id	sid	tid	token	lemma	pos
iajs-555	1	1	mathematics	mathematics	PROPN
iajs-555	1	2	377	377	NUM
iajs-555	1	3	مجلة	مجلة	NOUN
iajs-555	1	4	إبن	إبن	VERB
iajs-555	1	5	الهيثم	الهيثم	ADJ
iajs-555	1	6	للعلوم	للعلوم	NOUN
iajs-555	1	7	الصرفة	الصرفة	NOUN
iajs-555	2	1	و	و	PRON
iajs-555	2	2	التطبيقية	التطبيقية	ADJ
iajs-555	2	3	2012	2012	NUM
iajs-555	2	4	السنة	السنة	NOUN
iajs-555	2	5	25	25	NUM
iajs-555	2	6	المجلد	المجلد	NOUN
iajs-555	2	7	3	3	NUM
iajs-555	2	8	العدد	العدد	PROPN
iajs-555	2	9	ibn	ibn	PROPN
iajs-555	2	10	al	al	PROPN
iajs-555	2	11	-	-	PUNCT
iajs-555	2	12	haitham	haitham	PROPN
iajs-555	2	13	journal	journal	PROPN
iajs-555	2	14	for	for	ADP
iajs-555	2	15	pure	pure	ADJ
iajs-555	2	16	and	and	CCONJ
iajs-555	2	17	applied	apply	VERB
iajs-555	2	18	science	science	NOUN
iajs-555	2	19	no	no	NOUN
iajs-555	2	20	.	.	NOUN
iajs-555	2	21	3	3	NUM
iajs-555	2	22	vol	vol	NOUN
iajs-555	2	23	.	.	PUNCT
iajs-555	3	1	25	25	NUM
iajs-555	3	2	year	year	NOUN
iajs-555	3	3	2012	2012	NUM
iajs-555	3	4	on	on	ADP
iajs-555	3	5	generalized	generalize	VERB
iajs-555	3	6	regular	regular	ADJ
iajs-555	3	7	continuous	continuous	ADJ
iajs-555	3	8	functions	function	NOUN
iajs-555	3	9	in	in	ADP
iajs-555	3	10	topological	topological	ADJ
iajs-555	3	11	spaces	space	NOUN
iajs-555	3	12	s.	s.	PROPN
iajs-555	3	13	i.	i.	PROPN
iajs-555	3	14	mahmood	mahmood	PROPN
iajs-555	3	15	department	department	PROPN
iajs-555	3	16	of	of	ADP
iajs-555	3	17	mathematics	mathematics	PROPN
iajs-555	3	18	,	,	PUNCT
iajs-555	3	19	college	college	NOUN
iajs-555	3	20	of	of	ADP
iajs-555	3	21	science	science	PROPN
iajs-555	3	22	al	al	PROPN
iajs-555	3	23	-	-	PUNCT
iajs-555	3	24	mustansiriyah	mustansiriyah	NOUN
iajs-555	3	25	universityof	universityof	PROPN
iajs-555	3	26	baghdad	baghdad	PROPN
iajs-555	3	27	received	receive	VERB
iajs-555	3	28	in	in	ADP
iajs-555	3	29	:	:	PUNCT
iajs-555	3	30	30	30	NUM
iajs-555	3	31	january	january	PROPN
iajs-555	3	32	2012	2012	NUM
iajs-555	3	33	accepted	accept	VERB
iajs-555	3	34	in	in	ADP
iajs-555	3	35	:	:	PUNCT
iajs-555	3	36	21	21	NUM
iajs-555	3	37	may	may	PROPN
iajs-555	3	38	2012	2012	NUM
iajs-555	3	39	abstract	abstract	NOUN
iajs-555	3	40	in	in	ADP
iajs-555	3	41	this	this	DET
iajs-555	3	42	paper	paper	NOUN
iajs-555	3	43	we	we	PRON
iajs-555	3	44	introduce	introduce	VERB
iajs-555	3	45	a	a	DET
iajs-555	3	46	new	new	ADJ
iajs-555	3	47	type	type	NOUN
iajs-555	3	48	of	of	ADP
iajs-555	3	49	functions	function	NOUN
iajs-555	3	50	called	call	VERB
iajs-555	3	51	the	the	DET
iajs-555	3	52	generalized	generalized	ADJ
iajs-555	3	53	regular	regular	ADJ
iajs-555	3	54	continuous	continuous	ADJ
iajs-555	3	55	functions	function	NOUN
iajs-555	3	56	.these	.these	DET
iajs-555	3	57	functions	function	NOUN
iajs-555	3	58	are	be	AUX
iajs-555	3	59	weaker	weak	ADJ
iajs-555	3	60	than	than	ADP
iajs-555	3	61	regular	regular	ADJ
iajs-555	3	62	continuous	continuous	ADJ
iajs-555	3	63	functions	function	NOUN
iajs-555	3	64	and	and	CCONJ
iajs-555	3	65	stronger	strong	ADJ
iajs-555	3	66	than	than	ADP
iajs-555	3	67	regular	regular	ADJ
iajs-555	3	68	generalized	generalized	ADJ
iajs-555	3	69	continuous	continuous	ADJ
iajs-555	3	70	functions	function	NOUN
iajs-555	3	71	.	.	PUNCT
iajs-555	4	1	also	also	ADV
iajs-555	4	2	,	,	PUNCT
iajs-555	4	3	we	we	PRON
iajs-555	4	4	study	study	VERB
iajs-555	4	5	some	some	DET
iajs-555	4	6	characterizations	characterization	NOUN
iajs-555	4	7	and	and	CCONJ
iajs-555	4	8	basic	basic	ADJ
iajs-555	4	9	properties	property	NOUN
iajs-555	4	10	of	of	ADP
iajs-555	4	11	generalized	generalized	ADJ
iajs-555	4	12	regular	regular	ADJ
iajs-555	4	13	continuous	continuous	ADJ
iajs-555	4	14	functions	function	NOUN
iajs-555	4	15	.moreover	.moreover	SCONJ
iajs-555	4	16	we	we	PRON
iajs-555	4	17	study	study	VERB
iajs-555	4	18	another	another	DET
iajs-555	4	19	types	type	NOUN
iajs-555	4	20	of	of	ADP
iajs-555	4	21	generalized	generalized	ADJ
iajs-555	4	22	regular	regular	ADJ
iajs-555	4	23	continuous	continuous	ADJ
iajs-555	4	24	functions	function	NOUN
iajs-555	4	25	and	and	CCONJ
iajs-555	4	26	study	study	VERB
iajs-555	4	27	the	the	DET
iajs-555	4	28	relation	relation	NOUN
iajs-555	4	29	among	among	ADP
iajs-555	4	30	them	they	PRON
iajs-555	4	31	.	.	PUNCT
iajs-555	5	1	key	key	ADJ
iajs-555	5	2	words	word	NOUN
iajs-555	5	3	:	:	PUNCT
iajs-555	5	4	generalized	generalize	VERB
iajs-555	5	5	regular	regular	ADJ
iajs-555	5	6	continuous	continuous	ADJ
iajs-555	5	7	functions	function	NOUN
iajs-555	5	8	,	,	PUNCT
iajs-555	5	9	regular	regular	ADJ
iajs-555	5	10	continuous	continuous	ADJ
iajs-555	5	11	functions	function	NOUN
iajs-555	5	12	and	and	CCONJ
iajs-555	5	13	regular	regular	ADJ
iajs-555	5	14	generalized	generalized	ADJ
iajs-555	5	15	continuous	continuous	ADJ
iajs-555	5	16	functions	function	NOUN
iajs-555	5	17	.	.	PUNCT
iajs-555	6	1	introduction	introduction	NOUN
iajs-555	6	2	the	the	DET
iajs-555	6	3	concept	concept	NOUN
iajs-555	6	4	of	of	ADP
iajs-555	6	5	regular	regular	ADJ
iajs-555	6	6	continuous	continuous	ADJ
iajs-555	6	7	functions	function	NOUN
iajs-555	6	8	was	be	AUX
iajs-555	6	9	first	first	ADV
iajs-555	6	10	introduced	introduce	VERB
iajs-555	6	11	by	by	ADP
iajs-555	6	12	arya	arya	PROPN
iajs-555	6	13	,	,	PUNCT
iajs-555	6	14	s.p	s.p	PROPN
iajs-555	6	15	.	.	PROPN
iajs-555	6	16	and	and	CCONJ
iajs-555	6	17	gupta	gupta	PROPN
iajs-555	6	18	,	,	PUNCT
iajs-555	6	19	r.[1	r.[1	NOUN
iajs-555	6	20	]	]	PUNCT
iajs-555	6	21	.	.	PUNCT
iajs-555	7	1	later	later	ADV
iajs-555	7	2	palaniappan	palaniappan	PROPN
iajs-555	7	3	,	,	PUNCT
iajs-555	7	4	n.	n.	NOUN
iajs-555	7	5	and	and	CCONJ
iajs-555	7	6	rao	rao	PROPN
iajs-555	7	7	,	,	PUNCT
iajs-555	7	8	k.c.[2	k.c.[2	PROPN
iajs-555	7	9	]	]	PUNCT
iajs-555	7	10	studied	study	VERB
iajs-555	7	11	the	the	DET
iajs-555	7	12	concept	concept	NOUN
iajs-555	7	13	of	of	ADP
iajs-555	7	14	regular	regular	ADJ
iajs-555	7	15	generalized	generalized	ADJ
iajs-555	7	16	continuous	continuous	ADJ
iajs-555	7	17	functions	function	NOUN
iajs-555	7	18	.	.	PUNCT
iajs-555	8	1	also	also	ADV
iajs-555	8	2	,	,	PUNCT
iajs-555	8	3	the	the	DET
iajs-555	8	4	concept	concept	NOUN
iajs-555	8	5	of	of	ADP
iajs-555	8	6	generalized	generalized	ADJ
iajs-555	8	7	regular	regular	ADJ
iajs-555	8	8	closed	closed	ADJ
iajs-555	8	9	sets	set	NOUN
iajs-555	8	10	in	in	ADP
iajs-555	8	11	topological	topological	ADJ
iajs-555	8	12	spaces	space	NOUN
iajs-555	8	13	was	be	AUX
iajs-555	8	14	introduced	introduce	VERB
iajs-555	8	15	by	by	ADP
iajs-555	8	16	bhattacharya	bhattacharya	NOUN
iajs-555	8	17	,	,	PUNCT
iajs-555	8	18	s.[3	s.[3	PROPN
iajs-555	8	19	]	]	PUNCT
iajs-555	8	20	.the	.the	PUNCT
iajs-555	9	1	purpose	purpose	NOUN
iajs-555	9	2	of	of	ADP
iajs-555	9	3	this	this	DET
iajs-555	9	4	paper	paper	NOUN
iajs-555	9	5	is	be	AUX
iajs-555	9	6	to	to	PART
iajs-555	9	7	introduce	introduce	VERB
iajs-555	9	8	a	a	DET
iajs-555	9	9	new	new	ADJ
iajs-555	9	10	class	class	NOUN
iajs-555	9	11	of	of	ADP
iajs-555	9	12	functions	function	NOUN
iajs-555	9	13	,	,	PUNCT
iajs-555	9	14	namely	namely	ADV
iajs-555	9	15	,	,	PUNCT
iajs-555	9	16	generalized	generalize	VERB
iajs-555	9	17	regular	regular	ADJ
iajs-555	9	18	continuous	continuous	ADJ
iajs-555	9	19	functions	function	NOUN
iajs-555	9	20	.	.	PUNCT
iajs-555	10	1	this	this	DET
iajs-555	10	2	class	class	NOUN
iajs-555	10	3	is	be	AUX
iajs-555	10	4	placed	place	VERB
iajs-555	10	5	properly	properly	ADV
iajs-555	10	6	between	between	ADP
iajs-555	10	7	the	the	DET
iajs-555	10	8	class	class	NOUN
iajs-555	10	9	of	of	ADP
iajs-555	10	10	regular	regular	ADJ
iajs-555	10	11	continuous	continuous	ADJ
iajs-555	10	12	functions	function	NOUN
iajs-555	10	13	and	and	CCONJ
iajs-555	10	14	the	the	DET
iajs-555	10	15	class	class	NOUN
iajs-555	10	16	of	of	ADP
iajs-555	10	17	regular	regular	ADJ
iajs-555	10	18	generalized	generalized	ADJ
iajs-555	10	19	continuous	continuous	ADJ
iajs-555	10	20	functions	function	NOUN
iajs-555	10	21	.	.	PUNCT
iajs-555	11	1	also	also	ADV
iajs-555	11	2	,	,	PUNCT
iajs-555	11	3	we	we	PRON
iajs-555	11	4	study	study	VERB
iajs-555	11	5	some	some	DET
iajs-555	11	6	characterizations	characterization	NOUN
iajs-555	11	7	and	and	CCONJ
iajs-555	11	8	basic	basic	ADJ
iajs-555	11	9	properties	property	NOUN
iajs-555	11	10	of	of	ADP
iajs-555	11	11	generalized	generalized	ADJ
iajs-555	11	12	regular	regular	ADJ
iajs-555	11	13	continuous	continuous	ADJ
iajs-555	11	14	functions	function	NOUN
iajs-555	11	15	.	.	PUNCT
iajs-555	12	1	moreover	moreover	ADV
iajs-555	12	2	we	we	PRON
iajs-555	12	3	study	study	VERB
iajs-555	12	4	the	the	DET
iajs-555	12	5	perfectly	perfectly	ADV
iajs-555	12	6	generalized	generalized	ADJ
iajs-555	12	7	regular	regular	ADJ
iajs-555	12	8	continuous	continuous	ADJ
iajs-555	12	9	functions	function	NOUN
iajs-555	12	10	,	,	PUNCT
iajs-555	12	11	contra	contra	PROPN
iajs-555	12	12	generalized	generalize	VERB
iajs-555	12	13	regular	regular	ADJ
iajs-555	12	14	continuous	continuous	ADJ
iajs-555	12	15	functions	function	NOUN
iajs-555	12	16	,	,	PUNCT
iajs-555	12	17	generalized	generalize	VERB
iajs-555	12	18	regular	regular	ADJ
iajs-555	12	19	irresolute	irresolute	ADJ
iajs-555	12	20	functions	function	NOUN
iajs-555	12	21	,	,	PUNCT
iajs-555	12	22	contra	contra	PROPN
iajs-555	12	23	generalized	generalize	VERB
iajs-555	12	24	regular	regular	ADJ
iajs-555	12	25	irresolute	irresolute	ADJ
iajs-555	12	26	functions	function	NOUN
iajs-555	12	27	and	and	CCONJ
iajs-555	12	28	we	we	PRON
iajs-555	12	29	study	study	VERB
iajs-555	12	30	the	the	DET
iajs-555	12	31	relation	relation	NOUN
iajs-555	12	32	among	among	ADP
iajs-555	12	33	them	they	PRON
iajs-555	12	34	.	.	PUNCT
iajs-555	13	1	throughout	throughout	ADP
iajs-555	13	2	this	this	DET
iajs-555	13	3	paper	paper	NOUN
iajs-555	13	4	)	)	PUNCT
iajs-555	13	5	,	,	PUNCT
iajs-555	13	6	x	x	X
iajs-555	13	7	(	(	PUNCT
iajs-555	13	8	τ	τ	X
iajs-555	13	9	,	,	PUNCT
iajs-555	13	10	)	)	PUNCT
iajs-555	13	11	,	,	PUNCT
iajs-555	13	12	y	y	PROPN
iajs-555	13	13	(	(	PUNCT
iajs-555	13	14	τ′	τ′	X
iajs-555	13	15	and	and	CCONJ
iajs-555	13	16	)	)	PUNCT
iajs-555	13	17	,	,	PUNCT
iajs-555	13	18	z	z	X
iajs-555	13	19	(	(	PUNCT
iajs-555	13	20	τ	τ	X
iajs-555	13	21	′′	′′	PROPN
iajs-555	13	22	(	(	PUNCT
iajs-555	13	23	or	or	CCONJ
iajs-555	13	24	simply	simply	ADV
iajs-555	13	25	x	x	SYM
iajs-555	13	26	,	,	PUNCT
iajs-555	13	27	y	y	PROPN
iajs-555	13	28	and	and	CCONJ
iajs-555	13	29	z	z	PROPN
iajs-555	13	30	)	)	PUNCT
iajs-555	13	31	represent	represent	VERB
iajs-555	13	32	nonempty	nonempty	ADJ
iajs-555	13	33	topological	topological	ADJ
iajs-555	13	34	spaces	space	NOUN
iajs-555	13	35	on	on	ADP
iajs-555	13	36	which	which	PRON
iajs-555	13	37	no	no	DET
iajs-555	13	38	separation	separation	NOUN
iajs-555	13	39	axioms	axiom	NOUN
iajs-555	13	40	are	be	AUX
iajs-555	13	41	assumed	assume	VERB
iajs-555	13	42	,	,	PUNCT
iajs-555	13	43	unless	unless	SCONJ
iajs-555	13	44	otherwise	otherwise	ADV
iajs-555	13	45	mentioned	mention	VERB
iajs-555	13	46	.when	.when	ADP
iajs-555	13	47	a	a	PRON
iajs-555	13	48	is	be	AUX
iajs-555	13	49	a	a	DET
iajs-555	13	50	subset	subset	NOUN
iajs-555	13	51	of	of	ADP
iajs-555	13	52	x	x	X
iajs-555	13	53	,	,	PUNCT
iajs-555	13	54	)	)	PUNCT
iajs-555	13	55	a(cl	a(cl	PROPN
iajs-555	13	56	,	,	PUNCT
iajs-555	13	57	a	a	PROPN
iajs-555	13	58	and	and	CCONJ
iajs-555	13	59	ca	can	AUX
iajs-555	13	60	denote	denote	VERB
iajs-555	13	61	the	the	DET
iajs-555	13	62	closure	closure	NOUN
iajs-555	13	63	,	,	PUNCT
iajs-555	13	64	the	the	DET
iajs-555	13	65	interior	interior	NOUN
iajs-555	13	66	and	and	CCONJ
iajs-555	13	67	the	the	DET
iajs-555	13	68	complement	complement	NOUN
iajs-555	13	69	of	of	ADP
iajs-555	13	70	a	a	DET
iajs-555	13	71	set	set	NOUN
iajs-555	13	72	a	a	DET
iajs-555	13	73	respectively	respectively	ADV
iajs-555	13	74	.	.	PUNCT
iajs-555	14	1	preliminaries	preliminary	NOUN
iajs-555	14	2	first	first	ADV
iajs-555	14	3	we	we	PRON
iajs-555	14	4	recall	recall	VERB
iajs-555	14	5	the	the	DET
iajs-555	14	6	following	follow	VERB
iajs-555	14	7	definitions	definition	NOUN
iajs-555	14	8	:	:	PUNCT
iajs-555	14	9	(	(	PUNCT
iajs-555	14	10	1.1)definition	1.1)definition	NUM
iajs-555	14	11	:	:	PUNCT
iajs-555	14	12	a	a	DET
iajs-555	14	13	subset	subset	NOUN
iajs-555	14	14	a	a	PRON
iajs-555	14	15	of	of	ADP
iajs-555	14	16	a	a	DET
iajs-555	14	17	topological	topological	ADJ
iajs-555	14	18	space	space	NOUN
iajs-555	14	19	x	x	PRON
iajs-555	14	20	is	be	AUX
iajs-555	14	21	said	say	VERB
iajs-555	14	22	to	to	PART
iajs-555	14	23	be	be	AUX
iajs-555	14	24	:	:	PUNCT
iajs-555	14	25	i	i	X
iajs-555	14	26	)	)	PUNCT
iajs-555	14	27	a	a	DET
iajs-555	14	28	generalized	generalize	VERB
iajs-555	14	29	closed	close	VERB
iajs-555	14	30	(	(	PUNCT
iajs-555	14	31	briefly	briefly	NOUN
iajs-555	14	32	g	g	NOUN
iajs-555	14	33	-	-	PUNCT
iajs-555	14	34	closed	closed	ADJ
iajs-555	14	35	)	)	PUNCT
iajs-555	14	36	set	set	NOUN
iajs-555	14	37	[	[	X
iajs-555	14	38	4	4	X
iajs-555	14	39	]	]	PUNCT
iajs-555	14	40	if	if	SCONJ
iajs-555	14	41	u)a(cl	u)a(cl	NUM
iajs-555	14	42	⊆	⊆	NUM
iajs-555	14	43	whenever	whenever	SCONJ
iajs-555	14	44	ua	ua	PROPN
iajs-555	14	45	⊆	⊆	NUM
iajs-555	14	46	and	and	CCONJ
iajs-555	14	47	u	u	NOUN
iajs-555	14	48	is	be	AUX
iajs-555	14	49	open	open	ADJ
iajs-555	14	50	in	in	ADP
iajs-555	14	51	x	x	X
iajs-555	14	52	.	.	PUNCT
iajs-555	15	1	ii	ii	PROPN
iajs-555	15	2	)	)	PUNCT
iajs-555	15	3	a	a	DET
iajs-555	15	4	regular	regular	ADJ
iajs-555	15	5	closed	closed	ADJ
iajs-555	15	6	(	(	PUNCT
iajs-555	15	7	briefly	briefly	ADV
iajs-555	15	8	r	r	NOUN
iajs-555	15	9	-	-	PUNCT
iajs-555	15	10	closed	closed	ADJ
iajs-555	15	11	)	)	PUNCT
iajs-555	15	12	set	set	NOUN
iajs-555	15	13	[	[	X
iajs-555	15	14	5	5	NUM
iajs-555	15	15	]	]	PUNCT
iajs-555	15	16	if	if	SCONJ
iajs-555	15	17	a))a(int(cl	a))a(int(cl	PROPN
iajs-555	15	18	=	=	PUNCT
iajs-555	15	19	.	.	PUNCT
iajs-555	16	1	mathematics	mathematic	NOUN
iajs-555	16	2	378	378	NUM
iajs-555	16	3	مجلة	مجلة	NOUN
iajs-555	16	4	إبن	إبن	VERB
iajs-555	16	5	الهيثم	الهيثم	ADJ
iajs-555	16	6	للعلوم	للعلوم	NOUN
iajs-555	16	7	الصرفة	الصرفة	NOUN
iajs-555	16	8	و	و	PRON
iajs-555	16	9	التطبيقية	التطبيقية	ADJ
iajs-555	16	10	2012	2012	NUM
iajs-555	16	11	السنة	السنة	NOUN
iajs-555	16	12	25	25	NUM
iajs-555	16	13	المجلد	المجلد	NOUN
iajs-555	16	14	3	3	NUM
iajs-555	16	15	العدد	العدد	PROPN
iajs-555	16	16	ibn	ibn	PROPN
iajs-555	16	17	al	al	PROPN
iajs-555	16	18	-	-	PUNCT
iajs-555	16	19	haitham	haitham	PROPN
iajs-555	16	20	journal	journal	PROPN
iajs-555	16	21	for	for	ADP
iajs-555	16	22	pure	pure	ADJ
iajs-555	16	23	and	and	CCONJ
iajs-555	16	24	applied	apply	VERB
iajs-555	16	25	science	science	NOUN
iajs-555	16	26	no	no	NOUN
iajs-555	16	27	.	.	NOUN
iajs-555	16	28	3	3	NUM
iajs-555	16	29	vol	vol	NOUN
iajs-555	16	30	.	.	PUNCT
iajs-555	17	1	25	25	NUM
iajs-555	17	2	year	year	NOUN
iajs-555	17	3	2012	2012	NUM
iajs-555	17	4	iii	iii	NOUN
iajs-555	17	5	)	)	PUNCT
iajs-555	17	6	a	a	DET
iajs-555	17	7	regular	regular	ADJ
iajs-555	17	8	generalized	generalize	VERB
iajs-555	17	9	closed	close	VERB
iajs-555	17	10	(	(	PUNCT
iajs-555	17	11	briefly	briefly	NOUN
iajs-555	17	12	rg	rg	NOUN
iajs-555	17	13	-	-	PUNCT
iajs-555	17	14	closed	closed	ADJ
iajs-555	17	15	)	)	PUNCT
iajs-555	17	16	set	set	NOUN
iajs-555	17	17	[	[	X
iajs-555	17	18	2	2	NUM
iajs-555	17	19	]	]	PUNCT
iajs-555	17	20	if	if	SCONJ
iajs-555	17	21	u)a(cl	u)a(cl	NUM
iajs-555	17	22	⊆	⊆	NUM
iajs-555	17	23	whenever	whenever	SCONJ
iajs-555	17	24	ua	ua	PROPN
iajs-555	17	25	⊆	⊆	NUM
iajs-555	17	26	and	and	CCONJ
iajs-555	17	27	u	u	NOUN
iajs-555	17	28	is	be	AUX
iajs-555	17	29	regular	regular	ADJ
iajs-555	17	30	open	open	ADJ
iajs-555	17	31	in	in	ADP
iajs-555	17	32	x	x	X
iajs-555	17	33	.	.	PUNCT
iajs-555	18	1	iv	iv	X
iajs-555	18	2	)	)	PUNCT
iajs-555	18	3	a	a	DET
iajs-555	18	4	generalized	generalized	ADJ
iajs-555	18	5	regular	regular	ADJ
iajs-555	18	6	closed	close	VERB
iajs-555	18	7	(	(	PUNCT
iajs-555	18	8	briefly	briefly	ADV
iajs-555	18	9	gr	gr	ADV
iajs-555	18	10	-	-	PUNCT
iajs-555	18	11	closed	closed	ADJ
iajs-555	18	12	)	)	PUNCT
iajs-555	18	13	set	set	NOUN
iajs-555	18	14	[	[	X
iajs-555	18	15	3	3	NUM
iajs-555	18	16	]	]	PUNCT
iajs-555	18	17	if	if	SCONJ
iajs-555	18	18	u)a(rcl	u)a(rcl	NUM
iajs-555	18	19	⊆	⊆	NUM
iajs-555	18	20	whenever	whenever	SCONJ
iajs-555	18	21	ua	ua	PROPN
iajs-555	18	22	⊆	⊆	NUM
iajs-555	18	23	and	and	CCONJ
iajs-555	18	24	u	u	NOUN
iajs-555	18	25	is	be	AUX
iajs-555	18	26	open	open	ADJ
iajs-555	18	27	in	in	ADP
iajs-555	18	28	x	x	PUNCT
iajs-555	18	29	,	,	PUNCT
iajs-555	18	30	where	where	SCONJ
iajs-555	18	31	}	}	PUNCT
iajs-555	18	32	xofsubsetclosedregularaisf	xofsubsetclosedregularaisf	PROPN
iajs-555	18	33	,	,	PUNCT
iajs-555	18	34	fa	fa	NOUN
iajs-555	18	35	:	:	PUNCT
iajs-555	18	36	f{)a(rcl	f{)a(rcl	PROPN
iajs-555	18	37	⊆=	⊆=	PROPN
iajs-555	18	38			PROPN
iajs-555	18	39	.	.	PUNCT
iajs-555	19	1	v	v	X
iajs-555	19	2	)	)	PUNCT
iajs-555	19	3	a	a	DET
iajs-555	19	4	b	b	X
iajs-555	19	5	-	-	PUNCT
iajs-555	19	6	closed	closed	ADJ
iajs-555	19	7	set	set	NOUN
iajs-555	20	1	[	[	X
iajs-555	20	2	6	6	NUM
iajs-555	20	3	]	]	PUNCT
iajs-555	20	4	if	if	SCONJ
iajs-555	20	5	a))a(int(cl))a(clint	a))a(int(cl))a(clint	PROPN
iajs-555	20	6	(	(	PUNCT
iajs-555	20	7	⊆	⊆	ADJ
iajs-555	20	8	.	.	PUNCT
iajs-555	21	1	vi	vi	X
iajs-555	21	2	)	)	PUNCT
iajs-555	21	3	a	a	DET
iajs-555	21	4	generalized	generalized	ADJ
iajs-555	21	5	b	b	NOUN
iajs-555	21	6	-	-	PUNCT
iajs-555	21	7	closed	closed	ADJ
iajs-555	21	8	(	(	PUNCT
iajs-555	21	9	briefly	briefly	ADV
iajs-555	21	10	gb	gb	ADV
iajs-555	21	11	-	-	PUNCT
iajs-555	21	12	closed	closed	ADJ
iajs-555	21	13	)	)	PUNCT
iajs-555	22	1	set	set	NOUN
iajs-555	22	2	[	[	X
iajs-555	22	3	7	7	X
iajs-555	22	4	]	]	PUNCT
iajs-555	22	5	if	if	SCONJ
iajs-555	22	6	u)a(bcl	u)a(bcl	NUM
iajs-555	22	7	⊆	⊆	NUM
iajs-555	22	8	whenever	whenever	SCONJ
iajs-555	22	9	ua	ua	PROPN
iajs-555	22	10	⊆	⊆	NUM
iajs-555	22	11	and	and	CCONJ
iajs-555	22	12	u	u	NOUN
iajs-555	22	13	is	be	AUX
iajs-555	22	14	open	open	ADJ
iajs-555	22	15	in	in	ADP
iajs-555	22	16	x	x	PUNCT
iajs-555	22	17	,	,	PUNCT
iajs-555	22	18	where	where	SCONJ
iajs-555	22	19	}	}	PUNCT
iajs-555	22	20	xofsubsetclosedbaisf	xofsubsetclosedbaisf	PROPN
iajs-555	22	21	,	,	PUNCT
iajs-555	22	22	fa	fa	PROPN
iajs-555	22	23	:	:	PUNCT
iajs-555	22	24	f{)a(bcl	f{)a(bcl	NOUN
iajs-555	22	25	−⊆=	−⊆=	NUM
iajs-555	22	26			PROPN
iajs-555	22	27	.	.	PUNCT
iajs-555	23	1	the	the	DET
iajs-555	23	2	complement	complement	NOUN
iajs-555	23	3	of	of	ADP
iajs-555	23	4	a	a	DET
iajs-555	23	5	g	g	NOUN
iajs-555	23	6	-	-	PUNCT
iajs-555	23	7	closed	closed	ADJ
iajs-555	23	8	(	(	PUNCT
iajs-555	23	9	resp	resp	NOUN
iajs-555	23	10	.	.	PUNCT
iajs-555	24	1	r	r	X
iajs-555	24	2	-	-	PUNCT
iajs-555	24	3	closed	closed	ADJ
iajs-555	24	4	,	,	PUNCT
iajs-555	24	5	rg	rg	NOUN
iajs-555	24	6	-	-	PUNCT
iajs-555	24	7	closed	closed	ADJ
iajs-555	24	8	,	,	PUNCT
iajs-555	24	9	gr	gr	PRON
iajs-555	24	10	-	-	PUNCT
iajs-555	24	11	closed	closed	ADJ
iajs-555	24	12	,	,	PUNCT
iajs-555	24	13	b	b	X
iajs-555	24	14	-	-	PUNCT
iajs-555	24	15	closed	closed	ADJ
iajs-555	24	16	,	,	PUNCT
iajs-555	24	17	gb	gb	ADV
iajs-555	24	18	-	-	PUNCT
iajs-555	24	19	closed	closed	ADJ
iajs-555	24	20	)	)	PUNCT
iajs-555	24	21	set	set	NOUN
iajs-555	24	22	is	be	AUX
iajs-555	24	23	called	call	VERB
iajs-555	24	24	a	a	DET
iajs-555	24	25	g	g	NOUN
iajs-555	24	26	-	-	PUNCT
iajs-555	24	27	open	open	ADJ
iajs-555	24	28	(	(	PUNCT
iajs-555	24	29	resp	resp	NOUN
iajs-555	24	30	.	.	PUNCT
iajs-555	25	1	r	r	X
iajs-555	25	2	-	-	PUNCT
iajs-555	25	3	open	open	ADJ
iajs-555	25	4	,	,	PUNCT
iajs-555	25	5	rg	rg	NOUN
iajs-555	25	6	-	-	PUNCT
iajs-555	25	7	open	open	ADJ
iajs-555	25	8	,	,	PUNCT
iajs-555	25	9	gr	gr	NOUN
iajs-555	25	10	-	-	NOUN
iajs-555	25	11	open	open	ADJ
iajs-555	25	12	,	,	PUNCT
iajs-555	25	13	b	b	X
iajs-555	25	14	-	-	PUNCT
iajs-555	25	15	open	open	ADJ
iajs-555	25	16	,	,	PUNCT
iajs-555	25	17	gb	gb	ADV
iajs-555	25	18	-	-	PUNCT
iajs-555	25	19	open	open	ADJ
iajs-555	25	20	)	)	PUNCT
iajs-555	25	21	set	set	VERB
iajs-555	25	22	.	.	PUNCT
iajs-555	26	1	remarks	remark	NOUN
iajs-555	26	2	:	:	PUNCT
iajs-555	26	3	1	1	X
iajs-555	26	4	)	)	PUNCT
iajs-555	26	5	closed	close	VERB
iajs-555	26	6	sets	set	NOUN
iajs-555	26	7	and	and	CCONJ
iajs-555	26	8	gr	gr	NUM
iajs-555	26	9	-	-	PUNCT
iajs-555	26	10	closed	closed	ADJ
iajs-555	26	11	sets	set	NOUN
iajs-555	26	12	are	be	AUX
