id	sid	tid	token	lemma	pos
cana-5720	1	1	communications	communication	NOUN
cana-5720	1	2	on	on	ADP
cana-5720	1	3	applied	apply	VERB
cana-5720	1	4	nonlinear	nonlinear	ADJ
cana-5720	1	5	analysis	analysis	NOUN
cana-5720	1	6	issn	issn	NOUN
cana-5720	1	7	:	:	PUNCT
cana-5720	1	8	1074	1074	NUM
cana-5720	1	9	-	-	PUNCT
cana-5720	1	10	133x	133x	NUM
cana-5720	1	11	vol	vol	VERB
cana-5720	1	12	32	32	NUM
cana-5720	1	13	no	no	NOUN
cana-5720	1	14	.	.	PUNCT
cana-5720	2	1	10s	10	NOUN
cana-5720	2	2	(	(	PUNCT
cana-5720	2	3	2025	2025	NUM
cana-5720	2	4	)	)	PUNCT
cana-5720	2	5	2801	2801	NUM
cana-5720	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5720	2	7	almost	almost	ADV
cana-5720	2	8	gωα	gωα	ADJ
cana-5720	2	9	-	-	PUNCT
cana-5720	2	10	closed	close	VERB
cana-5720	2	11	functions	function	NOUN
cana-5720	2	12	and	and	CCONJ
cana-5720	2	13	separation	separation	NOUN
cana-5720	2	14	axioms	axioms	PROPN
cana-5720	2	15	a.	a.	NOUN
cana-5720	2	16	parveen	parveen	PROPN
cana-5720	3	1	banu1	banu1	PROPN
cana-5720	3	2	,	,	PUNCT
cana-5720	3	3	n.	n.	PROPN
cana-5720	3	4	selvanayaki2	selvanayaki2	PROPN
cana-5720	3	5	,	,	PUNCT
cana-5720	3	6	r.abinprakash3	r.abinprakash3	PROPN
cana-5720	3	7	1assistant	1assistant	NUM
cana-5720	3	8	professor	professor	NOUN
cana-5720	3	9	,	,	PUNCT
cana-5720	3	10	2assistant	2assistant	NUM
cana-5720	3	11	professor	professor	NOUN
cana-5720	3	12	(	(	PUNCT
cana-5720	3	13	selection	selection	NOUN
cana-5720	3	14	grade	grade	NOUN
cana-5720	3	15	)	)	PUNCT
cana-5720	3	16	,	,	PUNCT
cana-5720	3	17	3associate	3associate	NUM
cana-5720	3	18	professor	professor	NOUN
cana-5720	3	19	,	,	PUNCT
cana-5720	3	20	department	department	NOUN
cana-5720	3	21	of	of	ADP
cana-5720	3	22	mathematics	mathematic	NOUN
cana-5720	3	23	,	,	PUNCT
cana-5720	3	24	1	1	NUM
cana-5720	3	25	sri	sri	NOUN
cana-5720	3	26	g.v.g	g.v.g	ADJ
cana-5720	3	27	visalakshi	visalakshi	PROPN
cana-5720	3	28	college	college	PROPN
cana-5720	3	29	for	for	ADP
cana-5720	3	30	women	woman	NOUN
cana-5720	3	31	,	,	PUNCT
cana-5720	3	32	udumalpet	udumalpet	ADJ
cana-5720	3	33	,	,	PUNCT
cana-5720	3	34	tamil	tamil	PROPN
cana-5720	3	35	nadu	nadu	PROPN
cana-5720	3	36	,	,	PUNCT
cana-5720	3	37	india	india	PROPN
cana-5720	3	38	.	.	PUNCT
cana-5720	4	1	2,3	2,3	NUM
cana-5720	4	2	akshaya	akshaya	PROPN
cana-5720	4	3	college	college	PROPN
cana-5720	4	4	of	of	ADP
cana-5720	4	5	engineering	engineering	NOUN
cana-5720	4	6	and	and	CCONJ
cana-5720	4	7	technology	technology	NOUN
cana-5720	4	8	,	,	PUNCT
cana-5720	4	9	coimbatore	coimbatore	PROPN
cana-5720	4	10	,	,	PUNCT
cana-5720	4	11	tamil	tamil	PROPN
cana-5720	4	12	nadu	nadu	PROPN
cana-5720	4	13	,	,	PUNCT
cana-5720	4	14	india	india	PROPN
cana-5720	4	15	1e	1e	PROPN
cana-5720	4	16	-	-	PUNCT
cana-5720	4	17	mail	mail	NOUN
cana-5720	4	18	:	:	PUNCT
cana-5720	4	19	banuparveen14@gmail.com,2e	banuparveen14@gmail.com,2e	NUM
cana-5720	4	20	-	-	NOUN
cana-5720	4	21	mail	mail	NOUN
cana-5720	4	22	:	:	PUNCT
cana-5720	4	23	selvanayaki@acetcbe.edu.in	selvanayaki@acetcbe.edu.in	VERB
cana-5720	4	24	3e	3e	NOUN
cana-5720	4	25	-	-	NOUN
cana-5720	4	26	mail	mail	NOUN
cana-5720	4	27	:	:	PUNCT
cana-5720	4	28	abinprakash6343@gmail.com	abinprakash6343@gmail.com	X
cana-5720	5	1	article	article	PROPN
cana-5720	5	2	history	history	NOUN
cana-5720	5	3	:	:	PUNCT
cana-5720	5	4	received	receive	VERB
cana-5720	5	5	:	:	PUNCT
cana-5720	5	6	12	12	NUM
cana-5720	5	7	-	-	SYM
cana-5720	5	8	01	01	NUM
cana-5720	5	9	-	-	PUNCT
cana-5720	5	10	2025	2025	NUM
cana-5720	5	11	revised	revise	VERB
cana-5720	5	12	:	:	PUNCT
cana-5720	5	13	15	15	NUM
cana-5720	5	14	-	-	NUM
cana-5720	5	15	02	02	NUM
cana-5720	5	16	-	-	PUNCT
cana-5720	5	17	2025	2025	NUM
cana-5720	5	18	accepted	accept	VERB
cana-5720	5	19	:	:	PUNCT
cana-5720	5	20	01	01	NUM
cana-5720	5	21	-	-	SYM
cana-5720	5	22	03	03	NUM
cana-5720	5	23	-	-	PUNCT
cana-5720	5	24	2025	2025	NUM
cana-5720	5	25	abstract	abstract	NOUN
cana-5720	5	26	:	:	PUNCT
cana-5720	5	27	in	in	ADP
cana-5720	5	28	this	this	DET
cana-5720	5	29	article	article	NOUN
cana-5720	5	30	explores	explore	VERB
cana-5720	5	31	the	the	DET
cana-5720	5	32	concept	concept	NOUN
cana-5720	5	33	of	of	ADP
cana-5720	5	34	almost	almost	ADV
cana-5720	5	35	gωα	gωα	NOUN
cana-5720	5	36	-closed	-close	VERB
cana-5720	5	37	sets	set	NOUN
cana-5720	5	38	and	and	CCONJ
cana-5720	5	39	almost	almost	ADV
cana-5720	5	40	gωα	gωα	NOUN
cana-5720	5	41	-closed	-close	VERB
cana-5720	5	42	functions	function	NOUN
cana-5720	5	43	and	and	CCONJ
cana-5720	5	44	their	their	PRON
cana-5720	5	45	relationship	relationship	NOUN
cana-5720	5	46	with	with	ADP
cana-5720	5	47	separation	separation	NOUN
cana-5720	5	48	axioms	axiom	NOUN
cana-5720	5	49	in	in	ADP
cana-5720	5	50	topology	topology	NOUN
cana-5720	5	51	.	.	PUNCT
cana-5720	6	1	almost	almost	ADV
cana-5720	6	2	gωα	gωα	PROPN
cana-5720	6	3	-closed	-close	VERB
cana-5720	6	4	functions	function	NOUN
cana-5720	6	5	serve	serve	VERB
cana-5720	6	6	as	as	ADP
cana-5720	6	7	a	a	DET
cana-5720	6	8	generalization	generalization	NOUN
cana-5720	6	9	of	of	ADP
cana-5720	6	10	closed	close	VERB
cana-5720	6	11	functions	function	NOUN
cana-5720	6	12	and	and	CCONJ
cana-5720	6	13	play	play	VERB
cana-5720	6	14	a	a	DET
cana-5720	6	15	crucial	crucial	ADJ
cana-5720	6	16	role	role	NOUN
cana-5720	6	17	in	in	ADP
cana-5720	6	18	the	the	DET
cana-5720	6	19	study	study	NOUN
cana-5720	6	20	of	of	ADP
cana-5720	6	21	topological	topological	ADJ
cana-5720	6	22	properties	property	NOUN
cana-5720	6	23	.	.	PUNCT
cana-5720	7	1	we	we	PRON
cana-5720	7	2	investigate	investigate	VERB
cana-5720	7	3	various	various	ADJ
cana-5720	7	4	characterizations	characterization	NOUN
cana-5720	7	5	and	and	CCONJ
cana-5720	7	6	fundamental	fundamental	ADJ
cana-5720	7	7	properties	property	NOUN
cana-5720	7	8	of	of	ADP
cana-5720	7	9	almost	almost	ADV
cana-5720	7	10	gωα	gωα	NOUN
cana-5720	7	11	-closed	-close	VERB
cana-5720	7	12	functions	function	NOUN
cana-5720	7	13	,	,	PUNCT
cana-5720	7	14	analyzing	analyze	VERB
cana-5720	7	15	their	their	PRON
cana-5720	7	16	interaction	interaction	NOUN
cana-5720	7	17	with	with	ADP
cana-5720	7	18	different	different	ADJ
cana-5720	7	19	separation	separation	NOUN
cana-5720	7	20	axioms	axiom	NOUN
cana-5720	7	21	.	.	PUNCT
cana-5720	8	1	ams	am	NOUN
cana-5720	8	2	subject	subject	ADJ
cana-5720	8	3	classification	classification	NOUN
cana-5720	8	4	:	:	PUNCT
cana-5720	8	5	54c10	54c10	NUM
cana-5720	8	6	,	,	PUNCT
cana-5720	8	7	54c08	54c08	NUM
cana-5720	8	8	,	,	PUNCT
cana-5720	8	9	54c05	54c05	NUM
cana-5720	8	10	keywords	keyword	NOUN
cana-5720	8	11	:	:	PUNCT
cana-5720	8	12	almost	almost	ADV
cana-5720	8	13	gωα	gωα	ADJ
cana-5720	8	14	-	-	PUNCT
cana-5720	8	15	closed	closed	ADJ
cana-5720	8	16	sets	set	NOUN
cana-5720	8	17	,	,	PUNCT
cana-5720	8	18	almost	almost	ADV
cana-5720	8	19	gωα	gωα	NOUN
cana-5720	8	20	-closed	-close	VERB
cana-5720	8	21	functions	function	NOUN
cana-5720	8	22	,	,	PUNCT
cana-5720	8	23	normal	normal	ADJ
cana-5720	8	24	spaces	space	NOUN
cana-5720	8	25	,	,	PUNCT
cana-5720	8	26	weakly	weakly	ADJ
cana-5720	8	27	normal	normal	ADJ
cana-5720	8	28	spaces	space	NOUN
cana-5720	8	29	.	.	PUNCT
cana-5720	9	1	1	1	X
cana-5720	9	2	.	.	X
cana-5720	9	3	introduction	introduction	NOUN
cana-5720	9	4	in	in	ADP
cana-5720	9	5	topological	topological	ADJ
cana-5720	9	6	spaces	space	NOUN
cana-5720	9	7	,	,	PUNCT
cana-5720	9	8	it	it	PRON
cana-5720	9	9	is	be	AUX
cana-5720	9	10	well	well	ADV
cana-5720	9	11	known	know	VERB
cana-5720	9	12	that	that	SCONJ
cana-5720	9	13	normality	normality	NOUN
cana-5720	9	14	is	be	AUX
cana-5720	9	15	preserved	preserve	VERB
cana-5720	9	16	under	under	ADP
cana-5720	9	17	closed	closed	ADJ
cana-5720	9	18	continuous	continuous	ADJ
cana-5720	9	19	surjections	surjection	NOUN
cana-5720	9	20	.	.	PUNCT
cana-5720	10	1	many	many	ADJ
cana-5720	10	2	authors	author	NOUN
cana-5720	10	3	have	have	AUX
cana-5720	10	4	tried	try	VERB
cana-5720	10	5	to	to	PART
cana-5720	10	6	weaken	weaken	VERB
cana-5720	10	7	the	the	DET
cana-5720	10	8	condition	condition	NOUN
cana-5720	10	9	“	"	PUNCT
cana-5720	10	10	closed	close	VERB
cana-5720	10	11	”	"	PUNCT
cana-5720	10	12	in	in	ADP
cana-5720	10	13	this	this	DET
cana-5720	10	14	theorem	theorem	NOUN
cana-5720	10	15	.	.	PUNCT
cana-5720	11	1	in	in	ADP
cana-5720	11	2	1978	1978	NUM
cana-5720	11	3	,	,	PUNCT
cana-5720	11	4	long	long	ADJ
cana-5720	11	5	and	and	CCONJ
cana-5720	11	6	herrington	herrington	PROPN
cana-5720	11	7	[	[	X
cana-5720	11	8	5	5	NUM
cana-5720	11	9	]	]	PUNCT
cana-5720	11	10	used	use	VERB
cana-5720	11	11	almost	almost	ADV
cana-5720	11	12	closedness	closedness	ADJ
cana-5720	11	13	due	due	ADP
cana-5720	11	14	to	to	ADP
cana-5720	11	15	singal	singal	NOUN
cana-5720	11	16	[	[	X
cana-5720	11	17	17	17	NUM
cana-5720	11	18	]	]	PUNCT
cana-5720	11	19	.	.	PUNCT
cana-5720	12	1	in	in	ADP
cana-5720	12	2	1982	1982	NUM
cana-5720	12	3	,	,	PUNCT
cana-5720	12	4	malghan	malghan	PROPN
cana-5720	12	5	[	[	X
cana-5720	12	6	7	7	NUM
cana-5720	12	7	]	]	PUNCT
cana-5720	12	8	used	use	VERB
cana-5720	12	9	g	g	NOUN
cana-5720	12	10	-	-	PUNCT
cana-5720	12	11	closedness	closedness	NOUN
cana-5720	12	12	.	.	PUNCT
cana-5720	13	1	in	in	ADP
cana-5720	13	2	1986	1986	NUM
cana-5720	13	3	,	,	PUNCT
cana-5720	13	4	greenwood	greenwood	PROPN
cana-5720	13	5	and	and	CCONJ
cana-5720	13	6	reilly	reilly	ADV
cana-5720	13	7	[	[	X
cana-5720	13	8	4	4	X
cana-5720	13	9	]	]	PUNCT
cana-5720	13	10	used	use	VERB
cana-5720	13	11	-closedness	-closedness	PROPN
cana-5720	13	12	due	due	ADP
cana-5720	13	13	to	to	ADP
cana-5720	13	14	mashhour	mashhour	PROPN
cana-5720	13	15	et	et	PROPN
cana-5720	13	16	al	al	PROPN
cana-5720	13	17	.	.	PUNCT
cana-5720	14	1	[	[	X
cana-5720	14	2	8	8	NUM
cana-5720	14	3	]	]	PUNCT
cana-5720	14	4	.	.	PUNCT
cana-5720	15	1	in	in	ADP
cana-5720	15	2	1995	1995	NUM
cana-5720	15	3	,	,	PUNCT
cana-5720	15	4	yoshimura	yoshimura	PROPN
cana-5720	15	5	et	et	PROPN
cana-5720	15	6	al	al	PROPN
cana-5720	15	7	.	.	PUNCT
cana-5720	16	1	[	[	X
cana-5720	16	2	19	19	NUM
cana-5720	16	3	]	]	PUNCT
cana-5720	16	4	used	use	VERB
cana-5720	16	5	almost	almost	ADV
cana-5720	16	6	g	g	NOUN
cana-5720	16	7	-	-	PUNCT
cana-5720	16	8	closedness	closedness	NOUN
cana-5720	16	9	which	which	PRON
cana-5720	16	10	is	be	AUX
cana-5720	16	11	a	a	DET
cana-5720	16	12	generalization	generalization	NOUN
cana-5720	16	13	of	of	ADP
cana-5720	16	14	both	both	DET
cana-5720	16	15	almost	almost	ADV
cana-5720	16	16	closedness	closedness	ADJ
cana-5720	16	17	and	and	CCONJ
cana-5720	16	18	g	g	NOUN
cana-5720	16	19	-	-	PUNCT
cana-5720	16	20	closedness	closedness	NOUN
cana-5720	16	21	.	.	PUNCT
cana-5720	17	1	in	in	ADP
cana-5720	17	2	1999	1999	NUM
cana-5720	17	3	,	,	PUNCT
cana-5720	17	4	noiri	noiri	ADV
cana-5720	17	5	[	[	X
cana-5720	17	6	9	9	NUM
cana-5720	17	7	]	]	PUNCT
cana-5720	17	8	introduced	introduce	VERB
cana-5720	17	9	almost	almost	ADV
cana-5720	17	10	ag	ag	NOUN
cana-5720	17	11	-	-	PUNCT
cana-5720	17	12	closedness	closedness	NOUN
cana-5720	17	13	using	use	VERB
cana-5720	17	14	ag	ag	PROPN
cana-5720	17	15	-	-	PUNCT
cana-5720	17	16	closed	closed	ADJ
cana-5720	17	17	sets	set	NOUN
cana-5720	17	18	[	[	X
cana-5720	17	19	35	35	NUM
cana-5720	17	20	]	]	PUNCT
cana-5720	17	21	.	.	PUNCT
cana-5720	18	1	ravi	ravi	PROPN
cana-5720	18	2	et	et	PROPN
cana-5720	18	3	.	.	PUNCT
cana-5720	19	1	al	al	PROPN
cana-5720	19	2	.	.	PUNCT
cana-5720	20	1	[	[	X
cana-5720	20	2	14	14	NUM
cana-5720	20	3	]	]	PUNCT
cana-5720	20	4	introduced	introduce	VERB
cana-5720	20	5	almost	almost	ADV
cana-5720	20	6	ags	ag	NOUN
cana-5720	20	7	-	-	PUNCT
cana-5720	20	8	closedness	closedness	ADJ
cana-5720	20	9	using	use	VERB
cana-5720	20	10	ags	ag	NOUN
cana-5720	20	11	-	-	PUNCT
cana-5720	20	12	closed	close	VERB
cana-5720	20	13	sets	set	NOUN
cana-5720	20	14	[	[	X
cana-5720	20	15	13	13	NUM
cana-5720	20	16	]	]	PUNCT
cana-5720	20	17	.	.	PUNCT
cana-5720	21	1	we	we	PRON
cana-5720	21	2	use	use	VERB
cana-5720	21	3	gωα	gωα	VERB
cana-5720	21	4	-	-	PUNCT
cana-5720	21	5	closed	close	VERB
cana-5720	21	6	sets	set	NOUN
cana-5720	21	7	to	to	PART
cana-5720	21	8	define	define	VERB
cana-5720	21	9	a	a	DET
cana-5720	21	10	new	new	ADJ
cana-5720	21	11	class	class	NOUN
cana-5720	21	12	of	of	ADP
cana-5720	21	13	functions	function	NOUN
cana-5720	21	14	called	call	VERB
cana-5720	21	15	almost	almost	ADV
cana-5720	21	16	gωα	gωα	NOUN
cana-5720	21	17	-closed	-close	VERB
cana-5720	21	18	functions	function	NOUN
cana-5720	21	19	.	.	PUNCT
cana-5720	22	1	the	the	DET
cana-5720	22	2	purpose	purpose	NOUN
cana-5720	22	3	of	of	ADP
cana-5720	22	4	the	the	DET
cana-5720	22	5	present	present	ADJ
cana-5720	22	6	article	article	NOUN
cana-5720	22	7	is	be	AUX
cana-5720	22	8	to	to	PART
cana-5720	22	9	improve	improve	VERB
cana-5720	22	10	preservation	preservation	NOUN
cana-5720	22	11	theorems	theorem	NOUN
cana-5720	22	12	of	of	ADP
cana-5720	22	13	separation	separation	NOUN
cana-5720	22	14	axioms	axiom	NOUN
cana-5720	22	15	,	,	PUNCT
cana-5720	22	16	that	that	ADV
cana-5720	22	17	is	is	ADV
cana-5720	22	18	,	,	PUNCT
cana-5720	22	19	normality	normality	NOUN
cana-5720	22	20	,	,	PUNCT
cana-5720	22	21	weak	weak	ADJ
cana-5720	22	22	normality	normality	NOUN
cana-5720	22	23	,	,	PUNCT
cana-5720	22	24	mild	mild	ADJ
cana-5720	22	25	normality	normality	NOUN
cana-5720	22	26	,	,	PUNCT
cana-5720	22	27	almost	almost	ADV
cana-5720	22	28	normality	normality	NOUN
cana-5720	22	29	,	,	PUNCT
cana-5720	22	30	regularity	regularity	NOUN
cana-5720	22	31	,	,	PUNCT
cana-5720	22	32	almost	almost	ADV
cana-5720	22	33	regularity	regularity	NOUN
cana-5720	22	34	,	,	PUNCT
cana-5720	22	35	quasi	quasi	ADJ
cana-5720	22	36	-	-	NOUN
cana-5720	22	37	regularity	regularity	NOUN
cana-5720	22	38	and	and	CCONJ
cana-5720	22	39	strong	strong	ADJ
cana-5720	22	40	s	s	NOUN
cana-5720	22	41	-	-	NOUN
cana-5720	22	42	regularity	regularity	NOUN
cana-5720	22	43	.	.	PUNCT
cana-5720	23	1	theorem	theorem	VERB
cana-5720	23	2	a	a	DET
cana-5720	23	3	normality	normality	NOUN
cana-5720	23	4	and	and	CCONJ
cana-5720	23	5	weak	weak	ADJ
cana-5720	23	6	normality	normality	NOUN
cana-5720	23	7	are	be	AUX
cana-5720	23	8	preserved	preserve	VERB
cana-5720	23	9	under	under	ADP
cana-5720	23	10	almost	almost	ADV
cana-5720	23	11	gωα	gωα	NOUN
cana-5720	23	12	-closed	-close	VERB
cana-5720	23	13	continuous	continuous	ADJ
cana-5720	23	14	surjections	surjection	NOUN
cana-5720	23	15	.	.	PUNCT
cana-5720	24	1	theorem	theorem	NOUN
cana-5720	24	2	b	b	NOUN
cana-5720	24	3	regularity	regularity	NOUN
cana-5720	24	4	and	and	CCONJ
cana-5720	24	5	strong	strong	ADJ
cana-5720	24	6	s	s	NOUN
cana-5720	24	7	-	-	PUNCT
cana-5720	24	8	regularity	regularity	NOUN
cana-5720	24	9	are	be	AUX
cana-5720	24	10	preserved	preserve	VERB
cana-5720	24	11	under	under	ADP
cana-5720	24	12	almost	almost	ADV
cana-5720	24	13	a	a	PRON
cana-5720	24	14	-	-	PUNCT
cana-5720	24	15	open	open	ADJ
cana-5720	24	16	almost	almost	ADV
cana-5720	24	17	gωα	gωα	NOUN
cana-5720	24	18	-closed	-close	VERB
cana-5720	24	19	continuous	continuous	ADJ
cana-5720	24	20	surjections	surjection	NOUN
cana-5720	24	21	.	.	PUNCT
cana-5720	25	1	2	2	X
cana-5720	25	2	.	.	X
cana-5720	25	3	preliminaries	preliminary	NOUN
cana-5720	25	4	the	the	DET
cana-5720	25	5	family	family	NOUN
cana-5720	25	6	of	of	ADP
cana-5720	25	7	regular	regular	ADJ
cana-5720	25	8	open	open	ADJ
cana-5720	25	9	(	(	PUNCT
cana-5720	25	10	resp	resp	NOUN
cana-5720	25	11	.	.	PUNCT
cana-5720	26	1	regular	regular	ADJ
cana-5720	26	2	closed	closed	ADJ
cana-5720	26	3	)	)	PUNCT
cana-5720	26	4	sets	set	NOUN
cana-5720	26	5	of	of	ADP
cana-5720	26	6	a	a	DET
cana-5720	26	7	space	space	NOUN
cana-5720	26	8	(	(	PUNCT
cana-5720	26	9	x	x	X
cana-5720	26	10	,	,	PUNCT
cana-5720	26	11			PROPN
cana-5720	26	12	)	)	PUNCT
cana-5720	26	13	is	be	AUX
cana-5720	26	14	denoted	denote	VERB
cana-5720	26	15	by	by	ADP
cana-5720	26	16	ro	ro	PROPN
cana-5720	26	17	(	(	PUNCT
cana-5720	26	18	x	x	NOUN
cana-5720	26	19	,	,	PUNCT
cana-5720	26	20			PROPN
cana-5720	26	21	)	)	PUNCT
cana-5720	26	22	(	(	PUNCT
cana-5720	26	23	resp	resp	NOUN
cana-5720	26	24	.	.	PUNCT
cana-5720	27	1	rc	rc	PROPN
cana-5720	27	2	(	(	PUNCT
cana-5720	27	3	x	x	PROPN
cana-5720	27	4	,	,	PUNCT
cana-5720	27	5			PROPN
cana-5720	27	6	)	)	PUNCT
cana-5720	27	7	)	)	PUNCT
cana-5720	27	8	or	or	CCONJ
cana-5720	27	9	simply	simply	ADV
cana-5720	27	10	by	by	ADP
cana-5720	27	11	ro	ro	PROPN
cana-5720	27	12	(	(	PUNCT
cana-5720	27	13	x	x	NOUN
cana-5720	27	14	)	)	PUNCT
cana-5720	27	15	(	(	PUNCT
cana-5720	27	16	resp	resp	NOUN
cana-5720	27	17	.	.	PUNCT
cana-5720	28	1	rc	rc	PROPN
cana-5720	28	2	(	(	PUNCT
cana-5720	28	3	x	x	NOUN
cana-5720	28	4	)	)	PUNCT
cana-5720	28	5	)	)	PUNCT
cana-5720	28	6	.	.	PUNCT
cana-5720	29	1	mailto:selvanayaki@acetcbe.edu.in	mailto:selvanayaki@acetcbe.edu.in	PROPN
cana-5720	29	2	mailto:abinprakash6343@gmail.com	mailto:abinprakash6343@gmail.com	X
cana-5720	29	3	communications	communication	NOUN
cana-5720	29	4	on	on	ADP
cana-5720	29	5	applied	apply	VERB
cana-5720	29	6	nonlinear	nonlinear	ADJ
cana-5720	29	7	analysis	analysis	NOUN
cana-5720	29	8	issn	issn	NOUN
cana-5720	29	9	:	:	PUNCT
cana-5720	29	10	1074	1074	NUM
cana-5720	29	11	-	-	PUNCT
cana-5720	29	12	133x	133x	NUM
cana-5720	29	13	vol	vol	VERB
cana-5720	29	14	32	32	NUM
cana-5720	29	15	no	no	NOUN
cana-5720	29	16	.	.	PUNCT
cana-5720	30	1	10s	10	NOUN
cana-5720	30	2	(	(	PUNCT
cana-5720	30	3	2025	2025	NUM
cana-5720	30	4	)	)	PUNCT
cana-5720	30	5	2802	2802	NUM
cana-5720	30	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5720	30	7	definition	definition	NOUN
cana-5720	30	8	2.1	2.1	NUM
cana-5720	30	9	a	a	DET
cana-5720	30	10	subset	subset	NOUN
cana-5720	30	11	a	a	PRON
cana-5720	30	12	of	of	ADP
cana-5720	30	13	a	a	DET
cana-5720	30	14	space	space	NOUN
cana-5720	30	15	(	(	PUNCT
cana-5720	30	16	x	x	X
cana-5720	30	17	,	,	PUNCT
cana-5720	30	18			PROPN
cana-5720	30	19	)	)	PUNCT
cana-5720	30	20	is	be	AUX
cana-5720	30	21	called	call	VERB
cana-5720	30	22	a	a	DET
cana-5720	30	23	rg	rg	NOUN
cana-5720	30	24	-	-	PUNCT
cana-5720	30	25	closed	closed	ADJ
cana-5720	30	26	[	[	X
cana-5720	30	27	9	9	NUM
cana-5720	30	28	]	]	PUNCT
cana-5720	30	29	if	if	SCONJ
cana-5720	30	30	αcl(a	αcl(a	NUM
cana-5720	30	31	)	)	PUNCT
cana-5720	30	32			PROPN
cana-5720	30	33	u	u	PROPN
cana-5720	30	34	whenever	whenever	SCONJ
cana-5720	30	35	a	a	DET
cana-5720	30	36			PROPN
cana-5720	30	37	u	u	NOUN
cana-5720	30	38	and	and	CCONJ
cana-5720	30	39	u	u	NOUN
cana-5720	30	40	is	be	AUX
cana-5720	30	41	regular	regular	ADJ
cana-5720	30	42	open	open	ADJ
cana-5720	30	43	in	in	ADP
cana-5720	30	44	(	(	PUNCT
cana-5720	30	45	x	x	NOUN
cana-5720	30	46	,	,	PUNCT
cana-5720	30	47			PROPN
cana-5720	30	48	)	)	PUNCT
cana-5720	30	49	.	.	PUNCT
cana-5720	31	1	the	the	DET
cana-5720	31	2	complement	complement	NOUN
cana-5720	31	3	of	of	ADP
cana-5720	31	4	rαg	rαg	NOUN
cana-5720	31	5	-	-	PUNCT
cana-5720	31	6	closed	close	VERB
cana-5720	31	7	set	set	NOUN
cana-5720	31	8	is	be	AUX
cana-5720	31	9	called	call	VERB
cana-5720	31	10	rαg	rαg	NOUN
cana-5720	31	11	-	-	PUNCT
cana-5720	31	12	open	open	NOUN
cana-5720	31	13	set	set	NOUN
cana-5720	31	14	.	.	PUNCT
cana-5720	32	1	definition	definition	NOUN
cana-5720	32	2	2.2	2.2	NUM
cana-5720	32	3	a	a	DET
cana-5720	32	4	function	function	NOUN
cana-5720	32	5	f	f	NOUN
cana-5720	32	6	:	:	PUNCT
cana-5720	32	7	(	(	PUNCT
cana-5720	32	8	x	x	X
cana-5720	32	9	,	,	PUNCT
cana-5720	32	10			PROPN
cana-5720	32	11	)	)	PUNCT
cana-5720	32	12	→	→	SYM
cana-5720	32	13	(	(	PUNCT
cana-5720	32	14	y	y	NOUN
cana-5720	32	15	,	,	PUNCT
cana-5720	32	16			PRON
cana-5720	32	17	)	)	PUNCT
cana-5720	32	18	is	be	AUX
cana-5720	32	19	said	say	VERB
cana-5720	32	20	to	to	PART
cana-5720	32	21	be	be	AUX
cana-5720	32	22	(	(	PUNCT
cana-5720	32	23	i	i	NOUN
cana-5720	32	24	)	)	PUNCT
cana-5720	33	1	-closed	-close	VERB
cana-5720	33	2	[	[	X
cana-5720	33	3	40	40	NUM
cana-5720	33	4	]	]	PUNCT
cana-5720	33	5	(	(	PUNCT
cana-5720	33	6	resp	resp	NOUN
cana-5720	33	7	.	.	PUNCT
cana-5720	34	1	ĝ	ĝ	X
cana-5720	34	2	-	-	PUNCT
cana-5720	34	3	closed	closed	ADJ
cana-5720	34	4	[	[	X
cana-5720	34	5	14	14	NUM
cana-5720	34	6	]	]	SYM
cana-5720	34	7	,	,	PUNCT
cana-5720	34	8	gs	gs	PUNCT
cana-5720	34	9	-	-	PUNCT
cana-5720	34	10	closed	close	VERB
cana-5720	34	11	[	[	X
cana-5720	34	12	66	66	NUM
cana-5720	34	13	]	]	PUNCT
cana-5720	34	14	,	,	PUNCT
cana-5720	34	15	g	g	PROPN
cana-5720	34	16			NOUN
cana-5720	34	17	-closed	-close	VERB
cana-5720	34	18	)	)	PUNCT
cana-5720	34	19	if	if	SCONJ
cana-5720	34	20	for	for	ADP
cana-5720	34	21	each	each	DET
cana-5720	34	22	closed	close	VERB
cana-5720	34	23	set	set	VERB
cana-5720	34	24	f	f	PROPN
cana-5720	34	25	of	of	ADP
cana-5720	34	26	x	x	PROPN
cana-5720	34	27	,	,	PUNCT
cana-5720	34	28	f(f	f(f	PROPN
cana-5720	34	29	)	)	PUNCT
cana-5720	34	30	is	be	AUX
cana-5720	34	31	-closed	-close	VERB
cana-5720	34	32	(	(	PUNCT
cana-5720	34	33	resp	resp	NOUN
cana-5720	34	34	.	.	PUNCT
cana-5720	35	1	ĝ	ĝ	X
cana-5720	35	2	-	-	PUNCT
cana-5720	35	3	closed	closed	ADJ
cana-5720	35	4	,	,	PUNCT
cana-5720	35	5	gs	gs	PUNCT
cana-5720	35	6	-	-	PUNCT
cana-5720	35	7	closed	closed	ADJ
cana-5720	35	8	,	,	PUNCT
cana-5720	35	9	g	g	NUM
cana-5720	35	10			NOUN
cana-5720	35	11	-closed	-close	VERB
cana-5720	35	12	)	)	PUNCT
cana-5720	36	1	;	;	PUNCT
cana-5720	36	2	(	(	PUNCT
cana-5720	36	3	ii	ii	NOUN
cana-5720	36	4	)	)	PUNCT
cana-5720	36	5	almost	almost	ADV
cana-5720	36	6	-closed	-close	VERB
cana-5720	36	7	[	[	PUNCT
cana-5720	36	8	9	9	NUM
cana-5720	36	9	]	]	PUNCT
cana-5720	36	10	(	(	PUNCT
cana-5720	36	11	resp	resp	NOUN
cana-5720	36	12	.	.	PUNCT
cana-5720	37	1	almost	almost	ADV
cana-5720	37	2	ĝ	ĝ	ADV
cana-5720	37	3	-	-	PUNCT
cana-5720	37	4	closed	closed	ADJ
cana-5720	37	5	[	[	X
cana-5720	37	6	14	14	NUM
cana-5720	37	7	]	]	X
cana-5720	37	8	,	,	PUNCT
cana-5720	37	9	almost	almost	ADV
cana-5720	37	10	gs	gs	PUNCT
cana-5720	37	11	-	-	PUNCT
cana-5720	37	12	closed	close	VERB
cana-5720	37	13	[	[	X
cana-5720	37	14	14	14	NUM
cana-5720	37	15	]	]	X
cana-5720	37	16	,	,	PUNCT
cana-5720	37	17	almost	almost	ADV
cana-5720	37	18	g	g	NOUN
cana-5720	37	19			NOUN
cana-5720	37	20	-closed	-close	VERB
cana-5720	37	21	,	,	PUNCT
cana-5720	37	22	almost	almost	ADV
cana-5720	37	23	g	g	NUM
cana-5720	37	24			NOUN
cana-5720	37	25	-closed	-close	VERB
cana-5720	37	26	)	)	PUNCT
cana-5720	37	27	if	if	SCONJ
cana-5720	37	28	for	for	ADP
cana-5720	37	29	each	each	DET
cana-5720	37	30	f	f	NOUN
cana-5720	37	31	rc(x	rc(x	NOUN
cana-5720	37	32	,	,	PUNCT
cana-5720	37	33			PROPN
cana-5720	37	34	)	)	PUNCT
cana-5720	37	35	,	,	PUNCT
cana-5720	37	36	f(f	f(f	PROPN
cana-5720	37	37	)	)	PUNCT
cana-5720	37	38	is	be	AUX
cana-5720	37	39	-closed	-close	VERB
cana-5720	37	40	(	(	PUNCT
cana-5720	37	41	resp	resp	NOUN
cana-5720	37	42	.	.	PUNCT
cana-5720	38	1	ĝ	ĝ	X
cana-5720	38	2	-	-	PUNCT
cana-5720	38	3	closed	closed	ADJ
cana-5720	38	4	,	,	PUNCT
cana-5720	38	5	gs	gs	PUNCT
cana-5720	38	6	-	-	PUNCT
cana-5720	38	7	closed	closed	ADJ
cana-5720	38	8	,	,	PUNCT
cana-5720	38	9	g	g	PROPN
cana-5720	38	10			NOUN
cana-5720	38	11	closed	close	VERB
cana-5720	38	12	,	,	PUNCT
cana-5720	38	13	g	g	NUM
cana-5720	38	14			NOUN
cana-5720	38	15	-closed	-close	VERB
cana-5720	38	16	)	)	PUNCT
cana-5720	38	17	.	.	PUNCT
cana-5720	39	1	definition	definition	NOUN
cana-5720	39	2	2.3	2.3	NUM
cana-5720	39	3	a	a	DET
cana-5720	39	4	space	space	NOUN
cana-5720	39	5	x	x	PUNCT
cana-5720	39	6	is	be	AUX
cana-5720	39	7	said	say	VERB
cana-5720	39	8	to	to	PART
cana-5720	39	9	be	be	AUX
cana-5720	39	10	(	(	PUNCT
cana-5720	39	11	i	i	NOUN
cana-5720	39	12	)	)	PUNCT
cana-5720	39	13	weakly	weakly	ADV
cana-5720	39	14	normal	normal	ADJ
cana-5720	40	1	[	[	X
cana-5720	40	2	20	20	NUM
cana-5720	40	3	]	]	X
cana-5720	40	4	if	if	SCONJ
cana-5720	40	5	for	for	ADP
cana-5720	40	6	each	each	DET
cana-5720	40	7	decreasing	decrease	VERB
cana-5720	40	8	sequence	sequence	NOUN
cana-5720	40	9	{	{	PUNCT
cana-5720	40	10	fn	fn	NOUN
cana-5720	40	11	}	}	PUNCT
cana-5720	40	12	of	of	ADP
cana-5720	40	13	closed	closed	ADJ
cana-5720	40	14	sets	set	NOUN
cana-5720	40	15	of	of	ADP
cana-5720	40	16	x	x	SYM
cana-5720	40	17	such	such	ADJ
cana-5720	40	18	that	that	SCONJ
cana-5720	40	19			NOUN
cana-5720	40	20	{	{	PUNCT
cana-5720	40	21	fn	fn	NOUN
cana-5720	40	22	:	:	PUNCT
cana-5720	40	23	n	n	CCONJ
cana-5720	40	24			NOUN
cana-5720	40	25	n	n	CCONJ
cana-5720	40	26	}	}	PUNCT
cana-5720	40	27	=	=	NOUN
cana-5720	40	28			NOUN
cana-5720	40	29	and	and	CCONJ
cana-5720	40	30	each	each	DET
cana-5720	40	31	closed	close	VERB
cana-5720	40	32	set	set	ADJ
cana-5720	40	33	h	h	NOUN
cana-5720	40	34	of	of	ADP
cana-5720	40	35	x	x	PUNCT
cana-5720	40	36	with	with	ADP
cana-5720	40	37	h	h	NOUN
cana-5720	40	38			PUNCT
