id	sid	tid	token	lemma	pos
iajs-2382	1	1	757	757	NUM
iajs-2382	1	2	ibn	ibn	PROPN
iajs-2382	1	3	al	al	PROPN
iajs-2382	1	4	-	-	PUNCT
iajs-2382	1	5	haitham	haitham	PROPN
iajs-2382	1	6	jour	jour	X
iajs-2382	1	7	.	.	PROPN
iajs-2382	1	8	for	for	ADP
iajs-2382	1	9	pure	pure	ADJ
iajs-2382	1	10	&	&	CCONJ
iajs-2382	1	11	appl	appl	PROPN
iajs-2382	1	12	.	.	PUNCT
iajs-2382	2	1	sci	sci	PROPN
iajs-2382	2	2	.	.	PROPN
iajs-2382	3	1	33	33	NUM
iajs-2382	3	2	(	(	PUNCT
iajs-2382	3	3	1	1	NUM
iajs-2382	3	4	)	)	PUNCT
iajs-2382	3	5	2020	2020	NUM
iajs-2382	4	1	m.	m.	NOUN
iajs-2382	4	2	a.	a.	PROPN
iajs-2382	4	3	abdel	abdel	PROPN
iajs-2382	4	4	karim	karim	PROPN
iajs-2382	4	5	a.	a.	PROPN
iajs-2382	4	6	i.	i.	PROPN
iajs-2382	4	7	nasir	nasir	PROPN
iajs-2382	4	8	abstract	abstract	PROPN
iajs-2382	4	9	the	the	DET
iajs-2382	4	10	notions	notion	NOUN
iajs-2382	4	11	ǐ­semi­g­closedness	ǐ­semi­g­closedness	NOUN
iajs-2382	4	12	and	and	CCONJ
iajs-2382	4	13	ǐ­semi­g­openness	ǐ­semi­g­openness	NOUN
iajs-2382	4	14	were	be	AUX
iajs-2382	4	15	used	use	VERB
iajs-2382	4	16	to	to	PART
iajs-2382	4	17	generalize	generalize	VERB
iajs-2382	4	18	and	and	CCONJ
iajs-2382	4	19	introduced	introduce	VERB
iajs-2382	4	20	new	new	ADJ
iajs-2382	4	21	classes	class	NOUN
iajs-2382	4	22	of	of	ADP
iajs-2382	4	23	separation	separation	NOUN
iajs-2382	4	24	axioms	axiom	NOUN
iajs-2382	4	25	in	in	ADP
iajs-2382	4	26	ideal	ideal	ADJ
iajs-2382	4	27	spaces	space	NOUN
iajs-2382	4	28	.	.	PUNCT
iajs-2382	5	1	many	many	ADJ
iajs-2382	5	2	relations	relation	NOUN
iajs-2382	5	3	among	among	ADP
iajs-2382	5	4	several	several	ADJ
iajs-2382	5	5	sorts	sort	NOUN
iajs-2382	5	6	of	of	ADP
iajs-2382	5	7	these	these	DET
iajs-2382	5	8	classes	class	NOUN
iajs-2382	5	9	are	be	AUX
iajs-2382	5	10	summarized	summarize	VERB
iajs-2382	5	11	,	,	PUNCT
iajs-2382	5	12	also	also	ADV
iajs-2382	5	13	.	.	PUNCT
iajs-2382	6	1	keyword	keyword	NOUN
iajs-2382	6	2	:	:	PUNCT
iajs-2382	6	3	ideal	ideal	ADJ
iajs-2382	6	4	,	,	PUNCT
iajs-2382	6	5	separation	separation	NOUN
iajs-2382	6	6	axioms	axiom	NOUN
iajs-2382	6	7	,	,	PUNCT
iajs-2382	6	8	ǐ	ǐ	INTJ
iajs-2382	6	9	,	,	PUNCT
iajs-2382	6	10	ǐ	ǐ	INTJ
iajs-2382	6	11	,	,	PUNCT
iajs-2382	6	12	ǐ	ǐ	INTJ
iajs-2382	6	13	,	,	PUNCT
iajs-2382	6	14	ǐ	ǐ	INTJ
iajs-2382	6	15	.	.	PUNCT
iajs-2382	7	1	1	1	X
iajs-2382	7	2	.	.	X
iajs-2382	7	3	introduction	introduction	NOUN
iajs-2382	7	4	abdel	abdel	PROPN
iajs-2382	7	5	karim	karim	PROPN
iajs-2382	7	6	and	and	CCONJ
iajs-2382	7	7	nasir	nasir	PROPN
iajs-2382	7	8	[	[	X
iajs-2382	7	9	1	1	NUM
iajs-2382	7	10	]	]	PUNCT
iajs-2382	7	11	.	.	PUNCT
iajs-2382	7	12	introduced	introduce	VERB
iajs-2382	7	13	the	the	DET
iajs-2382	7	14	notion	notion	NOUN
iajs-2382	7	15	ǐ	ǐ	X
iajs-2382	7	16	set	set	VERB
iajs-2382	7	17	in	in	ADP
iajs-2382	7	18	ideal	ideal	ADJ
iajs-2382	7	19	spaces	space	NOUN
iajs-2382	7	20	.	.	PUNCT
iajs-2382	8	1	a	a	DET
iajs-2382	8	2	set	set	NOUN
iajs-2382	8	3	of	of	ADP
iajs-2382	8	4	(	(	PUNCT
iajs-2382	8	5	ǐ	ǐ	PROPN
iajs-2382	8	6	)	)	PUNCT
iajs-2382	8	7	is	be	AUX
iajs-2382	8	8	ǐ	ǐ	PROPN
iajs-2382	8	9	set	set	VERB
iajs-2382	8	10	(	(	PUNCT
iajs-2382	8	11	artlessly	artlessly	ADV
iajs-2382	8	12	,	,	PUNCT
iajs-2382	8	13	ǐ	ǐ	PROPN
iajs-2382	8	14	)	)	PUNCT
iajs-2382	8	15	,	,	PUNCT
iajs-2382	8	16	when	when	SCONJ
iajs-2382	8	17	prerequisite	prerequisite	ADJ
iajs-2382	8	18	ǐ	ǐ	PROPN
iajs-2382	8	19	and	and	CCONJ
iajs-2382	8	20	is	be	AUX
iajs-2382	8	21	semi	semi	ADJ
iajs-2382	8	22	-	-	ADJ
iajs-2382	8	23	open	open	ADJ
iajs-2382	8	24	,	,	PUNCT
iajs-2382	8	25	leads	lead	VERB
iajs-2382	8	26	to	to	ADP
iajs-2382	8	27	(	(	PUNCT
iajs-2382	8	28	)	)	PUNCT
iajs-2382	8	29	ǐ	ǐ	X
iajs-2382	8	30	.	.	PUNCT
iajs-2382	9	1	so	so	ADV
iajs-2382	9	2	,	,	PUNCT
iajs-2382	9	3	the	the	DET
iajs-2382	9	4	set	set	NOUN
iajs-2382	9	5	is	be	AUX
iajs-2382	9	6	nameable	nameable	ADJ
iajs-2382	9	7	ǐ	ǐ	NOUN
iajs-2382	9	8	(	(	PUNCT
iajs-2382	9	9	artlessly	artlessly	ADV
iajs-2382	9	10	,	,	PUNCT
iajs-2382	9	11	ǐ	ǐ	PROPN
iajs-2382	9	12	)	)	PUNCT
iajs-2382	9	13	whenever	whenever	SCONJ
iajs-2382	9	14	is	be	AUX
iajs-2382	9	15	ǐ	ǐ	PROPN
iajs-2382	9	16	set	set	VERB
iajs-2382	9	17	.	.	PUNCT
iajs-2382	10	1	the	the	DET
iajs-2382	10	2	collection	collection	NOUN
iajs-2382	10	3	of	of	ADP
iajs-2382	10	4	all	all	DET
iajs-2382	10	5	ǐ	ǐ	PROPN
iajs-2382	10	6	(	(	PUNCT
iajs-2382	10	7	respectively	respectively	ADV
iajs-2382	10	8	,	,	PUNCT
iajs-2382	10	9	ǐ	ǐ	PROPN
iajs-2382	10	10	)	)	PUNCT
iajs-2382	10	11	sets	set	NOUN
iajs-2382	10	12	in	in	ADP
iajs-2382	10	13	(	(	PUNCT
iajs-2382	10	14	ǐ	ǐ	NOUN
iajs-2382	10	15	)	)	PUNCT
iajs-2382	10	16	notate	notate	NOUN
iajs-2382	10	17	as	as	ADP
iajs-2382	10	18	ǐ	ǐ	PROPN
iajs-2382	10	19	(	(	PUNCT
iajs-2382	10	20	)	)	PUNCT
iajs-2382	10	21	(	(	PUNCT
iajs-2382	10	22	respectively	respectively	ADV
iajs-2382	10	23	,	,	PUNCT
iajs-2382	10	24	ǐ	ǐ	PROPN
iajs-2382	10	25	(	(	PUNCT
iajs-2382	10	26	)	)	PUNCT
iajs-2382	10	27	)	)	PUNCT
iajs-2382	10	28	.	.	PUNCT
iajs-2382	11	1	every	every	DET
iajs-2382	11	2	open	open	ADJ
iajs-2382	11	3	set	set	NOUN
iajs-2382	11	4	in	in	ADP
iajs-2382	11	5	(	(	PUNCT
iajs-2382	11	6	)	)	PUNCT
iajs-2382	11	7	is	be	AUX
iajs-2382	11	8	ǐ	ǐ	PROPN
iajs-2382	11	9	in	in	ADP
iajs-2382	11	10	(	(	PUNCT
iajs-2382	11	11	ǐ)[1	ǐ)[1	PROPN
iajs-2382	11	12	]	]	PUNCT
iajs-2382	11	13	.	.	PUNCT
iajs-2382	12	1	and	and	CCONJ
iajs-2382	12	2	the	the	DET
iajs-2382	12	3	reverse	reverse	NOUN
iajs-2382	12	4	of	of	ADP
iajs-2382	12	5	this	this	DET
iajs-2382	12	6	statement	statement	NOUN
iajs-2382	12	7	is	be	AUX
iajs-2382	12	8	incorrect	incorrect	ADJ
iajs-2382	12	9	[	[	X
iajs-2382	12	10	1	1	NUM
iajs-2382	12	11	]	]	PUNCT
iajs-2382	12	12	.	.	PUNCT
iajs-2382	13	1	the	the	DET
iajs-2382	13	2	idea	idea	NOUN
iajs-2382	13	3	of	of	ADP
iajs-2382	13	4	ideals	ideal	NOUN
iajs-2382	13	5	on	on	ADP
iajs-2382	13	6	a	a	DET
iajs-2382	13	7	nonempty	nonempty	ADJ
iajs-2382	13	8	set	set	NOUN
iajs-2382	13	9	was	be	AUX
iajs-2382	13	10	started	start	VERB
iajs-2382	13	11	by	by	ADP
iajs-2382	13	12	kuratowski	kuratowski	NOUN
iajs-2382	13	13	in	in	ADP
iajs-2382	13	14	1933[2	1933[2	NUM
iajs-2382	13	15	]	]	PUNCT
iajs-2382	13	16	.	.	PUNCT
iajs-2382	14	1	the	the	DET
iajs-2382	14	2	ideal	ideal	ADJ
iajs-2382	14	3	ǐ	ǐ	PROPN
iajs-2382	14	4	on	on	ADP
iajs-2382	14	5	where	where	SCONJ
iajs-2382	14	6	ǐ	ǐ	PROPN
iajs-2382	14	7	(	(	PUNCT
iajs-2382	14	8	)	)	PUNCT
iajs-2382	14	9	that	that	PRON
iajs-2382	14	10	is	be	AUX
iajs-2382	14	11	valid	valid	ADJ
iajs-2382	14	12	the	the	DET
iajs-2382	14	13	preconditions	precondition	NOUN
iajs-2382	14	14	finite	finite	VERB
iajs-2382	14	15	additivity	additivity	NOUN
iajs-2382	14	16	(	(	PUNCT
iajs-2382	14	17	ǐ	ǐ	NOUN
iajs-2382	14	18	ǐ	ǐ	PROPN
iajs-2382	14	19	)	)	PUNCT
iajs-2382	14	20	and	and	CCONJ
iajs-2382	14	21	heredity	heredity	NOUN
iajs-2382	14	22	(	(	PUNCT
iajs-2382	14	23	ǐ	ǐ	NOUN
iajs-2382	14	24	ǐ	ǐ	PROPN
iajs-2382	14	25	)	)	PUNCT
iajs-2382	15	1	[	[	X
iajs-2382	15	2	2	2	NUM
iajs-2382	15	3	]	]	PUNCT
iajs-2382	15	4	.	.	PUNCT
iajs-2382	16	1	in	in	ADP
iajs-2382	16	2	1945	1945	NUM
iajs-2382	16	3	,	,	PUNCT
iajs-2382	16	4	vaidynathaswamy	vaidynathaswamy	NOUN
iajs-2382	16	5	[	[	X
iajs-2382	16	6	3	3	NUM
iajs-2382	16	7	]	]	PUNCT
iajs-2382	16	8	.	.	PUNCT
iajs-2382	16	9	was	be	AUX
iajs-2382	16	10	the	the	DET
iajs-2382	16	11	first	first	ADJ
iajs-2382	16	12	mathematician	mathematician	NOUN
iajs-2382	16	13	who	who	PRON
iajs-2382	16	14	uses	use	VERB
iajs-2382	16	15	the	the	DET
iajs-2382	16	16	idea	idea	NOUN
iajs-2382	16	17	of	of	ADP
iajs-2382	16	18	ideal	ideal	NOUN
iajs-2382	16	19	in	in	ADP
iajs-2382	16	20	science	science	NOUN
iajs-2382	16	21	of	of	ADP
iajs-2382	16	22	topology	topology	NOUN
iajs-2382	16	23	,	,	PUNCT
iajs-2382	16	24	which	which	PRON
iajs-2382	16	25	used	use	VERB
iajs-2382	16	26	to	to	PART
iajs-2382	16	27	create	create	VERB
iajs-2382	16	28	a	a	DET
iajs-2382	16	29	new	new	ADJ
iajs-2382	16	30	generalization	generalization	NOUN
iajs-2382	16	31	of	of	ADP
iajs-2382	16	32	topological	topological	ADJ
iajs-2382	16	33	spaces	space	NOUN
iajs-2382	16	34	,	,	PUNCT
iajs-2382	16	35	which	which	PRON
iajs-2382	16	36	is	be	AUX
iajs-2382	16	37	called	call	VERB
iajs-2382	16	38	ideal	ideal	ADJ
iajs-2382	16	39	topological	topological	ADJ
iajs-2382	16	40	space	space	NOUN
iajs-2382	16	41	and	and	CCONJ
iajs-2382	16	42	notate	notate	NOUN
iajs-2382	16	43	as	as	ADP
iajs-2382	16	44	(	(	PUNCT
iajs-2382	16	45	ǐ)[4	ǐ)[4	X
iajs-2382	16	46	]	]	PUNCT
iajs-2382	16	47	.	.	PUNCT
