-153	73	9	28الھيثم	28الھيثم	NUM
iajs-153	73	10	للعلوم	للعلوم	PROPN
iajs-153	73	11	الصرفة	الصرفة	NOUN
iajs-153	74	1	و	و	PRON
iajs-153	74	2	التطبيقية	التطبيقية	ADV
iajs-153	74	3	المجلد	المجلد	ADV
iajs-153	74	4	مجلة	مجلة	VERB
iajs-153	74	5	إبن	إبن	VERB
iajs-153	74	6	ibn	ibn	PROPN
iajs-153	74	7	al	al	PROPN
iajs-153	74	8	-	-	PUNCT
iajs-153	74	9	haitham	haitham	PROPN
iajs-153	74	10	jour	jour	X
iajs-153	74	11	.	.	PROPN
iajs-153	74	12	for	for	ADP
iajs-153	74	13	pure	pure	ADJ
iajs-153	74	14	&	&	CCONJ
iajs-153	74	15	appl	appl	PROPN
iajs-153	74	16	.	.	PUNCT
iajs-153	75	1	sci	sci	PROPN
iajs-153	75	2	.	.	PUNCT
iajs-153	75	3	vol	vol	NOUN
iajs-153	75	4	.	.	PROPN
iajs-153	76	1	28	28	NUM
iajs-153	76	2	(	(	PUNCT
iajs-153	76	3	3	3	NUM
iajs-153	76	4	)	)	PUNCT
iajs-153	76	5	2015	2015	NUM
iajs-153	76	6	proof	proof	NOUN
iajs-153	76	7	:	:	PUNCT
iajs-153	76	8	let	let	VERB
iajs-153	76	9	u	u	PRON
iajs-153	76	10	be	be	AUX
iajs-153	76	11	a	a	DET
iajs-153	76	12	gb	gb	ADV
iajs-153	76	13	-open	-open	ADJ
iajs-153	76	14	set	set	NOUN
iajs-153	76	15	of	of	ADP
iajs-153	76	16	x	x	PRON
iajs-153	76	17	,	,	PUNCT
iajs-153	76	18	such	such	ADJ
iajs-153	76	19	that	that	PRON
iajs-153	76	20	b	b	PROPN
iajs-153	76	21	⊆	⊆	NUM
iajs-153	76	22	u	u	NOUN
iajs-153	76	23	.	.	PUNCT
iajs-153	77	1	then	then	ADV
iajs-153	77	2	a	a	DET
iajs-153	77	3	⊆	⊆	NUM
iajs-153	77	4	u	u	NOUN
iajs-153	77	5	.	.	PUNCT
iajs-153	78	1	since	since	SCONJ
iajs-153	78	2	a	a	PRON
iajs-153	78	3	is	be	AUX
iajs-153	78	4	gb	gb	ADP
iajs-153	78	5	*	*	NOUN
iajs-153	78	6	closed	closed	ADJ
iajs-153	78	7	,	,	PUNCT
iajs-153	78	8	then	then	ADV
iajs-153	78	9	int	int	VERB
iajs-153	78	10	cl	cl	NOUN
iajs-153	78	11	a	a	DET
iajs-153	78	12	⊆	⊆	NUM
iajs-153	78	13	u	u	NOUN
iajs-153	78	14	.now	.now	NOUN
iajs-153	78	15	int	int	NOUN
iajs-153	79	1	cl	cl	NOUN
iajs-153	79	2	b	b	NOUN
iajs-153	79	3	⊆	⊆	NUM
iajs-153	79	4	int	int	NOUN
iajs-153	79	5	cl	cl	NOUN
iajs-153	79	6	a	a	DET
iajs-153	79	7	⊆	⊆	NUM
iajs-153	79	8	u	u	NOUN
iajs-153	79	9	.therefore	.therefore	NOUN
iajs-153	79	10	b	b	PROPN
iajs-153	79	11	is	be	AUX
iajs-153	79	12	gb*closed	gb*close	VERB
iajs-153	79	13	set	set	VERB
iajs-153	79	14	in	in	ADP
iajs-153	79	15	x	x	PROPN
iajs-153	79	16	.	.	PUNCT
iajs-153	80	1	theorem	theorem	ADJ
iajs-153	80	2	3	3	NUM
iajs-153	80	3	-	-	SYM
iajs-153	80	4	9	9	NUM
iajs-153	80	5	:	:	PUNCT
iajs-153	80	6	the	the	DET
iajs-153	80	7	intersection	intersection	NOUN
iajs-153	80	8	of	of	ADP
iajs-153	80	9	a	a	DET
iajs-153	80	10	gb	gb	PROPN
iajs-153	80	11	*	*	PUNCT
iajs-153	80	12	-closed	-closed	ADJ
iajs-153	80	13	set	set	NOUN
iajs-153	80	14	and	and	CCONJ
iajs-153	80	15	a	a	DET
iajs-153	80	16	closed	closed	ADJ
iajs-153	80	17	set	set	NOUN
iajs-153	80	18	is	be	AUX
iajs-153	80	19	a	a	DET
iajs-153	80	20	gb	gb	ADV
iajs-153	80	21	*	*	PUNCT
iajs-153	80	22	-closed	-close	VERB
iajs-153	80	23	set	set	NOUN
iajs-153	80	24	.	.	PUNCT
iajs-153	81	1	proof	proof	NOUN
iajs-153	81	2	:	:	PUNCT
iajs-153	81	3	let	let	VERB
iajs-153	81	4	a	a	PRON
iajs-153	81	5	be	be	AUX
iajs-153	81	6	a	a	DET
iajs-153	81	7	gb	gb	NOUN
iajs-153	81	8	*	*	PUNCT
iajs-153	81	9	-closed	-closed	ADJ
iajs-153	81	10	set	set	NOUN
iajs-153	81	11	and	and	CCONJ
iajs-153	81	12	f	f	PROPN
iajs-153	81	13	be	be	AUX
iajs-153	81	14	a	a	DET
iajs-153	81	15	closed	closed	ADJ
iajs-153	81	16	set	set	NOUN
iajs-153	81	17	.	.	PUNCT
iajs-153	82	1	since	since	SCONJ
iajs-153	82	2	a	a	DET
iajs-153	82	3	is	be	AUX
iajs-153	82	4	gb	gb	ADP
iajs-153	82	5	*	*	PUNCT
iajs-153	82	6	-closed	-closed	ADJ
iajs-153	82	7	set	set	NOUN
iajs-153	82	8	,	,	PUNCT
iajs-153	82	9	int	int	NOUN
iajs-153	82	10	cl	cl	NOUN
iajs-153	82	11	a	a	DET
iajs-153	82	12	⊆	⊆	NUM
iajs-153	82	13	u	u	NOUN
iajs-153	82	14	whenever	whenever	SCONJ
iajs-153	82	15	a	a	DET
iajs-153	82	16	⊆	⊆	NUM
iajs-153	82	17	u	u	NOUN
iajs-153	82	18	,	,	PUNCT
iajs-153	82	19	where	where	SCONJ
iajs-153	82	20	u	u	NOUN
iajs-153	82	21	is	be	AUX
iajs-153	82	22	agb	agb	PROPN
iajs-153	82	23	-	-	PUNCT
iajs-153	82	24	open	open	ADJ
iajs-153	82	25	set	set	NOUN
iajs-153	82	26	.	.	PUNCT
iajs-153	83	1	to	to	PART
iajs-153	83	2	show	show	VERB
iajs-153	83	3	that	that	SCONJ
iajs-153	83	4	a	a	DET
iajs-153	83	5	∩	∩	NOUN
iajs-153	83	6	fis	fis	PROPN
iajs-153	83	7	gb*-closed	gb*-close	VERB
iajs-153	83	8	set	set	NOUN
iajs-153	83	9	,	,	PUNCT
iajs-153	83	10	it	it	PRON
iajs-153	83	11	is	be	AUX
iajs-153	83	12	enough	enough	ADJ
iajs-153	83	13	to	to	PART
iajs-153	83	14	show	show	VERB
iajs-153	83	15	that	that	DET
iajs-153	83	16	int	int	NOUN
iajs-153	83	17	cl	cl	NOUN
iajs-153	83	18	a	a	DET
iajs-153	83	19	∩	∩	NOUN
iajs-153	83	20	f	f	PROPN
iajs-153	83	21	⊆	⊆	NUM
iajs-153	83	22	u	u	NOUN
iajs-153	83	23	whenever	whenever	SCONJ
iajs-153	83	24	a	a	DET
iajs-153	83	25	∩	∩	NOUN
iajs-153	83	26	f	f	PROPN
iajs-153	83	27	⊆	⊆	NUM
iajs-153	83	28	u	u	NOUN
iajs-153	83	29	,	,	PUNCT
iajs-153	83	30	where	where	SCONJ
iajs-153	83	31	u	u	NOUN
iajs-153	83	32	is	be	AUX
iajs-153	83	33	gb	gb	ADV
iajs-153	83	34	-	-	PUNCT
iajs-153	83	35	open	open	ADJ
iajs-153	83	36	set	set	NOUN
iajs-153	83	37	.	.	PUNCT
iajs-153	84	1	let	let	VERB
iajs-153	84	2	g	g	PROPN
iajs-153	84	3	=	=	NOUN
iajs-153	84	4	x	x	PROPN
iajs-153	84	5	–	–	PUNCT
iajs-153	84	6	f	f	X
iajs-153	84	7	then	then	ADV
iajs-153	84	8	a	a	DET
iajs-153	84	9	⊆	⊆	NUM
iajs-153	84	10	u	u	NOUN
iajs-153	84	11	∪	∪	ADJ
iajs-153	84	12	g	g	NOUN
iajs-153	84	13	.since	.since	NOUN
iajs-153	85	1	g	g	PROPN
iajs-153	85	2	is	be	AUX
iajs-153	85	3	open	open	ADJ
iajs-153	85	4	set	set	VERB
iajs-153	85	5	,	,	PUNCT
iajs-153	85	6	u	u	NOUN
iajs-153	85	7	∪	∪	ADJ
iajs-153	85	8	g	g	PROPN
iajs-153	85	9	is	be	AUX
iajs-153	85	10	gb	gb	ADV
iajs-153	85	11	-	-	PUNCT
iajs-153	85	12	open	open	ADJ
iajs-153	85	13	set	set	NOUN
iajs-153	85	14	and	and	CCONJ
iajs-153	85	15	a	a	PRON
iajs-153	85	16	is	be	AUX
iajs-153	85	17	gb	gb	ADP
iajs-153	85	18	*	*	PUNCT
iajs-153	85	19	closed	closed	ADJ
iajs-153	85	20	set	set	VERB
iajs-153	85	21	,	,	PUNCT
iajs-153	85	22	int	int	NOUN
iajs-153	85	23	cl	cl	NOUN
iajs-153	85	24	a	a	DET
iajs-153	85	25	⊆	⊆	NUM
iajs-153	85	26	u	u	NOUN
iajs-153	85	27	∪	∪	ADJ
iajs-153	85	28	g	g	NOUN
iajs-153	85	29	.	.	PUNCT
iajs-153	86	1	now	now	ADV
iajs-153	86	2	int	int	VERB
iajs-153	86	3	cl	cl	NOUN
iajs-153	86	4	a	a	DET
iajs-153	86	5	∩	∩	NOUN
iajs-153	86	6	f	f	PROPN
iajs-153	86	7	⊆	⊆	NUM
iajs-153	86	8	int	int	NOUN
iajs-153	86	9	cl	cl	NOUN
iajs-153	86	10	a	a	DET
iajs-153	86	11	∩	∩	ADJ
iajs-153	86	12	int	int	NOUN
iajs-153	86	13	cl	cl	NOUN
iajs-153	86	14	f	f	PROPN
iajs-153	87	1	⊆	⊆	NUM
iajs-153	87	2	int	int	NOUN
iajs-153	87	3	cl	cl	NOUN
iajs-153	87	4	a	a	DET
iajs-153	87	5	∩	∩	NOUN
iajs-153	87	6	f	f	PROPN
iajs-153	87	7	⊆	⊆	NUM
iajs-153	87	8	u	u	NOUN
iajs-153	87	9	∪	∪	ADP
iajs-153	87	10	g	g	PROPN
iajs-153	87	11	∩	∩	NOUN
iajs-153	87	12	f	f	PROPN
iajs-153	87	13	⊆	⊆	NUM
iajs-153	87	14	u	u	NOUN
iajs-153	87	15	∩	∩	NOUN
iajs-153	87	16	f	f	PROPN
iajs-153	87	17	∪	∪	ADP
iajs-153	87	18	g	g	PROPN
iajs-153	87	19	∩	∩	NOUN
iajs-153	87	20	f	f	PROPN
iajs-153	87	21	⊆	⊆	NUM
iajs-153	87	22	u	u	NOUN
iajs-153	87	23	∩	∩	NOUN
iajs-153	87	24	f	f	PROPN
iajs-153	87	25	∪	∪	PROPN
iajs-153	87	26	⊆	⊆	NUM
iajs-153	87	27	u.	u.	VERB
iajs-153	87	28	this	this	PRON
iajs-153	87	29	implies	imply	VERB
iajs-153	87	30	that	that	SCONJ
iajs-153	87	31	a	a	DET
iajs-153	87	32	∩	∩	NOUN
iajs-153	87	33	f	f	X
iajs-153	87	34	is	be	AUX
iajs-153	87	35	gb	gb	ADV
iajs-153	87	36	*	*	PUNCT
iajs-153	87	37	-closed	-close	VERB
iajs-153	87	38	set	set	NOUN
iajs-153	87	39	.	.	PUNCT
iajs-153	88	1	theorem	theorem	VERB
iajs-153	88	2	3	3	NUM
iajs-153	88	3	-	-	SYM
iajs-153	88	4	10	10	NUM
iajs-153	88	5	:	:	PUNCT
iajs-153	88	6	if	if	SCONJ
iajs-153	88	7	a	a	PRON
iajs-153	88	8	and	and	CCONJ
iajs-153	88	9	b	b	NOUN
iajs-153	88	10	are	be	AUX
iajs-153	88	11	two	two	NUM
iajs-153	88	12	gb	gb	NOUN
iajs-153	88	13	*	*	PUNCT
iajs-153	88	14	-closed	-close	VERB
iajs-153	88	15	sets	set	NOUN
iajs-153	88	16	defined	define	VERB
iajs-153	88	17	for	for	ADP
iajs-153	88	18	a	a	DET
iajs-153	88	19	non	non	ADJ
iajs-153	88	20	–	–	PUNCT
iajs-153	88	21	empty	empty	ADJ
iajs-153	88	22	set	set	NOUN
iajs-153	88	23	x	x	NOUN
iajs-153	88	24	,	,	PUNCT
iajs-153	88	25	then	then	ADV
iajs-153	88	26	their	their	PRON
iajs-153	88	27	intersection	intersection	NOUN
iajs-153	88	28	a	a	DET
iajs-153	88	29	∩	∩	ADJ
iajs-153	88	30	b	b	NOUN
iajs-153	88	31	is	be	AUX
iajs-153	88	32	gb	gb	ADP
iajs-153	88	33	*	*	PUNCT
iajs-153	88	34	-closed	-closed	ADJ
iajs-153	88	35	set	set	NOUN
iajs-153	88	36	in	in	ADP
iajs-153	88	37	x.	x.	NOUN
iajs-153	88	38	proof	proof	NOUN
iajs-153	88	39	:	:	PUNCT
iajs-153	88	40	let	let	VERB
iajs-153	88	41	a	a	PRON
iajs-153	88	42	and	and	CCONJ
iajs-153	88	43	b	b	NOUN
iajs-153	88	44	are	be	AUX
iajs-153	88	45	two	two	NUM
iajs-153	88	46	gb	gb	NOUN
iajs-153	88	47	*	*	PUNCT
iajs-153	88	48	-closed	-close	VERB
iajs-153	88	49	sets	set	NOUN
iajs-153	88	50	in	in	ADP
iajs-153	88	51	x.	x.	NOUN
iajs-153	88	52	let	let	VERB
iajs-153	88	53	a	a	DET
iajs-153	88	54	∩	∩	ADJ
iajs-153	88	55	b	b	PROPN
iajs-153	88	56	⊆	⊆	NUM
iajs-153	88	57	u	u	NOUN
iajs-153	88	58	,	,	PUNCT
iajs-153	88	59	u	u	NOUN
iajs-153	88	60	is	be	AUX
iajs-153	88	61	gp	gp	NOUN
iajs-153	88	62	-	-	ADJ
iajs-153	88	63	open	open	ADJ
iajs-153	88	64	set	set	NOUN
iajs-153	88	65	in	in	ADP
iajs-153	88	66	x.	x.	NOUN
iajs-153	88	67	since	since	SCONJ
iajs-153	88	68	a	a	PRON
iajs-153	88	69	is	be	AUX
iajs-153	88	70	gb	gb	ADP
iajs-153	88	71	*	*	PUNCT
iajs-153	88	72	-closed	-closed	ADJ
iajs-153	88	73	,	,	PUNCT
iajs-153	88	74	int	int	NOUN
iajs-153	88	75	cl	cl	NOUN
iajs-153	88	76	a	a	DET
iajs-153	88	77	⊆	⊆	NUM
iajs-153	88	78	u	u	NOUN
iajs-153	88	79	,	,	PUNCT
iajs-153	88	80	whenever	whenever	SCONJ
iajs-153	88	81	a⊆	a⊆	VERB
iajs-153	88	82	u	u	PROPN
iajs-153	88	83	,	,	PUNCT
iajs-153	88	84	u	u	NOUN
iajs-153	88	85	is	be	AUX
iajs-153	88	86	g	g	NOUN
iajs-153	88	87	-	-	PUNCT
iajs-153	88	88	open	open	ADJ
iajs-153	88	89	set	set	NOUN
iajs-153	88	90	in	in	ADP
iajs-153	88	91	x	x	PROPN
iajs-153	88	92	.since	.since	PROPN
iajs-153	88	93	b	b	NOUN
iajs-153	88	94	is	be	AUX
iajs-153	88	95	gb	gb	ADV
iajs-153	88	96	*	*	PUNCT
iajs-153	88	97	-closed	-closed	ADJ
iajs-153	88	98	,	,	PUNCT
iajs-153	88	99	int	int	NOUN
iajs-153	88	100	cl	cl	NOUN
iajs-153	88	101	b	b	NOUN
iajs-153	88	102	⊆	⊆	NUM
iajs-153	88	103	u	u	NOUN
iajs-153	88	104	,	,	PUNCT
iajs-153	88	105	whenever	whenever	SCONJ
iajs-153	88	106	b⊆	b⊆	PROPN
iajs-153	88	107	u	u	PROPN
iajs-153	88	108	,	,	PUNCT
iajs-153	88	109	u	u	NOUN
iajs-153	88	110	is	be	AUX
iajs-153	88	111	g	g	NOUN
iajs-153	88	112	-	-	PUNCT
iajs-153	88	113	open	open	ADJ
iajs-153	88	114	set	set	NOUN
iajs-153	88	115	in	in	ADP
iajs-153	88	116	x	x	X
iajs-153	88	117	.	.	PUNCT
iajs-153	89	1	hence	hence	ADV
iajs-153	89	2	a	a	DET
iajs-153	89	3	∩	∩	ADJ
iajs-153	89	4	b	b	NOUN
iajs-153	89	5	is	be	AUX
iajs-153	89	6	gb	gb	ADV
iajs-153	89	7	*	*	PUNCT
