id	sid	tid	token	lemma	pos
iajs-2511	1	1	microsoft	microsoft	PROPN
iajs-2511	1	2	word	word	NOUN
iajs-2511	1	3	73	73	NUM
iajs-2511	1	4	-	-	SYM
iajs-2511	1	5	81	81	NUM
iajs-2511	1	6	ibn	ibn	PROPN
iajs-2511	1	7	al	al	PROPN
iajs-2511	1	8	-	-	PUNCT
iajs-2511	1	9	haitham	haitham	PROPN
iajs-2511	1	10	jour	jour	X
iajs-2511	1	11	.	.	PROPN
iajs-2511	2	1	for	for	ADP
iajs-2511	2	2	pure	pure	ADJ
iajs-2511	2	3	&	&	CCONJ
iajs-2511	2	4	appl	appl	PROPN
iajs-2511	2	5	.	.	PUNCT
iajs-2511	3	1	sci	sci	PROPN
iajs-2511	3	2	.	.	PROPN
iajs-2511	4	1	33	33	NUM
iajs-2511	4	2	(	(	PUNCT
iajs-2511	4	3	4	4	NUM
iajs-2511	4	4	)	)	PUNCT
iajs-2511	4	5	2020	2020	NUM
iajs-2511	5	1	73	73	NUM
iajs-2511	5	2	          	          	SPACE
iajs-2511	5	3	fuzzy	fuzzy	ADJ
iajs-2511	5	4	semi	semi	ADV
iajs-2511	5	5	pre	pre	VERB
iajs-2511	5	6	homeomorphism	homeomorphism	PROPN
iajs-2511	5	7	in	in	ADP
iajs-2511	5	8	fuzzy	fuzzy	ADJ
iajs-2511	5	9	topological	topological	ADJ
iajs-2511	5	10	spaces	space	NOUN
iajs-2511	5	11	saleem	saleem	PROPN
iajs-2511	5	12	y.	y.	PROPN
iajs-2511	5	13	majeed	majeed	PROPN
iajs-2511	5	14	department	department	PROPN
iajs-2511	5	15	of	of	ADP
iajs-2511	5	16	mathematics	mathematics	PROPN
iajs-2511	5	17	,	,	PUNCT
iajs-2511	5	18	college	college	NOUN
iajs-2511	5	19	of	of	ADP
iajs-2511	5	20	education	education	NOUN
iajs-2511	5	21	,	,	PUNCT
iajs-2511	5	22	university	university	NOUN
iajs-2511	5	23	of	of	ADP
iajs-2511	5	24	garmian	garmian	ADJ
iajs-2511	5	25	saleem.yaseen@garmian.edu.krd	saleem.yaseen@garmian.edu.krd	NOUN
iajs-2511	5	26	abstract	abstract	ADP
iajs-2511	5	27	the	the	DET
iajs-2511	5	28	aim	aim	NOUN
iajs-2511	5	29	of	of	ADP
iajs-2511	5	30	this	this	DET
iajs-2511	5	31	paper	paper	NOUN
iajs-2511	5	32	is	be	AUX
iajs-2511	5	33	to	to	PART
iajs-2511	5	34	introduce	introduce	VERB
iajs-2511	5	35	and	and	CCONJ
iajs-2511	5	36	study	study	VERB
iajs-2511	5	37	new	new	ADJ
iajs-2511	5	38	class	class	NOUN
iajs-2511	5	39	of	of	ADP
iajs-2511	5	40	fuzzy	fuzzy	ADJ
iajs-2511	5	41	function	function	NOUN
iajs-2511	5	42	called	call	VERB
iajs-2511	5	43	fuzzy	fuzzy	ADJ
iajs-2511	5	44	semi	semi	ADV
iajs-2511	5	45	pre	pre	VERB
iajs-2511	5	46	homeomorphism	homeomorphism	PROPN
iajs-2511	5	47	in	in	ADP
iajs-2511	5	48	a	a	DET
iajs-2511	5	49	fuzzy	fuzzy	ADJ
iajs-2511	5	50	topological	topological	ADJ
iajs-2511	5	51	space	space	NOUN
iajs-2511	5	52	by	by	ADP
iajs-2511	5	53	utilizing	utilize	VERB
iajs-2511	5	54	fuzzy	fuzzy	ADJ
iajs-2511	5	55	semi	semi	ADV
iajs-2511	5	56	pre	pre	ADJ
iajs-2511	5	57	-	-	ADJ
iajs-2511	5	58	open	open	ADJ
iajs-2511	5	59	sets	set	NOUN
iajs-2511	5	60	.	.	PUNCT
iajs-2511	6	1	therefore	therefore	ADV
iajs-2511	6	2	,	,	PUNCT
iajs-2511	6	3	some	some	PRON
iajs-2511	6	4	of	of	ADP
iajs-2511	6	5	their	their	PRON
iajs-2511	6	6	characterization	characterization	NOUN
iajs-2511	6	7	has	have	AUX
iajs-2511	6	8	been	be	AUX
iajs-2511	6	9	proved	prove	VERB
iajs-2511	6	10	;	;	PUNCT
iajs-2511	6	11	in	in	ADP
iajs-2511	6	12	addition	addition	NOUN
iajs-2511	6	13	to	to	ADP
iajs-2511	6	14	that	that	SCONJ
iajs-2511	6	15	we	we	PRON
iajs-2511	6	16	define	define	VERB
iajs-2511	6	17	,	,	PUNCT
iajs-2511	6	18	study	study	VERB
iajs-2511	6	19	and	and	CCONJ
iajs-2511	6	20	develop	develop	VERB
iajs-2511	6	21	corresponding	correspond	VERB
iajs-2511	6	22	to	to	ADP
iajs-2511	6	23	new	new	ADJ
iajs-2511	6	24	class	class	NOUN
iajs-2511	6	25	of	of	ADP
iajs-2511	6	26	fuzzy	fuzzy	ADJ
iajs-2511	6	27	semi	semi	ADJ
iajs-2511	6	28	pre	pre	VERB
iajs-2511	6	29	homeomorphism	homeomorphism	PROPN
iajs-2511	6	30	in	in	ADP
iajs-2511	6	31	fuzzy	fuzzy	ADJ
iajs-2511	6	32	topological	topological	ADJ
iajs-2511	6	33	spaces	space	NOUN
iajs-2511	6	34	using	use	VERB
iajs-2511	6	35	this	this	DET
iajs-2511	6	36	new	new	ADJ
iajs-2511	6	37	class	class	NOUN
iajs-2511	6	38	of	of	ADP
iajs-2511	6	39	functions	function	NOUN
iajs-2511	6	40	.	.	PUNCT
iajs-2511	7	1	keyword	keyword	NOUN
iajs-2511	7	2	:	:	PUNCT
iajs-2511	7	3	fuzzy	fuzzy	ADJ
iajs-2511	7	4	topological	topological	ADJ
iajs-2511	7	5	spaces	space	NOUN
iajs-2511	7	6	,	,	PUNCT
iajs-2511	7	7	fuzzy	fuzzy	ADJ
iajs-2511	7	8	semi	semi	ADV
iajs-2511	7	9	pre	pre	ADJ
iajs-2511	7	10	-	-	ADJ
iajs-2511	7	11	open	open	ADJ
iajs-2511	7	12	sets	set	NOUN
iajs-2511	7	13	,	,	PUNCT
iajs-2511	7	14	fuzzy	fuzzy	ADJ
iajs-2511	7	15	semi	semi	ADV
iajs-2511	7	16	pre	pre	PROPN
iajs-2511	7	17	homeomorphism	homeomorphism	PROPN
iajs-2511	7	18	function	function	NOUN
iajs-2511	7	19	and	and	CCONJ
iajs-2511	7	20	fuzzy	fuzzy	ADJ
iajs-2511	7	21	semi	semi	ADV
iajs-2511	7	22	pre	pre	PROPN
iajs-2511	7	23	*	*	PROPN
iajs-2511	7	24	homeomorphism	homeomorphism	PROPN
iajs-2511	7	25	function	function	NOUN
iajs-2511	7	26	.	.	PUNCT
iajs-2511	8	1	1	1	X
iajs-2511	8	2	.	.	X
iajs-2511	8	3	introduction	introduction	NOUN
iajs-2511	8	4	zadeh	zadeh	PROPN
iajs-2511	8	5	in	in	ADP
iajs-2511	8	6	[	[	X
iajs-2511	8	7	1	1	NUM
iajs-2511	8	8	]	]	PUNCT
iajs-2511	8	9	introduced	introduce	VERB
iajs-2511	8	10	the	the	DET
iajs-2511	8	11	fundamental	fundamental	ADJ
iajs-2511	8	12	concept	concept	NOUN
iajs-2511	8	13	of	of	ADP
iajs-2511	8	14	fuzzy	fuzzy	ADJ
iajs-2511	8	15	sets	set	NOUN
iajs-2511	8	16	and	and	CCONJ
iajs-2511	8	17	fuzzy	fuzzy	ADJ
iajs-2511	8	18	set	set	VERB
iajs-2511	8	19	operations	operation	NOUN
iajs-2511	8	20	in	in	ADP
iajs-2511	8	21	his	his	PRON
iajs-2511	8	22	standard	standard	ADJ
iajs-2511	8	23	paper	paper	NOUN
iajs-2511	8	24	.	.	PUNCT
iajs-2511	9	1	thereafter	thereafter	ADV
iajs-2511	9	2	,	,	PUNCT
iajs-2511	9	3	some	some	DET
iajs-2511	9	4	researchers	researcher	NOUN
iajs-2511	9	5	have	have	AUX
iajs-2511	9	6	applied	apply	VERB
iajs-2511	9	7	some	some	DET
iajs-2511	9	8	different	different	ADJ
iajs-2511	9	9	basic	basic	ADJ
iajs-2511	9	10	notions	notion	NOUN
iajs-2511	9	11	from	from	ADP
iajs-2511	9	12	general	general	ADJ
iajs-2511	9	13	topology	topology	NOUN
iajs-2511	9	14	by	by	ADP
iajs-2511	9	15	utilizing	utilize	VERB
iajs-2511	9	16	the	the	DET
iajs-2511	9	17	fundamental	fundamental	ADJ
iajs-2511	9	18	idea	idea	NOUN
iajs-2511	9	19	of	of	ADP
iajs-2511	9	20	fuzzy	fuzzy	ADJ
iajs-2511	9	21	sets	set	NOUN
iajs-2511	9	22	and	and	CCONJ
iajs-2511	9	23	was	be	AUX
iajs-2511	9	24	subsequently	subsequently	ADV
iajs-2511	9	25	expanded	expand	VERB
iajs-2511	9	26	by	by	ADP
iajs-2511	9	27	developing	develop	VERB
iajs-2511	9	28	important	important	ADJ
iajs-2511	9	29	theories	theory	NOUN
iajs-2511	9	30	of	of	ADP
iajs-2511	9	31	fuzzy	fuzzy	ADJ
iajs-2511	9	32	topological	topological	ADJ
iajs-2511	9	33	spaces	space	NOUN
iajs-2511	9	34	.	.	PUNCT
iajs-2511	10	1	the	the	DET
iajs-2511	10	2	notion	notion	NOUN
iajs-2511	10	3	of	of	ADP
iajs-2511	10	4	family	family	NOUN
iajs-2511	10	5	in	in	ADP
iajs-2511	10	6	fuzzy	fuzzy	ADJ
iajs-2511	10	7	sets	set	NOUN
iajs-2511	10	8	naturally	naturally	ADV
iajs-2511	10	9	plays	play	VERB
iajs-2511	10	10	a	a	DET
iajs-2511	10	11	very	very	ADV
iajs-2511	10	12	significant	significant	ADJ
iajs-2511	10	13	role	role	NOUN
iajs-2511	10	14	in	in	ADP
iajs-2511	10	15	the	the	DET
iajs-2511	10	16	study	study	NOUN
iajs-2511	10	17	of	of	ADP
iajs-2511	10	18	the	the	DET
iajs-2511	10	19	recent	recent	ADJ
iajs-2511	10	20	concept	concept	NOUN
iajs-2511	10	21	of	of	ADP
iajs-2511	10	22	fuzzy	fuzzy	ADJ
iajs-2511	10	23	topology	topology	NOUN
iajs-2511	10	24	introduced	introduce	VERB
iajs-2511	10	25	by	by	ADP
iajs-2511	10	26	chang	chang	PROPN
iajs-2511	11	1	[	[	X
iajs-2511	11	2	2	2	NUM
iajs-2511	11	3	]	]	PUNCT
iajs-2511	11	4	.	.	PUNCT
iajs-2511	12	1	while	while	SCONJ
iajs-2511	12	2	,	,	PUNCT
iajs-2511	12	3	ming	ming	PROPN
iajs-2511	12	4	,	,	PUNCT
iajs-2511	12	5	p.	p.	PROPN
iajs-2511	12	6	&	&	CCONJ
iajs-2511	12	7	ming	ming	PROPN
iajs-2511	12	8	,	,	PUNCT
iajs-2511	12	9	l.	l.	PROPN
iajs-2511	12	10	[	[	X
iajs-2511	12	11	3	3	NUM
iajs-2511	12	12	]	]	PUNCT
iajs-2511	12	13	introduced	introduce	VERB
iajs-2511	12	14	the	the	DET
iajs-2511	12	15	concept	concept	NOUN
iajs-2511	12	16	of	of	ADP
iajs-2511	12	17	extensions	extension	NOUN
iajs-2511	12	18	principle	principle	NOUN
iajs-2511	12	19	of	of	ADP
iajs-2511	12	20	functions	function	NOUN
iajs-2511	12	21	in	in	ADP
iajs-2511	12	22	fuzzy	fuzzy	ADJ
iajs-2511	12	23	setting	setting	NOUN
iajs-2511	12	24	.	.	PUNCT
iajs-2511	13	1	the	the	DET
iajs-2511	13	2	idea	idea	NOUN
iajs-2511	13	3	of	of	ADP
iajs-2511	13	4	semi	semi	ADJ
iajs-2511	13	5	pre	pre	ADJ
iajs-2511	13	6	-	-	ADJ
iajs-2511	13	7	open	open	ADJ
iajs-2511	13	8	set	set	NOUN
iajs-2511	13	9	in	in	ADP
iajs-2511	13	10	classical	classical	ADJ
iajs-2511	13	11	topology	topology	NOUN
iajs-2511	13	12	was	be	AUX
iajs-2511	13	13	introduced	introduce	VERB
iajs-2511	13	14	by	by	ADP
iajs-2511	13	15	andrijevic	andrijevic	PROPN
iajs-2511	13	16	,	,	PUNCT
iajs-2511	13	17	d.	d.	PROPN
iajs-2511	14	1	[	[	X
iajs-2511	14	2	4	4	NUM
iajs-2511	14	3	]	]	PUNCT
iajs-2511	14	4	.	.	PUNCT
iajs-2511	15	1	the	the	DET
iajs-2511	15	2	conception	conception	NOUN
iajs-2511	15	3	of	of	ADP
iajs-2511	15	4	fuzzy	fuzzy	ADJ
iajs-2511	15	5	semi	semi	ADJ
iajs-2511	15	6	pre	pre	ADJ
iajs-2511	15	7	-	-	ADJ
iajs-2511	15	8	open	open	ADJ
iajs-2511	15	9	set	set	ADJ
iajs-2511	15	10	and	and	CCONJ
iajs-2511	15	11	fuzzy	fuzzy	ADJ
iajs-2511	15	12	semi	semi	ADJ
iajs-2511	15	13	pre	pre	ADJ
iajs-2511	15	14	-	-	ADJ
iajs-2511	15	15	open	open	ADJ
iajs-2511	15	16	continuity	continuity	NOUN
iajs-2511	15	17	in	in	ADP
iajs-2511	15	18	fuzzy	fuzzy	ADJ
iajs-2511	15	19	topological	topological	ADJ
iajs-2511	15	20	spaces	space	NOUN
iajs-2511	15	21	was	be	AUX
iajs-2511	15	22	introduced	introduce	VERB
iajs-2511	15	23	by	by	ADP
iajs-2511	15	24	thakur	thakur	PROPN
iajs-2511	15	25	,	,	PUNCT
iajs-2511	15	26	s.	s.	PROPN
iajs-2511	15	27	s.	s.	PROPN
iajs-2511	15	28	and	and	CCONJ
iajs-2511	15	29	singh	singh	PROPN
iajs-2511	15	30	,	,	PUNCT
iajs-2511	15	31	s.	s.	PROPN
iajs-2511	16	1	[	[	X
iajs-2511	16	2	5	5	X
iajs-2511	16	3	]	]	PUNCT
iajs-2511	16	4	and	and	CCONJ
iajs-2511	16	5	investigated	investigate	VERB
iajs-2511	16	6	some	some	PRON
iajs-2511	16	7	of	of	ADP
iajs-2511	16	8	their	their	PRON
iajs-2511	16	9	properties	property	NOUN
iajs-2511	16	10	.	.	PUNCT
iajs-2511	17	1	this	this	DET
iajs-2511	17	2	paper	paper	NOUN
iajs-2511	17	3	is	be	AUX
iajs-2511	17	4	to	to	PART
iajs-2511	17	5	introduce	introduce	VERB
iajs-2511	17	6	and	and	CCONJ
iajs-2511	17	7	investigate	investigate	VERB
iajs-2511	17	8	some	some	DET
iajs-2511	17	9	new	new	ADJ
iajs-2511	17	10	types	type	NOUN
iajs-2511	17	11	of	of	ADP
iajs-2511	17	12	fuzzy	fuzzy	ADJ
iajs-2511	17	13	semi	semi	ADJ
iajs-2511	17	14	pre	pre	VERB
iajs-2511	17	15	continuous	continuous	ADJ
iajs-2511	17	16	functions	function	NOUN
iajs-2511	17	17	and	and	CCONJ
iajs-2511	17	18	fuzzy	fuzzy	ADJ
iajs-2511	17	19	semi	semi	ADJ
iajs-2511	17	20	pre	pre	PROPN
iajs-2511	17	21	homeomorphism	homeomorphism	PROPN
iajs-2511	17	22	functions	function	NOUN
iajs-2511	17	23	via	via	ADP
iajs-2511	17	24	fuzzy	fuzzy	ADJ
iajs-2511	17	25	semi	semi	ADJ
iajs-2511	17	26	pre	pre	ADJ
iajs-2511	17	27	-	-	ADJ
iajs-2511	17	28	open	open	ADJ
iajs-2511	17	29	sets	set	NOUN
iajs-2511	17	30	.	.	PUNCT
iajs-2511	18	1	also	also	ADV
iajs-2511	18	2	,	,	PUNCT
iajs-2511	18	3	the	the	DET
iajs-2511	18	4	relationships	relationship	NOUN
iajs-2511	18	5	between	between	ADP
iajs-2511	18	6	these	these	DET
iajs-2511	18	7	functions	function	NOUN
iajs-2511	18	8	and	and	CCONJ
iajs-2511	18	9	other	other	ADJ
iajs-2511	18	10	types	type	NOUN
iajs-2511	18	11	are	be	AUX
iajs-2511	18	12	discussed	discuss	VERB
iajs-2511	18	13	.	.	PUNCT
iajs-2511	19	1	several	several	ADJ
iajs-2511	19	2	properties	property	NOUN
iajs-2511	19	3	of	of	ADP
iajs-2511	19	4	ibn	ibn	PROPN
iajs-2511	19	5	al	al	PROPN
iajs-2511	19	6	haitham	haitham	PROPN
iajs-2511	19	7	journal	journal	PROPN
iajs-2511	19	8	for	for	ADP
iajs-2511	19	9	pure	pure	ADJ
iajs-2511	19	10	and	and	CCONJ
iajs-2511	19	11	applied	apply	VERB
iajs-2511	19	12	science	science	NOUN
iajs-2511	19	13	journal	journal	PROPN
iajs-2511	19	14	homepage	homepage	NOUN
iajs-2511	19	15	:	:	PUNCT
iajs-2511	19	16	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2511	19	17	doi	doi	NOUN
iajs-2511	19	18	:	:	PUNCT
iajs-2511	19	19	10.30526/33.4.2511	10.30526/33.4.2511	PROPN
iajs-2511	19	20	article	article	NOUN
iajs-2511	19	21	history	history	NOUN
iajs-2511	19	22	:	:	PUNCT
iajs-2511	19	23	received,2019	received,2019	PROPN
iajs-2511	19	24	,	,	PUNCT
iajs-2511	19	25	accepted,2020	accepted,2020	VERB
iajs-2511	19	26	,	,	PUNCT
iajs-2511	19	27	published	publish	VERB
iajs-2511	19	28	in	in	ADP
iajs-2511	19	29	october	october	PROPN
iajs-2511	19	30	2020	2020	NUM
iajs-2511	19	31	  	  	SPACE
iajs-2511	19	32	74	74	NUM
iajs-2511	19	33	  	  	SPACE
iajs-2511	19	34	ibn	ibn	PROPN
iajs-2511	19	35	al	al	PROPN
iajs-2511	19	36	-	-	PUNCT
iajs-2511	19	37	haitham	haitham	PROPN
iajs-2511	19	38	jour	jour	X
iajs-2511	19	39	.	.	PROPN
iajs-2511	19	40	for	for	ADP
iajs-2511	19	41	pure	pure	ADJ
iajs-2511	19	42	&	&	CCONJ
iajs-2511	19	43	appl	appl	PROPN
iajs-2511	19	44	.	.	PUNCT
iajs-2511	20	1	sci	sci	PROPN
iajs-2511	20	2	.	.	PROPN
iajs-2511	21	1	33	33	NUM
iajs-2511	21	2	(	(	PUNCT
iajs-2511	21	3	4	4	NUM
iajs-2511	21	4	)	)	PUNCT
iajs-2511	21	5	2020	2020	NUM
iajs-2511	22	1	these	these	DET
iajs-2511	22	2	new	new	ADJ
iajs-2511	22	3	notions	notion	NOUN
iajs-2511	22	4	are	be	AUX
iajs-2511	22	5	investigated	investigate	VERB
iajs-2511	22	6	and	and	CCONJ
iajs-2511	22	7	the	the	DET
iajs-2511	22	8	connections	connection	NOUN
iajs-2511	22	9	between	between	ADP
iajs-2511	22	10	them	they	PRON
iajs-2511	22	11	are	be	AUX
iajs-2511	22	12	studied	study	VERB
iajs-2511	22	13	.	.	PUNCT
iajs-2511	23	1	moreover	moreover	ADV
iajs-2511	23	2	,	,	PUNCT
iajs-2511	23	3	some	some	DET
iajs-2511	23	4	results	result	NOUN
iajs-2511	23	5	in	in	ADP
iajs-2511	23	6	this	this	DET
iajs-2511	23	7	topic	topic	NOUN
iajs-2511	23	8	with	with	ADP
iajs-2511	23	9	some	some	DET
iajs-2511	23	10	properties	property	NOUN
iajs-2511	23	11	and	and	CCONJ
iajs-2511	23	12	corollaries	corollary	NOUN
iajs-2511	23	13	are	be	AUX
iajs-2511	23	14	developed	develop	VERB
iajs-2511	23	15	.	.	PUNCT
iajs-2511	24	1	2	2	X
iajs-2511	24	2	.	.	X
iajs-2511	24	3	preliminaries	preliminary	NOUN
iajs-2511	24	4	throughout	throughout	ADP
iajs-2511	24	5	this	this	DET
iajs-2511	24	6	paper	paper	NOUN
iajs-2511	24	7	x	x	PUNCT
iajs-2511	24	8	denotes	denotes	PROPN
iajs-2511	24	9	anon	anon	PROPN
iajs-2511	24	10	empty	empty	ADJ
iajs-2511	24	11	set	set	NOUN
iajs-2511	25	1	and	and	CCONJ
iajs-2511	25	2	i	i	PRON
iajs-2511	25	3	denote	denote	VERB
iajs-2511	25	4	the	the	DET
iajs-2511	25	5	interval	interval	NOUN
iajs-2511	25	6	[	[	X
iajs-2511	25	7	0	0	NUM
iajs-2511	25	8	,	,	PUNCT
iajs-2511	25	9	1	1	NUM
iajs-2511	25	10	]	]	PUNCT
iajs-2511	25	11	.	.	PUNCT
iajs-2511	26	1	a	a	DET
iajs-2511	26	2	fuzzy	fuzzy	ADJ
iajs-2511	26	3	set	set	NOUN
iajs-2511	26	4	in	in	ADP
iajs-2511	26	5	x	x	PRON
iajs-2511	26	6	is	be	AUX
iajs-2511	26	7	a	a	DET
iajs-2511	26	8	function	function	NOUN
iajs-2511	26	9	𝜇	𝜇	ADP
iajs-2511	26	10	from	from	ADP
iajs-2511	26	11	x	x	PRON
iajs-2511	26	12	in	in	ADP
iajs-2511	26	13	to	to	PART
iajs-2511	26	14	i.	i.	NOUN
iajs-2511	26	15	the	the	DET
iajs-2511	26	16	value	value	NOUN
iajs-2511	26	17	𝜇	𝜇	ADP
iajs-2511	26	18	𝑥	𝑥	PROPN
iajs-2511	26	19	represents	represent	VERB
iajs-2511	26	20	the	the	DET
iajs-2511	26	21	degree	degree	NOUN
iajs-2511	26	22	of	of	ADP
iajs-2511	26	23	membership	membership	NOUN
iajs-2511	26	24	of	of	ADP
iajs-2511	26	25	𝑥	𝑥	DET
iajs-2511	26	26	∈	∈	PROPN
iajs-2511	26	27	𝑋	𝑋	NOUN
iajs-2511	26	28	in	in	ADP
iajs-2511	26	29	the	the	DET
iajs-2511	26	30	fuzzy	fuzzy	ADJ
iajs-2511	26	31	set	set	NOUN
iajs-2511	26	32	a.	a.	NOUN
iajs-2511	26	33	the	the	DET
iajs-2511	26	34	family	family	NOUN
iajs-2511	26	35	of	of	ADP
iajs-2511	26	36	all	all	DET
iajs-2511	26	37	fuzzy	fuzzy	ADJ
iajs-2511	26	38	sets	set	NOUN
iajs-2511	26	39	on	on	ADP
iajs-2511	26	40	a	a	DET
iajs-2511	26	41	crisp	crisp	ADJ
iajs-2511	26	42	set	set	NOUN
iajs-2511	26	43	x	x	PUNCT
iajs-2511	26	44	will	will	AUX
iajs-2511	26	45	be	be	AUX
iajs-2511	26	46	denoted	denote	VERB
iajs-2511	26	47	by	by	ADP
iajs-2511	26	48	ix	ix	PROPN
iajs-2511	26	49	.	.	PUNCT
iajs-2511	27	1	a	a	DET
iajs-2511	27	2	family	family	NOUN
iajs-2511	27	3	�	�	PROPN
iajs-2511	27	4	̃	̃	PROPN
iajs-2511	27	5	�	�	PROPN
iajs-2511	27	6	of	of	ADP
iajs-2511	27	7	fuzzy	fuzzy	ADJ
iajs-2511	27	8	sets	set	NOUN
iajs-2511	27	9	in	in	ADP
iajs-2511	27	10	x	x	PROPN
iajs-2511	27	11	is	be	AUX
iajs-2511	27	12	called	call	VERB
iajs-2511	27	13	a	a	DET
iajs-2511	27	14	fuzzy	fuzzy	ADJ
iajs-2511	27	15	topology	topology	NOUN
iajs-2511	27	16	for	for	ADP
iajs-2511	27	17	x	x	SYM
iajs-2511	27	18	iff	iff	PROPN
iajs-2511	27	19	(	(	PUNCT
iajs-2511	27	20	1	1	NUM
iajs-2511	27	21	)	)	PUNCT
iajs-2511	27	22	0	0	NUM
iajs-2511	27	23	,	,	PUNCT
iajs-2511	27	24	1	1	NUM
iajs-2511	27	25	∈	∈	PROPN
iajs-2511	27	26	�	�	PROPN
iajs-2511	27	27	̃	̃	PROPN
iajs-2511	27	28	�	�	PROPN
iajs-2511	27	29	(	(	PUNCT
iajs-2511	27	30	2	2	NUM
iajs-2511	27	31	)	)	PUNCT
iajs-2511	27	32	for	for	ADP
iajs-2511	27	33	all	all	DET
iajs-2511	27	34	𝐴	𝐴	PROPN
iajs-2511	27	35	,	,	PUNCT
iajs-2511	27	36	𝐵	𝐵	PROPN
iajs-2511	27	37	∈	∈	PROPN
iajs-2511	27	38	�	�	PROPN
iajs-2511	27	39	̃	̃	PROPN
iajs-2511	27	40	�	�	PROPN
iajs-2511	27	41	then	then	ADV
iajs-2511	27	42	𝑀𝑖𝑛	𝑀𝑖𝑛	VERB
iajs-2511	27	43	𝜇	𝜇	ADP
iajs-2511	27	44	𝑥	𝑥	X
iajs-2511	27	45	,	,	PUNCT
iajs-2511	27	46	𝜇	𝜇	ADP
iajs-2511	27	47	𝑥	𝑥	X
iajs-2511	27	48	∈	∈	PROPN
iajs-2511	27	49	�	�	PROPN
iajs-2511	27	50	̃	̃	PROPN
iajs-2511	27	51	�	�	PROPN
iajs-2511	27	52	(	(	PUNCT
iajs-2511	27	53	3	3	NUM
iajs-2511	27	54	)	)	PUNCT
iajs-2511	27	55	if	if	SCONJ
iajs-2511	27	56	𝐴	𝐴	PROPN
iajs-2511	27	57	∈	∈	PROPN
iajs-2511	27	58	�	�	PROPN
iajs-2511	27	59	̃	̃	PROPN
iajs-2511	27	60	�	�	PROPN
iajs-2511	27	61	for	for	ADP
iajs-2511	27	62	each	each	DET
iajs-2511	27	63	𝑖	𝑖	SYM
iajs-2511	27	64	∈	∈	PROPN
iajs-2511	27	65	𝐼	𝐼	PROPN
iajs-2511	27	66	,	,	PUNCT
iajs-2511	27	67	then	then	ADV
iajs-2511	27	68	𝑆𝑢𝑝	𝑆𝑢𝑝	PROPN
