id	sid	tid	token	lemma	pos
cana-2873	1	1	communications	communication	NOUN
cana-2873	1	2	on	on	ADP
cana-2873	1	3	applied	apply	VERB
cana-2873	1	4	nonlinear	nonlinear	ADJ
cana-2873	1	5	analysis	analysis	NOUN
cana-2873	1	6	issn	issn	NOUN
cana-2873	1	7	:	:	PUNCT
cana-2873	1	8	1074	1074	NUM
cana-2873	1	9	-	-	PUNCT
cana-2873	1	10	133x	133x	NUM
cana-2873	1	11	vol	vol	NOUN
cana-2873	1	12	32	32	NUM
cana-2873	1	13	no	no	NOUN
cana-2873	1	14	.	.	PUNCT
cana-2873	2	1	4s	4s	NUM
cana-2873	2	2	(	(	PUNCT
cana-2873	2	3	2025	2025	NUM
cana-2873	2	4	)	)	PUNCT
cana-2873	2	5	580	580	NUM
cana-2873	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	2	7	more	more	ADV
cana-2873	2	8	on	on	ADP
cana-2873	2	9	contra	contra	PROPN
cana-2873	2	10	β	β	NOUN
cana-2873	2	11	-	-	ADJ
cana-2873	2	12	open	open	ADJ
cana-2873	2	13	mappings	mapping	NOUN
cana-2873	2	14	in	in	ADP
cana-2873	2	15	a	a	DET
cana-2873	2	16	quadripartitioned	quadripartitione	VERB
cana-2873	2	17	neutrosophic	neutrosophic	ADJ
cana-2873	2	18	topological	topological	ADJ
cana-2873	2	19	spaces	space	NOUN
cana-2873	2	20	1mohanarao	1mohanarao	NUM
cana-2873	2	21	navuluri	navuluri	PROPN
cana-2873	2	22	,	,	PUNCT
cana-2873	2	23	2v	2v	PROPN
cana-2873	2	24	sathishkumar	sathishkumar	PROPN
cana-2873	2	25	1department	1department	PROPN
cana-2873	2	26	of	of	ADP
cana-2873	2	27	mathematics	mathematics	PROPN
cana-2873	2	28	,	,	PUNCT
cana-2873	2	29	annamalai	annamalai	PROPN
cana-2873	2	30	university	university	PROPN
cana-2873	2	31	,	,	PUNCT
cana-2873	2	32	annamalainagar	annamalainagar	NOUN
cana-2873	2	33	,	,	PUNCT
cana-2873	2	34	tamilnadu	tamilnadu	NOUN
cana-2873	2	35	,	,	PUNCT
cana-2873	2	36	india	india	PROPN
cana-2873	2	37	.	.	PUNCT
cana-2873	3	1	(	(	PUNCT
cana-2873	3	2	deputed	depute	VERB
cana-2873	3	3	to	to	ADP
cana-2873	3	4	government	government	NOUN
cana-2873	3	5	college	college	NOUN
cana-2873	3	6	of	of	ADP
cana-2873	3	7	engineering	engineering	NOUN
cana-2873	3	8	,	,	PUNCT
cana-2873	3	9	theni	theni	NOUN
cana-2873	3	10	,	,	PUNCT
cana-2873	3	11	tamilnadu	tamilnadu	NOUN
cana-2873	3	12	,	,	PUNCT
cana-2873	3	13	india	india	PROPN
cana-2873	3	14	.	.	PUNCT
cana-2873	3	15	)	)	PUNCT
cana-2873	4	1	2department	2department	NUM
cana-2873	4	2	of	of	ADP
cana-2873	4	3	mathematics	mathematic	NOUN
cana-2873	4	4	,	,	PUNCT
cana-2873	4	5	rajalakshmi	rajalakshmi	PROPN
cana-2873	4	6	institute	institute	PROPN
cana-2873	4	7	of	of	ADP
cana-2873	4	8	technology	technology	PROPN
cana-2873	4	9	(	(	PUNCT
cana-2873	4	10	autonomous	autonomous	ADJ
cana-2873	4	11	)	)	PUNCT
cana-2873	4	12	,	,	PUNCT
cana-2873	4	13	chennai	chennai	PROPN
cana-2873	4	14	;	;	PUNCT
cana-2873	4	15	department	department	NOUN
cana-2873	4	16	of	of	ADP
cana-2873	4	17	mathematics	mathematics	PROPN
cana-2873	4	18	,	,	PUNCT
cana-2873	4	19	annamalai	annamalai	PROPN
cana-2873	4	20	university	university	PROPN
cana-2873	4	21	,	,	PUNCT
cana-2873	4	22	annamalainagar	annamalainagar	NOUN
cana-2873	4	23	,	,	PUNCT
cana-2873	4	24	tamilnadu	tamilnadu	NOUN
cana-2873	4	25	,	,	PUNCT
cana-2873	4	26	india	india	PROPN
cana-2873	4	27	.	.	PUNCT
cana-2873	5	1	mohanaraonavuluri@gmail.com1	mohanaraonavuluri@gmail.com1	PROPN
cana-2873	5	2	,	,	PUNCT
cana-2873	5	3	vsathishkumar2020@gmail.com2	vsathishkumar2020@gmail.com2	ADP
cana-2873	5	4	article	article	NOUN
cana-2873	5	5	history	history	NOUN
cana-2873	5	6	:	:	PUNCT
cana-2873	5	7	received	receive	VERB
cana-2873	5	8	:	:	PUNCT
cana-2873	5	9	01	01	NUM
cana-2873	5	10	-	-	SYM
cana-2873	5	11	10	10	NUM
cana-2873	5	12	-	-	PUNCT
cana-2873	5	13	2024	2024	NUM
cana-2873	5	14	revised	revise	VERB
cana-2873	5	15	:	:	PUNCT
cana-2873	5	16	29	29	NUM
cana-2873	5	17	-	-	SYM
cana-2873	5	18	11	11	NUM
cana-2873	5	19	-	-	PUNCT
cana-2873	5	20	2024	2024	NUM
cana-2873	5	21	accepted	accept	VERB
cana-2873	5	22	:	:	PUNCT
cana-2873	5	23	07	07	NUM
cana-2873	5	24	-	-	SYM
cana-2873	5	25	12	12	NUM
cana-2873	5	26	-	-	PUNCT
cana-2873	5	27	2024	2024	NUM
cana-2873	5	28	abstract	abstract	NOUN
cana-2873	5	29	in	in	ADP
cana-2873	5	30	this	this	DET
cana-2873	5	31	article	article	NOUN
cana-2873	5	32	,	,	PUNCT
cana-2873	5	33	we	we	PRON
cana-2873	5	34	introduce	introduce	VERB
cana-2873	5	35	the	the	DET
cana-2873	5	36	concept	concept	NOUN
cana-2873	5	37	of	of	ADP
cana-2873	5	38	a	a	DET
cana-2873	5	39	quadripartitioned	quadripartitione	VERB
cana-2873	5	40	neutrosophic	neutrosophic	PROPN
cana-2873	5	41	contra	contra	PROPN
cana-2873	5	42	βcontinuous	βcontinuous	PROPN
cana-2873	5	43	,	,	PUNCT
cana-2873	5	44	quadripartitioned	quadripartitione	VERB
cana-2873	5	45	neutrosophic	neutrosophic	PROPN
cana-2873	5	46	contra	contra	PROPN
cana-2873	5	47	β	β	X
cana-2873	5	48	-	-	VERB
cana-2873	5	49	open	open	ADJ
cana-2873	5	50	and	and	CCONJ
cana-2873	5	51	a	a	DET
cana-2873	5	52	quadripartitioned	quadripartitione	VERB
cana-2873	5	53	neutrosophic	neutrosophic	PROPN
cana-2873	5	54	contra	contra	PROPN
cana-2873	5	55	β	β	PROPN
cana-2873	5	56	-	-	PUNCT
cana-2873	5	57	closed	close	VERB
cana-2873	5	58	mappings	mapping	NOUN
cana-2873	5	59	in	in	ADP
cana-2873	5	60	a	a	DET
cana-2873	5	61	quadripartitioned	quadripartitione	VERB
cana-2873	5	62	neutrosophic	neutrosophic	ADJ
cana-2873	5	63	topological	topological	ADJ
cana-2873	5	64	spaces	space	NOUN
cana-2873	5	65	and	and	CCONJ
cana-2873	5	66	studied	study	VERB
cana-2873	5	67	some	some	PRON
cana-2873	5	68	of	of	ADP
cana-2873	5	69	their	their	PRON
cana-2873	5	70	related	related	ADJ
cana-2873	5	71	properties	property	NOUN
cana-2873	5	72	.	.	PUNCT
cana-2873	6	1	further	far	ADV
cana-2873	6	2	the	the	DET
cana-2873	6	3	work	work	NOUN
cana-2873	6	4	is	be	AUX
cana-2873	6	5	extended	extend	VERB
cana-2873	6	6	to	to	ADP
cana-2873	6	7	a	a	DET
cana-2873	6	8	quadripartitioned	quadripartitione	VERB
cana-2873	6	9	neutrosophic	neutrosophic	PROPN
cana-2873	6	10	contra	contra	PROPN
cana-2873	6	11	β	β	PROPN
cana-2873	6	12	-	-	PUNCT
cana-2873	6	13	homeomorphism	homeomorphism	PROPN
cana-2873	6	14	and	and	CCONJ
cana-2873	6	15	a	a	DET
cana-2873	6	16	quadripartitioned	quadripartitione	VERB
cana-2873	6	17	neutrosophic	neutrosophic	PROPN
cana-2873	6	18	contra	contra	PROPN
cana-2873	6	19	β	β	X
cana-2873	6	20	-	-	PUNCT
cana-2873	6	21	completely	completely	ADV
cana-2873	6	22	homeomorphism	homeomorphism	NOUN
cana-2873	6	23	in	in	ADP
cana-2873	6	24	a	a	DET
cana-2873	6	25	quadripartitioned	quadripartitione	VERB
cana-2873	6	26	neutrosophic	neutrosophic	ADJ
cana-2873	6	27	topological	topological	ADJ
cana-2873	6	28	spaces	space	NOUN
cana-2873	6	29	and	and	CCONJ
cana-2873	6	30	establishes	establish	VERB
cana-2873	6	31	some	some	PRON
cana-2873	6	32	of	of	ADP
cana-2873	6	33	their	their	PRON
cana-2873	6	34	related	related	ADJ
cana-2873	6	35	properties	property	NOUN
cana-2873	6	36	.	.	PUNCT
cana-2873	7	1	keywords	keyword	NOUN
cana-2873	7	2	:	:	PUNCT
cana-2873	7	3	quadripartitioned	quadripartitione	VERB
cana-2873	7	4	neutrosophic	neutrosophic	ADJ
cana-2873	7	5	β	β	X
cana-2873	7	6	-	-	ADJ
cana-2873	7	7	open	open	ADJ
cana-2873	7	8	set	set	NOUN
cana-2873	7	9	,	,	PUNCT
cana-2873	7	10	quadripartitioned	quadripartitione	VERB
cana-2873	7	11	neutrosophic	neutrosophic	PROPN
cana-2873	7	12	contra	contra	PROPN
cana-2873	7	13	β	β	PROPN
cana-2873	7	14	-	-	ADJ
cana-2873	7	15	continuous	continuous	ADJ
cana-2873	7	16	map	map	NOUN
cana-2873	7	17	,	,	PUNCT
cana-2873	7	18	quadripartitioned	quadripartitione	VERB
cana-2873	7	19	neutrosophic	neutrosophic	PROPN
cana-2873	7	20	contra	contra	PROPN
cana-2873	7	21	β	β	PROPN
cana-2873	7	22	-	-	ADJ
cana-2873	7	23	open	open	ADJ
cana-2873	7	24	map	map	NOUN
cana-2873	7	25	,	,	PUNCT
cana-2873	7	26	quadripartitioned	quadripartitione	VERB
cana-2873	7	27	neutrosophic	neutrosophic	PROPN
cana-2873	7	28	contra	contra	PROPN
cana-2873	7	29	β	β	PROPN
cana-2873	7	30	-	-	PUNCT
cana-2873	7	31	closed	closed	ADJ
cana-2873	7	32	map	map	NOUN
cana-2873	7	33	,	,	PUNCT
cana-2873	7	34	quadripartitioned	quadripartitione	VERB
cana-2873	7	35	neutrosophic	neutrosophic	PROPN
cana-2873	7	36	contra	contra	PROPN
cana-2873	7	37	β	β	PROPN
cana-2873	7	38	-	-	PUNCT
cana-2873	7	39	homeomorphism	homeomorphism	PROPN
cana-2873	7	40	,	,	PUNCT