iajs-2382	17	1	since	since	SCONJ
iajs-2382	17	2	then	then	ADV
iajs-2382	17	3	,	,	PUNCT
iajs-2382	17	4	more	more	ADJ
iajs-2382	17	5	authors	author	NOUN
iajs-2382	17	6	are	be	AUX
iajs-2382	17	7	interested	interested	ADJ
iajs-2382	17	8	in	in	ADP
iajs-2382	17	9	this	this	DET
iajs-2382	17	10	scope	scope	NOUN
iajs-2382	17	11	of	of	ADP
iajs-2382	17	12	the	the	DET
iajs-2382	17	13	study	study	NOUN
iajs-2382	17	14	.	.	PUNCT
iajs-2382	18	1	many	many	ADJ
iajs-2382	18	2	results	result	NOUN
iajs-2382	18	3	have	have	AUX
iajs-2382	18	4	been	be	AUX
iajs-2382	18	5	achieved	achieve	VERB
iajs-2382	18	6	[	[	PUNCT
iajs-2382	18	7	5	5	NUM
iajs-2382	18	8	-	-	SYM
iajs-2382	18	9	8	8	NUM
iajs-2382	18	10	]	]	PUNCT
iajs-2382	18	11	.	.	PUNCT
iajs-2382	19	1	the	the	DET
iajs-2382	19	2	concept	concept	NOUN
iajs-2382	19	3	of	of	ADP
iajs-2382	19	4	"	"	PUNCT
iajs-2382	19	5	"	"	PUNCT
iajs-2382	19	6	was	be	AUX
iajs-2382	19	7	firstly	firstly	ADV
iajs-2382	19	8	offered	offer	VERB
iajs-2382	19	9	by	by	ADP
iajs-2382	19	10	n.levine	n.levine	PRON
iajs-2382	19	11	[	[	X
iajs-2382	19	12	9	9	NUM
iajs-2382	19	13	]	]	PUNCT
iajs-2382	19	14	.	.	PUNCT
iajs-2382	20	1	a	a	DET
iajs-2382	20	2	set	set	NOUN
iajs-2382	20	3	in	in	ADP
iajs-2382	20	4	(	(	PUNCT
iajs-2382	20	5	)	)	PUNCT
iajs-2382	20	6	is	be	AUX
iajs-2382	20	7	called	call	VERB
iajs-2382	20	8	if	if	SCONJ
iajs-2382	20	9	(	(	PUNCT
iajs-2382	20	10	(	(	PUNCT
iajs-2382	20	11	)	)	PUNCT
iajs-2382	20	12	)	)	PUNCT
iajs-2382	21	1	[	[	X
iajs-2382	21	2	9	9	NUM
iajs-2382	21	3	]	]	PUNCT
iajs-2382	21	4	.	.	PUNCT
iajs-2382	22	1	recently	recently	ADV
iajs-2382	22	2	,	,	PUNCT
iajs-2382	22	3	the	the	DET
iajs-2382	22	4	main	main	ADJ
iajs-2382	22	5	goal	goal	NOUN
iajs-2382	22	6	of	of	ADP
iajs-2382	22	7	our	our	PRON
iajs-2382	22	8	work	work	NOUN
iajs-2382	22	9	is	be	AUX
iajs-2382	22	10	to	to	PART
iajs-2382	22	11	construct	construct	VERB
iajs-2382	22	12	generalizations	generalization	NOUN
iajs-2382	22	13	of	of	ADP
iajs-2382	22	14	the	the	DET
iajs-2382	22	15	notion	notion	NOUN
iajs-2382	22	16	separation	separation	NOUN
iajs-2382	22	17	axioms	axiom	NOUN
iajs-2382	22	18	in	in	ADP
iajs-2382	22	19	topological	topological	ADJ
iajs-2382	22	20	space	space	NOUN
iajs-2382	22	21	by	by	ADP
iajs-2382	22	22	using	use	VERB
iajs-2382	22	23	the	the	DET
iajs-2382	22	24	notion	notion	NOUN
iajs-2382	22	25	of	of	ADP
iajs-2382	22	26	ǐ	ǐ	PROPN
iajs-2382	22	27	set	set	VERB
iajs-2382	22	28	.	.	PUNCT
iajs-2382	23	1	ibn	ibn	PROPN
iajs-2382	23	2	al	al	PROPN
iajs-2382	23	3	haitham	haitham	PROPN
iajs-2382	23	4	journal	journal	PROPN
iajs-2382	23	5	for	for	ADP
iajs-2382	23	6	pure	pure	ADJ
iajs-2382	23	7	and	and	CCONJ
iajs-2382	23	8	applied	apply	VERB
iajs-2382	23	9	science	science	NOUN
iajs-2382	23	10	journal	journal	PROPN
iajs-2382	23	11	homepage	homepage	NOUN
iajs-2382	23	12	:	:	PUNCT
iajs-2382	23	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2382	23	14	doi	doi	NOUN
iajs-2382	23	15	:	:	PUNCT
iajs-2382	23	16	10.30526/33.1.2382	10.30526/33.1.2382	PROPN
iajs-2382	23	17	department	department	NOUN
iajs-2382	23	18	of	of	ADP
iajs-2382	23	19	mathematics	mathematics	PROPN
iajs-2382	23	20	,	,	PUNCT
iajs-2382	23	21	college	college	NOUN
iajs-2382	23	22	of	of	ADP
iajs-2382	23	23	education	education	NOUN
iajs-2382	23	24	for	for	ADP
iajs-2382	23	25	pure	pure	ADJ
iajs-2382	23	26	sciences	science	NOUN
iajs-2382	23	27	,	,	PUNCT
iajs-2382	23	28	ibn	ibn	PROPN
iajs-2382	23	29	al	al	PROPN
iajs-2382	23	30	-	-	PUNCT
iajs-2382	23	31	haitham	haitham	PROPN
iajs-2382	23	32	,	,	PUNCT
iajs-2382	23	33	university	university	PROPN
iajs-2382	23	34	of	of	ADP
iajs-2382	23	35	baghdad	baghdad	PROPN
iajs-2382	23	36	,	,	PUNCT
iajs-2382	23	37	baghdad	baghdad	PROPN
iajs-2382	23	38	,	,	PUNCT
iajs-2382	23	39	iraq	iraq	PROPN
iajs-2382	23	40	.	.	PUNCT
iajs-2382	24	1	maherjaleel89@yahoo.com	maherjaleel89@yahoo.com	X
iajs-2382	24	2	ahmed_math06@yahoo.com	ahmed_math06@yahoo.com	NUM
iajs-2382	24	3	separation	separation	NOUN
iajs-2382	24	4	axioms	axiom	VERB
iajs-2382	24	5	via	via	ADP
iajs-2382	24	6	ǐ	ǐ	PROPN
iajs-2382	24	7	­	­	NUM
iajs-2382	24	8	semi­	semi­	NOUN
iajs-2382	24	9	g­	g­	NOUN
iajs-2382	24	10	open	open	ADJ
iajs-2382	24	11	sets	set	NOUN
iajs-2382	24	12	article	article	NOUN
iajs-2382	24	13	history	history	NOUN
iajs-2382	24	14	:	:	PUNCT
iajs-2382	24	15	received	receive	VERB
iajs-2382	24	16	2	2	NUM
iajs-2382	24	17	june	june	PROPN
iajs-2382	24	18	2019	2019	NUM
iajs-2382	24	19	,	,	PUNCT
iajs-2382	24	20	accepted	accept	VERB
iajs-2382	24	21	4	4	NUM
iajs-2382	24	22	july	july	PROPN
iajs-2382	24	23	2019	2019	NUM
iajs-2382	24	24	,	,	PUNCT
iajs-2382	24	25	publish	publish	VERB
iajs-2382	24	26	january	january	PROPN
iajs-2382	24	27	2020	2020	NUM
iajs-2382	24	28	.	.	PUNCT
iajs-2382	25	1	file:///c:/users/المجلة/desktop/عدد%20خاص/new%20folder/العدد%20كامل%20ومعدل/maherjaleel89@yahoo.com	file:///c:/users/المجلة/desktop/عدد%20خاص/new%20folder/العدد%20كامل%20ومعدل/maherjaleel89@yahoo.com	X
iajs-2382	25	2	file:///c:/users/المجلة/desktop/عدد%20خاص/new%20folder/العدد%20كامل%20ومعدل/ahmed_math06@yahoo.com	file:///c:/users/المجلة/desktop/عدد%20خاص/new%20folder/العدد%20كامل%20ومعدل/ahmed_math06@yahoo.com	X
iajs-2382	25	3	file:///c:/users/المجلة/desktop/عدد%20خاص/new%20folder/العدد%20كامل%20ومعدل/ahmed_math06@yahoo.com	file:///c:/users/المجلة/desktop/عدد%20خاص/new%20folder/العدد%20كامل%20ومعدل/ahmed_math06@yahoo.com	X
iajs-2382	26	1	758	758	NUM
iajs-2382	27	1	ibn	ibn	PROPN
iajs-2382	27	2	al	al	PROPN
iajs-2382	27	3	-	-	PUNCT
iajs-2382	27	4	haitham	haitham	PROPN
iajs-2382	27	5	jour	jour	X
iajs-2382	27	6	.	.	PROPN
iajs-2382	27	7	for	for	ADP
iajs-2382	27	8	pure	pure	ADJ
iajs-2382	27	9	&	&	CCONJ
iajs-2382	27	10	appl	appl	PROPN
iajs-2382	27	11	.	.	PUNCT
iajs-2382	28	1	sci	sci	PROPN
iajs-2382	28	2	.	.	PROPN
iajs-2382	29	1	33	33	NUM
iajs-2382	29	2	(	(	PUNCT
iajs-2382	29	3	1	1	NUM
iajs-2382	29	4	)	)	PUNCT
iajs-2382	29	5	2020	2020	NUM
iajs-2382	30	1	2	2	NUM
iajs-2382	30	2	.	.	PUNCT
iajs-2382	30	3	separation	separation	NOUN
iajs-2382	30	4	axioms	axiom	NOUN
iajs-2382	30	5	via	via	ADP
iajs-2382	30	6	ǐsg­open	ǐsg­open	ADJ
iajs-2382	30	7	sets	set	NOUN
iajs-2382	30	8	.	.	PUNCT
iajs-2382	31	1	here	here	ADV
iajs-2382	31	2	,	,	PUNCT
iajs-2382	31	3	we	we	PRON
iajs-2382	31	4	will	will	AUX
iajs-2382	31	5	present	present	VERB
iajs-2382	31	6	new	new	ADJ
iajs-2382	31	7	type	type	NOUN
iajs-2382	31	8	of	of	ADP
iajs-2382	31	9	separation	separation	NOUN
iajs-2382	31	10	axioms	axiom	NOUN
iajs-2382	31	11	in	in	ADP
iajs-2382	31	12	ideal	ideal	ADJ
iajs-2382	31	13	spaces	space	NOUN
iajs-2382	31	14	via	via	ADP
iajs-2382	31	15	ǐ	ǐ	PROPN
iajs-2382	31	16	set	set	VERB
iajs-2382	31	17	.	.	PUNCT
iajs-2382	32	1	also	also	ADV
iajs-2382	32	2	,	,	PUNCT
iajs-2382	32	3	relations	relation	NOUN
iajs-2382	32	4	between	between	ADP
iajs-2382	32	5	these	these	DET
iajs-2382	32	6	sorts	sort	NOUN
iajs-2382	32	7	are	be	AUX
iajs-2382	32	8	discussed	discuss	VERB
iajs-2382	32	9	.	.	PUNCT
iajs-2382	33	1	the	the	DET
iajs-2382	33	2	following	follow	VERB
iajs-2382	33	3	definition	definition	NOUN
iajs-2382	33	4	is	be	AUX
iajs-2382	33	5	for	for	ADP
iajs-2382	33	6	the	the	DET
iajs-2382	33	7	research	research	NOUN
iajs-2382	33	8	who	who	PRON
iajs-2382	33	9	did	do	VERB
iajs-2382	33	10	this	this	DET
iajs-2382	33	11	research	research	NOUN
iajs-2382	33	12	.	.	PUNCT
iajs-2382	34	1	definition	definition	NOUN
iajs-2382	34	2	2.1	2.1	NUM
iajs-2382	34	3	.	.	PUNCT
iajs-2382	35	1	the	the	DET
iajs-2382	35	2	triple	triple	ADJ
iajs-2382	35	3	(	(	PUNCT
iajs-2382	35	4	ǐ	ǐ	X
iajs-2382	35	5	)	)	PUNCT
iajs-2382	35	6	is	be	AUX
iajs-2382	35	7	called	call	VERB
iajs-2382	35	8	ǐ	ǐ	PROPN
iajs-2382	35	9	(	(	PUNCT
iajs-2382	35	10	shortly	shortly	ADV
iajs-2382	35	11	,	,	PUNCT
iajs-2382	35	12	ǐ	ǐ	PROPN
iajs-2382	35	13	)	)	PUNCT
iajs-2382	35	14	,	,	PUNCT
iajs-2382	35	15	if	if	SCONJ
iajs-2382	35	16	for	for	ADP
iajs-2382	35	17	any	any	DET
iajs-2382	35	18	element	element	NOUN
iajs-2382	35	19	,	,	PUNCT
iajs-2382	35	20	there	there	PRON
iajs-2382	35	21	is	be	VERB
iajs-2382	35	22	an	an	DET
iajs-2382	35	23	ǐ	ǐ	NOUN
iajs-2382	35	24	set	set	NOUN
iajs-2382	35	25	containing	contain	VERB
iajs-2382	35	26	only	only	ADV
iajs-2382	35	27	one	one	NUM
iajs-2382	35	28	of	of	ADP
iajs-2382	35	29	them	they	PRON
iajs-2382	35	30	.	.	PUNCT
iajs-2382	36	1	remark	remark	VERB
iajs-2382	36	2	2.2	2.2	NUM
iajs-2382	36	3	.	.	PUNCT
iajs-2382	37	1	if	if	SCONJ
iajs-2382	37	2	(	(	PUNCT
