id	sid	tid	token	lemma	pos
iajs-400	1	1	1	1	NUM
iajs-400	1	2	on	on	ADP
iajs-400	1	3	weak	weak	ADJ
iajs-400	1	4	g*sd	g*sd	NOUN
iajs-400	1	5	-sets	-set	NOUN
iajs-400	1	6	and	and	CCONJ
iajs-400	1	7	associative	associative	ADJ
iajs-400	1	8	separation	separation	NOUN
iajs-400	1	9	axioms	axiom	VERB
iajs-400	1	10	sabiha	sabiha	PROPN
iajs-400	1	11	i.	i.	PROPN
iajs-400	1	12	mahmood	mahmood	PROPN
iajs-400	1	13	department	department	PROPN
iajs-400	1	14	of	of	ADP
iajs-400	1	15	mathematics	mathematics	PROPN
iajs-400	1	16	/	/	SYM
iajs-400	1	17	college	college	NOUN
iajs-400	1	18	of	of	ADP
iajs-400	1	19	science	science	PROPN
iajs-400	1	20	/	/	SYM
iajs-400	1	21	al	al	PROPN
iajs-400	1	22	-	-	PUNCT
iajs-400	1	23	mustansiriyah	mustansiriyah	PROPN
iajs-400	1	24	university	university	NOUN
iajs-400	1	25	received	receive	VERB
iajs-400	1	26	in:3	in:3	PROPN
iajs-400	1	27	septamber	septamber	NOUN
iajs-400	1	28	2013	2013	NUM
iajs-400	1	29	,	,	PUNCT
iajs-400	1	30	accepted	accept	VERB
iajs-400	1	31	in	in	ADP
iajs-400	1	32	:	:	PUNCT
iajs-400	1	33	19	19	NUM
iajs-400	1	34	february	february	NOUN
iajs-400	1	35	2014	2014	NUM
iajs-400	1	36	abstract	abstract	NOUN
iajs-400	1	37	in	in	ADP
iajs-400	1	38	this	this	DET
iajs-400	1	39	paper	paper	NOUN
iajs-400	1	40	,	,	PUNCT
iajs-400	1	41	we	we	PRON
iajs-400	1	42	introduce	introduce	VERB
iajs-400	1	43	new	new	ADJ
iajs-400	1	44	classes	class	NOUN
iajs-400	1	45	of	of	ADP
iajs-400	1	46	sets	set	NOUN
iajs-400	1	47	called	call	VERB
iajs-400	1	48	g*sd	g*sd	PROPN
iajs-400	1	49	-sets	-set	NOUN
iajs-400	1	50	,	,	PUNCT
iajs-400	1	51	g*sd	g*sd	PROPN
iajs-400	1	52	−α	−α	PROPN
iajs-400	1	53	-sets	-set	NOUN
iajs-400	1	54	,	,	PUNCT
iajs-400	1	55	g*spred	g*spre	VERB
iajs-400	1	56	−	−	NOUN
iajs-400	1	57	sets	set	NOUN
iajs-400	1	58	,	,	PUNCT
iajs-400	1	59	g*sbd	g*sbd	VERB
iajs-400	1	60	−	−	NOUN
iajs-400	1	61	-sets	-set	NOUN
iajs-400	1	62	and	and	CCONJ
iajs-400	1	63	g*s	g*s	PROPN
iajs-400	1	64	d	d	X
iajs-400	1	65	−β	−β	ADJ
iajs-400	1	66	-sets	-set	NOUN
iajs-400	1	67	.	.	PUNCT
iajs-400	2	1	also	also	ADV
iajs-400	2	2	,	,	PUNCT
iajs-400	2	3	we	we	PRON
iajs-400	2	4	study	study	VERB
iajs-400	2	5	some	some	PRON
iajs-400	2	6	of	of	ADP
iajs-400	2	7	their	their	PRON
iajs-400	2	8	properties	property	NOUN
iajs-400	2	9	and	and	CCONJ
iajs-400	2	10	relations	relation	NOUN
iajs-400	2	11	among	among	ADP
iajs-400	2	12	them	they	PRON
iajs-400	2	13	.	.	PUNCT
iajs-400	3	1	moreover	moreover	ADV
iajs-400	3	2	,	,	PUNCT
iajs-400	3	3	we	we	PRON
iajs-400	3	4	use	use	VERB
iajs-400	3	5	these	these	DET
iajs-400	3	6	sets	set	NOUN
iajs-400	3	7	to	to	PART
iajs-400	3	8	define	define	VERB
iajs-400	3	9	and	and	CCONJ
iajs-400	3	10	study	study	VERB
iajs-400	3	11	some	some	DET
iajs-400	3	12	associative	associative	ADJ
iajs-400	3	13	separation	separation	NOUN
iajs-400	3	14	axioms	axiom	NOUN
iajs-400	3	15	.	.	PUNCT
iajs-400	4	1	keywords	keyword	NOUN
iajs-400	4	2	:	:	PUNCT
iajs-400	4	3	s*gid	s*gid	ADJ
iajs-400	4	4	-spaces	-space	NOUN
iajs-400	4	5	,	,	PUNCT
iajs-400	4	6	α	α	NOUN
iajs-400	4	7	-s*gid	-s*gid	ADJ
iajs-400	4	8	-spaces	-space	NOUN
iajs-400	4	9	,	,	PUNCT
iajs-400	4	10	pre	pre	ADJ
iajs-400	4	11	-	-	ADJ
iajs-400	4	12	s*gid	s*gid	ADJ
iajs-400	4	13	-space	-space	NOUN
iajs-400	4	14	,	,	PUNCT
iajs-400	4	15	b	b	X
iajs-400	4	16	-	-	PUNCT
iajs-400	4	17	s*gid	s*gid	ADJ
iajs-400	4	18	-spaces	-space	NOUN
iajs-400	4	19	,	,	PUNCT
iajs-400	4	20	β	β	X
iajs-400	4	21	-s*gid	-s*gid	X
iajs-400	4	22	-spaces	-space	NOUN
iajs-400	4	23	for	for	ADP
iajs-400	4	24	2,1,0i	2,1,0i	NUM
iajs-400	4	25	=	=	PRON
iajs-400	4	26	.	.	PUNCT
iajs-400	5	1	351	351	NUM
iajs-400	5	2	|	|	ADV
iajs-400	5	3	mathematics	mathematics	PROPN
iajs-400	5	4	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	5	5	�	�	NOUN
iajs-400	5	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	5	7	:	:	PUNCT
iajs-400	5	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	6	1	©	©	PROPN
iajs-400	6	2	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	6	3	ibn	ibn	PROPN
iajs-400	6	4	al	al	PROPN
iajs-400	6	5	-	-	PUNCT
iajs-400	6	6	haitham	haitham	PROPN
iajs-400	6	7	jour	jour	X
iajs-400	6	8	.	.	PROPN
iajs-400	6	9	for	for	ADP
iajs-400	6	10	pure	pure	ADJ
iajs-400	6	11	&	&	CCONJ
iajs-400	6	12	appl	appl	PROPN
iajs-400	6	13	.	.	PUNCT
iajs-400	7	1	sci	sci	PROPN
iajs-400	7	2	.	.	PUNCT
iajs-400	7	3	vol	vol	NOUN
iajs-400	7	4	.	.	PROPN
iajs-400	8	1	27	27	NUM
iajs-400	8	2	(	(	PUNCT
iajs-400	8	3	1	1	NUM
iajs-400	8	4	)	)	PUNCT
iajs-400	8	5	2014	2014	NUM
iajs-400	8	6	introduction	introduction	NOUN
iajs-400	8	7	tong	tong	PROPN
iajs-400	8	8	,	,	PUNCT
iajs-400	8	9	j	j	PROPN
iajs-400	8	10	.	.	PUNCT
iajs-400	9	1	[	[	X
iajs-400	9	2	1	1	NUM
iajs-400	9	3	]	]	PUNCT
iajs-400	9	4	,	,	PUNCT
iajs-400	9	5	calads	calad	NOUN
iajs-400	9	6	,	,	PUNCT
iajs-400	9	7	m.	m.	NOUN
iajs-400	10	1	[	[	X
iajs-400	10	2	2	2	NUM
iajs-400	10	3	]	]	PUNCT
iajs-400	10	4	,	,	PUNCT
iajs-400	10	5	calads	calad	NOUN
iajs-400	10	6	,	,	PUNCT
iajs-400	10	7	m.	m.	NOUN
iajs-400	10	8	and	and	CCONJ
iajs-400	10	9	et.al	et.al	ADJ
iajs-400	10	10	.	.	PUNCT
iajs-400	11	1	[	[	X
iajs-400	11	2	3	3	NUM
iajs-400	11	3	]	]	PUNCT
iajs-400	11	4	,	,	PUNCT
iajs-400	11	5	jafari	jafari	PROPN
iajs-400	11	6	,	,	PUNCT
iajs-400	11	7	s.	s.	PROPN
iajs-400	12	1	[	[	X
iajs-400	12	2	4	4	X
iajs-400	12	3	]	]	PUNCT
iajs-400	12	4	and	and	CCONJ
iajs-400	12	5	keskin	keskin	PROPN
iajs-400	12	6	,	,	PUNCT
iajs-400	12	7	a.	a.	NOUN
iajs-400	12	8	and	and	CCONJ
iajs-400	12	9	noiri	noiri	PROPN
iajs-400	12	10	,	,	PUNCT
iajs-400	12	11	t.	t.	PROPN
iajs-400	13	1	[	[	X
iajs-400	13	2	5	5	NUM
iajs-400	13	3	]	]	PUNCT
iajs-400	13	4	introduced	introduce	VERB
iajs-400	13	5	the	the	DET
iajs-400	13	6	notion	notion	NOUN
iajs-400	13	7	of	of	ADP
iajs-400	13	8	d	d	NOUN
iajs-400	13	9	-	-	PUNCT
iajs-400	13	10	sets	set	NOUN
iajs-400	13	11	,	,	PUNCT
iajs-400	13	12	sd	sd	ADP
iajs-400	13	13	-sets	-set	NOUN
iajs-400	13	14	,	,	PUNCT
iajs-400	13	15	αd	αd	PROPN
iajs-400	13	16	-sets	-set	NOUN
iajs-400	13	17	,	,	PUNCT
iajs-400	13	18	pred	pre	VERB
iajs-400	13	19	-sets	-set	NOUN
iajs-400	13	20	and	and	CCONJ
iajs-400	13	21	bd	bd	NOUN
iajs-400	13	22	-sets	-set	NOUN
iajs-400	13	23	respectively	respectively	ADV
iajs-400	13	24	by	by	ADP
iajs-400	13	25	using	use	VERB
iajs-400	13	26	open	open	ADJ
iajs-400	13	27	sets	set	NOUN
iajs-400	13	28	,	,	PUNCT
iajs-400	13	29	semi	semi	ADJ
iajs-400	13	30	-	-	ADJ
iajs-400	13	31	open	open	ADJ
iajs-400	13	32	sets	set	NOUN
iajs-400	13	33	,	,	PUNCT
iajs-400	13	34	α	α	NOUN
iajs-400	13	35	-	-	ADJ
iajs-400	13	36	open	open	ADJ
iajs-400	13	37	sets	set	NOUN
iajs-400	13	38	,	,	PUNCT
iajs-400	13	39	pre	pre	ADJ
iajs-400	13	40	-	-	ADJ
iajs-400	13	41	open	open	ADJ
iajs-400	13	42	sets	set	NOUN
iajs-400	13	43	and	and	CCONJ
iajs-400	13	44	b	b	X
iajs-400	13	45	-	-	PUNCT
iajs-400	13	46	open	open	ADJ
iajs-400	13	47	sets	set	NOUN
iajs-400	13	48	respectively	respectively	ADV
iajs-400	13	49	and	and	CCONJ
iajs-400	13	50	used	use	VERB
iajs-400	13	51	the	the	DET
iajs-400	13	52	notion	notion	NOUN
iajs-400	13	53	to	to	PART
iajs-400	13	54	define	define	VERB
iajs-400	13	55	some	some	DET
iajs-400	13	56	associative	associative	ADJ
iajs-400	13	57	separation	separation	NOUN
iajs-400	13	58	axioms	axiom	NOUN
iajs-400	13	59	.	.	PUNCT
iajs-400	14	1	khan	khan	PROPN
iajs-400	14	2	,	,	PUNCT
iajs-400	14	3	m.	m.	NOUN
iajs-400	14	4	and	and	CCONJ
iajs-400	14	5	et.al.[6	et.al.[6	NOUN
iajs-400	14	6	]	]	PUNCT
iajs-400	14	7	introduced	introduce	VERB
iajs-400	14	8	and	and	CCONJ
iajs-400	14	9	investigated	investigate	VERB
iajs-400	14	10	s*g	s*g	NOUN
iajs-400	14	11	-	-	PUNCT
iajs-400	14	12	closed	close	VERB
iajs-400	14	13	sets	set	NOUN
iajs-400	14	14	by	by	ADP
iajs-400	14	15	using	use	VERB
iajs-400	14	16	the	the	DET
iajs-400	14	17	concept	concept	NOUN
iajs-400	14	18	of	of	ADP
iajs-400	14	19	semi	semi	ADJ
iajs-400	14	20	-	-	ADJ
iajs-400	14	21	open	open	ADJ
iajs-400	14	22	sets	set	NOUN
iajs-400	14	23	.	.	PUNCT
iajs-400	15	1	in	in	ADP
iajs-400	15	2	this	this	DET
iajs-400	15	3	paper	paper	NOUN
iajs-400	15	4	we	we	PRON
iajs-400	15	5	introduce	introduce	VERB
iajs-400	15	6	and	and	CCONJ
iajs-400	15	7	investigate	investigate	VERB
iajs-400	15	8	new	new	ADJ
iajs-400	15	9	notions	notion	NOUN
iajs-400	15	10	called	call	VERB
iajs-400	15	11	g*sd	g*sd	PROPN
iajs-400	15	12	-sets	-set	NOUN
iajs-400	15	13	,	,	PUNCT
iajs-400	15	14	g*sd	g*sd	PROPN
iajs-400	15	15	−α	−α	PROPN
iajs-400	15	16	-sets	-set	NOUN
iajs-400	15	17	,	,	PUNCT
iajs-400	15	18	g*spred	g*spre	VERB
iajs-400	15	19	−	−	NOUN
iajs-400	15	20	sets	set	NOUN
iajs-400	15	21	,	,	PUNCT
iajs-400	15	22	g*sbd	g*sbd	VERB
iajs-400	15	23	−	−	NOUN
iajs-400	15	24	-sets	-set	NOUN
iajs-400	15	25	and	and	CCONJ
iajs-400	15	26	g*s	g*s	PROPN
iajs-400	16	1	d	d	X
iajs-400	16	2	−β	−β	ADJ
iajs-400	16	3	-sets	-set	NOUN
iajs-400	16	4	.	.	PUNCT
iajs-400	17	1	moreover	moreover	ADV
iajs-400	17	2	,	,	PUNCT
iajs-400	17	3	we	we	PRON
iajs-400	17	4	use	use	VERB
iajs-400	17	5	these	these	DET
iajs-400	17	6	notions	notion	NOUN
iajs-400	17	7	to	to	PART
iajs-400	17	8	define	define	VERB
iajs-400	17	9	some	some	DET
iajs-400	17	10	associative	associative	ADJ
iajs-400	17	11	separation	separation	NOUN
iajs-400	17	12	axioms	axiom	NOUN
iajs-400	17	13	.	.	PUNCT
iajs-400	18	1	recall	recall	VERB
iajs-400	18	2	that	that	SCONJ
iajs-400	18	3	a	a	DET
iajs-400	18	4	subset	subset	NOUN
iajs-400	18	5	a	a	PRON
iajs-400	18	6	of	of	ADP
iajs-400	18	7	a	a	DET
iajs-400	18	8	topological	topological	ADJ
iajs-400	18	9	space	space	NOUN
iajs-400	18	10	)	)	PUNCT
iajs-400	18	11	,	,	PUNCT
iajs-400	18	12	x	x	X
iajs-400	18	13	(	(	PUNCT
iajs-400	18	14	τ	τ	X
iajs-400	18	15	is	be	AUX
iajs-400	18	16	called	call	VERB
iajs-400	18	17	semi	semi	ADJ
iajs-400	18	18	-	-	ADJ
iajs-400	18	19	open	open	ADJ
iajs-400	18	20	[	[	X
iajs-400	18	21	7	7	NUM
iajs-400	18	22	]	]	X
iajs-400	18	23	(	(	PUNCT
iajs-400	18	24	resp	resp	NOUN
iajs-400	18	25	.	.	PUNCT
iajs-400	19	1	α	α	X
iajs-400	19	2	-open	-open	NOUN
iajs-400	20	1	[	[	X
iajs-400	20	2	8	8	NUM
iajs-400	20	3	]	]	PUNCT
iajs-400	20	4	,	,	PUNCT
iajs-400	20	5	pre	pre	ADJ
iajs-400	20	6	-	-	ADJ
iajs-400	20	7	open	open	ADJ
iajs-400	20	8	[	[	X
iajs-400	20	9	9	9	NUM
iajs-400	20	10	]	]	PUNCT
iajs-400	20	11	,	,	PUNCT
iajs-400	20	12	b	b	X
iajs-400	20	13	-	-	PUNCT
iajs-400	20	14	open[10	open[10	ADJ
iajs-400	20	15	]	]	PUNCT
iajs-400	20	16	and	and	CCONJ
iajs-400	20	17	β	β	X
iajs-400	20	18	-open	-open	NOUN
iajs-400	21	1	[	[	X
iajs-400	21	2	11	11	NUM
iajs-400	21	3	]	]	PUNCT
iajs-400	21	4	)	)	PUNCT
iajs-400	21	5	set	set	VERB
iajs-400	21	6	if	if	SCONJ
iajs-400	21	7	)	)	PUNCT
iajs-400	21	8	)	)	PUNCT
iajs-400	21	9	a(int(cla	a(int(cla	VERB
iajs-400	21	10	⊆	⊆	NUM
iajs-400	21	11	(	(	PUNCT
iajs-400	21	12	resp	resp	NOUN
iajs-400	21	13	.	.	PUNCT
iajs-400	21	14	)	)	PUNCT
iajs-400	21	15	)	)	PUNCT
iajs-400	21	16	)	)	PUNCT
iajs-400	21	17	a(int(clint(a	a(int(clint(a	PROPN
iajs-400	21	18	⊆	⊆	NUM
iajs-400	21	19	,	,	PUNCT
iajs-400	21	20	)	)	PUNCT
iajs-400	21	21	)	)	PUNCT
iajs-400	22	1	a(clint(a	a(clint(a	CCONJ
iajs-400	22	2	⊆	⊆	NUM
iajs-400	22	3	,	,	PUNCT
iajs-400	22	4	)	)	PUNCT
iajs-400	22	5	)	)	PUNCT
iajs-400	23	1	a(int(cl))a(clint(a	a(int(cl))a(clint(a	PROPN
iajs-400	23	2	⊆	⊆	PUNCT
iajs-400	23	3	and	and	CCONJ
iajs-400	23	4	)	)	PUNCT
iajs-400	23	5	)	)	PUNCT
iajs-400	23	6	)	)	PUNCT
iajs-400	23	7	a(cl(int(cla	a(cl(int(cla	VERB
iajs-400	23	8	⊆	⊆	NUM
iajs-400	23	9	)	)	PUNCT
iajs-400	23	10	.	.	PUNCT
iajs-400	24	1	also	also	ADV
iajs-400	24	2	,	,	PUNCT
iajs-400	24	3	a	a	DET
iajs-400	24	4	subset	subset	NOUN
iajs-400	24	5	a	a	PRON
iajs-400	24	6	of	of	ADP
iajs-400	24	7	a	a	DET
iajs-400	24	8	topological	topological	ADJ
iajs-400	24	9	space	space	NOUN
iajs-400	24	10	)	)	PUNCT
iajs-400	24	11	,	,	PUNCT
iajs-400	24	12	x	x	X
iajs-400	24	13	(	(	PUNCT
iajs-400	24	14	τ	τ	X
iajs-400	24	15	is	be	AUX
iajs-400	24	16	called	call	VERB
iajs-400	24	17	s*g	s*g	NOUN
iajs-400	24	18	-	-	PUNCT
iajs-400	24	19	closed	closed	ADJ
iajs-400	24	20	if	if	SCONJ
iajs-400	24	21	u)a(cl	u)a(cl	NUM
iajs-400	24	22	⊆	⊆	NUM
iajs-400	24	23	whenever	whenever	SCONJ
iajs-400	24	24	ua	ua	PROPN
iajs-400	24	25	⊆	⊆	NUM
iajs-400	24	26	and	and	CCONJ
iajs-400	24	27	u	u	NOUN
iajs-400	24	28	is	be	AUX
iajs-400	24	29	semi	semi	ADJ
iajs-400	24	30	-	-	ADJ
iajs-400	24	31	open	open	ADJ
iajs-400	24	32	in	in	ADP
iajs-400	24	33	x	x	PUNCT
iajs-400	24	34	[	[	X
iajs-400	24	35	6	6	NUM
iajs-400	24	36	]	]	PUNCT
iajs-400	24	37	.	.	PUNCT
iajs-400	25	1	the	the	DET
iajs-400	25	2	complement	complement	NOUN
iajs-400	25	3	of	of	ADP
iajs-400	25	4	an	an	DET
iajs-400	25	5	s*g	s*g	NOUN
iajs-400	25	6	-	-	PUNCT
iajs-400	25	7	closed	close	VERB
iajs-400	25	8	set	set	NOUN
iajs-400	25	9	is	be	AUX
iajs-400	25	10	defined	define	VERB
iajs-400	25	11	to	to	PART
iajs-400	25	12	be	be	AUX
iajs-400	25	13	s*g	s*g	NOUN
iajs-400	25	14	-	-	PUNCT
iajs-400	25	15	open	open	ADJ
iajs-400	25	16	.	.	PUNCT
iajs-400	26	1	the	the	DET
iajs-400	26	2	family	family	NOUN
iajs-400	26	3	of	of	ADP
iajs-400	26	4	all	all	DET
iajs-400	26	5	s*g	s*g	NOUN
iajs-400	26	6	-	-	PUNCT
iajs-400	26	7	open	open	ADJ
iajs-400	26	8	subsets	subset	NOUN
iajs-400	26	9	of	of	ADP
iajs-400	26	10	)	)	PUNCT
iajs-400	26	11	,	,	PUNCT
iajs-400	26	12	x	x	X
iajs-400	26	13	(	(	PUNCT
iajs-400	26	14	τ	τ	X
iajs-400	26	15	is	be	AUX
iajs-400	26	16	denoted	denote	VERB
iajs-400	26	17	by	by	ADP
iajs-400	26	18	)	)	PUNCT
iajs-400	26	19	,	,	PUNCT
iajs-400	26	20	x(go*s	x(go*s	PROPN
iajs-400	26	21	τ	τ	X
iajs-400	27	1	[	[	X
iajs-400	27	2	6	6	NUM
iajs-400	27	3	]	]	PUNCT
iajs-400	27	4	,	,	PUNCT
iajs-400	27	5	this	this	DET
iajs-400	27	6	family	family	NOUN
iajs-400	27	7	from	from	ADP
iajs-400	27	8	a	a	DET
iajs-400	27	9	topology	topology	NOUN
iajs-400	27	10	on	on	ADP
iajs-400	27	11	x	x	PUNCT
iajs-400	27	12	which	which	PRON
iajs-400	27	13	is	be	AUX
iajs-400	27	14	finer	fine	ADJ
iajs-400	27	15	than	than	ADP
iajs-400	27	16	τ	τ	PROPN
iajs-400	27	17	[	[	X
iajs-400	27	18	6	6	NUM
iajs-400	27	19	]	]	PUNCT
iajs-400	27	20	.	.	PUNCT
iajs-400	28	1	the	the	DET
iajs-400	28	2	s*g	s*g	NOUN
iajs-400	28	3	-	-	PUNCT
iajs-400	28	4	closure	closure	NOUN
iajs-400	28	5	of	of	ADP
iajs-400	28	6	a	a	PRON
iajs-400	28	7	,	,	PUNCT
iajs-400	28	8	denoted	denote	VERB
iajs-400	28	9	by	by	ADP
iajs-400	28	10	)	)	PUNCT
iajs-400	28	11	a(cl	a(cl	PROPN
iajs-400	28	12	g*s	g*s	PROPN
iajs-400	28	13	is	be	AUX
iajs-400	28	14	the	the	DET
iajs-400	28	15	intersection	intersection	NOUN
iajs-400	28	16	of	of	ADP
iajs-400	28	17	all	all	DET
iajs-400	28	18	s*g	s*g	NOUN
iajs-400	28	19	-	-	PUNCT
iajs-400	28	20	closed	close	VERB
iajs-400	28	21	subsets	subset	NOUN
iajs-400	28	22	of	of	ADP
iajs-400	28	23	x	x	PUNCT
iajs-400	28	24	which	which	PRON
iajs-400	28	25	contains	contain	VERB
iajs-400	28	26	a	a	PRON
iajs-400	28	27	and	and	CCONJ
iajs-400	28	28	the	the	DET
iajs-400	28	29	s*g	s*g	PROPN
iajs-400	28	30	-	-	PUNCT
iajs-400	28	31	interior	interior	NOUN
iajs-400	28	32	of	of	ADP
iajs-400	28	33	a	a	PRON
iajs-400	28	34	,	,	PUNCT
iajs-400	28	35	denoted	denote	VERB
iajs-400	28	36	by	by	ADP
iajs-400	28	37	)	)	PUNCT
iajs-400	28	38	a(int	a(int	PROPN
iajs-400	28	39	g*s	g*s	PROPN
iajs-400	28	40	is	be	AUX
iajs-400	28	41	the	the	DET
iajs-400	28	42	union	union	NOUN
iajs-400	28	43	of	of	ADP
iajs-400	28	44	all	all	DET
iajs-400	28	45	s*gopen	s*gopen	PROPN
iajs-400	28	46	sets	set	NOUN
iajs-400	28	47	in	in	ADP
iajs-400	28	48	x	x	PUNCT
iajs-400	28	49	which	which	PRON
iajs-400	28	50	are	be	AUX
iajs-400	28	51	contained	contain	VERB
iajs-400	28	52	in	in	ADP
iajs-400	28	53	a	a	DET
iajs-400	28	54	[	[	X
iajs-400	28	55	6	6	NUM
iajs-400	28	56	]	]	PUNCT
iajs-400	28	57	.	.	PUNCT
iajs-400	29	1	a	a	DET
iajs-400	29	2	function	function	NOUN
iajs-400	29	3	)	)	PUNCT
iajs-400	29	4	,	,	PUNCT
iajs-400	29	5	y(),x(:f	y(),x(:f	PROPN
iajs-400	29	6	σ→τ	σ→τ	NUM
iajs-400	29	7	is	be	AUX
iajs-400	29	8	called	call	VERB
iajs-400	29	9	s*gcontinuous	s*gcontinuous	ADJ
iajs-400	30	1	[	[	X
iajs-400	30	2	12	12	NUM
iajs-400	30	3	]	]	PUNCT
iajs-400	30	4	(	(	PUNCT
iajs-400	30	5	resp	resp	NOUN
iajs-400	30	6	.	.	PUNCT
iajs-400	30	7	s*g	s*g	PROPN
iajs-400	30	8	-	-	PUNCT
iajs-400	30	9	irresolute	irresolute	NOUN
iajs-400	31	1	[	[	X
iajs-400	31	2	12	12	NUM
iajs-400	31	3	]	]	PUNCT
iajs-400	31	4	)	)	PUNCT
iajs-400	32	1	if	if	SCONJ
iajs-400	32	2	the	the	DET
iajs-400	32	3	inverse	inverse	ADJ
iajs-400	32	4	image	image	NOUN
iajs-400	32	5	of	of	ADP
iajs-400	32	6	every	every	DET
iajs-400	32	7	open	open	ADJ
iajs-400	32	8	(	(	PUNCT
iajs-400	32	9	resp	resp	NOUN
iajs-400	32	10	.	.	PUNCT
iajs-400	32	11	s*g	s*g	NOUN
iajs-400	32	12	-	-	PUNCT
iajs-400	32	13	open	open	ADJ
iajs-400	32	14	)	)	PUNCT
iajs-400	32	15	subset	subset	NOUN
iajs-400	32	16	of	of	ADP
iajs-400	32	17	y	y	PROPN
iajs-400	32	18	is	be	AUX
iajs-400	32	19	an	an	DET
iajs-400	32	20	s*g	s*g	VERB
iajs-400	32	21	-	-	PUNCT
iajs-400	32	22	open	open	NOUN
iajs-400	32	23	set	set	NOUN
iajs-400	32	24	in	in	ADP
iajs-400	32	25	x	x	X
iajs-400	32	26	.	.	PUNCT
iajs-400	33	1	throughout	throughout	ADP
iajs-400	33	2	this	this	DET
iajs-400	33	3	paper	paper	NOUN
iajs-400	33	4	)	)	PUNCT
iajs-400	33	5	,	,	PUNCT
iajs-400	33	6	x	x	X
iajs-400	33	7	(	(	PUNCT
iajs-400	33	8	τ	τ	PROPN
iajs-400	33	9	and	and	CCONJ
iajs-400	33	10	)	)	PUNCT
iajs-400	33	11	,	,	PUNCT
iajs-400	33	12	y	y	PROPN
iajs-400	33	13	(	(	PUNCT
iajs-400	33	14	σ	σ	PROPN
iajs-400	33	15	(	(	PUNCT
iajs-400	33	16	or	or	CCONJ
iajs-400	33	17	simply	simply	ADV
iajs-400	33	18	x	x	X
iajs-400	33	19	and	and	CCONJ
iajs-400	33	20	y	y	X
iajs-400	33	21	)	)	PUNCT
iajs-400	33	22	represent	represent	VERB
iajs-400	33	23	non	non	ADJ
iajs-400	33	24	empty	empty	ADJ
iajs-400	33	25	topological	topological	ADJ
iajs-400	33	26	spaces	space	NOUN
iajs-400	33	27	on	on	ADP
iajs-400	33	28	which	which	PRON
iajs-400	33	29	no	no	DET
iajs-400	33	30	separation	separation	NOUN
iajs-400	33	31	axioms	axiom	NOUN
iajs-400	33	32	are	be	AUX
iajs-400	33	33	assumed	assume	VERB
iajs-400	33	34	,	,	PUNCT
iajs-400	33	35	unless	unless	SCONJ
iajs-400	33	36	otherwise	otherwise	ADV
iajs-400	33	37	mentioned	mention	VERB
iajs-400	33	38	.	.	PUNCT
iajs-400	34	1	preliminaries	preliminary	NOUN
iajs-400	34	2	first	first	ADV
iajs-400	34	3	we	we	PRON
iajs-400	34	4	recall	recall	VERB
iajs-400	34	5	the	the	DET
iajs-400	34	6	following	follow	VERB
iajs-400	34	7	definitions	definition	NOUN
iajs-400	34	8	.	.	PUNCT
iajs-400	35	1	definition(1.1)[1	definition(1.1)[1	PRON
iajs-400	35	2	]	]	X
iajs-400	35	3	:	:	PUNCT
iajs-400	35	4	a	a	DET
iajs-400	35	5	subset	subset	NOUN
iajs-400	35	6	a	a	PRON
iajs-400	35	7	of	of	ADP
iajs-400	35	8	a	a	DET
iajs-400	35	9	topological	topological	ADJ
iajs-400	35	10	space	space	NOUN
iajs-400	35	11	)	)	PUNCT
iajs-400	35	12	,	,	PUNCT
iajs-400	35	13	x	x	X
iajs-400	35	14	(	(	PUNCT
iajs-400	35	15	τ	τ	X
iajs-400	35	16	is	be	AUX
iajs-400	35	17	called	call	VERB
iajs-400	35	18	a	a	DET
iajs-400	35	19	d	d	NOUN
iajs-400	35	20	-	-	PUNCT
iajs-400	35	21	set	set	ADJ
iajs-400	35	22	if	if	SCONJ
iajs-400	35	23	there	there	PRON
iajs-400	35	24	are	be	VERB
iajs-400	35	25	two	two	NUM
iajs-400	35	26	open	open	ADJ
iajs-400	35	27	sets	set	NOUN
iajs-400	35	28	u	u	NOUN
iajs-400	35	29	and	and	CCONJ
iajs-400	35	30	v	v	NOUN
iajs-400	35	31	in	in	ADP
iajs-400	35	32	x	x	PUNCT
iajs-400	36	1	such	such	ADJ
iajs-400	36	2	that	that	SCONJ
iajs-400	36	3	xu	xu	PROPN
iajs-400	36	4	≠	≠	PROPN
iajs-400	36	5	and	and	CCONJ
iajs-400	36	6	v\ua	v\ua	PROPN
iajs-400	36	7	=	=	PUNCT
iajs-400	36	8	.	.	PUNCT
iajs-400	37	1	definition(1.2)[1	definition(1.2)[1	PROPN
iajs-400	37	2	]	]	PUNCT
iajs-400	37	3	:	:	PUNCT
iajs-400	37	4	a	a	DET
iajs-400	37	5	topological	topological	ADJ
iajs-400	37	6	space	space	NOUN
iajs-400	37	7	)	)	PUNCT
iajs-400	37	8	,	,	PUNCT
iajs-400	37	9	x	x	X
iajs-400	37	10	(	(	PUNCT
iajs-400	37	11	τ	τ	X
iajs-400	37	12	is	be	AUX
iajs-400	37	13	called	call	VERB
iajs-400	37	14	a	a	DET
iajs-400	37	15	0d	0d	NUM
iajs-400	37	16	-space	-space	NOUN
iajs-400	37	17	if	if	SCONJ
iajs-400	37	18	for	for	ADP
iajs-400	37	19	any	any	DET
iajs-400	37	20	two	two	NUM
iajs-400	37	21	distinct	distinct	ADJ
iajs-400	37	22	points	point	NOUN
iajs-400	37	23	x	x	PUNCT
iajs-400	37	24	and	and	CCONJ
iajs-400	37	25	y	y	PROPN
iajs-400	37	26	of	of	ADP
iajs-400	37	27	x	x	SYM
iajs-400	37	28	,	,	PUNCT
iajs-400	37	29	there	there	PRON
iajs-400	37	30	exists	exist	VERB
iajs-400	37	31	a	a	DET
iajs-400	37	32	d	d	NOUN
iajs-400	37	33	-	-	PUNCT
iajs-400	37	34	set	set	NOUN
iajs-400	37	35	of	of	ADP
iajs-400	37	36	x	x	PUNCT
iajs-400	37	37	containing	contain	VERB
iajs-400	37	38	one	one	NUM
iajs-400	37	39	of	of	ADP
iajs-400	37	40	the	the	DET
iajs-400	37	41	points	point	NOUN
iajs-400	37	42	but	but	CCONJ
iajs-400	37	43	not	not	PART
iajs-400	37	44	the	the	DET
iajs-400	37	45	other	other	ADJ
iajs-400	37	46	.	.	PUNCT
iajs-400	38	1	definition(1.3)[1	definition(1.3)[1	NOUN
iajs-400	38	2	]	]	X
iajs-400	38	3	:	:	PUNCT
iajs-400	38	4	a	a	DET
iajs-400	38	5	topological	topological	ADJ
iajs-400	38	6	space	space	NOUN
iajs-400	38	7	)	)	PUNCT
iajs-400	38	8	,	,	PUNCT
iajs-400	38	9	x	x	X
iajs-400	38	10	(	(	PUNCT
iajs-400	38	11	τ	τ	X
iajs-400	38	12	is	be	AUX
iajs-400	38	13	called	call	VERB
iajs-400	38	14	a	a	DET
iajs-400	38	15	1d	1d	NUM
iajs-400	38	16	-space	-space	NOUN
iajs-400	38	17	if	if	SCONJ
iajs-400	38	18	for	for	ADP
iajs-400	38	19	any	any	DET
iajs-400	38	20	two	two	NUM
iajs-400	38	21	distinct	distinct	ADJ
iajs-400	38	22	points	point	NOUN
iajs-400	38	23	x	x	PUNCT
iajs-400	38	24	and	and	CCONJ
iajs-400	38	25	y	y	PROPN
iajs-400	38	26	of	of	ADP
iajs-400	38	27	x	x	SYM
iajs-400	38	28	,	,	PUNCT
iajs-400	38	29	there	there	PRON
iajs-400	38	30	exists	exist	VERB
iajs-400	38	31	a	a	DET
iajs-400	38	32	d	d	NOUN
iajs-400	38	33	-	-	PUNCT
iajs-400	38	34	set	set	NOUN
iajs-400	38	35	of	of	ADP
iajs-400	38	36	x	x	PUNCT
iajs-400	38	37	containing	contain	VERB
iajs-400	38	38	x	x	NOUN
iajs-400	38	39	but	but	CCONJ
iajs-400	38	40	not	not	PART
iajs-400	38	41	y	y	PROPN
iajs-400	38	42	and	and	CCONJ
iajs-400	38	43	a	a	DET
iajs-400	38	44	d	d	NOUN
iajs-400	38	45	-	-	PUNCT
iajs-400	38	46	set	set	NOUN
iajs-400	38	47	of	of	ADP
iajs-400	38	48	x	x	PUNCT
iajs-400	38	49	containing	contain	VERB
iajs-400	38	50	y	y	NOUN
iajs-400	38	51	but	but	CCONJ
iajs-400	38	52	not	not	PART
iajs-400	38	53	x	x	X
iajs-400	38	54	.	.	PUNCT
iajs-400	39	1	definition(1.4)[1	definition(1.4)[1	PROPN
iajs-400	39	2	]	]	X
iajs-400	39	3	:	:	PUNCT
iajs-400	39	4	a	a	DET
iajs-400	39	5	topological	topological	ADJ
iajs-400	39	6	space	space	NOUN
iajs-400	39	7	)	)	PUNCT
iajs-400	39	8	,	,	PUNCT
iajs-400	39	9	x	x	X
iajs-400	39	10	(	(	PUNCT
iajs-400	39	11	τ	τ	X
iajs-400	39	12	is	be	AUX
iajs-400	39	13	called	call	VERB
iajs-400	39	14	a	a	DET
iajs-400	39	15	2d	2d	NUM
iajs-400	39	16	-space	-space	NOUN
iajs-400	39	17	if	if	SCONJ
iajs-400	39	18	for	for	ADP
iajs-400	39	19	any	any	DET
iajs-400	39	20	two	two	NUM
iajs-400	39	21	distinct	distinct	ADJ
iajs-400	39	22	points	point	NOUN
iajs-400	39	23	x	x	PUNCT
iajs-400	39	24	and	and	CCONJ
iajs-400	39	25	y	y	PROPN
iajs-400	39	26	of	of	ADP
iajs-400	39	27	x	x	SYM
iajs-400	39	28	,	,	PUNCT
iajs-400	39	29	there	there	PRON
iajs-400	39	30	are	be	VERB
iajs-400	39	31	two	two	NUM
iajs-400	39	32	d	d	NOUN
iajs-400	39	33	-	-	PUNCT
iajs-400	39	34	sets	set	NOUN
iajs-400	39	35	u	u	NOUN
iajs-400	39	36	and	and	CCONJ
iajs-400	39	37	v	v	NOUN
iajs-400	39	38	of	of	ADP
iajs-400	39	39	x	x	PUNCT
iajs-400	39	40	such	such	ADJ
iajs-400	39	41	that	that	SCONJ
iajs-400	39	42	ux∈	ux∈	PROPN
iajs-400	39	43	,	,	PUNCT
iajs-400	39	44	vy∈	vy∈	PROPN
iajs-400	39	45	and	and	CCONJ
iajs-400	39	46	φ	φ	NOUN
iajs-400	39	47	=	=	NOUN
iajs-400	39	48	vu	vu	X
iajs-400	39	49			PROPN
iajs-400	39	50	.	.	PUNCT
iajs-400	40	1	352	352	NUM
iajs-400	40	2	|	|	ADV
iajs-400	40	3	mathematics	mathematics	PROPN
iajs-400	40	4	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	40	5	�	�	NOUN
iajs-400	40	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	40	7	:	:	PUNCT
iajs-400	40	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	41	1	©	©	PROPN
iajs-400	41	2	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	41	3	ibn	ibn	PROPN
iajs-400	41	4	al	al	PROPN
iajs-400	41	5	-	-	PUNCT
iajs-400	41	6	haitham	haitham	PROPN
iajs-400	41	7	jour	jour	X
iajs-400	41	8	.	.	PROPN
iajs-400	41	9	for	for	ADP
iajs-400	41	10	pure	pure	ADJ
iajs-400	41	11	&	&	CCONJ
iajs-400	41	12	appl	appl	PROPN
iajs-400	41	13	.	.	PUNCT
iajs-400	42	1	sci	sci	PROPN
iajs-400	42	2	.	.	PUNCT
iajs-400	42	3	vol	vol	NOUN
iajs-400	42	4	.	.	PROPN
iajs-400	43	1	27	27	NUM
iajs-400	43	2	(	(	PUNCT
iajs-400	43	3	1	1	NUM
iajs-400	43	4	)	)	PUNCT
iajs-400	43	5	2014	2014	NUM
iajs-400	44	1	definition(1.5)[13	definition(1.5)[13	NOUN
iajs-400	44	2	]	]	PUNCT
iajs-400	44	3	:	:	PUNCT
iajs-400	44	4	a	a	DET
iajs-400	44	5	topological	topological	ADJ
iajs-400	44	6	space	space	NOUN
iajs-400	44	7	)	)	PUNCT
iajs-400	44	8	,	,	PUNCT
iajs-400	44	9	x	x	X
iajs-400	44	10	(	(	PUNCT
iajs-400	44	11	τ	τ	X
iajs-400	44	12	is	be	AUX
iajs-400	44	13	called	call	VERB
iajs-400	44	14	a	a	DET
iajs-400	44	15	door	door	NOUN
iajs-400	44	16	space	space	NOUN
iajs-400	44	17	if	if	SCONJ
iajs-400	44	18	each	each	DET
iajs-400	44	19	subset	subset	NOUN
iajs-400	44	20	of	of	ADP
iajs-400	44	21	x	x	PUNCT
iajs-400	44	22	is	be	AUX
iajs-400	44	23	either	either	CCONJ
iajs-400	44	24	open	open	ADJ
iajs-400	44	25	or	or	CCONJ
iajs-400	44	26	closed	closed	ADJ
iajs-400	44	27	.	.	PUNCT
iajs-400	45	1	theorem(1.6	theorem(1.6	NOUN
iajs-400	45	2	):	):	PUNCT
iajs-400	45	3	let	let	NOUN
iajs-400	45	4	)	)	PUNCT
iajs-400	45	5	,	,	PUNCT
iajs-400	45	6	x	x	X
iajs-400	45	7	(	(	PUNCT
iajs-400	45	8	τ	τ	X
iajs-400	45	9	be	be	AUX
iajs-400	45	10	a	a	DET
iajs-400	45	11	topological	topological	ADJ
iajs-400	45	12	space	space	NOUN
iajs-400	45	13	and	and	CCONJ
iajs-400	45	14	xb	xb	PROPN
iajs-400	45	15	,	,	PUNCT
iajs-400	45	16	a	a	DET
iajs-400	45	17	⊆	⊆	NUM
iajs-400	45	18	.	.	PUNCT
iajs-400	46	1	then	then	ADV
iajs-400	46	2	:	:	PUNCT
iajs-400	46	3	i	i	X
iajs-400	46	4	)	)	PUNCT
iajs-400	46	5	a)a(int)aint	a)a(int)aint	PROPN
iajs-400	46	6	(	(	PUNCT
iajs-400	46	7	g*s	g*s	PROPN
iajs-400	46	8	⊆⊆	⊆⊆	PROPN
iajs-400	46	9	and	and	CCONJ
iajs-400	46	10	)	)	PUNCT
iajs-400	46	11	a(cl)a(cla	a(cl)a(cla	NOUN
iajs-400	46	12	g*s	g*s	PROPN
iajs-400	46	13	⊆⊆	⊆⊆	PROPN
iajs-400	46	14	.	.	PUNCT
iajs-400	47	1	ii	ii	PROPN
iajs-400	47	2	)	)	PUNCT
iajs-400	47	3	)	)	PUNCT
iajs-400	48	1	a(int	a(int	PROPN
iajs-400	48	2	g*s	g*s	PROPN
iajs-400	48	3	is	be	AUX
iajs-400	48	4	an	an	DET
iajs-400	48	5	s*g	s*g	VERB
iajs-400	48	6	-	-	PUNCT
iajs-400	48	7	open	open	NOUN
iajs-400	48	8	set	set	NOUN
iajs-400	48	9	in	in	ADP
iajs-400	48	10	x	x	X
iajs-400	48	11	and	and	CCONJ
iajs-400	48	12	)	)	PUNCT
iajs-400	48	13	a(cl	a(cl	PROPN
iajs-400	48	14	g*s	g*s	PROPN
iajs-400	48	15	is	be	AUX
iajs-400	48	16	an	an	DET
iajs-400	48	17	s*g	s*g	NOUN
iajs-400	48	18	-	-	PUNCT
iajs-400	48	19	closed	close	VERB
iajs-400	48	20	set	set	NOUN
iajs-400	48	21	in	in	ADP
iajs-400	48	22	x	x	PROPN
iajs-400	48	23	.	.	PUNCT
iajs-400	48	24	iii	iii	X
iajs-400	48	25	)	)	PUNCT
iajs-400	48	26	if	if	SCONJ
iajs-400	48	27	ba	ba	PROPN
iajs-400	48	28	⊆	⊆	NUM
iajs-400	48	29	,	,	PUNCT
iajs-400	48	30	then	then	ADV
iajs-400	48	31	)	)	PUNCT
iajs-400	49	1	b(int)a(int	b(int)a(int	NOUN
iajs-400	49	2	g*sg*s	g*sg*s	PROPN
iajs-400	49	3	⊆	⊆	NUM
iajs-400	49	4	and	and	CCONJ
iajs-400	49	5	)	)	PUNCT
iajs-400	49	6	b(cl)a(cl	b(cl)a(cl	NOUN
iajs-400	49	7	g*sg*s	g*sg*s	PROPN
iajs-400	50	1	⊆	⊆	NUM
iajs-400	50	2	.	.	PUNCT
iajs-400	50	3	iv	iv	X
iajs-400	50	4	)	)	PUNCT
iajs-400	50	5	a	a	PRON
iajs-400	50	6	is	be	AUX
iajs-400	50	7	s*g	s*g	NOUN
iajs-400	50	8	-	-	PUNCT
iajs-400	50	9	open	open	ADJ
iajs-400	50	10	iff	iff	PROPN
iajs-400	50	11	a)a(int	a)a(int	PROPN
iajs-400	50	12	g*s	g*s	PROPN
iajs-400	51	1	=	=	PUNCT
iajs-400	51	2	and	and	CCONJ
iajs-400	51	3	a	a	PRON
iajs-400	51	4	is	be	AUX
iajs-400	51	5	s*g	s*g	NOUN
iajs-400	51	6	-	-	PUNCT
iajs-400	51	7	closed	close	VERB
iajs-400	51	8	iff	iff	PROPN
iajs-400	51	9	a)a(cl	a)a(cl	NOUN
iajs-400	51	10	g*s	g*s	PROPN
iajs-400	51	11	=	=	PUNCT
iajs-400	51	12	.	.	PUNCT
iajs-400	52	1	v	v	X
iajs-400	52	2	)	)	PUNCT
iajs-400	52	3	)	)	PUNCT
iajs-400	53	1	b(int)a(int)ba(int	b(int)a(int)ba(int	NOUN
iajs-400	53	2	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-400	53	3			PROPN
iajs-400	53	4	=	=	PUNCT
iajs-400	53	5	and	and	CCONJ
iajs-400	53	6	)	)	PUNCT
iajs-400	53	7	b(cl)a(cl)ba(cl	b(cl)a(cl)ba(cl	NOUN
iajs-400	53	8	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-400	54	1			PROPN
iajs-400	54	2	=	=	X
iajs-400	54	3	.	.	PUNCT
iajs-400	55	1	vi	vi	X
iajs-400	55	2	)	)	PUNCT
iajs-400	55	3	)	)	PUNCT
iajs-400	56	1	a(int))a((intint	a(int))a((intint	NOUN
iajs-400	56	2	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-400	56	3	=	=	SYM
iajs-400	56	4	and	and	CCONJ
iajs-400	56	5	)	)	PUNCT
iajs-400	56	6	a(cl))a(cl(cl	a(cl))a(cl(cl	NOUN
iajs-400	56	7	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-400	56	8	=	=	PUNCT
iajs-400	56	9	.	.	PUNCT
iajs-400	56	10	vii	vii	PROPN
iajs-400	56	11	)	)	PUNCT
iajs-400	56	12	)	)	PUNCT
iajs-400	57	1	ax(int)a(clx	ax(int)a(clx	PROPN
iajs-400	57	2	g*sg*s	g*sg*s	PROPN
iajs-400	57	3	−=−	−=−	PROPN
iajs-400	57	4	and	and	CCONJ
iajs-400	57	5	)	)	PUNCT
iajs-400	57	6	ax(cl)a(intx	ax(cl)a(intx	PROPN
iajs-400	57	7	g*sg*s	g*sg*s	PROPN
iajs-400	57	8	−=−	−=−	NOUN
iajs-400	57	9	.	.	PUNCT
iajs-400	58	1	viii	viii	ADJ
iajs-400	58	2	)	)	PUNCT
iajs-400	58	3	)	)	PUNCT
iajs-400	59	1	a(intx	a(intx	VERB
iajs-400	59	2	g*s∈	g*s∈	VERB
iajs-400	60	1	iff	iff	VERB
iajs-400	60	2	there	there	PRON
iajs-400	60	3	is	be	VERB
iajs-400	60	4	an	an	DET
iajs-400	60	5	s*g	s*g	NOUN
iajs-400	60	6	-	-	PUNCT
iajs-400	60	7	open	open	NOUN
iajs-400	60	8	set	set	NOUN
iajs-400	60	9	u	u	NOUN
iajs-400	60	10	in	in	ADP
iajs-400	60	11	x	x	X
iajs-400	60	12	s.t	s.t	PROPN
iajs-400	60	13	aux	aux	PROPN
iajs-400	60	14	⊆∈	⊆∈	NUM
iajs-400	60	15	.	.	PUNCT
iajs-400	61	1	ix	ix	ADV
iajs-400	61	2	)	)	PUNCT
iajs-400	61	3	)	)	PUNCT
iajs-400	62	1	a(clx	a(clx	NOUN
iajs-400	62	2	g*s∈	g*s∈	AUX
iajs-400	62	3	iff	iff	VERB
iajs-400	62	4	for	for	ADP
iajs-400	62	5	every	every	DET
iajs-400	62	6	s*g	s*g	NOUN
iajs-400	62	7	-	-	PUNCT
iajs-400	62	8	open	open	ADJ
iajs-400	62	9	set	set	NOUN
iajs-400	62	10	u	u	NOUN
iajs-400	62	11	containing	contain	VERB
iajs-400	62	12	x	x	PUNCT
iajs-400	62	13	,	,	PUNCT
iajs-400	62	14	φ≠au	φ≠au	PROPN
iajs-400	62	15			PROPN
iajs-400	62	16	.	.	PUNCT
iajs-400	63	1	x	x	X
iajs-400	63	2	)	)	PUNCT
iajs-400	63	3	)	)	PUNCT
iajs-400	63	4	u(cl)u(cl	u(cl)u(cl	PROPN
iajs-400	64	1	g*sg*s	g*sg*s	PROPN
iajs-400	64	2			ADJ
iajs-400	64	3	∧∈α	∧∈α	NOUN
iajs-400	65	1	α	α	PRON
iajs-400	65	2	∧∈α	∧∈α	NOUN
iajs-400	65	3	α	α	NOUN
iajs-400	65	4	⊆	⊆	NUM
iajs-400	65	5	and	and	CCONJ
iajs-400	65	6	)	)	PUNCT
iajs-400	65	7	u(int)u(int	u(int)u(int	PROPN
iajs-400	65	8	g*sg*s	g*sg*s	PROPN
iajs-400	66	1			ADJ
iajs-400	66	2	∧∈α	∧∈α	NOUN
iajs-400	67	1	α	α	DET
iajs-400	67	2	∧∈α	∧∈α	NOUN
iajs-400	67	3	α	α	NOUN
iajs-400	67	4	⊆	⊆	NUM
iajs-400	67	5	.	.	PUNCT
iajs-400	68	1	proof	proof	NOUN
iajs-400	68	2	:	:	PUNCT
iajs-400	68	3	it	it	PRON
iajs-400	68	4	is	be	AUX
iajs-400	68	5	a	a	DET
iajs-400	68	6	obvious	obvious	ADJ
iajs-400	68	7	.	.	PUNCT
iajs-400	69	1	in	in	ADP
iajs-400	69	2	this	this	DET
iajs-400	69	3	paper	paper	NOUN
iajs-400	69	4	we	we	PRON
iajs-400	69	5	introduce	introduce	VERB
iajs-400	69	6	and	and	CCONJ
iajs-400	69	7	investigate	investigate	VERB
iajs-400	69	8	new	new	ADJ
iajs-400	69	9	notions	notion	NOUN
iajs-400	69	10	called	call	VERB
iajs-400	69	11	α	α	DET
iajs-400	69	12	-s*g	-s*g	ADJ
iajs-400	69	13	-	-	PUNCT
iajs-400	69	14	open	open	ADJ
iajs-400	69	15	sets	set	NOUN
iajs-400	69	16	,	,	PUNCT
iajs-400	69	17	pre	pre	VERB
iajs-400	69	18	-s*gopen	-s*gopen	VERB
iajs-400	69	19	sets	set	NOUN
iajs-400	69	20	,	,	PUNCT
iajs-400	69	21	b	b	X
iajs-400	69	22	-	-	PUNCT
iajs-400	69	23	s*g	s*g	VERB
iajs-400	69	24	-	-	PUNCT
iajs-400	69	25	open	open	ADJ
iajs-400	69	26	sets	set	NOUN
iajs-400	69	27	andβ	andβ	ADV
iajs-400	69	28	-s*g	-s*g	ADJ
iajs-400	69	29	-	-	PUNCT
iajs-400	69	30	open	open	ADJ
iajs-400	69	31	sets	set	NOUN
iajs-400	69	32	which	which	PRON
iajs-400	69	33	are	be	AUX
iajs-400	69	34	weaker	weak	ADJ
iajs-400	69	35	than	than	SCONJ
iajs-400	69	36	s*g	s*g	VERB
iajs-400	69	37	-	-	PUNCT
iajs-400	69	38	open	open	ADJ
iajs-400	69	39	.	.	PUNCT
iajs-400	70	1	moreover	moreover	ADV
iajs-400	70	2	,	,	PUNCT
iajs-400	70	3	we	we	PRON
iajs-400	70	4	use	use	VERB
iajs-400	70	5	these	these	DET
iajs-400	70	6	notions	notion	NOUN
iajs-400	70	7	to	to	PART
iajs-400	70	8	define	define	VERB
iajs-400	70	9	some	some	DET
iajs-400	70	10	associative	associative	ADJ
iajs-400	70	11	separation	separation	NOUN
iajs-400	70	12	axioms	axiom	NOUN
iajs-400	70	13	.	.	PUNCT
iajs-400	71	1	2	2	X
iajs-400	71	2	.	.	X
iajs-400	71	3	weak	weak	ADJ
iajs-400	71	4	forms	form	NOUN
iajs-400	71	5	of	of	ADP
iajs-400	71	6	s*g	s*g	NOUN
iajs-400	71	7	-	-	PUNCT
iajs-400	71	8	open	open	ADJ
iajs-400	71	9	sets	set	NOUN
iajs-400	71	10	in	in	ADP
iajs-400	71	11	this	this	DET
iajs-400	71	12	section	section	NOUN
iajs-400	71	13	we	we	PRON