cana-2873	7	41	quadripartitioned	quadripartitione	VERB
cana-2873	7	42	neutrosophic	neutrosophic	PROPN
cana-2873	7	43	contra	contra	PROPN
cana-2873	7	44	βcompletely	βcompletely	ADV
cana-2873	7	45	homeomorphism	homeomorphism	X
cana-2873	7	46	.	.	PUNCT
cana-2873	8	1	1	1	NUM
cana-2873	8	2	introduction	introduction	NOUN
cana-2873	8	3	in	in	ADP
cana-2873	8	4	mathematics	mathematic	NOUN
cana-2873	8	5	,	,	PUNCT
cana-2873	8	6	zadeh25	zadeh25	PROPN
cana-2873	8	7	was	be	AUX
cana-2873	8	8	first	first	ADV
cana-2873	8	9	presented	present	VERB
cana-2873	8	10	a	a	DET
cana-2873	8	11	idea	idea	NOUN
cana-2873	8	12	of	of	ADP
cana-2873	8	13	fuzzy	fuzzy	ADJ
cana-2873	8	14	set	set	NOUN
cana-2873	8	15	between	between	ADP
cana-2873	8	16	the	the	DET
cana-2873	8	17	intervals	interval	NOUN
cana-2873	8	18	in	in	ADP
cana-2873	8	19	order	order	NOUN
cana-2873	8	20	of	of	ADP
cana-2873	8	21	logic	logic	NOUN
cana-2873	8	22	and	and	CCONJ
cana-2873	8	23	set	set	VERB
cana-2873	8	24	hypothesis	hypothesis	NOUN
cana-2873	8	25	.	.	PUNCT
cana-2873	9	1	the	the	DET
cana-2873	9	2	fuzzy	fuzzy	ADJ
cana-2873	9	3	set	set	NOUN
cana-2873	9	4	was	be	AUX
cana-2873	9	5	attempted	attempt	VERB
cana-2873	9	6	in	in	ADP
cana-2873	9	7	general	general	ADJ
cana-2873	9	8	topology	topology	NOUN
cana-2873	9	9	by	by	ADP
cana-2873	9	10	chang2	chang2	NOUN
cana-2873	9	11	as	as	ADP
cana-2873	9	12	fuzzy	fuzzy	ADJ
cana-2873	9	13	topological	topological	ADJ
cana-2873	9	14	space	space	NOUN
cana-2873	9	15	.	.	PUNCT
cana-2873	10	1	the	the	DET
cana-2873	10	2	intuitionistic	intuitionistic	ADJ
cana-2873	10	3	fuzzy	fuzzy	ADJ
cana-2873	10	4	set	set	NOUN
cana-2873	10	5	which	which	PRON
cana-2873	10	6	contains	contain	VERB
cana-2873	10	7	a	a	DET
cana-2873	10	8	membership	membership	NOUN
cana-2873	10	9	and	and	CCONJ
cana-2873	10	10	non	non	ADJ
cana-2873	10	11	-	-	ADJ
cana-2873	10	12	membership	membership	ADJ
cana-2873	10	13	values	value	NOUN
cana-2873	10	14	was	be	AUX
cana-2873	10	15	introduced	introduce	VERB
cana-2873	10	16	by	by	ADP
cana-2873	10	17	atanassov1	atanassov1	NOUN
cana-2873	10	18	in	in	ADP
cana-2873	10	19	1983	1983	NUM
cana-2873	10	20	.	.	PUNCT
cana-2873	11	1	coker4	coker4	PROPN
cana-2873	11	2	made	make	VERB
cana-2873	11	3	intuitionistic	intuitionistic	ADJ
cana-2873	11	4	fuzzy	fuzzy	ADJ
cana-2873	11	5	set	set	NOUN
cana-2873	11	6	in	in	ADP
cana-2873	11	7	a	a	DET
cana-2873	11	8	topology	topology	NOUN
cana-2873	11	9	entitled	entitle	VERB
cana-2873	11	10	as	as	ADP
cana-2873	11	11	intuitionistic	intuitionistic	ADJ
cana-2873	11	12	fuzzy	fuzzy	ADJ
cana-2873	11	13	topological	topological	ADJ
cana-2873	11	14	spaces	space	NOUN
cana-2873	11	15	.	.	PUNCT
cana-2873	12	1	the	the	DET
cana-2873	12	2	ideas	idea	NOUN
cana-2873	12	3	of	of	ADP
cana-2873	12	4	neutrosophy	neutrosophy	NOUN
cana-2873	12	5	and	and	CCONJ
cana-2873	12	6	neutrosophic	neutrosophic	ADJ
cana-2873	12	7	set	set	NOUN
cana-2873	12	8	was	be	AUX
cana-2873	12	9	presented	present	VERB
cana-2873	12	10	by	by	ADP
cana-2873	12	11	smarandache16,17	smarandache16,17	NOUN
cana-2873	12	12	toward	toward	ADP
cana-2873	12	13	the	the	DET
cana-2873	12	14	start	start	NOUN
cana-2873	12	15	of	of	ADP
cana-2873	12	16	20th	20th	ADJ
cana-2873	12	17	century	century	NOUN
cana-2873	12	18	.	.	PUNCT
cana-2873	13	1	salama	salama	NOUN
cana-2873	13	2	and	and	CCONJ
cana-2873	13	3	alblowi14,15	alblowi14,15	ADJ
cana-2873	13	4	in	in	ADP
cana-2873	13	5	2012	2012	NUM
cana-2873	13	6	,	,	PUNCT
cana-2873	13	7	originated	originate	VERB
cana-2873	13	8	neutrosophic	neutrosophic	ADJ
cana-2873	13	9	set	set	NOUN
cana-2873	13	10	and	and	CCONJ
cana-2873	13	11	neutrosophic	neutrosophic	ADJ
cana-2873	13	12	crisp	crisp	ADJ
cana-2873	13	13	set	set	NOUN
cana-2873	13	14	in	in	ADP
cana-2873	13	15	a	a	DET
cana-2873	13	16	neutrosophic	neutrosophic	ADJ
cana-2873	13	17	topological	topological	ADJ
cana-2873	13	18	space	space	NOUN
cana-2873	13	19	.	.	PUNCT
cana-2873	14	1	in	in	ADP
cana-2873	14	2	the	the	DET
cana-2873	14	3	year	year	NOUN
cana-2873	14	4	2016	2016	NUM
cana-2873	14	5	,	,	PUNCT
cana-2873	14	6	chatterjee	chatterjee	PROPN
cana-2873	14	7	et	et	NOUN
cana-2873	14	8	al.3	al.3	PROPN
cana-2873	14	9	grounded	ground	VERB
cana-2873	14	10	the	the	DET
cana-2873	14	11	idea	idea	NOUN
cana-2873	14	12	of	of	ADP
cana-2873	14	13	quadripartitioned	quadripartitione	VERB
cana-2873	14	14	neutrosophic	neutrosophic	ADJ
cana-2873	14	15	set	set	VERB
cana-2873	14	16	and	and	CCONJ
cana-2873	14	17	defined	define	VERB
cana-2873	14	18	several	several	ADJ
cana-2873	14	19	similarity	similarity	NOUN
cana-2873	14	20	measures	measure	NOUN
cana-2873	14	21	between	between	ADP
cana-2873	14	22	two	two	NUM
cana-2873	14	23	quadripartitioned	quadripartitione	VERB
cana-2873	14	24	neutrosophic	neutrosophic	ADJ
cana-2873	14	25	sets	set	NOUN
cana-2873	14	26	.	.	PUNCT
cana-2873	15	1	iswaraya	iswaraya	NOUN
cana-2873	15	2	and	and	CCONJ
cana-2873	15	3	bageerathi9	bageerathi9	PROPN
cana-2873	15	4	studied	study	VERB
cana-2873	15	5	the	the	DET
cana-2873	15	6	concept	concept	NOUN
cana-2873	15	7	of	of	ADP
cana-2873	15	8	neutrosophic	neutrosophic	ADJ
cana-2873	15	9	semi	semi	ADJ
cana-2873	15	10	-	-	ADJ
cana-2873	15	11	open	open	ADJ
cana-2873	15	12	sets	set	NOUN
cana-2873	15	13	and	and	CCONJ
cana-2873	15	14	neutrosophic	neutrosophic	ADJ
cana-2873	15	15	semi	semi	ADJ
cana-2873	15	16	-	-	ADJ
cana-2873	15	17	closed	closed	ADJ
cana-2873	15	18	sets	set	NOUN
cana-2873	15	19	.	.	PUNCT
cana-2873	16	1	pushpalatha	pushpalatha	NOUN
cana-2873	16	2	and	and	CCONJ
cana-2873	16	3	nandhini12grounded	nandhini12grounde	VERB
cana-2873	16	4	the	the	DET
cana-2873	16	5	idea	idea	NOUN
cana-2873	16	6	of	of	ADP
cana-2873	16	7	neutrosophic	neutrosophic	ADJ
cana-2873	16	8	generalized	generalize	VERB
cana-2873	16	9	closed	close	VERB
cana-2873	16	10	sets	set	NOUN
cana-2873	16	11	in	in	ADP
cana-2873	16	12	nts	nt	NOUN
cana-2873	16	13	’s	’s	PART
cana-2873	16	14	.	.	PUNCT
cana-2873	17	1	the	the	DET
cana-2873	17	2	notion	notion	NOUN
cana-2873	17	3	of	of	ADP
cana-2873	17	4	neutrosophic	neutrosophic	ADJ
cana-2873	17	5	b	b	X
cana-2873	17	6	-	-	PUNCT
cana-2873	17	7	open	open	ADJ
cana-2873	17	8	sets	set	NOUN
cana-2873	17	9	in	in	ADP
cana-2873	17	10	nts	nt	NOUN
cana-2873	17	11	’s	’s	PART
cana-2873	17	12	was	be	AUX
cana-2873	17	13	presented	present	VERB
cana-2873	17	14	by	by	ADP
cana-2873	17	15	ebenanjar	ebenanjar	PROPN
cana-2873	17	16	et	et	PROPN
cana-2873	17	17	al.8	al.8	PROPN
cana-2873	17	18	rao	rao	PROPN
cana-2873	17	19	and	and	CCONJ
cana-2873	17	20	srinivasa13	srinivasa13	NOUN
cana-2873	17	21	grounded	ground	VERB
cana-2873	17	22	the	the	DET
cana-2873	17	23	concept	concept	NOUN
cana-2873	17	24	of	of	ADP
cana-2873	17	25	pre	pre	ADJ
cana-2873	17	26	open	open	ADJ
cana-2873	17	27	set	set	NOUN
cana-2873	17	28	and	and	CCONJ
cana-2873	17	29	pre	pre	VERB
cana-2873	17	30	closed	closed	ADJ
cana-2873	17	31	set	set	VERB
cana-2873	17	32	via	via	ADP
cana-2873	17	33	neutrosophic	neutrosophic	ADJ
cana-2873	17	34	topological	topological	ADJ
cana-2873	17	35	spaces	space	NOUN
cana-2873	17	36	.	.	PUNCT
cana-2873	18	1	thereafter	thereafter	ADV
cana-2873	18	2	,	,	PUNCT
cana-2873	18	3	maheswari	maheswari	PROPN
cana-2873	18	4	et	et	PROPN
cana-2873	18	5	al.10	al.10	PROPN
cana-2873	18	6	studied	study	VERB
cana-2873	18	7	the	the	DET
cana-2873	18	8	neutrosophic	neutrosophic	ADJ
cana-2873	18	9	generalized	generalized	ADJ
cana-2873	18	10	b	b	X
cana-2873	18	11	-	-	PUNCT
cana-2873	18	12	closed	closed	ADJ
cana-2873	18	13	sets	set	NOUN
cana-2873	18	14	in	in	ADP
cana-2873	18	15	nts	nt	NOUN
cana-2873	18	16	’s	’s	PART
cana-2873	18	17	.	.	PUNCT
cana-2873	19	1	in	in	ADP
cana-2873	19	2	the	the	DET
cana-2873	19	3	year	year	NOUN
cana-2873	19	4	2019	2019	NUM
cana-2873	19	5	,	,	PUNCT
cana-2873	19	6	mohammed	mohammed	PROPN
cana-2873	19	7	ali	ali	PROPN
cana-2873	19	8	jaffer	jaffer	PROPN
cana-2873	19	9	and	and	CCONJ
cana-2873	19	10	ramesh11	ramesh11	PROPN
cana-2873	19	11	studied	study	VERB
cana-2873	19	12	the	the	DET
cana-2873	19	13	concept	concept	NOUN
cana-2873	19	14	of	of	ADP
cana-2873	19	15	neutrosophic	neutrosophic	ADJ
cana-2873	19	16	generalized	generalized	ADJ
