id	sid	tid	token	lemma	pos
iajs-2381	1	1	251	251	NUM
iajs-2381	1	2	ibn	ibn	PROPN
iajs-2381	1	3	al	al	PROPN
iajs-2381	1	4	-	-	PUNCT
iajs-2381	1	5	haitham	haitham	PROPN
iajs-2381	1	6	jour	jour	X
iajs-2381	1	7	.	.	PROPN
iajs-2381	1	8	for	for	ADP
iajs-2381	1	9	pure	pure	ADJ
iajs-2381	1	10	&	&	CCONJ
iajs-2381	1	11	appl	appl	PROPN
iajs-2381	1	12	.	.	PUNCT
iajs-2381	2	1	sci	sci	PROPN
iajs-2381	2	2	.	.	PROPN
iajs-2381	3	1	33	33	NUM
iajs-2381	3	2	(	(	PUNCT
iajs-2381	3	3	1	1	NUM
iajs-2381	3	4	)	)	PUNCT
iajs-2381	3	5	2020	2020	NUM
iajs-2381	3	6	ahmed	ahmed	PROPN
iajs-2381	3	7	.	.	PUNCT
iajs-2381	4	1	a.	a.	PROPN
iajs-2381	4	2	jassam	jassam	PROPN
iajs-2381	4	3	r.	r.	PROPN
iajs-2381	4	4	b.	b.	PROPN
iajs-2381	4	5	esmaeel	esmaeel	PROPN
iajs-2381	4	6	abstract	abstract	ADJ
iajs-2381	4	7	the	the	DET
iajs-2381	4	8	main	main	ADJ
iajs-2381	4	9	aim	aim	NOUN
iajs-2381	4	10	of	of	ADP
iajs-2381	4	11	this	this	DET
iajs-2381	4	12	paper	paper	NOUN
iajs-2381	4	13	is	be	AUX
iajs-2381	4	14	to	to	PART
iajs-2381	4	15	use	use	VERB
iajs-2381	4	16	the	the	DET
iajs-2381	4	17	notion	notion	NOUN
iajs-2381	4	18	ـ	ـ	X
iajs-2381	4	19	ـ	ـ	X
iajs-2381	4	20	ـ	ـ	X
iajs-2381	4	21	which	which	PRON
iajs-2381	4	22	was	be	AUX
iajs-2381	4	23	introduced	introduce	VERB
iajs-2381	4	24	in	in	ADP
iajs-2381	4	25	[	[	X
iajs-2381	4	26	1	1	NUM
iajs-2381	4	27	]	]	PUNCT
iajs-2381	4	28	.	.	PUNCT
iajs-2381	5	1	to	to	PART
iajs-2381	5	2	offered	offer	VERB
iajs-2381	5	3	new	new	ADJ
iajs-2381	5	4	classes	class	NOUN
iajs-2381	5	5	of	of	ADP
iajs-2381	5	6	separation	separation	NOUN
iajs-2381	5	7	axioms	axiom	NOUN
iajs-2381	5	8	in	in	ADP
iajs-2381	5	9	ideal	ideal	ADJ
iajs-2381	5	10	spaces	space	NOUN
iajs-2381	5	11	.	.	PUNCT
iajs-2381	6	1	so	so	ADV
iajs-2381	6	2	,	,	PUNCT
iajs-2381	6	3	we	we	PRON
iajs-2381	6	4	offered	offer	VERB
iajs-2381	6	5	new	new	ADJ
iajs-2381	6	6	type	type	NOUN
iajs-2381	6	7	of	of	ADP
iajs-2381	6	8	notions	notion	NOUN
iajs-2381	6	9	of	of	ADP
iajs-2381	6	10	convergence	convergence	NOUN
iajs-2381	6	11	in	in	ADP
iajs-2381	6	12	ideal	ideal	ADJ
iajs-2381	6	13	spaces	space	NOUN
iajs-2381	6	14	via	via	ADP
iajs-2381	6	15	the	the	DET
iajs-2381	6	16	ـ	ـ	X
iajs-2381	6	17	ـ	ـ	X
iajs-2381	6	18	ـ	ـ	X
iajs-2381	6	19	set	set	NOUN
iajs-2381	6	20	.	.	PUNCT
iajs-2381	7	1	relations	relation	NOUN
iajs-2381	7	2	among	among	ADP
iajs-2381	7	3	several	several	ADJ
iajs-2381	7	4	types	type	NOUN
iajs-2381	7	5	of	of	ADP
iajs-2381	7	6	separation	separation	NOUN
iajs-2381	7	7	axioms	axiom	NOUN
iajs-2381	7	8	that	that	PRON
iajs-2381	7	9	offered	offer	VERB
iajs-2381	7	10	were	be	AUX
iajs-2381	7	11	explained	explain	VERB
iajs-2381	7	12	.	.	PUNCT
iajs-2381	8	1	keyword	keyword	NOUN
iajs-2381	8	2	:	:	PUNCT
iajs-2381	8	3	ideal	ideal	ADJ
iajs-2381	8	4	,	,	PUNCT
iajs-2381	8	5	separation	separation	NOUN
iajs-2381	8	6	axioms	axiom	NOUN
iajs-2381	8	7	,	,	PUNCT
iajs-2381	8	8	ـ	ـ	X
iajs-2381	8	9	ـ	ـ	X
iajs-2381	8	10	ـ	ـ	PROPN
iajs-2381	8	11	,	,	PUNCT
iajs-2381	8	12	ـ	ـ	X
iajs-2381	8	13	ـ	ـ	X
iajs-2381	8	14	ـ	ـ	PROPN
iajs-2381	8	15	,	,	PUNCT
iajs-2381	8	16	ـ	ـ	X
iajs-2381	8	17	ـ	ـ	X
iajs-2381	8	18	ـ	ـ	PROPN
iajs-2381	8	19	,	,	PUNCT
iajs-2381	8	20	.	.	PUNCT
iajs-2381	9	1	ـ	ـ	X
iajs-2381	9	2	ـ	ـ	X
iajs-2381	9	3	ـ	ـ	PROPN
iajs-2381	9	4	,	,	PUNCT
iajs-2381	9	5	ـ	ـ	X
iajs-2381	9	6	ـ	ـ	X
iajs-2381	9	7	ـ	ـ	PROPN
iajs-2381	9	8	1	1	NUM
iajs-2381	9	9	.	.	PUNCT
iajs-2381	9	10	introduction	introduction	NOUN
iajs-2381	9	11	in	in	ADP
iajs-2381	9	12	1933	1933	NUM
iajs-2381	9	13	,	,	PUNCT
iajs-2381	9	14	kuratowski	kuratowski	VERB
iajs-2381	9	15	[	[	X
iajs-2381	9	16	2	2	NUM
iajs-2381	9	17	]	]	PUNCT
iajs-2381	9	18	.	.	PUNCT
iajs-2381	10	1	presented	present	VERB
iajs-2381	10	2	the	the	DET
iajs-2381	10	3	concept	concept	NOUN
iajs-2381	10	4	of	of	ADP
iajs-2381	10	5	ideals	ideal	NOUN
iajs-2381	10	6	on	on	ADP
iajs-2381	10	7	non	non	ADJ
iajs-2381	10	8	-	-	ADJ
iajs-2381	10	9	empty	empty	ADJ
iajs-2381	10	10	sets	set	NOUN
iajs-2381	10	11	.	.	PUNCT
iajs-2381	11	1	a	a	DET
iajs-2381	11	2	collection	collection	NOUN
iajs-2381	11	3	is	be	AUX
iajs-2381	11	4	namely	namely	ADV
iajs-2381	11	5	an	an	DET
iajs-2381	11	6	ideals	ideal	NOUN
iajs-2381	11	7	on	on	ADP
iajs-2381	11	8	a	a	DET
iajs-2381	11	9	nonempty	nonempty	ADV
iajs-2381	11	10	set	set	VERB
iajs-2381	11	11	when	when	SCONJ
iajs-2381	11	12	the	the	DET
iajs-2381	11	13	following	follow	VERB
iajs-2381	11	14	two	two	NUM
iajs-2381	11	15	conditions	condition	NOUN
iajs-2381	11	16	are	be	AUX
iajs-2381	11	17	met	meet	VERB
iajs-2381	11	18	;	;	PUNCT
iajs-2381	11	19	(	(	PUNCT
iajs-2381	11	20	i	i	NOUN
iajs-2381	11	21	)	)	PUNCT
iajs-2381	11	22	whenever	whenever	SCONJ
iajs-2381	11	23	and	and	CCONJ
iajs-2381	11	24	and	and	CCONJ
iajs-2381	11	25	(	(	PUNCT
iajs-2381	11	26	ii	ii	NOUN
iajs-2381	11	27	)	)	PUNCT
iajs-2381	11	28	whenever	whenever	SCONJ
iajs-2381	11	29	and	and	CCONJ
iajs-2381	11	30	are	be	AUX
iajs-2381	11	31	belong	belong	VERB
iajs-2381	11	32	to	to	ADP
iajs-2381	11	33	.	.	PUNCT
iajs-2381	12	1	vaidyanathaswamy	vaidyanathaswamy	VERB
iajs-2381	13	1	[	[	X
iajs-2381	13	2	3	3	NUM
iajs-2381	13	3	]	]	PUNCT
iajs-2381	13	4	.	.	PUNCT
iajs-2381	14	1	had	have	AUX
iajs-2381	14	2	offered	offer	VERB
iajs-2381	14	3	for	for	ADP
iajs-2381	14	4	initial	initial	ADJ
iajs-2381	14	5	the	the	DET
iajs-2381	14	6	idea	idea	NOUN
iajs-2381	14	7	of	of	ADP
iajs-2381	14	8	ideal	ideal	ADJ
iajs-2381	14	9	spaces	space	NOUN
iajs-2381	14	10	by	by	ADP
iajs-2381	14	11	introduced	introduce	VERB
iajs-2381	14	12	the	the	DET
iajs-2381	14	13	set	set	NOUN
iajs-2381	14	14	operator	operator	NOUN
iajs-2381	14	15	namely	namely	ADV
iajs-2381	14	16	local	local	ADJ
iajs-2381	14	17	function	function	NOUN
iajs-2381	14	18	.	.	PUNCT
iajs-2381	15	1	so	so	ADV
iajs-2381	15	2	he	he	PRON
iajs-2381	15	3	founded	found	VERB
iajs-2381	15	4	new	new	ADJ
iajs-2381	15	5	generalize	generalize	NOUN
iajs-2381	15	6	of	of	ADP
iajs-2381	15	7	the	the	DET
iajs-2381	15	8	topological	topological	ADJ
iajs-2381	15	9	spaces	space	NOUN
iajs-2381	15	10	,	,	PUNCT
iajs-2381	15	11	namely	namely	ADV
iajs-2381	15	12	ideal	ideal	ADJ
iajs-2381	15	13	space	space	NOUN
iajs-2381	15	14	and	and	CCONJ
iajs-2381	15	15	symbolizes	symbolize	VERB
iajs-2381	15	16	by	by	ADP
iajs-2381	15	17	,	,	PUNCT
iajs-2381	15	18	[	[	X
iajs-2381	15	19	4	4	NUM
iajs-2381	15	20	,	,	PUNCT
iajs-2381	15	21	5	5	NUM
iajs-2381	15	22	]	]	PUNCT
iajs-2381	15	23	.	.	PUNCT
iajs-2381	16	1	the	the	DET
iajs-2381	16	2	concept	concept	NOUN
iajs-2381	16	3	of	of	ADP
iajs-2381	16	4	"	"	PUNCT
iajs-2381	16	5	preـopen	preـopen	ADJ
iajs-2381	16	6	set	set	NOUN
iajs-2381	16	7	"	"	PUNCT
iajs-2381	16	8	was	be	AUX
iajs-2381	16	9	introduced	introduce	VERB
iajs-2381	16	10	by	by	ADP
iajs-2381	16	11	mashhour	mashhour	ADJ
iajs-2381	16	12	,	,	PUNCT
iajs-2381	16	13	abd	abd	PROPN
iajs-2381	16	14	elmonsef	elmonsef	NOUN
iajs-2381	16	15	and	and	CCONJ
iajs-2381	16	16	el	el	PROPN
iajs-2381	16	17	deeb	deeb	PROPN
iajs-2381	16	18	,	,	PUNCT
iajs-2381	16	19	a	a	DET
iajs-2381	16	20	set	set	NOUN
iajs-2381	16	21	in	in	ADP
iajs-2381	16	22	is	be	AUX
iajs-2381	16	23	a	a	DET
iajs-2381	16	24	pre	pre	NOUN
iajs-2381	16	25	-	-	ADJ
iajs-2381	16	26	open	open	ADJ
iajs-2381	17	1	when	when	SCONJ
iajs-2381	17	2	[	[	X
iajs-2381	17	3	6	6	NUM
iajs-2381	17	4	]	]	PUNCT
iajs-2381	17	5	.	.	PUNCT
iajs-2381	18	1	from	from	ADP
iajs-2381	18	2	that	that	DET
iajs-2381	18	3	time	time	NOUN
iajs-2381	18	4	many	many	ADJ
iajs-2381	18	5	researchers	researcher	NOUN
iajs-2381	18	6	have	have	AUX
iajs-2381	18	7	submitted	submit	VERB
iajs-2381	18	8	many	many	ADJ
iajs-2381	18	9	studies	study	NOUN
iajs-2381	18	10	in	in	ADP
iajs-2381	18	11	this	this	DET
iajs-2381	18	12	field	field	NOUN
iajs-2381	19	1	[	[	X
iajs-2381	19	2	7	7	NUM
iajs-2381	19	3	-	-	SYM
iajs-2381	19	4	9	9	NUM
iajs-2381	19	5	]	]	PUNCT
iajs-2381	19	6	.	.	PUNCT
iajs-2381	20	1	latterly	latterly	ADV
iajs-2381	20	2	,	,	PUNCT
iajs-2381	20	3	ahmed	ahme	VERB
iajs-2381	20	4	and	and	CCONJ
iajs-2381	20	5	esmaeel	esmaeel	VERB
iajs-2381	20	6	[	[	X
iajs-2381	20	7	1	1	NUM
iajs-2381	20	8	]	]	PUNCT
iajs-2381	20	9	.	.	PUNCT
iajs-2381	21	1	had	have	AUX
iajs-2381	21	2	submitted	submit	VERB
iajs-2381	21	3	the	the	DET
iajs-2381	21	4	concept	concept	NOUN
iajs-2381	21	5	of	of	ADP
iajs-2381	21	6	ـ	ـ	X
iajs-2381	21	7	ـ	ـ	X
iajs-2381	21	8	ـ	ـ	X
iajs-2381	21	9	(	(	PUNCT
iajs-2381	21	10	simply	simply	ADV
iajs-2381	21	11	,	,	PUNCT
