id	sid	tid	token	lemma	pos
cana-1033	1	1	communications	communication	NOUN
cana-1033	1	2	on	on	ADP
cana-1033	1	3	applied	apply	VERB
cana-1033	1	4	nonlinear	nonlinear	ADJ
cana-1033	1	5	analysis	analysis	NOUN
cana-1033	1	6	issn	issn	NOUN
cana-1033	1	7	:	:	PUNCT
cana-1033	1	8	1074	1074	NUM
cana-1033	1	9	-	-	PUNCT
cana-1033	1	10	133x	133x	NUM
cana-1033	1	11	vol	vol	NOUN
cana-1033	1	12	31	31	NUM
cana-1033	1	13	no	no	NOUN
cana-1033	1	14	.	.	PUNCT
cana-1033	2	1	5s	5s	NUM
cana-1033	2	2	(	(	PUNCT
cana-1033	2	3	2024	2024	NUM
cana-1033	2	4	)	)	PUNCT
cana-1033	2	5	259	259	NUM
cana-1033	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1033	2	7	compactness	compactness	NOUN
cana-1033	2	8	and	and	CCONJ
cana-1033	2	9	connectedness	connectedness	NOUN
cana-1033	2	10	in	in	ADP
cana-1033	2	11	beta	beta	ADJ
cana-1033	2	12	weakly	weakly	ADJ
cana-1033	2	13	semi	semi	ADJ
cana-1033	2	14	–	–	PUNCT
cana-1033	2	15	closed	closed	ADJ
cana-1033	2	16	sets	set	NOUN
cana-1033	2	17	in	in	ADP
cana-1033	2	18	topological	topological	ADJ
cana-1033	2	19	spaces	space	NOUN
cana-1033	2	20	s.	s.	PROPN
cana-1033	2	21	saranya*1	saranya*1	PROPN
cana-1033	2	22	,	,	PUNCT
cana-1033	2	23	v.e	v.e	PROPN
cana-1033	2	24	.	.	PROPN
cana-1033	2	25	sasikala*2	sasikala*2	PROPN
cana-1033	2	26	*	*	NUM
cana-1033	2	27	1	1	NUM
cana-1033	2	28	research	research	NOUN
cana-1033	2	29	scholar	scholar	NOUN
cana-1033	2	30	,	,	PUNCT
cana-1033	2	31	*	*	PROPN
cana-1033	2	32	2	2	NUM
cana-1033	2	33	assistant	assistant	NOUN
cana-1033	2	34	professor	professor	NOUN
cana-1033	2	35	,	,	PUNCT
cana-1033	2	36	research	research	NOUN
cana-1033	2	37	supervisor	supervisor	NOUN
cana-1033	2	38	corresponding	corresponding	ADJ
cana-1033	2	39	author	author	NOUN
cana-1033	2	40	,	,	PUNCT
cana-1033	2	41	department	department	NOUN
cana-1033	2	42	of	of	ADP
cana-1033	2	43	mathematics	mathematics	PROPN
cana-1033	2	44	,	,	PUNCT
cana-1033	2	45	vels	vels	PROPN
cana-1033	2	46	institute	institute	PROPN
cana-1033	2	47	of	of	ADP
cana-1033	2	48	science	science	NOUN
cana-1033	2	49	,	,	PUNCT
cana-1033	2	50	technology	technology	NOUN
cana-1033	2	51	and	and	CCONJ
cana-1033	2	52	advanced	advanced	ADJ
cana-1033	2	53	studies	study	NOUN
cana-1033	2	54	,	,	PUNCT
cana-1033	2	55	(	(	PUNCT
cana-1033	2	56	vistas	vista	NOUN
cana-1033	2	57	)	)	PUNCT
cana-1033	2	58	,	,	PUNCT
cana-1033	2	59	pallavaram	pallavaram	PROPN
cana-1033	2	60	,	,	PUNCT
cana-1033	2	61	chennai	chennai	PROPN
cana-1033	2	62	,	,	PUNCT
cana-1033	2	63	india	india	PROPN
cana-1033	2	64	.	.	PUNCT
cana-1033	3	1	corresponding	correspond	VERB
cana-1033	3	2	author	author	NOUN
cana-1033	3	3	mail	mail	NOUN
cana-1033	3	4	id.sasikala.sbs@velsuniv.ac.in	id.sasikala.sbs@velsuniv.ac.in	PROPN
cana-1033	3	5	article	article	NOUN
cana-1033	3	6	history	history	NOUN
cana-1033	3	7	:	:	PUNCT
cana-1033	3	8	received	receive	VERB
cana-1033	3	9	:	:	PUNCT
cana-1033	3	10	10	10	NUM
cana-1033	3	11	-	-	SYM
cana-1033	3	12	05	05	NUM
cana-1033	3	13	-	-	PUNCT
cana-1033	3	14	2024	2024	NUM
cana-1033	3	15	revised	revise	VERB
cana-1033	3	16	:	:	PUNCT
cana-1033	3	17	25	25	NUM
cana-1033	3	18	-	-	PUNCT
cana-1033	3	19	06	06	NUM
cana-1033	3	20	-	-	PUNCT
cana-1033	3	21	2024	2024	NUM
cana-1033	3	22	accepted	accept	VERB
cana-1033	3	23	:	:	PUNCT
cana-1033	3	24	07	07	NUM
cana-1033	3	25	-	-	PUNCT
cana-1033	3	26	07	07	NUM
cana-1033	3	27	-	-	PUNCT
cana-1033	3	28	2024	2024	NUM
cana-1033	3	29	abstract	abstract	NOUN
cana-1033	3	30	:	:	PUNCT
cana-1033	3	31	this	this	DET
cana-1033	3	32	research	research	NOUN
cana-1033	3	33	presents	present	VERB
cana-1033	3	34	an	an	DET
cana-1033	3	35	innovative	innovative	ADJ
cana-1033	3	36	class	class	NOUN
cana-1033	3	37	of	of	ADP
cana-1033	3	38	beta	beta	ADJ
cana-1033	3	39	weakly	weakly	ADJ
cana-1033	3	40	semi	semi	ADJ
cana-1033	3	41	-	-	ADJ
cana-1033	3	42	cs	cs	ADJ
cana-1033	3	43	,	,	PUNCT
cana-1033	3	44	namely	namely	ADV
cana-1033	3	45	compactness	compactness	NOUN
cana-1033	3	46	and	and	CCONJ
cana-1033	3	47	connectedness	connectedness	NOUN
cana-1033	3	48	in	in	ADP
cana-1033	3	49	beta	beta	ADJ
cana-1033	3	50	weakly	weakly	ADJ
cana-1033	3	51	semi	semi	NOUN
cana-1033	3	52	-	-	NOUN
cana-1033	3	53	cs	cs	ADJ
cana-1033	3	54	in	in	ADP
cana-1033	3	55	ts	ts	PROPN
cana-1033	3	56	.	.	PUNCT
cana-1033	4	1	throughout	throughout	ADP
cana-1033	4	2	this	this	DET
cana-1033	4	3	paper	paper	NOUN
cana-1033	4	4	,	,	PUNCT
cana-1033	4	5	wscompactness	wscompactness	NOUN
cana-1033	4	6	and	and	CCONJ
cana-1033	4	7	ws	ws	NOUN
cana-1033	4	8	-	-	PUNCT
cana-1033	4	9	connectedness	connectedness	NOUN
cana-1033	4	10	were	be	AUX
cana-1033	4	11	examined	examine	VERB
cana-1033	4	12	to	to	PART
cana-1033	4	13	get	get	VERB
cana-1033	4	14	the	the	DET
cana-1033	4	15	fundamental	fundamental	ADJ
cana-1033	4	16	facts	fact	NOUN
cana-1033	4	17	in	in	ADP
cana-1033	4	18	the	the	DET
cana-1033	4	19	beta	beta	ADJ
cana-1033	4	20	weakly	weakly	ADJ
cana-1033	4	21	semi	semi	NOUN
cana-1033	4	22	-	-	ADJ
cana-1033	4	23	cs	cs	ADJ
cana-1033	4	24	.	.	PROPN
cana-1033	4	25	in	in	ADP
cana-1033	4	26	this	this	DET
cana-1033	4	27	paper	paper	NOUN
cana-1033	4	28	,	,	PUNCT
cana-1033	4	29	the	the	DET
cana-1033	4	30	notion	notion	NOUN
cana-1033	4	31	of	of	ADP
cana-1033	4	32	countable	countable	ADJ
cana-1033	4	33	βwscompact	βwscompact	NOUN
cana-1033	4	34	in	in	ADP
cana-1033	4	35	ts	t	NOUN
cana-1033	4	36	were	be	AUX
cana-1033	4	37	explored	explore	VERB
cana-1033	4	38	and	and	CCONJ
cana-1033	4	39	ws	ws	ADJ
cana-1033	4	40	–	–	PUNCT
cana-1033	4	41	connectedness	connectedness	NOUN
cana-1033	4	42	(	(	PUNCT
cana-1033	4	43	cws	cws	NOUN
cana-1033	4	44	)	)	PUNCT
cana-1033	4	45	in	in	ADP
cana-1033	4	46	ts	t	NOUN
cana-1033	4	47	were	be	AUX
cana-1033	4	48	also	also	ADV
cana-1033	4	49	studied	study	VERB
cana-1033	4	50	to	to	PART
cana-1033	4	51	get	get	VERB
cana-1033	4	52	results	result	NOUN
cana-1033	4	53	.	.	PUNCT
cana-1033	5	1	the	the	DET
cana-1033	5	2	ws	ws	ADJ
cana-1033	5	3	cws	cws	NOUN
cana-1033	5	4	and	and	CCONJ
cana-1033	5	5	ws	ws	ADJ
cana-1033	5	6	–	–	PUNCT
cana-1033	5	7	compactness	compactness	NOUN
cana-1033	5	8	fulfilled	fulfil	VERB
cana-1033	5	9	most	most	ADJ
cana-1033	5	10	of	of	ADP
cana-1033	5	11	the	the	DET
cana-1033	5	12	connectedness	connectedness	NOUN
cana-1033	5	13	and	and	CCONJ
cana-1033	5	14	compactness	compactness	NOUN
cana-1033	5	15	properties	property	NOUN
cana-1033	5	16	in	in	ADP
cana-1033	5	17	ts	ts	PROPN
cana-1033	5	18	.	.	PUNCT
cana-1033	6	1	here	here	ADV
cana-1033	6	2	,	,	PUNCT
cana-1033	6	3	many	many	ADJ
cana-1033	6	4	characterizations	characterization	NOUN
cana-1033	6	5	were	be	AUX
cana-1033	6	6	obtained	obtain	VERB
cana-1033	6	7	along	along	ADP
cana-1033	6	8	with	with	ADP
cana-1033	6	9	some	some	PRON
cana-1033	6	10	of	of	ADP
cana-1033	6	11	their	their	PRON
cana-1033	6	12	features	feature	NOUN
cana-1033	6	13	.	.	PUNCT
cana-1033	7	1	the	the	DET
cana-1033	7	2	paper	paper	NOUN
cana-1033	7	3	concludes	conclude	VERB
cana-1033	7	4	on	on	ADP
cana-1033	7	5	how	how	SCONJ
cana-1033	7	6	it	it	PRON
cana-1033	7	7	relates	relate	VERB
cana-1033	7	8	to	to	ADP
cana-1033	7	9	other	other	ADJ
cana-1033	7	10	kinds	kind	NOUN
cana-1033	7	11	of	of	ADP
cana-1033	7	12	functions	function	NOUN
cana-1033	7	13	and	and	CCONJ
cana-1033	7	14	beta	beta	ADJ
cana-1033	7	15	ws	ws	NOUN
cana-1033	7	16	-	-	PUNCT
cana-1033	7	17	compactness	compactness	NOUN
cana-1033	7	18	in	in	ADP
cana-1033	7	19	ts	ts	ADP
cana-1033	7	20	and	and	CCONJ
cana-1033	7	21	its	its	PRON
cana-1033	7	22	characteristics	characteristic	NOUN
cana-1033	7	23	were	be	AUX
cana-1033	7	24	studied	study	VERB
cana-1033	7	25	to	to	PART
cana-1033	7	26	obtain	obtain	VERB
cana-1033	7	27	results	result	NOUN
cana-1033	7	28	theoretically	theoretically	ADV
cana-1033	7	29	.	.	PUNCT
cana-1033	8	1	keywords	keyword	NOUN
cana-1033	8	2	:	:	PUNCT
cana-1033	8	3	beta	beta	ADJ
cana-1033	8	4	weakly	weakly	ADJ
cana-1033	8	5	semi	semi	ADJ
cana-1033	8	6	–	–	PUNCT
cana-1033	8	7	closed	closed	ADJ
cana-1033	8	8	sets	set	NOUN
cana-1033	8	9	(	(	PUNCT
cana-1033	8	10	ws	ws	NOUN
cana-1033	8	11	closed	closed	ADJ
cana-1033	8	12	)	)	PUNCT
cana-1033	8	13	,	,	PUNCT
cana-1033	8	14	beta	beta	ADJ
cana-1033	8	15	weakly	weakly	ADJ
cana-1033	8	16	semi	semi	ADJ
cana-1033	8	17	–	–	PUNCT
cana-1033	8	18	open	open	ADJ
cana-1033	8	19	sets	set	NOUN
cana-1033	8	20	(	(	PUNCT
cana-1033	8	21	ws	ws	NOUN
cana-1033	8	22	-	-	PUNCT
cana-1033	8	23	open	open	ADJ
cana-1033	8	24	)	)	PUNCT
cana-1033	8	25	,	,	PUNCT
cana-1033	8	26	beta	beta	ADJ
cana-1033	8	27	weakly	weakly	ADJ
cana-1033	8	28	semi	semi	ADJ
cana-1033	8	29	-	-	ADJ
cana-1033	8	30	closed	closed	ADJ
cana-1033	8	31	sets	set	NOUN
cana-1033	8	32	–	–	PUNCT
cana-1033	8	33	compactness	compactness	NOUN
cana-1033	8	34	(	(	PUNCT
cana-1033	8	35	ws	ws	NOUN
cana-1033	8	36	–	–	PUNCT
cana-1033	8	37	compactness	compactness	NOUN
cana-1033	8	38	)	)	PUNCT
cana-1033	8	39	,	,	PUNCT
cana-1033	8	40	beta	beta	ADJ
cana-1033	8	41	weakly	weakly	ADJ
cana-1033	8	42	semi	semi	ADJ
cana-1033	8	43	closed	closed	ADJ
cana-1033	8	44	sets	set	NOUN
cana-1033	8	45	–	–	PUNCT
cana-1033	8	46	connectedness	connectedness	NOUN
cana-1033	8	47	(	(	PUNCT
cana-1033	8	48	ws	ws	ADJ
cana-1033	8	49	–	–	PUNCT
cana-1033	8	50	connectedness	connectedness	NOUN
cana-1033	8	51	)	)	PUNCT
cana-1033	8	52	.	.	PUNCT
cana-1033	9	1	1	1	X
cana-1033	9	2	.	.	X
cana-1033	9	3	introduction	introduction	NOUN
cana-1033	9	4	:	:	PUNCT
cana-1033	9	5	the	the	DET
cana-1033	9	6	fundamental	fundamental	ADJ
cana-1033	9	7	concepts	concept	NOUN
cana-1033	9	8	of	of	ADP
cana-1033	9	9	connectedness	connectedness	NOUN
cana-1033	9	10	and	and	CCONJ
cana-1033	9	11	compactness	compactness	NOUN
cana-1033	9	12	play	play	VERB
cana-1033	9	13	crucial	crucial	ADJ
cana-1033	9	14	roles	role	NOUN
cana-1033	9	15	in	in	ADP
cana-1033	9	16	general	general	ADJ
cana-1033	9	17	topology	topology	NOUN
cana-1033	9	18	and	and	CCONJ
cana-1033	9	19	various	various	ADJ
cana-1033	9	20	other	other	ADJ
cana-1033	9	21	branches	branch	NOUN
cana-1033	9	22	of	of	ADP
cana-1033	9	23	mathematics	mathematic	NOUN
cana-1033	9	24	.	.	PUNCT
cana-1033	10	1	numerous	numerous	ADJ
cana-1033	10	2	researchers	researcher	NOUN
cana-1033	10	3	have	have	AUX
cana-1033	10	4	investigated	investigate	VERB
cana-1033	10	5	into	into	ADP
cana-1033	10	6	exploring	explore	VERB
cana-1033	10	7	their	their	PRON
cana-1033	10	8	fundamental	fundamental	ADJ
cana-1033	10	9	properties	property	NOUN
cana-1033	10	10	,	,	PUNCT
cana-1033	10	11	leading	lead	VERB
cana-1033	10	12	to	to	ADP
cana-1033	10	13	inspirations	inspiration	NOUN
cana-1033	10	14	for	for	ADP
cana-1033	10	15	generalizing	generalize	VERB
cana-1033	10	16	these	these	DET
cana-1033	10	17	concepts	concept	NOUN
cana-1033	10	18	to	to	ADP
cana-1033	10	19	innovative	innovative	ADJ
cana-1033	10	20	extents	extent	NOUN
cana-1033	10	21	.	.	PUNCT
cana-1033	11	1	[	[	X
cana-1033	11	2	1	1	NUM
cana-1033	11	3	]	]	PUNCT
cana-1033	11	4	,	,	PUNCT
cana-1033	11	5	“	"	PUNCT
cana-1033	11	6	on	on	ADP
cana-1033	11	7	b	b	X
cana-1033	11	8	-	-	PUNCT
cana-1033	11	9	open	open	ADJ
cana-1033	11	10	sets	set	NOUN
cana-1033	11	11	,	,	PUNCT
cana-1033	11	12	math	math	NOUN
cana-1033	11	13	vesnik	vesnik	X
cana-1033	11	14	in	in	ADP
cana-1033	11	15	topological	topological	ADJ
cana-1033	11	16	spaces	space	NOUN
cana-1033	11	17	’’	’'	PUNCT
cana-1033	11	18	.	.	PUNCT
cana-1033	12	1	k.	k.	PROPN
cana-1033	12	2	rekha	rekha	PROPN
cana-1033	13	1	[	[	X
cana-1033	13	2	2	2	NUM
cana-1033	13	3	]	]	PUNCT
cana-1033	13	4	,	,	PUNCT
cana-1033	13	5	“	"	PUNCT
cana-1033	13	6	*	*	PUNCT
cana-1033	13	7	*	*	PUNCT
cana-1033	13	8	b	b	NOUN
cana-1033	13	9	-	-	PUNCT
cana-1033	13	10	compactness	compactness	NOUN
cana-1033	13	11	and	and	CCONJ
cana-1033	13	12	*	*	NOUN
cana-1033	13	13	*	*	PUNCT
cana-1033	13	14	b	b	NOUN
cana-1033	13	15	-	-	NOUN
cana-1033	13	16	connectedness	connectedness	NOUN
cana-1033	13	17	in	in	ADP
cana-1033	13	18	topological	topological	ADJ
cana-1033	13	19	spaces	space	NOUN
cana-1033	13	20	’’	’'	PUNCT
cana-1033	13	21	.	.	PUNCT
cana-1033	14	1	[	[	X
cana-1033	14	2	3	3	NUM
cana-1033	14	3	]	]	PUNCT
cana-1033	14	4	,	,	PUNCT
cana-1033	14	5	“	"	PUNCT
cana-1033	14	6	θ	θ	PROPN
cana-1033	14	7	-	-	PUNCT
cana-1033	14	8	b	b	NOUN
cana-1033	14	9	-	-	PUNCT
cana-1033	14	10	continuous	continuous	ADJ
cana-1033	14	11	functions	function	NOUN
cana-1033	14	12	,	,	PUNCT
cana-1033	14	13	acta	acta	PROPN
cana-1033	14	14	math	math	PROPN
cana-1033	14	15	.	.	PUNCT
cana-1033	15	1	hungar	hungar	NOUN
cana-1033	15	2	’’	’'	PUNCT
cana-1033	15	3	.	.	PUNCT
cana-1033	16	1	d.	d.	PROPN
cana-1033	16	2	sivaraj	sivaraj	PROPN
cana-1033	16	3	and	and	CCONJ
cana-1033	16	4	v.e	v.e	PROPN
cana-1033	16	5	.	.	PROPN
cana-1033	16	6	sasikala	sasikala	PROPN
cana-1033	17	1	[	[	X
cana-1033	17	2	4	4	NUM
cana-1033	17	3	-	-	SYM
cana-1033	17	4	6	6	NUM
cana-1033	17	5	]	]	PUNCT
cana-1033	17	6	,	,	PUNCT
cana-1033	17	7	“	"	PUNCT
cana-1033	17	8	a	a	DET
cana-1033	17	9	study	study	NOUN
cana-1033	17	10	on	on	ADP
cana-1033	17	11	soft	soft	ADJ
cana-1033	17	12	α−open	α−open	NOUN
cana-1033	17	13	sets	set	NOUN
cana-1033	17	14	”	"	PUNCT
cana-1033	17	15	in	in	ADP
cana-1033	17	16	topological	topological	ADJ
cana-1033	17	17	spaces	space	NOUN
cana-1033	17	18	.	.	PUNCT
cana-1033	18	1	“	"	PUNCT
cana-1033	18	2	on	on	ADP
cana-1033	18	3	soft	soft	ADJ
cana-1033	18	4	semi	semi	ADJ
cana-1033	18	5	weakly	weakly	ADJ
cana-1033	18	6	generalized	generalized	ADJ
cana-1033	18	7	closed	close	VERB
cana-1033	18	8	set	set	NOUN
cana-1033	18	9	’’	’'	PUNCT
cana-1033	18	10	and	and	CCONJ
cana-1033	18	11	“	"	PUNCT
cana-1033	18	12	soft	soft	ADJ
cana-1033	18	13	swg	swg	NOUN
cana-1033	18	14	separation	separation	NOUN
cana-1033	18	15	axioms	axiom	NOUN
cana-1033	18	16	in	in	ADP
cana-1033	18	17	soft	soft	ADJ
cana-1033	18	18	topological	topological	ADJ
cana-1033	18	19	spaces	space	NOUN
cana-1033	18	20	’’	’'	PUNCT
cana-1033	18	21	.	.	PUNCT
cana-1033	19	1	v.	v.	PROPN
cana-1033	19	2	kavitha	kavitha	PROPN
cana-1033	19	3	,	,	PUNCT
cana-1033	19	4	v.	v.	PROPN
cana-1033	19	5	e.	e.	PROPN
cana-1033	19	6	sasikala	sasikala	PROPN
cana-1033	20	1	[	[	X
