id	sid	tid	token	lemma	pos
cana-858	1	1	communications	communication	NOUN
cana-858	1	2	on	on	ADP
cana-858	1	3	applied	apply	VERB
cana-858	1	4	nonlinear	nonlinear	ADJ
cana-858	1	5	analysis	analysis	NOUN
cana-858	1	6	issn	issn	NOUN
cana-858	1	7	:	:	PUNCT
cana-858	1	8	1074	1074	NUM
cana-858	1	9	-	-	PUNCT
cana-858	1	10	133x	133x	NUM
cana-858	1	11	vol	vol	NOUN
cana-858	1	12	31	31	NUM
cana-858	1	13	no	no	NOUN
cana-858	1	14	.	.	PUNCT
cana-858	2	1	4s	4s	NUM
cana-858	2	2	(	(	PUNCT
cana-858	2	3	2024	2024	NUM
cana-858	2	4	)	)	PUNCT
cana-858	2	5	358	358	NUM
cana-858	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-858	2	7	on	on	ADP
cana-858	2	8	generalized	generalized	ADJ
cana-858	2	9	nano	nano	NOUN
cana-858	2	10	ℕ	ℕ	PROPN
cana-858	2	11	�	�	PROPN
cana-858	2	12	̌	̌	NUM
cana-858	2	13	�	�	NOUN
cana-858	2	14	closed	close	VERB
cana-858	2	15	and	and	CCONJ
cana-858	2	16	nano	nano	NOUN
cana-858	2	17	ℕα̂open	ℕα̂open	NOUN
cana-858	2	18	sets	set	VERB
cana-858	2	19	in	in	ADP
cana-858	2	20	nano	nano	NOUN
cana-858	2	21	topological	topological	ADJ
cana-858	2	22	spaces	space	NOUN
cana-858	2	23	abdulaziz	abdulaziz	PROPN
cana-858	2	24	.s	.s	PROPN
cana-858	2	25	.	.	PUNCT
cana-858	3	1	hameed1	hameed1	PROPN
cana-858	3	2	,	,	PUNCT
cana-858	3	3	layla	layla	PROPN
cana-858	3	4	hindi2	hindi2	PROPN
cana-858	3	5	,	,	PUNCT
cana-858	3	6	nabila	nabila	PROPN
cana-858	3	7	i.	i.	PROPN
cana-858	3	8	aziz3	aziz3	PROPN
cana-858	3	9	,	,	PUNCT
cana-858	3	10	faeyda	faeyda	NOUN
cana-858	3	11	yaseen	yaseen	PROPN
cana-858	3	12	taha4	taha4	VERB
cana-858	4	1	1ministry	1ministry	NUM
cana-858	4	2	of	of	ADP
cana-858	4	3	education	education	NOUN
cana-858	4	4	-	-	PUNCT
cana-858	4	5	general	general	ADJ
cana-858	4	6	directorate	directorate	NOUN
cana-858	4	7	for	for	ADP
cana-858	4	8	breeding	breed	VERB
cana-858	4	9	baghdad	baghdad	PROPN
cana-858	4	10	third	third	PROPN
cana-858	4	11	karkh	karkh	PROPN
cana-858	4	12	azizsaad201357@gmail.com	azizsaad201357@gmail.com	PUNCT
cana-858	5	1	2department	2department	NUM
cana-858	5	2	of	of	ADP
cana-858	5	3	mathematics	mathematic	NOUN
cana-858	5	4	,	,	PUNCT
cana-858	5	5	faculty	faculty	NOUN
cana-858	5	6	of	of	ADP
cana-858	5	7	computer	computer	NOUN
cana-858	5	8	science	science	NOUN
cana-858	5	9	and	and	CCONJ
cana-858	5	10	mathematics	mathematic	NOUN
cana-858	5	11	,	,	PUNCT
cana-858	5	12	university	university	PROPN
cana-858	5	13	of	of	ADP
cana-858	5	14	kufa	kufa	PROPN
cana-858	5	15	,	,	PUNCT
cana-858	5	16	al	al	PROPN
cana-858	5	17	-	-	PUNCT
cana-858	5	18	najaf	najaf	PROPN
cana-858	5	19	54001	54001	NUM
cana-858	5	20	,	,	PUNCT
cana-858	5	21	iraq	iraq	PROPN
cana-858	5	22	laylah.algharrawi@uokufa.edu.iq	laylah.algharrawi@uokufa.edu.iq	VERB
cana-858	5	23	3department	3department	NUM
cana-858	5	24	of	of	ADP
cana-858	5	25	physics	physics	PROPN
cana-858	5	26	,	,	PUNCT
cana-858	5	27	college	college	NOUN
cana-858	5	28	of	of	ADP
cana-858	5	29	education	education	PROPN
cana-858	5	30	-tuzkhurmatu	-tuzkhurmatu	NOUN
cana-858	5	31	,	,	PUNCT
cana-858	5	32	tikrit	tikrit	NOUN
cana-858	5	33	university	university	NOUN
cana-858	5	34	nabila.be@tu.edu.iq	nabila.be@tu.edu.iq	NOUN
cana-858	5	35	4samarra	4samarra	PROPN
cana-858	5	36	university	university	NOUN
cana-858	5	37	,	,	PUNCT
cana-858	5	38	college	college	NOUN
cana-858	5	39	of	of	ADP
cana-858	5	40	education	education	NOUN
cana-858	5	41	,	,	PUNCT
cana-858	5	42	department	department	NOUN
cana-858	5	43	of	of	ADP
cana-858	5	44	chemistry	chemistry	NOUN
cana-858	5	45	faedayaseen@	faedayaseen@	PROPN
cana-858	5	46	uosamarra	uosamarra	PROPN
cana-858	5	47	.	.	PUNCT
cana-858	6	1	edu	edu	PROPN
cana-858	6	2	.	.	PUNCT
cana-858	7	1	iq	iq	PROPN
cana-858	7	2	article	article	PROPN
cana-858	7	3	history	history	NOUN
cana-858	7	4	:	:	PUNCT
cana-858	7	5	received	receive	VERB
cana-858	7	6	:	:	PUNCT
cana-858	7	7	25	25	NUM
cana-858	7	8	-	-	PUNCT
cana-858	7	9	04	04	NUM
cana-858	7	10	-	-	PUNCT
cana-858	7	11	2024	2024	NUM
cana-858	7	12	revised	revise	VERB
cana-858	7	13	:	:	PUNCT
cana-858	7	14	10	10	NUM
cana-858	7	15	-	-	SYM
cana-858	7	16	06	06	NUM
cana-858	7	17	-	-	PUNCT
cana-858	7	18	2024	2024	NUM
cana-858	7	19	accepted	accept	VERB
cana-858	7	20	:	:	PUNCT
cana-858	7	21	21	21	NUM
cana-858	7	22	-	-	SYM
cana-858	7	23	06	06	NUM
cana-858	7	24	-	-	PUNCT
cana-858	7	25	2024	2024	NUM
cana-858	7	26	abstract	abstract	NOUN
cana-858	7	27	:	:	PUNCT
cana-858	7	28	this	this	DET
cana-858	7	29	work	work	NOUN
cana-858	7	30	aims	aim	VERB
cana-858	7	31	to	to	PART
cana-858	7	32	define	define	VERB
cana-858	7	33	a	a	DET
cana-858	7	34	new	new	ADJ
cana-858	7	35	class	class	NOUN
cana-858	7	36	of	of	ADP
cana-858	7	37	sets	set	NOUN
cana-858	7	38	in	in	ADP
cana-858	7	39	nano	nano	NOUN
cana-858	7	40	topological	topological	ADJ
cana-858	7	41	spaces	space	NOUN
cana-858	7	42	called	call	VERB
cana-858	7	43	nano	nano	NOUN
cana-858	7	44	(	(	PUNCT
cana-858	7	45	nα	nα	NOUN
cana-858	7	46	)	)	PUNCT
cana-858	7	47	̌	̌	NUM
cana-858	7	48	closed	closed	ADJ
cana-858	7	49	and	and	CCONJ
cana-858	7	50	(	(	PUNCT
cana-858	7	51	nα	nα	NOUN
cana-858	7	52	)	)	PUNCT
cana-858	7	53	̂-open	̂-open	NOUN
cana-858	7	54	sets	set	NOUN
cana-858	7	55	,	,	PUNCT
cana-858	7	56	and	and	CCONJ
cana-858	7	57	to	to	PART
cana-858	7	58	prove	prove	VERB
cana-858	7	59	its	its	PRON
cana-858	7	60	verifiable	verifiable	ADJ
cana-858	7	61	properties	property	NOUN
cana-858	7	62	and	and	CCONJ
cana-858	7	63	theorems	theorem	NOUN
cana-858	7	64	.	.	PUNCT
cana-858	8	1	subject	subject	ADJ
cana-858	8	2	classification	classification	NOUN
cana-858	8	3	:	:	PUNCT
cana-858	8	4	54a05	54a05	NUM
cana-858	8	5	,	,	PUNCT
cana-858	8	6	54a	54a	NUM
cana-858	8	7	10	10	NUM
cana-858	8	8	keywords	keyword	NOUN
cana-858	8	9	:	:	PUNCT
cana-858	8	10	nano	nano	NOUN
cana-858	8	11	topology	topology	NOUN
cana-858	8	12	,	,	PUNCT
cana-858	8	13	(	(	PUNCT
cana-858	8	14	nα	nα	NOUN
cana-858	8	15	)	)	PUNCT
cana-858	8	16	̌closed	̌close	VERB
cana-858	8	17	set	set	NOUN
cana-858	8	18	and	and	CCONJ
cana-858	8	19	nano	nano	NOUN
cana-858	8	20	(	(	PUNCT
cana-858	8	21	nα	nα	NOUN
cana-858	8	22	)	)	PUNCT
cana-858	8	23	̂open	̂open	NOUN
cana-858	8	24	set	set	NOUN
cana-858	8	25	.	.	PUNCT
cana-858	9	1	1	1	X
cana-858	9	2	.	.	X
cana-858	9	3	introduction	introduction	NOUN
cana-858	9	4	in	in	ADP
cana-858	9	5	2021	2021	NUM
cana-858	9	6	,	,	PUNCT
cana-858	9	7	ą	ą	PROPN
cana-858	9	8	regular	regular	ADJ
cana-858	9	9	closed	close	VERB
cana-858	9	10	sets	set	NOUN
cana-858	9	11	in	in	ADP
cana-858	9	12	nano	nano	NOUN
cana-858	9	13	topological	topological	ADJ
cana-858	9	14	spaces	space	NOUN
cana-858	9	15	were	be	AUX
cana-858	9	16	presented	present	VERB
cana-858	9	17	by	by	ADP
cana-858	9	18	narmatha	narmatha	PROPN
cana-858	9	19	s.	s.	PROPN
cana-858	9	20	,	,	PUNCT
cana-858	9	21	harshitha	harshitha	PROPN
cana-858	9	22	s.	s.	PROPN
cana-858	9	23	,	,	PUNCT
cana-858	9	24	and	and	CCONJ
cana-858	9	25	others	other	NOUN
cana-858	10	1	[	[	X
cana-858	10	2	3	3	NUM
cana-858	10	3	]	]	PUNCT
cana-858	10	4	.	.	PUNCT
cana-858	11	1	within	within	ADP
cana-858	11	2	micro	micro	PROPN
cana-858	11	3	topological	topological	ADJ
cana-858	11	4	spaces	space	NOUN
cana-858	11	5	,	,	PUNCT
cana-858	11	6	πgβ	πgβ	NOUN
cana-858	11	7	-	-	PUNCT
cana-858	11	8	closed	close	VERB
cana-858	11	9	sets	set	NOUN
cana-858	11	10	are	be	AUX
cana-858	11	11	studied	study	VERB
cana-858	11	12	by	by	ADP
cana-858	11	13	rajasekaran	rajasekaran	NOUN
cana-858	11	14	i.	i.	NOUN
cana-858	11	15	and	and	CCONJ
cana-858	11	16	others	other	NOUN
cana-858	12	1	[	[	X
cana-858	12	2	4	4	NUM
cana-858	12	3	]	]	PUNCT
cana-858	12	4	.	.	PUNCT
cana-858	13	1	in	in	ADP
cana-858	13	2	nano	nano	ADJ
cana-858	13	3	topological	topological	ADJ
cana-858	13	4	spaces	space	NOUN
cana-858	13	5	,	,	PUNCT
cana-858	13	6	ng∗α−	ng∗α−	ADJ
cana-858	13	7	closed	close	VERB
cana-858	13	8	sets	set	NOUN
cana-858	13	9	were	be	AUX
cana-858	13	10	first	first	ADV
cana-858	13	11	presented	present	VERB
cana-858	13	12	by	by	ADP
cana-858	13	13	rajendran	rajendran	PROPN
cana-858	13	14	v.	v.	PROPN
cana-858	13	15	and	and	CCONJ
cana-858	13	16	colleagues	colleague	NOUN
cana-858	13	17	[	[	X
cana-858	13	18	5]	5]	NOUN
cana-858	13	19	..	..	PUNCT
cana-858	13	20	crossley	crossley	NOUN
cana-858	13	21	and	and	CCONJ
cana-858	13	22	hildebrand	hildebrand	NOUN
cana-858	14	1	[	[	X
cana-858	14	2	7	7	NUM
cana-858	14	3	]	]	PUNCT
cana-858	14	4	conducted	conduct	VERB
cana-858	14	5	research	research	NOUN
cana-858	14	6	on	on	ADP
cana-858	14	7	semi	semi	NOUN
cana-858	14	8	-	-	ADJ
cana-858	14	9	closure	closure	ADJ
cana-858	14	10	in	in	ADP
cana-858	14	11	1971	1971	NUM
cana-858	14	12	.	.	PUNCT
cana-858	15	1	dunham	dunham	PROPN
cana-858	16	1	[	[	X
cana-858	16	2	14	14	NUM
cana-858	16	3	]	]	PUNCT
cana-858	16	4	provided	provide	VERB
cana-858	16	5	a	a	DET
cana-858	16	6	definition	definition	NOUN
cana-858	16	7	of	of	ADP
cana-858	16	8	the	the	DET
cana-858	16	9	closure	closure	NOUN
cana-858	16	10	operator	operator	NOUN
cana-858	16	11	c	c	NOUN
cana-858	16	12	*	*	NOUN
cana-858	16	13	notion	notion	NOUN
cana-858	16	14	along	along	ADP
cana-858	16	15	with	with	ADP
cana-858	16	16	various	various	ADJ
cana-858	16	17	attributes	attribute	NOUN
cana-858	16	18	.	.	PUNCT
cana-858	17	1	operator	operator	NOUN
cana-858	17	2	of	of	ADP
cana-858	17	3	regular	regular	ADJ
cana-858	17	4	closed	closed	ADJ
cana-858	17	5	sets	set	NOUN
cana-858	17	6	was	be	AUX
cana-858	17	7	first	first	ADV
cana-858	17	8	defined	define	VERB
cana-858	17	9	by	by	ADP
cana-858	17	10	s.	s.	PROPN