iajs-555	26	13	in	in	ADP
iajs-555	26	14	general	general	ADJ
iajs-555	26	15	independent	independent	ADJ
iajs-555	26	16	.consider	.consider	NOUN
iajs-555	27	1	the	the	DET
iajs-555	27	2	following	follow	VERB
iajs-555	27	3	examples	example	NOUN
iajs-555	27	4	:	:	PUNCT
iajs-555	27	5	examples	example	NOUN
iajs-555	27	6	:	:	PUNCT
iajs-555	27	7	i)let	i)let	NOUN
iajs-555	27	8	}	}	PUNCT
iajs-555	27	9	c	c	NOUN
iajs-555	27	10	,	,	PUNCT
iajs-555	27	11	b	b	NOUN
iajs-555	27	12	,	,	PUNCT
iajs-555	27	13	a{x	a{x	VERB
iajs-555	27	14	=	=	PUNCT
iajs-555	27	15	and	and	CCONJ
iajs-555	27	16	}	}	PUNCT
iajs-555	27	17	}	}	PUNCT
iajs-555	27	18	c	c	X
iajs-555	27	19	,	,	PUNCT
iajs-555	27	20	b{},a{,,x	b{},a{,,x	PROPN
iajs-555	27	21	{	{	PUNCT
iajs-555	27	22	φ	φ	PROPN
iajs-555	27	23	=	=	PROPN
iajs-555	27	24	τ	τ	X
iajs-555	27	25	.	.	PUNCT
iajs-555	28	1	then	then	ADV
iajs-555	28	2	}	}	PUNCT
iajs-555	28	3	b{a	b{a	NOUN
iajs-555	28	4	=	=	PUNCT
iajs-555	28	5	is	be	AUX
iajs-555	28	6	a	a	DET
iajs-555	28	7	gr	gr	ADV
iajs-555	28	8	-	-	PUNCT
iajs-555	28	9	closed	closed	ADJ
iajs-555	28	10	set	set	NOUN
iajs-555	28	11	,	,	PUNCT
iajs-555	28	12	but	but	CCONJ
iajs-555	28	13	not	not	PART
iajs-555	28	14	closed	close	VERB
iajs-555	28	15	.	.	PUNCT
iajs-555	29	1	ii)let	ii)let	ADJ
iajs-555	29	2	}	}	PUNCT
iajs-555	29	3	c	c	X
iajs-555	29	4	,	,	PUNCT
iajs-555	29	5	b	b	PROPN
iajs-555	29	6	,	,	PUNCT
iajs-555	29	7	a{x	a{x	VERB
iajs-555	29	8	=	=	PUNCT
iajs-555	29	9	and	and	CCONJ
iajs-555	29	10	}	}	PUNCT
iajs-555	29	11	}	}	PUNCT
iajs-555	29	12	b{},c	b{},c	PROPN
iajs-555	29	13	,	,	PUNCT
iajs-555	29	14	b{},b	b{},b	PROPN
iajs-555	29	15	,	,	PUNCT
iajs-555	29	16	a{,,x	a{,,x	PROPN
iajs-555	29	17	{	{	PUNCT
iajs-555	29	18	φ	φ	PROPN
iajs-555	29	19	=	=	PROPN
iajs-555	29	20	τ	τ	X
iajs-555	29	21	.	.	PUNCT
iajs-555	30	1	then	then	ADV
iajs-555	30	2	}	}	PUNCT
iajs-555	30	3	c{a	c{a	NOUN
iajs-555	30	4	=	=	PRON
iajs-555	30	5	is	be	AUX
iajs-555	30	6	a	a	DET
iajs-555	30	7	closed	closed	ADJ
iajs-555	30	8	set	set	NOUN
iajs-555	30	9	,	,	PUNCT
iajs-555	30	10	but	but	CCONJ
iajs-555	30	11	not	not	PART
iajs-555	30	12	gr	gr	PRON
iajs-555	30	13	closed	closed	ADJ
iajs-555	30	14	.	.	PUNCT
iajs-555	31	1	2)every	2)every	NUM
iajs-555	31	2	gr	gr	NUM
iajs-555	31	3	-	-	PUNCT
iajs-555	31	4	closed	closed	ADJ
iajs-555	31	5	set	set	NOUN
iajs-555	31	6	is	be	AUX
iajs-555	31	7	a	a	DET
iajs-555	31	8	g	g	NOUN
iajs-555	31	9	-	-	PUNCT
iajs-555	31	10	closed	close	VERB
iajs-555	31	11	set	set	NOUN
iajs-555	31	12	,	,	PUNCT
iajs-555	31	13	but	but	CCONJ
iajs-555	31	14	the	the	DET
iajs-555	31	15	converse	converse	NOUN
iajs-555	31	16	in	in	ADP
iajs-555	31	17	general	general	ADJ
iajs-555	31	18	is	be	AUX
iajs-555	31	19	not	not	PART
iajs-555	31	20	true	true	ADJ
iajs-555	31	21	.in	.in	PUNCT
iajs-555	31	22	(	(	PUNCT
iajs-555	31	23	1	1	X
iajs-555	31	24	)	)	PUNCT
iajs-555	31	25	no.(ii	no.(ii	NOUN
iajs-555	31	26	)	)	PUNCT
iajs-555	31	27	,	,	PUNCT
iajs-555	31	28	}	}	PUNCT
iajs-555	31	29	c{a	c{a	NOUN
iajs-555	31	30	=	=	PRON
iajs-555	31	31	is	be	AUX
iajs-555	31	32	a	a	DET
iajs-555	31	33	g	g	NOUN
iajs-555	31	34	-	-	PUNCT
iajs-555	31	35	closed	close	VERB
iajs-555	31	36	set	set	NOUN
iajs-555	31	37	,	,	PUNCT
iajs-555	31	38	but	but	CCONJ
iajs-555	31	39	not	not	PART
iajs-555	31	40	gr	gr	ADV
iajs-555	31	41	-	-	PUNCT
iajs-555	31	42	closed	closed	ADJ
iajs-555	31	43	.	.	PUNCT
iajs-555	32	1	3)every	3)every	NUM
iajs-555	32	2	gr	gr	ADJ
iajs-555	32	3	-	-	PUNCT
iajs-555	32	4	closed	closed	ADJ
iajs-555	32	5	set	set	NOUN
iajs-555	32	6	is	be	AUX
iajs-555	32	7	a	a	DET
iajs-555	32	8	rg	rg	NOUN
iajs-555	32	9	-	-	PUNCT
iajs-555	32	10	closed	closed	ADJ
iajs-555	32	11	set	set	NOUN
iajs-555	32	12	,	,	PUNCT
iajs-555	32	13	but	but	CCONJ
iajs-555	32	14	the	the	DET
iajs-555	32	15	converse	converse	NOUN
iajs-555	32	16	in	in	ADP
iajs-555	32	17	general	general	ADJ
iajs-555	32	18	is	be	AUX
iajs-555	32	19	not	not	PART
iajs-555	32	20	true	true	ADJ
iajs-555	32	21	.in	.in	PUNCT
iajs-555	32	22	(	(	PUNCT
iajs-555	32	23	1	1	X
iajs-555	32	24	)	)	PUNCT
iajs-555	32	25	no.(ii	no.(ii	NOUN
iajs-555	32	26	)	)	PUNCT
iajs-555	32	27	,	,	PUNCT
iajs-555	32	28	}	}	PUNCT
iajs-555	32	29	c{a	c{a	NOUN
iajs-555	32	30	=	=	PRON
iajs-555	32	31	is	be	AUX
iajs-555	32	32	a	a	DET
iajs-555	32	33	rg	rg	NOUN
iajs-555	32	34	-	-	PUNCT
iajs-555	32	35	closed	closed	ADJ
iajs-555	32	36	set	set	NOUN
iajs-555	32	37	,	,	PUNCT
iajs-555	32	38	but	but	CCONJ
iajs-555	32	39	not	not	PART
iajs-555	32	40	gr	gr	ADV
iajs-555	32	41	-	-	PUNCT
iajs-555	32	42	closed	closed	ADJ
iajs-555	32	43	.	.	PUNCT
iajs-555	33	1	4)every	4)every	NUM
iajs-555	33	2	gr	gr	ADJ
iajs-555	33	3	-	-	PUNCT
iajs-555	33	4	closed	closed	ADJ
iajs-555	33	5	set	set	NOUN
iajs-555	33	6	is	be	AUX
iajs-555	33	7	a	a	DET
iajs-555	33	8	gb	gb	ADV
iajs-555	33	9	-	-	PUNCT
iajs-555	33	10	closed	close	VERB
iajs-555	33	11	set	set	NOUN
iajs-555	33	12	,	,	PUNCT
iajs-555	33	13	but	but	CCONJ
iajs-555	33	14	the	the	DET
iajs-555	33	15	converse	converse	NOUN
iajs-555	33	16	in	in	ADP
iajs-555	33	17	general	general	ADJ
iajs-555	33	18	is	be	AUX
iajs-555	33	19	not	not	PART
iajs-555	33	20	true	true	ADJ
iajs-555	33	21	.in	.in	PUNCT
iajs-555	33	22	(	(	PUNCT
iajs-555	33	23	1	1	X
iajs-555	33	24	)	)	PUNCT
iajs-555	33	25	no.(ii	no.(ii	NOUN
iajs-555	33	26	)	)	PUNCT
iajs-555	33	27	,	,	PUNCT
iajs-555	33	28	}	}	PUNCT
iajs-555	33	29	c{a	c{a	NOUN
iajs-555	33	30	=	=	PRON
iajs-555	33	31	is	be	AUX
iajs-555	33	32	a	a	DET
iajs-555	33	33	gb	gb	ADV
iajs-555	33	34	-	-	PUNCT
iajs-555	33	35	closed	close	VERB
iajs-555	33	36	set	set	NOUN
iajs-555	33	37	,	,	PUNCT
iajs-555	33	38	but	but	CCONJ
iajs-555	33	39	not	not	PART
iajs-555	33	40	gr	gr	ADV
iajs-555	33	41	-	-	PUNCT
iajs-555	33	42	closed	closed	ADJ
iajs-555	33	43	.	.	PUNCT
iajs-555	34	1	5)every	5)every	NUM
iajs-555	34	2	r	r	NOUN
iajs-555	34	3	-	-	PUNCT
iajs-555	34	4	closed	closed	ADJ
iajs-555	34	5	set	set	NOUN
iajs-555	34	6	is	be	AUX
iajs-555	34	7	a	a	DET
iajs-555	34	8	gr	gr	NOUN
iajs-555	34	9	-	-	PUNCT
iajs-555	34	10	closed(resp	closed(resp	PROPN
iajs-555	34	11	.	.	PUNCT
iajs-555	35	1	g	g	NOUN
iajs-555	35	2	-	-	PUNCT
iajs-555	35	3	closed	closed	ADJ
iajs-555	35	4	,	,	PUNCT
iajs-555	35	5	gb	gb	ADV
iajs-555	35	6	-	-	PUNCT
iajs-555	35	7	closed	closed	ADJ
iajs-555	35	8	,	,	PUNCT
iajs-555	35	9	rg	rg	NOUN
iajs-555	35	10	-	-	PUNCT
iajs-555	35	11	closed	closed	ADJ
iajs-555	35	12	)	)	PUNCT
iajs-555	35	13	set	set	NOUN
iajs-555	35	14	,	,	PUNCT
iajs-555	35	15	but	but	CCONJ
iajs-555	35	16	the	the	DET
iajs-555	35	17	converse	converse	NOUN
iajs-555	35	18	in	in	ADP
iajs-555	35	19	general	general	ADJ
iajs-555	35	20	is	be	AUX
iajs-555	35	21	not	not	PART
iajs-555	35	22	true	true	ADJ
iajs-555	35	23	.in(1)no.(i	.in(1)no.(i	NOUN
iajs-555	35	24	)	)	PUNCT
iajs-555	35	25	,	,	PUNCT
iajs-555	35	26	}	}	PUNCT
iajs-555	35	27	b{a	b{a	NOUN
iajs-555	35	28	=	=	PUNCT
iajs-555	35	29	is	be	AUX
iajs-555	35	30	a	a	DET
iajs-555	35	31	gr	gr	ADV
iajs-555	35	32	-	-	PUNCT
iajs-555	35	33	closed	closed	ADJ
iajs-555	35	34	(	(	PUNCT
iajs-555	35	35	resp	resp	NOUN
iajs-555	35	36	.	.	PUNCT
iajs-555	36	1	g	g	NOUN
iajs-555	36	2	-	-	PUNCT
iajs-555	36	3	closed	closed	ADJ
iajs-555	36	4	,	,	PUNCT
iajs-555	36	5	gb	gb	ADV
iajs-555	36	6	-	-	PUNCT
iajs-555	36	7	closed	closed	ADJ
iajs-555	36	8	,	,	PUNCT
iajs-555	36	9	rg	rg	NOUN
iajs-555	36	10	-	-	PUNCT
iajs-555	36	11	closed	closed	ADJ
iajs-555	36	12	)	)	PUNCT
iajs-555	36	13	set	set	NOUN
iajs-555	36	14	,	,	PUNCT
iajs-555	36	15	but	but	CCONJ
iajs-555	36	16	not	not	PART
iajs-555	36	17	r	r	NOUN
iajs-555	36	18	-	-	PUNCT
iajs-555	36	19	closed	closed	ADJ
iajs-555	36	20	.	.	PUNCT
iajs-555	37	1	definition	definition	NOUN
iajs-555	37	2	:	:	PUNCT
iajs-555	37	3	the	the	DET
iajs-555	37	4	intersection	intersection	NOUN
iajs-555	37	5	of	of	ADP
iajs-555	37	6	all	all	DET
iajs-555	37	7	gr	gr	ADJ
iajs-555	37	8	-	-	PUNCT
iajs-555	37	9	closed	closed	ADJ
iajs-555	37	10	subsets	subset	NOUN
iajs-555	37	11	of	of	ADP
iajs-555	37	12	x	x	PUNCT
iajs-555	37	13	containing	contain	VERB
iajs-555	37	14	a	a	DET
iajs-555	37	15	set	set	NOUN
iajs-555	37	16	a	a	PRON
iajs-555	37	17	is	be	AUX
iajs-555	37	18	called	call	VERB
iajs-555	37	19	the	the	DET
iajs-555	37	20	generalized	generalized	ADJ
iajs-555	37	21	regular	regular	ADJ
iajs-555	37	22	-	-	PUNCT
iajs-555	37	23	closure	closure	NOUN
iajs-555	37	24	of	of	ADP
iajs-555	37	25	a	a	PRON
iajs-555	37	26	and	and	CCONJ
iajs-555	37	27	is	be	AUX
iajs-555	37	28	denoted	denote	VERB
iajs-555	37	29	by	by	ADP
iajs-555	37	30	grcl(a	grcl(a	NOUN
iajs-555	37	31	)	)	PUNCT
iajs-555	37	32	.	.	PUNCT
iajs-555	38	1	if	if	SCONJ
iajs-555	38	2	a	a	PRON
iajs-555	38	3	is	be	AUX
iajs-555	38	4	a	a	DET
iajs-555	38	5	gr	gr	ADJ
iajs-555	38	6	-	-	PUNCT
iajs-555	38	7	closed	closed	ADJ
iajs-555	38	8	set	set	NOUN
iajs-555	38	9	,	,	PUNCT
iajs-555	38	10	then	then	ADV
iajs-555	38	11	grcl(a	grcl(a	ADJ
iajs-555	38	12	)	)	PUNCT
iajs-555	38	13	=	=	VERB
iajs-555	38	14	a.	a.	NOUN
iajs-555	38	15	the	the	DET
iajs-555	38	16	converse	converse	NOUN
iajs-555	38	17	is	be	AUX
iajs-555	38	18	not	not	PART
iajs-555	38	19	true	true	ADJ
iajs-555	38	20	,	,	PUNCT
iajs-555	38	21	since	since	SCONJ
iajs-555	38	22	the	the	DET
iajs-555	38	23	intersection	intersection	NOUN
iajs-555	38	24	of	of	ADP
iajs-555	38	25	grclosed	grclose	VERB
iajs-555	38	26	sets	set	NOUN
iajs-555	38	27	need	need	AUX
iajs-555	38	28	not	not	PART
iajs-555	38	29	be	be	AUX
iajs-555	38	30	gr	gr	ADV
iajs-555	38	31	-	-	PUNCT
iajs-555	38	32	closed	closed	ADJ
iajs-555	38	33	.[3	.[3	NOUN
iajs-555	38	34	]	]	X
iajs-555	38	35	.	.	PUNCT
iajs-555	39	1	theorem	theorem	VERB
iajs-555	39	2	:	:	PUNCT
iajs-555	39	3	let	let	VERB
iajs-555	39	4	a	a	PRON
iajs-555	39	5	be	be	AUX
iajs-555	39	6	a	a	DET
iajs-555	39	7	subset	subset	NOUN
iajs-555	39	8	of	of	ADP
iajs-555	39	9	a	a	DET
iajs-555	39	10	topological	topological	ADJ
iajs-555	39	11	space	space	NOUN
iajs-555	39	12	x	x	NOUN
iajs-555	39	13	.then	.then	X
iajs-555	39	14	)	)	PUNCT
iajs-555	40	1	a(grclx∈	a(grclx∈	PROPN
iajs-555	40	2	if	if	SCONJ
iajs-555	40	3	and	and	CCONJ
iajs-555	40	4	only	only	ADV
iajs-555	40	5	if	if	SCONJ
iajs-555	40	6	for	for	ADP
iajs-555	40	7	any	any	DET
iajs-555	40	8	gr	gr	ADJ
iajs-555	40	9	-	-	PUNCT
iajs-555	40	10	open	open	ADJ
iajs-555	40	11	set	set	NOUN
iajs-555	40	12	u	u	NOUN
iajs-555	40	13	containing	contain	VERB
iajs-555	40	14	φ≠ua	φ≠ua	NOUN
iajs-555	40	15	,	,	PUNCT
iajs-555	40	16	x	x	SYM
iajs-555	40	17			PROPN
iajs-555	40	18	.	.	PUNCT
iajs-555	41	1	proof	proof	NOUN
iajs-555	41	2	:	:	PUNCT
iajs-555	41	3	⇒	⇒	NOUN
iajs-555	41	4	let	let	VERB
iajs-555	41	5	)	)	PUNCT
iajs-555	41	6	a(grclx∈	a(grclx∈	PROPN
iajs-555	41	7	and	and	CCONJ
iajs-555	41	8	suppose	suppose	VERB
iajs-555	41	9	that	that	SCONJ
iajs-555	41	10	,	,	PUNCT
iajs-555	41	11	there	there	PRON
iajs-555	41	12	is	be	VERB
iajs-555	41	13	a	a	DET
iajs-555	41	14	gr	gr	ADJ
iajs-555	41	15	-	-	PUNCT
iajs-555	41	16	open	open	ADJ
iajs-555	41	17	set	set	NOUN
iajs-555	41	18	u	u	NOUN
iajs-555	41	19	in	in	ADP
iajs-555	41	20	x	x	X
iajs-555	41	21	s.t	s.t	PROPN
iajs-555	41	22	ux∈	ux∈	PROPN
iajs-555	41	23	and	and	CCONJ
iajs-555	41	24	φ	φ	NUM
iajs-555	41	25	=	=	NOUN
iajs-555	41	26	ua	ua	X
iajs-555	41	27	cua	cua	X
iajs-555	41	28	⊂⇒	⊂⇒	NOUN
iajs-555	41	29	which	which	PRON
iajs-555	41	30	is	be	AUX
iajs-555	41	31	gr	gr	ADV
iajs-555	41	32	-	-	PUNCT
iajs-555	41	33	closed	closed	ADJ
iajs-555	41	34	in	in	ADP
iajs-555	41	35	x	x	X
iajs-555	41	36	⇒	⇒	NOUN
iajs-555	41	37	.u)u(grcl)a(grcl	.u)u(grcl)a(grcl	PUNCT
iajs-555	42	1	cc	cc	X
iajs-555	42	2	=	=	PROPN
iajs-555	42	3	⊆	⊆	NUM
iajs-555	42	4	ux∈	ux∈	ADJ
iajs-555	42	5	⇒	⇒	PROPN
iajs-555	42	6	cux∉	cux∉	PROPN
iajs-555	42	7	⇒	⇒	PROPN
iajs-555	42	8	)	)	PUNCT
iajs-555	43	1	a(grclx∉	a(grclx∉	PROPN
iajs-555	43	2	,	,	PUNCT
iajs-555	43	3	this	this	PRON
iajs-555	43	4	is	be	AUX
iajs-555	43	5	a	a	DET
iajs-555	43	6	contradiction	contradiction	NOUN
iajs-555	43	7	.	.	PUNCT
iajs-555	44	1	conversely	conversely	ADV
iajs-555	44	2	,	,	PUNCT
iajs-555	44	3	suppose	suppose	VERB
iajs-555	44	4	that	that	SCONJ
iajs-555	44	5	,	,	PUNCT
iajs-555	44	6	for	for	ADP
iajs-555	44	7	any	any	DET
iajs-555	44	8	gr	gr	ADJ
iajs-555	44	9	-	-	PUNCT
iajs-555	44	10	open	open	ADJ
iajs-555	44	11	set	set	NOUN
iajs-555	44	12	u	u	NOUN
iajs-555	44	13	containing	contain	VERB
iajs-555	44	14	x	x	PUNCT
iajs-555	44	15	,	,	PUNCT
iajs-555	44	16	φ≠ua	φ≠ua	NOUN
iajs-555	44	17			PROPN
iajs-555	44	18	.to	.to	PRON
iajs-555	44	19	prove	prove	VERB
iajs-555	44	20	that	that	PRON
iajs-555	44	21	)	)	PUNCT
iajs-555	44	22	a(grclx∈	a(grclx∈	PROPN
iajs-555	44	23	.	.	PUNCT
iajs-555	44	24	suppose	suppose	VERB
iajs-555	44	25	that	that	SCONJ
iajs-555	44	26	)	)	PUNCT
iajs-555	44	27	a(grclx∉	a(grclx∉	PROPN
iajs-555	44	28	,	,	PUNCT
iajs-555	44	29	then	then	ADV
iajs-555	44	30	there	there	PRON
iajs-555	44	31	is	be	VERB
iajs-555	44	32	a	a	DET
iajs-555	44	33	gr	gr	ADV
iajs-555	44	34	-	-	PUNCT
iajs-555	44	35	closed	closed	ADJ
iajs-555	44	36	set	set	NOUN
iajs-555	44	37	f	f	PROPN
iajs-555	44	38	in	in	ADP
iajs-555	44	39	x	x	PUNCT
iajs-555	44	40	such	such	ADJ
iajs-555	44	41	that	that	SCONJ
iajs-555	44	42	fx∉	fx∉	PROPN
iajs-555	44	43	and	and	CCONJ
iajs-555	44	44	fa	fa	NOUN
iajs-555	44	45	⊆	⊆	NUM
iajs-555	44	46	.	.	PUNCT
iajs-555	45	1	cfxfx	cfxfx	PROPN
iajs-555	45	2	∈⇒∉	∈⇒∉	PUNCT
iajs-555	45	3	which	which	PRON
iajs-555	45	4	is	be	AUX
iajs-555	45	5	gr	gr	ADV
iajs-555	45	6	-	-	NOUN
iajs-555	45	7	open	open	ADJ
iajs-555	45	8	in	in	ADP
iajs-555	45	9	x	x	X
iajs-555	45	10	.	.	PUNCT
iajs-555	45	11	φ=⇒⊆	φ=⇒⊆	PUNCT
iajs-555	45	12	cfafa	cfafa	VERB
iajs-555	45	13			PROPN
iajs-555	45	14	,	,	PUNCT
iajs-555	45	15	this	this	PRON
iajs-555	45	16	is	be	AUX
iajs-555	45	17	a	a	DET
iajs-555	45	18	contradiction	contradiction	NOUN
iajs-555	45	19	.	.	PUNCT
iajs-555	46	1	thus	thus	ADV
iajs-555	46	2	)	)	PUNCT
iajs-555	46	3	a(grclx∈	a(grclx∈	PROPN
iajs-555	46	4	.	.	PUNCT
iajs-555	47	1	definition	definition	NOUN
iajs-555	47	2	:	:	PUNCT
iajs-555	47	3	a	a	DET
iajs-555	47	4	function	function	NOUN
iajs-555	47	5	yx	yx	NOUN
iajs-555	47	6	:	:	PUNCT
iajs-555	47	7	f	f	PROPN
iajs-555	47	8	→	→	PUNCT
iajs-555	47	9	from	from	ADP
iajs-555	47	10	a	a	DET
iajs-555	47	11	topological	topological	ADJ
iajs-555	47	12	space	space	NOUN
iajs-555	47	13	x	x	PUNCT
iajs-555	47	14	into	into	ADP
iajs-555	47	15	a	a	DET
iajs-555	47	16	topological	topological	ADJ
iajs-555	47	17	space	space	NOUN
iajs-555	47	18	y	y	PROPN
iajs-555	47	19	is	be	AUX
iajs-555	47	20	called	call	VERB
iajs-555	47	21	:	:	PUNCT
iajs-555	47	22	1)a	1)a	NUM
iajs-555	47	23	generalized	generalize	VERB
iajs-555	47	24	continuous	continuous	ADJ
iajs-555	47	25	(	(	PUNCT
iajs-555	47	26	briefly	briefly	NOUN
iajs-555	47	27	g	g	NOUN
iajs-555	47	28	-	-	PUNCT
iajs-555	47	29	continuous)[8	continuous)[8	NUM
iajs-555	47	30	]	]	PUNCT
iajs-555	47	31	if	if	SCONJ
iajs-555	47	32	)	)	PUNCT
iajs-555	47	33	v(f	v(f	PROPN
iajs-555	47	34	1−	1−	NUM
iajs-555	47	35	is	be	AUX
iajs-555	47	36	g	g	NOUN
iajs-555	47	37	-	-	PUNCT
iajs-555	47	38	closed	close	VERB
iajs-555	47	39	set	set	NOUN
iajs-555	47	40	in	in	ADP
iajs-555	47	41	x	x	PUNCT
iajs-555	47	42	for	for	ADP
iajs-555	47	43	every	every	DET
iajs-555	47	44	closed	close	VERB
iajs-555	47	45	set	set	VERB
iajs-555	47	46	v	v	NOUN
iajs-555	47	47	in	in	ADP
iajs-555	47	48	y	y	PROPN
iajs-555	47	49	.	.	PUNCT
iajs-555	48	1	mathematics	mathematic	NOUN
iajs-555	48	2	379	379	NUM
iajs-555	48	3	مجلة	مجلة	PROPN
iajs-555	48	4	إبن	إبن	NOUN
iajs-555	48	5	الهيثم	الهيثم	ADJ
iajs-555	48	6	للعلوم	للعلوم	NOUN
iajs-555	48	7	الصرفة	الصرفة	NOUN
iajs-555	48	8	و	و	PRON
iajs-555	48	9	التطبيقية	التطبيقية	ADJ
iajs-555	48	10	2012	2012	NUM
iajs-555	48	11	السنة	السنة	NOUN
iajs-555	49	1	25	25	NUM
iajs-555	49	2	المجلد	المجلد	NOUN
iajs-555	49	3	3	3	NUM
iajs-555	49	4	العدد	العدد	PROPN
iajs-555	49	5	ibn	ibn	PROPN
iajs-555	49	6	al	al	PROPN
iajs-555	49	7	-	-	PUNCT
iajs-555	49	8	haitham	haitham	PROPN
iajs-555	49	9	journal	journal	PROPN
iajs-555	49	10	for	for	ADP
iajs-555	49	11	pure	pure	ADJ
iajs-555	49	12	and	and	CCONJ
iajs-555	49	13	applied	apply	VERB
iajs-555	49	14	science	science	NOUN
iajs-555	49	15	no	no	NOUN
iajs-555	49	16	.	.	NOUN
iajs-555	49	17	3	3	NUM
iajs-555	49	18	vol	vol	NOUN
iajs-555	49	19	.	.	PUNCT
iajs-555	49	20	25	25	NUM
iajs-555	49	21	year	year	NOUN
iajs-555	49	22	2012	2012	NUM
iajs-555	49	23	2)a	2)a	NUM
iajs-555	49	24	regular	regular	ADJ
iajs-555	49	25	generalized	generalized	ADJ
iajs-555	49	26	continuous	continuous	ADJ
iajs-555	49	27	(	(	PUNCT
iajs-555	49	28	briefly	briefly	NOUN
iajs-555	49	29	rg	rg	NOUN
iajs-555	49	30	-	-	PUNCT
iajs-555	49	31	continuous	continuous	ADJ
iajs-555	49	32	)	)	PUNCT
iajs-555	50	1	[	[	X
iajs-555	50	2	2	2	X
iajs-555	50	3	]	]	PUNCT
iajs-555	50	4	if	if	SCONJ
iajs-555	50	5	)	)	PUNCT
iajs-555	50	6	v(f	v(f	PROPN
iajs-555	50	7	1−	1−	NUM
iajs-555	50	8	is	be	AUX
iajs-555	50	9	rg	rg	NOUN
iajs-555	50	10	-	-	PUNCT
iajs-555	50	11	closed	close	VERB
iajs-555	50	12	set	set	NOUN
iajs-555	50	13	in	in	ADP
iajs-555	50	14	x	x	PUNCT
iajs-555	50	15	for	for	ADP
iajs-555	50	16	every	every	DET
iajs-555	50	17	closed	close	VERB
iajs-555	50	18	set	set	VERB
iajs-555	50	19	v	v	NOUN
iajs-555	50	20	in	in	ADP
iajs-555	50	21	y	y	PROPN
iajs-555	50	22	.	.	PUNCT
iajs-555	51	1	3)a	3)a	PROPN
iajs-555	51	2	regular	regular	ADJ
iajs-555	51	3	continuous	continuous	ADJ
iajs-555	51	4	(	(	PUNCT
iajs-555	51	5	briefly	briefly	NOUN
iajs-555	51	6	r	r	NOUN
iajs-555	51	7	-	-	PUNCT
iajs-555	51	8	continuous)[1	continuous)[1	NOUN
iajs-555	51	9	]	]	PUNCT
iajs-555	51	10	if	if	SCONJ
iajs-555	51	11	)	)	PUNCT
iajs-555	51	12	v(f	v(f	PROPN
iajs-555	51	13	1−	1−	NUM
iajs-555	51	14	is	be	AUX
iajs-555	51	15	r	r	NOUN
iajs-555	51	16	-	-	PUNCT
iajs-555	51	17	closed	closed	ADJ
iajs-555	51	18	set	set	NOUN
iajs-555	51	19	in	in	ADP
iajs-555	51	20	x	x	PUNCT
iajs-555	51	21	for	for	ADP
iajs-555	51	22	every	every	DET
iajs-555	51	23	closed	close	VERB
iajs-555	51	24	set	set	VERB
iajs-555	51	25	v	v	NOUN
iajs-555	51	26	in	in	ADP
iajs-555	51	27	y	y	PROPN
iajs-555	51	28	.	.	PUNCT
iajs-555	52	1	4	4	X
iajs-555	52	2	)	)	PUNCT
iajs-555	52	3	a	a	DET
iajs-555	52	4	generalized	generalized	ADJ
iajs-555	52	5	b	b	NOUN
iajs-555	52	6	-	-	ADJ
iajs-555	52	7	continuous	continuous	ADJ
iajs-555	52	8	(	(	PUNCT
iajs-555	52	9	briefly	briefly	NOUN
iajs-555	52	10	gb	gb	ADP
iajs-555	52	11	-	-	PUNCT
iajs-555	52	12	continuous)[9	continuous)[9	NUM
iajs-555	52	13	]	]	PUNCT
iajs-555	52	14	if	if	SCONJ
iajs-555	52	15	)	)	PUNCT
iajs-555	52	16	v(f	v(f	PROPN
iajs-555	52	17	1−	1−	NUM
iajs-555	52	18	is	be	AUX
iajs-555	52	19	gb	gb	ADV
iajs-555	52	20	-	-	PUNCT
iajs-555	52	21	closed	close	VERB
iajs-555	52	22	set	set	NOUN
iajs-555	52	23	in	in	ADP
iajs-555	52	24	x	x	PUNCT
iajs-555	52	25	for	for	ADP
iajs-555	52	26	every	every	DET
iajs-555	52	27	closed	close	VERB
iajs-555	52	28	set	set	VERB
iajs-555	52	29	v	v	NOUN
iajs-555	52	30	in	in	ADP
iajs-555	52	31	y	y	PROPN
iajs-555	52	32	.	.	PUNCT
iajs-555	53	1	5	5	X
iajs-555	53	2	)	)	PUNCT
iajs-555	53	3	a	a	DET
iajs-555	53	4	generalized	generalized	ADJ
iajs-555	53	5	irresolute	irresolute	NOUN
iajs-555	53	6	(	(	PUNCT
iajs-555	53	7	briefly	briefly	NOUN
iajs-555	53	8	g	g	NOUN
iajs-555	53	9	-	-	PUNCT
iajs-555	53	10	irresolute)[8	irresolute)[8	X
iajs-555	53	11	]	]	PUNCT
iajs-555	53	12	if	if	SCONJ
iajs-555	53	13	)	)	PUNCT
iajs-555	53	14	v(f	v(f	PROPN
iajs-555	53	15	1−	1−	NUM
iajs-555	53	16	is	be	AUX
iajs-555	53	17	g	g	NOUN
iajs-555	53	18	-	-	PUNCT
iajs-555	53	19	closed	close	VERB
iajs-555	53	20	set	set	NOUN
iajs-555	53	21	in	in	ADP
iajs-555	53	22	x	x	PUNCT
iajs-555	53	23	for	for	SCONJ
iajs-555	53	24	every	every	DET
iajs-555	53	25	g	g	NOUN
iajs-555	53	26	closed	close	VERB
iajs-555	53	27	set	set	VERB
iajs-555	53	28	v	v	NOUN
iajs-555	53	29	in	in	ADP
iajs-555	53	30	y	y	PROPN
iajs-555	53	31	.	.	PUNCT
iajs-555	54	1	6	6	X
iajs-555	54	2	)	)	PUNCT
iajs-555	54	3	a	a	DET
iajs-555	54	4	regular	regular	ADJ
iajs-555	54	5	generalized	generalized	ADJ
iajs-555	54	6	irresolute	irresolute	NOUN
iajs-555	54	7	(	(	PUNCT
iajs-555	54	8	briefly	briefly	NOUN
iajs-555	54	9	rg	rg	NOUN
iajs-555	54	10	-	-	PUNCT
iajs-555	54	11	irresolute	irresolute	NOUN
iajs-555	54	12	)	)	PUNCT
iajs-555	55	1	[	[	X
iajs-555	55	2	2	2	X
iajs-555	55	3	]	]	PUNCT
iajs-555	55	4	if	if	SCONJ