iajs-2382	37	3	)	)	PUNCT
iajs-2382	37	4	is	be	AUX
iajs-2382	37	5	then	then	ADV
iajs-2382	37	6	(	(	PUNCT
iajs-2382	37	7	ǐ	ǐ	X
iajs-2382	37	8	)	)	PUNCT
iajs-2382	37	9	ǐ	ǐ	PROPN
iajs-2382	37	10	.	.	PUNCT
iajs-2382	38	1	remark	remark	VERB
iajs-2382	38	2	2.3	2.3	NUM
iajs-2382	38	3	.	.	PUNCT
iajs-2382	39	1	the	the	DET
iajs-2382	39	2	below	below	ADJ
iajs-2382	39	3	phrases	phrase	NOUN
iajs-2382	39	4	are	be	AUX
iajs-2382	39	5	rewards	reward	NOUN
iajs-2382	39	6	;	;	PUNCT
iajs-2382	39	7	i.	i.	NOUN
iajs-2382	39	8	is	be	AUX
iajs-2382	39	9	ǐ	ǐ	PROPN
iajs-2382	39	10	.	.	PUNCT
iajs-2382	40	1	ii	ii	PROPN
iajs-2382	40	2	.	.	PUNCT
iajs-2382	41	1	for	for	ADP
iajs-2382	41	2	each	each	DET
iajs-2382	41	3	element	element	NOUN
iajs-2382	41	4	,	,	PUNCT
iajs-2382	41	5	there	there	PRON
iajs-2382	41	6	is	be	VERB
iajs-2382	41	7	an	an	DET
iajs-2382	41	8	ǐ	ǐ	NOUN
iajs-2382	41	9	set	set	NOUN
iajs-2382	41	10	containing	contain	VERB
iajs-2382	41	11	only	only	ADV
iajs-2382	41	12	one	one	NUM
iajs-2382	41	13	of	of	ADP
iajs-2382	41	14	them	they	PRON
iajs-2382	41	15	.	.	PUNCT
iajs-2382	42	1	definition	definition	NOUN
iajs-2382	42	2	2.4	2.4	NUM
iajs-2382	42	3	.	.	PUNCT
iajs-2382	43	1	(	(	PUNCT
iajs-2382	43	2	ǐ	ǐ	X
iajs-2382	43	3	)	)	PUNCT
iajs-2382	43	4	is	be	AUX
iajs-2382	43	5	called	call	VERB
iajs-2382	43	6	ǐ	ǐ	PROPN
iajs-2382	43	7	(	(	PUNCT
iajs-2382	43	8	artlessly	artlessly	ADV
iajs-2382	43	9	,	,	PUNCT
iajs-2382	43	10	ǐ	ǐ	PROPN
iajs-2382	43	11	)	)	PUNCT
iajs-2382	43	12	,	,	PUNCT
iajs-2382	43	13	if	if	SCONJ
iajs-2382	43	14	for	for	ADP
iajs-2382	43	15	any	any	DET
iajs-2382	43	16	elements	element	NOUN
iajs-2382	43	17	,	,	PUNCT
iajs-2382	43	18	there	there	PRON
iajs-2382	43	19	are	be	VERB
iajs-2382	43	20	ǐ	ǐ	PROPN
iajs-2382	43	21	sets	set	NOUN
iajs-2382	43	22	,	,	PUNCT
iajs-2382	43	23	whenever	whenever	SCONJ
iajs-2382	43	24	(	(	PUNCT
iajs-2382	43	25	)	)	PUNCT
iajs-2382	43	26	,	,	PUNCT
iajs-2382	43	27	(	(	PUNCT
iajs-2382	43	28	)	)	PUNCT
iajs-2382	43	29	.	.	PUNCT
iajs-2382	44	1	remark	remark	VERB
iajs-2382	44	2	2.5	2.5	NUM
iajs-2382	44	3	.	.	PUNCT
iajs-2382	45	1	if	if	SCONJ
iajs-2382	45	2	(	(	PUNCT
iajs-2382	45	3	)	)	PUNCT
iajs-2382	45	4	is	be	AUX
iajs-2382	45	5	then	then	ADV
iajs-2382	45	6	(	(	PUNCT
iajs-2382	45	7	ǐ	ǐ	X
iajs-2382	45	8	)	)	PUNCT
iajs-2382	45	9	ǐ	ǐ	PROPN
iajs-2382	45	10	.	.	PUNCT
iajs-2382	46	1	remark	remark	PROPN
iajs-2382	46	2	2.6	2.6	NUM
iajs-2382	46	3	.	.	PUNCT
iajs-2382	47	1	(	(	PUNCT
iajs-2382	47	2	ǐ	ǐ	X
iajs-2382	47	3	)	)	PUNCT
iajs-2382	47	4	is	be	AUX
iajs-2382	47	5	ǐ	ǐ	NOUN
iajs-2382	47	6	whenever	whenever	SCONJ
iajs-2382	47	7	it	it	PRON
iajs-2382	47	8	is	be	AUX
iajs-2382	47	9	an	an	DET
iajs-2382	47	10	ǐ	ǐ	NOUN
iajs-2382	47	11	.	.	PUNCT
iajs-2382	48	1	the	the	DET
iajs-2382	48	2	conclusions	conclusion	NOUN
iajs-2382	48	3	in	in	ADP
iajs-2382	48	4	remark	remark	NOUN
iajs-2382	48	5	2.6	2.6	NUM
iajs-2382	48	6	,	,	PUNCT
iajs-2382	48	7	is	be	AUX
iajs-2382	48	8	not	not	PART
iajs-2382	48	9	reversible	reversible	ADJ
iajs-2382	48	10	by	by	ADP
iajs-2382	48	11	example	example	NOUN
iajs-2382	48	12	below	below	ADV
iajs-2382	48	13	.	.	PUNCT
iajs-2382	49	1	example	example	NOUN
iajs-2382	49	2	2.7	2.7	NUM
iajs-2382	49	3	.	.	PUNCT
iajs-2382	50	1	the	the	DET
iajs-2382	50	2	ǐ	ǐ	PROPN
iajs-2382	50	3	(	(	PUNCT
iajs-2382	50	4	ǐ	ǐ	PROPN
iajs-2382	50	5	)	)	PUNCT
iajs-2382	50	6	(	(	PUNCT
iajs-2382	50	7	where	where	SCONJ
iajs-2382	50	8	*	*	PUNCT
iajs-2382	50	9	+	+	ADJ
iajs-2382	50	10	,	,	PUNCT
iajs-2382	50	11	*	*	PUNCT
iajs-2382	50	12	*	*	PUNCT
iajs-2382	51	1	+	+	PUNCT
iajs-2382	51	2	*	*	PUNCT
iajs-2382	52	1	+	+	PUNCT
iajs-2382	52	2	*	*	PUNCT
iajs-2382	52	3	+	+	PUNCT
iajs-2382	52	4	+	+	NUM
iajs-2382	52	5	and	and	CCONJ
iajs-2382	52	6	ǐ	ǐ	X
iajs-2382	52	7	*	*	PUNCT
iajs-2382	52	8	}	}	PUNCT
iajs-2382	52	9	)	)	PUNCT
iajs-2382	52	10	,	,	PUNCT
iajs-2382	52	11	is	be	AUX
iajs-2382	52	12	not	not	PART
iajs-2382	52	13	ǐ	ǐ	PROPN
iajs-2382	52	14	.	.	PUNCT
iajs-2382	53	1	remark	remark	VERB
iajs-2382	53	2	2.8	2.8	NUM
iajs-2382	53	3	.	.	PUNCT
iajs-2382	54	1	the	the	DET
iajs-2382	54	2	below	below	ADJ
iajs-2382	54	3	phrases	phrase	NOUN
iajs-2382	54	4	are	be	AUX
iajs-2382	54	5	rewards	reward	NOUN
iajs-2382	54	6	;	;	PUNCT
iajs-2382	54	7	i.	i.	NOUN
iajs-2382	54	8	is	be	AUX
iajs-2382	54	9	ǐ	ǐ	PROPN
iajs-2382	54	10	.	.	PUNCT
iajs-2382	55	1	ii	ii	PROPN
iajs-2382	55	2	.	.	PUNCT
iajs-2382	56	1	for	for	ADP
iajs-2382	56	2	each	each	DET
iajs-2382	56	3	elements	element	NOUN
iajs-2382	56	4	,	,	PUNCT
iajs-2382	56	5	there	there	PRON
iajs-2382	56	6	are	be	VERB
iajs-2382	56	7	two	two	NUM
iajs-2382	56	8	ǐ	ǐ	NOUN
iajs-2382	56	9	sets	set	NOUN
iajs-2382	56	10	and	and	CCONJ
iajs-2382	56	11	satisfy	satisfy	VERB
iajs-2382	56	12	(	(	PUNCT
iajs-2382	56	13	)	)	PUNCT
iajs-2382	56	14	and	and	CCONJ
iajs-2382	56	15	(	(	PUNCT
iajs-2382	56	16	)	)	PUNCT
iajs-2382	56	17	.	.	PUNCT
iajs-2382	57	1	remark	remark	PROPN
iajs-2382	57	2	2.9	2.9	NUM
iajs-2382	57	3	.	.	PUNCT
iajs-2382	58	1	for	for	ADP
iajs-2382	58	2	(	(	PUNCT
iajs-2382	58	3	ǐ	ǐ	PROPN
iajs-2382	58	4	)	)	PUNCT
iajs-2382	58	5	,	,	PUNCT
iajs-2382	58	6	if	if	SCONJ
iajs-2382	58	7	*	*	PUNCT
iajs-2382	58	8	+	+	PUNCT
iajs-2382	58	9	is	be	AUX
iajs-2382	58	10	ǐ	ǐ	PROPN
iajs-2382	58	11	set	set	VERB
iajs-2382	58	12	,	,	PUNCT
iajs-2382	58	13	then	then	ADV
iajs-2382	58	14	is	be	AUX
iajs-2382	58	15	ǐ	ǐ	PROPN
iajs-2382	58	16	.	.	PUNCT
iajs-2382	59	1	the	the	DET
iajs-2382	59	2	conclusions	conclusion	NOUN
iajs-2382	59	3	in	in	ADP
iajs-2382	59	4	remark	remark	NOUN
iajs-2382	59	5	2.9	2.9	NUM
iajs-2382	59	6	,	,	PUNCT
iajs-2382	59	7	is	be	AUX
iajs-2382	59	8	not	not	PART
iajs-2382	59	9	reversible	reversible	ADJ
iajs-2382	59	10	by	by	ADP
iajs-2382	59	11	example	example	NOUN
iajs-2382	59	12	below	below	ADV
iajs-2382	59	13	.	.	PUNCT
iajs-2382	60	1	example	example	NOUN
iajs-2382	60	2	2.10	2.10	NUM
iajs-2382	60	3	.	.	PUNCT
iajs-2382	61	1	given	give	VERB
iajs-2382	61	2	(	(	PUNCT
iajs-2382	61	3	ǐ	ǐ	PROPN
iajs-2382	61	4	)	)	PUNCT
iajs-2382	61	5	;	;	PUNCT
iajs-2382	61	6	(	(	PUNCT
iajs-2382	61	7	*	*	PUNCT
iajs-2382	61	8	+	+	ADJ
iajs-2382	61	9	,	,	PUNCT
iajs-2382	61	10	*	*	PUNCT
iajs-2382	61	11	+	+	PUNCT
iajs-2382	61	12	and	and	CCONJ
iajs-2382	61	13	ǐ	ǐ	X
iajs-2382	61	14	*	*	PUNCT
iajs-2382	61	15	*	*	PUNCT
iajs-2382	61	16	+	+	ADJ
iajs-2382	61	17	}	}	PUNCT
iajs-2382	61	18	)	)	PUNCT
iajs-2382	61	19	is	be	AUX
iajs-2382	61	20	ǐ	ǐ	NOUN
iajs-2382	61	21	,	,	PUNCT
iajs-2382	61	22	while	while	SCONJ
iajs-2382	61	23	*	*	PUNCT
iajs-2382	61	24	+	+	CCONJ
iajs-2382	61	25	is	be	AUX
iajs-2382	61	26	not	not	PART
iajs-2382	61	27	ǐ	ǐ	PROPN
iajs-2382	61	28	.	.	PUNCT
iajs-2382	62	1	definition	definition	NOUN
iajs-2382	62	2	2.11	2.11	NUM
iajs-2382	62	3	.	.	PUNCT
iajs-2382	63	1	(	(	PUNCT
iajs-2382	63	2	ǐ	ǐ	X
iajs-2382	63	3	)	)	PUNCT
iajs-2382	63	4	is	be	AUX
iajs-2382	63	5	called	call	VERB
iajs-2382	63	6	ǐ	ǐ	PROPN
iajs-2382	63	7	(	(	PUNCT
iajs-2382	63	8	artlessly	artlessly	ADV
iajs-2382	63	9	,	,	PUNCT
iajs-2382	63	10	ǐ	ǐ	PROPN
iajs-2382	63	11	)	)	PUNCT
iajs-2382	63	12	,	,	PUNCT
iajs-2382	63	13	if	if	SCONJ
iajs-2382	63	14	for	for	ADP
iajs-2382	63	15	any	any	DET
iajs-2382	63	16	elements	element	NOUN
iajs-2382	63	17	,	,	PUNCT
iajs-2382	63	18	there	there	PRON
iajs-2382	63	19	are	be	VERB
iajs-2382	63	20	ǐ	ǐ	PROPN
iajs-2382	63	21	sets	set	NOUN
iajs-2382	63	22	and	and	CCONJ
iajs-2382	63	23	satisfy	satisfy	VERB
iajs-2382	63	24	,	,	PUNCT
iajs-2382	63	25	and	and	CCONJ
iajs-2382	63	26	.	.	PUNCT
iajs-2382	63	27	remark	remark	VERB
iajs-2382	63	28	2.12	2.12	NUM
iajs-2382	63	29	.	.	PUNCT
iajs-2382	64	1	if	if	SCONJ
iajs-2382	64	2	(	(	PUNCT
iajs-2382	64	3	)	)	PUNCT
iajs-2382	64	4	is	be	AUX
iajs-2382	64	5	,	,	PUNCT
iajs-2382	64	6	then	then	ADV
iajs-2382	64	7	(	(	PUNCT
iajs-2382	64	8	ǐ	ǐ	X
iajs-2382	64	9	)	)	PUNCT
iajs-2382	64	10	is	be	AUX
iajs-2382	64	11	ǐ	ǐ	PROPN
iajs-2382	64	12	.	.	PUNCT
iajs-2382	65	1	remark	remark	PROPN
iajs-2382	65	2	2.13	2.13	NUM
iajs-2382	65	3	.	.	PUNCT
iajs-2382	66	1	a	a	DET
iajs-2382	66	2	space	space	NOUN
iajs-2382	66	3	(	(	PUNCT
iajs-2382	66	4	ǐ	ǐ	X
iajs-2382	66	5	)	)	PUNCT
iajs-2382	66	6	is	be	AUX
iajs-2382	66	7	ǐ	ǐ	NOUN
iajs-2382	66	8	whenever	whenever	SCONJ
iajs-2382	66	9	it	it	PRON
iajs-2382	66	10	is	be	AUX
iajs-2382	66	11	an	an	DET
iajs-2382	66	12	ǐ	ǐ	NOUN
iajs-2382	66	13	.	.	PUNCT
iajs-2382	67	1	the	the	DET
iajs-2382	67	2	conclusions	conclusion	NOUN
iajs-2382	67	3	in	in	ADP
iajs-2382	67	4	remark	remark	NOUN
iajs-2382	67	5	2.13	2.13	NUM