iajs-2511	27	69	∈	∈	PROPN
iajs-2511	27	70	𝜇	𝜇	ADP
iajs-2511	27	71	𝑥	𝑥	X
iajs-2511	27	72	∈	∈	PROPN
iajs-2511	27	73	�	�	PROPN
iajs-2511	27	74	̃	̃	PROPN
iajs-2511	27	75	�	�	PROPN
iajs-2511	27	76	.	.	PUNCT
iajs-2511	28	1	moreover	moreover	ADV
iajs-2511	28	2	,	,	PUNCT
iajs-2511	28	3	the	the	DET
iajs-2511	28	4	pair	pair	NOUN
iajs-2511	28	5	(	(	PUNCT
iajs-2511	28	6	x,	x,	PROPN
iajs-2511	28	7	�	�	PROPN
iajs-2511	28	8	̃	̃	PROPN
iajs-2511	28	9	�	�	PROPN
iajs-2511	28	10	)	)	PUNCT
iajs-2511	28	11	is	be	AUX
iajs-2511	28	12	called	call	VERB
iajs-2511	28	13	a	a	DET
iajs-2511	28	14	fuzzy	fuzzy	ADJ
iajs-2511	28	15	topological	topological	ADJ
iajs-2511	28	16	space	space	NOUN
iajs-2511	28	17	(	(	PUNCT
iajs-2511	28	18	abbreviated	abbreviate	VERB
iajs-2511	28	19	as	as	ADP
iajs-2511	28	20	f.t.s	f.t.s	ADJ
iajs-2511	28	21	)	)	PUNCT
iajs-2511	28	22	and	and	CCONJ
iajs-2511	28	23	every	every	DET
iajs-2511	28	24	member	member	NOUN
iajs-2511	28	25	of	of	ADP
iajs-2511	28	26	�	�	PROPN
iajs-2511	28	27	̃	̃	PROPN
iajs-2511	28	28	�	�	PROPN
iajs-2511	28	29	is	be	AUX
iajs-2511	28	30	called	call	VERB
iajs-2511	28	31	a	a	DET
iajs-2511	28	32	fuzzy	fuzzy	ADJ
iajs-2511	28	33	open	open	NOUN
iajs-2511	28	34	set	set	NOUN
iajs-2511	28	35	[	[	X
iajs-2511	28	36	2	2	NUM
iajs-2511	28	37	]	]	PUNCT
iajs-2511	28	38	.	.	PUNCT
iajs-2511	29	1	a	a	DET
iajs-2511	29	2	fuzzy	fuzzy	ADJ
iajs-2511	29	3	set	set	NOUN
iajs-2511	29	4	in	in	ADP
iajs-2511	29	5	a	a	DET
iajs-2511	29	6	crisp	crisp	ADJ
iajs-2511	29	7	set	set	NOUN
iajs-2511	29	8	x	x	PUNCT
iajs-2511	29	9	is	be	AUX
iajs-2511	29	10	called	call	VERB
iajs-2511	29	11	a	a	DET
iajs-2511	29	12	fuzzy	fuzzy	ADJ
iajs-2511	29	13	point	point	NOUN
iajs-2511	29	14	if	if	SCONJ
iajs-2511	29	15	it	it	PRON
iajs-2511	29	16	takes	take	VERB
iajs-2511	29	17	the	the	DET
iajs-2511	29	18	grade	grade	NOUN
iajs-2511	29	19	of	of	ADP
iajs-2511	29	20	membership	membership	NOUN
iajs-2511	29	21	(	(	PUNCT
iajs-2511	29	22	0	0	NUM
iajs-2511	29	23	)	)	PUNCT
iajs-2511	29	24	for	for	ADP
iajs-2511	29	25	all	all	DET
iajs-2511	29	26	𝑥	𝑥	DET
iajs-2511	29	27	∈	∈	NOUN
iajs-2511	29	28	𝑋	𝑋	NOUN
iajs-2511	29	29	1	1	NUM
iajs-2511	29	30	,	,	PUNCT
iajs-2511	29	31	say	say	INTJ
iajs-2511	29	32	,	,	PUNCT
iajs-2511	29	33	𝑝	𝑝	PROPN
iajs-2511	29	34	∈	∈	PROPN
iajs-2511	29	35	𝑋.	𝑋.	PROPN
iajs-2511	29	36	if	if	SCONJ
iajs-2511	29	37	its	its	PRON
iajs-2511	29	38	grade	grade	NOUN
iajs-2511	29	39	of	of	ADP
iajs-2511	29	40	membership	membership	NOUN
iajs-2511	29	41	at	at	ADP
iajs-2511	29	42	𝑥	𝑥	PROPN
iajs-2511	29	43	is	be	AUX
iajs-2511	29	44	𝛼	𝛼	PRON
iajs-2511	29	45	(	(	PUNCT
iajs-2511	29	46	0	0	NUM
iajs-2511	29	47	𝛼	𝛼	NOUN
iajs-2511	29	48	1	1	NUM
iajs-2511	29	49	)	)	PUNCT
iajs-2511	29	50	,	,	PUNCT
iajs-2511	29	51	we	we	PRON
iajs-2511	29	52	denote	denote	VERB
iajs-2511	29	53	this	this	DET
iajs-2511	29	54	fuzzy	fuzzy	ADJ
iajs-2511	29	55	point	point	NOUN
iajs-2511	29	56	by	by	ADP
iajs-2511	29	57	𝑝	𝑝	PROPN
iajs-2511	29	58	,	,	PUNCT
iajs-2511	29	59	where	where	SCONJ
iajs-2511	29	60	the	the	DET
iajs-2511	29	61	point	point	NOUN
iajs-2511	29	62	𝑝	𝑝	NOUN
iajs-2511	29	63	is	be	AUX
iajs-2511	29	64	called	call	VERB
iajs-2511	29	65	its	its	PRON
iajs-2511	29	66	support	support	NOUN
iajs-2511	29	67	[	[	X
iajs-2511	29	68	6	6	NUM
iajs-2511	29	69	]	]	PUNCT
iajs-2511	29	70	.	.	PUNCT
iajs-2511	30	1	for	for	ADP
iajs-2511	30	2	any	any	DET
iajs-2511	30	3	fuzzy	fuzzy	ADJ
iajs-2511	30	4	𝑝	𝑝	NOUN
iajs-2511	30	5	and	and	CCONJ
iajs-2511	30	6	any	any	DET
iajs-2511	30	7	fuzzy	fuzzy	ADJ
iajs-2511	30	8	set	set	VERB
iajs-2511	30	9	𝐴	𝐴	PROPN
iajs-2511	30	10	,	,	PUNCT
iajs-2511	30	11	we	we	PRON
iajs-2511	30	12	write	write	VERB
iajs-2511	30	13	𝑝	𝑝	PROPN
iajs-2511	30	14	∈	∈	PROPN
iajs-2511	30	15	𝐴	𝐴	PROPN
iajs-2511	30	16	iff	iff	PROPN
iajs-2511	30	17	𝜀	𝜀	PROPN
iajs-2511	30	18	𝜇	𝜇	ADP
iajs-2511	30	19	𝑥	𝑥	PROPN
iajs-2511	30	20	.	.	PUNCT
iajs-2511	31	1	definition	definition	NOUN
iajs-2511	31	2	2.1	2.1	NUM
iajs-2511	32	1	[	[	X
iajs-2511	32	2	7	7	NUM
iajs-2511	32	3	]	]	PUNCT
iajs-2511	32	4	:	:	PUNCT
iajs-2511	32	5	let	let	VERB
iajs-2511	32	6	𝑓	𝑓	PRON
iajs-2511	32	7	:	:	PUNCT
iajs-2511	32	8	𝑋	𝑋	PROPN
iajs-2511	32	9	,	,	PUNCT
iajs-2511	32	10	�	�	PROPN
iajs-2511	32	11	̃	̃	PROPN
iajs-2511	32	12	�	�	PROPN
iajs-2511	32	13			PROPN
iajs-2511	32	14	𝑌	𝑌	PROPN
iajs-2511	32	15	,	,	PUNCT
iajs-2511	32	16	𝜈	𝜈	X
iajs-2511	32	17	,	,	PUNCT
iajs-2511	32	18	let	let	VERB
iajs-2511	32	19	𝐵	𝐵	PRON
iajs-2511	32	20	be	be	AUX
iajs-2511	32	21	a	a	DET
iajs-2511	32	22	fuzzy	fuzzy	ADJ
iajs-2511	32	23	set	set	NOUN
iajs-2511	32	24	in	in	ADP
iajs-2511	32	25	y	y	PROPN
iajs-2511	32	26	with	with	ADP
iajs-2511	32	27	membership	membership	NOUN
iajs-2511	32	28	function	function	NOUN
iajs-2511	32	29	𝜇	𝜇	ADP
iajs-2511	32	30	𝑦	𝑦	NOUN
iajs-2511	32	31	.	.	PUNCT
iajs-2511	33	1	then	then	ADV
iajs-2511	33	2	the	the	DET
iajs-2511	33	3	inverse	inverse	NOUN
iajs-2511	33	4	of	of	ADP
iajs-2511	33	5	𝐵	𝐵	PROPN
iajs-2511	33	6	written	write	VERB
iajs-2511	33	7	as	as	SCONJ
iajs-2511	33	8	𝑓	𝑓	DET
iajs-2511	33	9	𝐵	𝐵	NOUN
iajs-2511	33	10	is	be	AUX
iajs-2511	33	11	a	a	DET
iajs-2511	33	12	fuzzy	fuzzy	ADJ
iajs-2511	33	13	set	set	NOUN
iajs-2511	33	14	in	in	ADP
iajs-2511	33	15	x	x	PUNCT
iajs-2511	33	16	whose	whose	DET
iajs-2511	33	17	membership	membership	NOUN
iajs-2511	33	18	function	function	NOUN
iajs-2511	33	19	is	be	AUX
iajs-2511	33	20	defined	define	VERB
iajs-2511	33	21	by	by	ADP
iajs-2511	33	22	𝜇	𝜇	ADP
iajs-2511	33	23	𝑥	𝑥	X
iajs-2511	33	24	𝜇	𝜇	ADP
iajs-2511	33	25	𝑓	𝑓	PRON
iajs-2511	33	26	𝑥	𝑥	X
iajs-2511	33	27	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
iajs-2511	33	28	𝑎𝑙𝑙	𝑎𝑙𝑙	VERB
iajs-2511	33	29	𝑥	𝑥	X
iajs-2511	33	30	∈	∈	PROPN
iajs-2511	33	31	𝑋.	𝑋.	PROPN
iajs-2511	33	32	conversely	conversely	ADV
iajs-2511	33	33	,	,	PUNCT
iajs-2511	33	34	let	let	VERB
iajs-2511	33	35	𝐴	𝐴	PROPN
iajs-2511	33	36	be	be	AUX
iajs-2511	33	37	a	a	DET
iajs-2511	33	38	fuzzy	fuzzy	ADJ
iajs-2511	33	39	set	set	NOUN
iajs-2511	33	40	in	in	ADP
iajs-2511	33	41	x	x	PUNCT
iajs-2511	33	42	with	with	ADP
iajs-2511	33	43	membership	membership	NOUN
iajs-2511	33	44	function	function	NOUN
iajs-2511	33	45	𝜇	𝜇	ADP
iajs-2511	33	46	𝑥	𝑥	PROPN
iajs-2511	33	47	.	.	PUNCT
iajs-2511	34	1	the	the	DET
iajs-2511	34	2	image	image	NOUN
iajs-2511	34	3	of	of	ADP
iajs-2511	34	4	𝐴	𝐴	PROPN
iajs-2511	34	5	written	write	VERB
iajs-2511	34	6	as	as	ADP
iajs-2511	34	7	𝑓	𝑓	DET
iajs-2511	34	8	𝐴	𝐴	PROPN
iajs-2511	34	9	is	be	AUX
iajs-2511	34	10	a	a	DET
iajs-2511	34	11	fuzzy	fuzzy	ADJ
iajs-2511	34	12	set	set	NOUN
iajs-2511	34	13	in	in	ADP
iajs-2511	34	14	y	y	PROPN
iajs-2511	34	15	whose	whose	DET
iajs-2511	34	16	membership	membership	NOUN
iajs-2511	34	17	function	function	NOUN
iajs-2511	34	18	is	be	AUX
iajs-2511	34	19	given	give	VERB
iajs-2511	34	20	by	by	ADP
iajs-2511	34	21	𝜇	𝜇	ADP
iajs-2511	34	22	𝑌	𝑌	PROPN
iajs-2511	34	23	sup	sup	NOUN
iajs-2511	34	24	∈	∈	PROPN
iajs-2511	34	25	𝜇	𝜇	ADP
iajs-2511	34	26	𝑥	𝑥	PROPN
iajs-2511	34	27	,	,	PUNCT
iajs-2511	34	28	𝑖𝑓	𝑖𝑓	ADP
iajs-2511	34	29	𝜇	𝜇	ADP
iajs-2511	35	1	𝑥	𝑥	X
iajs-2511	35	2	𝑖𝑠	𝑖𝑠	PROPN
iajs-2511	35	3	𝑛𝑜𝑡	𝑛𝑜𝑡	PROPN
iajs-2511	35	4	𝑒𝑚𝑝𝑡𝑦	𝑒𝑚𝑝𝑡𝑦	VERB
iajs-2511	35	5	0	0	NUM
iajs-2511	35	6	,	,	PUNCT
iajs-2511	35	7	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	VERB
iajs-2511	35	8	for	for	SCONJ
iajs-2511	35	9	each	each	DET
iajs-2511	35	10	y	y	PROPN
iajs-2511	35	11	belong	belong	VERB
iajs-2511	35	12	to	to	ADP
iajs-2511	35	13	y	y	PROPN
iajs-2511	35	14	,	,	PUNCT
iajs-2511	35	15	where	where	SCONJ
iajs-2511	35	16	𝜇	𝜇	ADP
iajs-2511	35	17	𝑥	𝑥	X
iajs-2511	35	18	𝜇	𝜇	ADP
iajs-2511	35	19	𝑌	𝑌	PROPN
iajs-2511	35	20	𝜇	𝜇	ADP
iajs-2511	35	21	𝑌	𝑌	PROPN
iajs-2511	35	22	.	.	PUNCT
iajs-2511	36	1	definition	definition	NOUN
iajs-2511	36	2	2.2	2.2	NUM
iajs-2511	36	3	:	:	PUNCT
iajs-2511	36	4	let	let	VERB
iajs-2511	36	5	𝑓	𝑓	PRON
iajs-2511	36	6	:	:	PUNCT
iajs-2511	36	7	𝑋	𝑋	PROPN
iajs-2511	36	8	,	,	PUNCT
iajs-2511	36	9	�	�	PROPN
iajs-2511	36	10	̃	̃	PROPN
iajs-2511	36	11	�	�	PROPN
iajs-2511	36	12			PROPN
iajs-2511	36	13	𝑌	𝑌	PROPN
iajs-2511	36	14	,	,	PUNCT
iajs-2511	36	15	𝜈	𝜈	X
iajs-2511	36	16	,	,	PUNCT
iajs-2511	36	17	then	then	ADV
iajs-2511	36	18	f	f	PROPN
iajs-2511	36	19	is	be	AUX
iajs-2511	36	20	called	call	VERB
iajs-2511	36	21	:	:	PUNCT
iajs-2511	36	22	(	(	PUNCT
iajs-2511	36	23	1	1	X
iajs-2511	36	24	)	)	PUNCT
iajs-2511	36	25	"	"	PUNCT
iajs-2511	36	26	a	a	DET
iajs-2511	36	27	fuzzy	fuzzy	ADJ
iajs-2511	36	28	continuous	continuous	ADJ
iajs-2511	36	29	function	function	NOUN
iajs-2511	36	30	"	"	PUNCT
iajs-2511	36	31	if	if	SCONJ
iajs-2511	36	32	the	the	DET
iajs-2511	36	33	𝜇	𝜇	X
iajs-2511	36	34	𝑥	𝑥	PROPN
iajs-2511	36	35	is	be	AUX
iajs-2511	36	36	a	a	DET
iajs-2511	36	37	fuzzy	fuzzy	ADJ
iajs-2511	36	38	open	open	NOUN
iajs-2511	36	39	set	set	VERB
iajs-2511	36	40	in	in	ADP
iajs-2511	36	41	x	x	PUNCT
iajs-2511	36	42	for	for	ADP
iajs-2511	36	43	each	each	DET
iajs-2511	36	44	𝑦	𝑦	NOUN
iajs-2511	36	45	∈	∈	ADJ
iajs-2511	36	46	𝜈	𝜈	X
iajs-2511	36	47	and	and	CCONJ
iajs-2511	36	48	denoted	denote	VERB
iajs-2511	36	49	𝑓.	𝑓.	PROPN
iajs-2511	36	50	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	36	51	𝑓.	𝑓.	NOUN
iajs-2511	36	52	.	.	PUNCT
iajs-2511	37	1	[	[	X
iajs-2511	37	2	8	8	NUM
iajs-2511	37	3	]	]	SYM
iajs-2511	37	4	(	(	PUNCT
iajs-2511	37	5	2	2	X
iajs-2511	37	6	)	)	PUNCT
iajs-2511	37	7	"	"	PUNCT
iajs-2511	37	8	a	a	DET
iajs-2511	37	9	fuzzy	fuzzy	ADJ
iajs-2511	37	10	open	open	ADJ
iajs-2511	37	11	function	function	NOUN
iajs-2511	37	12	"	"	PUNCT
iajs-2511	37	13	if	if	SCONJ
iajs-2511	37	14	the	the	PRON
iajs-2511	37	15	𝜇	𝜇	X
iajs-2511	37	16	𝑌	𝑌	PROPN
iajs-2511	37	17	is	be	AUX
iajs-2511	37	18	a	a	DET
iajs-2511	37	19	fuzzy	fuzzy	ADJ
iajs-2511	37	20	open	open	NOUN
iajs-2511	37	21	set	set	NOUN
iajs-2511	37	22	in	in	ADP
iajs-2511	37	23	y	y	PROPN
iajs-2511	37	24	,	,	PUNCT
iajs-2511	37	25	for	for	ADP
iajs-2511	37	26	each	each	DET
iajs-2511	37	27	𝑥	𝑥	PROPN
iajs-2511	37	28	∈	∈	PROPN
iajs-2511	37	29	�	�	PROPN
iajs-2511	37	30	̃	̃	PROPN
iajs-2511	37	31	�	�	PROPN
iajs-2511	37	32	and	and	CCONJ
iajs-2511	37	33	denoted	denote	VERB
iajs-2511	37	34	𝑓.	𝑓.	NOUN
iajs-2511	37	35	𝑜.	𝑜.	PROPN
iajs-2511	37	36	𝑓.	𝑓.	PROPN
iajs-2511	37	37	.	.	PUNCT
iajs-2511	38	1	[	[	X
iajs-2511	38	2	9	9	NUM
iajs-2511	38	3	]	]	SYM
iajs-2511	38	4	(	(	PUNCT
iajs-2511	38	5	3	3	X
iajs-2511	38	6	)	)	PUNCT
iajs-2511	38	7	"	"	PUNCT
iajs-2511	38	8	a	a	DET
iajs-2511	38	9	fuzzy	fuzzy	ADJ
iajs-2511	38	10	closed	closed	ADJ
iajs-2511	38	11	function	function	NOUN
iajs-2511	38	12	"	"	PUNCT
iajs-2511	38	13	if	if	SCONJ
iajs-2511	38	14	the	the	PRON
iajs-2511	38	15	𝜇	𝜇	X
iajs-2511	38	16	𝑌	𝑌	PROPN
iajs-2511	38	17	is	be	AUX
iajs-2511	38	18	a	a	DET
iajs-2511	38	19	fuzzy	fuzzy	ADJ
iajs-2511	38	20	closed	close	VERB
iajs-2511	38	21	set	set	VERB
iajs-2511	38	22	in	in	ADP
iajs-2511	38	23	y	y	PROPN
iajs-2511	38	24	,	,	PUNCT
iajs-2511	38	25	for	for	ADP
iajs-2511	38	26	each	each	DET
iajs-2511	38	27	𝑥	𝑥	PROPN
iajs-2511	38	28	∈	∈	PROPN
iajs-2511	38	29	�	�	PROPN
iajs-2511	38	30	̃	̃	PROPN
iajs-2511	38	31	�	�	PROPN
iajs-2511	38	32	and	and	CCONJ
iajs-2511	38	33	denoted	denote	VERB
iajs-2511	38	34	𝑓.	𝑓.	PROPN
iajs-2511	38	35	𝑐𝑙.	𝑐𝑙.	PROPN
iajs-2511	38	36	𝑓.	𝑓.	NOUN
iajs-2511	38	37	.	.	PUNCT
iajs-2511	39	1	[	[	X
iajs-2511	39	2	10	10	NUM
iajs-2511	39	3	]	]	PUNCT
iajs-2511	39	4	definition	definition	NOUN
iajs-2511	39	5	2.3	2.3	NUM
iajs-2511	40	1	[	[	X
iajs-2511	40	2	2	2	NUM
iajs-2511	40	3	]	]	PUNCT
iajs-2511	40	4	:	:	PUNCT
iajs-2511	40	5	let	let	VERB
iajs-2511	40	6	𝑓	𝑓	PRON
iajs-2511	40	7	:	:	PUNCT
iajs-2511	40	8	𝑋	𝑋	PROPN
iajs-2511	40	9	,	,	PUNCT
iajs-2511	40	10	�	�	PROPN
iajs-2511	40	11	̃	̃	PROPN
iajs-2511	40	12	�	�	PROPN
iajs-2511	40	13			PROPN
iajs-2511	40	14	𝑌	𝑌	PROPN
iajs-2511	40	15	,	,	PUNCT
iajs-2511	40	16	𝜈	𝜈	DET
iajs-2511	40	17	bijection	bijection	ADJ
iajs-2511	40	18	fuzzy	fuzzy	ADJ
iajs-2511	40	19	function	function	NOUN
iajs-2511	40	20	,	,	PUNCT
iajs-2511	40	21	f	f	PROPN
iajs-2511	40	22	is	be	AUX
iajs-2511	40	23	called	call	VERB
iajs-2511	40	24	a	a	DET
iajs-2511	40	25	fuzzy	fuzzy	ADJ
iajs-2511	40	26	homeomorphism	homeomorphism	NOUN
iajs-2511	40	27	if	if	SCONJ
iajs-2511	40	28	f	f	PROPN
iajs-2511	40	29	and	and	CCONJ
iajs-2511	40	30	f	f	PROPN
iajs-2511	40	31	-1	-1	X
iajs-2511	40	32	are	be	AUX
iajs-2511	40	33	𝑓.	𝑓.	PROPN
iajs-2511	40	34	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	40	35	𝑓.	𝑓.	NOUN
iajs-2511	40	36	(	(	PUNCT
iajs-2511	40	37	abbreviated	abbreviate	VERB
iajs-2511	40	38	as	as	ADP
iajs-2511	40	39	𝑓.	𝑓.	NOUN
iajs-2511	40	40	ℎ.	ℎ.	PROPN
iajs-2511	40	41	𝑓.	𝑓.	PROPN
iajs-2511	40	42	)	)	PUNCT
iajs-2511	40	43	  	  	SPACE
iajs-2511	40	44	75	75	NUM
iajs-2511	40	45	  	  	SPACE
iajs-2511	40	46	ibn	ibn	PROPN
iajs-2511	40	47	al	al	PROPN
iajs-2511	40	48	-	-	PUNCT
iajs-2511	40	49	haitham	haitham	PROPN
iajs-2511	40	50	jour	jour	X
iajs-2511	40	51	.	.	PROPN
iajs-2511	40	52	for	for	ADP
iajs-2511	40	53	pure	pure	ADJ
iajs-2511	40	54	&	&	CCONJ
iajs-2511	40	55	appl	appl	PROPN
iajs-2511	40	56	.	.	PUNCT
iajs-2511	41	1	sci	sci	PROPN
iajs-2511	41	2	.	.	PROPN
iajs-2511	42	1	33	33	NUM
iajs-2511	42	2	(	(	PUNCT
iajs-2511	42	3	4	4	NUM
iajs-2511	42	4	)	)	PUNCT
iajs-2511	42	5	2020	2020	NUM
iajs-2511	42	6	theorem	theorem	VERB
iajs-2511	42	7	2.4	2.4	NUM
iajs-2511	42	8	[	[	SYM
iajs-2511	42	9	6	6	NUM
iajs-2511	42	10	]	]	PUNCT
iajs-2511	42	11	:	:	PUNCT
iajs-2511	42	12	let	let	VERB
iajs-2511	42	13	𝑓	𝑓	PRON
iajs-2511	42	14	:	:	PUNCT
iajs-2511	42	15	𝑋	𝑋	PROPN
iajs-2511	42	16	,	,	PUNCT
iajs-2511	42	17	�	�	PROPN
iajs-2511	42	18	̃	̃	PROPN
iajs-2511	42	19	�	�	PROPN
iajs-2511	42	20			PROPN
iajs-2511	42	21	𝑌	𝑌	PROPN
iajs-2511	42	22	,	,	PUNCT
iajs-2511	42	23	𝜈	𝜈	X
iajs-2511	42	24	,	,	PUNCT
iajs-2511	42	25	then	then	ADV
iajs-2511	42	26	all	all	DET
iajs-2511	42	27	the	the	DET
iajs-2511	42	28	below	below	NOUN
iajs-2511	42	29	are	be	AUX
iajs-2511	42	30	true	true	ADJ
iajs-2511	42	31	:	:	PUNCT
iajs-2511	42	32	(	(	PUNCT
iajs-2511	42	33	1	1	X
iajs-2511	42	34	)	)	PUNCT
iajs-2511	42	35	for	for	ADP
iajs-2511	42	36	any	any	DET
iajs-2511	42	37	fuzzy	fuzzy	ADJ
iajs-2511	42	38	set	set	NOUN
iajs-2511	42	39	𝐵	𝐵	NOUN
iajs-2511	42	40	in	in	ADP
iajs-2511	42	41	y	y	PROPN
iajs-2511	42	42	,	,	PUNCT
iajs-2511	42	43	𝜇	𝜇	ADP
iajs-2511	42	44	𝑥	𝑥	ADP
iajs-2511	42	45	1	1	NUM
iajs-2511	42	46	𝜇	𝜇	ADP
iajs-2511	42	47	𝑥	𝑥	NOUN
iajs-2511	42	48	.	.	PUNCT
iajs-2511	43	1	(	(	PUNCT
iajs-2511	43	2	2	2	X
iajs-2511	43	3	)	)	PUNCT
iajs-2511	43	4	for	for	ADP
iajs-2511	43	5	any	any	DET
iajs-2511	43	6	fuzzy	fuzzy	ADJ
iajs-2511	43	7	set	set	VERB
iajs-2511	43	8	𝐴	𝐴	PROPN
iajs-2511	43	9	in	in	ADP
iajs-2511	43	10	x	x	PROPN
iajs-2511	43	11	,	,	PUNCT
iajs-2511	43	12	1	1	NUM
iajs-2511	43	13	𝜇	𝜇	ADP
iajs-2511	43	14	𝑌	𝑌	PROPN
iajs-2511	43	15	𝜇	𝜇	ADP
iajs-2511	43	16	𝑌	𝑌	PROPN
iajs-2511	43	17	.	.	PUNCT
iajs-2511	44	1	(	(	PUNCT
iajs-2511	44	2	3	3	X
iajs-2511	44	3	)	)	PUNCT
iajs-2511	44	4	for	for	ADP
iajs-2511	44	5	any	any	DET
iajs-2511	44	6	fuzzy	fuzzy	ADJ
iajs-2511	44	7	set	set	VERB
iajs-2511	44	8	𝐴	𝐴	PROPN
iajs-2511	44	9	in	in	ADP
iajs-2511	44	10	x	x	NOUN
iajs-2511	44	11	,	,	PUNCT
iajs-2511	44	12	𝜇	𝜇	ADP
iajs-2511	44	13	𝑥	𝑥	X
iajs-2511	44	14	𝜇	𝜇	ADP
iajs-2511	44	15	𝑥	𝑥	NOUN
iajs-2511	44	16	and	and	CCONJ
iajs-2511	44	17	𝜇	𝜇	ADP
iajs-2511	44	18	𝑥	𝑥	X
iajs-2511	44	19	𝜇	𝜇	ADP
iajs-2511	44	20	𝑥	𝑥	X
iajs-2511	44	21	if	if	SCONJ
iajs-2511	44	22	𝑓	𝑓	PRON
iajs-2511	44	23	is	be	AUX
iajs-2511	44	24	one	one	NUM
iajs-2511	44	25	-	-	PUNCT
iajs-2511	44	26	to	to	ADP
iajs-2511	44	27	-	-	PUNCT
iajs-2511	44	28	one	one	NUM
iajs-2511	44	29	.	.	PUNCT
iajs-2511	45	1	(	(	PUNCT
iajs-2511	45	2	4	4	NUM
iajs-2511	45	3	)	)	PUNCT
iajs-2511	45	4	for	for	ADP
iajs-2511	45	5	any	any	DET
iajs-2511	45	6	fuzzy	fuzzy	ADJ
iajs-2511	45	7	set	set	NOUN
iajs-2511	45	8	𝐵	𝐵	NOUN
iajs-2511	45	9	in	in	ADP
iajs-2511	45	10	y	y	PROPN
iajs-2511	45	11	,	,	PUNCT
iajs-2511	45	12	𝜇	𝜇	ADP
iajs-2511	45	13	𝑦	𝑦	NOUN
iajs-2511	45	14	𝜇	𝜇	ADP
iajs-2511	45	15	𝑦	𝑦	NOUN
iajs-2511	45	16	and	and	CCONJ
iajs-2511	45	17	𝜇	𝜇	ADP
iajs-2511	45	18	𝑦	𝑦	NOUN
iajs-2511	45	19	𝜇	𝜇	ADP
iajs-2511	45	20	𝑦	𝑦	NOUN
iajs-2511	45	21	if	if	SCONJ
iajs-2511	45	22	𝑓	𝑓	PRON
iajs-2511	45	23	is	be	AUX
iajs-2511	45	24	onto	onto	ADP
iajs-2511	45	25	.	.	PROPN
iajs-2511	46	1	3	3	X
iajs-2511	46	2	.	.	X
iajs-2511	46	3	fuzzy	fuzzy	ADJ
iajs-2511	46	4	semi	semi	ADV
iajs-2511	46	5	pre	pre	VERB
iajs-2511	46	6	open	open	ADJ
iajs-2511	46	7	sets	set	NOUN
iajs-2511	46	8	this	this	DET
iajs-2511	46	9	section	section	NOUN
iajs-2511	46	10	is	be	AUX
iajs-2511	46	11	devoted	devote	VERB
iajs-2511	46	12	to	to	ADP
iajs-2511	46	13	definitions	definition	NOUN
iajs-2511	46	14	,	,	PUNCT
iajs-2511	46	15	and	and	CCONJ
iajs-2511	46	16	some	some	DET
iajs-2511	46	17	theorems	theorem	NOUN
iajs-2511	46	18	of	of	ADP
iajs-2511	46	19	fuzzy	fuzzy	ADJ
iajs-2511	46	20	semi	semi	ADJ
iajs-2511	46	21	pre	pre	ADJ
iajs-2511	46	22	-	-	ADJ
iajs-2511	46	23	open	open	ADJ
iajs-2511	46	24	set	set	ADJ
iajs-2511	46	25	and	and	CCONJ
iajs-2511	46	26	fuzzy	fuzzy	ADJ
iajs-2511	46	27	semi	semi	ADV
iajs-2511	46	28	pre	pre	X
iajs-2511	46	29	closed	closed	ADJ
iajs-2511	46	30	set	set	NOUN
iajs-2511	46	31	.	.	PUNCT
iajs-2511	47	1	moreover	moreover	ADV
iajs-2511	47	2	,	,	PUNCT
iajs-2511	47	3	we	we	PRON
iajs-2511	47	4	study	study	VERB
iajs-2511	47	5	in	in	ADP
iajs-2511	47	6	this	this	DET
iajs-2511	47	7	section	section	NOUN
iajs-2511	47	8	some	some	DET
iajs-2511	47	9	remarks	remark	NOUN
iajs-2511	47	10	and	and	CCONJ
iajs-2511	47	11	relationship	relationship	NOUN
iajs-2511	47	12	between	between	ADP
iajs-2511	47	13	fuzzy	fuzzy	ADJ
iajs-2511	47	14	semi	semi	ADJ
iajs-2511	47	15	pre	pre	ADJ
iajs-2511	47	16	-	-	ADJ
iajs-2511	47	17	open	open	ADJ
iajs-2511	47	18	(	(	PUNCT
iajs-2511	47	19	semi	semi	ADV
iajs-2511	47	20	pre	pre	X
iajs-2511	47	21	closed	closed	ADJ
iajs-2511	47	22	)	)	PUNCT
iajs-2511	47	23	set	set	NOUN
iajs-2511	47	24	and	and	CCONJ
iajs-2511	47	25	fuzzy	fuzzy	ADJ
iajs-2511	47	26	open	open	ADJ
iajs-2511	47	27	(	(	PUNCT
iajs-2511	47	28	closed	closed	ADJ