cana-1033	20	2	7	7	NUM
cana-1033	20	3	]	]	PUNCT
cana-1033	20	4	,	,	PUNCT
cana-1033	20	5	“	"	PUNCT
cana-1033	20	6	beta	beta	ADJ
cana-1033	20	7	generalized	generalize	VERB
cana-1033	20	8	cs	cs	NOUN
cana-1033	20	9	’’	’'	PUNCT
cana-1033	20	10	in	in	ADP
cana-1033	20	11	topological	topological	ADJ
cana-1033	20	12	spaces	space	NOUN
cana-1033	20	13	.	.	PUNCT
cana-1033	21	1	[	[	X
cana-1033	21	2	8	8	NUM
cana-1033	21	3	]	]	PUNCT
cana-1033	21	4	,	,	PUNCT
cana-1033	21	5	“	"	PUNCT
cana-1033	21	6	minimal	minimal	ADJ
cana-1033	21	7	weakly	weakly	ADJ
cana-1033	21	8	open	open	ADJ
cana-1033	21	9	sets	set	NOUN
cana-1033	21	10	and	and	CCONJ
cana-1033	21	11	maximal	maximal	ADJ
cana-1033	21	12	weakly	weakly	ADJ
cana-1033	21	13	closed	closed	ADJ
cana-1033	21	14	sets	set	NOUN
cana-1033	21	15	in	in	ADP
cana-1033	21	16	topological	topological	ADJ
cana-1033	21	17	spaces	space	NOUN
cana-1033	21	18	”	"	PUNCT
cana-1033	21	19	.	.	PUNCT
cana-1033	22	1	[	[	X
cana-1033	22	2	9	9	NUM
cana-1033	22	3	]	]	PUNCT
cana-1033	22	4	,	,	PUNCT
cana-1033	22	5	“	"	PUNCT
cana-1033	22	6	some	some	DET
cana-1033	22	7	properties	property	NOUN
cana-1033	22	8	of	of	ADP
cana-1033	22	9	contra	contra	PROPN
cana-1033	22	10	-	-	PUNCT
cana-1033	22	11	γ	γ	ADJ
cana-1033	22	12	-	-	ADJ
cana-1033	22	13	continuous	continuous	ADJ
cana-1033	22	14	functions	function	NOUN
cana-1033	22	15	’’	’'	PUNCT
cana-1033	22	16	.	.	PUNCT
cana-1033	23	1	[	[	X
cana-1033	23	2	10	10	NUM
cana-1033	23	3	]	]	PUNCT
cana-1033	23	4	,	,	PUNCT
cana-1033	23	5	“	"	PUNCT
cana-1033	23	6	on	on	ADP
cana-1033	23	7	generalized	generalized	ADJ
cana-1033	23	8	continuous	continuous	ADJ
cana-1033	23	9	maps	map	NOUN
cana-1033	23	10	’’	’'	PUNCT
cana-1033	23	11	in	in	ADP
cana-1033	23	12	topological	topological	ADJ
cana-1033	23	13	spaces.[11	spaces.[11	PROPN
cana-1033	23	14	]	]	PUNCT
cana-1033	23	15	,	,	PUNCT
cana-1033	23	16	studies	study	NOUN
cana-1033	23	17	“	"	PUNCT
cana-1033	23	18	on	on	ADP
cana-1033	23	19	generalizations	generalization	NOUN
cana-1033	23	20	of	of	ADP
cana-1033	23	21	closed	closed	ADJ
cana-1033	23	22	maps	map	NOUN
cana-1033	23	23	and	and	CCONJ
cana-1033	23	24	homeomorphisms	homeomorphism	NOUN
cana-1033	23	25	in	in	ADP
cana-1033	23	26	topological	topological	ADJ
cana-1033	23	27	spaces”.[12],“on	spaces”.[12],“on	NOUN
cana-1033	23	28	gpr	gpr	PROPN
cana-1033	23	29	-	-	PUNCT
cana-1033	23	30	continuous	continuous	ADJ
cana-1033	23	31	functions	function	NOUN
cana-1033	23	32	’’	’'	PUNCT
cana-1033	23	33	in	in	ADP
cana-1033	23	34	topological	topological	ADJ
cana-1033	23	35	spaces	space	NOUN
cana-1033	23	36	.	.	PUNCT
cana-1033	24	1	a.	a.	PROPN
cana-1033	24	2	pushpalatha,[13	pushpalatha,[13	PROPN
cana-1033	24	3	]	]	PUNCT
cana-1033	24	4	studies	study	NOUN
cana-1033	24	5	“	"	PUNCT
cana-1033	24	6	on	on	ADP
cana-1033	24	7	generalizations	generalization	NOUN
cana-1033	24	8	of	of	ADP
cana-1033	24	9	mapping	mapping	NOUN
cana-1033	24	10	in	in	ADP
cana-1033	24	11	topological	topological	ADJ
cana-1033	24	12	spaces	space	NOUN
cana-1033	24	13	’’	’'	PUNCT
cana-1033	24	14	.	.	PUNCT
cana-1033	25	1	[	[	X
cana-1033	25	2	14	14	NUM
cana-1033	25	3	]	]	PUNCT
cana-1033	25	4	,	,	PUNCT
cana-1033	25	5	“	"	PUNCT
cana-1033	25	6	a	a	DET
cana-1033	25	7	study	study	NOUN
cana-1033	25	8	on	on	ADP
cana-1033	25	9	generalizations	generalization	NOUN
cana-1033	25	10	of	of	ADP
cana-1033	25	11	closed	closed	ADJ
cana-1033	25	12	sets	set	NOUN
cana-1033	25	13	and	and	CCONJ
cana-1033	25	14	continuous	continuous	ADJ
cana-1033	25	15	maps	map	NOUN
cana-1033	25	16	’’	’'	PUNCT
cana-1033	25	17	in	in	ADP
cana-1033	25	18	topological	topological	ADJ
cana-1033	25	19	and	and	CCONJ
cana-1033	25	20	bitopological	bitopological	ADJ
cana-1033	25	21	spaces	space	NOUN
cana-1033	25	22	.	.	PUNCT
cana-1033	26	1	this	this	DET
cana-1033	26	2	research	research	NOUN
cana-1033	26	3	aims	aim	VERB
cana-1033	26	4	to	to	ADP
cana-1033	26	5	communications	communication	NOUN
cana-1033	26	6	on	on	ADP
cana-1033	26	7	applied	apply	VERB
cana-1033	26	8	nonlinear	nonlinear	ADJ
cana-1033	26	9	analysis	analysis	NOUN
cana-1033	26	10	issn	issn	NOUN
cana-1033	26	11	:	:	PUNCT
cana-1033	26	12	1074	1074	NUM
cana-1033	26	13	-	-	PUNCT
cana-1033	26	14	133x	133x	NUM
cana-1033	26	15	vol	vol	NOUN
cana-1033	26	16	31	31	NUM
cana-1033	26	17	no	no	NOUN
cana-1033	26	18	.	.	PUNCT
cana-1033	27	1	5s	5s	NUM
cana-1033	27	2	(	(	PUNCT
cana-1033	27	3	2024	2024	NUM
cana-1033	27	4	)	)	PUNCT
cana-1033	27	5	260	260	NUM
cana-1033	28	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1033	28	2	introduce	introduce	VERB
cana-1033	28	3	the	the	DET
cana-1033	28	4	ideas	idea	NOUN
cana-1033	28	5	extending	extend	VERB
cana-1033	28	6	βws	βws	NOUN
cana-1033	28	7	compactness	compactness	NOUN
cana-1033	28	8	and	and	CCONJ
cana-1033	28	9	βws	βws	NOUN
cana-1033	28	10	–	–	PUNCT
cana-1033	28	11	connectedness	connectedness	NOUN
cana-1033	28	12	(	(	PUNCT
cana-1033	28	13	cws	cws	NOUN
cana-1033	28	14	)	)	PUNCT
cana-1033	28	15	within	within	ADP
cana-1033	28	16	ts	ts	PROPN
cana-1033	28	17	,	,	PUNCT
cana-1033	28	18	along	along	ADP
cana-1033	28	19	with	with	ADP
cana-1033	28	20	providing	provide	VERB
cana-1033	28	21	characterizations	characterization	NOUN
cana-1033	28	22	for	for	ADP
cana-1033	28	23	these	these	DET
cana-1033	28	24	concepts	concept	NOUN
cana-1033	28	25	.	.	PUNCT
cana-1033	29	1	review	review	NOUN
cana-1033	29	2	of	of	ADP
cana-1033	29	3	literature	literature	NOUN
cana-1033	29	4	:	:	PUNCT
cana-1033	29	5	a	a	DET
cana-1033	29	6	thorough	thorough	ADJ
cana-1033	29	7	review	review	NOUN
cana-1033	29	8	of	of	ADP
cana-1033	29	9	theoretical	theoretical	ADJ
cana-1033	29	10	contexts	context	NOUN
cana-1033	29	11	and	and	CCONJ
cana-1033	29	12	terminology	terminology	NOUN
cana-1033	29	13	that	that	PRON
cana-1033	29	14	have	have	AUX
cana-1033	29	15	contributed	contribute	VERB
cana-1033	29	16	to	to	ADP
cana-1033	29	17	the	the	DET
cana-1033	29	18	current	current	ADJ
cana-1033	29	19	knowledge	knowledge	NOUN
cana-1033	29	20	of	of	ADP
cana-1033	29	21	the	the	DET
cana-1033	29	22	beta	beta	ADJ
cana-1033	29	23	weakly	weakly	ADJ
cana-1033	29	24	semi	semi	ADJ
cana-1033	29	25	-	-	ADJ
cana-1033	29	26	closed	closed	ADJ
cana-1033	29	27	sets	set	NOUN
cana-1033	29	28	in	in	ADP
cana-1033	29	29	topological	topological	ADJ
cana-1033	29	30	spaces	space	NOUN
cana-1033	29	31	were	be	AUX
cana-1033	29	32	studied	study	VERB
cana-1033	29	33	.	.	PUNCT
cana-1033	30	1	whenever	whenever	SCONJ
cana-1033	30	2	a	a	PRON
cana-1033	30	3	is	be	AUX
cana-1033	30	4	g*s	g*s	ADJ
cana-1033	30	5	-	-	ADJ
cana-1033	30	6	compact	compact	ADJ
cana-1033	30	7	of	of	ADP
cana-1033	30	8	the	the	DET
cana-1033	30	9	subspace	subspace	NOUN
cana-1033	30	10	of	of	ADP
cana-1033	30	11	x	x	PROPN
cana-1033	30	12	is	be	AUX
cana-1033	30	13	called	call	VERB
cana-1033	30	14	g*s	g*s	ADJ
cana-1033	30	15	-	-	ADJ
cana-1033	30	16	compact	compact	ADJ
cana-1033	30	17	[	[	X
cana-1033	30	18	15	15	NUM
cana-1033	30	19	]	]	PUNCT
cana-1033	30	20	.	.	PUNCT
cana-1033	31	1	a	a	DET
cana-1033	31	2	topological	topological	ADJ
cana-1033	31	3	space	space	NOUN
cana-1033	31	4	𝑋	𝑋	NOUN
cana-1033	31	5	is	be	AUX
cana-1033	31	6	said	say	VERB
cana-1033	31	7	to	to	PART
cana-1033	31	8	be	be	AUX
cana-1033	31	9	generalized	generalize	VERB
cana-1033	31	10	semi	semi	ADJ
cana-1033	31	11	-	-	ADJ
cana-1033	31	12	open	open	ADJ
cana-1033	31	13	connected	connected	ADJ
cana-1033	31	14	(	(	PUNCT
cana-1033	31	15	briefly	briefly	ADV
cana-1033	31	16	𝑔𝑠𝑜-connected	𝑔𝑠𝑜-connecte	VERB
cana-1033	31	17	)	)	PUNCT
cana-1033	31	18	if	if	SCONJ
cana-1033	31	19	𝑋	𝑋	PROPN
cana-1033	31	20	can	can	AUX
cana-1033	31	21	not	not	PART
cana-1033	31	22	be	be	AUX
cana-1033	31	23	written	write	VERB
cana-1033	31	24	as	as	ADP
cana-1033	31	25	the	the	DET
cana-1033	31	26	union	union	NOUN
cana-1033	31	27	of	of	ADP
cana-1033	31	28	two	two	NUM
cana-1033	31	29	non	non	ADJ
cana-1033	31	30	-	-	ADJ
cana-1033	31	31	empty	empty	ADJ
cana-1033	31	32	disjoint	disjoint	ADJ
cana-1033	31	33	𝑔𝑠𝑜-open	𝑔𝑠𝑜-open	ADJ
cana-1033	31	34	sets	set	NOUN
cana-1033	31	35	[	[	X
cana-1033	31	36	16	16	NUM
cana-1033	31	37	]	]	PUNCT
cana-1033	31	38	.	.	PUNCT
cana-1033	32	1	a	a	DET
cana-1033	32	2	space	space	NOUN
cana-1033	32	3	x	x	PUNCT
cana-1033	32	4	is	be	AUX
cana-1033	32	5	said	say	VERB
cana-1033	32	6	to	to	PART
cana-1033	32	7	be	be	AUX
cana-1033	32	8	*	*	PUNCT
cana-1033	32	9	*	*	PUNCT
cana-1033	32	10	b	b	X
cana-1033	32	11	-	-	PUNCT
cana-1033	32	12	compact	compact	ADJ
cana-1033	32	13	if	if	SCONJ
cana-1033	32	14	every	every	PRON
cana-1033	32	15	“	"	PUNCT
cana-1033	32	16	*	*	NOUN
cana-1033	32	17	*	*	NOUN
cana-1033	32	18	b	b	X
cana-1033	32	19	-	-	PUNCT
cana-1033	32	20	open	open	ADJ
cana-1033	32	21	cover	cover	NOUN
cana-1033	32	22	{	{	PUNCT
cana-1033	32	23	𝐴	𝐴	NOUN
cana-1033	32	24	}	}	PUNCT
cana-1033	32	25	of	of	ADP
cana-1033	32	26	x	x	PUNCT
cana-1033	32	27	contains	contain	VERB
cana-1033	32	28	a	a	DET
cana-1033	32	29	finite	finite	ADJ
cana-1033	32	30	sub	sub	NOUN
cana-1033	32	31	collection	collection	NOUN
cana-1033	32	32	that	that	PRON
cana-1033	32	33	also	also	ADV
cana-1033	32	34	covers	cover	VERB
cana-1033	32	35	x	x	PRON
cana-1033	32	36	’’	’'	PUNCT
cana-1033	33	1	[	[	X
cana-1033	33	2	1	1	NUM
cana-1033	33	3	-	-	SYM
cana-1033	33	4	3	3	NUM
cana-1033	33	5	]	]	PUNCT
cana-1033	33	6	.	.	PUNCT
cana-1033	34	1	the	the	DET
cana-1033	34	2	methods	method	NOUN
cana-1033	34	3	applied	apply	VERB
cana-1033	34	4	for	for	ADP
cana-1033	34	5	studying	study	VERB
cana-1033	34	6	these	these	DET
cana-1033	34	7	sets	set	NOUN
cana-1033	34	8	,	,	PUNCT
cana-1033	34	9	the	the	DET
cana-1033	34	10	extensiveness	extensiveness	NOUN
cana-1033	34	11	of	of	ADP
cana-1033	34	12	the	the	DET
cana-1033	34	13	research	research	NOUN
cana-1033	34	14	,	,	PUNCT
cana-1033	34	15	and	and	CCONJ
cana-1033	34	16	the	the	DET
cana-1033	34	17	way	way	NOUN
cana-1033	34	18	these	these	DET
cana-1033	34	19	concepts	concept	NOUN
cana-1033	34	20	are	be	AUX
cana-1033	34	21	used	use	VERB
cana-1033	34	22	to	to	PART
cana-1033	34	23	better	well	ADV
cana-1033	34	24	comprehend	comprehend	VERB
cana-1033	34	25	authentic	authentic	ADJ
cana-1033	34	26	topological	topological	ADJ
cana-1033	34	27	issues	issue	NOUN
cana-1033	34	28	.	.	PUNCT
cana-1033	35	1	the	the	DET
cana-1033	35	2	emergence	emergence	NOUN
cana-1033	35	3	of	of	ADP
cana-1033	35	4	beta	beta	ADJ
cana-1033	35	5	weakly	weakly	ADJ
cana-1033	35	6	semi	semi	ADJ
cana-1033	35	7	-	-	ADJ
cana-1033	35	8	closed	closed	ADJ
cana-1033	35	9	sets	set	NOUN
cana-1033	35	10	in	in	ADP
cana-1033	35	11	topological	topological	ADJ
cana-1033	35	12	spaces	space	NOUN
cana-1033	35	13	,	,	PUNCT
cana-1033	35	14	which	which	PRON
cana-1033	35	15	provide	provide	VERB
cana-1033	35	16	an	an	DET
cana-1033	35	17	innovative	innovative	ADJ
cana-1033	35	18	viewpoint	viewpoint	NOUN
cana-1033	35	19	,	,	PUNCT
cana-1033	35	20	is	be	AUX
cana-1033	35	21	anticipated	anticipate	VERB
cana-1033	35	22	to	to	PART
cana-1033	35	23	advance	advance	VERB
cana-1033	35	24	our	our	PRON
cana-1033	35	25	understanding	understanding	NOUN
cana-1033	35	26	of	of	ADP
cana-1033	35	27	the	the	DET
cana-1033	35	28	field	field	NOUN
cana-1033	35	29	of	of	ADP
cana-1033	35	30	topological	topological	ADJ
cana-1033	35	31	spaces	space	NOUN
cana-1033	35	32	and	and	CCONJ
cana-1033	35	33	its	its	PRON
cana-1033	35	34	basic	basic	ADJ
cana-1033	35	35	features	feature	NOUN
cana-1033	35	36	.	.	PUNCT
cana-1033	36	1	2	2	X
cana-1033	36	2	.	.	X
cana-1033	36	3	preliminary	preliminary	ADJ
cana-1033	36	4	notes	note	NOUN
cana-1033	36	5	:	:	PUNCT
cana-1033	36	6	all	all	PRON
cana-1033	36	7	through	through	ADP
cana-1033	36	8	this	this	DET
cana-1033	36	9	study	study	NOUN
cana-1033	36	10	,	,	PUNCT
cana-1033	36	11	(	(	PUNCT
cana-1033	36	12	x	x	X
cana-1033	36	13	,	,	PUNCT
cana-1033	36	14	τ	τ	PROPN
cana-1033	36	15	)	)	PUNCT
cana-1033	36	16	and	and	CCONJ
cana-1033	36	17	(	(	PUNCT
cana-1033	36	18	y	y	PROPN
cana-1033	36	19	,	,	PUNCT
cana-1033	36	20	σ	σ	PROPN
cana-1033	36	21	)	)	PUNCT
cana-1033	36	22	as	as	SCONJ
cana-1033	36	23	generic	generic	ADJ
cana-1033	36	24	topological	topological	ADJ
cana-1033	36	25	spaces	space	NOUN
cana-1033	36	26	were	be	AUX
cana-1033	36	27	considered	consider	VERB
cana-1033	36	28	unless	unless	SCONJ
cana-1033	36	29	specified	specify	VERB
cana-1033	36	30	otherwise	otherwise	ADV
cana-1033	36	31	,	,	PUNCT
cana-1033	36	32	without	without	ADP
cana-1033	36	33	assuming	assume	VERB
cana-1033	36	34	any	any	DET
cana-1033	36	35	separation	separation	NOUN
cana-1033	36	36	axioms	axiom	VERB
cana-1033	36	37	.	.	PUNCT
cana-1033	37	1	for	for	ADP
cana-1033	37	2	the	the	DET
cana-1033	37	3	closure	closure	NOUN
cana-1033	37	4	of	of	ADP
cana-1033	37	5	set	set	NOUN
cana-1033	38	1	a	a	PRON
cana-1033	38	2	is	be	AUX
cana-1033	38	3	x	x	NOUN
cana-1033	38	4	,	,	PUNCT
cana-1033	38	5	we	we	PRON
cana-1033	38	6	denote	denote	VERB
cana-1033	38	7	it	it	PRON
cana-1033	38	8	as	as	ADP
cana-1033	38	9	cl	cl	NOUN
cana-1033	38	10	(	(	PUNCT
cana-1033	38	11	a	a	NOUN
cana-1033	38	12	)	)	PUNCT
cana-1033	38	13	,	,	PUNCT
cana-1033	38	14	and	and	CCONJ
cana-1033	38	15	int	int	NOUN
cana-1033	38	16	(	(	PUNCT
cana-1033	38	17	a	a	NOUN
cana-1033	38	18	)	)	PUNCT
cana-1033	38	19	represents	represent	VERB
cana-1033	38	20	the	the	DET
cana-1033	38	21	interior	interior	NOUN
cana-1033	38	22	of	of	ADP
cana-1033	38	23	a.	a.	NOUN
cana-1033	38	24	definition:2.1.[1	definition:2.1.[1	PROPN
cana-1033	38	25	]	]	PUNCT
cana-1033	38	26	“	"	PUNCT
cana-1033	38	27	a	a	DET
cana-1033	38	28	subset	subset	NOUN
cana-1033	38	29	a	a	PRON
cana-1033	38	30	of	of	ADP
cana-1033	38	31	x	x	SYM
cana-1033	38	32	is	be	AUX
cana-1033	38	33	said	say	VERB
cana-1033	38	34	to	to	PART
cana-1033	38	35	be	be	AUX
cana-1033	38	36	b	b	NOUN
cana-1033	38	37	-	-	PUNCT
cana-1033	38	38	open	open	ADJ
cana-1033	38	39	[	[	X
cana-1033	38	40	1	1	NUM
cana-1033	38	41	]	]	PUNCT
cana-1033	38	42	if	if	SCONJ
cana-1033	38	43	a⊆int(cl(a))∪cl(int(a	a⊆int(cl(a))∪cl(int(a	NOUN
cana-1033	38	44	)	)	PUNCT
cana-1033	38	45	)	)	PUNCT
cana-1033	38	46	.	.	PUNCT
cana-1033	39	1	the	the	DET
