id	sid	tid	token	lemma	pos
iajs-319	1	1	microsoft	microsoft	PROPN
iajs-319	1	2	word	word	NOUN
iajs-319	1	3	55	55	NUM
iajs-319	1	4	542	542	NUM
iajs-319	1	5	|	|	NOUN
iajs-319	1	6	mathematics	mathematic	NOUN
iajs-319	1	7	2014	2014	NUM
iajs-319	1	8	)	)	PUNCT
iajs-319	1	9	عام	عام	ADP
iajs-319	1	10	3العدد	3العدد	NUM
iajs-319	1	11	(	(	PUNCT
iajs-319	1	12	27مجلة	27مجلة	NUM
iajs-319	1	13	إبن	إبن	VERB
iajs-319	1	14	الھيثم	الھيثم	NOUN
iajs-319	1	15	للعلوم	للعلوم	NOUN
iajs-319	1	16	الصرفة	الصرفة	NOUN
iajs-319	2	1	و	و	PRON
iajs-319	2	2	التطبيقية	التطبيقية	ADV
iajs-319	2	3	المجلد	المجلد	VERB
iajs-319	2	4	ibn	ibn	PROPN
iajs-319	2	5	al	al	PROPN
iajs-319	2	6	-	-	PUNCT
iajs-319	2	7	haitham	haitham	PROPN
iajs-319	2	8	jour	jour	X
iajs-319	2	9	.	.	PROPN
iajs-319	3	1	for	for	ADP
iajs-319	3	2	pure	pure	ADJ
iajs-319	3	3	&	&	CCONJ
iajs-319	3	4	appl	appl	PROPN
iajs-319	3	5	.	.	PUNCT
iajs-319	4	1	sci	sci	PROPN
iajs-319	4	2	.	.	PUNCT
iajs-319	4	3	vol	vol	NOUN
iajs-319	4	4	.	.	PROPN
iajs-319	5	1	27	27	NUM
iajs-319	5	2	(	(	PUNCT
iajs-319	5	3	3	3	NUM
iajs-319	5	4	)	)	PUNCT
iajs-319	5	5	2014	2014	NUM
iajs-319	5	6	on	on	ADP
iajs-319	5	7	s*g-	s*g-	NOUN
iajs-319	5	8	-open	-open	PROPN
iajs-319	5	9	sets	set	NOUN
iajs-319	5	10	in	in	ADP
iajs-319	5	11	topological	topological	ADJ
iajs-319	5	12	spaces	space	NOUN
iajs-319	6	1	sabiha	sabiha	PROPN
iajs-319	6	2	i.	i.	PROPN
iajs-319	6	3	mahmood	mahmood	PROPN
iajs-319	6	4	jumana	jumana	PROPN
iajs-319	6	5	s	s	PROPN
iajs-319	6	6	.tareq	.tareq	PROPN
iajs-319	6	7	department	department	PROPN
iajs-319	6	8	of	of	ADP
iajs-319	6	9	mathematics	mathematics	PROPN
iajs-319	6	10	/	/	SYM
iajs-319	6	11	college	college	NOUN
iajs-319	6	12	of	of	ADP
iajs-319	6	13	science/	science/	NUM
iajs-319	6	14	university	university	PROPN
iajs-319	6	15	of	of	ADP
iajs-319	6	16	al	al	PROPN
iajs-319	6	17	-	-	PUNCT
iajs-319	6	18	mustansiriyah	mustansiriyah	NOUN
iajs-319	6	19	received	receive	VERB
iajs-319	6	20	in	in	ADP
iajs-319	6	21	:	:	PUNCT
iajs-319	6	22	9	9	NUM
iajs-319	6	23	april	april	PROPN
iajs-319	6	24	2014	2014	NUM
iajs-319	6	25	,	,	PUNCT
iajs-319	6	26	accepted	accept	VERB
iajs-319	6	27	in	in	ADP
iajs-319	6	28	:	:	PUNCT
iajs-319	6	29	1	1	NUM
iajs-319	6	30	september	september	PROPN
iajs-319	6	31	2014	2014	NUM
iajs-319	6	32	abstract	abstract	NOUN
iajs-319	6	33	in	in	ADP
iajs-319	6	34	this	this	DET
iajs-319	6	35	paper	paper	NOUN
iajs-319	6	36	,	,	PUNCT
iajs-319	6	37	we	we	PRON
iajs-319	6	38	introduce	introduce	VERB
iajs-319	6	39	a	a	DET
iajs-319	6	40	new	new	ADJ
iajs-319	6	41	class	class	NOUN
iajs-319	6	42	of	of	ADP
iajs-319	6	43	sets	set	NOUN
iajs-319	6	44	,	,	PUNCT
iajs-319	6	45	namely	namely	ADV
iajs-319	6	46	,	,	PUNCT
iajs-319	6	47	s*g-	s*g-	NOUN
iajs-319	6	48	-open	-open	NOUN
iajs-319	6	49	sets	set	NOUN
iajs-319	6	50	and	and	CCONJ
iajs-319	6	51	we	we	PRON
iajs-319	6	52	show	show	VERB
iajs-319	6	53	that	that	SCONJ
iajs-319	6	54	the	the	DET
iajs-319	6	55	family	family	NOUN
iajs-319	6	56	of	of	ADP
iajs-319	6	57	all	all	DET
iajs-319	6	58	s*g-	s*g-	NOUN
iajs-319	6	59	-open	-open	ADJ
iajs-319	6	60	subsets	subset	NOUN
iajs-319	6	61	of	of	ADP
iajs-319	6	62	a	a	DET
iajs-319	6	63	topological	topological	ADJ
iajs-319	6	64	space	space	NOUN
iajs-319	6	65	)	)	PUNCT
iajs-319	6	66	,	,	PUNCT
iajs-319	6	67	x	x	X
iajs-319	6	68	(	(	PUNCT
iajs-319	6	69			PROPN
iajs-319	6	70	from	from	ADP
iajs-319	6	71	a	a	DET
iajs-319	6	72	topology	topology	NOUN
iajs-319	6	73	on	on	ADP
iajs-319	6	74	x	x	PUNCT
iajs-319	6	75	which	which	PRON
iajs-319	6	76	is	be	AUX
iajs-319	6	77	finer	fine	ADJ
iajs-319	6	78	than	than	ADP
iajs-319	6	79			PROPN
iajs-319	6	80	.	.	PUNCT
iajs-319	7	1	also	also	ADV
iajs-319	7	2	,	,	PUNCT
iajs-319	7	3	we	we	PRON
iajs-319	7	4	study	study	VERB
iajs-319	7	5	the	the	DET
iajs-319	7	6	characterizations	characterization	NOUN
iajs-319	7	7	and	and	CCONJ
iajs-319	7	8	basic	basic	ADJ
iajs-319	7	9	properties	property	NOUN
iajs-319	7	10	of	of	ADP
iajs-319	7	11	s*g-	s*g-	NOUN
iajs-319	7	12	open	open	ADJ
iajs-319	7	13	sets	set	NOUN
iajs-319	7	14	and	and	CCONJ
iajs-319	7	15	s*g-	s*g-	NOUN
iajs-319	7	16	-closed	-close	VERB
iajs-319	7	17	sets	set	NOUN
iajs-319	7	18	.	.	PUNCT
iajs-319	8	1	moreover	moreover	ADV
iajs-319	8	2	,	,	PUNCT
iajs-319	8	3	we	we	PRON
iajs-319	8	4	use	use	VERB
iajs-319	8	5	these	these	DET
iajs-319	8	6	sets	set	NOUN
iajs-319	8	7	to	to	PART
iajs-319	8	8	define	define	VERB
iajs-319	8	9	and	and	CCONJ
iajs-319	8	10	study	study	VERB
iajs-319	8	11	a	a	DET
iajs-319	8	12	new	new	ADJ
iajs-319	8	13	class	class	NOUN
iajs-319	8	14	of	of	ADP
iajs-319	8	15	functions	function	NOUN
iajs-319	8	16	,	,	PUNCT
iajs-319	8	17	namely	namely	ADV
iajs-319	8	18	,	,	PUNCT
iajs-319	8	19	s*g	s*g	ADJ
iajs-319	8	20	-continuous	-continuous	ADJ
iajs-319	8	21	functions	function	NOUN
iajs-319	8	22	and	and	CCONJ
iajs-319	8	23	s*g	s*g	NOUN
iajs-319	8	24	-irresolute	-irresolute	NOUN
iajs-319	8	25	functions	function	NOUN
iajs-319	8	26	in	in	ADP
iajs-319	8	27	topological	topological	ADJ
iajs-319	8	28	spaces	space	NOUN
iajs-319	8	29	.	.	PUNCT
iajs-319	9	1	some	some	DET
iajs-319	9	2	properties	property	NOUN
iajs-319	9	3	of	of	ADP
iajs-319	9	4	these	these	DET
iajs-319	9	5	functions	function	NOUN
iajs-319	9	6	have	have	AUX
iajs-319	9	7	been	be	AUX
iajs-319	9	8	studied	study	VERB
iajs-319	9	9	.	.	PUNCT
iajs-319	10	1	keywords	keyword	NOUN
iajs-319	10	2	:	:	PUNCT
iajs-319	10	3	s*g-	s*g-	NOUN
iajs-319	10	4	-open	-open	NOUN
iajs-319	10	5	sets	set	NOUN
iajs-319	10	6	,	,	PUNCT
iajs-319	10	7	s*g-	s*g-	NOUN
iajs-319	10	8	-closed	-close	VERB
iajs-319	10	9	sets	set	NOUN
iajs-319	10	10	,	,	PUNCT
iajs-319	10	11	s*g-	s*g-	NOUN
iajs-319	10	12	-clopen	-clopen	NOUN
iajs-319	10	13	sets	set	NOUN
iajs-319	10	14	,	,	PUNCT
iajs-319	10	15	s*g-	s*g-	NOUN
iajs-319	10	16	-continuous	-continuous	ADJ
iajs-319	10	17	functions	function	NOUN
iajs-319	10	18	,	,	PUNCT
iajs-319	10	19	s*g-	s*g-	NOUN
iajs-319	10	20	-irresolute	-irresolute	NOUN
iajs-319	10	21	functions	function	NOUN
iajs-319	10	22	.	.	PUNCT
iajs-319	11	1	543	543	NUM
iajs-319	11	2	|	|	NOUN
iajs-319	11	3	mathematics	mathematic	NOUN
iajs-319	11	4	2014	2014	NUM
iajs-319	11	5	)	)	PUNCT
iajs-319	11	6	عام	عام	ADP
iajs-319	11	7	3العدد	3العدد	NUM
iajs-319	11	8	(	(	PUNCT
iajs-319	11	9	27مجلة	27مجلة	NUM
iajs-319	11	10	إبن	إبن	VERB
iajs-319	11	11	الھيثم	الھيثم	NOUN
iajs-319	11	12	للعلوم	للعلوم	NOUN
iajs-319	11	13	الصرفة	الصرفة	NOUN
iajs-319	12	1	و	و	PRON
iajs-319	12	2	التطبيقية	التطبيقية	ADV
iajs-319	12	3	المجلد	المجلد	VERB
iajs-319	12	4	ibn	ibn	PROPN
iajs-319	12	5	al	al	PROPN
iajs-319	12	6	-	-	PUNCT
iajs-319	12	7	haitham	haitham	PROPN
iajs-319	12	8	jour	jour	X
iajs-319	12	9	.	.	PROPN
iajs-319	13	1	for	for	ADP
iajs-319	13	2	pure	pure	ADJ
iajs-319	13	3	&	&	CCONJ
iajs-319	13	4	appl	appl	PROPN
iajs-319	13	5	.	.	PUNCT
iajs-319	14	1	sci	sci	PROPN
iajs-319	14	2	.	.	PUNCT
iajs-319	14	3	vol	vol	NOUN
iajs-319	14	4	.	.	PROPN
iajs-319	15	1	27	27	NUM
iajs-319	15	2	(	(	PUNCT
iajs-319	15	3	3	3	NUM
iajs-319	15	4	)	)	PUNCT
iajs-319	15	5	2014	2014	NUM
iajs-319	15	6	introduction	introduction	NOUN
iajs-319	15	7	levine	levine	PROPN
iajs-319	15	8	,	,	PUNCT
iajs-319	15	9	n.	n.	NOUN
iajs-319	16	1	[	[	X
iajs-319	16	2	1,2	1,2	NUM
iajs-319	16	3	]	]	PUNCT
iajs-319	16	4	introduced	introduce	VERB
iajs-319	16	5	and	and	CCONJ
iajs-319	16	6	studied	study	VERB
iajs-319	16	7	semi	semi	ADJ
iajs-319	16	8	-	-	ADJ
iajs-319	16	9	open	open	ADJ
iajs-319	16	10	sets	set	NOUN
iajs-319	16	11	and	and	CCONJ
iajs-319	16	12	generalized	generalize	VERB
iajs-319	16	13	open	open	ADJ
iajs-319	16	14	sets	set	NOUN
iajs-319	16	15	respectively	respectively	ADV
iajs-319	16	16	.	.	PUNCT
iajs-319	17	1	njastad	njastad	NOUN
iajs-319	17	2	,	,	PUNCT
iajs-319	17	3	o.	o.	PROPN
iajs-319	18	1	[	[	X
iajs-319	18	2	3	3	X
iajs-319	18	3	]	]	PUNCT
iajs-319	18	4	,	,	PUNCT
iajs-319	18	5	mashhour	mashhour	X
iajs-319	18	6	,	,	PUNCT
iajs-319	18	7	a.s	a.s	PROPN
iajs-319	18	8	.	.	PROPN
iajs-319	18	9	and	and	CCONJ
iajs-319	18	10	et.al	et.al	ADJ
iajs-319	18	11	.	.	PUNCT
iajs-319	19	1	[	[	X
iajs-319	19	2	4	4	NUM
iajs-319	19	3	]	]	PUNCT
iajs-319	19	4	,	,	PUNCT
iajs-319	19	5	andrijevic	andrijevic	VERB
iajs-319	19	6	,	,	PUNCT
iajs-319	19	7	d.	d.	PROPN
iajs-319	20	1	[	[	X
iajs-319	20	2	5	5	NUM
iajs-319	20	3	]	]	PUNCT
iajs-319	20	4	and	and	CCONJ
iajs-319	20	5	abd	abd	PROPN
iajs-319	20	6	elmonsef	elmonsef	PROPN
iajs-319	20	7	,	,	PUNCT
iajs-319	20	8	m.e	m.e	PROPN
iajs-319	20	9	.	.	PROPN
iajs-319	20	10	and	and	CCONJ
iajs-319	20	11	et.al	et.al	VERB
iajs-319	20	12	[	[	X
iajs-319	20	13	6	6	NUM
iajs-319	20	14	]	]	PUNCT
iajs-319	20	15	introduced	introduce	VERB
iajs-319	20	16	α	α	X
iajs-319	20	17	-	-	ADJ
iajs-319	20	18	open	open	ADJ
iajs-319	20	19	sets	set	NOUN
iajs-319	20	20	,	,	PUNCT
iajs-319	20	21	pre	pre	ADJ
iajs-319	20	22	-	-	ADJ
iajs-319	20	23	open	open	ADJ
iajs-319	20	24	sets	set	NOUN
iajs-319	20	25	,	,	PUNCT
iajs-319	20	26	b	b	X
iajs-319	20	27	-	-	PUNCT
iajs-319	20	28	open	open	ADJ
iajs-319	20	29	sets	set	NOUN
iajs-319	20	30	and	and	SYM
iajs-319	20	31	-open	-open	ADJ
iajs-319	20	32	sets	set	NOUN
iajs-319	20	33	respectively	respectively	ADV
iajs-319	20	34	.	.	PUNCT
iajs-319	21	1	also	also	ADV
iajs-319	21	2	,	,	PUNCT
iajs-319	21	3	arya	arya	PROPN
iajs-319	21	4	,	,	PUNCT
iajs-319	21	5	s.p	s.p	PROPN
iajs-319	21	6	.	.	PROPN
iajs-319	21	7	and	and	CCONJ
iajs-319	21	8	nour	nour	PROPN
iajs-319	21	9	,	,	PUNCT
iajs-319	21	10	t.m	t.m	PROPN
iajs-319	21	11	.	.	PUNCT
iajs-319	22	1	[	[	X
iajs-319	22	2	7	7	NUM
iajs-319	22	3	]	]	PUNCT
iajs-319	22	4	,	,	PUNCT
iajs-319	22	5	maki	maki	PROPN
iajs-319	22	6	,	,	PUNCT
iajs-319	22	7	h.	h.	PROPN
iajs-319	22	8	and	and	CCONJ
iajs-319	22	9	et.al	et.al	PROPN
iajs-319	23	1	[	[	X
iajs-319	23	2	8,9	8,9	NUM
iajs-319	23	3	]	]	PUNCT
iajs-319	23	4	,	,	PUNCT
iajs-319	23	5	khan	khan	PROPN
iajs-319	23	6	,	,	PUNCT
iajs-319	23	7	m.	m.	NOUN
iajs-319	23	8	and	and	CCONJ
iajs-319	23	9	et.al	et.al	VERB
iajs-319	24	1	[	[	X
iajs-319	24	2	10	10	NUM
iajs-319	24	3	]	]	PUNCT
iajs-319	24	4	introduced	introduce	VERB
iajs-319	24	5	and	and	CCONJ
iajs-319	24	6	investigated	investigate	VERB
iajs-319	24	7	generalized	generalize	VERB
iajs-319	24	8	semi	semi	ADJ
iajs-319	24	9	open	open	ADJ
iajs-319	24	10	sets	set	NOUN
iajs-319	24	11	,	,	PUNCT
iajs-319	24	12	generalized	generalized	ADJ
iajs-319	24	13	α	α	NOUN
iajs-319	24	14	-	-	ADJ
iajs-319	24	15	open	open	ADJ
iajs-319	24	16	sets	set	NOUN
iajs-319	24	17	,	,	PUNCT
iajs-319	24	18	αgeneralized	αgeneralize	VERB
iajs-319	24	19	open	open	ADJ
iajs-319	24	20	sets	set	NOUN
iajs-319	24	21	and	and	CCONJ
iajs-319	24	22	s*g	s*g	VERB
iajs-319	24	23	-	-	PUNCT
iajs-319	24	24	open	open	ADJ
iajs-319	24	25	sets	set	NOUN
iajs-319	24	26	respectively	respectively	ADV
iajs-319	24	27	.	.	PUNCT
iajs-319	25	1	in	in	ADP
iajs-319	25	2	this	this	DET
iajs-319	25	3	paper	paper	NOUN
iajs-319	25	4	,	,	PUNCT
iajs-319	25	5	we	we	PRON
iajs-319	25	6	introduce	introduce	VERB
iajs-319	25	7	a	a	DET
iajs-319	25	8	new	new	ADJ
iajs-319	25	9	class	class	NOUN
iajs-319	25	10	of	of	ADP
iajs-319	25	11	sets	set	NOUN
iajs-319	25	12	,	,	PUNCT
iajs-319	25	13	namely	namely	ADV
iajs-319	25	14	,	,	PUNCT
iajs-319	25	15	s*g-	s*g-	NOUN
iajs-319	25	16	-open	-open	NOUN
iajs-319	25	17	sets	set	NOUN
iajs-319	25	18	and	and	CCONJ
iajs-319	25	19	we	we	PRON
iajs-319	25	20	show	show	VERB
iajs-319	25	21	that	that	SCONJ
iajs-319	25	22	the	the	DET
iajs-319	25	23	family	family	NOUN
iajs-319	25	24	of	of	ADP
iajs-319	25	25	all	all	DET
iajs-319	25	26	s*g-	s*g-	NOUN
iajs-319	25	27	-open	-open	ADJ
iajs-319	25	28	subsets	subset	NOUN
iajs-319	25	29	of	of	ADP
iajs-319	25	30	a	a	DET
iajs-319	25	31	topological	topological	ADJ
iajs-319	25	32	space	space	NOUN
iajs-319	25	33	)	)	PUNCT
iajs-319	25	34	,	,	PUNCT
iajs-319	25	35	x	x	X
iajs-319	25	36	(	(	PUNCT
iajs-319	25	37			PROPN
iajs-319	25	38	from	from	ADP
iajs-319	25	39	a	a	DET
iajs-319	25	40	topology	topology	NOUN
iajs-319	25	41	on	on	ADP
iajs-319	25	42	x	x	PUNCT
iajs-319	25	43	which	which	PRON
iajs-319	25	44	is	be	AUX
iajs-319	25	45	finer	fine	ADJ
iajs-319	25	46	than	than	ADP
iajs-319	25	47			PROPN
iajs-319	25	48	.	.	PUNCT
iajs-319	26	1	this	this	DET
iajs-319	26	2	class	class	NOUN
iajs-319	26	3	of	of	ADP
iajs-319	26	4	open	open	ADJ
iajs-319	26	5	sets	set	NOUN
iajs-319	26	6	is	be	AUX
iajs-319	26	7	placed	place	VERB
iajs-319	26	8	properly	properly	ADV
iajs-319	26	9	between	between	ADP
iajs-319	26	10	the	the	DET
iajs-319	26	11	class	class	NOUN
iajs-319	26	12	of	of	ADP
iajs-319	26	13	open	open	ADJ
iajs-319	26	14	sets	set	NOUN
iajs-319	26	15	and	and	CCONJ
iajs-319	26	16	each	each	PRON
iajs-319	26	17	of	of	ADP
iajs-319	26	18	semi	semi	ADJ
iajs-319	26	19	-	-	ADJ
iajs-319	26	20	open	open	ADJ
iajs-319	26	21	sets	set	NOUN
iajs-319	26	22	,	,	PUNCT
iajs-319	26	23	α	α	NOUN
iajs-319	26	24	-	-	ADJ
iajs-319	26	25	open	open	ADJ
iajs-319	26	26	sets	set	NOUN
iajs-319	26	27	,	,	PUNCT
iajs-319	26	28	preopen	preopen	ADJ
iajs-319	26	29	sets	set	NOUN
iajs-319	26	30	,	,	PUNCT
iajs-319	26	31	b	b	X
iajs-319	26	32	-	-	PUNCT
iajs-319	26	33	open	open	ADJ
iajs-319	26	34	sets,	sets,	PROPN
iajs-319	26	35	-open	-open	PROPN
iajs-319	26	36	sets	set	NOUN
iajs-319	26	37	,	,	PUNCT
iajs-319	26	38	generalized	generalize	VERB
iajs-319	26	39	semi	semi	ADV
iajs-319	26	40	open	open	ADJ
iajs-319	26	41	sets	set	NOUN
iajs-319	26	42	,	,	PUNCT
iajs-319	26	43	generalized	generalized	ADJ
iajs-319	26	44	α	α	NOUN
iajs-319	26	45	-	-	ADJ
iajs-319	26	46	open	open	ADJ
iajs-319	26	47	sets	set	NOUN
iajs-319	26	48	and	and	CCONJ
iajs-319	26	49	αgeneralized	αgeneralize	VERB
iajs-319	26	50	open	open	ADJ
iajs-319	26	51	sets	set	NOUN
iajs-319	26	52	respectively	respectively	ADV
iajs-319	26	53	.	.	PUNCT
iajs-319	27	1	also	also	ADV
iajs-319	27	2	,	,	PUNCT
iajs-319	27	3	we	we	PRON
iajs-319	27	4	study	study	VERB
iajs-319	27	5	the	the	DET
iajs-319	27	6	characterizations	characterization	NOUN
iajs-319	27	7	and	and	CCONJ
iajs-319	27	8	basic	basic	ADJ
iajs-319	27	9	properties	property	NOUN
iajs-319	27	10	of	of	ADP
iajs-319	27	11	s*g-	s*g-	NOUN
iajs-319	27	12	-open	-open	NOUN
iajs-319	27	13	sets	set	NOUN
iajs-319	27	14	and	and	CCONJ
iajs-319	27	15	s*g-	s*g-	NOUN
iajs-319	27	16	-closed	-close	VERB
iajs-319	27	17	sets	set	NOUN
iajs-319	27	18	.	.	PUNCT
iajs-319	28	1	moreover	moreover	ADV
iajs-319	28	2	,	,	PUNCT
iajs-319	28	3	we	we	PRON
iajs-319	28	4	use	use	VERB
iajs-319	28	5	these	these	DET
iajs-319	28	6	sets	set	NOUN
iajs-319	28	7	to	to	PART
iajs-319	28	8	define	define	VERB
iajs-319	28	9	and	and	CCONJ
iajs-319	28	10	study	study	VERB
iajs-319	28	11	a	a	DET
iajs-319	28	12	new	new	ADJ
iajs-319	28	13	class	class	NOUN
iajs-319	28	14	of	of	ADP
iajs-319	28	15	functions	function	NOUN
iajs-319	28	16	,	,	PUNCT
iajs-319	28	17	namely	namely	ADV
iajs-319	28	18	,	,	PUNCT
iajs-319	28	19	s*g-	s*g-	NOUN
iajs-319	28	20	-continuous	-continuous	ADJ
iajs-319	28	21	functions	function	NOUN
iajs-319	28	22	and	and	CCONJ
iajs-319	28	23	s*g-	s*g-	NOUN
iajs-319	28	24	-irresolute	-irresolute	PROPN
iajs-319	28	25	functions	function	NOUN
iajs-319	28	26	in	in	ADP
iajs-319	28	27	topological	topological	ADJ
iajs-319	28	28	spaces	space	NOUN
iajs-319	28	29	.	.	PUNCT
iajs-319	29	1	some	some	DET
iajs-319	29	2	properties	property	NOUN
iajs-319	29	3	of	of	ADP
iajs-319	29	4	these	these	DET
iajs-319	29	5	functions	function	NOUN
iajs-319	29	6	have	have	AUX
iajs-319	29	7	been	be	AUX
iajs-319	29	8	studied	study	VERB
iajs-319	29	9	.	.	PUNCT
iajs-319	30	1	throughout	throughout	ADP
iajs-319	30	2	this	this	DET
iajs-319	30	3	paper	paper	NOUN
iajs-319	30	4	)	)	PUNCT
iajs-319	30	5	,	,	PUNCT
iajs-319	30	6	x	x	X
iajs-319	30	7	(	(	PUNCT
iajs-319	30	8			NOUN
iajs-319	30	9	,	,	PUNCT
iajs-319	30	10	)	)	PUNCT
iajs-319	30	11	,	,	PUNCT
iajs-319	30	12	y	y	PROPN
iajs-319	30	13	(	(	PUNCT
iajs-319	30	14			PROPN
iajs-319	30	15	and	and	CCONJ
iajs-319	30	16	)	)	PUNCT
iajs-319	30	17	,	,	PUNCT
iajs-319	30	18	z	z	X
iajs-319	30	19	(	(	PUNCT
iajs-319	30	20			PUNCT
iajs-319	30	21	(	(	PUNCT
iajs-319	30	22	or	or	CCONJ
iajs-319	30	23	simply	simply	ADV
iajs-319	30	24	x	x	SYM
iajs-319	30	25	,	,	PUNCT
iajs-319	30	26	y	y	PROPN
iajs-319	30	27	and	and	CCONJ
iajs-319	30	28	z	z	PROPN
iajs-319	30	29	)	)	PUNCT
iajs-319	30	30	represent	represent	VERB
iajs-319	30	31	non	non	ADJ
iajs-319	30	32	-	-	ADJ
iajs-319	30	33	empty	empty	ADJ
iajs-319	30	34	topological	topological	ADJ
iajs-319	30	35	spaces	space	NOUN
iajs-319	30	36	on	on	ADP
iajs-319	30	37	which	which	PRON
iajs-319	30	38	no	no	DET
iajs-319	30	39	separation	separation	NOUN
iajs-319	30	40	axioms	axiom	NOUN
iajs-319	30	41	are	be	AUX
iajs-319	30	42	assumed	assume	VERB
iajs-319	30	43	,	,	PUNCT
iajs-319	30	44	unless	unless	SCONJ
iajs-319	30	45	otherwise	otherwise	ADV
iajs-319	30	46	mentioned	mention	VERB
iajs-319	30	47	.	.	PUNCT
iajs-319	31	1	1.preliminaries	1.preliminaries	NUM
iajs-319	31	2	first	first	ADV
iajs-319	31	3	we	we	PRON
iajs-319	31	4	recall	recall	VERB
iajs-319	31	5	the	the	DET
iajs-319	31	6	following	follow	VERB
iajs-319	31	7	definitions	definition	NOUN
iajs-319	31	8	and	and	CCONJ
iajs-319	31	9	theorems	theorem	NOUN
iajs-319	31	10	.	.	PUNCT
iajs-319	32	1	definition(1.1	definition(1.1	NOUN
iajs-319	32	2	):	):	PUNCT
iajs-319	32	3	a	a	DET
iajs-319	32	4	subset	subset	NOUN
iajs-319	32	5	a	a	PRON
iajs-319	32	6	of	of	ADP
iajs-319	32	7	a	a	DET
iajs-319	32	8	topological	topological	ADJ
iajs-319	32	9	space	space	NOUN
iajs-319	32	10	)	)	PUNCT
iajs-319	32	11	,	,	PUNCT
iajs-319	32	12	x	x	X
iajs-319	32	13	(	(	PUNCT
iajs-319	32	14			NOUN
iajs-319	32	15	is	be	AUX
iajs-319	32	16	said	say	VERB
iajs-319	32	17	to	to	PART
iajs-319	32	18	be	be	AUX
iajs-319	32	19	:	:	PUNCT
iajs-319	32	20	i	i	X
iajs-319	32	21	)	)	PUNCT
iajs-319	32	22	an	an	DET
iajs-319	32	23	semi	semi	ADJ
iajs-319	32	24	-	-	ADJ
iajs-319	32	25	open	open	ADJ
iajs-319	32	26	(	(	PUNCT
iajs-319	32	27	briefly	briefly	NOUN
iajs-319	32	28	s	s	NOUN
iajs-319	32	29	-	-	ADJ
iajs-319	32	30	open	open	ADJ
iajs-319	32	31	)	)	PUNCT
iajs-319	32	32	set	set	VERB
iajs-319	32	33	[	[	X
iajs-319	32	34	1	1	X
iajs-319	32	35	]	]	PUNCT
iajs-319	32	36	if	if	SCONJ
iajs-319	32	37	)	)	PUNCT
iajs-319	32	38	)	)	PUNCT
iajs-319	32	39	a(int(cla	a(int(cla	VERB
iajs-319	32	40			PROPN
iajs-319	32	41	.	.	PUNCT
iajs-319	33	1	ii	ii	PROPN
iajs-319	33	2	)	)	PUNCT
iajs-319	33	3	an	an	DET
iajs-319	33	4	α	α	ADV
iajs-319	33	5	-	-	ADJ
iajs-319	33	6	open	open	ADJ
iajs-319	33	7	set	set	NOUN
iajs-319	33	8	[	[	X
iajs-319	33	9	3	3	X
iajs-319	33	10	]	]	PUNCT
iajs-319	33	11	if	if	SCONJ
iajs-319	33	12	)	)	PUNCT
iajs-319	33	13	)	)	PUNCT
iajs-319	33	14	)	)	PUNCT
iajs-319	33	15	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	33	16			PROPN
iajs-319	33	17	.	.	PUNCT
iajs-319	34	1	iii	iii	X
iajs-319	34	2	)	)	PUNCT
iajs-319	34	3	an	an	DET
iajs-319	34	4	pre	pre	ADJ
iajs-319	34	5	-	-	ADJ
iajs-319	34	6	open	open	ADJ
iajs-319	34	7	set	set	NOUN
iajs-319	34	8	[	[	X
iajs-319	34	9	4	4	X
iajs-319	34	10	]	]	X
iajs-319	34	11	if	if	SCONJ
iajs-319	34	12	)	)	PUNCT
iajs-319	34	13	)	)	PUNCT
iajs-319	35	1	a(clint(a	a(clint(a	CCONJ
iajs-319	35	2			PROPN
iajs-319	35	3	.	.	PUNCT
iajs-319	36	1	iv	iv	X
iajs-319	36	2	)	)	PUNCT
iajs-319	36	3	an	an	DET
iajs-319	36	4	b	b	NOUN
iajs-319	36	5	-	-	PUNCT
iajs-319	36	6	open	open	ADJ
iajs-319	36	7	set	set	NOUN
iajs-319	36	8	[	[	X
iajs-319	36	9	5	5	NUM
iajs-319	36	10	]	]	PUNCT
iajs-319	36	11	if	if	SCONJ
iajs-319	36	12	)	)	PUNCT
iajs-319	36	13	)	)	PUNCT
iajs-319	36	14	a(int(cl))a(clint(a	a(int(cl))a(clint(a	PROPN
iajs-319	36	15			PROPN
iajs-319	36	16	.	.	PUNCT
iajs-319	37	1	v	v	X
iajs-319	37	2	)	)	PUNCT
iajs-319	37	3	an	an	NOUN
iajs-319	37	4	-open	-open	NOUN
iajs-319	37	5	set	set	ADJ
iajs-319	37	6	[	[	X
iajs-319	37	7	6	6	NUM
iajs-319	37	8	]	]	PUNCT
iajs-319	37	9	if	if	SCONJ
iajs-319	37	10	)	)	PUNCT
iajs-319	37	11	)	)	PUNCT
iajs-319	37	12	)	)	PUNCT
iajs-319	38	1	a(cl(int(cla	a(cl(int(cla	NOUN
iajs-319	38	2			PROPN
iajs-319	38	3	.	.	PUNCT
iajs-319	39	1	the	the	DET
iajs-319	39	2	semi	semi	NOUN
iajs-319	39	3	-	-	ADJ
iajs-319	39	4	closure	closure	ADJ
iajs-319	39	5	(	(	PUNCT
iajs-319	39	6	resp	resp	NOUN
iajs-319	39	7	.	.	PUNCT
iajs-319	40	1	α	α	X
iajs-319	40	2	-	-	NOUN
iajs-319	40	3	closure	closure	NOUN
iajs-319	40	4	)	)	PUNCT
iajs-319	40	5	of	of	ADP
iajs-319	40	6	a	a	DET
iajs-319	40	7	subset	subset	NOUN
iajs-319	40	8	a	a	PRON
iajs-319	40	9	of	of	ADP
iajs-319	40	10	a	a	DET
iajs-319	40	11	topological	topological	ADJ
iajs-319	40	12	space	space	NOUN
iajs-319	40	13	)	)	PUNCT
iajs-319	40	14	,	,	PUNCT
iajs-319	40	15	x	x	X
iajs-319	40	16	(	(	PUNCT
iajs-319	40	17			NOUN
iajs-319	40	18	is	be	AUX
iajs-319	40	19	the	the	DET
iajs-319	40	20	intersection	intersection	NOUN
iajs-319	40	21	of	of	ADP
iajs-319	40	22	all	all	PRON
iajs-319	40	23	semi	semi	ADJ
iajs-319	40	24	-	-	ADJ
iajs-319	40	25	closed	closed	ADJ
iajs-319	40	26	(	(	PUNCT
iajs-319	40	27	resp	resp	NOUN
iajs-319	40	28	.	.	PUNCT
iajs-319	41	1	α	α	X
iajs-319	41	2	-	-	PUNCT
iajs-319	41	3	closed	closed	ADJ
iajs-319	41	4	)	)	PUNCT
iajs-319	41	5	sets	set	NOUN
iajs-319	41	6	which	which	PRON
iajs-319	41	7	contains	contain	VERB
iajs-319	41	8	a	a	PRON
iajs-319	41	9	and	and	CCONJ
iajs-319	41	10	is	be	AUX
iajs-319	41	11	denoted	denote	VERB
iajs-319	41	12	by	by	ADP
iajs-319	41	13	)	)	PUNCT
iajs-319	41	14	a(cls	a(cls	NOUN
iajs-319	41	15	(	(	PUNCT
iajs-319	41	16	resp	resp	NOUN
iajs-319	41	17	.	.	PUNCT
iajs-319	42	1	)	)	PUNCT
iajs-319	42	2	a(cl	a(cl	PROPN
iajs-319	42	3	)	)	PUNCT
iajs-319	42	4	.	.	PUNCT
iajs-319	43	1	clearly	clearly	ADV
iajs-319	43	2	)	)	PUNCT
iajs-319	43	3	a(cl)a(cl)a(cls	a(cl)a(cl)a(cls	PROPN
iajs-319	43	4			PRON
iajs-319	43	5			PROPN
iajs-319	43	6	.	.	PUNCT
iajs-319	44	1	definition(1.2	definition(1.2	ADJ
iajs-319	44	2	):	):	PUNCT
iajs-319	44	3	a	a	DET
iajs-319	44	4	subset	subset	NOUN
iajs-319	44	5	a	a	PRON
iajs-319	44	6	of	of	ADP
iajs-319	44	7	a	a	DET
iajs-319	44	8	topological	topological	ADJ
iajs-319	44	9	space	space	NOUN
iajs-319	44	10	)	)	PUNCT
iajs-319	44	11	,	,	PUNCT
iajs-319	44	12	x	x	X
iajs-319	44	13	(	(	PUNCT
iajs-319	44	14			NOUN
iajs-319	44	15	is	be	AUX
iajs-319	44	16	said	say	VERB
iajs-319	44	17	to	to	PART
iajs-319	44	18	be	be	AUX
iajs-319	44	19	:	:	PUNCT
iajs-319	44	20	i	i	X
iajs-319	44	21	)	)	PUNCT
iajs-319	44	22	a	a	DET
iajs-319	44	23	generalized	generalize	VERB
iajs-319	44	24	closed	close	VERB
iajs-319	44	25	(	(	PUNCT
iajs-319	44	26	briefly	briefly	NOUN
iajs-319	44	27	g	g	NOUN
iajs-319	44	28	-	-	PUNCT
iajs-319	44	29	closed	closed	ADJ
iajs-319	44	30	)	)	PUNCT
iajs-319	44	31	set	set	NOUN
iajs-319	44	32	[	[	X
iajs-319	44	33	2	2	NUM
iajs-319	44	34	]	]	PUNCT
iajs-319	44	35	if	if	SCONJ
iajs-319	44	36	u)a(cl	u)a(cl	PRON
iajs-319	44	37			PROPN
iajs-319	44	38	whenever	whenever	SCONJ
iajs-319	44	39	ua	ua	PROPN
iajs-319	44	40			PROPN
iajs-319	44	41	and	and	CCONJ
iajs-319	44	42	u	u	NOUN
iajs-319	44	43	is	be	AUX
iajs-319	44	44	open	open	ADJ
iajs-319	44	45	in	in	ADP
iajs-319	44	46	x	x	X
iajs-319	44	47	.	.	PUNCT
iajs-319	45	1	ii	ii	PROPN
iajs-319	45	2	)	)	PUNCT
iajs-319	45	3	a	a	DET
iajs-319	45	4	generalized	generalized	ADJ
iajs-319	45	5	semi	semi	ADJ
iajs-319	45	6	-	-	ADJ
iajs-319	45	7	closed	closed	ADJ
iajs-319	45	8	(	(	PUNCT
iajs-319	45	9	briefly	briefly	NOUN
iajs-319	45	10	gs	gs	NOUN
iajs-319	45	11	-	-	PUNCT
iajs-319	45	12	closed	closed	ADJ
iajs-319	45	13	)	)	PUNCT
iajs-319	45	14	set	set	NOUN
iajs-319	45	15	[	[	X
iajs-319	45	16	7	7	X
iajs-319	45	17	]	]	X
iajs-319	45	18	if	if	SCONJ
iajs-319	45	19	u)a(cls	u)a(cl	NOUN
iajs-319	45	20			PROPN
iajs-319	45	21	whenever	whenever	SCONJ
iajs-319	45	22	ua	ua	PROPN
iajs-319	45	23			PROPN
iajs-319	45	24	and	and	CCONJ
iajs-319	45	25	u	u	NOUN
iajs-319	45	26	is	be	AUX
iajs-319	45	27	open	open	ADJ
iajs-319	45	28	in	in	ADP
iajs-319	45	29	x	x	X
iajs-319	45	30	.	.	PUNCT
iajs-319	46	1	iii	iii	X
iajs-319	46	2	)	)	PUNCT
iajs-319	46	3	a	a	DET
iajs-319	46	4	generalized	generalized	ADJ
iajs-319	46	5	α	α	NOUN
iajs-319	46	6	-	-	ADJ
iajs-319	46	7	closed	closed	ADJ
iajs-319	46	8	(	(	PUNCT
iajs-319	46	9	briefly	briefly	NOUN
iajs-319	46	10	gα	gα	NOUN
iajs-319	46	11	-	-	PUNCT
iajs-319	46	12	closed	closed	ADJ
iajs-319	46	13	)	)	PUNCT
iajs-319	46	14	set	set	NOUN
iajs-319	46	15	[	[	X
iajs-319	46	16	8	8	NUM
iajs-319	46	17	]	]	PUNCT
iajs-319	46	18	if	if	SCONJ
iajs-319	46	19	u)a(cl	u)a(cl	NUM
iajs-319	46	20			NOUN
iajs-319	47	1	whenever	whenever	SCONJ
iajs-319	47	2	ua	ua	PROPN
iajs-319	47	3			PROPN
iajs-319	47	4	and	and	CCONJ
iajs-319	47	5	u	u	NOUN
iajs-319	47	6	is	be	AUX
iajs-319	47	7	α	α	NOUN
iajs-319	47	8	-	-	NOUN
iajs-319	47	9	open	open	ADJ
iajs-319	47	10	in	in	ADP
iajs-319	47	11	x	x	X
iajs-319	47	12	.	.	PUNCT
iajs-319	47	13	iv	iv	X
iajs-319	47	14	)	)	PUNCT
iajs-319	47	15	an	an	DET
iajs-319	47	16	α	α	ADV
iajs-319	47	17	-	-	PUNCT
iajs-319	47	18	generalized	generalize	VERB
iajs-319	47	19	closed	close	VERB
iajs-319	47	20	(	(	PUNCT
iajs-319	47	21	briefly	briefly	ADV
iajs-319	47	22	αg	αg	NOUN
iajs-319	47	23	-	-	PUNCT
iajs-319	47	24	closed	closed	ADJ
iajs-319	47	25	)	)	PUNCT
iajs-319	47	26	set	set	NOUN
iajs-319	47	27	[	[	X
iajs-319	47	28	9	9	NUM
iajs-319	47	29	]	]	PUNCT
iajs-319	47	30	if	if	SCONJ
iajs-319	47	31	u)a(cl	u)a(cl	NUM
iajs-319	47	32			NOUN
iajs-319	47	33	whenever	whenever	SCONJ
iajs-319	47	34	ua	ua	PROPN
iajs-319	47	35			PROPN
iajs-319	47	36	and	and	CCONJ
iajs-319	47	37	u	u	NOUN
iajs-319	47	38	is	be	AUX
iajs-319	47	39	open	open	ADJ
iajs-319	47	40	in	in	ADP
iajs-319	47	41	x	x	X
iajs-319	47	42	.	.	PUNCT
iajs-319	48	1	v	v	X
iajs-319	48	2	)	)	PUNCT
iajs-319	48	3	an	an	DET
iajs-319	48	4	s*g	s*g	NOUN
iajs-319	48	5	-	-	PUNCT
iajs-319	48	6	closed	close	VERB
iajs-319	48	7	set	set	NOUN
iajs-319	48	8	[	[	X
iajs-319	48	9	10	10	NUM
iajs-319	48	10	]	]	X
iajs-319	48	11	if	if	SCONJ
iajs-319	48	12	u)a(cl	u)a(cl	PRON
iajs-319	48	13			PROPN
iajs-319	48	14	whenever	whenever	SCONJ
iajs-319	48	15	ua	ua	PROPN
iajs-319	48	16			PROPN
iajs-319	48	17	and	and	CCONJ
iajs-319	48	18	u	u	NOUN
iajs-319	48	19	is	be	AUX
iajs-319	48	20	semi	semi	ADJ
iajs-319	48	21	-	-	ADJ
iajs-319	48	22	open	open	ADJ
iajs-319	48	23	in	in	ADP
iajs-319	48	24	x	x	X
iajs-319	48	25	.	.	PUNCT
iajs-319	49	1	the	the	DET
iajs-319	49	2	complement	complement	NOUN
iajs-319	49	3	of	of	ADP
iajs-319	49	4	a	a	DET
iajs-319	49	5	g	g	NOUN
iajs-319	49	6	-	-	PUNCT
iajs-319	49	7	closed	closed	ADJ
iajs-319	49	8	(	(	PUNCT
iajs-319	49	9	resp	resp	NOUN
iajs-319	49	10	.	.	PUNCT
iajs-319	50	1	gs	gs	NOUN
iajs-319	50	2	-	-	PUNCT
iajs-319	50	3	closed	closed	ADJ
iajs-319	50	4	,	,	PUNCT
iajs-319	50	5	gα	gα	NOUN
iajs-319	50	6	-	-	PUNCT
iajs-319	50	7	closed	closed	ADJ
iajs-319	50	8	,	,	PUNCT
iajs-319	50	9	αg	αg	NOUN
iajs-319	50	10	-	-	PUNCT
iajs-319	50	11	closed	closed	ADJ
iajs-319	50	12	,	,	PUNCT
iajs-319	50	13	s*g	s*g	NOUN
iajs-319	50	14	-	-	PUNCT
iajs-319	50	15	closed	closed	ADJ
iajs-319	50	16	)	)	PUNCT
iajs-319	50	17	set	set	NOUN
iajs-319	50	18	is	be	AUX
iajs-319	50	19	called	call	VERB
iajs-319	50	20	a	a	DET
iajs-319	50	21	g	g	NOUN
iajs-319	50	22	-	-	PUNCT
iajs-319	50	23	open	open	ADJ
iajs-319	50	24	(	(	PUNCT
iajs-319	50	25	resp	resp	NOUN
iajs-319	50	26	.	.	PUNCT
iajs-319	51	1	gs	g	VERB
iajs-319	51	2	-	-	PUNCT
iajs-319	51	3	open	open	ADJ
iajs-319	51	4	,	,	PUNCT
iajs-319	51	5	gα	gα	NOUN
iajs-319	51	6	-	-	PUNCT
iajs-319	51	7	open	open	ADJ
iajs-319	51	8	,	,	PUNCT
iajs-319	51	9	αg	αg	NOUN
iajs-319	51	10	-	-	PUNCT
iajs-319	51	11	open	open	ADJ
iajs-319	51	12	,	,	PUNCT
iajs-319	51	13	s*g	s*g	NOUN
iajs-319	51	14	-	-	PUNCT
iajs-319	51	15	open	open	ADJ
iajs-319	51	16	)	)	PUNCT
iajs-319	51	17	set	set	VERB
iajs-319	51	18	.	.	PUNCT
iajs-319	52	1	544	544	NUM
iajs-319	52	2	|	|	NOUN
iajs-319	52	3	mathematics	mathematic	NOUN
iajs-319	52	4	2014	2014	NUM
iajs-319	52	5	)	)	PUNCT
iajs-319	52	6	عام	عام	ADP
iajs-319	52	7	3العدد	3العدد	NUM
iajs-319	52	8	(	(	PUNCT
iajs-319	52	9	27مجلة	27مجلة	NUM
iajs-319	52	10	إبن	إبن	VERB
iajs-319	52	11	الھيثم	الھيثم	NOUN
iajs-319	52	12	للعلوم	للعلوم	NOUN
iajs-319	52	13	الصرفة	الصرفة	NOUN
iajs-319	53	1	و	و	PRON
iajs-319	53	2	التطبيقية	التطبيقية	ADV
iajs-319	53	3	المجلد	المجلد	VERB
iajs-319	53	4	ibn	ibn	PROPN
iajs-319	53	5	al	al	PROPN
iajs-319	53	6	-	-	PUNCT
iajs-319	53	7	haitham	haitham	PROPN
iajs-319	53	8	jour	jour	X
iajs-319	53	9	.	.	PROPN
iajs-319	54	1	for	for	ADP
iajs-319	54	2	pure	pure	ADJ
iajs-319	54	3	&	&	CCONJ
iajs-319	54	4	appl	appl	PROPN
iajs-319	54	5	.	.	PUNCT
iajs-319	55	1	sci	sci	PROPN
iajs-319	55	2	.	.	PUNCT
iajs-319	55	3	vol	vol	NOUN
iajs-319	55	4	.	.	PROPN
iajs-319	56	1	27	27	NUM
iajs-319	56	2	(	(	PUNCT
iajs-319	56	3	3	3	NUM
iajs-319	56	4	)	)	PUNCT
iajs-319	56	5	2014	2014	NUM
iajs-319	56	6	definition(1.3	definition(1.3	ADJ
iajs-319	56	7	):	):	PUNCT
iajs-319	56	8	a	a	DET
iajs-319	56	9	function	function	NOUN
iajs-319	56	10	)	)	PUNCT
iajs-319	56	11	,	,	PUNCT
iajs-319	56	12	y(),x(:f	y(),x(:f	PROPN
iajs-319	56	13			PROPN
iajs-319	56	14	is	be	AUX
iajs-319	56	15	called	call	VERB
iajs-319	56	16	:	:	PUNCT
iajs-319	56	17	i	i	X
iajs-319	56	18	)	)	PUNCT
iajs-319	56	19	semi	semi	ADJ
iajs-319	56	20	-	-	ADJ
iajs-319	56	21	continuous	continuous	ADJ
iajs-319	56	22	(	(	PUNCT
iajs-319	56	23	briefly	briefly	NOUN
iajs-319	56	24	s	s	NOUN
iajs-319	56	25	-	-	PUNCT
iajs-319	56	26	continuous)[1	continuous)[1	X
iajs-319	56	27	]	]	PUNCT
iajs-319	56	28	if	if	SCONJ
iajs-319	56	29	)	)	PUNCT
iajs-319	56	30	v(f	v(f	PROPN
iajs-319	56	31	1	1	NUM
iajs-319	56	32	is	be	AUX
iajs-319	56	33	s	s	NOUN
iajs-319	56	34	-	-	ADJ
iajs-319	56	35	open	open	ADJ
iajs-319	56	36	set	set	NOUN
iajs-319	56	37	in	in	ADP
iajs-319	56	38	x	x	PUNCT
iajs-319	56	39	for	for	SCONJ
iajs-319	56	40	every	every	DET
iajs-319	56	41	open	open	ADJ
iajs-319	56	42	set	set	VERB
iajs-319	56	43	vin	vin	NOUN
iajs-319	56	44	y	y	PROPN
iajs-319	56	45	ii)	ii)	PROPN
iajs-319	56	46	-continuous	-continuous	ADJ
iajs-319	56	47	[	[	X
iajs-319	56	48	11	11	NUM
iajs-319	56	49	]	]	PUNCT
iajs-319	56	50	if	if	SCONJ
iajs-319	56	51	)	)	PUNCT
iajs-319	56	52	v(f	v(f	PROPN
iajs-319	56	53	1	1	NUM
iajs-319	56	54	is	be	AUX
iajs-319	56	55			NOUN
iajs-319	56	56	-open	-open	VERB
iajs-319	56	57	set	set	VERB
iajs-319	56	58	in	in	ADP
iajs-319	56	59	x	x	PUNCT
iajs-319	56	60	for	for	ADP
iajs-319	56	61	every	every	DET