iajs-2511	47	29	)	)	PUNCT
iajs-2511	47	30	set	set	NOUN
iajs-2511	47	31	.	.	PUNCT
iajs-2511	48	1	also	also	ADV
iajs-2511	48	2	some	some	PRON
iajs-2511	48	3	of	of	ADP
iajs-2511	48	4	their	their	PRON
iajs-2511	48	5	properties	property	NOUN
iajs-2511	48	6	which	which	PRON
iajs-2511	48	7	we	we	PRON
iajs-2511	48	8	need	need	VERB
iajs-2511	48	9	them	they	PRON
iajs-2511	48	10	in	in	ADP
iajs-2511	48	11	our	our	PRON
iajs-2511	48	12	study	study	NOUN
iajs-2511	48	13	are	be	AUX
iajs-2511	48	14	discussed	discuss	VERB
iajs-2511	48	15	.	.	PUNCT
iajs-2511	49	1	definition	definition	NOUN
iajs-2511	49	2	3.1	3.1	NUM
iajs-2511	50	1	[	[	X
iajs-2511	50	2	11	11	NUM
iajs-2511	50	3	]	]	PUNCT
iajs-2511	50	4	:	:	PUNCT
iajs-2511	50	5	let	let	VERB
iajs-2511	50	6	(	(	PUNCT
iajs-2511	50	7	x,	x,	NUM
iajs-2511	50	8	�	�	PROPN
iajs-2511	50	9	̃	̃	PROPN
iajs-2511	50	10	�	�	PROPN
iajs-2511	50	11	)	)	PUNCT
iajs-2511	50	12	be	be	VERB
iajs-2511	50	13	a	a	DET
iajs-2511	50	14	f.t.s	f.t.s	NOUN
iajs-2511	50	15	,	,	PUNCT
iajs-2511	50	16	a	a	DET
iajs-2511	50	17	fuzzy	fuzzy	ADJ
iajs-2511	50	18	set	set	VERB
iajs-2511	50	19	𝐴	𝐴	PROPN
iajs-2511	50	20	in	in	ADP
iajs-2511	50	21	x	x	PROPN
iajs-2511	50	22	is	be	AUX
iajs-2511	50	23	called	call	VERB
iajs-2511	50	24	:	:	PUNCT
iajs-2511	50	25	(	(	PUNCT
iajs-2511	50	26	1	1	X
iajs-2511	50	27	)	)	PUNCT
iajs-2511	50	28	fuzzy	fuzzy	ADJ
iajs-2511	50	29	semi	semi	ADV
iajs-2511	50	30	pre	pre	ADJ
iajs-2511	50	31	-	-	ADJ
iajs-2511	50	32	open	open	ADJ
iajs-2511	50	33	set	set	NOUN
iajs-2511	50	34	if	if	SCONJ
iajs-2511	50	35	𝜇	𝜇	ADP
iajs-2511	50	36	𝑥	𝑥	X
iajs-2511	50	37	𝜇	𝜇	X
iajs-2511	50	38	𝑥	𝑥	X
iajs-2511	50	39	.	.	PUNCT
iajs-2511	51	1	(	(	PUNCT
iajs-2511	51	2	2	2	X
iajs-2511	51	3	)	)	PUNCT
iajs-2511	51	4	fuzzy	fuzzy	ADJ
iajs-2511	51	5	semi	semi	ADV
iajs-2511	51	6	pre	pre	X
iajs-2511	51	7	closed	closed	ADJ
iajs-2511	51	8	set	set	VERB
iajs-2511	51	9	if	if	SCONJ
iajs-2511	51	10	𝜇	𝜇	ADP
iajs-2511	51	11	𝑥	𝑥	X
iajs-2511	51	12	𝜇	𝜇	ADP
iajs-2511	51	13	𝑥	𝑥	X
iajs-2511	51	14	.	.	PUNCT
iajs-2511	52	1	notation	notation	NOUN
iajs-2511	52	2	3.2	3.2	NUM
iajs-2511	52	3	:	:	PUNCT
iajs-2511	52	4	in	in	ADP
iajs-2511	52	5	f.t.s	f.t.s	X
iajs-2511	52	6	(	(	PUNCT
iajs-2511	52	7	x,	x,	PROPN
iajs-2511	52	8	�	�	PROPN
iajs-2511	52	9	̃	̃	PROPN
iajs-2511	52	10	�	�	PROPN
iajs-2511	52	11	)	)	PUNCT
iajs-2511	52	12	,	,	PUNCT
iajs-2511	52	13	we	we	PRON
iajs-2511	52	14	denote	denote	VERB
iajs-2511	52	15	:	:	PUNCT
iajs-2511	52	16	(	(	PUNCT
iajs-2511	52	17	1	1	X
iajs-2511	52	18	)	)	PUNCT
iajs-2511	52	19	the	the	DET
iajs-2511	52	20	family	family	NOUN
iajs-2511	52	21	of	of	ADP
iajs-2511	52	22	all	all	DET
iajs-2511	52	23	fuzzy	fuzzy	ADJ
iajs-2511	52	24	semi	semi	ADV
iajs-2511	52	25	pre	pre	ADJ
iajs-2511	52	26	-	-	ADJ
iajs-2511	52	27	open	open	ADJ
iajs-2511	52	28	sets	set	NOUN
iajs-2511	52	29	of	of	ADP
iajs-2511	52	30	x	x	PUNCT
iajs-2511	52	31	by	by	ADP
iajs-2511	52	32	f.	f.	PROPN
iajs-2511	52	33	s.	s.	PROPN
iajs-2511	53	1	p.	p.	PROPN
iajs-2511	53	2	o.	o.	PROPN
iajs-2511	54	1	x	x	INTJ
iajs-2511	54	2	.	.	PUNCT
iajs-2511	55	1	(	(	PUNCT
iajs-2511	55	2	2	2	X
iajs-2511	55	3	)	)	PUNCT
iajs-2511	55	4	the	the	DET
iajs-2511	55	5	family	family	NOUN
iajs-2511	55	6	of	of	ADP
iajs-2511	55	7	all	all	DET
iajs-2511	55	8	fuzzy	fuzzy	ADJ
iajs-2511	55	9	semi	semi	ADV
iajs-2511	55	10	pre	pre	VERB
iajs-2511	55	11	closed	closed	ADJ
iajs-2511	55	12	sets	set	NOUN
iajs-2511	55	13	of	of	ADP
iajs-2511	55	14	x	x	PUNCT
iajs-2511	55	15	by	by	ADP
iajs-2511	55	16	f.	f.	PROPN
iajs-2511	55	17	s.	s.	PROPN
iajs-2511	56	1	p.	p.	PROPN
iajs-2511	56	2	c.	c.	PROPN
iajs-2511	57	1	x	x	PUNCT
iajs-2511	57	2	.	.	PUNCT
iajs-2511	58	1	theorem	theorem	VERB
iajs-2511	58	2	3.3	3.3	NUM
iajs-2511	59	1	[	[	SYM
iajs-2511	59	2	5	5	NUM
iajs-2511	59	3	]	]	PUNCT
iajs-2511	59	4	:	:	PUNCT
iajs-2511	59	5	let	let	VERB
iajs-2511	59	6	𝜌	𝜌	X
iajs-2511	59	7	in	in	ADP
iajs-2511	59	8	f.t.s	f.t.s	X
iajs-2511	59	9	(	(	PUNCT
iajs-2511	59	10	x,	x,	PROPN
iajs-2511	59	11	�	�	PROPN
iajs-2511	59	12	̃	̃	PROPN
iajs-2511	59	13	�	�	PROPN
iajs-2511	59	14	)	)	PUNCT
iajs-2511	59	15	,	,	PUNCT
iajs-2511	59	16	𝜇	𝜇	ADP
iajs-2511	59	17	𝑥	𝑥	PRON
iajs-2511	59	18	∈	∈	PROPN
iajs-2511	59	19	f.s.p.c(x	f.s.p.c(x	NOUN
iajs-2511	59	20	)	)	PUNCT
iajs-2511	59	21	if	if	SCONJ
iajs-2511	59	22	and	and	CCONJ
iajs-2511	59	23	only	only	ADV
iajs-2511	59	24	if	if	SCONJ
iajs-2511	59	25	1𝜇	1𝜇	NUM
iajs-2511	59	26	𝑥	𝑥	X
iajs-2511	59	27	∈	∈	PROPN
iajs-2511	59	28	f.s.p.o.(x	f.s.p.o.(x	NOUN
iajs-2511	59	29	)	)	PUNCT
iajs-2511	59	30	.	.	PUNCT
iajs-2511	60	1	remark	remark	VERB
iajs-2511	60	2	3.4	3.4	NUM
iajs-2511	60	3	:	:	PUNCT
iajs-2511	60	4	every	every	DET
iajs-2511	60	5	fuzzy	fuzzy	ADJ
iajs-2511	60	6	open	open	ADJ
iajs-2511	60	7	(	(	PUNCT
iajs-2511	60	8	resp	resp	NOUN
iajs-2511	60	9	.	.	PUNCT
iajs-2511	61	1	closed	closed	ADJ
iajs-2511	61	2	)	)	PUNCT
iajs-2511	61	3	set	set	NOUN
iajs-2511	61	4	is	be	AUX
iajs-2511	61	5	fuzzy	fuzzy	ADJ
iajs-2511	61	6	semi	semi	ADV
iajs-2511	61	7	pre	pre	ADJ
iajs-2511	61	8	-	-	ADJ
iajs-2511	61	9	open	open	ADJ
iajs-2511	61	10	(	(	PUNCT
iajs-2511	61	11	resp	resp	NOUN
iajs-2511	61	12	.	.	PUNCT
iajs-2511	62	1	semi	semi	ADJ
iajs-2511	62	2	pre	pre	VERB
iajs-2511	62	3	closed	closed	ADJ
iajs-2511	62	4	)	)	PUNCT
iajs-2511	62	5	set	set	NOUN
iajs-2511	62	6	.	.	PUNCT
iajs-2511	63	1	but	but	CCONJ
iajs-2511	63	2	the	the	DET
iajs-2511	63	3	converse	converse	NOUN
iajs-2511	63	4	is	be	AUX
iajs-2511	63	5	not	not	PART
iajs-2511	63	6	true	true	ADJ
iajs-2511	63	7	in	in	ADP
iajs-2511	63	8	general	general	ADJ
iajs-2511	63	9	.	.	PUNCT
iajs-2511	64	1	example	example	NOUN
iajs-2511	64	2	3.5	3.5	NUM
iajs-2511	64	3	:	:	PUNCT
iajs-2511	64	4	let	let	VERB
iajs-2511	64	5	𝑋	𝑋	PROPN
iajs-2511	64	6	𝛼	𝛼	PROPN
iajs-2511	64	7	,	,	PUNCT
iajs-2511	64	8	𝛽	𝛽	NOUN
iajs-2511	64	9	and	and	CCONJ
iajs-2511	64	10	let	let	VERB
iajs-2511	64	11	𝐴	𝐴	PROPN
iajs-2511	64	12	,	,	PUNCT
iajs-2511	64	13	𝐵	𝐵	PROPN
iajs-2511	64	14	are	be	AUX
iajs-2511	64	15	fuzzy	fuzzy	ADJ
iajs-2511	64	16	sets	set	NOUN
iajs-2511	64	17	of	of	ADP
iajs-2511	64	18	x	x	PUNCT
iajs-2511	64	19	defined	define	VERB
iajs-2511	64	20	as	as	SCONJ
iajs-2511	64	21	follows	follow	VERB
iajs-2511	64	22	:	:	PUNCT
iajs-2511	64	23	𝜇	𝜇	SCONJ
iajs-2511	64	24	𝛼	𝛼	PROPN
iajs-2511	64	25	0.4	0.4	NUM
iajs-2511	64	26	𝜇	𝜇	ADP
iajs-2511	64	27	𝛽	𝛽	PROPN
iajs-2511	64	28	0.4	0.4	NUM
iajs-2511	64	29	𝜇	𝜇	ADP
iajs-2511	64	30	𝛼	𝛼	SYM
iajs-2511	64	31	0.7	0.7	NUM
iajs-2511	64	32	𝜇	𝜇	ADP
iajs-2511	64	33	𝛽	𝛽	NOUN
iajs-2511	64	34	0.7	0.7	NUM
iajs-2511	64	35	𝜇	𝜇	ADP
iajs-2511	64	36	𝛼	𝛼	SYM
iajs-2511	64	37	0.8	0.8	NUM
iajs-2511	64	38	𝜇	𝜇	ADP
iajs-2511	64	39	𝛽	𝛽	PROPN
iajs-2511	64	40	0.6	0.6	NUM
iajs-2511	64	41	𝜇	𝜇	ADP
iajs-2511	64	42	𝛼	𝛼	PROPN
iajs-2511	64	43	0.3	0.3	NUM
iajs-2511	64	44	𝜇	𝜇	ADP
iajs-2511	64	45	𝛽	𝛽	NOUN
iajs-2511	64	46	0.7	0.7	NUM
iajs-2511	64	47	let	let	VERB
iajs-2511	64	48	�	�	PROPN
iajs-2511	64	49	̃	̃	PROPN
iajs-2511	64	50	�	�	PROPN
iajs-2511	64	51	0	0	NUM
iajs-2511	64	52	,	,	PUNCT
iajs-2511	64	53	1	1	NUM
iajs-2511	64	54	,	,	PUNCT
iajs-2511	64	55	𝐴	𝐴	PROPN
iajs-2511	64	56	,	,	PUNCT
iajs-2511	64	57	𝐵	𝐵	NOUN
iajs-2511	64	58	be	be	VERB
iajs-2511	64	59	a	a	DET
iajs-2511	64	60	f.t.s	f.t.s	NOUN
iajs-2511	64	61	.	.	PUNCT
iajs-2511	65	1	on	on	ADP
iajs-2511	65	2	x	x	SYM
iajs-2511	65	3	,	,	PUNCT
iajs-2511	65	4	it	it	PRON
iajs-2511	65	5	's	be	AUX
iajs-2511	65	6	clear	clear	ADJ
iajs-2511	65	7	that	that	SCONJ
iajs-2511	65	8	:	:	PUNCT
iajs-2511	65	9	(	(	PUNCT
iajs-2511	65	10	1	1	X
iajs-2511	65	11	)	)	PUNCT
iajs-2511	65	12	the	the	DET
iajs-2511	65	13	fuzzy	fuzzy	ADJ
iajs-2511	65	14	set	set	VERB
iajs-2511	65	15	𝐶	𝐶	PROPN
iajs-2511	65	16	is	be	AUX
iajs-2511	65	17	fuzzy	fuzzy	ADJ
iajs-2511	65	18	semi	semi	ADV
iajs-2511	65	19	pre	pre	ADJ
iajs-2511	65	20	-	-	ADJ
iajs-2511	65	21	open	open	ADJ
iajs-2511	65	22	set	set	NOUN
iajs-2511	65	23	in	in	ADP
iajs-2511	65	24	x	x	PUNCT
iajs-2511	66	1	but	but	CCONJ
iajs-2511	66	2	it	it	PRON
iajs-2511	66	3	is	be	AUX
iajs-2511	66	4	not	not	PART
iajs-2511	66	5	a	a	DET
iajs-2511	66	6	fuzzy	fuzzy	ADJ
iajs-2511	66	7	open	open	ADJ
iajs-2511	66	8	set	set	NOUN
iajs-2511	66	9	.	.	PUNCT
iajs-2511	67	1	(	(	PUNCT
iajs-2511	67	2	2	2	X
iajs-2511	67	3	)	)	PUNCT
iajs-2511	67	4	the	the	DET
iajs-2511	67	5	fuzzy	fuzzy	ADJ
iajs-2511	67	6	set	set	NOUN
iajs-2511	67	7	𝐸	𝐸	PROPN
iajs-2511	67	8	is	be	AUX
iajs-2511	67	9	fuzzy	fuzzy	ADJ
iajs-2511	67	10	semi	semi	ADV
iajs-2511	67	11	pre	pre	X
iajs-2511	67	12	closed	closed	ADJ
iajs-2511	67	13	set	set	VERB
iajs-2511	68	1	but	but	CCONJ
iajs-2511	68	2	it	it	PRON
iajs-2511	68	3	is	be	AUX
iajs-2511	68	4	not	not	PART
iajs-2511	68	5	a	a	DET
iajs-2511	68	6	fuzzy	fuzzy	ADJ
iajs-2511	68	7	closed	close	VERB
iajs-2511	68	8	set	set	NOUN
iajs-2511	68	9	.	.	PUNCT
iajs-2511	69	1	theorem	theorem	VERB
iajs-2511	69	2	3.6	3.6	NUM
iajs-2511	70	1	[	[	SYM
iajs-2511	70	2	5	5	NUM
iajs-2511	70	3	]	]	PUNCT
iajs-2511	70	4	:	:	PUNCT
iajs-2511	70	5	let	let	VERB
iajs-2511	70	6	(	(	PUNCT
iajs-2511	70	7	x,	x,	NUM
iajs-2511	70	8	�	�	PROPN
iajs-2511	70	9	̃	̃	PROPN
iajs-2511	70	10	�	�	PROPN
iajs-2511	70	11	)	)	PUNCT
iajs-2511	70	12	be	be	VERB
iajs-2511	70	13	a	a	DET
iajs-2511	70	14	f.t.s	f.t.s	NOUN
iajs-2511	70	15	,	,	PUNCT
iajs-2511	70	16	then	then	ADV
iajs-2511	70	17	:	:	PUNCT
iajs-2511	70	18	  	  	SPACE
iajs-2511	70	19	76	76	NUM
iajs-2511	70	20	  	  	SPACE
iajs-2511	70	21	ibn	ibn	PROPN
iajs-2511	70	22	al	al	PROPN
iajs-2511	70	23	-	-	PUNCT
iajs-2511	70	24	haitham	haitham	PROPN
iajs-2511	70	25	jour	jour	X
iajs-2511	70	26	.	.	PROPN
iajs-2511	71	1	for	for	ADP
iajs-2511	71	2	pure	pure	ADJ
iajs-2511	71	3	&	&	CCONJ
iajs-2511	71	4	appl	appl	PROPN
iajs-2511	71	5	.	.	PUNCT
iajs-2511	72	1	sci	sci	PROPN
iajs-2511	72	2	.	.	PROPN
iajs-2511	73	1	33	33	NUM
iajs-2511	73	2	(	(	PUNCT
iajs-2511	73	3	4	4	NUM
iajs-2511	73	4	)	)	PUNCT
iajs-2511	73	5	2020	2020	NUM
iajs-2511	73	6	(	(	PUNCT
iajs-2511	73	7	1	1	X
iajs-2511	73	8	)	)	PUNCT
iajs-2511	73	9	let	let	VERB
iajs-2511	73	10	𝐴	𝐴	PROPN
iajs-2511	73	11	∈	∈	PROPN
iajs-2511	74	1	f.	f.	PROPN
iajs-2511	74	2	s.	s.	PROPN
iajs-2511	74	3	p.	p.	PROPN
iajs-2511	75	1	o.	o.	PROPN
iajs-2511	76	1	x	x	PUNCT
iajs-2511	76	2	for	for	ADP
iajs-2511	76	3	each	each	DET
iajs-2511	76	4	𝑖	𝑖	SYM
iajs-2511	76	5	∈	∈	PROPN
iajs-2511	76	6	𝐼	𝐼	ADP
iajs-2511	76	7	then	then	ADV
iajs-2511	76	8	𝑆𝑢𝑝	𝑆𝑢𝑝	PROPN
iajs-2511	76	9	∈	∈	PROPN
iajs-2511	76	10	𝜇	𝜇	ADP
iajs-2511	76	11	𝑥	𝑥	X
iajs-2511	76	12	∈	∈	PROPN
iajs-2511	77	1	f.	f.	PROPN
iajs-2511	77	2	s.	s.	PROPN
iajs-2511	77	3	p.	p.	PROPN
iajs-2511	77	4	o.	o.	PROPN
iajs-2511	78	1	x	x	INTJ
iajs-2511	78	2	.	.	PUNCT
iajs-2511	79	1	(	(	PUNCT
iajs-2511	79	2	2	2	X
iajs-2511	79	3	)	)	PUNCT
iajs-2511	79	4	let	let	VERB
iajs-2511	79	5	𝐵	𝐵	PROPN
iajs-2511	79	6	∈	∈	PROPN
iajs-2511	80	1	f.	f.	PROPN
iajs-2511	80	2	s.	s.	PROPN
iajs-2511	81	1	p.	p.	PROPN
iajs-2511	81	2	c.	c.	PROPN
iajs-2511	82	1	x	x	PUNCT
iajs-2511	82	2	for	for	ADP
iajs-2511	82	3	each	each	DET
iajs-2511	82	4	𝑖	𝑖	SYM
iajs-2511	82	5	∈	∈	PROPN
iajs-2511	83	1	𝐼	𝐼	PROPN
iajs-2511	83	2	then	then	ADV
iajs-2511	83	3	𝐼𝑛𝑓	𝐼𝑛𝑓	PROPN
iajs-2511	83	4	∈	∈	PROPN
iajs-2511	83	5	𝜇	𝜇	ADP
iajs-2511	83	6	𝑥	𝑥	X
iajs-2511	83	7	∈	∈	PROPN
iajs-2511	84	1	f.	f.	PROPN
iajs-2511	84	2	s.	s.	PROPN
iajs-2511	85	1	p.	p.	PROPN
iajs-2511	85	2	c.	c.	PROPN
iajs-2511	86	1	x	x	PUNCT
iajs-2511	86	2	.	.	PUNCT
iajs-2511	87	1	remark	remark	NOUN
iajs-2511	87	2	3.7	3.7	NUM
iajs-2511	88	1	[	[	X
iajs-2511	88	2	5	5	NUM
iajs-2511	88	3	]	]	NUM
iajs-2511	88	4	:	:	PUNCT
iajs-2511	88	5	(	(	PUNCT
iajs-2511	88	6	1	1	X
iajs-2511	88	7	)	)	PUNCT
iajs-2511	88	8	let	let	VERB
iajs-2511	88	9	𝛿	𝛿	NOUN
iajs-2511	88	10	and	and	CCONJ
iajs-2511	88	11	𝜗	𝜗	NOUN
iajs-2511	88	12	be	be	AUX
iajs-2511	88	13	two	two	NUM
iajs-2511	88	14	fuzzy	fuzzy	ADJ
iajs-2511	88	15	semi	semi	ADJ
iajs-2511	88	16	pre	pre	ADJ
iajs-2511	88	17	-	-	ADJ
iajs-2511	88	18	open	open	ADJ
iajs-2511	88	19	sets	set	NOUN
iajs-2511	88	20	then	then	ADV
iajs-2511	88	21	𝑀𝑖𝑛	𝑀𝑖𝑛	VERB
iajs-2511	88	22	𝜇	𝜇	ADP
iajs-2511	88	23	𝑥	𝑥	X
iajs-2511	88	24	,	,	PUNCT
iajs-2511	88	25	𝜇	𝜇	ADP
iajs-2511	88	26	𝑥	𝑥	X
iajs-2511	88	27	need	need	NOUN
iajs-2511	88	28	not	not	PART
iajs-2511	88	29	to	to	PART
iajs-2511	88	30	be	be	AUX
iajs-2511	88	31	fuzzy	fuzzy	ADJ
iajs-2511	88	32	semi	semi	ADV
iajs-2511	88	33	pre	pre	VERB
iajs-2511	88	34	open	open	ADJ
iajs-2511	88	35	set	set	NOUN
iajs-2511	88	36	.	.	PUNCT
iajs-2511	89	1	(	(	PUNCT
iajs-2511	89	2	2	2	X
iajs-2511	89	3	)	)	PUNCT
iajs-2511	89	4	let	let	VERB
iajs-2511	89	5	𝜌	𝜌	PRON
iajs-2511	89	6	and	and	CCONJ
iajs-2511	89	7	𝜎	𝜎	PROPN
iajs-2511	89	8	be	be	AUX
iajs-2511	89	9	two	two	NUM
iajs-2511	89	10	fuzzy	fuzzy	ADJ
iajs-2511	89	11	semi	semi	ADV
iajs-2511	89	12	pre	pre	X
iajs-2511	89	13	closed	closed	ADJ
iajs-2511	89	14	sets	set	NOUN
iajs-2511	89	15	then	then	ADV
iajs-2511	89	16	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2511	89	17	𝜇	𝜇	ADP
iajs-2511	89	18	𝑥	𝑥	X
iajs-2511	89	19	,	,	PUNCT
iajs-2511	89	20	𝜇	𝜇	SCONJ
iajs-2511	89	21	𝑥	𝑥	X
iajs-2511	89	22	need	need	NOUN
iajs-2511	89	23	not	not	PART
iajs-2511	89	24	to	to	PART
iajs-2511	89	25	be	be	AUX
iajs-2511	89	26	fuzzy	fuzzy	ADJ
iajs-2511	89	27	semi	semi	ADV
iajs-2511	89	28	pre	pre	X
iajs-2511	89	29	closed	closed	ADJ
iajs-2511	89	30	set	set	NOUN
iajs-2511	89	31	.	.	PUNCT
iajs-2511	90	1	example	example	NOUN
iajs-2511	90	2	3.8	3.8	NUM
iajs-2511	90	3	:	:	PUNCT
iajs-2511	90	4	let	let	VERB
iajs-2511	90	5	𝑋	𝑋	PROPN
iajs-2511	90	6	𝛼	𝛼	PROPN
iajs-2511	90	7	,	,	PUNCT
iajs-2511	90	8	𝛽	𝛽	NOUN
iajs-2511	90	9	and	and	CCONJ
iajs-2511	90	10	let	let	VERB
iajs-2511	90	11	𝐴	𝐴	PROPN
iajs-2511	90	12	,	,	PUNCT
iajs-2511	90	13	𝐵	𝐵	PROPN
iajs-2511	90	14	are	be	AUX
iajs-2511	90	15	fuzzy	fuzzy	ADJ
iajs-2511	90	16	sets	set	NOUN
iajs-2511	90	17	of	of	ADP
iajs-2511	90	18	𝑋	𝑋	NOUN
iajs-2511	90	19	defined	define	VERB
iajs-2511	90	20	as	as	SCONJ
iajs-2511	90	21	follows	follow	VERB
iajs-2511	90	22	:	:	PUNCT
iajs-2511	90	23	𝜇	𝜇	SCONJ
iajs-2511	90	24	𝛼	𝛼	X
iajs-2511	90	25	0.6	0.6	NUM
iajs-2511	90	26	𝜇	𝜇	ADP
iajs-2511	90	27	𝛽	𝛽	NOUN
iajs-2511	90	28	0.5	0.5	NUM
iajs-2511	90	29	𝜇	𝜇	ADP
iajs-2511	90	30	𝛼	𝛼	SYM
iajs-2511	90	31	0.7	0.7	NUM
iajs-2511	90	32	𝜇	𝜇	ADP
iajs-2511	90	33	𝛽	𝛽	NOUN
iajs-2511	90	34	0.7	0.7	NUM
iajs-2511	90	35	𝜇	𝜇	ADP
iajs-2511	90	36	𝛼	𝛼	PROPN
iajs-2511	90	37	0.9	0.9	NUM
iajs-2511	90	38	𝜇	𝜇	ADP
iajs-2511	90	39	𝛽	𝛽	NOUN
iajs-2511	90	40	0.4	0.4	NUM
iajs-2511	90	41	𝜇	𝜇	ADP
iajs-2511	90	42	𝛼	𝛼	SYM
iajs-2511	90	43	0.4	0.4	NUM
iajs-2511	90	44	𝜇	𝜇	ADP
iajs-2511	90	45	𝛽	𝛽	NOUN
iajs-2511	90	46	0.8	0.8	NUM
iajs-2511	90	47	𝜇	𝜇	ADP
iajs-2511	90	48	𝛼	𝛼	SYM
iajs-2511	90	49	0.4	0.4	NUM
iajs-2511	90	50	𝜇	𝜇	ADP
iajs-2511	90	51	𝛽	𝛽	NOUN
iajs-2511	90	52	0.8	0.8	NUM
iajs-2511	90	53	𝜇	𝜇	ADP
iajs-2511	90	54	𝛼	𝛼	SYM
iajs-2511	90	55	0.7	0.7	NUM
iajs-2511	90	56	𝜇	𝜇	ADP
iajs-2511	90	57	𝛽	𝛽	NOUN
iajs-2511	90	58	0.4	0.4	NUM
iajs-2511	90	59	let	let	VERB
iajs-2511	90	60	�	�	PROPN
iajs-2511	90	61	̃	̃	PROPN
iajs-2511	90	62	�	�	PROPN
iajs-2511	90	63	0	0	NUM
iajs-2511	90	64	,	,	PUNCT
iajs-2511	90	65	1	1	NUM
iajs-2511	90	66	,	,	PUNCT
iajs-2511	90	67	𝐴	𝐴	PROPN
iajs-2511	90	68	,	,	PUNCT
iajs-2511	90	69	𝐵	𝐵	NOUN
iajs-2511	90	70	be	be	VERB
iajs-2511	90	71	a	a	DET
iajs-2511	90	72	f.t.s	f.t.s	NOUN
iajs-2511	90	73	.	.	PUNCT
iajs-2511	91	1	on	on	ADP
iajs-2511	91	2	x	x	SYM
iajs-2511	91	3	,	,	PUNCT
iajs-2511	91	4	it	it	PRON
iajs-2511	91	5	's	be	AUX
iajs-2511	91	6	clear	clear	ADJ
iajs-2511	91	7	that	that	SCONJ
iajs-2511	91	8	:	:	PUNCT
iajs-2511	91	9	(	(	PUNCT
iajs-2511	91	10	1	1	X
iajs-2511	91	11	)	)	PUNCT
iajs-2511	91	12	the	the	DET
iajs-2511	91	13	fuzzy	fuzzy	ADJ
iajs-2511	91	14	set	set	VERB
iajs-2511	91	15	𝐶	𝐶	PROPN
iajs-2511	91	16	and	and	CCONJ
iajs-2511	91	17	𝐷	𝐷	PROPN
iajs-2511	91	18	are	be	AUX
iajs-2511	91	19	fuzzy	fuzzy	ADJ
iajs-2511	91	20	semi	semi	ADJ
iajs-2511	91	21	pre	pre	ADJ
iajs-2511	91	22	-	-	ADJ
iajs-2511	91	23	open	open	ADJ
iajs-2511	91	24	sets	set	NOUN
iajs-2511	91	25	in	in	ADP
iajs-2511	91	26	x	x	NOUN
iajs-2511	91	27	,	,	PUNCT
iajs-2511	91	28	but	but	CCONJ
iajs-2511	91	29	𝑀𝑖𝑛	𝑀𝑖𝑛	PROPN
iajs-2511	91	30	𝜇	𝜇	ADP
iajs-2511	91	31	𝑥	𝑥	X
iajs-2511	91	32	,	,	PUNCT
iajs-2511	91	33	𝜇	𝜇	ADP
iajs-2511	91	34	𝑥	𝑥	PROPN
iajs-2511	91	35	is	be	AUX
iajs-2511	91	36	not	not	PART
iajs-2511	91	37	a	a	DET
iajs-2511	91	38	fuzzy	fuzzy	ADJ
iajs-2511	91	39	semi	semi	ADJ
iajs-2511	91	40	pre	pre	ADJ
iajs-2511	91	41	-	-	ADJ
iajs-2511	91	42	open	open	ADJ
iajs-2511	91	43	set	set	NOUN
iajs-2511	91	44	.	.	PUNCT
iajs-2511	92	1	(	(	PUNCT
iajs-2511	92	2	2	2	X
iajs-2511	92	3	)	)	PUNCT
iajs-2511	92	4	the	the	DET
iajs-2511	92	5	fuzzy	fuzzy	ADJ
iajs-2511	92	6	set	set	VERB
iajs-2511	92	7	𝐸	𝐸	PROPN
iajs-2511	92	8	and	and	CCONJ
iajs-2511	92	9	𝐹	𝐹	PROPN
iajs-2511	92	10	are	be	AUX
iajs-2511	92	11	fuzzy	fuzzy	ADJ
iajs-2511	92	12	semi	semi	ADV
iajs-2511	92	13	pre	pre	VERB
iajs-2511	92	14	closed	closed	ADJ
iajs-2511	92	15	sets	set	NOUN
iajs-2511	92	16	in	in	ADP
iajs-2511	92	17	x	x	NOUN
iajs-2511	92	18	,	,	PUNCT
iajs-2511	92	19	but	but	CCONJ
iajs-2511	92	20	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2511	92	21	𝜇	𝜇	ADP
iajs-2511	92	22	𝑥	𝑥	X
iajs-2511	92	23	,	,	PUNCT
iajs-2511	92	24	𝜇	𝜇	ADP
iajs-2511	92	25	𝑥	𝑥	PROPN
iajs-2511	92	26	is	be	AUX
iajs-2511	92	27	not	not	PART
iajs-2511	92	28	a	a	DET
iajs-2511	92	29	fuzzy	fuzzy	ADJ
iajs-2511	92	30	semi	semi	ADV
iajs-2511	92	31	pre	pre	X
iajs-2511	92	32	closed	closed	ADJ
iajs-2511	92	33	set	set	NOUN
iajs-2511	92	34	.	.	PUNCT
iajs-2511	93	1	definition	definition	NOUN
iajs-2511	93	2	3.9	3.9	NUM
iajs-2511	93	3	:	:	PUNCT
iajs-2511	93	4	let	let	VERB
iajs-2511	93	5	𝑓	𝑓	PRON
iajs-2511	93	6	:	:	PUNCT
iajs-2511	93	7	𝑋	𝑋	PROPN
iajs-2511	93	8	,	,	PUNCT
iajs-2511	93	9	�	�	PROPN
iajs-2511	93	10	̃	̃	PROPN
iajs-2511	93	11	�	�	PROPN
iajs-2511	93	12			PROPN
iajs-2511	93	13	𝑌	𝑌	PROPN
iajs-2511	93	14	,	,	PUNCT
iajs-2511	93	15	𝜈	𝜈	X
iajs-2511	93	16	,	,	PUNCT
iajs-2511	93	17	then	then	ADV
iajs-2511	93	18	f	f	PROPN
iajs-2511	93	19	is	be	AUX