iajs-2381	21	12	ـ	ـ	X
iajs-2381	21	13	a	a	DET
iajs-2381	21	14	set	set	NOUN
iajs-2381	21	15	in	in	ADP
iajs-2381	21	16	is	be	AUX
iajs-2381	21	17	so	so	ADV
iajs-2381	21	18	,	,	PUNCT
iajs-2381	21	19	the	the	DET
iajs-2381	21	20	set	set	NOUN
iajs-2381	21	21	.	.	PUNCT
iajs-2381	22	1	ـ	ـ	PROPN
iajs-2381	22	2	and	and	CCONJ
iajs-2381	22	3	is	be	AUX
iajs-2381	22	4	pre	pre	ADJ
iajs-2381	22	5	-	-	ADJ
iajs-2381	22	6	open	open	ADJ
iajs-2381	22	7	set	set	NOUN
iajs-2381	22	8	,	,	PUNCT
iajs-2381	22	9	implies	imply	VERB
iajs-2381	22	10	to	to	ADP
iajs-2381	22	11	ـ	ـ	PROPN
iajs-2381	22	12	if	if	SCONJ
iajs-2381	22	13	the	the	DET
iajs-2381	22	14	condition	condition	NOUN
iajs-2381	22	15	ـ	ـ	X
iajs-2381	22	16	in	in	ADP
iajs-2381	22	17	is	be	AUX
iajs-2381	22	18	namely	namely	ADV
iajs-2381	22	19	ـ	ـ	X
iajs-2381	22	20	ـ	ـ	X
iajs-2381	22	21	ـ	ـ	X
iajs-2381	22	22	(	(	PUNCT
iajs-2381	22	23	simply	simply	ADV
iajs-2381	22	24	,	,	PUNCT
iajs-2381	22	25	ـ	ـ	X
iajs-2381	22	26	if	if	SCONJ
iajs-2381	22	27	ـ	ـ	PROPN
iajs-2381	22	28	is	be	AUX
iajs-2381	22	29	ـ	ـ	X
iajs-2381	22	30	the	the	DET
iajs-2381	22	31	collection	collection	NOUN
iajs-2381	22	32	of	of	ADP
iajs-2381	22	33	all	all	DET
iajs-2381	22	34	ـ	ـ	X
iajs-2381	22	35	(	(	PUNCT
iajs-2381	22	36	respectively	respectively	ADV
iajs-2381	22	37	,	,	PUNCT
iajs-2381	22	38	ـ	ـ	X
iajs-2381	22	39	in	in	ADP
iajs-2381	22	40	simply	simply	ADV
iajs-2381	22	41	ـ	ـ	X
iajs-2381	22	42	(	(	PUNCT
iajs-2381	22	43	respectively	respectively	ADV
iajs-2381	22	44	,	,	PUNCT
iajs-2381	22	45	ـ	ـ	X
iajs-2381	22	46	)	)	PUNCT
iajs-2381	22	47	.	.	PUNCT
iajs-2381	23	1	for	for	ADP
iajs-2381	23	2	a	a	DET
iajs-2381	23	3	space	space	NOUN
iajs-2381	23	4	,	,	PUNCT
iajs-2381	23	5	ـ	ـ	X
iajs-2381	23	6	is	be	AUX
iajs-2381	23	7	finer	fine	ADJ
iajs-2381	23	8	than	than	ADP
iajs-2381	23	9	[	[	X
iajs-2381	23	10	1	1	NUM
iajs-2381	23	11	]	]	PUNCT
iajs-2381	23	12	.	.	PUNCT
iajs-2381	24	1	the	the	DET
iajs-2381	24	2	main	main	ADJ
iajs-2381	24	3	target	target	NOUN
iajs-2381	24	4	of	of	ADP
iajs-2381	24	5	this	this	DET
iajs-2381	24	6	article	article	NOUN
iajs-2381	24	7	is	be	AUX
iajs-2381	24	8	to	to	PART
iajs-2381	24	9	introduce	introduce	VERB
iajs-2381	24	10	new	new	ADJ
iajs-2381	24	11	kinds	kind	NOUN
iajs-2381	24	12	of	of	ADP
iajs-2381	24	13	separation	separation	NOUN
iajs-2381	24	14	axioms	axiom	NOUN
iajs-2381	24	15	in	in	ADP
iajs-2381	24	16	ideal	ideal	ADJ
iajs-2381	24	17	spaces	space	NOUN
iajs-2381	24	18	by	by	ADP
iajs-2381	24	19	using	use	VERB
iajs-2381	24	20	the	the	DET
iajs-2381	24	21	notion	notion	NOUN
iajs-2381	24	22	ـ	ـ	X
iajs-2381	24	23	ـ	ـ	X
iajs-2381	24	24	ـ	ـ	X
iajs-2381	24	25	ـ	ـ	PROPN
iajs-2381	24	26	.2	.2	NUM
iajs-2381	24	27	this	this	DET
iajs-2381	24	28	portion	portion	NOUN
iajs-2381	24	29	is	be	AUX
iajs-2381	24	30	to	to	PART
iajs-2381	24	31	submit	submit	VERB
iajs-2381	24	32	new	new	ADJ
iajs-2381	24	33	classes	class	NOUN
iajs-2381	24	34	of	of	ADP
iajs-2381	24	35	separation	separation	NOUN
iajs-2381	24	36	axioms	axiom	NOUN
iajs-2381	24	37	by	by	ADP
iajs-2381	24	38	using	use	VERB
iajs-2381	24	39	the	the	DET
iajs-2381	24	40	notion	notion	NOUN
iajs-2381	24	41	of	of	ADP
iajs-2381	24	42	ـ	ـ	X
iajs-2381	24	43	.	.	PUNCT
iajs-2381	25	1	properties	property	NOUN
iajs-2381	25	2	of	of	ADP
iajs-2381	25	3	these	these	DET
iajs-2381	25	4	sorts	sort	NOUN
iajs-2381	25	5	are	be	AUX
iajs-2381	25	6	studied	study	VERB
iajs-2381	25	7	and	and	CCONJ
iajs-2381	25	8	the	the	DET
iajs-2381	25	9	relations	relation	NOUN
iajs-2381	25	10	between	between	ADP
iajs-2381	25	11	it	it	PRON
iajs-2381	25	12	are	be	AUX
iajs-2381	25	13	discussed.also	discussed.also	PROPN
iajs-2381	25	14	.	.	PUNCT
iajs-2381	26	1	ibn	ibn	PROPN
iajs-2381	26	2	al	al	PROPN
iajs-2381	26	3	haitham	haitham	PROPN
iajs-2381	26	4	journal	journal	PROPN
iajs-2381	26	5	for	for	ADP
iajs-2381	26	6	pure	pure	ADJ
iajs-2381	26	7	and	and	CCONJ
iajs-2381	26	8	applied	apply	VERB
iajs-2381	26	9	science	science	NOUN
iajs-2381	26	10	journal	journal	PROPN
iajs-2381	26	11	homepage	homepage	NOUN
iajs-2381	26	12	:	:	PUNCT
iajs-2381	26	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2381	26	14	doi	doi	NOUN
iajs-2381	26	15	:	:	PUNCT
iajs-2381	27	1	10.30526/33.1.2381	10.30526/33.1.2381	PRON
iajs-2381	27	2	ahm7a7a@gmail.com	ahm7a7a@gmail.com	X
iajs-2381	28	1	ranamumosa@yahoo.com	ranamumosa@yahoo.com	PROPN
iajs-2381	28	2	article	article	NOUN
iajs-2381	28	3	history	history	NOUN
iajs-2381	28	4	:	:	PUNCT
iajs-2381	28	5	received	receive	VERB
iajs-2381	28	6	1	1	NUM
iajs-2381	28	7	june	june	PROPN
iajs-2381	28	8	2019	2019	NUM
iajs-2381	28	9	,	,	PUNCT
iajs-2381	28	10	accepted	accept	VERB
iajs-2381	28	11	10	10	NUM
iajs-2381	28	12	july	july	PROPN
iajs-2381	28	13	2019	2019	NUM
iajs-2381	28	14	,	,	PUNCT
iajs-2381	28	15	publish	publish	VERB
iajs-2381	28	16	january	january	PROPN
iajs-2381	28	17	2020	2020	NUM
iajs-2381	28	18	.	.	PUNCT
iajs-2381	29	1	convergences	convergence	NOUN
iajs-2381	29	2	via	via	ADP
iajs-2381	29	3	ẛ	ẛ	DET
iajs-2381	29	4	ـpre	ـpre	PROPN
iajs-2381	29	5	ـg	ـg	ADP
iajs-2381	29	6	ـopen	ـopen	VERB
iajs-2381	29	7	set	set	PROPN
iajs-2381	29	8	department	department	NOUN
iajs-2381	29	9	of	of	ADP
iajs-2381	29	10	mathematics	mathematics	PROPN
iajs-2381	29	11	,	,	PUNCT
iajs-2381	29	12	college	college	NOUN
iajs-2381	29	13	of	of	ADP
iajs-2381	29	14	education	education	NOUN
iajs-2381	29	15	for	for	ADP
iajs-2381	29	16	pure	pure	ADJ
iajs-2381	29	17	science	science	NOUN
iajs-2381	29	18	,	,	PUNCT
iajs-2381	29	19	ibn	ibn	PROPN
iajs-2381	29	20	-	-	PUNCT
iajs-2381	29	21	al	al	PROPN
iajs-2381	29	22	haitham	haitham	PROPN
iajs-2381	29	23	,	,	PUNCT
iajs-2381	29	24	university	university	PROPN
iajs-2381	29	25	of	of	ADP
iajs-2381	29	26	baghdad	baghdad	PROPN
iajs-2381	29	27	,	,	PUNCT
iajs-2381	29	28	iraq	iraq	PROPN
iajs-2381	29	29	file:///c:/users/mustafa/desktop/2020/رياضيات/ahm7a7a@gmail.com	file:///c:/users/mustafa/desktop/2020/رياضيات/ahm7a7a@gmail.com	PROPN
iajs-2381	29	30	file:///c:/users/mustafa/desktop/2020/رياضيات/ahm7a7a@gmail.com	file:///c:/users/mustafa/desktop/2020/رياضيات/ahm7a7a@gmail.com	PROPN
iajs-2381	29	31	file:///c:/users/mustafa/desktop/2020/رياضيات/ahm7a7a@gmail.com	file:///c:/users/mustafa/desktop/2020/رياضيات/ahm7a7a@gmail.com	PROPN
iajs-2381	29	32	file:///c:/users/mustafa/desktop/2020/رياضيات/ahm7a7a@gmail.com	file:///c:/users/mustafa/desktop/2020/رياضيات/ahm7a7a@gmail.com	PROPN
iajs-2381	30	1	file:///c:/users/mustafa/desktop/2020/رياضيات/ranamumosa@yahoo.com	file:///c:/users/mustafa/desktop/2020/رياضيات/ranamumosa@yahoo.com	X
iajs-2381	30	2	file:///c:/users/mustafa/desktop/2020/رياضيات/ranamumosa@yahoo.com	file:///c:/users/mustafa/desktop/2020/رياضيات/ranamumosa@yahoo.com	X
iajs-2381	30	3	251	251	NUM
iajs-2381	30	4	ibn	ibn	PROPN
iajs-2381	30	5	al	al	PROPN
iajs-2381	30	6	-	-	PUNCT
iajs-2381	30	7	haitham	haitham	PROPN
iajs-2381	30	8	jour	jour	X
iajs-2381	30	9	.	.	PROPN
iajs-2381	31	1	for	for	ADP
iajs-2381	31	2	pure	pure	ADJ
iajs-2381	31	3	&	&	CCONJ
iajs-2381	31	4	appl	appl	PROPN
iajs-2381	31	5	.	.	PUNCT
iajs-2381	32	1	sci	sci	PROPN
iajs-2381	32	2	.	.	PROPN
iajs-2381	33	1	33	33	NUM
iajs-2381	33	2	(	(	PUNCT
iajs-2381	33	3	1	1	NUM
iajs-2381	33	4	)	)	PUNCT
iajs-2381	33	5	2020	2020	NUM
iajs-2381	33	6	definition	definition	NOUN
iajs-2381	33	7	2.1	2.1	NUM
iajs-2381	33	8	:	:	PUNCT
iajs-2381	33	9	a	a	DET
iajs-2381	33	10	space	space	NOUN
iajs-2381	33	11	is	be	AUX
iajs-2381	33	12	namely	namely	ADV
iajs-2381	33	13	(	(	PUNCT
iajs-2381	33	14	frugally	frugally	ADV
iajs-2381	33	15	,	,	PUNCT
iajs-2381	33	16	)	)	PUNCT
iajs-2381	33	17	if	if	SCONJ
iajs-2381	33	18	for	for	ADP
iajs-2381	33	19	each	each	DET
iajs-2381	33	20	elements	element	NOUN
iajs-2381	33	21	,	,	PUNCT
iajs-2381	33	22	there	there	PRON
iajs-2381	33	23	exist	exist	VERB
iajs-2381	33	24	an	an	DET
iajs-2381	33	25	set	set	NOUN
iajs-2381	33	26	containing	contain	VERB
iajs-2381	33	27	only	only	ADV
iajs-2381	33	28	one	one	NUM
iajs-2381	33	29	of	of	ADP
iajs-2381	33	30	them	they	PRON
iajs-2381	33	31	.	.	PUNCT
iajs-2381	34	1	when	when	SCONJ
iajs-2381	34	2	is	be	AUX
iajs-2381	34	3	,	,	PUNCT
iajs-2381	34	4	it	it	PRON
iajs-2381	34	5	will	will	AUX
iajs-2381	34	6	lead	lead	VERB
iajs-2381	34	7	to	to	ADP
iajs-2381	34	8	that	that	PRON
iajs-2381	34	9	is	be	AUX
iajs-2381	34	10	for	for	ADP
iajs-2381	34	11	any	any	DET
iajs-2381	34	12	ideal	ideal	NOUN
