id	sid	tid	token	lemma	pos
iajs-2484	1	1	microsoft	microsoft	PROPN
iajs-2484	1	2	word	word	NOUN
iajs-2484	1	3	175	175	NUM
iajs-2484	1	4	-187	-187	PROPN
iajs-2484	1	5	  	  	SPACE
iajs-2484	1	6	175	175	NUM
iajs-2484	1	7	  	  	SPACE
iajs-2484	1	8	ibn	ibn	PROPN
iajs-2484	1	9	al	al	PROPN
iajs-2484	1	10	-	-	PUNCT
iajs-2484	1	11	haitham	haitham	PROPN
iajs-2484	1	12	jour	jour	X
iajs-2484	1	13	.	.	PROPN
iajs-2484	2	1	for	for	ADP
iajs-2484	2	2	pure	pure	ADJ
iajs-2484	2	3	&	&	CCONJ
iajs-2484	2	4	appl	appl	PROPN
iajs-2484	2	5	.	.	PUNCT
iajs-2484	3	1	sci	sci	PROPN
iajs-2484	3	2	.	.	PROPN
iajs-2484	4	1	33	33	NUM
iajs-2484	4	2	(	(	PUNCT
iajs-2484	4	3	3	3	NUM
iajs-2484	4	4	)	)	PUNCT
iajs-2484	4	5	2020	2020	NUM
iajs-2484	4	6	      	      	SPACE
iajs-2484	4	7	𝝎mc	𝝎mc	NOUN
iajs-2484	4	8	–	–	PUNCT
iajs-2484	4	9	functions	function	NOUN
iajs-2484	4	10	and	and	CCONJ
iajs-2484	4	11	𝑵mc	𝑵mc	NOUN
iajs-2484	4	12	-	-	PUNCT
iajs-2484	4	13	functions	function	NOUN
iajs-2484	4	14	abstract	abstract	NOUN
iajs-2484	4	15	in	in	ADP
iajs-2484	4	16	this	this	DET
iajs-2484	4	17	paper	paper	NOUN
iajs-2484	4	18	,	,	PUNCT
iajs-2484	4	19	we	we	PRON
iajs-2484	4	20	presented	present	VERB
iajs-2484	4	21	new	new	ADJ
iajs-2484	4	22	types	type	NOUN
iajs-2484	4	23	of	of	ADP
iajs-2484	4	24	mc	mc	PROPN
iajs-2484	4	25	-	-	PUNCT
iajs-2484	4	26	function	function	NOUN
iajs-2484	4	27	by	by	ADP
iajs-2484	4	28	using	use	VERB
iajs-2484	4	29	𝜔-open	𝜔-open	NOUN
iajs-2484	4	30	and	and	CCONJ
iajs-2484	4	31	𝑁-open	𝑁-open	PROPN
iajs-2484	4	32	sets	set	VERB
iajs-2484	4	33	some	some	PRON
iajs-2484	4	34	of	of	ADP
iajs-2484	4	35	them	they	PRON
iajs-2484	4	36	are	be	AUX
iajs-2484	4	37	weaker	weak	ADJ
iajs-2484	4	38	than	than	ADP
iajs-2484	4	39	mc	mc	NOUN
iajs-2484	4	40	-	-	PUNCT
iajs-2484	4	41	function	function	NOUN
iajs-2484	4	42	and	and	CCONJ
iajs-2484	4	43	some	some	PRON
iajs-2484	4	44	are	be	AUX
iajs-2484	4	45	stronger	strong	ADJ
iajs-2484	4	46	,	,	PUNCT
iajs-2484	4	47	which	which	PRON
iajs-2484	4	48	are	be	AUX
iajs-2484	4	49	𝜔mc	𝜔mc	ADJ
iajs-2484	4	50	-	-	PUNCT
iajs-2484	4	51	function	function	NOUN
iajs-2484	4	52	,	,	PUNCT
iajs-2484	4	53	m𝜔c	m𝜔c	NOUN
iajs-2484	4	54	-	-	PUNCT
iajs-2484	4	55	function	function	NOUN
iajs-2484	4	56	,	,	PUNCT
iajs-2484	4	57	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	4	58	-	-	PUNCT
iajs-2484	4	59	function	function	NOUN
iajs-2484	4	60	,	,	PUNCT
iajs-2484	4	61	𝑁mc	𝑁mc	NOUN
iajs-2484	4	62	-	-	PUNCT
iajs-2484	4	63	function	function	NOUN
iajs-2484	4	64	,	,	PUNCT
iajs-2484	4	65	m𝑁c	m𝑁c	NOUN
iajs-2484	4	66	-	-	PUNCT
iajs-2484	4	67	function	function	NOUN
iajs-2484	4	68	and	and	CCONJ
iajs-2484	4	69	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	4	70	-	-	PUNCT
iajs-2484	4	71	function	function	NOUN
iajs-2484	4	72	,	,	PUNCT
iajs-2484	4	73	also	also	ADV
iajs-2484	4	74	we	we	PRON
iajs-2484	4	75	submitted	submit	VERB
iajs-2484	4	76	new	new	ADJ
iajs-2484	4	77	kinds	kind	NOUN
iajs-2484	4	78	of	of	ADP
iajs-2484	4	79	continuous	continuous	ADJ
iajs-2484	4	80	functions	function	NOUN
iajs-2484	4	81	and	and	CCONJ
iajs-2484	4	82	compact	compact	ADJ
iajs-2484	4	83	functions	function	NOUN
iajs-2484	4	84	and	and	CCONJ
iajs-2484	4	85	we	we	PRON
iajs-2484	4	86	illustrated	illustrate	VERB
iajs-2484	4	87	the	the	DET
iajs-2484	4	88	relationships	relationship	NOUN
iajs-2484	4	89	between	between	ADP
iajs-2484	4	90	these	these	DET
iajs-2484	4	91	types	type	NOUN
iajs-2484	4	92	.	.	PUNCT
iajs-2484	5	1	the	the	DET
iajs-2484	5	2	purpose	purpose	NOUN
iajs-2484	5	3	of	of	ADP
iajs-2484	5	4	this	this	DET
iajs-2484	5	5	paper	paper	NOUN
iajs-2484	5	6	is	be	AUX
iajs-2484	5	7	to	to	PART
iajs-2484	5	8	expand	expand	VERB
iajs-2484	5	9	the	the	DET
iajs-2484	5	10	study	study	NOUN
iajs-2484	5	11	of	of	ADP
iajs-2484	5	12	mcfunction	mcfunction	NOUN
iajs-2484	5	13	and	and	CCONJ
iajs-2484	5	14	to	to	PART
iajs-2484	5	15	get	get	VERB
iajs-2484	5	16	results	result	NOUN
iajs-2484	5	17	that	that	SCONJ
iajs-2484	5	18	we	we	PRON
iajs-2484	5	19	need	need	VERB
iajs-2484	5	20	to	to	PART
iajs-2484	5	21	find	find	VERB
iajs-2484	5	22	the	the	DET
iajs-2484	5	23	relationship	relationship	NOUN
iajs-2484	5	24	with	with	ADP
iajs-2484	5	25	the	the	DET
iajs-2484	5	26	types	type	NOUN
iajs-2484	5	27	that	that	PRON
iajs-2484	5	28	have	have	AUX
iajs-2484	5	29	been	be	AUX
iajs-2484	5	30	introduced	introduce	VERB
iajs-2484	5	31	.	.	PUNCT
iajs-2484	6	1	keywords	keyword	NOUN
iajs-2484	6	2	:	:	PUNCT
iajs-2484	6	3	 	 	SPACE
iajs-2484	6	4	𝜔mc	𝜔mc	NOUN
iajs-2484	6	5	-	-	PUNCT
iajs-2484	6	6	function	function	NOUN
iajs-2484	6	7	,	,	PUNCT
iajs-2484	6	8	m𝜔c	m𝜔c	NOUN
iajs-2484	6	9	-	-	PUNCT
iajs-2484	6	10	function	function	NOUN
iajs-2484	6	11	,	,	PUNCT
iajs-2484	6	12	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	6	13	-	-	PUNCT
iajs-2484	6	14	function	function	NOUN
iajs-2484	6	15	,	,	PUNCT
iajs-2484	6	16	𝑁mc	𝑁mc	NOUN
iajs-2484	6	17	-	-	PUNCT
iajs-2484	6	18	function	function	NOUN
iajs-2484	6	19	,	,	PUNCT
iajs-2484	6	20	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	6	21	-	-	PUNCT
iajs-2484	6	22	function	function	NOUN
iajs-2484	6	23	.	.	PUNCT
iajs-2484	7	1	1	1	X
iajs-2484	7	2	.	.	X
iajs-2484	7	3	introduction	introduction	NOUN
iajs-2484	7	4	in	in	ADP
iajs-2484	7	5	(	(	PUNCT
iajs-2484	7	6	2011	2011	NUM
iajs-2484	7	7	)	)	PUNCT
iajs-2484	7	8	farhan	farhan	PROPN
iajs-2484	7	9	,	,	PUNCT
iajs-2484	7	10	ala’a	ala’a	NUM
iajs-2484	7	11	.	.	PUNCT
iajs-2484	8	1	mahmood	mahmood	PROPN
iajs-2484	9	1	[	[	X
iajs-2484	9	2	1	1	NUM
iajs-2484	9	3	]	]	PUNCT
iajs-2484	9	4	.	.	PUNCT
iajs-2484	10	1	introduced	introduce	VERB
iajs-2484	10	2	the	the	DET
iajs-2484	10	3	concept	concept	NOUN
iajs-2484	10	4	of	of	ADP
iajs-2484	10	5	new	new	ADJ
iajs-2484	10	6	function	function	NOUN
iajs-2484	10	7	which	which	PRON
iajs-2484	10	8	was	be	AUX
iajs-2484	10	9	named	name	VERB
iajs-2484	10	10	by	by	ADP
iajs-2484	10	11	mc	mc	PROPN
iajs-2484	10	12	-	-	PUNCT
iajs-2484	10	13	function	function	NOUN
iajs-2484	10	14	where	where	SCONJ
iajs-2484	10	15	he	he	PRON
iajs-2484	10	16	defined	define	VERB
iajs-2484	10	17	it	it	PRON
iajs-2484	10	18	as	as	ADP
iajs-2484	10	19	(	(	PUNCT
iajs-2484	10	20	a	a	DET
iajs-2484	10	21	function	function	NOUN
iajs-2484	10	22	𝑓	𝑓	PRON
iajs-2484	10	23	from	from	ADP
iajs-2484	10	24	any	any	DET
iajs-2484	10	25	topological	topological	ADJ
iajs-2484	10	26	space	space	NOUN
iajs-2484	10	27	𝑋	𝑋	PROPN
iajs-2484	10	28	,	,	PUNCT
iajs-2484	10	29	ʈ	ʈ	ADP
iajs-2484	10	30	into	into	ADP
iajs-2484	10	31	any	any	DET
iajs-2484	10	32	topological	topological	ADJ
iajs-2484	10	33	space	space	NOUN
iajs-2484	10	34	𝑌	𝑌	PROPN
iajs-2484	10	35	,	,	PUNCT
iajs-2484	10	36	ʈ	ʈ	AUX
iajs-2484	10	37	was	be	AUX
iajs-2484	10	38	called	call	VERB
iajs-2484	10	39	mc	mc	PROPN
iajs-2484	10	40	-	-	PUNCT
iajs-2484	10	41	function	function	NOUN
iajs-2484	10	42	iff	iff	PROPN
iajs-2484	10	43	𝑓	𝑓	DET
iajs-2484	10	44	𝒲	𝒲	PROPN
iajs-2484	10	45	was	be	AUX
iajs-2484	10	46	a	a	DET
iajs-2484	10	47	closed	closed	ADJ
iajs-2484	10	48	set	set	NOUN
iajs-2484	10	49	in	in	ADP
iajs-2484	10	50	𝑋	𝑋	NOUN
iajs-2484	10	51	for	for	ADP
iajs-2484	10	52	any	any	DET
iajs-2484	10	53	compact	compact	ADJ
iajs-2484	10	54	set	set	NOUN
iajs-2484	10	55	𝒲	𝒲	NOUN
iajs-2484	10	56	in	in	ADP
iajs-2484	10	57	𝑌	𝑌	PROPN
iajs-2484	10	58	)	)	PUNCT
iajs-2484	10	59	.	.	PUNCT
iajs-2484	11	1	moreover	moreover	ADV
iajs-2484	11	2	,	,	PUNCT
iajs-2484	11	3	in	in	ADP
iajs-2484	11	4	(	(	PUNCT
iajs-2484	11	5	2015	2015	NUM
iajs-2484	11	6	)	)	PUNCT
iajs-2484	11	7	the	the	DET
iajs-2484	11	8	researchers	researcher	NOUN
iajs-2484	11	9	in	in	ADP
iajs-2484	11	10	[	[	X
iajs-2484	11	11	2	2	NUM
iajs-2484	11	12	]	]	PUNCT
iajs-2484	11	13	.	.	PUNCT
iajs-2484	12	1	introduced	introduce	VERB
iajs-2484	12	2	new	new	ADJ
iajs-2484	12	3	types	type	NOUN
iajs-2484	12	4	of	of	ADP
iajs-2484	12	5	mc	mc	PROPN
iajs-2484	12	6	-	-	PUNCT
iajs-2484	12	7	functions	function	NOUN
iajs-2484	12	8	by	by	ADP
iajs-2484	12	9	using	use	VERB
iajs-2484	12	10	g	g	NOUN
iajs-2484	12	11	-	-	PUNCT
iajs-2484	12	12	closed	close	VERB
iajs-2484	12	13	sets	set	NOUN
iajs-2484	12	14	which	which	PRON
iajs-2484	12	15	were	be	AUX
iajs-2484	12	16	m	m	PROPN
iajs-2484	12	17	-	-	PUNCT
iajs-2484	12	18	gc	gc	PROPN
iajs-2484	12	19	,	,	PUNCT
iajs-2484	12	20	gm	gm	PROPN
iajs-2484	12	21	-	-	PUNCT
iajs-2484	12	22	c	c	PROPN
iajs-2484	12	23	and	and	CCONJ
iajs-2484	12	24	gm	gm	PROPN
iajs-2484	12	25	-	-	PUNCT
iajs-2484	12	26	gc	gc	PROPN
iajs-2484	12	27	functions	function	NOUN
iajs-2484	12	28	,	,	PUNCT
iajs-2484	12	29	where	where	SCONJ
iajs-2484	12	30	every	every	DET
iajs-2484	12	31	mc	mc	NOUN
iajs-2484	12	32	-	-	PUNCT
iajs-2484	12	33	function	function	NOUN
iajs-2484	12	34	was	be	AUX
iajs-2484	12	35	m	m	PROPN
iajs-2484	12	36	-	-	PUNCT
iajs-2484	12	37	gc	gc	ADJ
iajs-2484	12	38	function	function	NOUN
iajs-2484	12	39	and	and	CCONJ
iajs-2484	12	40	gmc	gmc	PROPN
iajs-2484	12	41	function	function	NOUN
iajs-2484	12	42	,	,	PUNCT
iajs-2484	12	43	the	the	DET
iajs-2484	12	44	notion	notion	NOUN
iajs-2484	12	45	of	of	ADP
iajs-2484	12	46	𝜔-open	𝜔-open	NOUN
iajs-2484	12	47	sets	set	NOUN
iajs-2484	12	48	submitted	submit	VERB
iajs-2484	12	49	at	at	ADP
iajs-2484	12	50	the	the	DET
iajs-2484	12	51	first	first	ADJ
iajs-2484	12	52	time	time	NOUN
iajs-2484	12	53	by	by	ADP
iajs-2484	12	54	hdeib	hdeib	NOUN
iajs-2484	12	55	in	in	ADP
iajs-2484	12	56	[	[	X
iajs-2484	12	57	3	3	NUM
iajs-2484	12	58	]	]	PUNCT
iajs-2484	12	59	.	.	PUNCT
iajs-2484	13	1	while	while	SCONJ
iajs-2484	13	2	the	the	DET
iajs-2484	13	3	notion	notion	NOUN
iajs-2484	13	4	of	of	ADP
iajs-2484	13	5	𝑁-open	𝑁-open	ADJ
iajs-2484	13	6	sets	set	NOUN
iajs-2484	13	7	submitted	submit	VERB
iajs-2484	13	8	by	by	ADP
iajs-2484	13	9	al	al	PROPN
iajs-2484	13	10	-	-	PUNCT
iajs-2484	13	11	omari	omari	PROPN
iajs-2484	13	12	in	in	ADP
iajs-2484	13	13	[	[	X
iajs-2484	13	14	4	4	NUM
iajs-2484	13	15	]	]	PUNCT
iajs-2484	13	16	.	.	PUNCT
iajs-2484	14	1	where	where	SCONJ
iajs-2484	14	2	they	they	PRON
iajs-2484	14	3	defined	define	VERB
iajs-2484	14	4	these	these	DET
iajs-2484	14	5	sets	set	NOUN
iajs-2484	14	6	as	as	ADP
iajs-2484	14	7	(	(	PUNCT
iajs-2484	14	8	any	any	DET
iajs-2484	14	9	set	set	NOUN
iajs-2484	14	10	𝒲	𝒲	NOUN
iajs-2484	14	11	in	in	ADP
iajs-2484	14	12	a	a	DET
iajs-2484	14	13	topological	topological	ADJ
iajs-2484	14	14	space	space	NOUN
iajs-2484	14	15	𝑋	𝑋	PROPN
iajs-2484	14	16	,	,	PUNCT
iajs-2484	14	17	ʈ	ʈ	AUX
iajs-2484	14	18	was	be	AUX
iajs-2484	14	19	called	call	VERB
iajs-2484	14	20	𝜔-open	𝜔-open	ADJ
iajs-2484	14	21	(	(	PUNCT
iajs-2484	14	22	respectively	respectively	ADV
iajs-2484	14	23	.	.	PUNCT
iajs-2484	15	1	𝑁-open	𝑁-open	ADJ
iajs-2484	15	2	)	)	PUNCT
iajs-2484	15	3	set	set	NOUN
iajs-2484	15	4	,	,	PUNCT
iajs-2484	15	5	if	if	SCONJ
iajs-2484	15	6	for	for	ADP
iajs-2484	15	7	any	any	DET
iajs-2484	15	8	element	element	NOUN
iajs-2484	15	9	𝑎	𝑎	PROPN
iajs-2484	15	10	∈	∈	PROPN
iajs-2484	15	11	𝒲	𝒲	NOUN
iajs-2484	15	12	there	there	PRON
iajs-2484	15	13	was	be	VERB
iajs-2484	15	14	an	an	DET
iajs-2484	15	15	open	open	ADJ
iajs-2484	15	16	set	set	NOUN
iajs-2484	15	17	ℬ	ℬ	NOUN
iajs-2484	15	18	containing	contain	VERB
iajs-2484	15	19	a	a	PRON
iajs-2484	15	20	,	,	PUNCT
iajs-2484	15	21	with	with	SCONJ
iajs-2484	15	22	ℬ-𝒲	ℬ-𝒲	PROPN
iajs-2484	15	23	was	be	AUX
iajs-2484	15	24	countable	countable	ADJ
iajs-2484	15	25	(	(	PUNCT
iajs-2484	15	26	respectively	respectively	ADV
iajs-2484	15	27	.	.	PUNCT
iajs-2484	16	1	finite	finite	PROPN
iajs-2484	16	2	)	)	PUNCT
iajs-2484	16	3	set	set	NOUN
iajs-2484	16	4	.	.	PUNCT
iajs-2484	17	1	𝒲	𝒲	NOUN
iajs-2484	17	2	was	be	AUX
iajs-2484	17	3	𝜔-closed	𝜔-close	VERB
iajs-2484	17	4	set	set	VERB
iajs-2484	17	5	(	(	PUNCT
iajs-2484	17	6	respectively	respectively	ADV
iajs-2484	17	7	.	.	PUNCT
iajs-2484	18	1	𝑁-closed	𝑁-closed	ADJ
iajs-2484	18	2	set	set	NOUN
iajs-2484	18	3	)	)	PUNCT
iajs-2484	18	4	.	.	PUNCT
iajs-2484	19	1	after	after	SCONJ
iajs-2484	19	2	that	that	DET
iajs-2484	19	3	many	many	ADJ
iajs-2484	19	4	researchers	researcher	NOUN
iajs-2484	19	5	used	use	VERB
iajs-2484	19	6	these	these	DET
iajs-2484	19	7	sets	set	NOUN
iajs-2484	19	8	and	and	CCONJ
iajs-2484	19	9	introduced	introduce	VERB
iajs-2484	19	10	new	new	ADJ
iajs-2484	19	11	concepts	concept	NOUN
iajs-2484	19	12	in	in	ADP
iajs-2484	19	13	different	different	ADJ
iajs-2484	19	14	kinds	kind	NOUN
iajs-2484	19	15	of	of	ADP
iajs-2484	19	16	topological	topological	ADJ
iajs-2484	19	17	spaces	space	NOUN
iajs-2484	19	18	.	.	PUNCT
iajs-2484	20	1	in	in	ADP
iajs-2484	20	2	this	this	DET
iajs-2484	20	3	paper	paper	NOUN
iajs-2484	20	4	,	,	PUNCT
iajs-2484	20	5	we	we	PRON
iajs-2484	20	6	used	use	VERB
iajs-2484	20	7	these	these	DET
iajs-2484	20	8	two	two	NUM
iajs-2484	20	9	sets	set	NOUN
iajs-2484	20	10	to	to	PART
iajs-2484	20	11	introduce	introduce	VERB
iajs-2484	20	12	new	new	ADJ
iajs-2484	20	13	types	type	NOUN
iajs-2484	20	14	of	of	ADP
iajs-2484	20	15	mc	mc	PROPN
iajs-2484	20	16	-	-	PUNCT
iajs-2484	20	17	function	function	NOUN
iajs-2484	20	18	,	,	PUNCT
iajs-2484	20	19	namely	namely	ADV
iajs-2484	20	20	𝜔mc	𝜔mc	NOUN
iajs-2484	20	21	-	-	PUNCT
iajs-2484	20	22	function	function	NOUN
iajs-2484	20	23	,	,	PUNCT
iajs-2484	20	24	m𝜔c	m𝜔c	NOUN
iajs-2484	20	25	-	-	PUNCT
iajs-2484	20	26	function	function	NOUN
iajs-2484	20	27	,	,	PUNCT
iajs-2484	20	28	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	20	29	-	-	PUNCT
iajs-2484	20	30	function	function	NOUN
iajs-2484	20	31	,	,	PUNCT
iajs-2484	20	32	𝑁mc	𝑁mc	NOUN
iajs-2484	20	33	-	-	PUNCT
iajs-2484	20	34	function	function	NOUN
iajs-2484	20	35	,	,	PUNCT
iajs-2484	20	36	m𝑁c	m𝑁c	NOUN
iajs-2484	20	37	-	-	PUNCT
iajs-2484	20	38	function	function	NOUN
iajs-2484	20	39	and	and	CCONJ
iajs-2484	20	40	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	20	41	-	-	PUNCT
iajs-2484	20	42	function	function	NOUN
iajs-2484	20	43	and	and	CCONJ
iajs-2484	20	44	we	we	PRON
iajs-2484	20	45	illustrated	illustrate	VERB
iajs-2484	20	46	the	the	DET
iajs-2484	20	47	relation	relation	NOUN
iajs-2484	20	48	between	between	ADP
iajs-2484	20	49	them	they	PRON
iajs-2484	20	50	and	and	CCONJ
iajs-2484	20	51	their	their	PRON
iajs-2484	20	52	relation	relation	NOUN
iajs-2484	20	53	with	with	ADP
iajs-2484	20	54	mc	mc	PROPN
iajs-2484	20	55	-	-	PUNCT
iajs-2484	20	56	function	function	NOUN
iajs-2484	20	57	,	,	PUNCT
iajs-2484	20	58	also	also	ADV
iajs-2484	20	59	we	we	PRON
iajs-2484	20	60	connected	connect	VERB
iajs-2484	20	61	between	between	ADP
iajs-2484	20	62	these	these	DET
iajs-2484	20	63	functions	function	NOUN
iajs-2484	20	64	and	and	CCONJ
iajs-2484	20	65	𝑇	𝑇	PROPN
iajs-2484	20	66	-space	-space	NOUN
iajs-2484	20	67	,	,	PUNCT
iajs-2484	20	68	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	20	69	-space	-space	NOUN
iajs-2484	20	70	,	,	PUNCT
iajs-2484	20	71	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	20	72	-space	-space	NOUN
iajs-2484	20	73	,	,	PUNCT
iajs-2484	20	74	kcspace	kcspace	NOUN
iajs-2484	20	75	,	,	PUNCT
iajs-2484	20	76	and	and	CCONJ
iajs-2484	20	77	c	c	X
iajs-2484	20	78	-	-	PUNCT
iajs-2484	20	79	c	c	NOUN
iajs-2484	20	80	space	space	NOUN
iajs-2484	20	81	.	.	PUNCT
iajs-2484	21	1	we	we	PRON
iajs-2484	21	2	used	use	VERB
iajs-2484	21	3	the	the	DET
iajs-2484	21	4	same	same	ADJ
iajs-2484	21	5	sets	set	NOUN
iajs-2484	21	6	to	to	PART
iajs-2484	21	7	define	define	VERB
iajs-2484	21	8	new	new	ADJ
iajs-2484	21	9	forms	form	NOUN
iajs-2484	21	10	of	of	ADP
iajs-2484	21	11	continuous	continuous	ADJ
iajs-2484	21	12	and	and	CCONJ
iajs-2484	21	13	compact	compact	ADJ
iajs-2484	21	14	functions	function	NOUN
iajs-2484	21	15	such	such	ADJ
iajs-2484	21	16	as	as	ADP
iajs-2484	21	17	strongly	strongly	ADV
iajs-2484	21	18	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	21	19	,	,	PUNCT
iajs-2484	21	20	strongly	strongly	ADV
iajs-2484	21	21	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	21	22	,	,	PUNCT
iajs-2484	21	23	𝜔-irresolute	𝜔-irresolute	NOUN
iajs-2484	21	24	,	,	PUNCT
iajs-2484	21	25	𝜔∗-compact	𝜔∗-compact	PROPN
iajs-2484	21	26	,	,	PUNCT
iajs-2484	21	27	𝑁∗-compact	𝑁∗-compact	NOUN
iajs-2484	21	28	,	,	PUNCT
iajs-2484	21	29	𝜔∗∗-compact	𝜔∗∗-compact	NOUN
iajs-2484	21	30	,	,	PUNCT
iajs-2484	21	31	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	21	32	function	function	NOUN
iajs-2484	21	33	,	,	PUNCT
iajs-2484	21	34	and	and	CCONJ
iajs-2484	21	35	we	we	PRON
iajs-2484	21	36	presented	present	VERB
iajs-2484	21	37	some	some	DET
iajs-2484	21	38	propositions	proposition	NOUN
iajs-2484	21	39	,	,	PUNCT
iajs-2484	21	40	remarks	remark	NOUN
iajs-2484	21	41	and	and	CCONJ
iajs-2484	21	42	examples	example	NOUN
iajs-2484	21	43	to	to	PART
iajs-2484	21	44	support	support	VERB
iajs-2484	21	45	our	our	PRON
iajs-2484	21	46	work	work	NOUN
iajs-2484	21	47	.	.	PUNCT
iajs-2484	22	1	ibn	ibn	PROPN
iajs-2484	22	2	al	al	PROPN
iajs-2484	22	3	haitham	haitham	PROPN
iajs-2484	22	4	journal	journal	PROPN
iajs-2484	22	5	for	for	ADP
iajs-2484	22	6	pure	pure	ADJ
iajs-2484	22	7	and	and	CCONJ
iajs-2484	22	8	applied	apply	VERB
iajs-2484	22	9	science	science	NOUN
iajs-2484	22	10	journal	journal	PROPN
iajs-2484	22	11	homepage	homepage	NOUN
iajs-2484	22	12	:	:	PUNCT
iajs-2484	22	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2484	22	14	doi	doi	NOUN
iajs-2484	22	15	:	:	PUNCT
iajs-2484	22	16	10.30526/	10.30526/	NUM
iajs-2484	22	17	33.3.2484	33.3.2484	NOUN
iajs-2484	22	18	article	article	NOUN
iajs-2484	22	19	history	history	NOUN
iajs-2484	22	20	:	:	PUNCT
iajs-2484	22	21	received	receive	VERB
iajs-2484	22	22	7	7	NUM
iajs-2484	22	23	september	september	PROPN
iajs-2484	22	24	2019	2019	NUM
iajs-2484	22	25	,	,	PUNCT
iajs-2484	22	26	accepted	accept	VERB
iajs-2484	22	27	13	13	NUM
iajs-2484	22	28	october	october	PROPN
iajs-2484	22	29	2019	2019	NUM
iajs-2484	22	30	,	,	PUNCT
iajs-2484	22	31	published	publish	VERB
iajs-2484	22	32	in	in	ADP
iajs-2484	22	33	july	july	PROPN
iajs-2484	22	34	2020	2020	NUM
iajs-2484	22	35	.	.	PUNCT
iajs-2484	23	1	nadia	nadia	PROPN
iajs-2484	23	2	kadum	kadum	PROPN
iajs-2484	23	3	humadi	humadi	PROPN
iajs-2484	23	4	haider	haider	PROPN
iajs-2484	23	5	jebur	jebur	PROPN
iajs-2484	23	6	ali	ali	PROPN
iajs-2484	23	7	department	department	PROPN
iajs-2484	23	8	of	of	ADP
iajs-2484	23	9	mathematics	mathematics	PROPN
iajs-2484	23	10	,	,	PUNCT
iajs-2484	23	11	college	college	NOUN
iajs-2484	23	12	of	of	ADP
iajs-2484	23	13	science	science	NOUN
iajs-2484	23	14	,	,	PUNCT
iajs-2484	23	15	mustansiriyah	mustansiriyah	NOUN
iajs-2484	23	16	university	university	PROPN
iajs-2484	23	17	,	,	PUNCT
iajs-2484	23	18	iraq	iraq	PROPN
iajs-2484	23	19	.	.	PUNCT
iajs-2484	24	1	m.a.nadia313@gmail.com	m.a.nadia313@gmail.com	X
iajs-2484	25	1	drhaiderjebur@uomustansiriyah.edu.iq	drhaiderjebur@uomustansiriyah.edu.iq	VERB
iajs-2484	25	2	  	  	SPACE
iajs-2484	25	3	176	176	NUM
iajs-2484	25	4	  	  	SPACE
iajs-2484	25	5	ibn	ibn	PROPN
iajs-2484	25	6	al	al	PROPN
iajs-2484	25	7	-	-	PUNCT
iajs-2484	25	8	haitham	haitham	PROPN
iajs-2484	25	9	jour	jour	X
iajs-2484	25	10	.	.	PROPN
iajs-2484	26	1	for	for	ADP
iajs-2484	26	2	pure	pure	ADJ
iajs-2484	26	3	&	&	CCONJ
iajs-2484	26	4	appl	appl	PROPN
iajs-2484	26	5	.	.	PUNCT
iajs-2484	27	1	sci	sci	PROPN
iajs-2484	27	2	.	.	PROPN
iajs-2484	28	1	33	33	NUM
iajs-2484	28	2	(	(	PUNCT
iajs-2484	28	3	3	3	NUM
iajs-2484	28	4	)	)	PUNCT
iajs-2484	28	5	2020	2020	NUM
iajs-2484	28	6	𝟏-𝝎mc	𝟏-𝝎mc	NOUN
iajs-2484	28	7	-	-	PUNCT
iajs-2484	28	8	functions	function	NOUN
iajs-2484	28	9	and	and	CCONJ
iajs-2484	28	10	𝑵mc	𝑵mc	NOUN
iajs-2484	28	11	-	-	PUNCT
iajs-2484	28	12	functions	function	NOUN
iajs-2484	28	13	.	.	PUNCT
iajs-2484	29	1	we	we	PRON
iajs-2484	29	2	recall	recall	VERB
iajs-2484	29	3	the	the	DET
iajs-2484	29	4	following	follow	VERB
iajs-2484	29	5	facts	fact	NOUN
iajs-2484	29	6	which	which	PRON
iajs-2484	29	7	we	we	PRON
iajs-2484	29	8	need	need	VERB
iajs-2484	29	9	in	in	ADP
iajs-2484	29	10	this	this	PRON
iajs-2484	29	11	our	our	PRON
iajs-2484	29	12	work	work	NOUN
iajs-2484	29	13	,	,	PUNCT
iajs-2484	29	14	after	after	ADP
iajs-2484	29	15	that	that	SCONJ
iajs-2484	29	16	we	we	PRON
iajs-2484	29	17	will	will	AUX
iajs-2484	29	18	introduce	introduce	VERB
iajs-2484	29	19	the	the	DET
iajs-2484	29	20	definitions	definition	NOUN
iajs-2484	29	21	of	of	ADP
iajs-2484	29	22	new	new	ADJ
iajs-2484	29	23	types	type	NOUN
iajs-2484	29	24	of	of	ADP
iajs-2484	29	25	mc	mc	PROPN
iajs-2484	29	26	-	-	PUNCT
iajs-2484	29	27	function	function	NOUN
iajs-2484	29	28	and	and	CCONJ
iajs-2484	29	29	illustrate	illustrate	VERB
iajs-2484	29	30	the	the	DET
iajs-2484	29	31	relation	relation	NOUN
iajs-2484	29	32	between	between	ADP
iajs-2484	29	33	these	these	DET
iajs-2484	29	34	types	type	NOUN
iajs-2484	29	35	.	.	PUNCT
iajs-2484	30	1	definition	definition	NOUN
iajs-2484	30	2	(	(	PUNCT
iajs-2484	30	3	1.1	1.1	NUM
iajs-2484	30	4	):	):	PUNCT
iajs-2484	30	5	a	a	DET
iajs-2484	30	6	space	space	NOUN
iajs-2484	30	7	𝑋	𝑋	NOUN
iajs-2484	30	8	,	,	PUNCT
iajs-2484	30	9	ʈ	ʈ	AUX
iajs-2484	30	10	is	be	AUX
iajs-2484	30	11	called	call	VERB
iajs-2484	30	12	:	:	PUNCT
iajs-2484	30	13	1a	1a	NUM
iajs-2484	30	14	compact	compact	ADJ
iajs-2484	30	15	space	space	NOUN
iajs-2484	30	16	if	if	SCONJ
iajs-2484	30	17	any	any	DET
iajs-2484	30	18	open	open	ADJ
iajs-2484	30	19	cover	cover	NOUN
iajs-2484	30	20	for	for	ADP
iajs-2484	30	21	𝑋	𝑋	PROPN
iajs-2484	30	22	possesses	possess	VERB
iajs-2484	30	23	a	a	DET
iajs-2484	30	24	finite	finite	ADJ
iajs-2484	30	25	sub	sub	NOUN
iajs-2484	30	26	cover	cover	NOUN
iajs-2484	30	27	[	[	X
iajs-2484	30	28	5	5	NUM
iajs-2484	30	29	]	]	PUNCT
iajs-2484	30	30	.	.	PUNCT
iajs-2484	31	1	2a	2a	NUM
iajs-2484	31	2	𝜔-compact	𝜔-compact	NOUN
iajs-2484	31	3	space	space	NOUN
iajs-2484	31	4	if	if	SCONJ
iajs-2484	31	5	any	any	DET
iajs-2484	31	6	𝜔-open	𝜔-open	ADJ
iajs-2484	31	7	cover	cover	NOUN
iajs-2484	31	8	for	for	ADP
iajs-2484	31	9	𝑋	𝑋	PROPN
iajs-2484	31	10	possesses	possess	VERB
iajs-2484	31	11	a	a	DET
iajs-2484	31	12	finite	finite	ADJ
iajs-2484	31	13	sub	sub	NOUN
iajs-2484	31	14	cover	cover	NOUN
iajs-2484	32	1	[	[	X
iajs-2484	32	2	5	5	NUM
iajs-2484	32	3	]	]	PUNCT
iajs-2484	32	4	.	.	PUNCT
iajs-2484	33	1	3an	3an	PROPN
iajs-2484	33	2	𝑁-compact	𝑁-compact	PROPN
iajs-2484	33	3	space	space	NOUN
iajs-2484	33	4	if	if	SCONJ
iajs-2484	33	5	any	any	DET
iajs-2484	33	6	𝑁-open	𝑁-open	ADJ
iajs-2484	33	7	cover	cover	NOUN
iajs-2484	33	8	for	for	ADP
iajs-2484	33	9	𝑋	𝑋	PROPN
iajs-2484	33	10	possesses	possess	VERB
iajs-2484	33	11	a	a	DET
iajs-2484	33	12	finite	finite	ADJ
iajs-2484	33	13	sub	sub	NOUN
iajs-2484	33	14	cover	cover	NOUN
iajs-2484	34	1	[	[	X
iajs-2484	34	2	6	6	NUM
iajs-2484	34	3	]	]	PUNCT
iajs-2484	34	4	.	.	PUNCT
iajs-2484	35	1	remark	remark	NOUN
iajs-2484	35	2	(	(	PUNCT
iajs-2484	35	3	1.2	1.2	NUM
iajs-2484	35	4	):	):	PUNCT
iajs-2484	35	5	every	every	DET
iajs-2484	35	6	closed	closed	ADJ
iajs-2484	35	7	set	set	NOUN
iajs-2484	35	8	is	be	AUX
iajs-2484	35	9	𝜔-closed	𝜔-close	VERB
iajs-2484	35	10	[	[	PUNCT
iajs-2484	35	11	7	7	NUM
iajs-2484	35	12	]	]	PUNCT
iajs-2484	35	13	.	.	PUNCT
iajs-2484	36	1	(	(	PUNCT
iajs-2484	36	2	respectively	respectively	ADV
iajs-2484	36	3	𝑁-closed	𝑁-closed	ADJ
iajs-2484	36	4	[	[	X
iajs-2484	36	5	6	6	NUM
iajs-2484	36	6	]	]	PUNCT
iajs-2484	36	7	.	.	PUNCT
iajs-2484	36	8	)	)	PUNCT
iajs-2484	37	1	set	set	VERB
iajs-2484	37	2	.	.	PUNCT
iajs-2484	38	1	and	and	CCONJ
iajs-2484	38	2	every	every	DET
iajs-2484	38	3	𝑁-open	𝑁-open	PROPN
iajs-2484	38	4	set	set	NOUN
iajs-2484	38	5	is	be	AUX
iajs-2484	38	6	𝜔-open	𝜔-open	ADJ
iajs-2484	38	7	set	set	VERB
iajs-2484	38	8	[	[	X
iajs-2484	38	9	8	8	NUM
iajs-2484	38	10	]	]	PUNCT
iajs-2484	38	11	.	.	PUNCT
iajs-2484	39	1	also	also	ADV
iajs-2484	39	2	every	every	DET
iajs-2484	39	3	𝑁-closed	𝑁-closed	PROPN
iajs-2484	39	4	set	set	NOUN
iajs-2484	39	5	is	be	AUX
iajs-2484	39	6	𝜔-closed	𝜔-close	VERB
iajs-2484	39	7	set	set	VERB
iajs-2484	39	8	[	[	X
iajs-2484	39	9	8	8	NUM
iajs-2484	39	10	]	]	PUNCT
iajs-2484	39	11	.	.	PUNCT
iajs-2484	40	1	as	as	ADV
iajs-2484	40	2	well	well	ADV
iajs-2484	40	3	as	as	ADP
iajs-2484	40	4	every	every	DET
iajs-2484	40	5	𝜔-compact	𝜔-compact	PROPN
iajs-2484	40	6	(	(	PUNCT
iajs-2484	40	7	respectively	respectively	ADV
iajs-2484	40	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	40	9	)	)	PUNCT
iajs-2484	40	10	set	set	NOUN
iajs-2484	40	11	is	be	AUX
iajs-2484	40	12	compact	compact	ADJ
iajs-2484	40	13	[	[	X
iajs-2484	40	14	5	5	NUM
iajs-2484	40	15	,	,	PUNCT
iajs-2484	40	16	9	9	NUM
iajs-2484	40	17	]	]	PUNCT
iajs-2484	40	18	.	.	PUNCT
iajs-2484	41	1	example	example	NOUN
iajs-2484	41	2	(	(	PUNCT
iajs-2484	41	3	1.3	1.3	NUM
iajs-2484	41	4	):	):	PUNCT
iajs-2484	41	5	1	1	NUM
iajs-2484	41	6	-	-	PUNCT
iajs-2484	41	7	in	in	ADP
iajs-2484	41	8	the	the	DET
iajs-2484	41	9	excluded	exclude	VERB
iajs-2484	41	10	point	point	NOUN
iajs-2484	41	11	topological	topological	ADJ
iajs-2484	41	12	space	space	NOUN
iajs-2484	41	13	(	(	PUNCT
iajs-2484	41	14	𝑋	𝑋	NOUN
iajs-2484	41	15	,	,	PUNCT
iajs-2484	41	16	ʈ	ʈ	PROPN
iajs-2484	41	17	)	)	PUNCT
iajs-2484	41	18	where	where	SCONJ
iajs-2484	41	19	𝑋	𝑋	PROPN
iajs-2484	41	20	is	be	AUX
iajs-2484	41	21	a	a	DET
iajs-2484	41	22	finite	finite	ADJ
iajs-2484	41	23	set	set	NOUN
iajs-2484	41	24	,	,	PUNCT
iajs-2484	41	25	the	the	DET
iajs-2484	41	26	set	set	NOUN
iajs-2484	41	27	{	{	PUNCT
iajs-2484	41	28	𝑥	𝑥	PRON
iajs-2484	41	29	∘	∘	PROPN
iajs-2484	41	30	is	be	AUX
iajs-2484	41	31	𝜔-closed	𝜔-close	VERB
iajs-2484	41	32	and	and	CCONJ
iajs-2484	41	33	𝑁-closed	𝑁-closed	ADJ
iajs-2484	41	34	set	set	NOUN
iajs-2484	41	35	but	but	CCONJ
iajs-2484	41	36	not	not	PART
iajs-2484	41	37	closed	closed	ADJ
iajs-2484	41	38	set	set	VERB
iajs-2484	41	39	,	,	PUNCT
iajs-2484	41	40	in	in	ADP
iajs-2484	41	41	which	which	PRON
iajs-2484	41	42	ʈ	ʈ	ADP
iajs-2484	41	43	=	=	SYM
iajs-2484	41	44	𝑈	𝑈	PROPN
iajs-2484	41	45	⊆	⊆	NUM
iajs-2484	41	46	𝑋	𝑋	PROPN
iajs-2484	41	47	,	,	PUNCT
iajs-2484	41	48	𝑥∘	𝑥∘	PROPN
iajs-2484	41	49	∉	∉	PROPN
iajs-2484	41	50	𝑈	𝑈	PROPN
iajs-2484	41	51	for	for	ADP
iajs-2484	41	52	some	some	DET
iajs-2484	41	53	𝑥∘	𝑥∘	PROPN
iajs-2484	41	54	∈	∈	NOUN
iajs-2484	41	55	𝑋	𝑋	PROPN
iajs-2484	41	56	⋃	⋃	NOUN
iajs-2484	41	57	𝑋	𝑋	NOUN
iajs-2484	41	58	.	.	PUNCT
iajs-2484	42	1	2	2	NUM
iajs-2484	42	2	-	-	NUM
iajs-2484	42	3	the	the	DET
iajs-2484	42	4	set	set	NOUN
iajs-2484	42	5	of	of	ADP
iajs-2484	42	6	irrational	irrational	ADJ
iajs-2484	42	7	number	number	NOUN
iajs-2484	42	8	𝒬	𝒬	NOUN
iajs-2484	42	9	in	in	ADP
iajs-2484	42	10	the	the	DET
iajs-2484	42	11	co	co	NOUN
iajs-2484	42	12	-	-	ADJ
iajs-2484	42	13	finite	finite	ADJ
iajs-2484	42	14	topological	topological	ADJ
iajs-2484	42	15	space	space	NOUN
iajs-2484	42	16	(	(	PUNCT
iajs-2484	42	17	ℛ	ℛ	NOUN
iajs-2484	42	18	,	,	PUNCT
iajs-2484	42	19	ʈ	ʈ	AUX
iajs-2484	42	20	is	be	AUX
iajs-2484	42	21	𝜔-open	𝜔-open	ADJ
iajs-2484	42	22	set	set	VERB
iajs-2484	42	23	but	but	CCONJ
iajs-2484	42	24	not	not	PART
iajs-2484	42	25	𝑁-open	𝑁-open	PROPN
iajs-2484	42	26	set	set	NOUN
iajs-2484	42	27	.	.	PUNCT
iajs-2484	43	1	3	3	NUM
iajs-2484	43	2	-	-	NUM
iajs-2484	43	3	the	the	DET
iajs-2484	43	4	set	set	NOUN
iajs-2484	43	5	of	of	ADP
iajs-2484	43	6	rational	rational	ADJ
iajs-2484	43	7	number	number	NOUN
iajs-2484	43	8	𝒬	𝒬	NOUN
iajs-2484	43	9	in	in	ADP
iajs-2484	43	10	the	the	DET
iajs-2484	43	11	co	co	NOUN
iajs-2484	43	12	-	-	ADJ
iajs-2484	43	13	finite	finite	ADJ
iajs-2484	43	14	topological	topological	ADJ
iajs-2484	43	15	space	space	NOUN
iajs-2484	43	16	(	(	PUNCT
iajs-2484	43	17	ℛ	ℛ	NOUN
iajs-2484	43	18	,	,	PUNCT
iajs-2484	43	19	ʈ	ʈ	VERB
iajs-2484	43	20	is	be	AUX
iajs-2484	43	21	𝜔-closed	𝜔-close	VERB
iajs-2484	43	22	set	set	VERB
iajs-2484	43	23	but	but	CCONJ
iajs-2484	43	24	not	not	PART
iajs-2484	43	25	𝑁-closed	𝑁-closed	ADJ
iajs-2484	43	26	set	set	NOUN
iajs-2484	43	27	.	.	PUNCT
iajs-2484	44	1	4	4	NUM
iajs-2484	44	2	-	-	X
iajs-2484	44	3	the	the	DET
iajs-2484	44	4	included	include	VERB
iajs-2484	44	5	point	point	NOUN
iajs-2484	44	6	topological	topological	ADJ
iajs-2484	44	7	space	space	NOUN
iajs-2484	44	8	(	(	PUNCT
iajs-2484	44	9	𝒵	𝒵	PROPN
iajs-2484	44	10	,	,	PUNCT
iajs-2484	44	11	ʈ	ʈ	ADP
iajs-2484	44	12	where	where	SCONJ
iajs-2484	44	13	ʈ	ʈ	ADV
iajs-2484	44	14	=	=	SYM
iajs-2484	44	15	{	{	PUNCT
iajs-2484	44	16	𝑈	𝑈	PROPN
iajs-2484	44	17	⊆	⊆	NUM
iajs-2484	44	18	𝑋	𝑋	PROPN
iajs-2484	44	19	,	,	PUNCT
iajs-2484	44	20	where	where	SCONJ
iajs-2484	44	21	𝑥∘	𝑥∘	PROPN
iajs-2484	44	22	∈	∈	PROPN
iajs-2484	44	23	𝑈	𝑈	PROPN
iajs-2484	44	24	,	,	PUNCT
iajs-2484	44	25	for	for	ADP
iajs-2484	44	26	some	some	DET
iajs-2484	44	27	𝑥	𝑥	PROPN
iajs-2484	44	28	°	°	NOUN
iajs-2484	44	29	in	in	ADP
iajs-2484	44	30	𝑋}⋃{∅	𝑋}⋃{∅	NOUN
iajs-2484	44	31	}	}	PUNCT
iajs-2484	44	32	is	be	AUX
iajs-2484	44	33	a	a	DET
iajs-2484	44	34	compact	compact	ADJ
iajs-2484	44	35	space	space	NOUN
iajs-2484	44	36	but	but	CCONJ
iajs-2484	44	37	not	not	PART
iajs-2484	44	38	𝜔-compact	𝜔-compact	PROPN
iajs-2484	44	39	.	.	PUNCT
iajs-2484	45	1	definition	definition	NOUN
iajs-2484	45	2	(	(	PUNCT
iajs-2484	45	3	1.4	1.4	NUM
iajs-2484	45	4	):	):	PUNCT
iajs-2484	45	5	the	the	DET
iajs-2484	45	6	space	space	NOUN
iajs-2484	45	7	𝑋	𝑋	PROPN
iajs-2484	45	8	,	,	PUNCT
iajs-2484	45	9	ʈ	ʈ	AUX
iajs-2484	45	10	is	be	AUX
iajs-2484	45	11	called	call	VERB
iajs-2484	45	12	:	:	PUNCT
iajs-2484	45	13	1a	1a	PROPN
iajs-2484	45	14	𝑇	𝑇	PROPN
iajs-2484	45	15	-space	-space	NOUN
iajs-2484	45	16	,	,	PUNCT
iajs-2484	45	17	if	if	SCONJ
iajs-2484	45	18	for	for	ADP
iajs-2484	45	19	each	each	DET
iajs-2484	45	20	non	non	ADJ
iajs-2484	45	21	-	-	ADJ
iajs-2484	45	22	equal	equal	ADJ
iajs-2484	45	23	elements	element	NOUN
iajs-2484	45	24	𝑥	𝑥	NOUN
iajs-2484	45	25	,	,	PUNCT
iajs-2484	45	26	𝑦	𝑦	NOUN
iajs-2484	45	27	in	in	ADP
iajs-2484	45	28	𝑋	𝑋	PROPN
iajs-2484	45	29	,	,	PUNCT
iajs-2484	45	30	there	there	PRON
iajs-2484	45	31	are	be	VERB
iajs-2484	45	32	disjoint	disjoint	NOUN
iajs-2484	45	33	𝒲	𝒲	PROPN
iajs-2484	45	34	,	,	PUNCT
iajs-2484	45	35	𝒲	𝒲	PROPN
iajs-2484	45	36	∈	∈	NOUN
iajs-2484	45	37	ʈ	ʈ	X
iajs-2484	45	38	with	with	ADP
iajs-2484	45	39	𝑥	𝑥	DET
iajs-2484	45	40	∈	∈	PROPN
iajs-2484	45	41	𝒲	𝒲	PROPN
iajs-2484	45	42	and	and	CCONJ
iajs-2484	45	43	𝑦	𝑦	NOUN
iajs-2484	45	44	∈	∈	NOUN
iajs-2484	45	45	𝒲	𝒲	NOUN
iajs-2484	46	1	[	[	X
iajs-2484	46	2	10	10	NUM
iajs-2484	46	3	]	]	PUNCT
iajs-2484	46	4	.	.	PUNCT
iajs-2484	47	1	2a	2a	NUM
iajs-2484	47	2	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	47	3	-space	-space	NOUN
iajs-2484	47	4	,	,	PUNCT
iajs-2484	47	5	if	if	SCONJ
iajs-2484	47	6	for	for	ADP
iajs-2484	47	7	each	each	DET
iajs-2484	47	8	non	non	ADJ
iajs-2484	47	9	-	-	ADJ
iajs-2484	47	10	equal	equal	ADJ
iajs-2484	47	11	elements	element	NOUN
iajs-2484	47	12	𝑥	𝑥	NOUN
iajs-2484	47	13	,	,	PUNCT
iajs-2484	47	14	𝑦	𝑦	NOUN
iajs-2484	47	15	in	in	ADP
iajs-2484	47	16	𝑋	𝑋	PROPN
iajs-2484	47	17	,	,	PUNCT
iajs-2484	47	18	there	there	PRON
iajs-2484	47	19	are	be	VERB
iajs-2484	47	20	disjoint	disjoint	NOUN
iajs-2484	47	21	𝜔-open	𝜔-open	NOUN
iajs-2484	47	22	sets	set	NOUN
iajs-2484	47	23	𝒲	𝒲	NOUN
iajs-2484	47	24	,	,	PUNCT
iajs-2484	47	25	𝒲	𝒲	PROPN
iajs-2484	47	26	in	in	ADP
iajs-2484	47	27	𝑋	𝑋	NOUN
iajs-2484	47	28	with	with	ADP
iajs-2484	47	29	𝑥	𝑥	DET
iajs-2484	47	30	∈	∈	PROPN
iajs-2484	47	31	𝒲	𝒲	PROPN
iajs-2484	47	32	and	and	CCONJ
iajs-2484	47	33	𝑦	𝑦	NOUN
iajs-2484	47	34	∈	∈	NOUN
iajs-2484	47	35	𝒲	𝒲	NOUN
iajs-2484	48	1	[	[	X
iajs-2484	48	2	11	11	NUM
iajs-2484	48	3	]	]	PUNCT
iajs-2484	48	4	.	.	PUNCT
iajs-2484	49	1	3an	3an	ADJ
iajs-2484	49	2	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	49	3	-space	-space	NOUN
iajs-2484	49	4	,	,	PUNCT
iajs-2484	49	5	if	if	SCONJ
iajs-2484	49	6	for	for	ADP
iajs-2484	49	7	each	each	DET
iajs-2484	49	8	non	non	ADJ
iajs-2484	49	9	-	-	ADJ
iajs-2484	49	10	equal	equal	ADJ
iajs-2484	49	11	elements	element	NOUN
iajs-2484	49	12	𝑥	𝑥	NOUN