iajs-319	56	62	open	open	ADJ
iajs-319	56	63	set	set	VERB
iajs-319	56	64	v	v	NOUN
iajs-319	56	65	in	in	ADP
iajs-319	56	66	y	y	PROPN
iajs-319	56	67	.	.	PUNCT
iajs-319	57	1	iii	iii	X
iajs-319	57	2	)	)	PUNCT
iajs-319	57	3	pre	pre	ADJ
iajs-319	57	4	-	-	ADJ
iajs-319	57	5	continuous	continuous	ADJ
iajs-319	57	6	[	[	X
iajs-319	57	7	4	4	NUM
iajs-319	57	8	]	]	X
iajs-319	57	9	if	if	SCONJ
iajs-319	57	10	)	)	PUNCT
iajs-319	57	11	v(f	v(f	PROPN
iajs-319	57	12	1	1	NUM
iajs-319	57	13	is	be	AUX
iajs-319	57	14	pre	pre	ADJ
iajs-319	57	15	-	-	ADJ
iajs-319	57	16	open	open	ADJ
iajs-319	57	17	set	set	NOUN
iajs-319	57	18	in	in	ADP
iajs-319	57	19	x	x	PUNCT
iajs-319	57	20	for	for	ADP
iajs-319	57	21	every	every	DET
iajs-319	57	22	open	open	ADJ
iajs-319	57	23	set	set	VERB
iajs-319	57	24	v	v	NOUN
iajs-319	57	25	in	in	ADP
iajs-319	57	26	y	y	PROPN
iajs-319	57	27	.	.	PUNCT
iajs-319	58	1	iv	iv	X
iajs-319	58	2	)	)	PUNCT
iajs-319	58	3	b	b	X
iajs-319	58	4	-	-	PUNCT
iajs-319	58	5	continuous	continuous	ADJ
iajs-319	58	6	[	[	X
iajs-319	58	7	12	12	NUM
iajs-319	58	8	]	]	PUNCT
iajs-319	58	9	if	if	SCONJ
iajs-319	58	10	)	)	PUNCT
iajs-319	58	11	v(f	v(f	PROPN
iajs-319	58	12	1	1	NUM
iajs-319	58	13	is	be	AUX
iajs-319	58	14	b	b	NOUN
iajs-319	58	15	-	-	PUNCT
iajs-319	58	16	open	open	ADJ
iajs-319	58	17	set	set	NOUN
iajs-319	58	18	in	in	ADP
iajs-319	58	19	x	x	PUNCT
iajs-319	58	20	for	for	ADP
iajs-319	58	21	every	every	DET
iajs-319	58	22	open	open	ADJ
iajs-319	58	23	set	set	VERB
iajs-319	58	24	v	v	NOUN
iajs-319	58	25	in	in	ADP
iajs-319	58	26	y	y	PROPN
iajs-319	58	27	.	.	PUNCT
iajs-319	59	1	v)	v)	PROPN
iajs-319	59	2	-continuous	-continuous	ADJ
iajs-319	59	3	[	[	X
iajs-319	59	4	6	6	NUM
iajs-319	59	5	]	]	PUNCT
iajs-319	59	6	if	if	SCONJ
iajs-319	59	7	)	)	PUNCT
iajs-319	59	8	v(f	v(f	PROPN
iajs-319	59	9	1	1	NUM
iajs-319	59	10	is	be	AUX
iajs-319	59	11			PROPN
iajs-319	59	12	-open	-open	NOUN
iajs-319	59	13	set	set	VERB
iajs-319	59	14	in	in	ADP
iajs-319	59	15	x	x	PUNCT
iajs-319	59	16	for	for	ADP
iajs-319	59	17	every	every	DET
iajs-319	59	18	open	open	ADJ
iajs-319	59	19	set	set	VERB
iajs-319	59	20	v	v	NOUN
iajs-319	59	21	in	in	ADP
iajs-319	59	22	y	y	PROPN
iajs-319	59	23	.	.	PUNCT
iajs-319	60	1	vi	vi	X
iajs-319	60	2	)	)	PUNCT
iajs-319	60	3	generalized	generalize	VERB
iajs-319	60	4	continuous	continuous	ADJ
iajs-319	60	5	(	(	PUNCT
iajs-319	60	6	briefly	briefly	NOUN
iajs-319	60	7	g	g	NOUN
iajs-319	60	8	-	-	PUNCT
iajs-319	60	9	continuous	continuous	ADJ
iajs-319	60	10	)	)	PUNCT
iajs-319	61	1	[	[	X
iajs-319	61	2	13	13	NUM
iajs-319	61	3	]	]	PUNCT
iajs-319	61	4	if	if	SCONJ
iajs-319	61	5	)	)	PUNCT
iajs-319	61	6	v(f	v(f	PROPN
iajs-319	61	7	1	1	NUM
iajs-319	61	8	is	be	AUX
iajs-319	61	9	g	g	NOUN
iajs-319	61	10	-	-	PUNCT
iajs-319	61	11	open	open	ADJ
iajs-319	61	12	set	set	NOUN
iajs-319	61	13	in	in	ADP
iajs-319	61	14	x	x	PUNCT
iajs-319	61	15	for	for	ADP
iajs-319	61	16	every	every	DET
iajs-319	61	17	open	open	ADJ
iajs-319	61	18	set	set	VERB
iajs-319	61	19	v	v	NOUN
iajs-319	61	20	in	in	ADP
iajs-319	61	21	y	y	PROPN
iajs-319	61	22	.	.	PUNCT
iajs-319	62	1	vii	vii	PROPN
iajs-319	62	2	)	)	PUNCT
iajs-319	62	3	generalized	generalize	VERB
iajs-319	62	4	semi	semi	ADV
iajs-319	62	5	continuous	continuous	ADJ
iajs-319	62	6	(	(	PUNCT
iajs-319	62	7	briefly	briefly	NOUN
iajs-319	62	8	gs	gs	NOUN
iajs-319	62	9	-	-	PUNCT
iajs-319	62	10	continuous)[14	continuous)[14	ADJ
iajs-319	62	11	]	]	PUNCT
iajs-319	62	12	if	if	SCONJ
iajs-319	62	13	)	)	PUNCT
iajs-319	62	14	v(f	v(f	PROPN
iajs-319	62	15	1	1	NUM
iajs-319	62	16	is	be	AUX
iajs-319	62	17	gs	gs	NOUN
iajs-319	62	18	-	-	PUNCT
iajs-319	62	19	open	open	ADJ
iajs-319	62	20	set	set	NOUN
iajs-319	62	21	in	in	ADP
iajs-319	62	22	x	x	PUNCT
iajs-319	62	23	for	for	ADP
iajs-319	62	24	every	every	DET
iajs-319	62	25	open	open	ADJ
iajs-319	62	26	set	set	VERB
iajs-319	62	27	v	v	NOUN
iajs-319	62	28	in	in	ADP
iajs-319	62	29	y	y	PROPN
iajs-319	62	30	.	.	PUNCT
iajs-319	63	1	viii	viii	PROPN
iajs-319	63	2	)	)	PUNCT
iajs-319	63	3	generalized	generalize	VERB
iajs-319	63	4	α	α	PRON
iajs-319	63	5	-	-	ADJ
iajs-319	63	6	continuous	continuous	ADJ
iajs-319	63	7	(	(	PUNCT
iajs-319	63	8	briefly	briefly	NOUN
iajs-319	63	9	gα	gα	NOUN
iajs-319	63	10	-	-	PUNCT
iajs-319	63	11	continuous	continuous	ADJ
iajs-319	63	12	)	)	PUNCT
iajs-319	64	1	[	[	X
iajs-319	64	2	8	8	NUM
iajs-319	64	3	]	]	X
iajs-319	64	4	if	if	SCONJ
iajs-319	64	5	)	)	PUNCT
iajs-319	64	6	v(f	v(f	PROPN
iajs-319	64	7	1	1	NUM
iajs-319	64	8	is	be	AUX
iajs-319	64	9	gα	gα	ADV
iajs-319	64	10	-	-	PUNCT
iajs-319	64	11	open	open	NOUN
iajs-319	64	12	set	set	NOUN
iajs-319	64	13	in	in	ADP
iajs-319	64	14	x	x	PUNCT
iajs-319	64	15	for	for	ADP
iajs-319	64	16	every	every	DET
iajs-319	64	17	open	open	ADJ
iajs-319	64	18	set	set	VERB
iajs-319	64	19	v	v	NOUN
iajs-319	64	20	in	in	ADP
iajs-319	64	21	y	y	PROPN
iajs-319	64	22	.	.	PUNCT
iajs-319	65	1	ix	ix	ADJ
iajs-319	65	2	)	)	PUNCT
iajs-319	65	3	α	α	X
iajs-319	65	4	-	-	PUNCT
iajs-319	65	5	generalized	generalize	VERB
iajs-319	65	6	continuous	continuous	ADJ
iajs-319	65	7	(	(	PUNCT
iajs-319	65	8	briefly	briefly	ADV
iajs-319	65	9	αg	αg	NOUN
iajs-319	65	10	-	-	PUNCT
iajs-319	65	11	continuous	continuous	ADJ
iajs-319	65	12	)	)	PUNCT
iajs-319	66	1	[	[	X
iajs-319	66	2	15	15	NUM
iajs-319	66	3	]	]	X
iajs-319	66	4	if	if	SCONJ
iajs-319	66	5	)	)	PUNCT
iajs-319	66	6	v(f	v(f	PROPN
iajs-319	66	7	1	1	NUM
iajs-319	66	8	is	be	AUX
iajs-319	66	9	αg	αg	NOUN
iajs-319	66	10	-	-	PUNCT
iajs-319	66	11	open	open	NOUN
iajs-319	66	12	set	set	NOUN
iajs-319	66	13	in	in	ADP
iajs-319	66	14	x	x	PUNCT
iajs-319	66	15	for	for	ADP
iajs-319	66	16	every	every	DET
iajs-319	66	17	open	open	ADJ
iajs-319	66	18	set	set	VERB
iajs-319	66	19	v	v	NOUN
iajs-319	66	20	in	in	ADP
iajs-319	66	21	y	y	PROPN
iajs-319	66	22	.	.	PUNCT
iajs-319	67	1	x	x	X
iajs-319	67	2	)	)	PUNCT
iajs-319	67	3	s*g	s*g	NOUN
iajs-319	67	4	-	-	PUNCT
iajs-319	67	5	continuous	continuous	ADJ
iajs-319	67	6	[	[	X
iajs-319	67	7	16	16	NUM
iajs-319	67	8	]	]	PUNCT
iajs-319	67	9	if	if	SCONJ
iajs-319	67	10	)	)	PUNCT
iajs-319	67	11	v(f	v(f	PROPN
iajs-319	67	12	1	1	NUM
iajs-319	67	13	is	be	AUX
iajs-319	67	14	s*g	s*g	NOUN
iajs-319	67	15	-	-	PUNCT
iajs-319	67	16	open	open	ADJ
iajs-319	67	17	set	set	NOUN
iajs-319	67	18	in	in	ADP
iajs-319	67	19	x	x	PUNCT
iajs-319	67	20	for	for	ADP
iajs-319	67	21	every	every	DET
iajs-319	67	22	open	open	ADJ
iajs-319	67	23	set	set	VERB
iajs-319	67	24	v	v	NOUN
iajs-319	67	25	in	in	ADP
iajs-319	67	26	y	y	PROPN
iajs-319	67	27	.	.	PUNCT
iajs-319	68	1	definition(1.4)[10],[17	definition(1.4)[10],[17	VERB
iajs-319	68	2	]	]	PUNCT
iajs-319	68	3	:	:	PUNCT
iajs-319	68	4	let	let	VERB
iajs-319	68	5	)	)	PUNCT
iajs-319	68	6	,	,	PUNCT
iajs-319	68	7	x	x	X
iajs-319	68	8	(	(	PUNCT
iajs-319	68	9			NOUN
iajs-319	68	10	be	be	VERB
iajs-319	68	11	a	a	DET
iajs-319	68	12	topological	topological	ADJ
iajs-319	68	13	space	space	NOUN
iajs-319	68	14	and	and	CCONJ
iajs-319	68	15	xa	xa	PROPN
iajs-319	68	16			PROPN
iajs-319	68	17	.	.	PUNCT
iajs-319	69	1	then	then	ADV
iajs-319	69	2	:	:	PUNCT
iajs-319	69	3	i	i	X
iajs-319	69	4	)	)	PUNCT
iajs-319	69	5	the	the	DET
iajs-319	69	6	s*g	s*g	NOUN
iajs-319	69	7	-	-	PUNCT
iajs-319	69	8	closure	closure	NOUN
iajs-319	69	9	of	of	ADP
iajs-319	69	10	a	a	PRON
iajs-319	69	11	,	,	PUNCT
iajs-319	69	12	denoted	denote	VERB
iajs-319	69	13	by	by	ADP
iajs-319	69	14	)	)	PUNCT
iajs-319	69	15	a(cl	a(cl	PROPN
iajs-319	69	16	g*s	g*s	PROPN
iajs-319	69	17	is	be	AUX
iajs-319	69	18	the	the	DET
iajs-319	69	19	intersection	intersection	NOUN
iajs-319	69	20	of	of	ADP
iajs-319	69	21	all	all	DET
iajs-319	69	22	s*g	s*g	NOUN
iajs-319	69	23	-	-	PUNCT
iajs-319	69	24	closed	close	VERB
iajs-319	69	25	subsets	subset	NOUN
iajs-319	69	26	of	of	ADP
iajs-319	69	27	x	x	PUNCT
iajs-319	69	28	which	which	PRON
iajs-319	69	29	contains	contain	VERB
iajs-319	69	30	a	a	DET
iajs-319	69	31	.	.	PUNCT
iajs-319	69	32	ii	ii	NOUN
iajs-319	69	33	)	)	PUNCT
iajs-319	69	34	the	the	DET
iajs-319	69	35	s*g	s*g	PROPN
iajs-319	69	36	-	-	PUNCT
iajs-319	69	37	interior	interior	NOUN
iajs-319	69	38	of	of	ADP
iajs-319	69	39	a	a	PRON
iajs-319	69	40	,	,	PUNCT
iajs-319	69	41	denoted	denote	VERB
iajs-319	69	42	by	by	ADP
iajs-319	69	43	)	)	PUNCT
iajs-319	69	44	a(int	a(int	PROPN
iajs-319	69	45	g*s	g*s	PROPN
iajs-319	69	46	is	be	AUX
iajs-319	69	47	the	the	DET
iajs-319	69	48	union	union	NOUN
iajs-319	69	49	of	of	ADP
iajs-319	69	50	all	all	DET
iajs-319	69	51	s*g	s*g	NOUN
iajs-319	69	52	-	-	PUNCT
iajs-319	69	53	open	open	ADJ
iajs-319	69	54	subsets	subset	NOUN
iajs-319	69	55	of	of	ADP
iajs-319	69	56	x	x	PUNCT
iajs-319	69	57	which	which	PRON
iajs-319	69	58	are	be	AUX
iajs-319	69	59	contained	contain	VERB
iajs-319	69	60	in	in	ADP
iajs-319	69	61	a	a	PRON
iajs-319	69	62	.	.	PUNCT
iajs-319	70	1	theorem(1.5)[17	theorem(1.5)[17	VERB
iajs-319	70	2	]	]	X
iajs-319	70	3	:	:	PUNCT
iajs-319	70	4	let	let	VERB
iajs-319	70	5	)	)	PUNCT
iajs-319	70	6	,	,	PUNCT
iajs-319	70	7	x	x	X
iajs-319	70	8	(	(	PUNCT
iajs-319	70	9			NOUN
iajs-319	70	10	be	be	VERB
iajs-319	70	11	a	a	DET
iajs-319	70	12	topological	topological	ADJ
iajs-319	70	13	space	space	NOUN
iajs-319	70	14	and	and	CCONJ
iajs-319	70	15	xb	xb	PROPN
iajs-319	70	16	,	,	PUNCT
iajs-319	70	17	a	a	DET
iajs-319	70	18			PROPN
iajs-319	70	19	.	.	PUNCT
iajs-319	71	1	then	then	ADV
iajs-319	71	2	:	:	PUNCT
iajs-319	71	3	i	i	PROPN
iajs-319	71	4	)	)	PUNCT
iajs-319	71	5	)	)	PUNCT
iajs-319	72	1	a(cl)a(cla	a(cl)a(cla	NOUN
iajs-319	72	2	g*s	g*s	PROPN
iajs-319	72	3			PROPN
iajs-319	72	4	.	.	PUNCT
iajs-319	73	1	ii	ii	X
iajs-319	73	2	)	)	PUNCT
iajs-319	73	3	a)a(int)aint	a)a(int)aint	PROPN
iajs-319	73	4	(	(	PUNCT
iajs-319	73	5	g*s	g*s	PROPN
iajs-319	73	6			PROPN
iajs-319	73	7	.	.	PUNCT
iajs-319	74	1	iii	iii	X
iajs-319	74	2	)	)	PUNCT
iajs-319	74	3	if	if	SCONJ
iajs-319	74	4	ba	ba	PROPN
iajs-319	74	5			PROPN
iajs-319	74	6	,	,	PUNCT
iajs-319	74	7	then	then	ADV
iajs-319	74	8	)	)	PUNCT
iajs-319	74	9	b(cl)a(cl	b(cl)a(cl	PROPN
iajs-319	74	10	g*sg*s	g*sg*s	PROPN
iajs-319	74	11			PROPN
iajs-319	74	12	.	.	PUNCT
iajs-319	75	1	iv	iv	X
iajs-319	75	2	)	)	PUNCT
iajs-319	75	3	a	a	PRON
iajs-319	75	4	is	be	AUX
iajs-319	75	5	s*g	s*g	NOUN
iajs-319	75	6	-	-	PUNCT
iajs-319	75	7	closed	close	VERB
iajs-319	75	8	iff	iff	PROPN
iajs-319	75	9	a)a(cl	a)a(cl	PROPN
iajs-319	75	10	g*s	g*s	PROPN
iajs-319	75	11			PROPN
iajs-319	75	12	.	.	PUNCT
iajs-319	76	1	v	v	X
iajs-319	76	2	)	)	PUNCT
iajs-319	76	3	)	)	PUNCT
iajs-319	76	4	a(cl))a(cl(cl	a(cl))a(cl(cl	NOUN
iajs-319	76	5	g*sg*sg*s	g*sg*sg*	VERB
iajs-319	76	6			PRON
iajs-319	76	7	.	.	PUNCT
iajs-319	77	1	vi	vi	X
iajs-319	77	2	)	)	PUNCT
iajs-319	77	3	)	)	PUNCT
iajs-319	77	4	ax(cl)a(intx	ax(cl)a(intx	VERB
iajs-319	77	5	g*sg*s	g*sg*s	PROPN
iajs-319	77	6			PROPN
iajs-319	77	7	.	.	PUNCT
iajs-319	78	1	vii	vii	PROPN
iajs-319	78	2	)	)	PUNCT
iajs-319	78	3	)	)	PUNCT
iajs-319	79	1	a(clx	a(clx	NUM
iajs-319	80	1	g*s	g*s	ADJ
iajs-319	80	2	iff	iff	VERB
iajs-319	80	3	for	for	ADP
iajs-319	80	4	every	every	DET
iajs-319	80	5	s*g	s*g	NOUN
iajs-319	80	6	-	-	PUNCT
iajs-319	80	7	open	open	ADJ
iajs-319	80	8	set	set	NOUN
iajs-319	80	9	u	u	NOUN
iajs-319	80	10	containing	contain	VERB
iajs-319	80	11	x	x	PUNCT
iajs-319	80	12	,	,	PUNCT
iajs-319	80	13	au	au	PROPN
iajs-319	80	14	.	.	PUNCT
iajs-319	81	1	viii	viii	PROPN
iajs-319	81	2	)	)	PUNCT
iajs-319	81	3	)	)	PUNCT
iajs-319	81	4	u(cl)u(cl	u(cl)u(cl	PROPN
iajs-319	82	1	g*sg*s	g*sg*s	PROPN
iajs-319	82	2			NOUN
iajs-319	82	3			ADP
iajs-319	82	4			NOUN
iajs-319	82	5			ADP
iajs-319	82	6			NOUN
iajs-319	82	7			PROPN
iajs-319	82	8	.	.	PUNCT
iajs-319	83	1	theorem(1.6)[18	theorem(1.6)[18	NUM
iajs-319	83	2	]	]	PUNCT
iajs-319	83	3	:	:	PUNCT
iajs-319	83	4	let	let	VERB
iajs-319	83	5	yx	yx	NOUN
iajs-319	83	6	be	be	AUX
iajs-319	83	7	the	the	DET
iajs-319	83	8	product	product	NOUN
iajs-319	83	9	space	space	NOUN
iajs-319	83	10	of	of	ADP
iajs-319	83	11	topological	topological	ADJ
iajs-319	83	12	spaces	space	NOUN
iajs-319	83	13	x	x	PUNCT
iajs-319	83	14	and	and	CCONJ
iajs-319	83	15	y	y	PROPN
iajs-319	83	16	.	.	PUNCT
iajs-319	84	1	if	if	SCONJ
iajs-319	84	2	xa	xa	PROPN
iajs-319	84	3			PROPN
iajs-319	84	4	and	and	CCONJ
iajs-319	84	5	yb	yb	PROPN
iajs-319	84	6			PROPN
iajs-319	84	7	.	.	PUNCT
iajs-319	85	1	then	then	ADV
iajs-319	85	2			NUM
iajs-319	85	3	)	)	PUNCT
iajs-319	85	4	b(cl)a(cl	b(cl)a(cl	PROPN
iajs-319	85	5	g*sg*s	g*sg*s	PROPN
iajs-319	85	6	)	)	PUNCT
iajs-319	85	7	ba(cl	ba(cl	PROPN
iajs-319	85	8	g*s	g*s	PROPN
iajs-319	85	9			INTJ
iajs-319	85	10	.	.	PUNCT
iajs-319	86	1	2	2	X
iajs-319	86	2	.	.	NUM
iajs-319	86	3	basic	basic	ADJ
iajs-319	86	4	properties	property	NOUN
iajs-319	86	5	of	of	ADP
iajs-319	86	6	s*g-	s*g-	NOUN
iajs-319	86	7	-open	-open	NOUN
iajs-319	86	8	sets	set	NOUN
iajs-319	86	9	in	in	ADP
iajs-319	86	10	this	this	DET
iajs-319	86	11	section	section	NOUN
iajs-319	86	12	we	we	PRON
iajs-319	86	13	introduce	introduce	VERB
iajs-319	86	14	a	a	DET
iajs-319	86	15	new	new	ADJ
iajs-319	86	16	class	class	NOUN
iajs-319	86	17	of	of	ADP
iajs-319	86	18	sets	set	NOUN
iajs-319	86	19	,	,	PUNCT
iajs-319	86	20	namely	namely	ADV
iajs-319	86	21	,	,	PUNCT
iajs-319	86	22	s*g-	s*g-	NOUN
iajs-319	86	23	-open	-open	NOUN
iajs-319	86	24	sets	set	NOUN
iajs-319	86	25	and	and	CCONJ
iajs-319	86	26	we	we	PRON
iajs-319	86	27	show	show	VERB
iajs-319	86	28	that	that	SCONJ
iajs-319	86	29	the	the	DET
iajs-319	86	30	family	family	NOUN
iajs-319	86	31	of	of	ADP
iajs-319	86	32	all	all	DET
iajs-319	86	33	s*g-	s*g-	NOUN
iajs-319	86	34	-open	-open	ADJ
iajs-319	86	35	subsets	subset	NOUN
iajs-319	86	36	of	of	ADP
iajs-319	86	37	a	a	DET
iajs-319	86	38	topological	topological	ADJ
iajs-319	86	39	space	space	NOUN
iajs-319	86	40	)	)	PUNCT
iajs-319	86	41	,	,	PUNCT
iajs-319	86	42	x	x	X
iajs-319	86	43	(	(	PUNCT
iajs-319	86	44			PROPN
iajs-319	86	45	from	from	ADP
iajs-319	86	46	a	a	DET
iajs-319	86	47	topology	topology	NOUN
iajs-319	86	48	on	on	ADP
iajs-319	86	49	x	x	PUNCT
iajs-319	86	50	which	which	PRON
iajs-319	86	51	is	be	AUX
iajs-319	86	52	finer	fine	ADJ
iajs-319	86	53	than	than	ADP
iajs-319	86	54			NOUN
iajs-319	86	55	.	.	PUNCT
iajs-319	87	1	545	545	NUM
iajs-319	87	2	|	|	ADV
iajs-319	87	3	mathematics	mathematic	NOUN
iajs-319	87	4	2014	2014	NUM
iajs-319	87	5	)	)	PUNCT
iajs-319	87	6	عام	عام	ADP
iajs-319	87	7	3العدد	3العدد	NUM
iajs-319	87	8	(	(	PUNCT
iajs-319	87	9	27مجلة	27مجلة	NUM
iajs-319	87	10	إبن	إبن	VERB
iajs-319	87	11	الھيثم	الھيثم	NOUN
iajs-319	87	12	للعلوم	للعلوم	NOUN
iajs-319	87	13	الصرفة	الصرفة	NOUN
iajs-319	88	1	و	و	PRON
iajs-319	88	2	التطبيقية	التطبيقية	ADV
iajs-319	88	3	المجلد	المجلد	VERB
iajs-319	88	4	ibn	ibn	PROPN
iajs-319	88	5	al	al	PROPN
iajs-319	88	6	-	-	PUNCT
iajs-319	88	7	haitham	haitham	PROPN
iajs-319	88	8	jour	jour	X
iajs-319	88	9	.	.	PROPN
iajs-319	89	1	for	for	ADP
iajs-319	89	2	pure	pure	ADJ
iajs-319	89	3	&	&	CCONJ
iajs-319	89	4	appl	appl	PROPN
iajs-319	89	5	.	.	PUNCT
iajs-319	90	1	sci	sci	PROPN
iajs-319	90	2	.	.	PUNCT
iajs-319	90	3	vol	vol	NOUN
iajs-319	90	4	.	.	PROPN
iajs-319	91	1	27	27	NUM
iajs-319	91	2	(	(	PUNCT
iajs-319	91	3	3	3	NUM
iajs-319	91	4	)	)	PUNCT
iajs-319	91	5	2014	2014	NUM
iajs-319	91	6	definition(2.1	definition(2.1	NOUN
iajs-319	91	7	):	):	PUNCT
iajs-319	91	8	a	a	DET
iajs-319	91	9	subset	subset	NOUN
iajs-319	91	10	a	a	PRON
iajs-319	91	11	of	of	ADP
iajs-319	91	12	a	a	DET
iajs-319	91	13	topological	topological	ADJ
iajs-319	91	14	space	space	NOUN
iajs-319	91	15	)	)	PUNCT
iajs-319	91	16	,	,	PUNCT
iajs-319	91	17	x	x	X
iajs-319	91	18	(	(	PUNCT
iajs-319	91	19			NOUN
iajs-319	91	20	is	be	AUX
iajs-319	91	21	called	call	VERB
iajs-319	91	22	an	an	DET
iajs-319	91	23	s*g-	s*g-	NOUN
iajs-319	91	24	-open	-open	NOUN
iajs-319	91	25	set	set	VERB
iajs-319	91	26	if	if	SCONJ
iajs-319	91	27	)	)	PUNCT
iajs-319	91	28	)	)	PUNCT
iajs-319	91	29	)	)	PUNCT
iajs-319	91	30	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	91	31	g*s	g*s	PROPN
iajs-319	91	32	.	.	PUNCT
iajs-319	92	1	the	the	DET
iajs-319	92	2	complement	complement	NOUN
iajs-319	92	3	of	of	ADP
iajs-319	92	4	an	an	DET
iajs-319	92	5	s*g-	s*g-	NOUN
iajs-319	92	6	-open	-open	NOUN
iajs-319	92	7	set	set	NOUN
iajs-319	92	8	is	be	AUX
iajs-319	92	9	defined	define	VERB
iajs-319	92	10	to	to	PART
iajs-319	92	11	be	be	AUX
iajs-319	92	12	s*g-	s*g-	NOUN
iajs-319	92	13	-closed	-close	VERB
iajs-319	92	14	.	.	PUNCT
iajs-319	93	1	the	the	DET
iajs-319	93	2	family	family	NOUN
iajs-319	93	3	of	of	ADP
iajs-319	93	4	all	all	DET
iajs-319	93	5	s*g-	s*g-	NOUN
iajs-319	93	6	-open	-open	ADJ
iajs-319	93	7	subsets	subset	NOUN
iajs-319	93	8	of	of	ADP
iajs-319	93	9	x	x	PROPN
iajs-319	93	10	is	be	AUX
iajs-319	93	11	denoted	denote	VERB
iajs-319	93	12	by	by	ADP
iajs-319	93	13			PROPN
iajs-319	93	14	g*s	g*s	PROPN
iajs-319	93	15	.	.	PUNCT
iajs-319	94	1	clearly	clearly	ADV
iajs-319	94	2	,	,	PUNCT
iajs-319	94	3	every	every	DET
iajs-319	94	4	open	open	ADJ
iajs-319	94	5	set	set	NOUN
iajs-319	94	6	is	be	AUX
iajs-319	94	7	an	an	DET
iajs-319	94	8	s*g-	s*g-	NOUN
iajs-319	94	9	-open	-open	NOUN
iajs-319	94	10	,	,	PUNCT
iajs-319	94	11	but	but	CCONJ
iajs-319	94	12	the	the	DET
iajs-319	94	13	converse	converse	NOUN
iajs-319	94	14	is	be	AUX
iajs-319	94	15	not	not	PART
iajs-319	94	16	true	true	ADJ
iajs-319	94	17	.	.	PUNCT
iajs-319	95	1	consider	consider	VERB
iajs-319	95	2	the	the	DET
iajs-319	95	3	following	follow	VERB
iajs-319	95	4	example	example	NOUN
iajs-319	95	5	.	.	PUNCT
iajs-319	96	1	example(2.2	example(2.2	NOUN
iajs-319	96	2	):	):	PUNCT
iajs-319	96	3	let	let	VERB
iajs-319	96	4	}	}	PUNCT
iajs-319	96	5	c	c	NOUN
iajs-319	96	6	,	,	PUNCT
iajs-319	96	7	b	b	NOUN
iajs-319	96	8	,	,	PUNCT
iajs-319	96	9	a{x	a{x	VERB
iajs-319	96	10			PROPN
iajs-319	96	11	and	and	CCONJ
iajs-319	96	12	}	}	PUNCT
iajs-319	96	13	}	}	PUNCT
iajs-319	96	14	a{,,x	a{,,x	PROPN
iajs-319	96	15	{	{	PUNCT
iajs-319	96	16			NOUN
iajs-319	96	17	be	be	AUX
iajs-319	96	18	a	a	DET
iajs-319	96	19	topology	topology	NOUN
iajs-319	96	20	on	on	ADP
iajs-319	96	21	x	x	X
iajs-319	96	22	.	.	PUNCT
iajs-319	97	1	then	then	ADV
iajs-319	97	2	}	}	PUNCT
iajs-319	97	3	b	b	X
iajs-319	97	4	,	,	PUNCT
iajs-319	97	5	a	a	PRON
iajs-319	97	6	{	{	PUNCT
iajs-319	97	7	is	be	AUX
iajs-319	97	8	an	an	DET
iajs-319	97	9	s*g-	s*g-	NOUN
iajs-319	97	10	-open	-open	NOUN
iajs-319	97	11	set	set	VERB
iajs-319	97	12	in	in	ADP
iajs-319	97	13	x	x	NOUN
iajs-319	97	14	,	,	PUNCT
iajs-319	97	15	since	since	SCONJ
iajs-319	97	16	}	}	PUNCT
iajs-319	97	17	)	)	PUNCT
iajs-319	97	18	)	)	PUNCT
iajs-319	97	19	)	)	PUNCT
iajs-319	98	1	b	b	X
iajs-319	98	2	,	,	PUNCT
iajs-319	98	3	a(int({clint(}b	a(int({clint(}b	PROPN
iajs-319	98	4	,	,	PUNCT
iajs-319	98	5	a	a	DET
iajs-319	98	6	{	{	PUNCT
iajs-319	98	7	g*s	g*s	PROPN
iajs-319	98	8	}	}	PUNCT
iajs-319	98	9	)	)	PUNCT
iajs-319	98	10	a({clint	a({clint	NOUN
iajs-319	98	11	(	(	PUNCT
iajs-319	98	12	g*s	g*s	NOUN
iajs-319	98	13	)	)	PUNCT
iajs-319	98	14	xint(	xint(	PROPN
iajs-319	98	15	x	x	X
iajs-319	98	16	.	.	PUNCT
iajs-319	99	1	but	but	CCONJ
iajs-319	99	2	}	}	PUNCT
iajs-319	99	3	b	b	NOUN
iajs-319	99	4	,	,	PUNCT
iajs-319	99	5	a	a	PRON
iajs-319	99	6	{	{	PUNCT
iajs-319	99	7	is	be	AUX
iajs-319	99	8	not	not	PART
iajs-319	99	9	open	open	ADJ
iajs-319	99	10	in	in	ADP
iajs-319	99	11	x	x	X
iajs-319	99	12	.	.	PUNCT
iajs-319	100	1	remark(2.3	remark(2.3	NOUN
iajs-319	100	2	):	):	PUNCT
iajs-319	100	3	s*g	s*g	NOUN
iajs-319	100	4	-	-	PUNCT
iajs-319	100	5	open	open	ADJ
iajs-319	100	6	sets	set	NOUN
iajs-319	100	7	and	and	CCONJ
iajs-319	100	8	s*g-	s*g-	NOUN
iajs-319	100	9	-open	-open	NOUN
iajs-319	100	10	sets	set	NOUN
iajs-319	100	11	are	be	AUX
iajs-319	100	12	in	in	ADP
iajs-319	100	13	general	general	ADJ
iajs-319	100	14	independent	independent	ADJ
iajs-319	100	15	.	.	PUNCT
iajs-319	101	1	consider	consider	VERB
iajs-319	101	2	the	the	DET
iajs-319	101	3	following	follow	VERB
iajs-319	101	4	examples	example	NOUN
iajs-319	101	5	:	:	PUNCT
iajs-319	101	6	example(2.4	example(2.4	ADV
iajs-319	101	7	):	):	PUNCT
iajs-319	101	8	let	let	VERB
iajs-319	101	9	}	}	PUNCT
iajs-319	101	10	c	c	NOUN
iajs-319	101	11	,	,	PUNCT
iajs-319	101	12	b	b	NOUN
iajs-319	101	13	,	,	PUNCT
iajs-319	101	14	a{x	a{x	VERB
iajs-319	101	15			PROPN
iajs-319	101	16	and	and	CCONJ
iajs-319	101	17	}	}	PUNCT
iajs-319	101	18	,	,	PUNCT
iajs-319	101	19	x	x	X
iajs-319	101	20	{	{	PUNCT
iajs-319	101	21			NOUN
iajs-319	101	22	be	be	AUX
iajs-319	101	23	a	a	DET
iajs-319	101	24	topology	topology	NOUN
iajs-319	101	25	on	on	ADP
iajs-319	101	26	x	x	X
iajs-319	101	27	.	.	PUNCT
iajs-319	102	1	then	then	ADV
iajs-319	102	2	}	}	PUNCT
iajs-319	102	3	b	b	X
iajs-319	102	4	{	{	PUNCT
iajs-319	102	5	is	be	AUX
iajs-319	102	6	an	an	DET
iajs-319	102	7	s*g	s*g	VERB
iajs-319	102	8	-	-	PUNCT
iajs-319	102	9	open	open	NOUN
iajs-319	102	10	set	set	NOUN
iajs-319	102	11	in	in	ADP
iajs-319	102	12	x	x	PUNCT
iajs-319	102	13	,	,	PUNCT
iajs-319	102	14	but	but	CCONJ
iajs-319	102	15	is	be	AUX
iajs-319	102	16	not	not	PART
iajs-319	102	17	s*g-	s*g-	NOUN
iajs-319	102	18	-open	-open	NOUN
iajs-319	102	19	set	set	VERB
iajs-319	102	20	,	,	PUNCT
iajs-319	102	21	since	since	SCONJ
iajs-319	102	22			NOUN
iajs-319	102	23	}	}	PUNCT
iajs-319	102	24	)	)	PUNCT
iajs-319	102	25	)	)	PUNCT
iajs-319	102	26	)	)	PUNCT
iajs-319	103	1	b(int({clint(}b	b(int({clint(}b	PROPN
iajs-319	103	2	{	{	PUNCT
iajs-319	103	3	g*s	g*s	PROPN
iajs-319	103	4	))(clint	))(clint	PROPN
iajs-319	103	5	(	(	PUNCT
iajs-319	103	6	g*s	g*s	PROPN
iajs-319	103	7	.	.	PUNCT
iajs-319	104	1	also	also	ADV
iajs-319	104	2	,	,	PUNCT
iajs-319	104	3	in	in	ADP
iajs-319	104	4	example	example	NOUN
iajs-319	104	5	(	(	PUNCT
iajs-319	104	6	2.2	2.2	NUM
iajs-319	104	7	)	)	PUNCT
iajs-319	104	8	}	}	PUNCT
iajs-319	104	9	b	b	X
iajs-319	104	10	,	,	PUNCT
iajs-319	104	11	a	a	PRON
iajs-319	104	12	{	{	PUNCT
iajs-319	104	13	is	be	AUX
iajs-319	104	14	an	an	DET
iajs-319	104	15	s*g-	s*g-	NOUN
iajs-319	104	16	-open	-open	NOUN
iajs-319	104	17	set	set	VERB
iajs-319	104	18	in	in	ADP
iajs-319	104	19	x	x	PUNCT
iajs-319	104	20	,	,	PUNCT
iajs-319	104	21	but	but	CCONJ
iajs-319	104	22	is	be	AUX
iajs-319	104	23	not	not	PART
iajs-319	104	24	s*g	s*g	NOUN
iajs-319	104	25	-	-	PUNCT
iajs-319	104	26	open	open	ADJ
iajs-319	104	27	,	,	PUNCT
iajs-319	104	28	since	since	SCONJ
iajs-319	104	29	}	}	PUNCT
iajs-319	104	30	c{}b	c{}b	NOUN
iajs-319	104	31	,	,	PUNCT
iajs-319	104	32	a	a	PRON
iajs-319	104	33	{	{	PUNCT
iajs-319	104	34	c	c	NOUN
iajs-319	104	35			NOUN
iajs-319	104	36	is	be	AUX
iajs-319	104	37	not	not	PART
iajs-319	104	38	s*g	s*g	NOUN
iajs-319	104	39	-	-	PUNCT
iajs-319	104	40	closed	close	VERB
iajs-319	104	41	set	set	NOUN
iajs-319	104	42	in	in	ADP
iajs-319	104	43	x	x	SYM
iajs-319	104	44	,	,	PUNCT
iajs-319	104	45	since	since	SCONJ
iajs-319	104	46	}	}	PUNCT
iajs-319	104	47	c	c	X
iajs-319	104	48	,	,	PUNCT
iajs-319	104	49	a	a	PRON
iajs-319	104	50	{	{	PUNCT
iajs-319	104	51	is	be	AUX
iajs-319	104	52	an	an	DET
iajs-319	104	53	semi	semi	ADJ
iajs-319	104	54	-	-	ADJ
iajs-319	104	55	open	open	ADJ
iajs-319	104	56	set	set	NOUN
iajs-319	104	57	in	in	ADP
iajs-319	104	58	x	x	X
iajs-319	104	59	and	and	CCONJ
iajs-319	104	60	}	}	SYM
iajs-319	104	61	c	c	X
iajs-319	104	62	,	,	PUNCT
iajs-319	104	63	a{}c	a{}c	ADV
iajs-319	104	64	{	{	PUNCT
iajs-319	104	65			PROPN
iajs-319	104	66	,	,	PUNCT
iajs-319	104	67	but	but	CCONJ
iajs-319	104	68	}	}	PUNCT
iajs-319	104	69	c	c	X
iajs-319	104	70	,	,	PUNCT
iajs-319	104	71	a{}c	a{}c	ADV
iajs-319	104	72	,	,	PUNCT
iajs-319	104	73	b{})c({cl	b{})c({cl	NOUN
iajs-319	104	74			PRON
iajs-319	104	75	.	.	PUNCT
iajs-319	105	1	theorem(2.5	theorem(2.5	NOUN
iajs-319	105	2	):	):	PUNCT
iajs-319	105	3	every	every	DET
iajs-319	105	4	s*g-	s*g-	NOUN
iajs-319	105	5	-open	-open	NOUN
iajs-319	105	6	set	set	NOUN
iajs-319	105	7	is	be	AUX
iajs-319	105	8			X
iajs-319	105	9	-open	-open	ADJ
iajs-319	105	10	(	(	PUNCT
iajs-319	105	11	resp	resp	NOUN
iajs-319	105	12	.	.	PUNCT
iajs-319	106	1	αg	αg	NOUN
iajs-319	106	2	-	-	PUNCT
iajs-319	106	3	open	open	ADJ
iajs-319	106	4	,	,	PUNCT
iajs-319	106	5	gα	gα	NOUN
iajs-319	106	6	-	-	PUNCT
iajs-319	106	7	open	open	ADJ
iajs-319	106	8	,	,	PUNCT
iajs-319	106	9	pre	pre	ADJ
iajs-319	106	10	-	-	ADJ
iajs-319	106	11	open	open	ADJ
iajs-319	106	12	,	,	PUNCT
iajs-319	106	13	b	b	X
iajs-319	106	14	-	-	PUNCT
iajs-319	106	15	open	open	ADJ
iajs-319	106	16	,	,	PUNCT
iajs-319	106	17			NOUN
iajs-319	106	18	-open	-open	NOUN
iajs-319	106	19	)	)	PUNCT
iajs-319	106	20	set	set	NOUN
iajs-319	106	21	.	.	PUNCT
iajs-319	107	1	proof	proof	NOUN
iajs-319	107	2	:	:	PUNCT
iajs-319	107	3	let	let	VERB
iajs-319	107	4	a	a	PRON
iajs-319	107	5	be	be	AUX
iajs-319	107	6	any	any	DET
iajs-319	107	7	s*g-	s*g-	NOUN
iajs-319	107	8	-open	-open	NOUN
iajs-319	107	9	set	set	VERB
iajs-319	107	10	in	in	ADP
iajs-319	107	11	x	x	SYM
iajs-319	107	12	,	,	PUNCT
iajs-319	107	13	then	then	ADV
iajs-319	107	14	)	)	PUNCT
iajs-319	107	15	)	)	PUNCT
iajs-319	107	16	)	)	PUNCT
iajs-319	107	17	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	107	18	g*s	g*s	PROPN
iajs-319	107	19	.	.	PUNCT
iajs-319	108	1	since	since	SCONJ
iajs-319	108	2	)	)	PUNCT
iajs-319	108	3	)	)	PUNCT
iajs-319	108	4	)	)	PUNCT
iajs-319	108	5	a(int(clint()))a(int(clint	a(int(clint()))a(int(clint	NOUN
iajs-319	108	6	(	(	PUNCT
iajs-319	108	7	g*s	g*s	PROPN
iajs-319	108	8			PROPN
iajs-319	108	9	,	,	PUNCT
iajs-319	108	10	thus	thus	ADV
iajs-319	108	11	)	)	PUNCT
iajs-319	108	12	)	)	PUNCT
iajs-319	108	13	)	)	PUNCT
iajs-319	108	14	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	108	15			PROPN
iajs-319	108	16	.	.	PUNCT
iajs-319	109	1	therefore	therefore	ADV
iajs-319	109	2	a	a	PRON
iajs-319	109	3	is	be	AUX
iajs-319	109	4	an	an	DET
iajs-319	109	5			X
iajs-319	109	6	-open	-open	NOUN
iajs-319	109	7	set	set	VERB
iajs-319	109	8	in	in	ADP
iajs-319	109	9	x	x	X
iajs-319	109	10	.	.	PUNCT
iajs-319	110	1	since	since	SCONJ
iajs-319	110	2	every	every	DET
iajs-319	110	3			NUM
iajs-319	110	4	-open	-open	ADJ
iajs-319	110	5	set	set	NOUN
iajs-319	110	6	is	be	AUX
iajs-319	110	7	αg	αg	NOUN
iajs-319	110	8	-	-	PUNCT
iajs-319	110	9	open	open	ADJ
iajs-319	110	10	(	(	PUNCT
iajs-319	110	11	resp	resp	NOUN
iajs-319	110	12	.	.	PUNCT
iajs-319	111	1	gα	gα	NOUN
iajs-319	111	2	-	-	PUNCT
iajs-319	111	3	open	open	ADJ
iajs-319	111	4	,	,	PUNCT
iajs-319	111	5	pre	pre	ADJ
iajs-319	111	6	-	-	ADJ
iajs-319	111	7	open	open	ADJ
iajs-319	111	8	,	,	PUNCT
iajs-319	111	9	b	b	X
iajs-319	111	10	-	-	PUNCT
iajs-319	111	11	open	open	ADJ
iajs-319	111	12	,	,	PUNCT
iajs-319	111	13			NOUN
iajs-319	111	14	-open	-open	NOUN
iajs-319	111	15	)	)	PUNCT
iajs-319	111	16	set	set	VERB
iajs-319	111	17	.thus	.thus	PUNCT
iajs-319	111	18	every	every	DET
iajs-319	111	19	s*g-	s*g-	NOUN
iajs-319	111	20	-open	-open	NOUN
iajs-319	111	21	set	set	NOUN
iajs-319	111	22	is	be	AUX
iajs-319	111	23			X
iajs-319	111	24	-open	-open	ADJ
iajs-319	111	25	(	(	PUNCT
iajs-319	111	26	resp	resp	NOUN
iajs-319	111	27	.	.	PUNCT
iajs-319	112	1	αg	αg	NOUN
iajs-319	112	2	-	-	PUNCT
iajs-319	112	3	open	open	ADJ
iajs-319	112	4	,	,	PUNCT
iajs-319	112	5	gα	gα	NOUN
iajs-319	112	6	-	-	PUNCT
iajs-319	112	7	open	open	ADJ
iajs-319	112	8	,	,	PUNCT
iajs-319	112	9	pre	pre	ADJ
iajs-319	112	10	-	-	ADJ
iajs-319	112	11	open	open	ADJ
iajs-319	112	12	,	,	PUNCT
iajs-319	112	13	b	b	X
iajs-319	112	14	-	-	PUNCT
iajs-319	112	15	open	open	ADJ
iajs-319	112	16	,	,	PUNCT
iajs-319	112	17			NOUN
iajs-319	112	18	-open	-open	NOUN
iajs-319	112	19	)	)	PUNCT
iajs-319	112	20	set	set	NOUN
iajs-319	112	21	.	.	PUNCT
iajs-319	113	1	remark(2.6	remark(2.6	NOUN
iajs-319	113	2	):	):	PUNCT
iajs-319	113	3	the	the	DET
iajs-319	113	4	converse	converse	NOUN
iajs-319	113	5	of	of	ADP
iajs-319	113	6	theorem	theorem	NOUN
iajs-319	113	7	(	(	PUNCT
iajs-319	113	8	2.5	2.5	NUM
iajs-319	113	9	)	)	PUNCT
iajs-319	113	10	may	may	AUX
iajs-319	113	11	not	not	PART
iajs-319	113	12	be	be	AUX
iajs-319	113	13	true	true	ADJ
iajs-319	113	14	in	in	ADP
iajs-319	113	15	general	general	ADJ
iajs-319	113	16	as	as	SCONJ
iajs-319	113	17	shown	show	VERB
iajs-319	113	18	in	in	ADP
iajs-319	113	19	the	the	DET
iajs-319	113	20	following	following	ADJ
iajs-319	113	21	example	example	NOUN
iajs-319	113	22	.	.	PUNCT
iajs-319	114	1	example(2.7	example(2.7	NOUN
iajs-319	114	2	):	):	PUNCT
iajs-319	114	3	let	let	VERB
iajs-319	114	4	}	}	PUNCT
iajs-319	114	5	c	c	NOUN
iajs-319	114	6	,	,	PUNCT
iajs-319	114	7	b	b	NOUN
iajs-319	114	8	,	,	PUNCT
iajs-319	114	9	a{x	a{x	VERB
iajs-319	114	10			PROPN
iajs-319	114	11	&	&	CCONJ
iajs-319	114	12	}	}	PUNCT
iajs-319	114	13	,	,	PUNCT
iajs-319	114	14	x	x	X
iajs-319	114	15	{	{	PUNCT
iajs-319	114	16			NOUN
iajs-319	114	17	be	be	AUX
iajs-319	114	18	a	a	DET
iajs-319	114	19	topology	topology	NOUN
iajs-319	114	20	on	on	ADP
iajs-319	114	21	x	x	X
iajs-319	114	22	.	.	PUNCT
iajs-319	115	1	then	then	ADV
iajs-319	115	2	the	the	DET
iajs-319	115	3	set	set	NOUN
iajs-319	115	4	}	}	PUNCT
iajs-319	115	5	c	c	NOUN
iajs-319	115	6	,	,	PUNCT
iajs-319	115	7	b	b	X
iajs-319	115	8	{	{	PUNCT
iajs-319	115	9	is	be	AUX
iajs-319	115	10	preopen	preopen	ADJ
iajs-319	115	11	(	(	PUNCT
iajs-319	115	12	resp	resp	NOUN
iajs-319	115	13	.	.	PUNCT
iajs-319	116	1	αg	αg	NOUN
iajs-319	116	2	-	-	PUNCT
iajs-319	116	3	open	open	ADJ
iajs-319	116	4	,	,	PUNCT
iajs-319	116	5	gα	gα	NOUN
iajs-319	116	6	-	-	PUNCT
iajs-319	116	7	open	open	ADJ
iajs-319	116	8	,	,	PUNCT
iajs-319	116	9	b	b	X
iajs-319	116	10	-	-	PUNCT
iajs-319	116	11	open	open	ADJ
iajs-319	116	12	,	,	PUNCT
iajs-319	116	13			NOUN
iajs-319	116	14	-open	-open	NOUN
iajs-319	116	15	)	)	PUNCT
iajs-319	117	1	in	in	ADP
iajs-319	117	2	x	x	X
iajs-319	117	3	,	,	PUNCT
iajs-319	117	4	but	but	CCONJ
iajs-319	117	5	is	be	AUX
iajs-319	117	6	not	not	PART
iajs-319	117	7	s*g-	s*g-	NOUN
iajs-319	117	8	-open	-open	NOUN
iajs-319	117	9	set	set	VERB
iajs-319	117	10	in	in	ADP
iajs-319	117	11	x	x	SYM
iajs-319	117	12	,	,	PUNCT
iajs-319	117	13	since	since	SCONJ
iajs-319	117	14	}	}	PUNCT
iajs-319	117	15	)	)	PUNCT
iajs-319	117	16	)	)	PUNCT
iajs-319	117	17	)	)	PUNCT
iajs-319	118	1	c	c	X
iajs-319	118	2	,	,	PUNCT
iajs-319	118	3	b(int({clint(}c	b(int({clint(}c	NOUN
iajs-319	118	4	,	,	PUNCT
iajs-319	118	5	b	b	NOUN
iajs-319	118	6	{	{	PUNCT
iajs-319	118	7	g*s	g*s	NOUN
iajs-319	118	8			PROPN
iajs-319	118	9	)	)	PUNCT
iajs-319	118	10	)	)	PUNCT
iajs-319	118	11	)	)	PUNCT
iajs-319	118	12	(	(	PUNCT