iajs-153	89	8	closed	closed	ADJ
iajs-153	89	9	set	set	VERB
iajs-153	89	10	.	.	PUNCT
iajs-153	90	1	remark	remark	VERB
iajs-153	90	2	3	3	NUM
iajs-153	90	3	-	-	SYM
iajs-153	90	4	11	11	NUM
iajs-153	90	5	:	:	PUNCT
iajs-153	90	6	the	the	DET
iajs-153	90	7	union	union	NOUN
iajs-153	90	8	of	of	ADP
iajs-153	90	9	two	two	NUM
iajs-153	90	10	gb	gb	NOUN
iajs-153	90	11	*	*	PUNCT
iajs-153	90	12	-closed	-close	VERB
iajs-153	90	13	sets	set	NOUN
iajs-153	90	14	need	need	VERB
iajs-153	90	15	not	not	PART
iajs-153	90	16	to	to	PART
iajs-153	90	17	be	be	AUX
iajs-153	90	18	gb	gb	ADP
iajs-153	90	19	*	*	PUNCT
iajs-153	90	20	-closed	-close	VERB
iajs-153	90	21	set	set	NOUN
iajs-153	90	22	.	.	PUNCT
iajs-153	91	1	example3	example3	PROPN
iajs-153	91	2	-	-	PUNCT
iajs-153	91	3	12	12	NUM
iajs-153	91	4	:	:	PUNCT
iajs-153	91	5	let	let	VERB
iajs-153	91	6	x	x	PUNCT
iajs-153	91	7	=	=	NOUN
iajs-153	91	8	{	{	PUNCT
iajs-153	91	9	a	a	DET
iajs-153	91	10	,	,	PUNCT
iajs-153	91	11	b	b	NOUN
iajs-153	91	12	,	,	PUNCT
iajs-153	91	13	c	c	NOUN
iajs-153	91	14	}	}	PUNCT
iajs-153	91	15	with	with	ADP
iajs-153	91	16	t={x	t={x	ADJ
iajs-153	91	17	,	,	PUNCT
iajs-153	91	18			ADJ
iajs-153	91	19	,	,	PUNCT
iajs-153	91	20	{	{	PUNCT
iajs-153	91	21	a},{c},{a	a},{c},{a	ADV
iajs-153	91	22	,	,	PUNCT
iajs-153	91	23	c	c	NOUN
iajs-153	91	24	}	}	PUNCT
iajs-153	91	25	}	}	PUNCT
iajs-153	91	26	.if	.if	PUNCT
iajs-153	92	1	a=	a=	NOUN
iajs-153	92	2	{	{	PUNCT
iajs-153	92	3	a	a	X
iajs-153	92	4	}	}	PUNCT
iajs-153	92	5	,	,	PUNCT
iajs-153	92	6	b=	b=	NOUN
iajs-153	92	7	{	{	PUNCT
iajs-153	92	8	c	c	X
iajs-153	92	9	}	}	PUNCT
iajs-153	92	10	are	be	AUX
iajs-153	92	11	gb	gb	ADP
iajs-153	92	12	*	*	PUNCT
iajs-153	92	13	-closed	-closed	ADJ
iajs-153	92	14	set	set	NOUN
iajs-153	92	15	in	in	ADP
iajs-153	92	16	x	x	X
iajs-153	92	17	.	.	PUNCT
iajs-153	93	1	then	then	ADV
iajs-153	93	2	a	a	DET
iajs-153	93	3	∪	∪	X
iajs-153	93	4	b	b	NOUN
iajs-153	93	5	is	be	AUX
iajs-153	93	6	not	not	PART
iajs-153	93	7	a	a	DET
iajs-153	93	8	gb	gb	NOUN
iajs-153	93	9	*	*	PUNCT
iajs-153	93	10	-closed	-closed	ADJ
iajs-153	93	11	set	set	NOUN
iajs-153	93	12	.	.	PUNCT
iajs-153	94	1	theorem	theorem	VERB
iajs-153	94	2	3	3	NUM
iajs-153	94	3	-	-	SYM
iajs-153	94	4	13	13	NUM
iajs-153	94	5	:	:	PUNCT
iajs-153	94	6	every	every	DET
iajs-153	94	7	gb	gb	NOUN
iajs-153	94	8	closed	closed	ADJ
iajs-153	94	9	set	set	NOUN
iajs-153	94	10	is	be	AUX
iajs-153	94	11	gb	gb	ADP
iajs-153	94	12	*	*	PUNCT
iajs-153	94	13	-closed	-close	VERB
iajs-153	94	14	set	set	NOUN
iajs-153	94	15	.	.	PUNCT
iajs-153	95	1	proof	proof	NOUN
iajs-153	95	2	:	:	PUNCT
iajs-153	95	3	assume	assume	VERB
iajs-153	95	4	that	that	SCONJ
iajs-153	95	5	a	a	DET
iajs-153	95	6	be	be	AUX
iajs-153	95	7	a	a	DET
iajs-153	95	8	g	g	PROPN
iajs-153	95	9	b	b	NOUN
iajs-153	95	10	closed	closed	ADJ
iajs-153	95	11	set	set	VERB
iajs-153	95	12	in	in	ADP
iajs-153	95	13	x.	x.	NOUN
iajs-153	95	14	and	and	CCONJ
iajs-153	95	15	let	let	VERB
iajs-153	95	16	u	u	PRON
iajs-153	95	17	be	be	AUX
iajs-153	95	18	an	an	DET
iajs-153	95	19	open	open	ADJ
iajs-153	95	20	set	set	NOUN
iajs-153	95	21	such	such	ADJ
iajs-153	95	22	that	that	SCONJ
iajs-153	95	23	a	a	DET
iajs-153	95	24	⊆	⊆	NUM
iajs-153	95	25	u.	u.	NOUN
iajs-153	95	26	since	since	SCONJ
iajs-153	95	27	every	every	DET
iajs-153	95	28	open	open	ADJ
iajs-153	95	29	set	set	NOUN
iajs-153	95	30	is	be	AUX
iajs-153	95	31	gb	gb	ADV
iajs-153	95	32	-	-	PUNCT
iajs-153	95	33	open	open	ADJ
iajs-153	95	34	set	set	NOUN
iajs-153	95	35	.	.	PUNCT
iajs-153	96	1	then	then	ADV
iajs-153	96	2	int	int	VERB
iajs-153	96	3	cl	cl	NOUN
iajs-153	96	4	a	a	DET
iajs-153	96	5	⊆	⊆	NUM
iajs-153	96	6	bcl	bcl	NOUN
iajs-153	96	7	a	a	DET
iajs-153	96	8	⊆	⊆	NUM
iajs-153	96	9	u.	u.	NOUN
iajs-153	96	10	hence	hence	ADV
iajs-153	96	11	a	a	PRON
iajs-153	96	12	is	be	AUX
iajs-153	96	13	gb*-closed	gb*-close	VERB
iajs-153	96	14	set	set	NOUN
iajs-153	96	15	.	.	PUNCT
iajs-153	97	1	remark	remark	VERB
iajs-153	97	2	3	3	NUM
iajs-153	97	3	-	-	SYM
iajs-153	97	4	14	14	NUM
iajs-153	97	5	:	:	PUNCT
iajs-153	97	6	the	the	DET
iajs-153	97	7	converse	converse	NOUN
iajs-153	97	8	of	of	ADP
iajs-153	97	9	the	the	DET
iajs-153	97	10	theorem	theorem	NOUN
iajs-153	97	11	[	[	X
iajs-153	97	12	3	3	NUM
iajs-153	97	13	-	-	SYM
iajs-153	97	14	13	13	NUM
iajs-153	97	15	]	]	PUNCT
iajs-153	97	16	need	need	AUX
iajs-153	97	17	not	not	PART
iajs-153	97	18	be	be	AUX
iajs-153	97	19	true	true	ADJ
iajs-153	97	20	as	as	SCONJ
iajs-153	97	21	seen	see	VERB
iajs-153	97	22	by	by	ADP
iajs-153	97	23	the	the	DET
iajs-153	97	24	following	follow	VERB
iajs-153	97	25	example	example	NOUN
iajs-153	97	26	.	.	PUNCT
iajs-153	98	1	example3	example3	PROPN
iajs-153	98	2	-	-	PUNCT
iajs-153	98	3	15	15	NUM
iajs-153	98	4	:	:	PUNCT
iajs-153	98	5	let	let	VERB
iajs-153	98	6	x=	x=	ADJ
iajs-153	98	7	{	{	PUNCT
iajs-153	98	8	a	a	DET
iajs-153	98	9	,	,	PUNCT
iajs-153	98	10	b	b	NOUN
iajs-153	98	11	,	,	PUNCT
iajs-153	98	12	c	c	NOUN
iajs-153	98	13	}	}	PUNCT
iajs-153	98	14	with	with	ADP
iajs-153	98	15	t={x	t={x	ADJ
iajs-153	98	16	,	,	PUNCT
iajs-153	98	17			ADJ
iajs-153	98	18	,	,	PUNCT
iajs-153	98	19	{	{	PUNCT
iajs-153	98	20	a	a	X
iajs-153	98	21	}	}	PUNCT
iajs-153	98	22	}	}	PUNCT
iajs-153	98	23	.in	.in	PUNCT
iajs-153	98	24	this	this	DET
iajs-153	98	25	topological	topological	ADJ
iajs-153	98	26	space	space	NOUN
iajs-153	98	27	,	,	PUNCT
iajs-153	98	28	the	the	DET
iajs-153	98	29	subset	subset	NOUN
iajs-153	98	30	a=	a=	PROPN
iajs-153	98	31	{	{	PUNCT
iajs-153	98	32	a	a	PRON
iajs-153	98	33	,	,	PUNCT
iajs-153	98	34	b	b	NOUN
iajs-153	98	35	}	}	PUNCT
iajs-153	98	36	is	be	AUX
iajs-153	98	37	gb	gb	ADP
iajs-153	98	38	*	*	PUNCT
iajs-153	98	39	-closed	-close	VERB
iajs-153	98	40	set	set	NOUN
iajs-153	98	41	,	,	PUNCT
iajs-153	98	42	but	but	CCONJ
iajs-153	98	43	not	not	PART
iajs-153	98	44	gbclosed	gbclose	VERB
iajs-153	98	45	set	set	NOUN
iajs-153	98	46	.	.	PUNCT
iajs-153	99	1	theorem	theorem	VERB
iajs-153	99	2	3	3	NUM
iajs-153	99	3	-	-	PUNCT
iajs-153	99	4	16::every	16::every	NOUN
iajs-153	99	5	gb*-closed	gb*-close	VERB
iajs-153	99	6	set	set	NOUN
iajs-153	99	7	is	be	AUX
iajs-153	99	8	b	b	NOUN
iajs-153	99	9	-	-	PUNCT
iajs-153	99	10	closed	closed	ADJ
iajs-153	99	11	set	set	NOUN
iajs-153	99	12	.	.	PUNCT
iajs-153	100	1	proof	proof	NOUN
iajs-153	100	2	:	:	PUNCT
iajs-153	100	3	assume	assume	VERB
iajs-153	100	4	that	that	SCONJ
iajs-153	100	5	a	a	PRON
iajs-153	100	6	is	be	AUX
iajs-153	100	7	a	a	DET
iajs-153	100	8	gb	gb	ADV
iajs-153	100	9	*	*	PUNCT
iajs-153	100	10	-closed	-closed	ADJ
iajs-153	100	11	set	set	NOUN
iajs-153	100	12	in	in	ADP
iajs-153	100	13	x	x	X
iajs-153	100	14	,	,	PUNCT
iajs-153	100	15	and	and	CCONJ
iajs-153	100	16	let	let	VERB
iajs-153	100	17	u	u	PRON
iajs-153	100	18	be	be	AUX
iajs-153	100	19	an	an	DET
iajs-153	100	20	open	open	ADJ
iajs-153	100	21	set	set	NOUN
iajs-153	100	22	such	such	ADJ
iajs-153	100	23	that	that	SCONJ
iajs-153	100	24	a	a	DET
iajs-153	100	25	⊆	⊆	NUM
iajs-153	100	26	u	u	NOUN
iajs-153	100	27	.since	.since	NOUN
iajs-153	100	28	every	every	DET
iajs-153	100	29	open	open	ADJ
iajs-153	100	30	set	set	NOUN
iajs-153	100	31	is	be	AUX
iajs-153	100	32	b	b	NOUN
iajs-153	100	33	-	-	PUNCT
iajs-153	100	34	open	open	ADJ
iajs-153	100	35	set	set	NOUN
iajs-153	100	36	and	and	CCONJ
iajs-153	100	37	a	a	PRON
iajs-153	100	38	is	be	AUX
iajs-153	100	39	gb*-closed	gb*-close	VERB
iajs-153	100	40	set	set	NOUN
iajs-153	100	41	,	,	PUNCT
iajs-153	100	42	then	then	ADV
iajs-153	100	43	int	int	VERB
iajs-153	100	44	cl	cl	NOUN
iajs-153	100	45	a	a	DET
iajs-153	100	46	⊆	⊆	NUM
iajs-153	100	47	intcl	intcl	NOUN
iajs-153	100	48	a	a	DET
iajs-153	100	49	⋃cl	⋃cl	NOUN
iajs-153	100	50	int	int	NOUN
iajs-153	100	51	a	a	DET
iajs-153	100	52	⊆	⊆	NUM
iajs-153	100	53	u.	u.	NOUN
iajs-153	100	54	therefore	therefore	ADV
iajs-153	100	55	a	a	PRON
iajs-153	100	56	is	be	AUX
iajs-153	100	57	b	b	NOUN
iajs-153	100	58	-	-	PUNCT
iajs-153	100	59	closed	closed	ADJ
iajs-153	100	60	set	set	NOUN
iajs-153	100	61	in	in	ADP
iajs-153	100	62	x	x	PROPN
iajs-153	100	63	.	.	PUNCT
iajs-153	101	1	209	209	NUM
iajs-153	101	2	|	|	ADV
iajs-153	101	3	mathematics	mathematic	NOUN
iajs-153	101	4	2015	2015	NUM
iajs-153	101	5	)	)	PUNCT
iajs-153	101	6	عام	عام	ADP
iajs-153	101	7	3العدد	3العدد	NUM
iajs-153	101	8	(	(	PUNCT
iajs-153	101	9	28الھيثم	28الھيثم	NUM
iajs-153	101	10	للعلوم	للعلوم	PROPN
iajs-153	101	11	الصرفة	الصرفة	NOUN
iajs-153	102	1	و	و	PRON
iajs-153	102	2	التطبيقية	التطبيقية	ADV
iajs-153	102	3	المجلد	المجلد	ADV
iajs-153	102	4	مجلة	مجلة	VERB
iajs-153	102	5	إبن	إبن	VERB
iajs-153	102	6	ibn	ibn	PROPN
iajs-153	102	7	al	al	PROPN
iajs-153	102	8	-	-	PUNCT
iajs-153	102	9	haitham	haitham	PROPN
iajs-153	102	10	jour	jour	X
iajs-153	102	11	.	.	PROPN
iajs-153	102	12	for	for	ADP
iajs-153	102	13	pure	pure	ADJ
iajs-153	102	14	&	&	CCONJ
iajs-153	102	15	appl	appl	PROPN
iajs-153	102	16	.	.	PUNCT
iajs-153	103	1	sci	sci	PROPN
iajs-153	103	2	.	.	PUNCT
iajs-153	103	3	vol	vol	NOUN
iajs-153	103	4	.	.	PROPN
iajs-153	104	1	28	28	NUM
iajs-153	104	2	(	(	PUNCT
iajs-153	104	3	3	3	NUM
iajs-153	104	4	)	)	PUNCT
iajs-153	104	5	2015	2015	NUM
iajs-153	104	6	remark	remark	NOUN
iajs-153	104	7	3	3	NUM
iajs-153	104	8	-	-	SYM
iajs-153	104	9	17	17	NUM
iajs-153	104	10	:	:	PUNCT
iajs-153	104	11	the	the	DET
iajs-153	104	12	converse	converse	NOUN
iajs-153	104	13	of	of	ADP
iajs-153	104	14	the	the	DET
iajs-153	104	15	theorem	theorem	NOUN
iajs-153	104	16	[	[	X
iajs-153	104	17	3	3	NUM
iajs-153	104	18	-	-	SYM
iajs-153	104	19	16	16	NUM
iajs-153	104	20	]	]	PUNCT
iajs-153	104	21	need	need	AUX
iajs-153	104	22	not	not	PART
iajs-153	104	23	be	be	AUX
iajs-153	104	24	true	true	ADJ
iajs-153	104	25	as	as	ADP
iajs-153	104	26	the	the	DET
iajs-153	104	27	following	follow	VERB
iajs-153	104	28	example	example	NOUN
iajs-153	104	29	shows	show	NOUN
iajs-153	104	30	.	.	PUNCT
iajs-153	105	1	example3	example3	PROPN
iajs-153	105	2	-	-	PUNCT
iajs-153	105	3	18	18	NUM
iajs-153	105	4	:	:	PUNCT
iajs-153	105	5	let	let	VERB
iajs-153	105	6	x=	x=	ADJ
iajs-153	105	7	{	{	PUNCT
iajs-153	105	8	a	a	DET
iajs-153	105	9	,	,	PUNCT
iajs-153	105	10	b	b	NOUN
iajs-153	105	11	,	,	PUNCT
iajs-153	105	12	c	c	NOUN
iajs-153	105	13	}	}	PUNCT
iajs-153	105	14	with	with	ADP
iajs-153	105	15	t={x	t={x	ADJ
iajs-153	105	16	,	,	PUNCT
iajs-153	105	17			ADJ
iajs-153	105	18	,	,	PUNCT
iajs-153	105	19	{	{	PUNCT
iajs-153	105	20	a	a	NOUN
iajs-153	105	21	}	}	PUNCT
iajs-153	105	22	,	,	PUNCT
iajs-153	105	23	{	{	PUNCT
iajs-153	105	24	b	b	NOUN
iajs-153	105	25	}	}	PUNCT
iajs-153	105	26	,	,	PUNCT
iajs-153	105	27	{	{	PUNCT
iajs-153	105	28	a	a	DET
iajs-153	105	29	,	,	PUNCT
iajs-153	105	30	b	b	NOUN
iajs-153	105	31	}	}	PUNCT
iajs-153	105	32	}	}	PUNCT
iajs-153	105	33	.	.	PUNCT
iajs-153	106	1	in	in	ADP
iajs-153	106	2	this	this	DET
iajs-153	106	3	topological	topological	ADJ
iajs-153	106	4	space	space	NOUN
iajs-153	106	5	,	,	PUNCT