cana-858	17	11	bhattacharya	bhattacharya	PROPN
cana-858	18	1	[	[	X
cana-858	18	2	6	6	NUM
cana-858	18	3	]	]	PUNCT
cana-858	18	4	in	in	ADP
cana-858	18	5	2011	2011	NUM
cana-858	18	6	.	.	PUNCT
cana-858	19	1	soft	soft	ADJ
cana-858	19	2	w	w	PROPN
cana-858	19	3	-int	-int	NOUN
cana-858	19	4	.	.	PUNCT
cana-858	20	1	and	and	CCONJ
cana-858	20	2	soft	soft	ADJ
cana-858	20	3	w	w	NOUN
cana-858	20	4	-cl	-cl	NOUN
cana-858	20	5	.	.	PUNCT
cana-858	21	1	in	in	ADP
cana-858	21	2	soft	soft	ADJ
cana-858	21	3	topological	topological	ADJ
cana-858	21	4	spaces	space	NOUN
cana-858	21	5	are	be	AUX
cana-858	21	6	studied	study	VERB
cana-858	21	7	by	by	ADP
cana-858	21	8	savita	savita	PROPN
cana-858	21	9	r.	r.	PROPN
cana-858	22	1	[	[	X
cana-858	22	2	8	8	NUM
cana-858	22	3	]	]	PUNCT
cana-858	22	4	.	.	PUNCT
cana-858	23	1	soft	soft	ADJ
cana-858	23	2	g	g	NOUN
cana-858	23	3	*	*	PUNCT
cana-858	23	4	closed	close	VERB
cana-858	23	5	in	in	ADP
cana-858	23	6	soft	soft	ADJ
cana-858	23	7	topological	topological	ADJ
cana-858	23	8	spaces	space	NOUN
cana-858	23	9	are	be	AUX
cana-858	23	10	studied	study	VERB
cana-858	23	11	by	by	ADP
cana-858	23	12	kalavathi	kalavathi	NOUN
cana-858	23	13	,	,	PUNCT
cana-858	23	14	a.	a.	NOUN
cana-858	23	15	and	and	CCONJ
cana-858	23	16	krishnan	krishnan	PROPN
cana-858	23	17	,	,	PUNCT
cana-858	23	18	g.[2	g.[2	NOUN
cana-858	23	19	]	]	PUNCT
cana-858	23	20	.	.	PUNCT
cana-858	24	1	regular	regular	ADJ
cana-858	24	2	generalized	generalize	VERB
cana-858	24	3	*	*	PUNCT
cana-858	24	4	in	in	ADP
cana-858	24	5	topological	topological	ADJ
cana-858	24	6	spaces	space	NOUN
cana-858	24	7	,	,	PUNCT
cana-858	24	8	closure	closure	NOUN
cana-858	24	9	regular	regular	ADJ
cana-858	24	10	generalized	generalize	VERB
cana-858	24	11	*	*	PUNCT
cana-858	24	12	closure	closure	NOUN
cana-858	24	13	regular	regular	ADJ
cana-858	24	14	generalized	generalize	VERB
cana-858	24	15	*	*	NOUN
cana-858	24	16	,	,	PUNCT
cana-858	24	17	and	and	CCONJ
cana-858	24	18	regular	regular	ADJ
cana-858	24	19	generalized	generalize	VERB
cana-858	24	20	closed	closed	ADJ
cana-858	24	21	sets	set	NOUN
cana-858	24	22	are	be	AUX
cana-858	24	23	new	new	ADJ
cana-858	24	24	classes	class	NOUN
cana-858	24	25	of	of	ADP
cana-858	24	26	operators	operator	NOUN
cana-858	24	27	introduced	introduce	VERB
cana-858	24	28	by	by	ADP
cana-858	24	29	siham	siham	PROPN
cana-858	24	30	i.	i.	PROPN
cana-858	24	31	aziz	aziz	PROPN
cana-858	24	32	and	and	CCONJ
cana-858	24	33	nabila	nabila	PROPN
cana-858	24	34	i.	i.	PROPN
cana-858	24	35	aziz	aziz	PROPN
cana-858	25	1	[	[	X
cana-858	25	2	9	9	NUM
cana-858	25	3	,	,	PUNCT
cana-858	25	4	10	10	NUM
cana-858	25	5	,	,	PUNCT
cana-858	25	6	11	11	NUM
cana-858	25	7	]	]	PUNCT
cana-858	25	8	and	and	CCONJ
cana-858	25	9	,	,	PUNCT
cana-858	25	10	respectively	respectively	ADV
cana-858	25	11	.	.	PUNCT
cana-858	25	12	2014	2014	NUM
cana-858	25	13	saw	see	VERB
cana-858	25	14	the	the	DET
cana-858	25	15	introduction	introduction	NOUN
cana-858	25	16	of	of	ADP
cana-858	25	17	nano	nano	NOUN
cana-858	25	18	closure	closure	NOUN
cana-858	25	19	and	and	CCONJ
cana-858	25	20	nano	nano	ADJ
cana-858	25	21	interior	interior	ADJ
cana-858	25	22	operator	operator	NOUN
cana-858	25	23	in	in	ADP
cana-858	25	24	nano	nano	NOUN
cana-858	25	25	topological	topological	ADJ
cana-858	25	26	spaces	space	NOUN
cana-858	25	27	by	by	ADP
cana-858	25	28	thivagar	thivagar	NOUN
cana-858	25	29	m.	m.	NOUN
cana-858	25	30	lellis	lellis	PROPN
cana-858	25	31	and	and	CCONJ
cana-858	25	32	carmel	carmel	PROPN
cana-858	25	33	rechard	rechard	NOUN
cana-858	26	1	[	[	X
cana-858	26	2	12	12	NUM
cana-858	26	3	]	]	X
cana-858	26	4	,	,	PUNCT
cana-858	26	5	a	a	DET
cana-858	26	6	novel	novel	ADJ
cana-858	26	7	class	class	NOUN
cana-858	26	8	of	of	ADP
cana-858	26	9	operators	operator	NOUN
cana-858	26	10	open	open	VERB
cana-858	26	11	and	and	CCONJ
cana-858	26	12	closed	close	VERB
cana-858	26	13	nano	nano	NOUN
cana-858	26	14	operators	operator	NOUN
cana-858	26	15	ɲ	ɲ	X
cana-858	26	16	̂	̂	PUNCT
cana-858	26	17	(	(	PUNCT
cana-858	26	18	ᾱ	ᾱ	NOUN
cana-858	26	19	)	)	PUNCT
cana-858	26	20	and	and	CCONJ
cana-858	26	21	ɲ	ɲ	NUM
cana-858	26	22	̌	̌	PROPN
cana-858	26	23	(	(	PUNCT
cana-858	26	24	ᾱ	ᾱ	NOUN
cana-858	26	25	)	)	PUNCT
cana-858	26	26	introduced	introduce	VERB
cana-858	26	27	by	by	ADP
cana-858	26	28	abdulaziz	abdulaziz	PROPN
cana-858	26	29	.s	.s	PROPN
cana-858	26	30	.	.	PUNCT
cana-858	27	1	[	[	PUNCT
cana-858	27	2	1	1	NUM
cana-858	27	3	]	]	PUNCT
cana-858	27	4	.	.	PUNCT
cana-858	28	1	the	the	DET
cana-858	28	2	aim	aim	NOUN
cana-858	28	3	of	of	ADP
cana-858	28	4	this	this	DET
cana-858	28	5	work	work	NOUN
cana-858	28	6	is	be	AUX
cana-858	28	7	to	to	PART
cana-858	28	8	investigate	investigate	VERB
cana-858	28	9	and	and	CCONJ
cana-858	28	10	characterize	characterize	VERB
cana-858	28	11	a	a	DET
cana-858	28	12	new	new	ADJ
cana-858	28	13	class	class	NOUN
cana-858	28	14	of	of	ADP
cana-858	28	15	operators	operator	NOUN
cana-858	28	16	in	in	ADP
cana-858	28	17	nano	nano	NOUN
cana-858	28	18	topological	topological	ADJ
cana-858	28	19	spaces	space	NOUN
cana-858	28	20	called	call	VERB
cana-858	28	21	nano	nano	NOUN
cana-858	28	22	ℕα̌closed	ℕα̌close	VERB
cana-858	28	23	and	and	CCONJ
cana-858	28	24	ℕα̂open	ℕα̂open	NOUN
cana-858	28	25	sets	set	VERB
cana-858	28	26	,	,	PUNCT
cana-858	28	27	and	and	CCONJ
cana-858	28	28	to	to	PART
cana-858	28	29	establish	establish	VERB
cana-858	28	30	their	their	PRON
cana-858	28	31	verifiable	verifiable	ADJ
cana-858	28	32	characteristics	characteristic	NOUN
cana-858	28	33	and	and	CCONJ
cana-858	28	34	theorems	theorem	NOUN
cana-858	28	35	.	.	PROPN
cana-858	29	1	2	2	X
cana-858	29	2	.	.	PUNCT
cana-858	29	3	preliminaries	preliminary	NOUN
cana-858	29	4	definition	definition	NOUN
cana-858	29	5	2.1	2.1	NUM
cana-858	30	1	[	[	X
cana-858	30	2	2	2	NUM
cana-858	30	3	]	]	PUNCT
cana-858	30	4	:	:	PUNCT
cana-858	30	5	suppose	suppose	VERB
cana-858	30	6	ϑ	ϑ	X
cana-858	30	7	be	be	AUX
cana-858	30	8	the	the	DET
cana-858	30	9	world	world	NOUN
cana-858	30	10	,	,	PUNCT
cana-858	30	11	ψ	ψ	VERB
cana-858	30	12	⊆	⊆	NUM
cana-858	30	13	ϑ	ϑ	X
cana-858	30	14	,	,	PUNCT
cana-858	30	15	and	and	CCONJ
cana-858	30	16	π	π	PROPN
cana-858	30	17	be	be	AUX
cana-858	30	18	an	an	DET
cana-858	30	19	equivalence	equivalence	NOUN
cana-858	30	20	relation	relation	NOUN
cana-858	30	21	on	on	ADP
cana-858	30	22	ϑ.	ϑ.	NOUN
cana-858	30	23	with	with	ADP
cana-858	30	24	regard	regard	NOUN
cana-858	30	25	to	to	ADP
cana-858	30	26	ψ	ψ	PROPN
cana-858	30	27	,	,	PUNCT
cana-858	30	28	τ	τ	PROPN
cana-858	30	29	ϕ(ψ	ϕ(ψ	PRON
cana-858	30	30	)	)	PUNCT
cana-858	31	1	=	=	NOUN
cana-858	31	2	{	{	PUNCT
cana-858	31	3	ϑ	ϑ	NOUN
cana-858	31	4	,	,	PUNCT
cana-858	31	5	∅	∅	NOUN
cana-858	31	6	,	,	PUNCT
cana-858	31	7	lr(ψ	lr(ψ	NOUN
cana-858	31	8	)	)	PUNCT
cana-858	31	9	,	,	PUNCT
cana-858	31	10	ϑ	ϑ	X
cana-858	31	11	φ(ψ	φ(ψ	PROPN
cana-858	31	12	)	)	PUNCT
cana-858	31	13	,	,	PUNCT
cana-858	31	14	bφ(ψ	bφ(ψ	NOUN
cana-858	31	15	)	)	PUNCT
cana-858	31	16	}	}	PUNCT
cana-858	31	17	and	and	CCONJ
cana-858	31	18	(	(	PUNCT
cana-858	31	19	ϑ	ϑ	X
cana-858	31	20	,	,	PUNCT
cana-858	31	21	τ	τ	PROPN
cana-858	31	22	φ(ψ	φ(ψ	PROPN
cana-858	31	23	)	)	PUNCT
cana-858	31	24	)	)	PUNCT
cana-858	31	25	define	define	VERB
cana-858	31	26	the	the	DET
cana-858	31	27	nano	nano	NOUN
cana-858	31	28	topology	topology	NOUN
cana-858	31	29	on	on	ADP
cana-858	31	30	u.	u.	NOUN
cana-858	31	31	communications	communication	NOUN
cana-858	31	32	on	on	ADP
cana-858	31	33	applied	apply	VERB
cana-858	31	34	nonlinear	nonlinear	ADJ
cana-858	31	35	analysis	analysis	NOUN
cana-858	31	36	issn	issn	NOUN
cana-858	31	37	:	:	PUNCT
cana-858	31	38	1074	1074	NUM
cana-858	31	39	-	-	PUNCT
cana-858	31	40	133x	133x	NUM
cana-858	31	41	vol	vol	NOUN
cana-858	31	42	31	31	NUM
cana-858	31	43	no	no	NOUN
cana-858	31	44	.	.	PUNCT
cana-858	32	1	4s	4s	NUM
cana-858	32	2	(	(	PUNCT
cana-858	32	3	2024	2024	NUM
cana-858	32	4	)	)	PUNCT
cana-858	32	5	359	359	NUM
cana-858	33	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-858	33	2	definition	definition	NOUN
cana-858	33	3	2.2	2.2	NUM
cana-858	33	4	[	[	PUNCT
cana-858	33	5	1	1	NUM
cana-858	33	6	]	]	PUNCT
cana-858	33	7	:	:	PUNCT
cana-858	33	8	assume	assume	VERB
cana-858	33	9	a	a	DET
cana-858	33	10	⊆	⊆	NUM
cana-858	33	11	ϑ	ϑ	X
cana-858	33	12	and	and	CCONJ
cana-858	33	13	(	(	PUNCT
cana-858	33	14	u	u	NOUN
cana-858	33	15	,	,	PUNCT
cana-858	33	16	τ	τ	X
cana-858	33	17	r(ψ	r(ψ	NOUN
cana-858	33	18	)	)	PUNCT
cana-858	33	19	)	)	PUNCT
cana-858	33	20	be	be	AUX
cana-858	33	21	a	a	DET
cana-858	33	22	nano	nano	ADJ
cana-858	33	23	topological	topological	ADJ
cana-858	33	24	space	space	NOUN
cana-858	33	25	.	.	PUNCT
cana-858	34	1	next	next	ADV
cana-858	34	2	,	,	PUNCT
cana-858	34	3	we	we	PRON
cana-858	34	4	established	establish	VERB
cana-858	34	5	1ℵ(a	1ℵ(a	NUM
cana-858	34	6	)	)	PUNCT
cana-858	35	1	=	=	NOUN
cana-858	35	2	∩	∩	NOUN
cana-858	35	3	{	{	PUNCT
cana-858	35	4	g	g	NOUN
cana-858	35	5	:	:	PUNCT
cana-858	35	6	a⊆	a⊆	VERB
cana-858	35	7	g	g	NOUN
cana-858	35	8	,	,	PUNCT
cana-858	35	9	g	g	PROPN
cana-858	35	10	∈	∈	PROPN
cana-858	35	11	n	n	PRON
cana-858	35	12	o(ϑ	o(ϑ	NOUN
cana-858	35	13	,	,	PUNCT
cana-858	35	14	ψ	ψ	NOUN
cana-858	35	15	)	)	PUNCT
cana-858	35	16	}	}	PUNCT
cana-858	35	17	and	and	CCONJ
cana-858	35	18	2	2	NUM
cana-858	35	19	-	-	PUNCT
cana-858	35	20	n	n	PRON
cana-858	35	21	̌	̌	NUM
cana-858	35	22	(	(	PUNCT
cana-858	35	23	a	a	X
cana-858	35	24	)	)	PUNCT
cana-858	35	25	=	=	SYM
cana-858	35	26	∪	∪	X