iajs-319	118	13	clint	clint	NOUN
iajs-319	118	14	(	(	PUNCT
iajs-319	118	15	g*s	g*s	PROPN
iajs-319	118	16	.	.	PUNCT
iajs-319	119	1	theorem(2.8	theorem(2.8	NOUN
iajs-319	119	2	):	):	PUNCT
iajs-319	119	3	every	every	DET
iajs-319	119	4	s*g-	s*g-	NOUN
iajs-319	119	5	-open	-open	NOUN
iajs-319	119	6	set	set	NOUN
iajs-319	119	7	is	be	AUX
iajs-319	119	8	semi	semi	ADJ
iajs-319	119	9	-	-	ADJ
iajs-319	119	10	open	open	ADJ
iajs-319	119	11	and	and	CCONJ
iajs-319	119	12	gs	gs	NOUN
iajs-319	119	13	-	-	PUNCT
iajs-319	119	14	open	open	ADJ
iajs-319	119	15	set	set	NOUN
iajs-319	119	16	.	.	PUNCT
iajs-319	120	1	proof	proof	NOUN
iajs-319	120	2	:	:	PUNCT
iajs-319	120	3	let	let	VERB
iajs-319	120	4	a	a	PRON
iajs-319	120	5	be	be	AUX
iajs-319	120	6	any	any	DET
iajs-319	120	7	s*g-	s*g-	NOUN
iajs-319	120	8	-open	-open	NOUN
iajs-319	120	9	set	set	VERB
iajs-319	120	10	in	in	ADP
iajs-319	120	11	x	x	SYM
iajs-319	120	12	,	,	PUNCT
iajs-319	120	13	then	then	ADV
iajs-319	120	14	)	)	PUNCT
iajs-319	120	15	)	)	PUNCT
iajs-319	120	16	)	)	PUNCT
iajs-319	120	17	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	120	18	g*s	g*s	PROPN
iajs-319	120	19	.	.	PUNCT
iajs-319	121	1	since	since	SCONJ
iajs-319	121	2	)	)	PUNCT
iajs-319	121	3	)	)	PUNCT
iajs-319	121	4	a(int(cl))a(int(cl)))a(int(clint	a(int(cl))a(int(cl)))a(int(clint	PROPN
iajs-319	121	5	(	(	PUNCT
iajs-319	121	6	g*sg*s	g*sg*s	PROPN
iajs-319	121	7			VERB
iajs-319	121	8	,	,	PUNCT
iajs-319	121	9	thus	thus	ADV
iajs-319	121	10	)	)	PUNCT
iajs-319	121	11	)	)	PUNCT
iajs-319	121	12	a(int(cla	a(int(cla	VERB
iajs-319	121	13			PROPN
iajs-319	121	14	.	.	PUNCT
iajs-319	122	1	therefore	therefore	ADV
iajs-319	122	2	a	a	PRON
iajs-319	122	3	is	be	AUX
iajs-319	122	4	a	a	DET
iajs-319	122	5	semiopen	semiopen	ADJ
iajs-319	122	6	set	set	NOUN
iajs-319	122	7	in	in	ADP
iajs-319	122	8	x	x	X
iajs-319	122	9	.	.	PUNCT
iajs-319	123	1	since	since	SCONJ
iajs-319	123	2	every	every	DET
iajs-319	123	3	semi	semi	ADJ
iajs-319	123	4	-	-	ADJ
iajs-319	123	5	open	open	ADJ
iajs-319	123	6	set	set	NOUN
iajs-319	123	7	is	be	AUX
iajs-319	123	8	gs	gs	ADJ
iajs-319	123	9	-	-	PUNCT
iajs-319	123	10	open	open	ADJ
iajs-319	123	11	set	set	NOUN
iajs-319	123	12	.	.	PUNCT
iajs-319	124	1	thus	thus	ADV
iajs-319	124	2	every	every	DET
iajs-319	124	3	s*g-	s*g-	NOUN
iajs-319	124	4	-open	-open	NOUN
iajs-319	124	5	set	set	NOUN
iajs-319	124	6	is	be	AUX
iajs-319	124	7	semiopen	semiopen	ADJ
iajs-319	124	8	and	and	CCONJ
iajs-319	124	9	gs	gs	NOUN
iajs-319	124	10	-	-	PUNCT
iajs-319	124	11	open	open	ADJ
iajs-319	124	12	set	set	NOUN
iajs-319	124	13	.	.	PUNCT
iajs-319	125	1	remark(2.9	remark(2.9	NOUN
iajs-319	125	2	):	):	PUNCT
iajs-319	125	3	the	the	DET
iajs-319	125	4	converse	converse	NOUN
iajs-319	125	5	of	of	ADP
iajs-319	125	6	theorem	theorem	NOUN
iajs-319	125	7	(	(	PUNCT
iajs-319	125	8	2.8	2.8	NUM
iajs-319	125	9	)	)	PUNCT
iajs-319	125	10	may	may	AUX
iajs-319	125	11	not	not	PART
iajs-319	125	12	be	be	AUX
iajs-319	125	13	true	true	ADJ
iajs-319	125	14	in	in	ADP
iajs-319	125	15	general	general	ADJ
iajs-319	125	16	as	as	SCONJ
iajs-319	125	17	shown	show	VERB
iajs-319	125	18	in	in	ADP
iajs-319	125	19	the	the	DET
iajs-319	125	20	following	following	ADJ
iajs-319	125	21	example	example	NOUN
iajs-319	125	22	.	.	PUNCT
iajs-319	126	1	example(2.10	example(2.10	NUM
iajs-319	126	2	):	):	PUNCT
iajs-319	126	3	let	let	VERB
iajs-319	126	4	}	}	PUNCT
iajs-319	126	5	c	c	NOUN
iajs-319	126	6	,	,	PUNCT
iajs-319	126	7	b	b	NOUN
iajs-319	126	8	,	,	PUNCT
iajs-319	126	9	a{x	a{x	VERB
iajs-319	126	10			PROPN
iajs-319	126	11	&	&	CCONJ
iajs-319	126	12	}	}	PUNCT
iajs-319	126	13	}	}	SYM
iajs-319	126	14	b	b	PROPN
iajs-319	126	15	,	,	PUNCT
iajs-319	126	16	a{},b{},a{,,x	a{},b{},a{,,x	PROPN
iajs-319	126	17	{	{	PUNCT
iajs-319	126	18			NOUN
iajs-319	126	19	be	be	AUX
iajs-319	126	20	a	a	DET
iajs-319	126	21	topology	topology	NOUN
iajs-319	126	22	on	on	ADP
iajs-319	126	23	x	x	X
iajs-319	126	24	.	.	PUNCT
iajs-319	127	1	then	then	ADV
iajs-319	127	2	the	the	DET
iajs-319	127	3	set	set	NOUN
iajs-319	127	4	}	}	PUNCT
iajs-319	127	5	c	c	X
iajs-319	127	6	,	,	PUNCT
iajs-319	127	7	a	a	PRON
iajs-319	127	8	{	{	PUNCT
iajs-319	127	9	is	be	AUX
iajs-319	127	10	semi	semi	ADJ
iajs-319	127	11	-	-	ADJ
iajs-319	127	12	open	open	ADJ
iajs-319	127	13	and	and	CCONJ
iajs-319	127	14	gs	gs	NOUN
iajs-319	127	15	-	-	PUNCT
iajs-319	127	16	open	open	ADJ
iajs-319	127	17	set	set	NOUN
iajs-319	127	18	in	in	ADP
iajs-319	127	19	x	x	PUNCT
iajs-319	127	20	,	,	PUNCT
iajs-319	127	21	but	but	CCONJ
iajs-319	127	22	is	be	AUX
iajs-319	127	23	not	not	PART
iajs-319	127	24	an	an	DET
iajs-319	127	25	s*g-	s*g-	NOUN
iajs-319	127	26	-open	-open	NOUN
iajs-319	127	27	set	set	VERB
iajs-319	127	28	in	in	ADP
iajs-319	127	29	x	x	SYM
iajs-319	127	30	,	,	PUNCT
iajs-319	127	31	since	since	SCONJ
iajs-319	127	32			NOUN
iajs-319	127	33	}	}	PUNCT
iajs-319	127	34	)	)	PUNCT
iajs-319	127	35	)	)	PUNCT
iajs-319	127	36	)	)	PUNCT
iajs-319	128	1	c	c	X
iajs-319	128	2	,	,	PUNCT
iajs-319	128	3	a(int({clint(}c	a(int({clint(}c	PROPN
iajs-319	128	4	,	,	PUNCT
iajs-319	128	5	a	a	PRON
iajs-319	128	6	{	{	PUNCT
iajs-319	128	7	g*s	g*s	PROPN
iajs-319	128	8	}	}	PUNCT
iajs-319	128	9	)	)	PUNCT
iajs-319	128	10	)	)	PUNCT
iajs-319	128	11	)	)	PUNCT
iajs-319	128	12	a({clint	a({clint	NOUN
iajs-319	128	13	(	(	PUNCT
iajs-319	128	14	g*s	g*s	PROPN
iajs-319	128	15	}	}	PUNCT
iajs-319	128	16	a{})c	a{})c	ADJ
iajs-319	128	17	,	,	PUNCT
iajs-319	128	18	aint	aint	NOUN
iajs-319	128	19	(	(	PUNCT
iajs-319	128	20	{	{	PUNCT
iajs-319	128	21			NUM
iajs-319	128	22	.	.	PUNCT
iajs-319	129	1	remark(2.11	remark(2.11	ADV
iajs-319	129	2	):	):	PUNCT
iajs-319	129	3	pre	pre	ADJ
iajs-319	129	4	-	-	ADJ
iajs-319	129	5	open	open	ADJ
iajs-319	129	6	sets	set	NOUN
iajs-319	129	7	and	and	CCONJ
iajs-319	129	8	αg	αg	NOUN
iajs-319	129	9	-	-	PUNCT
iajs-319	129	10	open	open	ADJ
iajs-319	129	11	sets	set	NOUN
iajs-319	129	12	are	be	AUX
iajs-319	129	13	in	in	ADP
iajs-319	129	14	general	general	ADJ
iajs-319	129	15	independent	independent	ADJ
iajs-319	129	16	.	.	PUNCT
iajs-319	130	1	consider	consider	VERB
iajs-319	130	2	the	the	DET
iajs-319	130	3	following	follow	VERB
iajs-319	130	4	examples	example	NOUN
iajs-319	130	5	:	:	PUNCT
iajs-319	130	6	example(2.12	example(2.12	NUM
iajs-319	130	7	):	):	PUNCT
iajs-319	130	8	let	let	NOUN
iajs-319	130	9	)	)	PUNCT
iajs-319	130	10	,	,	PUNCT
iajs-319	130	11	r	r	NOUN
iajs-319	130	12	(	(	PUNCT
iajs-319	130	13			NOUN
iajs-319	130	14	be	be	AUX
iajs-319	130	15	the	the	DET
iajs-319	130	16	usual	usual	ADJ
iajs-319	130	17	topological	topological	ADJ
iajs-319	130	18	space	space	NOUN
iajs-319	130	19	.	.	PUNCT
iajs-319	131	1	then	then	ADV
iajs-319	131	2	the	the	DET
iajs-319	131	3	set	set	NOUN
iajs-319	131	4	of	of	ADP
iajs-319	131	5	all	all	DET
iajs-319	131	6	rational	rational	ADJ
iajs-319	131	7	numbers	number	NOUN
iajs-319	131	8	q	q	NOUN
iajs-319	131	9	is	be	AUX
iajs-319	131	10	a	a	DET
iajs-319	131	11	pre	pre	ADJ
iajs-319	131	12	-	-	ADJ
iajs-319	131	13	open	open	ADJ
iajs-319	131	14	set	set	NOUN
iajs-319	131	15	,	,	PUNCT
iajs-319	131	16	but	but	CCONJ
iajs-319	131	17	is	be	AUX
iajs-319	131	18	not	not	PART
iajs-319	131	19	an	an	DET
iajs-319	131	20	αg	αg	NOUN
iajs-319	131	21	-	-	PUNCT
iajs-319	131	22	open	open	NOUN
iajs-319	131	23	set	set	NOUN
iajs-319	131	24	.	.	PUNCT
iajs-319	132	1	also	also	ADV
iajs-319	132	2	,	,	PUNCT
iajs-319	132	3	in	in	ADP
iajs-319	132	4	example	example	NOUN
iajs-319	132	5	(	(	PUNCT
iajs-319	132	6	2.2	2.2	NUM
iajs-319	132	7	)	)	PUNCT
iajs-319	132	8	}	}	PUNCT
iajs-319	132	9	b	b	X
iajs-319	132	10	{	{	PUNCT
iajs-319	132	11	is	be	AUX
iajs-319	132	12	an	an	DET
iajs-319	132	13	αg	αg	NOUN
iajs-319	132	14	-	-	PUNCT
iajs-319	132	15	open	open	NOUN
iajs-319	132	16	set	set	NOUN
iajs-319	132	17	,	,	PUNCT
iajs-319	132	18	since	since	SCONJ
iajs-319	132	19	,	,	PUNCT
iajs-319	132	20	}	}	PUNCT
iajs-319	132	21	c	c	X
iajs-319	132	22	,	,	PUNCT
iajs-319	132	23	a{}b	a{}b	NOUN
iajs-319	132	24	{	{	PUNCT
iajs-319	132	25	c	c	NOUN
iajs-319	132	26			NOUN
iajs-319	132	27	is	be	AUX
iajs-319	132	28	an	an	DET
iajs-319	132	29	αg	αg	NOUN
iajs-319	132	30	-	-	PUNCT
iajs-319	132	31	closed	close	VERB
iajs-319	132	32	set	set	NOUN
iajs-319	132	33	,	,	PUNCT
iajs-319	132	34	but	but	CCONJ
iajs-319	132	35	is	be	AUX
iajs-319	132	36	not	not	PART
iajs-319	132	37	a	a	DET
iajs-319	132	38	pre	pre	ADJ
iajs-319	132	39	-	-	ADJ
iajs-319	132	40	open	open	ADJ
iajs-319	132	41	set	set	NOUN
iajs-319	132	42	,	,	PUNCT
iajs-319	132	43	since	since	SCONJ
iajs-319	132	44			NOUN
iajs-319	132	45	}	}	PUNCT
iajs-319	132	46	)	)	PUNCT
iajs-319	132	47	)	)	PUNCT
iajs-319	133	1	b({clint(}b	b({clint(}b	PROPN
iajs-319	133	2	{	{	PUNCT
iajs-319	133	3	}	}	PUNCT
iajs-319	133	4	)	)	PUNCT
iajs-319	133	5	b	b	NOUN
iajs-319	133	6	,	,	PUNCT
iajs-319	133	7	cint	cint	NOUN
iajs-319	133	8	(	(	PUNCT
iajs-319	133	9	{	{	PUNCT
iajs-319	133	10			ADJ
iajs-319	133	11	.	.	PUNCT
iajs-319	134	1	546	546	NUM
iajs-319	134	2	|	|	ADV
iajs-319	134	3	mathematics	mathematic	NOUN
iajs-319	134	4	2014	2014	NUM
iajs-319	134	5	)	)	PUNCT
iajs-319	134	6	عام	عام	ADP
iajs-319	134	7	3العدد	3العدد	NUM
iajs-319	134	8	(	(	PUNCT
iajs-319	134	9	27مجلة	27مجلة	NUM
iajs-319	134	10	إبن	إبن	VERB
iajs-319	134	11	الھيثم	الھيثم	NOUN
iajs-319	134	12	للعلوم	للعلوم	NOUN
iajs-319	134	13	الصرفة	الصرفة	NOUN
iajs-319	135	1	و	و	PRON
iajs-319	135	2	التطبيقية	التطبيقية	ADV
iajs-319	135	3	المجلد	المجلد	VERB
iajs-319	135	4	ibn	ibn	PROPN
iajs-319	135	5	al	al	PROPN
iajs-319	135	6	-	-	PUNCT
iajs-319	135	7	haitham	haitham	PROPN
iajs-319	135	8	jour	jour	X
iajs-319	135	9	.	.	PROPN
iajs-319	136	1	for	for	ADP
iajs-319	136	2	pure	pure	ADJ
iajs-319	136	3	&	&	CCONJ
iajs-319	136	4	appl	appl	PROPN
iajs-319	136	5	.	.	PUNCT
iajs-319	137	1	sci	sci	PROPN
iajs-319	137	2	.	.	PUNCT
iajs-319	137	3	vol	vol	NOUN
iajs-319	137	4	.	.	PROPN
iajs-319	138	1	27	27	NUM
iajs-319	138	2	(	(	PUNCT
iajs-319	138	3	3	3	NUM
iajs-319	138	4	)	)	PUNCT
iajs-319	138	5	2014	2014	NUM
iajs-319	138	6	remark(2.13	remark(2.13	NUM
iajs-319	138	7	):	):	PUNCT
iajs-319	138	8	g	g	NOUN
iajs-319	138	9	-	-	PUNCT
iajs-319	138	10	open	open	ADJ
iajs-319	138	11	sets	set	NOUN
iajs-319	138	12	and	and	CCONJ
iajs-319	138	13	gα	gα	NOUN
iajs-319	138	14	-	-	PUNCT
iajs-319	138	15	open	open	ADJ
iajs-319	138	16	sets	set	NOUN
iajs-319	138	17	are	be	AUX
iajs-319	138	18	in	in	ADP
iajs-319	138	19	general	general	ADJ
iajs-319	138	20	independent	independent	ADJ
iajs-319	138	21	.	.	PUNCT
iajs-319	139	1	consider	consider	VERB
iajs-319	139	2	the	the	DET
iajs-319	139	3	following	follow	VERB
iajs-319	139	4	examples	example	NOUN
iajs-319	139	5	:	:	PUNCT
iajs-319	139	6	example(2.14	example(2.14	NUM
iajs-319	139	7	):	):	PUNCT
iajs-319	139	8	let	let	VERB
iajs-319	139	9	}	}	PUNCT
iajs-319	139	10	c	c	NOUN
iajs-319	139	11	,	,	PUNCT
iajs-319	139	12	b	b	NOUN
iajs-319	139	13	,	,	PUNCT
iajs-319	139	14	a{x	a{x	VERB
iajs-319	139	15			PROPN
iajs-319	139	16	&	&	CCONJ
iajs-319	139	17	}	}	PUNCT
iajs-319	139	18	}	}	PUNCT
iajs-319	139	19	c	c	AUX
iajs-319	139	20	,	,	PUNCT
iajs-319	139	21	a{},a{,,x	a{},a{,,x	PROPN
iajs-319	139	22	{	{	PUNCT
iajs-319	139	23			NOUN
iajs-319	139	24	be	be	AUX
iajs-319	139	25	a	a	DET
iajs-319	139	26	topology	topology	NOUN
iajs-319	139	27	on	on	ADP
iajs-319	139	28	x	x	X
iajs-319	139	29	.	.	PUNCT
iajs-319	140	1	then	then	ADV
iajs-319	140	2	the	the	DET
iajs-319	140	3	set	set	NOUN
iajs-319	140	4	}	}	SYM
iajs-319	140	5	b	b	NOUN
iajs-319	140	6	,	,	PUNCT
iajs-319	140	7	a	a	PRON
iajs-319	140	8	{	{	PUNCT
iajs-319	140	9	is	be	AUX
iajs-319	140	10	a	a	DET
iajs-319	140	11	gα	gα	NOUN
iajs-319	140	12	-	-	PUNCT
iajs-319	140	13	open	open	NOUN
iajs-319	140	14	set	set	NOUN
iajs-319	140	15	in	in	ADP
iajs-319	140	16	x	x	SYM
iajs-319	140	17	,	,	PUNCT
iajs-319	140	18	since	since	SCONJ
iajs-319	140	19	}	}	PUNCT
iajs-319	140	20	c{}b	c{}b	NOUN
iajs-319	140	21	,	,	PUNCT
iajs-319	140	22	a	a	PRON
iajs-319	140	23	{	{	PUNCT
iajs-319	140	24	c	c	NOUN
iajs-319	140	25			NOUN
iajs-319	140	26	is	be	AUX
iajs-319	140	27	gα	gα	NOUN
iajs-319	140	28	-	-	PUNCT
iajs-319	140	29	closed	closed	ADJ
iajs-319	140	30	,	,	PUNCT
iajs-319	140	31	but	but	CCONJ
iajs-319	140	32	is	be	AUX
iajs-319	140	33	not	not	PART
iajs-319	140	34	a	a	DET
iajs-319	140	35	g	g	NOUN
iajs-319	140	36	-	-	PUNCT
iajs-319	140	37	open	open	NOUN
iajs-319	140	38	set	set	NOUN
iajs-319	140	39	in	in	ADP
iajs-319	140	40	x	x	SYM
iajs-319	140	41	,	,	PUNCT
iajs-319	140	42	since	since	SCONJ
iajs-319	140	43	}	}	PUNCT
iajs-319	140	44	c{}b	c{}b	NOUN
iajs-319	140	45	,	,	PUNCT
iajs-319	140	46	a	a	PRON
iajs-319	140	47	{	{	PUNCT
iajs-319	140	48	c	c	NOUN
iajs-319	140	49			NOUN
iajs-319	140	50	is	be	AUX
iajs-319	140	51	not	not	PART
iajs-319	140	52	g	g	NOUN
iajs-319	140	53	-	-	PUNCT
iajs-319	140	54	closed	closed	ADJ
iajs-319	140	55	.	.	PUNCT
iajs-319	141	1	also	also	ADV
iajs-319	141	2	,	,	PUNCT
iajs-319	141	3	in	in	ADP
iajs-319	141	4	example	example	NOUN
iajs-319	141	5	(	(	PUNCT
iajs-319	141	6	2.2	2.2	NUM
iajs-319	141	7	)	)	PUNCT
iajs-319	141	8	}	}	PUNCT
iajs-319	141	9	c	c	X
iajs-319	141	10	{	{	PUNCT
iajs-319	141	11	is	be	AUX
iajs-319	141	12	a	a	DET
iajs-319	141	13	g	g	NOUN
iajs-319	141	14	-	-	PUNCT
iajs-319	141	15	open	open	NOUN
iajs-319	141	16	set	set	NOUN
iajs-319	141	17	in	in	ADP
iajs-319	141	18	x	x	SYM
iajs-319	141	19	,	,	PUNCT
iajs-319	141	20	since	since	SCONJ
iajs-319	141	21	,	,	PUNCT
iajs-319	141	22	}	}	PUNCT
iajs-319	141	23	b	b	NOUN
iajs-319	141	24	,	,	PUNCT
iajs-319	141	25	a{}c	a{}c	ADV
iajs-319	141	26	{	{	PUNCT
iajs-319	141	27	c	c	NOUN
iajs-319	141	28			PROPN
iajs-319	141	29	is	be	AUX
iajs-319	141	30	g	g	NOUN
iajs-319	141	31	-	-	PUNCT
iajs-319	141	32	closed	closed	ADJ
iajs-319	141	33	,	,	PUNCT
iajs-319	141	34	but	but	CCONJ
iajs-319	141	35	is	be	AUX
iajs-319	141	36	not	not	PART
iajs-319	141	37	a	a	DET
iajs-319	141	38	gα	gα	NOUN
iajs-319	141	39	-	-	PUNCT
iajs-319	141	40	open	open	NOUN
iajs-319	141	41	set	set	NOUN
iajs-319	141	42	in	in	ADP
iajs-319	141	43	x	x	SYM
iajs-319	141	44	,	,	PUNCT
iajs-319	141	45	since	since	SCONJ
iajs-319	141	46	}	}	PUNCT
iajs-319	141	47	b	b	NOUN
iajs-319	141	48	,	,	PUNCT
iajs-319	141	49	a{}c	a{}c	ADV
iajs-319	141	50	{	{	PUNCT
iajs-319	141	51	c	c	NOUN
iajs-319	141	52			PROPN
iajs-319	141	53	is	be	AUX
iajs-319	141	54	not	not	PART
iajs-319	141	55	gα	gα	NOUN
iajs-319	141	56	-	-	PUNCT
iajs-319	141	57	closed	closed	ADJ
iajs-319	141	58	.	.	PUNCT
iajs-319	142	1	the	the	DET
iajs-319	142	2	following	follow	VERB
iajs-319	142	3	diagram	diagram	NOUN
iajs-319	142	4	shows	show	VERB
iajs-319	142	5	the	the	DET
iajs-319	142	6	relationships	relationship	NOUN
iajs-319	142	7	between	between	ADP
iajs-319	142	8	s*g-	s*g-	NOUN
iajs-319	142	9	-open	-open	NOUN
iajs-319	142	10	sets	set	NOUN
iajs-319	142	11	and	and	CCONJ
iajs-319	142	12	some	some	DET
iajs-319	142	13	other	other	ADJ
iajs-319	142	14	open	open	ADJ
iajs-319	142	15	sets	set	NOUN
iajs-319	142	16	:	:	PUNCT
iajs-319	142	17	proposition(2.15	proposition(2.15	NUM
iajs-319	142	18	):	):	PUNCT
iajs-319	142	19	a	a	DET
iajs-319	142	20	subset	subset	NOUN
iajs-319	142	21	a	a	PRON
iajs-319	142	22	of	of	ADP
iajs-319	142	23	a	a	DET
iajs-319	142	24	topological	topological	ADJ
iajs-319	142	25	space	space	NOUN
iajs-319	142	26	)	)	PUNCT
iajs-319	142	27	,	,	PUNCT
iajs-319	142	28	x	x	X
iajs-319	142	29	(	(	PUNCT
iajs-319	142	30			NOUN
iajs-319	142	31	is	be	AUX
iajs-319	142	32	s*g-	s*g-	NOUN
iajs-319	142	33	-open	-open	ADJ
iajs-319	142	34	if	if	SCONJ
iajs-319	142	35	and	and	CCONJ
iajs-319	142	36	only	only	ADV
iajs-319	142	37	if	if	SCONJ
iajs-319	142	38	there	there	PRON
iajs-319	142	39	exists	exist	VERB
iajs-319	142	40	an	an	DET
iajs-319	142	41	open	open	ADJ
iajs-319	142	42	subset	subset	ADJ
iajs-319	142	43	u	u	NOUN
iajs-319	142	44	of	of	ADP
iajs-319	142	45	x	x	SYM
iajs-319	142	46	such	such	ADJ
iajs-319	142	47	that	that	PRON
iajs-319	142	48	)	)	PUNCT
iajs-319	142	49	)	)	PUNCT
iajs-319	142	50	u(clint(au	u(clint(au	NOUN
iajs-319	142	51	g*s	g*s	NOUN
iajs-319	142	52	.	.	PUNCT
iajs-319	143	1	proof	proof	NOUN
iajs-319	143	2	:	:	PUNCT
iajs-319	143	3			NOUN
iajs-319	143	4	suppose	suppose	VERB
iajs-319	143	5	that	that	SCONJ
iajs-319	143	6	a	a	PRON
iajs-319	143	7	is	be	AUX
iajs-319	143	8	a	a	DET
iajs-319	143	9	s*g-	s*g-	NOUN
iajs-319	143	10	-open	-open	NOUN
iajs-319	143	11	set	set	VERB
iajs-319	143	12	in	in	ADP
iajs-319	143	13	x	x	SYM
iajs-319	143	14	,	,	PUNCT
iajs-319	143	15	then	then	ADV
iajs-319	143	16	)	)	PUNCT
iajs-319	143	17	)	)	PUNCT
iajs-319	143	18	)	)	PUNCT
iajs-319	144	1	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	144	2	g*s	g*s	PROPN
iajs-319	144	3	.	.	PUNCT
iajs-319	145	1	since	since	SCONJ
iajs-319	145	2	a)aint	a)aint	PROPN
iajs-319	145	3	(	(	PUNCT
iajs-319	145	4			PROPN
iajs-319	145	5	,	,	PUNCT
iajs-319	145	6	thus	thus	ADV
iajs-319	145	7	)	)	PUNCT
iajs-319	145	8	)	)	PUNCT
iajs-319	145	9	)	)	PUNCT
iajs-319	145	10	a(int(clint(a)aint	a(int(clint(a)aint	NOUN
iajs-319	145	11	(	(	PUNCT
iajs-319	145	12	g*s	g*s	NOUN
iajs-319	145	13	.	.	PUNCT
iajs-319	146	1	put	put	VERB
iajs-319	146	2	)	)	PUNCT
iajs-319	146	3	aint(u	aint(u	PROPN
iajs-319	147	1			INTJ
iajs-319	148	1	,	,	PUNCT
iajs-319	148	2	hence	hence	ADV
iajs-319	148	3	there	there	PRON
iajs-319	148	4	exists	exist	VERB
iajs-319	148	5	an	an	DET
iajs-319	148	6	open	open	ADJ
iajs-319	148	7	subset	subset	ADJ
iajs-319	148	8	u	u	NOUN
iajs-319	148	9	of	of	ADP
iajs-319	148	10	x	x	SYM
iajs-319	148	11	such	such	ADJ
iajs-319	148	12	that	that	PRON
iajs-319	148	13	)	)	PUNCT
iajs-319	148	14	)	)	PUNCT
iajs-319	148	15	u(clint(au	u(clint(au	NOUN
iajs-319	148	16	g*s	g*s	NOUN
iajs-319	148	17	.	.	PUNCT
iajs-319	149	1	conversely	conversely	ADV
iajs-319	149	2	,	,	PUNCT
iajs-319	149	3	suppose	suppose	VERB
iajs-319	149	4	that	that	SCONJ
iajs-319	149	5	there	there	PRON
iajs-319	149	6	exists	exist	VERB
iajs-319	149	7	an	an	DET
iajs-319	149	8	open	open	ADJ
iajs-319	149	9	subset	subset	ADJ
iajs-319	149	10	u	u	NOUN
iajs-319	149	11	of	of	ADP
iajs-319	149	12	x	x	SYM
iajs-319	149	13	such	such	ADJ
iajs-319	149	14	that	that	PRON
iajs-319	149	15	)	)	PUNCT
iajs-319	149	16	)	)	PUNCT
iajs-319	149	17	u(clint(au	u(clint(au	NOUN
iajs-319	149	18	g*s	g*s	NOUN
iajs-319	149	19	.	.	PUNCT
iajs-319	150	1	since	since	SCONJ
iajs-319	150	2	au	au	PROPN
iajs-319	150	3			PROPN
iajs-319	150	4			PROPN
iajs-319	150	5	)	)	PUNCT
iajs-319	150	6	aint(u	aint(u	PROPN
iajs-319	150	7			PROPN
iajs-319	150	8			PROPN
iajs-319	150	9	)	)	PUNCT
iajs-319	150	10	)	)	PUNCT
iajs-319	150	11	a(int(cl)u(cl	a(int(cl)u(cl	PROPN
iajs-319	151	1	g*sg*s	g*sg*s	PROPN
iajs-319	151	2			PROPN
iajs-319	151	3			NOUN
iajs-319	151	4	)	)	PUNCT
iajs-319	151	5	)	)	PUNCT
iajs-319	151	6	)	)	PUNCT
iajs-319	152	1	a(int(clint())u(clint	a(int(clint())u(clint	PROPN
iajs-319	152	2	(	(	PUNCT
iajs-319	152	3	g*sg*s	g*sg*s	PROPN
iajs-319	152	4			PROPN
iajs-319	152	5	.	.	PUNCT
iajs-319	153	1	since	since	SCONJ
iajs-319	153	2	)	)	PUNCT
iajs-319	153	3	)	)	PUNCT
iajs-319	154	1	u(clint(a	u(clint(a	NOUN
iajs-319	155	1	g*s	g*s	PROPN
iajs-319	155	2	,	,	PUNCT
iajs-319	155	3	then	then	ADV
iajs-319	155	4	)	)	PUNCT
iajs-319	155	5	)	)	PUNCT
iajs-319	155	6	)	)	PUNCT
iajs-319	155	7	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	155	8	g*s	g*s	PROPN
iajs-319	155	9	.	.	PUNCT
iajs-319	156	1	thus	thus	ADV
iajs-319	156	2	a	a	PRON
iajs-319	156	3	is	be	AUX
iajs-319	156	4	an	an	DET
iajs-319	156	5	s*g-	s*g-	NOUN
iajs-319	156	6	-open	-open	NOUN
iajs-319	156	7	set	set	VERB
iajs-319	156	8	in	in	ADP
iajs-319	156	9	x	x	X
iajs-319	156	10	.	.	PUNCT
iajs-319	157	1	lemma(2.16	lemma(2.16	PROPN
iajs-319	157	2	):	):	PUNCT
iajs-319	157	3	let	let	VERB
iajs-319	157	4	)	)	PUNCT
iajs-319	157	5	,	,	PUNCT
iajs-319	157	6	x	x	X
iajs-319	157	7	(	(	PUNCT
iajs-319	157	8			NOUN
iajs-319	157	9	be	be	VERB
iajs-319	157	10	a	a	DET
iajs-319	157	11	topological	topological	ADJ
iajs-319	157	12	space	space	NOUN
iajs-319	157	13	.	.	PUNCT
iajs-319	158	1	if	if	SCONJ
iajs-319	158	2	u	u	NOUN
iajs-319	158	3	is	be	AUX
iajs-319	158	4	an	an	DET
iajs-319	158	5	open	open	ADJ
iajs-319	158	6	set	set	NOUN
iajs-319	158	7	in	in	ADP
iajs-319	158	8	x	x	SYM
iajs-319	158	9	,	,	PUNCT
iajs-319	158	10	then	then	ADV
iajs-319	158	11	)	)	PUNCT
iajs-319	158	12	au(cl)a(clu	au(cl)a(clu	NOUN
iajs-319	158	13	g*sg*s	g*sg*s	PROPN
iajs-319	158	14			PROPN
iajs-319	158	15			PROPN
iajs-319	158	16	for	for	ADP
iajs-319	158	17	any	any	DET
iajs-319	158	18	subset	subset	NOUN
iajs-319	158	19	a	a	PRON
iajs-319	158	20	of	of	ADP
iajs-319	158	21	x	x	X
iajs-319	158	22	.	.	PUNCT
iajs-319	159	1	proof	proof	NOUN
iajs-319	159	2	:	:	PUNCT
iajs-319	159	3	let	let	VERB
iajs-319	159	4	)	)	PUNCT
iajs-319	159	5	a(clux	a(clux	VERB
iajs-319	159	6	g*s	g*s	NOUN
iajs-319	159	7	and	and	CCONJ
iajs-319	159	8	v	v	NOUN
iajs-319	159	9	be	be	AUX
iajs-319	159	10	any	any	DET
iajs-319	159	11	s*g	s*g	NOUN
iajs-319	159	12	-	-	PUNCT
iajs-319	159	13	open	open	NOUN
iajs-319	159	14	set	set	NOUN
iajs-319	159	15	in	in	ADP
iajs-319	159	16	x	x	PUNCT
iajs-319	159	17	s.t	s.t	PROPN
iajs-319	159	18	vx	vx	PROPN
iajs-319	159	19	.	.	PUNCT
iajs-319	160	1	since	since	SCONJ
iajs-319	160	2	)	)	PUNCT
iajs-319	160	3	a(clx	a(clx	PROPN
iajs-319	160	4	g*s	g*s	PROPN
iajs-319	160	5	,	,	PUNCT
iajs-319	160	6	then	then	ADV
iajs-319	160	7	by	by	ADP
iajs-319	160	8	theorem	theorem	NOUN
iajs-319	160	9	(	(	PUNCT
iajs-319	160	10	(	(	PUNCT
iajs-319	160	11	1.5),vii	1.5),vii	NUM
iajs-319	160	12	)	)	PUNCT
iajs-319	160	13	,	,	PUNCT
iajs-319	160	14	av	av	NOUN
iajs-319	160	15	.	.	PUNCT
iajs-319	161	1	since	since	SCONJ
iajs-319	161	2	vu	vu	PRON
iajs-319	161	3	is	be	AUX
iajs-319	161	4	an	an	DET
iajs-319	161	5	s*g	s*g	VERB
iajs-319	161	6	-	-	PUNCT
iajs-319	161	7	open	open	NOUN
iajs-319	161	8	set	set	NOUN
iajs-319	161	9	in	in	ADP
iajs-319	161	10	x	x	PUNCT
iajs-319	161	11	and	and	CCONJ
iajs-319	161	12	uvx	uvx	PROPN
iajs-319	161	13			PROPN
iajs-319	161	14	,	,	PUNCT
iajs-319	161	15	then	then	ADV
iajs-319	161	16	a)uv	a)uv	PROPN
iajs-319	161	17	(	(	PUNCT
iajs-319	161	18			X
iajs-319	161	19	)au(v	)au(v	X
iajs-319	161	20			PROPN
iajs-319	161	21	.	.	PUNCT
iajs-319	162	1	therefore	therefore	ADV
iajs-319	162	2	)	)	PUNCT
iajs-319	162	3	au(clx	au(clx	PROPN
iajs-319	162	4	g*s	g*s	PROPN
iajs-319	162	5			PROPN
iajs-319	162	6	.	.	PUNCT
iajs-319	163	1	thus	thus	ADV
iajs-319	163	2	)a(clu	)a(clu	PROPN
iajs-319	163	3	g*s	g*s	ADJ
iajs-319	163	4	)	)	PUNCT
iajs-319	163	5	au(cl	au(cl	PROPN
iajs-319	163	6	g*s	g*s	PROPN
iajs-319	163	7			PROPN
iajs-319	163	8	for	for	ADP
iajs-319	163	9	any	any	DET
iajs-319	163	10	subset	subset	NOUN
iajs-319	163	11	a	a	PRON
iajs-319	163	12	of	of	ADP
iajs-319	163	13	x	x	PROPN
iajs-319	163	14	.	.	PUNCT
iajs-319	163	15	theorem(2.17	theorem(2.17	NUM
iajs-319	163	16	):	):	PUNCT
iajs-319	163	17	let	let	VERB
iajs-319	163	18	)	)	PUNCT
iajs-319	163	19	,	,	PUNCT
iajs-319	163	20	x	x	X
iajs-319	163	21	(	(	PUNCT
iajs-319	163	22			NOUN
iajs-319	163	23	be	be	VERB
iajs-319	163	24	a	a	DET
iajs-319	163	25	topological	topological	ADJ
iajs-319	163	26	space	space	NOUN
iajs-319	163	27	.	.	PUNCT
iajs-319	164	1	then	then	ADV
iajs-319	164	2	the	the	DET
iajs-319	164	3	family	family	NOUN
iajs-319	164	4	of	of	ADP
iajs-319	164	5	all	all	DET
iajs-319	164	6	s*g-	s*g-	NOUN
iajs-319	164	7	-open	-open	ADJ
iajs-319	164	8	subsets	subset	NOUN
iajs-319	164	9	of	of	ADP
iajs-319	164	10	x	x	NUM
iajs-319	164	11	from	from	ADP
iajs-319	164	12	a	a	DET
iajs-319	164	13	topology	topology	NOUN
iajs-319	164	14	on	on	ADP
iajs-319	164	15	x	x	X
iajs-319	164	16	.	.	PUNCT
iajs-319	165	1	proof:(i	proof:(i	PROPN
iajs-319	165	2	)	)	PUNCT
iajs-319	165	3	.	.	PUNCT
iajs-319	166	1	since	since	SCONJ
iajs-319	166	2	)	)	PUNCT
iajs-319	166	3	)	)	PUNCT
iajs-319	166	4	)	)	PUNCT
iajs-319	166	5	(	(	PUNCT
iajs-319	166	6	int(clint	int(clint	NOUN
iajs-319	166	7	(	(	PUNCT
iajs-319	166	8	g*s	g*s	PROPN
iajs-319	166	9			NOUN
iajs-319	166	10	and	and	CCONJ
iajs-319	166	11	)	)	PUNCT
iajs-319	166	12	)	)	PUNCT
iajs-319	166	13	)	)	PUNCT
iajs-319	166	14	x(int(clint(x	x(int(clint(x	PROPN
iajs-319	166	15	g*s	g*s	PROPN
iajs-319	166	16	,	,	PUNCT
iajs-319	166	17	then	then	ADV
iajs-319	166	18			DET
iajs-319	166	19	g*sx	g*sx	NOUN
iajs-319	166	20	,	,	PUNCT
iajs-319	166	21	.	.	PUNCT
iajs-319	167	1	(	(	PUNCT
iajs-319	167	2	ii	ii	NOUN
iajs-319	167	3	)	)	PUNCT
iajs-319	167	4	.	.	PUNCT
iajs-319	168	1	let	let	VERB
iajs-319	168	2			PROPN
iajs-319	168	3	g*sb	g*sb	PROPN
iajs-319	168	4	,	,	PUNCT
iajs-319	168	5	a	a	PRON
iajs-319	168	6	.	.	PUNCT
iajs-319	168	7	to	to	PART
iajs-319	168	8	prove	prove	VERB
iajs-319	168	9	that	that	SCONJ
iajs-319	168	10			NOUN
iajs-319	168	11	g*sba	g*sba	NOUN
iajs-319	168	12	.	.	PUNCT
iajs-319	169	1	by	by	ADP
iajs-319	169	2	proposition	proposition	NOUN
iajs-319	169	3	(	(	PUNCT
iajs-319	169	4	2.15	2.15	NUM
iajs-319	169	5	)	)	PUNCT
iajs-319	169	6	,	,	PUNCT
iajs-319	169	7	there	there	PRON
iajs-319	169	8	exists	exist	VERB
iajs-319	169	9	v	v	PROPN
iajs-319	169	10	,	,	PUNCT
iajs-319	169	11	u	u	NOUN
iajs-319	169	12	such	such	ADJ
iajs-319	169	13	that	that	PRON
iajs-319	169	14	)	)	PUNCT
iajs-319	169	15	)	)	PUNCT
iajs-319	170	1	u(clint(au	u(clint(au	NOUN
iajs-319	170	2	g*s	g*s	NOUN
iajs-319	170	3	and	and	CCONJ
iajs-319	170	4	)	)	PUNCT
iajs-319	170	5	)	)	PUNCT
iajs-319	171	1	v(clint(bv	v(clint(bv	PROPN
iajs-319	171	2	g*s	g*s	NOUN
iajs-319	171	3	.	.	PUNCT
iajs-319	172	1	notice	notice	VERB
iajs-319	172	2	that	that	SCONJ
iajs-319	172	3	vu	vu	PROPN
iajs-319	172	4	and	and	CCONJ
iajs-319	172	5	bavu	bavu	PROPN
iajs-319	172	6			PRON
iajs-319	172	7			PROPN
iajs-319	172	8	.	.	PUNCT
iajs-319	173	1	now	now	ADV
iajs-319	173	2	,	,	PUNCT
iajs-319	173	3			PROPN
iajs-319	173	4	)	)	PUNCT
iajs-319	173	5	)	)	PUNCT
iajs-319	173	6	v(clint())u(clint(ba	v(clint())u(clint(ba	X
iajs-319	173	7	g*sg*s	g*sg*s	PROPN
iajs-319	173	8			PROPN
iajs-319	173	9	)	)	PUNCT
iajs-319	173	10	)	)	PUNCT
iajs-319	174	1	v(cl))u(clint(int	v(cl))u(clint(int	PROPN
iajs-319	174	2	(	(	PUNCT
iajs-319	174	3	g*sg*s	g*sg*s	PROPN
iajs-319	174	4			ADP
iajs-319	174	5	547	547	NUM
iajs-319	174	6	|	|	NOUN
iajs-319	174	7	mathematics	mathematic	NOUN
iajs-319	174	8	2014	2014	NUM
iajs-319	174	9	)	)	PUNCT
iajs-319	174	10	عام	عام	ADP
iajs-319	174	11	3العدد	3العدد	NUM
iajs-319	174	12	(	(	PUNCT
iajs-319	174	13	27مجلة	27مجلة	NUM
iajs-319	174	14	إبن	إبن	VERB
iajs-319	174	15	الھيثم	الھيثم	NOUN
iajs-319	174	16	للعلوم	للعلوم	NOUN
iajs-319	174	17	الصرفة	الصرفة	NOUN
iajs-319	175	1	و	و	PRON
iajs-319	175	2	التطبيقية	التطبيقية	ADV
iajs-319	175	3	المجلد	المجلد	VERB
iajs-319	175	4	ibn	ibn	PROPN
iajs-319	175	5	al	al	PROPN
iajs-319	175	6	-	-	PUNCT
iajs-319	175	7	haitham	haitham	PROPN
iajs-319	175	8	jour	jour	X
iajs-319	175	9	.	.	PROPN
iajs-319	176	1	for	for	ADP
iajs-319	176	2	pure	pure	ADJ
iajs-319	176	3	&	&	CCONJ
iajs-319	176	4	appl	appl	PROPN
iajs-319	176	5	.	.	PUNCT
iajs-319	177	1	sci	sci	PROPN
iajs-319	177	2	.	.	PUNCT
iajs-319	177	3	vol	vol	NOUN
iajs-319	177	4	.	.	PROPN
iajs-319	178	1	27	27	NUM
iajs-319	178	2	(	(	PUNCT
iajs-319	178	3	3	3	NUM
iajs-319	178	4	)	)	PUNCT
iajs-319	178	5	2014	2014	NUM
iajs-319	178	6	)	)	PUNCT
iajs-319	178	7	)	)	PUNCT
iajs-319	178	8	v))u(cl(int(clint	v))u(cl(int(clint	NOUN
iajs-319	178	9	(	(	PUNCT
iajs-319	178	10	g*sg*s	g*sg*s	PROPN
iajs-319	178	11			VERB
iajs-319	178	12	(	(	PUNCT
iajs-319	178	13	by	by	ADP
iajs-319	178	14	lemma	lemma	PROPN
iajs-319	178	15	(	(	PUNCT
iajs-319	178	16	2.16	2.16	NUM
iajs-319	178	17	)	)	PUNCT
iajs-319	178	18	)	)	PUNCT
iajs-319	178	19	.	.	PUNCT
iajs-319	178	20	)	)	PUNCT
iajs-319	178	21	)	)	PUNCT
iajs-319	179	1	v)u(cl(clint	v)u(cl(clint	NOUN
iajs-319	179	2	(	(	PUNCT
iajs-319	179	3	g*sg*s	g*sg*s	PROPN
iajs-319	179	4			VERB
iajs-319	179	5	)	)	PUNCT
iajs-319	179	6	)	)	PUNCT
iajs-319	180	1	vu(cl(clint	vu(cl(clint	PROPN
iajs-319	180	2	(	(	PUNCT
iajs-319	180	3	g*sg*s	g*sg*s	PROPN
iajs-319	180	4			VERB
iajs-319	180	5	(	(	PUNCT
iajs-319	180	6	by	by	ADP
iajs-319	180	7	lemma	lemma	PROPN
iajs-319	180	8	(	(	PUNCT
iajs-319	180	9	2.16	2.16	NUM
iajs-319	180	10	)	)	PUNCT
iajs-319	180	11	)	)	PUNCT
iajs-319	180	12	.	.	PUNCT
iajs-319	180	13	)	)	PUNCT
iajs-319	180	14	)	)	PUNCT
iajs-319	181	1	vu(clint	vu(clint	PROPN
iajs-319	181	2	(	(	PUNCT
iajs-319	181	3	g*s	g*s	PROPN
iajs-319	181	4			PROPN
iajs-319	181	5	(	(	PUNCT
iajs-319	181	6	by	by	ADP
iajs-319	181	7	theorem	theorem	NOUN
iajs-319	181	8	(	(	PUNCT
iajs-319	181	9	1.5),v	1.5),v	NUM
iajs-319	181	10	)	)	PUNCT
iajs-319	181	11	.	.	PUNCT
iajs-319	182	1	thus	thus	ADV
iajs-319	182	2	)	)	PUNCT
iajs-319	182	3	)	)	PUNCT
iajs-319	183	1	vu(clint(bavu	vu(clint(bavu	PROPN
iajs-319	183	2	g*s	g*s	PROPN
iajs-319	183	3			PROPN
iajs-319	184	1			PROPN
iajs-319	184	2	.	.	PUNCT
iajs-319	185	1	therefore	therefore	ADV
iajs-319	185	2	by	by	ADP
iajs-319	185	3	proposition	proposition	NOUN
iajs-319	185	4	(	(	PUNCT
iajs-319	185	5	2.15	2.15	NUM
iajs-319	185	6	)	)	PUNCT
iajs-319	185	7	,	,	PUNCT
iajs-319	185	8			PROPN
iajs-319	185	9	g*sba	g*sba	NOUN
iajs-319	185	10	.	.	PUNCT
iajs-319	186	1	(	(	PUNCT
iajs-319	186	2	iii	iii	NOUN
iajs-319	186	3	)	)	PUNCT
iajs-319	186	4	.	.	PUNCT
iajs-319	187	1	let	let	VERB
iajs-319	187	2	}	}	PUNCT
iajs-319	187	3	:	:	PUNCT
iajs-319	187	4	u	u	NOUN
iajs-319	187	5	{	{	PUNCT
iajs-319	187	6			NOUN
iajs-319	187	7	be	be	AUX
iajs-319	187	8	any	any	DET
iajs-319	187	9	family	family	NOUN
iajs-319	187	10	of	of	ADP
iajs-319	187	11	s*g-	s*g-	NOUN
iajs-319	187	12	-open	-open	PROPN
iajs-319	187	13	subsets	subset	NOUN
iajs-319	187	14	of	of	ADP
iajs-319	187	15	x	x	X
iajs-319	187	16	,	,	PUNCT
iajs-319	187	17	then	then	ADV
iajs-319	187	18	)	)	PUNCT
iajs-319	187	19	)	)	PUNCT
iajs-319	187	20	)	)	PUNCT
iajs-319	188	1	u(int(clint(u	u(int(clint(u	PROPN
iajs-319	188	2	g*s	g*s	PROPN
iajs-319	188	3			PRON
iajs-319	188	4			NOUN
iajs-319	188	5	for	for	ADP
iajs-319	188	6	each	each	DET
iajs-319	188	7			PROPN
iajs-319	188	8	.	.	PUNCT
iajs-319	189	1	therefore	therefore	ADV
iajs-319	189	2	by	by	ADP
iajs-319	189	3	theorem	theorem	NOUN
iajs-319	189	4	(	(	PUNCT
iajs-319	189	5	(	(	PUNCT
iajs-319	189	6	1.5	1.5	NUM
iajs-319	189	7	)	)	PUNCT
iajs-319	189	8	viii	viii	NOUN
iajs-319	189	9	)	)	PUNCT
iajs-319	189	10	,	,	PUNCT
iajs-319	189	11	we	we	PRON
iajs-319	189	12	get	get	VERB
iajs-319	189	13	:	:	PUNCT
