id	sid	tid	token	lemma	pos
cana-537	1	1	communications	communication	NOUN
cana-537	1	2	on	on	ADP
cana-537	1	3	applied	apply	VERB
cana-537	1	4	nonlinear	nonlinear	ADJ
cana-537	1	5	analysis	analysis	NOUN
cana-537	1	6	issn	issn	NOUN
cana-537	1	7	:	:	PUNCT
cana-537	1	8	1074	1074	NUM
cana-537	1	9	-	-	PUNCT
cana-537	1	10	133x	133x	NUM
cana-537	1	11	vol	vol	NOUN
cana-537	1	12	31	31	NUM
cana-537	1	13	no	no	NOUN
cana-537	1	14	.	.	NOUN
cana-537	1	15	2	2	NUM
cana-537	1	16	(	(	PUNCT
cana-537	1	17	2024	2024	NUM
cana-537	1	18	)	)	PUNCT
cana-537	1	19	218	218	NUM
cana-537	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-537	1	21	a	a	DET
cana-537	1	22	study	study	NOUN
cana-537	1	23	of	of	ADP
cana-537	1	24	s	s	PROPN
cana-537	1	25	star	star	NOUN
cana-537	1	26	p	p	PROPN
cana-537	1	27	star	star	PROPN
cana-537	1	28	homeomorphism	homeomorphism	PROPN
cana-537	1	29	in	in	ADP
cana-537	1	30	topological	topological	ADJ
cana-537	1	31	spaces	space	NOUN
cana-537	1	32	*	*	PUNCT
cana-537	1	33	1	1	NUM
cana-537	1	34	r.	r.	PROPN
cana-537	1	35	sudha	sudha	PROPN
cana-537	1	36	,	,	PUNCT
cana-537	1	37	*	*	PROPN
cana-537	1	38	2	2	NUM
cana-537	1	39	v.e	v.e	PROPN
cana-537	1	40	.	.	PROPN
cana-537	1	41	sasikala	sasikala	PROPN
cana-537	1	42	*	*	SYM
cana-537	1	43	1	1	NUM
cana-537	1	44	research	research	NOUN
cana-537	1	45	scholar	scholar	NOUN
cana-537	1	46	,	,	PUNCT
cana-537	1	47	*	*	NOUN
cana-537	1	48	2	2	NUM
cana-537	1	49	corresponding	correspond	VERB
cana-537	1	50	author	author	NOUN
cana-537	1	51	,	,	PUNCT
cana-537	1	52	research	research	NOUN
cana-537	1	53	supervisor	supervisor	NOUN
cana-537	1	54	department	department	NOUN
cana-537	1	55	of	of	ADP
cana-537	1	56	mathematics	mathematics	PROPN
cana-537	1	57	,	,	PUNCT
cana-537	1	58	vels	vels	PROPN
cana-537	1	59	institute	institute	PROPN
cana-537	1	60	of	of	ADP
cana-537	1	61	science	science	NOUN
cana-537	1	62	,	,	PUNCT
cana-537	1	63	technology	technology	NOUN
cana-537	1	64	and	and	CCONJ
cana-537	1	65	advanced	advanced	ADJ
cana-537	1	66	studies	study	NOUN
cana-537	1	67	,	,	PUNCT
cana-537	1	68	(	(	PUNCT
cana-537	1	69	vistas	vista	NOUN
cana-537	1	70	)	)	PUNCT
cana-537	1	71	pallavaram	pallavaram	PROPN
cana-537	1	72	,	,	PUNCT
cana-537	1	73	chennai	chennai	PROPN
cana-537	1	74	.	.	PUNCT
cana-537	2	1	india	india	PROPN
cana-537	2	2	.	.	PUNCT
cana-537	3	1	corresponding	correspond	VERB
cana-537	3	2	author	author	NOUN
cana-537	3	3	mail	mail	NOUN
cana-537	3	4	i	i	PROPN
cana-537	3	5	d	d	PROPN
cana-537	3	6	:	:	PUNCT
cana-537	3	7	sasikala.sbs@velsuniv.ac.in	sasikala.sbs@velsuniv.ac.in	NOUN
cana-537	3	8	article	article	NOUN
cana-537	3	9	history	history	NOUN
cana-537	3	10	:	:	PUNCT
cana-537	3	11	received	receive	VERB
cana-537	3	12	:	:	PUNCT
cana-537	3	13	30	30	NUM
cana-537	3	14	-	-	SYM
cana-537	3	15	01	01	NUM
cana-537	3	16	-	-	PUNCT
cana-537	3	17	2024	2024	NUM
cana-537	3	18	revised	revise	VERB
cana-537	3	19	:	:	PUNCT
cana-537	3	20	10	10	NUM
cana-537	3	21	-	-	PUNCT
cana-537	3	22	04	04	NUM
cana-537	3	23	-	-	PUNCT
cana-537	3	24	2024	2024	NUM
cana-537	3	25	accepted	accept	VERB
cana-537	3	26	:	:	PUNCT
cana-537	3	27	28	28	NUM
cana-537	3	28	-	-	PUNCT
cana-537	3	29	04	04	NUM
cana-537	3	30	-	-	PUNCT
cana-537	3	31	2024	2024	NUM
cana-537	3	32	abstract	abstract	NOUN
cana-537	3	33	:	:	PUNCT
cana-537	3	34	the	the	DET
cana-537	3	35	present	present	ADJ
cana-537	3	36	study	study	NOUN
cana-537	3	37	aims	aim	VERB
cana-537	3	38	to	to	PART
cana-537	3	39	provide	provide	VERB
cana-537	3	40	an	an	DET
cana-537	3	41	overview	overview	NOUN
cana-537	3	42	and	and	CCONJ
cana-537	3	43	explore	explore	VERB
cana-537	3	44	the	the	DET
cana-537	3	45	new	new	ADJ
cana-537	3	46	class	class	NOUN
cana-537	3	47	of	of	ADP
cana-537	3	48	closed	closed	ADJ
cana-537	3	49	map	map	NOUN
cana-537	3	50	and	and	CCONJ
cana-537	3	51	open	open	ADJ
cana-537	3	52	map	map	NOUN
cana-537	3	53	is	be	AUX
cana-537	3	54	termed	term	VERB
cana-537	3	55	as	as	ADP
cana-537	3	56	semi	semi	ADV
cana-537	3	57	star	star	PROPN
cana-537	3	58	pre	pre	PROPN
cana-537	3	59	star	star	PROPN
cana-537	3	60	closed	closed	ADJ
cana-537	3	61	map	map	NOUN
cana-537	3	62	(	(	PUNCT
cana-537	3	63	briefly	briefly	ADV
cana-537	3	64	s*p*closed	s*p*close	VERB
cana-537	3	65	map	map	NOUN
cana-537	3	66	)	)	PUNCT
cana-537	3	67	,	,	PUNCT
cana-537	3	68	semi	semi	ADV
cana-537	3	69	star	star	PROPN
cana-537	3	70	pre	pre	PROPN
cana-537	3	71	star	star	PROPN
cana-537	3	72	open	open	PROPN
cana-537	3	73	map	map	NOUN
cana-537	3	74	(	(	PUNCT
cana-537	3	75	briefly	briefly	NOUN
cana-537	3	76	s*p*open	s*p*open	NUM
cana-537	3	77	map	map	NOUN
cana-537	3	78	)	)	PUNCT
cana-537	3	79	and	and	CCONJ
cana-537	3	80	some	some	PRON
cana-537	3	81	of	of	ADP
cana-537	3	82	its	its	PRON
cana-537	3	83	characterizations	characterization	NOUN
cana-537	3	84	are	be	AUX
cana-537	3	85	studied	study	VERB
cana-537	3	86	.	.	PUNCT
cana-537	4	1	more	more	ADV
cana-537	4	2	over	over	ADP
cana-537	4	3	semi	semi	ADV
cana-537	4	4	star	star	PROPN
cana-537	4	5	pre	pre	PROPN
cana-537	4	6	star	star	PROPN
cana-537	4	7	homeomorphism	homeomorphism	PROPN
cana-537	4	8	(	(	PUNCT
cana-537	4	9	briefly	briefly	NOUN
cana-537	4	10	s*p*homeomorphism	s*p*homeomorphism	NOUN
cana-537	4	11	)	)	PUNCT
cana-537	4	12	in	in	ADP
cana-537	4	13	topological	topological	ADJ
cana-537	4	14	spaces	space	NOUN
cana-537	4	15	is	be	AUX
cana-537	4	16	defined	define	VERB
cana-537	4	17	via	via	ADP
cana-537	4	18	s*p*open	s*p*open	NOUN
cana-537	4	19	map	map	NOUN
cana-537	4	20	and	and	CCONJ
cana-537	4	21	s*p*continuous	s*p*continuous	ADJ
cana-537	4	22	map	map	NOUN
cana-537	4	23	and	and	CCONJ
cana-537	4	24	to	to	PART
cana-537	4	25	get	get	VERB
cana-537	4	26	a	a	DET
cana-537	4	27	few	few	ADJ
cana-537	4	28	of	of	ADP
cana-537	4	29	their	their	PRON
cana-537	4	30	specific	specific	ADJ
cana-537	4	31	features	feature	NOUN
cana-537	4	32	.	.	PUNCT
cana-537	5	1	also	also	ADV
cana-537	5	2	,	,	PUNCT
cana-537	5	3	compared	compare	VERB
cana-537	5	4	with	with	ADP
cana-537	5	5	existing	exist	VERB
cana-537	5	6	one	one	NUM
cana-537	5	7	.	.	PUNCT
cana-537	6	1	keywords	keyword	NOUN
cana-537	6	2	:	:	PUNCT
cana-537	6	3	s*p*closed	s*p*close	VERB
cana-537	6	4	set	set	NOUN
cana-537	6	5	,	,	PUNCT
cana-537	6	6	s*p*open	s*p*open	PROPN
cana-537	6	7	set	set	NOUN
cana-537	6	8	,	,	PUNCT
cana-537	6	9	s*p*closed	s*p*close	VERB
cana-537	6	10	map	map	NOUN
cana-537	6	11	,	,	PUNCT
cana-537	6	12	s*p	s*p	PROPN
cana-537	6	13	*	*	PROPN
cana-537	6	14	open	open	PROPN
cana-537	6	15	map	map	NOUN
cana-537	6	16	,	,	PUNCT
cana-537	6	17	s*p*homeomorphism	s*p*homeomorphism	NOUN
cana-537	6	18	.	.	NOUN
cana-537	6	19	1	1	NUM
cana-537	6	20	.	.	X
cana-537	6	21	introduction	introduction	NOUN
cana-537	6	22	in	in	ADP
cana-537	6	23	topology	topology	NOUN
cana-537	6	24	,	,	PUNCT
cana-537	6	25	the	the	DET
cana-537	6	26	idea	idea	NOUN
cana-537	6	27	of	of	ADP
cana-537	6	28	homeomorphism	homeomorphism	PROPN
cana-537	6	29	is	be	AUX
cana-537	6	30	necessary	necessary	ADJ
cana-537	6	31	.	.	PUNCT
cana-537	7	1	homeomorphism	homeomorphism	PROPN
cana-537	7	2	is	be	AUX
cana-537	7	3	the	the	DET
cana-537	7	4	process	process	NOUN
cana-537	7	5	of	of	ADP
cana-537	7	6	continuously	continuously	ADV
cana-537	7	7	stretching	stretch	VERB
cana-537	7	8	and	and	CCONJ
cana-537	7	9	bending	bend	VERB
cana-537	7	10	an	an	DET
cana-537	7	11	object	object	NOUN
cana-537	7	12	into	into	ADP
cana-537	7	13	a	a	DET
cana-537	7	14	new	new	ADJ
cana-537	7	15	shape	shape	NOUN
cana-537	7	16	.	.	PUNCT
cana-537	8	1	a	a	DET
cana-537	8	2	homeomorphism	homeomorphism	NOUN
cana-537	8	3	is	be	AUX
cana-537	8	4	a	a	DET
cana-537	8	5	function	function	NOUN
cana-537	8	6	which	which	PRON
cana-537	8	7	is	be	AUX
cana-537	8	8	bijection	bijection	NOUN
cana-537	8	9	between	between	ADP
cana-537	8	10	topological	topological	ADJ
cana-537	8	11	spaces	space	NOUN
cana-537	8	12	so	so	SCONJ
cana-537	8	13	that	that	SCONJ
cana-537	8	14	the	the	DET
cana-537	8	15	map	map	NOUN
cana-537	8	16	and	and	CCONJ
cana-537	8	17	its	its	PRON
cana-537	8	18	inverse	inverse	NOUN
cana-537	8	19	are	be	AUX
cana-537	8	20	both	both	ADV
cana-537	8	21	continuous	continuous	ADJ
cana-537	8	22	.	.	PUNCT
cana-537	9	1	s.r.malghan	s.r.malghan	PROPN
cana-537	9	2	explores	explore	NOUN
cana-537	9	3	as	as	ADV
cana-537	9	4	well	well	ADV
cana-537	9	5	as	as	ADP
cana-537	9	6	establishes	establish	VERB
cana-537	9	7	the	the	DET
cana-537	9	8	generalized	generalize	VERB
cana-537	9	9	closed	closed	ADJ
cana-537	9	10	maps	map	NOUN
cana-537	9	11	[	[	X
cana-537	9	12	1	1	NUM
cana-537	9	13	]	]	PUNCT
cana-537	9	14	.	.	PUNCT
cana-537	10	1	benchalli	benchalli	PROPN
cana-537	11	1	[	[	X
cana-537	11	2	2	2	X
cana-537	11	3	]	]	PUNCT
cana-537	11	4	developed	develop	VERB
cana-537	11	5	regular	regular	ADJ
cana-537	11	6	closed	closed	ADJ
cana-537	11	7	maps	map	NOUN
cana-537	11	8	,	,	PUNCT
cana-537	11	9	rw	rw	NOUN
cana-537	11	10	-	-	PUNCT
cana-537	11	11	closed	close	VERB
cana-537	11	12	maps	map	NOUN
cana-537	11	13	and	and	CCONJ
cana-537	11	14	αrw	αrw	NOUN
cana-537	11	15	-	-	PUNCT
cana-537	11	16	closed	close	VERB
cana-537	11	17	maps	map	NOUN
cana-537	11	18	.	.	PUNCT
cana-537	12	1	rgα	rgα	NOUN
cana-537	12	2	-	-	PUNCT
cana-537	12	3	closed	closed	ADJ
cana-537	12	4	map	map	NOUN
cana-537	12	5	also	also	ADV
cana-537	12	6	rgα	rgα	VERB
cana-537	12	7	-	-	ADJ
cana-537	12	8	open	open	ADJ
cana-537	12	9	map	map	NOUN
cana-537	12	10	was	be	AUX
cana-537	12	11	introduced	introduce	VERB
cana-537	12	12	by	by	ADP
cana-537	12	13	a.vadivel	a.vadivel	NOUN
cana-537	12	14	and	and	CCONJ
cana-537	12	15	k.vairamanikcam	k.vairamanikcam	X
cana-537	13	1	[	[	X
cana-537	13	2	3	3	NUM
cana-537	13	3	]	]	PUNCT
cana-537	13	4	.	.	PUNCT
cana-537	14	1	sg	sg	PROPN
cana-537	14	2	homomorphism	homomorphism	PROPN
cana-537	14	3	and	and	CCONJ
cana-537	14	4	gs	gs	PROPN
cana-537	14	5	homomorphism	homomorphism	NOUN
cana-537	14	6	in	in	ADP
cana-537	14	7	topological	topological	ADJ
cana-537	14	8	spaces	space	NOUN
cana-537	14	9	was	be	AUX
cana-537	14	10	studied	study	VERB
cana-537	14	11	by	by	ADP
cana-537	14	12	devi	devi	PROPN
cana-537	14	13	et	et	PROPN
cana-537	14	14	al	al	PROPN
cana-537	15	1	[	[	X
cana-537	15	2	4	4	NUM
cana-537	15	3	]	]	PUNCT
cana-537	15	4	.	.	PUNCT
cana-537	16	1	generalized	generalized	ADJ
cana-537	16	2	homeomorphism	homeomorphism	PROPN
cana-537	16	3	were	be	AUX
cana-537	16	4	initially	initially	ADV
cana-537	16	5	stated	state	VERB
cana-537	16	6	and	and	CCONJ
cana-537	16	7	examined	examine	VERB
cana-537	16	8	by	by	ADP
cana-537	16	9	maki	maki	PROPN
cana-537	16	10	et	et	PROPN
cana-537	16	11	al	al	PROPN
cana-537	16	12	.	.	PUNCT
cana-537	17	1	[	[	X
cana-537	17	2	5	5	NUM
cana-537	17	3	]	]	PUNCT
cana-537	17	4	.	.	PUNCT
cana-537	17	5	rs	rs	PROPN
cana-537	17	6	wali	wali	PROPN
cana-537	17	7	et.al	et.al	PROPN
cana-537	17	8	[	[	X
cana-537	17	9	6	6	NUM
cana-537	17	10	]	]	PUNCT
cana-537	17	11	have	have	AUX
cana-537	17	12	introduced	introduce	VERB
cana-537	17	13	rgwα	rgwα	NOUN
cana-537	17	14	-	-	PUNCT
cana-537	17	15	homeomorphism	homeomorphism	PROPN
cana-537	17	16	in	in	ADP
cana-537	17	17	topological	topological	ADJ
cana-537	17	18	spaces	space	NOUN
cana-537	17	19	.	.	PUNCT
cana-537	18	1	gnanambal	gnanambal	PROPN
cana-537	19	1	[	[	X
cana-537	19	2	7	7	NUM
cana-537	19	3	]	]	PUNCT
cana-537	19	4	has	have	AUX
cana-537	19	5	defined	define	VERB
cana-537	19	6	gpr	gpr	PROPN
cana-537	19	7	-	-	PUNCT
cana-537	19	8	closed	close	VERB
cana-537	19	9	maps	map	NOUN
cana-537	19	10	and	and	CCONJ
cana-537	19	11	studied	study	VERB
cana-537	19	12	some	some	PRON
cana-537	19	13	of	of	ADP
cana-537	19	14	their	their	PRON
cana-537	19	15	unique	unique	ADJ
cana-537	19	16	features	feature	NOUN
cana-537	19	17	.	.	PUNCT
cana-537	20	1	d.iyappan	d.iyappan	ADP
cana-537	20	2	and	and	CCONJ
cana-537	20	3	n.nagaveni	n.nagaveni	ADV
cana-537	20	4	[	[	X
cana-537	20	5	8	8	NUM
cana-537	20	6	]	]	PUNCT
cana-537	20	7	was	be	AUX
cana-537	20	8	delivered	deliver	VERB
cana-537	20	9	on	on	ADP
cana-537	20	10	sgb	sgb	ADJ
cana-537	20	11	-	-	PUNCT
cana-537	20	12	continuous	continuous	ADJ
cana-537	20	13	map	map	NOUN
cana-537	20	14	,	,	PUNCT
cana-537	20	15	sgb	sgb	ADJ
cana-537	20	16	-	-	PUNCT
cana-537	20	17	closed	close	VERB
cana-537	20	18	maps	map	NOUN
cana-537	20	19	in	in	ADP
cana-537	20	20	topological	topological	ADJ
cana-537	20	21	space	space	NOUN
cana-537	20	22	.	.	PUNCT
cana-537	21	1	studies	study	NOUN
cana-537	21	2	on	on	ADP
cana-537	21	3	generalization	generalization	NOUN
cana-537	21	4	of	of	ADP
cana-537	21	5	homeomorphism	homeomorphism	PROPN
cana-537	21	6	in	in	ADP
cana-537	21	7	topological	topological	ADJ
cana-537	21	8	spaces	space	NOUN
cana-537	21	9	introduced	introduce	VERB
cana-537	21	10	by	by	ADP
cana-537	21	11	n.nagaveni	n.nagaveni	NOUN
cana-537	21	12	[	[	X
cana-537	21	13	9	9	NUM
cana-537	21	14	]	]	PUNCT
cana-537	21	15	.	.	PUNCT
cana-537	22	1	t.shyla	t.shyla	NUM
cana-537	22	2	isac	isac	PROPN
cana-537	22	3	mary	mary	PROPN
cana-537	22	4	and	and	CCONJ
cana-537	22	5	p.thangavelu	p.thangavelu	NOUN
cana-537	23	1	[	[	X
cana-537	23	2	10	10	NUM
cana-537	23	3	]	]	PUNCT
cana-537	23	4	studied	study	VERB
cana-537	23	5	and	and	CCONJ
cana-537	23	6	developed	develop	VERB
cana-537	23	7	rps	rps	PROPN
cana-537	23	8	-	-	PUNCT
cana-537	23	9	homeomorphism	homeomorphism	PROPN
cana-537	23	10	in	in	ADP
cana-537	23	11	topological	topological	ADJ
cana-537	23	12	spaces	space	NOUN
cana-537	23	13	.	.	PUNCT
cana-537	24	1	in	in	ADP
cana-537	24	2	topological	topological	ADJ
cana-537	24	3	spaces	space	NOUN
cana-537	24	4	,	,	PUNCT
cana-537	24	5	a.	a.	PROPN
cana-537	24	6	pushpalatha	pushpalatha	PROPN
cana-537	24	7	and	and	CCONJ
cana-537	24	8	k.	k.	PROPN
cana-537	24	9	anitha	anitha	PROPN
cana-537	25	1	[	[	X
cana-537	25	2	11	11	NUM
cana-537	25	3	]	]	PUNCT
cana-537	25	4	established	establish	VERB
cana-537	25	5	properties	property	NOUN
cana-537	25	6	of	of	ADP
cana-537	25	7	g*s	g*s	PROPN
cana-537	25	8	-	-	PUNCT
cana-537	25	9	closed	close	VERB
cana-537	25	10	set	set	NOUN
cana-537	25	11	and	and	CCONJ
cana-537	25	12	a.	a.	NOUN
cana-537	25	13	pushpalatha	pushpalatha	PROPN
cana-537	26	1	[	[	X
cana-537	26	2	12	12	NUM
cana-537	26	3	]	]	PUNCT
cana-537	26	4	looked	look	VERB
cana-537	26	5	on	on	ADP
cana-537	26	6	research	research	NOUN
cana-537	26	7	on	on	ADP
cana-537	26	8	topological	topological	ADJ
cana-537	26	9	space	space	NOUN
cana-537	26	10	generalizations	generalization	NOUN
cana-537	26	11	of	of	ADP
cana-537	26	12	mapping	mapping	NOUN
cana-537	26	13	.	.	PUNCT
cana-537	27	1	in	in	ADP
cana-537	27	2	topological	topological	ADJ
cana-537	27	3	spaces	space	NOUN
cana-537	27	4	,	,	PUNCT
cana-537	27	5	generalizations	generalization	NOUN
cana-537	27	6	of	of	ADP
cana-537	27	7	generalized	generalized	ADJ
cana-537	27	8	closed	closed	ADJ
cana-537	27	9	sets	set	NOUN
cana-537	27	10	and	and	CCONJ
cana-537	27	11	maps	map	NOUN
cana-537	27	12	was	be	AUX
cana-537	27	13	developed	develop	VERB
cana-537	27	14	by	by	ADP
cana-537	27	15	i.arockiarani	i.arockiarani	NOUN
cana-537	27	16	[	[	X
cana-537	27	17	13	13	NUM
cana-537	27	18	]	]	PUNCT
cana-537	27	19	.	.	PUNCT
cana-537	28	1	s.sekar	s.sekar	ADJ
cana-537	28	2	and	and	CCONJ
cana-537	28	3	b.jothilakshmi	b.jothilakshmi	ADJ
cana-537	28	4	[	[	X
cana-537	28	5	14	14	NUM
cana-537	28	6	]	]	PUNCT
cana-537	28	7	were	be	AUX
cana-537	28	8	created	create	VERB
cana-537	28	9	and	and	CCONJ
cana-537	28	10	explored	explore	VERB
cana-537	28	11	the	the	DET
cana-537	28	12	sg*b	sg*b	ADV
cana-537	28	13	-	-	PUNCT
cana-537	28	14	closed	closed	ADJ
cana-537	28	15	maps	map	NOUN
cana-537	28	16	in	in	ADP
cana-537	28	17	topological	topological	ADJ
cana-537	28	18	spaces	space	NOUN
cana-537	28	19	.	.	PUNCT
cana-537	29	1	fundamental	fundamental	ADJ
cana-537	29	2	topological	topological	ADJ
cana-537	29	3	ideas	idea	NOUN
cana-537	29	4	are	be	AUX
cana-537	29	5	explored	explore	VERB
cana-537	29	6	in	in	ADP
cana-537	29	7	this	this	DET
cana-537	29	8	paper	paper	NOUN
cana-537	29	9	with	with	ADP
cana-537	29	10	a	a	DET
cana-537	29	11	special	special	ADJ
cana-537	29	12	focus	focus	NOUN
cana-537	29	13	to	to	ADP
cana-537	29	14	the	the	DET
cana-537	29	15	s	s	PROPN
cana-537	29	16	star	star	NOUN
cana-537	29	17	p	p	PROPN
cana-537	29	18	star	star	PROPN
cana-537	29	19	homeomorphism	homeomorphism	PROPN
cana-537	29	20	.	.	PUNCT
cana-537	30	1	the	the	DET
cana-537	30	2	field	field	NOUN
cana-537	30	3	of	of	ADP
cana-537	30	4	topological	topological	ADJ
cana-537	30	5	spaces	space	NOUN
cana-537	30	6	and	and	CCONJ
cana-537	30	7	its	its	PRON
cana-537	30	8	fundamental	fundamental	ADJ
cana-537	30	9	properties	property	NOUN
cana-537	30	10	are	be	AUX
cana-537	30	11	expected	expect	VERB
cana-537	30	12	to	to	PART
cana-537	30	13	be	be	AUX
cana-537	30	14	better	well	ADV
cana-537	30	15	understood	understand	VERB
cana-537	30	16	with	with	ADP
cana-537	30	17	the	the	DET
cana-537	30	18	development	development	NOUN
cana-537	30	19	of	of	ADP
cana-537	30	20	s	s	PROPN
cana-537	30	21	star	star	NOUN
cana-537	30	22	p	p	PROPN
cana-537	30	23	star	star	PROPN
cana-537	30	24	homeomorphism	homeomorphism	PROPN
cana-537	30	25	ideas	idea	NOUN
cana-537	30	26	,	,	PUNCT
cana-537	30	27	which	which	PRON
cana-537	30	28	offer	offer	VERB
cana-537	30	29	a	a	DET
cana-537	30	30	new	new	ADJ
cana-537	30	31	point	point	NOUN
cana-537	30	32	of	of	ADP
cana-537	30	33	view	view	NOUN
cana-537	30	34	.	.	PUNCT
cana-537	31	1	in	in	ADP
cana-537	31	2	the	the	DET
cana-537	31	3	present	present	ADJ
cana-537	31	4	analysis	analysis	NOUN
cana-537	31	5	,	,	PUNCT
cana-537	31	6	topological	topological	ADJ
cana-537	31	7	spaces	space	NOUN
cana-537	31	8	are	be	AUX
cana-537	31	9	treated	treat	VERB
cana-537	31	10	as	as	ADP
cana-537	31	11	ts	ts	NOUN
cana-537	31	12	,	,	PUNCT
cana-537	31	13	s*p*closed	s*p*close	VERB
cana-537	31	14	set	set	VERB
cana-537	31	15	as	as	ADP
cana-537	31	16	s*p*-c	s*p*-c	PROPN
cana-537	31	17	set	set	PROPN
cana-537	31	18	,	,	PUNCT
cana-537	31	19	s*p	s*p	PROPN
cana-537	31	20	*	*	PROPN
cana-537	31	21	open	open	ADJ
cana-537	31	22	set	set	VERB
cana-537	31	23	as	as	ADP
cana-537	31	24	s*p*-o	s*p*-o	PROPN
cana-537	31	25	set	set	NOUN
cana-537	31	26	,	,	PUNCT
cana-537	31	27	s*p	s*p	PROPN
cana-537	31	28	*	*	PUNCT
cana-537	31	29	homeomorphism	homeomorphism	PROPN
cana-537	31	30	as	as	ADP
cana-537	31	31	s*p*-h	s*p*-h	NOUN
cana-537	31	32	.	.	PUNCT
cana-537	32	1	mailto:sasikala.sbs@velsuniv.ac.in	mailto:sasikala.sbs@velsuniv.ac.in	PROPN
cana-537	32	2	communications	communication	NOUN
cana-537	32	3	on	on	ADP
cana-537	32	4	applied	apply	VERB
cana-537	32	5	nonlinear	nonlinear	ADJ
cana-537	32	6	analysis	analysis	NOUN
cana-537	32	7	issn	issn	NOUN
cana-537	32	8	:	:	PUNCT
cana-537	32	9	1074	1074	NUM
cana-537	32	10	-	-	PUNCT
cana-537	32	11	133x	133x	NUM
cana-537	32	12	vol	vol	NOUN
cana-537	32	13	31	31	NUM
cana-537	32	14	no	no	NOUN
cana-537	32	15	.	.	NOUN
cana-537	32	16	2	2	NUM
cana-537	32	17	(	(	PUNCT
cana-537	32	18	2024	2024	NUM
cana-537	32	19	)	)	PUNCT
cana-537	32	20	219	219	NUM
cana-537	33	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-537	33	2	2	2	NUM
cana-537	33	3	.	.	X
cana-537	33	4	objectives	objective	VERB
cana-537	33	5	this	this	DET
cana-537	33	6	research	research	NOUN
cana-537	33	7	aims	aim	VERB
cana-537	33	8	to	to	PART
cana-537	33	9	define	define	VERB
cana-537	33	10	and	and	CCONJ
cana-537	33	11	analyses	analyse	VERB
cana-537	33	12	s	s	PART
cana-537	33	13	star	star	NOUN
cana-537	33	14	p	p	PROPN
cana-537	33	15	star	star	PROPN
cana-537	33	16	homeomorphism	homeomorphism	PROPN
cana-537	33	17	in	in	ADP
cana-537	33	18	topological	topological	ADJ
cana-537	33	19	spaces	space	NOUN
cana-537	33	20	in	in	ADP
cana-537	33	21	an	an	DET
cana-537	33	22	exact	exact	ADJ
cana-537	33	23	way	way	NOUN
cana-537	33	24	.	.	PUNCT
cana-537	34	1	formulate	formulate	VERB
cana-537	34	2	a	a	DET
cana-537	34	3	number	number	NOUN
cana-537	34	4	of	of	ADP
cana-537	34	5	theorems	theorem	NOUN
cana-537	34	6	that	that	PRON
cana-537	34	7	demonstrate	demonstrate	VERB
cana-537	34	8	these	these	DET
cana-537	34	9	sets	set	VERB
cana-537	34	10	features	feature	NOUN
cana-537	34	11	and	and	CCONJ
cana-537	34	12	implications	implication	NOUN
cana-537	34	13	.	.	PUNCT
cana-537	35	1	utilize	utilize	VERB
cana-537	35	2	the	the	DET
cana-537	35	3	illustrations	illustration	NOUN
cana-537	35	4	how	how	SCONJ
cana-537	35	5	these	these	DET
cana-537	35	6	concepts	concept	NOUN
cana-537	35	7	are	be	AUX
cana-537	35	8	effective	effective	ADJ
cana-537	35	9	.	.	PUNCT
cana-537	36	1	3	3	X
cana-537	36	2	.	.	X