iajs-2511	93	20	called	call	VERB
iajs-2511	93	21	:	:	PUNCT
iajs-2511	93	22	(	(	PUNCT
iajs-2511	93	23	1)"a	1)"a	NUM
iajs-2511	93	24	fuzzy	fuzzy	ADJ
iajs-2511	93	25	semi	semi	ADV
iajs-2511	93	26	pre	pre	ADJ
iajs-2511	93	27	-	-	ADJ
iajs-2511	93	28	open	open	ADJ
iajs-2511	93	29	function	function	NOUN
iajs-2511	93	30	"	"	PUNCT
iajs-2511	93	31	if	if	SCONJ
iajs-2511	93	32	the	the	PRON
iajs-2511	93	33	𝜇	𝜇	X
iajs-2511	93	34	𝑌	𝑌	PROPN
iajs-2511	93	35	∈	∈	PROPN
iajs-2511	93	36	𝐹.	𝐹.	NOUN
iajs-2511	93	37	𝑆.	𝑆.	PROPN
iajs-2511	93	38	𝑃.	𝑃.	PROPN
iajs-2511	93	39	𝑂.	𝑂.	PROPN
iajs-2511	93	40	𝑌	𝑌	PROPN
iajs-2511	93	41	,	,	PUNCT
iajs-2511	93	42	for	for	ADP
iajs-2511	93	43	each	each	DET
iajs-2511	93	44	𝑥	𝑥	PROPN
iajs-2511	93	45	∈	∈	PROPN
iajs-2511	93	46	�	�	PROPN
iajs-2511	93	47	̃	̃	PROPN
iajs-2511	93	48	�	�	PROPN
iajs-2511	93	49	and	and	CCONJ
iajs-2511	93	50	denoted	denote	VERB
iajs-2511	93	51	𝑓.	𝑓.	NOUN
iajs-2511	93	52	𝑠.	𝑠.	PROPN
iajs-2511	93	53	𝑝.	𝑝.	PROPN
iajs-2511	93	54	𝑜.	𝑜.	PROPN
iajs-2511	93	55	𝑓.	𝑓.	PROPN
iajs-2511	93	56	.	.	PUNCT
iajs-2511	94	1	[	[	X
iajs-2511	94	2	5	5	NUM
iajs-2511	94	3	]	]	PUNCT
iajs-2511	94	4	(	(	PUNCT
iajs-2511	94	5	2	2	X
iajs-2511	94	6	)	)	PUNCT
iajs-2511	94	7	"	"	PUNCT
iajs-2511	94	8	a	a	DET
iajs-2511	94	9	fuzzy	fuzzy	ADJ
iajs-2511	94	10	semi	semi	ADV
iajs-2511	94	11	pre	pre	X
iajs-2511	94	12	closed	closed	ADJ
iajs-2511	94	13	function	function	NOUN
iajs-2511	94	14	"	"	PUNCT
iajs-2511	94	15	if	if	SCONJ
iajs-2511	94	16	the	the	PRON
iajs-2511	94	17	𝜇	𝜇	X
iajs-2511	94	18	𝑌	𝑌	PROPN
iajs-2511	94	19	∈	∈	PROPN
iajs-2511	94	20	𝐹.	𝐹.	NOUN
iajs-2511	94	21	𝑆.	𝑆.	PROPN
iajs-2511	94	22	𝑃.	𝑃.	PROPN
iajs-2511	94	23	𝐶.	𝐶.	PROPN
iajs-2511	94	24	𝑌	𝑌	PROPN
iajs-2511	94	25	,	,	PUNCT
iajs-2511	94	26	for	for	ADP
iajs-2511	94	27	each	each	DET
iajs-2511	94	28	𝑥	𝑥	PROPN
iajs-2511	94	29	∈	∈	PROPN
iajs-2511	94	30	�	�	PROPN
iajs-2511	94	31	̃	̃	PROPN
iajs-2511	94	32	�	�	PROPN
iajs-2511	94	33	and	and	CCONJ
iajs-2511	94	34	denoted	denote	VERB
iajs-2511	94	35	𝑓.	𝑓.	PROPN
iajs-2511	94	36	𝑠.	𝑠.	PROPN
iajs-2511	94	37	𝑝.	𝑝.	PROPN
iajs-2511	94	38	𝑐𝑙.	𝑐𝑙.	PROPN
iajs-2511	94	39	𝑓.	𝑓.	PROPN
iajs-2511	94	40	.	.	PUNCT
iajs-2511	95	1	[	[	X
iajs-2511	95	2	5	5	NUM
iajs-2511	95	3	]	]	PUNCT
iajs-2511	95	4	(	(	PUNCT
iajs-2511	95	5	3)"a	3)"a	NUM
iajs-2511	95	6	fuzzy	fuzzy	ADJ
iajs-2511	95	7	semi	semi	ADJ
iajs-2511	95	8	preopen	preopen	ADJ
iajs-2511	95	9	function	function	NOUN
iajs-2511	95	10	"	"	PUNCT
iajs-2511	95	11	if	if	SCONJ
iajs-2511	95	12	the	the	PRON
iajs-2511	95	13	𝜇	𝜇	X
iajs-2511	95	14	𝑌	𝑌	PROPN
iajs-2511	95	15	∈	∈	PROPN
iajs-2511	95	16	𝐹.	𝐹.	NOUN
iajs-2511	95	17	𝑆.	𝑆.	PROPN
iajs-2511	95	18	𝑃.	𝑃.	PROPN
iajs-2511	95	19	𝑂.	𝑂.	PROPN
iajs-2511	95	20	𝑌	𝑌	PROPN
iajs-2511	95	21	,	,	PUNCT
iajs-2511	95	22	for	for	ADP
iajs-2511	95	23	each	each	DET
iajs-2511	95	24	𝑥	𝑥	PRON
iajs-2511	95	25	∈	∈	PROPN
iajs-2511	95	26	𝐹.	𝐹.	NOUN
iajs-2511	95	27	𝑆.	𝑆.	PROPN
iajs-2511	95	28	𝑃.	𝑃.	PROPN
iajs-2511	95	29	𝑂.	𝑂.	PROPN
iajs-2511	95	30	𝑋	𝑋	PROPN
iajs-2511	95	31	and	and	CCONJ
iajs-2511	95	32	denoted	denote	VERB
iajs-2511	95	33	𝑓.	𝑓.	NOUN
iajs-2511	95	34	𝑠.	𝑠.	PROPN
iajs-2511	95	35	𝑝∗.	𝑝∗.	PUNCT
iajs-2511	96	1	𝑜.	𝑜.	PROPN
iajs-2511	96	2	𝑓.	𝑓.	PROPN
iajs-2511	96	3	.	.	PUNCT
iajs-2511	97	1	(	(	PUNCT
iajs-2511	97	2	4	4	X
iajs-2511	97	3	)	)	PUNCT
iajs-2511	97	4	"	"	PUNCT
iajs-2511	97	5	a	a	DET
iajs-2511	97	6	fuzzy	fuzzy	ADJ
iajs-2511	97	7	semi	semi	ADJ
iajs-2511	97	8	pre	pre	NOUN
iajs-2511	97	9	closed	closed	ADJ
iajs-2511	97	10	function	function	NOUN
iajs-2511	97	11	"	"	PUNCT
iajs-2511	97	12	if	if	SCONJ
iajs-2511	97	13	the	the	PRON
iajs-2511	97	14	𝜇	𝜇	X
iajs-2511	97	15	𝑌	𝑌	PROPN
iajs-2511	97	16	∈	∈	PROPN
iajs-2511	97	17	𝐹.	𝐹.	NOUN
iajs-2511	97	18	𝑆.	𝑆.	PROPN
iajs-2511	97	19	𝑃.	𝑃.	PROPN
iajs-2511	97	20	𝐶.	𝐶.	PROPN
iajs-2511	97	21	𝑌	𝑌	PROPN
iajs-2511	97	22	,	,	PUNCT
iajs-2511	97	23	for	for	ADP
iajs-2511	97	24	each	each	DET
iajs-2511	97	25	𝑥	𝑥	PRON
iajs-2511	97	26	∈	∈	PROPN
iajs-2511	97	27	𝐹.	𝐹.	NOUN
iajs-2511	97	28	𝑆.	𝑆.	PROPN
iajs-2511	97	29	𝑃.	𝑃.	PROPN
iajs-2511	97	30	𝐶.	𝐶.	PROPN
iajs-2511	97	31	𝑋	𝑋	NOUN
iajs-2511	97	32	and	and	CCONJ
iajs-2511	97	33	denoted	denote	VERB
iajs-2511	97	34	𝑓.	𝑓.	NOUN
iajs-2511	97	35	𝑠.	𝑠.	PROPN
iajs-2511	97	36	𝑝∗.	𝑝∗.	PROPN
iajs-2511	97	37	𝑐𝑙.	𝑐𝑙.	PROPN
iajs-2511	97	38	𝑓.	𝑓.	PROPN
iajs-2511	97	39	.	.	PUNCT
iajs-2511	98	1	definition	definition	NOUN
iajs-2511	98	2	3.10	3.10	NUM
iajs-2511	98	3	:	:	PUNCT
iajs-2511	98	4	let	let	VERB
iajs-2511	98	5	f	f	X
iajs-2511	98	6	:	:	PUNCT
iajs-2511	98	7	x	x	X
iajs-2511	98	8	,	,	PUNCT
iajs-2511	98	9	τ	τ	PROPN
iajs-2511	98	10			PROPN
iajs-2511	98	11	y	y	PROPN
iajs-2511	98	12	,	,	PUNCT
iajs-2511	98	13	ν	ν	NOUN
iajs-2511	98	14	,	,	PUNCT
iajs-2511	98	15	then	then	ADV
iajs-2511	98	16	f	f	PROPN
iajs-2511	98	17	is	be	AUX
iajs-2511	98	18	called	call	VERB
iajs-2511	98	19	:	:	PUNCT
iajs-2511	98	20	(	(	PUNCT
iajs-2511	98	21	1	1	X
iajs-2511	98	22	)	)	PUNCT
iajs-2511	98	23	"	"	PUNCT
iajs-2511	98	24	a	a	DET
iajs-2511	98	25	fuzzy	fuzzy	ADJ
iajs-2511	98	26	semi	semi	ADV
iajs-2511	98	27	pre	pre	X
iajs-2511	98	28	continuous	continuous	ADJ
iajs-2511	98	29	function	function	NOUN
iajs-2511	98	30	"	"	PUNCT
iajs-2511	98	31	if	if	SCONJ
iajs-2511	98	32	the	the	PRON
iajs-2511	99	1	μ	μ	PROPN
iajs-2511	99	2	x	x	SYM
iajs-2511	99	3	∈	∈	PROPN
iajs-2511	99	4	f.	f.	PROPN
iajs-2511	99	5	s.	s.	PROPN
iajs-2511	99	6	p.	p.	PROPN
iajs-2511	100	1	o.	o.	PROPN
iajs-2511	101	1	x	x	PUNCT
iajs-2511	101	2	for	for	ADP
iajs-2511	101	3	each	each	DET
iajs-2511	101	4	y	y	PROPN
iajs-2511	101	5	∈	∈	PROPN
iajs-2511	101	6	ν	ν	NOUN
iajs-2511	101	7	and	and	CCONJ
iajs-2511	101	8	denoted	denote	VERB
iajs-2511	101	9	f.	f.	PROPN
iajs-2511	101	10	s.	s.	PROPN
iajs-2511	101	11	p.	p.	PROPN
iajs-2511	101	12	co.	co.	PROPN
iajs-2511	102	1	f.	f.	PROPN
iajs-2511	102	2	.	.	PUNCT
iajs-2511	103	1	[	[	X
iajs-2511	103	2	11	11	NUM
iajs-2511	103	3	]	]	SYM
iajs-2511	103	4	(	(	PUNCT
iajs-2511	103	5	2	2	X
iajs-2511	103	6	)	)	PUNCT
iajs-2511	103	7	"	"	PUNCT
iajs-2511	103	8	a	a	DET
iajs-2511	103	9	fuzzy	fuzzy	ADJ
iajs-2511	103	10	semi	semi	ADJ
iajs-2511	103	11	pre	pre	X
iajs-2511	103	12	irresolute	irresolute	ADJ
iajs-2511	103	13	function	function	NOUN
iajs-2511	103	14	"	"	PUNCT
iajs-2511	103	15	if	if	SCONJ
iajs-2511	103	16	the	the	PRON
iajs-2511	103	17	μ	μ	PROPN
iajs-2511	103	18	x	x	SYM
iajs-2511	103	19	∈	∈	PROPN
iajs-2511	103	20	f.	f.	PROPN
iajs-2511	103	21	s.	s.	PROPN
iajs-2511	104	1	p.	p.	PROPN
iajs-2511	104	2	o.	o.	PROPN
iajs-2511	105	1	x	x	PUNCT
iajs-2511	105	2	for	for	ADP
iajs-2511	105	3	each	each	DET
iajs-2511	105	4	y	y	PROPN
iajs-2511	105	5	∈	∈	PROPN
iajs-2511	105	6	f.	f.	PROPN
iajs-2511	105	7	s.	s.	PROPN
iajs-2511	106	1	p.	p.	PROPN
iajs-2511	106	2	o.	o.	PROPN
iajs-2511	106	3	y	y	PROPN
iajs-2511	107	1	and	and	CCONJ
iajs-2511	107	2	denoted	denote	VERB
iajs-2511	107	3	f.	f.	PROPN
iajs-2511	107	4	s.	s.	PROPN
iajs-2511	107	5	p.	p.	PROPN
iajs-2511	107	6	i.	i.	PROPN
iajs-2511	107	7	f.	f.	PROPN
iajs-2511	107	8	.	.	PUNCT
iajs-2511	108	1	[	[	X
iajs-2511	108	2	11	11	NUM
iajs-2511	108	3	]	]	SYM
iajs-2511	108	4	(	(	PUNCT
iajs-2511	108	5	3	3	X
iajs-2511	108	6	)	)	PUNCT
iajs-2511	108	7	"	"	PUNCT
iajs-2511	108	8	a	a	DET
iajs-2511	108	9	fuzzy	fuzzy	ADJ
iajs-2511	108	10	semi	semi	ADJ
iajs-2511	108	11	pre	pre	NOUN
iajs-2511	108	12	continuous	continuous	ADJ
iajs-2511	108	13	function	function	NOUN
iajs-2511	108	14	"	"	PUNCT
iajs-2511	108	15	if	if	SCONJ
iajs-2511	108	16	the	the	DET
iajs-2511	108	17	μ	μ	NOUN
iajs-2511	108	18	x	x	VERB
iajs-2511	108	19	is	be	AUX
iajs-2511	108	20	fuzzy	fuzzy	ADJ
iajs-2511	108	21	open	open	ADJ
iajs-2511	108	22	set	set	VERB
iajs-2511	108	23	in	in	ADP
iajs-2511	108	24	x	x	PUNCT
iajs-2511	108	25	for	for	ADP
iajs-2511	108	26	each	each	DET
iajs-2511	108	27	y	y	PROPN
iajs-2511	108	28	∈	∈	PROPN
iajs-2511	109	1	f.	f.	PROPN
iajs-2511	109	2	s.	s.	PROPN
iajs-2511	109	3	p.	p.	PROPN
iajs-2511	109	4	o.	o.	PROPN
iajs-2511	109	5	y	y	PROPN
iajs-2511	110	1	and	and	CCONJ
iajs-2511	110	2	denoted	denote	VERB
iajs-2511	110	3	f.	f.	PROPN
iajs-2511	110	4	s.	s.	PROPN
iajs-2511	110	5	p∗.	p∗.	PROPN
iajs-2511	110	6	co.	co.	PROPN
iajs-2511	111	1	f.	f.	PROPN
iajs-2511	111	2	.	.	PUNCT
iajs-2511	111	3	  	  	SPACE
iajs-2511	112	1	77	77	NUM
iajs-2511	112	2	  	  	SPACE
iajs-2511	112	3	ibn	ibn	PROPN
iajs-2511	112	4	al	al	PROPN
iajs-2511	112	5	-	-	PUNCT
iajs-2511	112	6	haitham	haitham	PROPN
iajs-2511	112	7	jour	jour	X
iajs-2511	112	8	.	.	PROPN
iajs-2511	112	9	for	for	ADP
iajs-2511	112	10	pure	pure	ADJ
iajs-2511	112	11	&	&	CCONJ
iajs-2511	112	12	appl	appl	PROPN
iajs-2511	112	13	.	.	PUNCT
iajs-2511	113	1	sci	sci	PROPN
iajs-2511	113	2	.	.	PROPN
iajs-2511	114	1	33	33	NUM
iajs-2511	114	2	(	(	PUNCT
iajs-2511	114	3	4	4	NUM
iajs-2511	114	4	)	)	PUNCT
iajs-2511	114	5	2020	2020	NUM
iajs-2511	114	6	proposition	proposition	NOUN
iajs-2511	114	7	3.11	3.11	NUM
iajs-2511	114	8	:	:	PUNCT
iajs-2511	114	9	(	(	PUNCT
iajs-2511	114	10	1	1	X
iajs-2511	114	11	)	)	PUNCT
iajs-2511	114	12	every	every	DET
iajs-2511	114	13	f.	f.	PROPN
iajs-2511	114	14	s.	s.	PROPN
iajs-2511	114	15	p∗.	p∗.	PROPN
iajs-2511	114	16	co.	co.	PROPN
iajs-2511	115	1	f.	f.	PROPN
iajs-2511	115	2	𝐢𝐬	𝐢𝐬	PROPN
iajs-2511	115	3	f.	f.	PROPN
iajs-2511	115	4	co.	co.	PROPN
iajs-2511	115	5	f.	f.	PROPN
iajs-2511	115	6	(	(	PUNCT
iajs-2511	115	7	2	2	X
iajs-2511	115	8	)	)	PUNCT
iajs-2511	115	9	every	every	DET
iajs-2511	115	10	𝑓.	𝑓.	NOUN
iajs-2511	115	11	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	115	12	𝑓.	𝑓.	NOUN
iajs-2511	115	13	𝐢𝐬	𝐢𝐬	VERB
iajs-2511	115	14	𝑓.	𝑓.	PROPN
iajs-2511	115	15	𝑠.	𝑠.	PROPN
iajs-2511	115	16	𝑝.	𝑝.	PROPN
iajs-2511	115	17	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	115	18	𝑓.	𝑓.	PROPN
iajs-2511	115	19	(	(	PUNCT
iajs-2511	115	20	3	3	NUM
iajs-2511	115	21	)	)	PUNCT
iajs-2511	115	22	every	every	DET
iajs-2511	115	23	𝑓.	𝑓.	NOUN
iajs-2511	115	24	𝑠.	𝑠.	PROPN
iajs-2511	115	25	𝑝∗.	𝑝∗.	PROPN
iajs-2511	116	1	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	116	2	𝑓.	𝑓.	NOUN
iajs-2511	116	3	𝐢𝐬	𝐢𝐬	VERB
iajs-2511	116	4	𝑓.	𝑓.	PROPN
iajs-2511	116	5	𝑠.	𝑠.	PROPN
iajs-2511	116	6	𝑝.	𝑝.	PROPN
iajs-2511	116	7	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	116	8	𝑓.	𝑓.	PROPN
iajs-2511	116	9	(	(	PUNCT
iajs-2511	116	10	4	4	NUM
iajs-2511	116	11	)	)	PUNCT
iajs-2511	116	12	every	every	DET
iajs-2511	116	13	𝑓.	𝑓.	NOUN
iajs-2511	116	14	𝑠.	𝑠.	PROPN
iajs-2511	116	15	𝑝∗.	𝑝∗.	PROPN
iajs-2511	117	1	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	117	2	𝑓.	𝑓.	NOUN
iajs-2511	117	3	𝐢𝐬	𝐢𝐬	VERB
iajs-2511	117	4	𝑓.	𝑓.	PROPN
iajs-2511	117	5	𝑠.	𝑠.	PROPN
iajs-2511	117	6	𝑝.	𝑝.	PROPN
iajs-2511	117	7	𝑖.	𝑖.	PROPN
iajs-2511	118	1	𝑓.	𝑓.	PROPN
iajs-2511	118	2	(	(	PUNCT
iajs-2511	118	3	5	5	NUM
iajs-2511	118	4	)	)	PUNCT
iajs-2511	118	5	every	every	DET
iajs-2511	118	6	𝑓.	𝑓.	NOUN
iajs-2511	118	7	𝑠.	𝑠.	PROPN
iajs-2511	118	8	𝑝.	𝑝.	PROPN
iajs-2511	118	9	𝑖.	𝑖.	PROPN
iajs-2511	118	10	𝑓.	𝑓.	PROPN
iajs-2511	119	1	𝐢𝐬	𝐢𝐬	VERB
iajs-2511	119	2	𝑓.	𝑓.	PROPN
iajs-2511	119	3	𝑠.	𝑠.	PROPN
iajs-2511	119	4	𝑝.	𝑝.	PROPN
iajs-2511	119	5	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	119	6	𝑓.	𝑓.	PROPN
iajs-2511	119	7	remark	remark	NOUN
iajs-2511	119	8	3.12	3.12	NUM
iajs-2511	119	9	:	:	PUNCT
iajs-2511	119	10	the	the	DET
iajs-2511	119	11	converse	converse	NOUN
iajs-2511	119	12	of	of	ADP
iajs-2511	119	13	proposition	proposition	NOUN
iajs-2511	119	14	(	(	PUNCT
iajs-2511	119	15	3.11	3.11	NUM
iajs-2511	119	16	)	)	PUNCT
iajs-2511	119	17	is	be	AUX
iajs-2511	119	18	not	not	PART
iajs-2511	119	19	true	true	ADJ
iajs-2511	119	20	in	in	ADP
iajs-2511	119	21	general	general	ADJ
iajs-2511	119	22	.	.	PUNCT
iajs-2511	120	1	example	example	NOUN
iajs-2511	120	2	3.13	3.13	NUM
iajs-2511	120	3	:	:	PUNCT
iajs-2511	120	4	let	let	VERB
iajs-2511	120	5	𝑋	𝑋	PROPN
iajs-2511	120	6	𝛼	𝛼	PROPN
iajs-2511	120	7	,	,	PUNCT
iajs-2511	120	8	𝛽	𝛽	NOUN
iajs-2511	120	9	,	,	PUNCT
iajs-2511	120	10	𝑌	𝑌	PROPN
iajs-2511	120	11	𝜌	𝜌	PROPN
iajs-2511	120	12	,	,	PUNCT
iajs-2511	120	13	𝜎	𝜎	PRON
iajs-2511	120	14	and	and	CCONJ
iajs-2511	120	15	let	let	VERB
iajs-2511	120	16	𝛿	𝛿	ADJ
iajs-2511	120	17	,	,	PUNCT
iajs-2511	120	18	𝜗	𝜗	NOUN
iajs-2511	120	19	,	,	PUNCT
iajs-2511	120	20	𝒢	𝒢	NOUN
iajs-2511	120	21	be	be	VERB
iajs-2511	120	22	fuzzy	fuzzy	ADJ
iajs-2511	120	23	sets	set	NOUN
iajs-2511	120	24	defined	define	VERB
iajs-2511	120	25	as	as	ADP
iajs-2511	120	26	follows	follow	VERB
iajs-2511	120	27	:	:	PUNCT
iajs-2511	120	28	𝜇	𝜇	ADP
iajs-2511	120	29	𝛼	𝛼	X
iajs-2511	120	30	0.6	0.6	NUM
iajs-2511	120	31	𝜇	𝜇	ADP
iajs-2511	120	32	𝛽	𝛽	NOUN
iajs-2511	120	33	0.5	0.5	NUM
iajs-2511	120	34	𝜇	𝜇	ADP
iajs-2511	120	35	𝜌	𝜌	ADP
iajs-2511	120	36	0.7	0.7	NUM
iajs-2511	120	37	𝜇	𝜇	ADP
iajs-2511	120	38	𝜎	𝜎	PROPN
iajs-2511	120	39	0.7	0.7	NUM
iajs-2511	120	40	𝜇𝒢	𝜇𝒢	NUM
iajs-2511	120	41	𝜌	𝜌	ADP
iajs-2511	120	42	0.9	0.9	NUM
iajs-2511	120	43	𝜇𝒢	𝜇𝒢	NOUN
iajs-2511	120	44	𝜎	𝜎	SYM
iajs-2511	120	45	0.7	0.7	NUM
iajs-2511	120	46	let	let	VERB
iajs-2511	120	47	�	�	PROPN
iajs-2511	120	48	̃	̃	PROPN
iajs-2511	120	49	�	�	PROPN
iajs-2511	120	50	0	0	NUM
iajs-2511	120	51	,	,	PUNCT
iajs-2511	120	52	1	1	NUM
iajs-2511	120	53	,	,	PUNCT
iajs-2511	120	54	𝛿	𝛿	ADJ
iajs-2511	120	55	,	,	PUNCT
iajs-2511	120	56	𝜗	𝜗	NOUN
iajs-2511	120	57	,	,	PUNCT
iajs-2511	120	58	𝜈	𝜈	PROPN
iajs-2511	120	59	0	0	NUM
iajs-2511	120	60	,	,	PUNCT
iajs-2511	120	61	1	1	NUM
iajs-2511	120	62	,	,	PUNCT
iajs-2511	120	63	𝜗	𝜗	VERB
iajs-2511	120	64	so	so	ADV
iajs-2511	120	65	,	,	PUNCT
iajs-2511	120	66	𝑋	𝑋	PROPN
iajs-2511	120	67	,	,	PUNCT
iajs-2511	120	68	�	�	PROPN
iajs-2511	120	69	̃	̃	PROPN
iajs-2511	120	70	�	�	PROPN
iajs-2511	120	71	and	and	CCONJ
iajs-2511	120	72	𝑌	𝑌	PROPN
iajs-2511	120	73	,	,	PUNCT
iajs-2511	120	74	𝜈	𝜈	PROPN
iajs-2511	120	75	are	be	AUX
iajs-2511	120	76	f.t.s	f.t.s	ADJ
iajs-2511	120	77	.	.	PUNCT
iajs-2511	121	1	then	then	ADV
iajs-2511	121	2	the	the	DET
iajs-2511	121	3	function	function	NOUN
iajs-2511	121	4	𝑓	𝑓	PROPN
iajs-2511	121	5	:	:	PUNCT
iajs-2511	121	6	𝑋	𝑋	PROPN
iajs-2511	121	7	,	,	PUNCT
iajs-2511	121	8	�	�	PROPN
iajs-2511	121	9	̃	̃	PROPN
iajs-2511	121	10	�	�	PROPN
iajs-2511	121	11			PROPN
iajs-2511	121	12	𝑌	𝑌	PROPN
iajs-2511	121	13	,	,	PUNCT
iajs-2511	121	14	𝜈	𝜈	PRON
iajs-2511	121	15	defined	define	VERB
iajs-2511	121	16	by	by	ADP
iajs-2511	121	17	𝑓	𝑓	DET
iajs-2511	121	18	𝛼	𝛼	PRON
iajs-2511	121	19	𝜌	𝜌	X
iajs-2511	121	20	,	,	PUNCT
iajs-2511	121	21	𝑓	𝑓	PRON
iajs-2511	121	22	𝛽	𝛽	NOUN
iajs-2511	121	23	𝜎	𝜎	PROPN
iajs-2511	121	24	is	be	AUX
iajs-2511	121	25	𝑓.	𝑓.	PROPN
iajs-2511	121	26	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	121	27	𝑓	𝑓	PROPN
iajs-2511	121	28	and	and	CCONJ
iajs-2511	121	29	𝑓.	𝑓.	NOUN
iajs-2511	121	30	𝑠.	𝑠.	NOUN
iajs-2511	122	1	𝑖.	𝑖.	NOUN
iajs-2511	122	2	𝑓	𝑓	PRON
iajs-2511	122	3	but	but	CCONJ
iajs-2511	122	4	not	not	PART
iajs-2511	122	5	𝑓.	𝑓.	NOUN
iajs-2511	122	6	𝑠.	𝑠.	PROPN
iajs-2511	122	7	𝑝∗.	𝑝∗.	PROPN
iajs-2511	123	1	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	123	2	𝑓.	𝑓.	PROPN
iajs-2511	123	3	example	example	NOUN
iajs-2511	123	4	3.14	3.14	NUM
iajs-2511	123	5	:	:	PUNCT
iajs-2511	123	6	let	let	VERB
iajs-2511	123	7	𝑋	𝑋	PROPN
iajs-2511	123	8	𝛼	𝛼	PROPN
iajs-2511	123	9	,	,	PUNCT
iajs-2511	123	10	𝛽	𝛽	PROPN
iajs-2511	123	11	,	,	PUNCT
iajs-2511	123	12	𝜆	𝜆	INTJ
iajs-2511	123	13	,	,	PUNCT
iajs-2511	123	14	𝑌	𝑌	PROPN
iajs-2511	123	15	𝜌	𝜌	PROPN
iajs-2511	123	16	,	,	PUNCT
iajs-2511	123	17	𝜎	𝜎	NOUN
iajs-2511	123	18	,	,	PUNCT
iajs-2511	123	19	𝜔	𝜔	VERB
iajs-2511	123	20	and	and	CCONJ
iajs-2511	123	21	let	let	VERB
iajs-2511	123	22	𝛿	𝛿	ADJ
iajs-2511	123	23	,	,	PUNCT
iajs-2511	123	24	𝜗	𝜗	X
iajs-2511	123	25	be	be	VERB
iajs-2511	123	26	fuzzy	fuzzy	ADJ
iajs-2511	123	27	sets	set	NOUN
iajs-2511	123	28	defined	define	VERB
iajs-2511	123	29	as	as	ADP
iajs-2511	123	30	follows	follow	VERB
iajs-2511	123	31	:	:	PUNCT
iajs-2511	123	32	𝜇	𝜇	SCONJ
iajs-2511	123	33	𝛼	𝛼	PROPN
iajs-2511	123	34	0.3	0.3	NUM
iajs-2511	123	35	𝜇	𝜇	ADP
iajs-2511	123	36	𝛽	𝛽	NOUN
iajs-2511	123	37	0.4	0.4	NUM
iajs-2511	123	38	𝜇	𝜇	ADP
iajs-2511	123	39	𝜆	𝜆	ADP
iajs-2511	123	40	0.5	0.5	NUM
iajs-2511	123	41	𝜇	𝜇	ADP
iajs-2511	123	42	𝜌	𝜌	X
iajs-2511	123	43	0.6	0.6	NUM
iajs-2511	123	44	𝜇	𝜇	ADP
iajs-2511	123	45	𝜎	𝜎	PROPN
iajs-2511	123	46	0.5	0.5	NUM
iajs-2511	123	47	𝜇	𝜇	ADP
iajs-2511	123	48	𝜔	𝜔	SYM
iajs-2511	123	49	0.2	0.2	NUM
iajs-2511	123	50	let	let	VERB
iajs-2511	123	51	�	�	PROPN
iajs-2511	123	52	̃	̃	PROPN
iajs-2511	123	53	�	�	PROPN
iajs-2511	123	54	0	0	NUM
iajs-2511	123	55	,	,	PUNCT
iajs-2511	123	56	1	1	NUM
iajs-2511	123	57	,	,	PUNCT
iajs-2511	123	58	𝛿	𝛿	ADJ
iajs-2511	123	59	,	,	PUNCT
iajs-2511	123	60	𝜈	𝜈	X
iajs-2511	123	61	0	0	NUM
iajs-2511	123	62	,	,	PUNCT
iajs-2511	123	63	1	1	NUM
iajs-2511	123	64	,	,	PUNCT
iajs-2511	123	65	𝜗	𝜗	VERB
iajs-2511	123	66	so	so	ADV
iajs-2511	123	67	,	,	PUNCT
iajs-2511	123	68	(	(	PUNCT
iajs-2511	123	69	x,	x,	PROPN
iajs-2511	123	70	�	�	PROPN
iajs-2511	123	71	̃	̃	PROPN
iajs-2511	123	72	�	�	PROPN
iajs-2511	123	73	)	)	PUNCT
iajs-2511	123	74	and	and	CCONJ
iajs-2511	123	75	(	(	PUNCT
iajs-2511	123	76	y,𝜈	y,𝜈	NOUN
iajs-2511	123	77	)	)	PUNCT
iajs-2511	123	78	are	be	AUX
iajs-2511	123	79	f.t.s	f.t.s	ADJ
iajs-2511	123	80	.	.	PUNCT
iajs-2511	124	1	then	then	ADV
iajs-2511	124	2	the	the	DET
iajs-2511	124	3	function	function	NOUN
iajs-2511	124	4	𝑓	𝑓	PROPN
iajs-2511	124	5	:	:	PUNCT
iajs-2511	124	6	𝑋	𝑋	PROPN
iajs-2511	124	7	,	,	PUNCT
iajs-2511	124	8	�	�	PROPN
iajs-2511	124	9	̃	̃	PROPN
iajs-2511	124	10	�	�	PROPN
iajs-2511	124	11	→	→	SYM
iajs-2511	124	12	𝑌	𝑌	PROPN
iajs-2511	124	13	,	,	PUNCT
iajs-2511	124	14	𝜈	𝜈	PRON
iajs-2511	124	15	defined	define	VERB
iajs-2511	124	16	by	by	ADP
iajs-2511	124	17	𝑓	𝑓	DET
iajs-2511	124	18	𝛼	𝛼	PRON
iajs-2511	124	19	𝜌	𝜌	X
iajs-2511	124	20	,	,	PUNCT
iajs-2511	124	21	𝑓	𝑓	DET
iajs-2511	124	22	𝛽	𝛽	PROPN
iajs-2511	124	23	𝜎	𝜎	PROPN
iajs-2511	124	24	,	,	PUNCT
iajs-2511	124	25	𝑓	𝑓	PRON
iajs-2511	124	26	𝜆	𝜆	NOUN
iajs-2511	124	27	𝜔	𝜔	NOUN
iajs-2511	124	28	is	be	AUX
iajs-2511	125	1	𝑓.	𝑓.	NOUN
iajs-2511	125	2	𝑠.	𝑠.	PROPN