iajs-2382	67	6	,	,	PUNCT
iajs-2382	67	7	is	be	AUX
iajs-2382	67	8	not	not	PART
iajs-2382	67	9	reversible	reversible	ADJ
iajs-2382	67	10	by	by	ADP
iajs-2382	67	11	example	example	NOUN
iajs-2382	67	12	below	below	ADV
iajs-2382	67	13	.	.	PUNCT
iajs-2382	68	1	example	example	NOUN
iajs-2382	68	2	2.14	2.14	NUM
iajs-2382	68	3	.	.	PUNCT
iajs-2382	69	1	a	a	DET
iajs-2382	69	2	space	space	NOUN
iajs-2382	69	3	(	(	PUNCT
iajs-2382	69	4	)	)	PUNCT
iajs-2382	69	5	when	when	SCONJ
iajs-2382	69	6	the	the	DET
iajs-2382	69	7	set	set	NOUN
iajs-2382	69	8	of	of	ADP
iajs-2382	69	9	all	all	DET
iajs-2382	69	10	natural	natural	ADJ
iajs-2382	69	11	numbers	number	NOUN
iajs-2382	69	12	,	,	PUNCT
iajs-2382	69	13	cof	cof	PROPN
iajs-2382	69	14	is	be	AUX
iajs-2382	69	15	the	the	DET
iajs-2382	69	16	cofinite	cofinite	NOUN
iajs-2382	69	17	topology	topology	NOUN
iajs-2382	69	18	on	on	ADP
iajs-2382	69	19	and	and	CCONJ
iajs-2382	69	20	ǐ	ǐ	X
iajs-2382	69	21	*	*	PUNCT
iajs-2382	70	1	+	+	X
iajs-2382	70	2	.	.	X
iajs-2382	70	3	clearly	clearly	ADV
iajs-2382	70	4	,	,	PUNCT
iajs-2382	70	5	that	that	SCONJ
iajs-2382	70	6	(	(	PUNCT
iajs-2382	70	7	ǐ	ǐ	X
iajs-2382	70	8	)	)	PUNCT
iajs-2382	70	9	is	be	AUX
iajs-2382	70	10	ǐ	ǐ	PRON
iajs-2382	70	11	which	which	PRON
iajs-2382	70	12	is	be	AUX
iajs-2382	70	13	not	not	PART
iajs-2382	70	14	ǐ	ǐ	PROPN
iajs-2382	70	15	.	.	PUNCT
iajs-2382	71	1	we	we	PRON
iajs-2382	71	2	have	have	AUX
iajs-2382	71	3	previously	previously	ADV
iajs-2382	71	4	noted	note	VERB
iajs-2382	71	5	that	that	SCONJ
iajs-2382	71	6	is	be	AUX
iajs-2382	71	7	ǐ	ǐ	NOUN
iajs-2382	71	8	whenever	whenever	SCONJ
iajs-2382	71	9	it	it	PRON
iajs-2382	71	10	is	be	AUX
iajs-2382	71	11	(	(	PUNCT
iajs-2382	71	12	)	)	PUNCT
iajs-2382	71	13	.	.	PUNCT
iajs-2382	72	1	the	the	DET
iajs-2382	72	2	opposite	opposite	NOUN
iajs-2382	72	3	is	be	AUX
iajs-2382	72	4	not	not	PART
iajs-2382	72	5	generally	generally	ADV
iajs-2382	72	6	achieved	achieve	VERB
iajs-2382	72	7	by	by	ADP
iajs-2382	72	8	example	example	NOUN
iajs-2382	72	9	below	below	ADV
iajs-2382	72	10	.	.	PUNCT
iajs-2382	73	1	example	example	NOUN
iajs-2382	73	2	2.15	2.15	NUM
iajs-2382	73	3	.	.	PUNCT
iajs-2382	74	1	(	(	PUNCT
iajs-2382	74	2	ǐ	ǐ	X
iajs-2382	74	3	)	)	PUNCT
iajs-2382	74	4	is	be	AUX
iajs-2382	74	5	ǐ	ǐ	PROPN
iajs-2382	74	6	(	(	PUNCT
iajs-2382	74	7	)	)	PUNCT
iajs-2382	74	8	where	where	SCONJ
iajs-2382	74	9	*	*	PUNCT
iajs-2382	75	1	+	+	ADJ
iajs-2382	75	2	,	,	PUNCT
iajs-2382	75	3	*	*	PUNCT
iajs-2382	75	4	+	+	PUNCT
iajs-2382	75	5	and	and	CCONJ
iajs-2382	75	6	ǐ	ǐ	PRON
iajs-2382	75	7	is	be	AUX
iajs-2382	75	8	the	the	DET
iajs-2382	75	9	class	class	NOUN
iajs-2382	75	10	of	of	ADP
iajs-2382	75	11	all	all	DET
iajs-2382	75	12	sets	set	NOUN
iajs-2382	75	13	in	in	ADP
iajs-2382	75	14	.	.	PUNCT
iajs-2382	76	1	but	but	CCONJ
iajs-2382	76	2	the	the	DET
iajs-2382	76	3	space	space	NOUN
iajs-2382	76	4	(	(	PUNCT
iajs-2382	76	5	)	)	PUNCT
iajs-2382	76	6	is	be	AUX
iajs-2382	76	7	not	not	PART
iajs-2382	76	8	.	.	PUNCT
iajs-2382	77	1	the	the	DET
iajs-2382	77	2	following	follow	VERB
iajs-2382	77	3	chart	chart	NOUN
iajs-2382	77	4	shows	show	VERB
iajs-2382	77	5	the	the	DET
iajs-2382	77	6	relationships	relationship	NOUN
iajs-2382	77	7	among	among	ADP
iajs-2382	77	8	the	the	DET
iajs-2382	77	9	various	various	ADJ
iajs-2382	77	10	types	type	NOUN
iajs-2382	77	11	of	of	ADP
iajs-2382	77	12	notions	notion	NOUN
iajs-2382	77	13	of	of	ADP
iajs-2382	77	14	our	our	PRON
iajs-2382	77	15	previously	previously	ADV
iajs-2382	77	16	mentioned	mention	VERB
iajs-2382	77	17	.	.	PUNCT
iajs-2382	78	1	759	759	NUM
iajs-2382	78	2	ibn	ibn	PROPN
iajs-2382	78	3	al	al	PROPN
iajs-2382	78	4	-	-	PUNCT
iajs-2382	78	5	haitham	haitham	PROPN
iajs-2382	78	6	jour	jour	X
iajs-2382	78	7	.	.	PROPN
iajs-2382	78	8	for	for	ADP
iajs-2382	78	9	pure	pure	ADJ
iajs-2382	78	10	&	&	CCONJ
iajs-2382	78	11	appl	appl	PROPN
iajs-2382	78	12	.	.	PUNCT
iajs-2382	79	1	sci	sci	PROPN
iajs-2382	79	2	.	.	PROPN
iajs-2382	80	1	33	33	NUM
iajs-2382	80	2	(	(	PUNCT
iajs-2382	80	3	1	1	NUM
iajs-2382	80	4	)	)	PUNCT
iajs-2382	80	5	2020	2020	NUM
iajs-2382	80	6	3	3	NUM
iajs-2382	80	7	.	.	PUNCT
iajs-2382	80	8	separation	separation	NOUN
iajs-2382	80	9	axioms	axiom	NOUN
iajs-2382	80	10	via	via	ADP
iajs-2382	80	11	some	some	DET
iajs-2382	80	12	types	type	NOUN
iajs-2382	80	13	of	of	ADP
iajs-2382	80	14	functions	function	NOUN
iajs-2382	80	15	in	in	ADP
iajs-2382	80	16	this	this	DET
iajs-2382	80	17	portion	portion	NOUN
iajs-2382	80	18	we	we	PRON
iajs-2382	80	19	will	will	AUX
iajs-2382	80	20	review	review	VERB
iajs-2382	80	21	some	some	DET
iajs-2382	80	22	sorts	sort	NOUN
iajs-2382	80	23	of	of	ADP
iajs-2382	80	24	functions	function	NOUN
iajs-2382	80	25	which	which	PRON
iajs-2382	80	26	presented	present	VERB
iajs-2382	80	27	by	by	ADP
iajs-2382	80	28	abdel	abdel	PROPN
iajs-2382	80	29	karim	karim	PROPN
iajs-2382	80	30	and	and	CCONJ
iajs-2382	80	31	nasir	nasir	PROPN
iajs-2382	80	32	[	[	X
iajs-2382	80	33	1	1	NUM
iajs-2382	80	34	]	]	PUNCT
iajs-2382	80	35	.	.	PUNCT
iajs-2382	81	1	and	and	CCONJ
iajs-2382	81	2	study	study	VERB
iajs-2382	81	3	their	their	PRON
iajs-2382	81	4	impact	impact	NOUN
iajs-2382	81	5	on	on	ADP
iajs-2382	81	6	the	the	DET
iajs-2382	81	7	notions	notion	NOUN
iajs-2382	81	8	of	of	ADP
iajs-2382	81	9	separated	separate	VERB
iajs-2382	81	10	axioms	axiom	NOUN
iajs-2382	81	11	.	.	PUNCT
iajs-2382	82	1	definition	definition	NOUN
iajs-2382	82	2	3.1:[1	3.1:[1	NUM
iajs-2382	82	3	]	]	PUNCT
iajs-2382	82	4	.	.	PUNCT
iajs-2382	83	1	(	(	PUNCT
iajs-2382	83	2	ǐ	ǐ	X
iajs-2382	83	3	)	)	PUNCT
iajs-2382	83	4	(	(	PUNCT
iajs-2382	83	5	)	)	PUNCT
iajs-2382	83	6	is	be	AUX
iajs-2382	83	7	;	;	PUNCT
iajs-2382	83	8	i.	i.	PROPN
iajs-2382	83	9	,	,	PUNCT
iajs-2382	83	10	,	,	PUNCT
iajs-2382	83	11	if	if	SCONJ
iajs-2382	83	12	the	the	DET
iajs-2382	83	13	precondition	precondition	NOUN
iajs-2382	83	14	is	be	AUX
iajs-2382	83	15	ǐ	ǐ	PROPN
iajs-2382	83	16	in	in	ADV
iajs-2382	83	17	,	,	PUNCT
iajs-2382	83	18	leads	lead	VERB
iajs-2382	83	19	to	to	ADP
iajs-2382	83	20	(	(	PUNCT
iajs-2382	83	21	)	)	PUNCT
iajs-2382	83	22	is	be	AUX
iajs-2382	83	23	in	in	ADP
iajs-2382	83	24	.	.	PUNCT
iajs-2382	84	1	ii	ii	X
iajs-2382	84	2	.	.	PROPN
iajs-2382	84	3	,	,	PUNCT
iajs-2382	84	4	,	,	PUNCT
iajs-2382	84	5	if	if	SCONJ
iajs-2382	84	6	the	the	DET
iajs-2382	84	7	precondition	precondition	NOUN
iajs-2382	84	8	is	be	AUX
iajs-2382	84	9	open	open	ADJ
iajs-2382	84	10	in	in	ADP
iajs-2382	84	11	,	,	PUNCT
iajs-2382	84	12	leads	lead	VERB
iajs-2382	84	13	to	to	ADP
iajs-2382	84	14	(	(	PUNCT
iajs-2382	84	15	)	)	PUNCT
iajs-2382	84	16	is	be	AUX
iajs-2382	84	17	in	in	ADP
iajs-2382	84	18	iii	iii	NOUN
iajs-2382	84	19	.	.	PROPN
iajs-2382	84	20	,	,	PUNCT
iajs-2382	84	21	,	,	PUNCT
iajs-2382	84	22	if	if	SCONJ
iajs-2382	84	23	the	the	DET
iajs-2382	84	24	precondition	precondition	NOUN
iajs-2382	84	25	is	be	AUX
iajs-2382	84	26	ǐ	ǐ	PROPN
iajs-2382	84	27	in	in	ADV
iajs-2382	84	28	,	,	PUNCT
iajs-2382	84	29	leads	lead	VERB
iajs-2382	84	30	to	to	ADP
iajs-2382	84	31	(	(	PUNCT
iajs-2382	84	32	)	)	PUNCT
iajs-2382	84	33	is	be	AUX
iajs-2382	84	34	open	open	ADJ
iajs-2382	84	35	in	in	ADP
iajs-2382	84	36	.	.	PUNCT
iajs-2382	85	1	proposition	proposition	NOUN
iajs-2382	85	2	3.2	3.2	NUM
iajs-2382	85	3	:	:	PUNCT
iajs-2382	85	4	is	be	AUX
iajs-2382	85	5	ǐ	ǐ	PROPN
iajs-2382	85	6	(	(	PUNCT
iajs-2382	85	7	)	)	PUNCT
iajs-2382	85	8	and	and	CCONJ
iajs-2382	85	9	is	be	AUX
iajs-2382	85	10	a	a	DET
iajs-2382	85	11	surjective	surjective	ADJ
iajs-2382	85	12	from	from	ADP
iajs-2382	85	13	(	(	PUNCT
iajs-2382	85	14	ǐ	ǐ	PROPN
iajs-2382	85	15	)	)	PUNCT
iajs-2382	85	16	(	(	PUNCT
iajs-2382	85	17	)	)	PUNCT
iajs-2382	85	18	implies	imply	VERB
iajs-2382	85	19	is	be	AUX
iajs-2382	85	20	.	.	PUNCT
iajs-2382	86	1	proof	proof	NOUN
iajs-2382	86	2	:	:	PUNCT
iajs-2382	86	3	follows	follow	VERB
iajs-2382	86	4	from	from	ADP
iajs-2382	86	5	(	(	PUNCT
iajs-2382	86	6	)	)	PUNCT
iajs-2382	86	7	is	be	AUX
iajs-2382	86	8	in	in	ADP
iajs-2382	86	9	for	for	SCONJ
iajs-2382	86	10	all	all	DET
iajs-2382	86	11	ǐ	ǐ	NOUN
iajs-2382	86	12	set	set	VERB
iajs-2382	86	13	in	in	ADP
iajs-2382	86	14	.	.	PUNCT
iajs-2382	87	1	proposition	proposition	NOUN
iajs-2382	87	2	3.3	3.3	NUM
iajs-2382	87	3	:	:	PUNCT
iajs-2382	87	4	is	be	AUX
iajs-2382	87	5	(	(	PUNCT
iajs-2382	87	6	)	)	PUNCT
iajs-2382	87	7	and	and	CCONJ
iajs-2382	87	8	is	be	AUX
iajs-2382	87	9	a	a	DET
iajs-2382	87	10	surjective	surjective	ADJ
iajs-2382	87	11	from	from	ADP
iajs-2382	87	12	(	(	PUNCT