iajs-153	106	6	the	the	DET
iajs-153	106	7	subset	subset	NOUN
iajs-153	106	8	a=	a=	PROPN
iajs-153	106	9	{	{	PUNCT
iajs-153	106	10	a	a	PRON
iajs-153	106	11	,	,	PUNCT
iajs-153	106	12	c	c	NOUN
iajs-153	106	13	}	}	PUNCT
iajs-153	106	14	is	be	AUX
iajs-153	106	15	b	b	NUM
iajs-153	106	16	-closed	-close	VERB
iajs-153	106	17	set	set	NOUN
iajs-153	106	18	but	but	CCONJ
iajs-153	106	19	not	not	PART
iajs-153	106	20	gb*closed	gb*close	VERB
iajs-153	106	21	set	set	NOUN
iajs-153	106	22	.	.	PUNCT
iajs-153	107	1	theorem	theorem	VERB
iajs-153	107	2	319	319	NUM
iajs-153	107	3	:	:	PUNCT
iajs-153	107	4	every	every	DET
iajs-153	107	5	w	w	NOUN
iajs-153	107	6	-	-	PUNCT
iajs-153	107	7	closed	closed	ADJ
iajs-153	107	8	set	set	NOUN
iajs-153	107	9	is	be	AUX
iajs-153	107	10	gb	gb	ADV
iajs-153	107	11	*	*	PUNCT
iajs-153	107	12	-closed	-closed	ADJ
iajs-153	107	13	set	set	NOUN
iajs-153	107	14	.	.	PUNCT
iajs-153	108	1	proof	proof	NOUN
iajs-153	108	2	:	:	PUNCT
iajs-153	108	3	assume	assume	VERB
iajs-153	108	4	that	that	SCONJ
iajs-153	108	5	a	a	PRON
iajs-153	108	6	is	be	AUX
iajs-153	108	7	w	w	NOUN
iajs-153	108	8	-	-	PUNCT
iajs-153	108	9	closed	closed	ADJ
iajs-153	108	10	set	set	NOUN
iajs-153	108	11	in	in	ADP
iajs-153	108	12	x	x	X
iajs-153	108	13	,	,	PUNCT
iajs-153	108	14	and	and	CCONJ
iajs-153	108	15	u	u	NOUN
iajs-153	108	16	is	be	AUX
iajs-153	108	17	semi	semi	ADJ
iajs-153	108	18	-	-	ADJ
iajs-153	108	19	open	open	ADJ
iajs-153	108	20	set	set	NOUN
iajs-153	108	21	such	such	ADJ
iajs-153	108	22	that	that	SCONJ
iajs-153	108	23	a	a	DET
iajs-153	108	24	⊆	⊆	NUM
iajs-153	108	25	u	u	NOUN
iajs-153	108	26	,	,	PUNCT
iajs-153	108	27	every	every	DET
iajs-153	108	28	semiopen	semiopen	ADJ
iajs-153	108	29	set	set	NOUN
iajs-153	108	30	is	be	AUX
iajs-153	108	31	gb	gb	ADV
iajs-153	108	32	-	-	PUNCT
iajs-153	108	33	open	open	ADJ
iajs-153	108	34	set	set	NOUN
iajs-153	108	35	then	then	ADV
iajs-153	108	36	cl	cl	VERB
iajs-153	108	37	a	a	DET
iajs-153	108	38	⊆int(cl(a	⊆int(cl(a	NOUN
iajs-153	108	39	)	)	PUNCT
iajs-153	108	40	)	)	PUNCT
iajs-153	108	41	therefore	therefore	ADV
iajs-153	108	42	a	a	PRON
iajs-153	108	43	is	be	AUX
iajs-153	108	44	gb	gb	ADP
iajs-153	108	45	*	*	PUNCT
iajs-153	108	46	-closed	-close	VERB
iajs-153	108	47	set	set	NOUN
iajs-153	108	48	.	.	PUNCT
iajs-153	109	1	remark	remark	PROPN
iajs-153	109	2	320	320	NUM
iajs-153	109	3	:	:	PUNCT
iajs-153	109	4	the	the	DET
iajs-153	109	5	converse	converse	NOUN
iajs-153	109	6	of	of	ADP
iajs-153	109	7	the	the	DET
iajs-153	109	8	theorem	theorem	NOUN
iajs-153	109	9	[	[	X
iajs-153	109	10	3	3	NUM
iajs-153	109	11	-	-	SYM
iajs-153	109	12	19	19	NUM
iajs-153	109	13	]	]	PUNCT
iajs-153	109	14	need	need	AUX
iajs-153	109	15	not	not	PART
iajs-153	109	16	be	be	AUX
iajs-153	109	17	true	true	ADJ
iajs-153	109	18	as	as	SCONJ
iajs-153	109	19	seen	see	VERB
iajs-153	109	20	by	by	ADP
iajs-153	109	21	the	the	DET
iajs-153	109	22	following	follow	VERB
iajs-153	109	23	example	example	NOUN
iajs-153	109	24	example	example	NOUN
iajs-153	109	25	3	3	NUM
iajs-153	109	26	-	-	SYM
iajs-153	109	27	21	21	NUM
iajs-153	109	28	:	:	PUNCT
iajs-153	109	29	let	let	VERB
iajs-153	109	30	x=	x=	ADJ
iajs-153	109	31	{	{	PUNCT
iajs-153	109	32	a	a	DET
iajs-153	109	33	,	,	PUNCT
iajs-153	109	34	b	b	NOUN
iajs-153	109	35	,	,	PUNCT
iajs-153	109	36	c	c	NOUN
iajs-153	109	37	}	}	PUNCT
iajs-153	109	38	with	with	ADP
iajs-153	109	39	t={x	t={x	ADJ
iajs-153	109	40	,	,	PUNCT
iajs-153	109	41			ADJ
iajs-153	109	42	,	,	PUNCT
iajs-153	109	43	{	{	PUNCT
iajs-153	109	44	a	a	NOUN
iajs-153	109	45	}	}	PUNCT
iajs-153	109	46	,	,	PUNCT
iajs-153	109	47	{	{	PUNCT
iajs-153	109	48	c	c	NOUN
iajs-153	109	49	}	}	PUNCT
iajs-153	109	50	,	,	PUNCT
iajs-153	109	51	{	{	PUNCT
iajs-153	109	52	a	a	DET
iajs-153	109	53	,	,	PUNCT
iajs-153	109	54	c	c	NOUN
iajs-153	109	55	}	}	PUNCT
iajs-153	109	56	}	}	PUNCT
iajs-153	109	57	.	.	PUNCT
iajs-153	110	1	in	in	ADP
iajs-153	110	2	this	this	DET
iajs-153	110	3	topological	topological	ADJ
iajs-153	110	4	spaces	space	NOUN
iajs-153	110	5	,	,	PUNCT
iajs-153	110	6	the	the	DET
iajs-153	110	7	subset	subset	NOUN
iajs-153	110	8	a=	a=	PROPN
iajs-153	110	9	{	{	PUNCT
iajs-153	110	10	a	a	PRON
iajs-153	110	11	}	}	PUNCT
iajs-153	110	12	is	be	AUX
iajs-153	110	13	gb*closed	gb*close	VERB
iajs-153	110	14	set	set	NOUN
iajs-153	110	15	but	but	CCONJ
iajs-153	110	16	not	not	PART
iajs-153	110	17	w	w	NOUN
iajs-153	110	18	-	-	PUNCT
iajs-153	110	19	closed	closed	ADJ
iajs-153	110	20	set	set	NOUN
iajs-153	110	21	.	.	PUNCT
iajs-153	111	1	theorem	theorem	VERB
iajs-153	111	2	322	322	NUM
iajs-153	111	3	:	:	PUNCT
iajs-153	111	4	every	every	DET
iajs-153	111	5	b	b	X
iajs-153	111	6	*	*	PUNCT
iajs-153	111	7	-closed	-closed	ADJ
iajs-153	111	8	set	set	NOUN
iajs-153	111	9	is	be	AUX
iajs-153	111	10	g	g	PROPN
iajs-153	111	11	b	b	PROPN
iajs-153	111	12	*	*	PUNCT
iajs-153	111	13	-closed	-closed	ADJ
iajs-153	111	14	set	set	NOUN
iajs-153	111	15	.	.	PUNCT
iajs-153	112	1	proof	proof	NOUN
iajs-153	112	2	:	:	PUNCT
iajs-153	112	3	assume	assume	VERB
iajs-153	112	4	that	that	SCONJ
iajs-153	112	5	a	a	PRON
iajs-153	112	6	is	be	AUX
iajs-153	112	7	a	a	DET
iajs-153	112	8	b*-closed	b*-closed	ADJ
iajs-153	112	9	set	set	NOUN
iajs-153	112	10	in	in	ADP
iajs-153	112	11	x	x	X
iajs-153	112	12	,	,	PUNCT
iajs-153	112	13	and	and	CCONJ
iajs-153	112	14	u	u	NOUN
iajs-153	112	15	is	be	AUX
iajs-153	112	16	bopen	bopen	ADJ
iajs-153	112	17	set	set	VERB
iajs-153	112	18	such	such	ADJ
iajs-153	112	19	that	that	SCONJ
iajs-153	112	20	a	a	DET
iajs-153	112	21	⊆	⊆	NUM
iajs-153	112	22	u.	u.	NOUN
iajs-153	112	23	every	every	DET
iajs-153	112	24	b	b	X
iajs-153	112	25	-	-	PUNCT
iajs-153	112	26	open	open	ADJ
iajs-153	112	27	set	set	NOUN
iajs-153	112	28	is	be	AUX
iajs-153	112	29	g	g	PROPN
iajs-153	112	30	b	b	NOUN
iajs-153	112	31	-	-	PUNCT
iajs-153	112	32	open	open	ADJ
iajs-153	112	33	set	set	NOUN
iajs-153	112	34	.	.	PUNCT
iajs-153	113	1	then	then	ADV
iajs-153	113	2	int	int	VERB
iajs-153	113	3	cl	cl	NOUN
iajs-153	113	4	a	a	DET
iajs-153	113	5	⊆	⊆	NUM
iajs-153	113	6	,	,	PUNCT
iajs-153	113	7	therefore	therefore	ADV
iajs-153	113	8	a	a	PRON
iajs-153	113	9	is	be	AUX
iajs-153	113	10	g	g	PROPN
iajs-153	113	11	b	b	PROPN
iajs-153	113	12	*	*	PUNCT
iajs-153	113	13	-closed	-close	VERB
iajs-153	113	14	set	set	NOUN
iajs-153	113	15	.	.	PUNCT
iajs-153	114	1	remark	remark	PROPN
iajs-153	114	2	323	323	NUM
iajs-153	114	3	:	:	PUNCT
iajs-153	114	4	the	the	DET
iajs-153	114	5	converse	converse	NOUN
iajs-153	114	6	of	of	ADP
iajs-153	114	7	the	the	DET
iajs-153	114	8	theorem	theorem	ADJ
iajs-153	114	9	3‐22	3‐22	NUM
iajs-153	114	10	need	need	AUX
iajs-153	114	11	not	not	PART
iajs-153	114	12	be	be	AUX
iajs-153	114	13	true	true	ADJ
iajs-153	114	14	as	as	SCONJ
iajs-153	114	15	seen	see	VERB
iajs-153	114	16	by	by	ADP
iajs-153	114	17	the	the	DET
iajs-153	114	18	following	follow	VERB
iajs-153	114	19	example	example	NOUN
iajs-153	114	20	.	.	PUNCT
iajs-153	115	1	example3	example3	PROPN
iajs-153	115	2	-	-	PUNCT
iajs-153	115	3	24	24	NUM
iajs-153	115	4	:	:	PUNCT
iajs-153	115	5	let	let	VERB
iajs-153	115	6	x=	x=	ADJ
iajs-153	115	7	{	{	PUNCT
iajs-153	115	8	a	a	DET
iajs-153	115	9	,	,	PUNCT
iajs-153	115	10	b	b	NOUN
iajs-153	115	11	,	,	PUNCT
iajs-153	115	12	c	c	X
iajs-153	115	13	,	,	PUNCT
iajs-153	115	14	d	d	NOUN
iajs-153	115	15	}	}	PUNCT
iajs-153	115	16	with	with	ADP
iajs-153	115	17	t={x	t={x	ADJ
iajs-153	115	18	,	,	PUNCT
iajs-153	115	19	,{b},{c	,{b},{c	PRON
iajs-153	115	20	,	,	PUNCT
iajs-153	115	21	d	d	NOUN
iajs-153	115	22	}	}	PUNCT
iajs-153	115	23	,	,	PUNCT
iajs-153	115	24	{	{	PUNCT
iajs-153	115	25	b	b	X
iajs-153	115	26	,	,	PUNCT
iajs-153	115	27	c	c	NOUN
iajs-153	115	28	,	,	PUNCT
iajs-153	115	29	d	d	NOUN
iajs-153	115	30	}	}	PUNCT
iajs-153	115	31	}	}	PUNCT
iajs-153	115	32	.	.	PUNCT
iajs-153	116	1	in	in	ADP
iajs-153	116	2	this	this	DET
iajs-153	116	3	topological	topological	ADJ
iajs-153	116	4	spaces	space	NOUN
iajs-153	116	5	the	the	DET
iajs-153	116	6	subset	subset	NOUN
iajs-153	116	7	a=	a=	PROPN
iajs-153	116	8	{	{	PUNCT
iajs-153	116	9	c	c	AUX
iajs-153	116	10	}	}	PUNCT
iajs-153	116	11	is	be	AUX
iajs-153	116	12	gb*-closed	gb*-close	VERB
iajs-153	116	13	set	set	VERB
iajs-153	116	14	,	,	PUNCT
iajs-153	116	15	but	but	CCONJ
iajs-153	116	16	not	not	PART
iajs-153	116	17	b*-closed	b*-close	VERB
iajs-153	116	18	set	set	NOUN
iajs-153	116	19	.	.	PUNCT
iajs-153	117	1	theorem	theorem	VERB
iajs-153	117	2	3	3	NUM
iajs-153	117	3	-	-	SYM
iajs-153	117	4	25	25	NUM
iajs-153	117	5	:	:	PUNCT
iajs-153	117	6	every	every	DET
iajs-153	117	7	gb*-closed	gb*-close	VERB
iajs-153	117	8	set	set	NOUN
iajs-153	117	9	is	be	AUX
iajs-153	117	10	g*b	g*b	NOUN
iajs-153	117	11	-	-	PUNCT
iajs-153	117	12	closed	close	VERB
iajs-153	117	13	set	set	NOUN
iajs-153	117	14	.	.	PUNCT
iajs-153	118	1	proof	proof	NOUN
iajs-153	118	2	:	:	PUNCT
iajs-153	118	3	assume	assume	VERB
iajs-153	118	4	that	that	SCONJ
iajs-153	118	5	a	a	PRON
iajs-153	118	6	is	be	AUX
iajs-153	118	7	a	a	DET
iajs-153	118	8	g	g	NOUN
iajs-153	118	9	b*-closed	b*-close	VERB
iajs-153	118	10	set	set	NOUN
iajs-153	118	11	in	in	ADP
iajs-153	118	12	x	x	X
iajs-153	118	13	.then	.then	X
iajs-153	118	14	int(cl(a	int(cl(a	PROPN
iajs-153	118	15	)	)	PUNCT
iajs-153	118	16	⊆	⊆	NUM
iajs-153	118	17	u	u	NOUN
iajs-153	118	18	,	,	PUNCT
iajs-153	118	19	u	u	PROPN
iajs-153	118	20	is	be	AUX
iajs-153	118	21	gb	gb	ADV
iajs-153	118	22	-	-	PUNCT
iajs-153	118	23	open	open	ADJ
iajs-153	118	24	set	set	NOUN
iajs-153	118	25	such	such	ADJ
iajs-153	118	26	that	that	SCONJ
iajs-153	118	27	a	a	DET
iajs-153	118	28	⊆	⊆	NUM
iajs-153	118	29	u.	u.	NOUN
iajs-153	118	30	then	then	ADV
iajs-153	118	31	bcl	bcl	VERB
iajs-153	118	32	a	a	DET
iajs-153	118	33	⊆	⊆	NUM
iajs-153	118	34	.	.	PUNCT
iajs-153	119	1	since	since	SCONJ
iajs-153	119	2	every	every	DET
iajs-153	119	3	g	g	NOUN
iajs-153	119	4	-	-	PUNCT
iajs-153	119	5	open	open	ADJ
iajs-153	119	6	set	set	NOUN
iajs-153	119	7	is	be	AUX
iajs-153	119	8	gb	gb	ADV
iajs-153	119	9	-	-	PUNCT
iajs-153	119	10	open	open	ADJ
iajs-153	119	11	set	set	NOUN
iajs-153	119	12	.then	.then	PUNCT
iajs-153	119	13	bcl	bcl	NOUN
iajs-153	119	14	a	a	DET
iajs-153	119	15	⊆	⊆	NUM
iajs-153	119	16	,	,	PUNCT
iajs-153	119	17	uis	uis	PROPN
iajs-153	119	18	g	g	NOUN
iajs-153	119	19	-	-	PUNCT
iajs-153	119	20	open	open	NOUN
iajs-153	119	21	set	set	NOUN
iajs-153	119	22	.therefore	.therefore	PUNCT
iajs-153	119	23	a	a	DET
iajs-153	119	24	is	be	AUX
iajs-153	119	25	g*b	g*b	NOUN
iajs-153	119	26	-	-	PUNCT
iajs-153	119	27	closed	close	VERB
iajs-153	119	28	set	set	NOUN
iajs-153	119	29	.	.	PUNCT
iajs-153	120	1	remark	remark	VERB
iajs-153	120	2	3	3	NUM
iajs-153	120	3	-	-	SYM
iajs-153	120	4	26	26	NUM
iajs-153	120	5	:	:	PUNCT
iajs-153	120	6	the	the	DET
iajs-153	120	7	converse	converse	NOUN
iajs-153	120	8	of	of	ADP
iajs-153	120	9	the	the	DET
iajs-153	120	10	theorem	theorem	NOUN