iajs-2484	49	13	,	,	PUNCT
iajs-2484	49	14	𝑦	𝑦	NOUN
iajs-2484	49	15	in	in	ADP
iajs-2484	49	16	𝑋	𝑋	PROPN
iajs-2484	49	17	,	,	PUNCT
iajs-2484	49	18	there	there	PRON
iajs-2484	49	19	are	be	VERB
iajs-2484	49	20	disjoint	disjoint	NOUN
iajs-2484	49	21	𝑁-open	𝑁-open	PROPN
iajs-2484	49	22	sets	set	VERB
iajs-2484	49	23	𝒲	𝒲	NOUN
iajs-2484	49	24	,	,	PUNCT
iajs-2484	49	25	𝒲	𝒲	NOUN
iajs-2484	49	26	with	with	ADP
iajs-2484	49	27	𝑥	𝑥	DET
iajs-2484	49	28	∈	∈	PROPN
iajs-2484	49	29	𝒲	𝒲	PROPN
iajs-2484	49	30	and	and	CCONJ
iajs-2484	49	31	𝑦	𝑦	NOUN
iajs-2484	49	32	∈	∈	NOUN
iajs-2484	49	33	𝒲	𝒲	NOUN
iajs-2484	50	1	[	[	X
iajs-2484	50	2	6	6	NUM
iajs-2484	50	3	]	]	PUNCT
iajs-2484	50	4	.	.	PUNCT
iajs-2484	51	1	example	example	NOUN
iajs-2484	51	2	(	(	PUNCT
iajs-2484	51	3	1.5	1.5	NUM
iajs-2484	51	4	)	)	PUNCT
iajs-2484	51	5	1ℛ	1ℛ	NOUN
iajs-2484	51	6	,	,	PUNCT
iajs-2484	51	7	ʈ	ʈ	X
iajs-2484	51	8	is	be	AUX
iajs-2484	51	9	𝑇	𝑇	PROPN
iajs-2484	51	10	-space	-space	NOUN
iajs-2484	51	11	.	.	PUNCT
iajs-2484	52	1	2𝑋	2𝑋	NOUN
iajs-2484	52	2	,	,	PUNCT
iajs-2484	52	3	ʈ	ʈ	ADP
iajs-2484	52	4	where	where	SCONJ
iajs-2484	52	5	𝑋	𝑋	NOUN
iajs-2484	52	6	is	be	AUX
iajs-2484	52	7	a	a	DET
iajs-2484	52	8	finite	finite	NOUN
iajs-2484	52	9	set	set	NOUN
iajs-2484	52	10	and	and	CCONJ
iajs-2484	52	11	ʈ	ʈ	ADP
iajs-2484	52	12	=	=	PUNCT
iajs-2484	52	13	{	{	PUNCT
iajs-2484	52	14	𝒲	𝒲	NOUN
iajs-2484	52	15	⊆	⊆	NUM
iajs-2484	52	16	𝑋	𝑋	NOUN
iajs-2484	52	17	|	|	NOUN
iajs-2484	52	18	𝒶∘	𝒶∘	PROPN
iajs-2484	52	19	∈	∈	PROPN
iajs-2484	52	20	𝒲	𝒲	PROPN
iajs-2484	52	21	,	,	PUNCT
iajs-2484	52	22	for	for	ADP
iajs-2484	52	23	some	some	DET
iajs-2484	52	24	𝒶∘	𝒶∘	PROPN
iajs-2484	52	25	∈	∈	PROPN
iajs-2484	52	26	x	x	PUNCT
iajs-2484	52	27	⋃	⋃	NOUN
iajs-2484	52	28	∅	∅	NOUN
iajs-2484	52	29	,	,	PUNCT
iajs-2484	52	30	is	be	AUX
iajs-2484	52	31	ωt	ωt	ADP
iajs-2484	52	32	-space	-space	NOUN
iajs-2484	52	33	and	and	CCONJ
iajs-2484	52	34	𝑁t	𝑁t	PROPN
iajs-2484	52	35	-space	-space	NOUN
iajs-2484	52	36	.	.	PUNCT
iajs-2484	53	1	remark	remark	NOUN
iajs-2484	53	2	(	(	PUNCT
iajs-2484	53	3	1.6	1.6	NUM
iajs-2484	53	4	)	)	PUNCT
iajs-2484	53	5	1every	1every	NUM
iajs-2484	53	6	closed	closed	ADJ
iajs-2484	53	7	subset	subset	NOUN
iajs-2484	53	8	of	of	ADP
iajs-2484	53	9	a	a	DET
iajs-2484	53	10	compact	compact	ADJ
iajs-2484	53	11	space	space	NOUN
iajs-2484	53	12	is	be	AUX
iajs-2484	53	13	a	a	DET
iajs-2484	53	14	compact	compact	ADJ
iajs-2484	53	15	set	set	NOUN
iajs-2484	54	1	[	[	X
iajs-2484	54	2	6	6	NUM
iajs-2484	54	3	]	]	PUNCT
iajs-2484	54	4	.	.	PUNCT
iajs-2484	55	1	2every	2every	NUM
iajs-2484	55	2	𝜔-closed	𝜔-close	VERB
iajs-2484	55	3	subset	subset	NOUN
iajs-2484	55	4	of	of	ADP
iajs-2484	55	5	an	an	DET
iajs-2484	55	6	𝜔-compact	𝜔-compact	NOUN
iajs-2484	55	7	space	space	NOUN
iajs-2484	55	8	is	be	AUX
iajs-2484	55	9	an	an	DET
iajs-2484	55	10	𝜔-compact	𝜔-compact	NOUN
iajs-2484	55	11	set	set	NOUN
iajs-2484	55	12	[	[	X
iajs-2484	55	13	12	12	NUM
iajs-2484	55	14	]	]	PUNCT
iajs-2484	55	15	.	.	PUNCT
iajs-2484	56	1	3-	3-	NOUN
iajs-2484	56	2	 	 	SPACE
iajs-2484	56	3	every	every	DET
iajs-2484	56	4	𝑁-closed	𝑁-closed	PROPN
iajs-2484	56	5	subset	subset	NOUN
iajs-2484	56	6	of	of	ADP
iajs-2484	56	7	an	an	DET
iajs-2484	56	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	56	9	space	space	NOUN
iajs-2484	56	10	is	be	AUX
iajs-2484	56	11	an	an	DET
iajs-2484	56	12	𝑁-compact	𝑁-compact	PROPN
iajs-2484	56	13	set	set	VERB
iajs-2484	56	14	[	[	PUNCT
iajs-2484	56	15	6	6	NUM
iajs-2484	56	16	]	]	PUNCT
iajs-2484	56	17	.	.	PUNCT
iajs-2484	57	1	4every	4every	NUM
iajs-2484	57	2	compact	compact	ADJ
iajs-2484	57	3	subset	subset	NOUN
iajs-2484	57	4	of	of	ADP
iajs-2484	57	5	a	a	DET
iajs-2484	57	6	𝑇	𝑇	PROPN
iajs-2484	57	7	-space	-space	NOUN
iajs-2484	57	8	is	be	AUX
iajs-2484	57	9	a	a	DET
iajs-2484	57	10	closed	closed	ADJ
iajs-2484	57	11	set	set	NOUN
iajs-2484	57	12	[	[	X
iajs-2484	57	13	12	12	NUM
iajs-2484	57	14	]	]	PUNCT
iajs-2484	57	15	.	.	PUNCT
iajs-2484	58	1	5every	5every	NUM
iajs-2484	58	2	𝜔-compact	𝜔-compact	NOUN
iajs-2484	58	3	subset	subset	NOUN
iajs-2484	58	4	of	of	ADP
iajs-2484	58	5	an	an	DET
iajs-2484	58	6	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	58	7	-space	-space	NOUN
iajs-2484	58	8	is	be	AUX
iajs-2484	58	9	an	an	DET
iajs-2484	58	10	𝜔-closed	𝜔-close	VERB
iajs-2484	58	11	set	set	NOUN
iajs-2484	58	12	[	[	X
iajs-2484	58	13	12	12	NUM
iajs-2484	58	14	]	]	PUNCT
iajs-2484	58	15	.	.	PUNCT
iajs-2484	59	1	6every	6every	NUM
iajs-2484	59	2	𝑁-compact	𝑁-compact	PROPN
iajs-2484	59	3	subset	subset	NOUN
iajs-2484	59	4	of	of	ADP
iajs-2484	59	5	an	an	DET
iajs-2484	59	6	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	59	7	-space	-space	NOUN
iajs-2484	59	8	is	be	AUX
iajs-2484	59	9	an	an	DET
iajs-2484	59	10	𝑁-closed	𝑁-closed	PROPN
iajs-2484	59	11	set	set	NOUN
iajs-2484	59	12	[	[	NOUN
iajs-2484	59	13	13	13	NUM
iajs-2484	59	14	]	]	PUNCT
iajs-2484	59	15	.	.	PUNCT
iajs-2484	60	1	7every	7every	NUM
iajs-2484	60	2	𝑇	𝑇	PROPN
iajs-2484	60	3	-space	-space	NOUN
iajs-2484	60	4	is	be	AUX
iajs-2484	60	5	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	60	6	-space	-space	NOUN
iajs-2484	60	7	[	[	X
iajs-2484	60	8	14	14	NUM
iajs-2484	60	9	]	]	PUNCT
iajs-2484	60	10	.	.	PUNCT
iajs-2484	61	1	8every	8every	NUM
iajs-2484	61	2	𝑇	𝑇	PROPN
iajs-2484	61	3	-space	-space	NOUN
iajs-2484	61	4	is	be	AUX
iajs-2484	61	5	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	61	6	-space	-space	NOUN
iajs-2484	61	7	[	[	X
iajs-2484	61	8	6	6	NUM
iajs-2484	61	9	]	]	PUNCT
iajs-2484	61	10	.	.	PUNCT
iajs-2484	61	11	  	  	SPACE
iajs-2484	62	1	177	177	NUM
iajs-2484	62	2	  	  	SPACE
iajs-2484	62	3	ibn	ibn	PROPN
iajs-2484	62	4	al	al	PROPN
iajs-2484	62	5	-	-	PUNCT
iajs-2484	62	6	haitham	haitham	PROPN
iajs-2484	62	7	jour	jour	X
iajs-2484	62	8	.	.	PROPN
iajs-2484	62	9	for	for	ADP
iajs-2484	62	10	pure	pure	ADJ
iajs-2484	62	11	&	&	CCONJ
iajs-2484	62	12	appl	appl	PROPN
iajs-2484	62	13	.	.	PUNCT
iajs-2484	63	1	sci	sci	PROPN
iajs-2484	63	2	.	.	PROPN
iajs-2484	64	1	33	33	NUM
iajs-2484	64	2	(	(	PUNCT
iajs-2484	64	3	3	3	NUM
iajs-2484	64	4	)	)	PUNCT
iajs-2484	64	5	2020	2020	NUM
iajs-2484	64	6	definition	definition	NOUN
iajs-2484	64	7	(	(	PUNCT
iajs-2484	64	8	1.7	1.7	NUM
iajs-2484	64	9	)	)	PUNCT
iajs-2484	64	10	a	a	DET
iajs-2484	64	11	function	function	NOUN
iajs-2484	64	12	𝑓	𝑓	NOUN
iajs-2484	64	13	:	:	PUNCT
iajs-2484	64	14	𝑋	𝑋	PROPN
iajs-2484	64	15	,	,	PUNCT
iajs-2484	64	16	ʈ	ʈ	ADP
iajs-2484	64	17	⟶	⟶	NOUN
iajs-2484	64	18	𝑌	𝑌	PROPN
iajs-2484	64	19	,	,	PUNCT
iajs-2484	64	20	ʈ	ʈ	AUX
iajs-2484	64	21	is	be	AUX
iajs-2484	64	22	called	call	VERB
iajs-2484	64	23	m𝜔c	m𝜔c	NOUN
iajs-2484	64	24	-	-	PUNCT
iajs-2484	64	25	function	function	NOUN
iajs-2484	64	26	if	if	SCONJ
iajs-2484	64	27	𝑓	𝑓	DET
iajs-2484	64	28	𝒲	𝒲	PROPN
iajs-2484	64	29	is	be	AUX
iajs-2484	64	30	a	a	DET
iajs-2484	64	31	𝜔-closed	𝜔-close	VERB
iajs-2484	64	32	set	set	NOUN
iajs-2484	64	33	in	in	ADP
iajs-2484	64	34	𝑋	𝑋	NOUN
iajs-2484	64	35	for	for	ADP
iajs-2484	64	36	any	any	DET
iajs-2484	64	37	compact	compact	ADJ
iajs-2484	64	38	set	set	NOUN
iajs-2484	64	39	𝒲	𝒲	NOUN
iajs-2484	64	40	in	in	ADP
iajs-2484	64	41	𝑌.	𝑌.	PROPN
iajs-2484	64	42	definition	definition	NOUN
iajs-2484	64	43	(	(	PUNCT
iajs-2484	64	44	1.8	1.8	NUM
iajs-2484	64	45	)	)	PUNCT
iajs-2484	64	46	a	a	DET
iajs-2484	64	47	function	function	NOUN
iajs-2484	64	48	𝑓	𝑓	NOUN
iajs-2484	64	49	:	:	PUNCT
iajs-2484	64	50	𝑋	𝑋	PROPN
iajs-2484	64	51	,	,	PUNCT
iajs-2484	64	52	ʈ	ʈ	ADP
iajs-2484	64	53	⟶	⟶	NOUN
iajs-2484	64	54	𝑌	𝑌	PROPN
iajs-2484	64	55	,	,	PUNCT
iajs-2484	64	56	ʈ	ʈ	AUX
iajs-2484	64	57	is	be	AUX
iajs-2484	64	58	called	call	VERB
iajs-2484	64	59	m𝑁c	m𝑁c	NOUN
iajs-2484	64	60	-	-	PUNCT
iajs-2484	64	61	function	function	NOUN
iajs-2484	64	62	if	if	SCONJ
iajs-2484	64	63	𝑓	𝑓	DET
iajs-2484	64	64	𝒲	𝒲	PROPN
iajs-2484	64	65	is	be	AUX
iajs-2484	64	66	an	an	DET
iajs-2484	64	67	𝑁-closed	𝑁-closed	PROPN
iajs-2484	64	68	set	set	NOUN
iajs-2484	64	69	in	in	ADP
iajs-2484	64	70	𝑋	𝑋	NOUN
iajs-2484	64	71	for	for	ADP
iajs-2484	64	72	any	any	DET
iajs-2484	64	73	compact	compact	ADJ
iajs-2484	64	74	set	set	NOUN
iajs-2484	64	75	𝒲	𝒲	NOUN
iajs-2484	64	76	in	in	ADP
iajs-2484	64	77	𝑌.	𝑌.	PROPN
iajs-2484	64	78	example	example	NOUN
iajs-2484	64	79	(	(	PUNCT
iajs-2484	64	80	1.9	1.9	NUM
iajs-2484	64	81	)	)	PUNCT
iajs-2484	64	82	the	the	DET
iajs-2484	64	83	identity	identity	NOUN
iajs-2484	64	84	function	function	NOUN
iajs-2484	64	85	𝐼	𝐼	PROPN
iajs-2484	64	86	:	:	PUNCT
iajs-2484	64	87	𝑋	𝑋	PROPN
iajs-2484	64	88	,	,	PUNCT
iajs-2484	64	89	ʈ	ʈ	ADP
iajs-2484	64	90	⟶	⟶	NOUN
iajs-2484	64	91	𝑋	𝑋	PROPN
iajs-2484	64	92	,	,	PUNCT
iajs-2484	64	93	ʈ	ʈ	ADP
iajs-2484	64	94	where	where	SCONJ
iajs-2484	64	95	𝑋	𝑋	NOUN
iajs-2484	64	96	is	be	AUX
iajs-2484	64	97	a	a	DET
iajs-2484	64	98	denumerable	denumerable	ADJ
iajs-2484	64	99	set	set	NOUN
iajs-2484	64	100	(	(	PUNCT
iajs-2484	64	101	infinite	infinite	ADJ
iajs-2484	64	102	countable	countable	ADJ
iajs-2484	64	103	set	set	NOUN
iajs-2484	64	104	)	)	PUNCT
iajs-2484	64	105	,	,	PUNCT
iajs-2484	64	106	is	be	AUX
iajs-2484	64	107	m𝜔c	m𝜔c	NOUN
iajs-2484	64	108	-	-	NOUN
iajs-2484	64	109	function	function	NOUN
iajs-2484	64	110	.	.	PUNCT
iajs-2484	65	1	but	but	CCONJ
iajs-2484	65	2	in	in	ADP
iajs-2484	65	3	case	case	NOUN
iajs-2484	65	4	𝑋	𝑋	NOUN
iajs-2484	65	5	is	be	AUX
iajs-2484	65	6	a	a	DET
iajs-2484	65	7	finite	finite	NOUN
iajs-2484	65	8	set	set	VERB
iajs-2484	65	9	then	then	ADV
iajs-2484	65	10	𝑓	𝑓	PRON
iajs-2484	65	11	is	be	AUX
iajs-2484	65	12	m𝑁c	m𝑁c	NOUN
iajs-2484	65	13	-	-	PUNCT
iajs-2484	65	14	function	function	NOUN
iajs-2484	65	15	.	.	PUNCT
iajs-2484	66	1	definition	definition	NOUN
iajs-2484	66	2	(	(	PUNCT
iajs-2484	66	3	1.10	1.10	NUM
iajs-2484	66	4	):	):	PUNCT
iajs-2484	66	5	a	a	DET
iajs-2484	66	6	function	function	NOUN
iajs-2484	66	7	𝑓	𝑓	NOUN
iajs-2484	66	8	:	:	PUNCT
iajs-2484	66	9	𝑋	𝑋	PROPN
iajs-2484	66	10	,	,	PUNCT
iajs-2484	66	11	ʈ	ʈ	ADP
iajs-2484	66	12	⟶	⟶	NOUN
iajs-2484	66	13	𝑌	𝑌	PROPN
iajs-2484	66	14	,	,	PUNCT
iajs-2484	66	15	ʈ	ʈ	AUX
iajs-2484	66	16	is	be	AUX
iajs-2484	66	17	called	call	VERB
iajs-2484	66	18	𝜔mc	𝜔mc	NOUN
iajs-2484	66	19	-	-	PUNCT
iajs-2484	66	20	function	function	NOUN
iajs-2484	66	21	if	if	SCONJ
iajs-2484	66	22	𝑓	𝑓	DET
iajs-2484	66	23	𝒲	𝒲	PROPN
iajs-2484	66	24	is	be	AUX
iajs-2484	66	25	a	a	DET
iajs-2484	66	26	closed	closed	ADJ
iajs-2484	66	27	set	set	NOUN
iajs-2484	66	28	in	in	ADP
iajs-2484	66	29	𝑋	𝑋	NOUN
iajs-2484	66	30	for	for	ADP
iajs-2484	66	31	any	any	DET
iajs-2484	66	32	𝜔-compact	𝜔-compact	NOUN
iajs-2484	66	33	set	set	VERB
iajs-2484	66	34	𝒲	𝒲	NOUN
iajs-2484	66	35	in	in	ADP
iajs-2484	66	36	𝑌.	𝑌.	PROPN
iajs-2484	66	37	definition	definition	NOUN
iajs-2484	66	38	(	(	PUNCT
iajs-2484	66	39	1.11	1.11	NUM
iajs-2484	66	40	)	)	PUNCT
iajs-2484	66	41	a	a	DET
iajs-2484	66	42	function	function	NOUN
iajs-2484	66	43	𝑓	𝑓	NOUN
iajs-2484	66	44	:	:	PUNCT
iajs-2484	66	45	𝑋	𝑋	PROPN
iajs-2484	66	46	,	,	PUNCT
iajs-2484	66	47	ʈ	ʈ	ADP
iajs-2484	66	48	⟶	⟶	NOUN
iajs-2484	66	49	𝑌	𝑌	PROPN
iajs-2484	66	50	,	,	PUNCT
iajs-2484	66	51	ʈ	ʈ	AUX
iajs-2484	66	52	is	be	AUX
iajs-2484	66	53	called	call	VERB
iajs-2484	66	54	𝑁mc	𝑁mc	NOUN
iajs-2484	66	55	-	-	PUNCT
iajs-2484	66	56	function	function	NOUN
iajs-2484	66	57	if	if	SCONJ
iajs-2484	66	58	𝑓	𝑓	DET
iajs-2484	66	59	𝒲	𝒲	PROPN
iajs-2484	66	60	is	be	AUX
iajs-2484	66	61	a	a	DET
iajs-2484	66	62	closed	closed	ADJ
iajs-2484	66	63	set	set	NOUN
iajs-2484	66	64	in	in	ADP
iajs-2484	66	65	𝑋	𝑋	NOUN
iajs-2484	66	66	for	for	ADP
iajs-2484	66	67	any	any	DET
iajs-2484	66	68	𝑁-compact	𝑁-compact	PROPN
iajs-2484	66	69	set	set	VERB
iajs-2484	66	70	𝒲	𝒲	NOUN
iajs-2484	66	71	in	in	ADP
iajs-2484	66	72	𝑌.	𝑌.	PROPN
iajs-2484	66	73	example	example	NOUN
iajs-2484	66	74	(	(	PUNCT
iajs-2484	66	75	1.12	1.12	NUM
iajs-2484	66	76	)	)	PUNCT
iajs-2484	66	77	the	the	DET
iajs-2484	66	78	identity	identity	NOUN
iajs-2484	66	79	function	function	NOUN
iajs-2484	66	80	𝐼ℛ	𝐼ℛ	PROPN
iajs-2484	66	81	:	:	PUNCT
iajs-2484	66	82	ℛ	ℛ	PROPN
iajs-2484	66	83	,	,	PUNCT
iajs-2484	66	84	ʈ	ʈ	ADP
iajs-2484	66	85	⟶	⟶	PROPN
iajs-2484	66	86	ℛ	ℛ	PROPN
iajs-2484	66	87	,	,	PUNCT
iajs-2484	66	88	ʈ	ʈ	X
iajs-2484	66	89	is	be	AUX
iajs-2484	66	90	𝜔mc	𝜔mc	NOUN
iajs-2484	66	91	-	-	PUNCT
iajs-2484	66	92	function	function	NOUN
iajs-2484	66	93	and	and	CCONJ
iajs-2484	66	94	𝑁mc	𝑁mc	NOUN
iajs-2484	66	95	-	-	PUNCT
iajs-2484	66	96	function	function	NOUN
iajs-2484	66	97	.	.	PUNCT
iajs-2484	67	1	definition	definition	NOUN
iajs-2484	67	2	(	(	PUNCT
iajs-2484	67	3	1.13	1.13	NUM
iajs-2484	67	4	)	)	PUNCT
iajs-2484	67	5	a	a	DET
iajs-2484	67	6	function	function	NOUN
iajs-2484	67	7	𝑓	𝑓	NOUN
iajs-2484	67	8	:	:	PUNCT
iajs-2484	67	9	𝑋	𝑋	PROPN
iajs-2484	67	10	,	,	PUNCT
iajs-2484	67	11	ʈ	ʈ	ADP
iajs-2484	67	12	⟶	⟶	NOUN
iajs-2484	67	13	𝑌	𝑌	PROPN
iajs-2484	67	14	,	,	PUNCT
iajs-2484	67	15	ʈ	ʈ	AUX
iajs-2484	67	16	is	be	AUX
iajs-2484	67	17	called	call	VERB
iajs-2484	67	18	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	67	19	-	-	PUNCT
iajs-2484	67	20	function	function	NOUN
iajs-2484	67	21	if	if	SCONJ
iajs-2484	67	22	𝑓	𝑓	DET
iajs-2484	67	23	𝒲	𝒲	PROPN
iajs-2484	67	24	is	be	AUX
iajs-2484	67	25	an	an	DET
iajs-2484	67	26	𝜔-closed	𝜔-close	VERB
iajs-2484	67	27	set	set	NOUN
iajs-2484	67	28	in	in	ADP
iajs-2484	67	29	𝑋	𝑋	NOUN
iajs-2484	67	30	for	for	ADP
iajs-2484	67	31	any	any	DET
iajs-2484	67	32	𝜔-compact	𝜔-compact	NOUN
iajs-2484	67	33	set	set	VERB
iajs-2484	67	34	𝒲	𝒲	NOUN
iajs-2484	67	35	in	in	ADP
iajs-2484	67	36	𝑌.	𝑌.	PROPN
iajs-2484	67	37	example	example	NOUN
iajs-2484	67	38	(	(	PUNCT
iajs-2484	67	39	1.14	1.14	NUM
iajs-2484	67	40	)	)	PUNCT
iajs-2484	67	41	the	the	DET
iajs-2484	67	42	function	function	NOUN
iajs-2484	67	43	𝑓	𝑓	NOUN
iajs-2484	67	44	:	:	PUNCT
iajs-2484	67	45	𝑁	𝑁	PROPN
iajs-2484	67	46	,	,	PUNCT
iajs-2484	67	47	ʈ	ʈ	ADP
iajs-2484	67	48	⟶	⟶	NOUN
iajs-2484	67	49	ℛ	ℛ	PROPN
iajs-2484	67	50	,	,	PUNCT
iajs-2484	67	51	ʈℛ	ʈℛ	PROPN
iajs-2484	67	52	is	be	AUX
iajs-2484	67	53	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	67	54	-	-	PUNCT
iajs-2484	67	55	function	function	NOUN
iajs-2484	67	56	.	.	PUNCT
iajs-2484	68	1	definition	definition	NOUN
iajs-2484	68	2	(	(	PUNCT
iajs-2484	68	3	1.15	1.15	NUM
iajs-2484	68	4	)	)	PUNCT
iajs-2484	68	5	the	the	DET
iajs-2484	68	6	function	function	NOUN
iajs-2484	68	7	𝑓	𝑓	PROPN
iajs-2484	68	8	:	:	PUNCT
iajs-2484	68	9	𝑋	𝑋	PROPN
iajs-2484	68	10	,	,	PUNCT
iajs-2484	68	11	ʈ	ʈ	ADP
iajs-2484	68	12	⟶	⟶	NOUN
iajs-2484	68	13	𝑌	𝑌	PROPN
iajs-2484	68	14	,	,	PUNCT
iajs-2484	68	15	ʈ	ʈ	AUX
iajs-2484	68	16	is	be	AUX
iajs-2484	68	17	called	call	VERB
iajs-2484	68	18	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	68	19	-	-	PUNCT
iajs-2484	68	20	function	function	NOUN
iajs-2484	68	21	if	if	SCONJ
iajs-2484	68	22	𝑓	𝑓	DET
iajs-2484	68	23	𝒲	𝒲	PROPN
iajs-2484	68	24	is	be	AUX
iajs-2484	68	25	an	an	DET
iajs-2484	68	26	𝑁-closed	𝑁-closed	PROPN
iajs-2484	68	27	set	set	NOUN
iajs-2484	68	28	in	in	ADP
iajs-2484	68	29	𝑋	𝑋	NOUN
iajs-2484	68	30	for	for	ADP
iajs-2484	68	31	any	any	DET
iajs-2484	68	32	𝑁-compact	𝑁-compact	PROPN
iajs-2484	68	33	set	set	VERB
iajs-2484	68	34	𝒲	𝒲	NOUN
iajs-2484	68	35	in	in	ADP
iajs-2484	68	36	𝑌.	𝑌.	PROPN
iajs-2484	68	37	example	example	NOUN
iajs-2484	68	38	(	(	PUNCT
iajs-2484	68	39	1.16	1.16	NUM
iajs-2484	68	40	)	)	PUNCT
iajs-2484	68	41	the	the	DET
iajs-2484	68	42	function	function	NOUN
iajs-2484	68	43	𝑓	𝑓	PROPN
iajs-2484	68	44	:	:	PUNCT
iajs-2484	68	45	𝑋	𝑋	PROPN
iajs-2484	68	46	,	,	PUNCT
iajs-2484	68	47	ʈ	ʈ	ADP
iajs-2484	68	48	⟶	⟶	NOUN
iajs-2484	68	49	ℛ	ℛ	PROPN
iajs-2484	68	50	,	,	PUNCT
iajs-2484	68	51	ʈℛ	ʈℛ	ADJ
iajs-2484	68	52	where	where	SCONJ
iajs-2484	68	53	𝑋	𝑋	PROPN
iajs-2484	68	54	is	be	AUX
iajs-2484	68	55	a	a	DET
iajs-2484	68	56	finite	finite	ADJ
iajs-2484	68	57	set	set	NOUN
iajs-2484	68	58	,	,	PUNCT
iajs-2484	68	59	is	be	AUX
iajs-2484	68	60	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	68	61	-	-	PUNCT
iajs-2484	68	62	function	function	NOUN
iajs-2484	68	63	.	.	PUNCT
iajs-2484	69	1	the	the	DET
iajs-2484	69	2	following	follow	VERB
iajs-2484	69	3	scheme	scheme	NOUN
iajs-2484	69	4	is	be	AUX
iajs-2484	69	5	helpful	helpful	ADJ
iajs-2484	69	6	mc	mc	NOUN
iajs-2484	69	7	-	-	PUNCT
iajs-2484	69	8	function	function	NOUN
iajs-2484	69	9	m𝜔c	m𝜔c	NOUN
iajs-2484	69	10	-	-	PUNCT
iajs-2484	69	11	function	function	NOUN
iajs-2484	69	12	(	(	PUNCT
iajs-2484	69	13	resp	resp	NOUN
iajs-2484	69	14	.	.	PUNCT
iajs-2484	70	1	m𝑁c	m𝑁c	NOUN
iajs-2484	70	2	-	-	PUNCT
iajs-2484	70	3	function	function	NOUN
iajs-2484	70	4	)	)	PUNCT
iajs-2484	70	5	𝜔mc	𝜔mc	NOUN
iajs-2484	70	6	-	-	PUNCT
iajs-2484	70	7	function	function	NOUN
iajs-2484	70	8	(	(	PUNCT
iajs-2484	70	9	resp	resp	NOUN
iajs-2484	70	10	.	.	PUNCT
iajs-2484	71	1	𝑁mc	𝑁mc	NOUN
iajs-2484	71	2	-	-	PUNCT
iajs-2484	71	3	function	function	NOUN
iajs-2484	71	4	)	)	PUNCT
iajs-2484	71	5	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	71	6	-	-	PUNCT
iajs-2484	71	7	function	function	NOUN
iajs-2484	71	8	(	(	PUNCT
iajs-2484	71	9	resp	resp	NOUN
iajs-2484	71	10	.	.	PUNCT
iajs-2484	72	1	𝑁m𝑁cfunction	𝑁m𝑁cfunction	NOUN
iajs-2484	72	2	)	)	PUNCT
iajs-2484	72	3	remark	remark	NOUN
iajs-2484	72	4	(	(	PUNCT
iajs-2484	72	5	1.17	1.17	NUM
iajs-2484	72	6	)	)	PUNCT
iajs-2484	72	7	1every	1every	NUM
iajs-2484	72	8	𝑁mc	𝑁mc	NOUN
iajs-2484	72	9	-	-	PUNCT
iajs-2484	72	10	function	function	NOUN
iajs-2484	72	11	is	be	AUX
iajs-2484	72	12	𝜔mc	𝜔mc	NOUN
iajs-2484	72	13	-	-	PUNCT
iajs-2484	72	14	function	function	NOUN
iajs-2484	72	15	.	.	PUNCT
iajs-2484	73	1	2every	2every	NUM
iajs-2484	73	2	m𝑁c	m𝑁c	VERB
iajs-2484	73	3	-	-	PUNCT
iajs-2484	73	4	function	function	NOUN
iajs-2484	73	5	is	be	AUX
iajs-2484	73	6	m𝜔c	m𝜔c	NOUN
iajs-2484	73	7	-	-	NOUN
iajs-2484	73	8	function	function	NOUN
iajs-2484	73	9	.	.	PUNCT
iajs-2484	74	1	3every	3every	NUM
iajs-2484	74	2	𝑁m𝑁c	𝑁m𝑁c	NOUN
iajs-2484	74	3	-	-	PUNCT
iajs-2484	74	4	function	function	NOUN
iajs-2484	74	5	is	be	AUX
iajs-2484	74	6	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	74	7	-	-	PUNCT
iajs-2484	74	8	function	function	NOUN
iajs-2484	74	9	.	.	PUNCT
iajs-2484	75	1	example	example	NOUN
iajs-2484	75	2	(	(	PUNCT
iajs-2484	75	3	1.18	1.18	NUM
iajs-2484	75	4	)	)	PUNCT
iajs-2484	75	5	1𝐼𝒵	1𝐼𝒵	NUM
iajs-2484	75	6	:	:	PUNCT
iajs-2484	75	7	𝒵	𝒵	NUM
iajs-2484	75	8	,	,	PUNCT
iajs-2484	75	9	ʈ	ʈ	ADP
iajs-2484	75	10	⟶	⟶	PROPN
iajs-2484	75	11	𝒵	𝒵	PROPN
iajs-2484	75	12	,	,	PUNCT
iajs-2484	75	13	ʈ	ʈ	X
iajs-2484	75	14	is	be	AUX
iajs-2484	75	15	m𝜔c	m𝜔c	NOUN
iajs-2484	75	16	-	-	PUNCT
iajs-2484	75	17	function	function	NOUN
iajs-2484	75	18	but	but	CCONJ
iajs-2484	75	19	neither	neither	DET
iajs-2484	75	20	m𝑁c	m𝑁c	NOUN
iajs-2484	75	21	-	-	PUNCT
iajs-2484	75	22	function	function	NOUN
iajs-2484	75	23	nor	nor	CCONJ
iajs-2484	75	24	mc	mc	NOUN
iajs-2484	75	25	-	-	PUNCT
iajs-2484	75	26	function	function	NOUN
iajs-2484	75	27	.	.	PUNCT
iajs-2484	76	1	2𝐼	2𝐼	NOUN
iajs-2484	76	2	:	:	PUNCT
iajs-2484	77	1	𝑋	𝑋	PROPN
iajs-2484	77	2	,	,	PUNCT
iajs-2484	77	3	ʈ	ʈ	ADP
iajs-2484	77	4	⟶	⟶	NOUN
iajs-2484	77	5	𝑋	𝑋	PROPN
iajs-2484	77	6	,	,	PUNCT
iajs-2484	77	7	ʈ	ʈ	ADP
iajs-2484	77	8	where	where	SCONJ
iajs-2484	77	9	𝑋	𝑋	NOUN
iajs-2484	77	10	is	be	AUX
iajs-2484	77	11	a	a	DET
iajs-2484	77	12	finite	finite	ADJ
iajs-2484	77	13	set	set	NOUN
iajs-2484	77	14	,	,	PUNCT
iajs-2484	77	15	is	be	AUX
iajs-2484	77	16	m𝑁c	m𝑁c	NOUN
iajs-2484	77	17	-	-	PUNCT
iajs-2484	77	18	function	function	NOUN
iajs-2484	77	19	but	but	CCONJ
iajs-2484	77	20	not	not	PART
iajs-2484	77	21	mc	mc	PROPN
iajs-2484	77	22	-	-	PUNCT
iajs-2484	77	23	function	function	NOUN
iajs-2484	77	24	.	.	PUNCT
iajs-2484	77	25	  	  	SPACE
iajs-2484	78	1	178	178	NUM
iajs-2484	78	2	  	  	SPACE
iajs-2484	78	3	ibn	ibn	PROPN
iajs-2484	78	4	al	al	PROPN
iajs-2484	78	5	-	-	PUNCT
iajs-2484	78	6	haitham	haitham	PROPN
iajs-2484	78	7	jour	jour	X
iajs-2484	78	8	.	.	PROPN
iajs-2484	78	9	for	for	ADP
iajs-2484	78	10	pure	pure	ADJ
iajs-2484	78	11	&	&	CCONJ
iajs-2484	78	12	appl	appl	PROPN
iajs-2484	78	13	.	.	PUNCT
iajs-2484	79	1	sci	sci	PROPN
iajs-2484	79	2	.	.	PROPN
iajs-2484	80	1	33	33	NUM
iajs-2484	80	2	(	(	PUNCT
iajs-2484	80	3	3	3	NUM
iajs-2484	80	4	)	)	PUNCT
iajs-2484	80	5	2020	2020	NUM
iajs-2484	80	6	3𝑓	3𝑓	NOUN
iajs-2484	80	7	:	:	PUNCT
iajs-2484	80	8	𝒵	𝒵	PROPN
iajs-2484	80	9	,	,	PUNCT
iajs-2484	80	10	ʈ	ʈ	ADP
iajs-2484	80	11	⟶	⟶	PROPN
iajs-2484	80	12	𝒵	𝒵	PROPN
iajs-2484	80	13	,	,	PUNCT
iajs-2484	80	14	ʈ	ʈ	PROPN
iajs-2484	80	15	is	be	AUX
iajs-2484	80	16	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	80	17	-	-	PUNCT
iajs-2484	80	18	function	function	NOUN
iajs-2484	80	19	but	but	CCONJ
iajs-2484	80	20	not	not	PART
iajs-2484	80	21	𝜔mc	𝜔mc	NOUN
iajs-2484	80	22	-	-	PUNCT
iajs-2484	80	23	function	function	NOUN
iajs-2484	80	24	.	.	PUNCT
iajs-2484	81	1	4𝑓	4𝑓	NUM
iajs-2484	81	2	:	:	PUNCT
iajs-2484	81	3	𝑋	𝑋	NOUN
iajs-2484	81	4	,	,	PUNCT
iajs-2484	81	5	ʈ	ʈ	PROPN
iajs-2484	81	6	⟶	⟶	NOUN
iajs-2484	81	7	𝑋	𝑋	PROPN
iajs-2484	81	8	,	,	PUNCT
iajs-2484	81	9	ʈ	ʈ	ADP
iajs-2484	81	10	where	where	SCONJ
iajs-2484	81	11	𝑋	𝑋	NOUN
iajs-2484	81	12	is	be	AUX
iajs-2484	81	13	a	a	DET
iajs-2484	81	14	finite	finite	ADJ
iajs-2484	81	15	set	set	NOUN
iajs-2484	81	16	,	,	PUNCT
iajs-2484	81	17	is	be	AUX
iajs-2484	81	18	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	81	19	-	-	PUNCT
iajs-2484	81	20	function	function	NOUN
iajs-2484	81	21	but	but	CCONJ
iajs-2484	81	22	not	not	PART
iajs-2484	81	23	𝑁mc	𝑁mc	NOUN
iajs-2484	81	24	-	-	PUNCT
iajs-2484	81	25	function	function	NOUN
iajs-2484	81	26	.	.	PUNCT
iajs-2484	82	1	5𝐼	5𝐼	NOUN
iajs-2484	82	2	:	:	PUNCT
iajs-2484	83	1	𝑋	𝑋	NOUN
iajs-2484	83	2	,	,	PUNCT
iajs-2484	83	3	ʈ	ʈ	ADP
iajs-2484	83	4	⟶	⟶	NOUN
iajs-2484	83	5	𝑋	𝑋	PROPN
iajs-2484	83	6	,	,	PUNCT
iajs-2484	83	7	ʈ	ʈ	ADP
iajs-2484	83	8	where	where	SCONJ
iajs-2484	83	9	𝑋=	𝑋=	NOUN
iajs-2484	83	10	{	{	PUNCT
iajs-2484	83	11	1	1	NUM
iajs-2484	83	12	,	,	PUNCT
iajs-2484	83	13	2	2	NUM
iajs-2484	83	14	,	,	PUNCT
iajs-2484	83	15	3	3	NUM
iajs-2484	83	16	}	}	PUNCT
iajs-2484	83	17	and	and	CCONJ
iajs-2484	83	18	ʈ=	ʈ=	NOUN
iajs-2484	83	19	{	{	PUNCT
iajs-2484	83	20	∅	∅	NOUN
iajs-2484	83	21	,	,	PUNCT
iajs-2484	83	22	𝑋	𝑋	PROPN
iajs-2484	83	23	,	,	PUNCT
iajs-2484	83	24	1	1	NUM
iajs-2484	83	25	}	}	PUNCT
iajs-2484	83	26	is	be	AUX
iajs-2484	83	27	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	83	28	-	-	PUNCT
iajs-2484	83	29	function	function	NOUN
iajs-2484	83	30	and	and	CCONJ
iajs-2484	83	31	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	83	32	-	-	PUNCT
iajs-2484	83	33	function	function	NOUN
iajs-2484	83	34	,	,	PUNCT
iajs-2484	83	35	but	but	CCONJ
iajs-2484	83	36	not	not	PART
iajs-2484	83	37	mc	mc	PROPN
iajs-2484	83	38	-	-	PUNCT
iajs-2484	83	39	function	function	NOUN
iajs-2484	83	40	.	.	PUNCT
iajs-2484	84	1	6	6	NUM
iajs-2484	84	2	𝐼𝒵	𝐼𝒵	NOUN
iajs-2484	84	3	:	:	PUNCT
iajs-2484	84	4	𝒵	𝒵	PROPN
iajs-2484	84	5	,	,	PUNCT
iajs-2484	84	6	ʈ	ʈ	ADP
iajs-2484	84	7	⟶	⟶	PROPN
iajs-2484	84	8	𝒵	𝒵	PROPN
iajs-2484	84	9	,	,	PUNCT
iajs-2484	84	10	ʈ	ʈ	X
iajs-2484	84	11	is	be	AUX
iajs-2484	84	12	m𝜔c	m𝜔c	NOUN
iajs-2484	84	13	-	-	NOUN
iajs-2484	84	14	function	function	NOUN
iajs-2484	84	15	,	,	PUNCT
iajs-2484	84	16	but	but	CCONJ
iajs-2484	84	17	not	not	PART
iajs-2484	84	18	𝜔mc	𝜔mc	NOUN
iajs-2484	84	19	-	-	PUNCT
iajs-2484	84	20	function	function	NOUN
iajs-2484	84	21	.	.	PUNCT
iajs-2484	85	1	7𝐼	7𝐼	ADJ
iajs-2484	85	2	:	:	PUNCT
iajs-2484	85	3	𝑋	𝑋	NOUN
iajs-2484	85	4	,	,	PUNCT
iajs-2484	85	5	ʈ	ʈ	ADP
iajs-2484	85	6	⟶	⟶	NOUN
iajs-2484	85	7	𝑋	𝑋	PROPN
iajs-2484	85	8	,	,	PUNCT
iajs-2484	85	9	ʈ	ʈ	ADP
iajs-2484	85	10	 	 	SPACE
iajs-2484	85	11	where	where	SCONJ
iajs-2484	85	12	𝑋	𝑋	PROPN
iajs-2484	85	13	is	be	AUX
iajs-2484	85	14	a	a	DET
iajs-2484	85	15	finite	finite	ADJ
iajs-2484	85	16	set	set	NOUN
iajs-2484	85	17	,	,	PUNCT
iajs-2484	85	18	is	be	AUX
iajs-2484	85	19	m𝑁c	m𝑁c	NOUN
iajs-2484	85	20	-	-	PUNCT
iajs-2484	85	21	function	function	NOUN
iajs-2484	85	22	but	but	CCONJ
iajs-2484	85	23	not	not	PART
iajs-2484	85	24	𝑁mc	𝑁mc	NOUN
iajs-2484	85	25	-	-	PUNCT
iajs-2484	85	26	function	function	NOUN
iajs-2484	85	27	.	.	PUNCT
iajs-2484	86	1	8𝐼𝒵	8𝐼𝒵	NUM
iajs-2484	86	2	:	:	PUNCT
iajs-2484	86	3	𝒵	𝒵	NUM
iajs-2484	86	4	,	,	PUNCT
iajs-2484	86	5	ʈ	ʈ	ADP
iajs-2484	86	6	⟶	⟶	PROPN
iajs-2484	86	7	𝒵	𝒵	PROPN
iajs-2484	86	8	,	,	PUNCT
iajs-2484	86	9	ʈ	ʈ	X
iajs-2484	86	10	is	be	AUX
iajs-2484	86	11	𝜔mc	𝜔mc	NOUN
iajs-2484	86	12	-	-	PUNCT
iajs-2484	86	13	function	function	NOUN
iajs-2484	86	14	but	but	CCONJ
iajs-2484	86	15	not	not	PART
iajs-2484	86	16	𝑁mc	𝑁mc	NOUN
iajs-2484	86	17	-	-	PUNCT
iajs-2484	86	18	function	function	NOUN
iajs-2484	86	19	.	.	PUNCT
iajs-2484	87	1	9𝐼𝒵	9𝐼𝒵	NUM
iajs-2484	87	2	:	:	PUNCT
iajs-2484	87	3	𝒵	𝒵	PROPN
iajs-2484	87	4	,	,	PUNCT
iajs-2484	87	5	ʈ	ʈ	ADP
iajs-2484	87	6	⟶	⟶	PROPN
iajs-2484	87	7	𝒵	𝒵	PROPN
iajs-2484	87	8	,	,	PUNCT
iajs-2484	87	9	ʈ	ʈ	X
iajs-2484	87	10	is	be	AUX
iajs-2484	87	11	m𝜔c	m𝜔c	NOUN
iajs-2484	87	12	-	-	PUNCT
iajs-2484	87	13	function	function	NOUN
iajs-2484	87	14	and	and	CCONJ
iajs-2484	87	15	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	87	16	-	-	PUNCT
iajs-2484	87	17	function	function	NOUN
iajs-2484	87	18	but	but	CCONJ
iajs-2484	87	19	neither	neither	CCONJ
iajs-2484	87	20	𝑁m𝑁cfunction	𝑁m𝑁cfunction	PROPN
iajs-2484	87	21	nor	nor	CCONJ
iajs-2484	87	22	m𝑁c	m𝑁c	NOUN
iajs-2484	87	23	-	-	PUNCT
iajs-2484	87	24	function	function	NOUN
iajs-2484	87	25	.	.	PUNCT
iajs-2484	88	1	definition	definition	NOUN
iajs-2484	88	2	(	(	PUNCT
iajs-2484	88	3	1.19	1.19	NUM
iajs-2484	88	4	)	)	PUNCT
iajs-2484	88	5	a	a	DET
iajs-2484	88	6	function	function	NOUN
iajs-2484	88	7	𝑓	𝑓	NOUN
iajs-2484	88	8	:	:	PUNCT
iajs-2484	88	9	𝑋	𝑋	PROPN
iajs-2484	88	10	,	,	PUNCT
iajs-2484	88	11	ʈ	ʈ	ADP
iajs-2484	88	12	⟶	⟶	NOUN
iajs-2484	88	13	𝑌	𝑌	PROPN
iajs-2484	88	14	,	,	PUNCT
iajs-2484	88	15	ʈ	ʈ	AUX
iajs-2484	88	16	is	be	AUX
iajs-2484	88	17	called	call	VERB
iajs-2484	88	18	:	:	PUNCT
iajs-2484	88	19	1a	1a	NUM
iajs-2484	88	20	continuous	continuous	ADJ
iajs-2484	88	21	function	function	NOUN
iajs-2484	88	22	if	if	SCONJ
iajs-2484	88	23	𝑓	𝑓	DET
iajs-2484	88	24	𝒲	𝒲	PROPN
iajs-2484	88	25	is	be	AUX
iajs-2484	88	26	open	open	ADJ
iajs-2484	88	27	set	set	VERB
iajs-2484	88	28	in	in	ADP
iajs-2484	88	29	𝑋	𝑋	NOUN
iajs-2484	88	30	for	for	ADP
iajs-2484	88	31	any	any	DET
iajs-2484	88	32	open	open	ADJ
iajs-2484	88	33	set	set	NOUN
iajs-2484	88	34	𝒲	𝒲	NOUN
iajs-2484	88	35	in	in	ADP
iajs-2484	88	36	the	the	DET
iajs-2484	88	37	space	space	NOUN
iajs-2484	88	38	𝑌	𝑌	PROPN
iajs-2484	89	1	[	[	X
iajs-2484	89	2	15	15	NUM
iajs-2484	89	3	]	]	PUNCT
iajs-2484	89	4	.	.	PUNCT
iajs-2484	90	1	2an	2an	ADJ
iajs-2484	90	2	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	90	3	function	function	NOUN
iajs-2484	90	4	if	if	SCONJ
iajs-2484	90	5	𝑓	𝑓	DET
iajs-2484	90	6	𝒲	𝒲	PROPN
iajs-2484	90	7	is	be	AUX
iajs-2484	90	8	𝜔-open	𝜔-open	ADJ
iajs-2484	90	9	set	set	VERB
iajs-2484	90	10	in	in	ADP
iajs-2484	90	11	𝑋	𝑋	NOUN
iajs-2484	90	12	for	for	ADP
iajs-2484	90	13	each	each	DET
iajs-2484	90	14	open	open	ADJ
iajs-2484	90	15	set	set	ADJ
iajs-2484	90	16	𝒲	𝒲	NOUN
iajs-2484	90	17	in	in	ADP
iajs-2484	90	18	𝑌	𝑌	PROPN
iajs-2484	91	1	[	[	X
iajs-2484	91	2	16	16	NUM
iajs-2484	91	3	]	]	PUNCT
iajs-2484	91	4	.	.	PUNCT
iajs-2484	92	1	3-	3-	NOUN
iajs-2484	92	2	 	 	SPACE
iajs-2484	92	3	an	an	DET
iajs-2484	92	4	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	92	5	function	function	NOUN
iajs-2484	92	6	if	if	SCONJ
iajs-2484	92	7	𝑓	𝑓	DET
iajs-2484	92	8	𝒲	𝒲	PROPN
iajs-2484	92	9	is	be	AUX
iajs-2484	92	10	𝑁-open	𝑁-open	PROPN
iajs-2484	92	11	set	set	VERB
iajs-2484	92	12	in	in	ADP
iajs-2484	92	13	𝑋	𝑋	NOUN
iajs-2484	92	14	for	for	ADP
iajs-2484	92	15	each	each	DET
iajs-2484	92	16	open	open	ADJ
iajs-2484	92	17	set	set	ADJ
iajs-2484	92	18	𝒲	𝒲	NOUN
iajs-2484	92	19	in	in	ADP
iajs-2484	92	20	𝑌	𝑌	PROPN
iajs-2484	92	21	[	[	X
iajs-2484	92	22	15	15	NUM
iajs-2484	92	23	]	]	PUNCT
iajs-2484	92	24	.	.	PUNCT
iajs-2484	93	1	4a	4a	NOUN
iajs-2484	93	2	strongly	strongly	ADV
iajs-2484	93	3	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	93	4	function	function	NOUN
iajs-2484	93	5	if	if	SCONJ
iajs-2484	93	6	𝑓	𝑓	DET
iajs-2484	93	7	𝒲	𝒲	PROPN
iajs-2484	93	8	is	be	AUX
iajs-2484	93	9	open	open	ADJ
iajs-2484	93	10	set	set	VERB
iajs-2484	93	11	in	in	ADP
iajs-2484	93	12	𝑋	𝑋	NOUN
iajs-2484	93	13	for	for	ADP
iajs-2484	93	14	each	each	DET
iajs-2484	93	15	𝜔-open	𝜔-open	NOUN
iajs-2484	93	16	set	set	VERB
iajs-2484	93	17	𝒲	𝒲	NOUN
iajs-2484	93	18	in	in	ADP
iajs-2484	93	19	𝑌.	𝑌.	PROPN
iajs-2484	93	20	5a	5a	NUM
iajs-2484	93	21	strongly	strongly	ADV
iajs-2484	93	22	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	93	23	function	function	NOUN
iajs-2484	93	24	if	if	SCONJ
iajs-2484	93	25	𝑓	𝑓	DET
iajs-2484	93	26	𝒲	𝒲	PROPN
iajs-2484	93	27	is	be	AUX
iajs-2484	93	28	open	open	ADJ
iajs-2484	93	29	set	set	VERB
iajs-2484	93	30	in	in	ADP
iajs-2484	93	31	𝑋	𝑋	NOUN
iajs-2484	93	32	for	for	ADP
iajs-2484	93	33	each	each	DET
iajs-2484	93	34	𝑁-open	𝑁-open	PROPN
iajs-2484	93	35	set	set	VERB
iajs-2484	93	36	𝒲	𝒲	NOUN
iajs-2484	93	37	in	in	ADP
iajs-2484	93	38	𝑌.	𝑌.	PROPN
iajs-2484	93	39	6-	6-	PROPN
iajs-2484	93	40	 	 	SPACE
iajs-2484	93	41	an	an	DET
iajs-2484	93	42	 	 	SPACE
iajs-2484	93	43	𝜔‐irresolute	𝜔‐irresolute	PUNCT
iajs-2484	93	44	function	function	NOUN
iajs-2484	93	45	 	 	SPACE
iajs-2484	93	46	if	if	SCONJ
iajs-2484	93	47	𝑓	𝑓	DET
iajs-2484	93	48	𝒲	𝒲	PROPN
iajs-2484	93	49	is	be	AUX
iajs-2484	93	50	𝜔-open	𝜔-open	ADJ
iajs-2484	93	51	set	set	VERB
iajs-2484	93	52	in	in	ADP
iajs-2484	93	53	𝑋	𝑋	NOUN
iajs-2484	93	54	for	for	ADP
iajs-2484	93	55	each	each	DET
iajs-2484	93	56	𝜔-open	𝜔-open	NOUN
iajs-2484	93	57	set	set	VERB
iajs-2484	93	58	in	in	ADP
iajs-2484	93	59	𝑌.	𝑌.	PROPN
iajs-2484	93	60	7an	7an	PROPN
iajs-2484	93	61	𝑁-irresolute	𝑁-irresolute	PROPN
iajs-2484	93	62	function	function	NOUN
iajs-2484	93	63	if	if	SCONJ
iajs-2484	93	64	𝑓	𝑓	DET
iajs-2484	93	65	𝒲	𝒲	PROPN
iajs-2484	93	66	is	be	AUX
iajs-2484	93	67	𝑁-open	𝑁-open	PROPN
iajs-2484	93	68	set	set	VERB
iajs-2484	93	69	in	in	ADP
iajs-2484	93	70	𝑋	𝑋	NOUN
iajs-2484	93	71	for	for	ADP
iajs-2484	93	72	each	each	DET
iajs-2484	93	73	𝑁-open	𝑁-open	PROPN
iajs-2484	93	74	set	set	VERB
iajs-2484	93	75	𝒲	𝒲	NOUN
iajs-2484	93	76	in	in	ADP
iajs-2484	93	77	𝑌	𝑌	PROPN
iajs-2484	94	1	[	[	X
iajs-2484	94	2	9	9	NUM
iajs-2484	94	3	]	]	PUNCT
iajs-2484	94	4	.	.	PUNCT
iajs-2484	95	1	example	example	NOUN
iajs-2484	95	2	(	(	PUNCT
iajs-2484	95	3	1.20	1.20	NUM
iajs-2484	95	4	)	)	PUNCT
iajs-2484	95	5	1𝑓	1𝑓	NUM
iajs-2484	95	6	:	:	PUNCT
iajs-2484	95	7	𝑋	𝑋	PROPN
iajs-2484	95	8	,	,	PUNCT
iajs-2484	95	9	ʈ	ʈ	ADP
iajs-2484	95	10	⟶	⟶	NOUN
iajs-2484	95	11	𝑌	𝑌	PROPN
iajs-2484	95	12	,	,	PUNCT
iajs-2484	95	13	ʈ	ʈ	AUX
iajs-2484	95	14	is	be	AUX
iajs-2484	95	15	continuous	continuous	ADJ
iajs-2484	95	16	function	function	NOUN
iajs-2484	95	17	.	.	PUNCT
iajs-2484	96	1	2the	2the	PRON
iajs-2484	96	2	function	function	NOUN
iajs-2484	96	3	𝑓	𝑓	ADV
iajs-2484	96	4	from	from	ADP
iajs-2484	96	5	the	the	DET
iajs-2484	96	6	excluded	exclude	VERB
iajs-2484	96	7	point	point	NOUN
iajs-2484	96	8	space	space	NOUN
iajs-2484	96	9	𝑋	𝑋	PROPN
iajs-2484	96	10	,	,	PUNCT
iajs-2484	96	11	ʈ	ʈ	ADP
iajs-2484	96	12	where	where	SCONJ
iajs-2484	96	13	𝑋	𝑋	NOUN
iajs-2484	96	14	is	be	AUX
iajs-2484	96	15	a	a	DET
iajs-2484	96	16	countable	countable	ADJ
iajs-2484	96	17	set	set	NOUN
iajs-2484	96	18	into	into	ADP
iajs-2484	96	19	any	any	DET
iajs-2484	96	20	space	space	NOUN
iajs-2484	96	21	𝑌	𝑌	PROPN
iajs-2484	96	22	,	,	PUNCT
iajs-2484	96	23	ʈ	ʈ	PROPN
iajs-2484	96	24	is	be	AUX
iajs-2484	96	25	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	96	26	function	function	NOUN
iajs-2484	96	27	,	,	PUNCT
iajs-2484	96	28	where	where	SCONJ
iajs-2484	96	29	ʈ	ʈ	ADP
iajs-2484	96	30	𝒲	𝒲	NOUN
iajs-2484	96	31	⊆	⊆	NUM
iajs-2484	96	32	𝑋	𝑋	PROPN