iajs-2382	87	13	ǐ	ǐ	PROPN
iajs-2382	87	14	)	)	PUNCT
iajs-2382	87	15	(	(	PUNCT
iajs-2382	87	16	)	)	PUNCT
iajs-2382	87	17	implies	imply	VERB
iajs-2382	87	18	is	be	AUX
iajs-2382	87	19	.	.	PUNCT
iajs-2382	88	1	proof	proof	NOUN
iajs-2382	88	2	:	:	PUNCT
iajs-2382	88	3	follows	follow	VERB
iajs-2382	88	4	from	from	ADP
iajs-2382	88	5	(	(	PUNCT
iajs-2382	88	6	)	)	PUNCT
iajs-2382	88	7	is	be	AUX
iajs-2382	88	8	in	in	ADP
iajs-2382	88	9	for	for	ADP
iajs-2382	88	10	all	all	PRON
iajs-2382	88	11	set	set	VERB
iajs-2382	88	12	in	in	ADP
iajs-2382	88	13	.	.	PUNCT
iajs-2382	89	1	proposition	proposition	NOUN
iajs-2382	89	2	3.4	3.4	NUM
iajs-2382	89	3	:	:	PUNCT
iajs-2382	89	4	is	be	AUX
iajs-2382	89	5	ǐ	ǐ	PROPN
iajs-2382	89	6	(	(	PUNCT
iajs-2382	89	7	)	)	PUNCT
iajs-2382	89	8	and	and	CCONJ
iajs-2382	89	9	is	be	AUX
iajs-2382	89	10	a	a	DET
iajs-2382	89	11	surjective	surjective	ADJ
iajs-2382	89	12	from	from	ADP
iajs-2382	89	13	(	(	PUNCT
iajs-2382	89	14	ǐ	ǐ	PROPN
iajs-2382	89	15	)	)	PUNCT
iajs-2382	89	16	(	(	PUNCT
iajs-2382	89	17	)	)	PUNCT
iajs-2382	89	18	implies	imply	VERB
iajs-2382	89	19	is	be	AUX
iajs-2382	89	20	.	.	PUNCT
iajs-2382	90	1	proof	proof	NOUN
iajs-2382	90	2	:	:	PUNCT
iajs-2382	90	3	follows	follow	VERB
iajs-2382	90	4	from	from	ADP
iajs-2382	90	5	(	(	PUNCT
iajs-2382	90	6	)	)	PUNCT
iajs-2382	90	7	is	be	AUX
iajs-2382	90	8	in	in	ADP
iajs-2382	90	9	for	for	SCONJ
iajs-2382	90	10	all	all	DET
iajs-2382	90	11	ǐ	ǐ	NOUN
iajs-2382	90	12	set	set	VERB
iajs-2382	90	13	in	in	ADP
iajs-2382	90	14	.	.	PUNCT
iajs-2382	91	1	remark	remark	NOUN
iajs-2382	91	2	3.5	3.5	NUM
iajs-2382	91	3	:	:	PUNCT
iajs-2382	91	4	if	if	SCONJ
iajs-2382	91	5	is	be	AUX
iajs-2382	91	6	bijective	bijective	ADJ
iajs-2382	91	7	open	open	ADJ
iajs-2382	91	8	function	function	NOUN
iajs-2382	91	9	from	from	ADP
iajs-2382	91	10	(	(	PUNCT
iajs-2382	91	11	)	)	PUNCT
iajs-2382	91	12	(	(	PUNCT
iajs-2382	91	13	)	)	PUNCT
iajs-2382	91	14	and	and	CCONJ
iajs-2382	91	15	is	be	AUX
iajs-2382	91	16	(	(	PUNCT
iajs-2382	91	17	)	)	PUNCT
iajs-2382	91	18	,	,	PUNCT
iajs-2382	91	19	then	then	ADV
iajs-2382	91	20	(	(	PUNCT
iajs-2382	91	21	)	)	PUNCT
iajs-2382	91	22	is	be	AUX
iajs-2382	91	23	,	,	PUNCT
iajs-2382	91	24	for	for	ADP
iajs-2382	91	25	any	any	DET
iajs-2382	91	26	ideal	ideal	NOUN
iajs-2382	91	27	on	on	ADP
iajs-2382	91	28	.	.	PUNCT
iajs-2382	92	1	definition	definition	NOUN
iajs-2382	92	2	3.6:[1	3.6:[1	NUM
iajs-2382	92	3	]	]	PUNCT
iajs-2382	92	4	.	.	PUNCT
iajs-2382	93	1	the	the	DET
iajs-2382	93	2	function	function	NOUN
iajs-2382	93	3	from	from	ADP
iajs-2382	93	4	(	(	PUNCT
iajs-2382	93	5	ǐ	ǐ	PROPN
iajs-2382	93	6	)	)	PUNCT
iajs-2382	93	7	(	(	PUNCT
iajs-2382	93	8	)	)	PUNCT
iajs-2382	93	9	is	be	AUX
iajs-2382	93	10	;	;	PUNCT
iajs-2382	93	11	i.	i.	PROPN
iajs-2382	93	12	,	,	PUNCT
iajs-2382	93	13	,	,	PUNCT
iajs-2382	93	14	if	if	SCONJ
iajs-2382	93	15	(	(	PUNCT
iajs-2382	93	16	)	)	PUNCT
iajs-2382	93	17	(	(	PUNCT
iajs-2382	93	18	)	)	PUNCT
iajs-2382	93	19	for	for	ADP
iajs-2382	93	20	every	every	PRON
iajs-2382	93	21	.	.	PUNCT
iajs-2382	94	1	ii	ii	PROPN
iajs-2382	94	2	.	.	PROPN
iajs-2382	94	3	,	,	PUNCT
iajs-2382	94	4	notate	notate	NOUN
iajs-2382	94	5	as	as	ADP
iajs-2382	94	6	function	function	NOUN
iajs-2382	94	7	,	,	PUNCT
iajs-2382	94	8	if	if	SCONJ
iajs-2382	94	9	(	(	PUNCT
iajs-2382	94	10	)	)	PUNCT
iajs-2382	94	11	for	for	ADP
iajs-2382	94	12	every	every	PRON
iajs-2382	94	13	(	(	PUNCT
iajs-2382	94	14	)	)	PUNCT
iajs-2382	94	15	.	.	PUNCT
iajs-2382	95	1	iii	iii	X
iajs-2382	95	2	.	.	PROPN
iajs-2382	95	3	,	,	PUNCT
iajs-2382	95	4	notate	notate	VERB
iajs-2382	95	5	as	as	ADP
iajs-2382	95	6	,	,	PUNCT
iajs-2382	95	7	if	if	SCONJ
iajs-2382	95	8	(	(	PUNCT
iajs-2382	95	9	)	)	PUNCT
iajs-2382	95	10	(	(	PUNCT
iajs-2382	95	11	)	)	PUNCT
iajs-2382	95	12	for	for	ADP
iajs-2382	95	13	every	every	PRON
iajs-2382	95	14	(	(	PUNCT
iajs-2382	95	15	)	)	PUNCT
iajs-2382	95	16	.	.	PUNCT
iajs-2382	96	1	proposition	proposition	NOUN
iajs-2382	96	2	3.7	3.7	NUM
iajs-2382	96	3	:	:	PUNCT
iajs-2382	96	4	if	if	SCONJ
iajs-2382	96	5	is	be	AUX
iajs-2382	96	6	(	(	PUNCT
iajs-2382	96	7	)	)	PUNCT
iajs-2382	96	8	and	and	CCONJ
iajs-2382	96	9	(	(	PUNCT
iajs-2382	96	10	ǐ	ǐ	NOUN
iajs-2382	96	11	)	)	PUNCT
iajs-2382	96	12	(	(	PUNCT
iajs-2382	96	13	)	)	PUNCT
iajs-2382	96	14	is	be	AUX
iajs-2382	96	15	an	an	DET
iajs-2382	96	16	injective	injective	NOUN
iajs-2382	96	17	then	then	ADV
iajs-2382	96	18	is	be	AUX
iajs-2382	96	19	ǐ	ǐ	PROPN
iajs-2382	96	20	.	.	PUNCT
iajs-2382	97	1	proof	proof	NOUN
iajs-2382	97	2	:	:	PUNCT
iajs-2382	97	3	since	since	SCONJ
iajs-2382	97	4	(	(	PUNCT
iajs-2382	97	5	)	)	PUNCT
iajs-2382	97	6	(	(	PUNCT
iajs-2382	97	7	)	)	PUNCT
iajs-2382	97	8	for	for	ADP
iajs-2382	97	9	all	all	PRON
iajs-2382	97	10	.	.	PUNCT
iajs-2382	98	1	𝑇	𝑇	PROPN
iajs-2382	98	2	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2382	98	3	𝑇	𝑇	PROPN
iajs-2382	98	4	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2382	98	5	𝑇	𝑇	PROPN
iajs-2382	98	6	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2382	98	7	ǐ𝑠𝑔	ǐ𝑠𝑔	PROPN
iajs-2382	98	8	𝑇	𝑇	PROPN
iajs-2382	98	9	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2382	98	10	ǐ𝑠𝑔	ǐ𝑠𝑔	PROPN
iajs-2382	98	11	𝑇	𝑇	PROPN
iajs-2382	98	12	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2382	98	13	ǐ𝑠𝑔	ǐ𝑠𝑔	PROPN
iajs-2382	98	14	𝑇	𝑇	PROPN
iajs-2382	98	15	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2382	98	16	761	761	NUM
iajs-2382	98	17	ibn	ibn	PROPN
iajs-2382	98	18	al	al	PROPN
iajs-2382	98	19	-	-	PUNCT
iajs-2382	98	20	haitham	haitham	PROPN
iajs-2382	98	21	jour	jour	X
iajs-2382	98	22	.	.	PROPN
iajs-2382	99	1	for	for	ADP
iajs-2382	99	2	pure	pure	ADJ
iajs-2382	99	3	&	&	CCONJ
iajs-2382	99	4	appl	appl	PROPN
iajs-2382	99	5	.	.	PUNCT
iajs-2382	100	1	sci	sci	PROPN
iajs-2382	100	2	.	.	PROPN
iajs-2382	101	1	33	33	NUM
iajs-2382	101	2	(	(	PUNCT
iajs-2382	101	3	1	1	NUM
iajs-2382	101	4	)	)	PUNCT
iajs-2382	101	5	2020	2020	NUM
iajs-2382	101	6	corollary	corollary	ADJ
iajs-2382	101	7	3.8	3.8	NUM
iajs-2382	101	8	:	:	PUNCT
iajs-2382	101	9	if	if	SCONJ
iajs-2382	101	10	is	be	AUX
iajs-2382	101	11	(	(	PUNCT
iajs-2382	101	12	)	)	PUNCT
iajs-2382	101	13	and	and	CCONJ
iajs-2382	101	14	(	(	PUNCT
iajs-2382	101	15	ǐ	ǐ	NOUN
iajs-2382	101	16	)	)	PUNCT
iajs-2382	101	17	(	(	PUNCT
iajs-2382	101	18	)	)	PUNCT
iajs-2382	101	19	is	be	AUX
iajs-2382	101	20	an	an	DET
iajs-2382	101	21	injective	injective	NOUN
iajs-2382	101	22	then	then	ADV
iajs-2382	101	23	is	be	AUX
iajs-2382	101	24	.	.	PUNCT
iajs-2382	102	1	proof	proof	NOUN
iajs-2382	102	2	:	:	PUNCT
iajs-2382	102	3	since	since	SCONJ
iajs-2382	102	4	,	,	PUNCT
iajs-2382	102	5	every	every	DET
iajs-2382	102	6	continuous	continuous	ADJ
iajs-2382	102	7	function	function	NOUN
iajs-2382	102	8	is	be	AUX
iajs-2382	102	9	[	[	X
iajs-2382	102	10	1	1	NUM
iajs-2382	102	11	]	]	PUNCT
iajs-2382	102	12	.	.	PUNCT
iajs-2382	103	1	and	and	CCONJ
iajs-2382	103	2	then	then	ADV
iajs-2382	103	3	proposition	proposition	VERB
iajs-2382	103	4	3.7	3.7	NUM
iajs-2382	103	5	is	be	AUX
iajs-2382	103	6	applicable	applicable	ADJ
iajs-2382	103	7	.	.	PUNCT
iajs-2382	104	1	proposition	proposition	NOUN
iajs-2382	104	2	3.9	3.9	NUM
iajs-2382	104	3	:	:	PUNCT
iajs-2382	104	4	if	if	SCONJ
iajs-2382	104	5	is	be	AUX
iajs-2382	104	6	(	(	PUNCT
iajs-2382	104	7	)	)	PUNCT
iajs-2382	104	8	and	and	CCONJ
iajs-2382	104	9	(	(	PUNCT
iajs-2382	104	10	ǐ	ǐ	NOUN
iajs-2382	104	11	)	)	PUNCT
iajs-2382	104	12	(	(	PUNCT
iajs-2382	104	13	)	)	PUNCT
iajs-2382	104	14	is	be	AUX
iajs-2382	104	15	an	an	DET
iajs-2382	104	16	injective	injective	NOUN
iajs-2382	104	17	then	then	ADV
iajs-2382	104	18	is	be	AUX
iajs-2382	104	19	.	.	PUNCT
iajs-2382	105	1	proof	proof	NOUN
iajs-2382	105	2	:	:	PUNCT
iajs-2382	105	3	follows	follow	VERB
iajs-2382	105	4	from	from	ADP
iajs-2382	105	5	,	,	PUNCT
iajs-2382	105	6	(	(	PUNCT
iajs-2382	105	7	)	)	PUNCT
iajs-2382	105	8	for	for	ADP
iajs-2382	105	9	all	all	PRON
iajs-2382	105	10	(	(	PUNCT
iajs-2382	105	11	)	)	PUNCT
iajs-2382	105	12	.	.	PUNCT
iajs-2382	106	1	proposition	proposition	NOUN
iajs-2382	106	2	3.10	3.10	NUM
iajs-2382	106	3	:	:	PUNCT
iajs-2382	106	4	if	if	SCONJ
iajs-2382	106	5	is	be	AUX
iajs-2382	106	6	(	(	PUNCT
iajs-2382	106	7	)	)	PUNCT
iajs-2382	106	8	and	and	CCONJ
iajs-2382	106	9	(	(	PUNCT
iajs-2382	106	10	ǐ	ǐ	NOUN
iajs-2382	106	11	)	)	PUNCT
iajs-2382	106	12	(	(	PUNCT
iajs-2382	106	13	)	)	PUNCT
iajs-2382	106	14	is	be	AUX
iajs-2382	106	15	an	an	DET
iajs-2382	106	16	injective	injective	NOUN