cana-5720	40	39	f1	f1	NOUN
cana-5720	40	40	=	=	SYM
cana-5720	40	41			NOUN
cana-5720	40	42	,	,	PUNCT
cana-5720	40	43	there	there	PRON
cana-5720	40	44	exist	exist	VERB
cana-5720	40	45	n	n	PRON
cana-5720	40	46			NOUN
cana-5720	40	47	n	n	CCONJ
cana-5720	40	48	and	and	CCONJ
cana-5720	40	49	an	an	DET
cana-5720	40	50	open	open	ADJ
cana-5720	40	51	set	set	NOUN
cana-5720	40	52	u	u	NOUN
cana-5720	40	53	of	of	ADP
cana-5720	40	54	x	x	SYM
cana-5720	40	55	such	such	ADJ
cana-5720	40	56	that	that	DET
cana-5720	40	57	fn	fn	NOUN
cana-5720	40	58			PROPN
cana-5720	40	59	u	u	NOUN
cana-5720	40	60	and	and	CCONJ
cana-5720	40	61	cl(u	cl(u	NOUN
cana-5720	40	62	)	)	PUNCT
cana-5720	40	63			PUNCT
cana-5720	40	64	h	h	NOUN
cana-5720	40	65	=	=	SYM
cana-5720	40	66			NOUN
cana-5720	40	67	;	;	PUNCT
cana-5720	40	68	(	(	PUNCT
cana-5720	40	69	ii	ii	NOUN
cana-5720	40	70	)	)	PUNCT
cana-5720	40	71	mildly	mildly	ADV
cana-5720	40	72	normal	normal	ADJ
cana-5720	40	73	[	[	X
cana-5720	40	74	18	18	NUM
cana-5720	40	75	]	]	X
cana-5720	40	76	if	if	SCONJ
cana-5720	40	77	for	for	ADP
cana-5720	40	78	any	any	DET
cana-5720	40	79	disjoint	disjoint	ADJ
cana-5720	40	80	regular	regular	ADJ
cana-5720	40	81	closed	closed	ADJ
cana-5720	40	82	sets	set	NOUN
cana-5720	40	83	a	a	PRON
cana-5720	40	84	and	and	CCONJ
cana-5720	40	85	b	b	NOUN
cana-5720	40	86	,	,	PUNCT
cana-5720	40	87	there	there	PRON
cana-5720	40	88	exist	exist	VERB
cana-5720	40	89	disjoint	disjoint	ADJ
cana-5720	40	90	open	open	ADJ
cana-5720	40	91	sets	set	NOUN
cana-5720	40	92	u	u	NOUN
cana-5720	40	93	and	and	CCONJ
cana-5720	40	94	v	v	ADP
cana-5720	40	95	such	such	ADJ
cana-5720	40	96	that	that	SCONJ
cana-5720	40	97	a	a	DET
cana-5720	40	98			PROPN
cana-5720	40	99	u	u	PROPN
cana-5720	40	100	and	and	CCONJ
cana-5720	40	101	b	b	PROPN
cana-5720	40	102			PROPN
cana-5720	40	103	v	v	PROPN
cana-5720	40	104	;	;	PUNCT
cana-5720	40	105	(	(	PUNCT
cana-5720	40	106	iii	iii	NOUN
cana-5720	40	107	)	)	PUNCT
cana-5720	40	108	almost	almost	ADV
cana-5720	40	109	normal	normal	ADJ
cana-5720	41	1	[	[	X
cana-5720	41	2	15	15	NUM
cana-5720	41	3	]	]	X
cana-5720	41	4	if	if	SCONJ
cana-5720	41	5	for	for	ADP
cana-5720	41	6	every	every	DET
cana-5720	41	7	pair	pair	NOUN
cana-5720	41	8	of	of	ADP
cana-5720	41	9	disjoint	disjoint	NOUN
cana-5720	41	10	sets	set	NOUN
cana-5720	41	11	a	a	PRON
cana-5720	41	12	and	and	CCONJ
cana-5720	41	13	b	b	NOUN
cana-5720	41	14	,	,	PUNCT
cana-5720	41	15	one	one	NUM
cana-5720	41	16	of	of	ADP
cana-5720	41	17	which	which	PRON
cana-5720	41	18	is	be	AUX
cana-5720	41	19	closed	close	VERB
cana-5720	41	20	and	and	CCONJ
cana-5720	41	21	the	the	DET
cana-5720	41	22	other	other	ADJ
cana-5720	41	23	is	be	AUX
cana-5720	41	24	regular	regular	ADJ
cana-5720	41	25	closed	closed	ADJ
cana-5720	41	26	,	,	PUNCT
cana-5720	41	27	there	there	PRON
cana-5720	41	28	exist	exist	VERB
cana-5720	41	29	disjoint	disjoint	ADJ
cana-5720	41	30	open	open	ADJ
cana-5720	41	31	sets	set	NOUN
cana-5720	41	32	u	u	NOUN
cana-5720	41	33	and	and	CCONJ
cana-5720	41	34	v	v	ADP
cana-5720	41	35	such	such	ADJ
cana-5720	41	36	that	that	SCONJ
cana-5720	41	37	a	a	DET
cana-5720	41	38			PROPN
cana-5720	41	39	u	u	PROPN
cana-5720	41	40	and	and	CCONJ
cana-5720	41	41	b	b	PROPN
cana-5720	41	42			PROPN
cana-5720	41	43	v.	v.	ADP
cana-5720	41	44	lemma	lemma	PROPN
cana-5720	42	1	2.4	2.4	NUM
cana-5720	42	2	[	[	SYM
cana-5720	42	3	9	9	NUM
cana-5720	42	4	]	]	X
cana-5720	42	5	if	if	SCONJ
cana-5720	42	6	a	a	PRON
cana-5720	42	7	is	be	AUX
cana-5720	42	8	an	an	DET
cana-5720	42	9	-open	-open	PROPN
cana-5720	42	10	set	set	NOUN
cana-5720	42	11	of	of	ADP
cana-5720	42	12	a	a	DET
cana-5720	42	13	space	space	NOUN
cana-5720	42	14	x	x	NOUN
cana-5720	42	15	,	,	PUNCT
cana-5720	42	16	then	then	ADV
cana-5720	42	17	the	the	DET
cana-5720	42	18	following	follow	VERB
cana-5720	42	19	hold	hold	NOUN
cana-5720	42	20	:	:	PUNCT
cana-5720	42	21	cl(a	cl(a	ADJ
cana-5720	42	22	)	)	PUNCT
cana-5720	42	23	=	=	SYM
cana-5720	42	24	cl(a	cl(a	X
cana-5720	42	25	)	)	PUNCT
cana-5720	42	26	=	=	SYM
cana-5720	42	27	cl(int(a	cl(int(a	PROPN
cana-5720	42	28	)	)	PUNCT
cana-5720	42	29	)	)	PUNCT
cana-5720	42	30	.	.	PUNCT
cana-5720	43	1	lemma	lemma	PROPN
cana-5720	43	2	2.5	2.5	NUM
cana-5720	44	1	[	[	SYM
cana-5720	44	2	10	10	NUM
cana-5720	44	3	]	]	PUNCT
cana-5720	44	4	a	a	DET
cana-5720	44	5	space	space	NOUN
cana-5720	44	6	x	x	PUNCT
cana-5720	44	7	is	be	AUX
cana-5720	44	8	weakly	weakly	ADV
cana-5720	44	9	normal	normal	ADJ
cana-5720	44	10	if	if	SCONJ
cana-5720	44	11	and	and	CCONJ
cana-5720	44	12	only	only	ADV
cana-5720	44	13	if	if	SCONJ
cana-5720	44	14	for	for	ADP
cana-5720	44	15	each	each	DET
cana-5720	44	16	decreasing	decrease	VERB
cana-5720	44	17	sequence	sequence	NOUN
cana-5720	44	18	{	{	PUNCT
cana-5720	44	19	fn	fn	NOUN
cana-5720	44	20	}	}	PUNCT
cana-5720	44	21	of	of	ADP
cana-5720	44	22	closed	closed	ADJ
cana-5720	44	23	sets	set	NOUN
cana-5720	44	24	of	of	ADP
cana-5720	44	25	x	x	SYM
cana-5720	44	26	such	such	ADJ
cana-5720	44	27	that	that	SCONJ
cana-5720	44	28			NOUN
cana-5720	44	29	{	{	PUNCT
cana-5720	44	30	fn	fn	NOUN
cana-5720	44	31	:	:	PUNCT
cana-5720	44	32	n	n	CCONJ
cana-5720	44	33			NOUN
cana-5720	44	34	n	n	CCONJ
cana-5720	44	35	}	}	PUNCT
cana-5720	44	36	=	=	NOUN
cana-5720	44	37			NOUN
cana-5720	44	38	and	and	CCONJ
cana-5720	44	39	each	each	DET
cana-5720	44	40	open	open	ADJ
cana-5720	44	41	set	set	VERB
cana-5720	44	42	u	u	NOUN
cana-5720	44	43	of	of	ADP
cana-5720	44	44	x	x	SYM
cana-5720	44	45	such	such	ADJ
cana-5720	44	46	that	that	DET
cana-5720	44	47	f1	f1	NOUN
cana-5720	44	48			PROPN
cana-5720	44	49	u	u	PROPN
cana-5720	44	50	,	,	PUNCT
cana-5720	44	51	there	there	PRON
cana-5720	44	52	exist	exist	VERB
cana-5720	44	53	n	n	PRON
cana-5720	44	54			NOUN
cana-5720	44	55	n	n	CCONJ
cana-5720	44	56	and	and	CCONJ
cana-5720	44	57	an	an	DET
cana-5720	44	58	open	open	ADJ
cana-5720	44	59	set	set	NOUN
cana-5720	44	60	g	g	NOUN
cana-5720	44	61	of	of	ADP
cana-5720	44	62	x	x	INTJ
cana-5720	44	63	such	such	ADJ
cana-5720	44	64	that	that	DET
cana-5720	44	65	fn	fn	NOUN
cana-5720	45	1			PROPN
cana-5720	45	2	g	g	PROPN
cana-5720	45	3			PROPN
cana-5720	45	4	cl(g	cl(g	NOUN
cana-5720	45	5	)	)	PUNCT
cana-5720	46	1			PROPN
cana-5720	46	2	u.	u.	PROPN
cana-5720	46	3	definition	definition	NOUN
cana-5720	46	4	2.6	2.6	NUM
cana-5720	46	5	a	a	DET
cana-5720	46	6	function	function	NOUN
cana-5720	46	7	f	f	NOUN
cana-5720	46	8	:	:	PUNCT
cana-5720	46	9	x	x	X
cana-5720	46	10	→	→	SYM
cana-5720	46	11	y	y	PROPN
cana-5720	46	12	is	be	AUX
cana-5720	46	13	said	say	VERB
cana-5720	46	14	to	to	PART
cana-5720	46	15	be	be	AUX
cana-5720	46	16	(	(	PUNCT
cana-5720	46	17	i	i	NOUN
cana-5720	46	18	)	)	PUNCT
cana-5720	46	19	r	r	NOUN
cana-5720	46	20	-	-	PUNCT
cana-5720	46	21	map	map	NOUN
cana-5720	47	1	[	[	X
cana-5720	47	2	1	1	NUM
cana-5720	47	3	]	]	PUNCT
cana-5720	47	4	(	(	PUNCT
cana-5720	47	5	resp	resp	NOUN
cana-5720	47	6	.	.	PUNCT
cana-5720	48	1	almost	almost	ADV
cana-5720	48	2	continuous	continuous	ADJ
cana-5720	48	3	[	[	X
cana-5720	48	4	79	79	NUM
cana-5720	48	5	]	]	SYM
cana-5720	48	6	)	)	PUNCT
cana-5720	48	7	if	if	SCONJ
cana-5720	48	8	f-1(v	f-1(v	NOUN
cana-5720	48	9	)	)	PUNCT
cana-5720	48	10	is	be	AUX
cana-5720	48	11	regular	regular	ADJ
cana-5720	48	12	open	open	ADJ
cana-5720	48	13	(	(	PUNCT
cana-5720	48	14	resp	resp	NOUN
cana-5720	48	15	.	.	PUNCT
cana-5720	49	1	open	open	ADJ
cana-5720	49	2	)	)	PUNCT
cana-5720	49	3	in	in	ADP
cana-5720	49	4	x	x	PUNCT
cana-5720	49	5	for	for	ADP
cana-5720	49	6	every	every	DET
cana-5720	49	7	v	v	NOUN
cana-5720	49	8			PROPN
cana-5720	49	9	ro	ro	X
cana-5720	49	10	(	(	PUNCT
cana-5720	49	11	y	y	PROPN
cana-5720	49	12	)	)	PUNCT
cana-5720	49	13	;	;	PUNCT
cana-5720	49	14	(	(	PUNCT
cana-5720	49	15	ii	ii	NOUN
cana-5720	49	16	)	)	PUNCT
cana-5720	49	17	almost	almost	ADV
cana-5720	49	18	open	open	ADJ
cana-5720	50	1	[	[	X
cana-5720	50	2	17	17	NUM
cana-5720	50	3	]	]	X
cana-5720	50	4	(	(	PUNCT
cana-5720	50	5	resp	resp	NOUN
cana-5720	50	6	.	.	PUNCT
cana-5720	51	1	almost	almost	ADV
cana-5720	51	2	-open	-open	PROPN
cana-5720	51	3	[	[	X
cana-5720	51	4	49	49	NUM
cana-5720	51	5	]	]	SYM
cana-5720	51	6	)	)	PUNCT
cana-5720	51	7	if	if	SCONJ
cana-5720	51	8	f(u	f(u	PROPN
cana-5720	51	9	)	)	PUNCT
cana-5720	51	10	is	be	AUX
cana-5720	51	11	open	open	ADJ
cana-5720	51	12	(	(	PUNCT
cana-5720	51	13	resp	resp	NOUN
cana-5720	51	14	.	.	PUNCT
cana-5720	52	1	-open	-open	PROPN
cana-5720	52	2	)	)	PUNCT
cana-5720	53	1	in	in	ADP
cana-5720	53	2	y	y	PROPN
cana-5720	53	3	for	for	ADP
cana-5720	53	4	every	every	DET
cana-5720	53	5	regular	regular	ADJ
cana-5720	53	6	open	open	ADJ
cana-5720	53	7	set	set	NOUN
cana-5720	53	8	u	u	NOUN
cana-5720	53	9	of	of	ADP
cana-5720	53	10	x	x	PRON
cana-5720	53	11	;	;	PUNCT
cana-5720	53	12	(	(	PUNCT
cana-5720	53	13	iii	iii	X
cana-5720	53	14	)	)	PUNCT
cana-5720	53	15	-open	-open	PROPN
cana-5720	54	1	[	[	X
cana-5720	54	2	8	8	X
cana-5720	54	3	]	]	X
cana-5720	54	4	if	if	SCONJ
cana-5720	54	5	f(u	f(u	PROPN
cana-5720	54	6	)	)	PUNCT
cana-5720	54	7	is	be	AUX
cana-5720	54	8	-open	-open	PROPN
cana-5720	54	9	in	in	ADP
cana-5720	54	10	y	y	PROPN
cana-5720	54	11	for	for	ADP
cana-5720	54	12	every	every	DET
cana-5720	54	13	open	open	ADJ
cana-5720	54	14	set	set	NOUN
cana-5720	54	15	u	u	NOUN
cana-5720	54	16	of	of	ADP
cana-5720	54	17	x	x	PRON
cana-5720	54	18	;	;	PUNCT
cana-5720	54	19	(	(	PUNCT
cana-5720	54	20	iv	iv	X
cana-5720	54	21	)	)	PUNCT
cana-5720	54	22	almost	almost	ADV
cana-5720	54	23	g	g	ADV
cana-5720	54	24	-	-	PUNCT
cana-5720	54	25	closed	closed	ADJ
cana-5720	54	26	[	[	X
cana-5720	54	27	9	9	NUM
cana-5720	54	28	]	]	X
cana-5720	54	29	if	if	SCONJ
cana-5720	54	30	f(u	f(u	PROPN
cana-5720	54	31	)	)	PUNCT
cana-5720	54	32	is	be	AUX
cana-5720	54	33	g	g	ADV
cana-5720	54	34	-	-	PUNCT
cana-5720	54	35	closed	closed	ADJ
cana-5720	54	36	in	in	ADP
cana-5720	54	37	y	y	PROPN
cana-5720	54	38	for	for	ADP
cana-5720	54	39	every	every	DET
cana-5720	54	40	regular	regular	ADJ
cana-5720	54	41	closed	close	VERB
cana-5720	54	42	set	set	NOUN
cana-5720	54	43	u	u	NOUN
cana-5720	54	44	of	of	ADP
cana-5720	54	45	x.	x.	PROPN
cana-5720	54	46	communications	communication	NOUN
cana-5720	54	47	on	on	ADP
cana-5720	54	48	applied	apply	VERB
cana-5720	54	49	nonlinear	nonlinear	ADJ
cana-5720	54	50	analysis	analysis	NOUN
cana-5720	54	51	issn	issn	NOUN
cana-5720	54	52	:	:	PUNCT
cana-5720	54	53	1074	1074	NUM
cana-5720	54	54	-	-	PUNCT
cana-5720	54	55	133x	133x	NUM
cana-5720	54	56	vol	vol	VERB
cana-5720	54	57	32	32	NUM
cana-5720	54	58	no	no	NOUN
cana-5720	54	59	.	.	PUNCT
cana-5720	55	1	10s	10	NOUN
cana-5720	55	2	(	(	PUNCT
cana-5720	55	3	2025	2025	NUM
cana-5720	55	4	)	)	PUNCT
cana-5720	55	5	2803	2803	NUM
cana-5720	55	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5720	56	1	lemma	lemma	PROPN
cana-5720	56	2	2.7	2.7	NUM
cana-5720	56	3	[	[	X
cana-5720	56	4	9	9	NUM
cana-5720	56	5	]	]	X
cana-5720	56	6	if	if	SCONJ
cana-5720	56	7	a	a	DET
cana-5720	56	8	function	function	NOUN
cana-5720	56	9	f	f	NOUN
cana-5720	56	10	:	:	PUNCT
cana-5720	56	11	x	x	X
cana-5720	56	12	→	→	SYM
cana-5720	56	13	y	y	PROPN
cana-5720	56	14	is	be	AUX
cana-5720	56	15	almost	almost	ADV
cana-5720	56	16	continuous	continuous	ADJ
cana-5720	56	17	almost	almost	ADV
cana-5720	56	18	-open	-open	PROPN
cana-5720	56	19	and	and	CCONJ
cana-5720	56	20	v	v	NOUN
cana-5720	56	21	is	be	AUX
cana-5720	56	22	regular	regular	ADJ
cana-5720	56	23	open	open	ADJ
cana-5720	56	24	in	in	ADP
cana-5720	56	25	y	y	PROPN
cana-5720	56	26	,	,	PUNCT
cana-5720	56	27	then	then	ADV
cana-5720	56	28	f-1(v	f-1(v	NOUN
cana-5720	56	29	)	)	PUNCT
cana-5720	56	30	is	be	AUX
cana-5720	56	31	regular	regular	ADJ
cana-5720	56	32	open	open	ADJ
cana-5720	56	33	in	in	ADP
cana-5720	56	34	x.	x.	PROPN
cana-5720	56	35	lemma	lemma	PROPN
cana-5720	56	36	2.8	2.8	NUM
cana-5720	56	37	(	(	PUNCT
cana-5720	56	38	i	i	NOUN
cana-5720	56	39	)	)	PUNCT
cana-5720	56	40	a	a	DET
cana-5720	56	41	subset	subset	NOUN
cana-5720	56	42	a	a	PRON
cana-5720	56	43	of	of	ADP
cana-5720	56	44	a	a	DET
cana-5720	56	45	space	space	NOUN
cana-5720	56	46	x	x	PUNCT
cana-5720	56	47	is	be	AUX
cana-5720	56	48	rg	rg	ADJ
cana-5720	56	49	-	-	ADJ
cana-5720	56	50	open	open	ADJ
cana-5720	56	51	if	if	SCONJ
cana-5720	56	52	and	and	CCONJ
cana-5720	56	53	only	only	ADV
cana-5720	56	54	if	if	SCONJ
cana-5720	56	55	f	f	PROPN
cana-5720	56	56			PROPN
cana-5720	56	57	int(a	int(a	PROPN
cana-5720	56	58	)	)	PUNCT
cana-5720	57	1	whenever	whenever	SCONJ
cana-5720	57	2	f	f	PROPN
cana-5720	57	3			PROPN
cana-5720	57	4	rc	rc	PROPN
cana-5720	57	5	(	(	PUNCT
cana-5720	57	6	x	x	NOUN
cana-5720	57	7	)	)	PUNCT
cana-5720	57	8	and	and	CCONJ
cana-5720	57	9	f	f	X
cana-5720	57	10			PROPN
cana-5720	57	11	a	a	PRON
cana-5720	58	1	[	[	X
cana-5720	58	2	9	9	NUM
cana-5720	58	3	]	]	PUNCT
cana-5720	58	4	.	.	PUNCT
cana-5720	59	1	(	(	PUNCT
cana-5720	59	2	ii	ii	NOUN
cana-5720	59	3	)	)	PUNCT
cana-5720	59	4	every	every	DET
cana-5720	59	5	gs	gs	ADV
cana-5720	59	6	-	-	PUNCT
cana-5720	59	7	closed	closed	ADJ
cana-5720	59	8	set	set	NOUN
cana-5720	59	9	is	be	AUX
cana-5720	59	10	g	g	ADV
cana-5720	59	11	-	-	PUNCT
cana-5720	59	12	closed	closed	ADJ
cana-5720	59	13	but	but	CCONJ
cana-5720	59	14	not	not	PART
cana-5720	59	15	conversely	conversely	ADV
cana-5720	59	16	[	[	X
cana-5720	59	17	14	14	NUM
cana-5720	59	18	]	]	PUNCT
cana-5720	59	19	.	.	PUNCT
cana-5720	60	1	(	(	PUNCT
cana-5720	60	2	iii	iii	X
cana-5720	60	3	)	)	PUNCT
cana-5720	60	4	every	every	DET
cana-5720	60	5	g	g	ADV
cana-5720	60	6	-	-	PUNCT
cana-5720	60	7	closed	closed	ADJ
cana-5720	60	8	set	set	NOUN
cana-5720	60	9	is	be	AUX
cana-5720	60	10	rg	rg	NOUN
cana-5720	60	11	-	-	PUNCT
cana-5720	60	12	closed	closed	ADJ
cana-5720	60	13	but	but	CCONJ
cana-5720	60	14	not	not	PART
cana-5720	60	15	conversely	conversely	ADV
cana-5720	60	16	[	[	X
cana-5720	60	17	9	9	NUM
cana-5720	60	18	]	]	PUNCT
cana-5720	60	19	.	.	PUNCT
cana-5720	61	1	definition	definition	NOUN
cana-5720	61	2	2.9	2.9	NUM
cana-5720	61	3	a	a	DET
cana-5720	61	4	space	space	NOUN
cana-5720	61	5	x	x	PUNCT
cana-5720	61	6	is	be	AUX
cana-5720	61	7	said	say	VERB
cana-5720	61	8	to	to	PART
cana-5720	61	9	be	be	AUX
cana-5720	61	10	(	(	PUNCT
cana-5720	61	11	i	i	NOUN
cana-5720	61	12	)	)	PUNCT
cana-5720	62	1	almost	almost	ADV
cana-5720	62	2	regular	regular	ADJ
cana-5720	62	3	[	[	X
cana-5720	62	4	16	16	NUM
cana-5720	62	5	]	]	X
cana-5720	62	6	if	if	SCONJ
cana-5720	62	7	for	for	ADP
cana-5720	62	8	each	each	DET
cana-5720	62	9	f	f	PROPN
cana-5720	62	10			PROPN
cana-5720	62	11	rc	rc	PROPN
cana-5720	62	12	(	(	PUNCT
cana-5720	62	13	x	x	NOUN
cana-5720	62	14	)	)	PUNCT
cana-5720	62	15	and	and	CCONJ
cana-5720	62	16	each	each	DET
cana-5720	62	17	x	x	ADJ
cana-5720	62	18			NOUN
cana-5720	62	19	x	x	X
cana-5720	62	20	−	−	PROPN
cana-5720	63	1	f	f	X
cana-5720	63	2	,	,	PUNCT
cana-5720	63	3	there	there	PRON
cana-5720	63	4	exist	exist	VERB
cana-5720	63	5	disjoint	disjoint	ADJ
cana-5720	63	6	open	open	ADJ
cana-5720	63	7	sets	set	NOUN
cana-5720	63	8	u	u	NOUN
cana-5720	63	9	and	and	CCONJ
cana-5720	63	10	v	v	NOUN
cana-5720	63	11	of	of	ADP
cana-5720	63	12	x	x	PUNCT
cana-5720	63	13	such	such	ADJ
cana-5720	63	14	that	that	SCONJ
cana-5720	63	15	x	x	SYM
cana-5720	63	16			NOUN
cana-5720	63	17	u	u	NOUN
cana-5720	63	18	and	and	CCONJ
cana-5720	63	19	f	f	PROPN
cana-5720	63	20			PROPN
cana-5720	63	21	v	v	PROPN
cana-5720	63	22	;	;	PUNCT
cana-5720	63	23	(	(	PUNCT
cana-5720	63	24	ii	ii	NOUN
cana-5720	63	25	)	)	PUNCT
cana-5720	63	26	quasi	quasi	NOUN
cana-5720	63	27	-	-	ADJ
cana-5720	63	28	regular	regular	ADJ
cana-5720	63	29	[	[	X
cana-5720	63	30	12	12	NUM
cana-5720	63	31	]	]	X
cana-5720	63	32	if	if	SCONJ
cana-5720	63	33	for	for	ADP
cana-5720	63	34	every	every	DET
cana-5720	63	35	nonempty	nonempty	ADJ
cana-5720	63	36	open	open	ADJ
cana-5720	63	37	set	set	VERB
cana-5720	63	38	v	v	NOUN
cana-5720	63	39	of	of	ADP
cana-5720	63	40	x	x	NOUN
cana-5720	63	41	,	,	PUNCT
cana-5720	63	42	there	there	PRON
cana-5720	63	43	exists	exist	VERB
cana-5720	63	44	a	a	DET
cana-5720	63	45	nonempty	nonempty	ADJ
cana-5720	63	46	open	open	ADJ
cana-5720	63	47	set	set	VERB
cana-5720	63	48	u	u	NOUN
cana-5720	63	49	in	in	ADP
cana-5720	63	50	x	x	SYM
cana-5720	63	51	such	such	ADJ
cana-5720	63	52	that	that	DET
cana-5720	63	53	cl(u	cl(u	NOUN
cana-5720	63	54	)	)	PUNCT
cana-5720	63	55			PROPN
cana-5720	63	56	v	v	ADP
cana-5720	63	57	;	;	PUNCT
cana-5720	63	58	(	(	PUNCT
cana-5720	63	59	iii	iii	NOUN
cana-5720	63	60	)	)	PUNCT
cana-5720	63	61	strongly	strongly	ADV
cana-5720	63	62	s	s	NOUN
cana-5720	63	63	-	-	ADJ
cana-5720	63	64	regular	regular	ADJ
cana-5720	63	65	[	[	X
cana-5720	63	66	3	3	NUM
cana-5720	63	67	]	]	X
cana-5720	63	68	if	if	SCONJ
cana-5720	63	69	for	for	ADP
cana-5720	63	70	any	any	DET
cana-5720	63	71	closed	closed	ADJ
cana-5720	63	72	set	set	NOUN
cana-5720	63	73	a	a	PRON
cana-5720	63	74	of	of	ADP
cana-5720	63	75	x	x	X
cana-5720	63	76	and	and	CCONJ
cana-5720	63	77	any	any	DET
cana-5720	63	78	point	point	NOUN
cana-5720	63	79	x	x	PUNCT
cana-5720	63	80			NOUN
cana-5720	63	81	x	x	X
cana-5720	63	82	−	−	NOUN
cana-5720	63	83	a	a	PRON
cana-5720	63	84	there	there	PRON
cana-5720	63	85	exists	exist	VERB
cana-5720	63	86	an	an	DET
cana-5720	63	87	f	f	PROPN
cana-5720	63	88			PROPN
cana-5720	63	89	rc	rc	PROPN
cana-5720	63	90	(	(	PUNCT
cana-5720	63	91	x	x	X
cana-5720	63	92	)	)	PUNCT
cana-5720	63	93	such	such	ADJ
cana-5720	63	94	that	that	SCONJ
cana-5720	63	95	x	x	PRON
cana-5720	63	96			PROPN
cana-5720	63	97	f	f	PROPN
cana-5720	63	98	and	and	CCONJ
cana-5720	63	99	f	f	PROPN
cana-5720	63	100			PUNCT
cana-5720	63	101	a	a	PRON
cana-5720	63	102	=	=	PUNCT
cana-5720	63	103	.	.	NOUN
cana-5720	63	104	definition	definition	NOUN
cana-5720	63	105	2.10	2.10	NUM
cana-5720	63	106	a	a	DET
cana-5720	63	107	function	function	NOUN
cana-5720	63	108	f	f	NOUN
cana-5720	63	109	:	:	PUNCT
cana-5720	63	110	x	x	X
cana-5720	63	111	→	→	SYM
cana-5720	63	112	y	y	PROPN
cana-5720	63	113	is	be	AUX
cana-5720	63	114	said	say	VERB
cana-5720	63	115	to	to	PART
cana-5720	63	116	be	be	AUX
cana-5720	63	117	(	(	PUNCT
cana-5720	63	118	i	i	NOUN
cana-5720	63	119	)	)	PUNCT
cana-5720	63	120	feebly	feebly	ADV
cana-5720	63	121	continuous	continuous	ADJ
cana-5720	63	122	[	[	X
cana-5720	63	123	2	2	NUM
cana-5720	63	124	]	]	X
cana-5720	63	125	if	if	SCONJ
cana-5720	63	126	int(f-1(v	int(f-1(v	NOUN
cana-5720	63	127	)	)	PUNCT
cana-5720	63	128	)	)	PUNCT
cana-5720	64	1			VERB
cana-5720	64	2			NOUN
cana-5720	64	3	for	for	ADP
cana-5720	64	4	every	every	DET
cana-5720	64	5	nonempty	nonempty	ADJ
cana-5720	64	6	open	open	ADJ
cana-5720	64	7	set	set	VERB
cana-5720	64	8	v	v	NOUN
cana-5720	64	9	of	of	ADP
cana-5720	64	10	y	y	PROPN
cana-5720	64	11	;	;	PUNCT
cana-5720	64	12	(	(	PUNCT
cana-5720	64	13	ii	ii	NOUN
cana-5720	64	14	)	)	PUNCT
cana-5720	64	15	feebly	feebly	ADV
cana-5720	64	16	open	open	ADJ
cana-5720	64	17	[	[	X
cana-5720	64	18	2	2	NUM
cana-5720	64	19	]	]	PUNCT
cana-5720	64	20	if	if	SCONJ
cana-5720	64	21	int(f(u	int(f(u	PROPN
cana-5720	64	22	)	)	PUNCT
cana-5720	64	23	)	)	PUNCT
cana-5720	65	1			VERB
cana-5720	65	2			NOUN
cana-5720	65	3	for	for	ADP
cana-5720	65	4	every	every	DET
cana-5720	65	5	nonempty	nonempty	ADJ
cana-5720	65	6	open	open	ADJ
cana-5720	65	7	set	set	VERB
cana-5720	65	8	u	u	NOUN
cana-5720	65	9	of	of	ADP
cana-5720	65	10	x	x	PRON
cana-5720	65	11	;	;	PUNCT
cana-5720	65	12	(	(	PUNCT
cana-5720	65	13	iii	iii	NOUN
cana-5720	65	14	)	)	PUNCT
cana-5720	65	15	almost	almost	ADV
cana-5720	65	16	feebly	feebly	ADV
cana-5720	65	17	open	open	ADJ
cana-5720	66	1	[	[	X
cana-5720	66	2	9	9	NUM
cana-5720	66	3	]	]	X
cana-5720	66	4	if	if	SCONJ
cana-5720	66	5	int(f(u	int(f(u	PROPN
cana-5720	66	6	)	)	PUNCT
cana-5720	66	7	)	)	PUNCT
cana-5720	67	1			VERB
cana-5720	67	2			NOUN
cana-5720	67	3	for	for	ADP
cana-5720	67	4	every	every	DET
cana-5720	67	5	nonempty	nonempty	ADJ
cana-5720	67	6	u	u	NOUN
cana-5720	67	7			NOUN
cana-5720	67	8	ro	ro	X
cana-5720	67	9	(	(	PUNCT
cana-5720	67	10	x	x	NOUN
cana-5720	67	11	)	)	PUNCT
cana-5720	67	12	.	.	PUNCT
cana-5720	68	1	theorem	theorem	VERB
cana-5720	68	2	2.11[9	2.11[9	NUM
cana-5720	68	3	]	]	X
cana-5720	68	4	the	the	DET
cana-5720	68	5	following	follow	VERB
cana-5720	68	6	are	be	AUX
cana-5720	68	7	equivalent	equivalent	ADJ
cana-5720	68	8	for	for	ADP
cana-5720	68	9	a	a	DET
cana-5720	68	10	space	space	NOUN
cana-5720	68	11	(	(	PUNCT
cana-5720	68	12	x	x	X
cana-5720	68	13	,	,	PUNCT
cana-5720	68	14			PROPN
cana-5720	68	15	):	):	PUNCT
cana-5720	68	16	(	(	PUNCT
cana-5720	68	17	i	i	NOUN
cana-5720	68	18	)	)	PUNCT
cana-5720	68	19	(	(	PUNCT
cana-5720	68	20	x	x	X
cana-5720	68	21	,	,	PUNCT
cana-5720	68	22			PROPN
cana-5720	68	23	)	)	PUNCT
cana-5720	68	24	is	be	AUX
cana-5720	68	25	regular	regular	ADJ
cana-5720	68	26	(	(	PUNCT
cana-5720	68	27	resp	resp	NOUN
cana-5720	68	28	.	.	PUNCT
cana-5720	69	1	almost	almost	ADV
cana-5720	69	2	regular	regular	ADV
cana-5720	69	3	)	)	PUNCT
cana-5720	70	1	;	;	PUNCT
cana-5720	70	2	(	(	PUNCT
cana-5720	70	3	ii	ii	NOUN
cana-5720	70	4	)	)	PUNCT
cana-5720	70	5	for	for	ADP
cana-5720	70	6	each	each	DET
cana-5720	70	7	closed	close	VERB
cana-5720	70	8	(	(	PUNCT
cana-5720	70	9	resp	resp	NOUN
cana-5720	70	10	.	.	PUNCT
cana-5720	71	1	regular	regular	ADJ
cana-5720	71	2	closed	closed	ADJ
cana-5720	71	3	)	)	PUNCT
cana-5720	71	4	set	set	NOUN
cana-5720	71	5	f	f	NOUN
cana-5720	71	6	and	and	CCONJ
cana-5720	71	7	each	each	DET
cana-5720	71	8	x	x	ADJ
cana-5720	71	9			NOUN
cana-5720	71	10	x	x	X
cana-5720	71	11	−	−	PROPN
cana-5720	72	1	f	f	X
cana-5720	72	2	,	,	PUNCT
cana-5720	72	3	there	there	PRON
cana-5720	72	4	exist	exist	VERB
cana-5720	72	5	disjoint	disjoint	NOUN
cana-5720	72	6	u	u	NOUN
cana-5720	72	7	,	,	PUNCT
cana-5720	72	8	v	v	ADV
cana-5720	72	9			NOUN
cana-5720	72	10			VERB
cana-5720	72	11	such	such	ADJ
cana-5720	72	12	that	that	SCONJ
cana-5720	72	13	x	x	SYM
cana-5720	72	14			NOUN
cana-5720	72	15	u	u	NOUN
cana-5720	72	16	and	and	CCONJ
cana-5720	72	17	f	f	PROPN
cana-5720	72	18			PROPN
cana-5720	72	19	v	v	PROPN
cana-5720	72	20	;	;	PUNCT
cana-5720	72	21	(	(	PUNCT
cana-5720	72	22	iii)for	iii)for	VERB
cana-5720	72	23	each	each	DET
cana-5720	72	24	open	open	ADJ
cana-5720	72	25	(	(	PUNCT
cana-5720	72	26	resp	resp	NOUN
cana-5720	72	27	.	.	PUNCT
cana-5720	73	1	regular	regular	ADJ
cana-5720	73	2	open	open	NOUN
cana-5720	73	3	)	)	PUNCT
cana-5720	73	4	set	set	VERB
cana-5720	73	5	v	v	NOUN
cana-5720	73	6	and	and	CCONJ
cana-5720	73	7	x	x	NOUN
cana-5720	73	8			NOUN
cana-5720	73	9	v	v	NOUN
cana-5720	73	10	,	,	PUNCT
cana-5720	73	11	there	there	PRON
cana-5720	73	12	exists	exist	VERB
cana-5720	73	13	u	u	NOUN
cana-5720	73	14			NOUN
cana-5720	73	15			VERB
cana-5720	73	16	such	such	ADJ
cana-5720	73	17	that	that	SCONJ
cana-5720	73	18	x	x	SYM
cana-5720	73	19			NOUN
cana-5720	73	20	u	u	NOUN
cana-5720	73	21			PROPN
cana-5720	73	22	cl(u	cl(u	PROPN
cana-5720	73	23	)	)	PUNCT
cana-5720	74	1			PROPN
cana-5720	74	2	v.	v.	ADP
cana-5720	74	3	3	3	X
cana-5720	74	4	.	.	PUNCT
cana-5720	74	5	almost	almost	ADV
cana-5720	74	6	gωα	gωα	NOUN
cana-5720	74	7	-closed	-close	VERB
cana-5720	74	8	functions	function	NOUN
cana-5720	74	9	definition	definition	NOUN
cana-5720	74	10	3.1	3.1	NUM
cana-5720	74	11	a	a	DET
cana-5720	74	12	function	function	NOUN
cana-5720	74	13	f	f	NOUN
cana-5720	74	14	:	:	PUNCT
cana-5720	74	15	(	(	PUNCT
cana-5720	74	16	x	x	X
cana-5720	74	17	,	,	PUNCT
cana-5720	74	18			PROPN
cana-5720	74	19	)	)	PUNCT
cana-5720	74	20	→	→	SYM
cana-5720	74	21	(	(	PUNCT
cana-5720	74	22	y	y	NOUN
cana-5720	74	23	,	,	PUNCT
cana-5720	74	24			PRON
cana-5720	74	25	)	)	PUNCT
cana-5720	74	26	is	be	AUX
cana-5720	74	27	said	say	VERB
cana-5720	74	28	to	to	PART
cana-5720	74	29	be	be	AUX
cana-5720	74	30	almost	almost	ADV
cana-5720	74	31	gωαclosed	gωαclose	VERB
cana-5720	74	32	if	if	SCONJ
cana-5720	74	33	for	for	ADP
cana-5720	74	34	each	each	DET
cana-5720	74	35	f	f	NOUN
cana-5720	74	36	rc(x	rc(x	NOUN
cana-5720	74	37	,	,	PUNCT
cana-5720	74	38			PROPN
cana-5720	74	39	)	)	PUNCT
cana-5720	74	40	,	,	PUNCT
cana-5720	74	41	f(f	f(f	PROPN
cana-5720	74	42	)	)	PUNCT
cana-5720	74	43	is	be	AUX
cana-5720	74	44	gωα	gωα	VERB
cana-5720	74	45	-	-	PUNCT
cana-5720	74	46	closed	closed	ADJ
cana-5720	74	47	.	.	PUNCT
cana-5720	75	1	theorem	theorem	VERB
cana-5720	75	2	:	:	PUNCT
cana-5720	75	3	3.2	3.2	NUM
cana-5720	75	4	every	every	DET
cana-5720	75	5	almost	almost	ADV
cana-5720	75	6	closed	close	VERB
cana-5720	75	7	function	function	NOUN
cana-5720	75	8	is	be	AUX
cana-5720	75	9	almost	almost	ADV
cana-5720	75	10	gω	gω	ADP
cana-5720	75	11	closed	closed	ADJ
cana-5720	75	12	function	function	NOUN
cana-5720	75	13	.	.	PUNCT