iajs-400	71	14	introduce	introduce	VERB
iajs-400	71	15	the	the	DET
iajs-400	71	16	following	follow	VERB
iajs-400	71	17	notions	notion	NOUN
iajs-400	71	18	.	.	PUNCT
iajs-400	72	1	definitions(2.1	definitions(2.1	NOUN
iajs-400	72	2	):	):	PUNCT
iajs-400	72	3	a	a	DET
iajs-400	72	4	subset	subset	NOUN
iajs-400	72	5	a	a	PRON
iajs-400	72	6	of	of	ADP
iajs-400	72	7	a	a	DET
iajs-400	72	8	topological	topological	ADJ
iajs-400	72	9	space	space	NOUN
iajs-400	72	10	)	)	PUNCT
iajs-400	72	11	,	,	PUNCT
iajs-400	72	12	x	x	X
iajs-400	72	13	(	(	PUNCT
iajs-400	72	14	τ	τ	X
iajs-400	72	15	is	be	AUX
iajs-400	72	16	said	say	VERB
iajs-400	72	17	to	to	PART
iajs-400	72	18	be	be	AUX
iajs-400	72	19	:	:	PUNCT
iajs-400	72	20	i	i	X
iajs-400	72	21	)	)	PUNCT
iajs-400	72	22	an	an	DET
iajs-400	72	23	α	α	NOUN
iajs-400	72	24	-s*g	-s*g	ADJ
iajs-400	72	25	-	-	PUNCT
iajs-400	72	26	open	open	NOUN
iajs-400	72	27	set	set	NOUN
iajs-400	72	28	if	if	SCONJ
iajs-400	72	29	)	)	PUNCT
iajs-400	72	30	)	)	PUNCT
iajs-400	72	31	)	)	PUNCT
iajs-400	73	1	a((intcl(inta	a((intcl(inta	PROPN
iajs-400	73	2	g*sg*s⊆	g*sg*s⊆	X
iajs-400	73	3	.	.	PUNCT
iajs-400	73	4	ii	ii	PROPN
iajs-400	73	5	)	)	PUNCT
iajs-400	73	6	a	a	DET
iajs-400	73	7	pre	pre	ADJ
iajs-400	73	8	-	-	ADJ
iajs-400	73	9	s*g	s*g	ADJ
iajs-400	73	10	-	-	PUNCT
iajs-400	73	11	open	open	NOUN
iajs-400	73	12	set	set	NOUN
iajs-400	73	13	if	if	SCONJ
iajs-400	73	14	)	)	PUNCT
iajs-400	73	15	)	)	PUNCT
iajs-400	73	16	a(cl(inta	a(cl(inta	ADP
iajs-400	73	17	g*s⊆	g*s⊆	NOUN
iajs-400	73	18	.	.	PUNCT
iajs-400	74	1	iii	iii	X
iajs-400	74	2	)	)	PUNCT
iajs-400	74	3	a	a	DET
iajs-400	74	4	b	b	X
iajs-400	74	5	-	-	PUNCT
iajs-400	74	6	s*g	s*g	VERB
iajs-400	74	7	-	-	PUNCT
iajs-400	74	8	open	open	NOUN
iajs-400	74	9	set	set	NOUN
iajs-400	74	10	if	if	SCONJ
iajs-400	74	11	)	)	PUNCT
iajs-400	74	12	)	)	PUNCT
iajs-400	74	13	a((intcl))a(cl(inta	a((intcl))a(cl(inta	PROPN
iajs-400	74	14	g*sg*s	g*sg*s	PROPN
iajs-400	74	15	⊆	⊆	PROPN
iajs-400	74	16	.	.	PUNCT
iajs-400	75	1	iv	iv	X
iajs-400	75	2	)	)	PUNCT
iajs-400	75	3	aβ	aβ	PRON
iajs-400	75	4	-s*g	-s*g	ADJ
iajs-400	75	5	-	-	PUNCT
iajs-400	75	6	open	open	NOUN
iajs-400	75	7	set	set	NOUN
iajs-400	75	8	if	if	SCONJ
iajs-400	75	9	)	)	PUNCT
iajs-400	75	10	)	)	PUNCT
iajs-400	75	11	)	)	PUNCT
iajs-400	75	12	a(cl((intcla	a(cl((intcla	VERB
iajs-400	75	13	g*s⊆	g*s⊆	NOUN
iajs-400	75	14	.	.	PUNCT
iajs-400	76	1	lemma(2.2	lemma(2.2	ADJ
iajs-400	76	2	):	):	PUNCT
iajs-400	76	3	let	let	NOUN
iajs-400	76	4	)	)	PUNCT
iajs-400	76	5	,	,	PUNCT
iajs-400	76	6	x	x	X
iajs-400	76	7	(	(	PUNCT
iajs-400	76	8	τ	τ	X
iajs-400	76	9	be	be	AUX
iajs-400	76	10	a	a	DET
iajs-400	76	11	topological	topological	ADJ
iajs-400	76	12	space	space	NOUN
iajs-400	76	13	,	,	PUNCT
iajs-400	76	14	then	then	ADV
iajs-400	76	15	the	the	DET
iajs-400	76	16	following	follow	VERB
iajs-400	76	17	properties	property	NOUN
iajs-400	76	18	hold	hold	VERB
iajs-400	76	19	:	:	PUNCT
iajs-400	77	1	i	i	NOUN
iajs-400	77	2	)	)	PUNCT
iajs-400	77	3	every	every	DET
iajs-400	77	4	α	α	PROPN
iajs-400	77	5	-open	-open	NOUN
iajs-400	77	6	(	(	PUNCT
iajs-400	77	7	resp	resp	NOUN
iajs-400	77	8	.	.	PUNCT
iajs-400	78	1	pre	pre	VERB
iajs-400	78	2	-	-	ADJ
iajs-400	78	3	open	open	ADJ
iajs-400	78	4	,	,	PUNCT
iajs-400	78	5	b	b	X
iajs-400	78	6	-	-	PUNCT
iajs-400	78	7	open	open	ADJ
iajs-400	78	8	,	,	PUNCT
iajs-400	78	9	β	β	X
iajs-400	78	10	-open	-open	NOUN
iajs-400	78	11	)	)	PUNCT
iajs-400	78	12	set	set	NOUN
iajs-400	78	13	is	be	AUX
iajs-400	78	14	α	α	DET
iajs-400	78	15	-s*g	-s*g	ADJ
iajs-400	78	16	-	-	PUNCT
iajs-400	78	17	open	open	ADJ
iajs-400	78	18	(	(	PUNCT
iajs-400	78	19	resp	resp	NOUN
iajs-400	78	20	.	.	PUNCT
iajs-400	79	1	pre	pre	ADJ
iajs-400	79	2	-	-	ADJ
iajs-400	79	3	s*g	s*g	ADJ
iajs-400	79	4	-	-	PUNCT
iajs-400	79	5	open	open	ADJ
iajs-400	79	6	,	,	PUNCT
iajs-400	79	7	bs*g	bs*g	X
iajs-400	79	8	open	open	ADJ
iajs-400	79	9	,	,	PUNCT
iajs-400	79	10	β	β	X
iajs-400	79	11	-s*g	-s*g	ADJ
iajs-400	79	12	-	-	PUNCT
iajs-400	79	13	open	open	ADJ
iajs-400	79	14	)	)	PUNCT
iajs-400	79	15	set	set	VERB
iajs-400	79	16	.	.	PUNCT
iajs-400	80	1	ii	ii	X
iajs-400	80	2	)	)	PUNCT
iajs-400	80	3	every	every	DET
iajs-400	80	4	s*g	s*g	NOUN
iajs-400	80	5	-	-	PUNCT
iajs-400	80	6	open	open	ADJ
iajs-400	80	7	set	set	NOUN
iajs-400	80	8	is	be	AUX
iajs-400	80	9	α	α	DET
iajs-400	80	10	-s*g	-s*g	NOUN
iajs-400	80	11	-	-	PUNCT
iajs-400	80	12	open	open	ADJ
iajs-400	80	13	.	.	PUNCT
iajs-400	81	1	iii	iii	X
iajs-400	81	2	)	)	PUNCT
iajs-400	81	3	every	every	DET
iajs-400	81	4	α	α	DET
iajs-400	81	5	-s*g	-s*g	ADJ
iajs-400	81	6	-	-	PUNCT
iajs-400	81	7	open	open	ADJ
iajs-400	81	8	set	set	NOUN
iajs-400	81	9	is	be	AUX
iajs-400	81	10	pre	pre	ADJ
iajs-400	81	11	-	-	ADJ
iajs-400	81	12	s*g	s*g	ADJ
iajs-400	81	13	-	-	PUNCT
iajs-400	81	14	open	open	ADJ
iajs-400	81	15	.	.	PUNCT
iajs-400	82	1	iv	iv	X
iajs-400	82	2	)	)	PUNCT
iajs-400	82	3	every	every	DET
iajs-400	82	4	pre	pre	ADJ
iajs-400	82	5	-	-	ADJ
iajs-400	82	6	s*g	s*g	ADJ
iajs-400	82	7	-	-	PUNCT
iajs-400	82	8	open	open	ADJ
iajs-400	82	9	set	set	NOUN
iajs-400	82	10	is	be	AUX
iajs-400	82	11	b	b	NOUN
iajs-400	82	12	-	-	PUNCT
iajs-400	82	13	s*g	s*g	NOUN
iajs-400	82	14	-	-	PUNCT
iajs-400	82	15	open	open	ADJ
iajs-400	82	16	.	.	PUNCT
iajs-400	83	1	v	v	X
iajs-400	83	2	)	)	PUNCT
iajs-400	83	3	every	every	DET
iajs-400	83	4	b	b	X
iajs-400	83	5	-	-	PUNCT
iajs-400	83	6	s*g	s*g	VERB
iajs-400	83	7	-	-	PUNCT
iajs-400	83	8	open	open	NOUN
iajs-400	83	9	set	set	VERB
iajs-400	83	10	isβ	isβ	PROPN
iajs-400	83	11	-s*g	-s*g	NOUN
iajs-400	83	12	-	-	PUNCT
iajs-400	83	13	open	open	ADJ
iajs-400	83	14	.	.	PUNCT
iajs-400	84	1	proof	proof	NOUN
iajs-400	84	2	:	:	PUNCT
iajs-400	84	3	it	it	PRON
iajs-400	84	4	is	be	AUX
iajs-400	84	5	obvious	obvious	ADJ
iajs-400	84	6	.	.	PUNCT
iajs-400	85	1	since	since	SCONJ
iajs-400	85	2	every	every	DET
iajs-400	85	3	open	open	ADJ
iajs-400	85	4	set	set	NOUN
iajs-400	85	5	is	be	AUX
iajs-400	85	6	s*g	s*g	NOUN
iajs-400	85	7	-	-	PUNCT
iajs-400	85	8	open	open	ADJ
iajs-400	85	9	,	,	PUNCT
iajs-400	85	10	then	then	ADV
iajs-400	85	11	we	we	PRON
iajs-400	85	12	have	have	VERB
iajs-400	85	13	the	the	DET
iajs-400	85	14	following	follow	VERB
iajs-400	85	15	diagram	diagram	NOUN
iajs-400	85	16	for	for	ADP
iajs-400	85	17	some	some	DET
iajs-400	85	18	types	type	NOUN
iajs-400	85	19	of	of	ADP
iajs-400	85	20	open	open	ADJ
iajs-400	85	21	sets	set	NOUN
iajs-400	85	22	and	and	CCONJ
iajs-400	85	23	s*g	s*g	VERB
iajs-400	85	24	-	-	PUNCT
iajs-400	85	25	open	open	ADJ
iajs-400	85	26	set	set	NOUN
iajs-400	85	27	.	.	PUNCT
iajs-400	86	1	353	353	NUM
iajs-400	87	1	|	|	ADV
iajs-400	87	2	mathematics	mathematics	PROPN
iajs-400	87	3	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	87	4	�	�	NOUN
iajs-400	87	5	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	87	6	:	:	PUNCT
iajs-400	87	7	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	87	8	©	©	PROPN
iajs-400	87	9	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	87	10	ibn	ibn	PROPN
iajs-400	87	11	al	al	PROPN
iajs-400	87	12	-	-	PUNCT
iajs-400	87	13	haitham	haitham	PROPN
iajs-400	87	14	jour	jour	X
iajs-400	87	15	.	.	PROPN
iajs-400	88	1	for	for	ADP
iajs-400	88	2	pure	pure	ADJ
iajs-400	88	3	&	&	CCONJ
iajs-400	88	4	appl	appl	PROPN
iajs-400	88	5	.	.	PUNCT
iajs-400	89	1	sci	sci	PROPN
iajs-400	89	2	.	.	PUNCT
iajs-400	89	3	vol	vol	NOUN
iajs-400	89	4	.	.	PROPN
iajs-400	90	1	27	27	NUM
iajs-400	90	2	(	(	PUNCT
iajs-400	90	3	1	1	NUM
iajs-400	90	4	)	)	PUNCT
iajs-400	90	5	2014	2014	NUM
iajs-400	90	6	figure	figure	NOUN
iajs-400	90	7	no	no	INTJ
iajs-400	90	8	.	.	PUNCT
iajs-400	91	1	(	(	PUNCT
iajs-400	91	2	1	1	NUM
iajs-400	91	3	):	):	PUNCT
iajs-400	91	4	relations	relation	NOUN
iajs-400	91	5	between	between	ADP
iajs-400	91	6	some	some	DET
iajs-400	91	7	types	type	NOUN
iajs-400	91	8	of	of	ADP
iajs-400	91	9	open	open	ADJ
iajs-400	91	10	sets	set	NOUN
iajs-400	91	11	and	and	CCONJ
iajs-400	91	12	s*g	s*g	VERB
iajs-400	91	13	-	-	PUNCT
iajs-400	91	14	open	open	ADJ
iajs-400	91	15	sets	set	VERB
iajs-400	91	16	the	the	DET
iajs-400	91	17	converses	converse	NOUN
iajs-400	91	18	need	need	AUX
iajs-400	91	19	not	not	PART
iajs-400	91	20	be	be	AUX
iajs-400	91	21	true	true	ADJ
iajs-400	91	22	in	in	ADP
iajs-400	91	23	general	general	ADJ
iajs-400	91	24	as	as	SCONJ
iajs-400	91	25	shown	show	VERB
iajs-400	91	26	by	by	ADP
iajs-400	91	27	the	the	DET
iajs-400	91	28	following	follow	VERB
iajs-400	91	29	examples	example	NOUN
iajs-400	91	30	.	.	PUNCT
iajs-400	92	1	example(2.3	example(2.3	ADJ
iajs-400	92	2	):	):	PUNCT
iajs-400	92	3	let	let	VERB
iajs-400	92	4	}	}	PUNCT
iajs-400	92	5	c	c	NOUN
iajs-400	92	6	,	,	PUNCT
iajs-400	92	7	b	b	NOUN
iajs-400	92	8	,	,	PUNCT
iajs-400	92	9	a{x	a{x	VERB
iajs-400	92	10	=	=	PUNCT
iajs-400	92	11	with	with	ADP
iajs-400	92	12	the	the	DET
iajs-400	92	13	indiscrete	indiscrete	ADJ
iajs-400	92	14	topology	topology	NOUN
iajs-400	92	15	}	}	PUNCT
iajs-400	92	16	,	,	PUNCT
iajs-400	92	17	x{i	x{i	PROPN
iajs-400	92	18	φ==τ	φ==τ	PROPN
iajs-400	92	19	.	.	PUNCT
iajs-400	93	1	then	then	ADV
iajs-400	93	2	}	}	PUNCT
iajs-400	93	3	b	b	X
iajs-400	93	4	,	,	PUNCT
iajs-400	93	5	a	a	PRON
iajs-400	93	6	{	{	PUNCT
iajs-400	93	7	is	be	AUX
iajs-400	93	8	an	an	DET
iajs-400	93	9	s*g	s*g	NOUN
iajs-400	93	10	-	-	PUNCT
iajs-400	93	11	open	open	ADJ
iajs-400	93	12	(	(	PUNCT
iajs-400	93	13	resp	resp	NOUN
iajs-400	93	14	.	.	PUNCT
iajs-400	94	1	α	α	DET
iajs-400	94	2	-s*g	-s*g	ADJ
iajs-400	94	3	-	-	PUNCT
iajs-400	94	4	open	open	ADJ
iajs-400	94	5	)	)	PUNCT
iajs-400	94	6	set	set	NOUN
iajs-400	94	7	,	,	PUNCT
iajs-400	94	8	but	but	CCONJ
iajs-400	94	9	it	it	PRON
iajs-400	94	10	is	be	AUX
iajs-400	94	11	not	not	PART
iajs-400	94	12	open	open	ADJ
iajs-400	94	13	(	(	PUNCT
iajs-400	94	14	resp	resp	NOUN
iajs-400	94	15	.	.	PUNCT
iajs-400	95	1	not	not	PART
iajs-400	95	2	α	α	NOUN
iajs-400	95	3	-open	-open	NOUN
iajs-400	95	4	)	)	PUNCT
iajs-400	95	5	set	set	NOUN
iajs-400	95	6	.	.	PUNCT
iajs-400	96	1	example(2.4	example(2.4	ADV
iajs-400	96	2	):	):	PUNCT
iajs-400	96	3	let	let	VERB
iajs-400	96	4	}	}	PUNCT
iajs-400	96	5	d	d	NOUN
iajs-400	96	6	,	,	PUNCT
iajs-400	96	7	c	c	X
iajs-400	96	8	,	,	PUNCT
iajs-400	96	9	b	b	PROPN
iajs-400	96	10	,	,	PUNCT
iajs-400	96	11	a{x	a{x	VERB
iajs-400	96	12	=	=	SYM
iajs-400	96	13	&	&	CCONJ
iajs-400	96	14	}	}	PUNCT
iajs-400	96	15	}	}	PUNCT
iajs-400	96	16	d	d	PROPN
iajs-400	96	17	,	,	PUNCT
iajs-400	96	18	b	b	PROPN
iajs-400	96	19	,	,	PUNCT
iajs-400	96	20	a{},c	a{},c	PROPN
iajs-400	96	21	,	,	PUNCT
iajs-400	96	22	a{},a{,,x	a{},a{,,x	PROPN
iajs-400	96	23	{	{	PUNCT
iajs-400	96	24	φ	φ	PROPN
iajs-400	96	25	=	=	PROPN
iajs-400	96	26	τ	τ	X
iajs-400	96	27	.	.	PUNCT
iajs-400	97	1	then	then	ADV
iajs-400	97	2	}	}	PUNCT
iajs-400	97	3	d	d	X
iajs-400	97	4	,	,	PUNCT
iajs-400	97	5	c	c	X
iajs-400	97	6	,	,	PUNCT
iajs-400	97	7	a	a	PRON
iajs-400	97	8	{	{	PUNCT
iajs-400	97	9	is	be	AUX
iajs-400	97	10	anα	anα	PROPN
iajs-400	97	11	-s*gopen	-s*gopen	PROPN
iajs-400	97	12	set	set	VERB
iajs-400	97	13	,	,	PUNCT
iajs-400	97	14	but	but	CCONJ
iajs-400	97	15	it	it	PRON
iajs-400	97	16	is	be	AUX
iajs-400	97	17	not	not	PART
iajs-400	97	18	s*g	s*g	NOUN
iajs-400	97	19	-	-	PUNCT
iajs-400	97	20	open	open	ADJ
iajs-400	97	21	.	.	PUNCT
iajs-400	98	1	example(2.5	example(2.5	NOUN
iajs-400	98	2	):	):	PUNCT
iajs-400	98	3	let	let	VERB
iajs-400	98	4	ℜ=x	ℜ=x	NOUN
iajs-400	98	5	with	with	ADP
iajs-400	98	6	the	the	DET
iajs-400	98	7	usual	usual	ADJ
iajs-400	98	8	topology	topology	NOUN
iajs-400	98	9	τ	τ	X
iajs-400	98	10	.	.	PUNCT
iajs-400	99	1	let	let	VERB
iajs-400	99	2	qa	qa	PROPN
iajs-400	99	3	=	=	PUNCT
iajs-400	99	4	be	be	AUX
iajs-400	99	5	the	the	DET
iajs-400	99	6	set	set	NOUN
iajs-400	99	7	of	of	ADP
iajs-400	99	8	all	all	DET
iajs-400	99	9	rational	rational	ADJ
iajs-400	99	10	numbers	number	NOUN
iajs-400	99	11	.	.	PUNCT
iajs-400	100	1	then	then	ADV
iajs-400	100	2	a	a	PRON
iajs-400	100	3	is	be	AUX
iajs-400	100	4	an	an	DET
iajs-400	100	5	pre	pre	ADJ
iajs-400	100	6	-	-	ADJ
iajs-400	100	7	s*g	s*g	ADJ
iajs-400	100	8	-	-	PUNCT
iajs-400	100	9	open	open	ADJ
iajs-400	100	10	set	set	NOUN
iajs-400	100	11	(	(	PUNCT
iajs-400	100	12	since	since	SCONJ
iajs-400	100	13	a	a	PRON
iajs-400	100	14	is	be	AUX
iajs-400	100	15	pre	pre	ADJ
iajs-400	100	16	-	-	ADJ
iajs-400	100	17	open	open	ADJ
iajs-400	100	18	set	set	NOUN
iajs-400	100	19	)	)	PUNCT
iajs-400	100	20	which	which	PRON
iajs-400	100	21	is	be	AUX
iajs-400	100	22	not	not	PART
iajs-400	100	23	α	α	DET
iajs-400	100	24	-s*g	-s*g	NOUN
iajs-400	100	25	-	-	PUNCT
iajs-400	100	26	open	open	ADJ
iajs-400	100	27	.	.	PUNCT
iajs-400	101	1	example(2.6	example(2.6	NOUN
iajs-400	101	2	):	):	PUNCT
iajs-400	101	3	let	let	VERB
iajs-400	101	4	ℜ=x	ℜ=x	NOUN
iajs-400	101	5	with	with	ADP
iajs-400	101	6	the	the	DET
iajs-400	101	7	usual	usual	ADJ
iajs-400	101	8	topology	topology	NOUN
iajs-400	101	9	τ	τ	X
iajs-400	101	10	.	.	PUNCT
iajs-400	102	1	let	let	VERB
iajs-400	102	2	]	]	PUNCT
iajs-400	102	3	1,0(a	1,0(a	NUM
iajs-400	102	4	=	=	NOUN
iajs-400	102	5	.	.	PUNCT
iajs-400	103	1	then	then	ADV
iajs-400	103	2	a	a	PRON
iajs-400	103	3	is	be	AUX
iajs-400	103	4	an	an	DET
iajs-400	103	5	b	b	X
iajs-400	103	6	-	-	PUNCT
iajs-400	103	7	s*gopen	s*gopen	ADJ
iajs-400	103	8	set	set	NOUN
iajs-400	103	9	(	(	PUNCT
iajs-400	103	10	since	since	SCONJ
iajs-400	103	11	a	a	PRON
iajs-400	103	12	is	be	AUX
iajs-400	103	13	b	b	NOUN
iajs-400	103	14	-	-	PUNCT
iajs-400	103	15	open	open	ADJ
iajs-400	103	16	set	set	NOUN
iajs-400	103	17	)	)	PUNCT
iajs-400	103	18	which	which	PRON
iajs-400	103	19	is	be	AUX
iajs-400	103	20	not	not	PART
iajs-400	103	21	pre	pre	ADJ
iajs-400	103	22	-	-	ADJ
iajs-400	103	23	s*g	s*g	ADJ
iajs-400	103	24	-	-	PUNCT
iajs-400	103	25	open	open	ADJ
iajs-400	103	26	.	.	PUNCT
iajs-400	104	1	example(2.7	example(2.7	NOUN
iajs-400	104	2	):	):	PUNCT
iajs-400	104	3	let	let	VERB
iajs-400	104	4	ℜ=x	ℜ=x	NOUN
iajs-400	104	5	with	with	ADP
iajs-400	104	6	the	the	DET
iajs-400	104	7	usual	usual	ADJ
iajs-400	104	8	topology	topology	NOUN
iajs-400	104	9	τ	τ	X
iajs-400	104	10	.	.	PUNCT
iajs-400	105	1	let	let	VERB
iajs-400	105	2	]	]	X
iajs-400	105	3	1,0[qa	1,0[qa	NUM
iajs-400	105	4	=	=	X
iajs-400	105	5	.	.	PUNCT
iajs-400	106	1	then	then	ADV
iajs-400	106	2	a	a	PRON
iajs-400	106	3	is	be	AUX
iajs-400	106	4	aβ	aβ	PRON
iajs-400	106	5	-s*g	-s*g	PROPN
iajs-400	106	6	open	open	ADJ
iajs-400	106	7	set	set	NOUN
iajs-400	106	8	(	(	PUNCT
iajs-400	106	9	since	since	SCONJ
iajs-400	106	10	a	a	DET
iajs-400	106	11	isβ	isβ	ADJ
iajs-400	106	12	-open	-open	NOUN
iajs-400	106	13	set	set	NOUN
iajs-400	106	14	)	)	PUNCT
iajs-400	106	15	which	which	PRON
iajs-400	106	16	is	be	AUX
iajs-400	106	17	not	not	PART
iajs-400	106	18	b	b	NOUN
iajs-400	106	19	-	-	PUNCT
iajs-400	106	20	s*g	s*g	NOUN
iajs-400	106	21	-	-	PUNCT
iajs-400	106	22	open	open	ADJ
iajs-400	106	23	.	.	PUNCT
iajs-400	107	1	theorem(2.8	theorem(2.8	NOUN
iajs-400	107	2	):	):	PUNCT
iajs-400	107	3	if	if	SCONJ
iajs-400	107	4	a	a	PRON
iajs-400	107	5	is	be	AUX
iajs-400	107	6	a	a	DET
iajs-400	107	7	pre	pre	ADJ
iajs-400	107	8	-	-	ADJ
iajs-400	107	9	s*g	s*g	ADJ
iajs-400	107	10	-	-	PUNCT
iajs-400	107	11	open	open	ADJ
iajs-400	107	12	subset	subset	NOUN
iajs-400	107	13	of	of	ADP
iajs-400	107	14	a	a	DET
iajs-400	107	15	topological	topological	ADJ
iajs-400	107	16	space	space	NOUN
iajs-400	107	17	)	)	PUNCT
iajs-400	107	18	,	,	PUNCT
iajs-400	107	19	x	x	X
iajs-400	107	20	(	(	PUNCT
iajs-400	107	21	τ	τ	X
iajs-400	107	22	such	such	ADJ
iajs-400	107	23	that	that	PRON
iajs-400	107	24	)	)	PUNCT
iajs-400	107	25	u(clau	u(clau	PROPN
iajs-400	107	26	⊆⊆	⊆⊆	PROPN
iajs-400	107	27	for	for	ADP
iajs-400	107	28	a	a	DET
iajs-400	107	29	subset	subset	ADJ
iajs-400	107	30	u	u	NOUN
iajs-400	107	31	of	of	ADP
iajs-400	107	32	x	x	SYM
iajs-400	107	33	,	,	PUNCT
iajs-400	107	34	then	then	ADV
iajs-400	107	35	u	u	NOUN
iajs-400	107	36	is	be	AUX
iajs-400	107	37	an	an	DET
iajs-400	107	38	pre	pre	ADJ
iajs-400	107	39	-	-	ADJ
iajs-400	107	40	s*g	s*g	ADJ
iajs-400	107	41	-	-	PUNCT
iajs-400	107	42	open	open	NOUN
iajs-400	107	43	set	set	NOUN
iajs-400	107	44	.	.	PUNCT
iajs-400	108	1	proof	proof	NOUN
iajs-400	108	2	:	:	PUNCT
iajs-400	108	3	since	since	SCONJ
iajs-400	108	4	)	)	PUNCT
iajs-400	108	5	u(cla	u(cla	VERB
iajs-400	108	6	⊆	⊆	NUM
iajs-400	108	7	⇒	⇒	NOUN
iajs-400	108	8	)	)	PUNCT
iajs-400	108	9	u(cl))u(cl(cl)a(cl	u(cl))u(cl(cl)a(cl	PUNCT
iajs-400	109	1	=	=	SYM
iajs-400	109	2	⊆	⊆	NUM
iajs-400	109	3	⇒	⇒	NOUN
iajs-400	109	4	)	)	PUNCT
iajs-400	109	5	)	)	PUNCT
iajs-400	110	1	u(cl(int))a(cl(int	u(cl(int))a(cl(int	PROPN
iajs-400	110	2	g*sg*s	g*sg*s	PROPN
iajs-400	110	3	⊆	⊆	NUM
iajs-400	110	4	.	.	PUNCT
iajs-400	111	1	since	since	SCONJ
iajs-400	111	2	)	)	PUNCT
iajs-400	111	3	)	)	PUNCT
iajs-400	111	4	a(cl(inta	a(cl(inta	ADP
iajs-400	111	5	g*s⊆	g*s⊆	NOUN
iajs-400	111	6	and	and	CCONJ
iajs-400	111	7	au	au	ADJ
iajs-400	111	8	⊆	⊆	NUM
iajs-400	111	9	⇒	⇒	NOUN
iajs-400	111	10	)	)	PUNCT
iajs-400	111	11	)	)	PUNCT
iajs-400	111	12	u(cl(intu	u(cl(intu	ADJ
iajs-400	111	13	g*s⊆	g*s⊆	NOUN
iajs-400	111	14	.	.	PUNCT
iajs-400	112	1	thus	thus	ADV
iajs-400	112	2	u	u	PRON
iajs-400	112	3	is	be	AUX
iajs-400	112	4	an	an	DET
iajs-400	112	5	pre	pre	ADJ
iajs-400	112	6	-	-	ADJ
iajs-400	112	7	s*g	s*g	ADJ
iajs-400	112	8	-	-	PUNCT
iajs-400	112	9	open	open	ADJ
iajs-400	112	10	set	set	NOUN
iajs-400	112	11	.	.	PUNCT
iajs-400	113	1	theorem(2.9	theorem(2.9	ADJ
iajs-400	113	2	):	):	PUNCT
iajs-400	113	3	a	a	DET
iajs-400	113	4	subset	subset	NOUN
iajs-400	113	5	a	a	PRON
iajs-400	113	6	of	of	ADP
iajs-400	113	7	a	a	DET
iajs-400	113	8	topological	topological	ADJ
iajs-400	113	9	space	space	NOUN
iajs-400	113	10	)	)	PUNCT
iajs-400	113	11	,	,	PUNCT
iajs-400	113	12	x	x	X
iajs-400	113	13	(	(	PUNCT
iajs-400	113	14	τ	τ	X
iajs-400	113	15	is	be	AUX
iajs-400	113	16	semi	semi	ADJ
iajs-400	113	17	-	-	ADJ
iajs-400	113	18	open	open	ADJ
iajs-400	113	19	if	if	SCONJ
iajs-400	113	20	and	and	CCONJ
iajs-400	113	21	only	only	ADV
iajs-400	113	22	if	if	SCONJ
iajs-400	113	23	a	a	PRON
iajs-400	113	24	is	be	AUX
iajs-400	113	25	β	β	X
iajs-400	113	26	s*g	s*g	VERB
iajs-400	113	27	-	-	PUNCT
iajs-400	113	28	open	open	ADJ
iajs-400	113	29	and	and	CCONJ
iajs-400	113	30	)	)	PUNCT
iajs-400	113	31	)	)	PUNCT
iajs-400	114	1	a(int(cl))a(cl(int	a(int(cl))a(cl(int	NOUN
iajs-400	114	2	g*s	g*s	PROPN
iajs-400	114	3	⊆	⊆	NUM
iajs-400	114	4	.	.	PUNCT
iajs-400	115	1	proof	proof	NOUN
iajs-400	115	2	:	:	PUNCT
iajs-400	115	3	let	let	VERB
iajs-400	115	4	a	a	PRON
iajs-400	115	5	be	be	AUX
iajs-400	115	6	semi	semi	ADJ
iajs-400	115	7	-	-	ADJ
iajs-400	115	8	open	open	ADJ
iajs-400	115	9	,	,	PUNCT
iajs-400	115	10	then	then	ADV
iajs-400	115	11	)	)	PUNCT
iajs-400	115	12	)	)	PUNCT
iajs-400	115	13	a(int(cla	a(int(cla	VERB
iajs-400	115	14	⊆	⊆	NUM
iajs-400	115	15	)	)	PUNCT
iajs-400	115	16	)	)	PUNCT
iajs-400	115	17	)	)	PUNCT
iajs-400	115	18	a(cl((intcl	a(cl((intcl	PROPN
iajs-400	115	19	g*s⊆	g*s⊆	NOUN
iajs-400	115	20	and	and	CCONJ
iajs-400	115	21	hence	hence	ADV
iajs-400	115	22	a	a	PRON
iajs-400	115	23	is	be	AUX
iajs-400	115	24	β	β	NOUN
iajs-400	115	25	-s*g	-s*g	X
iajs-400	115	26	open	open	ADJ
iajs-400	115	27	.	.	PUNCT
iajs-400	116	1	also	also	ADV
iajs-400	116	2	,	,	PUNCT
iajs-400	116	3	since	since	SCONJ
iajs-400	116	4	)	)	PUNCT
iajs-400	116	5	)	)	PUNCT
iajs-400	116	6	a(int(cla	a(int(cla	VERB
iajs-400	116	7	⊆	⊆	NUM
iajs-400	116	8	⇒	⇒	NOUN
iajs-400	116	9	)	)	PUNCT
iajs-400	116	10	)	)	PUNCT
iajs-400	116	11	a(int(cl)a(cl	a(int(cl)a(cl	PROPN
iajs-400	117	1	⊆	⊆	NUM
iajs-400	117	2	⇒	⇒	NOUN
iajs-400	117	3	)	)	PUNCT
iajs-400	117	4	)	)	PUNCT
iajs-400	117	5	a(int(cl))a(cl(int	a(int(cl))a(cl(int	PROPN
iajs-400	117	6	g*s	g*s	PROPN
iajs-400	117	7	⊆	⊆	NUM
iajs-400	117	8	.	.	PUNCT
iajs-400	118	1	conversely	conversely	ADV
iajs-400	118	2	,	,	PUNCT
iajs-400	118	3	let	let	VERB
iajs-400	118	4	a	a	PRON
iajs-400	118	5	be	be	AUX
iajs-400	118	6	β	β	X
iajs-400	118	7	-s*g	-s*g	ADJ
iajs-400	118	8	-	-	PUNCT
iajs-400	118	9	open	open	ADJ
iajs-400	118	10	and	and	CCONJ
iajs-400	118	11	)	)	PUNCT
iajs-400	118	12	)	)	PUNCT
iajs-400	118	13	a(int(cl))a(cl(int	a(int(cl))a(cl(int	NOUN
iajs-400	119	1	g*s	g*s	PROPN
iajs-400	119	2	⊆	⊆	NUM
iajs-400	119	3	.	.	PUNCT
iajs-400	120	1	then	then	ADV
iajs-400	120	2	)	)	PUNCT
iajs-400	120	3	)	)	PUNCT
iajs-400	120	4	)	)	PUNCT
iajs-400	121	1	a(int(cl(cl)))a(cl((intcla	a(int(cl(cl)))a(cl((intcla	ADP
iajs-400	121	2	g*s	g*s	PROPN
iajs-400	121	3	⊆⊆	⊆⊆	PROPN
iajs-400	121	4	)	)	PUNCT
iajs-400	121	5	)	)	PUNCT
iajs-400	122	1	a(int(cl=	a(int(cl=	PROPN
iajs-400	122	2	and	and	CCONJ
iajs-400	122	3	hence	hence	ADV
iajs-400	122	4	a	a	PRON
iajs-400	122	5	is	be	AUX
iajs-400	122	6	semi	semi	ADJ
iajs-400	122	7	-	-	ADJ
iajs-400	122	8	open	open	ADJ
iajs-400	122	9	.	.	PUNCT
iajs-400	123	1	lemma(2.10)[13	lemma(2.10)[13	PROPN
iajs-400	123	2	]	]	X
iajs-400	123	3	:	:	PUNCT
iajs-400	123	4	let	let	VERB
iajs-400	123	5	)	)	PUNCT
iajs-400	123	6	,	,	PUNCT
iajs-400	123	7	x	x	X
iajs-400	123	8	(	(	PUNCT
iajs-400	123	9	τ	τ	X
iajs-400	123	10	be	be	AUX
iajs-400	123	11	a	a	DET
iajs-400	123	12	topological	topological	ADJ
iajs-400	123	13	space	space	NOUN
iajs-400	123	14	.	.	PUNCT
iajs-400	124	1	if	if	SCONJ
iajs-400	124	2	u	u	NOUN
iajs-400	124	3	is	be	AUX
iajs-400	124	4	an	an	DET
iajs-400	124	5	open	open	ADJ
iajs-400	124	6	set	set	NOUN
iajs-400	124	7	in	in	ADP
iajs-400	124	8	x	x	NOUN
iajs-400	124	9	,	,	PUNCT
iajs-400	124	10	then	then	ADV
iajs-400	124	11	)	)	PUNCT
iajs-400	124	12	au(cl)a(clu	au(cl)a(clu	NOUN
iajs-400	124	13			NUM
iajs-400	124	14	⊆	⊆	NUM
iajs-400	124	15	for	for	ADP
iajs-400	124	16	any	any	DET
iajs-400	124	17	subset	subset	NOUN
iajs-400	124	18	a	a	PRON
iajs-400	124	19	of	of	ADP
iajs-400	124	20	x	x	X
iajs-400	124	21	.	.	PUNCT
iajs-400	124	22	propositions(2.11	propositions(2.11	NUM
iajs-400	124	23	):	):	PUNCT
iajs-400	124	24	let	let	NOUN
iajs-400	124	25	)	)	PUNCT
iajs-400	124	26	,	,	PUNCT
iajs-400	124	27	x	x	X
iajs-400	124	28	(	(	PUNCT
iajs-400	124	29	τ	τ	X
iajs-400	124	30	be	be	AUX
iajs-400	124	31	a	a	DET
iajs-400	124	32	topological	topological	ADJ
iajs-400	124	33	space	space	NOUN
iajs-400	124	34	,	,	PUNCT
iajs-400	124	35	then	then	ADV
iajs-400	124	36	:	:	PUNCT
iajs-400	124	37	i	i	X
iajs-400	124	38	)	)	PUNCT
iajs-400	124	39	the	the	DET
iajs-400	124	40	intersection	intersection	NOUN
iajs-400	124	41	of	of	ADP
iajs-400	124	42	a	a	DET
iajs-400	124	43	pre	pre	ADJ
iajs-400	124	44	-	-	ADJ
iajs-400	124	45	s*g	s*g	ADJ
iajs-400	124	46	-	-	PUNCT
iajs-400	124	47	open	open	NOUN
iajs-400	124	48	set	set	NOUN
iajs-400	124	49	and	and	CCONJ
iajs-400	124	50	an	an	DET
iajs-400	124	51	open	open	ADJ
iajs-400	124	52	set	set	NOUN
iajs-400	124	53	is	be	AUX
iajs-400	124	54	pre	pre	ADJ
iajs-400	124	55	-	-	ADJ
iajs-400	124	56	s*g	s*g	ADJ
iajs-400	124	57	-	-	PUNCT
iajs-400	124	58	open	open	ADJ
iajs-400	124	59	.	.	PUNCT
iajs-400	125	1	ii	ii	X
iajs-400	125	2	)	)	PUNCT
iajs-400	125	3	the	the	DET
iajs-400	125	4	intersection	intersection	NOUN
iajs-400	125	5	of	of	ADP
iajs-400	125	6	aβ	aβ	DET
iajs-400	125	7	-s*g	-s*g	ADJ
iajs-400	125	8	-	-	PUNCT
iajs-400	125	9	open	open	NOUN
iajs-400	125	10	set	set	NOUN
iajs-400	125	11	and	and	CCONJ
iajs-400	125	12	an	an	DET
iajs-400	125	13	open	open	ADJ
iajs-400	125	14	set	set	NOUN
iajs-400	125	15	is	be	AUX
iajs-400	125	16	β	β	X
iajs-400	125	17	-s*g	-s*g	ADJ
iajs-400	125	18	-	-	PUNCT
iajs-400	125	19	open	open	ADJ
iajs-400	125	20	.	.	PUNCT
iajs-400	126	1	354	354	NUM
iajs-400	127	1	|	|	ADV
iajs-400	127	2	mathematics	mathematics	PROPN
iajs-400	127	3	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	127	4	�	�	NOUN
iajs-400	127	5	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	127	6	:	:	PUNCT
iajs-400	127	7	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	127	8	©	©	PROPN
iajs-400	127	9	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	127	10	ibn	ibn	PROPN
iajs-400	127	11	al	al	PROPN
iajs-400	127	12	-	-	PUNCT
iajs-400	127	13	haitham	haitham	PROPN
iajs-400	127	14	jour	jour	X
iajs-400	127	15	.	.	PROPN
iajs-400	128	1	for	for	ADP
iajs-400	128	2	pure	pure	ADJ
iajs-400	128	3	&	&	CCONJ
iajs-400	128	4	appl	appl	PROPN
iajs-400	128	5	.	.	PUNCT
iajs-400	129	1	sci	sci	PROPN
iajs-400	129	2	.	.	PUNCT
iajs-400	129	3	vol	vol	NOUN
iajs-400	129	4	.	.	PROPN
iajs-400	130	1	27	27	NUM
iajs-400	130	2	(	(	PUNCT
iajs-400	130	3	1	1	NUM
iajs-400	130	4	)	)	PUNCT
iajs-400	130	5	2014	2014	NUM
iajs-400	130	6	iii	iii	NOUN
iajs-400	130	7	)	)	PUNCT
iajs-400	130	8	the	the	DET
iajs-400	130	9	intersection	intersection	NOUN
iajs-400	130	10	of	of	ADP
iajs-400	130	11	a	a	DET
iajs-400	130	12	b	b	NOUN
iajs-400	130	13	-	-	PUNCT
iajs-400	130	14	s*g	s*g	VERB
iajs-400	130	15	-	-	PUNCT
iajs-400	130	16	open	open	NOUN
iajs-400	130	17	set	set	NOUN
iajs-400	130	18	and	and	CCONJ
iajs-400	130	19	an	an	DET
iajs-400	130	20	open	open	ADJ
iajs-400	130	21	set	set	NOUN
iajs-400	130	22	is	be	AUX
iajs-400	130	23	b	b	NOUN
iajs-400	130	24	-	-	PUNCT
iajs-400	130	25	s*g	s*g	NOUN
iajs-400	130	26	-	-	PUNCT
iajs-400	130	27	open	open	ADJ
iajs-400	130	28	.	.	PUNCT
iajs-400	131	1	iv	iv	X
iajs-400	131	2	)	)	PUNCT
iajs-400	131	3	the	the	DET
iajs-400	131	4	intersection	intersection	NOUN
iajs-400	131	5	of	of	ADP
iajs-400	131	6	an	an	DET
iajs-400	131	7	α	α	NOUN
iajs-400	131	8	-s*g	-s*g	ADJ
iajs-400	131	9	-	-	PUNCT
iajs-400	131	10	open	open	NOUN
iajs-400	131	11	set	set	NOUN
iajs-400	131	12	and	and	CCONJ
iajs-400	131	13	an	an	DET
iajs-400	131	14	open	open	ADJ
iajs-400	131	15	set	set	NOUN
iajs-400	131	16	is	be	AUX
iajs-400	131	17	α	α	DET
iajs-400	131	18	-s*g	-s*g	NOUN
iajs-400	131	19	-	-	PUNCT
iajs-400	131	20	open	open	ADJ
iajs-400	131	21	.	.	PUNCT
iajs-400	132	1	proof	proof	NOUN
iajs-400	132	2	:	:	PUNCT
iajs-400	132	3	we	we	PRON
iajs-400	132	4	prove	prove	VERB
iajs-400	132	5	only	only	ADV
iajs-400	132	6	the	the	DET
iajs-400	132	7	first	first	ADJ
iajs-400	132	8	case	case	NOUN
iajs-400	132	9	since	since	SCONJ
iajs-400	132	10	the	the	DET
iajs-400	132	11	other	other	ADJ
iajs-400	132	12	cases	case	NOUN
iajs-400	132	13	are	be	AUX
iajs-400	132	14	similarly	similarly	ADV
iajs-400	132	15	shown	show	VERB
iajs-400	132	16	.	.	PUNCT
iajs-400	133	1	i	i	PRON
iajs-400	133	2	)	)	PUNCT
iajs-400	133	3	let	let	VERB
iajs-400	133	4	a	a	PRON
iajs-400	133	5	be	be	AUX
iajs-400	133	6	a	a	DET
iajs-400	133	7	pre	pre	ADJ
iajs-400	133	8	-	-	ADJ
iajs-400	133	9	s*g	s*g	ADJ
iajs-400	133	10	-	-	PUNCT
iajs-400	133	11	open	open	NOUN
iajs-400	133	12	set	set	NOUN
iajs-400	133	13	and	and	CCONJ
iajs-400	133	14	u	u	NOUN
iajs-400	133	15	be	be	VERB
iajs-400	133	16	an	an	DET
iajs-400	133	17	open	open	ADJ
iajs-400	133	18	set	set	NOUN
iajs-400	133	19	in	in	ADP
iajs-400	133	20	x	x	X
iajs-400	133	21	.	.	PUNCT
iajs-400	134	1	since	since	SCONJ
iajs-400	134	2	every	every	DET
iajs-400	134	3	open	open	ADJ
iajs-400	134	4	set	set	NOUN
iajs-400	134	5	is	be	AUX
iajs-400	134	6	s*g	s*g	NOUN
iajs-400	134	7	-	-	PUNCT
iajs-400	134	8	open	open	ADJ
iajs-400	134	9	,	,	PUNCT
iajs-400	134	10	then	then	ADV
iajs-400	134	11	)	)	PUNCT
iajs-400	134	12	)	)	PUNCT
iajs-400	135	1	a(cl(inta	a(cl(inta	ADP
iajs-400	135	2	g*s⊆	g*s⊆	NOUN
iajs-400	135	3	and	and	CCONJ
iajs-400	135	4	)	)	PUNCT
iajs-400	135	5	u(intu	u(intu	VERB
iajs-400	135	6	g*s=	g*s=	NOUN
iajs-400	135	7	.	.	PUNCT
iajs-400	136	1	by	by	ADP
iajs-400	136	2	lemma	lemma	PROPN
iajs-400	136	3	(	(	PUNCT
iajs-400	136	4	2.10	2.10	NUM
iajs-400	136	5	)	)	PUNCT
iajs-400	136	6	,	,	PUNCT
iajs-400	136	7	we	we	PRON
iajs-400	136	8	have	have	VERB
iajs-400	136	9	)	)	PUNCT
iajs-400	136	10	)	)	PUNCT
iajs-400	136	11	a(cl(int)u(intau	a(cl(int)u(intau	ADV
iajs-400	136	12	g*sg*s	g*sg*s	PROPN
iajs-400	136	13			NUM
iajs-400	136	14	⊆	⊆	NUM
iajs-400	136	15	)	)	PUNCT
iajs-400	136	16	)	)	PUNCT
iajs-400	137	1	a(clu(int	a(clu(int	NOUN
iajs-400	137	2	g*s	g*s	PROPN
iajs-400	137	3	=	=	NUM
iajs-400	137	4	)	)	PUNCT
iajs-400	137	5	)	)	PUNCT
iajs-400	137	6	au(cl(int	au(cl(int	PROPN
iajs-400	137	7	g*s	g*s	PROPN
iajs-400	137	8	⊆	⊆	PROPN
iajs-400	137	9	.	.	PUNCT
iajs-400	138	1	therefore	therefore	ADV
iajs-400	138	2	ua	ua	PROPN
iajs-400	138	3			PROPN
iajs-400	138	4	is	be	AUX
iajs-400	138	5	pre	pre	ADJ
iajs-400	138	6	-	-	ADJ
iajs-400	138	7	s*g	s*g	ADJ
iajs-400	138	8	-	-	PUNCT
iajs-400	138	9	open	open	ADJ
iajs-400	138	10	.	.	PUNCT
iajs-400	139	1	remark(2.12	remark(2.12	NUM
iajs-400	139	2	):	):	PUNCT
iajs-400	139	3	we	we	PRON
iajs-400	139	4	note	note	VERB
iajs-400	139	5	that	that	SCONJ
iajs-400	139	6	the	the	DET
iajs-400	139	7	intersection	intersection	NOUN
iajs-400	139	8	of	of	ADP
iajs-400	139	9	two	two	NUM
iajs-400	139	10	pre	pre	ADJ
iajs-400	139	11	-	-	ADJ
iajs-400	139	12	s*g	s*g	ADJ
iajs-400	139	13	-	-	PUNCT
iajs-400	139	14	open	open	ADJ
iajs-400	139	15	(	(	PUNCT
iajs-400	139	16	resp	resp	NOUN
iajs-400	139	17	.	.	PUNCT
iajs-400	140	1	b	b	X
iajs-400	140	2	-	-	PUNCT
iajs-400	140	3	s*g	s*g	NOUN
iajs-400	140	4	-	-	PUNCT
iajs-400	140	5	open	open	ADJ
iajs-400	140	6	,	,	PUNCT
iajs-400	140	7	β	β	X
iajs-400	140	8	-s*gopen	-s*gopen	PROPN
iajs-400	140	9	,	,	PUNCT
iajs-400	140	10	α	α	PRON
iajs-400	140	11	-s*g	-s*g	ADJ
iajs-400	140	12	-	-	PUNCT
iajs-400	140	13	open	open	ADJ
iajs-400	140	14	)	)	PUNCT
iajs-400	140	15	sets	set	NOUN
iajs-400	140	16	need	need	AUX
iajs-400	140	17	not	not	PART
iajs-400	140	18	be	be	AUX
iajs-400	140	19	pre	pre	ADJ
iajs-400	140	20	-	-	ADJ
iajs-400	140	21	s*g	s*g	ADJ
iajs-400	140	22	-	-	PUNCT
iajs-400	140	23	open	open	ADJ
iajs-400	140	24	(	(	PUNCT
iajs-400	140	25	resp	resp	NOUN
iajs-400	140	26	.	.	PUNCT
iajs-400	141	1	b	b	X
iajs-400	141	2	-	-	PUNCT
iajs-400	141	3	s*g	s*g	NOUN
iajs-400	141	4	-	-	PUNCT
iajs-400	141	5	open	open	ADJ
iajs-400	141	6	,	,	PUNCT
iajs-400	141	7	β	β	X
iajs-400	141	8	-s*g	-s*g	ADJ
iajs-400	141	9	-	-	PUNCT
iajs-400	141	10	open	open	ADJ
iajs-400	141	11	,	,	PUNCT
iajs-400	141	12	α	α	NOUN
iajs-400	141	13	-s*gopen	-s*gopen	NOUN
iajs-400	141	14	)	)	PUNCT
iajs-400	141	15	as	as	SCONJ
iajs-400	141	16	can	can	AUX
iajs-400	141	17	be	be	AUX
iajs-400	141	18	seen	see	VERB
iajs-400	141	19	from	from	ADP
iajs-400	141	20	the	the	DET
iajs-400	141	21	following	following	ADJ
iajs-400	141	22	examples	example	NOUN
iajs-400	141	23	:	:	PUNCT
iajs-400	141	24	example(2.13	example(2.13	NUM
iajs-400	141	25	):	):	PUNCT
iajs-400	141	26	let	let	VERB
iajs-400	141	27	ℜ=x	ℜ=x	NOUN
iajs-400	141	28	with	with	ADP
iajs-400	141	29	the	the	DET
iajs-400	141	30	usual	usual	ADJ
iajs-400	141	31	topology	topology	NOUN
iajs-400	141	32	τ	τ	X
iajs-400	141	33	.	.	PUNCT
iajs-400	142	1	let	let	VERB
iajs-400	142	2	qa	qa	PROPN
iajs-400	142	3	=	=	PUNCT
iajs-400	142	4	and	and	CCONJ
iajs-400	142	5	}	}	PUNCT
iajs-400	142	6	1{qb	1{qb	NOUN
iajs-400	142	7	c	c	PROPN
iajs-400	142	8	=	=	NOUN
iajs-400	142	9	,	,	PUNCT
iajs-400	142	10	then	then	ADV
iajs-400	142	11	a	a	PRON
iajs-400	142	12	and	and	CCONJ
iajs-400	142	13	b	b	NOUN
iajs-400	142	14	are	be	AUX
iajs-400	142	15	pre	pre	ADJ
iajs-400	142	16	-	-	ADJ
iajs-400	142	17	s*g	s*g	ADJ
iajs-400	142	18	-	-	PUNCT
iajs-400	142	19	open	open	ADJ
iajs-400	142	20	,	,	PUNCT
iajs-400	142	21	but	but	CCONJ
iajs-400	142	22	}	}	PUNCT
iajs-400	142	23	1{ba	1{ba	NUM
iajs-400	142	24	=	=	SYM
iajs-400	142	25			PROPN
iajs-400	142	26	which	which	PRON
iajs-400	142	27	is	be	AUX
iajs-400	142	28	not	not	PART
iajs-400	142	29	β	β	X
iajs-400	142	30	-s*g	-s*g	ADJ
iajs-400	142	31	-	-	PUNCT
iajs-400	142	32	open	open	ADJ
iajs-400	142	33	since	since	SCONJ
iajs-400	142	34	}	}	PUNCT
iajs-400	142	35	)	)	PUNCT
iajs-400	142	36	)	)	PUNCT
iajs-400	142	37	)	)	PUNCT
iajs-400	143	1	1({cl((intcl	1({cl((intcl	PROPN
iajs-400	143	2	g*s	g*s	PROPN
iajs-400	143	3	}	}	PUNCT
iajs-400	143	4	)	)	PUNCT
iajs-400	143	5	)	)	PUNCT
iajs-400	144	1	1({(intcl	1({(intcl	PROPN
iajs-400	144	2	g*s=	g*s=	PROPN
iajs-400	144	3	φ	φ	NUM
iajs-400	144	4	=	=	NOUN
iajs-400	144	5	φ=	φ=	NOUN
iajs-400	144	6	}	}	PUNCT
iajs-400	144	7	)	)	PUNCT
iajs-400	145	1	(	(	PUNCT
iajs-400	145	2	{	{	PUNCT
iajs-400	145	3	cl	cl	NOUN
iajs-400	145	4	.	.	PUNCT
iajs-400	146	1	example(2.14	example(2.14	X
iajs-400	146	2	):	):	PUNCT
iajs-400	146	3	let	let	VERB
iajs-400	146	4	}	}	PUNCT
iajs-400	146	5	c	c	NOUN
iajs-400	146	6	,	,	PUNCT
iajs-400	146	7	b	b	PROPN
iajs-400	146	8	,	,	PUNCT
iajs-400	146	9	a{x	a{x	VERB
iajs-400	146	10	=	=	SYM
iajs-400	146	11	&	&	CCONJ
iajs-400	146	12	}	}	PUNCT
iajs-400	146	13	}	}	PUNCT
iajs-400	146	14	c	c	X
iajs-400	146	15	,	,	PUNCT
iajs-400	146	16	b{,,x	b{,,x	PROPN
iajs-400	146	17	{	{	PUNCT
iajs-400	146	18	φ	φ	PROPN
iajs-400	146	19	=	=	PROPN
iajs-400	146	20	τ	τ	X
iajs-400	146	21	.	.	PUNCT
iajs-400	147	1	then	then	ADV
iajs-400	147	2	}	}	PUNCT
iajs-400	147	3	b	b	X
iajs-400	147	4	,	,	PUNCT
iajs-400	147	5	a	a	PRON
iajs-400	147	6	{	{	PUNCT
iajs-400	147	7	and	and	CCONJ
iajs-400	147	8	}	}	PUNCT
iajs-400	147	9	c	c	X
iajs-400	147	10	,	,	PUNCT
iajs-400	147	11	a	a	PRON
iajs-400	147	12	{	{	PUNCT
iajs-400	147	13	are	be	AUX
iajs-400	147	14	α	α	DET
iajs-400	147	15	-s*g	-s*g	ADJ
iajs-400	147	16	-	-	PUNCT
iajs-400	147	17	open	open	ADJ
iajs-400	147	18	sets	set	NOUN
iajs-400	147	19	,	,	PUNCT
iajs-400	147	20	but	but	CCONJ
iajs-400	147	21	}	}	PUNCT
iajs-400	147	22	a{}c	a{}c	ADV