iajs-2381	34	13	on	on	ADP
iajs-2381	34	14	.	.	PUNCT
iajs-2381	35	1	remark	remark	VERB
iajs-2381	35	2	2.2	2.2	NUM
iajs-2381	35	3	:	:	PUNCT
iajs-2381	35	4	for	for	ADP
iajs-2381	35	5	a	a	DET
iajs-2381	35	6	space	space	NOUN
iajs-2381	35	7	,	,	PUNCT
iajs-2381	35	8	the	the	DET
iajs-2381	35	9	below	below	ADJ
iajs-2381	35	10	sentences	sentence	NOUN
iajs-2381	35	11	are	be	AUX
iajs-2381	35	12	rewards	reward	NOUN
iajs-2381	35	13	;	;	PUNCT
iajs-2381	35	14	i.	i.	NOUN
iajs-2381	35	15	is	be	AUX
iajs-2381	35	16	an	an	DET
iajs-2381	35	17	.	.	PUNCT
iajs-2381	35	18	ii	ii	PROPN
iajs-2381	35	19	.	.	PUNCT
iajs-2381	36	1	for	for	ADP
iajs-2381	36	2	each	each	DET
iajs-2381	36	3	element	element	NOUN
iajs-2381	36	4	,	,	PUNCT
iajs-2381	36	5	there	there	PRON
iajs-2381	36	6	is	be	VERB
iajs-2381	36	7	an	an	DET
iajs-2381	36	8	set	set	NOUN
iajs-2381	36	9	containing	contain	VERB
iajs-2381	36	10	only	only	ADV
iajs-2381	36	11	one	one	NUM
iajs-2381	36	12	of	of	ADP
iajs-2381	36	13	them	they	PRON
iajs-2381	36	14	.	.	PUNCT
iajs-2381	37	1	definition	definition	NOUN
iajs-2381	37	2	2.3	2.3	NUM
iajs-2381	37	3	:	:	PUNCT
iajs-2381	37	4	a	a	DET
iajs-2381	37	5	space	space	NOUN
iajs-2381	37	6	is	be	AUX
iajs-2381	37	7	namely	namely	ADV
iajs-2381	37	8	(	(	PUNCT
iajs-2381	37	9	frugally	frugally	ADV
iajs-2381	37	10	,	,	PUNCT
iajs-2381	37	11	)	)	PUNCT
iajs-2381	37	12	if	if	SCONJ
iajs-2381	37	13	for	for	ADP
iajs-2381	37	14	each	each	DET
iajs-2381	37	15	elements	element	NOUN
iajs-2381	37	16	,	,	PUNCT
iajs-2381	37	17	there	there	PRON
iajs-2381	37	18	are	be	VERB
iajs-2381	37	19	ẛ	ẛ	PRON
iajs-2381	37	20	sets	set	NOUN
iajs-2381	37	21	and	and	CCONJ
iajs-2381	37	22	,	,	PUNCT
iajs-2381	37	23	satisfies	satisfie	NOUN
iajs-2381	37	24	ـ	ـ	X
iajs-2381	37	25	and	and	CCONJ
iajs-2381	37	26	.	.	PUNCT
iajs-2381	38	1	ـ	ـ	X
iajs-2381	38	2	when	when	SCONJ
iajs-2381	38	3	is	be	AUX
iajs-2381	38	4	,	,	PUNCT
iajs-2381	38	5	it	it	PRON
iajs-2381	38	6	will	will	AUX
iajs-2381	38	7	lead	lead	VERB
iajs-2381	38	8	to	to	ADP
iajs-2381	38	9	that	that	PRON
iajs-2381	38	10	is	be	AUX
iajs-2381	38	11	for	for	ADP
iajs-2381	38	12	any	any	DET
iajs-2381	38	13	ideal	ideal	NOUN
iajs-2381	38	14	on	on	ADP
iajs-2381	38	15	.	.	PUNCT
iajs-2381	39	1	remark	remark	VERB
iajs-2381	39	2	2.4	2.4	NUM
iajs-2381	39	3	:	:	PUNCT
iajs-2381	39	4	if	if	SCONJ
iajs-2381	39	5	is	is	ADV
iajs-2381	39	6	,	,	PUNCT
iajs-2381	39	7	implies	imply	VERB
iajs-2381	39	8	that	that	PRON
iajs-2381	39	9	.	.	PUNCT
iajs-2381	40	1	the	the	DET
iajs-2381	40	2	inverse	inverse	NOUN
iajs-2381	40	3	meaning	meaning	NOUN
iajs-2381	40	4	implied	imply	VERB
iajs-2381	40	5	in	in	ADP
iajs-2381	40	6	remark	remark	NOUN
iajs-2381	40	7	2.4	2.4	NUM
iajs-2381	40	8	,	,	PUNCT
iajs-2381	40	9	does	do	AUX
iajs-2381	40	10	not	not	PART
iajs-2381	40	11	valid	valid	ADJ
iajs-2381	40	12	,	,	PUNCT
iajs-2381	40	13	in	in	ADP
iajs-2381	40	14	general	general	ADJ
iajs-2381	40	15	.	.	PUNCT
iajs-2381	41	1	example	example	NOUN
iajs-2381	41	2	2.5	2.5	NUM
iajs-2381	41	3	:	:	PUNCT
iajs-2381	41	4	a	a	DET
iajs-2381	41	5	space	space	NOUN
iajs-2381	41	6	is	be	AUX
iajs-2381	41	7	a	a	DET
iajs-2381	41	8	where	where	SCONJ
iajs-2381	41	9	,	,	PUNCT
iajs-2381	41	10	{	{	PUNCT
iajs-2381	41	11	}	}	PUNCT
iajs-2381	41	12	and	and	CCONJ
iajs-2381	41	13	.	.	PUNCT
iajs-2381	42	1	the	the	DET
iajs-2381	42	2	space	space	NOUN
iajs-2381	42	3	is	be	AUX
iajs-2381	42	4	not	not	PART
iajs-2381	42	5	,	,	PUNCT
iajs-2381	42	6	since	since	SCONJ
iajs-2381	42	7	for	for	ADP
iajs-2381	42	8	the	the	DET
iajs-2381	42	9	elements	element	NOUN
iajs-2381	42	10	,	,	PUNCT
iajs-2381	42	11	there	there	PRON
iajs-2381	42	12	is	be	VERB
iajs-2381	42	13	no	no	DET
iajs-2381	42	14	ـ	ـ	NOUN
iajs-2381	42	15	set	set	NOUN
iajs-2381	42	16	containing	contain	VERB
iajs-2381	42	17	which	which	PRON
iajs-2381	42	18	does	do	AUX
iajs-2381	42	19	not	not	PART
iajs-2381	42	20	contain	contain	VERB
iajs-2381	42	21	.	.	PUNCT
iajs-2381	43	1	remark	remark	VERB
iajs-2381	43	2	2.6	2.6	NUM
iajs-2381	43	3	:	:	PUNCT
iajs-2381	43	4	for	for	ADP
iajs-2381	43	5	a	a	DET
iajs-2381	43	6	space	space	NOUN
iajs-2381	43	7	,	,	PUNCT
iajs-2381	43	8	the	the	DET
iajs-2381	43	9	below	below	ADJ
iajs-2381	43	10	sentences	sentence	NOUN
iajs-2381	43	11	are	be	AUX
iajs-2381	43	12	rewards	reward	NOUN
iajs-2381	43	13	;	;	PUNCT
iajs-2381	43	14	i.	i.	NOUN
iajs-2381	43	15	is	be	AUX
iajs-2381	43	16	an	an	DET
iajs-2381	43	17	.	.	PUNCT
iajs-2381	43	18	ii	ii	PROPN
iajs-2381	43	19	.	.	PUNCT
iajs-2381	44	1	for	for	ADP
iajs-2381	44	2	each	each	DET
iajs-2381	44	3	elements	element	NOUN
iajs-2381	44	4	,	,	PUNCT
iajs-2381	44	5	there	there	PRON
iajs-2381	44	6	are	be	VERB
iajs-2381	44	7	two	two	NUM
iajs-2381	44	8	sets	set	NOUN
iajs-2381	44	9	and	and	CCONJ
iajs-2381	44	10	,	,	PUNCT
iajs-2381	45	1	such	such	ADJ
iajs-2381	45	2	that	that	SCONJ
iajs-2381	45	3	ـ	ـ	PROPN
iajs-2381	45	4	and	and	CCONJ
iajs-2381	45	5	ـ	ـ	PROPN
iajs-2381	45	6	.	.	PUNCT
iajs-2381	45	7	remark	remark	PROPN
iajs-2381	45	8	2.7	2.7	NUM
iajs-2381	45	9	:	:	PUNCT
iajs-2381	45	10	if	if	SCONJ
iajs-2381	45	11	{	{	PUNCT
iajs-2381	45	12	r	r	NOUN
iajs-2381	45	13	}	}	PUNCT
iajs-2381	45	14	is	be	AUX
iajs-2381	45	15	set	set	VERB
iajs-2381	45	16	for	for	ADP
iajs-2381	45	17	each	each	PRON
iajs-2381	45	18	in	in	ADP
iajs-2381	45	19	ҳ	ҳ	PROPN
iajs-2381	45	20	,	,	PUNCT
iajs-2381	45	21	then	then	ADV
iajs-2381	45	22	is	be	AUX
iajs-2381	45	23	.	.	PUNCT
iajs-2381	46	1	definition	definition	NOUN
iajs-2381	46	2	2.8	2.8	NUM
iajs-2381	46	3	:	:	PUNCT
iajs-2381	46	4	a	a	DET
iajs-2381	46	5	space	space	NOUN
iajs-2381	46	6	is	be	AUX
iajs-2381	46	7	namely	namely	ADV
iajs-2381	46	8	(	(	PUNCT
iajs-2381	46	9	frugally	frugally	ADV
iajs-2381	46	10	,	,	PUNCT
iajs-2381	46	11	)	)	PUNCT
iajs-2381	46	12	,	,	PUNCT
iajs-2381	46	13	if	if	SCONJ
iajs-2381	46	14	for	for	ADP
iajs-2381	46	15	each	each	DET
iajs-2381	46	16	elements	element	NOUN
iajs-2381	46	17	,	,	PUNCT
iajs-2381	46	18	there	there	PRON
iajs-2381	46	19	are	be	VERB
iajs-2381	46	20	disjoint	disjoint	NOUN
iajs-2381	46	21	sets	set	NOUN
iajs-2381	46	22	and	and	CCONJ
iajs-2381	46	23	satisfies	satisfie	NOUN
iajs-2381	46	24	and	and	CCONJ
iajs-2381	46	25	.	.	PUNCT
iajs-2381	47	1	clearly	clearly	ADV
iajs-2381	47	2	;	;	PUNCT
iajs-2381	47	3	if	if	SCONJ
iajs-2381	47	4	is	be	AUX
iajs-2381	47	5	implie	implie	NOUN
iajs-2381	47	6	that	that	PRON
iajs-2381	47	7	is	is	ADV
iajs-2381	47	8	,	,	PUNCT
iajs-2381	47	9	for	for	ADP
iajs-2381	47	10	any	any	DET
iajs-2381	47	11	ideal	ideal	NOUN
iajs-2381	47	12	on	on	ADP
iajs-2381	47	13	.	.	PUNCT
iajs-2381	48	1	remark	remark	VERB
iajs-2381	48	2	2.9	2.9	NUM
iajs-2381	48	3	:	:	PUNCT
iajs-2381	48	4	if	if	SCONJ
iajs-2381	48	5	the	the	DET
iajs-2381	48	6	space	space	NOUN
iajs-2381	48	7	is	be	AUX
iajs-2381	48	8	then	then	ADV
iajs-2381	48	9	it	it	PRON
iajs-2381	48	10	is	be	AUX
iajs-2381	48	11	.	.	PUNCT
iajs-2381	49	1	the	the	DET
iajs-2381	49	2	inverse	inverse	NOUN
iajs-2381	49	3	meaning	meaning	NOUN
iajs-2381	49	4	implied	imply	VERB
iajs-2381	49	5	in	in	ADP
iajs-2381	49	6	remark	remark	NOUN
iajs-2381	49	7	2.9	2.9	NUM
iajs-2381	49	8	,	,	PUNCT
iajs-2381	49	9	does	do	AUX
iajs-2381	49	10	not	not	PART
iajs-2381	49	11	valid	valid	ADJ
iajs-2381	49	12	,	,	PUNCT
iajs-2381	49	13	in	in	ADP
iajs-2381	49	14	general	general	ADJ
iajs-2381	49	15	.	.	PUNCT
iajs-2381	50	1	example	example	NOUN
iajs-2381	51	1	2.10	2.10	NUM
iajs-2381	51	2	:	:	PUNCT
iajs-2381	51	3	the	the	PRON
iajs-2381	51	4	;	;	PUNCT
iajs-2381	51	5	such	such	ADJ
iajs-2381	51	6	that	that	PRON
iajs-2381	51	7	,	,	PUNCT
iajs-2381	51	8	and	and	CCONJ
iajs-2381	51	9	is	be	AUX
iajs-2381	51	10	not	not	PART
iajs-2381	51	11	.	.	PUNCT
iajs-2381	52	1	since	since	SCONJ
iajs-2381	52	2	,	,	PUNCT
iajs-2381	52	3	for	for	ADP
iajs-2381	52	4	the	the	DET
iajs-2381	52	5	elements	element	NOUN
iajs-2381	52	6	,	,	PUNCT
iajs-2381	52	7	there	there	PRON
iajs-2381	52	8	are	be	VERB
iajs-2381	52	9	no	no	DET
iajs-2381	52	10	disjoints	disjoint	NOUN
iajs-2381	52	11	ـ	ـ	NOUN
iajs-2381	52	12	sets	set	NOUN
iajs-2381	52	13	and	and	CCONJ
iajs-2381	52	14	such	such	ADJ
iajs-2381	52	15	that	that	PRON
iajs-2381	52	16	and	and	CCONJ
iajs-2381	52	17	.	.	PUNCT
iajs-2381	52	18	remark	remark	NOUN
iajs-2381	52	19	2.11	2.11	NUM
iajs-2381	52	20	:	:	PUNCT
iajs-2381	52	21	for	for	ADP
iajs-2381	52	22	a	a	DET
iajs-2381	52	23	space	space	NOUN
iajs-2381	52	24	,	,	PUNCT