cana-5720	76	1	communications	communication	NOUN
cana-5720	76	2	on	on	ADP
cana-5720	76	3	applied	apply	VERB
cana-5720	76	4	nonlinear	nonlinear	ADJ
cana-5720	76	5	analysis	analysis	NOUN
cana-5720	76	6	issn	issn	NOUN
cana-5720	76	7	:	:	PUNCT
cana-5720	76	8	1074	1074	NUM
cana-5720	76	9	-	-	PUNCT
cana-5720	76	10	133x	133x	NUM
cana-5720	76	11	vol	vol	VERB
cana-5720	76	12	32	32	NUM
cana-5720	76	13	no	no	NOUN
cana-5720	76	14	.	.	PUNCT
cana-5720	77	1	10s	10	NOUN
cana-5720	77	2	(	(	PUNCT
cana-5720	77	3	2025	2025	NUM
cana-5720	77	4	)	)	PUNCT
cana-5720	77	5	2804	2804	NUM
cana-5720	77	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5720	77	7	proof	proof	NOUN
cana-5720	77	8	let	let	VERB
cana-5720	77	9	f	f	PRON
cana-5720	77	10	be	be	AUX
cana-5720	77	11	regular	regular	ADJ
cana-5720	77	12	closed	closed	ADJ
cana-5720	77	13	space	space	NOUN
cana-5720	77	14	and	and	CCONJ
cana-5720	77	15	a	a	DET
cana-5720	77	16	function	function	NOUN
cana-5720	77	17	f	f	NOUN
cana-5720	77	18	:	:	PUNCT
cana-5720	77	19	(	(	PUNCT
cana-5720	77	20	x	x	X
cana-5720	77	21	,	,	PUNCT
cana-5720	77	22			PROPN
cana-5720	77	23	)	)	PUNCT
cana-5720	77	24	→	→	SYM
cana-5720	77	25	(	(	PUNCT
cana-5720	77	26	y	y	NOUN
cana-5720	77	27	,	,	PUNCT
cana-5720	77	28			PRON
cana-5720	77	29	)	)	PUNCT
cana-5720	77	30	be	be	VERB
cana-5720	77	31	almost	almost	ADV
cana-5720	77	32	closed	close	VERB
cana-5720	77	33	function	function	NOUN
cana-5720	77	34	.	.	PUNCT
cana-5720	78	1	then	then	ADV
cana-5720	78	2	if	if	SCONJ
cana-5720	78	3	for	for	ADP
cana-5720	78	4	each	each	DET
cana-5720	78	5	regular	regular	ADJ
cana-5720	78	6	closed	closed	ADJ
cana-5720	78	7	set	set	VERB
cana-5720	78	8	f	f	NOUN
cana-5720	78	9	,	,	PUNCT
cana-5720	78	10	f(f	f(f	PROPN
cana-5720	78	11	)	)	PUNCT
cana-5720	78	12	is	be	AUX
cana-5720	78	13	closed	close	VERB
cana-5720	78	14	and	and	CCONJ
cana-5720	78	15	every	every	DET
cana-5720	78	16	closed	close	VERB
cana-5720	78	17	set	set	NOUN
cana-5720	78	18	is	be	AUX
cana-5720	78	19	gω	gω	PROPN
cana-5720	78	20	closed	close	VERB
cana-5720	78	21	set	set	NOUN
cana-5720	78	22	.	.	PUNCT
cana-5720	79	1	hence	hence	ADV
cana-5720	79	2	f	f	PROPN
cana-5720	79	3	is	be	AUX
cana-5720	79	4	almost	almost	ADV
cana-5720	79	5	gω	gω	ADP
cana-5720	79	6	closed	closed	ADJ
cana-5720	79	7	function	function	NOUN
cana-5720	79	8	.	.	PUNCT
cana-5720	80	1	the	the	DET
cana-5720	80	2	following	follow	VERB
cana-5720	80	3	example	example	NOUN
cana-5720	80	4	shows	show	VERB
cana-5720	80	5	that	that	SCONJ
cana-5720	80	6	the	the	DET
cana-5720	80	7	converse	converse	NOUN
cana-5720	80	8	of	of	ADP
cana-5720	80	9	the	the	DET
cana-5720	80	10	above	above	ADJ
cana-5720	80	11	theorem	theorem	NOUN
cana-5720	80	12	is	be	AUX
cana-5720	80	13	not	not	PART
cana-5720	80	14	true	true	ADJ
cana-5720	80	15	.	.	PUNCT
cana-5720	81	1	example	example	NOUN
cana-5720	81	2	:	:	PUNCT
cana-5720	81	3	3.3	3.3	NUM
cana-5720	81	4	let	let	VERB
cana-5720	81	5	x	x	SYM
cana-5720	81	6	=	=	PUNCT
cana-5720	81	7	y	y	PROPN
cana-5720	81	8	=	=	PUNCT
cana-5720	81	9	{	{	PUNCT
cana-5720	81	10	a	a	PRON
cana-5720	81	11	,	,	PUNCT
cana-5720	81	12	b	b	NOUN
cana-5720	81	13	,	,	PUNCT
cana-5720	81	14	c	c	NOUN
cana-5720	81	15	}	}	PUNCT
cana-5720	81	16	,	,	PUNCT
cana-5720	81	17			NOUN
cana-5720	81	18	=	=	SYM
cana-5720	81	19	{	{	PUNCT
cana-5720	81	20			NOUN
cana-5720	81	21	,	,	PUNCT
cana-5720	81	22	{	{	PUNCT
cana-5720	81	23	a	a	X
cana-5720	81	24	}	}	PUNCT
cana-5720	81	25	,	,	PUNCT
cana-5720	81	26	{	{	PUNCT
cana-5720	81	27	b	b	NOUN
cana-5720	81	28	}	}	PUNCT
cana-5720	81	29	,	,	PUNCT
cana-5720	81	30	{	{	PUNCT
cana-5720	81	31	a	a	DET
cana-5720	81	32	,	,	PUNCT
cana-5720	81	33	b	b	NOUN
cana-5720	81	34	}	}	PUNCT
cana-5720	81	35	,	,	PUNCT
cana-5720	81	36	x	x	NOUN
cana-5720	81	37	}	}	PUNCT
cana-5720	81	38	and	and	CCONJ
cana-5720	81	39			PROPN
cana-5720	81	40	=	=	SYM
cana-5720	81	41	{	{	PUNCT
cana-5720	81	42			NOUN
cana-5720	81	43	,	,	PUNCT
cana-5720	81	44	{	{	PUNCT
cana-5720	81	45	a	a	DET
cana-5720	81	46	,	,	PUNCT
cana-5720	81	47	b	b	NOUN
cana-5720	81	48	}	}	PUNCT
cana-5720	81	49	,	,	PUNCT
cana-5720	81	50	y	y	PROPN
cana-5720	81	51	}	}	PUNCT
cana-5720	81	52	.	.	PUNCT
cana-5720	82	1	then	then	ADV
cana-5720	82	2	rc(x	rc(x	VERB
cana-5720	82	3	,	,	PUNCT
cana-5720	82	4			PROPN
cana-5720	82	5	)	)	PUNCT
cana-5720	82	6	=	=	SYM
cana-5720	82	7	{	{	PUNCT
cana-5720	82	8			NOUN
cana-5720	82	9	,	,	PUNCT
cana-5720	82	10	{	{	PUNCT
cana-5720	82	11	a	a	PRON
cana-5720	82	12	,	,	PUNCT
cana-5720	82	13	c	c	NOUN
cana-5720	82	14	}	}	PUNCT
cana-5720	82	15	,	,	PUNCT
cana-5720	82	16	{	{	PUNCT
cana-5720	82	17	b	b	X
cana-5720	82	18	,	,	PUNCT
cana-5720	82	19	c	c	NOUN
cana-5720	82	20	}	}	PUNCT
cana-5720	82	21	,	,	PUNCT
cana-5720	82	22	x	x	NOUN
cana-5720	82	23	}	}	PUNCT
cana-5720	82	24	and	and	CCONJ
cana-5720	82	25	gω	gω	PROPN
cana-5720	82	26	closed	close	VERB
cana-5720	82	27	in	in	ADP
cana-5720	82	28	y	y	PROPN
cana-5720	82	29	=	=	PUNCT
cana-5720	82	30	{	{	PUNCT
cana-5720	82	31			NOUN
cana-5720	82	32	,	,	PUNCT
cana-5720	82	33	{	{	PUNCT
cana-5720	82	34	c	c	NOUN
cana-5720	82	35	}	}	PUNCT
cana-5720	82	36	,	,	PUNCT
cana-5720	82	37	{	{	PUNCT
cana-5720	82	38	b	b	X
cana-5720	82	39	,	,	PUNCT
cana-5720	82	40	c	c	NOUN
cana-5720	82	41	}	}	PUNCT
cana-5720	82	42	,	,	PUNCT
cana-5720	82	43	{	{	PUNCT
cana-5720	82	44	a	a	X
cana-5720	82	45	,	,	PUNCT
cana-5720	82	46	c	c	NOUN
cana-5720	82	47	}	}	PUNCT
cana-5720	82	48	,	,	PUNCT
cana-5720	82	49	y	y	PROPN
cana-5720	82	50	}	}	PUNCT
cana-5720	82	51	then	then	ADV
cana-5720	82	52	the	the	DET
cana-5720	82	53	identity	identity	NOUN
cana-5720	82	54	function	function	NOUN
cana-5720	82	55	f	f	NOUN
cana-5720	82	56	:	:	PUNCT
cana-5720	82	57	(	(	PUNCT
cana-5720	82	58	x	x	X
cana-5720	82	59	,	,	PUNCT
cana-5720	82	60			PROPN
cana-5720	82	61	)	)	PUNCT
cana-5720	82	62	→	→	SYM
cana-5720	82	63	(	(	PUNCT
cana-5720	82	64	y	y	NOUN
cana-5720	82	65	,	,	PUNCT
cana-5720	82	66			PRON
cana-5720	82	67	)	)	PUNCT
cana-5720	82	68	is	be	AUX
cana-5720	82	69	almost	almost	ADV
cana-5720	82	70	gω	gω	PROPN
cana-5720	82	71	-closed	-close	VERB
cana-5720	82	72	.	.	PUNCT
cana-5720	83	1	however	however	ADV
cana-5720	83	2	,	,	PUNCT
cana-5720	83	3	it	it	PRON
cana-5720	83	4	is	be	AUX
cana-5720	83	5	not	not	PART
cana-5720	83	6	almost	almost	ADV
cana-5720	83	7	closed	close	VERB
cana-5720	83	8	since	since	SCONJ
cana-5720	83	9	there	there	PRON
cana-5720	83	10	exists	exist	VERB
cana-5720	83	11	{	{	PUNCT
cana-5720	83	12	b	b	NOUN
cana-5720	83	13	,	,	PUNCT
cana-5720	83	14	c	c	NOUN
cana-5720	83	15	}	}	PUNCT
cana-5720	83	16			PROPN
cana-5720	83	17	rc	rc	PROPN
cana-5720	83	18	(	(	PUNCT
cana-5720	83	19	x	x	PROPN
cana-5720	83	20	,	,	PUNCT
cana-5720	83	21			PROPN
cana-5720	83	22	)	)	PUNCT
cana-5720	83	23	such	such	ADJ
cana-5720	83	24	that	that	SCONJ
cana-5720	83	25	f({b	f({b	ADJ
cana-5720	83	26	,	,	PUNCT
cana-5720	83	27	c	c	NOUN
cana-5720	83	28	}	}	PUNCT
cana-5720	83	29	)	)	PUNCT
cana-5720	84	1	=	=	PRON
cana-5720	84	2	{	{	PUNCT
cana-5720	84	3	b	b	NOUN
cana-5720	84	4	,	,	PUNCT
cana-5720	84	5	c	c	NOUN
cana-5720	84	6	}	}	PUNCT
cana-5720	84	7	is	be	AUX
cana-5720	84	8	not	not	PART
cana-5720	84	9	closed	close	VERB
cana-5720	84	10	in	in	ADP
cana-5720	84	11	(	(	PUNCT
cana-5720	84	12	y	y	NOUN
cana-5720	84	13	,	,	PUNCT
cana-5720	84	14			PROPN
cana-5720	84	15	)	)	PUNCT
cana-5720	84	16	.	.	PUNCT
cana-5720	85	1	theorem	theorem	VERB
cana-5720	85	2	:	:	PUNCT
cana-5720	85	3	3.4	3.4	NUM
cana-5720	85	4	every	every	DET
cana-5720	85	5	almost	almost	ADV
cana-5720	85	6	α	α	ADV
cana-5720	85	7	-	-	PUNCT
cana-5720	85	8	closed	closed	ADJ
cana-5720	85	9	function	function	NOUN
cana-5720	85	10	is	be	AUX
cana-5720	85	11	almost	almost	ADV
cana-5720	85	12	gωα	gωα	NOUN
cana-5720	85	13	closed	closed	ADJ
cana-5720	85	14	function	function	NOUN
cana-5720	85	15	.	.	PUNCT
cana-5720	86	1	proof	proof	NOUN
cana-5720	86	2	let	let	VERB
cana-5720	86	3	f	f	PRON
cana-5720	86	4	be	be	AUX
cana-5720	86	5	regular	regular	ADJ
cana-5720	86	6	closed	closed	ADJ
cana-5720	86	7	space	space	NOUN
cana-5720	86	8	and	and	CCONJ
cana-5720	86	9	a	a	DET
cana-5720	86	10	function	function	NOUN
cana-5720	86	11	f	f	NOUN
cana-5720	86	12	:	:	PUNCT
cana-5720	86	13	(	(	PUNCT
cana-5720	86	14	x	x	X
cana-5720	86	15	,	,	PUNCT
cana-5720	86	16			PROPN
cana-5720	86	17	)	)	PUNCT
cana-5720	86	18	→	→	SYM
cana-5720	86	19	(	(	PUNCT
cana-5720	86	20	y	y	NOUN
cana-5720	86	21	,	,	PUNCT
cana-5720	86	22			PRON
cana-5720	86	23	)	)	PUNCT
cana-5720	86	24	be	be	VERB
cana-5720	86	25	almost	almost	ADV
cana-5720	86	26	α	α	ADV
cana-5720	86	27	-	-	PUNCT
cana-5720	86	28	closed	closed	ADJ
cana-5720	86	29	function	function	NOUN
cana-5720	86	30	.	.	PUNCT
cana-5720	87	1	then	then	ADV
cana-5720	87	2	if	if	SCONJ
cana-5720	87	3	for	for	ADP
cana-5720	87	4	each	each	DET
cana-5720	87	5	regular	regular	ADJ
cana-5720	87	6	closed	closed	ADJ
cana-5720	87	7	set	set	VERB
cana-5720	87	8	f	f	NOUN
cana-5720	87	9	,	,	PUNCT
cana-5720	87	10	f(f	f(f	PROPN
cana-5720	87	11	)	)	PUNCT
cana-5720	87	12	is	be	AUX
cana-5720	87	13	α	α	NOUN
cana-5720	87	14	-	-	PUNCT
cana-5720	87	15	closed	closed	ADJ
cana-5720	87	16	and	and	CCONJ
cana-5720	87	17	every	every	DET
cana-5720	87	18	α	α	X
cana-5720	87	19	-	-	PUNCT
cana-5720	87	20	closed	closed	ADJ
cana-5720	87	21	set	set	NOUN
cana-5720	87	22	is	be	AUX
cana-5720	87	23	gω	gω	PROPN
cana-5720	87	24	closed	close	VERB
cana-5720	87	25	set	set	NOUN
cana-5720	87	26	.	.	PUNCT
cana-5720	88	1	hence	hence	ADV
cana-5720	88	2	f	f	PROPN
cana-5720	88	3	is	be	AUX
cana-5720	88	4	almost	almost	ADV
cana-5720	88	5	gωα	gωα	NOUN
cana-5720	88	6	closed	closed	ADJ
cana-5720	88	7	function	function	NOUN
cana-5720	88	8	.	.	PUNCT
cana-5720	89	1	the	the	DET
cana-5720	89	2	following	follow	VERB
cana-5720	89	3	example	example	NOUN
cana-5720	89	4	shows	show	VERB
cana-5720	89	5	that	that	SCONJ
cana-5720	89	6	the	the	DET
cana-5720	89	7	converse	converse	NOUN
cana-5720	89	8	of	of	ADP
cana-5720	89	9	the	the	DET
cana-5720	89	10	above	above	ADJ
cana-5720	89	11	theorem	theorem	NOUN
cana-5720	89	12	is	be	AUX
cana-5720	89	13	not	not	PART
cana-5720	89	14	true	true	ADJ
cana-5720	89	15	.	.	PUNCT
cana-5720	90	1	example	example	NOUN
cana-5720	90	2	:	:	PUNCT
cana-5720	90	3	3.5	3.5	NUM
cana-5720	90	4	let	let	VERB
cana-5720	90	5	x	x	PUNCT
cana-5720	90	6	=	=	PUNCT
cana-5720	90	7	y	y	PROPN
cana-5720	90	8	=	=	PUNCT
cana-5720	90	9	{	{	PUNCT
cana-5720	90	10	a	a	PRON
cana-5720	90	11	,	,	PUNCT
cana-5720	90	12	b	b	NOUN
cana-5720	90	13	,	,	PUNCT
cana-5720	90	14	c	c	NOUN
cana-5720	90	15	}	}	PUNCT
cana-5720	90	16	,	,	PUNCT
cana-5720	90	17			NOUN
cana-5720	90	18	=	=	SYM
cana-5720	90	19	{	{	PUNCT
cana-5720	90	20			NOUN
cana-5720	90	21	,	,	PUNCT
cana-5720	90	22	{	{	PUNCT
cana-5720	90	23	a	a	X
cana-5720	90	24	}	}	PUNCT
cana-5720	90	25	,	,	PUNCT
cana-5720	90	26	{	{	PUNCT
cana-5720	90	27	b	b	NOUN
cana-5720	90	28	}	}	PUNCT
cana-5720	90	29	,	,	PUNCT
cana-5720	90	30	{	{	PUNCT
cana-5720	90	31	a	a	DET
cana-5720	90	32	,	,	PUNCT
cana-5720	90	33	b	b	NOUN
cana-5720	90	34	}	}	PUNCT
cana-5720	90	35	,	,	PUNCT
cana-5720	90	36	{	{	PUNCT
cana-5720	90	37	a	a	DET
cana-5720	90	38	,	,	PUNCT
cana-5720	90	39	c}x	c}x	NOUN
cana-5720	90	40	}	}	PUNCT
cana-5720	90	41	and	and	CCONJ
cana-5720	90	42			PROPN
cana-5720	90	43	=	=	SYM
cana-5720	90	44	{	{	PUNCT
cana-5720	90	45			NOUN
cana-5720	90	46	,	,	PUNCT
cana-5720	90	47	{	{	PUNCT
cana-5720	90	48	a	a	DET
cana-5720	90	49	,	,	PUNCT
cana-5720	90	50	b	b	NOUN
cana-5720	90	51	}	}	PUNCT
cana-5720	90	52	,	,	PUNCT
cana-5720	90	53	y	y	PROPN
cana-5720	90	54	}	}	PUNCT
cana-5720	90	55	.	.	PUNCT
cana-5720	91	1	then	then	ADV
cana-5720	91	2	rc(x	rc(x	VERB
cana-5720	91	3	,	,	PUNCT
cana-5720	91	4			PROPN
cana-5720	91	5	)	)	PUNCT
cana-5720	91	6	=	=	SYM
cana-5720	91	7	{	{	PUNCT
cana-5720	91	8			NOUN
cana-5720	91	9	,	,	PUNCT
cana-5720	91	10	{	{	PUNCT
cana-5720	91	11	a	a	PRON
cana-5720	91	12	,	,	PUNCT
cana-5720	91	13	c	c	NOUN
cana-5720	91	14	}	}	PUNCT
cana-5720	91	15	,	,	PUNCT
cana-5720	91	16	{	{	PUNCT
cana-5720	91	17	b	b	X
cana-5720	91	18	,	,	PUNCT
cana-5720	91	19	c	c	NOUN
cana-5720	91	20	}	}	PUNCT
cana-5720	91	21	,	,	PUNCT
cana-5720	91	22	x	x	X
cana-5720	91	23	}	}	PUNCT
cana-5720	91	24	,	,	PUNCT
cana-5720	91	25	αclosed	αclose	VERB
cana-5720	91	26	in	in	ADP
cana-5720	91	27	y	y	PROPN
cana-5720	91	28	=	=	PUNCT
cana-5720	91	29	{	{	PUNCT
cana-5720	91	30			NOUN
cana-5720	91	31	,	,	PUNCT
cana-5720	91	32	{	{	PUNCT
cana-5720	91	33	c	c	NOUN
cana-5720	91	34	}	}	PUNCT
cana-5720	91	35	,	,	PUNCT
cana-5720	91	36	y	y	PROPN
cana-5720	91	37	}	}	PUNCT
cana-5720	91	38	and	and	CCONJ
cana-5720	91	39	gωα	gωα	PROPN
cana-5720	91	40	closed	close	VERB
cana-5720	91	41	in	in	ADP
cana-5720	91	42	y	y	PROPN
cana-5720	91	43	=	=	PUNCT
cana-5720	91	44	{	{	PUNCT
cana-5720	91	45			NOUN
cana-5720	91	46	,	,	PUNCT
cana-5720	91	47	{	{	PUNCT
cana-5720	91	48	c},{a	c},{a	PROPN
cana-5720	91	49	,	,	PUNCT
cana-5720	91	50	b	b	NOUN
cana-5720	91	51	}	}	PUNCT
cana-5720	91	52	,	,	PUNCT
cana-5720	91	53	y	y	PROPN
cana-5720	91	54	}	}	PUNCT
cana-5720	91	55	then	then	ADV
cana-5720	91	56	the	the	DET
cana-5720	91	57	function	function	NOUN
cana-5720	91	58	f	f	NOUN
cana-5720	91	59	:	:	PUNCT
cana-5720	91	60	(	(	PUNCT
cana-5720	91	61	x	x	X
cana-5720	91	62	,	,	PUNCT
cana-5720	91	63			PROPN
cana-5720	91	64	)	)	PUNCT
cana-5720	91	65	→	→	SYM
cana-5720	91	66	(	(	PUNCT
cana-5720	91	67	y	y	NOUN
cana-5720	91	68	,	,	PUNCT
cana-5720	91	69			NUM
cana-5720	91	70	)	)	PUNCT
cana-5720	91	71	defined	define	VERB
cana-5720	91	72	as	as	ADP
cana-5720	91	73	f(a)=c	f(a)=c	PROPN
cana-5720	91	74	,	,	PUNCT
cana-5720	91	75	f(b)=b	f(b)=b	PROPN
cana-5720	91	76	,	,	PUNCT
cana-5720	91	77	f(c)=c	f(c)=c	PROPN
cana-5720	91	78	is	be	AUX
cana-5720	91	79	almost	almost	ADV
cana-5720	91	80	gωα	gωα	NOUN
cana-5720	91	81	-closed	-close	VERB
cana-5720	91	82	.	.	PUNCT
cana-5720	92	1	however	however	ADV
cana-5720	92	2	,	,	PUNCT
cana-5720	92	3	it	it	PRON
cana-5720	92	4	is	be	AUX
cana-5720	92	5	not	not	PART
cana-5720	92	6	almost	almost	ADV
cana-5720	92	7	α	α	NOUN
cana-5720	92	8	closed	close	VERB
cana-5720	92	9	since	since	SCONJ
cana-5720	92	10	there	there	PRON
cana-5720	92	11	exists	exist	VERB
cana-5720	92	12	{	{	PUNCT
cana-5720	92	13	b	b	NOUN
cana-5720	92	14	,	,	PUNCT
cana-5720	92	15	c	c	NOUN
cana-5720	92	16	}	}	PUNCT
cana-5720	92	17			PROPN
cana-5720	92	18	rc	rc	PROPN
cana-5720	92	19	(	(	PUNCT
cana-5720	92	20	x	x	PROPN
cana-5720	92	21	,	,	PUNCT
cana-5720	92	22			PROPN
cana-5720	92	23	)	)	PUNCT
cana-5720	92	24	such	such	ADJ
cana-5720	92	25	that	that	SCONJ
cana-5720	92	26	f({b	f({b	ADJ
cana-5720	92	27	,	,	PUNCT
cana-5720	92	28	c	c	NOUN
cana-5720	92	29	}	}	PUNCT
cana-5720	92	30	)	)	PUNCT
cana-5720	93	1	=	=	PRON
cana-5720	93	2	{	{	PUNCT
cana-5720	93	3	a	a	DET
cana-5720	93	4	,	,	PUNCT
cana-5720	93	5	b	b	X
cana-5720	93	6	}	}	PUNCT
cana-5720	93	7	is	be	AUX
cana-5720	93	8	αclosed	αclose	VERB
cana-5720	93	9	in	in	ADP
cana-5720	93	10	(	(	PUNCT
cana-5720	93	11	y	y	NOUN
cana-5720	93	12	,	,	PUNCT
cana-5720	93	13			PROPN
cana-5720	93	14	)	)	PUNCT
cana-5720	93	15	.	.	PUNCT
cana-5720	94	1	theorem	theorem	VERB
cana-5720	94	2	:	:	PUNCT
cana-5720	94	3	3.6	3.6	NUM
cana-5720	94	4	every	every	DET
cana-5720	94	5	gω	gω	PROPN
cana-5720	94	6	closed	closed	ADJ
cana-5720	94	7	function	function	NOUN
cana-5720	94	8	is	be	AUX
cana-5720	94	9	almost	almost	ADV
cana-5720	94	10	gω	gω	ADP
cana-5720	94	11	closed	closed	ADJ
cana-5720	94	12	function	function	NOUN
cana-5720	94	13	but	but	CCONJ
cana-5720	94	14	not	not	PART
cana-5720	94	15	conversely	conversely	ADV
cana-5720	94	16	proof	proof	NOUN
cana-5720	94	17	let	let	VERB
cana-5720	94	18	f	f	PRON
cana-5720	94	19	be	be	AUX
cana-5720	94	20	regular	regular	ADJ
cana-5720	94	21	closed	closed	ADJ
cana-5720	94	22	space	space	NOUN
cana-5720	94	23	.	.	PUNCT
cana-5720	95	1	then	then	ADV
cana-5720	95	2	every	every	DET
cana-5720	95	3	regular	regular	ADJ
cana-5720	95	4	closed	closed	ADJ
cana-5720	95	5	set	set	NOUN
cana-5720	95	6	is	be	AUX
cana-5720	95	7	closed	close	VERB
cana-5720	95	8	set	set	VERB
cana-5720	95	9	and	and	CCONJ
cana-5720	95	10	let	let	VERB
cana-5720	95	11	a	a	DET
cana-5720	95	12	function	function	NOUN
cana-5720	95	13	f	f	NOUN
cana-5720	95	14	:	:	PUNCT
cana-5720	95	15	(	(	PUNCT
cana-5720	95	16	x	x	X
cana-5720	95	17	,	,	PUNCT
cana-5720	95	18			PROPN
cana-5720	95	19	)	)	PUNCT
cana-5720	95	20	→	→	SYM
cana-5720	95	21	(	(	PUNCT
cana-5720	95	22	y	y	NOUN
cana-5720	95	23	,	,	PUNCT
cana-5720	95	24			PRON
cana-5720	95	25	)	)	PUNCT
cana-5720	95	26	be	be	VERB
cana-5720	95	27	gω	gω	PROPN
cana-5720	95	28	closed	closed	ADJ
cana-5720	95	29	function	function	NOUN
cana-5720	95	30	.	.	PUNCT
cana-5720	96	1	then	then	ADV
cana-5720	96	2	if	if	SCONJ
cana-5720	96	3	for	for	ADP
cana-5720	96	4	each	each	DET
cana-5720	96	5	closed	close	VERB
cana-5720	96	6	set	set	VERB
cana-5720	96	7	f	f	PROPN
cana-5720	96	8	,	,	PUNCT
cana-5720	96	9	f(f	f(f	PROPN
cana-5720	96	10	)	)	PUNCT
cana-5720	96	11	is	be	AUX
cana-5720	96	12	gω	gω	PROPN
cana-5720	96	13	-	-	PUNCT
cana-5720	96	14	closed	closed	ADJ
cana-5720	96	15	.	.	PUNCT
cana-5720	97	1	hence	hence	ADV
cana-5720	97	2	f	f	PROPN
cana-5720	97	3	is	be	AUX
cana-5720	97	4	almost	almost	ADV
cana-5720	97	5	gω	gω	ADP
cana-5720	97	6	closed	closed	ADJ
cana-5720	97	7	function	function	NOUN
cana-5720	97	8	.	.	PUNCT
cana-5720	98	1	the	the	DET
cana-5720	98	2	following	follow	VERB
cana-5720	98	3	example	example	NOUN
cana-5720	98	4	shows	show	VERB
cana-5720	98	5	that	that	SCONJ
cana-5720	98	6	the	the	DET
cana-5720	98	7	converse	converse	NOUN
cana-5720	98	8	of	of	ADP
cana-5720	98	9	the	the	DET
cana-5720	98	10	above	above	ADJ
cana-5720	98	11	theorem	theorem	NOUN
cana-5720	98	12	is	be	AUX
cana-5720	98	13	not	not	PART
cana-5720	98	14	true	true	ADJ
cana-5720	98	15	.	.	PUNCT
cana-5720	99	1	example	example	NOUN
cana-5720	99	2	3.7	3.7	NUM
cana-5720	99	3	let	let	VERB
cana-5720	99	4	x	x	SYM
cana-5720	99	5	=	=	PUNCT
cana-5720	99	6	y	y	PROPN
cana-5720	99	7	=	=	PUNCT
cana-5720	99	8	{	{	PUNCT
cana-5720	99	9	a	a	PRON
cana-5720	99	10	,	,	PUNCT
cana-5720	99	11	b	b	NOUN
cana-5720	99	12	,	,	PUNCT
cana-5720	99	13	c	c	NOUN
cana-5720	99	14	}	}	PUNCT
cana-5720	99	15	,	,	PUNCT
cana-5720	99	16			NOUN
cana-5720	99	17	=	=	SYM
cana-5720	99	18	{	{	PUNCT
cana-5720	99	19			NOUN
cana-5720	99	20	,	,	PUNCT
cana-5720	99	21	{	{	PUNCT
cana-5720	99	22	a	a	X
cana-5720	99	23	}	}	PUNCT
cana-5720	99	24	,	,	PUNCT
cana-5720	99	25	{	{	PUNCT
cana-5720	99	26	b	b	NOUN
cana-5720	99	27	}	}	PUNCT
cana-5720	99	28	,	,	PUNCT
cana-5720	99	29	{	{	PUNCT
cana-5720	99	30	a	a	DET
cana-5720	99	31	,	,	PUNCT
cana-5720	99	32	b	b	NOUN
cana-5720	99	33	}	}	PUNCT
cana-5720	99	34	,	,	PUNCT
cana-5720	99	35	{	{	PUNCT
cana-5720	99	36	a	a	DET
cana-5720	99	37	,	,	PUNCT
cana-5720	99	38	c}x	c}x	NOUN
cana-5720	99	39	}	}	PUNCT
cana-5720	99	40	and	and	CCONJ
cana-5720	99	41			PROPN
cana-5720	99	42	=	=	SYM
cana-5720	99	43	{	{	PUNCT
cana-5720	99	44			NOUN
cana-5720	99	45	,	,	PUNCT
cana-5720	99	46	{	{	PUNCT
cana-5720	99	47	a	a	DET
cana-5720	99	48	,	,	PUNCT
cana-5720	99	49	b	b	NOUN
cana-5720	99	50	}	}	PUNCT
cana-5720	99	51	,	,	PUNCT
cana-5720	99	52	y	y	PROPN
cana-5720	99	53	}	}	PUNCT
cana-5720	99	54	.	.	PUNCT
cana-5720	100	1	then	then	ADV
cana-5720	100	2	rc(x	rc(x	VERB
cana-5720	100	3	,	,	PUNCT
cana-5720	100	4			PROPN
cana-5720	100	5	)	)	PUNCT
cana-5720	100	6	=	=	SYM
cana-5720	100	7	{	{	PUNCT
cana-5720	100	8			NOUN
cana-5720	100	9	,	,	PUNCT
cana-5720	100	10	{	{	PUNCT
cana-5720	100	11	a	a	PRON
cana-5720	100	12	,	,	PUNCT
cana-5720	100	13	c	c	NOUN
cana-5720	100	14	}	}	PUNCT
cana-5720	100	15	,	,	PUNCT
cana-5720	100	16	{	{	PUNCT
cana-5720	100	17	b	b	X
cana-5720	100	18	,	,	PUNCT
cana-5720	100	19	c	c	NOUN
cana-5720	100	20	}	}	PUNCT
cana-5720	100	21	,	,	PUNCT
cana-5720	100	22	x	x	NOUN
cana-5720	100	23	}	}	PUNCT
cana-5720	100	24	and	and	CCONJ
cana-5720	100	25	gω	gω	PROPN
cana-5720	100	26	closed	close	VERB
cana-5720	100	27	in	in	ADP
cana-5720	100	28	y	y	PROPN
cana-5720	100	29	=	=	PUNCT
cana-5720	100	30	{	{	PUNCT
cana-5720	100	31			NOUN
cana-5720	100	32	,	,	PUNCT
cana-5720	100	33	{	{	PUNCT
cana-5720	100	34	c	c	NOUN
cana-5720	100	35	}	}	PUNCT
cana-5720	100	36	,	,	PUNCT
cana-5720	100	37	{	{	PUNCT
cana-5720	100	38	b	b	X
cana-5720	100	39	,	,	PUNCT
cana-5720	100	40	c	c	NOUN
cana-5720	100	41	}	}	PUNCT
cana-5720	100	42	,	,	PUNCT
cana-5720	100	43	{	{	PUNCT
cana-5720	100	44	a	a	X
cana-5720	100	45	,	,	PUNCT
cana-5720	100	46	c	c	NOUN
cana-5720	100	47	}	}	PUNCT
cana-5720	100	48	,	,	PUNCT
cana-5720	100	49	y	y	PROPN
cana-5720	100	50	}	}	PUNCT
cana-5720	100	51	then	then	ADV
cana-5720	100	52	the	the	DET
cana-5720	100	53	function	function	NOUN
cana-5720	100	54	f	f	NOUN
cana-5720	100	55	:	:	PUNCT
cana-5720	100	56	(	(	PUNCT
cana-5720	100	57	x	x	X
cana-5720	100	58	,	,	PUNCT
cana-5720	100	59			PROPN
cana-5720	100	60	)	)	PUNCT
cana-5720	100	61	→	→	SYM
cana-5720	100	62	(	(	PUNCT
cana-5720	100	63	y	y	NOUN
cana-5720	100	64	,	,	PUNCT
cana-5720	100	65			NUM
cana-5720	100	66	)	)	PUNCT
cana-5720	100	67	defined	define	VERB
cana-5720	100	68	as	as	ADP
cana-5720	100	69	f(a)=c	f(a)=c	PROPN
cana-5720	100	70	,	,	PUNCT
cana-5720	100	71	f(b)=b	f(b)=b	PROPN
cana-5720	100	72	,	,	PUNCT
cana-5720	100	73	f(c)=c	f(c)=c	PROPN
cana-5720	100	74	is	be	AUX
cana-5720	100	75	almost	almost	ADV
cana-5720	100	76	gω	gω	PROPN
cana-5720	100	77	-closed	-close	VERB
cana-5720	100	78	.	.	PUNCT
cana-5720	101	1	however	however	ADV
cana-5720	101	2	,	,	PUNCT
cana-5720	101	3	it	it	PRON
cana-5720	101	4	is	be	AUX
cana-5720	101	5	not	not	PART
cana-5720	101	6	gω	gω	PROPN
cana-5720	101	7	closed	close	VERB
cana-5720	101	8	since	since	SCONJ
cana-5720	101	9	there	there	PRON
cana-5720	101	10	exists	exist	VERB
cana-5720	101	11	{	{	PUNCT
cana-5720	101	12	b	b	NOUN
cana-5720	101	13	}	}	PUNCT
cana-5720	101	14			NOUN
cana-5720	101	15			NOUN
cana-5720	101	16	c	c	PROPN
cana-5720	101	17	such	such	ADJ
cana-5720	101	18	that	that	PRON
cana-5720	101	19	f({b	f({b	ADJ
cana-5720	101	20	}	}	PUNCT
cana-5720	101	21	)	)	PUNCT
cana-5720	102	1	=	=	PRON
cana-5720	102	2	{	{	PUNCT
cana-5720	102	3	b	b	NOUN
cana-5720	102	4	}	}	PUNCT
cana-5720	102	5	is	be	AUX
cana-5720	102	6	not	not	PART
cana-5720	102	7	gω	gω	PROPN
cana-5720	102	8	closed	close	VERB
cana-5720	102	9	in	in	ADP
cana-5720	102	10	(	(	PUNCT
cana-5720	102	11	y	y	NOUN
cana-5720	102	12	,	,	PUNCT
cana-5720	102	13			PROPN
cana-5720	102	14	)	)	PUNCT
cana-5720	102	15	.	.	PUNCT
cana-5720	103	1	theorem	theorem	VERB
cana-5720	103	2	:	:	PUNCT
cana-5720	103	3	3.8	3.8	NUM
cana-5720	103	4	every	every	DET
cana-5720	103	5	gωα	gωα	NOUN
cana-5720	103	6	closed	close	VERB
cana-5720	103	7	function	function	NOUN
cana-5720	103	8	is	be	AUX
cana-5720	103	9	almost	almost	ADV
cana-5720	103	10	gωα	gωα	NOUN
cana-5720	103	11	closed	closed	ADJ
cana-5720	103	12	function	function	NOUN
cana-5720	103	13	.	.	PUNCT
cana-5720	104	1	communications	communication	NOUN
cana-5720	104	2	on	on	ADP
cana-5720	104	3	applied	apply	VERB
cana-5720	104	4	nonlinear	nonlinear	ADJ
cana-5720	104	5	analysis	analysis	NOUN
cana-5720	104	6	issn	issn	NOUN
cana-5720	104	7	:	:	PUNCT
cana-5720	104	8	1074	1074	NUM
cana-5720	104	9	-	-	PUNCT
cana-5720	104	10	133x	133x	NUM
cana-5720	104	11	vol	vol	VERB
cana-5720	104	12	32	32	NUM
cana-5720	104	13	no	no	NOUN
cana-5720	104	14	.	.	PUNCT
cana-5720	105	1	10s	10	NOUN
cana-5720	105	2	(	(	PUNCT
cana-5720	105	3	2025	2025	NUM
cana-5720	105	4	)	)	PUNCT
cana-5720	105	5	2805	2805	NUM
cana-5720	105	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5720	105	7	proof	proof	NOUN
cana-5720	105	8	let	let	VERB
cana-5720	105	9	f	f	PRON
cana-5720	105	10	be	be	AUX
cana-5720	105	11	regular	regular	ADJ
cana-5720	105	12	closed	closed	ADJ
cana-5720	105	13	space	space	NOUN
cana-5720	105	14	.	.	PUNCT
cana-5720	106	1	then	then	ADV
cana-5720	106	2	every	every	DET
cana-5720	106	3	regular	regular	ADJ
cana-5720	106	4	closed	closed	ADJ
cana-5720	106	5	set	set	NOUN
cana-5720	106	6	is	be	AUX
cana-5720	106	7	closed	close	VERB
cana-5720	106	8	set	set	VERB
cana-5720	106	9	and	and	CCONJ
cana-5720	106	10	let	let	VERB
cana-5720	106	11	a	a	DET
cana-5720	106	12	function	function	NOUN
cana-5720	106	13	f	f	NOUN
cana-5720	106	14	:	:	PUNCT
cana-5720	106	15	(	(	PUNCT
cana-5720	106	16	x	x	X
cana-5720	106	17	,	,	PUNCT
cana-5720	106	18			PROPN
cana-5720	106	19	)	)	PUNCT
cana-5720	106	20	→	→	SYM
cana-5720	106	21	(	(	PUNCT
cana-5720	106	22	y	y	NOUN
cana-5720	106	23	,	,	PUNCT
cana-5720	106	24			PRON
cana-5720	106	25	)	)	PUNCT
cana-5720	106	26	be	be	VERB
cana-5720	106	27	gωα	gωα	NOUN
cana-5720	106	28	closed	close	VERB
cana-5720	106	29	function	function	NOUN