iajs-319	189	14	)	)	PUNCT
iajs-319	189	15	)	)	PUNCT
iajs-319	189	16	)	)	PUNCT
iajs-319	190	1	u(int(clint(u	u(int(clint(u	PROPN
iajs-319	190	2	g*s	g*s	PROPN
iajs-319	190	3			ADP
iajs-319	190	4			NOUN
iajs-319	190	5			ADP
iajs-319	190	6			NOUN
iajs-319	190	7			PROPN
iajs-319	190	8	)	)	PUNCT
iajs-319	190	9	)	)	PUNCT
iajs-319	190	10	)	)	PUNCT
iajs-319	191	1	u(int(clint	u(int(clint	NOUN
iajs-319	191	2	(	(	PUNCT
iajs-319	191	3	g*s	g*s	PROPN
iajs-319	191	4			PROPN
iajs-319	191	5			NUM
iajs-319	191	6	)	)	PUNCT
iajs-319	191	7	)	)	PUNCT
iajs-319	191	8	)	)	PUNCT
iajs-319	191	9	uint((clint	uint((clint	PROPN
iajs-319	191	10	(	(	PUNCT
iajs-319	191	11	g*s	g*s	PROPN
iajs-319	191	12			PROPN
iajs-319	191	13			PROPN
iajs-319	191	14			NUM
iajs-319	191	15	)	)	PUNCT
iajs-319	191	16	)	)	PUNCT
iajs-319	191	17	)	)	PUNCT
iajs-319	192	1	u(int(clint	u(int(clint	NOUN
iajs-319	192	2	(	(	PUNCT
iajs-319	192	3	g*s	g*s	PROPN
iajs-319	192	4			PROPN
iajs-319	192	5			PROPN
iajs-319	192	6			PROPN
iajs-319	192	7	.	.	PUNCT
iajs-319	193	1	hence	hence	ADV
iajs-319	193	2			X
iajs-319	193	3			NOUN
iajs-319	193	4			NOUN
iajs-319	193	5			PUNCT
iajs-319	193	6	g*su	g*su	NOUN
iajs-319	193	7	.	.	PUNCT
iajs-319	194	1	thus	thus	ADV
iajs-319	194	2			PROPN
iajs-319	194	3	g*s	g*s	PROPN
iajs-319	194	4	is	be	AUX
iajs-319	194	5	a	a	DET
iajs-319	194	6	topology	topology	NOUN
iajs-319	194	7	on	on	ADP
iajs-319	194	8	x	x	X
iajs-319	194	9	.	.	PUNCT
iajs-319	194	10	propositions(2.18	propositions(2.18	NUM
iajs-319	194	11	):	):	PUNCT
iajs-319	194	12	let	let	NOUN
iajs-319	194	13	)	)	PUNCT
iajs-319	194	14	,	,	PUNCT
iajs-319	194	15	x	x	X
iajs-319	194	16	(	(	PUNCT
iajs-319	194	17			NOUN
iajs-319	194	18	be	be	VERB
iajs-319	194	19	a	a	DET
iajs-319	194	20	topological	topological	ADJ
iajs-319	194	21	space	space	NOUN
iajs-319	194	22	and	and	CCONJ
iajs-319	194	23	b	b	NOUN
iajs-319	194	24	be	be	AUX
iajs-319	194	25	a	a	DET
iajs-319	194	26	subset	subset	NOUN
iajs-319	194	27	of	of	ADP
iajs-319	194	28	x	x	X
iajs-319	194	29	.	.	PUNCT
iajs-319	195	1	then	then	ADV
iajs-319	195	2	the	the	DET
iajs-319	195	3	following	follow	VERB
iajs-319	195	4	statements	statement	NOUN
iajs-319	195	5	are	be	AUX
iajs-319	195	6	equivalent	equivalent	ADJ
iajs-319	195	7	:	:	PUNCT
iajs-319	195	8	i	i	NOUN
iajs-319	195	9	)	)	PUNCT
iajs-319	195	10	b	b	PROPN
iajs-319	195	11	is	be	AUX
iajs-319	195	12	s*g-	s*g-	PROPN
iajs-319	195	13	-closed	-close	VERB
iajs-319	195	14	.	.	PUNCT
iajs-319	196	1	ii	ii	PROPN
iajs-319	196	2	)	)	PUNCT
iajs-319	196	3	b)))b(cl((intcl	b)))b(cl((intcl	PROPN
iajs-319	197	1	g*s	g*s	PROPN
iajs-319	197	2			PROPN
iajs-319	197	3	.	.	PUNCT
iajs-319	198	1	iii	iii	X
iajs-319	198	2	)	)	PUNCT
iajs-319	198	3	there	there	PRON
iajs-319	198	4	exists	exist	VERB
iajs-319	198	5	a	a	DET
iajs-319	198	6	closed	closed	ADJ
iajs-319	198	7	subset	subset	NOUN
iajs-319	198	8	f	f	PROPN
iajs-319	198	9	of	of	ADP
iajs-319	198	10	x	x	INTJ
iajs-319	198	11	such	such	ADJ
iajs-319	198	12	that	that	DET
iajs-319	198	13	fb))f((intcl	fb))f((intcl	NOUN
iajs-319	198	14	g*s	g*s	PROPN
iajs-319	198	15			VERB
iajs-319	198	16	.	.	PUNCT
iajs-319	199	1	proof	proof	NOUN
iajs-319	199	2	:	:	PUNCT
iajs-319	199	3	)	)	PUNCT
iajs-319	199	4	ii()i	ii()i	SYM
iajs-319	199	5	(	(	PUNCT
iajs-319	199	6			NOUN
iajs-319	199	7	.	.	PUNCT
iajs-319	200	1	since	since	SCONJ
iajs-319	200	2	b	b	PROPN
iajs-319	200	3	is	be	AUX
iajs-319	200	4	an	an	DET
iajs-319	200	5	s*g-	s*g-	NOUN
iajs-319	200	6	-closed	-close	VERB
iajs-319	200	7	set	set	VERB
iajs-319	200	8	in	in	ADP
iajs-319	200	9	x	x	PROPN
iajs-319	200	10			NOUN
iajs-319	200	11	bx	bx	PROPN
iajs-319	200	12			PROPN
iajs-319	200	13	is	be	AUX
iajs-319	200	14	an	an	DET
iajs-319	200	15	s*g-	s*g-	NOUN
iajs-319	200	16	-open	-open	NOUN
iajs-319	200	17	set	set	VERB
iajs-319	200	18	in	in	ADP
iajs-319	200	19	x	x	PROPN
iajs-319	200	20			NOUN
iajs-319	200	21	)	)	PUNCT
iajs-319	200	22	)	)	PUNCT
iajs-319	200	23	)	)	PUNCT
iajs-319	200	24	bx(int(clint(bx	bx(int(clint(bx	PROPN
iajs-319	201	1	g*s	g*	VERB
iajs-319	201	2			PROPN
iajs-319	201	3			NOUN
iajs-319	201	4	)	)	PUNCT
iajs-319	201	5	)	)	PUNCT
iajs-319	201	6	)	)	PUNCT
iajs-319	202	1	b(clx(clint(bx	b(clx(clint(bx	PROPN
iajs-319	202	2	g*s	g*s	PROPN
iajs-319	202	3			NOUN
iajs-319	202	4	.	.	PUNCT
iajs-319	203	1	by	by	ADP
iajs-319	203	2	theorem	theorem	NOUN
iajs-319	203	3	(	(	PUNCT
iajs-319	203	4	(	(	PUNCT
iajs-319	203	5	1.5	1.5	NUM
iajs-319	203	6	)	)	PUNCT
iajs-319	203	7	,	,	PUNCT
iajs-319	203	8	vi	vi	PROPN
iajs-319	203	9	)	)	PUNCT
iajs-319	203	10	,	,	PUNCT
iajs-319	203	11	we	we	PRON
iajs-319	203	12	get	get	VERB
iajs-319	203	13	)	)	PUNCT
iajs-319	203	14	)	)	PUNCT
iajs-319	204	1	b(clx(cl))b(cl(intx	b(clx(cl))b(cl(intx	VERB
iajs-319	204	2	g*sg*s	g*sg*s	PROPN
iajs-319	204	3			PROPN
iajs-319	204	4	.	.	PUNCT
iajs-319	205	1	hence	hence	ADV
iajs-319	205	2	)	)	PUNCT
iajs-319	205	3	)	)	PUNCT
iajs-319	205	4	)	)	PUNCT
iajs-319	206	1	b(cl(intxint(bx	b(cl(intxint(bx	NUM
iajs-319	206	2	g*s	g*s	NOUN
iajs-319	206	3			PROPN
iajs-319	206	4	)	)	PUNCT
iajs-319	206	5	)	)	PUNCT
iajs-319	206	6	)	)	PUNCT
iajs-319	207	1	b(cl((intclxbx	b(cl((intclxbx	PROPN
iajs-319	207	2	g*s	g*s	PROPN
iajs-319	207	3			PROPN
iajs-319	207	4	b)))b(cl((intcl	b)))b(cl((intcl	PROPN
iajs-319	208	1	g*s	g*s	PROPN
iajs-319	208	2			PROPN
iajs-319	208	3	.	.	PUNCT
iajs-319	208	4	)	)	PUNCT
iajs-319	209	1	iii()ii	iii()ii	NOUN
iajs-319	209	2	(	(	PUNCT
iajs-319	209	3			NOUN
iajs-319	209	4	.	.	PUNCT
iajs-319	210	1	since	since	SCONJ
iajs-319	210	2	b)))b(cl((intcl	b)))b(cl((intcl	PROPN
iajs-319	210	3	g*s	g*s	PROPN
iajs-319	210	4			PROPN
iajs-319	210	5	and	and	CCONJ
iajs-319	210	6	)	)	PUNCT
iajs-319	210	7	b(clb	b(clb	NOUN
iajs-319	210	8	,	,	PUNCT
iajs-319	210	9	then	then	ADV
iajs-319	210	10	)	)	PUNCT
iajs-319	210	11	b(clb)))b(cl((intcl	b(clb)))b(cl((intcl	PROPN
iajs-319	210	12	g*s	g*s	PROPN
iajs-319	210	13			PROPN
iajs-319	210	14	.	.	PUNCT
iajs-319	211	1	put	put	VERB
iajs-319	211	2	)	)	PUNCT
iajs-319	211	3	b(clf	b(clf	PROPN
iajs-319	211	4			PROPN
iajs-319	211	5	,	,	PUNCT
iajs-319	211	6	thus	thus	ADV
iajs-319	211	7	there	there	PRON
iajs-319	211	8	exists	exist	VERB
iajs-319	211	9	a	a	DET
iajs-319	211	10	closed	closed	ADJ
iajs-319	211	11	subset	subset	NOUN
iajs-319	211	12	f	f	PROPN
iajs-319	211	13	of	of	ADP
iajs-319	211	14	x	x	INTJ
iajs-319	211	15	such	such	ADJ
iajs-319	211	16	that	that	DET
iajs-319	211	17	fb))f((intcl	fb))f((intcl	NOUN
iajs-319	211	18	g*s	g*s	PROPN
iajs-319	211	19			VERB
iajs-319	211	20	.	.	PUNCT
iajs-319	211	21	)	)	PUNCT
iajs-319	212	1	i()iii	i()iii	PRON
iajs-319	212	2	(	(	PUNCT
iajs-319	212	3			NOUN
iajs-319	212	4	.	.	PUNCT
iajs-319	213	1	suppose	suppose	VERB
iajs-319	213	2	that	that	SCONJ
iajs-319	213	3	there	there	PRON
iajs-319	213	4	exists	exist	VERB
iajs-319	213	5	a	a	DET
iajs-319	213	6	closed	closed	ADJ
iajs-319	213	7	subset	subset	NOUN
iajs-319	213	8	f	f	PROPN
iajs-319	213	9	of	of	ADP
iajs-319	213	10	x	x	INTJ
iajs-319	213	11	such	such	ADJ
iajs-319	213	12	that	that	DET
iajs-319	213	13	fb))f((intcl	fb))f((intcl	NOUN
iajs-319	213	14	g*s	g*s	PROPN
iajs-319	213	15			VERB
iajs-319	213	16	.	.	PUNCT
iajs-319	214	1	hence	hence	ADV
iajs-319	214	2	)	)	PUNCT
iajs-319	214	3	)	)	PUNCT
iajs-319	215	1	f((intclxbxfx	f((intclxbxfx	NOUN
iajs-319	215	2	g*s	g*s	PROPN
iajs-319	215	3			NOUN
iajs-319	215	4	)	)	PUNCT
iajs-319	215	5	)	)	PUNCT
iajs-319	215	6	f(intxint	f(intxint	NOUN
iajs-319	215	7	(	(	PUNCT
iajs-319	215	8	g*s	g*s	NOUN
iajs-319	215	9	.	.	PUNCT
iajs-319	216	1	since	since	SCONJ
iajs-319	216	2	)	)	PUNCT
iajs-319	216	3	fx(cl)f(intx	fx(cl)f(intx	NOUN
iajs-319	216	4	g*sg*s	g*sg*s	PROPN
iajs-319	216	5			PROPN
iajs-319	216	6	,	,	PUNCT
iajs-319	216	7	then	then	ADV
iajs-319	216	8	)	)	PUNCT
iajs-319	216	9	)	)	PUNCT
iajs-319	216	10	fx(clint(bxfx	fx(clint(bxfx	PROPN
iajs-319	217	1	g*s	g*s	PROPN
iajs-319	217	2			PROPN
iajs-319	217	3	.	.	PUNCT
iajs-319	218	1	hence	hence	ADV
iajs-319	218	2	bx	bx	PROPN
iajs-319	218	3			PROPN
iajs-319	218	4	is	be	AUX
iajs-319	218	5	an	an	DET
iajs-319	218	6	s*g-	s*g-	NOUN
iajs-319	218	7	-open	-open	NOUN
iajs-319	218	8	set	set	VERB
iajs-319	218	9	in	in	ADP
iajs-319	218	10	x	x	X
iajs-319	218	11	.	.	PUNCT
iajs-319	219	1	thus	thus	ADV
iajs-319	219	2	b	b	X
iajs-319	219	3	is	be	AUX
iajs-319	219	4	an	an	DET
iajs-319	219	5	s*g-	s*g-	NOUN
iajs-319	219	6	closed	close	VERB
iajs-319	219	7	set	set	VERB
iajs-319	219	8	in	in	ADP
iajs-319	219	9	x	x	X
iajs-319	219	10	.	.	PUNCT
iajs-319	220	1	definition(2.19	definition(2.19	NUM
iajs-319	220	2	):	):	PUNCT
iajs-319	220	3	a	a	DET
iajs-319	220	4	subset	subset	NOUN
iajs-319	220	5	a	a	PRON
iajs-319	220	6	of	of	ADP
iajs-319	220	7	a	a	DET
iajs-319	220	8	topological	topological	ADJ
iajs-319	220	9	space	space	NOUN
iajs-319	220	10	)	)	PUNCT
iajs-319	220	11	,	,	PUNCT
iajs-319	220	12	x	x	X
iajs-319	220	13	(	(	PUNCT
iajs-319	220	14			NOUN
iajs-319	220	15	is	be	AUX
iajs-319	220	16	called	call	VERB
iajs-319	220	17	an	an	DET
iajs-319	220	18	s*g-	s*g-	NOUN
iajs-319	220	19	-neighborhood	-neighborhood	NOUN
iajs-319	220	20	of	of	ADP
iajs-319	220	21	a	a	DET
iajs-319	220	22	point	point	NOUN
iajs-319	220	23	x	x	PUNCT
iajs-319	220	24	in	in	ADP
iajs-319	220	25	x	x	PRON
iajs-319	220	26	if	if	SCONJ
iajs-319	220	27	there	there	PRON
iajs-319	220	28	exists	exist	VERB
iajs-319	220	29	an	an	DET
iajs-319	220	30	s*g-	s*g-	NOUN
iajs-319	220	31	-open	-open	NOUN
iajs-319	220	32	set	set	VERB
iajs-319	220	33	u	u	NOUN
iajs-319	220	34	in	in	ADP
iajs-319	220	35	x	x	SYM
iajs-319	220	36	such	such	ADJ
iajs-319	220	37	that	that	SCONJ
iajs-319	220	38	aux	aux	PROPN
iajs-319	220	39			PROPN
iajs-319	220	40	.	.	PUNCT
iajs-319	221	1	remark(2.20	remark(2.20	NUM
iajs-319	221	2	):	):	PUNCT
iajs-319	221	3	since	since	SCONJ
iajs-319	221	4	every	every	DET
iajs-319	221	5	open	open	ADJ
iajs-319	221	6	set	set	NOUN
iajs-319	221	7	is	be	AUX
iajs-319	221	8	an	an	DET
iajs-319	221	9	s*g-	s*g-	NOUN
iajs-319	221	10	-open	-open	NOUN
iajs-319	221	11	set	set	NOUN
iajs-319	221	12	,	,	PUNCT
iajs-319	221	13	then	then	ADV
iajs-319	221	14	every	every	DET
iajs-319	221	15	neighborhood	neighborhood	NOUN
iajs-319	221	16	of	of	ADP
iajs-319	221	17	x	x	PUNCT
iajs-319	221	18	is	be	AUX
iajs-319	221	19	an	an	DET
iajs-319	221	20	s*g-	s*g-	NOUN
iajs-319	221	21	-neighborhood	-neighborhood	NOUN
iajs-319	221	22	of	of	ADP
iajs-319	221	23	x	x	PRON
iajs-319	221	24	,	,	PUNCT
iajs-319	221	25	but	but	CCONJ
iajs-319	221	26	the	the	DET
iajs-319	221	27	converse	converse	NOUN
iajs-319	221	28	is	be	AUX
iajs-319	221	29	not	not	PART
iajs-319	221	30	true	true	ADJ
iajs-319	221	31	in	in	ADP
iajs-319	221	32	general	general	ADJ
iajs-319	221	33	.	.	PUNCT
iajs-319	222	1	in	in	ADP
iajs-319	222	2	example	example	NOUN
iajs-319	222	3	(	(	PUNCT
iajs-319	222	4	2.2	2.2	NUM
iajs-319	222	5	)	)	PUNCT
iajs-319	222	6	,	,	PUNCT
iajs-319	222	7	}	}	PUNCT
iajs-319	222	8	b	b	X
iajs-319	222	9	,	,	PUNCT
iajs-319	222	10	a	a	PRON
iajs-319	222	11	{	{	PUNCT
iajs-319	222	12	is	be	AUX
iajs-319	222	13	an	an	DET
iajs-319	222	14	s*g-	s*g-	NOUN
iajs-319	222	15	-neighborhood	-neighborhood	NOUN
iajs-319	222	16	of	of	ADP
iajs-319	222	17	a	a	DET
iajs-319	222	18	point	point	NOUN
iajs-319	222	19	b	b	NOUN
iajs-319	222	20	,	,	PUNCT
iajs-319	222	21	since	since	SCONJ
iajs-319	222	22	}	}	PUNCT
iajs-319	222	23	b	b	NOUN
iajs-319	222	24	,	,	PUNCT
iajs-319	222	25	a{}b	a{}b	NOUN
iajs-319	222	26	,	,	PUNCT
iajs-319	222	27	a{b	a{b	VERB
iajs-319	222	28			PROPN
iajs-319	222	29	.	.	PUNCT
iajs-319	223	1	but	but	CCONJ
iajs-319	223	2	}	}	PUNCT
iajs-319	223	3	b	b	NOUN
iajs-319	223	4	,	,	PUNCT
iajs-319	223	5	a	a	PRON
iajs-319	223	6	{	{	PUNCT
iajs-319	223	7	is	be	AUX
iajs-319	223	8	not	not	PART
iajs-319	223	9	a	a	DET
iajs-319	223	10	neighborhood	neighborhood	NOUN
iajs-319	223	11	of	of	ADP
iajs-319	223	12	a	a	DET
iajs-319	223	13	point	point	NOUN
iajs-319	223	14	b	b	NOUN
iajs-319	223	15	.	.	PUNCT
iajs-319	224	1	propositions(2.21	propositions(2.21	NOUN
iajs-319	224	2	):	):	PUNCT
iajs-319	224	3	a	a	DET
iajs-319	224	4	subset	subset	NOUN
iajs-319	224	5	a	a	PRON
iajs-319	224	6	of	of	ADP
iajs-319	224	7	a	a	DET
iajs-319	224	8	topological	topological	ADJ
iajs-319	224	9	space	space	NOUN
iajs-319	224	10	)	)	PUNCT
iajs-319	224	11	,	,	PUNCT
iajs-319	224	12	x	x	X
iajs-319	224	13	(	(	PUNCT
iajs-319	224	14			NOUN
iajs-319	224	15	is	be	AUX
iajs-319	224	16	s*g-	s*g-	NOUN
iajs-319	224	17	-open	-open	ADJ
iajs-319	224	18	if	if	SCONJ
iajs-319	224	19	and	and	CCONJ
iajs-319	224	20	only	only	ADV
iajs-319	224	21	if	if	SCONJ
iajs-319	224	22	it	it	PRON
iajs-319	224	23	is	be	AUX
iajs-319	224	24	an	an	DET
iajs-319	224	25	s*g-	s*g-	NOUN
iajs-319	224	26	-neighborhood	-neighborhood	NOUN
iajs-319	224	27	of	of	ADP
iajs-319	224	28	each	each	PRON
iajs-319	224	29	of	of	ADP
iajs-319	224	30	its	its	PRON
iajs-319	224	31	points	point	NOUN
iajs-319	224	32	.	.	PUNCT
iajs-319	225	1	548	548	NUM
iajs-319	225	2	|	|	ADV
iajs-319	225	3	mathematics	mathematic	NOUN
iajs-319	225	4	2014	2014	NUM
iajs-319	225	5	)	)	PUNCT
iajs-319	225	6	عام	عام	ADP
iajs-319	225	7	3العدد	3العدد	NUM
iajs-319	225	8	(	(	PUNCT
iajs-319	225	9	27مجلة	27مجلة	NUM
iajs-319	225	10	إبن	إبن	VERB
iajs-319	225	11	الھيثم	الھيثم	NOUN
iajs-319	225	12	للعلوم	للعلوم	NOUN
iajs-319	225	13	الصرفة	الصرفة	NOUN
iajs-319	226	1	و	و	PRON
iajs-319	226	2	التطبيقية	التطبيقية	ADV
iajs-319	226	3	المجلد	المجلد	VERB
iajs-319	226	4	ibn	ibn	PROPN
iajs-319	226	5	al	al	PROPN
iajs-319	226	6	-	-	PUNCT
iajs-319	226	7	haitham	haitham	PROPN
iajs-319	226	8	jour	jour	X
iajs-319	226	9	.	.	PROPN
iajs-319	227	1	for	for	ADP
iajs-319	227	2	pure	pure	ADJ
iajs-319	227	3	&	&	CCONJ
iajs-319	227	4	appl	appl	PROPN
iajs-319	227	5	.	.	PUNCT
iajs-319	228	1	sci	sci	PROPN
iajs-319	228	2	.	.	PUNCT
iajs-319	228	3	vol	vol	NOUN
iajs-319	228	4	.	.	PROPN
iajs-319	229	1	27	27	NUM
iajs-319	229	2	(	(	PUNCT
iajs-319	229	3	3	3	NUM
iajs-319	229	4	)	)	PUNCT
iajs-319	229	5	2014	2014	NUM
iajs-319	229	6	proof	proof	NOUN
iajs-319	229	7	:	:	PUNCT
iajs-319	229	8			NOUN
iajs-319	229	9	if	if	SCONJ
iajs-319	229	10	a	a	PRON
iajs-319	229	11	is	be	AUX
iajs-319	229	12	s*g-	s*g-	NOUN
iajs-319	229	13	-open	-open	ADJ
iajs-319	229	14	in	in	ADP
iajs-319	229	15	x	x	X
iajs-319	229	16	,	,	PUNCT
iajs-319	229	17	then	then	ADV
iajs-319	229	18	aax	aax	PROPN
iajs-319	229	19			PROPN
iajs-319	229	20	for	for	ADP
iajs-319	229	21	each	each	DET
iajs-319	229	22	ax	ax	NOUN
iajs-319	229	23	.	.	PUNCT
iajs-319	230	1	thus	thus	ADV
iajs-319	230	2	a	a	PRON
iajs-319	230	3	is	be	AUX
iajs-319	230	4	an	an	DET
iajs-319	230	5	s*g-	s*g-	NOUN
iajs-319	230	6	neighborhood	neighborhood	NOUN
iajs-319	230	7	of	of	ADP
iajs-319	230	8	each	each	PRON
iajs-319	230	9	of	of	ADP
iajs-319	230	10	its	its	PRON
iajs-319	230	11	points	point	NOUN
iajs-319	230	12	.	.	PUNCT
iajs-319	231	1	conversely	conversely	ADV
iajs-319	231	2	,	,	PUNCT
iajs-319	231	3	suppose	suppose	VERB
iajs-319	231	4	that	that	SCONJ
iajs-319	231	5	a	a	PRON
iajs-319	231	6	is	be	AUX
iajs-319	231	7	an	an	DET
iajs-319	231	8	s*g-	s*g-	NOUN
iajs-319	231	9	-neighborhood	-neighborhood	NOUN
iajs-319	231	10	of	of	ADP
iajs-319	231	11	each	each	PRON
iajs-319	231	12	of	of	ADP
iajs-319	231	13	its	its	PRON
iajs-319	231	14	points	point	NOUN
iajs-319	231	15	.	.	PUNCT
iajs-319	232	1	then	then	ADV
iajs-319	232	2	for	for	ADP
iajs-319	232	3	each	each	DET
iajs-319	232	4	ax	ax	NOUN
iajs-319	232	5	,	,	PUNCT
iajs-319	232	6	there	there	PRON
iajs-319	232	7	exists	exist	VERB
iajs-319	232	8	an	an	DET
iajs-319	232	9	s*g-	s*g-	NOUN
iajs-319	232	10	-open	-open	NOUN
iajs-319	232	11	set	set	VERB
iajs-319	232	12	xu	xu	INTJ
iajs-319	232	13	in	in	ADP
iajs-319	232	14	x	x	X
iajs-319	232	15	such	such	ADJ
iajs-319	232	16	that	that	SCONJ
iajs-319	232	17	aux	aux	PROPN
iajs-319	232	18	x	x	X
iajs-319	232	19			PROPN
iajs-319	232	20	.	.	PUNCT
iajs-319	233	1	hence	hence	ADV
iajs-319	233	2	au	au	VERB
iajs-319	233	3	ax	ax	NOUN
iajs-319	233	4	x	x	PUNCT
iajs-319	233	5			PROPN
iajs-319	233	6			PROPN
iajs-319	233	7			VERB
iajs-319	233	8	.	.	PUNCT
iajs-319	234	1	since	since	SCONJ
iajs-319	234	2			ADJ
iajs-319	234	3	ax	ax	NOUN
iajs-319	234	4	xua	xua	PROPN
iajs-319	234	5			PROPN
iajs-319	234	6			PROPN
iajs-319	234	7	,	,	PUNCT
iajs-319	234	8	therefore	therefore	ADV
iajs-319	234	9			ADJ
iajs-319	234	10	ax	ax	NOUN
iajs-319	234	11	xua	xua	PROPN
iajs-319	234	12			PROPN
iajs-319	234	13			PRON
iajs-319	234	14	.	.	PUNCT
iajs-319	235	1	thus	thus	ADV
iajs-319	235	2	a	a	PRON
iajs-319	235	3	is	be	AUX
iajs-319	235	4	an	an	DET
iajs-319	235	5	s*g-	s*g-	NOUN
iajs-319	235	6	-open	-open	NOUN
iajs-319	235	7	set	set	VERB
iajs-319	235	8	in	in	ADP
iajs-319	235	9	x	x	NOUN
iajs-319	235	10	,	,	PUNCT
iajs-319	235	11	since	since	SCONJ
iajs-319	235	12	it	it	PRON
iajs-319	235	13	is	be	AUX
iajs-319	235	14	a	a	DET
iajs-319	235	15	union	union	NOUN
iajs-319	235	16	of	of	ADP
iajs-319	235	17	s*g-	s*g-	NOUN
iajs-319	235	18	-open	-open	PROPN
iajs-319	235	19	sets	set	NOUN
iajs-319	235	20	.	.	PUNCT
iajs-319	236	1	proposition(2.22	proposition(2.22	X
iajs-319	236	2	):	):	PUNCT
iajs-319	236	3	if	if	SCONJ
iajs-319	236	4	a	a	PRON
iajs-319	236	5	is	be	AUX
iajs-319	236	6	an	an	DET
iajs-319	236	7	s*g-	s*g-	NOUN
iajs-319	236	8	-open	-open	NOUN
iajs-319	236	9	set	set	VERB
iajs-319	236	10	in	in	ADP
iajs-319	236	11	a	a	DET
iajs-319	236	12	topological	topological	ADJ
iajs-319	236	13	space	space	NOUN
iajs-319	236	14	)	)	PUNCT
iajs-319	236	15	,	,	PUNCT
iajs-319	236	16	x	x	X
iajs-319	236	17	(	(	PUNCT
iajs-319	236	18			NOUN
iajs-319	236	19	and	and	CCONJ
iajs-319	236	20	)	)	PUNCT
iajs-319	236	21	aint(ba	aint(ba	PROPN
iajs-319	236	22			PROPN
iajs-319	236	23	,	,	PUNCT
iajs-319	236	24	then	then	ADV
iajs-319	236	25	b	b	PROPN
iajs-319	236	26	is	be	AUX
iajs-319	236	27	an	an	DET
iajs-319	236	28	s*g-	s*g-	NOUN
iajs-319	236	29	-open	-open	NOUN
iajs-319	236	30	set	set	VERB
iajs-319	236	31	in	in	ADP
iajs-319	236	32	x	x	X
iajs-319	236	33	.	.	PUNCT
iajs-319	237	1	proof	proof	NOUN
iajs-319	237	2	:	:	PUNCT
iajs-319	237	3	since	since	SCONJ
iajs-319	237	4	a	a	PRON
iajs-319	237	5	is	be	AUX
iajs-319	237	6	an	an	DET
iajs-319	237	7	s*g-	s*g-	NOUN
iajs-319	237	8	-open	-open	NOUN
iajs-319	237	9	set	set	VERB
iajs-319	237	10	in	in	ADP
iajs-319	237	11	x	x	X
iajs-319	237	12	,	,	PUNCT
iajs-319	237	13	then	then	ADV
iajs-319	237	14	by	by	ADP
iajs-319	237	15	proposition	proposition	NOUN
iajs-319	237	16	(	(	PUNCT
iajs-319	237	17	2.15	2.15	NUM
iajs-319	237	18	)	)	PUNCT
iajs-319	237	19	,	,	PUNCT
iajs-319	237	20	there	there	PRON
iajs-319	237	21	exists	exist	VERB
iajs-319	237	22	an	an	DET
iajs-319	237	23	open	open	ADJ
iajs-319	237	24	subset	subset	ADJ
iajs-319	237	25	u	u	NOUN
iajs-319	237	26	of	of	ADP
iajs-319	237	27	x	x	SYM
iajs-319	237	28	such	such	ADJ
iajs-319	237	29	that	that	PRON
iajs-319	237	30	)	)	PUNCT
iajs-319	237	31	)	)	PUNCT
iajs-319	237	32	u(clint(au	u(clint(au	NOUN
iajs-319	237	33	g*s	g*s	NOUN
iajs-319	237	34	.	.	PUNCT
iajs-319	238	1	since	since	SCONJ
iajs-319	238	2	ba	ba	PROPN
iajs-319	238	3			PROPN
iajs-319	238	4			PROPN
iajs-319	238	5	bu	bu	PROPN
iajs-319	238	6			PROPN
iajs-319	238	7	.	.	PUNCT
iajs-319	239	1	but	but	CCONJ
iajs-319	239	2	)	)	PUNCT
iajs-319	239	3	)	)	PUNCT
iajs-319	240	1	u(clint()aint	u(clint()aint	PROPN
iajs-319	240	2	(	(	PUNCT
iajs-319	240	3	g*s	g*s	PROPN
iajs-319	240	4			PROPN
iajs-319	240	5	)	)	PUNCT
iajs-319	240	6	)	)	PUNCT
iajs-319	241	1	u(clint(bu	u(clint(bu	PROPN
iajs-319	241	2	g*s	g*s	NOUN
iajs-319	241	3	.	.	PUNCT
iajs-319	242	1	thus	thus	ADV
iajs-319	242	2	b	b	X
iajs-319	242	3	is	be	AUX
iajs-319	242	4	an	an	DET
iajs-319	242	5	s*g-	s*g-	NOUN
iajs-319	242	6	-open	-open	NOUN
iajs-319	242	7	set	set	VERB
iajs-319	242	8	in	in	ADP
iajs-319	242	9	x	x	X
iajs-319	242	10	.	.	PUNCT
iajs-319	243	1	proposition(2.23	proposition(2.23	NOUN
iajs-319	243	2	):	):	PUNCT
iajs-319	243	3	if	if	SCONJ
iajs-319	243	4	a	a	PRON
iajs-319	243	5	is	be	AUX
iajs-319	243	6	an	an	DET
iajs-319	243	7	s*g-	s*g-	NOUN
iajs-319	243	8	-closed	-close	VERB
iajs-319	243	9	set	set	NOUN
iajs-319	243	10	in	in	ADP
iajs-319	243	11	a	a	DET
iajs-319	243	12	topological	topological	ADJ
iajs-319	243	13	space	space	NOUN
iajs-319	243	14	)	)	PUNCT
iajs-319	243	15	,	,	PUNCT
iajs-319	243	16	x	x	X
iajs-319	243	17	(	(	PUNCT
iajs-319	243	18			NOUN
iajs-319	243	19	and	and	CCONJ
iajs-319	243	20	ab)a(cl	ab)a(cl	NOUN
iajs-319	243	21			PROPN
iajs-319	243	22	,	,	PUNCT
iajs-319	243	23	then	then	ADV
iajs-319	243	24	b	b	PROPN
iajs-319	243	25	is	be	AUX
iajs-319	243	26	an	an	DET
iajs-319	243	27	s*g-	s*g-	NOUN
iajs-319	243	28	-closed	-close	VERB
iajs-319	243	29	set	set	VERB
iajs-319	243	30	in	in	ADP
iajs-319	243	31	x	x	X
iajs-319	243	32	.	.	PUNCT
iajs-319	244	1	proof	proof	NOUN
iajs-319	244	2	:	:	PUNCT
iajs-319	244	3	since	since	SCONJ
iajs-319	244	4			NUM
iajs-319	244	5	)	)	PUNCT
iajs-319	244	6	a(clxbxax	a(clxbxax	NOUN
iajs-319	244	7	)	)	PUNCT
iajs-319	244	8	axint	axint	NOUN
iajs-319	244	9	(	(	PUNCT
iajs-319	244	10			NOUN
iajs-319	244	11	,	,	PUNCT
iajs-319	244	12	then	then	ADV
iajs-319	244	13	by	by	ADP
iajs-319	244	14	proposition	proposition	NOUN
iajs-319	244	15	(	(	PUNCT
iajs-319	244	16	2.22	2.22	NUM
iajs-319	244	17	)	)	PUNCT
iajs-319	244	18	bx	bx	PROPN
iajs-319	244	19			PROPN
iajs-319	244	20	is	be	AUX
iajs-319	244	21	an	an	DET
iajs-319	244	22	s*g-	s*g-	NOUN
iajs-319	244	23	-open	-open	NOUN
iajs-319	244	24	set	set	VERB
iajs-319	244	25	in	in	ADP
iajs-319	244	26	x	x	X
iajs-319	244	27	.	.	PUNCT
iajs-319	245	1	thus	thus	ADV
iajs-319	245	2	b	b	X
iajs-319	245	3	is	be	AUX
iajs-319	245	4	an	an	DET
iajs-319	245	5	s*g-	s*g-	NOUN
iajs-319	245	6	-closed	-close	VERB
iajs-319	245	7	set	set	VERB
iajs-319	245	8	in	in	ADP
iajs-319	245	9	x	x	X
iajs-319	245	10	.	.	PUNCT
iajs-319	246	1	theorem(2.24	theorem(2.24	NUM
iajs-319	246	2	):	):	PUNCT
iajs-319	246	3	a	a	DET
iajs-319	246	4	subset	subset	NOUN
iajs-319	246	5	a	a	PRON
iajs-319	246	6	of	of	ADP
iajs-319	246	7	a	a	DET
iajs-319	246	8	topological	topological	ADJ
iajs-319	246	9	space	space	NOUN
iajs-319	246	10	)	)	PUNCT
iajs-319	246	11	,	,	PUNCT
iajs-319	246	12	x	x	X
iajs-319	246	13	(	(	PUNCT
iajs-319	246	14			NOUN
iajs-319	246	15	is	be	AUX
iajs-319	246	16	clopen	clopen	ADJ
iajs-319	246	17	(	(	PUNCT
iajs-319	246	18	open	open	ADJ
iajs-319	246	19	and	and	CCONJ
iajs-319	246	20	closed	closed	ADJ
iajs-319	246	21	)	)	PUNCT
iajs-319	246	22	if	if	SCONJ
iajs-319	246	23	and	and	CCONJ
iajs-319	246	24	only	only	ADV
iajs-319	246	25	if	if	SCONJ
iajs-319	246	26	a	a	PRON
iajs-319	246	27	is	be	AUX
iajs-319	246	28	s*g-	s*g-	NOUN
iajs-319	246	29	-clopen	-clopen	ADJ
iajs-319	246	30	(	(	PUNCT
iajs-319	246	31	s*g-	s*g-	NOUN
iajs-319	246	32	-open	-open	NOUN
iajs-319	246	33	and	and	CCONJ
iajs-319	246	34	s*g-	s*g-	NOUN
iajs-319	246	35	-closed	-close	VERB
iajs-319	246	36	)	)	PUNCT
iajs-319	246	37	.	.	PUNCT
iajs-319	247	1	proof	proof	NOUN
iajs-319	247	2	:	:	PUNCT
iajs-319	247	3	(	(	PUNCT
iajs-319	247	4			NOUN
iajs-319	247	5	)	)	PUNCT
iajs-319	247	6	.	.	PUNCT
iajs-319	248	1	it	it	PRON
iajs-319	248	2	is	be	AUX
iajs-319	248	3	a	a	DET
iajs-319	248	4	obvious	obvious	ADJ
iajs-319	248	5	.	.	PUNCT
iajs-319	249	1	(	(	PUNCT
iajs-319	249	2			PROPN
iajs-319	249	3	)	)	PUNCT
iajs-319	249	4	.	.	PUNCT
iajs-319	250	1	suppose	suppose	VERB
iajs-319	250	2	that	that	SCONJ
iajs-319	250	3	a	a	PRON
iajs-319	250	4	is	be	AUX
iajs-319	250	5	an	an	DET
iajs-319	250	6	s*g-	s*g-	NOUN
iajs-319	250	7	-clopen	-clopen	NOUN
iajs-319	250	8	set	set	VERB
iajs-319	250	9	in	in	ADP
iajs-319	250	10	x	x	SYM
iajs-319	250	11	,	,	PUNCT
iajs-319	250	12	then	then	ADV
iajs-319	250	13	a	a	PRON
iajs-319	250	14	is	be	AUX
iajs-319	250	15	s*g-	s*g-	NOUN
iajs-319	250	16	-open	-open	ADJ
iajs-319	250	17	and	and	CCONJ
iajs-319	250	18	s*g-	s*g-	NOUN
iajs-319	250	19	-closed	-close	VERB
iajs-319	250	20	in	in	ADP
iajs-319	250	21	x	x	X
iajs-319	250	22	.	.	PUNCT
iajs-319	251	1	hence	hence	ADV
iajs-319	251	2	)	)	PUNCT
iajs-319	251	3	)	)	PUNCT
iajs-319	251	4	)	)	PUNCT
iajs-319	251	5	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	251	6	g*s	g*s	PROPN
iajs-319	251	7	and	and	CCONJ
iajs-319	251	8	a)))a(cl((intcl	a)))a(cl((intcl	PROPN
iajs-319	251	9	g*s	g*s	PROPN
iajs-319	251	10			PROPN
iajs-319	251	11	.	.	PUNCT
iajs-319	252	1	but	but	CCONJ
iajs-319	252	2	by	by	ADP
iajs-319	252	3	theorem	theorem	NOUN
iajs-319	252	4	(	(	PUNCT
iajs-319	252	5	(	(	PUNCT
iajs-319	252	6	1.5	1.5	NUM
iajs-319	252	7	)	)	PUNCT
iajs-319	252	8	,	,	PUNCT
iajs-319	252	9	i	i	PRON
iajs-319	252	10	,	,	PUNCT
iajs-319	252	11	ii	ii	PROPN
iajs-319	252	12	)	)	PUNCT
iajs-319	252	13	we	we	PRON
iajs-319	252	14	get	get	VERB
iajs-319	252	15	,	,	PUNCT
iajs-319	252	16	)	)	PUNCT
iajs-319	252	17	a(cl)a(cl	a(cl)a(cl	PROPN
iajs-319	253	1	g*s	g*s	PROPN
iajs-319	253	2			PROPN
iajs-319	253	3	and	and	CCONJ
iajs-319	253	4	)	)	PUNCT
iajs-319	253	5	a(int)aint	a(int)aint	PROPN
iajs-319	253	6	(	(	PUNCT
iajs-319	253	7	g*s	g*s	PROPN
iajs-319	253	8	,	,	PUNCT
iajs-319	253	9	thus	thus	ADV
iajs-319	253	10	:	:	PUNCT
iajs-319	253	11	)	)	PUNCT
iajs-319	253	12	)	)	PUNCT
iajs-319	253	13	)	)	PUNCT
iajs-319	253	14	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	253	15			PROPN
iajs-319	253	16	and	and	CCONJ
iajs-319	253	17	a)))a(cl(int(cl	a)))a(cl(int(cl	PROPN
iajs-319	253	18			PROPN
iajs-319	253	19	.	.	PUNCT
iajs-319	254	1	since	since	SCONJ
iajs-319	254	2	a)aint	a)aint	PROPN
iajs-319	254	3	(	(	PUNCT
iajs-319	254	4			PROPN
iajs-319	254	5			PROPN
iajs-319	254	6	)	)	PUNCT
iajs-319	254	7	a(cl))a(int(cl	a(cl))a(int(cl	NOUN
iajs-319	254	8			PROPN
iajs-319	254	9	----------	----------	PUNCT
iajs-319	254	10	(	(	PUNCT
iajs-319	254	11	1	1	NUM
iajs-319	254	12	)	)	PUNCT
iajs-319	254	13	since	since	SCONJ
iajs-319	254	14	)	)	PUNCT
iajs-319	254	15	)	)	PUNCT
iajs-319	254	16	a(int(cl)))a(int(clint	a(int(cl)))a(int(clint	PROPN
iajs-319	254	17	(	(	PUNCT
iajs-319	254	18			PROPN
iajs-319	254	19	,	,	PUNCT
iajs-319	254	20	thus	thus	ADV
iajs-319	254	21	)	)	PUNCT
iajs-319	254	22	)	)	PUNCT
iajs-319	255	1	a(int(cl)))a(int(clint(a	a(int(cl)))a(int(clint(a	ADP
iajs-319	255	2			ADJ
iajs-319	255	3			NOUN
iajs-319	255	4	)	)	PUNCT
iajs-319	255	5	)	)	PUNCT
iajs-319	255	6	a(int(cl)a(cl	a(int(cl)a(cl	PROPN
iajs-319	256	1			PROPN
iajs-319	256	2	----------	----------	PUNCT
iajs-319	256	3	(	(	PUNCT
iajs-319	256	4	2	2	NUM
iajs-319	256	5	)	)	PUNCT
iajs-319	256	6	therefore	therefore	ADV
iajs-319	256	7	from	from	ADP
iajs-319	256	8	(	(	PUNCT
iajs-319	256	9	1	1	NUM
iajs-319	256	10	)	)	PUNCT
iajs-319	256	11	and	and	CCONJ
iajs-319	256	12	(	(	PUNCT
iajs-319	256	13	2	2	NUM
iajs-319	256	14	)	)	PUNCT
iajs-319	256	15	,	,	PUNCT
iajs-319	256	16	we	we	PRON
iajs-319	256	17	get	get	VERB
iajs-319	256	18	)	)	PUNCT
iajs-319	256	19	a(cl))a(int(cl	a(cl))a(int(cl	NOUN
iajs-319	256	20			NUM
iajs-319	256	21	-----------(a	-----------(a	NOUN
iajs-319	256	22	)	)	PUNCT
iajs-319	256	23	similarly	similarly	ADV
iajs-319	256	24	,	,	PUNCT
iajs-319	256	25	since	since	SCONJ
iajs-319	256	26	)	)	PUNCT
iajs-319	256	27	a(cla	a(cla	ADP
iajs-319	256	28			PROPN
iajs-319	256	29			NOUN
iajs-319	256	30	)	)	PUNCT
iajs-319	256	31	)	)	PUNCT
iajs-319	256	32	a(clint()aint	a(clint()aint	NOUN
iajs-319	256	33	(	(	PUNCT
iajs-319	256	34			PROPN
iajs-319	256	35	----------	----------	PUNCT
iajs-319	256	36	(	(	PUNCT
iajs-319	256	37	3	3	NUM
iajs-319	256	38	)	)	PUNCT
iajs-319	256	39	now	now	ADV
iajs-319	256	40	,	,	PUNCT
iajs-319	256	41	a)))a(cl(int(cl))a(clint	a)))a(cl(int(cl))a(clint	PROPN
iajs-319	256	42	(	(	PUNCT
iajs-319	256	43			ADJ
iajs-319	256	44	,	,	PUNCT
iajs-319	256	45	thus	thus	ADV
iajs-319	256	46	)	)	PUNCT
iajs-319	257	1	aint())a(clint	aint())a(clint	PROPN
iajs-319	257	2	(	(	PUNCT
iajs-319	257	3			PROPN
iajs-319	257	4	-----------(4	-----------(4	PROPN
iajs-319	257	5	)	)	PUNCT
iajs-319	257	6	therefore	therefore	ADV
iajs-319	257	7	from	from	ADP
iajs-319	257	8	(	(	PUNCT
iajs-319	257	9	3	3	NUM
iajs-319	257	10	)	)	PUNCT
iajs-319	257	11	and	and	CCONJ
iajs-319	257	12	(	(	PUNCT
iajs-319	257	13	4	4	NUM
iajs-319	257	14	)	)	PUNCT
iajs-319	257	15	,	,	PUNCT
iajs-319	257	16	we	we	PRON
iajs-319	257	17	get	get	VERB
iajs-319	257	18	)	)	PUNCT
iajs-319	258	1	aint())a(clint	aint())a(clint	PROPN
iajs-319	258	2	(	(	PUNCT
iajs-319	258	3			NOUN
iajs-319	258	4	----------	----------	PUNCT
iajs-319	258	5	(	(	PUNCT
iajs-319	258	6	b	b	NOUN
iajs-319	258	7	)	)	PUNCT
iajs-319	258	8	since	since	SCONJ
iajs-319	258	9	)	)	PUNCT
iajs-319	259	1	aint())a(clint	aint())a(clint	PROPN
iajs-319	259	2	(	(	PUNCT
iajs-319	259	3			PROPN
iajs-319	259	4			NOUN
iajs-319	259	5	)	)	PUNCT
iajs-319	259	6	a(cl))a(int(cl)))a(cl(int(cl	a(cl))a(int(cl)))a(cl(int(cl	NOUN
iajs-319	259	7			NUM
iajs-319	259	8	(	(	PUNCT
iajs-319	259	9	by	by	ADP
iajs-319	259	10	(	(	PUNCT
iajs-319	259	11	a	a	NOUN
iajs-319	259	12	)	)	PUNCT
iajs-319	259	13	)	)	PUNCT
iajs-319	259	14	.	.	PUNCT
iajs-319	260	1	since	since	SCONJ
iajs-319	260	2	a)))a(cl(int(cl	a)))a(cl(int(cl	PROPN
iajs-319	260	3			PROPN
iajs-319	260	4	,	,	PUNCT
iajs-319	260	5	then	then	ADV
iajs-319	260	6	a)a(cl	a)a(cl	NOUN
iajs-319	260	7			PROPN
iajs-319	260	8	,	,	PUNCT
iajs-319	260	9	but	but	CCONJ
iajs-319	260	10	)	)	PUNCT
iajs-319	260	11	a(cla	a(cla	ADP
iajs-319	260	12			PROPN
iajs-319	260	13	,	,	PUNCT
iajs-319	260	14	therefore	therefore	ADV
iajs-319	260	15	)	)	PUNCT
iajs-319	260	16	a(cla	a(cla	ADP
iajs-319	260	17			PROPN
iajs-319	260	18	,	,	PUNCT
iajs-319	260	19	hence	hence	ADV
iajs-319	260	20	a	a	PRON
iajs-319	260	21	is	be	AUX
iajs-319	260	22	a	a	DET
iajs-319	260	23	closed	closed	ADJ
iajs-319	260	24	set	set	NOUN
iajs-319	260	25	in	in	ADP
iajs-319	260	26	x	x	X
iajs-319	260	27	.	.	PUNCT
iajs-319	261	1	similarly	similarly	ADV
iajs-319	261	2	,	,	PUNCT
iajs-319	261	3	since	since	SCONJ
iajs-319	261	4	)	)	PUNCT
iajs-319	261	5	a(cl))a(int(cl	a(cl))a(int(cl	NOUN
iajs-319	261	6			PROPN
iajs-319	261	7			NOUN
iajs-319	261	8	)	)	PUNCT
iajs-319	261	9	aint())a(clint()))a(int(clint	aint())a(clint()))a(int(clint	ADP
iajs-319	261	10	(	(	PUNCT
iajs-319	261	11			NUM
iajs-319	261	12	(	(	PUNCT
iajs-319	261	13	by	by	ADP
iajs-319	261	14	(	(	PUNCT
iajs-319	261	15	b	b	NOUN
iajs-319	261	16	)	)	PUNCT
iajs-319	261	17	)	)	PUNCT
iajs-319	261	18	.	.	PUNCT
iajs-319	262	1	since	since	SCONJ
iajs-319	262	2	)	)	PUNCT