iajs-555	55	5	)	)	PUNCT
iajs-555	55	6	v(f	v(f	PROPN
iajs-555	55	7	1−	1−	NUM
iajs-555	55	8	is	be	AUX
iajs-555	55	9	rg	rg	NOUN
iajs-555	55	10	-	-	PUNCT
iajs-555	55	11	closed	close	VERB
iajs-555	55	12	set	set	NOUN
iajs-555	55	13	in	in	ADP
iajs-555	55	14	x	x	PUNCT
iajs-555	55	15	for	for	ADP
iajs-555	55	16	every	every	DET
iajs-555	55	17	rg	rg	NOUN
iajs-555	55	18	-	-	PUNCT
iajs-555	55	19	closed	closed	ADJ
iajs-555	55	20	set	set	VERB
iajs-555	55	21	v	v	NOUN
iajs-555	55	22	in	in	ADP
iajs-555	55	23	y	y	PROPN
iajs-555	55	24	.	.	PUNCT
iajs-555	56	1	generalized	generalize	VERB
iajs-555	56	2	regular	regular	ADJ
iajs-555	56	3	continuous	continuous	ADJ
iajs-555	56	4	functions	function	NOUN
iajs-555	56	5	in	in	ADP
iajs-555	56	6	this	this	DET
iajs-555	56	7	section	section	NOUN
iajs-555	56	8	we	we	PRON
iajs-555	56	9	introduce	introduce	VERB
iajs-555	56	10	the	the	DET
iajs-555	56	11	concept	concept	NOUN
iajs-555	56	12	of	of	ADP
iajs-555	56	13	generalized	generalized	ADJ
iajs-555	56	14	regular	regular	ADJ
iajs-555	56	15	continuous	continuous	ADJ
iajs-555	56	16	functions	function	NOUN
iajs-555	56	17	in	in	ADP
iajs-555	56	18	topological	topological	ADJ
iajs-555	56	19	spaces	space	NOUN
iajs-555	56	20	and	and	CCONJ
iajs-555	56	21	study	study	VERB
iajs-555	56	22	the	the	DET
iajs-555	56	23	characterizations	characterization	NOUN
iajs-555	56	24	and	and	CCONJ
iajs-555	56	25	basic	basic	ADJ
iajs-555	56	26	properties	property	NOUN
iajs-555	56	27	of	of	ADP
iajs-555	56	28	generalized	generalized	ADJ
iajs-555	56	29	regular	regular	ADJ
iajs-555	56	30	continuous	continuous	ADJ
iajs-555	56	31	functions.also	functions.also	NOUN
iajs-555	56	32	,	,	PUNCT
iajs-555	56	33	we	we	PRON
iajs-555	56	34	study	study	VERB
iajs-555	56	35	another	another	DET
iajs-555	56	36	types	type	NOUN
iajs-555	56	37	of	of	ADP
iajs-555	56	38	generalized	generalized	ADJ
iajs-555	56	39	regular	regular	ADJ
iajs-555	56	40	continuous	continuous	ADJ
iajs-555	56	41	functions	function	NOUN
iajs-555	56	42	and	and	CCONJ
iajs-555	56	43	we	we	PRON
iajs-555	56	44	study	study	VERB
iajs-555	56	45	the	the	DET
iajs-555	56	46	relation	relation	NOUN
iajs-555	56	47	among	among	ADP
iajs-555	56	48	them	they	PRON
iajs-555	56	49	.	.	PUNCT
iajs-555	57	1	definition	definition	NOUN
iajs-555	57	2	:	:	PUNCT
iajs-555	57	3	a	a	DET
iajs-555	57	4	function	function	NOUN
iajs-555	57	5	yx	yx	NOUN
iajs-555	57	6	:	:	PUNCT
iajs-555	57	7	f	f	PROPN
iajs-555	57	8	→	→	PUNCT
iajs-555	57	9	from	from	ADP
iajs-555	57	10	a	a	DET
iajs-555	57	11	topological	topological	ADJ
iajs-555	57	12	space	space	NOUN
iajs-555	57	13	x	x	PUNCT
iajs-555	57	14	into	into	ADP
iajs-555	57	15	a	a	DET
iajs-555	57	16	topological	topological	ADJ
iajs-555	57	17	space	space	NOUN
iajs-555	57	18	y	y	PROPN
iajs-555	57	19	is	be	AUX
iajs-555	57	20	called	call	VERB
iajs-555	57	21	a	a	DET
iajs-555	57	22	generalized	generalized	ADJ
iajs-555	57	23	regular	regular	ADJ
iajs-555	57	24	continuous	continuous	ADJ
iajs-555	57	25	(	(	PUNCT
iajs-555	57	26	briefly	briefly	ADV
iajs-555	57	27	gr	gr	ADJ
iajs-555	57	28	-	-	PUNCT
iajs-555	57	29	continuous	continuous	ADJ
iajs-555	57	30	)	)	PUNCT
iajs-555	57	31	if	if	SCONJ
iajs-555	57	32	)	)	PUNCT
iajs-555	57	33	v(f	v(f	PROPN
iajs-555	57	34	1−	1−	NUM
iajs-555	57	35	is	be	AUX
iajs-555	57	36	gr	gr	PRON
iajs-555	57	37	-	-	PUNCT
iajs-555	57	38	closed	closed	ADJ
iajs-555	57	39	set	set	NOUN
iajs-555	57	40	in	in	ADP
iajs-555	57	41	x	x	PUNCT
iajs-555	57	42	for	for	ADP
iajs-555	57	43	every	every	DET
iajs-555	57	44	closed	close	VERB
iajs-555	57	45	set	set	VERB
iajs-555	57	46	v	v	NOUN
iajs-555	57	47	in	in	ADP
iajs-555	57	48	y	y	PROPN
iajs-555	57	49	.	.	PUNCT
iajs-555	58	1	theorem	theorem	NOUN
iajs-555	58	2	.	.	PUNCT
iajs-555	59	1	a	a	DET
iajs-555	59	2	function	function	NOUN
iajs-555	59	3	yx	yx	NOUN
iajs-555	59	4	:	:	PUNCT
iajs-555	59	5	f	f	PROPN
iajs-555	59	6	→	→	PUNCT
iajs-555	59	7	from	from	ADP
iajs-555	59	8	a	a	DET
iajs-555	59	9	topological	topological	ADJ
iajs-555	59	10	space	space	NOUN
iajs-555	59	11	x	x	PUNCT
iajs-555	59	12	into	into	ADP
iajs-555	59	13	a	a	DET
iajs-555	59	14	topological	topological	ADJ
iajs-555	59	15	space	space	NOUN
iajs-555	59	16	y	y	PROPN
iajs-555	59	17	is	be	AUX
iajs-555	59	18	gr	gr	ADJ
iajs-555	59	19	-	-	PUNCT
iajs-555	59	20	continuous	continuous	ADJ
iajs-555	59	21	iff	iff	PROPN
iajs-555	59	22	)	)	PUNCT
iajs-555	59	23	v(f	v(f	PROPN
iajs-555	59	24	1−	1−	NUM
iajs-555	59	25	is	be	AUX
iajs-555	59	26	gr	gr	ADV
iajs-555	59	27	-	-	PUNCT
iajs-555	59	28	open	open	NOUN
iajs-555	59	29	set	set	NOUN
iajs-555	59	30	in	in	ADP
iajs-555	59	31	x	x	PUNCT
iajs-555	59	32	for	for	ADP
iajs-555	59	33	every	every	DET
iajs-555	59	34	open	open	ADJ
iajs-555	59	35	set	set	VERB
iajs-555	59	36	v	v	NOUN
iajs-555	59	37	in	in	ADP
iajs-555	59	38	y	y	PROPN
iajs-555	59	39	.	.	PUNCT
iajs-555	60	1	proof	proof	NOUN
iajs-555	60	2	:	:	PUNCT
iajs-555	60	3	it	it	PRON
iajs-555	60	4	is	be	AUX
iajs-555	60	5	obvious	obvious	ADJ
iajs-555	60	6	.	.	PUNCT
iajs-555	61	1	theorem	theorem	VERB
iajs-555	61	2	:	:	PUNCT
iajs-555	61	3	let	let	VERB
iajs-555	61	4	yx	yx	NOUN
iajs-555	61	5	:	:	PUNCT
iajs-555	61	6	f	f	X
iajs-555	61	7	→	→	PUNCT
iajs-555	61	8	be	be	AUX
iajs-555	61	9	a	a	DET
iajs-555	61	10	function	function	NOUN
iajs-555	61	11	from	from	ADP
iajs-555	61	12	a	a	DET
iajs-555	61	13	topological	topological	ADJ
iajs-555	61	14	space	space	NOUN
iajs-555	61	15	x	x	PUNCT
iajs-555	61	16	into	into	ADP
iajs-555	61	17	a	a	DET
iajs-555	61	18	topological	topological	ADJ
iajs-555	61	19	space	space	NOUN
iajs-555	61	20	y.	y.	NOUN
iajs-555	61	21	if	if	SCONJ
iajs-555	61	22	yx	yx	ADP
iajs-555	61	23	:	:	PUNCT
iajs-555	61	24	f	f	PROPN
iajs-555	61	25	→	→	X
iajs-555	61	26	is	be	AUX
iajs-555	61	27	gr	gr	PRON
iajs-555	61	28	-	-	PUNCT
iajs-555	61	29	continuous	continuous	ADJ
iajs-555	61	30	,	,	PUNCT
iajs-555	61	31	then	then	ADV
iajs-555	61	32	)	)	PUNCT
iajs-555	61	33	)	)	PUNCT
iajs-555	61	34	a(f(cl))a(grcl(f	a(f(cl))a(grcl(f	NOUN
iajs-555	62	1	⊆	⊆	NUM
iajs-555	62	2	for	for	ADP
iajs-555	62	3	every	every	DET
iajs-555	62	4	subset	subset	NOUN
iajs-555	62	5	a	a	PRON
iajs-555	62	6	of	of	ADP
iajs-555	62	7	x	x	X
iajs-555	62	8	.	.	PUNCT
iajs-555	63	1	proof	proof	NOUN
iajs-555	63	2	:	:	PUNCT
iajs-555	63	3	since	since	SCONJ
iajs-555	63	4	)	)	PUNCT
iajs-555	63	5	)	)	PUNCT
iajs-555	63	6	a(f(cl)a(f	a(f(cl)a(f	X
iajs-555	63	7	⊆	⊆	NUM
iajs-555	63	8	⇒	⇒	NOUN
iajs-555	63	9	)	)	PUNCT
iajs-555	63	10	)	)	PUNCT
iajs-555	63	11	)	)	PUNCT
iajs-555	64	1	a(f(cl(fa	a(f(cl(fa	PROPN
iajs-555	64	2	1−⊆	1−⊆	INTJ
iajs-555	64	3	.	.	PUNCT
iajs-555	65	1	since	since	SCONJ
iajs-555	65	2	)	)	PUNCT
iajs-555	65	3	)	)	PUNCT
iajs-555	65	4	a(f(cl	a(f(cl	NOUN
iajs-555	65	5	is	be	AUX
iajs-555	65	6	a	a	DET
iajs-555	65	7	closed	closed	ADJ
iajs-555	65	8	set	set	NOUN
iajs-555	65	9	in	in	ADP
iajs-555	65	10	y	y	PROPN
iajs-555	65	11	and	and	CCONJ
iajs-555	65	12	f	f	PROPN
iajs-555	65	13	is	be	AUX
iajs-555	65	14	gr	gr	ADV
iajs-555	65	15	-	-	ADJ
iajs-555	65	16	continuous	continuous	ADJ
iajs-555	65	17	,	,	PUNCT
iajs-555	65	18	then	then	ADV
iajs-555	65	19	by	by	ADP
iajs-555	65	20	(	(	PUNCT
iajs-555	65	21	2.1	2.1	NUM
iajs-555	65	22	)	)	PUNCT
iajs-555	65	23	)	)	PUNCT
iajs-555	65	24	)	)	PUNCT
iajs-555	65	25	)	)	PUNCT
iajs-555	66	1	a(f(cl(f	a(f(cl(f	CCONJ
iajs-555	66	2	1−	1−	NUM
iajs-555	66	3	is	be	AUX
iajs-555	66	4	a	a	DET
iajs-555	66	5	gr	gr	ADV
iajs-555	66	6	-	-	PUNCT
iajs-555	66	7	closed	closed	ADJ
iajs-555	66	8	set	set	NOUN
iajs-555	66	9	in	in	ADP
iajs-555	66	10	x	x	PUNCT
iajs-555	66	11	containing	contain	VERB
iajs-555	66	12	a	a	PRON
iajs-555	66	13	.	.	PUNCT
iajs-555	67	1	hence	hence	ADV
iajs-555	67	2	)	)	PUNCT
iajs-555	67	3	)	)	PUNCT
iajs-555	67	4	)	)	PUNCT
iajs-555	68	1	a(f(cl(f)a(grcl	a(f(cl(f)a(grcl	NOUN
iajs-555	69	1	1−⊆	1−⊆	NOUN
iajs-555	69	2	.	.	PUNCT
iajs-555	70	1	therefore	therefore	ADV
iajs-555	70	2	)	)	PUNCT
iajs-555	70	3	)	)	PUNCT
iajs-555	70	4	a(f(cl))a(grcl(f	a(f(cl))a(grcl(f	PROPN
iajs-555	70	5	⊆	⊆	NUM
iajs-555	70	6	.	.	PUNCT
iajs-555	71	1	theorem	theorem	VERB
iajs-555	71	2	:	:	PUNCT
iajs-555	71	3	let	let	VERB
iajs-555	71	4	yx	yx	NOUN
iajs-555	71	5	:	:	PUNCT
iajs-555	71	6	f	f	X
iajs-555	71	7	→	→	PUNCT
iajs-555	71	8	be	be	AUX
iajs-555	71	9	a	a	DET
iajs-555	71	10	function	function	NOUN
iajs-555	71	11	from	from	ADP
iajs-555	71	12	a	a	DET
iajs-555	71	13	topological	topological	ADJ
iajs-555	71	14	space	space	NOUN
iajs-555	71	15	x	x	PUNCT
iajs-555	71	16	into	into	ADP
iajs-555	71	17	a	a	DET
iajs-555	71	18	topological	topological	ADJ
iajs-555	71	19	space	space	NOUN
iajs-555	71	20	y	y	PROPN
iajs-555	71	21	.	.	PUNCT
iajs-555	72	1	then	then	ADV
iajs-555	72	2	the	the	DET
iajs-555	72	3	following	follow	VERB
iajs-555	72	4	statements	statement	NOUN
iajs-555	72	5	are	be	AUX
iajs-555	72	6	equivalent	equivalent	ADJ
iajs-555	72	7	:	:	PUNCT
iajs-555	72	8	i)for	i)for	ADP
iajs-555	72	9	each	each	DET
iajs-555	72	10	point	point	NOUN
iajs-555	72	11	x	x	PUNCT
iajs-555	72	12	in	in	ADP
iajs-555	72	13	x	x	X
iajs-555	72	14	and	and	CCONJ
iajs-555	72	15	each	each	DET
iajs-555	72	16	open	open	ADJ
iajs-555	72	17	set	set	VERB
iajs-555	72	18	v	v	NOUN
iajs-555	72	19	in	in	ADP
iajs-555	72	20	y	y	PROPN
iajs-555	72	21	with	with	ADP
iajs-555	72	22	v)x(f	v)x(f	NOUN
iajs-555	72	23	∈	∈	PROPN
iajs-555	72	24	,	,	PUNCT
iajs-555	72	25	there	there	PRON
iajs-555	72	26	is	be	VERB
iajs-555	72	27	a	a	DET
iajs-555	72	28	gr	gr	ADJ
iajs-555	72	29	-	-	PUNCT
iajs-555	72	30	open	open	ADJ
iajs-555	72	31	set	set	NOUN
iajs-555	72	32	u	u	NOUN
iajs-555	72	33	in	in	ADP
iajs-555	72	34	x	x	SYM
iajs-555	72	35	such	such	ADJ
iajs-555	72	36	that	that	SCONJ
iajs-555	72	37	ux∈	ux∈	PROPN
iajs-555	72	38	and	and	CCONJ
iajs-555	72	39	v)u(f	v)u(f	PROPN
iajs-555	72	40	⊆	⊆	NUM
iajs-555	72	41	.	.	PUNCT
iajs-555	72	42	ii	ii	PROPN
iajs-555	72	43	)	)	PUNCT
iajs-555	72	44	for	for	ADP
iajs-555	72	45	each	each	PRON
iajs-555	72	46	subset	subset	VERB
iajs-555	72	47	a	a	PRON
iajs-555	72	48	of	of	ADP
iajs-555	72	49	x	x	PRON
iajs-555	72	50	,	,	PUNCT
iajs-555	72	51	)	)	PUNCT
iajs-555	72	52	)	)	PUNCT
iajs-555	72	53	a(f(cl))a(grcl(f	a(f(cl))a(grcl(f	PROPN
iajs-555	72	54	⊆	⊆	NUM
iajs-555	72	55	.	.	PUNCT
iajs-555	73	1	iii)for	iii)for	ADP
iajs-555	73	2	each	each	DET
iajs-555	73	3	subset	subset	NOUN
iajs-555	73	4	b	b	PROPN
iajs-555	73	5	of	of	ADP
iajs-555	73	6	y	y	PROPN
iajs-555	73	7	,	,	PUNCT
iajs-555	73	8	)	)	PUNCT
iajs-555	73	9	)	)	PUNCT
iajs-555	74	1	b(cl(f))b(f(grcl	b(cl(f))b(f(grcl	PROPN
iajs-555	74	2	11	11	NUM
iajs-555	74	3	−−	−−	NOUN
iajs-555	74	4	⊆	⊆	NUM
iajs-555	74	5	.	.	PUNCT
iajs-555	75	1	proof	proof	NOUN
iajs-555	75	2	:	:	PUNCT
iajs-555	75	3	)	)	PUNCT
iajs-555	75	4	ii()i	ii()i	SYM
iajs-555	75	5	(	(	PUNCT
iajs-555	75	6	→	→	PUNCT
iajs-555	75	7	.	.	PUNCT
iajs-555	75	8	suppose	suppose	VERB
iajs-555	75	9	that	that	SCONJ
iajs-555	75	10	(	(	PUNCT
iajs-555	75	11	i	i	NOUN
iajs-555	75	12	)	)	PUNCT
iajs-555	75	13	holds	hold	VERB
iajs-555	75	14	and	and	CCONJ
iajs-555	75	15	let	let	VERB
iajs-555	75	16	)	)	PUNCT
iajs-555	75	17	)	)	PUNCT
iajs-555	75	18	a(grcl(fy∈	a(grcl(fy∈	NOUN
iajs-555	75	19	and	and	CCONJ
iajs-555	75	20	let	let	VERB
iajs-555	75	21	v	v	PART
iajs-555	75	22	be	be	AUX
iajs-555	75	23	any	any	DET
iajs-555	75	24	open	open	ADJ
iajs-555	75	25	neighborhood	neighborhood	NOUN
iajs-555	75	26	of	of	ADP
iajs-555	75	27	y	y	PROPN
iajs-555	75	28	.	.	PUNCT
iajs-555	76	1	since	since	SCONJ
iajs-555	76	2	)	)	PUNCT
iajs-555	76	3	)	)	PUNCT
iajs-555	76	4	a(grcl(fy∈	a(grcl(fy∈	PROPN
iajs-555	76	5	⇒	⇒	NOUN
iajs-555	76	6	)	)	PUNCT
iajs-555	76	7	a(grclx∈∃	a(grclx∈∃	PROPN
iajs-555	76	8	s.t	s.t	PROPN
iajs-555	76	9	y)x(f	y)x(f	NOUN
iajs-555	76	10	=	=	PUNCT
iajs-555	76	11	.	.	PUNCT
iajs-555	77	1	since	since	SCONJ
iajs-555	77	2	v)x(f	v)x(f	PROPN
iajs-555	77	3	∈	∈	PROPN
iajs-555	77	4	,	,	PUNCT
iajs-555	77	5	then	then	ADV
iajs-555	77	6	by	by	ADP
iajs-555	77	7	(	(	PUNCT
iajs-555	77	8	i	i	NOUN
iajs-555	77	9	)	)	PUNCT
iajs-555	77	10	∃	∃	PROPN
iajs-555	77	11	a	a	DET
iajs-555	77	12	gr	gr	ADJ
iajs-555	77	13	-	-	PUNCT
iajs-555	77	14	open	open	ADJ
iajs-555	77	15	set	set	NOUN
iajs-555	77	16	u	u	NOUN
iajs-555	77	17	in	in	ADP
iajs-555	77	18	x	x	X
iajs-555	77	19	s.t	s.t	PROPN
iajs-555	77	20	ux∈	ux∈	PROPN
iajs-555	77	21	and	and	CCONJ
iajs-555	77	22	v)u(f	v)u(f	X
iajs-555	77	23	⊆	⊆	NUM
iajs-555	77	24	.	.	PUNCT
iajs-555	78	1	since	since	SCONJ
iajs-555	78	2	)	)	PUNCT
iajs-555	78	3	a(grclx∈	a(grclx∈	PROPN
iajs-555	78	4	,	,	PUNCT
iajs-555	78	5	then	then	ADV
iajs-555	78	6	by	by	ADP
iajs-555	78	7	(	(	PUNCT
iajs-555	78	8	1.4	1.4	NUM
iajs-555	78	9	)	)	PUNCT
iajs-555	78	10	φ≠au	φ≠au	PROPN
iajs-555	78	11			X
iajs-555	78	12	and	and	CCONJ
iajs-555	78	13	hence	hence	ADV
iajs-555	78	14	φ≠v)a(f	φ≠v)a(f	NUM
iajs-555	78	15			PROPN
iajs-555	78	16	.	.	PUNCT
iajs-555	79	1	therefore	therefore	ADV
iajs-555	79	2	we	we	PRON
iajs-555	79	3	have	have	VERB
iajs-555	79	4	)	)	PUNCT
iajs-555	79	5	)	)	PUNCT
iajs-555	79	6	a(f(cl)x(fy	a(f(cl)x(fy	X
iajs-555	79	7	∈=	∈=	PUNCT
iajs-555	79	8	.	.	PUNCT
iajs-555	80	1	hence	hence	ADV
iajs-555	80	2	)	)	PUNCT
iajs-555	80	3	)	)	PUNCT
iajs-555	80	4	a(f(cl))a(grcl(f	a(f(cl))a(grcl(f	NOUN
iajs-555	80	5	⊆	⊆	NUM
iajs-555	80	6	)	)	PUNCT
iajs-555	80	7	i()ii	i()ii	NOUN
iajs-555	80	8	(	(	PUNCT
iajs-555	80	9	→	→	SYM
iajs-555	80	10	mathematics	mathematics	NOUN
iajs-555	80	11	380	380	NUM
iajs-555	80	12	مجلة	مجلة	NOUN
iajs-555	80	13	إبن	إبن	VERB
iajs-555	80	14	الهيثم	الهيثم	ADJ
iajs-555	80	15	للعلوم	للعلوم	NOUN
iajs-555	80	16	الصرفة	الصرفة	NOUN
iajs-555	81	1	و	و	PRON
iajs-555	81	2	التطبيقية	التطبيقية	ADJ
iajs-555	81	3	2012	2012	NUM
iajs-555	81	4	السنة	السنة	NOUN
iajs-555	81	5	25	25	NUM
iajs-555	81	6	المجلد	المجلد	NOUN
iajs-555	81	7	3	3	NUM
iajs-555	81	8	العدد	العدد	PROPN
iajs-555	81	9	ibn	ibn	PROPN
iajs-555	81	10	al	al	PROPN
iajs-555	81	11	-	-	PUNCT
iajs-555	81	12	haitham	haitham	PROPN
iajs-555	81	13	journal	journal	PROPN
iajs-555	81	14	for	for	ADP
iajs-555	81	15	pure	pure	ADJ
iajs-555	81	16	and	and	CCONJ
iajs-555	81	17	applied	apply	VERB
iajs-555	81	18	science	science	NOUN
iajs-555	81	19	no	no	NOUN
iajs-555	81	20	.	.	NOUN
iajs-555	81	21	3	3	NUM
iajs-555	81	22	vol	vol	NOUN
iajs-555	81	23	.	.	PUNCT
iajs-555	82	1	25	25	NUM
iajs-555	82	2	year	year	NOUN
iajs-555	82	3	2012	2012	NUM
iajs-555	82	4	if	if	SCONJ
iajs-555	82	5	(	(	PUNCT
iajs-555	82	6	ii	ii	NOUN
iajs-555	82	7	)	)	PUNCT
iajs-555	82	8	holds	hold	VERB
iajs-555	82	9	and	and	CCONJ
iajs-555	82	10	let	let	VERB
iajs-555	82	11	xx∈	xx∈	PROPN
iajs-555	82	12	and	and	CCONJ
iajs-555	82	13	v	v	X
iajs-555	82	14	be	be	AUX
iajs-555	82	15	any	any	DET
iajs-555	82	16	open	open	ADJ
iajs-555	82	17	set	set	NOUN
iajs-555	82	18	in	in	ADP
iajs-555	82	19	y	y	NOUN
iajs-555	82	20	containing	contain	VERB
iajs-555	82	21	f(x	f(x	PROPN
iajs-555	82	22	)	)	PUNCT
iajs-555	82	23	.	.	PUNCT
iajs-555	83	1	let	let	VERB
iajs-555	83	2	)	)	PUNCT
iajs-555	83	3	v(fa	v(fa	PROPN
iajs-555	83	4	c1−=	c1−=	PROPN
iajs-555	83	5	⇒	⇒	PROPN
iajs-555	83	6	ax∉	ax∉	PROPN
iajs-555	83	7	.	.	PUNCT
iajs-555	84	1	since	since	SCONJ
iajs-555	84	2	cv))a(f(cl))a(grcl(f	cv))a(f(cl))a(grcl(f	PROPN
iajs-555	84	3	⊆⊆	⊆⊆	PROPN
iajs-555	84	4	⇒	⇒	PROPN
iajs-555	84	5	a)v(f)a(grcl	a)v(f)a(grcl	PROPN
iajs-555	84	6	c1	c1	NOUN
iajs-555	84	7	=	=	PROPN
iajs-555	84	8	⊆	⊆	NUM
iajs-555	84	9	−	−	NOUN
iajs-555	84	10	.	.	PUNCT
iajs-555	85	1	since	since	SCONJ
iajs-555	85	2	ax∉	ax∉	NOUN
iajs-555	85	3	⇒	⇒	NOUN
iajs-555	85	4	)	)	PUNCT
iajs-555	85	5	a(grclx∉	a(grclx∉	PROPN
iajs-555	85	6	and	and	CCONJ
iajs-555	85	7	by	by	ADP
iajs-555	85	8	(	(	PUNCT
iajs-555	85	9	1.4	1.4	NUM
iajs-555	85	10	)	)	PUNCT
iajs-555	85	11	there	there	PRON
iajs-555	85	12	exists	exist	VERB
iajs-555	85	13	a	a	DET
iajs-555	85	14	gr	gr	ADJ
iajs-555	85	15	-	-	PUNCT
iajs-555	85	16	open	open	ADJ
iajs-555	85	17	set	set	NOUN
iajs-555	85	18	u	u	NOUN
iajs-555	85	19	containing	contain	VERB
iajs-555	85	20	x	x	PUNCT
iajs-555	85	21	such	such	ADJ
iajs-555	85	22	that	that	SCONJ
iajs-555	85	23	φ	φ	PROPN
iajs-555	85	24	=	=	NOUN
iajs-555	85	25	au	au	X
iajs-555	85	26			NOUN
iajs-555	85	27	and	and	CCONJ
iajs-555	85	28	hence	hence	ADV
iajs-555	85	29	v)a(f)u(f	v)a(f)u(f	PROPN
iajs-555	85	30	c	c	PROPN
iajs-555	85	31	⊆⊆	⊆⊆	PROPN
iajs-555	85	32	.	.	PUNCT
iajs-555	86	1	)	)	PUNCT
iajs-555	86	2	iii()ii	iii()ii	NOUN
iajs-555	86	3	(	(	PUNCT
iajs-555	86	4	→	→	PUNCT
iajs-555	86	5	.	.	PUNCT
iajs-555	86	6	suppose	suppose	VERB
iajs-555	86	7	that	that	SCONJ
iajs-555	86	8	(	(	PUNCT
iajs-555	86	9	ii	ii	NOUN
iajs-555	86	10	)	)	PUNCT
iajs-555	86	11	holds	hold	VERB
iajs-555	86	12	and	and	CCONJ
iajs-555	86	13	let	let	VERB
iajs-555	86	14	b	b	X
iajs-555	86	15	be	be	AUX
iajs-555	86	16	any	any	DET
iajs-555	86	17	subset	subset	NOUN
iajs-555	86	18	of	of	ADP
iajs-555	86	19	y	y	PROPN
iajs-555	86	20	.	.	PUNCT
iajs-555	87	1	replacing	replace	VERB
iajs-555	87	2	a	a	DET
iajs-555	87	3	by	by	NOUN
iajs-555	87	4	)	)	PUNCT
iajs-555	87	5	b(f	b(f	PROPN
iajs-555	87	6	1−	1−	NUM
iajs-555	87	7	we	we	PRON
iajs-555	87	8	get	get	VERB
iajs-555	87	9	from	from	ADP
iajs-555	87	10	(	(	PUNCT
iajs-555	87	11	ii	ii	NOUN
iajs-555	87	12	)	)	PUNCT
iajs-555	87	13	)	)	PUNCT
iajs-555	88	1	b(cl)))b(f(f(cl)))b(f(grcl(f	b(cl)))b(f(f(cl)))b(f(grcl(f	NOUN
iajs-555	88	2	11	11	NUM
iajs-555	88	3	⊆⊆	⊆⊆	PROPN
iajs-555	88	4	−−	−−	NOUN
iajs-555	88	5	.	.	PUNCT
iajs-555	89	1	hence	hence	ADV
iajs-555	89	2	)	)	PUNCT
iajs-555	89	3	)	)	PUNCT
iajs-555	89	4	b(cl(f))b(f(grcl	b(cl(f))b(f(grcl	PROPN
iajs-555	89	5	11	11	NUM
iajs-555	89	6	−−	−−	NOUN
iajs-555	89	7	⊆	⊆	NUM
iajs-555	89	8	.	.	PUNCT
iajs-555	89	9	)	)	PUNCT
iajs-555	90	1	ii()iii	ii()iii	PROPN
iajs-555	90	2	(	(	PUNCT
iajs-555	90	3	→	→	PUNCT
iajs-555	90	4	.	.	PUNCT
iajs-555	90	5	suppose	suppose	VERB
iajs-555	90	6	that	that	SCONJ
iajs-555	90	7	(	(	PUNCT
iajs-555	90	8	iii	iii	NOUN
iajs-555	90	9	)	)	PUNCT
iajs-555	90	10	holds	hold	VERB
iajs-555	90	11	,	,	PUNCT
iajs-555	90	12	let	let	VERB
iajs-555	90	13	b	b	NOUN
iajs-555	90	14	=	=	SYM
iajs-555	90	15	f(a	f(a	PROPN
iajs-555	90	16	)	)	PUNCT
iajs-555	90	17	where	where	SCONJ
iajs-555	90	18	a	a	PRON
iajs-555	90	19	is	be	AUX
iajs-555	90	20	a	a	DET
iajs-555	90	21	subset	subset	NOUN
iajs-555	90	22	of	of	ADP
iajs-555	90	23	x	x	X
iajs-555	90	24	.	.	PUNCT
iajs-555	91	1	then	then	ADV
iajs-555	91	2	we	we	PRON
iajs-555	91	3	get	get	VERB
iajs-555	91	4	from	from	ADP
iajs-555	91	5	(	(	PUNCT
iajs-555	91	6	iii	iii	NOUN
iajs-555	91	7	)	)	PUNCT
iajs-555	91	8	)	)	PUNCT
iajs-555	91	9	)	)	PUNCT
iajs-555	91	10	)	)	PUNCT
iajs-555	92	1	a(f(cl(f))a(f(f(grcl)a(grcl	a(f(cl(f))a(f(f(grcl)a(grcl	X
iajs-555	92	2	11	11	NUM
iajs-555	92	3	−−	−−	PROPN
iajs-555	92	4	⊆⊆	⊆⊆	PROPN
iajs-555	92	5	.	.	PUNCT
iajs-555	93	1	therefore	therefore	ADV
iajs-555	93	2	)	)	PUNCT
iajs-555	93	3	)	)	PUNCT
iajs-555	93	4	a(f(cl))a(grcl(f	a(f(cl))a(grcl(f	PROPN
iajs-555	93	5	⊆	⊆	NUM
iajs-555	93	6	.	.	PUNCT
iajs-555	94	1	definition	definition	NOUN
iajs-555	94	2	:	:	PUNCT
iajs-555	94	3	a	a	DET
iajs-555	94	4	function	function	NOUN
iajs-555	94	5	yx	yx	NOUN
iajs-555	94	6	:	:	PUNCT
iajs-555	94	7	f	f	PROPN
iajs-555	94	8	→	→	PUNCT
iajs-555	94	9	from	from	ADP
iajs-555	94	10	a	a	DET
iajs-555	94	11	topological	topological	ADJ
iajs-555	94	12	space	space	NOUN
iajs-555	94	13	x	x	PUNCT
iajs-555	94	14	into	into	ADP
iajs-555	94	15	a	a	DET
iajs-555	94	16	topological	topological	ADJ
iajs-555	94	17	space	space	NOUN
iajs-555	94	18	y	y	PROPN
iajs-555	94	19	is	be	AUX
iajs-555	94	20	said	say	VERB
iajs-555	94	21	to	to	PART
iajs-555	94	22	be	be	AUX
iajs-555	94	23	perfectly	perfectly	ADV
iajs-555	94	24	generalized	generalize	VERB
iajs-555	94	25	regular	regular	ADJ
iajs-555	94	26	continuous	continuous	ADJ
iajs-555	94	27	(	(	PUNCT
iajs-555	94	28	briefly	briefly	ADV
iajs-555	94	29	perfectly	perfectly	ADV
iajs-555	94	30	gr	gr	ADV
iajs-555	94	31	-	-	PUNCT
iajs-555	94	32	continuous	continuous	ADJ
iajs-555	94	33	)	)	PUNCT
iajs-555	94	34	if	if	SCONJ
iajs-555	94	35	)	)	PUNCT
iajs-555	94	36	v(f	v(f	PROPN
iajs-555	94	37	1−	1−	NUM
iajs-555	94	38	is	be	AUX
iajs-555	94	39	gr	gr	ADV
iajs-555	94	40	-	-	PUNCT
iajs-555	94	41	clopen	clopen	ADJ
iajs-555	94	42	(	(	PUNCT
iajs-555	94	43	gr	gr	NOUN
iajs-555	94	44	-	-	PUNCT
iajs-555	94	45	open	open	ADJ
iajs-555	94	46	and	and	CCONJ
iajs-555	94	47	gr	gr	ADJ