cana-1033	39	2	complement	complement	NOUN
cana-1033	39	3	of	of	ADP
cana-1033	39	4	b	b	NOUN
cana-1033	39	5	-	-	PUNCT
cana-1033	39	6	open	open	ADJ
cana-1033	39	7	set	set	NOUN
cana-1033	39	8	is	be	AUX
cana-1033	39	9	said	say	VERB
cana-1033	39	10	to	to	PART
cana-1033	39	11	be	be	AUX
cana-1033	39	12	b	b	NOUN
cana-1033	39	13	-	-	PUNCT
cana-1033	39	14	closed	closed	ADJ
cana-1033	39	15	.	.	PUNCT
cana-1033	40	1	the	the	DET
cana-1033	40	2	family	family	NOUN
cana-1033	40	3	of	of	ADP
cana-1033	40	4	all	all	DET
cana-1033	40	5	b	b	NOUN
cana-1033	40	6	-	-	PUNCT
cana-1033	40	7	open	open	ADJ
cana-1033	40	8	sets	set	NOUN
cana-1033	40	9	(	(	PUNCT
cana-1033	40	10	respectively	respectively	ADV
cana-1033	40	11	b	b	X
cana-1033	40	12	-	-	PUNCT
cana-1033	40	13	closed	closed	ADJ
cana-1033	40	14	sets	set	NOUN
cana-1033	40	15	)	)	PUNCT
cana-1033	40	16	of	of	ADP
cana-1033	40	17	(	(	PUNCT
cana-1033	40	18	x	x	NOUN
cana-1033	40	19	,	,	PUNCT
cana-1033	40	20	τ	τ	X
cana-1033	40	21	)	)	PUNCT
cana-1033	40	22	is	be	AUX
cana-1033	40	23	denoted	denote	VERB
cana-1033	40	24	by	by	ADP
cana-1033	40	25	bo(x	bo(x	NUM
cana-1033	40	26	,	,	PUNCT
cana-1033	40	27	τ	τ	X
cana-1033	40	28	)	)	PUNCT
cana-1033	41	1	[	[	X
cana-1033	41	2	respectively	respectively	ADV
cana-1033	41	3	bcl(x	bcl(x	PROPN
cana-1033	41	4	,	,	PUNCT
cana-1033	41	5	τ	τ	PROPN
cana-1033	41	6	)	)	PUNCT
cana-1033	41	7	]	]	PUNCT
cana-1033	41	8	”	"	PUNCT
cana-1033	41	9	.	.	PUNCT
cana-1033	42	1	definition	definition	NOUN
cana-1033	42	2	2.2.[1	2.2.[1	NUM
cana-1033	42	3	]	]	PUNCT
cana-1033	42	4	let	let	VERB
cana-1033	42	5	a	a	DET
cana-1033	42	6			PROPN
cana-1033	42	7	x.	x.	NOUN
cana-1033	42	8	then	then	ADV
cana-1033	42	9	(	(	PUNCT
cana-1033	42	10	i	i	NOUN
cana-1033	42	11	)	)	PUNCT
cana-1033	42	12	“	"	PUNCT
cana-1033	42	13	b	b	X
cana-1033	42	14	-	-	PUNCT
cana-1033	42	15	interior	interior	ADJ
cana-1033	42	16	[	[	X
cana-1033	42	17	1	1	NUM
cana-1033	42	18	]	]	PUNCT
cana-1033	42	19	of	of	ADP
cana-1033	42	20	a	a	PRON
cana-1033	42	21	is	be	AUX
cana-1033	42	22	the	the	DET
cana-1033	42	23	union	union	NOUN
cana-1033	42	24	of	of	ADP
cana-1033	42	25	all	all	DET
cana-1033	42	26	b	b	NOUN
cana-1033	42	27	-	-	PUNCT
cana-1033	42	28	open	open	ADJ
cana-1033	42	29	sets	set	NOUN
cana-1033	42	30	contained	contain	VERB
cana-1033	42	31	in	in	ADP
cana-1033	42	32	a	a	PRON
cana-1033	42	33	”	"	PUNCT
cana-1033	42	34	.	.	PUNCT
cana-1033	43	1	(	(	PUNCT
cana-1033	43	2	ii)“b	ii)“b	NOUN
cana-1033	43	3	-	-	PUNCT
cana-1033	43	4	closure	closure	NOUN
cana-1033	43	5	[	[	X
cana-1033	43	6	1	1	NUM
cana-1033	43	7	]	]	PUNCT
cana-1033	43	8	of	of	ADP
cana-1033	43	9	a	a	PRON
cana-1033	43	10	is	be	AUX
cana-1033	43	11	the	the	DET
cana-1033	43	12	intersection	intersection	NOUN
cana-1033	43	13	of	of	ADP
cana-1033	43	14	all	all	DET
cana-1033	43	15	b	b	NOUN
cana-1033	43	16	-	-	PUNCT
cana-1033	43	17	closed	closed	ADJ
cana-1033	43	18	sets	set	NOUN
cana-1033	43	19	containing	contain	VERB
cana-1033	43	20	a.	a.	NOUN
cana-1033	43	21	the	the	DET
cana-1033	43	22	b	b	NOUN
cana-1033	43	23	-	-	PUNCT
cana-1033	43	24	interior	interior	ADJ
cana-1033	43	25	[	[	PUNCT
cana-1033	43	26	respectively	respectively	ADV
cana-1033	43	27	b	b	NOUN
cana-1033	43	28	-	-	PUNCT
cana-1033	43	29	closure	closure	NOUN
cana-1033	43	30	]	]	PUNCT
cana-1033	43	31	of	of	ADP
cana-1033	43	32	a	a	PRON
cana-1033	43	33	is	be	AUX
cana-1033	43	34	denoted	denote	VERB
cana-1033	43	35	by	by	ADP
cana-1033	43	36	b	b	NOUN
cana-1033	43	37	-	-	PUNCT
cana-1033	43	38	int(a	int(a	NOUN
cana-1033	43	39	)	)	PUNCT
cana-1033	44	1	[	[	X
cana-1033	44	2	respectively	respectively	ADV
cana-1033	44	3	b	b	NOUN
cana-1033	44	4	-	-	PUNCT
cana-1033	44	5	cl(a	cl(a	NUM
cana-1033	44	6	)	)	PUNCT
cana-1033	44	7	]	]	PUNCT
cana-1033	44	8	”	"	PUNCT
cana-1033	44	9	.	.	PUNCT
cana-1033	45	1	3	3	X
cana-1033	45	2	.	.	X
cana-1033	45	3	ws	ws	NOUN
cana-1033	45	4	-	-	PUNCT
cana-1033	45	5	compactness	compactness	NOUN
cana-1033	45	6	in	in	ADP
cana-1033	45	7	ts	ts	ADP
cana-1033	45	8	:	:	PUNCT
cana-1033	45	9	this	this	DET
cana-1033	45	10	section	section	NOUN
cana-1033	45	11	examines	examine	VERB
cana-1033	45	12	the	the	DET
cana-1033	45	13	idea	idea	NOUN
cana-1033	45	14	of	of	ADP
cana-1033	45	15	βws	βws	NOUN
cana-1033	45	16	-	-	PUNCT
cana-1033	45	17	compactness	compactness	NOUN
cana-1033	45	18	other	other	ADJ
cana-1033	45	19	than	than	ADP
cana-1033	45	20	subsequently	subsequently	ADV
cana-1033	45	21	explores	explore	VERB
cana-1033	45	22	it	it	PRON
cana-1033	45	23	’s	’	VERB
cana-1033	45	24	characteristics	characteristic	NOUN
cana-1033	45	25	and	and	CCONJ
cana-1033	45	26	also	also	ADV
cana-1033	45	27	provides	provide	VERB
cana-1033	45	28	its	its	PRON
cana-1033	45	29	fundamental	fundamental	ADJ
cana-1033	45	30	properties	property	NOUN
cana-1033	45	31	definition	definition	NOUN
cana-1033	45	32	3.1	3.1	NUM
cana-1033	45	33	.	.	PUNCT
cana-1033	46	1	the	the	DET
cana-1033	46	2	collection	collection	NOUN
cana-1033	46	3	{	{	PUNCT
cana-1033	46	4	ģi	ģi	NOUN
cana-1033	46	5	:	:	PUNCT
cana-1033	46	6	iϵi	iϵi	PROPN
cana-1033	46	7	}	}	PUNCT
cana-1033	46	8	of	of	ADP
cana-1033	46	9	ws	ws	NOUN
cana-1033	46	10	-	-	PUNCT
cana-1033	46	11	o	o	NOUN
cana-1033	46	12	-	-	NOUN
cana-1033	46	13	s	s	X
cana-1033	46	14	in	in	ADP
cana-1033	46	15	a	a	DET
cana-1033	46	16	ts	ts	NOUN
cana-1033	46	17	x	x	SYM
cana-1033	46	18	is	be	AUX
cana-1033	46	19	known	know	VERB
cana-1033	46	20	as	as	ADP
cana-1033	46	21	ws	ws	NOUN
cana-1033	46	22	-	-	PUNCT
cana-1033	46	23	o	o	NOUN
cana-1033	46	24	-	-	NOUN
cana-1033	46	25	c	c	NOUN
cana-1033	46	26			PROPN
cana-1033	46	27	ģ	ģ	PRON
cana-1033	46	28	related	relate	VERB
cana-1033	46	29	to	to	ADP
cana-1033	46	30	x	x	PRON
cana-1033	46	31	if	if	SCONJ
cana-1033	46	32	ģ⋃	ģ⋃	PROPN
cana-1033	46	33	iϵi	iϵi	VERB
cana-1033	46	34	ģi	ģi	NOUN
cana-1033	46	35	definition	definition	NOUN
cana-1033	46	36	3.2	3.2	NUM
cana-1033	46	37	.	.	PUNCT
cana-1033	47	1	the	the	DET
cana-1033	47	2	ts	ts	NOUN
cana-1033	47	3	x	x	AUX
cana-1033	47	4	were	be	AUX
cana-1033	47	5	named	name	VERB
cana-1033	47	6	as	as	ADP
cana-1033	47	7	ws	ws	NOUN
cana-1033	47	8	-	-	PUNCT
cana-1033	47	9	compact	compact	ADJ
cana-1033	47	10	with	with	ADP
cana-1033	47	11	each	each	PRON
cana-1033	47	12	and	and	CCONJ
cana-1033	47	13	every	every	DET
cana-1033	47	14	one	one	NUM
cana-1033	47	15	ws	ws	NOUN
cana-1033	47	16	-	-	PUNCT
cana-1033	47	17	o	o	NOUN
cana-1033	47	18	-	-	NOUN
cana-1033	47	19	c	c	NOUN
cana-1033	47	20	of	of	ADP
cana-1033	47	21	x	x	AUX
cana-1033	47	22	include	include	VERB
cana-1033	47	23	a	a	DET
cana-1033	47	24	finite	finite	ADJ
cana-1033	47	25	sub	sub	NOUN
cana-1033	47	26	cover	cover	NOUN
cana-1033	47	27	.	.	PUNCT
cana-1033	48	1	definition	definition	NOUN
cana-1033	48	2	3.3	3.3	NUM
cana-1033	48	3	.	.	PUNCT
cana-1033	49	1	a	a	DET
cana-1033	49	2			PROPN
cana-1033	49	3	ģ	ģ	PROPN
cana-1033	49	4	of	of	ADP
cana-1033	49	5	the	the	DET
cana-1033	49	6	ts	ts	NOUN
cana-1033	49	7	x	x	PRON
cana-1033	49	8	were	be	AUX
cana-1033	49	9	named	name	VERB
cana-1033	49	10	as	as	ADP
cana-1033	49	11	ws	ws	NOUN
cana-1033	49	12	-	-	PUNCT
cana-1033	49	13	compact	compact	NOUN
cana-1033	49	14	related	relate	VERB
cana-1033	49	15	to	to	ADP
cana-1033	49	16	x	x	PRON
cana-1033	49	17	,	,	PUNCT
cana-1033	49	18			NOUN
cana-1033	49	19	collection	collection	NOUN
cana-1033	49	20	{	{	PUNCT
cana-1033	49	21	ģ	ģ	NOUN
cana-1033	49	22	i	i	PRON
cana-1033	49	23	:	:	PUNCT
cana-1033	49	24	iϵi	iϵi	NOUN
cana-1033	49	25	}	}	PUNCT
cana-1033	49	26	of	of	ADP
cana-1033	49	27	ws	ws	NOUN
cana-1033	49	28	–	–	PUNCT
cana-1033	49	29	o	o	NOUN
cana-1033	49	30			PROPN
cana-1033	49	31	x	x	PUNCT
cana-1033	49	32			ADP
cana-1033	49	33	ģ	ģ	PRON
cana-1033	49	34			PROPN
cana-1033	49	35	⋃	⋃	PROPN
cana-1033	49	36	ai	ai	VERB
cana-1033	49	37	iϵi	iϵi	PROPN
cana-1033	49	38			PROPN
cana-1033	49	39	finite	finite	ADJ
cana-1033	49	40			PROPN
cana-1033	49	41	i0	i0	PROPN
cana-1033	49	42	of	of	ADP
cana-1033	49	43	i	i	PRON
cana-1033	49	44			PROPN
cana-1033	50	1	ģ	ģ	PROPN
cana-1033	50	2			PROPN
cana-1033	50	3	⋃	⋃	PROPN
cana-1033	50	4	ai	ai	VERB
cana-1033	50	5	iϵi	iϵi	NOUN
cana-1033	50	6	.	.	PUNCT
cana-1033	51	1	communications	communication	NOUN
cana-1033	51	2	on	on	ADP
cana-1033	51	3	applied	apply	VERB
cana-1033	51	4	nonlinear	nonlinear	ADJ
cana-1033	51	5	analysis	analysis	NOUN
cana-1033	51	6	issn	issn	NOUN
cana-1033	51	7	:	:	PUNCT
cana-1033	51	8	1074	1074	NUM
cana-1033	51	9	-	-	PUNCT
cana-1033	51	10	133x	133x	NUM
cana-1033	51	11	vol	vol	NOUN
cana-1033	51	12	31	31	NUM
cana-1033	51	13	no	no	NOUN
cana-1033	51	14	.	.	PUNCT
cana-1033	52	1	5s	5s	NUM
cana-1033	52	2	(	(	PUNCT
cana-1033	52	3	2024	2024	NUM
cana-1033	52	4	)	)	PUNCT
cana-1033	52	5	261	261	NUM
cana-1033	52	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1033	52	7	definition	definition	NOUN
cana-1033	52	8	3.4	3.4	NUM
cana-1033	52	9	.	.	PUNCT
cana-1033	53	1	a	a	DET
cana-1033	53	2			PROPN
cana-1033	53	3	ģ	ģ	PROPN
cana-1033	53	4	of	of	ADP
cana-1033	53	5	a	a	DET
cana-1033	53	6	ts	ts	NOUN
cana-1033	53	7	x	x	AUX
cana-1033	53	8	were	be	AUX
cana-1033	53	9	named	name	VERB
cana-1033	53	10	as	as	ADP
cana-1033	53	11	ws	ws	ADJ
cana-1033	53	12	compact	compact	ADJ
cana-1033	53	13	if	if	SCONJ
cana-1033	53	14	ģ	ģ	PROPN
cana-1033	53	15	is	be	AUX
cana-1033	53	16	ws	ws	ADJ
cana-1033	53	17	-	-	PUNCT
cana-1033	53	18	compact	compact	ADJ
cana-1033	53	19			PROPN
cana-1033	53	20	x.	x.	NOUN
cana-1033	53	21	theorem	theorem	VERB
cana-1033	53	22	3.5	3.5	NUM
cana-1033	53	23	.	.	PUNCT
cana-1033	54	1	a	a	DET
cana-1033	54	2	ws	ws	NOUN
cana-1033	54	3	-	-	PUNCT
cana-1033	54	4	c	c	NOUN
cana-1033	54	5			PROPN
cana-1033	54	6	ws	ws	ADJ
cana-1033	54	7	-compact	-compact	PROPN
cana-1033	54	8	space	space	NOUN
cana-1033	54	9	were	be	AUX
cana-1033	54	10	considered	consider	VERB
cana-1033	54	11	as	as	ADP
cana-1033	54	12	ws	ws	ADJ
cana-1033	54	13	-	-	PUNCT
cana-1033	54	14	compact	compact	ADJ
cana-1033	54	15	relative	relative	NOUN
cana-1033	54	16	to	to	ADP
cana-1033	54	17	x.	x.	NOUN
cana-1033	54	18	proof	proof	PROPN
cana-1033	54	19	.	.	PUNCT
cana-1033	55	1	assume	assume	VERB
cana-1033	55	2	that	that	SCONJ
cana-1033	55	3	ģ	ģ	PRON
cana-1033	55	4	be	be	VERB
cana-1033	55	5	a	a	DET
cana-1033	55	6	ws	ws	NOUN
cana-1033	55	7	-	-	PUNCT
cana-1033	55	8	c	c	NOUN
cana-1033	55	9			NOUN
cana-1033	55	10	ts	ts	ADP
cana-1033	55	11	in	in	ADP
cana-1033	55	12	x.	x.	PROPN
cana-1033	55	13	thence	thence	PROPN
cana-1033	55	14	ģc	ģc	PROPN
cana-1033	55	15	is	be	AUX
cana-1033	55	16	ws	ws	ADJ
cana-1033	55	17	-	-	PUNCT
cana-1033	55	18	o	o	NOUN
cana-1033	55	19	in	in	ADP
cana-1033	55	20	x	x	PROPN
cana-1033	55	21	,	,	PUNCT
cana-1033	55	22	𝒮	𝒮	PROPN
cana-1033	55	23	=	=	PRON
cana-1033	55	24	{	{	PUNCT
cana-1033	55	25	ģi	ģi	NOUN
cana-1033	55	26	:	:	PUNCT
cana-1033	55	27	iϵi	iϵi	PROPN
cana-1033	55	28	}	}	PUNCT
cana-1033	55	29	exist	exist	VERB
cana-1033	55	30	a	a	DET
cana-1033	55	31	ws	ws	ADJ
cana-1033	55	32	-	-	PUNCT
cana-1033	55	33	o	o	NOUN
cana-1033	55	34	-	-	NOUN
cana-1033	55	35	c	c	NOUN
cana-1033	55	36	of	of	ADP
cana-1033	55	37	ģ	ģ	PROPN
cana-1033	55	38	by	by	ADP
cana-1033	55	39	ws	ws	ADJ
cana-1033	55	40	-	-	PUNCT
cana-1033	55	41	o	o	NOUN
cana-1033	55	42			PROPN
cana-1033	55	43	x.	x.	NOUN
cana-1033	55	44	after	after	ADP
cana-1033	55	45	that	that	PRON
cana-1033	55	46	,	,	PUNCT
cana-1033	55	47	𝒮	𝒮	PROPN
cana-1033	55	48	*	*	SYM
cana-1033	55	49	=	=	SYM
cana-1033	55	50	𝒮	𝒮	PROPN
cana-1033	55	51	∪	∪	NOUN
cana-1033	55	52	ģc	ģc	NOUN
cana-1033	55	53	is	be	AUX
cana-1033	55	54	a	a	DET
cana-1033	55	55	ws	ws	ADJ
cana-1033	55	56	-	-	PUNCT
cana-1033	55	57	o	o	NOUN
cana-1033	55	58	-	-	NOUN
cana-1033	55	59	c	c	NOUN
cana-1033	55	60	of	of	ADP
cana-1033	55	61	x.	x.	NOUN
cana-1033	55	62	that	that	PRON
cana-1033	55	63	is	be	AUX
cana-1033	55	64	x	x	X
cana-1033	55	65	=	=	PUNCT
cana-1033	56	1	[	[	X
cana-1033	56	2	∪{ģi	∪{ģi	NUM
cana-1033	56	3	:	:	PUNCT
cana-1033	56	4	iϵi}]∪	iϵi}]∪	NOUN
cana-1033	56	5	ģc	ģc	NOUN
cana-1033	56	6	.	.	PUNCT
cana-1033	57	1	by	by	ADP
cana-1033	57	2	the	the	DET
cana-1033	57	3	assumption	assumption	NOUN
cana-1033	57	4	that	that	SCONJ
cana-1033	57	5	,	,	PUNCT
cana-1033	57	6	x	x	PRON
cana-1033	57	7	will	will	AUX
cana-1033	57	8	be	be	AUX
cana-1033	57	9	considered	consider	VERB
cana-1033	57	10	as	as	ADP
cana-1033	57	11	ws	ws	NOUN
cana-1033	57	12	-	-	PUNCT
cana-1033	57	13	compact	compact	ADJ
cana-1033	57	14	,	,	PUNCT
cana-1033	57	15	∴	∴	PROPN
cana-1033	57	16	,	,	PUNCT
cana-1033	57	17	𝒮	𝒮	PROPN
cana-1033	57	18	*	*	NOUN
cana-1033	57	19	reduction	reduction	NOUN
cana-1033	57	20	to	to	ADP
cana-1033	57	21	a	a	DET
cana-1033	57	22	finite	finite	ADJ
cana-1033	57	23	subcover	subcover	NOUN
cana-1033	57	24	of	of	ADP
cana-1033	57	25	x	x	PROPN
cana-1033	57	26	for	for	ADP
cana-1033	57	27	example	example	NOUN
cana-1033	57	28	,	,	PUNCT
cana-1033	57	29	x	x	PUNCT
cana-1033	57	30	=	=	PUNCT
cana-1033	57	31	ģi1∪	ģi1∪	NOUN
cana-1033	57	32	ģi2∪	ģi2∪	NOUN
cana-1033	57	33	…	…	PUNCT
cana-1033	57	34	∪	∪	X
cana-1033	57	35	ģin	ģin	PROPN
cana-1033	57	36	∪	∪	NOUN
cana-1033	57	37	ģc	ģc	PROPN
cana-1033	57	38	,	,	PUNCT
cana-1033	57	39	ģik	ģik	PROPN
cana-1033	57	40	𝒮	𝒮	PROPN
cana-1033	57	41	*	*	PROPN
cana-1033	57	42	.	.	PUNCT
cana-1033	58	1	since	since	SCONJ
cana-1033	58	2	ģ	ģ	PROPN
cana-1033	58	3	and	and	CCONJ
cana-1033	58	4	ģc	ģc	PROPN
cana-1033	58	5	are	be	AUX
cana-1033	58	6	disjoint	disjoint	ADJ
cana-1033	58	7	.	.	PUNCT
cana-1033	59	1	∴	∴	PROPN
cana-1033	59	2	,	,	PUNCT
cana-1033	59	3	ģ	ģ	PROPN
cana-1033	59	4			PROPN
cana-1033	59	5	ģi1∪	ģi1∪	NOUN
cana-1033	59	6	ģi2∪	ģi2∪	PROPN
cana-1033	59	7	…	…	PUNCT
cana-1033	59	8	..	..	PUNCT
cana-1033	59	9	∪	∪	ADP
cana-1033	59	10	ģin𝒮.	ģin𝒮.	NOUN
cana-1033	59	11	thus	thus	ADV
cana-1033	59	12	a	a	DET
cana-1033	59	13	ws	ws	ADJ
cana-1033	59	14	-	-	PUNCT
cana-1033	59	15	o	o	NOUN
cana-1033	59	16	-	-	NOUN
cana-1033	59	17	c	c	NOUN
cana-1033	59	18	𝒮	𝒮	PROPN
cana-1033	59	19	of	of	ADP
cana-1033	59	20	ģ	ģ	PROPN
cana-1033	59	21			PROPN
cana-1033	59	22	finite	finite	PROPN
cana-1033	59	23	subcover	subcover	PROPN
cana-1033	59	24	,	,	PUNCT
cana-1033	59	25	proving	prove	VERB