cana-2873	19	17	pre	pre	ADJ
cana-2873	19	18	-	-	ADJ
cana-2873	19	19	regular	regular	ADJ
cana-2873	19	20	closed	closed	ADJ
cana-2873	19	21	sets	set	NOUN
cana-2873	19	22	.	.	PUNCT
cana-2873	20	1	the	the	DET
cana-2873	20	2	generalized	generalize	VERB
cana-2873	20	3	neutrosophic	neutrosophic	ADJ
cana-2873	20	4	b	b	X
cana-2873	20	5	-	-	PUNCT
cana-2873	20	6	open	open	ADJ
cana-2873	20	7	sets	set	NOUN
cana-2873	20	8	in	in	ADP
cana-2873	20	9	nts	nt	NOUN
cana-2873	20	10	’s	’s	PART
cana-2873	20	11	was	be	AUX
cana-2873	20	12	introduced	introduce	VERB
cana-2873	20	13	by	by	ADP
cana-2873	20	14	das	das	PROPN
cana-2873	20	15	and	and	CCONJ
cana-2873	20	16	mailto	mailto	NOUN
cana-2873	20	17	:	:	PUNCT
cana-2873	20	18	mohanaraonavuluri@gmail.com1	mohanaraonavuluri@gmail.com1	PROPN
cana-2873	20	19	mailto	mailto	PROPN
cana-2873	20	20	:	:	PUNCT
cana-2873	20	21	vsathishkumar2020@gmail.com2	vsathishkumar2020@gmail.com2	ADP
cana-2873	20	22	communications	communication	NOUN
cana-2873	20	23	on	on	ADP
cana-2873	20	24	applied	apply	VERB
cana-2873	20	25	nonlinear	nonlinear	ADJ
cana-2873	20	26	analysis	analysis	NOUN
cana-2873	20	27	issn	issn	NOUN
cana-2873	20	28	:	:	PUNCT
cana-2873	20	29	1074	1074	NUM
cana-2873	20	30	-	-	PUNCT
cana-2873	20	31	133x	133x	NUM
cana-2873	20	32	vol	vol	NOUN
cana-2873	20	33	32	32	NUM
cana-2873	20	34	no	no	NOUN
cana-2873	20	35	.	.	PUNCT
cana-2873	21	1	4s	4s	NUM
cana-2873	21	2	(	(	PUNCT
cana-2873	21	3	2025	2025	NUM
cana-2873	21	4	)	)	PUNCT
cana-2873	21	5	581	581	NUM
cana-2873	21	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	21	7	pramanik.6	pramanik.6	PROPN
cana-2873	21	8	das	das	PROPN
cana-2873	21	9	and	and	CCONJ
cana-2873	21	10	pramanik7	pramanik7	NOUN
cana-2873	21	11	also	also	ADV
cana-2873	21	12	defined	define	VERB
cana-2873	21	13	the	the	DET
cana-2873	21	14	neutrosophic	neutrosophic	ADJ
cana-2873	21	15	φ	φ	VERB
cana-2873	21	16	-	-	ADJ
cana-2873	21	17	open	open	ADJ
cana-2873	21	18	sets	set	NOUN
cana-2873	21	19	and	and	CCONJ
cana-2873	21	20	neutrosophic	neutrosophic	ADJ
cana-2873	21	21	φcontinuous	φcontinuous	ADJ
cana-2873	21	22	mappings	mapping	NOUN
cana-2873	21	23	via	via	ADP
cana-2873	21	24	nts	nt	NOUN
cana-2873	21	25	’s	’s	PART
cana-2873	21	26	.	.	PUNCT
cana-2873	22	1	vadivel	vadivel	VERB
cana-2873	22	2	and	and	CCONJ
cana-2873	22	3	sundar	sundar	NOUN
cana-2873	22	4	defined	define	VERB
cana-2873	22	5	γ	γ	X
cana-2873	22	6	open	open	ADJ
cana-2873	22	7	sets,18	sets,18	PROPN
cana-2873	22	8	γ	γ	PROPN
cana-2873	22	9	continuous	continuous	ADJ
cana-2873	22	10	maps,20,21	maps,20,21	ADP
cana-2873	22	11	βopen	βopen	ADJ
cana-2873	22	12	sets19	sets19	NOUN
cana-2873	22	13	and	and	CCONJ
cana-2873	22	14	β	β	X
cana-2873	22	15	continuous	continuous	ADJ
cana-2873	22	16	maps22–24	maps22–24	NOUN
cana-2873	22	17	in	in	ADP
cana-2873	22	18	n	n	CCONJ
cana-2873	22	19	-neutrosophic	-neutrosophic	ADJ
cana-2873	22	20	crisp	crisp	ADJ
cana-2873	22	21	topological	topological	ADJ
cana-2873	22	22	spaces	space	NOUN
cana-2873	22	23	.	.	PUNCT
cana-2873	23	1	in	in	ADP
cana-2873	23	2	this	this	DET
cana-2873	23	3	paper	paper	NOUN
cana-2873	23	4	,	,	PUNCT
cana-2873	23	5	we	we	PRON
cana-2873	23	6	develop	develop	VERB
cana-2873	23	7	the	the	DET
cana-2873	23	8	concept	concept	NOUN
cana-2873	23	9	of	of	ADP
cana-2873	23	10	quadripartitioned	quadripartitione	VERB
cana-2873	23	11	neutrosophic	neutrosophic	PROPN
cana-2873	23	12	contra	contra	PROPN
cana-2873	23	13	β	β	PROPN
cana-2873	23	14	-	-	ADJ
cana-2873	23	15	continuous	continuous	ADJ
cana-2873	23	16	maps	map	NOUN
cana-2873	23	17	,	,	PUNCT
cana-2873	23	18	quadripartitioned	quadripartitione	VERB
cana-2873	23	19	neutrosophic	neutrosophic	PROPN
cana-2873	23	20	contra	contra	PROPN
cana-2873	23	21	β	β	PROPN
cana-2873	23	22	-	-	ADJ
cana-2873	23	23	open	open	ADJ
cana-2873	23	24	maps	map	NOUN
cana-2873	23	25	and	and	CCONJ
cana-2873	23	26	quadripartitioned	quadripartitione	VERB
cana-2873	23	27	neutrosophic	neutrosophic	PROPN
cana-2873	23	28	contra	contra	PROPN
cana-2873	23	29	βclosed	βclose	VERB
cana-2873	23	30	maps	map	NOUN
cana-2873	23	31	in	in	ADP
cana-2873	23	32	a	a	DET
cana-2873	23	33	quadripartitioned	quadripartitione	VERB
cana-2873	23	34	neutrosophic	neutrosophic	ADJ
cana-2873	23	35	topological	topological	ADJ
cana-2873	23	36	spaces	space	NOUN
cana-2873	23	37	and	and	CCONJ
cana-2873	23	38	also	also	ADV
cana-2873	23	39	specialized	specialize	VERB
cana-2873	23	40	some	some	PRON
cana-2873	23	41	of	of	ADP
cana-2873	23	42	their	their	PRON
cana-2873	23	43	basic	basic	ADJ
cana-2873	23	44	properties	property	NOUN
cana-2873	23	45	with	with	ADP
cana-2873	23	46	examples	example	NOUN
cana-2873	23	47	.	.	PUNCT
cana-2873	24	1	also	also	ADV
cana-2873	24	2	,	,	PUNCT
cana-2873	24	3	we	we	PRON
cana-2873	24	4	discuss	discuss	VERB
cana-2873	24	5	about	about	ADP
cana-2873	24	6	quadripartitioned	quadripartitione	VERB
cana-2873	24	7	neutrosophic	neutrosophic	PROPN
cana-2873	24	8	contra	contra	PROPN
cana-2873	24	9	βhomeomorphism	βhomeomorphism	NOUN
cana-2873	24	10	and	and	CCONJ
cana-2873	24	11	quadripartitioned	quadripartitione	VERB
cana-2873	24	12	neutrosophic	neutrosophic	PROPN
cana-2873	24	13	contra	contra	PROPN
cana-2873	24	14	β	β	PROPN
cana-2873	24	15	-	-	PUNCT
cana-2873	24	16	completely	completely	ADV
cana-2873	24	17	homeomorphism	homeomorphism	NOUN
cana-2873	24	18	in	in	ADP
cana-2873	24	19	a	a	DET
cana-2873	24	20	quadripartitioned	quadripartitione	VERB
cana-2873	24	21	neutrosophic	neutrosophic	ADJ
cana-2873	24	22	topological	topological	ADJ
cana-2873	24	23	spaces	space	NOUN
cana-2873	24	24	and	and	CCONJ
cana-2873	24	25	also	also	ADV
cana-2873	24	26	specialized	specialize	VERB
cana-2873	24	27	some	some	PRON
cana-2873	24	28	of	of	ADP
cana-2873	24	29	their	their	PRON
cana-2873	24	30	basic	basic	ADJ
cana-2873	24	31	properties	property	NOUN
cana-2873	24	32	with	with	ADP
cana-2873	24	33	examples	example	NOUN
cana-2873	24	34	.	.	PUNCT
cana-2873	25	1	2	2	NUM
cana-2873	25	2	preliminaries	preliminary	NOUN
cana-2873	25	3	the	the	DET
cana-2873	25	4	needful	needful	ADJ
cana-2873	25	5	basic	basic	ADJ
cana-2873	25	6	definitions	definition	NOUN
cana-2873	25	7	&	&	CCONJ
cana-2873	25	8	properties	property	NOUN
cana-2873	25	9	are	be	AUX
cana-2873	25	10	discussed	discuss	VERB
cana-2873	25	11	in	in	ADP
cana-2873	25	12	this	this	DET
cana-2873	25	13	section	section	NOUN
cana-2873	25	14	.	.	PUNCT
cana-2873	26	1	definition	definition	NOUN
cana-2873	26	2	2.1	2.1	NUM
cana-2873	26	3	.	.	PUNCT
cana-2873	26	4	3	3	NUM
cana-2873	26	5	let	let	VERB
cana-2873	26	6	z	z	NOUN
cana-2873	26	7	be	be	AUX
cana-2873	26	8	a	a	DET
cana-2873	26	9	fixed	fix	VERB
cana-2873	26	10	set	set	NOUN
cana-2873	26	11	.	.	PUNCT
cana-2873	27	1	then	then	ADV
cana-2873	27	2	,	,	PUNCT
cana-2873	27	3	a	a	DET
cana-2873	27	4	quadripartitioned	quadripartitione	VERB
cana-2873	27	5	neutrosophic	neutrosophic	ADJ
cana-2873	27	6	set	set	NOUN
cana-2873	27	7	(	(	PUNCT
cana-2873	27	8	in	in	ADP
cana-2873	27	9	-	-	PUNCT
cana-2873	27	10	short	short	ADJ
cana-2873	27	11	,	,	PUNCT
cana-2873	27	12	q	q	NOUN
cana-2873	27	13	-	-	PUNCT
cana-2873	27	14	nss	nss	ADJ
cana-2873	27	15	)	)	PUNCT
cana-2873	27	16	u	u	NOUN
cana-2873	27	17	over	over	ADP
cana-2873	27	18	z	z	PROPN
cana-2873	27	19	is	be	AUX
cana-2873	27	20	defined	define	VERB
cana-2873	27	21	by	by	ADP
cana-2873	27	22	u	u	X
cana-2873	27	23	=	=	PUNCT
cana-2873	27	24	{	{	PUNCT
cana-2873	27	25	(	(	PUNCT
cana-2873	27	26	u	u	NOUN
cana-2873	27	27	,	,	PUNCT
cana-2873	27	28	tu	tu	PROPN
cana-2873	27	29	(	(	PUNCT
cana-2873	27	30	u	u	NOUN
cana-2873	27	31	)	)	PUNCT
cana-2873	27	32	,	,	PUNCT
cana-2873	27	33	cu	cu	PROPN
cana-2873	27	34	(	(	PUNCT
cana-2873	27	35	u	u	NOUN
cana-2873	27	36	)	)	PUNCT
cana-2873	27	37	,	,	PUNCT
cana-2873	27	38	iu	iu	ADP
cana-2873	27	39	(	(	PUNCT
cana-2873	27	40	u	u	NOUN
cana-2873	27	41	)	)	PUNCT
cana-2873	27	42	,	,	PUNCT
cana-2873	27	43	fu	fu	NOUN
cana-2873	27	44	(	(	PUNCT
cana-2873	27	45	u	u	NOUN
cana-2873	27	46	)	)	PUNCT
cana-2873	27	47	)	)	PUNCT
cana-2873	27	48	:	:	PUNCT
cana-2873	28	1	u	u	PROPN
cana-2873	28	2	∈	∈	PROPN
cana-2873	28	3	z	z	PROPN