iajs-2484	96	33	,	,	PUNCT
iajs-2484	96	34	𝑎∘	𝑎∘	PROPN
iajs-2484	96	35	∉	∉	PROPN
iajs-2484	96	36	𝒲	𝒲	PROPN
iajs-2484	96	37	for	for	ADP
iajs-2484	96	38	some	some	DET
iajs-2484	96	39	𝑎∘	𝑎∘	PROPN
iajs-2484	96	40	∈	∈	PROPN
iajs-2484	96	41	𝑋	𝑋	PROPN
iajs-2484	96	42	⋃	⋃	PROPN
iajs-2484	96	43	𝑋	𝑋	NOUN
iajs-2484	96	44	.	.	PUNCT
iajs-2484	97	1	3the	3the	PRON
iajs-2484	97	2	function	function	NOUN
iajs-2484	97	3	𝑓	𝑓	PRON
iajs-2484	97	4	from	from	ADP
iajs-2484	97	5	the	the	DET
iajs-2484	97	6	included	include	VERB
iajs-2484	97	7	point	point	NOUN
iajs-2484	97	8	space	space	NOUN
iajs-2484	97	9	𝑋	𝑋	PROPN
iajs-2484	97	10	,	,	PUNCT
iajs-2484	97	11	ʈ	ʈ	ADP
iajs-2484	97	12	into	into	ADP
iajs-2484	97	13	the	the	DET
iajs-2484	97	14	discrete	discrete	ADJ
iajs-2484	97	15	space	space	NOUN
iajs-2484	97	16	𝑋	𝑋	PROPN
iajs-2484	97	17	,	,	PUNCT
iajs-2484	97	18	ʈ	ʈ	ADP
iajs-2484	97	19	where	where	SCONJ
iajs-2484	97	20	𝑋	𝑋	NOUN
iajs-2484	97	21	is	be	AUX
iajs-2484	97	22	a	a	DET
iajs-2484	97	23	finite	finite	ADJ
iajs-2484	97	24	set	set	NOUN
iajs-2484	97	25	,	,	PUNCT
iajs-2484	97	26	is	be	AUX
iajs-2484	97	27	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	97	28	function	function	NOUN
iajs-2484	97	29	.	.	PUNCT
iajs-2484	98	1	4𝑓	4𝑓	NUM
iajs-2484	98	2	:	:	PUNCT
iajs-2484	98	3	𝑋	𝑋	NOUN
iajs-2484	98	4	,	,	PUNCT
iajs-2484	98	5	ʈ	ʈ	PROPN
iajs-2484	98	6	⟶	⟶	NOUN
iajs-2484	98	7	𝑋	𝑋	PROPN
iajs-2484	98	8	,	,	PUNCT
iajs-2484	98	9	ʈ	ʈ	PROPN
iajs-2484	98	10	,	,	PUNCT
iajs-2484	98	11	where	where	SCONJ
iajs-2484	98	12	𝑓	𝑓	PRON
iajs-2484	98	13	𝑎	𝑎	NOUN
iajs-2484	98	14	𝑑	𝑑	NOUN
iajs-2484	98	15	for	for	ADP
iajs-2484	98	16	any	any	DET
iajs-2484	98	17	𝑎	𝑎	PROPN
iajs-2484	98	18	∈	∈	PROPN
iajs-2484	98	19	𝑋	𝑋	NOUN
iajs-2484	98	20	,	,	PUNCT
iajs-2484	98	21	is	be	AUX
iajs-2484	98	22	strongly	strongly	ADV
iajs-2484	98	23	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	98	24	function	function	NOUN
iajs-2484	98	25	.	.	PUNCT
iajs-2484	99	1	5the	5the	DET
iajs-2484	99	2	identity	identity	NOUN
iajs-2484	99	3	function	function	NOUN
iajs-2484	99	4	from	from	ADP
iajs-2484	99	5	the	the	DET
iajs-2484	99	6	co	co	ADJ
iajs-2484	99	7	-	-	ADJ
iajs-2484	99	8	countable	countable	ADJ
iajs-2484	99	9	space	space	NOUN
iajs-2484	99	10	𝑋	𝑋	PROPN
iajs-2484	99	11	,	,	PUNCT
iajs-2484	99	12	ʈ	ʈ	ADP
iajs-2484	99	13	into	into	ADP
iajs-2484	99	14	the	the	DET
iajs-2484	99	15	same	same	ADJ
iajs-2484	99	16	space	space	NOUN
iajs-2484	99	17	where	where	SCONJ
iajs-2484	99	18	𝑋	𝑋	NOUN
iajs-2484	99	19	is	be	AUX
iajs-2484	99	20	uncountable	uncountable	ADJ
iajs-2484	99	21	set	set	NOUN
iajs-2484	99	22	,	,	PUNCT
iajs-2484	99	23	is	be	AUX
iajs-2484	99	24	strongly	strongly	ADV
iajs-2484	99	25	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	99	26	function	function	NOUN
iajs-2484	99	27	.	.	PUNCT
iajs-2484	100	1	6-	6-	ADP
iajs-2484	100	2	 	 	SPACE
iajs-2484	100	3	a	a	DET
iajs-2484	100	4	function	function	NOUN
iajs-2484	100	5	𝑓	𝑓	PRON
iajs-2484	100	6	from	from	ADP
iajs-2484	100	7	the	the	DET
iajs-2484	100	8	included	include	VERB
iajs-2484	100	9	point	point	NOUN
iajs-2484	100	10	space	space	NOUN
iajs-2484	100	11	𝒵	𝒵	PROPN
iajs-2484	100	12	,	,	PUNCT
iajs-2484	100	13	ʈ	ʈ	ADP
iajs-2484	100	14	into	into	ADP
iajs-2484	100	15	the	the	DET
iajs-2484	100	16	co	co	NOUN
iajs-2484	100	17	-	-	ADJ
iajs-2484	100	18	finite	finite	ADJ
iajs-2484	100	19	space	space	NOUN
iajs-2484	100	20	𝒵	𝒵	PROPN
iajs-2484	100	21	,	,	PUNCT
iajs-2484	100	22	𝜇	𝜇	PRON
iajs-2484	100	23	is	be	AUX
iajs-2484	100	24	𝜔irresolute	𝜔irresolute	ADJ
iajs-2484	100	25	function	function	NOUN
iajs-2484	100	26	.	.	PUNCT
iajs-2484	101	1	7-	7-	X
iajs-2484	101	2	 	 	SPACE
iajs-2484	101	3	the	the	DET
iajs-2484	101	4	function	function	NOUN
iajs-2484	101	5	𝑓	𝑓	X
iajs-2484	101	6	from	from	ADP
iajs-2484	101	7	elective	elective	ADJ
iajs-2484	101	8	topology	topology	NOUN
iajs-2484	101	9	on	on	ADP
iajs-2484	101	10	an	an	DET
iajs-2484	101	11	infinite	infinite	ADJ
iajs-2484	101	12	set	set	NOUN
iajs-2484	101	13	to	to	ADP
iajs-2484	101	14	the	the	DET
iajs-2484	101	15	indiscrete	indiscrete	ADJ
iajs-2484	101	16	topology	topology	NOUN
iajs-2484	101	17	on	on	ADP
iajs-2484	101	18	the	the	DET
iajs-2484	101	19	same	same	ADJ
iajs-2484	101	20	set	set	NOUN
iajs-2484	101	21	in	in	ADP
iajs-2484	101	22	which	which	PRON
iajs-2484	101	23	𝑓	𝑓	X
iajs-2484	101	24	𝑎	𝑎	X
iajs-2484	101	25	𝑑	𝑑	NOUN
iajs-2484	101	26	for	for	ADP
iajs-2484	101	27	any	any	DET
iajs-2484	101	28	𝑎	𝑎	NOUN
iajs-2484	101	29	in	in	ADP
iajs-2484	101	30	the	the	DET
iajs-2484	101	31	domain	domain	NOUN
iajs-2484	101	32	,	,	PUNCT
iajs-2484	101	33	is	be	AUX
iajs-2484	101	34	𝑁-irresolute	𝑁-irresolute	PROPN
iajs-2484	101	35	function	function	NOUN
iajs-2484	101	36	.	.	PUNCT
iajs-2484	102	1	the	the	DET
iajs-2484	102	2	following	follow	VERB
iajs-2484	102	3	scheme	scheme	NOUN
iajs-2484	102	4	is	be	AUX
iajs-2484	102	5	useful	useful	ADJ
iajs-2484	102	6	.	.	PUNCT
iajs-2484	103	1	continuous	continuous	ADJ
iajs-2484	103	2	function	function	NOUN
iajs-2484	103	3	𝜔-continuous	𝜔-continuous	PROPN
iajs-2484	103	4	(	(	PUNCT
iajs-2484	103	5	resp	resp	NOUN
iajs-2484	103	6	.	.	PUNCT
iajs-2484	104	1	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	104	2	)	)	PUNCT
iajs-2484	104	3	function	function	NOUN
iajs-2484	104	4	strongly	strongly	ADV
iajs-2484	104	5	𝜔-continuous	𝜔-continuous	PROPN
iajs-2484	104	6	(	(	PUNCT
iajs-2484	104	7	resp	resp	NOUN
iajs-2484	104	8	.	.	PUNCT
iajs-2484	105	1	strongly	strongly	ADV
iajs-2484	105	2	𝜔-irresolute	𝜔-irresolute	PROPN
iajs-2484	105	3	(	(	PUNCT
iajs-2484	105	4	resp	resp	NOUN
iajs-2484	105	5	.	.	PUNCT
iajs-2484	106	1	𝑁-irresolute	𝑁-irresolute	ADJ
iajs-2484	106	2	)	)	PUNCT
iajs-2484	106	3	function	function	NOUN
iajs-2484	106	4	𝑁continuous	𝑁continuous	ADJ
iajs-2484	106	5	)	)	PUNCT
iajs-2484	106	6	function	function	NOUN
iajs-2484	106	7	remark	remark	NOUN
iajs-2484	106	8	(	(	PUNCT
iajs-2484	106	9	1.21	1.21	NUM
iajs-2484	106	10	)	)	PUNCT
iajs-2484	106	11	1every	1every	NUM
iajs-2484	107	1	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	107	2	function	function	NOUN
iajs-2484	107	3	 	 	SPACE
iajs-2484	107	4	is	be	AUX
iajs-2484	107	5	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	107	6	.	.	PUNCT
iajs-2484	108	1	2every	2every	NUM
iajs-2484	108	2	strongly	strongly	ADV
iajs-2484	108	3	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	108	4	function	function	NOUN
iajs-2484	108	5	is	be	AUX
iajs-2484	108	6	strongly	strongly	ADV
iajs-2484	108	7	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	108	8	.	.	NOUN
iajs-2484	108	9	3no	3no	ADJ
iajs-2484	108	10	relation	relation	NOUN
iajs-2484	108	11	between	between	ADP
iajs-2484	108	12	𝜔-irresolute	𝜔-irresolute	NOUN
iajs-2484	108	13	function	function	NOUN
iajs-2484	108	14	and	and	CCONJ
iajs-2484	108	15	𝑁-irresolute	𝑁-irresolute	PROPN
iajs-2484	108	16	.	.	PROPN
iajs-2484	108	17	  	  	SPACE
iajs-2484	108	18	179	179	NUM
iajs-2484	108	19	  	  	SPACE
iajs-2484	108	20	ibn	ibn	PROPN
iajs-2484	108	21	al	al	PROPN
iajs-2484	108	22	-	-	PUNCT
iajs-2484	108	23	haitham	haitham	PROPN
iajs-2484	108	24	jour	jour	X
iajs-2484	108	25	.	.	PROPN
iajs-2484	109	1	for	for	ADP
iajs-2484	109	2	pure	pure	ADJ
iajs-2484	109	3	&	&	CCONJ
iajs-2484	109	4	appl	appl	PROPN
iajs-2484	109	5	.	.	PUNCT
iajs-2484	110	1	sci	sci	PROPN
iajs-2484	110	2	.	.	PROPN
iajs-2484	111	1	33	33	NUM
iajs-2484	111	2	(	(	PUNCT
iajs-2484	111	3	3	3	NUM
iajs-2484	111	4	)	)	PUNCT
iajs-2484	111	5	2020	2020	NUM
iajs-2484	111	6	example	example	NOUN
iajs-2484	111	7	(	(	PUNCT
iajs-2484	111	8	1.22	1.22	NUM
iajs-2484	111	9	)	)	PUNCT
iajs-2484	111	10	1𝑓	1𝑓	NUM
iajs-2484	111	11	:	:	PUNCT
iajs-2484	111	12	𝒵	𝒵	PROPN
iajs-2484	111	13	,	,	PUNCT
iajs-2484	111	14	ʈ	ʈ	ADP
iajs-2484	111	15	⟶	⟶	PROPN
iajs-2484	111	16	𝒵	𝒵	PROPN
iajs-2484	111	17	,	,	PUNCT
iajs-2484	111	18	ʈ	ʈ	PRON
iajs-2484	111	19	 	 	SPACE
iajs-2484	111	20	is	be	AUX
iajs-2484	111	21	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	111	22	but	but	CCONJ
iajs-2484	111	23	not	not	PART
iajs-2484	111	24	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	111	25	function	function	NOUN
iajs-2484	111	26	.	.	PUNCT
iajs-2484	112	1	2𝐼𝒵	2𝐼𝒵	NUM
iajs-2484	112	2	:	:	PUNCT
iajs-2484	112	3	𝒵	𝒵	PROPN
iajs-2484	112	4	,	,	PUNCT
iajs-2484	112	5	ʈ	ʈ	ADP
iajs-2484	112	6	⟶	⟶	PROPN
iajs-2484	112	7	𝒵	𝒵	PROPN
iajs-2484	112	8	,	,	PUNCT
iajs-2484	112	9	ʈ	ʈ	AUX
iajs-2484	112	10	  	  	SPACE
iajs-2484	112	11	is	be	AUX
iajs-2484	112	12	strongly	strongly	ADV
iajs-2484	112	13	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	112	14	but	but	CCONJ
iajs-2484	112	15	not	not	PART
iajs-2484	112	16	strongly	strongly	ADV
iajs-2484	112	17	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	112	18	function	function	NOUN
iajs-2484	112	19	.	.	PUNCT
iajs-2484	113	1	3𝐼𝒵	3𝐼𝒵	NUM
iajs-2484	113	2	:	:	PUNCT
iajs-2484	113	3	𝒵	𝒵	PROPN
iajs-2484	113	4	,	,	PUNCT
iajs-2484	113	5	ʈ	ʈ	ADP
iajs-2484	113	6	⟶	⟶	PROPN
iajs-2484	113	7	𝒵	𝒵	PROPN
iajs-2484	113	8	,	,	PUNCT
iajs-2484	113	9	ʈ	ʈ	X
iajs-2484	113	10	is	be	AUX
iajs-2484	113	11	𝜔-irresolute	𝜔-irresolute	NUM
iajs-2484	113	12	but	but	CCONJ
iajs-2484	113	13	not	not	PART
iajs-2484	113	14	𝑁-irresolute	𝑁-irresolute	PROPN
iajs-2484	113	15	function	function	NOUN
iajs-2484	113	16	.	.	PUNCT
iajs-2484	114	1	definition	definition	NOUN
iajs-2484	114	2	(	(	PUNCT
iajs-2484	114	3	1.23	1.23	NUM
iajs-2484	114	4	)	)	PUNCT
iajs-2484	114	5	1a	1a	PROPN
iajs-2484	114	6	space	space	NOUN
iajs-2484	114	7	𝑋	𝑋	PROPN
iajs-2484	114	8	,	,	PUNCT
iajs-2484	114	9	ʈ	ʈ	ADJ
iajs-2484	114	10	)	)	PUNCT
iajs-2484	114	11	is	be	AUX
iajs-2484	114	12	called	call	VERB
iajs-2484	114	13	:	:	PUNCT
iajs-2484	114	14	1c	1c	NUM
iajs-2484	114	15	-	-	PUNCT
iajs-2484	114	16	c	c	NOUN
iajs-2484	114	17	space	space	NOUN
iajs-2484	114	18	if	if	SCONJ
iajs-2484	114	19	each	each	PRON
iajs-2484	114	20	closed	close	VERB
iajs-2484	114	21	set	set	VERB
iajs-2484	114	22	in	in	ADP
iajs-2484	114	23	𝑋	𝑋	PROPN
iajs-2484	114	24	is	be	AUX
iajs-2484	114	25	compact	compact	ADJ
iajs-2484	114	26	and	and	CCONJ
iajs-2484	114	27	each	each	DET
iajs-2484	114	28	compact	compact	ADJ
iajs-2484	114	29	set	set	NOUN
iajs-2484	114	30	is	be	AUX
iajs-2484	114	31	closed	close	VERB
iajs-2484	114	32	[	[	X
iajs-2484	114	33	17	17	NUM
iajs-2484	114	34	]	]	PUNCT
iajs-2484	114	35	.	.	PUNCT
iajs-2484	115	1	2kc	2kc	ADJ
iajs-2484	115	2	-	-	PUNCT
iajs-2484	115	3	space	space	NOUN
iajs-2484	115	4	if	if	SCONJ
iajs-2484	115	5	each	each	DET
iajs-2484	115	6	compact	compact	ADJ
iajs-2484	115	7	set	set	VERB
iajs-2484	115	8	in	in	ADP
iajs-2484	115	9	𝑋	𝑋	PROPN
iajs-2484	115	10	is	be	AUX
iajs-2484	115	11	closed	close	VERB
iajs-2484	115	12	[	[	X
iajs-2484	115	13	18	18	NUM
iajs-2484	115	14	]	]	PUNCT
iajs-2484	115	15	.	.	PUNCT
iajs-2484	116	1	example	example	NOUN
iajs-2484	116	2	(	(	PUNCT
iajs-2484	116	3	1.24	1.24	NUM
iajs-2484	116	4	)	)	PUNCT
iajs-2484	116	5	1𝑋	1𝑋	NOUN
iajs-2484	116	6	,	,	PUNCT
iajs-2484	116	7	ʈ	ʈ	PROPN
iajs-2484	116	8	)	)	PUNCT
iajs-2484	116	9	where	where	SCONJ
iajs-2484	116	10	𝑋	𝑋	PROPN
iajs-2484	116	11	is	be	AUX
iajs-2484	116	12	a	a	DET
iajs-2484	116	13	finite	finite	ADJ
iajs-2484	116	14	set	set	NOUN
iajs-2484	116	15	is	be	AUX
iajs-2484	116	16	c	c	NOUN
iajs-2484	116	17	-	-	PUNCT
iajs-2484	116	18	c	c	NOUN
iajs-2484	116	19	space	space	NOUN
iajs-2484	116	20	.	.	PUNCT
iajs-2484	117	1	2ℛ	2ℛ	PROPN
iajs-2484	117	2	,	,	PUNCT
iajs-2484	117	3	ʈ𝓊	ʈ𝓊	VERB
iajs-2484	117	4	is	be	AUX
iajs-2484	117	5	kc	kc	NOUN
iajs-2484	117	6	-	-	PUNCT
iajs-2484	117	7	space	space	NOUN
iajs-2484	117	8	.	.	PUNCT
iajs-2484	118	1	remark	remark	NOUN
iajs-2484	118	2	(	(	PUNCT
iajs-2484	118	3	1.25	1.25	NUM
iajs-2484	118	4	)	)	PUNCT
iajs-2484	118	5	every	every	DET
iajs-2484	118	6	𝑇	𝑇	PROPN
iajs-2484	118	7	-space	-space	NOUN
iajs-2484	118	8	is	be	AUX
iajs-2484	118	9	kc	kc	NOUN
iajs-2484	118	10	-	-	PUNCT
iajs-2484	118	11	space	space	NOUN
iajs-2484	118	12	.	.	PUNCT
iajs-2484	119	1	example	example	NOUN
iajs-2484	119	2	(	(	PUNCT
iajs-2484	119	3	1.26	1.26	NUM
iajs-2484	119	4	):	):	PUNCT
iajs-2484	119	5	(	(	PUNCT
iajs-2484	119	6	ℛ	ℛ	PROPN
iajs-2484	119	7	,	,	PUNCT
iajs-2484	119	8	ʈ	ʈ	X
iajs-2484	119	9	is	be	AUX
iajs-2484	119	10	kc	kc	NOUN
iajs-2484	119	11	-	-	PUNCT
iajs-2484	119	12	space	space	NOUN
iajs-2484	119	13	but	but	CCONJ
iajs-2484	119	14	not	not	PART
iajs-2484	119	15	𝑇	𝑇	PROPN
iajs-2484	119	16	-space	-space	NOUN
iajs-2484	119	17	.	.	PUNCT
iajs-2484	120	1	proposition	proposition	NOUN
iajs-2484	120	2	(	(	PUNCT
iajs-2484	120	3	1.27	1.27	NUM
iajs-2484	120	4	)	)	PUNCT
iajs-2484	120	5	if	if	SCONJ
iajs-2484	120	6	𝑓	𝑓	PRON
iajs-2484	120	7	:	:	PUNCT
iajs-2484	120	8	𝑋	𝑋	PROPN
iajs-2484	120	9	,	,	PUNCT
iajs-2484	120	10	ʈ	ʈ	ADP
iajs-2484	120	11	⟶	⟶	NOUN
iajs-2484	120	12	𝑌	𝑌	PROPN
iajs-2484	120	13	,	,	PUNCT
iajs-2484	120	14	ʈ	ʈ	AUX
iajs-2484	120	15	is	be	AUX
iajs-2484	120	16	a	a	DET
iajs-2484	120	17	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	120	18	function	function	NOUN
iajs-2484	120	19	where	where	SCONJ
iajs-2484	120	20	𝑌	𝑌	PROPN
iajs-2484	120	21	is	be	AUX
iajs-2484	120	22	a	a	DET
iajs-2484	120	23	𝑇	𝑇	PROPN
iajs-2484	120	24	-space	-space	NOUN
iajs-2484	120	25	,	,	PUNCT
iajs-2484	120	26	then	then	ADV
iajs-2484	120	27	it	it	PRON
iajs-2484	120	28	is	be	AUX
iajs-2484	120	29	an	an	DET
iajs-2484	120	30	m𝜔c	m𝜔c	NOUN
iajs-2484	120	31	-	-	NOUN
iajs-2484	120	32	function	function	NOUN
iajs-2484	120	33	.	.	PUNCT
iajs-2484	121	1	proof	proof	NOUN
iajs-2484	121	2	let	let	VERB
iajs-2484	121	3	𝒦	𝒦	PRON
iajs-2484	121	4	be	be	AUX
iajs-2484	121	5	a	a	DET
iajs-2484	121	6	compact	compact	ADJ
iajs-2484	121	7	subset	subset	NOUN
iajs-2484	121	8	of	of	ADP
iajs-2484	121	9	𝑌	𝑌	PROPN
iajs-2484	121	10	,	,	PUNCT
iajs-2484	121	11	since	since	SCONJ
iajs-2484	121	12	𝑌	𝑌	PROPN
iajs-2484	121	13	is	be	AUX
iajs-2484	121	14	a	a	DET
iajs-2484	121	15	𝑇	𝑇	PROPN
iajs-2484	121	16	-space	-space	NOUN
iajs-2484	121	17	then	then	ADV
iajs-2484	121	18	𝒦	𝒦	PROPN
iajs-2484	121	19	is	be	AUX
iajs-2484	121	20	closed	close	VERB
iajs-2484	121	21	(	(	PUNCT
iajs-2484	121	22	by	by	ADP
iajs-2484	121	23	remark	remark	NOUN
iajs-2484	121	24	(	(	PUNCT
iajs-2484	121	25	1.6	1.6	NUM
iajs-2484	121	26	)	)	PUNCT
iajs-2484	121	27	)	)	PUNCT
iajs-2484	121	28	,	,	PUNCT
iajs-2484	121	29	but	but	CCONJ
iajs-2484	121	30	𝑓	𝑓	PRON
iajs-2484	121	31	is	be	AUX
iajs-2484	121	32	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	121	33	function	function	NOUN
iajs-2484	121	34	,	,	PUNCT
iajs-2484	121	35	so	so	SCONJ
iajs-2484	121	36	𝑓	𝑓	DET
iajs-2484	121	37	𝒦	𝒦	PROPN
iajs-2484	121	38	is	be	AUX
iajs-2484	121	39	𝜔-closed	𝜔-close	VERB
iajs-2484	121	40	set	set	VERB
iajs-2484	121	41	in	in	ADP
iajs-2484	121	42	𝑋	𝑋	PROPN
iajs-2484	121	43	,	,	PUNCT
iajs-2484	121	44	therefore	therefore	ADV
iajs-2484	121	45	𝑓	𝑓	PRON
iajs-2484	121	46	is	be	AUX
iajs-2484	121	47	m𝜔c	m𝜔c	NOUN
iajs-2484	121	48	-	-	NOUN
iajs-2484	121	49	function	function	NOUN
iajs-2484	121	50	.	.	PUNCT
iajs-2484	122	1	by	by	ADP
iajs-2484	122	2	the	the	DET
iajs-2484	122	3	same	same	ADJ
iajs-2484	122	4	way	way	NOUN
iajs-2484	122	5	we	we	PRON
iajs-2484	122	6	can	can	AUX
iajs-2484	122	7	prove	prove	VERB
iajs-2484	122	8	the	the	DET
iajs-2484	122	9	following	follow	VERB
iajs-2484	122	10	proposition	proposition	NOUN
iajs-2484	122	11	.	.	PUNCT
iajs-2484	123	1	proposition	proposition	NOUN
iajs-2484	123	2	(	(	PUNCT
iajs-2484	123	3	1.28	1.28	NUM
iajs-2484	123	4	)	)	PUNCT
iajs-2484	123	5	if	if	SCONJ
iajs-2484	123	6	𝑓	𝑓	PRON
iajs-2484	123	7	:	:	PUNCT
iajs-2484	123	8	𝑋	𝑋	PROPN
iajs-2484	123	9	,	,	PUNCT
iajs-2484	123	10	ʈ	ʈ	ADP
iajs-2484	123	11	⟶	⟶	NOUN
iajs-2484	123	12	𝑌	𝑌	PROPN
iajs-2484	123	13	,	,	PUNCT
iajs-2484	123	14	ʈ	ʈ	X
iajs-2484	123	15	is	be	AUX
iajs-2484	123	16	:	:	PUNCT
iajs-2484	123	17	1-	1-	X
iajs-2484	123	18	 	 	SPACE
iajs-2484	123	19	an	an	DET
iajs-2484	123	20	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	123	21	function	function	NOUN
iajs-2484	123	22	where	where	SCONJ
iajs-2484	123	23	𝑌	𝑌	PROPN
iajs-2484	123	24	is	be	AUX
iajs-2484	123	25	a	a	DET
iajs-2484	123	26	𝑇	𝑇	PROPN
iajs-2484	123	27	-space	-space	NOUN
iajs-2484	123	28	,	,	PUNCT
iajs-2484	123	29	then	then	ADV
iajs-2484	123	30	it	it	PRON
iajs-2484	123	31	is	be	AUX
iajs-2484	123	32	an	an	DET
iajs-2484	123	33	m𝜔c	m𝜔c	NOUN
iajs-2484	123	34	-	-	PUNCT
iajs-2484	123	35	function	function	NOUN
iajs-2484	123	36	(	(	PUNCT
iajs-2484	123	37	respectively	respectively	ADV
iajs-2484	123	38	m𝑁c	m𝑁c	NOUN
iajs-2484	123	39	-	-	PUNCT
iajs-2484	123	40	function	function	NOUN
iajs-2484	123	41	)	)	PUNCT
iajs-2484	123	42	.	.	PUNCT
iajs-2484	124	1	2an	2an	ADJ
iajs-2484	124	2	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	124	3	function	function	NOUN
iajs-2484	124	4	where	where	SCONJ
iajs-2484	124	5	𝑌	𝑌	PROPN
iajs-2484	124	6	is	be	AUX
iajs-2484	124	7	a	a	DET
iajs-2484	124	8	kc	kc	NOUN
iajs-2484	124	9	-	-	PUNCT
iajs-2484	124	10	space	space	NOUN
iajs-2484	124	11	(	(	PUNCT
iajs-2484	124	12	respectively	respectively	ADV
iajs-2484	124	13	c	c	NOUN
iajs-2484	124	14	-	-	PUNCT
iajs-2484	124	15	c	c	NOUN
iajs-2484	124	16	space	space	NOUN
iajs-2484	124	17	)	)	PUNCT
iajs-2484	124	18	,	,	PUNCT
iajs-2484	124	19	then	then	ADV
iajs-2484	124	20	it	it	PRON
iajs-2484	124	21	is	be	AUX
iajs-2484	124	22	an	an	DET
iajs-2484	124	23	m𝜔c	m𝜔c	NOUN
iajs-2484	124	24	-	-	NOUN
iajs-2484	124	25	function	function	NOUN
iajs-2484	124	26	.	.	PUNCT
iajs-2484	125	1	3an	3an	ADJ
iajs-2484	125	2	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	125	3	function	function	NOUN
iajs-2484	125	4	where	where	SCONJ
iajs-2484	125	5	𝑌	𝑌	PROPN
iajs-2484	125	6	is	be	AUX
iajs-2484	125	7	a	a	DET
iajs-2484	125	8	kc	kc	NOUN
iajs-2484	125	9	-	-	PUNCT
iajs-2484	125	10	space	space	NOUN
iajs-2484	125	11	(	(	PUNCT
iajs-2484	125	12	respectively	respectively	ADV
iajs-2484	125	13	c	c	NOUN
iajs-2484	125	14	-	-	PUNCT
iajs-2484	125	15	c	c	NOUN
iajs-2484	125	16	space	space	NOUN
iajs-2484	125	17	)	)	PUNCT
iajs-2484	125	18	,	,	PUNCT
iajs-2484	125	19	then	then	ADV
iajs-2484	125	20	it	it	PRON
iajs-2484	125	21	is	be	AUX
iajs-2484	125	22	an	an	DET
iajs-2484	125	23	m𝑁c	m𝑁c	NOUN
iajs-2484	125	24	-	-	PUNCT
iajs-2484	125	25	function	function	NOUN
iajs-2484	125	26	.	.	PUNCT
iajs-2484	126	1	4a	4a	NOUN
iajs-2484	126	2	continuous	continuous	ADJ
iajs-2484	126	3	function	function	NOUN
iajs-2484	126	4	where	where	SCONJ
iajs-2484	126	5	𝑌	𝑌	PROPN
iajs-2484	126	6	is	be	AUX
iajs-2484	126	7	a	a	DET
iajs-2484	126	8	𝑇	𝑇	PROPN
iajs-2484	126	9	-space	-space	NOUN
iajs-2484	126	10	(	(	PUNCT
iajs-2484	126	11	respectively	respectively	ADV
iajs-2484	126	12	kc	kc	NOUN
iajs-2484	126	13	-	-	PUNCT
iajs-2484	126	14	space	space	NOUN
iajs-2484	126	15	,	,	PUNCT
iajs-2484	126	16	or	or	CCONJ
iajs-2484	126	17	c	c	X
iajs-2484	126	18	-	-	PUNCT
iajs-2484	126	19	c	c	NOUN
iajs-2484	126	20	space	space	NOUN
iajs-2484	126	21	)	)	PUNCT
iajs-2484	126	22	,	,	PUNCT
iajs-2484	126	23	then	then	ADV
iajs-2484	126	24	it	it	PRON
iajs-2484	126	25	is	be	AUX
iajs-2484	126	26	an	an	DET
iajs-2484	126	27	m𝜔c	m𝜔c	NOUN
iajs-2484	126	28	-	-	PUNCT
iajs-2484	126	29	function	function	NOUN
iajs-2484	126	30	,	,	PUNCT
iajs-2484	126	31	m𝑁c	m𝑁c	NOUN
iajs-2484	126	32	-	-	PUNCT
iajs-2484	126	33	function	function	NOUN
iajs-2484	126	34	,	,	PUNCT
iajs-2484	126	35	𝜔mc	𝜔mc	NOUN
iajs-2484	126	36	-	-	PUNCT
iajs-2484	126	37	function	function	NOUN
iajs-2484	126	38	,	,	PUNCT
iajs-2484	126	39	  	  	SPACE
iajs-2484	126	40	𝑁mc	𝑁mc	NOUN
iajs-2484	126	41	-	-	PUNCT
iajs-2484	126	42	function	function	NOUN
iajs-2484	126	43	,	,	PUNCT
iajs-2484	126	44	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	126	45	-	-	PUNCT
iajs-2484	126	46	function	function	NOUN
iajs-2484	126	47	and	and	CCONJ
iajs-2484	126	48	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	126	49	-	-	PUNCT
iajs-2484	126	50	function	function	NOUN
iajs-2484	126	51	.	.	PUNCT
iajs-2484	127	1	5a	5a	NUM
iajs-2484	127	2	strongly	strongly	ADV
iajs-2484	127	3	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	127	4	function	function	NOUN
iajs-2484	127	5	where	where	SCONJ
iajs-2484	127	6	𝑌	𝑌	PROPN
iajs-2484	127	7	is	be	AUX
iajs-2484	127	8	a	a	DET
iajs-2484	127	9	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	127	10	-space	-space	NOUN
iajs-2484	127	11	(	(	PUNCT
iajs-2484	127	12	respectively	respectively	ADV
iajs-2484	127	13	kc	kc	NOUN
iajs-2484	127	14	-	-	PUNCT
iajs-2484	127	15	space	space	NOUN
iajs-2484	127	16	,	,	PUNCT
iajs-2484	127	17	c	c	NOUN
iajs-2484	127	18	-	-	PUNCT
iajs-2484	127	19	c	c	NOUN
iajs-2484	127	20	space	space	NOUN
iajs-2484	127	21	)	)	PUNCT
iajs-2484	127	22	,	,	PUNCT
iajs-2484	127	23	then	then	ADV
iajs-2484	127	24	it	it	PRON
iajs-2484	127	25	is	be	AUX
iajs-2484	127	26	a	a	DET
iajs-2484	127	27	𝜔mc	𝜔mc	ADJ
iajs-2484	127	28	-	-	PUNCT
iajs-2484	127	29	function	function	NOUN
iajs-2484	127	30	and	and	CCONJ
iajs-2484	127	31	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	127	32	-	-	PUNCT
iajs-2484	127	33	function	function	NOUN
iajs-2484	127	34	.	.	PUNCT
iajs-2484	128	1	6a	6a	NOUN
iajs-2484	128	2	strongly	strongly	ADV
iajs-2484	128	3	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	128	4	function	function	NOUN
iajs-2484	128	5	where	where	SCONJ
iajs-2484	128	6	𝑌	𝑌	PROPN
iajs-2484	128	7	is	be	AUX
iajs-2484	128	8	a	a	DET
iajs-2484	128	9	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	128	10	-space	-space	NOUN
iajs-2484	128	11	(	(	PUNCT
iajs-2484	128	12	respectively	respectively	ADV
iajs-2484	128	13	kc	kc	NOUN
iajs-2484	128	14	-	-	PUNCT
iajs-2484	128	15	space	space	NOUN
iajs-2484	128	16	,	,	PUNCT
iajs-2484	128	17	c	c	NOUN
iajs-2484	128	18	-	-	PUNCT
iajs-2484	128	19	c	c	NOUN
iajs-2484	128	20	space	space	NOUN
iajs-2484	128	21	)	)	PUNCT
iajs-2484	128	22	,	,	PUNCT
iajs-2484	128	23	then	then	ADV
iajs-2484	128	24	it	it	PRON
iajs-2484	128	25	is	be	AUX
iajs-2484	128	26	an	an	DET
iajs-2484	128	27	𝑁mc	𝑁mc	NOUN
iajs-2484	128	28	-	-	PUNCT
iajs-2484	128	29	function	function	NOUN
iajs-2484	128	30	and	and	CCONJ
iajs-2484	128	31	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	128	32	-	-	PUNCT
iajs-2484	128	33	function	function	NOUN
iajs-2484	128	34	.	.	PUNCT
iajs-2484	129	1	7a	7a	NUM
iajs-2484	129	2	strongly	strongly	ADV
iajs-2484	129	3	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	129	4	function	function	NOUN
iajs-2484	129	5	where	where	SCONJ
iajs-2484	129	6	𝑌	𝑌	PROPN
iajs-2484	129	7	is	be	AUX
iajs-2484	129	8	a	a	DET
iajs-2484	129	9	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	129	10	-space	-space	NOUN
iajs-2484	129	11	,	,	PUNCT
iajs-2484	129	12	then	then	ADV
iajs-2484	129	13	it	it	PRON
iajs-2484	129	14	is	be	AUX
iajs-2484	129	15	an	an	DET
iajs-2484	129	16	𝑁mc	𝑁mc	NOUN
iajs-2484	129	17	-	-	PUNCT
iajs-2484	129	18	function	function	NOUN
iajs-2484	129	19	.	.	PUNCT
iajs-2484	130	1	8an	8an	ADJ
iajs-2484	130	2	𝜔-irresolute	𝜔-irresolute	NUM
iajs-2484	130	3	function	function	NOUN
iajs-2484	130	4	where	where	SCONJ
iajs-2484	130	5	𝑌	𝑌	PROPN
iajs-2484	130	6	is	be	AUX
iajs-2484	130	7	a	a	DET
iajs-2484	130	8	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	130	9	-space	-space	NOUN
iajs-2484	130	10	(	(	PUNCT
iajs-2484	130	11	respectively	respectively	ADV
iajs-2484	130	12	kc	kc	NOUN
iajs-2484	130	13	-	-	PUNCT
iajs-2484	130	14	space	space	NOUN
iajs-2484	130	15	,	,	PUNCT
iajs-2484	130	16	c	c	NOUN
iajs-2484	130	17	-	-	PUNCT
iajs-2484	130	18	c	c	NOUN
iajs-2484	130	19	space	space	NOUN
iajs-2484	130	20	)	)	PUNCT
iajs-2484	130	21	,	,	PUNCT
iajs-2484	130	22	then	then	ADV
iajs-2484	130	23	it	it	PRON
iajs-2484	130	24	is	be	AUX
iajs-2484	130	25	an	an	DET
iajs-2484	130	26	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	130	27	-	-	PUNCT
iajs-2484	130	28	function	function	NOUN
iajs-2484	130	29	.	.	PUNCT
iajs-2484	131	1	9an	9an	NOUN
iajs-2484	131	2	𝑁-irresolute	𝑁-irresolute	PROPN
iajs-2484	131	3	function	function	NOUN
iajs-2484	131	4	where	where	SCONJ
iajs-2484	131	5	𝑌	𝑌	PROPN
iajs-2484	131	6	is	be	AUX
iajs-2484	131	7	a	a	DET
iajs-2484	131	8	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	131	9	-space	-space	NOUN
iajs-2484	131	10	(	(	PUNCT
iajs-2484	131	11	respectively	respectively	ADV
iajs-2484	131	12	kc	kc	NOUN
iajs-2484	131	13	-	-	PUNCT
iajs-2484	131	14	space	space	NOUN
iajs-2484	131	15	,	,	PUNCT
iajs-2484	131	16	c	c	NOUN
iajs-2484	131	17	-	-	PUNCT
iajs-2484	131	18	c	c	NOUN
iajs-2484	131	19	space	space	NOUN
iajs-2484	131	20	)	)	PUNCT
iajs-2484	132	1	,	,	PUNCT
iajs-2484	132	2	then	then	ADV
iajs-2484	132	3	it	it	PRON
iajs-2484	132	4	is	be	AUX
iajs-2484	132	5	an	an	DET
iajs-2484	132	6	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	132	7	-	-	PUNCT
iajs-2484	132	8	function	function	NOUN
iajs-2484	132	9	.	.	PUNCT
iajs-2484	132	10	  	  	SPACE
iajs-2484	133	1	180	180	NUM
iajs-2484	133	2	  	  	SPACE
iajs-2484	133	3	ibn	ibn	PROPN
iajs-2484	133	4	al	al	PROPN
iajs-2484	133	5	-	-	PUNCT
iajs-2484	133	6	haitham	haitham	PROPN
iajs-2484	133	7	jour	jour	X
iajs-2484	133	8	.	.	PROPN
iajs-2484	133	9	for	for	ADP
iajs-2484	133	10	pure	pure	ADJ
iajs-2484	133	11	&	&	CCONJ
iajs-2484	133	12	appl	appl	PROPN
iajs-2484	133	13	.	.	PUNCT
iajs-2484	134	1	sci	sci	PROPN
iajs-2484	134	2	.	.	PROPN
iajs-2484	135	1	33	33	NUM
iajs-2484	135	2	(	(	PUNCT
iajs-2484	135	3	3	3	NUM
iajs-2484	135	4	)	)	PUNCT
iajs-2484	135	5	2020	2020	NUM
iajs-2484	136	1	proof	proof	NOUN
iajs-2484	136	2	:	:	PUNCT
iajs-2484	136	3	1let	1let	NUM
iajs-2484	136	4	k	k	AUX
iajs-2484	136	5	be	be	AUX
iajs-2484	136	6	a	a	DET
iajs-2484	136	7	compact	compact	ADJ
iajs-2484	136	8	set	set	NOUN
iajs-2484	136	9	in	in	ADP
iajs-2484	136	10	𝑌	𝑌	PROPN
iajs-2484	136	11	which	which	PRON
iajs-2484	136	12	is	be	AUX
iajs-2484	136	13	a	a	DET
iajs-2484	136	14	𝑇	𝑇	PROPN
iajs-2484	136	15	-space	-space	NOUN
iajs-2484	136	16	,	,	PUNCT
iajs-2484	136	17	so	so	SCONJ
iajs-2484	136	18	it	it	PRON
iajs-2484	136	19	is	be	AUX
iajs-2484	136	20	closed	close	VERB
iajs-2484	136	21	set	set	VERB
iajs-2484	136	22	(	(	PUNCT
iajs-2484	136	23	by	by	ADP
iajs-2484	136	24	remark	remark	NOUN
iajs-2484	136	25	(	(	PUNCT
iajs-2484	136	26	1.6	1.6	NUM
iajs-2484	136	27	)	)	PUNCT
iajs-2484	136	28	)	)	PUNCT
iajs-2484	136	29	,	,	PUNCT
iajs-2484	137	1	so	so	ADV
iajs-2484	137	2	𝑓	𝑓	ADV
iajs-2484	137	3	k	k	PROPN
iajs-2484	137	4	is	be	AUX
iajs-2484	137	5	𝜔-closed	𝜔-close	VERB
iajs-2484	137	6	(	(	PUNCT
iajs-2484	137	7	respectively	respectively	ADV
iajs-2484	137	8	𝑁-closed	𝑁-closed	PROPN
iajs-2484	137	9	)	)	PUNCT
iajs-2484	137	10	set	set	NOUN
iajs-2484	137	11	(	(	PUNCT
iajs-2484	137	12	since	since	SCONJ
iajs-2484	137	13	𝑓	𝑓	PRON
iajs-2484	137	14	is	be	AUX
iajs-2484	137	15	an	an	DET
iajs-2484	137	16	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	137	17	function	function	NOUN
iajs-2484	137	18	)	)	PUNCT
iajs-2484	137	19	,	,	PUNCT
iajs-2484	137	20	so	so	ADV
iajs-2484	137	21	𝑓	𝑓	PRON
iajs-2484	137	22	is	be	AUX
iajs-2484	137	23	an	an	DET
iajs-2484	137	24	m𝜔c	m𝜔c	NOUN
iajs-2484	137	25	-	-	PUNCT
iajs-2484	137	26	function	function	NOUN
iajs-2484	137	27	and	and	CCONJ
iajs-2484	137	28	an	an	DET
iajs-2484	137	29	m𝑁c	m𝑁c	NOUN
iajs-2484	137	30	-	-	PUNCT
iajs-2484	137	31	function	function	NOUN
iajs-2484	137	32	.	.	PUNCT
iajs-2484	138	1	by	by	ADP
iajs-2484	138	2	the	the	DET
iajs-2484	138	3	same	same	ADJ
iajs-2484	138	4	way	way	NOUN
iajs-2484	138	5	we	we	PRON
iajs-2484	138	6	can	can	AUX
iajs-2484	138	7	proof	proof	VERB
iajs-2484	138	8	the	the	DET
iajs-2484	138	9	rest	rest	NOUN
iajs-2484	138	10	.	.	PUNCT
iajs-2484	139	1	definition	definition	NOUN
iajs-2484	139	2	(	(	PUNCT
iajs-2484	139	3	1.29	1.29	NUM
iajs-2484	139	4	)	)	PUNCT
iajs-2484	139	5	a	a	DET
iajs-2484	139	6	function	function	NOUN
iajs-2484	139	7	𝑓	𝑓	DET
iajs-2484	139	8	∶	∶	NOUN
iajs-2484	139	9	𝑋	𝑋	NOUN
iajs-2484	139	10	⟶	⟶	NOUN
iajs-2484	139	11	𝑌	𝑌	PROPN
iajs-2484	139	12	is	be	AUX
iajs-2484	139	13	called	call	VERB
iajs-2484	139	14	:	:	PUNCT
iajs-2484	139	15	1a	1a	NUM
iajs-2484	139	16	compact	compact	ADJ
iajs-2484	139	17	function	function	NOUN
iajs-2484	139	18	if	if	SCONJ
iajs-2484	139	19	the	the	DET
iajs-2484	139	20	inverse	inverse	ADJ
iajs-2484	139	21	image	image	NOUN
iajs-2484	139	22	of	of	ADP
iajs-2484	139	23	any	any	DET
iajs-2484	139	24	compact	compact	ADJ
iajs-2484	139	25	set	set	NOUN
iajs-2484	139	26	in	in	ADP
iajs-2484	139	27	𝑌	𝑌	PROPN
iajs-2484	139	28	is	be	AUX
iajs-2484	139	29	a	a	DET
iajs-2484	139	30	compact	compact	ADJ
iajs-2484	139	31	set	set	NOUN
iajs-2484	139	32	in	in	ADP
iajs-2484	139	33	𝑋	𝑋	PROPN
iajs-2484	139	34	[	[	X
iajs-2484	139	35	2	2	NUM
iajs-2484	139	36	]	]	PUNCT
iajs-2484	139	37	.	.	PUNCT
iajs-2484	140	1	2an	2an	NOUN
iajs-2484	140	2	𝜔∗-compact	𝜔∗-compact	PROPN
iajs-2484	140	3	(	(	PUNCT
iajs-2484	140	4	respectively	respectively	ADV
iajs-2484	140	5	𝑁∗-compact	𝑁∗-compact	NOUN
iajs-2484	140	6	)	)	PUNCT
iajs-2484	140	7	function	function	NOUN
iajs-2484	140	8	if	if	SCONJ
iajs-2484	140	9	the	the	DET
iajs-2484	140	10	inverse	inverse	ADJ
iajs-2484	140	11	image	image	NOUN
iajs-2484	140	12	of	of	ADP
iajs-2484	140	13	any	any	DET
iajs-2484	140	14	compact	compact	ADJ
iajs-2484	140	15	set	set	NOUN
iajs-2484	140	16	in	in	ADP
iajs-2484	140	17	𝑌	𝑌	PROPN
iajs-2484	140	18	is	be	AUX
iajs-2484	140	19	an	an	DET
iajs-2484	140	20	𝜔-compact	𝜔-compact	PROPN
iajs-2484	140	21	(	(	PUNCT
iajs-2484	140	22	respectively	respectively	ADV
iajs-2484	140	23	𝑁-compact	𝑁-compact	PROPN
iajs-2484	140	24	)	)	PUNCT
iajs-2484	140	25	set	set	VERB
iajs-2484	140	26	in	in	ADP
iajs-2484	140	27	𝑋.	𝑋.	PROPN
iajs-2484	140	28	3an	3an	PROPN
iajs-2484	140	29	𝜔-compact	𝜔-compact	PROPN
iajs-2484	141	1	[	[	X
iajs-2484	141	2	12	12	NUM
iajs-2484	141	3	]	]	PUNCT
iajs-2484	141	4	.	.	PUNCT
iajs-2484	142	1	(	(	PUNCT
iajs-2484	142	2	respectively	respectively	ADV
iajs-2484	142	3	𝑁-compact	𝑁-compact	PROPN
iajs-2484	142	4	)	)	PUNCT
iajs-2484	142	5	function	function	VERB
iajs-2484	142	6	the	the	DET
iajs-2484	142	7	inverse	inverse	NOUN
iajs-2484	142	8	image	image	NOUN
iajs-2484	142	9	of	of	ADP
iajs-2484	142	10	any	any	DET
iajs-2484	142	11	𝜔compact	𝜔compact	ADJ
iajs-2484	142	12	(	(	PUNCT
iajs-2484	142	13	respectively	respectively	ADV
iajs-2484	142	14	𝑁-compact	𝑁-compact	PROPN
iajs-2484	142	15	)	)	PUNCT
iajs-2484	142	16	set	set	NOUN
iajs-2484	142	17	in	in	ADP
iajs-2484	142	18	𝑌	𝑌	PROPN
iajs-2484	142	19	is	be	AUX
iajs-2484	142	20	a	a	DET
iajs-2484	142	21	compact	compact	ADJ
iajs-2484	142	22	set	set	NOUN
iajs-2484	142	23	in	in	ADP
iajs-2484	142	24	𝑋.	𝑋.	PROPN
iajs-2484	142	25	4an	4an	PROPN
iajs-2484	142	26	𝜔∗∗-compact	𝜔∗∗-compact	PUNCT
iajs-2484	142	27	(	(	PUNCT
iajs-2484	142	28	respectively	respectively	ADV
iajs-2484	142	29	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	142	30	)	)	PUNCT
iajs-2484	142	31	function	function	VERB
iajs-2484	142	32	the	the	DET
iajs-2484	142	33	inverse	inverse	NOUN
iajs-2484	142	34	image	image	NOUN
iajs-2484	142	35	of	of	ADP
iajs-2484	142	36	any	any	DET
iajs-2484	142	37	𝜔-compact	𝜔-compact	NOUN
iajs-2484	142	38	(	(	PUNCT
iajs-2484	142	39	respectively	respectively	ADV
iajs-2484	142	40	𝑁-compact	𝑁-compact	PROPN
iajs-2484	142	41	)	)	PUNCT
iajs-2484	142	42	set	set	NOUN
iajs-2484	142	43	in	in	ADP
iajs-2484	142	44	𝑌	𝑌	PROPN
iajs-2484	142	45	is	be	AUX
iajs-2484	142	46	an	an	DET
iajs-2484	142	47	𝜔-compact	𝜔-compact	PROPN
iajs-2484	142	48	(	(	PUNCT
iajs-2484	142	49	respectively	respectively	ADV
iajs-2484	142	50	𝑁-compact	𝑁-compact	PROPN
iajs-2484	142	51	)	)	PUNCT
iajs-2484	142	52	set	set	VERB
iajs-2484	142	53	in	in	ADP
iajs-2484	142	54	𝑋.	𝑋.	PROPN
iajs-2484	142	55	(	(	PUNCT
iajs-2484	142	56	1.30	1.30	NUM
iajs-2484	142	57	)	)	PUNCT
iajs-2484	142	58	example	example	NOUN
iajs-2484	143	1	1𝑓	1𝑓	NUM
iajs-2484	143	2	:	:	PUNCT
iajs-2484	143	3	ℛ	ℛ	ADJ
iajs-2484	143	4	,	,	PUNCT