cana-1033	59	26	that	that	SCONJ
cana-1033	59	27	ģ	ģ	PRON
cana-1033	59	28	is	be	AUX
cana-1033	59	29	the	the	DET
cana-1033	59	30	βws	βws	ADV
cana-1033	59	31	compact	compact	ADJ
cana-1033	59	32	related	relate	VERB
cana-1033	59	33	to	to	ADP
cana-1033	59	34	x.	x.	NOUN
cana-1033	59	35	theorem	theorem	VERB
cana-1033	59	36	3.6	3.6	NUM
cana-1033	59	37	:	:	PUNCT
cana-1033	59	38	each	each	DET
cana-1033	59	39	ws	ws	ADJ
cana-1033	59	40	-	-	PUNCT
cana-1033	59	41	compact	compact	ADJ
cana-1033	59	42	space	space	NOUN
cana-1033	59	43	are	be	AUX
cana-1033	59	44	considered	consider	VERB
cana-1033	59	45	as	as	ADP
cana-1033	59	46	compact	compact	ADJ
cana-1033	59	47	.	.	PUNCT
cana-1033	60	1	proof	proof	NOUN
cana-1033	60	2	.	.	PUNCT
cana-1033	61	1	assume	assume	VERB
cana-1033	61	2	that	that	SCONJ
cana-1033	61	3	x	x	PRON
cana-1033	61	4	are	be	AUX
cana-1033	61	5	considered	consider	VERB
cana-1033	61	6	as	as	SCONJ
cana-1033	61	7	ws	ws	ADJ
cana-1033	61	8	-	-	PUNCT
cana-1033	61	9	compact	compact	ADJ
cana-1033	61	10	space.{ģi	space.{ģi	NOUN
cana-1033	61	11	:	:	PUNCT
cana-1033	61	12	iϵi	iϵi	NOUN
cana-1033	61	13	}	}	PUNCT
cana-1033	61	14	is	be	AUX
cana-1033	61	15	an	an	DET
cana-1033	61	16	o	o	NOUN
cana-1033	61	17	-	-	NOUN
cana-1033	61	18	c	c	NOUN
cana-1033	61	19	of	of	ADP
cana-1033	61	20	x.	x.	PROPN
cana-1033	61	21	thenceforth	thenceforth	NOUN
cana-1033	61	22	{	{	PUNCT
cana-1033	61	23	ģi	ģi	NOUN
cana-1033	61	24	:	:	PUNCT
cana-1033	61	25	iϵi	iϵi	PROPN
cana-1033	61	26	}	}	PUNCT
cana-1033	61	27	will	will	AUX
cana-1033	61	28	be	be	AUX
cana-1033	61	29	a	a	DET
cana-1033	61	30	ws	ws	ADJ
cana-1033	61	31	-	-	PUNCT
cana-1033	61	32	o	o	NOUN
cana-1033	61	33	-	-	NOUN
cana-1033	61	34	c	c	NOUN
cana-1033	61	35	of	of	ADP
cana-1033	61	36	x	x	PRON
cana-1033	61	37	since	since	SCONJ
cana-1033	61	38	every	every	DET
cana-1033	61	39	o	o	NOUN
cana-1033	61	40	-	-	PUNCT
cana-1033	61	41	s	s	X
cana-1033	61	42	is	be	AUX
cana-1033	61	43	also	also	ADV
cana-1033	61	44	a	a	DET
cana-1033	61	45	βws	βws	NOUN
cana-1033	61	46	–	–	PUNCT
cana-1033	61	47	o	o	NOUN
cana-1033	61	48	-	-	SYM
cana-1033	61	49	s	s	PROPN
cana-1033	61	50	,	,	PUNCT
cana-1033	61	51	∴	∴	PROPN
cana-1033	61	52	,	,	PUNCT
cana-1033	61	53	x	x	PRON
cana-1033	61	54	is	be	AUX
cana-1033	61	55	ws	ws	ADJ
cana-1033	61	56	-	-	PUNCT
cana-1033	61	57	compact	compact	ADJ
cana-1033	61	58	,	,	PUNCT
cana-1033	61	59	the	the	DET
cana-1033	61	60	ws	ws	NOUN
cana-1033	61	61	-	-	PUNCT
cana-1033	61	62	o	o	NOUN
cana-1033	61	63	-	-	NOUN
cana-1033	61	64	c	c	NOUN
cana-1033	61	65	{	{	PUNCT
cana-1033	61	66	ģi	ģi	NOUN
cana-1033	61	67	:	:	PUNCT
cana-1033	61	68	iϵi	iϵi	PROPN
cana-1033	61	69	}	}	PUNCT
cana-1033	61	70	of	of	ADP
cana-1033	61	71	x	x	PUNCT
cana-1033	61	72	includes	include	VERB
cana-1033	61	73	a	a	DET
cana-1033	61	74	finite	finite	ADJ
cana-1033	61	75	subcover	subcover	PROPN
cana-1033	61	76	talks	talk	NOUN
cana-1033	61	77	{	{	PUNCT
cana-1033	61	78	ģi	ģi	NOUN
cana-1033	61	79	,	,	PUNCT
cana-1033	61	80	i	i	PRON
cana-1033	61	81	ϵ	ϵ	PROPN
cana-1033	61	82	n	n	CCONJ
cana-1033	61	83	}	}	PUNCT
cana-1033	61	84	within	within	ADP
cana-1033	61	85	x.	x.	PROPN
cana-1033	61	86	∴	∴	PROPN
cana-1033	61	87	,	,	PUNCT
cana-1033	61	88	x	x	PRON
cana-1033	61	89	is	be	AUX
cana-1033	61	90	compact	compact	ADJ
cana-1033	61	91	.	.	PUNCT
cana-1033	62	1	theorem	theorem	VERB
cana-1033	62	2	3.7	3.7	NUM
cana-1033	62	3	:	:	PUNCT
cana-1033	62	4	each	each	PRON
cana-1033	62	5	and	and	CCONJ
cana-1033	62	6	all	all	DET
cana-1033	62	7	go	go	ADJ
cana-1033	62	8	-	-	ADJ
cana-1033	62	9	compact	compact	ADJ
cana-1033	62	10	space	space	NOUN
cana-1033	62	11	are	be	AUX
cana-1033	62	12	considered	consider	VERB
cana-1033	62	13	as	as	ADP
cana-1033	62	14	ws	ws	NOUN
cana-1033	62	15	-	-	PUNCT
cana-1033	62	16	compact	compact	ADJ
cana-1033	62	17	.	.	PUNCT
cana-1033	63	1	proof	proof	NOUN
cana-1033	63	2	.	.	PUNCT
cana-1033	64	1	assuming	assume	VERB
cana-1033	64	2	x	x	PRON
cana-1033	64	3	relate	relate	VERB
cana-1033	64	4	as	as	ADP
cana-1033	64	5	a	a	DET
cana-1033	64	6	go	go	NOUN
cana-1033	64	7	-	-	ADJ
cana-1033	64	8	compact	compact	ADJ
cana-1033	64	9	space	space	NOUN
cana-1033	64	10	.	.	PUNCT
cana-1033	65	1	assuming	assume	VERB
cana-1033	65	2	,	,	PUNCT
cana-1033	65	3	{	{	PUNCT
cana-1033	65	4	ģi	ģi	NOUN
cana-1033	65	5	:	:	PUNCT
cana-1033	65	6	iϵi	iϵi	ADJ
cana-1033	65	7	}	}	PUNCT
cana-1033	65	8	relate	relate	VERB
cana-1033	65	9	as	as	SCONJ
cana-1033	65	10	a	a	DET
cana-1033	65	11	ws	ws	NOUN
cana-1033	65	12	-	-	PUNCT
cana-1033	65	13	o	o	NOUN
cana-1033	65	14	-	-	NOUN
cana-1033	65	15	c	c	NOUN
cana-1033	65	16	of	of	ADP
cana-1033	65	17	x	x	PUNCT
cana-1033	65	18	by	by	ADP
cana-1033	65	19	wso	wso	NOUN
cana-1033	65	20	-	-	PUNCT
cana-1033	65	21	s	s	NOUN
cana-1033	65	22	in	in	ADP
cana-1033	65	23	x.	x.	NOUN
cana-1033	65	24	afterward	afterward	ADV
cana-1033	65	25	,	,	PUNCT
cana-1033	65	26	every	every	DET
cana-1033	65	27	ws	ws	NOUN
cana-1033	65	28	-	-	PUNCT
cana-1033	65	29	o	o	NOUN
cana-1033	65	30	-	-	NOUN
cana-1033	65	31	s	s	NOUN
cana-1033	65	32	is	be	AUX
cana-1033	65	33	g	g	X
cana-1033	65	34	-	-	PUNCT
cana-1033	65	35	o,∴	o,∴	ADJ
cana-1033	65	36	,	,	PUNCT
cana-1033	65	37	{	{	PUNCT
cana-1033	65	38	ģi	ģi	NOUN
cana-1033	65	39	:	:	PUNCT
cana-1033	65	40	iϵi	iϵi	PROPN
cana-1033	65	41	}	}	PUNCT
cana-1033	65	42	is	be	AUX
cana-1033	65	43	g	g	NOUN
cana-1033	65	44	-	-	PUNCT
cana-1033	65	45	o	o	NOUN
cana-1033	65	46	-	-	NOUN
cana-1033	65	47	c	c	NOUN
cana-1033	65	48	regarding	regard	VERB
cana-1033	65	49	x.	x.	PROPN
cana-1033	65	50	∴	∴	PROPN
cana-1033	65	51	,	,	PUNCT
cana-1033	65	52	x	x	X
cana-1033	65	53	is	be	AUX
cana-1033	65	54	gocompact	gocompact	ADJ
cana-1033	65	55	,	,	PUNCT
cana-1033	65	56	the	the	DET
cana-1033	65	57	g	g	NOUN
cana-1033	65	58	-	-	PUNCT
cana-1033	65	59	o	o	NOUN
cana-1033	65	60	-	-	NOUN
cana-1033	65	61	c	c	NOUN
cana-1033	65	62	{	{	PUNCT
cana-1033	65	63	ģi	ģi	NOUN
cana-1033	65	64	:	:	PUNCT
cana-1033	65	65	iϵi	iϵi	NOUN
cana-1033	65	66	}	}	PUNCT
cana-1033	65	67	x	x	PUNCT
cana-1033	65	68	has	have	VERB
cana-1033	65	69	a	a	DET
cana-1033	65	70	finite	finite	ADJ
cana-1033	65	71	sub	sub	NOUN
cana-1033	65	72	cover	cover	NOUN
cana-1033	65	73	say	say	VERB
cana-1033	65	74	{	{	PUNCT
cana-1033	65	75	ģi	ģi	INTJ
cana-1033	65	76	i	i	PROPN
cana-1033	65	77	ϵ	ϵ	PROPN
cana-1033	65	78	n	n	CCONJ
cana-1033	65	79	}	}	PUNCT
cana-1033	65	80	of	of	ADP
cana-1033	65	81	x	x	X
cana-1033	65	82	.	.	PUNCT
cana-1033	66	1	∴	∴	PROPN
cana-1033	66	2	,	,	PUNCT
cana-1033	66	3	x	x	X
cana-1033	66	4	is	be	AUX
cana-1033	66	5	ws	ws	ADJ
cana-1033	66	6	compact	compact	ADJ
cana-1033	66	7	.	.	PUNCT
cana-1033	67	1	4	4	X
cana-1033	67	2	.	.	X
cana-1033	67	3	countable	countable	ADJ
cana-1033	67	4	ws	ws	NOUN
cana-1033	67	5	-	-	PUNCT
cana-1033	67	6	compactness	compactness	NOUN
cana-1033	67	7	in	in	ADP
cana-1033	67	8	ts	ts	ADP
cana-1033	67	9	:	:	PUNCT
cana-1033	67	10	in	in	ADP
cana-1033	67	11	this	this	DET
cana-1033	67	12	section	section	NOUN
cana-1033	67	13	,	,	PUNCT
cana-1033	67	14	we	we	PRON
cana-1033	67	15	explored	explore	VERB
cana-1033	67	16	that	that	SCONJ
cana-1033	67	17	the	the	DET
cana-1033	67	18	notion	notion	NOUN
cana-1033	67	19	of	of	ADP
cana-1033	67	20	countable	countable	ADJ
cana-1033	67	21	βws	βws	NOUN
cana-1033	67	22	-	-	ADJ
cana-1033	67	23	compact	compact	ADJ
cana-1033	67	24	in	in	ADP
cana-1033	67	25	ts	t	NOUN
cana-1033	67	26	besides	besides	SCONJ
cana-1033	67	27	that	that	PRON
cana-1033	67	28	investigate	investigate	VERB
cana-1033	67	29	most	most	ADJ
cana-1033	67	30	of	of	ADP
cana-1033	67	31	its	its	PRON
cana-1033	67	32	characteristics	characteristic	NOUN
cana-1033	67	33	.	.	PUNCT
cana-1033	68	1	definition	definition	NOUN
cana-1033	68	2	4.1	4.1	NUM
cana-1033	68	3	.	.	PUNCT
cana-1033	69	1	a	a	DET
cana-1033	69	2	ts	ts	NOUN
cana-1033	69	3	x	x	VERB
cana-1033	69	4	is	be	AUX
cana-1033	69	5	named	name	VERB
cana-1033	69	6	as	as	ADP
cana-1033	69	7	countable	countable	ADJ
cana-1033	69	8	ws	ws	NOUN
cana-1033	69	9	-	-	PUNCT
cana-1033	69	10	compact	compact	ADJ
cana-1033	69	11	if	if	SCONJ
cana-1033	69	12	each	each	PRON
cana-1033	69	13	and	and	CCONJ
cana-1033	69	14	all	all	PRON
cana-1033	69	15	countable	countable	ADJ
cana-1033	69	16	ws	ws	NOUN
cana-1033	69	17	-	-	PUNCT
cana-1033	69	18	o	o	NOUN
cana-1033	69	19	-	-	NOUN
cana-1033	69	20	c	c	NOUN
cana-1033	69	21	of	of	ADP
cana-1033	69	22	`	`	PUNCT
cana-1033	69	23	x	x	PUNCT
cana-1033	69	24	includes	include	VERB
cana-1033	69	25	a	a	DET
cana-1033	69	26	finite	finite	ADJ
cana-1033	69	27	sub	sub	NOUN
cana-1033	69	28	cover	cover	NOUN
cana-1033	69	29	.	.	PUNCT
cana-1033	70	1	theorem	theorem	VERB
cana-1033	70	2	4.2	4.2	NUM
cana-1033	70	3	.	.	PUNCT
cana-1033	71	1	suppose	suppose	VERB
cana-1033	71	2	x	x	PRON
cana-1033	71	3	considered	consider	VERB
cana-1033	71	4	as	as	ADP
cana-1033	71	5	countable	countable	ADJ
cana-1033	71	6	ws	ws	ADJ
cana-1033	71	7	-	-	PUNCT
cana-1033	71	8	compact	compact	ADJ
cana-1033	71	9	space	space	NOUN
cana-1033	71	10	,	,	PUNCT
cana-1033	71	11	thenceforth	thenceforth	VERB
cana-1033	71	12	ⴇ	ⴇ	NOUN
cana-1033	71	13	would	would	AUX
cana-1033	71	14	be	be	AUX
cana-1033	71	15	considered	consider	VERB
cana-1033	71	16	as	as	ADP
cana-1033	71	17	countable	countable	ADJ
cana-1033	71	18	compact	compact	ADJ
cana-1033	71	19	.	.	PUNCT
cana-1033	72	1	proof	proof	NOUN
cana-1033	72	2	.	.	PUNCT
cana-1033	73	1	consider	consider	VERB
cana-1033	73	2	,	,	PUNCT
cana-1033	73	3	{	{	PUNCT
cana-1033	73	4	ģi	ģi	NOUN
cana-1033	73	5	:	:	PUNCT
cana-1033	73	6	iϵi	iϵi	AUX
cana-1033	73	7	}	}	PUNCT
cana-1033	73	8	be	be	AUX
cana-1033	73	9	present	present	ADJ
cana-1033	73	10	countable	countable	ADJ
cana-1033	73	11	o	o	NOUN
cana-1033	73	12	-	-	NOUN
cana-1033	73	13	c	c	NOUN
cana-1033	73	14	of	of	ADP
cana-1033	73	15	x	x	PUNCT
cana-1033	73	16	along	along	ADP
cana-1033	73	17	with	with	ADP
cana-1033	73	18	o	o	NOUN
cana-1033	73	19	-	-	PUNCT
cana-1033	73	20	s	s	NOUN
cana-1033	73	21	in	in	ADP
cana-1033	73	22	x.	x.	NOUN
cana-1033	73	23	thenceforth	thenceforth	NOUN
cana-1033	73	24	{	{	PUNCT
cana-1033	73	25	ģi	ģi	NOUN
cana-1033	73	26	:	:	PUNCT
cana-1033	73	27	iϵi	iϵi	PROPN
cana-1033	73	28	}	}	PUNCT
cana-1033	73	29	is	be	AUX
cana-1033	73	30	countable	countable	ADJ
cana-1033	73	31	ws	ws	ADJ
cana-1033	73	32	-	-	PUNCT
cana-1033	73	33	o	o	NOUN
cana-1033	73	34	-	-	NOUN
cana-1033	73	35	c	c	NOUN
cana-1033	73	36	regarding	regard	VERB
cana-1033	73	37	x.	x.	NOUN
cana-1033	73	38	given	give	VERB
cana-1033	73	39	that	that	SCONJ
cana-1033	73	40	x	x	PRON
cana-1033	73	41	would	would	AUX
cana-1033	73	42	be	be	AUX
cana-1033	73	43	countable	countable	ADJ
cana-1033	73	44	ws	ws	NOUN
cana-1033	73	45	-	-	PUNCT
cana-1033	73	46	compact	compact	ADJ
cana-1033	73	47	,	,	PUNCT
cana-1033	73	48	that	that	PRON
cana-1033	73	49	countable	countable	ADJ
cana-1033	73	50	communications	communication	NOUN
cana-1033	73	51	on	on	ADP
cana-1033	73	52	applied	apply	VERB
cana-1033	73	53	nonlinear	nonlinear	ADJ
cana-1033	73	54	analysis	analysis	NOUN
cana-1033	73	55	issn	issn	NOUN
cana-1033	73	56	:	:	PUNCT
cana-1033	73	57	1074	1074	NUM
cana-1033	73	58	-	-	PUNCT
cana-1033	73	59	133x	133x	NUM
cana-1033	73	60	vol	vol	NOUN
cana-1033	73	61	31	31	NUM
cana-1033	73	62	no	no	NOUN
cana-1033	73	63	.	.	PUNCT
cana-1033	74	1	5s	5s	NUM
cana-1033	74	2	(	(	PUNCT
cana-1033	74	3	2024	2024	NUM
cana-1033	74	4	)	)	PUNCT
cana-1033	74	5	262	262	NUM
cana-1033	74	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1033	74	7	ws	ws	NOUN
cana-1033	74	8	-	-	PUNCT
cana-1033	74	9	o	o	NOUN
cana-1033	74	10	-	-	NOUN
cana-1033	74	11	c	c	NOUN
cana-1033	74	12	of	of	ADP
cana-1033	74	13	x	x	PUNCT
cana-1033	74	14	includes	include	VERB
cana-1033	74	15	a	a	DET
cana-1033	74	16	finite	finite	ADJ
cana-1033	74	17	subcover	subcover	PROPN
cana-1033	74	18	,	,	PUNCT
cana-1033	74	19	for	for	ADP
cana-1033	74	20	example	example	NOUN
cana-1033	74	21	{	{	PUNCT
cana-1033	74	22	ģi	ģi	NOUN
cana-1033	74	23	.i	.i	PROPN
cana-1033	74	24	ϵn	ϵn	NOUN
cana-1033	74	25	}	}	PUNCT
cana-1033	74	26	.	.	PUNCT
cana-1033	75	1	∴	∴	NOUN
cana-1033	75	2	,	,	PUNCT
cana-1033	75	3	x	x	PRON
cana-1033	75	4	are	be	AUX
cana-1033	75	5	considered	consider	VERB
cana-1033	75	6	as	as	ADP
cana-1033	75	7	countable	countable	ADJ
cana-1033	75	8	compact	compact	ADJ
cana-1033	75	9	.	.	PUNCT
cana-1033	76	1	theorem	theorem	VERB
cana-1033	76	2	4.3	4.3	NUM
cana-1033	76	3	.	.	PUNCT
cana-1033	77	1	each	each	PRON
cana-1033	77	2	and	and	CCONJ
cana-1033	77	3	every	every	DET
cana-1033	77	4	ws	ws	ADJ
cana-1033	77	5	-	-	PUNCT
cana-1033	77	6	compact	compact	ADJ
cana-1033	77	7	space	space	NOUN
cana-1033	77	8	is	be	AUX
cana-1033	77	9	considered	consider	VERB
cana-1033	77	10	to	to	PART
cana-1033	77	11	be	be	AUX
cana-1033	77	12	countable	countable	ADJ
cana-1033	77	13	ws	ws	NOUN
cana-1033	77	14	-	-	PUNCT
cana-1033	77	15	compact	compact	ADJ
cana-1033	77	16	.	.	PUNCT
cana-1033	78	1	proof	proof	NOUN
cana-1033	78	2	.	.	PUNCT
cana-1033	79	1	suppose	suppose	VERB
cana-1033	79	2	that	that	SCONJ
cana-1033	79	3	ҳ	ҳ	PROPN
cana-1033	79	4	will	will	AUX
cana-1033	79	5	be	be	AUX
cana-1033	79	6	considered	consider	VERB
cana-1033	79	7	as	as	ADP
cana-1033	79	8	ws	ws	ADJ
cana-1033	79	9	-	-	PUNCT
cana-1033	79	10	compact	compact	ADJ
cana-1033	79	11	space	space	NOUN
cana-1033	79	12	,	,	PUNCT
cana-1033	79	13	{	{	PUNCT
cana-1033	79	14	ģi	ģi	NOUN
cana-1033	79	15	:	:	PUNCT
cana-1033	79	16	iϵi	iϵi	PROPN
cana-1033	79	17	}	}	PUNCT
cana-1033	79	18	will	will	AUX
cana-1033	79	19	be	be	AUX
cana-1033	79	20	considered	consider	VERB
cana-1033	79	21	as	as	ADP
cana-1033	79	22	countable	countable	ADJ
cana-1033	79	23	ws	ws	NOUN
cana-1033	79	24	-	-	PUNCT
cana-1033	79	25	o	o	NOUN
cana-1033	79	26	-	-	NOUN
cana-1033	79	27	c	c	NOUN
cana-1033	79	28	of	of	ADP
cana-1033	79	29	ҳ	ҳ	PROPN
cana-1033	79	30	including	include	VERB
cana-1033	79	31	ws	ws	NOUN
cana-1033	79	32	-	-	PUNCT
cana-1033	79	33	o	o	NOUN
cana-1033	79	34	-	-	PUNCT
cana-1033	79	35	s.	s.	PROPN
cana-1033	79	36	following	follow	VERB
cana-1033	79	37	that	that	SCONJ
cana-1033	79	38	{	{	PUNCT
cana-1033	79	39	ģi	ģi	NOUN
cana-1033	79	40	:	:	PUNCT