cana-2873	28	4	}	}	PUNCT
cana-2873	28	5	where	where	SCONJ
cana-2873	28	6	tu	tu	PROPN
cana-2873	28	7	,	,	PUNCT
cana-2873	28	8	cu	cu	PROPN
cana-2873	28	9	,	,	PUNCT
cana-2873	28	10	iu	iu	ADP
cana-2873	28	11	and	and	CCONJ
cana-2873	28	12	fu	fu	NOUN
cana-2873	28	13	(	(	PUNCT
cana-2873	28	14	∈	∈	PROPN
cana-2873	28	15	[	[	X
cana-2873	28	16	0	0	NUM
cana-2873	28	17	,	,	PUNCT
cana-2873	28	18	1	1	NUM
cana-2873	28	19	]	]	PUNCT
cana-2873	28	20	)	)	PUNCT
cana-2873	28	21	are	be	AUX
cana-2873	28	22	the	the	DET
cana-2873	28	23	truth	truth	NOUN
cana-2873	28	24	,	,	PUNCT
cana-2873	28	25	contradiction	contradiction	NOUN
cana-2873	28	26	,	,	PUNCT
cana-2873	28	27	ignorance	ignorance	NOUN
cana-2873	28	28	,	,	PUNCT
cana-2873	28	29	and	and	CCONJ
cana-2873	28	30	falsity	falsity	NOUN
cana-2873	28	31	membership	membership	NOUN
cana-2873	28	32	values	value	NOUN
cana-2873	28	33	of	of	ADP
cana-2873	28	34	u	u	PROPN
cana-2873	28	35	∈	∈	PROPN
cana-2873	28	36	z.	z.	PROPN
cana-2873	29	1	so	so	ADV
cana-2873	29	2	,	,	PUNCT
cana-2873	29	3	0	0	NUM
cana-2873	29	4	≤	≤	PROPN
cana-2873	29	5	tu	tu	X
cana-2873	29	6	(	(	PUNCT
cana-2873	29	7	u	u	NOUN
cana-2873	29	8	)	)	PUNCT
cana-2873	29	9	+	+	CCONJ
cana-2873	29	10	cu	cu	PROPN
cana-2873	29	11	(	(	PUNCT
cana-2873	29	12	u	u	NOUN
cana-2873	29	13	)	)	PUNCT
cana-2873	29	14	+	+	CCONJ
cana-2873	29	15	iu	iu	ADP
cana-2873	29	16	(	(	PUNCT
cana-2873	29	17	u	u	NOUN
cana-2873	29	18	)	)	PUNCT
cana-2873	29	19	+	+	NOUN
cana-2873	29	20	fu	fu	ADJ
cana-2873	29	21	(	(	PUNCT
cana-2873	29	22	u	u	NOUN
cana-2873	29	23	)	)	PUNCT
cana-2873	29	24	≤	≤	NUM
cana-2873	29	25	4	4	NUM
cana-2873	29	26	.	.	PUNCT
cana-2873	29	27	definition	definition	NOUN
cana-2873	29	28	2.2	2.2	NUM
cana-2873	29	29	.	.	NOUN
cana-2873	29	30	3	3	NUM
cana-2873	29	31	let	let	VERB
cana-2873	29	32	z	z	NOUN
cana-2873	29	33	be	be	AUX
cana-2873	29	34	a	a	DET
cana-2873	29	35	non	non	ADJ
cana-2873	29	36	-	-	ADJ
cana-2873	29	37	empty	empty	ADJ
cana-2873	29	38	set	set	NOUN
cana-2873	29	39	&	&	CCONJ
cana-2873	29	40	the	the	DET
cana-2873	29	41	q	q	NOUN
cana-2873	29	42	-	-	PUNCT
cana-2873	29	43	nss	nss	NOUN
cana-2873	29	44	’s	’s	PART
cana-2873	29	45	u	u	NOUN
cana-2873	29	46	&	&	CCONJ
cana-2873	29	47	u0	u0	PROPN
cana-2873	29	48	in	in	ADP
cana-2873	29	49	the	the	DET
cana-2873	29	50	form	form	NOUN
cana-2873	29	51	u	u	NOUN
cana-2873	29	52	=	=	X
cana-2873	29	53	{	{	PUNCT
cana-2873	29	54	(	(	PUNCT
cana-2873	29	55	u	u	NOUN
cana-2873	29	56	,	,	PUNCT
cana-2873	29	57	tu	tu	PROPN
cana-2873	29	58	(	(	PUNCT
cana-2873	29	59	u	u	NOUN
cana-2873	29	60	)	)	PUNCT
cana-2873	29	61	,	,	PUNCT
cana-2873	29	62	cu	cu	PROPN
cana-2873	29	63	(	(	PUNCT
cana-2873	29	64	u),iu	u),iu	PROPN
cana-2873	29	65	(	(	PUNCT
cana-2873	29	66	u	u	NOUN
cana-2873	29	67	)	)	PUNCT
cana-2873	29	68	,	,	PUNCT
cana-2873	29	69	fu	fu	NOUN
cana-2873	29	70	(	(	PUNCT
cana-2873	29	71	u	u	NOUN
cana-2873	29	72	)	)	PUNCT
cana-2873	29	73	)	)	PUNCT
cana-2873	29	74	:	:	PUNCT
cana-2873	30	1	u	u	PROPN
cana-2873	30	2	∈	∈	PROPN
cana-2873	30	3	z	z	PROPN
cana-2873	30	4	}	}	PUNCT
cana-2873	30	5	,	,	PUNCT
cana-2873	30	6	u	u	NOUN
cana-2873	30	7	=	=	PRON
cana-2873	30	8	{	{	PUNCT
cana-2873	30	9	(	(	PUNCT
cana-2873	30	10	u	u	NOUN
cana-2873	30	11	,	,	PUNCT
cana-2873	30	12	tu	tu	PROPN
cana-2873	30	13	(	(	PUNCT
cana-2873	30	14	u	u	NOUN
cana-2873	30	15	)	)	PUNCT
cana-2873	30	16	,	,	PUNCT
cana-2873	30	17	cu	cu	PROPN
cana-2873	30	18	(	(	PUNCT
cana-2873	30	19	u	u	NOUN
cana-2873	30	20	)	)	PUNCT
cana-2873	30	21	,	,	PUNCT
cana-2873	30	22	iu	iu	ADP
cana-2873	30	23	(	(	PUNCT
cana-2873	30	24	u	u	NOUN
cana-2873	30	25	)	)	PUNCT
cana-2873	30	26	,	,	PUNCT
cana-2873	30	27	fu	fu	NOUN
cana-2873	30	28	)	)	PUNCT
cana-2873	30	29	:	:	PUNCT
cana-2873	31	1	u	u	PROPN
cana-2873	31	2	∈	∈	PROPN
cana-2873	31	3	z	z	PROPN
cana-2873	31	4	}	}	PUNCT
cana-2873	31	5	,	,	PUNCT
cana-2873	31	6	then	then	ADV
cana-2873	31	7	(	(	PUNCT
cana-2873	31	8	i	i	NOUN
cana-2873	31	9	)	)	PUNCT
cana-2873	31	10	0qns	0qns	PROPN
cana-2873	32	1	=	=	PUNCT
cana-2873	32	2	(	(	PUNCT
cana-2873	32	3	u	u	NOUN
cana-2873	32	4	,	,	PUNCT
cana-2873	32	5	0	0	NUM
cana-2873	32	6	,	,	PUNCT
cana-2873	32	7	0	0	NUM
cana-2873	32	8	,	,	PUNCT
cana-2873	32	9	1	1	NUM
cana-2873	32	10	,	,	PUNCT
cana-2873	32	11	1	1	NUM
cana-2873	32	12	)	)	PUNCT
cana-2873	32	13	and	and	CCONJ
cana-2873	32	14	1qns	1qns	NUM
cana-2873	32	15	=	=	SYM
cana-2873	32	16	(	(	PUNCT
cana-2873	32	17	u	u	NOUN
cana-2873	32	18	,	,	PUNCT
cana-2873	32	19	1	1	NUM
cana-2873	32	20	,	,	PUNCT
cana-2873	32	21	1	1	NUM
cana-2873	32	22	,	,	PUNCT
cana-2873	32	23	0	0	NUM
cana-2873	32	24	,	,	PUNCT
cana-2873	32	25	0	0	NUM
cana-2873	32	26	)	)	PUNCT
cana-2873	32	27	,	,	PUNCT
cana-2873	32	28	(	(	PUNCT
cana-2873	32	29	ii	ii	NOUN
cana-2873	32	30	)	)	PUNCT
cana-2873	32	31	u	u	NOUN
cana-2873	32	32	⊆	⊆	NUM
cana-2873	32	33	u	u	NOUN
cana-2873	32	34	o	o	PROPN
cana-2873	32	35	iff	iff	PROPN
cana-2873	32	36	tu	tu	PROPN
cana-2873	32	37	(	(	PUNCT
cana-2873	32	38	u	u	NOUN
cana-2873	32	39	)	)	PUNCT
cana-2873	32	40	≤	≤	NOUN
cana-2873	32	41	tuo(u	tuo(u	NOUN
cana-2873	32	42	)	)	PUNCT
cana-2873	32	43	,	,	PUNCT
cana-2873	32	44	cu	cu	PROPN
cana-2873	32	45	(	(	PUNCT
cana-2873	32	46	u	u	NOUN
cana-2873	32	47	)	)	PUNCT
cana-2873	32	48	≤	≤	NOUN
cana-2873	32	49	cuo(u	cuo(u	NOUN
cana-2873	32	50	)	)	PUNCT
cana-2873	32	51	,	,	PUNCT
cana-2873	32	52	iu	iu	ADP
cana-2873	32	53	(	(	PUNCT
cana-2873	32	54	u	u	NOUN
cana-2873	32	55	)	)	PUNCT
cana-2873	32	56	≥	≥	X
cana-2873	32	57	iuo(u	iuo(u	PROPN
cana-2873	32	58	)	)	PUNCT
cana-2873	32	59	&	&	CCONJ
cana-2873	32	60	fu	fu	PROPN
cana-2873	32	61	(	(	PUNCT
cana-2873	32	62	u	u	NOUN
cana-2873	32	63	)	)	PUNCT
cana-2873	32	64	≥	≥	NOUN
cana-2873	32	65	fuo(u	fuo(u	PROPN
cana-2873	32	66	)	)	PUNCT
cana-2873	32	67	:	:	PUNCT
cana-2873	33	1	u	u	PROPN
cana-2873	33	2	∈	∈	PROPN
cana-2873	33	3	z	z	PROPN
cana-2873	33	4	,	,	PUNCT
cana-2873	33	5	(	(	PUNCT
cana-2873	33	6	iii	iii	NOUN
cana-2873	33	7	)	)	PUNCT
cana-2873	33	8	1qns	1qns	NUM
cana-2873	33	9	−	−	PROPN
cana-2873	33	10	u	u	NOUN
cana-2873	33	11	=	=	PUNCT
cana-2873	33	12	{	{	PUNCT
cana-2873	33	13	(	(	PUNCT
cana-2873	33	14	u	u	NOUN
cana-2873	33	15	,	,	PUNCT
cana-2873	33	16	fu	fu	NOUN
cana-2873	33	17	(	(	PUNCT
cana-2873	33	18	u	u	NOUN
cana-2873	33	19	)	)	PUNCT
cana-2873	33	20	,	,	PUNCT
cana-2873	33	21	iu	iu	ADP
cana-2873	33	22	(	(	PUNCT
cana-2873	33	23	u	u	NOUN
cana-2873	33	24	)	)	PUNCT
cana-2873	33	25	,	,	PUNCT
cana-2873	33	26	cu	cu	PROPN
cana-2873	33	27	(	(	PUNCT
cana-2873	33	28	u	u	NOUN
cana-2873	33	29	)	)	PUNCT
cana-2873	33	30	,	,	PUNCT
cana-2873	33	31	tu	tu	PROPN
cana-2873	33	32	(	(	PUNCT
cana-2873	33	33	u	u	NOUN
cana-2873	33	34	)	)	PUNCT
cana-2873	33	35	)	)	PUNCT
cana-2873	33	36	:	:	PUNCT
cana-2873	34	1	u	u	PROPN
cana-2873	34	2	∈	∈	PROPN
cana-2873	34	3	z	z	NOUN
cana-2873	34	4	}	}	PUNCT
cana-2873	34	5	=	=	SYM
cana-2873	34	6	uc	uc	PROPN
cana-2873	34	7	,	,	PUNCT
cana-2873	34	8	(	(	PUNCT
cana-2873	34	9	iv	iv	X
cana-2873	34	10	)	)	PUNCT
cana-2873	34	11	u	u	NOUN
cana-2873	34	12	∪u0	∪u0	PROPN
cana-2873	34	13	=	=	SYM
cana-2873	34	14	{	{	PUNCT
cana-2873	34	15	(	(	PUNCT
cana-2873	34	16	u	u	NOUN
cana-2873	34	17	,	,	PUNCT
cana-2873	34	18	max(tu	max(tu	X
cana-2873	34	19	(	(	PUNCT
cana-2873	34	20	u	u	NOUN
cana-2873	34	21	)	)	PUNCT
cana-2873	34	22	,	,	PUNCT
cana-2873	34	23	tu0	tu0	PROPN
cana-2873	34	24	(	(	PUNCT
cana-2873	34	25	u	u	NOUN
cana-2873	34	26	)	)	PUNCT
cana-2873	34	27	)	)	PUNCT
cana-2873	34	28	,	,	PUNCT
cana-2873	34	29	max(cu	max(cu	X
cana-2873	34	30	(	(	PUNCT
cana-2873	34	31	u	u	NOUN
cana-2873	34	32	)	)	PUNCT
cana-2873	34	33	,	,	PUNCT
cana-2873	34	34	cu0(u	cu0(u	PROPN
cana-2873	34	35	)	)	PUNCT
cana-2873	34	36	)	)	PUNCT
cana-2873	34	37	,	,	PUNCT
cana-2873	34	38	min(iu	min(iu	NUM
cana-2873	34	39	(	(	PUNCT
cana-2873	34	40	u	u	NOUN
cana-2873	34	41	)	)	PUNCT
cana-2873	34	42	,	,	PUNCT
cana-2873	34	43	iu	iu	ADP
cana-2873	34	44	(	(	PUNCT
cana-2873	34	45	u	u	NOUN
cana-2873	34	46	)	)	PUNCT
cana-2873	34	47	)	)	PUNCT
cana-2873	34	48	,	,	PUNCT
cana-2873	34	49	min(fu	min(fu	X
cana-2873	34	50	(	(	PUNCT
cana-2873	34	51	u	u	NOUN
cana-2873	34	52	)	)	PUNCT
cana-2873	34	53	,	,	PUNCT