cana-537	36	3	preliminaries	preliminary	NOUN
cana-537	36	4	definition	definition	NOUN
cana-537	36	5	:	:	PUNCT
cana-537	37	1	[	[	X
cana-537	37	2	15	15	NUM
cana-537	37	3	]	]	PUNCT
cana-537	37	4	let	let	VERB
cana-537	37	5	the	the	DET
cana-537	37	6	ts	ts	NOUN
cana-537	37	7	be	be	AUX
cana-537	37	8	x.	x.	NOUN
cana-537	37	9	let	let	VERB
cana-537	37	10	a	a	DET
cana-537	37	11			PROPN
cana-537	37	12	x	x	PUNCT
cana-537	37	13	is	be	AUX
cana-537	37	14	known	know	VERB
cana-537	37	15	as	as	ADP
cana-537	37	16	semi	semi	ADV
cana-537	37	17	star	star	PROPN
cana-537	37	18	pre	pre	PROPN
cana-537	37	19	star	star	PROPN
cana-537	37	20	closed	close	VERB
cana-537	37	21	sets	set	NOUN
cana-537	37	22	(	(	PUNCT
cana-537	37	23	briefly	briefly	NOUN
cana-537	37	24	s	s	PART
cana-537	37	25	*	*	X
cana-537	37	26	p	p	X
cana-537	37	27	*	*	PUNCT
cana-537	37	28	closed	closed	ADJ
cana-537	37	29	sets	set	NOUN
cana-537	37	30	)	)	PUNCT
cana-537	37	31	if	if	SCONJ
cana-537	37	32	scl	scl	PROPN
cana-537	37	33	of	of	ADP
cana-537	37	34	a	a	PRON
cana-537	37	35	is	be	AUX
cana-537	37	36	subset	subset	VERB
cana-537	37	37	of	of	ADP
cana-537	37	38	u	u	PRON
cana-537	37	39	when	when	SCONJ
cana-537	37	40	a	a	PRON
cana-537	37	41	is	be	AUX
cana-537	37	42			NOUN
cana-537	37	43	of	of	ADP
cana-537	37	44	u	u	NOUN
cana-537	37	45	and	and	CCONJ
cana-537	37	46	u	u	NOUN
cana-537	37	47	is	be	AUX
cana-537	37	48	pre	pre	VERB
cana-537	37	49	semi	semi	ADV
cana-537	37	50	open	open	ADJ
cana-537	37	51	set	set	NOUN
cana-537	37	52	.	.	PUNCT
cana-537	38	1	the	the	DET
cana-537	38	2	complement	complement	NOUN
cana-537	38	3	of	of	ADP
cana-537	38	4	s*p*-c	s*p*-c	PROPN
cana-537	38	5	set	set	PROPN
cana-537	38	6	is	be	AUX
cana-537	38	7	known	know	VERB
cana-537	38	8	as	as	ADP
cana-537	38	9	s*p*-o	s*p*-o	ADV
cana-537	38	10	set	set	NOUN
cana-537	38	11	.	.	PUNCT
cana-537	39	1	definition	definition	NOUN
cana-537	39	2	:	:	PUNCT
cana-537	39	3	the	the	DET
cana-537	39	4	term	term	NOUN
cana-537	39	5	s*p	s*p	PROPN
cana-537	39	6	*	*	PROPN
cana-537	39	7	continuous	continuous	ADJ
cana-537	39	8	refers	refer	VERB
cana-537	39	9	to	to	ADP
cana-537	39	10	a	a	DET
cana-537	39	11	function	function	NOUN
cana-537	40	1	f	f	NOUN
cana-537	40	2	:	:	PUNCT
cana-537	40	3	x1	x1	PROPN
cana-537	40	4	→	→	SYM
cana-537	40	5	x2	x2	PROPN
cana-537	40	6	where	where	SCONJ
cana-537	40	7	each	each	PRON
cana-537	40	8	closed	close	VERB
cana-537	40	9	set	set	VERB
cana-537	40	10	in	in	ADP
cana-537	40	11	x2	x2	PROPN
cana-537	40	12	has	have	VERB
cana-537	40	13	an	an	DET
cana-537	40	14	inverse	inverse	ADJ
cana-537	40	15	image	image	NOUN
cana-537	40	16	that	that	PRON
cana-537	40	17	is	be	AUX
cana-537	40	18	also	also	ADV
cana-537	40	19	s*p*-c	s*p*-c	PROPN
cana-537	40	20	set	set	VERB
cana-537	40	21	in	in	ADP
cana-537	40	22	of	of	ADP
cana-537	40	23	every	every	DET
cana-537	40	24	closed	close	VERB
cana-537	40	25	set	set	NOUN
cana-537	40	26	in	in	ADP
cana-537	40	27	x1	x1	PROPN
cana-537	40	28	.	.	PUNCT
cana-537	41	1	4	4	X
cana-537	41	2	.	.	X
cana-537	41	3	s*p	s*p	PROPN
cana-537	41	4	*	*	PROPN
cana-537	41	5	closed	closed	ADJ
cana-537	41	6	map	map	NOUN
cana-537	41	7	using	use	VERB
cana-537	41	8	the	the	DET
cana-537	41	9	basic	basic	ADJ
cana-537	41	10	ideas	idea	NOUN
cana-537	41	11	of	of	ADP
cana-537	41	12	s*p*-c	s*p*-c	PROPN
cana-537	41	13	sets	set	NOUN
cana-537	41	14	,	,	PUNCT
cana-537	41	15	we	we	PRON
cana-537	41	16	bring	bring	VERB
cana-537	41	17	about	about	ADP
cana-537	41	18	s*p*-c	s*p*-c	PROPN
cana-537	41	19	map	map	NOUN
cana-537	41	20	in	in	ADP
cana-537	41	21	topological	topological	ADJ
cana-537	41	22	spaces	space	NOUN
cana-537	41	23	in	in	ADP
cana-537	41	24	this	this	DET
cana-537	41	25	part	part	NOUN
cana-537	41	26	and	and	CCONJ
cana-537	41	27	go	go	VERB
cana-537	41	28	through	through	ADP
cana-537	41	29	some	some	PRON
cana-537	41	30	of	of	ADP
cana-537	41	31	its	its	PRON
cana-537	41	32	essential	essential	ADJ
cana-537	41	33	features	feature	NOUN
cana-537	41	34	.	.	PUNCT
cana-537	42	1	definition	definition	NOUN
cana-537	42	2	4.1	4.1	NUM
cana-537	42	3	:	:	PUNCT
cana-537	42	4	a	a	DET
cana-537	42	5	function	function	NOUN
cana-537	42	6	f	f	X
cana-537	42	7	:	:	PUNCT
cana-537	42	8	x1→x2	x1→x2	PROPN
cana-537	42	9	is	be	AUX
cana-537	42	10	referred	refer	VERB
cana-537	42	11	to	to	PART
cana-537	42	12	be	be	AUX
cana-537	42	13	a	a	DET
cana-537	42	14	s*p*-c	s*p*-c	PROPN
cana-537	42	15	(	(	PUNCT
cana-537	42	16	s*p*-o	s*p*-o	NOUN
cana-537	42	17	)	)	PUNCT
cana-537	42	18	map	map	NOUN
cana-537	42	19	if	if	SCONJ
cana-537	42	20	all	all	PRON
cana-537	42	21	closed	closed	ADJ
cana-537	42	22	(	(	PUNCT
cana-537	42	23	open	open	ADJ
cana-537	42	24	)	)	PUNCT
cana-537	42	25	set	set	VERB
cana-537	42	26	in	in	ADP
cana-537	42	27	x1	x1	PROPN
cana-537	42	28	has	have	VERB
cana-537	42	29	an	an	DET
cana-537	42	30	image	image	NOUN
cana-537	42	31	is	be	AUX
cana-537	42	32	in	in	ADP
cana-537	42	33	s*p*-c	s*p*-c	PROPN
cana-537	42	34	(	(	PUNCT
cana-537	42	35	s*p*-o	s*p*-o	NOUN
cana-537	42	36	)	)	PUNCT
cana-537	42	37	set	set	VERB
cana-537	42	38	in	in	ADP
cana-537	42	39	x2	x2	PROPN
cana-537	42	40	.	.	PUNCT
cana-537	43	1	example	example	NOUN
cana-537	43	2	4.2	4.2	NUM
cana-537	43	3	:	:	PUNCT
cana-537	43	4	let	let	VERB
cana-537	43	5	x1	x1	PROPN
cana-537	43	6	=	=	PUNCT
cana-537	44	1	x2=	x2=	PROPN
cana-537	45	1	{	{	PUNCT
cana-537	45	2	r	r	NOUN
cana-537	45	3	,	,	PUNCT
cana-537	45	4	s	s	PROPN
cana-537	45	5	,	,	PUNCT
cana-537	45	6	t	t	PROPN
cana-537	45	7	}	}	PUNCT
cana-537	45	8	;	;	PUNCT
cana-537	45	9	τ	τ	X
cana-537	45	10	=	=	PUNCT
cana-537	45	11	{	{	PUNCT
cana-537	45	12	x1	x1	PROPN
cana-537	45	13	,	,	PUNCT
cana-537	45	14	φ	φ	PROPN
cana-537	45	15	,	,	PUNCT
cana-537	45	16	{	{	PUNCT
cana-537	45	17	r	r	NOUN
cana-537	45	18	}	}	PUNCT
cana-537	45	19	,	,	PUNCT
cana-537	45	20	{	{	PUNCT
cana-537	45	21	t	t	NOUN
cana-537	45	22	}	}	PUNCT
cana-537	45	23	,	,	PUNCT
cana-537	45	24	{	{	PUNCT
cana-537	45	25	r	r	NOUN
cana-537	45	26	,	,	PUNCT
cana-537	45	27	t	t	NOUN
cana-537	45	28	}	}	PUNCT
cana-537	45	29	}	}	PUNCT
cana-537	45	30	and	and	CCONJ
cana-537	45	31	τc	τc	ADV
cana-537	45	32	=	=	PUNCT
cana-537	45	33	{	{	PUNCT
cana-537	45	34	x1	x1	PROPN
cana-537	45	35	,	,	PUNCT
cana-537	45	36	φ	φ	PROPN
cana-537	45	37	,	,	PUNCT
cana-537	45	38	{	{	PUNCT
cana-537	45	39	s	s	PROPN
cana-537	45	40	,	,	PUNCT
cana-537	45	41	t	t	PROPN
cana-537	45	42	}	}	PUNCT
cana-537	45	43	,	,	PUNCT
cana-537	45	44	{	{	PUNCT
cana-537	45	45	r	r	NOUN
cana-537	45	46	,	,	PUNCT
cana-537	45	47	s	s	PART
cana-537	45	48	}	}	PUNCT
cana-537	45	49	,	,	PUNCT
cana-537	45	50	{	{	PUNCT
cana-537	45	51	s	s	X
cana-537	45	52	}	}	PUNCT
cana-537	45	53	}	}	PUNCT
cana-537	45	54	.	.	PUNCT
cana-537	46	1	σ	σ	NOUN
cana-537	46	2	=	=	PRON
cana-537	46	3	{	{	PUNCT
cana-537	46	4	x2	x2	PROPN
cana-537	46	5	,	,	PUNCT
cana-537	46	6	φ	φ	PROPN
cana-537	46	7	,	,	PUNCT
cana-537	46	8	{	{	PUNCT
cana-537	46	9	s	s	X
cana-537	46	10	}	}	PUNCT
cana-537	46	11	,	,	PUNCT
cana-537	46	12	{	{	PUNCT
cana-537	46	13	r	r	NOUN
cana-537	46	14	,	,	PUNCT
cana-537	46	15	t	t	PROPN
cana-537	46	16	}	}	PUNCT
cana-537	46	17	}	}	PUNCT
cana-537	46	18	;	;	PUNCT
cana-537	46	19	σ	σ	NOUN
cana-537	46	20	c	c	NOUN
cana-537	46	21	=	=	PRON
cana-537	46	22	{	{	PUNCT
cana-537	46	23	x2	x2	PROPN
cana-537	46	24	,	,	PUNCT
cana-537	46	25	φ	φ	PROPN
cana-537	46	26	,	,	PUNCT
cana-537	46	27	{	{	PUNCT
cana-537	46	28	r	r	NOUN
cana-537	46	29	,	,	PUNCT
cana-537	46	30	t	t	PROPN
cana-537	46	31	}	}	PUNCT
cana-537	46	32	,	,	PUNCT
cana-537	46	33	{	{	PUNCT
cana-537	46	34	s	s	X
cana-537	46	35	}	}	PUNCT
cana-537	46	36	}	}	PUNCT
cana-537	46	37	and	and	CCONJ
cana-537	46	38	s*p*-c	s*p*-c	PROPN
cana-537	46	39	sets	set	NOUN
cana-537	46	40	of	of	ADP
cana-537	46	41	x2	x2	PROPN
cana-537	46	42	are	be	AUX
cana-537	46	43	{	{	PUNCT
cana-537	46	44	x2	x2	PROPN
cana-537	46	45	,	,	PUNCT
cana-537	46	46	φ	φ	PROPN
cana-537	46	47	,	,	PUNCT
cana-537	46	48	{	{	PUNCT
cana-537	46	49	r	r	NOUN
cana-537	46	50	}	}	PUNCT
cana-537	46	51	}	}	PUNCT
cana-537	46	52	.	.	PUNCT
cana-537	47	1	define	define	VERB
cana-537	47	2	a	a	DET
cana-537	47	3	map	map	NOUN
cana-537	48	1	f	f	X
cana-537	48	2	:	:	PUNCT
cana-537	48	3	x1→x2	x1→x2	NOUN
cana-537	48	4	by	by	ADP
cana-537	48	5	f(r	f(r	NOUN
cana-537	48	6	)	)	PUNCT
cana-537	49	1	=	=	SYM
cana-537	49	2	s	s	NOUN
cana-537	49	3	;	;	PUNCT
cana-537	49	4	f(s	f(s	X
cana-537	49	5	)	)	PUNCT
cana-537	49	6	=	=	SYM
cana-537	50	1	r	r	NOUN
cana-537	50	2	;	;	PUNCT
cana-537	50	3	f	f	PROPN
cana-537	50	4	(	(	PUNCT
cana-537	50	5	t	t	PROPN
cana-537	50	6	)	)	PUNCT
cana-537	50	7	=	=	SYM
cana-537	51	1	t.	t.	NOUN
cana-537	51	2	then	then	ADV
cana-537	51	3	f	f	PROPN
cana-537	51	4	is	be	AUX
cana-537	51	5	s*p*-c	s*p*-c	PROPN
cana-537	51	6	map	map	NOUN
cana-537	51	7	because	because	SCONJ
cana-537	51	8	the	the	DET
cana-537	51	9	image	image	NOUN
cana-537	51	10	of	of	ADP
cana-537	51	11	closed	closed	ADJ
cana-537	51	12	map	map	NOUN
cana-537	51	13	{	{	PUNCT
cana-537	51	14	s	s	NOUN
cana-537	51	15	}	}	PUNCT
cana-537	51	16	in	in	ADP
cana-537	51	17	(	(	PUNCT
cana-537	51	18	x1	x1	PROPN
cana-537	51	19	,	,	PUNCT
cana-537	51	20	τ	τ	PROPN
cana-537	51	21	)	)	PUNCT
cana-537	51	22	,	,	PUNCT
cana-537	51	23	f	f	PROPN
cana-537	51	24	{	{	PUNCT
cana-537	51	25	s	s	PROPN
cana-537	51	26	}	}	PUNCT
cana-537	51	27	=	=	SYM
cana-537	51	28	{	{	PUNCT
cana-537	51	29	r	r	NOUN
cana-537	51	30	}	}	PUNCT
cana-537	51	31	is	be	AUX
cana-537	51	32	in	in	ADP
cana-537	51	33	s	s	PROPN
cana-537	51	34	*	*	ADJ
cana-537	51	35	p*-c	p*-c	NOUN
cana-537	51	36	set	set	NOUN
cana-537	51	37	in	in	ADP
cana-537	51	38	x2	x2	PROPN
cana-537	51	39	.	.	PUNCT
cana-537	52	1	theorem	theorem	VERB
cana-537	52	2	4.3	4.3	NUM
cana-537	52	3	:	:	PUNCT
cana-537	52	4	a	a	DET
cana-537	52	5	closed	closed	ADJ
cana-537	52	6	map	map	NOUN
cana-537	52	7	is	be	AUX
cana-537	52	8	always	always	ADV
cana-537	52	9	a	a	DET
cana-537	52	10	s*p*-c	s*p*-c	PROPN
cana-537	52	11	map	map	NOUN
cana-537	52	12	.	.	PUNCT
cana-537	53	1	proof	proof	NOUN
cana-537	53	2	:	:	PUNCT
cana-537	53	3	consider	consider	VERB
cana-537	53	4	f	f	NOUN
cana-537	53	5	:	:	PUNCT
cana-537	53	6	x1→	x1→	X
cana-537	53	7	x2	x2	PRON
cana-537	53	8	be	be	VERB
cana-537	53	9	a	a	DET
cana-537	53	10	closed	closed	ADJ
cana-537	53	11	map	map	NOUN
cana-537	53	12	.	.	PUNCT
cana-537	54	1	assume	assume	VERB
cana-537	54	2	that	that	SCONJ
cana-537	54	3	v	v	NOUN
cana-537	54	4	is	be	AUX
cana-537	54	5	in	in	ADP
cana-537	54	6	x1	x1	PROPN
cana-537	54	7	.	.	PUNCT
cana-537	55	1	and	and	CCONJ
cana-537	55	2	it	it	PRON
cana-537	55	3	will	will	AUX
cana-537	55	4	be	be	AUX
cana-537	55	5	closed	close	VERB
cana-537	55	6	set	set	VERB
cana-537	55	7	.	.	PUNCT
cana-537	56	1	it	it	PRON
cana-537	56	2	therefore	therefore	ADV
cana-537	56	3	,	,	PUNCT
cana-537	56	4	the	the	DET
cana-537	56	5	image	image	NOUN
cana-537	56	6	of	of	ADP
cana-537	56	7	v	v	NOUN
cana-537	56	8	is	be	AUX
cana-537	56	9	in	in	ADP
cana-537	56	10	x2	x2	PROPN
cana-537	56	11	and	and	CCONJ
cana-537	56	12	that	that	PRON
cana-537	56	13	is	be	AUX
cana-537	56	14	closed	close	VERB
cana-537	56	15	set	set	VERB
cana-537	56	16	.	.	PUNCT
cana-537	57	1	all	all	DET
cana-537	57	2	closed	closed	ADJ
cana-537	57	3	set	set	NOUN
cana-537	57	4	is	be	AUX
cana-537	57	5	known	know	VERB
cana-537	57	6	to	to	PART
cana-537	57	7	be	be	AUX
cana-537	57	8	s*p*c	s*p*c	PROPN
cana-537	57	9	set	set	VERB
cana-537	57	10	.	.	PUNCT
cana-537	58	1	subsequently	subsequently	ADV
cana-537	58	2	,	,	PUNCT
cana-537	58	3	f(v	f(v	PROPN
cana-537	58	4	)	)	PUNCT
cana-537	58	5	is	be	AUX
cana-537	58	6	s*p*-c	s*p*-c	PROPN
cana-537	58	7	set	set	PROPN
cana-537	58	8	.	.	PUNCT
cana-537	59	1	thus	thus	ADV
cana-537	59	2	,	,	PUNCT
cana-537	59	3	f	f	PROPN
cana-537	59	4	is	be	AUX
cana-537	59	5	a	a	DET
cana-537	59	6	s*p*-c	s*p*-c	PROPN
cana-537	59	7	map	map	NOUN
cana-537	59	8	.	.	PUNCT
cana-537	60	1	this	this	DET
cana-537	60	2	theorem	theorem	ADJ
cana-537	60	3	reverse	reverse	ADJ
cana-537	60	4	implication	implication	NOUN
cana-537	60	5	may	may	AUX
cana-537	60	6	not	not	PART
cana-537	60	7	hold	hold	VERB
cana-537	60	8	,	,	PUNCT
cana-537	60	9	as	as	SCONJ
cana-537	60	10	shown	show	VERB
cana-537	60	11	by	by	ADP
cana-537	60	12	the	the	DET
cana-537	60	13	example	example	NOUN
cana-537	60	14	that	that	PRON
cana-537	60	15	follows	follow	VERB
cana-537	60	16	.	.	PUNCT
cana-537	61	1	example	example	NOUN
cana-537	61	2	4.4	4.4	NUM
cana-537	61	3	:	:	PUNCT
cana-537	61	4	let	let	VERB
cana-537	61	5	x1	x1	PROPN
cana-537	61	6	=	=	PUNCT
cana-537	61	7	x2=	x2=	PROPN
cana-537	62	1	{	{	PUNCT
cana-537	62	2	r	r	NOUN
cana-537	62	3	,	,	PUNCT
cana-537	62	4	s	s	PROPN
cana-537	62	5	,	,	PUNCT
cana-537	62	6	t	t	PROPN
cana-537	62	7	}	}	PUNCT
cana-537	62	8	;	;	PUNCT
cana-537	62	9	τ	τ	X
cana-537	62	10	=	=	PUNCT
cana-537	62	11	{	{	PUNCT
cana-537	62	12	x1	x1	PROPN
cana-537	62	13	,	,	PUNCT
cana-537	62	14	φ	φ	PROPN
cana-537	62	15	,	,	PUNCT
cana-537	62	16	{	{	PUNCT
cana-537	62	17	r	r	NOUN
cana-537	62	18	}	}	PUNCT
cana-537	62	19	,	,	PUNCT
cana-537	62	20	{	{	PUNCT
cana-537	62	21	s	s	X
cana-537	62	22	,	,	PUNCT
cana-537	62	23	t	t	NOUN
cana-537	62	24	}	}	PUNCT
cana-537	62	25	}	}	PUNCT
cana-537	62	26	and	and	CCONJ
cana-537	62	27	τc	τc	ADV
cana-537	62	28	=	=	PUNCT
cana-537	62	29	{	{	PUNCT
cana-537	62	30	x1	x1	PROPN
cana-537	62	31	,	,	PUNCT
cana-537	62	32	φ	φ	PROPN
cana-537	62	33	,	,	PUNCT
cana-537	62	34	{	{	PUNCT
cana-537	62	35	s	s	PROPN
cana-537	62	36	,	,	PUNCT
cana-537	62	37	t	t	PROPN
cana-537	62	38	}	}	PUNCT
cana-537	62	39	,	,	PUNCT
cana-537	62	40	{	{	PUNCT
cana-537	62	41	r	r	NOUN
cana-537	62	42	}	}	PUNCT
cana-537	62	43	}	}	PUNCT
cana-537	62	44	.	.	PUNCT
cana-537	63	1	σ	σ	NOUN
cana-537	63	2	=	=	PRON
cana-537	63	3	{	{	PUNCT
cana-537	63	4	x2	x2	PROPN
cana-537	63	5	,	,	PUNCT
cana-537	63	6	φ	φ	PROPN
cana-537	63	7	,	,	PUNCT
cana-537	63	8	{	{	PUNCT
cana-537	63	9	t	t	NOUN
cana-537	63	10	}	}	PUNCT
cana-537	63	11	,	,	PUNCT
cana-537	63	12	{	{	PUNCT
cana-537	63	13	r	r	NOUN
cana-537	63	14	,	,	PUNCT
cana-537	63	15	t	t	PROPN
cana-537	63	16	}	}	PUNCT
cana-537	63	17	}	}	PUNCT
cana-537	63	18	;	;	PUNCT
cana-537	63	19	σ	σ	NOUN
cana-537	63	20	c	c	NOUN
cana-537	63	21	=	=	PRON
cana-537	63	22	{	{	PUNCT
cana-537	63	23	x2	x2	PROPN
cana-537	63	24	,	,	PUNCT
cana-537	63	25	φ	φ	PROPN
cana-537	63	26	,	,	PUNCT
cana-537	63	27	{	{	PUNCT
cana-537	63	28	r	r	NOUN
cana-537	63	29	,	,	PUNCT
cana-537	63	30	s	s	PART
cana-537	63	31	}	}	PUNCT
cana-537	63	32	,	,	PUNCT
cana-537	63	33	{	{	PUNCT
cana-537	63	34	s	s	X
cana-537	63	35	}	}	PUNCT
cana-537	63	36	}	}	PUNCT
cana-537	63	37	and	and	CCONJ
cana-537	63	38	s*p*-c	s*p*-c	PROPN
cana-537	63	39	sets	set	NOUN
cana-537	63	40	of	of	ADP
cana-537	63	41	x2	x2	PROPN
cana-537	63	42	are	be	AUX
cana-537	63	43	{	{	PUNCT
cana-537	63	44	x2	x2	PROPN
cana-537	63	45	,	,	PUNCT
cana-537	63	46	φ	φ	PROPN
cana-537	63	47	,	,	PUNCT
cana-537	63	48	{	{	PUNCT
cana-537	63	49	r	r	NOUN
cana-537	63	50	}	}	PUNCT
cana-537	63	51	}	}	PUNCT
cana-537	63	52	.	.	PUNCT
cana-537	64	1	define	define	VERB
cana-537	64	2	a	a	DET
cana-537	64	3	map	map	NOUN
cana-537	65	1	f	f	X
cana-537	65	2	:	:	PUNCT
cana-537	65	3	x1→	x1→	X
cana-537	65	4	x2	x2	INTJ
cana-537	65	5	by	by	ADP
cana-537	65	6	f(r	f(r	NOUN
cana-537	65	7	)	)	PUNCT
cana-537	66	1	=	=	SYM
cana-537	66	2	r	r	NOUN
cana-537	66	3	;	;	PUNCT
cana-537	66	4	f(s	f(s	X
cana-537	66	5	)	)	PUNCT
cana-537	66	6	=	=	SYM
cana-537	66	7	s	s	X
cana-537	66	8	;	;	PUNCT
cana-537	66	9	f	f	PROPN
cana-537	66	10	(	(	PUNCT
cana-537	66	11	t	t	PROPN
cana-537	66	12	)	)	PUNCT
cana-537	66	13	=	=	SYM
cana-537	67	1	t.	t.	NOUN
cana-537	67	2	hence	hence	ADV
cana-537	67	3	f	f	PROPN
cana-537	67	4	does	do	AUX
cana-537	67	5	not	not	PART
cana-537	67	6	a	a	DET
cana-537	67	7	closed	close	VERB
cana-537	67	8	map	map	NOUN
cana-537	67	9	rather	rather	ADV
cana-537	67	10	a	a	DET
cana-537	67	11	s*p*-c	s*p*-c	PROPN
cana-537	67	12	map	map	NOUN
cana-537	67	13	.	.	PUNCT
cana-537	68	1	because	because	SCONJ
cana-537	68	2	the	the	DET
cana-537	68	3	image	image	NOUN
cana-537	68	4	of	of	ADP
cana-537	68	5	closed	closed	ADJ
cana-537	68	6	map	map	NOUN
cana-537	68	7	{	{	PUNCT
cana-537	68	8	a	a	NOUN
cana-537	68	9	}	}	PUNCT
cana-537	68	10	in	in	ADP
cana-537	68	11	(	(	PUNCT
cana-537	68	12	x1	x1	PROPN
cana-537	68	13	,	,	PUNCT
cana-537	68	14	τ	τ	PROPN
cana-537	68	15	)	)	PUNCT
cana-537	68	16	,	,	PUNCT
cana-537	68	17	f	f	PROPN
cana-537	68	18	{	{	PUNCT
cana-537	68	19	r	r	NOUN
cana-537	68	20	}	}	PUNCT
cana-537	68	21	=	=	SYM
cana-537	68	22	{	{	PUNCT
cana-537	68	23	r	r	NOUN
cana-537	68	24	}	}	PUNCT
cana-537	68	25	is	be	AUX
cana-537	68	26	not	not	PART
cana-537	68	27	in	in	ADP
cana-537	68	28	closed	closed	ADJ
cana-537	68	29	set	set	VERB
cana-537	68	30	in	in	ADP
cana-537	68	31	x2	x2	PROPN
cana-537	68	32	however	however	ADV
cana-537	68	33	it	it	PRON
cana-537	68	34	in	in	ADP
cana-537	68	35	s	s	PROPN
cana-537	68	36	*	*	PUNCT
cana-537	68	37	p*-c	p*-c	NOUN
cana-537	68	38	set	set	NOUN
cana-537	68	39	in	in	ADP
cana-537	68	40	x2	x2	PROPN
cana-537	68	41	.	.	PUNCT
cana-537	69	1	theorem	theorem	VERB
cana-537	69	2	4.5	4.5	NUM
cana-537	69	3	:	:	PUNCT
cana-537	69	4	every	every	DET
cana-537	69	5	map	map	NOUN
cana-537	69	6	that	that	PRON
cana-537	69	7	belongs	belong	VERB
cana-537	69	8	to	to	PART
cana-537	69	9	preclosed	preclose	VERB
cana-537	69	10	is	be	AUX
cana-537	69	11	s*p*-c	s*p*-c	PROPN
cana-537	69	12	map	map	NOUN
cana-537	69	13	.	.	PUNCT
cana-537	70	1	proof	proof	NOUN
cana-537	70	2	:	:	PUNCT
cana-537	70	3	let	let	VERB
cana-537	70	4	us	we	PRON
cana-537	70	5	consider	consider	VERB
cana-537	70	6	f	f	NOUN
cana-537	70	7	:	:	PUNCT
cana-537	70	8	x1→	x1→	X
cana-537	70	9	x2	x2	PRON
cana-537	70	10	be	be	VERB
cana-537	70	11	a	a	DET
cana-537	70	12	pre	pre	ADJ
cana-537	70	13	-	-	ADJ
cana-537	70	14	closed	closed	ADJ
cana-537	70	15	map	map	NOUN
cana-537	70	16	.	.	PUNCT
cana-537	71	1	let	let	VERB
cana-537	71	2	us	we	PRON
cana-537	71	3	consider	consider	VERB
cana-537	71	4	the	the	DET
cana-537	71	5	closed	closed	ADJ
cana-537	71	6	set	set	NOUN
cana-537	71	7	in	in	ADP
cana-537	71	8	x1	x1	PROPN
cana-537	71	9	which	which	PRON
cana-537	71	10	is	be	AUX
cana-537	71	11	denoted	denote	VERB
cana-537	71	12	by	by	ADP
cana-537	71	13	v.	v.	ADP
cana-537	71	14	thus	thus	ADV
cana-537	71	15	,	,	PUNCT
cana-537	71	16	its	its	PRON
cana-537	71	17	image	image	NOUN
cana-537	71	18	f(v	f(v	NOUN
cana-537	71	19	)	)	PUNCT
cana-537	71	20	is	be	AUX
cana-537	71	21	pre	pre	VERB
cana-537	71	22	closed	closed	ADJ
cana-537	71	23	set	set	VERB
cana-537	71	24	in	in	ADP
cana-537	71	25	x2	x2	PROPN
cana-537	71	26	.	.	PUNCT
cana-537	72	1	because	because	SCONJ
cana-537	72	2	each	each	DET
cana-537	72	3	pre	pre	ADJ
cana-537	72	4	-	-	ADJ
cana-537	72	5	closed	closed	ADJ
cana-537	72	6	set	set	NOUN
cana-537	72	7	is	be	AUX
cana-537	72	8	s*p*-c	s*p*-c	PROPN
cana-537	72	9	set	set	PROPN
cana-537	72	10	.	.	PUNCT
cana-537	73	1	so	so	ADV
cana-537	73	2	,	,	PUNCT
cana-537	73	3	the	the	DET
cana-537	73	4	image	image	NOUN
cana-537	73	5	of	of	ADP
cana-537	73	6	v	v	NOUN
cana-537	73	7	is	be	AUX
cana-537	73	8	in	in	ADP
cana-537	73	9	s*p*-c	s*p*-c	PROPN
cana-537	73	10	set	set	PROPN
cana-537	73	11	.	.	PUNCT
cana-537	74	1	hence	hence	ADV
cana-537	74	2	,	,	PUNCT
cana-537	74	3	f	f	PROPN
cana-537	74	4	is	be	AUX
cana-537	74	5	a	a	DET
cana-537	74	6	s*p*-c	s*p*-c	PROPN
cana-537	74	7	map	map	NOUN
cana-537	74	8	.	.	PUNCT
cana-537	75	1	upcoming	upcoming	ADJ
cana-537	75	2	example	example	NOUN
cana-537	75	3	shows	show	VERB
cana-537	75	4	the	the	DET
cana-537	75	5	reverse	reverse	NOUN
cana-537	75	6	of	of	ADP
cana-537	75	7	the	the	DET
cana-537	75	8	earlier	early	ADJ
cana-537	75	9	theorem	theorem	NOUN
cana-537	75	10	never	never	ADV
cana-537	75	11	hold	hold	VERB
cana-537	75	12	.	.	PUNCT
cana-537	76	1	example	example	NOUN
cana-537	76	2	4.6	4.6	NUM
cana-537	76	3	:	:	PUNCT
cana-537	76	4	let	let	VERB
cana-537	76	5	x1	x1	PROPN
cana-537	76	6	=	=	PUNCT
cana-537	77	1	x2=	x2=	PROPN
cana-537	78	1	{	{	PUNCT
cana-537	78	2	r	r	NOUN
cana-537	78	3	,	,	PUNCT
cana-537	78	4	s	s	PROPN
cana-537	78	5	,	,	PUNCT
cana-537	78	6	t	t	PROPN
cana-537	78	7	}	}	PUNCT
cana-537	78	8	;	;	PUNCT
cana-537	78	9	τ	τ	X
cana-537	78	10	=	=	PUNCT
cana-537	78	11	{	{	PUNCT
cana-537	78	12	x1	x1	PROPN
cana-537	78	13	,	,	PUNCT
cana-537	78	14	φ	φ	PROPN
cana-537	78	15	,	,	PUNCT
cana-537	78	16	{	{	PUNCT
cana-537	78	17	r	r	NOUN
cana-537	78	18	}	}	PUNCT
cana-537	78	19	,	,	PUNCT
cana-537	78	20	{	{	PUNCT
cana-537	78	21	s	s	X
cana-537	78	22	}	}	PUNCT
cana-537	78	23	,	,	PUNCT
cana-537	78	24	{	{	PUNCT
cana-537	78	25	r	r	NOUN
cana-537	78	26	,	,	PUNCT
cana-537	78	27	s	s	PART