cana-5720	106	30	.	.	PUNCT
cana-5720	107	1	then	then	ADV
cana-5720	107	2	if	if	SCONJ
cana-5720	107	3	for	for	ADP
cana-5720	107	4	each	each	DET
cana-5720	107	5	closed	close	VERB
cana-5720	107	6	set	set	VERB
cana-5720	107	7	f	f	PROPN
cana-5720	107	8	,	,	PUNCT
cana-5720	107	9	f(f	f(f	PROPN
cana-5720	107	10	)	)	PUNCT
cana-5720	107	11	is	be	AUX
cana-5720	107	12	gωα	gωα	VERB
cana-5720	107	13	-	-	PUNCT
cana-5720	107	14	closed	closed	ADJ
cana-5720	107	15	.	.	PUNCT
cana-5720	108	1	hence	hence	ADV
cana-5720	108	2	f	f	PROPN
cana-5720	108	3	is	be	AUX
cana-5720	108	4	almost	almost	ADV
cana-5720	108	5	gωα	gωα	NOUN
cana-5720	108	6	closed	closed	ADJ
cana-5720	108	7	function	function	NOUN
cana-5720	108	8	.	.	PUNCT
cana-5720	109	1	the	the	DET
cana-5720	109	2	following	follow	VERB
cana-5720	109	3	example	example	NOUN
cana-5720	109	4	shows	show	VERB
cana-5720	109	5	that	that	SCONJ
cana-5720	109	6	the	the	DET
cana-5720	109	7	converse	converse	NOUN
cana-5720	109	8	of	of	ADP
cana-5720	109	9	the	the	DET
cana-5720	109	10	above	above	ADJ
cana-5720	109	11	theorem	theorem	NOUN
cana-5720	109	12	is	be	AUX
cana-5720	109	13	not	not	PART
cana-5720	109	14	true	true	ADJ
cana-5720	109	15	.	.	PUNCT
cana-5720	110	1	example	example	NOUN
cana-5720	110	2	3.9	3.9	NUM
cana-5720	110	3	let	let	VERB
cana-5720	110	4	x	x	PUNCT
cana-5720	110	5	=	=	PUNCT
cana-5720	110	6	y	y	PROPN
cana-5720	110	7	=	=	PUNCT
cana-5720	110	8	{	{	PUNCT
cana-5720	110	9	a	a	PRON
cana-5720	110	10	,	,	PUNCT
cana-5720	110	11	b	b	NOUN
cana-5720	110	12	,	,	PUNCT
cana-5720	110	13	c	c	NOUN
cana-5720	110	14	}	}	PUNCT
cana-5720	110	15	,	,	PUNCT
cana-5720	110	16			NOUN
cana-5720	110	17	=	=	SYM
cana-5720	110	18	{	{	PUNCT
cana-5720	110	19			NOUN
cana-5720	110	20	,	,	PUNCT
cana-5720	110	21	{	{	PUNCT
cana-5720	110	22	a	a	X
cana-5720	110	23	}	}	PUNCT
cana-5720	110	24	,	,	PUNCT
cana-5720	110	25	{	{	PUNCT
cana-5720	110	26	b	b	NOUN
cana-5720	110	27	}	}	PUNCT
cana-5720	110	28	,	,	PUNCT
cana-5720	110	29	{	{	PUNCT
cana-5720	110	30	a	a	DET
cana-5720	110	31	,	,	PUNCT
cana-5720	110	32	b	b	NOUN
cana-5720	110	33	}	}	PUNCT
cana-5720	110	34	,	,	PUNCT
cana-5720	110	35	{	{	PUNCT
cana-5720	110	36	a	a	DET
cana-5720	110	37	,	,	PUNCT
cana-5720	110	38	c}x	c}x	NOUN
cana-5720	110	39	}	}	PUNCT
cana-5720	110	40	and	and	CCONJ
cana-5720	110	41			PROPN
cana-5720	110	42	=	=	SYM
cana-5720	110	43	{	{	PUNCT
cana-5720	110	44			NOUN
cana-5720	110	45	,	,	PUNCT
cana-5720	110	46	{	{	PUNCT
cana-5720	110	47	a	a	DET
cana-5720	110	48	,	,	PUNCT
cana-5720	110	49	b	b	NOUN
cana-5720	110	50	}	}	PUNCT
cana-5720	110	51	,	,	PUNCT
cana-5720	110	52	y	y	PROPN
cana-5720	110	53	}	}	PUNCT
cana-5720	110	54	.	.	PUNCT
cana-5720	111	1	then	then	ADV
cana-5720	111	2	rc(x	rc(x	VERB
cana-5720	111	3	,	,	PUNCT
cana-5720	111	4			PROPN
cana-5720	111	5	)	)	PUNCT
cana-5720	111	6	=	=	SYM
cana-5720	111	7	{	{	PUNCT
cana-5720	111	8			NOUN
cana-5720	111	9	,	,	PUNCT
cana-5720	111	10	{	{	PUNCT
cana-5720	111	11	a	a	PRON
cana-5720	111	12	,	,	PUNCT
cana-5720	111	13	c	c	NOUN
cana-5720	111	14	}	}	PUNCT
cana-5720	111	15	,	,	PUNCT
cana-5720	111	16	{	{	PUNCT
cana-5720	111	17	b	b	X
cana-5720	111	18	,	,	PUNCT
cana-5720	111	19	c	c	NOUN
cana-5720	111	20	}	}	PUNCT
cana-5720	111	21	,	,	PUNCT
cana-5720	111	22	x	x	NOUN
cana-5720	111	23	}	}	PUNCT
cana-5720	111	24	and	and	CCONJ
cana-5720	111	25	gωα	gωα	PROPN
cana-5720	111	26	closed	close	VERB
cana-5720	111	27	in	in	ADP
cana-5720	111	28	y	y	PROPN
cana-5720	111	29	=	=	PUNCT
cana-5720	111	30	{	{	PUNCT
cana-5720	111	31			NOUN
cana-5720	111	32	,	,	PUNCT
cana-5720	111	33	{	{	PUNCT
cana-5720	111	34	c	c	NOUN
cana-5720	111	35	}	}	PUNCT
cana-5720	111	36	,	,	PUNCT
cana-5720	111	37	{	{	PUNCT
cana-5720	111	38	a	a	DET
cana-5720	111	39	,	,	PUNCT
cana-5720	111	40	b	b	NOUN
cana-5720	111	41	}	}	PUNCT
cana-5720	111	42	,	,	PUNCT
cana-5720	111	43	y	y	PROPN
cana-5720	111	44	}	}	PUNCT
cana-5720	111	45	then	then	ADV
cana-5720	111	46	the	the	DET
cana-5720	111	47	function	function	NOUN
cana-5720	111	48	f	f	NOUN
cana-5720	111	49	:	:	PUNCT
cana-5720	111	50	(	(	PUNCT
cana-5720	111	51	x	x	X
cana-5720	111	52	,	,	PUNCT
cana-5720	111	53			PROPN
cana-5720	111	54	)	)	PUNCT
cana-5720	111	55	→	→	SYM
cana-5720	111	56	(	(	PUNCT
cana-5720	111	57	y	y	NOUN
cana-5720	111	58	,	,	PUNCT
cana-5720	111	59			NUM
cana-5720	111	60	)	)	PUNCT
cana-5720	111	61	defined	define	VERB
cana-5720	111	62	as	as	ADP
cana-5720	111	63	f(a)=c	f(a)=c	PROPN
cana-5720	111	64	,	,	PUNCT
cana-5720	111	65	f(b)=b	f(b)=b	PROPN
cana-5720	111	66	,	,	PUNCT
cana-5720	111	67	f(c)=c	f(c)=c	PROPN
cana-5720	111	68	is	be	AUX
cana-5720	111	69	almost	almost	ADV
cana-5720	111	70	gωα	gωα	NOUN
cana-5720	111	71	-closed	-close	VERB
cana-5720	111	72	.	.	PUNCT
cana-5720	112	1	however	however	ADV
cana-5720	112	2	,	,	PUNCT
cana-5720	112	3	it	it	PRON
cana-5720	112	4	is	be	AUX
cana-5720	112	5	not	not	PART
cana-5720	112	6	gω	gω	PROPN
cana-5720	112	7	closed	close	VERB
cana-5720	112	8	since	since	SCONJ
cana-5720	112	9	there	there	PRON
cana-5720	112	10	exists	exist	VERB
cana-5720	112	11	{	{	PUNCT
cana-5720	112	12	b	b	NOUN
cana-5720	112	13	}	}	PUNCT
cana-5720	112	14			NOUN
cana-5720	112	15			NOUN
cana-5720	112	16	c	c	PROPN
cana-5720	112	17	such	such	ADJ
cana-5720	112	18	that	that	PRON
cana-5720	112	19	f({b	f({b	ADJ
cana-5720	112	20	}	}	PUNCT
cana-5720	112	21	)	)	PUNCT
cana-5720	113	1	=	=	PRON
cana-5720	113	2	{	{	PUNCT
cana-5720	113	3	b	b	NOUN
cana-5720	113	4	}	}	PUNCT
cana-5720	113	5	is	be	AUX
cana-5720	113	6	not	not	PART
cana-5720	113	7	gωα	gωα	PROPN
cana-5720	113	8	closed	close	VERB
cana-5720	113	9	in	in	ADP
cana-5720	113	10	(	(	PUNCT
cana-5720	113	11	y	y	NOUN
cana-5720	113	12	,	,	PUNCT
cana-5720	113	13			PROPN
cana-5720	113	14	)	)	PUNCT
cana-5720	113	15	.	.	PUNCT
cana-5720	114	1	theorem	theorem	VERB
cana-5720	114	2	:	:	PUNCT
cana-5720	114	3	3.10	3.10	NUM
cana-5720	114	4	every	every	DET
cana-5720	114	5	almost	almost	ADV
cana-5720	114	6	gω	gω	PROPN
cana-5720	114	7	closed	closed	ADJ
cana-5720	114	8	function	function	NOUN
cana-5720	114	9	is	be	AUX
cana-5720	114	10	almost	almost	ADV
cana-5720	114	11	gωα	gωα	NOUN
cana-5720	114	12	closed	closed	ADJ
cana-5720	114	13	function	function	NOUN
cana-5720	114	14	.	.	PUNCT
cana-5720	115	1	proof	proof	NOUN
cana-5720	115	2	let	let	VERB
cana-5720	115	3	f	f	PRON
cana-5720	115	4	be	be	AUX
cana-5720	115	5	regular	regular	ADJ
cana-5720	115	6	closed	closed	ADJ
cana-5720	115	7	space	space	NOUN
cana-5720	115	8	and	and	CCONJ
cana-5720	115	9	a	a	DET
cana-5720	115	10	function	function	NOUN
cana-5720	115	11	f	f	NOUN
cana-5720	115	12	:	:	PUNCT
cana-5720	115	13	(	(	PUNCT
cana-5720	115	14	x	x	X
cana-5720	115	15	,	,	PUNCT
cana-5720	115	16			PROPN
cana-5720	115	17	)	)	PUNCT
cana-5720	115	18	→	→	SYM
cana-5720	115	19	(	(	PUNCT
cana-5720	115	20	y	y	NOUN
cana-5720	115	21	,	,	PUNCT
cana-5720	115	22			PRON
cana-5720	115	23	)	)	PUNCT
cana-5720	115	24	be	be	VERB
cana-5720	115	25	gω	gω	PROPN
cana-5720	115	26	closed	closed	ADJ
cana-5720	115	27	function	function	NOUN
cana-5720	115	28	.	.	PUNCT
cana-5720	116	1	then	then	ADV
cana-5720	116	2	if	if	SCONJ
cana-5720	116	3	for	for	ADP
cana-5720	116	4	each	each	DET
cana-5720	116	5	regular	regular	ADJ
cana-5720	116	6	closed	closed	ADJ
cana-5720	116	7	set	set	VERB
cana-5720	116	8	f	f	NOUN
cana-5720	116	9	,	,	PUNCT
cana-5720	116	10	f(f	f(f	PROPN
cana-5720	116	11	)	)	PUNCT
cana-5720	116	12	is	be	AUX
cana-5720	116	13	gω	gω	PROPN
cana-5720	116	14	-	-	PUNCT
cana-5720	116	15	closed	close	VERB
cana-5720	116	16	and	and	CCONJ
cana-5720	116	17	every	every	DET
cana-5720	116	18	gω	gω	PROPN
cana-5720	116	19	closed	close	VERB
cana-5720	116	20	set	set	NOUN
cana-5720	116	21	is	be	AUX
cana-5720	116	22	gωα	gωα	NOUN
cana-5720	116	23	closed	close	VERB
cana-5720	116	24	set	set	NOUN
cana-5720	116	25	.	.	PUNCT
cana-5720	117	1	hence	hence	ADV
cana-5720	117	2	f	f	PROPN
cana-5720	117	3	is	be	AUX
cana-5720	117	4	almost	almost	ADV
cana-5720	117	5	gωα	gωα	NOUN
cana-5720	117	6	closed	closed	ADJ
cana-5720	117	7	function	function	NOUN
cana-5720	117	8	.	.	PUNCT
cana-5720	118	1	example	example	NOUN
cana-5720	118	2	3.11	3.11	NUM
cana-5720	118	3	let	let	VERB
cana-5720	118	4	x	x	SYM
cana-5720	118	5	=	=	PUNCT
cana-5720	118	6	y	y	PROPN
cana-5720	118	7	=	=	PUNCT
cana-5720	118	8	{	{	PUNCT
cana-5720	118	9	a	a	PRON
cana-5720	118	10	,	,	PUNCT
cana-5720	118	11	b	b	NOUN
cana-5720	118	12	,	,	PUNCT
cana-5720	118	13	c	c	NOUN
cana-5720	118	14	}	}	PUNCT
cana-5720	118	15	,	,	PUNCT
cana-5720	118	16			NOUN
cana-5720	118	17	=	=	SYM
cana-5720	118	18	{	{	PUNCT
cana-5720	118	19			NOUN
cana-5720	118	20	,	,	PUNCT
cana-5720	118	21	{	{	PUNCT
cana-5720	118	22	a	a	X
cana-5720	118	23	}	}	PUNCT
cana-5720	118	24	,	,	PUNCT
cana-5720	118	25	{	{	PUNCT
cana-5720	118	26	b	b	NOUN
cana-5720	118	27	}	}	PUNCT
cana-5720	118	28	,	,	PUNCT
cana-5720	118	29	{	{	PUNCT
cana-5720	118	30	a	a	DET
cana-5720	118	31	,	,	PUNCT
cana-5720	118	32	b	b	NOUN
cana-5720	118	33	}	}	PUNCT
cana-5720	118	34	,	,	PUNCT
cana-5720	118	35	{	{	PUNCT
cana-5720	118	36	a	a	DET
cana-5720	118	37	,	,	PUNCT
cana-5720	118	38	c}x	c}x	NOUN
cana-5720	118	39	}	}	PUNCT
cana-5720	118	40	and	and	CCONJ
cana-5720	118	41			PROPN
cana-5720	118	42	=	=	SYM
cana-5720	118	43	{	{	PUNCT
cana-5720	118	44			NOUN
cana-5720	118	45	,	,	PUNCT
cana-5720	118	46	{	{	PUNCT
cana-5720	118	47	a	a	DET
cana-5720	118	48	,	,	PUNCT
cana-5720	118	49	b	b	NOUN
cana-5720	118	50	}	}	PUNCT
cana-5720	118	51	,	,	PUNCT
cana-5720	118	52	y	y	PROPN
cana-5720	118	53	}	}	PUNCT
cana-5720	118	54	.	.	PUNCT
cana-5720	119	1	then	then	ADV
cana-5720	119	2	rc(x	rc(x	VERB
cana-5720	119	3	,	,	PUNCT
cana-5720	119	4			PROPN
cana-5720	119	5	)	)	PUNCT
cana-5720	119	6	=	=	SYM
cana-5720	119	7	{	{	PUNCT
cana-5720	119	8			NOUN
cana-5720	119	9	,	,	PUNCT
cana-5720	119	10	{	{	PUNCT
cana-5720	119	11	a	a	PRON
cana-5720	119	12	,	,	PUNCT
cana-5720	119	13	c	c	NOUN
cana-5720	119	14	}	}	PUNCT
cana-5720	119	15	,	,	PUNCT
cana-5720	119	16	{	{	PUNCT
cana-5720	119	17	b	b	X
cana-5720	119	18	,	,	PUNCT
cana-5720	119	19	c	c	NOUN
cana-5720	119	20	}	}	PUNCT
cana-5720	119	21	,	,	PUNCT
cana-5720	119	22	x	x	NOUN
cana-5720	119	23	}	}	PUNCT
cana-5720	119	24	and	and	CCONJ
cana-5720	119	25	gωα	gωα	PROPN
cana-5720	119	26	closed	close	VERB
cana-5720	119	27	in	in	ADP
cana-5720	119	28	y	y	PROPN
cana-5720	119	29	=	=	PUNCT
cana-5720	119	30	{	{	PUNCT
cana-5720	119	31			NOUN
cana-5720	119	32	,	,	PUNCT
cana-5720	119	33	{	{	PUNCT
cana-5720	119	34	c	c	NOUN
cana-5720	119	35	}	}	PUNCT
cana-5720	119	36	,	,	PUNCT
cana-5720	119	37	{	{	PUNCT
cana-5720	119	38	a	a	DET
cana-5720	119	39	,	,	PUNCT
cana-5720	119	40	b	b	NOUN
cana-5720	119	41	}	}	PUNCT
cana-5720	119	42	,	,	PUNCT
cana-5720	119	43	y	y	PROPN
cana-5720	119	44	}	}	PUNCT
cana-5720	119	45	then	then	ADV
cana-5720	119	46	the	the	DET
cana-5720	119	47	function	function	NOUN
cana-5720	119	48	f	f	NOUN
cana-5720	119	49	:	:	PUNCT
cana-5720	119	50	(	(	PUNCT
cana-5720	119	51	x	x	X
cana-5720	119	52	,	,	PUNCT
cana-5720	119	53			PROPN
cana-5720	119	54	)	)	PUNCT
cana-5720	119	55	→	→	SYM
cana-5720	119	56	(	(	PUNCT
cana-5720	119	57	y	y	NOUN
cana-5720	119	58	,	,	PUNCT
cana-5720	119	59			NUM
cana-5720	119	60	)	)	PUNCT
cana-5720	119	61	defined	define	VERB
cana-5720	119	62	as	as	ADP
cana-5720	119	63	f(a)=c	f(a)=c	PROPN
cana-5720	119	64	,	,	PUNCT
cana-5720	119	65	f(b)=b	f(b)=b	PROPN
cana-5720	119	66	,	,	PUNCT
cana-5720	119	67	f(c)=c	f(c)=c	PROPN
cana-5720	119	68	is	be	AUX
cana-5720	119	69	almost	almost	ADV
cana-5720	119	70	gωα	gωα	NOUN
cana-5720	119	71	-closed	-close	VERB
cana-5720	119	72	.	.	PUNCT
cana-5720	120	1	however	however	ADV
cana-5720	120	2	,	,	PUNCT
cana-5720	120	3	it	it	PRON
cana-5720	120	4	is	be	AUX
cana-5720	120	5	not	not	PART
cana-5720	120	6	almost	almost	ADV
cana-5720	120	7	gω	gω	PROPN
cana-5720	120	8	closed	close	VERB
cana-5720	120	9	since	since	SCONJ
cana-5720	120	10	there	there	PRON
cana-5720	120	11	exists	exist	VERB
cana-5720	120	12	{	{	PUNCT
cana-5720	120	13	b	b	NOUN
cana-5720	120	14	,	,	PUNCT
cana-5720	120	15	c	c	NOUN
cana-5720	120	16	}	}	PUNCT
cana-5720	120	17			PROPN
cana-5720	120	18	rc	rc	PROPN
cana-5720	120	19	(	(	PUNCT
cana-5720	120	20	x	x	PROPN
cana-5720	120	21	,	,	PUNCT
cana-5720	120	22			PROPN
cana-5720	120	23	)	)	PUNCT
cana-5720	120	24	such	such	ADJ
cana-5720	120	25	that	that	SCONJ
cana-5720	120	26	f({b	f({b	ADJ
cana-5720	120	27	,	,	PUNCT
cana-5720	120	28	c	c	NOUN
cana-5720	120	29	}	}	PUNCT
cana-5720	120	30	)	)	PUNCT
cana-5720	120	31	=	=	PRON
cana-5720	120	32	{	{	PUNCT
cana-5720	120	33	a	a	DET
cana-5720	120	34	,	,	PUNCT
cana-5720	120	35	b	b	NOUN
cana-5720	120	36	}	}	PUNCT
cana-5720	120	37	is	be	AUX
cana-5720	120	38	not	not	PART
cana-5720	120	39	gωclosed	gωclose	VERB
cana-5720	120	40	in	in	ADP
cana-5720	120	41	(	(	PUNCT
cana-5720	120	42	y	y	NOUN
cana-5720	120	43	,	,	PUNCT
cana-5720	120	44			PROPN
cana-5720	120	45	)	)	PUNCT
cana-5720	120	46	.	.	PUNCT
cana-5720	121	1	remark	remark	NOUN
cana-5720	121	2	3.12	3.12	NUM
cana-5720	121	3	we	we	PRON
cana-5720	121	4	have	have	VERB
cana-5720	121	5	the	the	DET
cana-5720	121	6	following	follow	VERB
cana-5720	121	7	diagram	diagram	NOUN
cana-5720	121	8	for	for	ADP
cana-5720	121	9	properties	property	NOUN
cana-5720	121	10	of	of	ADP
cana-5720	121	11	functions	function	NOUN
cana-5720	121	12	:	:	PUNCT
cana-5720	121	13	gω	gω	PROPN
cana-5720	121	14	-	-	PUNCT
cana-5720	121	15	closed	close	VERB
cana-5720	121	16	almost	almost	ADV
cana-5720	121	17	closed	close	VERB
cana-5720	121	18	almost	almost	ADV
cana-5720	121	19	gω	gω	NOUN
cana-5720	121	20	-	-	PUNCT
cana-5720	121	21	closed	close	VERB
cana-5720	121	22	gωα	gωα	NOUN
cana-5720	121	23	-closed	-close	VERB
cana-5720	121	24	almost	almost	ADV
cana-5720	121	25	-closed	-closed	ADJ
cana-5720	121	26	almost	almost	ADV
cana-5720	121	27	gωα	gωα	NOUN
cana-5720	121	28	-closed	-closed	PROPN
cana-5720	121	29	theorem	theorem	VERB
cana-5720	121	30	3.13	3.13	NUM
cana-5720	121	31	a	a	DET
cana-5720	121	32	surjection	surjection	NOUN
cana-5720	122	1	f	f	X
cana-5720	122	2	:	:	PUNCT
cana-5720	122	3	x	x	X
cana-5720	122	4	→	→	SYM
cana-5720	122	5	y	y	PROPN
cana-5720	122	6	is	be	AUX
cana-5720	122	7	almost	almost	ADV
cana-5720	122	8	gωα	gωα	NOUN
cana-5720	122	9	-closed	-close	VERB
cana-5720	122	10	if	if	SCONJ
cana-5720	122	11	and	and	CCONJ
cana-5720	122	12	only	only	ADV
cana-5720	122	13	if	if	SCONJ
cana-5720	122	14	for	for	ADP
cana-5720	122	15	each	each	DET
cana-5720	122	16	subset	subset	NOUN
cana-5720	122	17	s	s	PROPN
cana-5720	122	18	of	of	ADP
cana-5720	122	19	y	y	PROPN
cana-5720	122	20	and	and	CCONJ
cana-5720	122	21	each	each	DET
cana-5720	122	22	u	u	NOUN
cana-5720	122	23			PROPN
cana-5720	122	24	ro	ro	X
cana-5720	122	25	(	(	PUNCT
cana-5720	122	26	x	x	X
cana-5720	122	27	)	)	PUNCT
cana-5720	122	28	containing	contain	VERB
cana-5720	122	29	f-1(s	f-1(	NOUN
cana-5720	122	30	)	)	PUNCT
cana-5720	122	31	there	there	PRON
cana-5720	122	32	exists	exist	VERB
cana-5720	122	33	an	an	DET
cana-5720	122	34	gωα	gωα	NOUN
cana-5720	122	35	-open	-open	NOUN
cana-5720	122	36	set	set	VERB
cana-5720	122	37	v	v	NOUN
cana-5720	122	38	of	of	ADP
cana-5720	122	39	y	y	PRON
cana-5720	122	40	such	such	ADJ
cana-5720	122	41	that	that	PRON
cana-5720	122	42	s	s	VERB
cana-5720	122	43			PROPN
cana-5720	122	44	v	v	PROPN
cana-5720	122	45	and	and	CCONJ
cana-5720	122	46	f-1(v	f-1(v	NOUN
cana-5720	122	47	)	)	PUNCT
cana-5720	123	1			PROPN
cana-5720	123	2	u.	u.	PROPN
cana-5720	123	3	communications	communication	NOUN
cana-5720	123	4	on	on	ADP
cana-5720	123	5	applied	apply	VERB
cana-5720	123	6	nonlinear	nonlinear	ADJ
cana-5720	123	7	analysis	analysis	NOUN
cana-5720	123	8	issn	issn	NOUN
cana-5720	123	9	:	:	PUNCT
cana-5720	123	10	1074	1074	NUM
cana-5720	123	11	-	-	PUNCT
cana-5720	123	12	133x	133x	NUM
cana-5720	123	13	vol	vol	VERB
cana-5720	123	14	32	32	NUM
cana-5720	123	15	no	no	NOUN
cana-5720	123	16	.	.	PUNCT
cana-5720	124	1	10s	10	NOUN
cana-5720	124	2	(	(	PUNCT
cana-5720	124	3	2025	2025	NUM
cana-5720	124	4	)	)	PUNCT
cana-5720	124	5	2806	2806	NUM
cana-5720	124	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5720	124	7	proof	proof	NOUN
cana-5720	124	8	necessity	necessity	NOUN
cana-5720	124	9	.	.	PUNCT
cana-5720	124	10	suppose	suppose	VERB
cana-5720	124	11	that	that	SCONJ
cana-5720	124	12	f	f	PROPN
cana-5720	124	13	is	be	AUX
cana-5720	124	14	almost	almost	ADV
cana-5720	124	15	gωα	gωα	NOUN
cana-5720	124	16	-closed	-close	VERB
cana-5720	124	17	.	.	PUNCT
cana-5720	125	1	let	let	VERB
cana-5720	125	2	s	s	PRON
cana-5720	125	3	be	be	AUX
cana-5720	125	4	a	a	DET
cana-5720	125	5	subset	subset	NOUN
cana-5720	125	6	of	of	ADP
cana-5720	125	7	y	y	PROPN
cana-5720	125	8	and	and	CCONJ
cana-5720	125	9	u	u	PRON
cana-5720	125	10			PROPN
cana-5720	125	11	ro	ro	X
cana-5720	125	12	(	(	PUNCT
cana-5720	125	13	x	x	X
cana-5720	125	14	)	)	PUNCT
cana-5720	125	15	containing	contain	VERB
cana-5720	125	16	f-1(s	f-1(	NOUN
cana-5720	125	17	)	)	PUNCT
cana-5720	125	18	.	.	PUNCT
cana-5720	126	1	put	put	VERB
cana-5720	126	2	v	v	NUM
cana-5720	126	3	=	=	SYM
cana-5720	126	4	y	y	PROPN
cana-5720	126	5	−	−	PROPN
cana-5720	127	1	f	f	PROPN
cana-5720	127	2	(	(	PUNCT
cana-5720	127	3	x	x	X
cana-5720	127	4	−	−	PROPN
cana-5720	127	5	u	u	NOUN
cana-5720	127	6	)	)	PUNCT
cana-5720	127	7	,	,	PUNCT
cana-5720	127	8	then	then	ADV
cana-5720	127	9	v	v	NOUN
cana-5720	127	10	is	be	AUX
cana-5720	127	11	an	an	DET
cana-5720	127	12	gωα	gωα	NOUN
cana-5720	127	13	-open	-open	NOUN
cana-5720	127	14	set	set	NOUN
cana-5720	127	15	of	of	ADP
cana-5720	127	16	y	y	PRON
cana-5720	127	17	such	such	ADJ
cana-5720	127	18	that	that	PRON
cana-5720	127	19	s	s	VERB
cana-5720	127	20			PROPN
cana-5720	127	21	v	v	PROPN
cana-5720	127	22	and	and	CCONJ
cana-5720	127	23	f-1(v	f-1(v	NOUN
cana-5720	127	24	)	)	PUNCT
cana-5720	128	1			PROPN
cana-5720	128	2	u.	u.	PROPN
cana-5720	128	3	sufficiency	sufficiency	PROPN
cana-5720	128	4	.	.	PUNCT
cana-5720	129	1	let	let	VERB
cana-5720	129	2	f	f	PRON
cana-5720	129	3	be	be	AUX
cana-5720	129	4	any	any	DET
cana-5720	129	5	regular	regular	ADJ
cana-5720	129	6	closed	closed	ADJ
cana-5720	129	7	set	set	NOUN
cana-5720	129	8	of	of	ADP
cana-5720	129	9	x.	x.	NOUN
cana-5720	129	10	then	then	ADV
cana-5720	129	11	f-1(y	f-1(y	VERB
cana-5720	130	1	−	−	PROPN
cana-5720	130	2	f	f	X
cana-5720	130	3	(	(	PUNCT
cana-5720	130	4	f	f	NOUN
cana-5720	130	5	)	)	PUNCT
cana-5720	130	6	)	)	PUNCT
cana-5720	131	1			PROPN
cana-5720	131	2	x	x	X
cana-5720	131	3	−	−	PROPN
cana-5720	131	4	f	f	PROPN
cana-5720	131	5	and	and	CCONJ
cana-5720	131	6	x	x	SYM
cana-5720	131	7	−	−	PROPN
cana-5720	131	8	f	f	PROPN
cana-5720	131	9			NOUN
cana-5720	131	10	ro	ro	X
cana-5720	131	11	(	(	PUNCT
cana-5720	131	12	x	x	NOUN
cana-5720	131	13	)	)	PUNCT
cana-5720	131	14	.	.	PUNCT
cana-5720	132	1	there	there	PRON
cana-5720	132	2	exists	exist	VERB
cana-5720	132	3	an	an	DET
cana-5720	132	4	gωα	gωα	NOUN
cana-5720	132	5	-	-	PUNCT
cana-5720	132	6	open	open	ADJ
cana-5720	132	7	set	set	NOUN
cana-5720	132	8	v	v	NOUN
cana-5720	132	9	of	of	ADP
cana-5720	132	10	y	y	PRON
cana-5720	132	11	such	such	ADJ
cana-5720	132	12	that	that	SCONJ
cana-5720	133	1	y	y	PROPN
cana-5720	133	2	−	−	PROPN
cana-5720	134	1	f	f	PROPN
cana-5720	134	2	(	(	PUNCT
cana-5720	134	3	f	f	X
cana-5720	134	4	)	)	PUNCT
cana-5720	134	5			PROPN
cana-5720	134	6	v	v	NOUN
cana-5720	134	7	and	and	CCONJ
cana-5720	134	8	f-1(v	f-1(v	NOUN
cana-5720	134	9	)	)	PUNCT
cana-5720	135	1			NOUN
cana-5720	135	2	x	x	X
cana-5720	136	1	−	−	PROPN
cana-5720	136	2	f.	f.	PROPN
cana-5720	136	3	therefore	therefore	ADV
cana-5720	136	4	,	,	PUNCT
cana-5720	136	5	we	we	PRON
cana-5720	136	6	have	have	VERB
cana-5720	136	7	f	f	PROPN
cana-5720	136	8	(	(	PUNCT
cana-5720	136	9	f	f	X
cana-5720	136	10	)	)	PUNCT
cana-5720	136	11			PROPN
cana-5720	136	12	y	y	PROPN
cana-5720	136	13	−	−	PROPN
cana-5720	136	14	v	v	PROPN
cana-5720	137	1	and	and	CCONJ
cana-5720	137	2	f	f	X
cana-5720	137	3			PROPN
cana-5720	137	4	f-1(y	f-1(y	VERB
cana-5720	137	5	−	−	PROPN
cana-5720	137	6	v	v	NOUN
cana-5720	137	7	)	)	PUNCT
cana-5720	137	8	.	.	PUNCT
cana-5720	138	1	hence	hence	ADV
cana-5720	138	2	,	,	PUNCT
cana-5720	138	3	we	we	PRON
cana-5720	138	4	obtain	obtain	VERB
cana-5720	138	5	f	f	X
cana-5720	138	6	(	(	PUNCT
cana-5720	138	7	f	f	X
cana-5720	138	8	)	)	PUNCT
cana-5720	139	1	=	=	SYM
cana-5720	139	2	y	y	PROPN
cana-5720	139	3	−	−	PROPN
cana-5720	139	4	v	v	PROPN
cana-5720	139	5	and	and	CCONJ
cana-5720	139	6	f	f	PROPN
cana-5720	139	7	(	(	PUNCT
cana-5720	139	8	f	f	X
cana-5720	139	9	)	)	PUNCT
cana-5720	139	10	is	be	AUX
cana-5720	139	11	gωα	gωα	VERB
cana-5720	139	12	-closed	-close	VERB
cana-5720	139	13	in	in	ADP
cana-5720	139	14	y.	y.	PROPN
cana-5720	139	15	this	this	PRON
cana-5720	139	16	shows	show	VERB
cana-5720	139	17	that	that	SCONJ
cana-5720	139	18	f	f	PROPN
cana-5720	139	19	is	be	AUX
cana-5720	139	20	almost	almost	ADV
cana-5720	139	21	gωα	gωα	NOUN
cana-5720	139	22	-closed	-close	VERB
cana-5720	139	23	.	.	PUNCT
cana-5720	140	1	corollary	corollary	ADJ
cana-5720	140	2	3.14	3.14	NUM
cana-5720	140	3	if	if	SCONJ
cana-5720	140	4	f	f	PROPN
cana-5720	140	5	:	:	PUNCT
cana-5720	140	6	x	x	X
cana-5720	140	7	→	→	SYM
cana-5720	140	8	y	y	PROPN
cana-5720	140	9	is	be	AUX
cana-5720	140	10	an	an	DET
cana-5720	140	11	almost	almost	ADV
cana-5720	140	12	gωα	gωα	ADJ
cana-5720	140	13	-	-	PUNCT
cana-5720	140	14	closed	close	VERB
cana-5720	140	15	surjection	surjection	NOUN
cana-5720	140	16	,	,	PUNCT
cana-5720	140	17	then	then	ADV
cana-5720	140	18	for	for	ADP
cana-5720	140	19	each	each	DET
cana-5720	140	20	sg	sg	NOUN
cana-5720	140	21	-	-	PUNCT
cana-5720	140	22	closed	close	VERB
cana-5720	140	23	set	set	ADJ
cana-5720	140	24	f	f	PROPN
cana-5720	140	25	of	of	ADP
cana-5720	140	26	y	y	PROPN
cana-5720	140	27	and	and	CCONJ
cana-5720	140	28	each	each	DET
cana-5720	140	29	u	u	NOUN
cana-5720	140	30			PROPN
cana-5720	140	31	ro	ro	X
cana-5720	140	32	(	(	PUNCT
cana-5720	140	33	x	x	X
cana-5720	140	34	)	)	PUNCT
cana-5720	140	35	containing	contain	VERB
cana-5720	140	36	f-1(f	f-1(f	NOUN
cana-5720	140	37	)	)	PUNCT
cana-5720	140	38	there	there	PRON
cana-5720	140	39	exists	exist	VERB
cana-5720	140	40	an	an	DET
cana-5720	140	41	-open	-open	PROPN
cana-5720	140	42	set	set	VERB
cana-5720	140	43	v	v	NOUN
cana-5720	140	44	of	of	ADP
cana-5720	140	45	y	y	PRON
cana-5720	140	46	such	such	ADJ
cana-5720	140	47	that	that	SCONJ
cana-5720	140	48	f	f	PROPN
cana-5720	140	49			PROPN
cana-5720	140	50	v	v	PROPN
cana-5720	140	51	and	and	CCONJ
cana-5720	140	52	f-1(v	f-1(v	NOUN
cana-5720	140	53	)	)	PUNCT
cana-5720	141	1			PROPN
cana-5720	141	2	u.	u.	PROPN
cana-5720	141	3	proof	proof	NOUN
cana-5720	141	4	let	let	VERB
cana-5720	141	5	f	f	PRON
cana-5720	141	6	be	be	AUX
cana-5720	141	7	a	a	DET
cana-5720	141	8	sg	sg	ADV
cana-5720	141	9	-	-	PUNCT
cana-5720	141	10	closed	close	VERB
cana-5720	141	11	set	set	NOUN
cana-5720	141	12	of	of	ADP
cana-5720	141	13	y	y	PROPN
cana-5720	141	14	and	and	CCONJ
cana-5720	141	15	u	u	PRON
cana-5720	141	16			PROPN
cana-5720	141	17	ro	ro	X
cana-5720	141	18	(	(	PUNCT
cana-5720	141	19	x	x	X
cana-5720	141	20	)	)	PUNCT
cana-5720	141	21	containing	contain	VERB
cana-5720	141	22	f-1(f	f-1(f	NOUN
cana-5720	141	23	)	)	PUNCT
cana-5720	141	24	.	.	PUNCT
cana-5720	142	1	by	by	ADP
cana-5720	142	2	theorem	theorem	NOUN
cana-5720	142	3	1.3.13	1.3.13	NUM
cana-5720	142	4	,	,	PUNCT
cana-5720	142	5	there	there	PRON
cana-5720	142	6	exists	exist	VERB
cana-5720	142	7	an	an	DET
cana-5720	142	8	gωα	gωα	NOUN
cana-5720	142	9	-open	-open	NOUN
cana-5720	142	10	set	set	VERB
cana-5720	142	11	w	w	NOUN
cana-5720	142	12	of	of	ADP
cana-5720	142	13	y	y	PRON
cana-5720	142	14	such	such	ADJ
cana-5720	142	15	that	that	SCONJ
cana-5720	142	16	f	f	PROPN
cana-5720	142	17			PROPN
cana-5720	142	18	w	w	PROPN
cana-5720	142	19	and	and	CCONJ
cana-5720	142	20	f-1(w	f-1(w	NOUN
cana-5720	142	21	)	)	PUNCT
cana-5720	142	22			PROPN
cana-5720	142	23	u.	u.	VERB
cana-5720	142	24	since	since	SCONJ
cana-5720	142	25	w	w	PROPN
cana-5720	142	26	is	be	AUX
cana-5720	142	27	gωα	gωα	PROPN
cana-5720	142	28	-open	-open	PROPN
cana-5720	142	29	,	,	PUNCT
cana-5720	142	30	we	we	PRON
cana-5720	142	31	have	have	VERB
cana-5720	142	32	f	f	PROPN
cana-5720	142	33			PROPN
cana-5720	142	34	int(w	int(w	PROPN
cana-5720	142	35	)	)	PUNCT
cana-5720	142	36	.	.	PUNCT
cana-5720	143	1	put	put	VERB
cana-5720	143	2	v	v	NOUN
cana-5720	143	3	=	=	SYM
cana-5720	143	4	int(w	int(w	NOUN
cana-5720	143	5	)	)	PUNCT
cana-5720	143	6	,	,	PUNCT
cana-5720	143	7	then	then	ADV
cana-5720	143	8	v	v	NOUN
cana-5720	143	9	is	be	AUX
cana-5720	143	10	-open	-open	PROPN
cana-5720	143	11	in	in	ADP