cana-2873	34	54	fu0(u	fu0(u	PROPN
cana-2873	34	55	)	)	PUNCT
cana-2873	34	56	)	)	PUNCT
cana-2873	34	57	)	)	PUNCT
cana-2873	34	58	:	:	PUNCT
cana-2873	35	1	u	u	NOUN
cana-2873	35	2	∈	∈	PROPN
cana-2873	35	3	z	z	PROPN
cana-2873	35	4	}	}	PUNCT
cana-2873	35	5	,	,	PUNCT
cana-2873	35	6	(	(	PUNCT
cana-2873	35	7	v	v	NOUN
cana-2873	35	8	)	)	PUNCT
cana-2873	35	9	u	u	NOUN
cana-2873	35	10	∩u	∩u	NOUN
cana-2873	35	11	=	=	PUNCT
cana-2873	35	12	{	{	PUNCT
cana-2873	35	13	(	(	PUNCT
cana-2873	35	14	u	u	NOUN
cana-2873	35	15	,	,	PUNCT
cana-2873	35	16	min(tu	min(tu	ADJ
cana-2873	35	17	(	(	PUNCT
cana-2873	35	18	u	u	NOUN
cana-2873	35	19	)	)	PUNCT
cana-2873	35	20	,	,	PUNCT
cana-2873	35	21	tu0u	tu0u	PROPN
cana-2873	35	22	)	)	PUNCT
cana-2873	35	23	)	)	PUNCT
cana-2873	35	24	,	,	PUNCT
cana-2873	35	25	min(cu	min(cu	X
cana-2873	35	26	(	(	PUNCT
cana-2873	35	27	u	u	NOUN
cana-2873	35	28	)	)	PUNCT
cana-2873	35	29	,	,	PUNCT
cana-2873	35	30	cu0(u	cu0(u	PROPN
cana-2873	35	31	)	)	PUNCT
cana-2873	35	32	)	)	PUNCT
cana-2873	35	33	,	,	PUNCT
cana-2873	35	34	max(iu	max(iu	NOUN
cana-2873	35	35	(	(	PUNCT
cana-2873	35	36	u	u	NOUN
cana-2873	35	37	)	)	PUNCT
cana-2873	35	38	,	,	PUNCT
cana-2873	35	39	iu0(u	iu0(u	ADV
cana-2873	35	40	)	)	PUNCT
cana-2873	35	41	)	)	PUNCT
cana-2873	35	42	,	,	PUNCT
cana-2873	35	43	max(fu	max(fu	X
cana-2873	35	44	(	(	PUNCT
cana-2873	35	45	u	u	NOUN
cana-2873	35	46	)	)	PUNCT
cana-2873	35	47	,	,	PUNCT
cana-2873	35	48	fu0(u	fu0(u	PROPN
cana-2873	35	49	)	)	PUNCT
cana-2873	35	50	)	)	PUNCT
cana-2873	35	51	)	)	PUNCT
cana-2873	35	52	:	:	PUNCT
cana-2873	36	1	u	u	NOUN
cana-2873	36	2	∈	∈	PROPN
cana-2873	36	3	z	z	NOUN
cana-2873	36	4	}	}	PUNCT
cana-2873	36	5	.	.	PUNCT
cana-2873	37	1	definition	definition	NOUN
cana-2873	37	2	2.3	2.3	NUM
cana-2873	37	3	.	.	PUNCT
cana-2873	37	4	5	5	NUM
cana-2873	37	5	let	let	VERB
cana-2873	37	6	z	z	PRON
cana-2873	37	7	be	be	AUX
cana-2873	37	8	a	a	DET
cana-2873	37	9	fixed	fix	VERB
cana-2873	37	10	set	set	NOUN
cana-2873	37	11	.	.	PUNCT
cana-2873	38	1	a	a	DET
cana-2873	38	2	collection	collection	NOUN
cana-2873	38	3	γq	γq	ADP
cana-2873	38	4	of	of	ADP
cana-2873	38	5	some	some	DET
cana-2873	38	6	q	q	NOUN
cana-2873	38	7	-	-	PUNCT
cana-2873	38	8	nss	nss	NOUN
cana-2873	38	9	’s	’s	NOUN
cana-2873	38	10	over	over	ADP
cana-2873	38	11	z	z	PROPN
cana-2873	38	12	is	be	AUX
cana-2873	38	13	called	call	VERB
cana-2873	38	14	a	a	DET
cana-2873	38	15	quadripartitioned	quadripartitione	VERB
cana-2873	38	16	neutrosophic	neutrosophic	ADJ
cana-2873	38	17	topology	topology	NOUN
cana-2873	38	18	(	(	PUNCT
cana-2873	38	19	in	in	ADP
cana-2873	38	20	-	-	PUNCT
cana-2873	38	21	short	short	ADJ
cana-2873	38	22	,	,	PUNCT
cana-2873	38	23	q	q	NOUN
cana-2873	38	24	-	-	PUNCT
cana-2873	38	25	nst	nst	NOUN
cana-2873	38	26	)	)	PUNCT
cana-2873	38	27	on	on	ADP
cana-2873	38	28	z	z	PROPN
cana-2873	38	29	,	,	PUNCT
cana-2873	38	30	if	if	SCONJ
cana-2873	38	31	the	the	DET
cana-2873	38	32	following	follow	VERB
cana-2873	38	33	conditions	condition	NOUN
cana-2873	38	34	holds	hold	VERB
cana-2873	38	35	:	:	PUNCT
cana-2873	38	36	(	(	PUNCT
cana-2873	38	37	i	i	NOUN
cana-2873	38	38	)	)	PUNCT
cana-2873	38	39	0n	0n	NOUN
cana-2873	38	40	,	,	PUNCT
cana-2873	39	1	1n	1n	NUM
cana-2873	39	2	∈	∈	PROPN
cana-2873	39	3	γq	γq	VERB
cana-2873	39	4	.	.	PUNCT
cana-2873	40	1	(	(	PUNCT
cana-2873	40	2	ii	ii	NOUN
cana-2873	40	3	)	)	PUNCT
cana-2873	40	4	gϕ	gϕ	PROPN
cana-2873	40	5	∩	∩	PROPN
cana-2873	40	6	gφ	gφ	PROPN
cana-2873	40	7	∈	∈	PROPN
cana-2873	40	8	γq	γq	ADP
cana-2873	40	9	for	for	ADP
cana-2873	40	10	any	any	DET
cana-2873	40	11	gϕ	gϕ	PROPN
cana-2873	40	12	,	,	PUNCT
cana-2873	40	13	gφ	gφ	PROPN
cana-2873	40	14	∈	∈	PROPN
cana-2873	40	15	γq	γq	VERB
cana-2873	40	16	.	.	PUNCT
cana-2873	41	1	(	(	PUNCT
cana-2873	41	2	iii	iii	X
cana-2873	41	3	)	)	PUNCT
cana-2873	41	4	∪gϕ	∪gϕ	PROPN
cana-2873	41	5	∈	∈	PROPN
cana-2873	41	6	γq	γq	ADP
cana-2873	41	7	,	,	PUNCT
cana-2873	41	8	∀	∀	X
cana-2873	41	9	{	{	PUNCT
cana-2873	41	10	gϕ	gϕ	PROPN
cana-2873	41	11	:	:	PUNCT
cana-2873	41	12	ϕ	ϕ	PROPN
cana-2873	41	13	∈	∈	PROPN
cana-2873	41	14	z	z	PROPN
cana-2873	41	15	}	}	PUNCT
cana-2873	41	16	⊆	⊆	NUM
cana-2873	41	17	γq	γq	NOUN
cana-2873	41	18	.	.	PUNCT
cana-2873	42	1	then	then	ADV
cana-2873	42	2	(	(	PUNCT
cana-2873	42	3	z	z	NOUN
cana-2873	42	4	,	,	PUNCT
cana-2873	42	5	γq	γq	VERB
cana-2873	42	6	)	)	PUNCT
cana-2873	42	7	is	be	AUX
cana-2873	42	8	called	call	VERB
cana-2873	42	9	a	a	DET
cana-2873	42	10	quadripartitioned	quadripartitione	VERB
cana-2873	42	11	neutrosophic	neutrosophic	ADJ
cana-2873	42	12	topological	topological	ADJ
cana-2873	42	13	space	space	NOUN
cana-2873	42	14	(	(	PUNCT
cana-2873	42	15	in	in	ADP
cana-2873	42	16	-	-	PUNCT
cana-2873	42	17	short	short	ADJ
cana-2873	42	18	,	,	PUNCT
cana-2873	42	19	q	q	NOUN
cana-2873	42	20	-	-	NOUN
cana-2873	42	21	nsts	nst	NOUN
cana-2873	42	22	)	)	PUNCT
cana-2873	42	23	in	in	ADP
cana-2873	42	24	z.	z.	PROPN
cana-2873	43	1	every	every	DET
cana-2873	43	2	element	element	NOUN
cana-2873	43	3	of	of	ADP
cana-2873	43	4	γq	γq	ADV
cana-2873	43	5	are	be	AUX
cana-2873	43	6	called	call	VERB
cana-2873	43	7	a	a	DET
cana-2873	43	8	quadripartitioned	quadripartitione	VERB
cana-2873	43	9	neutrosophic	neutrosophic	ADJ
cana-2873	43	10	open	open	ADJ
cana-2873	43	11	sets	set	NOUN
cana-2873	43	12	(	(	PUNCT
cana-2873	43	13	in	in	ADP
cana-2873	43	14	-	-	PUNCT
cana-2873	43	15	short	short	ADJ
cana-2873	43	16	,	,	PUNCT
cana-2873	43	17	q	q	ADJ
cana-2873	43	18	-	-	PUNCT
cana-2873	43	19	nso	nso	NOUN
cana-2873	43	20	set	set	NOUN
cana-2873	43	21	)	)	PUNCT
cana-2873	43	22	.	.	PUNCT
cana-2873	44	1	if	if	SCONJ
cana-2873	44	2	c∈γq	c∈γq	NOUN
cana-2873	44	3	,	,	PUNCT
cana-2873	44	4	then	then	ADV
cana-2873	44	5	cc	cc	PROPN
cana-2873	44	6	is	be	AUX
cana-2873	44	7	called	call	VERB
cana-2873	44	8	a	a	DET
cana-2873	44	9	quadripartitioned	quadripartitione	VERB
cana-2873	44	10	neutrosophic	neutrosophic	ADJ
cana-2873	44	11	closed	closed	ADJ
cana-2873	44	12	sets	set	NOUN
cana-2873	44	13	(	(	PUNCT
cana-2873	44	14	in	in	ADP
cana-2873	44	15	-	-	PUNCT
cana-2873	44	16	short	short	ADJ
cana-2873	44	17	,	,	PUNCT
cana-2873	44	18	q	q	ADJ
cana-2873	44	19	-	-	PUNCT
cana-2873	44	20	nsc	nsc	NOUN
cana-2873	44	21	set	set	NOUN
cana-2873	44	22	)	)	PUNCT
cana-2873	44	23	.	.	PUNCT
cana-2873	45	1	communications	communication	NOUN
cana-2873	45	2	on	on	ADP
cana-2873	45	3	applied	apply	VERB
cana-2873	45	4	nonlinear	nonlinear	ADJ
cana-2873	45	5	analysis	analysis	NOUN
cana-2873	45	6	issn	issn	NOUN
cana-2873	45	7	:	:	PUNCT
cana-2873	45	8	1074	1074	NUM
cana-2873	45	9	-	-	PUNCT
cana-2873	45	10	133x	133x	NUM
cana-2873	45	11	vol	vol	NOUN
cana-2873	45	12	32	32	NUM
cana-2873	45	13	no	no	NOUN
cana-2873	45	14	.	.	PUNCT
cana-2873	46	1	4s	4s	NUM
cana-2873	46	2	(	(	PUNCT
cana-2873	46	3	2025	2025	NUM
cana-2873	46	4	)	)	PUNCT
cana-2873	46	5	582	582	NUM
cana-2873	46	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	46	7	definition	definition	NOUN
cana-2873	46	8	2.4	2.4	NUM
cana-2873	46	9	.	.	PUNCT
cana-2873	46	10	5	5	NUM
cana-2873	46	11	let	let	VERB
cana-2873	46	12	(	(	PUNCT
cana-2873	46	13	z	z	NOUN
cana-2873	46	14	,	,	PUNCT
cana-2873	46	15	γq	γq	VERB
cana-2873	46	16	)	)	PUNCT
cana-2873	46	17	be	be	AUX
cana-2873	46	18	q	q	NOUN
cana-2873	46	19	-	-	NOUN
cana-2873	46	20	nsts	nst	NOUN
cana-2873	46	21	on	on	ADP
cana-2873	46	22	z	z	PROPN
cana-2873	46	23	and	and	CCONJ
cana-2873	46	24	u	u	PRON
cana-2873	46	25	be	be	VERB
cana-2873	46	26	an	an	DET
cana-2873	46	27	q	q	NOUN
cana-2873	46	28	-	-	PUNCT
cana-2873	46	29	nss	nss	NOUN
cana-2873	46	30	on	on	ADP
cana-2873	46	31	z	z	PROPN
cana-2873	46	32	,	,	PUNCT
cana-2873	46	33	then	then	ADV
cana-2873	46	34	a	a	DET
cana-2873	46	35	quadripartitioned	quadripartitioned	ADJ
cana-2873	46	36	neutrosophic	neutrosophic	ADJ
cana-2873	46	37	interior	interior	NOUN
cana-2873	46	38	(	(	PUNCT
cana-2873	46	39	resp	resp	NOUN
cana-2873	46	40	.	.	PUNCT
cana-2873	47	1	closure	closure	NOUN
cana-2873	47	2	)	)	PUNCT
cana-2873	47	3	of	of	ADP
cana-2873	47	4	u	u	PROPN
cana-2873	47	5	(	(	PUNCT
cana-2873	47	6	in	in	ADP
cana-2873	47	7	-	-	PUNCT
cana-2873	47	8	short	short	ADJ
cana-2873	47	9	,	,	PUNCT