iajs-153	120	11	[	[	X
iajs-153	120	12	3	3	NUM
iajs-153	120	13	-	-	SYM
iajs-153	120	14	25	25	NUM
iajs-153	120	15	]	]	PUNCT
iajs-153	120	16	need	need	AUX
iajs-153	120	17	not	not	PART
iajs-153	120	18	be	be	AUX
iajs-153	120	19	true	true	ADJ
iajs-153	120	20	as	as	SCONJ
iajs-153	120	21	seen	see	VERB
iajs-153	120	22	by	by	ADP
iajs-153	120	23	the	the	DET
iajs-153	120	24	following	follow	VERB
iajs-153	120	25	example	example	NOUN
iajs-153	120	26	.	.	PUNCT
iajs-153	121	1	example3	example3	PROPN
iajs-153	121	2	-	-	PUNCT
iajs-153	121	3	27	27	NUM
iajs-153	121	4	:	:	PUNCT
iajs-153	121	5	let	let	VERB
iajs-153	121	6	x=	x=	ADJ
iajs-153	121	7	{	{	PUNCT
iajs-153	121	8	a	a	DET
iajs-153	121	9	,	,	PUNCT
iajs-153	121	10	b	b	NOUN
iajs-153	121	11	,	,	PUNCT
iajs-153	121	12	c	c	NOUN
iajs-153	121	13	}	}	PUNCT
iajs-153	121	14	with	with	ADP
iajs-153	121	15	t={x	t={x	ADJ
iajs-153	121	16	,	,	PUNCT
iajs-153	121	17			PROPN
iajs-153	121	18	}	}	PUNCT
iajs-153	121	19	.in	.in	PUNCT
iajs-153	121	20	this	this	DET
iajs-153	121	21	topological	topological	ADJ
iajs-153	121	22	spaces	space	NOUN
iajs-153	121	23	,	,	PUNCT
iajs-153	121	24	the	the	DET
iajs-153	121	25	subset	subset	NOUN
iajs-153	121	26	a=	a=	PROPN
iajs-153	121	27	{	{	PUNCT
iajs-153	121	28	a	a	DET
iajs-153	121	29	,	,	PUNCT
iajs-153	121	30	b	b	NOUN
iajs-153	121	31	}	}	PUNCT
iajs-153	121	32	is	be	AUX
iajs-153	121	33	g*b	g*b	NOUN
iajs-153	121	34	-closed	-close	VERB
iajs-153	121	35	set	set	NOUN
iajs-153	121	36	but	but	CCONJ
iajs-153	121	37	not	not	PART
iajs-153	121	38	gb*closed	gb*close	VERB
iajs-153	121	39	set	set	NOUN
iajs-153	121	40	.	.	PUNCT
iajs-153	122	1	theorem	theorem	VERB
iajs-153	122	2	328	328	NUM
iajs-153	122	3	:	:	PUNCT
iajs-153	122	4	every	every	DET
iajs-153	122	5	gb*-closed	gb*-close	VERB
iajs-153	122	6	set	set	NOUN
iajs-153	122	7	is	be	AUX
iajs-153	122	8	sg	sg	ADP
iajs-153	122	9	-closed	-close	VERB
iajs-153	122	10	set	set	NOUN
iajs-153	122	11	.	.	PUNCT
iajs-153	123	1	proof	proof	NOUN
iajs-153	123	2	:	:	PUNCT
iajs-153	123	3	assume	assume	VERB
iajs-153	123	4	that	that	SCONJ
iajs-153	123	5	a	a	PRON
iajs-153	123	6	is	be	AUX
iajs-153	123	7	gb*-closed	gb*-close	VERB
iajs-153	123	8	set	set	VERB
iajs-153	123	9	in	in	ADP
iajs-153	123	10	x	x	X
iajs-153	123	11	,	,	PUNCT
iajs-153	123	12	and	and	CCONJ
iajs-153	123	13	u	u	NOUN
iajs-153	123	14	is	be	AUX
iajs-153	123	15	open	open	ADJ
iajs-153	123	16	set	set	VERB
iajs-153	123	17	such	such	ADJ
iajs-153	123	18	that	that	SCONJ
iajs-153	123	19	a	a	DET
iajs-153	123	20	⊆	⊆	NUM
iajs-153	123	21	u	u	NOUN
iajs-153	123	22	every	every	DET
iajs-153	123	23	open	open	ADJ
iajs-153	123	24	set	set	NOUN
iajs-153	123	25	is	be	AUX
iajs-153	123	26	semi	semi	ADJ
iajs-153	123	27	-	-	ADJ
iajs-153	123	28	open	open	ADJ
iajs-153	123	29	set	set	NOUN
iajs-153	123	30	,	,	PUNCT
iajs-153	123	31	a	a	PRON
iajs-153	123	32	is	be	AUX
iajs-153	123	33	gb*-closed	gb*-close	VERB
iajs-153	123	34	and	and	CCONJ
iajs-153	123	35	u	u	NOUN
iajs-153	123	36	is	be	AUX
iajs-153	123	37	gb	gb	ADV
iajs-153	123	38	-	-	PUNCT
iajs-153	123	39	closed	closed	ADJ
iajs-153	123	40	then	then	ADV
iajs-153	123	41	int	int	NOUN
iajs-153	123	42	cl	cl	NOUN
iajs-153	123	43	a	a	DET
iajs-153	123	44	⊆	⊆	NUM
iajs-153	123	45	a	a	DET
iajs-153	123	46	∪	∪	ADJ
iajs-153	123	47	scl	scl	PROPN
iajs-153	123	48	a	a	DET
iajs-153	123	49	⊆	⊆	NUM
iajs-153	123	50	u	u	NOUN
iajs-153	123	51	therefore	therefore	ADV
iajs-153	123	52	a	a	PRON
iajs-153	123	53	is	be	AUX
iajs-153	123	54	sg	sg	ADP
iajs-153	123	55	-closed	-close	VERB
iajs-153	123	56	set	set	NOUN
iajs-153	123	57	.	.	PUNCT
iajs-153	124	1	210	210	NUM
iajs-153	124	2	|	|	ADV
iajs-153	124	3	mathematics	mathematic	NOUN
iajs-153	124	4	2015	2015	NUM
iajs-153	124	5	)	)	PUNCT
iajs-153	124	6	عام	عام	ADP
iajs-153	124	7	3العدد	3العدد	NUM
iajs-153	124	8	(	(	PUNCT
iajs-153	124	9	28الھيثم	28الھيثم	NUM
iajs-153	124	10	للعلوم	للعلوم	PROPN
iajs-153	124	11	الصرفة	الصرفة	NOUN
iajs-153	125	1	و	و	PRON
iajs-153	125	2	التطبيقية	التطبيقية	ADV
iajs-153	125	3	المجلد	المجلد	ADV
iajs-153	125	4	مجلة	مجلة	VERB
iajs-153	125	5	إبن	إبن	VERB
iajs-153	125	6	ibn	ibn	PROPN
iajs-153	125	7	al	al	PROPN
iajs-153	125	8	-	-	PUNCT
iajs-153	125	9	haitham	haitham	PROPN
iajs-153	125	10	jour	jour	X
iajs-153	125	11	.	.	PROPN
iajs-153	125	12	for	for	ADP
iajs-153	125	13	pure	pure	ADJ
iajs-153	125	14	&	&	CCONJ
iajs-153	125	15	appl	appl	PROPN
iajs-153	125	16	.	.	PUNCT
iajs-153	126	1	sci	sci	PROPN
iajs-153	126	2	.	.	PUNCT
iajs-153	126	3	vol	vol	NOUN
iajs-153	126	4	.	.	PROPN
iajs-153	127	1	28	28	NUM
iajs-153	127	2	(	(	PUNCT
iajs-153	127	3	3	3	NUM
iajs-153	127	4	)	)	PUNCT
iajs-153	127	5	2015	2015	NUM
iajs-153	127	6	remark	remark	NOUN
iajs-153	127	7	329	329	NUM
iajs-153	127	8	:	:	PUNCT
iajs-153	127	9	the	the	DET
iajs-153	127	10	converse	converse	NOUN
iajs-153	127	11	of	of	ADP
iajs-153	127	12	the	the	DET
iajs-153	127	13	theorem	theorem	NOUN
iajs-153	127	14	[	[	X
iajs-153	127	15	3	3	NUM
iajs-153	127	16	-	-	SYM
iajs-153	127	17	28	28	NUM
iajs-153	127	18	]	]	PUNCT
iajs-153	127	19	need	need	AUX
iajs-153	127	20	not	not	PART
iajs-153	127	21	be	be	AUX
iajs-153	127	22	true	true	ADJ
iajs-153	127	23	as	as	SCONJ
iajs-153	127	24	seen	see	VERB
iajs-153	127	25	by	by	ADP
iajs-153	127	26	the	the	DET
iajs-153	127	27	following	follow	VERB
iajs-153	127	28	example	example	NOUN
iajs-153	127	29	.	.	PUNCT
iajs-153	128	1	example3	example3	PROPN
iajs-153	128	2	-	-	PUNCT
iajs-153	128	3	30	30	NUM
iajs-153	128	4	:	:	PUNCT
iajs-153	128	5	let	let	VERB
iajs-153	128	6	x=	x=	PUNCT
iajs-153	128	7	{	{	PUNCT
iajs-153	128	8	a	a	DET
iajs-153	128	9	,	,	PUNCT
iajs-153	128	10	b	b	NOUN
iajs-153	128	11	,	,	PUNCT
iajs-153	128	12	c	c	NOUN
iajs-153	128	13	}	}	PUNCT
iajs-153	128	14	,	,	PUNCT
iajs-153	128	15	t={x,,{a	t={x,,{a	PROPN
iajs-153	128	16	,	,	PUNCT
iajs-153	128	17	b	b	NOUN
iajs-153	128	18	}	}	PUNCT
iajs-153	128	19	,	,	PUNCT
iajs-153	128	20	{	{	PUNCT
iajs-153	128	21	c	c	X
iajs-153	128	22	}	}	PUNCT
iajs-153	128	23	}	}	PUNCT
iajs-153	128	24	in	in	ADP
iajs-153	128	25	this	this	DET
iajs-153	128	26	example	example	NOUN
iajs-153	128	27	a={a	a={a	NOUN
iajs-153	128	28	,	,	PUNCT
iajs-153	128	29	b	b	X
iajs-153	128	30	}	}	PUNCT
iajs-153	128	31	is	be	AUX
iajs-153	128	32	sgclosed	sgclose	VERB
iajs-153	128	33	set	set	ADJ
iajs-153	128	34	but	but	CCONJ
iajs-153	128	35	not	not	PART
iajs-153	128	36	gb	gb	ADV
iajs-153	128	37	*	*	PUNCT
iajs-153	128	38	-closed	-close	VERB
iajs-153	128	39	set	set	NOUN
iajs-153	128	40	.	.	PUNCT
iajs-153	129	1	theorem	theorem	VERB
iajs-153	129	2	331	331	NUM
iajs-153	129	3	:	:	PUNCT
iajs-153	129	4	every	every	DET
iajs-153	129	5	gb	gb	NOUN
iajs-153	129	6	*	*	PUNCT
iajs-153	129	7	-closed	-closed	ADJ
iajs-153	129	8	set	set	NOUN
iajs-153	129	9	is	be	AUX
iajs-153	129	10	gβ	gβ	NOUN
iajs-153	129	11	-	-	PUNCT
iajs-153	129	12	closed	closed	ADJ
iajs-153	129	13	set	set	NOUN
iajs-153	129	14	.	.	PUNCT
iajs-153	130	1	proof	proof	NOUN
iajs-153	130	2	:	:	PUNCT
iajs-153	130	3	assume	assume	VERB
iajs-153	130	4	that	that	SCONJ
iajs-153	130	5	a	a	PRON
iajs-153	130	6	is	be	AUX
iajs-153	130	7	g*b	g*b	PROPN
iajs-153	130	8	*	*	SYM
iajs-153	130	9	-closed	-closed	ADJ
iajs-153	130	10	set	set	NOUN
iajs-153	130	11	in	in	ADP
iajs-153	130	12	x	x	X
iajs-153	130	13	,	,	PUNCT
iajs-153	130	14	and	and	CCONJ
iajs-153	130	15	u	u	NOUN
iajs-153	130	16	is	be	AUX
iajs-153	130	17	open	open	ADJ
iajs-153	130	18	set	set	VERB
iajs-153	130	19	such	such	ADJ
iajs-153	130	20	that	that	SCONJ
iajs-153	130	21	a	a	DET
iajs-153	130	22	⊆	⊆	NUM
iajs-153	130	23	u	u	NOUN
iajs-153	130	24	,	,	PUNCT
iajs-153	130	25	every	every	DET
iajs-153	130	26	open	open	ADJ
iajs-153	130	27	set	set	NOUN
iajs-153	130	28	is	be	AUX
iajs-153	130	29	gb	gb	ADV
iajs-153	130	30	-	-	PUNCT
iajs-153	130	31	open	open	NOUN
iajs-153	130	32	set	set	NOUN
iajs-153	130	33	then	then	ADV
iajs-153	130	34	int	int	NOUN
iajs-153	130	35	cl	cl	NOUN
iajs-153	130	36	a	a	DET
iajs-153	130	37	⊆	⊆	NUM
iajs-153	130	38	a	a	DET
iajs-153	130	39	∪	∪	NOUN
iajs-153	130	40	β	β	PRON
iajs-153	130	41	closed	close	VERB
iajs-153	130	42	⊆	⊆	NUM
iajs-153	130	43	u	u	NOUN
iajs-153	130	44	therefore	therefore	ADV
iajs-153	130	45	a	a	PRON
iajs-153	130	46	is	be	AUX
iajs-153	130	47	g*b	g*b	PROPN
iajs-153	130	48	*	*	PUNCT
iajs-153	130	49	-closed	-close	VERB
iajs-153	130	50	set	set	NOUN
iajs-153	130	51	.	.	PUNCT
iajs-153	131	1	remark	remark	VERB
iajs-153	131	2	332	332	NUM
iajs-153	131	3	:	:	PUNCT
iajs-153	131	4	the	the	DET
iajs-153	131	5	converse	converse	NOUN
iajs-153	131	6	of	of	ADP
iajs-153	131	7	the	the	DET
iajs-153	131	8	theorem	theorem	NOUN
iajs-153	131	9	[	[	X
iajs-153	131	10	3	3	NUM
iajs-153	131	11	-	-	SYM
iajs-153	131	12	31	31	NUM
iajs-153	131	13	]	]	PUNCT
iajs-153	131	14	need	need	AUX
iajs-153	131	15	not	not	PART
iajs-153	131	16	be	be	AUX
iajs-153	131	17	true	true	ADJ
iajs-153	131	18	as	as	SCONJ
iajs-153	131	19	seen	see	VERB
iajs-153	131	20	by	by	ADP
iajs-153	131	21	the	the	DET
iajs-153	131	22	following	follow	VERB
iajs-153	131	23	example	example	NOUN
iajs-153	131	24	.	.	PUNCT
iajs-153	132	1	example3	example3	PROPN
iajs-153	132	2	-	-	PUNCT
iajs-153	132	3	33	33	NUM
iajs-153	132	4	:	:	PUNCT
iajs-153	132	5	let	let	VERB
iajs-153	132	6	x=	x=	PUNCT
iajs-153	132	7	{	{	PUNCT
iajs-153	132	8	a	a	DET
iajs-153	132	9	,	,	PUNCT
iajs-153	132	10	b	b	NOUN
iajs-153	132	11	,	,	PUNCT
iajs-153	132	12	c	c	NOUN
iajs-153	132	13	}	}	PUNCT
iajs-153	132	14	,	,	PUNCT
iajs-153	132	15	t={x,,{b	t={x,,{b	PROPN
iajs-153	132	16	}	}	PUNCT
iajs-153	132	17	,	,	PUNCT
iajs-153	132	18	{	{	PUNCT
iajs-153	132	19	b	b	X
iajs-153	132	20	,	,	PUNCT
iajs-153	132	21	c	c	NOUN
iajs-153	132	22	}	}	PUNCT
iajs-153	132	23	}	}	PUNCT
iajs-153	132	24	.	.	PUNCT
iajs-153	133	1	in	in	ADP
iajs-153	133	2	this	this	DET
iajs-153	133	3	example	example	NOUN
iajs-153	133	4	a={a	a={a	NOUN
iajs-153	133	5	,	,	PUNCT
iajs-153	133	6	b	b	X
iajs-153	133	7	}	}	PUNCT
iajs-153	133	8	is	be	AUX
iajs-153	133	9	gβ	gβ	ADJ
iajs-153	133	10	–	–	PUNCT
iajs-153	133	11	closed	closed	ADJ
iajs-153	133	12	set	set	ADJ
iajs-153	133	13	but	but	CCONJ
iajs-153	133	14	not	not	PART
iajs-153	133	15	gb	gb	ADV
iajs-153	133	16	*	*	PUNCT
iajs-153	133	17	-closed	-close	VERB
iajs-153	133	18	set	set	NOUN
iajs-153	133	19	.	.	PUNCT
iajs-153	134	1	theorem	theorem	NOUN
iajs-153	134	2	334	334	NUM
iajs-153	134	3	:	:	PUNCT
iajs-153	134	4	every	every	DET
iajs-153	134	5	gb	gb	NOUN
iajs-153	134	6	*	*	PUNCT
iajs-153	134	7	-closed	-closed	ADJ
iajs-153	134	8	set	set	NOUN
iajs-153	134	9	is	be	AUX
iajs-153	134	10	b	b	NOUN
iajs-153	134	11	*	*	PUNCT
iajs-153	134	12	*	*	PUNCT
iajs-153	134	13	-closed	-closed	ADJ
iajs-153	134	14	set	set	NOUN
iajs-153	134	15	.	.	PUNCT
iajs-153	135	1	proof	proof	NOUN
iajs-153	135	2	:	:	PUNCT
iajs-153	135	3	assume	assume	VERB
iajs-153	135	4	that	that	SCONJ
iajs-153	135	5	a	a	PRON
iajs-153	135	6	is	be	AUX
iajs-153	135	7	g*b	g*b	PROPN