iajs-2484	143	5	ʈ	ʈ	ADP
iajs-2484	143	6	⟶	⟶	PROPN
iajs-2484	143	7	ℛ	ℛ	PROPN
iajs-2484	143	8	,	,	PUNCT
iajs-2484	143	9	ʈ	ʈ	X
iajs-2484	143	10	is	be	AUX
iajs-2484	143	11	compact	compact	ADJ
iajs-2484	143	12	,	,	PUNCT
iajs-2484	143	13	𝜔∗-compact	𝜔∗-compact	PROPN
iajs-2484	143	14	,	,	PUNCT
iajs-2484	143	15	𝑁∗-compact	𝑁∗-compact	PROPN
iajs-2484	143	16	,	,	PUNCT
iajs-2484	143	17	𝜔-compact	𝜔-compact	PROPN
iajs-2484	143	18	,	,	PUNCT
iajs-2484	143	19	𝑁-compact	𝑁-compact	PROPN
iajs-2484	143	20	,	,	PUNCT
iajs-2484	143	21	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	143	22	and	and	CCONJ
iajs-2484	143	23	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	143	24	function	function	NOUN
iajs-2484	143	25	.	.	PUNCT
iajs-2484	144	1	proposition	proposition	NOUN
iajs-2484	144	2	(	(	PUNCT
iajs-2484	144	3	1.31	1.31	NUM
iajs-2484	144	4	):	):	PUNCT
iajs-2484	144	5	if	if	SCONJ
iajs-2484	144	6	𝑓	𝑓	X
iajs-2484	144	7	:	:	PUNCT
iajs-2484	144	8	𝑋	𝑋	PROPN
iajs-2484	144	9	⟶	⟶	NOUN
iajs-2484	144	10	𝑌	𝑌	PROPN
iajs-2484	144	11	is	be	AUX
iajs-2484	144	12	:	:	PUNCT
iajs-2484	144	13	1𝜔-compact	1𝜔-compact	NUM
iajs-2484	144	14	(	(	PUNCT
iajs-2484	144	15	respectively	respectively	ADV
iajs-2484	144	16	𝑁-compact	𝑁-compact	PROPN
iajs-2484	144	17	)	)	PUNCT
iajs-2484	144	18	function	function	NOUN
iajs-2484	144	19	where	where	SCONJ
iajs-2484	144	20	𝑋	𝑋	PROPN
iajs-2484	144	21	is	be	AUX
iajs-2484	144	22	a	a	DET
iajs-2484	144	23	𝑇	𝑇	PROPN
iajs-2484	144	24	-space	-space	NOUN
iajs-2484	144	25	,	,	PUNCT
iajs-2484	144	26	and	and	CCONJ
iajs-2484	144	27	then	then	ADV
iajs-2484	144	28	it	it	PRON
iajs-2484	144	29	is	be	AUX
iajs-2484	144	30	𝜔mcfunction	𝜔mcfunction	NOUN
iajs-2484	144	31	and	and	CCONJ
iajs-2484	144	32	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	144	33	-	-	PUNCT
iajs-2484	144	34	function	function	NOUN
iajs-2484	144	35	(	(	PUNCT
iajs-2484	144	36	respectively	respectively	ADV
iajs-2484	144	37	 	 	SPACE
iajs-2484	144	38	𝑁mc	𝑁mc	PROPN
iajs-2484	144	39	-	-	PUNCT
iajs-2484	144	40	function	function	NOUN
iajs-2484	144	41	and	and	CCONJ
iajs-2484	144	42	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	144	43	-	-	PUNCT
iajs-2484	144	44	function	function	NOUN
iajs-2484	144	45	)	)	PUNCT
iajs-2484	144	46	.	.	PUNCT
iajs-2484	145	1	2𝜔-compact	2𝜔-compact	NUM
iajs-2484	145	2	(	(	PUNCT
iajs-2484	145	3	respectively	respectively	ADV
iajs-2484	145	4	𝑁-compact	𝑁-compact	PROPN
iajs-2484	145	5	)	)	PUNCT
iajs-2484	145	6	function	function	NOUN
iajs-2484	145	7	where	where	SCONJ
iajs-2484	145	8	𝑋	𝑋	PROPN
iajs-2484	145	9	is	be	AUX
iajs-2484	145	10	a	a	DET
iajs-2484	145	11	kc	kc	NOUN
iajs-2484	145	12	-	-	PUNCT
iajs-2484	145	13	space	space	NOUN
iajs-2484	145	14	,	,	PUNCT
iajs-2484	145	15	and	and	CCONJ
iajs-2484	145	16	then	then	ADV
iajs-2484	145	17	it	it	PRON
iajs-2484	145	18	is	be	AUX
iajs-2484	145	19	𝜔mcfunction	𝜔mcfunction	NOUN
iajs-2484	145	20	and	and	CCONJ
iajs-2484	145	21	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	145	22	-	-	PUNCT
iajs-2484	145	23	function	function	NOUN
iajs-2484	145	24	(	(	PUNCT
iajs-2484	145	25	respectively	respectively	ADV
iajs-2484	145	26	𝑁mc	𝑁mc	NOUN
iajs-2484	145	27	-	-	PUNCT
iajs-2484	145	28	function	function	NOUN
iajs-2484	145	29	and	and	CCONJ
iajs-2484	145	30	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	145	31	-	-	PUNCT
iajs-2484	145	32	function	function	NOUN
iajs-2484	145	33	)	)	PUNCT
iajs-2484	145	34	.	.	PUNCT
iajs-2484	146	1	3𝜔-compact	3𝜔-compact	NUM
iajs-2484	146	2	(	(	PUNCT
iajs-2484	146	3	respectively	respectively	ADV
iajs-2484	146	4	𝑁-compact	𝑁-compact	PROPN
iajs-2484	146	5	)	)	PUNCT
iajs-2484	146	6	function	function	NOUN
iajs-2484	146	7	where	where	SCONJ
iajs-2484	146	8	𝑋	𝑋	PROPN
iajs-2484	146	9	is	be	AUX
iajs-2484	146	10	a	a	DET
iajs-2484	146	11	c	c	NOUN
iajs-2484	146	12	-	-	PUNCT
iajs-2484	146	13	c	c	NOUN
iajs-2484	146	14	space	space	NOUN
iajs-2484	146	15	,	,	PUNCT
iajs-2484	146	16	and	and	CCONJ
iajs-2484	146	17	then	then	ADV
iajs-2484	146	18	it	it	PRON
iajs-2484	146	19	is	be	AUX
iajs-2484	146	20	𝜔mcfunction	𝜔mcfunction	NOUN
iajs-2484	146	21	and	and	CCONJ
iajs-2484	146	22	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	146	23	-	-	PUNCT
iajs-2484	146	24	function	function	NOUN
iajs-2484	146	25	(	(	PUNCT
iajs-2484	146	26	respectively	respectively	ADV
iajs-2484	146	27	𝑁mc	𝑁mc	NOUN
iajs-2484	146	28	-	-	PUNCT
iajs-2484	146	29	function	function	NOUN
iajs-2484	146	30	and	and	CCONJ
iajs-2484	146	31	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	146	32	-	-	PUNCT
iajs-2484	146	33	function	function	NOUN
iajs-2484	146	34	)	)	PUNCT
iajs-2484	146	35	.	.	PUNCT
iajs-2484	147	1	4compact	4compact	NUM
iajs-2484	147	2	function	function	NOUN
iajs-2484	147	3	where	where	SCONJ
iajs-2484	147	4	𝑋	𝑋	PROPN
iajs-2484	147	5	is	be	AUX
iajs-2484	147	6	a	a	DET
iajs-2484	147	7	𝑇	𝑇	PROPN
iajs-2484	147	8	-space	-space	NOUN
iajs-2484	147	9	(	(	PUNCT
iajs-2484	147	10	respectively	respectively	ADV
iajs-2484	147	11	kc	kc	NOUN
iajs-2484	147	12	-	-	PUNCT
iajs-2484	147	13	space	space	NOUN
iajs-2484	147	14	,	,	PUNCT
iajs-2484	147	15	c	c	NOUN
iajs-2484	147	16	-	-	PUNCT
iajs-2484	147	17	c	c	NOUN
iajs-2484	147	18	space	space	NOUN
iajs-2484	147	19	)	)	PUNCT
iajs-2484	147	20	,	,	PUNCT
iajs-2484	147	21	and	and	CCONJ
iajs-2484	147	22	then	then	ADV
iajs-2484	147	23	it	it	PRON
iajs-2484	147	24	is	be	AUX
iajs-2484	147	25	𝜔mc	𝜔mc	ADJ
iajs-2484	147	26	-	-	PUNCT
iajs-2484	147	27	function	function	NOUN
iajs-2484	147	28	and	and	CCONJ
iajs-2484	147	29	𝑁mc	𝑁mc	NOUN
iajs-2484	147	30	-	-	PUNCT
iajs-2484	147	31	function	function	NOUN
iajs-2484	147	32	.	.	PUNCT
iajs-2484	148	1	5𝜔∗∗-compact	5𝜔∗∗-compact	INTJ
iajs-2484	148	2	(	(	PUNCT
iajs-2484	148	3	respectively	respectively	ADV
iajs-2484	148	4	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	148	5	)	)	PUNCT
iajs-2484	148	6	function	function	NOUN
iajs-2484	148	7	where	where	SCONJ
iajs-2484	148	8	x	x	PRON
iajs-2484	148	9	is	be	AUX
iajs-2484	148	10	a	a	DET
iajs-2484	148	11	t	t	NOUN
iajs-2484	148	12	-space	-space	NOUN
iajs-2484	148	13	,	,	PUNCT
iajs-2484	148	14	and	and	CCONJ
iajs-2484	148	15	then	then	ADV
iajs-2484	148	16	it	it	PRON
iajs-2484	148	17	is	be	AUX
iajs-2484	148	18	ωmωc	ωmωc	NOUN
iajs-2484	148	19	-	-	PUNCT
iajs-2484	148	20	function	function	NOUN
iajs-2484	148	21	(	(	PUNCT
iajs-2484	148	22	respectively	respectively	ADV
iajs-2484	148	23	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	148	24	-	-	PUNCT
iajs-2484	148	25	function	function	NOUN
iajs-2484	148	26	)	)	PUNCT
iajs-2484	148	27	.	.	PUNCT
iajs-2484	149	1	6𝜔∗∗-compact	6𝜔∗∗-compact	NUM
iajs-2484	149	2	(	(	PUNCT
iajs-2484	149	3	respectively	respectively	ADV
iajs-2484	149	4	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	149	5	)	)	PUNCT
iajs-2484	149	6	function	function	NOUN
iajs-2484	149	7	where	where	SCONJ
iajs-2484	149	8	𝑋	𝑋	PROPN
iajs-2484	149	9	is	be	AUX
iajs-2484	149	10	a	a	DET
iajs-2484	149	11	kc	kc	NOUN
iajs-2484	149	12	-	-	PUNCT
iajs-2484	149	13	space	space	NOUN
iajs-2484	149	14	,	,	PUNCT
iajs-2484	149	15	and	and	CCONJ
iajs-2484	149	16	then	then	ADV
iajs-2484	149	17	it	it	PRON
iajs-2484	149	18	is	be	AUX
iajs-2484	149	19	𝜔m𝜔cfunction	𝜔m𝜔cfunction	NOUN
iajs-2484	149	20	(	(	PUNCT
iajs-2484	149	21	respectively	respectively	ADV
iajs-2484	149	22	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	149	23	-	-	PUNCT
iajs-2484	149	24	function	function	NOUN
iajs-2484	149	25	)	)	PUNCT
iajs-2484	149	26	.	.	PUNCT
iajs-2484	150	1	7𝜔∗∗-compact	7𝜔∗∗-compact	NOUN
iajs-2484	150	2	(	(	PUNCT
iajs-2484	150	3	respectively	respectively	ADV
iajs-2484	150	4	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	150	5	)	)	PUNCT
iajs-2484	150	6	function	function	NOUN
iajs-2484	150	7	where	where	SCONJ
iajs-2484	150	8	𝑋	𝑋	PROPN
iajs-2484	150	9	is	be	AUX
iajs-2484	150	10	a	a	DET
iajs-2484	150	11	c	c	NOUN
iajs-2484	150	12	-	-	PUNCT
iajs-2484	150	13	c	c	NOUN
iajs-2484	150	14	space	space	NOUN
iajs-2484	150	15	,	,	PUNCT
iajs-2484	150	16	and	and	CCONJ
iajs-2484	150	17	then	then	ADV
iajs-2484	150	18	it	it	PRON
iajs-2484	150	19	is	be	AUX
iajs-2484	150	20	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	150	21	-	-	PUNCT
iajs-2484	150	22	function	function	NOUN
iajs-2484	150	23	(	(	PUNCT
iajs-2484	150	24	respectively	respectively	ADV
iajs-2484	150	25	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	150	26	-	-	PUNCT
iajs-2484	150	27	function	function	NOUN
iajs-2484	150	28	)	)	PUNCT
iajs-2484	150	29	.	.	PUNCT
iajs-2484	151	1	8𝜔∗-compact	8𝜔∗-compact	PROPN
iajs-2484	151	2	(	(	PUNCT
iajs-2484	151	3	respectively	respectively	ADV
iajs-2484	151	4	𝑁∗-compact	𝑁∗-compact	NOUN
iajs-2484	151	5	)	)	PUNCT
iajs-2484	151	6	function	function	NOUN
iajs-2484	151	7	where	where	SCONJ
iajs-2484	151	8	𝑋	𝑋	PROPN
iajs-2484	151	9	is	be	AUX
iajs-2484	151	10	a	a	DET
iajs-2484	151	11	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	151	12	-space	-space	NOUN
iajs-2484	151	13	(	(	PUNCT
iajs-2484	151	14	respectively	respectively	ADV
iajs-2484	151	15	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	151	16	space	space	NOUN
iajs-2484	151	17	)	)	PUNCT
iajs-2484	151	18	,	,	PUNCT
iajs-2484	151	19	and	and	CCONJ
iajs-2484	151	20	then	then	ADV
iajs-2484	151	21	it	it	PRON
iajs-2484	151	22	is	be	AUX
iajs-2484	151	23	m𝜔c	m𝜔c	NOUN
iajs-2484	151	24	-	-	PUNCT
iajs-2484	151	25	function	function	NOUN
iajs-2484	151	26	(	(	PUNCT
iajs-2484	151	27	resp	resp	NOUN
iajs-2484	151	28	.	.	PUNCT
iajs-2484	152	1	m𝑁c	m𝑁c	NOUN
iajs-2484	152	2	-	-	PUNCT
iajs-2484	152	3	function	function	NOUN
iajs-2484	152	4	)	)	PUNCT
iajs-2484	152	5	.	.	PUNCT
iajs-2484	153	1	9𝜔∗-compact	9𝜔∗-compact	NOUN
iajs-2484	153	2	(	(	PUNCT
iajs-2484	153	3	respectively	respectively	ADV
iajs-2484	153	4	𝑁∗-compact	𝑁∗-compact	NOUN
iajs-2484	153	5	)	)	PUNCT
iajs-2484	153	6	function	function	NOUN
iajs-2484	153	7	where	where	SCONJ
iajs-2484	153	8	𝑋	𝑋	PROPN
iajs-2484	153	9	is	be	AUX
iajs-2484	153	10	a	a	DET
iajs-2484	153	11	kc	kc	NOUN
iajs-2484	153	12	-	-	PUNCT
iajs-2484	153	13	space	space	NOUN
iajs-2484	153	14	,	,	PUNCT
iajs-2484	153	15	and	and	CCONJ
iajs-2484	153	16	then	then	ADV
iajs-2484	153	17	it	it	PRON
iajs-2484	153	18	is	be	AUX
iajs-2484	153	19	m𝜔c	m𝜔c	NOUN
iajs-2484	153	20	-	-	PUNCT
iajs-2484	153	21	function	function	NOUN
iajs-2484	153	22	(	(	PUNCT
iajs-2484	153	23	respectively	respectively	ADV
iajs-2484	153	24	m𝑁c	m𝑁c	NOUN
iajs-2484	153	25	-	-	PUNCT
iajs-2484	153	26	function	function	NOUN
iajs-2484	153	27	)	)	PUNCT
iajs-2484	153	28	.	.	PUNCT
iajs-2484	154	1	10𝜔∗-compact	10𝜔∗-compact	NUM
iajs-2484	154	2	(	(	PUNCT
iajs-2484	154	3	respectively	respectively	ADV
iajs-2484	154	4	𝑁∗-compact	𝑁∗-compact	NOUN
iajs-2484	154	5	)	)	PUNCT
iajs-2484	154	6	function	function	NOUN
iajs-2484	154	7	where	where	SCONJ
iajs-2484	154	8	𝑋	𝑋	PROPN
iajs-2484	154	9	is	be	AUX
iajs-2484	154	10	a	a	DET
iajs-2484	154	11	c	c	NOUN
iajs-2484	154	12	-	-	PUNCT
iajs-2484	154	13	c	c	NOUN
iajs-2484	154	14	space	space	NOUN
iajs-2484	154	15	,	,	PUNCT
iajs-2484	154	16	and	and	CCONJ
iajs-2484	154	17	then	then	ADV
iajs-2484	154	18	it	it	PRON
iajs-2484	154	19	is	be	AUX
iajs-2484	154	20	m𝜔c	m𝜔c	NOUN
iajs-2484	154	21	-	-	PUNCT
iajs-2484	154	22	function	function	NOUN
iajs-2484	154	23	(	(	PUNCT
iajs-2484	154	24	respectively	respectively	ADV
iajs-2484	154	25	m𝑁c	m𝑁c	NOUN
iajs-2484	154	26	-	-	PUNCT
iajs-2484	154	27	function	function	NOUN
iajs-2484	154	28	)	)	PUNCT
iajs-2484	154	29	.	.	PUNCT
iajs-2484	155	1	11𝜔∗∗-compact	11𝜔∗∗-compact	NUM
iajs-2484	155	2	(	(	PUNCT
iajs-2484	155	3	respectively	respectively	ADV
iajs-2484	155	4	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	155	5	)	)	PUNCT
iajs-2484	155	6	function	function	NOUN
iajs-2484	155	7	where	where	SCONJ
iajs-2484	155	8	𝑋	𝑋	PROPN
iajs-2484	155	9	is	be	AUX
iajs-2484	155	10	a	a	DET
iajs-2484	155	11	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	155	12	-space	-space	NOUN
iajs-2484	155	13	(	(	PUNCT
iajs-2484	155	14	respectively	respectively	ADV
iajs-2484	155	15	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	155	16	-space	-space	NOUN
iajs-2484	155	17	)	)	PUNCT
iajs-2484	155	18	,	,	PUNCT
iajs-2484	155	19	and	and	CCONJ
iajs-2484	155	20	then	then	ADV
iajs-2484	155	21	it	it	PRON
iajs-2484	155	22	is	be	AUX
iajs-2484	155	23	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	155	24	-	-	PUNCT
iajs-2484	155	25	function	function	NOUN
iajs-2484	155	26	(	(	PUNCT
iajs-2484	155	27	respectively	respectively	ADV
iajs-2484	155	28	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	155	29	-	-	PUNCT
iajs-2484	155	30	function	function	NOUN
iajs-2484	155	31	)	)	PUNCT
iajs-2484	155	32	.	.	PUNCT
iajs-2484	156	1	proof	proof	NOUN
iajs-2484	156	2	:	:	PUNCT
iajs-2484	156	3	suppose	suppose	VERB
iajs-2484	156	4	𝑓	𝑓	PRON
iajs-2484	156	5	is	be	AUX
iajs-2484	156	6	𝜔-compact	𝜔-compact	PROPN
iajs-2484	156	7	(	(	PUNCT
iajs-2484	156	8	respectively	respectively	ADV
iajs-2484	156	9	𝑁-compact	𝑁-compact	PROPN
iajs-2484	156	10	)	)	PUNCT
iajs-2484	156	11	function	function	NOUN
iajs-2484	156	12	and	and	CCONJ
iajs-2484	156	13	𝑋	𝑋	NOUN
iajs-2484	156	14	is	be	AUX
iajs-2484	156	15	a	a	DET
iajs-2484	156	16	𝑇	𝑇	PROPN
iajs-2484	156	17	-space	-space	NOUN
iajs-2484	156	18	,	,	PUNCT
iajs-2484	156	19	let	let	VERB
iajs-2484	156	20	𝒲	𝒲	NOUN
iajs-2484	156	21	be	be	AUX
iajs-2484	156	22	an	an	DET
iajs-2484	156	23	𝜔-compact	𝜔-compact	NOUN
iajs-2484	156	24	set	set	VERB
iajs-2484	156	25	in	in	ADP
iajs-2484	156	26	𝑌	𝑌	PROPN
iajs-2484	156	27	,	,	PUNCT
iajs-2484	156	28	so	so	SCONJ
iajs-2484	156	29	𝑓	𝑓	PRON
iajs-2484	156	30	𝒲	𝒲	NOUN
iajs-2484	156	31	is	be	AUX
iajs-2484	156	32	compact	compact	ADJ
iajs-2484	156	33	set	set	VERB
iajs-2484	156	34	in	in	ADP
iajs-2484	156	35	𝑋	𝑋	PROPN
iajs-2484	156	36	which	which	PRON
iajs-2484	156	37	is	be	AUX
iajs-2484	156	38	a	a	DET
iajs-2484	156	39	𝑇	𝑇	PROPN
iajs-2484	156	40	-space	-space	NOUN
iajs-2484	156	41	,	,	PUNCT
iajs-2484	156	42	thus	thus	ADV
iajs-2484	156	43	𝑓	𝑓	PRON
iajs-2484	156	44	𝒲	𝒲	PROPN
iajs-2484	156	45	is	be	AUX
iajs-2484	156	46	  	  	SPACE
iajs-2484	156	47	181	181	NUM
iajs-2484	156	48	  	  	SPACE
iajs-2484	156	49	ibn	ibn	PROPN
iajs-2484	156	50	al	al	PROPN
iajs-2484	156	51	-	-	PUNCT
iajs-2484	156	52	haitham	haitham	PROPN
iajs-2484	156	53	jour	jour	X
iajs-2484	156	54	.	.	PROPN
iajs-2484	157	1	for	for	ADP
iajs-2484	157	2	pure	pure	ADJ
iajs-2484	157	3	&	&	CCONJ
iajs-2484	157	4	appl	appl	PROPN
iajs-2484	157	5	.	.	PUNCT
iajs-2484	158	1	sci	sci	PROPN
iajs-2484	158	2	.	.	PROPN
iajs-2484	159	1	33	33	NUM
iajs-2484	159	2	(	(	PUNCT
iajs-2484	159	3	3	3	NUM
iajs-2484	159	4	)	)	PUNCT
iajs-2484	159	5	2020	2020	NUM
iajs-2484	159	6	closed	close	VERB
iajs-2484	159	7	set	set	VERB
iajs-2484	159	8	(	(	PUNCT
iajs-2484	159	9	by	by	ADP
iajs-2484	159	10	remark	remark	NOUN
iajs-2484	159	11	(	(	PUNCT
iajs-2484	159	12	1.6	1.6	NUM
iajs-2484	159	13	)	)	PUNCT
iajs-2484	159	14	)	)	PUNCT
iajs-2484	159	15	,	,	PUNCT
iajs-2484	159	16	therefore	therefore	ADV
iajs-2484	159	17	𝑓	𝑓	PRON
iajs-2484	159	18	is	be	AUX
iajs-2484	159	19	𝜔mc	𝜔mc	NOUN
iajs-2484	159	20	-	-	PUNCT
iajs-2484	159	21	function	function	NOUN
iajs-2484	159	22	(	(	PUNCT
iajs-2484	159	23	respectively	respectively	ADV
iajs-2484	159	24	𝑁mc	𝑁mc	NOUN
iajs-2484	159	25	-	-	PUNCT
iajs-2484	159	26	function	function	NOUN
iajs-2484	159	27	)	)	PUNCT
iajs-2484	159	28	.	.	PUNCT
iajs-2484	160	1	now	now	ADV
iajs-2484	160	2	,	,	PUNCT
iajs-2484	160	3	since	since	SCONJ
iajs-2484	160	4	every	every	DET
iajs-2484	160	5	closed	closed	ADJ
iajs-2484	160	6	set	set	NOUN
iajs-2484	160	7	is	be	AUX
iajs-2484	160	8	𝑁-closed	𝑁-closed	ADJ
iajs-2484	160	9	and	and	CCONJ
iajs-2484	160	10	𝜔-closed	𝜔-close	VERB
iajs-2484	160	11	set	set	NOUN
iajs-2484	160	12	,	,	PUNCT
iajs-2484	160	13	so	so	ADV
iajs-2484	160	14	𝑓	𝑓	PRON
iajs-2484	160	15	is	be	AUX
iajs-2484	160	16	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	160	17	-	-	PUNCT
iajs-2484	160	18	function	function	NOUN
iajs-2484	160	19	(	(	PUNCT
iajs-2484	160	20	respectively	respectively	ADV
iajs-2484	160	21	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	160	22	-	-	PUNCT
iajs-2484	160	23	function	function	NOUN
iajs-2484	160	24	)	)	PUNCT
iajs-2484	160	25	.	.	PUNCT
iajs-2484	161	1	we	we	PRON
iajs-2484	161	2	can	can	AUX
iajs-2484	161	3	prove	prove	VERB
iajs-2484	161	4	the	the	DET
iajs-2484	161	5	rest	rest	NOUN
iajs-2484	161	6	by	by	ADP
iajs-2484	161	7	the	the	DET
iajs-2484	161	8	same	same	ADJ
iajs-2484	161	9	way	way	NOUN
iajs-2484	161	10	.	.	PUNCT
iajs-2484	162	1	proposition	proposition	NOUN
iajs-2484	162	2	(	(	PUNCT
iajs-2484	162	3	1.32	1.32	NUM
iajs-2484	162	4	)	)	PUNCT
iajs-2484	163	1	[	[	X
iajs-2484	163	2	19	19	NUM
iajs-2484	163	3	]	]	PUNCT
iajs-2484	163	4	.	.	PUNCT
iajs-2484	164	1	1if	1if	PROPN
iajs-2484	164	2	𝑌	𝑌	PROPN
iajs-2484	164	3	is	be	AUX
iajs-2484	164	4	a	a	DET
iajs-2484	164	5	subspace	subspace	NOUN
iajs-2484	164	6	of	of	ADP
iajs-2484	164	7	𝑋	𝑋	PROPN
iajs-2484	164	8	,	,	PUNCT
iajs-2484	164	9	ʈ	ʈ	PROPN
iajs-2484	164	10	and	and	CCONJ
iajs-2484	164	11	𝒲	𝒲	NOUN
iajs-2484	164	12	is	be	AUX
iajs-2484	164	13	𝜔-open	𝜔-open	ADJ
iajs-2484	164	14	set	set	VERB
iajs-2484	164	15	in	in	ADP
iajs-2484	164	16	𝑋	𝑋	PROPN
iajs-2484	164	17	,	,	PUNCT
iajs-2484	164	18	then	then	ADV
iajs-2484	164	19	𝒲	𝒲	NOUN
iajs-2484	164	20	is	be	AUX
iajs-2484	164	21	𝜔-open	𝜔-open	ADJ
iajs-2484	164	22	set	set	VERB
iajs-2484	164	23	in	in	ADP
iajs-2484	164	24	𝑌	𝑌	PROPN
iajs-2484	164	25	provided	provide	VERB
iajs-2484	164	26	that	that	SCONJ
iajs-2484	164	27	𝒲	𝒲	PROPN
iajs-2484	164	28	⊆	⊆	NUM
iajs-2484	164	29	𝑌.	𝑌.	PROPN
iajs-2484	165	1	2-	2-	X
iajs-2484	165	2	 	 	SPACE
iajs-2484	165	3	if	if	SCONJ
iajs-2484	165	4	𝑌	𝑌	PROPN
iajs-2484	165	5	is	be	AUX
iajs-2484	165	6	a	a	DET
iajs-2484	165	7	subspace	subspace	NOUN
iajs-2484	165	8	of	of	ADP
iajs-2484	165	9	𝑋	𝑋	PROPN
iajs-2484	165	10	,	,	PUNCT
iajs-2484	165	11	ʈ	ʈ	PROPN
iajs-2484	165	12	and	and	CCONJ
iajs-2484	165	13	𝒲	𝒲	NOUN
iajs-2484	165	14	is	be	AUX
iajs-2484	165	15	𝜔-closed	𝜔-close	VERB
iajs-2484	165	16	set	set	VERB
iajs-2484	165	17	in	in	ADP
iajs-2484	165	18	𝑋	𝑋	PROPN
iajs-2484	165	19	,	,	PUNCT
iajs-2484	165	20	then	then	ADV
iajs-2484	165	21	𝒲	𝒲	NOUN
iajs-2484	165	22	is	be	AUX
iajs-2484	165	23	𝜔-closed	𝜔-close	VERB
iajs-2484	165	24	set	set	VERB
iajs-2484	165	25	in	in	ADP
iajs-2484	165	26	𝑌	𝑌	PROPN
iajs-2484	165	27	provided	provide	VERB
iajs-2484	165	28	that	that	SCONJ
iajs-2484	165	29	𝒲	𝒲	PROPN
iajs-2484	165	30	⊆	⊆	NUM
iajs-2484	165	31	𝑌.	𝑌.	PROPN
iajs-2484	165	32	proposition	proposition	NOUN
iajs-2484	165	33	(	(	PUNCT
iajs-2484	165	34	1.33	1.33	NUM
iajs-2484	165	35	)	)	PUNCT
iajs-2484	165	36	if	if	SCONJ
iajs-2484	165	37	𝑓	𝑓	X
iajs-2484	165	38	:	:	PUNCT
iajs-2484	165	39	𝑋	𝑋	PROPN
iajs-2484	165	40	⟶	⟶	NOUN
iajs-2484	165	41	𝑌	𝑌	PROPN
iajs-2484	165	42	is	be	AUX
iajs-2484	165	43	a	a	DET
iajs-2484	165	44	𝜔mc	𝜔mc	ADJ
iajs-2484	165	45	-	-	PUNCT
iajs-2484	165	46	function	function	NOUN
iajs-2484	165	47	(	(	PUNCT
iajs-2484	165	48	respectively	respectively	ADV
iajs-2484	165	49	𝑁mc	𝑁mc	NOUN
iajs-2484	165	50	-	-	PUNCT
iajs-2484	165	51	function	function	NOUN
iajs-2484	165	52	)	)	PUNCT
iajs-2484	165	53	and	and	CCONJ
iajs-2484	165	54	𝒲	𝒲	NOUN
iajs-2484	165	55	⊆	⊆	NUM
iajs-2484	165	56	𝑋	𝑋	PROPN
iajs-2484	165	57	then	then	ADV
iajs-2484	165	58	𝑓|𝒲	𝑓|𝒲	PROPN
iajs-2484	165	59	:	:	PUNCT
iajs-2484	165	60	𝒲	𝒲	NOUN
iajs-2484	165	61	⟶	⟶	NOUN
iajs-2484	165	62	𝑌	𝑌	PROPN
iajs-2484	165	63	is	be	AUX
iajs-2484	165	64	a	a	DET
iajs-2484	165	65	𝜔mc	𝜔mc	ADJ
iajs-2484	165	66	-	-	PUNCT
iajs-2484	165	67	function	function	NOUN
iajs-2484	165	68	(	(	PUNCT
iajs-2484	165	69	respectively	respectively	ADV
iajs-2484	165	70	𝑁mc	𝑁mc	NOUN
iajs-2484	165	71	-	-	PUNCT
iajs-2484	165	72	function	function	NOUN
iajs-2484	165	73	)	)	PUNCT
iajs-2484	165	74	.	.	PUNCT
iajs-2484	166	1	proof	proof	NOUN
iajs-2484	166	2	:	:	PUNCT
iajs-2484	166	3	let	let	VERB
iajs-2484	166	4	𝒢=𝑓|𝒲	𝒢=𝑓|𝒲	VERB
iajs-2484	166	5	:	:	PUNCT
iajs-2484	166	6	𝒲	𝒲	NOUN
iajs-2484	166	7	⟶	⟶	NOUN
iajs-2484	166	8	𝑌	𝑌	PROPN
iajs-2484	166	9	and	and	CCONJ
iajs-2484	166	10	let	let	VERB
iajs-2484	166	11	k	k	PROPN
iajs-2484	166	12	be	be	AUX
iajs-2484	166	13	an	an	DET
iajs-2484	166	14	𝜔-compact	𝜔-compact	PROPN
iajs-2484	166	15	(	(	PUNCT
iajs-2484	166	16	respectively	respectively	ADV
iajs-2484	166	17	𝑁-compact	𝑁-compact	PROPN
iajs-2484	166	18	)	)	PUNCT
iajs-2484	166	19	subset	subset	NOUN
iajs-2484	166	20	of	of	ADP
iajs-2484	166	21	𝑌	𝑌	PROPN
iajs-2484	166	22	,	,	PUNCT
iajs-2484	166	23	since	since	SCONJ
iajs-2484	166	24	𝑓	𝑓	PRON
iajs-2484	166	25	is	be	AUX
iajs-2484	166	26	an	an	DET
iajs-2484	166	27	𝜔mc	𝜔mc	ADJ
iajs-2484	166	28	-	-	PUNCT
iajs-2484	166	29	function	function	NOUN
iajs-2484	166	30	(	(	PUNCT
iajs-2484	166	31	respectively	respectively	ADV
iajs-2484	166	32	𝑁mc	𝑁mc	NOUN
iajs-2484	166	33	-	-	PUNCT
iajs-2484	166	34	function	function	NOUN
iajs-2484	166	35	)	)	PUNCT
iajs-2484	166	36	,	,	PUNCT
iajs-2484	166	37	then	then	ADV
iajs-2484	166	38	𝑓	𝑓	X
iajs-2484	166	39	𝐾	𝐾	PROPN
iajs-2484	166	40	is	be	AUX
iajs-2484	166	41	a	a	DET
iajs-2484	166	42	closed	closed	ADJ
iajs-2484	166	43	subset	subset	NOUN
iajs-2484	166	44	of	of	ADP
iajs-2484	166	45	𝑋.	𝑋.	PROPN
iajs-2484	166	46	now	now	ADV
iajs-2484	166	47	𝒢	𝒢	PROPN
iajs-2484	166	48	(	(	PUNCT
iajs-2484	166	49	k	k	NOUN
iajs-2484	166	50	)	)	PUNCT
iajs-2484	166	51	=	=	SYM
iajs-2484	167	1	𝑓	𝑓	PROPN
iajs-2484	167	2	(	(	PUNCT
iajs-2484	167	3	k)⋂𝒲	k)⋂𝒲	NOUN
iajs-2484	167	4	,	,	PUNCT
iajs-2484	167	5	hence	hence	ADV
iajs-2484	167	6	𝒢	𝒢	PROPN
iajs-2484	167	7	(	(	PUNCT
iajs-2484	167	8	k	k	NOUN
iajs-2484	167	9	)	)	PUNCT
iajs-2484	167	10	is	be	AUX
iajs-2484	167	11	a	a	DET
iajs-2484	167	12	closed	closed	ADJ
iajs-2484	167	13	subset	subset	NOUN
iajs-2484	167	14	of	of	ADP
iajs-2484	167	15	𝒲.	𝒲.	PROPN
iajs-2484	167	16	therefore	therefore	ADV
iajs-2484	167	17	𝒢	𝒢	PROPN
iajs-2484	167	18	𝑓|𝒲	𝑓|𝒲	NOUN
iajs-2484	167	19	:	:	PUNCT
iajs-2484	167	20	𝒲	𝒲	NOUN
iajs-2484	167	21	⟶	⟶	NOUN
iajs-2484	167	22	𝑌	𝑌	PROPN
iajs-2484	167	23	is	be	AUX
iajs-2484	167	24	a	a	DET
iajs-2484	167	25	𝜔mc	𝜔mc	ADJ
iajs-2484	167	26	-	-	PUNCT
iajs-2484	167	27	function	function	NOUN
iajs-2484	167	28	(	(	PUNCT
iajs-2484	167	29	respectively	respectively	ADV
iajs-2484	167	30	𝑁mc	𝑁mc	NOUN
iajs-2484	167	31	-	-	PUNCT
iajs-2484	167	32	function	function	NOUN
iajs-2484	167	33	)	)	PUNCT
iajs-2484	167	34	.	.	PUNCT
iajs-2484	168	1	by	by	ADP
iajs-2484	168	2	the	the	DET
iajs-2484	168	3	same	same	ADJ
iajs-2484	168	4	way	way	NOUN
iajs-2484	168	5	we	we	PRON
iajs-2484	168	6	can	can	AUX
iajs-2484	168	7	prove	prove	VERB
iajs-2484	168	8	the	the	DET
iajs-2484	168	9	following	follow	VERB
iajs-2484	168	10	proposition	proposition	NOUN
iajs-2484	168	11	.	.	PUNCT
iajs-2484	169	1	proposition	proposition	NOUN
iajs-2484	169	2	(	(	PUNCT
iajs-2484	169	3	1.34	1.34	NUM
iajs-2484	169	4	)	)	PUNCT
iajs-2484	169	5	if	if	SCONJ
iajs-2484	169	6	𝒲	𝒲	NOUN
iajs-2484	169	7	⊆	⊆	NUM
iajs-2484	169	8	𝑋	𝑋	NOUN
iajs-2484	169	9	and	and	CCONJ
iajs-2484	169	10	𝑓	𝑓	X
iajs-2484	169	11	:	:	PUNCT
iajs-2484	169	12	𝑋	𝑋	PROPN
iajs-2484	169	13	⟶	⟶	NOUN
iajs-2484	169	14	𝑌	𝑌	PROPN
iajs-2484	169	15	is	be	AUX
iajs-2484	169	16	:	:	PUNCT
iajs-2484	169	17	1an	1an	ADJ
iajs-2484	169	18	m𝜔c	m𝜔c	NOUN
iajs-2484	169	19	-	-	PUNCT
iajs-2484	169	20	function	function	NOUN
iajs-2484	169	21	(	(	PUNCT
iajs-2484	169	22	respectively	respectively	ADV
iajs-2484	169	23	m𝑁c	m𝑁c	NOUN
iajs-2484	169	24	-	-	PUNCT
iajs-2484	169	25	function	function	NOUN
iajs-2484	169	26	)	)	PUNCT
iajs-2484	169	27	,	,	PUNCT
iajs-2484	169	28	then	then	ADV
iajs-2484	169	29	𝑓|𝒲	𝑓|𝒲	NOUN
iajs-2484	169	30	:	:	PUNCT
iajs-2484	169	31	𝒲	𝒲	NOUN
iajs-2484	169	32	⟶	⟶	NOUN
iajs-2484	169	33	𝑌	𝑌	PROPN
iajs-2484	169	34	is	be	AUX
iajs-2484	169	35	an	an	DET
iajs-2484	169	36	m𝜔c	m𝜔c	NOUN
iajs-2484	169	37	-	-	PUNCT
iajs-2484	169	38	function	function	NOUN
iajs-2484	169	39	(	(	PUNCT
iajs-2484	169	40	respectively	respectively	ADV
iajs-2484	169	41	m𝑁c	m𝑁c	NOUN
iajs-2484	169	42	-	-	PUNCT
iajs-2484	169	43	function	function	NOUN
iajs-2484	169	44	)	)	PUNCT
iajs-2484	169	45	.	.	PUNCT
iajs-2484	170	1	2an	2an	ADJ
iajs-2484	170	2	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	170	3	-	-	PUNCT
iajs-2484	170	4	function	function	NOUN
iajs-2484	170	5	(	(	PUNCT
iajs-2484	170	6	respectively	respectively	ADV
iajs-2484	170	7	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	170	8	-	-	PUNCT
iajs-2484	170	9	function	function	NOUN
iajs-2484	170	10	)	)	PUNCT
iajs-2484	170	11	,	,	PUNCT
iajs-2484	170	12	then	then	ADV
iajs-2484	170	13	𝑓|𝒲	𝑓|𝒲	NOUN
iajs-2484	170	14	:	:	PUNCT
iajs-2484	170	15	𝒲	𝒲	NOUN
iajs-2484	170	16	⟶	⟶	NOUN
iajs-2484	170	17	𝑌	𝑌	PROPN
iajs-2484	170	18	is	be	AUX
iajs-2484	170	19	a	a	DET
iajs-2484	170	20	𝜔m𝜔cfunction	𝜔m𝜔cfunction	NOUN
iajs-2484	170	21	(	(	PUNCT
iajs-2484	170	22	respectively	respectively	ADV
iajs-2484	170	23	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	170	24	-	-	PUNCT
iajs-2484	170	25	function	function	NOUN
iajs-2484	170	26	)	)	PUNCT
iajs-2484	170	27	.	.	PUNCT
iajs-2484	171	1	proposition	proposition	NOUN
iajs-2484	171	2	(	(	PUNCT
iajs-2484	171	3	1.35	1.35	NUM
iajs-2484	171	4	)	)	PUNCT
iajs-2484	171	5	if	if	SCONJ
iajs-2484	171	6	𝑓	𝑓	X
iajs-2484	171	7	:	:	PUNCT
iajs-2484	171	8	𝑋	𝑋	PROPN
iajs-2484	171	9	⟶	⟶	NOUN
iajs-2484	171	10	𝑌	𝑌	PROPN
iajs-2484	171	11	is	be	AUX
iajs-2484	171	12	𝜔mc	𝜔mc	NOUN
iajs-2484	171	13	-	-	PUNCT
iajs-2484	171	14	function	function	NOUN
iajs-2484	171	15	(	(	PUNCT
iajs-2484	171	16	respectively	respectively	ADV
iajs-2484	171	17	𝑁mc	𝑁mc	NOUN
iajs-2484	171	18	-	-	PUNCT
iajs-2484	171	19	function	function	NOUN
iajs-2484	171	20	)	)	PUNCT
iajs-2484	171	21	where	where	SCONJ
iajs-2484	171	22	𝑋	𝑋	NOUN
iajs-2484	171	23	is	be	AUX
iajs-2484	171	24	a	a	DET
iajs-2484	171	25	compact	compact	ADJ
iajs-2484	171	26	space	space	NOUN
iajs-2484	171	27	,	,	PUNCT
iajs-2484	171	28	then	then	ADV
iajs-2484	171	29	it	it	PRON
iajs-2484	171	30	is	be	AUX
iajs-2484	171	31	𝜔-compact	𝜔-compact	NOUN
iajs-2484	171	32	(	(	PUNCT
iajs-2484	171	33	respectively	respectively	ADV
iajs-2484	171	34	𝑁-compact	𝑁-compact	PROPN
iajs-2484	171	35	)	)	PUNCT
iajs-2484	171	36	function	function	NOUN
iajs-2484	171	37	.	.	PUNCT
iajs-2484	172	1	proof	proof	NOUN
iajs-2484	172	2	:	:	PUNCT
iajs-2484	172	3	suppose	suppose	VERB
iajs-2484	172	4	k	k	PROPN
iajs-2484	172	5	is	be	AUX
iajs-2484	172	6	a	a	DET
iajs-2484	172	7	𝜔-compact	𝜔-compact	PROPN
iajs-2484	172	8	(	(	PUNCT
iajs-2484	172	9	respectively	respectively	ADV
iajs-2484	172	10	𝑁-compact	𝑁-compact	PROPN
iajs-2484	172	11	)	)	PUNCT
iajs-2484	172	12	subset	subset	NOUN
iajs-2484	172	13	of	of	ADP
iajs-2484	172	14	𝑌	𝑌	PROPN
iajs-2484	172	15	,	,	PUNCT
iajs-2484	172	16	so	so	ADV
iajs-2484	172	17	𝑓	𝑓	PRON
iajs-2484	172	18	(	(	PUNCT
iajs-2484	172	19	k	k	NOUN
iajs-2484	172	20	)	)	PUNCT
iajs-2484	172	21	is	be	AUX
iajs-2484	172	22	a	a	DET
iajs-2484	172	23	closed	closed	ADJ
iajs-2484	172	24	subset	subset	NOUN
iajs-2484	172	25	of	of	ADP
iajs-2484	172	26	𝑋(since	𝑋(since	NOUN
iajs-2484	173	1	𝑓	𝑓	PROPN
iajs-2484	173	2	is	be	AUX
iajs-2484	173	3	𝜔mc	𝜔mc	NOUN
iajs-2484	173	4	-	-	PUNCT
iajs-2484	173	5	function	function	NOUN
iajs-2484	173	6	(	(	PUNCT
iajs-2484	173	7	respectively	respectively	ADV
iajs-2484	173	8	𝑁mc	𝑁mc	NOUN
iajs-2484	173	9	-	-	PUNCT
iajs-2484	173	10	function	function	NOUN
iajs-2484	173	11	)	)	PUNCT
iajs-2484	173	12	)	)	PUNCT
iajs-2484	173	13	,	,	PUNCT
iajs-2484	173	14	but	but	CCONJ
iajs-2484	173	15	𝑋	𝑋	NOUN
iajs-2484	173	16	is	be	AUX
iajs-2484	173	17	compact	compact	ADJ
iajs-2484	173	18	,	,	PUNCT
iajs-2484	173	19	hence	hence	ADV
iajs-2484	173	20	𝑓	𝑓	PROPN
iajs-2484	173	21	(	(	PUNCT
iajs-2484	173	22	k	k	NOUN
iajs-2484	173	23	)	)	PUNCT
iajs-2484	173	24	is	be	AUX
iajs-2484	173	25	compact	compact	ADJ
iajs-2484	173	26	(	(	PUNCT
iajs-2484	173	27	by	by	ADP
iajs-2484	173	28	remark	remark	NOUN
iajs-2484	173	29	(	(	PUNCT
iajs-2484	173	30	1.6	1.6	NUM
iajs-2484	173	31	)	)	PUNCT
iajs-2484	173	32	)	)	PUNCT
iajs-2484	173	33	,	,	PUNCT
iajs-2484	173	34	therefore	therefore	ADV
iajs-2484	173	35	𝑓	𝑓	PRON
iajs-2484	173	36	is	be	AUX
iajs-2484	173	37	𝜔-compact	𝜔-compact	NOUN
iajs-2484	173	38	(	(	PUNCT
iajs-2484	173	39	respectively	respectively	ADV
iajs-2484	173	40	𝑁compact	𝑁compact	PROPN
iajs-2484	173	41	)	)	PUNCT
iajs-2484	173	42	function	function	NOUN
iajs-2484	173	43	.	.	PUNCT
iajs-2484	174	1	in	in	ADP
iajs-2484	174	2	a	a	DET
iajs-2484	174	3	same	same	ADJ
iajs-2484	174	4	manner	manner	NOUN
iajs-2484	174	5	,	,	PUNCT
iajs-2484	174	6	we	we	PRON
iajs-2484	174	7	can	can	AUX
iajs-2484	174	8	prove	prove	VERB
iajs-2484	174	9	the	the	DET
iajs-2484	174	10	following	follow	VERB
iajs-2484	174	11	corollary	corollary	NOUN
iajs-2484	174	12	.	.	PUNCT
iajs-2484	175	1	corollary	corollary	ADJ
iajs-2484	175	2	(	(	PUNCT
iajs-2484	175	3	1.36	1.36	NUM
iajs-2484	175	4	)	)	PUNCT
iajs-2484	175	5	if	if	SCONJ
iajs-2484	175	6	𝑓	𝑓	X
iajs-2484	175	7	:	:	PUNCT
iajs-2484	175	8	𝑋	𝑋	PROPN
iajs-2484	175	9	⟶	⟶	NOUN
iajs-2484	175	10	𝑌	𝑌	PROPN
iajs-2484	175	11	is	be	AUX
iajs-2484	175	12	:	:	PUNCT
iajs-2484	175	13	1𝜔mc	1𝜔mc	NUM
iajs-2484	175	14	-	-	PUNCT
iajs-2484	175	15	function	function	NOUN
iajs-2484	175	16	(	(	PUNCT
iajs-2484	175	17	respectively	respectively	ADV
iajs-2484	175	18	𝑁mc	𝑁mc	NOUN
iajs-2484	175	19	-	-	PUNCT
iajs-2484	175	20	function	function	NOUN
iajs-2484	175	21	)	)	PUNCT
iajs-2484	175	22	where	where	SCONJ
iajs-2484	175	23	𝑋	𝑋	PROPN
iajs-2484	175	24	is	be	AUX
iajs-2484	175	25	a	a	DET
iajs-2484	175	26	c	c	NOUN
iajs-2484	175	27	-	-	PUNCT
iajs-2484	175	28	c	c	NOUN
iajs-2484	175	29	space	space	NOUN
iajs-2484	175	30	,	,	PUNCT
iajs-2484	175	31	then	then	ADV
iajs-2484	175	32	it	it	PRON
iajs-2484	175	33	is	be	AUX
iajs-2484	175	34	𝜔-compact	𝜔-compact	NOUN
iajs-2484	175	35	(	(	PUNCT
iajs-2484	175	36	respectively	respectively	ADV
iajs-2484	175	37	𝑁-compact	𝑁-compact	PROPN
iajs-2484	175	38	)	)	PUNCT
iajs-2484	175	39	function	function	NOUN
iajs-2484	175	40	.	.	PUNCT
iajs-2484	176	1	2mc	2mc	VERB
iajs-2484	176	2	-	-	PUNCT
iajs-2484	176	3	function	function	NOUN
iajs-2484	176	4	where	where	SCONJ
iajs-2484	176	5	𝑋	𝑋	NOUN
iajs-2484	176	6	is	be	AUX
iajs-2484	176	7	a	a	DET
iajs-2484	176	8	compact	compact	ADJ
iajs-2484	176	9	space	space	NOUN
iajs-2484	176	10	,	,	PUNCT
iajs-2484	176	11	then	then	ADV
iajs-2484	176	12	it	it	PRON
iajs-2484	176	13	is	be	AUX
iajs-2484	176	14	𝜔-compact	𝜔-compact	NOUN
iajs-2484	176	15	(	(	PUNCT
iajs-2484	176	16	respectively	respectively	ADV
iajs-2484	176	17	𝑁-compact	𝑁-compact	PROPN
iajs-2484	176	18	)	)	PUNCT
iajs-2484	176	19	function	function	NOUN
iajs-2484	176	20	.	.	PUNCT
iajs-2484	177	1	3mc	3mc	ADJ
iajs-2484	177	2	-	-	PUNCT
iajs-2484	177	3	function	function	NOUN
iajs-2484	177	4	where	where	SCONJ
iajs-2484	177	5	𝑋	𝑋	NOUN
iajs-2484	177	6	is	be	AUX
iajs-2484	177	7	a	a	DET
iajs-2484	177	8	c	c	NOUN
iajs-2484	177	9	-	-	PUNCT
iajs-2484	177	10	c	c	NOUN
iajs-2484	177	11	space	space	NOUN
iajs-2484	177	12	,	,	PUNCT
iajs-2484	177	13	then	then	ADV
iajs-2484	177	14	it	it	PRON
iajs-2484	177	15	is	be	AUX
iajs-2484	177	16	𝜔-compact	𝜔-compact	NOUN
iajs-2484	177	17	(	(	PUNCT
iajs-2484	177	18	respectively	respectively	ADV
iajs-2484	177	19	𝑁-compact	𝑁-compact	PROPN
iajs-2484	177	20	)	)	PUNCT
iajs-2484	177	21	function	function	NOUN
iajs-2484	177	22	.	.	PUNCT
iajs-2484	178	1	4mc	4mc	ADJ
iajs-2484	178	2	-	-	PUNCT
iajs-2484	178	3	function	function	NOUN
iajs-2484	178	4	where	where	SCONJ
iajs-2484	178	5	𝑋	𝑋	PROPN
iajs-2484	178	6	is	be	AUX
iajs-2484	178	7	an	an	DET
iajs-2484	178	8	𝜔-compact	𝜔-compact	PROPN
iajs-2484	178	9	(	(	PUNCT
iajs-2484	178	10	respectively	respectively	ADV
iajs-2484	178	11	𝑁-compact	𝑁-compact	PROPN
iajs-2484	178	12	)	)	PUNCT
iajs-2484	178	13	space	space	NOUN