cana-537	78	28	}	}	PUNCT
cana-537	78	29	,	,	PUNCT
cana-537	78	30	{	{	PUNCT
cana-537	78	31	s	s	X
cana-537	78	32	,	,	PUNCT
cana-537	78	33	t	t	NOUN
cana-537	78	34	}	}	PUNCT
cana-537	78	35	}	}	PUNCT
cana-537	78	36	and	and	CCONJ
cana-537	78	37	τc	τc	ADV
cana-537	78	38	=	=	PUNCT
cana-537	78	39	{	{	PUNCT
cana-537	78	40	x1	x1	PROPN
cana-537	78	41	,	,	PUNCT
cana-537	78	42	φ	φ	PROPN
cana-537	78	43	,	,	PUNCT
cana-537	78	44	{	{	PUNCT
cana-537	78	45	s	s	PROPN
cana-537	78	46	,	,	PUNCT
cana-537	78	47	t	t	PROPN
cana-537	78	48	}	}	PUNCT
cana-537	78	49	,	,	PUNCT
cana-537	78	50	{	{	PUNCT
cana-537	78	51	r	r	NOUN
cana-537	78	52	,	,	PUNCT
cana-537	78	53	t	t	PROPN
cana-537	78	54	}	}	PUNCT
cana-537	78	55	,	,	PUNCT
cana-537	78	56	{	{	PUNCT
cana-537	78	57	t	t	NOUN
cana-537	78	58	}	}	PUNCT
cana-537	78	59	,	,	PUNCT
cana-537	78	60	{	{	PUNCT
cana-537	78	61	r	r	NOUN
cana-537	78	62	}	}	PUNCT
cana-537	78	63	}	}	PUNCT
cana-537	78	64	.	.	PUNCT
cana-537	79	1	σ	σ	NOUN
cana-537	79	2	=	=	PRON
cana-537	79	3	{	{	PUNCT
cana-537	79	4	x2	x2	PROPN
cana-537	79	5	,	,	PUNCT
cana-537	79	6	φ	φ	PROPN
cana-537	79	7	,	,	PUNCT
cana-537	79	8	{	{	PUNCT
cana-537	79	9	r	r	NOUN
cana-537	79	10	}	}	PUNCT
cana-537	79	11	,	,	PUNCT
cana-537	79	12	{	{	PUNCT
cana-537	79	13	s	s	X
cana-537	79	14	}	}	PUNCT
cana-537	79	15	,	,	PUNCT
cana-537	79	16	{	{	PUNCT
cana-537	79	17	r	r	NOUN
cana-537	79	18	,	,	PUNCT
cana-537	79	19	s	s	PART
cana-537	79	20	}	}	PUNCT
cana-537	79	21	}	}	PUNCT
cana-537	79	22	;	;	PUNCT
cana-537	79	23	σc	σc	PROPN
cana-537	79	24	=	=	SYM
cana-537	79	25	{	{	PUNCT
cana-537	79	26	x2	x2	PROPN
cana-537	79	27	,	,	PUNCT
cana-537	79	28	φ	φ	PROPN
cana-537	79	29	,	,	PUNCT
cana-537	79	30	{	{	PUNCT
cana-537	79	31	s	s	PROPN
cana-537	79	32	,	,	PUNCT
cana-537	79	33	t	t	PROPN
cana-537	79	34	}	}	PUNCT
cana-537	79	35	,	,	PUNCT
cana-537	79	36	{	{	PUNCT
cana-537	79	37	r	r	NOUN
cana-537	79	38	,	,	PUNCT
cana-537	79	39	t	t	PROPN
cana-537	79	40	}	}	PUNCT
cana-537	79	41	,	,	PUNCT
cana-537	79	42	{	{	PUNCT
cana-537	79	43	t	t	NOUN
cana-537	79	44	}	}	PUNCT
cana-537	79	45	}	}	PUNCT
cana-537	79	46	and	and	CCONJ
cana-537	79	47	s*p*-c	s*p*-c	PROPN
cana-537	79	48	sets	set	NOUN
cana-537	79	49	of	of	ADP
cana-537	79	50	x2	x2	PROPN
cana-537	79	51	are	be	AUX
cana-537	79	52	{	{	PUNCT
cana-537	79	53	x2	x2	PROPN
cana-537	79	54	,	,	PUNCT
cana-537	79	55	φ	φ	PROPN
cana-537	79	56	,	,	PUNCT
cana-537	79	57	{	{	PUNCT
cana-537	79	58	r	r	NOUN
cana-537	79	59	}	}	PUNCT
cana-537	79	60	,	,	PUNCT
cana-537	79	61	{	{	PUNCT
cana-537	79	62	s	s	X
cana-537	79	63	}	}	PUNCT
cana-537	79	64	}	}	PUNCT
cana-537	79	65	.	.	PUNCT
cana-537	80	1	pre	pre	ADJ
cana-537	80	2	-	-	ADJ
cana-537	80	3	closed	closed	ADJ
cana-537	80	4	sets	set	NOUN
cana-537	80	5	are	be	AUX
cana-537	80	6	{	{	PUNCT
cana-537	80	7	x2	x2	PROPN
cana-537	80	8	,	,	PUNCT
cana-537	80	9	φ	φ	PROPN
cana-537	80	10	,	,	PUNCT
cana-537	80	11	{	{	PUNCT
cana-537	80	12	s	s	PROPN
cana-537	80	13	,	,	PUNCT
cana-537	80	14	t	t	PROPN
cana-537	80	15	}	}	PUNCT
cana-537	80	16	,	,	PUNCT
cana-537	80	17	{	{	PUNCT
cana-537	80	18	r	r	NOUN
cana-537	80	19	,	,	PUNCT
cana-537	80	20	t	t	PROPN
cana-537	80	21	}	}	PUNCT
cana-537	80	22	,	,	PUNCT
cana-537	80	23	{	{	PUNCT
cana-537	80	24	t	t	NOUN
cana-537	80	25	}	}	PUNCT
cana-537	80	26	}	}	PUNCT
cana-537	80	27	.	.	PUNCT
cana-537	81	1	define	define	VERB
cana-537	81	2	a	a	DET
cana-537	81	3	map	map	NOUN
cana-537	82	1	f	f	X
cana-537	82	2	:	:	PUNCT
cana-537	82	3	x1→	x1→	X
cana-537	82	4	x2	x2	INTJ
cana-537	82	5	by	by	ADP
cana-537	82	6	f(r	f(r	NOUN
cana-537	82	7	)	)	PUNCT
cana-537	83	1	=	=	SYM
cana-537	83	2	s	s	NOUN
cana-537	83	3	;	;	PUNCT
cana-537	83	4	f(s	f(s	X
cana-537	83	5	)	)	PUNCT
cana-537	83	6	=	=	SYM
cana-537	83	7	t	t	PROPN
cana-537	83	8	;	;	PUNCT
cana-537	83	9	f	f	PROPN
cana-537	83	10	(	(	PUNCT
cana-537	83	11	t	t	PROPN
cana-537	83	12	)	)	PUNCT
cana-537	83	13	=	=	VERB
cana-537	84	1	r.	r.	PROPN
cana-537	84	2	hence	hence	ADV
cana-537	84	3	f	f	PROPN
cana-537	84	4	is	be	AUX
cana-537	84	5	s*p*-c	s*p*-c	PROPN
cana-537	84	6	map	map	NOUN
cana-537	84	7	.	.	PUNCT
cana-537	85	1	however	however	ADV
cana-537	85	2	,	,	PUNCT
cana-537	85	3	it	it	PRON
cana-537	85	4	is	be	AUX
cana-537	85	5	not	not	PART
cana-537	85	6	pre	pre	ADJ
cana-537	85	7	-	-	ADJ
cana-537	85	8	closed	closed	ADJ
cana-537	85	9	map	map	NOUN
cana-537	85	10	.	.	PUNCT
cana-537	86	1	because	because	SCONJ
cana-537	86	2	the	the	DET
cana-537	86	3	closed	closed	ADJ
cana-537	86	4	map	map	NOUN
cana-537	86	5	{	{	PUNCT
cana-537	86	6	r	r	NOUN
cana-537	86	7	}	}	PUNCT
cana-537	86	8	in	in	ADP
cana-537	86	9	(	(	PUNCT
cana-537	86	10	x1	x1	PROPN
cana-537	86	11	,	,	PUNCT
cana-537	86	12	τ	τ	PROPN
cana-537	86	13	)	)	PUNCT
cana-537	86	14	,	,	PUNCT
cana-537	86	15	its	its	PRON
cana-537	86	16	image	image	NOUN
cana-537	86	17	f	f	X
cana-537	86	18	(	(	PUNCT
cana-537	86	19	r	r	NOUN
cana-537	86	20	)	)	PUNCT
cana-537	86	21	=	=	SYM
cana-537	86	22	{	{	PUNCT
cana-537	86	23	s	s	X
cana-537	86	24	}	}	PUNCT
cana-537	86	25	is	be	AUX
cana-537	86	26	not	not	PART
cana-537	86	27	in	in	ADP
cana-537	86	28	preclosed	preclose	VERB
cana-537	86	29	set	set	VERB
cana-537	86	30	in	in	ADP
cana-537	86	31	x2	x2	PROPN
cana-537	87	1	but	but	CCONJ
cana-537	87	2	it	it	PRON
cana-537	87	3	in	in	ADP
cana-537	87	4	s*p*-c	s*p*-c	PROPN
cana-537	87	5	set	set	VERB
cana-537	87	6	in	in	ADP
cana-537	87	7	x2	x2	PROPN
cana-537	87	8	.	.	PUNCT
cana-537	88	1	theorem	theorem	VERB
cana-537	88	2	4.7	4.7	NUM
cana-537	88	3	:	:	PUNCT
cana-537	88	4	every	every	DET
cana-537	88	5	map	map	NOUN
cana-537	88	6	which	which	PRON
cana-537	88	7	is	be	AUX
cana-537	88	8	g*-closed	g*-close	VERB
cana-537	88	9	map	map	NOUN
cana-537	88	10	is	be	AUX
cana-537	88	11	also	also	ADV
cana-537	88	12	s*p*-c	s*p*-c	PROPN
cana-537	88	13	map	map	NOUN
cana-537	88	14	.	.	PUNCT
cana-537	89	1	proof	proof	NOUN
cana-537	89	2	:	:	PUNCT
cana-537	89	3	consider	consider	VERB
cana-537	89	4	f	f	NOUN
cana-537	89	5	:	:	PUNCT
cana-537	89	6	x1→	x1→	X
cana-537	89	7	x2	x2	PRON
cana-537	89	8	be	be	VERB
cana-537	89	9	a	a	DET
cana-537	89	10	g*-closed	g*-close	VERB
cana-537	89	11	map	map	NOUN
cana-537	89	12	.	.	PUNCT
cana-537	90	1	let	let	VERB
cana-537	90	2	us	we	PRON
cana-537	90	3	assume	assume	VERB
cana-537	90	4	the	the	DET
cana-537	90	5	closed	closed	ADJ
cana-537	90	6	set	set	NOUN
cana-537	90	7	in	in	ADP
cana-537	90	8	x1	x1	PROPN
cana-537	90	9	it	it	PRON
cana-537	90	10	is	be	AUX
cana-537	90	11	denoted	denote	VERB
cana-537	90	12	by	by	ADP
cana-537	90	13	v.	v.	ADV
cana-537	90	14	after	after	ADP
cana-537	90	15	that	that	PRON
cana-537	90	16	the	the	DET
cana-537	90	17	image	image	NOUN
cana-537	90	18	of	of	ADP
cana-537	90	19	v	v	NOUN
cana-537	90	20	that	that	PRON
cana-537	90	21	is	be	AUX
cana-537	90	22	f(v	f(v	NOUN
cana-537	90	23	)	)	PUNCT
cana-537	90	24	in	in	ADP
cana-537	90	25	x2	x2	PROPN
cana-537	90	26	is	be	AUX
cana-537	90	27	g*closed	g*close	VERB
cana-537	90	28	set	set	VERB
cana-537	90	29	.	.	PUNCT
cana-537	91	1	each	each	DET
cana-537	91	2	g*closed	g*close	VERB
cana-537	91	3	set	set	NOUN
cana-537	91	4	is	be	AUX
cana-537	91	5	s*p*-c	s*p*-c	PROPN
cana-537	91	6	set	set	NOUN
cana-537	91	7	.	.	PUNCT
cana-537	92	1	thus	thus	ADV
cana-537	92	2	,	,	PUNCT
cana-537	92	3	the	the	DET
cana-537	92	4	image	image	NOUN
cana-537	92	5	of	of	ADP
cana-537	92	6	v	v	NOUN
cana-537	92	7	is	be	AUX
cana-537	92	8	s*p*-c	s*p*-c	PROPN
cana-537	92	9	set	set	NOUN
cana-537	92	10	.	.	PUNCT
cana-537	93	1	hence	hence	ADV
cana-537	93	2	,	,	PUNCT
cana-537	93	3	it	it	PRON
cana-537	93	4	is	be	AUX
cana-537	93	5	s*p*-c	s*p*-c	PROPN
cana-537	93	6	map	map	NOUN
cana-537	93	7	.	.	PUNCT
cana-537	94	1	communications	communication	NOUN
cana-537	94	2	on	on	ADP
cana-537	94	3	applied	apply	VERB
cana-537	94	4	nonlinear	nonlinear	ADJ
cana-537	94	5	analysis	analysis	NOUN
cana-537	94	6	issn	issn	NOUN
cana-537	94	7	:	:	PUNCT
cana-537	94	8	1074	1074	NUM
cana-537	94	9	-	-	PUNCT
cana-537	94	10	133x	133x	NUM
cana-537	94	11	vol	vol	NOUN
cana-537	94	12	31	31	NUM
cana-537	94	13	no	no	NOUN
cana-537	94	14	.	.	NOUN
cana-537	94	15	2	2	NUM
cana-537	94	16	(	(	PUNCT
cana-537	94	17	2024	2024	NUM
cana-537	94	18	)	)	PUNCT
cana-537	94	19	220	220	NUM
cana-537	94	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-537	94	21	reverse	reverse	ADJ
cana-537	94	22	implication	implication	NOUN
cana-537	94	23	of	of	ADP
cana-537	94	24	the	the	DET
cana-537	94	25	previously	previously	ADV
cana-537	94	26	stated	state	VERB
cana-537	94	27	theorem	theorem	NOUN
cana-537	94	28	does	do	AUX
cana-537	94	29	not	not	PART
cana-537	94	30	valid	valid	VERB
cana-537	94	31	by	by	ADP
cana-537	94	32	the	the	DET
cana-537	94	33	following	follow	VERB
cana-537	94	34	example	example	NOUN
cana-537	94	35	.	.	PUNCT
cana-537	95	1	example	example	NOUN
cana-537	95	2	4.8	4.8	NUM
cana-537	96	1	:	:	PUNCT
cana-537	96	2	let	let	VERB
cana-537	96	3	x1	x1	PROPN
cana-537	96	4	=	=	PUNCT
cana-537	96	5	x2=	x2=	PROPN
cana-537	96	6	{	{	PUNCT
cana-537	96	7	r	r	NOUN
cana-537	96	8	,	,	PUNCT
cana-537	96	9	s	s	PROPN
cana-537	96	10	,	,	PUNCT
cana-537	96	11	t	t	PROPN
cana-537	96	12	}	}	PUNCT
cana-537	96	13	;	;	PUNCT
cana-537	96	14	τ	τ	X
cana-537	96	15	=	=	PUNCT
cana-537	96	16	{	{	PUNCT
cana-537	96	17	x1	x1	PROPN
cana-537	96	18	,	,	PUNCT
cana-537	96	19	φ	φ	PROPN
cana-537	96	20	,	,	PUNCT
cana-537	96	21	{	{	PUNCT
cana-537	96	22	r	r	NOUN
cana-537	96	23	}	}	PUNCT
cana-537	96	24	,	,	PUNCT
cana-537	96	25	{	{	PUNCT
cana-537	96	26	t	t	NOUN
cana-537	96	27	}	}	PUNCT
cana-537	96	28	,	,	PUNCT
cana-537	96	29	{	{	PUNCT
cana-537	96	30	r	r	NOUN
cana-537	96	31	,	,	PUNCT
cana-537	96	32	t	t	NOUN
cana-537	96	33	}	}	PUNCT
cana-537	96	34	}	}	PUNCT
cana-537	96	35	and	and	CCONJ
cana-537	96	36	τc	τc	ADV
cana-537	96	37	=	=	PUNCT
cana-537	96	38	{	{	PUNCT
cana-537	96	39	x1	x1	PROPN
cana-537	96	40	,	,	PUNCT
cana-537	96	41	φ	φ	PROPN
cana-537	96	42	,	,	PUNCT
cana-537	96	43	{	{	PUNCT
cana-537	96	44	s	s	PROPN
cana-537	96	45	,	,	PUNCT
cana-537	96	46	t	t	PROPN
cana-537	96	47	}	}	PUNCT
cana-537	96	48	,	,	PUNCT
cana-537	96	49	{	{	PUNCT
cana-537	96	50	r	r	NOUN
cana-537	96	51	,	,	PUNCT
cana-537	96	52	s	s	PART
cana-537	96	53	}	}	PUNCT
cana-537	96	54	,	,	PUNCT
cana-537	96	55	{	{	PUNCT
cana-537	96	56	s	s	X
cana-537	96	57	}	}	PUNCT
cana-537	96	58	}	}	PUNCT
cana-537	96	59	.	.	PUNCT
cana-537	97	1	σ	σ	NOUN
cana-537	97	2	=	=	PRON
cana-537	97	3	{	{	PUNCT
cana-537	97	4	x2	x2	PROPN
cana-537	97	5	,	,	PUNCT
cana-537	97	6	φ	φ	PROPN
cana-537	97	7	,	,	PUNCT
cana-537	97	8	{	{	PUNCT
cana-537	97	9	r	r	NOUN
cana-537	97	10	}	}	PUNCT
cana-537	97	11	,	,	PUNCT
cana-537	97	12	{	{	PUNCT
cana-537	97	13	r	r	NOUN
cana-537	97	14	,	,	PUNCT
cana-537	97	15	s	s	PART
cana-537	97	16	}	}	PUNCT
cana-537	97	17	}	}	PUNCT
cana-537	97	18	;	;	PUNCT
cana-537	97	19	σc	σc	PROPN
cana-537	97	20	=	=	SYM
cana-537	97	21	{	{	PUNCT
cana-537	97	22	x2	x2	PROPN
cana-537	97	23	,	,	PUNCT
cana-537	97	24	φ	φ	PROPN
cana-537	97	25	,	,	PUNCT
cana-537	97	26	{	{	PUNCT
cana-537	97	27	s	s	PROPN
cana-537	97	28	,	,	PUNCT
cana-537	97	29	t	t	PROPN
cana-537	97	30	}	}	PUNCT
cana-537	97	31	,	,	PUNCT
cana-537	97	32	{	{	PUNCT
cana-537	97	33	t	t	NOUN
cana-537	97	34	}	}	PUNCT
cana-537	97	35	}	}	PUNCT
cana-537	97	36	and	and	CCONJ
cana-537	97	37	s*p*-c	s*p*-c	PROPN
cana-537	97	38	sets	set	NOUN
cana-537	97	39	of	of	ADP
cana-537	97	40	x2	x2	PROPN
cana-537	97	41	are	be	AUX
cana-537	97	42	{	{	PUNCT
cana-537	97	43	x2	x2	PROPN
cana-537	97	44	,	,	PUNCT
cana-537	97	45	φ	φ	PROPN
cana-537	97	46	,	,	PUNCT
cana-537	97	47	{	{	PUNCT
cana-537	97	48	s	s	NOUN
cana-537	97	49	}	}	PUNCT
cana-537	97	50	}	}	PUNCT
cana-537	97	51	.	.	PUNCT
cana-537	98	1	g*closed	g*close	VERB
cana-537	98	2	sets	set	NOUN
cana-537	98	3	are	be	AUX
cana-537	98	4	{	{	PUNCT
cana-537	98	5	x2	x2	PROPN
cana-537	98	6	,	,	PUNCT
cana-537	98	7	φ	φ	PROPN
cana-537	98	8	,	,	PUNCT
cana-537	98	9	{	{	PUNCT
cana-537	98	10	s	s	PROPN
cana-537	98	11	,	,	PUNCT
cana-537	98	12	t	t	PROPN
cana-537	98	13	}	}	PUNCT
cana-537	98	14	,	,	PUNCT
cana-537	98	15	{	{	PUNCT
cana-537	98	16	r	r	NOUN
cana-537	98	17	,	,	PUNCT
cana-537	98	18	t	t	PROPN
cana-537	98	19	}	}	PUNCT
cana-537	98	20	,	,	PUNCT
cana-537	98	21	{	{	PUNCT
cana-537	98	22	t	t	NOUN
cana-537	98	23	}	}	PUNCT
cana-537	98	24	}	}	PUNCT
cana-537	98	25	.	.	PUNCT
cana-537	99	1	assume	assume	VERB
cana-537	99	2	f	f	X
cana-537	99	3	:	:	PUNCT
cana-537	100	1	x1→	x1→	X
cana-537	100	2	x2	x2	INTJ
cana-537	100	3	by	by	ADP
cana-537	100	4	f(r	f(r	NOUN
cana-537	100	5	)	)	PUNCT
cana-537	100	6	=	=	SYM
cana-537	100	7	t	t	PROPN
cana-537	100	8	;	;	PUNCT
cana-537	100	9	f(s	f(s	X
cana-537	100	10	)	)	PUNCT
cana-537	100	11	=	=	SYM
cana-537	100	12	s	s	X
cana-537	100	13	;	;	PUNCT
cana-537	100	14	f	f	PROPN
cana-537	100	15	(	(	PUNCT
cana-537	100	16	t	t	PROPN
cana-537	100	17	)	)	PUNCT
cana-537	100	18	=	=	VERB
cana-537	101	1	r.	r.	PROPN
cana-537	101	2	hence	hence	ADV
cana-537	101	3	f	f	PROPN
cana-537	101	4	is	be	AUX
cana-537	101	5	not	not	PART
cana-537	101	6	g*closed	g*close	VERB
cana-537	101	7	map	map	NOUN
cana-537	101	8	however	however	ADV
cana-537	101	9	it	it	PRON
cana-537	101	10	is	be	AUX
cana-537	101	11	in	in	ADP
cana-537	101	12	s*p*-c	s*p*-c	PROPN
cana-537	101	13	map	map	NOUN
cana-537	101	14	.	.	PUNCT
cana-537	102	1	hence	hence	ADV
cana-537	102	2	the	the	DET
cana-537	102	3	image	image	NOUN
cana-537	102	4	of	of	ADP
cana-537	102	5	closed	closed	ADJ
cana-537	102	6	map	map	NOUN
cana-537	102	7	{	{	PUNCT
cana-537	102	8	r	r	NOUN
cana-537	102	9	}	}	PUNCT
cana-537	102	10	in	in	ADP
cana-537	102	11	(	(	PUNCT
cana-537	102	12	x1	x1	PROPN
cana-537	102	13	,	,	PUNCT
cana-537	102	14	τ	τ	PROPN
cana-537	102	15	)	)	PUNCT
cana-537	102	16	,	,	PUNCT
cana-537	102	17	f{r	f{r	PROPN
cana-537	102	18	}	}	PUNCT
cana-537	102	19	=	=	PUNCT
cana-537	102	20	{	{	PUNCT
cana-537	102	21	s	s	X
cana-537	102	22	}	}	PUNCT
cana-537	102	23	is	be	AUX
cana-537	102	24	not	not	PART
cana-537	102	25	in	in	ADP
cana-537	102	26	g	g	NOUN
cana-537	102	27	*	*	PUNCT
cana-537	102	28	closed	closed	ADJ
cana-537	102	29	set	set	VERB
cana-537	102	30	in	in	ADP
cana-537	102	31	x2	x2	PROPN
cana-537	102	32	but	but	CCONJ
cana-537	102	33	it	it	PRON
cana-537	102	34	in	in	ADP
cana-537	102	35	s	s	PROPN
cana-537	102	36	*	*	PUNCT
cana-537	102	37	p*-c	p*-c	NOUN
cana-537	102	38	set	set	NOUN
cana-537	102	39	in	in	ADP
cana-537	102	40	x2	x2	PROPN
cana-537	102	41	.	.	PUNCT
cana-537	103	1	theorem	theorem	VERB
cana-537	103	2	4.9	4.9	NUM
cana-537	103	3	:	:	PUNCT
cana-537	103	4	s*p*-c	s*p*-c	PROPN
cana-537	103	5	maps	maps	PROPN
cana-537	103	6	are	be	AUX
cana-537	103	7	all	all	PRON
cana-537	103	8	gpr	gpr	PROPN
cana-537	103	9	closed	close	VERB
cana-537	103	10	maps	map	NOUN
cana-537	103	11	.	.	PUNCT
cana-537	104	1	proof	proof	NOUN
cana-537	104	2	:	:	PUNCT
cana-537	104	3	suppose	suppose	VERB
cana-537	104	4	f	f	X
cana-537	104	5	:	:	PUNCT
cana-537	104	6	x1	x1	PROPN
cana-537	104	7	→	→	PUNCT
cana-537	104	8	x2	x2	PROPN
cana-537	104	9	be	be	AUX
cana-537	104	10	a	a	DET
cana-537	104	11	gpr	gpr	PROPN
cana-537	104	12	closed	closed	ADJ
cana-537	104	13	map	map	NOUN
cana-537	104	14	.	.	PUNCT
cana-537	105	1	assume	assume	VERB
cana-537	105	2	that	that	SCONJ
cana-537	105	3	v	v	NOUN
cana-537	105	4	be	be	AUX
cana-537	105	5	in	in	ADP
cana-537	105	6	x1	x1	PROPN
cana-537	105	7	.	.	PUNCT
cana-537	106	1	it	it	PRON
cana-537	106	2	is	be	AUX
cana-537	106	3	closed	close	VERB
cana-537	106	4	set	set	VERB
cana-537	106	5	.	.	PUNCT
cana-537	107	1	then	then	ADV
cana-537	107	2	image	image	NOUN
cana-537	107	3	of	of	ADP
cana-537	107	4	v	v	NOUN
cana-537	107	5	that	that	PRON
cana-537	107	6	is	be	AUX
cana-537	107	7	f(v	f(v	NOUN
cana-537	107	8	)	)	PUNCT
cana-537	107	9	is	be	AUX
cana-537	107	10	gpr	gpr	PROPN
cana-537	107	11	closed	close	VERB
cana-537	107	12	set	set	VERB
cana-537	107	13	in	in	ADP
cana-537	107	14	x2	x2	PROPN
cana-537	107	15	.	.	PUNCT
cana-537	108	1	since	since	SCONJ
cana-537	108	2	any	any	DET
cana-537	108	3	gpr	gpr	PROPN
cana-537	108	4	-	-	PUNCT
cana-537	108	5	closed	close	VERB
cana-537	108	6	set	set	NOUN
cana-537	108	7	is	be	AUX
cana-537	108	8	s*p*-c	s*p*-c	NOUN
cana-537	108	9	set	set	VERB
cana-537	108	10	thus	thus	ADV
cana-537	108	11	image	image	NOUN
cana-537	108	12	of	of	ADP
cana-537	108	13	v	v	NOUN
cana-537	108	14	is	be	AUX
cana-537	108	15	gpr	gpr	PROPN
cana-537	108	16	closed	close	VERB
cana-537	108	17	set	set	NOUN
cana-537	108	18	.	.	PUNCT
cana-537	109	1	so	so	ADV
cana-537	109	2	that	that	SCONJ
cana-537	109	3	f	f	PROPN
cana-537	109	4	is	be	AUX
cana-537	109	5	s*p*-c	s*p*-c	PROPN
cana-537	109	6	map	map	NOUN
cana-537	109	7	.	.	PUNCT
cana-537	110	1	upcoming	upcoming	ADJ
cana-537	110	2	illustration	illustration	NOUN
cana-537	110	3	shows	show	VERB
cana-537	110	4	the	the	DET
cana-537	110	5	opposite	opposite	NOUN
cana-537	110	6	of	of	ADP
cana-537	110	7	the	the	DET
cana-537	110	8	previously	previously	ADV
cana-537	110	9	stated	state	VERB
cana-537	110	10	theorem	theorem	NOUN
cana-537	110	11	is	be	AUX
cana-537	110	12	not	not	PART
cana-537	110	13	always	always	ADV
cana-537	110	14	right	right	ADJ
cana-537	110	15	.	.	PUNCT
cana-537	111	1	example	example	NOUN
cana-537	111	2	4.10	4.10	NUM
cana-537	111	3	:	:	PUNCT
cana-537	111	4	let	let	VERB
cana-537	111	5	x1	x1	NOUN
cana-537	111	6	=	=	PUNCT
cana-537	112	1	x2	x2	PROPN
cana-537	112	2	=	=	PRON
cana-537	112	3	{	{	PUNCT
cana-537	112	4	r	r	NOUN
cana-537	112	5	,	,	PUNCT
cana-537	112	6	s	s	PROPN
cana-537	112	7	,	,	PUNCT
cana-537	112	8	t	t	PROPN
cana-537	112	9	}	}	PUNCT
cana-537	112	10	;	;	PUNCT
cana-537	112	11	τ	τ	X
cana-537	112	12	=	=	PUNCT
cana-537	112	13	{	{	PUNCT
cana-537	112	14	x1	x1	PROPN
cana-537	112	15	,	,	PUNCT
cana-537	112	16	φ	φ	PROPN
cana-537	112	17	,	,	PUNCT
cana-537	112	18	{	{	PUNCT
cana-537	112	19	s	s	X
cana-537	112	20	}	}	PUNCT
cana-537	112	21	,	,	PUNCT
cana-537	112	22	{	{	PUNCT
cana-537	112	23	t	t	NOUN
cana-537	112	24	}	}	PUNCT
cana-537	112	25	,	,	PUNCT
cana-537	112	26	{	{	PUNCT
cana-537	112	27	r	r	NOUN
cana-537	112	28	,	,	PUNCT
cana-537	112	29	s	s	PART
cana-537	112	30	}	}	PUNCT
cana-537	112	31	,	,	PUNCT
cana-537	112	32	{	{	PUNCT
cana-537	112	33	s	s	X
cana-537	112	34	,	,	PUNCT
cana-537	112	35	t	t	NOUN
cana-537	112	36	}	}	PUNCT
cana-537	112	37	}	}	PUNCT
cana-537	112	38	and	and	CCONJ
cana-537	112	39	τc	τc	ADV
cana-537	112	40	=	=	PUNCT
cana-537	112	41	{	{	PUNCT
cana-537	112	42	x1	x1	PROPN
cana-537	112	43	,	,	PUNCT
cana-537	112	44	φ	φ	PROPN
cana-537	112	45	,	,	PUNCT
cana-537	112	46	{	{	PUNCT
cana-537	112	47	r	r	NOUN
cana-537	112	48	,	,	PUNCT
cana-537	112	49	t	t	PROPN
cana-537	112	50	}	}	PUNCT
cana-537	112	51	,	,	PUNCT
cana-537	112	52	{	{	PUNCT
cana-537	112	53	r	r	NOUN
cana-537	112	54	,	,	PUNCT
cana-537	112	55	s	s	PART
cana-537	112	56	}	}	PUNCT
cana-537	112	57	,	,	PUNCT
cana-537	112	58	{	{	PUNCT
cana-537	112	59	t	t	NOUN
cana-537	112	60	}	}	PUNCT
cana-537	112	61	,	,	PUNCT
cana-537	112	62	{	{	PUNCT
cana-537	112	63	r	r	NOUN
cana-537	112	64	}	}	PUNCT
cana-537	112	65	}	}	PUNCT
cana-537	112	66	.	.	PUNCT
cana-537	113	1	σ	σ	NOUN
cana-537	113	2	=	=	PRON
cana-537	113	3	{	{	PUNCT
cana-537	113	4	x2	x2	PROPN
cana-537	113	5	,	,	PUNCT
cana-537	113	6	φ	φ	PROPN
cana-537	113	7	,	,	PUNCT
cana-537	113	8	{	{	PUNCT
cana-537	113	9	r	r	NOUN
cana-537	113	10	}	}	PUNCT
cana-537	113	11	,	,	PUNCT
cana-537	113	12	{	{	PUNCT
cana-537	113	13	s	s	X
cana-537	113	14	}	}	PUNCT
cana-537	113	15	,	,	PUNCT
cana-537	113	16	{	{	PUNCT
cana-537	113	17	r	r	NOUN
cana-537	113	18	,	,	PUNCT
cana-537	113	19	s	s	PART
cana-537	113	20	}	}	PUNCT
cana-537	113	21	}	}	PUNCT
cana-537	113	22	;	;	PUNCT
cana-537	113	23	σc	σc	PROPN
cana-537	113	24	=	=	SYM
cana-537	113	25	{	{	PUNCT
cana-537	113	26	x2	x2	PROPN
cana-537	113	27	,	,	PUNCT
cana-537	113	28	φ	φ	PROPN
cana-537	113	29	,	,	PUNCT
cana-537	113	30	{	{	PUNCT
cana-537	113	31	s	s	PROPN
cana-537	113	32	,	,	PUNCT
cana-537	113	33	t	t	PROPN
cana-537	113	34	}	}	PUNCT
cana-537	113	35	,	,	PUNCT
cana-537	113	36	{	{	PUNCT
cana-537	113	37	r	r	NOUN
cana-537	113	38	,	,	PUNCT
cana-537	113	39	t	t	PROPN
cana-537	113	40	}	}	PUNCT
cana-537	113	41	,	,	PUNCT
cana-537	113	42	{	{	PUNCT
cana-537	113	43	t	t	NOUN
cana-537	113	44	}	}	PUNCT
cana-537	113	45	}	}	PUNCT
cana-537	113	46	and	and	CCONJ
cana-537	113	47	s*p*-c	s*p*-c	PROPN
cana-537	113	48	sets	set	NOUN
cana-537	113	49	of	of	ADP
cana-537	113	50	x2	x2	PROPN
cana-537	113	51	are	be	AUX
cana-537	113	52	{	{	PUNCT
cana-537	113	53	x2	x2	PROPN
cana-537	113	54	,	,	PUNCT
cana-537	113	55	φ	φ	PROPN
cana-537	113	56	,	,	PUNCT
cana-537	113	57	{	{	PUNCT
cana-537	113	58	s	s	NOUN
cana-537	113	59	}	}	PUNCT
cana-537	113	60	}	}	PUNCT