cana-1033	79	41	iϵi	iϵi	PROPN
cana-1033	79	42	}	}	PUNCT
cana-1033	79	43	is	be	AUX
cana-1033	79	44	a	a	DET
cana-1033	79	45	ws	ws	ADJ
cana-1033	79	46	-	-	PUNCT
cana-1033	79	47	o	o	NOUN
cana-1033	79	48	-	-	NOUN
cana-1033	79	49	c	c	NOUN
cana-1033	79	50	{	{	PUNCT
cana-1033	79	51	ģi	ģi	NOUN
cana-1033	79	52	:	:	PUNCT
cana-1033	79	53	iϵi	iϵi	PROPN
cana-1033	79	54	}	}	PUNCT
cana-1033	79	55	of	of	ADP
cana-1033	79	56	x	x	PUNCT
cana-1033	79	57	whose	whose	DET
cana-1033	79	58	finite	finite	ADJ
cana-1033	79	59	sub	sub	NOUN
cana-1033	79	60	cover	cover	NOUN
cana-1033	79	61	say	say	VERB
cana-1033	79	62	{	{	PUNCT
cana-1033	79	63	ģi	ģi	NOUN
cana-1033	79	64	,	,	PUNCT
cana-1033	79	65	iϵn	iϵn	ADJ
cana-1033	79	66	}	}	PUNCT
cana-1033	79	67	.	.	PUNCT
cana-1033	80	1	∴	∴	NOUN
cana-1033	80	2	,	,	PUNCT
cana-1033	80	3	x	x	PRON
cana-1033	80	4	is	be	AUX
cana-1033	80	5	countable	countable	ADJ
cana-1033	80	6	ws	ws	ADJ
cana-1033	80	7	-	-	PUNCT
cana-1033	80	8	compact	compact	ADJ
cana-1033	80	9	.	.	PUNCT
cana-1033	81	1	theorem	theorem	VERB
cana-1033	81	2	4.4	4.4	NUM
cana-1033	81	3	.	.	PUNCT
cana-1033	82	1	the	the	DET
cana-1033	82	2	countable	countable	ADJ
cana-1033	82	3	ws	ws	ADJ
cana-1033	82	4	-	-	PUNCT
cana-1033	82	5	compact	compact	ADJ
cana-1033	82	6	space	space	NOUN
cana-1033	82	7	under	under	ADP
cana-1033	82	8	ws	ws	NOUN
cana-1033	82	9	-	-	PUNCT
cana-1033	82	10	irresolute	irresolute	ADJ
cana-1033	82	11	function	function	NOUN
cana-1033	82	12	are	be	AUX
cana-1033	82	13	considered	consider	VERB
cana-1033	82	14	as	as	ADP
cana-1033	82	15	countable	countable	ADJ
cana-1033	82	16	wscompact	wscompact	ADJ
cana-1033	82	17	.	.	PUNCT
cana-1033	83	1	proof	proof	NOUN
cana-1033	83	2	.	.	PUNCT
cana-1033	84	1	suppose	suppose	VERB
cana-1033	84	2	ⴇ	ⴇ	NOUN
cana-1033	84	3	:	:	PUNCT
cana-1033	84	4	x	x	SYM
cana-1033	84	5	→	→	SYM
cana-1033	84	6	y	y	PRON
cana-1033	84	7	have	have	VERB
cana-1033	84	8	a	a	DET
cana-1033	84	9	ws	ws	NOUN
cana-1033	84	10	-	-	PUNCT
cana-1033	84	11	irresolute	irresolute	ADJ
cana-1033	84	12	function	function	NOUN
cana-1033	84	13	after	after	SCONJ
cana-1033	84	14	a	a	DET
cana-1033	84	15	countable	countable	ADJ
cana-1033	84	16	ws	ws	ADJ
cana-1033	84	17	-	-	PUNCT
cana-1033	84	18	compact	compact	ADJ
cana-1033	84	19	space	space	NOUN
cana-1033	84	20	ҳ	ҳ	PROPN
cana-1033	84	21	continuously	continuously	ADV
cana-1033	84	22	ts	ts	ADP
cana-1033	84	23	y	y	PROPN
cana-1033	84	24	,	,	PUNCT
cana-1033	84	25	{	{	PUNCT
cana-1033	84	26	ģi	ģi	NOUN
cana-1033	84	27	:	:	PUNCT
cana-1033	84	28	iϵi	iϵi	PROPN
cana-1033	84	29	}	}	PUNCT
cana-1033	84	30	will	will	AUX
cana-1033	84	31	be	be	AUX
cana-1033	84	32	considered	consider	VERB
cana-1033	84	33	as	as	ADP
cana-1033	84	34	countable	countable	ADJ
cana-1033	84	35	ws	ws	NOUN
cana-1033	84	36	-	-	PUNCT
cana-1033	84	37	o	o	NOUN
cana-1033	84	38	-	-	NOUN
cana-1033	84	39	c	c	NOUN
cana-1033	84	40	of	of	ADP
cana-1033	84	41	y.	y.	PROPN
cana-1033	84	42	subsequently	subsequently	ADV
cana-1033	84	43	,	,	PUNCT
cana-1033	84	44	{	{	PUNCT
cana-1033	84	45	ⴇ	ⴇ	NOUN
cana-1033	84	46	1(ģi	1(ģi	NUM
cana-1033	84	47	):	):	PUNCT
cana-1033	84	48	iϵi	iϵi	NOUN
cana-1033	84	49	}	}	PUNCT
cana-1033	84	50	are	be	AUX
cana-1033	84	51	considered	consider	VERB
cana-1033	84	52	as	as	SCONJ
cana-1033	84	53	countable	countable	ADJ
cana-1033	84	54	ws	ws	NOUN
cana-1033	84	55	-	-	PUNCT
cana-1033	84	56	o	o	NOUN
cana-1033	84	57	-	-	PUNCT
cana-1033	84	58	s	s	X
cana-1033	84	59	of	of	ADP
cana-1033	84	60	x	x	SYM
cana-1033	84	61	such	such	ADJ
cana-1033	84	62	as	as	ADP
cana-1033	84	63	ⴇ	ⴇ	PROPN
cana-1033	84	64	remains	remain	VERB
cana-1033	84	65	ws	ws	NOUN
cana-1033	84	66	-	-	PUNCT
cana-1033	84	67	irresolute	irresolute	NOUN
cana-1033	84	68	.	.	PUNCT
cana-1033	85	1	when	when	SCONJ
cana-1033	85	2	x	x	PRON
cana-1033	85	3	is	be	AUX
cana-1033	85	4	countable	countable	ADJ
cana-1033	85	5	ws	ws	ADJ
cana-1033	85	6	-	-	PUNCT
cana-1033	85	7	compact	compact	ADJ
cana-1033	85	8	,	,	PUNCT
cana-1033	85	9	the	the	DET
cana-1033	85	10	countable	countable	ADJ
cana-1033	85	11	ws	ws	ADJ
cana-1033	85	12	-	-	PUNCT
cana-1033	85	13	o	o	NOUN
cana-1033	85	14	-	-	NOUN
cana-1033	85	15	c	c	NOUN
cana-1033	85	16	{	{	PUNCT
cana-1033	85	17	ⴇ	ⴇ	NOUN
cana-1033	85	18	-1(ģi	-1(ģi	PROPN
cana-1033	85	19	)	)	PUNCT
cana-1033	85	20	:	:	PUNCT
cana-1033	85	21	iϵi	iϵi	NOUN
cana-1033	85	22	}	}	PUNCT
cana-1033	85	23	of	of	ADP
cana-1033	85	24	x	x	PRON
cana-1033	85	25	include	include	VERB
cana-1033	85	26	a	a	DET
cana-1033	85	27	finite	finite	ADJ
cana-1033	85	28	subcover	subcover	PROPN
cana-1033	85	29	say	say	VERB
cana-1033	85	30	{	{	PUNCT
cana-1033	85	31	ⴇ	ⴇ	NOUN
cana-1033	85	32	-1(ģi	-1(ģi	PROPN
cana-1033	85	33	)	)	PUNCT
cana-1033	85	34	:	:	PUNCT
cana-1033	85	35	in	in	NOUN
cana-1033	85	36	}	}	PUNCT
cana-1033	85	37	.	.	PUNCT
cana-1033	86	1	∴	∴	NOUN
cana-1033	86	2	,	,	PUNCT
cana-1033	86	3	x	x	PUNCT
cana-1033	86	4	=	=	VERB
cana-1033	86	5	∪i∈i	∪i∈i	NUM
cana-1033	86	6	ⴇ	ⴇ	NOUN
cana-1033	86	7	-1	-1	PUNCT
cana-1033	86	8	(	(	PUNCT
cana-1033	86	9	ģi	ģi	NOUN
cana-1033	86	10	)	)	PUNCT
cana-1033	86	11	ⴇ	ⴇ	NOUN
cana-1033	86	12	(	(	PUNCT
cana-1033	86	13	x	x	X
cana-1033	86	14	)	)	PUNCT
cana-1033	86	15	=	=	PUNCT
cana-1033	86	16	∪i∈i	∪i∈i	NUM
cana-1033	86	17	ģi	ģi	NOUN
cana-1033	86	18	.	.	PUNCT
cana-1033	87	1	then	then	ADV
cana-1033	87	2	y	y	PROPN
cana-1033	87	3	=	=	PROPN
cana-1033	87	4	∪i∈i	∪i∈i	PRON
cana-1033	87	5	ģi	ģi	PROPN
cana-1033	87	6	{	{	PUNCT
cana-1033	87	7	ģ1	ģ1	PROPN
cana-1033	87	8	,	,	PUNCT
cana-1033	87	9	ģ2	ģ2	PROPN
cana-1033	87	10	,	,	PUNCT
cana-1033	87	11	ģ3	ģ3	NOUN
cana-1033	87	12	,	,	PUNCT
cana-1033	87	13	…	…	PUNCT
cana-1033	87	14	,	,	PUNCT
cana-1033	87	15	ģn	ģn	AUX
cana-1033	87	16	}	}	PUNCT
cana-1033	87	17	is	be	AUX
cana-1033	87	18	a	a	DET
cana-1033	87	19	finite	finite	ADJ
cana-1033	87	20			NOUN
cana-1033	87	21	{	{	PUNCT
cana-1033	87	22	ģi	ģi	NOUN
cana-1033	87	23	:	:	PUNCT
cana-1033	87	24	iϵi	iϵi	PROPN
cana-1033	87	25	}	}	PUNCT
cana-1033	87	26	used	use	VERB
cana-1033	87	27	for	for	ADP
cana-1033	87	28	y.	y.	PROPN
cana-1033	87	29	∴	∴	PROPN
cana-1033	87	30	,	,	PUNCT
cana-1033	87	31	y	y	PROPN
cana-1033	87	32	is	be	AUX
cana-1033	87	33	countable	countable	ADJ
cana-1033	87	34	ws	ws	ADJ
cana-1033	87	35	compact	compact	ADJ
cana-1033	87	36	.	.	PUNCT
cana-1033	88	1	theorem	theorem	VERB
cana-1033	88	2	4.5	4.5	NUM
cana-1033	88	3	:	:	PUNCT
cana-1033	88	4	a	a	DET
cana-1033	88	5	space	space	NOUN
cana-1033	88	6	x	x	PUNCT
cana-1033	88	7	is	be	AUX
cana-1033	88	8	countable	countable	ADJ
cana-1033	88	9	ws	ws	ADJ
cana-1033	88	10	compact	compact	NOUN
cana-1033	88	11	if	if	SCONJ
cana-1033	88	12	all	all	DET
cana-1033	88	13	countable	countable	ADJ
cana-1033	88	14	unit	unit	NOUN
cana-1033	88	15	of	of	ADP
cana-1033	88	16	ws	ws	NOUN
cana-1033	88	17	-	-	PUNCT
cana-1033	88	18	cs	cs	NOUN
cana-1033	88	19	that	that	PRON
cana-1033	88	20	is	be	AUX
cana-1033	88	21	x	x	PUNCT
cana-1033	88	22	having	have	VERB
cana-1033	88	23	finite	finite	ADJ
cana-1033	88	24	intersection	intersection	NOUN
cana-1033	88	25	property	property	NOUN
cana-1033	88	26	has	have	VERB
cana-1033	88	27	a	a	DET
cana-1033	88	28	non	non	ADJ
cana-1033	88	29	-	-	ADJ
cana-1033	88	30	empty	empty	ADJ
cana-1033	88	31	intersection	intersection	NOUN
cana-1033	88	32	.	.	PUNCT
cana-1033	89	1	proof	proof	NOUN
cana-1033	89	2	:	:	PUNCT
cana-1033	89	3	the	the	PRON
cana-1033	89	4	x	x	PUNCT
cana-1033	89	5	is	be	AUX
cana-1033	89	6	considered	consider	VERB
cana-1033	89	7	as	as	ADP
cana-1033	89	8	countable	countable	ADJ
cana-1033	89	9	ws	ws	NOUN
cana-1033	89	10	-	-	PUNCT
cana-1033	89	11	compact	compact	ADJ
cana-1033	89	12	,	,	PUNCT
cana-1033	89	13	{	{	PUNCT
cana-1033	89	14	fi	fi	NOUN
cana-1033	89	15	:	:	PUNCT
cana-1033	89	16	iϵi	iϵi	NOUN
cana-1033	89	17	}	}	PUNCT
cana-1033	89	18	is	be	AUX
cana-1033	89	19	included	include	VERB
cana-1033	89	20	to	to	PART
cana-1033	89	21	countable	countable	VERB
cana-1033	89	22	unit	unit	NOUN
cana-1033	89	23	of	of	ADP
cana-1033	89	24	ws	ws	NOUN
cana-1033	89	25	-	-	PUNCT
cana-1033	89	26	cs	cs	PROPN
cana-1033	89	27	along	along	ADV
cana-1033	89	28	through	through	ADP
cana-1033	89	29	finite	finite	ADJ
cana-1033	89	30	∩	∩	ADJ
cana-1033	89	31	property	property	NOUN
cana-1033	89	32	.	.	PUNCT
cana-1033	90	1	to	to	PART
cana-1033	90	2	show	show	VERB
cana-1033	90	3	that	that	SCONJ
cana-1033	90	4	∩i∈i	∩i∈i	ADJ
cana-1033	90	5	n	n	PROPN
cana-1033	90	6	(	(	PUNCT
cana-1033	90	7	fi	fi	NOUN
cana-1033	90	8	)	)	PUNCT
cana-1033	90	9			NOUN
cana-1033	90	10	.	.	PUNCT
cana-1033	90	11	to	to	PART
cana-1033	90	12	take	take	VERB
cana-1033	90	13	∩i∈i	∩i∈i	ADJ
cana-1033	90	14	n	n	PROPN
cana-1033	90	15	(	(	PUNCT
cana-1033	90	16	fi	fi	NOUN
cana-1033	90	17	)	)	PUNCT
cana-1033	90	18	=	=	SYM
cana-1033	90	19			NOUN
cana-1033	90	20	,	,	PUNCT
cana-1033	90	21	then	then	ADV
cana-1033	90	22	x	x	PUNCT
cana-1033	90	23	∪i∈i	∪i∈i	NUM
cana-1033	90	24	fi	fi	NOUN
cana-1033	90	25	=	=	NOUN
cana-1033	90	26	x	x	SYM
cana-1033	90	27			NOUN
cana-1033	90	28	∪i∈i	∪i∈i	NUM
cana-1033	90	29	(	(	PUNCT
cana-1033	90	30	x	x	SYM
cana-1033	90	31	fi	fi	NOUN
cana-1033	90	32	)	)	PUNCT
cana-1033	90	33	=	=	PUNCT
cana-1033	91	1	x.	x.	NOUN
cana-1033	91	2	the	the	DET
cana-1033	91	3	{	{	PUNCT
cana-1033	91	4	x	x	PROPN
cana-1033	91	5	fi	fi	NOUN
cana-1033	91	6	:	:	PUNCT
cana-1033	91	7	iϵi	iϵi	NOUN
cana-1033	91	8	}	}	PUNCT
cana-1033	91	9	is	be	AUX
cana-1033	91	10	a	a	DET
cana-1033	91	11	countable	countable	ADJ
cana-1033	91	12	ws	ws	NOUN
cana-1033	91	13	-	-	PUNCT
cana-1033	91	14	o	o	NOUN
cana-1033	91	15	-	-	NOUN
cana-1033	91	16	c	c	NOUN
cana-1033	91	17	{	{	PUNCT
cana-1033	91	18	x	x	X
cana-1033	91	19	fi	fi	NOUN
cana-1033	91	20	:	:	PUNCT
cana-1033	91	21	iϵi	iϵi	NOUN
cana-1033	91	22	}	}	PUNCT
cana-1033	91	23	has	have	AUX
cana-1033	91	24	finite	finite	ADJ
cana-1033	91	25	sub	sub	NOUN
cana-1033	91	26	cover	cover	NOUN
cana-1033	91	27	say	say	VERB
cana-1033	91	28	{	{	PUNCT
cana-1033	91	29	x	x	X
cana-1033	91	30	fi	fi	NOUN
cana-1033	91	31	:	:	PUNCT
cana-1033	91	32	i	i	NOUN
cana-1033	91	33	=	=	NOUN
cana-1033	91	34	1,	1,	NUM
cana-1033	91	35	…	…	PUNCT
cana-1033	91	36	,n	,n	NOUN
cana-1033	91	37	}	}	PUNCT
cana-1033	91	38	.	.	PUNCT
cana-1033	92	1	where	where	SCONJ
cana-1033	92	2	,	,	PUNCT
cana-1033	92	3	x	x	PROPN
cana-1033	92	4	=	=	VERB
cana-1033	92	5	∪i=1	∪i=1	PROPN
cana-1033	92	6	n	n	INTJ
cana-1033	92	7	(	(	PUNCT
cana-1033	92	8	x	x	SYM
cana-1033	92	9	fi	fi	NOUN
cana-1033	92	10	)	)	PUNCT
cana-1033	92	11	⟺	⟺	NOUN
cana-1033	92	12	x	x	X
cana-1033	93	1	=	=	PUNCT
cana-1033	93	2	x	x	PUNCT
cana-1033	94	1	=	=	NOUN
cana-1033	94	2	∩i=1	∩i=1	ADV
cana-1033	94	3	n	n	NUM
cana-1033	94	4	fi	fi	NOUN
cana-1033	94	5	⟹	⟹	X
cana-1033	94	6	x	x	SYM
cana-1033	94	7	x	x	PUNCT
cana-1033	94	8	=	=	PUNCT
cana-1033	94	9	x	x	PUNCT
cana-1033	94	10	-∩i=1	-∩i=1	NOUN
cana-1033	94	11	n	n	PRON
cana-1033	94	12	fi	fi	NOUN
cana-1033	94	13	.	.	PUNCT
cana-1033	95	1	hence	hence	ADV
cana-1033	95	2	,	,	PUNCT
cana-1033	95	3			NOUN
cana-1033	95	4	=	=	SYM
cana-1033	95	5	∩i=1	∩i=1	NOUN
cana-1033	95	6	n	n	PRON
cana-1033	95	7	fi	fi	NOUN
cana-1033	95	8	.	.	PUNCT
cana-1033	96	1			PROPN
cana-1033	96	2	finite	finite	ADJ
cana-1033	96	3	subcollection	subcollection	NOUN
cana-1033	96	4	{	{	PUNCT
cana-1033	96	5	fi.in	fi.in	NOUN
cana-1033	96	6	}	}	PUNCT
cana-1033	96	7	of	of	ADP
cana-1033	96	8	{	{	PUNCT
cana-1033	96	9	fi	fi	NOUN
cana-1033	96	10	:	:	PUNCT
cana-1033	96	11	iϵi}∋	iϵi}∋	NOUN
cana-1033	96	12	x	x	PUNCT
cana-1033	97	1	=	=	PRON
cana-1033	97	2	∪i=1	∪i=1	PROPN
cana-1033	97	3	n	n	INTJ
cana-1033	97	4	(	(	PUNCT
cana-1033	97	5	x	x	X
cana-1033	97	6	fi	fi	NOUN
cana-1033	97	7	)	)	PUNCT
cana-1033	97	8	.	.	PUNCT
cana-1033	98	1	then	then	ADV
cana-1033	98	2	,	,	PUNCT
cana-1033	98	3			NOUN
cana-1033	98	4	=	=	SYM
cana-1033	98	5	∩i=1	∩i=1	NOUN
cana-1033	98	6	n	n	PRON
cana-1033	98	7	fi	fi	NOUN
cana-1033	98	8	.	.	PROPN
cana-1033	98	9	which	which	PRON
cana-1033	98	10	contradicts	contradict	VERB
cana-1033	98	11	the	the	DET
cana-1033	98	12	assumption	assumption	NOUN
cana-1033	98	13	,	,	PUNCT
cana-1033	98	14	∩i∈i	∩i∈i	ADJ
cana-1033	98	15	n	n	CCONJ
cana-1033	98	16	(	(	PUNCT
cana-1033	98	17	fi	fi	NOUN
cana-1033	98	18	)	)	PUNCT
cana-1033	98	19			NOUN
cana-1033	98	20	.	.	PUNCT
cana-1033	98	21	theorem	theorem	VERB
cana-1033	98	22	4.6	4.6	NUM
cana-1033	98	23	.	.	PUNCT
cana-1033	99	1	in	in	ADP
cana-1033	99	2	case	case	NOUN
cana-1033	99	3	a	a	DET
cana-1033	99	4	map	map	NOUN
cana-1033	99	5	ⴇ	ⴇ	NOUN
cana-1033	99	6	:	:	PUNCT
cana-1033	99	7	x	x	SYM
cana-1033	99	8	→	→	SYM
cana-1033	99	9	y	y	PROPN
cana-1033	99	10	is	be	AUX
cana-1033	99	11	ws	ws	NOUN
cana-1033	99	12	-	-	PUNCT
cana-1033	99	13	irresolute	irresolute	ADJ
cana-1033	99	14	besides	besides	SCONJ
cana-1033	99	15	b	b	NOUN
cana-1033	99	16	subset	subset	NOUN
cana-1033	99	17	of	of	ADP
cana-1033	99	18	x	x	PUNCT
cana-1033	99	19	is	be	AUX
cana-1033	99	20	ws	ws	ADJ
cana-1033	99	21	–	–	PUNCT
cana-1033	99	22	compact	compact	ADJ
cana-1033	99	23	related	relate	VERB
cana-1033	99	24	to	to	ADP
cana-1033	99	25	x	x	PRON
cana-1033	99	26	,	,	PUNCT
cana-1033	99	27	thereafter	thereafter	ADV
cana-1033	99	28	,	,	PUNCT
cana-1033	99	29	the	the	DET
cana-1033	99	30	illustration	illustration	NOUN
cana-1033	99	31	ⴇ	ⴇ	X
cana-1033	99	32	(	(	PUNCT
cana-1033	99	33	b	b	NOUN
cana-1033	99	34	)	)	PUNCT
cana-1033	99	35	is	be	AUX
cana-1033	99	36	ws	ws	ADJ
cana-1033	99	37	-	-	PUNCT
cana-1033	99	38	compact	compact	ADJ
cana-1033	99	39	related	relate	VERB
cana-1033	99	40	towards	towards	ADP
cana-1033	99	41	y.	y.	PROPN
cana-1033	99	42	proof	proof	NOUN
cana-1033	99	43	:	:	PUNCT
cana-1033	99	44	suppose	suppose	VERB
cana-1033	99	45	that	that	SCONJ
cana-1033	99	46	{	{	PUNCT
cana-1033	99	47	ģi	ģi	NOUN
cana-1033	99	48	:	:	PUNCT
cana-1033	99	49	i∆0	i∆0	ADJ
cana-1033	99	50	}	}	PUNCT
cana-1033	99	51	be	be	AUX
cana-1033	99	52	multiples	multiple	NOUN
cana-1033	99	53	of	of	ADP
cana-1033	99	54	ws	ws	NOUN
cana-1033	99	55	-	-	PUNCT
cana-1033	99	56	o	o	NOUN
cana-1033	99	57			PROPN
cana-1033	99	58	y	y	PROPN
cana-1033	99	59	∋	∋	NOUN
cana-1033	99	60	ⴇ	ⴇ	PROPN
cana-1033	99	61	(	(	PUNCT
cana-1033	99	62	b)∪	b)∪	PROPN