iajs-400	147	23	,	,	PUNCT
iajs-400	147	24	a{}b	a{}b	NOUN
iajs-400	147	25	,	,	PUNCT
iajs-400	147	26	a	a	PRON
iajs-400	147	27	{	{	PUNCT
iajs-400	147	28	=	=	NOUN
iajs-400	147	29			NOUN
iajs-400	147	30	is	be	AUX
iajs-400	147	31	not	not	PART
iajs-400	147	32	α	α	DET
iajs-400	147	33	-s*g	-s*g	NOUN
iajs-400	147	34	-	-	PUNCT
iajs-400	147	35	open	open	ADJ
iajs-400	147	36	.	.	PUNCT
iajs-400	148	1	theorem(2.15	theorem(2.15	NUM
iajs-400	148	2	):	):	PUNCT
iajs-400	148	3	if	if	SCONJ
iajs-400	148	4	}	}	PUNCT
iajs-400	148	5	:	:	PUNCT
iajs-400	148	6	a	a	PRON
iajs-400	148	7	{	{	PUNCT
iajs-400	148	8	∧∈αα	∧∈αα	NOUN
iajs-400	148	9	is	be	AUX
iajs-400	148	10	a	a	DET
iajs-400	148	11	collection	collection	NOUN
iajs-400	148	12	of	of	ADP
iajs-400	148	13	b	b	NOUN
iajs-400	148	14	-	-	PUNCT
iajs-400	148	15	s*g	s*g	VERB
iajs-400	148	16	-	-	PUNCT
iajs-400	148	17	open	open	ADJ
iajs-400	148	18	(	(	PUNCT
iajs-400	148	19	resp	resp	NOUN
iajs-400	148	20	.	.	PUNCT
iajs-400	149	1	pre	pre	ADJ
iajs-400	149	2	-	-	ADJ
iajs-400	149	3	s*g	s*g	ADJ
iajs-400	149	4	-	-	PUNCT
iajs-400	149	5	open	open	ADJ
iajs-400	149	6	,	,	PUNCT
iajs-400	149	7	β	β	X
iajs-400	149	8	-s*gopen	-s*gopen	PROPN
iajs-400	149	9	,	,	PUNCT
iajs-400	149	10	α	α	PRON
iajs-400	149	11	-s*g	-s*g	ADJ
iajs-400	149	12	-	-	PUNCT
iajs-400	149	13	open	open	ADJ
iajs-400	149	14	)	)	PUNCT
iajs-400	149	15	sets	set	NOUN
iajs-400	149	16	of	of	ADP
iajs-400	149	17	a	a	DET
iajs-400	149	18	topological	topological	ADJ
iajs-400	149	19	space	space	NOUN
iajs-400	149	20	)	)	PUNCT
iajs-400	149	21	,	,	PUNCT
iajs-400	149	22	x	x	X
iajs-400	149	23	(	(	PUNCT
iajs-400	149	24	τ	τ	X
iajs-400	149	25	,	,	PUNCT
iajs-400	149	26	then	then	PROPN
iajs-400	149	27	∧∈α	∧∈α	NOUN
iajs-400	149	28	αa	αa	ADV
iajs-400	149	29	is	be	AUX
iajs-400	149	30	b	b	NOUN
iajs-400	149	31	-	-	PUNCT
iajs-400	149	32	s*g	s*g	VERB
iajs-400	149	33	-	-	PUNCT
iajs-400	149	34	open	open	ADJ
iajs-400	149	35	(	(	PUNCT
iajs-400	149	36	resp	resp	NOUN
iajs-400	149	37	.	.	PUNCT
iajs-400	150	1	pre	pre	ADJ
iajs-400	150	2	-	-	ADJ
iajs-400	150	3	s*g	s*g	ADJ
iajs-400	150	4	-	-	PUNCT
iajs-400	150	5	open	open	ADJ
iajs-400	150	6	,	,	PUNCT
iajs-400	150	7	β	β	X
iajs-400	150	8	s*g	s*g	NOUN
iajs-400	150	9	-	-	PUNCT
iajs-400	150	10	open	open	ADJ
iajs-400	150	11	,	,	PUNCT
iajs-400	150	12	α	α	PRON
iajs-400	150	13	-s*g	-s*g	NOUN
iajs-400	150	14	-	-	PUNCT
iajs-400	150	15	open	open	ADJ
iajs-400	150	16	)	)	PUNCT
iajs-400	150	17	.	.	PUNCT
iajs-400	151	1	proof	proof	NOUN
iajs-400	151	2	:	:	PUNCT
iajs-400	151	3	we	we	PRON
iajs-400	151	4	prove	prove	VERB
iajs-400	151	5	only	only	ADV
iajs-400	151	6	the	the	DET
iajs-400	151	7	first	first	ADJ
iajs-400	151	8	case	case	NOUN
iajs-400	151	9	since	since	SCONJ
iajs-400	151	10	the	the	DET
iajs-400	151	11	other	other	ADJ
iajs-400	151	12	cases	case	NOUN
iajs-400	151	13	are	be	AUX
iajs-400	151	14	similarly	similarly	ADV
iajs-400	151	15	shown	show	VERB
iajs-400	151	16	.	.	PUNCT
iajs-400	152	1	since	since	SCONJ
iajs-400	152	2	)	)	PUNCT
iajs-400	152	3	)	)	PUNCT
iajs-400	152	4	a((intcl))a(cl(inta	a((intcl))a(cl(inta	PROPN
iajs-400	152	5	g*sg*s	g*sg*s	PROPN
iajs-400	152	6	ααα	ααα	VERB
iajs-400	152	7	⊆	⊆	NUM
iajs-400	152	8			NOUN
iajs-400	152	9	for	for	ADP
iajs-400	152	10	every	every	DET
iajs-400	152	11	∧∈α	∧∈α	NOUN
iajs-400	152	12	,	,	PUNCT
iajs-400	152	13	we	we	PRON
iajs-400	152	14	have	have	VERB
iajs-400	152	15	:	:	PUNCT
iajs-400	152	16	)	)	PUNCT
iajs-400	152	17	)	)	PUNCT
iajs-400	153	1	]	]	PUNCT
iajs-400	153	2	a((intcl))a(cl([inta	a((intcl))a(cl([inta	PROPN
iajs-400	153	3	g*sg*s	g*sg*s	PROPN
iajs-400	153	4	αα	αα	PROPN
iajs-400	153	5	∧∈α∧∈α	∧∈α∧∈α	PROPN
iajs-400	153	6	α	α	NOUN
iajs-400	153	7	⊆	⊆	NUM
iajs-400	153	8			NOUN
iajs-400	153	9	)	)	PUNCT
iajs-400	153	10	)	)	PUNCT
iajs-400	154	1	]	]	X
iajs-400	155	1	a((intcl[))]a(cl(int	a((intcl[))]a(cl(int	PROPN
iajs-400	155	2	[	[	PUNCT
iajs-400	155	3	g*sg*s	g*sg*s	PROPN
iajs-400	155	4			PROPN
iajs-400	155	5			ADJ
iajs-400	155	6	∧∈α	∧∈α	NOUN
iajs-400	155	7	αα	αα	NOUN
iajs-400	155	8	∧∈α	∧∈α	NOUN
iajs-400	155	9	=	=	SYM
iajs-400	155	10	)	)	PUNCT
iajs-400	155	11	)	)	PUNCT
iajs-400	156	1	]	]	PUNCT
iajs-400	156	2	a(int(cl[]))a(cl([int	a(int(cl[]))a(cl([int	VERB
iajs-400	156	3	g*sg*s	g*sg*s	PROPN
iajs-400	156	4			PROPN
iajs-400	156	5			ADJ
iajs-400	156	6	∧∈α	∧∈α	NOUN
iajs-400	157	1	α	α	NOUN
iajs-400	157	2	∧∈α	∧∈α	NOUN
iajs-400	157	3	α⊆	α⊆	NOUN
iajs-400	157	4	)	)	PUNCT
iajs-400	157	5	)	)	PUNCT
iajs-400	158	1	]	]	PUNCT
iajs-400	158	2	a((intcl[]))a(cl([int	a((intcl[]))a(cl([int	PROPN
iajs-400	158	3	g*sg*s	g*sg*s	PROPN
iajs-400	158	4			PROPN
iajs-400	158	5			ADJ
iajs-400	158	6	∧∈α	∧∈α	NOUN
iajs-400	158	7	α	α	NOUN
iajs-400	158	8	∧∈α	∧∈α	NOUN
iajs-400	158	9	α⊆	α⊆	NOUN
iajs-400	158	10	therefore	therefore	ADV
iajs-400	158	11			ADJ
iajs-400	158	12	∧∈α	∧∈α	NOUN
iajs-400	158	13	αa	αa	ADV
iajs-400	158	14	is	be	AUX
iajs-400	158	15	b	b	NUM
iajs-400	158	16	-	-	PUNCT
iajs-400	158	17	s*g	s*g	NOUN
iajs-400	158	18	-	-	PUNCT
iajs-400	158	19	open	open	ADJ
iajs-400	158	20	.	.	PUNCT
iajs-400	159	1	proposition(2.16	proposition(2.16	NOUN
iajs-400	159	2	):	):	PUNCT
iajs-400	159	3	let	let	NOUN
iajs-400	159	4	)	)	PUNCT
iajs-400	159	5	,	,	PUNCT
iajs-400	159	6	x	x	X
iajs-400	159	7	(	(	PUNCT
iajs-400	159	8	τ	τ	X
iajs-400	159	9	be	be	AUX
iajs-400	159	10	a	a	DET
iajs-400	159	11	topological	topological	ADJ
iajs-400	159	12	space	space	NOUN
iajs-400	159	13	and	and	CCONJ
iajs-400	159	14	xa	xa	PROPN
iajs-400	159	15	⊆	⊆	NUM
iajs-400	159	16	.	.	PUNCT
iajs-400	160	1	if	if	SCONJ
iajs-400	160	2	a	a	PRON
iajs-400	160	3	is	be	AUX
iajs-400	160	4	a	a	DET
iajs-400	160	5	b	b	NOUN
iajs-400	160	6	-	-	PUNCT
iajs-400	160	7	s*g	s*g	VERB
iajs-400	160	8	-	-	PUNCT
iajs-400	160	9	open	open	NOUN
iajs-400	160	10	set	set	NOUN
iajs-400	160	11	such	such	DET
iajs-400	160	12	that	that	DET
iajs-400	160	13	φ=)a(int	φ=)a(int	NOUN
iajs-400	160	14	g*s	g*s	PROPN
iajs-400	160	15	,	,	PUNCT
iajs-400	160	16	then	then	ADV
iajs-400	160	17	a	a	PRON
iajs-400	160	18	is	be	AUX
iajs-400	160	19	pre	pre	ADJ
iajs-400	160	20	-	-	ADJ
iajs-400	160	21	s*g	s*g	ADJ
iajs-400	160	22	-	-	PUNCT
iajs-400	160	23	open	open	ADJ
iajs-400	160	24	.	.	PUNCT
iajs-400	161	1	proof	proof	NOUN
iajs-400	161	2	:	:	PUNCT
iajs-400	161	3	since	since	SCONJ
iajs-400	161	4	a	a	PRON
iajs-400	161	5	is	be	AUX
iajs-400	161	6	b	b	NOUN
iajs-400	161	7	-	-	PUNCT
iajs-400	161	8	s*g	s*g	NOUN
iajs-400	161	9	-	-	PUNCT
iajs-400	161	10	open	open	ADJ
iajs-400	161	11	,	,	PUNCT
iajs-400	161	12	then	then	ADV
iajs-400	161	13	)	)	PUNCT
iajs-400	161	14	)	)	PUNCT
iajs-400	161	15	a((intcl))a(cl(inta	a((intcl))a(cl(inta	PROPN
iajs-400	161	16	g*sg*s	g*sg*s	PROPN
iajs-400	161	17	⊆	⊆	PUNCT
iajs-400	161	18	.	.	PUNCT
iajs-400	162	1	since	since	SCONJ
iajs-400	162	2	φ=)a(int	φ=)a(int	NOUN
iajs-400	162	3	g*s	g*s	PROPN
iajs-400	162	4	,	,	PUNCT
iajs-400	162	5	then	then	ADV
iajs-400	162	6	φ=))a((intcl	φ=))a((intcl	PROPN
iajs-400	162	7	g*s	g*s	PROPN
iajs-400	162	8	,	,	PUNCT
iajs-400	162	9	therefore	therefore	ADV
iajs-400	162	10	)	)	PUNCT
iajs-400	162	11	)	)	PUNCT
iajs-400	162	12	a(cl(inta	a(cl(inta	ADP
iajs-400	162	13	g*s⊆	g*s⊆	NOUN
iajs-400	162	14	.	.	PUNCT
iajs-400	163	1	thus	thus	ADV
iajs-400	163	2	a	a	PRON
iajs-400	163	3	is	be	AUX
iajs-400	163	4	a	a	DET
iajs-400	163	5	pre	pre	ADJ
iajs-400	163	6	-	-	ADJ
iajs-400	163	7	s*g	s*g	ADJ
iajs-400	163	8	-	-	PUNCT
iajs-400	163	9	open	open	NOUN
iajs-400	163	10	set	set	NOUN
iajs-400	163	11	.	.	PUNCT
iajs-400	164	1	propositions(2.17	propositions(2.17	X
iajs-400	164	2	):	):	PUNCT
iajs-400	164	3	if	if	SCONJ
iajs-400	164	4	)	)	PUNCT
iajs-400	164	5	,	,	PUNCT
iajs-400	164	6	x	x	X
iajs-400	164	7	(	(	PUNCT
iajs-400	164	8	τ	τ	X
iajs-400	164	9	is	be	AUX
iajs-400	164	10	a	a	DET
iajs-400	164	11	door	door	NOUN
iajs-400	164	12	space	space	NOUN
iajs-400	164	13	,	,	PUNCT
iajs-400	164	14	then	then	ADV
iajs-400	164	15	:	:	PUNCT
iajs-400	164	16	i	i	NOUN
iajs-400	164	17	)	)	PUNCT
iajs-400	164	18	every	every	DET
iajs-400	164	19	pre	pre	ADJ
iajs-400	164	20	-	-	ADJ
iajs-400	164	21	s*g	s*g	ADJ
iajs-400	164	22	-	-	PUNCT
iajs-400	164	23	open	open	ADJ
iajs-400	164	24	set	set	NOUN
iajs-400	164	25	is	be	AUX
iajs-400	164	26	s*g	s*g	NOUN
iajs-400	164	27	-	-	PUNCT
iajs-400	164	28	open	open	ADJ
iajs-400	164	29	.	.	PUNCT
iajs-400	165	1	ii	ii	X
iajs-400	165	2	)	)	PUNCT
iajs-400	165	3	everyβ	everyβ	NOUN
iajs-400	165	4	-s*g	-s*g	NOUN
iajs-400	165	5	-	-	PUNCT
iajs-400	165	6	open	open	ADJ
iajs-400	165	7	set	set	NOUN
iajs-400	165	8	is	be	AUX
iajs-400	165	9	b	b	NOUN
iajs-400	165	10	-	-	PUNCT
iajs-400	165	11	s*g	s*g	NOUN
iajs-400	165	12	-	-	PUNCT
iajs-400	165	13	open	open	ADJ
iajs-400	165	14	.	.	PUNCT
iajs-400	166	1	355	355	NUM
iajs-400	167	1	|	|	ADV
iajs-400	167	2	mathematics	mathematics	PROPN
iajs-400	167	3	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	167	4	�	�	NOUN
iajs-400	167	5	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	167	6	:	:	PUNCT
iajs-400	167	7	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	167	8	©	©	PROPN
iajs-400	167	9	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	167	10	ibn	ibn	PROPN
iajs-400	167	11	al	al	PROPN
iajs-400	167	12	-	-	PUNCT
iajs-400	167	13	haitham	haitham	PROPN
iajs-400	167	14	jour	jour	X
iajs-400	167	15	.	.	PROPN
iajs-400	168	1	for	for	ADP
iajs-400	168	2	pure	pure	ADJ
iajs-400	168	3	&	&	CCONJ
iajs-400	168	4	appl	appl	PROPN
iajs-400	168	5	.	.	PUNCT
iajs-400	169	1	sci	sci	PROPN
iajs-400	169	2	.	.	PUNCT
iajs-400	169	3	vol	vol	NOUN
iajs-400	169	4	.	.	PROPN
iajs-400	170	1	27	27	NUM
iajs-400	170	2	(	(	PUNCT
iajs-400	170	3	1	1	NUM
iajs-400	170	4	)	)	PUNCT
iajs-400	170	5	2014	2014	NUM
iajs-400	170	6	proof	proof	NOUN
iajs-400	170	7	:	:	PUNCT
iajs-400	170	8	i	i	PRON
iajs-400	170	9	)	)	PUNCT
iajs-400	170	10	let	let	VERB
iajs-400	170	11	a	a	PRON
iajs-400	170	12	be	be	AUX
iajs-400	170	13	an	an	DET
iajs-400	170	14	pre	pre	ADJ
iajs-400	170	15	-	-	ADJ
iajs-400	170	16	s*g	s*g	ADJ
iajs-400	170	17	-	-	PUNCT
iajs-400	170	18	open	open	ADJ
iajs-400	170	19	set	set	NOUN
iajs-400	170	20	.	.	PUNCT
iajs-400	171	1	if	if	SCONJ
iajs-400	171	2	a	a	PRON
iajs-400	171	3	is	be	AUX
iajs-400	171	4	open	open	ADJ
iajs-400	171	5	,	,	PUNCT
iajs-400	171	6	then	then	ADV
iajs-400	171	7	a	a	PRON
iajs-400	171	8	is	be	AUX
iajs-400	171	9	s*g	s*g	NOUN
iajs-400	171	10	-	-	PUNCT
iajs-400	171	11	open	open	ADJ
iajs-400	171	12	.	.	PUNCT
iajs-400	172	1	otherwise	otherwise	ADV
iajs-400	172	2	,	,	PUNCT
iajs-400	172	3	a	a	PRON
iajs-400	172	4	is	be	AUX
iajs-400	172	5	closed	closed	ADJ
iajs-400	172	6	and	and	CCONJ
iajs-400	172	7	hence	hence	ADV
iajs-400	172	8	)	)	PUNCT
iajs-400	172	9	)	)	PUNCT
iajs-400	173	1	a(cl(inta	a(cl(inta	ADP
iajs-400	173	2	g*s⊆	g*s⊆	NOUN
iajs-400	173	3	)	)	PUNCT
iajs-400	173	4	a(int	a(int	PROPN
iajs-400	173	5	g*s=	g*s=	PROPN
iajs-400	173	6	.	.	PUNCT
iajs-400	174	1	therefore	therefore	ADV
iajs-400	174	2	,	,	PUNCT
iajs-400	174	3	)	)	PUNCT
iajs-400	174	4	a(inta	a(inta	NOUN
iajs-400	174	5	g*s=	g*s=	PROPN
iajs-400	174	6	and	and	CCONJ
iajs-400	174	7	thus	thus	ADV
iajs-400	174	8	a	a	PRON
iajs-400	174	9	is	be	AUX
iajs-400	174	10	an	an	DET
iajs-400	174	11	s*g	s*g	VERB
iajs-400	174	12	-	-	PUNCT
iajs-400	174	13	open	open	ADJ
iajs-400	174	14	set	set	NOUN
iajs-400	174	15	.	.	PUNCT
iajs-400	175	1	ii	ii	PROPN
iajs-400	175	2	)	)	PUNCT
iajs-400	175	3	let	let	VERB
iajs-400	175	4	a	a	DET
iajs-400	175	5	be	be	AUX
iajs-400	175	6	anβ	anβ	NOUN
iajs-400	175	7	-s*g	-s*g	ADJ
iajs-400	175	8	-	-	PUNCT
iajs-400	175	9	open	open	NOUN
iajs-400	175	10	set	set	NOUN
iajs-400	175	11	.	.	PUNCT
iajs-400	176	1	if	if	SCONJ
iajs-400	176	2	a	a	PRON
iajs-400	176	3	is	be	AUX
iajs-400	176	4	open	open	ADJ
iajs-400	176	5	,	,	PUNCT
iajs-400	176	6	then	then	ADV
iajs-400	176	7	a	a	PRON
iajs-400	176	8	is	be	AUX
iajs-400	176	9	b	b	NOUN
iajs-400	176	10	-	-	PUNCT
iajs-400	176	11	s*g	s*g	NOUN
iajs-400	176	12	-	-	PUNCT
iajs-400	176	13	open	open	ADJ
iajs-400	176	14	.	.	PUNCT
iajs-400	177	1	otherwise	otherwise	ADV
iajs-400	177	2	,	,	PUNCT
iajs-400	177	3	a	a	PRON
iajs-400	177	4	is	be	AUX
iajs-400	177	5	closed	closed	ADJ
iajs-400	177	6	and	and	CCONJ
iajs-400	177	7	hence	hence	ADV
iajs-400	177	8	)	)	PUNCT
iajs-400	177	9	)	)	PUNCT
iajs-400	177	10	)	)	PUNCT
iajs-400	177	11	a(cl((intcla	a(cl((intcla	VERB
iajs-400	177	12	g*s⊆	g*s⊆	NOUN
iajs-400	177	13	)	)	PUNCT
iajs-400	177	14	)	)	PUNCT
iajs-400	178	1	a((intcl	a((intcl	PROPN
iajs-400	178	2	g*s=	g*s=	PROPN
iajs-400	178	3	)	)	PUNCT
iajs-400	178	4	)	)	PUNCT
iajs-400	178	5	a((intcl))a(cl(int	a((intcl))a(cl(int	PROPN
iajs-400	178	6	g*sg*s	g*sg*s	PROPN
iajs-400	178	7	⊆	⊆	PUNCT
iajs-400	178	8	.	.	PUNCT
iajs-400	179	1	therefore	therefore	ADV
iajs-400	179	2	a	a	PRON
iajs-400	179	3	is	be	AUX
iajs-400	179	4	an	an	DET
iajs-400	179	5	b	b	NOUN
iajs-400	179	6	-	-	PUNCT
iajs-400	179	7	s*g	s*g	VERB
iajs-400	179	8	-	-	PUNCT
iajs-400	179	9	open	open	NOUN
iajs-400	179	10	set	set	NOUN
iajs-400	179	11	.	.	PUNCT
iajs-400	180	1	definitions(2.18	definitions(2.18	X
iajs-400	180	2	):	):	PUNCT
iajs-400	180	3	a	a	DET
iajs-400	180	4	subset	subset	NOUN
iajs-400	180	5	a	a	PRON
iajs-400	180	6	of	of	ADP
iajs-400	180	7	a	a	DET
iajs-400	180	8	topological	topological	ADJ
iajs-400	180	9	space	space	NOUN
iajs-400	180	10	)	)	PUNCT
iajs-400	180	11	,	,	PUNCT
iajs-400	180	12	x	x	X
iajs-400	180	13	(	(	PUNCT
iajs-400	180	14	τ	τ	X
iajs-400	180	15	is	be	AUX
iajs-400	180	16	called	call	VERB
iajs-400	180	17	:	:	PUNCT
iajs-400	180	18	i	i	X
iajs-400	180	19	)	)	PUNCT
iajs-400	180	20	an	an	DET
iajs-400	180	21	s*g	s*g	PROPN
iajs-400	180	22	-	-	PUNCT
iajs-400	180	23	t	t	NOUN
iajs-400	180	24	-	-	PUNCT
iajs-400	180	25	set	set	VERB
iajs-400	180	26	if	if	SCONJ
iajs-400	180	27	)	)	PUNCT
iajs-400	180	28	)	)	PUNCT
iajs-400	181	1	a(cl(int)aint	a(cl(int)aint	PROPN
iajs-400	181	2	(	(	PUNCT
iajs-400	181	3	g*s=	g*s=	PROPN
iajs-400	181	4	.	.	PUNCT
iajs-400	182	1	ii	ii	PROPN
iajs-400	182	2	)	)	PUNCT
iajs-400	182	3	an	an	DET
iajs-400	182	4	s*g	s*g	PROPN
iajs-400	182	5	-	-	PUNCT
iajs-400	182	6	b	b	NOUN
iajs-400	182	7	-	-	PUNCT
iajs-400	182	8	set	set	VERB
iajs-400	182	9	if	if	SCONJ
iajs-400	182	10	vua	vua	PROPN
iajs-400	182	11	=	=	X
iajs-400	182	12	,	,	PUNCT
iajs-400	182	13	where	where	SCONJ
iajs-400	182	14	τ∈u	τ∈u	PRON
iajs-400	182	15	and	and	CCONJ
iajs-400	182	16	v	v	NOUN
iajs-400	182	17	is	be	AUX
iajs-400	182	18	an	an	DET
iajs-400	182	19	s*g	s*g	PROPN
iajs-400	182	20	-	-	PUNCT
iajs-400	182	21	t	t	NOUN
iajs-400	182	22	-	-	PUNCT
iajs-400	182	23	set	set	VERB
iajs-400	182	24	.	.	PUNCT
iajs-400	183	1	proposition(2.19	proposition(2.19	NUM
iajs-400	183	2	):	):	PUNCT
iajs-400	183	3	let	let	VERB
iajs-400	183	4	a	a	PRON
iajs-400	183	5	and	and	CCONJ
iajs-400	183	6	b	b	NOUN
iajs-400	183	7	be	be	AUX
iajs-400	183	8	subsets	subset	NOUN
iajs-400	183	9	of	of	ADP
iajs-400	183	10	a	a	DET
iajs-400	183	11	topological	topological	ADJ
iajs-400	183	12	space	space	NOUN
iajs-400	183	13	)	)	PUNCT
iajs-400	183	14	,	,	PUNCT
iajs-400	183	15	x	x	X
iajs-400	183	16	(	(	PUNCT
iajs-400	183	17	τ	τ	X
iajs-400	183	18	.	.	PUNCT
iajs-400	184	1	if	if	SCONJ
iajs-400	184	2	a	a	PRON
iajs-400	184	3	and	and	CCONJ
iajs-400	184	4	b	b	NOUN
iajs-400	184	5	are	be	AUX
iajs-400	184	6	s*gt	s*gt	NOUN
iajs-400	184	7	-	-	PUNCT
iajs-400	184	8	sets	set	NOUN
iajs-400	184	9	,	,	PUNCT
iajs-400	184	10	then	then	ADV
iajs-400	184	11	ba	ba	ADJ
iajs-400	184	12	is	be	AUX
iajs-400	184	13	an	an	DET
iajs-400	184	14	s*g	s*g	PROPN
iajs-400	184	15	-	-	PUNCT
iajs-400	184	16	t	t	NOUN
iajs-400	184	17	-	-	PUNCT
iajs-400	184	18	set	set	NOUN
iajs-400	184	19	.	.	PUNCT
iajs-400	185	1	proof	proof	NOUN
iajs-400	185	2	:	:	PUNCT
iajs-400	185	3	let	let	VERB
iajs-400	185	4	a	a	PRON
iajs-400	185	5	and	and	CCONJ
iajs-400	185	6	b	b	NOUN
iajs-400	185	7	be	be	AUX
iajs-400	185	8	s*g	s*g	NOUN
iajs-400	185	9	-	-	PUNCT
iajs-400	185	10	t	t	NOUN
iajs-400	185	11	-	-	PUNCT
iajs-400	185	12	sets	set	NOUN
iajs-400	185	13	.	.	PUNCT
iajs-400	186	1	then	then	ADV
iajs-400	186	2	we	we	PRON
iajs-400	186	3	have	have	VERB
iajs-400	186	4	:	:	PUNCT
iajs-400	186	5	)	)	PUNCT
iajs-400	186	6	)	)	PUNCT
iajs-400	186	7	ba(cl(int	ba(cl(int	PROPN
iajs-400	186	8	g*s	g*s	PROPN
iajs-400	186	9			PROPN
iajs-400	186	10	)	)	PUNCT
iajs-400	186	11	)	)	PUNCT
iajs-400	187	1	b(cl)a(cl(int	b(cl)a(cl(int	PROPN
iajs-400	187	2	g*s	g*s	PROPN
iajs-400	187	3	⊆	⊆	PROPN
iajs-400	187	4	)	)	PUNCT
iajs-400	187	5	)	)	PUNCT
iajs-400	188	1	b(cl(int))a(cl(int	b(cl(int))a(cl(int	PUNCT
iajs-400	188	2	g*sg*s	g*sg*s	PROPN
iajs-400	188	3	=	=	X
iajs-400	188	4	)	)	PUNCT
iajs-400	188	5	bint()aint	bint()aint	NOUN
iajs-400	188	6	(	(	PUNCT
iajs-400	188	7	=	=	X
iajs-400	188	8	)	)	PUNCT
iajs-400	188	9	baint	baint	NOUN
iajs-400	188	10	(	(	PUNCT
iajs-400	188	11	=	=	X
iajs-400	188	12	.	.	PUNCT
iajs-400	189	1	since	since	SCONJ
iajs-400	189	2	)	)	PUNCT
iajs-400	189	3	)	)	PUNCT
iajs-400	189	4	ba(cl(int)baint	ba(cl(int)baint	NOUN
iajs-400	189	5	(	(	PUNCT
iajs-400	189	6	g*s	g*s	PROPN
iajs-400	189	7			NUM
iajs-400	189	8	⊆	⊆	NUM
iajs-400	189	9	,	,	PUNCT
iajs-400	189	10	then	then	ADV
iajs-400	189	11	)	)	PUNCT
iajs-400	189	12	)	)	PUNCT
iajs-400	189	13	ba(cl(int)baint	ba(cl(int)baint	NOUN
iajs-400	189	14	(	(	PUNCT
iajs-400	189	15	g*s	g*s	PROPN
iajs-400	189	16			X
iajs-400	189	17	=	=	PUNCT
iajs-400	190	1	and	and	CCONJ
iajs-400	190	2	hence	hence	ADV
iajs-400	190	3	ba	ba	PROPN
iajs-400	190	4			PROPN
iajs-400	190	5	is	be	AUX
iajs-400	190	6	an	an	DET
iajs-400	190	7	s*g	s*g	PROPN
iajs-400	190	8	-	-	PUNCT
iajs-400	190	9	t	t	NOUN
iajs-400	190	10	-	-	PUNCT
iajs-400	190	11	set	set	NOUN
iajs-400	190	12	.	.	PUNCT
iajs-400	191	1	from	from	ADP
iajs-400	191	2	the	the	DET
iajs-400	191	3	following	following	ADJ
iajs-400	191	4	example	example	NOUN
iajs-400	191	5	one	one	PRON
iajs-400	191	6	can	can	AUX
iajs-400	191	7	deduce	deduce	VERB
iajs-400	191	8	that	that	SCONJ
iajs-400	191	9	a	a	DET
iajs-400	191	10	pre	pre	ADJ
iajs-400	191	11	-	-	ADJ
iajs-400	191	12	s*g	s*g	ADJ
iajs-400	191	13	-	-	PUNCT
iajs-400	191	14	open	open	NOUN
iajs-400	191	15	set	set	NOUN
iajs-400	191	16	and	and	CCONJ
iajs-400	191	17	a	a	DET
iajs-400	191	18	s*g	s*g	PROPN
iajs-400	191	19	-	-	PUNCT
iajs-400	191	20	b	b	NOUN
iajs-400	191	21	-	-	PUNCT
iajs-400	191	22	set	set	NOUN
iajs-400	191	23	are	be	AUX
iajs-400	191	24	independent	independent	ADJ
iajs-400	191	25	.	.	PUNCT
iajs-400	192	1	example(2.20	example(2.20	X
iajs-400	192	2	):	):	PUNCT
iajs-400	192	3	let	let	VERB
iajs-400	192	4	x	x	PUNCT
iajs-400	192	5	=	=	PUNCT
iajs-400	192	6	r	r	NOUN
iajs-400	192	7	with	with	ADP
iajs-400	192	8	the	the	DET
iajs-400	192	9	usual	usual	ADJ
iajs-400	192	10	topology	topology	NOUN
iajs-400	192	11	τ	τ	PROPN
iajs-400	192	12	.	.	PUNCT
iajs-400	193	1	then	then	ADV
iajs-400	193	2	q\r	q\r	PROPN
iajs-400	193	3	is	be	AUX
iajs-400	193	4	pre	pre	ADJ
iajs-400	193	5	-	-	ADJ
iajs-400	193	6	s*g	s*g	ADJ
iajs-400	193	7	-	-	PUNCT
iajs-400	193	8	open	open	ADJ
iajs-400	193	9	,	,	PUNCT
iajs-400	193	10	but	but	CCONJ
iajs-400	193	11	it	it	PRON
iajs-400	193	12	is	be	AUX
iajs-400	193	13	not	not	PART
iajs-400	193	14	an	an	DET
iajs-400	193	15	s*g	s*g	NOUN
iajs-400	193	16	-	-	PUNCT
iajs-400	193	17	b	b	NOUN
iajs-400	193	18	-	-	PUNCT
iajs-400	193	19	set	set	NOUN
iajs-400	193	20	(	(	PUNCT
iajs-400	193	21	since	since	SCONJ
iajs-400	193	22	q\rrq\r	q\rrq\r	PROPN
iajs-400	193	23	=	=	X
iajs-400	193	24	,	,	PUNCT
iajs-400	194	1	where	where	SCONJ
iajs-400	194	2	τ∈r	τ∈r	NOUN
iajs-400	194	3	,	,	PUNCT
iajs-400	194	4	but	but	CCONJ
iajs-400	194	5	q\r	q\r	NOUN
iajs-400	194	6	is	be	AUX
iajs-400	194	7	not	not	PART
iajs-400	194	8	an	an	DET
iajs-400	194	9	s*g	s*g	PROPN
iajs-400	194	10	-	-	PUNCT
iajs-400	194	11	t	t	NOUN
iajs-400	194	12	-	-	PUNCT
iajs-400	194	13	set	set	NOUN
iajs-400	194	14	)	)	PUNCT
iajs-400	194	15	and	and	CCONJ
iajs-400	194	16	(	(	PUNCT
iajs-400	194	17	0,1	0,1	NUM
iajs-400	194	18	]	]	PUNCT
iajs-400	194	19	is	be	AUX
iajs-400	194	20	an	an	DET
iajs-400	194	21	s*g	s*g	PROPN
iajs-400	194	22	-	-	PUNCT
iajs-400	194	23	b	b	NOUN
iajs-400	194	24	-	-	PUNCT
iajs-400	194	25	set	set	NOUN
iajs-400	194	26	(	(	PUNCT
iajs-400	194	27	since	since	SCONJ
iajs-400	194	28	]	]	X
iajs-400	194	29	1,0(r]1,0	1,0(r]1,0	NUM
iajs-400	194	30	(	(	PUNCT
iajs-400	194	31	=	=	X
iajs-400	194	32	,	,	PUNCT
iajs-400	194	33	where	where	SCONJ
iajs-400	194	34	τ∈r	τ∈r	NOUN
iajs-400	194	35	and	and	CCONJ
iajs-400	194	36	(	(	PUNCT
iajs-400	194	37	0,1	0,1	NUM
iajs-400	194	38	]	]	PUNCT
iajs-400	194	39	is	be	AUX
iajs-400	194	40	an	an	DET
iajs-400	194	41	s*g	s*g	PROPN
iajs-400	194	42	-	-	PUNCT
iajs-400	194	43	t	t	NOUN
iajs-400	194	44	-	-	PUNCT
iajs-400	194	45	set	set	NOUN
iajs-400	194	46	)	)	PUNCT
iajs-400	194	47	which	which	PRON
iajs-400	194	48	is	be	AUX
iajs-400	194	49	not	not	PART
iajs-400	194	50	pre	pre	ADJ
iajs-400	194	51	-	-	ADJ
iajs-400	194	52	s*g	s*g	ADJ
iajs-400	194	53	-	-	PUNCT
iajs-400	194	54	open	open	ADJ
iajs-400	194	55	(	(	PUNCT
iajs-400	194	56	since	since	SCONJ
iajs-400	194	57	)	)	PUNCT
iajs-400	194	58	1,0(]))1,0((cl(int]1,0	1,0(]))1,0((cl(int]1,0	NUM
iajs-400	194	59	(	(	PUNCT
iajs-400	194	60	g*s	g*s	PROPN
iajs-400	194	61	=	=	PRON
iajs-400	194	62	⊄	⊄	NOUN
iajs-400	194	63	)	)	PUNCT
iajs-400	194	64	.	.	PUNCT
iajs-400	195	1	proposition(2.21	proposition(2.21	NUM
iajs-400	195	2	):	):	PUNCT
iajs-400	195	3	let	let	NOUN
iajs-400	195	4	)	)	PUNCT
iajs-400	195	5	,	,	PUNCT
iajs-400	195	6	x	x	X
iajs-400	195	7	(	(	PUNCT
iajs-400	195	8	τ	τ	X
iajs-400	195	9	be	be	AUX
iajs-400	195	10	a	a	DET
iajs-400	195	11	topological	topological	ADJ
iajs-400	195	12	space	space	NOUN
iajs-400	195	13	and	and	CCONJ
iajs-400	195	14	xa	xa	PROPN
iajs-400	195	15	⊆	⊆	NUM
iajs-400	195	16	.	.	PUNCT
iajs-400	196	1	then	then	ADV
iajs-400	196	2	the	the	DET
iajs-400	196	3	following	follow	VERB
iajs-400	196	4	are	be	AUX
iajs-400	196	5	equivalent	equivalent	ADJ
iajs-400	196	6	:	:	PUNCT
iajs-400	196	7	i	i	X
iajs-400	196	8	)	)	PUNCT
iajs-400	196	9	a	a	PRON
iajs-400	196	10	is	be	AUX
iajs-400	196	11	open	open	ADJ
iajs-400	196	12	.	.	PUNCT
iajs-400	197	1	ii	ii	X
iajs-400	197	2	)	)	PUNCT
iajs-400	197	3	a	a	PRON
iajs-400	197	4	is	be	AUX
iajs-400	197	5	pre	pre	ADJ
iajs-400	197	6	-	-	ADJ
iajs-400	197	7	s*g	s*g	ADJ
iajs-400	197	8	-	-	PUNCT
iajs-400	197	9	open	open	ADJ
iajs-400	197	10	and	and	CCONJ
iajs-400	197	11	an	an	DET
iajs-400	197	12	s*g	s*g	PROPN
iajs-400	197	13	-	-	PUNCT
iajs-400	197	14	b	b	NOUN
iajs-400	197	15	-	-	PUNCT
iajs-400	197	16	set	set	NOUN
iajs-400	197	17	.	.	PUNCT
iajs-400	198	1	proof	proof	NOUN
iajs-400	198	2	:	:	PUNCT
iajs-400	198	3	)	)	PUNCT
iajs-400	198	4	ii()i	ii()i	NOUN
iajs-400	198	5	(	(	PUNCT
iajs-400	198	6	⇒	⇒	NOUN
iajs-400	198	7	.	.	PUNCT
iajs-400	199	1	let	let	VERB
iajs-400	199	2	a	a	PRON
iajs-400	199	3	be	be	AUX
iajs-400	199	4	open	open	ADJ
iajs-400	199	5	.	.	PUNCT
iajs-400	200	1	then	then	ADV
iajs-400	200	2	)	)	PUNCT
iajs-400	200	3	a(inta	a(inta	PROPN
iajs-400	200	4	g*s=	g*s=	PROPN
iajs-400	200	5	)	)	PUNCT
iajs-400	200	6	)	)	PUNCT
iajs-400	200	7	a(cl(int	a(cl(int	NOUN
iajs-400	200	8	g*s⊆	g*s⊆	NOUN
iajs-400	200	9	and	and	CCONJ
iajs-400	200	10	a	a	PRON
iajs-400	200	11	is	be	AUX
iajs-400	200	12	pre	pre	ADJ
iajs-400	200	13	-	-	ADJ
iajs-400	200	14	s*g	s*g	ADJ
iajs-400	200	15	-	-	PUNCT
iajs-400	200	16	open	open	ADJ
iajs-400	200	17	.	.	PUNCT
iajs-400	201	1	also	also	ADV
iajs-400	201	2	,	,	PUNCT
iajs-400	201	3	xaa	xaa	PROPN
iajs-400	201	4	=	=	X
iajs-400	201	5	,	,	PUNCT
iajs-400	201	6	where	where	SCONJ
iajs-400	201	7	τ∈a	τ∈a	NOUN
iajs-400	201	8	and	and	CCONJ
iajs-400	201	9	x	x	PRON
iajs-400	201	10	is	be	AUX
iajs-400	201	11	an	an	DET
iajs-400	201	12	s*g	s*g	PROPN
iajs-400	201	13	-	-	PUNCT
iajs-400	201	14	t	t	NOUN
iajs-400	201	15	-	-	PUNCT
iajs-400	201	16	set	set	VERB
iajs-400	201	17	and	and	CCONJ
iajs-400	201	18	hence	hence	ADV
iajs-400	201	19	a	a	PRON
iajs-400	201	20	is	be	AUX
iajs-400	201	21	an	an	DET
iajs-400	201	22	s*g	s*g	PROPN
iajs-400	201	23	-	-	PUNCT
iajs-400	201	24	b	b	NOUN
iajs-400	201	25	-	-	PUNCT
iajs-400	201	26	set	set	VERB
iajs-400	201	27	.	.	PUNCT
iajs-400	201	28	)	)	PUNCT
iajs-400	202	1	i()ii	i()ii	NOUN
iajs-400	202	2	(	(	PUNCT
iajs-400	202	3	⇒	⇒	NOUN
iajs-400	202	4	.	.	PUNCT
iajs-400	203	1	since	since	SCONJ
iajs-400	203	2	a	a	PRON
iajs-400	203	3	is	be	AUX
iajs-400	203	4	an	an	DET
iajs-400	203	5	s*g	s*g	PROPN
iajs-400	203	6	-	-	PUNCT
iajs-400	203	7	b	b	NOUN
iajs-400	203	8	-	-	PUNCT
iajs-400	203	9	set	set	NOUN
iajs-400	203	10	,	,	PUNCT
iajs-400	203	11	we	we	PRON
iajs-400	203	12	have	have	VERB
iajs-400	203	13	vua	vua	VERB
iajs-400	203	14	=	=	PROPN
iajs-400	203	15	,	,	PUNCT
iajs-400	203	16	where	where	SCONJ
iajs-400	203	17	τ∈u	τ∈u	PRON
iajs-400	203	18	and	and	CCONJ
iajs-400	203	19	v	v	NOUN
iajs-400	203	20	is	be	AUX
iajs-400	203	21	an	an	DET
iajs-400	203	22	s*g	s*g	PROPN
iajs-400	203	23	-	-	PUNCT
iajs-400	203	24	t	t	NOUN
iajs-400	203	25	-	-	PUNCT
iajs-400	203	26	set	set	NOUN
iajs-400	203	27	.	.	PUNCT
iajs-400	204	1	by	by	ADP
iajs-400	204	2	the	the	DET
iajs-400	204	3	hypothesis	hypothesis	NOUN
iajs-400	204	4	,	,	PUNCT
iajs-400	204	5	a	a	PRON
iajs-400	204	6	is	be	AUX
iajs-400	204	7	also	also	ADV
iajs-400	204	8	pre	pre	ADJ
iajs-400	204	9	-	-	ADJ
iajs-400	204	10	s*g	s*g	ADJ
iajs-400	204	11	-	-	PUNCT
iajs-400	204	12	open	open	ADJ
iajs-400	204	13	and	and	CCONJ
iajs-400	204	14	we	we	PRON
iajs-400	204	15	have	have	VERB
iajs-400	204	16	:	:	PUNCT
iajs-400	204	17	)	)	PUNCT
iajs-400	204	18	)	)	PUNCT
iajs-400	205	1	a(cl(inta	a(cl(inta	ADP
iajs-400	205	2	g*s⊆	g*s⊆	NOUN
iajs-400	205	3	)	)	PUNCT
iajs-400	205	4	)	)	PUNCT
iajs-400	205	5	vu(cl(int	vu(cl(int	PROPN
iajs-400	205	6	g*s	g*s	PROPN
iajs-400	205	7	=	=	NUM
iajs-400	205	8	)	)	PUNCT
iajs-400	205	9	)	)	PUNCT
iajs-400	206	1	v(cl)u(cl(int	v(cl)u(cl(int	PROPN
iajs-400	207	1	g*s	g*s	PROPN
iajs-400	207	2	⊆	⊆	PROPN
iajs-400	207	3	)	)	PUNCT
iajs-400	207	4	)	)	PUNCT
iajs-400	208	1	v(cl(int))u(cl(int	v(cl(int))u(cl(int	X
iajs-400	209	1	g*sg*s	g*sg*s	PROPN
iajs-400	209	2	=	=	X
iajs-400	209	3	)	)	PUNCT
iajs-400	210	1	vint())u(cl(int	vint())u(cl(int	NOUN
iajs-400	210	2	g*s	g*s	PROPN
iajs-400	210	3	=	=	PUNCT
iajs-400	210	4	hence	hence	ADV
iajs-400	210	5	u)vu(vua	u)vu(vua	VERB
iajs-400	210	6			PUNCT
iajs-400	211	1	=	=	SYM
iajs-400	211	2	=	=	SYM
iajs-400	211	3	u))vint())u(cl((int	u))vint())u(cl((int	PROPN
iajs-400	211	4	g*s	g*s	PROPN
iajs-400	211	5	⊆	⊆	PROPN
iajs-400	211	6	)	)	PUNCT
iajs-400	211	7	vint()u))u(cl((int	vint()u))u(cl((int	PROPN
iajs-400	211	8	g*s	g*s	PROPN
iajs-400	211	9	=	=	PROPN
iajs-400	211	10	)	)	PUNCT
iajs-400	211	11	vint(u	vint(u	ADJ
iajs-400	211	12	=	=	PUNCT
iajs-400	211	13	)	)	PUNCT
iajs-400	211	14	vint()uint	vint()uint	NOUN
iajs-400	211	15	(	(	PUNCT
iajs-400	211	16	=	=	X
iajs-400	211	17	)	)	PUNCT
iajs-400	211	18	vuint	vuint	NOUN
iajs-400	211	19	(	(	PUNCT
iajs-400	211	20	=	=	X
iajs-400	211	21	)	)	PUNCT
iajs-400	211	22	aint(=	aint(=	PROPN
iajs-400	211	23	.	.	PUNCT
iajs-400	212	1	therefore	therefore	ADV
iajs-400	212	2	)	)	PUNCT
iajs-400	212	3	aint(a	aint(a	PROPN
iajs-400	212	4	=	=	PUNCT
iajs-400	212	5	and	and	CCONJ
iajs-400	212	6	a	a	PRON
iajs-400	212	7	is	be	AUX
iajs-400	212	8	open	open	ADJ
iajs-400	212	9	.	.	PUNCT
iajs-400	213	1	356	356	NUM
iajs-400	213	2	|	|	ADV
iajs-400	213	3	mathematics	mathematics	PROPN
iajs-400	213	4	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	213	5	�	�	NOUN
iajs-400	213	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	213	7	:	:	PUNCT
iajs-400	213	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	213	9	©	©	PROPN
iajs-400	213	10	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	213	11	ibn	ibn	PROPN
iajs-400	213	12	al	al	PROPN
iajs-400	213	13	-	-	PUNCT
iajs-400	213	14	haitham	haitham	PROPN
iajs-400	213	15	jour	jour	X
iajs-400	213	16	.	.	PROPN
iajs-400	214	1	for	for	ADP
iajs-400	214	2	pure	pure	ADJ
iajs-400	214	3	&	&	CCONJ
iajs-400	214	4	appl	appl	PROPN
iajs-400	214	5	.	.	PUNCT
iajs-400	215	1	sci	sci	PROPN
iajs-400	215	2	.	.	PUNCT
iajs-400	215	3	vol	vol	NOUN
iajs-400	215	4	.	.	PROPN
iajs-400	216	1	27	27	NUM
iajs-400	216	2	(	(	PUNCT
iajs-400	216	3	1	1	NUM
iajs-400	216	4	)	)	PUNCT
iajs-400	216	5	2014	2014	NUM
iajs-400	216	6	definitions(2.22	definitions(2.22	NOUN
iajs-400	216	7	):	):	PUNCT
iajs-400	216	8	a	a	DET
iajs-400	216	9	subset	subset	NOUN
iajs-400	216	10	a	a	PRON
iajs-400	216	11	of	of	ADP
iajs-400	216	12	a	a	DET
iajs-400	216	13	topological	topological	ADJ
iajs-400	216	14	space	space	NOUN
iajs-400	216	15	)	)	PUNCT
iajs-400	216	16	,	,	PUNCT
iajs-400	216	17	x	x	X
iajs-400	216	18	(	(	PUNCT
iajs-400	216	19	τ	τ	X
iajs-400	216	20	is	be	AUX
iajs-400	216	21	called	call	VERB
iajs-400	216	22	:	:	PUNCT
iajs-400	216	23	i	i	X
iajs-400	216	24	)	)	PUNCT
iajs-400	216	25	an	an	DET
iajs-400	216	26	s*gαt	s*gαt	PROPN
iajs-400	216	27	-set	-set	PUNCT
iajs-400	216	28	if	if	SCONJ
iajs-400	216	29	)	)	PUNCT
iajs-400	216	30	)	)	PUNCT
iajs-400	216	31	)	)	PUNCT
iajs-400	216	32	a((intcl(int)aint	a((intcl(int)aint	NOUN
iajs-400	216	33	(	(	PUNCT
iajs-400	216	34	g*sg*s=	g*sg*s=	PROPN
iajs-400	216	35	.	.	PUNCT
iajs-400	217	1	ii	ii	PROPN
iajs-400	217	2	)	)	PUNCT
iajs-400	217	3	an	an	DET
iajs-400	217	4	s*gαb	s*gαb	NOUN
iajs-400	217	5	-set	-set	PUNCT
iajs-400	217	6	if	if	SCONJ
iajs-400	217	7	vua	vua	PROPN
iajs-400	217	8	=	=	X
iajs-400	217	9	,	,	PUNCT
iajs-400	217	10	where	where	SCONJ
iajs-400	217	11	τ∈u	τ∈u	PRON
iajs-400	217	12	and	and	CCONJ
iajs-400	217	13	v	v	NOUN
iajs-400	217	14	is	be	AUX
iajs-400	217	15	an	an	DET
iajs-400	217	16	s*gαt	s*gαt	PROPN
iajs-400	217	17	-set	-set	PUNCT
iajs-400	217	18	.	.	PUNCT
iajs-400	218	1	proposition(2.23	proposition(2.23	NOUN
iajs-400	218	2	):	):	PUNCT
iajs-400	218	3	let	let	VERB
iajs-400	218	4	a	a	PRON
iajs-400	218	5	and	and	CCONJ
iajs-400	218	6	b	b	NOUN
iajs-400	218	7	be	be	AUX
iajs-400	218	8	subsets	subset	NOUN
iajs-400	218	9	of	of	ADP
iajs-400	218	10	a	a	DET
iajs-400	218	11	topological	topological	ADJ
iajs-400	218	12	space	space	NOUN
iajs-400	218	13	)	)	PUNCT
iajs-400	218	14	,	,	PUNCT
iajs-400	218	15	x	x	X
iajs-400	218	16	(	(	PUNCT
iajs-400	218	17	τ	τ	X
iajs-400	218	18	.	.	PUNCT
iajs-400	219	1	if	if	SCONJ
iajs-400	219	2	a	a	PRON
iajs-400	219	3	and	and	CCONJ
iajs-400	219	4	b	b	NOUN
iajs-400	219	5	are	be	AUX
iajs-400	219	6	s*gαt	s*gαt	ADJ
iajs-400	219	7	-sets	-set	NOUN
iajs-400	219	8	,	,	PUNCT
iajs-400	219	9	then	then	ADV
iajs-400	219	10	ba	ba	ADJ
iajs-400	219	11	is	be	AUX
iajs-400	219	12	an	an	DET
iajs-400	219	13	s*gαt	s*gαt	PROPN
iajs-400	219	14	-set	-set	PUNCT
iajs-400	219	15	.	.	PUNCT
iajs-400	220	1	proof	proof	NOUN
iajs-400	220	2	:	:	PUNCT
iajs-400	220	3	let	let	VERB
iajs-400	220	4	a	a	PRON
iajs-400	220	5	and	and	CCONJ
iajs-400	220	6	b	b	NOUN
iajs-400	220	7	be	be	AUX
iajs-400	220	8	s*gαt	s*gαt	ADJ
iajs-400	220	9	-sets	-set	NOUN
iajs-400	220	10	.	.	PUNCT
iajs-400	221	1	then	then	ADV
iajs-400	221	2	we	we	PRON
iajs-400	221	3	have	have	VERB
iajs-400	221	4	:	:	PUNCT
iajs-400	221	5	)	)	PUNCT
iajs-400	221	6	)	)	PUNCT
iajs-400	222	1	ba((intcl(int	ba((intcl(int	PROPN
iajs-400	222	2	g*sg*s	g*sg*s	PROPN
iajs-400	222	3			PROPN
iajs-400	222	4	)	)	PUNCT
iajs-400	222	5	)	)	PUNCT
iajs-400	222	6	)	)	PUNCT
iajs-400	223	1	b(int)a((intcl(int	b(int)a((intcl(int	PROPN
iajs-400	223	2	g*sg*sg*s	g*sg*sg*s	ADJ
iajs-400	223	3	=	=	NOUN
iajs-400	223	4	)	)	PUNCT
iajs-400	223	5	)	)	PUNCT
iajs-400	223	6	)	)	PUNCT
iajs-400	224	1	b((intcl)a((intcl(int	b((intcl)a((intcl(int	NOUN
iajs-400	224	2	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-400	224	3	⊆	⊆	PROPN
iajs-400	224	4	)	)	PUNCT
iajs-400	224	5	)	)	PUNCT
iajs-400	224	6	)	)	PUNCT
iajs-400	224	7	b((intcl(int)))a((intcl(int	b((intcl(int)))a((intcl(int	NOUN
iajs-400	224	8	g*sg*sg*sg*s	g*sg*sg*sg*s	NOUN
iajs-400	224	9	=	=	X
iajs-400	224	10	)	)	PUNCT
iajs-400	224	11	bint()aint	bint()aint	NOUN
iajs-400	224	12	(	(	PUNCT
iajs-400	224	13	=	=	X
iajs-400	224	14	)	)	PUNCT
iajs-400	224	15	baint	baint	NOUN
iajs-400	224	16	(	(	PUNCT
iajs-400	224	17	=	=	X
iajs-400	224	18	.	.	PUNCT
iajs-400	225	1	since	since	SCONJ
iajs-400	225	2	)	)	PUNCT
iajs-400	225	3	)	)	PUNCT
iajs-400	225	4	)	)	PUNCT
iajs-400	225	5	ba((intcl(int)baint	ba((intcl(int)baint	PROPN
iajs-400	226	1	(	(	PUNCT
iajs-400	226	2	g*sg*s	g*sg*s	PROPN
iajs-400	226	3			PROPN
iajs-400	226	4	⊆	⊆	NUM
iajs-400	226	5	,	,	PUNCT
iajs-400	226	6	then	then	ADV
iajs-400	226	7	)	)	PUNCT
iajs-400	226	8	)	)	PUNCT
iajs-400	226	9	ba((intcl(int)baint	ba((intcl(int)baint	PROPN
iajs-400	226	10	(	(	PUNCT
iajs-400	226	11	g*sg*s	g*sg*s	PROPN
iajs-400	226	12			PROPN
iajs-400	226	13	=	=	PUNCT
iajs-400	227	1	and	and	CCONJ
iajs-400	227	2	hence	hence	ADV
iajs-400	227	3	ba	ba	PROPN
iajs-400	227	4			PROPN
iajs-400	227	5	is	be	AUX
iajs-400	227	6	an	an	DET
iajs-400	227	7	s*gαt	s*gαt	PROPN
iajs-400	227	8	-set	-set	X
iajs-400	227	9	.	.	PUNCT
iajs-400	228	1	from	from	ADP
iajs-400	228	2	the	the	DET
iajs-400	228	3	following	following	ADJ
iajs-400	228	4	example	example	NOUN
iajs-400	228	5	one	one	PRON
iajs-400	228	6	can	can	AUX
iajs-400	228	7	deduce	deduce	VERB
iajs-400	228	8	that	that	SCONJ
iajs-400	228	9	an	an	DET
iajs-400	228	10	α	α	NOUN