iajs-555	94	48	-	-	PUNCT
iajs-555	94	49	closed	closed	ADJ
iajs-555	94	50	)	)	PUNCT
iajs-555	94	51	set	set	VERB
iajs-555	94	52	in	in	ADP
iajs-555	94	53	x	x	PUNCT
iajs-555	94	54	for	for	ADP
iajs-555	94	55	every	every	DET
iajs-555	94	56	open	open	ADJ
iajs-555	94	57	set	set	VERB
iajs-555	94	58	v	v	NOUN
iajs-555	94	59	in	in	ADP
iajs-555	94	60	y	y	PROPN
iajs-555	94	61	.	.	PUNCT
iajs-555	95	1	definition	definition	NOUN
iajs-555	95	2	:	:	PUNCT
iajs-555	95	3	a	a	DET
iajs-555	95	4	function	function	NOUN
iajs-555	95	5	yx	yx	NOUN
iajs-555	95	6	:	:	PUNCT
iajs-555	95	7	f	f	PROPN
iajs-555	95	8	→	→	PUNCT
iajs-555	95	9	from	from	ADP
iajs-555	95	10	a	a	DET
iajs-555	95	11	topological	topological	ADJ
iajs-555	95	12	space	space	NOUN
iajs-555	95	13	x	x	PUNCT
iajs-555	95	14	into	into	ADP
iajs-555	95	15	a	a	DET
iajs-555	95	16	topological	topological	ADJ
iajs-555	95	17	space	space	NOUN
iajs-555	95	18	y	y	PROPN
iajs-555	95	19	is	be	AUX
iajs-555	95	20	said	say	VERB
iajs-555	95	21	to	to	PART
iajs-555	95	22	be	be	AUX
iajs-555	95	23	contra	contra	PROPN
iajs-555	95	24	generalized	generalize	VERB
iajs-555	95	25	regular	regular	ADJ
iajs-555	95	26	continuous	continuous	ADJ
iajs-555	95	27	(	(	PUNCT
iajs-555	95	28	briefly	briefly	NOUN
iajs-555	95	29	contra	contra	PROPN
iajs-555	95	30	gr	gr	PROPN
iajs-555	95	31	-	-	PUNCT
iajs-555	95	32	continuous	continuous	ADJ
iajs-555	95	33	)	)	PUNCT
iajs-555	95	34	if	if	SCONJ
iajs-555	95	35	)	)	PUNCT
iajs-555	95	36	v(f	v(f	PROPN
iajs-555	95	37	1−	1−	NUM
iajs-555	95	38	is	be	AUX
iajs-555	95	39	grclosed	grclose	VERB
iajs-555	95	40	set	set	VERB
iajs-555	95	41	in	in	ADP
iajs-555	95	42	x	x	PUNCT
iajs-555	95	43	for	for	ADP
iajs-555	95	44	every	every	DET
iajs-555	95	45	open	open	ADJ
iajs-555	95	46	set	set	VERB
iajs-555	95	47	v	v	NOUN
iajs-555	95	48	in	in	ADP
iajs-555	95	49	y	y	PROPN
iajs-555	95	50	.	.	PUNCT
iajs-555	96	1	theorem	theorem	VERB
iajs-555	96	2	:	:	PUNCT
iajs-555	96	3	let	let	VERB
iajs-555	96	4	yx	yx	NOUN
iajs-555	96	5	:	:	PUNCT
iajs-555	96	6	f	f	X
iajs-555	96	7	→	→	PUNCT
iajs-555	96	8	be	be	AUX
iajs-555	96	9	a	a	DET
iajs-555	96	10	function	function	NOUN
iajs-555	96	11	.	.	PUNCT
iajs-555	97	1	then	then	ADV
iajs-555	97	2	1	1	X
iajs-555	97	3	)	)	PUNCT
iajs-555	97	4	if	if	SCONJ
iajs-555	97	5	f	f	PROPN
iajs-555	97	6	is	be	AUX
iajs-555	97	7	r	r	NOUN
iajs-555	97	8	-	-	ADJ
iajs-555	97	9	continuous	continuous	ADJ
iajs-555	97	10	,	,	PUNCT
iajs-555	97	11	then	then	ADV
iajs-555	97	12	f	f	PROPN
iajs-555	97	13	is	be	AUX
iajs-555	97	14	gr	gr	ADV
iajs-555	97	15	-	-	ADJ
iajs-555	97	16	continuous	continuous	ADJ
iajs-555	97	17	.	.	PUNCT
iajs-555	98	1	2	2	X
iajs-555	98	2	)	)	PUNCT
iajs-555	98	3	if	if	SCONJ
iajs-555	98	4	f	f	PROPN
iajs-555	98	5	is	be	AUX
iajs-555	98	6	gr	gr	ADV
iajs-555	98	7	-	-	ADJ
iajs-555	98	8	continuous	continuous	ADJ
iajs-555	98	9	,	,	PUNCT
iajs-555	98	10	then	then	ADV
iajs-555	98	11	f	f	PROPN
iajs-555	98	12	is	be	AUX
iajs-555	98	13	g	g	NOUN
iajs-555	98	14	-	-	PUNCT
iajs-555	98	15	continuous	continuous	ADJ
iajs-555	98	16	.	.	PUNCT
iajs-555	99	1	3	3	X
iajs-555	99	2	)	)	PUNCT
iajs-555	99	3	if	if	SCONJ
iajs-555	99	4	f	f	PROPN
iajs-555	99	5	is	be	AUX
iajs-555	99	6	gr	gr	ADV
iajs-555	99	7	-	-	ADJ
iajs-555	99	8	continuous	continuous	ADJ
iajs-555	99	9	,	,	PUNCT
iajs-555	99	10	then	then	ADV
iajs-555	99	11	f	f	PROPN
iajs-555	99	12	is	be	AUX
iajs-555	99	13	rg	rg	NOUN
iajs-555	99	14	-	-	ADJ
iajs-555	99	15	continuous	continuous	ADJ
iajs-555	99	16	.	.	PUNCT
iajs-555	100	1	4	4	X
iajs-555	100	2	)	)	PUNCT
iajs-555	100	3	if	if	SCONJ
iajs-555	100	4	f	f	PROPN
iajs-555	100	5	is	be	AUX
iajs-555	100	6	gr	gr	ADV
iajs-555	100	7	-	-	ADJ
iajs-555	100	8	continuous	continuous	ADJ
iajs-555	100	9	,	,	PUNCT
iajs-555	100	10	then	then	ADV
iajs-555	100	11	f	f	PROPN
iajs-555	100	12	is	be	AUX
iajs-555	100	13	gb	gb	ADV
iajs-555	100	14	-	-	PUNCT
iajs-555	100	15	continuous	continuous	ADJ
iajs-555	100	16	.	.	PUNCT
iajs-555	101	1	5	5	X
iajs-555	101	2	)	)	PUNCT
iajs-555	101	3	if	if	SCONJ
iajs-555	101	4	f	f	PROPN
iajs-555	101	5	is	be	AUX
iajs-555	101	6	continuous	continuous	ADJ
iajs-555	101	7	,	,	PUNCT
iajs-555	101	8	then	then	ADV
iajs-555	101	9	f	f	PROPN
iajs-555	101	10	is	be	AUX
iajs-555	101	11	rg	rg	NOUN
iajs-555	101	12	-	-	ADJ
iajs-555	101	13	continuous	continuous	ADJ
iajs-555	101	14	.	.	PUNCT
iajs-555	102	1	6	6	X
iajs-555	102	2	)	)	PUNCT
iajs-555	102	3	if	if	SCONJ
iajs-555	102	4	f	f	PROPN
iajs-555	102	5	is	be	AUX
iajs-555	102	6	perfectly	perfectly	ADV
iajs-555	102	7	gr	gr	ADV
iajs-555	102	8	-	-	ADJ
iajs-555	102	9	continuous	continuous	ADJ
iajs-555	102	10	,	,	PUNCT
iajs-555	102	11	then	then	ADV
iajs-555	102	12	f	f	PROPN
iajs-555	102	13	is	be	AUX
iajs-555	102	14	gr	gr	ADV
iajs-555	102	15	-	-	ADJ
iajs-555	102	16	continuous	continuous	ADJ
iajs-555	102	17	.	.	PUNCT
iajs-555	103	1	7	7	X
iajs-555	103	2	)	)	PUNCT
iajs-555	103	3	if	if	SCONJ
iajs-555	103	4	f	f	PROPN
iajs-555	103	5	is	be	AUX
iajs-555	103	6	perfectly	perfectly	ADV
iajs-555	103	7	gr	gr	ADV
iajs-555	103	8	-	-	ADJ
iajs-555	103	9	continuous	continuous	ADJ
iajs-555	103	10	,	,	PUNCT
iajs-555	103	11	then	then	ADV
iajs-555	103	12	f	f	PROPN
iajs-555	103	13	is	be	AUX
iajs-555	103	14	rg	rg	NOUN
iajs-555	103	15	-	-	ADJ
iajs-555	103	16	continuous	continuous	ADJ
iajs-555	103	17	.	.	PUNCT
iajs-555	104	1	8)	8)	NUM
iajs-555	104	2	if	if	SCONJ
iajs-555	104	3	f	f	PROPN
iajs-555	104	4	is	be	AUX
iajs-555	104	5	perfectly	perfectly	ADV
iajs-555	104	6	gr	gr	ADV
iajs-555	104	7	-	-	ADJ
iajs-555	104	8	continuous	continuous	ADJ
iajs-555	104	9	,	,	PUNCT
iajs-555	104	10	then	then	ADV
iajs-555	104	11	f	f	PROPN
iajs-555	104	12	is	be	AUX
iajs-555	104	13	g	g	NOUN
iajs-555	104	14	-	-	PUNCT
iajs-555	104	15	continuous	continuous	ADJ
iajs-555	104	16	.	.	PUNCT
iajs-555	105	1	9	9	X
iajs-555	105	2	)	)	PUNCT
iajs-555	105	3	if	if	SCONJ
iajs-555	105	4	f	f	PROPN
iajs-555	105	5	is	be	AUX
iajs-555	105	6	perfectly	perfectly	ADV
iajs-555	105	7	gr	gr	ADV
iajs-555	105	8	-	-	ADJ
iajs-555	105	9	continuous	continuous	ADJ
iajs-555	105	10	,	,	PUNCT
iajs-555	105	11	then	then	ADV
iajs-555	105	12	f	f	PROPN
iajs-555	105	13	is	be	AUX
iajs-555	105	14	gb	gb	ADV
iajs-555	105	15	-	-	PUNCT
iajs-555	105	16	continuous	continuous	ADJ
iajs-555	105	17	.	.	PUNCT
iajs-555	106	1	10	10	NUM
iajs-555	106	2	)	)	PUNCT
iajs-555	106	3	if	if	SCONJ
iajs-555	106	4	f	f	PROPN
iajs-555	106	5	is	be	AUX
iajs-555	106	6	perfectly	perfectly	ADV
iajs-555	106	7	gr	gr	ADV
iajs-555	106	8	-	-	ADJ
iajs-555	106	9	continuous	continuous	ADJ
iajs-555	106	10	,	,	PUNCT
iajs-555	106	11	then	then	ADV
iajs-555	106	12	f	f	PROPN
iajs-555	106	13	is	be	AUX
iajs-555	106	14	contra	contra	PROPN
iajs-555	106	15	gr	gr	PROPN
iajs-555	106	16	-	-	PUNCT
iajs-555	106	17	continuous	continuous	ADJ
iajs-555	106	18	.	.	PUNCT
iajs-555	107	1	proof	proof	NOUN
iajs-555	107	2	:	:	PUNCT
iajs-555	107	3	1	1	X
iajs-555	107	4	)	)	PUNCT
iajs-555	107	5	let	let	VERB
iajs-555	107	6	f	f	PRON
iajs-555	107	7	be	be	AUX
iajs-555	107	8	a	a	DET
iajs-555	107	9	closed	closed	ADJ
iajs-555	107	10	set	set	NOUN
iajs-555	107	11	in	in	ADP
iajs-555	107	12	y	y	PROPN
iajs-555	107	13	,	,	PUNCT
iajs-555	107	14	since	since	SCONJ
iajs-555	107	15	f	f	PROPN
iajs-555	107	16	is	be	AUX
iajs-555	107	17	r	r	NOUN
iajs-555	107	18	-	-	PUNCT
iajs-555	107	19	continuous	continuous	ADJ
iajs-555	107	20	,	,	PUNCT
iajs-555	107	21	then	then	ADV
iajs-555	107	22	by	by	ADP
iajs-555	107	23	(	(	PUNCT
iajs-555	107	24	1.5	1.5	NUM
iajs-555	107	25	)	)	PUNCT
iajs-555	107	26	no.3	no.3	PROPN
iajs-555	107	27	,	,	PUNCT
iajs-555	107	28	)	)	PUNCT
iajs-555	107	29	f(f	f(f	PROPN
iajs-555	107	30	1−	1−	NUM
iajs-555	107	31	is	be	AUX
iajs-555	107	32	r	r	NOUN
iajs-555	107	33	-	-	PUNCT
iajs-555	107	34	closed	closed	ADJ
iajs-555	107	35	in	in	ADP
iajs-555	107	36	x	x	X
iajs-555	107	37	.	.	PUNCT
iajs-555	108	1	since	since	SCONJ
iajs-555	108	2	every	every	DET
iajs-555	108	3	r	r	NOUN
iajs-555	108	4	-	-	PUNCT
iajs-555	108	5	closed	closed	ADJ
iajs-555	108	6	set	set	NOUN
iajs-555	108	7	is	be	AUX
iajs-555	108	8	gr	gr	PRON
iajs-555	108	9	-	-	PUNCT
iajs-555	108	10	closed	closed	ADJ
iajs-555	108	11	,	,	PUNCT
iajs-555	108	12	then	then	ADV
iajs-555	108	13	)	)	PUNCT
iajs-555	108	14	f(f	f(f	PROPN
iajs-555	108	15	1−	1−	NUM
iajs-555	108	16	is	be	AUX
iajs-555	108	17	gr	gr	ADV
iajs-555	108	18	-	-	PUNCT
iajs-555	108	19	closed	closed	ADJ
iajs-555	108	20	in	in	ADP
iajs-555	108	21	x	x	X
iajs-555	108	22	.	.	PUNCT
iajs-555	109	1	hence	hence	ADV
iajs-555	109	2	f	f	PROPN
iajs-555	109	3	is	be	AUX
iajs-555	109	4	gr	gr	ADV
iajs-555	109	5	-	-	ADJ
iajs-555	109	6	continuous	continuous	ADJ
iajs-555	109	7	.	.	PUNCT
iajs-555	110	1	3	3	X
iajs-555	110	2	)	)	PUNCT
iajs-555	110	3	let	let	VERB
iajs-555	110	4	f	f	PRON
iajs-555	110	5	be	be	AUX
iajs-555	110	6	a	a	DET
iajs-555	110	7	closed	closed	ADJ
iajs-555	110	8	set	set	NOUN
iajs-555	110	9	in	in	ADP
iajs-555	110	10	y	y	PROPN
iajs-555	110	11	,	,	PUNCT
iajs-555	110	12	since	since	SCONJ
iajs-555	110	13	f	f	PROPN
iajs-555	110	14	is	be	AUX
iajs-555	110	15	gr	gr	ADJ
iajs-555	110	16	-	-	PUNCT
iajs-555	110	17	continuous	continuous	ADJ
iajs-555	110	18	,	,	PUNCT
iajs-555	110	19	then	then	ADV
iajs-555	110	20	by	by	ADP
iajs-555	110	21	(	(	PUNCT
iajs-555	110	22	2.1	2.1	NUM
iajs-555	110	23	)	)	PUNCT
iajs-555	110	24	,	,	PUNCT
iajs-555	110	25	)	)	PUNCT
iajs-555	110	26	f(f	f(f	PROPN
iajs-555	110	27	1−	1−	NUM
iajs-555	110	28	is	be	AUX
iajs-555	110	29	gr	gr	ADV
iajs-555	110	30	-	-	PUNCT
iajs-555	110	31	closed	closed	ADJ
iajs-555	110	32	in	in	ADP
iajs-555	110	33	x	x	X
iajs-555	110	34	.	.	PUNCT
iajs-555	111	1	since	since	SCONJ
iajs-555	111	2	every	every	DET
iajs-555	111	3	gr	gr	NOUN
iajs-555	111	4	-	-	PUNCT
iajs-555	111	5	closed	closed	ADJ
iajs-555	111	6	set	set	NOUN
iajs-555	111	7	is	be	AUX
iajs-555	111	8	rg	rg	NOUN
iajs-555	111	9	-	-	PUNCT
iajs-555	111	10	closed	closed	ADJ
iajs-555	111	11	,	,	PUNCT
iajs-555	111	12	then	then	ADV
iajs-555	111	13	)	)	PUNCT
iajs-555	111	14	f(f	f(f	PROPN
iajs-555	111	15	1−	1−	NUM
iajs-555	111	16	is	be	AUX
iajs-555	111	17	rg	rg	NOUN
iajs-555	111	18	-	-	PUNCT
iajs-555	111	19	closed	closed	ADJ
iajs-555	111	20	in	in	ADP
iajs-555	111	21	x	x	X
iajs-555	111	22	.	.	PUNCT
iajs-555	112	1	hence	hence	ADV
iajs-555	112	2	f	f	PROPN
iajs-555	112	3	is	be	AUX
iajs-555	112	4	rg	rg	NOUN
iajs-555	112	5	-	-	ADJ
iajs-555	112	6	continuous	continuous	ADJ
iajs-555	112	7	.	.	PUNCT
iajs-555	113	1	5	5	X
iajs-555	113	2	)	)	PUNCT
iajs-555	113	3	let	let	VERB
iajs-555	113	4	f	f	PRON
iajs-555	113	5	be	be	AUX
iajs-555	113	6	a	a	DET
iajs-555	113	7	closed	closed	ADJ
iajs-555	113	8	set	set	NOUN
iajs-555	113	9	in	in	ADP
iajs-555	113	10	y	y	PROPN
iajs-555	113	11	,	,	PUNCT
iajs-555	113	12	since	since	SCONJ
iajs-555	113	13	f	f	PROPN
iajs-555	113	14	is	be	AUX
iajs-555	113	15	continuous	continuous	ADJ
iajs-555	113	16	,	,	PUNCT
iajs-555	113	17	then	then	ADV
iajs-555	113	18	)	)	PUNCT
iajs-555	113	19	f(f	f(f	PROPN
iajs-555	113	20	1−	1−	NUM
iajs-555	113	21	is	be	AUX
iajs-555	113	22	closed	close	VERB
iajs-555	113	23	in	in	ADP
iajs-555	113	24	x	x	X
iajs-555	113	25	.	.	PUNCT
iajs-555	114	1	since	since	SCONJ
iajs-555	114	2	every	every	DET
iajs-555	114	3	closed	closed	ADJ
iajs-555	114	4	set	set	NOUN
iajs-555	114	5	is	be	AUX
iajs-555	114	6	rg	rg	NOUN
iajs-555	114	7	-	-	PUNCT
iajs-555	114	8	closed	closed	ADJ
iajs-555	114	9	,	,	PUNCT
iajs-555	114	10	then	then	ADV
iajs-555	114	11	)	)	PUNCT
iajs-555	114	12	f(f	f(f	PROPN
iajs-555	114	13	1−	1−	NUM
iajs-555	114	14	is	be	AUX
iajs-555	114	15	rg	rg	NOUN
iajs-555	114	16	-	-	PUNCT
iajs-555	114	17	closed	closed	ADJ
iajs-555	114	18	in	in	ADP
iajs-555	114	19	x	x	X
iajs-555	114	20	.	.	PUNCT
iajs-555	115	1	hence	hence	ADV
iajs-555	115	2	f	f	PROPN
iajs-555	115	3	is	be	AUX
iajs-555	115	4	rg	rg	NOUN
iajs-555	115	5	-	-	ADJ
iajs-555	115	6	continuous	continuous	ADJ
iajs-555	115	7	.	.	PUNCT
iajs-555	116	1	9	9	X
iajs-555	116	2	)	)	PUNCT
iajs-555	116	3	let	let	VERB
iajs-555	116	4	u	u	PRON
iajs-555	116	5	be	be	AUX
iajs-555	116	6	an	an	DET
iajs-555	116	7	open	open	ADJ
iajs-555	116	8	set	set	NOUN
iajs-555	116	9	in	in	ADP
iajs-555	116	10	y	y	PROPN
iajs-555	116	11	,	,	PUNCT
iajs-555	116	12	since	since	SCONJ
iajs-555	116	13	f	f	PROPN
iajs-555	116	14	is	be	AUX
iajs-555	116	15	perfectly	perfectly	ADV
iajs-555	116	16	gr	gr	ADV
iajs-555	116	17	-	-	PUNCT
iajs-555	116	18	continuous	continuous	ADJ
iajs-555	116	19	,	,	PUNCT
iajs-555	116	20	then	then	ADV
iajs-555	116	21	by	by	ADP
iajs-555	116	22	(	(	PUNCT
iajs-555	116	23	2.5	2.5	NUM
iajs-555	116	24	)	)	PUNCT
iajs-555	116	25	,	,	PUNCT
iajs-555	116	26	)	)	PUNCT
iajs-555	116	27	u(f	u(f	PROPN
iajs-555	116	28	1−	1−	NUM
iajs-555	116	29	is	be	AUX
iajs-555	116	30	gr	gr	ADP
iajs-555	116	31	closed	closed	ADJ
iajs-555	116	32	and	and	CCONJ
iajs-555	116	33	gr	gr	NOUN
iajs-555	116	34	-	-	NOUN
iajs-555	116	35	open	open	ADJ
iajs-555	116	36	in	in	ADP
iajs-555	116	37	x	x	X
iajs-555	116	38	.	.	PUNCT
iajs-555	117	1	since	since	SCONJ
iajs-555	117	2	every	every	DET
iajs-555	117	3	gr	gr	NOUN
iajs-555	117	4	-	-	PUNCT
iajs-555	117	5	open	open	ADJ
iajs-555	117	6	set	set	NOUN
iajs-555	117	7	is	be	AUX
iajs-555	117	8	gb	gb	ADV
iajs-555	117	9	-	-	PUNCT
iajs-555	117	10	open	open	ADJ
iajs-555	117	11	,	,	PUNCT
iajs-555	117	12	then	then	ADV
iajs-555	117	13	)	)	PUNCT
iajs-555	117	14	u(f	u(f	PROPN
iajs-555	117	15	1−	1−	NUM
iajs-555	117	16	is	be	AUX
iajs-555	117	17	gb	gb	ADV
iajs-555	117	18	-	-	PUNCT
iajs-555	117	19	open	open	ADJ
iajs-555	117	20	in	in	ADP
iajs-555	117	21	x	x	X
iajs-555	117	22	.	.	PUNCT
iajs-555	118	1	hence	hence	ADV
iajs-555	118	2	f	f	PROPN
iajs-555	118	3	is	be	AUX
iajs-555	118	4	gb	gb	ADV
iajs-555	118	5	-	-	PUNCT
iajs-555	118	6	continuous	continuous	ADJ
iajs-555	118	7	.	.	PUNCT
iajs-555	119	1	similarly	similarly	ADV
iajs-555	119	2	,	,	PUNCT
iajs-555	119	3	we	we	PRON
iajs-555	119	4	can	can	AUX
iajs-555	119	5	prove	prove	VERB
iajs-555	119	6	(	(	PUNCT
iajs-555	119	7	2),(4),(6),(7),(8	2),(4),(6),(7),(8	PROPN
iajs-555	119	8	)	)	PUNCT
iajs-555	119	9	and	and	CCONJ
iajs-555	119	10	(	(	PUNCT
iajs-555	119	11	10	10	NUM
iajs-555	119	12	)	)	PUNCT
iajs-555	119	13	.	.	PUNCT
iajs-555	120	1	mathematics	mathematic	NOUN
iajs-555	120	2	381	381	NUM
iajs-555	120	3	مجلة	مجلة	NOUN
iajs-555	120	4	إبن	إبن	VERB
iajs-555	120	5	الهيثم	الهيثم	ADJ
iajs-555	120	6	للعلوم	للعلوم	NOUN
iajs-555	120	7	الصرفة	الصرفة	NOUN
iajs-555	121	1	و	و	PRON
iajs-555	121	2	التطبيقية	التطبيقية	ADJ
iajs-555	121	3	2012	2012	NUM
iajs-555	121	4	السنة	السنة	NOUN
iajs-555	121	5	25	25	NUM
iajs-555	121	6	المجلد	المجلد	NOUN
iajs-555	121	7	3	3	NUM
iajs-555	121	8	العدد	العدد	PROPN
iajs-555	121	9	ibn	ibn	PROPN
iajs-555	121	10	al	al	PROPN
iajs-555	121	11	-	-	PUNCT
iajs-555	121	12	haitham	haitham	PROPN
iajs-555	121	13	journal	journal	PROPN
iajs-555	121	14	for	for	ADP
iajs-555	121	15	pure	pure	ADJ
iajs-555	121	16	and	and	CCONJ
iajs-555	121	17	applied	apply	VERB
iajs-555	121	18	science	science	NOUN
iajs-555	121	19	no	no	NOUN
iajs-555	121	20	.	.	NOUN
iajs-555	121	21	3	3	NUM
iajs-555	121	22	vol	vol	NOUN
iajs-555	121	23	.	.	PUNCT
iajs-555	122	1	25	25	NUM
iajs-555	122	2	year	year	NOUN
iajs-555	122	3	2012	2012	NUM
iajs-555	122	4	remarks	remark	VERB
iajs-555	122	5	:	:	PUNCT
iajs-555	122	6	1)continuous	1)continuous	NUM
iajs-555	122	7	functions	function	NOUN
iajs-555	122	8	and	and	CCONJ
iajs-555	122	9	gr	gr	ADJ
iajs-555	122	10	-	-	PUNCT
iajs-555	122	11	continuous	continuous	ADJ
iajs-555	122	12	functions	function	NOUN
iajs-555	122	13	are	be	AUX
iajs-555	122	14	in	in	ADP
iajs-555	122	15	general	general	ADJ
iajs-555	122	16	independent	independent	ADJ
iajs-555	122	17	.consider	.consider	NOUN
iajs-555	123	1	the	the	DET
iajs-555	123	2	following	follow	VERB
iajs-555	123	3	examples	example	NOUN
iajs-555	123	4	:	:	PUNCT
iajs-555	123	5	examples	example	NOUN
iajs-555	123	6	i)let	i)let	NOUN
iajs-555	123	7	}	}	PUNCT
iajs-555	123	8	c	c	NOUN
iajs-555	123	9	,	,	PUNCT
iajs-555	123	10	b	b	PROPN
iajs-555	123	11	,	,	PUNCT
iajs-555	123	12	a{x	a{x	VERB
iajs-555	123	13	=	=	NOUN
iajs-555	123	14	,	,	PUNCT
iajs-555	123	15	}	}	PUNCT
iajs-555	123	16	}	}	PUNCT
iajs-555	123	17	b{},c	b{},c	PROPN
iajs-555	123	18	,	,	PUNCT
iajs-555	123	19	b{},b	b{},b	PROPN
iajs-555	123	20	,	,	PUNCT
iajs-555	123	21	a{,,x	a{,,x	PROPN
iajs-555	123	22	{	{	PUNCT
iajs-555	123	23	φ	φ	PROPN
iajs-555	123	24	=	=	PROPN
iajs-555	123	25	τ	τ	X
iajs-555	123	26	and	and	CCONJ
iajs-555	123	27	}	}	PUNCT
iajs-555	123	28	}	}	SYM
iajs-555	123	29	b	b	NOUN
iajs-555	123	30	,	,	PUNCT
iajs-555	123	31	a{,,x	a{,,x	PROPN
iajs-555	123	32	{	{	PUNCT
iajs-555	123	33	φ	φ	NOUN
iajs-555	123	34	=	=	PRON
iajs-555	123	35	τ′	τ′	X
iajs-555	123	36	.	.	PUNCT
iajs-555	124	1	let	let	VERB
iajs-555	124	2	)	)	PUNCT
iajs-555	124	3	,	,	PUNCT
iajs-555	124	4	x(),x(:f	x(),x(:f	PROPN
iajs-555	124	5	τ′→τ	τ′→τ	NOUN
iajs-555	124	6	be	be	AUX
iajs-555	124	7	a	a	DET
iajs-555	124	8	function	function	NOUN
iajs-555	124	9	defined	define	VERB
iajs-555	124	10	by	by	ADP
iajs-555	124	11	:	:	PUNCT
iajs-555	124	12	a)a(f	a)a(f	PROPN
iajs-555	124	13	=	=	SYM
iajs-555	124	14	,	,	PUNCT
iajs-555	124	15	b)b(f	b)b(f	NOUN
iajs-555	124	16	=	=	SYM
iajs-555	124	17	and	and	CCONJ
iajs-555	124	18	c)c(f	c)c(f	NOUN
iajs-555	124	19	=	=	PUNCT
iajs-555	124	20	.	.	PUNCT
iajs-555	125	1	it	it	PRON
iajs-555	125	2	is	be	AUX
iajs-555	125	3	clear	clear	ADJ
iajs-555	125	4	that	that	SCONJ
iajs-555	125	5	f	f	PROPN
iajs-555	125	6	is	be	AUX
iajs-555	125	7	continuous	continuous	ADJ
iajs-555	125	8	,	,	PUNCT
iajs-555	125	9	but	but	CCONJ
iajs-555	125	10	f	f	PROPN
iajs-555	125	11	is	be	AUX
iajs-555	125	12	not	not	PART
iajs-555	125	13	gr	gr	ADJ
iajs-555	125	14	-	-	ADJ
iajs-555	125	15	continuous	continuous	ADJ
iajs-555	125	16	,	,	PUNCT
iajs-555	125	17	since{c}is	since{c}is	PROPN
iajs-555	125	18	closed	close	VERB
iajs-555	125	19	in	in	ADP
iajs-555	125	20	)	)	PUNCT
iajs-555	125	21	,	,	PUNCT
iajs-555	125	22	x	x	X
iajs-555	125	23	(	(	PUNCT
iajs-555	125	24	τ′	τ′	X
iajs-555	125	25	,	,	PUNCT
iajs-555	125	26	but	but	CCONJ
iajs-555	125	27	}	}	PUNCT
iajs-555	125	28	c{})c({f	c{})c({f	X
iajs-555	125	29	1	1	NUM
iajs-555	126	1	=	=	NOUN
iajs-555	126	2	−	−	PROPN
iajs-555	126	3	is	be	AUX
iajs-555	126	4	not	not	PART
iajs-555	126	5	gr	gr	ADV
iajs-555	126	6	-	-	PUNCT
iajs-555	126	7	closed	closed	ADJ
iajs-555	126	8	in	in	ADP
iajs-555	126	9	)	)	PUNCT
iajs-555	126	10	,	,	PUNCT
iajs-555	126	11	x	x	X
iajs-555	126	12	(	(	PUNCT
iajs-555	126	13	τ	τ	X
iajs-555	126	14	.	.	PUNCT
iajs-555	127	1	ii)let	ii)let	ADJ
iajs-555	127	2	}	}	PUNCT
iajs-555	127	3	c	c	X
iajs-555	127	4	,	,	PUNCT
iajs-555	127	5	b	b	PROPN
iajs-555	127	6	,	,	PUNCT
iajs-555	127	7	a{x	a{x	VERB
iajs-555	128	1	=	=	NOUN
iajs-555	128	2	,	,	PUNCT
iajs-555	128	3	}	}	PUNCT
iajs-555	128	4	,	,	PUNCT
iajs-555	128	5	x	x	X
iajs-555	128	6	{	{	PUNCT
iajs-555	128	7	φ	φ	PROPN
iajs-555	128	8	=	=	NOUN
iajs-555	128	9	τ	τ	X
iajs-555	128	10	and	and	CCONJ
iajs-555	128	11	}	}	PUNCT
iajs-555	128	12	}	}	PUNCT
iajs-555	128	13	a{,,x	a{,,x	PROPN
iajs-555	128	14	{	{	PUNCT
iajs-555	128	15	φ	φ	NOUN
iajs-555	128	16	=	=	PRON
iajs-555	128	17	τ′	τ′	X
iajs-555	128	18	.	.	PUNCT
iajs-555	129	1	let	let	VERB
iajs-555	129	2	)	)	PUNCT
iajs-555	129	3	,	,	PUNCT
iajs-555	129	4	x(),x(:f	x(),x(:f	PROPN
iajs-555	129	5	τ′→τ	τ′→τ	NOUN
iajs-555	129	6	be	be	AUX
iajs-555	129	7	a	a	DET
iajs-555	129	8	function	function	NOUN
iajs-555	129	9	defined	define	VERB
iajs-555	129	10	by	by	ADP
iajs-555	129	11	:	:	PUNCT
iajs-555	129	12	a)a(f	a)a(f	PROPN
iajs-555	129	13	=	=	SYM
iajs-555	129	14	,	,	PUNCT
iajs-555	129	15	b)b(f	b)b(f	NOUN
iajs-555	129	16	=	=	SYM
iajs-555	129	17	and	and	CCONJ
iajs-555	129	18	c)c(f	c)c(f	NOUN
iajs-555	129	19	=	=	PUNCT
iajs-555	129	20	.	.	PUNCT
iajs-555	130	1	it	it	PRON
iajs-555	130	2	is	be	AUX
iajs-555	130	3	clear	clear	ADJ
iajs-555	130	4	that	that	SCONJ
iajs-555	130	5	f	f	PROPN
iajs-555	130	6	is	be	AUX
iajs-555	130	7	not	not	PART
iajs-555	130	8	continuous	continuous	ADJ
iajs-555	130	9	,	,	PUNCT
iajs-555	130	10	but	but	CCONJ
iajs-555	130	11	f	f	PROPN
iajs-555	130	12	is	be	AUX
iajs-555	130	13	gr	gr	ADV
iajs-555	130	14	-	-	ADJ
iajs-555	130	15	continuous	continuous	ADJ
iajs-555	130	16	,	,	PUNCT
iajs-555	130	17	since	since	SCONJ
iajs-555	130	18	φ	φ	NOUN
iajs-555	130	19	=	=	NOUN