iajs-153	135	8	*	*	SYM
iajs-153	135	9	-closed	-closed	ADJ
iajs-153	135	10	set	set	NOUN
iajs-153	135	11	in	in	ADP
iajs-153	135	12	x	x	X
iajs-153	135	13	,	,	PUNCT
iajs-153	135	14	and	and	CCONJ
iajs-153	135	15	u	u	NOUN
iajs-153	135	16	is	be	AUX
iajs-153	135	17	open	open	ADJ
iajs-153	135	18	set	set	VERB
iajs-153	135	19	such	such	ADJ
iajs-153	135	20	that	that	SCONJ
iajs-153	135	21	a	a	DET
iajs-153	135	22	⊆	⊆	NUM
iajs-153	135	23	u	u	NOUN
iajs-153	135	24	,	,	PUNCT
iajs-153	135	25	every	every	DET
iajs-153	135	26	open	open	ADJ
iajs-153	135	27	set	set	NOUN
iajs-153	135	28	is	be	AUX
iajs-153	135	29	gb	gb	ADV
iajs-153	135	30	-	-	PUNCT
iajs-153	135	31	open	open	NOUN
iajs-153	135	32	set	set	NOUN
iajs-153	135	33	then	then	ADV
iajs-153	135	34	int	int	NOUN
iajs-153	135	35	cl	cl	NOUN
iajs-153	135	36	a	a	DET
iajs-153	135	37	⊆	⊆	NUM
iajs-153	135	38	cl	cl	NOUN
iajs-153	135	39	int	int	NOUN
iajs-153	135	40	cl	cl	NOUN
iajs-153	135	41	a	a	DET
iajs-153	135	42	∪	∪	ADJ
iajs-153	135	43	int	int	NOUN
iajs-153	135	44	cl	cl	NOUN
iajs-153	135	45	int	int	NOUN
iajs-153	135	46	a	a	DET
iajs-153	135	47	⊆	⊆	NUM
iajs-153	135	48	u.therefore	u.therefore	NOUN
iajs-153	135	49	a	a	DET
iajs-153	135	50	is	be	AUX
iajs-153	135	51	b**-closed	b**-close	VERB
iajs-153	135	52	set	set	NOUN
iajs-153	135	53	.	.	PUNCT
iajs-153	136	1	remark	remark	PROPN
iajs-153	136	2	335	335	NUM
iajs-153	136	3	:	:	PUNCT
iajs-153	136	4	the	the	DET
iajs-153	136	5	converse	converse	NOUN
iajs-153	136	6	of	of	ADP
iajs-153	136	7	the	the	DET
iajs-153	136	8	theorem	theorem	NOUN
iajs-153	136	9	[	[	X
iajs-153	136	10	3	3	NUM
iajs-153	136	11	-	-	SYM
iajs-153	136	12	34	34	NUM
iajs-153	136	13	]	]	PUNCT
iajs-153	136	14	need	need	AUX
iajs-153	136	15	not	not	PART
iajs-153	136	16	be	be	AUX
iajs-153	136	17	true	true	ADJ
iajs-153	136	18	as	as	SCONJ
iajs-153	136	19	seen	see	VERB
iajs-153	136	20	by	by	ADP
iajs-153	136	21	the	the	DET
iajs-153	136	22	following	follow	VERB
iajs-153	136	23	example	example	NOUN
iajs-153	136	24	.	.	PUNCT
iajs-153	137	1	example3	example3	PROPN
iajs-153	137	2	-	-	PUNCT
iajs-153	137	3	36	36	NUM
iajs-153	137	4	:	:	PUNCT
iajs-153	137	5	let	let	VERB
iajs-153	137	6	x=	x=	PUNCT
iajs-153	137	7	{	{	PUNCT
iajs-153	137	8	a	a	DET
iajs-153	137	9	,	,	PUNCT
iajs-153	137	10	b	b	NOUN
iajs-153	137	11	,	,	PUNCT
iajs-153	137	12	c	c	NOUN
iajs-153	137	13	}	}	PUNCT
iajs-153	137	14	,	,	PUNCT
iajs-153	137	15	t={x,,{a	t={x,,{a	ADV
iajs-153	137	16	,	,	PUNCT
iajs-153	137	17	b	b	X
iajs-153	137	18	}	}	PUNCT
iajs-153	137	19	,	,	PUNCT
iajs-153	137	20	{	{	PUNCT
iajs-153	137	21	c	c	X
iajs-153	137	22	}	}	PUNCT
iajs-153	137	23	}	}	PUNCT
iajs-153	137	24	.	.	PUNCT
iajs-153	138	1	in	in	ADP
iajs-153	138	2	this	this	DET
iajs-153	138	3	topological	topological	ADJ
iajs-153	138	4	spaces	space	NOUN
iajs-153	138	5	the	the	DET
iajs-153	138	6	subset	subset	NOUN
iajs-153	138	7	a={b	a={b	NOUN
iajs-153	138	8	,	,	PUNCT
iajs-153	138	9	c	c	NOUN
iajs-153	138	10	}	}	PUNCT
iajs-153	138	11	is	be	AUX
iajs-153	138	12	b**-closed	b**-close	VERB
iajs-153	138	13	set	set	NOUN
iajs-153	138	14	but	but	CCONJ
iajs-153	138	15	not	not	PART
iajs-153	138	16	g	g	PROPN
iajs-153	138	17	b	b	PROPN
iajs-153	138	18	*	*	PUNCT
iajs-153	138	19	-closed	-close	VERB
iajs-153	138	20	set	set	NOUN
iajs-153	138	21	.	.	PUNCT
iajs-153	138	22	                                                     	                                                     	SPACE
iajs-153	139	1	gb‐closed	gb‐close	VERB
iajs-153	139	2	closed	closed	ADJ
iajs-153	139	3	set	set	NOUN
iajs-153	139	4	                                                                                                                                        	                                                                                                                                        	SPACE
iajs-153	139	5	wclosed	wclose	VERB
iajs-153	139	6	  	  	SPACE
iajs-153	139	7	gβ	gβ	NOUN
iajs-153	139	8	-	-	PUNCT
iajs-153	139	9	closed	close	VERB
iajs-153	139	10	                                                                                                      	                                                                                                      	SPACE
iajs-153	139	11	sg	sg	NOUN
iajs-153	139	12	-	-	PUNCT
iajs-153	139	13	closed	close	VERB
iajs-153	139	14	                                                 	                                                 	SPACE
iajs-153	139	15	gb*-closed	gb*-close	VERB
iajs-153	139	16	set	set	VERB
iajs-153	139	17	                       	                       	SPACE
iajs-153	139	18	b	b	NOUN
iajs-153	139	19	-	-	PUNCT
iajs-153	139	20	closed	closed	ADJ
iajs-153	139	21	                                                                                              	                                                                                              	SPACE
iajs-153	139	22	g*b	g*b	NOUN
iajs-153	139	23	-	-	PUNCT
iajs-153	139	24	closed	close	VERB
iajs-153	139	25	                                	                                	SPACE
iajs-153	139	26	b*-closed	b*-closed	ADJ
iajs-153	139	27	                      	                      	SPACE
iajs-153	139	28	b**-closed	b**-close	VERB
iajs-153	139	29	  	  	SPACE
iajs-153	139	30	diagram	diagram	NOUN
iajs-153	139	31	(	(	PUNCT
iajs-153	139	32	1	1	X
iajs-153	139	33	)	)	PUNCT
iajs-153	139	34	211	211	NUM
iajs-153	139	35	|	|	ADV
iajs-153	139	36	mathematics	mathematic	NOUN
iajs-153	139	37	2015	2015	NUM
iajs-153	139	38	)	)	PUNCT
iajs-153	139	39	عام	عام	ADP
iajs-153	139	40	3العدد	3العدد	NUM
iajs-153	139	41	(	(	PUNCT
iajs-153	139	42	28الھيثم	28الھيثم	NUM
iajs-153	139	43	للعلوم	للعلوم	PROPN
iajs-153	139	44	الصرفة	الصرفة	NOUN
iajs-153	140	1	و	و	PRON
iajs-153	140	2	التطبيقية	التطبيقية	ADV
iajs-153	140	3	المجلد	المجلد	ADV
iajs-153	140	4	مجلة	مجلة	VERB
iajs-153	140	5	إبن	إبن	VERB
iajs-153	140	6	ibn	ibn	PROPN
iajs-153	140	7	al	al	PROPN
iajs-153	140	8	-	-	PUNCT
iajs-153	140	9	haitham	haitham	PROPN
iajs-153	140	10	jour	jour	X
iajs-153	140	11	.	.	PROPN
iajs-153	140	12	for	for	ADP
iajs-153	140	13	pure	pure	ADJ
iajs-153	140	14	&	&	CCONJ
iajs-153	140	15	appl	appl	PROPN
iajs-153	140	16	.	.	PUNCT
iajs-153	141	1	sci	sci	PROPN
iajs-153	141	2	.	.	PUNCT
iajs-153	141	3	vol	vol	NOUN
iajs-153	141	4	.	.	PROPN
iajs-153	142	1	28	28	NUM
iajs-153	142	2	(	(	PUNCT
iajs-153	142	3	3	3	NUM
iajs-153	142	4	)	)	PUNCT
iajs-153	142	5	2015	2015	NUM
iajs-153	142	6	4.gb*-closed	4.gb*-closed	NUM
iajs-153	142	7	set	set	NOUN
iajs-153	142	8	is	be	AUX
iajs-153	142	9	independent	independent	ADJ
iajs-153	142	10	of	of	ADP
iajs-153	142	11	other	other	ADJ
iajs-153	142	12	closed	closed	ADJ
iajs-153	142	13	sets	set	NOUN
iajs-153	142	14	in	in	ADP
iajs-153	142	15	this	this	DET
iajs-153	142	16	section	section	NOUN
iajs-153	142	17	,	,	PUNCT
iajs-153	142	18	we	we	PRON
iajs-153	142	19	explain	explain	VERB
iajs-153	142	20	independency	independency	NOUN
iajs-153	142	21	of	of	ADP
iajs-153	142	22	gb*-closed	gb*-close	VERB
iajs-153	142	23	set	set	VERB
iajs-153	142	24	with	with	ADP
iajs-153	142	25	some	some	DET
iajs-153	142	26	other	other	ADJ
iajs-153	142	27	closed	closed	ADJ
iajs-153	142	28	sets	set	NOUN
iajs-153	142	29	.	.	PUNCT
iajs-153	143	1	remark	remark	VERB
iajs-153	143	2	41	41	NUM
iajs-153	143	3	:	:	PUNCT
iajs-153	143	4	the	the	DET
iajs-153	143	5	following	follow	VERB
iajs-153	143	6	example	example	NOUN
iajs-153	143	7	shows	show	VERB
iajs-153	143	8	that	that	SCONJ
iajs-153	143	9	the	the	DET
iajs-153	143	10	concept	concept	NOUN
iajs-153	143	11	of	of	ADP
iajs-153	143	12	g	g	NOUN
iajs-153	143	13	-	-	PUNCT
iajs-153	143	14	closed	close	VERB
iajs-153	143	15	and	and	CCONJ
iajs-153	143	16	gb*-closed	gb*-close	VERB
iajs-153	143	17	sets	set	NOUN
iajs-153	143	18	are	be	AUX
iajs-153	143	19	independent	independent	ADJ
iajs-153	143	20	.	.	PUNCT
iajs-153	144	1	example4	example4	NOUN
iajs-153	144	2	-	-	PUNCT
iajs-153	144	3	2	2	NUM
iajs-153	144	4	:	:	PUNCT
iajs-153	144	5	let	let	VERB
iajs-153	144	6	x=	x=	PUNCT
iajs-153	144	7	{	{	PUNCT
iajs-153	144	8	a	a	PRON
iajs-153	144	9	,	,	PUNCT
iajs-153	144	10	b	b	NOUN
iajs-153	144	11	,	,	PUNCT
iajs-153	144	12	c	c	NOUN
iajs-153	144	13	}	}	PUNCT
iajs-153	144	14	,	,	PUNCT
iajs-153	144	15	t={x,	t={x,	NOUN
iajs-153	144	16	,	,	PUNCT
iajs-153	144	17	{	{	PUNCT
iajs-153	144	18	b	b	NOUN
iajs-153	144	19	}	}	PUNCT
iajs-153	144	20	,	,	PUNCT
iajs-153	144	21	{	{	PUNCT
iajs-153	144	22	b	b	X
iajs-153	144	23	,	,	PUNCT
iajs-153	144	24	c	c	NOUN
iajs-153	144	25	}	}	PUNCT
iajs-153	144	26	}	}	PUNCT
iajs-153	144	27	,	,	PUNCT
iajs-153	144	28	in	in	ADP
iajs-153	144	29	this	this	DET
iajs-153	144	30	topological	topological	ADJ
iajs-153	144	31	space	space	NOUN
iajs-153	144	32	,	,	PUNCT
iajs-153	144	33	the	the	DET
iajs-153	144	34	subset	subset	NOUN
iajs-153	144	35	a={a	a={a	NOUN
iajs-153	144	36	,	,	PUNCT
iajs-153	144	37	b}is	b}is	DET
iajs-153	144	38	g	g	ADV
iajs-153	144	39	-	-	PUNCT
iajs-153	144	40	closed	close	VERB
iajs-153	144	41	set	set	NOUN
iajs-153	144	42	but	but	CCONJ
iajs-153	144	43	not	not	PART
iajs-153	144	44	gb*-closed	gb*-close	VERB
iajs-153	144	45	set	set	NOUN
iajs-153	144	46	.	.	PUNCT
iajs-153	145	1	and	and	CCONJ
iajs-153	145	2	,	,	PUNCT
iajs-153	145	3	in	in	ADP
iajs-153	145	4	this	this	DET
iajs-153	145	5	topological	topological	ADJ
iajs-153	145	6	space	space	NOUN
iajs-153	145	7	,	,	PUNCT
iajs-153	145	8	the	the	DET
iajs-153	145	9	subset	subset	NOUN
iajs-153	145	10	b={c}is	b={c}is	PROPN
iajs-153	145	11	gb*-closed	gb*-close	VERB
iajs-153	145	12	set	set	NOUN
iajs-153	145	13	but	but	CCONJ
iajs-153	145	14	not	not	PART
iajs-153	145	15	g	g	NOUN
iajs-153	145	16	-	-	PUNCT
iajs-153	145	17	closed	close	VERB
iajs-153	145	18	set	set	NOUN
iajs-153	145	19	.	.	PUNCT
iajs-153	146	1	remark	remark	PROPN
iajs-153	146	2	43	43	NUM
iajs-153	146	3	:	:	PUNCT
iajs-153	146	4	the	the	DET
iajs-153	146	5	following	follow	VERB
iajs-153	146	6	example	example	NOUN
iajs-153	146	7	shows	show	VERB
iajs-153	146	8	that	that	SCONJ
iajs-153	146	9	the	the	DET
iajs-153	146	10	concept	concept	NOUN
iajs-153	146	11	of	of	ADP
iajs-153	146	12	sb*-closed	sb*-close	VERB
iajs-153	146	13	and	and	CCONJ
iajs-153	146	14	gb*-closed	gb*-close	VERB
iajs-153	146	15	sets	set	NOUN
iajs-153	146	16	are	be	AUX
iajs-153	146	17	independent	independent	ADJ
iajs-153	146	18	.	.	PUNCT
iajs-153	147	1	example4	example4	NOUN
iajs-153	147	2	-	-	PUNCT
iajs-153	147	3	4	4	NUM
iajs-153	147	4	:	:	PUNCT
iajs-153	147	5	let	let	VERB
iajs-153	147	6	x=	x=	PUNCT
iajs-153	147	7	{	{	PUNCT
iajs-153	147	8	a	a	PRON
iajs-153	147	9	,	,	PUNCT
iajs-153	147	10	b	b	NOUN
iajs-153	147	11	,	,	PUNCT
iajs-153	147	12	c	c	NOUN
iajs-153	147	13	}	}	PUNCT
iajs-153	147	14	,	,	PUNCT
iajs-153	147	15	t={x,	t={x,	NOUN
iajs-153	147	16	,	,	PUNCT
iajs-153	147	17	{	{	PUNCT
iajs-153	147	18	a},{c	a},{c	ADP
iajs-153	147	19	}	}	PUNCT