iajs-2511	125	3	𝑝.	𝑝.	PROPN
iajs-2511	125	4	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	126	1	𝑓	𝑓	PROPN
iajs-2511	126	2	but	but	CCONJ
iajs-2511	126	3	not	not	PART
iajs-2511	126	4	𝑓.	𝑓.	PROPN
iajs-2511	126	5	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	126	6	𝑓.	𝑓.	NOUN
iajs-2511	126	7	and	and	CCONJ
iajs-2511	126	8	𝑓.	𝑓.	PROPN
iajs-2511	126	9	𝑠.	𝑠.	PROPN
iajs-2511	126	10	𝑝∗.	𝑝∗.	PROPN
iajs-2511	126	11	𝑐𝑜.	𝑐𝑜.	NOUN
iajs-2511	126	12	𝑓.	𝑓.	NOUN
iajs-2511	126	13	remark	remark	VERB
iajs-2511	126	14	3.15	3.15	NUM
iajs-2511	126	15	:	:	PUNCT
iajs-2511	126	16	the	the	DET
iajs-2511	126	17	following	follow	VERB
iajs-2511	126	18	diagram	diagram	NOUN
iajs-2511	126	19	explains	explain	VERB
iajs-2511	126	20	the	the	DET
iajs-2511	126	21	relationship	relationship	NOUN
iajs-2511	126	22	among	among	ADP
iajs-2511	126	23	some	some	DET
iajs-2511	126	24	fuzzy	fuzzy	ADJ
iajs-2511	126	25	continuous	continuous	ADJ
iajs-2511	126	26	function	function	NOUN
iajs-2511	126	27	.	.	PUNCT
iajs-2511	127	1	diagram	diagram	NOUN
iajs-2511	127	2	(	(	PUNCT
iajs-2511	127	3	1	1	NUM
iajs-2511	127	4	):	):	PUNCT
iajs-2511	127	5	the	the	DET
iajs-2511	127	6	relationship	relationship	NOUN
iajs-2511	127	7	among	among	ADP
iajs-2511	127	8	the	the	DET
iajs-2511	127	9	some	some	DET
iajs-2511	127	10	fuzzy	fuzzy	ADJ
iajs-2511	127	11	continuous	continuous	ADJ
iajs-2511	127	12	function	function	NOUN
iajs-2511	127	13	𝑓.	𝑓.	PROPN
iajs-2511	127	14	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	127	15	𝑓.	𝑓.	PROPN
iajs-2511	127	16	  	  	SPACE
iajs-2511	127	17	𝑓.	𝑓.	PROPN
iajs-2511	127	18	𝑠.	𝑠.	PROPN
iajs-2511	127	19	𝑝.	𝑝.	PROPN
iajs-2511	127	20	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	127	21	𝑓.	𝑓.	PROPN
iajs-2511	127	22	 	 	SPACE
iajs-2511	127	23	𝑓.	𝑓.	NOUN
iajs-2511	127	24	𝑠.	𝑠.	PROPN
iajs-2511	127	25	𝑝∗.	𝑝∗.	PROPN
iajs-2511	128	1	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	128	2	𝑓.	𝑓.	NOUN
iajs-2511	128	3	  	  	SPACE
iajs-2511	128	4	𝑓.	𝑓.	NOUN
iajs-2511	128	5	𝑠.	𝑠.	PROPN
iajs-2511	128	6	𝑝.	𝑝.	PROPN
iajs-2511	128	7	𝑖.	𝑖.	PROPN
iajs-2511	128	8	𝑓.	𝑓.	NOUN
iajs-2511	128	9	    	    	SPACE
iajs-2511	128	10	78	78	NUM
iajs-2511	128	11	  	  	SPACE
iajs-2511	128	12	ibn	ibn	PROPN
iajs-2511	128	13	al	al	PROPN
iajs-2511	128	14	-	-	PUNCT
iajs-2511	128	15	haitham	haitham	PROPN
iajs-2511	128	16	jour	jour	X
iajs-2511	128	17	.	.	PROPN
iajs-2511	129	1	for	for	ADP
iajs-2511	129	2	pure	pure	ADJ
iajs-2511	129	3	&	&	CCONJ
iajs-2511	129	4	appl	appl	PROPN
iajs-2511	129	5	.	.	PUNCT
iajs-2511	130	1	sci	sci	PROPN
iajs-2511	130	2	.	.	PROPN
iajs-2511	131	1	33	33	NUM
iajs-2511	131	2	(	(	PUNCT
iajs-2511	131	3	4	4	NUM
iajs-2511	131	4	)	)	PUNCT
iajs-2511	131	5	2020	2020	NUM
iajs-2511	131	6	4	4	NUM
iajs-2511	131	7	.	.	PUNCT
iajs-2511	132	1	fuzzy	fuzzy	ADJ
iajs-2511	132	2	semi	semi	ADV
iajs-2511	132	3	pre	pre	VERB
iajs-2511	132	4	homeomorphism	homeomorphism	PROPN
iajs-2511	132	5	in	in	ADP
iajs-2511	132	6	fuzzy	fuzzy	ADJ
iajs-2511	132	7	topological	topological	ADJ
iajs-2511	132	8	spaces	space	NOUN
iajs-2511	132	9	.	.	PUNCT
iajs-2511	133	1	in	in	ADP
iajs-2511	133	2	this	this	DET
iajs-2511	133	3	section	section	NOUN
iajs-2511	133	4	we	we	PRON
iajs-2511	133	5	introduce	introduce	VERB
iajs-2511	133	6	the	the	DET
iajs-2511	133	7	fuzzy	fuzzy	ADJ
iajs-2511	133	8	semi	semi	ADJ
iajs-2511	133	9	pre	pre	PROPN
iajs-2511	133	10	homeomorphism	homeomorphism	PROPN
iajs-2511	133	11	functions	function	NOUN
iajs-2511	133	12	and	and	CCONJ
iajs-2511	133	13	fuzzy	fuzzy	ADJ
iajs-2511	133	14	semi	semi	ADV
iajs-2511	133	15	pre	pre	PROPN
iajs-2511	133	16	*	*	NOUN
iajs-2511	133	17	homeomorphism	homeomorphism	NOUN
iajs-2511	133	18	functions	function	NOUN
iajs-2511	133	19	in	in	ADP
iajs-2511	133	20	fuzzy	fuzzy	ADJ
iajs-2511	133	21	topological	topological	ADJ
iajs-2511	133	22	spaces	space	NOUN
iajs-2511	133	23	.	.	PUNCT
iajs-2511	134	1	some	some	PRON
iajs-2511	134	2	of	of	ADP
iajs-2511	134	3	their	their	PRON
iajs-2511	134	4	properties	property	NOUN
iajs-2511	134	5	and	and	CCONJ
iajs-2511	134	6	characterization	characterization	NOUN
iajs-2511	134	7	have	have	AUX
iajs-2511	134	8	been	be	AUX
iajs-2511	134	9	proved	prove	VERB
iajs-2511	134	10	and	and	CCONJ
iajs-2511	134	11	discussed	discuss	VERB
iajs-2511	134	12	in	in	ADP
iajs-2511	134	13	details	detail	NOUN
iajs-2511	134	14	.	.	PUNCT
iajs-2511	135	1	definition	definition	NOUN
iajs-2511	135	2	4.1	4.1	NUM
iajs-2511	135	3	:	:	PUNCT
iajs-2511	135	4	let	let	VERB
iajs-2511	135	5	𝑓	𝑓	PRON
iajs-2511	135	6	:	:	PUNCT
iajs-2511	135	7	𝑋	𝑋	PROPN
iajs-2511	135	8	,	,	PUNCT
iajs-2511	135	9	�	�	PROPN
iajs-2511	135	10	̃	̃	PROPN
iajs-2511	135	11	�	�	PROPN
iajs-2511	135	12			PROPN
iajs-2511	135	13	𝑌	𝑌	PROPN
iajs-2511	135	14	,	,	PUNCT
iajs-2511	135	15	𝜈	𝜈	X
iajs-2511	135	16	be	be	VERB
iajs-2511	135	17	bijection	bijection	ADJ
iajs-2511	135	18	fuzzy	fuzzy	ADJ
iajs-2511	135	19	function	function	NOUN
iajs-2511	135	20	,	,	PUNCT
iajs-2511	135	21	f	f	PROPN
iajs-2511	135	22	is	be	AUX
iajs-2511	135	23	called	call	VERB
iajs-2511	136	1	a	a	DET
iajs-2511	136	2	fuzzy	fuzzy	ADJ
iajs-2511	136	3	semi	semi	ADV
iajs-2511	136	4	pre	pre	PROPN
iajs-2511	136	5	homeomorphism	homeomorphism	PROPN
iajs-2511	136	6	iff	iff	PROPN
iajs-2511	136	7	f	f	PROPN
iajs-2511	136	8	and	and	CCONJ
iajs-2511	136	9	f	f	PROPN
iajs-2511	136	10	-1	-1	X
iajs-2511	136	11	are	be	AUX
iajs-2511	136	12	𝑓.	𝑓.	PROPN
iajs-2511	136	13	𝑠.	𝑠.	PROPN
iajs-2511	136	14	𝑝.	𝑝.	PROPN
iajs-2511	136	15	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	136	16	𝑓𝑠.	𝑓𝑠.	PROPN
iajs-2511	136	17	(	(	PUNCT
iajs-2511	136	18	abbreviated	abbreviate	VERB
iajs-2511	136	19	as	as	SCONJ
iajs-2511	136	20	𝑓.	𝑓.	NOUN
iajs-2511	136	21	𝑠.	𝑠.	PROPN
iajs-2511	136	22	𝑝.	𝑝.	PROPN
iajs-2511	136	23	ℎ.	ℎ.	PROPN
iajs-2511	136	24	𝑓.	𝑓.	PROPN
iajs-2511	136	25	)	)	PUNCT
iajs-2511	136	26	theorem	theorem	VERB
iajs-2511	136	27	4.2	4.2	NUM
iajs-2511	136	28	:	:	PUNCT
iajs-2511	136	29	every	every	DET
iajs-2511	136	30	fuzzy	fuzzy	ADJ
iajs-2511	136	31	homeomorphism	homeomorphism	PROPN
iajs-2511	136	32	function	function	NOUN
iajs-2511	136	33	is	be	AUX
iajs-2511	136	34	a	a	DET
iajs-2511	136	35	fuzzy	fuzzy	ADJ
iajs-2511	136	36	semi	semi	ADJ
iajs-2511	136	37	pre	pre	PROPN
iajs-2511	136	38	homeomorphism	homeomorphism	PROPN
iajs-2511	136	39	function	function	NOUN
iajs-2511	136	40	.	.	PUNCT
iajs-2511	137	1	proof	proof	NOUN
iajs-2511	137	2	:	:	PUNCT
iajs-2511	137	3	let	let	VERB
iajs-2511	137	4	𝑓	𝑓	PRON
iajs-2511	137	5	:	:	PUNCT
iajs-2511	137	6	𝑋	𝑋	PROPN
iajs-2511	137	7	,	,	PUNCT
iajs-2511	137	8	�	�	PROPN
iajs-2511	137	9	̃	̃	PROPN
iajs-2511	137	10	�	�	PROPN
iajs-2511	137	11			PROPN
iajs-2511	137	12	𝑌	𝑌	PROPN
iajs-2511	137	13	,	,	PUNCT
iajs-2511	137	14	𝜈	𝜈	PRON
iajs-2511	137	15	be	be	VERB
iajs-2511	137	16	a	a	DET
iajs-2511	137	17	fuzzy	fuzzy	ADJ
iajs-2511	137	18	homeomorphism	homeomorphism	NOUN
iajs-2511	137	19	function	function	NOUN
iajs-2511	137	20	.	.	PUNCT
iajs-2511	138	1	so	so	ADV
iajs-2511	138	2	,	,	PUNCT
iajs-2511	138	3	f	f	PROPN
iajs-2511	138	4	and	and	CCONJ
iajs-2511	138	5	f	f	PROPN
iajs-2511	138	6	-1	-1	X
iajs-2511	138	7	are	be	AUX
iajs-2511	138	8	fuzzy	fuzzy	ADJ
iajs-2511	138	9	continuous	continuous	ADJ
iajs-2511	138	10	functions	function	NOUN
iajs-2511	138	11	.	.	PUNCT
iajs-2511	139	1	hence	hence	ADV
iajs-2511	139	2	,	,	PUNCT
iajs-2511	139	3	by	by	ADP
iajs-2511	139	4	proposition	proposition	NOUN
iajs-2511	139	5	(	(	PUNCT
iajs-2511	139	6	3.11	3.11	NUM
iajs-2511	139	7	)	)	PUNCT
iajs-2511	139	8	f	f	PROPN
iajs-2511	139	9	and	and	CCONJ
iajs-2511	139	10	f	f	PROPN
iajs-2511	139	11	-1	-1	X
iajs-2511	139	12	are	be	AUX
iajs-2511	139	13	fuzzy	fuzzy	ADJ
iajs-2511	139	14	semi	semi	ADV
iajs-2511	139	15	pre	pre	VERB
iajs-2511	139	16	continuous	continuous	ADJ
iajs-2511	139	17	functions	function	NOUN
iajs-2511	139	18	.	.	PUNCT
iajs-2511	140	1	thus	thus	ADV
iajs-2511	140	2	,	,	PUNCT
iajs-2511	140	3	f	f	PROPN
iajs-2511	140	4	is	be	AUX
iajs-2511	140	5	a	a	DET
iajs-2511	140	6	fuzzy	fuzzy	ADJ
iajs-2511	140	7	semi	semi	ADV
iajs-2511	140	8	pre	pre	VERB
iajs-2511	140	9	homeomorphism	homeomorphism	VERB
iajs-2511	140	10	the	the	DET
iajs-2511	140	11	converse	converse	NOUN
iajs-2511	140	12	of	of	ADP
iajs-2511	140	13	theorem	theorem	ADJ
iajs-2511	140	14	4.2	4.2	NUM
iajs-2511	140	15	is	be	AUX
iajs-2511	140	16	not	not	PART
iajs-2511	140	17	true	true	ADJ
iajs-2511	140	18	in	in	ADP
iajs-2511	140	19	general	general	ADJ
iajs-2511	140	20	,	,	PUNCT
iajs-2511	140	21	so	so	SCONJ
iajs-2511	140	22	the	the	DET
iajs-2511	140	23	below	below	ADJ
iajs-2511	140	24	example	example	NOUN
iajs-2511	140	25	explain	explain	VERB
iajs-2511	140	26	that	that	PRON
iajs-2511	140	27	.	.	PUNCT
iajs-2511	141	1	example	example	NOUN
iajs-2511	141	2	4.3	4.3	NUM
iajs-2511	141	3	:	:	PUNCT
iajs-2511	141	4	let	let	VERB
iajs-2511	141	5	𝑋	𝑋	PROPN
iajs-2511	141	6	𝑥	𝑥	PROPN
iajs-2511	141	7	,	,	PUNCT
iajs-2511	141	8	𝑦	𝑦	PROPN
iajs-2511	141	9	,	,	PUNCT
iajs-2511	141	10	𝑧	𝑧	X
iajs-2511	141	11	,	,	PUNCT
iajs-2511	141	12	𝑌	𝑌	PROPN
iajs-2511	141	13	𝛼	𝛼	PROPN
iajs-2511	141	14	,	,	PUNCT
iajs-2511	141	15	𝛽	𝛽	PROPN
iajs-2511	141	16	,	,	PUNCT
iajs-2511	141	17	𝜎	𝜎	PROPN
iajs-2511	141	18	and	and	CCONJ
iajs-2511	141	19	let	let	VERB
iajs-2511	141	20	𝐴	𝐴	PROPN
iajs-2511	141	21	,	,	PUNCT
iajs-2511	141	22	𝐵	𝐵	NOUN
iajs-2511	141	23	be	be	VERB
iajs-2511	141	24	fuzzy	fuzzy	ADJ
iajs-2511	141	25	sets	set	NOUN
iajs-2511	141	26	defined	define	VERB
iajs-2511	141	27	as	as	ADP
iajs-2511	141	28	follows	follow	VERB
iajs-2511	141	29	:	:	PUNCT
iajs-2511	141	30	𝜇	𝜇	ADP
iajs-2511	141	31	𝑥	𝑥	ADP
iajs-2511	141	32	0.2	0.2	NUM
iajs-2511	141	33	𝜇	𝜇	ADP
iajs-2511	141	34	𝑦	𝑦	NOUN
iajs-2511	141	35	0.3	0.3	NUM
iajs-2511	141	36	𝜇	𝜇	ADP
iajs-2511	141	37	𝑧	𝑧	ADP
iajs-2511	141	38	0.5	0.5	NUM
iajs-2511	141	39	𝜇	𝜇	ADP
iajs-2511	141	40	𝛼	𝛼	SYM
iajs-2511	141	41	0.5	0.5	NUM
iajs-2511	141	42	𝜇	𝜇	ADP
iajs-2511	141	43	𝛽	𝛽	NOUN
iajs-2511	141	44	0.4	0.4	NUM
iajs-2511	141	45	𝜇	𝜇	ADP
iajs-2511	141	46	𝜎	𝜎	PROPN
iajs-2511	141	47	0.1	0.1	NUM
iajs-2511	141	48	let	let	VERB
iajs-2511	141	49	�	�	PROPN
iajs-2511	141	50	̃	̃	PROPN
iajs-2511	141	51	�	�	PROPN
iajs-2511	141	52	0	0	NUM
iajs-2511	141	53	,	,	PUNCT
iajs-2511	141	54	1	1	NUM
iajs-2511	141	55	,	,	PUNCT
iajs-2511	141	56	𝐴	𝐴	PROPN
iajs-2511	141	57	,	,	PUNCT
iajs-2511	141	58	𝜈	𝜈	PROPN
iajs-2511	141	59	0	0	NUM
iajs-2511	141	60	,	,	PUNCT
iajs-2511	141	61	1	1	NUM
iajs-2511	141	62	,	,	PUNCT
iajs-2511	141	63	𝐵	𝐵	NOUN
iajs-2511	141	64	so	so	ADV
iajs-2511	141	65	,	,	PUNCT
iajs-2511	141	66	(	(	PUNCT
iajs-2511	141	67	x,	x,	PROPN
iajs-2511	141	68	�	�	PROPN
iajs-2511	141	69	̃	̃	PROPN
iajs-2511	141	70	�	�	PROPN
iajs-2511	141	71	)	)	PUNCT
iajs-2511	141	72	and	and	CCONJ
iajs-2511	141	73	(	(	PUNCT
iajs-2511	141	74	y,𝜈	y,𝜈	NOUN
iajs-2511	141	75	)	)	PUNCT
iajs-2511	141	76	are	be	AUX
iajs-2511	141	77	f.t.s	f.t.s	ADJ
iajs-2511	141	78	.	.	PUNCT
iajs-2511	142	1	then	then	ADV
iajs-2511	142	2	the	the	DET
iajs-2511	142	3	function	function	NOUN
iajs-2511	142	4	𝑓	𝑓	PROPN
iajs-2511	142	5	:	:	PUNCT
iajs-2511	142	6	𝑋	𝑋	PROPN
iajs-2511	142	7	,	,	PUNCT
iajs-2511	142	8	�	�	PROPN
iajs-2511	142	9	̃	̃	PROPN
iajs-2511	142	10	�	�	PROPN
iajs-2511	142	11	→	→	SYM
iajs-2511	142	12	𝑌	𝑌	PROPN
iajs-2511	142	13	,	,	PUNCT
iajs-2511	142	14	𝜈	𝜈	PRON
iajs-2511	142	15	defined	define	VERB
iajs-2511	142	16	by	by	ADP
iajs-2511	142	17	𝑓	𝑓	DET
iajs-2511	142	18	𝑥	𝑥	X
iajs-2511	142	19	𝛼	𝛼	NOUN
iajs-2511	142	20	,	,	PUNCT
iajs-2511	142	21	𝑓	𝑓	PROPN
iajs-2511	142	22	𝑦	𝑦	PROPN
iajs-2511	142	23	𝛽	𝛽	NOUN
iajs-2511	142	24	,	,	PUNCT
iajs-2511	142	25	𝑓	𝑓	PRON
iajs-2511	142	26	𝑧	𝑧	PRON
iajs-2511	142	27	𝜎	𝜎	PROPN
iajs-2511	142	28	is	be	AUX
iajs-2511	142	29	𝑓.	𝑓.	PROPN
iajs-2511	142	30	𝑠.	𝑠.	PROPN
iajs-2511	142	31	𝑝.	𝑝.	PROPN
iajs-2511	143	1	ℎ.	ℎ.	PROPN
iajs-2511	143	2	𝑓	𝑓	PROPN
iajs-2511	143	3	but	but	CCONJ
iajs-2511	143	4	not	not	PART
iajs-2511	143	5	𝑓.	𝑓.	PROPN
iajs-2511	143	6	ℎ.	ℎ.	ADJ
iajs-2511	143	7	𝑓.	𝑓.	PROPN
iajs-2511	143	8	since	since	SCONJ
iajs-2511	143	9	f	f	PROPN
iajs-2511	143	10	and	and	CCONJ
iajs-2511	143	11	f	f	PROPN
iajs-2511	143	12	-1	-1	X
iajs-2511	143	13	are	be	AUX
iajs-2511	143	14	not	not	PART
iajs-2511	143	15	𝑓.	𝑓.	PROPN
iajs-2511	143	16	𝑐𝑜.	𝑐𝑜.	PROPN
iajs-2511	143	17	𝑓.	𝑓.	PROPN
iajs-2511	143	18	theorem	theorem	VERB
iajs-2511	143	19	4.4	4.4	NUM
iajs-2511	143	20	:	:	PUNCT
iajs-2511	143	21	let	let	VERB
iajs-2511	143	22	𝑓	𝑓	PRON
iajs-2511	143	23	:	:	PUNCT
iajs-2511	143	24	𝑋	𝑋	PROPN
iajs-2511	143	25	,	,	PUNCT
iajs-2511	143	26	�	�	PROPN
iajs-2511	143	27	̃	̃	PROPN
iajs-2511	143	28	�	�	PROPN
iajs-2511	143	29			PROPN
iajs-2511	143	30	𝑌	𝑌	PROPN
iajs-2511	143	31	,	,	PUNCT
iajs-2511	143	32	𝜈	𝜈	X
iajs-2511	143	33	be	be	VERB
iajs-2511	143	34	bijection	bijection	ADJ
iajs-2511	143	35	fuzzy	fuzzy	ADJ
iajs-2511	143	36	function	function	NOUN
iajs-2511	143	37	then	then	ADV
iajs-2511	143	38	the	the	DET
iajs-2511	143	39	below	below	ADJ
iajs-2511	143	40	statements	statement	NOUN
iajs-2511	143	41	are	be	AUX
iajs-2511	143	42	equivalent	equivalent	ADJ
iajs-2511	143	43	.	.	PUNCT
iajs-2511	144	1	(	(	PUNCT
iajs-2511	144	2	1	1	X
iajs-2511	144	3	)	)	PUNCT
iajs-2511	144	4	f	f	PROPN
iajs-2511	144	5	is	be	AUX
iajs-2511	144	6	a	a	DET
iajs-2511	144	7	fuzzy	fuzzy	ADJ
iajs-2511	144	8	semi	semi	ADJ
iajs-2511	144	9	pre	pre	ADJ
iajs-2511	144	10	-	-	ADJ
iajs-2511	144	11	open	open	ADJ
iajs-2511	144	12	function	function	NOUN
iajs-2511	144	13	.	.	PUNCT
iajs-2511	145	1	(	(	PUNCT
iajs-2511	145	2	2	2	X
iajs-2511	145	3	)	)	PUNCT
iajs-2511	145	4	f	f	PROPN
iajs-2511	145	5	is	be	AUX
iajs-2511	145	6	a	a	DET
iajs-2511	145	7	fuzzy	fuzzy	ADJ
iajs-2511	145	8	semi	semi	ADV
iajs-2511	145	9	pre	pre	X
iajs-2511	145	10	closed	closed	ADJ
iajs-2511	145	11	function	function	NOUN
iajs-2511	145	12	.	.	PUNCT
iajs-2511	146	1	(	(	PUNCT
iajs-2511	146	2	3	3	X
iajs-2511	146	3	)	)	PUNCT
iajs-2511	146	4	f	f	NOUN
iajs-2511	147	1	-1	-1	X
iajs-2511	147	2	is	be	AUX
iajs-2511	147	3	a	a	DET
iajs-2511	147	4	fuzzy	fuzzy	ADJ
iajs-2511	147	5	semi	semi	ADV
iajs-2511	147	6	pre	pre	VERB
iajs-2511	147	7	continuous	continuous	ADJ
iajs-2511	147	8	function	function	NOUN
iajs-2511	147	9	.	.	PUNCT
iajs-2511	148	1	proof	proof	NOUN
iajs-2511	148	2	:	:	PUNCT
iajs-2511	148	3	(	(	PUNCT
iajs-2511	148	4	1	1	X
iajs-2511	148	5	)	)	PUNCT
iajs-2511	148	6	→	→	X
iajs-2511	148	7	(	(	PUNCT
iajs-2511	148	8	2	2	X
iajs-2511	148	9	)	)	PUNCT
iajs-2511	148	10	let	let	VERB
iajs-2511	148	11	𝜌	𝜌	PART
iajs-2511	148	12	be	be	AUX
iajs-2511	148	13	fuzzy	fuzzy	ADJ
iajs-2511	148	14	closed	closed	ADJ
iajs-2511	148	15	set	set	VERB
iajs-2511	148	16	belong	belong	VERB
iajs-2511	148	17	to	to	ADP
iajs-2511	148	18	x	x	PRON
iajs-2511	148	19	,	,	PUNCT
iajs-2511	148	20	then	then	ADV
iajs-2511	148	21	1	1	NUM
iajs-2511	148	22	𝜇	𝜇	PRON
iajs-2511	148	23	𝑥	𝑥	NOUN
iajs-2511	148	24	is	be	AUX
iajs-2511	148	25	a	a	DET
iajs-2511	148	26	fuzzy	fuzzy	ADJ
iajs-2511	148	27	open	open	ADJ
iajs-2511	148	28	set	set	NOUN
iajs-2511	148	29	belong	belong	VERB
iajs-2511	148	30	to	to	ADP
iajs-2511	148	31	x	x	PRON
iajs-2511	148	32	since	since	SCONJ
iajs-2511	148	33	f	f	PROPN
iajs-2511	148	34	is	be	AUX
iajs-2511	148	35	a	a	DET
iajs-2511	148	36	fuzzy	fuzzy	ADJ
iajs-2511	148	37	semi	semi	ADJ
iajs-2511	148	38	pre	pre	ADJ
iajs-2511	148	39	-	-	ADJ
iajs-2511	148	40	open	open	ADJ
iajs-2511	148	41	function	function	NOUN
iajs-2511	148	42	.	.	PUNCT
iajs-2511	149	1	then	then	ADV
iajs-2511	149	2	𝑓	𝑓	X
iajs-2511	149	3	1	1	NUM
iajs-2511	149	4	𝜇	𝜇	ADP
iajs-2511	149	5	𝑥	𝑥	PRON
iajs-2511	149	6	∈	∈	PROPN
iajs-2511	149	7	𝐹.	𝐹.	NOUN
iajs-2511	149	8	𝑆.	𝑆.	PROPN
iajs-2511	149	9	𝑃.	𝑃.	PROPN
iajs-2511	149	10	𝑂.	𝑂.	PROPN
iajs-2511	149	11	𝑌	𝑌	PROPN
iajs-2511	149	12	.	.	PUNCT
iajs-2511	150	1	so	so	ADV
iajs-2511	150	2	,	,	PUNCT
iajs-2511	150	3	by	by	ADP
iajs-2511	150	4	[	[	PUNCT
iajs-2511	150	5	theorem	theorem	ADJ
iajs-2511	150	6	2.4	2.4	NUM
iajs-2511	150	7	]	]	PUNCT
iajs-2511	150	8	we	we	PRON
iajs-2511	150	9	obtain	obtain	VERB
iajs-2511	150	10	1	1	NUM
iajs-2511	150	11	–	–	PUNCT
iajs-2511	150	12	𝜇	𝜇	ADP
iajs-2511	150	13	𝑓	𝑓	PRON
iajs-2511	150	14	𝑥	𝑥	PROPN
iajs-2511	150	15	1	1	NUM
iajs-2511	150	16	–	–	PUNCT
iajs-2511	150	17	𝜇	𝜇	ADP
iajs-2511	150	18	𝑦	𝑦	NOUN
iajs-2511	150	19	∈	∈	NOUN
iajs-2511	150	20	𝐹.	𝐹.	NOUN
iajs-2511	150	21	𝑆.	𝑆.	PROPN
iajs-2511	150	22	𝑃.	𝑃.	PROPN
iajs-2511	150	23	𝑂.	𝑂.	PROPN
iajs-2511	150	24	𝑌	𝑌	PROPN
iajs-2511	150	25	.	.	PUNCT
iajs-2511	151	1	thus	thus	ADV
iajs-2511	151	2	,	,	PUNCT
iajs-2511	151	3	by	by	ADP
iajs-2511	151	4	[	[	PUNCT
iajs-2511	151	5	theorem	theorem	ADJ
iajs-2511	151	6	3.3	3.3	NUM
iajs-2511	151	7	]	]	PUNCT
iajs-2511	151	8	𝜇	𝜇	ADP
iajs-2511	151	9	𝑦	𝑦	NOUN
iajs-2511	151	10	∈	∈	NOUN
iajs-2511	151	11	𝐹.	𝐹.	NOUN
iajs-2511	151	12	𝑆.	𝑆.	PROPN
iajs-2511	151	13	𝑃.	𝑃.	PROPN
iajs-2511	151	14	𝐶.	𝐶.	PROPN
iajs-2511	151	15	𝑌	𝑌	PROPN
iajs-2511	151	16	.	.	PUNCT
iajs-2511	152	1	hence	hence	ADV
iajs-2511	152	2	,	,	PUNCT
iajs-2511	152	3	f	f	PROPN
iajs-2511	152	4	is	be	AUX
iajs-2511	152	5	a	a	DET
iajs-2511	152	6	fuzzy	fuzzy	ADJ
iajs-2511	152	7	semi	semi	ADV
iajs-2511	152	8	pre	pre	NOUN
iajs-2511	152	9	closed	closed	ADJ
iajs-2511	152	10	function	function	NOUN
iajs-2511	152	11	(	(	PUNCT
iajs-2511	152	12	2	2	NUM
iajs-2511	152	13	)	)	PUNCT
iajs-2511	152	14	→	→	X
iajs-2511	152	15	(	(	PUNCT
iajs-2511	152	16	3	3	X
iajs-2511	152	17	)	)	PUNCT
iajs-2511	152	18	let	let	VERB
iajs-2511	152	19	𝛿	𝛿	PRON
iajs-2511	152	20	be	be	AUX
iajs-2511	152	21	any	any	DET
iajs-2511	152	22	fuzzy	fuzzy	ADJ
iajs-2511	152	23	open	open	ADJ
iajs-2511	152	24	set	set	NOUN
iajs-2511	152	25	belong	belong	VERB
iajs-2511	152	26	to	to	ADP
iajs-2511	152	27	x.	x.	NOUN
iajs-2511	152	28	so	so	ADV
iajs-2511	152	29	,	,	PUNCT
iajs-2511	152	30	1	1	NUM
iajs-2511	152	31	𝜇	𝜇	PRON
iajs-2511	152	32	𝑥	𝑥	NOUN
iajs-2511	152	33	is	be	AUX
iajs-2511	152	34	a	a	DET
iajs-2511	152	35	fuzzy	fuzzy	ADJ
iajs-2511	152	36	closed	close	VERB
iajs-2511	152	37	set	set	VERB
iajs-2511	152	38	belong	belong	VERB
iajs-2511	152	39	to	to	ADP