cana-537	113	61	.	.	PUNCT
cana-537	114	1	gpr	gpr	PROPN
cana-537	114	2	closed	closed	ADJ
cana-537	114	3	sets	set	NOUN
cana-537	114	4	of	of	ADP
cana-537	114	5	x2	x2	PROPN
cana-537	114	6	are	be	AUX
cana-537	114	7	{	{	PUNCT
cana-537	114	8	x2	x2	PROPN
cana-537	114	9	,	,	PUNCT
cana-537	114	10	φ	φ	PROPN
cana-537	114	11	,	,	PUNCT
cana-537	114	12	{	{	PUNCT
cana-537	114	13	r	r	NOUN
cana-537	114	14	,	,	PUNCT
cana-537	114	15	t	t	PROPN
cana-537	114	16	}	}	PUNCT
cana-537	114	17	}	}	PUNCT
cana-537	114	18	.	.	PUNCT
cana-537	115	1	define	define	VERB
cana-537	115	2	a	a	DET
cana-537	115	3	map	map	NOUN
cana-537	116	1	f	f	X
cana-537	116	2	:	:	PUNCT
cana-537	116	3	x1	x1	PROPN
cana-537	116	4	→	→	SYM
cana-537	116	5	x2	x2	PROPN
cana-537	116	6	by	by	ADP
cana-537	116	7	f(r	f(r	NOUN
cana-537	116	8	)	)	PUNCT
cana-537	116	9	=	=	SYM
cana-537	116	10	t	t	PROPN
cana-537	116	11	;	;	PUNCT
cana-537	116	12	f(s	f(s	X
cana-537	116	13	)	)	PUNCT
cana-537	116	14	=	=	SYM
cana-537	117	1	r	r	NOUN
cana-537	117	2	;	;	PUNCT
cana-537	117	3	f	f	PROPN
cana-537	117	4	(	(	PUNCT
cana-537	117	5	t	t	PROPN
cana-537	117	6	)	)	PUNCT
cana-537	117	7	=	=	VERB
cana-537	118	1	s.	s.	PROPN
cana-537	118	2	hence	hence	ADV
cana-537	118	3	f	f	PROPN
cana-537	118	4	does	do	AUX
cana-537	118	5	not	not	PART
cana-537	118	6	a	a	DET
cana-537	118	7	gpr	gpr	PROPN
cana-537	118	8	closed	closed	ADJ
cana-537	118	9	map	map	NOUN
cana-537	118	10	rather	rather	ADV
cana-537	118	11	than	than	ADP
cana-537	118	12	s*p*-c	s*p*-c	PROPN
cana-537	118	13	map	map	NOUN
cana-537	118	14	.	.	PUNCT
cana-537	119	1	consequently	consequently	ADV
cana-537	119	2	,	,	PUNCT
cana-537	119	3	the	the	DET
cana-537	119	4	image	image	NOUN
cana-537	119	5	of	of	ADP
cana-537	119	6	closed	closed	ADJ
cana-537	119	7	map	map	NOUN
cana-537	119	8	{	{	PUNCT
cana-537	119	9	c	c	NOUN
cana-537	119	10	}	}	PUNCT
cana-537	119	11	in	in	ADP
cana-537	119	12	(	(	PUNCT
cana-537	119	13	x1	x1	PROPN
cana-537	119	14	,	,	PUNCT
cana-537	119	15	τ	τ	PROPN
cana-537	119	16	)	)	PUNCT
cana-537	119	17	,	,	PUNCT
cana-537	119	18	f{t	f{t	NOUN
cana-537	119	19	}	}	PUNCT
cana-537	119	20	=	=	PUNCT
cana-537	119	21	{	{	PUNCT
cana-537	119	22	s	s	X
cana-537	119	23	}	}	PUNCT
cana-537	119	24	is	be	AUX
cana-537	119	25	not	not	PART
cana-537	119	26	in	in	ADP
cana-537	119	27	gpr	gpr	PROPN
cana-537	119	28	closed	close	VERB
cana-537	119	29	set	set	VERB
cana-537	119	30	in	in	ADP
cana-537	119	31	x2	x2	PROPN
cana-537	120	1	but	but	CCONJ
cana-537	120	2	it	it	PRON
cana-537	120	3	in	in	ADP
cana-537	120	4	s*p*c	s*p*c	NOUN
cana-537	120	5	set	set	VERB
cana-537	120	6	in	in	ADP
cana-537	120	7	x2	x2	PROPN
cana-537	120	8	.	.	PUNCT
cana-537	121	1	theorem	theorem	VERB
cana-537	121	2	4.11	4.11	NUM
cana-537	121	3	:	:	PUNCT
cana-537	121	4	every	every	DET
cana-537	121	5	αg	αg	NOUN
cana-537	121	6	closed	closed	ADJ
cana-537	121	7	map	map	NOUN
cana-537	121	8	is	be	AUX
cana-537	121	9	a	a	DET
cana-537	121	10	s*p*-c	s*p*-c	PROPN
cana-537	121	11	map	map	NOUN
cana-537	121	12	.	.	PUNCT
cana-537	122	1	proof	proof	NOUN
cana-537	122	2	:	:	PUNCT
cana-537	122	3	consider	consider	VERB
cana-537	122	4	f	f	NOUN
cana-537	122	5	:	:	PUNCT
cana-537	123	1	x1	x1	PROPN
cana-537	123	2	→	→	SYM
cana-537	123	3	x2	x2	PROPN
cana-537	123	4	as	as	ADP
cana-537	123	5	an	an	DET
cana-537	123	6	αg	αg	NOUN
cana-537	123	7	closed	close	VERB
cana-537	123	8	map	map	NOUN
cana-537	123	9	.	.	PUNCT
cana-537	124	1	take	take	VERB
cana-537	124	2	v	v	NOUN
cana-537	124	3	in	in	ADP
cana-537	124	4	x1	x1	PROPN
cana-537	124	5	be	be	AUX
cana-537	124	6	a	a	DET
cana-537	124	7	closed	closed	ADJ
cana-537	124	8	set	set	NOUN
cana-537	124	9	.	.	PUNCT
cana-537	125	1	thus	thus	ADV
cana-537	125	2	,	,	PUNCT
cana-537	125	3	its	its	PRON
cana-537	125	4	image	image	NOUN
cana-537	125	5	is	be	AUX
cana-537	125	6	in	in	ADP
cana-537	125	7	αg	αg	NOUN
cana-537	125	8	closed	close	VERB
cana-537	125	9	set	set	VERB
cana-537	125	10	in	in	ADP
cana-537	125	11	x2	x2	PROPN
cana-537	125	12	.	.	PUNCT
cana-537	126	1	because	because	SCONJ
cana-537	126	2	all	all	DET
cana-537	126	3	αg	αg	NOUN
cana-537	126	4	closed	closed	ADJ
cana-537	126	5	set	set	NOUN
cana-537	126	6	is	be	AUX
cana-537	126	7	s*p*-c	s*p*-c	NOUN
cana-537	126	8	set	set	NOUN
cana-537	126	9	,	,	PUNCT
cana-537	126	10	then	then	ADV
cana-537	126	11	the	the	DET
cana-537	126	12	image	image	NOUN
cana-537	126	13	of	of	ADP
cana-537	126	14	v	v	NOUN
cana-537	126	15	is	be	AUX
cana-537	126	16	in	in	ADP
cana-537	126	17	s*p*c	s*p*c	NOUN
cana-537	126	18	in	in	ADP
cana-537	126	19	x2	x2	PROPN
cana-537	126	20	.	.	PUNCT
cana-537	127	1	hence	hence	ADV
cana-537	127	2	,	,	PUNCT
cana-537	127	3	f	f	PROPN
cana-537	127	4	is	be	AUX
cana-537	127	5	s*p*-c	s*p*-c	PROPN
cana-537	127	6	map	map	NOUN
cana-537	127	7	.	.	PUNCT
cana-537	128	1	our	our	PRON
cana-537	128	2	next	next	ADJ
cana-537	128	3	illustration	illustration	NOUN
cana-537	128	4	reveals	reveal	VERB
cana-537	128	5	why	why	SCONJ
cana-537	128	6	the	the	DET
cana-537	128	7	other	other	ADJ
cana-537	128	8	side	side	NOUN
cana-537	128	9	of	of	ADP
cana-537	128	10	the	the	DET
cana-537	128	11	above	above	ADV
cana-537	128	12	-	-	PUNCT
cana-537	128	13	mentioned	mention	VERB
cana-537	128	14	theorem	theorem	NOUN
cana-537	128	15	may	may	AUX
cana-537	128	16	not	not	PART
cana-537	128	17	be	be	AUX
cana-537	128	18	correct	correct	ADJ
cana-537	128	19	.	.	PUNCT
cana-537	129	1	example	example	NOUN
cana-537	129	2	4.12	4.12	NUM
cana-537	129	3	:	:	PUNCT
cana-537	129	4	let	let	VERB
cana-537	129	5	x1	x1	PROPN
cana-537	130	1	=	=	PUNCT
cana-537	130	2	x2=	x2=	PROPN
cana-537	130	3	{	{	PUNCT
cana-537	130	4	q	q	NOUN
cana-537	130	5	,	,	PUNCT
cana-537	130	6	r	r	NOUN
cana-537	130	7	,	,	PUNCT
cana-537	130	8	s	s	PROPN
cana-537	130	9	,	,	PUNCT
cana-537	130	10	t	t	PROPN
cana-537	130	11	}	}	PUNCT
cana-537	130	12	;	;	PUNCT
cana-537	130	13	τ	τ	X
cana-537	130	14	=	=	PUNCT
cana-537	130	15	{	{	PUNCT
cana-537	130	16	x1	x1	PROPN
cana-537	130	17	,	,	PUNCT
cana-537	130	18	φ	φ	PROPN
cana-537	130	19	,	,	PUNCT
cana-537	130	20	{	{	PUNCT
cana-537	130	21	q	q	X
cana-537	130	22	}	}	PUNCT
cana-537	130	23	,	,	PUNCT
cana-537	130	24	{	{	PUNCT
cana-537	130	25	r	r	NOUN
cana-537	130	26	}	}	PUNCT
cana-537	130	27	,	,	PUNCT
cana-537	130	28	{	{	PUNCT
cana-537	130	29	q	q	X
cana-537	130	30	,	,	PUNCT
cana-537	130	31	r	r	NOUN
cana-537	130	32	}	}	PUNCT
cana-537	130	33	,	,	PUNCT
cana-537	130	34	{	{	PUNCT
cana-537	130	35	q	q	X
cana-537	130	36	,	,	PUNCT
cana-537	130	37	r	r	NOUN
cana-537	130	38	,	,	PUNCT
cana-537	130	39	s	s	PART
cana-537	130	40	}	}	PUNCT
cana-537	130	41	}	}	PUNCT
cana-537	130	42	and	and	CCONJ
cana-537	130	43	τc	τc	ADV
cana-537	130	44	=	=	PUNCT
cana-537	130	45	{	{	PUNCT
cana-537	130	46	x1	x1	PROPN
cana-537	130	47	,	,	PUNCT
cana-537	130	48	φ	φ	PROPN
cana-537	130	49	,	,	PUNCT
cana-537	130	50	{	{	PUNCT
cana-537	130	51	r	r	NOUN
cana-537	130	52	,	,	PUNCT
cana-537	130	53	s	s	PROPN
cana-537	130	54	,	,	PUNCT
cana-537	130	55	t	t	PROPN
cana-537	130	56	}	}	PUNCT
cana-537	130	57	,	,	PUNCT
cana-537	130	58	{	{	PUNCT
cana-537	130	59	q	q	X
cana-537	130	60	,	,	PUNCT
cana-537	130	61	s	s	PROPN
cana-537	130	62	,	,	PUNCT
cana-537	130	63	t	t	PROPN
cana-537	130	64	}	}	PUNCT
cana-537	130	65	,	,	PUNCT
cana-537	130	66	{	{	PUNCT
cana-537	130	67	s	s	X
cana-537	130	68	,	,	PUNCT
cana-537	130	69	t	t	PROPN
cana-537	130	70	}	}	PUNCT
cana-537	130	71	,	,	PUNCT
cana-537	130	72	{	{	PUNCT
cana-537	130	73	t	t	NOUN
cana-537	130	74	}	}	PUNCT
cana-537	130	75	}	}	PUNCT
cana-537	130	76	.	.	PUNCT
cana-537	131	1	σ	σ	NOUN
cana-537	131	2	=	=	PRON
cana-537	131	3	{	{	PUNCT
cana-537	131	4	x2	x2	PROPN
cana-537	131	5	,	,	PUNCT
cana-537	131	6	φ	φ	PROPN
cana-537	131	7	,	,	PUNCT
cana-537	131	8	{	{	PUNCT
cana-537	131	9	q	q	X
cana-537	131	10	}	}	PUNCT
cana-537	131	11	,	,	PUNCT
cana-537	131	12	{	{	PUNCT
cana-537	131	13	s	s	X
cana-537	131	14	}	}	PUNCT
cana-537	131	15	,	,	PUNCT
cana-537	131	16	{	{	PUNCT
cana-537	131	17	t	t	NOUN
cana-537	131	18	}	}	PUNCT
cana-537	131	19	,	,	PUNCT
cana-537	131	20	{	{	PUNCT
cana-537	131	21	q	q	X
cana-537	131	22	,	,	PUNCT
cana-537	131	23	s	s	PART
cana-537	131	24	}	}	PUNCT
cana-537	131	25	,	,	PUNCT
cana-537	131	26	{	{	PUNCT
cana-537	131	27	q	q	NOUN
cana-537	131	28	,	,	PUNCT
cana-537	131	29	t	t	PROPN
cana-537	131	30	}	}	PUNCT
cana-537	131	31	,	,	PUNCT
cana-537	131	32	{	{	PUNCT
cana-537	131	33	s	s	X
cana-537	131	34	,	,	PUNCT
cana-537	131	35	t	t	PROPN
cana-537	131	36	}	}	PUNCT
cana-537	131	37	,	,	PUNCT
cana-537	131	38	{	{	PUNCT
cana-537	131	39	q	q	X
cana-537	131	40	,	,	PUNCT
cana-537	131	41	s	s	PROPN
cana-537	131	42	,	,	PUNCT
cana-537	131	43	t	t	PROPN
cana-537	131	44	}	}	PUNCT
cana-537	131	45	}	}	PUNCT
cana-537	131	46	;	;	PUNCT
cana-537	131	47	σc	σc	PROPN
cana-537	131	48	=	=	SYM
cana-537	131	49	{	{	PUNCT
cana-537	131	50	x2	x2	PROPN
cana-537	131	51	,	,	PUNCT
cana-537	131	52	φ	φ	PROPN
cana-537	131	53	,	,	PUNCT
cana-537	131	54	{	{	PUNCT
cana-537	131	55	r	r	NOUN
cana-537	131	56	,	,	PUNCT
cana-537	131	57	s	s	PROPN
cana-537	131	58	,	,	PUNCT
cana-537	131	59	t	t	PROPN
cana-537	131	60	}	}	PUNCT
cana-537	131	61	,	,	PUNCT
cana-537	131	62	{	{	PUNCT
cana-537	131	63	q	q	X
cana-537	131	64	,	,	PUNCT
cana-537	131	65	r	r	NOUN
cana-537	131	66	,	,	PUNCT
cana-537	131	67	t	t	PROPN
cana-537	131	68	}	}	PUNCT
cana-537	131	69	,	,	PUNCT
cana-537	131	70	{	{	PUNCT
cana-537	131	71	q	q	X
cana-537	131	72	,	,	PUNCT
cana-537	131	73	r	r	NOUN
cana-537	131	74	,	,	PUNCT
cana-537	131	75	s	s	PART
cana-537	131	76	}	}	PUNCT
cana-537	131	77	,	,	PUNCT
cana-537	131	78	{	{	PUNCT
cana-537	131	79	r	r	NOUN
cana-537	131	80	,	,	PUNCT
cana-537	131	81	t	t	PROPN
cana-537	131	82	}	}	PUNCT
cana-537	131	83	,	,	PUNCT
cana-537	131	84	{	{	PUNCT
cana-537	131	85	r	r	NOUN
cana-537	131	86	,	,	PUNCT
cana-537	131	87	s	s	PART
cana-537	131	88	}	}	PUNCT
cana-537	131	89	,	,	PUNCT
cana-537	131	90	{	{	PUNCT
cana-537	131	91	q	q	X
cana-537	131	92	,	,	PUNCT
cana-537	131	93	r	r	NOUN
cana-537	131	94	}	}	PUNCT
cana-537	131	95	,	,	PUNCT
cana-537	131	96	{	{	PUNCT
cana-537	131	97	r	r	NOUN
cana-537	131	98	}	}	PUNCT
cana-537	131	99	}	}	PUNCT
cana-537	131	100	and	and	CCONJ
cana-537	131	101	s*p*-c	s*p*-c	PROPN
cana-537	131	102	sets	set	NOUN
cana-537	131	103	of	of	ADP
cana-537	131	104	x2	x2	PROPN
cana-537	131	105	are	be	AUX
cana-537	131	106	{	{	PUNCT
cana-537	131	107	x2	x2	PROPN
cana-537	131	108	,	,	PUNCT
cana-537	131	109	φ	φ	PROPN
cana-537	131	110	,	,	PUNCT
cana-537	131	111	{	{	PUNCT
cana-537	131	112	q	q	X
cana-537	131	113	}	}	PUNCT
cana-537	131	114	,	,	PUNCT
cana-537	131	115	{	{	PUNCT
cana-537	131	116	s	s	X
cana-537	131	117	}	}	PUNCT
cana-537	131	118	,	,	PUNCT
cana-537	131	119	{	{	PUNCT
cana-537	131	120	t	t	NOUN
cana-537	131	121	}	}	PUNCT
cana-537	131	122	,	,	PUNCT
cana-537	131	123	{	{	PUNCT
cana-537	131	124	q	q	X
cana-537	131	125	,	,	PUNCT
cana-537	131	126	s	s	PART
cana-537	131	127	}	}	PUNCT
cana-537	131	128	,	,	PUNCT
cana-537	131	129	{	{	PUNCT
cana-537	131	130	q	q	NOUN
cana-537	131	131	,	,	PUNCT
cana-537	131	132	t	t	PROPN
cana-537	131	133	}	}	PUNCT
cana-537	131	134	,	,	PUNCT
cana-537	131	135	{	{	PUNCT
cana-537	131	136	s	s	PROPN
cana-537	131	137	,	,	PUNCT
cana-537	131	138	t	t	PROPN
cana-537	131	139	}	}	PUNCT
cana-537	131	140	}	}	PUNCT
cana-537	131	141	.	.	PUNCT
cana-537	132	1	αg	αg	PROPN
cana-537	132	2	closed	close	VERB
cana-537	132	3	sets	set	NOUN
cana-537	132	4	of	of	ADP
cana-537	132	5	x2	x2	PROPN
cana-537	132	6	are	be	AUX
cana-537	132	7	{	{	PUNCT
cana-537	132	8	x2	x2	PROPN
cana-537	132	9	,	,	PUNCT
cana-537	132	10	φ	φ	PROPN
cana-537	132	11	,	,	PUNCT
cana-537	132	12	{	{	PUNCT
cana-537	132	13	r	r	NOUN
cana-537	132	14	}	}	PUNCT
cana-537	132	15	,	,	PUNCT
cana-537	132	16	{	{	PUNCT
cana-537	132	17	q	q	X
cana-537	132	18	,	,	PUNCT
cana-537	132	19	r	r	NOUN
cana-537	132	20	}	}	PUNCT
cana-537	132	21	,	,	PUNCT
cana-537	132	22	{	{	PUNCT
cana-537	132	23	r	r	NOUN
cana-537	132	24	,	,	PUNCT
cana-537	132	25	t	t	PROPN
cana-537	132	26	}	}	PUNCT
cana-537	132	27	,	,	PUNCT
cana-537	132	28	{	{	PUNCT
cana-537	132	29	q	q	X
cana-537	132	30	,	,	PUNCT
cana-537	132	31	r	r	NOUN
cana-537	132	32	,	,	PUNCT
cana-537	132	33	t	t	PROPN
cana-537	132	34	}	}	PUNCT
cana-537	132	35	,	,	PUNCT
cana-537	132	36	{	{	PUNCT
cana-537	132	37	q	q	X
cana-537	132	38	,	,	PUNCT
cana-537	132	39	r	r	NOUN
cana-537	132	40	,	,	PUNCT
cana-537	132	41	t	t	PROPN
cana-537	132	42	}	}	PUNCT
cana-537	132	43	,	,	PUNCT
cana-537	132	44	{	{	PUNCT
cana-537	132	45	r	r	NOUN
cana-537	132	46	,	,	PUNCT
cana-537	132	47	s	s	PROPN
cana-537	132	48	,	,	PUNCT
cana-537	132	49	t	t	PROPN
cana-537	132	50	}	}	PUNCT
cana-537	132	51	}	}	PUNCT
cana-537	132	52	.	.	PUNCT
cana-537	133	1	declare	declare	VERB
cana-537	133	2	a	a	DET
cana-537	133	3	map	map	NOUN
cana-537	134	1	f	f	X
cana-537	134	2	:	:	PUNCT
cana-537	134	3	x1	x1	PROPN
cana-537	134	4	→	→	SYM
cana-537	134	5	x2	x2	PROPN
cana-537	134	6	by	by	ADP
cana-537	134	7	f(q	f(q	NOUN
cana-537	134	8	)	)	PUNCT
cana-537	134	9	=	=	SYM
cana-537	135	1	s	s	X
cana-537	135	2	;	;	PUNCT
cana-537	135	3	f(r	f(r	X
cana-537	135	4	)	)	PUNCT
cana-537	136	1	=	=	SYM
cana-537	136	2	r	r	NOUN
cana-537	136	3	;	;	PUNCT
cana-537	136	4	f	f	X
cana-537	136	5	(	(	PUNCT
cana-537	136	6	s	s	X
cana-537	136	7	)	)	PUNCT
cana-537	136	8	=	=	SYM
cana-537	137	1	q	q	NOUN
cana-537	137	2	;	;	PUNCT
cana-537	137	3	f(t	f(t	NOUN
cana-537	137	4	)	)	PUNCT
cana-537	137	5	=	=	SYM
cana-537	138	1	t.	t.	NOUN
cana-537	138	2	hence	hence	ADV
cana-537	138	3	f	f	PROPN
cana-537	138	4	does	do	AUX
cana-537	138	5	not	not	PART
cana-537	138	6	a	a	DET
cana-537	138	7	αg	αg	NOUN
cana-537	138	8	closed	close	VERB
cana-537	138	9	map	map	NOUN
cana-537	138	10	rather	rather	ADV
cana-537	138	11	than	than	ADP
cana-537	138	12	s*p*-c	s*p*-c	PROPN
cana-537	138	13	map	map	NOUN
cana-537	138	14	.	.	PUNCT
cana-537	139	1	because	because	SCONJ
cana-537	139	2	the	the	DET
cana-537	139	3	image	image	NOUN
cana-537	139	4	of	of	ADP
cana-537	139	5	closed	closed	ADJ
cana-537	139	6	map	map	NOUN
cana-537	139	7	{	{	PUNCT
cana-537	139	8	s	s	PROPN
cana-537	139	9	,	,	PUNCT
cana-537	139	10	t	t	PROPN
cana-537	139	11	}	}	PUNCT
cana-537	139	12	in	in	ADP
cana-537	139	13	(	(	PUNCT
cana-537	139	14	x1	x1	PROPN
cana-537	139	15	,	,	PUNCT
cana-537	139	16	τ	τ	PROPN
cana-537	139	17	)	)	PUNCT
cana-537	139	18	,	,	PUNCT
cana-537	139	19	f	f	PROPN
cana-537	139	20	{	{	PUNCT
cana-537	139	21	s	s	PROPN
cana-537	139	22	,	,	PUNCT
cana-537	139	23	t	t	PROPN
cana-537	139	24	}	}	PUNCT
cana-537	139	25	=	=	PUNCT
cana-537	139	26	{	{	PUNCT
cana-537	139	27	q	q	PROPN
cana-537	139	28	,	,	PUNCT
cana-537	139	29	t	t	PROPN
cana-537	139	30	}	}	PUNCT
cana-537	139	31	is	be	AUX
cana-537	139	32	not	not	PART
cana-537	139	33	in	in	ADP
cana-537	139	34	αg	αg	NOUN
cana-537	139	35	closed	close	VERB
cana-537	139	36	set	set	VERB
cana-537	139	37	in	in	ADP
cana-537	139	38	x2	x2	PROPN
cana-537	139	39	but	but	CCONJ
cana-537	139	40	it	it	PRON
cana-537	139	41	in	in	ADP
cana-537	139	42	s*p*-c	s*p*-c	PROPN
cana-537	139	43	set	set	VERB
cana-537	139	44	in	in	ADP
cana-537	139	45	x2	x2	PROPN
cana-537	139	46	.	.	PUNCT
cana-537	140	1	theorem	theorem	VERB
cana-537	140	2	4.13	4.13	NUM
cana-537	140	3	:	:	PUNCT
cana-537	140	4	all	all	DET
cana-537	140	5	-closed	-closed	ADJ
cana-537	140	6	maps	map	NOUN
cana-537	140	7	are	be	AUX
cana-537	140	8	s*p*-c	s*p*-c	PROPN
cana-537	140	9	map	map	NOUN
cana-537	140	10	.	.	PUNCT
cana-537	141	1	proof	proof	NOUN
cana-537	141	2	:	:	PUNCT
cana-537	141	3	given	give	VERB
cana-537	141	4	the	the	DET
cana-537	141	5	idea	idea	NOUN
cana-537	141	6	and	and	CCONJ
cana-537	141	7	fact	fact	NOUN
cana-537	141	8	that	that	SCONJ
cana-537	141	9	any	any	DET
cana-537	141	10	-closed	-closed	ADJ
cana-537	141	11	set	set	NOUN
cana-537	141	12	is	be	AUX
cana-537	141	13	s*p*-c	s*p*-c	PROPN
cana-537	141	14	set	set	PROPN
cana-537	141	15	,	,	PUNCT
cana-537	141	16	the	the	DET
cana-537	141	17	proof	proof	NOUN
cana-537	141	18	is	be	AUX
cana-537	141	19	obvious	obvious	ADJ
cana-537	141	20	.	.	PUNCT
cana-537	142	1	as	as	ADP
cana-537	142	2	this	this	DET
cana-537	142	3	next	next	ADJ
cana-537	142	4	illustration	illustration	NOUN
cana-537	142	5	clarifies	clarifie	NOUN
cana-537	142	6	,	,	PUNCT
cana-537	142	7	the	the	DET
cana-537	142	8	opposite	opposite	NOUN
cana-537	142	9	of	of	ADP
cana-537	142	10	given	give	VERB
cana-537	142	11	theorem	theorem	NOUN
cana-537	142	12	is	be	AUX
cana-537	142	13	not	not	PART
cana-537	142	14	valid	valid	ADJ
cana-537	142	15	.	.	PUNCT
cana-537	143	1	example	example	NOUN
cana-537	143	2	4.14	4.14	NUM
cana-537	143	3	:	:	PUNCT
cana-537	143	4	let	let	VERB
cana-537	143	5	x1	x1	NOUN
cana-537	143	6	=	=	PUNCT
cana-537	144	1	x2	x2	PROPN
cana-537	144	2	=	=	PRON
cana-537	144	3	{	{	PUNCT
cana-537	144	4	r	r	NOUN
cana-537	144	5	,	,	PUNCT
cana-537	144	6	s	s	PROPN
cana-537	144	7	,	,	PUNCT
cana-537	144	8	t	t	PROPN
cana-537	144	9	}	}	PUNCT
cana-537	144	10	;	;	PUNCT
cana-537	144	11	τ	τ	X
cana-537	144	12	=	=	PUNCT
cana-537	144	13	{	{	PUNCT
cana-537	144	14	x1	x1	PROPN
cana-537	144	15	,	,	PUNCT
cana-537	144	16	φ	φ	PROPN
cana-537	144	17	,	,	PUNCT
cana-537	144	18	{	{	PUNCT
cana-537	144	19	r	r	NOUN
cana-537	144	20	}	}	PUNCT
cana-537	144	21	,	,	PUNCT
cana-537	144	22	{	{	PUNCT
cana-537	144	23	r	r	NOUN
cana-537	144	24	,	,	PUNCT
cana-537	144	25	s	s	PART
cana-537	144	26	}	}	PUNCT
cana-537	144	27	}	}	PUNCT
cana-537	144	28	and	and	CCONJ
cana-537	144	29	τc	τc	ADV
cana-537	144	30	=	=	PUNCT
cana-537	144	31	{	{	PUNCT
cana-537	144	32	x1	x1	PROPN
cana-537	144	33	,	,	PUNCT
cana-537	144	34	φ	φ	PROPN
cana-537	144	35	,	,	PUNCT
cana-537	144	36	{	{	PUNCT
cana-537	144	37	s	s	PROPN
cana-537	144	38	,	,	PUNCT
cana-537	144	39	t	t	PROPN
cana-537	144	40	}	}	PUNCT
cana-537	144	41	,	,	PUNCT
cana-537	144	42	{	{	PUNCT
cana-537	144	43	t	t	NOUN
cana-537	144	44	}	}	PUNCT
cana-537	144	45	}	}	PUNCT
cana-537	144	46	.	.	PUNCT
cana-537	145	1	σ	σ	NOUN
cana-537	145	2	=	=	PRON
cana-537	145	3	{	{	PUNCT
cana-537	145	4	x2	x2	PROPN
cana-537	145	5	,	,	PUNCT
cana-537	145	6	φ	φ	PROPN
cana-537	145	7	,	,	PUNCT
cana-537	145	8	{	{	PUNCT
cana-537	145	9	r	r	NOUN
cana-537	145	10	}	}	PUNCT
cana-537	145	11	,	,	PUNCT
cana-537	145	12	{	{	PUNCT
cana-537	145	13	r	r	NOUN
cana-537	145	14	,	,	PUNCT
cana-537	145	15	t	t	PROPN
cana-537	145	16	}	}	PUNCT
cana-537	145	17	}	}	PUNCT
cana-537	145	18	;	;	PUNCT
cana-537	145	19	σc	σc	PROPN
cana-537	145	20	=	=	SYM
cana-537	145	21	{	{	PUNCT
cana-537	145	22	x2	x2	PROPN
cana-537	145	23	,	,	PUNCT
cana-537	145	24	φ	φ	PROPN
cana-537	145	25	,	,	PUNCT
cana-537	145	26	{	{	PUNCT
cana-537	145	27	s	s	PROPN
cana-537	145	28	,	,	PUNCT
cana-537	145	29	t	t	PROPN
cana-537	145	30	}	}	PUNCT
cana-537	145	31	,	,	PUNCT
cana-537	145	32	{	{	PUNCT
cana-537	145	33	s	s	X
cana-537	145	34	}	}	PUNCT
cana-537	145	35	}	}	PUNCT
cana-537	145	36	and	and	CCONJ
cana-537	145	37	s*p*-c	s*p*-c	PROPN
cana-537	145	38	sets	set	NOUN
cana-537	145	39	of	of	ADP
cana-537	145	40	x2	x2	PROPN
cana-537	145	41	are	be	AUX
cana-537	145	42	{	{	PUNCT
cana-537	145	43	x2	x2	PROPN
cana-537	145	44	,	,	PUNCT
cana-537	145	45	φ	φ	PROPN
cana-537	145	46	,	,	PUNCT
cana-537	145	47	{	{	PUNCT
cana-537	145	48	t	t	NOUN
cana-537	145	49	}	}	PUNCT
cana-537	145	50	}	}	PUNCT
cana-537	145	51	.	.	PUNCT
cana-537	146	1			PROPN
cana-537	146	2	closed	close	VERB
cana-537	146	3	sets	set	NOUN
cana-537	146	4	of	of	ADP
cana-537	146	5	x2	x2	PROPN
cana-537	146	6	are	be	AUX
cana-537	146	7	{	{	PUNCT
cana-537	146	8	x2	x2	PROPN
cana-537	146	9	,	,	PUNCT
cana-537	146	10	φ	φ	PROPN
cana-537	146	11	,	,	PUNCT
cana-537	146	12	{	{	PUNCT
cana-537	146	13	s	s	X
cana-537	146	14	}	}	PUNCT
cana-537	146	15	,	,	PUNCT
cana-537	146	16	{	{	PUNCT
cana-537	146	17	r	r	NOUN
cana-537	146	18	,	,	PUNCT
cana-537	146	19	s	s	PART
cana-537	146	20	}	}	PUNCT
cana-537	146	21	,	,	PUNCT
cana-537	146	22	{	{	PUNCT
cana-537	146	23	s	s	PROPN
cana-537	146	24	,	,	PUNCT
cana-537	146	25	t	t	PROPN
cana-537	146	26	}	}	PUNCT
cana-537	146	27	}	}	PUNCT
cana-537	146	28	.	.	PUNCT
cana-537	147	1	define	define	VERB
cana-537	147	2	a	a	DET
cana-537	147	3	map	map	NOUN
cana-537	148	1	f	f	X
cana-537	148	2	:	:	PUNCT
cana-537	148	3	x1→	x1→	X
cana-537	148	4	x2	x2	INTJ
cana-537	148	5	by	by	ADP
cana-537	148	6	f(r	f(r	NOUN
cana-537	148	7	)	)	PUNCT
cana-537	149	1	=	=	SYM
cana-537	149	2	s	s	NOUN
cana-537	149	3	;	;	PUNCT
cana-537	149	4	f(s	f(s	X
cana-537	149	5	)	)	PUNCT
cana-537	149	6	=	=	SYM
cana-537	150	1	r	r	NOUN
cana-537	150	2	;	;	PUNCT
cana-537	150	3	f	f	PROPN
cana-537	150	4	(	(	PUNCT
cana-537	150	5	t	t	PROPN
cana-537	150	6	)	)	PUNCT
cana-537	150	7	=	=	SYM
cana-537	151	1	t.	t.	NOUN