iajs-153	147	20	,	,	PUNCT
iajs-153	147	21	{	{	PUNCT
iajs-153	147	22	a	a	DET
iajs-153	147	23	,	,	PUNCT
iajs-153	147	24	c	c	NOUN
iajs-153	147	25	}	}	PUNCT
iajs-153	147	26	}	}	PUNCT
iajs-153	147	27	,	,	PUNCT
iajs-153	147	28	in	in	ADP
iajs-153	147	29	this	this	DET
iajs-153	147	30	topological	topological	ADJ
iajs-153	147	31	space	space	NOUN
iajs-153	147	32	,	,	PUNCT
iajs-153	147	33	the	the	DET
iajs-153	147	34	subset	subset	NOUN
iajs-153	147	35	a={a	a={a	NOUN
iajs-153	147	36	,	,	PUNCT
iajs-153	147	37	c}is	c}is	PROPN
iajs-153	147	38	sb*-closed	sb*-close	VERB
iajs-153	147	39	set	set	NOUN
iajs-153	147	40	but	but	CCONJ
iajs-153	147	41	not	not	PART
iajs-153	147	42	gb*-closed	gb*-close	VERB
iajs-153	147	43	set	set	NOUN
iajs-153	147	44	.	.	PUNCT
iajs-153	148	1	and	and	CCONJ
iajs-153	148	2	,	,	PUNCT
iajs-153	148	3	in	in	ADP
iajs-153	148	4	this	this	DET
iajs-153	148	5	topological	topological	ADJ
iajs-153	148	6	space	space	NOUN
iajs-153	148	7	,	,	PUNCT
iajs-153	148	8	the	the	DET
iajs-153	148	9	subset	subset	NOUN
iajs-153	148	10	b={c}is	b={c}is	PROPN
iajs-153	148	11	gb*-closed	gb*-close	VERB
iajs-153	148	12	set	set	NOUN
iajs-153	148	13	but	but	CCONJ
iajs-153	148	14	not	not	PART
iajs-153	148	15	sb*-closed	sb*-close	VERB
iajs-153	148	16	set	set	NOUN
iajs-153	148	17	.	.	PUNCT
iajs-153	149	1	remark	remark	NOUN
iajs-153	149	2	45	45	NUM
iajs-153	149	3	:	:	PUNCT
iajs-153	149	4	the	the	DET
iajs-153	149	5	following	follow	VERB
iajs-153	149	6	example	example	NOUN
iajs-153	149	7	shows	show	VERB
iajs-153	149	8	that	that	SCONJ
iajs-153	149	9	the	the	DET
iajs-153	149	10	concept	concept	NOUN
iajs-153	149	11	of	of	ADP
iajs-153	149	12	g*-closed	g*-close	VERB
iajs-153	149	13	and	and	CCONJ
iajs-153	149	14	gb*-closed	gb*-close	VERB
iajs-153	149	15	sets	set	NOUN
iajs-153	149	16	are	be	AUX
iajs-153	149	17	independent	independent	ADJ
iajs-153	149	18	.	.	PUNCT
iajs-153	150	1	example4	example4	NOUN
iajs-153	150	2	-	-	PUNCT
iajs-153	150	3	6	6	NUM
iajs-153	150	4	:	:	PUNCT
iajs-153	150	5	let	let	VERB
iajs-153	150	6	x=	x=	PUNCT
iajs-153	150	7	{	{	PUNCT
iajs-153	150	8	a	a	PRON
iajs-153	150	9	,	,	PUNCT
iajs-153	150	10	b	b	NOUN
iajs-153	150	11	,	,	PUNCT
iajs-153	150	12	c	c	NOUN
iajs-153	150	13	}	}	PUNCT
iajs-153	150	14	,	,	PUNCT
iajs-153	150	15	t={x,	t={x,	NOUN
iajs-153	150	16	,	,	PUNCT
iajs-153	150	17	{	{	PUNCT
iajs-153	150	18	b	b	NOUN
iajs-153	150	19	}	}	PUNCT
iajs-153	150	20	,	,	PUNCT
iajs-153	150	21	{	{	PUNCT
iajs-153	150	22	b	b	X
iajs-153	150	23	,	,	PUNCT
iajs-153	150	24	c	c	NOUN
iajs-153	150	25	}	}	PUNCT
iajs-153	150	26	}	}	PUNCT
iajs-153	150	27	,	,	PUNCT
iajs-153	150	28	in	in	ADP
iajs-153	150	29	this	this	DET
iajs-153	150	30	topological	topological	ADJ
iajs-153	150	31	space	space	NOUN
iajs-153	150	32	,	,	PUNCT
iajs-153	150	33	the	the	DET
iajs-153	150	34	subset	subset	NOUN
iajs-153	150	35	a={a	a={a	NOUN
iajs-153	150	36	,	,	PUNCT
iajs-153	150	37	b}is	b}is	PRON
iajs-153	150	38	g*-closed	g*-closed	ADJ
iajs-153	150	39	set	set	NOUN
iajs-153	150	40	but	but	CCONJ
iajs-153	150	41	not	not	PART
iajs-153	150	42	gb*-closed	gb*-close	VERB
iajs-153	150	43	set	set	NOUN
iajs-153	150	44	.	.	PUNCT
iajs-153	151	1	and	and	CCONJ
iajs-153	151	2	,	,	PUNCT
iajs-153	151	3	in	in	ADP
iajs-153	151	4	this	this	DET
iajs-153	151	5	topological	topological	ADJ
iajs-153	151	6	space	space	NOUN
iajs-153	151	7	,	,	PUNCT
iajs-153	151	8	the	the	DET
iajs-153	151	9	subset	subset	NOUN
iajs-153	151	10	b={c}is	b={c}is	PROPN
iajs-153	151	11	gb*-closed	gb*-close	VERB
iajs-153	151	12	set	set	NOUN
iajs-153	151	13	but	but	CCONJ
iajs-153	151	14	not	not	PART
iajs-153	151	15	g*-closed	g*-close	VERB
iajs-153	151	16	set	set	NOUN
iajs-153	151	17	.	.	PUNCT
iajs-153	152	1	remark	remark	NOUN
iajs-153	152	2	47	47	NUM
iajs-153	152	3	:	:	PUNCT
iajs-153	152	4	the	the	DET
iajs-153	152	5	following	follow	VERB
iajs-153	152	6	example	example	NOUN
iajs-153	152	7	shows	show	VERB
iajs-153	152	8	that	that	SCONJ
iajs-153	152	9	the	the	DET
iajs-153	152	10	concept	concept	NOUN
iajs-153	152	11	of	of	ADP
iajs-153	152	12	gα	gα	NOUN
iajs-153	152	13	-	-	PUNCT
iajs-153	152	14	closed	close	VERB
iajs-153	152	15	and	and	CCONJ
iajs-153	152	16	gb*-closed	gb*-close	VERB
iajs-153	152	17	sets	set	NOUN
iajs-153	152	18	are	be	AUX
iajs-153	152	19	independent	independent	ADJ
iajs-153	152	20	.	.	PUNCT
iajs-153	153	1	example4	example4	NOUN
iajs-153	153	2	-	-	PUNCT
iajs-153	153	3	8	8	NUM
iajs-153	153	4	:	:	PUNCT
iajs-153	153	5	let	let	VERB
iajs-153	153	6	x=	x=	PUNCT
iajs-153	153	7	{	{	PUNCT
iajs-153	153	8	a	a	PRON
iajs-153	153	9	,	,	PUNCT
iajs-153	153	10	b	b	NOUN
iajs-153	153	11	,	,	PUNCT
iajs-153	153	12	c	c	NOUN
iajs-153	153	13	}	}	PUNCT
iajs-153	153	14	,	,	PUNCT
iajs-153	153	15	t={x,	t={x,	NOUN
iajs-153	153	16	,	,	PUNCT
iajs-153	153	17	{	{	PUNCT
iajs-153	153	18	a},{c	a},{c	ADP
iajs-153	153	19	}	}	PUNCT
iajs-153	153	20	,	,	PUNCT
iajs-153	153	21	{	{	PUNCT
iajs-153	153	22	a	a	DET
iajs-153	153	23	,	,	PUNCT
iajs-153	153	24	c	c	NOUN
iajs-153	153	25	}	}	PUNCT
iajs-153	153	26	}	}	PUNCT
iajs-153	153	27	,	,	PUNCT
iajs-153	153	28	in	in	ADP
iajs-153	153	29	this	this	DET
iajs-153	153	30	topological	topological	ADJ
iajs-153	153	31	space	space	NOUN
iajs-153	153	32	,	,	PUNCT
iajs-153	153	33	the	the	DET
iajs-153	153	34	subset	subset	NOUN
iajs-153	153	35	a={b	a={b	NOUN
iajs-153	153	36	,	,	PUNCT
iajs-153	153	37	c}is	c}i	NOUN
iajs-153	153	38	gα	gα	ADP
iajs-153	153	39	-closed	-close	VERB
iajs-153	153	40	set	set	NOUN
iajs-153	153	41	but	but	CCONJ
iajs-153	153	42	not	not	PART
iajs-153	153	43	gb*-closed	gb*-close	VERB
iajs-153	153	44	set	set	NOUN
iajs-153	153	45	.	.	PUNCT
iajs-153	154	1	and	and	CCONJ
iajs-153	154	2	,	,	PUNCT
iajs-153	154	3	in	in	ADP
iajs-153	154	4	this	this	DET
iajs-153	154	5	topological	topological	ADJ
iajs-153	154	6	space	space	NOUN
iajs-153	154	7	,	,	PUNCT
iajs-153	154	8	the	the	DET
iajs-153	154	9	subset	subset	NOUN
iajs-153	154	10	b={a}is	b={a}is	PROPN
iajs-153	154	11	gb*-closed	gb*-close	VERB
iajs-153	154	12	set	set	NOUN
iajs-153	154	13	but	but	CCONJ
iajs-153	154	14	not	not	PART
iajs-153	154	15	gα	gα	ADP
iajs-153	154	16	-closed	-close	VERB
iajs-153	154	17	set	set	NOUN
iajs-153	154	18	remark	remark	NOUN
iajs-153	154	19	49	49	NUM
iajs-153	154	20	:	:	PUNCT
iajs-153	154	21	the	the	DET
iajs-153	154	22	following	follow	VERB
iajs-153	154	23	example	example	NOUN
iajs-153	154	24	shows	show	VERB
iajs-153	154	25	that	that	SCONJ
iajs-153	154	26	the	the	DET
iajs-153	154	27	concept	concept	NOUN
iajs-153	154	28	of	of	ADP
iajs-153	154	29	gp	gp	NOUN
iajs-153	154	30	-	-	PUNCT
iajs-153	154	31	closed	closed	ADJ
iajs-153	154	32	and	and	CCONJ
iajs-153	154	33	gb*-closed	gb*-close	VERB
iajs-153	154	34	sets	set	NOUN
iajs-153	154	35	are	be	AUX
iajs-153	154	36	independent	independent	ADJ
iajs-153	154	37	.	.	PUNCT
iajs-153	155	1	example4	example4	NOUN
iajs-153	155	2	-	-	PUNCT
iajs-153	155	3	10	10	NUM
iajs-153	155	4	:	:	PUNCT
iajs-153	155	5	let	let	VERB
iajs-153	155	6	x=	x=	PUNCT
iajs-153	155	7	{	{	PUNCT
iajs-153	155	8	a	a	DET
iajs-153	155	9	,	,	PUNCT
iajs-153	155	10	b	b	NOUN
iajs-153	155	11	,	,	PUNCT
iajs-153	155	12	c	c	NOUN
iajs-153	155	13	}	}	PUNCT
iajs-153	155	14	with	with	ADP
iajs-153	155	15	the	the	DET
iajs-153	155	16	topology	topology	NOUN
iajs-153	155	17	,	,	PUNCT
iajs-153	155	18	t1={x,	t1={x,	PROPN
iajs-153	155	19	,	,	PUNCT
iajs-153	155	20	{	{	PUNCT
iajs-153	155	21	a	a	DET
iajs-153	155	22	,	,	PUNCT
iajs-153	155	23	b},{,c	b},{,c	ADJ
iajs-153	155	24	}	}	PUNCT
iajs-153	155	25	}	}	PUNCT
iajs-153	155	26	,	,	PUNCT
iajs-153	155	27	in	in	ADP
iajs-153	155	28	this	this	DET
iajs-153	155	29	topological	topological	ADJ
iajs-153	155	30	space	space	NOUN
iajs-153	155	31	,	,	PUNCT
iajs-153	155	32	the	the	DET
iajs-153	155	33	subset	subset	NOUN
iajs-153	155	34	a={a	a={a	NOUN
iajs-153	155	35	,	,	PUNCT
iajs-153	155	36	c}is	c}is	PROPN
iajs-153	155	37	gp	gp	NOUN
iajs-153	155	38	-closed	-close	VERB
iajs-153	155	39	set	set	NOUN
iajs-153	155	40	but	but	CCONJ
iajs-153	155	41	not	not	PART
iajs-153	155	42	gb*-closed	gb*-close	VERB
iajs-153	155	43	set	set	NOUN
iajs-153	155	44	.	.	PUNCT
iajs-153	156	1	for	for	ADP
iajs-153	156	2	the	the	DET
iajs-153	156	3	topology	topology	NOUN
iajs-153	156	4	t2={x,	t2={x,	NOUN
iajs-153	156	5	,	,	PUNCT
iajs-153	156	6	{	{	PUNCT
iajs-153	156	7	a	a	PRON
iajs-153	156	8	}	}	PUNCT
iajs-153	156	9	,	,	PUNCT
iajs-153	156	10	{	{	PUNCT
iajs-153	156	11	b	b	NOUN
iajs-153	156	12	}	}	PUNCT
iajs-153	156	13	,	,	PUNCT
iajs-153	156	14	{	{	PUNCT
iajs-153	156	15	a	a	PRON
iajs-153	156	16	,	,	PUNCT
iajs-153	156	17	b	b	NOUN
iajs-153	156	18	}	}	PUNCT
iajs-153	156	19	}	}	PUNCT
iajs-153	156	20	topological	topological	ADJ
iajs-153	156	21	,	,	PUNCT
iajs-153	156	22	the	the	DET
iajs-153	156	23	subset	subset	NOUN
iajs-153	156	24	b={b}is	b={b}is	PROPN
iajs-153	156	25	gb*-closed	gb*-close	VERB
iajs-153	156	26	set	set	NOUN
iajs-153	156	27	but	but	CCONJ
iajs-153	156	28	not	not	PART
iajs-153	156	29	gp	gp	NOUN
iajs-153	156	30	-	-	PUNCT
iajs-153	156	31	closed	closed	ADJ
iajs-153	156	32	set	set	NOUN
iajs-153	156	33	.	.	PUNCT
iajs-153	157	1	remark	remark	PROPN
iajs-153	157	2	411	411	NUM
iajs-153	157	3	:	:	PUNCT
iajs-153	157	4	the	the	DET
iajs-153	157	5	following	follow	VERB
iajs-153	157	6	example	example	NOUN
iajs-153	157	7	shows	show	VERB
iajs-153	157	8	that	that	SCONJ
iajs-153	157	9	the	the	DET
iajs-153	157	10	concept	concept	NOUN
iajs-153	157	11	of	of	ADP
iajs-153	157	12	wg	wg	NOUN
iajs-153	157	13	-	-	PUNCT
iajs-153	157	14	closed	close	VERB
iajs-153	157	15	and	and	CCONJ
iajs-153	157	16	gb*closed	gb*close	VERB
iajs-153	157	17	sets	set	NOUN
iajs-153	157	18	are	be	AUX
iajs-153	157	19	independent	independent	ADJ
iajs-153	157	20	.	.	PUNCT
iajs-153	158	1	example4	example4	NOUN
iajs-153	158	2	-	-	PUNCT
iajs-153	158	3	12	12	NUM
iajs-153	158	4	:	:	PUNCT
iajs-153	158	5	let	let	VERB
iajs-153	158	6	x=	x=	PUNCT
iajs-153	158	7	{	{	PUNCT
iajs-153	158	8	a	a	DET
iajs-153	158	9	,	,	PUNCT
iajs-153	158	10	b	b	NOUN
iajs-153	158	11	,	,	PUNCT
iajs-153	158	12	c	c	NOUN
iajs-153	158	13	}	}	PUNCT
iajs-153	158	14	with	with	ADP
iajs-153	158	15	the	the	DET
iajs-153	158	16	topology	topology	NOUN
iajs-153	158	17	,	,	PUNCT
iajs-153	158	18	t1={x,	t1={x,	PROPN
iajs-153	158	19	,	,	PUNCT
iajs-153	158	20	{	{	PUNCT
iajs-153	158	21	a	a	PRON
iajs-153	158	22	}	}	PUNCT
iajs-153	158	23	}	}	PUNCT
iajs-153	158	24	,	,	PUNCT
iajs-153	158	25	in	in	ADP
iajs-153	158	26	this	this	DET
iajs-153	158	27	topological	topological	ADJ
iajs-153	158	28	space	space	NOUN
iajs-153	158	29	,	,	PUNCT
iajs-153	158	30	the	the	DET
iajs-153	158	31	subset	subset	NOUN
iajs-153	158	32	a={a	a={a	NOUN
iajs-153	158	33	,	,	PUNCT
iajs-153	158	34	b}is	b}is	PROPN
iajs-153	158	35	wg	wg	PROPN
iajs-153	158	36	-	-	PUNCT
iajs-153	158	37	closed	close	VERB
iajs-153	158	38	set	set	NOUN