iajs-555	130	20	φ−	φ−	PROPN
iajs-555	130	21	)	)	PUNCT
iajs-555	130	22	(	(	PUNCT
iajs-555	130	23	f	f	NOUN
iajs-555	130	24	1	1	NUM
iajs-555	130	25	,	,	PUNCT
iajs-555	130	26	x)x(f	x)x(f	X
iajs-555	130	27	1	1	NUM
iajs-555	130	28	=	=	NOUN
iajs-555	130	29	−	−	PROPN
iajs-555	130	30	and	and	CCONJ
iajs-555	130	31	}	}	SYM
iajs-555	130	32	c	c	NOUN
iajs-555	130	33	,	,	PUNCT
iajs-555	130	34	b{})c	b{})c	ADJ
iajs-555	130	35	,	,	PUNCT
iajs-555	130	36	b({f	b({f	NOUN
iajs-555	130	37	1	1	NUM
iajs-555	130	38	=	=	NOUN
iajs-555	130	39	−	−	NOUN
iajs-555	130	40	are	be	AUX
iajs-555	130	41	gr	gr	ADV
iajs-555	130	42	-	-	PUNCT
iajs-555	130	43	closed	closed	ADJ
iajs-555	130	44	in	in	ADP
iajs-555	130	45	)	)	PUNCT
iajs-555	130	46	,	,	PUNCT
iajs-555	130	47	x	x	X
iajs-555	130	48	(	(	PUNCT
iajs-555	130	49	τ	τ	X
iajs-555	130	50	.	.	PUNCT
iajs-555	131	1	2)the	2)the	NUM
iajs-555	131	2	converse	converse	NOUN
iajs-555	131	3	of	of	ADP
iajs-555	131	4	(	(	PUNCT
iajs-555	131	5	(	(	PUNCT
iajs-555	131	6	2.7),no.1	2.7),no.1	NOUN
iajs-555	131	7	)	)	PUNCT
iajs-555	131	8	in	in	ADP
iajs-555	131	9	general	general	ADJ
iajs-555	131	10	is	be	AUX
iajs-555	131	11	not	not	PART
iajs-555	131	12	true	true	ADJ
iajs-555	131	13	.consider	.consider	PUNCT
iajs-555	132	1	the	the	DET
iajs-555	132	2	following	follow	VERB
iajs-555	132	3	examples	example	NOUN
iajs-555	132	4	:	:	PUNCT
iajs-555	132	5	let	let	VERB
iajs-555	132	6	}	}	PUNCT
iajs-555	132	7	d	d	X
iajs-555	132	8	,	,	PUNCT
iajs-555	132	9	c	c	X
iajs-555	132	10	,	,	PUNCT
iajs-555	132	11	b	b	PROPN
iajs-555	132	12	,	,	PUNCT
iajs-555	132	13	a{x	a{x	VERB
iajs-555	133	1	=	=	NOUN
iajs-555	133	2	,	,	PUNCT
iajs-555	133	3	}	}	PUNCT
iajs-555	133	4	q	q	X
iajs-555	133	5	,	,	PUNCT
iajs-555	133	6	p{y	p{y	NOUN
iajs-555	133	7	=	=	PUNCT
iajs-555	133	8	,	,	PUNCT
iajs-555	133	9	}	}	PUNCT
iajs-555	133	10	}	}	PUNCT
iajs-555	133	11	d	d	X
iajs-555	133	12	,	,	PUNCT
iajs-555	133	13	c{,,x	c{,,x	PROPN
iajs-555	133	14	{	{	PUNCT
iajs-555	133	15	φ	φ	PROPN
iajs-555	133	16	=	=	PROPN
iajs-555	133	17	τ	τ	X
iajs-555	133	18	and	and	CCONJ
iajs-555	133	19	}	}	PUNCT
iajs-555	133	20	}	}	PUNCT
iajs-555	133	21	p{,,y	p{,,y	NOUN
iajs-555	133	22	{	{	PUNCT
iajs-555	133	23	φ	φ	NOUN
iajs-555	133	24	=	=	NOUN
iajs-555	133	25	τ′	τ′	X
iajs-555	133	26	.	.	PUNCT
iajs-555	134	1	let	let	VERB
iajs-555	134	2	)	)	PUNCT
iajs-555	134	3	,	,	PUNCT
iajs-555	134	4	y(),x(:f	y(),x(:f	PROPN
iajs-555	134	5	τ′→τ	τ′→τ	NOUN
iajs-555	134	6	be	be	AUX
iajs-555	134	7	a	a	DET
iajs-555	134	8	function	function	NOUN
iajs-555	134	9	defined	define	VERB
iajs-555	134	10	by	by	ADP
iajs-555	134	11	:	:	PUNCT
iajs-555	134	12	q)d(f)b(f)a(f	q)d(f)b(f)a(f	ADJ
iajs-555	134	13	=	=	PROPN
iajs-555	134	14	=	=	SYM
iajs-555	134	15	=	=	SYM
iajs-555	134	16	and	and	CCONJ
iajs-555	134	17	p)c(f	p)c(f	NOUN
iajs-555	134	18	=	=	X
iajs-555	134	19	.	.	PUNCT
iajs-555	135	1	f	f	PROPN
iajs-555	135	2	is	be	AUX
iajs-555	135	3	gr	gr	ADV
iajs-555	135	4	-	-	ADJ
iajs-555	135	5	continuous	continuous	ADJ
iajs-555	135	6	,	,	PUNCT
iajs-555	135	7	since	since	SCONJ
iajs-555	135	8	φ	φ	NOUN
iajs-555	135	9	=	=	NOUN
iajs-555	135	10	φ−	φ−	PROPN
iajs-555	135	11	)	)	PUNCT
iajs-555	135	12	(	(	PUNCT
iajs-555	135	13	f	f	PROPN
iajs-555	135	14	1	1	NUM
iajs-555	135	15	,	,	PUNCT
iajs-555	135	16	x)y(f	x)y(f	PROPN
iajs-555	135	17	1	1	NUM
iajs-555	135	18	=	=	NOUN
iajs-555	135	19	−	−	PROPN
iajs-555	135	20	and	and	CCONJ
iajs-555	135	21	}	}	SYM
iajs-555	135	22	d	d	PROPN
iajs-555	135	23	,	,	PUNCT
iajs-555	135	24	b	b	PROPN
iajs-555	135	25	,	,	PUNCT
iajs-555	135	26	a{})q({f	a{})q({f	PROPN
iajs-555	135	27	1	1	NUM
iajs-555	135	28	=	=	NOUN
iajs-555	135	29	−	−	PROPN
iajs-555	135	30	are	be	AUX
iajs-555	135	31	gr	gr	ADV
iajs-555	135	32	-	-	PUNCT
iajs-555	135	33	closed	closed	ADJ
iajs-555	135	34	in	in	ADP
iajs-555	135	35	)	)	PUNCT
iajs-555	135	36	,	,	PUNCT
iajs-555	135	37	x	x	X
iajs-555	135	38	(	(	PUNCT
iajs-555	135	39	τ	τ	X
iajs-555	135	40	.	.	PUNCT
iajs-555	136	1	but	but	CCONJ
iajs-555	136	2	f	f	PROPN
iajs-555	136	3	is	be	AUX
iajs-555	136	4	not	not	PART
iajs-555	136	5	r	r	NOUN
iajs-555	136	6	-	-	ADJ
iajs-555	136	7	continuous	continuous	ADJ
iajs-555	136	8	,	,	PUNCT
iajs-555	136	9	since{q}is	since{q}is	PROPN
iajs-555	136	10	closed	close	VERB
iajs-555	136	11	in	in	ADP
iajs-555	136	12	)	)	PUNCT
iajs-555	136	13	,	,	PUNCT
iajs-555	136	14	y	y	PROPN
iajs-555	136	15	(	(	PUNCT
iajs-555	136	16	τ′	τ′	X
iajs-555	136	17	,	,	PUNCT
iajs-555	136	18	but	but	CCONJ
iajs-555	136	19	}	}	PUNCT
iajs-555	136	20	d	d	NOUN
iajs-555	136	21	,	,	PUNCT
iajs-555	136	22	b	b	PROPN
iajs-555	136	23	,	,	PUNCT
iajs-555	136	24	a{})q({f	a{})q({f	PROPN
iajs-555	136	25	1	1	NUM
iajs-555	137	1	=	=	NOUN
iajs-555	137	2	−	−	PROPN
iajs-555	137	3	is	be	AUX
iajs-555	137	4	not	not	PART
iajs-555	137	5	r	r	NOUN
iajs-555	137	6	-	-	PUNCT
iajs-555	137	7	closed	closed	ADJ
iajs-555	137	8	in	in	ADP
iajs-555	137	9	)	)	PUNCT
iajs-555	137	10	,	,	PUNCT
iajs-555	137	11	x	x	X
iajs-555	137	12	(	(	PUNCT
iajs-555	137	13	τ	τ	X
iajs-555	137	14	.	.	PUNCT
iajs-555	138	1	3)the	3)the	DET
iajs-555	138	2	converse	converse	NOUN
iajs-555	138	3	of	of	ADP
iajs-555	138	4	(	(	PUNCT
iajs-555	138	5	(	(	PUNCT
iajs-555	138	6	2.7),no.2,3,4	2.7),no.2,3,4	NUM
iajs-555	138	7	)	)	PUNCT
iajs-555	138	8	in	in	ADP
iajs-555	138	9	general	general	ADJ
iajs-555	138	10	is	be	AUX
iajs-555	138	11	not	not	PART
iajs-555	138	12	true	true	ADJ
iajs-555	138	13	.in	.in	PUNCT
iajs-555	138	14	(	(	PUNCT
iajs-555	138	15	1,(i)),f	1,(i)),f	NUM
iajs-555	138	16	is	be	AUX
iajs-555	138	17	g	g	NOUN
iajs-555	138	18	-	-	PUNCT
iajs-555	138	19	continuous(resp	continuous(resp	NOUN
iajs-555	138	20	.	.	PUNCT
iajs-555	139	1	rg	rg	PROPN
iajs-555	139	2	continuous	continuous	ADJ
iajs-555	139	3	,	,	PUNCT
iajs-555	139	4	gb	gb	ADV
iajs-555	139	5	-	-	PUNCT
iajs-555	139	6	continuous	continuous	ADJ
iajs-555	139	7	)	)	PUNCT
iajs-555	139	8	since	since	SCONJ
iajs-555	139	9	f	f	PROPN
iajs-555	139	10	is	be	AUX
iajs-555	139	11	continuous	continuous	ADJ
iajs-555	139	12	,	,	PUNCT
iajs-555	139	13	but	but	CCONJ
iajs-555	139	14	f	f	PROPN
iajs-555	139	15	is	be	AUX
iajs-555	139	16	not	not	PART
iajs-555	139	17	gr	gr	ADV
iajs-555	139	18	-	-	NOUN
iajs-555	139	19	continuous	continuous	ADJ
iajs-555	139	20	.	.	PUNCT
iajs-555	140	1	4)the	4)the	DET
iajs-555	140	2	converse	converse	NOUN
iajs-555	140	3	of	of	ADP
iajs-555	140	4	(	(	PUNCT
iajs-555	140	5	(	(	PUNCT
iajs-555	140	6	2.7),no.5)in	2.7),no.5)in	PROPN
iajs-555	140	7	general	general	NOUN
iajs-555	140	8	is	be	AUX
iajs-555	140	9	not	not	PART
iajs-555	140	10	true	true	ADJ
iajs-555	140	11	.in	.in	PUNCT
iajs-555	140	12	(	(	PUNCT
iajs-555	140	13	1,(ii	1,(ii	NUM
iajs-555	140	14	)	)	PUNCT
iajs-555	140	15	)	)	PUNCT
iajs-555	140	16	,	,	PUNCT
iajs-555	140	17	f	f	PROPN
iajs-555	140	18	is	be	AUX
iajs-555	140	19	rg	rg	NOUN
iajs-555	140	20	-	-	ADJ
iajs-555	140	21	continuous	continuous	ADJ
iajs-555	140	22	,	,	PUNCT
iajs-555	140	23	but	but	CCONJ
iajs-555	140	24	f	f	PROPN
iajs-555	140	25	is	be	AUX
iajs-555	140	26	not	not	PART
iajs-555	140	27	continuous	continuous	ADJ
iajs-555	140	28	.	.	PUNCT
iajs-555	141	1	5)the	5)the	DET
iajs-555	141	2	converse	converse	NOUN
iajs-555	141	3	of	of	ADP
iajs-555	141	4	(	(	PUNCT
iajs-555	141	5	(	(	PUNCT
iajs-555	141	6	2.7),no.6,7,8,9	2.7),no.6,7,8,9	NUM
iajs-555	141	7	)	)	PUNCT
iajs-555	141	8	in	in	ADP
iajs-555	141	9	general	general	ADJ
iajs-555	141	10	is	be	AUX
iajs-555	141	11	not	not	PART
iajs-555	141	12	true	true	ADJ
iajs-555	141	13	.in	.in	PUNCT
iajs-555	141	14	(	(	PUNCT
iajs-555	141	15	2),f	2),f	PROPN
iajs-555	141	16	is	be	AUX
iajs-555	141	17	gr	gr	ADJ
iajs-555	141	18	-	-	ADJ
iajs-555	141	19	continuous	continuous	ADJ
iajs-555	141	20	(	(	PUNCT
iajs-555	141	21	resp	resp	NOUN
iajs-555	141	22	.	.	PUNCT
iajs-555	142	1	rg	rg	PROPN
iajs-555	142	2	continuous	continuous	ADJ
iajs-555	142	3	,	,	PUNCT
iajs-555	142	4	g	g	NOUN
iajs-555	142	5	-	-	PUNCT
iajs-555	142	6	continuous	continuous	ADJ
iajs-555	142	7	,	,	PUNCT
iajs-555	142	8	gb	gb	ADV
iajs-555	142	9	-	-	PUNCT
iajs-555	142	10	continuous	continuous	ADJ
iajs-555	142	11	)	)	PUNCT
iajs-555	142	12	,	,	PUNCT
iajs-555	142	13	but	but	CCONJ
iajs-555	142	14	f	f	PROPN
iajs-555	142	15	is	be	AUX
iajs-555	142	16	not	not	PART
iajs-555	142	17	perfectly	perfectly	ADV
iajs-555	142	18	gr	gr	ADJ
iajs-555	142	19	-	-	ADJ
iajs-555	142	20	continuous	continuous	ADJ
iajs-555	142	21	,	,	PUNCT
iajs-555	142	22	since{p}is	since{p}is	PROPN
iajs-555	142	23	open	open	ADJ
iajs-555	142	24	in	in	ADP
iajs-555	142	25	)	)	PUNCT
iajs-555	142	26	,	,	PUNCT
iajs-555	142	27	y	y	PROPN
iajs-555	142	28	(	(	PUNCT
iajs-555	142	29	τ′	τ′	X
iajs-555	142	30	,	,	PUNCT
iajs-555	142	31	but	but	CCONJ
iajs-555	142	32	}	}	PUNCT
iajs-555	142	33	c{})p({f	c{})p({f	VERB
iajs-555	142	34	1	1	NUM
iajs-555	143	1	=	=	SYM
iajs-555	143	2	−	−	PROPN
iajs-555	143	3	is	be	AUX
iajs-555	143	4	gr	gr	ADV
iajs-555	143	5	-	-	NOUN
iajs-555	143	6	open	open	ADJ
iajs-555	143	7	,	,	PUNCT
iajs-555	143	8	but	but	CCONJ
iajs-555	143	9	not	not	PART
iajs-555	143	10	gr	gr	ADV
iajs-555	143	11	-	-	PUNCT
iajs-555	143	12	closed	closed	ADJ
iajs-555	143	13	in	in	ADP
iajs-555	143	14	)	)	PUNCT
iajs-555	143	15	,	,	PUNCT
iajs-555	143	16	x	x	X
iajs-555	143	17	(	(	PUNCT
iajs-555	143	18	τ	τ	X
iajs-555	143	19	.	.	PUNCT
iajs-555	144	1	6)the	6)the	DET
iajs-555	144	2	converse	converse	NOUN
iajs-555	144	3	of	of	ADP
iajs-555	144	4	(	(	PUNCT
iajs-555	144	5	(	(	PUNCT
iajs-555	144	6	2.7),no.10	2.7),no.10	NUM
iajs-555	144	7	)	)	PUNCT
iajs-555	144	8	in	in	ADP
iajs-555	144	9	general	general	ADJ
iajs-555	144	10	is	be	AUX
iajs-555	144	11	not	not	PART
iajs-555	144	12	true	true	ADJ
iajs-555	144	13	.consider	.consider	PUNCT
iajs-555	145	1	the	the	DET
iajs-555	145	2	following	follow	VERB
iajs-555	145	3	examples	example	NOUN
iajs-555	145	4	:	:	PUNCT
iajs-555	145	5	let	let	VERB
iajs-555	145	6	}	}	PUNCT
iajs-555	145	7	b	b	NOUN
iajs-555	145	8	,	,	PUNCT
iajs-555	145	9	a{yx	a{yx	PROPN
iajs-555	145	10	=	=	NOUN
iajs-555	145	11	=	=	PROPN
iajs-555	145	12	and	and	CCONJ
iajs-555	145	13	}	}	PUNCT
iajs-555	145	14	}	}	PUNCT
iajs-555	145	15	a{,,x	a{,,x	PROPN
iajs-555	145	16	{	{	PUNCT
iajs-555	145	17	φ	φ	NOUN
iajs-555	145	18	=	=	NOUN
iajs-555	145	19	τ′=τ	τ′=τ	ADJ
iajs-555	145	20	.	.	PUNCT
iajs-555	146	1	let	let	VERB
iajs-555	146	2	)	)	PUNCT
iajs-555	146	3	,	,	PUNCT
iajs-555	146	4	x(),x(:f	x(),x(:f	PROPN
iajs-555	146	5	τ′→τ	τ′→τ	NOUN
iajs-555	146	6	be	be	AUX
iajs-555	146	7	a	a	DET
iajs-555	146	8	function	function	NOUN
iajs-555	146	9	defined	define	VERB
iajs-555	146	10	by	by	ADP
iajs-555	146	11	:	:	PUNCT
iajs-555	146	12	b)a(f	b)a(f	NOUN
iajs-555	146	13	=	=	PUNCT
iajs-555	146	14	and	and	CCONJ
iajs-555	146	15	a)b(f	a)b(f	PROPN
iajs-555	146	16	=	=	PUNCT
iajs-555	146	17	.	.	PUNCT
iajs-555	147	1	f	f	PROPN
iajs-555	147	2	is	be	AUX
iajs-555	147	3	contra	contra	PROPN
iajs-555	147	4	gr	gr	PROPN
iajs-555	147	5	-	-	PUNCT
iajs-555	147	6	continuous	continuous	ADJ
iajs-555	147	7	,	,	PUNCT
iajs-555	147	8	since	since	SCONJ
iajs-555	147	9	φ	φ	NOUN
iajs-555	147	10	=	=	NOUN
iajs-555	147	11	φ−	φ−	PROPN
iajs-555	147	12	)	)	PUNCT
iajs-555	147	13	(	(	PUNCT
iajs-555	147	14	f	f	PROPN
iajs-555	147	15	1	1	NUM
iajs-555	147	16	,	,	PUNCT
iajs-555	147	17	x)y(f	x)y(f	PROPN
iajs-555	147	18	1	1	NUM
iajs-555	147	19	=	=	NOUN
iajs-555	147	20	−	−	NOUN
iajs-555	147	21	and	and	CCONJ
iajs-555	147	22	}	}	PUNCT
iajs-555	147	23	b{})a({f	b{})a({f	VERB
iajs-555	147	24	1	1	NUM
iajs-555	147	25	=	=	NOUN
iajs-555	147	26	−	−	NOUN
iajs-555	147	27	are	be	AUX
iajs-555	147	28	gr	gr	ADV
iajs-555	147	29	-	-	PUNCT
iajs-555	147	30	closed	closed	ADJ
iajs-555	147	31	in	in	ADP
iajs-555	147	32	)	)	PUNCT
iajs-555	147	33	,	,	PUNCT
iajs-555	147	34	x	x	X
iajs-555	147	35	(	(	PUNCT
iajs-555	147	36	τ	τ	X
iajs-555	147	37	.but	.but	PUNCT
iajs-555	148	1	f	f	PROPN
iajs-555	148	2	is	be	AUX
iajs-555	148	3	not	not	PART
iajs-555	148	4	perfectly	perfectly	ADV
iajs-555	148	5	gr	gr	ADJ
iajs-555	148	6	-	-	ADJ
iajs-555	148	7	continuous	continuous	ADJ
iajs-555	148	8	,	,	PUNCT
iajs-555	148	9	since{a}is	since{a}is	PROPN
iajs-555	148	10	open	open	ADJ
iajs-555	148	11	in	in	ADP
iajs-555	148	12	)	)	PUNCT
iajs-555	148	13	,	,	PUNCT
iajs-555	148	14	x	x	X
iajs-555	148	15	(	(	PUNCT
iajs-555	148	16	τ′	τ′	X
iajs-555	148	17	,	,	PUNCT
iajs-555	148	18	but	but	CCONJ
iajs-555	148	19	}	}	PUNCT
iajs-555	148	20	b{})a({f	b{})a({f	VERB
iajs-555	148	21	1	1	NUM
iajs-555	148	22	=	=	NOUN
iajs-555	148	23	−	−	PROPN
iajs-555	148	24	is	be	AUX
iajs-555	148	25	gr	gr	ADV
iajs-555	148	26	closed	closed	ADJ
iajs-555	148	27	,	,	PUNCT
iajs-555	148	28	but	but	CCONJ
iajs-555	148	29	not	not	PART
iajs-555	148	30	gr	gr	ADV
iajs-555	148	31	-	-	NOUN
iajs-555	148	32	open	open	ADJ
iajs-555	148	33	in	in	ADP
iajs-555	148	34	)	)	PUNCT
iajs-555	148	35	,	,	PUNCT
iajs-555	148	36	x	x	X
iajs-555	148	37	(	(	PUNCT
iajs-555	148	38	τ	τ	X
iajs-555	148	39	.	.	PUNCT
iajs-555	148	40	7)continuous	7)continuous	ADJ
iajs-555	148	41	functions	function	NOUN
iajs-555	148	42	and	and	CCONJ
iajs-555	148	43	contra	contra	PROPN
iajs-555	148	44	gr	gr	ADJ
iajs-555	148	45	-	-	PUNCT
iajs-555	148	46	continuous	continuous	ADJ
iajs-555	148	47	functions	function	NOUN
iajs-555	148	48	are	be	AUX
iajs-555	148	49	in	in	ADP
iajs-555	148	50	general	general	ADJ
iajs-555	148	51	independent	independent	ADJ
iajs-555	148	52	.	.	PUNCT
iajs-555	149	1	consider	consider	VERB
iajs-555	149	2	the	the	DET
iajs-555	149	3	following	follow	VERB
iajs-555	149	4	examples	example	NOUN
iajs-555	149	5	:	:	PUNCT
iajs-555	149	6	i	i	X
iajs-555	149	7	)	)	PUNCT
iajs-555	149	8	it	it	PRON
iajs-555	149	9	is	be	AUX
iajs-555	149	10	clear	clear	ADJ
iajs-555	149	11	that	that	SCONJ
iajs-555	149	12	in	in	ADP
iajs-555	149	13	(	(	PUNCT
iajs-555	149	14	1,(i)),f	1,(i)),f	NUM
iajs-555	149	15	is	be	AUX
iajs-555	149	16	continuous	continuous	ADJ
iajs-555	149	17	,	,	PUNCT
iajs-555	149	18	but	but	CCONJ
iajs-555	149	19	f	f	PROPN
iajs-555	149	20	is	be	AUX
iajs-555	149	21	not	not	PART
iajs-555	149	22	contra	contra	PROPN
iajs-555	149	23	gr	gr	ADV
iajs-555	149	24	-	-	PUNCT
iajs-555	149	25	continuous	continuous	ADJ
iajs-555	149	26	.	.	PUNCT
iajs-555	150	1	ii	ii	X
iajs-555	150	2	)	)	PUNCT
iajs-555	151	1	it	it	PRON
iajs-555	151	2	is	be	AUX
iajs-555	151	3	clear	clear	ADJ
iajs-555	151	4	that	that	SCONJ
iajs-555	151	5	in	in	SCONJ
iajs-555	151	6	(	(	PUNCT
iajs-555	151	7	6),f	6),f	PROPN
iajs-555	151	8	is	be	AUX
iajs-555	151	9	contra	contra	PROPN
iajs-555	151	10	gr	gr	PROPN
iajs-555	151	11	-	-	PUNCT
iajs-555	151	12	continuous	continuous	ADJ
iajs-555	151	13	,	,	PUNCT
iajs-555	151	14	but	but	CCONJ
iajs-555	151	15	f	f	PROPN
iajs-555	151	16	is	be	AUX
iajs-555	151	17	not	not	PART
iajs-555	151	18	continuous	continuous	ADJ
iajs-555	151	19	.	.	PUNCT
iajs-555	152	1	8)contra	8)contra	NUM
iajs-555	152	2	gr	gr	NUM
iajs-555	152	3	-	-	PUNCT
iajs-555	152	4	continuous	continuous	ADJ
iajs-555	152	5	functions	function	NOUN
iajs-555	152	6	and	and	CCONJ
iajs-555	152	7	r	r	NOUN
iajs-555	152	8	-	-	PUNCT
iajs-555	152	9	continuous	continuous	ADJ
iajs-555	152	10	functions	function	NOUN
iajs-555	152	11	are	be	AUX
iajs-555	152	12	in	in	ADP
iajs-555	152	13	general	general	ADJ
iajs-555	152	14	independent	independent	ADJ
iajs-555	152	15	.	.	PUNCT
iajs-555	153	1	consider	consider	VERB
iajs-555	153	2	the	the	DET
iajs-555	153	3	following	follow	VERB
iajs-555	153	4	examples	example	NOUN
iajs-555	153	5	:	:	PUNCT
iajs-555	153	6	i	i	X
iajs-555	153	7	)	)	PUNCT
iajs-555	153	8	it	it	PRON
iajs-555	153	9	is	be	AUX
iajs-555	153	10	clear	clear	ADJ
iajs-555	153	11	that	that	SCONJ
iajs-555	153	12	in	in	SCONJ
iajs-555	153	13	(	(	PUNCT
iajs-555	153	14	6),f	6),f	PROPN
iajs-555	153	15	is	be	AUX
iajs-555	153	16	contra	contra	PROPN
iajs-555	153	17	gr	gr	PROPN
iajs-555	153	18	-	-	PUNCT
iajs-555	153	19	continuous	continuous	ADJ
iajs-555	153	20	,	,	PUNCT
iajs-555	153	21	but	but	CCONJ
iajs-555	153	22	f	f	PROPN
iajs-555	153	23	is	be	AUX
iajs-555	153	24	not	not	PART
iajs-555	153	25	r	r	NOUN
iajs-555	153	26	-	-	NOUN
iajs-555	153	27	continuous	continuous	ADJ
iajs-555	153	28	.	.	PUNCT
iajs-555	154	1	ii)let	ii)let	ADJ
iajs-555	154	2	}	}	PUNCT
iajs-555	154	3	d	d	X
iajs-555	154	4	,	,	PUNCT
iajs-555	154	5	c	c	X
iajs-555	154	6	,	,	PUNCT
iajs-555	154	7	b	b	NOUN
iajs-555	154	8	,	,	PUNCT
iajs-555	154	9	a{yx	a{yx	PROPN
iajs-555	154	10	=	=	NOUN
iajs-555	154	11	=	=	NOUN
iajs-555	154	12	,	,	PUNCT
iajs-555	154	13	}	}	PUNCT
iajs-555	154	14	}	}	PUNCT
iajs-555	154	15	d	d	PROPN
iajs-555	154	16	,	,	PUNCT
iajs-555	154	17	b	b	PROPN
iajs-555	154	18	,	,	PUNCT
iajs-555	154	19	a{},c	a{},c	PROPN
iajs-555	154	20	,	,	PUNCT
iajs-555	154	21	b	b	PROPN
iajs-555	154	22	,	,	PUNCT
iajs-555	154	23	a{},b	a{},b	PROPN
iajs-555	154	24	,	,	PUNCT
iajs-555	154	25	a{},b{},a{,,x	a{},b{},a{,,x	PROPN
iajs-555	154	26	{	{	PUNCT
iajs-555	154	27	φ	φ	PROPN
iajs-555	154	28	=	=	PROPN
iajs-555	154	29	τ	τ	X
iajs-555	154	30	and	and	CCONJ
iajs-555	154	31	}	}	PUNCT
iajs-555	154	32	}	}	PUNCT
iajs-555	154	33	a{,,y	a{,,y	NOUN
iajs-555	154	34	{	{	PUNCT
iajs-555	154	35	φ	φ	NOUN
iajs-555	154	36	=	=	PRON
iajs-555	154	37	τ′	τ′	X
iajs-555	154	38	.	.	PUNCT
iajs-555	155	1	let	let	VERB
iajs-555	155	2	)	)	PUNCT
iajs-555	155	3	,	,	PUNCT
iajs-555	155	4	y(),x(:f	y(),x(:f	PROPN
iajs-555	155	5	τ′→τ	τ′→τ	NOUN
iajs-555	155	6	be	be	AUX
iajs-555	155	7	a	a	DET
iajs-555	155	8	function	function	NOUN
iajs-555	155	9	defined	define	VERB
iajs-555	155	10	by	by	ADP
iajs-555	155	11	:	:	PUNCT
iajs-555	155	12	a)a(f	a)a(f	PROPN
iajs-555	155	13	=	=	SYM
iajs-555	155	14	,	,	PUNCT
iajs-555	155	15	b)b(f	b)b(f	NOUN
iajs-555	155	16	=	=	X
iajs-555	155	17	,	,	PUNCT
iajs-555	155	18	c)c(f	c)c(f	NOUN
iajs-555	155	19	=	=	PUNCT
iajs-555	155	20	and	and	CCONJ
iajs-555	155	21	d)d(f	d)d(f	NOUN
iajs-555	155	22	=	=	PUNCT
iajs-555	155	23	.	.	PUNCT
iajs-555	156	1	f	f	PROPN
iajs-555	156	2	is	be	AUX
iajs-555	156	3	r	r	NOUN
iajs-555	156	4	-	-	ADJ
iajs-555	156	5	continuous	continuous	ADJ
iajs-555	156	6	,	,	PUNCT
iajs-555	156	7	since	since	SCONJ
iajs-555	156	8	φ	φ	NOUN
iajs-555	156	9	=	=	NOUN
iajs-555	156	10	φ−	φ−	PROPN
iajs-555	156	11	)	)	PUNCT
iajs-555	156	12	(	(	PUNCT
iajs-555	156	13	f	f	PROPN
iajs-555	156	14	1	1	NUM
iajs-555	156	15	,	,	PUNCT
iajs-555	156	16	x)y(f	x)y(f	PROPN
iajs-555	156	17	1	1	NUM
iajs-555	156	18	=	=	NOUN
iajs-555	156	19	−	−	PROPN
iajs-555	156	20	and	and	CCONJ
iajs-555	156	21	}	}	SYM
iajs-555	156	22	d	d	PROPN
iajs-555	156	23	,	,	PUNCT
iajs-555	156	24	c	c	NOUN
iajs-555	156	25	,	,	PUNCT
iajs-555	156	26	b{})d	b{})d	X
iajs-555	156	27	,	,	PUNCT
iajs-555	156	28	c	c	X
iajs-555	156	29	,	,	PUNCT
iajs-555	156	30	b({f	b({f	NOUN
iajs-555	156	31	1	1	NUM
iajs-555	156	32	=	=	NOUN
iajs-555	156	33	−	−	NOUN
iajs-555	156	34	are	be	AUX
iajs-555	156	35	r	r	NOUN
iajs-555	156	36	-	-	PUNCT
iajs-555	156	37	closed	closed	ADJ
iajs-555	156	38	in	in	ADP
iajs-555	156	39	)	)	PUNCT
iajs-555	156	40	,	,	PUNCT
iajs-555	156	41	x	x	X
iajs-555	156	42	(	(	PUNCT
iajs-555	156	43	τ	τ	X
iajs-555	156	44	.	.	PUNCT
iajs-555	157	1	but	but	CCONJ
iajs-555	157	2	f	f	PROPN
iajs-555	157	3	is	be	AUX
iajs-555	157	4	not	not	PART
iajs-555	157	5	contra	contra	PROPN
iajs-555	157	6	gr	gr	ADV
iajs-555	157	7	-	-	PUNCT
iajs-555	157	8	continuous	continuous	ADJ
iajs-555	157	9	,	,	PUNCT
iajs-555	157	10	since{a}is	since{a}is	PROPN
iajs-555	157	11	open	open	ADJ
iajs-555	157	12	in	in	ADP
iajs-555	157	13	)	)	PUNCT
iajs-555	157	14	,	,	PUNCT
iajs-555	157	15	y	y	PROPN
iajs-555	157	16	(	(	PUNCT
iajs-555	157	17	τ′	τ′	X
iajs-555	157	18	,	,	PUNCT
iajs-555	157	19	but	but	CCONJ
iajs-555	157	20	}	}	PUNCT
iajs-555	157	21	a{})a({f	a{})a({f	PROPN
iajs-555	157	22	1	1	NUM
iajs-555	157	23	=	=	NOUN
iajs-555	157	24	−	−	PROPN
iajs-555	157	25	is	be	AUX
iajs-555	157	26	not	not	PART
iajs-555	157	27	gr	gr	ADV
iajs-555	157	28	-	-	PUNCT
iajs-555	157	29	closed	closed	ADJ
iajs-555	157	30	in	in	ADP
iajs-555	157	31	)	)	PUNCT
iajs-555	157	32	,	,	PUNCT
iajs-555	157	33	x	x	X
iajs-555	157	34	(	(	PUNCT
iajs-555	157	35	τ	τ	X
iajs-555	157	36	.	.	PUNCT
iajs-555	158	1	mathematics	mathematic	NOUN
iajs-555	158	2	382	382	NUM
iajs-555	158	3	مجلة	مجلة	NOUN
iajs-555	158	4	إبن	إبن	VERB
iajs-555	158	5	الهيثم	الهيثم	ADJ
iajs-555	158	6	للعلوم	للعلوم	NOUN
iajs-555	158	7	الصرفة	الصرفة	NOUN
iajs-555	159	1	و	و	PRON