iajs-400	228	11	-s*g	-s*g	ADJ
iajs-400	228	12	-	-	PUNCT
iajs-400	228	13	open	open	NOUN
iajs-400	228	14	set	set	NOUN
iajs-400	228	15	and	and	CCONJ
iajs-400	228	16	an	an	DET
iajs-400	228	17	s*gαb	s*gαb	NOUN
iajs-400	228	18	-set	-set	PUNCT
iajs-400	228	19	are	be	AUX
iajs-400	228	20	independent	independent	ADJ
iajs-400	228	21	.	.	PUNCT
iajs-400	229	1	example(2.24	example(2.24	NOUN
iajs-400	229	2	):	):	PUNCT
iajs-400	229	3	let	let	VERB
iajs-400	229	4	x	x	PUNCT
iajs-400	229	5	=	=	PUNCT
iajs-400	229	6	r	r	NOUN
iajs-400	229	7	with	with	ADP
iajs-400	229	8	the	the	DET
iajs-400	229	9	usual	usual	ADJ
iajs-400	229	10	topology	topology	NOUN
iajs-400	229	11	τ	τ	X
iajs-400	229	12	.	.	PUNCT
iajs-400	230	1	then	then	ADV
iajs-400	230	2	(	(	PUNCT
iajs-400	230	3	0,1	0,1	NOUN
iajs-400	230	4	]	]	PUNCT
iajs-400	230	5	is	be	AUX
iajs-400	230	6	an	an	DET
iajs-400	230	7	s*gαb	s*gαb	NOUN
iajs-400	230	8	-set	-set	NUM
iajs-400	230	9	which	which	PRON
iajs-400	230	10	is	be	AUX
iajs-400	230	11	not	not	PART
iajs-400	230	12	α	α	DET
iajs-400	230	13	-s*g	-s*g	NOUN
iajs-400	230	14	-	-	PUNCT
iajs-400	230	15	open	open	ADJ
iajs-400	230	16	.	.	PUNCT
iajs-400	231	1	also	also	ADV
iajs-400	231	2	,	,	PUNCT
iajs-400	231	3	in	in	ADP
iajs-400	231	4	example	example	NOUN
iajs-400	231	5	(	(	PUNCT
iajs-400	231	6	2.3	2.3	NUM
iajs-400	231	7	)	)	PUNCT
iajs-400	231	8	,	,	PUNCT
iajs-400	231	9	}	}	PUNCT
iajs-400	231	10	b	b	NOUN
iajs-400	231	11	,	,	PUNCT
iajs-400	231	12	a{a	a{a	X
iajs-400	232	1	=	=	PRON
iajs-400	232	2	is	be	AUX
iajs-400	232	3	anα	anα	ADJ
iajs-400	232	4	-s*g	-s*g	ADJ
iajs-400	232	5	-	-	PUNCT
iajs-400	232	6	open	open	NOUN
iajs-400	232	7	set	set	NOUN
iajs-400	232	8	,	,	PUNCT
iajs-400	232	9	but	but	CCONJ
iajs-400	232	10	is	be	AUX
iajs-400	232	11	not	not	PART
iajs-400	232	12	an	an	DET
iajs-400	232	13	s*gαb	s*gαb	NOUN
iajs-400	232	14	-set	-set	ADJ
iajs-400	232	15	.	.	PUNCT
iajs-400	233	1	proposition(2.25	proposition(2.25	NOUN
iajs-400	233	2	):	):	PUNCT
iajs-400	233	3	let	let	NOUN
iajs-400	233	4	)	)	PUNCT
iajs-400	233	5	,	,	PUNCT
iajs-400	233	6	x	x	X
iajs-400	233	7	(	(	PUNCT
iajs-400	233	8	τ	τ	X
iajs-400	233	9	be	be	AUX
iajs-400	233	10	a	a	DET
iajs-400	233	11	topological	topological	ADJ
iajs-400	233	12	space	space	NOUN
iajs-400	233	13	and	and	CCONJ
iajs-400	233	14	xa	xa	PROPN
iajs-400	233	15	⊆	⊆	NUM
iajs-400	233	16	.	.	PUNCT
iajs-400	234	1	then	then	ADV
iajs-400	234	2	the	the	DET
iajs-400	234	3	following	follow	VERB
iajs-400	234	4	are	be	AUX
iajs-400	234	5	equivalent	equivalent	ADJ
iajs-400	234	6	:	:	PUNCT
iajs-400	234	7	i	i	X
iajs-400	234	8	)	)	PUNCT
iajs-400	234	9	a	a	PRON
iajs-400	234	10	is	be	AUX
iajs-400	234	11	open	open	ADJ
iajs-400	234	12	.	.	PUNCT
iajs-400	235	1	ii	ii	X
iajs-400	235	2	)	)	PUNCT
iajs-400	235	3	a	a	PRON
iajs-400	235	4	is	be	AUX
iajs-400	235	5	α	α	DET
iajs-400	235	6	-s*g	-s*g	NOUN
iajs-400	235	7	-	-	PUNCT
iajs-400	235	8	open	open	ADJ
iajs-400	235	9	and	and	CCONJ
iajs-400	235	10	an	an	DET
iajs-400	235	11	s*gαb	s*gαb	NOUN
iajs-400	235	12	-set	-set	PUNCT
iajs-400	235	13	.	.	PUNCT
iajs-400	236	1	proof	proof	NOUN
iajs-400	236	2	:	:	PUNCT
iajs-400	236	3	)	)	PUNCT
iajs-400	236	4	ii()i	ii()i	NOUN
iajs-400	236	5	(	(	PUNCT
iajs-400	236	6	⇒	⇒	NOUN
iajs-400	236	7	.	.	PUNCT
iajs-400	237	1	let	let	VERB
iajs-400	237	2	a	a	PRON
iajs-400	237	3	be	be	AUX
iajs-400	237	4	open	open	ADJ
iajs-400	237	5	.	.	PUNCT
iajs-400	238	1	then	then	ADV
iajs-400	238	2	)	)	PUNCT
iajs-400	238	3	a(inta	a(inta	PROPN
iajs-400	238	4	g*s=	g*s=	PROPN
iajs-400	238	5	)	)	PUNCT
iajs-400	238	6	)	)	PUNCT
iajs-400	238	7	a((intcl	a((intcl	PROPN
iajs-400	238	8	g*s⊆	g*s⊆	PROPN
iajs-400	238	9	and	and	CCONJ
iajs-400	238	10	)	)	PUNCT
iajs-400	238	11	)	)	PUNCT
iajs-400	239	1	a((intcl(inta	a((intcl(inta	PROPN
iajs-400	239	2	g*sg*s⊆	g*sg*s⊆	X
iajs-400	239	3	therefore	therefore	ADV
iajs-400	239	4	a	a	PRON
iajs-400	239	5	is	be	AUX
iajs-400	239	6	α	α	DET
iajs-400	239	7	-s*g	-s*g	NOUN
iajs-400	239	8	-	-	PUNCT
iajs-400	239	9	open	open	ADJ
iajs-400	239	10	.	.	PUNCT
iajs-400	240	1	also	also	ADV
iajs-400	240	2	,	,	PUNCT
iajs-400	240	3	xaa	xaa	PROPN
iajs-400	240	4	=	=	PROPN
iajs-400	240	5	,	,	PUNCT
iajs-400	240	6	where	where	SCONJ
iajs-400	240	7	τ∈a	τ∈a	NOUN
iajs-400	240	8	and	and	CCONJ
iajs-400	240	9	x	x	PRON
iajs-400	240	10	is	be	AUX
iajs-400	240	11	an	an	DET
iajs-400	240	12	s*gαt	s*gαt	PROPN
iajs-400	240	13	-set	-set	PUNCT
iajs-400	240	14	and	and	CCONJ
iajs-400	240	15	hence	hence	ADV
iajs-400	240	16	a	a	PRON
iajs-400	240	17	is	be	AUX
iajs-400	240	18	an	an	DET
iajs-400	240	19	s*gαb	s*gαb	NOUN
iajs-400	240	20	-set	-set	PUNCT
iajs-400	240	21	.	.	PUNCT
iajs-400	241	1	)	)	PUNCT
iajs-400	241	2	i()ii	i()ii	NOUN
iajs-400	241	3	(	(	PUNCT
iajs-400	241	4	⇒	⇒	NOUN
iajs-400	241	5	.	.	PUNCT
iajs-400	242	1	since	since	SCONJ
iajs-400	242	2	a	a	PRON
iajs-400	242	3	is	be	AUX
iajs-400	242	4	an	an	DET
iajs-400	242	5	s*gαb	s*gαb	NOUN
iajs-400	242	6	-set	-set	NUM
iajs-400	242	7	,	,	PUNCT
iajs-400	242	8	we	we	PRON
iajs-400	242	9	have	have	VERB
iajs-400	242	10	vua	vua	VERB
iajs-400	242	11	=	=	PROPN
iajs-400	242	12	,	,	PUNCT
iajs-400	242	13	where	where	SCONJ
iajs-400	242	14	τ∈u	τ∈u	PRON
iajs-400	242	15	and	and	CCONJ
iajs-400	242	16	v	v	NOUN
iajs-400	242	17	is	be	AUX
iajs-400	242	18	an	an	DET
iajs-400	242	19	s*gαt	s*gαt	ADJ
iajs-400	242	20	set	set	NOUN
iajs-400	242	21	.	.	PUNCT
iajs-400	243	1	by	by	ADP
iajs-400	243	2	the	the	DET
iajs-400	243	3	hypothesis	hypothesis	NOUN
iajs-400	243	4	,	,	PUNCT
iajs-400	243	5	a	a	PRON
iajs-400	243	6	is	be	AUX
iajs-400	243	7	also	also	ADV
iajs-400	243	8	α	α	DET
iajs-400	243	9	-s*g	-s*g	ADJ
iajs-400	243	10	-	-	PUNCT
iajs-400	243	11	open	open	ADJ
iajs-400	243	12	,	,	PUNCT
iajs-400	243	13	and	and	CCONJ
iajs-400	243	14	we	we	PRON
iajs-400	243	15	have	have	VERB
iajs-400	243	16	:	:	PUNCT
iajs-400	243	17	)	)	PUNCT
iajs-400	243	18	)	)	PUNCT
iajs-400	243	19	)	)	PUNCT
iajs-400	243	20	a((intcl(inta	a((intcl(inta	PROPN
iajs-400	243	21	g*sg*s⊆	g*sg*s⊆	PROPN
iajs-400	243	22	)	)	PUNCT
iajs-400	243	23	)	)	PUNCT
iajs-400	243	24	)	)	PUNCT
iajs-400	244	1	vu((intcl(int	vu((intcl(int	PROPN
iajs-400	244	2	g*sg*s	g*sg*s	PROPN
iajs-400	244	3	=	=	X
iajs-400	244	4	)	)	PUNCT
iajs-400	244	5	)	)	PUNCT
iajs-400	244	6	)	)	PUNCT
iajs-400	245	1	v(int)u((intcl(int	v(int)u((intcl(int	PROPN
iajs-400	245	2	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-400	245	3	=	=	NOUN
iajs-400	245	4	)	)	PUNCT
iajs-400	245	5	)	)	PUNCT
iajs-400	245	6	)	)	PUNCT
iajs-400	246	1	v((intcl)u((intcl(int	v((intcl)u((intcl(int	NOUN
iajs-400	246	2	g*sg*sg*s	g*sg*sg*s	NOUN
iajs-400	246	3	⊆	⊆	PROPN
iajs-400	246	4	)	)	PUNCT
iajs-400	246	5	)	)	PUNCT
iajs-400	246	6	)	)	PUNCT
iajs-400	246	7	v((intcl(int)u((intcl(int	v((intcl(int)u((intcl(int	NOUN
iajs-400	246	8	g*sg*sg*sg*s	g*sg*sg*sg*s	NOUN
iajs-400	246	9	=	=	X
iajs-400	246	10	)	)	PUNCT
iajs-400	247	1	vint())u(cl(int	vint())u(cl(int	NOUN
iajs-400	247	2	g*s	g*s	PROPN
iajs-400	247	3	⊆	⊆	PROPN
iajs-400	247	4	hence	hence	ADV
iajs-400	247	5	u)vu(vua	u)vu(vua	VERB
iajs-400	247	6			PUNCT
iajs-400	248	1	=	=	SYM
iajs-400	248	2	=	=	SYM
iajs-400	248	3	u))vint())u(cl((int	u))vint())u(cl((int	PROPN
iajs-400	248	4	g*s	g*s	PROPN
iajs-400	248	5	⊆	⊆	PROPN
iajs-400	248	6	)	)	PUNCT
iajs-400	248	7	vint()u))u(cl((int	vint()u))u(cl((int	PROPN
iajs-400	248	8	g*s	g*s	PROPN
iajs-400	248	9	=	=	PROPN
iajs-400	248	10	)	)	PUNCT
iajs-400	248	11	vint(u	vint(u	ADJ
iajs-400	248	12	=	=	PUNCT
iajs-400	248	13	)	)	PUNCT
iajs-400	248	14	vint()uint	vint()uint	NOUN
iajs-400	248	15	(	(	PUNCT
iajs-400	248	16	=	=	X
iajs-400	248	17	)	)	PUNCT
iajs-400	248	18	vuint	vuint	NOUN
iajs-400	248	19	(	(	PUNCT
iajs-400	248	20	=	=	X
iajs-400	248	21	)	)	PUNCT
iajs-400	248	22	aint(=	aint(=	PROPN
iajs-400	248	23	.	.	PUNCT
iajs-400	249	1	therefore	therefore	ADV
iajs-400	249	2	)	)	PUNCT
iajs-400	249	3	aint(a	aint(a	PROPN
iajs-400	249	4	=	=	PUNCT
iajs-400	249	5	and	and	CCONJ
iajs-400	249	6	a	a	PRON
iajs-400	249	7	is	be	AUX
iajs-400	249	8	open	open	ADJ
iajs-400	249	9	.	.	PUNCT
iajs-400	250	1	357	357	NUM
iajs-400	250	2	|	|	ADV
iajs-400	250	3	mathematics	mathematics	PROPN
iajs-400	250	4	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	250	5	�	�	NOUN
iajs-400	250	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	250	7	:	:	PUNCT
iajs-400	250	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	250	9	©	©	PROPN
iajs-400	250	10	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	250	11	ibn	ibn	PROPN
iajs-400	250	12	al	al	PROPN
iajs-400	250	13	-	-	PUNCT
iajs-400	250	14	haitham	haitham	PROPN
iajs-400	250	15	jour	jour	X
iajs-400	250	16	.	.	PROPN
iajs-400	251	1	for	for	ADP
iajs-400	251	2	pure	pure	ADJ
iajs-400	251	3	&	&	CCONJ
iajs-400	251	4	appl	appl	PROPN
iajs-400	251	5	.	.	PUNCT
iajs-400	252	1	sci	sci	PROPN
iajs-400	252	2	.	.	PUNCT
iajs-400	252	3	vol	vol	NOUN
iajs-400	252	4	.	.	PROPN
iajs-400	253	1	27	27	NUM
iajs-400	253	2	(	(	PUNCT
iajs-400	253	3	1	1	NUM
iajs-400	253	4	)	)	PUNCT
iajs-400	253	5	2014	2014	NUM
iajs-400	253	6	definition(2.26	definition(2.26	NOUN
iajs-400	253	7	):	):	PUNCT
iajs-400	253	8	a	a	DET
iajs-400	253	9	subset	subset	NOUN
iajs-400	253	10	a	a	PRON
iajs-400	253	11	of	of	ADP
iajs-400	253	12	a	a	DET
iajs-400	253	13	topological	topological	ADJ
iajs-400	253	14	space	space	NOUN
iajs-400	253	15	)	)	PUNCT
iajs-400	253	16	,	,	PUNCT
iajs-400	253	17	x	x	X
iajs-400	253	18	(	(	PUNCT
iajs-400	253	19	τ	τ	X
iajs-400	253	20	is	be	AUX
iajs-400	253	21	called	call	VERB
iajs-400	253	22	an	an	DET
iajs-400	253	23	s*g	s*g	NOUN
iajs-400	253	24	-	-	PUNCT
iajs-400	253	25	set	set	VERB
iajs-400	253	26	if	if	SCONJ
iajs-400	253	27	vua	vua	PROPN
iajs-400	253	28	=	=	X
iajs-400	253	29	,	,	PUNCT
iajs-400	253	30	where	where	SCONJ
iajs-400	253	31	τ∈u	τ∈u	NOUN
iajs-400	253	32	and	and	CCONJ
iajs-400	253	33	)	)	PUNCT
iajs-400	253	34	v(int)vint	v(int)vint	NOUN
iajs-400	253	35	(	(	PUNCT
iajs-400	253	36	g*s=	g*s=	PROPN
iajs-400	253	37	.	.	PUNCT
iajs-400	254	1	from	from	ADP
iajs-400	254	2	the	the	DET
iajs-400	254	3	following	following	ADJ
iajs-400	254	4	example	example	NOUN
iajs-400	254	5	one	one	PRON
iajs-400	254	6	can	can	AUX
iajs-400	254	7	deduce	deduce	VERB
iajs-400	254	8	that	that	SCONJ
iajs-400	254	9	an	an	DET
iajs-400	254	10	s*g	s*g	NOUN
iajs-400	254	11	-	-	PUNCT
iajs-400	254	12	open	open	NOUN
iajs-400	254	13	set	set	NOUN
iajs-400	254	14	and	and	CCONJ
iajs-400	254	15	an	an	DET
iajs-400	254	16	s*g	s*g	NOUN
iajs-400	254	17	-	-	PUNCT
iajs-400	254	18	set	set	NOUN
iajs-400	254	19	are	be	AUX
iajs-400	254	20	independent	independent	ADJ
iajs-400	254	21	.	.	PUNCT
iajs-400	255	1	example(2.27	example(2.27	ADJ
iajs-400	255	2	):	):	PUNCT
iajs-400	255	3	let	let	VERB
iajs-400	255	4	x	x	PUNCT
iajs-400	255	5	=	=	PUNCT
iajs-400	255	6	r	r	NOUN
iajs-400	255	7	with	with	ADP
iajs-400	255	8	the	the	DET
iajs-400	255	9	usual	usual	ADJ
iajs-400	255	10	topology	topology	NOUN
iajs-400	255	11	τ	τ	X
iajs-400	255	12	.	.	PUNCT
iajs-400	256	1	then	then	ADV
iajs-400	256	2	q)1,0(a	q)1,0(a	PROPN
iajs-400	256	3	=	=	X
iajs-400	256	4	is	be	AUX
iajs-400	256	5	an	an	DET
iajs-400	256	6	s*g	s*g	NOUN
iajs-400	256	7	-	-	PUNCT
iajs-400	256	8	set	set	NOUN
iajs-400	256	9	which	which	PRON
iajs-400	256	10	is	be	AUX
iajs-400	256	11	not	not	PART
iajs-400	256	12	s*g	s*g	NOUN
iajs-400	256	13	-	-	PUNCT
iajs-400	256	14	open	open	ADJ
iajs-400	256	15	.	.	PUNCT
iajs-400	257	1	also	also	ADV
iajs-400	257	2	,	,	PUNCT
iajs-400	257	3	in	in	ADP
iajs-400	257	4	example	example	NOUN
iajs-400	257	5	(	(	PUNCT
iajs-400	257	6	2.3	2.3	NUM
iajs-400	257	7	)	)	PUNCT
iajs-400	257	8	,	,	PUNCT
iajs-400	257	9	}	}	PUNCT
iajs-400	257	10	b	b	NOUN
iajs-400	257	11	,	,	PUNCT
iajs-400	257	12	a{a	a{a	X
iajs-400	258	1	=	=	PRON
iajs-400	258	2	is	be	AUX
iajs-400	258	3	an	an	DET
iajs-400	258	4	s*g	s*g	VERB
iajs-400	258	5	-	-	PUNCT
iajs-400	258	6	open	open	NOUN
iajs-400	258	7	set	set	NOUN
iajs-400	258	8	,	,	PUNCT
iajs-400	258	9	but	but	CCONJ
iajs-400	258	10	is	be	AUX
iajs-400	258	11	not	not	PART
iajs-400	258	12	an	an	DET
iajs-400	258	13	s*g	s*g	NOUN
iajs-400	258	14	-	-	PUNCT
iajs-400	258	15	set	set	VERB
iajs-400	258	16	.	.	PUNCT
iajs-400	259	1	proposition(2.28	proposition(2.28	NUM
iajs-400	259	2	):	):	PUNCT
iajs-400	259	3	let	let	NOUN
iajs-400	259	4	)	)	PUNCT
iajs-400	259	5	,	,	PUNCT
iajs-400	259	6	x	x	X
iajs-400	259	7	(	(	PUNCT
iajs-400	259	8	τ	τ	X
iajs-400	259	9	be	be	AUX
iajs-400	259	10	a	a	DET
iajs-400	259	11	topological	topological	ADJ
iajs-400	259	12	space	space	NOUN
iajs-400	259	13	and	and	CCONJ
iajs-400	259	14	xa	xa	PROPN
iajs-400	259	15	⊆	⊆	NUM
iajs-400	259	16	.	.	PUNCT
iajs-400	260	1	then	then	ADV
iajs-400	260	2	the	the	DET
iajs-400	260	3	following	follow	VERB
iajs-400	260	4	are	be	AUX
iajs-400	260	5	equivalent	equivalent	ADJ
iajs-400	260	6	:	:	PUNCT
iajs-400	260	7	i	i	X
iajs-400	260	8	)	)	PUNCT
iajs-400	260	9	a	a	PRON
iajs-400	260	10	is	be	AUX
iajs-400	260	11	open	open	ADJ
iajs-400	260	12	.	.	PUNCT
iajs-400	261	1	ii	ii	X
iajs-400	261	2	)	)	PUNCT
iajs-400	261	3	a	a	PRON
iajs-400	261	4	is	be	AUX
iajs-400	261	5	s*g	s*g	NOUN
iajs-400	261	6	-	-	PUNCT
iajs-400	261	7	open	open	ADJ
iajs-400	261	8	and	and	CCONJ
iajs-400	261	9	an	an	DET
iajs-400	261	10	s*g	s*g	NOUN
iajs-400	261	11	-	-	PUNCT
iajs-400	261	12	set	set	NOUN
iajs-400	261	13	.	.	PUNCT
iajs-400	262	1	proof	proof	NOUN
iajs-400	262	2	:	:	PUNCT
iajs-400	262	3	)	)	PUNCT
iajs-400	262	4	ii()i	ii()i	NOUN
iajs-400	262	5	(	(	PUNCT
iajs-400	262	6	⇒	⇒	NOUN
iajs-400	262	7	.	.	PUNCT
iajs-400	263	1	this	this	PRON
iajs-400	263	2	is	be	AUX
iajs-400	263	3	obvious	obvious	ADJ
iajs-400	263	4	.	.	PUNCT
iajs-400	263	5	)	)	PUNCT
iajs-400	264	1	i()ii	i()ii	NOUN
iajs-400	264	2	(	(	PUNCT
iajs-400	264	3	⇒	⇒	NOUN
iajs-400	264	4	.	.	PUNCT
iajs-400	265	1	since	since	SCONJ
iajs-400	265	2	a	a	PRON
iajs-400	265	3	is	be	AUX
iajs-400	265	4	an	an	DET
iajs-400	265	5	s*g	s*g	NOUN
iajs-400	265	6	-	-	PUNCT
iajs-400	265	7	set	set	NOUN
iajs-400	265	8	,	,	PUNCT
iajs-400	265	9	we	we	PRON
iajs-400	265	10	have	have	VERB
iajs-400	265	11	vua	vua	VERB
iajs-400	265	12	=	=	PROPN
iajs-400	265	13	,	,	PUNCT
iajs-400	265	14	where	where	SCONJ
iajs-400	265	15	τ∈u	τ∈u	NOUN
iajs-400	265	16	and	and	CCONJ
iajs-400	265	17	)	)	PUNCT
iajs-400	265	18	v(int)vint	v(int)vint	NOUN
iajs-400	265	19	(	(	PUNCT
iajs-400	265	20	g*s=	g*s=	PROPN
iajs-400	265	21	.	.	PUNCT
iajs-400	266	1	by	by	ADP
iajs-400	266	2	the	the	DET
iajs-400	266	3	hypothesis	hypothesis	NOUN
iajs-400	266	4	,	,	PUNCT
iajs-400	266	5	a	a	PRON
iajs-400	266	6	is	be	AUX
iajs-400	266	7	also	also	ADV
iajs-400	266	8	s*g	s*g	NOUN
iajs-400	266	9	-	-	PUNCT
iajs-400	266	10	open	open	ADJ
iajs-400	266	11	and	and	CCONJ
iajs-400	266	12	we	we	PRON
iajs-400	266	13	have	have	VERB
iajs-400	266	14	:	:	PUNCT
iajs-400	266	15	)	)	PUNCT
iajs-400	266	16	a(inta	a(inta	PROPN
iajs-400	266	17	g*s=	g*s=	PROPN
iajs-400	266	18	)	)	PUNCT
iajs-400	266	19	vu(int	vu(int	NOUN
iajs-400	266	20	g*s	g*s	PROPN
iajs-400	266	21	=	=	PUNCT
iajs-400	266	22	)	)	PUNCT
iajs-400	267	1	v(int)u(int	v(int)u(int	PROPN
iajs-400	267	2	g*sg*s	g*sg*s	PROPN
iajs-400	267	3	=	=	X
iajs-400	267	4	)	)	PUNCT
iajs-400	267	5	vint(u	vint(u	INTJ
iajs-400	267	6	=	=	PUNCT
iajs-400	267	7	)	)	PUNCT
iajs-400	267	8	vint()uint	vint()uint	NOUN
iajs-400	267	9	(	(	PUNCT
iajs-400	267	10	=	=	X
iajs-400	267	11	)	)	PUNCT
iajs-400	267	12	vuint	vuint	NOUN
iajs-400	267	13	(	(	PUNCT
iajs-400	267	14	=	=	X
iajs-400	267	15	)	)	PUNCT
iajs-400	267	16	aint(=	aint(=	PROPN
iajs-400	267	17	.	.	PUNCT
iajs-400	268	1	therefore	therefore	ADV
iajs-400	268	2	a	a	PRON
iajs-400	268	3	is	be	AUX
iajs-400	268	4	open	open	ADJ
iajs-400	268	5	.	.	PUNCT
iajs-400	269	1	definitions(2.29	definitions(2.29	NOUN
iajs-400	269	2	):	):	PUNCT
iajs-400	269	3	a	a	DET
iajs-400	269	4	topological	topological	ADJ
iajs-400	269	5	space	space	NOUN
iajs-400	269	6	)	)	PUNCT
iajs-400	269	7	,	,	PUNCT
iajs-400	269	8	x	x	X
iajs-400	269	9	(	(	PUNCT
iajs-400	269	10	τ	τ	X
iajs-400	269	11	is	be	AUX
iajs-400	269	12	said	say	VERB
iajs-400	269	13	to	to	PART
iajs-400	269	14	satisfy	satisfy	VERB
iajs-400	269	15	:	:	PUNCT
iajs-400	269	16	i	i	X
iajs-400	269	17	)	)	PUNCT
iajs-400	269	18	the	the	DET
iajs-400	269	19	s*g	s*g	NOUN
iajs-400	269	20	-	-	PUNCT
iajs-400	269	21	condition	condition	NOUN
iajs-400	269	22	if	if	SCONJ
iajs-400	269	23	every	every	DET
iajs-400	269	24	s*g	s*g	NOUN
iajs-400	269	25	-	-	PUNCT
iajs-400	269	26	open	open	ADJ
iajs-400	269	27	set	set	NOUN
iajs-400	269	28	is	be	AUX
iajs-400	269	29	s*g	s*g	NOUN
iajs-400	269	30	-	-	PUNCT
iajs-400	269	31	t	t	NOUN
iajs-400	269	32	-	-	PUNCT
iajs-400	269	33	set	set	VERB
iajs-400	269	34	.	.	PUNCT
iajs-400	270	1	ii	ii	X
iajs-400	270	2	)	)	PUNCT
iajs-400	270	3	the	the	DET
iajs-400	270	4	s*gαb	s*gαb	NOUN
iajs-400	270	5	-condition	-condition	PROPN
iajs-400	270	6	if	if	SCONJ
iajs-400	270	7	every	every	DET
iajs-400	270	8	α	α	NOUN
iajs-400	270	9	-s*g	-s*g	ADJ
iajs-400	270	10	-	-	PUNCT
iajs-400	270	11	open	open	ADJ
iajs-400	270	12	set	set	NOUN
iajs-400	270	13	is	be	AUX
iajs-400	270	14	s*gαb	s*gαb	NOUN
iajs-400	270	15	-set	-set	ADJ
iajs-400	270	16	.	.	PUNCT
iajs-400	271	1	iii	iii	X
iajs-400	271	2	)	)	PUNCT
iajs-400	271	3	the	the	DET
iajs-400	271	4	s*g	s*g	PROPN
iajs-400	271	5	-	-	PUNCT
iajs-400	271	6	b	b	NOUN
iajs-400	271	7	-	-	PUNCT
iajs-400	271	8	condition	condition	NOUN
iajs-400	271	9	if	if	SCONJ
iajs-400	271	10	every	every	DET
iajs-400	271	11	pre	pre	ADJ
iajs-400	271	12	-	-	ADJ
iajs-400	271	13	s*g	s*g	ADJ
iajs-400	271	14	-	-	PUNCT
iajs-400	271	15	open	open	ADJ
iajs-400	271	16	set	set	NOUN
iajs-400	271	17	is	be	AUX
iajs-400	271	18	s*g	s*g	NOUN
iajs-400	271	19	-	-	PUNCT
iajs-400	271	20	b	b	NOUN
iajs-400	271	21	-	-	PUNCT
iajs-400	271	22	set	set	NOUN
iajs-400	271	23	.	.	PUNCT
iajs-400	272	1	definition(2.30	definition(2.30	NOUN
iajs-400	272	2	):	):	PUNCT
iajs-400	272	3	a	a	DET
iajs-400	272	4	topological	topological	ADJ
iajs-400	272	5	space	space	NOUN
iajs-400	272	6	)	)	PUNCT
iajs-400	272	7	,	,	PUNCT
iajs-400	272	8	x	x	X
iajs-400	272	9	(	(	PUNCT
iajs-400	272	10	τ	τ	X
iajs-400	272	11	is	be	AUX
iajs-400	272	12	called	call	VERB
iajs-400	272	13	an	an	DET
iajs-400	272	14	s*g0	s*g0	PROPN
iajs-400	272	15	t	t	NOUN
iajs-400	272	16	-space	-space	NOUN
iajs-400	272	17	[	[	X
iajs-400	272	18	14	14	NUM
iajs-400	272	19	]	]	X
iajs-400	272	20	(	(	PUNCT
iajs-400	272	21	resp	resp	NOUN
iajs-400	272	22	.	.	PUNCT
iajs-400	273	1	α	α	PROPN
iajs-400	273	2	-s*g0	-s*g0	NOUN
iajs-400	273	3	t	t	PROPN
iajs-400	273	4	space	space	NOUN
iajs-400	273	5	,	,	PUNCT
iajs-400	273	6	pre	pre	ADJ
iajs-400	273	7	-	-	ADJ
iajs-400	273	8	s*g0	s*g0	ADJ
iajs-400	273	9	t	t	NOUN
iajs-400	273	10	-space	-space	NOUN
iajs-400	273	11	,	,	PUNCT
iajs-400	273	12	b	b	X
iajs-400	273	13	-	-	PUNCT
iajs-400	273	14	s*g0	s*g0	NOUN
iajs-400	273	15	t	t	NOUN
iajs-400	273	16	-space	-space	NOUN
iajs-400	273	17	,	,	PUNCT
iajs-400	273	18	β	β	X
iajs-400	273	19	-s*g0	-s*g0	NOUN
iajs-400	273	20	t	t	NOUN
iajs-400	273	21	-space	-space	NOUN
iajs-400	273	22	)	)	PUNCT
iajs-400	273	23	if	if	SCONJ
iajs-400	273	24	for	for	ADP
iajs-400	273	25	any	any	DET
iajs-400	273	26	two	two	NUM
iajs-400	273	27	distinct	distinct	ADJ
iajs-400	273	28	points	point	NOUN
iajs-400	273	29	x	x	PUNCT
iajs-400	273	30	and	and	CCONJ
iajs-400	273	31	y	y	PROPN
iajs-400	273	32	of	of	ADP
iajs-400	273	33	x	x	SYM
iajs-400	273	34	,	,	PUNCT
iajs-400	273	35	there	there	PRON
iajs-400	273	36	exists	exist	VERB
iajs-400	273	37	an	an	DET
iajs-400	273	38	s*g	s*g	NOUN
iajs-400	273	39	-	-	PUNCT
iajs-400	273	40	open	open	ADJ
iajs-400	273	41	(	(	PUNCT
iajs-400	273	42	resp	resp	NOUN
iajs-400	273	43	.	.	PUNCT
iajs-400	274	1	α	α	DET
iajs-400	274	2	-s*g	-s*g	ADJ
iajs-400	274	3	-	-	PUNCT
iajs-400	274	4	open	open	ADJ
iajs-400	274	5	,	,	PUNCT
iajs-400	274	6	pre	pre	ADJ
iajs-400	274	7	-	-	ADJ
iajs-400	274	8	s*g	s*g	ADJ
iajs-400	274	9	-	-	PUNCT
iajs-400	274	10	open	open	ADJ
iajs-400	274	11	,	,	PUNCT
iajs-400	274	12	b	b	X
iajs-400	274	13	-	-	PUNCT
iajs-400	274	14	s*g	s*g	NOUN
iajs-400	274	15	-	-	PUNCT
iajs-400	274	16	open	open	ADJ
iajs-400	274	17	,	,	PUNCT
iajs-400	274	18	β	β	X
iajs-400	274	19	-s*gopen	-s*gopen	NOUN
iajs-400	274	20	)	)	PUNCT
iajs-400	274	21	set	set	NOUN
iajs-400	274	22	of	of	ADP
iajs-400	274	23	x	x	PUNCT
iajs-400	274	24	containing	contain	VERB
iajs-400	274	25	one	one	NUM
iajs-400	274	26	of	of	ADP
iajs-400	274	27	the	the	DET
iajs-400	274	28	points	point	NOUN
iajs-400	274	29	but	but	CCONJ
iajs-400	274	30	not	not	PART
iajs-400	274	31	the	the	DET
iajs-400	274	32	other	other	ADJ
iajs-400	274	33	.	.	PUNCT
iajs-400	275	1	definition(2.31	definition(2.31	VERB
iajs-400	275	2	):	):	PUNCT
iajs-400	275	3	a	a	DET
iajs-400	275	4	topological	topological	ADJ
iajs-400	275	5	space	space	NOUN
iajs-400	275	6	)	)	PUNCT
iajs-400	275	7	,	,	PUNCT
iajs-400	275	8	x	x	X
iajs-400	275	9	(	(	PUNCT
iajs-400	275	10	τ	τ	X
iajs-400	275	11	is	be	AUX
iajs-400	275	12	called	call	VERB
iajs-400	275	13	an	an	DET
iajs-400	275	14	s*g1	s*g1	PROPN
iajs-400	275	15	t	t	NOUN
iajs-400	275	16	-space	-space	NOUN
iajs-400	275	17	[	[	X
iajs-400	275	18	14	14	NUM
iajs-400	275	19	]	]	X
iajs-400	275	20	(	(	PUNCT
iajs-400	275	21	resp	resp	NOUN
iajs-400	275	22	.	.	PUNCT
iajs-400	276	1	α	α	PROPN
iajs-400	276	2	-s*g1	-s*g1	PROPN
iajs-400	276	3	t	t	PROPN
iajs-400	276	4	space	space	NOUN
iajs-400	276	5	,	,	PUNCT
iajs-400	276	6	pre	pre	ADJ
iajs-400	276	7	-	-	ADJ
iajs-400	276	8	s*g1	s*g1	PROPN
iajs-400	276	9	t	t	NOUN
iajs-400	276	10	-space	-space	NOUN
iajs-400	276	11	,	,	PUNCT
iajs-400	276	12	b	b	X
iajs-400	276	13	-	-	PUNCT
iajs-400	276	14	s*g1	s*g1	PROPN
iajs-400	276	15	t	t	NOUN
iajs-400	276	16	-space	-space	NOUN
iajs-400	276	17	,	,	PUNCT
iajs-400	276	18	β	β	X
iajs-400	276	19	-s*g1	-s*g1	PROPN
iajs-400	276	20	t	t	PROPN
iajs-400	276	21	-space	-space	NOUN
iajs-400	276	22	)	)	PUNCT
iajs-400	276	23	if	if	SCONJ
iajs-400	276	24	for	for	ADP
iajs-400	276	25	any	any	DET
iajs-400	276	26	two	two	NUM
iajs-400	276	27	distinct	distinct	ADJ
iajs-400	276	28	points	point	NOUN
iajs-400	276	29	x	x	PUNCT
iajs-400	276	30	and	and	CCONJ
iajs-400	276	31	y	y	PROPN
iajs-400	276	32	of	of	ADP
iajs-400	276	33	x	x	SYM
iajs-400	276	34	,	,	PUNCT
iajs-400	276	35	there	there	PRON
iajs-400	276	36	exists	exist	VERB
iajs-400	276	37	an	an	DET
iajs-400	276	38	s*g	s*g	NOUN
iajs-400	276	39	-	-	PUNCT
iajs-400	276	40	open	open	ADJ
iajs-400	276	41	(	(	PUNCT
iajs-400	276	42	resp	resp	NOUN
iajs-400	276	43	.	.	PUNCT
iajs-400	277	1	α	α	PRON
iajs-400	277	2	-s*g	-s*g	ADJ
iajs-400	277	3	-	-	PUNCT
iajs-400	277	4	open	open	ADJ
iajs-400	277	5	,	,	PUNCT
iajs-400	277	6	pre	pre	ADJ
iajs-400	277	7	-	-	ADJ
iajs-400	277	8	s*g	s*g	ADJ
iajs-400	277	9	-	-	PUNCT
iajs-400	277	10	open	open	ADJ
iajs-400	277	11	,	,	PUNCT
iajs-400	277	12	b	b	X
iajs-400	277	13	-	-	PUNCT
iajs-400	277	14	s*g	s*g	NOUN
iajs-400	277	15	-	-	PUNCT
iajs-400	277	16	open	open	ADJ
iajs-400	277	17	,	,	PUNCT
iajs-400	277	18	β	β	X
iajs-400	277	19	-s*g	-s*g	ADJ
iajs-400	277	20	-	-	PUNCT
iajs-400	277	21	open	open	ADJ
iajs-400	277	22	)	)	PUNCT
iajs-400	277	23	set	set	NOUN
iajs-400	277	24	of	of	ADP
iajs-400	277	25	x	x	PUNCT
iajs-400	277	26	containing	contain	VERB
iajs-400	277	27	x	x	NOUN
iajs-400	277	28	but	but	CCONJ
iajs-400	277	29	not	not	PART
iajs-400	277	30	y	y	PROPN
iajs-400	277	31	and	and	CCONJ
iajs-400	277	32	an	an	DET
iajs-400	277	33	s*g	s*g	NOUN
iajs-400	277	34	-	-	PUNCT
iajs-400	277	35	open	open	ADJ
iajs-400	277	36	(	(	PUNCT
iajs-400	277	37	resp	resp	NOUN
iajs-400	277	38	.	.	PUNCT
iajs-400	278	1	α	α	PRON
iajs-400	278	2	-s*g	-s*g	ADJ
iajs-400	278	3	-	-	PUNCT
iajs-400	278	4	open	open	ADJ
iajs-400	278	5	,	,	PUNCT
iajs-400	278	6	pre	pre	ADJ
iajs-400	278	7	-	-	ADJ
iajs-400	278	8	s*g	s*g	ADJ
iajs-400	278	9	-	-	PUNCT
iajs-400	278	10	open	open	ADJ
iajs-400	278	11	,	,	PUNCT
iajs-400	278	12	b	b	X
iajs-400	278	13	-	-	PUNCT
iajs-400	278	14	s*g	s*g	NOUN
iajs-400	278	15	-	-	PUNCT
iajs-400	278	16	open	open	ADJ
iajs-400	278	17	,	,	PUNCT
iajs-400	278	18	β	β	X
iajs-400	278	19	-s*g	-s*g	ADJ
iajs-400	278	20	-	-	PUNCT
iajs-400	278	21	open	open	ADJ
iajs-400	278	22	)	)	PUNCT
iajs-400	278	23	set	set	NOUN
iajs-400	278	24	of	of	ADP
iajs-400	278	25	x	x	PUNCT
iajs-400	278	26	containing	contain	VERB
iajs-400	278	27	y	y	NOUN
iajs-400	278	28	but	but	CCONJ
iajs-400	278	29	not	not	PART
iajs-400	278	30	x	x	PROPN
iajs-400	278	31	.	.	PROPN
iajs-400	279	1	definition(2.32	definition(2.32	NUM
iajs-400	279	2	):	):	PUNCT
iajs-400	279	3	a	a	DET
iajs-400	279	4	topological	topological	ADJ
iajs-400	279	5	space	space	NOUN
iajs-400	279	6	)	)	PUNCT
iajs-400	279	7	,	,	PUNCT
iajs-400	279	8	x	x	X
iajs-400	279	9	(	(	PUNCT
iajs-400	279	10	τ	τ	X
iajs-400	279	11	is	be	AUX
iajs-400	279	12	called	call	VERB
iajs-400	279	13	an	an	DET
iajs-400	279	14	s*g2	s*g2	NOUN
iajs-400	279	15	t	t	NOUN
iajs-400	279	16	-space	-space	NOUN
iajs-400	279	17	[	[	X
iajs-400	279	18	14	14	NUM
iajs-400	279	19	]	]	X
iajs-400	279	20	(	(	PUNCT
iajs-400	279	21	resp	resp	NOUN
iajs-400	279	22	.	.	PUNCT
iajs-400	280	1	α	α	PROPN
iajs-400	280	2	-s*g2	-s*g2	PROPN
iajs-400	280	3	t	t	PROPN
iajs-400	280	4	space	space	NOUN
iajs-400	280	5	,	,	PUNCT
iajs-400	280	6	pre	pre	ADJ
iajs-400	280	7	-	-	NOUN
iajs-400	280	8	s*g2	s*g2	NOUN
iajs-400	280	9	t	t	NOUN
iajs-400	280	10	-space	-space	NOUN
iajs-400	280	11	,	,	PUNCT
iajs-400	280	12	b	b	X
iajs-400	280	13	-	-	PUNCT
iajs-400	280	14	s*g2	s*g2	NOUN
iajs-400	280	15	t	t	NOUN
iajs-400	280	16	-space	-space	NOUN
iajs-400	280	17	,	,	PUNCT
iajs-400	280	18	β	β	PROPN
iajs-400	280	19	-s*g2	-s*g2	PROPN
iajs-400	280	20	t	t	PROPN
iajs-400	280	21	-space	-space	NOUN
iajs-400	280	22	)	)	PUNCT
iajs-400	280	23	if	if	SCONJ
iajs-400	280	24	for	for	ADP
iajs-400	280	25	any	any	DET
iajs-400	280	26	two	two	NUM
iajs-400	280	27	distinct	distinct	ADJ
iajs-400	280	28	points	point	NOUN
iajs-400	280	29	x	x	PUNCT
iajs-400	280	30	and	and	CCONJ
iajs-400	280	31	y	y	PROPN
iajs-400	280	32	of	of	ADP
iajs-400	280	33	x	x	SYM
iajs-400	280	34	,	,	PUNCT
iajs-400	280	35	there	there	PRON
iajs-400	280	36	are	be	VERB
iajs-400	280	37	two	two	NUM
iajs-400	280	38	s*g	s*g	NOUN
iajs-400	280	39	-	-	PUNCT
iajs-400	280	40	open	open	ADJ
iajs-400	280	41	(	(	PUNCT
iajs-400	280	42	resp	resp	NOUN
iajs-400	280	43	.	.	PUNCT
iajs-400	281	1	α	α	PRON
iajs-400	281	2	-s*g	-s*g	ADJ
iajs-400	281	3	-	-	PUNCT
iajs-400	281	4	open	open	ADJ
iajs-400	281	5	,	,	PUNCT
iajs-400	281	6	pre	pre	ADJ
iajs-400	281	7	-	-	ADJ
iajs-400	281	8	s*g	s*g	ADJ
iajs-400	281	9	-	-	PUNCT
iajs-400	281	10	open	open	ADJ
iajs-400	281	11	,	,	PUNCT
iajs-400	281	12	b	b	X
iajs-400	281	13	-	-	PUNCT
iajs-400	281	14	s*g	s*g	NOUN
iajs-400	281	15	-	-	PUNCT
iajs-400	281	16	open	open	ADJ
iajs-400	281	17	,	,	PUNCT
iajs-400	281	18	β	β	X
iajs-400	281	19	-s*gopen	-s*gopen	NOUN
iajs-400	281	20	)	)	PUNCT
iajs-400	281	21	sets	set	VERB
iajs-400	281	22	u	u	NOUN
iajs-400	281	23	and	and	CCONJ
iajs-400	281	24	v	v	NOUN
iajs-400	281	25	of	of	ADP
iajs-400	281	26	x	x	PUNCT
iajs-400	281	27	such	such	ADJ
iajs-400	281	28	that	that	SCONJ
iajs-400	281	29	ux∈	ux∈	PROPN
iajs-400	281	30	,	,	PUNCT
iajs-400	281	31	vy∈	vy∈	PROPN
iajs-400	281	32	and	and	CCONJ
iajs-400	281	33	φ	φ	NOUN
iajs-400	281	34	=	=	NOUN
iajs-400	281	35	vu	vu	X
iajs-400	281	36			PROPN
iajs-400	281	37	.	.	PUNCT
iajs-400	282	1	3	3	X
iajs-400	282	2	.	.	X
iajs-400	282	3	weak	weak	ADJ
iajs-400	282	4	g*sd	g*sd	NOUN
iajs-400	282	5	-sets	-set	NOUN
iajs-400	282	6	and	and	CCONJ
iajs-400	282	7	associative	associative	ADJ
iajs-400	282	8	separation	separation	NOUN
iajs-400	282	9	axioms	axiom	VERB
iajs-400	282	10	358	358	NUM
iajs-400	282	11	|	|	ADV
iajs-400	282	12	mathematics	mathematics	PROPN
iajs-400	282	13	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	282	14	�	�	NOUN
iajs-400	282	15	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	282	16	:	:	PUNCT
iajs-400	282	17	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	283	1	©	©	PROPN
iajs-400	283	2	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	283	3	ibn	ibn	PROPN
iajs-400	283	4	al	al	PROPN
iajs-400	283	5	-	-	PUNCT
iajs-400	283	6	haitham	haitham	PROPN
iajs-400	283	7	jour	jour	X
iajs-400	283	8	.	.	PROPN
iajs-400	283	9	for	for	ADP
iajs-400	283	10	pure	pure	ADJ
iajs-400	283	11	&	&	CCONJ
iajs-400	283	12	appl	appl	PROPN
iajs-400	283	13	.	.	PUNCT
iajs-400	284	1	sci	sci	PROPN
iajs-400	284	2	.	.	PUNCT
iajs-400	284	3	vol	vol	NOUN
iajs-400	284	4	.	.	PROPN
iajs-400	285	1	27	27	NUM
iajs-400	285	2	(	(	PUNCT
iajs-400	285	3	1	1	NUM
iajs-400	285	4	)	)	PUNCT
iajs-400	285	5	2014	2014	NUM
iajs-400	285	6	in	in	ADP
iajs-400	285	7	this	this	DET
iajs-400	285	8	section	section	NOUN
iajs-400	285	9	we	we	PRON
iajs-400	285	10	introduce	introduce	VERB
iajs-400	285	11	and	and	CCONJ
iajs-400	285	12	investigate	investigate	VERB
iajs-400	285	13	new	new	ADJ
iajs-400	285	14	notions	notion	NOUN
iajs-400	285	15	called	call	VERB
iajs-400	285	16	g*sd	g*sd	PROPN
iajs-400	285	17	-sets	-set	NOUN
iajs-400	285	18	,	,	PUNCT
iajs-400	285	19	g*sd	g*sd	PROPN
iajs-400	285	20	−α	−α	PROPN
iajs-400	285	21	-sets	-set	NOUN
iajs-400	285	22	,	,	PUNCT
iajs-400	285	23	g*spred	g*spre	VERB
iajs-400	285	24	−	−	NOUN
iajs-400	285	25	-sets	-set	NOUN
iajs-400	285	26	,	,	PUNCT
iajs-400	285	27	g*sbd	g*sbd	VERB
iajs-400	285	28	−	−	NOUN
iajs-400	285	29	-sets	-set	NOUN
iajs-400	285	30	and	and	CCONJ
iajs-400	285	31	g*s	g*s	PROPN
iajs-400	286	1	d	d	PROPN
iajs-400	286	2	−β	−β	ADJ
iajs-400	286	3	-sets	-set	NOUN
iajs-400	287	1	and	and	CCONJ
iajs-400	287	2	we	we	PRON
iajs-400	287	3	use	use	VERB
iajs-400	287	4	these	these	DET
iajs-400	287	5	notions	notion	NOUN
iajs-400	287	6	to	to	PART
iajs-400	287	7	define	define	VERB
iajs-400	287	8	and	and	CCONJ
iajs-400	287	9	study	study	VERB
iajs-400	287	10	some	some	DET
iajs-400	287	11	associative	associative	ADJ
iajs-400	287	12	separation	separation	NOUN
iajs-400	287	13	axioms	axiom	NOUN
iajs-400	287	14	.	.	PUNCT
iajs-400	288	1	definition(3.1	definition(3.1	ADJ
iajs-400	288	2	):	):	PUNCT
iajs-400	288	3	a	a	DET
iajs-400	288	4	subset	subset	NOUN
iajs-400	288	5	a	a	PRON
iajs-400	288	6	of	of	ADP
iajs-400	288	7	a	a	DET
iajs-400	288	8	topological	topological	ADJ
iajs-400	288	9	space	space	NOUN
iajs-400	288	10	)	)	PUNCT
iajs-400	288	11	,	,	PUNCT
iajs-400	288	12	x	x	X
iajs-400	288	13	(	(	PUNCT
iajs-400	288	14	τ	τ	X
iajs-400	288	15	is	be	AUX
iajs-400	288	16	called	call	VERB
iajs-400	288	17	an	an	DET
iajs-400	288	18	g*sd	g*sd	PROPN
iajs-400	288	19	-set	-set	PUNCT
iajs-400	288	20	(	(	PUNCT
iajs-400	288	21	resp	resp	NOUN
iajs-400	288	22	.	.	PUNCT
iajs-400	289	1	g*sd	g*sd	PROPN
iajs-400	289	2	−α	−α	PROPN
iajs-400	289	3	set	set	VERB
iajs-400	289	4	,	,	PUNCT
iajs-400	289	5	g*spred	g*spre	VERB
iajs-400	289	6	−	−	NOUN
iajs-400	289	7	-set	-set	NUM
iajs-400	289	8	,	,	PUNCT
iajs-400	289	9	g*sbd	g*sbd	NOUN
iajs-400	289	10	−	−	PROPN
iajs-400	289	11	-set	-set	NUM
iajs-400	289	12	,	,	PUNCT
iajs-400	289	13	g*s	g*s	PROPN
iajs-400	289	14	d	d	PROPN
iajs-400	289	15	−β	−β	PROPN
iajs-400	289	16	-set	-set	ADJ
iajs-400	289	17	)	)	PUNCT
iajs-400	290	1	if	if	SCONJ
iajs-400	290	2	there	there	PRON
iajs-400	290	3	are	be	VERB
iajs-400	290	4	two	two	NUM
iajs-400	290	5	s*g	s*g	NOUN
iajs-400	290	6	-	-	PUNCT
iajs-400	290	7	open	open	ADJ
iajs-400	290	8	(	(	PUNCT
iajs-400	290	9	resp	resp	NOUN
iajs-400	290	10	.	.	PUNCT
iajs-400	291	1	α	α	PRON
iajs-400	291	2	-s*g	-s*g	ADJ
iajs-400	291	3	-	-	PUNCT
iajs-400	291	4	open	open	ADJ
iajs-400	291	5	,	,	PUNCT
iajs-400	291	6	pre	pre	ADJ
iajs-400	291	7	-	-	ADJ
iajs-400	291	8	s*gopen	s*gopen	ADJ
iajs-400	291	9	,	,	PUNCT
iajs-400	291	10	b	b	X
iajs-400	291	11	-	-	PUNCT
iajs-400	291	12	s*g	s*g	NOUN
iajs-400	291	13	-	-	PUNCT
iajs-400	291	14	open	open	ADJ
iajs-400	291	15	,	,	PUNCT
iajs-400	291	16	β	β	X
iajs-400	291	17	-s*g	-s*g	ADJ
iajs-400	291	18	-	-	PUNCT
iajs-400	291	19	open	open	ADJ
iajs-400	291	20	)	)	PUNCT
iajs-400	291	21	sets	set	VERB
iajs-400	291	22	u	u	NOUN
iajs-400	291	23	and	and	CCONJ
iajs-400	291	24	v	v	NOUN
iajs-400	291	25	in	in	ADP
iajs-400	291	26	x	x	PUNCT
iajs-400	291	27	such	such	ADJ
iajs-400	291	28	that	that	SCONJ
iajs-400	291	29	xu	xu	PROPN
iajs-400	291	30	≠	≠	PROPN
iajs-400	291	31	and	and	CCONJ
iajs-400	291	32	v\ua	v\ua	PROPN
iajs-400	291	33	=	=	PUNCT
iajs-400	291	34	.	.	PUNCT
iajs-400	292	1	remark(3.2	remark(3.2	PROPN
iajs-400	292	2	):	):	PUNCT
iajs-400	292	3	in	in	ADP
iajs-400	292	4	definition	definition	NOUN
iajs-400	292	5	(	(	PUNCT
iajs-400	292	6	3.1	3.1	NUM
iajs-400	292	7	)	)	PUNCT
iajs-400	292	8	,	,	PUNCT
iajs-400	292	9	if	if	SCONJ
iajs-400	292	10	xu	xu	PROPN
iajs-400	292	11	≠	≠	PROPN
iajs-400	292	12	and	and	CCONJ
iajs-400	292	13	φ	φ	NUM
iajs-400	292	14	=	=	NOUN
iajs-400	292	15	v	v	NOUN
iajs-400	292	16	,	,	PUNCT
iajs-400	292	17	then	then	ADV
iajs-400	292	18	every	every	DET
iajs-400	292	19	proper	proper	ADJ
iajs-400	292	20	s*g	s*g	NOUN
iajs-400	292	21	-	-	PUNCT
iajs-400	292	22	open	open	ADJ
iajs-400	292	23	(	(	PUNCT
iajs-400	292	24	resp	resp	NOUN
iajs-400	292	25	.	.	PUNCT
iajs-400	293	1	α	α	PRON
iajs-400	293	2	s*g	s*g	NOUN
iajs-400	293	3	-	-	PUNCT
iajs-400	293	4	open	open	ADJ