cana-5720	143	12	y	y	PROPN
cana-5720	143	13	and	and	CCONJ
cana-5720	143	14	f-1(v	f-1(v	PROPN
cana-5720	143	15	)	)	PUNCT
cana-5720	144	1			PROPN
cana-5720	144	2	u.	u.	PROPN
cana-5720	144	3	4	4	NUM
cana-5720	144	4	.	.	PUNCT
cana-5720	144	5	normal	normal	ADJ
cana-5720	144	6	spaces	space	NOUN
cana-5720	144	7	in	in	ADP
cana-5720	144	8	this	this	DET
cana-5720	144	9	section	section	NOUN
cana-5720	144	10	,	,	PUNCT
cana-5720	144	11	we	we	PRON
cana-5720	144	12	make	make	VERB
cana-5720	144	13	use	use	NOUN
cana-5720	144	14	of	of	ADP
cana-5720	144	15	gωα	gωα	NOUN
cana-5720	144	16	-	-	PUNCT
cana-5720	144	17	closed	close	VERB
cana-5720	144	18	sets	set	NOUN
cana-5720	144	19	to	to	PART
cana-5720	144	20	obtain	obtain	VERB
cana-5720	144	21	further	further	ADJ
cana-5720	144	22	characterizations	characterization	NOUN
cana-5720	144	23	and	and	CCONJ
cana-5720	144	24	preservation	preservation	NOUN
cana-5720	144	25	theorems	theorem	NOUN
cana-5720	144	26	of	of	ADP
cana-5720	144	27	normal	normal	ADJ
cana-5720	144	28	spaces	space	NOUN
cana-5720	144	29	.	.	PUNCT
cana-5720	145	1	theorem	theorem	VERB
cana-5720	145	2	4.1	4.1	NUM
cana-5720	145	3	the	the	DET
cana-5720	145	4	following	following	NOUN
cana-5720	145	5	are	be	AUX
cana-5720	145	6	equivalent	equivalent	ADJ
cana-5720	145	7	for	for	ADP
cana-5720	145	8	a	a	DET
cana-5720	145	9	space	space	NOUN
cana-5720	145	10	x	x	NOUN
cana-5720	145	11	:	:	PUNCT
cana-5720	145	12	(	(	PUNCT
cana-5720	145	13	i	i	NOUN
cana-5720	145	14	)	)	PUNCT
cana-5720	145	15	x	x	X
cana-5720	145	16	is	be	AUX
cana-5720	145	17	normal	normal	ADJ
cana-5720	145	18	;	;	PUNCT
cana-5720	145	19	(	(	PUNCT
cana-5720	145	20	ii	ii	NOUN
cana-5720	145	21	)	)	PUNCT
cana-5720	145	22	for	for	ADP
cana-5720	145	23	any	any	DET
cana-5720	145	24	disjoint	disjoint	NOUN
cana-5720	145	25	closed	close	VERB
cana-5720	145	26	sets	set	NOUN
cana-5720	145	27	a	a	PRON
cana-5720	145	28	and	and	CCONJ
cana-5720	145	29	b	b	NOUN
cana-5720	145	30	,	,	PUNCT
cana-5720	145	31	there	there	PRON
cana-5720	145	32	exist	exist	VERB
cana-5720	145	33	disjoint	disjoint	ADJ
cana-5720	145	34	gωα	gωα	NOUN
cana-5720	145	35	-	-	PUNCT
cana-5720	145	36	open	open	ADJ
cana-5720	145	37	sets	set	NOUN
cana-5720	145	38	u	u	NOUN
cana-5720	145	39	,	,	PUNCT
cana-5720	145	40	v	v	ADP
cana-5720	145	41	such	such	ADJ
cana-5720	145	42	that	that	SCONJ
cana-5720	145	43	a	a	DET
cana-5720	145	44			PROPN
cana-5720	145	45	u	u	PROPN
cana-5720	145	46	and	and	CCONJ
cana-5720	145	47	b	b	PROPN
cana-5720	145	48			PROPN
cana-5720	145	49	v	v	PROPN
cana-5720	145	50	;	;	PUNCT
cana-5720	145	51	(	(	PUNCT
cana-5720	145	52	iii	iii	NOUN
cana-5720	145	53	)	)	PUNCT
cana-5720	145	54	for	for	ADP
cana-5720	145	55	any	any	DET
cana-5720	145	56	closed	closed	ADJ
cana-5720	145	57	set	set	NOUN
cana-5720	145	58	a	a	PRON
cana-5720	145	59	and	and	CCONJ
cana-5720	145	60	any	any	DET
cana-5720	145	61	open	open	ADJ
cana-5720	145	62	set	set	VERB
cana-5720	145	63	v	v	NOUN
cana-5720	145	64	containing	contain	VERB
cana-5720	145	65	a	a	PRON
cana-5720	145	66	,	,	PUNCT
cana-5720	145	67	there	there	PRON
cana-5720	145	68	exists	exist	VERB
cana-5720	145	69	an	an	DET
cana-5720	145	70	gωα	gωα	NOUN
cana-5720	145	71	-open	-open	NOUN
cana-5720	145	72	set	set	VERB
cana-5720	145	73	u	u	NOUN
cana-5720	145	74	of	of	ADP
cana-5720	145	75	x	x	SYM
cana-5720	145	76	such	such	ADJ
cana-5720	145	77	that	that	SCONJ
cana-5720	145	78	a	a	DET
cana-5720	145	79			PROPN
cana-5720	145	80	u	u	PROPN
cana-5720	145	81			PROPN
cana-5720	145	82	cl(u	cl(u	PROPN
cana-5720	145	83	)	)	PUNCT
cana-5720	146	1			PROPN
cana-5720	146	2	v.	v.	ADP
cana-5720	146	3	proof	proof	NOUN
cana-5720	146	4	(	(	PUNCT
cana-5720	146	5	i	i	NOUN
cana-5720	146	6	)	)	PUNCT
cana-5720	146	7			PROPN
cana-5720	146	8	(	(	PUNCT
cana-5720	146	9	ii	ii	NOUN
cana-5720	146	10	)	)	PUNCT
cana-5720	146	11	.	.	PUNCT
cana-5720	147	1	this	this	PRON
cana-5720	147	2	is	be	AUX
cana-5720	147	3	obvious	obvious	ADJ
cana-5720	147	4	since	since	SCONJ
cana-5720	147	5	every	every	DET
cana-5720	147	6	open	open	ADJ
cana-5720	147	7	set	set	NOUN
cana-5720	147	8	is	be	AUX
cana-5720	147	9	gωα	gωα	NOUN
cana-5720	147	10	-open	-open	NOUN
cana-5720	147	11	.	.	PUNCT
cana-5720	148	1	(	(	PUNCT
cana-5720	148	2	ii	ii	PROPN
cana-5720	148	3	)	)	PUNCT
cana-5720	148	4			NOUN
cana-5720	148	5	(	(	PUNCT
cana-5720	148	6	iii	iii	NOUN
cana-5720	148	7	)	)	PUNCT
cana-5720	148	8	.	.	PUNCT
cana-5720	149	1	let	let	VERB
cana-5720	149	2	a	a	DET
cana-5720	149	3	be	be	AUX
cana-5720	149	4	a	a	DET
cana-5720	149	5	closed	closed	ADJ
cana-5720	149	6	set	set	NOUN
cana-5720	149	7	and	and	CCONJ
cana-5720	149	8	v	v	ADP
cana-5720	149	9	an	an	DET
cana-5720	149	10	open	open	ADJ
cana-5720	149	11	set	set	NOUN
cana-5720	149	12	containing	contain	VERB
cana-5720	149	13	a.	a.	NOUN
cana-5720	149	14	then	then	ADV
cana-5720	149	15	a	a	PRON
cana-5720	149	16	and	and	CCONJ
cana-5720	149	17	x	x	SYM
cana-5720	149	18	−	−	NOUN
cana-5720	149	19	v	v	NOUN
cana-5720	149	20	are	be	AUX
cana-5720	149	21	disjoint	disjoint	NOUN
cana-5720	149	22	closed	closed	ADJ
cana-5720	149	23	sets	set	NOUN
cana-5720	149	24	.	.	PUNCT
cana-5720	150	1	there	there	PRON
cana-5720	150	2	exist	exist	VERB
cana-5720	150	3	disjoint	disjoint	NOUN
cana-5720	150	4	gωα	gωα	X
cana-5720	150	5	-open	-open	PROPN
cana-5720	150	6	sets	set	VERB
cana-5720	150	7	u	u	NOUN
cana-5720	150	8	and	and	CCONJ
cana-5720	150	9	w	w	ADP
cana-5720	150	10	such	such	ADJ
cana-5720	150	11	that	that	SCONJ
cana-5720	150	12	a	a	DET
cana-5720	150	13			PROPN
cana-5720	150	14	u	u	PROPN
cana-5720	150	15	and	and	CCONJ
cana-5720	150	16	x	x	NOUN
cana-5720	150	17	−	−	PROPN
cana-5720	150	18	v	v	NUM
cana-5720	150	19			PROPN
cana-5720	150	20	w.	w.	PROPN
cana-5720	150	21	since	since	SCONJ
cana-5720	150	22	x	x	PROPN
cana-5720	150	23	−	−	PROPN
cana-5720	150	24	v	v	NOUN
cana-5720	150	25	is	be	AUX
cana-5720	150	26	closed	closed	ADJ
cana-5720	150	27	and	and	CCONJ
cana-5720	150	28	hence	hence	ADV
cana-5720	150	29	sg	sg	ADV
cana-5720	150	30	-	-	PUNCT
cana-5720	150	31	closed	closed	ADJ
cana-5720	150	32	,	,	PUNCT
cana-5720	150	33	we	we	PRON
cana-5720	150	34	have	have	VERB
cana-5720	150	35	x	x	X
cana-5720	150	36	−	−	NOUN
cana-5720	150	37	v	v	ADP
cana-5720	150	38			PROPN
cana-5720	150	39	int(w	int(w	VERB
cana-5720	150	40	)	)	PUNCT
cana-5720	150	41	and	and	CCONJ
cana-5720	150	42	u	u	NOUN
cana-5720	150	43			X
cana-5720	150	44	int(w	int(w	NOUN
cana-5720	150	45	)	)	PUNCT
cana-5720	150	46	=	=	PUNCT
cana-5720	150	47	.	.	X
cana-5720	150	48	therefore	therefore	ADV
cana-5720	150	49	,	,	PUNCT
cana-5720	150	50	we	we	PRON
cana-5720	150	51	obtain	obtain	VERB
cana-5720	150	52	cl(u	cl(u	NOUN
cana-5720	150	53	)	)	PUNCT
cana-5720	150	54			X
cana-5720	150	55	int(w	int(w	NOUN
cana-5720	150	56	)	)	PUNCT
cana-5720	150	57	=	=	SYM
cana-5720	150	58			NOUN
cana-5720	150	59	and	and	CCONJ
cana-5720	150	60	hence	hence	ADV
cana-5720	150	61	a	a	DET
cana-5720	150	62			PROPN
cana-5720	150	63	u	u	PROPN
cana-5720	150	64			PROPN
cana-5720	150	65	cl(u	cl(u	PROPN
cana-5720	150	66	)	)	PUNCT
cana-5720	151	1			PROPN
cana-5720	151	2	x	x	X
cana-5720	152	1	−	−	ADP
cana-5720	152	2	int(w	int(w	NOUN
cana-5720	152	3	)	)	PUNCT
cana-5720	153	1			PROPN
cana-5720	153	2	v.	v.	ADP
cana-5720	153	3	(	(	PUNCT
cana-5720	153	4	iii	iii	PROPN
cana-5720	153	5	)	)	PUNCT
cana-5720	153	6			NOUN
cana-5720	153	7	(	(	PUNCT
cana-5720	153	8	i	i	NOUN
cana-5720	153	9	)	)	PUNCT
cana-5720	153	10	.	.	PUNCT
cana-5720	154	1	let	let	VERB
cana-5720	154	2	a	a	DET
cana-5720	154	3	,	,	PUNCT
cana-5720	154	4	b	b	PROPN
cana-5720	154	5	be	be	AUX
cana-5720	154	6	disjoint	disjoint	X
cana-5720	154	7	closed	closed	ADJ
cana-5720	154	8	sets	set	NOUN
cana-5720	154	9	of	of	ADP
cana-5720	154	10	x.	x.	NOUN
cana-5720	154	11	then	then	ADV
cana-5720	154	12	a	a	DET
cana-5720	154	13			PROPN
cana-5720	154	14	x	x	PUNCT
cana-5720	154	15	−	−	PROPN
cana-5720	154	16	b	b	PROPN
cana-5720	154	17	and	and	CCONJ
cana-5720	154	18	x	x	SYM
cana-5720	154	19	−	−	PROPN
cana-5720	154	20	b	b	NOUN
cana-5720	154	21	is	be	AUX
cana-5720	154	22	open	open	ADJ
cana-5720	154	23	.	.	PUNCT
cana-5720	155	1	there	there	PRON
cana-5720	155	2	exists	exist	VERB
cana-5720	155	3	an	an	DET
cana-5720	155	4	gωα	gωα	NOUN
cana-5720	155	5	-open	-open	NOUN
cana-5720	155	6	set	set	VERB
cana-5720	155	7	g	g	NOUN
cana-5720	155	8	of	of	ADP
cana-5720	155	9	x	x	SYM
cana-5720	155	10	such	such	ADJ
cana-5720	155	11	that	that	SCONJ
cana-5720	155	12	a	a	DET
cana-5720	155	13			PROPN
cana-5720	155	14	g	g	PROPN
cana-5720	155	15			PROPN
cana-5720	155	16	cl(g	cl(g	PROPN
cana-5720	155	17	)	)	PUNCT
cana-5720	156	1			PROPN
cana-5720	156	2	x	x	X
cana-5720	156	3	−	−	PROPN
cana-5720	156	4	b.	b.	NOUN
cana-5720	156	5	since	since	SCONJ
cana-5720	156	6	a	a	PRON
cana-5720	156	7	is	be	AUX
cana-5720	156	8	closed	closed	ADJ
cana-5720	156	9	,	,	PUNCT
cana-5720	156	10	we	we	PRON
cana-5720	156	11	have	have	VERB
cana-5720	156	12	a	a	DET
cana-5720	156	13			PROPN
cana-5720	156	14	int(g	int(g	NUM
cana-5720	156	15	)	)	PUNCT
cana-5720	156	16	.	.	PUNCT
cana-5720	157	1	put	put	VERB
cana-5720	157	2	u	u	NOUN
cana-5720	157	3	=	=	NOUN
cana-5720	157	4	int(cl(int(int(g	int(cl(int(int(g	PROPN
cana-5720	157	5	)	)	PUNCT
cana-5720	157	6	)	)	PUNCT
cana-5720	157	7	)	)	PUNCT
cana-5720	157	8	)	)	PUNCT
cana-5720	158	1	and	and	CCONJ
cana-5720	158	2	v	v	X
cana-5720	158	3	=	=	SYM
cana-5720	158	4	int(cl(int(x	int(cl(int(x	PROPN
cana-5720	158	5	−	−	PROPN
cana-5720	158	6	cl(g	cl(g	PROPN
cana-5720	158	7	)	)	PUNCT
cana-5720	158	8	)	)	PUNCT
cana-5720	158	9	)	)	PUNCT
cana-5720	158	10	)	)	PUNCT
cana-5720	158	11	.	.	PUNCT
cana-5720	159	1	then	then	ADV
cana-5720	159	2	u	u	NOUN
cana-5720	159	3	and	and	CCONJ
cana-5720	159	4	v	v	NOUN
cana-5720	159	5	are	be	AUX
cana-5720	159	6	disjoint	disjoint	ADJ
cana-5720	159	7	open	open	ADJ
cana-5720	159	8	sets	set	NOUN
cana-5720	159	9	of	of	ADP
cana-5720	159	10	x	x	SYM
cana-5720	159	11	such	such	ADJ
cana-5720	159	12	that	that	SCONJ
cana-5720	159	13	a	a	DET
cana-5720	159	14			PROPN
cana-5720	159	15	u	u	PROPN
cana-5720	159	16	and	and	CCONJ
cana-5720	159	17	b	b	PROPN
cana-5720	159	18			PROPN
cana-5720	159	19	v.	v.	CCONJ
cana-5720	159	20	therefore	therefore	ADV
cana-5720	159	21	,	,	PUNCT
cana-5720	159	22	x	x	PUNCT
cana-5720	159	23	is	be	AUX
cana-5720	159	24	normal	normal	ADJ
cana-5720	159	25	.	.	PUNCT
cana-5720	160	1	theorem	theorem	VERB
cana-5720	160	2	4.2	4.2	NUM
cana-5720	160	3	if	if	SCONJ
cana-5720	160	4	f	f	X
cana-5720	160	5	:	:	PUNCT
cana-5720	160	6	x	x	X
cana-5720	160	7	→	→	SYM
cana-5720	160	8	y	y	PROPN
cana-5720	160	9	is	be	AUX
cana-5720	160	10	a	a	DET
cana-5720	160	11	continuous	continuous	ADJ
cana-5720	160	12	almost	almost	ADV
cana-5720	160	13	gωα	gωα	NOUN
cana-5720	160	14	-closed	-close	VERB
cana-5720	160	15	surjection	surjection	PROPN
cana-5720	160	16	and	and	CCONJ
cana-5720	160	17	x	x	NOUN
cana-5720	160	18	is	be	AUX
cana-5720	160	19	a	a	DET
cana-5720	160	20	normal	normal	ADJ
cana-5720	160	21	space	space	NOUN
cana-5720	160	22	,	,	PUNCT
cana-5720	160	23	then	then	ADV
cana-5720	160	24	y	y	PROPN
cana-5720	160	25	is	be	AUX
cana-5720	160	26	normal	normal	ADJ
cana-5720	160	27	.	.	PUNCT
cana-5720	161	1	communications	communication	NOUN
cana-5720	161	2	on	on	ADP
cana-5720	161	3	applied	apply	VERB
cana-5720	161	4	nonlinear	nonlinear	ADJ
cana-5720	161	5	analysis	analysis	NOUN
cana-5720	161	6	issn	issn	NOUN
cana-5720	161	7	:	:	PUNCT
cana-5720	161	8	1074	1074	NUM
cana-5720	161	9	-	-	PUNCT
cana-5720	161	10	133x	133x	NUM
cana-5720	161	11	vol	vol	VERB
cana-5720	161	12	32	32	NUM
cana-5720	161	13	no	no	NOUN
cana-5720	161	14	.	.	PUNCT
cana-5720	162	1	10s	10	NOUN
cana-5720	162	2	(	(	PUNCT
cana-5720	162	3	2025	2025	NUM
cana-5720	162	4	)	)	PUNCT
cana-5720	162	5	2807	2807	NUM
cana-5720	162	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5720	162	7	proof	proof	NOUN
cana-5720	162	8	let	let	VERB
cana-5720	162	9	a	a	PRON
cana-5720	162	10	and	and	CCONJ
cana-5720	162	11	b	b	NOUN
cana-5720	162	12	be	be	AUX
cana-5720	162	13	any	any	DET
cana-5720	162	14	disjoint	disjoint	NOUN
cana-5720	162	15	closed	close	VERB
cana-5720	162	16	sets	set	NOUN
cana-5720	162	17	of	of	ADP
cana-5720	162	18	y.	y.	NOUN
cana-5720	162	19	then	then	ADV
cana-5720	162	20	f-1(a	f-1(a	NOUN
cana-5720	162	21	)	)	PUNCT
cana-5720	162	22	and	and	CCONJ
cana-5720	162	23	f-1(b	f-1(b	NOUN
cana-5720	162	24	)	)	PUNCT
cana-5720	162	25	are	be	AUX
cana-5720	162	26	disjoint	disjoint	NOUN
cana-5720	162	27	closed	closed	ADJ
cana-5720	162	28	sets	set	NOUN
cana-5720	162	29	of	of	ADP
cana-5720	162	30	x.	x.	NOUN
cana-5720	162	31	since	since	SCONJ
cana-5720	162	32	x	x	PRON
cana-5720	162	33	is	be	AUX
cana-5720	162	34	normal	normal	ADJ
cana-5720	162	35	,	,	PUNCT
cana-5720	162	36	there	there	PRON
cana-5720	162	37	exist	exist	VERB
cana-5720	162	38	disjoint	disjoint	ADJ
cana-5720	162	39	open	open	ADJ
cana-5720	162	40	sets	set	NOUN
cana-5720	162	41	u	u	NOUN
cana-5720	162	42	and	and	CCONJ
cana-5720	162	43	v	v	ADP
cana-5720	162	44	such	such	ADJ
cana-5720	162	45	that	that	DET
cana-5720	162	46	f-1(a	f-1(a	NOUN
cana-5720	162	47	)	)	PUNCT
cana-5720	162	48			PROPN
cana-5720	162	49	u	u	NOUN
cana-5720	162	50	and	and	CCONJ
cana-5720	162	51	f-1(b	f-1(b	NOUN
cana-5720	162	52	)	)	PUNCT
cana-5720	163	1			PROPN
cana-5720	164	1	v.	v.	CCONJ
cana-5720	164	2	let	let	VERB
cana-5720	164	3	g	g	PROPN
cana-5720	164	4	=	=	PROPN
cana-5720	164	5	int(cl(u	int(cl(u	PROPN
cana-5720	164	6	)	)	PUNCT
cana-5720	164	7	)	)	PUNCT
cana-5720	165	1	and	and	CCONJ
cana-5720	165	2	h	h	NOUN
cana-5720	165	3	=	=	SYM
cana-5720	165	4	int(cl(v	int(cl(v	PROPN
cana-5720	165	5	)	)	PUNCT
cana-5720	165	6	)	)	PUNCT
cana-5720	166	1	,	,	PUNCT
cana-5720	166	2	then	then	ADV
cana-5720	166	3	g	g	PROPN
cana-5720	166	4	and	and	CCONJ
cana-5720	166	5	h	h	NOUN
cana-5720	166	6	are	be	AUX
cana-5720	166	7	disjoint	disjoint	VERB
cana-5720	166	8	regular	regular	ADJ
cana-5720	166	9	open	open	ADJ
cana-5720	166	10	sets	set	NOUN
cana-5720	166	11	of	of	ADP
cana-5720	166	12	x	x	SYM
cana-5720	166	13	such	such	ADJ
cana-5720	166	14	that	that	DET
cana-5720	166	15	f-1(a	f-1(a	NOUN
cana-5720	166	16	)	)	PUNCT
cana-5720	166	17			PROPN
cana-5720	166	18	g	g	NOUN
cana-5720	166	19	and	and	CCONJ
cana-5720	166	20	f-1(b	f-1(b	PROPN
cana-5720	166	21	)	)	PUNCT
cana-5720	167	1			PROPN
cana-5720	167	2	h.	h.	PROPN
cana-5720	167	3	by	by	ADP
cana-5720	167	4	theorem	theorem	PROPN
cana-5720	167	5	1.3.13	1.3.13	NUM
cana-5720	167	6	,	,	PUNCT
cana-5720	167	7	there	there	PRON
cana-5720	167	8	exists	exist	VERB
cana-5720	167	9	gωα	gωα	PROPN
cana-5720	167	10	-open	-open	PROPN
cana-5720	167	11	sets	set	VERB
cana-5720	167	12	k	k	NOUN
cana-5720	167	13	and	and	CCONJ
cana-5720	167	14	l	l	NOUN
cana-5720	167	15	of	of	ADP
cana-5720	167	16	y	y	PRON
cana-5720	167	17	such	such	ADJ
cana-5720	167	18	that	that	SCONJ
cana-5720	167	19	a	a	DET
cana-5720	167	20			PROPN
cana-5720	167	21	k	k	PROPN
cana-5720	167	22	,	,	PUNCT
cana-5720	167	23	b	b	PROPN
cana-5720	167	24			PROPN
cana-5720	167	25	l	l	PROPN
cana-5720	167	26	,	,	PUNCT
cana-5720	167	27	f-1(k	f-1(k	NOUN
cana-5720	167	28	)	)	PUNCT
cana-5720	167	29			PROPN
cana-5720	167	30	g	g	PROPN
cana-5720	167	31	and	and	CCONJ
cana-5720	167	32	f-1(l	f-1(l	NOUN
cana-5720	167	33	)	)	PUNCT
cana-5720	168	1			PROPN
cana-5720	168	2	h.	h.	PROPN
cana-5720	168	3	since	since	SCONJ
cana-5720	168	4	g	g	PROPN
cana-5720	168	5	and	and	CCONJ
cana-5720	168	6	h	h	NOUN
cana-5720	168	7	are	be	AUX
cana-5720	168	8	disjoint	disjoint	ADJ
cana-5720	168	9	,	,	PUNCT
cana-5720	168	10	so	so	ADV
cana-5720	168	11	are	be	AUX
cana-5720	168	12	k	k	PROPN
cana-5720	168	13	and	and	CCONJ
cana-5720	168	14	l.	l.	PROPN
cana-5720	168	15	it	it	PRON
cana-5720	168	16	follows	follow	VERB
cana-5720	168	17	from	from	ADP
cana-5720	168	18	theorem	theorem	ADJ
cana-5720	168	19	1.4.1	1.4.1	NUM
cana-5720	168	20	that	that	SCONJ
cana-5720	168	21	y	y	PROPN
cana-5720	168	22	is	be	AUX
cana-5720	168	23	normal	normal	ADJ
cana-5720	168	24	.	.	PUNCT
cana-5720	169	1	theorem	theorem	VERB
cana-5720	169	2	4.3	4.3	NUM
cana-5720	169	3	if	if	SCONJ
cana-5720	169	4	f	f	X
cana-5720	169	5	:	:	PUNCT
cana-5720	169	6	x	x	X
cana-5720	169	7	→	→	SYM
cana-5720	169	8	y	y	PROPN
cana-5720	169	9	is	be	AUX
cana-5720	169	10	an	an	DET
cana-5720	169	11	almost	almost	ADV
cana-5720	169	12	gωα	gωα	NOUN
cana-5720	169	13	-closed	-closed	ADJ
cana-5720	169	14	continuous	continuous	ADJ
cana-5720	169	15	surjection	surjection	NOUN
cana-5720	169	16	and	and	CCONJ
cana-5720	169	17	x	x	NOUN
cana-5720	169	18	is	be	AUX
cana-5720	169	19	a	a	DET
cana-5720	169	20	weakly	weakly	ADJ
cana-5720	169	21	normal	normal	ADJ
cana-5720	169	22	space	space	NOUN
cana-5720	169	23	,	,	PUNCT
cana-5720	169	24	then	then	ADV
cana-5720	169	25	y	y	PROPN
cana-5720	169	26	is	be	AUX
cana-5720	169	27	weakly	weakly	ADV
cana-5720	169	28	normal	normal	ADJ
cana-5720	169	29	.	.	PUNCT
cana-5720	170	1	proof	proof	NOUN
cana-5720	170	2	let	let	VERB
cana-5720	170	3	{	{	PUNCT
cana-5720	170	4	fn	fn	AUX
cana-5720	170	5	}	}	PUNCT
cana-5720	170	6	be	be	AUX
cana-5720	170	7	any	any	DET
cana-5720	170	8	decreasing	decrease	VERB
cana-5720	170	9	sequence	sequence	NOUN
cana-5720	170	10	of	of	ADP
cana-5720	170	11	closed	closed	ADJ
cana-5720	170	12	sets	set	NOUN
cana-5720	170	13	of	of	ADP
cana-5720	170	14	y	y	PROPN
cana-5720	170	15	with	with	ADP
cana-5720	170	16	no	no	DET
cana-5720	170	17	common	common	ADJ
cana-5720	170	18	point	point	NOUN
cana-5720	170	19	and	and	CCONJ
cana-5720	170	20	any	any	DET
cana-5720	170	21	open	open	ADJ
cana-5720	170	22	set	set	NOUN
cana-5720	170	23	v	v	NOUN
cana-5720	170	24	of	of	ADP
cana-5720	170	25	y	y	PRON
cana-5720	170	26	such	such	ADJ
cana-5720	170	27	that	that	DET
cana-5720	170	28	f1	f1	NOUN
cana-5720	171	1			PROPN
cana-5720	171	2	v.	v.	PROPN
cana-5720	171	3	then	then	ADV
cana-5720	171	4	{	{	PUNCT
cana-5720	171	5	f-1(fn	f-1(fn	NOUN
cana-5720	171	6	)	)	PUNCT
cana-5720	171	7	}	}	PUNCT
cana-5720	171	8	is	be	AUX
cana-5720	171	9	a	a	DET
cana-5720	171	10	decreasing	decrease	VERB
cana-5720	171	11	sequence	sequence	NOUN
cana-5720	171	12	of	of	ADP
cana-5720	171	13	closed	closed	ADJ
cana-5720	171	14	sets	set	NOUN
cana-5720	171	15	of	of	ADP
cana-5720	171	16	x	x	PUNCT
cana-5720	171	17	with	with	ADP
cana-5720	171	18	no	no	DET
cana-5720	171	19	common	common	ADJ
cana-5720	171	20	point	point	NOUN
cana-5720	171	21	and	and	CCONJ
cana-5720	171	22	f-1(v	f-1(v	NOUN
cana-5720	171	23	)	)	PUNCT
cana-5720	171	24	is	be	AUX
cana-5720	171	25	an	an	DET
cana-5720	171	26	open	open	ADJ
cana-5720	171	27	set	set	NOUN
cana-5720	171	28	of	of	ADP
cana-5720	171	29	x	x	INTJ
cana-5720	171	30	such	such	ADJ
cana-5720	171	31	that	that	DET
cana-5720	171	32	f-1(f1	f-1(f1	NOUN
cana-5720	171	33	)	)	PUNCT
cana-5720	171	34			PROPN
cana-5720	171	35	f-1(v	f-1(v	PROPN
cana-5720	171	36	)	)	PUNCT
cana-5720	171	37	.	.	PUNCT
cana-5720	172	1	since	since	SCONJ
cana-5720	172	2	x	x	PRON
cana-5720	172	3	is	be	AUX
cana-5720	172	4	weakly	weakly	ADV
cana-5720	172	5	normal	normal	ADJ
cana-5720	172	6	,	,	PUNCT
cana-5720	172	7	by	by	ADP
cana-5720	172	8	lemma	lemma	PROPN
cana-5720	172	9	1.4.7	1.4.7	PROPN
cana-5720	172	10	,	,	PUNCT
cana-5720	172	11	there	there	PRON
cana-5720	172	12	exist	exist	VERB
cana-5720	172	13	n	n	PRON
cana-5720	172	14			NOUN
cana-5720	172	15	n	n	CCONJ
cana-5720	172	16	and	and	CCONJ
cana-5720	172	17	an	an	DET
cana-5720	172	18	open	open	ADJ
cana-5720	172	19	set	set	NOUN
cana-5720	172	20	u	u	NOUN
cana-5720	172	21	of	of	ADP
cana-5720	172	22	x	x	SYM
cana-5720	172	23	such	such	ADJ
cana-5720	172	24	that	that	PRON
cana-5720	172	25	f-1(fn	f-1(fn	NOUN
cana-5720	172	26	)	)	PUNCT
cana-5720	172	27			PROPN
cana-5720	172	28	u	u	NOUN
cana-5720	172	29			PROPN
cana-5720	172	30	cl(u	cl(u	PROPN
cana-5720	172	31	)	)	PUNCT
cana-5720	172	32			PROPN
cana-5720	172	33	f-1(v	f-1(v	PROPN
cana-5720	172	34	)	)	PUNCT
cana-5720	172	35	.	.	PUNCT
cana-5720	173	1	therefore	therefore	ADV
cana-5720	173	2	,	,	PUNCT
cana-5720	173	3	f1(fn	f1(fn	PROPN
cana-5720	173	4	)	)	PUNCT
cana-5720	173	5			PROPN
cana-5720	173	6	int(cl(u	int(cl(u	PROPN
cana-5720	173	7	)	)	PUNCT
cana-5720	173	8	)	)	PUNCT
cana-5720	173	9	and	and	CCONJ
cana-5720	173	10	by	by	ADP
cana-5720	173	11	corollary	corollary	ADJ
cana-5720	173	12	1.3.14	1.3.14	NUM
cana-5720	173	13	,	,	PUNCT
cana-5720	173	14	there	there	PRON
cana-5720	173	15	exists	exist	VERB
cana-5720	173	16	an	an	DET
cana-5720	173	17	-open	-open	PROPN
cana-5720	173	18	set	set	VERB
cana-5720	173	19	g	g	NOUN
cana-5720	173	20	of	of	ADP
cana-5720	173	21	y	y	PRON
cana-5720	173	22	such	such	ADJ
cana-5720	173	23	that	that	DET
cana-5720	173	24	fn	fn	VERB
cana-5720	173	25			PROPN
cana-5720	173	26	g	g	PROPN
cana-5720	173	27	and	and	CCONJ
cana-5720	173	28	f1(g	f1(g	NUM
cana-5720	173	29	)	)	PUNCT
cana-5720	173	30			PROPN
cana-5720	173	31	int(cl(u	int(cl(u	PROPN
cana-5720	173	32	)	)	PUNCT
cana-5720	173	33	)	)	PUNCT
cana-5720	173	34	.	.	PUNCT
cana-5720	174	1	since	since	SCONJ
cana-5720	174	2	cl(u	cl(u	NUM
cana-5720	174	3	)	)	PUNCT
cana-5720	174	4	is	be	AUX
cana-5720	174	5	regular	regular	ADJ
cana-5720	174	6	closed	closed	ADJ
cana-5720	174	7	and	and	CCONJ
cana-5720	174	8	f	f	NOUN
cana-5720	174	9	is	be	AUX
cana-5720	174	10	almost	almost	ADV
cana-5720	174	11	gωα	gωα	NOUN
cana-5720	174	12	-closed	-close	VERB
cana-5720	174	13	,	,	PUNCT
cana-5720	174	14	f(cl(u	f(cl(u	PROPN
cana-5720	174	15	)	)	PUNCT
cana-5720	174	16	)	)	PUNCT
cana-5720	174	17	is	be	AUX
cana-5720	174	18	gωα	gωα	PROPN
cana-5720	174	19	-closed	-close	VERB
cana-5720	174	20	in	in	ADP
cana-5720	174	21	y.	y.	PROPN
cana-5720	174	22	thus	thus	ADV
cana-5720	174	23	,	,	PUNCT
cana-5720	174	24	we	we	PRON
cana-5720	174	25	obtain	obtain	VERB
cana-5720	174	26	fn	fn	NOUN
cana-5720	174	27			PROPN
cana-5720	174	28	g	g	PROPN
cana-5720	174	29			PROPN
cana-5720	174	30	cl(g	cl(g	PROPN
cana-5720	174	31	)	)	PUNCT
cana-5720	175	1			PROPN
cana-5720	175	2	cl(f(cl(u	cl(f(cl(u	PROPN
cana-5720	175	3	)	)	PUNCT
cana-5720	175	4	)	)	PUNCT
cana-5720	175	5	)	)	PUNCT
cana-5720	176	1			PROPN
cana-5720	176	2	v.	v.	CCONJ
cana-5720	176	3	let	let	VERB
cana-5720	176	4	h	h	NOUN
cana-5720	176	5	=	=	SYM
cana-5720	176	6	int(cl(int(g	int(cl(int(g	PROPN
cana-5720	176	7	)	)	PUNCT
cana-5720	176	8	)	)	PUNCT
cana-5720	176	9	)	)	PUNCT
cana-5720	176	10	,	,	PUNCT
cana-5720	176	11	then	then	ADV
cana-5720	176	12	by	by	ADP
cana-5720	176	13	lemma	lemma	PROPN
cana-5720	176	14	7.2.4	7.2.4	NUM
cana-5720	176	15	we	we	PRON
cana-5720	176	16	have	have	VERB
cana-5720	176	17	fn	fn	NOUN
cana-5720	177	1			PROPN
cana-5720	177	2	h	h	NOUN
cana-5720	177	3			PROPN
cana-5720	177	4	cl(h	cl(h	VERB
cana-5720	177	5	)	)	PUNCT
cana-5720	177	6	=	=	SYM
cana-5720	177	7	cl(g	cl(g	PROPN
cana-5720	177	8	)	)	PUNCT
cana-5720	178	1			PROPN
cana-5720	178	2	v.	v.	ADP
cana-5720	178	3	it	it	PRON
cana-5720	178	4	follows	follow	VERB
cana-5720	178	5	from	from	ADP
cana-5720	178	6	lemma	lemma	PROPN
cana-5720	178	7	1.2.5	1.2.5	NUM
cana-5720	178	8	that	that	PRON
cana-5720	178	9	y	y	PROPN
cana-5720	178	10	is	be	AUX
cana-5720	178	11	weakly	weakly	ADV
cana-5720	178	12	normal	normal	ADJ
cana-5720	178	13	.	.	PUNCT
cana-5720	179	1	theorem	theorem	VERB
cana-5720	179	2	4.4	4.4	NUM
cana-5720	179	3	the	the	DET
cana-5720	179	4	following	following	NOUN
cana-5720	179	5	are	be	AUX
cana-5720	179	6	equivalent	equivalent	ADJ
cana-5720	179	7	for	for	ADP
cana-5720	179	8	a	a	DET
cana-5720	179	9	space	space	NOUN
cana-5720	179	10	x	x	NOUN
cana-5720	179	11	:	:	PUNCT
cana-5720	179	12	(	(	PUNCT
cana-5720	179	13	i	i	NOUN
cana-5720	179	14	)	)	PUNCT
cana-5720	179	15	x	x	VERB
cana-5720	179	16	is	be	AUX
cana-5720	179	17	mildly	mildly	ADV
cana-5720	179	18	normal	normal	ADJ
cana-5720	179	19	;	;	PUNCT
cana-5720	179	20	(	(	PUNCT
cana-5720	179	21	ii	ii	NOUN
cana-5720	179	22	)	)	PUNCT
cana-5720	179	23	for	for	ADP
cana-5720	179	24	any	any	DET
cana-5720	179	25	disjoint	disjoint	ADJ
cana-5720	179	26	h	h	NOUN
cana-5720	179	27	,	,	PUNCT
cana-5720	179	28	k	k	PROPN
cana-5720	180	1			PROPN
cana-5720	180	2	rc	rc	PROPN
cana-5720	180	3	(	(	PUNCT
cana-5720	180	4	x	x	NOUN
cana-5720	180	5	)	)	PUNCT
cana-5720	180	6	,	,	PUNCT
cana-5720	180	7	there	there	PRON
cana-5720	180	8	exist	exist	VERB
cana-5720	180	9	disjoint	disjoint	NOUN
cana-5720	180	10	gωα	gωα	X
cana-5720	180	11	-open	-open	PROPN
cana-5720	180	12	sets	set	VERB
cana-5720	180	13	u	u	NOUN
cana-5720	180	14	,	,	PUNCT
cana-5720	180	15	v	v	ADP
cana-5720	180	16	such	such	ADJ
cana-5720	180	17	that	that	DET
cana-5720	180	18	h	h	NOUN
cana-5720	180	19			PROPN
cana-5720	180	20	u	u	PROPN