cana-2873	47	10	q	q	NOUN
cana-2873	47	11	-	-	PUNCT
cana-2873	47	12	nsint(u	nsint(u	PROPN
cana-2873	47	13	)	)	PUNCT
cana-2873	47	14	(	(	PUNCT
cana-2873	47	15	resp	resp	NOUN
cana-2873	47	16	.	.	PUNCT
cana-2873	48	1	q	q	X
cana-2873	48	2	-	-	PUNCT
cana-2873	48	3	nscl(u	nscl(u	NOUN
cana-2873	48	4	)	)	PUNCT
cana-2873	48	5	)	)	PUNCT
cana-2873	48	6	)	)	PUNCT
cana-2873	48	7	are	be	AUX
cana-2873	48	8	defined	define	VERB
cana-2873	48	9	as	as	ADP
cana-2873	48	10	q	q	NOUN
cana-2873	48	11	-	-	PUNCT
cana-2873	48	12	nsint(u	nsint(u	ADJ
cana-2873	48	13	)	)	PUNCT
cana-2873	49	1	=	=	PUNCT
cana-2873	49	2	∪{u	∪{u	VERB
cana-2873	49	3	o	o	X
cana-2873	49	4	:	:	PUNCT
cana-2873	49	5	u	u	NOUN
cana-2873	49	6	o	o	NOUN
cana-2873	49	7	⊆	⊆	NUM
cana-2873	49	8	u	u	NOUN
cana-2873	49	9	&	&	CCONJ
cana-2873	49	10	u	u	PROPN
cana-2873	49	11	o	o	NOUN
cana-2873	49	12	is	be	AUX
cana-2873	49	13	a	a	DET
cana-2873	49	14	q	q	NOUN
cana-2873	49	15	-	-	NOUN
cana-2873	49	16	nso	nso	NOUN
cana-2873	49	17	in	in	ADP
cana-2873	49	18	z	z	PROPN
cana-2873	49	19	}	}	PUNCT
cana-2873	49	20	,	,	PUNCT
cana-2873	49	21	q	q	X
cana-2873	49	22	-	-	PUNCT
cana-2873	49	23	nscl(u	nscl(u	NOUN
cana-2873	49	24	)	)	PUNCT
cana-2873	49	25	=	=	PUNCT
cana-2873	50	1	∩{u	∩{u	NUM
cana-2873	50	2	o	o	NOUN
cana-2873	50	3	:	:	PUNCT
cana-2873	50	4	u	u	NOUN
cana-2873	50	5	⊆	⊆	NUM
cana-2873	50	6	u	u	SYM
cana-2873	50	7	o	o	NOUN
cana-2873	50	8	&	&	CCONJ
cana-2873	50	9	u	u	PROPN
cana-2873	50	10	o	o	NOUN
cana-2873	50	11	is	be	AUX
cana-2873	50	12	a	a	DET
cana-2873	50	13	q	q	NOUN
cana-2873	50	14	-	-	PUNCT
cana-2873	50	15	nsc	nsc	NOUN
cana-2873	50	16	in	in	ADP
cana-2873	50	17	z	z	PROPN
cana-2873	50	18	}	}	PUNCT
cana-2873	50	19	,	,	PUNCT
cana-2873	50	20	definition	definition	NOUN
cana-2873	50	21	2.5	2.5	NUM
cana-2873	50	22	.	.	PUNCT
cana-2873	51	1	5	5	NUM
cana-2873	51	2	let	let	VERB
cana-2873	51	3	(	(	PUNCT
cana-2873	51	4	z	z	NOUN
cana-2873	51	5	,	,	PUNCT
cana-2873	51	6	γq	γq	VERB
cana-2873	51	7	)	)	PUNCT
cana-2873	51	8	be	be	AUX
cana-2873	51	9	q	q	NOUN
cana-2873	51	10	-	-	NOUN
cana-2873	51	11	nsts	nst	NOUN
cana-2873	51	12	on	on	ADP
cana-2873	51	13	z	z	PROPN
cana-2873	51	14	and	and	CCONJ
cana-2873	51	15	u	u	PRON
cana-2873	51	16	be	be	VERB
cana-2873	51	17	an	an	DET
cana-2873	51	18	q	q	NOUN
cana-2873	51	19	-	-	PUNCT
cana-2873	51	20	nss	nss	NOUN
cana-2873	51	21	on	on	ADP
cana-2873	51	22	z.	z.	PROPN
cana-2873	51	23	then	then	ADV
cana-2873	51	24	u	u	NOUN
cana-2873	51	25	is	be	AUX
cana-2873	51	26	said	say	VERB
cana-2873	51	27	to	to	PART
cana-2873	51	28	be	be	AUX
cana-2873	51	29	a	a	DET
cana-2873	51	30	quadripartitioned	quadripartitioned	ADJ
cana-2873	51	31	neutrosophic	neutrosophic	ADJ
cana-2873	51	32	pre	pre	PROPN
cana-2873	51	33	(	(	PUNCT
cana-2873	51	34	resp	resp	NOUN
cana-2873	51	35	.	.	PUNCT
cana-2873	52	1	semi	semi	ADV
cana-2873	52	2	,	,	PUNCT
cana-2873	52	3	α	α	PROPN
cana-2873	52	4	&	&	CCONJ
cana-2873	52	5	b	b	NOUN
cana-2873	52	6	)	)	PUNCT
cana-2873	52	7	open	open	ADJ
cana-2873	52	8	set	set	NOUN
cana-2873	52	9	(	(	PUNCT
cana-2873	52	10	in	in	ADP
cana-2873	52	11	-	-	PUNCT
cana-2873	52	12	short	short	ADJ
cana-2873	52	13	,	,	PUNCT
cana-2873	52	14	q	q	NOUN
cana-2873	52	15	-	-	PUNCT
cana-2873	52	16	ns	ns	NOUN
cana-2873	52	17	ƿo	ƿo	ADP
cana-2873	52	18	set	set	NOUN
cana-2873	52	19	(	(	PUNCT
cana-2873	52	20	resp	resp	NOUN
cana-2873	52	21	.	.	PUNCT
cana-2873	53	1	q	q	X
cana-2873	53	2	-	-	PUNCT
cana-2873	53	3	ns	ns	ADJ
cana-2873	53	4	α	α	NOUN
cana-2873	53	5	o	o	NOUN
cana-2873	53	6	set	set	NOUN
cana-2873	53	7	,	,	PUNCT
cana-2873	53	8	q	q	ADJ
cana-2873	53	9	-	-	PUNCT
cana-2873	53	10	nsαo	nsαo	NOUN
cana-2873	53	11	set	set	PROPN
cana-2873	53	12	&	&	CCONJ
cana-2873	53	13	q	q	NOUN
cana-2873	53	14	-	-	PUNCT
cana-2873	53	15	nsbo	nsbo	NOUN
cana-2873	53	16	set	set	NOUN
cana-2873	53	17	)	)	PUNCT
cana-2873	53	18	)	)	PUNCT
cana-2873	54	1	if	if	SCONJ
cana-2873	54	2	u⊆q	u⊆q	PROPN
cana-2873	54	3	-	-	PUNCT
cana-2873	54	4	nsint(q	nsint(q	NOUN
cana-2873	54	5	-	-	PUNCT
cana-2873	54	6	nscl(u	nscl(u	NOUN
cana-2873	54	7	)	)	PUNCT
cana-2873	54	8	)	)	PUNCT
cana-2873	54	9	(	(	PUNCT
cana-2873	54	10	resp	resp	NOUN
cana-2873	54	11	.	.	PUNCT
cana-2873	55	1	u⊆q	u⊆q	PROPN
cana-2873	55	2	-	-	PUNCT
cana-2873	55	3	nscl(q	nscl(q	ADP
cana-2873	55	4	-	-	PUNCT
cana-2873	55	5	nsint(u	nsint(u	PROPN
cana-2873	55	6	)	)	PUNCT
cana-2873	55	7	)	)	PUNCT
cana-2873	55	8	,	,	PUNCT
cana-2873	55	9	u⊆q	u⊆q	PROPN
cana-2873	55	10	-	-	PUNCT
cana-2873	55	11	nsint(q	nsint(q	NOUN
cana-2873	55	12	-	-	PUNCT
cana-2873	55	13	nscl(q	nscl(q	ADP
cana-2873	55	14	-	-	PUNCT
cana-2873	55	15	nsint(u	nsint(u	PROPN
cana-2873	55	16	)	)	PUNCT
cana-2873	55	17	)	)	PUNCT
cana-2873	55	18	)	)	PUNCT
cana-2873	55	19	&	&	CCONJ
cana-2873	55	20	u⊆q	u⊆q	PROPN
cana-2873	55	21	-	-	PUNCT
cana-2873	55	22	nscl(q	nscl(q	ADP
cana-2873	55	23	-	-	PUNCT
cana-2873	55	24	nsint(u	nsint(u	PROPN
cana-2873	55	25	)	)	PUNCT
cana-2873	55	26	)	)	PUNCT
cana-2873	55	27	∪	∪	ADP
cana-2873	55	28	q	q	NOUN
cana-2873	55	29	-	-	PUNCT
cana-2873	55	30	nsint(q	nsint(q	NOUN
cana-2873	55	31	-	-	PUNCT
cana-2873	55	32	nscl(u	nscl(u	NOUN
cana-2873	55	33	)	)	PUNCT
cana-2873	55	34	)	)	PUNCT
cana-2873	55	35	)	)	PUNCT
cana-2873	55	36	.	.	PUNCT
cana-2873	56	1	the	the	DET
cana-2873	56	2	complement	complement	NOUN
cana-2873	56	3	of	of	ADP
cana-2873	56	4	an	an	DET
cana-2873	56	5	q	q	NOUN
cana-2873	56	6	-	-	PUNCT
cana-2873	56	7	ns	ns	ADJ
cana-2873	56	8	o	o	NOUN
cana-2873	56	9	set	set	NOUN
cana-2873	56	10	(	(	PUNCT
cana-2873	56	11	resp	resp	NOUN
cana-2873	56	12	.	.	PUNCT
cana-2873	57	1	q	q	X
cana-2873	57	2	-	-	PUNCT
cana-2873	57	3	ns	ns	ADJ
cana-2873	57	4	o	o	NOUN
cana-2873	57	5	set	set	NOUN
cana-2873	57	6	,	,	PUNCT
cana-2873	57	7	q	q	ADJ
cana-2873	57	8	-	-	PUNCT
cana-2873	57	9	nsαo	nsαo	NOUN
cana-2873	57	10	set	set	PROPN
cana-2873	57	11	&	&	CCONJ
cana-2873	57	12	q	q	NOUN
cana-2873	57	13	-	-	PUNCT
cana-2873	57	14	nsbo	nsbo	PROPN
cana-2873	57	15	set	set	NOUN
cana-2873	57	16	)	)	PUNCT
cana-2873	57	17	is	be	AUX
cana-2873	57	18	called	call	VERB
cana-2873	57	19	a	a	DET
cana-2873	57	20	quadripar	quadripar	NOUN
cana-2873	57	21	titioned	titione	VERB
cana-2873	57	22	neutrosophic	neutrosophic	ADJ
cana-2873	57	23	pre	pre	X
cana-2873	57	24	(	(	PUNCT
cana-2873	57	25	resp	resp	NOUN
cana-2873	57	26	.	.	PUNCT
cana-2873	58	1	semi	semi	ADV
cana-2873	58	2	,	,	PUNCT
cana-2873	58	3	α	α	PROPN
cana-2873	58	4	&	&	CCONJ
cana-2873	58	5	b	b	PROPN
cana-2873	58	6	)	)	PUNCT
cana-2873	58	7	closed	close	VERB
cana-2873	58	8	set	set	NOUN
cana-2873	58	9	(	(	PUNCT
cana-2873	58	10	in	in	ADP
cana-2873	58	11	-	-	PUNCT
cana-2873	58	12	short	short	ADJ
cana-2873	58	13	,	,	PUNCT
cana-2873	58	14	q	q	ADJ
cana-2873	58	15	-	-	PUNCT
cana-2873	58	16	ns	ns	ADJ
cana-2873	58	17	c	c	NOUN
cana-2873	58	18	set	set	NOUN
cana-2873	58	19	(	(	PUNCT
cana-2873	58	20	resp	resp	NOUN
cana-2873	58	21	.	.	PUNCT
cana-2873	59	1	q	q	X
cana-2873	59	2	-	-	PUNCT
cana-2873	59	3	ns	ns	ADJ
cana-2873	59	4	ƿ	ƿ	PROPN
cana-2873	59	5	c	c	NOUN
cana-2873	59	6	set	set	NOUN
cana-2873	59	7	,	,	PUNCT
cana-2873	59	8	qnsαc	qnsαc	NOUN
cana-2873	59	9	set	set	NOUN
cana-2873	59	10	&	&	CCONJ
cana-2873	59	11	q	q	PROPN
cana-2873	59	12	-	-	PUNCT
cana-2873	59	13	nsbc	nsbc	ADJ
cana-2873	59	14	set	set	NOUN
cana-2873	59	15	)	)	PUNCT
cana-2873	59	16	)	)	PUNCT
cana-2873	59	17	in	in	ADP
cana-2873	59	18	z.	z.	PROPN
cana-2873	59	19	the	the	DET
cana-2873	59	20	family	family	NOUN
cana-2873	59	21	of	of	ADP
cana-2873	59	22	all	all	DET
cana-2873	59	23	q	q	NOUN
cana-2873	59	24	-	-	PUNCT
cana-2873	59	25	nspo	nspo	NOUN
cana-2873	59	26	set	set	NOUN
cana-2873	59	27	(	(	PUNCT
cana-2873	59	28	resp	resp	NOUN
cana-2873	59	29	.	.	PUNCT
cana-2873	60	1	q	q	X
cana-2873	60	2	-	-	PUNCT
cana-2873	60	3	nspc	nspc	NOUN
cana-2873	60	4	set	set	NOUN
cana-2873	60	5	,	,	PUNCT
cana-2873	60	6	q	q	ADJ
cana-2873	60	7	-	-	PUNCT
cana-2873	60	8	nsso	nsso	ADJ
cana-2873	60	9	set	set	NOUN
cana-2873	60	10	,	,	PUNCT
cana-2873	60	11	q	q	ADJ
cana-2873	60	12	-	-	PUNCT
cana-2873	60	13	nssc	nssc	NOUN
cana-2873	60	14	set	set	NOUN
cana-2873	60	15	,	,	PUNCT
cana-2873	60	16	q	q	ADJ
cana-2873	60	17	-	-	PUNCT