iajs-400	293	5	,	,	PUNCT
iajs-400	293	6	pre	pre	ADJ
iajs-400	293	7	-	-	ADJ
iajs-400	293	8	s*g	s*g	ADJ
iajs-400	293	9	-	-	PUNCT
iajs-400	293	10	open	open	ADJ
iajs-400	293	11	,	,	PUNCT
iajs-400	293	12	b	b	X
iajs-400	293	13	-	-	PUNCT
iajs-400	293	14	s*g	s*g	NOUN
iajs-400	293	15	-	-	PUNCT
iajs-400	293	16	open	open	ADJ
iajs-400	293	17	,	,	PUNCT
iajs-400	293	18	β	β	X
iajs-400	293	19	-s*g	-s*g	ADJ
iajs-400	293	20	-	-	PUNCT
iajs-400	293	21	open	open	ADJ
iajs-400	293	22	)	)	PUNCT
iajs-400	293	23	subset	subset	VERB
iajs-400	293	24	u	u	NOUN
iajs-400	293	25	of	of	ADP
iajs-400	293	26	x	x	SYM
iajs-400	293	27	is	be	AUX
iajs-400	293	28	an	an	DET
iajs-400	293	29	g*sd	g*sd	PROPN
iajs-400	293	30	-set	-set	PUNCT
iajs-400	293	31	(	(	PUNCT
iajs-400	293	32	resp	resp	NOUN
iajs-400	293	33	.	.	PUNCT
iajs-400	294	1	g*sd	g*sd	PROPN
iajs-400	294	2	−α	−α	PROPN
iajs-400	294	3	set	set	VERB
iajs-400	294	4	,	,	PUNCT
iajs-400	294	5	g*spred	g*spre	VERB
iajs-400	294	6	−	−	NOUN
iajs-400	294	7	-set	-set	NUM
iajs-400	294	8	,	,	PUNCT
iajs-400	294	9	g*sbd	g*sbd	NOUN
iajs-400	294	10	−	−	PROPN
iajs-400	294	11	-set	-set	NUM
iajs-400	294	12	,	,	PUNCT
iajs-400	294	13	g*s	g*s	PROPN
iajs-400	294	14	d	d	PROPN
iajs-400	294	15	−β	−β	PROPN
iajs-400	294	16	-set	-set	NUM
iajs-400	294	17	)	)	PUNCT
iajs-400	294	18	.	.	PUNCT
iajs-400	295	1	proposition(3.3	proposition(3.3	NOUN
iajs-400	295	2	):	):	PUNCT
iajs-400	295	3	in	in	ADP
iajs-400	295	4	any	any	DET
iajs-400	295	5	topological	topological	ADJ
iajs-400	295	6	space	space	NOUN
iajs-400	295	7	)	)	PUNCT
iajs-400	295	8	,	,	PUNCT
iajs-400	295	9	x	x	X
iajs-400	295	10	(	(	PUNCT
iajs-400	295	11	τ	τ	X
iajs-400	295	12	.	.	PUNCT
iajs-400	296	1	i	i	PRON
iajs-400	296	2	)	)	PUNCT
iajs-400	297	1	any	any	PRON
iajs-400	297	2	d	d	X
iajs-400	297	3	-	-	PUNCT
iajs-400	297	4	set	set	NOUN
iajs-400	297	5	is	be	AUX
iajs-400	297	6	g*sd	g*sd	PROPN
iajs-400	297	7	-set	-set	ADJ
iajs-400	297	8	.	.	PUNCT
iajs-400	298	1	ii	ii	X
iajs-400	298	2	)	)	PUNCT
iajs-400	298	3	any	any	DET
iajs-400	298	4	g*sd	g*sd	PROPN
iajs-400	298	5	-set	-set	PROPN
iajs-400	298	6	is	be	AUX
iajs-400	298	7	g*sd	g*sd	PROPN
iajs-400	298	8	−α	−α	PROPN
iajs-400	298	9	-set	-set	PUNCT
iajs-400	298	10	.	.	PUNCT
iajs-400	299	1	iii	iii	X
iajs-400	299	2	)	)	PUNCT
iajs-400	299	3	any	any	DET
iajs-400	299	4	g*sd	g*sd	PROPN
iajs-400	299	5	−α	−α	PROPN
iajs-400	299	6	-set	-set	PUNCT
iajs-400	299	7	is	be	AUX
iajs-400	299	8	g*spred	g*spre	VERB
iajs-400	299	9	−	−	NOUN
iajs-400	299	10	-set	-set	PUNCT
iajs-400	299	11	.	.	PUNCT
iajs-400	300	1	iv	iv	X
iajs-400	300	2	)	)	PUNCT
iajs-400	300	3	any	any	PRON
iajs-400	300	4	g*spred	g*spre	VERB
iajs-400	300	5	−	−	NOUN
iajs-400	300	6	-set	-set	PUNCT
iajs-400	300	7	is	be	AUX
iajs-400	300	8	g*sbd	g*sbd	NOUN
iajs-400	300	9	−	−	PROPN
iajs-400	300	10	-set	-set	PUNCT
iajs-400	300	11	.	.	PUNCT
iajs-400	301	1	v	v	X
iajs-400	301	2	)	)	PUNCT
iajs-400	301	3	any	any	DET
iajs-400	301	4	g*sbd	g*sbd	NOUN
iajs-400	301	5	−	−	PROPN
iajs-400	301	6	-set	-set	PUNCT
iajs-400	301	7	is	be	AUX
iajs-400	301	8	g*s	g*s	PROPN
iajs-400	301	9	d	d	PROPN
iajs-400	301	10	−β	−β	PROPN
iajs-400	301	11	-set	-set	PUNCT
iajs-400	301	12	.	.	PUNCT
iajs-400	302	1	proof	proof	NOUN
iajs-400	302	2	:	:	PUNCT
iajs-400	302	3	follows	follow	VERB
iajs-400	302	4	from	from	ADP
iajs-400	302	5	lemma	lemma	PROPN
iajs-400	302	6	(	(	PUNCT
iajs-400	302	7	2.2	2.2	NUM
iajs-400	302	8	)	)	PUNCT
iajs-400	302	9	.	.	PUNCT
iajs-400	303	1	proposition(3.4	proposition(3.4	NOUN
iajs-400	303	2	):	):	PUNCT
iajs-400	303	3	in	in	ADP
iajs-400	303	4	any	any	DET
iajs-400	303	5	door	door	NOUN
iajs-400	303	6	space	space	NOUN
iajs-400	303	7	)	)	PUNCT
iajs-400	303	8	,	,	PUNCT
iajs-400	303	9	x	x	X
iajs-400	303	10	(	(	PUNCT
iajs-400	303	11	τ	τ	X
iajs-400	303	12	.	.	PUNCT
iajs-400	304	1	i	i	PRON
iajs-400	304	2	)	)	PUNCT
iajs-400	304	3	any	any	DET
iajs-400	304	4	g*spred	g*spre	VERB
iajs-400	304	5	−	−	NOUN
iajs-400	304	6	-set	-set	PUNCT
iajs-400	304	7	is	be	AUX
iajs-400	304	8	g*sd	g*sd	PROPN
iajs-400	304	9	-set	-set	ADJ
iajs-400	304	10	.	.	PUNCT
iajs-400	305	1	ii	ii	X
iajs-400	305	2	)	)	PUNCT
iajs-400	306	1	any	any	PRON
iajs-400	306	2	g*s	g*s	PROPN
iajs-400	307	1	d	d	X
iajs-400	307	2	−β	−β	PROPN
iajs-400	307	3	-set	-set	VERB
iajs-400	307	4	is	be	AUX
iajs-400	307	5	g*sbd	g*sbd	NOUN
iajs-400	307	6	−	−	PROPN
iajs-400	307	7	-set	-set	PUNCT
iajs-400	307	8	.	.	PUNCT
iajs-400	308	1	proof	proof	NOUN
iajs-400	308	2	:	:	PUNCT
iajs-400	308	3	follows	follow	VERB
iajs-400	308	4	from	from	ADP
iajs-400	308	5	proposition	proposition	NOUN
iajs-400	308	6	(	(	PUNCT
iajs-400	308	7	2.17	2.17	NUM
iajs-400	308	8	)	)	PUNCT
iajs-400	308	9	.	.	PUNCT
iajs-400	309	1	proposition(3.5	proposition(3.5	NOUN
iajs-400	309	2	):	):	PUNCT
iajs-400	309	3	in	in	ADP
iajs-400	309	4	any	any	DET
iajs-400	309	5	topological	topological	ADJ
iajs-400	309	6	space	space	NOUN
iajs-400	309	7	satisfies	satisfie	NOUN
iajs-400	309	8	s*g	s*g	VERB
iajs-400	309	9	-	-	PUNCT
iajs-400	309	10	condition	condition	NOUN
iajs-400	309	11	any	any	DET
iajs-400	309	12	g*sd	g*sd	PROPN
iajs-400	309	13	-set	-set	PUNCT
iajs-400	309	14	is	be	AUX
iajs-400	309	15	d	d	NOUN
iajs-400	309	16	-	-	PUNCT
iajs-400	309	17	set	set	ADJ
iajs-400	309	18	.	.	PUNCT
iajs-400	310	1	proof	proof	NOUN
iajs-400	310	2	:	:	PUNCT
iajs-400	310	3	suppose	suppose	VERB
iajs-400	310	4	that	that	SCONJ
iajs-400	310	5	a	a	PRON
iajs-400	310	6	is	be	AUX
iajs-400	310	7	an	an	DET
iajs-400	310	8	g*sd	g*sd	PROPN
iajs-400	310	9	-set	-set	PROPN
iajs-400	310	10	,	,	PUNCT
iajs-400	310	11	then	then	ADV
iajs-400	310	12	there	there	PRON
iajs-400	310	13	are	be	VERB
iajs-400	310	14	two	two	NUM
iajs-400	310	15	s*g	s*g	NOUN
iajs-400	310	16	-	-	PUNCT
iajs-400	310	17	open	open	ADJ
iajs-400	310	18	sets	set	NOUN
iajs-400	310	19	u	u	NOUN
iajs-400	310	20	and	and	CCONJ
iajs-400	310	21	v	v	NOUN
iajs-400	310	22	in	in	ADP
iajs-400	310	23	x	x	PUNCT
iajs-400	310	24	such	such	ADJ
iajs-400	310	25	that	that	SCONJ
iajs-400	310	26	xu	xu	PROPN
iajs-400	310	27	≠	≠	PROPN
iajs-400	310	28	and	and	CCONJ
iajs-400	310	29	v\ua	v\ua	PROPN
iajs-400	310	30	=	=	PUNCT
iajs-400	310	31	.	.	PUNCT
iajs-400	311	1	hence	hence	ADV
iajs-400	311	2	)	)	PUNCT
iajs-400	311	3	)	)	PUNCT
iajs-400	312	1	u(cl(int)u(intu	u(cl(int)u(intu	PROPN
iajs-400	312	2	g*sg*s	g*sg*s	PROPN
iajs-400	312	3	⊆=	⊆=	PROPN
iajs-400	312	4	and	and	CCONJ
iajs-400	312	5	)	)	PUNCT
iajs-400	312	6	)	)	PUNCT
iajs-400	312	7	v(cl(int)v(intv	v(cl(int)v(intv	VERB
iajs-400	312	8	g*sg*s	g*sg*s	PROPN
iajs-400	312	9	⊆=	⊆=	PROPN
iajs-400	312	10	.	.	PUNCT
iajs-400	313	1	since	since	SCONJ
iajs-400	313	2	x	x	PRON
iajs-400	313	3	is	be	AUX
iajs-400	313	4	satisfy	satisfy	VERB
iajs-400	313	5	the	the	DET
iajs-400	313	6	s*g	s*g	NOUN
iajs-400	313	7	-	-	PUNCT
iajs-400	313	8	condition	condition	NOUN
iajs-400	313	9	,	,	PUNCT
iajs-400	313	10	then	then	ADV
iajs-400	313	11	u	u	NOUN
iajs-400	313	12	and	and	CCONJ
iajs-400	313	13	v	v	NOUN
iajs-400	313	14	are	be	AUX
iajs-400	313	15	s*g	s*g	NOUN
iajs-400	313	16	-	-	PUNCT
iajs-400	313	17	tsets	tset	NOUN
iajs-400	313	18	.	.	PUNCT
iajs-400	314	1	therefore	therefore	ADV
iajs-400	314	2	)	)	PUNCT
iajs-400	314	3	uint(u	uint(u	PROPN
iajs-400	314	4	⊆	⊆	NUM
iajs-400	314	5	and	and	CCONJ
iajs-400	314	6	)	)	PUNCT
iajs-400	314	7	vint(v	vint(v	NOUN
iajs-400	314	8	⊆	⊆	NUM
iajs-400	314	9	.	.	PUNCT
iajs-400	315	1	hence	hence	ADV
iajs-400	315	2	u	u	NOUN
iajs-400	315	3	and	and	CCONJ
iajs-400	315	4	v	v	NOUN
iajs-400	315	5	are	be	AUX
iajs-400	315	6	open	open	ADJ
iajs-400	315	7	-	-	PUNCT
iajs-400	315	8	sets	set	NOUN
iajs-400	315	9	.	.	PUNCT
iajs-400	316	1	thus	thus	ADV
iajs-400	316	2	a	a	PRON
iajs-400	316	3	is	be	AUX
iajs-400	316	4	d	d	NOUN
iajs-400	316	5	-	-	PUNCT
iajs-400	316	6	set	set	ADJ
iajs-400	316	7	.	.	PUNCT
iajs-400	317	1	proposition(3.6	proposition(3.6	NOUN
iajs-400	317	2	):	):	PUNCT
iajs-400	317	3	in	in	ADP
iajs-400	317	4	any	any	DET
iajs-400	317	5	topological	topological	ADJ
iajs-400	317	6	space	space	NOUN
iajs-400	317	7	satisfies	satisfie	NOUN
iajs-400	317	8	s*gαb	s*gαb	NOUN
iajs-400	317	9	-condition	-condition	PROPN
iajs-400	317	10	any	any	DET
iajs-400	317	11	g*sd	g*sd	PROPN
iajs-400	317	12	−α	−α	PROPN
iajs-400	317	13	-set	-set	PUNCT
iajs-400	317	14	is	be	AUX
iajs-400	317	15	d	d	NOUN
iajs-400	317	16	-	-	PUNCT
iajs-400	317	17	set	set	ADJ
iajs-400	317	18	.	.	PUNCT
iajs-400	318	1	proof	proof	NOUN
iajs-400	318	2	:	:	PUNCT
iajs-400	318	3	follows	follow	VERB
iajs-400	318	4	from	from	ADP
iajs-400	318	5	proposition	proposition	NOUN
iajs-400	318	6	(	(	PUNCT
iajs-400	318	7	2.25	2.25	NUM
iajs-400	318	8	)	)	PUNCT
iajs-400	318	9	.	.	PUNCT
iajs-400	319	1	359	359	NUM
iajs-400	320	1	|	|	ADV
iajs-400	320	2	mathematics	mathematics	PROPN
iajs-400	320	3	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	320	4	�	�	NOUN
iajs-400	320	5	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	320	6	:	:	PUNCT
iajs-400	320	7	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	320	8	©	©	PROPN
iajs-400	320	9	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	320	10	ibn	ibn	PROPN
iajs-400	320	11	al	al	PROPN
iajs-400	320	12	-	-	PUNCT
iajs-400	320	13	haitham	haitham	PROPN
iajs-400	320	14	jour	jour	X
iajs-400	320	15	.	.	PROPN
iajs-400	321	1	for	for	ADP
iajs-400	321	2	pure	pure	ADJ
iajs-400	321	3	&	&	CCONJ
iajs-400	321	4	appl	appl	PROPN
iajs-400	321	5	.	.	PUNCT
iajs-400	322	1	sci	sci	PROPN
iajs-400	322	2	.	.	PUNCT
iajs-400	322	3	vol	vol	NOUN
iajs-400	322	4	.	.	PROPN
iajs-400	323	1	27	27	NUM
iajs-400	323	2	(	(	PUNCT
iajs-400	323	3	1	1	NUM
iajs-400	323	4	)	)	PUNCT
iajs-400	323	5	2014	2014	NUM
iajs-400	323	6	proposition(3.7	proposition(3.7	NOUN
iajs-400	323	7	):	):	PUNCT
iajs-400	323	8	in	in	ADP
iajs-400	323	9	any	any	DET
iajs-400	323	10	topological	topological	ADJ
iajs-400	323	11	space	space	NOUN
iajs-400	323	12	satisfies	satisfie	NOUN
iajs-400	323	13	s*g	s*g	VERB
iajs-400	323	14	-	-	PUNCT
iajs-400	323	15	b	b	NOUN
iajs-400	323	16	-	-	PUNCT
iajs-400	323	17	condition	condition	NOUN
iajs-400	323	18	any	any	DET
iajs-400	323	19	g*spred	g*spre	VERB
iajs-400	323	20	−	−	NOUN
iajs-400	323	21	-set	-set	PUNCT
iajs-400	323	22	is	be	AUX
iajs-400	323	23	d	d	NOUN
iajs-400	323	24	-	-	PUNCT
iajs-400	323	25	set	set	ADJ
iajs-400	323	26	.	.	PUNCT
iajs-400	324	1	proof	proof	NOUN
iajs-400	324	2	:	:	PUNCT
iajs-400	324	3	follows	follow	VERB
iajs-400	324	4	from	from	ADP
iajs-400	324	5	proposition	proposition	NOUN
iajs-400	324	6	(	(	PUNCT
iajs-400	324	7	2.21	2.21	NUM
iajs-400	324	8	)	)	PUNCT
iajs-400	324	9	.	.	PUNCT
iajs-400	325	1	from	from	ADP
iajs-400	325	2	above	above	ADP
iajs-400	325	3	propositions	proposition	NOUN
iajs-400	325	4	we	we	PRON
iajs-400	325	5	can	can	AUX
iajs-400	325	6	get	get	VERB
iajs-400	325	7	the	the	DET
iajs-400	325	8	following	follow	VERB
iajs-400	325	9	diagram	diagram	NOUN
iajs-400	325	10	.	.	PUNCT
iajs-400	326	1	(	(	PUNCT
iajs-400	326	2	1	1	X
iajs-400	326	3	)	)	PUNCT
iajs-400	326	4	s*g	s*g	NOUN
iajs-400	326	5	-	-	PUNCT
iajs-400	326	6	bα	bα	NOUN
iajs-400	326	7	-	-	PUNCT
iajs-400	326	8	condition	condition	NOUN
iajs-400	326	9	(	(	PUNCT
iajs-400	326	10	2	2	NUM
iajs-400	326	11	)	)	PUNCT
iajs-400	326	12	s*g	s*g	NOUN
iajs-400	326	13	-	-	PUNCT
iajs-400	326	14	condition	condition	NOUN
iajs-400	326	15	(	(	PUNCT
iajs-400	326	16	3	3	NUM
iajs-400	326	17	)	)	PUNCT
iajs-400	326	18	s*g	s*g	NOUN
iajs-400	326	19	-	-	PUNCT
iajs-400	326	20	b	b	NOUN
iajs-400	326	21	-	-	PUNCT
iajs-400	326	22	condition	condition	NOUN
iajs-400	326	23	(	(	PUNCT
iajs-400	326	24	4	4	NUM
iajs-400	326	25	)	)	PUNCT
iajs-400	326	26	door	door	NOUN
iajs-400	326	27	space	space	NOUN
iajs-400	326	28	figure	figure	NOUN
iajs-400	326	29	no	no	INTJ
iajs-400	326	30	.	.	PUNCT
iajs-400	327	1	(	(	PUNCT
iajs-400	327	2	2	2	NUM
iajs-400	327	3	):	):	PUNCT
iajs-400	327	4	relations	relation	NOUN
iajs-400	327	5	among	among	ADP
iajs-400	327	6	the	the	DET
iajs-400	327	7	weak	weak	ADJ
iajs-400	327	8	g*sd	g*sd	PROPN
iajs-400	327	9	sets	set	NOUN
iajs-400	327	10	definition(3.8	definition(3.8	VERB
iajs-400	327	11	):	):	PUNCT
iajs-400	327	12	a	a	DET
iajs-400	327	13	function	function	NOUN
iajs-400	327	14	)	)	PUNCT
iajs-400	327	15	,	,	PUNCT
iajs-400	327	16	y(),x(:f	y(),x(:f	PROPN
iajs-400	327	17	σ→τ	σ→τ	NUM
iajs-400	327	18	is	be	AUX
iajs-400	327	19	said	say	VERB
iajs-400	327	20	to	to	PART
iajs-400	327	21	be	be	AUX
iajs-400	327	22	α	α	DET
iajs-400	327	23	-s*g	-s*g	ADJ
iajs-400	327	24	-	-	PUNCT
iajs-400	327	25	continuous	continuous	ADJ
iajs-400	327	26	(	(	PUNCT
iajs-400	327	27	resp	resp	NOUN
iajs-400	327	28	.	.	PUNCT
iajs-400	328	1	pre	pre	ADJ
iajs-400	328	2	-	-	ADJ
iajs-400	328	3	s*gcontinuous	s*gcontinuous	ADJ
iajs-400	328	4	,	,	PUNCT
iajs-400	328	5	b	b	X
iajs-400	328	6	-	-	PUNCT
iajs-400	328	7	s*g	s*g	NOUN
iajs-400	328	8	-	-	PUNCT
iajs-400	328	9	continuous	continuous	ADJ
iajs-400	328	10	,	,	PUNCT
iajs-400	328	11	β	β	X
iajs-400	328	12	-s*g	-s*g	ADJ
iajs-400	328	13	-	-	PUNCT
iajs-400	328	14	continuous	continuous	ADJ
iajs-400	328	15	)	)	PUNCT
iajs-400	328	16	if	if	SCONJ
iajs-400	328	17	)	)	PUNCT
iajs-400	328	18	v(f	v(f	PROPN
iajs-400	328	19	1−	1−	NUM
iajs-400	328	20	is	be	AUX
iajs-400	328	21	α	α	DET
iajs-400	328	22	-s*g	-s*g	NOUN
iajs-400	328	23	-	-	PUNCT
iajs-400	328	24	open	open	ADJ
iajs-400	328	25	(	(	PUNCT
iajs-400	328	26	resp	resp	NOUN
iajs-400	328	27	.	.	PUNCT
iajs-400	329	1	pre	pre	ADJ
iajs-400	329	2	-	-	ADJ
iajs-400	329	3	s*gopen	s*gopen	ADJ
iajs-400	329	4	,	,	PUNCT
iajs-400	329	5	b	b	X
iajs-400	329	6	-	-	PUNCT
iajs-400	329	7	s*g	s*g	NOUN
iajs-400	329	8	-	-	PUNCT
iajs-400	329	9	open	open	ADJ
iajs-400	329	10	,	,	PUNCT
iajs-400	329	11	β	β	X
iajs-400	329	12	-s*g	-s*g	ADJ
iajs-400	329	13	-	-	PUNCT
iajs-400	329	14	open	open	ADJ
iajs-400	329	15	)	)	PUNCT
iajs-400	329	16	set	set	VERB
iajs-400	329	17	in	in	ADP
iajs-400	329	18	x	x	PUNCT
iajs-400	329	19	for	for	SCONJ
iajs-400	329	20	each	each	DET
iajs-400	329	21	open	open	ADJ
iajs-400	329	22	set	set	VERB
iajs-400	329	23	v	v	NOUN
iajs-400	329	24	in	in	ADP
iajs-400	329	25	y	y	PROPN
iajs-400	329	26	.	.	PUNCT
iajs-400	330	1	definition(3.9	definition(3.9	NOUN
iajs-400	330	2	):	):	PUNCT
iajs-400	330	3	a	a	DET
iajs-400	330	4	function	function	NOUN
iajs-400	330	5	)	)	PUNCT
iajs-400	330	6	,	,	PUNCT
iajs-400	330	7	y(),x(:f	y(),x(:f	PROPN
iajs-400	330	8	σ→τ	σ→τ	NUM
iajs-400	330	9	is	be	AUX
iajs-400	330	10	said	say	VERB
iajs-400	330	11	to	to	PART
iajs-400	330	12	be	be	AUX
iajs-400	330	13	α	α	DET
iajs-400	330	14	-s*g	-s*g	NOUN
iajs-400	330	15	-	-	PUNCT
iajs-400	330	16	irresolute	irresolute	ADJ
iajs-400	330	17	(	(	PUNCT
iajs-400	330	18	resp	resp	NOUN
iajs-400	330	19	.	.	PUNCT
iajs-400	331	1	pres*g	pres*g	PROPN
iajs-400	331	2	irresolute	irresolute	PROPN
iajs-400	331	3	,	,	PUNCT
iajs-400	331	4	b	b	X
iajs-400	331	5	-	-	PUNCT
iajs-400	331	6	s*g	s*g	NOUN
iajs-400	331	7	-	-	PUNCT
iajs-400	331	8	irresolute	irresolute	ADJ
iajs-400	331	9	,	,	PUNCT
iajs-400	331	10	β	β	X
iajs-400	331	11	-s*g	-s*g	ADJ
iajs-400	331	12	-	-	PUNCT
iajs-400	331	13	irresolute	irresolute	NOUN
iajs-400	331	14	)	)	PUNCT
iajs-400	331	15	if	if	SCONJ
iajs-400	331	16	)	)	PUNCT
iajs-400	331	17	v(f	v(f	PROPN
iajs-400	331	18	1−	1−	NUM
iajs-400	331	19	is	be	AUX
iajs-400	331	20	α	α	DET
iajs-400	331	21	-s*g	-s*g	NOUN
iajs-400	331	22	-	-	PUNCT
iajs-400	331	23	open	open	ADJ
iajs-400	331	24	(	(	PUNCT
iajs-400	331	25	resp	resp	NOUN
iajs-400	331	26	.	.	PUNCT
iajs-400	332	1	pre	pre	ADJ
iajs-400	332	2	-	-	ADJ
iajs-400	332	3	s*g	s*g	ADJ
iajs-400	332	4	-	-	PUNCT
iajs-400	332	5	open	open	ADJ
iajs-400	332	6	,	,	PUNCT
iajs-400	332	7	bs*g	bs*g	X
iajs-400	332	8	-	-	ADJ
iajs-400	332	9	open	open	ADJ
iajs-400	332	10	,	,	PUNCT
iajs-400	332	11	β	β	X
iajs-400	332	12	-s*g	-s*g	ADJ
iajs-400	332	13	-	-	PUNCT
iajs-400	332	14	open	open	ADJ
iajs-400	332	15	)	)	PUNCT
iajs-400	332	16	set	set	VERB
iajs-400	332	17	in	in	ADP
iajs-400	332	18	x	x	PUNCT
iajs-400	332	19	for	for	ADP
iajs-400	332	20	each	each	DET
iajs-400	332	21	α	α	DET
iajs-400	332	22	-s*g	-s*g	ADJ
iajs-400	332	23	-	-	PUNCT
iajs-400	332	24	open	open	ADJ
iajs-400	332	25	(	(	PUNCT
iajs-400	332	26	resp	resp	NOUN
iajs-400	332	27	.	.	PUNCT
iajs-400	333	1	pre	pre	ADJ
iajs-400	333	2	-	-	ADJ
iajs-400	333	3	s*g	s*g	ADJ
iajs-400	333	4	-	-	PUNCT
iajs-400	333	5	open	open	ADJ
iajs-400	333	6	,	,	PUNCT
iajs-400	333	7	b	b	X
iajs-400	333	8	-	-	PUNCT
iajs-400	333	9	s*g	s*g	NOUN
iajs-400	333	10	-	-	PUNCT
iajs-400	333	11	open	open	ADJ
iajs-400	333	12	,	,	PUNCT
iajs-400	333	13	β	β	X
iajs-400	333	14	-s*gopen	-s*gopen	NOUN
iajs-400	333	15	)	)	PUNCT
iajs-400	333	16	set	set	VERB
iajs-400	333	17	v	v	NOUN
iajs-400	333	18	in	in	ADP
iajs-400	333	19	y	y	PROPN
iajs-400	333	20	.	.	PUNCT
iajs-400	334	1	theorem(3.10	theorem(3.10	PROPN
iajs-400	334	2	):	):	PUNCT
iajs-400	334	3	if	if	SCONJ
iajs-400	334	4	)	)	PUNCT
iajs-400	334	5	,	,	PUNCT
iajs-400	334	6	y(),x(:f	y(),x(:f	PROPN
iajs-400	334	7	σ→τ	σ→τ	NUM
iajs-400	334	8	is	be	AUX
iajs-400	334	9	an	an	DET
iajs-400	334	10	α	α	NOUN
iajs-400	334	11	-s*g	-s*g	ADJ
iajs-400	334	12	-	-	PUNCT
iajs-400	334	13	continuous	continuous	ADJ
iajs-400	334	14	(	(	PUNCT
iajs-400	334	15	resp	resp	NOUN
iajs-400	334	16	.	.	PUNCT
iajs-400	335	1	s*g	s*g	PROPN
iajs-400	335	2	-	-	PUNCT
iajs-400	335	3	continuous	continuous	ADJ
iajs-400	335	4	,	,	PUNCT
iajs-400	335	5	pres*g	pres*g	ADJ
iajs-400	335	6	-	-	PUNCT
iajs-400	335	7	continuous	continuous	ADJ
iajs-400	335	8	,	,	PUNCT
iajs-400	335	9	b	b	X
iajs-400	335	10	-	-	PUNCT
iajs-400	335	11	s*g	s*g	NOUN
iajs-400	335	12	-	-	PUNCT
iajs-400	335	13	continuous	continuous	ADJ
iajs-400	335	14	,	,	PUNCT
iajs-400	335	15	β	β	X
iajs-400	335	16	-s*g	-s*g	ADJ
iajs-400	335	17	-	-	PUNCT
iajs-400	335	18	continuous	continuous	ADJ
iajs-400	335	19	)	)	PUNCT
iajs-400	335	20	surjective	surjective	ADJ
iajs-400	335	21	function	function	NOUN
iajs-400	335	22	and	and	CCONJ
iajs-400	335	23	s	s	NOUN
iajs-400	335	24	is	be	AUX
iajs-400	335	25	a	a	DET
iajs-400	335	26	d	d	NOUN
iajs-400	335	27	-	-	PUNCT
iajs-400	335	28	set	set	NOUN
iajs-400	335	29	in	in	ADP
iajs-400	335	30	y	y	PROPN
iajs-400	335	31	,	,	PUNCT
iajs-400	335	32	then	then	ADV
iajs-400	335	33	the	the	DET
iajs-400	335	34	inverse	inverse	ADJ
iajs-400	335	35	image	image	NOUN
iajs-400	335	36	of	of	ADP
iajs-400	335	37	s	s	PROPN
iajs-400	335	38	is	be	AUX
iajs-400	335	39	an	an	DET
iajs-400	335	40	g*sd	g*sd	PROPN
iajs-400	335	41	−α	−α	PROPN
iajs-400	335	42	-set	-set	PUNCT
iajs-400	335	43	(	(	PUNCT
iajs-400	335	44	resp	resp	NOUN
iajs-400	335	45	.	.	PUNCT
iajs-400	336	1	g*sd	g*sd	PROPN
iajs-400	336	2	-set	-set	PROPN
iajs-400	336	3	,	,	PUNCT
iajs-400	336	4	g*spred	g*spre	VERB
iajs-400	336	5	−	−	NOUN
iajs-400	336	6	-set	-set	NUM
iajs-400	336	7	,	,	PUNCT
iajs-400	336	8	g*sbd	g*sbd	NOUN
iajs-400	336	9	−	−	PROPN
iajs-400	336	10	-set	-set	NUM
iajs-400	336	11	,	,	PUNCT
iajs-400	336	12	g*s	g*s	PROPN
iajs-400	336	13	d	d	PROPN
iajs-400	336	14	−β	−β	PROPN
iajs-400	336	15	set	set	PROPN
iajs-400	336	16	)	)	PUNCT
iajs-400	336	17	in	in	ADP
iajs-400	336	18	x	x	X
iajs-400	336	19	.	.	PUNCT
iajs-400	337	1	proof	proof	NOUN
iajs-400	337	2	:	:	PUNCT
iajs-400	337	3	let	let	VERB
iajs-400	337	4	s	s	PRON
iajs-400	337	5	be	be	AUX
iajs-400	337	6	a	a	DET
iajs-400	337	7	d	d	NOUN
iajs-400	337	8	-	-	PUNCT
iajs-400	337	9	set	set	NOUN
iajs-400	337	10	in	in	ADP
iajs-400	337	11	y	y	PROPN
iajs-400	337	12	,	,	PUNCT
iajs-400	337	13	then	then	ADV
iajs-400	337	14	there	there	PRON
iajs-400	337	15	are	be	VERB
iajs-400	337	16	two	two	NUM
iajs-400	337	17	open	open	ADJ
iajs-400	337	18	sets	set	NOUN
iajs-400	337	19	1u	1u	PRON
iajs-400	337	20	and	and	CCONJ
iajs-400	337	21	2u	2u	NOUN
iajs-400	337	22	in	in	ADP
iajs-400	337	23	y	y	PROPN
iajs-400	337	24	such	such	ADJ
iajs-400	337	25	that	that	SCONJ
iajs-400	337	26	21	21	NUM
iajs-400	337	27	u\us	u\u	NOUN
iajs-400	337	28	=	=	PUNCT
iajs-400	337	29	and	and	CCONJ
iajs-400	337	30	yu1	yu1	NOUN
iajs-400	337	31	≠	≠	PROPN
iajs-400	337	32	.	.	PUNCT
iajs-400	338	1	since	since	SCONJ
iajs-400	338	2	f	f	PROPN
iajs-400	338	3	is	be	AUX
iajs-400	338	4	α	α	PRON
iajs-400	338	5	-s*g	-s*g	ADJ
iajs-400	338	6	-	-	PUNCT
iajs-400	338	7	continuous	continuous	ADJ
iajs-400	338	8	,	,	PUNCT
iajs-400	338	9	then	then	ADV
iajs-400	338	10	)	)	PUNCT
iajs-400	338	11	u(f	u(f	PROPN
iajs-400	338	12	1	1	NUM
iajs-400	338	13	1−	1−	NUM
iajs-400	338	14	and	and	CCONJ
iajs-400	338	15	)	)	PUNCT
iajs-400	338	16	u(f	u(f	PROPN
iajs-400	338	17	2	2	NUM
iajs-400	338	18	1−	1−	NUM
iajs-400	338	19	are	be	AUX
iajs-400	338	20	α	α	PRON
iajs-400	338	21	-s*gopen	-s*gopen	NOUN
iajs-400	338	22	sets	set	NOUN
iajs-400	338	23	in	in	ADP
iajs-400	338	24	x.	x.	NOUN
iajs-400	338	25	since	since	SCONJ
iajs-400	338	26	yu1	yu1	NOUN
iajs-400	338	27	≠	≠	PROPN
iajs-400	338	28	and	and	CCONJ
iajs-400	338	29	f	f	PROPN
iajs-400	338	30	is	be	AUX
iajs-400	338	31	surjective	surjective	ADJ
iajs-400	338	32	,	,	PUNCT
iajs-400	338	33	then	then	ADV
iajs-400	338	34	x)u(f	x)u(f	PROPN
iajs-400	338	35	1	1	NUM
iajs-400	338	36	1	1	NUM
iajs-400	338	37	≠−	≠−	NOUN
iajs-400	338	38	.	.	PUNCT
iajs-400	339	1	hence	hence	ADV
iajs-400	339	2	)	)	PUNCT
iajs-400	339	3	u(f\)u(f)s(f	u(f\)u(f)s(f	ADJ
iajs-400	339	4	2	2	NUM
iajs-400	339	5	1	1	NUM
iajs-400	339	6	1	1	NUM
iajs-400	339	7	11	11	NUM
iajs-400	339	8	−−−	−−−	NUM
iajs-400	339	9	=	=	PUNCT
iajs-400	339	10	is	be	AUX
iajs-400	339	11	a	a	DET
iajs-400	339	12	g*sd	g*sd	PROPN
iajs-400	339	13	−α	−α	PROPN
iajs-400	339	14	-set	-set	PUNCT
iajs-400	339	15	in	in	ADP
iajs-400	339	16	x	x	X
iajs-400	339	17	.	.	PUNCT
iajs-400	340	1	by	by	ADP
iajs-400	340	2	the	the	DET
iajs-400	340	3	same	same	ADJ
iajs-400	340	4	way	way	NOUN
iajs-400	340	5	we	we	PRON
iajs-400	340	6	can	can	AUX
iajs-400	340	7	prove	prove	VERB
iajs-400	340	8	that	that	SCONJ
iajs-400	340	9	other	other	ADJ
iajs-400	340	10	cases	case	NOUN
iajs-400	340	11	.	.	PUNCT
iajs-400	341	1	theorem(3.11	theorem(3.11	X
iajs-400	341	2	):	):	PUNCT
iajs-400	341	3	if	if	SCONJ
iajs-400	341	4	)	)	PUNCT
iajs-400	341	5	,	,	PUNCT
iajs-400	341	6	y(),x(:f	y(),x(:f	PROPN
iajs-400	341	7	σ→τ	σ→τ	NUM
iajs-400	341	8	is	be	AUX
iajs-400	341	9	an	an	DET
iajs-400	341	10	α	α	NOUN
iajs-400	341	11	-s*g	-s*g	NOUN
iajs-400	341	12	-	-	PUNCT
iajs-400	341	13	irresolute	irresolute	ADJ
iajs-400	341	14	(	(	PUNCT
iajs-400	341	15	resp	resp	NOUN
iajs-400	341	16	.	.	PUNCT
iajs-400	342	1	s*g	s*g	PROPN
iajs-400	342	2	-	-	PUNCT
iajs-400	342	3	irresolute	irresolute	ADJ
iajs-400	342	4	,	,	PUNCT
iajs-400	342	5	pres*g	pres*g	X
iajs-400	342	6	-	-	PUNCT
iajs-400	342	7	irresolute	irresolute	ADJ
iajs-400	342	8	,	,	PUNCT
iajs-400	342	9	b	b	X
iajs-400	342	10	-	-	PUNCT
iajs-400	342	11	s*g	s*g	NOUN
iajs-400	342	12	-	-	PUNCT
iajs-400	342	13	irresolute	irresolute	ADJ
iajs-400	342	14	,	,	PUNCT
iajs-400	342	15	β	β	X
iajs-400	342	16	-s*g	-s*g	ADJ
iajs-400	342	17	-	-	PUNCT
iajs-400	342	18	irresolute	irresolute	NOUN
iajs-400	342	19	)	)	PUNCT
iajs-400	342	20	surjective	surjective	ADJ
iajs-400	342	21	function	function	NOUN
iajs-400	342	22	and	and	CCONJ
iajs-400	342	23	s	s	NOUN
iajs-400	342	24	is	be	AUX
iajs-400	342	25	an	an	DET
iajs-400	342	26	g*sd	g*sd	PROPN
iajs-400	342	27	−α	−α	PROPN
iajs-400	342	28	set	set	NOUN
iajs-400	342	29	(	(	PUNCT
iajs-400	342	30	resp	resp	NOUN
iajs-400	342	31	.	.	PUNCT
iajs-400	343	1	360	360	NUM
iajs-400	343	2	|	|	ADV
iajs-400	343	3	mathematics	mathematics	PROPN
iajs-400	343	4	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	343	5	�	�	NOUN
iajs-400	343	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	343	7	:	:	PUNCT
iajs-400	343	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	343	9	©	©	PROPN
iajs-400	343	10	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	343	11	ibn	ibn	PROPN
iajs-400	343	12	al	al	PROPN
iajs-400	343	13	-	-	PUNCT
iajs-400	343	14	haitham	haitham	PROPN
iajs-400	343	15	jour	jour	X
iajs-400	343	16	.	.	PROPN
iajs-400	344	1	for	for	ADP
iajs-400	344	2	pure	pure	ADJ
iajs-400	344	3	&	&	CCONJ
iajs-400	344	4	appl	appl	PROPN
iajs-400	344	5	.	.	PUNCT
iajs-400	345	1	sci	sci	PROPN
iajs-400	345	2	.	.	PUNCT
iajs-400	345	3	vol	vol	NOUN
iajs-400	345	4	.	.	PROPN
iajs-400	346	1	27	27	NUM
iajs-400	346	2	(	(	PUNCT
iajs-400	346	3	1	1	NUM
iajs-400	346	4	)	)	PUNCT
iajs-400	346	5	2014	2014	NUM
iajs-400	346	6	g*sd	g*sd	PROPN
iajs-400	346	7	-set	-set	PUNCT
iajs-400	346	8	,	,	PUNCT
iajs-400	346	9	g*spred	g*spre	VERB
iajs-400	346	10	−	−	NOUN
iajs-400	346	11	-set	-set	PUNCT
iajs-400	346	12	,	,	PUNCT
iajs-400	346	13	g*sbd	g*sbd	NOUN
iajs-400	346	14	−	−	PROPN
iajs-400	346	15	-set	-set	PUNCT
iajs-400	346	16	,	,	PUNCT
iajs-400	346	17	g*s	g*s	PROPN
iajs-400	346	18	d	d	PROPN
iajs-400	346	19	−β	−β	PROPN
iajs-400	346	20	-set	-set	NUM
iajs-400	346	21	)	)	PUNCT
iajs-400	346	22	in	in	ADP
iajs-400	346	23	y	y	PROPN
iajs-400	346	24	,	,	PUNCT
iajs-400	346	25	then	then	ADV
iajs-400	346	26	the	the	DET
iajs-400	346	27	inverse	inverse	ADJ
iajs-400	346	28	image	image	NOUN
iajs-400	346	29	of	of	ADP
iajs-400	346	30	s	s	PROPN
iajs-400	346	31	is	be	AUX
iajs-400	346	32	an	an	DET
iajs-400	346	33	g*sd	g*sd	PROPN
iajs-400	346	34	−α	−α	PROPN
iajs-400	346	35	set	set	NOUN
iajs-400	346	36	(	(	PUNCT
iajs-400	346	37	resp	resp	NOUN
iajs-400	346	38	.	.	PUNCT
iajs-400	347	1	g*sd	g*sd	PROPN
iajs-400	347	2	-set	-set	PUNCT
iajs-400	347	3	,	,	PUNCT
iajs-400	347	4	g*spred	g*spre	VERB
iajs-400	347	5	−	−	NOUN
iajs-400	347	6	-set	-set	PUNCT
iajs-400	347	7	,	,	PUNCT
iajs-400	347	8	g*sbd	g*sbd	NOUN
iajs-400	347	9	−	−	PROPN
iajs-400	347	10	-set	-set	PUNCT
iajs-400	347	11	,	,	PUNCT
iajs-400	347	12	g*s	g*s	PROPN
iajs-400	347	13	d	d	PROPN
iajs-400	347	14	−β	−β	PROPN
iajs-400	347	15	-set	-set	ADJ
iajs-400	347	16	)	)	PUNCT
iajs-400	347	17	in	in	ADP
iajs-400	347	18	x	x	X
iajs-400	347	19	.	.	PUNCT
iajs-400	348	1	proof	proof	NOUN
iajs-400	348	2	:	:	PUNCT
iajs-400	348	3	let	let	VERB
iajs-400	348	4	s	s	PRON
iajs-400	348	5	be	be	AUX
iajs-400	348	6	an	an	DET
iajs-400	348	7	g*sd	g*sd	PROPN
iajs-400	348	8	−α	−α	PROPN
iajs-400	348	9	-set	-set	PUNCT
iajs-400	348	10	in	in	ADP
iajs-400	348	11	y	y	PROPN
iajs-400	348	12	,	,	PUNCT
iajs-400	348	13	then	then	ADV
iajs-400	348	14	there	there	PRON
iajs-400	348	15	are	be	VERB
iajs-400	348	16	two	two	NUM
iajs-400	348	17	α	α	PRON
iajs-400	348	18	-s*g	-s*g	ADJ
iajs-400	348	19	-	-	PUNCT
iajs-400	348	20	open	open	ADJ
iajs-400	348	21	sets	set	VERB
iajs-400	348	22	1u	1u	PRON
iajs-400	348	23	and	and	CCONJ
iajs-400	348	24	2u	2u	NOUN
iajs-400	348	25	in	in	ADP
iajs-400	348	26	y	y	PROPN
iajs-400	348	27	such	such	ADJ
iajs-400	348	28	that	that	SCONJ
iajs-400	348	29	21	21	NUM
iajs-400	348	30	u\us	u\u	NOUN
iajs-400	348	31	=	=	PUNCT
iajs-400	348	32	and	and	CCONJ
iajs-400	348	33	yu1	yu1	NOUN
iajs-400	348	34	≠	≠	PROPN
iajs-400	348	35	.	.	PUNCT
iajs-400	349	1	since	since	SCONJ
iajs-400	349	2	f	f	PROPN
iajs-400	349	3	is	be	AUX
iajs-400	349	4	α	α	PROPN
iajs-400	349	5	-s*girresolute	-s*girresolute	PROPN
iajs-400	349	6	,	,	PUNCT
iajs-400	349	7	then	then	ADV
iajs-400	349	8	)	)	PUNCT
iajs-400	349	9	u(f	u(f	PROPN
iajs-400	349	10	1	1	NUM
iajs-400	349	11	1−	1−	NUM
iajs-400	349	12	and	and	CCONJ
iajs-400	349	13	)	)	PUNCT
iajs-400	349	14	u(f	u(f	PROPN
iajs-400	349	15	2	2	NUM
iajs-400	349	16	1−	1−	NUM
iajs-400	349	17	are	be	AUX
iajs-400	349	18	α	α	DET
iajs-400	349	19	-s*g	-s*g	ADJ
iajs-400	349	20	-	-	PUNCT
iajs-400	349	21	open	open	ADJ
iajs-400	349	22	sets	set	NOUN
iajs-400	349	23	in	in	ADP
iajs-400	349	24	x	x	X
iajs-400	349	25	.	.	PUNCT
iajs-400	350	1	since	since	SCONJ
iajs-400	350	2	yu1	yu1	NOUN
iajs-400	350	3	≠	≠	PROPN
iajs-400	350	4	and	and	CCONJ
iajs-400	350	5	f	f	PROPN
iajs-400	350	6	is	be	AUX
iajs-400	350	7	surjective	surjective	ADJ
iajs-400	350	8	,	,	PUNCT
iajs-400	350	9	then	then	ADV
iajs-400	350	10	x)u(f	x)u(f	PROPN
iajs-400	350	11	1	1	NUM
iajs-400	350	12	1	1	NUM
iajs-400	350	13	≠−	≠−	NOUN
iajs-400	350	14	.	.	PUNCT
iajs-400	351	1	hence	hence	ADV
iajs-400	351	2	)	)	PUNCT
iajs-400	351	3	u(f\)u(f)s(f	u(f\)u(f)s(f	ADJ
iajs-400	351	4	2	2	NUM
iajs-400	351	5	1	1	NUM
iajs-400	351	6	1	1	NUM
iajs-400	351	7	11	11	NUM
iajs-400	351	8	−−−	−−−	NUM
iajs-400	351	9	=	=	PUNCT
iajs-400	351	10	is	be	AUX
iajs-400	351	11	an	an	DET
iajs-400	351	12	g*sd	g*sd	PROPN
iajs-400	351	13	−α	−α	PROPN
iajs-400	351	14	-set	-set	PUNCT
iajs-400	351	15	in	in	ADP
iajs-400	351	16	x.	x.	NOUN
iajs-400	351	17	by	by	ADP
iajs-400	351	18	the	the	DET
iajs-400	351	19	same	same	ADJ
iajs-400	351	20	way	way	NOUN
iajs-400	351	21	we	we	PRON
iajs-400	351	22	can	can	AUX
iajs-400	351	23	prove	prove	VERB
iajs-400	351	24	that	that	SCONJ
iajs-400	351	25	other	other	ADJ
iajs-400	351	26	cases	case	NOUN
iajs-400	351	27	.	.	PUNCT
iajs-400	352	1	definitions(3.12	definitions(3.12	NOUN
iajs-400	352	2	):	):	PUNCT
iajs-400	352	3	a	a	DET
iajs-400	352	4	topological	topological	ADJ
iajs-400	352	5	space	space	NOUN
iajs-400	352	6	)	)	PUNCT
iajs-400	352	7	,	,	PUNCT
iajs-400	352	8	x	x	X
iajs-400	352	9	(	(	PUNCT
iajs-400	352	10	τ	τ	X
iajs-400	352	11	is	be	AUX
iajs-400	352	12	called	call	VERB
iajs-400	352	13	:	:	PUNCT
iajs-400	352	14	(	(	PUNCT
iajs-400	352	15	i	i	NOUN
iajs-400	352	16	)	)	PUNCT
iajs-400	352	17	an	an	DET
iajs-400	352	18	s*g0d	s*g0d	ADJ
iajs-400	352	19	-space	-space	NOUN
iajs-400	352	20	(	(	PUNCT
iajs-400	352	21	resp	resp	NOUN
iajs-400	352	22	.	.	PUNCT
iajs-400	353	1	α	α	PRON
iajs-400	353	2	-s*g0d	-s*g0d	ADJ
iajs-400	353	3	-space	-space	PROPN
iajs-400	353	4	,	,	PUNCT
iajs-400	353	5	pre	pre	ADJ
iajs-400	353	6	-	-	ADJ
iajs-400	353	7	s*g0d	s*g0d	ADJ
iajs-400	353	8	-space	-space	NOUN
iajs-400	353	9	,	,	PUNCT
iajs-400	353	10	b	b	X
iajs-400	353	11	-	-	PUNCT
iajs-400	353	12	s*g0d	s*g0d	ADJ
iajs-400	353	13	-space	-space	NOUN
iajs-400	353	14	,	,	PUNCT
iajs-400	353	15	β	β	X
iajs-400	353	16	-s*g0d	-s*g0d	ADJ
iajs-400	353	17	-space	-space	NOUN
iajs-400	353	18	)	)	PUNCT
iajs-400	353	19	if	if	SCONJ
iajs-400	353	20	for	for	ADP
iajs-400	353	21	any	any	DET
iajs-400	353	22	two	two	NUM
iajs-400	353	23	distinct	distinct	ADJ
iajs-400	353	24	points	point	NOUN
iajs-400	353	25	x	x	PUNCT
iajs-400	353	26	and	and	CCONJ
iajs-400	353	27	y	y	PROPN
iajs-400	353	28	of	of	ADP
iajs-400	353	29	x	x	SYM
iajs-400	353	30	,	,	PUNCT
iajs-400	353	31	there	there	PRON
iajs-400	353	32	exists	exist	VERB
iajs-400	353	33	an	an	DET
iajs-400	353	34	g*sd	g*sd	PROPN
iajs-400	353	35	-set	-set	PUNCT
iajs-400	353	36	(	(	PUNCT
iajs-400	353	37	resp	resp	NOUN
iajs-400	353	38	.	.	PUNCT
iajs-400	354	1	g*sd	g*sd	PROPN
iajs-400	354	2	−α	−α	PROPN
iajs-400	354	3	-set	-set	PROPN
iajs-400	354	4	,	,	PUNCT
iajs-400	354	5	g*spred	g*spre	VERB
iajs-400	354	6	−	−	NOUN
iajs-400	354	7	-set	-set	PUNCT
iajs-400	354	8	,	,	PUNCT
iajs-400	354	9	g*sbd	g*sbd	NOUN
iajs-400	354	10	−	−	PROPN
iajs-400	354	11	-set	-set	NUM
iajs-400	354	12	,	,	PUNCT
iajs-400	354	13	g*s	g*s	PROPN
iajs-400	354	14	d	d	PROPN
iajs-400	354	15	−β	−β	PROPN
iajs-400	354	16	-set	-set	NUM
iajs-400	354	17	)	)	PUNCT
iajs-400	354	18	of	of	ADP
iajs-400	354	19	x	x	SYM
iajs-400	354	20	containing	contain	VERB
iajs-400	354	21	one	one	NUM
iajs-400	354	22	of	of	ADP
iajs-400	354	23	the	the	DET
iajs-400	354	24	points	point	NOUN
iajs-400	354	25	but	but	CCONJ
iajs-400	354	26	not	not	PART
iajs-400	354	27	the	the	DET
iajs-400	354	28	other	other	ADJ
iajs-400	354	29	.	.	PUNCT
iajs-400	355	1	(	(	PUNCT
iajs-400	355	2	ii	ii	NOUN
iajs-400	355	3	)	)	PUNCT
iajs-400	355	4	an	an	DET
iajs-400	355	5	s*g1d	s*g1d	NOUN
iajs-400	355	6	-space	-space	NOUN
iajs-400	355	7	(	(	PUNCT
iajs-400	355	8	resp	resp	NOUN
iajs-400	355	9	.	.	PUNCT
iajs-400	356	1	α	α	PRON
iajs-400	356	2	-s*g1d	-s*g1d	NOUN
iajs-400	356	3	-space	-space	NOUN
iajs-400	356	4	,	,	PUNCT
iajs-400	356	5	pre	pre	ADJ
iajs-400	356	6	-	-	ADJ
iajs-400	356	7	s*g1d	s*g1d	ADJ
iajs-400	356	8	-space	-space	NOUN
iajs-400	356	9	,	,	PUNCT
iajs-400	356	10	b	b	X
iajs-400	356	11	-	-	PUNCT
iajs-400	356	12	s*g1d	s*g1d	NOUN
iajs-400	356	13	-space	-space	NOUN
iajs-400	356	14	,	,	PUNCT
iajs-400	356	15	β	β	NOUN
iajs-400	356	16	-s*g1d	-s*g1d	NOUN
iajs-400	356	17	space	space	NOUN
iajs-400	356	18	)	)	PUNCT
iajs-400	356	19	if	if	SCONJ
iajs-400	356	20	for	for	ADP
iajs-400	356	21	any	any	DET
iajs-400	356	22	two	two	NUM
iajs-400	356	23	distinct	distinct	ADJ
iajs-400	356	24	points	point	NOUN
iajs-400	356	25	x	x	PUNCT
iajs-400	356	26	and	and	CCONJ
iajs-400	356	27	y	y	PROPN
iajs-400	356	28	of	of	ADP
iajs-400	356	29	x	x	SYM
iajs-400	356	30	,	,	PUNCT
iajs-400	356	31	there	there	PRON
iajs-400	356	32	exists	exist	VERB
iajs-400	356	33	an	an	DET
iajs-400	356	34	g*sd	g*sd	PROPN
iajs-400	356	35	-set	-set	PUNCT
iajs-400	356	36	(	(	PUNCT
iajs-400	356	37	resp	resp	NOUN
iajs-400	356	38	.	.	PUNCT
iajs-400	357	1	g*sd	g*sd	PROPN
iajs-400	357	2	−α	−α	PROPN
iajs-400	357	3	-set	-set	PROPN
iajs-400	357	4	,	,	PUNCT
iajs-400	357	5	g*spred	g*spre	VERB
iajs-400	357	6	−	−	NOUN
iajs-400	357	7	-set	-set	PUNCT
iajs-400	357	8	,	,	PUNCT
iajs-400	357	9	g*sbd	g*sbd	NOUN
iajs-400	357	10	−	−	PROPN
iajs-400	357	11	-set	-set	NUM
iajs-400	357	12	,	,	PUNCT
iajs-400	357	13	g*s	g*s	PROPN
iajs-400	357	14	d	d	PROPN
iajs-400	357	15	−β	−β	PROPN
iajs-400	357	16	-set	-set	NUM