iajs-319	262	3	)	)	PUNCT
iajs-319	262	4	)	)	PUNCT
iajs-319	262	5	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	262	6			PROPN
iajs-319	262	7	,	,	PUNCT
iajs-319	262	8	then	then	ADV
iajs-319	262	9	)	)	PUNCT
iajs-319	262	10	aint(a	aint(a	NOUN
iajs-319	262	11			PROPN
iajs-319	262	12	,	,	PUNCT
iajs-319	262	13	but	but	CCONJ
iajs-319	262	14	a)aint	a)aint	NOUN
iajs-319	262	15	(	(	PUNCT
iajs-319	262	16			PROPN
iajs-319	262	17	,	,	PUNCT
iajs-319	262	18	therefore	therefore	ADV
iajs-319	262	19	)	)	PUNCT
iajs-319	262	20	aint(a	aint(a	VERB
iajs-319	262	21			PRON
iajs-319	262	22	,	,	PUNCT
iajs-319	262	23	hence	hence	ADV
iajs-319	262	24	a	a	PRON
iajs-319	262	25	is	be	AUX
iajs-319	262	26	an	an	DET
iajs-319	262	27	open	open	ADJ
iajs-319	262	28	set	set	NOUN
iajs-319	262	29	in	in	ADP
iajs-319	262	30	x	x	X
iajs-319	262	31	.	.	PUNCT
iajs-319	263	1	thus	thus	ADV
iajs-319	263	2	a	a	PRON
iajs-319	263	3	is	be	AUX
iajs-319	263	4	a	a	DET
iajs-319	263	5	clopen	clopen	ADJ
iajs-319	263	6	set	set	NOUN
iajs-319	263	7	in	in	ADP
iajs-319	263	8	x	x	PROPN
iajs-319	263	9	.	.	PUNCT
iajs-319	264	1	definition(2.25	definition(2.25	NOUN
iajs-319	264	2	):	):	PUNCT
iajs-319	264	3	let	let	NOUN
iajs-319	264	4	)	)	PUNCT
iajs-319	264	5	,	,	PUNCT
iajs-319	264	6	x	x	X
iajs-319	264	7	(	(	PUNCT
iajs-319	264	8			NOUN
iajs-319	264	9	be	be	VERB
iajs-319	264	10	a	a	DET
iajs-319	264	11	topological	topological	ADJ
iajs-319	264	12	space	space	NOUN
iajs-319	264	13	and	and	CCONJ
iajs-319	264	14	xa	xa	PROPN
iajs-319	264	15			PROPN
iajs-319	264	16	.	.	PUNCT
iajs-319	265	1	then	then	ADV
iajs-319	265	2	i	i	PRON
iajs-319	265	3	)	)	PUNCT
iajs-319	265	4	the	the	DET
iajs-319	265	5	s*g-	s*g-	NOUN
iajs-319	265	6	-closure	-closure	NOUN
iajs-319	265	7	of	of	ADP
iajs-319	265	8	a	a	PRON
iajs-319	265	9	,	,	PUNCT
iajs-319	265	10	denoted	denote	VERB
iajs-319	265	11	by	by	ADP
iajs-319	265	12	)	)	PUNCT
iajs-319	265	13	a(cl	a(cl	PROPN
iajs-319	265	14	g*s	g*s	PROPN
iajs-319	265	15			X
iajs-319	265	16	is	be	AUX
iajs-319	265	17	the	the	DET
iajs-319	265	18	intersection	intersection	NOUN
iajs-319	265	19	of	of	ADP
iajs-319	265	20	all	all	DET
iajs-319	265	21	s*g-	s*g-	NOUN
iajs-319	265	22	-closed	-close	VERB
iajs-319	265	23	subsets	subset	NOUN
iajs-319	265	24	of	of	ADP
iajs-319	265	25	x	x	PUNCT
iajs-319	265	26	which	which	PRON
iajs-319	265	27	contains	contain	VERB
iajs-319	265	28	a	a	DET
iajs-319	265	29	.	.	PUNCT
iajs-319	265	30	549	549	NUM
iajs-319	265	31	|	|	NOUN
iajs-319	265	32	mathematics	mathematic	NOUN
iajs-319	265	33	2014	2014	NUM
iajs-319	265	34	)	)	PUNCT
iajs-319	265	35	عام	عام	ADP
iajs-319	265	36	3العدد	3العدد	NUM
iajs-319	265	37	(	(	PUNCT
iajs-319	265	38	27مجلة	27مجلة	NUM
iajs-319	265	39	إبن	إبن	VERB
iajs-319	265	40	الھيثم	الھيثم	NOUN
iajs-319	265	41	للعلوم	للعلوم	NOUN
iajs-319	265	42	الصرفة	الصرفة	NOUN
iajs-319	266	1	و	و	PRON
iajs-319	266	2	التطبيقية	التطبيقية	ADV
iajs-319	266	3	المجلد	المجلد	VERB
iajs-319	266	4	ibn	ibn	PROPN
iajs-319	266	5	al	al	PROPN
iajs-319	266	6	-	-	PUNCT
iajs-319	266	7	haitham	haitham	PROPN
iajs-319	266	8	jour	jour	X
iajs-319	266	9	.	.	PROPN
iajs-319	267	1	for	for	ADP
iajs-319	267	2	pure	pure	ADJ
iajs-319	267	3	&	&	CCONJ
iajs-319	267	4	appl	appl	PROPN
iajs-319	267	5	.	.	PUNCT
iajs-319	268	1	sci	sci	PROPN
iajs-319	268	2	.	.	PUNCT
iajs-319	268	3	vol	vol	NOUN
iajs-319	268	4	.	.	PROPN
iajs-319	269	1	27	27	NUM
iajs-319	269	2	(	(	PUNCT
iajs-319	269	3	3	3	NUM
iajs-319	269	4	)	)	PUNCT
iajs-319	269	5	2014	2014	NUM
iajs-319	269	6	ii	ii	NOUN
iajs-319	269	7	)	)	PUNCT
iajs-319	269	8	the	the	DET
iajs-319	269	9	s*g-	s*g-	NOUN
iajs-319	269	10	-interior	-interior	NOUN
iajs-319	269	11	of	of	ADP
iajs-319	269	12	a	a	PRON
iajs-319	269	13	,	,	PUNCT
iajs-319	269	14	denoted	denote	VERB
iajs-319	269	15	by	by	ADP
iajs-319	269	16	)	)	PUNCT
iajs-319	269	17	a(int	a(int	PROPN
iajs-319	269	18	g*s	g*s	PROPN
iajs-319	269	19			X
iajs-319	269	20	is	be	AUX
iajs-319	269	21	the	the	DET
iajs-319	269	22	union	union	NOUN
iajs-319	269	23	of	of	ADP
iajs-319	269	24	all	all	DET
iajs-319	269	25	s*g-	s*g-	NOUN
iajs-319	269	26	-open	-open	NOUN
iajs-319	269	27	sets	set	NOUN
iajs-319	269	28	in	in	ADP
iajs-319	269	29	x	x	PUNCT
iajs-319	269	30	which	which	PRON
iajs-319	269	31	are	be	AUX
iajs-319	269	32	contained	contain	VERB
iajs-319	269	33	in	in	ADP
iajs-319	269	34	a	a	DET
iajs-319	269	35	.	.	PUNCT
iajs-319	269	36	theorem(2.26	theorem(2.26	ADJ
iajs-319	269	37	):	):	PUNCT
iajs-319	269	38	let	let	NOUN
iajs-319	269	39	)	)	PUNCT
iajs-319	269	40	,	,	PUNCT
iajs-319	269	41	x	x	X
iajs-319	269	42	(	(	PUNCT
iajs-319	269	43			NOUN
iajs-319	269	44	be	be	VERB
iajs-319	269	45	a	a	DET
iajs-319	269	46	topological	topological	ADJ
iajs-319	269	47	space	space	NOUN
iajs-319	269	48	and	and	CCONJ
iajs-319	269	49	xb	xb	PROPN
iajs-319	269	50	,	,	PUNCT
iajs-319	269	51	a	a	DET
iajs-319	269	52			PROPN
iajs-319	269	53	.	.	PUNCT
iajs-319	270	1	then	then	ADV
iajs-319	270	2	:	:	PUNCT
iajs-319	270	3	i	i	X
iajs-319	270	4	)	)	PUNCT
iajs-319	270	5	a)a(int)aint	a)a(int)aint	PROPN
iajs-319	270	6	(	(	PUNCT
iajs-319	270	7	g*s	g*s	PROPN
iajs-319	270	8			ADJ
iajs-319	270	9			X
iajs-319	270	10	and	and	CCONJ
iajs-319	270	11	)	)	PUNCT
iajs-319	270	12	a(cl)a(cla	a(cl)a(cla	NOUN
iajs-319	270	13	g*s	g*s	PROPN
iajs-319	270	14			PRON
iajs-319	270	15			PROPN
iajs-319	270	16	.	.	PUNCT
iajs-319	270	17	ii	ii	PROPN
iajs-319	270	18	)	)	PUNCT
iajs-319	270	19	)	)	PUNCT
iajs-319	271	1	a(int	a(int	PROPN
iajs-319	271	2	g*s	g*s	PROPN
iajs-319	271	3			X
iajs-319	271	4	is	be	AUX
iajs-319	271	5	an	an	DET
iajs-319	271	6	s*g-	s*g-	NOUN
iajs-319	271	7	-open	-open	NOUN
iajs-319	271	8	set	set	VERB
iajs-319	271	9	in	in	ADP
iajs-319	271	10	x	x	X
iajs-319	271	11	and	and	CCONJ
iajs-319	271	12	)	)	PUNCT
iajs-319	271	13	a(cl	a(cl	PROPN
iajs-319	271	14	g*s	g*s	PROPN
iajs-319	271	15			X
iajs-319	271	16	is	be	AUX
iajs-319	271	17	an	an	DET
iajs-319	271	18	s*g-	s*g-	NOUN
iajs-319	271	19	-closed	-close	VERB
iajs-319	271	20	set	set	VERB
iajs-319	271	21	in	in	ADP
iajs-319	271	22	x	x	PROPN
iajs-319	271	23	.	.	PUNCT
iajs-319	271	24	iii	iii	X
iajs-319	271	25	)	)	PUNCT
iajs-319	272	1	if	if	SCONJ
iajs-319	272	2	ba	ba	PROPN
iajs-319	272	3			PROPN
iajs-319	272	4	,	,	PUNCT
iajs-319	272	5	then	then	ADV
iajs-319	272	6	)	)	PUNCT
iajs-319	272	7	b(int)a(int	b(int)a(int	NOUN
iajs-319	272	8	g*sg*s	g*sg*s	PROPN
iajs-319	272	9			PRON
iajs-319	272	10			NOUN
iajs-319	272	11	and	and	CCONJ
iajs-319	272	12	)	)	PUNCT
iajs-319	272	13	b(cl)a(cl	b(cl)a(cl	NOUN
iajs-319	272	14	g*sg*s	g*sg*s	PROPN
iajs-319	272	15			PRON
iajs-319	272	16			PROPN
iajs-319	272	17	.	.	PUNCT
iajs-319	273	1	iv	iv	X
iajs-319	273	2	)	)	PUNCT
iajs-319	273	3	a	a	PRON
iajs-319	273	4	is	be	AUX
iajs-319	273	5	s*g-	s*g-	NOUN
iajs-319	273	6	-open	-open	PROPN
iajs-319	273	7	iff	iff	PROPN
iajs-319	273	8	a)a(int	a)a(int	PROPN
iajs-319	273	9	g*s	g*s	PROPN
iajs-319	273	10			VERB
iajs-319	273	11	and	and	CCONJ
iajs-319	273	12	a	a	PRON
iajs-319	273	13	is	be	AUX
iajs-319	273	14	s*g-	s*g-	NOUN
iajs-319	273	15	-closed	-close	VERB
iajs-319	273	16	iff	iff	PROPN
iajs-319	273	17	a)a(cl	a)a(cl	NOUN
iajs-319	273	18	g*s	g*s	PROPN
iajs-319	273	19			NOUN
iajs-319	273	20	.	.	PUNCT
iajs-319	274	1	v	v	X
iajs-319	274	2	)	)	PUNCT
iajs-319	274	3	)	)	PUNCT
iajs-319	275	1	b(int)a(int)ba(int	b(int)a(int)ba(int	NOUN
iajs-319	275	2	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-319	275	3			ADP
iajs-319	275	4			PROPN
iajs-319	275	5			PROPN
iajs-319	275	6	and	and	CCONJ
iajs-319	275	7	)	)	PUNCT
iajs-319	275	8	b(cl)a(cl)ba(cl	b(cl)a(cl)ba(cl	NOUN
iajs-319	275	9	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-319	275	10			ADP
iajs-319	275	11			PROPN
iajs-319	275	12			PROPN
iajs-319	275	13	.	.	PUNCT
iajs-319	276	1	vi	vi	X
iajs-319	276	2	)	)	PUNCT
iajs-319	276	3	)	)	PUNCT
iajs-319	277	1	a(int))a((intint	a(int))a((intint	NOUN
iajs-319	277	2	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-319	277	3			ADP
iajs-319	277	4			NOUN
iajs-319	277	5	and	and	CCONJ
iajs-319	277	6	)	)	PUNCT
iajs-319	277	7	a(cl))a(cl(cl	a(cl))a(cl(cl	NOUN
iajs-319	277	8	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-319	277	9			ADP
iajs-319	277	10			PROPN
iajs-319	277	11	.	.	PUNCT
iajs-319	278	1	vii	vii	PROPN
iajs-319	278	2	)	)	PUNCT
iajs-319	278	3	)	)	PUNCT
iajs-319	279	1	a(intx	a(intx	PROPN
iajs-319	279	2	g*s	g*s	PROPN
iajs-319	279	3			NUM
iajs-319	279	4	iff	iff	PROPN
iajs-319	279	5	there	there	PRON
iajs-319	279	6	is	be	VERB
iajs-319	279	7	an	an	DET
iajs-319	279	8	s*g-	s*g-	NOUN
iajs-319	279	9	-open	-open	NOUN
iajs-319	279	10	set	set	VERB
iajs-319	279	11	u	u	NOUN
iajs-319	279	12	in	in	ADP
iajs-319	279	13	x	x	X
iajs-319	279	14	s.t	s.t	PROPN
iajs-319	279	15	aux	aux	PROPN
iajs-319	279	16			PROPN
iajs-319	279	17	.	.	PUNCT
iajs-319	280	1	viii	viii	PROPN
iajs-319	280	2	)	)	PUNCT
iajs-319	280	3	)	)	PUNCT
iajs-319	281	1	a(clx	a(clx	PROPN
iajs-319	281	2	g*s	g*s	PROPN
iajs-319	281	3			NUM
iajs-319	281	4	iff	iff	PROPN
iajs-319	281	5	for	for	ADP
iajs-319	281	6	every	every	DET
iajs-319	281	7	s*g-	s*g-	NOUN
iajs-319	281	8	-open	-open	NOUN
iajs-319	281	9	set	set	VERB
iajs-319	281	10	u	u	NOUN
iajs-319	281	11	containing	contain	VERB
iajs-319	281	12	x	x	PUNCT
iajs-319	281	13	,	,	PUNCT
iajs-319	281	14	au	au	NOUN
iajs-319	281	15	.	.	PUNCT
iajs-319	282	1	proof	proof	NOUN
iajs-319	282	2	:	:	PUNCT
iajs-319	282	3	it	it	PRON
iajs-319	282	4	is	be	AUX
iajs-319	282	5	obvious	obvious	ADJ
iajs-319	282	6	.	.	PUNCT
iajs-319	283	1	proposition(2.27	proposition(2.27	PUNCT
iajs-319	283	2	):	):	PUNCT
iajs-319	283	3	let	let	VERB
iajs-319	283	4	x	x	PRON
iajs-319	283	5	and	and	CCONJ
iajs-319	283	6	y	y	PROPN
iajs-319	283	7	be	be	AUX
iajs-319	283	8	topological	topological	ADJ
iajs-319	283	9	spaces	space	NOUN
iajs-319	283	10	.	.	PUNCT
iajs-319	284	1	if	if	SCONJ
iajs-319	284	2	xa	xa	PROPN
iajs-319	284	3			PROPN
iajs-319	284	4	and	and	CCONJ
iajs-319	284	5	yb	yb	NOUN
iajs-319	284	6	.	.	PUNCT
iajs-319	285	1	then	then	ADV
iajs-319	285	2	ba	ba	PROPN
iajs-319	285	3	is	be	AUX
iajs-319	285	4	an	an	DET
iajs-319	285	5	s*g	s*g	NOUN
iajs-319	285	6	-open	-open	NOUN
iajs-319	285	7	set	set	VERB
iajs-319	285	8	in	in	ADP
iajs-319	285	9	yx	yx	PROPN
iajs-319	285	10	if	if	SCONJ
iajs-319	285	11	and	and	CCONJ
iajs-319	285	12	only	only	ADV
iajs-319	285	13	if	if	SCONJ
iajs-319	285	14	a	a	PRON
iajs-319	285	15	and	and	CCONJ
iajs-319	285	16	b	b	NOUN
iajs-319	285	17	are	be	AUX
iajs-319	285	18	s*g-	s*g-	NOUN
iajs-319	285	19	-open	-open	NOUN
iajs-319	285	20	sets	set	NOUN
iajs-319	285	21	in	in	ADP
iajs-319	285	22	x	x	PUNCT
iajs-319	285	23	and	and	CCONJ
iajs-319	285	24	y	y	PROPN
iajs-319	285	25	respectevely	respectevely	ADV
iajs-319	285	26	.	.	PUNCT
iajs-319	286	1	proof	proof	NOUN
iajs-319	286	2	:	:	PUNCT
iajs-319	286	3			PROPN
iajs-319	286	4	since	since	SCONJ
iajs-319	286	5	a	a	PRON
iajs-319	286	6	and	and	CCONJ
iajs-319	286	7	b	b	NOUN
iajs-319	286	8	are	be	AUX
iajs-319	286	9	s*g-	s*g-	NOUN
iajs-319	286	10	-open	-open	NOUN
iajs-319	286	11	sets	set	NOUN
iajs-319	286	12	in	in	ADP
iajs-319	286	13	x	x	PUNCT
iajs-319	286	14	and	and	CCONJ
iajs-319	286	15	y	y	PROPN
iajs-319	286	16	respectevely	respectevely	ADV
iajs-319	286	17	,	,	PUNCT
iajs-319	286	18	then	then	ADV
iajs-319	286	19	by	by	ADP
iajs-319	286	20	definition	definition	NOUN
iajs-319	286	21	(	(	PUNCT
iajs-319	286	22	2.1	2.1	NUM
iajs-319	286	23	)	)	PUNCT
iajs-319	286	24	,	,	PUNCT
iajs-319	286	25	we	we	PRON
iajs-319	286	26	get	get	VERB
iajs-319	286	27	)	)	PUNCT
iajs-319	286	28	)	)	PUNCT
iajs-319	286	29	)	)	PUNCT
iajs-319	286	30	a(int(clint(a	a(int(clint(a	PROPN
iajs-319	286	31	g*s	g*s	PROPN
iajs-319	286	32	and	and	CCONJ
iajs-319	286	33	)	)	PUNCT
iajs-319	286	34	)	)	PUNCT
iajs-319	286	35	)	)	PUNCT
iajs-319	287	1	b(int(clint(b	b(int(clint(b	PROPN
iajs-319	287	2	g*s	g*s	PROPN
iajs-319	287	3	.	.	PUNCT
iajs-319	288	1	hence	hence	ADV
iajs-319	288	2	)	)	PUNCT
iajs-319	288	3	)	)	PUNCT
iajs-319	288	4	)	)	PUNCT
iajs-319	289	1	b(int(clint()))a(int(clint(ba	b(int(clint()))a(int(clint(ba	PROPN
iajs-319	289	2	g*sg*s	g*sg*s	PROPN
iajs-319	289	3			PROPN
iajs-319	289	4	)	)	PUNCT
iajs-319	289	5	)	)	PUNCT
iajs-319	289	6	)	)	PUNCT
iajs-319	290	1	b(int(cl))a(int(clint	b(int(cl))a(int(clint	NOUN
iajs-319	290	2	(	(	PUNCT
iajs-319	290	3	g*sg*s	g*sg*s	PROPN
iajs-319	290	4			NOUN
iajs-319	290	5	.	.	PUNCT
iajs-319	291	1	since	since	SCONJ
iajs-319	291	2			PROPN
iajs-319	291	3	)	)	PUNCT
iajs-319	291	4	b(cl)a(cl	b(cl)a(cl	PROPN
iajs-319	291	5	g*sg*s	g*sg*s	PROPN
iajs-319	291	6	)	)	PUNCT
iajs-319	291	7	ba(cl	ba(cl	PROPN
iajs-319	291	8	g*s	g*s	PROPN
iajs-319	291	9			INTJ
iajs-319	291	10	,	,	PUNCT
iajs-319	291	11	then	then	ADV
iajs-319	291	12	)	)	PUNCT
iajs-319	291	13	)	)	PUNCT
iajs-319	291	14	)	)	PUNCT
iajs-319	291	15	ba(int(clint(ba	ba(int(clint(ba	PROPN
iajs-319	292	1	g*s	g*s	PROPN
iajs-319	292	2			X
iajs-319	292	3	.	.	PUNCT
iajs-319	293	1	thus	thus	ADV
iajs-319	293	2	ba	ba	PROPN
iajs-319	293	3	is	be	AUX
iajs-319	293	4	an	an	DET
iajs-319	293	5	s*g-	s*g-	NOUN
iajs-319	293	6	open	open	NOUN
iajs-319	293	7	set	set	VERB
iajs-319	293	8	in	in	ADP
iajs-319	293	9	yx	yx	PROPN
iajs-319	293	10	.	.	PUNCT
iajs-319	294	1	by	by	ADP
iajs-319	294	2	the	the	DET
iajs-319	294	3	same	same	ADJ
iajs-319	294	4	way	way	NOUN
iajs-319	294	5	,	,	PUNCT
iajs-319	294	6	we	we	PRON
iajs-319	294	7	can	can	AUX
iajs-319	294	8	prove	prove	VERB
iajs-319	294	9	that	that	SCONJ
iajs-319	294	10	a	a	PRON
iajs-319	294	11	and	and	CCONJ
iajs-319	294	12	b	b	NOUN
iajs-319	294	13	are	be	AUX
iajs-319	294	14	s*g-	s*g-	NOUN
iajs-319	294	15	-open	-open	NOUN
iajs-319	294	16	sets	set	NOUN
iajs-319	294	17	in	in	ADP
iajs-319	294	18	x	x	PUNCT
iajs-319	294	19	and	and	CCONJ
iajs-319	294	20	y	y	PROPN
iajs-319	294	21	respectevely	respectevely	ADV
iajs-319	294	22	if	if	SCONJ
iajs-319	294	23	ba	ba	PROPN
iajs-319	294	24	is	be	AUX
iajs-319	294	25	an	an	DET
iajs-319	294	26	s*g-	s*g-	NOUN
iajs-319	294	27	-open	-open	NOUN
iajs-319	294	28	set	set	VERB
iajs-319	294	29	in	in	ADP
iajs-319	294	30	yx	yx	PROPN
iajs-319	294	31	.	.	PUNCT
iajs-319	295	1	3	3	X
iajs-319	295	2	.	.	PUNCT
iajs-319	296	1	s*g-	s*g-	NOUN
iajs-319	296	2	continuous	continuous	ADJ
iajs-319	296	3	functions	function	NOUN
iajs-319	296	4	and	and	CCONJ
iajs-319	296	5	s*g-	s*g-	NOUN
iajs-319	296	6	irresolute	irresolute	ADJ
iajs-319	296	7	functions	function	NOUN
iajs-319	296	8	in	in	ADP
iajs-319	296	9	this	this	DET
iajs-319	296	10	section	section	NOUN
iajs-319	296	11	,	,	PUNCT
iajs-319	296	12	we	we	PRON
iajs-319	296	13	introduce	introduce	VERB
iajs-319	296	14	a	a	DET
iajs-319	296	15	new	new	ADJ
iajs-319	296	16	class	class	NOUN
iajs-319	296	17	of	of	ADP
iajs-319	296	18	functions	function	NOUN
iajs-319	296	19	,	,	PUNCT
iajs-319	296	20	namely	namely	ADV
iajs-319	296	21	,	,	PUNCT
iajs-319	296	22	s*g-	s*g-	NOUN
iajs-319	296	23	-continuous	-continuous	ADJ
iajs-319	296	24	functions	function	NOUN
iajs-319	296	25	and	and	CCONJ
iajs-319	296	26	s*g-	s*g-	NOUN
iajs-319	296	27	-irresolute	-irresolute	PROPN
iajs-319	296	28	functions	function	NOUN
iajs-319	296	29	in	in	ADP
iajs-319	296	30	topological	topological	ADJ
iajs-319	296	31	spaces	space	NOUN
iajs-319	296	32	and	and	CCONJ
iajs-319	296	33	study	study	VERB
iajs-319	296	34	some	some	PRON
iajs-319	296	35	of	of	ADP
iajs-319	296	36	their	their	PRON
iajs-319	296	37	properties	property	NOUN
iajs-319	296	38	.	.	PUNCT
iajs-319	297	1	definition(3.1	definition(3.1	ADJ
iajs-319	297	2	):	):	PUNCT
iajs-319	297	3	a	a	DET
iajs-319	297	4	function	function	NOUN
iajs-319	297	5	)	)	PUNCT
iajs-319	297	6	,	,	PUNCT
iajs-319	297	7	y(),x(:f	y(),x(:f	PROPN
iajs-319	297	8			PROPN
iajs-319	297	9	is	be	AUX
iajs-319	297	10	called	call	VERB
iajs-319	297	11	s*g-	s*g-	NOUN
iajs-319	297	12	-continuous	-continuous	ADJ
iajs-319	297	13	if	if	SCONJ
iajs-319	297	14	)	)	PUNCT
iajs-319	297	15	v(f	v(f	PROPN
iajs-319	297	16	1	1	NUM
iajs-319	297	17	is	be	AUX
iajs-319	297	18	an	an	DET
iajs-319	297	19	s*g	s*g	NOUN
iajs-319	297	20	-open	-open	NOUN
iajs-319	297	21	set	set	VERB
iajs-319	297	22	in	in	ADP
iajs-319	297	23	x	x	PUNCT
iajs-319	297	24	for	for	ADP
iajs-319	297	25	every	every	DET
iajs-319	297	26	open	open	ADJ
iajs-319	297	27	set	set	VERB
iajs-319	297	28	v	v	NOUN
iajs-319	297	29	in	in	ADP
iajs-319	297	30	y	y	PROPN
iajs-319	297	31	.	.	PUNCT
iajs-319	298	1	proposition(3.2	proposition(3.2	NOUN
iajs-319	298	2	):	):	PUNCT
iajs-319	298	3	a	a	DET
iajs-319	298	4	function	function	NOUN
iajs-319	298	5	)	)	PUNCT
iajs-319	298	6	,	,	PUNCT
iajs-319	298	7	y(),x(:f	y(),x(:f	PROPN
iajs-319	298	8			PROPN
iajs-319	298	9	is	be	AUX
iajs-319	298	10	s*g-	s*g-	NOUN
iajs-319	298	11	-continuous	-continuous	ADJ
iajs-319	298	12	iff	iff	PROPN
iajs-319	298	13	)	)	PUNCT
iajs-319	298	14	v(f	v(f	PROPN
iajs-319	298	15	1	1	NUM
iajs-319	298	16	is	be	AUX
iajs-319	298	17	an	an	DET
iajs-319	298	18	s*g-	s*g-	NOUN
iajs-319	298	19	closed	close	VERB
iajs-319	298	20	set	set	VERB
iajs-319	298	21	in	in	ADP
iajs-319	298	22	x	x	PUNCT
iajs-319	298	23	for	for	ADP
iajs-319	298	24	every	every	DET
iajs-319	298	25	closed	close	VERB
iajs-319	298	26	set	set	VERB
iajs-319	298	27	v	v	NOUN
iajs-319	298	28	in	in	ADP
iajs-319	298	29	y	y	PROPN
iajs-319	298	30	.	.	PUNCT
iajs-319	299	1	proof	proof	NOUN
iajs-319	299	2	:	:	PUNCT
iajs-319	299	3	it	it	PRON
iajs-319	299	4	is	be	AUX
iajs-319	299	5	obvious	obvious	ADJ
iajs-319	299	6	.	.	PUNCT
iajs-319	300	1	proposition(3.3	proposition(3.3	NOUN
iajs-319	300	2	):	):	PUNCT
iajs-319	300	3	every	every	DET
iajs-319	300	4	continuous	continuous	ADJ
iajs-319	300	5	function	function	NOUN
iajs-319	300	6	is	be	AUX
iajs-319	300	7	s*g-	s*g-	NOUN
iajs-319	300	8	-continuous	-continuous	ADJ
iajs-319	300	9	.	.	PUNCT
iajs-319	301	1	proof	proof	NOUN
iajs-319	301	2	:	:	PUNCT
iajs-319	301	3	follows	follow	VERB
iajs-319	301	4	from	from	ADP
iajs-319	301	5	the	the	DET
iajs-319	301	6	definition	definition	NOUN
iajs-319	301	7	(	(	PUNCT
iajs-319	301	8	3.1	3.1	NUM
iajs-319	301	9	)	)	PUNCT
iajs-319	301	10	and	and	CCONJ
iajs-319	301	11	the	the	DET
iajs-319	301	12	fact	fact	NOUN
iajs-319	301	13	that	that	SCONJ
iajs-319	301	14	every	every	DET
iajs-319	301	15	open	open	ADJ
iajs-319	301	16	set	set	NOUN
iajs-319	301	17	is	be	AUX
iajs-319	301	18	s*g-	s*g-	NOUN
iajs-319	301	19	-open	-open	NOUN
iajs-319	301	20	.	.	PUNCT
iajs-319	302	1	remark(3.4	remark(3.4	NOUN
iajs-319	302	2	):	):	PUNCT
iajs-319	302	3	the	the	DET
iajs-319	302	4	converse	converse	NOUN
iajs-319	302	5	of	of	ADP
iajs-319	302	6	proposition	proposition	NOUN
iajs-319	302	7	(	(	PUNCT
iajs-319	302	8	3.3	3.3	NUM
iajs-319	302	9	)	)	PUNCT
iajs-319	302	10	may	may	AUX
iajs-319	302	11	not	not	PART
iajs-319	302	12	be	be	AUX
iajs-319	302	13	true	true	ADJ
iajs-319	302	14	in	in	ADP
iajs-319	302	15	general	general	ADJ
iajs-319	302	16	as	as	SCONJ
iajs-319	302	17	shown	show	VERB
iajs-319	302	18	in	in	ADP
iajs-319	302	19	the	the	DET
iajs-319	302	20	following	follow	VERB
iajs-319	302	21	example	example	NOUN
iajs-319	302	22	:	:	PUNCT
iajs-319	302	23	example(3.5	example(3.5	ADJ
iajs-319	302	24	):	):	PUNCT
iajs-319	302	25	let	let	VERB
iajs-319	302	26	}	}	PUNCT
iajs-319	302	27	c	c	NOUN
iajs-319	302	28	,	,	PUNCT
iajs-319	302	29	b	b	NOUN
iajs-319	302	30	,	,	PUNCT
iajs-319	302	31	a{yx	a{yx	PUNCT
iajs-319	302	32			NUM
iajs-319	302	33	,	,	PUNCT
iajs-319	302	34	}	}	PUNCT
iajs-319	302	35	}	}	PUNCT
iajs-319	302	36	a{,,x	a{,,x	PROPN
iajs-319	302	37	{	{	PUNCT
iajs-319	302	38			PROPN
iajs-319	302	39	&	&	CCONJ
iajs-319	302	40	}	}	PUNCT
iajs-319	302	41	}	}	PUNCT
iajs-319	302	42	c	c	X
iajs-319	302	43	,	,	PUNCT
iajs-319	302	44	a{},a{,,y	a{},a{,,y	PROPN
iajs-319	302	45	{	{	PUNCT
iajs-319	302	46			X
iajs-319	302	47			NOUN
iajs-319	302	48	}	}	PUNCT
iajs-319	302	49	,	,	PUNCT
iajs-319	302	50	a{,,x{g*s	a{,,x{g*s	PROPN
iajs-319	302	51			PROPN
iajs-319	302	52			X
iajs-319	302	53	}	}	PUNCT
iajs-319	302	54	}	}	PUNCT
iajs-319	302	55	c	c	X
iajs-319	302	56	,	,	PUNCT
iajs-319	302	57	a{},b	a{},b	PROPN
iajs-319	302	58	,	,	PUNCT
iajs-319	302	59	a	a	PRON
iajs-319	302	60	{	{	PUNCT
iajs-319	302	61	.	.	PUNCT
iajs-319	303	1	define	define	VERB
iajs-319	303	2	)	)	PUNCT
iajs-319	303	3	,	,	PUNCT
iajs-319	303	4	y(),x(:f	y(),x(:f	PROPN
iajs-319	303	5			PUNCT
iajs-319	303	6	by	by	ADP
iajs-319	303	7	:	:	PUNCT
iajs-319	303	8	a)a(f	a)a(f	PROPN
iajs-319	303	9			PROPN
iajs-319	303	10	,	,	PUNCT
iajs-319	303	11	b)b(f	b)b(f	PROPN
iajs-319	303	12			PROPN
iajs-319	303	13	&	&	CCONJ
iajs-319	303	14	c)c(f	c)c(f	PROPN
iajs-319	303	15			PROPN
iajs-319	304	1			NOUN
iajs-319	305	1	f	f	NOUN
iajs-319	305	2	is	be	AUX
iajs-319	305	3	not	not	PART
iajs-319	305	4	continuous	continuous	ADJ
iajs-319	305	5	,	,	PUNCT
iajs-319	305	6	but	but	CCONJ
iajs-319	305	7	f	f	PROPN
iajs-319	305	8	is	be	AUX
iajs-319	305	9	s*g-	s*g-	NOUN
iajs-319	305	10	-continuous	-continuous	ADJ
iajs-319	305	11	,	,	PUNCT
iajs-319	305	12	since	since	SCONJ
iajs-319	305	13	x)y(f	x)y(f	PROPN
iajs-319	305	14	1	1	NUM
iajs-319	305	15			NOUN
iajs-319	305	16	,	,	PUNCT
iajs-319	305	17			ADJ
iajs-319	305	18	)	)	PUNCT
iajs-319	306	1	(	(	PUNCT
iajs-319	306	2	f	f	NOUN
iajs-319	306	3	1	1	NUM
iajs-319	306	4	,	,	PUNCT
iajs-319	306	5	}	}	PUNCT
iajs-319	306	6	c	c	NOUN
iajs-319	306	7	,	,	PUNCT
iajs-319	306	8	a{})c	a{})c	ADJ
iajs-319	306	9	,	,	PUNCT
iajs-319	306	10	a({f	a({f	PROPN
iajs-319	306	11	1	1	NUM
iajs-319	306	12			NOUN
iajs-319	306	13	,	,	PUNCT
iajs-319	306	14	and	and	CCONJ
iajs-319	306	15	}	}	PUNCT
iajs-319	306	16	a{})a({f	a{})a({f	PROPN
iajs-319	306	17	1	1	NUM
iajs-319	306	18			NOUN
iajs-319	306	19	are	be	AUX
iajs-319	306	20	s*g-	s*g-	NOUN
iajs-319	306	21	-open	-open	NOUN
iajs-319	306	22	sets	set	NOUN
iajs-319	306	23	in	in	ADP
iajs-319	306	24	x	x	X
iajs-319	306	25	.	.	PUNCT
iajs-319	307	1	remark(3.6	remark(3.6	NOUN
iajs-319	307	2	):	):	PUNCT
iajs-319	307	3	s*g	s*g	NOUN
iajs-319	307	4	-	-	PUNCT
iajs-319	307	5	continuous	continuous	ADJ
iajs-319	307	6	functions	function	NOUN
iajs-319	307	7	and	and	CCONJ
iajs-319	307	8	s*g-	s*g-	NOUN
iajs-319	307	9	-continuous	-continuous	ADJ
iajs-319	307	10	functions	function	NOUN
iajs-319	307	11	are	be	AUX
iajs-319	307	12	in	in	ADP
iajs-319	307	13	general	general	ADJ
iajs-319	307	14	independent	independent	ADJ
iajs-319	307	15	.	.	PUNCT
iajs-319	308	1	consider	consider	VERB
iajs-319	308	2	the	the	DET
iajs-319	308	3	following	follow	VERB
iajs-319	308	4	examples	example	NOUN
iajs-319	308	5	:	:	PUNCT
iajs-319	308	6	550	550	NUM
iajs-319	308	7	|	|	NOUN
iajs-319	308	8	mathematics	mathematic	NOUN
iajs-319	308	9	2014	2014	NUM
iajs-319	308	10	)	)	PUNCT
iajs-319	308	11	عام	عام	ADP
iajs-319	308	12	3العدد	3العدد	NUM
iajs-319	308	13	(	(	PUNCT
iajs-319	308	14	27مجلة	27مجلة	NUM
iajs-319	308	15	إبن	إبن	VERB
iajs-319	308	16	الھيثم	الھيثم	NOUN
iajs-319	308	17	للعلوم	للعلوم	NOUN
iajs-319	308	18	الصرفة	الصرفة	NOUN
iajs-319	309	1	و	و	PRON
iajs-319	309	2	التطبيقية	التطبيقية	ADV
iajs-319	309	3	المجلد	المجلد	VERB
iajs-319	309	4	ibn	ibn	PROPN
iajs-319	309	5	al	al	PROPN
iajs-319	309	6	-	-	PUNCT
iajs-319	309	7	haitham	haitham	PROPN
iajs-319	309	8	jour	jour	X
iajs-319	309	9	.	.	PROPN
iajs-319	310	1	for	for	ADP
iajs-319	310	2	pure	pure	ADJ
iajs-319	310	3	&	&	CCONJ
iajs-319	310	4	appl	appl	PROPN
iajs-319	310	5	.	.	PUNCT
iajs-319	311	1	sci	sci	PROPN
iajs-319	311	2	.	.	PUNCT
iajs-319	311	3	vol	vol	NOUN
iajs-319	311	4	.	.	PROPN
iajs-319	312	1	27	27	NUM
iajs-319	312	2	(	(	PUNCT
iajs-319	312	3	3	3	NUM
iajs-319	312	4	)	)	PUNCT
iajs-319	312	5	2014	2014	NUM
iajs-319	312	6	example(3.7	example(3.7	NOUN
iajs-319	312	7	):	):	PUNCT
iajs-319	312	8	let	let	VERB
iajs-319	312	9	}	}	PUNCT
iajs-319	312	10	c	c	NOUN
iajs-319	312	11	,	,	PUNCT
iajs-319	312	12	b	b	NOUN
iajs-319	312	13	,	,	PUNCT
iajs-319	312	14	a{yx	a{yx	PUNCT
iajs-319	312	15			NUM
iajs-319	312	16	,	,	PUNCT
iajs-319	312	17	}	}	PUNCT
iajs-319	312	18	,	,	PUNCT
iajs-319	312	19	x	x	X
iajs-319	312	20	{	{	PUNCT
iajs-319	312	21			PROPN
iajs-319	312	22	&	&	CCONJ
iajs-319	312	23	}	}	PUNCT
iajs-319	312	24	}	}	PUNCT
iajs-319	312	25	a{,,y	a{,,y	NOUN
iajs-319	312	26	{	{	PUNCT
iajs-319	312	27			PUNCT
iajs-319	312	28			NOUN
iajs-319	312	29			PROPN
iajs-319	312	30	g*s	g*s	PROPN
iajs-319	312	31	and	and	CCONJ
iajs-319	312	32	}	}	PUNCT
iajs-319	312	33	}	}	PUNCT
iajs-319	312	34	c	c	PROPN
iajs-319	312	35	,	,	PUNCT
iajs-319	312	36	b{},c	b{},c	PROPN
iajs-319	312	37	,	,	PUNCT
iajs-319	312	38	a{},b	a{},b	PROPN
iajs-319	312	39	,	,	PUNCT
iajs-319	312	40	a{},c{},b{},a{,,x{g*s	a{},c{},b{},a{,,x{g*s	PROPN
iajs-319	312	41			PROPN
iajs-319	312	42	.	.	PUNCT
iajs-319	313	1	define	define	VERB
iajs-319	313	2	)	)	PUNCT
iajs-319	313	3	,	,	PUNCT
iajs-319	313	4	y(),x(:f	y(),x(:f	PROPN
iajs-319	313	5			PUNCT
iajs-319	313	6	by	by	ADP
iajs-319	313	7	:	:	PUNCT
iajs-319	313	8	a)a(f	a)a(f	PROPN
iajs-319	313	9			PROPN
iajs-319	313	10	,	,	PUNCT
iajs-319	313	11	b)b(f	b)b(f	PROPN
iajs-319	313	12			PROPN
iajs-319	313	13	&	&	CCONJ
iajs-319	313	14	c)c(f	c)c(f	PROPN
iajs-319	313	15			PROPN
iajs-319	313	16			NOUN
iajs-319	314	1	f	f	PROPN
iajs-319	314	2	is	be	AUX
iajs-319	314	3	s*g	s*g	NOUN
iajs-319	314	4	-	-	PUNCT
iajs-319	314	5	continuous	continuous	ADJ
iajs-319	314	6	,	,	PUNCT
iajs-319	314	7	but	but	CCONJ
iajs-319	314	8	f	f	PROPN
iajs-319	314	9	is	be	AUX
iajs-319	314	10	not	not	PART
iajs-319	314	11	s*g-	s*g-	NOUN
iajs-319	314	12	-continuous	-continuous	ADJ
iajs-319	314	13	,	,	PUNCT
iajs-319	314	14	since	since	SCONJ
iajs-319	314	15	}	}	PUNCT
iajs-319	314	16	a	a	PRON
iajs-319	314	17	{	{	PUNCT
iajs-319	314	18	is	be	AUX
iajs-319	314	19	open	open	ADJ
iajs-319	314	20	set	set	VERB
iajs-319	314	21	in	in	ADP
iajs-319	314	22	y	y	PROPN
iajs-319	314	23	,	,	PUNCT
iajs-319	314	24	but	but	CCONJ
iajs-319	314	25	}	}	PUNCT
iajs-319	314	26	a{})a({f	a{})a({f	PROPN
iajs-319	314	27	1	1	NUM
iajs-319	314	28			NOUN
iajs-319	314	29	is	be	AUX
iajs-319	314	30	not	not	PART
iajs-319	314	31	s*g-	s*g-	NOUN
iajs-319	314	32	-open	-open	ADJ
iajs-319	314	33	in	in	ADP
iajs-319	314	34	x	x	X
iajs-319	314	35	.	.	PUNCT
iajs-319	315	1	also	also	ADV
iajs-319	315	2	,	,	PUNCT
iajs-319	315	3	in	in	ADP
iajs-319	315	4	example	example	NOUN
iajs-319	315	5	(	(	PUNCT
iajs-319	315	6	3.5	3.5	NUM
iajs-319	315	7	)	)	PUNCT
iajs-319	315	8	f	f	PROPN
iajs-319	315	9	is	be	AUX
iajs-319	315	10	s*g-	s*g-	NOUN
iajs-319	315	11	continuous	continuous	ADJ
iajs-319	315	12	,	,	PUNCT
iajs-319	315	13	but	but	CCONJ
iajs-319	315	14	is	be	AUX
iajs-319	315	15	not	not	PART
iajs-319	315	16	s*g	s*g	NOUN
iajs-319	315	17	-	-	PUNCT
iajs-319	315	18	continuous	continuous	ADJ
iajs-319	315	19	,	,	PUNCT
iajs-319	315	20	since	since	SCONJ
iajs-319	315	21	}	}	PUNCT
iajs-319	315	22	c	c	X
iajs-319	315	23	,	,	PUNCT
iajs-319	315	24	a	a	PRON
iajs-319	315	25	{	{	PUNCT
iajs-319	315	26	is	be	AUX
iajs-319	315	27	open	open	ADJ
iajs-319	315	28	set	set	VERB
iajs-319	315	29	in	in	ADP
iajs-319	315	30	y	y	PROPN
iajs-319	315	31	,	,	PUNCT
iajs-319	315	32	but	but	CCONJ
iajs-319	315	33	}	}	PUNCT
iajs-319	315	34	c	c	X
iajs-319	315	35	,	,	PUNCT
iajs-319	315	36	a{})c	a{})c	ADJ
iajs-319	315	37	,	,	PUNCT
iajs-319	315	38	a({f	a({f	PROPN
iajs-319	315	39	1	1	NUM
iajs-319	315	40			NOUN
iajs-319	315	41	is	be	AUX
iajs-319	315	42	not	not	PART
iajs-319	315	43	s*g	s*g	NOUN
iajs-319	315	44	-	-	PUNCT
iajs-319	315	45	open	open	ADJ
iajs-319	315	46	in	in	ADP
iajs-319	315	47	x	x	X
iajs-319	315	48	.	.	PUNCT
iajs-319	316	1	theorem(3.8	theorem(3.8	NOUN
iajs-319	316	2	):	):	PUNCT
iajs-319	316	3	every	every	DET
iajs-319	316	4	s*g-	s*g-	NOUN
iajs-319	316	5	-continuous	-continuous	ADJ
iajs-319	316	6	function	function	NOUN
iajs-319	316	7	is	be	AUX
iajs-319	316	8			X
iajs-319	316	9	-continuous	-continuous	ADJ
iajs-319	316	10	(	(	PUNCT
iajs-319	316	11	resp	resp	NOUN
iajs-319	316	12	.	.	PUNCT
iajs-319	317	1	αg	αg	NOUN
iajs-319	317	2	-	-	PUNCT
iajs-319	317	3	continuous	continuous	ADJ
iajs-319	317	4	,	,	PUNCT
iajs-319	317	5	gα	gα	ADP
iajs-319	317	6	continuous	continuous	ADJ
iajs-319	317	7	,	,	PUNCT
iajs-319	317	8	pre	pre	ADJ
iajs-319	317	9	-	-	ADJ
iajs-319	317	10	continuous	continuous	ADJ
iajs-319	317	11	,	,	PUNCT
iajs-319	317	12	b	b	X
iajs-319	317	13	-	-	PUNCT
iajs-319	317	14	continuous	continuous	ADJ
iajs-319	317	15	,	,	PUNCT
iajs-319	317	16			NOUN
iajs-319	317	17	-continuous	-continuous	ADJ
iajs-319	317	18	)	)	PUNCT
iajs-319	317	19	function	function	NOUN
iajs-319	317	20	.	.	PUNCT
iajs-319	318	1	proof	proof	NOUN
iajs-319	318	2	:	:	PUNCT
iajs-319	318	3	follows	follow	VERB
iajs-319	318	4	from	from	ADP
iajs-319	318	5	the	the	DET
iajs-319	318	6	theorem	theorem	NOUN
iajs-319	318	7	(	(	PUNCT
iajs-319	318	8	2.5	2.5	NUM
iajs-319	318	9	)	)	PUNCT
iajs-319	318	10	.	.	PUNCT
iajs-319	319	1	remark(3.9	remark(3.9	PROPN
iajs-319	319	2	):	):	PUNCT
iajs-319	319	3	the	the	DET
iajs-319	319	4	converse	converse	NOUN
iajs-319	319	5	of	of	ADP
iajs-319	319	6	theorem	theorem	NOUN
iajs-319	319	7	(	(	PUNCT
iajs-319	319	8	3.8	3.8	NUM
iajs-319	319	9	)	)	PUNCT
iajs-319	319	10	may	may	AUX
iajs-319	319	11	not	not	PART
iajs-319	319	12	be	be	AUX
iajs-319	319	13	true	true	ADJ
iajs-319	319	14	in	in	ADP
iajs-319	319	15	general	general	ADJ
iajs-319	319	16	.	.	PUNCT
iajs-319	320	1	observe	observe	VERB
iajs-319	320	2	that	that	SCONJ
iajs-319	320	3	in	in	ADP
iajs-319	320	4	example	example	NOUN
iajs-319	320	5	(	(	PUNCT
iajs-319	320	6	3.7	3.7	NUM
iajs-319	320	7	)	)	PUNCT
iajs-319	320	8	f	f	PROPN
iajs-319	320	9	is	be	AUX
iajs-319	320	10	pre	pre	ADJ
iajs-319	320	11	-	-	ADJ
iajs-319	320	12	continuous	continuous	ADJ
iajs-319	320	13	(	(	PUNCT
iajs-319	320	14	resp	resp	NOUN
iajs-319	320	15	.	.	PUNCT
iajs-319	321	1	b	b	X
iajs-319	321	2	-	-	PUNCT
iajs-319	321	3	continuous	continuous	ADJ
iajs-319	321	4	,	,	PUNCT
iajs-319	321	5			NOUN
iajs-319	321	6	-continuous	-continuous	ADJ
iajs-319	321	7	,	,	PUNCT
iajs-319	321	8	gα	gα	NOUN
iajs-319	321	9	-	-	PUNCT
iajs-319	321	10	continuous	continuous	ADJ
iajs-319	321	11	,	,	PUNCT
iajs-319	321	12	αgcontinuous	αgcontinuous	ADJ
iajs-319	321	13	)	)	PUNCT
iajs-319	321	14	function	function	NOUN
iajs-319	321	15	,	,	PUNCT
iajs-319	321	16	but	but	CCONJ
iajs-319	321	17	f	f	PROPN
iajs-319	321	18	is	be	AUX
iajs-319	321	19	not	not	PART
iajs-319	321	20	s*g-	s*g-	NOUN
iajs-319	321	21	-continuous	-continuous	ADJ
iajs-319	321	22	.	.	PUNCT