cana-5720	180	21	and	and	CCONJ
cana-5720	180	22	k	k	PROPN
cana-5720	180	23			PROPN
cana-5720	180	24	v	v	PROPN
cana-5720	180	25	;	;	PUNCT
cana-5720	180	26	(	(	PUNCT
cana-5720	180	27	iii	iii	NOUN
cana-5720	180	28	)	)	PUNCT
cana-5720	180	29	for	for	ADP
cana-5720	180	30	any	any	DET
cana-5720	180	31	disjoint	disjoint	ADJ
cana-5720	180	32	h	h	NOUN
cana-5720	180	33	,	,	PUNCT
cana-5720	180	34	k	k	PROPN
cana-5720	180	35			PROPN
cana-5720	180	36	rc	rc	PROPN
cana-5720	180	37	(	(	PUNCT
cana-5720	180	38	x	x	NOUN
cana-5720	180	39	)	)	PUNCT
cana-5720	180	40	,	,	PUNCT
cana-5720	180	41	there	there	PRON
cana-5720	180	42	exist	exist	VERB
cana-5720	180	43	disjoint	disjoint	NOUN
cana-5720	180	44	gs	gs	PUNCT
cana-5720	180	45	-	-	ADJ
cana-5720	180	46	open	open	ADJ
cana-5720	180	47	sets	set	VERB
cana-5720	180	48	u	u	NOUN
cana-5720	180	49	,	,	PUNCT
cana-5720	180	50	v	v	ADP
cana-5720	180	51	such	such	ADJ
cana-5720	180	52	that	that	DET
cana-5720	180	53	h	h	NOUN
cana-5720	180	54			PROPN
cana-5720	180	55	u	u	PROPN
cana-5720	180	56	and	and	CCONJ
cana-5720	180	57	k	k	PROPN
cana-5720	180	58			PROPN
cana-5720	180	59	v	v	PROPN
cana-5720	180	60	;	;	PUNCT
cana-5720	180	61	(	(	PUNCT
cana-5720	180	62	iv	iv	X
cana-5720	180	63	)	)	PUNCT
cana-5720	180	64	for	for	ADP
cana-5720	180	65	any	any	DET
cana-5720	180	66	disjoint	disjoint	ADJ
cana-5720	180	67	h	h	NOUN
cana-5720	180	68	,	,	PUNCT
cana-5720	180	69	k	k	PROPN
cana-5720	180	70			PROPN
cana-5720	180	71	rc	rc	PROPN
cana-5720	180	72	(	(	PUNCT
cana-5720	180	73	x	x	NOUN
cana-5720	180	74	)	)	PUNCT
cana-5720	180	75	,	,	PUNCT
cana-5720	180	76	there	there	PRON
cana-5720	180	77	exist	exist	VERB
cana-5720	180	78	disjoint	disjoint	ADJ
cana-5720	180	79	rg	rg	NOUN
cana-5720	180	80	-	-	PUNCT
cana-5720	180	81	open	open	ADJ
cana-5720	180	82	sets	set	VERB
cana-5720	180	83	u	u	NOUN
cana-5720	180	84	,	,	PUNCT
cana-5720	180	85	v	v	ADP
cana-5720	180	86	such	such	ADJ
cana-5720	180	87	that	that	DET
cana-5720	180	88	h	h	NOUN
cana-5720	180	89			PROPN
cana-5720	180	90	u	u	PROPN
cana-5720	180	91	and	and	CCONJ
cana-5720	180	92	k	k	PROPN
cana-5720	180	93			PROPN
cana-5720	180	94	v	v	PROPN
cana-5720	180	95	;	;	PUNCT
cana-5720	180	96	(	(	PUNCT
cana-5720	180	97	v	v	NOUN
cana-5720	180	98	)	)	PUNCT
cana-5720	180	99	for	for	ADP
cana-5720	180	100	any	any	DET
cana-5720	180	101	h	h	NOUN
cana-5720	180	102			PROPN
cana-5720	180	103	rc	rc	PROPN
cana-5720	180	104	(	(	PUNCT
cana-5720	180	105	x	x	NOUN
cana-5720	180	106	)	)	PUNCT
cana-5720	180	107	and	and	CCONJ
cana-5720	180	108	any	any	DET
cana-5720	180	109	v	v	NOUN
cana-5720	180	110			PROPN
cana-5720	180	111	ro	ro	X
cana-5720	180	112	(	(	PUNCT
cana-5720	180	113	x	x	X
cana-5720	180	114	)	)	PUNCT
cana-5720	180	115	containing	contain	VERB
cana-5720	180	116	h	h	NOUN
cana-5720	180	117	,	,	PUNCT
cana-5720	180	118	there	there	PRON
cana-5720	180	119	exists	exist	VERB
cana-5720	180	120	an	an	DET
cana-5720	180	121	rg	rg	NOUN
cana-5720	180	122	-	-	PUNCT
cana-5720	180	123	open	open	ADJ
cana-5720	180	124	set	set	NOUN
cana-5720	180	125	u	u	NOUN
cana-5720	180	126	of	of	ADP
cana-5720	180	127	x	x	SYM
cana-5720	180	128	such	such	ADJ
cana-5720	180	129	that	that	DET
cana-5720	180	130	h	h	NOUN
cana-5720	180	131			PROPN
cana-5720	180	132	u	u	PROPN
cana-5720	180	133			PROPN
cana-5720	180	134	cl(u	cl(u	PROPN
cana-5720	180	135	)	)	PUNCT
cana-5720	181	1			PROPN
cana-5720	181	2	v	v	ADP
cana-5720	181	3	;	;	PUNCT
cana-5720	181	4	(	(	PUNCT
cana-5720	181	5	vi	vi	NOUN
cana-5720	181	6	)	)	PUNCT
cana-5720	181	7	for	for	ADP
cana-5720	181	8	any	any	DET
cana-5720	181	9	h	h	NOUN
cana-5720	181	10			PROPN
cana-5720	181	11	rc	rc	PROPN
cana-5720	181	12	(	(	PUNCT
cana-5720	181	13	x	x	NOUN
cana-5720	181	14	)	)	PUNCT
cana-5720	181	15	and	and	CCONJ
cana-5720	181	16	any	any	DET
cana-5720	181	17	v	v	NOUN
cana-5720	181	18			PROPN
cana-5720	181	19	ro	ro	X
cana-5720	181	20	(	(	PUNCT
cana-5720	181	21	x	x	X
cana-5720	181	22	)	)	PUNCT
cana-5720	181	23	containing	contain	VERB
cana-5720	181	24	h	h	NOUN
cana-5720	181	25	,	,	PUNCT
cana-5720	181	26	there	there	PRON
cana-5720	181	27	exists	exist	VERB
cana-5720	181	28	an	an	DET
cana-5720	181	29	-open	-open	PROPN
cana-5720	181	30	set	set	VERB
cana-5720	181	31	u	u	NOUN
cana-5720	181	32	of	of	ADP
cana-5720	181	33	x	x	SYM
cana-5720	181	34	such	such	ADJ
cana-5720	181	35	that	that	DET
cana-5720	181	36	h	h	NOUN
cana-5720	181	37			PROPN
cana-5720	181	38	u	u	PROPN
cana-5720	181	39			PROPN
cana-5720	181	40	cl(u	cl(u	PROPN
cana-5720	181	41	)	)	PUNCT
cana-5720	182	1			PROPN
cana-5720	182	2	v	v	ADP
cana-5720	182	3	;	;	PUNCT
cana-5720	182	4	(	(	PUNCT
cana-5720	182	5	vii	vii	PROPN
cana-5720	182	6	)	)	PUNCT
cana-5720	182	7	for	for	ADP
cana-5720	182	8	any	any	DET
cana-5720	182	9	disjoint	disjoint	ADJ
cana-5720	182	10	h	h	NOUN
cana-5720	182	11	,	,	PUNCT
cana-5720	182	12	k	k	PROPN
cana-5720	182	13			PROPN
cana-5720	182	14	rc	rc	PROPN
cana-5720	182	15	(	(	PUNCT
cana-5720	182	16	x	x	NOUN
cana-5720	182	17	)	)	PUNCT
cana-5720	182	18	,	,	PUNCT
cana-5720	182	19	there	there	PRON
cana-5720	182	20	exist	exist	VERB
cana-5720	182	21	disjoint	disjoint	NOUN
cana-5720	182	22	-open	-open	PROPN
cana-5720	182	23	sets	set	VERB
cana-5720	182	24	u	u	NOUN
cana-5720	182	25	,	,	PUNCT
cana-5720	182	26	v	v	ADP
cana-5720	182	27	such	such	ADJ
cana-5720	182	28	that	that	DET
cana-5720	182	29	h	h	NOUN
cana-5720	182	30			PROPN
cana-5720	182	31	u	u	PROPN
cana-5720	182	32	and	and	CCONJ
cana-5720	182	33	k	k	PROPN
cana-5720	182	34			PROPN
cana-5720	182	35	v.	v.	ADP
cana-5720	182	36	proof	proof	NOUN
cana-5720	182	37	it	it	PRON
cana-5720	182	38	is	be	AUX
cana-5720	182	39	obvious	obvious	ADJ
cana-5720	182	40	that	that	SCONJ
cana-5720	182	41	(	(	PUNCT
cana-5720	182	42	i	i	NOUN
cana-5720	182	43	)	)	PUNCT
cana-5720	182	44			PROPN
cana-5720	182	45	(	(	PUNCT
cana-5720	182	46	ii	ii	NOUN
cana-5720	182	47	)	)	PUNCT
cana-5720	182	48	,	,	PUNCT
cana-5720	182	49	(	(	PUNCT
cana-5720	182	50	ii	ii	NOUN
cana-5720	182	51	)	)	PUNCT
cana-5720	182	52			NOUN
cana-5720	182	53	(	(	PUNCT
cana-5720	182	54	iii	iii	NOUN
cana-5720	182	55	)	)	PUNCT
cana-5720	182	56	and	and	CCONJ
cana-5720	182	57	(	(	PUNCT
cana-5720	182	58	iii	iii	X
cana-5720	182	59	)	)	PUNCT
cana-5720	182	60			NOUN
cana-5720	182	61	(	(	PUNCT
cana-5720	182	62	iv	iv	NOUN
cana-5720	182	63	)	)	PUNCT
cana-5720	182	64	.	.	PUNCT
cana-5720	183	1	communications	communication	NOUN
cana-5720	183	2	on	on	ADP
cana-5720	183	3	applied	apply	VERB
cana-5720	183	4	nonlinear	nonlinear	ADJ
cana-5720	183	5	analysis	analysis	NOUN
cana-5720	183	6	issn	issn	NOUN
cana-5720	183	7	:	:	PUNCT
cana-5720	183	8	1074	1074	NUM
cana-5720	183	9	-	-	PUNCT
cana-5720	183	10	133x	133x	NUM
cana-5720	183	11	vol	vol	VERB
cana-5720	183	12	32	32	NUM
cana-5720	183	13	no	no	NOUN
cana-5720	183	14	.	.	PUNCT
cana-5720	184	1	10s	10	NOUN
cana-5720	184	2	(	(	PUNCT
cana-5720	184	3	2025	2025	NUM
cana-5720	184	4	)	)	PUNCT
cana-5720	184	5	2808	2808	NUM
cana-5720	184	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5720	184	7	(	(	PUNCT
cana-5720	184	8	iv	iv	X
cana-5720	184	9	)	)	PUNCT
cana-5720	184	10			NOUN
cana-5720	184	11	(	(	PUNCT
cana-5720	184	12	v	v	NOUN
cana-5720	184	13	)	)	PUNCT
cana-5720	184	14	.	.	PUNCT
cana-5720	185	1	let	let	VERB
cana-5720	185	2	h	h	PRON
cana-5720	185	3			PROPN
cana-5720	185	4	rc	rc	PROPN
cana-5720	185	5	(	(	PUNCT
cana-5720	185	6	x	x	NOUN
cana-5720	185	7	)	)	PUNCT
cana-5720	185	8	and	and	CCONJ
cana-5720	185	9	v	v	ADP
cana-5720	185	10			PROPN
cana-5720	185	11	ro	ro	PROPN
cana-5720	185	12	(	(	PUNCT
cana-5720	185	13	x	x	X
cana-5720	185	14	)	)	PUNCT
cana-5720	185	15	containing	contain	VERB
cana-5720	185	16	h.	h.	NOUN
cana-5720	185	17	there	there	PRON
cana-5720	185	18	exist	exist	VERB
cana-5720	185	19	disjoint	disjoint	ADJ
cana-5720	185	20	rg	rg	NOUN
cana-5720	185	21	-	-	PUNCT
cana-5720	185	22	open	open	ADJ
cana-5720	185	23	sets	set	VERB
cana-5720	185	24	u	u	PROPN
cana-5720	185	25	,	,	PUNCT
cana-5720	185	26	w	w	ADP
cana-5720	185	27	such	such	ADJ
cana-5720	185	28	that	that	DET
cana-5720	185	29	h	h	NOUN
cana-5720	185	30			PROPN
cana-5720	185	31	u	u	PROPN
cana-5720	185	32	and	and	CCONJ
cana-5720	185	33	x	x	NOUN
cana-5720	185	34	−	−	NOUN
cana-5720	185	35	v	v	NUM
cana-5720	185	36			PROPN
cana-5720	185	37	w.	w.	PROPN
cana-5720	185	38	by	by	ADP
cana-5720	185	39	lemma	lemma	PROPN
cana-5720	185	40	7.2.8	7.2.8	PROPN
cana-5720	185	41	,	,	PUNCT
cana-5720	185	42	we	we	PRON
cana-5720	185	43	have	have	VERB
cana-5720	185	44	x	x	X
cana-5720	185	45	−	−	NOUN
cana-5720	185	46	v	v	ADP
cana-5720	185	47			PROPN
cana-5720	185	48	int(w	int(w	VERB
cana-5720	185	49	)	)	PUNCT
cana-5720	185	50	and	and	CCONJ
cana-5720	185	51	u	u	NOUN
cana-5720	185	52			X
cana-5720	185	53	int(w	int(w	NOUN
cana-5720	185	54	)	)	PUNCT
cana-5720	185	55	=	=	PUNCT
cana-5720	185	56	.	.	X
cana-5720	185	57	therefore	therefore	ADV
cana-5720	185	58	,	,	PUNCT
cana-5720	185	59	we	we	PRON
cana-5720	185	60	obtain	obtain	VERB
cana-5720	185	61	cl(u	cl(u	NOUN
cana-5720	185	62	)	)	PUNCT
cana-5720	186	1			X
cana-5720	186	2	int(w	int(w	NOUN
cana-5720	186	3	)	)	PUNCT
cana-5720	186	4	=	=	SYM
cana-5720	186	5			NOUN
cana-5720	186	6	and	and	CCONJ
cana-5720	186	7	hence	hence	ADV
cana-5720	186	8	h	h	NOUN
cana-5720	186	9			PROPN
cana-5720	186	10	u	u	PROPN
cana-5720	186	11			PROPN
cana-5720	186	12	cl(u	cl(u	PROPN
cana-5720	186	13	)	)	PUNCT
cana-5720	187	1			PROPN
cana-5720	187	2	x	x	X
cana-5720	188	1	−	−	ADP
cana-5720	188	2	int(w	int(w	NOUN
cana-5720	188	3	)	)	PUNCT
cana-5720	189	1			PROPN
cana-5720	189	2	v.	v.	ADP
cana-5720	189	3	(	(	PUNCT
cana-5720	189	4	v	v	NOUN
cana-5720	189	5	)	)	PUNCT
cana-5720	189	6			NOUN
cana-5720	189	7	(	(	PUNCT
cana-5720	189	8	vi	vi	NOUN
cana-5720	189	9	)	)	PUNCT
cana-5720	189	10	.	.	PUNCT
cana-5720	190	1	let	let	VERB
cana-5720	190	2	h	h	PRON
cana-5720	190	3			PROPN
cana-5720	190	4	rc	rc	PROPN
cana-5720	190	5	(	(	PUNCT
cana-5720	190	6	x	x	NOUN
cana-5720	190	7	)	)	PUNCT
cana-5720	190	8	and	and	CCONJ
cana-5720	190	9	v	v	ADP
cana-5720	190	10			PROPN
cana-5720	190	11	ro	ro	PROPN
cana-5720	190	12	(	(	PUNCT
cana-5720	190	13	x	x	X
cana-5720	190	14	)	)	PUNCT
cana-5720	190	15	containing	contain	VERB
cana-5720	190	16	h.	h.	PROPN
cana-5720	190	17	there	there	PRON
cana-5720	190	18	exists	exist	VERB
cana-5720	190	19	an	an	DET
cana-5720	190	20	rg	rg	NOUN
cana-5720	190	21	-	-	PUNCT
cana-5720	190	22	open	open	NOUN
cana-5720	190	23	set	set	NOUN
cana-5720	190	24	g	g	NOUN
cana-5720	190	25	of	of	ADP
cana-5720	190	26	x	x	SYM
cana-5720	190	27	such	such	ADJ
cana-5720	190	28	that	that	DET
cana-5720	190	29	h	h	NOUN
cana-5720	190	30			PROPN
cana-5720	190	31	g	g	PROPN
cana-5720	190	32			PROPN
cana-5720	190	33	cl(g	cl(g	PROPN
cana-5720	190	34	)	)	PUNCT
cana-5720	191	1			PROPN
cana-5720	191	2	v.	v.	CCONJ
cana-5720	191	3	since	since	SCONJ
cana-5720	191	4	h	h	PROPN
cana-5720	191	5			PROPN
cana-5720	191	6	rc	rc	PROPN
cana-5720	191	7	(	(	PUNCT
cana-5720	191	8	x	x	NOUN
cana-5720	191	9	)	)	PUNCT
cana-5720	191	10	,	,	PUNCT
cana-5720	191	11	by	by	ADP
cana-5720	191	12	lemma	lemma	PROPN
cana-5720	191	13	1.2.8	1.2.8	NUM
cana-5720	191	14	,	,	PUNCT
cana-5720	191	15	we	we	PRON
cana-5720	191	16	have	have	VERB
cana-5720	191	17	h	h	NOUN
cana-5720	191	18			PROPN
cana-5720	191	19	int(g	int(g	NUM
cana-5720	191	20	)	)	PUNCT
cana-5720	191	21	.	.	PUNCT
cana-5720	192	1	put	put	VERB
cana-5720	192	2	u	u	NOUN
cana-5720	192	3	=	=	PUNCT
cana-5720	192	4	int(g	int(g	NUM
cana-5720	192	5	)	)	PUNCT
cana-5720	192	6	,	,	PUNCT
cana-5720	192	7	then	then	ADV
cana-5720	192	8	u	u	NOUN
cana-5720	192	9	is	be	AUX
cana-5720	192	10	-open	-open	PROPN
cana-5720	192	11	in	in	ADP
cana-5720	192	12	x	x	PUNCT
cana-5720	192	13	and	and	CCONJ
cana-5720	192	14	h	h	NOUN
cana-5720	192	15			PROPN
cana-5720	192	16	u	u	PROPN
cana-5720	192	17			PROPN
cana-5720	192	18	cl(u	cl(u	PROPN
cana-5720	192	19	)	)	PUNCT
cana-5720	193	1			PROPN
cana-5720	193	2	v.	v.	ADP
cana-5720	193	3	(	(	PUNCT
cana-5720	193	4	vi	vi	PROPN
cana-5720	193	5	)	)	PUNCT
cana-5720	193	6			NOUN
cana-5720	193	7	(	(	PUNCT
cana-5720	193	8	vii	vii	PROPN
cana-5720	193	9	)	)	PUNCT
cana-5720	193	10	.	.	PUNCT
cana-5720	194	1	let	let	VERB
cana-5720	194	2	h	h	NOUN
cana-5720	194	3	and	and	CCONJ
cana-5720	194	4	k	k	PROPN
cana-5720	194	5	be	be	AUX
cana-5720	194	6	any	any	DET
cana-5720	194	7	disjoint	disjoint	ADJ
cana-5720	194	8	regular	regular	ADJ
cana-5720	194	9	closed	closed	ADJ
cana-5720	194	10	sets	set	NOUN
cana-5720	194	11	of	of	ADP
cana-5720	194	12	x.	x.	NOUN
cana-5720	194	13	then	then	ADV
cana-5720	194	14	,	,	PUNCT
cana-5720	194	15	since	since	SCONJ
cana-5720	194	16	h	h	NOUN
cana-5720	194	17			PROPN
cana-5720	194	18	x	x	PUNCT
cana-5720	195	1	−	−	PROPN
cana-5720	196	1	k	k	PROPN
cana-5720	197	1	and	and	CCONJ
cana-5720	197	2	x	x	SYM
cana-5720	197	3	−	−	PROPN
cana-5720	197	4	k	k	X
cana-5720	198	1			PROPN
cana-5720	198	2	ro	ro	X
cana-5720	198	3	(	(	PUNCT
cana-5720	198	4	x	x	NOUN
cana-5720	198	5	)	)	PUNCT
cana-5720	198	6	,	,	PUNCT
cana-5720	198	7	there	there	PRON
cana-5720	198	8	exists	exist	VERB
cana-5720	198	9	an	an	DET
cana-5720	198	10	-open	-open	PROPN
cana-5720	198	11	set	set	VERB
cana-5720	198	12	u	u	NOUN
cana-5720	198	13	of	of	ADP
cana-5720	198	14	x	x	SYM
cana-5720	198	15	such	such	ADJ
cana-5720	198	16	that	that	DET
cana-5720	198	17	h	h	NOUN
cana-5720	198	18			PROPN
cana-5720	198	19	u	u	PROPN
cana-5720	198	20			PROPN
cana-5720	198	21	cl(u	cl(u	PROPN
cana-5720	198	22	)	)	PUNCT
cana-5720	199	1			PROPN
cana-5720	199	2	x	x	PUNCT
cana-5720	199	3	−	−	PROPN
cana-5720	199	4	k.	k.	NOUN
cana-5720	199	5	put	put	VERB
cana-5720	199	6	v	v	NOUN
cana-5720	199	7	=	=	NOUN
cana-5720	199	8	x	x	NOUN
cana-5720	199	9	−	−	PROPN
cana-5720	199	10	cl(u	cl(u	PROPN
cana-5720	199	11	)	)	PUNCT
cana-5720	199	12	,	,	PUNCT
cana-5720	199	13	then	then	ADV
cana-5720	199	14	u	u	NOUN
cana-5720	199	15	and	and	CCONJ
cana-5720	199	16	v	v	NOUN
cana-5720	199	17	are	be	AUX
cana-5720	199	18	disjoint	disjoint	ADJ
cana-5720	199	19	-open	-open	PROPN
cana-5720	199	20	sets	set	NOUN
cana-5720	199	21	of	of	ADP
cana-5720	199	22	x	x	SYM
cana-5720	199	23	such	such	ADJ
cana-5720	199	24	that	that	DET
cana-5720	199	25	h	h	NOUN
cana-5720	200	1			PROPN
cana-5720	200	2	u	u	PROPN
cana-5720	200	3	and	and	CCONJ
cana-5720	200	4	k	k	PROPN
cana-5720	200	5			PROPN
cana-5720	200	6	v.	v.	PROPN
cana-5720	200	7	(	(	PUNCT
cana-5720	200	8	vii	vii	PROPN
cana-5720	200	9	)	)	PUNCT
cana-5720	200	10			NOUN
cana-5720	200	11	(	(	PUNCT
cana-5720	200	12	i	i	NOUN
cana-5720	200	13	)	)	PUNCT
cana-5720	200	14	.	.	PUNCT
cana-5720	201	1	let	let	VERB
cana-5720	201	2	h	h	NOUN
cana-5720	201	3	and	and	CCONJ
cana-5720	201	4	k	k	PROPN
cana-5720	201	5	be	be	AUX
cana-5720	201	6	any	any	DET
cana-5720	201	7	disjoint	disjoint	ADJ
cana-5720	201	8	regular	regular	ADJ
cana-5720	201	9	closed	closed	ADJ
cana-5720	201	10	sets	set	NOUN
cana-5720	201	11	of	of	ADP
cana-5720	201	12	x.	x.	NOUN
cana-5720	201	13	then	then	ADV
cana-5720	201	14	there	there	PRON
cana-5720	201	15	exist	exist	VERB
cana-5720	201	16	disjoint	disjoint	NOUN
cana-5720	201	17	-open	-open	PROPN
cana-5720	201	18	sets	set	VERB
cana-5720	201	19	a	a	DET
cana-5720	201	20	and	and	CCONJ
cana-5720	201	21	b	b	NOUN
cana-5720	201	22	of	of	ADP
cana-5720	201	23	x	x	SYM
cana-5720	201	24	such	such	ADJ
cana-5720	201	25	that	that	DET
cana-5720	201	26	h	h	NOUN
cana-5720	202	1			PROPN
cana-5720	202	2	a	a	PROPN
cana-5720	202	3	and	and	CCONJ
cana-5720	202	4	k	k	PROPN
cana-5720	202	5			PROPN
cana-5720	202	6	b.	b.	PROPN
cana-5720	203	1	since	since	SCONJ
cana-5720	203	2	a	a	PRON
cana-5720	203	3	and	and	CCONJ
cana-5720	203	4	b	b	NOUN
cana-5720	203	5	are	be	AUX
cana-5720	203	6	disjoint	disjoint	ADJ
cana-5720	203	7	,	,	PUNCT
cana-5720	203	8	we	we	PRON
cana-5720	203	9	have	have	VERB
cana-5720	203	10	int(cl(int(a	int(cl(int(a	PROPN
cana-5720	203	11	)	)	PUNCT
cana-5720	203	12	)	)	PUNCT
cana-5720	203	13	)	)	PUNCT
cana-5720	204	1			X
cana-5720	204	2	int(cl(int(b	int(cl(int(b	PROPN
cana-5720	204	3	)	)	PUNCT
cana-5720	204	4	)	)	PUNCT
cana-5720	204	5	)	)	PUNCT
cana-5720	205	1	=	=	NOUN
cana-5720	205	2	.	.	X
cana-5720	205	3	now	now	ADV
cana-5720	205	4	,	,	PUNCT
cana-5720	205	5	put	put	VERB
cana-5720	205	6	u	u	NOUN
cana-5720	205	7	=	=	SYM
cana-5720	205	8	int(cl(int(a	int(cl(int(a	PROPN
cana-5720	205	9	)	)	PUNCT
cana-5720	205	10	)	)	PUNCT
cana-5720	205	11	)	)	PUNCT
cana-5720	205	12	and	and	CCONJ
cana-5720	205	13	v	v	X
cana-5720	205	14	=	=	SYM
cana-5720	205	15	int(cl(int(b	int(cl(int(b	PROPN
cana-5720	205	16	)	)	PUNCT
cana-5720	205	17	)	)	PUNCT
cana-5720	205	18	)	)	PUNCT
cana-5720	205	19	,	,	PUNCT
cana-5720	205	20	then	then	ADV
cana-5720	205	21	u	u	NOUN
cana-5720	205	22	and	and	CCONJ
cana-5720	205	23	v	v	NOUN
cana-5720	205	24	are	be	AUX
cana-5720	205	25	disjoint	disjoint	ADJ
cana-5720	205	26	open	open	ADJ
cana-5720	205	27	sets	set	NOUN
cana-5720	205	28	of	of	ADP
cana-5720	205	29	x	x	SYM
cana-5720	205	30	such	such	ADJ
cana-5720	205	31	that	that	DET
cana-5720	205	32	h	h	NOUN
cana-5720	205	33			PROPN
cana-5720	205	34	u	u	PROPN
cana-5720	205	35	and	and	CCONJ
cana-5720	205	36	k	k	PROPN
cana-5720	205	37			PROPN
cana-5720	205	38	v.	v.	CCONJ
cana-5720	205	39	therefore	therefore	ADV
cana-5720	205	40	,	,	PUNCT
cana-5720	205	41	x	x	PUNCT
cana-5720	205	42	is	be	AUX
cana-5720	205	43	mildly	mildly	ADV
cana-5720	205	44	normal	normal	ADJ
cana-5720	205	45	.	.	PUNCT
cana-5720	206	1	theorem	theorem	VERB
cana-5720	206	2	4.5	4.5	NUM
cana-5720	206	3	let	let	VERB
cana-5720	206	4	f	f	NOUN
cana-5720	206	5	:	:	PUNCT
cana-5720	206	6	x	x	X
cana-5720	206	7	→	→	SYM
cana-5720	206	8	y	y	X
cana-5720	206	9	be	be	AUX
cana-5720	206	10	an	an	DET
cana-5720	206	11	r	r	NOUN
cana-5720	206	12	-	-	PUNCT
cana-5720	206	13	map	map	NOUN
cana-5720	206	14	and	and	CCONJ
cana-5720	206	15	an	an	DET
cana-5720	206	16	almost	almost	ADV
cana-5720	206	17	gωα	gωα	NOUN
cana-5720	206	18	-closed	-close	VERB
cana-5720	206	19	surjection	surjection	PROPN
cana-5720	206	20	and	and	CCONJ
cana-5720	206	21	x	x	NOUN
cana-5720	206	22	is	be	AUX
cana-5720	206	23	mildly	mildly	ADV
cana-5720	206	24	normal	normal	ADJ
cana-5720	206	25	then	then	ADV
cana-5720	206	26	y	y	PROPN
cana-5720	206	27	is	be	AUX
cana-5720	206	28	mildly	mildly	ADV
cana-5720	206	29	normal	normal	ADJ
cana-5720	206	30	.	.	PUNCT
cana-5720	207	1	proof	proof	NOUN
cana-5720	207	2	let	let	VERB
cana-5720	207	3	a	a	PRON
cana-5720	207	4	and	and	CCONJ
cana-5720	207	5	b	b	NOUN
cana-5720	207	6	be	be	AUX
cana-5720	207	7	any	any	DET
cana-5720	207	8	disjoint	disjoint	ADJ
cana-5720	207	9	regular	regular	ADJ
cana-5720	207	10	closed	closed	ADJ
cana-5720	207	11	sets	set	NOUN
cana-5720	207	12	of	of	ADP
cana-5720	207	13	y.	y.	NOUN
cana-5720	207	14	then	then	ADV
cana-5720	207	15	f-1(a	f-1(a	NOUN
cana-5720	207	16	)	)	PUNCT
cana-5720	207	17	and	and	CCONJ
cana-5720	207	18	f-1(b	f-1(b	NOUN
cana-5720	207	19	)	)	PUNCT
cana-5720	207	20	are	be	AUX
cana-5720	207	21	disjoint	disjoint	NOUN
cana-5720	207	22	regular	regular	ADJ
cana-5720	207	23	closed	closed	ADJ
cana-5720	207	24	sets	set	NOUN
cana-5720	207	25	of	of	ADP
cana-5720	207	26	x.	x.	NOUN
cana-5720	207	27	since	since	SCONJ
cana-5720	207	28	x	x	PRON
cana-5720	207	29	is	be	AUX
cana-5720	207	30	mildly	mildly	ADV
cana-5720	207	31	normal	normal	ADJ
cana-5720	207	32	,	,	PUNCT
cana-5720	207	33	there	there	PRON
cana-5720	207	34	exist	exist	VERB
cana-5720	207	35	disjoint	disjoint	ADJ
cana-5720	207	36	open	open	ADJ
cana-5720	207	37	sets	set	NOUN
cana-5720	207	38	u	u	NOUN
cana-5720	207	39	and	and	CCONJ
cana-5720	207	40	v	v	NOUN
cana-5720	207	41	of	of	ADP
cana-5720	207	42	x	x	PUNCT
cana-5720	207	43	such	such	ADJ
cana-5720	207	44	that	that	SCONJ
cana-5720	207	45	f	f	PROPN
cana-5720	207	46	-1(a	-1(a	PROPN
cana-5720	207	47	)	)	PUNCT
cana-5720	208	1			PROPN
cana-5720	208	2	u	u	NOUN
cana-5720	208	3	and	and	CCONJ
cana-5720	208	4	f-1(b	f-1(b	NOUN
cana-5720	208	5	)	)	PUNCT
cana-5720	208	6			PROPN
cana-5720	208	7	v	v	X
cana-5720	208	8	.	.	PUNCT
cana-5720	209	1	put	put	VERB
cana-5720	209	2	g	g	PROPN
cana-5720	209	3	=	=	PUNCT
cana-5720	209	4	int(cl(u	int(cl(u	PROPN
cana-5720	209	5	)	)	PUNCT
cana-5720	209	6	)	)	PUNCT
cana-5720	210	1	and	and	CCONJ
cana-5720	210	2	h	h	NOUN
cana-5720	210	3	=	=	SYM
cana-5720	210	4	int(cl(v	int(cl(v	PROPN
cana-5720	210	5	)	)	PUNCT
cana-5720	210	6	)	)	PUNCT
cana-5720	211	1	,	,	PUNCT
cana-5720	211	2	then	then	ADV
cana-5720	211	3	g	g	PROPN
cana-5720	211	4	and	and	CCONJ
cana-5720	211	5	h	h	NOUN
cana-5720	211	6	are	be	AUX
cana-5720	211	7	disjoint	disjoint	VERB
cana-5720	211	8	regular	regular	ADJ
cana-5720	211	9	open	open	ADJ
cana-5720	211	10	sets	set	NOUN
cana-5720	211	11	of	of	ADP
cana-5720	211	12	x	x	SYM
cana-5720	211	13	such	such	ADJ
cana-5720	211	14	that	that	DET
cana-5720	211	15	f-1(a	f-1(a	NOUN
cana-5720	211	16	)	)	PUNCT
cana-5720	211	17			PROPN
cana-5720	211	18	g	g	NOUN
cana-5720	211	19	and	and	CCONJ
cana-5720	211	20	f-1(b	f-1(b	PROPN
cana-5720	211	21	)	)	PUNCT
cana-5720	212	1			PROPN
cana-5720	212	2	h.	h.	PROPN
cana-5720	212	3	by	by	ADP
cana-5720	212	4	theorem	theorem	NOUN
cana-5720	212	5	3.13	3.13	NUM
cana-5720	212	6	[	[	X
cana-5720	212	7	14	14	NUM
cana-5720	212	8	]	]	PUNCT
cana-5720	212	9	,	,	PUNCT
cana-5720	212	10	there	there	PRON
cana-5720	212	11	exist	exist	VERB
cana-5720	212	12	gωα	gωα	X
cana-5720	212	13	-open	-open	PROPN
cana-5720	212	14	sets	set	NOUN
cana-5720	212	15	k	k	NOUN
cana-5720	212	16	and	and	CCONJ
cana-5720	212	17	l	l	NOUN
cana-5720	212	18	of	of	ADP
cana-5720	212	19	y	y	PRON
cana-5720	212	20	such	such	ADJ
cana-5720	212	21	that	that	SCONJ
cana-5720	212	22	a	a	DET
cana-5720	212	23			PROPN
cana-5720	212	24	k	k	PROPN
cana-5720	212	25	,	,	PUNCT
cana-5720	212	26	b	b	PROPN
cana-5720	212	27			PROPN
cana-5720	212	28	l	l	PROPN
cana-5720	212	29	,	,	PUNCT
cana-5720	212	30	f-1(k	f-1(k	NOUN
cana-5720	212	31	)	)	PUNCT
cana-5720	213	1			PROPN
cana-5720	213	2	g	g	PROPN
cana-5720	213	3	and	and	CCONJ
cana-5720	213	4	f-1(l	f-1(l	NOUN
cana-5720	213	5	)	)	PUNCT
cana-5720	213	6			PROPN
cana-5720	213	7	h.	h.	PROPN
cana-5720	213	8	since	since	SCONJ
cana-5720	213	9	g	g	PROPN
cana-5720	213	10	and	and	CCONJ
cana-5720	213	11	h	h	NOUN
cana-5720	213	12	are	be	AUX
cana-5720	213	13	disjoint	disjoint	ADJ
cana-5720	213	14	,	,	PUNCT
cana-5720	213	15	so	so	ADV
cana-5720	213	16	are	be	AUX
cana-5720	213	17	k	k	PROPN
cana-5720	213	18	and	and	CCONJ
cana-5720	213	19	l.	l.	PROPN
cana-5720	213	20	it	it	PRON
cana-5720	213	21	follows	follow	VERB
cana-5720	213	22	from	from	ADP
cana-5720	213	23	theorem	theorem	ADJ
cana-5720	213	24	1.4.4	1.4.4	NUM
cana-5720	213	25	that	that	SCONJ
cana-5720	213	26	y	y	PROPN
cana-5720	213	27	is	be	AUX
cana-5720	213	28	mildly	mildly	ADV
cana-5720	213	29	normal	normal	ADJ
cana-5720	213	30	.	.	PUNCT
cana-5720	214	1	theorem	theorem	VERB
cana-5720	214	2	4.6	4.6	NUM
cana-5720	214	3	if	if	SCONJ
cana-5720	214	4	f	f	X
cana-5720	214	5	:	:	PUNCT
cana-5720	214	6	x	x	X
cana-5720	214	7	→	→	SYM
cana-5720	214	8	y	y	PROPN
cana-5720	214	9	is	be	AUX
cana-5720	214	10	an	an	DET
cana-5720	214	11	almost	almost	ADV
cana-5720	214	12	-open	-open	PROPN
cana-5720	214	13	almost	almost	ADV
cana-5720	214	14	gs	g	NOUN
cana-5720	214	15	-	-	PUNCT
cana-5720	214	16	closed	close	VERB
cana-5720	214	17	continuous	continuous	ADJ
cana-5720	214	18	surjection	surjection	NOUN
cana-5720	214	19	and	and	CCONJ
cana-5720	214	20	x	x	NOUN
cana-5720	214	21	is	be	AUX
cana-5720	214	22	an	an	DET
cana-5720	214	23	almost	almost	ADV
cana-5720	214	24	normal	normal	ADJ
cana-5720	214	25	space	space	NOUN
cana-5720	214	26	,	,	PUNCT
cana-5720	214	27	then	then	ADV
cana-5720	214	28	y	y	PROPN
cana-5720	214	29	is	be	AUX
cana-5720	214	30	almost	almost	ADV
cana-5720	214	31	normal	normal	ADJ
cana-5720	214	32	.	.	PUNCT
cana-5720	215	1	proof	proof	NOUN
cana-5720	215	2	let	let	VERB
cana-5720	215	3	b	b	X
cana-5720	215	4	be	be	AUX
cana-5720	215	5	any	any	DET
cana-5720	215	6	closed	closed	ADJ
cana-5720	215	7	set	set	NOUN
cana-5720	215	8	of	of	ADP
cana-5720	215	9	y	y	PROPN
cana-5720	215	10	and	and	CCONJ
cana-5720	215	11	v	v	AUX
cana-5720	215	12			PROPN
cana-5720	215	13	ro	ro	PROPN
cana-5720	215	14	(	(	PUNCT
cana-5720	215	15	y	y	NOUN
cana-5720	215	16	)	)	PUNCT
cana-5720	215	17	containing	contain	VERB
cana-5720	215	18	b.	b.	PROPN
cana-5720	215	19	since	since	SCONJ
cana-5720	215	20	f	f	PROPN
cana-5720	215	21	is	be	AUX
cana-5720	215	22	continuous	continuous	ADJ
cana-5720	215	23	and	and	CCONJ
cana-5720	215	24	almost	almost	ADV
cana-5720	215	25	-open	-open	PROPN
cana-5720	215	26	,	,	PUNCT
cana-5720	215	27	f-1(b	f-1(b	NOUN