cana-858	35	27	{	{	PUNCT
cana-858	35	28	g	g	NOUN
cana-858	35	29	:	:	PUNCT
cana-858	35	30	g⊆	g⊆	PROPN
cana-858	35	31	a	a	NOUN
cana-858	35	32	,	,	PUNCT
cana-858	35	33	g	g	PROPN
cana-858	35	34	∈	∈	PROPN
cana-858	35	35	nc	nc	PROPN
cana-858	35	36	(	(	PUNCT
cana-858	35	37	ϑ	ϑ	X
cana-858	35	38	,	,	PUNCT
cana-858	35	39	ψ	ψ	NOUN
cana-858	35	40	)	)	PUNCT
cana-858	35	41	}	}	PUNCT
cana-858	35	42	.	.	PUNCT
cana-858	36	1	definition	definition	NOUN
cana-858	36	2	2.3	2.3	NUM
cana-858	37	1	[	[	X
cana-858	37	2	2	2	NUM
cana-858	37	3	]	]	PUNCT
cana-858	37	4	:	:	PUNCT
cana-858	37	5	assuming	assume	VERB
cana-858	37	6	ψ	ψ	X
cana-858	37	7	,	,	PUNCT
cana-858	37	8	ψ	ψ	VERB
cana-858	37	9	⊆	⊆	NUM
cana-858	37	10	ϑ	ϑ	X
cana-858	37	11	,	,	PUNCT
cana-858	37	12	let	let	VERB
cana-858	37	13	(	(	PUNCT
cana-858	37	14	u	u	NOUN
cana-858	37	15	,	,	PUNCT
cana-858	37	16	τ	τ	X
cana-858	37	17	r(ψ	r(ψ	NOUN
cana-858	37	18	)	)	PUNCT
cana-858	37	19	)	)	PUNCT
cana-858	37	20	be	be	AUX
cana-858	37	21	a	a	DET
cana-858	37	22	nano	nano	ADJ
cana-858	37	23	topological	topological	ADJ
cana-858	37	24	space	space	NOUN
cana-858	37	25	.	.	PUNCT
cana-858	38	1	if	if	SCONJ
cana-858	38	2	a	a	PRON
cana-858	38	3	is	be	AUX
cana-858	38	4	not	not	PART
cana-858	38	5	equal	equal	ADJ
cana-858	38	6	to	to	ADP
cana-858	38	7	ϑ	ϑ	PRON
cana-858	38	8	,	,	PUNCT
cana-858	38	9	then	then	ADV
cana-858	38	10	:	:	PUNCT
cana-858	38	11	the	the	DET
cana-858	38	12	union	union	NOUN
cana-858	38	13	of	of	ADP
cana-858	38	14	all	all	PRON
cana-858	38	15	of	of	ADP
cana-858	38	16	a	a	DET
cana-858	38	17	's	's	PART
cana-858	38	18	open	open	ADJ
cana-858	38	19	subsets	subset	NOUN
cana-858	38	20	is	be	AUX
cana-858	38	21	a	a	PRON
cana-858	38	22	's	's	PART
cana-858	38	23	nanointerior	nanointerior	ADJ
cana-858	38	24	,	,	PUNCT
cana-858	38	25	and	and	CCONJ
cana-858	38	26	it	it	PRON
cana-858	38	27	is	be	AUX
cana-858	38	28	represented	represent	VERB
cana-858	38	29	by	by	ADP
cana-858	38	30	nint(a	nint(a	PROPN
cana-858	38	31	)	)	PUNCT
cana-858	38	32	.	.	PUNCT
cana-858	39	1	ncl(a	ncl(a	PROPN
cana-858	39	2	)	)	PUNCT
cana-858	39	3	represents	represent	VERB
cana-858	39	4	the	the	DET
cana-858	39	5	nano	nano	NOUN
cana-858	39	6	closure	closure	NOUN
cana-858	39	7	of	of	ADP
cana-858	39	8	a	a	PRON
cana-858	39	9	,	,	PUNCT
cana-858	39	10	which	which	PRON
cana-858	39	11	is	be	AUX
cana-858	39	12	the	the	DET
cana-858	39	13	intersection	intersection	NOUN
cana-858	39	14	of	of	ADP
cana-858	39	15	all	all	DET
cana-858	39	16	nano	nano	NOUN
cana-858	39	17	closed	close	VERB
cana-858	39	18	subsets	subset	NOUN
cana-858	39	19	containing	contain	VERB
cana-858	39	20	a.	a.	NOUN
cana-858	39	21	definition	definition	NOUN
cana-858	39	22	2.4	2.4	NUM
cana-858	40	1	[	[	SYM
cana-858	40	2	13	13	NUM
cana-858	40	3	]	]	PUNCT
cana-858	40	4	:	:	PUNCT
cana-858	40	5	when	when	SCONJ
cana-858	40	6	m	m	PROPN
cana-858	40	7	⊆	⊆	NUM
cana-858	40	8	nint	nint	NOUN
cana-858	40	9	(	(	PUNCT
cana-858	40	10	ncl	ncl	NOUN
cana-858	40	11	(	(	PUNCT
cana-858	40	12	nint	nint	NOUN
cana-858	40	13	m	m	PROPN
cana-858	40	14	)	)	PUNCT
cana-858	40	15	)	)	PUNCT
cana-858	40	16	,	,	PUNCT
cana-858	40	17	a	a	DET
cana-858	40	18	subset	subset	NOUN
cana-858	40	19	m	m	VERB
cana-858	40	20	of	of	ADP
cana-858	40	21	(	(	PUNCT
cana-858	40	22	ϑ	ϑ	X
cana-858	40	23	,	,	PUNCT
cana-858	40	24	τ	τ	X
cana-858	40	25	r(ψ	r(ψ	PROPN
cana-858	40	26	)	)	PUNCT
cana-858	40	27	)	)	PUNCT
cana-858	40	28	is	be	AUX
cana-858	40	29	referred	refer	VERB
cana-858	40	30	to	to	ADP
cana-858	40	31	as	as	ADP
cana-858	40	32	a	a	DET
cana-858	40	33	nano	nano	NOUN
cana-858	40	34	α	α	PRON
cana-858	40	35	open	open	ADJ
cana-858	40	36	set	set	NOUN
cana-858	40	37	(	(	PUNCT
cana-858	40	38	briefly	briefly	ADV
cana-858	40	39	,	,	PUNCT
cana-858	40	40	n𝛼-o	n𝛼-o	PROPN
cana-858	40	41	-	-	PUNCT
cana-858	40	42	s.	s.	PROPN
cana-858	40	43	)	)	PUNCT
cana-858	40	44	.	.	PUNCT
cana-858	41	1	in	in	ADP
cana-858	41	2	(	(	PUNCT
cana-858	41	3	u	u	NOUN
cana-858	41	4	,	,	PUNCT
cana-858	41	5	τ	τ	X
cana-858	41	6	r(ψ	r(ψ	PROPN
cana-858	41	7	)	)	PUNCT
cana-858	41	8	)	)	PUNCT
cana-858	41	9	,	,	PUNCT
cana-858	41	10	the	the	DET
cana-858	41	11	complement	complement	NOUN
cana-858	41	12	of	of	ADP
cana-858	41	13	a	a	DET
cana-858	41	14	n𝛼-o	n𝛼-o	PROPN
cana-858	41	15	-	-	PUNCT
cana-858	41	16	s.	s.	PROPN
cana-858	41	17	is	be	AUX
cana-858	41	18	referred	refer	VERB
cana-858	41	19	to	to	ADP
cana-858	41	20	as	as	ADP
cana-858	41	21	a	a	DET
cana-858	41	22	nano	nano	NOUN
cana-858	41	23	𝛼-closed	𝛼-close	VERB
cana-858	41	24	set	set	NOUN
cana-858	41	25	(	(	PUNCT
cana-858	41	26	briefly	briefly	ADV
cana-858	41	27	,	,	PUNCT
cana-858	41	28	n𝛼-c	n𝛼-c	PROPN
cana-858	41	29	-	-	PUNCT
cana-858	41	30	s.	s.	PROPN
cana-858	41	31	)	)	PUNCT
cana-858	41	32	.	.	PUNCT
cana-858	42	1	n𝛼-o-	n𝛼-o-	PROPN
cana-858	42	2	(	(	PUNCT
cana-858	42	3	ϑ	ϑ	X
cana-858	42	4	,	,	PUNCT
cana-858	42	5	ψ	ψ	NOUN
cana-858	42	6	)	)	PUNCT
cana-858	42	7	(	(	PUNCT
cana-858	42	8	resp	resp	NOUN
cana-858	42	9	.	.	PUNCT
cana-858	43	1	n𝛼-c-	n𝛼-c-	X
cana-858	43	2	(	(	PUNCT
cana-858	43	3	ϑ	ϑ	X
cana-858	43	4	,	,	PUNCT
cana-858	43	5	ψ	ψ	NOUN
cana-858	43	6	)	)	PUNCT
cana-858	43	7	)	)	PUNCT
cana-858	44	1	represents	represent	VERB
cana-858	44	2	the	the	DET
cana-858	44	3	family	family	NOUN
cana-858	44	4	of	of	ADP
cana-858	44	5	all	all	DET
cana-858	44	6	n𝛼-o	n𝛼-o	PROPN
cana-858	44	7	-	-	PUNCT
cana-858	44	8	s.	s.	PROPN
cana-858	44	9	(	(	PUNCT
cana-858	44	10	resp	resp	NOUN
cana-858	44	11	.	.	PUNCT
cana-858	45	1	n𝛼-c	n𝛼-c	NOUN
cana-858	45	2	-	-	PUNCT
cana-858	45	3	s.	s.	PROPN
cana-858	45	4	)	)	PUNCT
cana-858	45	5	of	of	ADP
cana-858	45	6	u.	u.	NOUN
cana-858	45	7	3	3	NUM
cana-858	45	8	on	on	ADP
cana-858	45	9	generalized	generalized	ADJ
cana-858	45	10	nano	nano	NOUN
cana-858	45	11	ℕ	ℕ	PROPN
cana-858	45	12	�	�	PROPN
cana-858	45	13	̌	̌	NUM
cana-858	45	14	�	�	NOUN
cana-858	45	15	closed	close	VERB
cana-858	45	16	and	and	CCONJ
cana-858	45	17	nano	nano	ADJ
cana-858	45	18	ℵ	ℵ	NOUN
cana-858	45	19	�	�	PROPN
cana-858	45	20	̂	̂	SYM
cana-858	45	21	�	�	NOUN
cana-858	45	22	open	open	ADJ
cana-858	45	23	sets	set	NOUN
cana-858	45	24	in	in	ADP
cana-858	45	25	nanotopological	nanotopological	ADJ
cana-858	45	26	spaces	space	NOUN
cana-858	45	27	definition	definition	NOUN
cana-858	45	28	3.1assume	3.1assume	NUM
cana-858	46	1	that	that	SCONJ
cana-858	46	2	a	a	DET
cana-858	46	3	⊆	⊆	NUM
cana-858	46	4	u	u	NOUN
cana-858	46	5	and	and	CCONJ
cana-858	46	6	that	that	SCONJ
cana-858	46	7	(	(	PUNCT
cana-858	46	8	u	u	NOUN
cana-858	46	9	,	,	PUNCT
cana-858	46	10	τ	τ	X
cana-858	46	11	r(ψ	r(ψ	NOUN
cana-858	46	12	)	)	PUNCT
cana-858	46	13	)	)	PUNCT
cana-858	46	14	is	be	AUX
cana-858	46	15	a	a	DET
cana-858	46	16	nano	nano	ADJ
cana-858	46	17	topological	topological	ADJ
cana-858	46	18	space	space	NOUN
cana-858	46	19	.	.	PUNCT
cana-858	47	1	if	if	SCONJ
cana-858	47	2	a	a	DET
cana-858	47	3	⊆	⊆	NUM
cana-858	47	4	ℵ	ℵ	NOUN
cana-858	47	5	(	(	PUNCT
cana-858	47	6	(	(	PUNCT
cana-858	47	7	n	n	CCONJ
cana-858	47	8	)	)	PUNCT
cana-858	47	9	̌	̌	PROPN
cana-858	47	10	(	(	PUNCT
cana-858	47	11	ℵ(a	ℵ(a	NOUN
cana-858	47	12	)	)	PUNCT
cana-858	47	13	)	)	PUNCT
cana-858	47	14	)	)	PUNCT
cana-858	47	15	,	,	PUNCT
cana-858	47	16	then	then	ADV
cana-858	47	17	a	a	DET
cana-858	47	18	subset	subset	NOUN
cana-858	47	19	a	a	PRON
cana-858	47	20	is	be	AUX
cana-858	47	21	referred	refer	VERB
cana-858	47	22	to	to	ADP
cana-858	47	23	as	as	ADP
cana-858	47	24	an	an	DET
cana-858	47	25	open	open	ADJ
cana-858	47	26	set	set	NOUN
cana-858	47	27	(	(	PUNCT
cana-858	47	28	nα	nα	NOUN
cana-858	47	29	)	)	PUNCT
cana-858	47	30	̂.the	̂.the	DET
cana-858	47	31	closed	closed	ADJ
cana-858	47	32	set	set	ADJ
cana-858	47	33	nano	nano	NOUN
cana-858	47	34	(	(	PUNCT
cana-858	47	35	ℵδ	ℵδ	NOUN
cana-858	47	36	)	)	PUNCT
cana-858	47	37	is	be	AUX
cana-858	47	38	the	the	DET
cana-858	47	39	complement	complement	NOUN
cana-858	47	40	of	of	ADP
cana-858	47	41	the	the	DET
cana-858	47	42	open	open	ADJ
cana-858	47	43	set	set	NOUN
cana-858	47	44	nano	nano	NOUN
cana-858	47	45	(	(	PUNCT
cana-858	47	46	nα	nα	NOUN
cana-858	47	47	)	)	PUNCT
cana-858	47	48	̂	̂	PUNCT
cana-858	47	49	and	and	CCONJ
cana-858	47	50	is	be	AUX
cana-858	47	51	defined	define	VERB
cana-858	47	52	as	as	ADP
cana-858	47	53	[	[	X
cana-858	47	54	a	a	DET
cana-858	47	55	⊇	⊇	X
cana-858	47	56	(	(	PUNCT
cana-858	47	57	n	n	CCONJ
cana-858	47	58	)	)	PUNCT
cana-858	47	59	̌	̌	PROPN
cana-858	47	60	(	(	PUNCT
cana-858	47	61	ℵ	ℵ	NOUN
cana-858	47	62	(	(	PUNCT
cana-858	47	63	(	(	PUNCT
cana-858	47	64	(	(	PUNCT
cana-858	47	65	n	n	CCONJ
cana-858	47	66	)	)	PUNCT
cana-858	47	67	̌	̌	PROPN
cana-858	48	1	(	(	PUNCT
cana-858	48	2	a	a	NOUN
cana-858	48	3	)	)	PUNCT
cana-858	48	4	)	)	PUNCT
cana-858	48	5	)	)	PUNCT
cana-858	48	6	]	]	PUNCT
cana-858	48	7	example	example	NOUN
cana-858	48	8	3.2	3.2	NUM
cana-858	48	9	:	:	PUNCT
cana-858	48	10	assuming	assume	VERB
cana-858	48	11	u	u	NOUN
cana-858	48	12	/	/	SYM
cana-858	48	13	r	r	NOUN
cana-858	48	14	=	=	PUNCT
cana-858	48	15	{	{	PUNCT
cana-858	48	16	{	{	PUNCT
cana-858	48	17	r	r	NOUN
cana-858	48	18	,	,	PUNCT
cana-858	48	19	p	p	NOUN
cana-858	48	20	}	}	PUNCT
cana-858	48	21	,	,	PUNCT
cana-858	48	22	{	{	PUNCT
cana-858	48	23	q	q	X
cana-858	48	24	}	}	PUNCT
cana-858	48	25	}	}	PUNCT
cana-858	48	26	and	and	CCONJ
cana-858	48	27	ψ	ψ	X
cana-858	48	28	=	=	SYM
cana-858	48	29	{	{	PUNCT
cana-858	48	30	r	r	NOUN
cana-858	48	31	,	,	PUNCT
cana-858	48	32	q	q	NOUN
cana-858	48	33	}	}	PUNCT
cana-858	48	34	,	,	PUNCT
cana-858	48	35	let	let	VERB
cana-858	48	36	u	u	PRON