iajs-555	159	2	التطبيقية	التطبيقية	ADJ
iajs-555	159	3	2012	2012	NUM
iajs-555	159	4	السنة	السنة	NOUN
iajs-555	159	5	25	25	NUM
iajs-555	159	6	المجلد	المجلد	NOUN
iajs-555	159	7	3	3	NUM
iajs-555	159	8	العدد	العدد	PROPN
iajs-555	159	9	ibn	ibn	PROPN
iajs-555	159	10	al	al	PROPN
iajs-555	159	11	-	-	PUNCT
iajs-555	159	12	haitham	haitham	PROPN
iajs-555	159	13	journal	journal	PROPN
iajs-555	159	14	for	for	ADP
iajs-555	159	15	pure	pure	ADJ
iajs-555	159	16	and	and	CCONJ
iajs-555	159	17	applied	apply	VERB
iajs-555	159	18	science	science	NOUN
iajs-555	159	19	no	no	NOUN
iajs-555	159	20	.	.	NOUN
iajs-555	159	21	3	3	NUM
iajs-555	159	22	vol	vol	NOUN
iajs-555	159	23	.	.	PUNCT
iajs-555	160	1	25	25	NUM
iajs-555	160	2	year	year	NOUN
iajs-555	160	3	2012	2012	NUM
iajs-555	160	4	thus	thus	ADV
iajs-555	160	5	we	we	PRON
iajs-555	160	6	have	have	VERB
iajs-555	160	7	the	the	DET
iajs-555	160	8	following	follow	VERB
iajs-555	160	9	diagram	diagram	NOUN
iajs-555	160	10	:	:	PUNCT
iajs-555	160	11	definition	definition	NOUN
iajs-555	160	12	:	:	PUNCT
iajs-555	160	13	a	a	DET
iajs-555	160	14	topological	topological	ADJ
iajs-555	160	15	space	space	NOUN
iajs-555	160	16	)	)	PUNCT
iajs-555	160	17	,	,	PUNCT
iajs-555	160	18	x	x	X
iajs-555	160	19	(	(	PUNCT
iajs-555	160	20	τ	τ	X
iajs-555	160	21	is	be	AUX
iajs-555	160	22	called	call	VERB
iajs-555	160	23	a	a	DET
iajs-555	160	24	grt	grt	NOUN
iajs-555	160	25	space	space	NOUN
iajs-555	160	26	if	if	SCONJ
iajs-555	160	27	every	every	DET
iajs-555	160	28	rg	rg	NOUN
iajs-555	160	29	-	-	PUNCT
iajs-555	160	30	closed	closed	ADJ
iajs-555	160	31	set	set	NOUN
iajs-555	160	32	is	be	AUX
iajs-555	160	33	gr	gr	PRON
iajs-555	160	34	-	-	PUNCT
iajs-555	160	35	closed	closed	ADJ
iajs-555	160	36	set	set	NOUN
iajs-555	160	37	.	.	PUNCT
iajs-555	161	1	examples	example	NOUN
iajs-555	161	2	:	:	PUNCT
iajs-555	161	3	1)in	1)in	NUM
iajs-555	161	4	remarks	remark	NOUN
iajs-555	161	5	(	(	PUNCT
iajs-555	161	6	(	(	PUNCT
iajs-555	161	7	2.8	2.8	NUM
iajs-555	161	8	)	)	PUNCT
iajs-555	161	9	no.1(ii	no.1(ii	PROPN
iajs-555	161	10	)	)	PUNCT
iajs-555	161	11	)	)	PUNCT
iajs-555	161	12	,	,	PUNCT
iajs-555	161	13	)	)	PUNCT
iajs-555	161	14	,	,	PUNCT
iajs-555	161	15	x	x	X
iajs-555	161	16	(	(	PUNCT
iajs-555	161	17	τ	τ	X
iajs-555	161	18	is	be	AUX
iajs-555	161	19	a	a	DET
iajs-555	161	20	grt	grt	NOUN
iajs-555	161	21	space	space	NOUN
iajs-555	161	22	,	,	PUNCT
iajs-555	161	23	since	since	SCONJ
iajs-555	161	24	rg	rg	NOUN
iajs-555	161	25	-	-	PUNCT
iajs-555	161	26	closed	closed	ADJ
iajs-555	161	27	set	set	NOUN
iajs-555	161	28	=	=	SYM
iajs-555	161	29	{	{	PUNCT
iajs-555	161	30	x	x	PROPN
iajs-555	161	31	,	,	PUNCT
iajs-555	161	32	φ	φ	PROPN
iajs-555	161	33	,	,	PUNCT
iajs-555	161	34	{	{	PUNCT
iajs-555	161	35	a},{b},{c	a},{b},{c	X
iajs-555	161	36	}	}	PUNCT
iajs-555	161	37	,	,	PUNCT
iajs-555	161	38	{	{	PUNCT
iajs-555	161	39	a	a	PRON
iajs-555	161	40	,	,	PUNCT
iajs-555	161	41	b},{a	b},{a	ADV
iajs-555	161	42	,	,	PUNCT
iajs-555	161	43	c},{b	c},{b	NOUN
iajs-555	161	44	,	,	PUNCT
iajs-555	161	45	c	c	NOUN
iajs-555	161	46	}	}	PUNCT
iajs-555	161	47	}	}	PUNCT
iajs-555	161	48	=	=	SYM
iajs-555	161	49	gr	gr	VERB
iajs-555	161	50	-	-	PUNCT
iajs-555	161	51	closed	closed	ADJ
iajs-555	161	52	.	.	PUNCT
iajs-555	162	1	2)in	2)in	NUM
iajs-555	162	2	remarks	remark	VERB
iajs-555	162	3	(	(	PUNCT
iajs-555	162	4	(	(	PUNCT
iajs-555	162	5	1.2	1.2	NUM
iajs-555	162	6	)	)	PUNCT
iajs-555	162	7	no.1(ii	no.1(ii	PROPN
iajs-555	162	8	)	)	PUNCT
iajs-555	162	9	)	)	PUNCT
iajs-555	162	10	,	,	PUNCT
iajs-555	162	11	)	)	PUNCT
iajs-555	162	12	,	,	PUNCT
iajs-555	162	13	x	x	X
iajs-555	162	14	(	(	PUNCT
iajs-555	162	15	τ	τ	X
iajs-555	162	16	is	be	AUX
iajs-555	162	17	not	not	PART
iajs-555	162	18	a	a	DET
iajs-555	162	19	grt	grt	NOUN
iajs-555	162	20	space	space	NOUN
iajs-555	162	21	,	,	PUNCT
iajs-555	162	22	since	since	SCONJ
iajs-555	162	23	}	}	PUNCT
iajs-555	162	24	c	c	X
iajs-555	162	25	{	{	PUNCT
iajs-555	162	26	is	be	AUX
iajs-555	162	27	rg	rg	NOUN
iajs-555	162	28	-	-	PUNCT
iajs-555	162	29	closed	closed	ADJ
iajs-555	162	30	set	set	NOUN
iajs-555	162	31	,	,	PUNCT
iajs-555	162	32	but	but	CCONJ
iajs-555	162	33	not	not	PART
iajs-555	162	34	gr	gr	PRON
iajs-555	162	35	closed	closed	ADJ
iajs-555	162	36	.	.	PUNCT
iajs-555	163	1	theorem	theorem	VERB
iajs-555	163	2	:	:	PUNCT
iajs-555	163	3	let	let	VERB
iajs-555	163	4	yx	yx	NOUN
iajs-555	163	5	:	:	PUNCT
iajs-555	163	6	f	f	X
iajs-555	163	7	→	→	PUNCT
iajs-555	163	8	be	be	AUX
iajs-555	163	9	a	a	DET
iajs-555	163	10	function	function	NOUN
iajs-555	163	11	such	such	ADJ
iajs-555	163	12	that	that	SCONJ
iajs-555	163	13	x	x	PRON
iajs-555	163	14	is	be	AUX
iajs-555	163	15	a	a	DET
iajs-555	163	16	grt	grt	NOUN
iajs-555	163	17	space	space	NOUN
iajs-555	163	18	,	,	PUNCT
iajs-555	163	19	then	then	ADV
iajs-555	163	20	:	:	PUNCT
iajs-555	163	21	i)every	i)every	NOUN
iajs-555	163	22	continuous	continuous	ADJ
iajs-555	163	23	function	function	NOUN
iajs-555	163	24	is	be	AUX
iajs-555	163	25	gr	gr	ADJ
iajs-555	163	26	-	-	PUNCT
iajs-555	163	27	continuous	continuous	ADJ
iajs-555	163	28	.	.	PUNCT
iajs-555	164	1	ii)every	ii)every	NOUN
iajs-555	164	2	rg	rg	NOUN
iajs-555	164	3	-	-	PUNCT
iajs-555	164	4	continuous	continuous	ADJ
iajs-555	164	5	function	function	NOUN
iajs-555	164	6	is	be	AUX
iajs-555	164	7	gr	gr	ADJ
iajs-555	164	8	-	-	ADJ
iajs-555	164	9	continuous	continuous	ADJ
iajs-555	164	10	.	.	PUNCT
iajs-555	165	1	iii)every	iii)every	NOUN
iajs-555	165	2	g	g	NOUN
iajs-555	165	3	-	-	PUNCT
iajs-555	165	4	continuous	continuous	ADJ
iajs-555	165	5	function	function	NOUN
iajs-555	165	6	is	be	AUX
iajs-555	165	7	gr	gr	ADJ
iajs-555	165	8	-	-	PUNCT
iajs-555	165	9	continuous	continuous	ADJ
iajs-555	165	10	.	.	PUNCT
iajs-555	166	1	proof	proof	NOUN
iajs-555	166	2	:	:	PUNCT
iajs-555	167	1	i)let	i)let	NOUN
iajs-555	167	2	f	f	PROPN
iajs-555	167	3	be	be	AUX
iajs-555	167	4	a	a	DET
iajs-555	167	5	closed	closed	ADJ
iajs-555	167	6	set	set	NOUN
iajs-555	167	7	in	in	ADP
iajs-555	167	8	y	y	PROPN
iajs-555	167	9	,	,	PUNCT
iajs-555	167	10	since	since	SCONJ
iajs-555	167	11	f	f	PROPN
iajs-555	167	12	is	be	AUX
iajs-555	167	13	continuous	continuous	ADJ
iajs-555	167	14	,	,	PUNCT
iajs-555	167	15	then	then	ADV
iajs-555	167	16	)	)	PUNCT
iajs-555	167	17	f(f	f(f	PROPN
iajs-555	167	18	1−	1−	NUM
iajs-555	167	19	is	be	AUX
iajs-555	167	20	closed	close	VERB
iajs-555	167	21	in	in	ADP
iajs-555	167	22	x.	x.	NOUN
iajs-555	167	23	since	since	SCONJ
iajs-555	167	24	every	every	DET
iajs-555	167	25	closed	closed	ADJ
iajs-555	167	26	set	set	NOUN
iajs-555	167	27	is	be	AUX
iajs-555	167	28	rg	rg	NOUN
iajs-555	167	29	-	-	PUNCT
iajs-555	167	30	closed	closed	ADJ
iajs-555	167	31	,	,	PUNCT
iajs-555	167	32	then	then	ADV
iajs-555	167	33	)	)	PUNCT
iajs-555	167	34	f(f	f(f	PROPN
iajs-555	167	35	1−	1−	NUM
iajs-555	167	36	is	be	AUX
iajs-555	167	37	rg	rg	NOUN
iajs-555	167	38	-	-	PUNCT
iajs-555	167	39	closed	closed	ADJ
iajs-555	167	40	in	in	ADP
iajs-555	167	41	x.	x.	NOUN
iajs-555	167	42	since	since	SCONJ
iajs-555	167	43	x	x	PRON
iajs-555	167	44	is	be	AUX
iajs-555	167	45	a	a	DET
iajs-555	167	46	grt	grt	NOUN
iajs-555	167	47	space	space	NOUN
iajs-555	167	48	,	,	PUNCT
iajs-555	167	49	then	then	ADV
iajs-555	167	50	)	)	PUNCT
iajs-555	167	51	f(f	f(f	PROPN
iajs-555	167	52	1−	1−	NUM
iajs-555	167	53	is	be	AUX
iajs-555	167	54	gr	gr	ADV
iajs-555	167	55	-	-	PUNCT
iajs-555	167	56	closed	closed	ADJ
iajs-555	167	57	in	in	ADP
iajs-555	167	58	x	x	X
iajs-555	167	59	.	.	PUNCT
iajs-555	168	1	hence	hence	ADV
iajs-555	168	2	f	f	PROPN
iajs-555	168	3	is	be	AUX
iajs-555	168	4	gr	gr	ADV
iajs-555	168	5	-	-	PUNCT
iajs-555	168	6	continuous	continuous	ADJ
iajs-555	168	7	.	.	PUNCT
iajs-555	169	1	similarly	similarly	ADV
iajs-555	169	2	,	,	PUNCT
iajs-555	169	3	we	we	PRON
iajs-555	169	4	can	can	AUX
iajs-555	169	5	prove	prove	VERB
iajs-555	169	6	(	(	PUNCT
iajs-555	169	7	ii	ii	NOUN
iajs-555	169	8	)	)	PUNCT
iajs-555	169	9	and	and	CCONJ
iajs-555	169	10	(	(	PUNCT
iajs-555	169	11	iii	iii	NOUN
iajs-555	169	12	)	)	PUNCT
iajs-555	169	13	.	.	PUNCT
iajs-555	170	1	generalized	generalize	VERB
iajs-555	170	2	regular	regular	ADJ
iajs-555	170	3	irresolute	irresolute	ADJ
iajs-555	170	4	functions	function	NOUN
iajs-555	170	5	definition	definition	NOUN
iajs-555	170	6	:	:	PUNCT
iajs-555	170	7	a	a	DET
iajs-555	170	8	function	function	NOUN
iajs-555	170	9	yx	yx	NOUN
iajs-555	170	10	:	:	PUNCT
iajs-555	170	11	f	f	PROPN
iajs-555	170	12	→	→	PUNCT
iajs-555	170	13	from	from	ADP
iajs-555	170	14	a	a	DET
iajs-555	170	15	topological	topological	ADJ
iajs-555	170	16	space	space	NOUN
iajs-555	170	17	x	x	PUNCT
iajs-555	170	18	into	into	ADP
iajs-555	170	19	a	a	DET
iajs-555	170	20	topological	topological	ADJ
iajs-555	170	21	space	space	NOUN
iajs-555	170	22	y	y	PROPN
iajs-555	170	23	is	be	AUX
iajs-555	170	24	called	call	VERB
iajs-555	170	25	a	a	DET
iajs-555	170	26	generalized	generalized	ADJ
iajs-555	170	27	regular	regular	ADJ
iajs-555	170	28	irresolute	irresolute	NOUN
iajs-555	170	29	(	(	PUNCT
iajs-555	170	30	briefly	briefly	ADV
iajs-555	170	31	gr	gr	NOUN
iajs-555	170	32	-	-	PUNCT
iajs-555	170	33	irresolute	irresolute	NOUN
iajs-555	170	34	)	)	PUNCT
iajs-555	170	35	if	if	SCONJ
iajs-555	170	36	)	)	PUNCT
iajs-555	170	37	v(f	v(f	PROPN
iajs-555	170	38	1−	1−	NUM
iajs-555	170	39	is	be	AUX
iajs-555	170	40	gr	gr	PRON
iajs-555	170	41	-	-	PUNCT
iajs-555	170	42	closed	closed	ADJ
iajs-555	170	43	set	set	NOUN
iajs-555	170	44	in	in	ADP
iajs-555	170	45	x	x	PUNCT
iajs-555	170	46	for	for	ADP
iajs-555	170	47	every	every	DET
iajs-555	170	48	gr	gr	NOUN
iajs-555	170	49	-	-	PUNCT
iajs-555	170	50	closed	closed	ADJ
iajs-555	170	51	set	set	VERB
iajs-555	170	52	v	v	NOUN
iajs-555	170	53	in	in	ADP
iajs-555	170	54	y	y	PROPN
iajs-555	170	55	.	.	PUNCT
iajs-555	171	1	theorem	theorem	VERB
iajs-555	171	2	:	:	PUNCT
iajs-555	171	3	a	a	DET
iajs-555	171	4	function	function	NOUN
iajs-555	171	5	yx	yx	NOUN
iajs-555	171	6	:	:	PUNCT
iajs-555	171	7	f	f	PROPN
iajs-555	171	8	→	→	PUNCT
iajs-555	171	9	from	from	ADP
iajs-555	171	10	a	a	DET
iajs-555	171	11	topological	topological	ADJ
iajs-555	171	12	space	space	NOUN
iajs-555	171	13	x	x	PUNCT
iajs-555	171	14	into	into	ADP
iajs-555	171	15	a	a	DET
iajs-555	171	16	topological	topological	ADJ
iajs-555	171	17	space	space	NOUN
iajs-555	171	18	y	y	PROPN
iajs-555	171	19	is	be	AUX
iajs-555	171	20	grirresolute	grirresolute	VERB
iajs-555	171	21	iff	iff	PROPN
iajs-555	171	22	)	)	PUNCT
iajs-555	171	23	v(f	v(f	PROPN
iajs-555	171	24	1−	1−	NUM
iajs-555	171	25	is	be	AUX
iajs-555	171	26	gr	gr	ADV
iajs-555	171	27	-	-	PUNCT
iajs-555	171	28	open	open	NOUN
iajs-555	171	29	set	set	NOUN
iajs-555	171	30	in	in	ADP
iajs-555	171	31	x	x	PUNCT
iajs-555	171	32	for	for	ADP
iajs-555	171	33	every	every	DET
iajs-555	171	34	gr	gr	NOUN
iajs-555	171	35	-	-	PUNCT
iajs-555	171	36	open	open	NOUN
iajs-555	171	37	set	set	VERB
iajs-555	171	38	v	v	NOUN
iajs-555	171	39	in	in	ADP
iajs-555	171	40	y	y	PROPN
iajs-555	171	41	.	.	PUNCT
iajs-555	172	1	proof	proof	NOUN
iajs-555	172	2	:	:	PUNCT
iajs-555	172	3	it	it	PRON
iajs-555	172	4	is	be	AUX
iajs-555	172	5	obvious	obvious	ADJ
iajs-555	172	6	.	.	PUNCT
iajs-555	173	1	definition	definition	NOUN
iajs-555	173	2	:	:	PUNCT
iajs-555	173	3	a	a	DET
iajs-555	173	4	function	function	NOUN
iajs-555	173	5	yx	yx	NOUN
iajs-555	173	6	:	:	PUNCT
iajs-555	173	7	f	f	PROPN
iajs-555	173	8	→	→	PUNCT
iajs-555	173	9	from	from	ADP
iajs-555	173	10	a	a	DET
iajs-555	173	11	topological	topological	ADJ
iajs-555	173	12	space	space	NOUN
iajs-555	173	13	x	x	PUNCT
iajs-555	173	14	into	into	ADP
iajs-555	173	15	a	a	DET
iajs-555	173	16	topological	topological	ADJ
iajs-555	173	17	space	space	NOUN
iajs-555	173	18	y	y	PROPN
iajs-555	173	19	is	be	AUX
iajs-555	173	20	said	say	VERB
iajs-555	173	21	to	to	PART
iajs-555	173	22	be	be	AUX
iajs-555	173	23	contra	contra	PROPN
iajs-555	173	24	generalized	generalize	VERB
iajs-555	173	25	regular	regular	ADJ
iajs-555	173	26	irresolute	irresolute	NOUN
iajs-555	173	27	(	(	PUNCT
iajs-555	173	28	briefly	briefly	NOUN
iajs-555	173	29	contra	contra	PROPN
iajs-555	173	30	gr	gr	PROPN
iajs-555	173	31	-	-	PUNCT
iajs-555	173	32	irresolute	irresolute	NOUN
iajs-555	173	33	)	)	PUNCT
iajs-555	173	34	if	if	SCONJ
iajs-555	173	35	)	)	PUNCT
iajs-555	173	36	v(f	v(f	PROPN
iajs-555	173	37	1−	1−	NUM
iajs-555	173	38	is	be	AUX
iajs-555	173	39	grclosed	grclose	VERB
iajs-555	173	40	set	set	VERB
iajs-555	173	41	in	in	ADP
iajs-555	173	42	x	x	PUNCT
iajs-555	173	43	for	for	ADP
iajs-555	173	44	every	every	DET
iajs-555	173	45	gr	gr	NOUN
iajs-555	173	46	-	-	PUNCT
iajs-555	173	47	open	open	NOUN
iajs-555	173	48	set	set	VERB
iajs-555	173	49	v	v	NOUN
iajs-555	173	50	in	in	ADP
iajs-555	173	51	y	y	PROPN
iajs-555	173	52	.	.	PUNCT
iajs-555	174	1	remarks	remark	NOUN
iajs-555	174	2	:	:	PUNCT
iajs-555	174	3	1	1	X
iajs-555	174	4	)	)	PUNCT
iajs-555	174	5	gr	gr	NUM
iajs-555	174	6	-	-	PUNCT
iajs-555	174	7	irresolute	irresolute	ADJ
iajs-555	174	8	functions	function	NOUN
iajs-555	174	9	and	and	CCONJ
iajs-555	174	10	gr	gr	ADJ
iajs-555	174	11	-	-	PUNCT
iajs-555	174	12	continuous	continuous	ADJ
iajs-555	174	13	functions	function	NOUN
iajs-555	174	14	are	be	AUX
iajs-555	174	15	in	in	ADP
iajs-555	174	16	general	general	ADJ
iajs-555	174	17	independent	independent	ADJ
iajs-555	174	18	.consider	.consider	NOUN
iajs-555	174	19	the	the	DET
iajs-555	174	20	following	follow	VERB
iajs-555	174	21	examples	example	NOUN
iajs-555	174	22	:	:	PUNCT
iajs-555	174	23	mathematics	mathematic	NOUN
iajs-555	174	24	383	383	NUM
iajs-555	174	25	مجلة	مجلة	NOUN
iajs-555	174	26	إبن	إبن	VERB
iajs-555	174	27	الهيثم	الهيثم	ADJ
iajs-555	174	28	للعلوم	للعلوم	NOUN
iajs-555	174	29	الصرفة	الصرفة	NOUN
iajs-555	175	1	و	و	PRON
iajs-555	175	2	التطبيقية	التطبيقية	ADJ
iajs-555	175	3	2012	2012	NUM
iajs-555	175	4	السنة	السنة	NOUN
iajs-555	175	5	25	25	NUM
iajs-555	175	6	المجلد	المجلد	NOUN
iajs-555	175	7	3	3	NUM
iajs-555	175	8	العدد	العدد	PROPN
iajs-555	175	9	ibn	ibn	PROPN
iajs-555	175	10	al	al	PROPN
iajs-555	175	11	-	-	PUNCT
iajs-555	175	12	haitham	haitham	PROPN
iajs-555	175	13	journal	journal	PROPN
iajs-555	175	14	for	for	ADP
iajs-555	175	15	pure	pure	ADJ
iajs-555	175	16	and	and	CCONJ
iajs-555	175	17	applied	apply	VERB
iajs-555	175	18	science	science	NOUN
iajs-555	175	19	no	no	NOUN
iajs-555	175	20	.	.	NOUN
iajs-555	175	21	3	3	NUM
iajs-555	175	22	vol	vol	NOUN
iajs-555	175	23	.	.	PUNCT
iajs-555	176	1	25	25	NUM
iajs-555	176	2	year	year	NOUN
iajs-555	176	3	2012	2012	NUM
iajs-555	176	4	examples	example	NOUN
iajs-555	176	5	:	:	PUNCT
iajs-555	176	6	i)let	i)let	NOUN
iajs-555	176	7	}	}	PUNCT
iajs-555	176	8	c	c	NOUN
iajs-555	176	9	,	,	PUNCT
iajs-555	176	10	b	b	PROPN
iajs-555	176	11	,	,	PUNCT
iajs-555	176	12	a{x	a{x	VERB
iajs-555	176	13	=	=	NOUN
iajs-555	176	14	,	,	PUNCT
iajs-555	176	15	}	}	PUNCT
iajs-555	176	16	}	}	PUNCT
iajs-555	176	17	a{,,x	a{,,x	PROPN
iajs-555	176	18	{	{	PUNCT
iajs-555	176	19	φ	φ	PROPN
iajs-555	176	20	=	=	PROPN
iajs-555	176	21	τ	τ	X
iajs-555	176	22	and	and	CCONJ
iajs-555	176	23	}	}	PUNCT
iajs-555	176	24	,	,	PUNCT
iajs-555	176	25	x	x	X
iajs-555	176	26	{	{	PUNCT
iajs-555	176	27	φ	φ	NOUN
iajs-555	176	28	=	=	NOUN
iajs-555	176	29	τ′	τ′	X
iajs-555	176	30	.	.	PUNCT
iajs-555	177	1	let	let	VERB
iajs-555	177	2	)	)	PUNCT
iajs-555	177	3	,	,	PUNCT
iajs-555	177	4	x(),x(:f	x(),x(:f	PROPN
iajs-555	177	5	τ′→τ	τ′→τ	NOUN
iajs-555	177	6	be	be	AUX
iajs-555	177	7	a	a	DET
iajs-555	177	8	function	function	NOUN
iajs-555	177	9	defined	define	VERB
iajs-555	177	10	by	by	ADP
iajs-555	177	11	:	:	PUNCT
iajs-555	177	12	a)a(f	a)a(f	PROPN
iajs-555	177	13	=	=	SYM
iajs-555	177	14	,	,	PUNCT
iajs-555	177	15	b)b(f	b)b(f	NOUN
iajs-555	177	16	=	=	SYM
iajs-555	177	17	and	and	CCONJ
iajs-555	177	18	c)c(f	c)c(f	NOUN
iajs-555	177	19	=	=	PUNCT
iajs-555	177	20	.	.	PUNCT
iajs-555	178	1	it	it	PRON
iajs-555	178	2	is	be	AUX
iajs-555	178	3	clear	clear	ADJ
iajs-555	178	4	that	that	SCONJ
iajs-555	178	5	f	f	PROPN
iajs-555	178	6	is	be	AUX
iajs-555	178	7	gr	gr	ADV
iajs-555	178	8	-	-	ADJ
iajs-555	178	9	continuous	continuous	ADJ
iajs-555	178	10	,	,	PUNCT
iajs-555	178	11	but	but	CCONJ
iajs-555	178	12	f	f	PROPN
iajs-555	178	13	is	be	AUX
iajs-555	178	14	not	not	PART
iajs-555	178	15	gr	gr	NOUN
iajs-555	178	16	-	-	PUNCT
iajs-555	178	17	irresolute	irresolute	ADJ
iajs-555	178	18	,	,	PUNCT
iajs-555	178	19	since{a}is	since{a}is	PROPN
iajs-555	178	20	gr	gr	NOUN
iajs-555	178	21	-	-	PUNCT
iajs-555	178	22	closed	closed	ADJ
iajs-555	178	23	in	in	ADP
iajs-555	178	24	)	)	PUNCT
iajs-555	178	25	,	,	PUNCT
iajs-555	178	26	x	x	X
iajs-555	178	27	(	(	PUNCT
iajs-555	178	28	τ′	τ′	X
iajs-555	178	29	,	,	PUNCT
iajs-555	178	30	but	but	CCONJ
iajs-555	178	31	}	}	PUNCT
iajs-555	178	32	a{})a({f	a{})a({f	PROPN
iajs-555	178	33	1	1	NUM
iajs-555	178	34	=	=	NOUN
iajs-555	178	35	−	−	PROPN
iajs-555	178	36	is	be	AUX
iajs-555	178	37	not	not	PART
iajs-555	178	38	gr	gr	ADV
iajs-555	178	39	-	-	PUNCT
iajs-555	178	40	closed	closed	ADJ
iajs-555	178	41	in	in	ADP
iajs-555	178	42	)	)	PUNCT
iajs-555	178	43	,	,	PUNCT
iajs-555	178	44	x	x	X
iajs-555	178	45	(	(	PUNCT
iajs-555	178	46	τ	τ	X
iajs-555	178	47	.	.	PUNCT
iajs-555	179	1	ii)let	ii)let	ADJ
iajs-555	179	2	}	}	PUNCT
iajs-555	179	3	c	c	X
iajs-555	179	4	,	,	PUNCT
iajs-555	179	5	b	b	PROPN
iajs-555	179	6	,	,	PUNCT
iajs-555	179	7	a{x	a{x	VERB
iajs-555	179	8	=	=	NOUN
iajs-555	179	9	,	,	PUNCT
iajs-555	179	10	}	}	PUNCT
iajs-555	179	11	}	}	PUNCT
iajs-555	179	12	a{,,x	a{,,x	PROPN
iajs-555	179	13	{	{	PUNCT
iajs-555	179	14	φ	φ	PROPN
iajs-555	179	15	=	=	PROPN
iajs-555	179	16	τ	τ	X
iajs-555	179	17	and	and	CCONJ
iajs-555	179	18	}	}	PUNCT
iajs-555	179	19	}	}	PUNCT
iajs-555	179	20	b{},c	b{},c	PROPN
iajs-555	179	21	,	,	PUNCT
iajs-555	179	22	b{},b	b{},b	PROPN
iajs-555	179	23	,	,	PUNCT
iajs-555	179	24	a{,,x	a{,,x	PROPN
iajs-555	179	25	{	{	PUNCT
iajs-555	179	26	φ	φ	NOUN
iajs-555	179	27	=	=	PRON
iajs-555	179	28	τ′	τ′	X
iajs-555	179	29	.	.	PUNCT
iajs-555	180	1	let	let	VERB
iajs-555	180	2	)	)	PUNCT
iajs-555	180	3	,	,	PUNCT
iajs-555	180	4	x(),x(:f	x(),x(:f	PROPN
iajs-555	180	5	τ′→τ	τ′→τ	NOUN
iajs-555	180	6	be	be	AUX
iajs-555	180	7	a	a	DET
iajs-555	180	8	function	function	NOUN
iajs-555	180	9	defined	define	VERB
iajs-555	180	10	by	by	ADP
iajs-555	180	11	:	:	PUNCT
iajs-555	180	12	a)a(f	a)a(f	PROPN
iajs-555	180	13	=	=	SYM
iajs-555	180	14	,	,	PUNCT
iajs-555	180	15	b)b(f	b)b(f	NOUN
iajs-555	180	16	=	=	SYM
iajs-555	180	17	and	and	CCONJ
iajs-555	180	18	c)c(f	c)c(f	PROPN
iajs-555	180	19	=	=	PUNCT
iajs-555	180	20	.	.	PUNCT
iajs-555	181	1	f	f	PROPN
iajs-555	181	2	is	be	AUX
iajs-555	181	3	gr	gr	NOUN
iajs-555	181	4	-	-	PUNCT
iajs-555	181	5	irresolute	irresolute	ADJ
iajs-555	181	6	,	,	PUNCT
iajs-555	181	7	since	since	SCONJ
iajs-555	181	8	φ	φ	NOUN
iajs-555	181	9	=	=	NOUN
iajs-555	181	10	φ−	φ−	PROPN
iajs-555	181	11	)	)	PUNCT
iajs-555	181	12	(	(	PUNCT
iajs-555	181	13	f	f	NOUN
iajs-555	181	14	1	1	NUM
iajs-555	181	15	,	,	PUNCT
iajs-555	181	16	x)x(f	x)x(f	X
iajs-555	181	17	1	1	NUM
iajs-555	181	18	=	=	NOUN
iajs-555	181	19	−	−	PROPN
iajs-555	181	20	and	and	CCONJ
iajs-555	181	21	}	}	SYM
iajs-555	181	22	c	c	NOUN
iajs-555	181	23	,	,	PUNCT
iajs-555	181	24	a{})c	a{})c	ADJ
iajs-555	181	25	,	,	PUNCT
iajs-555	181	26	a({f	a({f	NOUN
iajs-555	181	27	1	1	NUM
iajs-555	181	28	=	=	NOUN
iajs-555	181	29	−	−	NOUN
iajs-555	181	30	are	be	AUX
iajs-555	181	31	gr	gr	ADV
iajs-555	181	32	-	-	PUNCT
iajs-555	181	33	closed	closed	ADJ
iajs-555	181	34	in	in	ADP
iajs-555	181	35	)	)	PUNCT
iajs-555	181	36	,	,	PUNCT
iajs-555	181	37	x	x	X
iajs-555	181	38	(	(	PUNCT
iajs-555	181	39	τ	τ	X
iajs-555	181	40	.	.	PUNCT
iajs-555	182	1	but	but	CCONJ
iajs-555	182	2	f	f	PROPN
iajs-555	182	3	is	be	AUX
iajs-555	182	4	not	not	PART
iajs-555	182	5	gr	gr	ADJ
iajs-555	182	6	-	-	ADJ
iajs-555	182	7	continuous	continuous	ADJ
iajs-555	182	8	,	,	PUNCT
iajs-555	182	9	since{a}is	since{a}is	PROPN
iajs-555	182	10	closed	close	VERB
iajs-555	182	11	in	in	ADP
iajs-555	182	12	)	)	PUNCT
iajs-555	182	13	,	,	PUNCT
iajs-555	182	14	x	x	X
iajs-555	182	15	(	(	PUNCT
iajs-555	182	16	τ′	τ′	X
iajs-555	182	17	,	,	PUNCT
iajs-555	182	18	but	but	CCONJ
iajs-555	182	19	}	}	PUNCT
iajs-555	182	20	a{})a({f	a{})a({f	PROPN
iajs-555	182	21	1	1	NUM
iajs-555	182	22	=	=	NOUN
iajs-555	182	23	−	−	PROPN
iajs-555	182	24	is	be	AUX