iajs-2382	106	17	then	then	ADV
iajs-2382	106	18	is	be	AUX
iajs-2382	106	19	.	.	PUNCT
iajs-2382	107	1	proof	proof	NOUN
iajs-2382	107	2	:	:	PUNCT
iajs-2382	107	3	since	since	SCONJ
iajs-2382	107	4	(	(	PUNCT
iajs-2382	107	5	)	)	PUNCT
iajs-2382	107	6	(	(	PUNCT
iajs-2382	107	7	)	)	PUNCT
iajs-2382	107	8	for	for	ADP
iajs-2382	107	9	all	all	PRON
iajs-2382	107	10	(	(	PUNCT
iajs-2382	107	11	)	)	PUNCT
iajs-2382	107	12	.	.	PUNCT
iajs-2382	108	1	4	4	X
iajs-2382	108	2	.	.	X
iajs-2382	108	3	i­	i­	NOUN
iajs-2382	108	4	semi­	semi­	PROPN
iajs-2382	108	5	g­	g­	PROPN
iajs-2382	108	6	convergence	convergence	NOUN
iajs-2382	108	7	sequence	sequence	NOUN
iajs-2382	108	8	sequences	sequence	NOUN
iajs-2382	108	9	are	be	AUX
iajs-2382	108	10	one	one	NUM
iajs-2382	108	11	of	of	ADP
iajs-2382	108	12	important	important	ADJ
iajs-2382	108	13	topics	topic	NOUN
iajs-2382	108	14	in	in	ADP
iajs-2382	108	15	all	all	DET
iajs-2382	108	16	branches	branch	NOUN
iajs-2382	108	17	of	of	ADP
iajs-2382	108	18	mathematics	mathematic	NOUN
iajs-2382	108	19	,	,	PUNCT
iajs-2382	108	20	especially	especially	ADV
iajs-2382	108	21	mathematical	mathematical	ADJ
iajs-2382	108	22	analysis	analysis	NOUN
iajs-2382	108	23	and	and	CCONJ
iajs-2382	108	24	topology	topology	NOUN
iajs-2382	108	25	.	.	PUNCT
iajs-2382	109	1	so	so	ADV
iajs-2382	109	2	the	the	DET
iajs-2382	109	3	convergence	convergence	NOUN
iajs-2382	109	4	is	be	AUX
iajs-2382	109	5	the	the	DET
iajs-2382	109	6	important	important	ADJ
iajs-2382	109	7	property	property	NOUN
iajs-2382	109	8	for	for	ADP
iajs-2382	109	9	the	the	DET
iajs-2382	109	10	sequence	sequence	NOUN
iajs-2382	109	11	[	[	X
iajs-2382	109	12	10	10	NUM
iajs-2382	109	13	,	,	PUNCT
iajs-2382	109	14	11	11	NUM
iajs-2382	109	15	]	]	PUNCT
iajs-2382	109	16	.	.	PUNCT
iajs-2382	110	1	in	in	ADP
iajs-2382	110	2	this	this	DET
iajs-2382	110	3	paragraph	paragraph	NOUN
iajs-2382	110	4	,	,	PUNCT
iajs-2382	110	5	we	we	PRON
iajs-2382	110	6	will	will	AUX
iajs-2382	110	7	use	use	VERB
iajs-2382	110	8	the	the	DET
iajs-2382	110	9	notion	notion	NOUN
iajs-2382	110	10	of	of	ADP
iajs-2382	110	11	set	set	NOUN
iajs-2382	110	12	to	to	PART
iajs-2382	110	13	create	create	VERB
iajs-2382	110	14	new	new	ADJ
iajs-2382	110	15	class	class	NOUN
iajs-2382	110	16	of	of	ADP
iajs-2382	110	17	convergence	convergence	NOUN
iajs-2382	110	18	.	.	PUNCT
iajs-2382	111	1	definition	definition	NOUN
iajs-2382	111	2	4.1	4.1	NUM
iajs-2382	111	3	.	.	PUNCT
iajs-2382	112	1	given	give	VERB
iajs-2382	112	2	a	a	DET
iajs-2382	112	3	space	space	NOUN
iajs-2382	112	4	(	(	PUNCT
iajs-2382	112	5	ǐ	ǐ	NOUN
iajs-2382	112	6	)	)	PUNCT
iajs-2382	112	7	where	where	SCONJ
iajs-2382	112	8	and	and	CCONJ
iajs-2382	112	9	the	the	DET
iajs-2382	112	10	sequence	sequence	NOUN
iajs-2382	112	11	(	(	PUNCT
iajs-2382	112	12	)	)	PUNCT
iajs-2382	112	13	in	in	ADP
iajs-2382	112	14	.	.	PUNCT
iajs-2382	113	1	then	then	ADV
iajs-2382	113	2	(	(	PUNCT
iajs-2382	113	3	)	)	PUNCT
iajs-2382	113	4	is	be	AUX
iajs-2382	113	5	called	call	VERB
iajs-2382	113	6	ǐ	ǐ	PROPN
iajs-2382	113	7	to	to	ADP
iajs-2382	113	8	(	(	PUNCT
iajs-2382	113	9	artlessly	artlessly	ADV
iajs-2382	113	10	,	,	PUNCT
iajs-2382	113	11	)	)	PUNCT
iajs-2382	113	12	if	if	SCONJ
iajs-2382	113	13	for	for	SCONJ
iajs-2382	113	14	every	every	DET
iajs-2382	113	15	ǐsg­open	ǐsg­open	ADJ
iajs-2382	113	16	set	set	NOUN
iajs-2382	113	17	contained	contain	VERB
iajs-2382	113	18	,	,	PUNCT
iajs-2382	113	19	where	where	SCONJ
iajs-2382	113	20	.	.	PUNCT
iajs-2382	114	1	a	a	DET
iajs-2382	114	2	sequence	sequence	NOUN
iajs-2382	114	3	(	(	PUNCT
iajs-2382	114	4	)	)	PUNCT
iajs-2382	114	5	is	be	AUX
iajs-2382	114	6	nameable	nameable	ADJ
iajs-2382	114	7	ǐ	ǐ	NOUN
iajs-2382	114	8	if	if	SCONJ
iajs-2382	114	9	it	it	PRON
iajs-2382	114	10	is	be	AUX
iajs-2382	114	11	not	not	PART
iajs-2382	114	12	ǐ	ǐ	PROPN
iajs-2382	114	13	.	.	PUNCT
iajs-2382	115	1	proposition	proposition	NOUN
iajs-2382	115	2	4.2	4.2	NUM
iajs-2382	115	3	.	.	PUNCT
iajs-2382	116	1	if	if	SCONJ
iajs-2382	116	2	(	(	PUNCT
iajs-2382	116	3	ǐ	ǐ	X
iajs-2382	116	4	)	)	PUNCT
iajs-2382	116	5	is	be	AUX
iajs-2382	116	6	ǐ	ǐ	PRON
iajs-2382	116	7	then	then	ADV
iajs-2382	116	8	every	every	DET
iajs-2382	116	9	ǐ	ǐ	NOUN
iajs-2382	116	10	sequence	sequence	NOUN
iajs-2382	116	11	in	in	ADV
iajs-2382	116	12	has	have	VERB
iajs-2382	116	13	only	only	ADV
iajs-2382	116	14	one	one	NUM
iajs-2382	116	15	limit	limit	NOUN
iajs-2382	116	16	point	point	NOUN
iajs-2382	116	17	.	.	PUNCT
iajs-2382	117	1	proof	proof	NOUN
iajs-2382	117	2	:	:	PUNCT
iajs-2382	117	3	if	if	SCONJ
iajs-2382	117	4	we	we	PRON
iajs-2382	117	5	consider	consider	VERB
iajs-2382	117	6	(	(	PUNCT
iajs-2382	117	7	)	)	PUNCT
iajs-2382	117	8	is	be	AUX
iajs-2382	117	9	a	a	DET
iajs-2382	117	10	seq	seq	NOUN
iajs-2382	117	11	.	.	PUNCT
iajs-2382	118	1	in	in	ADP
iajs-2382	118	2	and	and	CCONJ
iajs-2382	118	3	so	so	ADV
iajs-2382	118	4	;	;	PUNCT
iajs-2382	118	5	where	where	SCONJ
iajs-2382	118	6	.	.	PUNCT
iajs-2382	119	1	since	since	SCONJ
iajs-2382	119	2	is	be	AUX
iajs-2382	119	3	ǐ	ǐ	PROPN
iajs-2382	119	4	,	,	PUNCT
iajs-2382	119	5	then	then	ADV
iajs-2382	119	6	there	there	PRON
iajs-2382	119	7	are	be	VERB
iajs-2382	119	8	disjoint	disjoint	ADJ
iajs-2382	119	9	ǐ	ǐ	X
iajs-2382	119	10	-open	-open	NOUN
iajs-2382	119	11	sets	set	VERB
iajs-2382	119	12	such	such	ADJ
iajs-2382	119	13	that	that	PRON
iajs-2382	119	14	and	and	CCONJ
iajs-2382	119	15	.	.	PUNCT
iajs-2382	120	1	now	now	ADV
iajs-2382	120	2	,	,	PUNCT
iajs-2382	120	3	since	since	SCONJ
iajs-2382	120	4	and	and	CCONJ
iajs-2382	120	5	implies	imply	VERB
iajs-2382	120	6	;	;	PUNCT
iajs-2382	120	7	so	so	CCONJ
iajs-2382	120	8	,	,	PUNCT
iajs-2382	120	9	and	and	CCONJ
iajs-2382	120	10	implies	imply	VERB
iajs-2382	120	11	;	;	PUNCT
iajs-2382	120	12	leads	lead	VERB
iajs-2382	120	13	to	to	ADP
iajs-2382	120	14	where	where	SCONJ
iajs-2382	120	15	that	that	DET
iajs-2382	120	16	contradiction	contradiction	NOUN
iajs-2382	120	17	.	.	PUNCT
iajs-2382	121	1	the	the	DET
iajs-2382	121	2	precondition	precondition	NOUN
iajs-2382	121	3	that	that	SCONJ
iajs-2382	121	4	a	a	DET
iajs-2382	121	5	space	space	NOUN
iajs-2382	121	6	is	be	AUX
iajs-2382	121	7	ǐ	ǐ	NOUN
iajs-2382	121	8	is	be	AUX
iajs-2382	121	9	very	very	ADV
iajs-2382	121	10	requisite	requisite	ADJ
iajs-2382	121	11	to	to	PART
iajs-2382	121	12	make	make	VERB
iajs-2382	121	13	proposition	proposition	NOUN
iajs-2382	121	14	4.2	4.2	NUM
iajs-2382	121	15	,	,	PUNCT
iajs-2382	121	16	is	be	AUX
iajs-2382	121	17	valid	valid	ADJ
iajs-2382	121	18	.	.	PUNCT
iajs-2382	121	19	example	example	NOUN
iajs-2382	122	1	4.3	4.3	NUM
iajs-2382	122	2	.	.	PUNCT
iajs-2382	123	1	consider	consider	VERB
iajs-2382	123	2	(	(	PUNCT
iajs-2382	123	3	ǐ	ǐ	NOUN
iajs-2382	123	4	)	)	PUNCT
iajs-2382	124	1	where	where	SCONJ
iajs-2382	124	2	*	*	PUNCT
iajs-2382	124	3	+	+	ADJ
iajs-2382	124	4	,	,	PUNCT
iajs-2382	124	5	*	*	PUNCT
iajs-2382	124	6	+	+	PUNCT
iajs-2382	124	7	and	and	CCONJ
iajs-2382	124	8	ǐ	ǐ	X
iajs-2382	124	9	*	*	PUNCT
iajs-2382	125	1	+	+	X
iajs-2382	125	2	.	.	PUNCT
iajs-2382	125	3	obviously	obviously	ADV
iajs-2382	125	4	;	;	PUNCT
iajs-2382	125	5	the	the	DET
iajs-2382	125	6	sequence	sequence	NOUN
iajs-2382	125	7	(	(	PUNCT
iajs-2382	125	8	)	)	PUNCT
iajs-2382	125	9	in	in	ADP
iajs-2382	125	10	,	,	PUNCT
iajs-2382	125	11	where	where	SCONJ
iajs-2382	125	12	for	for	ADP
iajs-2382	125	13	all	all	PRON
iajs-2382	125	14	,	,	PUNCT
iajs-2382	125	15	has	have	VERB
iajs-2382	125	16	more	more	ADJ
iajs-2382	125	17	than	than	ADP
iajs-2382	125	18	one	one	NUM
iajs-2382	125	19	limit	limit	NOUN
iajs-2382	125	20	point	point	NOUN
iajs-2382	125	21	;	;	PUNCT
iajs-2382	125	22	that	that	SCONJ
iajs-2382	125	23	,	,	PUNCT
iajs-2382	125	24	and	and	CCONJ
iajs-2382	125	25	.	.	PUNCT
iajs-2382	126	1	proposition	proposition	NOUN
iajs-2382	126	2	4.4	4.4	NUM
iajs-2382	126	3	.	.	PUNCT
iajs-2382	127	1	if	if	SCONJ
iajs-2382	127	2	a	a	DET
iajs-2382	127	3	sequence	sequence	NOUN
iajs-2382	127	4	(	(	PUNCT
iajs-2382	127	5	)	)	PUNCT
iajs-2382	127	6	is	be	AUX
iajs-2382	127	7	ǐ	ǐ	PROPN
iajs-2382	127	8	to	to	ADP
iajs-2382	127	9	in	in	ADP
iajs-2382	127	10	an	an	DET
iajs-2382	127	11	ideal	ideal	ADJ
iajs-2382	127	12	space	space	NOUN
iajs-2382	127	13	,	,	PUNCT
iajs-2382	127	14	then	then	ADV
iajs-2382	127	15	it	it	PRON
iajs-2382	127	16	is	be	AUX
iajs-2382	127	17	convergent	convergent	ADJ
iajs-2382	127	18	to	to	PART
iajs-2382	127	19	.	.	PUNCT
iajs-2382	128	1	proof	proof	NOUN
iajs-2382	128	2	.	.	PUNCT