cana-1033	99	63	{	{	PUNCT
cana-1033	99	64	ģi	ģi	NOUN
cana-1033	99	65	:	:	PUNCT
cana-1033	99	66	i∆	i∆	NOUN
cana-1033	99	67	}	}	PUNCT
cana-1033	99	68	holds	hold	VERB
cana-1033	99	69	.	.	PUNCT
cana-1033	100	1	by	by	ADP
cana-1033	100	2	hypothesis	hypothesis	NOUN
cana-1033	100	3			NUM
cana-1033	100	4	a	a	DET
cana-1033	100	5	finite	finite	ADJ
cana-1033	100	6			NOUN
cana-1033	100	7			PROPN
cana-1033	100	8	b∪	b∪	ADJ
cana-1033	100	9	{	{	PUNCT
cana-1033	100	10	ⴇ	ⴇ	NOUN
cana-1033	100	11	-1(ģi	-1(ģi	PROPN
cana-1033	100	12	)	)	PUNCT
cana-1033	100	13	:	:	PUNCT
cana-1033	101	1	i∆0	i∆0	ADJ
cana-1033	101	2	}	}	PUNCT
cana-1033	101	3	.	.	PUNCT
cana-1033	102	1	∴	∴	NOUN
cana-1033	102	2	,	,	PUNCT
cana-1033	102	3	here	here	ADV
cana-1033	102	4	,	,	PUNCT
cana-1033	102	5	we	we	PRON
cana-1033	102	6	have	have	VERB
cana-1033	102	7	ⴇ	ⴇ	NOUN
cana-1033	102	8	(	(	PUNCT
cana-1033	102	9	b	b	X
cana-1033	102	10	)	)	PUNCT
cana-1033	102	11			PROPN
cana-1033	102	12	(ģi	(ģi	NOUN
cana-1033	102	13	:	:	PUNCT
cana-1033	103	1	i∆0	i∆0	X
cana-1033	103	2	}	}	PUNCT
cana-1033	103	3	,	,	PUNCT
cana-1033	103	4	showing	show	VERB
cana-1033	103	5	that	that	SCONJ
cana-1033	103	6	ⴇ	ⴇ	NOUN
cana-1033	103	7	(	(	PUNCT
cana-1033	103	8	b	b	NOUN
cana-1033	103	9	)	)	PUNCT
cana-1033	103	10	are	be	AUX
cana-1033	103	11	communications	communication	NOUN
cana-1033	103	12	on	on	ADP
cana-1033	103	13	applied	apply	VERB
cana-1033	103	14	nonlinear	nonlinear	ADJ
cana-1033	103	15	analysis	analysis	NOUN
cana-1033	103	16	issn	issn	NOUN
cana-1033	103	17	:	:	PUNCT
cana-1033	103	18	1074	1074	NUM
cana-1033	103	19	-	-	PUNCT
cana-1033	103	20	133x	133x	NUM
cana-1033	103	21	vol	vol	NOUN
cana-1033	103	22	31	31	NUM
cana-1033	103	23	no	no	NOUN
cana-1033	103	24	.	.	PUNCT
cana-1033	104	1	5s	5s	NUM
cana-1033	104	2	(	(	PUNCT
cana-1033	104	3	2024	2024	NUM
cana-1033	104	4	)	)	PUNCT
cana-1033	104	5	263	263	NUM
cana-1033	105	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1033	105	2	considered	consider	VERB
cana-1033	105	3	as	as	ADP
cana-1033	105	4	ws	ws	ADJ
cana-1033	105	5	-	-	PUNCT
cana-1033	105	6	compact	compact	ADJ
cana-1033	105	7	related	relate	VERB
cana-1033	105	8	towards	towards	ADP
cana-1033	105	9	y.	y.	PROPN
cana-1033	105	10	theorem	theorem	VERB
cana-1033	105	11	4.7	4.7	NUM
cana-1033	105	12	.	.	PUNCT
cana-1033	106	1	the	the	DET
cana-1033	106	2	x	x	SYM
cana-1033	106	3	×	×	PROPN
cana-1033	106	4	y	y	PROPN
cana-1033	106	5	of	of	ADP
cana-1033	106	6	two	two	NUM
cana-1033	106	7	non	non	ADJ
cana-1033	106	8	-	-	ADJ
cana-1033	106	9	empty	empty	ADJ
cana-1033	106	10	space	space	NOUN
cana-1033	106	11	is	be	AUX
cana-1033	106	12	ws	ws	ADJ
cana-1033	106	13	-	-	PUNCT
cana-1033	106	14	compact	compact	ADJ
cana-1033	106	15	.	.	PUNCT
cana-1033	107	1	proof	proof	NOUN
cana-1033	107	2	.	.	PUNCT
cana-1033	108	1	considering	consider	VERB
cana-1033	108	2	x	x	SYM
cana-1033	108	3	→y	→y	AUX
cana-1033	108	4	represent	represent	VERB
cana-1033	108	5	the	the	DET
cana-1033	108	6	non	non	ADJ
cana-1033	108	7	-	-	ADJ
cana-1033	108	8	empty	empty	ADJ
cana-1033	108	9	spaces	space	NOUN
cana-1033	108	10	'	'	PART
cana-1033	108	11	product	product	NOUN
cana-1033	108	12	space	space	NOUN
cana-1033	108	13	x	x	PUNCT
cana-1033	108	14	and	and	CCONJ
cana-1033	108	15	y	y	PROPN
cana-1033	108	16	also	also	ADV
cana-1033	108	17	considering	consider	VERB
cana-1033	108	18	x	x	SYM
cana-1033	108	19	×	×	PROPN
cana-1033	108	20	y	y	PROPN
cana-1033	108	21	is	be	AUX
cana-1033	108	22	a	a	DET
cana-1033	108	23	ws	ws	ADJ
cana-1033	108	24	compact	compact	NOUN
cana-1033	108	25	.	.	PUNCT
cana-1033	109	1	subsequently	subsequently	ADV
cana-1033	109	2	,	,	PUNCT
cana-1033	109	3	the	the	DET
cana-1033	109	4	projection	projection	NOUN
cana-1033	109	5	∏	∏	PROPN
cana-1033	109	6	∶	∶	NOUN
cana-1033	109	7	x	x	X
cana-1033	109	8	×	×	NOUN
cana-1033	109	9	y	y	PROPN
cana-1033	109	10	are	be	AUX
cana-1033	109	11	considered	consider	VERB
cana-1033	109	12	as	as	ADP
cana-1033	109	13	ws	ws	ADJ
cana-1033	109	14	-irresolute	-irresolute	NOUN
cana-1033	109	15	map	map	NOUN
cana-1033	109	16	.	.	PUNCT
cana-1033	110	1	∴	∴	NOUN
cana-1033	110	2	,	,	PUNCT
cana-1033	110	3	(	(	PUNCT
cana-1033	110	4	x	x	SYM
cana-1033	110	5	×	×	PROPN
cana-1033	110	6	y	y	PROPN
cana-1033	110	7	)	)	PUNCT
cana-1033	110	8	=	=	PUNCT
cana-1033	111	1	x	x	X
cana-1033	111	2	is	be	AUX
cana-1033	111	3	ws	ws	ADJ
cana-1033	111	4	compact	compact	ADJ
cana-1033	111	5	.	.	PUNCT
cana-1033	112	1	likewise	likewise	ADV
cana-1033	112	2	,	,	PUNCT
cana-1033	112	3	we	we	PRON
cana-1033	112	4	illustrate	illustrate	VERB
cana-1033	112	5	aimed	aim	VERB
cana-1033	112	6	at	at	ADP
cana-1033	112	7	the	the	DET
cana-1033	112	8	space	space	NOUN
cana-1033	112	9	y.	y.	NOUN
cana-1033	112	10	5	5	NUM
cana-1033	112	11	.	.	PUNCT
cana-1033	113	1	ws	ws	ADJ
cana-1033	113	2	–	–	PUNCT
cana-1033	113	3	connectedness	connectedness	NOUN
cana-1033	113	4	(	(	PUNCT
cana-1033	113	5	cws	cws	NOUN
cana-1033	113	6	)	)	PUNCT
cana-1033	113	7	in	in	ADP
cana-1033	113	8	ts	ts	NOUN
cana-1033	113	9	:	:	PUNCT
cana-1033	113	10	definition	definition	NOUN
cana-1033	113	11	5.1	5.1	NUM
cana-1033	113	12	.	.	PUNCT
cana-1033	114	1	a	a	DET
cana-1033	114	2	ts	ts	NOUN
cana-1033	114	3	x	x	VERB
cana-1033	114	4	is	be	AUX
cana-1033	114	5	named	name	VERB
cana-1033	114	6	as	as	ADP
cana-1033	114	7	ws	ws	NOUN
cana-1033	114	8	-	-	PUNCT
cana-1033	114	9	cws	cws	NOUN
cana-1033	114	10	if	if	SCONJ
cana-1033	114	11	x	x	PRON
cana-1033	114	12	can	can	AUX
cana-1033	114	13	not	not	PART
cana-1033	114	14	be	be	AUX
cana-1033	114	15	indicated	indicate	VERB
cana-1033	114	16	as	as	ADP
cana-1033	114	17	a	a	DET
cana-1033	114	18	disjoint	disjoint	NOUN
cana-1033	114	19	union	union	NOUN
cana-1033	114	20	of	of	ADP
cana-1033	114	21	two	two	NUM
cana-1033	114	22	non	non	X
cana-1033	114	23	empty	empty	ADJ
cana-1033	114	24	wso	wso	PROPN
cana-1033	114	25	-	-	PUNCT
cana-1033	114	26	s.	s.	PROPN
cana-1033	114	27	example	example	NOUN
cana-1033	115	1	5.2	5.2	NUM
cana-1033	115	2	.	.	PUNCT
cana-1033	116	1	ӽ	ӽ	X
cana-1033	116	2	=	=	SYM
cana-1033	116	3	{	{	PUNCT
cana-1033	116	4	l	l	NOUN
cana-1033	116	5	,	,	PUNCT
cana-1033	116	6	g	g	PROPN
cana-1033	116	7	,	,	PUNCT
cana-1033	116	8	h	h	NOUN
cana-1033	116	9	,	,	PUNCT
cana-1033	116	10	k	k	NOUN
cana-1033	116	11	}	}	PUNCT
cana-1033	116	12			NOUN
cana-1033	116	13	=	=	SYM
cana-1033	116	14	{	{	PUNCT
cana-1033	116	15	ӽ	ӽ	X
cana-1033	116	16	,	,	PUNCT
cana-1033	116	17			ADJ
cana-1033	116	18	,	,	PUNCT
cana-1033	116	19	{	{	PUNCT
cana-1033	116	20	l	l	NOUN
cana-1033	116	21	}	}	PUNCT
cana-1033	116	22	,	,	PUNCT
cana-1033	116	23	{	{	PUNCT
cana-1033	116	24	k	k	X
cana-1033	116	25	}	}	PUNCT
cana-1033	116	26	,	,	PUNCT
cana-1033	116	27	{	{	PUNCT
cana-1033	116	28	l	l	NOUN
cana-1033	116	29	,	,	PUNCT
cana-1033	116	30	k	k	NOUN
cana-1033	116	31	}	}	PUNCT
cana-1033	116	32	}	}	PUNCT
cana-1033	116	33	,	,	PUNCT
cana-1033	116	34	ws	ws	NOUN
cana-1033	116	35	–	–	PUNCT
cana-1033	116	36	cs	cs	PROPN
cana-1033	116	37	are	be	AUX
cana-1033	116	38	{	{	PUNCT
cana-1033	116	39	ӽ	ӽ	PRON
cana-1033	116	40	,	,	PUNCT
cana-1033	116	41			PROPN
cana-1033	116	42	,	,	PUNCT
cana-1033	116	43	{	{	PUNCT
cana-1033	116	44	g	g	NOUN
cana-1033	116	45	}	}	PUNCT
cana-1033	116	46	,	,	PUNCT
cana-1033	116	47	{	{	PUNCT
cana-1033	116	48	h	h	NOUN
cana-1033	116	49	}	}	PUNCT
cana-1033	116	50	,	,	PUNCT
cana-1033	116	51	{	{	PUNCT
cana-1033	116	52	k	k	NOUN
cana-1033	116	53	}	}	PUNCT
cana-1033	116	54	,	,	PUNCT
cana-1033	116	55	{	{	PUNCT
cana-1033	116	56	g	g	NOUN
cana-1033	116	57	,	,	PUNCT
cana-1033	116	58	h	h	NOUN
cana-1033	116	59	}	}	PUNCT
cana-1033	116	60	,	,	PUNCT
cana-1033	116	61	{	{	PUNCT
cana-1033	116	62	g	g	PROPN
cana-1033	116	63	,	,	PUNCT
cana-1033	116	64	k	k	PROPN
cana-1033	116	65	}	}	PUNCT
cana-1033	116	66	,	,	PUNCT
cana-1033	116	67	{	{	PUNCT
cana-1033	116	68	h	h	NOUN
cana-1033	116	69	,	,	PUNCT
cana-1033	116	70	k	k	NOUN
cana-1033	116	71	}	}	PUNCT
cana-1033	116	72	}	}	PUNCT
cana-1033	116	73	.	.	PUNCT
cana-1033	117	1	ws	ws	ADJ
cana-1033	117	2	–	–	PUNCT
cana-1033	117	3	o	o	X
cana-1033	117	4	-	-	PUNCT
cana-1033	117	5	s	s	X
cana-1033	117	6	are	be	AUX
cana-1033	117	7	{	{	PUNCT
cana-1033	117	8	ӽ	ӽ	NOUN
cana-1033	117	9	,	,	PUNCT
cana-1033	117	10			ADJ
cana-1033	117	11	,	,	PUNCT
cana-1033	117	12	{	{	PUNCT
cana-1033	117	13	l	l	NOUN
cana-1033	117	14	,	,	PUNCT
cana-1033	117	15	h	h	NOUN
cana-1033	117	16	,	,	PUNCT
cana-1033	117	17	k	k	PROPN
cana-1033	117	18	}	}	PUNCT
cana-1033	117	19	,	,	PUNCT
cana-1033	117	20	{	{	PUNCT
cana-1033	117	21	l	l	NOUN
cana-1033	117	22	,	,	PUNCT
cana-1033	117	23	g	g	PROPN
cana-1033	117	24	,	,	PUNCT
cana-1033	117	25	k	k	PROPN
cana-1033	117	26	}	}	PUNCT
cana-1033	117	27	,	,	PUNCT
cana-1033	117	28	{	{	PUNCT
cana-1033	117	29	l	l	NOUN
cana-1033	117	30	,	,	PUNCT
cana-1033	117	31	g	g	PROPN
cana-1033	117	32	,	,	PUNCT
cana-1033	117	33	h	h	NOUN
cana-1033	117	34	}	}	PUNCT
cana-1033	117	35	,	,	PUNCT
cana-1033	117	36	{	{	PUNCT
cana-1033	117	37	l	l	NOUN
cana-1033	117	38	,	,	PUNCT
cana-1033	117	39	k	k	NOUN
cana-1033	117	40	}	}	PUNCT
cana-1033	117	41	,	,	PUNCT
cana-1033	117	42	{	{	PUNCT
cana-1033	117	43	l	l	NOUN
cana-1033	117	44	,	,	PUNCT
cana-1033	117	45	h	h	NOUN
cana-1033	117	46	}	}	PUNCT
cana-1033	117	47	,	,	PUNCT
cana-1033	117	48	{	{	PUNCT
cana-1033	117	49	l	l	NOUN
cana-1033	117	50	,	,	PUNCT
cana-1033	117	51	g	g	NOUN
cana-1033	117	52	}	}	PUNCT
cana-1033	117	53	}	}	PUNCT
cana-1033	117	54	.	.	PUNCT
cana-1033	118	1	let	let	VERB
cana-1033	118	2	u	u	PRON
cana-1033	118	3	=	=	PUNCT
cana-1033	118	4	{	{	PUNCT
cana-1033	118	5	l	l	NOUN
cana-1033	118	6	,	,	PUNCT
cana-1033	118	7	g	g	NOUN
cana-1033	118	8	}	}	PUNCT
cana-1033	118	9	and	and	CCONJ
cana-1033	118	10	v	v	NOUN
cana-1033	118	11	=	=	SYM
cana-1033	118	12	{	{	PUNCT
cana-1033	118	13	l	l	NOUN
cana-1033	118	14	,	,	PUNCT
cana-1033	118	15	k	k	NOUN
cana-1033	118	16	}	}	PUNCT
cana-1033	118	17	.	.	PUNCT
cana-1033	119	1	here	here	ADV
cana-1033	119	2	x	x	PUNCT
cana-1033	119	3	can	can	AUX
cana-1033	119	4	not	not	PART
cana-1033	119	5	be	be	AUX
cana-1033	119	6	expressed	express	VERB
cana-1033	119	7	as	as	SCONJ
cana-1033	119	8	the	the	DET
cana-1033	119	9	union	union	NOUN
cana-1033	119	10	of	of	ADP
cana-1033	119	11	two	two	NUM
cana-1033	119	12	non	non	ADJ
cana-1033	119	13	-	-	ADJ
cana-1033	119	14	empty	empty	ADJ
cana-1033	119	15	disjoint	disjoint	NOUN
cana-1033	119	16	ws	ws	NOUN
cana-1033	119	17	–	–	PUNCT
cana-1033	119	18	o	o	NOUN
cana-1033	119	19	-	-	PUNCT
cana-1033	119	20	s.	s.	PROPN
cana-1033	119	21	∴	∴	PROPN
cana-1033	119	22	,	,	PUNCT
cana-1033	119	23	x	x	X
cana-1033	119	24	is	be	AUX
cana-1033	119	25	ws	ws	ADJ
cana-1033	119	26	–	–	PUNCT
cana-1033	119	27	cws	cws	NOUN
cana-1033	119	28	.	.	PUNCT
cana-1033	119	29	theorem	theorem	VERB
cana-1033	119	30	5.3	5.3	NUM
cana-1033	119	31	.	.	PUNCT
cana-1033	120	1	every	every	DET
cana-1033	120	2	ws	ws	ADJ
cana-1033	120	3	-	-	PUNCT
cana-1033	120	4	cws	cws	NOUN
cana-1033	120	5	space	space	NOUN
cana-1033	120	6	is	be	AUX
cana-1033	120	7	cws	cws	ADJ
cana-1033	120	8	.	.	PUNCT
cana-1033	121	1	proof	proof	NOUN
cana-1033	121	2	.	.	PUNCT
cana-1033	122	1	considering	consider	VERB
cana-1033	122	2	(	(	PUNCT
cana-1033	122	3	ҳ	ҳ	NOUN
cana-1033	122	4	,	,	PUNCT
cana-1033	122	5			NOUN
cana-1033	122	6	)	)	PUNCT
cana-1033	122	7	is	be	AUX
cana-1033	122	8	known	know	VERB
cana-1033	122	9	as	as	ADP
cana-1033	122	10	ws	ws	NOUN
cana-1033	122	11	-	-	PUNCT
cana-1033	122	12	cws	cws	NOUN
cana-1033	122	13	space	space	NOUN
cana-1033	122	14	.	.	PUNCT
cana-1033	123	1	supposing	suppose	VERB
cana-1033	123	2	that	that	PRON
cana-1033	123	3	(	(	PUNCT
cana-1033	123	4	ҳ	ҳ	NOUN
cana-1033	123	5	,	,	PUNCT
cana-1033	123	6			NOUN
cana-1033	123	7	)	)	PUNCT
cana-1033	123	8	is	be	AUX
cana-1033	123	9	not	not	PART
cana-1033	123	10	that	that	SCONJ
cana-1033	123	11	cws	cws	NOUN
cana-1033	123	12	.	.	PUNCT
cana-1033	124	1	later	later	ADV
cana-1033	124	2	,	,	PUNCT
cana-1033	124	3	ҳ	ҳ	NOUN
cana-1033	124	4	=	=	SYM
cana-1033	124	5	ģ∪q	ģ∪q	NOUN
cana-1033	124	6	,	,	PUNCT
cana-1033	124	7	where	where	SCONJ
cana-1033	124	8	ģ	ģ	PRON
cana-1033	124	9	and	and	CCONJ
cana-1033	124	10	q	q	NOUN
cana-1033	124	11	be	be	AUX
cana-1033	124	12	there	there	ADV
cana-1033	124	13	disjoint	disjoint	VERB
cana-1033	124	14	nonempty	nonempty	ADJ
cana-1033	124	15	o	o	NOUN
cana-1033	124	16	-	-	PUNCT
cana-1033	124	17	s	s	X
cana-1033	124	18	in	in	ADP
cana-1033	124	19	(	(	PUNCT
cana-1033	124	20	ҳ	ҳ	NOUN
cana-1033	124	21	,	,	PUNCT
cana-1033	124	22			NOUN
cana-1033	124	23	)	)	PUNCT
cana-1033	124	24	.	.	PUNCT
cana-1033	125	1	as	as	SCONJ
cana-1033	125	2	it	it	PRON
cana-1033	125	3	is	be	AUX
cana-1033	125	4	already	already	ADV
cana-1033	125	5	known	know	VERB
cana-1033	125	6	,	,	PUNCT
cana-1033	125	7	arbitrary	arbitrary	ADJ
cana-1033	125	8	∪	∪	ADJ
cana-1033	125	9	ws	ws	NOUN
cana-1033	125	10	-	-	PUNCT
cana-1033	125	11	o	o	NOUN
cana-1033	125	12	-	-	PUNCT
cana-1033	125	13	s	s	NOUN
cana-1033	125	14	is	be	AUX
cana-1033	125	15	ws	ws	ADJ
cana-1033	125	16	-	-	PUNCT
cana-1033	125	17	o	o	NOUN
cana-1033	125	18	,	,	PUNCT
cana-1033	125	19	ģ	ģ	PROPN
cana-1033	125	20	and	and	CCONJ
cana-1033	125	21	q	q	PROPN
cana-1033	125	22	are	be	AUX
cana-1033	125	23	ws	ws	ADJ
cana-1033	125	24	o	o	NOUN
cana-1033	125	25	,	,	PUNCT
cana-1033	125	26	ҳ	ҳ	NOUN
cana-1033	125	27	=	=	SYM
cana-1033	125	28	ģ∪q	ģ∪q	NOUN
cana-1033	125	29	,	,	PUNCT
cana-1033	125	30	where	where	SCONJ
cana-1033	125	31	ģ	ģ	PRON
cana-1033	125	32	and	and	CCONJ
cana-1033	125	33	q	q	PROPN
cana-1033	125	34	are	be	AUX
cana-1033	125	35	disjoint	disjoint	X
cana-1033	125	36	nonempty	nonempty	ADJ
cana-1033	125	37	and	and	CCONJ
cana-1033	125	38	wso	wso	PROPN
cana-1033	125	39	-	-	PUNCT
cana-1033	125	40	s	s	NOUN
cana-1033	125	41	in	in	ADP
cana-1033	125	42	(	(	PUNCT
cana-1033	125	43	ҳ	ҳ	NOUN
cana-1033	125	44	,	,	PUNCT
cana-1033	125	45			NOUN
cana-1033	125	46	)	)	PUNCT
cana-1033	125	47	.	.	PUNCT
cana-1033	126	1	this	this	PRON
cana-1033	126	2	opposes	oppose	VERB
cana-1033	126	3	the	the	DET
cana-1033	126	4	point	point	NOUN
cana-1033	126	5	that	that	SCONJ
cana-1033	126	6	(	(	PUNCT
cana-1033	126	7	ҳ	ҳ	NOUN
cana-1033	126	8	,	,	PUNCT