iajs-2381	52	25	the	the	DET
iajs-2381	52	26	below	below	ADJ
iajs-2381	52	27	sentences	sentence	NOUN
iajs-2381	52	28	are	be	AUX
iajs-2381	52	29	rewards	reward	NOUN
iajs-2381	52	30	;	;	PUNCT
iajs-2381	52	31	i.	i.	NOUN
iajs-2381	52	32	is	be	AUX
iajs-2381	52	33	an	an	DET
iajs-2381	52	34	.	.	PUNCT
iajs-2381	52	35	ii	ii	PROPN
iajs-2381	52	36	.	.	PUNCT
iajs-2381	53	1	for	for	ADP
iajs-2381	53	2	each	each	DET
iajs-2381	53	3	elements	element	NOUN
iajs-2381	53	4	,	,	PUNCT
iajs-2381	53	5	there	there	PRON
iajs-2381	53	6	are	be	VERB
iajs-2381	53	7	disjoint	disjoint	NOUN
iajs-2381	53	8	sets	set	NOUN
iajs-2381	53	9	and	and	CCONJ
iajs-2381	53	10	,	,	PUNCT
iajs-2381	53	11	satisfies	satisfie	NOUN
iajs-2381	53	12	and	and	CCONJ
iajs-2381	53	13	.	.	PUNCT
iajs-2381	54	1	we	we	PRON
iajs-2381	54	2	have	have	VERB
iajs-2381	54	3	the	the	DET
iajs-2381	54	4	truth	truth	NOUN
iajs-2381	54	5	that	that	PRON
iajs-2381	54	6	confirms	confirm	VERB
iajs-2381	54	7	that	that	SCONJ
iajs-2381	54	8	if	if	SCONJ
iajs-2381	54	9	is	be	AUX
iajs-2381	54	10	a	a	PRON
iajs-2381	54	11	(	(	PUNCT
iajs-2381	54	12	)	)	PUNCT
iajs-2381	54	13	,	,	PUNCT
iajs-2381	54	14	then	then	ADV
iajs-2381	54	15	the	the	DET
iajs-2381	54	16	ideal	ideal	ADJ
iajs-2381	54	17	space	space	NOUN
iajs-2381	54	18	is	be	AUX
iajs-2381	54	19	a	a	PRON
iajs-2381	54	20	.	.	PUNCT
iajs-2381	55	1	but	but	CCONJ
iajs-2381	55	2	the	the	DET
iajs-2381	55	3	inverse	inverse	NOUN
iajs-2381	55	4	meaning	meaning	NOUN
iajs-2381	55	5	implied	imply	VERB
iajs-2381	55	6	may	may	AUX
iajs-2381	55	7	be	be	AUX
iajs-2381	55	8	invalid	invalid	ADJ
iajs-2381	55	9	,	,	PUNCT
iajs-2381	55	10	as	as	SCONJ
iajs-2381	55	11	shown	show	VERB
iajs-2381	55	12	in	in	ADP
iajs-2381	55	13	the	the	DET
iajs-2381	55	14	following	follow	VERB
iajs-2381	55	15	diagram	diagram	NOUN
iajs-2381	55	16	.	.	PUNCT
iajs-2381	56	1	example	example	NOUN
iajs-2381	56	2	below	below	ADV
iajs-2381	56	3	shows	show	VERB
iajs-2381	56	4	the	the	DET
iajs-2381	56	5	relationships	relationship	NOUN
iajs-2381	56	6	between	between	ADP
iajs-2381	56	7	the	the	DET
iajs-2381	56	8	unlike	unlike	ADJ
iajs-2381	56	9	classes	class	NOUN
iajs-2381	56	10	of	of	ADP
iajs-2381	56	11	notions	notion	NOUN
iajs-2381	56	12	that	that	PRON
iajs-2381	56	13	presented	present	VERB
iajs-2381	56	14	previously	previously	ADV
iajs-2381	56	15	.	.	PUNCT
iajs-2381	57	1	ҳ	ҳ	NOUN
iajs-2381	57	2	is	be	AUX
iajs-2381	57	3	ҳ	ҳ	NOUN
iajs-2381	57	4	is	be	AUX
iajs-2381	57	5	e	e	NOUN
iajs-2381	57	6	ҳ	ҳ	NOUN
iajs-2381	57	7	is	be	AUX
iajs-2381	57	8	ҳ	ҳ	NOUN
iajs-2381	57	9	is	be	AUX
iajs-2381	57	10	ҳ	ҳ	NOUN
iajs-2381	57	11	is	be	AUX
iajs-2381	57	12	ҳ	ҳ	NOUN
iajs-2381	57	13	is	be	AUX
iajs-2381	57	14	251	251	NUM
iajs-2381	57	15	ibn	ibn	PROPN
iajs-2381	57	16	al	al	PROPN
iajs-2381	57	17	-	-	PUNCT
iajs-2381	57	18	haitham	haitham	PROPN
iajs-2381	57	19	jour	jour	X
iajs-2381	57	20	.	.	PROPN
iajs-2381	57	21	for	for	ADP
iajs-2381	57	22	pure	pure	ADJ
iajs-2381	57	23	&	&	CCONJ
iajs-2381	57	24	appl	appl	PROPN
iajs-2381	57	25	.	.	PUNCT
iajs-2381	58	1	sci	sci	PROPN
iajs-2381	58	2	.	.	PROPN
iajs-2381	59	1	33	33	NUM
iajs-2381	59	2	(	(	PUNCT
iajs-2381	59	3	1	1	NUM
iajs-2381	59	4	)	)	PUNCT
iajs-2381	59	5	2020	2020	NUM
iajs-2381	59	6	example	example	NOUN
iajs-2381	59	7	2.12	2.12	NUM
iajs-2381	59	8	:	:	PUNCT
iajs-2381	59	9	the	the	DET
iajs-2381	59	10	where	where	SCONJ
iajs-2381	59	11	,	,	PUNCT
iajs-2381	59	12	and	and	CCONJ
iajs-2381	59	13	is	be	AUX
iajs-2381	59	14	not	not	PART
iajs-2381	59	15	(	(	PUNCT
iajs-2381	59	16	where	where	SCONJ
iajs-2381	59	17	and	and	CCONJ
iajs-2381	59	18	)	)	PUNCT
iajs-2381	59	19	.	.	PUNCT
iajs-2381	60	1	3	3	X
iajs-2381	60	2	.	.	X
iajs-2381	60	3	separation	separation	NOUN
iajs-2381	60	4	axioms	axiom	NOUN
iajs-2381	60	5	by	by	ADP
iajs-2381	60	6	using	use	VERB
iajs-2381	60	7	some	some	DET
iajs-2381	60	8	types	type	NOUN
iajs-2381	60	9	of	of	ADP
iajs-2381	60	10	function	function	NOUN
iajs-2381	60	11	in	in	ADP
iajs-2381	60	12	this	this	DET
iajs-2381	60	13	part	part	NOUN
iajs-2381	60	14	,	,	PUNCT
iajs-2381	60	15	we	we	PRON
iajs-2381	60	16	will	will	AUX
iajs-2381	60	17	using	use	VERB
iajs-2381	60	18	some	some	DET
iajs-2381	60	19	types	type	NOUN
iajs-2381	60	20	of	of	ADP
iajs-2381	60	21	functions	function	NOUN
iajs-2381	60	22	that	that	PRON
iajs-2381	60	23	we	we	PRON
iajs-2381	60	24	were	be	AUX
iajs-2381	60	25	offered	offer	VERB
iajs-2381	60	26	it	it	PRON
iajs-2381	60	27	in	in	ADP
iajs-2381	60	28	ahmed	ahmed	PROPN
iajs-2381	60	29	and	and	CCONJ
iajs-2381	60	30	esmaeel	esmaeel	VERB
iajs-2381	60	31	[	[	X
iajs-2381	60	32	1	1	NUM
iajs-2381	60	33	]	]	PUNCT
iajs-2381	60	34	.	.	PUNCT
iajs-2381	61	1	and	and	CCONJ
iajs-2381	61	2	study	study	VERB
iajs-2381	61	3	the	the	DET
iajs-2381	61	4	notions	notion	NOUN
iajs-2381	61	5	of	of	ADP
iajs-2381	61	6	new	new	ADJ
iajs-2381	61	7	separation	separation	NOUN
iajs-2381	61	8	axioms	axiom	VERB
iajs-2381	61	9	under	under	ADP
iajs-2381	61	10	influence	influence	NOUN
iajs-2381	61	11	of	of	ADP
iajs-2381	61	12	these	these	DET
iajs-2381	61	13	functions	function	NOUN
iajs-2381	61	14	.	.	PUNCT
iajs-2381	62	1	definition	definition	NOUN
iajs-2381	62	2	3.1	3.1	NUM
iajs-2381	62	3	:	:	PUNCT
iajs-2381	63	1	[	[	X
iajs-2381	63	2	1	1	NUM
iajs-2381	63	3	]	]	PUNCT
iajs-2381	63	4	.	.	PUNCT
iajs-2381	64	1	a	a	DET
iajs-2381	64	2	function	function	NOUN
iajs-2381	64	3	ὑ	ὑ	PROPN
iajs-2381	64	4	is	be	AUX
iajs-2381	64	5	i.	i.	NOUN
iajs-2381	64	6	,	,	PUNCT
iajs-2381	64	7	symbolizes	symbolize	VERB
iajs-2381	64	8	,	,	PUNCT
iajs-2381	64	9	if	if	SCONJ
iajs-2381	64	10	is	be	AUX
iajs-2381	64	11	set	set	VERB
iajs-2381	64	12	in	in	ADP
iajs-2381	64	13	ὑ	ὑ	X
iajs-2381	64	14	whenever	whenever	SCONJ
iajs-2381	64	15	is	be	AUX
iajs-2381	64	16	set	set	VERB
iajs-2381	64	17	in	in	ADP
iajs-2381	64	18	ҳ.	ҳ.	PROPN
iajs-2381	64	19	ii	ii	PROPN
iajs-2381	64	20	.	.	PROPN
iajs-2381	65	1	,	,	PUNCT
iajs-2381	65	2	symbolizes	symbolize	VERB
iajs-2381	65	3	,	,	PUNCT
iajs-2381	65	4	if	if	SCONJ
iajs-2381	65	5	is	be	AUX
iajs-2381	65	6	set	set	VERB
iajs-2381	65	7	in	in	ADP
iajs-2381	65	8	ὑ	ὑ	X
iajs-2381	65	9	whenever	whenever	SCONJ
iajs-2381	65	10	is	be	AUX
iajs-2381	65	11	open	open	ADJ
iajs-2381	65	12	set	set	VERB
iajs-2381	65	13	in	in	ADP
iajs-2381	65	14	ҳ.	ҳ.	PROPN
iajs-2381	65	15	iii	iii	PROPN
iajs-2381	65	16	.	.	PROPN
iajs-2381	65	17	,	,	PUNCT
iajs-2381	65	18	symbolizes	symbolize	VERB
iajs-2381	65	19	,	,	PUNCT
iajs-2381	65	20	if	if	SCONJ
iajs-2381	65	21	is	be	AUX
iajs-2381	65	22	open	open	ADJ
iajs-2381	65	23	in	in	ADP
iajs-2381	65	24	ὑ	ὑ	X
iajs-2381	65	25	whenever	whenever	SCONJ
iajs-2381	65	26	is	be	AUX
iajs-2381	65	27	set	set	VERB
iajs-2381	65	28	in	in	ADP
iajs-2381	65	29	ҳ.	ҳ.	ADJ
iajs-2381	65	30	proposition	proposition	NOUN
iajs-2381	65	31	3.2	3.2	NUM
iajs-2381	65	32	:	:	PUNCT
iajs-2381	65	33	if	if	SCONJ
iajs-2381	65	34	is	be	AUX
iajs-2381	65	35	an	an	DET
iajs-2381	65	36	(	(	PUNCT
iajs-2381	65	37	respectively	respectively	ADV
iajs-2381	65	38	,	,	PUNCT
iajs-2381	65	39	and	and	CCONJ
iajs-2381	65	40	)	)	PUNCT
iajs-2381	65	41	and	and	CCONJ
iajs-2381	65	42	ὑ	ὑ	PROPN
iajs-2381	65	43	is	be	AUX
iajs-2381	65	44	surjective	surjective	ADJ
iajs-2381	65	45	,	,	PUNCT
iajs-2381	65	46	then	then	ADV
iajs-2381	65	47	ὑ	ὑ	PROPN
iajs-2381	65	48	is	be	AUX
iajs-2381	65	49	(	(	PUNCT
iajs-2381	65	50	respectively	respectively	ADV
iajs-2381	65	51	,	,	PUNCT
iajs-2381	65	52	and	and	CCONJ
iajs-2381	65	53	)	)	PUNCT
iajs-2381	65	54	.	.	PUNCT
iajs-2381	66	1	proof	proof	NOUN
iajs-2381	66	2	:	:	PUNCT
iajs-2381	66	3	since	since	SCONJ
iajs-2381	66	4	is	be	AUX
iajs-2381	66	5	in	in	ADP
iajs-2381	66	6	ὑ	ὑ	ADV
iajs-2381	66	7	whenever	whenever	SCONJ
iajs-2381	66	8	is	be	AUX
iajs-2381	66	9	set	set	VERB
iajs-2381	66	10	in	in	ADP
iajs-2381	66	11	ҳ.	ҳ.	ADJ
iajs-2381	66	12	proposition	proposition	NOUN
iajs-2381	66	13	3.3	3.3	NUM
iajs-2381	66	14	:	:	PUNCT
iajs-2381	66	15	if	if	SCONJ
iajs-2381	66	16	a	a	DET
iajs-2381	66	17	space	space	NOUN
iajs-2381	66	18	is	be	AUX
iajs-2381	66	19	(	(	PUNCT
iajs-2381	66	20	respectively	respectively	ADV
iajs-2381	66	21	,	,	PUNCT
iajs-2381	66	22	and	and	CCONJ
iajs-2381	66	23	)	)	PUNCT
iajs-2381	66	24	and	and	CCONJ
iajs-2381	66	25	ὑ	ὑ	PROPN
iajs-2381	66	26	is	be	AUX
iajs-2381	66	27	surjective	surjective	ADJ
iajs-2381	66	28	,	,	PUNCT
iajs-2381	66	29	then	then	ADV
iajs-2381	66	30	ὑ	ὑ	PROPN
iajs-2381	66	31	is	be	AUX