cana-858	48	37	=	=	X
cana-858	48	38	{	{	PUNCT
cana-858	48	39	r	r	PROPN
cana-858	48	40	,	,	PUNCT
cana-858	48	41	μ	μ	NOUN
cana-858	48	42	,	,	PUNCT
cana-858	48	43	q	q	NOUN
cana-858	48	44	}	}	PUNCT
cana-858	48	45	.	.	PUNCT
cana-858	49	1	assuming	assume	VERB
cana-858	49	2	τr(ψ)={∅,u	τr(ψ)={∅,u	PROPN
cana-858	49	3	,	,	PUNCT
cana-858	49	4	{	{	PUNCT
cana-858	49	5	q},{r	q},{r	NOUN
cana-858	49	6	,	,	PUNCT
cana-858	49	7	p	p	NOUN
cana-858	49	8	}	}	PUNCT
cana-858	49	9	}	}	PUNCT
cana-858	49	10	,	,	PUNCT
cana-858	49	11	we	we	PRON
cana-858	49	12	get	get	VERB
cana-858	49	13	τcr(ψ	τcr(ψ	NOUN
cana-858	49	14	)	)	PUNCT
cana-858	50	1	=	=	SYM
cana-858	50	2	{	{	PUNCT
cana-858	50	3	∅,u	∅,u	NOUN
cana-858	50	4	,	,	PUNCT
cana-858	50	5	{	{	PUNCT
cana-858	50	6	q},{r	q},{r	NOUN
cana-858	50	7	,	,	PUNCT
cana-858	50	8	p	p	NOUN
cana-858	50	9	}	}	PUNCT
cana-858	50	10	}	}	PUNCT
cana-858	50	11	.	.	PUNCT
cana-858	51	1	(	(	PUNCT
cana-858	51	2	nα	nα	NOUN
cana-858	51	3	)	)	PUNCT
cana-858	51	4	-o(x)={u	-o(x)={u	NOUN
cana-858	51	5	,	,	PUNCT
cana-858	51	6	ϕ,{r},{μ	ϕ,{r},{μ	PROPN
cana-858	51	7	}	}	PUNCT
cana-858	51	8	,	,	PUNCT
cana-858	51	9	{	{	PUNCT
cana-858	51	10	q},{r	q},{r	NOUN
cana-858	51	11	,	,	PUNCT
cana-858	51	12	}	}	PUNCT
cana-858	51	13	,	,	PUNCT
cana-858	51	14	{	{	PUNCT
cana-858	51	15	r	r	NOUN
cana-858	51	16	,	,	PUNCT
cana-858	51	17	q},{μ	q},{μ	ADJ
cana-858	51	18	,	,	PUNCT
cana-858	51	19	q	q	NOUN
cana-858	51	20	}	}	PUNCT
cana-858	51	21	}	}	PUNCT
cana-858	51	22	.	.	PUNCT
cana-858	52	1	theorem	theorem	VERB
cana-858	52	2	3.3	3.3	NUM
cana-858	52	3	all	all	DET
cana-858	52	4	subsets	subset	NOUN
cana-858	52	5	of	of	ADP
cana-858	52	6	u	u	PRON
cana-858	52	7	r(ψ	r(ψ	NOUN
cana-858	52	8	)	)	PUNCT
cana-858	52	9	are	be	AUX
cana-858	52	10	not	not	PART
cana-858	52	11	(	(	PUNCT
cana-858	52	12	nα	nα	NOUN
cana-858	52	13	)	)	PUNCT
cana-858	52	14	̂	̂	PUNCT
cana-858	52	15	open	open	ADJ
cana-858	52	16	sets	set	NOUN
cana-858	52	17	if	if	SCONJ
cana-858	52	18	τ	τ	PROPN
cana-858	52	19	r(ψ	r(ψ	PROPN
cana-858	52	20	)	)	PUNCT
cana-858	52	21	is	be	AUX
cana-858	52	22	not	not	PART
cana-858	52	23	highly	highly	ADV
cana-858	52	24	disconnected	disconnected	ADJ
cana-858	52	25	.	.	PUNCT
cana-858	53	1	proof	proof	ADJ
cana-858	53	2	case	case	NOUN
cana-858	53	3	1	1	NUM
cana-858	53	4	in	in	ADP
cana-858	53	5	the	the	DET
cana-858	53	6	event	event	NOUN
cana-858	53	7	that	that	PRON
cana-858	53	8	τ	τ	PROPN
cana-858	53	9	r(ψ	r(ψ	PROPN
cana-858	53	10	)	)	PUNCT
cana-858	54	1	=	=	NOUN
cana-858	54	2	{	{	PUNCT
cana-858	54	3	u	u	NOUN
cana-858	54	4	,	,	PUNCT
cana-858	54	5	ø	ø	PROPN
cana-858	54	6	,	,	PUNCT
cana-858	54	7	u	u	NOUN
cana-858	54	8	r(ψ	r(ψ	NOUN
cana-858	54	9	)	)	PUNCT
cana-858	54	10	}	}	PUNCT
cana-858	54	11	.	.	PUNCT
cana-858	55	1	to	to	PART
cana-858	55	2	begin	begin	VERB
cana-858	55	3	with	with	ADP
cana-858	55	4	,	,	PUNCT
cana-858	55	5	assume	assume	VERB
cana-858	55	6	a	a	DET
cana-858	55	7	=	=	X
cana-858	55	8	u	u	NOUN
cana-858	55	9	r(ψ	r(ψ	PROPN
cana-858	55	10	)	)	PUNCT
cana-858	55	11	⇒ℵ(a	⇒ℵ(a	NOUN
cana-858	55	12	)	)	PUNCT
cana-858	56	1	=	=	PUNCT
cana-858	56	2	u	u	NOUN
cana-858	56	3	r(ψ	r(ψ	PROPN
cana-858	56	4	)	)	PUNCT
cana-858	56	5	⇒	⇒	NOUN
cana-858	56	6	(	(	PUNCT
cana-858	56	7	n	n	CCONJ
cana-858	56	8	)	)	PUNCT
cana-858	56	9	̌	̌	PROPN
cana-858	57	1	(	(	PUNCT
cana-858	57	2	ℵ(u	ℵ(u	PROPN
cana-858	57	3	r(ψ))=∅⇒ℵ	r(ψ))=∅⇒ℵ	X
cana-858	57	4	(	(	PUNCT
cana-858	57	5	n	n	CCONJ
cana-858	57	6	)	)	PUNCT
cana-858	57	7	̌(ℵ(∅))=∅.	̌(ℵ(∅))=∅.	VERB
cana-858	57	8	if	if	SCONJ
cana-858	57	9	a⊉	a⊉	ADJ
cana-858	57	10	∅	∅	NOUN
cana-858	57	11	∅	∅	NOUN
cana-858	57	12	⇒	⇒	VERB
cana-858	57	13	a	a	DET
cana-858	57	14	⊈	⊈	PROPN
cana-858	57	15	ℵ((n	ℵ((n	NOUN
cana-858	57	16	)	)	PUNCT
cana-858	57	17	̌(ℵ(a	̌(ℵ(a	PROPN
cana-858	57	18	)	)	PUNCT
cana-858	57	19	)	)	PUNCT
cana-858	57	20	,	,	PUNCT
cana-858	57	21	then	then	ADV
cana-858	57	22	a∉	a∉	PROPN
cana-858	57	23	(	(	PUNCT
cana-858	57	24	nα	nα	NOUN
cana-858	57	25	)	)	PUNCT
cana-858	57	26	̂.	̂.	NOUN
cana-858	57	27	2	2	NUM
cana-858	57	28	-	-	PUNCT
cana-858	57	29	take	take	VERB
cana-858	57	30	a⊆	a⊆	NOUN
cana-858	57	31	uc	uc	PROPN
cana-858	57	32	r(ψ)⇒	r(ψ)⇒	PROPN
cana-858	57	33	n̂(a)=u	n̂(a)=u	PROPN
cana-858	57	34	·	·	PUNCT
cana-858	57	35	(	(	PUNCT
cana-858	57	36	n	n	CCONJ
cana-858	57	37	)	)	PUNCT
cana-858	57	38	·	·	PUNCT
cana-858	57	39	(	(	PUNCT
cana-858	57	40	n̂(u)=u	n̂(u)=u	PROPN
cana-858	57	41	·	·	PUNCT
cana-858	57	42	n̂((n)œ(n̂(u))=u	n̂((n)œ(n̂(u))=u	PROPN
cana-858	57	43	⇒	⇒	VERB
cana-858	57	44	a	a	DET
cana-858	57	45	⊆n̂	⊆n̂	PROPN
cana-858	57	46	(	(	PUNCT
cana-858	57	47	(	(	PUNCT
cana-858	57	48	n	n	CCONJ
cana-858	57	49	)	)	PUNCT
cana-858	57	50	̌(n̂(a	̌(n̂(a	ADJ
cana-858	57	51	)	)	PUNCT
cana-858	57	52	)	)	PUNCT
cana-858	57	53	.	.	PUNCT
cana-858	58	1	3	3	X
cana-858	58	2	.	.	X
cana-858	59	1	if	if	SCONJ
cana-858	59	2	[	[	X
cana-858	59	3	u	u	X
cana-858	59	4	r(ψ	r(ψ	NOUN
cana-858	59	5	)	)	PUNCT
cana-858	59	6	and	and	CCONJ
cana-858	59	7	uc	uc	ADJ
cana-858	59	8	r(ψ	r(ψ	PROPN
cana-858	59	9	)	)	PUNCT
cana-858	59	10	]	]	PUNCT
cana-858	60	1	intersect	intersect	ADJ
cana-858	60	2	at	at	ADP
cana-858	60	3	a	a	PRON
cana-858	60	4	,	,	PUNCT
cana-858	60	5	then	then	ADV
cana-858	60	6	ℵ(a)=	ℵ(a)=	PROPN
cana-858	60	7	u	u	NOUN
cana-858	60	8	⇒	⇒	NOUN
cana-858	60	9	(	(	PUNCT
cana-858	60	10	n	n	CCONJ
cana-858	60	11	)	)	PUNCT
cana-858	60	12	̌	̌	NUM
cana-858	60	13	(	(	PUNCT
cana-858	60	14	ℵ(u)=u	ℵ(u)=u	NOUN
cana-858	60	15	⇒	⇒	NOUN
cana-858	60	16	ℵ((n	ℵ((n	NOUN
cana-858	60	17	)	)	PUNCT
cana-858	60	18	̌(ℵ(u))=u	̌(ℵ(u))=u	NOUN
cana-858	60	19	⇒	⇒	VERB
cana-858	60	20	a	a	DET
cana-858	60	21	⊆ℵ	⊆ℵ	X
cana-858	60	22	(	(	PUNCT
cana-858	60	23	(	(	PUNCT
cana-858	60	24	n	n	CCONJ
cana-858	60	25	)	)	PUNCT
cana-858	60	26	̌(ℵ(a	̌(ℵ(a	NOUN
cana-858	60	27	)	)	PUNCT
cana-858	60	28	)	)	PUNCT
cana-858	60	29	.	.	PUNCT
cana-858	61	1	case	case	NOUN
cana-858	61	2	2	2	NUM
cana-858	61	3	:	:	PUNCT
cana-858	61	4	if	if	SCONJ
cana-858	61	5	𝜏	𝜏	PRON
cana-858	61	6	r(ψ	r(ψ	NOUN
cana-858	61	7	)	)	PUNCT
cana-858	62	1	=	=	NOUN
cana-858	62	2	{	{	PUNCT
cana-858	62	3	u	u	NOUN
cana-858	62	4	,	,	PUNCT
cana-858	62	5	ø	ø	PROPN
cana-858	62	6	,	,	PUNCT
cana-858	62	7	l	l	NOUN
cana-858	62	8	r(ψ	r(ψ	NOUN
cana-858	62	9	)	)	PUNCT
cana-858	62	10	,	,	PUNCT
cana-858	62	11	b	b	X
cana-858	62	12	r(ψ),u	r(ψ),u	PROPN
cana-858	62	13	r(ψ	r(ψ	PROPN
cana-858	62	14	)	)	PUNCT
cana-858	62	15	}	}	PUNCT
cana-858	62	16	.	.	PUNCT
cana-858	63	1	first	first	ADV
cana-858	63	2	,	,	PUNCT
cana-858	63	3	suppose	suppose	VERB
cana-858	63	4	that	that	SCONJ
cana-858	63	5	a⊆	a⊆	VERB
cana-858	63	6	l	l	NOUN
cana-858	63	7	r(ψ	r(ψ	NOUN
cana-858	63	8	)	)	PUNCT
cana-858	63	9	⇒ℵ(a)=	⇒ℵ(a)=	PROPN
cana-858	63	10	l	l	PROPN
cana-858	63	11	r(ψ)⇒	r(ψ)⇒	PROPN
cana-858	63	12	(	(	PUNCT
cana-858	63	13	n	n	CCONJ
cana-858	63	14	)	)	PUNCT
cana-858	63	15	̌	̌	PROPN
cana-858	64	1	(	(	PUNCT
cana-858	64	2	ℵ(l	ℵ(l	PROPN
cana-858	64	3	r(ψ	r(ψ	PROPN
cana-858	64	4	)	)	PUNCT
cana-858	64	5	)	)	PUNCT
cana-858	65	1	=	=	NOUN
cana-858	65	2	∅	∅	NOUN
cana-858	65	3	⇒ℵ	⇒ℵ	NOUN
cana-858	65	4	(	(	PUNCT
cana-858	65	5	n	n	CCONJ
cana-858	65	6	)	)	PUNCT
cana-858	65	7	̌(ℵ(∅))=∉.	̌(ℵ(∅))=∉.	PROPN
cana-858	65	8	a⊈	a⊈	NOUN
cana-858	65	9	∅	∅	NOUN
cana-858	65	10	⍒	⍒	PROPN
cana-858	65	11	⇒	⇒	PROPN
cana-858	65	12	a⊈	a⊈	PROPN
cana-858	65	13	ℵ((n	ℵ((n	PROPN
cana-858	65	14	)	)	PUNCT
cana-858	65	15	̌(ℵ(a	̌(ℵ(a	PROPN
cana-858	65	16	)	)	PUNCT
cana-858	65	17	)	)	PUNCT
cana-858	65	18	.	.	PUNCT
cana-858	66	1	afterwards	afterwards	ADV
cana-858	66	2	,	,	PUNCT
cana-858	66	3	a∉	a∉	PROPN
cana-858	66	4	(	(	PUNCT
cana-858	66	5	nα	nα	NOUN
cana-858	66	6	)	)	PUNCT
cana-858	66	7	̂	̂	VERB
cana-858	66	8	2	2	NUM
cana-858	66	9	.	.	X
cana-858	66	10	in	in	ADP
cana-858	66	11	the	the	DET
cana-858	66	12	event	event	NOUN
cana-858	66	13	when	when	SCONJ
cana-858	66	14	a	a	DET
cana-858	66	15	⊆	⊆	NUM
cana-858	66	16	b	b	X
cana-858	66	17	r(ψ	r(ψ	NOUN
cana-858	66	18	)	)	PUNCT
cana-858	66	19	⇒	⇒	NOUN
cana-858	66	20	ℵ(a)=	ℵ(a)=	PROPN
cana-858	66	21	b	b	X
cana-858	66	22	r(ψ	r(ψ	NOUN
cana-858	66	23	)	)	PUNCT
cana-858	66	24	⇒	⇒	NOUN
cana-858	66	25	(	(	PUNCT
cana-858	66	26	n	n	CCONJ
cana-858	66	27	)	)	PUNCT
cana-858	66	28	̌	̌	NUM
cana-858	67	1	(	(	PUNCT
cana-858	67	2	ℵ(b	ℵ(b	NOUN
cana-858	67	3	r(ψ	r(ψ	NOUN
cana-858	67	4	)	)	PUNCT
cana-858	67	5	)	)	PUNCT
cana-858	68	1	=	=	NOUN
cana-858	68	2	∅	∅	NOUN
cana-858	68	3	⇒ℵ	⇒ℵ	NOUN
cana-858	68	4	(	(	PUNCT
cana-858	68	5	n	n	CCONJ
cana-858	68	6	)	)	PUNCT
cana-858	68	7	̌(ℵ(∅))=∪.	̌(ℵ(∅))=∪.	NOUN
cana-858	68	8	a⊈_∅_⇒	a⊈_∅_⇒	ADP
cana-858	68	9	a⊈_ℵ((n	a⊈_ℵ((n	NOUN
cana-858	68	10	)	)	PUNCT
cana-858	68	11	̌(ℵ(a	̌(ℵ(a	PROPN
cana-858	68	12	)	)	PUNCT
cana-858	68	13	)	)	PUNCT
cana-858	68	14	.	.	PUNCT
cana-858	69	1	afterwards	afterwards	ADV
cana-858	69	2	,	,	PUNCT
cana-858	69	3	a∉	a∉	PROPN
cana-858	69	4	(	(	PUNCT
cana-858	69	5	nα	nα	NOUN
cana-858	69	6	)	)	PUNCT
cana-858	69	7	̂	̂	VERB
cana-858	69	8	3	3	X
cana-858	69	9	.	.	PUNCT
cana-858	70	1	at	at	ADP
cana-858	70	2	the	the	DET
cana-858	70	3	intersection	intersection	NOUN
cana-858	70	4	of	of	ADP
cana-858	70	5	a	a	DET
cana-858	70	6	with	with	ADP
cana-858	70	7	[	[	X
cana-858	70	8	l	l	X
cana-858	70	9	r(ψ	r(ψ	NOUN
cana-858	70	10	)	)	PUNCT
cana-858	70	11	and	and	CCONJ
cana-858	70	12	b	b	X
cana-858	70	13	r(ψ	r(ψ	NOUN
cana-858	70	14	)	)	PUNCT
cana-858	70	15	]	]	PUNCT
cana-858	70	16	,	,	PUNCT
cana-858	70	17	ℵ(a)=	ℵ(a)=	PUNCT
cana-858	70	18	u	u	PRON
cana-858	70	19	r(ψ	r(ψ	NOUN
cana-858	70	20	)	)	PUNCT