iajs-319	322	1	theorem(3.10	theorem(3.10	NUM
iajs-319	322	2	):	):	PUNCT
iajs-319	322	3	every	every	DET
iajs-319	322	4	s*g-	s*g-	NOUN
iajs-319	322	5	-continuous	-continuous	ADJ
iajs-319	322	6	function	function	NOUN
iajs-319	322	7	is	be	AUX
iajs-319	322	8	semi	semi	ADJ
iajs-319	322	9	-	-	ADJ
iajs-319	322	10	continuous	continuous	ADJ
iajs-319	322	11	function	function	NOUN
iajs-319	322	12	and	and	CCONJ
iajs-319	322	13	gscontinuous	gscontinuous	ADJ
iajs-319	322	14	function	function	NOUN
iajs-319	322	15	.	.	PUNCT
iajs-319	323	1	proof	proof	NOUN
iajs-319	323	2	:	:	PUNCT
iajs-319	323	3	follows	follow	VERB
iajs-319	323	4	from	from	ADP
iajs-319	323	5	the	the	DET
iajs-319	323	6	theorem	theorem	NOUN
iajs-319	323	7	(	(	PUNCT
iajs-319	323	8	2.8	2.8	NUM
iajs-319	323	9	)	)	PUNCT
iajs-319	323	10	.	.	PUNCT
iajs-319	324	1	remark(3.11	remark(3.11	X
iajs-319	324	2	):	):	PUNCT
iajs-319	324	3	the	the	DET
iajs-319	324	4	converse	converse	NOUN
iajs-319	324	5	of	of	ADP
iajs-319	324	6	theorem	theorem	NOUN
iajs-319	324	7	(	(	PUNCT
iajs-319	324	8	3.10	3.10	NUM
iajs-319	324	9	)	)	PUNCT
iajs-319	324	10	may	may	AUX
iajs-319	324	11	not	not	PART
iajs-319	324	12	be	be	AUX
iajs-319	324	13	true	true	ADJ
iajs-319	324	14	in	in	ADP
iajs-319	324	15	general	general	ADJ
iajs-319	324	16	as	as	SCONJ
iajs-319	324	17	shown	show	VERB
iajs-319	324	18	in	in	ADP
iajs-319	324	19	the	the	DET
iajs-319	324	20	following	follow	VERB
iajs-319	324	21	example	example	NOUN
iajs-319	324	22	:	:	PUNCT
iajs-319	324	23	example(3.12	example(3.12	NUM
iajs-319	324	24	):	):	PUNCT
iajs-319	324	25	let	let	VERB
iajs-319	324	26	}	}	PUNCT
iajs-319	324	27	c	c	NOUN
iajs-319	324	28	,	,	PUNCT
iajs-319	324	29	b	b	NOUN
iajs-319	324	30	,	,	PUNCT
iajs-319	324	31	a{yx	a{yx	PUNCT
iajs-319	324	32			NUM
iajs-319	324	33	,	,	PUNCT
iajs-319	324	34	}	}	PUNCT
iajs-319	324	35	}	}	PUNCT
iajs-319	324	36	b	b	NOUN
iajs-319	324	37	,	,	PUNCT
iajs-319	324	38	a{},b{},a{,,x	a{},b{},a{,,x	PROPN
iajs-319	324	39	{	{	PUNCT
iajs-319	324	40			PROPN
iajs-319	324	41	&	&	CCONJ
iajs-319	324	42	}	}	PUNCT
iajs-319	324	43	}	}	PUNCT
iajs-319	324	44	c	c	X
iajs-319	324	45	,	,	PUNCT
iajs-319	324	46	a{},a{,,y	a{},a{,,y	PROPN
iajs-319	324	47	{	{	PUNCT
iajs-319	324	48			X
iajs-319	324	49	.	.	PUNCT
iajs-319	325	1	define	define	NOUN
iajs-319	325	2	)	)	PUNCT
iajs-319	325	3	,	,	PUNCT
iajs-319	325	4	y(),x(:f	y(),x(:f	PROPN
iajs-319	325	5			PUNCT
iajs-319	325	6	by	by	ADP
iajs-319	325	7	:	:	PUNCT
iajs-319	325	8	a)a(f	a)a(f	PROPN
iajs-319	325	9			PROPN
iajs-319	325	10	,	,	PUNCT
iajs-319	325	11	b)b(f	b)b(f	PROPN
iajs-319	325	12			PROPN
iajs-319	325	13	&	&	CCONJ
iajs-319	325	14	c)c(f	c)c(f	PROPN
iajs-319	325	15			PROPN
iajs-319	325	16			NOUN
iajs-319	326	1	f	f	NOUN
iajs-319	326	2	is	be	AUX
iajs-319	326	3	semi	semi	ADJ
iajs-319	326	4	-	-	ADJ
iajs-319	326	5	continuous	continuous	ADJ
iajs-319	326	6	and	and	CCONJ
iajs-319	326	7	gs	gs	NOUN
iajs-319	326	8	-	-	PUNCT
iajs-319	326	9	continuous	continuous	ADJ
iajs-319	326	10	,	,	PUNCT
iajs-319	326	11	but	but	CCONJ
iajs-319	326	12	f	f	PROPN
iajs-319	326	13	is	be	AUX
iajs-319	326	14	not	not	PART
iajs-319	326	15	s*g-	s*g-	NOUN
iajs-319	326	16	-continuous	-continuous	ADJ
iajs-319	326	17	,	,	PUNCT
iajs-319	326	18	since	since	SCONJ
iajs-319	326	19	}	}	PUNCT
iajs-319	326	20	c	c	X
iajs-319	326	21	,	,	PUNCT
iajs-319	326	22	a	a	PRON
iajs-319	326	23	{	{	PUNCT
iajs-319	326	24	is	be	AUX
iajs-319	326	25	open	open	ADJ
iajs-319	326	26	in	in	ADP
iajs-319	326	27	y	y	PROPN
iajs-319	326	28	,	,	PUNCT
iajs-319	326	29	but	but	CCONJ
iajs-319	326	30	}	}	PUNCT
iajs-319	326	31	c	c	X
iajs-319	326	32	,	,	PUNCT
iajs-319	326	33	a{})c	a{})c	ADJ
iajs-319	326	34	,	,	PUNCT
iajs-319	326	35	a({f	a({f	PROPN
iajs-319	326	36	1	1	NUM
iajs-319	326	37			NOUN
iajs-319	326	38	is	be	AUX
iajs-319	326	39	not	not	PART
iajs-319	326	40	s*g-	s*g-	NOUN
iajs-319	326	41	-open	-open	ADJ
iajs-319	326	42	in	in	ADP
iajs-319	326	43	x	x	SYM
iajs-319	326	44	,	,	PUNCT
iajs-319	326	45	since	since	SCONJ
iajs-319	326	46			NOUN
iajs-319	326	47	}	}	PUNCT
iajs-319	326	48	)	)	PUNCT
iajs-319	326	49	)	)	PUNCT
iajs-319	326	50	)	)	PUNCT
iajs-319	327	1	c	c	X
iajs-319	327	2	,	,	PUNCT
iajs-319	327	3	a(int({clint(}c	a(int({clint(}c	PROPN
iajs-319	327	4	,	,	PUNCT
iajs-319	327	5	a	a	PRON
iajs-319	327	6	{	{	PUNCT
iajs-319	327	7	g*s	g*s	PROPN
iajs-319	327	8	}	}	PUNCT
iajs-319	327	9	)	)	PUNCT
iajs-319	327	10	)	)	PUNCT
iajs-319	327	11	)	)	PUNCT
iajs-319	327	12	a({clint	a({clint	NOUN
iajs-319	327	13	(	(	PUNCT
iajs-319	327	14	g*s	g*s	PROPN
iajs-319	327	15	}	}	PUNCT
iajs-319	327	16	a{})c	a{})c	ADJ
iajs-319	327	17	,	,	PUNCT
iajs-319	327	18	aint	aint	NOUN
iajs-319	327	19	(	(	PUNCT
iajs-319	327	20	{	{	PUNCT
iajs-319	327	21			NUM
iajs-319	327	22	.	.	PUNCT
iajs-319	328	1	remark(3.13	remark(3.13	NUM
iajs-319	328	2	):	):	PUNCT
iajs-319	328	3	pre	pre	ADJ
iajs-319	328	4	-	-	ADJ
iajs-319	328	5	continuous	continuous	ADJ
iajs-319	328	6	functions	function	NOUN
iajs-319	328	7	and	and	CCONJ
iajs-319	328	8			NOUN
iajs-319	328	9	g	g	NOUN
iajs-319	328	10	-	-	PUNCT
iajs-319	328	11	continuous	continuous	ADJ
iajs-319	328	12	functions	function	NOUN
iajs-319	328	13	are	be	AUX
iajs-319	328	14	in	in	ADP
iajs-319	328	15	general	general	ADJ
iajs-319	328	16	independent	independent	ADJ
iajs-319	328	17	.	.	PUNCT
iajs-319	329	1	consider	consider	VERB
iajs-319	329	2	the	the	DET
iajs-319	329	3	following	follow	VERB
iajs-319	329	4	examples	example	NOUN
iajs-319	329	5	:	:	PUNCT
iajs-319	329	6	example(3.14	example(3.14	X
iajs-319	329	7	):	):	PUNCT
iajs-319	329	8	let	let	VERB
iajs-319	329	9	}	}	PUNCT
iajs-319	329	10	c	c	NOUN
iajs-319	329	11	,	,	PUNCT
iajs-319	329	12	b	b	NOUN
iajs-319	329	13	,	,	PUNCT
iajs-319	329	14	a{yx	a{yx	PUNCT
iajs-319	329	15			NUM
iajs-319	329	16	,	,	PUNCT
iajs-319	329	17	}	}	PUNCT
iajs-319	329	18	}	}	PUNCT
iajs-319	329	19	c	c	X
iajs-319	329	20	,	,	PUNCT
iajs-319	329	21	a{},a{,,x	a{},a{,,x	PROPN
iajs-319	329	22	{	{	PUNCT
iajs-319	329	23			PROPN
iajs-319	329	24	&	&	CCONJ
iajs-319	329	25	}	}	PUNCT
iajs-319	329	26	}	}	SYM
iajs-319	329	27	b	b	PROPN
iajs-319	329	28	,	,	PUNCT
iajs-319	329	29	a{},b{},a{,,y	a{},b{},a{,,y	PROPN
iajs-319	329	30	{	{	PUNCT
iajs-319	329	31			X
iajs-319	329	32	.	.	PUNCT
iajs-319	330	1	define	define	NOUN
iajs-319	330	2	)	)	PUNCT
iajs-319	330	3	,	,	PUNCT
iajs-319	330	4	y(),x(:f	y(),x(:f	PROPN
iajs-319	330	5			PUNCT
iajs-319	330	6	by	by	ADP
iajs-319	330	7	:	:	PUNCT
iajs-319	330	8	a)a(f	a)a(f	PROPN
iajs-319	330	9			PROPN
iajs-319	330	10	,	,	PUNCT
iajs-319	330	11	c)b(f	c)b(f	PROPN
iajs-319	331	1			PROPN
iajs-319	331	2	&	&	CCONJ
iajs-319	331	3	b)c(f	b)c(f	PROPN
iajs-319	332	1			PROPN
iajs-319	332	2			NOUN
iajs-319	333	1	f	f	NOUN
iajs-319	333	2	is	is	NOUN
iajs-319	333	3	g	g	NOUN
iajs-319	333	4	-	-	PUNCT
iajs-319	333	5	continuous	continuous	ADJ
iajs-319	333	6	,	,	PUNCT
iajs-319	333	7	but	but	CCONJ
iajs-319	333	8	f	f	PROPN
iajs-319	333	9	is	be	AUX
iajs-319	333	10	not	not	PART
iajs-319	333	11	pre	pre	ADJ
iajs-319	333	12	-	-	ADJ
iajs-319	333	13	continuous	continuous	ADJ
iajs-319	333	14	,	,	PUNCT
iajs-319	333	15	since	since	SCONJ
iajs-319	333	16	}	}	PUNCT
iajs-319	333	17	b	b	X
iajs-319	333	18	{	{	PUNCT
iajs-319	333	19	is	be	AUX
iajs-319	333	20	open	open	ADJ
iajs-319	333	21	set	set	VERB
iajs-319	333	22	in	in	ADP
iajs-319	333	23	y	y	PROPN
iajs-319	333	24	,	,	PUNCT
iajs-319	333	25	but	but	CCONJ
iajs-319	333	26	}	}	PUNCT
iajs-319	333	27	c{})b({f	c{})b({f	NOUN
iajs-319	333	28	1	1	NUM
iajs-319	333	29			NOUN
iajs-319	333	30	is	be	AUX
iajs-319	333	31	not	not	PART
iajs-319	333	32	pre	pre	ADJ
iajs-319	333	33	-	-	ADJ
iajs-319	333	34	open	open	ADJ
iajs-319	333	35	set	set	NOUN
iajs-319	333	36	in	in	ADP
iajs-319	333	37	x	x	SYM
iajs-319	333	38	,	,	PUNCT
iajs-319	333	39	since	since	SCONJ
iajs-319	333	40	}	}	PUNCT
iajs-319	333	41	)	)	PUNCT
iajs-319	333	42	)	)	PUNCT
iajs-319	334	1	c({clint(}c	c({clint(}c	PROPN
iajs-319	334	2	{	{	PUNCT
iajs-319	334	3			PROPN
iajs-319	334	4	}	}	PUNCT
iajs-319	334	5	)	)	PUNCT
iajs-319	335	1	c	c	X
iajs-319	335	2	,	,	PUNCT
iajs-319	335	3	bint({	bint({	X
iajs-319	335	4			X
iajs-319	335	5	.	.	PUNCT
iajs-319	336	1	example(3.15	example(3.15	NUM
iajs-319	336	2	):	):	PUNCT
iajs-319	336	3	let	let	VERB
iajs-319	336	4			PROPN
iajs-319	336	5	yx	yx	PROPN
iajs-319	336	6	,	,	PUNCT
iajs-319	336	7			PROPN
iajs-319	336	8	usual	usual	ADJ
iajs-319	336	9	topology	topology	NOUN
iajs-319	336	10	&	&	CCONJ
iajs-319	336	11	}	}	PUNCT
iajs-319	336	12	}	}	PUNCT
iajs-319	336	13	q	q	X
iajs-319	336	14	{	{	PUNCT
iajs-319	336	15	,	,	PUNCT
iajs-319	336	16	,	,	PUNCT
iajs-319	336	17	{	{	PUNCT
iajs-319	336	18			NOUN
iajs-319	336	19	.	.	PUNCT
iajs-319	337	1	define	define	VERB
iajs-319	337	2	)	)	PUNCT
iajs-319	337	3	,	,	PUNCT
iajs-319	337	4	(	(	PUNCT
iajs-319	337	5	)	)	PUNCT
iajs-319	337	6	,	,	PUNCT
iajs-319	337	7	(:	(:	PROPN
iajs-319	337	8	f	f	PROPN
iajs-319	337	9			NOUN
iajs-319	337	10	by	by	ADP
iajs-319	337	11	:	:	PUNCT
iajs-319	337	12	x)x(f	x)x(f	PROPN
iajs-319	337	13			NOUN
iajs-319	337	14	for	for	ADP
iajs-319	337	15	each	each	DET
iajs-319	337	16	x	x	NOUN
iajs-319	337	17			NOUN
iajs-319	338	1	f	f	PROPN
iajs-319	338	2	is	be	AUX
iajs-319	338	3	not	not	PART
iajs-319	338	4	g	g	ADV
iajs-319	338	5	-	-	ADJ
iajs-319	338	6	continuous	continuous	ADJ
iajs-319	338	7	,	,	PUNCT
iajs-319	338	8	since	since	SCONJ
iajs-319	338	9	q	q	NOUN
iajs-319	338	10	is	be	AUX
iajs-319	338	11	open	open	ADJ
iajs-319	338	12	in	in	ADP
iajs-319	338	13	y	y	PROPN
iajs-319	338	14	,	,	PUNCT
iajs-319	338	15	but	but	CCONJ
iajs-319	338	16	q})q({f	q})q({f	PROPN
iajs-319	338	17	1	1	NUM
iajs-319	338	18			NOUN
iajs-319	338	19	is	be	AUX
iajs-319	338	20	not	not	PART
iajs-319	338	21			NOUN
iajs-319	338	22	g	g	NOUN
iajs-319	338	23	-	-	PUNCT
iajs-319	338	24	open	open	NOUN
iajs-319	338	25	set	set	NOUN
iajs-319	338	26	in	in	ADP
iajs-319	338	27	x	x	X
iajs-319	338	28	.	.	PUNCT
iajs-319	339	1	but	but	CCONJ
iajs-319	339	2	f	f	PROPN
iajs-319	339	3	is	be	AUX
iajs-319	339	4	pre	pre	ADJ
iajs-319	339	5	-	-	ADJ
iajs-319	339	6	continuous	continuous	ADJ
iajs-319	339	7	.	.	PUNCT
iajs-319	340	1	remark(3.16	remark(3.16	NUM
iajs-319	340	2	):	):	PUNCT
iajs-319	340	3	g	g	NOUN
iajs-319	340	4	-	-	PUNCT
iajs-319	340	5	continuous	continuous	ADJ
iajs-319	340	6	functions	function	NOUN
iajs-319	340	7	and	and	CCONJ
iajs-319	340	8	g	g	NOUN
iajs-319	340	9	-continuous	-continuous	ADJ
iajs-319	340	10	functions	function	NOUN
iajs-319	340	11	are	be	AUX
iajs-319	340	12	in	in	ADP
iajs-319	340	13	general	general	ADJ
iajs-319	340	14	independent	independent	ADJ
iajs-319	340	15	.	.	PUNCT
iajs-319	341	1	consider	consider	VERB
iajs-319	341	2	the	the	DET
iajs-319	341	3	following	follow	VERB
iajs-319	341	4	examples	example	NOUN
iajs-319	341	5	:	:	PUNCT
iajs-319	341	6	example(3.17	example(3.17	NUM
iajs-319	341	7	):	):	PUNCT
iajs-319	341	8	let	let	VERB
iajs-319	341	9	}	}	PUNCT
iajs-319	341	10	c	c	NOUN
iajs-319	341	11	,	,	PUNCT
iajs-319	341	12	b	b	NOUN
iajs-319	341	13	,	,	PUNCT
iajs-319	341	14	a{yx	a{yx	PUNCT
iajs-319	341	15			NUM
iajs-319	341	16	,	,	PUNCT
iajs-319	341	17	}	}	PUNCT
iajs-319	341	18	}	}	PUNCT
iajs-319	341	19	a{,,x	a{,,x	PROPN
iajs-319	341	20	{	{	PUNCT
iajs-319	341	21			PROPN
iajs-319	341	22	&	&	CCONJ
iajs-319	341	23	}	}	PUNCT
iajs-319	341	24	}	}	PUNCT
iajs-319	341	25	b{,,y	b{,,y	NOUN
iajs-319	341	26	{	{	PUNCT
iajs-319	341	27			NOUN
iajs-319	341	28	.	.	PUNCT
iajs-319	342	1	define	define	NOUN
iajs-319	342	2	)	)	PUNCT
iajs-319	342	3	,	,	PUNCT
iajs-319	342	4	y(),x(:f	y(),x(:f	PROPN
iajs-319	342	5			PUNCT
iajs-319	342	6	by	by	ADP
iajs-319	342	7	:	:	PUNCT
iajs-319	342	8	a)a(f	a)a(f	PROPN
iajs-319	342	9			PROPN
iajs-319	342	10	,	,	PUNCT
iajs-319	342	11	c)b(f	c)b(f	PROPN
iajs-319	343	1			PROPN
iajs-319	343	2	&	&	CCONJ
iajs-319	343	3	b)c(f	b)c(f	PROPN
iajs-319	344	1			PROPN
iajs-319	344	2			NOUN
iajs-319	345	1	f	f	NOUN
iajs-319	345	2	is	be	AUX
iajs-319	345	3	g	g	NOUN
iajs-319	345	4	-	-	PUNCT
iajs-319	345	5	continuous	continuous	ADJ
iajs-319	345	6	,	,	PUNCT
iajs-319	345	7	but	but	CCONJ
iajs-319	345	8	f	f	PROPN
iajs-319	345	9	is	be	AUX
iajs-319	345	10	not	not	PART
iajs-319	345	11	g	g	NOUN
iajs-319	345	12	continuous	continuous	ADJ
iajs-319	345	13	,	,	PUNCT
iajs-319	345	14	since	since	SCONJ
iajs-319	345	15	}	}	PUNCT
iajs-319	345	16	b	b	X
iajs-319	345	17	{	{	PUNCT
iajs-319	345	18	is	be	AUX
iajs-319	345	19	open	open	ADJ
iajs-319	345	20	set	set	VERB
iajs-319	345	21	in	in	ADP
iajs-319	345	22	y	y	PROPN
iajs-319	345	23	,	,	PUNCT
iajs-319	345	24	but	but	CCONJ
iajs-319	345	25	}	}	PUNCT
iajs-319	345	26	c{})b({f	c{})b({f	NOUN
iajs-319	345	27	1	1	NUM
iajs-319	345	28			NOUN
iajs-319	345	29	is	be	AUX
iajs-319	345	30	not	not	PART
iajs-319	345	31	g	g	ADJ
iajs-319	345	32	-open	-open	NOUN
iajs-319	345	33	set	set	VERB
iajs-319	345	34	in	in	ADP
iajs-319	345	35	x	x	SYM
iajs-319	345	36	,	,	PUNCT
iajs-319	345	37	since	since	SCONJ
iajs-319	345	38	c}c	c}c	NOUN
iajs-319	345	39	{	{	PUNCT
iajs-319	345	40	}	}	PUNCT
iajs-319	345	41	b	b	NOUN
iajs-319	345	42	,	,	PUNCT
iajs-319	345	43	a	a	PRON
iajs-319	345	44	{	{	PUNCT
iajs-319	345	45	is	be	AUX
iajs-319	345	46	not	not	PART
iajs-319	345	47	g	g	NOUN
iajs-319	345	48	-closed	-close	VERB
iajs-319	345	49	set	set	NOUN
iajs-319	345	50	in	in	ADP
iajs-319	345	51	x	x	X
iajs-319	345	52	.	.	PUNCT
iajs-319	345	53	example(3.18	example(3.18	NUM
iajs-319	345	54	):	):	PUNCT
iajs-319	345	55	let	let	VERB
iajs-319	345	56	}	}	PUNCT
iajs-319	345	57	c	c	NOUN
iajs-319	345	58	,	,	PUNCT
iajs-319	345	59	b	b	NOUN
iajs-319	345	60	,	,	PUNCT
iajs-319	345	61	a{yx	a{yx	PUNCT
iajs-319	345	62			NUM
iajs-319	345	63	,	,	PUNCT
iajs-319	345	64	}	}	PUNCT
iajs-319	345	65	}	}	PUNCT
iajs-319	345	66	c	c	X
iajs-319	345	67	,	,	PUNCT
iajs-319	345	68	a{},a{,,x	a{},a{,,x	PROPN
iajs-319	345	69	{	{	PUNCT
iajs-319	345	70			PROPN
iajs-319	345	71	&	&	CCONJ
iajs-319	345	72	}	}	PUNCT
iajs-319	345	73	}	}	PUNCT
iajs-319	345	74	b{,,y	b{,,y	NOUN
iajs-319	345	75	{	{	PUNCT
iajs-319	345	76			NOUN
iajs-319	345	77	.	.	PUNCT
iajs-319	346	1	define	define	NOUN
iajs-319	346	2	)	)	PUNCT
iajs-319	346	3	,	,	PUNCT
iajs-319	346	4	y(),x(:f	y(),x(:f	PROPN
iajs-319	346	5			PUNCT
iajs-319	346	6	by	by	ADP
iajs-319	346	7	:	:	PUNCT
iajs-319	346	8	b)a(f	b)a(f	ADJ
iajs-319	346	9			NUM
iajs-319	346	10	,	,	PUNCT
iajs-319	346	11	b)b(f	b)b(f	PROPN
iajs-319	346	12			PROPN
iajs-319	346	13	&	&	CCONJ
iajs-319	346	14	a)c(f	a)c(f	PROPN
iajs-319	347	1			PROPN
iajs-319	347	2			NOUN
iajs-319	348	1	f	f	NOUN
iajs-319	348	2	is	be	AUX
iajs-319	348	3	g	g	NOUN
iajs-319	348	4	-continuous	-continuous	ADJ
iajs-319	348	5	,	,	PUNCT
iajs-319	348	6	but	but	CCONJ
iajs-319	348	7	f	f	PROPN
iajs-319	348	8	is	be	AUX
iajs-319	348	9	not	not	PART
iajs-319	348	10	g	g	NOUN
iajs-319	348	11	-	-	NOUN
iajs-319	348	12	continuous	continuous	ADJ
iajs-319	348	13	,	,	PUNCT
iajs-319	348	14	since	since	SCONJ
iajs-319	348	15	}	}	PUNCT
iajs-319	348	16	b	b	X
iajs-319	348	17	{	{	PUNCT
iajs-319	348	18	is	be	AUX
iajs-319	348	19	open	open	ADJ
iajs-319	348	20	set	set	VERB
iajs-319	348	21	in	in	ADP
iajs-319	348	22	y	y	PROPN
iajs-319	348	23	,	,	PUNCT
iajs-319	348	24	but	but	CCONJ
iajs-319	348	25	}	}	PUNCT
iajs-319	348	26	b	b	NOUN
iajs-319	348	27	,	,	PUNCT
iajs-319	348	28	a{})b({f	a{})b({f	NOUN
iajs-319	348	29	1	1	NUM
iajs-319	348	30			NOUN
iajs-319	348	31	is	be	AUX
iajs-319	348	32	not	not	PART
iajs-319	348	33	g	g	NOUN
iajs-319	348	34	-	-	PUNCT
iajs-319	348	35	open	open	ADJ
iajs-319	348	36	set	set	NOUN
iajs-319	348	37	in	in	ADP
iajs-319	348	38	x	x	SYM
iajs-319	348	39	,	,	PUNCT
iajs-319	348	40	since	since	SCONJ
iajs-319	348	41	}	}	PUNCT
iajs-319	348	42	c{}b	c{}b	NOUN
iajs-319	348	43	,	,	PUNCT
iajs-319	348	44	a	a	PRON
iajs-319	348	45	{	{	PUNCT
iajs-319	348	46	c	c	NOUN
iajs-319	348	47			NOUN
iajs-319	348	48	is	be	AUX
iajs-319	348	49	not	not	PART
iajs-319	348	50	g	g	NOUN
iajs-319	348	51	-	-	PUNCT
iajs-319	348	52	closed	closed	ADJ
iajs-319	348	53	in	in	ADP
iajs-319	348	54	x	x	X
iajs-319	348	55	.	.	PUNCT
iajs-319	349	1	551	551	NUM
iajs-319	350	1	|	|	ADV
iajs-319	350	2	mathematics	mathematic	NOUN
iajs-319	350	3	2014	2014	NUM
iajs-319	350	4	)	)	PUNCT
iajs-319	350	5	عام	عام	ADP
iajs-319	350	6	3العدد	3العدد	NUM
iajs-319	350	7	(	(	PUNCT
iajs-319	350	8	27مجلة	27مجلة	NUM
iajs-319	350	9	إبن	إبن	VERB
iajs-319	350	10	الھيثم	الھيثم	NOUN
iajs-319	350	11	للعلوم	للعلوم	NOUN
iajs-319	350	12	الصرفة	الصرفة	NOUN
iajs-319	351	1	و	و	PRON
iajs-319	351	2	التطبيقية	التطبيقية	ADV
iajs-319	351	3	المجلد	المجلد	VERB
iajs-319	351	4	ibn	ibn	PROPN
iajs-319	351	5	al	al	PROPN
iajs-319	351	6	-	-	PUNCT
iajs-319	351	7	haitham	haitham	PROPN
iajs-319	351	8	jour	jour	X
iajs-319	351	9	.	.	PROPN
iajs-319	352	1	for	for	ADP
iajs-319	352	2	pure	pure	ADJ
iajs-319	352	3	&	&	CCONJ
iajs-319	352	4	appl	appl	PROPN
iajs-319	352	5	.	.	PUNCT
iajs-319	353	1	sci	sci	PROPN
iajs-319	353	2	.	.	PUNCT
iajs-319	353	3	vol	vol	NOUN
iajs-319	353	4	.	.	PROPN
iajs-319	354	1	27	27	NUM
iajs-319	354	2	(	(	PUNCT
iajs-319	354	3	3	3	NUM
iajs-319	354	4	)	)	PUNCT
iajs-319	354	5	2014	2014	NUM
iajs-319	354	6	the	the	DET
iajs-319	354	7	following	follow	VERB
iajs-319	354	8	diagram	diagram	NOUN
iajs-319	354	9	shows	show	VERB
iajs-319	354	10	the	the	DET
iajs-319	354	11	relationships	relationship	NOUN
iajs-319	354	12	between	between	ADP
iajs-319	354	13	s*g-	s*g-	NOUN
iajs-319	354	14	-continuous	-continuous	ADJ
iajs-319	354	15	functions	function	NOUN
iajs-319	354	16	and	and	CCONJ
iajs-319	354	17	some	some	DET
iajs-319	354	18	other	other	ADJ
iajs-319	354	19	continuous	continuous	ADJ
iajs-319	354	20	functions	function	NOUN
iajs-319	354	21	:	:	PUNCT
iajs-319	354	22	proposition(3.19	proposition(3.19	NUM
iajs-319	354	23	):	):	PUNCT
iajs-319	354	24	if	if	SCONJ
iajs-319	354	25	)	)	PUNCT
iajs-319	354	26	,	,	PUNCT
iajs-319	354	27	y(),x(:f	y(),x(:f	PROPN
iajs-319	354	28			PROPN
iajs-319	354	29	is	be	AUX
iajs-319	354	30	s*g-	s*g-	NOUN
iajs-319	354	31	-continuous	-continuous	ADJ
iajs-319	354	32	,	,	PUNCT
iajs-319	354	33	then	then	ADV
iajs-319	354	34	)	)	PUNCT
iajs-319	354	35	)	)	PUNCT
iajs-319	355	1	a(f(cl))a(cl(f	a(f(cl))a(cl(f	PROPN
iajs-319	355	2	g*s	g*s	PROPN
iajs-319	355	3			NOUN
iajs-319	355	4	for	for	ADP
iajs-319	355	5	every	every	DET
iajs-319	355	6	subset	subset	NOUN
iajs-319	355	7	a	a	PRON
iajs-319	355	8	of	of	ADP
iajs-319	355	9	x	x	X
iajs-319	355	10	.	.	PUNCT
iajs-319	356	1	proof	proof	NOUN
iajs-319	356	2	:	:	PUNCT
iajs-319	356	3	since	since	SCONJ
iajs-319	356	4	)	)	PUNCT
iajs-319	356	5	)	)	PUNCT
iajs-319	356	6	a(f(cl)a(f	a(f(cl)a(f	VERB
iajs-319	356	7			PROPN
iajs-319	356	8			PROPN
iajs-319	356	9	)	)	PUNCT
iajs-319	356	10	)	)	PUNCT
iajs-319	356	11	)	)	PUNCT
iajs-319	357	1	a(f(cl(fa	a(f(cl(fa	PROPN
iajs-319	357	2	1	1	NUM
iajs-319	357	3	.	.	PUNCT
iajs-319	358	1	since	since	SCONJ
iajs-319	358	2	)	)	PUNCT
iajs-319	358	3	)	)	PUNCT
iajs-319	358	4	a(f(cl	a(f(cl	NOUN
iajs-319	358	5	is	be	AUX
iajs-319	358	6	a	a	DET
iajs-319	358	7	closed	closed	ADJ
iajs-319	358	8	set	set	NOUN
iajs-319	358	9	in	in	ADP
iajs-319	358	10	y	y	PROPN
iajs-319	358	11	and	and	CCONJ
iajs-319	358	12	f	f	PROPN
iajs-319	358	13	is	be	AUX
iajs-319	358	14	s*g-	s*g-	NOUN
iajs-319	358	15	-continuous	-continuous	ADJ
iajs-319	358	16	,	,	PUNCT
iajs-319	358	17	then	then	ADV
iajs-319	358	18	by	by	ADP
iajs-319	358	19	(	(	PUNCT
iajs-319	358	20	3.2	3.2	NUM
iajs-319	358	21	)	)	PUNCT
iajs-319	358	22	)	)	PUNCT
iajs-319	358	23	)	)	PUNCT
iajs-319	358	24	)	)	PUNCT
iajs-319	359	1	a(f(cl(f	a(f(cl(f	ADV
iajs-319	359	2	1	1	NUM
iajs-319	359	3	is	be	AUX
iajs-319	359	4	an	an	DET
iajs-319	359	5	s*g-	s*g-	NOUN
iajs-319	359	6	-closed	-close	VERB
iajs-319	359	7	set	set	VERB
iajs-319	359	8	in	in	ADP
iajs-319	359	9	x	x	PUNCT
iajs-319	359	10	containing	contain	VERB
iajs-319	359	11	a	a	DET
iajs-319	359	12	.	.	PUNCT
iajs-319	360	1	hence	hence	ADV
iajs-319	360	2	)	)	PUNCT
iajs-319	360	3	)	)	PUNCT
iajs-319	360	4	)	)	PUNCT
iajs-319	361	1	a(f(cl(f)a(cl	a(f(cl(f)a(cl	X
iajs-319	361	2	1	1	NUM
iajs-319	361	3	g*s	g*s	PROPN
iajs-319	361	4			PROPN
iajs-319	361	5			X
iajs-319	361	6			PROPN
iajs-319	361	7	.	.	PUNCT
iajs-319	362	1	therefore	therefore	ADV
iajs-319	362	2	)	)	PUNCT
iajs-319	362	3	)	)	PUNCT
iajs-319	362	4	a(f(cl))a(cl(f	a(f(cl))a(cl(f	PROPN
iajs-319	362	5	g*s	g*s	PROPN
iajs-319	362	6			NOUN
iajs-319	362	7	.	.	PUNCT
iajs-319	363	1	theorem(3.20	theorem(3.20	NUM
iajs-319	363	2	:	:	PUNCT
iajs-319	363	3	let	let	VERB
iajs-319	363	4	)	)	PUNCT
iajs-319	363	5	,	,	PUNCT
iajs-319	363	6	y(),x(:f	y(),x(:f	PROPN
iajs-319	363	7			PROPN
iajs-319	363	8	be	be	VERB
iajs-319	363	9	a	a	DET
iajs-319	363	10	function	function	NOUN
iajs-319	363	11	.	.	PUNCT
iajs-319	364	1	then	then	ADV
iajs-319	364	2	the	the	DET
iajs-319	364	3	following	follow	VERB
iajs-319	364	4	statements	statement	NOUN
iajs-319	364	5	are	be	AUX
iajs-319	364	6	equivalent	equivalent	ADJ
iajs-319	364	7	:	:	PUNCT
iajs-319	364	8	i	i	X
iajs-319	364	9	)	)	PUNCT
iajs-319	365	1	f	f	PROPN
iajs-319	365	2	is	be	AUX
iajs-319	365	3	s*g-	s*g-	NOUN
iajs-319	365	4	-continuous	-continuous	ADJ
iajs-319	365	5	.	.	PUNCT
iajs-319	366	1	ii	ii	X
iajs-319	366	2	)	)	PUNCT
iajs-319	366	3	for	for	ADP
iajs-319	366	4	each	each	DET
iajs-319	366	5	point	point	NOUN
iajs-319	366	6	x	x	PUNCT
iajs-319	366	7	in	in	ADP
iajs-319	366	8	x	x	X
iajs-319	366	9	and	and	CCONJ
iajs-319	366	10	each	each	DET
iajs-319	366	11	open	open	ADJ
iajs-319	366	12	set	set	VERB
iajs-319	366	13	v	v	NOUN
iajs-319	366	14	in	in	ADP
iajs-319	366	15	y	y	PROPN
iajs-319	366	16	with	with	ADP
iajs-319	366	17	v)x(f	v)x(f	NOUN
iajs-319	366	18			NOUN
iajs-319	366	19	,	,	PUNCT
iajs-319	366	20	there	there	PRON
iajs-319	366	21	is	be	VERB
iajs-319	366	22	an	an	DET
iajs-319	366	23	s*g-	s*g-	NOUN
iajs-319	366	24	-open	-open	NOUN
iajs-319	366	25	set	set	VERB
iajs-319	366	26	u	u	NOUN
iajs-319	366	27	in	in	ADP
iajs-319	366	28	x	x	PUNCT
iajs-319	366	29	such	such	ADJ
iajs-319	366	30	that	that	SCONJ
iajs-319	366	31	ux	ux	NOUN
iajs-319	366	32	and	and	CCONJ
iajs-319	366	33	v)u(f	v)u(f	PROPN
iajs-319	366	34			PROPN
iajs-319	366	35	.	.	PUNCT
iajs-319	366	36	iii	iii	X
iajs-319	366	37	)	)	PUNCT
iajs-319	366	38	for	for	SCONJ
iajs-319	366	39	each	each	PRON
iajs-319	366	40	subset	subset	VERB
iajs-319	366	41	a	a	PRON
iajs-319	366	42	of	of	ADP
iajs-319	366	43	x	x	PRON
iajs-319	366	44	,	,	PUNCT
iajs-319	366	45	)	)	PUNCT
iajs-319	366	46	)	)	PUNCT
iajs-319	367	1	a(f(cl))a(cl(f	a(f(cl))a(cl(f	PROPN
iajs-319	367	2	g*s	g*s	PROPN
iajs-319	367	3			NOUN
iajs-319	367	4	.	.	PUNCT
iajs-319	368	1	iv	iv	X
iajs-319	368	2	)	)	PUNCT
iajs-319	368	3	for	for	ADP
iajs-319	368	4	each	each	DET
iajs-319	368	5	subset	subset	NOUN
iajs-319	368	6	b	b	PROPN
iajs-319	368	7	of	of	ADP
iajs-319	368	8	y	y	PROPN
iajs-319	368	9	,	,	PUNCT
iajs-319	368	10	)	)	PUNCT
iajs-319	368	11	)	)	PUNCT
iajs-319	368	12	b(cl(f))b(f(cl	b(cl(f))b(f(cl	NOUN
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iajs-319	368	16			NOUN
iajs-319	368	17			ADJ
iajs-319	368	18	.	.	PUNCT
iajs-319	369	1	proof	proof	NOUN
iajs-319	369	2	:	:	PUNCT
iajs-319	369	3	)	)	PUNCT
iajs-319	369	4	ii()i	ii()i	SYM
iajs-319	369	5	(	(	PUNCT
iajs-319	369	6			NOUN
iajs-319	369	7	.	.	PUNCT
iajs-319	370	1	let	let	VERB
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iajs-319	370	3	:	:	PUNCT
iajs-319	370	4	f	f	X
iajs-319	370	5			PROPN
iajs-319	370	6	be	be	AUX
iajs-319	370	7	an	an	DET
iajs-319	370	8	s*g-	s*g-	NOUN
iajs-319	370	9	-continuous	-continuous	ADJ
iajs-319	370	10	function	function	NOUN
iajs-319	370	11	and	and	CCONJ
iajs-319	370	12	v	v	AUX
iajs-319	370	13	be	be	AUX
iajs-319	370	14	an	an	DET
iajs-319	370	15	open	open	ADJ
iajs-319	370	16	set	set	NOUN
iajs-319	370	17	in	in	ADP
iajs-319	370	18	y	y	PROPN
iajs-319	370	19	s.t	s.t	PROPN
iajs-319	370	20	v)x(f	v)x(f	PROPN
iajs-319	370	21			NOUN
iajs-319	370	22	.	.	PUNCT
iajs-319	371	1	to	to	PART
iajs-319	371	2	prove	prove	VERB
iajs-319	371	3	that	that	SCONJ
iajs-319	371	4	,	,	PUNCT
iajs-319	371	5	there	there	PRON
iajs-319	371	6	is	be	VERB
iajs-319	371	7	an	an	DET
iajs-319	371	8	s*g-	s*g-	NOUN
iajs-319	371	9	-open	-open	NOUN
iajs-319	371	10	set	set	VERB
iajs-319	371	11	u	u	NOUN
iajs-319	371	12	in	in	ADP
iajs-319	371	13	x	x	X
iajs-319	371	14	s.t	s.t	PROPN
iajs-319	371	15	ux	ux	NOUN
iajs-319	371	16	and	and	CCONJ
iajs-319	371	17	v)u(f	v)u(f	PROPN
iajs-319	371	18			PROPN
iajs-319	371	19	.	.	PUNCT
iajs-319	372	1	since	since	SCONJ
iajs-319	372	2	f	f	PROPN
iajs-319	372	3	is	be	AUX
iajs-319	372	4	s*g-	s*g-	NOUN
iajs-319	372	5	-continuous	-continuous	ADJ
iajs-319	372	6	,	,	PUNCT
iajs-319	372	7	then	then	ADV
iajs-319	372	8	)	)	PUNCT
iajs-319	372	9	v(f	v(f	PROPN
iajs-319	372	10	1	1	NUM
iajs-319	372	11	is	be	AUX
iajs-319	372	12	an	an	DET
iajs-319	372	13	s*g-	s*g-	NOUN
iajs-319	372	14	-open	-open	NOUN
iajs-319	372	15	set	set	VERB
iajs-319	372	16	in	in	ADP
iajs-319	372	17	x	x	PROPN
iajs-319	372	18	s.t	s.t	PROPN
iajs-319	372	19	)	)	PUNCT
iajs-319	372	20	v(fx	v(fx	PROPN
iajs-319	372	21	1	1	NUM
iajs-319	372	22	.	.	PUNCT
iajs-319	373	1	let	let	VERB
iajs-319	373	2	)	)	PUNCT
iajs-319	373	3	v(fu	v(fu	PROPN
iajs-319	373	4	1	1	NUM
iajs-319	373	5			NOUN
iajs-319	373	6	v))v(f(f)u(f	v))v(f(f)u(f	NOUN
iajs-319	373	7	1	1	NUM
iajs-319	373	8			NOUN
iajs-319	373	9			NOUN
iajs-319	373	10			NOUN
iajs-319	373	11	v)u(f	v)u(f	NOUN
iajs-319	373	12			PROPN
iajs-319	373	13	.	.	PUNCT
iajs-319	373	14	)	)	PUNCT
iajs-319	374	1	i()ii	i()ii	PROPN
iajs-319	374	2	(	(	PUNCT
iajs-319	374	3			NOUN
iajs-319	374	4	.	.	PUNCT
iajs-319	375	1	to	to	PART
iajs-319	375	2	prove	prove	VERB
iajs-319	375	3	that	that	PRON
iajs-319	375	4	yx	yx	ADP
iajs-319	375	5	:	:	PUNCT
iajs-319	375	6	f	f	NOUN
iajs-319	375	7			PROPN
iajs-319	375	8	is	be	AUX
iajs-319	375	9	s*g-	s*g-	NOUN
iajs-319	375	10	-continuous	-continuous	ADJ
iajs-319	375	11	.	.	PUNCT
iajs-319	376	1	let	let	VERB
iajs-319	376	2	v	v	PART
iajs-319	376	3	be	be	AUX
iajs-319	376	4	any	any	DET
iajs-319	376	5	open	open	ADJ
iajs-319	376	6	set	set	NOUN
iajs-319	376	7	in	in	ADP
iajs-319	376	8	y	y	PROPN
iajs-319	376	9	.	.	PUNCT
iajs-319	377	1	to	to	PART
iajs-319	377	2	prove	prove	VERB
iajs-319	377	3	that	that	PRON
iajs-319	377	4	)	)	PUNCT
iajs-319	378	1	v(f	v(f	PROPN
iajs-319	378	2	1	1	NUM
iajs-319	378	3	is	be	AUX
iajs-319	378	4	an	an	DET
iajs-319	378	5	s*g-	s*g-	NOUN
iajs-319	378	6	-open	-open	NOUN
iajs-319	378	7	set	set	VERB
iajs-319	378	8	in	in	ADP
iajs-319	378	9	x	x	X
iajs-319	378	10	.	.	PUNCT
iajs-319	379	1	let	let	VERB
iajs-319	379	2	)	)	PUNCT
iajs-319	379	3	v(fx	v(fx	NOUN
iajs-319	379	4	1	1	NUM
iajs-319	379	5			NOUN
iajs-319	379	6	v)x(f	v)x(f	PROPN
iajs-319	379	7			NOUN
iajs-319	379	8	.by	.by	PUNCT
iajs-319	380	1	hypothesis	hypothesis	NOUN
iajs-319	380	2	there	there	PRON
iajs-319	380	3	is	be	VERB
iajs-319	380	4	an	an	DET
iajs-319	380	5	s*g-	s*g-	NOUN
iajs-319	380	6	-open	-open	NOUN
iajs-319	380	7	set	set	VERB
iajs-319	380	8	u	u	NOUN
iajs-319	380	9	in	in	ADP
iajs-319	380	10	x	x	X
iajs-319	380	11	s.t	s.t	PROPN
iajs-319	380	12	ux	ux	NOUN
iajs-319	380	13	and	and	CCONJ
iajs-319	380	14	v)u(f	v)u(f	PROPN
iajs-319	380	15			PROPN
iajs-319	380	16			PROPN
iajs-319	380	17	)	)	PUNCT
iajs-319	380	18	v(fux	v(fux	PROPN
iajs-319	380	19	1	1	NOUN
iajs-319	380	20	.	.	PUNCT
iajs-319	381	1	thus	thus	ADV
iajs-319	381	2	by	by	ADP
iajs-319	381	3	theorem	theorem	NOUN
iajs-319	381	4	(	(	PUNCT
iajs-319	381	5	(	(	PUNCT
iajs-319	381	6	2.26),vii	2.26),vii	VERB
iajs-319	381	7	)	)	PUNCT
iajs-319	381	8	)	)	PUNCT
iajs-319	382	1	v(f	v(f	PROPN
iajs-319	382	2	1	1	NUM
iajs-319	382	3	is	be	AUX
iajs-319	382	4	an	an	DET
iajs-319	382	5	s*g-	s*g-	NOUN
iajs-319	382	6	-open	-open	NOUN
iajs-319	382	7	set	set	VERB
iajs-319	382	8	in	in	ADP
iajs-319	382	9	x	x	X
iajs-319	382	10	.	.	PUNCT
iajs-319	383	1	hence	hence	ADV
iajs-319	383	2	yx	yx	NOUN
iajs-319	383	3	:	:	PUNCT
iajs-319	383	4	f	f	X
iajs-319	383	5			X
iajs-319	383	6	is	be	AUX
iajs-319	383	7	an	an	DET
iajs-319	383	8	s*g-	s*g-	NOUN
iajs-319	383	9	-continuous	-continuous	ADJ
iajs-319	383	10	function	function	NOUN
iajs-319	383	11	.	.	PUNCT
iajs-319	384	1	)	)	PUNCT
iajs-319	384	2	iii()ii	iii()ii	NOUN
iajs-319	384	3	(	(	PUNCT
iajs-319	384	4			NOUN
iajs-319	384	5	.	.	PUNCT
iajs-319	384	6	suppose	suppose	VERB
iajs-319	384	7	that	that	SCONJ
iajs-319	384	8	(	(	PUNCT
iajs-319	384	9	ii	ii	NOUN
iajs-319	384	10	)	)	PUNCT
iajs-319	384	11	holds	hold	VERB
iajs-319	384	12	and	and	CCONJ
iajs-319	384	13	let	let	VERB
iajs-319	384	14	)	)	PUNCT
iajs-319	384	15	)	)	PUNCT
iajs-319	384	16	a(cl(fy	a(cl(fy	PROPN
iajs-319	384	17	g*s	g*s	PROPN
iajs-319	384	18			NUM
iajs-319	384	19	and	and	CCONJ
iajs-319	384	20	let	let	VERB
iajs-319	384	21	v	v	PART
iajs-319	384	22	be	be	AUX
iajs-319	384	23	any	any	DET
iajs-319	384	24	open	open	ADJ
iajs-319	384	25	neighborhood	neighborhood	NOUN
iajs-319	384	26	of	of	ADP
iajs-319	384	27	y	y	PROPN
iajs-319	384	28	in	in	ADP
iajs-319	384	29	y	y	PROPN
iajs-319	384	30	.	.	PUNCT
iajs-319	385	1	since	since	SCONJ
iajs-319	385	2	)	)	PUNCT
iajs-319	385	3	)	)	PUNCT
iajs-319	385	4	a(cl(fy	a(cl(fy	PROPN
iajs-319	386	1	g*s	g*s	PROPN
iajs-319	386	2			NUM
iajs-319	386	3			NOUN
iajs-319	386	4	)	)	PUNCT
iajs-319	387	1	a(clx	a(clx	NUM
iajs-319	388	1	g*s	g*s	PROPN
iajs-319	388	2			VERB
iajs-319	388	3	s.t	s.t	PROPN
iajs-319	388	4	y)x(f	y)x(f	NOUN
iajs-319	388	5			PROPN
iajs-319	388	6	.	.	PUNCT
iajs-319	389	1	since	since	SCONJ
iajs-319	389	2	v)x(f	v)x(f	NOUN
iajs-319	389	3			NOUN
iajs-319	389	4	,	,	PUNCT
iajs-319	389	5	then	then	ADV
iajs-319	389	6	by	by	ADP
iajs-319	389	7	(	(	PUNCT
iajs-319	389	8	ii	ii	NOUN
iajs-319	389	9	)	)	PUNCT
iajs-319	389	10			ADP
iajs-319	389	11	an	an	DET
iajs-319	389	12	s*g-	s*g-	NOUN
iajs-319	389	13	-open	-open	NOUN
iajs-319	389	14	set	set	VERB
iajs-319	389	15	u	u	NOUN
iajs-319	389	16	in	in	ADP
iajs-319	389	17	x	x	X
iajs-319	389	18	s.t	s.t	PROPN
iajs-319	389	19	ux	ux	NOUN
iajs-319	389	20	and	and	CCONJ
iajs-319	389	21	v)u(f	v)u(f	PROPN
iajs-319	389	22			PROPN
iajs-319	389	23	.	.	PUNCT
iajs-319	390	1	since	since	SCONJ
iajs-319	390	2	)	)	PUNCT
iajs-319	390	3	a(clx	a(clx	PROPN
iajs-319	390	4	g*s	g*s	PROPN
iajs-319	390	5			NUM
iajs-319	390	6	,	,	PUNCT
iajs-319	390	7	then	then	ADV
iajs-319	390	8	by	by	ADP
iajs-319	390	9	theorem	theorem	NOUN
iajs-319	390	10	(	(	PUNCT