cana-1033	126	9			NOUN
cana-1033	126	10	)	)	PUNCT
cana-1033	126	11	is	be	AUX
cana-1033	126	12	ws	ws	ADJ
cana-1033	126	13	-	-	PUNCT
cana-1033	126	14	cws	cws	NOUN
cana-1033	126	15	and	and	CCONJ
cana-1033	126	16	so	so	ADV
cana-1033	126	17	(	(	PUNCT
cana-1033	126	18	ҳ	ҳ	NOUN
cana-1033	126	19	,	,	PUNCT
cana-1033	126	20			NOUN
cana-1033	126	21	)	)	PUNCT
cana-1033	126	22	is	be	AUX
cana-1033	126	23	cws	cws	NOUN
cana-1033	126	24	.	.	PUNCT
cana-1033	127	1	definition	definition	NOUN
cana-1033	127	2	5.4	5.4	NUM
cana-1033	127	3	.	.	PUNCT
cana-1033	128	1	a	a	DET
cana-1033	128	2	function	function	NOUN
cana-1033	128	3	ⴇ	ⴇ	NOUN
cana-1033	128	4	:	:	PUNCT
cana-1033	128	5	x	x	SYM
cana-1033	128	6	→y	→y	PROPN
cana-1033	128	7	is	be	AUX
cana-1033	128	8	named	name	VERB
cana-1033	128	9	as	as	ADP
cana-1033	128	10	ws	ws	NOUN
cana-1033	128	11	-	-	PUNCT
cana-1033	128	12	irresolute	irresolute	ADJ
cana-1033	128	13	if	if	SCONJ
cana-1033	128	14	ⴇ	ⴇ	NOUN
cana-1033	128	15	-1(v	-1(v	NOUN
cana-1033	128	16	)	)	PUNCT
cana-1033	128	17	is	be	AUX
cana-1033	128	18	ws	ws	NOUN
cana-1033	128	19	-	-	PUNCT
cana-1033	128	20	c	c	NOUN
cana-1033	128	21	in	in	ADP
cana-1033	128	22	x	x	PUNCT
cana-1033	128	23			NOUN
cana-1033	128	24	ws	ws	NOUN
cana-1033	128	25	-	-	PUNCT
cana-1033	128	26	cs	cs	PROPN
cana-1033	128	27	v	v	NOUN
cana-1033	128	28	of	of	ADP
cana-1033	128	29	y.	y.	PROPN
cana-1033	128	30	theorem	theorem	PROPN
cana-1033	128	31	:	:	PUNCT
cana-1033	128	32	5.5	5.5	NUM
cana-1033	128	33	if	if	SCONJ
cana-1033	128	34	ⴇ	ⴇ	NOUN
cana-1033	128	35	x	x	X
cana-1033	128	36	→	→	SYM
cana-1033	128	37	y	y	PROPN
cana-1033	128	38	is	be	AUX
cana-1033	128	39	a	a	DET
cana-1033	128	40	ws	ws	ADJ
cana-1033	128	41	irresolute	irresolute	ADJ
cana-1033	128	42	surjection	surjection	NOUN
cana-1033	128	43	and	and	CCONJ
cana-1033	128	44	x	x	NOUN
cana-1033	128	45	is	be	AUX
cana-1033	128	46	ws	ws	NOUN
cana-1033	128	47	-	-	PUNCT
cana-1033	128	48	cws	cws	NOUN
cana-1033	128	49	,	,	PUNCT
cana-1033	128	50	hence	hence	ADV
cana-1033	128	51	y	y	PROPN
cana-1033	128	52	is	be	AUX
cana-1033	128	53	ws	ws	NOUN
cana-1033	128	54	-	-	PUNCT
cana-1033	128	55	cws	cws	NOUN
cana-1033	128	56	.	.	PUNCT
cana-1033	129	1	proof	proof	NOUN
cana-1033	129	2	.	.	PUNCT
cana-1033	130	1	considering	consider	VERB
cana-1033	130	2	y	y	PROPN
cana-1033	130	3	is	be	AUX
cana-1033	130	4	not	not	PART
cana-1033	130	5	that	that	SCONJ
cana-1033	130	6	ws	ws	NOUN
cana-1033	130	7	-	-	PUNCT
cana-1033	130	8	cws	cws	NOUN
cana-1033	130	9	,	,	PUNCT
cana-1033	130	10	y	y	PROPN
cana-1033	130	11	=	=	PUNCT
cana-1033	130	12	ģ∪q	ģ∪q	VERB
cana-1033	130	13	where	where	SCONJ
cana-1033	130	14	ģ	ģ	PRON
cana-1033	130	15	and	and	CCONJ
cana-1033	130	16	q	q	PROPN
cana-1033	130	17	are	be	AUX
cana-1033	130	18	disjoint	disjoint	ADJ
cana-1033	130	19	non	non	ADJ
cana-1033	130	20	-	-	ADJ
cana-1033	130	21	empty	empty	ADJ
cana-1033	130	22	ws	ws	NOUN
cana-1033	130	23	-	-	PUNCT
cana-1033	130	24	o	o	NOUN
cana-1033	130	25	-	-	NOUN
cana-1033	130	26	s	s	X
cana-1033	130	27	throughout	throughout	ADP
cana-1033	130	28	y.	y.	NOUN
cana-1033	130	29	subsequently	subsequently	ADV
cana-1033	130	30	,	,	PUNCT
cana-1033	130	31	ⴇ	ⴇ	PROPN
cana-1033	130	32	is	be	AUX
cana-1033	130	33	ws	ws	NOUN
cana-1033	130	34	-	-	PUNCT
cana-1033	130	35	irresolute	irresolute	ADJ
cana-1033	130	36	besides	besides	SCONJ
cana-1033	130	37	on	on	ADP
cana-1033	130	38	,	,	PUNCT
cana-1033	130	39	x	x	PUNCT
cana-1033	130	40	=	=	PUNCT
cana-1033	130	41	ⴇ	ⴇ	NOUN
cana-1033	130	42	-1(ģ	-1(ģ	NOUN
cana-1033	130	43	)	)	PUNCT
cana-1033	130	44	∪	∪	ADP
cana-1033	130	45	ⴇ	ⴇ	PROPN
cana-1033	130	46	-1	-1	PUNCT
cana-1033	130	47	(	(	PUNCT
cana-1033	130	48	q	q	NOUN
cana-1033	130	49	)	)	PUNCT
cana-1033	130	50	where	where	SCONJ
cana-1033	130	51	ⴇ	ⴇ	NOUN
cana-1033	130	52	-1(ģ	-1(ģ	NOUN
cana-1033	130	53	)	)	PUNCT
cana-1033	130	54	and	and	CCONJ
cana-1033	130	55	ⴇ	ⴇ	PROPN
cana-1033	130	56	-1(q	-1(q	X
cana-1033	130	57	)	)	PUNCT
cana-1033	130	58	are	be	AUX
cana-1033	130	59	disjoint	disjoint	ADJ
cana-1033	130	60	non	non	ADJ
cana-1033	130	61	-	-	ADJ
cana-1033	130	62	empty	empty	ADJ
cana-1033	130	63	ws	ws	NOUN
cana-1033	130	64	-	-	PUNCT
cana-1033	130	65	o	o	NOUN
cana-1033	130	66	-	-	NOUN
cana-1033	130	67	s	s	NOUN
cana-1033	130	68	in	in	ADP
cana-1033	130	69	x.	x.	NOUN
cana-1033	131	1	the	the	DET
cana-1033	131	2	fact	fact	NOUN
cana-1033	131	3	x	x	PUNCT
cana-1033	131	4	is	be	AUX
cana-1033	131	5	contradicted	contradict	VERB
cana-1033	131	6	by	by	ADP
cana-1033	131	7	this	this	DET
cana-1033	131	8	ws	ws	NOUN
cana-1033	131	9	-	-	PUNCT
cana-1033	131	10	cws	cws	NOUN
cana-1033	131	11	.	.	PUNCT
cana-1033	132	1	∴	∴	PROPN
cana-1033	132	2	,	,	PUNCT
cana-1033	132	3	y	y	PROPN
cana-1033	132	4	is	be	AUX
cana-1033	132	5	cws	cws	NOUN
cana-1033	132	6	.	.	PUNCT
cana-1033	133	1	communications	communication	NOUN
cana-1033	133	2	on	on	ADP
cana-1033	133	3	applied	apply	VERB
cana-1033	133	4	nonlinear	nonlinear	ADJ
cana-1033	133	5	analysis	analysis	NOUN
cana-1033	133	6	issn	issn	NOUN
cana-1033	133	7	:	:	PUNCT
cana-1033	133	8	1074	1074	NUM
cana-1033	133	9	-	-	PUNCT
cana-1033	133	10	133x	133x	NUM
cana-1033	133	11	vol	vol	NOUN
cana-1033	133	12	31	31	NUM
cana-1033	133	13	no	no	NOUN
cana-1033	133	14	.	.	PUNCT
cana-1033	134	1	5s	5s	NUM
cana-1033	134	2	(	(	PUNCT
cana-1033	134	3	2024	2024	NUM
cana-1033	134	4	)	)	PUNCT
cana-1033	134	5	264	264	NUM
cana-1033	135	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1033	135	2	remark	remark	NOUN
cana-1033	135	3	5.6	5.6	NUM
cana-1033	135	4	.	.	PUNCT
cana-1033	136	1	any	any	DET
cana-1033	136	2	indiscrete	indiscrete	ADJ
cana-1033	136	3	space	space	NOUN
cana-1033	136	4	with	with	ADP
cana-1033	136	5	two	two	NUM
cana-1033	136	6	points	point	NOUN
cana-1033	136	7	is	be	AUX
cana-1033	136	8	ws	ws	ADJ
cana-1033	136	9	–	–	PUNCT
cana-1033	136	10	cws	cws	NOUN
cana-1033	136	11	,	,	PUNCT
cana-1033	136	12	but	but	CCONJ
cana-1033	136	13	any	any	DET
cana-1033	136	14	two	two	NUM
cana-1033	136	15	–	–	PUNCT
cana-1033	136	16	point	point	NOUN
cana-1033	136	17	set	set	VERB
cana-1033	136	18	with	with	ADP
cana-1033	136	19	discrete	discrete	ADJ
cana-1033	136	20	topology	topology	NOUN
cana-1033	136	21	is	be	AUX
cana-1033	136	22	not	not	PART
cana-1033	136	23	wscws	wscws	ADJ
cana-1033	136	24	.	.	PUNCT
cana-1033	137	1	theorem	theorem	VERB
cana-1033	137	2	5.7	5.7	NUM
cana-1033	137	3	.	.	PUNCT
cana-1033	138	1	if	if	SCONJ
cana-1033	138	2	the	the	DET
cana-1033	138	3	ws	ws	NOUN
cana-1033	138	4	-	-	PUNCT
cana-1033	138	5	o	o	NOUN
cana-1033	138	6	-	-	NOUN
cana-1033	138	7	s	s	X
cana-1033	138	8	q	q	NOUN
cana-1033	138	9	and	and	CCONJ
cana-1033	138	10	℘	℘	PROPN
cana-1033	138	11	leads	lead	VERB
cana-1033	138	12	to	to	ADP
cana-1033	138	13	separation	separation	NOUN
cana-1033	138	14	of	of	ADP
cana-1033	138	15	x	x	PUNCT
cana-1033	138	16	besides	besides	ADV
cana-1033	138	17	if	if	SCONJ
cana-1033	138	18	y	y	PROPN
cana-1033	138	19	is	be	AUX
cana-1033	138	20	ws	ws	ADJ
cana-1033	138	21	-	-	PUNCT
cana-1033	138	22	cws	cws	NOUN
cana-1033	138	23	subspace	subspace	NOUN
cana-1033	138	24	of	of	ADP
cana-1033	138	25	x	x	PRON
cana-1033	138	26	,	,	PUNCT
cana-1033	138	27	then	then	ADV
cana-1033	138	28	y	y	PROPN
cana-1033	138	29	exists	exist	VERB
cana-1033	138	30	mainly	mainly	ADV
cana-1033	138	31	in	in	ADP
cana-1033	138	32	q	q	PROPN
cana-1033	138	33	and	and	CCONJ
cana-1033	138	34	℘.	℘.	PROPN
cana-1033	138	35	proof	proof	NOUN
cana-1033	138	36	.	.	PUNCT
cana-1033	139	1	when	when	SCONJ
cana-1033	139	2	q	q	NOUN
cana-1033	139	3	and	and	CCONJ
cana-1033	139	4	℘	℘	PROPN
cana-1033	139	5	are	be	AUX
cana-1033	139	6	both	both	CCONJ
cana-1033	139	7	ws	ws	ADJ
cana-1033	139	8	-	-	PUNCT
cana-1033	139	9	o	o	NOUN
cana-1033	139	10	in	in	ADP
cana-1033	139	11	x	x	PUNCT
cana-1033	139	12	the	the	DET
cana-1033	139	13	sets	set	NOUN
cana-1033	139	14	q	q	X
cana-1033	139	15	∩℘	∩℘	PUNCT
cana-1033	139	16	and	and	CCONJ
cana-1033	139	17	℘∩y	℘∩y	NOUN
cana-1033	139	18	are	be	AUX
cana-1033	139	19	ws	ws	ADJ
cana-1033	139	20	-	-	PUNCT
cana-1033	139	21	o	o	NOUN
cana-1033	139	22	in	in	ADP
cana-1033	139	23	y	y	PROPN
cana-1033	139	24	these	these	DET
cana-1033	139	25	two	two	NUM
cana-1033	139	26	sets	set	NOUN
cana-1033	139	27	are	be	AUX
cana-1033	139	28	disjoint	disjoint	NOUN
cana-1033	139	29	∪	∪	ADJ
cana-1033	139	30	in	in	ADP
cana-1033	139	31	y.	y.	PROPN
cana-1033	139	32	if	if	SCONJ
cana-1033	139	33	both	both	PRON
cana-1033	139	34	were	be	AUX
cana-1033	139	35	non	non	ADJ
cana-1033	139	36	-	-	ADJ
cana-1033	139	37	empty	empty	ADJ
cana-1033	139	38	,	,	PUNCT
cana-1033	139	39	they	they	PRON
cana-1033	139	40	would	would	AUX
cana-1033	139	41	represent	represent	VERB
cana-1033	139	42	a	a	DET
cana-1033	139	43	division	division	NOUN
cana-1033	139	44	y.	y.	PROPN
cana-1033	139	45	∴	∴	PROPN
cana-1033	139	46	,	,	PUNCT
cana-1033	139	47	there	there	PRON
cana-1033	139	48	are	be	VERB
cana-1033	139	49	only	only	ADV
cana-1033	139	50	one	one	NUM
cana-1033	139	51	empty	empty	ADJ
cana-1033	139	52	one	one	NUM
cana-1033	139	53	.	.	PUNCT
cana-1033	140	1	∴	∴	PROPN
cana-1033	140	2	,	,	PUNCT
cana-1033	140	3	y	y	PROPN
cana-1033	140	4	has	have	VERB
cana-1033	140	5	to	to	PART
cana-1033	140	6	completely	completely	ADV
cana-1033	140	7	lie	lie	VERB
cana-1033	140	8	in	in	ADP
cana-1033	140	9	q	q	PROPN
cana-1033	140	10	or	or	CCONJ
cana-1033	140	11	in	in	ADP
cana-1033	140	12	℘.	℘.	PROPN
cana-1033	140	13	6	6	NUM
cana-1033	140	14	.	.	PUNCT
cana-1033	141	1	conclusion	conclusion	NOUN
cana-1033	141	2	:	:	PUNCT
cana-1033	141	3	the	the	DET
cana-1033	141	4	definition	definition	NOUN
cana-1033	141	5	of	of	ADP
cana-1033	141	6	two	two	NUM
cana-1033	141	7	new	new	ADJ
cana-1033	141	8	concepts	concept	NOUN
cana-1033	141	9	of	of	ADP
cana-1033	141	10	connectedness	connectedness	NOUN
cana-1033	141	11	and	and	CCONJ
cana-1033	141	12	compactness	compactness	NOUN
cana-1033	141	13	ws	ws	NOUN
cana-1033	141	14	(	(	PUNCT
cana-1033	141	15	compactness	compactness	NOUN
cana-1033	141	16	)	)	PUNCT
cana-1033	141	17	and	and	CCONJ
cana-1033	141	18	ws	ws	NOUN
cana-1033	141	19	(	(	PUNCT
cana-1033	141	20	connectedness	connectedness	NOUN
cana-1033	141	21	)	)	PUNCT
cana-1033	141	22	.	.	PUNCT
cana-1033	142	1	an	an	PRON
cana-1033	142	2	x	x	NOUN
cana-1033	142	3	represents	represent	VERB
cana-1033	142	4	ws	ws	ADJ
cana-1033	142	5	–	–	PUNCT
cana-1033	142	6	compact	compact	ADJ
cana-1033	142	7	if	if	SCONJ
cana-1033	142	8	every	every	DET
cana-1033	142	9	ws	ws	NOUN
cana-1033	142	10	–	–	PUNCT
cana-1033	142	11	o	o	NOUN
cana-1033	142	12	–	–	PUNCT
cana-1033	142	13	c	c	NOUN
cana-1033	142	14	of	of	ADP
cana-1033	142	15	x	x	PUNCT
cana-1033	142	16	have	have	VERB
cana-1033	142	17	a	a	DET
cana-1033	142	18	finite	finite	ADJ
cana-1033	142	19	subcover	subcover	PROPN
cana-1033	142	20	.	.	PUNCT
cana-1033	143	1	the	the	DET
cana-1033	143	2	ws	ws	ADJ
cana-1033	143	3	cws	cws	NOUN
cana-1033	143	4	and	and	CCONJ
cana-1033	143	5	ws	ws	ADJ
cana-1033	143	6	–	–	PUNCT
cana-1033	143	7	compactness	compactness	NOUN
cana-1033	143	8	fulfilled	fulfil	VERB
cana-1033	143	9	most	most	ADJ
cana-1033	143	10	of	of	ADP
cana-1033	143	11	the	the	DET
cana-1033	143	12	connectedness	connectedness	NOUN
cana-1033	143	13	and	and	CCONJ
cana-1033	143	14	compactness	compactness	NOUN
cana-1033	143	15	properties	property	NOUN
cana-1033	143	16	in	in	ADP
cana-1033	143	17	ts	ts	PROPN
cana-1033	143	18	.	.	PUNCT
cana-1033	144	1	the	the	DET
cana-1033	144	2	primary	primary	ADJ
cana-1033	144	3	goal	goal	NOUN
cana-1033	144	4	of	of	ADP
cana-1033	144	5	this	this	DET
cana-1033	144	6	work	work	NOUN
cana-1033	144	7	was	be	AUX
cana-1033	144	8	to	to	PART
cana-1033	144	9	get	get	VERB
cana-1033	144	10	a	a	DET
cana-1033	144	11	deeper	deep	ADJ
cana-1033	144	12	understanding	understanding	NOUN
cana-1033	144	13	of	of	ADP
cana-1033	144	14	the	the	DET
cana-1033	144	15	consequences	consequence	NOUN
cana-1033	144	16	of	of	ADP
cana-1033	144	17	compactness	compactness	NOUN
cana-1033	144	18	and	and	CCONJ
cana-1033	144	19	connectedness	connectedness	NOUN
cana-1033	144	20	in	in	ADP
cana-1033	144	21	beta	beta	ADJ
cana-1033	144	22	weakly	weakly	ADJ
cana-1033	144	23	semi	semi	NOUN
cana-1033	144	24	-	-	NOUN
cana-1033	144	25	cs	cs	ADJ
cana-1033	144	26	in	in	ADP
cana-1033	144	27	ts	ts	ADV
cana-1033	144	28	and	and	CCONJ
cana-1033	144	29	suggest	suggest	VERB
cana-1033	144	30	future	future	ADJ
cana-1033	144	31	lines	line	NOUN
cana-1033	144	32	of	of	ADP
cana-1033	144	33	research	research	NOUN
cana-1033	144	34	.	.	PUNCT
cana-1033	145	1	we	we	PRON
cana-1033	145	2	have	have	AUX
cana-1033	145	3	obtained	obtain	VERB
cana-1033	145	4	several	several	ADJ
cana-1033	145	5	noteworthy	noteworthy	ADJ
cana-1033	145	6	results	result	NOUN
cana-1033	145	7	from	from	ADP
cana-1033	145	8	our	our	PRON
cana-1033	145	9	analysis	analysis	NOUN
cana-1033	145	10	of	of	ADP
cana-1033	145	11	beta	beta	ADJ
cana-1033	145	12	weakly	weakly	ADJ
cana-1033	145	13	closed	closed	ADJ
cana-1033	145	14	sets	set	NOUN
cana-1033	145	15	.	.	PUNCT
cana-1033	146	1	the	the	DET
cana-1033	146	2	study	study	NOUN
cana-1033	146	3	has	have	AUX
cana-1033	146	4	strengthened	strengthen	VERB
cana-1033	146	5	the	the	DET
cana-1033	146	6	theoretical	theoretical	ADJ
cana-1033	146	7	foundations	foundation	NOUN
cana-1033	146	8	of	of	ADP
cana-1033	146	9	these	these	DET
cana-1033	146	10	concepts	concept	NOUN
cana-1033	146	11	by	by	ADP
cana-1033	146	12	developing	develop	VERB
cana-1033	146	13	and	and	CCONJ
cana-1033	146	14	verifying	verify	VERB
cana-1033	146	15	several	several	ADJ
cana-1033	146	16	theorems	theorem	NOUN
cana-1033	146	17	that	that	PRON
cana-1033	146	18	show	show	VERB
cana-1033	146	19	these	these	DET
cana-1033	146	20	ideas	idea	NOUN
cana-1033	146	21	may	may	AUX
cana-1033	146	22	hold	hold	VERB
cana-1033	146	23	true	true	ADJ
cana-1033	146	24	in	in	ADP
cana-1033	146	25	various	various	ADJ
cana-1033	146	26	topological	topological	ADJ
cana-1033	146	27	domains	domain	NOUN
cana-1033	146	28	.	.	PUNCT
cana-1033	147	1	there	there	PRON
cana-1033	147	2	are	be	VERB
cana-1033	147	3	a	a	DET
cana-1033	147	4	number	number	NOUN