cana-537	151	2	hence	hence	ADV
cana-537	151	3	f	f	PROPN
cana-537	151	4	is	be	AUX
cana-537	151	5	not	not	PART
cana-537	151	6			PROPN
cana-537	151	7	closed	closed	ADJ
cana-537	151	8	map	map	NOUN
cana-537	151	9	but	but	CCONJ
cana-537	151	10	it	it	PRON
cana-537	151	11	is	be	AUX
cana-537	151	12	s*p*-c	s*p*-c	PROPN
cana-537	151	13	map	map	NOUN
cana-537	151	14	.	.	PUNCT
cana-537	152	1	because	because	SCONJ
cana-537	152	2	the	the	DET
cana-537	152	3	image	image	NOUN
cana-537	152	4	of	of	ADP
cana-537	152	5	closed	closed	ADJ
cana-537	152	6	map	map	NOUN
cana-537	152	7	{	{	PUNCT
cana-537	152	8	t	t	NOUN
cana-537	152	9	}	}	PUNCT
cana-537	152	10	in	in	ADP
cana-537	152	11	(	(	PUNCT
cana-537	152	12	x1	x1	PROPN
cana-537	152	13	,	,	PUNCT
cana-537	152	14	τ	τ	PROPN
cana-537	152	15	)	)	PUNCT
cana-537	152	16	,	,	PUNCT
cana-537	152	17	f	f	PROPN
cana-537	152	18	{	{	PUNCT
cana-537	152	19	t	t	PROPN
cana-537	152	20	}	}	PUNCT
cana-537	152	21	=	=	SYM
cana-537	152	22	{	{	PUNCT
cana-537	152	23	t	t	NOUN
cana-537	152	24	}	}	PUNCT
cana-537	152	25	is	be	AUX
cana-537	152	26	not	not	PART
cana-537	152	27	in	in	ADP
cana-537	152	28			PROPN
cana-537	152	29	closed	closed	ADJ
cana-537	152	30	set	set	NOUN
cana-537	152	31	in	in	ADP
cana-537	152	32	x2	x2	PROPN
cana-537	152	33	but	but	CCONJ
cana-537	152	34	it	it	PRON
cana-537	152	35	in	in	ADP
cana-537	152	36	s*p*-c	s*p*-c	PROPN
cana-537	152	37	set	set	VERB
cana-537	152	38	in	in	ADP
cana-537	152	39	x2	x2	PROPN
cana-537	152	40	.	.	PUNCT
cana-537	153	1	remark	remark	PROPN
cana-537	153	2	4.15	4.15	NUM
cana-537	153	3	:	:	PUNCT
cana-537	154	1	an	an	DET
cana-537	154	2	upcoming	upcoming	ADJ
cana-537	154	3	example	example	NOUN
cana-537	154	4	shows	show	VERB
cana-537	154	5	that	that	SCONJ
cana-537	154	6	g	g	NOUN
cana-537	154	7	-	-	PUNCT
cana-537	154	8	closed	close	VERB
cana-537	154	9	map	map	NOUN
cana-537	154	10	and	and	CCONJ
cana-537	154	11	s*p*-c	s*p*-c	NOUN
cana-537	154	12	map	map	NOUN
cana-537	154	13	are	be	AUX
cana-537	154	14	not	not	PART
cana-537	154	15	dependent	dependent	ADJ
cana-537	154	16	.	.	PUNCT
cana-537	155	1	let	let	VERB
cana-537	155	2	x1	x1	NOUN
cana-537	156	1	=	=	PUNCT
cana-537	156	2	x2	x2	PROPN
cana-537	156	3	=	=	PRON
cana-537	156	4	{	{	PUNCT
cana-537	156	5	q	q	NOUN
cana-537	156	6	,	,	PUNCT
cana-537	156	7	r	r	NOUN
cana-537	156	8	,	,	PUNCT
cana-537	156	9	s	s	PROPN
cana-537	156	10	,	,	PUNCT
cana-537	156	11	t	t	PROPN
cana-537	156	12	}	}	PUNCT
cana-537	156	13	;	;	PUNCT
cana-537	156	14	τ	τ	X
cana-537	156	15	=	=	PUNCT
cana-537	156	16	{	{	PUNCT
cana-537	156	17	x1	x1	PROPN
cana-537	156	18	,	,	PUNCT
cana-537	156	19	φ	φ	PROPN
cana-537	156	20	,	,	PUNCT
cana-537	156	21	{	{	PUNCT
cana-537	156	22	q	q	X
cana-537	156	23	}	}	PUNCT
cana-537	156	24	,	,	PUNCT
cana-537	156	25	{	{	PUNCT
cana-537	156	26	r	r	NOUN
cana-537	156	27	}	}	PUNCT
cana-537	156	28	,	,	PUNCT
cana-537	156	29	{	{	PUNCT
cana-537	156	30	q	q	X
cana-537	156	31	,	,	PUNCT
cana-537	156	32	r	r	NOUN
cana-537	156	33	}	}	PUNCT
cana-537	156	34	,	,	PUNCT
cana-537	156	35	{	{	PUNCT
cana-537	156	36	r	r	NOUN
cana-537	156	37	,	,	PUNCT
cana-537	156	38	s	s	PART
cana-537	156	39	}	}	PUNCT
cana-537	156	40	,	,	PUNCT
cana-537	156	41	{	{	PUNCT
cana-537	156	42	q	q	X
cana-537	156	43	,	,	PUNCT
cana-537	156	44	r	r	NOUN
cana-537	156	45	,	,	PUNCT
cana-537	156	46	s	s	PART
cana-537	156	47	}	}	PUNCT
cana-537	156	48	}	}	PUNCT
cana-537	156	49	and	and	CCONJ
cana-537	156	50	τc	τc	ADV
cana-537	156	51	=	=	PUNCT
cana-537	156	52	{	{	PUNCT
cana-537	156	53	x1	x1	PROPN
cana-537	156	54	,	,	PUNCT
cana-537	156	55	φ	φ	PROPN
cana-537	156	56	,	,	PUNCT
cana-537	156	57	{	{	PUNCT
cana-537	156	58	r	r	NOUN
cana-537	156	59	,	,	PUNCT
cana-537	156	60	s	s	PROPN
cana-537	156	61	,	,	PUNCT
cana-537	156	62	t	t	PROPN
cana-537	156	63	}	}	PUNCT
cana-537	156	64	,	,	PUNCT
cana-537	156	65	{	{	PUNCT
cana-537	156	66	q	q	X
cana-537	156	67	,	,	PUNCT
cana-537	156	68	s	s	PROPN
cana-537	156	69	,	,	PUNCT
cana-537	156	70	t	t	PROPN
cana-537	156	71	}	}	PUNCT
cana-537	156	72	,	,	PUNCT
cana-537	156	73	{	{	PUNCT
cana-537	156	74	s	s	X
cana-537	156	75	,	,	PUNCT
cana-537	156	76	t	t	PROPN
cana-537	156	77	}	}	PUNCT
cana-537	156	78	,	,	PUNCT
cana-537	156	79	{	{	PUNCT
cana-537	156	80	q	q	NOUN
cana-537	156	81	,	,	PUNCT
cana-537	156	82	t	t	PROPN
cana-537	156	83	}	}	PUNCT
cana-537	156	84	,	,	PUNCT
cana-537	156	85	{	{	PUNCT
cana-537	156	86	t	t	NOUN
cana-537	156	87	}	}	PUNCT
cana-537	156	88	}	}	PUNCT
cana-537	156	89	.	.	PUNCT
cana-537	157	1	σ	σ	NOUN
cana-537	157	2	=	=	PRON
cana-537	157	3	{	{	PUNCT
cana-537	157	4	x2	x2	PROPN
cana-537	157	5	,	,	PUNCT
cana-537	157	6	φ	φ	PROPN
cana-537	157	7	,	,	PUNCT
cana-537	157	8	{	{	PUNCT
cana-537	157	9	r	r	NOUN
cana-537	157	10	}	}	PUNCT
cana-537	157	11	,	,	PUNCT
cana-537	157	12	{	{	PUNCT
cana-537	157	13	t	t	NOUN
cana-537	157	14	}	}	PUNCT
cana-537	157	15	,	,	PUNCT
cana-537	157	16	{	{	PUNCT
cana-537	157	17	r	r	NOUN
cana-537	157	18	,	,	PUNCT
cana-537	157	19	t	t	PROPN
cana-537	157	20	}	}	PUNCT
cana-537	157	21	,	,	PUNCT
cana-537	157	22	{	{	PUNCT
cana-537	157	23	r	r	NOUN
cana-537	157	24	,	,	PUNCT
cana-537	157	25	s	s	PROPN
cana-537	157	26	,	,	PUNCT
cana-537	157	27	t	t	PROPN
cana-537	157	28	}	}	PUNCT
cana-537	157	29	}	}	PUNCT
cana-537	157	30	;	;	PUNCT
cana-537	157	31	σc	σc	PROPN
cana-537	157	32	=	=	SYM
cana-537	157	33	{	{	PUNCT
cana-537	157	34	x2	x2	PROPN
cana-537	157	35	,	,	PUNCT
cana-537	157	36	φ	φ	PROPN
cana-537	157	37	,	,	PUNCT
cana-537	157	38	{	{	PUNCT
cana-537	157	39	q	q	X
cana-537	157	40	,	,	PUNCT
cana-537	157	41	s	s	PROPN
cana-537	157	42	,	,	PUNCT
cana-537	157	43	t	t	PROPN
cana-537	157	44	}	}	PUNCT
cana-537	157	45	,	,	PUNCT
cana-537	157	46	{	{	PUNCT
cana-537	157	47	q	q	X
cana-537	157	48	,	,	PUNCT
cana-537	157	49	r	r	NOUN
cana-537	157	50	,	,	PUNCT
cana-537	157	51	s	s	PART
cana-537	157	52	}	}	PUNCT
cana-537	157	53	,	,	PUNCT
cana-537	157	54	{	{	PUNCT
cana-537	157	55	q	q	X
cana-537	157	56	,	,	PUNCT
cana-537	157	57	s	s	PART
cana-537	157	58	}	}	PUNCT
cana-537	157	59	,	,	PUNCT
cana-537	157	60	{	{	PUNCT
cana-537	157	61	q	q	NOUN
cana-537	157	62	}	}	PUNCT
cana-537	157	63	}	}	PUNCT
cana-537	157	64	and	and	CCONJ
cana-537	157	65	s*p*-c	s*p*-c	PROPN
cana-537	157	66	sets	set	NOUN
cana-537	157	67	of	of	ADP
cana-537	157	68	x2	x2	PROPN
cana-537	157	69	are	be	AUX
cana-537	157	70	{	{	PUNCT
cana-537	157	71	x2	x2	PROPN
cana-537	157	72	,	,	PUNCT
cana-537	157	73	φ	φ	PROPN
cana-537	157	74	,	,	PUNCT
cana-537	157	75	{	{	PUNCT
cana-537	157	76	r	r	NOUN
cana-537	157	77	}	}	PUNCT
cana-537	157	78	,	,	PUNCT
cana-537	157	79	{	{	PUNCT
cana-537	157	80	s	s	X
cana-537	157	81	}	}	PUNCT
cana-537	157	82	,	,	PUNCT
cana-537	157	83	{	{	PUNCT
cana-537	157	84	t	t	NOUN
cana-537	157	85	}	}	PUNCT
cana-537	157	86	,	,	PUNCT
cana-537	157	87	{	{	PUNCT
cana-537	157	88	r	r	NOUN
cana-537	157	89	,	,	PUNCT
cana-537	157	90	s	s	PART
cana-537	157	91	}	}	PUNCT
cana-537	157	92	,	,	PUNCT
cana-537	157	93	{	{	PUNCT
cana-537	157	94	s	s	PROPN
cana-537	157	95	,	,	PUNCT
cana-537	157	96	t	t	PROPN
cana-537	157	97	}	}	PUNCT
cana-537	157	98	}	}	PUNCT
cana-537	157	99	.	.	PUNCT
cana-537	158	1	g	g	PROPN
cana-537	158	2	closed	close	VERB
cana-537	158	3	sets	set	NOUN
cana-537	158	4	of	of	ADP
cana-537	158	5	x2	x2	PROPN
cana-537	158	6	are	be	AUX
cana-537	158	7	{	{	PUNCT
cana-537	158	8	x2	x2	PROPN
cana-537	158	9	,	,	PUNCT
cana-537	158	10	φ	φ	PROPN
cana-537	158	11	,	,	PUNCT
cana-537	158	12	{	{	PUNCT
cana-537	158	13	q	q	X
cana-537	158	14	}	}	PUNCT
cana-537	158	15	,	,	PUNCT
cana-537	158	16	{	{	PUNCT
cana-537	158	17	q	q	X
cana-537	158	18	,	,	PUNCT
cana-537	158	19	r	r	NOUN
cana-537	158	20	}	}	PUNCT
cana-537	158	21	,	,	PUNCT
cana-537	158	22	{	{	PUNCT
cana-537	158	23	q	q	X
cana-537	158	24	,	,	PUNCT
cana-537	158	25	s	s	PART
cana-537	158	26	}	}	PUNCT
cana-537	158	27	,	,	PUNCT
cana-537	158	28	{	{	PUNCT
cana-537	158	29	q	q	NOUN
cana-537	158	30	,	,	PUNCT
cana-537	158	31	t	t	PROPN
cana-537	158	32	}	}	PUNCT
cana-537	158	33	,	,	PUNCT
cana-537	158	34	{	{	PUNCT
cana-537	158	35	q	q	X
cana-537	158	36	,	,	PUNCT
cana-537	158	37	r	r	NOUN
cana-537	158	38	,	,	PUNCT
cana-537	158	39	s	s	PART
cana-537	158	40	}	}	PUNCT
cana-537	158	41	,	,	PUNCT
cana-537	158	42	{	{	PUNCT
cana-537	158	43	q	q	X
cana-537	158	44	,	,	PUNCT
cana-537	158	45	r	r	NOUN
cana-537	158	46	,	,	PUNCT
cana-537	158	47	t	t	PROPN
cana-537	158	48	}	}	PUNCT
cana-537	158	49	,	,	PUNCT
cana-537	158	50	{	{	PUNCT
cana-537	158	51	q	q	X
cana-537	158	52	,	,	PUNCT
cana-537	158	53	s	s	PROPN
cana-537	158	54	,	,	PUNCT
cana-537	158	55	t	t	PROPN
cana-537	158	56	}	}	PUNCT
cana-537	158	57	}	}	PUNCT
cana-537	158	58	.	.	PUNCT
cana-537	159	1	define	define	VERB
cana-537	159	2	a	a	DET
cana-537	159	3	map	map	NOUN
cana-537	160	1	f	f	X
cana-537	160	2	:	:	PUNCT
cana-537	160	3	x1→	x1→	X
cana-537	160	4	x2	x2	INTJ
cana-537	160	5	by	by	ADP
cana-537	160	6	f(q	f(q	NOUN
cana-537	160	7	)	)	PUNCT
cana-537	161	1	=	=	SYM
cana-537	161	2	r	r	NOUN
cana-537	161	3	;	;	PUNCT
cana-537	161	4	f(r	f(r	NOUN
cana-537	161	5	)	)	PUNCT
cana-537	162	1	=	=	SYM
cana-537	163	1	q	q	NOUN
cana-537	163	2	;	;	PUNCT
cana-537	163	3	f	f	X
cana-537	163	4	(	(	PUNCT
cana-537	163	5	s	s	X
cana-537	163	6	)	)	PUNCT
cana-537	163	7	=	=	SYM
cana-537	163	8	s	s	NOUN
cana-537	163	9	;	;	PUNCT
cana-537	163	10	f(t	f(t	NOUN
cana-537	163	11	)	)	PUNCT
cana-537	163	12	=	=	SYM
cana-537	164	1	t.	t.	NOUN
cana-537	164	2	hence	hence	ADV
cana-537	164	3	f	f	PROPN
cana-537	164	4	does	do	AUX
cana-537	164	5	not	not	PART
cana-537	164	6	a	a	DET
cana-537	164	7	g	g	NOUN
cana-537	164	8	closed	closed	ADJ
cana-537	164	9	map	map	NOUN
cana-537	164	10	rather	rather	ADV
cana-537	164	11	than	than	ADP
cana-537	164	12	s*p*-c	s*p*-c	PROPN
cana-537	164	13	map	map	NOUN
cana-537	164	14	.	.	PUNCT
cana-537	165	1	when	when	SCONJ
cana-537	165	2	the	the	DET
cana-537	165	3	image	image	NOUN
cana-537	165	4	of	of	ADP
cana-537	165	5	closed	closed	ADJ
cana-537	165	6	map	map	NOUN
cana-537	165	7	{	{	PUNCT
cana-537	165	8	s	s	PROPN
cana-537	165	9	,	,	PUNCT
cana-537	165	10	t	t	PROPN
cana-537	165	11	}	}	PUNCT
cana-537	165	12	in	in	ADP
cana-537	165	13	(	(	PUNCT
cana-537	165	14	x1	x1	PROPN
cana-537	165	15	,	,	PUNCT
cana-537	165	16	τ	τ	PROPN
cana-537	165	17	)	)	PUNCT
cana-537	165	18	,	,	PUNCT
cana-537	165	19	f	f	PROPN
cana-537	165	20	{	{	PUNCT
cana-537	165	21	s	s	PROPN
cana-537	165	22	,	,	PUNCT
cana-537	165	23	t	t	PROPN
cana-537	165	24	}	}	PUNCT
cana-537	165	25	=	=	PUNCT
cana-537	165	26	{	{	PUNCT
cana-537	165	27	s	s	PROPN
cana-537	165	28	,	,	PUNCT
cana-537	165	29	t	t	PROPN
cana-537	165	30	}	}	PUNCT
cana-537	165	31	is	be	AUX
cana-537	165	32	not	not	PART
cana-537	165	33	in	in	ADP
cana-537	165	34	g	g	NOUN
cana-537	165	35	closed	close	VERB
cana-537	165	36	set	set	VERB
cana-537	165	37	in	in	ADP
cana-537	165	38	x2	x2	PROPN
cana-537	166	1	but	but	CCONJ
cana-537	166	2	it	it	PRON
cana-537	166	3	in	in	ADP
cana-537	166	4	s*p*-c	s*p*-c	PROPN
cana-537	166	5	set	set	VERB
cana-537	166	6	in	in	ADP
cana-537	166	7	x2	x2	PROPN
cana-537	166	8	.	.	PUNCT
cana-537	167	1	similarly	similarly	ADV
cana-537	167	2	,	,	PUNCT
cana-537	167	3	f	f	PROPN
cana-537	167	4	is	be	AUX
cana-537	167	5	g	g	NOUN
cana-537	167	6	closed	closed	ADJ
cana-537	167	7	but	but	CCONJ
cana-537	167	8	not	not	PART
cana-537	167	9	communications	communication	NOUN
cana-537	167	10	on	on	ADP
cana-537	167	11	applied	apply	VERB
cana-537	167	12	nonlinear	nonlinear	ADJ
cana-537	167	13	analysis	analysis	NOUN
cana-537	167	14	issn	issn	NOUN
cana-537	167	15	:	:	PUNCT
cana-537	167	16	1074	1074	NUM
cana-537	167	17	-	-	PUNCT
cana-537	167	18	133x	133x	NUM
cana-537	167	19	vol	vol	NOUN
cana-537	167	20	31	31	NUM
cana-537	167	21	no	no	NOUN
cana-537	167	22	.	.	NOUN
cana-537	167	23	2	2	NUM
cana-537	167	24	(	(	PUNCT
cana-537	167	25	2024	2024	NUM
cana-537	167	26	)	)	PUNCT
cana-537	167	27	221	221	NUM
cana-537	167	28	https://internationalpubls.com	https://internationalpubls.com	X
cana-537	167	29	s*p*-c	s*p*-c	PROPN
cana-537	167	30	map	map	NOUN
cana-537	167	31	.	.	PUNCT
cana-537	168	1	thus	thus	ADV
cana-537	168	2	,	,	PUNCT
cana-537	168	3	the	the	DET
cana-537	168	4	closed	closed	ADJ
cana-537	168	5	set	set	NOUN
cana-537	168	6	{	{	PUNCT
cana-537	168	7	r	r	NOUN
cana-537	168	8	,	,	PUNCT
cana-537	168	9	s	s	PROPN
cana-537	168	10	,	,	PUNCT
cana-537	168	11	t	t	PROPN
cana-537	168	12	}	}	PUNCT
cana-537	168	13	in	in	ADP
cana-537	168	14	(	(	PUNCT
cana-537	168	15	x1	x1	PROPN
cana-537	168	16	,	,	PUNCT
cana-537	168	17	τ	τ	PROPN
cana-537	168	18	)	)	PUNCT
cana-537	168	19	,	,	PUNCT
cana-537	168	20	f	f	PROPN
cana-537	168	21	{	{	PUNCT
cana-537	168	22	r	r	PROPN
cana-537	168	23	,	,	PUNCT
cana-537	168	24	s	s	PROPN
cana-537	168	25	,	,	PUNCT
cana-537	168	26	t	t	PROPN
cana-537	168	27	}	}	PUNCT
cana-537	168	28	=	=	PUNCT
cana-537	168	29	{	{	PUNCT
cana-537	168	30	q	q	X
cana-537	168	31	,	,	PUNCT
cana-537	168	32	s	s	PROPN
cana-537	168	33	,	,	PUNCT
cana-537	168	34	t	t	PROPN
cana-537	168	35	}	}	PUNCT
cana-537	168	36	is	be	AUX
cana-537	168	37	in	in	ADP
cana-537	168	38	g	g	NOUN
cana-537	168	39	closed	close	VERB
cana-537	168	40	set	set	VERB
cana-537	168	41	in	in	ADP
cana-537	168	42	x2	x2	PROPN
cana-537	168	43	but	but	CCONJ
cana-537	168	44	not	not	PART
cana-537	168	45	in	in	ADP
cana-537	168	46	s*p*-c	s*p*-c	PROPN
cana-537	168	47	set	set	VERB
cana-537	168	48	in	in	ADP
cana-537	168	49	x2	x2	PROPN
cana-537	168	50	.	.	PUNCT
cana-537	169	1	5	5	X
cana-537	169	2	.	.	X
cana-537	169	3	s*p	s*p	PROPN
cana-537	169	4	*	*	PROPN
cana-537	169	5	homeomorphism	homeomorphism	PROPN
cana-537	169	6	this	this	DET
cana-537	169	7	portion	portion	NOUN
cana-537	169	8	deals	deal	VERB
cana-537	169	9	with	with	ADP
cana-537	169	10	s*p*-homeomorphism	s*p*-homeomorphism	NOUN
cana-537	169	11	(	(	PUNCT
cana-537	169	12	s*p*-h	s*p*-h	NOUN
cana-537	169	13	)	)	PUNCT
cana-537	169	14	using	use	VERB
cana-537	169	15	s*p*-c	s*p*-c	PROPN
cana-537	169	16	maps	map	NOUN
cana-537	169	17	and	and	CCONJ
cana-537	169	18	s*p*-o	s*p*-o	ADJ
cana-537	169	19	maps	map	NOUN
cana-537	169	20	.	.	PUNCT
cana-537	170	1	definition	definition	NOUN
cana-537	170	2	5.1	5.1	NUM
cana-537	170	3	:	:	PUNCT
cana-537	170	4	a	a	DET
cana-537	170	5	bijection	bijection	NOUN
cana-537	170	6	maps	map	NOUN
cana-537	170	7	f	f	NOUN
cana-537	170	8	:	:	PUNCT
cana-537	171	1	x1→	x1→	X
cana-537	171	2	x2	x2	PROPN
cana-537	171	3	is	be	AUX
cana-537	171	4	known	know	VERB
cana-537	171	5	as	as	ADP
cana-537	171	6	s*p*homeomorphism(s*p*-h	s*p*homeomorphism(s*p*-h	NOUN
cana-537	171	7	)	)	PUNCT
cana-537	171	8	if	if	SCONJ
cana-537	171	9	f	f	PROPN
cana-537	171	10	and	and	CCONJ
cana-537	171	11	its	its	PRON
cana-537	171	12	inverse	inverse	NOUN
cana-537	171	13	are	be	AUX
cana-537	171	14	s*p*continuous	s*p*continuous	ADJ
cana-537	171	15	maps	map	NOUN
cana-537	171	16	.	.	PUNCT
cana-537	172	1	example	example	NOUN
cana-537	172	2	5.2	5.2	NUM
cana-537	172	3	:	:	PUNCT
cana-537	172	4	let	let	VERB
cana-537	172	5	x1	x1	PROPN
cana-537	173	1	=	=	PUNCT
cana-537	173	2	x2=	x2=	PROPN
cana-537	173	3	{	{	PUNCT
cana-537	173	4	r	r	NOUN
cana-537	173	5	,	,	PUNCT
cana-537	173	6	s	s	PROPN
cana-537	173	7	,	,	PUNCT
cana-537	173	8	t	t	PROPN
cana-537	173	9	}	}	PUNCT
cana-537	173	10	;	;	PUNCT
cana-537	173	11	τ	τ	X
cana-537	173	12	=	=	PUNCT
cana-537	173	13	{	{	PUNCT
cana-537	173	14	x1	x1	PROPN
cana-537	173	15	,	,	PUNCT
cana-537	173	16	φ	φ	PROPN
cana-537	173	17	,	,	PUNCT
cana-537	173	18	{	{	PUNCT
cana-537	173	19	r	r	NOUN
cana-537	173	20	}	}	PUNCT
cana-537	173	21	,	,	PUNCT
cana-537	173	22	{	{	PUNCT
cana-537	173	23	s	s	X
cana-537	173	24	}	}	PUNCT
cana-537	173	25	,	,	PUNCT
cana-537	173	26	{	{	PUNCT
cana-537	173	27	r	r	NOUN
cana-537	173	28	,	,	PUNCT
cana-537	173	29	s	s	PART
cana-537	173	30	}	}	PUNCT
cana-537	173	31	}	}	PUNCT
cana-537	173	32	and	and	CCONJ
cana-537	173	33	τc	τc	ADV
cana-537	173	34	=	=	PUNCT
cana-537	173	35	{	{	PUNCT
cana-537	173	36	x1	x1	PROPN
cana-537	173	37	,	,	PUNCT
cana-537	173	38	φ	φ	PROPN
cana-537	173	39	,	,	PUNCT
cana-537	173	40	{	{	PUNCT
cana-537	173	41	s	s	PROPN
cana-537	173	42	,	,	PUNCT
cana-537	173	43	t	t	PROPN
cana-537	173	44	}	}	PUNCT
cana-537	173	45	,	,	PUNCT
cana-537	173	46	{	{	PUNCT
cana-537	173	47	r	r	NOUN
cana-537	173	48	,	,	PUNCT
cana-537	173	49	t	t	PROPN
cana-537	173	50	}	}	PUNCT
cana-537	173	51	,	,	PUNCT
cana-537	173	52	{	{	PUNCT
cana-537	173	53	t	t	NOUN
cana-537	173	54	}	}	PUNCT
cana-537	173	55	}	}	PUNCT
cana-537	173	56	.	.	PUNCT
cana-537	174	1	s*p*-c	s*p*-c	PROPN
cana-537	174	2	sets	set	NOUN
cana-537	174	3	of	of	ADP
cana-537	174	4	x1	x1	PROPN
cana-537	174	5	are	be	AUX
cana-537	174	6	{	{	PUNCT
cana-537	174	7	x1	x1	PROPN
cana-537	174	8	,	,	PUNCT
cana-537	174	9	φ	φ	PROPN
cana-537	174	10	,	,	PUNCT
cana-537	174	11	{	{	PUNCT
cana-537	174	12	r	r	NOUN
cana-537	174	13	}	}	PUNCT
cana-537	174	14	,	,	PUNCT
cana-537	174	15	{	{	PUNCT
cana-537	174	16	s	s	X
cana-537	174	17	}	}	PUNCT
cana-537	174	18	}	}	PUNCT
cana-537	174	19	.	.	PUNCT
cana-537	175	1	σ	σ	NOUN
cana-537	175	2	=	=	PRON
cana-537	175	3	{	{	PUNCT
cana-537	175	4	x2	x2	PROPN
cana-537	175	5	,	,	PUNCT
cana-537	175	6	φ	φ	PROPN
cana-537	175	7	,	,	PUNCT
cana-537	175	8	{	{	PUNCT
cana-537	175	9	s	s	X
cana-537	175	10	}	}	PUNCT
cana-537	175	11	,	,	PUNCT
cana-537	175	12	{	{	PUNCT
cana-537	175	13	t	t	NOUN
cana-537	175	14	}	}	PUNCT
cana-537	175	15	,	,	PUNCT
cana-537	175	16	{	{	PUNCT
cana-537	175	17	r	r	NOUN
cana-537	175	18	,	,	PUNCT
cana-537	175	19	s	s	PART
cana-537	175	20	}	}	PUNCT
cana-537	175	21	,	,	PUNCT
cana-537	175	22	{	{	PUNCT
cana-537	175	23	s	s	PROPN
cana-537	175	24	,	,	PUNCT
cana-537	175	25	t	t	PROPN
cana-537	175	26	}	}	PUNCT
cana-537	175	27	}	}	PUNCT
cana-537	175	28	;	;	PUNCT
cana-537	175	29	σc	σc	PROPN
cana-537	175	30	=	=	SYM
cana-537	175	31	{	{	PUNCT
cana-537	175	32	x2	x2	PROPN
cana-537	175	33	,	,	PUNCT
cana-537	175	34	φ	φ	PROPN
cana-537	175	35	,	,	PUNCT
cana-537	175	36	{	{	PUNCT
cana-537	175	37	r	r	NOUN
cana-537	175	38	,	,	PUNCT
cana-537	175	39	t	t	PROPN
cana-537	175	40	}	}	PUNCT
cana-537	175	41	,	,	PUNCT
cana-537	175	42	{	{	PUNCT
cana-537	175	43	r	r	NOUN
cana-537	175	44	,	,	PUNCT
cana-537	175	45	s	s	PART
cana-537	175	46	}	}	PUNCT
cana-537	175	47	,	,	PUNCT
cana-537	175	48	{	{	PUNCT
cana-537	175	49	t	t	NOUN
cana-537	175	50	}	}	PUNCT
cana-537	175	51	,	,	PUNCT
cana-537	175	52	{	{	PUNCT
cana-537	175	53	r	r	NOUN
cana-537	175	54	}	}	PUNCT
cana-537	175	55	}	}	PUNCT
cana-537	175	56	and	and	CCONJ
cana-537	175	57	s*p*-c	s*p*-c	PROPN
cana-537	175	58	sets	set	NOUN
cana-537	175	59	of	of	ADP
cana-537	175	60	x2	x2	PROPN
cana-537	175	61	are	be	AUX
cana-537	175	62	{	{	PUNCT
cana-537	175	63	x2	x2	PROPN
cana-537	175	64	,	,	PUNCT
cana-537	175	65	φ	φ	PROPN
cana-537	175	66	,	,	PUNCT
cana-537	175	67	{	{	PUNCT
cana-537	175	68	r	r	NOUN
cana-537	175	69	}	}	PUNCT
cana-537	175	70	,	,	PUNCT
cana-537	175	71	{	{	PUNCT
cana-537	175	72	r	r	NOUN
cana-537	175	73	,	,	PUNCT
cana-537	175	74	s	s	PART
cana-537	175	75	}	}	PUNCT
cana-537	175	76	}	}	PUNCT
cana-537	175	77	.	.	PUNCT
cana-537	176	1	define	define	VERB
cana-537	176	2	a	a	DET
cana-537	176	3	map	map	NOUN
cana-537	177	1	f	f	X
cana-537	177	2	:	:	PUNCT
cana-537	177	3	x1→	x1→	X
cana-537	177	4	x2	x2	INTJ
cana-537	177	5	by	by	ADP
cana-537	177	6	f(r	f(r	NOUN
cana-537	177	7	)	)	PUNCT
cana-537	178	1	=	=	SYM
cana-537	178	2	s	s	NOUN
cana-537	178	3	;	;	PUNCT
cana-537	178	4	f(s	f(s	X
cana-537	178	5	)	)	PUNCT
cana-537	178	6	=	=	SYM
cana-537	178	7	t	t	PROPN
cana-537	178	8	;	;	PUNCT
cana-537	178	9	f	f	PROPN
cana-537	178	10	(	(	PUNCT
cana-537	178	11	t	t	PROPN
cana-537	178	12	)	)	PUNCT
cana-537	178	13	=	=	VERB
cana-537	179	1	r.	r.	NOUN
cana-537	179	2	here	here	ADV
cana-537	179	3	the	the	DET
cana-537	179	4	inverse	inverse	ADJ
cana-537	179	5	image	image	NOUN
cana-537	179	6	of	of	ADP
cana-537	179	7	the	the	DET
cana-537	179	8	closed	closed	ADJ
cana-537	179	9	set	set	NOUN
cana-537	179	10	{	{	PUNCT
cana-537	179	11	c	c	NOUN
cana-537	179	12	}	}	PUNCT
cana-537	179	13	in	in	ADP
cana-537	179	14	x2	x2	PROPN
cana-537	179	15	is	be	AUX
cana-537	179	16	s*p*-c	s*p*-c	PROPN
cana-537	179	17	set	set	NOUN
cana-537	179	18	in	in	ADP
cana-537	179	19	x1	x1	PROPN
cana-537	179	20	and	and	CCONJ
cana-537	179	21	(	(	PUNCT
cana-537	179	22	f-1	f-1	NOUN
cana-537	179	23	)	)	PUNCT
cana-537	179	24	-1	-1	PUNCT
cana-537	180	1	(	(	PUNCT
cana-537	180	2	t	t	NOUN
cana-537	180	3	)	)	PUNCT
cana-537	180	4	=	=	SYM
cana-537	180	5	f(t	f(t	NOUN
cana-537	180	6	)	)	PUNCT
cana-537	180	7	=	=	PRON
cana-537	180	8	{	{	PUNCT
cana-537	180	9	r	r	NOUN
cana-537	180	10	}	}	PUNCT
cana-537	180	11	is	be	AUX
cana-537	180	12	in	in	ADP
cana-537	180	13	s*p*-c	s*p*-c	PROPN