iajs-2511	152	40	x.	x.	NOUN
iajs-2511	153	1	but	but	CCONJ
iajs-2511	153	2	f	f	PROPN
iajs-2511	153	3	is	be	AUX
iajs-2511	153	4	a	a	DET
iajs-2511	153	5	fuzzy	fuzzy	ADJ
iajs-2511	153	6	semi	semi	ADV
iajs-2511	153	7	pre	pre	X
iajs-2511	153	8	closed	closed	ADJ
iajs-2511	153	9	function	function	NOUN
iajs-2511	153	10	.	.	PUNCT
iajs-2511	154	1	so	so	ADV
iajs-2511	154	2	,	,	PUNCT
iajs-2511	154	3	𝑓	𝑓	DET
iajs-2511	154	4	1	1	NUM
iajs-2511	154	5	𝜇	𝜇	ADP
iajs-2511	154	6	𝑥	𝑥	PRON
iajs-2511	154	7	∈	∈	PROPN
iajs-2511	154	8	𝐹.	𝐹.	NOUN
iajs-2511	154	9	𝑆.	𝑆.	PROPN
iajs-2511	154	10	𝑃.	𝑃.	PROPN
iajs-2511	154	11	𝐶.	𝐶.	PROPN
iajs-2511	154	12	𝑌	𝑌	PROPN
iajs-2511	154	13	by	by	ADP
iajs-2511	154	14	[	[	X
iajs-2511	154	15	theorem	theorem	ADJ
iajs-2511	154	16	(	(	PUNCT
iajs-2511	154	17	2.4	2.4	NUM
iajs-2511	154	18	)	)	PUNCT
iajs-2511	154	19	]	]	PUNCT
iajs-2511	155	1	we	we	PRON
iajs-2511	155	2	obtain	obtain	VERB
iajs-2511	155	3	1	1	NUM
iajs-2511	155	4	–	–	PUNCT
iajs-2511	155	5	𝜇	𝜇	ADP
iajs-2511	155	6	𝑓	𝑓	PRON
iajs-2511	155	7	𝑥	𝑥	PROPN
iajs-2511	155	8	1	1	NUM
iajs-2511	155	9	–	–	PUNCT
iajs-2511	155	10	𝜇	𝜇	ADP
iajs-2511	155	11	𝑦	𝑦	NOUN
iajs-2511	155	12	∈	∈	NOUN
iajs-2511	155	13	𝐹.	𝐹.	NOUN
iajs-2511	155	14	𝑆.	𝑆.	PROPN
iajs-2511	155	15	𝑃.	𝑃.	PROPN
iajs-2511	155	16	𝐶.	𝐶.	PROPN
iajs-2511	155	17	𝑌	𝑌	PROPN
iajs-2511	155	18	.	.	PUNCT
iajs-2511	156	1	thus	thus	ADV
iajs-2511	156	2	,	,	PUNCT
iajs-2511	156	3	by	by	ADP
iajs-2511	156	4	[	[	PUNCT
iajs-2511	156	5	theorem	theorem	ADJ
iajs-2511	156	6	(	(	PUNCT
iajs-2511	156	7	3.3	3.3	NUM
iajs-2511	156	8	)	)	PUNCT
iajs-2511	156	9	]	]	PUNCT
iajs-2511	157	1	𝜇	𝜇	ADP
iajs-2511	157	2	𝑦	𝑦	ADP
iajs-2511	157	3	𝜇	𝜇	X
iajs-2511	157	4	𝑦	𝑦	NOUN
iajs-2511	157	5	∈	∈	NOUN
iajs-2511	157	6	𝐹.	𝐹.	NOUN
iajs-2511	157	7	𝑆.	𝑆.	PROPN
iajs-2511	157	8	𝑃.	𝑃.	PROPN
iajs-2511	157	9	𝑂.	𝑂.	PROPN
iajs-2511	157	10	𝑌	𝑌	PROPN
iajs-2511	157	11	.	.	PUNCT
iajs-2511	158	1	hence	hence	ADV
iajs-2511	158	2	,	,	PUNCT
iajs-2511	158	3	f	f	PROPN
iajs-2511	158	4	-1	-1	X
iajs-2511	158	5	is	be	AUX
iajs-2511	158	6	a	a	DET
iajs-2511	158	7	fuzzy	fuzzy	ADJ
iajs-2511	158	8	semi	semi	ADV
iajs-2511	158	9	pre	pre	X
iajs-2511	158	10	continuous	continuous	ADJ
iajs-2511	158	11	function	function	NOUN
iajs-2511	158	12	  	  	SPACE
iajs-2511	158	13	79	79	NUM
iajs-2511	158	14	  	  	SPACE
iajs-2511	158	15	ibn	ibn	PROPN
iajs-2511	158	16	al	al	PROPN
iajs-2511	158	17	-	-	PUNCT
iajs-2511	158	18	haitham	haitham	PROPN
iajs-2511	158	19	jour	jour	X
iajs-2511	158	20	.	.	PROPN
iajs-2511	159	1	for	for	ADP
iajs-2511	159	2	pure	pure	ADJ
iajs-2511	159	3	&	&	CCONJ
iajs-2511	159	4	appl	appl	PROPN
iajs-2511	159	5	.	.	PUNCT
iajs-2511	160	1	sci	sci	PROPN
iajs-2511	160	2	.	.	PROPN
iajs-2511	161	1	33	33	NUM
iajs-2511	161	2	(	(	PUNCT
iajs-2511	161	3	4	4	NUM
iajs-2511	161	4	)	)	PUNCT
iajs-2511	161	5	2020	2020	NUM
iajs-2511	161	6	(	(	PUNCT
iajs-2511	161	7	3	3	NUM
iajs-2511	161	8	)	)	PUNCT
iajs-2511	161	9	→	→	X
iajs-2511	161	10	(	(	PUNCT
iajs-2511	161	11	1	1	X
iajs-2511	161	12	)	)	PUNCT
iajs-2511	161	13	let	let	VERB
iajs-2511	161	14	𝜔	𝜔	PART
iajs-2511	161	15	be	be	AUX
iajs-2511	161	16	any	any	DET
iajs-2511	161	17	fuzzy	fuzzy	ADJ
iajs-2511	161	18	open	open	ADJ
iajs-2511	161	19	set	set	NOUN
iajs-2511	161	20	belong	belong	VERB
iajs-2511	161	21	to	to	ADP
iajs-2511	161	22	x.	x.	NOUN
iajs-2511	161	23	and	and	CCONJ
iajs-2511	161	24	since	since	ADV
iajs-2511	161	25	,	,	PUNCT
iajs-2511	161	26	f	f	PROPN
iajs-2511	161	27	-1	-1	X
iajs-2511	161	28	is	be	AUX
iajs-2511	161	29	a	a	DET
iajs-2511	161	30	fuzzy	fuzzy	ADJ
iajs-2511	161	31	semi	semi	ADV
iajs-2511	161	32	pre	pre	VERB
iajs-2511	161	33	continuous	continuous	ADJ
iajs-2511	161	34	function	function	NOUN
iajs-2511	161	35	.	.	PUNCT
iajs-2511	162	1	so	so	ADV
iajs-2511	162	2	,	,	PUNCT
iajs-2511	162	3	𝜇	𝜇	ADP
iajs-2511	162	4	𝑦	𝑦	ADP
iajs-2511	162	5	𝜇	𝜇	X
iajs-2511	162	6	𝑦	𝑦	NOUN
iajs-2511	162	7	∈	∈	NOUN
iajs-2511	162	8	𝐹.	𝐹.	NOUN
iajs-2511	162	9	𝑆.	𝑆.	PROPN
iajs-2511	162	10	𝑃.	𝑃.	PROPN
iajs-2511	162	11	𝑂.	𝑂.	PROPN
iajs-2511	162	12	𝑌	𝑌	PROPN
iajs-2511	162	13	.	.	PUNCT
iajs-2511	163	1	hence	hence	ADV
iajs-2511	163	2	,	,	PUNCT
iajs-2511	163	3	f	f	PROPN
iajs-2511	163	4	is	be	AUX
iajs-2511	163	5	a	a	DET
iajs-2511	163	6	fuzzy	fuzzy	ADJ
iajs-2511	163	7	semi	semi	ADJ
iajs-2511	163	8	pre	pre	ADJ
iajs-2511	163	9	-	-	ADJ
iajs-2511	163	10	open	open	ADJ
iajs-2511	163	11	function	function	NOUN
iajs-2511	163	12	corollary	corollary	ADJ
iajs-2511	163	13	4.5	4.5	NUM
iajs-2511	163	14	:	:	PUNCT
iajs-2511	163	15	let	let	VERB
iajs-2511	163	16	𝑓	𝑓	PRON
iajs-2511	163	17	:	:	PUNCT
iajs-2511	163	18	𝑋	𝑋	PROPN
iajs-2511	163	19	,	,	PUNCT
iajs-2511	163	20	�	�	PROPN
iajs-2511	163	21	̃	̃	PROPN
iajs-2511	163	22	�	�	PROPN
iajs-2511	163	23			PROPN
iajs-2511	163	24	𝑌	𝑌	PROPN
iajs-2511	163	25	,	,	PUNCT
iajs-2511	163	26	𝜈	𝜈	PRON
iajs-2511	163	27	be	be	VERB
iajs-2511	163	28	a	a	DET
iajs-2511	163	29	bijective	bijective	ADJ
iajs-2511	163	30	fuzzy	fuzzy	ADJ
iajs-2511	163	31	function	function	NOUN
iajs-2511	163	32	,	,	PUNCT
iajs-2511	163	33	then	then	ADV
iajs-2511	163	34	the	the	DET
iajs-2511	163	35	below	below	ADJ
iajs-2511	163	36	statements	statement	NOUN
iajs-2511	163	37	are	be	AUX
iajs-2511	163	38	equivalent	equivalent	ADJ
iajs-2511	163	39	.	.	PUNCT
iajs-2511	164	1	(	(	PUNCT
iajs-2511	164	2	1	1	X
iajs-2511	164	3	)	)	PUNCT
iajs-2511	164	4	f	f	PROPN
iajs-2511	164	5	is	be	AUX
iajs-2511	164	6	a	a	DET
iajs-2511	164	7	fuzzy	fuzzy	ADJ
iajs-2511	164	8	semi	semi	ADV
iajs-2511	164	9	pre	pre	VERB
iajs-2511	164	10	continuous	continuous	ADJ
iajs-2511	164	11	and	and	CCONJ
iajs-2511	164	12	a	a	DET
iajs-2511	164	13	fuzzy	fuzzy	ADJ
iajs-2511	164	14	semi	semi	ADJ
iajs-2511	164	15	pre	pre	ADJ
iajs-2511	164	16	-	-	ADJ
iajs-2511	164	17	open	open	ADJ
iajs-2511	164	18	functions	function	NOUN
iajs-2511	164	19	.	.	PUNCT
iajs-2511	165	1	(	(	PUNCT
iajs-2511	165	2	2	2	X
iajs-2511	165	3	)	)	PUNCT
iajs-2511	165	4	f	f	PROPN
iajs-2511	165	5	is	be	AUX
iajs-2511	165	6	a	a	DET
iajs-2511	165	7	fuzzy	fuzzy	ADJ
iajs-2511	165	8	semi	semi	ADV
iajs-2511	165	9	pre	pre	VERB
iajs-2511	165	10	continuous	continuous	ADJ
iajs-2511	165	11	and	and	CCONJ
iajs-2511	165	12	a	a	DET
iajs-2511	165	13	fuzzy	fuzzy	ADJ
iajs-2511	165	14	semi	semi	ADJ
iajs-2511	165	15	pre	pre	X
iajs-2511	165	16	closed	closed	ADJ
iajs-2511	165	17	functions	function	NOUN
iajs-2511	165	18	.	.	PUNCT
iajs-2511	166	1	(	(	PUNCT
iajs-2511	166	2	3	3	X
iajs-2511	166	3	)	)	PUNCT
iajs-2511	166	4	f	f	PROPN
iajs-2511	166	5	is	be	AUX
iajs-2511	166	6	a	a	DET
iajs-2511	166	7	fuzzy	fuzzy	ADJ
iajs-2511	166	8	semi	semi	ADJ
iajs-2511	166	9	pre	pre	PROPN
iajs-2511	166	10	homeomorphism	homeomorphism	PROPN
iajs-2511	166	11	function	function	NOUN
iajs-2511	166	12	.	.	PUNCT
iajs-2511	167	1	proof	proof	NOUN
iajs-2511	167	2	:	:	PUNCT
iajs-2511	167	3	(	(	PUNCT
iajs-2511	167	4	1	1	X
iajs-2511	167	5	)	)	PUNCT
iajs-2511	167	6	→	→	X
iajs-2511	167	7	(	(	PUNCT
iajs-2511	167	8	2	2	X
iajs-2511	167	9	)	)	PUNCT
iajs-2511	167	10	follows	follow	VERB
iajs-2511	167	11	from	from	ADP
iajs-2511	167	12	proof	proof	NOUN
iajs-2511	167	13	theorem	theorem	NOUN
iajs-2511	167	14	(	(	PUNCT
iajs-2511	167	15	4.4	4.4	NUM
iajs-2511	167	16	)	)	PUNCT
iajs-2511	168	1	[	[	X
iajs-2511	168	2	(	(	PUNCT
iajs-2511	168	3	1	1	NUM
iajs-2511	168	4	)	)	PUNCT
iajs-2511	168	5	→	→	SYM
iajs-2511	168	6	(	(	PUNCT
iajs-2511	168	7	2)]	2)]	NUM
iajs-2511	168	8	(	(	PUNCT
iajs-2511	168	9	2	2	NUM
iajs-2511	168	10	)	)	PUNCT
iajs-2511	168	11	→	→	X
iajs-2511	168	12	(	(	PUNCT
iajs-2511	168	13	3	3	X
iajs-2511	168	14	)	)	PUNCT
iajs-2511	168	15	follows	follow	VERB
iajs-2511	168	16	from	from	ADP
iajs-2511	168	17	proof	proof	NOUN
iajs-2511	168	18	theorem	theorem	NOUN
iajs-2511	168	19	(	(	PUNCT
iajs-2511	168	20	4.4	4.4	NUM
iajs-2511	168	21	)	)	PUNCT
iajs-2511	169	1	[	[	X
iajs-2511	169	2	(	(	PUNCT
iajs-2511	169	3	2	2	NUM
iajs-2511	169	4	)	)	PUNCT
iajs-2511	169	5	→	→	SYM
iajs-2511	169	6	(	(	PUNCT
iajs-2511	169	7	3)]	3)]	NUM
iajs-2511	169	8	(	(	PUNCT
iajs-2511	169	9	3	3	NUM
iajs-2511	169	10	)	)	PUNCT
iajs-2511	169	11	→(1	→(1	PUNCT
iajs-2511	169	12	)	)	PUNCT
iajs-2511	169	13	follows	follow	VERB
iajs-2511	169	14	from	from	ADP
iajs-2511	169	15	definition	definition	NOUN
iajs-2511	169	16	(	(	PUNCT
iajs-2511	169	17	4.1	4.1	NUM
iajs-2511	169	18	)	)	PUNCT
iajs-2511	169	19	and	and	CCONJ
iajs-2511	169	20	proof	proof	NOUN
iajs-2511	169	21	theorem	theorem	NOUN
iajs-2511	169	22	(	(	PUNCT
iajs-2511	169	23	4.4	4.4	NUM
iajs-2511	169	24	)	)	PUNCT
iajs-2511	170	1	[	[	X
iajs-2511	170	2	(	(	PUNCT
iajs-2511	170	3	3	3	NUM
iajs-2511	170	4	)	)	PUNCT
iajs-2511	170	5	→(1)]	→(1)]	NOUN
iajs-2511	170	6	definition	definition	NOUN
iajs-2511	170	7	4.6	4.6	NUM
iajs-2511	170	8	:	:	PUNCT
iajs-2511	170	9	let	let	VERB
iajs-2511	170	10	𝑓	𝑓	PRON
iajs-2511	170	11	:	:	PUNCT
iajs-2511	170	12	𝑋	𝑋	PROPN
iajs-2511	170	13	,	,	PUNCT
iajs-2511	170	14	�	�	PROPN
iajs-2511	170	15	̃	̃	PROPN
iajs-2511	170	16	�	�	PROPN
iajs-2511	170	17			PROPN
iajs-2511	170	18	𝑌	𝑌	PROPN
iajs-2511	170	19	,	,	PUNCT
iajs-2511	170	20	𝜈	𝜈	X
iajs-2511	170	21	be	be	VERB
iajs-2511	170	22	bijection	bijection	ADJ
iajs-2511	170	23	fuzzy	fuzzy	ADJ
iajs-2511	170	24	function	function	NOUN
iajs-2511	170	25	,	,	PUNCT
iajs-2511	170	26	f	f	PROPN
iajs-2511	170	27	is	be	AUX
iajs-2511	170	28	called	call	VERB
iajs-2511	170	29	a	a	DET
iajs-2511	170	30	fuzzy	fuzzy	ADJ
iajs-2511	170	31	semi	semi	ADJ
iajs-2511	170	32	pre	pre	PROPN
iajs-2511	170	33	homeomorphism	homeomorphism	PROPN
iajs-2511	170	34	iff	iff	PROPN
iajs-2511	170	35	f	f	PROPN
iajs-2511	170	36	and	and	CCONJ
iajs-2511	170	37	f	f	PROPN
iajs-2511	170	38	-1	-1	X
iajs-2511	170	39	are	be	AUX
iajs-2511	170	40	fuzzy	fuzzy	ADJ
iajs-2511	170	41	semi	semi	ADV
iajs-2511	170	42	pre	pre	X
iajs-2511	170	43	irresolute	irresolute	ADJ
iajs-2511	170	44	functions	function	NOUN
iajs-2511	170	45	(	(	PUNCT
iajs-2511	170	46	abbreviated	abbreviate	VERB
iajs-2511	170	47	as	as	ADP
iajs-2511	170	48	𝑓.	𝑓.	NOUN
iajs-2511	170	49	𝑠.	𝑠.	PROPN
iajs-2511	170	50	𝑝∗.	𝑝∗.	PROPN
iajs-2511	170	51	ℎ.	ℎ.	ADJ
iajs-2511	170	52	𝑓.	𝑓.	PROPN
iajs-2511	170	53	)	)	PUNCT
iajs-2511	170	54	.we	.we	PUNCT
iajs-2511	171	1	say	say	VERB
iajs-2511	171	2	the	the	DET
iajs-2511	171	3	spaces	space	NOUN
iajs-2511	171	4	(	(	PUNCT
iajs-2511	171	5	x,	x,	PROPN
iajs-2511	171	6	�	�	PROPN
iajs-2511	171	7	̃	̃	PROPN
iajs-2511	171	8	�	�	PROPN
iajs-2511	171	9	)	)	PUNCT
iajs-2511	171	10	and	and	CCONJ
iajs-2511	171	11	(	(	PUNCT
iajs-2511	171	12	y,𝜈	y,𝜈	NOUN
iajs-2511	171	13	)	)	PUNCT
iajs-2511	171	14	are	be	AUX
iajs-2511	171	15	fuzzy	fuzzy	ADJ
iajs-2511	171	16	semi	semi	ADV
iajs-2511	171	17	pre	pre	NOUN
iajs-2511	171	18	homeomorphism	homeomorphism	PROPN
iajs-2511	171	19	if	if	SCONJ
iajs-2511	171	20	there	there	PRON
iajs-2511	171	21	exist	exist	VERB
iajs-2511	171	22	a	a	DET
iajs-2511	171	23	fuzzy	fuzzy	ADJ
iajs-2511	171	24	semi	semi	ADJ
iajs-2511	171	25	pre	pre	PROPN
iajs-2511	171	26	homeomorphism	homeomorphism	PROPN
iajs-2511	171	27	from	from	ADP
iajs-2511	171	28	(	(	PUNCT
iajs-2511	171	29	x,	x,	PROPN
iajs-2511	171	30	�	�	PROPN
iajs-2511	171	31	̃	̃	PROPN
iajs-2511	171	32	�	�	PROPN
iajs-2511	171	33	)	)	PUNCT
iajs-2511	171	34	on	on	ADP
iajs-2511	171	35	to	to	ADP
iajs-2511	171	36	(	(	PUNCT
iajs-2511	171	37	y,𝜈	y,𝜈	NOUN
iajs-2511	171	38	)	)	PUNCT
iajs-2511	171	39	.	.	PUNCT
iajs-2511	172	1	the	the	DET
iajs-2511	172	2	family	family	NOUN
iajs-2511	172	3	of	of	ADP
iajs-2511	172	4	fuzzy	fuzzy	ADJ
iajs-2511	172	5	semi	semi	ADJ
iajs-2511	172	6	pre	pre	PROPN
iajs-2511	172	7	homeomorphism	homeomorphism	PROPN
iajs-2511	172	8	from	from	ADP
iajs-2511	172	9	a	a	DET
iajs-2511	172	10	f.t.s	f.t.s	NOUN
iajs-2511	172	11	(	(	PUNCT
iajs-2511	172	12	x,	x,	PROPN
iajs-2511	172	13	�	�	PROPN
iajs-2511	172	14	̃	̃	PROPN
iajs-2511	172	15	�	�	PROPN
iajs-2511	172	16	)	)	PUNCT
iajs-2511	172	17	to	to	ADP
iajs-2511	172	18	itself	itself	PRON
iajs-2511	172	19	is	be	AUX
iajs-2511	172	20	denoted	denote	VERB
iajs-2511	172	21	by	by	ADP
iajs-2511	172	22	fuzzy	fuzzy	ADJ
iajs-2511	172	23	semi	semi	ADJ
iajs-2511	172	24	pre	pre	PROPN
iajs-2511	172	25	homeomorphism(x,	homeomorphism(x,	PROPN
iajs-2511	172	26	�	�	PROPN
iajs-2511	172	27	̃	̃	PROPN
iajs-2511	172	28	�	�	PROPN
iajs-2511	172	29	)	)	PUNCT
iajs-2511	172	30	(	(	PUNCT
iajs-2511	172	31	abbreviated	abbreviate	VERB
iajs-2511	172	32	as	as	ADP
iajs-2511	172	33	𝑓.	𝑓.	NOUN
iajs-2511	172	34	𝑠.	𝑠.	PROPN
iajs-2511	172	35	𝑝∗.	𝑝∗.	PROPN
iajs-2511	172	36	ℎ.(x,	ℎ.(x,	PROPN
iajs-2511	172	37	�	�	PROPN
iajs-2511	172	38	̃	̃	PROPN
iajs-2511	172	39	�	�	PROPN
iajs-2511	172	40	)	)	PUNCT
iajs-2511	172	41	)	)	PUNCT
iajs-2511	172	42	.	.	PUNCT
iajs-2511	173	1	theorem	theorem	VERB
iajs-2511	173	2	4.7	4.7	NUM
iajs-2511	173	3	every	every	DET
iajs-2511	173	4	fuzzy	fuzzy	ADJ
iajs-2511	173	5	semi	semi	ADJ
iajs-2511	173	6	pre	pre	PROPN
iajs-2511	173	7	homeomorphism	homeomorphism	PROPN
iajs-2511	173	8	function	function	NOUN
iajs-2511	173	9	is	be	AUX
iajs-2511	173	10	a	a	DET
iajs-2511	173	11	fuzzy	fuzzy	ADJ
iajs-2511	173	12	semi	semi	ADJ
iajs-2511	173	13	pre	pre	PROPN
iajs-2511	173	14	homeomorphism	homeomorphism	PROPN
iajs-2511	173	15	function	function	NOUN
iajs-2511	173	16	.	.	PUNCT
iajs-2511	174	1	proof	proof	NOUN
iajs-2511	174	2	:	:	PUNCT
iajs-2511	174	3	let	let	VERB
iajs-2511	174	4	𝑓	𝑓	PRON
iajs-2511	174	5	:	:	PUNCT
iajs-2511	174	6	𝑋	𝑋	PROPN
iajs-2511	174	7	,	,	PUNCT
iajs-2511	174	8	�	�	PROPN
iajs-2511	174	9	̃	̃	PROPN
iajs-2511	174	10	�	�	PROPN
iajs-2511	174	11			PROPN
iajs-2511	174	12	𝑌	𝑌	PROPN
iajs-2511	174	13	,	,	PUNCT
iajs-2511	174	14	𝜈	𝜈	PRON
iajs-2511	174	15	be	be	VERB
iajs-2511	174	16	a	a	DET
iajs-2511	174	17	fuzzy	fuzzy	ADJ
iajs-2511	174	18	semi	semi	ADJ
iajs-2511	174	19	pre	pre	PROPN
iajs-2511	174	20	homeomorphism	homeomorphism	PROPN
iajs-2511	174	21	function	function	NOUN
iajs-2511	174	22	,	,	PUNCT
iajs-2511	174	23	so	so	ADV
iajs-2511	174	24	,	,	PUNCT
iajs-2511	174	25	f	f	PROPN
iajs-2511	174	26	and	and	CCONJ
iajs-2511	174	27	f	f	PROPN
iajs-2511	174	28	-1	-1	X
iajs-2511	174	29	are	be	AUX
iajs-2511	174	30	fuzzy	fuzzy	ADJ
iajs-2511	174	31	semi	semi	ADV
iajs-2511	174	32	pre	pre	X
iajs-2511	174	33	irresolute	irresolute	ADJ
iajs-2511	174	34	functions	function	NOUN
iajs-2511	174	35	.	.	PUNCT
iajs-2511	175	1	hence	hence	ADV
iajs-2511	175	2	,	,	PUNCT
iajs-2511	175	3	by	by	ADP
iajs-2511	175	4	proposition	proposition	NOUN
iajs-2511	175	5	(	(	PUNCT
iajs-2511	175	6	3.11	3.11	NUM
iajs-2511	175	7	)	)	PUNCT
iajs-2511	175	8	f	f	PROPN
iajs-2511	175	9	and	and	CCONJ
iajs-2511	175	10	f	f	PROPN
iajs-2511	175	11	-1	-1	X
iajs-2511	175	12	are	be	AUX
iajs-2511	175	13	fuzzy	fuzzy	ADJ
iajs-2511	175	14	semi	semi	ADV
iajs-2511	175	15	pre	pre	VERB
iajs-2511	175	16	continuous	continuous	ADJ
iajs-2511	175	17	functions	function	NOUN
iajs-2511	175	18	.	.	PUNCT
iajs-2511	176	1	thus	thus	ADV
iajs-2511	176	2	,	,	PUNCT
iajs-2511	176	3	𝑓	𝑓	PRON
iajs-2511	176	4	is	be	AUX
iajs-2511	176	5	a	a	DET
iajs-2511	176	6	fuzzy	fuzzy	ADJ
iajs-2511	176	7	semi	semi	ADJ
iajs-2511	176	8	pre	pre	VERB
iajs-2511	176	9	homeomorphism	homeomorphism	PROPN
iajs-2511	176	10	function	function	VERB
iajs-2511	176	11	theorem	theorem	VERB
iajs-2511	176	12	4.8	4.8	NUM
iajs-2511	176	13	:	:	PUNCT
iajs-2511	176	14	let	let	VERB
iajs-2511	176	15	𝑓	𝑓	PRON
iajs-2511	176	16	:	:	PUNCT
iajs-2511	176	17	𝑋	𝑋	PROPN
iajs-2511	176	18	,	,	PUNCT
iajs-2511	176	19	�	�	PROPN
iajs-2511	176	20	̃	̃	PROPN
iajs-2511	176	21	�	�	PROPN
iajs-2511	176	22			PROPN
iajs-2511	176	23	𝑌	𝑌	PROPN
iajs-2511	176	24	,	,	PUNCT
iajs-2511	176	25	𝜈	𝜈	PRON
iajs-2511	176	26	be	be	VERB
iajs-2511	176	27	a	a	DET
iajs-2511	176	28	bijective	bijective	ADJ
iajs-2511	176	29	fuzzy	fuzzy	ADJ
iajs-2511	176	30	function	function	NOUN
iajs-2511	176	31	,	,	PUNCT
iajs-2511	176	32	then	then	ADV
iajs-2511	176	33	the	the	DET
iajs-2511	176	34	below	below	ADJ
iajs-2511	176	35	statements	statement	NOUN
iajs-2511	176	36	are	be	AUX
iajs-2511	176	37	equivalent	equivalent	ADJ
iajs-2511	176	38	.	.	PUNCT
iajs-2511	177	1	(	(	PUNCT
iajs-2511	177	2	1	1	X
iajs-2511	177	3	)	)	PUNCT
iajs-2511	177	4	f	f	PROPN
iajs-2511	177	5	is	be	AUX
iajs-2511	177	6	a	a	DET
iajs-2511	177	7	fuzzy	fuzzy	ADJ
iajs-2511	177	8	semi	semi	ADJ
iajs-2511	177	9	pre	pre	X
iajs-2511	177	10	irresolute	irresolute	ADJ
iajs-2511	177	11	and	and	CCONJ
iajs-2511	177	12	a	a	DET
iajs-2511	177	13	fuzzy	fuzzy	ADJ
iajs-2511	177	14	semi	semi	ADJ
iajs-2511	177	15	preopen	preopen	ADJ
iajs-2511	177	16	functions	function	NOUN
iajs-2511	177	17	.	.	PUNCT
iajs-2511	178	1	(	(	PUNCT
iajs-2511	178	2	2	2	X
iajs-2511	178	3	)	)	PUNCT
iajs-2511	178	4	f	f	PROPN
iajs-2511	178	5	is	be	AUX
iajs-2511	178	6	a	a	DET
iajs-2511	178	7	fuzzy	fuzzy	ADJ
iajs-2511	178	8	semi	semi	ADJ
iajs-2511	178	9	pre	pre	X
iajs-2511	178	10	irresolute	irresolute	ADJ
iajs-2511	178	11	and	and	CCONJ
iajs-2511	178	12	a	a	DET
iajs-2511	178	13	fuzzy	fuzzy	ADJ
iajs-2511	178	14	semi	semi	ADJ
iajs-2511	178	15	pre	pre	NOUN
iajs-2511	178	16	closed	closed	ADJ
iajs-2511	178	17	functions	function	NOUN
iajs-2511	178	18	.	.	PUNCT
iajs-2511	179	1	(	(	PUNCT
iajs-2511	179	2	3	3	X
iajs-2511	179	3	)	)	PUNCT
iajs-2511	179	4	f	f	PROPN
iajs-2511	179	5	is	be	AUX
iajs-2511	179	6	a	a	DET
iajs-2511	179	7	fuzzy	fuzzy	ADJ
iajs-2511	179	8	semi	semi	ADJ
iajs-2511	179	9	pre	pre	PROPN
iajs-2511	179	10	homeomorphism	homeomorphism	PROPN
iajs-2511	179	11	function	function	NOUN
iajs-2511	179	12	.	.	PUNCT
iajs-2511	180	1	proof	proof	NOUN
iajs-2511	180	2	:	:	PUNCT
iajs-2511	180	3	(	(	PUNCT
iajs-2511	180	4	1	1	X
iajs-2511	180	5	)	)	PUNCT
iajs-2511	180	6	→	→	X
iajs-2511	180	7	(	(	PUNCT
iajs-2511	180	8	2	2	X
iajs-2511	180	9	)	)	PUNCT
iajs-2511	180	10	let	let	VERB
iajs-2511	180	11	𝜌	𝜌	X
iajs-2511	180	12	∈	∈	VERB
iajs-2511	180	13	𝐹.	𝐹.	NOUN
iajs-2511	180	14	𝑆.	𝑆.	PROPN
iajs-2511	180	15	𝑃.	𝑃.	PROPN
iajs-2511	180	16	𝐶.	𝐶.	PROPN
iajs-2511	180	17	𝑋	𝑋	NOUN
iajs-2511	180	18	.then	.then	PUNCT
iajs-2511	180	19	1	1	NUM
iajs-2511	180	20	𝜇	𝜇	ADP
iajs-2511	180	21	𝑥	𝑥	X