cana-858	70	21	and	and	CCONJ
cana-858	70	22	(	(	PUNCT
cana-858	70	23	n	n	CCONJ
cana-858	70	24	)	)	PUNCT
cana-858	70	25	̌	̌	PROPN
cana-858	70	26	(	(	PUNCT
cana-858	70	27	ℵ(u	ℵ(u	NOUN
cana-858	70	28	r(ψ	r(ψ	NOUN
cana-858	70	29	)	)	PUNCT
cana-858	70	30	)	)	PUNCT
cana-858	71	1	=	=	NOUN
cana-858	71	2	∅	∅	NOUN
cana-858	71	3	⇒ℵ	⇒ℵ	NOUN
cana-858	71	4	(	(	PUNCT
cana-858	71	5	n	n	CCONJ
cana-858	71	6	)	)	PUNCT
cana-858	71	7	̌(ℵ(∅	̌(ℵ(∅	NOUN
cana-858	71	8	)	)	PUNCT
cana-858	71	9	)	)	PUNCT
cana-858	72	1	=	=	VERB
cana-858	72	2	∅.	∅.	ADP
cana-858	72	3	a⊈	a⊈	NOUN
cana-858	72	4	∅	∅	NOUN
cana-858	72	5	⍒	⍒	PROPN
cana-858	72	6	⇒	⇒	PROPN
cana-858	72	7	a⊈	a⊈	PROPN
cana-858	72	8	ℵ((n	ℵ((n	PROPN
cana-858	72	9	)	)	PUNCT
cana-858	72	10	̌(ℵ(a	̌(ℵ(a	PROPN
cana-858	72	11	)	)	PUNCT
cana-858	72	12	)	)	PUNCT
cana-858	72	13	.	.	PUNCT
cana-858	73	1	afterwards	afterwards	ADV
cana-858	73	2	,	,	PUNCT
cana-858	73	3	a∉	a∉	PROPN
cana-858	73	4	(	(	PUNCT
cana-858	73	5	nα	nα	NOUN
cana-858	73	6	)	)	PUNCT
cana-858	73	7	4	4	NUM
cana-858	73	8	-	-	PUNCT
cana-858	73	9	if	if	NOUN
cana-858	73	10	a⊆	a⊆	VERB
cana-858	73	11	uc	uc	PROPN
cana-858	73	12	r(ψ	r(ψ	PROPN
cana-858	73	13	)	)	PUNCT
cana-858	73	14	⇒	⇒	NOUN
cana-858	73	15	n̂(a)=	n̂(a)=	PROPN
cana-858	73	16	u	u	PROPN
cana-858	73	17	⇒	⇒	VERB
cana-858	73	18	(	(	PUNCT
cana-858	73	19	n	n	CCONJ
cana-858	73	20	)	)	PUNCT
cana-858	73	21	̌	̌	NUM
cana-858	74	1	(	(	PUNCT
cana-858	74	2	n̂(u)=u	n̂(u)=u	NOUN
cana-858	74	3	⇒	⇒	NOUN
cana-858	74	4	n̂	n̂	NUM
cana-858	74	5	(	(	PUNCT
cana-858	74	6	(	(	PUNCT
cana-858	74	7	n	n	CCONJ
cana-858	74	8	)	)	PUNCT
cana-858	74	9	̌(n̂(u))=u	̌(n̂(u))=u	ADJ
cana-858	74	10	⇒	⇒	VERB
cana-858	74	11	a	a	DET
cana-858	74	12	⊆n̂	⊆n̂	PROPN
cana-858	74	13	(	(	PUNCT
cana-858	74	14	(	(	PUNCT
cana-858	74	15	n	n	CCONJ
cana-858	74	16	)	)	PUNCT
cana-858	74	17	̌(n̂(a	̌(n̂(a	ADJ
cana-858	74	18	)	)	PUNCT
cana-858	74	19	)	)	PUNCT
cana-858	74	20	.	.	PUNCT
cana-858	75	1	5	5	X
cana-858	75	2	.	.	X
cana-858	75	3	in	in	ADP
cana-858	75	4	the	the	DET
cana-858	75	5	event	event	NOUN
cana-858	75	6	when	when	SCONJ
cana-858	75	7	a	a	DET
cana-858	75	8	intersects	intersect	NOUN
cana-858	75	9	[	[	X
cana-858	75	10	l	l	NOUN
cana-858	75	11	r(ψ	r(ψ	NOUN
cana-858	75	12	)	)	PUNCT
cana-858	75	13	and	and	CCONJ
cana-858	75	14	uc	uc	ADJ
cana-858	75	15	r(ψ	r(ψ	PROPN
cana-858	75	16	)	)	PUNCT
cana-858	75	17	]	]	PUNCT
cana-858	75	18	⇒	⇒	NOUN
cana-858	75	19	ℵ(a)=	ℵ(a)=	PROPN
cana-858	75	20	u	u	PRON
cana-858	75	21	⇒	⇒	NOUN
cana-858	75	22	(	(	PUNCT
cana-858	75	23	n	n	CCONJ
cana-858	75	24	)	)	PUNCT
cana-858	75	25	̌	̌	NUM
cana-858	75	26	(	(	PUNCT
cana-858	75	27	ℵ(u)=u	ℵ(u)=u	NOUN
cana-858	75	28	⇒	⇒	NOUN
cana-858	75	29	ℵ	ℵ	NOUN
cana-858	75	30	(	(	PUNCT
cana-858	75	31	(	(	PUNCT
cana-858	75	32	n	n	CCONJ
cana-858	75	33	)	)	PUNCT
cana-858	75	34	̌(ℵ(u))=u	̌(ℵ(u))=u	NOUN
cana-858	75	35	⇒	⇒	NOUN
cana-858	75	36	a	a	DET
cana-858	75	37	⊆ℵ	⊆ℵ	X
cana-858	75	38	(	(	PUNCT
cana-858	75	39	(	(	PUNCT
cana-858	75	40	n	n	CCONJ
cana-858	75	41	)	)	PUNCT
cana-858	75	42	̌(ℵ(a	̌(ℵ(a	NOUN
cana-858	75	43	)	)	PUNCT
cana-858	75	44	)	)	PUNCT
cana-858	75	45	.	.	PUNCT
cana-858	76	1	communications	communication	NOUN
cana-858	76	2	on	on	ADP
cana-858	76	3	applied	apply	VERB
cana-858	76	4	nonlinear	nonlinear	ADJ
cana-858	76	5	analysis	analysis	NOUN
cana-858	76	6	issn	issn	NOUN
cana-858	76	7	:	:	PUNCT
cana-858	76	8	1074	1074	NUM
cana-858	76	9	-	-	PUNCT
cana-858	76	10	133x	133x	NUM
cana-858	76	11	vol	vol	NOUN
cana-858	76	12	31	31	NUM
cana-858	76	13	no	no	NOUN
cana-858	76	14	.	.	PUNCT
cana-858	77	1	4s	4s	NUM
cana-858	77	2	(	(	PUNCT
cana-858	77	3	2024	2024	NUM
cana-858	77	4	)	)	PUNCT
cana-858	77	5	360	360	NUM
cana-858	77	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-858	77	7	6	6	NUM
cana-858	77	8	-	-	PUNCT
cana-858	77	9	if	if	SCONJ
cana-858	77	10	[	[	X
cana-858	77	11	b	b	X
cana-858	77	12	r(ψ	r(ψ	NOUN
cana-858	77	13	)	)	PUNCT
cana-858	77	14	and	and	CCONJ
cana-858	77	15	uc	uc	ADJ
cana-858	77	16	r(ψ	r(ψ	PROPN
cana-858	77	17	)	)	PUNCT
cana-858	77	18	]	]	PUNCT
cana-858	78	1	intersect	intersect	ADJ
cana-858	78	2	a	a	DET
cana-858	78	3	,	,	PUNCT
cana-858	78	4	then	then	ADV
cana-858	78	5	n̂(a)=	n̂(a)=	PROPN
cana-858	78	6	u	u	PROPN
cana-858	78	7	⇒	⇒	X
cana-858	78	8	(	(	PUNCT
cana-858	78	9	ℵ	ℵ	NOUN
cana-858	78	10	)	)	PUNCT
cana-858	78	11	̌	̌	NUM
cana-858	78	12	(	(	PUNCT
cana-858	78	13	n̂(u)=u	n̂(u)=u	NOUN
cana-858	78	14	⇒	⇒	NOUN
cana-858	78	15	ℵ	ℵ	NUM
cana-858	78	16	(	(	PUNCT
cana-858	78	17	(	(	PUNCT
cana-858	78	18	ℵ	ℵ	NOUN
cana-858	78	19	)	)	PUNCT
cana-858	78	20	̌(n̂(u))=u	̌(n̂(u))=u	NOUN
cana-858	78	21	⇒	⇒	VERB
cana-858	78	22	a	a	DET
cana-858	78	23	⊆ℵ	⊆ℵ	X
cana-858	78	24	(	(	PUNCT
cana-858	78	25	(	(	PUNCT
cana-858	78	26	n	n	CCONJ
cana-858	78	27	)	)	PUNCT
cana-858	78	28	̌(ℵ(a	̌(ℵ(a	NOUN
cana-858	78	29	)	)	PUNCT
cana-858	78	30	)	)	PUNCT
cana-858	78	31	.	.	PUNCT
cana-858	79	1	theorem	theorem	VERB
cana-858	79	2	3.4	3.4	NUM
cana-858	79	3	:	:	PUNCT
cana-858	79	4	all	all	PRON
cana-858	79	5	subset	subset	NOUN
cana-858	79	6	of	of	ADP
cana-858	79	7	uc	uc	PROPN
cana-858	79	8	r(ψ	r(ψ	PROPN
cana-858	79	9	)	)	PUNCT
cana-858	79	10	is	be	AUX
cana-858	79	11	ℕα̂	ℕα̂	ADJ
cana-858	79	12	open	open	ADJ
cana-858	79	13	set	set	NOUN
cana-858	79	14	.	.	PUNCT
cana-858	80	1	proof	proof	NOUN
cana-858	80	2	:	:	PUNCT
cana-858	81	1	case	case	NOUN
cana-858	81	2	1if	1if	NOUN
cana-858	81	3	τ	τ	X
cana-858	81	4	r(ψ	r(ψ	PROPN
cana-858	81	5	)	)	PUNCT
cana-858	81	6	=	=	NOUN
cana-858	81	7	{	{	PUNCT
cana-858	81	8	u	u	NOUN
cana-858	81	9	,	,	PUNCT
cana-858	81	10	ø	ø	PROPN
cana-858	81	11	,	,	PUNCT
cana-858	81	12	u	u	NOUN
cana-858	81	13	r(ψ	r(ψ	NOUN
cana-858	81	14	)	)	PUNCT
cana-858	81	15	}	}	PUNCT
cana-858	81	16	.	.	PUNCT
cana-858	82	1	if	if	SCONJ
cana-858	82	2	a⊆	a⊆	VERB
cana-858	82	3	uc	uc	PROPN
cana-858	82	4	r(ψ	r(ψ	PROPN
cana-858	82	5	)	)	PUNCT
cana-858	82	6	⇒	⇒	NOUN
cana-858	82	7	ℕ̂(a)=u	ℕ̂(a)=u	ADJ
cana-858	82	8	⇒	⇒	PROPN
cana-858	82	9	ℕ̌	ℕ̌	PROPN
cana-858	82	10	(	(	PUNCT
cana-858	82	11	ℕ̂(u	ℕ̂(u	PROPN
cana-858	82	12	)	)	PUNCT
cana-858	83	1	=	=	SYM
cana-858	83	2	u	u	NOUN
cana-858	83	3	⇒	⇒	NOUN
cana-858	83	4	ℕ̂	ℕ̂	PROPN
cana-858	83	5	(	(	PUNCT
cana-858	83	6	ℕ̌(ℕ̂(u))=u	ℕ̌(ℕ̂(u))=u	AUX
cana-858	83	7	⇒	⇒	VERB
cana-858	83	8	a	a	DET
cana-858	83	9	⊆	⊆	NUM
cana-858	83	10	ℕ̂	ℕ̂	NOUN
cana-858	83	11	(	(	PUNCT
cana-858	83	12	ℕ̌(ℕ̂(a	ℕ̌(ℕ̂(a	NOUN
cana-858	83	13	)	)	PUNCT
cana-858	83	14	)	)	PUNCT
cana-858	83	15	.	.	PUNCT
cana-858	84	1	then	then	ADV
cana-858	84	2	a∈	a∈	PROPN
cana-858	84	3	ℕα̂.	ℕα̂.	PROPN
cana-858	84	4	case	case	NOUN
cana-858	84	5	2	2	NUM
cana-858	84	6	:	:	PUNCT
cana-858	84	7	when	when	SCONJ
cana-858	84	8	τ	τ	X
cana-858	84	9	r(ψ	r(ψ	PROPN
cana-858	84	10	)	)	PUNCT
cana-858	85	1	=	=	NOUN
cana-858	85	2	{	{	PUNCT
cana-858	85	3	u	u	NOUN
cana-858	85	4	,	,	PUNCT
cana-858	85	5	ø	ø	PROPN
cana-858	85	6	,	,	PUNCT
cana-858	85	7	l	l	NOUN
cana-858	85	8	r(ψ	r(ψ	NOUN
cana-858	85	9	)	)	PUNCT
cana-858	85	10	,	,	PUNCT
cana-858	85	11	b	b	X
cana-858	85	12	r(ψ	r(ψ	NOUN
cana-858	85	13	)	)	PUNCT
cana-858	85	14	,	,	PUNCT
cana-858	85	15	u	u	NOUN
cana-858	85	16	r(ψ	r(ψ	NOUN
cana-858	85	17	)	)	PUNCT
cana-858	85	18	}	}	PUNCT
cana-858	85	19	.	.	PUNCT
cana-858	86	1	if	if	SCONJ
cana-858	86	2	a⊆	a⊆	VERB
cana-858	86	3	uc	uc	PROPN
cana-858	86	4	r(ψ	r(ψ	PROPN
cana-858	86	5	)	)	PUNCT
cana-858	86	6	⇒	⇒	NOUN
cana-858	86	7	ℕ̂(a)=u	ℕ̂(a)=u	ADJ
cana-858	86	8	⇒	⇒	PROPN
cana-858	86	9	ℕ̌	ℕ̌	PROPN
cana-858	86	10	(	(	PUNCT
cana-858	86	11	ℕ̂(u	ℕ̂(u	PROPN
cana-858	86	12	)	)	PUNCT
cana-858	87	1	=	=	SYM
cana-858	87	2	u	u	NOUN
cana-858	87	3	⇒	⇒	NOUN
cana-858	87	4	ℕ̂	ℕ̂	PROPN
cana-858	87	5	(	(	PUNCT
cana-858	87	6	ℕ̌(ℕ̂(u))=u	ℕ̌(ℕ̂(u))=u	AUX
cana-858	87	7	⇒	⇒	VERB
cana-858	87	8	a	a	DET
cana-858	87	9	⊆	⊆	NUM
cana-858	87	10	ℕ̂	ℕ̂	NOUN
cana-858	87	11	(	(	PUNCT
cana-858	87	12	ℕ̌(ℕ̂(a	ℕ̌(ℕ̂(a	NOUN
cana-858	87	13	)	)	PUNCT
cana-858	87	14	)	)	PUNCT
cana-858	87	15	.	.	PUNCT
cana-858	88	1	then	then	ADV
cana-858	88	2	a∈	a∈	PROPN
cana-858	88	3	ℕα̂.	ℕα̂.	PROPN
cana-858	88	4	theorem	theorem	VERB
cana-858	88	5	3	3	NUM
cana-858	88	6	.	.	NOUN
cana-858	88	7	5	5	NUM
cana-858	88	8	:	:	PUNCT
cana-858	88	9	all	all	PRON
cana-858	88	10	subset	subset	NOUN
cana-858	88	11	of	of	ADP
cana-858	88	12	u	u	PRON
cana-858	88	13	which	which	PRON
cana-858	88	14	intersect	intersect	VERB
cana-858	88	15	[	[	X
cana-858	88	16	u	u	NOUN
cana-858	88	17	r(ψ	r(ψ	NOUN
cana-858	88	18	)	)	PUNCT
cana-858	88	19	and	and	CCONJ
cana-858	88	20	uc	uc	ADJ
cana-858	88	21	r(ψ	r(ψ	PROPN
cana-858	88	22	)	)	PUNCT
cana-858	88	23	]	]	PUNCT
cana-858	88	24	is	be	AUX
cana-858	88	25	ℕα̂	ℕα̂	ADJ
cana-858	88	26	open	open	ADJ
cana-858	88	27	set	set	NOUN
cana-858	88	28	.	.	PUNCT
cana-858	89	1	proof	proof	NOUN
cana-858	89	2	:	:	PUNCT
cana-858	90	1	case	case	NOUN
cana-858	90	2	1if	1if	NOUN
cana-858	90	3	τ	τ	X
cana-858	90	4	r(ψ	r(ψ	PROPN
cana-858	90	5	)	)	PUNCT
cana-858	90	6	=	=	NOUN
cana-858	90	7	{	{	PUNCT
cana-858	90	8	u	u	NOUN
cana-858	90	9	,	,	PUNCT
cana-858	90	10	ø	ø	PROPN
cana-858	90	11	,	,	PUNCT
cana-858	90	12	u	u	NOUN
cana-858	90	13	r(ψ	r(ψ	NOUN
cana-858	90	14	)	)	PUNCT
cana-858	90	15	}	}	PUNCT
cana-858	90	16	let	let	VERB
cana-858	90	17	a	a	DET
cana-858	90	18	⊆	⊆	NUM
cana-858	90	19	u	u	NOUN
cana-858	90	20	such	such	ADJ
cana-858	90	21	that	that	SCONJ
cana-858	90	22	a	a	DET
cana-858	90	23	intersect	intersect	ADJ
cana-858	90	24	[	[	PUNCT
cana-858	90	25	u	u	NOUN
cana-858	90	26	r(ψ	r(ψ	NOUN
cana-858	90	27	)	)	PUNCT
cana-858	90	28	and	and	CCONJ
cana-858	90	29	uc	uc	ADJ