cana-5720	215	28	)	)	PUNCT
cana-5720	215	29	is	be	AUX
cana-5720	215	30	closed	closed	ADJ
cana-5720	215	31	and	and	CCONJ
cana-5720	215	32	f-1(v	f-1(v	ADJ
cana-5720	215	33	)	)	PUNCT
cana-5720	215	34			NOUN
cana-5720	215	35	ro(x	ro(x	PUNCT
cana-5720	215	36	)	)	PUNCT
cana-5720	215	37	by	by	ADP
cana-5720	215	38	lemma	lemma	PROPN
cana-5720	215	39	1.2.7	1.2.7	NUM
cana-5720	215	40	.	.	PUNCT
cana-5720	216	1	since	since	SCONJ
cana-5720	216	2	x	x	PRON
cana-5720	216	3	is	be	AUX
cana-5720	216	4	almost	almost	ADV
cana-5720	216	5	normal	normal	ADJ
cana-5720	216	6	and	and	CCONJ
cana-5720	216	7	f-1(b	f-1(b	ADJ
cana-5720	216	8	)	)	PUNCT
cana-5720	216	9			PROPN
cana-5720	216	10	f-1(v	f-1(v	NOUN
cana-5720	216	11	)	)	PUNCT
cana-5720	216	12	,	,	PUNCT
cana-5720	216	13	there	there	PRON
cana-5720	216	14	exists	exist	VERB
cana-5720	216	15	u	u	PRON
cana-5720	216	16			PROPN
cana-5720	216	17	ro	ro	X
cana-5720	216	18	(	(	PUNCT
cana-5720	216	19	x	x	X
cana-5720	216	20	)	)	PUNCT
cana-5720	216	21	such	such	ADJ
cana-5720	216	22	that	that	DET
cana-5720	216	23	f-1(b	f-1(b	NOUN
cana-5720	216	24	)	)	PUNCT
cana-5720	216	25			PROPN
cana-5720	216	26	u	u	NOUN
cana-5720	216	27			PROPN
cana-5720	216	28	cl(u	cl(u	PROPN
cana-5720	216	29	)	)	PUNCT
cana-5720	216	30			PROPN
cana-5720	216	31	f-1(v	f-1(v	PROPN
cana-5720	216	32	)	)	PUNCT
cana-5720	217	1	[	[	X
cana-5720	217	2	15	15	NUM
cana-5720	217	3	,	,	PUNCT
cana-5720	217	4	theorem	theorem	VERB
cana-5720	217	5	2.1	2.1	NUM
cana-5720	217	6	]	]	PUNCT
cana-5720	217	7	.	.	PUNCT
cana-5720	218	1	since	since	SCONJ
cana-5720	218	2	f	f	PROPN
cana-5720	218	3	is	be	AUX
cana-5720	218	4	almost	almost	ADV
cana-5720	218	5	-open	-open	PROPN
cana-5720	218	6	and	and	CCONJ
cana-5720	218	7	almost	almost	ADV
cana-5720	218	8	gs	g	NOUN
cana-5720	218	9	-	-	PUNCT
cana-5720	218	10	closed	closed	ADJ
cana-5720	218	11	,	,	PUNCT
cana-5720	218	12	f(u	f(u	PROPN
cana-5720	218	13	)	)	PUNCT
cana-5720	218	14	is	be	AUX
cana-5720	218	15	-open	-open	PROPN
cana-5720	218	16	and	and	CCONJ
cana-5720	218	17	f(cl(u	f(cl(u	NUM
cana-5720	218	18	)	)	PUNCT
cana-5720	218	19	)	)	PUNCT
cana-5720	219	1	is	be	AUX
cana-5720	219	2	gs	g	NOUN
cana-5720	219	3	-	-	PUNCT
cana-5720	219	4	closed	closed	ADJ
cana-5720	219	5	in	in	ADP
cana-5720	219	6	y.	y.	PROPN
cana-5720	219	7	therefore	therefore	ADV
cana-5720	219	8	,	,	PUNCT
cana-5720	219	9	we	we	PRON
cana-5720	219	10	obtain	obtain	VERB
cana-5720	219	11	b	b	PROPN
cana-5720	219	12			PROPN
cana-5720	219	13	f(u	f(u	PROPN
cana-5720	219	14	)	)	PUNCT
cana-5720	220	1			PROPN
cana-5720	220	2	cl(f(u	cl(f(u	PROPN
cana-5720	220	3	)	)	PUNCT
cana-5720	220	4	)	)	PUNCT
cana-5720	221	1			PROPN
cana-5720	221	2	cl(f(cl(u	cl(f(cl(u	PROPN
cana-5720	221	3	)	)	PUNCT
cana-5720	221	4	)	)	PUNCT
cana-5720	222	1			PROPN
cana-5720	222	2	v.	v.	CCONJ
cana-5720	222	3	put	put	VERB
cana-5720	222	4	g	g	PROPN
cana-5720	222	5	=	=	SYM
cana-5720	222	6	int(cl(int(f(u	int(cl(int(f(u	PROPN
cana-5720	222	7	)	)	PUNCT
cana-5720	222	8	)	)	PUNCT
cana-5720	222	9	)	)	PUNCT
cana-5720	222	10	)	)	PUNCT
cana-5720	222	11	.	.	PUNCT
cana-5720	223	1	then	then	ADV
cana-5720	223	2	g	g	PROPN
cana-5720	223	3	is	be	AUX
cana-5720	223	4	open	open	ADJ
cana-5720	223	5	in	in	ADP
cana-5720	223	6	y	y	PROPN
cana-5720	223	7	and	and	CCONJ
cana-5720	223	8	cl(f(u	cl(f(u	PROPN
cana-5720	223	9	)	)	PUNCT
cana-5720	223	10	)	)	PUNCT
cana-5720	224	1	=	=	SYM
cana-5720	224	2	cl(int(f(u	cl(int(f(u	PROPN
cana-5720	224	3	)	)	PUNCT
cana-5720	224	4	)	)	PUNCT
cana-5720	224	5	)	)	PUNCT
cana-5720	225	1	=	=	PUNCT
cana-5720	225	2	cl(g	cl(g	X
cana-5720	225	3	)	)	PUNCT
cana-5720	225	4	by	by	ADP
cana-5720	225	5	lemma	lemma	PROPN
cana-5720	225	6	1.2.4	1.2.4	NUM
cana-5720	225	7	.	.	PUNCT
cana-5720	225	8	therefore	therefore	ADV
cana-5720	225	9	,	,	PUNCT
cana-5720	225	10	we	we	PRON
cana-5720	225	11	obtain	obtain	VERB
cana-5720	225	12	b	b	PROPN
cana-5720	225	13			PROPN
cana-5720	225	14	f(u	f(u	PROPN
cana-5720	225	15	)	)	PUNCT
cana-5720	226	1			PROPN
cana-5720	226	2	g	g	PROPN
cana-5720	226	3			PROPN
cana-5720	226	4	cl(g	cl(g	X
cana-5720	226	5	)	)	PUNCT
cana-5720	227	1			PROPN
cana-5720	227	2	v.	v.	ADP
cana-5720	227	3	it	it	PRON
cana-5720	227	4	follows	follow	VERB
cana-5720	227	5	from	from	ADP
cana-5720	227	6	[	[	X
cana-5720	227	7	15	15	NUM
cana-5720	227	8	,	,	PUNCT
cana-5720	227	9	theorem	theorem	VERB
cana-5720	227	10	2.1	2.1	NUM
cana-5720	227	11	]	]	PUNCT
cana-5720	227	12	that	that	SCONJ
cana-5720	227	13	y	y	PROPN
cana-5720	227	14	is	be	AUX
cana-5720	227	15	almost	almost	ADV
cana-5720	227	16	normal	normal	ADJ
cana-5720	227	17	.	.	PUNCT
cana-5720	228	1	5	5	X
cana-5720	228	2	.	.	X
cana-5720	228	3	regular	regular	ADJ
cana-5720	228	4	spaces	space	NOUN
cana-5720	228	5	in	in	ADP
cana-5720	228	6	this	this	DET
cana-5720	228	7	section	section	NOUN
cana-5720	228	8	,	,	PUNCT
cana-5720	228	9	we	we	PRON
cana-5720	228	10	improve	improve	VERB
cana-5720	228	11	preservation	preservation	NOUN
cana-5720	228	12	theorems	theorem	NOUN
cana-5720	228	13	of	of	ADP
cana-5720	228	14	regularity	regularity	NOUN
cana-5720	228	15	almost	almost	ADV
cana-5720	228	16	regularity	regularity	NOUN
cana-5720	228	17	and	and	CCONJ
cana-5720	228	18	quasiregularity	quasiregularity	NOUN
cana-5720	228	19	.	.	PUNCT
cana-5720	229	1	theorem	theorem	VERB
cana-5720	229	2	5.1	5.1	NUM
cana-5720	229	3	if	if	SCONJ
cana-5720	229	4	f	f	X
cana-5720	229	5	:	:	PUNCT
cana-5720	229	6	x	x	X
cana-5720	229	7	→	→	SYM
cana-5720	229	8	y	y	PROPN
cana-5720	229	9	is	be	AUX
cana-5720	229	10	an	an	DET
cana-5720	229	11	almost	almost	ADV
cana-5720	229	12	-open	-open	PROPN
cana-5720	229	13	almost	almost	ADV
cana-5720	229	14	gωα	gωα	NOUN
cana-5720	229	15	-closed	-close	VERB
cana-5720	229	16	continuous	continuous	ADJ
cana-5720	229	17	surjection	surjection	NOUN
cana-5720	229	18	and	and	CCONJ
cana-5720	229	19	x	x	NOUN
cana-5720	229	20	is	be	AUX
cana-5720	229	21	a	a	DET
cana-5720	229	22	regular	regular	ADJ
cana-5720	229	23	space	space	NOUN
cana-5720	229	24	,	,	PUNCT
cana-5720	229	25	then	then	ADV
cana-5720	229	26	y	y	PROPN
cana-5720	229	27	is	be	AUX
cana-5720	229	28	regular	regular	ADJ
cana-5720	229	29	.	.	PUNCT
cana-5720	230	1	communications	communication	NOUN
cana-5720	230	2	on	on	ADP
cana-5720	230	3	applied	apply	VERB
cana-5720	230	4	nonlinear	nonlinear	ADJ
cana-5720	230	5	analysis	analysis	NOUN
cana-5720	230	6	issn	issn	NOUN
cana-5720	230	7	:	:	PUNCT
cana-5720	230	8	1074	1074	NUM
cana-5720	230	9	-	-	PUNCT
cana-5720	230	10	133x	133x	NUM
cana-5720	230	11	vol	vol	VERB
cana-5720	230	12	32	32	NUM
cana-5720	230	13	no	no	NOUN
cana-5720	230	14	.	.	PUNCT
cana-5720	231	1	10s	10	NOUN
cana-5720	231	2	(	(	PUNCT
cana-5720	231	3	2025	2025	NUM
cana-5720	231	4	)	)	PUNCT
cana-5720	231	5	2809	2809	NUM
cana-5720	231	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5720	231	7	proof	proof	NOUN
cana-5720	231	8	let	let	VERB
cana-5720	231	9	y	y	PRON
cana-5720	231	10	be	be	AUX
cana-5720	231	11	any	any	DET
cana-5720	231	12	point	point	NOUN
cana-5720	231	13	of	of	ADP
cana-5720	231	14	y	y	PROPN
cana-5720	231	15	and	and	CCONJ
cana-5720	231	16	v	v	ADP
cana-5720	231	17	any	any	DET
cana-5720	231	18	open	open	ADJ
cana-5720	231	19	neighbourhood	neighbourhood	NOUN
cana-5720	231	20	of	of	ADP
cana-5720	231	21	y.	y.	PROPN
cana-5720	231	22	there	there	PRON
cana-5720	231	23	exists	exist	VERB
cana-5720	231	24	a	a	DET
cana-5720	231	25	point	point	NOUN
cana-5720	231	26	x	x	PUNCT
cana-5720	231	27			NOUN
cana-5720	231	28	x	x	PUNCT
cana-5720	231	29	with	with	ADP
cana-5720	231	30	f(x	f(x	PROPN
cana-5720	231	31	)	)	PUNCT
cana-5720	232	1	=	=	PUNCT
cana-5720	232	2	y.	y.	NOUN
cana-5720	232	3	since	since	SCONJ
cana-5720	232	4	x	x	PRON
cana-5720	232	5	is	be	AUX
cana-5720	232	6	regular	regular	ADJ
cana-5720	232	7	and	and	CCONJ
cana-5720	232	8	f	f	PROPN
cana-5720	232	9	is	be	AUX
cana-5720	232	10	continuous	continuous	ADJ
cana-5720	232	11	,	,	PUNCT
cana-5720	232	12	there	there	PRON
cana-5720	232	13	exists	exist	VERB
cana-5720	232	14	an	an	DET
cana-5720	232	15	open	open	ADJ
cana-5720	232	16	set	set	NOUN
cana-5720	232	17	u	u	NOUN
cana-5720	232	18	of	of	ADP
cana-5720	232	19	x	x	SYM
cana-5720	232	20	such	such	ADJ
cana-5720	232	21	that	that	SCONJ
cana-5720	232	22	x	x	SYM
cana-5720	232	23			NOUN
cana-5720	232	24	u	u	NOUN
cana-5720	232	25			PROPN
cana-5720	232	26	cl(u	cl(u	PROPN
cana-5720	232	27	)	)	PUNCT
cana-5720	232	28			PROPN
cana-5720	232	29	f-1(v	f-1(v	PROPN
cana-5720	232	30	)	)	PUNCT
cana-5720	232	31	.	.	PUNCT
cana-5720	233	1	therefore	therefore	ADV
cana-5720	233	2	,	,	PUNCT
cana-5720	233	3	we	we	PRON
cana-5720	233	4	have	have	VERB
cana-5720	233	5	y	y	PROPN
cana-5720	233	6			PROPN
cana-5720	233	7	f(u	f(u	PROPN
cana-5720	233	8	)	)	PUNCT
cana-5720	234	1			PROPN
cana-5720	234	2	f(int(cl(u	f(int(cl(u	PROPN
cana-5720	234	3	)	)	PUNCT
cana-5720	234	4	)	)	PUNCT
cana-5720	234	5	)	)	PUNCT
cana-5720	235	1			PROPN
cana-5720	235	2	f(cl(u	f(cl(u	PROPN
cana-5720	235	3	)	)	PUNCT
cana-5720	235	4	)	)	PUNCT
cana-5720	236	1			PROPN
cana-5720	236	2	v	v	NOUN
cana-5720	236	3	and	and	CCONJ
cana-5720	236	4	f(int(cl(u	f(int(cl(u	PROPN
cana-5720	236	5	)	)	PUNCT
cana-5720	236	6	)	)	PUNCT
cana-5720	236	7	is	be	AUX
cana-5720	236	8	-open	-open	PROPN
cana-5720	236	9	because	because	SCONJ
cana-5720	236	10	int(cl(u	int(cl(u	PROPN
cana-5720	236	11	)	)	PUNCT
cana-5720	236	12	)	)	PUNCT
cana-5720	237	1			NOUN
cana-5720	237	2	ro	ro	X
cana-5720	237	3	(	(	PUNCT
cana-5720	237	4	x	x	NOUN
cana-5720	237	5	)	)	PUNCT
cana-5720	237	6	and	and	CCONJ
cana-5720	237	7	f	f	PROPN
cana-5720	237	8	is	be	AUX
cana-5720	237	9	almost	almost	ADV
cana-5720	237	10	-open	-open	PROPN
cana-5720	237	11	.	.	PUNCT
cana-5720	238	1	since	since	SCONJ
cana-5720	238	2	cl(u	cl(u	NUM
cana-5720	238	3	)	)	PUNCT
cana-5720	238	4			PROPN
cana-5720	238	5	rc	rc	PROPN
cana-5720	238	6	(	(	PUNCT
cana-5720	238	7	x	x	NOUN
cana-5720	238	8	)	)	PUNCT
cana-5720	238	9	and	and	CCONJ
cana-5720	238	10	f	f	PROPN
cana-5720	238	11	is	be	AUX
cana-5720	238	12	almost	almost	ADV
cana-5720	238	13	gωα	gωα	NOUN
cana-5720	238	14	-closed	-close	VERB
cana-5720	238	15	,	,	PUNCT
cana-5720	238	16	f(cl(u	f(cl(u	PROPN
cana-5720	238	17	)	)	PUNCT
cana-5720	238	18	)	)	PUNCT
cana-5720	238	19	is	be	AUX
cana-5720	238	20	gωα	gωα	NOUN
cana-5720	238	21	-closed	-close	VERB
cana-5720	238	22	and	and	CCONJ
cana-5720	238	23	hence	hence	ADV
cana-5720	238	24	y	y	PROPN
cana-5720	238	25			PROPN
cana-5720	238	26	f(int(cl(u	f(int(cl(u	PROPN
cana-5720	238	27	)	)	PUNCT
cana-5720	238	28	)	)	PUNCT
cana-5720	238	29	)	)	PUNCT
cana-5720	239	1			PROPN
cana-5720	239	2	cl(f(int(cl(u	cl(f(int(cl(u	PROPN
cana-5720	239	3	)	)	PUNCT
cana-5720	239	4	)	)	PUNCT
cana-5720	239	5	)	)	PUNCT
cana-5720	239	6	)	)	PUNCT
cana-5720	240	1			PROPN
cana-5720	240	2	cl(f(cl(u	cl(f(cl(u	PROPN
cana-5720	240	3	)	)	PUNCT
cana-5720	240	4	)	)	PUNCT
cana-5720	240	5	)	)	PUNCT
cana-5720	241	1			PROPN
cana-5720	241	2	v.	v.	CCONJ
cana-5720	241	3	it	it	PRON
cana-5720	241	4	follows	follow	VERB
cana-5720	241	5	from	from	ADP
cana-5720	241	6	theorem	theorem	ADJ
cana-5720	241	7	1.2.11	1.2.11	NUM
cana-5720	241	8	that	that	PRON
cana-5720	241	9	y	y	PROPN
cana-5720	241	10	is	be	AUX
cana-5720	241	11	regular	regular	ADJ
cana-5720	241	12	.	.	PUNCT
cana-5720	242	1	theorem	theorem	VERB
cana-5720	242	2	5.2	5.2	NUM
cana-5720	242	3	if	if	SCONJ
cana-5720	242	4	f	f	X
cana-5720	242	5	:	:	PUNCT
cana-5720	242	6	x	x	X
cana-5720	242	7	→	→	SYM
cana-5720	242	8	y	y	PROPN
cana-5720	242	9	is	be	AUX
cana-5720	242	10	an	an	DET
cana-5720	242	11	almost	almost	ADV
cana-5720	242	12	-open	-open	PROPN
cana-5720	242	13	almost	almost	ADV
cana-5720	242	14	gs	gs	PUNCT
cana-5720	242	15	-	-	PUNCT
cana-5720	242	16	closed	close	VERB
cana-5720	242	17	almost	almost	ADV
cana-5720	242	18	continuous	continuous	ADJ
cana-5720	242	19	surjection	surjection	NOUN
cana-5720	242	20	and	and	CCONJ
cana-5720	242	21	x	x	NOUN
cana-5720	242	22	is	be	AUX
cana-5720	242	23	an	an	DET
cana-5720	242	24	almost	almost	ADV
cana-5720	242	25	regular	regular	ADJ
cana-5720	242	26	space	space	NOUN
cana-5720	242	27	,	,	PUNCT
cana-5720	242	28	then	then	ADV
cana-5720	242	29	y	y	PROPN
cana-5720	242	30	is	be	AUX
cana-5720	242	31	almost	almost	ADV
cana-5720	242	32	regular	regular	ADJ
cana-5720	242	33	.	.	PUNCT
cana-5720	243	1	proof	proof	NOUN
cana-5720	243	2	let	let	VERB
cana-5720	243	3	y	y	PRON
cana-5720	243	4	be	be	AUX
cana-5720	243	5	any	any	DET
cana-5720	243	6	point	point	NOUN
cana-5720	243	7	of	of	ADP
cana-5720	243	8	y	y	PROPN
cana-5720	243	9	and	and	CCONJ
cana-5720	243	10	v	v	ADP
cana-5720	243	11			PROPN
cana-5720	243	12	ro	ro	PROPN
cana-5720	243	13	(	(	PUNCT
cana-5720	243	14	y	y	NOUN
cana-5720	243	15	)	)	PUNCT
cana-5720	243	16	containing	contain	VERB
cana-5720	243	17	y.	y.	NOUN
cana-5720	243	18	since	since	SCONJ
cana-5720	243	19	f	f	PROPN
cana-5720	243	20	is	be	AUX
cana-5720	243	21	almost	almost	ADV
cana-5720	243	22	-open	-open	ADJ
cana-5720	244	1	almost	almost	ADV
cana-5720	244	2	continuous	continuous	ADJ
cana-5720	244	3	,	,	PUNCT
cana-5720	244	4	f-1(v	f-1(v	NOUN
cana-5720	244	5	)	)	PUNCT
cana-5720	244	6			NOUN
cana-5720	244	7	ro	ro	X
cana-5720	244	8	(	(	PUNCT
cana-5720	244	9	y	y	NOUN
cana-5720	244	10	)	)	PUNCT
cana-5720	244	11	by	by	ADP
cana-5720	244	12	lemma	lemma	PROPN
cana-5720	244	13	1.2.7	1.2.7	NUM
cana-5720	244	14	.	.	PUNCT
cana-5720	244	15	take	take	VERB
cana-5720	244	16	a	a	DET
cana-5720	244	17	point	point	NOUN
cana-5720	244	18	x	x	PUNCT
cana-5720	244	19			NOUN
cana-5720	244	20	f-1(y	f-1(y	PROPN
cana-5720	244	21	)	)	PUNCT
cana-5720	244	22	.	.	PUNCT
cana-5720	245	1	since	since	SCONJ
cana-5720	245	2	x	x	PRON
cana-5720	245	3	is	be	AUX
cana-5720	245	4	almost	almost	ADV
cana-5720	245	5	regular	regular	ADJ
cana-5720	245	6	,	,	PUNCT
cana-5720	245	7	there	there	PRON
cana-5720	245	8	exists	exist	VERB
cana-5720	245	9	u	u	PRON
cana-5720	245	10			PROPN
cana-5720	245	11	ro	ro	X
cana-5720	245	12	(	(	PUNCT
cana-5720	245	13	x	x	X
cana-5720	245	14	)	)	PUNCT
cana-5720	245	15	such	such	ADJ
cana-5720	245	16	that	that	SCONJ
cana-5720	245	17	x	x	SYM
cana-5720	245	18			NOUN
cana-5720	245	19	u	u	NOUN
cana-5720	245	20			PROPN
cana-5720	245	21	cl(u	cl(u	PROPN
cana-5720	245	22	)	)	PUNCT
cana-5720	245	23			PROPN
cana-5720	245	24	f-1(v	f-1(v	PROPN
cana-5720	245	25	)	)	PUNCT
cana-5720	246	1	[	[	X
cana-5720	246	2	16	16	NUM
cana-5720	246	3	,	,	PUNCT
cana-5720	246	4	theorem	theorem	VERB
cana-5720	246	5	2.2	2.2	NUM
cana-5720	246	6	]	]	PUNCT
cana-5720	246	7	.	.	PUNCT
cana-5720	247	1	hence	hence	ADV
cana-5720	247	2	y	y	PROPN
cana-5720	247	3			PROPN
cana-5720	247	4	f(u	f(u	PROPN
cana-5720	247	5	)	)	PUNCT
cana-5720	248	1			PROPN
cana-5720	248	2	f(cl(u	f(cl(u	PROPN
cana-5720	248	3	)	)	PUNCT
cana-5720	248	4	)	)	PUNCT
cana-5720	249	1			PROPN
cana-5720	249	2	v.	v.	CCONJ
cana-5720	249	3	since	since	SCONJ
cana-5720	249	4	f	f	PROPN
cana-5720	249	5	is	be	AUX
cana-5720	249	6	almost	almost	ADV
cana-5720	249	7	-open	-open	ADJ
cana-5720	249	8	almost	almost	ADV
cana-5720	249	9	gs	g	NOUN
cana-5720	249	10	-	-	PUNCT
cana-5720	249	11	closed	closed	ADJ
cana-5720	249	12	,	,	PUNCT
cana-5720	249	13	f(u	f(u	PROPN
cana-5720	249	14	)	)	PUNCT
cana-5720	249	15	is	be	AUX
cana-5720	249	16	-open	-open	PROPN
cana-5720	249	17	in	in	ADP
cana-5720	249	18	y	y	PROPN
cana-5720	249	19	and	and	CCONJ
cana-5720	249	20	f(cl(u	f(cl(u	PROPN
cana-5720	249	21	)	)	PUNCT
cana-5720	249	22	)	)	PUNCT
cana-5720	249	23	is	be	AUX
cana-5720	249	24	gs	g	NOUN
cana-5720	249	25	-	-	PUNCT
cana-5720	249	26	closed	closed	ADJ
cana-5720	249	27	in	in	ADP
cana-5720	249	28	y	y	PROPN
cana-5720	249	29	and	and	CCONJ
cana-5720	249	30	hence	hence	ADV
cana-5720	249	31	we	we	PRON
cana-5720	249	32	have	have	VERB
cana-5720	249	33	y	y	PROPN
cana-5720	249	34			PROPN
cana-5720	249	35	f(u	f(u	PROPN
cana-5720	249	36	)	)	PUNCT
cana-5720	250	1			PROPN
cana-5720	250	2	cl(f(u	cl(f(u	PROPN
cana-5720	250	3	)	)	PUNCT
cana-5720	250	4	)	)	PUNCT
cana-5720	251	1			PROPN
cana-5720	251	2	cl(f(cl(u	cl(f(cl(u	PROPN
cana-5720	251	3	)	)	PUNCT
cana-5720	251	4	)	)	PUNCT
cana-5720	251	5	)	)	PUNCT
cana-5720	252	1			PROPN
cana-5720	252	2	v.	v.	CCONJ
cana-5720	252	3	it	it	PRON
cana-5720	252	4	follows	follow	VERB
cana-5720	252	5	from	from	ADP
cana-5720	252	6	theorem	theorem	ADJ
cana-5720	252	7	1.2.11	1.2.11	NUM
cana-5720	252	8	that	that	PRON
cana-5720	252	9	y	y	PROPN
cana-5720	252	10	is	be	AUX
cana-5720	252	11	almost	almost	ADV
cana-5720	252	12	regular	regular	ADJ
cana-5720	252	13	.	.	PUNCT
cana-5720	253	1	theorem	theorem	VERB
cana-5720	253	2	5.3	5.3	NUM
cana-5720	253	3	if	if	SCONJ
cana-5720	253	4	f	f	X
cana-5720	253	5	:	:	PUNCT
cana-5720	253	6	x	x	X
cana-5720	253	7	→	→	SYM
cana-5720	253	8	y	y	PROPN
cana-5720	253	9	is	be	AUX
cana-5720	253	10	an	an	DET
cana-5720	253	11	almost	almost	ADV
cana-5720	253	12	feebly	feebly	ADV
cana-5720	253	13	open	open	ADJ
cana-5720	253	14	feebly	feebly	ADV
cana-5720	253	15	continuous	continuous	ADJ
cana-5720	253	16	almost	almost	ADV
cana-5720	253	17	gωα	gωα	NOUN
cana-5720	253	18	-closed	-close	VERB
cana-5720	253	19	surjection	surjection	PROPN
cana-5720	253	20	and	and	CCONJ
cana-5720	253	21	x	x	NOUN
cana-5720	253	22	is	be	AUX
cana-5720	253	23	a	a	DET
cana-5720	253	24	quasi	quasi	ADJ
cana-5720	253	25	-	-	ADJ
cana-5720	253	26	regular	regular	ADJ
cana-5720	253	27	space	space	NOUN
cana-5720	253	28	,	,	PUNCT
cana-5720	253	29	then	then	ADV
cana-5720	253	30	y	y	PROPN
cana-5720	253	31	is	be	AUX
cana-5720	253	32	quasi	quasi	ADJ
cana-5720	253	33	-	-	ADJ
cana-5720	253	34	regular	regular	ADJ
cana-5720	253	35	.	.	PUNCT
cana-5720	254	1	proof	proof	NOUN
cana-5720	254	2	let	let	VERB
cana-5720	254	3	v	v	PART
cana-5720	254	4	be	be	AUX
cana-5720	254	5	any	any	DET
cana-5720	254	6	nonempty	nonempty	ADJ
cana-5720	254	7	open	open	ADJ
cana-5720	254	8	set	set	NOUN
cana-5720	254	9	of	of	ADP
cana-5720	254	10	y.	y.	PROPN
cana-5720	254	11	since	since	SCONJ
cana-5720	254	12	f	f	PROPN
cana-5720	254	13	is	be	AUX
cana-5720	254	14	feebly	feebly	ADV
cana-5720	254	15	continuous	continuous	ADJ
cana-5720	254	16	,	,	PUNCT
cana-5720	254	17	int(f-1(v	int(f-1(v	NOUN
cana-5720	254	18	)	)	PUNCT
cana-5720	254	19	)	)	PUNCT
cana-5720	255	1			VERB
cana-5720	255	2			NOUN
cana-5720	255	3	and	and	CCONJ
cana-5720	255	4	by	by	ADP
cana-5720	255	5	the	the	DET
cana-5720	255	6	quasiregularity	quasiregularity	NOUN
cana-5720	255	7	of	of	ADP
cana-5720	255	8	x	x	SYM
cana-5720	255	9	there	there	PRON
cana-5720	255	10	exists	exist	VERB
cana-5720	255	11	a	a	DET
cana-5720	255	12	nonempty	nonempty	ADJ
cana-5720	255	13	open	open	ADJ
cana-5720	255	14	set	set	NOUN
cana-5720	255	15	u	u	NOUN
cana-5720	255	16	of	of	ADP
cana-5720	255	17	x	x	SYM
cana-5720	255	18	such	such	ADJ
cana-5720	255	19	that	that	SCONJ
cana-5720	255	20	u	u	NOUN
cana-5720	255	21			PROPN
cana-5720	255	22	cl(u	cl(u	PROPN
cana-5720	255	23	)	)	PUNCT
cana-5720	256	1			PROPN
cana-5720	256	2	int(f-1(v	int(f-1(v	NOUN
cana-5720	256	3	)	)	PUNCT
cana-5720	256	4	)	)	PUNCT
cana-5720	256	5	.	.	PUNCT
cana-5720	257	1	we	we	PRON
cana-5720	257	2	have	have	VERB
cana-5720	257	3	f(int(cl(u	f(int(cl(u	PROPN
cana-5720	257	4	)	)	PUNCT
cana-5720	257	5	)	)	PUNCT
cana-5720	257	6	)	)	PUNCT
cana-5720	258	1			PROPN
cana-5720	258	2	f(cl(u	f(cl(u	PROPN
cana-5720	258	3	)	)	PUNCT
cana-5720	258	4	)	)	PUNCT
cana-5720	259	1			PROPN
cana-5720	259	2	v.	v.	CCONJ
cana-5720	259	3	since	since	SCONJ
cana-5720	259	4	f	f	PROPN
cana-5720	259	5	is	be	AUX
cana-5720	259	6	almost	almost	ADV
cana-5720	259	7	feebly	feebly	ADV
cana-5720	259	8	open	open	ADJ
cana-5720	259	9	,	,	PUNCT
cana-5720	259	10	int(f(int(cl(u	int(f(int(cl(u	PROPN
cana-5720	259	11	)	)	PUNCT
cana-5720	259	12	)	)	PUNCT
cana-5720	259	13	)	)	PUNCT
cana-5720	259	14	)	)	PUNCT
cana-5720	260	1			NOUN
cana-5720	260	2	.	.	PUNCT
cana-5720	260	3	since	since	SCONJ
cana-5720	260	4	f	f	PROPN
cana-5720	260	5	is	be	AUX
cana-5720	260	6	almost	almost	ADV
cana-5720	260	7	gωα	gωα	NOUN
cana-5720	260	8	-closed	-close	VERB
cana-5720	260	9	,	,	PUNCT
cana-5720	260	10	f(cl(u	f(cl(u	PROPN
cana-5720	260	11	)	)	PUNCT
cana-5720	260	12	)	)	PUNCT
cana-5720	260	13	is	be	AUX
cana-5720	260	14	gωα	gωα	NOUN
cana-5720	260	15	-closed	-close	VERB
cana-5720	260	16	and	and	CCONJ
cana-5720	260	17	hence	hence	ADV
cana-5720	260	18	cl(f(cl(u	cl(f(cl(u	NOUN
cana-5720	260	19	)	)	PUNCT
cana-5720	260	20	)	)	PUNCT
cana-5720	260	21	)	)	PUNCT
cana-5720	261	1			PROPN
cana-5720	261	2	v.	v.	ADP
cana-5720	261	3	now	now	ADV
cana-5720	261	4	,	,	PUNCT
cana-5720	261	5	put	put	VERB
cana-5720	261	6	g	g	PROPN
cana-5720	261	7	=	=	PUNCT
cana-5720	261	8	int(f(int(cl(u	int(f(int(cl(u	PROPN
cana-5720	261	9	)	)	PUNCT
cana-5720	261	10	)	)	PUNCT
cana-5720	261	11	)	)	PUNCT
cana-5720	261	12	)	)	PUNCT
cana-5720	261	13	,	,	PUNCT
cana-5720	261	14	then	then	ADV
cana-5720	261	15	by	by	ADP
cana-5720	261	16	lemma	lemma	PROPN
cana-5720	261	17	1.2.4	1.2.4	NUM
cana-5720	261	18	we	we	PRON
cana-5720	261	19	obtain	obtain	VERB
cana-5720	261	20			NOUN
cana-5720	261	21			NOUN
cana-5720	261	22	g	g	NOUN
cana-5720	261	23			PROPN
cana-5720	261	24	cl(g	cl(g	X
cana-5720	261	25	)	)	PUNCT
cana-5720	261	26	=	=	SYM
cana-5720	261	27	cl(g	cl(g	PROPN
cana-5720	261	28	)	)	PUNCT
cana-5720	262	1			PROPN
cana-5720	262	2	cl(f(cl(u	cl(f(cl(u	PROPN
cana-5720	262	3	)	)	PUNCT
cana-5720	262	4	)	)	PUNCT
cana-5720	262	5	)	)	PUNCT
cana-5720	263	1			PROPN
cana-5720	263	2	v.	v.	ADP
cana-5720	263	3	this	this	PRON
cana-5720	263	4	shows	show	VERB
cana-5720	263	5	that	that	SCONJ
cana-5720	263	6	y	y	PROPN
cana-5720	263	7	is	be	AUX
cana-5720	263	8	quasiregular	quasiregular	ADJ
cana-5720	263	9	.	.	PUNCT
cana-5720	264	1	theorem	theorem	VERB
cana-5720	264	2	5.4	5.4	NUM
cana-5720	264	3	if	if	SCONJ
cana-5720	264	4	f	f	X
cana-5720	264	5	:	:	PUNCT
cana-5720	264	6	x	x	X
cana-5720	264	7	→	→	SYM
cana-5720	264	8	y	y	PROPN
cana-5720	264	9	is	be	AUX
cana-5720	264	10	an	an	DET
cana-5720	264	11	almost	almost	ADV
cana-5720	264	12	-open	-open	PROPN
cana-5720	264	13	almost	almost	ADV
cana-5720	264	14	gωα	gωα	NOUN
cana-5720	264	15	-closed	-close	VERB
cana-5720	264	16	continuous	continuous	ADJ
cana-5720	264	17	surjection	surjection	NOUN
cana-5720	264	18	and	and	CCONJ
cana-5720	264	19	x	x	NOUN
cana-5720	264	20	is	be	AUX
cana-5720	264	21	a	a	DET
cana-5720	264	22	strongly	strongly	ADV
cana-5720	264	23	s	s	NOUN
cana-5720	264	24	-	-	ADJ
cana-5720	264	25	regular	regular	ADJ
cana-5720	264	26	space	space	NOUN
cana-5720	264	27	,	,	PUNCT
cana-5720	264	28	then	then	ADV
cana-5720	264	29	y	y	PROPN
cana-5720	264	30	is	be	AUX
cana-5720	264	31	strongly	strongly	ADV
cana-5720	264	32	s	s	NOUN
cana-5720	264	33	-	-	NOUN
cana-5720	264	34	regular	regular	ADJ
cana-5720	264	35	.	.	PUNCT
cana-5720	265	1	proof	proof	NOUN
cana-5720	265	2	let	let	VERB
cana-5720	265	3	v	v	PART
cana-5720	265	4	be	be	AUX
cana-5720	265	5	any	any	DET
cana-5720	265	6	open	open	ADJ
cana-5720	265	7	set	set	NOUN
cana-5720	265	8	of	of	ADP
cana-5720	265	9	y	y	PROPN
cana-5720	265	10	and	and	CCONJ
cana-5720	265	11	y	y	PROPN
cana-5720	265	12	any	any	DET
cana-5720	265	13	point	point	NOUN
cana-5720	265	14	of	of	ADP
cana-5720	265	15	v.	v.	ADV
cana-5720	265	16	since	since	SCONJ
cana-5720	265	17	f	f	PROPN
cana-5720	265	18	is	be	AUX
cana-5720	265	19	continuous	continuous	ADJ
cana-5720	265	20	,	,	PUNCT
cana-5720	265	21	f-1(v	f-1(v	NOUN
cana-5720	265	22	)	)	PUNCT
cana-5720	265	23	is	be	AUX
cana-5720	265	24	open	open	ADJ
cana-5720	265	25	in	in	ADP
cana-5720	265	26	x.	x.	NOUN
cana-5720	265	27	for	for	ADP
cana-5720	265	28	a	a	DET
cana-5720	265	29	point	point	NOUN
cana-5720	265	30	x	x	PUNCT
cana-5720	265	31			NOUN
cana-5720	265	32	f-1(y	f-1(y	PROPN
cana-5720	265	33	)	)	PUNCT
cana-5720	265	34	,	,	PUNCT
cana-5720	265	35	there	there	PRON
cana-5720	265	36	exists	exist	VERB
cana-5720	265	37	f	f	PROPN
cana-5720	265	38			PROPN
cana-5720	265	39	rc(x	rc(x	NOUN
cana-5720	265	40	)	)	PUNCT
cana-5720	265	41	such	such	ADJ
cana-5720	265	42	that	that	SCONJ
cana-5720	265	43	x	x	PRON
cana-5720	265	44			NOUN
cana-5720	265	45	f	f	PROPN
cana-5720	265	46			PROPN
cana-5720	265	47	f-1(v	f-1(v	PROPN
cana-5720	265	48	)	)	PUNCT
cana-5720	265	49	;	;	PUNCT
cana-5720	265	50	hence	hence	ADV
cana-5720	265	51	y	y	PROPN
cana-5720	265	52	=	=	SYM
cana-5720	265	53	f(x	f(x	PROPN
cana-5720	265	54	)	)	PUNCT
cana-5720	265	55			NOUN
cana-5720	265	56	f(f	f(f	PROPN
cana-5720	265	57	)	)	PUNCT
cana-5720	266	1			PROPN
cana-5720	266	2	v.	v.	CCONJ
cana-5720	266	3	since	since	SCONJ
cana-5720	266	4	f	f	PROPN
cana-5720	266	5	is	be	AUX
cana-5720	266	6	continuous	continuous	ADJ
cana-5720	266	7	,	,	PUNCT