iajs-2381	66	32	(	(	PUNCT
iajs-2381	66	33	respectively	respectively	ADV
iajs-2381	66	34	,	,	PUNCT
iajs-2381	66	35	and	and	CCONJ
iajs-2381	66	36	)	)	PUNCT
iajs-2381	66	37	.	.	PUNCT
iajs-2381	67	1	proof	proof	NOUN
iajs-2381	67	2	:	:	PUNCT
iajs-2381	67	3	since	since	SCONJ
iajs-2381	67	4	is	be	AUX
iajs-2381	67	5	set	set	VERB
iajs-2381	67	6	in	in	ADP
iajs-2381	67	7	ὑ	ὑ	X
iajs-2381	67	8	whenever	whenever	SCONJ
iajs-2381	67	9	is	be	AUX
iajs-2381	67	10	open	open	ADJ
iajs-2381	67	11	in	in	ADP
iajs-2381	67	12	ҳ.	ҳ.	ADJ
iajs-2381	67	13	proposition	proposition	NOUN
iajs-2381	67	14	3.4	3.4	NUM
iajs-2381	67	15	:	:	PUNCT
iajs-2381	67	16	if	if	SCONJ
iajs-2381	67	17	a	a	DET
iajs-2381	67	18	space	space	NOUN
iajs-2381	67	19	is	be	AUX
iajs-2381	67	20	(	(	PUNCT
iajs-2381	67	21	respectively	respectively	ADV
iajs-2381	67	22	,	,	PUNCT
iajs-2381	67	23	and	and	CCONJ
iajs-2381	67	24	)	)	PUNCT
iajs-2381	67	25	and	and	CCONJ
iajs-2381	67	26	ὑ	ὑ	PROPN
iajs-2381	67	27	is	be	AUX
iajs-2381	67	28	surjective	surjective	ADJ
iajs-2381	67	29	,	,	PUNCT
iajs-2381	67	30	then	then	ADV
iajs-2381	67	31	ὑ	ὑ	PROPN
iajs-2381	67	32	is	be	AUX
iajs-2381	67	33	(	(	PUNCT
iajs-2381	67	34	respectively	respectively	ADV
iajs-2381	67	35	,	,	PUNCT
iajs-2381	67	36	and	and	CCONJ
iajs-2381	67	37	)	)	PUNCT
iajs-2381	67	38	.	.	PUNCT
iajs-2381	68	1	proof	proof	NOUN
iajs-2381	68	2	:	:	PUNCT
iajs-2381	68	3	since	since	SCONJ
iajs-2381	68	4	is	be	AUX
iajs-2381	68	5	open	open	ADJ
iajs-2381	68	6	in	in	ADP
iajs-2381	68	7	ὑ	ὑ	X
iajs-2381	68	8	whenever	whenever	SCONJ
iajs-2381	68	9	is	be	AUX
iajs-2381	68	10	set	set	VERB
iajs-2381	68	11	in	in	ADP
iajs-2381	68	12	ҳ.	ҳ.	ADJ
iajs-2381	68	13	remark	remark	NOUN
iajs-2381	68	14	3.5	3.5	NUM
iajs-2381	68	15	:	:	PUNCT
iajs-2381	68	16	if	if	SCONJ
iajs-2381	68	17	ὑ	ὑ	PROPN
iajs-2381	68	18	is	be	AUX
iajs-2381	68	19	a	a	DET
iajs-2381	68	20	bijective	bijective	ADJ
iajs-2381	68	21	open	open	ADJ
iajs-2381	68	22	function	function	NOUN
iajs-2381	68	23	and	and	CCONJ
iajs-2381	68	24	a	a	DET
iajs-2381	68	25	space	space	NOUN
iajs-2381	68	26	is	be	AUX
iajs-2381	68	27	a	a	DET
iajs-2381	68	28	(	(	PUNCT
iajs-2381	68	29	respectively	respectively	ADV
iajs-2381	68	30	,	,	PUNCT
iajs-2381	68	31	and	and	CCONJ
iajs-2381	68	32	)	)	PUNCT
iajs-2381	68	33	,	,	PUNCT
iajs-2381	68	34	then	then	ADV
iajs-2381	68	35	the	the	DET
iajs-2381	68	36	space	space	NOUN
iajs-2381	68	37	ὑ	ὑ	PROPN
iajs-2381	68	38	is	be	AUX
iajs-2381	68	39	a	a	DET
iajs-2381	68	40	(	(	PUNCT
iajs-2381	68	41	respectively	respectively	ADV
iajs-2381	68	42	,	,	PUNCT
iajs-2381	68	43	and	and	CCONJ
iajs-2381	68	44	)	)	PUNCT
iajs-2381	68	45	,	,	PUNCT
iajs-2381	68	46	for	for	ADP
iajs-2381	68	47	any	any	DET
iajs-2381	68	48	ideal	ideal	NOUN
iajs-2381	68	49	on	on	ADP
iajs-2381	68	50	ὑ.	ὑ.	ADJ
iajs-2381	68	51	definition	definition	NOUN
iajs-2381	68	52	3.6	3.6	NUM
iajs-2381	68	53	:	:	PUNCT
iajs-2381	69	1	[	[	X
iajs-2381	69	2	2	2	NUM
iajs-2381	69	3	]	]	PUNCT
iajs-2381	69	4	.	.	PUNCT
iajs-2381	70	1	a	a	DET
iajs-2381	70	2	function	function	NOUN
iajs-2381	70	3	ὑ	ὑ	NOUN
iajs-2381	70	4	is	be	AUX
iajs-2381	70	5	;	;	PUNCT
iajs-2381	70	6	i.	i.	PROPN
iajs-2381	70	7	ẛ	ẛ	PROPN
iajs-2381	70	8	,	,	PUNCT
iajs-2381	70	9	symbolizes	symbolize	VERB
iajs-2381	70	10	,	,	PUNCT
iajs-2381	70	11	if	if	SCONJ
iajs-2381	70	12	for	for	ADP
iajs-2381	70	13	all	all	PRON
iajs-2381	70	14	.	.	PUNCT
iajs-2381	71	1	ii	ii	X
iajs-2381	71	2	.	.	PUNCT
iajs-2381	72	1	ẛ	ẛ	PROPN
iajs-2381	72	2	symbolizes	symbolize	VERB
iajs-2381	72	3	ẛ	ẛ	PRON
iajs-2381	72	4	if	if	SCONJ
iajs-2381	72	5	,	,	PUNCT
iajs-2381	72	6	for	for	ADP
iajs-2381	72	7	all	all	DET
iajs-2381	72	8	ὑ	ὑ	NOUN
iajs-2381	72	9	.	.	PUNCT
iajs-2381	73	1	iii	iii	X
iajs-2381	74	1	.	.	PUNCT
iajs-2381	74	2	ẛ	ẛ	PROPN
iajs-2381	74	3	,	,	PUNCT
iajs-2381	74	4	symbolizes	symbolize	VERB
iajs-2381	74	5	ẛ	ẛ	NOUN
iajs-2381	74	6	,	,	PUNCT
iajs-2381	74	7	if	if	SCONJ
iajs-2381	74	8	for	for	ADP
iajs-2381	74	9	all	all	DET
iajs-2381	74	10	ὑ	ὑ	NOUN
iajs-2381	74	11	.	.	PUNCT
iajs-2381	75	1	proposition	proposition	NOUN
iajs-2381	75	2	3.7	3.7	NUM
iajs-2381	75	3	:	:	PUNCT
iajs-2381	75	4	if	if	SCONJ
iajs-2381	75	5	ὑ	ὑ	PROPN
iajs-2381	75	6	is	be	AUX
iajs-2381	75	7	(	(	PUNCT
iajs-2381	75	8	respectively	respectively	ADV
iajs-2381	75	9	,	,	PUNCT
iajs-2381	75	10	and	and	CCONJ
iajs-2381	75	11	)	)	PUNCT
iajs-2381	75	12	and	and	CCONJ
iajs-2381	75	13	ὑ	ὑ	PROPN
iajs-2381	75	14	is	be	AUX
iajs-2381	75	15	injective	injective	ADJ
iajs-2381	75	16	,	,	PUNCT
iajs-2381	75	17	ـ	ـ	X
iajs-2381	75	18	function	function	NOUN
iajs-2381	75	19	,	,	PUNCT
iajs-2381	75	20	then	then	ADV
iajs-2381	75	21	is	be	AUX
iajs-2381	75	22	an	an	DET
iajs-2381	75	23	(	(	PUNCT
iajs-2381	75	24	respectively	respectively	ADV
iajs-2381	75	25	,	,	PUNCT
iajs-2381	75	26	and	and	CCONJ
iajs-2381	75	27	)	)	PUNCT
iajs-2381	75	28	.	.	PUNCT
iajs-2381	76	1	proof	proof	NOUN
iajs-2381	76	2	:	:	PUNCT
iajs-2381	76	3	since	since	SCONJ
iajs-2381	76	4	for	for	ADP
iajs-2381	76	5	all	all	PRON
iajs-2381	76	6	.	.	PUNCT
iajs-2381	77	1	corollary	corollary	ADJ
iajs-2381	77	2	3.8	3.8	NUM
iajs-2381	77	3	:	:	PUNCT
iajs-2381	77	4	if	if	SCONJ
iajs-2381	77	5	a	a	DET
iajs-2381	77	6	space	space	NOUN
iajs-2381	77	7	ὑ	ὑ	NOUN
iajs-2381	77	8	is	be	AUX
iajs-2381	77	9	(	(	PUNCT
iajs-2381	77	10	respectively	respectively	ADV
iajs-2381	77	11	,	,	PUNCT
iajs-2381	77	12	and	and	CCONJ
iajs-2381	77	13	)	)	PUNCT
iajs-2381	78	1	and	and	CCONJ
iajs-2381	78	2	ὑ	ὑ	PROPN
iajs-2381	78	3	is	be	AUX
iajs-2381	78	4	injective	injective	ADJ
iajs-2381	78	5	,	,	PUNCT
iajs-2381	78	6	continuous	continuous	ADJ
iajs-2381	78	7	function	function	NOUN
iajs-2381	78	8	then	then	ADV
iajs-2381	78	9	is	be	AUX
iajs-2381	78	10	an	an	DET
iajs-2381	78	11	ـ	ـ	X
iajs-2381	78	12	(	(	PUNCT
iajs-2381	78	13	respectively	respectively	ADV
iajs-2381	78	14	,	,	PUNCT
iajs-2381	78	15	and	and	CCONJ
iajs-2381	78	16	)	)	PUNCT
iajs-2381	78	17	.	.	PUNCT
iajs-2381	79	1	proof	proof	NOUN
iajs-2381	79	2	:	:	PUNCT
iajs-2381	79	3	clearly	clearly	ADV
iajs-2381	79	4	,	,	PUNCT
iajs-2381	79	5	the	the	DET
iajs-2381	79	6	continuity	continuity	NOUN
iajs-2381	79	7	leads	lead	VERB
iajs-2381	79	8	to	to	ADP
iajs-2381	79	9	ـ	ـ	NOUN
iajs-2381	79	10	continuity	continuity	NOUN
iajs-2381	79	11	[	[	X
iajs-2381	79	12	2	2	NUM
iajs-2381	79	13	]	]	PUNCT
iajs-2381	79	14	.	.	PUNCT
iajs-2381	80	1	so	so	ADV
iajs-2381	80	2	proposition	proposition	NOUN
iajs-2381	80	3	3.7	3.7	NUM
iajs-2381	80	4	is	be	AUX
iajs-2381	80	5	valid	valid	ADJ
iajs-2381	80	6	.	.	PUNCT
iajs-2381	81	1	255	255	NUM
iajs-2381	82	1	ibn	ibn	PROPN
iajs-2381	82	2	al	al	PROPN
iajs-2381	82	3	-	-	PUNCT
iajs-2381	82	4	haitham	haitham	PROPN
iajs-2381	82	5	jour	jour	X
iajs-2381	82	6	.	.	PROPN
iajs-2381	82	7	for	for	ADP
iajs-2381	82	8	pure	pure	ADJ
iajs-2381	82	9	&	&	CCONJ
iajs-2381	82	10	appl	appl	PROPN
iajs-2381	82	11	.	.	PUNCT
iajs-2381	83	1	sci	sci	PROPN
iajs-2381	83	2	.	.	PROPN
iajs-2381	84	1	33	33	NUM
iajs-2381	84	2	(	(	PUNCT
iajs-2381	84	3	1	1	NUM
iajs-2381	84	4	)	)	PUNCT
iajs-2381	84	5	2020	2020	NUM
iajs-2381	84	6	proposition	proposition	NOUN
iajs-2381	84	7	3.9	3.9	NUM
iajs-2381	84	8	:	:	PUNCT
iajs-2381	84	9	if	if	SCONJ
iajs-2381	84	10	is	be	AUX
iajs-2381	84	11	(	(	PUNCT
iajs-2381	84	12	respectively	respectively	ADV
iajs-2381	84	13	,	,	PUNCT
iajs-2381	84	14	and	and	CCONJ
iajs-2381	84	15	)	)	PUNCT
iajs-2381	84	16	and	and	CCONJ
iajs-2381	84	17	ὑ	ὑ	PROPN
iajs-2381	84	18	is	be	AUX
iajs-2381	84	19	injective	injective	ADJ
iajs-2381	84	20	,	,	PUNCT
iajs-2381	84	21	ـ	ـ	X
iajs-2381	84	22	then	then	ADV
iajs-2381	84	23	the	the	DET
iajs-2381	84	24	space	space	NOUN
iajs-2381	84	25	is	be	AUX
iajs-2381	84	26	(	(	PUNCT
iajs-2381	84	27	respectively	respectively	ADV
iajs-2381	84	28	,	,	PUNCT
iajs-2381	84	29	and	and	CCONJ
iajs-2381	84	30	)	)	PUNCT
iajs-2381	84	31	.	.	PUNCT
iajs-2381	85	1	proof	proof	NOUN
iajs-2381	85	2	:	:	PUNCT
iajs-2381	85	3	follows	follow	VERB
iajs-2381	85	4	by	by	ADP
iajs-2381	85	5	the	the	DET
iajs-2381	85	6	result	result	NOUN
iajs-2381	85	7	,	,	PUNCT
iajs-2381	85	8	for	for	ADP
iajs-2381	85	9	all	all	DET
iajs-2381	85	10	ὑ	ὑ	NOUN
iajs-2381	85	11	.	.	PUNCT
iajs-2381	86	1	proposition	proposition	NOUN
iajs-2381	86	2	3.10	3.10	NUM
iajs-2381	86	3	:	:	PUNCT
iajs-2381	86	4	if	if	SCONJ
iajs-2381	86	5	a	a	DET
iajs-2381	86	6	space	space	NOUN
iajs-2381	86	7	ὑ	ὑ	NOUN
iajs-2381	86	8	is	be	AUX