cana-858	90	30	r(ψ	r(ψ	PROPN
cana-858	90	31	)	)	PUNCT
cana-858	90	32	]	]	PUNCT
cana-858	90	33	ℕ̂(a)=u	ℕ̂(a)=u	ADP
cana-858	90	34	⇒	⇒	NOUN
cana-858	90	35	ℵ̌	ℵ̌	PROPN
cana-858	90	36	(	(	PUNCT
cana-858	90	37	ℕ̂(u	ℕ̂(u	PROPN
cana-858	90	38	)	)	PUNCT
cana-858	91	1	=	=	SYM
cana-858	91	2	u	u	NOUN
cana-858	91	3	⇒	⇒	NOUN
cana-858	91	4	ℵ̂	ℵ̂	PUNCT
cana-858	91	5	(	(	PUNCT
cana-858	91	6	ℕ̌(ℵ̂(u))=u	ℕ̌(ℵ̂(u))=u	VERB
cana-858	91	7	⇒	⇒	VERB
cana-858	91	8	a	a	DET
cana-858	91	9	⊆	⊆	NUM
cana-858	91	10	ℵ̂	ℵ̂	SYM
cana-858	91	11	(	(	PUNCT
cana-858	91	12	ℕ̌(ℵ̂(a	ℕ̌(ℵ̂(a	ADJ
cana-858	91	13	)	)	PUNCT
cana-858	91	14	)	)	PUNCT
cana-858	91	15	.	.	PUNCT
cana-858	92	1	then	then	ADV
cana-858	92	2	a∈	a∈	PROPN
cana-858	92	3	ℕα̂	ℕα̂	ADJ
cana-858	92	4	open	open	ADJ
cana-858	92	5	set	set	NOUN
cana-858	92	6	.	.	PUNCT
cana-858	93	1	case	case	NOUN
cana-858	93	2	2	2	NUM
cana-858	93	3	:	:	PUNCT
cana-858	93	4	𝜏	𝜏	PRON
cana-858	93	5	r(ψ	r(ψ	NOUN
cana-858	93	6	)	)	PUNCT
cana-858	94	1	=	=	NOUN
cana-858	94	2	{	{	PUNCT
cana-858	94	3	u	u	NOUN
cana-858	94	4	,	,	PUNCT
cana-858	94	5	ø	ø	PROPN
cana-858	94	6	,	,	PUNCT
cana-858	94	7	l	l	NOUN
cana-858	94	8	r(ψ	r(ψ	NOUN
cana-858	94	9	)	)	PUNCT
cana-858	94	10	,	,	PUNCT
cana-858	94	11	b	b	X
cana-858	94	12	r(ψ	r(ψ	NOUN
cana-858	94	13	)	)	PUNCT
cana-858	94	14	,	,	PUNCT
cana-858	94	15	u	u	NOUN
cana-858	94	16	r(ψ	r(ψ	NOUN
cana-858	94	17	)	)	PUNCT
cana-858	94	18	}	}	PUNCT
cana-858	94	19	.	.	PUNCT
cana-858	95	1	1let	1let	PROPN
cana-858	95	2	a⊆	a⊆	PROPN
cana-858	95	3	u	u	NOUN
cana-858	95	4	such	such	ADJ
cana-858	95	5	that	that	SCONJ
cana-858	95	6	a	a	DET
cana-858	95	7	intersect	intersect	ADJ
cana-858	95	8	[	[	X
cana-858	95	9	l	l	X
cana-858	95	10	r(ψ	r(ψ	NOUN
cana-858	95	11	)	)	PUNCT
cana-858	95	12	and	and	CCONJ
cana-858	95	13	uc	uc	ADJ
cana-858	95	14	r(ψ	r(ψ	PROPN
cana-858	95	15	)	)	PUNCT
cana-858	95	16	]	]	PUNCT
cana-858	95	17	.	.	PUNCT
cana-858	96	1	ℕ̂(a)=u	ℕ̂(a)=u	ADJ
cana-858	96	2	⇒	⇒	PROPN
cana-858	96	3	ℕ̌	ℕ̌	PROPN
cana-858	96	4	(	(	PUNCT
cana-858	96	5	ℵ(u	ℵ(u	PROPN
cana-858	96	6	)	)	PUNCT
cana-858	96	7	=	=	SYM
cana-858	96	8	u	u	NOUN
cana-858	96	9	⇒	⇒	NOUN
cana-858	96	10	ℵ̂	ℵ̂	PUNCT
cana-858	96	11	(	(	PUNCT
cana-858	96	12	ℕ̌(ℵ̂(u))=u	ℕ̌(ℵ̂(u))=u	VERB
cana-858	96	13	⇒	⇒	VERB
cana-858	96	14	a	a	DET
cana-858	96	15	⊆	⊆	NUM
cana-858	96	16	ℵ̂	ℵ̂	SYM
cana-858	96	17	(	(	PUNCT
cana-858	96	18	ℕ̌(ℵ̂(a	ℕ̌(ℵ̂(a	ADJ
cana-858	96	19	)	)	PUNCT
cana-858	96	20	)	)	PUNCT
cana-858	96	21	.	.	PUNCT
cana-858	97	1	then	then	ADV
cana-858	97	2	a∈	a∈	PROPN
cana-858	97	3	ℕα̂	ℕα̂	ADJ
cana-858	97	4	open	open	ADJ
cana-858	97	5	set	set	NOUN
cana-858	97	6	.	.	PUNCT
cana-858	98	1	2let	2let	PROPN
cana-858	98	2	a⊆	a⊆	VERB
cana-858	98	3	u	u	NOUN
cana-858	98	4	such	such	ADJ
cana-858	98	5	that	that	SCONJ
cana-858	98	6	a	a	DET
cana-858	98	7	intersect	intersect	ADJ
cana-858	98	8	[	[	X
cana-858	98	9	b	b	X
cana-858	98	10	r(ψ	r(ψ	NOUN
cana-858	98	11	)	)	PUNCT
cana-858	98	12	and	and	CCONJ
cana-858	98	13	uc	uc	ADJ
cana-858	98	14	r(ψ	r(ψ	PROPN
cana-858	98	15	)	)	PUNCT
cana-858	98	16	]	]	PUNCT
cana-858	98	17	.	.	PUNCT
cana-858	99	1	ℕ̂(a)=u	ℕ̂(a)=u	PROPN
cana-858	99	2	⇒	⇒	PROPN
cana-858	99	3	ℕ̌	ℕ̌	PROPN
cana-858	99	4	(	(	PUNCT
cana-858	99	5	ℕ̂(u	ℕ̂(u	PROPN
cana-858	99	6	)	)	PUNCT
cana-858	99	7	=	=	SYM
cana-858	99	8	u	u	NOUN
cana-858	99	9	⇒	⇒	NOUN
cana-858	99	10	ℵ̂	ℵ̂	PUNCT
cana-858	99	11	(	(	PUNCT
cana-858	99	12	ℕ̌(ℵ̂(u))=u	ℕ̌(ℵ̂(u))=u	VERB
cana-858	99	13	⇒	⇒	VERB
cana-858	99	14	a	a	DET
cana-858	99	15	⊆	⊆	NUM
cana-858	99	16	ℵ̂	ℵ̂	SYM
cana-858	99	17	(	(	PUNCT
cana-858	99	18	ℕ̌(ℵ̂(a	ℕ̌(ℵ̂(a	ADJ
cana-858	99	19	)	)	PUNCT
cana-858	99	20	)	)	PUNCT
cana-858	99	21	.	.	PUNCT
cana-858	100	1	then	then	ADV
cana-858	100	2	a∈	a∈	PROPN
cana-858	100	3	ℕα̂	ℕα̂	ADJ
cana-858	100	4	open	open	ADJ
cana-858	100	5	set	set	NOUN
cana-858	100	6	.	.	PUNCT
cana-858	101	1	3let	3let	PROPN
cana-858	101	2	a⊆	a⊆	VERB
cana-858	101	3	u	u	NOUN
cana-858	101	4	such	such	ADJ
cana-858	101	5	that	that	SCONJ
cana-858	101	6	a	a	DET
cana-858	101	7	intersect	intersect	ADJ
cana-858	101	8	[	[	X
cana-858	101	9	l	l	X
cana-858	101	10	r(ψ	r(ψ	NOUN
cana-858	101	11	)	)	PUNCT
cana-858	101	12	and	and	CCONJ
cana-858	101	13	b	b	X
cana-858	101	14	r(ψ	r(ψ	NOUN
cana-858	101	15	)	)	PUNCT
cana-858	101	16	and	and	CCONJ
cana-858	101	17	uc	uc	ADJ
cana-858	101	18	r(ψ	r(ψ	PROPN
cana-858	101	19	)	)	PUNCT
cana-858	101	20	]	]	PUNCT
cana-858	101	21	.	.	PUNCT
cana-858	102	1	ℕ̂(a)=u	ℕ̂(a)=u	PROPN
cana-858	102	2	⇒	⇒	PROPN
cana-858	102	3	ℕ̌	ℕ̌	PROPN
cana-858	102	4	(	(	PUNCT
cana-858	102	5	ℕ̂(u	ℕ̂(u	PROPN
cana-858	102	6	)	)	PUNCT
cana-858	102	7	=	=	SYM
cana-858	102	8	u	u	NOUN
cana-858	102	9	⇒	⇒	NOUN
cana-858	102	10	ℵ̂	ℵ̂	PUNCT
cana-858	102	11	(	(	PUNCT
cana-858	102	12	ℕ̌(ℕ̂(u))=u	ℕ̌(ℕ̂(u))=u	AUX
cana-858	102	13	⇒	⇒	VERB
cana-858	102	14	a	a	DET
cana-858	102	15	⊆	⊆	NUM
cana-858	102	16	ℵ̂	ℵ̂	SYM
cana-858	102	17	(	(	PUNCT
cana-858	102	18	ℕ̌(ℕ̂(a	ℕ̌(ℕ̂(a	NOUN
cana-858	102	19	)	)	PUNCT
cana-858	102	20	)	)	PUNCT
cana-858	102	21	.	.	PUNCT
cana-858	103	1	then	then	ADV
cana-858	103	2	a∈	a∈	PROPN
cana-858	103	3	ℕα̂	ℕα̂	ADJ
cana-858	103	4	open	open	ADJ
cana-858	103	5	set	set	NOUN
cana-858	103	6	.	.	PUNCT
cana-858	104	1	theorem	theorem	VERB
cana-858	104	2	3.6	3.6	NUM
cana-858	104	3	:	:	PUNCT
cana-858	104	4	when	when	SCONJ
cana-858	104	5	the	the	DET
cana-858	104	6	nano	nano	NOUN
cana-858	104	7	space	space	NOUN
cana-858	104	8	u	u	NOUN
cana-858	104	9	is	be	AUX
cana-858	104	10	extremely	extremely	ADV
cana-858	104	11	disconnected	disconnected	ADJ
cana-858	104	12	then	then	ADV
cana-858	104	13	all	all	PRON
cana-858	104	14	subset	subset	NOUN
cana-858	104	15	of	of	ADP
cana-858	104	16	u	u	NOUN
cana-858	104	17	is	be	AUX
cana-858	104	18	ℕα̂	ℕα̂	ADJ
cana-858	104	19	−open	−open	VERB
cana-858	104	20	set	set	VERB
cana-858	104	21	.	.	PUNCT
cana-858	105	1	proof	proof	NOUN
cana-858	105	2	:	:	PUNCT
cana-858	105	3	𝜏	𝜏	PRON
cana-858	105	4	r(ψ	r(ψ	NOUN
cana-858	105	5	)	)	PUNCT
cana-858	105	6	=	=	NOUN
cana-858	105	7	{	{	PUNCT
cana-858	105	8	u	u	NOUN
cana-858	105	9	,	,	PUNCT
cana-858	105	10	ø	ø	PROPN
cana-858	105	11	,	,	PUNCT
cana-858	105	12	l	l	NOUN
cana-858	105	13	r(ψ	r(ψ	NOUN
cana-858	105	14	)	)	PUNCT
cana-858	105	15	,	,	PUNCT
cana-858	105	16	b	b	X
cana-858	105	17	r(ψ	r(ψ	NOUN
cana-858	105	18	)	)	PUNCT
cana-858	105	19	}	}	PUNCT
cana-858	105	20	.	.	PUNCT
cana-858	106	1	assuming	assume	VERB
cana-858	106	2	that	that	SCONJ
cana-858	106	3	a	a	DET
cana-858	106	4	⊆	⊆	NUM
cana-858	106	5	l	l	NOUN
cana-858	106	6	r(ψ	r(ψ	NOUN
cana-858	106	7	)	)	PUNCT
cana-858	106	8	⇒ℵ(a)=	⇒ℵ(a)=	PROPN
cana-858	106	9	l	l	PROPN
cana-858	106	10	r(ψ)⇒	r(ψ)⇒	PROPN
cana-858	106	11	(	(	PUNCT
cana-858	106	12	n	n	CCONJ
cana-858	106	13	)	)	PUNCT
cana-858	106	14	̌	̌	PROPN
cana-858	106	15	(	(	PUNCT
cana-858	106	16	ℵ(l	ℵ(l	PROPN
cana-858	106	17	r(ψ	r(ψ	PROPN
cana-858	106	18	)	)	PUNCT
cana-858	106	19	)	)	PUNCT
cana-858	107	1	=	=	PUNCT
cana-858	107	2	l	l	NOUN
cana-858	107	3	r(ψ)⇒	r(ψ)⇒	NOUN
cana-858	107	4	ℵ	ℵ	PROPN
cana-858	107	5	(	(	PUNCT
cana-858	107	6	n	n	CCONJ
cana-858	107	7	)	)	PUNCT
cana-858	107	8	̌	̌	PROPN
cana-858	107	9	(	(	PUNCT
cana-858	107	10	ℵ(l	ℵ(l	PROPN
cana-858	107	11	r(ψ	r(ψ	PROPN
cana-858	107	12	)	)	PUNCT
cana-858	107	13	)	)	PUNCT
cana-858	108	1	=	=	SYM
cana-858	108	2	l	l	PRON
cana-858	108	3	r(ψ)a	r(ψ)a	NOUN
cana-858	108	4	⊆	⊆	NUM
cana-858	108	5	ℵ((n	ℵ((n	NOUN
cana-858	108	6	)	)	PUNCT
cana-858	108	7	̌(ℵ(a	̌(ℵ(a	NOUN
cana-858	108	8	)	)	PUNCT
cana-858	108	9	)	)	PUNCT
cana-858	109	1	if	if	SCONJ
cana-858	109	2	a⊆	a⊆	ADP
cana-858	109	3	l	l	NOUN
cana-858	109	4	r(ψ	r(ψ	NOUN
cana-858	109	5	)	)	PUNCT
cana-858	109	6	⇒	⇒	NOUN
cana-858	109	7	a.	a.	NOUN
cana-858	109	8	after	after	ADP
cana-858	109	9	that	that	PRON
cana-858	109	10	,	,	PUNCT
cana-858	109	11	a∈(nα	a∈(nα	NOUN
cana-858	109	12	)	)	PUNCT
cana-858	109	13	̂	̂	PUNCT
cana-858	109	14	open	open	ADJ
cana-858	109	15	set	set	NOUN
cana-858	109	16	.	.	PUNCT
cana-858	110	1	in	in	ADP
cana-858	110	2	the	the	DET
cana-858	110	3	event	event	NOUN
cana-858	110	4	that	that	SCONJ
cana-858	110	5	a	a	DET
cana-858	110	6	⊆	⊆	NUM
cana-858	110	7	b	b	SYM
cana-858	110	8	r(ψ	r(ψ	NOUN
cana-858	110	9	)	)	PUNCT
cana-858	110	10	⇒	⇒	NOUN
cana-858	110	11	ℵ(a)=	ℵ(a)=	PROPN
cana-858	110	12	b	b	X
cana-858	110	13	r(ψ	r(ψ	NOUN
cana-858	110	14	)	)	PUNCT
cana-858	110	15	⇒	⇒	NOUN
cana-858	110	16	(	(	PUNCT
cana-858	110	17	n	n	CCONJ
cana-858	110	18	)	)	PUNCT
cana-858	110	19	̌	̌	NUM
cana-858	111	1	(	(	PUNCT
cana-858	111	2	ℵ(b	ℵ(b	NOUN
cana-858	111	3	r(ψ	r(ψ	NOUN
cana-858	111	4	)	)	PUNCT
cana-858	111	5	)	)	PUNCT
cana-858	112	1	=	=	SYM
cana-858	112	2	b	b	X
cana-858	112	3	r(ψ	r(ψ	NOUN
cana-858	112	4	)	)	PUNCT
cana-858	112	5	⇒	⇒	PROPN
cana-858	112	6	ℵ	ℵ	X
cana-858	112	7	(	(	PUNCT
cana-858	112	8	n	n	CCONJ
cana-858	112	9	)	)	PUNCT
cana-858	112	10	̌	̌	NUM
cana-858	112	11	(	(	PUNCT
cana-858	112	12	ℵ(b	ℵ(b	NOUN
cana-858	112	13	r(ψ))=	r(ψ))=	X
cana-858	113	1	b	b	X
cana-858	113	2	r(ψ	r(ψ	NOUN
cana-858	113	3	)	)	PUNCT
cana-858	113	4	⇒\	⇒\	PROPN
cana-858	113	5	a⊆	a⊆	VERB
cana-858	113	6	b	b	PRON
cana-858	113	7	r(ψ	r(ψ	NOUN
cana-858	113	8	)	)	PUNCT
cana-858	113	9	⇒	⇒	VERB
cana-858	113	10	a	a	DET
cana-858	113	11	⊆	⊆	NUM
cana-858	113	12	b	b	X
cana-858	113	13	r(ψ	r(ψ	NOUN
cana-858	113	14	)	)	PUNCT
cana-858	113	15	⇒	⇒	PROPN
cana-858	113	16	b	b	X
cana-858	113	17	r(ψ	r(ψ	NOUN
cana-858	113	18	)	)	PUNCT
cana-858	113	19	⇒	⇒	VERB
cana-858	113	20	a	a	DET
cana-858	113	21	⊆	⊆	NUM
cana-858	113	22	ℵ((n	ℵ((n	NOUN
cana-858	113	23	)	)	PUNCT