iajs-400	357	17	)	)	PUNCT
iajs-400	357	18	of	of	ADP
iajs-400	357	19	x	x	SYM
iajs-400	357	20	containing	contain	VERB
iajs-400	357	21	x	x	NOUN
iajs-400	357	22	but	but	CCONJ
iajs-400	357	23	not	not	PART
iajs-400	357	24	y	y	PROPN
iajs-400	357	25	and	and	CCONJ
iajs-400	357	26	an	an	DET
iajs-400	357	27	g*sd	g*sd	PROPN
iajs-400	357	28	-set	-set	PUNCT
iajs-400	357	29	(	(	PUNCT
iajs-400	357	30	resp	resp	NOUN
iajs-400	357	31	.	.	PUNCT
iajs-400	358	1	g*sd	g*sd	PROPN
iajs-400	358	2	−α	−α	PROPN
iajs-400	358	3	set	set	VERB
iajs-400	358	4	,	,	PUNCT
iajs-400	358	5	g*spred	g*spre	VERB
iajs-400	358	6	−	−	NOUN
iajs-400	358	7	-set	-set	PUNCT
iajs-400	358	8	,	,	PUNCT
iajs-400	358	9	g*sbd	g*sbd	NOUN
iajs-400	358	10	−	−	PROPN
iajs-400	358	11	-set	-set	NUM
iajs-400	358	12	,	,	PUNCT
iajs-400	358	13	g*s	g*s	PROPN
iajs-400	358	14	d	d	PROPN
iajs-400	358	15	−β	−β	PROPN
iajs-400	358	16	-set	-set	NUM
iajs-400	358	17	)	)	PUNCT
iajs-400	358	18	of	of	ADP
iajs-400	358	19	x	x	SYM
iajs-400	358	20	containing	contain	VERB
iajs-400	358	21	y	y	NOUN
iajs-400	358	22	but	but	CCONJ
iajs-400	358	23	not	not	PART
iajs-400	358	24	x	x	X
iajs-400	358	25	.	.	PUNCT
iajs-400	359	1	(	(	PUNCT
iajs-400	359	2	iii	iii	X
iajs-400	359	3	)	)	PUNCT
iajs-400	359	4	an	an	DET
iajs-400	359	5	s*g2d	s*g2d	PROPN
iajs-400	359	6	-space	-space	NOUN
iajs-400	359	7	(	(	PUNCT
iajs-400	359	8	resp	resp	NOUN
iajs-400	359	9	.	.	PUNCT
iajs-400	360	1	α	α	NOUN
iajs-400	360	2	-s*g2d	-s*g2d	PROPN
iajs-400	360	3	space	space	NOUN
iajs-400	360	4	,	,	PUNCT
iajs-400	360	5	pre	pre	ADJ
iajs-400	360	6	-	-	ADJ
iajs-400	360	7	s*g2d	s*g2d	ADJ
iajs-400	360	8	-space	-space	NOUN
iajs-400	360	9	,	,	PUNCT
iajs-400	360	10	b	b	X
iajs-400	360	11	-	-	PUNCT
iajs-400	360	12	s*g2d	s*g2d	X
iajs-400	360	13	-space	-space	NOUN
iajs-400	360	14	,	,	PUNCT
iajs-400	360	15	β	β	NOUN
iajs-400	360	16	-s*g2d	-s*g2d	PUNCT
iajs-400	360	17	-space	-space	NOUN
iajs-400	360	18	)	)	PUNCT
iajs-400	360	19	if	if	SCONJ
iajs-400	360	20	for	for	ADP
iajs-400	360	21	any	any	DET
iajs-400	360	22	two	two	NUM
iajs-400	360	23	distinct	distinct	ADJ
iajs-400	360	24	points	point	NOUN
iajs-400	360	25	x	x	PUNCT
iajs-400	360	26	and	and	CCONJ
iajs-400	360	27	y	y	PROPN
iajs-400	360	28	of	of	ADP
iajs-400	360	29	x	x	SYM
iajs-400	360	30	,	,	PUNCT
iajs-400	360	31	there	there	PRON
iajs-400	360	32	are	be	VERB
iajs-400	360	33	two	two	NUM
iajs-400	360	34	g*sd	g*sd	NOUN
iajs-400	360	35	-sets	-set	NOUN
iajs-400	360	36	(	(	PUNCT
iajs-400	360	37	resp	resp	NOUN
iajs-400	360	38	.	.	PUNCT
iajs-400	361	1	g*sd	g*sd	PROPN
iajs-400	361	2	−α	−α	PROPN
iajs-400	361	3	sets	set	VERB
iajs-400	361	4	,	,	PUNCT
iajs-400	361	5	g*spred	g*spre	VERB
iajs-400	361	6	−	−	NOUN
iajs-400	361	7	-sets	-set	NOUN
iajs-400	361	8	,	,	PUNCT
iajs-400	361	9	g*sbd	g*sbd	NOUN
iajs-400	361	10	−	−	NOUN
iajs-400	361	11	-sets	-set	NOUN
iajs-400	361	12	,	,	PUNCT
iajs-400	361	13	g*s	g*s	PROPN
iajs-400	361	14	d	d	ADP
iajs-400	361	15	−β	−β	ADJ
iajs-400	361	16	-sets	-set	NOUN
iajs-400	361	17	)	)	PUNCT
iajs-400	361	18	u	u	NOUN
iajs-400	361	19	and	and	CCONJ
iajs-400	361	20	v	v	NOUN
iajs-400	361	21	of	of	ADP
iajs-400	361	22	x	x	PUNCT
iajs-400	361	23	such	such	ADJ
iajs-400	361	24	that	that	SCONJ
iajs-400	361	25	ux∈	ux∈	PROPN
iajs-400	361	26	,	,	PUNCT
iajs-400	361	27	vy∈	vy∈	PROPN
iajs-400	361	28	and	and	CCONJ
iajs-400	361	29	φ	φ	NOUN
iajs-400	361	30	=	=	NOUN
iajs-400	361	31	vu	vu	X
iajs-400	361	32			PROPN
iajs-400	361	33	.	.	PUNCT
iajs-400	362	1	theorem(3.13	theorem(3.13	NUM
iajs-400	362	2	):	):	PUNCT
iajs-400	362	3	(	(	PUNCT
iajs-400	362	4	i	i	NOUN
iajs-400	362	5	)	)	PUNCT
iajs-400	362	6	every	every	DET
iajs-400	362	7	s*git	s*git	ADJ
iajs-400	362	8	-space	-space	NOUN
iajs-400	362	9	(	(	PUNCT
iajs-400	362	10	resp	resp	NOUN
iajs-400	362	11	.	.	PUNCT
iajs-400	363	1	α	α	NOUN
iajs-400	363	2	-s*git	-s*git	PUNCT
iajs-400	363	3	-space	-space	NOUN
iajs-400	363	4	,	,	PUNCT
iajs-400	363	5	pre	pre	ADJ
iajs-400	363	6	-	-	ADJ
iajs-400	363	7	s*git	s*git	ADJ
iajs-400	363	8	-space	-space	NOUN
iajs-400	363	9	,	,	PUNCT
iajs-400	363	10	b	b	X
iajs-400	363	11	-	-	PUNCT
iajs-400	363	12	s*git	s*git	ADJ
iajs-400	363	13	-space	-space	NOUN
iajs-400	363	14	,	,	PUNCT
iajs-400	363	15	β	β	X
iajs-400	363	16	-s*git	-s*git	PUNCT
iajs-400	363	17	-space	-space	NOUN
iajs-400	363	18	)	)	PUNCT
iajs-400	363	19	is	be	AUX
iajs-400	363	20	s*g1it	s*g1it	NOUN
iajs-400	363	21	−	−	NOUN
iajs-400	363	22	-space	-space	NOUN
iajs-400	363	23	(	(	PUNCT
iajs-400	363	24	resp	resp	NOUN
iajs-400	363	25	.	.	PUNCT
iajs-400	364	1	α	α	PROPN
iajs-400	364	2	-s*g1it	-s*g1it	ADJ
iajs-400	364	3	−	−	PROPN
iajs-400	364	4	-space	-space	NOUN
iajs-400	364	5	,	,	PUNCT
iajs-400	364	6	pre	pre	ADJ
iajs-400	364	7	-	-	NOUN
iajs-400	364	8	s*g1it	s*g1it	ADJ
iajs-400	364	9	−	−	NOUN
iajs-400	364	10	-space	-space	NOUN
iajs-400	364	11	,	,	PUNCT
iajs-400	364	12	bs*g1it	bs*g1it	ADJ
iajs-400	364	13	−	−	PROPN
iajs-400	364	14	-space	-space	NOUN
iajs-400	364	15	,	,	PUNCT
iajs-400	364	16	β	β	X
iajs-400	364	17	-s*g	-s*g	PROPN
iajs-400	364	18	1it	1it	NOUN
iajs-400	364	19	−	−	PROPN
iajs-400	364	20	-space	-space	NOUN
iajs-400	364	21	)	)	PUNCT
iajs-400	364	22	,	,	PUNCT
iajs-400	364	23	2,1i	2,1i	NOUN
iajs-400	365	1	=	=	PUNCT
iajs-400	365	2	.	.	PUNCT
iajs-400	366	1	(	(	PUNCT
iajs-400	366	2	ii	ii	NOUN
iajs-400	366	3	)	)	PUNCT
iajs-400	366	4	every	every	DET
iajs-400	366	5	s*git	s*git	ADJ
iajs-400	366	6	-space	-space	NOUN
iajs-400	366	7	(	(	PUNCT
iajs-400	366	8	resp	resp	NOUN
iajs-400	366	9	.	.	PUNCT
iajs-400	367	1	α	α	NOUN
iajs-400	367	2	-s*git	-s*git	PUNCT
iajs-400	367	3	-space	-space	NOUN
iajs-400	367	4	,	,	PUNCT
iajs-400	367	5	pre	pre	ADJ
iajs-400	367	6	-	-	ADJ
iajs-400	367	7	s*git	s*git	ADJ
iajs-400	367	8	-space	-space	NOUN
iajs-400	367	9	,	,	PUNCT
iajs-400	367	10	b	b	X
iajs-400	367	11	-	-	PUNCT
iajs-400	367	12	s*git	s*git	ADJ
iajs-400	367	13	-space	-space	NOUN
iajs-400	367	14	,	,	PUNCT
iajs-400	367	15	β	β	X
iajs-400	367	16	-s*git	-s*git	PUNCT
iajs-400	367	17	-space	-space	NOUN
iajs-400	367	18	)	)	PUNCT
iajs-400	367	19	is	be	AUX
iajs-400	367	20	s*gid	s*gid	ADJ
iajs-400	367	21	-space	-space	NOUN
iajs-400	367	22	(	(	PUNCT
iajs-400	367	23	resp	resp	NOUN
iajs-400	367	24	.	.	PUNCT
iajs-400	368	1	α	α	PRON
iajs-400	368	2	-s*gid	-s*gid	ADJ
iajs-400	368	3	-space	-space	NOUN
iajs-400	368	4	,	,	PUNCT
iajs-400	368	5	pre	pre	ADJ
iajs-400	368	6	-	-	ADJ
iajs-400	368	7	s*gid	s*gid	ADJ
iajs-400	368	8	-space	-space	NOUN
iajs-400	368	9	,	,	PUNCT
iajs-400	368	10	b	b	X
iajs-400	368	11	-	-	PUNCT
iajs-400	368	12	s*gid	s*gid	ADJ
iajs-400	368	13	-space	-space	NOUN
iajs-400	368	14	,	,	PUNCT
iajs-400	368	15	β	β	X
iajs-400	368	16	s*gid	s*gid	ADJ
iajs-400	368	17	-space	-space	NOUN
iajs-400	368	18	)	)	PUNCT
iajs-400	368	19	,	,	PUNCT
iajs-400	368	20	2,1,0i	2,1,0i	PROPN
iajs-400	368	21	=	=	PUNCT
iajs-400	368	22	.	.	PUNCT
iajs-400	369	1	(	(	PUNCT
iajs-400	369	2	iii	iii	X
iajs-400	369	3	)	)	PUNCT
iajs-400	369	4	every	every	DET
iajs-400	369	5	s*gid	s*gid	ADJ
iajs-400	369	6	-space	-space	NOUN
iajs-400	369	7	(	(	PUNCT
iajs-400	369	8	resp	resp	NOUN
iajs-400	369	9	.	.	PUNCT
iajs-400	370	1	α	α	PRON
iajs-400	370	2	-s*gid	-s*gid	ADJ
iajs-400	370	3	-space	-space	NOUN
iajs-400	370	4	,	,	PUNCT
iajs-400	370	5	pre	pre	ADJ
iajs-400	370	6	-	-	ADJ
iajs-400	370	7	s*gid	s*gid	ADJ
iajs-400	370	8	-space	-space	NOUN
iajs-400	370	9	,	,	PUNCT
iajs-400	370	10	b	b	X
iajs-400	370	11	-	-	PUNCT
iajs-400	370	12	s*gid	s*gid	ADJ
iajs-400	370	13	-space	-space	NOUN
iajs-400	370	14	,	,	PUNCT
iajs-400	370	15	β	β	NOUN
iajs-400	370	16	s*gid	s*gid	ADJ
iajs-400	370	17	-space	-space	NOUN
iajs-400	370	18	)	)	PUNCT
iajs-400	370	19	is	be	AUX
iajs-400	370	20	s*g1id	s*g1id	NOUN
iajs-400	370	21	−	−	NOUN
iajs-400	370	22	-space	-space	NOUN
iajs-400	370	23	(	(	PUNCT
iajs-400	370	24	resp	resp	NOUN
iajs-400	370	25	.	.	PUNCT
iajs-400	371	1	α	α	PROPN
iajs-400	371	2	-s*g1id	-s*g1id	NOUN
iajs-400	371	3	−	−	PROPN
iajs-400	371	4	-space	-space	NOUN
iajs-400	371	5	,	,	PUNCT
iajs-400	371	6	pre	pre	ADJ
iajs-400	371	7	-	-	ADJ
iajs-400	371	8	s*g1id	s*g1id	ADJ
iajs-400	371	9	−	−	NOUN
iajs-400	371	10	-space	-space	NOUN
iajs-400	371	11	,	,	PUNCT
iajs-400	371	12	b	b	X
iajs-400	371	13	-	-	PUNCT
iajs-400	371	14	s*g1id	s*g1id	NOUN
iajs-400	371	15	−	−	NOUN
iajs-400	371	16	space	space	NOUN
iajs-400	371	17	,	,	PUNCT
iajs-400	371	18	β	β	X
iajs-400	371	19	-s*g	-s*g	PROPN
iajs-400	371	20	1id	1id	NOUN
iajs-400	371	21	−	−	PROPN
iajs-400	371	22	-space	-space	NOUN
iajs-400	371	23	)	)	PUNCT
iajs-400	371	24	,	,	PUNCT
iajs-400	371	25	2,1i	2,1i	NOUN
iajs-400	371	26	=	=	PUNCT
iajs-400	371	27	.	.	PUNCT
iajs-400	372	1	proof	proof	NOUN
iajs-400	372	2	:	:	PUNCT
iajs-400	372	3	(	(	PUNCT
iajs-400	372	4	i	i	NOUN
iajs-400	372	5	)	)	PUNCT
iajs-400	372	6	it	it	PRON
iajs-400	372	7	is	be	AUX
iajs-400	372	8	obvious	obvious	ADJ
iajs-400	372	9	.	.	PUNCT
iajs-400	373	1	(	(	PUNCT
iajs-400	373	2	ii	ii	NOUN
iajs-400	373	3	)	)	PUNCT
iajs-400	373	4	follows	follow	VERB
iajs-400	373	5	from	from	ADP
iajs-400	373	6	remark	remark	NOUN
iajs-400	373	7	(	(	PUNCT
iajs-400	373	8	3.2	3.2	NUM
iajs-400	373	9	)	)	PUNCT
iajs-400	373	10	.	.	PUNCT
iajs-400	374	1	(	(	PUNCT
iajs-400	374	2	iii	iii	X
iajs-400	374	3	)	)	PUNCT
iajs-400	374	4	it	it	PRON
iajs-400	374	5	is	be	AUX
iajs-400	374	6	obvious	obvious	ADJ
iajs-400	374	7	.	.	PUNCT
iajs-400	375	1	remark(3.14	remark(3.14	PRON
iajs-400	375	2	):	):	PUNCT
iajs-400	375	3	the	the	DET
iajs-400	375	4	converse	converse	NOUN
iajs-400	375	5	of	of	ADP
iajs-400	375	6	theorem	theorem	NOUN
iajs-400	375	7	(	(	PUNCT
iajs-400	375	8	3.13	3.13	NUM
iajs-400	375	9	)	)	PUNCT
iajs-400	375	10	,	,	PUNCT
iajs-400	375	11	no	no	INTJ
iajs-400	375	12	.	.	PUNCT
iajs-400	376	1	(	(	PUNCT
iajs-400	376	2	i	i	NOUN
iajs-400	376	3	)	)	PUNCT
iajs-400	376	4	may	may	AUX
iajs-400	376	5	not	not	PART
iajs-400	376	6	be	be	AUX
iajs-400	376	7	true	true	ADJ
iajs-400	376	8	.	.	PUNCT
iajs-400	377	1	consider	consider	VERB
iajs-400	377	2	the	the	DET
iajs-400	377	3	following	follow	VERB
iajs-400	377	4	examples	example	NOUN
iajs-400	377	5	:	:	PUNCT
iajs-400	377	6	361	361	NUM
iajs-400	377	7	|	|	ADV
iajs-400	377	8	mathematics	mathematics	PROPN
iajs-400	377	9	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	377	10	�	�	NOUN
iajs-400	377	11	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	377	12	:	:	PUNCT
iajs-400	377	13	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	377	14	©	©	PROPN
iajs-400	377	15	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	377	16	ibn	ibn	PROPN
iajs-400	377	17	al	al	PROPN
iajs-400	377	18	-	-	PUNCT
iajs-400	377	19	haitham	haitham	PROPN
iajs-400	377	20	jour	jour	X
iajs-400	377	21	.	.	PROPN
iajs-400	378	1	for	for	ADP
iajs-400	378	2	pure	pure	ADJ
iajs-400	378	3	&	&	CCONJ
iajs-400	378	4	appl	appl	PROPN
iajs-400	378	5	.	.	PUNCT
iajs-400	379	1	sci	sci	PROPN
iajs-400	379	2	.	.	PUNCT
iajs-400	379	3	vol	vol	NOUN
iajs-400	379	4	.	.	PROPN
iajs-400	380	1	27	27	NUM
iajs-400	380	2	(	(	PUNCT
iajs-400	380	3	1	1	NUM
iajs-400	380	4	)	)	PUNCT
iajs-400	380	5	2014	2014	NUM
iajs-400	380	6	example(3.15	example(3.15	NUM
iajs-400	380	7	):	):	PUNCT
iajs-400	380	8	let	let	VERB
iajs-400	380	9	x	x	PRON
iajs-400	380	10	be	be	AUX
iajs-400	380	11	any	any	DET
iajs-400	380	12	infinte	infinte	NOUN
iajs-400	380	13	set	set	NOUN
iajs-400	380	14	and	and	CCONJ
iajs-400	380	15	let	let	VERB
iajs-400	380	16	τ=	τ=	NOUN
iajs-400	380	17	{	{	PUNCT
iajs-400	380	18	cu	cu	PROPN
iajs-400	380	19	:	:	PUNCT
iajs-400	380	20	xu	xu	PROPN
iajs-400	380	21	⊆	⊆	NUM
iajs-400	380	22	is	be	AUX
iajs-400	380	23	finite	finite	ADJ
iajs-400	380	24	}	}	PUNCT
iajs-400	380	25	}	}	PUNCT
iajs-400	380	26	{	{	PUNCT
iajs-400	380	27	φ	φ	PROPN
iajs-400	380	28	.	.	PUNCT
iajs-400	381	1	then	then	ADV
iajs-400	381	2	)	)	PUNCT
iajs-400	381	3	,	,	PUNCT
iajs-400	381	4	x	x	X
iajs-400	381	5	(	(	PUNCT
iajs-400	381	6	τ	τ	X
iajs-400	381	7	is	be	AUX
iajs-400	381	8	an	an	DET
iajs-400	381	9	s*g	s*g	NOUN
iajs-400	381	10	1	1	NUM
iajs-400	381	11	t	t	NOUN
iajs-400	381	12	-space	-space	NOUN
iajs-400	381	13	(	(	PUNCT
iajs-400	381	14	resp	resp	NOUN
iajs-400	381	15	.	.	PUNCT
iajs-400	382	1	α	α	PROPN
iajs-400	382	2	-s*g1	-s*g1	PROPN
iajs-400	382	3	t	t	PROPN
iajs-400	382	4	-space	-space	NOUN
iajs-400	382	5	,	,	PUNCT
iajs-400	382	6	pre	pre	ADJ
iajs-400	382	7	-	-	ADJ
iajs-400	382	8	s*g1	s*g1	PROPN
iajs-400	382	9	t	t	NOUN
iajs-400	382	10	-space	-space	NOUN
iajs-400	382	11	,	,	PUNCT
iajs-400	382	12	b	b	X
iajs-400	382	13	-	-	PUNCT
iajs-400	382	14	s*g1	s*g1	PROPN
iajs-400	382	15	t	t	NOUN
iajs-400	382	16	-space	-space	NOUN
iajs-400	382	17	,	,	PUNCT
iajs-400	382	18	β	β	PROPN
iajs-400	382	19	-s*g1	-s*g1	PROPN
iajs-400	382	20	t	t	PROPN
iajs-400	382	21	-space	-space	NOUN
iajs-400	382	22	)	)	PUNCT
iajs-400	382	23	,	,	PUNCT
iajs-400	382	24	but	but	CCONJ
iajs-400	382	25	is	be	AUX
iajs-400	382	26	not	not	PART
iajs-400	382	27	an	an	DET
iajs-400	382	28	s*g2	s*g2	NOUN
iajs-400	382	29	t	t	NOUN
iajs-400	382	30	-space	-space	NOUN
iajs-400	382	31	(	(	PUNCT
iajs-400	382	32	resp	resp	NOUN
iajs-400	382	33	.	.	PUNCT
iajs-400	383	1	α	α	PROPN
iajs-400	383	2	-s*g2	-s*g2	PROPN
iajs-400	383	3	t	t	PROPN
iajs-400	383	4	-space	-space	NOUN
iajs-400	383	5	,	,	PUNCT
iajs-400	383	6	pre	pre	ADJ
iajs-400	383	7	-	-	NOUN
iajs-400	383	8	s*g2	s*g2	NOUN
iajs-400	383	9	t	t	NOUN
iajs-400	383	10	-space	-space	NOUN
iajs-400	383	11	,	,	PUNCT
iajs-400	383	12	b	b	X
iajs-400	383	13	-	-	PUNCT
iajs-400	383	14	s*g2	s*g2	NOUN
iajs-400	383	15	t	t	NOUN
iajs-400	383	16	-space	-space	NOUN
iajs-400	383	17	,	,	PUNCT
iajs-400	383	18	β	β	PROPN
iajs-400	383	19	-s*g2	-s*g2	PROPN
iajs-400	383	20	t	t	PROPN
iajs-400	383	21	-space	-space	NOUN
iajs-400	383	22	)	)	PUNCT
iajs-400	383	23	.	.	PUNCT
iajs-400	384	1	example(3.16	example(3.16	PROPN
iajs-400	384	2	):	):	PUNCT
iajs-400	384	3	let	let	VERB
iajs-400	384	4	}	}	PUNCT
iajs-400	384	5	b	b	PROPN
iajs-400	384	6	,	,	PUNCT
iajs-400	384	7	a{x	a{x	VERB
iajs-400	384	8	=	=	PUNCT
iajs-400	384	9	and	and	CCONJ
iajs-400	384	10	}	}	PUNCT
iajs-400	384	11	}	}	PUNCT
iajs-400	384	12	a{,,x	a{,,x	PROPN
iajs-400	384	13	{	{	PUNCT
iajs-400	384	14	φ	φ	PROPN
iajs-400	384	15	=	=	PROPN
iajs-400	384	16	τ	τ	X
iajs-400	384	17	.	.	PUNCT
iajs-400	385	1	then	then	ADV
iajs-400	385	2	)	)	PUNCT
iajs-400	385	3	,	,	PUNCT
iajs-400	385	4	x	x	X
iajs-400	385	5	(	(	PUNCT
iajs-400	385	6	τ	τ	X
iajs-400	385	7	is	be	AUX
iajs-400	385	8	s*g0	s*g0	ADJ
iajs-400	385	9	t	t	NOUN
iajs-400	385	10	-space	-space	NOUN
iajs-400	385	11	(	(	PUNCT
iajs-400	385	12	resp	resp	NOUN
iajs-400	385	13	.	.	PUNCT
iajs-400	386	1	α	α	PROPN
iajs-400	386	2	-s*g0	-s*g0	NOUN
iajs-400	386	3	t	t	PROPN
iajs-400	386	4	space	space	NOUN
iajs-400	386	5	,	,	PUNCT
iajs-400	386	6	pre	pre	ADJ
iajs-400	386	7	-	-	ADJ
iajs-400	386	8	s*g0	s*g0	ADJ
iajs-400	386	9	t	t	NOUN
iajs-400	386	10	-space	-space	NOUN
iajs-400	386	11	,	,	PUNCT
iajs-400	386	12	b	b	X
iajs-400	386	13	-	-	PUNCT
iajs-400	386	14	s*g0	s*g0	NOUN
iajs-400	386	15	t	t	NOUN
iajs-400	386	16	-space	-space	NOUN
iajs-400	386	17	,	,	PUNCT
iajs-400	386	18	β	β	X
iajs-400	386	19	-s*g0	-s*g0	NOUN
iajs-400	386	20	t	t	NOUN
iajs-400	386	21	-space	-space	NOUN
iajs-400	386	22	)	)	PUNCT
iajs-400	386	23	,	,	PUNCT
iajs-400	386	24	but	but	CCONJ
iajs-400	386	25	is	be	AUX
iajs-400	386	26	not	not	PART
iajs-400	386	27	s*g1	s*g1	PROPN
iajs-400	386	28	t	t	NOUN
iajs-400	386	29	-space	-space	NOUN
iajs-400	386	30	(	(	PUNCT
iajs-400	386	31	resp	resp	NOUN
iajs-400	386	32	.	.	PUNCT
iajs-400	387	1	α	α	PRON
iajs-400	387	2	s*g1	s*g1	X
iajs-400	387	3	t	t	NOUN
iajs-400	387	4	-space	-space	NOUN
iajs-400	387	5	,	,	PUNCT
iajs-400	387	6	pre	pre	ADJ
iajs-400	387	7	-	-	ADJ
iajs-400	387	8	s*g1	s*g1	PROPN
iajs-400	387	9	t	t	NOUN
iajs-400	387	10	-space	-space	NOUN
iajs-400	387	11	,	,	PUNCT
iajs-400	387	12	b	b	X
iajs-400	387	13	-	-	PUNCT
iajs-400	387	14	s*g1	s*g1	PROPN
iajs-400	387	15	t	t	NOUN
iajs-400	387	16	-space	-space	NOUN
iajs-400	387	17	,	,	PUNCT
iajs-400	387	18	β	β	X
iajs-400	387	19	-s*g1	-s*g1	PROPN
iajs-400	387	20	t	t	PROPN
iajs-400	387	21	-space	-space	NOUN
iajs-400	387	22	)	)	PUNCT
iajs-400	387	23	.	.	PUNCT
iajs-400	388	1	remark(3.17	remark(3.17	X
iajs-400	388	2	):	):	PUNCT
iajs-400	388	3	the	the	DET
iajs-400	388	4	converse	converse	NOUN
iajs-400	388	5	of	of	ADP
iajs-400	388	6	theorem	theorem	NOUN
iajs-400	388	7	(	(	PUNCT
iajs-400	388	8	3.13	3.13	NUM
iajs-400	388	9	)	)	PUNCT
iajs-400	388	10	,	,	PUNCT
iajs-400	388	11	no.(ii	no.(ii	NOUN
iajs-400	388	12	)	)	PUNCT
iajs-400	388	13	may	may	AUX
iajs-400	388	14	not	not	PART
iajs-400	388	15	be	be	AUX
iajs-400	388	16	true	true	ADJ
iajs-400	388	17	.	.	PUNCT
iajs-400	389	1	consider	consider	VERB
iajs-400	389	2	the	the	DET
iajs-400	389	3	following	follow	VERB
iajs-400	389	4	examples	example	NOUN
iajs-400	389	5	:	:	PUNCT
iajs-400	389	6	example(3.18	example(3.18	NUM
iajs-400	389	7	):	):	PUNCT
iajs-400	389	8	let	let	VERB
iajs-400	389	9	}	}	PUNCT
iajs-400	389	10	c	c	NOUN
iajs-400	389	11	,	,	PUNCT
iajs-400	389	12	b	b	PROPN
iajs-400	389	13	,	,	PUNCT
iajs-400	389	14	a{x	a{x	VERB
iajs-400	389	15	=	=	PUNCT
iajs-400	389	16	and	and	CCONJ
iajs-400	389	17	}	}	PUNCT
iajs-400	389	18	}	}	PUNCT
iajs-400	389	19	c	c	X
iajs-400	389	20	,	,	PUNCT
iajs-400	389	21	a{},b	a{},b	PROPN
iajs-400	389	22	,	,	PUNCT
iajs-400	389	23	a{},a{,,x	a{},a{,,x	PROPN
iajs-400	389	24	{	{	PUNCT
iajs-400	389	25	φ	φ	PROPN
iajs-400	389	26	=	=	PROPN
iajs-400	389	27	τ	τ	X
iajs-400	389	28	.	.	PUNCT
iajs-400	390	1	then	then	ADV
iajs-400	390	2	s*g	s*g	VERB
iajs-400	390	3	-	-	PUNCT
iajs-400	390	4	open	open	ADJ
iajs-400	390	5	sets	set	NOUN
iajs-400	390	6	in	in	ADP
iajs-400	390	7	x	x	X
iajs-400	390	8	=	=	SYM
iajs-400	390	9	open	open	ADJ
iajs-400	390	10	sets	set	NOUN
iajs-400	390	11	in	in	ADP
iajs-400	390	12	x	x	X
iajs-400	390	13	.	.	PUNCT
iajs-400	391	1	hence	hence	ADV
iajs-400	391	2	)	)	PUNCT
iajs-400	391	3	,	,	PUNCT
iajs-400	391	4	x	x	X
iajs-400	391	5	(	(	PUNCT
iajs-400	391	6	τ	τ	X
iajs-400	391	7	is	be	AUX
iajs-400	391	8	s*gid	s*gid	ADJ
iajs-400	391	9	-space	-space	NOUN
iajs-400	391	10	,	,	PUNCT
iajs-400	391	11	but	but	CCONJ
iajs-400	391	12	is	be	AUX
iajs-400	391	13	not	not	PART
iajs-400	391	14	s*git	s*git	ADJ
iajs-400	391	15	-space	-space	NOUN
iajs-400	391	16	,	,	PUNCT
iajs-400	391	17	2,1i	2,1i	NOUN
iajs-400	391	18	=	=	SYM
iajs-400	391	19	.	.	PUNCT
iajs-400	392	1	example(3.19	example(3.19	NUM
iajs-400	392	2	):	):	PUNCT
iajs-400	392	3	let	let	VERB
iajs-400	392	4	}	}	PUNCT
iajs-400	392	5	c	c	NOUN
iajs-400	392	6	,	,	PUNCT
iajs-400	392	7	b	b	PROPN
iajs-400	392	8	,	,	PUNCT
iajs-400	392	9	a{x	a{x	VERB
iajs-400	392	10	=	=	PUNCT
iajs-400	392	11	and	and	CCONJ
iajs-400	392	12	}	}	PUNCT
iajs-400	392	13	}	}	PUNCT
iajs-400	392	14	a{,,x	a{,,x	PROPN
iajs-400	392	15	{	{	PUNCT
iajs-400	392	16	φ	φ	PROPN
iajs-400	392	17	=	=	PROPN
iajs-400	392	18	τ	τ	X
iajs-400	392	19	.	.	PUNCT
iajs-400	393	1	then	then	ADV
iajs-400	393	2	α	α	PROPN
iajs-400	393	3	-s*g	-s*g	ADJ
iajs-400	393	4	-	-	PUNCT
iajs-400	393	5	open	open	ADJ
iajs-400	393	6	sets	set	NOUN
iajs-400	393	7	in	in	ADP
iajs-400	393	8	x	x	X
iajs-400	393	9	=	=	SYM
iajs-400	393	10	pre	pre	ADJ
iajs-400	393	11	-	-	ADJ
iajs-400	393	12	s*gopen	s*gopen	ADJ
iajs-400	393	13	sets	set	NOUN
iajs-400	393	14	in	in	ADP
iajs-400	393	15	x	x	X
iajs-400	393	16	=	=	SYM
iajs-400	393	17	b	b	X
iajs-400	393	18	-	-	PUNCT
iajs-400	393	19	s*g	s*g	VERB
iajs-400	393	20	-	-	PUNCT
iajs-400	393	21	open	open	ADJ
iajs-400	393	22	sets	set	NOUN
iajs-400	393	23	in	in	ADP
iajs-400	393	24	x	x	NOUN
iajs-400	393	25	=	=	PUNCT
iajs-400	393	26	β	β	X
iajs-400	393	27	-s*g	-s*g	ADJ
iajs-400	393	28	-	-	PUNCT
iajs-400	393	29	open	open	ADJ
iajs-400	393	30	sets	set	NOUN
iajs-400	393	31	in	in	ADP
iajs-400	393	32	x	x	X
iajs-400	393	33	=	=	PUNCT
iajs-400	393	34	}	}	PUNCT
iajs-400	393	35	}	}	PUNCT
iajs-400	393	36	c	c	X
iajs-400	393	37	,	,	PUNCT
iajs-400	393	38	a{},b	a{},b	PROPN
iajs-400	393	39	,	,	PUNCT
iajs-400	393	40	a{},a{,,x	a{},a{,,x	PROPN
iajs-400	393	41	{	{	PUNCT
iajs-400	393	42	φ	φ	PROPN
iajs-400	393	43	.	.	PUNCT
iajs-400	394	1	hence	hence	ADV
iajs-400	394	2	)	)	PUNCT
iajs-400	394	3	,	,	PUNCT
iajs-400	394	4	x	x	X
iajs-400	394	5	(	(	PUNCT
iajs-400	394	6	τ	τ	X
iajs-400	394	7	is	be	AUX
iajs-400	394	8	α	α	PRON
iajs-400	394	9	-s*gid	-s*gid	ADJ
iajs-400	394	10	-space	-space	NOUN
iajs-400	394	11	(	(	PUNCT
iajs-400	394	12	resp	resp	NOUN
iajs-400	394	13	.	.	PUNCT
iajs-400	395	1	pre	pre	ADJ
iajs-400	395	2	-	-	ADJ
iajs-400	395	3	s*gid	s*gid	ADJ
iajs-400	395	4	-space	-space	NOUN
iajs-400	395	5	,	,	PUNCT
iajs-400	395	6	b	b	X
iajs-400	395	7	-	-	PUNCT
iajs-400	395	8	s*gid	s*gid	ADJ
iajs-400	395	9	-space	-space	NOUN
iajs-400	395	10	,	,	PUNCT
iajs-400	395	11	β	β	X
iajs-400	395	12	-s*gid	-s*gid	X
iajs-400	395	13	-space	-space	NOUN
iajs-400	395	14	)	)	PUNCT
iajs-400	395	15	,	,	PUNCT
iajs-400	395	16	but	but	CCONJ
iajs-400	395	17	is	be	AUX
iajs-400	395	18	not	not	PART
iajs-400	395	19	α	α	PRON
iajs-400	395	20	-s*git	-s*git	PUNCT
iajs-400	395	21	-space	-space	NOUN
iajs-400	395	22	(	(	PUNCT
iajs-400	395	23	resp	resp	NOUN
iajs-400	395	24	.	.	PUNCT
iajs-400	396	1	pre	pre	ADJ
iajs-400	396	2	-	-	ADJ
iajs-400	396	3	s*git	s*git	ADJ
iajs-400	396	4	-space	-space	NOUN
iajs-400	396	5	,	,	PUNCT
iajs-400	396	6	b	b	X
iajs-400	396	7	-	-	PUNCT
iajs-400	396	8	s*git	s*git	ADJ
iajs-400	396	9	-space	-space	NOUN
iajs-400	396	10	,	,	PUNCT
iajs-400	396	11	β	β	X
iajs-400	396	12	-s*git	-s*git	PUNCT
iajs-400	396	13	-space	-space	PROPN
iajs-400	396	14	)	)	PUNCT
iajs-400	396	15	,	,	PUNCT
iajs-400	396	16	2,1i	2,1i	NOUN
iajs-400	396	17	=	=	SYM
iajs-400	396	18	.	.	PUNCT
iajs-400	397	1	remark(3.20	remark(3.20	PROPN
iajs-400	397	2	):	):	PUNCT
iajs-400	397	3	the	the	DET
iajs-400	397	4	converse	converse	NOUN
iajs-400	397	5	of	of	ADP
iajs-400	397	6	theorem	theorem	NOUN
iajs-400	397	7	(	(	PUNCT
iajs-400	397	8	3.13	3.13	NUM
iajs-400	397	9	)	)	PUNCT
iajs-400	397	10	,	,	PUNCT
iajs-400	397	11	no	no	INTJ
iajs-400	397	12	.	.	PUNCT
iajs-400	398	1	(	(	PUNCT
iajs-400	398	2	iii	iii	NOUN
iajs-400	398	3	)	)	PUNCT
iajs-400	398	4	may	may	AUX
iajs-400	398	5	not	not	PART
iajs-400	398	6	be	be	AUX
iajs-400	398	7	true	true	ADJ
iajs-400	398	8	.	.	PUNCT
iajs-400	399	1	in	in	ADP
iajs-400	399	2	example	example	NOUN
iajs-400	399	3	(	(	PUNCT
iajs-400	399	4	3.16	3.16	NUM
iajs-400	399	5	)	)	PUNCT
iajs-400	399	6	,	,	PUNCT
iajs-400	399	7	)	)	PUNCT
iajs-400	399	8	,	,	PUNCT
iajs-400	399	9	x	x	X
iajs-400	399	10	(	(	PUNCT
iajs-400	399	11	τ	τ	X
iajs-400	399	12	is	be	AUX
iajs-400	399	13	s*g0d	s*g0d	ADJ
iajs-400	399	14	-space	-space	NOUN
iajs-400	399	15	(	(	PUNCT
iajs-400	399	16	resp	resp	NOUN
iajs-400	399	17	.	.	PUNCT
iajs-400	400	1	α	α	PROPN
iajs-400	400	2	-s*g0d	-s*g0d	ADJ
iajs-400	400	3	space	space	NOUN
iajs-400	400	4	,	,	PUNCT
iajs-400	400	5	pre	pre	ADJ
iajs-400	400	6	-	-	ADJ
iajs-400	400	7	s*g0d	s*g0d	ADJ
iajs-400	400	8	-space	-space	NOUN
iajs-400	400	9	,	,	PUNCT
iajs-400	400	10	b	b	X
iajs-400	400	11	-	-	PUNCT
iajs-400	400	12	s*g0d	s*g0d	ADJ
iajs-400	400	13	-space	-space	NOUN
iajs-400	400	14	,	,	PUNCT
iajs-400	400	15	β	β	X
iajs-400	400	16	-s*g0d	-s*g0d	ADJ
iajs-400	400	17	-space	-space	NOUN
iajs-400	400	18	)	)	PUNCT
iajs-400	400	19	,	,	PUNCT
iajs-400	400	20	but	but	CCONJ
iajs-400	400	21	is	be	AUX
iajs-400	400	22	not	not	PART
iajs-400	400	23	s*g1d	s*g1d	NOUN
iajs-400	400	24	-space	-space	NOUN
iajs-400	400	25	(	(	PUNCT
iajs-400	400	26	resp	resp	NOUN
iajs-400	400	27	.	.	PUNCT
iajs-400	401	1	α	α	PRON
iajs-400	401	2	-s*g1d	-s*g1d	NOUN
iajs-400	401	3	-space	-space	NOUN
iajs-400	401	4	,	,	PUNCT
iajs-400	401	5	pre	pre	ADJ
iajs-400	401	6	-	-	ADJ
iajs-400	401	7	s*g1d	s*g1d	ADJ
iajs-400	401	8	-space	-space	NOUN
iajs-400	401	9	,	,	PUNCT
iajs-400	401	10	b	b	X
iajs-400	401	11	-	-	PUNCT
iajs-400	401	12	s*g1d	s*g1d	NOUN
iajs-400	401	13	space	space	NOUN
iajs-400	401	14	,	,	PUNCT
iajs-400	401	15	β	β	NOUN
iajs-400	401	16	-s*g1d	-s*g1d	NOUN
iajs-400	401	17	-space	-space	NOUN
iajs-400	401	18	)	)	PUNCT
iajs-400	401	19	.	.	PUNCT
iajs-400	402	1	theorem(3.21	theorem(3.21	NUM
iajs-400	402	2	):	):	PUNCT
iajs-400	402	3	a	a	DET
iajs-400	402	4	topological	topological	ADJ
iajs-400	402	5	space	space	NOUN
iajs-400	402	6	)	)	PUNCT
iajs-400	402	7	,	,	PUNCT
iajs-400	402	8	x	x	X
iajs-400	402	9	(	(	PUNCT
iajs-400	402	10	τ	τ	X
iajs-400	402	11	is	be	AUX
iajs-400	402	12	anα	anα	ADJ
iajs-400	402	13	-s*g0d	-s*g0d	ADJ
iajs-400	402	14	-space	-space	NOUN
iajs-400	402	15	(	(	PUNCT
iajs-400	402	16	resp	resp	NOUN
iajs-400	402	17	.	.	PUNCT
iajs-400	403	1	s*g0d	s*g0d	ADJ
iajs-400	403	2	-space	-space	NOUN
iajs-400	403	3	,	,	PUNCT
iajs-400	403	4	pre	pre	ADJ
iajs-400	403	5	-	-	ADJ
iajs-400	403	6	s*g0d	s*g0d	ADJ
iajs-400	403	7	-space	-space	NOUN
iajs-400	403	8	,	,	PUNCT
iajs-400	403	9	b	b	X
iajs-400	403	10	-	-	PUNCT
iajs-400	403	11	s*g0d	s*g0d	ADJ
iajs-400	403	12	-space	-space	NOUN
iajs-400	403	13	,	,	PUNCT
iajs-400	403	14	β	β	X
iajs-400	403	15	-s*g0d	-s*g0d	ADJ
iajs-400	403	16	-space	-space	NOUN
iajs-400	403	17	)	)	PUNCT
iajs-400	404	1	if	if	SCONJ
iajs-400	404	2	and	and	CCONJ
iajs-400	404	3	only	only	ADV
iajs-400	404	4	if	if	SCONJ
iajs-400	404	5	it	it	PRON
iajs-400	404	6	is	be	AUX
iajs-400	404	7	an	an	DET
iajs-400	404	8	α	α	NOUN
iajs-400	404	9	-s*g0	-s*g0	NOUN
iajs-400	404	10	t	t	NOUN
iajs-400	404	11	-space	-space	NOUN
iajs-400	404	12	(	(	PUNCT
iajs-400	404	13	resp	resp	NOUN
iajs-400	404	14	.	.	PUNCT
iajs-400	405	1	s*g0	s*g0	PROPN
iajs-400	405	2	t	t	NOUN
iajs-400	405	3	space	space	NOUN
iajs-400	405	4	,	,	PUNCT
iajs-400	405	5	pre	pre	ADJ
iajs-400	405	6	-	-	ADJ
iajs-400	405	7	s*g0	s*g0	ADJ
iajs-400	405	8	t	t	NOUN
iajs-400	405	9	-space	-space	NOUN
iajs-400	405	10	,	,	PUNCT
iajs-400	405	11	b	b	X
iajs-400	405	12	-	-	PUNCT
iajs-400	405	13	s*g0	s*g0	NOUN
iajs-400	405	14	t	t	NOUN
iajs-400	405	15	-space	-space	NOUN
iajs-400	405	16	,	,	PUNCT
iajs-400	405	17	β	β	X
iajs-400	405	18	-s*g0	-s*g0	NOUN
iajs-400	405	19	t	t	NOUN
iajs-400	405	20	-space	-space	NOUN
iajs-400	405	21	)	)	PUNCT
iajs-400	405	22	.	.	PUNCT
iajs-400	406	1	proof	proof	NOUN
iajs-400	406	2	:	:	PUNCT
iajs-400	406	3	sufficiency	sufficiency	PROPN
iajs-400	406	4	.	.	PUNCT
iajs-400	406	5	follows	follow	VERB
iajs-400	406	6	from	from	ADP
iajs-400	406	7	theorem	theorem	NOUN
iajs-400	406	8	(	(	PUNCT
iajs-400	406	9	3.13	3.13	NUM
iajs-400	406	10	)	)	PUNCT
iajs-400	406	11	,	,	PUNCT
iajs-400	406	12	no	no	INTJ
iajs-400	406	13	.	.	PUNCT
iajs-400	407	1	(	(	PUNCT
iajs-400	407	2	ii	ii	NOUN
iajs-400	407	3	)	)	PUNCT
iajs-400	407	4	.	.	PUNCT
iajs-400	408	1	necessity	necessity	NOUN
iajs-400	408	2	.	.	PUNCT
iajs-400	409	1	let	let	VERB
iajs-400	409	2	xy	xy	PRON
iajs-400	409	3	,	,	PUNCT
iajs-400	409	4	x	x	PROPN
iajs-400	409	5	∈	∈	PRON
iajs-400	409	6	such	such	ADJ
iajs-400	409	7	that	that	DET
iajs-400	409	8	yx	yx	NOUN
iajs-400	409	9	≠	≠	PROPN
iajs-400	409	10	.	.	PUNCT
iajs-400	410	1	since	since	SCONJ
iajs-400	410	2	)	)	PUNCT
iajs-400	410	3	,	,	PUNCT
iajs-400	410	4	x	x	X
iajs-400	410	5	(	(	PUNCT
iajs-400	410	6	τ	τ	X
iajs-400	410	7	is	be	AUX
iajs-400	410	8	α	α	DET
iajs-400	410	9	-s*g0d	-s*g0d	ADJ
iajs-400	410	10	-space	-space	NOUN
iajs-400	410	11	,	,	PUNCT
iajs-400	410	12	then	then	ADV
iajs-400	410	13	there	there	PRON
iajs-400	410	14	exists	exist	VERB
iajs-400	410	15	an	an	DET
iajs-400	410	16	g*sd	g*sd	PROPN
iajs-400	410	17	−α	−α	PROPN
iajs-400	410	18	-set	-set	PUNCT
iajs-400	410	19	u	u	PRON
iajs-400	410	20	such	such	ADJ
iajs-400	410	21	that	that	SCONJ
iajs-400	410	22	ux∈	ux∈	PROPN
iajs-400	410	23	,	,	PUNCT
iajs-400	410	24	uy∉	uy∉	PROPN
iajs-400	410	25	.	.	PUNCT
iajs-400	411	1	let	let	VERB
iajs-400	411	2	21	21	NUM
iajs-400	411	3	p\pu	p\pu	NOUN
iajs-400	411	4	=	=	PUNCT
iajs-400	411	5	,	,	PUNCT
iajs-400	411	6	where	where	SCONJ
iajs-400	411	7	xp1	xp1	PROPN
iajs-400	411	8	≠	≠	PROPN
iajs-400	411	9	and	and	CCONJ
iajs-400	411	10	21	21	NUM
iajs-400	411	11	p	p	NOUN
iajs-400	411	12	,	,	PUNCT
iajs-400	411	13	p	p	NOUN
iajs-400	411	14	are	be	AUX
iajs-400	411	15	α	α	PRON
iajs-400	411	16	-s*gopen	-s*gopen	NOUN
iajs-400	411	17	sets	set	NOUN
iajs-400	411	18	in	in	ADP
iajs-400	411	19	x	x	X
iajs-400	411	20	.	.	PUNCT
iajs-400	412	1	by	by	ADP
iajs-400	412	2	uy∉	uy∉	PROPN
iajs-400	412	3	we	we	PRON
iajs-400	412	4	have	have	VERB
iajs-400	412	5	two	two	NUM
iajs-400	412	6	cases	case	NOUN
iajs-400	412	7	:	:	PUNCT
iajs-400	412	8	(	(	PUNCT
iajs-400	412	9	i	i	NOUN
iajs-400	412	10	)	)	PUNCT
iajs-400	412	11	1py∉	1py∉	PROPN
iajs-400	412	12	(	(	PUNCT
iajs-400	412	13	ii	ii	NOUN
iajs-400	412	14	)	)	PUNCT
iajs-400	412	15	1py∈	1py∈	PROPN
iajs-400	412	16	and	and	CCONJ
iajs-400	412	17	2py∈	2py∈	NUM
iajs-400	412	18	.	.	PUNCT
iajs-400	413	1	in	in	ADP
iajs-400	413	2	case	case	NOUN
iajs-400	413	3	(	(	PUNCT
iajs-400	413	4	i	i	NOUN
iajs-400	413	5	)	)	PUNCT
iajs-400	413	6	1py∉	1py∉	NUM
iajs-400	413	7	and	and	CCONJ
iajs-400	413	8	21	21	NUM
iajs-400	413	9	p\pux	p\pux	X
iajs-400	413	10	=	=	PUNCT
iajs-400	413	11	∈	∈	PROPN
iajs-400	413	12	⇒	⇒	NOUN
iajs-400	413	13	1px∈	1px∈	NUM
iajs-400	413	14	and	and	CCONJ
iajs-400	413	15	1py∉	1py∉	NUM
iajs-400	413	16	.	.	PUNCT
iajs-400	414	1	in	in	ADP
iajs-400	414	2	case	case	NOUN
iajs-400	414	3	(	(	PUNCT
iajs-400	414	4	ii	ii	NOUN
iajs-400	414	5	)	)	PUNCT
iajs-400	414	6	1py∈	1py∈	PROPN
iajs-400	414	7	and	and	CCONJ
iajs-400	414	8	2py∈	2py∈	NUM
iajs-400	414	9	and	and	CCONJ
iajs-400	414	10	21	21	NUM
iajs-400	414	11	p\px∈	p\px∈	NOUN
iajs-400	414	12	⇒	⇒	VERB
iajs-400	414	13	2px∉	2px∉	NUM
iajs-400	414	14	⇒	⇒	NOUN
iajs-400	414	15	2py∈	2py∈	PROPN
iajs-400	414	16	and	and	CCONJ
iajs-400	414	17	2px∉	2px∉	NUM
iajs-400	414	18	.	.	PUNCT
iajs-400	415	1	thus	thus	ADV
iajs-400	415	2	in	in	ADP
iajs-400	415	3	both	both	DET
iajs-400	415	4	cases	case	NOUN
iajs-400	415	5	,	,	PUNCT
iajs-400	415	6	we	we	PRON
iajs-400	415	7	obtain	obtain	VERB
iajs-400	415	8	that	that	PRON
iajs-400	415	9	)	)	PUNCT
iajs-400	415	10	,	,	PUNCT
iajs-400	415	11	x	x	X
iajs-400	415	12	(	(	PUNCT
iajs-400	415	13	τ	τ	X
iajs-400	415	14	is	be	AUX
iajs-400	415	15	an	an	DET
iajs-400	415	16	α	α	NOUN
iajs-400	415	17	-s*g0	-s*g0	NOUN
iajs-400	415	18	t	t	NOUN
iajs-400	415	19	-space	-space	NOUN
iajs-400	415	20	.	.	PUNCT
iajs-400	416	1	by	by	ADP
iajs-400	416	2	the	the	DET
iajs-400	416	3	same	same	ADJ
iajs-400	416	4	way	way	NOUN
iajs-400	416	5	we	we	PRON
iajs-400	416	6	can	can	AUX
iajs-400	416	7	prove	prove	VERB
iajs-400	416	8	that	that	SCONJ
iajs-400	416	9	other	other	ADJ
iajs-400	416	10	cases	case	NOUN
iajs-400	416	11	.	.	PUNCT
iajs-400	417	1	theorem(3.22	theorem(3.22	X
iajs-400	417	2	):	):	PUNCT
iajs-400	417	3	a	a	DET
iajs-400	417	4	topological	topological	ADJ
iajs-400	417	5	space	space	NOUN
iajs-400	417	6	)	)	PUNCT
iajs-400	417	7	,	,	PUNCT
iajs-400	417	8	x	x	X
iajs-400	417	9	(	(	PUNCT
iajs-400	417	10	τ	τ	X
iajs-400	417	11	is	be	AUX
iajs-400	417	12	an	an	DET
iajs-400	417	13	α	α	PRON
iajs-400	417	14	-s*g1d	-s*g1d	NOUN
iajs-400	417	15	-space	-space	NOUN
iajs-400	417	16	(	(	PUNCT
iajs-400	417	17	resp	resp	NOUN
iajs-400	417	18	.	.	PUNCT
iajs-400	418	1	s*g1d	s*g1d	NOUN
iajs-400	418	2	-space	-space	NOUN
iajs-400	418	3	,	,	PUNCT
iajs-400	418	4	pre	pre	ADJ
iajs-400	418	5	-	-	ADJ
iajs-400	418	6	s*g1d	s*g1d	ADJ
iajs-400	418	7	-space	-space	NOUN
iajs-400	418	8	,	,	PUNCT
iajs-400	418	9	b	b	X
iajs-400	418	10	-	-	PUNCT
iajs-400	418	11	s*g1d	s*g1d	NOUN
iajs-400	418	12	-space	-space	NOUN
iajs-400	418	13	,	,	PUNCT
iajs-400	418	14	β	β	NOUN
iajs-400	418	15	-s*g1d	-s*g1d	NOUN
iajs-400	418	16	-space	-space	NOUN
iajs-400	418	17	)	)	PUNCT
iajs-400	419	1	if	if	SCONJ
iajs-400	419	2	and	and	CCONJ
iajs-400	419	3	only	only	ADV
iajs-400	419	4	if	if	SCONJ
iajs-400	419	5	it	it	PRON
iajs-400	419	6	is	be	AUX
iajs-400	419	7	an	an	DET
iajs-400	419	8	α	α	NOUN
iajs-400	419	9	-s*g2d	-s*g2d	PUNCT
iajs-400	419	10	-space	-space	NOUN
iajs-400	419	11	(	(	PUNCT
iajs-400	419	12	resp	resp	NOUN
iajs-400	419	13	.	.	PUNCT
iajs-400	420	1	s*g2d	s*g2d	PROPN
iajs-400	420	2	space	space	NOUN
iajs-400	420	3	,	,	PUNCT
iajs-400	420	4	pre	pre	ADJ
iajs-400	420	5	-	-	ADJ
iajs-400	420	6	s*g2d	s*g2d	ADJ
iajs-400	420	7	-space	-space	NOUN
iajs-400	420	8	,	,	PUNCT
iajs-400	420	9	b	b	X
iajs-400	420	10	-	-	PUNCT
iajs-400	420	11	s*g2d	s*g2d	X
iajs-400	420	12	-space	-space	NOUN
iajs-400	420	13	,	,	PUNCT
iajs-400	420	14	β	β	NOUN
iajs-400	420	15	-s*g2d	-s*g2d	PUNCT
iajs-400	420	16	-space	-space	NOUN
iajs-400	420	17	)	)	PUNCT
iajs-400	420	18	.	.	PUNCT
iajs-400	421	1	362	362	NUM
iajs-400	421	2	|	|	ADV
iajs-400	421	3	mathematics	mathematics	PROPN
iajs-400	421	4	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	421	5	�	�	NOUN
iajs-400	421	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	421	7	:	:	PUNCT
iajs-400	421	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	421	9	©	©	PROPN
iajs-400	421	10	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	421	11	ibn	ibn	PROPN
iajs-400	421	12	al	al	PROPN
iajs-400	421	13	-	-	PUNCT
iajs-400	421	14	haitham	haitham	PROPN
iajs-400	421	15	jour	jour	X
iajs-400	421	16	.	.	PROPN
iajs-400	422	1	for	for	ADP
iajs-400	422	2	pure	pure	ADJ
iajs-400	422	3	&	&	CCONJ