cana-5720	266	8	we	we	PRON
cana-5720	266	9	have	have	VERB
cana-5720	266	10	f(f	f(f	PROPN
cana-5720	266	11	)	)	PUNCT
cana-5720	266	12	=	=	SYM
cana-5720	266	13	f(cl(int(f	f(cl(int(f	PROPN
cana-5720	266	14	)	)	PUNCT
cana-5720	266	15	)	)	PUNCT
cana-5720	266	16	)	)	PUNCT
cana-5720	267	1			PROPN
cana-5720	267	2	cl(f(int(f	cl(f(int(f	PROPN
cana-5720	267	3	)	)	PUNCT
cana-5720	267	4	)	)	PUNCT
cana-5720	267	5	)	)	PUNCT
cana-5720	267	6	.	.	PUNCT
cana-5720	268	1	since	since	SCONJ
cana-5720	268	2	f	f	PROPN
cana-5720	268	3	is	be	AUX
cana-5720	268	4	almost	almost	ADV
cana-5720	268	5	gωα	gωα	NOUN
cana-5720	268	6	-closed	-close	VERB
cana-5720	268	7	,	,	PUNCT
cana-5720	268	8	f(f	f(f	PROPN
cana-5720	268	9	)	)	PUNCT
cana-5720	268	10	is	be	AUX
cana-5720	268	11	gωα	gωα	NOUN
cana-5720	268	12	-closed	-close	VERB
cana-5720	268	13	and	and	CCONJ
cana-5720	268	14	cl(f(f	cl(f(f	NUM
cana-5720	268	15	)	)	PUNCT
cana-5720	268	16	)	)	PUNCT
cana-5720	269	1			PROPN
cana-5720	269	2	v.	v.	ADP
cana-5720	269	3	moreover	moreover	ADV
cana-5720	269	4	,	,	PUNCT
cana-5720	269	5	f	f	PROPN
cana-5720	269	6	is	be	AUX
cana-5720	269	7	almost	almost	ADV
cana-5720	269	8	-open	-open	PROPN
cana-5720	269	9	,	,	PUNCT
cana-5720	269	10	f(int(f	f(int(f	NOUN
cana-5720	269	11	)	)	PUNCT
cana-5720	269	12	)	)	PUNCT
cana-5720	269	13	is	be	AUX
cana-5720	269	14	-open	-open	PROPN
cana-5720	269	15	in	in	ADP
cana-5720	269	16	y	y	PROPN
cana-5720	269	17	and	and	CCONJ
cana-5720	269	18	by	by	ADP
cana-5720	269	19	lemma	lemma	PROPN
cana-5720	269	20	1.2.4	1.2.4	PROPN
cana-5720	269	21	we	we	PRON
cana-5720	269	22	have	have	VERB
cana-5720	269	23	cl(f(int(f	cl(f(int(f	NOUN
cana-5720	269	24	)	)	PUNCT
cana-5720	269	25	)	)	PUNCT
cana-5720	269	26	)	)	PUNCT
cana-5720	270	1	=	=	SYM
cana-5720	270	2	cl(int(f(int(f	cl(int(f(int(f	NOUN
cana-5720	270	3	)	)	PUNCT
cana-5720	270	4	)	)	PUNCT
cana-5720	270	5	)	)	PUNCT
cana-5720	270	6	)	)	PUNCT
cana-5720	271	1	=	=	SYM
cana-5720	271	2	cl(f(int(f	cl(f(int(f	PROPN
cana-5720	271	3	)	)	PUNCT
cana-5720	271	4	)	)	PUNCT
cana-5720	271	5	)	)	PUNCT
cana-5720	272	1			PROPN
cana-5720	272	2	cl(f(f	cl(f(f	PROPN
cana-5720	272	3	)	)	PUNCT
cana-5720	272	4	)	)	PUNCT
cana-5720	272	5	.	.	PUNCT
cana-5720	273	1	therefore	therefore	ADV
cana-5720	273	2	,	,	PUNCT
cana-5720	273	3	we	we	PRON
cana-5720	273	4	obtain	obtain	VERB
cana-5720	273	5	cl(int(f(int(f	cl(int(f(int(f	NOUN
cana-5720	273	6	)	)	PUNCT
cana-5720	273	7	)	)	PUNCT
cana-5720	273	8	)	)	PUNCT
cana-5720	273	9	)	)	PUNCT
cana-5720	274	1			PROPN
cana-5720	274	2	rc	rc	PROPN
cana-5720	274	3	(	(	PUNCT
cana-5720	274	4	y	y	NOUN
cana-5720	274	5	)	)	PUNCT
cana-5720	274	6	and	and	CCONJ
cana-5720	274	7	y	y	PROPN
cana-5720	274	8			PROPN
cana-5720	274	9	f(f	f(f	PROPN
cana-5720	274	10	)	)	PUNCT
cana-5720	275	1			PROPN
cana-5720	275	2	cl(f(int(f	cl(f(int(f	PROPN
cana-5720	275	3	)	)	PUNCT
cana-5720	275	4	)	)	PUNCT
cana-5720	275	5	)	)	PUNCT
cana-5720	276	1	=	=	SYM
cana-5720	276	2	cl(int(f(int(f	cl(int(f(int(f	NOUN
cana-5720	276	3	)	)	PUNCT
cana-5720	276	4	)	)	PUNCT
cana-5720	276	5	)	)	PUNCT
cana-5720	276	6	)	)	PUNCT
cana-5720	277	1			PROPN
cana-5720	277	2	cl(f(f	cl(f(f	NUM
cana-5720	277	3	)	)	PUNCT
cana-5720	277	4	)	)	PUNCT
cana-5720	278	1			PROPN
cana-5720	278	2	v.	v.	ADP
cana-5720	278	3	it	it	PRON
cana-5720	278	4	follows	follow	VERB
cana-5720	278	5	from	from	ADP
cana-5720	278	6	[	[	X
cana-5720	278	7	3	3	NUM
cana-5720	278	8	,	,	PUNCT
cana-5720	278	9	theorem	theorem	VERB
cana-5720	278	10	1	1	NUM
cana-5720	278	11	]	]	PUNCT
cana-5720	278	12	that	that	SCONJ
cana-5720	278	13	y	y	PROPN
cana-5720	278	14	is	be	AUX
cana-5720	278	15	strongly	strongly	ADV
cana-5720	278	16	s	s	NOUN
cana-5720	278	17	-	-	ADJ
cana-5720	278	18	regular	regular	ADJ
cana-5720	278	19	.	.	PUNCT
cana-5720	279	1	communications	communication	NOUN
cana-5720	279	2	on	on	ADP
cana-5720	279	3	applied	apply	VERB
cana-5720	279	4	nonlinear	nonlinear	ADJ
cana-5720	279	5	analysis	analysis	NOUN
cana-5720	279	6	issn	issn	NOUN
cana-5720	279	7	:	:	PUNCT
cana-5720	279	8	1074	1074	NUM
cana-5720	279	9	-	-	PUNCT
cana-5720	279	10	133x	133x	NUM
cana-5720	279	11	vol	vol	VERB
cana-5720	279	12	32	32	NUM
cana-5720	279	13	no	no	NOUN
cana-5720	279	14	.	.	PUNCT
cana-5720	280	1	10s	10	NOUN
cana-5720	280	2	(	(	PUNCT
cana-5720	280	3	2025	2025	NUM
cana-5720	280	4	)	)	PUNCT
cana-5720	280	5	2810	2810	NUM
cana-5720	280	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5720	280	7	references	reference	NOUN
cana-5720	280	8	[	[	X
cana-5720	280	9	1	1	NUM
cana-5720	280	10	]	]	PUNCT
cana-5720	280	11	carnation	carnation	NOUN
cana-5720	280	12	,	,	PUNCT
cana-5720	280	13	d.	d.	PROPN
cana-5720	280	14	,	,	PUNCT
cana-5720	280	15	some	some	DET
cana-5720	280	16	properties	property	NOUN
cana-5720	280	17	related	relate	VERB
cana-5720	280	18	to	to	ADP
cana-5720	280	19	compactness	compactness	NOUN
cana-5720	280	20	in	in	ADP
cana-5720	280	21	topological	topological	ADJ
cana-5720	280	22	spaces	space	NOUN
cana-5720	280	23	,	,	PUNCT
cana-5720	280	24	ph	ph	PROPN
cana-5720	280	25	.	.	PROPN
cana-5720	280	26	d.	d.	PROPN
cana-5720	280	27	thesis	thesis	PROPN
cana-5720	280	28	,	,	PUNCT
cana-5720	280	29	university	university	NOUN
cana-5720	280	30	of	of	ADP
cana-5720	280	31	arkansas	arkansas	PROPN
cana-5720	280	32	,	,	PUNCT
cana-5720	280	33	1977	1977	NUM
cana-5720	280	34	.	.	PUNCT
cana-5720	281	1	[	[	X
cana-5720	281	2	2	2	NUM
cana-5720	281	3	]	]	PUNCT
cana-5720	281	4	frolik	frolik	NOUN
cana-5720	281	5	,	,	PUNCT
cana-5720	281	6	z.	z.	PROPN
cana-5720	281	7	,	,	PUNCT
cana-5720	281	8	remarks	remark	NOUN
cana-5720	281	9	concerning	concern	VERB
cana-5720	281	10	the	the	DET
cana-5720	281	11	invariance	invariance	NOUN
cana-5720	281	12	of	of	ADP
cana-5720	281	13	baire	baire	NOUN
cana-5720	281	14	spaces	space	VERB
cana-5720	281	15	under	under	ADP
cana-5720	281	16	mappings	mapping	NOUN
cana-5720	281	17	,	,	PUNCT
cana-5720	281	18	czechoslovak	czechoslovak	ADJ
cana-5720	281	19	math	math	NOUN
cana-5720	281	20	.	.	PUNCT
cana-5720	282	1	j.	j.	PROPN
cana-5720	282	2	,	,	PUNCT
cana-5720	282	3	11(86	11(86	NUM
cana-5720	282	4	)	)	PUNCT
cana-5720	282	5	(	(	PUNCT
cana-5720	282	6	1961	1961	NUM
cana-5720	282	7	)	)	PUNCT
cana-5720	282	8	,	,	PUNCT
cana-5720	282	9	381	381	NUM
cana-5720	282	10	-	-	SYM
cana-5720	282	11	385	385	NUM
cana-5720	282	12	.	.	PUNCT
cana-5720	283	1	[	[	X
cana-5720	283	2	3	3	NUM
cana-5720	283	3	]	]	X
cana-5720	283	4	ganster	ganster	NOUN
cana-5720	283	5	,	,	PUNCT
cana-5720	283	6	m.	m.	NOUN
cana-5720	283	7	,	,	PUNCT
cana-5720	283	8	on	on	ADP
cana-5720	283	9	strongly	strongly	ADV
cana-5720	283	10	s	s	NOUN
cana-5720	283	11	-	-	ADJ
cana-5720	283	12	regular	regular	ADJ
cana-5720	283	13	spaces	space	NOUN
cana-5720	283	14	,	,	PUNCT
cana-5720	283	15	glasnik	glasnik	PROPN
cana-5720	283	16	mat	mat	PROPN
cana-5720	283	17	.	.	PROPN
cana-5720	283	18	,	,	PUNCT
cana-5720	283	19	25(45)(1990	25(45)(1990	NUM
cana-5720	283	20	)	)	PUNCT
cana-5720	283	21	,	,	PUNCT
cana-5720	283	22	195	195	NUM
cana-5720	283	23	-	-	PUNCT
cana-5720	283	24	201	201	NUM
cana-5720	283	25	.	.	PUNCT
cana-5720	284	1	[	[	X
cana-5720	284	2	4	4	NUM
cana-5720	284	3	]	]	X
cana-5720	284	4	greenwood	greenwood	PROPN
cana-5720	284	5	,	,	PUNCT
cana-5720	284	6	s.	s.	PROPN
cana-5720	284	7	and	and	CCONJ
cana-5720	284	8	reilly	reilly	PROPN
cana-5720	284	9	,	,	PUNCT
cana-5720	284	10	i.	i.	PROPN
cana-5720	284	11	l.	l.	PROPN
cana-5720	284	12	,	,	PUNCT
cana-5720	284	13	on	on	ADP
cana-5720	284	14	feebly	feebly	ADJ
cana-5720	284	15	closed	closed	ADJ
cana-5720	284	16	mappings	mapping	NOUN
cana-5720	284	17	,	,	PUNCT
cana-5720	284	18	indian	indian	ADJ
cana-5720	284	19	j.	j.	PROPN
cana-5720	284	20	pure	pure	PROPN
cana-5720	284	21	appl	appl	PROPN
cana-5720	284	22	.	.	PUNCT
cana-5720	284	23	math	math	PROPN
cana-5720	284	24	.	.	PUNCT
cana-5720	284	25	,	,	PUNCT
cana-5720	284	26	17	17	NUM
cana-5720	284	27	(	(	PUNCT
cana-5720	284	28	1986	1986	NUM
cana-5720	284	29	)	)	PUNCT
cana-5720	284	30	,	,	PUNCT
cana-5720	284	31	1101	1101	NUM
cana-5720	284	32	-	-	PUNCT
cana-5720	284	33	1105	1105	NUM
cana-5720	284	34	.	.	PUNCT
cana-5720	285	1	[	[	X
cana-5720	285	2	5	5	NUM
cana-5720	285	3	]	]	X
cana-5720	285	4	long	long	ADV
cana-5720	285	5	,	,	PUNCT
cana-5720	285	6	p.	p.	PROPN
cana-5720	285	7	e.	e.	PROPN
cana-5720	285	8	and	and	CCONJ
cana-5720	285	9	herrington	herrington	PROPN
cana-5720	285	10	,	,	PUNCT
cana-5720	285	11	l.	l.	PROPN
cana-5720	285	12	l.	l.	PROPN
cana-5720	285	13	,	,	PUNCT
cana-5720	285	14	basic	basic	ADJ
cana-5720	285	15	properties	property	NOUN
cana-5720	285	16	of	of	ADP
cana-5720	285	17	regular	regular	ADJ
cana-5720	285	18	-	-	PUNCT
cana-5720	285	19	closed	close	VERB
cana-5720	285	20	functions	function	NOUN
cana-5720	285	21	,	,	PUNCT
cana-5720	285	22	rend	rend	VERB
cana-5720	285	23	.	.	PUNCT
cana-5720	286	1	circ	circ	PROPN
cana-5720	286	2	.	.	PUNCT
cana-5720	287	1	mat	mat	PROPN
cana-5720	287	2	.	.	PUNCT
cana-5720	287	3	palermo	palermo	PROPN
cana-5720	287	4	(	(	PUNCT
cana-5720	287	5	2	2	NUM
cana-5720	287	6	)	)	PUNCT
cana-5720	287	7	,	,	PUNCT
cana-5720	287	8	27	27	NUM
cana-5720	287	9	(	(	PUNCT
cana-5720	287	10	1978	1978	NUM
cana-5720	287	11	)	)	PUNCT
cana-5720	287	12	,	,	PUNCT
cana-5720	287	13	20	20	NUM
cana-5720	287	14	-	-	SYM
cana-5720	287	15	28	28	NUM
cana-5720	287	16	.	.	PUNCT
cana-5720	288	1	[	[	X
cana-5720	288	2	6	6	NUM
cana-5720	288	3	]	]	X
cana-5720	288	4	maki	maki	X
cana-5720	288	5	,	,	PUNCT
cana-5720	288	6	h.	h.	PROPN
cana-5720	288	7	,	,	PUNCT
cana-5720	288	8	devi	devi	PROPN
cana-5720	288	9	,	,	PUNCT
cana-5720	288	10	r.	r.	PROPN
cana-5720	288	11	and	and	CCONJ
cana-5720	288	12	balachandran	balachandran	PROPN
cana-5720	288	13	,	,	PUNCT
cana-5720	288	14	k.	k.	PROPN
cana-5720	288	15	,	,	PUNCT
cana-5720	288	16	associated	associate	VERB
cana-5720	288	17	topologies	topology	NOUN
cana-5720	288	18	of	of	ADP
cana-5720	288	19	generalized	generalized	ADJ
cana-5720	288	20			NOUN
cana-5720	288	21	-closed	-close	VERB
cana-5720	288	22	sets	set	NOUN
cana-5720	288	23	and	and	CCONJ
cana-5720	288	24			NOUN
cana-5720	288	25	-generalized	-generalize	VERB
cana-5720	288	26	closed	closed	ADJ
cana-5720	288	27	sets	set	NOUN
cana-5720	288	28	,	,	PUNCT
cana-5720	288	29	mem	mem	PROPN
cana-5720	288	30	.	.	PUNCT
cana-5720	289	1	fac	fac	PROPN
cana-5720	289	2	.	.	PUNCT
cana-5720	290	1	sci	sci	PROPN
cana-5720	290	2	.	.	PROPN
cana-5720	290	3	kochi	kochi	PROPN
cana-5720	290	4	.	.	PUNCT
cana-5720	291	1	univ	univ	PROPN
cana-5720	291	2	.	.	PUNCT
cana-5720	291	3	ser	ser	PROPN
cana-5720	291	4	.	.	PUNCT
cana-5720	291	5	a.	a.	PROPN
cana-5720	291	6	math	math	PROPN
cana-5720	291	7	.	.	PUNCT
cana-5720	291	8	,	,	PUNCT
cana-5720	291	9	15	15	NUM
cana-5720	291	10	(	(	PUNCT
cana-5720	291	11	1994	1994	NUM
cana-5720	291	12	)	)	PUNCT
cana-5720	291	13	,	,	PUNCT
cana-5720	291	14	51	51	NUM
cana-5720	291	15	-	-	SYM
cana-5720	291	16	63	63	NUM
cana-5720	291	17	.	.	PUNCT
cana-5720	292	1	[	[	X
cana-5720	292	2	7	7	NUM
cana-5720	292	3	]	]	SYM
cana-5720	292	4	malghan	malghan	PROPN
cana-5720	292	5	,	,	PUNCT
cana-5720	292	6	s.	s.	PROPN
cana-5720	292	7	r.	r.	PROPN
cana-5720	292	8	,	,	PUNCT
cana-5720	292	9	generalized	generalize	VERB
cana-5720	292	10	closed	closed	ADJ
cana-5720	292	11	maps	map	NOUN
cana-5720	292	12	,	,	PUNCT
cana-5720	292	13	j.	j.	PROPN
cana-5720	292	14	karnatak	karnatak	PROPN
cana-5720	292	15	univ	univ	PROPN
cana-5720	292	16	.	.	PUNCT
cana-5720	293	1	sci	sci	PROPN
cana-5720	293	2	.	.	PROPN
cana-5720	293	3	,	,	PUNCT
cana-5720	293	4	27	27	NUM
cana-5720	293	5	(	(	PUNCT
cana-5720	293	6	1982	1982	NUM
cana-5720	293	7	)	)	PUNCT
cana-5720	293	8	,	,	PUNCT
cana-5720	293	9	82	82	NUM
cana-5720	293	10	-	-	SYM
cana-5720	293	11	88	88	NUM
cana-5720	293	12	.	.	PUNCT
cana-5720	294	1	[	[	X
cana-5720	294	2	8	8	NUM
cana-5720	294	3	]	]	X
cana-5720	294	4	mashhour	mashhour	ADJ
cana-5720	294	5	,	,	PUNCT
cana-5720	294	6	a.	a.	PROPN
cana-5720	294	7	s.	s.	PROPN
cana-5720	294	8	,	,	PUNCT
cana-5720	294	9	hasanein	hasanein	ADV
cana-5720	294	10	,	,	PUNCT
cana-5720	294	11	i.	i.	PROPN
cana-5720	294	12	a.	a.	PROPN
cana-5720	294	13	and	and	CCONJ
cana-5720	294	14	el	el	PROPN
cana-5720	294	15	-	-	PUNCT
cana-5720	294	16	deep	deep	ADJ
cana-5720	294	17	,	,	PUNCT
cana-5720	294	18	s.	s.	PROPN
cana-5720	294	19	n.	n.	PROPN
cana-5720	294	20	,	,	PUNCT
cana-5720	294	21			NOUN
cana-5720	294	22	-continuous	-continuous	ADJ
cana-5720	294	23	and	and	CCONJ
cana-5720	294	24			NOUN
cana-5720	294	25	-open	-open	NOUN
cana-5720	294	26	mappings	mapping	NOUN
cana-5720	294	27	,	,	PUNCT
cana-5720	294	28	acta	acta	PROPN
cana-5720	294	29	math	math	PROPN
cana-5720	294	30	.	.	PUNCT
cana-5720	295	1	hungar	hungar	PROPN
cana-5720	295	2	.	.	PUNCT
cana-5720	295	3	,	,	PUNCT
cana-5720	295	4	41	41	NUM
cana-5720	295	5	(	(	PUNCT
cana-5720	295	6	1983	1983	NUM
cana-5720	295	7	)	)	PUNCT
cana-5720	295	8	,	,	PUNCT
cana-5720	295	9	213	213	NUM
cana-5720	295	10	-	-	SYM
cana-5720	295	11	218	218	NUM
cana-5720	295	12	.	.	PUNCT
cana-5720	296	1	[	[	X
cana-5720	296	2	9	9	NUM
cana-5720	296	3	]	]	SYM
cana-5720	296	4	noiri	noiri	NOUN
cana-5720	296	5	,	,	PUNCT
cana-5720	296	6	t.	t.	PROPN
cana-5720	296	7	,	,	PUNCT
cana-5720	296	8	almost	almost	ADV
cana-5720	296	9	g	g	NUM
cana-5720	296	10	-	-	PUNCT
cana-5720	296	11	closed	close	VERB
cana-5720	296	12	functions	function	NOUN
cana-5720	296	13	and	and	CCONJ
cana-5720	296	14	separation	separation	NOUN
cana-5720	296	15	axioms	axiom	NOUN
cana-5720	296	16	,	,	PUNCT
cana-5720	296	17	acta	acta	PROPN
cana-5720	296	18	math	math	PROPN
cana-5720	296	19	.	.	PUNCT
cana-5720	297	1	hungar	hungar	NOUN
cana-5720	297	2	,	,	PUNCT
cana-5720	297	3	82(3	82(3	NUM
cana-5720	297	4	)	)	PUNCT
cana-5720	297	5	(	(	PUNCT
cana-5720	297	6	1999	1999	NUM
cana-5720	297	7	)	)	PUNCT
cana-5720	297	8	,	,	PUNCT
cana-5720	297	9	193	193	NUM
cana-5720	297	10	-	-	SYM
cana-5720	297	11	205	205	NUM
cana-5720	297	12	.	.	PUNCT
cana-5720	298	1	[	[	X
cana-5720	298	2	10	10	NUM
cana-5720	298	3	]	]	X
cana-5720	298	4	noiri	noiri	PROPN
cana-5720	298	5	,	,	PUNCT
cana-5720	298	6	t.	t.	PROPN
cana-5720	298	7	,	,	PUNCT
cana-5720	298	8	almost	almost	ADV
cana-5720	298	9	-	-	PUNCT
cana-5720	298	10	closed	close	VERB
cana-5720	298	11	images	image	NOUN
cana-5720	298	12	of	of	ADP
cana-5720	298	13	countably	countably	ADV
cana-5720	298	14	paracompact	paracompact	ADJ
cana-5720	298	15	spaces	space	NOUN
cana-5720	298	16	,	,	PUNCT
cana-5720	298	17	prace	prace	PROPN
cana-5720	298	18	mat	mat	PROPN
cana-5720	298	19	.	.	PROPN
cana-5720	298	20	,	,	PUNCT
cana-5720	298	21	20(1978	20(1978	NUM
cana-5720	298	22	)	)	PUNCT
cana-5720	298	23	,	,	PUNCT
cana-5720	298	24	423426	423426	NUM
cana-5720	298	25	.	.	PUNCT
cana-5720	299	1	[	[	X
cana-5720	299	2	11	11	NUM
cana-5720	299	3	]	]	PUNCT
cana-5720	299	4	parveen	parveen	PROPN
cana-5720	299	5	banu	banu	PROPN
cana-5720	299	6	a.	a.	PROPN
cana-5720	299	7	,	,	PUNCT
cana-5720	299	8	new	new	ADJ
cana-5720	299	9	classes	class	NOUN
cana-5720	299	10	of	of	ADP
cana-5720	299	11	topological	topological	ADJ
cana-5720	299	12	mapping	mapping	NOUN
cana-5720	299	13	,	,	PUNCT
cana-5720	299	14	international	international	ADJ
cana-5720	299	15	journal	journal	NOUN
cana-5720	299	16	of	of	ADP
cana-5720	299	17	emerging	emerge	VERB
cana-5720	299	18	technologies	technology	NOUN
cana-5720	299	19	and	and	CCONJ
cana-5720	299	20	innovative	innovative	ADJ
cana-5720	299	21	research	research	NOUN
cana-5720	299	22	,	,	PUNCT
cana-5720	299	23	vol-6	vol-6	NOUN
cana-5720	299	24	,	,	PUNCT
cana-5720	299	25	issue-6,(2019),45	issue-6,(2019),45	NOUN
cana-5720	299	26	-	-	PUNCT
cana-5720	299	27	53	53	NUM
cana-5720	299	28	.	.	PUNCT
cana-5720	300	1	[	[	X
cana-5720	300	2	12	12	NUM
cana-5720	300	3	]	]	X
cana-5720	300	4	porter	porter	NOUN
cana-5720	300	5	,	,	PUNCT
cana-5720	300	6	j.	j.	PROPN
cana-5720	300	7	and	and	CCONJ
cana-5720	300	8	woods	woods	PROPN
cana-5720	300	9	,	,	PUNCT
cana-5720	300	10	r.	r.	PROPN
cana-5720	300	11	g.	g.	PROPN
cana-5720	300	12	,	,	PUNCT
cana-5720	300	13	extensions	extension	NOUN
cana-5720	300	14	and	and	CCONJ
cana-5720	300	15	absolute	absolute	ADJ
cana-5720	300	16	of	of	ADP
cana-5720	300	17	hausdorff	hausdorff	NOUN
cana-5720	300	18	spaces	space	NOUN
cana-5720	300	19	,	,	PUNCT
cana-5720	300	20	springer	springer	NOUN
cana-5720	300	21	verlag	verlag	NOUN
cana-5720	300	22	,	,	PUNCT
cana-5720	300	23	1988	1988	NUM
cana-5720	300	24	.	.	PUNCT
cana-5720	301	1	[	[	X
cana-5720	301	2	13	13	NUM
cana-5720	301	3	]	]	PUNCT
cana-5720	301	4	rajamani	rajamani	NOUN
cana-5720	301	5	,	,	PUNCT
cana-5720	301	6	m.	m.	NOUN
cana-5720	301	7	and	and	CCONJ
cana-5720	301	8	viswanathan	viswanathan	PROPN
cana-5720	301	9	,	,	PUNCT
cana-5720	301	10	k.	k.	PROPN
cana-5720	301	11	,	,	PUNCT
cana-5720	301	12	on	on	ADP
cana-5720	301	13	gs	gs	ADJ
cana-5720	301	14	-	-	PUNCT
cana-5720	301	15	closed	closed	ADJ
cana-5720	301	16	sets	set	NOUN
cana-5720	301	17	in	in	ADP
cana-5720	301	18	topological	topological	ADJ
cana-5720	301	19	spaces	space	NOUN
cana-5720	301	20	,	,	PUNCT
cana-5720	301	21	acta	acta	PROPN
cana-5720	301	22	ciencia	ciencia	PROPN
cana-5720	301	23	indica	indica	PROPN
cana-5720	301	24	,	,	PUNCT
cana-5720	301	25	xxxm	xxxm	PROPN
cana-5720	301	26	(	(	PUNCT
cana-5720	301	27	3	3	NUM
cana-5720	301	28	)	)	PUNCT
cana-5720	301	29	(	(	PUNCT
cana-5720	301	30	2004	2004	NUM
cana-5720	301	31	)	)	PUNCT
cana-5720	301	32	,	,	PUNCT
cana-5720	301	33	21	21	NUM
cana-5720	301	34	-	-	SYM
cana-5720	301	35	25	25	NUM
cana-5720	301	36	.	.	PUNCT
cana-5720	302	1	[	[	X
cana-5720	302	2	14	14	NUM
cana-5720	302	3	]	]	X
cana-5720	302	4	ravi	ravi	NOUN
cana-5720	302	5	,	,	PUNCT
cana-5720	302	6	o.	o.	PROPN
cana-5720	302	7	,	,	PUNCT
cana-5720	302	8	ganesan	ganesan	PROPN
cana-5720	302	9	,	,	PUNCT
cana-5720	302	10	s.	s.	PROPN
cana-5720	302	11	and	and	CCONJ
cana-5720	302	12	chandrasekar	chandrasekar	PROPN
cana-5720	302	13	,	,	PUNCT
cana-5720	302	14	s.	s.	PROPN
cana-5720	302	15	,	,	PUNCT
cana-5720	302	16	almost	almost	ADV
cana-5720	302	17	gs	gs	ADJ
cana-5720	302	18	-	-	PUNCT
cana-5720	302	19	closed	close	VERB
cana-5720	302	20	functions	function	NOUN
cana-5720	302	21	and	and	CCONJ
cana-5720	302	22	separation	separation	NOUN
cana-5720	302	23	axioms	axiom	NOUN
cana-5720	302	24	,	,	PUNCT
cana-5720	302	25	bulletin	bulletin	NOUN
cana-5720	302	26	of	of	ADP
cana-5720	302	27	mathematical	mathematical	ADJ
cana-5720	302	28	analysis	analysis	NOUN
cana-5720	302	29	and	and	CCONJ
cana-5720	302	30	applications	application	NOUN
cana-5720	302	31	,	,	PUNCT
cana-5720	302	32	3(1	3(1	NUM
cana-5720	302	33	)	)	PUNCT
cana-5720	302	34	(	(	PUNCT
cana-5720	302	35	2011	2011	NUM
cana-5720	302	36	)	)	PUNCT
cana-5720	302	37	,	,	PUNCT
cana-5720	302	38	165	165	NUM
cana-5720	302	39	-	-	SYM
cana-5720	302	40	177	177	NUM
cana-5720	302	41	.	.	PUNCT
cana-5720	303	1	[	[	X
cana-5720	303	2	15	15	NUM
cana-5720	303	3	]	]	X
cana-5720	303	4	singal	singal	NOUN
cana-5720	303	5	,	,	PUNCT
cana-5720	303	6	m.	m.	NOUN
cana-5720	303	7	k.	k.	PROPN
cana-5720	303	8	and	and	CCONJ
cana-5720	303	9	arya	arya	PROPN
cana-5720	303	10	,	,	PUNCT
cana-5720	303	11	s.	s.	PROPN
cana-5720	303	12	p.	p.	PROPN
cana-5720	303	13	,	,	PUNCT
cana-5720	303	14	almost	almost	ADV
cana-5720	303	15	normal	normal	ADJ
cana-5720	303	16	and	and	CCONJ
cana-5720	303	17	almost	almost	ADV
cana-5720	303	18	completely	completely	ADV
cana-5720	303	19	regular	regular	ADJ
cana-5720	303	20	spaces	space	NOUN
cana-5720	303	21	,	,	PUNCT
cana-5720	303	22	glasnik	glasnik	PROPN
cana-5720	303	23	mat	mat	PROPN
cana-5720	303	24	.	.	PROPN
cana-5720	303	25	,	,	PUNCT
cana-5720	303	26	5(25	5(25	NUM
cana-5720	303	27	)	)	PUNCT
cana-5720	303	28	(	(	PUNCT
cana-5720	303	29	1970	1970	NUM
cana-5720	303	30	)	)	PUNCT
cana-5720	303	31	,	,	PUNCT
cana-5720	303	32	141	141	NUM
cana-5720	303	33	-	-	SYM
cana-5720	303	34	152	152	NUM
cana-5720	303	35	.	.	PUNCT
cana-5720	304	1	[	[	X
cana-5720	304	2	16	16	NUM
cana-5720	304	3	]	]	X
cana-5720	304	4	singal	singal	NOUN
cana-5720	304	5	,	,	PUNCT
cana-5720	304	6	m.	m.	NOUN
cana-5720	304	7	k.	k.	PROPN
cana-5720	304	8	and	and	CCONJ
cana-5720	304	9	arya	arya	PROPN
cana-5720	304	10	,	,	PUNCT
cana-5720	304	11	s.	s.	PROPN
cana-5720	304	12	p.	p.	PROPN
cana-5720	304	13	,on	,on	PUNCT
cana-5720	304	14	almost	almost	ADV
cana-5720	304	15	-	-	PUNCT
cana-5720	304	16	regular	regular	ADJ
cana-5720	304	17	spaces	space	NOUN
cana-5720	304	18	,	,	PUNCT
cana-5720	304	19	glasnik	glasnik	PROPN
cana-5720	304	20	mat	mat	PROPN
cana-5720	304	21	.	.	PROPN
cana-5720	304	22	,	,	PUNCT
cana-5720	304	23	4(24	4(24	NUM
cana-5720	304	24	)	)	PUNCT
cana-5720	304	25	(	(	PUNCT
cana-5720	304	26	1969	1969	NUM
cana-5720	304	27	)	)	PUNCT
cana-5720	304	28	,	,	PUNCT
cana-5720	304	29	89	89	NUM
cana-5720	304	30	-	-	SYM
cana-5720	304	31	99	99	NUM
cana-5720	304	32	.	.	PUNCT
cana-5720	305	1	[	[	X
cana-5720	305	2	17	17	NUM
cana-5720	305	3	]	]	X
cana-5720	305	4	singal	singal	NOUN
cana-5720	305	5	,	,	PUNCT
cana-5720	305	6	m.	m.	NOUN
cana-5720	305	7	k.	k.	PROPN
cana-5720	305	8	and	and	CCONJ
cana-5720	305	9	singal	singal	PROPN
cana-5720	305	10	,	,	PUNCT
cana-5720	305	11	a.	a.	PROPN
cana-5720	305	12	r.	r.	PROPN
cana-5720	305	13	,almost	,almost	PUNCT
cana-5720	305	14	-	-	PUNCT
cana-5720	305	15	continuous	continuous	ADJ
cana-5720	305	16	mappings	mapping	NOUN
cana-5720	305	17	,	,	PUNCT
cana-5720	305	18	yokohama	yokohama	PROPN
cana-5720	305	19	math	math	PROPN
cana-5720	305	20	.	.	PUNCT
cana-5720	306	1	j.	j.	PROPN
cana-5720	306	2	,	,	PUNCT
cana-5720	306	3	16	16	NUM
cana-5720	306	4	(	(	PUNCT
cana-5720	306	5	1968	1968	NUM
cana-5720	306	6	)	)	PUNCT
cana-5720	306	7	,	,	PUNCT
cana-5720	306	8	63	63	NUM
cana-5720	306	9	-	-	SYM
cana-5720	306	10	73	73	NUM
cana-5720	306	11	.	.	PUNCT
cana-5720	307	1	[	[	X
cana-5720	307	2	18	18	NUM
cana-5720	307	3	]	]	X
cana-5720	307	4	singal	singal	NOUN
cana-5720	307	5	,	,	PUNCT
cana-5720	307	6	m.	m.	NOUN
cana-5720	307	7	k.	k.	PROPN
cana-5720	307	8	and	and	CCONJ
cana-5720	307	9	singal	singal	PROPN
cana-5720	307	10	,	,	PUNCT
cana-5720	307	11	a.	a.	PROPN
cana-5720	307	12	r.	r.	PROPN
cana-5720	307	13	,mildly	,mildly	PUNCT
cana-5720	307	14	normal	normal	ADJ
cana-5720	307	15	spaces	space	NOUN
cana-5720	307	16	,	,	PUNCT
cana-5720	307	17	kyungpook	kyungpook	PROPN
cana-5720	307	18	math	math	NOUN
cana-5720	307	19	.	.	PUNCT
cana-5720	308	1	j.	j.	PROPN
cana-5720	308	2	,	,	PUNCT
cana-5720	308	3	13	13	NUM
cana-5720	308	4	(	(	PUNCT
cana-5720	308	5	1973	1973	NUM
cana-5720	308	6	)	)	PUNCT
cana-5720	308	7	,	,	PUNCT
cana-5720	308	8	27	27	NUM
cana-5720	308	9	-	-	SYM
cana-5720	308	10	31	31	NUM
cana-5720	308	11	.	.	PUNCT
cana-5720	309	1	[	[	X
cana-5720	309	2	19	19	NUM
cana-5720	309	3	]	]	PUNCT
cana-5720	309	4	yoshimura	yoshimura	NOUN
cana-5720	309	5	,	,	PUNCT
cana-5720	309	6	m.	m.	NOUN
cana-5720	309	7	,	,	PUNCT
cana-5720	309	8	miwa	miwa	PROPN
cana-5720	309	9	,	,	PUNCT
cana-5720	309	10	t.	t.	PROPN
cana-5720	309	11	and	and	CCONJ
cana-5720	309	12	noiri	noiri	PROPN
cana-5720	309	13	,	,	PUNCT
cana-5720	309	14	t.	t.	PROPN
cana-5720	309	15	,	,	PUNCT
cana-5720	309	16	a	a	DET
cana-5720	309	17	generalization	generalization	NOUN
cana-5720	309	18	of	of	ADP
cana-5720	309	19	regular	regular	ADJ
cana-5720	309	20	closed	closed	ADJ
cana-5720	309	21	and	and	CCONJ
cana-5720	309	22	g	g	NOUN
cana-5720	309	23	-	-	PUNCT
cana-5720	309	24	closed	close	VERB
cana-5720	309	25	functions	function	NOUN
cana-5720	309	26	,	,	PUNCT
cana-5720	309	27	stud	stud	NOUN
cana-5720	309	28	.	.	PUNCT
cana-5720	309	29	cerc	cerc	PROPN
cana-5720	309	30	.	.	PUNCT
cana-5720	310	1	mat	mat	PROPN
cana-5720	310	2	.	.	PROPN
cana-5720	310	3	,	,	PUNCT
cana-5720	310	4	47	47	NUM
cana-5720	310	5	(	(	PUNCT
cana-5720	310	6	1995	1995	NUM
cana-5720	310	7	)	)	PUNCT
cana-5720	310	8	,	,	PUNCT
cana-5720	310	9	353	353	NUM
cana-5720	310	10	-	-	SYM
cana-5720	310	11	358	358	NUM
cana-5720	310	12	.	.	PUNCT
cana-5720	311	1	[	[	X
cana-5720	311	2	20	20	NUM
cana-5720	311	3	]	]	PUNCT
cana-5720	311	4	zenor	zenor	NOUN
cana-5720	311	5	,	,	PUNCT
cana-5720	311	6	p.	p.	PROPN
cana-5720	311	7	,on	,on	PUNCT
cana-5720	311	8	countable	countable	ADJ
cana-5720	311	9	paracompactness	paracompactness	NOUN
cana-5720	311	10	and	and	CCONJ
cana-5720	311	11	normality	normality	NOUN
cana-5720	311	12	,	,	PUNCT
cana-5720	311	13	prace	prace	PROPN
cana-5720	311	14	mat	mat	PROPN
cana-5720	311	15	.	.	PROPN
cana-5720	311	16	,	,	PUNCT
cana-5720	311	17	13	13	NUM
cana-5720	311	18	(	(	PUNCT
cana-5720	311	19	1969	1969	NUM
cana-5720	311	20	)	)	PUNCT
cana-5720	311	21	,	,	PUNCT
cana-5720	311	22	23	23	NUM
cana-5720	311	23	-	-	SYM
cana-5720	311	24	32	32	NUM
cana-5720	311	25	.	.	PUNCT