iajs-555	182	25	not	not	PART
iajs-555	182	26	gr	gr	ADV
iajs-555	182	27	-	-	PUNCT
iajs-555	182	28	closed	closed	ADJ
iajs-555	182	29	in	in	ADP
iajs-555	182	30	)	)	PUNCT
iajs-555	182	31	,	,	PUNCT
iajs-555	182	32	x	x	X
iajs-555	182	33	(	(	PUNCT
iajs-555	182	34	τ	τ	X
iajs-555	182	35	.	.	PUNCT
iajs-555	183	1	theorem	theorem	VERB
iajs-555	183	2	:	:	PUNCT
iajs-555	183	3	let	let	VERB
iajs-555	183	4	yx	yx	NOUN
iajs-555	183	5	:	:	PUNCT
iajs-555	183	6	f	f	X
iajs-555	183	7	→	→	PUNCT
iajs-555	183	8	be	be	AUX
iajs-555	183	9	a	a	DET
iajs-555	183	10	function	function	NOUN
iajs-555	183	11	such	such	ADJ
iajs-555	183	12	that	that	SCONJ
iajs-555	183	13	x	x	PRON
iajs-555	183	14	is	be	AUX
iajs-555	183	15	a	a	DET
iajs-555	183	16	grt	grt	NOUN
iajs-555	183	17	space	space	NOUN
iajs-555	183	18	,	,	PUNCT
iajs-555	183	19	then	then	ADV
iajs-555	183	20	:	:	PUNCT
iajs-555	184	1	i)every	i)every	PROPN
iajs-555	184	2	rg	rg	PROPN
iajs-555	184	3	-	-	PUNCT
iajs-555	184	4	irresolute	irresolute	ADJ
iajs-555	184	5	function	function	NOUN
iajs-555	184	6	is	be	AUX
iajs-555	184	7	gr	gr	PRON
iajs-555	184	8	-	-	PUNCT
iajs-555	184	9	irresolute	irresolute	ADJ
iajs-555	184	10	.	.	PUNCT
iajs-555	185	1	ii)every	ii)every	NOUN
iajs-555	185	2	g	g	NOUN
iajs-555	185	3	-	-	PUNCT
iajs-555	185	4	irresolute	irresolute	ADJ
iajs-555	185	5	function	function	NOUN
iajs-555	185	6	is	be	AUX
iajs-555	185	7	gr	gr	NOUN
iajs-555	185	8	-	-	PUNCT
iajs-555	185	9	irresolute	irresolute	ADJ
iajs-555	185	10	.	.	PUNCT
iajs-555	186	1	proof	proof	NOUN
iajs-555	186	2	:	:	PUNCT
iajs-555	187	1	i)let	i)let	NOUN
iajs-555	187	2	f	f	PROPN
iajs-555	187	3	be	be	AUX
iajs-555	187	4	a	a	DET
iajs-555	187	5	gr	gr	ADV
iajs-555	187	6	-	-	PUNCT
iajs-555	187	7	closed	closed	ADJ
iajs-555	187	8	set	set	NOUN
iajs-555	187	9	in	in	ADP
iajs-555	187	10	y	y	PROPN
iajs-555	187	11	,	,	PUNCT
iajs-555	187	12	then	then	ADV
iajs-555	187	13	by	by	ADP
iajs-555	187	14	(	(	PUNCT
iajs-555	187	15	1.2	1.2	NUM
iajs-555	187	16	)	)	PUNCT
iajs-555	187	17	no.3	no.3	PROPN
iajs-555	187	18	,	,	PUNCT
iajs-555	187	19	f	f	PROPN
iajs-555	187	20	is	be	AUX
iajs-555	187	21	rg	rg	NOUN
iajs-555	187	22	-	-	PUNCT
iajs-555	187	23	closed	closed	ADJ
iajs-555	187	24	in	in	ADP
iajs-555	187	25	y	y	PROPN
iajs-555	187	26	.	.	PUNCT
iajs-555	188	1	since	since	SCONJ
iajs-555	188	2	f	f	PROPN
iajs-555	188	3	is	be	AUX
iajs-555	188	4	rg	rg	NOUN
iajs-555	188	5	-	-	PUNCT
iajs-555	188	6	irresolute	irresolute	ADJ
iajs-555	188	7	,	,	PUNCT
iajs-555	188	8	then	then	ADV
iajs-555	188	9	by	by	ADP
iajs-555	188	10	(	(	PUNCT
iajs-555	188	11	1.5	1.5	NUM
iajs-555	188	12	)	)	PUNCT
iajs-555	188	13	no.6	no.6	PROPN
iajs-555	188	14	,	,	PUNCT
iajs-555	188	15	)	)	PUNCT
iajs-555	188	16	f(f	f(f	PROPN
iajs-555	188	17	1−	1−	NUM
iajs-555	188	18	is	be	AUX
iajs-555	188	19	rg	rg	NOUN
iajs-555	188	20	-	-	PUNCT
iajs-555	188	21	closed	closed	ADJ
iajs-555	188	22	in	in	ADP
iajs-555	188	23	x	x	X
iajs-555	188	24	.	.	PUNCT
iajs-555	189	1	since	since	SCONJ
iajs-555	189	2	x	x	PRON
iajs-555	189	3	is	be	AUX
iajs-555	189	4	a	a	DET
iajs-555	189	5	grt	grt	NOUN
iajs-555	189	6	space	space	NOUN
iajs-555	189	7	,	,	PUNCT
iajs-555	189	8	then	then	ADV
iajs-555	189	9	)	)	PUNCT
iajs-555	189	10	f(f	f(f	PROPN
iajs-555	189	11	1−	1−	NUM
iajs-555	189	12	is	be	AUX
iajs-555	189	13	gr	gr	ADV
iajs-555	189	14	-	-	PUNCT
iajs-555	189	15	closed	closed	ADJ
iajs-555	189	16	in	in	ADP
iajs-555	189	17	x	x	X
iajs-555	189	18	.	.	PUNCT
iajs-555	190	1	hence	hence	ADV
iajs-555	190	2	f	f	PROPN
iajs-555	190	3	is	be	AUX
iajs-555	190	4	gr	gr	NOUN
iajs-555	190	5	-	-	PUNCT
iajs-555	190	6	irresolute	irresolute	NOUN
iajs-555	190	7	.	.	PUNCT
iajs-555	191	1	ii)let	ii)let	PROPN
iajs-555	191	2	f	f	PROPN
iajs-555	191	3	be	be	AUX
iajs-555	191	4	a	a	DET
iajs-555	191	5	gr	gr	ADV
iajs-555	191	6	-	-	PUNCT
iajs-555	191	7	closed	closed	ADJ
iajs-555	191	8	set	set	NOUN
iajs-555	191	9	in	in	ADP
iajs-555	191	10	y	y	PROPN
iajs-555	191	11	,	,	PUNCT
iajs-555	191	12	then	then	ADV
iajs-555	191	13	by	by	ADP
iajs-555	191	14	(	(	PUNCT
iajs-555	191	15	1.2	1.2	NUM
iajs-555	191	16	)	)	PUNCT
iajs-555	191	17	no.2	no.2	PROPN
iajs-555	191	18	,	,	PUNCT
iajs-555	191	19	f	f	PROPN
iajs-555	191	20	is	be	AUX
iajs-555	191	21	g	g	NOUN
iajs-555	191	22	-	-	PUNCT
iajs-555	191	23	closed	closed	ADJ
iajs-555	191	24	in	in	ADP
iajs-555	191	25	y	y	PROPN
iajs-555	191	26	.	.	PUNCT
iajs-555	192	1	since	since	SCONJ
iajs-555	192	2	f	f	PROPN
iajs-555	192	3	is	be	AUX
iajs-555	192	4	g	g	NOUN
iajs-555	192	5	-	-	PUNCT
iajs-555	192	6	irresolute	irresolute	ADJ
iajs-555	192	7	,	,	PUNCT
iajs-555	192	8	then	then	ADV
iajs-555	192	9	by	by	ADP
iajs-555	192	10	(	(	PUNCT
iajs-555	192	11	1.5	1.5	NUM
iajs-555	192	12	)	)	PUNCT
iajs-555	192	13	no.5	no.5	PROPN
iajs-555	192	14	,	,	PUNCT
iajs-555	192	15	)	)	PUNCT
iajs-555	192	16	f(f	f(f	PROPN
iajs-555	192	17	1−	1−	NUM
iajs-555	192	18	is	be	AUX
iajs-555	192	19	g	g	NOUN
iajs-555	192	20	-	-	PUNCT
iajs-555	192	21	closed	closed	ADJ
iajs-555	192	22	in	in	ADP
iajs-555	192	23	x	x	X
iajs-555	192	24	.	.	PUNCT
iajs-555	193	1	since	since	SCONJ
iajs-555	193	2	every	every	DET
iajs-555	193	3	g	g	NOUN
iajs-555	193	4	-	-	PUNCT
iajs-555	193	5	closed	close	VERB
iajs-555	193	6	set	set	NOUN
iajs-555	193	7	is	be	AUX
iajs-555	193	8	rg	rg	NOUN
iajs-555	193	9	-	-	PUNCT
iajs-555	193	10	closed	closed	ADJ
iajs-555	193	11	,	,	PUNCT
iajs-555	193	12	then	then	ADV
iajs-555	193	13	)	)	PUNCT
iajs-555	193	14	f(f	f(f	PROPN
iajs-555	193	15	1−	1−	NUM
iajs-555	193	16	is	be	AUX
iajs-555	193	17	rg	rg	NOUN
iajs-555	193	18	-	-	PUNCT
iajs-555	193	19	closed	closed	ADJ
iajs-555	193	20	in	in	ADP
iajs-555	193	21	x	x	X
iajs-555	193	22	.	.	PUNCT
iajs-555	194	1	since	since	SCONJ
iajs-555	194	2	x	x	PRON
iajs-555	194	3	is	be	AUX
iajs-555	194	4	a	a	DET
iajs-555	194	5	grt	grt	NOUN
iajs-555	194	6	space	space	NOUN
iajs-555	194	7	,	,	PUNCT
iajs-555	194	8	then	then	ADV
iajs-555	194	9	)	)	PUNCT
iajs-555	194	10	f(f	f(f	PROPN
iajs-555	194	11	1−	1−	NUM
iajs-555	194	12	is	be	AUX
iajs-555	194	13	gr	gr	ADV
iajs-555	194	14	-	-	PUNCT
iajs-555	194	15	closed	closed	ADJ
iajs-555	194	16	in	in	ADP
iajs-555	194	17	x	x	X
iajs-555	194	18	.	.	PUNCT
iajs-555	195	1	hence	hence	ADV
iajs-555	195	2	f	f	PROPN
iajs-555	195	3	is	be	AUX
iajs-555	195	4	gr	gr	NOUN
iajs-555	195	5	-	-	PUNCT
iajs-555	195	6	irresolute	irresolute	NOUN
iajs-555	195	7	.	.	PUNCT
iajs-555	196	1	theorem	theorem	VERB
iajs-555	196	2	:	:	PUNCT
iajs-555	196	3	if	if	SCONJ
iajs-555	196	4	yx	yx	ADJ
iajs-555	196	5	:	:	PUNCT
iajs-555	196	6	f	f	PROPN
iajs-555	196	7	→	→	PUNCT
iajs-555	196	8	and	and	CCONJ
iajs-555	196	9	zy	zy	NOUN
iajs-555	196	10	:	:	PUNCT
iajs-555	196	11	g	g	PROPN
iajs-555	196	12	→	→	NOUN
iajs-555	196	13	are	be	AUX
iajs-555	196	14	functions	function	NOUN
iajs-555	196	15	,	,	PUNCT
iajs-555	196	16	then	then	ADV
iajs-555	196	17	:	:	PUNCT
iajs-555	196	18	1	1	X
iajs-555	196	19	)	)	PUNCT
iajs-555	196	20	if	if	SCONJ
iajs-555	196	21	yx	yx	ADJ
iajs-555	196	22	:	:	PUNCT
iajs-555	196	23	f	f	PROPN
iajs-555	196	24	→	→	PUNCT
iajs-555	196	25	and	and	CCONJ
iajs-555	196	26	zy	zy	NOUN
iajs-555	196	27	:	:	PUNCT
iajs-555	196	28	g	g	PROPN
iajs-555	196	29	→	→	SYM
iajs-555	196	30	are	be	AUX
iajs-555	196	31	both	both	DET
iajs-555	196	32	gr	gr	ADJ
iajs-555	196	33	-	-	PUNCT
iajs-555	196	34	irresolute	irresolute	ADJ
iajs-555	196	35	functions	function	NOUN
iajs-555	196	36	,	,	PUNCT
iajs-555	196	37	then	then	ADV
iajs-555	196	38	zx	zx	NUM
iajs-555	196	39	:	:	PUNCT
iajs-555	196	40	fg	fg	PROPN
iajs-555	196	41	→	→	PROPN
iajs-555	196	42	is	be	AUX
iajs-555	196	43	gr	gr	PRON
iajs-555	196	44	-	-	PUNCT
iajs-555	196	45	irresolute	irresolute	ADJ
iajs-555	196	46	.	.	NOUN
iajs-555	197	1	2	2	NUM
iajs-555	197	2	)	)	PUNCT
iajs-555	197	3	if	if	SCONJ
iajs-555	197	4	yx	yx	ADJ
iajs-555	197	5	:	:	PUNCT
iajs-555	197	6	f	f	PROPN
iajs-555	197	7	→	→	X
iajs-555	197	8	is	be	AUX
iajs-555	197	9	contra	contra	PROPN
iajs-555	197	10	gr	gr	PROPN
iajs-555	197	11	-	-	PUNCT
iajs-555	197	12	irresolute	irresolute	ADJ
iajs-555	197	13	and	and	CCONJ
iajs-555	197	14	zy	zy	NOUN
iajs-555	197	15	:	:	PUNCT
iajs-555	197	16	g	g	PROPN
iajs-555	197	17	→	→	PUNCT
iajs-555	197	18	is	be	AUX
iajs-555	197	19	gr	gr	PRON
iajs-555	197	20	-	-	PUNCT
iajs-555	197	21	irresolute	irresolute	ADJ
iajs-555	197	22	,	,	PUNCT
iajs-555	197	23	then	then	ADV
iajs-555	197	24	zx	zx	NUM
iajs-555	197	25	:	:	PUNCT
iajs-555	197	26	fg	fg	PROPN
iajs-555	197	27	→	→	PROPN
iajs-555	197	28	is	be	AUX
iajs-555	197	29	contra	contra	PROPN
iajs-555	197	30	gr	gr	NOUN
iajs-555	197	31	-	-	PUNCT
iajs-555	197	32	irresolute	irresolute	ADJ
iajs-555	197	33	.	.	PUNCT
iajs-555	198	1	3	3	X
iajs-555	198	2	)	)	PUNCT
iajs-555	198	3	if	if	SCONJ
iajs-555	198	4	yx	yx	ADJ
iajs-555	198	5	:	:	PUNCT
iajs-555	198	6	f	f	PROPN
iajs-555	198	7	→	→	X
iajs-555	198	8	is	be	AUX
iajs-555	198	9	gr	gr	PRON
iajs-555	198	10	-	-	PUNCT
iajs-555	198	11	irresolute	irresolute	ADJ
iajs-555	198	12	and	and	CCONJ
iajs-555	198	13	zy	zy	NOUN
iajs-555	198	14	:	:	PUNCT
iajs-555	198	15	g	g	PROPN
iajs-555	198	16	→	→	PUNCT
iajs-555	198	17	is	be	AUX
iajs-555	198	18	gr	gr	ADV
iajs-555	198	19	-	-	ADJ
iajs-555	198	20	continuous	continuous	ADJ
iajs-555	198	21	,	,	PUNCT
iajs-555	198	22	then	then	ADV
iajs-555	198	23	zx	zx	NUM
iajs-555	198	24	:	:	PUNCT
iajs-555	198	25	fg	fg	PROPN
iajs-555	198	26	→	→	PROPN
iajs-555	198	27	is	be	AUX
iajs-555	198	28	gr	gr	ADJ
iajs-555	198	29	-	-	ADJ
iajs-555	198	30	continuous	continuous	ADJ
iajs-555	198	31	.	.	PUNCT
iajs-555	199	1	4	4	X
iajs-555	199	2	)	)	PUNCT
iajs-555	199	3	if	if	SCONJ
iajs-555	199	4	yx	yx	ADJ
iajs-555	199	5	:	:	PUNCT
iajs-555	199	6	f	f	PROPN
iajs-555	199	7	→	→	X
iajs-555	199	8	is	be	AUX
iajs-555	199	9	gr	gr	ADV
iajs-555	199	10	-	-	PUNCT
iajs-555	199	11	continuous	continuous	ADJ
iajs-555	199	12	and	and	CCONJ
iajs-555	199	13	zy	zy	NOUN
iajs-555	199	14	:	:	PUNCT
iajs-555	199	15	g	g	PROPN
iajs-555	199	16	→	→	PUNCT
iajs-555	199	17	is	be	AUX
iajs-555	199	18	r	r	NOUN
iajs-555	199	19	-	-	ADJ
iajs-555	199	20	continuous	continuous	ADJ
iajs-555	199	21	,	,	PUNCT
iajs-555	199	22	then	then	ADV
iajs-555	199	23	zx	zx	NUM
iajs-555	199	24	:	:	PUNCT
iajs-555	199	25	fg	fg	PROPN
iajs-555	199	26	→	→	PROPN
iajs-555	199	27	is	be	AUX
iajs-555	199	28	gr	gr	ADJ
iajs-555	199	29	-	-	ADJ
iajs-555	199	30	continuous	continuous	ADJ
iajs-555	199	31	.	.	PUNCT
iajs-555	200	1	5	5	X
iajs-555	200	2	)	)	PUNCT
iajs-555	200	3	if	if	SCONJ
iajs-555	200	4	yx	yx	ADJ
iajs-555	200	5	:	:	PUNCT
iajs-555	200	6	f	f	PROPN
iajs-555	200	7	→	→	X
iajs-555	200	8	is	be	AUX
iajs-555	200	9	gr	gr	ADV
iajs-555	200	10	-	-	PUNCT
iajs-555	200	11	continuous	continuous	ADJ
iajs-555	200	12	and	and	CCONJ
iajs-555	200	13	zy	zy	NOUN
iajs-555	200	14	:	:	PUNCT
iajs-555	200	15	g	g	PROPN
iajs-555	200	16	→	→	PUNCT
iajs-555	200	17	is	be	AUX
iajs-555	200	18	continuous	continuous	ADJ
iajs-555	200	19	,	,	PUNCT
iajs-555	200	20	then	then	ADV
iajs-555	200	21	zx	zx	NUM
iajs-555	200	22	:	:	PUNCT
iajs-555	200	23	fg	fg	PROPN
iajs-555	200	24	→	→	PROPN
iajs-555	200	25	is	be	AUX
iajs-555	200	26	gr	gr	ADJ
iajs-555	200	27	-	-	ADJ
iajs-555	200	28	continuous	continuous	ADJ
iajs-555	200	29	.	.	PUNCT
iajs-555	201	1	6	6	X
iajs-555	201	2	)	)	PUNCT
iajs-555	201	3	if	if	SCONJ
iajs-555	201	4	yx	yx	ADJ
iajs-555	201	5	:	:	PUNCT
iajs-555	201	6	f	f	PROPN
iajs-555	201	7	→	→	X
iajs-555	201	8	is	be	AUX
iajs-555	201	9	contra	contra	PROPN
iajs-555	201	10	gr	gr	PROPN
iajs-555	201	11	-	-	PUNCT
iajs-555	201	12	irresolute	irresolute	ADJ
iajs-555	201	13	and	and	CCONJ
iajs-555	201	14	zy	zy	NOUN
iajs-555	201	15	:	:	PUNCT
iajs-555	201	16	g	g	PROPN
iajs-555	201	17	→	→	PUNCT
iajs-555	201	18	is	be	AUX
iajs-555	201	19	gr	gr	ADV
iajs-555	201	20	-	-	ADJ
iajs-555	201	21	continuous	continuous	ADJ
iajs-555	201	22	,	,	PUNCT
iajs-555	201	23	then	then	ADV
iajs-555	201	24	zx	zx	NUM
iajs-555	201	25	:	:	PUNCT
iajs-555	201	26	fg	fg	PROPN
iajs-555	201	27	→	→	PROPN
iajs-555	201	28	is	be	AUX
iajs-555	201	29	contra	contra	PROPN
iajs-555	201	30	gr	gr	PROPN
iajs-555	201	31	-	-	PUNCT
iajs-555	201	32	continuous	continuous	ADJ
iajs-555	201	33	.	.	PUNCT
iajs-555	202	1	proof	proof	NOUN
iajs-555	202	2	:	:	PUNCT
iajs-555	202	3	1)let	1)let	NUM
iajs-555	202	4	u	u	NOUN
iajs-555	202	5	be	be	VERB
iajs-555	202	6	a	a	DET
iajs-555	202	7	gr	gr	ADJ
iajs-555	202	8	-	-	PUNCT
iajs-555	202	9	open	open	ADJ
iajs-555	202	10	set	set	NOUN
iajs-555	202	11	in	in	ADP
iajs-555	202	12	z	z	PROPN
iajs-555	202	13	,	,	PUNCT
iajs-555	202	14	since	since	SCONJ
iajs-555	202	15	g	g	PROPN
iajs-555	202	16	is	be	AUX
iajs-555	202	17	gr	gr	NOUN
iajs-555	202	18	-	-	PUNCT
iajs-555	202	19	irresolute	irresolute	ADJ
iajs-555	202	20	,	,	PUNCT
iajs-555	202	21	then	then	ADV
iajs-555	202	22	)	)	PUNCT
iajs-555	202	23	u(g	u(g	PROPN
iajs-555	202	24	1−	1−	NUM
iajs-555	202	25	is	be	AUX
iajs-555	202	26	gr	gr	ADV
iajs-555	202	27	-	-	PUNCT
iajs-555	202	28	open	open	ADJ
iajs-555	202	29	in	in	ADP
iajs-555	202	30	y	y	PROPN
iajs-555	202	31	,	,	PUNCT
iajs-555	202	32	since	since	SCONJ
iajs-555	202	33	f	f	PROPN
iajs-555	202	34	is	be	AUX
iajs-555	202	35	gr	gr	NOUN
iajs-555	202	36	-	-	PUNCT
iajs-555	202	37	irresolute	irresolute	ADJ
iajs-555	202	38	,	,	PUNCT
iajs-555	202	39	then	then	ADV
iajs-555	202	40	)	)	PUNCT
iajs-555	202	41	)	)	PUNCT
iajs-555	203	1	u(g(f	u(g(f	PROPN
iajs-555	203	2	11	11	NUM
iajs-555	203	3	−−	−−	NOUN
iajs-555	203	4	is	be	AUX
iajs-555	203	5	gr	gr	ADJ
iajs-555	203	6	-	-	NOUN
iajs-555	203	7	open	open	ADJ
iajs-555	203	8	in	in	ADP
iajs-555	203	9	x	x	X
iajs-555	203	10	.	.	PUNCT
iajs-555	204	1	since	since	SCONJ
iajs-555	204	2	)	)	PUNCT
iajs-555	204	3	)	)	PUNCT
iajs-555	205	1	u(g(f)u()fg	u(g(f)u()fg	ADJ
iajs-555	205	2	(	(	PUNCT
iajs-555	205	3	111	111	NUM
iajs-555	205	4	−−−	−−−	NOUN
iajs-555	205	5	=	=	NOUN
iajs-555	205	6			NOUN
iajs-555	205	7	,	,	PUNCT
iajs-555	205	8	then	then	ADV
iajs-555	205	9	)	)	PUNCT
iajs-555	205	10	u()fg	u()fg	NOUN
iajs-555	205	11	(	(	PUNCT
iajs-555	205	12	1−	1−	NUM
iajs-555	205	13	is	be	AUX
iajs-555	205	14	a	a	DET
iajs-555	205	15	gr	gr	ADJ
iajs-555	205	16	-	-	PUNCT
iajs-555	205	17	open	open	NOUN
iajs-555	205	18	set	set	NOUN
iajs-555	205	19	in	in	ADP
iajs-555	205	20	x	x	X
iajs-555	205	21	.	.	PUNCT
iajs-555	206	1	thus	thus	ADV
iajs-555	206	2	fg	fg	PROPN
iajs-555	206	3			PROPN
iajs-555	206	4	is	be	AUX
iajs-555	206	5	gr	gr	NOUN
iajs-555	206	6	-	-	PUNCT
iajs-555	206	7	irresolute	irresolute	ADJ
iajs-555	206	8	.	.	PUNCT
iajs-555	207	1	2)let	2)let	NUM
iajs-555	207	2	u	u	NOUN
iajs-555	207	3	be	be	VERB
iajs-555	207	4	a	a	DET
iajs-555	207	5	gr	gr	ADJ
iajs-555	207	6	-	-	PUNCT
iajs-555	207	7	open	open	ADJ
iajs-555	207	8	set	set	NOUN
iajs-555	207	9	in	in	ADP
iajs-555	207	10	z	z	PROPN
iajs-555	207	11	,	,	PUNCT
iajs-555	207	12	since	since	SCONJ
iajs-555	207	13	g	g	PROPN
iajs-555	207	14	is	be	AUX
iajs-555	207	15	gr	gr	NOUN
iajs-555	207	16	-	-	PUNCT
iajs-555	207	17	irresolute	irresolute	ADJ
iajs-555	207	18	,	,	PUNCT
iajs-555	207	19	then	then	ADV
iajs-555	207	20	)	)	PUNCT
iajs-555	208	1	u(g	u(g	PROPN
iajs-555	208	2	1−	1−	NUM
iajs-555	208	3	is	be	AUX
iajs-555	208	4	gr	gr	ADV
iajs-555	208	5	-	-	PUNCT
iajs-555	208	6	open	open	ADJ
iajs-555	208	7	in	in	ADP
iajs-555	208	8	y	y	PROPN
iajs-555	208	9	,	,	PUNCT
iajs-555	208	10	since	since	SCONJ
iajs-555	208	11	f	f	PROPN
iajs-555	208	12	is	be	AUX
iajs-555	208	13	contra	contra	PROPN
iajs-555	208	14	gr	gr	PROPN
iajs-555	208	15	-	-	PUNCT
iajs-555	208	16	irresolute	irresolute	ADJ
iajs-555	208	17	,	,	PUNCT
iajs-555	208	18	then	then	ADV
iajs-555	208	19	)	)	PUNCT
iajs-555	208	20	)	)	PUNCT
iajs-555	209	1	u(g(f	u(g(f	PROPN
iajs-555	209	2	11	11	NUM
iajs-555	209	3	−−	−−	NOUN
iajs-555	209	4	is	be	AUX
iajs-555	209	5	gr	gr	ADV
iajs-555	209	6	-	-	PUNCT
iajs-555	209	7	closed	closed	ADJ
iajs-555	209	8	in	in	ADP
iajs-555	209	9	x	x	X
iajs-555	209	10	.since	.since	NOUN
iajs-555	209	11	)	)	PUNCT
iajs-555	209	12	)	)	PUNCT
iajs-555	210	1	u(g(f)u()fg	u(g(f)u()fg	ADP
iajs-555	210	2	(	(	PUNCT
iajs-555	210	3	111	111	NUM
iajs-555	210	4	−−−	−−−	NOUN
iajs-555	210	5	=	=	PRON
iajs-555	210	6			NOUN
iajs-555	210	7	,	,	PUNCT
iajs-555	210	8	then	then	ADV
iajs-555	210	9	mathematics	mathematics	NOUN
iajs-555	210	10	384	384	NUM
iajs-555	210	11	مجلة	مجلة	NOUN
iajs-555	210	12	إبن	إبن	NOUN
iajs-555	210	13	الهيثم	الهيثم	ADJ
iajs-555	210	14	للعلوم	للعلوم	NOUN
iajs-555	210	15	الصرفة	الصرفة	NOUN
iajs-555	210	16	و	و	PRON
iajs-555	210	17	التطبيقية	التطبيقية	ADJ
iajs-555	210	18	2012	2012	NUM
iajs-555	210	19	السنة	السنة	NOUN
iajs-555	210	20	25	25	NUM
iajs-555	210	21	المجلد	المجلد	NOUN
iajs-555	210	22	3	3	NUM
iajs-555	210	23	العدد	العدد	PROPN
iajs-555	210	24	ibn	ibn	PROPN
iajs-555	210	25	al	al	PROPN
iajs-555	210	26	-	-	PUNCT
iajs-555	210	27	haitham	haitham	PROPN
iajs-555	210	28	journal	journal	PROPN
iajs-555	210	29	for	for	ADP
iajs-555	210	30	pure	pure	ADJ
iajs-555	210	31	and	and	CCONJ
iajs-555	210	32	applied	apply	VERB
iajs-555	210	33	science	science	NOUN
iajs-555	210	34	no	no	NOUN
iajs-555	210	35	.	.	NOUN
iajs-555	210	36	3	3	NUM
iajs-555	210	37	vol	vol	NOUN
iajs-555	210	38	.	.	PUNCT
iajs-555	211	1	25	25	NUM
iajs-555	211	2	year	year	NOUN
iajs-555	211	3	2012	2012	NUM
iajs-555	211	4	)	)	PUNCT
iajs-555	211	5	u()fg	u()fg	NOUN
iajs-555	211	6	(	(	PUNCT
iajs-555	211	7	1−	1−	NUM
iajs-555	211	8	is	be	AUX
iajs-555	211	9	a	a	DET
iajs-555	211	10	gr	gr	ADV
iajs-555	211	11	-	-	PUNCT
iajs-555	211	12	closed	closed	ADJ
iajs-555	211	13	set	set	NOUN
iajs-555	211	14	in	in	ADP
iajs-555	211	15	x	x	X
iajs-555	211	16	.	.	PUNCT
iajs-555	212	1	thus	thus	ADV
iajs-555	212	2	fg	fg	PROPN
iajs-555	212	3			PROPN
iajs-555	212	4	is	be	AUX
iajs-555	212	5	contra	contra	PROPN
iajs-555	212	6	gr	gr	NOUN
iajs-555	212	7	-	-	PUNCT
iajs-555	212	8	irresolute	irresolute	NOUN
iajs-555	212	9	.	.	PUNCT
iajs-555	213	1	3)let	3)let	NUM
iajs-555	213	2	f	f	AUX
iajs-555	213	3	be	be	AUX
iajs-555	213	4	a	a	DET
iajs-555	213	5	closed	closed	ADJ
iajs-555	213	6	set	set	NOUN
iajs-555	213	7	in	in	ADP
iajs-555	213	8	z	z	PROPN
iajs-555	213	9	,	,	PUNCT
iajs-555	213	10	since	since	SCONJ
iajs-555	213	11	g	g	PROPN
iajs-555	213	12	is	be	AUX
iajs-555	213	13	gr	gr	ADJ
iajs-555	213	14	-	-	ADJ
iajs-555	213	15	continuous	continuous	ADJ
iajs-555	213	16	,	,	PUNCT
iajs-555	213	17	then	then	ADV
iajs-555	213	18	)	)	PUNCT
iajs-555	213	19	f(g	f(g	PROPN
iajs-555	213	20	1−	1−	NUM
iajs-555	213	21	is	be	AUX
iajs-555	213	22	gr	gr	ADV
iajs-555	213	23	-	-	PUNCT
iajs-555	213	24	closed	closed	ADJ
iajs-555	213	25	in	in	ADP
iajs-555	213	26	y	y	PROPN
iajs-555	213	27	,	,	PUNCT
iajs-555	213	28	since	since	SCONJ
iajs-555	213	29	f	f	PROPN
iajs-555	213	30	is	be	AUX
iajs-555	213	31	gr	gr	NOUN
iajs-555	213	32	-	-	PUNCT
iajs-555	213	33	irresolute	irresolute	ADJ
iajs-555	213	34	,	,	PUNCT
iajs-555	213	35	then	then	ADV
iajs-555	213	36	)	)	PUNCT
iajs-555	213	37	)	)	PUNCT
iajs-555	214	1	f(g(f	f(g(f	NOUN
iajs-555	214	2	11	11	NUM
iajs-555	214	3	−−	−−	NOUN
iajs-555	214	4	is	be	AUX
iajs-555	214	5	gr	gr	ADV
iajs-555	214	6	-	-	PUNCT
iajs-555	214	7	closed	closed	ADJ
iajs-555	214	8	in	in	ADP
iajs-555	214	9	x	x	X
iajs-555	214	10	.	.	PUNCT
iajs-555	215	1	since	since	SCONJ
iajs-555	215	2	)	)	PUNCT
iajs-555	215	3	)	)	PUNCT
iajs-555	215	4	f(g(f)f()fg	f(g(f)f()fg	NOUN
iajs-555	215	5	(	(	PUNCT
iajs-555	215	6	111	111	NUM
iajs-555	215	7	−−−	−−−	NOUN
iajs-555	215	8	=	=	NOUN
iajs-555	215	9			NOUN
iajs-555	215	10	,	,	PUNCT
iajs-555	215	11	then	then	ADV
iajs-555	215	12	)	)	PUNCT
iajs-555	215	13	f()fg	f()fg	NOUN
iajs-555	215	14	(	(	PUNCT
iajs-555	215	15	1−	1−	NUM
iajs-555	215	16	is	be	AUX
iajs-555	215	17	a	a	DET
iajs-555	215	18	gr	gr	ADV
iajs-555	215	19	-	-	PUNCT
iajs-555	215	20	closed	closed	ADJ
iajs-555	215	21	set	set	NOUN
iajs-555	215	22	in	in	ADP
iajs-555	215	23	x	x	X
iajs-555	215	24	.	.	PUNCT
iajs-555	216	1	thus	thus	ADV
iajs-555	216	2	fg	fg	PROPN
iajs-555	216	3			PROPN
iajs-555	216	4	is	be	AUX
iajs-555	216	5	gr	gr	ADV
iajs-555	216	6	-	-	PUNCT
iajs-555	216	7	continuous	continuous	ADJ
iajs-555	216	8	.	.	PUNCT
iajs-555	217	1	4)let	4)let	NUM
iajs-555	217	2	f	f	PROPN
iajs-555	217	3	be	be	AUX
iajs-555	217	4	a	a	DET
iajs-555	217	5	closed	closed	ADJ
iajs-555	217	6	set	set	NOUN
iajs-555	217	7	in	in	ADP
iajs-555	217	8	z	z	PROPN
iajs-555	217	9	,	,	PUNCT
iajs-555	217	10	since	since	SCONJ
iajs-555	217	11	g	g	PROPN