iajs-319	390	11	(	(	PUNCT
iajs-319	390	12	2.26),viii	2.26),viii	NUM
iajs-319	390	13	)	)	PUNCT
iajs-319	390	14	au	au	NOUN
iajs-319	390	15	and	and	CCONJ
iajs-319	390	16	hence	hence	ADV
iajs-319	390	17	v)a(f	v)a(f	NOUN
iajs-319	390	18			PROPN
iajs-319	390	19	.	.	PUNCT
iajs-319	391	1	therefore	therefore	ADV
iajs-319	391	2	we	we	PRON
iajs-319	391	3	have	have	VERB
iajs-319	391	4	)	)	PUNCT
iajs-319	391	5	)	)	PUNCT
iajs-319	392	1	a(f(cly	a(f(cly	PROPN
iajs-319	392	2	.	.	PUNCT
iajs-319	393	1	hence	hence	ADV
iajs-319	393	2	)	)	PUNCT
iajs-319	393	3	)	)	PUNCT
iajs-319	394	1	a(f(cl))a(cl(f	a(f(cl))a(cl(f	PROPN
iajs-319	394	2	g*s	g*s	PROPN
iajs-319	394	3			NOUN
iajs-319	394	4	.	.	PUNCT
iajs-319	395	1	552	552	NUM
iajs-319	395	2	|	|	ADV
iajs-319	395	3	mathematics	mathematic	NOUN
iajs-319	395	4	2014	2014	NUM
iajs-319	395	5	)	)	PUNCT
iajs-319	395	6	عام	عام	ADP
iajs-319	395	7	3العدد	3العدد	NUM
iajs-319	395	8	(	(	PUNCT
iajs-319	395	9	27مجلة	27مجلة	NUM
iajs-319	395	10	إبن	إبن	VERB
iajs-319	395	11	الھيثم	الھيثم	NOUN
iajs-319	395	12	للعلوم	للعلوم	NOUN
iajs-319	395	13	الصرفة	الصرفة	NOUN
iajs-319	396	1	و	و	PRON
iajs-319	396	2	التطبيقية	التطبيقية	ADV
iajs-319	396	3	المجلد	المجلد	VERB
iajs-319	396	4	ibn	ibn	PROPN
iajs-319	396	5	al	al	PROPN
iajs-319	396	6	-	-	PUNCT
iajs-319	396	7	haitham	haitham	PROPN
iajs-319	396	8	jour	jour	X
iajs-319	396	9	.	.	PROPN
iajs-319	397	1	for	for	ADP
iajs-319	397	2	pure	pure	ADJ
iajs-319	397	3	&	&	CCONJ
iajs-319	397	4	appl	appl	PROPN
iajs-319	397	5	.	.	PUNCT
iajs-319	398	1	sci	sci	PROPN
iajs-319	398	2	.	.	PUNCT
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iajs-319	398	4	.	.	PROPN
iajs-319	399	1	27	27	NUM
iajs-319	399	2	(	(	PUNCT
iajs-319	399	3	3	3	NUM
iajs-319	399	4	)	)	PUNCT
iajs-319	399	5	2014	2014	NUM
iajs-319	399	6	)	)	PUNCT
iajs-319	400	1	ii()iii	ii()iii	PROPN
iajs-319	400	2	(	(	PUNCT
iajs-319	400	3			NOUN
iajs-319	400	4	.	.	PUNCT
iajs-319	401	1	let	let	VERB
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iajs-319	401	3	and	and	CCONJ
iajs-319	401	4	v	v	X
iajs-319	401	5	be	be	AUX
iajs-319	401	6	any	any	DET
iajs-319	401	7	open	open	ADJ
iajs-319	401	8	set	set	NOUN
iajs-319	401	9	in	in	ADP
iajs-319	401	10	y	y	NOUN
iajs-319	401	11	containing	contain	VERB
iajs-319	401	12	)	)	PUNCT
iajs-319	402	1	x(f	x(f	PROPN
iajs-319	402	2	.	.	PUNCT
iajs-319	403	1	let	let	VERB
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iajs-319	403	3	v(fa	v(fa	PROPN
iajs-319	403	4	c1	c1	PROPN
iajs-319	403	5			NOUN
iajs-319	403	6	ax	ax	NOUN
iajs-319	403	7	.	.	PUNCT
iajs-319	404	1	since	since	SCONJ
iajs-319	404	2	c	c	PROPN
iajs-319	404	3	g*s	g*s	PROPN
iajs-319	404	4	v))a(f(cl))a(cl(f	v))a(f(cl))a(cl(f	PROPN
iajs-319	404	5			NOUN
iajs-319	404	6			NOUN
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iajs-319	404	8	c1	c1	PROPN
iajs-319	404	9	g*s	g*s	PROPN
iajs-319	404	10			PROPN
iajs-319	404	11			PROPN
iajs-319	404	12			NOUN
iajs-319	404	13	.	.	PUNCT
iajs-319	405	1	since	since	SCONJ
iajs-319	405	2	ax	ax	NOUN
iajs-319	405	3			NOUN
iajs-319	405	4	)	)	PUNCT
iajs-319	405	5	a(clx	a(clx	PROPN
iajs-319	405	6	g*s	g*s	PROPN
iajs-319	405	7			NOUN
iajs-319	405	8	and	and	CCONJ
iajs-319	405	9	by	by	ADP
iajs-319	405	10	theorem	theorem	NOUN
iajs-319	405	11	(	(	PUNCT
iajs-319	405	12	(	(	PUNCT
iajs-319	405	13	2.26),viii	2.26),viii	X
iajs-319	405	14	)	)	PUNCT
iajs-319	405	15	there	there	PRON
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iajs-319	405	18	s*g-	s*g-	NOUN
iajs-319	405	19	-open	-open	NOUN
iajs-319	405	20	set	set	VERB
iajs-319	405	21	u	u	NOUN
iajs-319	405	22	containing	contain	VERB
iajs-319	405	23	x	x	PUNCT
iajs-319	405	24	such	such	ADJ
iajs-319	405	25	that	that	DET
iajs-319	405	26	au	au	NOUN
iajs-319	405	27	and	and	CCONJ
iajs-319	405	28	hence	hence	ADV
iajs-319	405	29	v)a(f)u(f	v)a(f)u(f	PROPN
iajs-319	405	30	c	c	PROPN
iajs-319	405	31			PROPN
iajs-319	405	32	.	.	PUNCT
iajs-319	405	33	)	)	PUNCT
iajs-319	406	1	iv()iii	iv()iii	PROPN
iajs-319	406	2	(	(	PUNCT
iajs-319	406	3			NOUN
iajs-319	406	4	.	.	PUNCT
iajs-319	407	1	suppose	suppose	VERB
iajs-319	407	2	that	that	SCONJ
iajs-319	407	3	(	(	PUNCT
iajs-319	407	4	iii	iii	NOUN
iajs-319	407	5	)	)	PUNCT
iajs-319	407	6	holds	hold	VERB
iajs-319	407	7	and	and	CCONJ
iajs-319	407	8	let	let	VERB
iajs-319	407	9	b	b	X
iajs-319	407	10	be	be	AUX
iajs-319	407	11	any	any	DET
iajs-319	407	12	subset	subset	NOUN
iajs-319	407	13	of	of	ADP
iajs-319	407	14	y	y	PROPN
iajs-319	407	15	.	.	PUNCT
iajs-319	408	1	replacing	replace	VERB
iajs-319	408	2	a	a	DET
iajs-319	408	3	by	by	NOUN
iajs-319	408	4	)	)	PUNCT
iajs-319	408	5	b(f	b(f	PROPN
iajs-319	408	6	1	1	NUM
iajs-319	408	7	we	we	PRON
iajs-319	408	8	get	get	VERB
iajs-319	408	9	from	from	ADP
iajs-319	408	10	(	(	PUNCT
iajs-319	408	11	iii	iii	NOUN
iajs-319	408	12	)	)	PUNCT
iajs-319	408	13	)	)	PUNCT
iajs-319	409	1	b(cl)))b(f(f(cl)))b(f(cl(f	b(cl)))b(f(f(cl)))b(f(cl(f	NOUN
iajs-319	409	2	11	11	NUM
iajs-319	410	1	g*s	g*s	NOUN
iajs-319	410	2			PRON
iajs-319	410	3			NOUN
iajs-319	410	4			NOUN
iajs-319	410	5	.	.	PUNCT
iajs-319	411	1	hence	hence	ADV
iajs-319	411	2	)	)	PUNCT
iajs-319	411	3	)	)	PUNCT
iajs-319	412	1	b(cl(f))b(f(cl	b(cl(f))b(f(cl	NOUN
iajs-319	412	2	11	11	NUM
iajs-319	412	3	g*s	g*s	PROPN
iajs-319	412	4			NOUN
iajs-319	412	5			NOUN
iajs-319	412	6			PROPN
iajs-319	412	7	.	.	PUNCT
iajs-319	412	8	)	)	PUNCT
iajs-319	412	9	iii()iv	iii()iv	ADV
iajs-319	412	10	(	(	PUNCT
iajs-319	412	11			NOUN
iajs-319	412	12	.	.	PUNCT
iajs-319	412	13	suppose	suppose	VERB
iajs-319	412	14	that	that	SCONJ
iajs-319	412	15	(	(	PUNCT
iajs-319	412	16	iv	iv	X
iajs-319	412	17	)	)	PUNCT
iajs-319	412	18	holds	hold	VERB
iajs-319	412	19	and	and	CCONJ
iajs-319	412	20	let	let	VERB
iajs-319	412	21	)	)	PUNCT
iajs-319	412	22	a(fb	a(fb	PROPN
iajs-319	412	23			NOUN
iajs-319	412	24	where	where	SCONJ
iajs-319	412	25	a	a	PRON
iajs-319	412	26	is	be	AUX
iajs-319	412	27	a	a	DET
iajs-319	412	28	subset	subset	NOUN
iajs-319	412	29	of	of	ADP
iajs-319	412	30	x	x	X
iajs-319	412	31	.	.	PUNCT
iajs-319	413	1	then	then	ADV
iajs-319	413	2	we	we	PRON
iajs-319	413	3	get	get	VERB
iajs-319	413	4	from	from	ADP
iajs-319	413	5	(	(	PUNCT
iajs-319	413	6	iv	iv	NOUN
iajs-319	413	7	)	)	PUNCT
iajs-319	413	8	)	)	PUNCT
iajs-319	413	9	)	)	PUNCT
iajs-319	413	10	)	)	PUNCT
iajs-319	414	1	a(f(cl(f))a(f(f(cl)a(cl	a(f(cl(f))a(f(f(cl)a(cl	PROPN
iajs-319	414	2	11	11	NUM
iajs-319	414	3	g*sg*s	g*sg*s	PROPN
iajs-319	414	4			PROPN
iajs-319	414	5			NUM
iajs-319	414	6			ADJ
iajs-319	414	7	.	.	PUNCT
iajs-319	415	1	therefore	therefore	ADV
iajs-319	415	2	)	)	PUNCT
iajs-319	415	3	)	)	PUNCT
iajs-319	416	1	a(f(cl))a(cl(f	a(f(cl))a(cl(f	PROPN
iajs-319	416	2	g*s	g*s	PROPN
iajs-319	416	3			NOUN
iajs-319	416	4	.	.	PUNCT
iajs-319	417	1	definition(3.21	definition(3.21	NUM
iajs-319	417	2	):	):	PUNCT
iajs-319	417	3	a	a	DET
iajs-319	417	4	function	function	NOUN
iajs-319	417	5	)	)	PUNCT
iajs-319	417	6	,	,	PUNCT
iajs-319	417	7	y(),x(:f	y(),x(:f	PROPN
iajs-319	417	8			PROPN
iajs-319	417	9	is	be	AUX
iajs-319	417	10	called	call	VERB
iajs-319	417	11	s*g-	s*g-	NOUN
iajs-319	417	12	-irresolute	-irresolute	NOUN
iajs-319	417	13	if	if	SCONJ
iajs-319	417	14	the	the	DET
iajs-319	417	15	inverse	inverse	ADJ
iajs-319	417	16	image	image	NOUN
iajs-319	417	17	of	of	ADP
iajs-319	417	18	every	every	DET
iajs-319	417	19	s*g-	s*g-	NOUN
iajs-319	417	20	-open	-open	NOUN
iajs-319	417	21	set	set	VERB
iajs-319	417	22	in	in	ADP
iajs-319	417	23	y	y	PROPN
iajs-319	417	24	is	be	AUX
iajs-319	417	25	an	an	DET
iajs-319	417	26	s*g-	s*g-	NOUN
iajs-319	417	27	-open	-open	NOUN
iajs-319	417	28	set	set	VERB
iajs-319	417	29	in	in	ADP
iajs-319	417	30	x	x	X
iajs-319	417	31	.	.	PUNCT
iajs-319	418	1	proposition(3.22	proposition(3.22	NUM
iajs-319	418	2	):	):	PUNCT
iajs-319	418	3	every	every	DET
iajs-319	418	4	s*g-	s*g-	NOUN
iajs-319	418	5	-irresolute	-irresolute	PROPN
iajs-319	418	6	function	function	NOUN
iajs-319	418	7	is	be	AUX
iajs-319	418	8	s*g-	s*g-	NOUN
iajs-319	418	9	-continuous	-continuous	ADJ
iajs-319	418	10	.	.	PUNCT
iajs-319	419	1	proof	proof	NOUN
iajs-319	419	2	:	:	PUNCT
iajs-319	419	3	it	it	PRON
iajs-319	419	4	is	be	AUX
iajs-319	419	5	obvious	obvious	ADJ
iajs-319	419	6	.	.	PUNCT
iajs-319	420	1	remark(3.23	remark(3.23	NOUN
iajs-319	420	2	):	):	PUNCT
iajs-319	420	3	the	the	DET
iajs-319	420	4	converse	converse	NOUN
iajs-319	420	5	of	of	ADP
iajs-319	420	6	proposition	proposition	NOUN
iajs-319	420	7	(	(	PUNCT
iajs-319	420	8	3.22	3.22	NUM
iajs-319	420	9	)	)	PUNCT
iajs-319	420	10	may	may	AUX
iajs-319	420	11	not	not	PART
iajs-319	420	12	be	be	AUX
iajs-319	420	13	true	true	ADJ
iajs-319	420	14	in	in	ADP
iajs-319	420	15	general	general	ADJ
iajs-319	420	16	as	as	SCONJ
iajs-319	420	17	shown	show	VERB
iajs-319	420	18	in	in	ADP
iajs-319	420	19	the	the	DET
iajs-319	420	20	following	follow	VERB
iajs-319	420	21	example	example	NOUN
iajs-319	420	22	:	:	PUNCT
iajs-319	420	23	example(3.24	example(3.24	NUM
iajs-319	420	24	):	):	PUNCT
iajs-319	420	25	let	let	VERB
iajs-319	420	26	}	}	PUNCT
iajs-319	420	27	c	c	NOUN
iajs-319	420	28	,	,	PUNCT
iajs-319	420	29	b	b	NOUN
iajs-319	420	30	,	,	PUNCT
iajs-319	420	31	a{yx	a{yx	PUNCT
iajs-319	420	32			NUM
iajs-319	420	33	,	,	PUNCT
iajs-319	420	34	}	}	PUNCT
iajs-319	420	35	}	}	PUNCT
iajs-319	420	36	c	c	X
iajs-319	420	37	,	,	PUNCT
iajs-319	420	38	a{},c{},a{,,x	a{},c{},a{,,x	PROPN
iajs-319	420	39	{	{	PUNCT
iajs-319	420	40			PROPN
iajs-319	420	41	&	&	CCONJ
iajs-319	420	42	}	}	PUNCT
iajs-319	420	43	}	}	PUNCT
iajs-319	420	44	c	c	X
iajs-319	420	45	,	,	PUNCT
iajs-319	420	46	a{},a{,,y	a{},a{,,y	PROPN
iajs-319	420	47	{	{	PUNCT
iajs-319	420	48			X
iajs-319	420	49			NOUN
iajs-319	420	50			PROPN
iajs-319	420	51	g*s	g*s	PROPN
iajs-319	420	52	and	and	CCONJ
iajs-319	420	53	}	}	PUNCT
iajs-319	420	54	}	}	PUNCT
iajs-319	420	55	c	c	X
iajs-319	420	56	,	,	PUNCT
iajs-319	420	57	a{},b	a{},b	PROPN
iajs-319	420	58	,	,	PUNCT
iajs-319	420	59	a{},a{,,y{g*s	a{},a{,,y{g*s	PROPN
iajs-319	420	60			PROPN
iajs-319	420	61			X
iajs-319	420	62	.	.	PUNCT
iajs-319	421	1	define	define	NOUN
iajs-319	421	2	)	)	PUNCT
iajs-319	421	3	,	,	PUNCT
iajs-319	421	4	y(),x(:f	y(),x(:f	PROPN
iajs-319	421	5			PUNCT
iajs-319	421	6	by	by	ADP
iajs-319	421	7	:	:	PUNCT
iajs-319	421	8	a)a(f	a)a(f	PROPN
iajs-319	421	9			PROPN
iajs-319	421	10	,	,	PUNCT
iajs-319	421	11	b)b(f	b)b(f	PROPN
iajs-319	421	12			PROPN
iajs-319	421	13	&	&	CCONJ
iajs-319	421	14	c)c(f	c)c(f	PROPN
iajs-319	421	15			PROPN
iajs-319	422	1			NOUN
iajs-319	423	1	f	f	PROPN
iajs-319	423	2	is	be	AUX
iajs-319	423	3	s*g-	s*g-	NOUN
iajs-319	423	4	-continuous	-continuous	ADJ
iajs-319	423	5	,	,	PUNCT
iajs-319	423	6	but	but	CCONJ
iajs-319	423	7	f	f	PROPN
iajs-319	423	8	is	be	AUX
iajs-319	423	9	not	not	PART
iajs-319	423	10	s*g-	s*g-	NOUN
iajs-319	423	11	-irresolute	-irresolute	NOUN
iajs-319	423	12	since	since	SCONJ
iajs-319	423	13	}	}	PUNCT
iajs-319	423	14	b	b	NOUN
iajs-319	423	15	,	,	PUNCT
iajs-319	423	16	a	a	PRON
iajs-319	423	17	{	{	PUNCT
iajs-319	423	18	is	be	AUX
iajs-319	423	19	an	an	DET
iajs-319	423	20	s*g-	s*g-	NOUN
iajs-319	423	21	-open	-open	NOUN
iajs-319	423	22	set	set	VERB
iajs-319	423	23	in	in	ADP
iajs-319	423	24	y	y	PROPN
iajs-319	423	25	,	,	PUNCT
iajs-319	423	26	but	but	CCONJ
iajs-319	423	27	}	}	PUNCT
iajs-319	423	28	b	b	NOUN
iajs-319	423	29	,	,	PUNCT
iajs-319	423	30	a{})b	a{})b	NOUN
iajs-319	423	31	,	,	PUNCT
iajs-319	423	32	a({f	a({f	PROPN
iajs-319	423	33	1	1	NUM
iajs-319	423	34			NOUN
iajs-319	423	35	is	be	AUX
iajs-319	423	36	not	not	PART
iajs-319	423	37	s*g-	s*g-	NOUN
iajs-319	423	38	-open	-open	NOUN
iajs-319	423	39	set	set	VERB
iajs-319	423	40	in	in	ADP
iajs-319	423	41	x	x	X
iajs-319	423	42	.	.	PUNCT
iajs-319	424	1	remark(3.25	remark(3.25	ADJ
iajs-319	424	2	):	):	PUNCT
iajs-319	424	3	continuous	continuous	ADJ
iajs-319	424	4	functions	function	NOUN
iajs-319	424	5	and	and	CCONJ
iajs-319	424	6	s*g-	s*g-	NOUN
iajs-319	424	7	-irresolute	-irresolute	PROPN
iajs-319	424	8	functions	function	NOUN
iajs-319	424	9	are	be	AUX
iajs-319	424	10	in	in	ADP
iajs-319	424	11	general	general	ADJ
iajs-319	424	12	independent	independent	NOUN
iajs-319	424	13	consider	consider	VERB
iajs-319	424	14	the	the	DET
iajs-319	424	15	following	follow	VERB
iajs-319	424	16	examples	example	NOUN
iajs-319	424	17	:	:	PUNCT
iajs-319	424	18	example(3.26	example(3.26	NOUN
iajs-319	424	19	):	):	PUNCT
iajs-319	424	20	let	let	VERB
iajs-319	424	21	}	}	PUNCT
iajs-319	424	22	c	c	NOUN
iajs-319	424	23	,	,	PUNCT
iajs-319	424	24	b	b	NOUN
iajs-319	424	25	,	,	PUNCT
iajs-319	424	26	a{yx	a{yx	PUNCT
iajs-319	424	27			NUM
iajs-319	424	28	,	,	PUNCT
iajs-319	424	29	}	}	PUNCT
iajs-319	424	30	}	}	PUNCT
iajs-319	424	31	c	c	X
iajs-319	424	32	,	,	PUNCT
iajs-319	424	33	b{},a{,,x	b{},a{,,x	PROPN
iajs-319	424	34	{	{	PUNCT
iajs-319	424	35			PROPN
iajs-319	424	36	&	&	CCONJ
iajs-319	424	37	}	}	PUNCT
iajs-319	424	38	}	}	PUNCT
iajs-319	424	39	a{,,y	a{,,y	NOUN
iajs-319	424	40	{	{	PUNCT
iajs-319	424	41			NOUN
iajs-319	424	42	.	.	PUNCT
iajs-319	425	1	also	also	ADV
iajs-319	425	2	,	,	PUNCT
iajs-319	425	3	}	}	PUNCT
iajs-319	425	4	}	}	PUNCT
iajs-319	425	5	c	c	X
iajs-319	425	6	,	,	PUNCT
iajs-319	425	7	b{},a{,,x{g*s	b{},a{,,x{g*s	PROPN
iajs-319	425	8			PROPN
iajs-319	425	9			PROPN
iajs-319	425	10	&	&	CCONJ
iajs-319	425	11	}	}	PUNCT
iajs-319	425	12	}	}	PUNCT
iajs-319	425	13	c	c	X
iajs-319	425	14	,	,	PUNCT
iajs-319	425	15	a{},b	a{},b	PROPN
iajs-319	425	16	,	,	PUNCT
iajs-319	425	17	a{},a{,,y{g*s	a{},a{,,y{g*s	PROPN
iajs-319	425	18			PROPN
iajs-319	425	19			X
iajs-319	425	20	.	.	PUNCT
iajs-319	426	1	define	define	NOUN
iajs-319	426	2	)	)	PUNCT
iajs-319	426	3	,	,	PUNCT
iajs-319	426	4	y(),x(:f	y(),x(:f	PROPN
iajs-319	426	5			PUNCT
iajs-319	426	6	by	by	ADP
iajs-319	426	7	:	:	PUNCT
iajs-319	426	8	a)a(f	a)a(f	PROPN
iajs-319	426	9			PROPN
iajs-319	426	10	,	,	PUNCT
iajs-319	426	11	b)b(f	b)b(f	PROPN
iajs-319	426	12			PROPN
iajs-319	426	13	&	&	CCONJ
iajs-319	426	14	c)c(f	c)c(f	PROPN
iajs-319	426	15			PROPN
iajs-319	427	1			NOUN
iajs-319	428	1	f	f	NOUN
iajs-319	428	2	is	be	AUX
iajs-319	428	3	continuous	continuous	ADJ
iajs-319	428	4	,	,	PUNCT
iajs-319	428	5	but	but	CCONJ
iajs-319	428	6	f	f	PROPN
iajs-319	428	7	is	be	AUX
iajs-319	428	8	not	not	PART
iajs-319	428	9	s*g-	s*g-	NOUN
iajs-319	428	10	-irresolute	-irresolute	ADJ
iajs-319	428	11	,	,	PUNCT
iajs-319	428	12	since	since	SCONJ
iajs-319	428	13	}	}	PUNCT
iajs-319	428	14	b	b	NOUN
iajs-319	428	15	,	,	PUNCT
iajs-319	428	16	a	a	PRON
iajs-319	428	17	{	{	PUNCT
iajs-319	428	18	is	be	AUX
iajs-319	428	19	s*g	s*g	NOUN
iajs-319	428	20	-open	-open	NOUN
iajs-319	428	21	set	set	VERB
iajs-319	428	22	in	in	ADP
iajs-319	428	23	y	y	PROPN
iajs-319	428	24	,	,	PUNCT
iajs-319	428	25	but	but	CCONJ
iajs-319	428	26	}	}	PUNCT
iajs-319	428	27	b	b	NOUN
iajs-319	428	28	,	,	PUNCT
iajs-319	428	29	a{})b	a{})b	NOUN
iajs-319	428	30	,	,	PUNCT
iajs-319	428	31	a({f	a({f	PROPN
iajs-319	428	32	1	1	NUM
iajs-319	428	33			NOUN
iajs-319	428	34	is	be	AUX
iajs-319	428	35	not	not	PART
iajs-319	428	36	s*g-	s*g-	NOUN
iajs-319	428	37	-open	-open	NOUN
iajs-319	428	38	set	set	VERB
iajs-319	428	39	in	in	ADP
iajs-319	428	40	x	x	PROPN
iajs-319	428	41	.	.	PUNCT
iajs-319	428	42	example(3.27	example(3.27	PROPN
iajs-319	428	43	):	):	PUNCT
iajs-319	429	1	let	let	VERB
iajs-319	429	2	}	}	PUNCT
iajs-319	429	3	c	c	NOUN
iajs-319	429	4	,	,	PUNCT
iajs-319	429	5	b	b	NOUN
iajs-319	429	6	,	,	PUNCT
iajs-319	429	7	a{yx	a{yx	PUNCT
iajs-319	429	8			NUM
iajs-319	429	9	,	,	PUNCT
iajs-319	429	10	}	}	PUNCT
iajs-319	429	11	}	}	PUNCT
iajs-319	429	12	a{,,x	a{,,x	PROPN
iajs-319	429	13	{	{	PUNCT
iajs-319	429	14			PROPN
iajs-319	429	15	&	&	CCONJ
iajs-319	429	16	}	}	PUNCT
iajs-319	429	17	}	}	SYM
iajs-319	429	18	b	b	NOUN
iajs-319	429	19	,	,	PUNCT
iajs-319	429	20	a{,,y	a{,,y	NOUN
iajs-319	429	21	{	{	PUNCT
iajs-319	429	22			NOUN
iajs-319	429	23	.	.	PUNCT
iajs-319	430	1	also	also	ADV
iajs-319	430	2	,	,	PUNCT
iajs-319	430	3	}	}	PUNCT
iajs-319	430	4	}	}	PUNCT
iajs-319	430	5	c	c	X
iajs-319	430	6	,	,	PUNCT
iajs-319	430	7	a{},b	a{},b	PROPN
iajs-319	430	8	,	,	PUNCT
iajs-319	430	9	a{},a{,,x{g*s	a{},a{,,x{g*s	PROPN
iajs-319	430	10			PROPN
iajs-319	430	11			X
iajs-319	430	12	&	&	CCONJ
iajs-319	430	13	}	}	PUNCT
iajs-319	430	14	}	}	SYM
iajs-319	430	15	b	b	NOUN
iajs-319	430	16	,	,	PUNCT
iajs-319	430	17	a{,,y{g*s	a{,,y{g*s	PROPN
iajs-319	430	18			PUNCT
iajs-319	430	19			X
iajs-319	430	20	.	.	PUNCT
iajs-319	431	1	define	define	VERB
iajs-319	431	2	)	)	PUNCT
iajs-319	431	3	,	,	PUNCT
iajs-319	431	4	y(),x(:f	y(),x(:f	PROPN
iajs-319	431	5			PUNCT
iajs-319	431	6	by	by	ADP
iajs-319	431	7	:	:	PUNCT
iajs-319	431	8	a)a(f	a)a(f	PROPN
iajs-319	431	9			PROPN
iajs-319	431	10	,	,	PUNCT
iajs-319	431	11	b)b(f	b)b(f	PROPN
iajs-319	431	12			PROPN
iajs-319	431	13	&	&	CCONJ
iajs-319	431	14	c)c(f	c)c(f	PROPN
iajs-319	431	15			PROPN
iajs-319	432	1			NOUN
iajs-319	433	1	f	f	PROPN
iajs-319	433	2	is	be	AUX
iajs-319	433	3	s*g-	s*g-	NOUN
iajs-319	433	4	-irresolute	-irresolute	ADJ
iajs-319	433	5	,	,	PUNCT
iajs-319	433	6	but	but	CCONJ
iajs-319	433	7	f	f	PROPN
iajs-319	433	8	is	be	AUX
iajs-319	433	9	not	not	PART
iajs-319	433	10	continuous	continuous	ADJ
iajs-319	433	11	,	,	PUNCT
iajs-319	433	12	since	since	SCONJ
iajs-319	433	13	}	}	PUNCT
iajs-319	433	14	b	b	NOUN
iajs-319	433	15	,	,	PUNCT
iajs-319	433	16	a	a	PRON
iajs-319	433	17	{	{	PUNCT
iajs-319	433	18	is	be	AUX
iajs-319	433	19	open	open	ADJ
iajs-319	433	20	in	in	ADP
iajs-319	433	21	y	y	PROPN
iajs-319	433	22	,	,	PUNCT
iajs-319	433	23	but	but	CCONJ
iajs-319	433	24	}	}	PUNCT
iajs-319	433	25	b	b	NOUN
iajs-319	433	26	,	,	PUNCT
iajs-319	433	27	a{})b	a{})b	NOUN
iajs-319	433	28	,	,	PUNCT
iajs-319	433	29	a({f	a({f	PROPN
iajs-319	433	30	1	1	NUM
iajs-319	433	31			NOUN
iajs-319	433	32	is	be	AUX
iajs-319	433	33	not	not	PART
iajs-319	433	34	open	open	ADJ
iajs-319	433	35	in	in	ADP
iajs-319	433	36	x	x	X
iajs-319	433	37	.	.	PUNCT
iajs-319	434	1	theorem(3.28	theorem(3.28	PROPN
iajs-319	434	2	):	):	PUNCT
iajs-319	435	1	let	let	NOUN
iajs-319	435	2	)	)	PUNCT
iajs-319	435	3	,	,	PUNCT
iajs-319	435	4	y(),x(:f	y(),x(:f	PROPN
iajs-319	435	5			PROPN
iajs-319	435	6	be	be	VERB
iajs-319	435	7	a	a	DET
iajs-319	435	8	function	function	NOUN
iajs-319	435	9	.	.	PUNCT
iajs-319	436	1	then	then	ADV
iajs-319	436	2	the	the	DET
iajs-319	436	3	following	follow	VERB
iajs-319	436	4	statements	statement	NOUN
iajs-319	436	5	are	be	AUX
iajs-319	436	6	equivalent	equivalent	ADJ
iajs-319	436	7	:	:	PUNCT
iajs-319	436	8	(	(	PUNCT
iajs-319	436	9	i	i	NOUN
iajs-319	436	10	)	)	PUNCT
iajs-319	436	11	f	f	PROPN
iajs-319	436	12	is	be	AUX
iajs-319	436	13	s*g-	s*g-	NOUN
iajs-319	436	14	-irresolute	-irresolute	ADJ
iajs-319	436	15	.	.	PUNCT
iajs-319	437	1	(	(	PUNCT
iajs-319	437	2	ii	ii	NOUN
iajs-319	437	3	)	)	PUNCT
iajs-319	437	4	for	for	ADP
iajs-319	437	5	each	each	DET
iajs-319	437	6	xx	xx	PROPN
iajs-319	437	7	and	and	CCONJ
iajs-319	437	8	each	each	DET
iajs-319	437	9	s*g-	s*g-	NOUN
iajs-319	437	10	-neighborhood	-neighborhood	PROPN
iajs-319	437	11	v	v	NOUN
iajs-319	437	12	of	of	ADP
iajs-319	437	13	)	)	PUNCT
iajs-319	437	14	x(f	x(f	PROPN
iajs-319	437	15	in	in	ADP
iajs-319	437	16	y	y	PROPN
iajs-319	437	17	,	,	PUNCT
iajs-319	437	18	there	there	PRON
iajs-319	437	19	is	be	VERB
iajs-319	437	20	an	an	DET
iajs-319	437	21	s*g-	s*g-	NOUN
iajs-319	437	22	neighborhood	neighborhood	NOUN
iajs-319	437	23	553	553	NUM
iajs-319	437	24	|	|	NOUN
iajs-319	437	25	mathematics	mathematic	NOUN
iajs-319	437	26	2014	2014	NUM
iajs-319	437	27	)	)	PUNCT
iajs-319	437	28	عام	عام	ADP
iajs-319	437	29	3العدد	3العدد	NUM
iajs-319	437	30	(	(	PUNCT
iajs-319	437	31	27مجلة	27مجلة	NUM
iajs-319	437	32	إبن	إبن	VERB
iajs-319	437	33	الھيثم	الھيثم	NOUN
iajs-319	437	34	للعلوم	للعلوم	NOUN
iajs-319	437	35	الصرفة	الصرفة	NOUN
iajs-319	438	1	و	و	PRON
iajs-319	438	2	التطبيقية	التطبيقية	ADV
iajs-319	438	3	المجلد	المجلد	VERB
iajs-319	438	4	ibn	ibn	PROPN
iajs-319	438	5	al	al	PROPN
iajs-319	438	6	-	-	PUNCT
iajs-319	438	7	haitham	haitham	PROPN
iajs-319	438	8	jour	jour	X
iajs-319	438	9	.	.	PROPN
iajs-319	439	1	for	for	ADP
iajs-319	439	2	pure	pure	ADJ
iajs-319	439	3	&	&	CCONJ
iajs-319	439	4	appl	appl	PROPN
iajs-319	439	5	.	.	PUNCT
iajs-319	440	1	sci	sci	PROPN
iajs-319	440	2	.	.	PUNCT
iajs-319	440	3	vol	vol	NOUN
iajs-319	440	4	.	.	PROPN
iajs-319	441	1	27	27	NUM
iajs-319	441	2	(	(	PUNCT
iajs-319	441	3	3	3	NUM
iajs-319	441	4	)	)	PUNCT
iajs-319	441	5	2014	2014	NUM
iajs-319	441	6	u	u	NOUN
iajs-319	441	7	of	of	ADP
iajs-319	441	8	x	x	PUNCT
iajs-319	441	9	in	in	ADP
iajs-319	441	10	x	x	X
iajs-319	441	11	such	such	ADJ
iajs-319	441	12	that	that	DET
iajs-319	441	13	v)u(f	v)u(f	PROPN
iajs-319	441	14			PROPN
iajs-319	441	15	.	.	PUNCT
iajs-319	442	1	(	(	PUNCT
iajs-319	442	2	iii	iii	X
iajs-319	442	3	)	)	PUNCT
iajs-319	442	4	the	the	DET
iajs-319	442	5	inverse	inverse	ADJ
iajs-319	442	6	image	image	NOUN
iajs-319	442	7	of	of	ADP
iajs-319	442	8	every	every	DET
iajs-319	442	9	s*g-	s*g-	NOUN
iajs-319	442	10	-closed	-close	VERB
iajs-319	442	11	subset	subset	NOUN
iajs-319	442	12	of	of	ADP
iajs-319	442	13	y	y	PROPN
iajs-319	442	14	is	be	AUX
iajs-319	442	15	an	an	DET
iajs-319	442	16	s*g-	s*g-	NOUN
iajs-319	442	17	-closed	-close	VERB
iajs-319	442	18	subset	subset	NOUN
iajs-319	442	19	of	of	ADP
iajs-319	442	20	x	x	X
iajs-319	442	21	.	.	PUNCT
iajs-319	443	1	proof	proof	NOUN
iajs-319	443	2	:	:	PUNCT
iajs-319	443	3	)	)	PUNCT
iajs-319	443	4	ii()i	ii()i	SYM
iajs-319	443	5	(	(	PUNCT
iajs-319	443	6			NOUN
iajs-319	443	7	.	.	PUNCT
iajs-319	444	1	let	let	VERB
iajs-319	444	2	yx	yx	NOUN
iajs-319	444	3	:	:	PUNCT
iajs-319	444	4	f	f	X
iajs-319	444	5			PROPN
iajs-319	444	6	be	be	AUX
iajs-319	444	7	an	an	DET
iajs-319	444	8	s*g-	s*g-	NOUN
iajs-319	444	9	-irresolute	-irresolute	NOUN
iajs-319	444	10	function	function	NOUN
iajs-319	444	11	and	and	CCONJ
iajs-319	444	12	v	v	AUX
iajs-319	444	13	be	be	AUX
iajs-319	444	14	an	an	DET
iajs-319	444	15	s*g-	s*g-	NOUN
iajs-319	444	16	neighborhood	neighborhood	NOUN
iajs-319	444	17	of	of	ADP
iajs-319	444	18	)	)	PUNCT
iajs-319	444	19	x(f	x(f	PROPN
iajs-319	444	20	in	in	ADP
iajs-319	444	21	y	y	PROPN
iajs-319	444	22	.	.	PUNCT
iajs-319	445	1	to	to	PART
iajs-319	445	2	prove	prove	VERB
iajs-319	445	3	that	that	SCONJ
iajs-319	445	4	,	,	PUNCT
iajs-319	445	5	there	there	PRON
iajs-319	445	6	is	be	VERB
iajs-319	445	7	an	an	DET
iajs-319	445	8	s*g-	s*g-	NOUN
iajs-319	445	9	-neighborhood	-neighborhood	NOUN
iajs-319	445	10	u	u	NOUN
iajs-319	445	11	of	of	ADP
iajs-319	445	12	x	x	PUNCT
iajs-319	445	13	in	in	ADP
iajs-319	445	14	x	x	X
iajs-319	445	15	such	such	ADJ
iajs-319	445	16	that	that	DET
iajs-319	445	17	v)u(f	v)u(f	PROPN
iajs-319	445	18			PROPN
iajs-319	445	19	.	.	PUNCT
iajs-319	446	1	since	since	SCONJ
iajs-319	446	2	f	f	PROPN
iajs-319	446	3	is	be	AUX
iajs-319	446	4	an	an	DET
iajs-319	446	5	s*g-	s*g-	NOUN
iajs-319	446	6	-irresolute	-irresolute	NOUN
iajs-319	446	7	then	then	ADV
iajs-319	446	8	,	,	PUNCT
iajs-319	446	9	)	)	PUNCT
iajs-319	446	10	v(f	v(f	PROPN
iajs-319	446	11	1	1	NUM
iajs-319	446	12	is	be	AUX
iajs-319	446	13	an	an	DET
iajs-319	446	14	s*g-	s*g-	NOUN
iajs-319	446	15	-neighborhood	-neighborhood	NOUN
iajs-319	446	16	of	of	ADP
iajs-319	446	17	x	x	PUNCT
iajs-319	446	18	in	in	ADP
iajs-319	446	19	x	x	X
iajs-319	446	20	.	.	PUNCT
iajs-319	447	1	let	let	VERB
iajs-319	447	2	)	)	PUNCT
iajs-319	447	3	v(fu	v(fu	PROPN
iajs-319	447	4	1	1	NUM
iajs-319	447	5			NOUN
iajs-319	447	6	v))v(f(f)u(f	v))v(f(f)u(f	NOUN
iajs-319	447	7	1	1	NUM
iajs-319	447	8			NOUN
iajs-319	447	9			NOUN
iajs-319	447	10			NOUN
iajs-319	447	11	v)u(f	v)u(f	NOUN
iajs-319	447	12			PROPN
iajs-319	447	13	.	.	PUNCT
iajs-319	447	14	)	)	PUNCT
iajs-319	448	1	i()ii	i()ii	PROPN
iajs-319	448	2	(	(	PUNCT
iajs-319	448	3			NOUN
iajs-319	448	4	.	.	PUNCT
iajs-319	449	1	to	to	PART
iajs-319	449	2	prove	prove	VERB
iajs-319	449	3	that	that	PRON
iajs-319	449	4	yx	yx	ADP
iajs-319	449	5	:	:	PUNCT
iajs-319	449	6	f	f	NOUN
iajs-319	449	7			PROPN
iajs-319	449	8	is	be	AUX
iajs-319	449	9	s*g-	s*g-	NOUN
iajs-319	449	10	-irresolute	-irresolute	ADJ
iajs-319	449	11	.	.	PUNCT
iajs-319	450	1	let	let	VERB
iajs-319	450	2	v	v	PART
iajs-319	450	3	be	be	AUX
iajs-319	450	4	an	an	DET
iajs-319	450	5	s*g-	s*g-	NOUN
iajs-319	450	6	-open	-open	NOUN
iajs-319	450	7	set	set	VERB
iajs-319	450	8	in	in	ADP
iajs-319	450	9	y	y	PROPN
iajs-319	450	10	.	.	PUNCT
iajs-319	451	1	to	to	PART
iajs-319	451	2	prove	prove	VERB
iajs-319	451	3	that	that	PRON
iajs-319	451	4	)	)	PUNCT
iajs-319	452	1	v(f	v(f	PROPN
iajs-319	452	2	1	1	NUM
iajs-319	452	3	is	be	AUX
iajs-319	452	4	an	an	DET
iajs-319	452	5	s*g-	s*g-	NOUN
iajs-319	452	6	-open	-open	NOUN
iajs-319	452	7	set	set	VERB
iajs-319	452	8	in	in	ADP
iajs-319	452	9	x	x	X
iajs-319	452	10	.	.	PUNCT
iajs-319	453	1	let	let	VERB
iajs-319	453	2	)	)	PUNCT
iajs-319	453	3	v(fx	v(fx	NOUN
iajs-319	453	4	1	1	NUM
iajs-319	453	5			NOUN
iajs-319	453	6	v)x(f	v)x(f	PROPN
iajs-319	453	7			PROPN
iajs-319	453	8			NOUN
iajs-319	453	9	v	v	NOUN
iajs-319	453	10	is	be	AUX
iajs-319	453	11	an	an	DET
iajs-319	453	12	s*g	s*g	NOUN
iajs-319	453	13	-neighborhood	-neighborhood	NOUN
iajs-319	453	14	of	of	ADP
iajs-319	453	15	)	)	PUNCT
iajs-319	453	16	x(f	x(f	PROPN
iajs-319	453	17	.by	.by	PROPN
iajs-319	454	1	hypothesis	hypothesis	NOUN
iajs-319	454	2	there	there	PRON
iajs-319	454	3	is	be	VERB
iajs-319	454	4	an	an	DET
iajs-319	454	5	s*g-	s*g-	NOUN
iajs-319	454	6	-neighborhood	-neighborhood	NOUN
iajs-319	455	1	xu	xu	PROPN
iajs-319	455	2	of	of	ADP
iajs-319	455	3	x	x	SYM
iajs-319	455	4	such	such	ADJ
iajs-319	455	5	that	that	DET
iajs-319	455	6	v)u(f	v)u(f	X
iajs-319	455	7	x	x	X
iajs-319	455	8			PROPN
iajs-319	455	9			PROPN
iajs-319	455	10	)	)	PUNCT
iajs-319	455	11	v(fu	v(fu	PROPN
iajs-319	455	12	1	1	NUM
iajs-319	455	13	x	x	SYM
iajs-319	455	14			NOUN
iajs-319	455	15	,	,	PUNCT
iajs-319	455	16	)	)	PUNCT
iajs-319	455	17	v(fx	v(fx	NOUN
iajs-319	455	18	1	1	NUM
iajs-319	455	19			NOUN
iajs-319	455	20			ADP
iajs-319	455	21	an	an	DET
iajs-319	455	22	s*g-	s*g-	NOUN
iajs-319	455	23	-open	-open	NOUN
iajs-319	455	24	set	set	VERB
iajs-319	455	25	xw	xw	PROPN
iajs-319	455	26	of	of	ADP
iajs-319	455	27	x	x	INTJ
iajs-319	455	28	such	such	ADJ
iajs-319	455	29	that	that	PRON
iajs-319	455	30	)	)	PUNCT
iajs-319	455	31	v(fuw	v(fuw	PROPN
iajs-319	455	32	1	1	NUM
iajs-319	455	33	xx	xx	NUM
iajs-319	455	34			PROPN
iajs-319	455	35	,	,	PUNCT
iajs-319	455	36	)	)	PUNCT
iajs-319	455	37	v(fx	v(fx	NOUN
iajs-319	455	38	1	1	NUM
iajs-319	455	39			NOUN
iajs-319	455	40	)	)	PUNCT
iajs-319	455	41	v(fw	v(fw	PROPN
iajs-319	455	42	1	1	NUM
iajs-319	455	43	)	)	PUNCT
iajs-319	455	44	v(fx	v(fx	NOUN
iajs-319	455	45	x	x	SYM
iajs-319	455	46	1	1	NUM
iajs-319	455	47			PROPN
iajs-319	455	48			NOUN
iajs-319	455	49			PROPN
iajs-319	455	50			PROPN
iajs-319	455	51			NOUN
iajs-319	455	52	.	.	PUNCT
iajs-319	456	1	since	since	SCONJ
iajs-319	456	2			NOUN
iajs-319	456	3	)	)	PUNCT
iajs-319	456	4	v(fx	v(fx	ADV
iajs-319	456	5	1	1	NUM
iajs-319	456	6	1	1	NUM
iajs-319	456	7	}	}	PUNCT
iajs-319	456	8	x{)v(f	x{)v(f	PUNCT
iajs-319	456	9			PROPN
iajs-319	456	10			VERB
iajs-319	456	11			NOUN
iajs-319	456	12			NOUN
iajs-319	456	13	)	)	PUNCT
iajs-319	456	14	v(fx	v(fx	NOUN
iajs-319	456	15	x	x	SYM
iajs-319	456	16	1	1	NUM
iajs-319	456	17	w	w	PROPN
iajs-319	456	18			PROPN
iajs-319	456	19			PROPN
iajs-319	456	20			NOUN
iajs-319	456	21			ADJ
iajs-319	456	22	)	)	PUNCT
iajs-319	456	23	v(fx	v(fx	NOUN
iajs-319	456	24	x	x	SYM
iajs-319	456	25	1	1	NUM
iajs-319	456	26	1	1	NUM
iajs-319	456	27	w)v(f	w)v(f	NOUN
iajs-319	456	28			PROPN
iajs-319	456	29			PROPN
iajs-319	456	30			PROPN
iajs-319	456	31			NOUN
iajs-319	456	32	)	)	PUNCT
iajs-319	457	1	v(f	v(f	PROPN
iajs-319	457	2	1	1	NUM
iajs-319	457	3	is	be	AUX
iajs-319	457	4	an	an	DET
iajs-319	457	5	s*g-	s*g-	NOUN
iajs-319	457	6	-open	-open	NOUN
iajs-319	457	7	set	set	VERB
iajs-319	457	8	in	in	ADP
iajs-319	457	9	y	y	PROPN
iajs-319	457	10	,	,	PUNCT
iajs-319	457	11	since	since	SCONJ
iajs-319	457	12	its	its	PRON
iajs-319	457	13	a	a	DET
iajs-319	457	14	union	union	NOUN
iajs-319	457	15	of	of	ADP
iajs-319	457	16	s*g-	s*g-	NOUN
iajs-319	457	17	-open	-open	PROPN
iajs-319	457	18	sets	set	NOUN
iajs-319	457	19	.	.	PUNCT
iajs-319	458	1	thus	thus	ADV
iajs-319	458	2	yx	yx	ADP
iajs-319	458	3	:	:	PUNCT
iajs-319	458	4	f	f	NOUN
iajs-319	458	5			X
iajs-319	458	6	is	be	AUX
iajs-319	458	7	an	an	DET
iajs-319	458	8	s*g-	s*g-	NOUN
iajs-319	458	9	-irresolute	-irresolute	NOUN
iajs-319	458	10	function	function	NOUN
iajs-319	458	11	.	.	PUNCT
iajs-319	458	12	)	)	PUNCT
iajs-319	459	1	iii()i	iii()i	PROPN
iajs-319	459	2	(	(	PUNCT
iajs-319	459	3			PROPN
iajs-319	459	4	.	.	PUNCT
iajs-319	460	1	it	it	PRON
iajs-319	460	2	is	be	AUX
iajs-319	460	3	a	a	DET
iajs-319	460	4	obvious	obvious	ADJ
iajs-319	460	5	.	.	PUNCT
iajs-319	461	1	corollary(3.29	corollary(3.29	NOUN
iajs-319	461	2	):	):	PUNCT
iajs-319	461	3	let	let	NOUN
iajs-319	461	4	)	)	PUNCT
iajs-319	461	5	,	,	PUNCT
iajs-319	461	6	x	x	X
iajs-319	461	7	(	(	PUNCT
iajs-319	461	8	11	11	NUM
iajs-319	461	9			NOUN
iajs-319	461	10	and	and	CCONJ
iajs-319	461	11	)	)	PUNCT
iajs-319	461	12	,	,	PUNCT
iajs-319	461	13	x	x	X
iajs-319	461	14	(	(	PUNCT
iajs-319	461	15	22	22	NUM
iajs-319	461	16			NOUN
iajs-319	461	17	be	be	VERB
iajs-319	461	18	topological	topological	ADJ
iajs-319	461	19	spaces	space	NOUN
iajs-319	461	20	.	.	PUNCT
iajs-319	462	1	then	then	ADV
iajs-319	462	2	the	the	DET
iajs-319	462	3	projection	projection	NOUN
iajs-319	462	4	functions	function	NOUN
iajs-319	462	5	1211	1211	NUM
iajs-319	462	6	xxx	xxx	NOUN
iajs-319	462	7	:	:	PUNCT
iajs-319	462	8			PROPN
iajs-319	462	9	and	and	CCONJ
iajs-319	462	10	2212	2212	NUM
iajs-319	462	11	xxx	xxx	NOUN
iajs-319	462	12	:	:	PUNCT
iajs-319	462	13			PROPN
iajs-319	462	14	are	be	AUX
iajs-319	462	15	s*g-	s*g-	NOUN
iajs-319	462	16	-irresolute	-irresolute	NOUN
iajs-319	462	17	functions	function	NOUN
iajs-319	462	18	.	.	PUNCT
iajs-319	463	1	proof	proof	NOUN
iajs-319	463	2	:	:	PUNCT
iajs-319	463	3	let	let	VERB
iajs-319	463	4	u	u	PRON
iajs-319	463	5	be	be	AUX
iajs-319	463	6	an	an	DET
iajs-319	463	7	s*g-	s*g-	NOUN
iajs-319	463	8	-open	-open	NOUN
iajs-319	463	9	set	set	VERB
iajs-319	463	10	in	in	ADP
iajs-319	463	11	1x	1x	NUM