cana-537	180	14	set	set	VERB
cana-537	180	15	in	in	ADP
cana-537	180	16	x2	x2	PROPN
cana-537	180	17	.	.	PUNCT
cana-537	181	1	hence	hence	ADV
cana-537	181	2	,	,	PUNCT
cana-537	181	3	f	f	PROPN
cana-537	181	4	and	and	CCONJ
cana-537	181	5	its	its	PRON
cana-537	181	6	inverse	inverse	NOUN
cana-537	181	7	are	be	AUX
cana-537	181	8	s*p*continuous	s*p*continuous	ADJ
cana-537	181	9	.	.	PUNCT
cana-537	182	1	which	which	PRON
cana-537	182	2	leads	lead	VERB
cana-537	182	3	to	to	ADP
cana-537	182	4	f	f	PROPN
cana-537	182	5	is	be	AUX
cana-537	182	6	s*p*-h	s*p*-h	NOUN
cana-537	182	7	.	.	PUNCT
cana-537	183	1	theorem	theorem	VERB
cana-537	183	2	5.3	5.3	NUM
cana-537	183	3	:	:	PUNCT
cana-537	183	4	all	all	DET
cana-537	183	5	homeomorphism	homeomorphism	NOUN
cana-537	183	6	may	may	AUX
cana-537	183	7	be	be	AUX
cana-537	183	8	expressed	express	VERB
cana-537	183	9	as	as	ADP
cana-537	183	10	s*p*homeomorphism	s*p*homeomorphism	NOUN
cana-537	183	11	.	.	PUNCT
cana-537	184	1	proof	proof	NOUN
cana-537	184	2	:	:	PUNCT
cana-537	184	3	a	a	DET
cana-537	184	4	homeomorphism	homeomorphism	NOUN
cana-537	184	5	is	be	AUX
cana-537	184	6	defined	define	VERB
cana-537	184	7	as	as	ADP
cana-537	184	8	f	f	PROPN
cana-537	184	9	:	:	PUNCT
cana-537	184	10	x1	x1	PROPN
cana-537	184	11	→	→	SYM
cana-537	184	12	x2	x2	PROPN
cana-537	184	13	.	.	PUNCT
cana-537	185	1	consequently	consequently	ADV
cana-537	185	2	,	,	PUNCT
cana-537	185	3	f	f	PROPN
cana-537	185	4	and	and	CCONJ
cana-537	185	5	its	its	PRON
cana-537	185	6	inverse	inverse	NOUN
cana-537	185	7	are	be	AUX
cana-537	185	8	continuous	continuous	ADJ
cana-537	185	9	and	and	CCONJ
cana-537	185	10	bijection	bijection	ADJ
cana-537	185	11	.	.	PUNCT
cana-537	186	1	so	so	ADV
cana-537	186	2	that	that	SCONJ
cana-537	186	3	f	f	PROPN
cana-537	186	4	is	be	AUX
cana-537	186	5	s*p*-h	s*p*-h	NOUN
cana-537	186	6	if	if	SCONJ
cana-537	186	7	any	any	DET
cana-537	186	8	continuous	continuous	ADJ
cana-537	186	9	function	function	NOUN
cana-537	186	10	is	be	AUX
cana-537	186	11	s*p*continuous	s*p*continuous	ADJ
cana-537	186	12	.	.	PUNCT
cana-537	187	1	the	the	DET
cana-537	187	2	subsequent	subsequent	ADJ
cana-537	187	3	example	example	NOUN
cana-537	187	4	explains	explain	VERB
cana-537	187	5	that	that	SCONJ
cana-537	187	6	the	the	DET
cana-537	187	7	theorems	theorem	NOUN
cana-537	187	8	in	in	ADP
cana-537	187	9	contradiction	contradiction	NOUN
cana-537	187	10	does	do	AUX
cana-537	187	11	not	not	PART
cana-537	187	12	always	always	ADV
cana-537	187	13	valid	valid	ADJ
cana-537	187	14	.	.	PUNCT
cana-537	188	1	example	example	NOUN
cana-537	188	2	5.4	5.4	NUM
cana-537	188	3	:	:	PUNCT
cana-537	188	4	let	let	VERB
cana-537	188	5	x1	x1	PROPN
cana-537	188	6	=	=	PUNCT
cana-537	189	1	x2=	x2=	PROPN
cana-537	189	2	{	{	PUNCT
cana-537	189	3	r	r	NOUN
cana-537	189	4	,	,	PUNCT
cana-537	189	5	s	s	PROPN
cana-537	189	6	,	,	PUNCT
cana-537	189	7	t	t	PROPN
cana-537	189	8	}	}	PUNCT
cana-537	189	9	;	;	PUNCT
cana-537	189	10	τ	τ	X
cana-537	189	11	=	=	PUNCT
cana-537	189	12	{	{	PUNCT
cana-537	189	13	x1	x1	PROPN
cana-537	189	14	,	,	PUNCT
cana-537	189	15	φ	φ	PROPN
cana-537	189	16	,	,	PUNCT
cana-537	189	17	{	{	PUNCT
cana-537	189	18	t	t	NOUN
cana-537	189	19	}	}	PUNCT
cana-537	189	20	,	,	PUNCT
cana-537	189	21	{	{	PUNCT
cana-537	189	22	r	r	NOUN
cana-537	189	23	,	,	PUNCT
cana-537	189	24	t	t	NOUN
cana-537	189	25	}	}	PUNCT
cana-537	189	26	}	}	PUNCT
cana-537	189	27	and	and	CCONJ
cana-537	189	28	τc	τc	ADV
cana-537	189	29	=	=	PUNCT
cana-537	189	30	{	{	PUNCT
cana-537	189	31	x1	x1	PROPN
cana-537	189	32	,	,	PUNCT
cana-537	189	33	φ	φ	PROPN
cana-537	189	34	,	,	PUNCT
cana-537	189	35	{	{	PUNCT
cana-537	189	36	r	r	NOUN
cana-537	189	37	,	,	PUNCT
cana-537	189	38	s	s	PART
cana-537	189	39	}	}	PUNCT
cana-537	189	40	,	,	PUNCT
cana-537	189	41	{	{	PUNCT
cana-537	189	42	s	s	X
cana-537	189	43	}	}	PUNCT
cana-537	189	44	}	}	PUNCT
cana-537	189	45	.	.	PUNCT
cana-537	190	1	s*p*c	s*p*c	NOUN
cana-537	190	2	sets	set	NOUN
cana-537	190	3	of	of	ADP
cana-537	190	4	x1	x1	PROPN
cana-537	190	5	are	be	AUX
cana-537	190	6	{	{	PUNCT
cana-537	190	7	x1	x1	PROPN
cana-537	190	8	,	,	PUNCT
cana-537	190	9	φ	φ	PROPN
cana-537	190	10	,	,	PUNCT
cana-537	190	11	{	{	PUNCT
cana-537	190	12	r	r	NOUN
cana-537	190	13	}	}	PUNCT
cana-537	190	14	}	}	PUNCT
cana-537	190	15	.	.	PUNCT
cana-537	191	1	σ	σ	NOUN
cana-537	191	2	=	=	PRON
cana-537	191	3	{	{	PUNCT
cana-537	191	4	x2	x2	PROPN
cana-537	191	5	,	,	PUNCT
cana-537	191	6	φ	φ	PROPN
cana-537	191	7	,	,	PUNCT
cana-537	191	8	{	{	PUNCT
cana-537	191	9	r	r	NOUN
cana-537	191	10	}	}	PUNCT
cana-537	191	11	,	,	PUNCT
cana-537	191	12	{	{	PUNCT
cana-537	191	13	t	t	NOUN
cana-537	191	14	}	}	PUNCT
cana-537	191	15	,	,	PUNCT
cana-537	191	16	{	{	PUNCT
cana-537	191	17	s	s	X
cana-537	191	18	,	,	PUNCT
cana-537	191	19	t	t	PROPN
cana-537	191	20	}	}	PUNCT
cana-537	191	21	,	,	PUNCT
cana-537	191	22	{	{	PUNCT
cana-537	191	23	r	r	NOUN
cana-537	191	24	,	,	PUNCT
cana-537	191	25	t	t	PROPN
cana-537	191	26	}	}	PUNCT
cana-537	191	27	}	}	PUNCT
cana-537	191	28	;	;	PUNCT
cana-537	191	29	σc	σc	PROPN
cana-537	191	30	=	=	SYM
cana-537	191	31	{	{	PUNCT
cana-537	191	32	x2	x2	PROPN
cana-537	191	33	,	,	PUNCT
cana-537	191	34	φ	φ	PROPN
cana-537	191	35	,	,	PUNCT
cana-537	191	36	{	{	PUNCT
cana-537	191	37	s	s	PROPN
cana-537	191	38	,	,	PUNCT
cana-537	191	39	t	t	PROPN
cana-537	191	40	}	}	PUNCT
cana-537	191	41	,	,	PUNCT
cana-537	191	42	{	{	PUNCT
cana-537	191	43	r	r	NOUN
cana-537	191	44	,	,	PUNCT
cana-537	191	45	s	s	PART
cana-537	191	46	}	}	PUNCT
cana-537	191	47	,	,	PUNCT
cana-537	191	48	{	{	PUNCT
cana-537	191	49	r	r	NOUN
cana-537	191	50	}	}	PUNCT
cana-537	191	51	,	,	PUNCT
cana-537	191	52	{	{	PUNCT
cana-537	191	53	s	s	X
cana-537	191	54	}	}	PUNCT
cana-537	191	55	}	}	PUNCT
cana-537	191	56	and	and	CCONJ
cana-537	191	57	s*p	s*p	PROPN
cana-537	191	58	*	*	PUNCT
cana-537	191	59	c	c	PROPN
cana-537	191	60	sets	set	NOUN
cana-537	191	61	of	of	ADP
cana-537	191	62	x2	x2	PROPN
cana-537	191	63	are	be	AUX
cana-537	191	64	{	{	PUNCT
cana-537	191	65	x2	x2	PROPN
cana-537	191	66	,	,	PUNCT
cana-537	191	67	φ	φ	PROPN
cana-537	191	68	,	,	PUNCT
cana-537	191	69	{	{	PUNCT
cana-537	191	70	s	s	X
cana-537	191	71	}	}	PUNCT
cana-537	191	72	,	,	PUNCT
cana-537	191	73	{	{	PUNCT
cana-537	191	74	t	t	NOUN
cana-537	191	75	}	}	PUNCT
cana-537	191	76	,	,	PUNCT
cana-537	191	77	{	{	PUNCT
cana-537	191	78	s	s	PROPN
cana-537	191	79	,	,	PUNCT
cana-537	191	80	t	t	PROPN
cana-537	191	81	}	}	PUNCT
cana-537	191	82	}	}	PUNCT
cana-537	191	83	.	.	PUNCT
cana-537	192	1	assume	assume	VERB
cana-537	192	2	a	a	DET
cana-537	192	3	map	map	NOUN
cana-537	193	1	f	f	X
cana-537	193	2	:	:	PUNCT
cana-537	193	3	x1	x1	PROPN
cana-537	193	4	→	→	SYM
cana-537	193	5	x2	x2	PROPN
cana-537	193	6	by	by	ADP
cana-537	193	7	f(r	f(r	NOUN
cana-537	193	8	)	)	PUNCT
cana-537	194	1	=	=	SYM
cana-537	194	2	r	r	NOUN
cana-537	194	3	;	;	PUNCT
cana-537	194	4	f(s	f(s	X
cana-537	194	5	)	)	PUNCT
cana-537	194	6	=	=	SYM
cana-537	194	7	t	t	PROPN
cana-537	194	8	;	;	PUNCT
cana-537	194	9	f	f	PROPN
cana-537	194	10	(	(	PUNCT
cana-537	194	11	t	t	PROPN
cana-537	194	12	)	)	PUNCT
cana-537	194	13	=	=	VERB
cana-537	195	1	s.	s.	PROPN
cana-537	195	2	then	then	ADV
cana-537	195	3	f	f	PROPN
cana-537	195	4	and	and	CCONJ
cana-537	195	5	its	its	PRON
cana-537	195	6	inverse	inverse	NOUN
cana-537	195	7	are	be	AUX
cana-537	195	8	s*p*continuous	s*p*continuous	ADJ
cana-537	195	9	.	.	PUNCT
cana-537	196	1	so	so	ADV
cana-537	196	2	,	,	PUNCT
cana-537	196	3	f	f	PROPN
cana-537	196	4	does	do	VERB
cana-537	196	5	not	not	PART
cana-537	196	6	a	a	DET
cana-537	196	7	homeomorphism	homeomorphism	NOUN
cana-537	196	8	rather	rather	ADV
cana-537	196	9	than	than	ADP
cana-537	196	10	a	a	DET
cana-537	196	11	s*p*-h	s*p*-h	NOUN
cana-537	196	12	.	.	PUNCT
cana-537	197	1	because	because	SCONJ
cana-537	197	2	the	the	DET
cana-537	197	3	inverse	inverse	NOUN
cana-537	197	4	image	image	NOUN
cana-537	197	5	of	of	ADP
cana-537	197	6	closed	closed	ADJ
cana-537	197	7	map	map	NOUN
cana-537	197	8	{	{	PUNCT
cana-537	197	9	r	r	NOUN
cana-537	197	10	,	,	PUNCT
cana-537	197	11	s	s	PART
cana-537	197	12	}	}	PUNCT
cana-537	197	13	in	in	ADP
cana-537	197	14	(	(	PUNCT
cana-537	197	15	x1	x1	PROPN
cana-537	197	16	,	,	PUNCT
cana-537	197	17	τ	τ	PROPN
cana-537	197	18	)	)	PUNCT
cana-537	197	19	,	,	PUNCT
cana-537	197	20	(	(	PUNCT
cana-537	197	21	f	f	X
cana-537	197	22	-1	-1	ADJ
cana-537	197	23	)	)	PUNCT
cana-537	197	24	-1	-1	PUNCT
cana-537	198	1	(	(	PUNCT
cana-537	198	2	r	r	NOUN
cana-537	198	3	,	,	PUNCT
cana-537	198	4	s	s	NOUN
cana-537	198	5	)	)	PUNCT
cana-537	199	1	=	=	SYM
cana-537	199	2	f	f	X
cana-537	199	3	(	(	PUNCT
cana-537	199	4	r	r	NOUN
cana-537	199	5	,	,	PUNCT
cana-537	199	6	s	s	NOUN
cana-537	199	7	)	)	PUNCT
cana-537	199	8	=	=	SYM
cana-537	199	9	{	{	PUNCT
cana-537	199	10	r	r	NOUN
cana-537	199	11	,	,	PUNCT
cana-537	199	12	t	t	PROPN
cana-537	199	13	}	}	PUNCT
cana-537	199	14	is	be	AUX
cana-537	199	15	not	not	PART
cana-537	199	16	in	in	ADP
cana-537	199	17	closed	closed	ADJ
cana-537	199	18	set	set	VERB
cana-537	199	19	x2	x2	PROPN
cana-537	199	20	.	.	PUNCT
cana-537	200	1	theorem	theorem	VERB
cana-537	200	2	5.5	5.5	NUM
cana-537	200	3	:	:	PUNCT
cana-537	200	4	every	every	DET
cana-537	200	5	𝘢-homeomorphism	𝘢-homeomorphism	NOUN
cana-537	200	6	is	be	AUX
cana-537	200	7	a	a	DET
cana-537	200	8	s*p*-homeomorphism	s*p*-homeomorphism	NOUN
cana-537	200	9	.	.	PUNCT
cana-537	201	1	proof	proof	NOUN
cana-537	201	2	:	:	PUNCT
cana-537	201	3	a	a	DET
cana-537	201	4	α	α	PROPN
cana-537	201	5	homeomorphism	homeomorphism	PROPN
cana-537	201	6	is	be	AUX
cana-537	201	7	x1	x1	PROPN
cana-537	201	8	→	→	SYM
cana-537	201	9	x2	x2	PROPN
cana-537	201	10	.	.	PUNCT
cana-537	202	1	following	follow	VERB
cana-537	202	2	that	that	PRON
cana-537	202	3	f	f	PROPN
cana-537	202	4	and	and	CCONJ
cana-537	202	5	its	its	PRON
cana-537	202	6	inverse	inverse	NOUN
cana-537	202	7	are	be	AUX
cana-537	202	8	α	α	X
cana-537	202	9	-	-	ADJ
cana-537	202	10	continuous	continuous	ADJ
cana-537	202	11	and	and	CCONJ
cana-537	202	12	f	f	PROPN
cana-537	202	13	is	be	AUX
cana-537	202	14	bijection	bijection	ADJ
cana-537	202	15	.	.	PUNCT
cana-537	203	1	f	f	PROPN
cana-537	203	2	and	and	CCONJ
cana-537	203	3	its	its	PRON
cana-537	203	4	inverse	inverse	NOUN
cana-537	203	5	are	be	AUX
cana-537	203	6	s*p	s*p	VERB
cana-537	203	7	*	*	PUNCT
cana-537	203	8	continuous	continuous	ADJ
cana-537	203	9	obtained	obtain	VERB
cana-537	203	10	through	through	ADP
cana-537	203	11	each	each	DET
cana-537	203	12	𝘢continuous	𝘢continuous	ADJ
cana-537	203	13	function	function	NOUN
cana-537	203	14	that	that	PRON
cana-537	203	15	is	be	AUX
cana-537	203	16	s*p*-continuous	s*p*-continuous	ADJ
cana-537	203	17	.	.	PUNCT
cana-537	204	1	accordingly	accordingly	ADV
cana-537	204	2	,	,	PUNCT
cana-537	204	3	f	f	PROPN
cana-537	204	4	is	be	AUX
cana-537	204	5	s*p*-homeomorphism	s*p*-homeomorphism	NOUN
cana-537	204	6	.	.	PUNCT
cana-537	205	1	a	a	DET
cana-537	205	2	further	further	ADJ
cana-537	205	3	illustration	illustration	NOUN
cana-537	205	4	demonstrates	demonstrate	VERB
cana-537	205	5	that	that	SCONJ
cana-537	205	6	the	the	DET
cana-537	205	7	previously	previously	ADV
cana-537	205	8	stated	state	VERB
cana-537	205	9	theorems	theorem	NOUN
cana-537	205	10	reversal	reversal	NOUN
cana-537	205	11	is	be	AUX
cana-537	205	12	not	not	PART
cana-537	205	13	generally	generally	ADV
cana-537	205	14	correct	correct	ADJ
cana-537	205	15	.	.	PUNCT
cana-537	206	1	example	example	NOUN
cana-537	206	2	5.6	5.6	NUM
cana-537	206	3	:	:	PUNCT
cana-537	206	4	let	let	VERB
cana-537	206	5	x1	x1	PROPN
cana-537	206	6	=	=	PUNCT
cana-537	207	1	x2=	x2=	PROPN
cana-537	208	1	{	{	PUNCT
cana-537	208	2	r	r	NOUN
cana-537	208	3	,	,	PUNCT
cana-537	208	4	s	s	PROPN
cana-537	208	5	,	,	PUNCT
cana-537	208	6	t	t	PROPN
cana-537	208	7	}	}	PUNCT
cana-537	208	8	;	;	PUNCT
cana-537	208	9	τ	τ	X
cana-537	208	10	=	=	PUNCT
cana-537	208	11	{	{	PUNCT
cana-537	208	12	x1	x1	PROPN
cana-537	208	13	,	,	PUNCT
cana-537	208	14	φ	φ	PROPN
cana-537	208	15	,	,	PUNCT
cana-537	208	16	{	{	PUNCT
cana-537	208	17	r	r	NOUN
cana-537	208	18	}	}	PUNCT
cana-537	208	19	,	,	PUNCT
cana-537	208	20	{	{	PUNCT
cana-537	208	21	s	s	X
cana-537	208	22	}	}	PUNCT
cana-537	208	23	,	,	PUNCT
cana-537	208	24	{	{	PUNCT
cana-537	208	25	r	r	NOUN
cana-537	208	26	,	,	PUNCT
cana-537	208	27	s	s	PART
cana-537	208	28	}	}	PUNCT
cana-537	208	29	}	}	PUNCT
cana-537	208	30	and	and	CCONJ
cana-537	208	31	τc	τc	ADV
cana-537	208	32	=	=	PUNCT
cana-537	208	33	{	{	PUNCT
cana-537	208	34	x1	x1	PROPN
cana-537	208	35	,	,	PUNCT
cana-537	208	36	φ	φ	PROPN
cana-537	208	37	,	,	PUNCT
cana-537	208	38	{	{	PUNCT
cana-537	208	39	s	s	PROPN
cana-537	208	40	,	,	PUNCT
cana-537	208	41	t	t	PROPN
cana-537	208	42	}	}	PUNCT
cana-537	208	43	,	,	PUNCT
cana-537	208	44	{	{	PUNCT
cana-537	208	45	r	r	NOUN
cana-537	208	46	,	,	PUNCT
cana-537	208	47	t	t	PROPN
cana-537	208	48	}	}	PUNCT
cana-537	208	49	,	,	PUNCT
cana-537	208	50	{	{	PUNCT
cana-537	208	51	t	t	NOUN
cana-537	208	52	}	}	PUNCT
cana-537	208	53	}	}	PUNCT
cana-537	208	54	.	.	PUNCT
cana-537	209	1	s*p*-c	s*p*-c	PROPN
cana-537	209	2	sets	set	NOUN
cana-537	209	3	of	of	ADP
cana-537	209	4	x1	x1	PROPN
cana-537	209	5	are	be	AUX
cana-537	209	6	{	{	PUNCT
cana-537	209	7	x1	x1	PROPN
cana-537	209	8	,	,	PUNCT
cana-537	209	9	φ	φ	PROPN
cana-537	209	10	,	,	PUNCT
cana-537	209	11	{	{	PUNCT
cana-537	209	12	r	r	NOUN
cana-537	209	13	}	}	PUNCT
cana-537	209	14	,	,	PUNCT
cana-537	209	15	{	{	PUNCT
cana-537	209	16	s	s	X
cana-537	209	17	}	}	PUNCT
cana-537	209	18	}	}	PUNCT
cana-537	209	19	and	and	CCONJ
cana-537	209	20	𝘢-closed	𝘢-close	VERB
cana-537	209	21	sets	set	NOUN
cana-537	209	22	of	of	ADP
cana-537	209	23	x1	x1	PROPN
cana-537	209	24	are	be	AUX
cana-537	209	25	{	{	PUNCT
cana-537	209	26	x1	x1	PROPN
cana-537	209	27	,	,	PUNCT
cana-537	209	28	φ	φ	PROPN
cana-537	209	29	,	,	PUNCT
cana-537	209	30	{	{	PUNCT
cana-537	209	31	r	r	NOUN
cana-537	209	32	}	}	PUNCT
cana-537	209	33	,	,	PUNCT
cana-537	209	34	{	{	PUNCT
cana-537	209	35	s	s	X
cana-537	209	36	}	}	PUNCT
cana-537	209	37	,	,	PUNCT
cana-537	209	38	{	{	PUNCT
cana-537	209	39	t	t	NOUN
cana-537	209	40	}	}	PUNCT
cana-537	209	41	,	,	PUNCT
cana-537	209	42	{	{	PUNCT
cana-537	209	43	s	s	X
cana-537	209	44	,	,	PUNCT
cana-537	209	45	t	t	PROPN
cana-537	209	46	}	}	PUNCT
cana-537	209	47	,	,	PUNCT
cana-537	209	48	{	{	PUNCT
cana-537	209	49	r	r	NOUN
cana-537	209	50	,	,	PUNCT
cana-537	209	51	t	t	PROPN
cana-537	209	52	}	}	PUNCT
cana-537	209	53	}	}	PUNCT
cana-537	209	54	.	.	PUNCT
cana-537	210	1	σ	σ	NOUN
cana-537	210	2	=	=	PRON
cana-537	210	3	{	{	PUNCT
cana-537	210	4	x2	x2	PROPN
cana-537	210	5	,	,	PUNCT
cana-537	210	6	φ	φ	PROPN
cana-537	210	7	,	,	PUNCT
cana-537	210	8	{	{	PUNCT
cana-537	210	9	s	s	X
cana-537	210	10	}	}	PUNCT
cana-537	210	11	,	,	PUNCT
cana-537	210	12	{	{	PUNCT
cana-537	210	13	t	t	NOUN
cana-537	210	14	}	}	PUNCT
cana-537	210	15	,	,	PUNCT
cana-537	210	16	{	{	PUNCT
cana-537	210	17	r	r	NOUN
cana-537	210	18	,	,	PUNCT
cana-537	210	19	s	s	PART
cana-537	210	20	}	}	PUNCT
cana-537	210	21	,	,	PUNCT
cana-537	210	22	{	{	PUNCT
cana-537	210	23	s	s	PROPN
cana-537	210	24	,	,	PUNCT
cana-537	210	25	t	t	PROPN
cana-537	210	26	}	}	PUNCT
cana-537	210	27	}	}	PUNCT
cana-537	210	28	;	;	PUNCT
cana-537	210	29	σ	σ	NOUN
cana-537	210	30	c	c	NOUN
cana-537	210	31	=	=	PRON
cana-537	210	32	{	{	PUNCT
cana-537	210	33	x2	x2	PROPN
cana-537	210	34	,	,	PUNCT
cana-537	210	35	φ	φ	PROPN
cana-537	210	36	,	,	PUNCT
cana-537	210	37	{	{	PUNCT
cana-537	210	38	r	r	NOUN
cana-537	210	39	,	,	PUNCT
cana-537	210	40	t	t	PROPN
cana-537	210	41	}	}	PUNCT
cana-537	210	42	,	,	PUNCT
cana-537	210	43	{	{	PUNCT
cana-537	210	44	r	r	NOUN
cana-537	210	45	,	,	PUNCT
cana-537	210	46	s	s	PART
cana-537	210	47	}	}	PUNCT
cana-537	210	48	,	,	PUNCT
cana-537	210	49	{	{	PUNCT
cana-537	210	50	t	t	NOUN
cana-537	210	51	}	}	PUNCT
cana-537	210	52	,	,	PUNCT
cana-537	210	53	{	{	PUNCT
cana-537	210	54	r	r	NOUN
cana-537	210	55	}	}	PUNCT
cana-537	210	56	}	}	PUNCT
cana-537	210	57	and	and	CCONJ
cana-537	210	58	s*p*c	s*p*c	VERB
cana-537	210	59	sets	set	NOUN
cana-537	210	60	of	of	ADP
cana-537	210	61	x2	x2	PRON
cana-537	210	62	are	be	AUX
cana-537	210	63	{	{	PUNCT
cana-537	210	64	x2	x2	PROPN
cana-537	210	65	,	,	PUNCT
cana-537	210	66	φ	φ	PROPN
cana-537	210	67	,	,	PUNCT
cana-537	210	68	{	{	PUNCT
cana-537	210	69	r	r	NOUN
cana-537	210	70	}	}	PUNCT
cana-537	210	71	,	,	PUNCT
cana-537	210	72	{	{	PUNCT
cana-537	210	73	r	r	NOUN
cana-537	210	74	,	,	PUNCT
cana-537	210	75	s	s	PART
cana-537	210	76	}	}	PUNCT
cana-537	210	77	}	}	PUNCT
cana-537	210	78	.	.	PUNCT
cana-537	211	1	𝘢-closed	𝘢-close	VERB
cana-537	211	2	sets	set	NOUN
cana-537	211	3	of	of	ADP
cana-537	211	4	x2	x2	PROPN
cana-537	211	5	are	be	AUX
cana-537	211	6	{	{	PUNCT
cana-537	211	7	x2	x2	PROPN
cana-537	211	8	,	,	PUNCT
cana-537	211	9	φ	φ	PROPN
cana-537	211	10	,	,	PUNCT
cana-537	211	11	{	{	PUNCT
cana-537	211	12	r	r	NOUN
cana-537	211	13	}	}	PUNCT
cana-537	211	14	,	,	PUNCT
cana-537	211	15	{	{	PUNCT
cana-537	211	16	s	s	X
cana-537	211	17	}	}	PUNCT
cana-537	211	18	,	,	PUNCT
cana-537	211	19	{	{	PUNCT
cana-537	211	20	r	r	NOUN
cana-537	211	21	,	,	PUNCT
cana-537	211	22	s	s	PART
cana-537	211	23	}	}	PUNCT
cana-537	211	24	,	,	PUNCT
cana-537	211	25	{	{	PUNCT
cana-537	211	26	r	r	NOUN
cana-537	211	27	,	,	PUNCT
cana-537	211	28	t	t	PROPN
cana-537	211	29	}	}	PUNCT
cana-537	211	30	}	}	PUNCT
cana-537	211	31	.	.	PUNCT
cana-537	212	1	define	define	VERB
cana-537	212	2	a	a	DET
cana-537	212	3	map	map	NOUN
cana-537	213	1	f	f	X
cana-537	213	2	:	:	PUNCT
cana-537	213	3	x1→	x1→	X
cana-537	213	4	x2	x2	INTJ
cana-537	213	5	by	by	ADP
cana-537	213	6	f(r	f(r	NOUN
cana-537	213	7	)	)	PUNCT
cana-537	214	1	=	=	SYM
cana-537	214	2	s	s	NOUN
cana-537	214	3	;	;	PUNCT
cana-537	214	4	f(s	f(s	X
cana-537	214	5	)	)	PUNCT
cana-537	214	6	=	=	SYM
cana-537	215	1	r	r	NOUN
cana-537	215	2	;	;	PUNCT
cana-537	215	3	f	f	PROPN
cana-537	215	4	(	(	PUNCT
cana-537	215	5	t	t	PROPN
cana-537	215	6	)	)	PUNCT
cana-537	215	7	=	=	PUNCT
cana-537	216	1	t.	t.	NOUN
cana-537	216	2	here	here	ADV
cana-537	216	3	f	f	PROPN
cana-537	216	4	is	be	AUX
cana-537	216	5	s*p*-h	s*p*-h	NOUN
cana-537	216	6	but	but	CCONJ
cana-537	216	7	not	not	PART
cana-537	216	8	𝘢homeomorphism	𝘢homeomorphism	NOUN
cana-537	216	9	because	because	SCONJ
cana-537	216	10	the	the	DET
cana-537	216	11	inverse	inverse	NOUN
cana-537	216	12	image	image	NOUN
cana-537	216	13	of	of	ADP
cana-537	216	14	the	the	DET
cana-537	216	15	closed	closed	ADJ
cana-537	216	16	set	set	NOUN
cana-537	216	17	{	{	PUNCT
cana-537	216	18	t	t	NOUN
cana-537	216	19	}	}	PUNCT
cana-537	216	20	in	in	ADP
cana-537	216	21	x1	x1	PROPN
cana-537	216	22	and	and	CCONJ
cana-537	216	23	(	(	PUNCT
cana-537	216	24	f-1	f-1	NOUN
cana-537	216	25	)	)	PUNCT
cana-537	216	26	-1	-1	PUNCT
cana-537	216	27	(	(	PUNCT
cana-537	216	28	t	t	NOUN
cana-537	216	29	)	)	PUNCT
cana-537	216	30	=	=	SYM
cana-537	216	31	f(t	f(t	NOUN
cana-537	216	32	)	)	PUNCT
cana-537	216	33	=	=	PRON
cana-537	216	34	{	{	PUNCT
cana-537	216	35	t	t	NOUN
cana-537	216	36	}	}	PUNCT
cana-537	216	37	is	be	AUX
cana-537	216	38	not	not	PART
cana-537	216	39	in	in	ADP
cana-537	216	40	αclosed	αclosed	ADJ
cana-537	216	41	set	set	NOUN
cana-537	216	42	in	in	ADP
cana-537	216	43	x2	x2	PROPN
cana-537	216	44	.	.	PUNCT
cana-537	217	1	theorem	theorem	VERB
cana-537	217	2	5.7	5.7	NUM
cana-537	217	3	:	:	PUNCT
cana-537	217	4	all	all	DET
cana-537	217	5	ghomeomorphisms	ghomeomorphism	NOUN
cana-537	217	6	are	be	AUX
cana-537	217	7	equivalent	equivalent	ADJ
cana-537	217	8	to	to	ADP
cana-537	217	9	s*p*-homeomorphism	s*p*-homeomorphism	NOUN
cana-537	217	10	.	.	PUNCT
cana-537	218	1	proof	proof	NOUN
cana-537	218	2	:	:	PUNCT
cana-537	218	3	consider	consider	VERB
cana-537	218	4	a	a	DET
cana-537	218	5	ghomeomorphism	ghomeomorphism	NOUN
cana-537	218	6	x1→x2	x1→x2	NOUN
cana-537	218	7	.	.	PUNCT
cana-537	219	1	thus	thus	ADV
cana-537	219	2	,	,	PUNCT
cana-537	219	3	f	f	PROPN
cana-537	219	4	and	and	CCONJ
cana-537	219	5	its	its	PRON
cana-537	219	6	inverse	inverse	NOUN
cana-537	219	7	are	be	AUX
cana-537	219	8	g	g	NOUN
cana-537	219	9	continuous	continuous	ADJ
cana-537	219	10	as	as	ADV
cana-537	219	11	well	well	ADV
cana-537	219	12	as	as	ADP
cana-537	219	13	bijection	bijection	NOUN
cana-537	219	14	.	.	PUNCT
cana-537	220	1	f	f	PROPN
cana-537	220	2	and	and	CCONJ
cana-537	220	3	its	its	PRON
cana-537	220	4	inverse	inverse	NOUN
cana-537	220	5	are	be	AUX
cana-537	220	6	s*p	s*p	VERB
cana-537	220	7	*	*	PUNCT
cana-537	220	8	continuous	continuous	ADJ
cana-537	220	9	this	this	PRON