iajs-2484	178	14	,	,	PUNCT
iajs-2484	178	15	then	then	ADV
iajs-2484	178	16	it	it	PRON
iajs-2484	178	17	is	be	AUX
iajs-2484	178	18	𝜔∗compact	𝜔∗compact	NOUN
iajs-2484	178	19	(	(	PUNCT
iajs-2484	178	20	respectively	respectively	ADV
iajs-2484	178	21	𝑁∗-compact	𝑁∗-compact	NOUN
iajs-2484	178	22	)	)	PUNCT
iajs-2484	178	23	function	function	NOUN
iajs-2484	178	24	.	.	PUNCT
iajs-2484	179	1	5m𝜔c	5m𝜔c	NUM
iajs-2484	179	2	-	-	PUNCT
iajs-2484	179	3	function	function	NOUN
iajs-2484	179	4	(	(	PUNCT
iajs-2484	179	5	respectively	respectively	ADV
iajs-2484	179	6	m𝑁c	m𝑁c	VERB
iajs-2484	179	7	-	-	PUNCT
iajs-2484	179	8	function	function	NOUN
iajs-2484	179	9	)	)	PUNCT
iajs-2484	179	10	where	where	SCONJ
iajs-2484	179	11	𝑋	𝑋	PROPN
iajs-2484	179	12	is	be	AUX
iajs-2484	179	13	an	an	DET
iajs-2484	179	14	𝜔-compact	𝜔-compact	PROPN
iajs-2484	179	15	(	(	PUNCT
iajs-2484	179	16	respectively	respectively	ADV
iajs-2484	179	17	𝑁compact	𝑁compact	PROPN
iajs-2484	179	18	)	)	PUNCT
iajs-2484	179	19	space	space	NOUN
iajs-2484	179	20	,	,	PUNCT
iajs-2484	179	21	then	then	ADV
iajs-2484	179	22	it	it	PRON
iajs-2484	179	23	is	be	AUX
iajs-2484	179	24	𝜔∗-compact	𝜔∗-compact	PROPN
iajs-2484	179	25	(	(	PUNCT
iajs-2484	179	26	respectively	respectively	ADV
iajs-2484	179	27	𝑁∗-compact	𝑁∗-compact	NOUN
iajs-2484	179	28	)	)	PUNCT
iajs-2484	179	29	function	function	NOUN
iajs-2484	179	30	.	.	PUNCT
iajs-2484	179	31	  	  	SPACE
iajs-2484	180	1	182	182	NUM
iajs-2484	180	2	  	  	SPACE
iajs-2484	180	3	ibn	ibn	PROPN
iajs-2484	180	4	al	al	PROPN
iajs-2484	180	5	-	-	PUNCT
iajs-2484	180	6	haitham	haitham	PROPN
iajs-2484	180	7	jour	jour	X
iajs-2484	180	8	.	.	PROPN
iajs-2484	180	9	for	for	ADP
iajs-2484	180	10	pure	pure	ADJ
iajs-2484	180	11	&	&	CCONJ
iajs-2484	180	12	appl	appl	PROPN
iajs-2484	180	13	.	.	PUNCT
iajs-2484	181	1	sci	sci	PROPN
iajs-2484	181	2	.	.	PROPN
iajs-2484	182	1	33	33	NUM
iajs-2484	182	2	(	(	PUNCT
iajs-2484	182	3	3	3	NUM
iajs-2484	182	4	)	)	PUNCT
iajs-2484	182	5	2020	2020	NUM
iajs-2484	183	1	6𝜔m𝜔c	6𝜔m𝜔c	NOUN
iajs-2484	183	2	-	-	PUNCT
iajs-2484	183	3	function	function	NOUN
iajs-2484	183	4	(	(	PUNCT
iajs-2484	183	5	respectively	respectively	ADV
iajs-2484	183	6	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	183	7	-	-	PUNCT
iajs-2484	183	8	function	function	NOUN
iajs-2484	183	9	)	)	PUNCT
iajs-2484	183	10	where	where	SCONJ
iajs-2484	183	11	𝑋	𝑋	PROPN
iajs-2484	183	12	is	be	AUX
iajs-2484	183	13	an	an	DET
iajs-2484	183	14	𝜔-compact	𝜔-compact	PROPN
iajs-2484	183	15	(	(	PUNCT
iajs-2484	183	16	respectively	respectively	ADV
iajs-2484	183	17	𝑁compact	𝑁compact	PROPN
iajs-2484	183	18	)	)	PUNCT
iajs-2484	183	19	space	space	NOUN
iajs-2484	183	20	,	,	PUNCT
iajs-2484	183	21	then	then	ADV
iajs-2484	183	22	it	it	PRON
iajs-2484	183	23	is	be	AUX
iajs-2484	183	24	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	183	25	(	(	PUNCT
iajs-2484	183	26	respectively	respectively	ADV
iajs-2484	183	27	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	183	28	)	)	PUNCT
iajs-2484	183	29	function	function	NOUN
iajs-2484	183	30	.	.	PUNCT
iajs-2484	184	1	7m𝜔c	7m𝜔c	NUM
iajs-2484	184	2	-	-	PUNCT
iajs-2484	184	3	function	function	NOUN
iajs-2484	184	4	(	(	PUNCT
iajs-2484	184	5	respectively	respectively	ADV
iajs-2484	184	6	m𝑁c	m𝑁c	VERB
iajs-2484	184	7	-	-	PUNCT
iajs-2484	184	8	function	function	NOUN
iajs-2484	184	9	)	)	PUNCT
iajs-2484	184	10	where	where	SCONJ
iajs-2484	184	11	𝑋	𝑋	PROPN
iajs-2484	184	12	is	be	AUX
iajs-2484	184	13	an	an	DET
iajs-2484	184	14	𝜔-compact	𝜔-compact	PROPN
iajs-2484	184	15	(	(	PUNCT
iajs-2484	184	16	respectively	respectively	ADV
iajs-2484	184	17	𝑁compact	𝑁compact	PROPN
iajs-2484	184	18	)	)	PUNCT
iajs-2484	184	19	space	space	NOUN
iajs-2484	184	20	,	,	PUNCT
iajs-2484	184	21	then	then	ADV
iajs-2484	184	22	it	it	PRON
iajs-2484	184	23	is	be	AUX
iajs-2484	184	24	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	184	25	(	(	PUNCT
iajs-2484	184	26	respectively	respectively	ADV
iajs-2484	184	27	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	184	28	)	)	PUNCT
iajs-2484	184	29	function	function	NOUN
iajs-2484	184	30	.	.	PUNCT
iajs-2484	185	1	8mc	8mc	ADJ
iajs-2484	185	2	-	-	PUNCT
iajs-2484	185	3	function	function	NOUN
iajs-2484	185	4	where	where	SCONJ
iajs-2484	185	5	𝑋	𝑋	PROPN
iajs-2484	185	6	is	be	AUX
iajs-2484	185	7	an	an	DET
iajs-2484	185	8	𝜔-compact	𝜔-compact	PROPN
iajs-2484	185	9	(	(	PUNCT
iajs-2484	185	10	respectively	respectively	ADV
iajs-2484	185	11	𝑁-compact	𝑁-compact	PROPN
iajs-2484	185	12	)	)	PUNCT
iajs-2484	185	13	space	space	NOUN
iajs-2484	185	14	,	,	PUNCT
iajs-2484	185	15	then	then	ADV
iajs-2484	185	16	it	it	PRON
iajs-2484	185	17	is	be	AUX
iajs-2484	185	18	𝜔∗∗compact	𝜔∗∗compact	PUNCT
iajs-2484	185	19	(	(	PUNCT
iajs-2484	185	20	respectively	respectively	ADV
iajs-2484	185	21	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	185	22	)	)	PUNCT
iajs-2484	185	23	function	function	NOUN
iajs-2484	185	24	.	.	PUNCT
iajs-2484	186	1	proof	proof	NOUN
iajs-2484	186	2	1suppose	1suppose	NUM
iajs-2484	186	3	k	k	PROPN
iajs-2484	186	4	is	be	AUX
iajs-2484	186	5	a	a	DET
iajs-2484	186	6	𝜔-compact	𝜔-compact	PROPN
iajs-2484	186	7	(	(	PUNCT
iajs-2484	186	8	respectively	respectively	ADV
iajs-2484	186	9	𝑁-compact	𝑁-compact	PROPN
iajs-2484	186	10	)	)	PUNCT
iajs-2484	186	11	subset	subset	NOUN
iajs-2484	186	12	of	of	ADP
iajs-2484	186	13	𝑌	𝑌	PROPN
iajs-2484	186	14	,	,	PUNCT
iajs-2484	186	15	so	so	ADV
iajs-2484	186	16	𝑓	𝑓	PRON
iajs-2484	186	17	(	(	PUNCT
iajs-2484	186	18	k	k	NOUN
iajs-2484	186	19	)	)	PUNCT
iajs-2484	186	20	is	be	AUX
iajs-2484	186	21	a	a	DET
iajs-2484	186	22	closed	closed	ADJ
iajs-2484	186	23	subset	subset	NOUN
iajs-2484	186	24	of	of	ADP
iajs-2484	186	25	𝑋(since	𝑋(since	NOUN
iajs-2484	186	26	𝑓	𝑓	PROPN
iajs-2484	186	27	is	be	AUX
iajs-2484	186	28	𝜔mc	𝜔mc	NOUN
iajs-2484	186	29	-	-	PUNCT
iajs-2484	186	30	function	function	NOUN
iajs-2484	186	31	(	(	PUNCT
iajs-2484	186	32	respectively	respectively	ADV
iajs-2484	186	33	𝑁mc	𝑁mc	NOUN
iajs-2484	186	34	-	-	PUNCT
iajs-2484	186	35	function	function	NOUN
iajs-2484	186	36	)	)	PUNCT
iajs-2484	186	37	)	)	PUNCT
iajs-2484	186	38	,	,	PUNCT
iajs-2484	186	39	but	but	CCONJ
iajs-2484	186	40	𝑋	𝑋	NOUN
iajs-2484	186	41	is	be	AUX
iajs-2484	186	42	c	c	NOUN
iajs-2484	186	43	-	-	PUNCT
iajs-2484	186	44	c	c	NOUN
iajs-2484	186	45	space	space	NOUN
iajs-2484	186	46	,	,	PUNCT
iajs-2484	186	47	hence	hence	ADV
iajs-2484	186	48	𝑓	𝑓	PROPN
iajs-2484	186	49	(	(	PUNCT
iajs-2484	186	50	k	k	NOUN
iajs-2484	186	51	)	)	PUNCT
iajs-2484	186	52	is	be	AUX
iajs-2484	186	53	compact	compact	ADJ
iajs-2484	186	54	,	,	PUNCT
iajs-2484	186	55	therefore	therefore	ADV
iajs-2484	186	56	𝑓	𝑓	PRON
iajs-2484	186	57	is	be	AUX
iajs-2484	186	58	𝜔-compact	𝜔-compact	NOUN
iajs-2484	186	59	(	(	PUNCT
iajs-2484	186	60	respectively	respectively	ADV
iajs-2484	186	61	𝑁-compact	𝑁-compact	PROPN
iajs-2484	186	62	)	)	PUNCT
iajs-2484	186	63	function	function	NOUN
iajs-2484	186	64	.	.	PUNCT
iajs-2484	187	1	2suppose	2suppose	NUM
iajs-2484	187	2	k	k	X
iajs-2484	187	3	is	be	AUX
iajs-2484	187	4	a	a	DET
iajs-2484	187	5	𝜔-compact	𝜔-compact	PROPN
iajs-2484	187	6	(	(	PUNCT
iajs-2484	187	7	respectively	respectively	ADV
iajs-2484	187	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	187	9	)	)	PUNCT
iajs-2484	187	10	subset	subset	NOUN
iajs-2484	187	11	of	of	ADP
iajs-2484	187	12	𝑌	𝑌	PROPN
iajs-2484	187	13	,	,	PUNCT
iajs-2484	187	14	so	so	SCONJ
iajs-2484	187	15	it	it	PRON
iajs-2484	187	16	is	be	AUX
iajs-2484	187	17	compact	compact	ADJ
iajs-2484	187	18	(	(	PUNCT
iajs-2484	187	19	by	by	ADP
iajs-2484	187	20	remark	remark	NOUN
iajs-2484	187	21	(	(	PUNCT
iajs-2484	187	22	1.2	1.2	NUM
iajs-2484	187	23	)	)	PUNCT
iajs-2484	187	24	)	)	PUNCT
iajs-2484	187	25	,	,	PUNCT
iajs-2484	187	26	hence	hence	ADV
iajs-2484	187	27	𝑓	𝑓	PROPN
iajs-2484	187	28	(	(	PUNCT
iajs-2484	187	29	k	k	NOUN
iajs-2484	187	30	)	)	PUNCT
iajs-2484	187	31	is	be	AUX
iajs-2484	187	32	a	a	DET
iajs-2484	187	33	closed	closed	ADJ
iajs-2484	187	34	subset	subset	NOUN
iajs-2484	187	35	of	of	ADP
iajs-2484	187	36	𝑋(since	𝑋(since	NOUN
iajs-2484	187	37	𝑓	𝑓	PROPN
iajs-2484	187	38	is	be	AUX
iajs-2484	187	39	mc	mc	NOUN
iajs-2484	187	40	-	-	PUNCT
iajs-2484	187	41	function	function	NOUN
iajs-2484	187	42	)	)	PUNCT
iajs-2484	187	43	,	,	PUNCT
iajs-2484	187	44	but	but	CCONJ
iajs-2484	187	45	𝑋	𝑋	NOUN
iajs-2484	187	46	is	be	AUX
iajs-2484	187	47	compact	compact	ADJ
iajs-2484	187	48	space	space	NOUN
iajs-2484	187	49	,	,	PUNCT
iajs-2484	187	50	hence	hence	ADV
iajs-2484	187	51	𝑓	𝑓	PROPN
iajs-2484	187	52	(	(	PUNCT
iajs-2484	187	53	k	k	NOUN
iajs-2484	187	54	)	)	PUNCT
iajs-2484	187	55	is	be	AUX
iajs-2484	187	56	compact	compact	ADJ
iajs-2484	187	57	(	(	PUNCT
iajs-2484	187	58	by	by	ADP
iajs-2484	187	59	remark	remark	NOUN
iajs-2484	187	60	(	(	PUNCT
iajs-2484	187	61	1.6	1.6	NUM
iajs-2484	187	62	)	)	PUNCT
iajs-2484	187	63	)	)	PUNCT
iajs-2484	187	64	,	,	PUNCT
iajs-2484	187	65	therefore	therefore	ADV
iajs-2484	187	66	𝑓	𝑓	PRON
iajs-2484	187	67	is	be	AUX
iajs-2484	187	68	𝜔-compact	𝜔-compact	NOUN
iajs-2484	187	69	(	(	PUNCT
iajs-2484	187	70	respectively	respectively	ADV
iajs-2484	187	71	𝑁compact	𝑁compact	PROPN
iajs-2484	187	72	)	)	PUNCT
iajs-2484	187	73	function	function	NOUN
iajs-2484	187	74	.	.	PUNCT
iajs-2484	188	1	3suppose	3suppose	NUM
iajs-2484	188	2	k	k	NOUN
iajs-2484	188	3	is	be	AUX
iajs-2484	188	4	an	an	DET
iajs-2484	188	5	𝜔-compact	𝜔-compact	PROPN
iajs-2484	188	6	(	(	PUNCT
iajs-2484	188	7	respectively	respectively	ADV
iajs-2484	188	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	188	9	)	)	PUNCT
iajs-2484	188	10	subset	subset	NOUN
iajs-2484	188	11	of	of	ADP
iajs-2484	188	12	𝑌	𝑌	PROPN
iajs-2484	188	13	,	,	PUNCT
iajs-2484	188	14	so	so	SCONJ
iajs-2484	188	15	it	it	PRON
iajs-2484	188	16	is	be	AUX
iajs-2484	188	17	compact	compact	ADJ
iajs-2484	188	18	(	(	PUNCT
iajs-2484	188	19	by	by	ADP
iajs-2484	188	20	remark	remark	NOUN
iajs-2484	188	21	(	(	PUNCT
iajs-2484	188	22	1.2	1.2	NUM
iajs-2484	188	23	)	)	PUNCT
iajs-2484	188	24	)	)	PUNCT
iajs-2484	188	25	,	,	PUNCT
iajs-2484	188	26	hence	hence	ADV
iajs-2484	188	27	𝑓	𝑓	PROPN
iajs-2484	188	28	(	(	PUNCT
iajs-2484	188	29	k	k	NOUN
iajs-2484	188	30	)	)	PUNCT
iajs-2484	188	31	is	be	AUX
iajs-2484	188	32	a	a	DET
iajs-2484	188	33	closed	closed	ADJ
iajs-2484	188	34	subset	subset	NOUN
iajs-2484	188	35	of	of	ADP
iajs-2484	188	36	𝑋(since	𝑋(since	NOUN
iajs-2484	188	37	𝑓	𝑓	PROPN
iajs-2484	188	38	is	be	AUX
iajs-2484	188	39	mc	mc	NOUN
iajs-2484	188	40	-	-	PUNCT
iajs-2484	188	41	function	function	NOUN
iajs-2484	188	42	)	)	PUNCT
iajs-2484	188	43	,	,	PUNCT
iajs-2484	188	44	but	but	CCONJ
iajs-2484	188	45	𝑋	𝑋	NOUN
iajs-2484	188	46	is	be	AUX
iajs-2484	188	47	c	c	NOUN
iajs-2484	188	48	-	-	PUNCT
iajs-2484	188	49	c	c	NOUN
iajs-2484	188	50	space	space	NOUN
iajs-2484	188	51	,	,	PUNCT
iajs-2484	188	52	hence	hence	ADV
iajs-2484	188	53	𝑓	𝑓	PROPN
iajs-2484	188	54	(	(	PUNCT
iajs-2484	188	55	k	k	NOUN
iajs-2484	188	56	)	)	PUNCT
iajs-2484	188	57	is	be	AUX
iajs-2484	188	58	compact	compact	ADJ
iajs-2484	188	59	,	,	PUNCT
iajs-2484	188	60	therefore	therefore	ADV
iajs-2484	188	61	𝑓	𝑓	PRON
iajs-2484	188	62	is	be	AUX
iajs-2484	188	63	𝜔-compact	𝜔-compact	NOUN
iajs-2484	188	64	(	(	PUNCT
iajs-2484	188	65	respectively	respectively	ADV
iajs-2484	188	66	𝑁-compact	𝑁-compact	PROPN
iajs-2484	188	67	)	)	PUNCT
iajs-2484	188	68	function	function	NOUN
iajs-2484	188	69	.	.	PUNCT
iajs-2484	189	1	4suppose	4suppose	NUM
iajs-2484	189	2	k	k	NOUN
iajs-2484	189	3	is	be	AUX
iajs-2484	189	4	a	a	DET
iajs-2484	189	5	compact	compact	ADJ
iajs-2484	189	6	subset	subset	NOUN
iajs-2484	189	7	of	of	ADP
iajs-2484	189	8	𝑌	𝑌	PROPN
iajs-2484	189	9	,	,	PUNCT
iajs-2484	189	10	hence	hence	ADV
iajs-2484	189	11	𝑓	𝑓	PROPN
iajs-2484	189	12	(	(	PUNCT
iajs-2484	189	13	k	k	NOUN
iajs-2484	189	14	)	)	PUNCT
iajs-2484	189	15	is	be	AUX
iajs-2484	189	16	a	a	DET
iajs-2484	189	17	closed	closed	ADJ
iajs-2484	189	18	subset	subset	NOUN
iajs-2484	189	19	of	of	ADP
iajs-2484	189	20	𝑋(since	𝑋(since	NOUN
iajs-2484	189	21	𝑓	𝑓	PROPN
iajs-2484	189	22	is	be	AUX
iajs-2484	189	23	mcfunction	mcfunction	NOUN
iajs-2484	189	24	)	)	PUNCT
iajs-2484	189	25	,	,	PUNCT
iajs-2484	189	26	and	and	CCONJ
iajs-2484	189	27	by	by	ADP
iajs-2484	189	28	remark	remark	NOUN
iajs-2484	189	29	(	(	PUNCT
iajs-2484	189	30	1.2	1.2	NUM
iajs-2484	189	31	)	)	PUNCT
iajs-2484	189	32	it	it	PRON
iajs-2484	189	33	is	be	AUX
iajs-2484	189	34	𝜔-closed	𝜔-close	VERB
iajs-2484	189	35	(	(	PUNCT
iajs-2484	189	36	respectively	respectively	ADV
iajs-2484	189	37	𝑁-closed	𝑁-closed	PROPN
iajs-2484	189	38	)	)	PUNCT
iajs-2484	189	39	subset	subset	NOUN
iajs-2484	189	40	of	of	ADP
iajs-2484	189	41	𝑋	𝑋	PROPN
iajs-2484	189	42	which	which	PRON
iajs-2484	189	43	is	be	AUX
iajs-2484	189	44	𝜔compact	𝜔compact	ADJ
iajs-2484	189	45	(	(	PUNCT
iajs-2484	189	46	respectively	respectively	ADV
iajs-2484	189	47	𝑁-compact	𝑁-compact	ADJ
iajs-2484	189	48	)	)	PUNCT
iajs-2484	189	49	space	space	NOUN
iajs-2484	189	50	,	,	PUNCT
iajs-2484	189	51	hence	hence	ADV
iajs-2484	189	52	𝑓	𝑓	PROPN
iajs-2484	189	53	(	(	PUNCT
iajs-2484	189	54	k	k	NOUN
iajs-2484	189	55	)	)	PUNCT
iajs-2484	189	56	is	be	AUX
iajs-2484	189	57	𝜔-compact	𝜔-compact	PROPN
iajs-2484	189	58	(	(	PUNCT
iajs-2484	189	59	respectively	respectively	ADV
iajs-2484	189	60	𝑁compact	𝑁compact	PROPN
iajs-2484	189	61	)	)	PUNCT
iajs-2484	189	62	(	(	PUNCT
iajs-2484	189	63	by	by	ADP
iajs-2484	189	64	remark	remark	NOUN
iajs-2484	189	65	(	(	PUNCT
iajs-2484	189	66	1.6	1.6	NUM
iajs-2484	189	67	)	)	PUNCT
iajs-2484	189	68	)	)	PUNCT
iajs-2484	189	69	,	,	PUNCT
iajs-2484	189	70	therefore	therefore	ADV
iajs-2484	189	71	𝑓	𝑓	PRON
iajs-2484	189	72	is	be	AUX
iajs-2484	189	73	𝜔∗-compact	𝜔∗-compact	PROPN
iajs-2484	189	74	(	(	PUNCT
iajs-2484	189	75	respectively	respectively	ADV
iajs-2484	189	76	𝑁∗-compact	𝑁∗-compact	NOUN
iajs-2484	189	77	)	)	PUNCT
iajs-2484	189	78	function	function	NOUN
iajs-2484	189	79	.	.	PUNCT
iajs-2484	190	1	5suppose	5suppose	NUM
iajs-2484	190	2	k	k	PROPN
iajs-2484	190	3	is	be	AUX
iajs-2484	190	4	a	a	DET
iajs-2484	190	5	compact	compact	ADJ
iajs-2484	190	6	subset	subset	NOUN
iajs-2484	190	7	of	of	ADP
iajs-2484	190	8	𝑌	𝑌	PROPN
iajs-2484	190	9	,	,	PUNCT
iajs-2484	190	10	hence	hence	ADV
iajs-2484	190	11	𝑓	𝑓	PROPN
iajs-2484	190	12	(	(	PUNCT
iajs-2484	190	13	k	k	NOUN
iajs-2484	190	14	)	)	PUNCT
iajs-2484	190	15	is	be	AUX
iajs-2484	190	16	an	an	DET
iajs-2484	190	17	𝜔-closed	𝜔-close	VERB
iajs-2484	190	18	(	(	PUNCT
iajs-2484	190	19	respectively	respectively	ADV
iajs-2484	190	20	𝑁-closed	𝑁-closed	PROPN
iajs-2484	190	21	)	)	PUNCT
iajs-2484	190	22	subset	subset	NOUN
iajs-2484	190	23	of	of	ADP
iajs-2484	190	24	𝑋	𝑋	PROPN
iajs-2484	190	25	(	(	PUNCT
iajs-2484	190	26	since	since	SCONJ
iajs-2484	190	27	𝑓	𝑓	PRON
iajs-2484	190	28	is	be	AUX
iajs-2484	190	29	m𝜔c	m𝜔c	NOUN
iajs-2484	190	30	-	-	PUNCT
iajs-2484	190	31	function	function	NOUN
iajs-2484	190	32	(	(	PUNCT
iajs-2484	190	33	respectively	respectively	ADV
iajs-2484	190	34	m𝑁c	m𝑁c	NOUN
iajs-2484	190	35	-	-	PUNCT
iajs-2484	190	36	function	function	NOUN
iajs-2484	190	37	)	)	PUNCT
iajs-2484	190	38	)	)	PUNCT
iajs-2484	190	39	,	,	PUNCT
iajs-2484	190	40	but	but	CCONJ
iajs-2484	190	41	𝑋	𝑋	NOUN
iajs-2484	190	42	is	be	AUX
iajs-2484	190	43	𝜔-compact	𝜔-compact	NOUN
iajs-2484	190	44	(	(	PUNCT
iajs-2484	190	45	respectively	respectively	ADV
iajs-2484	190	46	𝑁-compact	𝑁-compact	PROPN
iajs-2484	190	47	)	)	PUNCT
iajs-2484	190	48	space	space	NOUN
iajs-2484	190	49	,	,	PUNCT
iajs-2484	190	50	hence	hence	ADV
iajs-2484	190	51	𝑓	𝑓	PROPN
iajs-2484	190	52	(	(	PUNCT
iajs-2484	190	53	k	k	NOUN
iajs-2484	190	54	)	)	PUNCT
iajs-2484	190	55	is	be	AUX
iajs-2484	190	56	𝜔-compact	𝜔-compact	PROPN
iajs-2484	190	57	(	(	PUNCT
iajs-2484	190	58	respectively	respectively	ADV
iajs-2484	190	59	𝑁-compact	𝑁-compact	PROPN
iajs-2484	190	60	)	)	PUNCT
iajs-2484	190	61	(	(	PUNCT
iajs-2484	190	62	by	by	ADP
iajs-2484	190	63	remark	remark	NOUN
iajs-2484	190	64	(	(	PUNCT
iajs-2484	190	65	1.6	1.6	NUM
iajs-2484	190	66	)	)	PUNCT
iajs-2484	190	67	)	)	PUNCT
iajs-2484	190	68	,	,	PUNCT
iajs-2484	190	69	therefore	therefore	ADV
iajs-2484	190	70	𝑓	𝑓	PRON
iajs-2484	190	71	is	be	AUX
iajs-2484	190	72	𝜔∗-compact	𝜔∗-compact	PROPN
iajs-2484	190	73	(	(	PUNCT
iajs-2484	190	74	respectively	respectively	ADV
iajs-2484	190	75	𝑁∗-compact	𝑁∗-compact	NOUN
iajs-2484	190	76	)	)	PUNCT
iajs-2484	190	77	function	function	NOUN
iajs-2484	190	78	.	.	PUNCT
iajs-2484	191	1	6suppose	6suppose	NUM
iajs-2484	191	2	k	k	NOUN
iajs-2484	191	3	is	be	AUX
iajs-2484	191	4	an	an	DET
iajs-2484	191	5	𝜔-compact	𝜔-compact	PROPN
iajs-2484	191	6	(	(	PUNCT
iajs-2484	191	7	respectively	respectively	ADV
iajs-2484	191	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	191	9	)	)	PUNCT
iajs-2484	191	10	subset	subset	NOUN
iajs-2484	191	11	of	of	ADP
iajs-2484	191	12	𝑌	𝑌	PROPN
iajs-2484	191	13	,	,	PUNCT
iajs-2484	191	14	hence	hence	ADV
iajs-2484	191	15	𝑓	𝑓	PROPN
iajs-2484	191	16	(	(	PUNCT
iajs-2484	191	17	k	k	NOUN
iajs-2484	191	18	)	)	PUNCT
iajs-2484	191	19	is	be	AUX
iajs-2484	191	20	an	an	DET
iajs-2484	191	21	𝜔closed	𝜔close	VERB
iajs-2484	191	22	(	(	PUNCT
iajs-2484	191	23	respectively	respectively	ADV
iajs-2484	191	24	𝑁-closed	𝑁-closed	PROPN
iajs-2484	191	25	)	)	PUNCT
iajs-2484	191	26	subset	subset	NOUN
iajs-2484	191	27	of	of	ADP
iajs-2484	191	28	𝑋	𝑋	PROPN
iajs-2484	191	29	(	(	PUNCT
iajs-2484	191	30	since	since	SCONJ
iajs-2484	191	31	𝑓	𝑓	PRON
iajs-2484	191	32	is	be	AUX
iajs-2484	191	33	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	191	34	-	-	PUNCT
iajs-2484	191	35	function	function	NOUN
iajs-2484	191	36	(	(	PUNCT
iajs-2484	191	37	respectively	respectively	ADV
iajs-2484	191	38	𝑁m𝑁cfunction	𝑁m𝑁cfunction	PROPN
iajs-2484	191	39	)	)	PUNCT
iajs-2484	191	40	)	)	PUNCT
iajs-2484	191	41	,	,	PUNCT
iajs-2484	191	42	but	but	CCONJ
iajs-2484	191	43	𝑋	𝑋	NOUN
iajs-2484	191	44	is	be	AUX
iajs-2484	191	45	an	an	DET
iajs-2484	191	46	𝜔-compact	𝜔-compact	PROPN
iajs-2484	191	47	(	(	PUNCT
iajs-2484	191	48	respectively	respectively	ADV
iajs-2484	191	49	𝑁-compact	𝑁-compact	PROPN
iajs-2484	191	50	)	)	PUNCT
iajs-2484	191	51	space	space	NOUN
iajs-2484	191	52	,	,	PUNCT
iajs-2484	191	53	hence	hence	ADV
iajs-2484	191	54	𝑓	𝑓	PROPN
iajs-2484	191	55	(	(	PUNCT
iajs-2484	191	56	k	k	NOUN
iajs-2484	191	57	)	)	PUNCT
iajs-2484	191	58	is	be	AUX
iajs-2484	191	59	𝜔compact	𝜔compact	ADJ
iajs-2484	191	60	(	(	PUNCT
iajs-2484	191	61	respectively	respectively	ADV
iajs-2484	191	62	𝑁-compact	𝑁-compact	PROPN
iajs-2484	191	63	)	)	PUNCT
iajs-2484	191	64	(	(	PUNCT
iajs-2484	191	65	by	by	ADP
iajs-2484	191	66	remark	remark	NOUN
iajs-2484	191	67	(	(	PUNCT
iajs-2484	191	68	1.6	1.6	NUM
iajs-2484	191	69	)	)	PUNCT
iajs-2484	191	70	)	)	PUNCT
iajs-2484	191	71	,	,	PUNCT
iajs-2484	191	72	therefore	therefore	ADV
iajs-2484	191	73	𝑓	𝑓	PRON
iajs-2484	191	74	is	be	AUX
iajs-2484	191	75	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	191	76	(	(	PUNCT
iajs-2484	191	77	respectively	respectively	ADV
iajs-2484	191	78	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	191	79	)	)	PUNCT
iajs-2484	191	80	function	function	NOUN
iajs-2484	191	81	.	.	PUNCT
iajs-2484	192	1	7suppose	7suppose	NUM
iajs-2484	192	2	k	k	NOUN
iajs-2484	192	3	is	be	AUX
iajs-2484	192	4	an	an	DET
iajs-2484	192	5	𝜔-compact	𝜔-compact	PROPN
iajs-2484	192	6	(	(	PUNCT
iajs-2484	192	7	respectively	respectively	ADV
iajs-2484	192	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	192	9	)	)	PUNCT
iajs-2484	192	10	subset	subset	NOUN
iajs-2484	192	11	of	of	ADP
iajs-2484	192	12	𝑌	𝑌	PROPN
iajs-2484	192	13	,	,	PUNCT
iajs-2484	192	14	so	so	SCONJ
iajs-2484	192	15	it	it	PRON
iajs-2484	192	16	is	be	AUX
iajs-2484	192	17	compact	compact	ADJ
iajs-2484	192	18	(	(	PUNCT
iajs-2484	192	19	by	by	ADP
iajs-2484	192	20	remark	remark	NOUN
iajs-2484	192	21	(	(	PUNCT
iajs-2484	192	22	1.2	1.2	NUM
iajs-2484	192	23	)	)	PUNCT
iajs-2484	192	24	)	)	PUNCT
iajs-2484	192	25	,	,	PUNCT
iajs-2484	192	26	hence	hence	ADV
iajs-2484	192	27	𝑓	𝑓	PROPN
iajs-2484	192	28	(	(	PUNCT
iajs-2484	192	29	k	k	NOUN
iajs-2484	192	30	)	)	PUNCT
iajs-2484	192	31	is	be	AUX
iajs-2484	192	32	an	an	DET
iajs-2484	192	33	𝜔-closed	𝜔-close	VERB
iajs-2484	192	34	(	(	PUNCT
iajs-2484	192	35	respectively	respectively	ADV
iajs-2484	192	36	𝑁-closed	𝑁-closed	PROPN
iajs-2484	192	37	)	)	PUNCT
iajs-2484	192	38	subset	subset	NOUN
iajs-2484	192	39	of	of	ADP
iajs-2484	192	40	𝑋	𝑋	PROPN
iajs-2484	192	41	(	(	PUNCT
iajs-2484	192	42	since	since	SCONJ
iajs-2484	192	43	𝑓	𝑓	PRON
iajs-2484	192	44	is	be	AUX
iajs-2484	192	45	m𝜔c	m𝜔c	NOUN
iajs-2484	192	46	-	-	PUNCT
iajs-2484	192	47	function	function	NOUN
iajs-2484	192	48	(	(	PUNCT
iajs-2484	192	49	respectively	respectively	ADV
iajs-2484	192	50	m𝑁c	m𝑁c	NOUN
iajs-2484	192	51	-	-	PUNCT
iajs-2484	192	52	function	function	NOUN
iajs-2484	192	53	)	)	PUNCT
iajs-2484	192	54	)	)	PUNCT
iajs-2484	192	55	,	,	PUNCT
iajs-2484	192	56	but	but	CCONJ
iajs-2484	192	57	𝑋	𝑋	NOUN
iajs-2484	192	58	is	be	AUX
iajs-2484	192	59	𝜔-compact	𝜔-compact	NOUN
iajs-2484	192	60	(	(	PUNCT
iajs-2484	192	61	respectively	respectively	ADV
iajs-2484	192	62	𝑁-compact	𝑁-compact	PROPN
iajs-2484	192	63	)	)	PUNCT
iajs-2484	192	64	space	space	NOUN
iajs-2484	192	65	,	,	PUNCT
iajs-2484	192	66	hence	hence	ADV
iajs-2484	192	67	𝑓	𝑓	PROPN
iajs-2484	192	68	(	(	PUNCT
iajs-2484	192	69	k	k	NOUN
iajs-2484	192	70	)	)	PUNCT
iajs-2484	192	71	is	be	AUX
iajs-2484	192	72	𝜔-compact	𝜔-compact	PROPN
iajs-2484	192	73	(	(	PUNCT
iajs-2484	192	74	respectively	respectively	ADV
iajs-2484	192	75	𝑁-compact	𝑁-compact	PROPN
iajs-2484	192	76	)	)	PUNCT
iajs-2484	192	77	(	(	PUNCT
iajs-2484	192	78	by	by	ADP
iajs-2484	192	79	remark	remark	NOUN
iajs-2484	192	80	(	(	PUNCT
iajs-2484	192	81	1.6	1.6	NUM
iajs-2484	192	82	)	)	PUNCT
iajs-2484	192	83	)	)	PUNCT
iajs-2484	192	84	,	,	PUNCT
iajs-2484	192	85	therefore	therefore	ADV
iajs-2484	192	86	𝑓	𝑓	PRON
iajs-2484	192	87	is	be	AUX
iajs-2484	192	88	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	192	89	(	(	PUNCT
iajs-2484	192	90	respectively	respectively	ADV
iajs-2484	192	91	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	192	92	)	)	PUNCT
iajs-2484	192	93	function	function	NOUN
iajs-2484	192	94	.	.	PUNCT
iajs-2484	193	1	8suppose	8suppose	NUM
iajs-2484	193	2	k	k	NOUN
iajs-2484	193	3	is	be	AUX
iajs-2484	193	4	an	an	DET
iajs-2484	193	5	𝜔-compact	𝜔-compact	PROPN
iajs-2484	193	6	(	(	PUNCT
iajs-2484	193	7	respectively	respectively	ADV
iajs-2484	193	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	193	9	)	)	PUNCT
iajs-2484	193	10	subset	subset	NOUN
iajs-2484	193	11	of	of	ADP
iajs-2484	193	12	𝑌	𝑌	PROPN
iajs-2484	193	13	,	,	PUNCT
iajs-2484	193	14	so	so	SCONJ
iajs-2484	193	15	it	it	PRON
iajs-2484	193	16	is	be	AUX
iajs-2484	193	17	compact	compact	ADJ
iajs-2484	193	18	(	(	PUNCT
iajs-2484	193	19	by	by	ADP
iajs-2484	193	20	remark	remark	NOUN
iajs-2484	193	21	(	(	PUNCT
iajs-2484	193	22	1.2	1.2	NUM
iajs-2484	193	23	)	)	PUNCT
iajs-2484	193	24	)	)	PUNCT
iajs-2484	193	25	,	,	PUNCT
iajs-2484	193	26	hence	hence	ADV
iajs-2484	193	27	𝑓	𝑓	PROPN
iajs-2484	193	28	(	(	PUNCT
iajs-2484	193	29	k	k	NOUN
iajs-2484	193	30	)	)	PUNCT
iajs-2484	193	31	is	be	AUX
iajs-2484	193	32	closed	close	VERB
iajs-2484	193	33	subset	subset	NOUN
iajs-2484	193	34	of	of	ADP
iajs-2484	193	35	𝑋	𝑋	PROPN
iajs-2484	193	36	(	(	PUNCT
iajs-2484	193	37	since	since	SCONJ
iajs-2484	193	38	𝑓	𝑓	PRON
iajs-2484	193	39	is	be	AUX
iajs-2484	193	40	mc	mc	NOUN
iajs-2484	193	41	-	-	PUNCT
iajs-2484	193	42	function	function	NOUN
iajs-2484	193	43	(	(	PUNCT
iajs-2484	193	44	respectively	respectively	ADV
iajs-2484	193	45	mcfunction	mcfunction	NOUN
iajs-2484	193	46	)	)	PUNCT
iajs-2484	193	47	)	)	PUNCT
iajs-2484	193	48	,	,	PUNCT
iajs-2484	193	49	and	and	CCONJ
iajs-2484	193	50	by	by	ADP
iajs-2484	193	51	remark	remark	NOUN
iajs-2484	193	52	(	(	PUNCT
iajs-2484	193	53	1.2	1.2	NUM
iajs-2484	193	54	)	)	PUNCT
iajs-2484	193	55	)	)	PUNCT
iajs-2484	194	1	it	it	PRON
iajs-2484	194	2	is	be	AUX
iajs-2484	194	3	an	an	DET
iajs-2484	194	4	𝜔-closed	𝜔-close	VERB
iajs-2484	194	5	(	(	PUNCT
iajs-2484	194	6	respectively	respectively	ADV
iajs-2484	194	7	𝑁-closed	𝑁-closed	PROPN
iajs-2484	194	8	)	)	PUNCT
iajs-2484	194	9	,	,	PUNCT
iajs-2484	194	10	but	but	CCONJ
iajs-2484	194	11	𝑋	𝑋	NOUN
iajs-2484	194	12	is	be	AUX
iajs-2484	194	13	𝜔-compact	𝜔-compact	NOUN
iajs-2484	194	14	(	(	PUNCT
iajs-2484	194	15	respectively	respectively	ADV
iajs-2484	194	16	𝑁-compact	𝑁-compact	PROPN
iajs-2484	194	17	)	)	PUNCT
iajs-2484	194	18	space	space	NOUN
iajs-2484	194	19	,	,	PUNCT
iajs-2484	194	20	hence	hence	ADV
iajs-2484	194	21	𝑓	𝑓	PROPN
iajs-2484	194	22	(	(	PUNCT
iajs-2484	194	23	k	k	NOUN
iajs-2484	194	24	)	)	PUNCT
iajs-2484	194	25	is	be	AUX
iajs-2484	194	26	𝜔-compact	𝜔-compact	PROPN
iajs-2484	194	27	(	(	PUNCT
iajs-2484	194	28	respectively	respectively	ADV
iajs-2484	194	29	𝑁-compact	𝑁-compact	PROPN
iajs-2484	194	30	)	)	PUNCT
iajs-2484	194	31	(	(	PUNCT
iajs-2484	194	32	by	by	ADP
iajs-2484	194	33	remark	remark	NOUN
iajs-2484	194	34	(	(	PUNCT
iajs-2484	194	35	1.6	1.6	NUM
iajs-2484	194	36	)	)	PUNCT
iajs-2484	194	37	)	)	PUNCT
iajs-2484	194	38	,	,	PUNCT
iajs-2484	194	39	therefore	therefore	ADV
iajs-2484	194	40	𝑓	𝑓	PRON
iajs-2484	194	41	is	be	AUX
iajs-2484	194	42	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	194	43	(	(	PUNCT
iajs-2484	194	44	respectively	respectively	ADV
iajs-2484	194	45	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	194	46	)	)	PUNCT
iajs-2484	194	47	function	function	NOUN
iajs-2484	194	48	.	.	PUNCT
iajs-2484	195	1	proposition	proposition	NOUN
iajs-2484	195	2	(	(	PUNCT
iajs-2484	195	3	1.37	1.37	NUM
iajs-2484	195	4	)	)	PUNCT
iajs-2484	195	5	if	if	SCONJ
iajs-2484	195	6	𝑋	𝑋	PROPN
iajs-2484	195	7	is	be	AUX
iajs-2484	195	8	an	an	DET
iajs-2484	195	9	𝜔-compact	𝜔-compact	NOUN
iajs-2484	195	10	and	and	CCONJ
iajs-2484	195	11	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	195	12	-space	-space	NOUN
iajs-2484	195	13	(	(	PUNCT
iajs-2484	195	14	respectively	respectively	ADV
iajs-2484	195	15	𝑁-compact	𝑁-compact	PROPN
iajs-2484	195	16	and	and	CCONJ
iajs-2484	195	17	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	195	18	-space	-space	NOUN
iajs-2484	195	19	)	)	PUNCT
iajs-2484	195	20	,	,	PUNCT
iajs-2484	195	21	then	then	ADV
iajs-2484	195	22	a	a	DET
iajs-2484	195	23	function	function	NOUN
iajs-2484	195	24	𝑓	𝑓	NOUN
iajs-2484	195	25	:	:	PUNCT
iajs-2484	195	26	𝑋	𝑋	PROPN
iajs-2484	195	27	⟶	⟶	NOUN
iajs-2484	195	28	𝑌	𝑌	PROPN
iajs-2484	195	29	is	be	AUX
iajs-2484	195	30	an	an	DET
iajs-2484	195	31	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	195	32	(	(	PUNCT
iajs-2484	195	33	respectively	respectively	ADV
iajs-2484	195	34	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	195	35	)	)	PUNCT
iajs-2484	195	36	function	function	NOUN
iajs-2484	195	37	iff	iff	NOUN
iajs-2484	195	38	it	it	PRON
iajs-2484	195	39	is	be	AUX
iajs-2484	195	40	𝜔m𝜔cfunction	𝜔m𝜔cfunction	NOUN
iajs-2484	195	41	(	(	PUNCT
iajs-2484	195	42	respectively	respectively	ADV
iajs-2484	195	43	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	195	44	-	-	PUNCT
iajs-2484	195	45	function	function	NOUN
iajs-2484	195	46	)	)	PUNCT
iajs-2484	195	47	.	.	PUNCT
iajs-2484	195	48	  	  	SPACE
iajs-2484	196	1	183	183	NUM
iajs-2484	196	2	  	  	SPACE
iajs-2484	196	3	ibn	ibn	PROPN
iajs-2484	196	4	al	al	PROPN
iajs-2484	196	5	-	-	PUNCT
iajs-2484	196	6	haitham	haitham	PROPN
iajs-2484	196	7	jour	jour	X
iajs-2484	196	8	.	.	PROPN
iajs-2484	196	9	for	for	ADP
iajs-2484	196	10	pure	pure	ADJ
iajs-2484	196	11	&	&	CCONJ
iajs-2484	196	12	appl	appl	PROPN
iajs-2484	196	13	.	.	PUNCT
iajs-2484	197	1	sci	sci	PROPN
iajs-2484	197	2	.	.	PROPN
iajs-2484	198	1	33	33	NUM
iajs-2484	198	2	(	(	PUNCT
iajs-2484	198	3	3	3	NUM
iajs-2484	198	4	)	)	PUNCT
iajs-2484	198	5	2020	2020	NUM
iajs-2484	199	1	proof	proof	NOUN
iajs-2484	199	2	:	:	PUNCT
iajs-2484	199	3	let	let	VERB
iajs-2484	199	4	𝑋	𝑋	NOUN
iajs-2484	199	5	be	be	AUX
iajs-2484	199	6	an	an	DET
iajs-2484	199	7	𝜔-compact	𝜔-compact	NOUN
iajs-2484	199	8	and	and	CCONJ
iajs-2484	199	9	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	199	10	-space	-space	NOUN
iajs-2484	199	11	(	(	PUNCT
iajs-2484	199	12	respectively	respectively	ADV
iajs-2484	199	13	𝑁-compact	𝑁-compact	PROPN
iajs-2484	199	14	and	and	CCONJ
iajs-2484	199	15	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	199	16	-space	-space	NOUN
iajs-2484	199	17	)	)	PUNCT
iajs-2484	199	18	,	,	PUNCT
iajs-2484	199	19	let	let	VERB
iajs-2484	199	20	𝑓	𝑓	PRON
iajs-2484	199	21	be	be	AUX
iajs-2484	199	22	an	an	DET
iajs-2484	199	23	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	199	24	(	(	PUNCT
iajs-2484	199	25	respectively	respectively	ADV
iajs-2484	199	26	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	199	27	)	)	PUNCT
iajs-2484	199	28	.	.	PUNCT
iajs-2484	200	1	to	to	PART
iajs-2484	200	2	prove	prove	VERB
iajs-2484	200	3	𝑓	𝑓	PRON
iajs-2484	200	4	is	be	AUX
iajs-2484	200	5	an	an	DET
iajs-2484	200	6	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	200	7	-	-	PUNCT
iajs-2484	200	8	function	function	NOUN
iajs-2484	200	9	(	(	PUNCT
iajs-2484	200	10	respectively	respectively	ADV
iajs-2484	200	11	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	200	12	-	-	PUNCT
iajs-2484	200	13	function	function	NOUN
iajs-2484	200	14	)	)	PUNCT
iajs-2484	200	15	.	.	PUNCT
iajs-2484	201	1	let	let	VERB
iajs-2484	201	2	ℳ	ℳ	PRON
iajs-2484	201	3	be	be	AUX
iajs-2484	201	4	an	an	DET
iajs-2484	201	5	𝜔-compact	𝜔-compact	NOUN
iajs-2484	201	6	(	(	PUNCT
iajs-2484	201	7	respectively	respectively	ADV
iajs-2484	201	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	201	9	)	)	PUNCT
iajs-2484	201	10	set	set	NOUN
iajs-2484	201	11	in	in	ADP
iajs-2484	201	12	𝑌	𝑌	PROPN
iajs-2484	201	13	,	,	PUNCT
iajs-2484	201	14	then	then	ADV
iajs-2484	201	15	𝑓	𝑓	PRON
iajs-2484	201	16	ℳ	ℳ	PROPN
iajs-2484	201	17	is	be	AUX
iajs-2484	201	18	𝜔-compact	𝜔-compact	NOUN
iajs-2484	201	19	(	(	PUNCT
iajs-2484	201	20	respectively	respectively	ADV
iajs-2484	201	21	𝑁-compact	𝑁-compact	PROPN
iajs-2484	201	22	)	)	PUNCT
iajs-2484	201	23	set	set	NOUN
iajs-2484	201	24	in	in	ADP
iajs-2484	201	25	𝑋	𝑋	PROPN
iajs-2484	201	26	(	(	PUNCT
iajs-2484	201	27	since	since	SCONJ
iajs-2484	201	28	𝑓	𝑓	PRON
iajs-2484	201	29	is	be	AUX
iajs-2484	201	30	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	201	31	(	(	PUNCT
iajs-2484	201	32	respectively	respectively	ADV
iajs-2484	201	33	𝑁∗∗compact	𝑁∗∗compact	NOUN
iajs-2484	201	34	)	)	PUNCT
iajs-2484	201	35	)	)	PUNCT
iajs-2484	201	36	,	,	PUNCT
iajs-2484	201	37	and	and	CCONJ
iajs-2484	201	38	since	since	SCONJ
iajs-2484	201	39	𝑋	𝑋	NOUN
iajs-2484	201	40	is	be	AUX
iajs-2484	201	41	𝜔𝑇	𝜔𝑇	ADJ
iajs-2484	201	42	-space	-space	NOUN
iajs-2484	201	43	(	(	PUNCT
iajs-2484	201	44	respectively	respectively	ADV
iajs-2484	201	45	𝑁𝑇	𝑁𝑇	NOUN
iajs-2484	201	46	-space	-space	NOUN
iajs-2484	201	47	)	)	PUNCT
iajs-2484	201	48	,	,	PUNCT
iajs-2484	201	49	so	so	ADV
iajs-2484	201	50	𝑓	𝑓	PRON
iajs-2484	201	51	ℳ	ℳ	PROPN
iajs-2484	201	52	is	be	AUX
iajs-2484	201	53	𝜔-closed	𝜔-close	VERB
iajs-2484	201	54	(	(	PUNCT
iajs-2484	201	55	respectively	respectively	ADV
iajs-2484	201	56	𝑁-closed	𝑁-closed	PROPN
iajs-2484	201	57	)	)	PUNCT
iajs-2484	201	58	set	set	NOUN
iajs-2484	201	59	in	in	ADP
iajs-2484	201	60	𝑋	𝑋	PROPN
iajs-2484	201	61	,	,	PUNCT
iajs-2484	201	62	hence	hence	ADV
iajs-2484	201	63	𝑓	𝑓	PRON
iajs-2484	201	64	is	be	AUX
iajs-2484	201	65	an	an	DET
iajs-2484	201	66	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	201	67	-	-	PUNCT
iajs-2484	201	68	funtion	funtion	NOUN
iajs-2484	201	69	(	(	PUNCT
iajs-2484	201	70	respectively	respectively	ADV
iajs-2484	201	71	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	201	72	-	-	PUNCT