iajs-400	422	4	appl	appl	PROPN
iajs-400	422	5	.	.	PUNCT
iajs-400	423	1	sci	sci	PROPN
iajs-400	423	2	.	.	PUNCT
iajs-400	423	3	vol	vol	NOUN
iajs-400	423	4	.	.	PROPN
iajs-400	424	1	27	27	NUM
iajs-400	424	2	(	(	PUNCT
iajs-400	424	3	1	1	NUM
iajs-400	424	4	)	)	PUNCT
iajs-400	424	5	2014	2014	NUM
iajs-400	424	6	proof	proof	NOUN
iajs-400	424	7	:	:	PUNCT
iajs-400	424	8	sufficiency	sufficiency	PROPN
iajs-400	424	9	.	.	PUNCT
iajs-400	424	10	follows	follow	VERB
iajs-400	424	11	from	from	ADP
iajs-400	424	12	theorem	theorem	NOUN
iajs-400	424	13	(	(	PUNCT
iajs-400	424	14	3.13	3.13	NUM
iajs-400	424	15	)	)	PUNCT
iajs-400	424	16	,	,	PUNCT
iajs-400	424	17	no	no	INTJ
iajs-400	424	18	.	.	PUNCT
iajs-400	425	1	(	(	PUNCT
iajs-400	425	2	iii	iii	NOUN
iajs-400	425	3	)	)	PUNCT
iajs-400	425	4	.	.	PUNCT
iajs-400	426	1	necessity	necessity	NOUN
iajs-400	426	2	.	.	PUNCT
iajs-400	427	1	let	let	VERB
iajs-400	427	2	xy	xy	PRON
iajs-400	427	3	,	,	PUNCT
iajs-400	427	4	x	x	PROPN
iajs-400	427	5	∈	∈	PRON
iajs-400	427	6	such	such	ADJ
iajs-400	427	7	that	that	DET
iajs-400	427	8	yx	yx	NOUN
iajs-400	427	9	≠	≠	PROPN
iajs-400	427	10	.	.	PUNCT
iajs-400	428	1	since	since	SCONJ
iajs-400	428	2	)	)	PUNCT
iajs-400	428	3	,	,	PUNCT
iajs-400	428	4	x	x	X
iajs-400	428	5	(	(	PUNCT
iajs-400	428	6	τ	τ	X
iajs-400	428	7	is	be	AUX
iajs-400	428	8	an	an	DET
iajs-400	428	9	α	α	NOUN
iajs-400	428	10	-s*g1d	-s*g1d	NOUN
iajs-400	428	11	-space	-space	NOUN
iajs-400	428	12	,	,	PUNCT
iajs-400	428	13	then	then	ADV
iajs-400	428	14	there	there	PRON
iajs-400	428	15	exists	exist	VERB
iajs-400	428	16	g*sd	g*sd	PROPN
iajs-400	428	17	−α	−α	PROPN
iajs-400	428	18	-sets	-set	VERB
iajs-400	428	19	u	u	NOUN
iajs-400	428	20	and	and	CCONJ
iajs-400	428	21	v	v	NOUN
iajs-400	428	22	in	in	ADP
iajs-400	428	23	x	x	X
iajs-400	428	24	such	such	ADJ
iajs-400	428	25	ux∈	ux∈	PROPN
iajs-400	428	26	,	,	PUNCT
iajs-400	428	27	uy∉	uy∉	PROPN
iajs-400	428	28	and	and	CCONJ
iajs-400	428	29	vy∈	vy∈	NOUN
iajs-400	428	30	,	,	PUNCT
iajs-400	428	31	vx∉	vx∉	PROPN
iajs-400	428	32	.	.	PUNCT
iajs-400	429	1	let	let	VERB
iajs-400	429	2	21	21	NUM
iajs-400	429	3	p\pu	p\pu	NOUN
iajs-400	429	4	=	=	PUNCT
iajs-400	429	5	and	and	CCONJ
iajs-400	429	6	43	43	NUM
iajs-400	429	7	p\pv	p\pv	PROPN
iajs-400	429	8	=	=	PUNCT
iajs-400	429	9	,	,	PUNCT
iajs-400	429	10	where	where	SCONJ
iajs-400	429	11	4321	4321	NUM
iajs-400	429	12	p	p	NOUN
iajs-400	429	13	,	,	PUNCT
iajs-400	429	14	p	p	X
iajs-400	429	15	,	,	PUNCT
iajs-400	429	16	p	p	X
iajs-400	429	17	,	,	PUNCT
iajs-400	429	18	p	p	NOUN
iajs-400	429	19	are	be	AUX
iajs-400	429	20	α	α	DET
iajs-400	429	21	-s*g	-s*g	ADJ
iajs-400	429	22	-	-	PUNCT
iajs-400	429	23	open	open	ADJ
iajs-400	429	24	sets	set	NOUN
iajs-400	429	25	in	in	ADP
iajs-400	429	26	x	x	PUNCT
iajs-400	429	27	and	and	CCONJ
iajs-400	429	28	xp1	xp1	PROPN
iajs-400	429	29	≠	≠	PROPN
iajs-400	429	30	and	and	CCONJ
iajs-400	429	31	xp3	xp3	PROPN
iajs-400	429	32	≠	≠	PROPN
iajs-400	429	33	.	.	PUNCT
iajs-400	430	1	by	by	ADP
iajs-400	430	2	vx∉	vx∉	NOUN
iajs-400	430	3	we	we	PRON
iajs-400	430	4	have	have	VERB
iajs-400	430	5	two	two	NUM
iajs-400	430	6	cases	case	NOUN
iajs-400	430	7	:	:	PUNCT
iajs-400	430	8	(	(	PUNCT
iajs-400	430	9	i	i	NOUN
iajs-400	430	10	)	)	PUNCT
iajs-400	430	11	3px∉	3px∉	NUM
iajs-400	430	12	(	(	PUNCT
iajs-400	430	13	ii	ii	NOUN
iajs-400	430	14	)	)	PUNCT
iajs-400	430	15	3px∈	3px∈	NUM
iajs-400	430	16	and	and	CCONJ
iajs-400	430	17	4px∈	4px∈	NOUN
iajs-400	430	18	.	.	PUNCT
iajs-400	431	1	in	in	ADP
iajs-400	431	2	case	case	NOUN
iajs-400	431	3	(	(	PUNCT
iajs-400	431	4	i	i	NOUN
iajs-400	431	5	):	):	PUNCT
iajs-400	431	6	3px∉	3px∉	NUM
iajs-400	431	7	.	.	PUNCT
iajs-400	432	1	by	by	ADP
iajs-400	432	2	uy∉	uy∉	PROPN
iajs-400	432	3	we	we	PRON
iajs-400	432	4	have	have	VERB
iajs-400	432	5	two	two	NUM
iajs-400	432	6	subcases	subcase	NOUN
iajs-400	432	7	:	:	PUNCT
iajs-400	432	8	(	(	PUNCT
iajs-400	432	9	a	a	X
iajs-400	432	10	)	)	PUNCT
iajs-400	432	11	1py∈	1py∈	PROPN
iajs-400	432	12	and	and	CCONJ
iajs-400	432	13	2py∈	2py∈	NUM
iajs-400	432	14	(	(	PUNCT
iajs-400	432	15	b	b	NOUN
iajs-400	432	16	)	)	PUNCT
iajs-400	432	17	1py∉	1py∉	NUM
iajs-400	432	18	.	.	PUNCT
iajs-400	433	1	subcase	subcase	PROPN
iajs-400	433	2	(	(	PUNCT
iajs-400	433	3	a	a	X
iajs-400	433	4	):	):	PUNCT
iajs-400	433	5	1py∈	1py∈	NUM
iajs-400	433	6	and	and	CCONJ
iajs-400	433	7	2py∈	2py∈	NUM
iajs-400	433	8	.	.	PUNCT
iajs-400	434	1	we	we	PRON
iajs-400	434	2	have	have	VERB
iajs-400	434	3	21	21	NUM
iajs-400	434	4	p\px∈	p\px∈	NOUN
iajs-400	434	5	,	,	PUNCT
iajs-400	434	6	2py∈	2py∈	NUM
iajs-400	434	7	and	and	CCONJ
iajs-400	434	8	φ=221	φ=221	NOUN
iajs-400	434	9	p)p\p	p)p\p	PROPN
iajs-400	434	10	(	(	PUNCT
iajs-400	434	11			PROPN
iajs-400	434	12	.	.	PUNCT
iajs-400	435	1	observe	observe	VERB
iajs-400	435	2	that	that	SCONJ
iajs-400	435	3	xp2	xp2	PROPN
iajs-400	435	4	≠	≠	PROPN
iajs-400	435	5	since	since	SCONJ
iajs-400	435	6	φ≠u	φ≠u	X
iajs-400	435	7	,	,	PUNCT
iajs-400	435	8	thus	thus	ADV
iajs-400	435	9	by	by	ADP
iajs-400	435	10	remark	remark	NOUN
iajs-400	435	11	(	(	PUNCT
iajs-400	435	12	3.2	3.2	NUM
iajs-400	435	13	)	)	PUNCT
iajs-400	435	14	2p	2p	NOUN
iajs-400	435	15	is	be	AUX
iajs-400	435	16	an	an	DET
iajs-400	435	17	g*sd	g*sd	PROPN
iajs-400	435	18	−α	−α	PROPN
iajs-400	435	19	-set	-set	PUNCT
iajs-400	435	20	.	.	PUNCT
iajs-400	436	1	subcase	subcase	NOUN
iajs-400	436	2	(	(	PUNCT
iajs-400	436	3	b	b	NOUN
iajs-400	436	4	):	):	PUNCT
iajs-400	436	5	1py∉	1py∉	NOUN
iajs-400	436	6	.	.	PUNCT
iajs-400	437	1	since	since	SCONJ
iajs-400	437	2	21	21	NUM
iajs-400	437	3	p\px∈	p\px∈	NOUN
iajs-400	437	4	and	and	CCONJ
iajs-400	437	5	3px∉	3px∉	NUM
iajs-400	437	6	,	,	PUNCT
iajs-400	437	7	then	then	ADV
iajs-400	437	8	)	)	PUNCT
iajs-400	437	9	pp(\px	pp(\px	ADP
iajs-400	437	10	321	321	NUM
iajs-400	437	11	∈	∈	ADJ
iajs-400	437	12	and	and	CCONJ
iajs-400	437	13	since	since	SCONJ
iajs-400	437	14	43	43	NUM
iajs-400	437	15	p\py∈	p\py∈	NOUN
iajs-400	437	16	and	and	CCONJ
iajs-400	437	17	1py∉	1py∉	NUM
iajs-400	437	18	,	,	PUNCT
iajs-400	437	19	then	then	ADV
iajs-400	437	20	)	)	PUNCT
iajs-400	437	21	pp(\py	pp(\py	PROPN
iajs-400	437	22	143	143	PRON
iajs-400	437	23	∈	∈	PROPN
iajs-400	437	24	.	.	PUNCT
iajs-400	438	1	observe	observe	VERB
iajs-400	438	2	also	also	ADV
iajs-400	438	3	from	from	ADP
iajs-400	438	4	theorem	theorem	ADJ
iajs-400	438	5	(	(	PUNCT
iajs-400	438	6	2.15	2.15	NUM
iajs-400	438	7	)	)	PUNCT
iajs-400	438	8	that	that	PRON
iajs-400	438	9	)	)	PUNCT
iajs-400	439	1	pp	pp	PROPN
iajs-400	439	2	(	(	PUNCT
iajs-400	439	3	32	32	NUM
iajs-400	439	4			NOUN
iajs-400	439	5	and	and	CCONJ
iajs-400	439	6	)	)	PUNCT
iajs-400	439	7	pp	pp	CCONJ
iajs-400	439	8	(	(	PUNCT
iajs-400	439	9	14	14	NUM
iajs-400	439	10			NOUN
iajs-400	439	11	are	be	AUX
iajs-400	439	12	α	α	DET
iajs-400	439	13	-s*g	-s*g	ADJ
iajs-400	439	14	-	-	PUNCT
iajs-400	439	15	open	open	ADJ
iajs-400	439	16	sets	set	NOUN
iajs-400	439	17	.	.	PUNCT
iajs-400	440	1	hence	hence	ADV
iajs-400	440	2	)	)	PUNCT
iajs-400	440	3	pp(\px	pp(\px	VERB
iajs-400	440	4	321	321	NUM
iajs-400	440	5	∈	∈	NOUN
iajs-400	440	6	,	,	PUNCT
iajs-400	440	7	)	)	PUNCT
iajs-400	440	8	pp(\py	pp(\py	NOUN
iajs-400	440	9	143	143	NOUN
iajs-400	440	10	∈	∈	NOUN
iajs-400	440	11	and	and	CCONJ
iajs-400	440	12	φ=))pp(\p())pp(\p	φ=))pp(\p())pp(\p	PROPN
iajs-400	440	13	(	(	PUNCT
iajs-400	440	14	143321	143321	NUM
iajs-400	440	15			NOUN
iajs-400	440	16	.	.	PUNCT
iajs-400	441	1	in	in	ADP
iajs-400	441	2	case	case	NOUN
iajs-400	441	3	(	(	PUNCT
iajs-400	441	4	ii	ii	NOUN
iajs-400	441	5	):	):	PUNCT
iajs-400	441	6	3px∈	3px∈	NUM
iajs-400	441	7	and	and	CCONJ
iajs-400	441	8	4px∈	4px∈	NOUN
iajs-400	441	9	.	.	PUNCT
iajs-400	442	1	we	we	PRON
iajs-400	442	2	have	have	VERB
iajs-400	442	3	43	43	NUM
iajs-400	442	4	p\py∈	p\py∈	NOUN
iajs-400	442	5	,	,	PUNCT
iajs-400	442	6	4px∈	4px∈	NOUN
iajs-400	442	7	and	and	CCONJ
iajs-400	442	8	φ=443	φ=443	NUM
iajs-400	442	9	p)p\p	p)p\p	PROPN
iajs-400	442	10	(	(	PUNCT
iajs-400	442	11			PROPN
iajs-400	442	12	.	.	PUNCT
iajs-400	443	1	observe	observe	VERB
iajs-400	443	2	that	that	SCONJ
iajs-400	443	3	xp4	xp4	PROPN
iajs-400	443	4	≠	≠	PROPN
iajs-400	443	5	since	since	SCONJ
iajs-400	443	6	φ≠v	φ≠v	VERB
iajs-400	443	7	,	,	PUNCT
iajs-400	443	8	thus	thus	ADV
iajs-400	443	9	by	by	ADP
iajs-400	443	10	remark	remark	NOUN
iajs-400	443	11	(	(	PUNCT
iajs-400	443	12	3.2	3.2	NUM
iajs-400	443	13	)	)	PUNCT
iajs-400	443	14	4p	4p	NOUN
iajs-400	443	15	is	be	AUX
iajs-400	443	16	an	an	DET
iajs-400	443	17	g*sd	g*sd	PROPN
iajs-400	443	18	−α	−α	PROPN
iajs-400	443	19	-set	-set	PUNCT
iajs-400	443	20	.	.	PUNCT
iajs-400	444	1	hence	hence	ADV
iajs-400	444	2	)	)	PUNCT
iajs-400	444	3	,	,	PUNCT
iajs-400	444	4	x	x	X
iajs-400	444	5	(	(	PUNCT
iajs-400	444	6	τ	τ	X
iajs-400	444	7	is	be	AUX
iajs-400	444	8	an	an	DET
iajs-400	444	9	α	α	NOUN
iajs-400	444	10	-s*g2d	-s*g2d	PUNCT
iajs-400	444	11	-space	-space	NOUN
iajs-400	444	12	.	.	PUNCT
iajs-400	445	1	by	by	ADP
iajs-400	445	2	the	the	DET
iajs-400	445	3	same	same	ADJ
iajs-400	445	4	way	way	NOUN
iajs-400	445	5	we	we	PRON
iajs-400	445	6	can	can	AUX
iajs-400	445	7	prove	prove	VERB
iajs-400	445	8	that	that	SCONJ
iajs-400	445	9	other	other	ADJ
iajs-400	445	10	cases	case	NOUN
iajs-400	445	11	.	.	PUNCT
iajs-400	446	1	corollary(3.23	corollary(3.23	X
iajs-400	446	2	):	):	PUNCT
iajs-400	446	3	if	if	SCONJ
iajs-400	446	4	)	)	PUNCT
iajs-400	446	5	,	,	PUNCT
iajs-400	446	6	x	x	X
iajs-400	446	7	(	(	PUNCT
iajs-400	446	8	τ	τ	X
iajs-400	446	9	is	be	AUX
iajs-400	446	10	anα	anα	PROPN
iajs-400	446	11	-s*g1d	-s*g1d	PROPN
iajs-400	446	12	-space	-space	PROPN
iajs-400	446	13	(	(	PUNCT
iajs-400	446	14	resp	resp	NOUN
iajs-400	446	15	.	.	PUNCT
iajs-400	447	1	s*g1d	s*g1d	NOUN
iajs-400	447	2	-space	-space	NOUN
iajs-400	447	3	,	,	PUNCT
iajs-400	447	4	pre	pre	ADJ
iajs-400	447	5	-	-	ADJ
iajs-400	447	6	s*g1d	s*g1d	ADJ
iajs-400	447	7	-space	-space	NOUN
iajs-400	447	8	,	,	PUNCT
iajs-400	447	9	bs*g1d	bs*g1d	ADJ
iajs-400	447	10	-space	-space	NOUN
iajs-400	447	11	,	,	PUNCT
iajs-400	447	12	β	β	NOUN
iajs-400	447	13	-s*g1d	-s*g1d	NOUN
iajs-400	447	14	-space	-space	NOUN
iajs-400	447	15	)	)	PUNCT
iajs-400	447	16	,	,	PUNCT
iajs-400	447	17	then	then	ADV
iajs-400	447	18	it	it	PRON
iajs-400	447	19	is	be	AUX
iajs-400	447	20	anα	anα	PROPN
iajs-400	447	21	-s*g0	-s*g0	PROPN
iajs-400	447	22	t	t	PROPN
iajs-400	447	23	-space	-space	NOUN
iajs-400	447	24	(	(	PUNCT
iajs-400	447	25	resp	resp	NOUN
iajs-400	447	26	.	.	PUNCT
iajs-400	448	1	s*g0	s*g0	PROPN
iajs-400	448	2	t	t	NOUN
iajs-400	448	3	-space	-space	NOUN
iajs-400	448	4	,	,	PUNCT
iajs-400	448	5	pre	pre	ADJ
iajs-400	448	6	-	-	ADJ
iajs-400	448	7	s*g0	s*g0	ADJ
iajs-400	448	8	t	t	NOUN
iajs-400	448	9	-space	-space	NOUN
iajs-400	448	10	,	,	PUNCT
iajs-400	448	11	b	b	X
iajs-400	448	12	-	-	PUNCT
iajs-400	448	13	s*g0	s*g0	NOUN
iajs-400	448	14	t	t	NOUN
iajs-400	448	15	-space	-space	NOUN
iajs-400	448	16	,	,	PUNCT
iajs-400	448	17	β	β	X
iajs-400	448	18	-s*g0	-s*g0	NOUN
iajs-400	448	19	t	t	NOUN
iajs-400	448	20	-space	-space	NOUN
iajs-400	448	21	)	)	PUNCT
iajs-400	448	22	.	.	PUNCT
iajs-400	449	1	proof	proof	NOUN
iajs-400	449	2	:	:	PUNCT
iajs-400	449	3	follows	follow	VERB
iajs-400	449	4	from	from	ADP
iajs-400	449	5	theorem	theorem	NOUN
iajs-400	449	6	(	(	PUNCT
iajs-400	449	7	3.13	3.13	NUM
iajs-400	449	8	)	)	PUNCT
iajs-400	449	9	,	,	PUNCT
iajs-400	449	10	no	no	INTJ
iajs-400	449	11	.	.	PUNCT
iajs-400	450	1	(	(	PUNCT
iajs-400	450	2	iii	iii	NOUN
iajs-400	450	3	)	)	PUNCT
iajs-400	450	4	and	and	CCONJ
iajs-400	450	5	theorem	theorem	VERB
iajs-400	450	6	(	(	PUNCT
iajs-400	450	7	3.21	3.21	NUM
iajs-400	450	8	)	)	PUNCT
iajs-400	450	9	.	.	PUNCT
iajs-400	451	1	remark(3.24	remark(3.24	NOUN
iajs-400	451	2	):	):	PUNCT
iajs-400	451	3	the	the	DET
iajs-400	451	4	converse	converse	NOUN
iajs-400	451	5	of	of	ADP
iajs-400	451	6	corollary	corollary	ADJ
iajs-400	451	7	(	(	PUNCT
iajs-400	451	8	3.23	3.23	NUM
iajs-400	451	9	)	)	PUNCT
iajs-400	451	10	may	may	AUX
iajs-400	451	11	not	not	PART
iajs-400	451	12	be	be	AUX
iajs-400	451	13	true	true	ADJ
iajs-400	451	14	.	.	PUNCT
iajs-400	452	1	in	in	ADP
iajs-400	452	2	example	example	NOUN
iajs-400	452	3	(	(	PUNCT
iajs-400	452	4	3.16	3.16	NUM
iajs-400	452	5	)	)	PUNCT
iajs-400	452	6	,	,	PUNCT
iajs-400	452	7	)	)	PUNCT
iajs-400	452	8	,	,	PUNCT
iajs-400	452	9	x	x	X
iajs-400	452	10	(	(	PUNCT
iajs-400	452	11	τ	τ	X
iajs-400	452	12	is	be	AUX
iajs-400	452	13	α	α	PRON
iajs-400	452	14	-s*g0	-s*g0	NOUN
iajs-400	452	15	t	t	NOUN
iajs-400	452	16	-space	-space	NOUN
iajs-400	452	17	(	(	PUNCT
iajs-400	452	18	resp	resp	NOUN
iajs-400	452	19	.	.	PUNCT
iajs-400	453	1	s*g0	s*g0	PROPN
iajs-400	453	2	t	t	NOUN
iajs-400	453	3	-space	-space	NOUN
iajs-400	453	4	,	,	PUNCT
iajs-400	453	5	pre	pre	ADJ
iajs-400	453	6	-	-	ADJ
iajs-400	453	7	s*g0	s*g0	ADJ
iajs-400	453	8	t	t	NOUN
iajs-400	453	9	-space	-space	NOUN
iajs-400	453	10	,	,	PUNCT
iajs-400	453	11	b	b	X
iajs-400	453	12	-	-	PUNCT
iajs-400	453	13	s*g0	s*g0	NOUN
iajs-400	453	14	t	t	NOUN
iajs-400	453	15	-space	-space	NOUN
iajs-400	453	16	,	,	PUNCT
iajs-400	453	17	β	β	X
iajs-400	453	18	-s*g0	-s*g0	NOUN
iajs-400	453	19	t	t	NOUN
iajs-400	453	20	-space	-space	NOUN
iajs-400	453	21	)	)	PUNCT
iajs-400	453	22	,	,	PUNCT
iajs-400	453	23	but	but	CCONJ
iajs-400	453	24	is	be	AUX
iajs-400	453	25	not	not	PART
iajs-400	453	26	an	an	DET
iajs-400	453	27	α	α	NOUN
iajs-400	453	28	-s*g1d	-s*g1d	NOUN
iajs-400	453	29	-space	-space	NOUN
iajs-400	453	30	(	(	PUNCT
iajs-400	453	31	resp	resp	NOUN
iajs-400	453	32	.	.	PUNCT
iajs-400	454	1	s*g1d	s*g1d	NOUN
iajs-400	454	2	-space	-space	NOUN
iajs-400	454	3	,	,	PUNCT
iajs-400	454	4	pre	pre	ADJ
iajs-400	454	5	-	-	ADJ
iajs-400	454	6	s*g1d	s*g1d	ADJ
iajs-400	454	7	-space	-space	NOUN
iajs-400	454	8	,	,	PUNCT
iajs-400	454	9	b	b	X
iajs-400	454	10	-	-	PUNCT
iajs-400	454	11	s*g1d	s*g1d	NOUN
iajs-400	454	12	-space	-space	NOUN
iajs-400	454	13	,	,	PUNCT
iajs-400	454	14	β	β	NOUN
iajs-400	454	15	s*g1d	s*g1d	NOUN
iajs-400	454	16	-space	-space	NOUN
iajs-400	454	17	)	)	PUNCT
iajs-400	454	18	.	.	PUNCT
iajs-400	455	1	propositions(3.25	propositions(3.25	NUM
iajs-400	455	2	):	):	PUNCT
iajs-400	455	3	(	(	PUNCT
iajs-400	455	4	i	i	NOUN
iajs-400	455	5	)	)	PUNCT
iajs-400	455	6	every	every	DET
iajs-400	455	7	s*gid	s*gid	ADJ
iajs-400	455	8	-space	-space	NOUN
iajs-400	455	9	is	be	AUX
iajs-400	455	10	α	α	DET
iajs-400	455	11	-s*gid	-s*gid	ADJ
iajs-400	455	12	-space	-space	NOUN
iajs-400	455	13	,	,	PUNCT
iajs-400	455	14	2,1,0i	2,1,0i	PROPN
iajs-400	455	15	=	=	PRON
iajs-400	455	16	.	.	PUNCT
iajs-400	456	1	(	(	PUNCT
iajs-400	456	2	ii	ii	NOUN
iajs-400	456	3	)	)	PUNCT
iajs-400	456	4	every	every	DET
iajs-400	456	5	α	α	PROPN
iajs-400	456	6	-s*gid	-s*gid	ADJ
iajs-400	456	7	-space	-space	NOUN
iajs-400	456	8	is	be	AUX
iajs-400	456	9	pre	pre	ADJ
iajs-400	456	10	-	-	ADJ
iajs-400	456	11	s*gid	s*gid	ADJ
iajs-400	456	12	-space	-space	NOUN
iajs-400	456	13	,	,	PUNCT
iajs-400	456	14	2,1,0i	2,1,0i	PROPN
iajs-400	456	15	=	=	PRON
iajs-400	456	16	.	.	PUNCT
iajs-400	457	1	(	(	PUNCT
iajs-400	457	2	iii	iii	NOUN
iajs-400	457	3	)	)	PUNCT
iajs-400	457	4	every	every	DET
iajs-400	457	5	pre	pre	ADJ
iajs-400	457	6	-	-	ADJ
iajs-400	457	7	s*gid	s*gid	ADJ
iajs-400	457	8	-space	-space	NOUN
iajs-400	457	9	is	be	AUX
iajs-400	457	10	b	b	NUM
iajs-400	457	11	-	-	PUNCT
iajs-400	457	12	s*gid	s*gid	ADJ
iajs-400	457	13	-space	-space	NOUN
iajs-400	457	14	,	,	PUNCT
iajs-400	457	15	2,1,0i	2,1,0i	PROPN
iajs-400	457	16	=	=	PUNCT
iajs-400	457	17	.	.	PUNCT
iajs-400	458	1	(	(	PUNCT
iajs-400	458	2	iv	iv	X
iajs-400	458	3	)	)	PUNCT
iajs-400	458	4	every	every	DET
iajs-400	458	5	b	b	X
iajs-400	458	6	-	-	PUNCT
iajs-400	458	7	s*gid	s*gid	ADJ
iajs-400	458	8	-space	-space	NOUN
iajs-400	458	9	isβ	isβ	ADJ
iajs-400	458	10	-s*gid	-s*gid	ADJ
iajs-400	458	11	-space	-space	NOUN
iajs-400	458	12	,	,	PUNCT
iajs-400	458	13	2,1,0i	2,1,0i	PROPN
iajs-400	458	14	=	=	PUNCT
iajs-400	458	15	.	.	PUNCT
iajs-400	459	1	remark(3.26	remark(3.26	ADJ
iajs-400	459	2	):	):	PUNCT
iajs-400	459	3	the	the	DET
iajs-400	459	4	converse	converse	NOUN
iajs-400	459	5	of	of	ADP
iajs-400	459	6	proposition	proposition	NOUN
iajs-400	459	7	(	(	PUNCT
iajs-400	459	8	3.25	3.25	NUM
iajs-400	459	9	)	)	PUNCT
iajs-400	459	10	,	,	PUNCT
iajs-400	459	11	no.(i	no.(i	NUM
iajs-400	459	12	)	)	PUNCT
iajs-400	459	13	may	may	AUX
iajs-400	459	14	not	not	PART
iajs-400	459	15	be	be	AUX
iajs-400	459	16	true	true	ADJ
iajs-400	459	17	.	.	PUNCT
iajs-400	460	1	in	in	ADP
iajs-400	460	2	example	example	NOUN
iajs-400	460	3	(	(	PUNCT
iajs-400	460	4	3.19	3.19	NUM
iajs-400	460	5	)	)	PUNCT
iajs-400	460	6	,	,	PUNCT
iajs-400	460	7	)	)	PUNCT
iajs-400	460	8	,	,	PUNCT
iajs-400	460	9	x	x	X
iajs-400	460	10	(	(	PUNCT
iajs-400	460	11	τ	τ	X
iajs-400	460	12	is	be	AUX
iajs-400	460	13	α	α	PRON
iajs-400	460	14	-s*gid	-s*gid	ADJ
iajs-400	460	15	-space	-space	NOUN
iajs-400	460	16	,	,	PUNCT
iajs-400	460	17	but	but	CCONJ
iajs-400	460	18	is	be	AUX
iajs-400	460	19	not	not	PART
iajs-400	460	20	s*gid	s*gid	ADJ
iajs-400	460	21	-space	-space	NOUN
iajs-400	460	22	,	,	PUNCT
iajs-400	460	23	2,1,0i	2,1,0i	PROPN
iajs-400	460	24	=	=	PUNCT
iajs-400	460	25	.	.	PUNCT
iajs-400	461	1	remark(3.27	remark(3.27	PROPN
iajs-400	461	2	):	):	PUNCT
iajs-400	461	3	the	the	DET
iajs-400	461	4	converse	converse	NOUN
iajs-400	461	5	of	of	ADP
iajs-400	461	6	proposition	proposition	NOUN
iajs-400	461	7	(	(	PUNCT
iajs-400	461	8	3.25	3.25	NUM
iajs-400	461	9	)	)	PUNCT
iajs-400	461	10	,	,	PUNCT
iajs-400	461	11	no	no	INTJ
iajs-400	461	12	.	.	PUNCT
iajs-400	462	1	(	(	PUNCT
iajs-400	462	2	iii	iii	NOUN
iajs-400	462	3	)	)	PUNCT
iajs-400	462	4	may	may	AUX
iajs-400	462	5	not	not	PART
iajs-400	462	6	be	be	AUX
iajs-400	462	7	true	true	ADJ
iajs-400	462	8	.	.	PUNCT
iajs-400	463	1	consider	consider	VERB
iajs-400	463	2	the	the	DET
iajs-400	463	3	following	follow	VERB
iajs-400	463	4	example	example	NOUN
iajs-400	463	5	:	:	PUNCT
iajs-400	463	6	363	363	NUM
iajs-400	463	7	|	|	ADV
iajs-400	463	8	mathematics	mathematics	PROPN
iajs-400	463	9	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	463	10	�	�	NOUN
iajs-400	463	11	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	463	12	:	:	PUNCT
iajs-400	463	13	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	463	14	©	©	PROPN
iajs-400	463	15	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	463	16	ibn	ibn	PROPN
iajs-400	463	17	al	al	PROPN
iajs-400	463	18	-	-	PUNCT
iajs-400	463	19	haitham	haitham	PROPN
iajs-400	463	20	jour	jour	X
iajs-400	463	21	.	.	PROPN
iajs-400	464	1	for	for	ADP
iajs-400	464	2	pure	pure	ADJ
iajs-400	464	3	&	&	CCONJ
iajs-400	464	4	appl	appl	PROPN
iajs-400	464	5	.	.	PUNCT
iajs-400	465	1	sci	sci	PROPN
iajs-400	465	2	.	.	PUNCT
iajs-400	465	3	vol	vol	NOUN
iajs-400	465	4	.	.	PROPN
iajs-400	466	1	27	27	NUM
iajs-400	466	2	(	(	PUNCT
iajs-400	466	3	1	1	NUM
iajs-400	466	4	)	)	PUNCT
iajs-400	466	5	2014	2014	NUM
iajs-400	466	6	example(3.28	example(3.28	NUM
iajs-400	466	7	):	):	PUNCT
iajs-400	466	8	let	let	VERB
iajs-400	466	9	}	}	PUNCT
iajs-400	466	10	c	c	NOUN
iajs-400	466	11	,	,	PUNCT
iajs-400	466	12	b	b	PROPN
iajs-400	466	13	,	,	PUNCT
iajs-400	466	14	a{x	a{x	VERB
iajs-400	466	15	=	=	SYM
iajs-400	466	16	&	&	CCONJ
iajs-400	466	17	}	}	PUNCT
iajs-400	466	18	}	}	SYM
iajs-400	466	19	b	b	PROPN
iajs-400	466	20	,	,	PUNCT
iajs-400	466	21	a{},b{},a{,,x	a{},b{},a{,,x	PROPN
iajs-400	466	22	{	{	PUNCT
iajs-400	466	23	φ	φ	PROPN
iajs-400	466	24	=	=	PROPN
iajs-400	466	25	τ	τ	X
iajs-400	466	26	.	.	PUNCT
iajs-400	467	1	then	then	ADV
iajs-400	467	2	pre	pre	ADJ
iajs-400	467	3	-	-	ADJ
iajs-400	467	4	s*g	s*g	ADJ
iajs-400	467	5	-	-	PUNCT
iajs-400	467	6	open	open	ADJ
iajs-400	467	7	sets	set	NOUN
iajs-400	467	8	in	in	ADP
iajs-400	467	9	x	x	X
iajs-400	467	10	=	=	SYM
iajs-400	467	11	open	open	ADJ
iajs-400	467	12	sets	set	NOUN
iajs-400	467	13	in	in	ADP
iajs-400	467	14	x	x	PUNCT
iajs-400	467	15	and	and	CCONJ
iajs-400	467	16	b	b	X
iajs-400	467	17	-	-	PUNCT
iajs-400	467	18	s*g	s*g	VERB
iajs-400	467	19	-	-	PUNCT
iajs-400	467	20	open	open	ADJ
iajs-400	467	21	sets	set	NOUN
iajs-400	467	22	in	in	ADP
iajs-400	467	23	x=	x=	PROPN
iajs-400	467	24	}	}	PUNCT
iajs-400	467	25	}	}	PUNCT
iajs-400	467	26	c	c	X
iajs-400	467	27	,	,	PUNCT
iajs-400	467	28	b{},c	b{},c	PROPN
iajs-400	467	29	,	,	PUNCT
iajs-400	467	30	a}{b	a}{b	PROPN
iajs-400	467	31	,	,	PUNCT
iajs-400	467	32	a{},b{},a{,,x	a{},b{},a{,,x	PROPN
iajs-400	467	33	{	{	PUNCT
iajs-400	468	1	φ	φ	PROPN
iajs-400	468	2	.	.	PUNCT
iajs-400	469	1	hence	hence	ADV
iajs-400	469	2	)	)	PUNCT
iajs-400	469	3	,	,	PUNCT
iajs-400	469	4	x	x	X
iajs-400	469	5	(	(	PUNCT
iajs-400	469	6	τ	τ	X
iajs-400	469	7	is	be	AUX
iajs-400	469	8	bs*gid	bs*gid	ADJ
iajs-400	469	9	-space	-space	NOUN
iajs-400	469	10	,	,	PUNCT
iajs-400	469	11	but	but	CCONJ
iajs-400	469	12	is	be	AUX
iajs-400	469	13	not	not	PART
iajs-400	469	14	pre	pre	ADJ
iajs-400	469	15	-	-	ADJ
iajs-400	469	16	s*gid	s*gid	ADJ
iajs-400	469	17	-space	-space	NOUN
iajs-400	469	18	,	,	PUNCT
iajs-400	469	19	2,1i	2,1i	NOUN
iajs-400	469	20	=	=	PUNCT
iajs-400	469	21	.	.	PUNCT
iajs-400	470	1	from	from	ADP
iajs-400	470	2	above	above	ADP
iajs-400	470	3	we	we	PRON
iajs-400	470	4	can	can	AUX
iajs-400	470	5	get	get	VERB
iajs-400	470	6	the	the	DET
iajs-400	470	7	following	follow	VERB
iajs-400	470	8	diagram	diagram	NOUN
iajs-400	470	9	.	.	PUNCT
iajs-400	471	1	figure	figure	VERB
iajs-400	471	2	no	no	INTJ
iajs-400	471	3	.	.	PUNCT
iajs-400	472	1	(	(	PUNCT
iajs-400	472	2	3	3	NUM
iajs-400	472	3	):	):	PUNCT
iajs-400	472	4	relations	relation	NOUN
iajs-400	472	5	among	among	ADP
iajs-400	472	6	the	the	DET
iajs-400	472	7	types	type	NOUN
iajs-400	472	8	of	of	ADP
iajs-400	472	9	separation	separation	NOUN
iajs-400	472	10	axioms	axiom	VERB
iajs-400	472	11	definition(3.29	definition(3.29	NUM
iajs-400	472	12	):	):	PUNCT
iajs-400	472	13	a	a	DET
iajs-400	472	14	subset	subset	NOUN
iajs-400	472	15	a	a	PRON
iajs-400	472	16	of	of	ADP
iajs-400	472	17	a	a	DET
iajs-400	472	18	topological	topological	ADJ
iajs-400	472	19	space	space	NOUN
iajs-400	472	20	)	)	PUNCT
iajs-400	472	21	,	,	PUNCT
iajs-400	472	22	x	x	X
iajs-400	472	23	(	(	PUNCT
iajs-400	472	24	τ	τ	X
iajs-400	472	25	is	be	AUX
iajs-400	472	26	called	call	VERB
iajs-400	472	27	anα	anα	ADJ
iajs-400	472	28	-s*g	-s*g	ADJ
iajs-400	472	29	-	-	PUNCT
iajs-400	472	30	neighborhood	neighborhood	NOUN
iajs-400	472	31	(	(	PUNCT
iajs-400	472	32	resp	resp	NOUN
iajs-400	472	33	.	.	PUNCT
iajs-400	473	1	s*g	s*g	PROPN
iajs-400	473	2	-	-	PUNCT
iajs-400	473	3	neighborhood	neighborhood	NOUN
iajs-400	473	4	,	,	PUNCT
iajs-400	473	5	pre	pre	ADJ
iajs-400	473	6	-	-	ADJ
iajs-400	473	7	s*g	s*g	ADJ
iajs-400	473	8	-	-	PUNCT
iajs-400	473	9	neighborhood	neighborhood	NOUN
iajs-400	473	10	,	,	PUNCT
iajs-400	473	11	b	b	X
iajs-400	473	12	-	-	PUNCT
iajs-400	473	13	s*g	s*g	NOUN
iajs-400	473	14	-	-	PUNCT
iajs-400	473	15	neighborhood	neighborhood	NOUN
iajs-400	473	16	,	,	PUNCT
iajs-400	473	17	β	β	X
iajs-400	473	18	-s*g	-s*g	ADJ
iajs-400	473	19	-	-	PUNCT
iajs-400	473	20	neighborhood	neighborhood	NOUN
iajs-400	473	21	)	)	PUNCT
iajs-400	473	22	of	of	ADP
iajs-400	473	23	a	a	DET
iajs-400	473	24	point	point	NOUN
iajs-400	473	25	x	x	PUNCT
iajs-400	473	26	in	in	ADP
iajs-400	473	27	x	x	PRON
iajs-400	473	28	if	if	SCONJ
iajs-400	473	29	there	there	PRON
iajs-400	473	30	exists	exist	VERB
iajs-400	473	31	an	an	DET
iajs-400	473	32	α	α	NOUN
iajs-400	473	33	-s*g	-s*g	ADJ
iajs-400	473	34	-	-	PUNCT
iajs-400	473	35	open	open	ADJ
iajs-400	473	36	(	(	PUNCT
iajs-400	473	37	resp	resp	NOUN
iajs-400	473	38	.	.	PUNCT
iajs-400	474	1	s*g	s*g	NOUN
iajs-400	474	2	-	-	PUNCT
iajs-400	474	3	open	open	ADJ
iajs-400	474	4	,	,	PUNCT
iajs-400	474	5	pre	pre	ADJ
iajs-400	474	6	-	-	ADJ
iajs-400	474	7	s*g	s*g	ADJ
iajs-400	474	8	-	-	PUNCT
iajs-400	474	9	open	open	ADJ
iajs-400	474	10	,	,	PUNCT
iajs-400	474	11	b	b	X
iajs-400	474	12	-	-	PUNCT
iajs-400	474	13	s*g	s*g	NOUN
iajs-400	474	14	-	-	PUNCT
iajs-400	474	15	open	open	ADJ
iajs-400	474	16	,	,	PUNCT
iajs-400	474	17	β	β	X
iajs-400	474	18	-s*gopen	-s*gopen	NOUN
iajs-400	474	19	)	)	PUNCT
iajs-400	474	20	set	set	VERB
iajs-400	474	21	u	u	NOUN
iajs-400	474	22	in	in	ADP
iajs-400	474	23	x	x	SYM
iajs-400	474	24	such	such	ADJ
iajs-400	474	25	that	that	SCONJ
iajs-400	474	26	aux	aux	PROPN
iajs-400	474	27	⊆∈	⊆∈	NUM
iajs-400	474	28	.	.	PUNCT
iajs-400	475	1	definition(3.30	definition(3.30	NOUN
iajs-400	475	2	):	):	PUNCT
iajs-400	475	3	let	let	VERB
iajs-400	475	4	)	)	PUNCT
iajs-400	475	5	,	,	PUNCT
iajs-400	475	6	x	x	X
iajs-400	475	7	(	(	PUNCT
iajs-400	475	8	τ	τ	X
iajs-400	475	9	be	be	AUX
iajs-400	475	10	a	a	DET
iajs-400	475	11	topological	topological	ADJ
iajs-400	475	12	space	space	NOUN
iajs-400	475	13	.	.	PUNCT
iajs-400	476	1	a	a	DET
iajs-400	476	2	point	point	NOUN
iajs-400	476	3	xx∈	xx∈	NOUN
iajs-400	476	4	which	which	PRON
iajs-400	476	5	has	have	VERB
iajs-400	476	6	x	x	SYM
iajs-400	476	7	as	as	ADP
iajs-400	476	8	the	the	DET
iajs-400	476	9	only	only	ADJ
iajs-400	476	10	α	α	PROPN
iajs-400	476	11	s*g	s*g	NOUN
iajs-400	476	12	-	-	PUNCT
iajs-400	476	13	neighborhood	neighborhood	NOUN
iajs-400	476	14	(	(	PUNCT
iajs-400	476	15	resp	resp	NOUN
iajs-400	476	16	.	.	PUNCT
iajs-400	477	1	s*g	s*g	PROPN
iajs-400	477	2	-	-	PUNCT
iajs-400	477	3	neighborhood	neighborhood	NOUN
iajs-400	477	4	,	,	PUNCT
iajs-400	477	5	pre	pre	ADJ
iajs-400	477	6	-	-	ADJ
iajs-400	477	7	s*g	s*g	ADJ
iajs-400	477	8	-	-	PUNCT
iajs-400	477	9	neighborhood	neighborhood	NOUN
iajs-400	477	10	,	,	PUNCT
iajs-400	477	11	b	b	X
iajs-400	477	12	-	-	PUNCT
iajs-400	477	13	s*g	s*g	NOUN
iajs-400	477	14	-	-	PUNCT
iajs-400	477	15	neighborhood	neighborhood	NOUN
iajs-400	477	16	,	,	PUNCT
iajs-400	477	17	β	β	NOUN
iajs-400	477	18	s*g	s*g	NOUN
iajs-400	477	19	-	-	PUNCT
iajs-400	477	20	neighborhood	neighborhood	NOUN
iajs-400	477	21	)	)	PUNCT
iajs-400	477	22	is	be	AUX
iajs-400	477	23	called	call	VERB
iajs-400	477	24	an	an	PRON
iajs-400	477	25	α	α	NOUN
iajs-400	477	26	-s*g	-s*g	ADJ
iajs-400	477	27	-	-	PUNCT
iajs-400	477	28	neat	neat	ADJ
iajs-400	477	29	(	(	PUNCT
iajs-400	477	30	resp	resp	NOUN
iajs-400	477	31	.	.	PUNCT
iajs-400	478	1	s*g	s*g	PROPN
iajs-400	478	2	-	-	PUNCT
iajs-400	478	3	neat	neat	ADJ
iajs-400	478	4	,	,	PUNCT
iajs-400	478	5	pre	pre	ADJ
iajs-400	478	6	-	-	ADJ
iajs-400	478	7	s*g	s*g	ADJ
iajs-400	478	8	-	-	PUNCT
iajs-400	478	9	neat	neat	ADJ
iajs-400	478	10	,	,	PUNCT
iajs-400	478	11	b	b	X
iajs-400	478	12	-	-	PUNCT
iajs-400	478	13	s*g	s*g	NOUN
iajs-400	478	14	-	-	PUNCT
iajs-400	478	15	neat	neat	ADJ
iajs-400	478	16	,	,	PUNCT
iajs-400	478	17	β	β	PROPN
iajs-400	478	18	-s*gneat	-s*gneat	ADJ
iajs-400	478	19	)	)	PUNCT
iajs-400	478	20	point	point	NOUN
iajs-400	478	21	.	.	PUNCT
iajs-400	479	1	theorem(3.31	theorem(3.31	NUM
iajs-400	479	2	):	):	PUNCT
iajs-400	479	3	for	for	ADP
iajs-400	479	4	anα	anα	PROPN
iajs-400	479	5	-s*g0	-s*g0	PROPN
iajs-400	479	6	t	t	PROPN
iajs-400	479	7	-space	-space	NOUN
iajs-400	479	8	(	(	PUNCT
iajs-400	479	9	resp	resp	NOUN
iajs-400	479	10	.	.	PUNCT
iajs-400	480	1	s*g0	s*g0	PROPN
iajs-400	480	2	t	t	NOUN
iajs-400	480	3	-space	-space	NOUN
iajs-400	480	4	,	,	PUNCT
iajs-400	480	5	pre	pre	ADJ
iajs-400	480	6	-	-	ADJ
iajs-400	480	7	s*g0	s*g0	ADJ
iajs-400	480	8	t	t	NOUN
iajs-400	480	9	-space	-space	NOUN
iajs-400	480	10	,	,	PUNCT
iajs-400	480	11	b	b	X
iajs-400	480	12	-	-	PUNCT
iajs-400	480	13	s*g0	s*g0	VERB
iajs-400	480	14	t	t	NOUN
iajs-400	480	15	-space	-space	NOUN
iajs-400	480	16	,	,	PUNCT
iajs-400	480	17	β	β	PROPN
iajs-400	480	18	-s*g0	-s*g0	NOUN
iajs-400	480	19	t	t	NOUN
iajs-400	480	20	-space	-space	NOUN
iajs-400	480	21	)	)	PUNCT
iajs-400	480	22	)	)	PUNCT
iajs-400	481	1	,	,	PUNCT
iajs-400	481	2	x	x	X
iajs-400	481	3	(	(	PUNCT
iajs-400	481	4	τ	τ	X
iajs-400	481	5	the	the	DET
iajs-400	481	6	following	following	NOUN
iajs-400	481	7	are	be	AUX
iajs-400	481	8	equivalent	equivalent	ADJ
iajs-400	481	9	.	.	PUNCT
iajs-400	482	1	(	(	PUNCT
iajs-400	482	2	i	i	NOUN
iajs-400	482	3	)	)	PUNCT
iajs-400	482	4	)	)	PUNCT
iajs-400	482	5	,	,	PUNCT
iajs-400	482	6	x	x	X
iajs-400	482	7	(	(	PUNCT
iajs-400	482	8	τ	τ	X
iajs-400	482	9	is	be	AUX
iajs-400	482	10	anα	anα	PROPN
iajs-400	482	11	-s*g1d	-s*g1d	PROPN
iajs-400	482	12	-space	-space	PROPN
iajs-400	482	13	(	(	PUNCT
iajs-400	482	14	resp	resp	NOUN
iajs-400	482	15	.	.	PUNCT
iajs-400	483	1	s*g1d	s*g1d	NOUN
iajs-400	483	2	-space	-space	NOUN
iajs-400	483	3	,	,	PUNCT
iajs-400	483	4	pre	pre	ADJ
iajs-400	483	5	-	-	ADJ
iajs-400	483	6	s*g1d	s*g1d	ADJ
iajs-400	483	7	-space	-space	NOUN
iajs-400	483	8	,	,	PUNCT
iajs-400	483	9	b	b	X
iajs-400	483	10	-	-	PUNCT
iajs-400	483	11	s*g1d	s*g1d	NOUN
iajs-400	483	12	-space	-space	NOUN
iajs-400	483	13	,	,	PUNCT
iajs-400	483	14	β	β	X
iajs-400	483	15	s*g	s*g	VERB
iajs-400	483	16	1d	1d	NUM
iajs-400	483	17	-space	-space	NOUN
iajs-400	483	18	)	)	PUNCT
iajs-400	483	19	.	.	PUNCT
iajs-400	484	1	(	(	PUNCT
iajs-400	484	2	ii	ii	NOUN
iajs-400	484	3	)	)	PUNCT
iajs-400	484	4	)	)	PUNCT
iajs-400	484	5	,	,	PUNCT
iajs-400	484	6	x	x	X
iajs-400	484	7	(	(	PUNCT
iajs-400	484	8	τ	τ	X
iajs-400	484	9	has	have	AUX
iajs-400	485	1	no	no	DET
iajs-400	485	2	α	α	PRON
iajs-400	485	3	-s*g	-s*g	NOUN
iajs-400	485	4	-	-	PUNCT
iajs-400	485	5	neat	neat	ADJ
iajs-400	485	6	(	(	PUNCT
iajs-400	485	7	resp	resp	NOUN
iajs-400	485	8	.	.	PUNCT
iajs-400	486	1	s*g	s*g	PROPN
iajs-400	486	2	-	-	PUNCT
iajs-400	486	3	neat	neat	ADJ
iajs-400	486	4	,	,	PUNCT
iajs-400	486	5	pre	pre	ADJ
iajs-400	486	6	-	-	ADJ
iajs-400	486	7	s*g	s*g	ADJ
iajs-400	486	8	-	-	PUNCT
iajs-400	486	9	neat	neat	ADJ
iajs-400	486	10	,	,	PUNCT
iajs-400	486	11	b	b	X
iajs-400	486	12	-	-	PUNCT
iajs-400	486	13	s*g	s*g	NOUN
iajs-400	486	14	-	-	PUNCT
iajs-400	486	15	neat	neat	ADJ
iajs-400	486	16	,	,	PUNCT
iajs-400	486	17	β	β	X
iajs-400	486	18	-s*g	-s*g	ADJ
iajs-400	486	19	-	-	PUNCT
iajs-400	486	20	neat	neat	ADJ
iajs-400	486	21	)	)	PUNCT
iajs-400	486	22	point	point	NOUN
iajs-400	486	23	.	.	PUNCT
iajs-400	487	1	proof	proof	NOUN
iajs-400	487	2	:	:	PUNCT
iajs-400	487	3	)	)	PUNCT
iajs-400	487	4	ii()i	ii()i	NOUN
iajs-400	487	5	(	(	PUNCT
iajs-400	487	6	⇒	⇒	NOUN
iajs-400	487	7	.	.	PUNCT
iajs-400	488	1	since	since	SCONJ
iajs-400	488	2	)	)	PUNCT
iajs-400	488	3	,	,	PUNCT
iajs-400	488	4	x	x	X
iajs-400	488	5	(	(	PUNCT
iajs-400	488	6	τ	τ	X
iajs-400	488	7	is	be	AUX
iajs-400	488	8	anα	anα	PROPN
iajs-400	488	9	-s*g1d	-s*g1d	PROPN
iajs-400	488	10	-space	-space	NOUN
iajs-400	488	11	,	,	PUNCT
iajs-400	488	12	then	then	ADV
iajs-400	488	13	each	each	DET
iajs-400	488	14	point	point	NOUN
iajs-400	488	15	x	x	PUNCT
iajs-400	488	16	of	of	ADP
iajs-400	488	17	x	x	PRON
iajs-400	488	18	is	be	AUX
iajs-400	488	19	contained	contain	VERB
iajs-400	488	20	in	in	ADP
iajs-400	488	21	a	a	DET
iajs-400	488	22	g*sd	g*sd	PROPN
iajs-400	488	23	−α	−α	PROPN
iajs-400	488	24	-set	-set	PUNCT
iajs-400	489	1	v\ug	v\ug	PROPN
iajs-400	489	2	=	=	PUNCT
iajs-400	489	3	,	,	PUNCT
iajs-400	489	4	where	where	SCONJ
iajs-400	489	5	u	u	NOUN
iajs-400	489	6	and	and	CCONJ
iajs-400	489	7	v	v	NOUN
iajs-400	489	8	are	be	AUX
iajs-400	489	9	α	α	DET
iajs-400	489	10	-s*g	-s*g	ADJ
iajs-400	489	11	-	-	PUNCT
iajs-400	489	12	open	open	ADJ
iajs-400	489	13	sets	set	NOUN
iajs-400	489	14	and	and	CCONJ
iajs-400	489	15	thus	thus	ADV
iajs-400	489	16	in	in	ADP
iajs-400	489	17	u	u	PROPN
iajs-400	489	18	.	.	PUNCT
iajs-400	490	1	by	by	ADP
iajs-400	490	2	definition	definition	NOUN
iajs-400	490	3	xu	xu	PROPN
iajs-400	490	4	≠	≠	PROPN
iajs-400	490	5	.	.	PUNCT
iajs-400	491	1	this	this	PRON
iajs-400	491	2	implies	imply	VERB
iajs-400	491	3	that	that	SCONJ
iajs-400	491	4	x	x	PRON
iajs-400	491	5	is	be	AUX
iajs-400	491	6	not	not	PART
iajs-400	491	7	anα	anα	ADJ
iajs-400	491	8	-s*g	-s*g	ADJ
iajs-400	491	9	-	-	PUNCT
iajs-400	491	10	neat	neat	ADJ
iajs-400	491	11	point	point	NOUN
iajs-400	491	12	.	.	PUNCT
iajs-400	491	13	)	)	PUNCT
iajs-400	492	1	i()ii	i()ii	NOUN
iajs-400	492	2	(	(	PUNCT
iajs-400	492	3	⇒	⇒	NOUN
iajs-400	492	4	.	.	PUNCT
iajs-400	493	1	if	if	SCONJ
iajs-400	493	2	)	)	PUNCT
iajs-400	493	3	,	,	PUNCT
iajs-400	493	4	x	x	X
iajs-400	493	5	(	(	PUNCT
iajs-400	493	6	τ	τ	X
iajs-400	493	7	is	be	AUX
iajs-400	493	8	anα	anα	PROPN
iajs-400	493	9	-s*g0	-s*g0	PROPN
iajs-400	493	10	t	t	NOUN
iajs-400	493	11	-space	-space	NOUN
iajs-400	493	12	,	,	PUNCT
iajs-400	493	13	then	then	ADV
iajs-400	493	14	for	for	ADP
iajs-400	493	15	each	each	DET
iajs-400	493	16	distinct	distinct	ADJ
iajs-400	493	17	points	point	NOUN
iajs-400	493	18	xy	xy	PRON
iajs-400	493	19	,	,	PUNCT
iajs-400	493	20	x	x	SYM
iajs-400	493	21	∈	∈	PROPN
iajs-400	493	22	,	,	PUNCT
iajs-400	493	23	at	at	ADP
iajs-400	493	24	least	least	ADJ
iajs-400	493	25	one	one	NUM
iajs-400	493	26	of	of	ADP
iajs-400	493	27	them	they	PRON
iajs-400	493	28	,	,	PUNCT
iajs-400	493	29	say	say	VERB
iajs-400	493	30	x	x	PUNCT
iajs-400	493	31	has	have	VERB
iajs-400	493	32	an	an	DET
iajs-400	493	33	α	α	DET
iajs-400	493	34	-s*g	-s*g	ADJ
iajs-400	493	35	-	-	PUNCT
iajs-400	493	36	neighborhood	neighborhood	NOUN
iajs-400	493	37	u	u	NOUN
iajs-400	493	38	containing	contain	VERB
iajs-400	493	39	x	x	PUNCT
iajs-400	493	40	,	,	PUNCT
iajs-400	493	41	but	but	CCONJ