iajs-2511	180	22	∈	∈	PROPN
iajs-2511	180	23	𝐹.	𝐹.	NOUN
iajs-2511	180	24	𝑆.	𝑆.	PROPN
iajs-2511	180	25	𝑃.	𝑃.	PROPN
iajs-2511	180	26	𝑂.	𝑂.	PROPN
iajs-2511	180	27	𝑋	𝑋	PROPN
iajs-2511	180	28	since	since	SCONJ
iajs-2511	180	29	f	f	PROPN
iajs-2511	180	30	is	be	AUX
iajs-2511	180	31	a	a	DET
iajs-2511	180	32	fuzzy	fuzzy	ADJ
iajs-2511	180	33	semi	semi	ADJ
iajs-2511	180	34	preopen	preopen	PROPN
iajs-2511	180	35	function	function	NOUN
iajs-2511	180	36	.	.	PUNCT
iajs-2511	181	1	then	then	ADV
iajs-2511	181	2	𝑓	𝑓	X
iajs-2511	181	3	1	1	NUM
iajs-2511	181	4	𝜇	𝜇	ADP
iajs-2511	181	5	𝑥	𝑥	PRON
iajs-2511	181	6	∈	∈	PROPN
iajs-2511	181	7	𝐹.	𝐹.	NOUN
iajs-2511	181	8	𝑆.	𝑆.	PROPN
iajs-2511	181	9	𝑃.	𝑃.	PROPN
iajs-2511	181	10	𝑂.	𝑂.	PROPN
iajs-2511	181	11	𝑌	𝑌	PROPN
iajs-2511	181	12	.	.	PUNCT
iajs-2511	182	1	so	so	ADV
iajs-2511	182	2	,	,	PUNCT
iajs-2511	182	3	by	by	ADP
iajs-2511	182	4	[	[	PUNCT
iajs-2511	182	5	theorem	theorem	ADJ
iajs-2511	182	6	2.4	2.4	NUM
iajs-2511	182	7	]	]	PUNCT
iajs-2511	182	8	we	we	PRON
iajs-2511	182	9	obtain	obtain	VERB
iajs-2511	182	10	1	1	NUM
iajs-2511	182	11	–	–	PUNCT
iajs-2511	182	12	𝜇	𝜇	ADP
iajs-2511	182	13	𝑓	𝑓	PRON
iajs-2511	182	14	𝑥	𝑥	PROPN
iajs-2511	182	15	1	1	NUM
iajs-2511	182	16	–	–	PUNCT
iajs-2511	182	17	𝜇	𝜇	ADP
iajs-2511	182	18	𝑦	𝑦	NOUN
iajs-2511	182	19	∈	∈	NOUN
iajs-2511	182	20	𝐹.	𝐹.	NOUN
iajs-2511	182	21	𝑆.	𝑆.	PROPN
iajs-2511	182	22	𝑃.	𝑃.	PROPN
iajs-2511	182	23	𝑂.	𝑂.	PROPN
iajs-2511	182	24	𝑌	𝑌	PROPN
iajs-2511	182	25	.thus	.thus	ADV
iajs-2511	182	26	,	,	PUNCT
iajs-2511	182	27	𝜇	𝜇	ADP
iajs-2511	182	28	𝑦	𝑦	NOUN
iajs-2511	182	29	∈	∈	NOUN
iajs-2511	182	30	  	  	SPACE
iajs-2511	182	31	80	80	NUM
iajs-2511	182	32	  	  	SPACE
iajs-2511	182	33	ibn	ibn	PROPN
iajs-2511	182	34	al	al	PROPN
iajs-2511	182	35	-	-	PUNCT
iajs-2511	182	36	haitham	haitham	PROPN
iajs-2511	182	37	jour	jour	X
iajs-2511	182	38	.	.	PROPN
iajs-2511	183	1	for	for	ADP
iajs-2511	183	2	pure	pure	ADJ
iajs-2511	183	3	&	&	CCONJ
iajs-2511	183	4	appl	appl	PROPN
iajs-2511	183	5	.	.	PUNCT
iajs-2511	184	1	sci	sci	PROPN
iajs-2511	184	2	.	.	PROPN
iajs-2511	185	1	33	33	NUM
iajs-2511	185	2	(	(	PUNCT
iajs-2511	185	3	4	4	NUM
iajs-2511	185	4	)	)	PUNCT
iajs-2511	185	5	2020	2020	NUM
iajs-2511	185	6	𝐹.	𝐹.	PROPN
iajs-2511	185	7	𝑆.	𝑆.	PROPN
iajs-2511	185	8	𝑃.	𝑃.	PROPN
iajs-2511	185	9	𝐶.	𝐶.	PROPN
iajs-2511	185	10	𝑌	𝑌	PROPN
iajs-2511	185	11	.	.	PUNCT
iajs-2511	186	1	hence	hence	ADV
iajs-2511	186	2	,	,	PUNCT
iajs-2511	186	3	f	f	PROPN
iajs-2511	186	4	is	be	AUX
iajs-2511	186	5	a	a	DET
iajs-2511	186	6	fuzzy	fuzzy	ADJ
iajs-2511	186	7	semi	semi	ADJ
iajs-2511	186	8	pre	pre	X
iajs-2511	186	9	irresolute	irresolute	ADJ
iajs-2511	186	10	and	and	CCONJ
iajs-2511	186	11	a	a	DET
iajs-2511	186	12	fuzzy	fuzzy	ADJ
iajs-2511	186	13	semi	semi	ADJ
iajs-2511	186	14	pre	pre	NOUN
iajs-2511	186	15	closed	closed	ADJ
iajs-2511	186	16	functions	function	NOUN
iajs-2511	186	17			PROPN
iajs-2511	186	18	(	(	PUNCT
iajs-2511	186	19	2	2	NUM
iajs-2511	186	20	)	)	PUNCT
iajs-2511	186	21	→	→	X
iajs-2511	186	22	(	(	PUNCT
iajs-2511	186	23	3	3	X
iajs-2511	186	24	)	)	PUNCT
iajs-2511	186	25	let	let	VERB
iajs-2511	186	26	𝛿	𝛿	PROPN
iajs-2511	186	27	∈	∈	PROPN
iajs-2511	186	28	𝐹.	𝐹.	NOUN
iajs-2511	186	29	𝑆.	𝑆.	PROPN
iajs-2511	186	30	𝑃.	𝑃.	PROPN
iajs-2511	186	31	𝑂.	𝑂.	PROPN
iajs-2511	186	32	𝑋	𝑋	PROPN
iajs-2511	186	33	.	.	PUNCT
iajs-2511	187	1	so	so	ADV
iajs-2511	187	2	,	,	PUNCT
iajs-2511	187	3	1	1	NUM
iajs-2511	187	4	𝜇	𝜇	ADP
iajs-2511	187	5	𝑥	𝑥	X
iajs-2511	187	6	∈	∈	PROPN
iajs-2511	187	7	𝐹.	𝐹.	NOUN
iajs-2511	187	8	𝑆.	𝑆.	PROPN
iajs-2511	187	9	𝑃.	𝑃.	PROPN
iajs-2511	187	10	𝐶.	𝐶.	PROPN
iajs-2511	187	11	𝑋	𝑋	NOUN
iajs-2511	187	12	.	.	PUNCT
iajs-2511	188	1	but	but	CCONJ
iajs-2511	188	2	f	f	PROPN
iajs-2511	188	3	is	be	AUX
iajs-2511	188	4	a	a	DET
iajs-2511	188	5	fuzzy	fuzzy	ADJ
iajs-2511	188	6	semi	semi	ADJ
iajs-2511	188	7	pre	pre	NOUN
iajs-2511	188	8	closed	closed	ADJ
iajs-2511	188	9	functions	function	NOUN
iajs-2511	188	10	.	.	PUNCT
iajs-2511	189	1	so	so	ADV
iajs-2511	189	2	,	,	PUNCT
iajs-2511	189	3	𝑓	𝑓	PRON
iajs-2511	189	4	1	1	NUM
iajs-2511	189	5	𝜇	𝜇	ADP
iajs-2511	189	6	𝑥	𝑥	PRON
iajs-2511	189	7	∈	∈	PROPN
iajs-2511	189	8	𝐹.	𝐹.	NOUN
iajs-2511	189	9	𝑆.	𝑆.	PROPN
iajs-2511	189	10	𝑃.	𝑃.	PROPN
iajs-2511	189	11	𝐶.	𝐶.	PROPN
iajs-2511	189	12	𝑌	𝑌	PROPN
iajs-2511	189	13	.	.	PUNCT
iajs-2511	190	1	by	by	ADP
iajs-2511	190	2	[	[	X
iajs-2511	190	3	theorem	theorem	X
iajs-2511	190	4	(	(	PUNCT
iajs-2511	190	5	2.4	2.4	NUM
iajs-2511	190	6	)	)	PUNCT
iajs-2511	190	7	]	]	PUNCT
iajs-2511	190	8	we	we	PRON
iajs-2511	190	9	obtain	obtain	VERB
iajs-2511	190	10	1	1	NUM
iajs-2511	190	11	–	–	PUNCT
iajs-2511	190	12	𝜇	𝜇	ADP
iajs-2511	190	13	𝑓	𝑓	PRON
iajs-2511	190	14	𝑥	𝑥	X
iajs-2511	190	15	=	=	SYM
iajs-2511	190	16	1	1	NUM
iajs-2511	190	17	–	–	PUNCT
iajs-2511	190	18	𝜇	𝜇	ADP
iajs-2511	190	19	𝑦	𝑦	NOUN
iajs-2511	190	20	∈	∈	NOUN
iajs-2511	190	21	𝐹.	𝐹.	NOUN
iajs-2511	190	22	𝑆.	𝑆.	PROPN
iajs-2511	190	23	𝑃.	𝑃.	PROPN
iajs-2511	190	24	𝐶.	𝐶.	PROPN
iajs-2511	190	25	𝑌	𝑌	PROPN
iajs-2511	190	26	.thus	.thus	ADV
iajs-2511	190	27	,	,	PUNCT
iajs-2511	190	28	𝜇	𝜇	ADP
iajs-2511	190	29	𝑦	𝑦	ADP
iajs-2511	190	30	𝜇	𝜇	X
iajs-2511	190	31	𝑦	𝑦	NOUN
iajs-2511	190	32	∈	∈	NOUN
iajs-2511	190	33	𝐹.	𝐹.	NOUN
iajs-2511	190	34	𝑆.	𝑆.	PROPN
iajs-2511	190	35	𝑃.	𝑃.	PROPN
iajs-2511	190	36	𝑂.	𝑂.	PROPN
iajs-2511	190	37	𝑌	𝑌	PROPN
iajs-2511	190	38	.	.	PUNCT
iajs-2511	191	1	hence	hence	ADV
iajs-2511	191	2	,	,	PUNCT
iajs-2511	191	3	𝑓	𝑓	PRON
iajs-2511	191	4	is	be	AUX
iajs-2511	191	5	a	a	DET
iajs-2511	191	6	fuzzy	fuzzy	ADJ
iajs-2511	191	7	semi	semi	ADJ
iajs-2511	191	8	pre	pre	X
iajs-2511	191	9	irresolute	irresolute	ADJ
iajs-2511	191	10	function	function	NOUN
iajs-2511	191	11	and	and	CCONJ
iajs-2511	191	12	we	we	PRON
iajs-2511	191	13	know	know	VERB
iajs-2511	191	14	f	f	PROPN
iajs-2511	191	15	is	be	AUX
iajs-2511	191	16	a	a	DET
iajs-2511	191	17	fuzzy	fuzzy	ADJ
iajs-2511	191	18	semi	semi	ADJ
iajs-2511	191	19	pre	pre	X
iajs-2511	191	20	irresolute	irresolute	ADJ
iajs-2511	191	21	function	function	NOUN
iajs-2511	191	22	.	.	PUNCT
iajs-2511	192	1	therefor	therefor	ADV
iajs-2511	192	2	;	;	PUNCT
iajs-2511	192	3	f	f	PROPN
iajs-2511	192	4	is	be	AUX
iajs-2511	192	5	a	a	DET
iajs-2511	192	6	fuzzy	fuzzy	ADJ
iajs-2511	192	7	semi	semi	ADJ
iajs-2511	192	8	pre	pre	NOUN
iajs-2511	192	9	homeomorphism	homeomorphism	NOUN
iajs-2511	192	10	function	function	NOUN
iajs-2511	192	11	(	(	PUNCT
iajs-2511	192	12	3	3	NUM
iajs-2511	192	13	)	)	PUNCT
iajs-2511	192	14	→	→	X
iajs-2511	192	15	(	(	PUNCT
iajs-2511	192	16	1	1	X
iajs-2511	192	17	)	)	PUNCT
iajs-2511	192	18	let	let	VERB
iajs-2511	192	19	𝜔	𝜔	AUX
iajs-2511	192	20	∈	∈	VERB
iajs-2511	192	21	𝐹.	𝐹.	NOUN
iajs-2511	192	22	𝑆.	𝑆.	PROPN
iajs-2511	192	23	𝑃.	𝑃.	PROPN
iajs-2511	192	24	𝑂.	𝑂.	PROPN
iajs-2511	192	25	𝑋	𝑋	PROPN
iajs-2511	192	26	.since	.since	NOUN
iajs-2511	192	27	,	,	PUNCT
iajs-2511	192	28	𝑓	𝑓	PRON
iajs-2511	192	29	is	be	AUX
iajs-2511	192	30	a	a	DET
iajs-2511	192	31	fuzzy	fuzzy	ADJ
iajs-2511	192	32	semi	semi	ADJ
iajs-2511	192	33	pre	pre	X
iajs-2511	192	34	irresolute	irresolute	ADJ
iajs-2511	192	35	function	function	NOUN
iajs-2511	192	36	so	so	ADV
iajs-2511	192	37	,	,	PUNCT
iajs-2511	192	38	𝜇	𝜇	ADP
iajs-2511	192	39	𝑦	𝑦	ADP
iajs-2511	192	40	𝜇	𝜇	X
iajs-2511	192	41	𝑦	𝑦	NOUN
iajs-2511	192	42	∈	∈	NOUN
iajs-2511	192	43	𝐹.	𝐹.	NOUN
iajs-2511	192	44	𝑆.	𝑆.	PROPN
iajs-2511	192	45	𝑃.	𝑃.	PROPN
iajs-2511	192	46	𝑂.	𝑂.	PROPN
iajs-2511	192	47	𝑌	𝑌	PROPN
iajs-2511	192	48	.	.	PUNCT
iajs-2511	193	1	hence	hence	ADV
iajs-2511	193	2	,	,	PUNCT
iajs-2511	193	3	by	by	ADP
iajs-2511	193	4	[	[	X
iajs-2511	193	5	definition	definition	NOUN
iajs-2511	193	6	(	(	PUNCT
iajs-2511	193	7	4.6	4.6	NUM
iajs-2511	193	8	)	)	PUNCT
iajs-2511	193	9	]	]	PUNCT
iajs-2511	194	1	f	f	X
iajs-2511	194	2	is	be	AUX
iajs-2511	194	3	a	a	DET
iajs-2511	194	4	fuzzy	fuzzy	ADJ
iajs-2511	194	5	semi	semi	ADJ
iajs-2511	194	6	pre	pre	X
iajs-2511	194	7	irresolute	irresolute	ADJ
iajs-2511	194	8	function	function	NOUN
iajs-2511	194	9	and	and	CCONJ
iajs-2511	194	10	a	a	DET
iajs-2511	194	11	fuzzy	fuzzy	ADJ
iajs-2511	194	12	semi	semi	ADJ
iajs-2511	194	13	preopen	preopen	ADJ
iajs-2511	194	14	function	function	NOUN
iajs-2511	194	15	theorem	theorem	VERB
iajs-2511	194	16	4.9	4.9	NUM
iajs-2511	194	17	:	:	PUNCT
iajs-2511	194	18	let	let	VERB
iajs-2511	194	19	𝑓	𝑓	PRON
iajs-2511	194	20	:	:	PUNCT
iajs-2511	194	21	𝑋	𝑋	PROPN
iajs-2511	194	22	,	,	PUNCT
iajs-2511	194	23	�	�	PROPN
iajs-2511	194	24	̃	̃	PROPN
iajs-2511	194	25	�	�	PROPN
iajs-2511	194	26			PROPN
iajs-2511	194	27	𝑌	𝑌	PROPN
iajs-2511	194	28	,	,	PUNCT
iajs-2511	194	29	𝜈	𝜈	X
iajs-2511	194	30	and	and	CCONJ
iajs-2511	194	31	ℎ	ℎ	PROPN
iajs-2511	194	32	:	:	PUNCT
iajs-2511	194	33	𝑌	𝑌	PROPN
iajs-2511	194	34	,	,	PUNCT
iajs-2511	194	35	𝜈	𝜈	PROPN
iajs-2511	194	36			PROPN
iajs-2511	194	37	𝑍	𝑍	PROPN
iajs-2511	194	38	,	,	PUNCT
iajs-2511	194	39	𝑢	𝑢	NOUN
iajs-2511	194	40	are	be	AUX
iajs-2511	194	41	two	two	NUM
iajs-2511	194	42	fuzzy	fuzzy	ADJ
iajs-2511	194	43	semi	semi	ADJ
iajs-2511	194	44	pre	pre	PROPN
iajs-2511	194	45	homeomorphism	homeomorphism	PROPN
iajs-2511	194	46	function	function	NOUN
iajs-2511	194	47	then	then	ADV
iajs-2511	194	48	the	the	DET
iajs-2511	194	49	function	function	NOUN
iajs-2511	194	50	ℎ	ℎ	X
iajs-2511	194	51	∘	∘	VERB
iajs-2511	194	52	𝑓	𝑓	PRON
iajs-2511	194	53	:	:	PUNCT
iajs-2511	194	54	𝑋	𝑋	PROPN
iajs-2511	194	55	,	,	PUNCT
iajs-2511	194	56	�	�	PROPN
iajs-2511	194	57	̃	̃	PROPN
iajs-2511	194	58	�	�	PROPN
iajs-2511	194	59			PROPN
iajs-2511	194	60	𝑍	𝑍	PROPN
iajs-2511	194	61	,	,	PUNCT
iajs-2511	194	62	𝑢	𝑢	PRON
iajs-2511	194	63	is	be	AUX
iajs-2511	194	64	also	also	ADV
iajs-2511	194	65	a	a	DET
iajs-2511	194	66	fuzzy	fuzzy	ADJ
iajs-2511	194	67	semi	semi	ADJ
iajs-2511	194	68	pre	pre	PROPN
iajs-2511	194	69	homeomorphism	homeomorphism	PROPN
iajs-2511	194	70	function	function	NOUN
iajs-2511	194	71	.	.	PUNCT
iajs-2511	195	1	proof	proof	NOUN
iajs-2511	195	2	:	:	PUNCT
iajs-2511	195	3	let	let	VERB
iajs-2511	195	4	𝜇	𝜇	ADP
iajs-2511	195	5	𝑧	𝑧	VERB
iajs-2511	195	6	𝜇	𝜇	X
iajs-2511	195	7	𝑧	𝑧	X
iajs-2511	195	8	∈	∈	PROPN
iajs-2511	195	9	𝐹.	𝐹.	NOUN
iajs-2511	195	10	𝑆.	𝑆.	PROPN
iajs-2511	195	11	𝑃.	𝑃.	PROPN
iajs-2511	195	12	𝑂.	𝑂.	PROPN
iajs-2511	195	13	𝑍	𝑍	PROPN
iajs-2511	195	14	,	,	PUNCT
iajs-2511	195	15	since	since	SCONJ
iajs-2511	195	16	h	h	NOUN
iajs-2511	195	17	is	be	AUX
iajs-2511	195	18	a	a	DET
iajs-2511	195	19	fuzzy	fuzzy	ADJ
iajs-2511	195	20	semi	semi	ADJ
iajs-2511	195	21	pre	pre	X
iajs-2511	195	22	irresolute	irresolute	ADJ
iajs-2511	195	23	function	function	NOUN
iajs-2511	195	24	.	.	PUNCT
iajs-2511	196	1	so	so	ADV
iajs-2511	196	2	,	,	PUNCT
iajs-2511	196	3	𝜇	𝜇	SCONJ
iajs-2511	196	4	𝑦	𝑦	NOUN
iajs-2511	196	5	∈	∈	X
iajs-2511	196	6	𝐹.	𝐹.	NOUN
iajs-2511	196	7	𝑆.	𝑆.	PROPN
iajs-2511	196	8	𝑃.	𝑃.	PROPN
iajs-2511	196	9	𝑂.	𝑂.	PROPN
iajs-2511	196	10	𝑌	𝑌	PROPN
iajs-2511	196	11	also	also	ADV
iajs-2511	196	12	since	since	SCONJ
iajs-2511	196	13	f	f	PROPN
iajs-2511	196	14	is	be	AUX
iajs-2511	196	15	a	a	DET
iajs-2511	196	16	fuzzy	fuzzy	ADJ
iajs-2511	196	17	semi	semi	ADJ
iajs-2511	196	18	pre	pre	X
iajs-2511	196	19	irresolute	irresolute	ADJ
iajs-2511	196	20	function	function	NOUN
iajs-2511	196	21	.	.	PUNCT
iajs-2511	197	1	so	so	ADV
iajs-2511	197	2	,	,	PUNCT
iajs-2511	197	3	we	we	PRON
iajs-2511	197	4	obtain	obtain	VERB
iajs-2511	197	5	𝜇	𝜇	ADP
iajs-2511	197	6	𝑥	𝑥	NOUN
iajs-2511	197	7	𝜇	𝜇	ADP
iajs-2511	197	8	ℎ∘𝑓	ℎ∘𝑓	PROPN
iajs-2511	197	9	𝑥	𝑥	PRON
iajs-2511	197	10	∈	∈	PROPN
iajs-2511	197	11	𝐹.	𝐹.	NOUN
iajs-2511	197	12	𝑆.	𝑆.	PROPN
iajs-2511	197	13	𝑃.	𝑃.	PROPN
iajs-2511	197	14	𝑂.	𝑂.	PROPN
iajs-2511	197	15	𝑋	𝑋	PROPN
iajs-2511	197	16	.	.	PUNCT
iajs-2511	198	1	thus	thus	ADV
iajs-2511	198	2	,	,	PUNCT
iajs-2511	198	3	ℎ	ℎ	PROPN
iajs-2511	198	4	∘	∘	VERB
iajs-2511	198	5	𝑓	𝑓	PRON
iajs-2511	198	6	is	be	AUX
iajs-2511	198	7	a	a	DET
iajs-2511	198	8	fuzzy	fuzzy	ADJ
iajs-2511	198	9	semi	semi	ADJ
iajs-2511	198	10	pre	pre	X
iajs-2511	198	11	irresolute	irresolute	ADJ
iajs-2511	198	12	function	function	NOUN
iajs-2511	198	13	.	.	PUNCT
iajs-2511	199	1	and	and	CCONJ
iajs-2511	199	2	let	let	VERB
iajs-2511	199	3	𝜇	𝜇	ADP
iajs-2511	199	4	𝑥	𝑥	VERB
iajs-2511	199	5	𝜇	𝜇	ADP
iajs-2511	199	6	𝑥	𝑥	X
iajs-2511	199	7	∈	∈	PROPN
iajs-2511	199	8	𝐹.	𝐹.	NOUN
iajs-2511	199	9	𝑆.	𝑆.	PROPN
iajs-2511	199	10	𝑃.	𝑃.	PROPN
iajs-2511	199	11	𝑂.	𝑂.	PROPN
iajs-2511	199	12	𝑋	𝑋	PROPN
iajs-2511	199	13	,	,	PUNCT
iajs-2511	199	14	since	since	SCONJ
iajs-2511	199	15	f	f	PROPN
iajs-2511	199	16	-1	-1	PROPN
iajs-2511	199	17	is	be	AUX
iajs-2511	199	18	a	a	DET
iajs-2511	199	19	fuzzy	fuzzy	ADJ
iajs-2511	199	20	semi	semi	ADJ
iajs-2511	199	21	pre	pre	X
iajs-2511	199	22	irresolute	irresolute	ADJ
iajs-2511	199	23	function	function	NOUN
iajs-2511	199	24	.	.	PUNCT
iajs-2511	200	1	so	so	ADV
iajs-2511	200	2	,	,	PUNCT
iajs-2511	200	3	𝜇	𝜇	ADP
iajs-2511	200	4	𝑦	𝑦	ADP
iajs-2511	200	5	𝜇	𝜇	X
iajs-2511	200	6	𝑦	𝑦	NOUN
iajs-2511	200	7	∈	∈	NOUN
iajs-2511	200	8	𝐹.	𝐹.	NOUN
iajs-2511	200	9	𝑆.	𝑆.	PROPN
iajs-2511	200	10	𝑃.	𝑃.	PROPN
iajs-2511	200	11	𝑂.	𝑂.	PROPN
iajs-2511	200	12	𝑌	𝑌	PROPN
iajs-2511	200	13	and	and	CCONJ
iajs-2511	200	14	since	since	SCONJ
iajs-2511	200	15	h-1	h-1	NOUN
iajs-2511	200	16	is	be	AUX
iajs-2511	200	17	a	a	DET
iajs-2511	200	18	fuzzy	fuzzy	ADJ
iajs-2511	200	19	semi	semi	ADJ
iajs-2511	200	20	pre	pre	X
iajs-2511	200	21	irresolute	irresolute	ADJ
iajs-2511	200	22	function	function	NOUN
iajs-2511	200	23	,	,	PUNCT
iajs-2511	200	24	so	so	ADV
iajs-2511	200	25	,	,	PUNCT
iajs-2511	200	26	𝜇	𝜇	SCONJ
iajs-2511	200	27	𝑧	𝑧	X
iajs-2511	200	28	𝜇	𝜇	ADP
iajs-2511	200	29	𝑧	𝑧	X
iajs-2511	200	30	𝜇	𝜇	ADP
iajs-2511	200	31	∘	∘	NOUN
iajs-2511	200	32	𝑧	𝑧	PRON
iajs-2511	200	33	𝜇	𝜇	ADP
iajs-2511	200	34	∘	∘	NOUN
iajs-2511	200	35	𝑧	𝑧	ADP
iajs-2511	200	36	∈	∈	PROPN
iajs-2511	200	37	𝐹.	𝐹.	NOUN
iajs-2511	200	38	𝑆.	𝑆.	PROPN
iajs-2511	200	39	𝑃.	𝑃.	PROPN
iajs-2511	200	40	𝑂.	𝑂.	PROPN
iajs-2511	200	41	𝑍	𝑍	PROPN
iajs-2511	200	42	.	.	PUNCT
iajs-2511	201	1	thus	thus	ADV
iajs-2511	201	2	,	,	PUNCT
iajs-2511	201	3	(	(	PUNCT
iajs-2511	201	4	ℎ	ℎ	PROPN
iajs-2511	201	5	∘	∘	PROPN
iajs-2511	201	6	𝑓)-1	𝑓)-1	VERB
iajs-2511	201	7	is	be	AUX
iajs-2511	201	8	a	a	DET
iajs-2511	201	9	fuzzy	fuzzy	ADJ
iajs-2511	201	10	semi	semi	ADJ
iajs-2511	201	11	pre	pre	X
iajs-2511	201	12	irresolute	irresolute	ADJ
iajs-2511	201	13	function	function	NOUN
iajs-2511	201	14	.	.	PUNCT
iajs-2511	202	1	therefore	therefore	ADV
iajs-2511	202	2	,	,	PUNCT
iajs-2511	202	3	ℎ	ℎ	PROPN
iajs-2511	202	4	∘	∘	VERB
iajs-2511	202	5	𝑓	𝑓	PRON
iajs-2511	202	6	is	be	AUX
iajs-2511	202	7	a	a	DET
iajs-2511	202	8	fuzzy	fuzzy	ADJ
iajs-2511	202	9	semi	semi	ADJ
iajs-2511	202	10	pre	pre	NOUN
iajs-2511	202	11	homeomorphism	homeomorphism	PROPN
iajs-2511	202	12	function	function	NOUN
iajs-2511	202	13	theorem	theorem	VERB
iajs-2511	202	14	4.10	4.10	NUM
iajs-2511	202	15	:	:	PUNCT
iajs-2511	202	16	let	let	VERB
iajs-2511	202	17	𝑋	𝑋	PROPN
iajs-2511	202	18	,	,	PUNCT
iajs-2511	202	19	�	�	PROPN
iajs-2511	202	20	̃	̃	PROPN
iajs-2511	202	21	�	�	PROPN
iajs-2511	202	22	be	be	VERB
iajs-2511	202	23	the	the	DET
iajs-2511	202	24	set	set	NOUN
iajs-2511	202	25	of	of	ADP
iajs-2511	202	26	all	all	DET
iajs-2511	202	27	fuzzy	fuzzy	ADJ
iajs-2511	202	28	semi	semi	ADV
iajs-2511	202	29	pre	pre	PROPN
iajs-2511	202	30	homeomorphism	homeomorphism	X
iajs-2511	202	31	(	(	PUNCT
iajs-2511	202	32	or	or	CCONJ
iajs-2511	202	33	𝑓.	𝑓.	NOUN
iajs-2511	202	34	𝑠.	𝑠.	NOUN
iajs-2511	202	35	𝑝∗.	𝑝∗.	PROPN
iajs-2511	202	36	ℎ.	ℎ.	PROPN
iajs-2511	202	37	𝑋	𝑋	PROPN
iajs-2511	202	38	,	,	PUNCT
iajs-2511	202	39	�	�	PROPN
iajs-2511	202	40	̃	̃	PROPN
iajs-2511	202	41	�	�	PROPN
iajs-2511	202	42	for	for	ADP
iajs-2511	202	43	short	short	ADJ
iajs-2511	202	44	)	)	PUNCT
iajs-2511	202	45	,	,	PUNCT
iajs-2511	202	46	then	then	ADV
iajs-2511	202	47	𝑋	𝑋	PROPN
iajs-2511	202	48	,	,	PUNCT
iajs-2511	202	49	�	�	PROPN
iajs-2511	202	50	̃	̃	PROPN
iajs-2511	202	51	�	�	PROPN
iajs-2511	202	52	is	be	AUX
iajs-2511	202	53	a	a	DET
iajs-2511	202	54	group	group	NOUN
iajs-2511	202	55	under	under	ADP
iajs-2511	202	56	the	the	DET
iajs-2511	202	57	usual	usual	ADJ
iajs-2511	202	58	composition	composition	NOUN
iajs-2511	202	59	functions	function	NOUN
iajs-2511	202	60	.	.	PUNCT
iajs-2511	203	1	proof	proof	NOUN
iajs-2511	203	2	:	:	PUNCT
iajs-2511	203	3	assume	assume	VERB
iajs-2511	203	4	that	that	SCONJ
iajs-2511	203	5	∗	∗	NOUN
iajs-2511	203	6	:	:	PUNCT
iajs-2511	203	7	𝑓.	𝑓.	NOUN
iajs-2511	203	8	𝑠.	𝑠.	PROPN
iajs-2511	203	9	𝑝∗.	𝑝∗.	PROPN
iajs-2511	203	10	ℎ.	ℎ.	PROPN
iajs-2511	203	11	𝑋	𝑋	PROPN
iajs-2511	203	12	,	,	PUNCT
iajs-2511	203	13	�	�	PROPN
iajs-2511	203	14	̃	̃	PROPN
iajs-2511	203	15	�	�	PROPN
iajs-2511	203	16	𝑓.	𝑓.	NOUN
iajs-2511	203	17	𝑠.	𝑠.	PROPN
iajs-2511	203	18	𝑝∗.	𝑝∗.	PROPN
iajs-2511	203	19	ℎ.	ℎ.	PROPN
iajs-2511	203	20	𝑋	𝑋	PROPN
iajs-2511	203	21	,	,	PUNCT
iajs-2511	203	22	�	�	PROPN
iajs-2511	203	23	̃	̃	PROPN
iajs-2511	203	24	�	�	PROPN
iajs-2511	203	25	→	→	SYM
iajs-2511	203	26	𝑓.	𝑓.	NOUN
iajs-2511	203	27	𝑠.	𝑠.	PROPN
iajs-2511	203	28	𝑝∗.	𝑝∗.	PROPN
iajs-2511	203	29	ℎ.	ℎ.	PROPN
iajs-2511	203	30	𝑋	𝑋	PROPN
iajs-2511	203	31	,	,	PUNCT
iajs-2511	203	32	�	�	PROPN
iajs-2511	203	33	̃	̃	PROPN
iajs-2511	203	34	�	�	PROPN
iajs-2511	203	35	is	be	AUX
iajs-2511	203	36	a	a	DET
iajs-2511	203	37	binary	binary	ADJ
iajs-2511	203	38	operation	operation	NOUN
iajs-2511	203	39	function	function	NOUN
iajs-2511	203	40	defined	define	VERB
iajs-2511	203	41	by	by	ADP
iajs-2511	203	42	𝜇	𝜇	ADP
iajs-2511	203	43	∗𝑓	∗𝑓	PROPN
iajs-2511	203	44	𝑥	𝑥	NOUN
iajs-2511	203	45	𝜇	𝜇	X
iajs-2511	203	46	∘𝑓	∘𝑓	NOUN
iajs-2511	203	47	𝑥	𝑥	INTJ
iajs-2511	203	48	,	,	PUNCT
iajs-2511	203	49	for	for	ADP
iajs-2511	203	50	all	all	PRON
iajs-2511	203	51	𝜇	𝜇	ADP
iajs-2511	203	52	𝑥	𝑥	X
iajs-2511	203	53	,	,	PUNCT
iajs-2511	203	54	𝜇	𝜇	X
iajs-2511	203	55	𝑥	𝑥	X
iajs-2511	203	56	𝜇	𝜇	X
iajs-2511	203	57	.	.	PUNCT
iajs-2511	203	58	.	.	PUNCT
iajs-2511	204	1	∗.	∗.	PROPN
iajs-2511	204	2	.	.	PUNCT
iajs-2511	205	1	,	,	PUNCT
iajs-2511	205	2	𝑥	𝑥	X
iajs-2511	205	3	.	.	PUNCT
iajs-2511	206	1	now	now	ADV