cana-1033	147	5	of	of	ADP
cana-1033	147	6	interesting	interesting	ADJ
cana-1033	147	7	avenues	avenue	NOUN
cana-1033	147	8	for	for	ADP
cana-1033	147	9	further	further	ADJ
cana-1033	147	10	research	research	NOUN
cana-1033	147	11	in	in	ADP
cana-1033	147	12	the	the	DET
cana-1033	147	13	future	future	NOUN
cana-1033	147	14	.	.	PUNCT
cana-1033	148	1	the	the	DET
cana-1033	148	2	application	application	NOUN
cana-1033	148	3	of	of	ADP
cana-1033	148	4	connectedness	connectedness	NOUN
cana-1033	148	5	and	and	CCONJ
cana-1033	148	6	compactness	compactness	NOUN
cana-1033	148	7	in	in	ADP
cana-1033	148	8	beta	beta	ADJ
cana-1033	148	9	weakly	weakly	ADJ
cana-1033	148	10	semi	semi	NOUN
cana-1033	148	11	-	-	NOUN
cana-1033	148	12	cs	cs	ADJ
cana-1033	148	13	in	in	ADP
cana-1033	148	14	ts	ts	PROPN
cana-1033	148	15	.	.	PUNCT
cana-1033	149	1	the	the	DET
cana-1033	149	2	study	study	NOUN
cana-1033	149	3	of	of	ADP
cana-1033	149	4	compactness	compactness	NOUN
cana-1033	149	5	and	and	CCONJ
cana-1033	149	6	connectedness	connectedness	NOUN
cana-1033	149	7	in	in	ADP
cana-1033	149	8	beta	beta	ADJ
cana-1033	149	9	weakly	weakly	ADJ
cana-1033	149	10	semi	semi	NOUN
cana-1033	149	11	-	-	NOUN
cana-1033	149	12	cs	cs	ADJ
cana-1033	149	13	in	in	ADP
cana-1033	149	14	ts	ts	PROPN
cana-1033	149	15	has	have	AUX
cana-1033	149	16	led	lead	VERB
cana-1033	149	17	to	to	ADP
cana-1033	149	18	significant	significant	ADJ
cana-1033	149	19	discoveries	discovery	NOUN
cana-1033	149	20	in	in	ADP
cana-1033	149	21	the	the	DET
cana-1033	149	22	ts	ts	NOUN
cana-1033	149	23	.	.	PUNCT
cana-1033	150	1	references	reference	NOUN
cana-1033	150	2	[	[	X
cana-1033	150	3	1	1	X
cana-1033	150	4	]	]	PUNCT
cana-1033	150	5	d.	d.	PROPN
cana-1033	150	6	andrijevic	andrijevic	PROPN
cana-1033	150	7	,	,	PUNCT
cana-1033	150	8	on	on	ADP
cana-1033	150	9	b	b	X
cana-1033	150	10	-	-	PUNCT
cana-1033	150	11	open	open	ADJ
cana-1033	150	12	sets	set	NOUN
cana-1033	150	13	,	,	PUNCT
cana-1033	150	14	math	math	NOUN
cana-1033	150	15	.	.	PUNCT
cana-1033	151	1	vesnik	vesnik	PROPN
cana-1033	151	2	,	,	PUNCT
cana-1033	151	3	48	48	NUM
cana-1033	151	4	(	(	PUNCT
cana-1033	151	5	1996	1996	NUM
cana-1033	151	6	)	)	PUNCT
cana-1033	151	7	,	,	PUNCT
cana-1033	151	8	no	no	INTJ
cana-1033	151	9	.	.	NOUN
cana-1033	152	1	1	1	NUM
cana-1033	152	2	-	-	SYM
cana-1033	152	3	2	2	NUM
cana-1033	152	4	,	,	PUNCT
cana-1033	152	5	59	59	NUM
cana-1033	152	6	-	-	SYM
cana-1033	152	7	64	64	NUM
cana-1033	152	8	.	.	PUNCT
cana-1033	153	1	doi.10.12691	doi.10.12691	PROPN
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cana-1033	153	6	-	-	SYM
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cana-1033	153	49	,	,	PUNCT
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cana-1033	153	51	.	.	PUNCT
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cana-1033	154	2	-	-	SYM
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cana-1033	155	2	,	,	PUNCT
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cana-1033	155	4	.	.	PUNCT
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cana-1033	156	3	]	]	PUNCT
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cana-1033	156	7	,	,	PUNCT
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cana-1033	156	9	-	-	PUNCT
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cana-1033	156	11	-	-	PUNCT
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cana-1033	157	7	,	,	PUNCT
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cana-1033	157	9	-	-	SYM
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cana-1033	157	11	.	.	PUNCT
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cana-1033	159	3	]	]	PUNCT
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cana-1033	159	23	,	,	PUNCT
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cana-1033	159	27	.	.	PUNCT
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cana-1033	160	7	.	.	PROPN
cana-1033	160	8	sasikala	sasikala	PROPN
cana-1033	160	9	,	,	PUNCT
cana-1033	160	10	d.	d.	PROPN
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cana-1033	160	28	,	,	PUNCT
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cana-1033	160	37	,	,	PUNCT
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cana-1033	160	47	,	,	PUNCT
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cana-1033	160	58	.	.	PUNCT
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cana-1033	164	35	,	,	PUNCT
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cana-1033	164	42	,	,	PUNCT
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cana-1033	165	2	-	-	SYM
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cana-1033	167	32	,	,	PUNCT
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cana-1033	168	2	-	-	SYM
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cana-1033	168	8	.	.	PUNCT
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cana-1033	169	7	,	,	PUNCT
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cana-1033	169	9	,	,	PUNCT
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cana-1033	169	11	891	891	NUM
cana-1033	169	12	-	-	SYM
cana-1033	169	13	898	898	NUM
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cana-1033	169	15	issn.1309	issn.1309	PROPN
cana-1033	169	16	-	-	SYM
cana-1033	169	17	3452	3452	NUM
cana-1033	169	18	.	.	PUNCT
cana-1033	170	1	[	[	X
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cana-1033	170	3	]	]	X
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cana-1033	170	8	,	,	PUNCT
cana-1033	170	9	“	"	PUNCT
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cana-1033	170	14	and	and	CCONJ
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cana-1033	170	16	weakly	weakly	ADJ
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cana-1033	170	22	”	"	PUNCT
cana-1033	170	23	;	;	PUNCT
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cana-1033	173	13	on	on	ADP
cana-1033	173	14	generalized	generalized	ADJ
cana-1033	173	15	continuous	continuous	ADJ
cana-1033	173	16	maps	map	NOUN
cana-1033	173	17	in	in	ADP
cana-1033	173	18	topological	topological	ADJ
cana-1033	173	19	spaces	space	NOUN
cana-1033	173	20	,	,	PUNCT
cana-1033	173	21	mem	mem	PROPN
cana-1033	173	22	.	.	PUNCT
cana-1033	174	1	fac	fac	PROPN
cana-1033	174	2	.	.	PROPN
cana-1033	174	3	kochi	kochi	PROPN
cana-1033	174	4	univ	univ	PROPN
cana-1033	174	5	.	.	PUNCT
cana-1033	175	1	ser	ser	PROPN
cana-1033	175	2	.	.	PUNCT
cana-1033	176	1	a	a	DET
cana-1033	176	2	,	,	PUNCT
cana-1033	176	3	math	math	NOUN
cana-1033	176	4	.	.	PUNCT
cana-1033	177	1	12	12	NUM
cana-1033	177	2	(	(	PUNCT
cana-1033	177	3	1991	1991	NUM
cana-1033	177	4	)	)	PUNCT
cana-1033	177	5	5–13	5–13	PROPN
cana-1033	177	6	.	.	PUNCT
cana-1033	178	1	doi.https://doi.org/10.14445/22315373/ijmtt-v6p506	doi.https://doi.org/10.14445/22315373/ijmtt-v6p506	NOUN
cana-1033	179	1	[	[	X
cana-1033	179	2	11	11	NUM
cana-1033	179	3	]	]	X
cana-1033	179	4	r.	r.	PROPN
cana-1033	179	5	devi	devi	PROPN
cana-1033	179	6	,	,	PUNCT
cana-1033	179	7	studies	study	NOUN
cana-1033	179	8	on	on	ADP
cana-1033	179	9	generalizations	generalization	NOUN
cana-1033	179	10	of	of	ADP
cana-1033	179	11	closed	closed	ADJ
cana-1033	179	12	maps	map	NOUN
cana-1033	179	13	and	and	CCONJ
cana-1033	179	14	homeomorphisms	homeomorphism	NOUN
cana-1033	179	15	in	in	ADP
cana-1033	179	16	topological	topological	ADJ
cana-1033	179	17	spaces	space	NOUN
cana-1033	179	18	,	,	PUNCT
cana-1033	179	19	ph.d	ph.d	PROPN
cana-1033	179	20	.	.	PUNCT
cana-1033	180	1	thesis	thesis	PROPN
cana-1033	180	2	,	,	PUNCT
cana-1033	180	3	bharathiar	bharathiar	PROPN
cana-1033	180	4	university	university	PROPN
cana-1033	180	5	,	,	PUNCT
cana-1033	180	6	coimbatore	coimbatore	PROPN
cana-1033	180	7	,	,	PUNCT
cana-1033	180	8	1994	1994	NUM
cana-1033	180	9	.	.	PUNCT
cana-1033	181	1	https://doi.org/10.26713/jims.v9i3.755	https://doi.org/10.26713/jims.v9i3.755	PROPN
cana-1033	181	2	[	[	X
cana-1033	181	3	12	12	NUM
cana-1033	181	4	]	]	X
cana-1033	181	5	y.	y.	PROPN
cana-1033	181	6	gnanambal	gnanambal	PROPN
cana-1033	181	7	,	,	PUNCT
cana-1033	181	8	k.	k.	PROPN
cana-1033	181	9	balachandran	balachandran	PROPN
cana-1033	181	10	,	,	PUNCT
cana-1033	181	11	on	on	ADP
cana-1033	181	12	gpr	gpr	NOUN
cana-1033	181	13	-	-	PUNCT
cana-1033	181	14	continuous	continuous	ADJ
cana-1033	181	15	functions	function	NOUN
cana-1033	181	16	in	in	ADP
cana-1033	181	17	topological	topological	ADJ
cana-1033	181	18	spaces	space	NOUN
cana-1033	181	19	,	,	PUNCT
cana-1033	181	20	indian	indian	PROPN
cana-1033	181	21	j.	j.	PROPN
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cana-1033	181	24	.	.	PUNCT
cana-1033	181	25	math	math	NOUN
cana-1033	181	26	.	.	PUNCT
cana-1033	182	1	30	30	NUM
cana-1033	182	2	(	(	PUNCT
cana-1033	182	3	6	6	NUM
cana-1033	182	4	)	)	PUNCT
cana-1033	182	5	(	(	PUNCT
cana-1033	182	6	1999	1999	NUM
cana-1033	182	7	)	)	PUNCT
cana-1033	183	1	581–593	581–593	NUM
cana-1033	183	2	.	.	PUNCT
cana-1033	183	3	doi	doi	PROPN
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cana-1033	184	1	[	[	X
cana-1033	184	2	13	13	NUM
cana-1033	184	3	]	]	PUNCT
cana-1033	184	4	a.	a.	NOUN
cana-1033	184	5	pushpalatha	pushpalatha	PROPN
cana-1033	184	6	,	,	PUNCT
cana-1033	184	7	studies	study	NOUN
cana-1033	184	8	on	on	ADP
cana-1033	184	9	generalizations	generalization	NOUN
cana-1033	184	10	of	of	ADP
cana-1033	184	11	mappings	mapping	NOUN
cana-1033	184	12	in	in	ADP
cana-1033	184	13	topological	topological	ADJ
cana-1033	184	14	spaces	space	NOUN
cana-1033	184	15	,	,	PUNCT
cana-1033	184	16	ph.d	ph.d	PROPN
cana-1033	184	17	.	.	PUNCT
cana-1033	185	1	thesis	thesis	PROPN
cana-1033	185	2	,	,	PUNCT
cana-1033	185	3	bharathiar	bharathiar	PROPN
cana-1033	185	4	university	university	PROPN
cana-1033	185	5	,	,	PUNCT
cana-1033	185	6	coimbatore	coimbatore	PROPN
cana-1033	185	7	,	,	PUNCT
cana-1033	185	8	2000	2000	NUM
cana-1033	185	9	.	.	PUNCT
cana-1033	186	1	doi:10.29322	doi:10.29322	NOUN
cana-1033	186	2	/	/	SYM
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cana-1033	186	5	14	14	NUM
cana-1033	186	6	]	]	PUNCT
cana-1033	186	7	m.	m.	NOUN
cana-1033	186	8	sheik	sheik	PROPN
cana-1033	186	9	john	john	PROPN
cana-1033	186	10	,	,	PUNCT
cana-1033	186	11	a	a	DET
cana-1033	186	12	study	study	NOUN
cana-1033	186	13	on	on	ADP
cana-1033	186	14	generalizations	generalization	NOUN
cana-1033	186	15	of	of	ADP
cana-1033	186	16	closed	closed	ADJ
cana-1033	186	17	sets	set	NOUN
cana-1033	186	18	and	and	CCONJ
cana-1033	186	19	continuous	continuous	ADJ
cana-1033	186	20	maps	map	NOUN
cana-1033	186	21	in	in	ADP
cana-1033	186	22	topological	topological	ADJ
cana-1033	186	23	and	and	CCONJ
cana-1033	186	24	bitopological	bitopological	ADJ
cana-1033	186	25	spaces	space	NOUN
cana-1033	186	26	,	,	PUNCT
cana-1033	186	27	ph.d	ph.d	PROPN
cana-1033	186	28	.	.	PUNCT
cana-1033	187	1	thesis	thesis	PROPN
cana-1033	187	2	,	,	PUNCT
cana-1033	187	3	bharathiar	bharathiar	PROPN
cana-1033	187	4	university	university	PROPN
cana-1033	187	5	,	,	PUNCT
cana-1033	187	6	coimbatore	coimbatore	PROPN
cana-1033	187	7	,	,	PUNCT
cana-1033	187	8	2002	2002	NUM
cana-1033	187	9	.	.	PUNCT
cana-1033	188	1	10.26637	10.26637	NUM
cana-1033	188	2	/	/	SYM
cana-1033	188	3	mjm0s20/0108	mjm0s20/0108	PROPN
cana-1033	188	4	.	.	PUNCT
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cana-1033	189	2	15	15	NUM
cana-1033	189	3	]	]	X
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cana-1033	189	5	-	-	PUNCT
cana-1033	189	6	compactness	compactness	NOUN
cana-1033	189	7	and	and	CCONJ
cana-1033	189	8	g*sconnectedness	g*sconnectedness	NOUN
cana-1033	189	9	in	in	ADP
cana-1033	189	10	topological	topological	ADJ
cana-1033	189	11	spaces	space	NOUN
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cana-1033	189	13	m.	m.	PROPN
cana-1033	189	14	patil1	patil1	PROPN
cana-1033	189	15	and	and	CCONJ
cana-1033	189	16	t.	t.	PROPN
cana-1033	189	17	d.	d.	PROPN
cana-1033	189	18	rayanagoudar	rayanagoudar	PROPN
cana-1033	189	19	2	2	NUM
cana-1033	189	20	*	*	PROPN
cana-1033	189	21	department	department	NOUN
cana-1033	189	22	of	of	ADP
cana-1033	189	23	mathematics	mathematics	PROPN
cana-1033	189	24	government	government	NOUN
cana-1033	189	25	first	first	ADJ
cana-1033	189	26	grade	grade	NOUN
cana-1033	189	27	college	college	NOUN
cana-1033	189	28	,	,	PUNCT
cana-1033	189	29	rajnagar	rajnagar	ADJ
cana-1033	189	30	,	,	PUNCT
cana-1033	189	31	hubli	hubli	NOUN
cana-1033	189	32	-580	-580	PROPN
cana-1033	189	33	032	032	NUM
cana-1033	189	34	,	,	PUNCT
cana-1033	189	35	karnataka	karnataka	PROPN
cana-1033	189	36	state	state	PROPN
cana-1033	189	37	,	,	PUNCT
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cana-1033	189	39	.	.	PUNCT
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cana-1033	190	2	16	16	NUM
cana-1033	190	3	]	]	X
cana-1033	190	4	"	"	PUNCT
cana-1033	190	5	gso	gso	X
cana-1033	190	6	-	-	NOUN
cana-1033	190	7	connectedness	connectedness	NOUN
cana-1033	190	8	and	and	CCONJ
cana-1033	190	9	gso	gso	NOUN
cana-1033	190	10	-	-	NOUN
cana-1033	190	11	compactness	compactness	NOUN
cana-1033	190	12	in	in	ADP
cana-1033	190	13	topological	topological	ADJ
cana-1033	190	14	spaces	space	NOUN
cana-1033	190	15	"	"	PUNCT
cana-1033	190	16	,	,	PUNCT
cana-1033	190	17	international	international	ADJ
cana-1033	190	18	journal	journal	NOUN
cana-1033	190	19	of	of	ADP
cana-1033	190	20	emerging	emerge	VERB
cana-1033	190	21	technologies	technology	NOUN
cana-1033	190	22	and	and	CCONJ
cana-1033	190	23	innovative	innovative	ADJ
cana-1033	190	24	research	research	NOUN
cana-1033	190	25	(	(	PUNCT
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cana-1033	190	27	)	)	PUNCT
cana-1033	190	28	,	,	PUNCT
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cana-1033	190	30	-	-	ADJ
cana-1033	190	31	5162	5162	NUM
cana-1033	190	32	,	,	PUNCT
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cana-1033	190	34	,	,	PUNCT
cana-1033	190	35	issue	issue	NOUN
cana-1033	190	36	11,pageno.c119	11,pageno.c119	NOUN
cana-1033	190	37	-	-	PUNCT
cana-1033	190	38	c122,november2022,available	c122,november2022,available	ADJ
cana-1033	190	39	:	:	PUNCT
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