cana-858	113	24	̌(ℵ(a	̌(ℵ(a	NOUN
cana-858	113	25	)	)	PUNCT
cana-858	113	26	)	)	PUNCT
cana-858	113	27	.	.	PUNCT
cana-858	114	1	a∈(nα	a∈(nα	PROPN
cana-858	114	2	)	)	PUNCT
cana-858	115	1	̂	̂	VERB
cana-858	115	2	is	be	AUX
cana-858	115	3	thus	thus	ADV
cana-858	115	4	an	an	DET
cana-858	115	5	open	open	NOUN
cana-858	115	6	set.when	set.when	ADV
cana-858	115	7	a	a	DET
cana-858	115	8	crosses	crosse	NOUN
cana-858	115	9	across	across	ADP
cana-858	115	10	[	[	X
cana-858	115	11	l	l	NOUN
cana-858	115	12	r(ψ	r(ψ	NOUN
cana-858	115	13	)	)	PUNCT
cana-858	115	14	and	and	CCONJ
cana-858	115	15	b	b	NOUN
cana-858	115	16	r(ψ)].n	r(ψ)].n	X
cana-858	115	17	(	(	PUNCT
cana-858	115	18	a)=u	a)=u	X
cana-858	115	19	⇒	⇒	NOUN
cana-858	115	20	(	(	PUNCT
cana-858	115	21	n	n	CCONJ
cana-858	115	22	)	)	PUNCT
cana-858	115	23	(	(	PUNCT
cana-858	115	24	n̂(u	n̂(u	NUM
cana-858	115	25	)	)	PUNCT
cana-858	115	26	=	=	SYM
cana-858	115	27	u	u	X
cana-858	115	28	·	·	SYM
cana-858	115	29	n̂((n)(n̂(u))=u	n̂((n)(n̂(u))=u	X
cana-858	115	30	·	·	PUNCT
cana-858	115	31	a	a	DET
cana-858	115	32	⊆n̂((n)(ℵ(a	⊆n̂((n)(ℵ(a	NOUN
cana-858	115	33	)	)	PUNCT
cana-858	115	34	)	)	PUNCT
cana-858	115	35	.	.	PUNCT
cana-858	116	1	a∈(nα	a∈(nα	PROPN
cana-858	116	2	)	)	PUNCT
cana-858	117	1	̂	̂	VERB
cana-858	117	2	is	be	AUX
cana-858	117	3	thus	thus	ADV
cana-858	117	4	an	an	DET
cana-858	117	5	open	open	ADJ
cana-858	117	6	set	set	NOUN
cana-858	117	7	.	.	PUNCT
cana-858	118	1	4.conclusion	4.conclusion	NUM
cana-858	118	2	the	the	DET
cana-858	118	3	purpose	purpose	NOUN
cana-858	118	4	of	of	ADP
cana-858	118	5	this	this	DET
cana-858	118	6	study	study	NOUN
cana-858	118	7	is	be	AUX
cana-858	118	8	to	to	PART
cana-858	118	9	define	define	VERB
cana-858	118	10	a	a	DET
cana-858	118	11	novel	novel	ADJ
cana-858	118	12	class	class	NOUN
cana-858	118	13	called	call	VERB
cana-858	118	14	(	(	PUNCT
cana-858	118	15	ℕα̌closed	ℕα̌close	VERB
cana-858	118	16	and	and	CCONJ
cana-858	118	17	ℕα̂open	ℕα̂open	CCONJ
cana-858	118	18	)	)	PUNCT
cana-858	118	19	sets	set	NOUN
cana-858	118	20	in	in	ADP
cana-858	118	21	nanotopological	nanotopological	ADJ
cana-858	118	22	spaces	space	NOUN
cana-858	118	23	and	and	CCONJ
cana-858	118	24	to	to	PART
cana-858	118	25	demonstrate	demonstrate	VERB
cana-858	118	26	its	its	PRON
cana-858	118	27	verifiable	verifiable	ADJ
cana-858	118	28	characteristics	characteristic	NOUN
cana-858	118	29	and	and	CCONJ
cana-858	118	30	theorems	theorem	NOUN
cana-858	118	31	.	.	PUNCT
cana-858	119	1	the	the	DET
cana-858	119	2	(	(	PUNCT
cana-858	119	3	𝛽	𝛽	PROPN
cana-858	119	4	,	,	PUNCT
cana-858	119	5	b	b	NOUN
cana-858	119	6	,	,	PUNCT
cana-858	119	7	regular	regular	ADJ
cana-858	119	8	,	,	PUNCT
cana-858	119	9	and	and	CCONJ
cana-858	119	10	semi	semi	ADJ
cana-858	119	11	)	)	PUNCT
cana-858	119	12	sets	set	NOUN
cana-858	119	13	can	can	AUX
cana-858	119	14	be	be	AUX
cana-858	119	15	included	include	VERB
cana-858	119	16	in	in	ADP
cana-858	119	17	the	the	DET
cana-858	119	18	future	future	ADJ
cana-858	119	19	generalization	generalization	NOUN
cana-858	119	20	of	of	ADP
cana-858	119	21	the	the	DET
cana-858	119	22	new	new	ADJ
cana-858	119	23	concept	concept	NOUN
cana-858	119	24	.	.	PUNCT
cana-858	120	1	communications	communication	NOUN
cana-858	120	2	on	on	ADP
cana-858	120	3	applied	apply	VERB
cana-858	120	4	nonlinear	nonlinear	ADJ
cana-858	120	5	analysis	analysis	NOUN
cana-858	120	6	issn	issn	NOUN
cana-858	120	7	:	:	PUNCT
cana-858	120	8	1074	1074	NUM
cana-858	120	9	-	-	PUNCT
cana-858	120	10	133x	133x	NUM
cana-858	120	11	vol	vol	NOUN
cana-858	120	12	31	31	NUM
cana-858	120	13	no	no	NOUN
cana-858	120	14	.	.	PUNCT
cana-858	121	1	4s	4s	NUM
cana-858	121	2	(	(	PUNCT
cana-858	121	3	2024	2024	NUM
cana-858	121	4	)	)	PUNCT
cana-858	121	5	361	361	NUM
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cana-858	122	2	references	reference	NOUN
cana-858	122	3	[	[	X
cana-858	122	4	1	1	NUM
cana-858	122	5	]	]	PUNCT
cana-858	122	6	abdulaziz	abdulaziz	ADJ
cana-858	122	7	.s	.s	PROPN
cana-858	122	8	.	.	PUNCT
cana-858	123	1	hameed	hameed	PROPN
cana-858	123	2	,	,	PUNCT
cana-858	123	3	,	,	PUNCT
cana-858	123	4	nabila	nabila	PROPN
cana-858	123	5	i.	i.	PROPN
cana-858	123	6	aziz	aziz	PROPN
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cana-858	123	8	siham	siham	PROPN
cana-858	123	9	i.	i.	PROPN
cana-858	123	10	aziz	aziz	PROPN
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cana-858	123	12	inside	inside	ADV
cana-858	123	13	of	of	ADP
cana-858	123	14	nano	nano	NOUN
cana-858	123	15	topological	topological	ADJ
cana-858	123	16	spaces	space	NOUN
cana-858	123	17	a	a	DET
cana-858	123	18	novel	novel	NOUN
cana-858	123	19	generalized	generalize	VERB
cana-858	123	20	open	open	ADJ
cana-858	123	21	and	and	CCONJ
cana-858	123	22	closed	close	VERB
cana-858	123	23	nano	nano	NOUN
cana-858	123	24	operators	operator	NOUN
cana-858	123	25	,	,	PUNCT
cana-858	123	26	under	under	ADP
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cana-858	123	28	[	[	X
cana-858	123	29	2	2	NUM
cana-858	123	30	]	]	X
cana-858	123	31	kalavathi	kalavathi	NOUN
cana-858	123	32	,	,	PUNCT
cana-858	123	33	a.	a.	NOUN
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cana-858	123	42	closed	closed	ADJ
cana-858	123	43	and	and	CCONJ
cana-858	123	44	soft	soft	ADJ
cana-858	123	45	g	g	NOUN
cana-858	123	46	*	*	PUNCT
cana-858	123	47	open	open	ADJ
cana-858	123	48	sets	set	NOUN
cana-858	123	49	in	in	ADP
cana-858	123	50	soft	soft	ADJ
cana-858	123	51	topological	topological	ADJ
cana-858	123	52	spaces	space	NOUN
cana-858	123	53	.	.	PUNCT
cana-858	124	1	journal	journal	NOUN
cana-858	124	2	of	of	ADP
cana-858	124	3	interdisciplinary	interdisciplinary	ADJ
cana-858	124	4	mathematics	mathematic	NOUN
cana-858	124	5	,	,	PUNCT
cana-858	124	6	19(1	19(1	NUM
cana-858	124	7	)	)	PUNCT
cana-858	124	8	,	,	PUNCT
cana-858	124	9	65	65	NUM
cana-858	124	10	-	-	SYM
cana-858	124	11	82	82	NUM
cana-858	124	12	,	,	PUNCT
cana-858	124	13	https://doi.org/10.1080/09720502.2015.1103110	https://doi.org/10.1080/09720502.2015.1103110	PROPN
cana-858	124	14	,	,	PUNCT
cana-858	124	15	(	(	PUNCT
cana-858	124	16	2016	2016	NUM
cana-858	124	17	)	)	PUNCT
cana-858	124	18	.	.	PUNCT
cana-858	125	1	[	[	X
cana-858	125	2	3	3	X
cana-858	125	3	]	]	X
cana-858	125	4	narmatha	narmatha	PROPN
cana-858	125	5	s.	s.	PROPN
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cana-858	125	7	harshitha	harshitha	PROPN
cana-858	125	8	s.	s.	PROPN
cana-858	125	9	,	,	PUNCT
cana-858	125	10	kaaviya	kaaviya	PROPN
cana-858	125	11	p.	p.	PROPN
cana-858	125	12	,	,	PUNCT
cana-858	125	13	harshini	harshini	PROPN
cana-858	125	14	r.	r.	PROPN
cana-858	125	15	,	,	PUNCT
cana-858	125	16	indhuja	indhuja	PROPN
cana-858	125	17	s.	s.	PROPN
cana-858	125	18	.(2021	.(2021	PROPN
cana-858	125	19	)	)	PUNCT
cana-858	125	20	.	.	PUNCT
cana-858	126	1	"	"	PUNCT
cana-858	126	2	on	on	ADP
cana-858	126	3	generalizd	generalizd	PROPN
cana-858	126	4	α	α	DET
cana-858	126	5	regular	regular	ADJ
cana-858	126	6	-	-	PUNCT
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cana-858	126	8	set	set	NOUN
cana-858	126	9	in	in	ADP
cana-858	126	10	nano	nano	NOUN
cana-858	126	11	topoloical	topoloical	ADJ
cana-858	126	12	spaces".jour	spaces".jour	PROPN
cana-858	126	13	.	.	PUNCT
cana-858	127	1	nat	nat	PROPN
cana-858	127	2	.	.	PUNCT
cana-858	128	1	volatiles	volatile	NOUN
cana-858	128	2	&	&	CCONJ
cana-858	128	3	essent	essent	NOUN
cana-858	128	4	.	.	PUNCT
cana-858	129	1	oils	oil	NOUN
cana-858	129	2	.	.	PUNCT
cana-858	130	1	no.8	no.8	NOUN
cana-858	130	2	.	.	PUNCT
cana-858	131	1	vol.5,pp	vol.5,pp	NOUN
cana-858	131	2	.	.	PUNCT
cana-858	132	1	5057	5057	NUM
cana-858	132	2	–	–	PUNCT
cana-858	132	3	5061	5061	NUM
cana-858	132	4	.	.	PUNCT
cana-858	133	1	[	[	X
cana-858	133	2	4	4	NUM
cana-858	133	3	]	]	X
cana-858	133	4	rajasekaran	rajasekaran	NOUN
cana-858	133	5	i.	i.	NOUN
cana-858	133	6	,	,	PUNCT
cana-858	133	7	nethaji	nethaji	PROPN
cana-858	133	8	o.	o.	NOUN
cana-858	133	9	and	and	CCONJ
cana-858	133	10	sajan	sajan	PROPN
cana-858	133	11	joseph	joseph	PROPN
cana-858	133	12	m.	m.	PROPN
cana-858	133	13	"	"	PUNCT
cana-858	133	14	.	.	PUNCT
cana-858	134	1	(	(	PUNCT
cana-858	134	2	2018	2018	NUM
cana-858	134	3	)	)	PUNCT
cana-858	134	4	.	.	PUNCT
cana-858	135	1	on	on	ADP
cana-858	135	2	nano	nano	ADJ
cana-858	135	3	πgβ	πgβ	NOUN
cana-858	135	4	-	-	PUNCT
cana-858	135	5	closed	close	VERB
cana-858	135	6	sets	set	NOUN
cana-858	135	7	.	.	PUNCT
cana-858	135	8	"	"	PUNCT
cana-858	135	9	global	global	ADJ
cana-858	135	10	journal	journal	NOUN
cana-858	135	11	of	of	ADP
cana-858	135	12	pure	pure	ADJ
cana-858	135	13	and	and	CCONJ
cana-858	135	14	applied	applied	ADJ
cana-858	135	15	mathematics	mathematics	PROPN
cana-858	135	16	no.1.vol	no.1.vol	PROPN
cana-858	135	17	.	.	PROPN
cana-858	135	18	14	14	NUM
cana-858	135	19	,	,	PUNCT
cana-858	135	20	pp	pp	ADJ
cana-858	135	21	.	.	PUNCT
cana-858	136	1	181	181	NUM
cana-858	136	2	-	-	SYM
cana-858	136	3	187	187	NUM
cana-858	136	4	.	.	PUNCT
cana-858	137	1	[	[	X
cana-858	137	2	5	5	NUM
cana-858	137	3	]	]	X
cana-858	137	4	rajendran	rajendran	NOUN
cana-858	137	5	v.	v.	ADV
cana-858	137	6	,	,	PUNCT
cana-858	137	7	sathish	sathish	PROPN
cana-858	137	8	mohan	mohan	PROPN
cana-858	137	9	p.	p.	PROPN
cana-858	137	10	and	and	CCONJ
cana-858	137	11	chitra	chitra	PROPN
cana-858	137	12	m.(2020	m.(2020	PROPN
cana-858	137	13	)	)	PUNCT
cana-858	137	14	.	.	PUNCT
cana-858	137	15	"	"	PUNCT
cana-858	138	1	on	on	ADP
cana-858	138	2	ng∗α−	ng∗α−	ADJ
cana-858	138	3	closed	close	VERB