cana-537	220	10	comes	come	VERB
cana-537	220	11	from	from	ADP
cana-537	220	12	any	any	DET
cana-537	220	13	g	g	NOUN
cana-537	220	14	-	-	PUNCT
cana-537	220	15	continuous	continuous	ADJ
cana-537	220	16	function	function	NOUN
cana-537	220	17	being	be	AUX
cana-537	220	18	s*p	s*p	VERB
cana-537	220	19	*	*	PUNCT
cana-537	220	20	continuous	continuous	ADJ
cana-537	220	21	.	.	PUNCT
cana-537	221	1	because	because	SCONJ
cana-537	221	2	of	of	ADP
cana-537	221	3	this	this	DET
cana-537	221	4	f	f	NOUN
cana-537	221	5	is	be	AUX
cana-537	221	6	s*p*homeomorphism	s*p*homeomorphism	NOUN
cana-537	221	7	.	.	PUNCT
cana-537	222	1	the	the	DET
cana-537	222	2	reverse	reverse	ADJ
cana-537	222	3	implications	implication	NOUN
cana-537	222	4	are	be	AUX
cana-537	222	5	not	not	PART
cana-537	222	6	valid	valid	ADJ
cana-537	222	7	as	as	SCONJ
cana-537	222	8	demonstrated	demonstrate	VERB
cana-537	222	9	from	from	ADP
cana-537	222	10	the	the	DET
cana-537	222	11	below	below	ADJ
cana-537	222	12	example	example	NOUN
cana-537	222	13	.	.	PUNCT
cana-537	223	1	example	example	NOUN
cana-537	223	2	5.8	5.8	NUM
cana-537	223	3	:	:	PUNCT
cana-537	223	4	let	let	VERB
cana-537	223	5	x1	x1	PROPN
cana-537	223	6	=	=	PUNCT
cana-537	224	1	x2=	x2=	PROPN
cana-537	224	2	{	{	PUNCT
cana-537	224	3	r	r	NOUN
cana-537	224	4	,	,	PUNCT
cana-537	224	5	s	s	PROPN
cana-537	224	6	,	,	PUNCT
cana-537	224	7	t	t	PROPN
cana-537	224	8	}	}	PUNCT
cana-537	224	9	;	;	PUNCT
cana-537	224	10	τ	τ	X
cana-537	224	11	=	=	PUNCT
cana-537	224	12	{	{	PUNCT
cana-537	224	13	x1	x1	PROPN
cana-537	224	14	,	,	PUNCT
cana-537	224	15	φ	φ	PROPN
cana-537	224	16	,	,	PUNCT
cana-537	224	17	{	{	PUNCT
cana-537	224	18	t	t	NOUN
cana-537	224	19	}	}	PUNCT
cana-537	224	20	,	,	PUNCT
cana-537	224	21	{	{	PUNCT
cana-537	224	22	r	r	NOUN
cana-537	224	23	,	,	PUNCT
cana-537	224	24	t	t	NOUN
cana-537	224	25	}	}	PUNCT
cana-537	224	26	}	}	PUNCT
cana-537	224	27	and	and	CCONJ
cana-537	224	28	τ	τ	PROPN
cana-537	224	29	c=	c=	NOUN
cana-537	224	30	{	{	PUNCT
cana-537	224	31	x1	x1	PROPN
cana-537	224	32	,	,	PUNCT
cana-537	224	33	φ	φ	PROPN
cana-537	224	34	,	,	PUNCT
cana-537	224	35	{	{	PUNCT
cana-537	224	36	r	r	NOUN
cana-537	224	37	,	,	PUNCT
cana-537	224	38	s	s	PART
cana-537	224	39	}	}	PUNCT
cana-537	224	40	,	,	PUNCT
cana-537	224	41	{	{	PUNCT
cana-537	224	42	s	s	X
cana-537	224	43	}	}	PUNCT
cana-537	224	44	}	}	PUNCT
cana-537	224	45	and	and	CCONJ
cana-537	224	46	s*p*closed	s*p*close	VERB
cana-537	224	47	sets	set	NOUN
cana-537	224	48	of	of	ADP
cana-537	224	49	x1	x1	NOUN
cana-537	224	50	=	=	SYM
cana-537	224	51	{	{	PUNCT
cana-537	224	52	x1	x1	PROPN
cana-537	224	53	,	,	PUNCT
cana-537	224	54	φ	φ	PROPN
cana-537	224	55	,	,	PUNCT
cana-537	224	56	{	{	PUNCT
cana-537	224	57	r	r	NOUN
cana-537	224	58	}	}	PUNCT
cana-537	224	59	}	}	PUNCT
cana-537	224	60	.	.	PUNCT
cana-537	225	1	g	g	PROPN
cana-537	225	2	closed	close	VERB
cana-537	225	3	sets	set	NOUN
cana-537	225	4	of	of	ADP
cana-537	225	5	x1	x1	NOUN
cana-537	225	6	=	=	SYM
cana-537	225	7	{	{	PUNCT
cana-537	225	8	x1	x1	PROPN
cana-537	225	9	,	,	PUNCT
cana-537	225	10	φ	φ	PROPN
cana-537	225	11	,	,	PUNCT
cana-537	225	12	{	{	PUNCT
cana-537	225	13	s	s	X
cana-537	225	14	}	}	PUNCT
cana-537	225	15	,	,	PUNCT
cana-537	225	16	{	{	PUNCT
cana-537	225	17	r	r	NOUN
cana-537	225	18	,	,	PUNCT
cana-537	225	19	s	s	PART
cana-537	225	20	}	}	PUNCT
cana-537	225	21	,	,	PUNCT
cana-537	225	22	{	{	PUNCT
cana-537	225	23	s	s	PROPN
cana-537	225	24	,	,	PUNCT
cana-537	225	25	t	t	PROPN
cana-537	225	26	}	}	PUNCT
cana-537	225	27	}	}	PUNCT
cana-537	225	28	.	.	PUNCT
cana-537	226	1	σ	σ	NOUN
cana-537	226	2	=	=	PRON
cana-537	226	3	{	{	PUNCT
cana-537	226	4	x2	x2	PROPN
cana-537	226	5	,	,	PUNCT
cana-537	226	6	φ	φ	PROPN
cana-537	226	7	,	,	PUNCT
cana-537	226	8	{	{	PUNCT
cana-537	226	9	r	r	NOUN
cana-537	226	10	}	}	PUNCT
cana-537	226	11	,	,	PUNCT
cana-537	226	12	{	{	PUNCT
cana-537	226	13	t	t	NOUN
cana-537	226	14	}	}	PUNCT
cana-537	226	15	,	,	PUNCT
cana-537	226	16	{	{	PUNCT
cana-537	226	17	s	s	X
cana-537	226	18	,	,	PUNCT
cana-537	226	19	t	t	PROPN
cana-537	226	20	}	}	PUNCT
cana-537	226	21	,	,	PUNCT
cana-537	226	22	{	{	PUNCT
cana-537	226	23	r	r	NOUN
cana-537	226	24	,	,	PUNCT
cana-537	226	25	t	t	PROPN
cana-537	226	26	}	}	PUNCT
cana-537	226	27	}	}	PUNCT
cana-537	226	28	;	;	PUNCT
cana-537	226	29	σc	σc	PROPN
cana-537	226	30	=	=	SYM
cana-537	226	31	{	{	PUNCT
cana-537	226	32	x2	x2	PROPN
cana-537	226	33	,	,	PUNCT
cana-537	226	34	φ	φ	PROPN
cana-537	226	35	,	,	PUNCT
cana-537	226	36	{	{	PUNCT
cana-537	226	37	s	s	PROPN
cana-537	226	38	,	,	PUNCT
cana-537	226	39	t	t	PROPN
cana-537	226	40	}	}	PUNCT
cana-537	226	41	,	,	PUNCT
cana-537	226	42	{	{	PUNCT
cana-537	226	43	r	r	NOUN
cana-537	226	44	,	,	PUNCT
cana-537	226	45	s	s	PART
cana-537	226	46	}	}	PUNCT
cana-537	226	47	,	,	PUNCT
cana-537	226	48	{	{	PUNCT
cana-537	226	49	r	r	NOUN
cana-537	226	50	}	}	PUNCT
cana-537	226	51	,	,	PUNCT
cana-537	226	52	{	{	PUNCT
cana-537	226	53	s	s	X
cana-537	226	54	}	}	PUNCT
cana-537	226	55	}	}	PUNCT
cana-537	226	56	and	and	CCONJ
cana-537	226	57	s*p*-c	s*p*-c	PROPN
cana-537	226	58	sets	set	NOUN
cana-537	226	59	of	of	ADP
cana-537	226	60	x2	x2	PROPN
cana-537	226	61	are	be	AUX
cana-537	226	62	{	{	PUNCT
cana-537	226	63	x2	x2	PROPN
cana-537	226	64	,	,	PUNCT
cana-537	226	65	φ	φ	PROPN
cana-537	226	66	,	,	PUNCT
cana-537	226	67	{	{	PUNCT
cana-537	226	68	s	s	X
cana-537	226	69	}	}	PUNCT
cana-537	226	70	,	,	PUNCT
cana-537	226	71	{	{	PUNCT
cana-537	226	72	t	t	NOUN
cana-537	226	73	}	}	PUNCT
cana-537	226	74	,	,	PUNCT
cana-537	226	75	{	{	PUNCT
cana-537	226	76	s	s	PROPN
cana-537	226	77	,	,	PUNCT
cana-537	226	78	t	t	PROPN
cana-537	226	79	}	}	PUNCT
cana-537	226	80	}	}	PUNCT
cana-537	226	81	.	.	PUNCT
cana-537	227	1	g	g	PROPN
cana-537	227	2	closed	close	VERB
cana-537	227	3	sets	set	NOUN
cana-537	227	4	of	of	ADP
cana-537	227	5	x2	x2	PROPN
cana-537	227	6	are	be	AUX
cana-537	227	7	{	{	PUNCT
cana-537	227	8	x2	x2	PROPN
cana-537	227	9	,	,	PUNCT
cana-537	227	10	φ	φ	PROPN
cana-537	227	11	,	,	PUNCT
cana-537	227	12	{	{	PUNCT
cana-537	227	13	s	s	X
cana-537	227	14	}	}	PUNCT
cana-537	227	15	,	,	PUNCT
cana-537	227	16	{	{	PUNCT
cana-537	227	17	t	t	NOUN
cana-537	227	18	}	}	PUNCT
cana-537	227	19	,	,	PUNCT
cana-537	227	20	{	{	PUNCT
cana-537	227	21	s	s	PROPN
cana-537	227	22	,	,	PUNCT
cana-537	227	23	t	t	PROPN
cana-537	227	24	}	}	PUNCT
cana-537	227	25	}	}	PUNCT
cana-537	227	26	.	.	PUNCT
cana-537	228	1	declare	declare	VERB
cana-537	228	2	a	a	DET
cana-537	228	3	map	map	NOUN
cana-537	229	1	f	f	X
cana-537	229	2	:	:	PUNCT
cana-537	229	3	x1→	x1→	X
cana-537	229	4	x2	x2	INTJ
cana-537	229	5	by	by	ADP
cana-537	229	6	f(r	f(r	NOUN
cana-537	229	7	)	)	PUNCT
cana-537	230	1	=	=	SYM
cana-537	230	2	r	r	NOUN
cana-537	230	3	;	;	PUNCT
cana-537	230	4	f(s	f(s	X
cana-537	230	5	)	)	PUNCT
cana-537	230	6	=	=	SYM
cana-537	230	7	s	s	X
cana-537	230	8	;	;	PUNCT
cana-537	230	9	f	f	PROPN
cana-537	230	10	(	(	PUNCT
cana-537	230	11	t	t	PROPN
cana-537	230	12	)	)	PUNCT
cana-537	230	13	=	=	SYM
cana-537	231	1	t.	t.	NOUN
cana-537	231	2	hence	hence	ADV
cana-537	231	3	f	f	PROPN
cana-537	231	4	does	do	VERB
cana-537	231	5	not	not	PART
cana-537	231	6	a	a	DET
cana-537	231	7	g	g	NOUN
cana-537	231	8	-	-	PUNCT
cana-537	231	9	homeomorphism	homeomorphism	PROPN
cana-537	231	10	rather	rather	ADV
cana-537	231	11	than	than	ADP
cana-537	231	12	a	a	DET
cana-537	231	13	s*p*-h	s*p*-h	NOUN
cana-537	231	14	.	.	PUNCT
cana-537	232	1	because	because	SCONJ
cana-537	232	2	the	the	DET
cana-537	232	3	inverse	inverse	NOUN
cana-537	232	4	image	image	NOUN
cana-537	232	5	of	of	ADP
cana-537	232	6	closed	closed	ADJ
cana-537	232	7	map	map	NOUN
cana-537	232	8	{	{	PUNCT
cana-537	232	9	s	s	NOUN
cana-537	232	10	}	}	PUNCT
cana-537	232	11	in	in	ADP
cana-537	232	12	(	(	PUNCT
cana-537	232	13	x1	x1	PROPN
cana-537	232	14	,	,	PUNCT
cana-537	232	15	τ	τ	PROPN
cana-537	232	16	)	)	PUNCT
cana-537	232	17	,	,	PUNCT
cana-537	232	18	(	(	PUNCT
cana-537	232	19	f-1)-1	f-1)-1	NOUN
cana-537	232	20	(	(	PUNCT
cana-537	232	21	r	r	NOUN
cana-537	232	22	,	,	PUNCT
cana-537	232	23	s	s	NOUN
cana-537	232	24	)	)	PUNCT
cana-537	232	25	=	=	SYM
cana-537	232	26	f	f	X
cana-537	232	27	(	(	PUNCT
cana-537	232	28	r	r	NOUN
cana-537	232	29	,	,	PUNCT
cana-537	232	30	s	s	NOUN
cana-537	232	31	)	)	PUNCT
cana-537	232	32	=	=	SYM
cana-537	232	33	{	{	PUNCT
cana-537	232	34	r	r	NOUN
cana-537	232	35	,	,	PUNCT
cana-537	232	36	s	s	PART
cana-537	232	37	}	}	PUNCT
cana-537	232	38	is	be	AUX
cana-537	232	39	not	not	PART
cana-537	232	40	in	in	ADP
cana-537	232	41	gclosed	gclosed	ADJ
cana-537	232	42	set	set	VERB
cana-537	232	43	in	in	ADP
cana-537	232	44	x2	x2	PROPN
cana-537	232	45	.	.	PUNCT
cana-537	233	1	communications	communication	NOUN
cana-537	233	2	on	on	ADP
cana-537	233	3	applied	apply	VERB
cana-537	233	4	nonlinear	nonlinear	ADJ
cana-537	233	5	analysis	analysis	NOUN
cana-537	233	6	issn	issn	NOUN
cana-537	233	7	:	:	PUNCT
cana-537	233	8	1074	1074	NUM
cana-537	233	9	-	-	PUNCT
cana-537	233	10	133x	133x	NUM
cana-537	233	11	vol	vol	NOUN
cana-537	233	12	31	31	NUM
cana-537	233	13	no	no	NOUN
cana-537	233	14	.	.	NOUN
cana-537	233	15	2	2	NUM
cana-537	233	16	(	(	PUNCT
cana-537	233	17	2024	2024	NUM
cana-537	233	18	)	)	PUNCT
cana-537	233	19	222	222	NUM
cana-537	233	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-537	233	21	remark	remark	NOUN
cana-537	233	22	5.9	5.9	NUM
cana-537	233	23	:	:	PUNCT
cana-537	233	24	the	the	DET
cana-537	233	25	example	example	NOUN
cana-537	233	26	that	that	PRON
cana-537	233	27	comes	come	VERB
cana-537	233	28	next	next	ADJ
cana-537	233	29	points	point	NOUN
cana-537	233	30	out	out	ADP
cana-537	233	31	the	the	DET
cana-537	233	32	independence	independence	NOUN
cana-537	233	33	of	of	ADP
cana-537	233	34	s*p*-h	s*p*-h	NOUN
cana-537	233	35	and	and	CCONJ
cana-537	233	36	αg	αg	NOUN
cana-537	233	37	homeomorphism	homeomorphism	NOUN
cana-537	233	38	.	.	PUNCT
cana-537	234	1	example	example	NOUN
cana-537	234	2	5.10	5.10	NUM
cana-537	234	3	:	:	PUNCT
cana-537	234	4	let	let	VERB
cana-537	234	5	x1=	x1=	PROPN
cana-537	234	6	x2=	x2=	PROPN
cana-537	235	1	{	{	PUNCT
cana-537	235	2	q	q	NOUN
cana-537	235	3	,	,	PUNCT
cana-537	235	4	r	r	NOUN
cana-537	235	5	,	,	PUNCT
cana-537	235	6	s	s	PROPN
cana-537	235	7	,	,	PUNCT
cana-537	235	8	t	t	PROPN
cana-537	235	9	}	}	PUNCT
cana-537	235	10	;	;	PUNCT
cana-537	235	11	τ	τ	X
cana-537	235	12	=	=	PUNCT
cana-537	235	13	{	{	PUNCT
cana-537	235	14	x1	x1	PROPN
cana-537	235	15	,	,	PUNCT
cana-537	235	16	φ	φ	PROPN
cana-537	235	17	,	,	PUNCT
cana-537	235	18	{	{	PUNCT
cana-537	235	19	q	q	X
cana-537	235	20	}	}	PUNCT
cana-537	235	21	,	,	PUNCT
cana-537	235	22	{	{	PUNCT
cana-537	235	23	r	r	NOUN
cana-537	235	24	}	}	PUNCT
cana-537	235	25	,	,	PUNCT
cana-537	235	26	{	{	PUNCT
cana-537	235	27	q	q	X
cana-537	235	28	,	,	PUNCT
cana-537	235	29	r	r	NOUN
cana-537	235	30	}	}	PUNCT
cana-537	235	31	,	,	PUNCT
cana-537	235	32	{	{	PUNCT
cana-537	235	33	q	q	X
cana-537	235	34	,	,	PUNCT
cana-537	235	35	r	r	NOUN
cana-537	235	36	,	,	PUNCT
cana-537	235	37	s	s	PART
cana-537	235	38	}	}	PUNCT
cana-537	235	39	}	}	PUNCT
cana-537	235	40	and	and	CCONJ
cana-537	235	41	τc	τc	ADV
cana-537	235	42	=	=	PUNCT
cana-537	235	43	{	{	PUNCT
cana-537	235	44	x1	x1	PROPN
cana-537	235	45	,	,	PUNCT
cana-537	235	46	φ	φ	PROPN
cana-537	235	47	,	,	PUNCT
cana-537	235	48	{	{	PUNCT
cana-537	235	49	r	r	NOUN
cana-537	235	50	,	,	PUNCT
cana-537	235	51	s	s	PROPN
cana-537	235	52	,	,	PUNCT
cana-537	235	53	t	t	PROPN
cana-537	235	54	}	}	PUNCT
cana-537	235	55	,	,	PUNCT
cana-537	235	56	{	{	PUNCT
cana-537	235	57	q	q	X
cana-537	235	58	,	,	PUNCT
cana-537	235	59	s	s	PROPN
cana-537	235	60	,	,	PUNCT
cana-537	235	61	t	t	PROPN
cana-537	235	62	}	}	PUNCT
cana-537	235	63	,	,	PUNCT
cana-537	235	64	{	{	PUNCT
cana-537	235	65	s	s	X
cana-537	235	66	,	,	PUNCT
cana-537	235	67	t	t	PROPN
cana-537	235	68	}	}	PUNCT
cana-537	235	69	,	,	PUNCT
cana-537	235	70	{	{	PUNCT
cana-537	235	71	t	t	NOUN
cana-537	235	72	}	}	PUNCT
cana-537	235	73	}	}	PUNCT
cana-537	235	74	.	.	PUNCT
cana-537	236	1	s*p*-c	s*p*-c	PROPN
cana-537	236	2	sets	set	NOUN
cana-537	236	3	of	of	ADP
cana-537	236	4	x1	x1	PROPN
cana-537	236	5	are	be	AUX
cana-537	236	6	{	{	PUNCT
cana-537	236	7	x1	x1	PROPN
cana-537	236	8	,	,	PUNCT
cana-537	236	9	φ	φ	PROPN
cana-537	236	10	,	,	PUNCT
cana-537	236	11	{	{	PUNCT
cana-537	236	12	q	q	X
cana-537	236	13	}	}	PUNCT
cana-537	236	14	,	,	PUNCT
cana-537	236	15	{	{	PUNCT
cana-537	236	16	r	r	NOUN
cana-537	236	17	}	}	PUNCT
cana-537	236	18	,	,	PUNCT
cana-537	236	19	{	{	PUNCT
cana-537	236	20	t	t	NOUN
cana-537	236	21	}	}	PUNCT
cana-537	236	22	,	,	PUNCT
cana-537	236	23	{	{	PUNCT
cana-537	236	24	r	r	NOUN
cana-537	236	25	,	,	PUNCT
cana-537	236	26	t	t	PROPN
cana-537	236	27	}	}	PUNCT
cana-537	236	28	,	,	PUNCT
cana-537	236	29	{	{	PUNCT
cana-537	236	30	q	q	NOUN
cana-537	236	31	,	,	PUNCT
cana-537	236	32	t	t	PROPN
cana-537	236	33	}	}	PUNCT
cana-537	236	34	}	}	PUNCT
cana-537	236	35	.	.	PUNCT
cana-537	237	1	σ	σ	NOUN
cana-537	237	2	=	=	PRON
cana-537	237	3	{	{	PUNCT
cana-537	237	4	x2	x2	PROPN
cana-537	237	5	,	,	PUNCT
cana-537	237	6	φ	φ	PROPN
cana-537	237	7	,	,	PUNCT
cana-537	237	8	{	{	PUNCT
cana-537	237	9	q	q	X
cana-537	237	10	}	}	PUNCT
cana-537	237	11	,	,	PUNCT
cana-537	237	12	{	{	PUNCT
cana-537	237	13	s	s	X
cana-537	237	14	}	}	PUNCT
cana-537	237	15	,	,	PUNCT
cana-537	237	16	{	{	PUNCT
cana-537	237	17	t	t	NOUN
cana-537	237	18	}	}	PUNCT
cana-537	237	19	,	,	PUNCT
cana-537	237	20	{	{	PUNCT
cana-537	237	21	q	q	X
cana-537	237	22	,	,	PUNCT
cana-537	237	23	s	s	PART
cana-537	237	24	}	}	PUNCT
cana-537	237	25	,	,	PUNCT
cana-537	237	26	{	{	PUNCT
cana-537	237	27	q	q	NOUN
cana-537	237	28	,	,	PUNCT
cana-537	237	29	t	t	PROPN
cana-537	237	30	}	}	PUNCT
cana-537	237	31	,	,	PUNCT
cana-537	237	32	{	{	PUNCT
cana-537	237	33	s	s	X
cana-537	237	34	,	,	PUNCT
cana-537	237	35	t	t	PROPN
cana-537	237	36	}	}	PUNCT
cana-537	237	37	,	,	PUNCT
cana-537	237	38	{	{	PUNCT
cana-537	237	39	q	q	X
cana-537	237	40	,	,	PUNCT
cana-537	237	41	s	s	PROPN
cana-537	237	42	,	,	PUNCT
cana-537	237	43	t	t	PROPN
cana-537	237	44	}	}	PUNCT
cana-537	237	45	}	}	PUNCT
cana-537	237	46	and	and	CCONJ
cana-537	237	47	σc	σc	PROPN
cana-537	237	48	=	=	SYM
cana-537	237	49	{	{	PUNCT
cana-537	237	50	x2	x2	PROPN
cana-537	237	51	,	,	PUNCT
cana-537	237	52	φ	φ	PROPN
cana-537	237	53	,	,	PUNCT
cana-537	237	54	{	{	PUNCT
cana-537	237	55	r	r	NOUN
cana-537	237	56	,	,	PUNCT
cana-537	237	57	s	s	PROPN
cana-537	237	58	,	,	PUNCT
cana-537	237	59	t	t	PROPN
cana-537	237	60	}	}	PUNCT
cana-537	237	61	,	,	PUNCT
cana-537	237	62	{	{	PUNCT
cana-537	237	63	q	q	X
cana-537	237	64	,	,	PUNCT
cana-537	237	65	r	r	NOUN
cana-537	237	66	,	,	PUNCT
cana-537	237	67	t	t	PROPN
cana-537	237	68	}	}	PUNCT
cana-537	237	69	,	,	PUNCT
cana-537	237	70	{	{	PUNCT
cana-537	237	71	q	q	X
cana-537	237	72	,	,	PUNCT
cana-537	237	73	r	r	NOUN
cana-537	237	74	,	,	PUNCT
cana-537	237	75	s	s	PART
cana-537	237	76	}	}	PUNCT
cana-537	237	77	,	,	PUNCT
cana-537	237	78	{	{	PUNCT
cana-537	237	79	r	r	NOUN
cana-537	237	80	,	,	PUNCT
cana-537	237	81	t	t	PROPN
cana-537	237	82	}	}	PUNCT
cana-537	237	83	,	,	PUNCT
cana-537	237	84	{	{	PUNCT
cana-537	237	85	r	r	NOUN
cana-537	237	86	,	,	PUNCT
cana-537	237	87	s	s	PART
cana-537	237	88	}	}	PUNCT
cana-537	237	89	,	,	PUNCT
cana-537	237	90	{	{	PUNCT
cana-537	237	91	q	q	X
cana-537	237	92	,	,	PUNCT
cana-537	237	93	r	r	NOUN
cana-537	237	94	}	}	PUNCT
cana-537	237	95	,	,	PUNCT
cana-537	237	96	{	{	PUNCT
cana-537	237	97	r	r	NOUN
cana-537	237	98	}	}	PUNCT
cana-537	237	99	}	}	PUNCT
cana-537	237	100	and	and	CCONJ
cana-537	237	101	s*p*-c	s*p*-c	PROPN
cana-537	237	102	sets	set	NOUN
cana-537	237	103	of	of	ADP
cana-537	237	104	x2	x2	PROPN
cana-537	237	105	are	be	AUX
cana-537	237	106	{	{	PUNCT
cana-537	237	107	x2	x2	PROPN
cana-537	237	108	,	,	PUNCT
cana-537	237	109	φ	φ	PROPN
cana-537	237	110	,	,	PUNCT
cana-537	237	111	{	{	PUNCT
cana-537	237	112	q	q	X
cana-537	237	113	}	}	PUNCT
cana-537	237	114	,	,	PUNCT
cana-537	237	115	{	{	PUNCT
cana-537	237	116	s	s	X
cana-537	237	117	}	}	PUNCT
cana-537	237	118	,	,	PUNCT
cana-537	237	119	{	{	PUNCT
cana-537	237	120	t	t	NOUN
cana-537	237	121	}	}	PUNCT
cana-537	237	122	,	,	PUNCT
cana-537	237	123	{	{	PUNCT
cana-537	237	124	q	q	X
cana-537	237	125	,	,	PUNCT
cana-537	237	126	s	s	PART
cana-537	237	127	}	}	PUNCT
cana-537	237	128	,	,	PUNCT
cana-537	237	129	{	{	PUNCT
cana-537	237	130	q	q	NOUN
cana-537	237	131	,	,	PUNCT
cana-537	237	132	t	t	PROPN
cana-537	237	133	}	}	PUNCT
cana-537	237	134	,	,	PUNCT
cana-537	237	135	{	{	PUNCT
cana-537	237	136	s	s	PROPN
cana-537	237	137	,	,	PUNCT
cana-537	237	138	t	t	PROPN
cana-537	237	139	}	}	PUNCT
cana-537	237	140	}	}	PUNCT
cana-537	237	141	.	.	PUNCT
cana-537	238	1	αg	αg	PROPN
cana-537	238	2	closed	close	VERB
cana-537	238	3	sets	set	NOUN
cana-537	238	4	of	of	ADP
cana-537	238	5	x2	x2	PROPN
cana-537	238	6	are	be	AUX
cana-537	238	7	{	{	PUNCT
cana-537	238	8	x2	x2	PROPN
cana-537	238	9	,	,	PUNCT
cana-537	238	10	φ	φ	PROPN
cana-537	238	11	,	,	PUNCT
cana-537	238	12	{	{	PUNCT
cana-537	238	13	r	r	NOUN
cana-537	238	14	}	}	PUNCT
cana-537	238	15	,	,	PUNCT
cana-537	238	16	{	{	PUNCT
cana-537	238	17	q	q	X
cana-537	238	18	,	,	PUNCT
cana-537	238	19	r	r	NOUN
cana-537	238	20	}	}	PUNCT
cana-537	238	21	,	,	PUNCT
cana-537	238	22	{	{	PUNCT
cana-537	238	23	r	r	NOUN
cana-537	238	24	,	,	PUNCT
cana-537	238	25	t	t	PROPN
cana-537	238	26	}	}	PUNCT
cana-537	238	27	,	,	PUNCT
cana-537	238	28	{	{	PUNCT
cana-537	238	29	q	q	X
cana-537	238	30	,	,	PUNCT
cana-537	238	31	r	r	NOUN
cana-537	238	32	,	,	PUNCT
cana-537	238	33	s	s	PART
cana-537	238	34	}	}	PUNCT
cana-537	238	35	,	,	PUNCT
cana-537	238	36	{	{	PUNCT
cana-537	238	37	q	q	X
cana-537	238	38	,	,	PUNCT
cana-537	238	39	r	r	NOUN
cana-537	238	40	,	,	PUNCT
cana-537	238	41	t	t	PROPN
cana-537	238	42	}	}	PUNCT
cana-537	238	43	,	,	PUNCT
cana-537	238	44	{	{	PUNCT
cana-537	238	45	r	r	NOUN
cana-537	238	46	,	,	PUNCT
cana-537	238	47	s	s	PROPN
cana-537	238	48	,	,	PUNCT
cana-537	238	49	t	t	PROPN
cana-537	238	50	}	}	PUNCT
cana-537	238	51	}	}	PUNCT
cana-537	238	52	.	.	PUNCT
cana-537	239	1	assume	assume	VERB
cana-537	239	2	a	a	DET
cana-537	239	3	map	map	NOUN
cana-537	240	1	f	f	X
cana-537	240	2	:	:	PUNCT
cana-537	240	3	x1→	x1→	X
cana-537	240	4	x2	x2	INTJ
cana-537	240	5	by	by	ADP
cana-537	240	6	f(q	f(q	NOUN
cana-537	240	7	)	)	PUNCT
cana-537	240	8	=	=	SYM
cana-537	241	1	q	q	ADJ
cana-537	241	2	;	;	PUNCT
cana-537	241	3	f(r	f(r	X
cana-537	241	4	)	)	PUNCT
cana-537	241	5	=	=	SYM
cana-537	241	6	t	t	PROPN
cana-537	241	7	;	;	PUNCT
cana-537	241	8	f	f	PROPN
cana-537	241	9	(	(	PUNCT
cana-537	241	10	s	s	NOUN
cana-537	241	11	)	)	PUNCT
cana-537	241	12	=	=	SYM
cana-537	241	13	r	r	NOUN
cana-537	241	14	;	;	PUNCT
cana-537	241	15	f(t	f(t	NOUN
cana-537	241	16	)	)	PUNCT
cana-537	241	17	=	=	SYM
cana-537	242	1	s.	s.	PROPN
cana-537	242	2	hence	hence	ADV
cana-537	242	3	f	f	PROPN
cana-537	242	4	does	do	VERB
cana-537	242	5	not	not	PART
cana-537	242	6	a	a	DET
cana-537	242	7	αg	αg	NOUN
cana-537	242	8	homeomorphism	homeomorphism	NOUN
cana-537	242	9	rather	rather	ADV
cana-537	242	10	than	than	ADP
cana-537	242	11	s*p*-h	s*p*-h	NOUN
cana-537	242	12	.	.	PUNCT
cana-537	243	1	hence	hence	ADV
cana-537	243	2	the	the	DET
cana-537	243	3	image	image	NOUN
cana-537	243	4	of	of	ADP
cana-537	243	5	closed	closed	ADJ
cana-537	243	6	set	set	NOUN
cana-537	243	7	{	{	PUNCT
cana-537	243	8	u	u	NOUN
cana-537	243	9	}	}	PUNCT
cana-537	243	10	in	in	ADP
cana-537	243	11	(	(	PUNCT
cana-537	243	12	x1	x1	PROPN
cana-537	243	13	,	,	PUNCT
cana-537	243	14	τ	τ	PROPN
cana-537	243	15	)	)	PUNCT
cana-537	243	16	,	,	PUNCT
cana-537	243	17	(	(	PUNCT
cana-537	243	18	f-1	f-1	NOUN
cana-537	243	19	)	)	PUNCT
cana-537	243	20	-1	-1	PUNCT
cana-537	244	1	(	(	PUNCT
cana-537	244	2	t	t	NOUN
cana-537	244	3	)	)	PUNCT
cana-537	244	4	=	=	SYM
cana-537	245	1	f	f	PROPN
cana-537	245	2	(	(	PUNCT
cana-537	245	3	t	t	PROPN
cana-537	245	4	)	)	PUNCT
cana-537	245	5	=	=	PRON
cana-537	245	6	{	{	PUNCT
cana-537	245	7	s	s	X
cana-537	245	8	}	}	PUNCT
cana-537	245	9	is	be	AUX
cana-537	245	10	does	do	AUX
cana-537	245	11	not	not	PART
cana-537	245	12	in	in	ADP
cana-537	245	13	αg	αg	NUM
cana-537	245	14	closed	close	VERB
cana-537	245	15	set	set	VERB
cana-537	245	16	in	in	ADP
cana-537	245	17	x2	x2	PROPN
cana-537	245	18	.	.	PUNCT
cana-537	246	1	also	also	ADV
cana-537	246	2	,	,	PUNCT
cana-537	246	3	f	f	PROPN
cana-537	246	4	is	be	AUX
cana-537	246	5	αg	αg	PROPN
cana-537	246	6	homeomorphism	homeomorphism	NOUN
cana-537	246	7	but	but	CCONJ
cana-537	246	8	not	not	PART
cana-537	246	9	s*p	s*p	PROPN
cana-537	246	10	*	*	PROPN