iajs-555	217	12	is	be	AUX
iajs-555	217	13	r	r	NOUN
iajs-555	217	14	-	-	ADJ
iajs-555	217	15	continuous	continuous	ADJ
iajs-555	217	16	,	,	PUNCT
iajs-555	217	17	then	then	ADV
iajs-555	217	18	)	)	PUNCT
iajs-555	217	19	f(g	f(g	NOUN
iajs-555	217	20	1−	1−	NUM
iajs-555	217	21	is	be	AUX
iajs-555	217	22	r	r	NOUN
iajs-555	217	23	-	-	PUNCT
iajs-555	217	24	closed	closed	ADJ
iajs-555	217	25	in	in	ADP
iajs-555	217	26	y	y	PROPN
iajs-555	217	27	,	,	PUNCT
iajs-555	217	28	since	since	SCONJ
iajs-555	217	29	every	every	DET
iajs-555	217	30	r	r	NOUN
iajs-555	217	31	-	-	PUNCT
iajs-555	217	32	closed	closed	ADJ
iajs-555	217	33	set	set	NOUN
iajs-555	217	34	is	be	AUX
iajs-555	217	35	closed	closed	ADJ
iajs-555	217	36	,	,	PUNCT
iajs-555	217	37	then	then	ADV
iajs-555	217	38	)	)	PUNCT
iajs-555	217	39	f(g	f(g	PROPN
iajs-555	217	40	1−	1−	NUM
iajs-555	217	41	is	be	AUX
iajs-555	217	42	closed	close	VERB
iajs-555	217	43	in	in	ADP
iajs-555	217	44	y	y	PROPN
iajs-555	217	45	,	,	PUNCT
iajs-555	217	46	since	since	SCONJ
iajs-555	217	47	f	f	PROPN
iajs-555	217	48	is	be	AUX
iajs-555	217	49	gr	gr	ADV
iajs-555	217	50	-	-	ADJ
iajs-555	217	51	continuous	continuous	ADJ
iajs-555	217	52	,	,	PUNCT
iajs-555	217	53	then	then	ADV
iajs-555	217	54	)	)	PUNCT
iajs-555	217	55	)	)	PUNCT
iajs-555	218	1	f(g(f	f(g(f	NOUN
iajs-555	218	2	11	11	NUM
iajs-555	218	3	−−	−−	NOUN
iajs-555	218	4	is	be	AUX
iajs-555	218	5	gr	gr	ADV
iajs-555	218	6	-	-	PUNCT
iajs-555	218	7	closed	closed	ADJ
iajs-555	218	8	in	in	ADP
iajs-555	218	9	x	x	X
iajs-555	218	10	.	.	PUNCT
iajs-555	219	1	since	since	SCONJ
iajs-555	219	2	)	)	PUNCT
iajs-555	219	3	)	)	PUNCT
iajs-555	219	4	f(g(f)f()fg	f(g(f)f()fg	NOUN
iajs-555	219	5	(	(	PUNCT
iajs-555	219	6	111	111	NUM
iajs-555	219	7	−−−	−−−	NOUN
iajs-555	219	8	=	=	NOUN
iajs-555	219	9			NOUN
iajs-555	219	10	,	,	PUNCT
iajs-555	219	11	then	then	ADV
iajs-555	219	12	)	)	PUNCT
iajs-555	219	13	f()fg	f()fg	NOUN
iajs-555	219	14	(	(	PUNCT
iajs-555	219	15	1−	1−	NUM
iajs-555	219	16	is	be	AUX
iajs-555	219	17	a	a	DET
iajs-555	219	18	gr	gr	ADV
iajs-555	219	19	-	-	PUNCT
iajs-555	219	20	closed	closed	ADJ
iajs-555	219	21	set	set	NOUN
iajs-555	219	22	in	in	ADP
iajs-555	219	23	x	x	X
iajs-555	219	24	.	.	PUNCT
iajs-555	220	1	thus	thus	ADV
iajs-555	220	2	fg	fg	PROPN
iajs-555	220	3			PROPN
iajs-555	220	4	is	be	AUX
iajs-555	220	5	gr	gr	ADJ
iajs-555	220	6	-	-	ADJ
iajs-555	220	7	continuous	continuous	ADJ
iajs-555	220	8	5)let	5)let	NUM
iajs-555	220	9	f	f	AUX
iajs-555	220	10	be	be	AUX
iajs-555	220	11	a	a	DET
iajs-555	220	12	closed	closed	ADJ
iajs-555	220	13	set	set	NOUN
iajs-555	220	14	in	in	ADP
iajs-555	220	15	z	z	PROPN
iajs-555	220	16	,	,	PUNCT
iajs-555	220	17	since	since	SCONJ
iajs-555	220	18	g	g	PROPN
iajs-555	220	19	is	be	AUX
iajs-555	220	20	continuous	continuous	ADJ
iajs-555	220	21	,	,	PUNCT
iajs-555	220	22	then	then	ADV
iajs-555	220	23	)	)	PUNCT
iajs-555	220	24	f(g	f(g	NOUN
iajs-555	220	25	1−	1−	NUM
iajs-555	220	26	is	be	AUX
iajs-555	220	27	closed	close	VERB
iajs-555	220	28	iny	iny	ADJ
iajs-555	220	29	,	,	PUNCT
iajs-555	220	30	since	since	SCONJ
iajs-555	220	31	f	f	PROPN
iajs-555	220	32	is	be	AUX
iajs-555	220	33	gr	gr	ADV
iajs-555	220	34	continuous	continuous	ADJ
iajs-555	220	35	,	,	PUNCT
iajs-555	220	36	then	then	ADV
iajs-555	220	37	)	)	PUNCT
iajs-555	220	38	)	)	PUNCT
iajs-555	221	1	f(g(f	f(g(f	NOUN
iajs-555	221	2	11	11	NUM
iajs-555	221	3	−−	−−	NOUN
iajs-555	221	4	is	be	AUX
iajs-555	221	5	gr	gr	ADV
iajs-555	221	6	-	-	PUNCT
iajs-555	221	7	closed	closed	ADJ
iajs-555	221	8	in	in	ADP
iajs-555	221	9	x	x	X
iajs-555	221	10	.	.	PUNCT
iajs-555	222	1	since	since	SCONJ
iajs-555	222	2	)	)	PUNCT
iajs-555	222	3	)	)	PUNCT
iajs-555	222	4	f(g(f)f()fg	f(g(f)f()fg	NOUN
iajs-555	222	5	(	(	PUNCT
iajs-555	222	6	111	111	NUM
iajs-555	222	7	−−−	−−−	NOUN
iajs-555	222	8	=	=	NOUN
iajs-555	222	9			NOUN
iajs-555	222	10	,	,	PUNCT
iajs-555	222	11	then	then	ADV
iajs-555	222	12	)	)	PUNCT
iajs-555	222	13	f()fg	f()fg	NOUN
iajs-555	222	14	(	(	PUNCT
iajs-555	222	15	1−	1−	NUM
iajs-555	222	16	is	be	AUX
iajs-555	222	17	a	a	DET
iajs-555	222	18	gr	gr	ADV
iajs-555	222	19	-	-	PUNCT
iajs-555	222	20	closed	closed	ADJ
iajs-555	222	21	set	set	NOUN
iajs-555	222	22	in	in	ADP
iajs-555	222	23	x	x	X
iajs-555	222	24	.	.	PUNCT
iajs-555	223	1	thus	thus	ADV
iajs-555	223	2	fg	fg	PROPN
iajs-555	223	3			PROPN
iajs-555	223	4	is	be	AUX
iajs-555	223	5	gr	gr	ADV
iajs-555	223	6	-	-	ADJ
iajs-555	223	7	continuous	continuous	ADJ
iajs-555	223	8	.	.	PUNCT
iajs-555	224	1	6)let	6)let	NUM
iajs-555	224	2	u	u	NOUN
iajs-555	224	3	be	be	VERB
iajs-555	224	4	an	an	DET
iajs-555	224	5	open	open	ADJ
iajs-555	224	6	set	set	NOUN
iajs-555	224	7	in	in	ADP
iajs-555	224	8	z	z	PROPN
iajs-555	224	9	,	,	PUNCT
iajs-555	224	10	since	since	SCONJ
iajs-555	224	11	g	g	PROPN
iajs-555	224	12	is	be	AUX
iajs-555	224	13	gr	gr	ADJ
iajs-555	224	14	-	-	ADJ
iajs-555	224	15	continuous	continuous	ADJ
iajs-555	224	16	,	,	PUNCT
iajs-555	224	17	then	then	ADV
iajs-555	224	18	)	)	PUNCT
iajs-555	224	19	u(g	u(g	PROPN
iajs-555	224	20	1−	1−	NUM
iajs-555	224	21	is	be	AUX
iajs-555	224	22	gr	gr	ADV
iajs-555	224	23	-	-	PUNCT
iajs-555	224	24	open	open	ADJ
iajs-555	224	25	in	in	ADP
iajs-555	224	26	y	y	PROPN
iajs-555	224	27	,	,	PUNCT
iajs-555	224	28	since	since	SCONJ
iajs-555	224	29	f	f	PROPN
iajs-555	224	30	is	be	AUX
iajs-555	224	31	contra	contra	PROPN
iajs-555	224	32	gr	gr	PROPN
iajs-555	224	33	-	-	PUNCT
iajs-555	224	34	irresolute	irresolute	ADJ
iajs-555	224	35	,	,	PUNCT
iajs-555	224	36	then	then	ADV
iajs-555	224	37	)	)	PUNCT
iajs-555	224	38	)	)	PUNCT
iajs-555	225	1	u(g(f	u(g(f	PROPN
iajs-555	225	2	11	11	NUM
iajs-555	225	3	−−	−−	NOUN
iajs-555	225	4	is	be	AUX
iajs-555	225	5	gr	gr	ADV
iajs-555	225	6	-	-	PUNCT
iajs-555	225	7	closed	closed	ADJ
iajs-555	225	8	in	in	ADP
iajs-555	225	9	x	x	X
iajs-555	225	10	.	.	PUNCT
iajs-555	226	1	since	since	SCONJ
iajs-555	226	2	)	)	PUNCT
iajs-555	226	3	)	)	PUNCT
iajs-555	227	1	u(g(f)u()fg	u(g(f)u()fg	ADJ
iajs-555	227	2	(	(	PUNCT
iajs-555	227	3	111	111	NUM
iajs-555	227	4	−−−	−−−	NOUN
iajs-555	227	5	=	=	NOUN
iajs-555	227	6			X
iajs-555	227	7	,	,	PUNCT
iajs-555	227	8	then	then	ADV
iajs-555	227	9	)	)	PUNCT
iajs-555	227	10	u()fg	u()fg	NOUN
iajs-555	227	11	(	(	PUNCT
iajs-555	227	12	1−	1−	NUM
iajs-555	227	13	is	be	AUX
iajs-555	227	14	a	a	DET
iajs-555	227	15	gr	gr	ADV
iajs-555	227	16	-	-	PUNCT
iajs-555	227	17	closed	closed	ADJ
iajs-555	227	18	set	set	NOUN
iajs-555	227	19	in	in	ADP
iajs-555	227	20	x	x	X
iajs-555	227	21	.	.	PUNCT
iajs-555	228	1	thus	thus	ADV
iajs-555	228	2	fg	fg	PROPN
iajs-555	228	3			PROPN
iajs-555	228	4	is	be	AUX
iajs-555	228	5	contra	contra	PROPN
iajs-555	228	6	gr	gr	PROPN
iajs-555	228	7	-	-	PUNCT
iajs-555	228	8	continuous	continuous	ADJ
iajs-555	228	9	.	.	PUNCT
iajs-555	229	1	references	reference	NOUN
iajs-555	229	2	1	1	NUM
iajs-555	229	3	.	.	PUNCT
iajs-555	229	4	arya	arya	PROPN
iajs-555	229	5	,	,	PUNCT
iajs-555	229	6	s.	s.	PROPN
iajs-555	229	7	p.	p.	PROPN
iajs-555	229	8	and	and	CCONJ
iajs-555	229	9	gupta	gupta	PROPN
iajs-555	229	10	,	,	PUNCT
iajs-555	229	11	r.	r.	PROPN
iajs-555	229	12	(	(	PUNCT
iajs-555	229	13	1974	1974	NUM
iajs-555	229	14	)	)	PUNCT
iajs-555	229	15	on	on	ADP
iajs-555	229	16	strongly	strongly	ADV
iajs-555	229	17	continuous	continuous	ADJ
iajs-555	229	18	functions	function	NOUN
iajs-555	229	19	,	,	PUNCT
iajs-555	229	20	kyungpook	kyungpook	PROPN
iajs-555	229	21	math	math	NOUN
iajs-555	229	22	.	.	PUNCT
iajs-555	230	1	j.	j.	PROPN
iajs-555	230	2	,	,	PUNCT
iajs-555	230	3	14	14	NUM
iajs-555	230	4	:	:	SYM
iajs-555	230	5	131	131	NUM
iajs-555	230	6	-	-	SYM
iajs-555	230	7	143	143	NUM
iajs-555	230	8	.	.	NOUN
iajs-555	231	1	2	2	X
iajs-555	231	2	.	.	X
iajs-555	231	3	palaniappan	palaniappan	NOUN
iajs-555	231	4	,	,	PUNCT
iajs-555	231	5	n.	n.	PROPN
iajs-555	231	6	and	and	CCONJ
iajs-555	231	7	rao	rao	PROPN
iajs-555	231	8	,	,	PUNCT
iajs-555	231	9	k.c.(1993	k.c.(1993	PROPN
iajs-555	231	10	)	)	PUNCT
iajs-555	231	11	regular	regular	ADJ
iajs-555	231	12	generalized	generalize	VERB
iajs-555	231	13	closed	close	VERB
iajs-555	231	14	sets	set	NOUN
iajs-555	231	15	,	,	PUNCT
iajs-555	231	16	kyungpook	kyungpook	PROPN
iajs-555	231	17	math	math	NOUN
iajs-555	231	18	.	.	PUNCT
iajs-555	232	1	j.	j.	PROPN
iajs-555	232	2	,	,	PUNCT
iajs-555	232	3	33	33	NUM
iajs-555	232	4	:	:	PUNCT
iajs-555	232	5	(	(	PUNCT
iajs-555	232	6	2	2	X
iajs-555	232	7	)	)	PUNCT
iajs-555	232	8	211	211	NUM
iajs-555	232	9	-	-	SYM
iajs-555	232	10	219	219	NUM
iajs-555	232	11	.	.	PUNCT
iajs-555	233	1	3	3	X
iajs-555	233	2	.	.	X
iajs-555	233	3	bhattacharya	bhattacharya	PROPN
iajs-555	233	4	,	,	PUNCT
iajs-555	233	5	s.	s.	PROPN
iajs-555	233	6	(	(	PUNCT
iajs-555	233	7	2011	2011	NUM
iajs-555	233	8	)	)	PUNCT
iajs-555	233	9	on	on	ADP
iajs-555	233	10	generalized	generalize	VERB
iajs-555	233	11	regular	regular	ADJ
iajs-555	233	12	closed	closed	ADJ
iajs-555	233	13	sets	set	NOUN
iajs-555	233	14	,	,	PUNCT
iajs-555	233	15	int	int	NOUN
iajs-555	233	16	.	.	PUNCT
iajs-555	234	1	j.	j.	PROPN
iajs-555	234	2	contemp	contemp	PROPN
iajs-555	234	3	.	.	PUNCT
iajs-555	235	1	math	math	NOUN
iajs-555	235	2	.	.	PUNCT
iajs-555	236	1	sciences	science	NOUN
iajs-555	236	2	,	,	PUNCT
iajs-555	236	3	6	6	NUM
iajs-555	236	4	:	:	PUNCT
iajs-555	236	5	(	(	PUNCT
iajs-555	236	6	3	3	X
iajs-555	236	7	)	)	PUNCT
iajs-555	236	8	145	145	NUM
iajs-555	236	9	-	-	SYM
iajs-555	236	10	152	152	NUM
iajs-555	236	11	.	.	PUNCT
iajs-555	237	1	4	4	X
iajs-555	237	2	.	.	X
iajs-555	237	3	levine	levine	PROPN
iajs-555	237	4	,	,	PUNCT
iajs-555	237	5	n.(1970	n.(1970	PROPN
iajs-555	237	6	)	)	PUNCT
iajs-555	237	7	generalized	generalize	VERB
iajs-555	237	8	closed	closed	ADJ
iajs-555	237	9	sets	set	NOUN
iajs-555	237	10	in	in	ADP
iajs-555	237	11	topology	topology	NOUN
iajs-555	237	12	,	,	PUNCT
iajs-555	237	13	rend	rend	VERB
iajs-555	237	14	.	.	PUNCT
iajs-555	238	1	circ	circ	PROPN
iajs-555	238	2	.	.	PUNCT
iajs-555	239	1	math	math	NOUN
iajs-555	239	2	.	.	PUNCT
iajs-555	240	1	palermo	palermo	NOUN
iajs-555	240	2	,	,	PUNCT
iajs-555	240	3	19	19	NUM
iajs-555	240	4	:	:	PUNCT
iajs-555	240	5	(	(	PUNCT
iajs-555	240	6	2	2	NUM
iajs-555	240	7	)	)	PUNCT
iajs-555	240	8	89	89	NUM
iajs-555	240	9	-	-	SYM
iajs-555	240	10	96	96	NUM
iajs-555	240	11	.	.	PUNCT
iajs-555	241	1	5	5	X
iajs-555	241	2	.	.	X
iajs-555	241	3	stone	stone	NOUN
iajs-555	241	4	,	,	PUNCT
iajs-555	241	5	m.(1937	m.(1937	PROPN
iajs-555	241	6	)	)	PUNCT
iajs-555	241	7	applications	application	NOUN
iajs-555	241	8	of	of	ADP
iajs-555	241	9	the	the	DET
iajs-555	241	10	theory	theory	NOUN
iajs-555	241	11	of	of	ADP
iajs-555	241	12	boolean	boolean	ADJ
iajs-555	241	13	rings	ring	NOUN
iajs-555	241	14	to	to	ADP
iajs-555	241	15	general	general	ADJ
iajs-555	241	16	topology	topology	NOUN
iajs-555	241	17	,	,	PUNCT
iajs-555	241	18	trans	trans	PROPN
iajs-555	241	19	.	.	PROPN
iajs-555	242	1	amer	amer	PROPN
iajs-555	242	2	.	.	PUNCT
iajs-555	242	3	math	math	PROPN
iajs-555	242	4	.	.	PUNCT
iajs-555	243	1	soc	soc	PROPN
iajs-555	243	2	.	.	PUNCT
iajs-555	243	3	,	,	PUNCT
iajs-555	243	4	41	41	NUM
iajs-555	243	5	:	:	SYM
iajs-555	243	6	375	375	NUM
iajs-555	243	7	-	-	SYM
iajs-555	243	8	381	381	NUM
iajs-555	243	9	.	.	PUNCT
iajs-555	244	1	6	6	X
iajs-555	244	2	.	.	X
iajs-555	244	3	andrijevic	andrijevic	VERB
iajs-555	244	4	,	,	PUNCT
iajs-555	244	5	d.(1996	d.(1996	NOUN
iajs-555	244	6	)	)	PUNCT
iajs-555	244	7	on	on	ADP
iajs-555	244	8	b	b	X
iajs-555	244	9	-	-	PUNCT
iajs-555	244	10	open	open	ADJ
iajs-555	244	11	sets	set	NOUN
iajs-555	244	12	,	,	PUNCT
iajs-555	244	13	mat	mat	PROPN
iajs-555	244	14	.	.	PROPN
iajs-555	244	15	vesnik	vesnik	PROPN
iajs-555	244	16	,	,	PUNCT
iajs-555	244	17	48	48	NUM
iajs-555	244	18	:	:	PUNCT
iajs-555	244	19	(	(	PUNCT
iajs-555	244	20	1	1	NUM
iajs-555	244	21	-	-	SYM
iajs-555	244	22	2	2	NUM
iajs-555	244	23	)	)	PUNCT
iajs-555	244	24	59	59	NUM
iajs-555	244	25	-	-	SYM
iajs-555	244	26	64	64	NUM
iajs-555	244	27	.	.	PUNCT
iajs-555	245	1	7	7	X
iajs-555	245	2	.	.	X
iajs-555	245	3	ganster	ganster	NOUN
iajs-555	245	4	,	,	PUNCT
iajs-555	245	5	m.	m.	NOUN
iajs-555	245	6	and	and	CCONJ
iajs-555	245	7	steiner	steiner	NOUN
iajs-555	245	8	,	,	PUNCT
iajs-555	245	9	m.	m.	NOUN
iajs-555	245	10	,2007	,2007	PUNCT
iajs-555	245	11	,	,	PUNCT
iajs-555	245	12	on	on	ADP
iajs-555	245	13	b	b	PROPN
iajs-555	245	14	τ	τ	X
iajs-555	245	15	-closed	-close	VERB
iajs-555	245	16	sets	set	NOUN
iajs-555	245	17	,	,	PUNCT
iajs-555	245	18	applied	apply	VERB
iajs-555	245	19	general	general	ADJ
iajs-555	245	20	topology	topology	NOUN
iajs-555	245	21	,	,	PUNCT
iajs-555	245	22	8	8	NUM
iajs-555	245	23	:(	:(	SYM
iajs-555	245	24	2	2	NUM
iajs-555	245	25	)	)	PUNCT
iajs-555	245	26	243	243	NUM
iajs-555	245	27	-	-	SYM
iajs-555	245	28	247	247	NUM
iajs-555	245	29	.	.	NOUN
iajs-555	245	30	8	8	NUM
iajs-555	245	31	.	.	X
iajs-555	245	32	balachandran	balachandran	NOUN
iajs-555	245	33	,	,	PUNCT
iajs-555	245	34	k.	k.	PROPN
iajs-555	245	35	;	;	PUNCT
iajs-555	245	36	sundaram	sundaram	PROPN
iajs-555	245	37	,	,	PUNCT
iajs-555	245	38	p.	p.	NOUN
iajs-555	245	39	and	and	CCONJ
iajs-555	245	40	maki	maki	PROPN
iajs-555	245	41	,	,	PUNCT
iajs-555	245	42	h.(1991	h.(1991	PROPN
iajs-555	245	43	)	)	PUNCT
iajs-555	245	44	on	on	ADP
iajs-555	245	45	generalized	generalized	ADJ
iajs-555	245	46	continuous	continuous	ADJ
iajs-555	245	47	maps	map	NOUN
iajs-555	245	48	in	in	ADP
iajs-555	245	49	topological	topological	ADJ
iajs-555	245	50	spaces	space	NOUN
iajs-555	245	51	,	,	PUNCT
iajs-555	245	52	mem	mem	PROPN
iajs-555	245	53	.	.	PUNCT
iajs-555	246	1	fac	fac	PROPN
iajs-555	246	2	.	.	PUNCT
iajs-555	247	1	sci	sci	PROPN
iajs-555	247	2	.	.	PROPN
iajs-555	247	3	kochi	kochi	PROPN
iajs-555	247	4	univ	univ	PROPN
iajs-555	247	5	.	.	PUNCT
iajs-555	248	1	ser	ser	PROPN
iajs-555	248	2	.	.	PUNCT
iajs-555	248	3	a.	a.	PROPN
iajs-555	248	4	math	math	PROPN
iajs-555	248	5	.	.	PUNCT
iajs-555	248	6	,	,	PUNCT
iajs-555	248	7	12	12	NUM
iajs-555	248	8	:	:	SYM
iajs-555	248	9	5	5	NUM
iajs-555	248	10	-	-	SYM
iajs-555	248	11	13	13	NUM
iajs-555	248	12	.	.	PUNCT
iajs-555	249	1	9	9	X
iajs-555	249	2	.	.	X
iajs-555	250	1	al	al	PROPN
iajs-555	250	2	-	-	PUNCT
iajs-555	250	3	omari	omari	PROPN
iajs-555	250	4	,	,	PUNCT
iajs-555	250	5	a.	a.	NOUN
iajs-555	250	6	and	and	CCONJ
iajs-555	250	7	noorani	noorani	PROPN
iajs-555	250	8	,	,	PUNCT
iajs-555	250	9	m.s	m.s	PROPN
iajs-555	250	10	.	.	PROPN
iajs-555	250	11	,2009	,2009	PUNCT
iajs-555	250	12	,	,	PUNCT
iajs-555	250	13	on	on	ADP
iajs-555	250	14	generalized	generalized	ADJ
iajs-555	250	15	b	b	X
iajs-555	250	16	-	-	PUNCT
iajs-555	250	17	closed	closed	ADJ
iajs-555	250	18	sets	set	NOUN
iajs-555	250	19	,	,	PUNCT
iajs-555	250	20	bull	bull	NOUN
iajs-555	250	21	.	.	PUNCT
iajs-555	251	1	malays	malays	PROPN
iajs-555	251	2	.	.	PUNCT
iajs-555	252	1	math	math	NOUN
iajs-555	252	2	.	.	PUNCT
iajs-555	253	1	sci	sci	PROPN
iajs-555	253	2	.	.	PROPN
iajs-555	253	3	soc	soc	PROPN
iajs-555	253	4	.	.	PUNCT
iajs-555	253	5	,	,	PUNCT
iajs-555	253	6	2	2	NUM
iajs-555	253	7	:	:	PUNCT
iajs-555	253	8	(	(	PUNCT
iajs-555	253	9	32	32	NUM
iajs-555	253	10	)	)	PUNCT
iajs-555	253	11	19	19	NUM
iajs-555	253	12	-	-	SYM
iajs-555	253	13	30	30	NUM
iajs-555	253	14	.	.	PUNCT
iajs-555	254	1	mathematics	mathematic	NOUN
iajs-555	254	2	385	385	NUM
iajs-555	254	3	مجلة	مجلة	PROPN
iajs-555	254	4	إبن	إبن	VERB
iajs-555	254	5	الهيثم	الهيثم	ADJ
iajs-555	254	6	للعلوم	للعلوم	NOUN
iajs-555	254	7	الصرفة	الصرفة	NOUN
iajs-555	255	1	و	و	PRON
iajs-555	255	2	التطبيقية	التطبيقية	ADJ
iajs-555	255	3	2012	2012	NUM
iajs-555	255	4	السنة	السنة	NOUN
iajs-555	255	5	25	25	NUM
iajs-555	255	6	المجلد	المجلد	NOUN
iajs-555	255	7	3	3	NUM
iajs-555	255	8	العدد	العدد	PROPN
iajs-555	255	9	ibn	ibn	PROPN
iajs-555	255	10	al	al	PROPN
iajs-555	255	11	-	-	PUNCT
iajs-555	255	12	haitham	haitham	PROPN
iajs-555	255	13	journal	journal	PROPN
iajs-555	255	14	for	for	ADP
iajs-555	255	15	pure	pure	ADJ
iajs-555	255	16	and	and	CCONJ
iajs-555	255	17	applied	apply	VERB
iajs-555	255	18	science	science	NOUN
iajs-555	255	19	no	no	NOUN
iajs-555	255	20	.	.	NOUN
iajs-555	255	21	3	3	NUM
iajs-555	255	22	vol	vol	NOUN
iajs-555	255	23	.	.	PUNCT
iajs-555	256	1	25	25	NUM
iajs-555	256	2	year	year	NOUN
iajs-555	256	3	2012	2012	NUM
iajs-555	256	4	في	في	SCONJ
iajs-555	256	5	الفضاءات	الفضاءات	PROPN
iajs-555	256	6	التبولوجية	التبولوجية	PROPN
iajs-555	256	7	حول	حول	PROPN
iajs-555	256	8	الدوال	الدوال	PROPN
iajs-555	256	9	المستمرة	المستمرة	PROPN
iajs-555	256	10	المنتظمة	المنتظمة	PROPN
iajs-555	256	11	المعممة	المعممة	PROPN
iajs-555	256	12	صبيحة	صبيحة	VERB
iajs-555	256	13	إبراهيم	إبراهيم	NOUN
iajs-555	256	14	محمود	محمود	ADJ
iajs-555	256	15	الجامعة	الجامعة	NOUN
iajs-555	256	16	المستنصرية	المستنصرية	PROPN
iajs-555	256	17	،	،	NOUN
iajs-555	256	18	كلية	كلية	PROPN
iajs-555	256	19	العلوم	العلوم	PROPN
iajs-555	256	20	،	،	PROPN
iajs-555	257	1	قسم	قسم	PROPN
iajs-555	257	2	الرياضيات	الرياضيات	PROPN
iajs-555	257	3	2012ايار	2012ايار	PROPN
iajs-555	257	4	21قبل	21قبل	NUM
iajs-555	257	5	البحث	البحث	NOUN
iajs-555	257	6	في	في	ADP
iajs-555	257	7	:	:	PUNCT
iajs-555	257	8	2012كانون	2012كانون	PROPN
iajs-555	257	9	الثاني	الثاني	NOUN
iajs-555	257	10	30استلم	30استلم	NUM
iajs-555	257	11	البحث	البحث	VERB
iajs-555	257	12	في	في	ADP
iajs-555	257	13	:	:	PUNCT
iajs-555	257	14	الخالصة	الخالصة	NOUN
iajs-555	257	15	generalized	generalize	VERB
iajs-555	257	16	regular)أسميناها	regular)أسميناها	VERB
iajs-555	257	17	بالدوال	بالدوال	ADJ
iajs-555	257	18	المستمرة	المستمرة	PROPN
iajs-555	257	19	المنتظمة	المنتظمة	PROPN
iajs-555	257	20	المعممة	المعممة	PROPN
iajs-555	257	21	في	في	ADP
iajs-555	257	22	هذا	هذا	NOUN
iajs-555	257	23	البحث	البحث	PROPN
iajs-555	257	24	قدمنا	قدمنا	PROPN
iajs-555	257	25	نوعا	نوعا	PROPN
iajs-555	257	26	جديدا	جديدا	NOUN
iajs-555	257	27	من	من	DET
iajs-555	257	28	الدوال	الدوال	ADJ
iajs-555	257	29	continuous	continuous	ADJ
iajs-555	257	30	functions	function	NOUN
iajs-555	257	31	هذه	هذه	PROPN
iajs-555	257	32	الدوال	الدوال	NOUN
iajs-555	257	33	اضعف	اضعف	PROPN
iajs-555	258	1	من	من	PROPN
iajs-555	259	1	الدوال	الدوال	PROPN
iajs-555	259	2	المستمرة	المستمرة	PROPN
iajs-555	259	3	المنتظمة)(regular	المنتظمة)(regular	PROPN
iajs-555	259	4	continuous	continuous	ADJ
iajs-555	259	5	functions	function	NOUN
iajs-555	259	6	كذلك	كذلك	VERB
iajs-555	259	7	درسنا	درسنا	ADJ
iajs-555	259	8	بعض	بعض	NOUN
iajs-555	259	9	.	.	PUNCT
iajs-555	259	10	)	)	PUNCT
iajs-555	260	1	(	(	PUNCT
iajs-555	260	2	regular	regular	ADJ
iajs-555	260	3	generalized	generalize	VERB
iajs-555	260	4	continuous	continuous	ADJ
iajs-555	260	5	functionsمن	functionsمن	PROPN
iajs-555	260	6	الدوال	الدوال	PROPN
iajs-555	260	7	المستمرة	المستمرة	PROPN
iajs-555	260	8	المعممة	المعممة	PROPN
iajs-555	260	9	المنتظمة	المنتظمة	PROPN
iajs-555	260	10	وأقوى	وأقوى	PROPN
iajs-555	260	11	ذلك	ذلك	PROPN
iajs-555	260	12	درسنا	درسنا	PROPN
iajs-555	260	13	أنواعا	أنواعا	PROPN
iajs-555	260	14	أخرى	أخرى	PROPN
iajs-555	260	15	من	من	DET
iajs-555	260	16	الدوال	الدوال	PROPN
iajs-555	260	17	المستمرة	المستمرة	PROPN
iajs-555	260	18	فضًال	فضًال	PROPN
iajs-555	260	19	عنوالخواص	عنوالخواص	PROPN
iajs-555	260	20	األساسية	األساسية	PROPN
iajs-555	260	21	للدوال	للدوال	ADP
iajs-555	260	22	المستمرة	المستمرة	PROPN
iajs-555	260	23	المنتظمة	المنتظمة	PROPN
iajs-555	260	24	المعممة	المعممة	PROPN
iajs-555	260	25	.	.	PUNCT
iajs-555	261	1	أتفالمكا	أتفالمكا	PROPN
iajs-555	261	2	المعممة	المعممة	PROPN
iajs-555	261	3	ومن	ومن	VERB
iajs-555	261	4	ثم	ثم	ADP
iajs-555	261	5	درسنا	درسنا	ADJ
iajs-555	261	6	العالقة	العالقة	PROPN
iajs-555	261	7	بينها	بينها	VERB
iajs-555	261	8	.	.	PUNCT
iajs-555	262	1	المنتظمة	المنتظمة	PROPN
iajs-555	262	2	ة	ة	DET
iajs-555	262	3	.دوال	.دوال	PROPN
iajs-555	262	4	المستمرة	المستمرة	PROPN
iajs-555	262	5	المعممة	المعممة	PROPN
iajs-555	262	6	المنتظمالدوال	المنتظمالدوال	PROPN
iajs-555	262	7	المستمرة	المستمرة	PROPN
iajs-555	262	8	المنتظمة	المنتظمة	PROPN
iajs-555	262	9	المعممة	المعممة	PROPN
iajs-555	262	10	،	،	PROPN
iajs-555	262	11	الدوال	الدوال	PROPN
iajs-555	262	12	المستمرة	المستمرة	PROPN
iajs-555	262	13	المنتظمة	المنتظمة	PROPN
iajs-555	262	14	،	،	PROPN
iajs-555	262	15	ال	ال	ADP
iajs-555	262	16	الكلمات	الكلمات	VERB
iajs-555	262	17	المفتاحية	المفتاحية	PROPN
iajs-555	262	18	:	:	PUNCT
iajs-555	262	19	s.	s.	PROPN
iajs-555	262	20	i.	i.	PROPN
iajs-555	262	21	mahmood	mahmood	PROPN