iajs-2382	129	1	since	since	SCONJ
iajs-2382	129	2	every	every	DET
iajs-2382	129	3	open	open	ADJ
iajs-2382	129	4	set	set	NOUN
iajs-2382	129	5	in	in	ADP
iajs-2382	129	6	(	(	PUNCT
iajs-2382	129	7	ǐ)is	ǐ)is	PROPN
iajs-2382	129	8	ǐsg­open	ǐsg­open	ADJ
iajs-2382	129	9	,	,	PUNCT
iajs-2382	129	10	then	then	ADV
iajs-2382	129	11	the	the	DET
iajs-2382	129	12	proof	proof	NOUN
iajs-2382	129	13	is	be	AUX
iajs-2382	129	14	over	over	ADV
iajs-2382	129	15	.	.	PUNCT
iajs-2382	130	1	the	the	DET
iajs-2382	130	2	meaningfulness	meaningfulness	NOUN
iajs-2382	130	3	in	in	ADP
iajs-2382	130	4	proposition	proposition	NOUN
iajs-2382	130	5	4.4	4.4	NUM
iajs-2382	130	6	,	,	PUNCT
iajs-2382	130	7	is	be	AUX
iajs-2382	130	8	not	not	PART
iajs-2382	130	9	reversible	reversible	ADJ
iajs-2382	130	10	,	,	PUNCT
iajs-2382	130	11	in	in	ADP
iajs-2382	130	12	general	general	ADJ
iajs-2382	130	13	.	.	PUNCT
iajs-2382	130	14	example	example	NOUN
iajs-2382	131	1	4.5	4.5	NUM
iajs-2382	131	2	.	.	PUNCT
iajs-2382	132	1	for	for	ADP
iajs-2382	132	2	an	an	DET
iajs-2382	132	3	ideal	ideal	ADJ
iajs-2382	132	4	space	space	NOUN
iajs-2382	132	5	(	(	PUNCT
iajs-2382	132	6	ǐ	ǐ	PROPN
iajs-2382	132	7	)	)	PUNCT
iajs-2382	132	8	,	,	PUNCT
iajs-2382	132	9	where	where	SCONJ
iajs-2382	132	10	,	,	PUNCT
iajs-2382	132	11	*	*	PUNCT
iajs-2382	132	12	+	+	PUNCT
iajs-2382	132	13	and	and	CCONJ
iajs-2382	132	14	ǐ	ǐ	PROPN
iajs-2382	132	15	(	(	PUNCT
iajs-2382	132	16	)	)	PUNCT
iajs-2382	132	17	.	.	PUNCT
iajs-2382	133	1	the	the	DET
iajs-2382	133	2	sequence	sequence	NOUN
iajs-2382	133	3	(	(	PUNCT
iajs-2382	133	4	)	)	PUNCT
iajs-2382	133	5	,	,	PUNCT
iajs-2382	133	6	where	where	SCONJ
iajs-2382	133	7	,	,	PUNCT
iajs-2382	133	8	is	be	AUX
iajs-2382	133	9	convergent	convergent	ADJ
iajs-2382	133	10	to	to	PART
iajs-2382	133	11	which	which	PRON
iajs-2382	133	12	is	be	AUX
iajs-2382	133	13	notǐ	notǐ	NOUN
iajs-2382	133	14	.	.	PUNCT
iajs-2382	134	1	proposition	proposition	NOUN
iajs-2382	134	2	4.6	4.6	NUM
iajs-2382	134	3	.	.	PUNCT
iajs-2382	135	1	let	let	AUX
iajs-2382	135	2	be	be	AUX
iajs-2382	135	3	function	function	NOUN
iajs-2382	135	4	from	from	ADP
iajs-2382	135	5	and	and	CCONJ
iajs-2382	135	6	(	(	PUNCT
iajs-2382	135	7	)	)	PUNCT
iajs-2382	135	8	be	be	AUX
iajs-2382	135	9	a	a	DET
iajs-2382	135	10	sequence	sequence	NOUN
iajs-2382	135	11	in	in	ADP
iajs-2382	135	12	,	,	PUNCT
iajs-2382	135	13	(	(	PUNCT
iajs-2382	135	14	)	)	PUNCT
iajs-2382	135	15	(	(	PUNCT
iajs-2382	135	16	)	)	PUNCT
iajs-2382	135	17	in	in	ADP
iajs-2382	135	18	whenever	whenever	SCONJ
iajs-2382	135	19	in	in	ADV
iajs-2382	135	20	.	.	PUNCT
iajs-2382	136	1	767	767	NUM
iajs-2382	136	2	ibn	ibn	PROPN
iajs-2382	136	3	al	al	PROPN
iajs-2382	136	4	-	-	PUNCT
iajs-2382	136	5	haitham	haitham	PROPN
iajs-2382	136	6	jour	jour	X
iajs-2382	136	7	.	.	PROPN
iajs-2382	136	8	for	for	ADP
iajs-2382	136	9	pure	pure	ADJ
iajs-2382	136	10	&	&	CCONJ
iajs-2382	136	11	appl	appl	PROPN
iajs-2382	136	12	.	.	PUNCT
iajs-2382	137	1	sci	sci	PROPN
iajs-2382	137	2	.	.	PROPN
iajs-2382	138	1	33	33	NUM
iajs-2382	138	2	(	(	PUNCT
iajs-2382	138	3	1	1	NUM
iajs-2382	138	4	)	)	PUNCT
iajs-2382	138	5	2020	2020	NUM
iajs-2382	138	6	proposition	proposition	NOUN
iajs-2382	138	7	4.7	4.7	NUM
iajs-2382	138	8	.	.	PUNCT
iajs-2382	139	1	let	let	AUX
iajs-2382	139	2	be	be	AUX
iajs-2382	139	3	function	function	NOUN
iajs-2382	139	4	from	from	ADP
iajs-2382	139	5	and	and	CCONJ
iajs-2382	139	6	(	(	PUNCT
iajs-2382	139	7	)	)	PUNCT
iajs-2382	139	8	be	be	AUX
iajs-2382	139	9	a	a	DET
iajs-2382	139	10	sequence	sequence	NOUN
iajs-2382	139	11	in	in	ADP
iajs-2382	139	12	.	.	PUNCT
iajs-2382	140	1	(	(	PUNCT
iajs-2382	140	2	)	)	PUNCT
iajs-2382	140	3	(	(	PUNCT
iajs-2382	140	4	)	)	PUNCT
iajs-2382	140	5	in	in	ADP
iajs-2382	140	6	whenever	whenever	SCONJ
iajs-2382	140	7	in	in	ADV
iajs-2382	140	8	.	.	PUNCT
iajs-2382	141	1	proposition	proposition	NOUN
iajs-2382	141	2	4.8	4.8	NUM
iajs-2382	141	3	.	.	PUNCT
iajs-2382	142	1	let	let	AUX
iajs-2382	142	2	be	be	AUX
iajs-2382	142	3	function	function	NOUN
iajs-2382	142	4	from	from	ADP
iajs-2382	142	5	and	and	CCONJ
iajs-2382	142	6	(	(	PUNCT
iajs-2382	142	7	)	)	PUNCT
iajs-2382	142	8	be	be	AUX
iajs-2382	142	9	a	a	DET
iajs-2382	142	10	sequence	sequence	NOUN
iajs-2382	142	11	in	in	ADP
iajs-2382	142	12	,	,	PUNCT
iajs-2382	142	13	(	(	PUNCT
iajs-2382	142	14	)	)	PUNCT
iajs-2382	142	15	(	(	PUNCT
iajs-2382	142	16	)	)	PUNCT
iajs-2382	142	17	in	in	ADP
iajs-2382	142	18	whenever	whenever	SCONJ
iajs-2382	142	19	in	in	ADV
iajs-2382	142	20	.	.	PUNCT
iajs-2382	143	1	5	5	X
iajs-2382	143	2	.	.	X
iajs-2382	143	3	conclusion	conclusion	NOUN
iajs-2382	143	4	the	the	DET
iajs-2382	143	5	separation	separation	NOUN
iajs-2382	143	6	axioms	axiom	NOUN
iajs-2382	143	7	appeared	appear	VERB
iajs-2382	143	8	in	in	ADP
iajs-2382	143	9	new	new	ADJ
iajs-2382	143	10	types	type	NOUN
iajs-2382	143	11	and	and	CCONJ
iajs-2382	143	12	generalizations	generalization	NOUN
iajs-2382	143	13	by	by	ADP
iajs-2382	143	14	used	use	VERB
iajs-2382	143	15	ǐ­semi­g­openness	ǐ­semi­g­openness	NOUN
iajs-2382	143	16	,	,	PUNCT
iajs-2382	143	17	in	in	ADP
iajs-2382	143	18	addition	addition	NOUN
iajs-2382	143	19	a	a	DET
iajs-2382	143	20	new	new	ADJ
iajs-2382	143	21	types	type	NOUN
iajs-2382	143	22	of	of	ADP
iajs-2382	143	23	convergence	convergence	NOUN
iajs-2382	143	24	in	in	ADP
iajs-2382	143	25	ideal	ideal	ADJ
iajs-2382	143	26	spaces	space	NOUN
iajs-2382	143	27	were	be	AUX
iajs-2382	143	28	studied	study	VERB
iajs-2382	143	29	such	such	ADJ
iajs-2382	143	30	as	as	ADP
iajs-2382	143	31	ǐ	ǐ	PROPN
iajs-2382	143	32	,	,	PUNCT
iajs-2382	143	33	and	and	CCONJ
iajs-2382	143	34	the	the	DET
iajs-2382	143	35	relationships	relationship	NOUN
iajs-2382	143	36	between	between	ADP
iajs-2382	143	37	them	they	PRON
iajs-2382	143	38	was	be	AUX
iajs-2382	143	39	clarified	clarify	VERB
iajs-2382	143	40	by	by	ADP
iajs-2382	143	41	using	use	VERB
iajs-2382	143	42	several	several	ADJ
iajs-2382	143	43	example	example	NOUN
iajs-2382	143	44	.	.	PUNCT
iajs-2382	144	1	references	reference	NOUN
iajs-2382	144	2	1	1	NUM
iajs-2382	144	3	.	.	PUNCT
iajs-2382	145	1	abdel	abdel	PROPN
iajs-2382	145	2	karim	karim	PROPN
iajs-2382	145	3	,	,	PUNCT
iajs-2382	145	4	m.a	m.a	PROPN
iajs-2382	145	5	.	.	PROPN
iajs-2382	145	6	;	;	PUNCT
iajs-2382	145	7	nasir	nasir	PROPN
iajs-2382	145	8	,	,	PUNCT
iajs-2382	145	9	a.i	a.i	PROPN
iajs-2382	145	10	.	.	PROPN
iajs-2382	145	11	on	on	ADP
iajs-2382	145	12	i	i	PROPN
iajs-2382	145	13	-	-	PUNCT
iajs-2382	145	14	semi	semi	ADJ
iajs-2382	145	15	-	-	ADJ
iajs-2382	145	16	g	g	ADV
iajs-2382	145	17	-	-	PUNCT
iajs-2382	145	18	closed	close	VERB
iajs-2382	145	19	sets	set	NOUN
iajs-2382	145	20	and	and	CCONJ
iajs-2382	145	21	i	i	PRON
iajs-2382	145	22	-	-	PUNCT
iajs-2382	145	23	semi	semi	ADJ
iajs-2382	145	24	-	-	ADJ
iajs-2382	145	25	g	g	ADV
iajs-2382	145	26	-	-	PUNCT
iajs-2382	145	27	continuous	continuous	ADJ
iajs-2382	145	28	functions	function	NOUN
iajs-2382	145	29	.	.	PUNCT
iajs-2382	146	1	journal	journal	NOUN
iajs-2382	146	2	of	of	ADP
iajs-2382	146	3	the	the	DET
iajs-2382	146	4	indian	indian	PROPN
iajs-2382	146	5	mathematical	mathematical	PROPN
iajs-2382	146	6	society.2019	society.2019	PROPN
iajs-2382	146	7	.	.	PROPN
iajs-2382	146	8	2	2	NUM
iajs-2382	146	9	.	.	X
iajs-2382	147	1	kuratowski	kuratowski	PROPN
iajs-2382	147	2	,	,	PUNCT
iajs-2382	147	3	k.	k.	PROPN
iajs-2382	147	4	topology	topology	PROPN
iajs-2382	147	5	.	.	PUNCT
iajs-2382	148	1	new	new	PROPN
iajs-2382	148	2	york	york	PROPN
iajs-2382	148	3	:	:	PUNCT
iajs-2382	148	4	academic	academic	PROPN
iajs-2382	148	5	press.1933	press.1933	PROPN
iajs-2382	148	6	,	,	PUNCT
iajs-2382	148	7	i.	i.	NOUN
iajs-2382	148	8	3	3	NUM
iajs-2382	148	9	.	.	PUNCT
iajs-2382	148	10	vaidyanathaswamy	vaidyanathaswamy	NOUN
iajs-2382	148	11	,	,	PUNCT
iajs-2382	148	12	v.	v.	ADP
iajs-2382	148	13	the	the	DET
iajs-2382	148	14	localization	localization	NOUN
iajs-2382	148	15	theory	theory	NOUN
iajs-2382	148	16	in	in	ADP
iajs-2382	148	17	set	set	NOUN
iajs-2382	148	18	topology	topology	NOUN
iajs-2382	148	19	.	.	PUNCT
iajs-2382	149	1	proc	proc	NOUN
iajs-2382	149	2	.	.	PUNCT
iajs-2382	150	1	indian	indian	PROPN
iajs-2382	150	2	acad	acad	PROPN
iajs-2382	150	3	.	.	PUNCT
iajs-2382	151	1	sci	sci	PROPN
iajs-2382	151	2	.	.	PROPN
iajs-2382	151	3	1945	1945	NUM
iajs-2382	151	4	,	,	PUNCT
iajs-2382	151	5	20	20	NUM
iajs-2382	151	6	,	,	PUNCT
iajs-2382	151	7	51	51	NUM
iajs-2382	151	8	-	-	SYM
iajs-2382	151	9	61	61	NUM
iajs-2382	151	10	.	.	PUNCT