iajs-2484	201	73	function	function	NOUN
iajs-2484	201	74	)	)	PUNCT
iajs-2484	201	75	.	.	PUNCT
iajs-2484	202	1	conversely	conversely	ADV
iajs-2484	202	2	,	,	PUNCT
iajs-2484	202	3	let	let	VERB
iajs-2484	202	4	𝑓	𝑓	PRON
iajs-2484	202	5	be	be	AUX
iajs-2484	202	6	an	an	DET
iajs-2484	202	7	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	202	8	-	-	PUNCT
iajs-2484	202	9	function	function	NOUN
iajs-2484	202	10	(	(	PUNCT
iajs-2484	202	11	respectively	respectively	ADV
iajs-2484	202	12	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	202	13	-	-	PUNCT
iajs-2484	202	14	function	function	NOUN
iajs-2484	202	15	)	)	PUNCT
iajs-2484	202	16	.	.	PUNCT
iajs-2484	203	1	to	to	PART
iajs-2484	203	2	prove	prove	VERB
iajs-2484	203	3	𝑓	𝑓	PRON
iajs-2484	203	4	is	be	AUX
iajs-2484	203	5	an	an	DET
iajs-2484	203	6	𝜔∗∗compact	𝜔∗∗compact	PROPN
iajs-2484	203	7	(	(	PUNCT
iajs-2484	203	8	respectively	respectively	ADV
iajs-2484	203	9	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	203	10	)	)	PUNCT
iajs-2484	203	11	.	.	PUNCT
iajs-2484	204	1	let	let	VERB
iajs-2484	204	2	ℳ	ℳ	PRON
iajs-2484	204	3	be	be	AUX
iajs-2484	204	4	an	an	DET
iajs-2484	204	5	𝜔-compact	𝜔-compact	NOUN
iajs-2484	204	6	(	(	PUNCT
iajs-2484	204	7	respectively	respectively	ADV
iajs-2484	204	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	204	9	)	)	PUNCT
iajs-2484	204	10	set	set	NOUN
iajs-2484	204	11	in	in	ADP
iajs-2484	204	12	𝑌	𝑌	PROPN
iajs-2484	204	13	,	,	PUNCT
iajs-2484	204	14	so	so	ADV
iajs-2484	204	15	𝑓	𝑓	DET
iajs-2484	204	16	ℳ	ℳ	NOUN
iajs-2484	204	17	)	)	PUNCT
iajs-2484	204	18	is	be	AUX
iajs-2484	204	19	𝜔-closed	𝜔-close	VERB
iajs-2484	204	20	(	(	PUNCT
iajs-2484	204	21	respectively	respectively	ADV
iajs-2484	204	22	𝑁-closed	𝑁-closed	PROPN
iajs-2484	204	23	)	)	PUNCT
iajs-2484	204	24	set	set	NOUN
iajs-2484	204	25	in	in	ADP
iajs-2484	204	26	𝑋	𝑋	PROPN
iajs-2484	204	27	(	(	PUNCT
iajs-2484	204	28	because	because	SCONJ
iajs-2484	204	29	𝑓	𝑓	PRON
iajs-2484	204	30	is	be	AUX
iajs-2484	204	31	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	204	32	-	-	PUNCT
iajs-2484	204	33	function	function	NOUN
iajs-2484	204	34	(	(	PUNCT
iajs-2484	204	35	respectively	respectively	ADV
iajs-2484	204	36	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	204	37	-	-	PUNCT
iajs-2484	204	38	function	function	NOUN
iajs-2484	204	39	)	)	PUNCT
iajs-2484	204	40	)	)	PUNCT
iajs-2484	204	41	,	,	PUNCT
iajs-2484	204	42	but	but	CCONJ
iajs-2484	204	43	𝑋	𝑋	NOUN
iajs-2484	204	44	is	be	AUX
iajs-2484	204	45	𝜔-compact	𝜔-compact	PROPN
iajs-2484	204	46	(	(	PUNCT
iajs-2484	204	47	respectively	respectively	ADV
iajs-2484	204	48	.	.	PUNCT
iajs-2484	205	1	𝑁-compact	𝑁-compact	ADJ
iajs-2484	205	2	)	)	PUNCT
iajs-2484	205	3	space	space	NOUN
iajs-2484	205	4	,	,	PUNCT
iajs-2484	205	5	hence	hence	ADV
iajs-2484	205	6	𝑓	𝑓	PRON
iajs-2484	205	7	ℳ	ℳ	PROPN
iajs-2484	205	8	is	be	AUX
iajs-2484	205	9	𝜔-compact	𝜔-compact	NOUN
iajs-2484	205	10	(	(	PUNCT
iajs-2484	205	11	respectively	respectively	ADV
iajs-2484	205	12	𝑁-compact	𝑁-compact	PROPN
iajs-2484	205	13	)	)	PUNCT
iajs-2484	205	14	set	set	NOUN
iajs-2484	205	15	,	,	PUNCT
iajs-2484	205	16	therefore	therefore	ADV
iajs-2484	205	17	𝑓	𝑓	PRON
iajs-2484	205	18	is	be	AUX
iajs-2484	205	19	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	205	20	(	(	PUNCT
iajs-2484	205	21	respectively	respectively	ADV
iajs-2484	205	22	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	205	23	)	)	PUNCT
iajs-2484	205	24	function	function	NOUN
iajs-2484	205	25	.	.	PUNCT
iajs-2484	206	1	corollary	corollary	ADJ
iajs-2484	206	2	(	(	PUNCT
iajs-2484	206	3	1.38	1.38	NUM
iajs-2484	206	4	)	)	PUNCT
iajs-2484	206	5	   	   	SPACE
iajs-2484	207	1	1‐	1‐	NOUN
iajs-2484	207	2	 	 	SPACE
iajs-2484	207	3	if	if	SCONJ
iajs-2484	207	4	𝑋	𝑋	PROPN
iajs-2484	207	5	is	be	AUX
iajs-2484	207	6	a	a	DET
iajs-2484	207	7	kc	kc	NOUN
iajs-2484	207	8	-	-	PUNCT
iajs-2484	207	9	space	space	NOUN
iajs-2484	207	10	,	,	PUNCT
iajs-2484	207	11	and	and	CCONJ
iajs-2484	207	12	𝑓	𝑓	X
iajs-2484	207	13	:	:	PUNCT
iajs-2484	207	14	𝑋	𝑋	PROPN
iajs-2484	207	15	⟶	⟶	NOUN
iajs-2484	207	16	𝑌	𝑌	PROPN
iajs-2484	207	17	is	be	AUX
iajs-2484	207	18	an	an	DET
iajs-2484	207	19	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	207	20	(	(	PUNCT
iajs-2484	207	21	respectively	respectively	ADV
iajs-2484	207	22	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	207	23	)	)	PUNCT
iajs-2484	207	24	function	function	NOUN
iajs-2484	207	25	,	,	PUNCT
iajs-2484	207	26	then	then	ADV
iajs-2484	207	27	it	it	PRON
iajs-2484	207	28	is	be	AUX
iajs-2484	207	29	an	an	DET
iajs-2484	207	30	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	207	31	-	-	PUNCT
iajs-2484	207	32	function	function	NOUN
iajs-2484	207	33	(	(	PUNCT
iajs-2484	207	34	respectively	respectively	ADV
iajs-2484	207	35	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	207	36	-	-	PUNCT
iajs-2484	207	37	function	function	NOUN
iajs-2484	207	38	)	)	PUNCT
iajs-2484	207	39	.	.	PUNCT
iajs-2484	208	1	2-	2-	X
iajs-2484	208	2	 	 	SPACE
iajs-2484	208	3	if	if	SCONJ
iajs-2484	208	4	𝑋	𝑋	PROPN
iajs-2484	208	5	is	be	AUX
iajs-2484	208	6	an	an	DET
iajs-2484	208	7	𝜔-compact	𝜔-compact	PROPN
iajs-2484	208	8	(	(	PUNCT
iajs-2484	208	9	respectively	respectively	ADV
iajs-2484	208	10	𝑁-compact	𝑁-compact	PROPN
iajs-2484	208	11	)	)	PUNCT
iajs-2484	208	12	space	space	NOUN
iajs-2484	208	13	and	and	CCONJ
iajs-2484	208	14	kc	kc	NOUN
iajs-2484	208	15	-	-	PUNCT
iajs-2484	208	16	space	space	NOUN
iajs-2484	208	17	,	,	PUNCT
iajs-2484	208	18	then	then	ADV
iajs-2484	208	19	a	a	DET
iajs-2484	208	20	function	function	NOUN
iajs-2484	208	21	𝑓	𝑓	NOUN
iajs-2484	208	22	:	:	PUNCT
iajs-2484	208	23	𝑋	𝑋	PROPN
iajs-2484	208	24	⟶	⟶	NOUN
iajs-2484	208	25	𝑌	𝑌	PROPN
iajs-2484	208	26	is	be	AUX
iajs-2484	208	27	an	an	DET
iajs-2484	208	28	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	208	29	(	(	PUNCT
iajs-2484	208	30	respectively	respectively	ADV
iajs-2484	208	31	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	208	32	)	)	PUNCT
iajs-2484	208	33	function	function	NOUN
iajs-2484	208	34	iff	iff	NOUN
iajs-2484	208	35	it	it	PRON
iajs-2484	208	36	is	be	AUX
iajs-2484	208	37	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	208	38	-	-	PUNCT
iajs-2484	208	39	function	function	NOUN
iajs-2484	208	40	(	(	PUNCT
iajs-2484	208	41	respectively	respectively	ADV
iajs-2484	208	42	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	208	43	-	-	PUNCT
iajs-2484	208	44	function	function	NOUN
iajs-2484	208	45	)	)	PUNCT
iajs-2484	208	46	.	.	PUNCT
iajs-2484	209	1	3if	3if	ADJ
iajs-2484	209	2	𝑋	𝑋	PROPN
iajs-2484	209	3	is	be	AUX
iajs-2484	209	4	a	a	DET
iajs-2484	209	5	c	c	NOUN
iajs-2484	209	6	-	-	PUNCT
iajs-2484	209	7	c	c	NOUN
iajs-2484	209	8	space	space	NOUN
iajs-2484	209	9	,	,	PUNCT
iajs-2484	209	10	and	and	CCONJ
iajs-2484	209	11	𝑓	𝑓	X
iajs-2484	209	12	:	:	PUNCT
iajs-2484	209	13	𝑋	𝑋	PROPN
iajs-2484	209	14	⟶	⟶	NOUN
iajs-2484	209	15	𝑌	𝑌	PROPN
iajs-2484	209	16	is	be	AUX
iajs-2484	209	17	an	an	DET
iajs-2484	209	18	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	209	19	(	(	PUNCT
iajs-2484	209	20	respectively	respectively	ADV
iajs-2484	209	21	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	209	22	)	)	PUNCT
iajs-2484	209	23	function	function	NOUN
iajs-2484	209	24	,	,	PUNCT
iajs-2484	209	25	then	then	ADV
iajs-2484	209	26	it	it	PRON
iajs-2484	209	27	is	be	AUX
iajs-2484	209	28	an	an	DET
iajs-2484	209	29	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	209	30	-	-	PUNCT
iajs-2484	209	31	function	function	NOUN
iajs-2484	209	32	(	(	PUNCT
iajs-2484	209	33	respectively	respectively	ADV
iajs-2484	209	34	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	209	35	-	-	PUNCT
iajs-2484	209	36	function	function	NOUN
iajs-2484	209	37	)	)	PUNCT
iajs-2484	209	38	.	.	PUNCT
iajs-2484	210	1	4if	4if	NOUN
iajs-2484	211	1	𝑋	𝑋	NOUN
iajs-2484	211	2	is	be	AUX
iajs-2484	211	3	an	an	DET
iajs-2484	211	4	𝜔-compact	𝜔-compact	PROPN
iajs-2484	211	5	(	(	PUNCT
iajs-2484	211	6	respectively	respectively	ADV
iajs-2484	211	7	𝑁-compact	𝑁-compact	PROPN
iajs-2484	211	8	)	)	PUNCT
iajs-2484	211	9	and	and	CCONJ
iajs-2484	211	10	c	c	NOUN
iajs-2484	211	11	-	-	PUNCT
iajs-2484	211	12	c	c	NOUN
iajs-2484	211	13	space	space	NOUN
iajs-2484	211	14	,	,	PUNCT
iajs-2484	211	15	then	then	ADV
iajs-2484	211	16	a	a	DET
iajs-2484	211	17	function	function	NOUN
iajs-2484	211	18	𝑓	𝑓	NOUN
iajs-2484	211	19	:	:	PUNCT
iajs-2484	211	20	𝑋	𝑋	PROPN
iajs-2484	211	21	⟶	⟶	NOUN
iajs-2484	211	22	𝑌	𝑌	PROPN
iajs-2484	211	23	is	be	AUX
iajs-2484	211	24	an	an	DET
iajs-2484	211	25	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	211	26	(	(	PUNCT
iajs-2484	211	27	respectively	respectively	ADV
iajs-2484	211	28	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	211	29	)	)	PUNCT
iajs-2484	211	30	function	function	NOUN
iajs-2484	211	31	iff	iff	NOUN
iajs-2484	211	32	it	it	PRON
iajs-2484	211	33	is	be	AUX
iajs-2484	211	34	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	211	35	-	-	PUNCT
iajs-2484	211	36	function	function	NOUN
iajs-2484	211	37	(	(	PUNCT
iajs-2484	211	38	respectively	respectively	ADV
iajs-2484	211	39	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	211	40	-	-	PUNCT
iajs-2484	211	41	function	function	NOUN
iajs-2484	211	42	)	)	PUNCT
iajs-2484	211	43	.	.	PUNCT
iajs-2484	212	1	5if	5if	ADJ
iajs-2484	212	2	𝑋	𝑋	PROPN
iajs-2484	212	3	is	be	AUX
iajs-2484	212	4	an	an	DET
iajs-2484	212	5	𝜔-compact	𝜔-compact	PROPN
iajs-2484	212	6	(	(	PUNCT
iajs-2484	212	7	respectively	respectively	ADV
iajs-2484	212	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	212	9	)	)	PUNCT
iajs-2484	212	10	and	and	CCONJ
iajs-2484	212	11	𝑇	𝑇	PROPN
iajs-2484	212	12	-space	-space	NOUN
iajs-2484	212	13	,	,	PUNCT
iajs-2484	212	14	then	then	ADV
iajs-2484	212	15	a	a	DET
iajs-2484	212	16	function	function	NOUN
iajs-2484	212	17	𝑓	𝑓	NOUN
iajs-2484	212	18	:	:	PUNCT
iajs-2484	212	19	𝑋	𝑋	PROPN
iajs-2484	212	20	⟶	⟶	NOUN
iajs-2484	212	21	𝑌	𝑌	PROPN
iajs-2484	212	22	is	be	AUX
iajs-2484	212	23	an	an	DET
iajs-2484	212	24	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	212	25	(	(	PUNCT
iajs-2484	212	26	respectively	respectively	ADV
iajs-2484	212	27	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	212	28	)	)	PUNCT
iajs-2484	212	29	function	function	NOUN
iajs-2484	212	30	iff	iff	NOUN
iajs-2484	212	31	it	it	PRON
iajs-2484	212	32	is	be	AUX
iajs-2484	212	33	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	212	34	-	-	PUNCT
iajs-2484	212	35	function	function	NOUN
iajs-2484	212	36	(	(	PUNCT
iajs-2484	212	37	respectively	respectively	ADV
iajs-2484	212	38	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	212	39	-	-	PUNCT
iajs-2484	212	40	function	function	NOUN
iajs-2484	212	41	)	)	PUNCT
iajs-2484	212	42	.	.	PUNCT
iajs-2484	213	1	proof	proof	NOUN
iajs-2484	213	2	:	:	PUNCT
iajs-2484	214	1	1let	1let	NUM
iajs-2484	214	2	k	k	AUX
iajs-2484	214	3	be	be	AUX
iajs-2484	214	4	an	an	DET
iajs-2484	214	5	𝜔-compact	𝜔-compact	PROPN
iajs-2484	214	6	(	(	PUNCT
iajs-2484	214	7	respectively	respectively	ADV
iajs-2484	214	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	214	9	)	)	PUNCT
iajs-2484	214	10	subset	subset	NOUN
iajs-2484	214	11	of	of	ADP
iajs-2484	214	12	𝑌	𝑌	PROPN
iajs-2484	214	13	,	,	PUNCT
iajs-2484	214	14	so	so	ADV
iajs-2484	214	15	𝑓	𝑓	PRON
iajs-2484	214	16	(	(	PUNCT
iajs-2484	214	17	k	k	NOUN
iajs-2484	214	18	)	)	PUNCT
iajs-2484	214	19	is	be	AUX
iajs-2484	214	20	𝜔-compact	𝜔-compact	PROPN
iajs-2484	214	21	(	(	PUNCT
iajs-2484	214	22	respectively	respectively	ADV
iajs-2484	214	23	𝑁-compact	𝑁-compact	PROPN
iajs-2484	214	24	)	)	PUNCT
iajs-2484	214	25	subset	subset	NOUN
iajs-2484	214	26	of	of	ADP
iajs-2484	214	27	𝑋	𝑋	PROPN
iajs-2484	214	28	(	(	PUNCT
iajs-2484	214	29	since	since	SCONJ
iajs-2484	214	30	𝑓	𝑓	PRON
iajs-2484	214	31	is	be	AUX
iajs-2484	214	32	an	an	DET
iajs-2484	214	33	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	214	34	(	(	PUNCT
iajs-2484	214	35	respectively	respectively	ADV
iajs-2484	214	36	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	214	37	)	)	PUNCT
iajs-2484	214	38	function	function	NOUN
iajs-2484	214	39	)	)	PUNCT
iajs-2484	214	40	)	)	PUNCT
iajs-2484	214	41	,	,	PUNCT
iajs-2484	214	42	and	and	CCONJ
iajs-2484	214	43	then	then	ADV
iajs-2484	214	44	it	it	PRON
iajs-2484	214	45	is	be	AUX
iajs-2484	214	46	compact	compact	ADJ
iajs-2484	214	47	subset	subset	NOUN
iajs-2484	214	48	of	of	ADP
iajs-2484	214	49	𝑋	𝑋	PROPN
iajs-2484	214	50	(	(	PUNCT
iajs-2484	214	51	by	by	ADP
iajs-2484	214	52	remark	remark	NOUN
iajs-2484	214	53	(	(	PUNCT
iajs-2484	214	54	1.2	1.2	NUM
iajs-2484	214	55	)	)	PUNCT
iajs-2484	214	56	)	)	PUNCT
iajs-2484	214	57	which	which	PRON
iajs-2484	214	58	is	be	AUX
iajs-2484	214	59	kc	kc	NOUN
iajs-2484	214	60	-	-	PUNCT
iajs-2484	214	61	space	space	NOUN
iajs-2484	214	62	,	,	PUNCT
iajs-2484	214	63	so	so	ADV
iajs-2484	214	64	𝑓	𝑓	PRON
iajs-2484	214	65	(	(	PUNCT
iajs-2484	214	66	k	k	NOUN
iajs-2484	214	67	)	)	PUNCT
iajs-2484	214	68	is	be	AUX
iajs-2484	214	69	closed	close	VERB
iajs-2484	214	70	subset	subset	NOUN
iajs-2484	214	71	of	of	ADP
iajs-2484	214	72	𝑋	𝑋	PROPN
iajs-2484	214	73	,	,	PUNCT
iajs-2484	214	74	and	and	CCONJ
iajs-2484	214	75	by	by	ADP
iajs-2484	214	76	remark	remark	NOUN
iajs-2484	214	77	(	(	PUNCT
iajs-2484	214	78	1.2	1.2	NUM
iajs-2484	214	79	)	)	PUNCT
iajs-2484	214	80	)	)	PUNCT
iajs-2484	215	1	it	it	PRON
iajs-2484	215	2	is	be	AUX
iajs-2484	215	3	𝜔-closed	𝜔-close	VERB
iajs-2484	215	4	(	(	PUNCT
iajs-2484	215	5	respectively	respectively	ADV
iajs-2484	215	6	𝑁-closed	𝑁-closed	PROPN
iajs-2484	215	7	)	)	PUNCT
iajs-2484	215	8	,	,	PUNCT
iajs-2484	215	9	so	so	ADV
iajs-2484	215	10	𝑓	𝑓	PRON
iajs-2484	215	11	is	be	AUX
iajs-2484	215	12	an	an	DET
iajs-2484	215	13	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	215	14	-	-	PUNCT
iajs-2484	215	15	function	function	NOUN
iajs-2484	215	16	(	(	PUNCT
iajs-2484	215	17	respectively	respectively	ADV
iajs-2484	215	18	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	215	19	-	-	PUNCT
iajs-2484	215	20	function	function	NOUN
iajs-2484	215	21	)	)	PUNCT
iajs-2484	215	22	.	.	PUNCT
iajs-2484	216	1	2let	2let	NUM
iajs-2484	216	2	𝑓	𝑓	PRON
iajs-2484	216	3	be	be	AUX
iajs-2484	216	4	an	an	DET
iajs-2484	216	5	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	216	6	(	(	PUNCT
iajs-2484	216	7	respectively	respectively	ADV
iajs-2484	216	8	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	216	9	)	)	PUNCT
iajs-2484	216	10	function	function	NOUN
iajs-2484	216	11	,	,	PUNCT
iajs-2484	216	12	and	and	CCONJ
iajs-2484	216	13	k	k	PROPN
iajs-2484	216	14	be	be	AUX
iajs-2484	216	15	an	an	DET
iajs-2484	216	16	𝜔-compact	𝜔-compact	PROPN
iajs-2484	216	17	(	(	PUNCT
iajs-2484	216	18	respectively	respectively	ADV
iajs-2484	216	19	𝑁-compact	𝑁-compact	PROPN
iajs-2484	216	20	)	)	PUNCT
iajs-2484	216	21	subset	subset	NOUN
iajs-2484	216	22	of	of	ADP
iajs-2484	216	23	𝑌	𝑌	PROPN
iajs-2484	216	24	,	,	PUNCT
iajs-2484	216	25	so	so	ADV
iajs-2484	216	26	𝑓	𝑓	PRON
iajs-2484	216	27	(	(	PUNCT
iajs-2484	216	28	k	k	NOUN
iajs-2484	216	29	)	)	PUNCT
iajs-2484	216	30	is	be	AUX
iajs-2484	216	31	𝜔-compact	𝜔-compact	PROPN
iajs-2484	216	32	(	(	PUNCT
iajs-2484	216	33	respectively	respectively	ADV
iajs-2484	216	34	𝑁-compact	𝑁-compact	PROPN
iajs-2484	216	35	)	)	PUNCT
iajs-2484	216	36	subset	subset	NOUN
iajs-2484	216	37	of	of	ADP
iajs-2484	216	38	𝑋	𝑋	PROPN
iajs-2484	216	39	(	(	PUNCT
iajs-2484	216	40	since	since	SCONJ
iajs-2484	216	41	𝑓	𝑓	PRON
iajs-2484	216	42	is	be	AUX
iajs-2484	216	43	an	an	DET
iajs-2484	216	44	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	216	45	(	(	PUNCT
iajs-2484	216	46	respectively	respectively	ADV
iajs-2484	216	47	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	216	48	)	)	PUNCT
iajs-2484	216	49	function	function	NOUN
iajs-2484	216	50	)	)	PUNCT
iajs-2484	216	51	)	)	PUNCT
iajs-2484	216	52	,	,	PUNCT
iajs-2484	216	53	and	and	CCONJ
iajs-2484	216	54	then	then	ADV
iajs-2484	216	55	it	it	PRON
iajs-2484	216	56	is	be	AUX
iajs-2484	216	57	compact	compact	ADJ
iajs-2484	216	58	subset	subset	NOUN
iajs-2484	216	59	of	of	ADP
iajs-2484	216	60	𝑋	𝑋	PROPN
iajs-2484	216	61	(	(	PUNCT
iajs-2484	216	62	by	by	ADP
iajs-2484	216	63	remark	remark	NOUN
iajs-2484	216	64	(	(	PUNCT
iajs-2484	216	65	1.2	1.2	NUM
iajs-2484	216	66	)	)	PUNCT
iajs-2484	216	67	)	)	PUNCT
iajs-2484	216	68	which	which	PRON
iajs-2484	216	69	is	be	AUX
iajs-2484	216	70	kc	kc	NOUN
iajs-2484	216	71	-	-	PUNCT
iajs-2484	216	72	space	space	NOUN
iajs-2484	216	73	,	,	PUNCT
iajs-2484	216	74	so	so	ADV
iajs-2484	216	75	𝑓	𝑓	PRON
iajs-2484	216	76	(	(	PUNCT
iajs-2484	216	77	k	k	NOUN
iajs-2484	216	78	)	)	PUNCT
iajs-2484	216	79	is	be	AUX
iajs-2484	216	80	closed	close	VERB
iajs-2484	216	81	subset	subset	NOUN
iajs-2484	216	82	of	of	ADP
iajs-2484	216	83	𝑋	𝑋	PROPN
iajs-2484	216	84	,	,	PUNCT
iajs-2484	216	85	and	and	CCONJ
iajs-2484	216	86	by	by	ADP
iajs-2484	216	87	remark	remark	NOUN
iajs-2484	216	88	(	(	PUNCT
iajs-2484	216	89	1.2	1.2	NUM
iajs-2484	216	90	)	)	PUNCT
iajs-2484	216	91	)	)	PUNCT
iajs-2484	217	1	it	it	PRON
iajs-2484	217	2	is	be	AUX
iajs-2484	217	3	𝜔-closed	𝜔-close	VERB
iajs-2484	217	4	(	(	PUNCT
iajs-2484	217	5	respectively	respectively	ADV
iajs-2484	217	6	𝑁-closed	𝑁-closed	PROPN
iajs-2484	217	7	)	)	PUNCT
iajs-2484	217	8	,	,	PUNCT
iajs-2484	217	9	so	so	ADV
iajs-2484	217	10	𝑓	𝑓	PRON
iajs-2484	217	11	is	be	AUX
iajs-2484	217	12	an	an	DET
iajs-2484	217	13	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	217	14	-	-	PUNCT
iajs-2484	217	15	function	function	NOUN
iajs-2484	217	16	(	(	PUNCT
iajs-2484	217	17	respectively	respectively	ADV
iajs-2484	217	18	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	217	19	-	-	PUNCT
iajs-2484	217	20	function	function	NOUN
iajs-2484	217	21	)	)	PUNCT
iajs-2484	217	22	.	.	PUNCT
iajs-2484	218	1	conversely	conversely	ADV
iajs-2484	218	2	,	,	PUNCT
iajs-2484	218	3	let	let	VERB
iajs-2484	218	4	k	k	PRON
iajs-2484	218	5	be	be	AUX
iajs-2484	218	6	an	an	DET
iajs-2484	218	7	𝜔-compact	𝜔-compact	PROPN
iajs-2484	218	8	(	(	PUNCT
iajs-2484	218	9	respectively	respectively	ADV
iajs-2484	218	10	𝑁-compact	𝑁-compact	PROPN
iajs-2484	218	11	)	)	PUNCT
iajs-2484	218	12	subset	subset	NOUN
iajs-2484	218	13	of	of	ADP
iajs-2484	218	14	𝑌	𝑌	PROPN
iajs-2484	218	15	so	so	ADV
iajs-2484	218	16	𝑓	𝑓	PROPN
iajs-2484	218	17	(	(	PUNCT
iajs-2484	218	18	k	k	NOUN
iajs-2484	218	19	)	)	PUNCT
iajs-2484	218	20	is	be	AUX
iajs-2484	218	21	𝜔-closed	𝜔-close	VERB
iajs-2484	218	22	(	(	PUNCT
iajs-2484	218	23	respectively	respectively	ADV
iajs-2484	218	24	𝑁-closed	𝑁-closed	PROPN
iajs-2484	218	25	)	)	PUNCT
iajs-2484	218	26	subset	subset	NOUN
iajs-2484	218	27	of	of	ADP
iajs-2484	218	28	𝑋	𝑋	PROPN
iajs-2484	218	29	(	(	PUNCT
iajs-2484	218	30	since	since	SCONJ
iajs-2484	218	31	𝑓	𝑓	PRON
iajs-2484	218	32	is	be	AUX
iajs-2484	218	33	an	an	DET
iajs-2484	218	34	𝜔m𝜔cfunction	𝜔m𝜔cfunction	NOUN
iajs-2484	218	35	(	(	PUNCT
iajs-2484	218	36	respectively	respectively	ADV
iajs-2484	218	37	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	218	38	-	-	PUNCT
iajs-2484	218	39	function	function	NOUN
iajs-2484	218	40	)	)	PUNCT
iajs-2484	218	41	)	)	PUNCT
iajs-2484	218	42	,	,	PUNCT
iajs-2484	218	43	but	but	CCONJ
iajs-2484	218	44	𝑋	𝑋	NOUN
iajs-2484	218	45	is	be	AUX
iajs-2484	218	46	an	an	DET
iajs-2484	218	47	𝜔-compact	𝜔-compact	PROPN
iajs-2484	218	48	(	(	PUNCT
iajs-2484	218	49	respectively	respectively	ADV
iajs-2484	218	50	𝑁-compact	𝑁-compact	PROPN
iajs-2484	218	51	)	)	PUNCT
iajs-2484	218	52	space	space	NOUN
iajs-2484	218	53	,	,	PUNCT
iajs-2484	218	54	so	so	ADV
iajs-2484	218	55	𝑓	𝑓	PRON
iajs-2484	218	56	(	(	PUNCT
iajs-2484	218	57	k	k	NOUN
iajs-2484	218	58	)	)	PUNCT
iajs-2484	218	59	is	be	AUX
iajs-2484	218	60	an	an	DET
iajs-2484	218	61	𝜔-compact	𝜔-compact	PROPN
iajs-2484	218	62	(	(	PUNCT
iajs-2484	218	63	respectively	respectively	ADV
iajs-2484	218	64	𝑁-compact	𝑁-compact	PROPN
iajs-2484	218	65	)	)	PUNCT
iajs-2484	218	66	subset	subset	NOUN
iajs-2484	218	67	of	of	ADP
iajs-2484	218	68	𝑋	𝑋	PROPN
iajs-2484	218	69	,	,	PUNCT
iajs-2484	218	70	therefore	therefore	ADV
iajs-2484	218	71	𝑓	𝑓	PRON
iajs-2484	218	72	is	be	AUX
iajs-2484	218	73	an	an	DET
iajs-2484	218	74	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	218	75	(	(	PUNCT
iajs-2484	218	76	respectively	respectively	ADV
iajs-2484	218	77	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	218	78	)	)	PUNCT
iajs-2484	218	79	function	function	NOUN
iajs-2484	218	80	.	.	PUNCT
iajs-2484	218	81	  	  	SPACE
iajs-2484	219	1	184	184	NUM
iajs-2484	219	2	  	  	SPACE
iajs-2484	219	3	ibn	ibn	PROPN
iajs-2484	219	4	al	al	PROPN
iajs-2484	219	5	-	-	PUNCT
iajs-2484	219	6	haitham	haitham	PROPN
iajs-2484	219	7	jour	jour	X
iajs-2484	219	8	.	.	PROPN
iajs-2484	219	9	for	for	ADP
iajs-2484	219	10	pure	pure	ADJ
iajs-2484	219	11	&	&	CCONJ
iajs-2484	219	12	appl	appl	PROPN
iajs-2484	219	13	.	.	PUNCT
iajs-2484	220	1	sci	sci	PROPN
iajs-2484	220	2	.	.	PROPN
iajs-2484	221	1	33	33	NUM
iajs-2484	221	2	(	(	PUNCT
iajs-2484	221	3	3	3	NUM
iajs-2484	221	4	)	)	PUNCT
iajs-2484	221	5	2020	2020	NUM
iajs-2484	222	1	3let	3let	NUM
iajs-2484	222	2	k	k	X
iajs-2484	222	3	be	be	AUX
iajs-2484	222	4	an	an	DET
iajs-2484	222	5	𝜔-compact	𝜔-compact	PROPN
iajs-2484	222	6	(	(	PUNCT
iajs-2484	222	7	respectively	respectively	ADV
iajs-2484	222	8	𝑁-compact	𝑁-compact	PROPN
iajs-2484	222	9	)	)	PUNCT
iajs-2484	222	10	subset	subset	NOUN
iajs-2484	222	11	of	of	ADP
iajs-2484	222	12	𝑌	𝑌	PROPN
iajs-2484	222	13	,	,	PUNCT
iajs-2484	222	14	so	so	ADV
iajs-2484	222	15	𝑓	𝑓	PRON
iajs-2484	222	16	(	(	PUNCT
iajs-2484	222	17	k	k	NOUN
iajs-2484	222	18	)	)	PUNCT
iajs-2484	222	19	is	be	AUX
iajs-2484	222	20	𝜔-compact	𝜔-compact	PROPN
iajs-2484	222	21	(	(	PUNCT
iajs-2484	222	22	respectively	respectively	ADV
iajs-2484	222	23	𝑁-compact	𝑁-compact	PROPN
iajs-2484	222	24	)	)	PUNCT
iajs-2484	222	25	subset	subset	NOUN
iajs-2484	222	26	of	of	ADP
iajs-2484	222	27	𝑋	𝑋	PROPN
iajs-2484	222	28	(	(	PUNCT
iajs-2484	222	29	since	since	SCONJ
iajs-2484	222	30	𝑓	𝑓	PRON
iajs-2484	222	31	is	be	AUX
iajs-2484	222	32	an	an	DET
iajs-2484	222	33	𝜔∗∗-compact	𝜔∗∗-compact	ADJ
iajs-2484	222	34	(	(	PUNCT
iajs-2484	222	35	resp	resp	NOUN
iajs-2484	222	36	.	.	PUNCT
iajs-2484	223	1	𝑁∗∗-compact	𝑁∗∗-compact	NOUN
iajs-2484	223	2	)	)	PUNCT
iajs-2484	223	3	function	function	NOUN
iajs-2484	223	4	)	)	PUNCT
iajs-2484	223	5	)	)	PUNCT
iajs-2484	223	6	,	,	PUNCT
iajs-2484	223	7	and	and	CCONJ
iajs-2484	223	8	then	then	ADV
iajs-2484	223	9	it	it	PRON
iajs-2484	223	10	is	be	AUX
iajs-2484	223	11	compact	compact	ADJ
iajs-2484	223	12	subset	subset	NOUN
iajs-2484	223	13	of	of	ADP
iajs-2484	223	14	𝑋	𝑋	PROPN
iajs-2484	223	15	(	(	PUNCT
iajs-2484	223	16	by	by	ADP
iajs-2484	223	17	remark	remark	NOUN
iajs-2484	223	18	(	(	PUNCT
iajs-2484	223	19	1.2	1.2	NUM
iajs-2484	223	20	)	)	PUNCT
iajs-2484	223	21	)	)	PUNCT
iajs-2484	223	22	which	which	PRON
iajs-2484	223	23	is	be	AUX
iajs-2484	223	24	c	c	NOUN
iajs-2484	223	25	-	-	PUNCT
iajs-2484	223	26	c	c	NOUN
iajs-2484	223	27	space	space	NOUN
iajs-2484	223	28	,	,	PUNCT
iajs-2484	223	29	so	so	ADV
iajs-2484	223	30	𝑓	𝑓	PRON
iajs-2484	223	31	(	(	PUNCT
iajs-2484	223	32	k	k	NOUN
iajs-2484	223	33	)	)	PUNCT
iajs-2484	223	34	is	be	AUX
iajs-2484	223	35	closed	close	VERB
iajs-2484	223	36	subset	subset	NOUN
iajs-2484	223	37	of	of	ADP
iajs-2484	223	38	𝑋	𝑋	PROPN
iajs-2484	223	39	,	,	PUNCT
iajs-2484	223	40	and	and	CCONJ
iajs-2484	223	41	by	by	ADP
iajs-2484	223	42	remark	remark	NOUN
iajs-2484	223	43	(	(	PUNCT
iajs-2484	223	44	1.2	1.2	NUM
iajs-2484	223	45	)	)	PUNCT
iajs-2484	223	46	)	)	PUNCT
iajs-2484	224	1	it	it	PRON
iajs-2484	224	2	is	be	AUX
iajs-2484	224	3	𝜔-closed	𝜔-close	VERB
iajs-2484	224	4	(	(	PUNCT
iajs-2484	224	5	respectively	respectively	ADV
iajs-2484	224	6	𝑁-closed	𝑁-closed	PROPN
iajs-2484	224	7	)	)	PUNCT
iajs-2484	224	8	subset	subset	NOUN
iajs-2484	224	9	of	of	ADP
iajs-2484	224	10	𝑋	𝑋	PROPN
iajs-2484	224	11	,	,	PUNCT
iajs-2484	224	12	so	so	ADV
iajs-2484	224	13	𝑓	𝑓	PRON
iajs-2484	224	14	is	be	AUX
iajs-2484	224	15	an	an	DET
iajs-2484	224	16	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	224	17	-	-	PUNCT
iajs-2484	224	18	function	function	NOUN
iajs-2484	224	19	(	(	PUNCT
iajs-2484	224	20	respectively	respectively	ADV
iajs-2484	224	21	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	224	22	-	-	PUNCT
iajs-2484	224	23	function	function	NOUN
iajs-2484	224	24	)	)	PUNCT
iajs-2484	224	25	.	.	PUNCT
iajs-2484	225	1	4let	4let	NOUN
iajs-2484	225	2	𝑓	𝑓	PROPN
iajs-2484	225	3	be	be	AUX
iajs-2484	225	4	an	an	DET
iajs-2484	225	5	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	225	6	(	(	PUNCT
iajs-2484	225	7	respectively	respectively	ADV
iajs-2484	225	8	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	225	9	)	)	PUNCT
iajs-2484	225	10	function	function	NOUN
iajs-2484	225	11	,	,	PUNCT
iajs-2484	225	12	and	and	CCONJ
iajs-2484	225	13	k	k	PROPN
iajs-2484	225	14	be	be	AUX
iajs-2484	225	15	an	an	DET
iajs-2484	225	16	𝜔-compact	𝜔-compact	PROPN
iajs-2484	225	17	(	(	PUNCT
iajs-2484	225	18	respectively	respectively	ADV
iajs-2484	225	19	𝑁-compact	𝑁-compact	PROPN
iajs-2484	225	20	)	)	PUNCT
iajs-2484	225	21	subset	subset	NOUN
iajs-2484	225	22	of	of	ADP
iajs-2484	225	23	𝑌	𝑌	PROPN
iajs-2484	225	24	,	,	PUNCT
iajs-2484	225	25	so	so	ADV
iajs-2484	225	26	𝑓	𝑓	PRON
iajs-2484	225	27	(	(	PUNCT
iajs-2484	225	28	k	k	NOUN
iajs-2484	225	29	)	)	PUNCT
iajs-2484	225	30	is	be	AUX
iajs-2484	225	31	𝜔-compact	𝜔-compact	PROPN
iajs-2484	225	32	(	(	PUNCT
iajs-2484	225	33	respectively	respectively	ADV
iajs-2484	225	34	𝑁-compact	𝑁-compact	PROPN
iajs-2484	225	35	)	)	PUNCT
iajs-2484	225	36	subset	subset	NOUN
iajs-2484	225	37	of	of	ADP
iajs-2484	225	38	𝑋	𝑋	PROPN
iajs-2484	225	39	(	(	PUNCT
iajs-2484	225	40	since	since	SCONJ
iajs-2484	225	41	𝑓	𝑓	PRON
iajs-2484	225	42	is	be	AUX
iajs-2484	225	43	an	an	DET
iajs-2484	225	44	𝜔∗∗-compact	𝜔∗∗-compact	ADJ
iajs-2484	225	45	(	(	PUNCT
iajs-2484	225	46	resp	resp	NOUN
iajs-2484	225	47	.	.	PUNCT
iajs-2484	226	1	𝑁∗∗-compact	𝑁∗∗-compact	NOUN
iajs-2484	226	2	)	)	PUNCT
iajs-2484	226	3	function	function	NOUN
iajs-2484	226	4	)	)	PUNCT
iajs-2484	226	5	)	)	PUNCT
iajs-2484	226	6	,	,	PUNCT
iajs-2484	226	7	and	and	CCONJ
iajs-2484	226	8	then	then	ADV
iajs-2484	226	9	it	it	PRON
iajs-2484	226	10	is	be	AUX
iajs-2484	226	11	compact	compact	ADJ
iajs-2484	226	12	subset	subset	NOUN
iajs-2484	226	13	of	of	ADP
iajs-2484	226	14	𝑋	𝑋	PROPN
iajs-2484	226	15	(	(	PUNCT
iajs-2484	226	16	by	by	ADP
iajs-2484	226	17	remark	remark	NOUN
iajs-2484	226	18	(	(	PUNCT
iajs-2484	226	19	1.2	1.2	NUM
iajs-2484	226	20	)	)	PUNCT
iajs-2484	226	21	)	)	PUNCT
iajs-2484	226	22	which	which	PRON
iajs-2484	226	23	is	be	AUX
iajs-2484	226	24	c	c	NOUN
iajs-2484	226	25	-	-	PUNCT
iajs-2484	226	26	c	c	NOUN
iajs-2484	226	27	space	space	NOUN
iajs-2484	226	28	,	,	PUNCT
iajs-2484	226	29	so	so	ADV
iajs-2484	226	30	𝑓	𝑓	PRON
iajs-2484	226	31	(	(	PUNCT
iajs-2484	226	32	k	k	NOUN
iajs-2484	226	33	)	)	PUNCT
iajs-2484	226	34	is	be	AUX
iajs-2484	226	35	closed	close	VERB
iajs-2484	226	36	subset	subset	NOUN
iajs-2484	226	37	of	of	ADP
iajs-2484	226	38	𝑋	𝑋	PROPN
iajs-2484	226	39	,	,	PUNCT
iajs-2484	226	40	and	and	CCONJ
iajs-2484	226	41	by	by	ADP
iajs-2484	226	42	remark	remark	NOUN
iajs-2484	226	43	(	(	PUNCT
iajs-2484	226	44	1.2	1.2	NUM
iajs-2484	226	45	)	)	PUNCT
iajs-2484	226	46	)	)	PUNCT
iajs-2484	227	1	it	it	PRON
iajs-2484	227	2	is	be	AUX
iajs-2484	227	3	𝜔-closed	𝜔-close	VERB
iajs-2484	227	4	(	(	PUNCT
iajs-2484	227	5	respectively	respectively	ADV
iajs-2484	227	6	𝑁-closed	𝑁-closed	PROPN
iajs-2484	227	7	)	)	PUNCT
iajs-2484	227	8	subset	subset	NOUN
iajs-2484	227	9	of	of	ADP
iajs-2484	227	10	𝑋	𝑋	PROPN
iajs-2484	227	11	,	,	PUNCT
iajs-2484	227	12	so	so	ADV
iajs-2484	227	13	𝑓	𝑓	PRON
iajs-2484	227	14	is	be	AUX
iajs-2484	227	15	an	an	DET
iajs-2484	227	16	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	227	17	-	-	PUNCT
iajs-2484	227	18	function	function	NOUN
iajs-2484	227	19	(	(	PUNCT
iajs-2484	227	20	respectively	respectively	ADV
iajs-2484	227	21	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	227	22	-	-	PUNCT
iajs-2484	227	23	function	function	NOUN
iajs-2484	227	24	)	)	PUNCT
iajs-2484	227	25	.	.	PUNCT
iajs-2484	228	1	conversely	conversely	ADV
iajs-2484	228	2	,	,	PUNCT
iajs-2484	228	3	let	let	VERB
iajs-2484	228	4	k	k	PRON
iajs-2484	228	5	be	be	AUX
iajs-2484	228	6	an	an	DET
iajs-2484	228	7	𝜔-compact	𝜔-compact	PROPN
iajs-2484	228	8	(	(	PUNCT
iajs-2484	228	9	respectively	respectively	ADV
iajs-2484	228	10	𝑁-compact	𝑁-compact	PROPN
iajs-2484	228	11	)	)	PUNCT
iajs-2484	228	12	subset	subset	NOUN
iajs-2484	228	13	of	of	ADP
iajs-2484	228	14	𝑌	𝑌	PROPN
iajs-2484	228	15	,	,	PUNCT
iajs-2484	228	16	so	so	ADV
iajs-2484	228	17	𝑓	𝑓	PRON
iajs-2484	228	18	(	(	PUNCT
iajs-2484	228	19	k	k	NOUN
iajs-2484	228	20	)	)	PUNCT
iajs-2484	228	21	is	be	AUX
iajs-2484	228	22	𝜔-closed	𝜔-close	VERB
iajs-2484	228	23	(	(	PUNCT
iajs-2484	228	24	respectively	respectively	ADV
iajs-2484	228	25	𝑁-closed	𝑁-closed	PROPN
iajs-2484	228	26	)	)	PUNCT
iajs-2484	228	27	subset	subset	NOUN
iajs-2484	228	28	of	of	ADP
iajs-2484	228	29	𝑋	𝑋	PROPN
iajs-2484	228	30	(	(	PUNCT
iajs-2484	228	31	since	since	SCONJ
iajs-2484	228	32	𝑓	𝑓	PRON
iajs-2484	228	33	is	be	AUX
iajs-2484	228	34	an	an	DET
iajs-2484	228	35	𝜔m𝜔cfunction	𝜔m𝜔cfunction	NOUN
iajs-2484	228	36	(	(	PUNCT
iajs-2484	228	37	respectively	respectively	ADV
iajs-2484	228	38	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	228	39	-	-	PUNCT
iajs-2484	228	40	function	function	NOUN
iajs-2484	228	41	)	)	PUNCT
iajs-2484	228	42	which	which	PRON
iajs-2484	228	43	is	be	AUX
iajs-2484	228	44	an	an	DET
iajs-2484	228	45	𝜔-compact	𝜔-compact	PROPN
iajs-2484	228	46	(	(	PUNCT
iajs-2484	228	47	respectively	respectively	ADV
iajs-2484	228	48	𝑁-compact	𝑁-compact	PROPN
iajs-2484	228	49	)	)	PUNCT
iajs-2484	228	50	space	space	NOUN
iajs-2484	228	51	,	,	PUNCT
iajs-2484	228	52	so	so	ADV
iajs-2484	228	53	𝑓	𝑓	PRON
iajs-2484	228	54	(	(	PUNCT
iajs-2484	228	55	k	k	NOUN
iajs-2484	228	56	)	)	PUNCT
iajs-2484	228	57	is	be	AUX
iajs-2484	228	58	an	an	DET
iajs-2484	228	59	𝜔-compact	𝜔-compact	PROPN
iajs-2484	228	60	(	(	PUNCT
iajs-2484	228	61	respectively	respectively	ADV
iajs-2484	228	62	𝑁-compact	𝑁-compact	PROPN
iajs-2484	228	63	)	)	PUNCT
iajs-2484	228	64	subset	subset	NOUN
iajs-2484	228	65	of	of	ADP
iajs-2484	228	66	𝑋(by	𝑋(by	PROPN
iajs-2484	228	67	remark	remark	NOUN
iajs-2484	228	68	(	(	PUNCT
iajs-2484	228	69	1.6	1.6	NUM
iajs-2484	228	70	)	)	PUNCT
iajs-2484	228	71	)	)	PUNCT
iajs-2484	228	72	,	,	PUNCT
iajs-2484	228	73	so	so	ADV
iajs-2484	228	74	𝑓	𝑓	PRON
iajs-2484	228	75	be	be	AUX
iajs-2484	228	76	an	an	DET
iajs-2484	228	77	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	228	78	(	(	PUNCT
iajs-2484	228	79	respectively	respectively	ADV
iajs-2484	228	80	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	228	81	)	)	PUNCT
iajs-2484	228	82	function	function	NOUN
iajs-2484	228	83	.	.	PUNCT
iajs-2484	229	1	5let	5let	NUM
iajs-2484	229	2	𝑓	𝑓	PROPN
iajs-2484	229	3	be	be	AUX
iajs-2484	229	4	a	a	DET
iajs-2484	229	5	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	229	6	(	(	PUNCT
iajs-2484	229	7	respectively	respectively	ADV
iajs-2484	229	8	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	229	9	)	)	PUNCT
iajs-2484	229	10	function	function	NOUN
iajs-2484	229	11	,	,	PUNCT
iajs-2484	229	12	and	and	CCONJ
iajs-2484	229	13	k	k	PROPN
iajs-2484	229	14	be	be	AUX
iajs-2484	229	15	an	an	DET
iajs-2484	229	16	𝜔-compact	𝜔-compact	PROPN
iajs-2484	229	17	(	(	PUNCT
iajs-2484	229	18	respectively	respectively	ADV
iajs-2484	229	19	𝑁-compact	𝑁-compact	PROPN
iajs-2484	229	20	)	)	PUNCT
iajs-2484	229	21	subset	subset	NOUN
iajs-2484	229	22	of	of	ADP