iajs-2381	86	9	a	a	DET
iajs-2381	86	10	(	(	PUNCT
iajs-2381	86	11	respectively	respectively	ADV
iajs-2381	86	12	,	,	PUNCT
iajs-2381	86	13	and	and	CCONJ
iajs-2381	86	14	)	)	PUNCT
iajs-2381	86	15	and	and	CCONJ
iajs-2381	86	16	ὑ	ὑ	PROPN
iajs-2381	86	17	is	be	AUX
iajs-2381	86	18	an	an	DET
iajs-2381	86	19	injective	injective	ADJ
iajs-2381	86	20	,	,	PUNCT
iajs-2381	86	21	function	function	NOUN
iajs-2381	86	22	,	,	PUNCT
iajs-2381	86	23	then	then	ADV
iajs-2381	86	24	is	be	AUX
iajs-2381	86	25	an	an	DET
iajs-2381	86	26	(	(	PUNCT
iajs-2381	86	27	respectively	respectively	ADV
iajs-2381	86	28	,	,	PUNCT
iajs-2381	86	29	and	and	CCONJ
iajs-2381	86	30	)	)	PUNCT
iajs-2381	86	31	.	.	PUNCT
iajs-2381	87	1	proof	proof	NOUN
iajs-2381	87	2	:	:	PUNCT
iajs-2381	87	3	follows	follow	VERB
iajs-2381	87	4	by	by	ADP
iajs-2381	87	5	the	the	DET
iajs-2381	87	6	result	result	NOUN
iajs-2381	87	7	if	if	SCONJ
iajs-2381	87	8	for	for	ADP
iajs-2381	87	9	all	all	DET
iajs-2381	87	10	ὑ	ὑ	NOUN
iajs-2381	87	11	ـ	ـ	NOUN
iajs-2381	87	12	.4	.4	NUM
iajs-2381	87	13	in	in	ADP
iajs-2381	87	14	this	this	DET
iajs-2381	87	15	part	part	NOUN
iajs-2381	87	16	we	we	PRON
iajs-2381	87	17	will	will	AUX
iajs-2381	87	18	use	use	VERB
iajs-2381	87	19	the	the	DET
iajs-2381	87	20	notion	notion	NOUN
iajs-2381	87	21	ـ	ـ	X
iajs-2381	87	22	to	to	PART
iajs-2381	87	23	erection	erection	VERB
iajs-2381	87	24	some	some	DET
iajs-2381	87	25	class	class	NOUN
iajs-2381	87	26	of	of	ADP
iajs-2381	87	27	convergence	convergence	NOUN
iajs-2381	87	28	in	in	ADP
iajs-2381	87	29	ideal	ideal	ADJ
iajs-2381	87	30	spaces	space	NOUN
iajs-2381	87	31	namely	namely	ADV
iajs-2381	87	32	ـ	ـ	X
iajs-2381	87	33	.	.	PUNCT
iajs-2381	88	1	so	so	ADV
iajs-2381	88	2	,	,	PUNCT
iajs-2381	88	3	the	the	DET
iajs-2381	88	4	action	action	NOUN
iajs-2381	88	5	of	of	ADP
iajs-2381	88	6	some	some	DET
iajs-2381	88	7	sorts	sort	NOUN
iajs-2381	88	8	of	of	ADP
iajs-2381	88	9	functions	function	NOUN
iajs-2381	88	10	are	be	AUX
iajs-2381	88	11	discussed	discuss	VERB
iajs-2381	88	12	like	like	ADP
iajs-2381	88	13	,	,	PUNCT
iajs-2381	88	14	ـ	ـ	X
iajs-2381	88	15	,	,	PUNCT
iajs-2381	88	16	ẛ	ẛ	PROPN
iajs-2381	88	17	and	and	CCONJ
iajs-2381	88	18	ẛ	ẛ	X
iajs-2381	89	1	[	[	X
iajs-2381	89	2	1	1	NUM
iajs-2381	89	3	]	]	PUNCT
iajs-2381	89	4	.	.	PUNCT
iajs-2381	90	1	definition	definition	NOUN
iajs-2381	90	2	4.1	4.1	NUM
iajs-2381	90	3	:	:	PUNCT
iajs-2381	90	4	let	let	AUX
iajs-2381	90	5	be	be	AUX
iajs-2381	90	6	an	an	DET
iajs-2381	90	7	ideal	ideal	ADJ
iajs-2381	90	8	space	space	NOUN
iajs-2381	90	9	,	,	PUNCT
iajs-2381	90	10	and	and	CCONJ
iajs-2381	90	11	be	be	AUX
iajs-2381	90	12	a	a	DET
iajs-2381	90	13	sequence	sequence	NOUN
iajs-2381	90	14	in	in	ADP
iajs-2381	90	15	.	.	PUNCT
iajs-2381	91	1	then	then	ADV
iajs-2381	91	2	is	be	AUX
iajs-2381	91	3	namely	namely	ADV
iajs-2381	91	4	ـ	ـ	X
iajs-2381	91	5	to	to	PART
iajs-2381	91	6	(	(	PUNCT
iajs-2381	91	7	frugally	frugally	ADV
iajs-2381	91	8	,	,	PUNCT
iajs-2381	91	9	)	)	PUNCT
iajs-2381	91	10	if	if	SCONJ
iajs-2381	91	11	for	for	SCONJ
iajs-2381	91	12	every	every	DET
iajs-2381	91	13	ـ	ـ	PROPN
iajs-2381	91	14	set	set	NOUN
iajs-2381	91	15	contained	contain	VERB
iajs-2381	91	16	,	,	PUNCT
iajs-2381	91	17	such	such	ADJ
iajs-2381	91	18	that	that	SCONJ
iajs-2381	91	19	a	a	DET
iajs-2381	91	20	sequence	sequence	NOUN
iajs-2381	91	21	is	be	AUX
iajs-2381	91	22	namely	namely	ADV
iajs-2381	91	23	ـ	ـ	X
iajs-2381	91	24	if	if	SCONJ
iajs-2381	91	25	it	it	PRON
iajs-2381	91	26	is	be	AUX
iajs-2381	91	27	not	not	PART
iajs-2381	91	28	ـ	ـ	X
iajs-2381	91	29	.	.	PUNCT
iajs-2381	92	1	proposition	proposition	NOUN
iajs-2381	92	2	4.2	4.2	NUM
iajs-2381	92	3	:	:	PUNCT
iajs-2381	92	4	if	if	SCONJ
iajs-2381	92	5	is	be	AUX
iajs-2381	92	6	ـ	ـ	X
iajs-2381	92	7	then	then	ADV
iajs-2381	92	8	every	every	DET
iajs-2381	92	9	ـ	ـ	NOUN
iajs-2381	92	10	sequence	sequence	NOUN
iajs-2381	92	11	in	in	ADP
iajs-2381	92	12	has	have	VERB
iajs-2381	92	13	a	a	DET
iajs-2381	92	14	unique	unique	ADJ
iajs-2381	92	15	limit	limit	NOUN
iajs-2381	92	16	point	point	NOUN
iajs-2381	92	17	.	.	PUNCT
iajs-2381	93	1	proof	proof	NOUN
iajs-2381	93	2	:	:	PUNCT
iajs-2381	93	3	let	let	AUX
iajs-2381	93	4	be	be	AUX
iajs-2381	93	5	a	a	DET
iajs-2381	93	6	sequence	sequence	NOUN
iajs-2381	93	7	in	in	ADP
iajs-2381	93	8	where	where	SCONJ
iajs-2381	93	9	and	and	CCONJ
iajs-2381	93	10	;	;	PUNCT
iajs-2381	93	11	where	where	SCONJ
iajs-2381	93	12	.	.	PUNCT
iajs-2381	94	1	since	since	SCONJ
iajs-2381	94	2	is	be	AUX
iajs-2381	94	3	ـ	ـ	PROPN
iajs-2381	94	4	ـ	ـ	PROPN
iajs-2381	94	5	,	,	PUNCT
iajs-2381	94	6	then	then	ADV
iajs-2381	94	7	such	such	ADJ
iajs-2381	94	8	that	that	PRON
iajs-2381	94	9	and	and	CCONJ
iajs-2381	94	10	,	,	PUNCT
iajs-2381	94	11	where	where	SCONJ
iajs-2381	94	12	.	.	PUNCT
iajs-2381	95	1	since	since	SCONJ
iajs-2381	95	2	and	and	CCONJ
iajs-2381	95	3	leads	lead	VERB
iajs-2381	95	4	to	to	ADP
iajs-2381	95	5	;	;	PUNCT
iajs-2381	95	6	so	so	ADV
iajs-2381	95	7	and	and	CCONJ
iajs-2381	95	8	leads	lead	VERB
iajs-2381	95	9	to	to	ADP
iajs-2381	95	10	;	;	PUNCT
iajs-2381	95	11	.	.	PUNCT
iajs-2381	96	1	hence	hence	ADV
iajs-2381	96	2	,	,	PUNCT
iajs-2381	96	3	,	,	PUNCT
iajs-2381	96	4	that	that	PRON
iajs-2381	96	5	is	be	AUX
iajs-2381	96	6	contradiction	contradiction	NOUN
iajs-2381	96	7	.	.	PUNCT
iajs-2381	97	1	the	the	DET
iajs-2381	97	2	precondition	precondition	NOUN
iajs-2381	97	3	that	that	SCONJ
iajs-2381	97	4	a	a	DET
iajs-2381	97	5	space	space	NOUN
iajs-2381	97	6	is	be	AUX
iajs-2381	97	7	ـ	ـ	PROPN
iajs-2381	97	8	ـ	ـ	PROPN
iajs-2381	97	9	is	be	AUX
iajs-2381	97	10	very	very	ADV
iajs-2381	97	11	requisite	requisite	ADJ
iajs-2381	97	12	to	to	PART
iajs-2381	97	13	make	make	VERB
iajs-2381	97	14	proposition	proposition	NOUN
iajs-2381	97	15	4.2	4.2	NUM
iajs-2381	97	16	,	,	PUNCT
iajs-2381	97	17	is	be	AUX
iajs-2381	97	18	valid	valid	ADJ
iajs-2381	97	19	.	.	PUNCT
iajs-2381	97	20	example	example	NOUN
iajs-2381	97	21	4.3	4.3	NUM
iajs-2381	97	22	:	:	PUNCT
iajs-2381	97	23	for	for	ADP
iajs-2381	97	24	a	a	DET
iajs-2381	97	25	space	space	NOUN
iajs-2381	97	26	where	where	SCONJ
iajs-2381	97	27	,	,	PUNCT
iajs-2381	97	28	and	and	CCONJ
iajs-2381	97	29	.	.	PUNCT
iajs-2381	98	1	obviously	obviously	ADV
iajs-2381	98	2	;	;	PUNCT
iajs-2381	98	3	the	the	DET
iajs-2381	98	4	sequence	sequence	NOUN
iajs-2381	98	5	in	in	ADP
iajs-2381	98	6	,	,	PUNCT
iajs-2381	98	7	where	where	SCONJ
iajs-2381	98	8	for	for	ADP
iajs-2381	98	9	all	all	PRON
iajs-2381	98	10	,	,	PUNCT
iajs-2381	98	11	has	have	VERB
iajs-2381	98	12	three	three	NUM
iajs-2381	98	13	limit	limit	NOUN
iajs-2381	98	14	points	point	NOUN
iajs-2381	98	15	;	;	PUNCT
iajs-2381	98	16	that	that	SCONJ
iajs-2381	98	17	,	,	PUNCT
iajs-2381	98	18	and	and	CCONJ
iajs-2381	98	19	.	.	PUNCT
iajs-2381	99	1	in	in	ADP
iajs-2381	99	2	mathematics	mathematic	NOUN
iajs-2381	99	3	,	,	PUNCT
iajs-2381	99	4	convergence	convergence	NOUN
iajs-2381	99	5	sequence	sequence	NOUN
iajs-2381	99	6	was	be	AUX
iajs-2381	99	7	an	an	DET
iajs-2381	99	8	important	important	ADJ
iajs-2381	99	9	subject	subject	NOUN
iajs-2381	99	10	[	[	X
iajs-2381	99	11	10	10	NUM
iajs-2381	99	12	,	,	PUNCT
iajs-2381	99	13	11	11	NUM
iajs-2381	99	14	]	]	PUNCT
iajs-2381	99	15	.	.	PUNCT
iajs-2381	100	1	the	the	DET
iajs-2381	100	2	following	follow	VERB
iajs-2381	100	3	proposition	proposition	NOUN
iajs-2381	100	4	explains	explain	VERB
iajs-2381	100	5	the	the	DET
iajs-2381	100	6	relationships	relationship	NOUN
iajs-2381	100	7	between	between	ADP
iajs-2381	100	8	convergence	convergence	NOUN
iajs-2381	100	9	and	and	CCONJ
iajs-2381	100	10	ـ	ـ	X
iajs-2381	100	11	to	to	PART
iajs-2381	100	12	.	.	PUNCT
iajs-2381	101	1	proposition	proposition	NOUN
iajs-2381	101	2	4.4	4.4	NUM
iajs-2381	101	3	:	:	PUNCT
iajs-2381	101	4	if	if	SCONJ
iajs-2381	101	5	a	a	DET
iajs-2381	101	6	sequence	sequence	NOUN
iajs-2381	101	7	is	be	AUX
iajs-2381	101	8	ـ	ـ	NOUN
iajs-2381	101	9	to	to	PART
iajs-2381	101	10	in	in	ADP
iajs-2381	101	11	,	,	PUNCT
iajs-2381	101	12	then	then	ADV
iajs-2381	101	13	it	it	PRON
iajs-2381	101	14	is	be	AUX
iajs-2381	101	15	convergence	convergence	NOUN
iajs-2381	101	16	to	to	ADP
iajs-2381	101	17	.	.	PUNCT
iajs-2381	102	1	proof	proof	NOUN
iajs-2381	102	2	:	:	PUNCT
iajs-2381	102	3	since	since	SCONJ
iajs-2381	102	4	every	every	DET
iajs-2381	102	5	open	open	ADJ
iajs-2381	102	6	set	set	NOUN
iajs-2381	102	7	in	in	ADP
iajs-2381	102	8	is	be	AUX