iajs-153	158	39	but	but	CCONJ
iajs-153	158	40	not	not	PART
iajs-153	158	41	gb*-closed	gb*-close	VERB
iajs-153	158	42	set	set	NOUN
iajs-153	158	43	.	.	PUNCT
iajs-153	159	1	for	for	ADP
iajs-153	159	2	the	the	DET
iajs-153	159	3	topology	topology	NOUN
iajs-153	159	4	t2={x,	t2={x,	NOUN
iajs-153	159	5	,	,	PUNCT
iajs-153	159	6	{	{	PUNCT
iajs-153	159	7	a	a	PRON
iajs-153	159	8	}	}	PUNCT
iajs-153	159	9	,	,	PUNCT
iajs-153	159	10	{	{	PUNCT
iajs-153	159	11	c	c	NOUN
iajs-153	159	12	}	}	PUNCT
iajs-153	159	13	,	,	PUNCT
iajs-153	159	14	{	{	PUNCT
iajs-153	159	15	a	a	PRON
iajs-153	159	16	,	,	PUNCT
iajs-153	159	17	c	c	NOUN
iajs-153	159	18	}	}	PUNCT
iajs-153	159	19	topological	topological	ADJ
iajs-153	159	20	,	,	PUNCT
iajs-153	159	21	the	the	DET
iajs-153	159	22	subset	subset	NOUN
iajs-153	159	23	b={a}is	b={a}is	PROPN
iajs-153	159	24	gb*-closed	gb*-close	VERB
iajs-153	159	25	set	set	NOUN
iajs-153	159	26	but	but	CCONJ
iajs-153	159	27	not	not	PART
iajs-153	159	28	wg	wg	ADV
iajs-153	159	29	-	-	PUNCT
iajs-153	159	30	closed	close	VERB
iajs-153	159	31	set	set	NOUN
iajs-153	159	32	.	.	PUNCT
iajs-153	160	1	212	212	NUM
iajs-153	160	2	|	|	NOUN
iajs-153	160	3	mathematics	mathematic	NOUN
iajs-153	160	4	2015	2015	NUM
iajs-153	160	5	)	)	PUNCT
iajs-153	160	6	عام	عام	ADP
iajs-153	160	7	3العدد	3العدد	NUM
iajs-153	160	8	(	(	PUNCT
iajs-153	160	9	28الھيثم	28الھيثم	NUM
iajs-153	160	10	للعلوم	للعلوم	PROPN
iajs-153	160	11	الصرفة	الصرفة	NOUN
iajs-153	161	1	و	و	PRON
iajs-153	161	2	التطبيقية	التطبيقية	ADV
iajs-153	161	3	المجلد	المجلد	ADV
iajs-153	161	4	مجلة	مجلة	VERB
iajs-153	161	5	إبن	إبن	VERB
iajs-153	161	6	ibn	ibn	PROPN
iajs-153	161	7	al	al	PROPN
iajs-153	161	8	-	-	PUNCT
iajs-153	161	9	haitham	haitham	PROPN
iajs-153	161	10	jour	jour	X
iajs-153	161	11	.	.	PROPN
iajs-153	161	12	for	for	ADP
iajs-153	161	13	pure	pure	ADJ
iajs-153	161	14	&	&	CCONJ
iajs-153	161	15	appl	appl	PROPN
iajs-153	161	16	.	.	PUNCT
iajs-153	162	1	sci	sci	PROPN
iajs-153	162	2	.	.	PUNCT
iajs-153	162	3	vol	vol	NOUN
iajs-153	162	4	.	.	PROPN
iajs-153	163	1	28	28	NUM
iajs-153	163	2	(	(	PUNCT
iajs-153	163	3	3	3	NUM
iajs-153	163	4	)	)	PUNCT
iajs-153	163	5	2015	2015	NUM
iajs-153	163	6	                                                                                	                                                                                	SPACE
iajs-153	163	7	gp	gp	NOUN
iajs-153	163	8	-	-	PUNCT
iajs-153	163	9	closed	closed	ADJ
iajs-153	163	10	                                            	                                            	SPACE
iajs-153	163	11	sb*-closed	sb*-close	VERB
iajs-153	163	12	                                                                 	                                                                 	SPACE
iajs-153	163	13	gα	gα	NOUN
iajs-153	163	14	-	-	PUNCT
iajs-153	163	15	closed	close	VERB
iajs-153	163	16	                                                                                	                                                                                	SPACE
iajs-153	163	17	gb*-closed	gb*-close	VERB
iajs-153	163	18	set	set	NOUN
iajs-153	163	19	                                                                                                                            	                                                                                                                            	SPACE
iajs-153	163	20	g	g	NOUN
iajs-153	163	21	-	-	PUNCT
iajs-153	163	22	closed	close	VERB
iajs-153	163	23	                             	                             	SPACE
iajs-153	163	24	g*-closed	g*-closed	ADJ
iajs-153	163	25	                	                	SPACE
iajs-153	163	26	wg	wg	PROPN
iajs-153	163	27	-	-	PUNCT
iajs-153	163	28	closed	closed	ADJ
iajs-153	163	29	  	  	SPACE
iajs-153	163	30	diagram	diagram	NOUN
iajs-153	163	31	(	(	PUNCT
iajs-153	163	32	2	2	NUM
iajs-153	163	33	)	)	PUNCT
iajs-153	163	34	reference	reference	NOUN
iajs-153	163	35	1	1	NUM
iajs-153	163	36	.	.	PUNCT
iajs-153	164	1	el	el	NOUN
iajs-153	164	2	-	-	PUNCT
iajs-153	164	3	monsef	monsef	ADJ
iajs-153	164	4	,	,	PUNCT
iajs-153	164	5	m.d	m.d	PROPN
iajs-153	164	6	.	.	PROPN
iajs-153	164	7	;	;	PUNCT
iajs-153	165	1	abd	abd	PROPN
iajs-153	165	2	,	,	PUNCT
iajs-153	165	3	el	el	PROPN
iajs-153	165	4	-	-	PUNCT
iajs-153	165	5	atik	atik	PROPN
iajs-153	165	6	,	,	PUNCT
iajs-153	165	7	a.	a.	NOUN
iajs-153	165	8	a.	a.	PROPN
iajs-153	165	9	and	and	CCONJ
iajs-153	165	10	el	el	PROPN
iajs-153	165	11	-	-	PROPN
iajs-153	165	12	sharkasy	sharkasy	PROPN
iajs-153	165	13	,	,	PUNCT
iajs-153	165	14	m.	m.	NOUN
iajs-153	165	15	m.	m.	NOUN
iajs-153	165	16	,	,	PUNCT
iajs-153	165	17	(	(	PUNCT
iajs-153	165	18	2005	2005	NUM
iajs-153	165	19	)	)	PUNCT
iajs-153	165	20	,	,	PUNCT
iajs-153	165	21	some	some	DET
iajs-153	165	22	topologies	topology	NOUN
iajs-153	165	23	induced	induce	VERB
iajs-153	165	24	by	by	ADP
iajs-153	165	25	b	b	NOUN
iajs-153	165	26	-	-	PUNCT
iajs-153	165	27	open	open	ADJ
iajs-153	165	28	sets	set	NOUN
iajs-153	165	29	,	,	PUNCT
iajs-153	165	30	kyungpook	kyungpook	NOUN
iajs-153	165	31	math	math	NOUN
iajs-153	165	32	.	.	PUNCT
iajs-153	166	1	j.	j.	PROPN
iajs-153	166	2	45	45	NUM
iajs-153	166	3	.	.	PROPN
iajs-153	167	1	4	4	NUM
iajs-153	167	2	,	,	PUNCT
iajs-153	167	3	539{547	539{547	PROPN
iajs-153	167	4	.	.	NOUN
iajs-153	168	1	2	2	NUM
iajs-153	168	2	.	.	X
iajs-153	168	3	ahmad	ahmad	PROPN
iajs-153	168	4	al	al	PROPN
iajs-153	168	5	-	-	PUNCT
iajs-153	168	6	omari	omari	PROPN
iajs-153	168	7	and	and	CCONJ
iajs-153	168	8	mohd	mohd	PROPN
iajs-153	168	9	.	.	PUNCT
iajs-153	169	1	salmi	salmi	PROPN
iajs-153	169	2	,	,	PUNCT
iajs-153	169	3	md	md	PROPN
iajs-153	169	4	.	.	PROPN
iajs-153	169	5	noorani	noorani	PROPN
iajs-153	169	6	,	,	PUNCT
iajs-153	169	7	(	(	PUNCT
iajs-153	169	8	2009	2009	NUM
iajs-153	169	9	)	)	PUNCT
iajs-153	169	10	,	,	PUNCT
iajs-153	169	11	on	on	ADP
iajs-153	169	12	generalized	generalized	ADJ
iajs-153	169	13	b	b	X
iajs-153	169	14	-	-	PUNCT
iajs-153	169	15	closed	closed	ADJ
iajs-153	169	16	sets	set	NOUN
iajs-153	169	17	,	,	PUNCT
iajs-153	169	18	bull	bull	NOUN
iajs-153	169	19	.	.	PUNCT
iajs-153	170	1	malays	malays	PROPN
iajs-153	170	2	.	.	PUNCT
iajs-153	171	1	math	math	NOUN
iajs-153	171	2	.	.	PUNCT
iajs-153	172	1	sci	sci	PROPN
iajs-153	172	2	.	.	PUNCT
iajs-153	172	3	soc(2)32(1	soc(2)32(1	NOUN
iajs-153	172	4	)	)	PUNCT
iajs-153	172	5	.19	.19	NUM
iajs-153	172	6	-	-	SYM
iajs-153	172	7	30	30	NUM
iajs-153	172	8	.	.	PUNCT
iajs-153	173	1	3	3	X
iajs-153	173	2	.	.	X
iajs-153	173	3	andrijevic.d	andrijevic.d	ADP
iajs-153	173	4	,	,	PUNCT
iajs-153	173	5	(	(	PUNCT
iajs-153	173	6	1986	1986	NUM
iajs-153	173	7	)	)	PUNCT
iajs-153	173	8	,	,	PUNCT
iajs-153	173	9	semi	semi	ADJ
iajs-153	173	10	-	-	ADJ
iajs-153	173	11	preopen	preopen	ADJ
iajs-153	173	12	sets	set	NOUN
iajs-153	173	13	,	,	PUNCT
iajs-153	173	14	mat	mat	NOUN
iajs-153	173	15	.	.	PROPN
iajs-153	173	16	vesink	vesink	NOUN
iajs-153	173	17	,	,	PUNCT
iajs-153	173	18	38	38	NUM
iajs-153	173	19	,	,	PUNCT
iajs-153	173	20	24	24	NUM
iajs-153	173	21	32	32	NUM
iajs-153	173	22	.	.	PUNCT
iajs-153	174	1	4	4	NUM
iajs-153	174	2	.	.	X
iajs-153	174	3	andrijevic.d	andrijevic.d	ADP
iajs-153	174	4	,	,	PUNCT
iajs-153	174	5	(	(	PUNCT
iajs-153	174	6	1996	1996	NUM
iajs-153	174	7	)	)	PUNCT
iajs-153	174	8	,	,	PUNCT
iajs-153	174	9	on	on	ADP
iajs-153	174	10	b	b	X
iajs-153	174	11	-	-	PUNCT
iajs-153	174	12	open	open	ADJ
iajs-153	174	13	sets	set	NOUN
iajs-153	174	14	,	,	PUNCT
iajs-153	174	15	mat	mat	NOUN
iajs-153	174	16	.	.	PROPN
iajs-153	174	17	vesink	vesink	NOUN
iajs-153	174	18	,	,	PUNCT
iajs-153	174	19	48	48	NUM
iajs-153	174	20	,	,	PUNCT
iajs-153	174	21	59	59	NUM
iajs-153	174	22	64	64	NUM
iajs-153	174	23	.	.	PUNCT
iajs-153	174	24	5	5	NUM
iajs-153	174	25	.	.	X
iajs-153	174	26	a.poongothai	a.poongothai	ADJ
iajs-153	174	27	and	and	CCONJ
iajs-153	174	28	r	r	NOUN
iajs-153	174	29	,	,	PUNCT
iajs-153	174	30	parimelazhagan	parimelazhagan	NOUN
iajs-153	174	31	,	,	PUNCT
iajs-153	174	32	(	(	PUNCT
iajs-153	174	33	2012	2012	NUM
iajs-153	174	34	)	)	PUNCT
iajs-153	174	35	sb*-closed	sb*-close	VERB
iajs-153	174	36	sets	set	NOUN
iajs-153	174	37	in	in	ADP
iajs-153	174	38	topological	topological	ADJ
iajs-153	174	39	spaces	space	NOUN
iajs-153	174	40	,	,	PUNCT
iajs-153	174	41	math	math	NOUN
iajs-153	174	42	.	.	PUNCT
iajs-153	175	1	j.	j.	PROPN
iajs-153	175	2	6	6	NUM
iajs-153	175	3	,	,	PUNCT
iajs-153	175	4	47,2325	47,2325	NUM
iajs-153	175	5	-	-	PUNCT
iajs-153	175	6	2333	2333	NUM
iajs-153	175	7	.	.	PUNCT
iajs-153	176	1	6	6	NUM
iajs-153	176	2	.	.	X
iajs-153	176	3	arya	arya	PROPN
iajs-153	176	4	,	,	PUNCT
iajs-153	176	5	s.	s.	PROPN
iajs-153	176	6	p.	p.	PROPN
iajs-153	176	7	and	and	CCONJ
iajs-153	176	8	nour	nour	PROPN
iajs-153	176	9	,	,	PUNCT
iajs-153	176	10	t.	t.	PROPN
iajs-153	176	11	:	:	PUNCT
iajs-153	176	12	(	(	PUNCT
iajs-153	176	13	1990	1990	NUM
iajs-153	176	14	)	)	PUNCT
iajs-153	176	15	,	,	PUNCT
iajs-153	176	16	characterizations	characterization	NOUN
iajs-153	176	17	of	of	ADP
iajs-153	176	18	s	s	NOUN
iajs-153	176	19	-	-	ADJ
iajs-153	176	20	normal	normal	ADJ
iajs-153	176	21	spaces	space	NOUN
iajs-153	176	22	,	,	PUNCT
iajs-153	176	23	indian	indian	ADJ
iajs-153	176	24	j.pure	j.pure	NOUN
iajs-153	176	25	.	.	PUNCT
iajs-153	177	1	appl	appl	PROPN
iajs-153	177	2	.	.	PROPN
iajs-153	177	3	math	math	NOUN
iajs-153	177	4	.	.	PUNCT
iajs-153	178	1	21	21	NUM
iajs-153	178	2	(	(	PUNCT
iajs-153	178	3	8)	8)	NUM
iajs-153	178	4	,	,	PUNCT
iajs-153	178	5	717–719	717–719	NUM
iajs-153	178	6	.	.	PUNCT
iajs-153	178	7	7	7	NUM
iajs-153	178	8	.	.	PUNCT
iajs-153	179	1	bhattacharya	bhattacharya	PROPN
iajs-153	179	2	,	,	PUNCT
iajs-153	179	3	p.	p.	NOUN
iajs-153	179	4	and	and	CCONJ
iajs-153	179	5	lahiri.b.k	lahiri.b.k	PROPN
iajs-153	179	6	,	,	PUNCT
iajs-153	179	7	(	(	PUNCT
iajs-153	179	8	1987	1987	NUM
iajs-153	179	9	)	)	PUNCT
iajs-153	179	10	,	,	PUNCT
iajs-153	179	11	semi	semi	ADJ
iajs-153	179	12	-	-	ADJ
iajs-153	179	13	generalised	generalised	ADJ
iajs-153	179	14	closed	closed	ADJ
iajs-153	179	15	sets	set	NOUN
iajs-153	179	16	in	in	ADP
iajs-153	179	17	topology	topology	NOUN
iajs-153	179	18	,	,	PUNCT
iajs-153	179	19	indian	indian	PROPN
iajs-153	179	20	j.	j.	PROPN
iajs-153	179	21	math	math	PROPN
iajs-153	179	22	.	.	PUNCT
iajs-153	179	23	,	,	PUNCT
iajs-153	179	24	29(3	29(3	NUM
iajs-153	179	25	)	)	PUNCT
iajs-153	179	26	,	,	PUNCT
iajs-153	179	27	375	375	NUM
iajs-153	179	28	382	382	NUM
iajs-153	179	29	.	.	PUNCT
iajs-153	179	30	8	8	NUM
iajs-153	179	31	.	.	X
iajs-153	180	1	dontchev.j	dontchev.j	NOUN
iajs-153	180	2	,	,	PUNCT
iajs-153	180	3	(	(	PUNCT
iajs-153	180	4	1995	1995	NUM
iajs-153	180	5	)	)	PUNCT
iajs-153	180	6	,	,	PUNCT
iajs-153	180	7	on	on	ADP
iajs-153	180	8	generalizing	generalize	VERB
iajs-153	180	9	semi	semi	ADJ
iajs-153	180	10	preopen	preopen	ADJ
iajs-153	180	11	sets	set	NOUN
iajs-153	180	12	,	,	PUNCT