iajs-2511	206	2	by	by	ADP
iajs-2511	206	3	the	the	DET
iajs-2511	206	4	above	above	ADJ
iajs-2511	206	5	[	[	X
iajs-2511	206	6	theorem	theorem	NOUN
iajs-2511	206	7	(	(	PUNCT
iajs-2511	206	8	4.9	4.9	NUM
iajs-2511	206	9	)	)	PUNCT
iajs-2511	206	10	]	]	PUNCT
iajs-2511	206	11	,	,	PUNCT
iajs-2511	206	12	we	we	PRON
iajs-2511	206	13	get	get	VERB
iajs-2511	206	14	𝜇	𝜇	ADP
iajs-2511	206	15	∘𝑓	∘𝑓	NOUN
iajs-2511	206	16	𝑥	𝑥	NOUN
iajs-2511	206	17	𝜇	𝜇	X
iajs-2511	206	18	.	.	PUNCT
iajs-2511	206	19	.	.	PUNCT
iajs-2511	207	1	∗.	∗.	PROPN
iajs-2511	207	2	.	.	PUNCT
iajs-2511	208	1	,	,	PUNCT
iajs-2511	208	2	𝑥	𝑥	X
iajs-2511	208	3	i.e	i.e	X
iajs-2511	208	4	,	,	PUNCT
iajs-2511	208	5	(	(	PUNCT
iajs-2511	208	6	∗	∗	NOUN
iajs-2511	208	7	)	)	PUNCT
iajs-2511	208	8	is	be	AUX
iajs-2511	208	9	closed	close	VERB
iajs-2511	208	10	and	and	CCONJ
iajs-2511	208	11	by	by	ADP
iajs-2511	208	12	usual	usual	ADJ
iajs-2511	208	13	definition	definition	NOUN
iajs-2511	208	14	of	of	ADP
iajs-2511	208	15	composition	composition	NOUN
iajs-2511	208	16	functions	function	NOUN
iajs-2511	208	17	we	we	PRON
iajs-2511	208	18	know	know	VERB
iajs-2511	208	19	(	(	PUNCT
iajs-2511	208	20	∗	∗	NOUN
iajs-2511	208	21	)	)	PUNCT
iajs-2511	208	22	is	be	AUX
iajs-2511	208	23	associative	associative	ADJ
iajs-2511	208	24	and	and	CCONJ
iajs-2511	208	25	there	there	PRON
iajs-2511	208	26	exists	exist	VERB
iajs-2511	208	27	the	the	DET
iajs-2511	208	28	identity	identity	NOUN
iajs-2511	208	29	function	function	NOUN
iajs-2511	208	30	𝐼	𝐼	PROPN
iajs-2511	208	31	:	:	PUNCT
iajs-2511	208	32	𝑓.	𝑓.	NOUN
iajs-2511	208	33	𝑠.	𝑠.	PROPN
iajs-2511	208	34	𝑝∗.	𝑝∗.	PROPN
iajs-2511	208	35	ℎ.	ℎ.	PROPN
iajs-2511	208	36	𝑋	𝑋	PROPN
iajs-2511	208	37	,	,	PUNCT
iajs-2511	208	38	�	�	PROPN
iajs-2511	208	39	̃	̃	PROPN
iajs-2511	208	40	�	�	PROPN
iajs-2511	208	41	→	→	SYM
iajs-2511	208	42	𝑓.	𝑓.	NOUN
iajs-2511	208	43	𝑠.	𝑠.	PROPN
iajs-2511	208	44	𝑝∗.	𝑝∗.	PROPN
iajs-2511	208	45	ℎ.	ℎ.	PROPN
iajs-2511	208	46	𝑋	𝑋	PROPN
iajs-2511	208	47	,	,	PUNCT
iajs-2511	208	48	�	�	PROPN
iajs-2511	208	49	̃	̃	NOUN
iajs-2511	208	50	�	�	NOUN
iajs-2511	208	51	such	such	ADJ
iajs-2511	208	52	that	that	SCONJ
iajs-2511	208	53	𝜇	𝜇	ADP
iajs-2511	208	54	∘𝐼	∘𝐼	ADP
iajs-2511	208	55	𝑥	𝑥	PRON
iajs-2511	208	56	𝜇	𝜇	ADV
iajs-2511	208	57	∘𝑓	∘𝑓	NOUN
iajs-2511	209	1	𝑥	𝑥	NOUN
iajs-2511	209	2	𝜇	𝜇	ADP
iajs-2511	209	3	𝑥	𝑥	X
iajs-2511	209	4	i.e.	i.e.	X
iajs-2511	209	5	,	,	PUNCT
iajs-2511	209	6	𝜇	𝜇	ADP
iajs-2511	209	7	∗𝐼	∗𝐼	X
iajs-2511	209	8	𝑥	𝑥	X
iajs-2511	209	9	𝜇	𝜇	ADP
iajs-2511	209	10	∗𝑓	∗𝑓	PROPN
iajs-2511	209	11	𝑥	𝑥	NOUN
iajs-2511	209	12	𝜇	𝜇	X
iajs-2511	209	13	𝑥	𝑥	X
iajs-2511	209	14	and	and	CCONJ
iajs-2511	209	15	finely	finely	ADV
iajs-2511	209	16	for	for	ADP
iajs-2511	209	17	all	all	PRON
iajs-2511	209	18	𝜇	𝜇	ADP
iajs-2511	209	19	𝑥	𝑥	NOUN
iajs-2511	209	20	𝜇	𝜇	X
iajs-2511	209	21	.	.	PUNCT
iajs-2511	209	22	.	.	PUNCT
iajs-2511	210	1	∗.	∗.	PROPN
iajs-2511	210	2	.	.	PUNCT
iajs-2511	211	1	,	,	PUNCT
iajs-2511	211	2	𝑥	𝑥	X
iajs-2511	211	3	there	there	PRON
iajs-2511	211	4	exists	exist	VERB
iajs-2511	211	5	𝜇	𝜇	ADP
iajs-2511	211	6	𝑥	𝑥	X
iajs-2511	211	7	𝜇	𝜇	X
iajs-2511	211	8	.	.	PUNCT
iajs-2511	211	9	.	.	PUNCT
iajs-2511	212	1	∗.	∗.	PROPN
iajs-2511	212	2	.	.	PUNCT
iajs-2511	213	1	,	,	PUNCT
iajs-2511	213	2	𝑥	𝑥	X
iajs-2511	213	3	such	such	ADJ
iajs-2511	213	4	that	that	PRON
iajs-2511	213	5	𝜇	𝜇	ADP
iajs-2511	213	6	∘	∘	NOUN
iajs-2511	213	7	𝑥	𝑥	NOUN
iajs-2511	213	8	𝜇	𝜇	X
iajs-2511	213	9	∘𝑓	∘𝑓	NOUN
iajs-2511	213	10	𝑥	𝑥	PART
iajs-2511	213	11	𝜇	𝜇	ADP
iajs-2511	213	12	𝑥	𝑥	X
iajs-2511	213	13	i.e	i.e	X
iajs-2511	213	14	,	,	PUNCT
iajs-2511	213	15	𝜇	𝜇	ADP
iajs-2511	213	16	∗	∗	NOUN
iajs-2511	213	17	𝑥	𝑥	NOUN
iajs-2511	213	18	𝜇	𝜇	ADP
iajs-2511	213	19	∗𝑓	∗𝑓	PROPN
iajs-2511	213	20	𝑥	𝑥	NOUN
iajs-2511	213	21	𝜇	𝜇	ADP
iajs-2511	213	22	𝑥	𝑥	X
iajs-2511	213	23	.thus	.thus	INTJ
iajs-2511	214	1	it	it	PRON
iajs-2511	214	2	's	be	AUX
iajs-2511	214	3	clear	clear	ADJ
iajs-2511	214	4	𝑓.	𝑓.	NOUN
iajs-2511	214	5	𝑠.	𝑠.	PROPN
iajs-2511	214	6	𝑝∗.	𝑝∗.	PROPN
iajs-2511	214	7	ℎ.	ℎ.	PROPN
iajs-2511	214	8	𝑋	𝑋	PROPN
iajs-2511	214	9	,	,	PUNCT
iajs-2511	214	10	�	�	PROPN
iajs-2511	214	11	̃	̃	PROPN
iajs-2511	214	12	�	�	PROPN
iajs-2511	214	13	,	,	PUNCT
iajs-2511	214	14	∘	∘	PROPN
iajs-2511	214	15	is	be	AUX
iajs-2511	214	16	a	a	DET
iajs-2511	214	17	group	group	ADJ
iajs-2511	214	18	  	  	SPACE
iajs-2511	214	19	81	81	NUM
iajs-2511	214	20	  	  	SPACE
iajs-2511	214	21	ibn	ibn	PROPN
iajs-2511	214	22	al	al	PROPN
iajs-2511	214	23	-	-	PUNCT
iajs-2511	214	24	haitham	haitham	PROPN
iajs-2511	214	25	jour	jour	X
iajs-2511	214	26	.	.	PROPN
iajs-2511	215	1	for	for	ADP
iajs-2511	215	2	pure	pure	ADJ
iajs-2511	215	3	&	&	CCONJ
iajs-2511	215	4	appl	appl	PROPN
iajs-2511	215	5	.	.	PUNCT
iajs-2511	216	1	sci	sci	PROPN
iajs-2511	216	2	.	.	PROPN
iajs-2511	217	1	33	33	NUM
iajs-2511	217	2	(	(	PUNCT
iajs-2511	217	3	4	4	NUM
iajs-2511	217	4	)	)	PUNCT
iajs-2511	217	5	2020	2020	NUM
iajs-2511	217	6	5	5	NUM
iajs-2511	217	7	.	.	PUNCT
iajs-2511	217	8	conclusions	conclusion	NOUN
iajs-2511	217	9	in	in	ADP
iajs-2511	217	10	this	this	DET
iajs-2511	217	11	paper	paper	NOUN
iajs-2511	217	12	,	,	PUNCT
iajs-2511	217	13	we	we	PRON
iajs-2511	217	14	been	been	AUX
iajs-2511	217	15	developed	develop	VERB
iajs-2511	217	16	the	the	DET
iajs-2511	217	17	new	new	ADJ
iajs-2511	217	18	types	type	NOUN
iajs-2511	217	19	of	of	ADP
iajs-2511	217	20	fuzzy	fuzzy	ADJ
iajs-2511	217	21	homeomorphism	homeomorphism	PROPN
iajs-2511	217	22	function	function	NOUN
iajs-2511	217	23	in	in	ADP
iajs-2511	217	24	fuzzy	fuzzy	ADJ
iajs-2511	217	25	topological	topological	ADJ
iajs-2511	217	26	spaces	space	NOUN
iajs-2511	217	27	called	call	VERB
iajs-2511	217	28	fuzzy	fuzzy	ADJ
iajs-2511	217	29	semi	semi	ADV
iajs-2511	217	30	pre	pre	PROPN
iajs-2511	217	31	homeomorphism	homeomorphism	PROPN
iajs-2511	217	32	function	function	NOUN
iajs-2511	217	33	and	and	CCONJ
iajs-2511	217	34	fuzzy	fuzzy	ADJ
iajs-2511	217	35	semi	semi	ADV
iajs-2511	217	36	pre	pre	PROPN
iajs-2511	217	37	*	*	PROPN
iajs-2511	217	38	homeomorphism	homeomorphism	PROPN
iajs-2511	217	39	function	function	NOUN
iajs-2511	217	40	.	.	PUNCT
iajs-2511	218	1	in	in	ADP
iajs-2511	218	2	addition	addition	NOUN
iajs-2511	218	3	to	to	ADP
iajs-2511	218	4	that	that	SCONJ
iajs-2511	218	5	we	we	PRON
iajs-2511	218	6	developed	develop	VERB
iajs-2511	218	7	the	the	DET
iajs-2511	218	8	relationship	relationship	NOUN
iajs-2511	218	9	between	between	ADP
iajs-2511	218	10	these	these	DET
iajs-2511	218	11	new	new	ADJ
iajs-2511	218	12	types	type	NOUN
iajs-2511	218	13	of	of	ADP
iajs-2511	218	14	fuzzy	fuzzy	ADJ
iajs-2511	218	15	homeomorphism	homeomorphism	PROPN
iajs-2511	218	16	function	function	NOUN
iajs-2511	218	17	in	in	ADP
iajs-2511	218	18	fuzzy	fuzzy	ADJ
iajs-2511	218	19	topological	topological	ADJ
iajs-2511	218	20	spaces	space	NOUN
iajs-2511	218	21	with	with	ADP
iajs-2511	218	22	some	some	DET
iajs-2511	218	23	new	new	ADJ
iajs-2511	218	24	kinds	kind	NOUN
iajs-2511	218	25	of	of	ADP
iajs-2511	218	26	fuzzy	fuzzy	ADJ
iajs-2511	218	27	semi	semi	ADJ
iajs-2511	218	28	pre	pre	VERB
iajs-2511	218	29	continuous	continuous	ADJ
iajs-2511	218	30	function	function	NOUN
iajs-2511	218	31	.	.	PUNCT
iajs-2511	219	1	finally	finally	ADV
iajs-2511	219	2	,	,	PUNCT
iajs-2511	219	3	we	we	PRON
iajs-2511	219	4	structure	structure	VERB
iajs-2511	219	5	a	a	DET
iajs-2511	219	6	group	group	NOUN
iajs-2511	219	7	under	under	ADP
iajs-2511	219	8	the	the	DET
iajs-2511	219	9	usual	usual	ADJ
iajs-2511	219	10	composition	composition	NOUN
iajs-2511	219	11	functions	function	NOUN
iajs-2511	219	12	by	by	ADP
iajs-2511	219	13	using	use	VERB
iajs-2511	219	14	these	these	DET
iajs-2511	219	15	new	new	ADJ
iajs-2511	219	16	types	type	NOUN
iajs-2511	219	17	of	of	ADP
iajs-2511	219	18	fuzzy	fuzzy	ADJ
iajs-2511	219	19	homeomorphism	homeomorphism	PROPN
iajs-2511	219	20	function	function	NOUN
iajs-2511	219	21	.	.	PUNCT
iajs-2511	220	1	as	as	SCONJ
iajs-2511	220	2	follows	follow	VERB
iajs-2511	220	3	:	:	PUNCT
iajs-2511	220	4	(	(	PUNCT
iajs-2511	220	5	i	i	NOUN
iajs-2511	220	6	)	)	PUNCT
iajs-2511	220	7	every	every	DET
iajs-2511	220	8	fuzzy	fuzzy	ADJ
iajs-2511	220	9	semi	semi	ADV
iajs-2511	220	10	pre	pre	PROPN
iajs-2511	220	11	homeomorphism	homeomorphism	PROPN
iajs-2511	220	12	function	function	NOUN
iajs-2511	220	13	is	be	AUX
iajs-2511	220	14	a	a	DET
iajs-2511	220	15	fuzzy	fuzzy	ADJ
iajs-2511	220	16	semi	semi	ADJ
iajs-2511	220	17	pre	pre	PROPN
iajs-2511	220	18	homeomorphism	homeomorphism	PROPN
iajs-2511	220	19	function	function	NOUN
iajs-2511	220	20	.	.	PUNCT
iajs-2511	221	1	(	(	PUNCT
iajs-2511	221	2	ii	ii	NOUN
iajs-2511	221	3	)	)	PUNCT
iajs-2511	221	4	let	let	VERB
iajs-2511	221	5	𝑓	𝑓	DET
iajs-2511	221	6	:	:	PUNCT
iajs-2511	221	7	𝑋	𝑋	PROPN
iajs-2511	221	8	,	,	PUNCT
iajs-2511	221	9	�	�	PROPN
iajs-2511	221	10	̃	̃	PROPN
iajs-2511	221	11	�	�	PROPN
iajs-2511	221	12			PROPN
iajs-2511	221	13	𝑌	𝑌	PROPN
iajs-2511	221	14	,	,	PUNCT
iajs-2511	221	15	𝜈	𝜈	PRON
iajs-2511	221	16	be	be	VERB
iajs-2511	221	17	a	a	DET
iajs-2511	221	18	bijective	bijective	ADJ
iajs-2511	221	19	fuzzy	fuzzy	ADJ
iajs-2511	221	20	function	function	NOUN
iajs-2511	221	21	,	,	PUNCT
iajs-2511	221	22	then	then	ADV
iajs-2511	221	23	the	the	DET
iajs-2511	221	24	below	below	ADJ
iajs-2511	221	25	statements	statement	NOUN
iajs-2511	221	26	are	be	AUX
iajs-2511	221	27	equivalent	equivalent	ADJ
iajs-2511	221	28	.	.	PUNCT
iajs-2511	222	1	(	(	PUNCT
iajs-2511	222	2	1	1	X
iajs-2511	222	3	)	)	PUNCT
iajs-2511	222	4	f	f	PROPN
iajs-2511	222	5	is	be	AUX
iajs-2511	222	6	a	a	DET
iajs-2511	222	7	fuzzy	fuzzy	ADJ
iajs-2511	222	8	semi	semi	ADJ
iajs-2511	222	9	pre	pre	X
iajs-2511	222	10	irresolute	irresolute	ADJ
iajs-2511	222	11	and	and	CCONJ
iajs-2511	222	12	a	a	DET
iajs-2511	222	13	fuzzy	fuzzy	ADJ
iajs-2511	222	14	semi	semi	ADJ
iajs-2511	222	15	preopen	preopen	ADJ
iajs-2511	222	16	functions	function	NOUN
iajs-2511	222	17	.	.	PUNCT
iajs-2511	223	1	(	(	PUNCT
iajs-2511	223	2	2	2	X
iajs-2511	223	3	)	)	PUNCT
iajs-2511	223	4	f	f	PROPN
iajs-2511	223	5	is	be	AUX
iajs-2511	223	6	a	a	DET
iajs-2511	223	7	fuzzy	fuzzy	ADJ
iajs-2511	223	8	semi	semi	ADJ
iajs-2511	223	9	pre	pre	X
iajs-2511	223	10	irresolute	irresolute	ADJ
iajs-2511	223	11	and	and	CCONJ
iajs-2511	223	12	a	a	DET
iajs-2511	223	13	fuzzy	fuzzy	ADJ
iajs-2511	223	14	semi	semi	ADJ
iajs-2511	223	15	pre	pre	NOUN
iajs-2511	223	16	closed	closed	ADJ
iajs-2511	223	17	functions	function	NOUN
iajs-2511	223	18	.	.	PUNCT
iajs-2511	224	1	(	(	PUNCT
iajs-2511	224	2	3	3	X
iajs-2511	224	3	)	)	PUNCT
iajs-2511	224	4	f	f	PROPN
iajs-2511	224	5	is	be	AUX
iajs-2511	224	6	a	a	DET
iajs-2511	224	7	fuzzy	fuzzy	ADJ
iajs-2511	224	8	semi	semi	ADJ
iajs-2511	224	9	pre	pre	PROPN
iajs-2511	224	10	homeomorphism	homeomorphism	PROPN
iajs-2511	224	11	function	function	NOUN
iajs-2511	224	12	.	.	PUNCT
iajs-2511	225	1	(	(	PUNCT
iajs-2511	225	2	iii	iii	X
iajs-2511	225	3	)	)	PUNCT
iajs-2511	225	4	let	let	VERB
iajs-2511	225	5	𝑋	𝑋	PROPN
iajs-2511	225	6	,	,	PUNCT
iajs-2511	225	7	�	�	PROPN
iajs-2511	225	8	̃	̃	PROPN
iajs-2511	225	9	�	�	PROPN
iajs-2511	225	10	be	be	VERB
iajs-2511	225	11	the	the	DET
iajs-2511	225	12	set	set	NOUN
iajs-2511	225	13	of	of	ADP
iajs-2511	225	14	all	all	DET
iajs-2511	225	15	fuzzy	fuzzy	ADJ
iajs-2511	225	16	semi	semi	ADV
iajs-2511	225	17	pre	pre	PROPN
iajs-2511	225	18	homeomorphism	homeomorphism	X
iajs-2511	225	19	(	(	PUNCT
iajs-2511	225	20	or	or	CCONJ
iajs-2511	225	21	𝑓.	𝑓.	NOUN
iajs-2511	225	22	𝑠.	𝑠.	NOUN
iajs-2511	225	23	𝑝∗.	𝑝∗.	PROPN
iajs-2511	225	24	ℎ.	ℎ.	PROPN
iajs-2511	225	25	𝑋	𝑋	PROPN
iajs-2511	225	26	,	,	PUNCT
iajs-2511	225	27	�	�	PROPN
iajs-2511	225	28	̃	̃	PROPN
iajs-2511	225	29	�	�	PROPN
iajs-2511	225	30	for	for	ADP
iajs-2511	225	31	short	short	ADJ
iajs-2511	225	32	)	)	PUNCT
iajs-2511	225	33	,	,	PUNCT
iajs-2511	225	34	then	then	ADV
iajs-2511	225	35	𝑋	𝑋	PROPN
iajs-2511	225	36	,	,	PUNCT
iajs-2511	225	37	�	�	PROPN
iajs-2511	225	38	̃	̃	PROPN
iajs-2511	225	39	�	�	PROPN
iajs-2511	225	40	is	be	AUX
iajs-2511	225	41	a	a	DET
iajs-2511	225	42	group	group	NOUN
iajs-2511	225	43	under	under	ADP
iajs-2511	225	44	the	the	DET
iajs-2511	225	45	usual	usual	ADJ
iajs-2511	225	46	composition	composition	NOUN
iajs-2511	225	47	functions	function	NOUN
iajs-2511	225	48	.	.	PUNCT
iajs-2511	226	1	references	reference	NOUN
iajs-2511	226	2	1	1	NUM
iajs-2511	226	3	.	.	PUNCT
iajs-2511	227	1	zadeh	zadeh	PROPN
iajs-2511	227	2	,	,	PUNCT
iajs-2511	227	3	l.a	l.a	PROPN
iajs-2511	227	4	.	.	PROPN
iajs-2511	227	5	fuzzy	fuzzy	ADJ
iajs-2511	227	6	sets	set	NOUN
iajs-2511	227	7	.	.	PUNCT
iajs-2511	228	1	inform	inform	NOUN
iajs-2511	228	2	.	.	PUNCT
iajs-2511	229	1	control	control	NOUN
iajs-2511	229	2	.	.	PUNCT
iajs-2511	230	1	1965	1965	NUM
iajs-2511	230	2	,	,	PUNCT
iajs-2511	230	3	8	8	NUM
iajs-2511	230	4	,	,	PUNCT
iajs-2511	230	5	338	338	NUM
iajs-2511	230	6	-	-	SYM
iajs-2511	230	7	353	353	NUM
iajs-2511	230	8	.	.	NOUN
iajs-2511	231	1	2	2	NUM
iajs-2511	231	2	.	.	X
iajs-2511	231	3	chang	chang	PROPN
iajs-2511	231	4	,	,	PUNCT
iajs-2511	231	5	c.	c.	PROPN
iajs-2511	231	6	l.	l.	PROPN
iajs-2511	231	7	fuzzy	fuzzy	PROPN
iajs-2511	231	8	topological	topological	ADJ
iajs-2511	231	9	spaces	space	NOUN
iajs-2511	231	10	.	.	PUNCT
iajs-2511	232	1	j.	j.	PROPN
iajs-2511	232	2	math	math	PROPN
iajs-2511	232	3	.	.	PUNCT
iajs-2511	233	1	anal	anal	PROPN
iajs-2511	233	2	.	.	PUNCT
iajs-2511	233	3	appl	appl	PROPN
iajs-2511	233	4	.	.	PUNCT
iajs-2511	234	1	1968	1968	NUM
iajs-2511	234	2	,	,	PUNCT
iajs-2511	234	3	24,182190	24,182190	NUM
iajs-2511	234	4	.	.	PUNCT
iajs-2511	235	1	3	3	X
iajs-2511	235	2	.	.	X
iajs-2511	235	3	ming	ming	NOUN
iajs-2511	235	4	,	,	PUNCT
iajs-2511	235	5	p.	p.	PROPN
iajs-2511	235	6	p.	p.	NOUN
iajs-2511	235	7	;	;	PUNCT
iajs-2511	236	1	ming	ming	PROPN
iajs-2511	236	2	,	,	PUNCT
iajs-2511	236	3	l.	l.	PROPN
iajs-2511	236	4	y.	y.	PROPN
iajs-2511	236	5	fuzzy	fuzzy	PROPN
iajs-2511	236	6	topology	topology	PROPN
iajs-2511	236	7	i.	i.	PROPN
iajs-2511	236	8	neighborhood	neighborhood	PROPN
iajs-2511	236	9	structure	structure	NOUN
iajs-2511	236	10	of	of	ADP
iajs-2511	236	11	a	a	DET
iajs-2511	236	12	fuzzy	fuzzy	ADJ
iajs-2511	236	13	point	point	NOUN
iajs-2511	236	14	and	and	CCONJ
iajs-2511	236	15	moor	moor	PROPN
iajs-2511	236	16	-	-	PUNCT
iajs-2511	236	17	smith	smith	PROPN
iajs-2511	236	18	convergence	convergence	NOUN
iajs-2511	236	19	.	.	PUNCT
iajs-2511	237	1	j.	j.	PROPN
iajs-2511	237	2	math	math	PROPN
iajs-2511	237	3	.	.	PUNCT
iajs-2511	238	1	anal	anal	PROPN
iajs-2511	238	2	.	.	PUNCT
iajs-2511	238	3	appl	appl	PROPN
iajs-2511	238	4	.	.	PUNCT
iajs-2511	239	1	1980	1980	NUM
iajs-2511	239	2	,	,	PUNCT
iajs-2511	239	3	76,571	76,571	NUM
iajs-2511	239	4	-	-	SYM
iajs-2511	239	5	599	599	NUM
iajs-2511	239	6	.	.	PUNCT
iajs-2511	240	1	4	4	X
iajs-2511	240	2	.	.	X
iajs-2511	240	3	andrijevic	andrijevic	VERB
iajs-2511	240	4	,	,	PUNCT
iajs-2511	240	5	d.	d.	PROPN
iajs-2511	240	6	semi	semi	ADV
iajs-2511	240	7	preopen	preopen	ADJ
iajs-2511	240	8	sets	set	NOUN
iajs-2511	240	9	.	.	PUNCT
iajs-2511	241	1	mat.vesnik.1986	mat.vesnik.1986	PROPN
iajs-2511	241	2	,	,	PUNCT
iajs-2511	241	3	38	38	NUM
iajs-2511	241	4	,	,	PUNCT
iajs-2511	241	5	2432	2432	NUM
iajs-2511	241	6	.	.	PUNCT
iajs-2511	242	1	5	5	NUM
iajs-2511	242	2	.	.	X
iajs-2511	242	3	thakur	thakur	PROPN
iajs-2511	242	4	,	,	PUNCT
iajs-2511	242	5	s.	s.	PROPN
iajs-2511	242	6	s.	s.	PROPN
iajs-2511	242	7	;	;	PUNCT
iajs-2511	242	8	singh	singh	PROPN
iajs-2511	242	9	,	,	PUNCT
iajs-2511	242	10	s.	s.	PROPN
iajs-2511	242	11	on	on	ADP
iajs-2511	242	12	fuzzy	fuzzy	ADJ
iajs-2511	242	13	semi	semi	ADJ
iajs-2511	242	14	-	-	ADJ
iajs-2511	242	15	preopen	preopen	ADJ
iajs-2511	242	16	sets	set	NOUN
iajs-2511	242	17	and	and	CCONJ
iajs-2511	242	18	fuzzy	fuzzy	ADJ
iajs-2511	242	19	semi	semi	NOUN
iajs-2511	242	20	-	-	NOUN
iajs-2511	242	21	precontinuity	precontinuity	NOUN
iajs-2511	242	22	.	.	PUNCT
iajs-2511	243	1	j.	j.	PROPN
iajs-2511	243	2	fuzzy	fuzzy	PROPN
iajs-2511	243	3	sets	set	NOUN
iajs-2511	243	4	and	and	CCONJ
iajs-2511	243	5	systems	system	NOUN
iajs-2511	243	6	.	.	PUNCT
iajs-2511	244	1	1998	1998	NUM
iajs-2511	244	2	,	,	PUNCT
iajs-2511	244	3	98	98	NUM
iajs-2511	244	4	,	,	PUNCT
iajs-2511	244	5	383	383	NUM
iajs-2511	244	6	-	-	SYM
iajs-2511	244	7	391	391	NUM
iajs-2511	244	8	.	.	NOUN
iajs-2511	245	1	6	6	NUM
iajs-2511	245	2	.	.	X
iajs-2511	245	3	mageed	mageed	NOUN
iajs-2511	245	4	,	,	PUNCT
iajs-2511	245	5	s.	s.	PROPN
iajs-2511	245	6	y.	y.	PROPN
iajs-2511	245	7	on	on	ADP
iajs-2511	245	8	fuzzy	fuzzy	ADJ
iajs-2511	245	9	compact	compact	ADJ
iajs-2511	245	10	spaces	space	NOUN
iajs-2511	245	11	.	.	PUNCT
iajs-2511	246	1	m.sc	m.sc	NOUN
iajs-2511	246	2	.	.	PUNCT
iajs-2511	247	1	thesis	thesis	NOUN
iajs-2511	247	2	,	,	PUNCT
iajs-2511	247	3	college	college	NOUN
iajs-2511	247	4	of	of	ADP
iajs-2511	247	5	education	education	NOUN
iajs-2511	247	6	,	,	PUNCT
iajs-2511	247	7	almustansiryah	almustansiryah	PROPN
iajs-2511	247	8	university	university	NOUN
iajs-2511	247	9	,	,	PUNCT
iajs-2511	247	10	2012	2012	NUM
iajs-2511	247	11	.	.	PUNCT
iajs-2511	248	1	7	7	X
iajs-2511	248	2	.	.	X
iajs-2511	248	3	ali	ali	PROPN
iajs-2511	248	4	,	,	PUNCT
iajs-2511	248	5	t.	t.	PROPN
iajs-2511	248	6	;	;	PUNCT
iajs-2511	248	7	das	das	PROPN
iajs-2511	248	8	,	,	PUNCT
iajs-2511	248	9	s.	s.	PROPN
iajs-2511	248	10	fuzzy	fuzzy	PROPN
iajs-2511	248	11	topological	topological	ADJ
iajs-2511	248	12	transformation	transformation	NOUN
iajs-2511	248	13	groups	group	NOUN
iajs-2511	248	14	.	.	PUNCT
iajs-2511	249	1	j.	j.	PROPN
iajs-2511	249	2	math	math	PROPN
iajs-2511	249	3	.	.	PUNCT
iajs-2511	250	1	rese.2009,1	rese.2009,1	PROPN
iajs-2511	250	2	,	,	PUNCT
iajs-2511	250	3	1,78	1,78	NUM
iajs-2511	250	4	-	-	SYM
iajs-2511	250	5	86	86	NUM
iajs-2511	250	6	.	.	NOUN
iajs-2511	250	7	8	8	NUM
iajs-2511	250	8	.	.	X
iajs-2511	250	9	cahit	cahit	VERB
iajs-2511	250	10	,	,	PUNCT
iajs-2511	250	11	t.	t.	NOUN
iajs-2511	250	12	some	some	DET
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iajs-2511	264	11	  	  	SPACE