iajs-2381	102	9	ẛpg	ẛpg	ADJ
iajs-2381	102	10	-	-	PUNCT
iajs-2381	102	11	open	open	ADJ
iajs-2381	102	12	,	,	PUNCT
iajs-2381	102	13	then	then	ADV
iajs-2381	102	14	the	the	DET
iajs-2381	102	15	proof	proof	NOUN
iajs-2381	102	16	is	be	AUX
iajs-2381	102	17	over	over	ADV
iajs-2381	102	18	.	.	PUNCT
iajs-2381	103	1	the	the	DET
iajs-2381	103	2	meaningfulness	meaningfulness	NOUN
iajs-2381	103	3	in	in	ADP
iajs-2381	103	4	proposition	proposition	NOUN
iajs-2381	103	5	4.4	4.4	NUM
iajs-2381	103	6	,	,	PUNCT
iajs-2381	103	7	can	can	AUX
iajs-2381	103	8	not	not	PART
iajs-2381	103	9	be	be	AUX
iajs-2381	103	10	inverting	invert	VERB
iajs-2381	103	11	,	,	PUNCT
iajs-2381	103	12	in	in	ADP
iajs-2381	103	13	general	general	ADJ
iajs-2381	103	14	.	.	PUNCT
iajs-2381	104	1	example	example	NOUN
iajs-2381	104	2	4.5	4.5	NUM
iajs-2381	104	3	:	:	PUNCT
iajs-2381	104	4	for	for	ADP
iajs-2381	104	5	a	a	DET
iajs-2381	104	6	space	space	NOUN
iajs-2381	104	7	,	,	PUNCT
iajs-2381	104	8	where	where	SCONJ
iajs-2381	104	9	set	set	NOUN
iajs-2381	104	10	of	of	ADP
iajs-2381	104	11	all	all	DET
iajs-2381	104	12	neutral	neutral	ADJ
iajs-2381	104	13	numbers	number	NOUN
iajs-2381	104	14	,	,	PUNCT
iajs-2381	104	15	and	and	CCONJ
iajs-2381	104	16	.	.	PUNCT
iajs-2381	105	1	the	the	DET
iajs-2381	105	2	sequence	sequence	NOUN
iajs-2381	105	3	,	,	PUNCT
iajs-2381	105	4	where	where	SCONJ
iajs-2381	105	5	,	,	PUNCT
iajs-2381	105	6	is	be	AUX
iajs-2381	105	7	convergence	convergence	NOUN
iajs-2381	105	8	to	to	PART
iajs-2381	105	9	which	which	PRON
iajs-2381	105	10	is	be	AUX
iajs-2381	105	11	not	not	PART
iajs-2381	105	12	ـ	ـ	X
iajs-2381	105	13	.	.	PUNCT
iajs-2381	106	1	proposition	proposition	NOUN
iajs-2381	106	2	4.6	4.6	NUM
iajs-2381	106	3	:	:	PUNCT
iajs-2381	106	4	let	let	VERB
iajs-2381	106	5	ὑ	ὑ	PART
iajs-2381	106	6	be	be	AUX
iajs-2381	106	7	ـ	ـ	NOUN
iajs-2381	106	8	function	function	NOUN
iajs-2381	106	9	and	and	CCONJ
iajs-2381	106	10	be	be	AUX
iajs-2381	106	11	a	a	DET
iajs-2381	106	12	sequence	sequence	NOUN
iajs-2381	106	13	in	in	ADP
iajs-2381	106	14	.	.	PUNCT
iajs-2381	107	1	if	if	SCONJ
iajs-2381	107	2	in	in	ADV
iajs-2381	107	3	,	,	PUNCT
iajs-2381	107	4	then	then	ADV
iajs-2381	107	5	in	in	ADP
iajs-2381	107	6	proposition	proposition	NOUN
iajs-2381	107	7	4.7	4.7	NUM
iajs-2381	107	8	:	:	PUNCT
iajs-2381	107	9	let	let	VERB
iajs-2381	107	10	ὑ	ὑ	PART
iajs-2381	107	11	be	be	AUX
iajs-2381	107	12	ـ	ـ	NOUN
iajs-2381	107	13	function	function	NOUN
iajs-2381	107	14	and	and	CCONJ
iajs-2381	107	15	be	be	AUX
iajs-2381	107	16	a	a	DET
iajs-2381	107	17	sequence	sequence	NOUN
iajs-2381	107	18	in	in	ADP
iajs-2381	107	19	.	.	PUNCT
iajs-2381	108	1	if	if	SCONJ
iajs-2381	108	2	in	in	ADV
iajs-2381	108	3	,	,	PUNCT
iajs-2381	108	4	then	then	ADV
iajs-2381	108	5	in	in	ADP
iajs-2381	108	6	251	251	NUM
iajs-2381	108	7	ibn	ibn	PROPN
iajs-2381	108	8	al	al	PROPN
iajs-2381	108	9	-	-	PUNCT
iajs-2381	108	10	haitham	haitham	PROPN
iajs-2381	108	11	jour	jour	X
iajs-2381	108	12	.	.	PROPN
iajs-2381	109	1	for	for	ADP
iajs-2381	109	2	pure	pure	ADJ
iajs-2381	109	3	&	&	CCONJ
iajs-2381	109	4	appl	appl	PROPN
iajs-2381	109	5	.	.	PUNCT
iajs-2381	110	1	sci	sci	PROPN
iajs-2381	110	2	.	.	PROPN
iajs-2381	111	1	33	33	NUM
iajs-2381	111	2	(	(	PUNCT
iajs-2381	111	3	1	1	NUM
iajs-2381	111	4	)	)	PUNCT
iajs-2381	111	5	2020	2020	NUM
iajs-2381	111	6	proposition	proposition	NOUN
iajs-2381	111	7	4.8	4.8	NUM
iajs-2381	111	8	:	:	PUNCT
iajs-2381	111	9	let	let	VERB
iajs-2381	111	10	ὑ	ὑ	PART
iajs-2381	111	11	be	be	AUX
iajs-2381	111	12	ـ	ـ	X
iajs-2381	111	13	ـ	ـ	NOUN
iajs-2381	111	14	function	function	NOUN
iajs-2381	111	15	and	and	CCONJ
iajs-2381	111	16	be	be	AUX
iajs-2381	111	17	a	a	DET
iajs-2381	111	18	sequence	sequence	NOUN
iajs-2381	111	19	in	in	ADP
iajs-2381	111	20	.	.	PUNCT
iajs-2381	112	1	if	if	SCONJ
iajs-2381	112	2	in	in	ADV
iajs-2381	112	3	,	,	PUNCT
iajs-2381	112	4	then	then	ADV
iajs-2381	112	5	in	in	ADP
iajs-2381	112	6	5	5	NUM
iajs-2381	112	7	.	.	PUNCT
iajs-2381	112	8	conclusion	conclusion	NOUN
iajs-2381	112	9	the	the	DET
iajs-2381	112	10	notion	notion	NOUN
iajs-2381	112	11	ـ	ـ	X
iajs-2381	112	12	ـ	ـ	X
iajs-2381	112	13	ـ	ـ	PROPN
iajs-2381	112	14	was	be	AUX
iajs-2381	112	15	use	use	NOUN
iajs-2381	112	16	to	to	PART
iajs-2381	112	17	offered	offer	VERB
iajs-2381	112	18	new	new	ADJ
iajs-2381	112	19	classes	class	NOUN
iajs-2381	112	20	of	of	ADP
iajs-2381	112	21	separation	separation	NOUN
iajs-2381	112	22	axioms	axiom	NOUN
iajs-2381	112	23	and	and	CCONJ
iajs-2381	112	24	new	new	ADJ
iajs-2381	112	25	type	type	NOUN
iajs-2381	112	26	of	of	ADP
iajs-2381	112	27	convergence	convergence	NOUN
iajs-2381	112	28	in	in	ADP
iajs-2381	112	29	ideal	ideal	ADJ
iajs-2381	112	30	spaces	space	NOUN
iajs-2381	112	31	.	.	PUNCT
iajs-2381	113	1	some	some	DET
iajs-2381	113	2	relations	relation	NOUN
iajs-2381	113	3	and	and	CCONJ
iajs-2381	113	4	examples	example	NOUN
iajs-2381	113	5	among	among	ADP
iajs-2381	113	6	several	several	ADJ
iajs-2381	113	7	types	type	NOUN
iajs-2381	113	8	of	of	ADP
iajs-2381	113	9	separation	separation	NOUN
iajs-2381	113	10	axioms	axiom	NOUN
iajs-2381	113	11	that	that	PRON
iajs-2381	113	12	offered	offer	VERB
iajs-2381	113	13	were	be	AUX
iajs-2381	113	14	explained	explain	VERB
iajs-2381	113	15	.	.	PUNCT
iajs-2381	114	1	references	reference	NOUN
iajs-2381	114	2	1	1	NUM
iajs-2381	114	3	.	.	PUNCT
iajs-2381	115	1	ahmed	ahmed	PROPN
iajs-2381	115	2	,	,	PUNCT
iajs-2381	115	3	a.	a.	NOUN
iajs-2381	115	4	;	;	PUNCT
iajs-2381	115	5	esmaeel	esmaeel	VERB
iajs-2381	115	6	r.b	r.b	PROPN
iajs-2381	115	7	.	.	PROPN
iajs-2381	116	1	on	on	ADP
iajs-2381	116	2	ẛ	ẛ	NOUN
iajs-2381	116	3	-	-	PUNCT
iajs-2381	116	4	pre	pre	ADJ
iajs-2381	116	5	-	-	ADJ
iajs-2381	116	6	g	g	NOUN
iajs-2381	116	7	-	-	PUNCT
iajs-2381	116	8	closed	close	VERB
iajs-2381	116	9	sets	set	NOUN
iajs-2381	116	10	and	and	CCONJ
iajs-2381	116	11	ẛ	ẛ	NOUN
iajs-2381	116	12	-	-	PUNCT
iajs-2381	116	13	pre	pre	ADJ
iajs-2381	116	14	-	-	ADJ
iajs-2381	116	15	g	g	ADV
iajs-2381	116	16	-	-	PUNCT
iajs-2381	116	17	continuous	continuous	ADJ
iajs-2381	116	18	functions	function	NOUN
iajs-2381	116	19	.	.	PUNCT
iajs-2381	117	1	ready	ready	ADJ
iajs-2381	117	2	to	to	PART
iajs-2381	117	3	be	be	AUX
iajs-2381	117	4	published	publish	VERB
iajs-2381	117	5	in	in	ADP
iajs-2381	117	6	the	the	DET
iajs-2381	117	7	journal	journal	NOUN
iajs-2381	117	8	of	of	ADP
iajs-2381	117	9	the	the	DET
iajs-2381	117	10	indian	indian	ADJ
iajs-2381	117	11	mathamatical	mathamatical	ADJ
iajs-2381	117	12	society	society	NOUN
iajs-2381	117	13	,	,	PUNCT
iajs-2381	117	14	2019	2019	NUM
iajs-2381	117	15	.	.	PUNCT
iajs-2381	118	1	2	2	X
iajs-2381	118	2	.	.	X
iajs-2381	118	3	kuratowski	kuratowski	PROPN
iajs-2381	118	4	,	,	PUNCT
iajs-2381	118	5	k.	k.	PROPN
iajs-2381	118	6	topology	topology	PROPN
iajs-2381	118	7	.	.	PUNCT
iajs-2381	119	1	new	new	PROPN
iajs-2381	119	2	york	york	PROPN
iajs-2381	119	3	:	:	PUNCT
iajs-2381	119	4	acadeic	acadeic	PROPN
iajs-2381	119	5	press.1933	press.1933	PROPN
iajs-2381	119	6	,	,	PUNCT
iajs-2381	119	7	i.	i.	NOUN
iajs-2381	119	8	3	3	NUM
iajs-2381	119	9	.	.	PUNCT
iajs-2381	119	10	vaidyanathaswamy	vaidyanathaswamy	PROPN
iajs-2381	119	11	v.	v.	ADP
iajs-2381	119	12	;	;	PUNCT
iajs-2381	119	13	the	the	DET
iajs-2381	119	14	localization	localization	NOUN
iajs-2381	119	15	theory	theory	NOUN
iajs-2381	119	16	in	in	ADP
iajs-2381	119	17	set	set	NOUN
iajs-2381	119	18	topology	topology	NOUN
iajs-2381	119	19	,	,	PUNCT
iajs-2381	119	20	proc	proc	NOUN
iajs-2381	119	21	.	.	PUNCT
iajs-2381	120	1	indian	indian	PROPN
iajs-2381	120	2	acad	acad	PROPN
iajs-2381	120	3	.	.	PUNCT
iajs-2381	121	1	sci	sci	PROPN
iajs-2381	121	2	.	.	PROPN
iajs-2381	121	3	1945	1945	NUM
iajs-2381	121	4	,	,	PUNCT
iajs-2381	121	5	20	20	NUM
iajs-2381	121	6	,	,	PUNCT
iajs-2381	121	7	1	1	NUM
iajs-2381	121	8	,	,	PUNCT
iajs-2381	121	9	51	51	NUM
iajs-2381	121	10	-	-	SYM
iajs-2381	121	11	61	61	NUM
iajs-2381	121	12	.	.	PUNCT
iajs-2381	121	13	4	4	X
iajs-2381	121	14	.	.	X
iajs-2381	121	15	abd	abd	PROPN
iajs-2381	121	16	elmonsef	elmonsef	PROPN
iajs-2381	121	17	,	,	PUNCT
iajs-2381	121	18	m.e	m.e	PROPN
iajs-2381	121	19	.	.	PROPN
iajs-2381	121	20	;	;	PUNCT
iajs-2381	121	21	nasef	nasef	PROPN
iajs-2381	121	22	,	,	PUNCT
iajs-2381	121	23	a.a	a.a	PROPN
iajs-2381	121	24	.	.	PROPN
iajs-2381	121	25	;	;	PUNCT
iajs-2381	121	26	radwan	radwan	NOUN
iajs-2381	121	27	,	,	PUNCT