iajs-400	493	42	not	not	PART
iajs-400	493	43	y	y	PROPN
iajs-400	493	44	.	.	PUNCT
iajs-400	494	1	thus	thus	ADV
iajs-400	494	2	u	u	PRON
iajs-400	494	3	is	be	AUX
iajs-400	494	4	different	different	ADJ
iajs-400	494	5	364	364	NUM
iajs-400	494	6	|	|	NOUN
iajs-400	494	7	mathematics	mathematics	PROPN
iajs-400	494	8	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	494	9	�	�	NOUN
iajs-400	494	10	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	494	11	:	:	PUNCT
iajs-400	494	12	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	495	1	©	©	PROPN
iajs-400	495	2	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	495	3	ibn	ibn	PROPN
iajs-400	495	4	al	al	PROPN
iajs-400	495	5	-	-	PUNCT
iajs-400	495	6	haitham	haitham	PROPN
iajs-400	495	7	jour	jour	X
iajs-400	495	8	.	.	PROPN
iajs-400	495	9	for	for	ADP
iajs-400	495	10	pure	pure	ADJ
iajs-400	495	11	&	&	CCONJ
iajs-400	495	12	appl	appl	PROPN
iajs-400	495	13	.	.	PUNCT
iajs-400	496	1	sci	sci	PROPN
iajs-400	496	2	.	.	PUNCT
iajs-400	496	3	vol	vol	NOUN
iajs-400	496	4	.	.	PROPN
iajs-400	497	1	27	27	NUM
iajs-400	497	2	(	(	PUNCT
iajs-400	497	3	1	1	NUM
iajs-400	497	4	)	)	PUNCT
iajs-400	497	5	2014	2014	NUM
iajs-400	497	6	from	from	ADP
iajs-400	497	7	x	x	PUNCT
iajs-400	497	8	and	and	CCONJ
iajs-400	497	9	therefore	therefore	ADV
iajs-400	497	10	by	by	ADP
iajs-400	497	11	remark	remark	NOUN
iajs-400	497	12	(	(	PUNCT
iajs-400	497	13	3.2	3.2	NUM
iajs-400	497	14	)	)	PUNCT
iajs-400	497	15	,	,	PUNCT
iajs-400	497	16	u	u	NOUN
iajs-400	497	17	is	be	AUX
iajs-400	497	18	an	an	DET
iajs-400	497	19	g*sd	g*sd	PROPN
iajs-400	497	20	−α	−α	PROPN
iajs-400	497	21	-set	-set	PUNCT
iajs-400	497	22	.	.	PUNCT
iajs-400	498	1	since	since	SCONJ
iajs-400	498	2	x	x	PRON
iajs-400	498	3	has	have	AUX
iajs-400	498	4	noα	noα	ADP
iajs-400	498	5	-s*g	-s*g	ADJ
iajs-400	498	6	-	-	PUNCT
iajs-400	498	7	neat	neat	ADJ
iajs-400	498	8	point	point	NOUN
iajs-400	498	9	,	,	PUNCT
iajs-400	498	10	then	then	ADV
iajs-400	498	11	y	y	PROPN
iajs-400	498	12	is	be	AUX
iajs-400	498	13	not	not	PART
iajs-400	498	14	an	an	DET
iajs-400	498	15	α	α	NOUN
iajs-400	498	16	-s*g	-s*g	ADJ
iajs-400	498	17	-	-	PUNCT
iajs-400	498	18	neat	neat	ADJ
iajs-400	498	19	point	point	NOUN
iajs-400	498	20	.	.	PUNCT
iajs-400	499	1	thus	thus	ADV
iajs-400	499	2	there	there	PRON
iajs-400	499	3	exists	exist	VERB
iajs-400	499	4	an	an	DET
iajs-400	499	5	α	α	NOUN
iajs-400	499	6	-s*g	-s*g	ADJ
iajs-400	499	7	-	-	PUNCT
iajs-400	499	8	neighborhood	neighborhood	NOUN
iajs-400	499	9	v	v	NOUN
iajs-400	499	10	of	of	ADP
iajs-400	499	11	y	y	PRON
iajs-400	499	12	such	such	ADJ
iajs-400	499	13	that	that	SCONJ
iajs-400	499	14	xv	xv	PROPN
iajs-400	499	15	≠	≠	PROPN
iajs-400	499	16	.	.	PUNCT
iajs-400	500	1	therefore	therefore	ADV
iajs-400	500	2	,	,	PUNCT
iajs-400	500	3	u\vy∈	u\vy∈	NOUN
iajs-400	500	4	,	,	PUNCT
iajs-400	500	5	u\vx∉	u\vx∉	PROPN
iajs-400	500	6	and	and	CCONJ
iajs-400	500	7	u\v	u\v	PROPN
iajs-400	500	8	is	be	AUX
iajs-400	500	9	an	an	DET
iajs-400	500	10	g*sd	g*sd	PROPN
iajs-400	500	11	−α	−α	PROPN
iajs-400	500	12	-set	-set	PUNCT
iajs-400	500	13	.	.	PUNCT
iajs-400	501	1	hence	hence	ADV
iajs-400	501	2	)	)	PUNCT
iajs-400	501	3	,	,	PUNCT
iajs-400	501	4	x	x	X
iajs-400	501	5	(	(	PUNCT
iajs-400	501	6	τ	τ	X
iajs-400	501	7	is	be	AUX
iajs-400	501	8	anα	anα	PROPN
iajs-400	501	9	-s*g1d	-s*g1d	NOUN
iajs-400	501	10	space	space	NOUN
iajs-400	501	11	.	.	PUNCT
iajs-400	502	1	theorem(3.32	theorem(3.32	NOUN
iajs-400	502	2	):	):	PUNCT
iajs-400	502	3	let	let	NOUN
iajs-400	502	4	)	)	PUNCT
iajs-400	502	5	,	,	PUNCT
iajs-400	502	6	y(),x(:f	y(),x(:f	PROPN
iajs-400	502	7	σ→τ	σ→τ	NUM
iajs-400	502	8	be	be	VERB
iajs-400	502	9	anα	anα	ADJ
iajs-400	502	10	-s*g	-s*g	ADJ
iajs-400	502	11	-	-	PUNCT
iajs-400	502	12	continuous	continuous	ADJ
iajs-400	502	13	(	(	PUNCT
iajs-400	502	14	resp	resp	NOUN
iajs-400	502	15	.	.	PUNCT
iajs-400	503	1	s*g	s*g	PROPN
iajs-400	503	2	-	-	PUNCT
iajs-400	503	3	continuous	continuous	ADJ
iajs-400	503	4	,	,	PUNCT
iajs-400	503	5	pre	pre	ADJ
iajs-400	503	6	-	-	ADJ
iajs-400	503	7	s*g	s*g	ADJ
iajs-400	503	8	-	-	PUNCT
iajs-400	503	9	continuous	continuous	ADJ
iajs-400	503	10	,	,	PUNCT
iajs-400	503	11	b	b	X
iajs-400	503	12	-	-	PUNCT
iajs-400	503	13	s*g	s*g	NOUN
iajs-400	503	14	-	-	PUNCT
iajs-400	503	15	continuous	continuous	ADJ
iajs-400	503	16	,	,	PUNCT
iajs-400	503	17	β	β	X
iajs-400	503	18	-s*g	-s*g	ADJ
iajs-400	503	19	-	-	PUNCT
iajs-400	503	20	continuous	continuous	ADJ
iajs-400	503	21	)	)	PUNCT
iajs-400	503	22	bijective	bijective	ADJ
iajs-400	503	23	function	function	NOUN
iajs-400	503	24	.	.	PUNCT
iajs-400	504	1	if	if	SCONJ
iajs-400	504	2	)	)	PUNCT
iajs-400	504	3	,	,	PUNCT
iajs-400	504	4	y	y	PROPN
iajs-400	504	5	(	(	PUNCT
iajs-400	504	6	σ	σ	PROPN
iajs-400	504	7	is	be	AUX
iajs-400	504	8	a	a	DET
iajs-400	504	9	i	i	PROPN
iajs-400	504	10	d	d	PROPN
iajs-400	504	11	space	space	NOUN
iajs-400	504	12	,	,	PUNCT
iajs-400	504	13	then	then	ADV
iajs-400	504	14	)	)	PUNCT
iajs-400	504	15	,	,	PUNCT
iajs-400	504	16	x	x	X
iajs-400	504	17	(	(	PUNCT
iajs-400	504	18	τ	τ	X
iajs-400	504	19	is	be	AUX
iajs-400	504	20	anα	anα	ADJ
iajs-400	504	21	-s*gid	-s*gid	ADJ
iajs-400	504	22	-space	-space	NOUN
iajs-400	504	23	(	(	PUNCT
iajs-400	504	24	resp	resp	NOUN
iajs-400	504	25	.	.	PUNCT
iajs-400	505	1	s*gid	s*gid	ADJ
iajs-400	505	2	-space	-space	NOUN
iajs-400	505	3	,	,	PUNCT
iajs-400	505	4	pre	pre	ADJ
iajs-400	505	5	-	-	ADJ
iajs-400	505	6	s*gid	s*gid	ADJ
iajs-400	505	7	-space	-space	NOUN
iajs-400	505	8	,	,	PUNCT
iajs-400	505	9	b	b	X
iajs-400	505	10	-	-	PUNCT
iajs-400	505	11	s*gid	s*gid	ADJ
iajs-400	505	12	-space	-space	NOUN
iajs-400	505	13	,	,	PUNCT
iajs-400	505	14	β	β	X
iajs-400	505	15	-s*gid	-s*gid	ADJ
iajs-400	505	16	-space	-space	NOUN
iajs-400	505	17	)	)	PUNCT
iajs-400	505	18	,	,	PUNCT
iajs-400	505	19	2,1,0i	2,1,0i	NUM
iajs-400	505	20	=	=	PUNCT
iajs-400	505	21	.	.	PUNCT
iajs-400	506	1	proof	proof	NOUN
iajs-400	506	2	:	:	PUNCT
iajs-400	506	3	suppose	suppose	VERB
iajs-400	506	4	that	that	SCONJ
iajs-400	506	5	)	)	PUNCT
iajs-400	506	6	,	,	PUNCT
iajs-400	506	7	y	y	PROPN
iajs-400	506	8	(	(	PUNCT
iajs-400	506	9	σ	σ	PROPN
iajs-400	506	10	is	be	AUX
iajs-400	506	11	a	a	DET
iajs-400	506	12	2d	2d	NUM
iajs-400	506	13	-space	-space	NOUN
iajs-400	506	14	.	.	PUNCT
iajs-400	507	1	let	let	VERB
iajs-400	507	2	xy	xy	PRON
iajs-400	507	3	,	,	PUNCT
iajs-400	507	4	x	x	PROPN
iajs-400	507	5	∈	∈	PRON
iajs-400	507	6	such	such	ADJ
iajs-400	507	7	that	that	DET
iajs-400	507	8	yx	yx	NOUN
iajs-400	507	9	≠	≠	PROPN
iajs-400	507	10	.	.	PUNCT
iajs-400	508	1	since	since	SCONJ
iajs-400	508	2	f	f	PROPN
iajs-400	508	3	is	be	AUX
iajs-400	508	4	injective	injective	ADJ
iajs-400	508	5	and	and	CCONJ
iajs-400	508	6	y	y	PROPN
iajs-400	508	7	is	be	AUX
iajs-400	508	8	a	a	DET
iajs-400	508	9	2d	2d	NUM
iajs-400	508	10	-space	-space	NOUN
iajs-400	508	11	,	,	PUNCT
iajs-400	508	12	then	then	ADV
iajs-400	508	13	there	there	PRON
iajs-400	508	14	exists	exist	VERB
iajs-400	508	15	disjoint	disjoint	NOUN
iajs-400	508	16	d	d	NOUN
iajs-400	508	17	-	-	NOUN
iajs-400	508	18	sets	set	VERB
iajs-400	508	19	1	1	NUM
iajs-400	508	20	g	g	NOUN
iajs-400	508	21	and	and	CCONJ
iajs-400	508	22	2	2	NUM
iajs-400	508	23	g	g	NOUN
iajs-400	508	24	of	of	ADP
iajs-400	508	25	y	y	PRON
iajs-400	508	26	such	such	ADJ
iajs-400	508	27	that	that	SCONJ
iajs-400	508	28	1g)x(f	1g)x(f	NUM
iajs-400	508	29	∈	∈	NOUN
iajs-400	508	30	and	and	CCONJ
iajs-400	508	31	2g)y(f	2g)y(f	NUM
iajs-400	508	32	∈	∈	PROPN
iajs-400	508	33	.	.	PUNCT
iajs-400	509	1	by	by	ADP
iajs-400	509	2	theorem	theorem	NOUN
iajs-400	509	3	(	(	PUNCT
iajs-400	509	4	3.10	3.10	NUM
iajs-400	509	5	)	)	PUNCT
iajs-400	509	6	,	,	PUNCT
iajs-400	509	7	)	)	PUNCT
iajs-400	509	8	g(f	g(f	PROPN
iajs-400	509	9	1	1	NUM
iajs-400	509	10	1−	1−	NUM
iajs-400	509	11	and	and	CCONJ
iajs-400	509	12	)	)	PUNCT
iajs-400	509	13	g(f	g(f	PROPN
iajs-400	509	14	2	2	NUM
iajs-400	509	15	1−	1−	NUM
iajs-400	509	16	are	be	AUX
iajs-400	509	17	g*sd	g*sd	PROPN
iajs-400	509	18	−α	−α	NOUN
iajs-400	509	19	-sets	-set	NOUN
iajs-400	509	20	in	in	ADP
iajs-400	509	21	x	x	SYM
iajs-400	509	22	such	such	ADJ
iajs-400	509	23	that	that	PRON
iajs-400	509	24	)	)	PUNCT
iajs-400	509	25	g(fx	g(fx	NOUN
iajs-400	509	26	1	1	NUM
iajs-400	509	27	1−∈	1−∈	NUM
iajs-400	509	28	,	,	PUNCT
iajs-400	509	29	)	)	PUNCT
iajs-400	509	30	g(fy	g(fy	PROPN
iajs-400	509	31	2	2	NUM
iajs-400	509	32	1−∈	1−∈	NUM
iajs-400	509	33	and	and	CCONJ
iajs-400	509	34	φ=−−	φ=−−	NOUN
iajs-400	509	35	)	)	PUNCT
iajs-400	509	36	g(f)g(f	g(f)g(f	PROPN
iajs-400	509	37	2	2	NUM
iajs-400	509	38	1	1	NUM
iajs-400	509	39	1	1	NUM
iajs-400	509	40	1	1	NUM
iajs-400	509	41			NOUN
iajs-400	509	42	.	.	PUNCT
iajs-400	510	1	hence	hence	ADV
iajs-400	510	2	)	)	PUNCT
iajs-400	510	3	,	,	PUNCT
iajs-400	510	4	x	x	X
iajs-400	510	5	(	(	PUNCT
iajs-400	510	6	τ	τ	X
iajs-400	510	7	is	be	AUX
iajs-400	510	8	anα	anα	NOUN
iajs-400	510	9	-s*g2d	-s*g2d	PUNCT
iajs-400	510	10	-space	-space	NOUN
iajs-400	510	11	.	.	PUNCT
iajs-400	511	1	theorem(3.33	theorem(3.33	NUM
iajs-400	511	2	):	):	PUNCT
iajs-400	511	3	let	let	NOUN
iajs-400	511	4	)	)	PUNCT
iajs-400	511	5	,	,	PUNCT
iajs-400	511	6	y(),x(:f	y(),x(:f	PROPN
iajs-400	511	7	σ→τ	σ→τ	NUM
iajs-400	511	8	be	be	VERB
iajs-400	511	9	an	an	DET
iajs-400	511	10	α	α	DET
iajs-400	511	11	-s*g	-s*g	NOUN
iajs-400	511	12	-	-	PUNCT
iajs-400	511	13	irresolute	irresolute	ADJ
iajs-400	511	14	(	(	PUNCT
iajs-400	511	15	resp	resp	NOUN
iajs-400	511	16	.	.	PUNCT
iajs-400	512	1	s*g	s*g	PROPN
iajs-400	512	2	-	-	PUNCT
iajs-400	512	3	irresolute	irresolute	ADJ
iajs-400	512	4	,	,	PUNCT
iajs-400	512	5	pres*g	pres*g	X
iajs-400	512	6	irresolute	irresolute	PROPN
iajs-400	512	7	,	,	PUNCT
iajs-400	512	8	b	b	X
iajs-400	512	9	-	-	PUNCT
iajs-400	512	10	s*g	s*g	NOUN
iajs-400	512	11	-	-	PUNCT
iajs-400	512	12	irresolute	irresolute	ADJ
iajs-400	512	13	,	,	PUNCT
iajs-400	512	14	β	β	X
iajs-400	512	15	-s*g	-s*g	ADJ
iajs-400	512	16	-	-	PUNCT
iajs-400	512	17	irresolute	irresolute	NOUN
iajs-400	512	18	)	)	PUNCT
iajs-400	512	19	bijective	bijective	ADJ
iajs-400	512	20	function	function	NOUN
iajs-400	512	21	.	.	PUNCT
iajs-400	513	1	if	if	SCONJ
iajs-400	513	2	)	)	PUNCT
iajs-400	513	3	,	,	PUNCT
iajs-400	513	4	y	y	PROPN
iajs-400	513	5	(	(	PUNCT
iajs-400	513	6	σ	σ	PROPN
iajs-400	513	7	is	be	AUX
iajs-400	513	8	anα	anα	PROPN
iajs-400	513	9	-s*gid	-s*gid	ADJ
iajs-400	513	10	space	space	NOUN
iajs-400	513	11	(	(	PUNCT
iajs-400	513	12	resp	resp	NOUN
iajs-400	513	13	.	.	PUNCT
iajs-400	514	1	s*gid	s*gid	ADJ
iajs-400	514	2	-space	-space	NOUN
iajs-400	514	3	,	,	PUNCT
iajs-400	514	4	pre	pre	ADJ
iajs-400	514	5	-	-	ADJ
iajs-400	514	6	s*gid	s*gid	ADJ
iajs-400	514	7	-space	-space	NOUN
iajs-400	514	8	,	,	PUNCT
iajs-400	514	9	b	b	X
iajs-400	514	10	-	-	PUNCT
iajs-400	514	11	s*gid	s*gid	ADJ
iajs-400	514	12	-space	-space	NOUN
iajs-400	514	13	,	,	PUNCT
iajs-400	514	14	β	β	X
iajs-400	514	15	-s*gid	-s*gid	X
iajs-400	514	16	-space	-space	NOUN
iajs-400	514	17	)	)	PUNCT
iajs-400	514	18	,	,	PUNCT
iajs-400	514	19	then	then	ADV
iajs-400	514	20	)	)	PUNCT
iajs-400	514	21	,	,	PUNCT
iajs-400	514	22	x	x	X
iajs-400	514	23	(	(	PUNCT
iajs-400	514	24	τ	τ	X
iajs-400	514	25	is	be	AUX
iajs-400	514	26	an	an	DET
iajs-400	514	27	α	α	NOUN
iajs-400	514	28	-s*gid	-s*gid	ADJ
iajs-400	514	29	-space	-space	NOUN
iajs-400	514	30	(	(	PUNCT
iajs-400	514	31	resp	resp	NOUN
iajs-400	514	32	.	.	PUNCT
iajs-400	515	1	s*gid	s*gid	ADJ
iajs-400	515	2	-space	-space	NOUN
iajs-400	515	3	,	,	PUNCT
iajs-400	515	4	pre	pre	ADJ
iajs-400	515	5	-	-	ADJ
iajs-400	515	6	s*gid	s*gid	ADJ
iajs-400	515	7	-space	-space	NOUN
iajs-400	515	8	,	,	PUNCT
iajs-400	515	9	b	b	X
iajs-400	515	10	-	-	PUNCT
iajs-400	515	11	s*gid	s*gid	ADJ
iajs-400	515	12	-space	-space	NOUN
iajs-400	515	13	,	,	PUNCT
iajs-400	515	14	β	β	X
iajs-400	515	15	-s*gid	-s*gid	X
iajs-400	515	16	space	space	NOUN
iajs-400	515	17	)	)	PUNCT
iajs-400	515	18	,	,	PUNCT
iajs-400	515	19	2,1,0i	2,1,0i	NUM
iajs-400	515	20	=	=	PUNCT
iajs-400	515	21	.	.	PUNCT
iajs-400	516	1	proof	proof	NOUN
iajs-400	516	2	:	:	PUNCT
iajs-400	516	3	suppose	suppose	VERB
iajs-400	516	4	that	that	SCONJ
iajs-400	516	5	)	)	PUNCT
iajs-400	516	6	,	,	PUNCT
iajs-400	516	7	y	y	PROPN
iajs-400	516	8	(	(	PUNCT
iajs-400	516	9	σ	σ	PROPN
iajs-400	516	10	is	be	AUX
iajs-400	516	11	an	an	DET
iajs-400	516	12	α	α	NOUN
iajs-400	516	13	-s*g2d	-s*g2d	PUNCT
iajs-400	516	14	-space	-space	NOUN
iajs-400	516	15	.	.	PUNCT
iajs-400	517	1	let	let	VERB
iajs-400	517	2	xy	xy	PRON
iajs-400	517	3	,	,	PUNCT
iajs-400	517	4	x	x	PROPN
iajs-400	517	5	∈	∈	PRON
iajs-400	517	6	such	such	ADJ
iajs-400	517	7	that	that	DET
iajs-400	517	8	yx	yx	NOUN
iajs-400	517	9	≠	≠	PROPN
iajs-400	517	10	.	.	PUNCT
iajs-400	518	1	since	since	SCONJ
iajs-400	518	2	f	f	PROPN
iajs-400	518	3	is	be	AUX
iajs-400	518	4	injective	injective	ADJ
iajs-400	518	5	and	and	CCONJ
iajs-400	518	6	y	y	PROPN
iajs-400	518	7	is	be	AUX
iajs-400	518	8	anα	anα	PROPN
iajs-400	518	9	-s*g2d	-s*g2d	PUNCT
iajs-400	518	10	-space	-space	NOUN
iajs-400	518	11	,	,	PUNCT
iajs-400	518	12	then	then	ADV
iajs-400	518	13	there	there	PRON
iajs-400	518	14	exists	exist	VERB
iajs-400	518	15	disjoint	disjoint	PROPN
iajs-400	518	16	g*sd	g*sd	PROPN
iajs-400	518	17	−α	−α	PROPN
iajs-400	518	18	-sets	-set	VERB
iajs-400	518	19	1	1	NUM
iajs-400	518	20	g	g	NOUN
iajs-400	518	21	and	and	CCONJ
iajs-400	518	22	2	2	NUM
iajs-400	518	23	g	g	NOUN
iajs-400	518	24	of	of	ADP
iajs-400	518	25	y	y	PRON
iajs-400	518	26	such	such	ADJ
iajs-400	518	27	that	that	SCONJ
iajs-400	518	28	1g)x(f	1g)x(f	NUM
iajs-400	518	29	∈	∈	NOUN
iajs-400	518	30	and	and	CCONJ
iajs-400	518	31	2g)y(f	2g)y(f	NUM
iajs-400	518	32	∈	∈	PROPN
iajs-400	518	33	.	.	PUNCT
iajs-400	519	1	by	by	ADP
iajs-400	519	2	theorem	theorem	NOUN
iajs-400	519	3	(	(	PUNCT
iajs-400	519	4	3.11	3.11	NUM
iajs-400	519	5	)	)	PUNCT
iajs-400	519	6	,	,	PUNCT
iajs-400	519	7	)	)	PUNCT
iajs-400	519	8	g(f	g(f	PROPN
iajs-400	519	9	1	1	NUM
iajs-400	519	10	1−	1−	NUM
iajs-400	519	11	and	and	CCONJ
iajs-400	519	12	)	)	PUNCT
iajs-400	519	13	g(f	g(f	PROPN
iajs-400	519	14	2	2	NUM
iajs-400	519	15	1−	1−	NUM
iajs-400	519	16	are	be	AUX
iajs-400	519	17	g*sd	g*sd	PROPN
iajs-400	519	18	−α	−α	PROPN
iajs-400	519	19	sets	set	VERB
iajs-400	519	20	in	in	ADP
iajs-400	519	21	x	x	SYM
iajs-400	519	22	such	such	ADJ
iajs-400	519	23	that	that	PRON
iajs-400	519	24	)	)	PUNCT
iajs-400	519	25	g(fx	g(fx	NOUN
iajs-400	519	26	1	1	NUM
iajs-400	519	27	1−∈	1−∈	NUM
iajs-400	519	28	,	,	PUNCT
iajs-400	519	29	)	)	PUNCT
iajs-400	519	30	g(fy	g(fy	PROPN
iajs-400	519	31	2	2	NUM
iajs-400	519	32	1−∈	1−∈	NUM
iajs-400	519	33	and	and	CCONJ
iajs-400	519	34	φ=−−	φ=−−	NOUN
iajs-400	519	35	)	)	PUNCT
iajs-400	519	36	g(f)g(f	g(f)g(f	PROPN
iajs-400	519	37	2	2	NUM
iajs-400	519	38	1	1	NUM
iajs-400	519	39	1	1	NUM
iajs-400	519	40	1	1	NUM
iajs-400	519	41			NOUN
iajs-400	519	42	.	.	PUNCT
iajs-400	520	1	hence	hence	ADV
iajs-400	520	2	)	)	PUNCT
iajs-400	520	3	,	,	PUNCT
iajs-400	520	4	x	x	X
iajs-400	520	5	(	(	PUNCT
iajs-400	520	6	τ	τ	X
iajs-400	520	7	is	be	AUX
iajs-400	520	8	an	an	DET
iajs-400	520	9	α	α	NOUN
iajs-400	520	10	-s*g2d	-s*g2d	PUNCT
iajs-400	520	11	-space	-space	NOUN
iajs-400	520	12	.	.	PUNCT
iajs-400	521	1	365	365	NUM
iajs-400	521	2	|	|	ADV
iajs-400	521	3	mathematics	mathematics	PROPN
iajs-400	521	4	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	521	5	�	�	NOUN
iajs-400	521	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	521	7	:	:	PUNCT
iajs-400	521	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	521	9	©	©	PROPN
iajs-400	521	10	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	521	11	ibn	ibn	PROPN
iajs-400	521	12	al	al	PROPN
iajs-400	521	13	-	-	PUNCT
iajs-400	521	14	haitham	haitham	PROPN
iajs-400	521	15	jour	jour	X
iajs-400	521	16	.	.	PROPN
iajs-400	522	1	for	for	ADP
iajs-400	522	2	pure	pure	ADJ
iajs-400	522	3	&	&	CCONJ
iajs-400	522	4	appl	appl	PROPN
iajs-400	522	5	.	.	PUNCT
iajs-400	523	1	sci	sci	PROPN
iajs-400	523	2	.	.	PUNCT
iajs-400	523	3	vol	vol	NOUN
iajs-400	523	4	.	.	PROPN
iajs-400	524	1	27	27	NUM
iajs-400	524	2	(	(	PUNCT
iajs-400	524	3	1	1	NUM
iajs-400	524	4	)	)	PUNCT
iajs-400	524	5	2014	2014	NUM
iajs-400	524	6	references	reference	NOUN
iajs-400	524	7	1	1	NUM
iajs-400	524	8	.	.	PUNCT
iajs-400	525	1	tong	tong	PROPN
iajs-400	525	2	,	,	PUNCT
iajs-400	525	3	j.	j.	PROPN
iajs-400	525	4	(	(	PUNCT
iajs-400	525	5	1982	1982	NUM
iajs-400	525	6	)	)	PUNCT
iajs-400	525	7	a	a	DET
iajs-400	525	8	separation	separation	NOUN
iajs-400	525	9	axioms	axiom	VERB
iajs-400	525	10	between	between	ADP
iajs-400	525	11	0	0	NUM
iajs-400	525	12	t	t	NOUN
iajs-400	525	13	and	and	CCONJ
iajs-400	525	14	1	1	NUM
iajs-400	525	15	t	t	NOUN
iajs-400	525	16	,	,	PUNCT
iajs-400	525	17	ann	ann	PROPN
iajs-400	525	18	.	.	PROPN
iajs-400	525	19	soc	soc	PROPN
iajs-400	525	20	.	.	PUNCT
iajs-400	526	1	sci	sci	PROPN
iajs-400	526	2	.	.	PUNCT
iajs-400	527	1	bruxelles	bruxelles	PROPN
iajs-400	527	2	96	96	NUM
iajs-400	527	3	ii,8590	ii,8590	NOUN
iajs-400	527	4	.	.	PUNCT
iajs-400	528	1	2	2	X
iajs-400	528	2	.	.	NUM
iajs-400	528	3	calads	calad	NOUN
iajs-400	528	4	,	,	PUNCT
iajs-400	528	5	m.	m.	NOUN
iajs-400	528	6	(	(	PUNCT
iajs-400	528	7	1997	1997	NUM
iajs-400	528	8	)	)	PUNCT
iajs-400	528	9	a	a	DET
iajs-400	528	10	separation	separation	NOUN
iajs-400	528	11	axioms	axiom	NOUN
iajs-400	528	12	between	between	ADP
iajs-400	528	13	semi0	semi0	PROPN
iajs-400	528	14	t	t	PROPN
iajs-400	528	15	and	and	CCONJ
iajs-400	528	16	semi1	semi1	PROPN
iajs-400	528	17	t	t	PROPN
iajs-400	528	18	,	,	PUNCT
iajs-400	528	19	mem	mem	PROPN
iajs-400	528	20	.	.	PUNCT
iajs-400	529	1	fac	fac	PROPN
iajs-400	529	2	.	.	PUNCT
iajs-400	530	1	sci	sci	PROPN
iajs-400	530	2	.	.	PROPN
iajs-400	530	3	kochi	kochi	PROPN
iajs-400	530	4	univ	univ	PROPN
iajs-400	530	5	.	.	PUNCT
iajs-400	531	1	ser	ser	PROPN
iajs-400	531	2	.	.	PUNCT
iajs-400	532	1	a	a	DET
iajs-400	532	2	math	math	NOUN
iajs-400	532	3	.	.	PUNCT
iajs-400	533	1	181,37	181,37	NUM
iajs-400	533	2	-	-	PUNCT
iajs-400	533	3	42	42	NUM
iajs-400	533	4	.	.	PUNCT
iajs-400	534	1	3	3	X
iajs-400	534	2	.	.	NUM
iajs-400	534	3	calads	calad	NOUN
iajs-400	534	4	,	,	PUNCT
iajs-400	534	5	m.	m.	NOUN
iajs-400	534	6	;	;	PUNCT
iajs-400	534	7	georgiou	georgiou	PROPN
iajs-400	534	8	,	,	PUNCT
iajs-400	534	9	d.n	d.n	PROPN
iajs-400	534	10	.	.	PROPN
iajs-400	534	11	and	and	CCONJ
iajs-400	534	12	jafari	jafari	PROPN
iajs-400	534	13	,	,	PUNCT
iajs-400	534	14	s.	s.	PROPN
iajs-400	534	15	(	(	PUNCT
iajs-400	534	16	2003	2003	NUM
iajs-400	534	17	)	)	PUNCT
iajs-400	534	18	characterization	characterization	NOUN
iajs-400	534	19	of	of	ADP
iajs-400	534	20	low	low	ADJ
iajs-400	534	21	separation	separation	NOUN
iajs-400	534	22	axioms	axiom	NOUN
iajs-400	534	23	via	via	ADP
iajs-400	534	24	α	α	NOUN
iajs-400	534	25	-open	-open	NOUN
iajs-400	534	26	sets	set	NOUN
iajs-400	534	27	and	and	CCONJ
iajs-400	534	28	α	α	NOUN
iajs-400	534	29	-closure	-closure	NOUN
iajs-400	534	30	operator	operator	NOUN
iajs-400	534	31	,	,	PUNCT
iajs-400	534	32	bol	bol	NOUN
iajs-400	534	33	.	.	PUNCT
iajs-400	535	1	soc	soc	PROPN
iajs-400	535	2	.	.	PUNCT
iajs-400	536	1	paran	paran	PROPN
iajs-400	536	2	.	.	PUNCT
iajs-400	536	3	mat.(3s	mat.(3s	PROPN
iajs-400	536	4	)	)	PUNCT
iajs-400	536	5	,	,	PUNCT
iajs-400	536	6	21(1/2	21(1/2	NUM
iajs-400	536	7	)	)	PUNCT
iajs-400	536	8	,	,	PUNCT
iajs-400	536	9	1	1	NUM
iajs-400	536	10	-	-	SYM
iajs-400	536	11	14	14	NUM
iajs-400	536	12	.	.	PUNCT
iajs-400	537	1	4	4	X
iajs-400	537	2	.	.	X
iajs-400	537	3	jafari	jafari	PROPN
iajs-400	537	4	,	,	PUNCT
iajs-400	537	5	s.	s.	PROPN
iajs-400	537	6	on	on	ADP
iajs-400	537	7	a	a	DET
iajs-400	537	8	weak	weak	ADJ
iajs-400	537	9	separation	separation	NOUN
iajs-400	537	10	axioms	axiom	NOUN
iajs-400	537	11	,	,	PUNCT
iajs-400	537	12	far	far	PROPN
iajs-400	537	13	east	east	PROPN
iajs-400	537	14	j.	j.	PROPN
iajs-400	537	15	math	math	PROPN
iajs-400	537	16	.	.	PUNCT
iajs-400	538	1	sci	sci	PROPN
iajs-400	538	2	.	.	PUNCT
iajs-400	539	1	(	(	PUNCT
iajs-400	539	2	to	to	PART
iajs-400	539	3	appear	appear	VERB
iajs-400	539	4	)	)	PUNCT
iajs-400	539	5	.	.	PUNCT
iajs-400	540	1	5	5	X
iajs-400	540	2	.	.	X
iajs-400	540	3	keskin	keskin	PROPN
iajs-400	540	4	,	,	PUNCT
iajs-400	540	5	a.	a.	NOUN
iajs-400	540	6	and	and	CCONJ
iajs-400	540	7	noiri	noiri	PROPN
iajs-400	540	8	,	,	PUNCT
iajs-400	540	9	t.	t.	PROPN
iajs-400	540	10	(	(	PUNCT
iajs-400	540	11	2009	2009	NUM
iajs-400	540	12	)	)	PUNCT
iajs-400	540	13	on	on	ADP
iajs-400	540	14	bd	bd	NOUN
iajs-400	540	15	-	-	PUNCT
iajs-400	540	16	sets	set	NOUN
iajs-400	540	17	and	and	CCONJ
iajs-400	540	18	associated	associated	ADJ
iajs-400	540	19	separation	separation	NOUN
iajs-400	540	20	axioms	axiom	NOUN
iajs-400	540	21	,	,	PUNCT
iajs-400	540	22	bulletin	bulletin	NOUN
iajs-400	540	23	of	of	ADP
iajs-400	540	24	the	the	DET
iajs-400	540	25	iranian	iranian	ADJ
iajs-400	540	26	math	math	PROPN
iajs-400	540	27	.	.	PUNCT
iajs-400	541	1	soc	soc	NOUN
iajs-400	541	2	.	.	PUNCT
iajs-400	542	1	35,1,179	35,1,179	NUM
iajs-400	542	2	-	-	SYM
iajs-400	542	3	198	198	NUM
iajs-400	542	4	.	.	PUNCT
iajs-400	543	1	6	6	NUM
iajs-400	543	2	.	.	X
iajs-400	543	3	khan	khan	PROPN
iajs-400	543	4	,	,	PUNCT
iajs-400	543	5	m.	m.	NOUN
iajs-400	543	6	;	;	PUNCT
iajs-400	543	7	noiri	noiri	PROPN
iajs-400	543	8	,	,	PUNCT
iajs-400	543	9	t	t	PROPN
iajs-400	543	10	.	.	PUNCT
iajs-400	543	11	and	and	CCONJ
iajs-400	543	12	hussain	hussain	PROPN
iajs-400	543	13	,	,	PUNCT
iajs-400	543	14	m	m	NOUN
iajs-400	543	15	.(2008	.(2008	NOUN
iajs-400	543	16	)	)	PUNCT
iajs-400	543	17	on	on	ADP
iajs-400	543	18	s*g	s*g	NOUN
iajs-400	543	19	-	-	PUNCT
iajs-400	543	20	closed	close	VERB
iajs-400	543	21	sets	set	NOUN
iajs-400	543	22	and	and	CCONJ
iajs-400	543	23	s*-normal	s*-normal	ADJ
iajs-400	543	24	spaces	space	NOUN
iajs-400	543	25	,	,	PUNCT
iajs-400	543	26	48	48	NUM
iajs-400	543	27	,	,	PUNCT
iajs-400	543	28	31	31	NUM
iajs-400	543	29	-	-	SYM
iajs-400	543	30	41	41	NUM
iajs-400	543	31	.	.	PUNCT
iajs-400	544	1	7	7	X
iajs-400	544	2	.	.	X
iajs-400	544	3	levine	levine	PROPN
iajs-400	544	4	,	,	PUNCT
iajs-400	544	5	n.	n.	PROPN
iajs-400	544	6	(	(	PUNCT
iajs-400	544	7	1963	1963	NUM
iajs-400	544	8	)	)	PUNCT
iajs-400	544	9	semi	semi	ADJ
iajs-400	544	10	-	-	ADJ
iajs-400	544	11	open	open	ADJ
iajs-400	544	12	sets	set	NOUN
iajs-400	544	13	and	and	CCONJ
iajs-400	544	14	semi	semi	ADJ
iajs-400	544	15	-	-	NOUN
iajs-400	544	16	continuity	continuity	NOUN
iajs-400	544	17	in	in	ADP
iajs-400	544	18	topological	topological	ADJ
iajs-400	544	19	spaces	space	NOUN
iajs-400	544	20	,	,	PUNCT
iajs-400	544	21	amer	amer	PROPN
iajs-400	544	22	.	.	PROPN
iajs-400	544	23	math	math	PROPN
iajs-400	544	24	.	.	PUNCT
iajs-400	545	1	monthly	monthly	ADJ
iajs-400	545	2	70	70	NUM
iajs-400	545	3	,	,	PUNCT
iajs-400	545	4	36	36	NUM
iajs-400	545	5	-	-	SYM
iajs-400	545	6	41	41	NUM
iajs-400	545	7	.	.	PUNCT
iajs-400	546	1	8	8	X
iajs-400	546	2	.	.	X
iajs-400	547	1	njastad	njastad	NOUN
iajs-400	547	2	,	,	PUNCT
iajs-400	547	3	o.	o.	PROPN
iajs-400	547	4	(	(	PUNCT
iajs-400	547	5	1965	1965	NUM
iajs-400	547	6	)	)	PUNCT
iajs-400	547	7	on	on	ADP
iajs-400	547	8	some	some	DET
iajs-400	547	9	classes	class	NOUN
iajs-400	547	10	of	of	ADP
iajs-400	547	11	nearly	nearly	ADV
iajs-400	547	12	open	open	ADJ
iajs-400	547	13	sets	set	NOUN
iajs-400	547	14	,	,	PUNCT
iajs-400	547	15	pacific	pacific	PROPN
iajs-400	547	16	j.	j.	PROPN
iajs-400	547	17	math	math	PROPN
iajs-400	547	18	.	.	PUNCT
iajs-400	548	1	15	15	NUM
iajs-400	548	2	,	,	PUNCT
iajs-400	548	3	961	961	NUM
iajs-400	548	4	-	-	SYM
iajs-400	548	5	970	970	NUM
iajs-400	548	6	.	.	PUNCT
iajs-400	549	1	9	9	X
iajs-400	549	2	.	.	X
iajs-400	550	1	mashhour	mashhour	PROPN
iajs-400	550	2	,	,	PUNCT
iajs-400	550	3	a.s	a.s	PROPN
iajs-400	550	4	.	.	PROPN
iajs-400	550	5	;	;	PUNCT
iajs-400	550	6	abd	abd	PROPN
iajs-400	550	7	el	el	PROPN
iajs-400	550	8	-	-	PUNCT
iajs-400	550	9	monsef	monsef	ADJ
iajs-400	550	10	,	,	PUNCT
iajs-400	550	11	m.e	m.e	PROPN
iajs-400	550	12	.	.	PROPN
iajs-400	550	13	and	and	CCONJ
iajs-400	550	14	el	el	PROPN
iajs-400	550	15	-	-	PUNCT
iajs-400	550	16	deeb	deeb	PROPN
iajs-400	550	17	,	,	PUNCT
iajs-400	550	18	s.n	s.n	PROPN
iajs-400	550	19	.	.	PROPN
iajs-400	550	20	(	(	PUNCT
iajs-400	550	21	1982	1982	NUM
iajs-400	550	22	)	)	PUNCT
iajs-400	550	23	on	on	ADP
iajs-400	550	24	precontinuous	precontinuous	ADJ
iajs-400	550	25	and	and	CCONJ
iajs-400	550	26	weak	weak	ADJ
iajs-400	550	27	precontinuous	precontinuous	ADJ
iajs-400	550	28	functions	function	NOUN
iajs-400	550	29	,	,	PUNCT
iajs-400	550	30	proc	proc	NOUN
iajs-400	550	31	.	.	PUNCT
iajs-400	551	1	math	math	NOUN
iajs-400	551	2	.	.	PUNCT
iajs-400	552	1	phys	phy	NOUN
iajs-400	552	2	.	.	PUNCT
iajs-400	553	1	soc	soc	PROPN
iajs-400	553	2	.	.	PUNCT
iajs-400	554	1	egypt	egypt	PROPN
iajs-400	554	2	51	51	NUM
iajs-400	554	3	,	,	PUNCT
iajs-400	554	4	47	47	NUM
iajs-400	554	5	-	-	SYM
iajs-400	554	6	53	53	NUM
iajs-400	554	7	.	.	PUNCT
iajs-400	554	8	10	10	NUM
iajs-400	554	9	.	.	PUNCT
iajs-400	555	1	andrijevic	andrijevic	PROPN
iajs-400	555	2	,	,	PUNCT
iajs-400	555	3	d.	d.	PROPN
iajs-400	555	4	(	(	PUNCT
iajs-400	555	5	1996	1996	NUM
iajs-400	555	6	)	)	PUNCT
iajs-400	555	7	on	on	ADP
iajs-400	555	8	b	b	X
iajs-400	555	9	-	-	PUNCT
iajs-400	555	10	open	open	ADJ
iajs-400	555	11	sets	set	NOUN
iajs-400	555	12	,	,	PUNCT
iajs-400	555	13	mat	mat	X
iajs-400	555	14	.	.	PROPN
iajs-400	555	15	vesnik	vesnik	PROPN
iajs-400	555	16	,	,	PUNCT
iajs-400	555	17	48	48	NUM
iajs-400	555	18	(	(	PUNCT
iajs-400	555	19	1	1	NUM
iajs-400	555	20	-	-	SYM
iajs-400	555	21	2	2	NUM
iajs-400	555	22	)	)	PUNCT
iajs-400	555	23	,	,	PUNCT
iajs-400	555	24	59	59	NUM
iajs-400	555	25	-	-	SYM
iajs-400	555	26	64	64	NUM
iajs-400	555	27	.	.	PUNCT
iajs-400	556	1	11	11	NUM
iajs-400	556	2	.	.	X
iajs-400	557	1	abd	abd	PROPN
iajs-400	557	2	el	el	PROPN
iajs-400	557	3	-	-	PUNCT
iajs-400	557	4	monsef	monsef	ADJ
iajs-400	557	5	,	,	PUNCT
iajs-400	557	6	m.e	m.e	PROPN
iajs-400	557	7	.	.	PROPN
iajs-400	557	8	;	;	PUNCT
iajs-400	557	9	el	el	PROPN
iajs-400	557	10	-	-	PUNCT
iajs-400	557	11	deeb	deeb	PROPN
iajs-400	557	12	,	,	PUNCT
iajs-400	557	13	s.n	s.n	PROPN
iajs-400	557	14	.	.	PROPN
iajs-400	557	15	and	and	CCONJ
iajs-400	557	16	mahmoud	mahmoud	PROPN
iajs-400	557	17	,	,	PUNCT
iajs-400	557	18	r.a	r.a	PROPN
iajs-400	557	19	.	.	PROPN
iajs-400	557	20	(	(	PUNCT
iajs-400	557	21	1983	1983	NUM
iajs-400	557	22	)	)	PUNCT
iajs-400	557	23	β	β	X
iajs-400	557	24	-open	-open	NOUN
iajs-400	557	25	sets	set	NOUN
iajs-400	557	26	andβ	andβ	ADP
iajs-400	557	27	continuous	continuous	ADJ
iajs-400	557	28	mappings	mapping	NOUN
iajs-400	557	29	,	,	PUNCT
iajs-400	557	30	bull	bull	NOUN
iajs-400	557	31	.	.	PUNCT
iajs-400	558	1	fac	fac	PROPN
iajs-400	558	2	.	.	PUNCT
iajs-400	559	1	sci	sci	PROPN
iajs-400	559	2	.	.	PUNCT
iajs-400	559	3	assuit	assuit	PROPN
iajs-400	559	4	univ	univ	PROPN
iajs-400	559	5	.	.	PROPN
iajs-400	560	1	12	12	NUM
iajs-400	560	2	,	,	PUNCT
iajs-400	560	3	77	77	NUM
iajs-400	560	4	-	-	SYM
iajs-400	560	5	90	90	NUM
iajs-400	560	6	.	.	PUNCT
iajs-400	561	1	12	12	NUM
iajs-400	561	2	.	.	X
iajs-400	562	1	veerakumar	veerakumar	PROPN
iajs-400	562	2	,	,	PUNCT
iajs-400	562	3	m.k.r.s	m.k.r.s	PROPN
iajs-400	562	4	.	.	PUNCT
iajs-400	563	1	(	(	PUNCT
iajs-400	563	2	2001	2001	NUM
iajs-400	563	3	)	)	PUNCT
iajs-400	563	4	ĝ	ĝ	PROPN
iajs-400	563	5	-closed	-close	VERB
iajs-400	563	6	sets	set	NOUN
iajs-400	563	7	and	and	CCONJ
iajs-400	563	8	g	g	NOUN
iajs-400	563	9	l̂	l̂	NUM
iajs-400	563	10	c	c	NOUN
iajs-400	563	11	-	-	PUNCT
iajs-400	563	12	functions	function	NOUN
iajs-400	563	13	,	,	PUNCT
iajs-400	563	14	indian	indian	PROPN
iajs-400	563	15	j.math	j.math	NOUN
iajs-400	563	16	.	.	PROPN
iajs-400	563	17	,	,	PUNCT
iajs-400	563	18	43,2	43,2	NOUN
iajs-400	563	19	,	,	PUNCT
iajs-400	563	20	231	231	NUM
iajs-400	563	21	-	-	SYM
iajs-400	563	22	247	247	NUM
iajs-400	563	23	.	.	NOUN
iajs-400	563	24	13	13	NUM
iajs-400	563	25	.	.	PUNCT
iajs-400	564	1	kelly	kelly	PROPN
iajs-400	564	2	,	,	PUNCT
iajs-400	564	3	j.l.(1955	j.l.(1955	NOUN
iajs-400	564	4	)	)	PUNCT
iajs-400	564	5	general	general	ADJ
iajs-400	564	6	topology	topology	NOUN
iajs-400	564	7	,	,	PUNCT
iajs-400	564	8	van	van	PROPN
iajs-400	564	9	nostrand	nostrand	PROPN
iajs-400	564	10	,	,	PUNCT
iajs-400	564	11	new	new	PROPN
iajs-400	564	12	york	york	PROPN
iajs-400	564	13	.	.	PUNCT
iajs-400	565	1	14	14	NUM
iajs-400	565	2	.	.	PUNCT
iajs-400	566	1	s.i	s.i	PROPN
iajs-400	566	2	.	.	PROPN
iajs-400	566	3	and	and	CCONJ
iajs-400	566	4	afrah	afrah	PROPN
iajs-400	566	5	,	,	PUNCT
iajs-400	566	6	m	m	PROPN
iajs-400	566	7	.	.	PUNCT
iajs-400	567	1	(	(	PUNCT
iajs-400	567	2	2010	2010	NUM
iajs-400	567	3	)	)	PUNCT
iajs-400	567	4	s*-separation	s*-separation	NOUN
iajs-400	567	5	axioms	axiom	NOUN
iajs-400	567	6	,	,	PUNCT
iajs-400	567	7	iraqi	iraqi	ADJ
iajs-400	567	8	journal	journal	NOUN
iajs-400	567	9	of	of	ADP
iajs-400	567	10	science	science	NOUN
iajs-400	567	11	,	,	PUNCT
iajs-400	567	12	university	university	NOUN
iajs-400	567	13	of	of	ADP
iajs-400	567	14	baghdad	baghdad	PROPN
iajs-400	567	15	,	,	PUNCT
iajs-400	567	16	51	51	NUM
iajs-400	567	17	,	,	PUNCT
iajs-400	567	18	1	1	NUM
iajs-400	567	19	,	,	PUNCT
iajs-400	567	20	145	145	NUM
iajs-400	567	21	-	-	SYM
iajs-400	567	22	153	153	NUM
iajs-400	567	23	.	.	PUNCT
iajs-400	568	1	366	366	NUM
iajs-400	568	2	|	|	ADV
iajs-400	568	3	mathematics	mathematics	PROPN
iajs-400	568	4	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-400	568	5	�	�	NOUN
iajs-400	568	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-400	568	7	:	:	PUNCT
iajs-400	568	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-400	568	9	©	©	PROPN
iajs-400	568	10	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-400	568	11	ibn	ibn	PROPN
iajs-400	568	12	al	al	PROPN
iajs-400	568	13	-	-	PUNCT
iajs-400	568	14	haitham	haitham	PROPN
iajs-400	568	15	jour	jour	X
iajs-400	568	16	.	.	PROPN
iajs-400	569	1	for	for	ADP
iajs-400	569	2	pure	pure	ADJ
iajs-400	569	3	&	&	CCONJ
iajs-400	569	4	appl	appl	PROPN
iajs-400	569	5	.	.	PUNCT
iajs-400	570	1	sci	sci	PROPN
iajs-400	570	2	.	.	PUNCT
iajs-400	570	3	vol	vol	NOUN
iajs-400	570	4	.	.	PROPN
iajs-400	571	1	27	27	NUM
iajs-400	571	2	(	(	PUNCT
iajs-400	571	3	1	1	NUM
iajs-400	571	4	)	)	PUNCT
iajs-400	571	5	2014	2014	NUM
iajs-400	571	6	صل	صل	ADP
iajs-400	571	7	المشتقة	المشتقة	PROPN
iajs-400	571	8	منھافال	منھافال	PROPN
iajs-400	571	9	وبدیھیات	وبدیھیات	NOUN
iajs-400	571	10	الضعیفة	الضعیفة	VERB
iajs-400	571	11	g*sd	g*sd	PROPN
iajs-400	571	12	-	-	PUNCT
iajs-400	571	13	مجموعات	مجموعات	VERB
iajs-400	571	14	حول	حول	NOUN
iajs-400	571	15	ال	ال	ADP
iajs-400	571	16	صبیحة	صبیحة	PROPN
iajs-400	571	17	إبراھیم	إبراھیم	PROPN
iajs-400	572	1	محمود	محمود	PROPN
iajs-400	572	2	المستنصریةالجامعة	المستنصریةالجامعة	NOUN
iajs-400	572	3	-كلیة	-كلیة	NOUN
iajs-400	572	4	العلوم	العلوم	NOUN
iajs-400	572	5	-قسم	-قسم	PUNCT
iajs-400	572	6	الریاضیات	الریاضیات	VERB
iajs-400	572	7	2014شباط	2014شباط	NUM
iajs-400	572	8	19	19	NUM
iajs-400	572	9	:	:	SYM
iajs-400	572	10	،	،	PROPN
iajs-400	572	11	قبل	قبل	PROPN
iajs-400	572	12	البحث	البحث	VERB
iajs-400	572	13	في	في	ADP
iajs-400	572	14	2013ایلول	2013ایلول	ADJ
iajs-400	572	15	3أستلم	3أستلم	PROPN
iajs-400	572	16	البحث	البحث	NOUN
iajs-400	572	17	في	في	NOUN
iajs-400	572	18	:	:	PUNCT
iajs-400	572	19	الخالصة	الخالصة	PROPN
iajs-400	572	20	-المجموعات	-المجموعات	PROPN
iajs-400	572	21	,	,	PUNCT
iajs-400	572	22	g*sd	g*sd	PROPN
iajs-400	572	23	-بالمجموعات	-بالمجموعات	PROPN
iajs-400	572	24	اسمیناھا	اسمیناھا	NOUN
iajs-400	572	25	جدیدة	جدیدة	PROPN
iajs-400	572	26	من	من	PROPN
iajs-400	572	27	المجموعات	المجموعات	PROPN
iajs-400	572	28	اصناف	اصناف	NOUN
iajs-400	572	29	یمقدبت	یمقدبت	NOUN
iajs-400	572	30	قمنا	قمنا	ADP
iajs-400	572	31	في	في	ADP
iajs-400	573	1	ھذا	ھذا	NOUN
iajs-400	573	2	البحث	البحث	PROPN
iajs-400	573	3	g*sd	g*sd	PROPN
iajs-400	573	4	−α	−α	PROPN
iajs-400	573	5	-المجموعات	-المجموعات	PROPN
iajs-400	573	6	,	,	PUNCT
iajs-400	573	7	g*spred	g*spre	VERB
iajs-400	573	8	−	−	PROPN
iajs-400	573	9	g*sbd	g*sbd	NOUN
iajs-400	573	10	-المجموعات	-المجموعات	ADJ
iajs-400	573	11	,	,	PUNCT
iajs-400	573	12	-والمجموعات	-والمجموعات	NOUN
iajs-400	573	13	−	−	PROPN
iajs-400	573	14	g*s	g*s	PROPN
iajs-400	574	1	d	d	NOUN
iajs-400	574	2	−βھذه	−βھذه	NOUN
iajs-400	574	3	خواص	خواص	ADV
iajs-400	574	4	بعض	بعض	NOUN
iajs-400	574	5	درسنا	درسنا	ADV
iajs-400	574	6	.	.	PUNCT
iajs-400	575	1	كذلك	كذلك	PROPN
iajs-400	575	2	بعض	بعض	NOUN
iajs-400	575	3	بدیھیات	بدیھیات	VERB
iajs-400	575	4	الفصلوالعالقات	الفصلوالعالقات	PROPN
iajs-400	575	5	بینھم	بینھم	PROPN
iajs-400	575	6	.	.	PUNCT
iajs-400	576	1	فضال	فضال	PROPN
iajs-400	576	2	عن	عن	PROPN
iajs-400	576	3	ذلك	ذلك	PROPN
iajs-400	576	4	استخدمنا	استخدمنا	PROPN
iajs-400	576	5	ھذه	ھذه	VERB
iajs-400	576	6	المجموعات	المجموعات	PROPN
iajs-400	576	7	في	في	SCONJ
iajs-400	576	8	تعریف	تعریف	NOUN
iajs-400	576	9	ودراسھ	ودراسھ	VERB
iajs-400	576	10	المجموعات	المجموعات	PROPN
iajs-400	576	11	.	.	PUNCT
iajs-400	577	1	المشتقة	المشتقة	PROPN
iajs-400	577	2	منھا	منھا	VERB
iajs-400	577	3	i	i	PROPN
iajs-400	577	4	d	d	NOUN
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