cana-2873	60	18	nsαo	nsαo	NOUN
cana-2873	60	19	set	set	NOUN
cana-2873	60	20	,	,	PUNCT
cana-2873	60	21	q	q	ADJ
cana-2873	60	22	-	-	PUNCT
cana-2873	60	23	nsαc	nsαc	NOUN
cana-2873	60	24	set	set	NOUN
cana-2873	60	25	,	,	PUNCT
cana-2873	60	26	q	q	NOUN
cana-2873	60	27	-	-	PUNCT
cana-2873	60	28	nsbo	nsbo	NOUN
cana-2873	60	29	set	set	PROPN
cana-2873	60	30	&	&	CCONJ
cana-2873	60	31	q	q	PROPN
cana-2873	60	32	-	-	PUNCT
cana-2873	60	33	nsbc	nsbc	ADJ
cana-2873	60	34	set	set	NOUN
cana-2873	60	35	)	)	PUNCT
cana-2873	60	36	of	of	ADP
cana-2873	60	37	z	z	PROPN
cana-2873	60	38	is	be	AUX
cana-2873	60	39	denoted	denote	VERB
cana-2873	60	40	by	by	ADP
cana-2873	60	41	q	q	NOUN
cana-2873	60	42	-	-	PUNCT
cana-2873	60	43	nspos(z	nspos(z	NOUN
cana-2873	60	44	)	)	PUNCT
cana-2873	60	45	(	(	PUNCT
cana-2873	60	46	resp	resp	NOUN
cana-2873	60	47	.	.	PUNCT
cana-2873	61	1	q	q	X
cana-2873	61	2	-	-	PUNCT
cana-2873	61	3	nspcs(z	nspcs(z	NOUN
cana-2873	61	4	)	)	PUNCT
cana-2873	61	5	,	,	PUNCT
cana-2873	61	6	qnssos(z	qnssos(z	NOUN
cana-2873	61	7	)	)	PUNCT
cana-2873	61	8	,	,	PUNCT
cana-2873	61	9	qnsscs(z	qnsscs(z	PROPN
cana-2873	61	10	)	)	PUNCT
cana-2873	61	11	,	,	PUNCT
cana-2873	61	12	q	q	PROPN
cana-2873	61	13	-	-	PUNCT
cana-2873	61	14	nsαos(z	nsαos(z	NOUN
cana-2873	61	15	)	)	PUNCT
cana-2873	61	16	,	,	PUNCT
cana-2873	61	17	q	q	NOUN
cana-2873	61	18	-	-	PUNCT
cana-2873	61	19	nsαcs(z	nsαcs(z	NOUN
cana-2873	61	20	)	)	PUNCT
cana-2873	61	21	,	,	PUNCT
cana-2873	61	22	q	q	NOUN
cana-2873	61	23	-	-	PUNCT
cana-2873	61	24	nsbos(z	nsbos(z	NOUN
cana-2873	61	25	)	)	PUNCT
cana-2873	61	26	&	&	CCONJ
cana-2873	61	27	q	q	NOUN
cana-2873	61	28	-	-	PUNCT
cana-2873	61	29	nsbcs(z	nsbcs(z	NOUN
cana-2873	61	30	)	)	PUNCT
cana-2873	61	31	)	)	PUNCT
cana-2873	61	32	.	.	PUNCT
cana-2873	62	1	definition	definition	NOUN
cana-2873	62	2	2.6	2.6	NUM
cana-2873	62	3	.	.	PUNCT
cana-2873	63	1	let	let	VERB
cana-2873	63	2	(	(	PUNCT
cana-2873	63	3	z	z	NOUN
cana-2873	63	4	,	,	PUNCT
cana-2873	63	5	γq	γq	AUX
cana-2873	63	6	)	)	PUNCT
cana-2873	63	7	be	be	AUX
cana-2873	63	8	q	q	NOUN
cana-2873	63	9	-	-	NOUN
cana-2873	63	10	nsts	nst	NOUN
cana-2873	63	11	on	on	ADP
cana-2873	63	12	z	z	PROPN
cana-2873	63	13	and	and	CCONJ
cana-2873	63	14	u	u	PRON
cana-2873	63	15	be	be	VERB
cana-2873	63	16	an	an	DET
cana-2873	63	17	q	q	NOUN
cana-2873	63	18	-	-	PUNCT
cana-2873	63	19	nss	nss	NOUN
cana-2873	63	20	on	on	ADP
cana-2873	63	21	z.	z.	PROPN
cana-2873	63	22	then	then	ADV
cana-2873	63	23	u	u	NOUN
cana-2873	63	24	is	be	AUX
cana-2873	63	25	said	say	VERB
cana-2873	63	26	to	to	PART
cana-2873	63	27	be	be	AUX
cana-2873	63	28	a	a	DET
cana-2873	63	29	quadripartitioned	quadripartitioned	ADJ
cana-2873	63	30	neutrosophic	neutrosophic	ADJ
cana-2873	63	31	β	β	X
cana-2873	63	32	open	open	ADJ
cana-2873	63	33	set	set	NOUN
cana-2873	63	34	(	(	PUNCT
cana-2873	63	35	in	in	ADP
cana-2873	63	36	-	-	PUNCT
cana-2873	63	37	short	short	ADJ
cana-2873	63	38	,	,	PUNCT
cana-2873	63	39	q	q	NOUN
cana-2873	63	40	-	-	PUNCT
cana-2873	63	41	nsβo	nsβo	ADJ
cana-2873	63	42	)	)	PUNCT
cana-2873	63	43	set	set	VERB
cana-2873	63	44	if	if	SCONJ
cana-2873	63	45	u⊆q	u⊆q	NOUN
cana-2873	63	46	-	-	PUNCT
cana-2873	63	47	nscl(q	nscl(q	ADP
cana-2873	63	48	-	-	PUNCT
cana-2873	63	49	nsint(q	nsint(q	NOUN
cana-2873	63	50	-	-	PUNCT
cana-2873	63	51	nscl(u	nscl(u	NOUN
cana-2873	63	52	)	)	PUNCT
cana-2873	63	53	)	)	PUNCT
cana-2873	63	54	)	)	PUNCT
cana-2873	63	55	.	.	PUNCT
cana-2873	64	1	the	the	DET
cana-2873	64	2	complement	complement	NOUN
cana-2873	64	3	of	of	ADP
cana-2873	64	4	an	an	DET
cana-2873	64	5	q	q	NOUN
cana-2873	64	6	-	-	PUNCT
cana-2873	64	7	nsβo	nsβo	ADJ
cana-2873	64	8	set	set	NOUN
cana-2873	64	9	is	be	AUX
cana-2873	64	10	called	call	VERB
cana-2873	64	11	a	a	DET
cana-2873	64	12	quadripartitioned	quadripartitione	VERB
cana-2873	64	13	neutrosophic	neutrosophic	PROPN
cana-2873	64	14	β	β	X
cana-2873	64	15	closed	close	VERB
cana-2873	64	16	set	set	NOUN
cana-2873	64	17	(	(	PUNCT
cana-2873	64	18	in	in	ADP
cana-2873	64	19	-	-	PUNCT
cana-2873	64	20	short	short	ADJ
cana-2873	64	21	,	,	PUNCT
cana-2873	64	22	qnsβc	qnsβc	PROPN
cana-2873	64	23	set	set	VERB
cana-2873	64	24	in	in	ADP
cana-2873	64	25	z.	z.	PROPN
cana-2873	64	26	the	the	DET
cana-2873	64	27	family	family	NOUN
cana-2873	64	28	of	of	ADP
cana-2873	64	29	all	all	DET
cana-2873	64	30	q	q	ADJ
cana-2873	64	31	-	-	PUNCT
cana-2873	64	32	nsβo	nsβo	ADJ
cana-2873	64	33	set	set	NOUN
cana-2873	64	34	(	(	PUNCT
cana-2873	64	35	resp	resp	NOUN
cana-2873	64	36	.	.	PUNCT
cana-2873	65	1	q	q	X
cana-2873	65	2	-	-	PUNCT
cana-2873	65	3	nsβc	nsβc	NOUN
cana-2873	65	4	set	set	NOUN
cana-2873	65	5	)	)	PUNCT
cana-2873	65	6	of	of	ADP
cana-2873	65	7	z	z	PROPN
cana-2873	65	8	is	be	AUX
cana-2873	65	9	denoted	denote	VERB
cana-2873	65	10	by	by	ADP
cana-2873	65	11	q	q	NOUN
cana-2873	65	12	-	-	PUNCT
cana-2873	65	13	nsβos(z	nsβos(z	NOUN
cana-2873	65	14	)	)	PUNCT
cana-2873	65	15	(	(	PUNCT
cana-2873	65	16	resp	resp	NOUN
cana-2873	65	17	.	.	PUNCT
cana-2873	66	1	qnsβcs(z	qnsβcs(z	NOUN
cana-2873	66	2	)	)	PUNCT
cana-2873	66	3	)	)	PUNCT
cana-2873	66	4	.	.	PUNCT
cana-2873	67	1	definition	definition	NOUN
cana-2873	67	2	2.7.the	2.7.the	DET
cana-2873	67	3	q	q	ADJ
cana-2873	67	4	-	-	PUNCT
cana-2873	67	5	nsβ	nsβ	ADJ
cana-2873	67	6	interior	interior	NOUN
cana-2873	67	7	of	of	ADP
cana-2873	67	8	u	u	PROPN
cana-2873	67	9	(	(	PUNCT
cana-2873	67	10	briefly	briefly	ADV
cana-2873	67	11	,	,	PUNCT
cana-2873	67	12	q	q	NOUN
cana-2873	67	13	-	-	NOUN
cana-2873	67	14	nsβint(u	nsβint(u	ADJ
cana-2873	67	15	)	)	PUNCT
cana-2873	67	16	)	)	PUNCT
cana-2873	67	17	and	and	CCONJ
cana-2873	67	18	q	q	X
cana-2873	67	19	-	-	PUNCT
cana-2873	67	20	nsβ	nsβ	ADV
cana-2873	67	21	closure	closure	NOUN
cana-2873	67	22	of	of	ADP
cana-2873	67	23	u	u	NOUN
cana-2873	67	24	(	(	PUNCT
cana-2873	67	25	briefly	briefly	ADV
cana-2873	67	26	,	,	PUNCT
cana-2873	67	27	q	q	NOUN
cana-2873	67	28	-	-	PUNCT
cana-2873	67	29	nsβcl(u	nsβcl(u	NOUN
cana-2873	67	30	)	)	PUNCT
cana-2873	67	31	)	)	PUNCT
cana-2873	67	32	are	be	AUX
cana-2873	67	33	defined	define	VERB
cana-2873	67	34	as	as	ADP
cana-2873	67	35	(	(	PUNCT
cana-2873	67	36	i	i	NOUN
cana-2873	67	37	)	)	PUNCT
cana-2873	67	38	q	q	NOUN
cana-2873	67	39	-	-	NOUN
cana-2873	67	40	nsβint(u	nsβint(u	ADJ
cana-2873	67	41	)	)	PUNCT
cana-2873	68	1	=	=	SYM
cana-2873	68	2	∪{uo	∪{uo	PROPN
cana-2873	68	3	:	:	PUNCT
cana-2873	68	4	uo	uo	NUM
cana-2873	68	5	⊆	⊆	NUM
cana-2873	68	6	u	u	NOUN
cana-2873	68	7	&	&	CCONJ
cana-2873	68	8	uo	uo	PROPN
cana-2873	68	9	is	be	AUX
cana-2873	68	10	a	a	DET
cana-2873	68	11	q	q	NOUN
cana-2873	68	12	-	-	PUNCT
cana-2873	68	13	nsβo	nsβo	ADJ
cana-2873	68	14	set	set	NOUN
cana-2873	68	15	in	in	ADP
cana-2873	68	16	z	z	NOUN
cana-2873	68	17	}	}	PUNCT
cana-2873	68	18	.	.	PUNCT
cana-2873	69	1	(	(	PUNCT
cana-2873	69	2	ii	ii	NOUN
cana-2873	69	3	)	)	PUNCT
cana-2873	69	4	q	q	NOUN
cana-2873	69	5	-	-	PUNCT
cana-2873	69	6	nsβcl(u	nsβcl(u	NOUN
cana-2873	69	7	)	)	PUNCT
cana-2873	70	1	=	=	PUNCT
cana-2873	70	2	∩{uo	∩{uo	NUM
cana-2873	70	3	:	:	PUNCT
cana-2873	70	4	u	u	PROPN
cana-2873	70	5	⊆	⊆	NUM
cana-2873	70	6	uo	uo	NOUN
cana-2873	70	7	&	&	CCONJ
cana-2873	70	8	uo	uo	PROPN
cana-2873	70	9	is	be	AUX
cana-2873	70	10	a	a	DET
cana-2873	70	11	q	q	ADJ
cana-2873	70	12	-	-	PUNCT
cana-2873	70	13	nsβc	nsβc	NOUN
cana-2873	70	14	set	set	NOUN
cana-2873	70	15	in	in	ADP
cana-2873	70	16	z	z	NOUN
cana-2873	70	17	}	}	PUNCT
cana-2873	70	18	.	.	PUNCT
cana-2873	71	1	definition	definition	NOUN
cana-2873	71	2	2.8	2.8	NUM
cana-2873	71	3	.	.	PUNCT
cana-2873	72	1	let	let	VERB
cana-2873	72	2	(	(	PUNCT
cana-2873	72	3	z1	z1	VERB
cana-2873	72	4	,	,	PUNCT
cana-2873	72	5	γq	γq	NOUN
cana-2873	72	6	)	)	PUNCT
cana-2873	72	7	and	and	CCONJ
cana-2873	72	8	(	(	PUNCT
cana-2873	72	9	z2	z2	PROPN
cana-2873	72	10	,	,	PUNCT
cana-2873	72	11	σq	σq	NOUN
cana-2873	72	12	)	)	PUNCT
cana-2873	72	13	be	be	VERB
cana-2873	72	14	any	any	DET
cana-2873	72	15	two	two	NUM
cana-2873	72	16	q	q	NOUN
cana-2873	72	17	-	-	PUNCT
cana-2873	72	18	nsts	nst	NOUN
cana-2873	72	19	’s	’s	NOUN
cana-2873	72	20	.	.	PUNCT
cana-2873	73	1	a	a	DET
cana-2873	73	2	map	map	NOUN
cana-2873	73	3	k	k	X
cana-2873	73	4	:	:	PUNCT