iajs-2382	151	11	4	4	X
iajs-2382	151	12	.	.	X
iajs-2382	151	13	abd	abd	PROPN
iajs-2382	151	14	elmonsef	elmonsef	PROPN
iajs-2382	151	15	,	,	PUNCT
iajs-2382	151	16	m.e	m.e	PROPN
iajs-2382	151	17	.	.	PROPN
iajs-2382	151	18	;	;	PUNCT
iajs-2382	151	19	nasef	nasef	PROPN
iajs-2382	151	20	,	,	PUNCT
iajs-2382	151	21	a.a	a.a	PROPN
iajs-2382	151	22	.	.	PROPN
iajs-2382	151	23	;	;	PUNCT
iajs-2382	151	24	radwan	radwan	NOUN
iajs-2382	151	25	,	,	PUNCT
iajs-2382	151	26	a.e	a.e	PROPN
iajs-2382	151	27	.	.	PROPN
iajs-2382	151	28	;	;	PUNCT
iajs-2382	151	29	esmaeel	esmaeel	NOUN
iajs-2382	151	30	,	,	PUNCT
iajs-2382	151	31	r.b	r.b	NOUN
iajs-2382	151	32	.	.	PROPN
iajs-2382	152	1	on	on	ADP
iajs-2382	152	2	αopen	αopen	ADJ
iajs-2382	152	3	sets	set	NOUN
iajs-2382	152	4	with	with	ADP
iajs-2382	152	5	respect	respect	NOUN
iajs-2382	152	6	to	to	ADP
iajs-2382	152	7	an	an	DET
iajs-2382	152	8	ideal	ideal	NOUN
iajs-2382	152	9	.	.	PUNCT
iajs-2382	153	1	journal	journal	NOUN
iajs-2382	153	2	of	of	ADP
iajs-2382	153	3	advances	advance	NOUN
iajs-2382	153	4	studies	study	NOUN
iajs-2382	153	5	in	in	ADP
iajs-2382	153	6	topology.2014	topology.2014	PROPN
iajs-2382	153	7	,	,	PUNCT
iajs-2382	153	8	5	5	NUM
iajs-2382	153	9	,	,	PUNCT
iajs-2382	153	10	3	3	NUM
iajs-2382	153	11	,	,	PUNCT
iajs-2382	153	12	1	1	NUM
iajs-2382	153	13	-	-	SYM
iajs-2382	153	14	10	10	NUM
iajs-2382	153	15	.	.	PUNCT
iajs-2382	154	1	5	5	NUM
iajs-2382	154	2	.	.	X
iajs-2382	154	3	alhawez	alhawez	NOUN
iajs-2382	154	4	,	,	PUNCT
iajs-2382	154	5	z.t	z.t	PROPN
iajs-2382	154	6	.	.	PROPN
iajs-2382	154	7	on	on	ADP
iajs-2382	154	8	generalized	generalized	ADJ
iajs-2382	154	9	-closed	-close	VERB
iajs-2382	154	10	set	set	NOUN
iajs-2382	154	11	in	in	ADP
iajs-2382	154	12	topological	topological	ADJ
iajs-2382	154	13	spaces	space	NOUN
iajs-2382	154	14	.	.	PUNCT
iajs-2382	155	1	ibn	ibn	PROPN
iajs-2382	155	2	al	al	PROPN
iajs-2382	155	3	-	-	PUNCT
iajs-2382	155	4	haithatham	haithatham	PROPN
iajs-2382	155	5	journal	journal	NOUN
iajs-2382	155	6	for	for	ADP
iajs-2382	155	7	pure	pure	ADJ
iajs-2382	155	8	and	and	CCONJ
iajs-2382	155	9	applied	apply	VERB
iajs-2382	155	10	science.2015	science.2015	PROPN
iajs-2382	155	11	,	,	PUNCT
iajs-2382	155	12	28	28	NUM
iajs-2382	155	13	,	,	PUNCT
iajs-2382	155	14	204	204	NUM
iajs-2382	155	15	-	-	SYM
iajs-2382	155	16	213	213	NUM
iajs-2382	155	17	.	.	NOUN
iajs-2382	156	1	6	6	NUM
iajs-2382	156	2	.	.	X
iajs-2382	157	1	mahmood	mahmood	PROPN
iajs-2382	157	2	,	,	PUNCT
iajs-2382	157	3	s.i	s.i	PROPN
iajs-2382	157	4	.	.	PROPN
iajs-2382	157	5	on	on	ADP
iajs-2382	157	6	generalized	generalized	ADJ
iajs-2382	157	7	regular	regular	ADJ
iajs-2382	157	8	continuous	continuous	ADJ
iajs-2382	157	9	functions	function	NOUN
iajs-2382	157	10	in	in	ADP
iajs-2382	157	11	topological	topological	ADJ
iajs-2382	157	12	spaces	space	NOUN
iajs-2382	157	13	.	.	PUNCT
iajs-2382	158	1	ibn	ibn	PROPN
iajs-2382	158	2	al	al	PROPN
iajs-2382	158	3	-	-	PUNCT
iajs-2382	158	4	haithatham	haithatham	PROPN
iajs-2382	158	5	journal	journal	NOUN
iajs-2382	158	6	for	for	ADP
iajs-2382	158	7	pure	pure	ADJ
iajs-2382	158	8	and	and	CCONJ
iajs-2382	158	9	applied	apply	VERB
iajs-2382	158	10	science.2017	science.2017	PROPN
iajs-2382	158	11	,	,	PUNCT
iajs-2382	158	12	25	25	NUM
iajs-2382	158	13	,	,	PUNCT
iajs-2382	158	14	3	3	NUM
iajs-2382	158	15	,	,	PUNCT
iajs-2382	158	16	77	77	NUM
iajs-2382	158	17	-	-	SYM
iajs-2382	158	18	385	385	NUM
iajs-2382	158	19	.	.	PUNCT
iajs-2382	159	1	7	7	NUM
iajs-2382	159	2	.	.	X
iajs-2382	159	3	hatir	hatir	PROPN
iajs-2382	159	4	,	,	PUNCT
iajs-2382	159	5	e.	e.	PROPN
iajs-2382	159	6	;	;	PUNCT
iajs-2382	159	7	noiri	noiri	PROPN
iajs-2382	159	8	,	,	PUNCT
iajs-2382	159	9	t.	t.	NOUN
iajs-2382	159	10	on	on	ADP
iajs-2382	159	11	semi	semi	ADJ
iajs-2382	159	12	-	-	ADJ
iajs-2382	159	13	i	i	PRON
iajs-2382	159	14	-	-	PUNCT
iajs-2382	159	15	open	open	ADJ
iajs-2382	159	16	sets	set	NOUN
iajs-2382	159	17	and	and	CCONJ
iajs-2382	159	18	semi	semi	ADJ
iajs-2382	159	19	-	-	ADJ
iajs-2382	159	20	i	i	ADV
iajs-2382	159	21	-	-	PUNCT
iajs-2382	159	22	continuous	continuous	ADJ
iajs-2382	159	23	functions	function	NOUN
iajs-2382	159	24	.	.	PUNCT
iajs-2382	160	1	act	act	PROPN
iajs-2382	160	2	mathematical	mathematical	PROPN
iajs-2382	160	3	hungarian.2005	hungarian.2005	PROPN
iajs-2382	160	4	,	,	PUNCT
iajs-2382	160	5	107	107	NUM
iajs-2382	160	6	,	,	PUNCT
iajs-2382	160	7	4	4	NUM
iajs-2382	160	8	,	,	PUNCT
iajs-2382	160	9	345353	345353	NUM
iajs-2382	160	10	.	.	PUNCT
iajs-2382	161	1	8	8	NUM
iajs-2382	161	2	.	.	X
iajs-2382	162	1	abd	abd	PROPN
iajs-2382	162	2	el	el	PROPN
iajs-2382	162	3	-	-	PUNCT
iajs-2382	162	4	monsef	monsef	ADJ
iajs-2382	162	5	,	,	PUNCT
iajs-2382	162	6	m.e	m.e	PROPN
iajs-2382	162	7	.	.	PROPN
iajs-2382	162	8	;	;	PUNCT
iajs-2382	162	9	radwan	radwan	NOUN
iajs-2382	162	10	,	,	PUNCT
iajs-2382	162	11	a.e	a.e	PROPN
iajs-2382	162	12	.	.	PROPN
iajs-2382	162	13	;	;	PUNCT
iajs-2382	162	14	ibrahem	ibrahem	NOUN
iajs-2382	162	15	,	,	PUNCT
iajs-2382	162	16	f.a	f.a	PROPN
iajs-2382	162	17	.	.	PROPN
iajs-2382	162	18	;	;	PUNCT
iajs-2382	162	19	naser	naser	PROPN
iajs-2382	162	20	,	,	PUNCT
iajs-2382	162	21	a.i	a.i	PROPN
iajs-2382	162	22	.	.	PROPN
iajs-2382	163	1	some	some	DET
iajs-2382	163	2	generalized	generalized	ADJ
iajs-2382	163	3	forms	form	NOUN
iajs-2382	163	4	of	of	ADP
iajs-2382	163	5	compactness	compactness	NOUN
iajs-2382	163	6	.	.	PUNCT
iajs-2382	164	1	international	international	ADJ
iajs-2382	164	2	mathematical	mathematical	ADJ
iajs-2382	164	3	form	form	NOUN
iajs-2382	164	4	,	,	PUNCT
iajs-2382	164	5	bulgaria	bulgaria	PROPN
iajs-2382	164	6	,	,	PUNCT
iajs-2382	164	7	hiker	hiker	NOUN
iajs-2382	164	8	ltd.2012	ltd.2012	PROPN
iajs-2382	164	9	,	,	PUNCT
iajs-2382	164	10	7	7	NUM
iajs-2382	164	11	,	,	PUNCT
iajs-2382	164	12	56	56	NUM
iajs-2382	164	13	,	,	PUNCT
iajs-2382	164	14	2767	2767	NUM
iajs-2382	164	15	-	-	SYM
iajs-2382	164	16	2782	2782	NUM
iajs-2382	164	17	.	.	PUNCT
iajs-2382	165	1	9	9	NUM
iajs-2382	165	2	.	.	X
iajs-2382	165	3	levine	levine	PROPN
iajs-2382	165	4	,	,	PUNCT
iajs-2382	165	5	n.	n.	PROPN
iajs-2382	165	6	semi	semi	ADJ
iajs-2382	165	7	-	-	ADJ
iajs-2382	165	8	open	open	ADJ
iajs-2382	165	9	sets	set	NOUN
iajs-2382	165	10	and	and	CCONJ
iajs-2382	165	11	semi	semi	ADJ
iajs-2382	165	12	-	-	NOUN
iajs-2382	165	13	continuity	continuity	NOUN
iajs-2382	165	14	in	in	ADP
iajs-2382	165	15	topological	topological	ADJ
iajs-2382	165	16	spaces	space	NOUN
iajs-2382	165	17	.	.	PUNCT
iajs-2382	166	1	american	american	PROPN
iajs-2382	166	2	mathematical	mathematical	PROPN
iajs-2382	166	3	monthly.1963	monthly.1963	PROPN
iajs-2382	166	4	,	,	PUNCT
iajs-2382	166	5	70	70	NUM
iajs-2382	166	6	,	,	PUNCT
iajs-2382	166	7	1	1	NUM
iajs-2382	166	8	,	,	PUNCT
iajs-2382	166	9	36	36	NUM
iajs-2382	166	10	-	-	SYM
iajs-2382	166	11	41	41	NUM
iajs-2382	166	12	.	.	PUNCT
iajs-2382	167	1	10	10	NUM
iajs-2382	167	2	.	.	PUNCT
iajs-2382	168	1	munkres	munkre	NOUN
iajs-2382	168	2	,	,	PUNCT
iajs-2382	168	3	j.r	j.r	PROPN
iajs-2382	168	4	.	.	PROPN
iajs-2382	168	5	topology	topology	PROPN
iajs-2382	168	6	.	.	PUNCT
iajs-2382	169	1	prentice	prentice	NOUN
iajs-2382	169	2	-	-	PUNCT
iajs-2382	169	3	hall	hall	PROPN
iajs-2382	169	4	,	,	PUNCT
iajs-2382	169	5	inc	inc	PROPN
iajs-2382	169	6	.	.	PROPN
iajs-2382	169	7	,	,	PUNCT
iajs-2382	169	8	englewood	englewood	PROPN
iajs-2382	169	9	cliffs	cliffs	PROPN
iajs-2382	169	10	,	,	PUNCT
iajs-2382	169	11	new	new	PROPN
iajs-2382	169	12	jersey	jersey	PROPN
iajs-2382	169	13	,	,	PUNCT
iajs-2382	169	14	1975	1975	NUM
iajs-2382	169	15	.	.	PUNCT
iajs-2382	170	1	11	11	NUM
iajs-2382	170	2	.	.	PUNCT
iajs-2382	170	3	dugundji	dugundji	PROPN
iajs-2382	170	4	,	,	PUNCT
iajs-2382	170	5	j.	j.	PROPN
iajs-2382	170	6	topology	topology	PROPN
iajs-2382	170	7	,	,	PUNCT
iajs-2382	170	8	university	university	PROPN
iajs-2382	170	9	of	of	ADP
iajs-2382	170	10	southey	southey	PROPN
iajs-2382	170	11	california	california	PROPN
iajs-2382	170	12	,	,	PUNCT
iajs-2382	170	13	los	los	PROPN
iajs-2382	170	14	angeles	angeles	PROPN
iajs-2382	170	15	,	,	PUNCT
iajs-2382	170	16	ally	ally	NOUN
iajs-2382	170	17	and	and	CCONJ
iajs-2382	170	18	bacon	bacon	NOUN
iajs-2382	170	19	,	,	PUNCT
iajs-2382	170	20	inc	inc	PROPN
iajs-2382	170	21	.	.	PROPN
iajs-2382	170	22	,	,	PUNCT
iajs-2382	170	23	boston	boston	PROPN
iajs-2382	170	24	,	,	PUNCT
iajs-2382	170	25	mass	mass	PROPN
iajs-2382	170	26	,	,	PUNCT
iajs-2382	170	27	1966	1966	NUM
iajs-2382	170	28	.	.	PUNCT