iajs-2381	121	28	a.e	a.e	PROPN
iajs-2381	121	29	.	.	PROPN
iajs-2381	121	30	;	;	PUNCT
iajs-2381	121	31	esmaeel	esmaeel	NOUN
iajs-2381	121	32	,	,	PUNCT
iajs-2381	121	33	r.b	r.b	NOUN
iajs-2381	121	34	.	.	PROPN
iajs-2381	122	1	on	on	ADP
iajs-2381	122	2	αopen	αopen	ADJ
iajs-2381	122	3	sets	set	NOUN
iajs-2381	122	4	with	with	ADP
iajs-2381	122	5	respect	respect	NOUN
iajs-2381	122	6	to	to	ADP
iajs-2381	122	7	an	an	DET
iajs-2381	122	8	ideal	ideal	NOUN
iajs-2381	122	9	.	.	PUNCT
iajs-2381	123	1	journal	journal	NOUN
iajs-2381	123	2	of	of	ADP
iajs-2381	123	3	advances	advance	NOUN
iajs-2381	123	4	studies	study	NOUN
iajs-2381	123	5	in	in	ADP
iajs-2381	123	6	topology.2014	topology.2014	PROPN
iajs-2381	123	7	,	,	PUNCT
iajs-2381	123	8	5	5	NUM
iajs-2381	123	9	,	,	PUNCT
iajs-2381	123	10	3	3	NUM
iajs-2381	123	11	,	,	PUNCT
iajs-2381	123	12	1	1	NUM
iajs-2381	123	13	-	-	SYM
iajs-2381	123	14	9	9	NUM
iajs-2381	123	15	.	.	NOUN
iajs-2381	123	16	5	5	NUM
iajs-2381	123	17	.	.	X
iajs-2381	123	18	nasef	nasef	PROPN
iajs-2381	123	19	,	,	PUNCT
iajs-2381	123	20	a.a	a.a	PROPN
iajs-2381	123	21	.	.	PROPN
iajs-2381	123	22	;	;	PUNCT
iajs-2381	123	23	radwan	radwan	NOUN
iajs-2381	123	24	,	,	PUNCT
iajs-2381	123	25	a.e	a.e	PROPN
iajs-2381	123	26	.	.	PROPN
iajs-2381	123	27	;	;	PUNCT
iajs-2381	123	28	esmaeeln	esmaeeln	PROPN
iajs-2381	123	29	,	,	PUNCT
iajs-2381	123	30	r.b	r.b	NOUN
iajs-2381	123	31	.	.	PUNCT
iajs-2381	124	1	some	some	DET
iajs-2381	124	2	properties	property	NOUN
iajs-2381	124	3	of	of	ADP
iajs-2381	124	4	α	α	NOUN
iajs-2381	124	5	-	-	ADJ
iajs-2381	124	6	open	open	ADJ
iajs-2381	124	7	sets	set	NOUN
iajs-2381	124	8	with	with	ADP
iajs-2381	124	9	repect	repect	NOUN
iajs-2381	124	10	to	to	ADP
iajs-2381	124	11	an	an	DET
iajs-2381	124	12	ideal	ideal	ADJ
iajs-2381	124	13	,	,	PUNCT
iajs-2381	124	14	iternational	iternational	ADJ
iajs-2381	124	15	journal	journal	NOUN
iajs-2381	124	16	of	of	ADP
iajs-2381	124	17	pur	pur	NOUN
iajs-2381	124	18	and	and	CCONJ
iajs-2381	124	19	applied	apply	VERB
iajs-2381	124	20	mathematics.2015	mathematics.2015	PROPN
iajs-2381	124	21	,	,	PUNCT
iajs-2381	124	22	102	102	NUM
iajs-2381	124	23	,	,	PUNCT
iajs-2381	124	24	4	4	NUM
iajs-2381	124	25	,	,	PUNCT
iajs-2381	124	26	613	613	NUM
iajs-2381	124	27	-	-	SYM
iajs-2381	124	28	630	630	NUM
iajs-2381	124	29	.	.	PUNCT
iajs-2381	125	1	6	6	NUM
iajs-2381	125	2	.	.	X
iajs-2381	126	1	mashhour	mashhour	PROPN
iajs-2381	126	2	,	,	PUNCT
iajs-2381	126	3	a.s	a.s	PROPN
iajs-2381	126	4	.	.	PROPN
iajs-2381	126	5	;	;	PUNCT
iajs-2381	126	6	abd	abd	PROPN
iajs-2381	126	7	elmonsef	elmonsef	PROPN
iajs-2381	126	8	,	,	PUNCT
iajs-2381	126	9	m.e	m.e	PROPN
iajs-2381	126	10	.	.	PROPN
iajs-2381	126	11	;	;	PUNCT
iajs-2381	126	12	eldeeb	eldeeb	PROPN
iajs-2381	126	13	,	,	PUNCT
iajs-2381	126	14	s.n	s.n	PROPN
iajs-2381	126	15	.	.	PROPN
iajs-2381	126	16	on	on	ADP
iajs-2381	126	17	pre	pre	ADJ
iajs-2381	126	18	topological	topological	ADJ
iajs-2381	126	19	spaces	space	NOUN
iajs-2381	126	20	.	.	PUNCT
iajs-2381	127	1	bull	bull	NOUN
iajs-2381	127	2	.	.	PUNCT
iajs-2381	128	1	math	math	NOUN
iajs-2381	128	2	.	.	PUNCT
iajs-2381	129	1	dela	dela	PROPN
iajs-2381	129	2	soc	soc	PROPN
iajs-2381	129	3	.	.	PUNCT
iajs-2381	130	1	r.s	r.s	PROPN
iajs-2381	130	2	.	.	PROPN
iajs-2381	130	3	de	de	PROPN
iajs-2381	130	4	roumanie.1984	roumanie.1984	PROPN
iajs-2381	130	5	,	,	PUNCT
iajs-2381	130	6	28	28	NUM
iajs-2381	130	7	,	,	PUNCT
iajs-2381	130	8	3945	3945	NUM
iajs-2381	130	9	ـ	ـ	X
iajs-2381	130	10	.	.	PROPN
iajs-2381	130	11	7	7	NUM
iajs-2381	130	12	.	.	X
iajs-2381	131	1	dawood	dawood	PROPN
iajs-2381	131	2	,	,	PUNCT
iajs-2381	131	3	n.a	n.a	PROPN
iajs-2381	131	4	.	.	PROPN
iajs-2381	131	5	;	;	PUNCT
iajs-2381	131	6	nasir	nasir	PROPN
iajs-2381	131	7	,	,	PUNCT
iajs-2381	131	8	a.i	a.i	PROPN
iajs-2381	131	9	.	.	PROPN
iajs-2381	132	1	some	some	DET
iajs-2381	132	2	types	type	NOUN
iajs-2381	132	3	of	of	ADP
iajs-2381	132	4	compactness	compactness	NOUN
iajs-2381	132	5	in	in	ADP
iajs-2381	132	6	bitopological	bitopological	ADJ
iajs-2381	132	7	spaces	space	NOUN
iajs-2381	132	8	and	and	CCONJ
iajs-2381	132	9	it	it	PRON
iajs-2381	132	10	is	be	AUX
iajs-2381	132	11	associated	associate	VERB
iajs-2381	132	12	topology	topology	NOUN
iajs-2381	132	13	of	of	ADP
iajs-2381	132	14	α	α	NOUN
iajs-2381	132	15	-	-	PUNCT
iajs-2381	132	16	subsets	subset	NOUN
iajs-2381	132	17	.	.	PUNCT
iajs-2381	133	1	indian	indian	PROPN
iajs-2381	133	2	j.	j.	PROPN
iajs-2381	133	3	pure	pure	PROPN
iajs-2381	133	4	appl	appl	PROPN
iajs-2381	133	5	.	.	PUNCT
iajs-2381	134	1	math.2010	math.2010	PROPN
iajs-2381	134	2	,	,	PUNCT
iajs-2381	134	3	27	27	NUM
iajs-2381	134	4	,	,	PUNCT
iajs-2381	134	5	995	995	NUM
iajs-2381	134	6	-	-	SYM
iajs-2381	134	7	1004	1004	NUM
iajs-2381	134	8	.	.	PUNCT
iajs-2381	135	1	8	8	NUM
iajs-2381	135	2	.	.	X
iajs-2381	136	1	mahmood	mahmood	PROPN
iajs-2381	136	2	,	,	PUNCT
iajs-2381	136	3	s.i	s.i	PROPN
iajs-2381	136	4	.	.	PROPN
iajs-2381	136	5	on	on	ADP
iajs-2381	136	6	generalized	generalized	ADJ
iajs-2381	136	7	regular	regular	ADJ
iajs-2381	136	8	continuous	continuous	ADJ
iajs-2381	136	9	functions	function	NOUN
iajs-2381	136	10	in	in	ADP
iajs-2381	136	11	topological	topological	ADJ
iajs-2381	136	12	spaces	space	NOUN
iajs-2381	136	13	.	.	PUNCT
iajs-2381	137	1	ibn	ibn	PROPN
iajs-2381	137	2	al	al	PROPN
iajs-2381	137	3	-	-	PUNCT
iajs-2381	137	4	haithatham	haithatham	PROPN
iajs-2381	137	5	journal	journal	NOUN
iajs-2381	137	6	for	for	ADP
iajs-2381	137	7	pure	pure	ADJ
iajs-2381	137	8	and	and	CCONJ
iajs-2381	137	9	applied	apply	VERB
iajs-2381	137	10	science.2017	science.2017	PROPN
iajs-2381	137	11	,	,	PUNCT
iajs-2381	137	12	25	25	NUM
iajs-2381	137	13	,	,	PUNCT
iajs-2381	137	14	3	3	NUM
iajs-2381	137	15	,	,	PUNCT
iajs-2381	137	16	377	377	NUM
iajs-2381	137	17	-	-	SYM
iajs-2381	137	18	376	376	NUM
iajs-2381	137	19	.	.	PUNCT
iajs-2381	138	1	9	9	X
iajs-2381	138	2	.	.	PUNCT
iajs-2381	139	1	alhawez	alhawez	PROPN
iajs-2381	139	2	zinah	zinah	PROPN
iajs-2381	139	3	,	,	PUNCT
iajs-2381	139	4	.t	.t	PROPN
iajs-2381	139	5	.	.	PUNCT
iajs-2381	140	1	on	on	ADP
iajs-2381	140	2	generalized	generalized	ADJ
iajs-2381	140	3	-closed	-close	VERB
iajs-2381	140	4	set	set	NOUN
iajs-2381	140	5	in	in	ADP
iajs-2381	140	6	topological	topological	ADJ
iajs-2381	140	7	spaces	space	NOUN
iajs-2381	140	8	.	.	PUNCT
iajs-2381	141	1	ibn	ibn	PROPN
iajs-2381	141	2	alhaithatham	alhaithatham	PROPN
iajs-2381	141	3	journal	journal	PROPN
iajs-2381	141	4	for	for	ADP
iajs-2381	141	5	pure	pure	ADJ
iajs-2381	141	6	and	and	CCONJ
iajs-2381	141	7	applied	apply	VERB
iajs-2381	141	8	science.2015	science.2015	PROPN
iajs-2381	141	9	,	,	PUNCT
iajs-2381	141	10	28	28	NUM
iajs-2381	141	11	,	,	PUNCT
iajs-2381	141	12	204	204	NUM
iajs-2381	141	13	-	-	SYM
iajs-2381	141	14	213	213	NUM
iajs-2381	141	15	.	.	PUNCT
iajs-2381	142	1	10	10	NUM
iajs-2381	142	2	.	.	PUNCT
iajs-2381	142	3	dugundji	dugundji	PROPN
iajs-2381	142	4	,	,	PUNCT
iajs-2381	142	5	j.	j.	PROPN
iajs-2381	142	6	topology	topology	PROPN
iajs-2381	142	7	.	.	PUNCT
iajs-2381	143	1	university	university	NOUN
iajs-2381	143	2	of	of	ADP
iajs-2381	143	3	south	south	PROPN
iajs-2381	143	4	california	california	PROPN
iajs-2381	143	5	,	,	PUNCT
iajs-2381	143	6	los	los	PROPN
iajs-2381	143	7	angeles	angeles	PROPN
iajs-2381	143	8	,	,	PUNCT
iajs-2381	143	9	allyn	allyn	PROPN
iajs-2381	143	10	and	and	CCONJ
iajs-2381	143	11	bacon	bacon	PROPN
iajs-2381	143	12	,	,	PUNCT
iajs-2381	143	13	inc	inc	PROPN
iajs-2381	143	14	.	.	PROPN
iajs-2381	143	15	,	,	PUNCT
iajs-2381	143	16	boston	boston	PROPN
iajs-2381	143	17	,	,	PUNCT
iajs-2381	143	18	mass	mass	PROPN
iajs-2381	143	19	,	,	PUNCT
iajs-2381	143	20	1966	1966	NUM
iajs-2381	143	21	.	.	PUNCT
iajs-2381	144	1	11	11	NUM
iajs-2381	144	2	.	.	PUNCT
iajs-2381	145	1	munkres	munkre	NOUN
iajs-2381	145	2	,	,	PUNCT
iajs-2381	145	3	j.r	j.r	PROPN
iajs-2381	145	4	.	.	PROPN
iajs-2381	145	5	topology	topology	PROPN
iajs-2381	145	6	.	.	PUNCT
iajs-2381	146	1	prentice	prentice	NOUN
iajs-2381	146	2	-	-	PUNCT
iajs-2381	146	3	hall	hall	PROPN
iajs-2381	146	4	,	,	PUNCT
iajs-2381	146	5	inc	inc	PROPN
iajs-2381	146	6	.	.	PROPN
iajs-2381	146	7	,	,	PUNCT
iajs-2381	146	8	englwood	englwood	ADJ
iajs-2381	146	9	cliffs	cliff	NOUN
iajs-2381	146	10	,	,	PUNCT
iajs-2381	146	11	newjersey	newjersey	NOUN
iajs-2381	146	12	,	,	PUNCT
iajs-2381	146	13	1975	1975	NUM
iajs-2381	146	14	.	.	PUNCT