iajs-153	180	13	mem	mem	ADJ
iajs-153	180	14	.fac.sci.k	.fac.sci.k	PROPN
iajs-153	180	15	ochi.ser	ochi.ser	X
iajs-153	180	16	.a	.a	PROPN
iajs-153	180	17	,	,	PUNCT
iajs-153	180	18	math	math	NOUN
iajs-153	180	19	.	.	PUNCT
iajs-153	180	20	,	,	PUNCT
iajs-153	180	21	16	16	NUM
iajs-153	180	22	,	,	PUNCT
iajs-153	180	23	35	35	NUM
iajs-153	180	24	-	-	SYM
iajs-153	180	25	48	48	NUM
iajs-153	180	26	.	.	PUNCT
iajs-153	181	1	9	9	NUM
iajs-153	181	2	.	.	X
iajs-153	181	3	levine.n	levine.n	PROPN
iajs-153	181	4	,	,	PUNCT
iajs-153	181	5	(	(	PUNCT
iajs-153	181	6	1970	1970	NUM
iajs-153	181	7	)	)	PUNCT
iajs-153	181	8	,	,	PUNCT
iajs-153	181	9	generalized	generalize	VERB
iajs-153	181	10	closed	closed	ADJ
iajs-153	181	11	sets	set	NOUN
iajs-153	181	12	in	in	ADP
iajs-153	181	13	topology	topology	NOUN
iajs-153	181	14	,	,	PUNCT
iajs-153	181	15	rend	rend	VERB
iajs-153	181	16	.circ	.circ	PROPN
iajs-153	181	17	.	.	PUNCT
iajs-153	182	1	math	math	NOUN
iajs-153	182	2	.	.	PUNCT
iajs-153	183	1	palermo,19	palermo,19	PROPN
iajs-153	183	2	,	,	PUNCT
iajs-153	183	3	89	89	NUM
iajs-153	183	4	96	96	NUM
iajs-153	183	5	.	.	PUNCT
iajs-153	184	1	10	10	NUM
iajs-153	184	2	.	.	PUNCT
iajs-153	185	1	levine.n	levine.n	PROPN
iajs-153	185	2	,	,	PUNCT
iajs-153	185	3	(	(	PUNCT
iajs-153	185	4	1963	1963	NUM
iajs-153	185	5	)	)	PUNCT
iajs-153	185	6	,	,	PUNCT
iajs-153	185	7	semi	semi	ADJ
iajs-153	185	8	-	-	ADJ
iajs-153	185	9	open	open	ADJ
iajs-153	185	10	sets	set	NOUN
iajs-153	185	11	and	and	CCONJ
iajs-153	185	12	semi	semi	ADJ
iajs-153	185	13	-	-	NOUN
iajs-153	185	14	continuity	continuity	NOUN
iajs-153	185	15	in	in	ADP
iajs-153	185	16	topological	topological	ADJ
iajs-153	185	17	spaces	space	NOUN
iajs-153	185	18	,	,	PUNCT
iajs-153	185	19	amer.math.monthly	amer.math.monthly	ADV
iajs-153	185	20	,	,	PUNCT
iajs-153	185	21	70	70	NUM
iajs-153	185	22	,	,	PUNCT
iajs-153	185	23	36	36	NUM
iajs-153	185	24	41	41	NUM
iajs-153	185	25	.	.	PUNCT
iajs-153	186	1	11	11	NUM
iajs-153	186	2	.	.	PUNCT
iajs-153	187	1	mashhour	mashhour	PROPN
iajs-153	187	2	.	.	PUNCT
iajs-153	187	3	a.	a.	PROPN
iajs-153	187	4	s	s	PROPN
iajs-153	187	5	,	,	PUNCT
iajs-153	187	6	;	;	PUNCT
iajs-153	187	7	abd	abd	PROPN
iajs-153	187	8	ei	ei	PROPN
iajs-153	187	9	-	-	PUNCT
iajs-153	187	10	monsef.m.e	monsef.m.e	NOUN
iajs-153	187	11	.	.	PUNCT
iajs-153	188	1	and	and	CCONJ
iajs-153	188	2	ei	ei	NOUN
iajs-153	188	3	-	-	PUNCT
iajs-153	188	4	deeb	deeb	PROPN
iajs-153	188	5	.	.	PUNCT
iajs-153	189	1	s.	s.	PROPN
iajs-153	189	2	n.	n.	PROPN
iajs-153	189	3	,	,	PUNCT
iajs-153	189	4	(	(	PUNCT
iajs-153	189	5	1982	1982	NUM
iajs-153	189	6	)	)	PUNCT
iajs-153	189	7	,	,	PUNCT
iajs-153	189	8	on	on	ADP
iajs-153	189	9	precontinuous	precontinuous	ADJ
iajs-153	189	10	and	and	CCONJ
iajs-153	189	11	weak	weak	ADJ
iajs-153	189	12	pre	pre	ADJ
iajs-153	189	13	-	-	ADJ
iajs-153	189	14	continuous	continuous	ADJ
iajs-153	189	15	mapping	mapping	NOUN
iajs-153	189	16	,	,	PUNCT
iajs-153	189	17	proc	proc	NOUN
iajs-153	189	18	.	.	PUNCT
iajs-153	190	1	math	math	NOUN
iajs-153	190	2	.	.	PUNCT
iajs-153	191	1	,	,	PUNCT
iajs-153	191	2	phys	phy	NOUN
iajs-153	191	3	.	.	PUNCT
iajs-153	191	4	soc	soc	PROPN
iajs-153	191	5	.	.	PUNCT
iajs-153	192	1	egypt	egypt	PROPN
iajs-153	192	2	,	,	PUNCT
iajs-153	192	3	53	53	NUM
iajs-153	192	4	,	,	PUNCT
iajs-153	192	5	47	47	NUM
iajs-153	192	6	–	–	SYM
iajs-153	192	7	53	53	NUM
iajs-153	192	8	.	.	NOUN
iajs-153	192	9	12	12	NUM
iajs-153	192	10	.	.	PUNCT
iajs-153	193	1	s.muthuvel	s.muthuvel	NOUN
iajs-153	193	2	and	and	CCONJ
iajs-153	193	3	r	r	NOUN
iajs-153	193	4	,	,	PUNCT
iajs-153	193	5	parimelazhagan	parimelazhagan	NOUN
iajs-153	193	6	,	,	PUNCT
iajs-153	193	7	(	(	PUNCT
iajs-153	193	8	2012	2012	NUM
iajs-153	193	9	)	)	PUNCT
iajs-153	193	10	b*-closed	b*-close	VERB
iajs-153	193	11	sets	set	NOUN
iajs-153	193	12	in	in	ADP
iajs-153	193	13	topological	topological	ADJ
iajs-153	193	14	spaces	space	NOUN
iajs-153	193	15	,	,	PUNCT
iajs-153	193	16	math	math	NOUN
iajs-153	193	17	.	.	PUNCT
iajs-153	194	1	j	j	PROPN
iajs-153	194	2	.	.	PUNCT
iajs-153	195	1	6	6	NUM
iajs-153	195	2	,	,	PUNCT
iajs-153	195	3	,	,	PUNCT
iajs-153	195	4	47,2317	47,2317	PROPN
iajs-153	195	5	-	-	SYM
iajs-153	195	6	2323	2323	NUM
iajs-153	195	7	.	.	PUNCT
iajs-153	196	1	13	13	NUM
iajs-153	196	2	.	.	X
iajs-153	196	3	njastad	njastad	NOUN
iajs-153	196	4	.	.	PUNCT
iajs-153	197	1	o	o	NOUN
iajs-153	197	2	,	,	PUNCT
iajs-153	197	3	(	(	PUNCT
iajs-153	197	4	1965	1965	NUM
iajs-153	197	5	)	)	PUNCT
iajs-153	197	6	,	,	PUNCT
iajs-153	197	7	on	on	ADP
iajs-153	197	8	some	some	DET
iajs-153	197	9	classes	class	NOUN
iajs-153	197	10	of	of	ADP
iajs-153	197	11	nearly	nearly	ADV
iajs-153	197	12	open	open	ADJ
iajs-153	197	13	sets	set	NOUN
iajs-153	197	14	,	,	PUNCT
iajs-153	197	15	pacific	pacific	PROPN
iajs-153	197	16	j.math	j.math	PROPN
iajs-153	197	17	.	.	PROPN
iajs-153	197	18	,	,	PUNCT
iajs-153	197	19	,	,	PUNCT
iajs-153	197	20	15	15	NUM
iajs-153	197	21	961	961	NUM
iajs-153	197	22	-	-	SYM
iajs-153	197	23	970	970	NUM
iajs-153	197	24	.	.	PUNCT
iajs-153	198	1	14	14	NUM
iajs-153	198	2	.	.	PUNCT
iajs-153	198	3	omari.a.a	omari.a.a	PROPN
iajs-153	198	4	and	and	CCONJ
iajs-153	198	5	noorani	noorani	PROPN
iajs-153	198	6	.m.s.m	.m.s.m	PROPN
iajs-153	198	7	,	,	PUNCT
iajs-153	198	8	on	on	ADP
iajs-153	198	9	generalized	generalized	ADJ
iajs-153	198	10	b	b	X
iajs-153	198	11	-	-	PUNCT
iajs-153	198	12	closed	closed	ADJ
iajs-153	198	13	sets	set	NOUN
iajs-153	198	14	,	,	PUNCT
iajs-153	198	15	bull	bull	NOUN
iajs-153	198	16	.	.	PUNCT
iajs-153	199	1	malays	malays	PROPN
iajs-153	199	2	.	.	PUNCT
iajs-153	200	1	math	math	NOUN
iajs-153	200	2	.	.	PUNCT
iajs-153	201	1	sci	sci	PROPN
iajs-153	201	2	.	.	PROPN
iajs-153	201	3	sco	sco	PROPN
iajs-153	201	4	.	.	PUNCT
iajs-153	202	1	(	(	PUNCT
iajs-153	202	2	2	2	NUM
iajs-153	202	3	)	)	PUNCT
iajs-153	202	4	32	32	NUM
iajs-153	202	5	(	(	PUNCT
iajs-153	202	6	1	1	NUM
iajs-153	202	7	)	)	PUNCT
iajs-153	202	8	(	(	PUNCT
iajs-153	202	9	2009	2009	NUM
iajs-153	202	10	)	)	PUNCT
iajs-153	202	11	,	,	PUNCT
iajs-153	202	12	19	19	NUM
iajs-153	202	13	-	-	SYM
iajs-153	202	14	36	36	NUM
iajs-153	202	15	.	.	PUNCT
iajs-153	203	1	15	15	NUM
iajs-153	203	2	.	.	PUNCT
iajs-153	204	1	sundaram	sundaram	PROPN
iajs-153	204	2	,	,	PUNCT
iajs-153	204	3	p.	p.	PROPN
iajs-153	204	4	and	and	CCONJ
iajs-153	204	5	shiek	shiek	PROPN
iajs-153	204	6	john	john	PROPN
iajs-153	204	7	,	,	PUNCT
iajs-153	204	8	m.	m.	NOUN
iajs-153	204	9	,	,	PUNCT
iajs-153	204	10	(	(	PUNCT
iajs-153	204	11	2000	2000	NUM
iajs-153	204	12	)	)	PUNCT
iajs-153	204	13	on	on	ADP
iajs-153	204	14	w	w	ADJ
iajs-153	204	15	-	-	PUNCT
iajs-153	204	16	closed	closed	ADJ
iajs-153	204	17	sets	set	NOUN
iajs-153	204	18	in	in	ADP
iajs-153	204	19	topology	topology	NOUN
iajs-153	204	20	,	,	PUNCT
iajs-153	204	21	acta	acta	PROPN
iajs-153	204	22	ciencia	ciencia	PROPN
iajs-153	204	23	indica	indica	PROPN
iajs-153	204	24	,	,	PUNCT
iajs-153	204	25	4,389	4,389	NUM
iajs-153	204	26	-	-	SYM
iajs-153	204	27	392	392	NUM
iajs-153	204	28	.	.	NOUN
iajs-153	204	29	213	213	NUM
iajs-153	204	30	|	|	NOUN
iajs-153	204	31	mathematics	mathematic	NOUN
iajs-153	204	32	2015	2015	NUM
iajs-153	204	33	)	)	PUNCT
iajs-153	204	34	عام	عام	ADP
iajs-153	204	35	3العدد	3العدد	NUM
iajs-153	204	36	(	(	PUNCT
iajs-153	204	37	28الھيثم	28الھيثم	NUM
iajs-153	204	38	للعلوم	للعلوم	PROPN
iajs-153	204	39	الصرفة	الصرفة	NOUN
iajs-153	204	40	و	و	PRON
iajs-153	204	41	التطبيقية	التطبيقية	ADV
iajs-153	204	42	المجلد	المجلد	ADV
iajs-153	204	43	مجلة	مجلة	VERB
iajs-153	204	44	إبن	إبن	VERB
iajs-153	204	45	ibn	ibn	PROPN
iajs-153	204	46	al	al	PROPN
iajs-153	204	47	-	-	PUNCT
iajs-153	204	48	haitham	haitham	PROPN
iajs-153	204	49	jour	jour	X
iajs-153	204	50	.	.	PROPN
iajs-153	204	51	for	for	ADP
iajs-153	204	52	pure	pure	ADJ
iajs-153	204	53	&	&	CCONJ
iajs-153	204	54	appl	appl	PROPN
iajs-153	204	55	.	.	PUNCT
iajs-153	205	1	sci	sci	PROPN
iajs-153	205	2	.	.	PUNCT
iajs-153	205	3	vol	vol	NOUN
iajs-153	205	4	.	.	PROPN
iajs-153	206	1	28	28	NUM
iajs-153	206	2	(	(	PUNCT
iajs-153	206	3	3	3	NUM
iajs-153	206	4	)	)	PUNCT
iajs-153	206	5	2015	2015	NUM
iajs-153	206	6	*	*	PUNCT
iajs-153	206	7	gb	gb	ADP
iajs-153	206	8	–	–	PUNCT
iajs-153	206	9	حول	حول	NOUN
iajs-153	206	10	المجموعات	المجموعات	PROPN
iajs-153	206	11	المغلقة	المغلقة	PROPN
iajs-153	206	12	بالنمط	بالنمط	NOUN
iajs-153	206	13	زينة	زينة	NOUN
iajs-153	206	14	طه	طه	PRON
iajs-153	206	15	الحويز	الحويز	ADV
iajs-153	206	16	قسم	قسم	PRON
iajs-153	206	17	الرياضيات	الرياضيات	PROPN
iajs-153	206	18	/كلية	/كلية	PROPN
iajs-153	206	19	التربية	التربية	PROPN
iajs-153	206	20	للبنات	للبنات	PROPN
iajs-153	206	21	/جامعة	/جامعة	PROPN
iajs-153	206	22	تكريت	تكريت	VERB
iajs-153	206	23	2015	2015	NUM
iajs-153	206	24	/	/	SYM
iajs-153	206	25	أيلول/20قبل	أيلول/20قبل	PROPN
iajs-153	206	26	البحث	البحث	VERB
iajs-153	206	27	في	في	PROPN
iajs-153	206	28	:	:	PUNCT
iajs-153	206	29	،	،	NOUN
iajs-153	206	30	2014	2014	NUM
iajs-153	206	31	/	/	SYM
iajs-153	206	32	كانون	كانون	NOUN
iajs-153	206	33	األول/22	األول/22	NOUN
iajs-153	206	34	:	:	PUNCT
iajs-153	206	35	استلم	استلم	PROPN
iajs-153	206	36	البحث	البحث	VERB
iajs-153	206	37	في	في	ADP
iajs-153	206	38	الخالصة	الخالصة	PROPN
iajs-153	206	39	*	*	PUNCT
iajs-153	206	40	gbدراسة	gbدراسة	PROPN
iajs-153	206	41	مفھوم	مفھوم	PROPN
iajs-153	206	42	جديد	جديد	PROPN
iajs-153	206	43	من	من	PROPN
iajs-153	206	44	المجموعات	المجموعات	PROPN
iajs-153	206	45	المغلقة	المغلقة	PROPN
iajs-153	206	46	يسمى	يسمى	PROPN
iajs-153	206	47	المجموعات	المجموعات	PROPN
iajs-153	206	48	المعممة	المعممة	PROPN
iajs-153	206	49	المغلقة	المغلقة	PROPN
iajs-153	206	50	يعرض	يعرض	PROPN
iajs-153	207	1	ھذا	ھذا	PROPN
iajs-153	207	2	البحث	البحث	VERB
iajs-153	207	3	كما	كما	PROPN
iajs-153	207	4	نقوم	نقوم	ADJ
iajs-153	207	5	بدراسة	بدراسة	NOUN
iajs-153	207	6	بعض	بعض	NOUN
iajs-153	207	7	الخصائص	الخصائص	VERB
iajs-153	207	8	األساسية	األساسية	PROPN
iajs-153	207	9	،	،	PROPN
iajs-153	207	10	ودراسة	ودراسة	PROPN
iajs-153	207	11	العالقات	العالقات	NOUN
iajs-153	207	12	بينھا	بينھا	NOUN
iajs-153	207	13	وبين	وبين	ADV
iajs-153	207	14	المجموعات	المجموعات	PROPN
iajs-153	207	15	المغلقة	المغلقة	PROPN
iajs-153	207	16	ةفي	ةفي	ADV
iajs-153	207	17	الفضاءات	الفضاءات	PROPN
iajs-153	207	18	التبولوجي	التبولوجي	PROPN
iajs-153	207	19	في	في	DET
iajs-153	207	20	الفضاء	الفضاء	PROPN
iajs-153	207	21	التبولوجي	التبولوجي	PROPN
iajs-153	207	22	.	.	PUNCT
iajs-153	208	1	:	:	PUNCT
iajs-153	208	2	والمجموعات	والمجموعات	ADJ
iajs-153	208	3	المعممة	المعممة	PROPN
iajs-153	208	4	المغلقة	المغلقة	PROPN
iajs-153	208	5	.	.	PUNCT
iajs-153	209	1	-bوالمجموعات	-bوالمجموعات	ADJ
iajs-153	209	2	المعممة	المعممة	NOUN
iajs-153	209	3	المغلقه	المغلقه	VERB
iajs-153	209	4	-*bالمجموعات	-*bالمجموعات	ADJ
iajs-153	209	5	المعممة	المعممة	PROPN
iajs-153	209	6	المغلقة	المغلقة	PROPN
iajs-153	209	7	:	:	PUNCT
iajs-153	209	8	الكلمات	الكلمات	VERB
iajs-153	209	9	ألمفتاحيه	ألمفتاحيه	NOUN