iajs-319	463	12	,	,	PUNCT
iajs-319	463	13	then	then	ADV
iajs-319	463	14	2	2	NUM
iajs-319	463	15	1	1	NUM
iajs-319	463	16	1	1	NUM
iajs-319	463	17	xu)u	xu)u	PROPN
iajs-319	463	18	(	(	PUNCT
iajs-319	463	19			ADJ
iajs-319	463	20			NOUN
iajs-319	463	21	.	.	PUNCT
iajs-319	464	1	since	since	SCONJ
iajs-319	464	2	u	u	NOUN
iajs-319	464	3	is	be	AUX
iajs-319	464	4	s*g-	s*g-	NOUN
iajs-319	464	5	-open	-open	ADJ
iajs-319	464	6	in	in	ADP
iajs-319	464	7	1x	1x	NUM
iajs-319	464	8	and	and	CCONJ
iajs-319	464	9	2x	2x	NUM
iajs-319	464	10	is	be	AUX
iajs-319	464	11	s*g-	s*g-	NOUN
iajs-319	464	12	-open	-open	NOUN
iajs-319	464	13	in	in	ADP
iajs-319	464	14	2x	2x	NUM
iajs-319	464	15	,	,	PUNCT
iajs-319	464	16	then	then	ADV
iajs-319	464	17	by	by	ADP
iajs-319	464	18	proposition	proposition	NOUN
iajs-319	464	19	(	(	PUNCT
iajs-319	464	20	2.27	2.27	NUM
iajs-319	464	21	)	)	PUNCT
iajs-319	464	22	2xu	2xu	ADJ
iajs-319	464	23			NOUN
iajs-319	464	24	is	be	AUX
iajs-319	464	25	s*g-	s*g-	NOUN
iajs-319	464	26	-open	-open	ADJ
iajs-319	464	27	in	in	ADP
iajs-319	464	28	21	21	NUM
iajs-319	464	29	xx	xx	NUM
iajs-319	464	30			NOUN
iajs-319	464	31	.	.	PUNCT
iajs-319	465	1	thus	thus	ADV
iajs-319	465	2	1211	1211	NUM
iajs-319	465	3	xxx	xxx	NOUN
iajs-319	465	4	:	:	PUNCT
iajs-319	465	5			PROPN
iajs-319	465	6	is	be	AUX
iajs-319	465	7	an	an	DET
iajs-319	465	8	s*g-	s*g-	NOUN
iajs-319	465	9	-irresolute	-irresolute	PROPN
iajs-319	465	10	function	function	NOUN
iajs-319	465	11	.	.	PUNCT
iajs-319	466	1	similaly	similaly	PROPN
iajs-319	466	2	we	we	PRON
iajs-319	466	3	can	can	AUX
iajs-319	466	4	prove	prove	VERB
iajs-319	466	5	that	that	SCONJ
iajs-319	466	6	2212	2212	NUM
iajs-319	466	7	xxx	xxx	NOUN
iajs-319	466	8	:	:	PUNCT
iajs-319	466	9			PROPN
iajs-319	466	10	is	be	AUX
iajs-319	466	11	s*g-	s*g-	NOUN
iajs-319	466	12	-irresolute	-irresolute	ADJ
iajs-319	466	13	function	function	NOUN
iajs-319	466	14	.	.	PUNCT
iajs-319	467	1	however	however	ADV
iajs-319	467	2	the	the	DET
iajs-319	467	3	following	follow	VERB
iajs-319	467	4	theorem	theorem	NOUN
iajs-319	467	5	holds	hold	VERB
iajs-319	467	6	.	.	PUNCT
iajs-319	468	1	the	the	DET
iajs-319	468	2	proof	proof	NOUN
iajs-319	468	3	is	be	AUX
iajs-319	468	4	easy	easy	ADJ
iajs-319	468	5	and	and	CCONJ
iajs-319	468	6	hence	hence	ADV
iajs-319	468	7	omitted	omit	VERB
iajs-319	468	8	.	.	PUNCT
iajs-319	469	1	theorem(3.30	theorem(3.30	X
iajs-319	469	2	):	):	PUNCT
iajs-319	469	3	if	if	SCONJ
iajs-319	469	4	)	)	PUNCT
iajs-319	469	5	,	,	PUNCT
iajs-319	469	6	y(),x(:f	y(),x(:f	PROPN
iajs-319	469	7			PROPN
iajs-319	469	8	and	and	CCONJ
iajs-319	469	9	)	)	PUNCT
iajs-319	469	10	,	,	PUNCT
iajs-319	469	11	z(),y(:f	z(),y(:f	PROPN
iajs-319	469	12			NOUN
iajs-319	469	13	are	be	AUX
iajs-319	469	14	functions	function	NOUN
iajs-319	469	15	,	,	PUNCT
iajs-319	469	16	then	then	ADV
iajs-319	469	17	:	:	PUNCT
iajs-319	469	18	i	i	X
iajs-319	469	19	)	)	PUNCT
iajs-319	469	20	if	if	SCONJ
iajs-319	469	21	f	f	PROPN
iajs-319	469	22	and	and	CCONJ
iajs-319	469	23	g	g	PROPN
iajs-319	469	24	are	be	AUX
iajs-319	469	25	both	both	DET
iajs-319	469	26	s*g-	s*g-	NOUN
iajs-319	469	27	-irresolute	-irresolute	PROPN
iajs-319	469	28	functions	function	NOUN
iajs-319	469	29	,	,	PUNCT
iajs-319	469	30	then	then	ADV
iajs-319	469	31	so	so	ADV
iajs-319	469	32	is	be	AUX
iajs-319	469	33	fg	fg	PROPN
iajs-319	469	34			PROPN
iajs-319	469	35	.	.	PUNCT
iajs-319	469	36	ii	ii	PROPN
iajs-319	469	37	)	)	PUNCT
iajs-319	469	38	if	if	SCONJ
iajs-319	469	39	f	f	PROPN
iajs-319	469	40	is	be	AUX
iajs-319	469	41	s*g-	s*g-	NOUN
iajs-319	469	42	-irresolute	-irresolute	ADJ
iajs-319	469	43	and	and	CCONJ
iajs-319	469	44	g	g	PROPN
iajs-319	469	45	is	be	AUX
iajs-319	469	46	s*g-	s*g-	NOUN
iajs-319	469	47	-continuous	-continuous	ADJ
iajs-319	469	48	,	,	PUNCT
iajs-319	469	49	then	then	ADV
iajs-319	469	50	fg	fg	PROPN
iajs-319	469	51			PROPN
iajs-319	469	52	is	be	AUX
iajs-319	469	53	s*g-	s*g-	NOUN
iajs-319	469	54	-continuous	-continuous	ADJ
iajs-319	469	55	.	.	PUNCT
iajs-319	470	1	iii	iii	X
iajs-319	470	2	)	)	PUNCT
iajs-319	470	3	if	if	SCONJ
iajs-319	470	4	f	f	PROPN
iajs-319	470	5	is	be	AUX
iajs-319	470	6	s*g-	s*g-	NOUN
iajs-319	470	7	-continuous	-continuous	ADJ
iajs-319	470	8	and	and	CCONJ
iajs-319	470	9	g	g	NOUN
iajs-319	470	10	is	be	AUX
iajs-319	470	11	continuous	continuous	ADJ
iajs-319	470	12	,	,	PUNCT
iajs-319	470	13	then	then	ADV
iajs-319	470	14	fg	fg	PROPN
iajs-319	470	15			PROPN
iajs-319	470	16	is	be	AUX
iajs-319	470	17	s*g-	s*g-	NOUN
iajs-319	470	18	-continuous	-continuous	ADJ
iajs-319	470	19	.	.	PUNCT
iajs-319	471	1	references	reference	NOUN
iajs-319	471	2	1	1	NUM
iajs-319	471	3	.	.	PUNCT
iajs-319	472	1	levine	levine	PROPN
iajs-319	472	2	,	,	PUNCT
iajs-319	472	3	n.	n.	PROPN
iajs-319	472	4	(	(	PUNCT
iajs-319	472	5	1963	1963	NUM
iajs-319	472	6	)	)	PUNCT
iajs-319	472	7	semi	semi	ADJ
iajs-319	472	8	-	-	ADJ
iajs-319	472	9	open	open	ADJ
iajs-319	472	10	sets	set	NOUN
iajs-319	472	11	and	and	CCONJ
iajs-319	472	12	semi	semi	ADJ
iajs-319	472	13	-	-	NOUN
iajs-319	472	14	continuity	continuity	NOUN
iajs-319	472	15	in	in	ADP
iajs-319	472	16	topological	topological	ADJ
iajs-319	472	17	spaces	space	NOUN
iajs-319	472	18	,	,	PUNCT
iajs-319	472	19	amer	amer	PROPN
iajs-319	472	20	.	.	PROPN
iajs-319	472	21	math	math	PROPN
iajs-319	472	22	.	.	PUNCT
iajs-319	473	1	monthly	monthly	ADJ
iajs-319	473	2	,	,	PUNCT
iajs-319	473	3	70	70	NUM
iajs-319	473	4	,	,	PUNCT
iajs-319	473	5	36	36	NUM
iajs-319	473	6	-	-	SYM
iajs-319	473	7	41	41	NUM
iajs-319	473	8	.	.	PUNCT
iajs-319	473	9	2	2	NUM
iajs-319	473	10	.	.	PUNCT
iajs-319	474	1	levine	levine	PROPN
iajs-319	474	2	,	,	PUNCT
iajs-319	474	3	n.(1970)generalized	n.(1970)generalized	ADJ
iajs-319	474	4	closed	close	VERB
iajs-319	474	5	sets	set	NOUN
iajs-319	474	6	in	in	ADP
iajs-319	474	7	topology	topology	NOUN
iajs-319	474	8	,	,	PUNCT
iajs-319	474	9	rend.circ.math.palermo	rend.circ.math.palermo	PROPN
iajs-319	474	10	,	,	PUNCT
iajs-319	474	11	19	19	NUM
iajs-319	474	12	(	(	PUNCT
iajs-319	474	13	2	2	NUM
iajs-319	474	14	)	)	PUNCT
iajs-319	474	15	,	,	PUNCT
iajs-319	474	16	89	89	NUM
iajs-319	474	17	-	-	SYM
iajs-319	474	18	96	96	NUM
iajs-319	474	19	.	.	PUNCT
iajs-319	474	20	3	3	NUM
iajs-319	474	21	.	.	PUNCT
iajs-319	474	22	njasta	njasta	NOUN
iajs-319	474	23	,	,	PUNCT
iajs-319	474	24	o.	o.	PROPN
iajs-319	474	25	(	(	PUNCT
iajs-319	474	26	1965	1965	NUM
iajs-319	474	27	)	)	PUNCT
iajs-319	474	28	on	on	ADP
iajs-319	474	29	some	some	DET
iajs-319	474	30	classes	class	NOUN
iajs-319	474	31	of	of	ADP
iajs-319	474	32	nearly	nearly	ADV
iajs-319	474	33	open	open	ADJ
iajs-319	474	34	sets	set	NOUN
iajs-319	474	35	,	,	PUNCT
iajs-319	474	36	pacific	pacific	PROPN
iajs-319	474	37	j.	j.	PROPN
iajs-319	474	38	math	math	PROPN
iajs-319	474	39	.	.	PUNCT
iajs-319	475	1	15	15	NUM
iajs-319	475	2	,	,	PUNCT
iajs-319	475	3	961	961	NUM
iajs-319	475	4	-	-	SYM
iajs-319	475	5	970	970	NUM
iajs-319	475	6	.	.	PUNCT
iajs-319	476	1	4	4	NUM
iajs-319	476	2	.	.	PUNCT
iajs-319	477	1	mashhour	mashhour	PROPN
iajs-319	477	2	,	,	PUNCT
iajs-319	477	3	a.s	a.s	PROPN
iajs-319	477	4	.	.	PROPN
iajs-319	477	5	;	;	PUNCT
iajs-319	477	6	abd	abd	PROPN
iajs-319	477	7	el	el	PROPN
iajs-319	477	8	-	-	PUNCT
iajs-319	477	9	monsef	monsef	ADJ
iajs-319	477	10	,	,	PUNCT
iajs-319	477	11	m.e	m.e	PROPN
iajs-319	477	12	.	.	PROPN
iajs-319	477	13	and	and	CCONJ
iajs-319	477	14	el	el	PROPN
iajs-319	477	15	-	-	PUNCT
iajs-319	477	16	deeb	deeb	PROPN
iajs-319	477	17	,	,	PUNCT
iajs-319	477	18	s.n	s.n	PROPN
iajs-319	477	19	.	.	PROPN
iajs-319	477	20	(	(	PUNCT
iajs-319	477	21	1982	1982	NUM
iajs-319	477	22	)	)	PUNCT
iajs-319	477	23	on	on	ADP
iajs-319	477	24	precontinuous	precontinuous	ADJ
iajs-319	477	25	and	and	CCONJ
iajs-319	477	26	weak	weak	ADJ
iajs-319	477	27	precontinuous	precontinuous	ADJ
iajs-319	477	28	functions	function	NOUN
iajs-319	477	29	,	,	PUNCT
iajs-319	477	30	proc	proc	NOUN
iajs-319	477	31	.	.	PUNCT
iajs-319	478	1	math	math	NOUN
iajs-319	478	2	.	.	PUNCT
iajs-319	479	1	phys	phy	NOUN
iajs-319	479	2	.	.	PUNCT
iajs-319	480	1	soc	soc	PROPN
iajs-319	480	2	.	.	PUNCT
iajs-319	481	1	egypt	egypt	PROPN
iajs-319	481	2	,	,	PUNCT
iajs-319	481	3	51	51	NUM
iajs-319	481	4	,	,	PUNCT
iajs-319	481	5	47	47	NUM
iajs-319	481	6	-	-	SYM
iajs-319	481	7	53	53	NUM
iajs-319	481	8	.	.	NUM
iajs-319	481	9	5	5	NUM
iajs-319	481	10	.	.	PUNCT
iajs-319	482	1	andrijevic	andrijevic	PROPN
iajs-319	482	2	,	,	PUNCT
iajs-319	482	3	d.	d.	PROPN
iajs-319	482	4	(	(	PUNCT
iajs-319	482	5	1996	1996	NUM
iajs-319	482	6	)	)	PUNCT
iajs-319	482	7	on	on	ADP
iajs-319	482	8	b	b	X
iajs-319	482	9	-	-	PUNCT
iajs-319	482	10	open	open	ADJ
iajs-319	482	11	sets	set	NOUN
iajs-319	482	12	,	,	PUNCT
iajs-319	482	13	mat	mat	X
iajs-319	482	14	.	.	PROPN
iajs-319	482	15	vesnik	vesnik	PROPN
iajs-319	482	16	,	,	PUNCT
iajs-319	482	17	48	48	NUM
iajs-319	482	18	(	(	PUNCT
iajs-319	482	19	1	1	NUM
iajs-319	482	20	-	-	SYM
iajs-319	482	21	2	2	NUM
iajs-319	482	22	)	)	PUNCT
iajs-319	482	23	,	,	PUNCT
iajs-319	482	24	59	59	NUM
iajs-319	482	25	-	-	SYM
iajs-319	482	26	64	64	NUM
iajs-319	482	27	.	.	PUNCT
iajs-319	483	1	6	6	NUM
iajs-319	483	2	.	.	PUNCT
iajs-319	484	1	abd	abd	PROPN
iajs-319	484	2	el	el	PROPN
iajs-319	484	3	-	-	PUNCT
iajs-319	484	4	monsef	monsef	ADJ
iajs-319	484	5	,	,	PUNCT
iajs-319	484	6	m.e	m.e	PROPN
iajs-319	484	7	;	;	PUNCT
iajs-319	484	8	el	el	PROPN
iajs-319	484	9	-	-	PUNCT
iajs-319	484	10	deeb	deeb	PROPN
iajs-319	484	11	,	,	PUNCT
iajs-319	484	12	s.n	s.n	PROPN
iajs-319	484	13	.	.	PROPN
iajs-319	484	14	and	and	CCONJ
iajs-319	484	15	mahmoud	mahmoud	PROPN
iajs-319	484	16	,	,	PUNCT
iajs-319	484	17	r.a	r.a	PROPN
iajs-319	484	18	.	.	PROPN
iajs-319	484	19	(	(	PUNCT
iajs-319	484	20	1983	1983	NUM
iajs-319	484	21	)	)	PUNCT
iajs-319	484	22			NOUN
iajs-319	484	23	-open	-open	NOUN
iajs-319	484	24	sets	set	NOUN
iajs-319	484	25	and	and	VERB
iajs-319	484	26	continuous	continuous	ADJ
iajs-319	484	27	mappings	mapping	NOUN
iajs-319	484	28	,	,	PUNCT
iajs-319	484	29	bull	bull	NOUN
iajs-319	484	30	.	.	PUNCT
iajs-319	485	1	fac	fac	PROPN
iajs-319	485	2	.	.	PUNCT
iajs-319	486	1	sci	sci	PROPN
iajs-319	486	2	.	.	PUNCT
iajs-319	486	3	assuit	assuit	PROPN
iajs-319	486	4	univ	univ	PROPN
iajs-319	486	5	.	.	PROPN
iajs-319	487	1	12	12	NUM
iajs-319	487	2	,	,	PUNCT
iajs-319	487	3	77	77	NUM
iajs-319	487	4	-	-	SYM
iajs-319	487	5	90	90	NUM
iajs-319	487	6	.	.	PUNCT
iajs-319	488	1	554	554	NUM
iajs-319	488	2	|	|	ADV
iajs-319	488	3	mathematics	mathematic	NOUN
iajs-319	488	4	2014	2014	NUM
iajs-319	488	5	)	)	PUNCT
iajs-319	488	6	عام	عام	ADP
iajs-319	488	7	3العدد	3العدد	NUM
iajs-319	488	8	(	(	PUNCT
iajs-319	488	9	27مجلة	27مجلة	NUM
iajs-319	488	10	إبن	إبن	VERB
iajs-319	488	11	الھيثم	الھيثم	NOUN
iajs-319	488	12	للعلوم	للعلوم	NOUN
iajs-319	488	13	الصرفة	الصرفة	NOUN
iajs-319	489	1	و	و	PRON
iajs-319	489	2	التطبيقية	التطبيقية	ADV
iajs-319	489	3	المجلد	المجلد	VERB
iajs-319	489	4	ibn	ibn	PROPN
iajs-319	489	5	al	al	PROPN
iajs-319	489	6	-	-	PUNCT
iajs-319	489	7	haitham	haitham	PROPN
iajs-319	489	8	jour	jour	X
iajs-319	489	9	.	.	PROPN
iajs-319	490	1	for	for	ADP
iajs-319	490	2	pure	pure	ADJ
iajs-319	490	3	&	&	CCONJ
iajs-319	490	4	appl	appl	PROPN
iajs-319	490	5	.	.	PUNCT
iajs-319	491	1	sci	sci	PROPN
iajs-319	491	2	.	.	PUNCT
iajs-319	491	3	vol	vol	NOUN
iajs-319	491	4	.	.	PROPN
iajs-319	492	1	27	27	NUM
iajs-319	492	2	(	(	PUNCT
iajs-319	492	3	3	3	NUM
iajs-319	492	4	)	)	PUNCT
iajs-319	492	5	2014	2014	NUM
iajs-319	492	6	7	7	NUM
iajs-319	492	7	.	.	PUNCT
iajs-319	493	1	arya	arya	PROPN
iajs-319	493	2	,	,	PUNCT
iajs-319	493	3	s.p	s.p	PROPN
iajs-319	493	4	.	.	PROPN
iajs-319	493	5	and	and	CCONJ
iajs-319	493	6	nour	nour	PROPN
iajs-319	493	7	,	,	PUNCT
iajs-319	493	8	t.m	t.m	PROPN
iajs-319	493	9	.	.	PROPN
iajs-319	493	10	(	(	PUNCT
iajs-319	493	11	1990	1990	NUM
iajs-319	493	12	)	)	PUNCT
iajs-319	493	13	characterizations	characterization	NOUN
iajs-319	493	14	of	of	ADP
iajs-319	493	15	s	s	NOUN
iajs-319	493	16	-	-	ADJ
iajs-319	493	17	normal	normal	ADJ
iajs-319	493	18	spaces	space	NOUN
iajs-319	493	19	,	,	PUNCT
iajs-319	493	20	indian	indian	ADJ
iajs-319	493	21	j.	j.	PROPN
iajs-319	493	22	pure	pure	PROPN
iajs-319	493	23	appl	appl	PROPN
iajs-319	493	24	.	.	PUNCT
iajs-319	493	25	math	math	NOUN
iajs-319	493	26	.	.	PUNCT
iajs-319	494	1	21	21	NUM
iajs-319	494	2	(	(	PUNCT
iajs-319	494	3	8)	8)	NUM
iajs-319	494	4	,	,	PUNCT
iajs-319	494	5	717	717	NUM
iajs-319	494	6	-	-	SYM
iajs-319	494	7	719	719	NUM
iajs-319	494	8	.	.	NUM
iajs-319	494	9	8	8	NUM
iajs-319	494	10	.	.	PUNCT
iajs-319	495	1	maki	maki	PROPN
iajs-319	495	2	,	,	PUNCT
iajs-319	495	3	h.	h.	PROPN
iajs-319	495	4	;	;	PUNCT
iajs-319	495	5	devi	devi	PROPN
iajs-319	495	6	,	,	PUNCT
iajs-319	495	7	r.	r.	PROPN
iajs-319	495	8	and	and	CCONJ
iajs-319	495	9	balachandran	balachandran	PROPN
iajs-319	495	10	,	,	PUNCT
iajs-319	495	11	k.	k.	PROPN
iajs-319	495	12	(	(	PUNCT
iajs-319	495	13	1993	1993	NUM
iajs-319	495	14	)	)	PUNCT
iajs-319	495	15	generalized	generalize	VERB
iajs-319	495	16	α	α	PRON
iajs-319	495	17	-	-	PUNCT
iajs-319	495	18	closed	closed	ADJ
iajs-319	495	19	sets	set	NOUN
iajs-319	495	20	in	in	ADP
iajs-319	495	21	topology	topology	NOUN
iajs-319	495	22	,	,	PUNCT
iajs-319	495	23	bull.fukuoka	bull.fukuoka	PROPN
iajs-319	495	24	univ	univ	PROPN
iajs-319	495	25	.	.	PUNCT
iajs-319	496	1	ed	ed	NOUN
iajs-319	496	2	.	.	PUNCT
iajs-319	497	1	part	part	PROPN
iajs-319	497	2	iii	iii	PROPN
iajs-319	497	3	,	,	PUNCT
iajs-319	497	4	42	42	NUM
iajs-319	497	5	,	,	PUNCT
iajs-319	497	6	13	13	NUM
iajs-319	497	7	-	-	SYM
iajs-319	497	8	21	21	NUM
iajs-319	497	9	.	.	PUNCT
iajs-319	497	10	9	9	NUM
iajs-319	497	11	.	.	PUNCT
iajs-319	498	1	maki	maki	PROPN
iajs-319	498	2	,	,	PUNCT
iajs-319	498	3	h.	h.	PROPN
iajs-319	498	4	;	;	PUNCT
iajs-319	498	5	devi	devi	PROPN
iajs-319	498	6	,	,	PUNCT
iajs-319	498	7	r.	r.	PROPN
iajs-319	498	8	and	and	CCONJ
iajs-319	498	9	balachandran	balachandran	PROPN
iajs-319	498	10	,	,	PUNCT
iajs-319	498	11	k.	k.	PROPN
iajs-319	498	12	(	(	PUNCT
iajs-319	498	13	1994	1994	NUM
iajs-319	498	14	)	)	PUNCT
iajs-319	498	15	associated	associate	VERB
iajs-319	498	16	topologies	topology	NOUN
iajs-319	498	17	of	of	ADP
iajs-319	498	18	generalized	generalized	ADJ
iajs-319	498	19	α	α	NOUN
iajs-319	498	20	closed	close	VERB
iajs-319	498	21	sets	set	NOUN
iajs-319	498	22	and	and	CCONJ
iajs-319	498	23	α	α	X
iajs-319	498	24	-	-	ADJ
iajs-319	498	25	generalized	generalize	VERB
iajs-319	498	26	closed	closed	ADJ
iajs-319	498	27	sets	set	NOUN
iajs-319	498	28	,	,	PUNCT
iajs-319	498	29	mem	mem	PROPN
iajs-319	498	30	.	.	PUNCT
iajs-319	499	1	fac	fac	PROPN
iajs-319	499	2	.	.	PUNCT
iajs-319	500	1	sci	sci	PROPN
iajs-319	500	2	.	.	PROPN
iajs-319	500	3	kochi	kochi	PROPN
iajs-319	500	4	univ	univ	PROPN
iajs-319	500	5	.	.	PUNCT
iajs-319	501	1	ser.a.math	ser.a.math	NOUN
iajs-319	501	2	.	.	PUNCT
iajs-319	502	1	15	15	NUM
iajs-319	502	2	,	,	PUNCT
iajs-319	502	3	51	51	NUM
iajs-319	502	4	-	-	SYM
iajs-319	502	5	63	63	NUM
iajs-319	502	6	.	.	PUNCT
iajs-319	503	1	10	10	NUM
iajs-319	503	2	.	.	PUNCT
iajs-319	504	1	khan	khan	PROPN
iajs-319	504	2	,	,	PUNCT
iajs-319	504	3	m.	m.	NOUN
iajs-319	504	4	;	;	PUNCT
iajs-319	504	5	noiri	noiri	PROPN
iajs-319	504	6	,	,	PUNCT
iajs-319	504	7	t	t	PROPN
iajs-319	504	8	.	.	PUNCT
iajs-319	504	9	and	and	CCONJ
iajs-319	504	10	hussain	hussain	PROPN
iajs-319	504	11	,	,	PUNCT
iajs-319	504	12	m	m	NOUN
iajs-319	504	13	.(2008	.(2008	NOUN
iajs-319	504	14	)	)	PUNCT
iajs-319	504	15	on	on	ADP
iajs-319	504	16	s*g	s*g	NOUN
iajs-319	504	17	-	-	PUNCT
iajs-319	504	18	closed	close	VERB
iajs-319	504	19	sets	set	NOUN
iajs-319	504	20	and	and	CCONJ
iajs-319	504	21	s*-normal	s*-normal	ADJ
iajs-319	504	22	spaces	space	NOUN
iajs-319	504	23	,	,	PUNCT
iajs-319	504	24	48	48	NUM
iajs-319	504	25	,	,	PUNCT
iajs-319	504	26	31	31	NUM
iajs-319	504	27	-	-	SYM
iajs-319	504	28	41	41	NUM
iajs-319	504	29	.	.	PUNCT
iajs-319	504	30	11	11	NUM
iajs-319	504	31	.	.	PUNCT
iajs-319	505	1	mashhour	mashhour	PROPN
iajs-319	505	2	,	,	PUNCT
iajs-319	505	3	a.s	a.s	PROPN
iajs-319	505	4	.	.	PROPN
iajs-319	505	5	;	;	PUNCT
iajs-319	505	6	hasanein	hasanein	PROPN
iajs-319	505	7	,	,	PUNCT
iajs-319	505	8	i.a	i.a	PROPN
iajs-319	505	9	and	and	CCONJ
iajs-319	505	10	el	el	PROPN
iajs-319	505	11	-	-	PUNCT
iajs-319	505	12	deeb	deeb	PROPN
iajs-319	505	13	,	,	PUNCT
iajs-319	505	14	s.n	s.n	PROPN
iajs-319	505	15	.	.	PROPN
iajs-319	505	16	(	(	PUNCT
iajs-319	505	17	1983)	1983)	NUM
iajs-319	505	18	-continuous	-continuous	ADJ
iajs-319	505	19	and	and	CCONJ
iajs-319	505	20			NOUN
iajs-319	505	21	-open	-open	NOUN
iajs-319	505	22	mappings	mapping	NOUN
iajs-319	505	23	,	,	PUNCT
iajs-319	505	24	acta	acta	PROPN
iajs-319	505	25	math	math	PROPN
iajs-319	505	26	hung	hung	PROPN
iajs-319	505	27	.	.	PUNCT
iajs-319	506	1	41	41	NUM
iajs-319	506	2	(	(	PUNCT
iajs-319	506	3	3	3	NUM
iajs-319	506	4	-	-	SYM
iajs-319	506	5	4	4	NUM
iajs-319	506	6	)	)	PUNCT
iajs-319	506	7	,	,	PUNCT
iajs-319	506	8	213	213	NUM
iajs-319	506	9	-	-	SYM
iajs-319	506	10	218	218	NUM
iajs-319	506	11	.	.	PUNCT
iajs-319	507	1	12	12	NUM
iajs-319	507	2	.	.	PUNCT
iajs-319	508	1	ekici	ekici	PROPN
iajs-319	508	2	,	,	PUNCT
iajs-319	508	3	e.	e.	PROPN
iajs-319	508	4	and	and	CCONJ
iajs-319	508	5	caldas	caldas	PROPN
iajs-319	508	6	,	,	PUNCT
iajs-319	508	7	m.	m.	NOUN
iajs-319	508	8	(	(	PUNCT
iajs-319	508	9	2004	2004	NUM
iajs-319	508	10	)	)	PUNCT
iajs-319	508	11	slightly	slightly	ADV
iajs-319	508	12			NUM
iajs-319	508	13	-continuous	-continuous	ADJ
iajs-319	508	14	functions	function	NOUN
iajs-319	508	15	,	,	PUNCT
iajs-319	508	16	bol	bol	NOUN
iajs-319	508	17	.	.	PUNCT
iajs-319	509	1	soc	soc	PROPN
iajs-319	509	2	.	.	PUNCT
iajs-319	510	1	parana	parana	PROPN
iajs-319	510	2	mat	mat	PROPN
iajs-319	510	3	.	.	PROPN
iajs-319	510	4	22	22	NUM
iajs-319	510	5	(	(	PUNCT
iajs-319	510	6	2	2	NUM
iajs-319	510	7	)	)	PUNCT
iajs-319	510	8	,	,	PUNCT
iajs-319	510	9	63	63	NUM
iajs-319	510	10	-	-	SYM
iajs-319	510	11	74	74	NUM
iajs-319	510	12	.	.	PUNCT
iajs-319	510	13	13	13	NUM
iajs-319	510	14	.	.	PUNCT
iajs-319	511	1	balachandran	balachandran	PROPN
iajs-319	511	2	,	,	PUNCT
iajs-319	511	3	k.	k.	PROPN
iajs-319	511	4	;	;	PUNCT
iajs-319	511	5	sundaram	sundaram	PROPN
iajs-319	511	6	,	,	PUNCT
iajs-319	511	7	p.	p.	NOUN
iajs-319	511	8	and	and	CCONJ
iajs-319	511	9	maki	maki	PROPN
iajs-319	511	10	,	,	PUNCT
iajs-319	511	11	h.	h.	PROPN
iajs-319	511	12	(	(	PUNCT
iajs-319	511	13	1991	1991	NUM
iajs-319	511	14	)	)	PUNCT
iajs-319	511	15	on	on	ADP
iajs-319	511	16	generalized	generalized	ADJ
iajs-319	511	17	continuous	continuous	ADJ
iajs-319	511	18	maps	map	NOUN
iajs-319	511	19	in	in	ADP
iajs-319	511	20	topological	topological	ADJ
iajs-319	511	21	spaces	space	NOUN
iajs-319	511	22	,	,	PUNCT
iajs-319	511	23	mem	mem	PROPN
iajs-319	511	24	.	.	PUNCT
iajs-319	512	1	fac	fac	PROPN
iajs-319	512	2	.	.	PUNCT
iajs-319	513	1	sci	sci	PROPN
iajs-319	513	2	.	.	PROPN
iajs-319	513	3	kochi	kochi	PROPN
iajs-319	513	4	univ	univ	PROPN
iajs-319	513	5	.	.	PUNCT
iajs-319	514	1	ser	ser	PROPN
iajs-319	514	2	.	.	PUNCT
iajs-319	514	3	a.	a.	PROPN
iajs-319	514	4	math	math	PROPN
iajs-319	514	5	.	.	PUNCT
iajs-319	515	1	12	12	NUM
iajs-319	515	2	,	,	PUNCT
iajs-319	515	3	5	5	NUM
iajs-319	515	4	-	-	SYM
iajs-319	515	5	13	13	NUM
iajs-319	515	6	.	.	PUNCT
iajs-319	516	1	14	14	NUM
iajs-319	516	2	.	.	PUNCT
iajs-319	517	1	devi	devi	PROPN
iajs-319	517	2	,	,	PUNCT
iajs-319	517	3	r.	r.	PROPN
iajs-319	517	4	;	;	PUNCT
iajs-319	517	5	balachandran	balachandran	NOUN
iajs-319	517	6	,	,	PUNCT
iajs-319	517	7	k.	k.	PROPN
iajs-319	517	8	and	and	CCONJ
iajs-319	517	9	maki	maki	PROPN
iajs-319	517	10	,	,	PUNCT
iajs-319	517	11	h.	h.	PROPN
iajs-319	517	12	(	(	PUNCT
iajs-319	517	13	1995	1995	NUM
iajs-319	517	14	)	)	PUNCT
iajs-319	517	15	semi	semi	ADJ
iajs-319	517	16	-	-	ADJ
iajs-319	517	17	generalized	generalized	ADJ
iajs-319	517	18	homeomorphisms	homeomorphism	NOUN
iajs-319	517	19	and	and	CCONJ
iajs-319	517	20	generalized	generalize	VERB
iajs-319	517	21	semi	semi	NOUN
iajs-319	517	22	-	-	NOUN
iajs-319	517	23	homeomorphisms	homeomorphism	NOUN
iajs-319	517	24	in	in	ADP
iajs-319	517	25	topological	topological	ADJ
iajs-319	517	26	spaces	space	NOUN
iajs-319	517	27	,	,	PUNCT
iajs-319	517	28	indian	indian	PROPN
iajs-319	517	29	j.	j.	PROPN
iajs-319	517	30	pure	pure	PROPN
iajs-319	517	31	appl	appl	PROPN
iajs-319	517	32	.	.	PUNCT
iajs-319	517	33	math	math	NOUN
iajs-319	517	34	.	.	PUNCT
iajs-319	518	1	26	26	NUM
iajs-319	518	2	(	(	PUNCT
iajs-319	518	3	3	3	NUM
iajs-319	518	4	)	)	PUNCT
iajs-319	518	5	,	,	PUNCT
iajs-319	518	6	271	271	NUM
iajs-319	518	7	-	-	SYM
iajs-319	518	8	284	284	NUM
iajs-319	518	9	.	.	PUNCT
iajs-319	519	1	15	15	NUM
iajs-319	519	2	.	.	PUNCT
iajs-319	520	1	gnanambal	gnanambal	PROPN
iajs-319	520	2	,	,	PUNCT
iajs-319	520	3	y.	y.	PROPN
iajs-319	520	4	(	(	PUNCT
iajs-319	520	5	1997	1997	NUM
iajs-319	520	6	)	)	PUNCT
iajs-319	520	7	on	on	ADP
iajs-319	520	8	generalized	generalize	VERB
iajs-319	520	9	preregular	preregular	ADJ
iajs-319	520	10	closed	close	VERB
iajs-319	520	11	sets	set	NOUN
iajs-319	520	12	in	in	ADP
iajs-319	520	13	topological	topological	ADJ
iajs-319	520	14	spaces	space	NOUN
iajs-319	520	15	,	,	PUNCT
iajs-319	520	16	indian	indian	PROPN
iajs-319	520	17	j.	j.	PROPN
iajs-319	520	18	pure	pure	PROPN
iajs-319	520	19	appl	appl	PROPN
iajs-319	520	20	.math	.math	PROPN
iajs-319	520	21	.	.	PUNCT
iajs-319	521	1	28(3	28(3	NUM
iajs-319	521	2	)	)	PUNCT
iajs-319	521	3	,	,	PUNCT
iajs-319	521	4	351	351	NUM
iajs-319	521	5	-	-	SYM
iajs-319	521	6	360	360	NUM
iajs-319	521	7	.	.	PUNCT
iajs-319	522	1	16	16	NUM
iajs-319	522	2	.	.	PUNCT
iajs-319	523	1	s.	s.	PROPN
iajs-319	523	2	i	i	PRON
iajs-319	523	3	.	.	PUNCT
iajs-319	524	1	and	and	CCONJ
iajs-319	524	2	afrah	afrah	PROPN
iajs-319	524	3	m	m	PROPN
iajs-319	524	4	.(2010	.(2010	NOUN
iajs-319	524	5	)	)	PUNCT
iajs-319	525	1	s*-separation	s*-separation	NOUN
iajs-319	525	2	axioms	axiom	NOUN
iajs-319	525	3	,	,	PUNCT
iajs-319	525	4	iraqi	iraqi	ADJ
iajs-319	525	5	journal	journal	NOUN
iajs-319	525	6	of	of	ADP
iajs-319	525	7	science	science	NOUN
iajs-319	525	8	,	,	PUNCT
iajs-319	525	9	university	university	NOUN
iajs-319	525	10	of	of	ADP
iajs-319	525	11	baghdad	baghdad	PROPN
iajs-319	525	12	,	,	PUNCT
iajs-319	525	13	51(1	51(1	NUM
iajs-319	525	14	)	)	PUNCT
iajs-319	525	15	,	,	PUNCT
iajs-319	525	16	145	145	NUM
iajs-319	525	17	-	-	SYM
iajs-319	525	18	153	153	NUM
iajs-319	525	19	.	.	PUNCT
iajs-319	525	20	17	17	NUM
iajs-319	525	21	.	.	PUNCT
iajs-319	526	1	s.	s.	PROPN
iajs-319	526	2	i	i	PRON
iajs-319	526	3	.	.	PUNCT
iajs-319	527	1	(	(	PUNCT
iajs-319	527	2	2014	2014	NUM
iajs-319	527	3	)	)	PUNCT
iajs-319	527	4	on	on	ADP
iajs-319	527	5	weak	weak	ADJ
iajs-319	527	6	g*sd	g*sd	NOUN
iajs-319	527	7	-sets	-set	NOUN
iajs-319	527	8	and	and	CCONJ
iajs-319	527	9	associative	associative	ADJ
iajs-319	527	10	separation	separation	NOUN
iajs-319	527	11	axioms	axiom	NOUN
iajs-319	527	12	,	,	PUNCT
iajs-319	527	13	ibn	ibn	PROPN
iajs-319	527	14	al	al	PROPN
iajs-319	527	15	-	-	PUNCT
iajs-319	527	16	haitham	haitham	PROPN
iajs-319	527	17	journal	journal	PROPN
iajs-319	527	18	for	for	ADP
iajs-319	527	19	pure	pure	ADJ
iajs-319	527	20	and	and	CCONJ
iajs-319	527	21	applied	apply	VERB
iajs-319	527	22	science	science	NOUN
iajs-319	527	23	,	,	PUNCT
iajs-319	527	24	(	(	PUNCT
iajs-319	527	25	to	to	PART
iajs-319	527	26	appear	appear	VERB
iajs-319	527	27	)	)	PUNCT
iajs-319	527	28	.	.	PUNCT
iajs-319	528	1	18	18	NUM
iajs-319	528	2	.	.	PUNCT
iajs-319	529	1	s.	s.	PROPN
iajs-319	529	2	i.	i.	PROPN
iajs-319	529	3	,	,	PUNCT
iajs-319	529	4	(	(	PUNCT
iajs-319	529	5	2014	2014	NUM
iajs-319	529	6	)	)	PUNCT
iajs-319	529	7	another	another	DET
iajs-319	529	8	type	type	NOUN
iajs-319	529	9	of	of	ADP
iajs-319	529	10	compactness	compactness	NOUN
iajs-319	529	11	in	in	ADP
iajs-319	529	12	bitopological	bitopological	ADJ
iajs-319	529	13	spaces	space	NOUN
iajs-319	529	14	,	,	PUNCT
iajs-319	529	15	journal	journal	NOUN
iajs-319	529	16	of	of	ADP
iajs-319	529	17	al	al	PROPN
iajs-319	529	18	rafidain	rafidain	PROPN
iajs-319	529	19	university	university	PROPN
iajs-319	529	20	college	college	NOUN
iajs-319	529	21	,	,	PUNCT
iajs-319	529	22	(	(	PUNCT
iajs-319	529	23	to	to	PART
iajs-319	529	24	appear	appear	VERB
iajs-319	529	25	)	)	PUNCT
iajs-319	529	26	.	.	PUNCT
iajs-319	530	1	555	555	NUM
iajs-319	530	2	|	|	ADV
iajs-319	530	3	mathematics	mathematic	NOUN
iajs-319	530	4	2014	2014	NUM
iajs-319	530	5	)	)	PUNCT
iajs-319	530	6	عام	عام	ADP
iajs-319	530	7	3العدد	3العدد	NUM
iajs-319	530	8	(	(	PUNCT
iajs-319	530	9	27مجلة	27مجلة	NUM
iajs-319	530	10	إبن	إبن	VERB
iajs-319	530	11	الھيثم	الھيثم	NOUN
iajs-319	530	12	للعلوم	للعلوم	NOUN
iajs-319	530	13	الصرفة	الصرفة	NOUN
iajs-319	531	1	و	و	PRON
iajs-319	531	2	التطبيقية	التطبيقية	ADV
iajs-319	531	3	المجلد	المجلد	VERB
iajs-319	531	4	ibn	ibn	PROPN
iajs-319	531	5	al	al	PROPN
iajs-319	531	6	-	-	PUNCT
iajs-319	531	7	haitham	haitham	PROPN
iajs-319	531	8	jour	jour	X
iajs-319	531	9	.	.	PROPN
iajs-319	532	1	for	for	ADP
iajs-319	532	2	pure	pure	ADJ
iajs-319	532	3	&	&	CCONJ
iajs-319	532	4	appl	appl	PROPN
iajs-319	532	5	.	.	PUNCT
iajs-319	533	1	sci	sci	PROPN
iajs-319	533	2	.	.	PUNCT
iajs-319	533	3	vol	vol	NOUN
iajs-319	533	4	.	.	PROPN
iajs-319	534	1	27	27	NUM
iajs-319	534	2	(	(	PUNCT
iajs-319	534	3	3	3	NUM
iajs-319	534	4	)	)	PUNCT
iajs-319	534	5	2014	2014	NUM
iajs-319	534	6	في	في	SCONJ
iajs-319	534	7	الفضاءات	الفضاءات	PROPN
iajs-319	534	8	التبولوجية	التبولوجية	PROPN
iajs-319	534	9			X
iajs-319	534	10	-s*gالمجموعات	-s*gالمجموعات	X
iajs-319	534	11	المفتوحة	المفتوحة	NOUN
iajs-319	534	12	ولح	ولح	NOUN
iajs-319	534	13	صبيحة	صبيحة	ADJ
iajs-319	534	14	إبراھيم	إبراھيم	NOUN
iajs-319	534	15	محمود	محمود	PROPN
iajs-319	534	16	سري	سري	PROPN
iajs-319	534	17	طارق	طارق	NOUN
iajs-319	534	18	جمانة	جمانة	VERB
iajs-319	534	19	الجامعة	الجامعة	NOUN
iajs-319	534	20	المستنصرية	المستنصرية	NOUN
iajs-319	534	21	/	/	SYM
iajs-319	534	22	كلية	كلية	NOUN
iajs-319	534	23	العلوم	العلوم	NOUN
iajs-319	534	24	/	/	SYM
iajs-319	534	25	قسم	قسم	NUM
iajs-319	534	26	الرياضيات	الرياضيات	NOUN
iajs-319	534	27	2014أيلول	2014أيلول	NUM
iajs-319	534	28	1	1	NUM
iajs-319	534	29	،	،	NOUN
iajs-319	534	30	قبل	قبل	NOUN
iajs-319	535	1	في	في	ADP
iajs-319	535	2	2014نيسان	2014نيسان	NOUN
iajs-319	535	3	9استلم	9استلم	NUM
iajs-319	535	4	في	في	X
iajs-319	535	5	الخالصة	الخالصة	PROPN
iajs-319	535	6	-s*gالنمط	-s*gالنمط	PROPN
iajs-319	535	7	من	من	PROPN
iajs-319	535	8	أسميناھا	أسميناھا	VERB
iajs-319	535	9	بالمجموعات	بالمجموعات	ADJ
iajs-319	535	10	المفتوحة	المفتوحة	NOUN
iajs-319	535	11	من	من	PRON
iajs-319	535	12	المجموعات	المجموعات	PROPN
iajs-319	535	13	اجديد	اجديد	PROPN
iajs-319	535	14	ا	ا	PROPN
iajs-319	536	1	ھذا	ھذا	NOUN
iajs-319	536	2	البحث	البحث	VERB
iajs-319	536	3	صنف	صنف	VERB
iajs-319	536	4	قدمنا	قدمنا	PROPN
iajs-319	536	5	في	في	PART
iajs-319	536	6	-s*g	-s*g	NOUN
iajs-319	536	7	المفتوحة	المفتوحة	NOUN
iajs-319	536	8	من	من	PRON
iajs-319	536	9	النمط	النمط	NOUN
iajs-319	537	1	و	و	PRON
iajs-319	537	2	من	من	INTJ
iajs-319	537	3	ثم	ثم	ADV
iajs-319	537	4	اثبتنا	اثبتنا	VERB
iajs-319	537	5	ان	ان	ADP
iajs-319	537	6	عائلة	عائلة	PROPN
iajs-319	537	7	كل	كل	PROPN
iajs-319	537	8	المجموعات	المجموعات	PROPN
iajs-319	537	9	الجزئية--s*g	الجزئية--s*g	PROPN
iajs-319	537	10	الفضاء	الفضاء	NOUN
iajs-319	537	11	التبولوجي	التبولوجي	NOUN
iajs-319	537	12	من	من	PROPN
iajs-319	537	13	)	)	PUNCT
iajs-319	537	14	,	,	PUNCT
iajs-319	537	15	x	x	X
iajs-319	537	16	(	(	PUNCT
iajs-319	537	17			NOUN
iajs-319	537	18	تشكل	تشكل	PROPN
iajs-319	537	19	تبولوجي	تبولوجي	AUX
iajs-319	537	20	على	على	VERB
iajs-319	537	21	x	x	X
iajs-319	537	22	الذي	الذي	PROPN
iajs-319	537	23	ھو	ھو	PROPN
iajs-319	537	24	انعم	انعم	PROPN
iajs-319	537	25	من	من	PROPN
iajs-319	537	26	.	.	PUNCT
iajs-319	538	1	األساسية	األساسية	PROPN
iajs-319	538	2	والخواص	والخواص	PROPN
iajs-319	538	3	المكافئات	المكافئات	PROPN
iajs-319	538	4	كذلك	كذلك	PROPN
iajs-319	538	5	درسنا	درسنا	PROPN
iajs-319	538	6	هاستخدمنا	هاستخدمنا	PROPN
iajs-319	538	7	ھذ	ھذ	PROPN
iajs-319	538	8	ذلك	ذلك	NOUN
iajs-319	538	9	عن	عن	PROPN
iajs-319	538	10	فضال	فضال	NOUN
iajs-319	538	11	-	-	ADJ
iajs-319	538	12	.	.	PUNCT
iajs-319	538	13	s*g	s*g	PROPN
iajs-319	538	14	-	-	PUNCT
iajs-319	538	15	المغلقة	المغلقة	PROPN
iajs-319	538	16	من	من	PROPN
iajs-319	538	17	النمط	النمط	PROPN
iajs-319	538	18	والمجموعات	والمجموعات	ADJ
iajs-319	538	19	-s*g	-s*g	ADJ
iajs-319	538	20	-	-	PUNCT
iajs-319	538	21	للمجموعات	للمجموعات	ADJ
iajs-319	538	22	المفتوحة	المفتوحة	NOUN
iajs-319	538	23	من	من	PRON
iajs-319	538	24	النمط	النمط	PROPN
iajs-319	538	25	النمطمن	النمطمن	PROPN
iajs-319	538	26	بالدوال	بالدوال	PROPN
iajs-319	538	27	المستمرة	المستمرة	VERB
iajs-319	538	28	صنف	صنف	PROPN
iajs-319	538	29	جديد	جديد	PROPN
iajs-319	538	30	من	من	DET
iajs-319	538	31	الدوال	الدوال	NOUN
iajs-319	538	32	في	في	PRON
iajs-319	538	33	الفضاءات	الفضاءات	PROPN
iajs-319	538	34	التبولوجية	التبولوجية	VERB
iajs-319	538	35	أسميناه	أسميناه	ADV
iajs-319	538	36	المجموعة	المجموعة	ADJ
iajs-319	538	37	في	في	INTJ
iajs-319	538	38	تعريف	تعريف	NOUN
iajs-319	538	39	ودراسة	ودراسة	PROPN
iajs-319	539	1	-	-	PROPN
iajs-319	539	2	-s*g	-s*g	PROPN
iajs-319	539	3	النمطمن	النمطمن	NOUN
iajs-319	539	4	والدوال	والدوال	INTJ
iajs-319	539	5	المحيرة--s*g	المحيرة--s*g	NOUN
iajs-319	539	6	بعض	بعض	NOUN
iajs-319	539	7	خواص	خواص	ADV
iajs-319	539	8	ھذه	ھذه	VERB
iajs-319	539	9	الدوال	الدوال	NOUN
iajs-319	539	10	.	.	PUNCT
iajs-319	540	1	قد	قد	INTJ
iajs-319	541	1	درستو	درستو	NOUN
iajs-319	541	2	الدوال	الدوال	NOUN
iajs-319	541	3	,	,	PUNCT
iajs-319	541	4	-s*g-المجموعات	-s*g-المجموعات	PROPN
iajs-319	541	5	المغلقة	المغلقة	NOUN
iajs-319	541	6	من	من	PRON
iajs-319	541	7	النمط	النمط	NOUN
iajs-319	541	8	,	,	PUNCT
iajs-319	541	9	s*g--المجموعات	s*g--المجموعات	VERB
iajs-319	541	10	المفتوحة	المفتوحة	NOUN
iajs-319	541	11	من	من	DET
iajs-319	541	12	النمط	النمط	NOUN
iajs-319	541	13	المفتاحية	المفتاحية	PROPN
iajs-319	541	14	:	:	PUNCT
iajs-319	541	15	الكلمات	الكلمات	VERB
iajs-319	541	16	s*g	s*g	NOUN
iajs-319	541	17	.--الدوال	.--الدوال	PROPN
iajs-319	541	18	المحيرة	المحيرة	PROPN
iajs-319	542	1	من	من	PROPN
iajs-319	542	2	النمط	النمط	PROPN
iajs-319	542	3	s*g	s*g	NOUN
iajs-319	542	4	,	,	PUNCT
iajs-319	542	5	--المستمرة	--المستمرة	PROPN
iajs-319	542	6	من	من	PRON
iajs-319	542	7	النمط	النمط	NOUN