cana-537	246	11	h	h	NOUN
cana-537	246	12	,	,	PUNCT
cana-537	246	13	consider	consider	VERB
cana-537	246	14	the	the	DET
cana-537	246	15	closed	closed	ADJ
cana-537	246	16	set	set	NOUN
cana-537	246	17	{	{	PUNCT
cana-537	246	18	q	q	NOUN
cana-537	246	19	,	,	PUNCT
cana-537	246	20	s	s	PROPN
cana-537	246	21	,	,	PUNCT
cana-537	246	22	t	t	PROPN
cana-537	246	23	}	}	PUNCT
cana-537	246	24	in	in	ADP
cana-537	246	25	(	(	PUNCT
cana-537	246	26	x1	x1	PROPN
cana-537	246	27	,	,	PUNCT
cana-537	246	28	τ	τ	PROPN
cana-537	246	29	)	)	PUNCT
cana-537	246	30	,	,	PUNCT
cana-537	246	31	then	then	ADV
cana-537	246	32	its	its	PRON
cana-537	246	33	inverse	inverse	NOUN
cana-537	246	34	image	image	NOUN
cana-537	246	35	(	(	PUNCT
cana-537	246	36	f-1)-1	f-1)-1	PROPN
cana-537	246	37	(	(	PUNCT
cana-537	246	38	q	q	NOUN
cana-537	246	39	,	,	PUNCT
cana-537	246	40	s	s	PROPN
cana-537	246	41	,	,	PUNCT
cana-537	246	42	t	t	PROPN
cana-537	246	43	)	)	PUNCT
cana-537	247	1	=	=	SYM
cana-537	247	2	f	f	X
cana-537	247	3	(	(	PUNCT
cana-537	247	4	q	q	PROPN
cana-537	247	5	,	,	PUNCT
cana-537	247	6	s	s	PROPN
cana-537	247	7	,	,	PUNCT
cana-537	247	8	t	t	PROPN
cana-537	247	9	)	)	PUNCT
cana-537	247	10	=	=	PRON
cana-537	247	11	{	{	PUNCT
cana-537	247	12	q	q	X
cana-537	247	13	,	,	PUNCT
cana-537	247	14	r	r	NOUN
cana-537	247	15	,	,	PUNCT
cana-537	247	16	s	s	PART
cana-537	247	17	}	}	PUNCT
cana-537	247	18	is	be	AUX
cana-537	247	19	not	not	PART
cana-537	247	20	in	in	ADP
cana-537	247	21	s*p*-c	s*p*-c	PROPN
cana-537	247	22	set	set	VERB
cana-537	247	23	in	in	ADP
cana-537	247	24	x2	x2	PROPN
cana-537	247	25	.	.	PUNCT
cana-537	248	1	6	6	NUM
cana-537	248	2	.	.	X
cana-537	248	3	conclusion	conclusion	NOUN
cana-537	248	4	in	in	ADP
cana-537	248	5	this	this	DET
cana-537	248	6	paper	paper	NOUN
cana-537	248	7	,	,	PUNCT
cana-537	248	8	we	we	PRON
cana-537	248	9	derived	derive	VERB
cana-537	248	10	unique	unique	ADJ
cana-537	248	11	features	feature	NOUN
cana-537	248	12	of	of	ADP
cana-537	248	13	s*p*closed	s*p*close	VERB
cana-537	248	14	map	map	NOUN
cana-537	248	15	and	and	CCONJ
cana-537	248	16	even	even	ADV
cana-537	248	17	s*p*homeomorphism	s*p*homeomorphism	NOUN
cana-537	248	18	via	via	ADP
cana-537	248	19	s*p*continuous	s*p*continuous	ADJ
cana-537	248	20	and	and	CCONJ
cana-537	248	21	many	many	ADJ
cana-537	248	22	of	of	ADP
cana-537	248	23	the	the	DET
cana-537	248	24	implications	implication	NOUN
cana-537	248	25	,	,	PUNCT
cana-537	248	26	relations	relation	NOUN
cana-537	248	27	and	and	CCONJ
cana-537	248	28	independence	independence	NOUN
cana-537	248	29	of	of	ADP
cana-537	248	30	relationship	relationship	NOUN
cana-537	248	31	with	with	ADP
cana-537	248	32	few	few	ADJ
cana-537	248	33	of	of	ADP
cana-537	248	34	the	the	DET
cana-537	248	35	existing	exist	VERB
cana-537	248	36	closed	closed	ADJ
cana-537	248	37	sets	set	NOUN
cana-537	248	38	are	be	AUX
cana-537	248	39	studied	study	VERB
cana-537	248	40	.	.	PUNCT
cana-537	249	1	references	reference	NOUN
cana-537	249	2	[	[	X
cana-537	249	3	1	1	NUM
cana-537	249	4	]	]	X
cana-537	249	5	s.r	s.r	PROPN
cana-537	249	6	.	.	PROPN
cana-537	249	7	malghan	malghan	PROPN
cana-537	249	8	.	.	PROPN
cana-537	249	9	,	,	PUNCT
cana-537	249	10	“	"	PUNCT
cana-537	249	11	generalized	generalize	VERB
cana-537	249	12	closed	closed	ADJ
cana-537	249	13	maps	map	NOUN
cana-537	249	14	”	"	PUNCT
cana-537	249	15	.	.	PUNCT
cana-537	249	16	,	,	PUNCT
cana-537	249	17	j.	j.	PROPN
cana-537	249	18	karnatak	karnatak	PROPN
cana-537	249	19	univ	univ	PROPN
cana-537	249	20	.	.	PUNCT
cana-537	250	1	sci	sci	PROPN
cana-537	250	2	.	.	PROPN
cana-537	250	3	,	,	PUNCT
cana-537	250	4	vol.27	vol.27	PROPN
cana-537	250	5	.	.	PROPN
cana-537	250	6	,	,	PUNCT
cana-537	250	7	pp	pp	PROPN
cana-537	250	8	.	.	PUNCT
cana-537	250	9	8288	8288	NUM
cana-537	250	10	.	.	PUNCT
cana-537	250	11	,	,	PUNCT
cana-537	250	12	1982	1982	NUM
cana-537	250	13	.	.	PUNCT
cana-537	251	1	[	[	X
cana-537	251	2	2	2	NUM
cana-537	251	3	]	]	PUNCT
cana-537	251	4	benchalli.s.s	benchalli.s.s	PROPN
cana-537	251	5	and	and	CCONJ
cana-537	251	6	wali.r.s	wali.r.s	PROPN
cana-537	251	7	.	.	PUNCT
cana-537	251	8	,	,	PUNCT
cana-537	251	9	“	"	PUNCT
cana-537	251	10	on	on	ADP
cana-537	251	11	r-closed	r-close	VERB
cana-537	251	12	sets	set	NOUN
cana-537	251	13	in	in	ADP
cana-537	251	14	topological	topological	ADJ
cana-537	251	15	spaces	space	NOUN
cana-537	251	16	”	"	PUNCT
cana-537	251	17	.	.	PUNCT
cana-537	251	18	,	,	PUNCT
cana-537	251	19	bull.malays.math.sci.soc	bull.malays.math.sci.soc	PROPN
cana-537	251	20	.	.	PUNCT
cana-537	251	21	,	,	PUNCT
cana-537	251	22	vol.2	vol.2	PROPN
cana-537	251	23	.	.	PUNCT
cana-537	251	24	,	,	PUNCT
cana-537	251	25	issue.30	issue.30	PROPN
cana-537	251	26	.	.	PUNCT
cana-537	251	27	,	,	PUNCT
cana-537	251	28	pp.99	pp.99	NOUN
cana-537	251	29	-	-	PUNCT
cana-537	251	30	110	110	NUM
cana-537	251	31	.	.	PUNCT
cana-537	251	32	,	,	PUNCT
cana-537	251	33	2007	2007	NUM
cana-537	251	34	.	.	PUNCT
cana-537	252	1	[	[	X
cana-537	252	2	3	3	X
cana-537	252	3	]	]	PUNCT
cana-537	252	4	a.vadivel	a.vadivel	NOUN
cana-537	252	5	and	and	CCONJ
cana-537	252	6	k.vairamanickam	k.vairamanickam	NOUN
cana-537	252	7	.	.	PROPN
cana-537	252	8	,	,	PUNCT
cana-537	252	9	“	"	PUNCT
cana-537	252	10	rgα	rgα	NOUN
cana-537	252	11	-	-	PUNCT
cana-537	252	12	closed	closed	ADJ
cana-537	252	13	and	and	CCONJ
cana-537	252	14	rgα	rgα	NOUN
cana-537	252	15	-	-	ADJ
cana-537	252	16	open	open	ADJ
cana-537	252	17	maps	map	NOUN
cana-537	252	18	in	in	ADP
cana-537	252	19	topological	topological	ADJ
cana-537	252	20	spaces	space	NOUN
cana-537	252	21	”	"	PUNCT
cana-537	252	22	.	.	PUNCT
cana-537	252	23	,	,	PUNCT
cana-537	252	24	int	int	PROPN
cana-537	252	25	.	.	PUNCT
cana-537	253	1	journal	journal	PROPN
cana-537	253	2	of	of	ADP
cana-537	253	3	math	math	NOUN
cana-537	253	4	.	.	PUNCT
cana-537	254	1	analysis	analysis	NOUN
cana-537	254	2	.	.	PUNCT
cana-537	254	3	,	,	PUNCT
cana-537	254	4	vol.4	vol.4	PROPN
cana-537	254	5	.	.	PROPN
cana-537	254	6	,	,	PUNCT
cana-537	254	7	no.10	no.10	PROPN
cana-537	254	8	.	.	NOUN
cana-537	254	9	,	,	PUNCT
cana-537	254	10	pp.453	pp.453	NOUN
cana-537	254	11	-	-	PUNCT
cana-537	254	12	468	468	NUM
cana-537	254	13	.	.	NUM
cana-537	254	14	,	,	PUNCT
cana-537	254	15	2010	2010	NUM
cana-537	254	16	.	.	PUNCT
cana-537	255	1	[	[	X
cana-537	255	2	4	4	NUM
cana-537	255	3	]	]	SYM
cana-537	255	4	devi	devi	X
cana-537	255	5	.	.	PUNCT
cana-537	256	1	r	r	NOUN
cana-537	256	2	,	,	PUNCT
cana-537	256	3	balachandran	balachandran	NOUN
cana-537	256	4	.	.	PUNCT
cana-537	257	1	k	k	PROPN
cana-537	257	2	and	and	CCONJ
cana-537	257	3	maki	maki	PROPN
cana-537	257	4	.	.	PUNCT
cana-537	258	1	h.	h.	PROPN
cana-537	258	2	,	,	PUNCT
cana-537	258	3	“	"	PUNCT
cana-537	258	4	semi	semi	ADJ
cana-537	258	5	-	-	ADJ
cana-537	258	6	generalized	generalized	ADJ
cana-537	258	7	homeomorphism	homeomorphism	NOUN
cana-537	258	8	and	and	CCONJ
cana-537	258	9	generalized	generalize	VERB
cana-537	258	10	semi	semi	ADJ
cana-537	258	11	homeomorphism	homeomorphism	PROPN
cana-537	258	12	in	in	ADP
cana-537	258	13	topological	topological	ADJ
cana-537	258	14	spaces	space	NOUN
cana-537	258	15	”	"	PUNCT
cana-537	258	16	.	.	PUNCT
cana-537	258	17	,	,	PUNCT
cana-537	258	18	indian	indian	PROPN
cana-537	258	19	j	j	PROPN
cana-537	258	20	pure	pure	ADJ
cana-537	258	21	appl	appl	PROPN
cana-537	258	22	.	.	PUNCT
cana-537	258	23	math	math	PROPN
cana-537	258	24	.	.	PUNCT
cana-537	258	25	,	,	PUNCT
cana-537	259	1	vol.26	vol.26	PROPN
cana-537	259	2	.	.	PROPN
cana-537	259	3	,	,	PUNCT
cana-537	259	4	no.3	no.3	PROPN
cana-537	259	5	.	.	PROPN
cana-537	259	6	,	,	PUNCT
cana-537	259	7	pp.271	pp.271	PROPN
cana-537	259	8	-	-	SYM
cana-537	259	9	284	284	NUM
cana-537	259	10	.	.	NUM
cana-537	259	11	,	,	PUNCT
cana-537	259	12	1995	1995	NUM
cana-537	259	13	.	.	PUNCT
cana-537	260	1	[	[	X
cana-537	260	2	5	5	X
cana-537	260	3	]	]	PUNCT
cana-537	260	4	h.	h.	NOUN
cana-537	260	5	maki	maki	PROPN
cana-537	260	6	,	,	PUNCT
cana-537	260	7	p.	p.	NOUN
cana-537	260	8	sundaram	sundaram	PROPN
cana-537	260	9	and	and	CCONJ
cana-537	260	10	k.	k.	PROPN
cana-537	260	11	balachandran	balachandran	PROPN
cana-537	260	12	.	.	PUNCT
cana-537	260	13	,	,	PUNCT
cana-537	260	14	“	"	PUNCT
cana-537	260	15	on	on	ADP
cana-537	260	16	generalized	generalized	ADJ
cana-537	260	17	homeomorphisms	homeomorphism	NOUN
cana-537	260	18	in	in	ADP
cana-537	260	19	topological	topological	ADJ
cana-537	260	20	spaces	space	NOUN
cana-537	260	21	”	"	PUNCT
cana-537	260	22	.	.	PUNCT
cana-537	260	23	,	,	PUNCT
cana-537	260	24	bull	bull	NOUN
cana-537	260	25	.	.	PUNCT
cana-537	261	1	fukuoka	fukuoka	PROPN
cana-537	261	2	univ.ed	univ.ed	PROPN
cana-537	261	3	,	,	PUNCT
cana-537	261	4	part	part	NOUN
cana-537	261	5	iii	iii	PROPN
cana-537	261	6	,	,	PUNCT
cana-537	261	7	vol.40	vol.40	PROPN
cana-537	261	8	.	.	PROPN
cana-537	261	9	,	,	PUNCT
cana-537	261	10	pp.13	pp.13	NOUN
cana-537	261	11	-	-	NOUN
cana-537	261	12	21.,1991	21.,1991	NUM
cana-537	261	13	.	.	PUNCT
cana-537	262	1	[	[	X
cana-537	262	2	6	6	NUM
cana-537	262	3	]	]	SYM
cana-537	262	4	rs	rs	X
cana-537	262	5	wali	wali	PROPN
cana-537	262	6	and	and	CCONJ
cana-537	262	7	vijayalaxmi	vijayalaxmi	NOUN
cana-537	262	8	r	r	PROPN
cana-537	262	9	patil	patil	PROPN
cana-537	262	10	.	.	PUNCT
cana-537	262	11	,	,	PUNCT
cana-537	262	12	“	"	PUNCT
cana-537	262	13	on	on	ADP
cana-537	262	14	rgwαhomeomorphism	rgwαhomeomorphism	NOUN
cana-537	262	15	in	in	ADP
cana-537	262	16	topological	topological	ADJ
cana-537	262	17	spaces	space	NOUN
cana-537	262	18	”	"	PUNCT
cana-537	262	19	.	.	PUNCT
cana-537	262	20	,	,	PUNCT
cana-537	262	21	international	international	ADJ
cana-537	262	22	journal	journal	NOUN
cana-537	262	23	of	of	ADP
cana-537	262	24	statistics	statistic	NOUN
cana-537	262	25	and	and	CCONJ
cana-537	262	26	applied	apply	VERB
cana-537	262	27	mathematics	mathematic	NOUN
cana-537	262	28	.	.	PUNCT
cana-537	262	29	,	,	PUNCT
cana-537	263	1	vol.2	vol.2	PROPN
cana-537	263	2	.	.	PROPN
cana-537	263	3	,	,	PUNCT
cana-537	263	4	no.4	no.4	PROPN
cana-537	263	5	.	.	PROPN
cana-537	263	6	,	,	PUNCT
cana-537	263	7	pp.22	pp.22	NOUN
cana-537	263	8	-	-	PUNCT
cana-537	263	9	27	27	NUM
cana-537	263	10	.	.	NUM
cana-537	263	11	,	,	PUNCT
cana-537	263	12	2017	2017	NUM
cana-537	263	13	.	.	PUNCT
cana-537	264	1	[	[	X
cana-537	264	2	7	7	X
cana-537	264	3	]	]	X
cana-537	264	4	gnanambal	gnanambal	PROPN
cana-537	264	5	y.	y.	PROPN
cana-537	264	6	,	,	PUNCT
cana-537	264	7	“	"	PUNCT
cana-537	264	8	on	on	ADP
cana-537	264	9	generalized	generalized	ADJ
cana-537	264	10	pre	pre	ADJ
cana-537	264	11	-	-	ADJ
cana-537	264	12	regular	regular	ADJ
cana-537	264	13	closed	closed	ADJ
cana-537	264	14	sets	set	NOUN
cana-537	264	15	in	in	ADP
cana-537	264	16	topological	topological	ADJ
cana-537	264	17	spaces	space	NOUN
cana-537	264	18	”	"	PUNCT
cana-537	264	19	.	.	PUNCT
cana-537	264	20	,	,	PUNCT
cana-537	264	21	indian	indian	PROPN
cana-537	264	22	j.	j.	PROPN
cana-537	264	23	pure	pure	PROPN
cana-537	264	24	appl	appl	PROPN
cana-537	264	25	.	.	PUNCT
cana-537	264	26	math	math	PROPN
cana-537	264	27	.	.	PUNCT
cana-537	265	1	,	,	PUNCT
cana-537	265	2	vol.28	vol.28	PROPN
cana-537	265	3	.	.	PROPN
cana-537	265	4	,	,	PUNCT
cana-537	265	5	pp.351	pp.351	NOUN
cana-537	265	6	-	-	PUNCT
cana-537	265	7	360	360	NUM
cana-537	265	8	.	.	NUM
cana-537	265	9	,	,	PUNCT
cana-537	265	10	1997	1997	NUM
cana-537	265	11	.	.	PUNCT
cana-537	266	1	[	[	X
cana-537	266	2	8	8	NUM
cana-537	266	3	]	]	SYM
cana-537	266	4	d.iyappan	d.iyappan	ADP
cana-537	266	5	and	and	CCONJ
cana-537	266	6	n.nagaveni	n.nagaveni	NOUN
cana-537	266	7	.	.	PUNCT
cana-537	266	8	,	,	PUNCT
cana-537	266	9	“	"	PUNCT
cana-537	266	10	on	on	ADP
cana-537	266	11	semi	semi	ADV
cana-537	266	12	generalized	generalized	ADJ
cana-537	266	13	b	b	X
cana-537	266	14	-	-	ADJ
cana-537	266	15	continuous	continuous	ADJ
cana-537	266	16	maps	map	NOUN
cana-537	266	17	,	,	PUNCT
cana-537	266	18	semi	semi	ADV
cana-537	266	19	genealized	genealize	VERB
cana-537	266	20	b	b	X
cana-537	266	21	-	-	PUNCT
cana-537	266	22	closed	close	VERB
cana-537	266	23	maps	map	NOUN
cana-537	266	24	in	in	ADP
cana-537	266	25	topological	topological	ADJ
cana-537	266	26	space	space	NOUN
cana-537	266	27	”	"	PUNCT
cana-537	266	28	.	.	PUNCT
cana-537	266	29	,	,	PUNCT
cana-537	267	1	int	int	PROPN
cana-537	267	2	.	.	PUNCT
cana-537	268	1	journal	journal	PROPN
cana-537	268	2	of	of	ADP
cana-537	268	3	math	math	NOUN
cana-537	268	4	.	.	PUNCT
cana-537	269	1	analysis	analysis	NOUN
cana-537	269	2	.	.	PUNCT
cana-537	269	3	,	,	PUNCT
cana-537	269	4	vol.6	vol.6	PROPN
cana-537	269	5	.	.	PROPN
cana-537	269	6	,	,	PUNCT
cana-537	269	7	no.26	no.26	PROPN
cana-537	269	8	.	.	PROPN
cana-537	269	9	,	,	PUNCT
cana-537	269	10	pp.1251	pp.1251	PROPN
cana-537	269	11	-	-	PUNCT
cana-537	269	12	1264	1264	NUM
cana-537	269	13	.	.	PUNCT
cana-537	269	14	,	,	PUNCT
cana-537	269	15	2012	2012	NUM
cana-537	269	16	.	.	PUNCT
cana-537	270	1	[	[	X
cana-537	270	2	9	9	NUM
cana-537	270	3	]	]	SYM
cana-537	270	4	n.nagaveni	n.nagaveni	NOUN
cana-537	270	5	.	.	PUNCT
cana-537	270	6	,	,	PUNCT
cana-537	270	7	“	"	PUNCT
cana-537	270	8	studies	study	NOUN
cana-537	270	9	on	on	ADP
cana-537	270	10	generalizations	generalization	NOUN
cana-537	270	11	of	of	ADP
cana-537	270	12	homeomorphisms	homeomorphisms	PROPN
cana-537	270	13	in	in	ADP
cana-537	270	14	topological	topological	ADJ
cana-537	270	15	spaces	space	NOUN
cana-537	270	16	.	.	PUNCT
cana-537	270	17	,	,	PUNCT
cana-537	270	18	ph.d	ph.d	PROPN
cana-537	270	19	thesis	thesis	NOUN
cana-537	270	20	.	.	PUNCT
cana-537	270	21	,	,	PUNCT
cana-537	270	22	bharathiyar	bharathiyar	PROPN
cana-537	270	23	university	university	PROPN
cana-537	270	24	.	.	PUNCT
cana-537	270	25	,	,	PUNCT
cana-537	270	26	coimbatore	coimbatore	PROPN
cana-537	270	27	.	.	PROPN
cana-537	270	28	,	,	PUNCT
cana-537	270	29	july1999	july1999	PROPN
cana-537	270	30	.	.	PUNCT
cana-537	271	1	[	[	X
cana-537	271	2	10	10	NUM
cana-537	271	3	]	]	PUNCT
cana-537	271	4	t.shyla	t.shyla	NOUN
cana-537	271	5	isac	isac	PROPN
cana-537	271	6	mary	mary	PROPN
cana-537	271	7	and	and	CCONJ
cana-537	271	8	p.thangavelu	p.thangavelu	NOUN
cana-537	271	9	.	.	PROPN
cana-537	271	10	,	,	PUNCT
cana-537	271	11	“	"	PUNCT
cana-537	271	12	rps	rps	PROPN
cana-537	271	13	-	-	PUNCT
cana-537	271	14	homeomorphism	homeomorphism	PROPN
cana-537	271	15	in	in	ADP
cana-537	271	16	topological	topological	ADJ
cana-537	271	17	spaces	space	NOUN
cana-537	271	18	”	"	PUNCT
cana-537	271	19	.	.	PUNCT
cana-537	271	20	,	,	PUNCT
cana-537	271	21	asian	asian	ADJ
cana-537	271	22	journal	journal	NOUN
cana-537	271	23	of	of	ADP
cana-537	271	24	current	current	ADJ
cana-537	271	25	engineering	engineering	NOUN
cana-537	271	26	and	and	CCONJ
cana-537	271	27	maths2	maths2	NOUN
cana-537	271	28	.	.	PROPN
cana-537	271	29	,	,	PUNCT
cana-537	271	30	pp.14	pp.14	NOUN
cana-537	271	31	-	-	SYM
cana-537	271	32	16	16	NUM
cana-537	271	33	.	.	PUNCT
cana-537	271	34	,	,	PUNCT
cana-537	271	35	2013	2013	NUM
cana-537	271	36	.	.	PUNCT
cana-537	272	1	[	[	X
cana-537	272	2	11	11	NUM
cana-537	272	3	]	]	X
cana-537	272	4	a.pushpalatha	a.pushpalatha	NOUN
cana-537	272	5	and	and	CCONJ
cana-537	272	6	k.anitha	k.anitha	NOUN
cana-537	272	7	.	.	PROPN
cana-537	272	8	,	,	PUNCT
cana-537	272	9	“	"	PUNCT
cana-537	272	10	g*s	g*s	NOUN
cana-537	272	11	-	-	PUNCT
cana-537	272	12	closed	close	VERB
cana-537	272	13	sets	set	NOUN
cana-537	272	14	in	in	ADP
cana-537	272	15	topological	topological	ADJ
cana-537	272	16	spaces	space	NOUN
cana-537	272	17	”	"	PUNCT
cana-537	272	18	.	.	PUNCT
cana-537	272	19	,	,	PUNCT
cana-537	272	20	int	int	NOUN
cana-537	272	21	.	.	PUNCT
cana-537	273	1	j.contemp	j.contemp	ADJ
cana-537	273	2	.	.	PUNCT
cana-537	274	1	math	math	NOUN
cana-537	274	2	.	.	PUNCT
cana-537	275	1	sciences	sciences	PROPN
cana-537	275	2	.	.	PUNCT
cana-537	275	3	,	,	PUNCT
cana-537	275	4	vol.6	vol.6	PROPN
cana-537	275	5	.	.	PROPN
cana-537	275	6	,	,	PUNCT
cana-537	275	7	no.19	no.19	PROPN
cana-537	275	8	.	.	PUNCT
cana-537	275	9	,	,	PUNCT
cana-537	275	10	pp.917	pp.917	NOUN
cana-537	275	11	-	-	SYM
cana-537	275	12	929.,2011	929.,2011	PROPN
cana-537	276	1	[	[	X
cana-537	276	2	12	12	NUM
cana-537	276	3	]	]	PUNCT
cana-537	276	4	a.	a.	NOUN
cana-537	276	5	pushpalatha	pushpalatha	PROPN
cana-537	276	6	.	.	PUNCT
cana-537	276	7	,	,	PUNCT
cana-537	276	8	“	"	PUNCT
cana-537	276	9	studies	study	NOUN
cana-537	276	10	on	on	ADP
cana-537	276	11	generalizations	generalization	NOUN
cana-537	276	12	of	of	ADP
cana-537	276	13	mappings	mapping	NOUN
cana-537	276	14	in	in	ADP
cana-537	276	15	topological	topological	ADJ
cana-537	276	16	spaces	space	NOUN
cana-537	276	17	.	.	PUNCT
cana-537	276	18	,	,	PUNCT
cana-537	276	19	ph.d	ph.d	PROPN
cana-537	276	20	.	.	PUNCT
cana-537	277	1	thesis	thesis	PROPN
cana-537	277	2	.	.	PUNCT
cana-537	277	3	,	,	PUNCT
cana-537	277	4	bharathiar	bharathiar	PROPN
cana-537	277	5	university	university	PROPN
cana-537	277	6	.	.	PUNCT
cana-537	277	7	,	,	PUNCT
cana-537	277	8	coimbatore	coimbatore	PROPN
cana-537	277	9	.	.	PUNCT
cana-537	277	10	,2000	,2000	PROPN
cana-537	277	11	.	.	PUNCT
cana-537	278	1	[	[	X
cana-537	278	2	13	13	NUM
cana-537	278	3	]	]	SYM
cana-537	278	4	i.arockiarani	i.arockiarani	NOUN
cana-537	278	5	.	.	PUNCT
cana-537	278	6	,	,	PUNCT
cana-537	278	7	“	"	PUNCT
cana-537	278	8	studies	study	NOUN
cana-537	278	9	on	on	ADP
cana-537	278	10	generalizations	generalization	NOUN
cana-537	278	11	of	of	ADP
cana-537	278	12	generalized	generalize	VERB
cana-537	278	13	closed	closed	ADJ
cana-537	278	14	sets	set	NOUN
cana-537	278	15	and	and	CCONJ
cana-537	278	16	maps	map	NOUN
cana-537	278	17	in	in	ADP
cana-537	278	18	topological	topological	ADJ
cana-537	278	19	spaces	space	NOUN
cana-537	278	20	.	.	PUNCT
cana-537	278	21	,	,	PUNCT
cana-537	278	22	ph.d	ph.d	PROPN
cana-537	278	23	.	.	PUNCT
cana-537	279	1	thesis	thesis	PROPN
cana-537	279	2	.	.	PUNCT
cana-537	279	3	,	,	PUNCT
cana-537	279	4	bharathiar	bharathiar	PROPN
cana-537	279	5	university	university	PROPN
cana-537	279	6	.	.	PUNCT
cana-537	279	7	,	,	PUNCT
cana-537	279	8	coimbatore	coimbatore	PROPN
cana-537	279	9	.	.	PROPN
cana-537	279	10	,	,	PUNCT
cana-537	279	11	1997	1997	NUM
cana-537	279	12	.	.	PUNCT
cana-537	280	1	[	[	X
cana-537	280	2	14	14	NUM
cana-537	280	3	]	]	X
cana-537	280	4	s.sekar	s.sekar	ADJ
cana-537	280	5	and	and	CCONJ
cana-537	280	6	b.jothilakshmi	b.jothilakshmi	ADJ
cana-537	280	7	.	.	PUNCT
cana-537	280	8	,	,	PUNCT
cana-537	280	9	“	"	PUNCT
cana-537	280	10	on	on	ADP
cana-537	280	11	semi	semi	ADV
cana-537	280	12	generalized	generalized	ADJ
cana-537	280	13	star	star	NOUN
cana-537	280	14	b	b	X
cana-537	280	15	-	-	PUNCT
cana-537	280	16	closed	close	VERB
cana-537	280	17	maps	map	NOUN
cana-537	280	18	in	in	ADP
cana-537	280	19	topological	topological	ADJ
cana-537	280	20	spaces	space	NOUN
cana-537	280	21	”	"	PUNCT
cana-537	280	22	.	.	PUNCT
cana-537	280	23	,	,	PUNCT
cana-537	280	24	international	international	ADJ
cana-537	280	25	journal	journal	NOUN
cana-537	280	26	of	of	ADP
cana-537	280	27	pure	pure	ADJ
cana-537	280	28	and	and	CCONJ
cana-537	280	29	applied	applied	ADJ
cana-537	280	30	mathematics	mathematic	NOUN
cana-537	280	31	.	.	PUNCT
cana-537	280	32	,	,	PUNCT
cana-537	280	33	vol.113	vol.113	PROPN
cana-537	280	34	.	.	PROPN
cana-537	280	35	,	,	PUNCT
cana-537	280	36	no.1.,pp.93	no.1.,pp.93	NUM
cana-537	280	37	-	-	SYM
cana-537	280	38	102	102	NUM
cana-537	280	39	.	.	PUNCT
cana-537	280	40	,	,	PUNCT
cana-537	280	41	2017	2017	NUM
cana-537	280	42	.	.	PUNCT
cana-537	281	1	[	[	X
cana-537	281	2	15	15	NUM
cana-537	281	3	]	]	SYM
cana-537	281	4	r.sudha	r.sudha	NOUN
cana-537	281	5	and	and	CCONJ
cana-537	281	6	v.e.sasikala	v.e.sasikala	NOUN
cana-537	281	7	,	,	PUNCT
cana-537	281	8	“	"	PUNCT
cana-537	281	9	on	on	ADP
cana-537	281	10	semi	semi	ADV
cana-537	281	11	star	star	PROPN
cana-537	281	12	pre	pre	PROPN
cana-537	281	13	star	star	PROPN
cana-537	281	14	closed	close	VERB
cana-537	281	15	set	set	VERB
cana-537	281	16	in	in	ADP
cana-537	281	17	topological	topological	ADJ
cana-537	281	18	spaces	space	NOUN
cana-537	281	19	”	"	PUNCT
cana-537	281	20	,	,	PUNCT
cana-537	281	21	patent	patent	NOUN
cana-537	281	22	publication	publication	NOUN
cana-537	281	23	,	,	PUNCT
cana-537	281	24	application	application	NOUN
cana-537	281	25	no	no	NOUN
cana-537	281	26	.	.	PROPN
cana-537	282	1	202341031746	202341031746	NUM
cana-537	282	2	a	a	PRON
cana-537	282	3	,	,	PUNCT
cana-537	282	4	publication	publication	NOUN
cana-537	282	5	date	date	NOUN
cana-537	282	6	:	:	PUNCT
cana-537	283	1	18.08.23	18.08.23	X
cana-537	283	2	.	.	PUNCT