iajs-2484	229	23	𝑌	𝑌	PROPN
iajs-2484	229	24	,	,	PUNCT
iajs-2484	229	25	so	so	ADV
iajs-2484	229	26	𝑓	𝑓	PRON
iajs-2484	229	27	(	(	PUNCT
iajs-2484	229	28	k	k	NOUN
iajs-2484	229	29	)	)	PUNCT
iajs-2484	229	30	is	be	AUX
iajs-2484	229	31	𝜔-compact	𝜔-compact	PROPN
iajs-2484	229	32	(	(	PUNCT
iajs-2484	229	33	respectively	respectively	ADV
iajs-2484	229	34	𝑁-compact	𝑁-compact	PROPN
iajs-2484	229	35	)	)	PUNCT
iajs-2484	229	36	subset	subset	NOUN
iajs-2484	229	37	of	of	ADP
iajs-2484	229	38	𝑋	𝑋	PROPN
iajs-2484	229	39	(	(	PUNCT
iajs-2484	229	40	since	since	SCONJ
iajs-2484	229	41	𝑓	𝑓	PRON
iajs-2484	229	42	is	be	AUX
iajs-2484	229	43	an	an	DET
iajs-2484	229	44	𝜔∗∗-compact	𝜔∗∗-compact	ADJ
iajs-2484	229	45	(	(	PUNCT
iajs-2484	229	46	resp	resp	NOUN
iajs-2484	229	47	.	.	PUNCT
iajs-2484	230	1	𝑁∗∗-compact	𝑁∗∗-compact	NOUN
iajs-2484	230	2	)	)	PUNCT
iajs-2484	230	3	function	function	NOUN
iajs-2484	230	4	)	)	PUNCT
iajs-2484	230	5	)	)	PUNCT
iajs-2484	230	6	,	,	PUNCT
iajs-2484	230	7	and	and	CCONJ
iajs-2484	230	8	then	then	ADV
iajs-2484	230	9	it	it	PRON
iajs-2484	230	10	is	be	AUX
iajs-2484	230	11	compact	compact	ADJ
iajs-2484	230	12	subset	subset	NOUN
iajs-2484	230	13	of	of	ADP
iajs-2484	230	14	𝑋	𝑋	PROPN
iajs-2484	230	15	(	(	PUNCT
iajs-2484	230	16	by	by	ADP
iajs-2484	230	17	remark	remark	NOUN
iajs-2484	230	18	(	(	PUNCT
iajs-2484	230	19	1.2	1.2	NUM
iajs-2484	230	20	)	)	PUNCT
iajs-2484	230	21	)	)	PUNCT
iajs-2484	230	22	which	which	PRON
iajs-2484	230	23	is	be	AUX
iajs-2484	230	24	a	a	DET
iajs-2484	230	25	𝑇	𝑇	PROPN
iajs-2484	230	26	-space	-space	NOUN
iajs-2484	230	27	,	,	PUNCT
iajs-2484	230	28	so	so	SCONJ
iajs-2484	230	29	𝑓	𝑓	PRON
iajs-2484	230	30	(	(	PUNCT
iajs-2484	230	31	k	k	NOUN
iajs-2484	230	32	)	)	PUNCT
iajs-2484	230	33	is	be	AUX
iajs-2484	230	34	closed	close	VERB
iajs-2484	230	35	subset	subset	NOUN
iajs-2484	230	36	of	of	ADP
iajs-2484	230	37	𝑋	𝑋	PROPN
iajs-2484	230	38	(	(	PUNCT
iajs-2484	230	39	by	by	ADP
iajs-2484	230	40	remark	remark	NOUN
iajs-2484	230	41	(	(	PUNCT
iajs-2484	230	42	1.6	1.6	NUM
iajs-2484	230	43	)	)	PUNCT
iajs-2484	230	44	)	)	PUNCT
iajs-2484	230	45	,	,	PUNCT
iajs-2484	230	46	and	and	CCONJ
iajs-2484	230	47	by	by	ADP
iajs-2484	230	48	remark	remark	NOUN
iajs-2484	230	49	(	(	PUNCT
iajs-2484	230	50	1.2	1.2	NUM
iajs-2484	230	51	)	)	PUNCT
iajs-2484	230	52	)	)	PUNCT
iajs-2484	231	1	it	it	PRON
iajs-2484	231	2	is	be	AUX
iajs-2484	231	3	𝜔-closed	𝜔-close	VERB
iajs-2484	231	4	(	(	PUNCT
iajs-2484	231	5	respectively	respectively	ADV
iajs-2484	231	6	𝑁-closed	𝑁-closed	PROPN
iajs-2484	231	7	)	)	PUNCT
iajs-2484	231	8	subset	subset	NOUN
iajs-2484	231	9	of	of	ADP
iajs-2484	231	10	𝑋	𝑋	PROPN
iajs-2484	231	11	,	,	PUNCT
iajs-2484	231	12	so	so	ADV
iajs-2484	231	13	𝑓	𝑓	PRON
iajs-2484	231	14	is	be	AUX
iajs-2484	231	15	an	an	DET
iajs-2484	231	16	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	231	17	-	-	PUNCT
iajs-2484	231	18	function	function	NOUN
iajs-2484	231	19	(	(	PUNCT
iajs-2484	231	20	respectively	respectively	ADV
iajs-2484	231	21	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	231	22	-	-	PUNCT
iajs-2484	231	23	function	function	NOUN
iajs-2484	231	24	)	)	PUNCT
iajs-2484	231	25	.	.	PUNCT
iajs-2484	232	1	conversely	conversely	ADV
iajs-2484	232	2	,	,	PUNCT
iajs-2484	232	3	let	let	VERB
iajs-2484	232	4	k	k	PRON
iajs-2484	232	5	be	be	AUX
iajs-2484	232	6	a	a	DET
iajs-2484	232	7	𝜔-compact	𝜔-compact	PROPN
iajs-2484	232	8	(	(	PUNCT
iajs-2484	232	9	respectively	respectively	ADV
iajs-2484	232	10	𝑁-compact	𝑁-compact	PROPN
iajs-2484	232	11	)	)	PUNCT
iajs-2484	232	12	subset	subset	NOUN
iajs-2484	232	13	of	of	ADP
iajs-2484	232	14	𝑌	𝑌	PROPN
iajs-2484	232	15	,	,	PUNCT
iajs-2484	232	16	so	so	ADV
iajs-2484	232	17	𝑓	𝑓	PRON
iajs-2484	232	18	(	(	PUNCT
iajs-2484	232	19	k	k	NOUN
iajs-2484	232	20	)	)	PUNCT
iajs-2484	232	21	is	be	AUX
iajs-2484	232	22	𝜔-closed	𝜔-close	VERB
iajs-2484	232	23	(	(	PUNCT
iajs-2484	232	24	respectively	respectively	ADV
iajs-2484	232	25	𝑁-closed	𝑁-closed	PROPN
iajs-2484	232	26	)	)	PUNCT
iajs-2484	232	27	subset	subset	NOUN
iajs-2484	232	28	of	of	ADP
iajs-2484	232	29	𝑋	𝑋	PROPN
iajs-2484	232	30	(	(	PUNCT
iajs-2484	232	31	since	since	SCONJ
iajs-2484	232	32	𝑓	𝑓	PRON
iajs-2484	232	33	is	be	AUX
iajs-2484	232	34	an	an	DET
iajs-2484	232	35	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	232	36	-	-	PUNCT
iajs-2484	232	37	function	function	NOUN
iajs-2484	232	38	(	(	PUNCT
iajs-2484	232	39	respectively	respectively	ADV
iajs-2484	232	40	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	232	41	-	-	PUNCT
iajs-2484	232	42	function	function	NOUN
iajs-2484	232	43	)	)	PUNCT
iajs-2484	232	44	which	which	PRON
iajs-2484	232	45	is	be	AUX
iajs-2484	232	46	an	an	DET
iajs-2484	232	47	𝜔-compact	𝜔-compact	PROPN
iajs-2484	232	48	(	(	PUNCT
iajs-2484	232	49	respectively	respectively	ADV
iajs-2484	232	50	𝑁-compact	𝑁-compact	PROPN
iajs-2484	232	51	)	)	PUNCT
iajs-2484	232	52	space	space	NOUN
iajs-2484	232	53	,	,	PUNCT
iajs-2484	232	54	so	so	ADV
iajs-2484	232	55	𝑓	𝑓	PRON
iajs-2484	232	56	(	(	PUNCT
iajs-2484	232	57	k	k	NOUN
iajs-2484	232	58	)	)	PUNCT
iajs-2484	232	59	is	be	AUX
iajs-2484	232	60	a	a	DET
iajs-2484	232	61	𝜔-compact	𝜔-compact	PROPN
iajs-2484	232	62	(	(	PUNCT
iajs-2484	232	63	respectively	respectively	ADV
iajs-2484	232	64	𝑁-compact	𝑁-compact	PROPN
iajs-2484	232	65	)	)	PUNCT
iajs-2484	232	66	subset	subset	NOUN
iajs-2484	232	67	of	of	ADP
iajs-2484	232	68	𝑋(by	𝑋(by	PROPN
iajs-2484	232	69	remark	remark	NOUN
iajs-2484	232	70	(	(	PUNCT
iajs-2484	232	71	1.6	1.6	NUM
iajs-2484	232	72	)	)	PUNCT
iajs-2484	232	73	)	)	PUNCT
iajs-2484	232	74	,	,	PUNCT
iajs-2484	232	75	so	so	ADV
iajs-2484	232	76	𝑓	𝑓	PRON
iajs-2484	232	77	be	be	AUX
iajs-2484	232	78	an	an	DET
iajs-2484	232	79	𝜔∗∗-compact	𝜔∗∗-compact	VERB
iajs-2484	232	80	(	(	PUNCT
iajs-2484	232	81	respectively	respectively	ADV
iajs-2484	232	82	𝑁∗∗-compact	𝑁∗∗-compact	PROPN
iajs-2484	232	83	)	)	PUNCT
iajs-2484	232	84	function	function	NOUN
iajs-2484	232	85	.	.	PUNCT
iajs-2484	233	1	proposition	proposition	NOUN
iajs-2484	233	2	(	(	PUNCT
iajs-2484	233	3	1.39	1.39	NUM
iajs-2484	233	4	)	)	PUNCT
iajs-2484	233	5	the	the	DET
iajs-2484	233	6	composition	composition	NOUN
iajs-2484	233	7	between	between	ADP
iajs-2484	233	8	:	:	PUNCT
iajs-2484	233	9	1strongly	1strongly	NUM
iajs-2484	233	10	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	233	11	function	function	NOUN
iajs-2484	233	12	and	and	CCONJ
iajs-2484	233	13	m𝜔c	m𝜔c	NOUN
iajs-2484	233	14	-	-	PUNCT
iajs-2484	233	15	function	function	NOUN
iajs-2484	233	16	(	(	PUNCT
iajs-2484	233	17	respectively	respectively	ADV
iajs-2484	233	18	m𝑁c	m𝑁c	NOUN
iajs-2484	233	19	-	-	PUNCT
iajs-2484	233	20	function	function	NOUN
iajs-2484	233	21	)	)	PUNCT
iajs-2484	233	22	is	be	AUX
iajs-2484	233	23	mcfunction	mcfunction	NOUN
iajs-2484	233	24	.	.	PUNCT
iajs-2484	234	1	2𝜔-continuous	2𝜔-continuous	NUM
iajs-2484	234	2	(	(	PUNCT
iajs-2484	234	3	respectively	respectively	ADV
iajs-2484	234	4	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	234	5	)	)	PUNCT
iajs-2484	234	6	function	function	NOUN
iajs-2484	234	7	and	and	CCONJ
iajs-2484	234	8	𝜔mc	𝜔mc	NOUN
iajs-2484	234	9	-	-	PUNCT
iajs-2484	234	10	function	function	NOUN
iajs-2484	234	11	(	(	PUNCT
iajs-2484	234	12	respectively	respectively	ADV
iajs-2484	234	13	𝑁mcfunction	𝑁mcfunction	PROPN
iajs-2484	234	14	)	)	PUNCT
iajs-2484	234	15	is	be	AUX
iajs-2484	234	16	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	234	17	-	-	PUNCT
iajs-2484	234	18	function	function	NOUN
iajs-2484	234	19	(	(	PUNCT
iajs-2484	234	20	respectively	respectively	ADV
iajs-2484	234	21	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	234	22	-	-	PUNCT
iajs-2484	234	23	function	function	NOUN
iajs-2484	234	24	)	)	PUNCT
iajs-2484	234	25	.	.	PUNCT
iajs-2484	235	1	3strongly	3strongly	NUM
iajs-2484	235	2	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	235	3	(	(	PUNCT
iajs-2484	235	4	respectively	respectively	ADV
iajs-2484	235	5	strongly	strongly	ADV
iajs-2484	235	6	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	235	7	)	)	PUNCT
iajs-2484	235	8	function	function	NOUN
iajs-2484	235	9	and	and	CCONJ
iajs-2484	235	10	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	235	11	-	-	PUNCT
iajs-2484	235	12	function	function	NOUN
iajs-2484	235	13	(	(	PUNCT
iajs-2484	235	14	respectively	respectively	ADV
iajs-2484	235	15	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	235	16	-	-	PUNCT
iajs-2484	235	17	function	function	NOUN
iajs-2484	235	18	)	)	PUNCT
iajs-2484	235	19	is	be	AUX
iajs-2484	235	20	𝜔mc	𝜔mc	NOUN
iajs-2484	235	21	-	-	PUNCT
iajs-2484	235	22	function	function	NOUN
iajs-2484	235	23	(	(	PUNCT
iajs-2484	235	24	respectively	respectively	ADV
iajs-2484	235	25	𝑁mc	𝑁mc	NOUN
iajs-2484	235	26	-	-	PUNCT
iajs-2484	235	27	function	function	NOUN
iajs-2484	235	28	)	)	PUNCT
iajs-2484	235	29	.	.	PUNCT
iajs-2484	236	1	4strongly	4strongly	ADV
iajs-2484	236	2	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	236	3	(	(	PUNCT
iajs-2484	236	4	respectively	respectively	ADV
iajs-2484	236	5	strongly	strongly	ADV
iajs-2484	236	6	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	236	7	)	)	PUNCT
iajs-2484	236	8	function	function	NOUN
iajs-2484	236	9	and	and	CCONJ
iajs-2484	236	10	mc	mc	PROPN
iajs-2484	236	11	-	-	PUNCT
iajs-2484	236	12	function	function	PROPN
iajs-2484	236	13	is	be	AUX
iajs-2484	236	14	mc	mc	NOUN
iajs-2484	236	15	-	-	PUNCT
iajs-2484	236	16	function	function	NOUN
iajs-2484	236	17	.	.	PUNCT
iajs-2484	237	1	5strongly	5strongly	ADV
iajs-2484	237	2	𝜔-continuous	𝜔-continuous	ADV
iajs-2484	237	3	(	(	PUNCT
iajs-2484	237	4	respectively	respectively	ADV
iajs-2484	237	5	strongly	strongly	ADV
iajs-2484	237	6	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	237	7	)	)	PUNCT
iajs-2484	237	8	function	function	NOUN
iajs-2484	237	9	and	and	CCONJ
iajs-2484	237	10	𝜔mc	𝜔mc	NOUN
iajs-2484	237	11	-	-	PUNCT
iajs-2484	237	12	function	function	NOUN
iajs-2484	237	13	(	(	PUNCT
iajs-2484	237	14	respectively	respectively	ADV
iajs-2484	237	15	𝑁mc	𝑁mc	NOUN
iajs-2484	237	16	-	-	PUNCT
iajs-2484	237	17	function	function	NOUN
iajs-2484	237	18	)	)	PUNCT
iajs-2484	237	19	is	be	AUX
iajs-2484	237	20	𝜔mc	𝜔mc	NOUN
iajs-2484	237	21	-	-	PUNCT
iajs-2484	237	22	function	function	NOUN
iajs-2484	237	23	(	(	PUNCT
iajs-2484	237	24	respectively	respectively	ADV
iajs-2484	237	25	𝑁mc	𝑁mc	NOUN
iajs-2484	237	26	-	-	PUNCT
iajs-2484	237	27	function	function	NOUN
iajs-2484	237	28	)	)	PUNCT
iajs-2484	237	29	.	.	PUNCT
iajs-2484	238	1	6strongly	6strongly	ADV
iajs-2484	238	2	𝜔-continuous	𝜔-continuous	ADV
iajs-2484	238	3	(	(	PUNCT
iajs-2484	238	4	respectively	respectively	ADV
iajs-2484	238	5	strongly	strongly	ADV
iajs-2484	238	6	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	238	7	)	)	PUNCT
iajs-2484	238	8	function	function	NOUN
iajs-2484	238	9	and	and	CCONJ
iajs-2484	238	10	m𝜔c	m𝜔c	NOUN
iajs-2484	238	11	-	-	PUNCT
iajs-2484	238	12	function	function	NOUN
iajs-2484	238	13	(	(	PUNCT
iajs-2484	238	14	respectively	respectively	ADV
iajs-2484	238	15	m𝑁c	m𝑁c	NOUN
iajs-2484	238	16	-	-	PUNCT
iajs-2484	238	17	function	function	NOUN
iajs-2484	238	18	)	)	PUNCT
iajs-2484	238	19	is	be	AUX
iajs-2484	238	20	mc	mc	PROPN
iajs-2484	238	21	-	-	PUNCT
iajs-2484	238	22	function	function	NOUN
iajs-2484	238	23	.	.	PUNCT
iajs-2484	239	1	proof	proof	NOUN
iajs-2484	239	2	:	:	PUNCT
iajs-2484	239	3	1let	1let	NUM
iajs-2484	239	4	𝑓	𝑓	X
iajs-2484	239	5	:	:	PUNCT
iajs-2484	239	6	𝑋	𝑋	PROPN
iajs-2484	239	7	⟶	⟶	NOUN
iajs-2484	239	8	𝑌	𝑌	PROPN
iajs-2484	239	9	be	be	VERB
iajs-2484	239	10	strongly	strongly	ADV
iajs-2484	239	11	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	239	12	function	function	NOUN
iajs-2484	239	13	and	and	CCONJ
iajs-2484	239	14	𝒢	𝒢	PROPN
iajs-2484	239	15	:	:	PUNCT
iajs-2484	239	16	𝑌	𝑌	PROPN
iajs-2484	239	17	⟶	⟶	NOUN
iajs-2484	239	18	𝒵	𝒵	PRON
iajs-2484	239	19	be	be	VERB
iajs-2484	239	20	m𝜔c	m𝜔c	NOUN
iajs-2484	239	21	-	-	PUNCT
iajs-2484	239	22	function	function	NOUN
iajs-2484	239	23	(	(	PUNCT
iajs-2484	239	24	resp	resp	NOUN
iajs-2484	239	25	.	.	PUNCT
iajs-2484	240	1	m𝑁c	m𝑁c	NOUN
iajs-2484	240	2	-	-	PUNCT
iajs-2484	240	3	function	function	NOUN
iajs-2484	240	4	)	)	PUNCT
iajs-2484	240	5	,	,	PUNCT
iajs-2484	240	6	and	and	CCONJ
iajs-2484	240	7	let	let	VERB
iajs-2484	240	8	k	k	PRON
iajs-2484	240	9	be	be	AUX
iajs-2484	240	10	a	a	DET
iajs-2484	240	11	compact	compact	ADJ
iajs-2484	240	12	set	set	NOUN
iajs-2484	240	13	in	in	ADP
iajs-2484	240	14	𝒵	𝒵	PROPN
iajs-2484	240	15	,	,	PUNCT
iajs-2484	240	16	so	so	ADV
iajs-2484	240	17	𝒢	𝒢	PROPN
iajs-2484	240	18	k	k	PROPN
iajs-2484	240	19	is	be	AUX
iajs-2484	240	20	𝜔-closed	𝜔-close	VERB
iajs-2484	240	21	(	(	PUNCT
iajs-2484	240	22	respectively	respectively	ADV
iajs-2484	240	23	𝑁closed	𝑁close	VERB
iajs-2484	240	24	)	)	PUNCT
iajs-2484	240	25	set	set	NOUN
iajs-2484	240	26	in	in	ADP
iajs-2484	240	27	𝑌	𝑌	PROPN
iajs-2484	240	28	,	,	PUNCT
iajs-2484	241	1	so	so	ADV
iajs-2484	241	2	𝑓	𝑓	PRON
iajs-2484	241	3	(	(	PUNCT
iajs-2484	241	4	𝒢	𝒢	NOUN
iajs-2484	241	5	k	k	NOUN
iajs-2484	241	6	=	=	PUNCT
iajs-2484	241	7	𝒢	𝒢	NOUN
iajs-2484	241	8	∘	∘	NOUN
iajs-2484	241	9	𝑓	𝑓	PROPN
iajs-2484	241	10	(	(	PUNCT
iajs-2484	241	11	k	k	NOUN
iajs-2484	241	12	)	)	PUNCT
iajs-2484	241	13	is	be	AUX
iajs-2484	241	14	closed	close	VERB
iajs-2484	241	15	set	set	VERB
iajs-2484	241	16	in	in	ADP
iajs-2484	241	17	𝑋(since	𝑋(since	NOUN
iajs-2484	241	18	every	every	DET
iajs-2484	241	19	𝑁-closed	𝑁-closed	PROPN
iajs-2484	241	20	set	set	NOUN
iajs-2484	241	21	is	be	AUX
iajs-2484	241	22	𝜔-closed	𝜔-close	VERB
iajs-2484	241	23	)	)	PUNCT
iajs-2484	241	24	,	,	PUNCT
iajs-2484	241	25	so	so	ADV
iajs-2484	241	26	𝒢	𝒢	ADJ
iajs-2484	241	27	∘	∘	NOUN
iajs-2484	241	28	𝑓	𝑓	PROPN
iajs-2484	241	29	is	be	AUX
iajs-2484	241	30	mc	mc	NOUN
iajs-2484	241	31	-	-	PUNCT
iajs-2484	241	32	function	function	NOUN
iajs-2484	241	33	.	.	PUNCT
iajs-2484	241	34	  	  	SPACE
iajs-2484	242	1	185	185	NUM
iajs-2484	242	2	  	  	SPACE
iajs-2484	242	3	ibn	ibn	PROPN
iajs-2484	242	4	al	al	PROPN
iajs-2484	242	5	-	-	PUNCT
iajs-2484	242	6	haitham	haitham	PROPN
iajs-2484	242	7	jour	jour	X
iajs-2484	242	8	.	.	PROPN
iajs-2484	242	9	for	for	ADP
iajs-2484	242	10	pure	pure	ADJ
iajs-2484	242	11	&	&	CCONJ
iajs-2484	242	12	appl	appl	PROPN
iajs-2484	242	13	.	.	PUNCT
iajs-2484	243	1	sci	sci	PROPN
iajs-2484	243	2	.	.	PROPN
iajs-2484	244	1	33	33	NUM
iajs-2484	244	2	(	(	PUNCT
iajs-2484	244	3	3	3	NUM
iajs-2484	244	4	)	)	PUNCT
iajs-2484	244	5	2020	2020	NUM
iajs-2484	245	1	2let	2let	NUM
iajs-2484	245	2	𝑓	𝑓	X
iajs-2484	245	3	:	:	PUNCT
iajs-2484	245	4	𝑋	𝑋	PROPN
iajs-2484	245	5	⟶	⟶	NOUN
iajs-2484	245	6	𝑌	𝑌	PROPN
iajs-2484	245	7	be	be	VERB
iajs-2484	245	8	an	an	DET
iajs-2484	245	9	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	245	10	(	(	PUNCT
iajs-2484	245	11	respectively	respectively	ADV
iajs-2484	245	12	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	245	13	)	)	PUNCT
iajs-2484	245	14	function	function	NOUN
iajs-2484	245	15	and	and	CCONJ
iajs-2484	245	16	𝒢	𝒢	NOUN
iajs-2484	245	17	:	:	PUNCT
iajs-2484	245	18	𝑌	𝑌	PROPN
iajs-2484	245	19	⟶	⟶	NOUN
iajs-2484	245	20	𝒵	𝒵	PRON
iajs-2484	245	21	be	be	VERB
iajs-2484	245	22	𝜔mc	𝜔mc	ADJ
iajs-2484	245	23	-	-	PUNCT
iajs-2484	245	24	function	function	NOUN
iajs-2484	245	25	(	(	PUNCT
iajs-2484	245	26	respectively	respectively	ADV
iajs-2484	245	27	𝑁mc	𝑁mc	NOUN
iajs-2484	245	28	-	-	PUNCT
iajs-2484	245	29	function	function	NOUN
iajs-2484	245	30	)	)	PUNCT
iajs-2484	245	31	,	,	PUNCT
iajs-2484	245	32	and	and	CCONJ
iajs-2484	245	33	let	let	VERB
iajs-2484	245	34	k	k	PRON
iajs-2484	245	35	be	be	AUX
iajs-2484	245	36	an	an	DET
iajs-2484	245	37	𝜔-compact	𝜔-compact	PROPN
iajs-2484	245	38	(	(	PUNCT
iajs-2484	245	39	respectively	respectively	ADV
iajs-2484	245	40	𝑁compact	𝑁compact	PROPN
iajs-2484	245	41	)	)	PUNCT
iajs-2484	245	42	set	set	VERB
iajs-2484	245	43	in	in	ADP
iajs-2484	245	44	𝒵	𝒵	PROPN
iajs-2484	245	45	,	,	PUNCT
iajs-2484	245	46	so	so	ADV
iajs-2484	245	47	𝒢	𝒢	PROPN
iajs-2484	245	48	k	k	PROPN
iajs-2484	245	49	is	be	AUX
iajs-2484	245	50	closed	close	VERB
iajs-2484	245	51	set	set	VERB
iajs-2484	245	52	in	in	ADP
iajs-2484	245	53	𝑌	𝑌	PROPN
iajs-2484	245	54	,	,	PUNCT
iajs-2484	245	55	and	and	CCONJ
iajs-2484	245	56	then	then	ADV
iajs-2484	246	1	𝑓	𝑓	X
iajs-2484	246	2	(	(	PUNCT
iajs-2484	246	3	𝒢	𝒢	NOUN
iajs-2484	246	4	k	k	NOUN
iajs-2484	246	5	=	=	PUNCT
iajs-2484	246	6	𝒢	𝒢	NOUN
iajs-2484	246	7	∘	∘	NOUN
iajs-2484	246	8	𝑓	𝑓	PROPN
iajs-2484	246	9	(	(	PUNCT
iajs-2484	246	10	k	k	NOUN
iajs-2484	246	11	)	)	PUNCT
iajs-2484	246	12	is	be	AUX
iajs-2484	246	13	𝜔closed	𝜔close	VERB
iajs-2484	246	14	(	(	PUNCT
iajs-2484	246	15	respectively	respectively	ADV
iajs-2484	246	16	𝑁-closed	𝑁-closed	PROPN
iajs-2484	246	17	)	)	PUNCT
iajs-2484	246	18	set	set	NOUN
iajs-2484	246	19	in	in	ADP
iajs-2484	246	20	𝑋	𝑋	PROPN
iajs-2484	246	21	,	,	PUNCT
iajs-2484	246	22	so	so	SCONJ
iajs-2484	246	23	𝒢	𝒢	ADJ
iajs-2484	246	24	∘	∘	NOUN
iajs-2484	246	25	𝑓	𝑓	PROPN
iajs-2484	246	26	is	be	AUX
iajs-2484	246	27	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	246	28	-	-	PUNCT
iajs-2484	246	29	function	function	NOUN
iajs-2484	246	30	(	(	PUNCT
iajs-2484	246	31	resp	resp	NOUN
iajs-2484	246	32	.	.	PUNCT
iajs-2484	247	1	𝑁m𝑁c	𝑁m𝑁c	NOUN
iajs-2484	247	2	-	-	PUNCT
iajs-2484	247	3	function	function	NOUN
iajs-2484	247	4	)	)	PUNCT
iajs-2484	247	5	.	.	PUNCT
iajs-2484	248	1	3let	3let	NUM
iajs-2484	248	2	𝑓	𝑓	NOUN
iajs-2484	248	3	:	:	PUNCT
iajs-2484	248	4	𝑋	𝑋	PROPN
iajs-2484	248	5	⟶	⟶	NOUN
iajs-2484	248	6	𝑌	𝑌	PROPN
iajs-2484	248	7	be	be	VERB
iajs-2484	248	8	strongly	strongly	ADV
iajs-2484	248	9	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	248	10	(	(	PUNCT
iajs-2484	248	11	respectively	respectively	ADV
iajs-2484	248	12	strongly	strongly	ADV
iajs-2484	248	13	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	248	14	)	)	PUNCT
iajs-2484	248	15	function	function	NOUN
iajs-2484	248	16	and	and	CCONJ
iajs-2484	248	17	𝒢	𝒢	NOUN
iajs-2484	248	18	:	:	PUNCT
iajs-2484	248	19	𝑌	𝑌	PROPN
iajs-2484	248	20	⟶	⟶	NOUN
iajs-2484	248	21	𝒵	𝒵	PRON
iajs-2484	248	22	be	be	VERB
iajs-2484	248	23	an	an	DET
iajs-2484	248	24	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	248	25	-	-	PUNCT
iajs-2484	248	26	function	function	NOUN
iajs-2484	248	27	(	(	PUNCT
iajs-2484	248	28	respectively	respectively	ADV
iajs-2484	248	29	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	248	30	-	-	PUNCT
iajs-2484	248	31	function	function	NOUN
iajs-2484	248	32	)	)	PUNCT
iajs-2484	248	33	,	,	PUNCT
iajs-2484	248	34	and	and	CCONJ
iajs-2484	248	35	let	let	VERB
iajs-2484	248	36	k	k	PRON
iajs-2484	248	37	be	be	AUX
iajs-2484	248	38	an	an	DET
iajs-2484	248	39	𝜔-compact	𝜔-compact	PROPN
iajs-2484	248	40	(	(	PUNCT
iajs-2484	248	41	respectively	respectively	ADV
iajs-2484	248	42	𝑁-compact	𝑁-compact	PROPN
iajs-2484	248	43	)	)	PUNCT
iajs-2484	248	44	set	set	NOUN
iajs-2484	248	45	in	in	ADP
iajs-2484	248	46	𝒵	𝒵	PROPN
iajs-2484	248	47	,	,	PUNCT
iajs-2484	248	48	so	so	ADV
iajs-2484	248	49	𝒢	𝒢	PROPN
iajs-2484	248	50	k	k	PROPN
iajs-2484	248	51	is	be	AUX
iajs-2484	248	52	𝜔-closed	𝜔-close	VERB
iajs-2484	248	53	(	(	PUNCT
iajs-2484	248	54	respectively	respectively	ADV
iajs-2484	248	55	𝑁-closed	𝑁-closed	PROPN
iajs-2484	248	56	)	)	PUNCT
iajs-2484	248	57	set	set	NOUN
iajs-2484	248	58	in	in	ADP
iajs-2484	248	59	𝑌	𝑌	PROPN
iajs-2484	248	60	,	,	PUNCT
iajs-2484	249	1	so	so	ADV
iajs-2484	249	2	𝑓	𝑓	PRON
iajs-2484	249	3	(	(	PUNCT
iajs-2484	249	4	𝒢	𝒢	NOUN
iajs-2484	249	5	k	k	NOUN
iajs-2484	249	6	=	=	PUNCT
iajs-2484	249	7	𝒢	𝒢	NOUN
iajs-2484	249	8	∘	∘	NOUN
iajs-2484	249	9	𝑓	𝑓	PROPN
iajs-2484	249	10	(	(	PUNCT
iajs-2484	249	11	k	k	NOUN
iajs-2484	249	12	)	)	PUNCT
iajs-2484	249	13	is	be	AUX
iajs-2484	249	14	closed	close	VERB
iajs-2484	249	15	set	set	VERB
iajs-2484	249	16	in	in	ADP
iajs-2484	249	17	𝑋(since	𝑋(since	NOUN
iajs-2484	249	18	every	every	DET
iajs-2484	249	19	𝑁-closed	𝑁-closed	PROPN
iajs-2484	249	20	set	set	NOUN
iajs-2484	249	21	is	be	AUX
iajs-2484	249	22	𝜔-closed	𝜔-close	VERB
iajs-2484	249	23	)	)	PUNCT
iajs-2484	249	24	,	,	PUNCT
iajs-2484	249	25	so	so	ADV
iajs-2484	249	26	𝒢	𝒢	ADJ
iajs-2484	249	27	∘	∘	NOUN
iajs-2484	249	28	𝑓	𝑓	PROPN
iajs-2484	249	29	is	be	AUX
iajs-2484	249	30	𝜔mc	𝜔mc	NOUN
iajs-2484	249	31	-	-	PUNCT
iajs-2484	249	32	function	function	NOUN
iajs-2484	249	33	(	(	PUNCT
iajs-2484	249	34	respectively	respectively	ADV
iajs-2484	249	35	𝑁mc	𝑁mc	NOUN
iajs-2484	249	36	-	-	PUNCT
iajs-2484	249	37	function	function	NOUN
iajs-2484	249	38	)	)	PUNCT
iajs-2484	249	39	.	.	PUNCT
iajs-2484	250	1	4let	4let	PROPN
iajs-2484	250	2	𝑓	𝑓	X
iajs-2484	250	3	:	:	PUNCT
iajs-2484	250	4	𝑋	𝑋	PROPN
iajs-2484	250	5	⟶	⟶	NOUN
iajs-2484	250	6	𝑌	𝑌	PROPN
iajs-2484	250	7	be	be	VERB
iajs-2484	250	8	strongly	strongly	ADV
iajs-2484	250	9	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	250	10	(	(	PUNCT
iajs-2484	250	11	respectively	respectively	ADV
iajs-2484	250	12	strongly	strongly	ADV
iajs-2484	250	13	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	250	14	)	)	PUNCT
iajs-2484	250	15	function	function	NOUN
iajs-2484	250	16	and	and	CCONJ
iajs-2484	250	17	𝒢	𝒢	NOUN
iajs-2484	250	18	:	:	PUNCT
iajs-2484	250	19	𝑌	𝑌	PROPN
iajs-2484	250	20	⟶	⟶	NOUN
iajs-2484	250	21	𝒵	𝒵	PRON
iajs-2484	250	22	be	be	VERB
iajs-2484	250	23	mc	mc	NOUN
iajs-2484	250	24	-	-	PUNCT
iajs-2484	250	25	function	function	NOUN
iajs-2484	250	26	,	,	PUNCT
iajs-2484	250	27	and	and	CCONJ
iajs-2484	250	28	let	let	VERB
iajs-2484	250	29	k	k	PRON
iajs-2484	250	30	be	be	AUX
iajs-2484	250	31	a	a	DET
iajs-2484	250	32	compact	compact	ADJ
iajs-2484	250	33	set	set	NOUN
iajs-2484	250	34	in	in	ADP
iajs-2484	250	35	𝒵	𝒵	PROPN
iajs-2484	250	36	,	,	PUNCT
iajs-2484	250	37	so	so	ADV
iajs-2484	250	38	𝒢	𝒢	PROPN
iajs-2484	250	39	k	k	PROPN
iajs-2484	250	40	is	be	AUX
iajs-2484	250	41	closed	close	VERB
iajs-2484	250	42	set	set	VERB
iajs-2484	250	43	in	in	ADP
iajs-2484	250	44	𝑌	𝑌	PROPN
iajs-2484	250	45	,	,	PUNCT
iajs-2484	250	46	and	and	CCONJ
iajs-2484	250	47	by	by	ADP
iajs-2484	250	48	remark	remark	NOUN
iajs-2484	250	49	(	(	PUNCT
iajs-2484	250	50	1.2	1.2	NUM
iajs-2484	250	51	)	)	PUNCT
iajs-2484	250	52	it	it	PRON
iajs-2484	250	53	is	be	AUX
iajs-2484	250	54	𝜔-closed	𝜔-close	VERB
iajs-2484	250	55	(	(	PUNCT
iajs-2484	250	56	respectively	respectively	ADV
iajs-2484	250	57	𝑁-closed	𝑁-closed	PROPN
iajs-2484	250	58	)	)	PUNCT
iajs-2484	250	59	set	set	NOUN
iajs-2484	250	60	in	in	ADP
iajs-2484	250	61	𝑌	𝑌	PROPN
iajs-2484	250	62	,	,	PUNCT
iajs-2484	251	1	so	so	ADV
iajs-2484	251	2	𝑓	𝑓	PRON
iajs-2484	251	3	(	(	PUNCT
iajs-2484	251	4	𝒢	𝒢	NOUN
iajs-2484	251	5	k	k	NOUN
iajs-2484	251	6	=	=	PUNCT
iajs-2484	251	7	𝒢	𝒢	NOUN
iajs-2484	251	8	∘	∘	NOUN
iajs-2484	251	9	𝑓	𝑓	PROPN
iajs-2484	251	10	(	(	PUNCT
iajs-2484	251	11	k	k	NOUN
iajs-2484	251	12	)	)	PUNCT
iajs-2484	251	13	is	be	AUX
iajs-2484	251	14	closed	close	VERB
iajs-2484	251	15	set	set	VERB
iajs-2484	251	16	in	in	ADP
iajs-2484	251	17	𝑋	𝑋	PROPN
iajs-2484	251	18	,	,	PUNCT
iajs-2484	251	19	so	so	SCONJ
iajs-2484	251	20	𝒢	𝒢	ADJ
iajs-2484	251	21	∘	∘	NOUN
iajs-2484	251	22	𝑓	𝑓	PROPN
iajs-2484	251	23	is	be	AUX
iajs-2484	251	24	mc	mc	NOUN
iajs-2484	251	25	-	-	PUNCT
iajs-2484	251	26	function	function	NOUN
iajs-2484	251	27	.	.	PUNCT
iajs-2484	252	1	5let	5let	NUM
iajs-2484	252	2	𝑓	𝑓	NOUN
iajs-2484	252	3	:	:	PUNCT
iajs-2484	252	4	𝑋	𝑋	PROPN
iajs-2484	252	5	⟶	⟶	NOUN
iajs-2484	252	6	𝑌	𝑌	PROPN
iajs-2484	252	7	be	be	VERB
iajs-2484	252	8	strongly	strongly	ADV
iajs-2484	252	9	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	252	10	(	(	PUNCT
iajs-2484	252	11	respectively	respectively	ADV
iajs-2484	252	12	strongly	strongly	ADV
iajs-2484	252	13	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	252	14	)	)	PUNCT
iajs-2484	252	15	function	function	NOUN
iajs-2484	252	16	and	and	CCONJ
iajs-2484	252	17	𝒢	𝒢	NOUN
iajs-2484	252	18	:	:	PUNCT
iajs-2484	252	19	𝑌	𝑌	PROPN
iajs-2484	252	20	⟶	⟶	NOUN
iajs-2484	252	21	𝒵	𝒵	PRON
iajs-2484	252	22	be	be	VERB
iajs-2484	252	23	𝜔mc	𝜔mc	ADJ
iajs-2484	252	24	-	-	PUNCT
iajs-2484	252	25	function	function	NOUN
iajs-2484	252	26	(	(	PUNCT
iajs-2484	252	27	respectively	respectively	ADV
iajs-2484	252	28	𝑁mc	𝑁mc	NOUN
iajs-2484	252	29	-	-	PUNCT
iajs-2484	252	30	function	function	NOUN
iajs-2484	252	31	)	)	PUNCT
iajs-2484	252	32	,	,	PUNCT
iajs-2484	252	33	and	and	CCONJ
iajs-2484	252	34	let	let	VERB
iajs-2484	252	35	k	k	PRON
iajs-2484	252	36	be	be	AUX
iajs-2484	252	37	an	an	DET
iajs-2484	252	38	𝜔-compact	𝜔-compact	PROPN
iajs-2484	252	39	(	(	PUNCT
iajs-2484	252	40	respectively	respectively	ADV
iajs-2484	252	41	𝑁-compact	𝑁-compact	PROPN
iajs-2484	252	42	)	)	PUNCT
iajs-2484	252	43	set	set	NOUN
iajs-2484	252	44	in	in	ADP
iajs-2484	252	45	𝒵	𝒵	PROPN
iajs-2484	252	46	,	,	PUNCT
iajs-2484	252	47	so	so	ADV
iajs-2484	252	48	𝒢	𝒢	PROPN
iajs-2484	252	49	k	k	PROPN
iajs-2484	252	50	is	be	AUX
iajs-2484	252	51	closed	close	VERB
iajs-2484	252	52	set	set	VERB
iajs-2484	252	53	in	in	ADP
iajs-2484	252	54	𝑌	𝑌	PROPN
iajs-2484	252	55	,	,	PUNCT
iajs-2484	252	56	and	and	CCONJ
iajs-2484	252	57	by	by	ADP
iajs-2484	252	58	remark	remark	NOUN
iajs-2484	252	59	(	(	PUNCT
iajs-2484	252	60	1.2	1.2	NUM
iajs-2484	252	61	)	)	PUNCT
iajs-2484	252	62	it	it	PRON
iajs-2484	252	63	is	be	AUX
iajs-2484	252	64	𝜔closed	𝜔close	VERB
iajs-2484	252	65	(	(	PUNCT
iajs-2484	252	66	respectively	respectively	ADV
iajs-2484	252	67	𝑁-closed	𝑁-closed	PROPN
iajs-2484	252	68	)	)	PUNCT
iajs-2484	252	69	set	set	NOUN
iajs-2484	252	70	in	in	ADP
iajs-2484	252	71	𝑌	𝑌	PROPN
iajs-2484	252	72	,	,	PUNCT
iajs-2484	253	1	so	so	ADV
iajs-2484	253	2	𝑓	𝑓	PRON
iajs-2484	253	3	(	(	PUNCT
iajs-2484	253	4	𝒢	𝒢	NOUN
iajs-2484	253	5	k	k	NOUN
iajs-2484	253	6	=	=	PUNCT
iajs-2484	253	7	𝒢	𝒢	NOUN
iajs-2484	253	8	∘	∘	NOUN
iajs-2484	253	9	𝑓	𝑓	PROPN
iajs-2484	253	10	(	(	PUNCT
iajs-2484	253	11	k	k	NOUN
iajs-2484	253	12	)	)	PUNCT
iajs-2484	253	13	is	be	AUX
iajs-2484	253	14	closed	close	VERB
iajs-2484	253	15	set	set	VERB
iajs-2484	253	16	in	in	ADP
iajs-2484	253	17	𝑋	𝑋	PROPN
iajs-2484	253	18	,	,	PUNCT
iajs-2484	253	19	so	so	SCONJ
iajs-2484	253	20	𝒢	𝒢	ADJ
iajs-2484	253	21	∘	∘	NOUN
iajs-2484	253	22	𝑓	𝑓	PROPN
iajs-2484	253	23	is	be	AUX
iajs-2484	253	24	𝜔mc	𝜔mc	NOUN
iajs-2484	253	25	-	-	PUNCT
iajs-2484	253	26	function	function	NOUN
iajs-2484	253	27	(	(	PUNCT
iajs-2484	253	28	resp	resp	NOUN
iajs-2484	253	29	.	.	PUNCT
iajs-2484	254	1	𝑁mc	𝑁mc	NOUN
iajs-2484	254	2	-	-	PUNCT
iajs-2484	254	3	function	function	NOUN
iajs-2484	254	4	)	)	PUNCT
iajs-2484	254	5	.	.	PUNCT
iajs-2484	255	1	6let	6let	NUM
iajs-2484	255	2	𝑓	𝑓	X
iajs-2484	255	3	:	:	PUNCT
iajs-2484	255	4	𝑋	𝑋	PROPN
iajs-2484	255	5	⟶	⟶	NOUN
iajs-2484	255	6	𝑌	𝑌	PROPN
iajs-2484	255	7	be	be	VERB
iajs-2484	255	8	strongly	strongly	ADV
iajs-2484	255	9	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	255	10	(	(	PUNCT
iajs-2484	255	11	respectively	respectively	ADV
iajs-2484	255	12	strongly	strongly	ADV
iajs-2484	255	13	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	255	14	)	)	PUNCT
iajs-2484	255	15	function	function	NOUN
iajs-2484	255	16	and	and	CCONJ
iajs-2484	255	17	𝒢	𝒢	NOUN
iajs-2484	255	18	:	:	PUNCT
iajs-2484	255	19	𝑌	𝑌	PROPN
iajs-2484	255	20	⟶	⟶	NOUN
iajs-2484	255	21	𝒵	𝒵	PRON
iajs-2484	255	22	be	be	VERB
iajs-2484	255	23	m𝜔c	m𝜔c	NOUN
iajs-2484	255	24	-	-	PUNCT
iajs-2484	255	25	function	function	NOUN
iajs-2484	255	26	(	(	PUNCT
iajs-2484	255	27	respectively	respectively	ADV
iajs-2484	255	28	m𝑁c	m𝑁c	NOUN
iajs-2484	255	29	-	-	PUNCT
iajs-2484	255	30	function	function	NOUN
iajs-2484	255	31	)	)	PUNCT
iajs-2484	255	32	,	,	PUNCT
iajs-2484	255	33	and	and	CCONJ
iajs-2484	255	34	let	let	VERB
iajs-2484	255	35	k	k	PRON
iajs-2484	255	36	be	be	AUX
iajs-2484	255	37	a	a	DET
iajs-2484	255	38	compact	compact	ADJ
iajs-2484	255	39	set	set	NOUN
iajs-2484	255	40	in	in	ADP
iajs-2484	255	41	𝒵	𝒵	PROPN
iajs-2484	255	42	,	,	PUNCT
iajs-2484	255	43	so	so	ADV
iajs-2484	255	44	𝒢	𝒢	PROPN
iajs-2484	255	45	k	k	PROPN
iajs-2484	255	46	is	be	AUX
iajs-2484	255	47	𝜔-closed	𝜔-close	VERB
iajs-2484	255	48	(	(	PUNCT
iajs-2484	255	49	respectively	respectively	ADV
iajs-2484	255	50	𝑁-closed	𝑁-closed	PROPN
iajs-2484	255	51	)	)	PUNCT
iajs-2484	255	52	set	set	NOUN
iajs-2484	255	53	in	in	ADP
iajs-2484	255	54	𝑌	𝑌	PROPN
iajs-2484	255	55	,	,	PUNCT
iajs-2484	256	1	so	so	ADV
iajs-2484	256	2	𝑓	𝑓	PRON
iajs-2484	256	3	(	(	PUNCT
iajs-2484	256	4	𝒢	𝒢	NOUN
iajs-2484	256	5	k	k	NOUN
iajs-2484	256	6	=	=	PUNCT
iajs-2484	256	7	𝒢	𝒢	NOUN
iajs-2484	256	8	∘	∘	NOUN
iajs-2484	256	9	𝑓	𝑓	PROPN
iajs-2484	256	10	(	(	PUNCT
iajs-2484	256	11	k	k	NOUN
iajs-2484	256	12	)	)	PUNCT
iajs-2484	256	13	is	be	AUX
iajs-2484	256	14	closed	close	VERB
iajs-2484	256	15	set	set	VERB
iajs-2484	256	16	in	in	ADP
iajs-2484	256	17	𝑋	𝑋	PROPN
iajs-2484	256	18	(	(	PUNCT
iajs-2484	256	19	since	since	SCONJ
iajs-2484	256	20	every	every	DET
iajs-2484	256	21	𝑁-closed	𝑁-closed	PROPN
iajs-2484	256	22	set	set	NOUN
iajs-2484	256	23	is	be	AUX
iajs-2484	256	24	𝜔-closed	𝜔-close	VERB
iajs-2484	256	25	)	)	PUNCT
iajs-2484	256	26	,	,	PUNCT
iajs-2484	256	27	so	so	ADV
iajs-2484	256	28	𝒢	𝒢	ADJ
iajs-2484	256	29	∘	∘	NOUN
iajs-2484	256	30	𝑓	𝑓	PROPN
iajs-2484	256	31	is	be	AUX
iajs-2484	256	32	mc	mc	NOUN
iajs-2484	256	33	-	-	PUNCT
iajs-2484	256	34	function	function	NOUN
iajs-2484	256	35	.	.	PUNCT
iajs-2484	257	1	proposition	proposition	NOUN
iajs-2484	257	2	(	(	PUNCT
iajs-2484	257	3	1.40	1.40	NUM
iajs-2484	257	4	)	)	PUNCT
iajs-2484	257	5	if	if	SCONJ
iajs-2484	257	6	𝑓	𝑓	X
iajs-2484	257	7	:	:	PUNCT
iajs-2484	257	8	𝑋	𝑋	PROPN
iajs-2484	257	9	⟶	⟶	NOUN
iajs-2484	257	10	𝑌	𝑌	PROPN
iajs-2484	257	11	and	and	CCONJ
iajs-2484	257	12	𝒢	𝒢	PROPN
iajs-2484	257	13	:	:	PUNCT
iajs-2484	257	14	𝑌	𝑌	PROPN
iajs-2484	257	15	⟶	⟶	NOUN
iajs-2484	257	16	𝒵	𝒵	NOUN
iajs-2484	257	17	are	be	AUX
iajs-2484	257	18	two	two	NUM
iajs-2484	257	19	functions	function	NOUN
iajs-2484	257	20	:	:	PUNCT
iajs-2484	257	21	1if	1if	NOUN
iajs-2484	257	22	𝑓	𝑓	PROPN
iajs-2484	257	23	is	be	AUX
iajs-2484	257	24	m𝜔c	m𝜔c	NOUN
iajs-2484	257	25	-	-	PUNCT
iajs-2484	257	26	function	function	NOUN
iajs-2484	257	27	(	(	PUNCT
iajs-2484	257	28	respectively	respectively	ADV
iajs-2484	257	29	m𝑁c	m𝑁c	NOUN
iajs-2484	257	30	-	-	PUNCT
iajs-2484	257	31	function	function	NOUN
iajs-2484	257	32	)	)	PUNCT
iajs-2484	257	33	and	and	CCONJ
iajs-2484	257	34	𝒢	𝒢	PROPN
iajs-2484	257	35	is	be	AUX
iajs-2484	257	36	strongly	strongly	ADV
iajs-2484	257	37	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	257	38	function	function	NOUN
iajs-2484	257	39	where	where	SCONJ
iajs-2484	257	40	𝑌	𝑌	PROPN
iajs-2484	257	41	is	be	AUX
iajs-2484	257	42	a	a	DET
iajs-2484	257	43	compact	compact	ADJ
iajs-2484	257	44	space	space	NOUN
iajs-2484	257	45	,	,	PUNCT
iajs-2484	257	46	then	then	ADV
iajs-2484	257	47	𝒢	𝒢	PROPN
iajs-2484	257	48	∘	∘	NOUN
iajs-2484	257	49	𝑓	𝑓	PRON
iajs-2484	257	50	is	be	AUX
iajs-2484	257	51	an	an	DET
iajs-2484	257	52	𝜔-irresolute	𝜔-irresolute	NOUN
iajs-2484	257	53	(	(	PUNCT
iajs-2484	257	54	respectively	respectively	ADV
iajs-2484	257	55	𝑁-irresolute	𝑁-irresolute	PROPN
iajs-2484	257	56	)	)	PUNCT
iajs-2484	257	57	function	function	NOUN
iajs-2484	257	58	.	.	PUNCT
iajs-2484	258	1	2if	2if	NOUN
iajs-2484	258	2	𝑓	𝑓	PROPN
iajs-2484	258	3	is	be	AUX
iajs-2484	258	4	𝜔mc	𝜔mc	NOUN
iajs-2484	258	5	-	-	PUNCT
iajs-2484	258	6	function	function	NOUN
iajs-2484	258	7	(	(	PUNCT
iajs-2484	258	8	respectively	respectively	ADV
iajs-2484	258	9	𝑁mc	𝑁mc	NOUN
iajs-2484	258	10	-	-	PUNCT
iajs-2484	258	11	function	function	NOUN
iajs-2484	258	12	)	)	PUNCT
iajs-2484	258	13	and	and	CCONJ
iajs-2484	258	14	𝒢	𝒢	PROPN
iajs-2484	258	15	is	be	AUX
iajs-2484	258	16	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	258	17	(	(	PUNCT
iajs-2484	258	18	respectively	respectively	ADV