cana-858	138	4	sets	set	NOUN
cana-858	138	5	in	in	ADP
cana-858	138	6	nano	nano	ADJ
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cana-858	138	8	spaces	space	NOUN
cana-858	138	9	.	.	PUNCT
cana-858	138	10	"	"	PUNCT
cana-858	138	11	journal	journal	NOUN
cana-858	138	12	of	of	ADP
cana-858	138	13	critical	critical	ADJ
cana-858	138	14	reviews	review	NOUN
cana-858	138	15	.	.	PUNCT
cana-858	139	1	no.13.vol.7	no.13.vol.7	ADJ
cana-858	139	2	,	,	PUNCT
cana-858	139	3	pp	pp	ADJ
cana-858	139	4	.	.	PUNCT
cana-858	140	1	4121	4121	NUM
cana-858	140	2	-	-	SYM
cana-858	140	3	4127	4127	NUM
cana-858	140	4	.	.	PUNCT
cana-858	141	1	[	[	X
cana-858	141	2	6	6	NUM
cana-858	141	3	]	]	PUNCT
cana-858	141	4	s.	s.	PROPN
cana-858	141	5	bhattacharya	bhattacharya	PROPN
cana-858	141	6	.	.	PUNCT
cana-858	142	1	on	on	ADP
cana-858	142	2	generalized	generalized	ADJ
cana-858	142	3	regular	regular	ADJ
cana-858	142	4	closed	closed	ADJ
cana-858	142	5	sets	set	NOUN
cana-858	142	6	.	.	PUNCT
cana-858	143	1	contemp	contemp	NOUN
cana-858	143	2	.	.	PUNCT
cana-858	144	1	math	math	NOUN
cana-858	144	2	.	.	PUNCT
cana-858	145	1	sciences	science	NOUN
cana-858	145	2	,	,	PUNCT
cana-858	145	3	6(3),pp	6(3),pp	NUM
cana-858	145	4	.	.	PUNCT
cana-858	146	1	145	145	NUM
cana-858	146	2	-	-	SYM
cana-858	146	3	152	152	NUM
cana-858	146	4	,	,	PUNCT
cana-858	146	5	(	(	PUNCT
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cana-858	146	7	)	)	PUNCT
cana-858	146	8	.	.	PUNCT
cana-858	147	1	[	[	X
cana-858	147	2	7	7	X
cana-858	147	3	]	]	X
cana-858	147	4	s.	s.	PROPN
cana-858	147	5	g.	g.	PROPN
cana-858	147	6	crossley	crossley	PROPN
cana-858	147	7	and	and	CCONJ
cana-858	147	8	s.	s.	PROPN
cana-858	147	9	k.	k.	PROPN
cana-858	147	10	hildebrand	hildebrand	PROPN
cana-858	147	11	,	,	PUNCT
cana-858	147	12	''	''	PUNCT
cana-858	147	13	semi	semi	ADJ
cana-858	147	14	-	-	ADJ
cana-858	147	15	closure	closure	ADJ
cana-858	147	16	''	''	PUNCT
cana-858	147	17	,	,	PUNCT
cana-858	147	18	teψas	teψas	PROPN
cana-858	147	19	j.	j.	PROPN
cana-858	147	20	sci	sci	PROPN
cana-858	147	21	.	.	PROPN
cana-858	147	22	,	,	PUNCT
cana-858	147	23	22	22	NUM
cana-858	147	24	,	,	PUNCT
cana-858	147	25	99–112	99–112	NUM
cana-858	147	26	,	,	PUNCT
cana-858	147	27	(	(	PUNCT
cana-858	147	28	1971	1971	NUM
cana-858	147	29	)	)	PUNCT
cana-858	147	30	.	.	PUNCT
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cana-858	148	2	8	8	NUM
cana-858	148	3	]	]	X
cana-858	148	4	mustafa	mustafa	PROPN
cana-858	148	5	,	,	PUNCT
cana-858	148	6	m.a	m.a	PROPN
cana-858	148	7	.	.	PROPN
cana-858	148	8	,	,	PUNCT
cana-858	148	9	kadham	kadham	PROPN
cana-858	148	10	,	,	PUNCT
cana-858	148	11	s.m	s.m	PROPN
cana-858	148	12	.	.	PROPN
cana-858	148	13	,	,	PUNCT
cana-858	148	14	abbass	abbass	PROPN
cana-858	148	15	,	,	PUNCT
cana-858	148	16	n.k	n.k	PROPN
cana-858	148	17	.	.	PROPN
cana-858	148	18	et	et	PROPN
cana-858	148	19	al	al	PROPN
cana-858	148	20	.	.	PUNCT
cana-858	149	1	a	a	DET
cana-858	149	2	novel	novel	ADJ
cana-858	149	3	fuzzy	fuzzy	ADJ
cana-858	149	4	m	m	NOUN
cana-858	149	5	-	-	PUNCT
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cana-858	149	7	technique	technique	NOUN
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cana-858	149	10	ground	ground	NOUN
cana-858	149	11	water	water	NOUN
cana-858	149	12	level	level	NOUN
cana-858	149	13	prediction	prediction	NOUN
cana-858	149	14	.	.	PUNCT
cana-858	150	1	appl	appl	PROPN
cana-858	150	2	geomat	geomat	PROPN
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cana-858	150	4	,	,	PUNCT
cana-858	150	5	9–15	9–15	PROPN
cana-858	150	6	(	(	PUNCT
cana-858	150	7	2024	2024	NUM
cana-858	150	8	)	)	PUNCT
cana-858	150	9	.	.	PUNCT
cana-858	151	1	https://doi.org/10.1007/s12518-022-00486-4	https://doi.org/10.1007/s12518-022-00486-4	NUM
cana-858	151	2	)	)	PUNCT
cana-858	152	1	[	[	X
cana-858	152	2	9	9	NUM
cana-858	152	3	]	]	PUNCT
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cana-858	152	5	i.	i.	PROPN
cana-858	152	6	aziz	aziz	PROPN
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cana-858	152	8	nabila	nabila	PROPN
cana-858	152	9	i.	i.	PROPN
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cana-858	152	13	some	some	DET
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cana-858	152	15	recent	recent	ADJ
cana-858	152	16	operators	operator	NOUN
cana-858	152	17	in	in	ADP
cana-858	152	18	topological	topological	ADJ
cana-858	152	19	spaces	space	NOUN
cana-858	152	20	.	.	PUNCT
cana-858	153	1	tikrit	tikrit	NOUN
cana-858	153	2	journal	journal	NOUN
cana-858	153	3	of	of	ADP
cana-858	153	4	pure	pure	ADJ
cana-858	153	5	science	science	NOUN
cana-858	153	6	,	,	PUNCT
cana-858	153	7	vol	vol	NOUN
cana-858	153	8	.	.	PROPN
cana-858	153	9	27	27	NUM
cana-858	153	10	(	(	PUNCT
cana-858	153	11	4	4	NUM
cana-858	153	12	)	)	PUNCT
cana-858	153	13	,	,	PUNCT
cana-858	153	14	(	(	PUNCT
cana-858	153	15	2022	2022	NUM
cana-858	153	16	)	)	PUNCT
cana-858	154	1	[	[	X
cana-858	154	2	10	10	NUM
cana-858	154	3	]	]	X
cana-858	154	4	kadham	kadham	PROPN
cana-858	154	5	,	,	PUNCT
cana-858	154	6	s.m	s.m	PROPN
cana-858	154	7	.	.	PROPN
cana-858	154	8	acute	acute	PROPN
cana-858	154	9	interstitial	interstitial	ADJ
cana-858	154	10	pneumonia	pneumonia	NOUN
cana-858	154	11	image	image	NOUN
cana-858	154	12	enhancement	enhancement	NOUN
cana-858	154	13	using	use	VERB
cana-858	154	14	fuzzy	fuzzy	ADJ
cana-858	154	15	partial	partial	ADJ
cana-858	154	16	transforms	transform	NOUN
cana-858	154	17	.	.	PUNCT
cana-858	155	1	appl	appl	PROPN
cana-858	155	2	geomat	geomat	PROPN
cana-858	155	3	16	16	NUM
cana-858	155	4	,	,	PUNCT
cana-858	155	5	35–39	35–39	NUM
cana-858	155	6	(	(	PUNCT
cana-858	155	7	2024	2024	NUM
cana-858	155	8	)	)	PUNCT
cana-858	155	9	.	.	PUNCT
cana-858	156	1	https://doi.org/10.1007/s12518-023-00509-8	https://doi.org/10.1007/s12518-023-00509-8	NUM
cana-858	157	1	[	[	X
cana-858	157	2	11	11	NUM
cana-858	157	3	]	]	PUNCT
cana-858	157	4	siham	siham	PROPN
cana-858	157	5	i.	i.	PROPN
cana-858	157	6	aziz	aziz	PROPN
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cana-858	157	8	nabila	nabila	PROPN
cana-858	157	9	i	i	PRON
cana-858	157	10	.	.	PUNCT
cana-858	158	1	aziz	aziz	PROPN
cana-858	158	2	,	,	PUNCT
cana-858	158	3	new	new	ADJ
cana-858	158	4	generalized	generalized	ADJ
cana-858	158	5	operator	operator	NOUN
cana-858	158	6	in	in	ADP
cana-858	158	7	topological	topological	ADJ
cana-858	158	8	spaces	space	NOUN
cana-858	158	9	.	.	PUNCT
cana-858	159	1	v.	v.	ADP
cana-858	159	2	international	international	ADJ
cana-858	159	3	scientific	scientific	ADJ
cana-858	159	4	congress	congress	NOUN
cana-858	159	5	of	of	ADP
cana-858	159	6	pure	pure	ADJ
cana-858	159	7	,	,	PUNCT
cana-858	159	8	applied	applied	ADJ
cana-858	159	9	and	and	CCONJ
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cana-858	159	12	)	)	PUNCT
cana-858	159	13	.	.	PUNCT
cana-858	160	1	[	[	X
cana-858	160	2	12	12	NUM
cana-858	160	3	]	]	PUNCT
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cana-858	160	5	m.	m.	NOUN
cana-858	160	6	lellis	lellis	PROPN
cana-858	160	7	,	,	PUNCT
cana-858	160	8	carmel	carmel	PROPN
cana-858	160	9	rechard	rechard	NOUN
cana-858	160	10	,	,	PUNCT
cana-858	160	11	note	note	NOUN
cana-858	160	12	on	on	ADP
cana-858	160	13	nano	nano	NOUN
cana-858	160	14	topological	topological	ADJ
cana-858	160	15	space	space	NOUN
cana-858	160	16	,	,	PUNCT
cana-858	160	17	communicated	communicate	VERB
cana-858	160	18	,	,	PUNCT
cana-858	160	19	(	(	PUNCT
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cana-858	160	21	)	)	PUNCT
cana-858	160	22	.	.	PUNCT
cana-858	161	1	[	[	X
cana-858	161	2	13	13	NUM
cana-858	161	3	]	]	SYM
cana-858	161	4	thivagar	thivagar	NOUN
cana-858	161	5	,	,	PUNCT
cana-858	161	6	m.l	m.l	PROPN
cana-858	161	7	.	.	PROPN
cana-858	161	8	,	,	PUNCT
cana-858	161	9	richard	richard	PROPN
cana-858	161	10	,	,	PUNCT
cana-858	161	11	c.	c.	PROPN
cana-858	161	12	,	,	PUNCT
cana-858	161	13	on	on	ADP
cana-858	161	14	nano	nano	NOUN
cana-858	161	15	forms	form	NOUN
cana-858	161	16	of	of	ADP
cana-858	161	17	weakly	weakly	ADJ
cana-858	161	18	open	open	ADJ
cana-858	161	19	sets	set	NOUN
cana-858	161	20	,	,	PUNCT
cana-858	161	21	int	int	NOUN
cana-858	161	22	.	.	PUNCT
cana-858	162	1	j.	j.	PROPN
cana-858	162	2	math	math	PROPN
cana-858	162	3	statistics	statistics	PROPN
cana-858	162	4	invention	invention	NOUN
cana-858	162	5	,	,	PUNCT
cana-858	162	6	1(1	1(1	NUM
cana-858	162	7	)	)	PUNCT
cana-858	162	8	,	,	PUNCT
cana-858	162	9	31	31	NUM
cana-858	162	10	-	-	SYM
cana-858	162	11	37	37	NUM
cana-858	162	12	,	,	PUNCT
cana-858	162	13	2013	2013	NUM
cana-858	162	14	.	.	PUNCT
cana-858	163	1	[	[	X
cana-858	163	2	14	14	NUM
cana-858	163	3	]	]	X
cana-858	163	4	w.	w.	PROPN
cana-858	163	5	dunham	dunham	PROPN
cana-858	163	6	,	,	PUNCT
cana-858	163	7	''	''	PUNCT
cana-858	163	8	a	a	DET
cana-858	163	9	new	new	ADJ
cana-858	163	10	closure	closure	NOUN
cana-858	163	11	operator	operator	NOUN
cana-858	163	12	for	for	ADP
cana-858	163	13	non	non	NOUN
cana-858	163	14	-	-	ADJ
cana-858	163	15	t1topologies	t1topologie	NOUN
cana-858	163	16	''	''	PUNCT
cana-858	163	17	,	,	PUNCT
cana-858	163	18	kyungpook	kyungpook	NOUN
cana-858	163	19	,	,	PUNCT
cana-858	163	20	math.j	math.j	ADJ
cana-858	163	21	"	"	PUNCT
cana-858	163	22	.	.	PUNCT
cana-858	164	1	22	22	NUM
cana-858	164	2	,	,	PUNCT
cana-858	164	3	55	55	NUM
cana-858	164	4	-	-	SYM
cana-858	164	5	602009	602009	NUM
cana-858	164	6	,	,	PUNCT
cana-858	164	7	(	(	PUNCT
cana-858	164	8	1982	1982	NUM
cana-858	164	9	)	)	PUNCT
cana-858	164	10	.	.	PUNCT