iajs-2484	258	19	𝑁continuous	𝑁continuous	ADJ
iajs-2484	258	20	)	)	PUNCT
iajs-2484	258	21	function	function	NOUN
iajs-2484	258	22	where	where	SCONJ
iajs-2484	258	23	𝑌	𝑌	PROPN
iajs-2484	258	24	is	be	AUX
iajs-2484	258	25	a	a	DET
iajs-2484	258	26	𝜔-compact	𝜔-compact	PROPN
iajs-2484	258	27	(	(	PUNCT
iajs-2484	258	28	respectively	respectively	ADV
iajs-2484	258	29	𝑁-compact	𝑁-compact	PROPN
iajs-2484	258	30	)	)	PUNCT
iajs-2484	258	31	space	space	NOUN
iajs-2484	258	32	,	,	PUNCT
iajs-2484	258	33	then	then	ADV
iajs-2484	258	34	𝒢	𝒢	PROPN
iajs-2484	258	35	∘	∘	NOUN
iajs-2484	258	36	𝑓	𝑓	PRON
iajs-2484	258	37	is	be	AUX
iajs-2484	258	38	a	a	DET
iajs-2484	258	39	continuous	continuous	ADJ
iajs-2484	258	40	function	function	NOUN
iajs-2484	258	41	.	.	PUNCT
iajs-2484	259	1	3if	3if	NOUN
iajs-2484	259	2	𝑓	𝑓	PROPN
iajs-2484	259	3	is	be	AUX
iajs-2484	259	4	𝜔m𝜔c	𝜔m𝜔c	NOUN
iajs-2484	259	5	-	-	PUNCT
iajs-2484	259	6	function	function	NOUN
iajs-2484	259	7	(	(	PUNCT
iajs-2484	259	8	respectively	respectively	ADV
iajs-2484	259	9	𝑁m𝑁c	𝑁m𝑁c	PROPN
iajs-2484	259	10	-	-	PUNCT
iajs-2484	259	11	function	function	NOUN
iajs-2484	259	12	)	)	PUNCT
iajs-2484	259	13	and	and	CCONJ
iajs-2484	259	14	𝒢	𝒢	PROPN
iajs-2484	259	15	is	be	AUX
iajs-2484	259	16	strongly	strongly	ADV
iajs-2484	259	17	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	259	18	(	(	PUNCT
iajs-2484	259	19	respectively	respectively	ADV
iajs-2484	259	20	strongly	strongly	ADV
iajs-2484	259	21	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	259	22	)	)	PUNCT
iajs-2484	259	23	function	function	NOUN
iajs-2484	259	24	where	where	SCONJ
iajs-2484	259	25	𝑌	𝑌	PROPN
iajs-2484	259	26	is	be	AUX
iajs-2484	259	27	an	an	DET
iajs-2484	259	28	𝜔-compact	𝜔-compact	PROPN
iajs-2484	259	29	(	(	PUNCT
iajs-2484	259	30	respectively	respectively	ADV
iajs-2484	259	31	𝑁compact	𝑁compact	PROPN
iajs-2484	259	32	)	)	PUNCT
iajs-2484	259	33	space	space	NOUN
iajs-2484	259	34	,	,	PUNCT
iajs-2484	259	35	then	then	ADV
iajs-2484	259	36	𝒢	𝒢	PROPN
iajs-2484	259	37	∘	∘	NOUN
iajs-2484	259	38	𝑓	𝑓	PRON
iajs-2484	259	39	is	be	AUX
iajs-2484	259	40	an	an	DET
iajs-2484	259	41	𝜔-irresolute	𝜔-irresolute	NOUN
iajs-2484	259	42	(	(	PUNCT
iajs-2484	259	43	respectively	respectively	ADV
iajs-2484	259	44	𝑁-irresolute	𝑁-irresolute	PROPN
iajs-2484	259	45	)	)	PUNCT
iajs-2484	259	46	function	function	NOUN
iajs-2484	259	47	.	.	PUNCT
iajs-2484	260	1	4if	4if	NOUN
iajs-2484	261	1	𝑓	𝑓	PRON
iajs-2484	261	2	is	be	AUX
iajs-2484	261	3	mc	mc	NOUN
iajs-2484	261	4	-	-	PUNCT
iajs-2484	261	5	function	function	NOUN
iajs-2484	261	6	and	and	CCONJ
iajs-2484	261	7	𝒢	𝒢	PROPN
iajs-2484	261	8	is	be	AUX
iajs-2484	261	9	𝜔mc	𝜔mc	NOUN
iajs-2484	261	10	-	-	PUNCT
iajs-2484	261	11	function	function	NOUN
iajs-2484	261	12	(	(	PUNCT
iajs-2484	261	13	respectively	respectively	ADV
iajs-2484	261	14	𝑁mc	𝑁mc	NOUN
iajs-2484	261	15	-	-	PUNCT
iajs-2484	261	16	function	function	NOUN
iajs-2484	261	17	)	)	PUNCT
iajs-2484	261	18	function	function	NOUN
iajs-2484	261	19	where	where	SCONJ
iajs-2484	261	20	𝑌	𝑌	PROPN
iajs-2484	261	21	is	be	AUX
iajs-2484	261	22	a	a	DET
iajs-2484	261	23	compact	compact	ADJ
iajs-2484	261	24	space	space	NOUN
iajs-2484	261	25	,	,	PUNCT
iajs-2484	261	26	then	then	ADV
iajs-2484	261	27	𝒢	𝒢	PROPN
iajs-2484	261	28	∘	∘	NOUN
iajs-2484	261	29	𝑓	𝑓	PROPN
iajs-2484	261	30	is	be	AUX
iajs-2484	261	31	𝜔mc	𝜔mc	NOUN
iajs-2484	261	32	-	-	PUNCT
iajs-2484	261	33	function	function	NOUN
iajs-2484	261	34	(	(	PUNCT
iajs-2484	261	35	respectively	respectively	ADV
iajs-2484	261	36	𝑁mc	𝑁mc	NOUN
iajs-2484	261	37	-	-	PUNCT
iajs-2484	261	38	function	function	NOUN
iajs-2484	261	39	)	)	PUNCT
iajs-2484	261	40	.	.	PUNCT
iajs-2484	262	1	5if	5if	NOUN
iajs-2484	262	2	𝑓	𝑓	PRON
iajs-2484	262	3	is	be	AUX
iajs-2484	262	4	a	a	DET
iajs-2484	262	5	compact	compact	ADJ
iajs-2484	262	6	function	function	NOUN
iajs-2484	262	7	and	and	CCONJ
iajs-2484	262	8	𝒢	𝒢	NOUN
iajs-2484	262	9	is	be	AUX
iajs-2484	262	10	𝜔mc	𝜔mc	NOUN
iajs-2484	262	11	-	-	PUNCT
iajs-2484	262	12	function	function	NOUN
iajs-2484	262	13	(	(	PUNCT
iajs-2484	262	14	respectively	respectively	ADV
iajs-2484	262	15	𝑁mc	𝑁mc	NOUN
iajs-2484	262	16	-	-	PUNCT
iajs-2484	262	17	function	function	NOUN
iajs-2484	262	18	)	)	PUNCT
iajs-2484	262	19	where	where	SCONJ
iajs-2484	262	20	𝑌	𝑌	PROPN
iajs-2484	262	21	is	be	AUX
iajs-2484	262	22	a	a	DET
iajs-2484	262	23	compact	compact	ADJ
iajs-2484	262	24	space	space	NOUN
iajs-2484	262	25	,	,	PUNCT
iajs-2484	262	26	then	then	ADV
iajs-2484	262	27	𝒢	𝒢	PROPN
iajs-2484	262	28	∘	∘	NOUN
iajs-2484	262	29	𝑓	𝑓	PRON
iajs-2484	262	30	is	be	AUX
iajs-2484	262	31	a	a	DET
iajs-2484	262	32	𝜔-compact	𝜔-compact	PROPN
iajs-2484	262	33	(	(	PUNCT
iajs-2484	262	34	respectively	respectively	ADV
iajs-2484	262	35	𝑁-compact	𝑁-compact	PROPN
iajs-2484	262	36	)	)	PUNCT
iajs-2484	262	37	function	function	NOUN
iajs-2484	262	38	6if	6if	NOUN
iajs-2484	262	39	𝑓	𝑓	PROPN
iajs-2484	262	40	is	be	AUX
iajs-2484	262	41	mc	mc	NOUN
iajs-2484	262	42	-	-	PUNCT
iajs-2484	262	43	function	function	NOUN
iajs-2484	262	44	and	and	CCONJ
iajs-2484	262	45	𝒢	𝒢	NOUN
iajs-2484	262	46	is	be	AUX
iajs-2484	262	47	strongly	strongly	ADV
iajs-2484	262	48	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	262	49	(	(	PUNCT
iajs-2484	262	50	respectively	respectively	ADV
iajs-2484	262	51	strongly	strongly	ADV
iajs-2484	262	52	𝑁-continuous	𝑁-continuous	ADJ
iajs-2484	262	53	)	)	PUNCT
iajs-2484	262	54	function	function	NOUN
iajs-2484	262	55	where	where	SCONJ
iajs-2484	262	56	𝑌	𝑌	PROPN
iajs-2484	262	57	is	be	AUX
iajs-2484	262	58	a	a	DET
iajs-2484	262	59	c	c	NOUN
iajs-2484	262	60	-	-	PUNCT
iajs-2484	262	61	c	c	NOUN
iajs-2484	262	62	space	space	NOUN
iajs-2484	262	63	,	,	PUNCT
iajs-2484	262	64	then	then	ADV
iajs-2484	262	65	𝒢	𝒢	PROPN
iajs-2484	262	66	∘	∘	NOUN
iajs-2484	262	67	𝑓	𝑓	PRON
iajs-2484	262	68	is	be	AUX
iajs-2484	262	69	strongly	strongly	ADV
iajs-2484	262	70	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	262	71	(	(	PUNCT
iajs-2484	262	72	respectively	respectively	ADV
iajs-2484	262	73	strongly	strongly	ADV
iajs-2484	262	74	𝑁continuous	𝑁continuous	ADJ
iajs-2484	262	75	)	)	PUNCT
iajs-2484	262	76	function	function	NOUN
iajs-2484	262	77	.	.	PUNCT
iajs-2484	263	1	7if	7if	ADJ
iajs-2484	263	2	𝑓	𝑓	PRON
iajs-2484	263	3	is	be	AUX
iajs-2484	263	4	m𝜔c	m𝜔c	NOUN
iajs-2484	263	5	-	-	PUNCT
iajs-2484	263	6	function	function	NOUN
iajs-2484	263	7	(	(	PUNCT
iajs-2484	263	8	respectively	respectively	ADV
iajs-2484	263	9	m𝑁c	m𝑁c	NOUN
iajs-2484	263	10	-	-	PUNCT
iajs-2484	263	11	function	function	NOUN
iajs-2484	263	12	)	)	PUNCT
iajs-2484	263	13	and	and	CCONJ
iajs-2484	263	14	𝒢	𝒢	PROPN
iajs-2484	263	15	is	be	AUX
iajs-2484	263	16	strongly	strongly	ADV
iajs-2484	263	17	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	263	18	function	function	NOUN
iajs-2484	263	19	where	where	SCONJ
iajs-2484	263	20	𝑌	𝑌	PROPN
iajs-2484	263	21	is	be	AUX
iajs-2484	263	22	a	a	DET
iajs-2484	263	23	c	c	NOUN
iajs-2484	263	24	-	-	PUNCT
iajs-2484	263	25	c	c	NOUN
iajs-2484	263	26	space	space	NOUN
iajs-2484	263	27	,	,	PUNCT
iajs-2484	263	28	then	then	ADV
iajs-2484	263	29	𝒢	𝒢	PROPN
iajs-2484	263	30	∘	∘	NOUN
iajs-2484	263	31	𝑓	𝑓	PRON
iajs-2484	263	32	is	be	AUX
iajs-2484	263	33	an	an	DET
iajs-2484	263	34	𝜔-irresolute	𝜔-irresolute	NOUN
iajs-2484	263	35	(	(	PUNCT
iajs-2484	263	36	respectively	respectively	ADV
iajs-2484	263	37	𝑁-irresolute	𝑁-irresolute	PROPN
iajs-2484	263	38	)	)	PUNCT
iajs-2484	263	39	function	function	NOUN
iajs-2484	263	40	.	.	PUNCT
iajs-2484	264	1	and	and	CCONJ
iajs-2484	264	2	there	there	PRON
iajs-2484	264	3	are	be	VERB
iajs-2484	264	4	many	many	ADJ
iajs-2484	264	5	other	other	ADJ
iajs-2484	264	6	cases	case	NOUN
iajs-2484	264	7	.	.	PUNCT
iajs-2484	264	8	  	  	SPACE
iajs-2484	265	1	186	186	NUM
iajs-2484	265	2	  	  	SPACE
iajs-2484	265	3	ibn	ibn	PROPN
iajs-2484	265	4	al	al	PROPN
iajs-2484	265	5	-	-	PUNCT
iajs-2484	265	6	haitham	haitham	PROPN
iajs-2484	265	7	jour	jour	X
iajs-2484	265	8	.	.	PROPN
iajs-2484	265	9	for	for	ADP
iajs-2484	265	10	pure	pure	ADJ
iajs-2484	265	11	&	&	CCONJ
iajs-2484	265	12	appl	appl	PROPN
iajs-2484	265	13	.	.	PUNCT
iajs-2484	266	1	sci	sci	PROPN
iajs-2484	266	2	.	.	PROPN
iajs-2484	267	1	33	33	NUM
iajs-2484	267	2	(	(	PUNCT
iajs-2484	267	3	3	3	NUM
iajs-2484	267	4	)	)	PUNCT
iajs-2484	267	5	2020	2020	NUM
iajs-2484	268	1	proof	proof	NOUN
iajs-2484	268	2	:	:	PUNCT
iajs-2484	268	3	1let	1let	NUM
iajs-2484	268	4	𝑓	𝑓	PRON
iajs-2484	268	5	be	be	AUX
iajs-2484	268	6	an	an	DET
iajs-2484	268	7	m𝜔c	m𝜔c	NOUN
iajs-2484	268	8	-	-	PUNCT
iajs-2484	268	9	function	function	NOUN
iajs-2484	268	10	(	(	PUNCT
iajs-2484	268	11	respectively	respectively	ADV
iajs-2484	268	12	m𝑁c	m𝑁c	NOUN
iajs-2484	268	13	-	-	PUNCT
iajs-2484	268	14	function	function	NOUN
iajs-2484	268	15	)	)	PUNCT
iajs-2484	268	16	and	and	CCONJ
iajs-2484	268	17	𝒢	𝒢	PROPN
iajs-2484	268	18	be	be	VERB
iajs-2484	268	19	a	a	DET
iajs-2484	268	20	strongly	strongly	ADV
iajs-2484	268	21	𝜔-continuous	𝜔-continuous	ADJ
iajs-2484	268	22	function	function	NOUN
iajs-2484	268	23	,	,	PUNCT
iajs-2484	268	24	and	and	CCONJ
iajs-2484	268	25	let	let	VERB
iajs-2484	268	26	𝒲	𝒲	NOUN
iajs-2484	268	27	be	be	AUX
iajs-2484	268	28	𝜔-open	𝜔-open	ADJ
iajs-2484	268	29	set	set	VERB
iajs-2484	268	30	in	in	ADP
iajs-2484	268	31	𝒵	𝒵	PROPN
iajs-2484	268	32	,	,	PUNCT
iajs-2484	268	33	so	so	SCONJ
iajs-2484	268	34	𝒢	𝒢	PROPN
iajs-2484	268	35	𝒲	𝒲	PROPN
iajs-2484	268	36	is	be	AUX
iajs-2484	268	37	open	open	ADJ
iajs-2484	268	38	set	set	VERB
iajs-2484	268	39	in	in	ADP
iajs-2484	268	40	𝑌	𝑌	PROPN
iajs-2484	268	41	,	,	PUNCT
iajs-2484	268	42	so	so	ADV
iajs-2484	268	43	(	(	PUNCT
iajs-2484	268	44	𝒢	𝒢	PROPN
iajs-2484	268	45	𝒲	𝒲	PROPN
iajs-2484	268	46	is	be	AUX
iajs-2484	268	47	closed	close	VERB
iajs-2484	268	48	set	set	VERB
iajs-2484	268	49	in	in	ADP
iajs-2484	268	50	𝑌	𝑌	PROPN
iajs-2484	268	51	which	which	PRON
iajs-2484	268	52	is	be	AUX
iajs-2484	268	53	compact	compact	ADJ
iajs-2484	268	54	space	space	NOUN
iajs-2484	268	55	,	,	PUNCT
iajs-2484	268	56	so	so	SCONJ
iajs-2484	268	57	𝒢	𝒢	PROPN
iajs-2484	268	58	𝒲	𝒲	PROPN
iajs-2484	268	59	is	be	AUX
iajs-2484	268	60	compact	compact	ADJ
iajs-2484	268	61	set	set	VERB
iajs-2484	268	62	in	in	ADP
iajs-2484	268	63	𝑌	𝑌	PROPN
iajs-2484	268	64	,	,	PUNCT
iajs-2484	268	65	then	then	ADV
iajs-2484	268	66	𝑓	𝑓	DET
iajs-2484	268	67	𝒢	𝒢	PROPN
iajs-2484	268	68	𝒲	𝒲	PROPN
iajs-2484	268	69	)	)	PUNCT
iajs-2484	268	70	]	]	PUNCT
iajs-2484	269	1	=[	=[	NOUN
iajs-2484	270	1	𝒢	𝒢	NOUN
iajs-2484	270	2	∘	∘	NOUN
iajs-2484	270	3	𝑓	𝑓	DET
iajs-2484	270	4	𝒲	𝒲	PROPN
iajs-2484	270	5	is	be	AUX
iajs-2484	270	6	𝜔-closed	𝜔-close	VERB
iajs-2484	270	7	(	(	PUNCT
iajs-2484	270	8	respectively	respectively	ADV
iajs-2484	270	9	𝑁-closed	𝑁-closed	PROPN
iajs-2484	270	10	)	)	PUNCT
iajs-2484	270	11	set	set	NOUN
iajs-2484	270	12	in	in	ADP
iajs-2484	270	13	𝑋	𝑋	PROPN
iajs-2484	270	14	(	(	PUNCT
iajs-2484	270	15	since	since	SCONJ
iajs-2484	270	16	𝑓	𝑓	DET
iajs-2484	270	17	𝒢	𝒢	PROPN
iajs-2484	270	18	𝒲	𝒲	PROPN
iajs-2484	270	19	]	]	PUNCT
iajs-2484	271	1	=	=	NUM
iajs-2484	271	2	𝑓	𝑓	PRON
iajs-2484	271	3	𝑌	𝑌	PROPN
iajs-2484	271	4	𝒢	𝒢	PROPN
iajs-2484	271	5	𝒲	𝒲	PROPN
iajs-2484	271	6	𝑋	𝑋	PROPN
iajs-2484	271	7	𝑓	𝑓	PRON
iajs-2484	271	8	𝒢	𝒢	PROPN
iajs-2484	271	9	𝒲	𝒲	PROPN
iajs-2484	271	10	𝑋	𝑋	NOUN
iajs-2484	271	11	𝒢	𝒢	PROPN
iajs-2484	271	12	∘	∘	VERB
iajs-2484	271	13	𝑓	𝑓	DET
iajs-2484	271	14	𝒲	𝒲	PROPN
iajs-2484	271	15	𝒢	𝒢	PROPN
iajs-2484	271	16	∘	∘	NOUN
iajs-2484	271	17	𝑓	𝑓	DET
iajs-2484	271	18	𝒲	𝒲	PROPN
iajs-2484	271	19	)	)	PUNCT
iajs-2484	271	20	,	,	PUNCT
iajs-2484	271	21	and	and	CCONJ
iajs-2484	271	22	then	then	ADV
iajs-2484	271	23	𝒢	𝒢	ADV
iajs-2484	271	24	∘	∘	NOUN
iajs-2484	271	25	𝑓	𝑓	PRON
iajs-2484	271	26	𝒲	𝒲	PROPN
iajs-2484	271	27	is	be	AUX
iajs-2484	271	28	𝜔-open	𝜔-open	ADJ
iajs-2484	271	29	(	(	PUNCT
iajs-2484	271	30	respectively	respectively	ADV
iajs-2484	271	31	𝑁-open	𝑁-open	ADJ
iajs-2484	271	32	)	)	PUNCT
iajs-2484	271	33	set	set	NOUN
iajs-2484	271	34	in	in	ADP
iajs-2484	271	35	𝑋	𝑋	PROPN
iajs-2484	271	36	,	,	PUNCT
iajs-2484	271	37	hence	hence	ADV
iajs-2484	271	38	𝒢	𝒢	ADJ
iajs-2484	271	39	∘	∘	NOUN
iajs-2484	271	40	𝑓	𝑓	ADV
iajs-2484	271	41	is	be	AUX
iajs-2484	271	42	𝜔-irresolute	𝜔-irresolute	X
iajs-2484	271	43	(	(	PUNCT
iajs-2484	271	44	respectively	respectively	ADV
iajs-2484	271	45	𝑁-irresolute	𝑁-irresolute	PROPN
iajs-2484	271	46	)	)	PUNCT
iajs-2484	271	47	function	function	NOUN
iajs-2484	271	48	.	.	PUNCT
iajs-2484	272	1	by	by	ADP
iajs-2484	272	2	the	the	DET
iajs-2484	272	3	same	same	ADJ
iajs-2484	272	4	way	way	NOUN
iajs-2484	272	5	we	we	PRON
iajs-2484	272	6	can	can	AUX
iajs-2484	272	7	prove	prove	VERB
iajs-2484	272	8	the	the	DET
iajs-2484	272	9	rest	rest	NOUN
iajs-2484	272	10	.	.	PUNCT
iajs-2484	273	1	references	reference	NOUN
iajs-2484	273	2	1	1	NUM
iajs-2484	273	3	.	.	PUNCT
iajs-2484	273	4	farhan	farhan	PROPN
iajs-2484	273	5	,	,	PUNCT
iajs-2484	273	6	a.a.m	a.a.m	PROPN
iajs-2484	273	7	.	.	PUNCT
iajs-2484	274	1	on	on	ADP
iajs-2484	274	2	-	-	PUNCT
iajs-2484	274	3	mc	mc	NOUN
iajs-2484	274	4	-	-	PUNCT
iajs-2484	274	5	functions	function	NOUN
iajs-2484	274	6	,	,	PUNCT
iajs-2484	274	7	tikrit	tikrit	NOUN
iajs-2484	274	8	journal	journal	NOUN
iajs-2484	274	9	of	of	ADP
iajs-2484	274	10	pure	pure	ADJ
iajs-2484	274	11	science.2011	science.2011	PROPN
iajs-2484	274	12	,	,	PUNCT
iajs-2484	274	13	16	16	NUM
iajs-2484	274	14	,	,	PUNCT
iajs-2484	274	15	4	4	NUM
iajs-2484	274	16	,	,	PUNCT
iajs-2484	274	17	287	287	NUM
iajs-2484	274	18	-	-	SYM
iajs-2484	274	19	289	289	NUM
iajs-2484	274	20	.	.	PUNCT
iajs-2484	275	1	2	2	X
iajs-2484	275	2	.	.	X
iajs-2484	275	3	al	al	PROPN
iajs-2484	275	4	-	-	PUNCT
iajs-2484	275	5	saidy	saidy	ADJ
iajs-2484	275	6	,	,	PUNCT
iajs-2484	275	7	s.k	s.k	PROPN
iajs-2484	275	8	.	.	PROPN
iajs-2484	275	9	;	;	PUNCT
iajs-2484	275	10	abtan	abtan	PROPN
iajs-2484	275	11	,	,	PUNCT
iajs-2484	275	12	r.g	r.g	PROPN
iajs-2484	275	13	.	.	PROPN
iajs-2484	275	14	;	;	PUNCT
iajs-2484	275	15	ali	ali	PROPN
iajs-2484	275	16	,	,	PUNCT
iajs-2484	275	17	h.j	h.j	PROPN
iajs-2484	275	18	.	.	PROPN
iajs-2484	275	19	more	more	ADJ
iajs-2484	275	20	on	on	ADP
iajs-2484	275	21	mc	mc	PROPN
iajs-2484	275	22	-	-	PUNCT
iajs-2484	275	23	functions	function	NOUN
iajs-2484	275	24	,	,	PUNCT
iajs-2484	275	25	journal	journal	NOUN
iajs-2484	275	26	of	of	ADP
iajs-2484	275	27	the	the	DET
iajs-2484	275	28	college	college	NOUN
iajs-2484	275	29	of	of	ADP
iajs-2484	275	30	basic	basic	ADJ
iajs-2484	275	31	education.2015	education.2015	PROPN
iajs-2484	275	32	,	,	PUNCT
iajs-2484	275	33	21	21	NUM
iajs-2484	275	34	,	,	PUNCT
iajs-2484	275	35	89	89	NUM
iajs-2484	275	36	,	,	PUNCT
iajs-2484	275	37	149	149	NUM
iajs-2484	275	38	-	-	SYM
iajs-2484	275	39	156	156	NUM
iajs-2484	275	40	.	.	PUNCT
iajs-2484	276	1	3	3	X
iajs-2484	276	2	.	.	X
iajs-2484	276	3	hdeib	hdeib	PROPN
iajs-2484	276	4	,	,	PUNCT
iajs-2484	276	5	h.z	h.z	PROPN
iajs-2484	276	6	.	.	PROPN
iajs-2484	276	7	𝜔-closed	𝜔-close	VERB
iajs-2484	276	8	mappings	mapping	NOUN
iajs-2484	276	9	,	,	PUNCT
iajs-2484	276	10	revista	revista	PROPN
iajs-2484	276	11	colombiana	colombiana	PROPN
iajs-2484	276	12	de	de	PROPN
iajs-2484	276	13	matemáticas.1982	matemáticas.1982	PROPN
iajs-2484	276	14	,	,	PUNCT
iajs-2484	276	15	16	16	NUM
iajs-2484	276	16	,	,	PUNCT
iajs-2484	276	17	1	1	NUM
iajs-2484	276	18	-	-	SYM
iajs-2484	276	19	2	2	NUM
iajs-2484	276	20	,	,	PUNCT
iajs-2484	276	21	6578	6578	NUM
iajs-2484	276	22	.	.	PUNCT
iajs-2484	277	1	4	4	X
iajs-2484	277	2	.	.	X
iajs-2484	277	3	al	al	PROPN
iajs-2484	277	4	-	-	PUNCT
iajs-2484	277	5	omari	omari	PROPN
iajs-2484	277	6	,	,	PUNCT
iajs-2484	277	7	a.h.m.a.d	a.h.m.a.d	ADV
iajs-2484	277	8	.	.	PUNCT
iajs-2484	277	9	;	;	PUNCT
iajs-2484	277	10	noorani	noorani	PROPN
iajs-2484	277	11	,	,	PUNCT
iajs-2484	277	12	m.m	m.m	PROPN
iajs-2484	277	13	.	.	PROPN
iajs-2484	277	14	new	new	ADJ
iajs-2484	277	15	characterizations	characterization	NOUN
iajs-2484	277	16	of	of	ADP
iajs-2484	277	17	compact	compact	ADJ
iajs-2484	277	18	spaces	space	NOUN
iajs-2484	277	19	,	,	PUNCT
iajs-2484	277	20	in	in	ADP
iajs-2484	277	21	proceedings	proceeding	NOUN
iajs-2484	277	22	of	of	ADP
iajs-2484	277	23	the	the	DET
iajs-2484	277	24	5th	5th	ADJ
iajs-2484	277	25	asian	asian	ADJ
iajs-2484	277	26	mathematical	mathematical	NOUN
iajs-2484	277	27	conference.2009	conference.2009	PROPN
iajs-2484	277	28	,	,	PUNCT
iajs-2484	277	29	53	53	NUM
iajs-2484	277	30	-	-	SYM
iajs-2484	277	31	60	60	NUM
iajs-2484	277	32	.	.	PUNCT
iajs-2484	278	1	5	5	NUM
iajs-2484	278	2	.	.	NOUN
iajs-2484	278	3	alshams	alsham	NOUN
iajs-2484	278	4	,	,	PUNCT
iajs-2484	278	5	h.a	h.a	PROPN
iajs-2484	278	6	.	.	PROPN
iajs-2484	278	7	on	on	ADP
iajs-2484	278	8	the	the	DET
iajs-2484	278	9	𝜔b	𝜔b	NOUN
iajs-2484	278	10	-	-	NOUN
iajs-2484	278	11	compactspace	compactspace	NOUN
iajs-2484	278	12	,	,	PUNCT
iajs-2484	278	13	journal	journal	NOUN
iajs-2484	278	14	of	of	ADP
iajs-2484	278	15	advances	advance	NOUN
iajs-2484	278	16	in	in	ADP
iajs-2484	278	17	mathematics	mathematic	NOUN
iajs-2484	278	18	.	.	PUNCT
iajs-2484	279	1	2017	2017	NUM
iajs-2484	279	2	,	,	PUNCT
iajs-2484	279	3	13	13	NUM
iajs-2484	279	4	,	,	PUNCT
iajs-2484	279	5	4	4	NUM
iajs-2484	279	6	,	,	PUNCT
iajs-2484	279	7	7295	7295	NUM
iajs-2484	279	8	-	-	SYM
iajs-2484	279	9	7301	7301	NUM
iajs-2484	279	10	.	.	PUNCT
iajs-2484	280	1	6	6	NUM
iajs-2484	280	2	.	.	X
iajs-2484	280	3	ali	ali	PROPN
iajs-2484	280	4	,	,	PUNCT
iajs-2484	280	5	e.r	e.r	PROPN
iajs-2484	280	6	.	.	PROPN
iajs-2484	280	7	;	;	PUNCT
iajs-2484	281	1	hussain	hussain	PROPN
iajs-2484	281	2	,	,	PUNCT
iajs-2484	281	3	r.a	r.a	PROPN
iajs-2484	281	4	.	.	PROPN
iajs-2484	281	5	on	on	ADP
iajs-2484	281	6	dimension	dimension	NOUN
iajs-2484	281	7	theory	theory	NOUN
iajs-2484	281	8	by	by	ADP
iajs-2484	281	9	using	use	VERB
iajs-2484	281	10	n	n	CCONJ
iajs-2484	281	11	-	-	PUNCT
iajs-2484	281	12	open	open	ADJ
iajs-2484	281	13	sets	set	NOUN
iajs-2484	281	14	,	,	PUNCT
iajs-2484	281	15	journal	journal	NOUN
iajs-2484	281	16	of	of	ADP
iajs-2484	281	17	university	university	PROPN
iajs-2484	281	18	of	of	ADP
iajs-2484	281	19	babylon.2015	babylon.2015	PROPN
iajs-2484	281	20	,	,	PUNCT
iajs-2484	281	21	23	23	NUM
iajs-2484	281	22	,	,	PUNCT
iajs-2484	281	23	2	2	NUM
iajs-2484	281	24	,	,	PUNCT
iajs-2484	281	25	595	595	NUM
iajs-2484	281	26	-	-	SYM
iajs-2484	281	27	604	604	NUM
iajs-2484	281	28	.	.	PUNCT
iajs-2484	282	1	7	7	X
iajs-2484	282	2	.	.	X
iajs-2484	282	3	ravi	ravi	NOUN
iajs-2484	282	4	,	,	PUNCT
iajs-2484	282	5	o.	o.	PROPN
iajs-2484	282	6	;	;	PUNCT
iajs-2484	282	7	sekar	sekar	PROPN
iajs-2484	282	8	,	,	PUNCT
iajs-2484	282	9	p.	p.	NOUN
iajs-2484	282	10	;	;	PUNCT
iajs-2484	282	11	vidhyalakshmi	vidhyalakshmi	NOUN
iajs-2484	282	12	,	,	PUNCT
iajs-2484	282	13	k.	k.	PROPN
iajs-2484	282	14	𝜔-topology	𝜔-topology	PROPN
iajs-2484	282	15	and⋆-topology	and⋆-topology	PROPN
iajs-2484	282	16	.	.	PUNCT
iajs-2484	282	17	bulletin	bulletin	NOUN
iajs-2484	282	18	of	of	ADP
iajs-2484	282	19	international	international	ADJ
iajs-2484	282	20	mathematical	mathematical	ADJ
iajs-2484	282	21	virtual	virtual	ADJ
iajs-2484	282	22	institute.2017	institute.2017	PROPN
iajs-2484	282	23	,	,	PUNCT
iajs-2484	282	24	7	7	NUM
iajs-2484	282	25	,	,	PUNCT
iajs-2484	282	26	1	1	NUM
iajs-2484	282	27	,	,	PUNCT
iajs-2484	282	28	139	139	NUM
iajs-2484	282	29	-	-	SYM
iajs-2484	282	30	151	151	NUM
iajs-2484	282	31	.	.	NOUN
iajs-2484	282	32	8	8	NUM
iajs-2484	282	33	.	.	X
iajs-2484	282	34	amer	amer	PROPN
iajs-2484	282	35	,	,	PUNCT
iajs-2484	282	36	i.	i.	PROPN
iajs-2484	282	37	weak	weak	ADJ
iajs-2484	282	38	n	n	CCONJ
iajs-2484	282	39	-	-	PUNCT
iajs-2484	282	40	open	open	ADJ
iajs-2484	282	41	sets	set	NOUN
iajs-2484	282	42	.	.	PUNCT
iajs-2484	283	1	ibn	ibn	PROPN
iajs-2484	283	2	al	al	PROPN
iajs-2484	283	3	-	-	PUNCT
iajs-2484	283	4	haitham	haitham	PROPN
iajs-2484	283	5	journal	journal	PROPN
iajs-2484	283	6	for	for	ADP
iajs-2484	283	7	pure	pure	ADJ
iajs-2484	283	8	and	and	CCONJ
iajs-2484	283	9	applied	applied	ADJ
iajs-2484	283	10	science	science	NOUN
iajs-2484	283	11	.	.	PUNCT
iajs-2484	284	1	2016	2016	NUM
iajs-2484	284	2	,	,	PUNCT
iajs-2484	284	3	29	29	NUM
iajs-2484	284	4	,	,	PUNCT
iajs-2484	284	5	1	1	NUM
iajs-2484	284	6	,	,	PUNCT
iajs-2484	284	7	267	267	NUM
iajs-2484	284	8	-	-	SYM
iajs-2484	284	9	276	276	NUM
iajs-2484	284	10	.	.	PUNCT
iajs-2484	285	1	9	9	NUM
iajs-2484	285	2	.	.	X
iajs-2484	285	3	hamza	hamza	PROPN
iajs-2484	285	4	,	,	PUNCT
iajs-2484	285	5	s.h	s.h	PROPN
iajs-2484	285	6	.	.	PROPN
iajs-2484	285	7	;	;	PUNCT
iajs-2484	285	8	majhool	majhool	PROPN
iajs-2484	285	9	,	,	PUNCT
iajs-2484	285	10	f.m	f.m	PROPN
iajs-2484	285	11	.	.	PROPN
iajs-2484	285	12	strongly	strongly	ADV
iajs-2484	285	13	n	n	CCONJ
iajs-2484	285	14	-	-	PUNCT
iajs-2484	285	15	proper	proper	ADJ
iajs-2484	285	16	functions	function	NOUN
iajs-2484	285	17	,	,	PUNCT
iajs-2484	285	18	journal	journal	NOUN
iajs-2484	285	19	of	of	ADP
iajs-2484	285	20	al	al	PROPN
iajs-2484	285	21	-	-	PUNCT
iajs-2484	285	22	qadisiyah	qadisiyah	NOUN
iajs-2484	285	23	for	for	ADP
iajs-2484	285	24	computer	computer	NOUN
iajs-2484	285	25	science	science	NOUN
iajs-2484	285	26	and	and	CCONJ
iajs-2484	285	27	mathematics.2011	mathematics.2011	PROPN
iajs-2484	285	28	,	,	PUNCT
iajs-2484	285	29	3	3	NUM
iajs-2484	285	30	,	,	PUNCT
iajs-2484	285	31	2	2	NUM
iajs-2484	285	32	,	,	PUNCT
iajs-2484	285	33	183	183	NUM
iajs-2484	285	34	-	-	SYM
iajs-2484	285	35	199	199	NUM
iajs-2484	285	36	.	.	PUNCT
iajs-2484	286	1	10	10	NUM
iajs-2484	286	2	.	.	X
iajs-2484	287	1	hussain	hussain	PROPN
iajs-2484	287	2	,	,	PUNCT
iajs-2484	287	3	r.a	r.a	PROPN
iajs-2484	287	4	.	.	PROPN
iajs-2484	287	5	;	;	PUNCT
iajs-2484	287	6	nasser	nasser	PROPN
iajs-2484	287	7	,	,	PUNCT
iajs-2484	287	8	z.a	z.a	PROPN
iajs-2484	287	9	.	.	PROPN
iajs-2484	288	1	on	on	ADP
iajs-2484	288	2	the	the	DET
iajs-2484	288	3	𝜔b	𝜔b	NOUN
iajs-2484	288	4	-	-	PUNCT
iajs-2484	288	5	separation	separation	NOUN
iajs-2484	288	6	axioms	axiom	NOUN
iajs-2484	288	7	,	,	PUNCT
iajs-2484	288	8	international	international	ADJ
iajs-2484	288	9	journal	journal	NOUN
iajs-2484	288	10	of	of	ADP
iajs-2484	288	11	science	science	NOUN
iajs-2484	288	12	and	and	CCONJ
iajs-2484	288	13	research	research	NOUN
iajs-2484	288	14	(	(	PUNCT
iajs-2484	288	15	ijsr).2015	ijsr).2015	PROPN
iajs-2484	288	16	,	,	PUNCT
iajs-2484	288	17	6	6	NUM
iajs-2484	288	18	,	,	PUNCT
iajs-2484	288	19	2	2	NUM
iajs-2484	288	20	,	,	PUNCT
iajs-2484	288	21	78	78	NUM
iajs-2484	288	22	-	-	SYM
iajs-2484	288	23	96	96	NUM
iajs-2484	288	24	.	.	PUNCT
iajs-2484	288	25	11	11	NUM
iajs-2484	288	26	.	.	PUNCT
iajs-2484	288	27	rosas	rosa	NOUN
iajs-2484	288	28	,	,	PUNCT
iajs-2484	288	29	e.r	e.r	PROPN
iajs-2484	288	30	.	.	PROPN
iajs-2484	288	31	;	;	PUNCT
iajs-2484	288	32	carpintero	carpintero	NOUN
iajs-2484	288	33	,	,	PUNCT
iajs-2484	288	34	c.	c.	PROPN
iajs-2484	288	35	;	;	PUNCT
iajs-2484	288	36	pacheco	pacheco	PROPN
iajs-2484	288	37	,	,	PUNCT
iajs-2484	288	38	j.	j.	PROPN
iajs-2484	288	39	;	;	PUNCT
iajs-2484	288	40	rajesh	rajesh	PROPN
iajs-2484	288	41	,	,	PUNCT
iajs-2484	288	42	n.	n.	PROPN
iajs-2484	288	43	;	;	PUNCT
iajs-2484	288	44	saranyasri	saranyasri	PROPN
iajs-2484	288	45	,	,	PUNCT
iajs-2484	288	46	s.	s.	PROPN
iajs-2484	288	47	almost	almost	ADV
iajs-2484	288	48	nearly	nearly	ADV
iajs-2484	288	49	𝜔continuious	𝜔continuious	ADJ
iajs-2484	288	50	multifunctions	multifunction	NOUN
iajs-2484	288	51	,	,	PUNCT
iajs-2484	288	52	eurasian	eurasian	ADJ
iajs-2484	288	53	bulletin	bulletin	NOUN
iajs-2484	288	54	of	of	ADP
iajs-2484	288	55	mathematics.2018	mathematics.2018	PROPN
iajs-2484	288	56	,	,	PUNCT
iajs-2484	288	57	1	1	NUM
iajs-2484	288	58	,	,	PUNCT
iajs-2484	288	59	1	1	NUM
iajs-2484	288	60	,	,	PUNCT
iajs-2484	288	61	24	24	NUM
iajs-2484	288	62	-	-	SYM
iajs-2484	288	63	33	33	NUM
iajs-2484	288	64	.	.	PUNCT
iajs-2484	288	65	12	12	NUM
iajs-2484	288	66	.	.	PUNCT
iajs-2484	289	1	abdullah	abdullah	PROPN
iajs-2484	289	2	,	,	PUNCT
iajs-2484	289	3	h.k	h.k	PROPN
iajs-2484	289	4	.	.	PROPN
iajs-2484	289	5	;	;	PUNCT
iajs-2484	289	6	hamza	hamza	PROPN
iajs-2484	289	7	,	,	PUNCT
iajs-2484	289	8	z.	z.	PROPN
iajs-2484	289	9	m.	m.	PROPN
iajs-2484	289	10	compactly	compactly	ADV
iajs-2484	289	11	𝜔-closed	𝜔-close	VERB
iajs-2484	289	12	set	set	NOUN
iajs-2484	289	13	and	and	CCONJ
iajs-2484	289	14	compactly	compactly	ADV
iajs-2484	289	15	𝜔-k	𝜔-k	NOUN
iajs-2484	289	16	-	-	PUNCT
iajs-2484	289	17	closed	closed	ADJ
iajs-2484	289	18	set	set	NOUN
iajs-2484	289	19	,	,	PUNCT
iajs-2484	289	20	journal	journal	NOUN
iajs-2484	289	21	of	of	ADP
iajs-2484	289	22	kerbala	kerbala	PROPN
iajs-2484	289	23	university.2013	university.2013	PROPN
iajs-2484	289	24	,	,	PUNCT
iajs-2484	289	25	11	11	NUM
iajs-2484	289	26	,	,	PUNCT
iajs-2484	289	27	4	4	NUM
iajs-2484	289	28	,	,	PUNCT
iajs-2484	289	29	113	113	NUM
iajs-2484	289	30	-	-	SYM
iajs-2484	289	31	118	118	NUM
iajs-2484	289	32	.	.	NOUN
iajs-2484	290	1	13	13	NUM
iajs-2484	290	2	.	.	PUNCT
iajs-2484	290	3	hamza	hamza	PROPN
iajs-2484	290	4	,	,	PUNCT
iajs-2484	290	5	s.h	s.h	PROPN
iajs-2484	290	6	.	.	PROPN
iajs-2484	290	7	;	;	PUNCT
iajs-2484	290	8	majhool	majhool	PROPN
iajs-2484	290	9	,	,	PUNCT
iajs-2484	290	10	f.m	f.m	PROPN
iajs-2484	290	11	.	.	PROPN
iajs-2484	290	12	on	on	ADP
iajs-2484	290	13	nproper	nproper	ADJ
iajs-2484	290	14	actions	action	NOUN
iajs-2484	290	15	.	.	PUNCT
iajs-2484	291	1	master	master	NOUN
iajs-2484	291	2	thesis	thesis	NOUN
iajs-2484	291	3	.	.	PUNCT
iajs-2484	292	1	al	al	PROPN
iajs-2484	292	2	-	-	PUNCT
iajs-2484	292	3	qadisiyah	qadisiyah	PROPN
iajs-2484	292	4	university	university	NOUN
iajs-2484	292	5	,	,	PUNCT
iajs-2484	292	6	2011	2011	NUM
iajs-2484	292	7	.	.	PUNCT
iajs-2484	293	1	14	14	NUM
iajs-2484	293	2	.	.	PUNCT
iajs-2484	294	1	al	al	PROPN
iajs-2484	294	2	ghour	ghour	PROPN
iajs-2484	294	3	,	,	PUNCT
iajs-2484	294	4	s.	s.	PROPN
iajs-2484	294	5	;	;	PUNCT
iajs-2484	294	6	irshidat	irshidat	PROPN
iajs-2484	294	7	,	,	PUNCT
iajs-2484	294	8	b.	b.	PROPN
iajs-2484	294	9	the	the	DET
iajs-2484	294	10	topology	topology	NOUN
iajs-2484	294	11	of	of	ADP
iajs-2484	294	12	theta	theta	NOUN
iajs-2484	294	13	omega	omega	NOUN
iajs-2484	294	14	open	open	ADJ
iajs-2484	294	15	sets	set	NOUN
iajs-2484	294	16	,	,	PUNCT
iajs-2484	294	17	filomat.2017	filomat.2017	PROPN
iajs-2484	294	18	,	,	PUNCT
iajs-2484	294	19	31	31	NUM
iajs-2484	294	20	,	,	PUNCT
iajs-2484	294	21	16	16	NUM
iajs-2484	294	22	,	,	PUNCT
iajs-2484	294	23	5369	5369	NUM
iajs-2484	294	24	-	-	SYM
iajs-2484	294	25	5377	5377	NUM
iajs-2484	294	26	.	.	PUNCT
iajs-2484	295	1	15	15	NUM
iajs-2484	295	2	.	.	PUNCT
iajs-2484	296	1	hussein	hussein	PROPN
iajs-2484	296	2	,	,	PUNCT
iajs-2484	296	3	h.j.a	h.j.a	PROPN
iajs-2484	296	4	.	.	PUNCT
iajs-2484	296	5	new	new	ADJ
iajs-2484	296	6	characterization	characterization	NOUN
iajs-2484	296	7	of	of	ADP
iajs-2484	296	8	topological	topological	ADJ
iajs-2484	296	9	transitivity	transitivity	NOUN
iajs-2484	296	10	,	,	PUNCT
iajs-2484	296	11	iraqi	iraqi	ADJ
iajs-2484	296	12	journal	journal	NOUN
iajs-2484	296	13	of	of	ADP
iajs-2484	296	14	science.2013	science.2013	PROPN
iajs-2484	296	15	,	,	PUNCT
iajs-2484	296	16	54	54	NUM
iajs-2484	296	17	,	,	PUNCT
iajs-2484	296	18	3	3	NUM
iajs-2484	296	19	,	,	PUNCT
iajs-2484	296	20	817	817	NUM
iajs-2484	296	21	-	-	SYM
iajs-2484	296	22	821	821	NUM
iajs-2484	296	23	.	.	PUNCT
iajs-2484	296	24	16	16	NUM
iajs-2484	296	25	.	.	PUNCT
iajs-2484	297	1	labendia	labendia	PROPN
iajs-2484	297	2	,	,	PUNCT
iajs-2484	297	3	m.	m.	NOUN
iajs-2484	297	4	a.	a.	PROPN
iajs-2484	297	5	;	;	PUNCT
iajs-2484	297	6	sasam	sasam	NOUN
iajs-2484	297	7	,	,	PUNCT
iajs-2484	297	8	j.a.c	j.a.c	PROPN
iajs-2484	297	9	.	.	PUNCT
iajs-2484	298	1	on	on	ADP
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iajs-2484	298	5	and	and	CCONJ
iajs-2484	298	6	omega	omega	NOUN
iajs-2484	298	7	-	-	PUNCT
iajs-2484	298	8	continuity	continuity	NOUN
iajs-2484	298	9	in	in	ADP
iajs-2484	298	10	the	the	DET
iajs-2484	298	11	product	product	NOUN
iajs-2484	298	12	space	space	NOUN
iajs-2484	298	13	,	,	PUNCT
iajs-2484	298	14	european	european	PROPN
iajs-2484	298	15	journal	journal	PROPN
iajs-2484	298	16	of	of	ADP
iajs-2484	298	17	pure	pure	ADJ
iajs-2484	298	18	and	and	CCONJ
iajs-2484	298	19	applied	apply	VERB
iajs-2484	298	20	mathematics.2018	mathematics.2018	NOUN
iajs-2484	298	21	,	,	PUNCT
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iajs-2484	298	23	,	,	PUNCT
iajs-2484	298	24	3	3	NUM
iajs-2484	298	25	,	,	PUNCT
iajs-2484	298	26	834843	834843	NUM
iajs-2484	298	27	.	.	PUNCT
iajs-2484	298	28	  	  	SPACE
iajs-2484	299	1	187	187	NUM
iajs-2484	299	2	  	  	SPACE
iajs-2484	299	3	ibn	ibn	PROPN
iajs-2484	299	4	al	al	PROPN
iajs-2484	299	5	-	-	PUNCT
iajs-2484	299	6	haitham	haitham	PROPN
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iajs-2484	299	8	.	.	PROPN
iajs-2484	299	9	for	for	ADP
iajs-2484	299	10	pure	pure	ADJ
iajs-2484	299	11	&	&	CCONJ
iajs-2484	299	12	appl	appl	PROPN
iajs-2484	299	13	.	.	PUNCT
iajs-2484	300	1	sci	sci	PROPN
iajs-2484	300	2	.	.	PROPN
iajs-2484	301	1	33	33	NUM
iajs-2484	301	2	(	(	PUNCT
iajs-2484	301	3	3	3	NUM
iajs-2484	301	4	)	)	PUNCT
iajs-2484	301	5	2020	2020	NUM
iajs-2484	301	6	17	17	NUM
iajs-2484	301	7	.	.	PUNCT
iajs-2484	302	1	levine	levine	PROPN
iajs-2484	302	2	,	,	PUNCT
iajs-2484	302	3	n.	n.	PROPN
iajs-2484	302	4	when	when	SCONJ
iajs-2484	302	5	are	be	AUX
iajs-2484	302	6	compact	compact	ADJ
iajs-2484	302	7	and	and	CCONJ
iajs-2484	302	8	closed	closed	ADJ
iajs-2484	302	9	equivalent	equivalent	ADJ
iajs-2484	302	10	,	,	PUNCT
iajs-2484	302	11	the	the	DET
iajs-2484	302	12	american	american	PROPN
iajs-2484	302	13	mathematical	mathematical	PROPN
iajs-2484	302	14	monthly.1965	monthly.1965	PROPN
iajs-2484	302	15	,	,	PUNCT
iajs-2484	302	16	72	72	NUM
iajs-2484	302	17	,	,	PUNCT
iajs-2484	302	18	1	1	NUM
iajs-2484	302	19	,	,	PUNCT
iajs-2484	302	20	41	41	NUM
iajs-2484	302	21	-	-	SYM
iajs-2484	302	22	44	44	NUM
iajs-2484	302	23	.	.	PUNCT
iajs-2484	302	24	18	18	NUM
iajs-2484	302	25	.	.	X
iajs-2484	302	26	bella	bella	PROPN
iajs-2484	302	27	,	,	PUNCT
iajs-2484	302	28	a.	a.	NOUN
iajs-2484	302	29	;	;	PUNCT
iajs-2484	302	30	costantini	costantini	PROPN
iajs-2484	302	31	,	,	PUNCT
iajs-2484	302	32	c.	c.	PROPN
iajs-2484	302	33	minimal	minimal	PROPN
iajs-2484	302	34	kc	kc	PROPN
iajs-2484	302	35	spaces	space	NOUN
iajs-2484	302	36	are	be	AUX
iajs-2484	302	37	compact	compact	ADJ
iajs-2484	302	38	,	,	PUNCT
iajs-2484	302	39	topology	topology	NOUN
iajs-2484	302	40	and	and	CCONJ
iajs-2484	302	41	its	its	PRON
iajs-2484	302	42	applications.2008	applications.2008	PROPN
iajs-2484	302	43	,	,	PUNCT
iajs-2484	302	44	155	155	NUM
iajs-2484	302	45	,	,	PUNCT
iajs-2484	302	46	13	13	NUM
iajs-2484	302	47	,	,	PUNCT
iajs-2484	302	48	1426	1426	NUM
iajs-2484	302	49	-	-	SYM
iajs-2484	302	50	1429	1429	NUM
iajs-2484	302	51	.	.	PUNCT
iajs-2484	303	1	19	19	NUM
iajs-2484	303	2	.	.	PUNCT
iajs-2484	303	3	hadi	hadi	PROPN
iajs-2484	303	4	,	,	PUNCT
iajs-2484	303	5	m.h	m.h	PROPN
iajs-2484	303	6	.	.	PROPN
iajs-2484	304	1	a	a	DET
iajs-2484	304	2	comparison	comparison	NOUN
iajs-2484	304	3	between	between	ADP
iajs-2484	304	4	two	two	NUM
iajs-2484	304	5	kinds	kind	NOUN
iajs-2484	304	6	of	of	ADP
iajs-2484	304	7	subspaces	subspace	NOUN
iajs-2484	304	8	topologies	topology	NOUN
iajs-2484	304	9	,	,	PUNCT
iajs-2484	304	10	journal	journal	NOUN
iajs-2484	304	11	of	of	ADP
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iajs-2484	304	13	and	and	CCONJ
iajs-2484	304	14	arts.2017	arts.2017	PROPN
iajs-2484	304	15	,	,	PUNCT
iajs-2484	304	16	3	3	NUM
iajs-2484	304	17	,	,	PUNCT
iajs-2484	304	18	40	40	NUM
iajs-2484	304	19	,	,	PUNCT
iajs-2484	304	20	449	449	NUM
iajs-2484	304	21	-	-	NUM
iajs-2484	304	22	456	456	NUM
iajs-2484	304	23	.	.	PUNCT