cana-2873	73	5	(	(	PUNCT
cana-2873	73	6	z1	z1	VERB
cana-2873	73	7	,	,	PUNCT
cana-2873	73	8	γq	γq	ADP
cana-2873	73	9	)	)	PUNCT
cana-2873	73	10	→	→	SYM
cana-2873	73	11	(	(	PUNCT
cana-2873	73	12	z2	z2	PROPN
cana-2873	73	13	,	,	PUNCT
cana-2873	73	14	σq	σq	NOUN
cana-2873	73	15	)	)	PUNCT
cana-2873	73	16	is	be	AUX
cana-2873	73	17	said	say	VERB
cana-2873	73	18	to	to	PART
cana-2873	73	19	be	be	AUX
cana-2873	73	20	quadripartitioned	quadripartitione	VERB
cana-2873	73	21	neutrosophic	neutrosophic	ADJ
cana-2873	73	22	(	(	PUNCT
cana-2873	73	23	resp	resp	NOUN
cana-2873	73	24	.	.	PUNCT
cana-2873	74	1	semi	semi	ADJ
cana-2873	74	2	,	,	PUNCT
cana-2873	74	3	pre	pre	ADJ
cana-2873	74	4	,	,	PUNCT
cana-2873	74	5	b	b	PROPN
cana-2873	74	6	&	&	CCONJ
cana-2873	74	7	β	β	NOUN
cana-2873	74	8	)	)	PUNCT
cana-2873	74	9	continuous	continuous	ADJ
cana-2873	74	10	(	(	PUNCT
cana-2873	74	11	briefly	briefly	ADV
cana-2873	74	12	,	,	PUNCT
cana-2873	74	13	q	q	NOUN
cana-2873	74	14	-	-	PUNCT
cana-2873	74	15	nscts	nsct	NOUN
cana-2873	74	16	(	(	PUNCT
cana-2873	74	17	resp	resp	NOUN
cana-2873	74	18	.	.	PUNCT
cana-2873	75	1	q	q	X
cana-2873	75	2	-	-	PUNCT
cana-2873	75	3	nsscts	nssct	NOUN
cana-2873	75	4	,	,	PUNCT
cana-2873	75	5	q	q	NOUN
cana-2873	75	6	-	-	PUNCT
cana-2873	75	7	nspcts	nspcts	NOUN
cana-2873	75	8	,	,	PUNCT
cana-2873	75	9	q	q	NOUN
cana-2873	75	10	-	-	PUNCT
cana-2873	75	11	nsbcts	nsbct	NOUN
cana-2873	75	12	&	&	CCONJ
cana-2873	75	13	q	q	NOUN
cana-2873	75	14	-	-	PUNCT
cana-2873	75	15	nsβcts	nsβct	NOUN
cana-2873	75	16	)	)	PUNCT
cana-2873	75	17	)	)	PUNCT
cana-2873	76	1	if	if	SCONJ
cana-2873	76	2	the	the	DET
cana-2873	76	3	inverse	inverse	ADJ
cana-2873	76	4	image	image	NOUN
cana-2873	76	5	of	of	ADP
cana-2873	76	6	every	every	DET
cana-2873	76	7	q	q	NOUN
cana-2873	76	8	-	-	PUNCT
cana-2873	76	9	nso	nso	NOUN
cana-2873	76	10	set	set	VERB
cana-2873	76	11	in	in	ADP
cana-2873	76	12	(	(	PUNCT
cana-2873	76	13	z2	z2	PROPN
cana-2873	76	14	,	,	PUNCT
cana-2873	76	15	σq	σq	NOUN
cana-2873	76	16	)	)	PUNCT
cana-2873	76	17	is	be	AUX
cana-2873	76	18	a	a	DET
cana-2873	76	19	q	q	NOUN
cana-2873	76	20	-	-	PUNCT
cana-2873	76	21	nso	nso	NOUN
cana-2873	76	22	set	set	NOUN
cana-2873	76	23	(	(	PUNCT
cana-2873	76	24	resp	resp	NOUN
cana-2873	76	25	.	.	PUNCT
cana-2873	77	1	q	q	X
cana-2873	77	2	-	-	ADJ
cana-2873	77	3	nsso	nsso	ADJ
cana-2873	77	4	set	set	NOUN
cana-2873	77	5	,	,	PUNCT
cana-2873	77	6	q	q	NOUN
cana-2873	77	7	-	-	PUNCT
cana-2873	77	8	nspo	nspo	NOUN
cana-2873	77	9	set	set	NOUN
cana-2873	77	10	,	,	PUNCT
cana-2873	77	11	q	q	NOUN
cana-2873	77	12	-	-	PUNCT
cana-2873	77	13	nsbo	nsbo	NOUN
cana-2873	77	14	set	set	PROPN
cana-2873	77	15	&	&	CCONJ
cana-2873	77	16	q	q	NOUN
cana-2873	77	17	-	-	PUNCT
cana-2873	77	18	nsβo	nsβo	ADJ
cana-2873	77	19	set	set	NOUN
cana-2873	77	20	)	)	PUNCT
cana-2873	77	21	in	in	ADP
cana-2873	77	22	(	(	PUNCT
cana-2873	77	23	z1	z1	NOUN
cana-2873	77	24	,	,	PUNCT
cana-2873	77	25	γq	γq	ADP
cana-2873	77	26	)	)	PUNCT
cana-2873	77	27	.	.	PUNCT
cana-2873	78	1	definition	definition	NOUN
cana-2873	78	2	2.9	2.9	NUM
cana-2873	78	3	.	.	PUNCT
cana-2873	79	1	a	a	DET
cana-2873	79	2	map	map	NOUN
cana-2873	79	3	k	k	X
cana-2873	79	4	:	:	PUNCT
cana-2873	79	5	(	(	PUNCT
cana-2873	79	6	z1	z1	VERB
cana-2873	79	7	,	,	PUNCT
cana-2873	79	8	γq)→	γq)→	X
cana-2873	79	9	(	(	PUNCT
cana-2873	79	10	z2	z2	PROPN
cana-2873	79	11	,	,	PUNCT
cana-2873	79	12	σq	σq	NOUN
cana-2873	79	13	)	)	PUNCT
cana-2873	79	14	is	be	AUX
cana-2873	79	15	called	call	VERB
cana-2873	79	16	a	a	DET
cana-2873	79	17	quadripartitioned	quadripartitione	VERB
cana-2873	79	18	neutrosophic	neutrosophic	ADJ
cana-2873	79	19	β	β	X
cana-2873	79	20	-	-	NOUN
cana-2873	79	21	irresolute	irresolute	ADJ
cana-2873	79	22	(	(	PUNCT
cana-2873	79	23	briefly	briefly	ADV
cana-2873	79	24	,	,	PUNCT
cana-2873	79	25	q	q	ADJ
cana-2873	79	26	-	-	PUNCT
cana-2873	79	27	nsβirr	nsβirr	NOUN
cana-2873	79	28	)	)	PUNCT
cana-2873	79	29	map	map	NOUN
cana-2873	79	30	if	if	SCONJ
cana-2873	79	31	k−1(λ	k−1(λ	NOUN
cana-2873	79	32	)	)	PUNCT
cana-2873	79	33	is	be	AUX
cana-2873	79	34	a	a	DET
cana-2873	79	35	q	q	NOUN
cana-2873	79	36	-	-	PUNCT
cana-2873	79	37	nsβo	nsβo	ADJ
cana-2873	79	38	set	set	NOUN
cana-2873	79	39	in	in	ADP
cana-2873	79	40	(	(	PUNCT
cana-2873	79	41	z1	z1	NOUN
cana-2873	79	42	,	,	PUNCT
cana-2873	79	43	γq	γq	ADP
cana-2873	79	44	)	)	PUNCT
cana-2873	79	45	for	for	ADP
cana-2873	79	46	every	every	DET
cana-2873	79	47	q	q	NOUN
cana-2873	79	48	-	-	PUNCT
cana-2873	79	49	nsβo	nsβo	ADJ
cana-2873	79	50	set	set	ADJ
cana-2873	79	51	λ	λ	PROPN
cana-2873	79	52	of	of	ADP
cana-2873	79	53	(	(	PUNCT
cana-2873	79	54	z2	z2	PROPN
cana-2873	79	55	,	,	PUNCT
cana-2873	79	56	σq	σq	NOUN
cana-2873	79	57	)	)	PUNCT
cana-2873	79	58	.	.	PUNCT
cana-2873	80	1	definition	definition	NOUN
cana-2873	80	2	2.10	2.10	NUM
cana-2873	80	3	.	.	PUNCT
cana-2873	81	1	a	a	DET
cana-2873	81	2	q	q	NOUN
cana-2873	81	3	-	-	PUNCT
cana-2873	81	4	nsts	nst	NOUN
cana-2873	81	5	(	(	PUNCT
cana-2873	81	6	z	z	NOUN
cana-2873	81	7	,	,	PUNCT
cana-2873	81	8	γq	γq	ADP
cana-2873	81	9	)	)	PUNCT
cana-2873	81	10	is	be	AUX
cana-2873	81	11	said	say	VERB
cana-2873	81	12	to	to	PART
cana-2873	81	13	be	be	AUX
cana-2873	81	14	an	an	DET
cana-2873	81	15	quadripartitioned	quadripartitioned	ADJ
cana-2873	81	16	neutrosophic	neutrosophic	ADJ
cana-2873	81	17	β	β	SYM
cana-2873	81	18	u	u	PROPN
cana-2873	81	19	1/2	1/2	NUM
cana-2873	81	20	(	(	PUNCT
cana-2873	81	21	in	in	ADP
cana-2873	81	22	short	short	ADJ
cana-2873	81	23	q	q	ADJ
cana-2873	81	24	-	-	PUNCT
cana-2873	81	25	nsβu	nsβu	NOUN
cana-2873	81	26	1/2	1/2	NUM
cana-2873	81	27	)	)	PUNCT
cana-2873	81	28	-space	-space	NOUN
cana-2873	81	29	,	,	PUNCT
cana-2873	81	30	if	if	SCONJ
cana-2873	81	31	every	every	DET
cana-2873	81	32	q	q	NOUN
cana-2873	81	33	-	-	PUNCT
cana-2873	81	34	nsβo	nsβo	ADJ
cana-2873	81	35	set	set	NOUN
cana-2873	81	36	in	in	ADP
cana-2873	81	37	z	z	PROPN
cana-2873	81	38	is	be	AUX
cana-2873	81	39	a	a	DET
cana-2873	81	40	q	q	NOUN
cana-2873	81	41	-	-	PUNCT
cana-2873	81	42	nso	nso	NOUN
cana-2873	81	43	set	set	VERB
cana-2873	81	44	in	in	ADP
cana-2873	81	45	z.	z.	PROPN
cana-2873	81	46	definition	definition	NOUN
cana-2873	81	47	2.11	2.11	NUM
cana-2873	81	48	.	.	PUNCT
cana-2873	82	1	let	let	VERB
cana-2873	82	2	(	(	PUNCT
cana-2873	82	3	z1	z1	VERB
cana-2873	82	4	,	,	PUNCT
cana-2873	82	5	γq	γq	NOUN
cana-2873	82	6	)	)	PUNCT
cana-2873	82	7	and	and	CCONJ
cana-2873	82	8	(	(	PUNCT
cana-2873	82	9	z2	z2	PROPN
cana-2873	82	10	,	,	PUNCT
cana-2873	82	11	σq	σq	NOUN
cana-2873	82	12	)	)	PUNCT
cana-2873	82	13	be	be	VERB
cana-2873	82	14	any	any	DET
cana-2873	82	15	two	two	NUM
cana-2873	82	16	q	q	NOUN
cana-2873	82	17	-	-	PUNCT
cana-2873	82	18	nsts	nst	NOUN
cana-2873	82	19	’s	’s	NOUN
cana-2873	82	20	.	.	PUNCT
cana-2873	83	1	a	a	DET
cana-2873	83	2	map	map	NOUN
cana-2873	83	3	k	k	X
cana-2873	83	4	:	:	PUNCT
cana-2873	83	5	(	(	PUNCT
cana-2873	83	6	z1	z1	VERB
cana-2873	83	7	,	,	PUNCT
cana-2873	83	8	γq	γq	ADP
cana-2873	83	9	)	)	PUNCT
cana-2873	83	10	→	→	SYM
cana-2873	83	11	(	(	PUNCT
cana-2873	83	12	z2	z2	PROPN
cana-2873	83	13	,	,	PUNCT
cana-2873	83	14	σq	σq	NOUN
cana-2873	83	15	)	)	PUNCT
cana-2873	83	16	is	be	AUX
cana-2873	83	17	said	say	VERB
cana-2873	83	18	to	to	PART
cana-2873	83	19	be	be	AUX
cana-2873	83	20	quadripartitioned	quadripartitione	VERB
cana-2873	83	21	neutrosophic	neutrosophic	ADJ
cana-2873	83	22	(	(	PUNCT
cana-2873	83	23	resp	resp	NOUN
cana-2873	83	24	.	.	PUNCT
cana-2873	84	1	semi	semi	ADJ
cana-2873	84	2	,	,	PUNCT
cana-2873	84	3	pre	pre	ADJ
cana-2873	84	4	,	,	PUNCT
cana-2873	84	5	b	b	PROPN
cana-2873	84	6	&	&	CCONJ
cana-2873	84	7	β	β	NOUN
cana-2873	84	8	)	)	PUNCT
cana-2873	84	9	open	open	ADJ
cana-2873	84	10	map	map	NOUN
cana-2873	84	11	(	(	PUNCT
cana-2873	84	12	briefly	briefly	ADV
cana-2873	84	13	,	,	PUNCT
cana-2873	84	14	q	q	ADJ
cana-2873	84	15	-	-	PUNCT
cana-2873	84	16	nso	nso	NOUN
cana-2873	84	17	communications	communication	NOUN
cana-2873	84	18	on	on	ADP
cana-2873	84	19	applied	apply	VERB
cana-2873	84	20	nonlinear	nonlinear	ADJ
cana-2873	84	21	analysis	analysis	NOUN
cana-2873	84	22	issn	issn	NOUN
cana-2873	84	23	:	:	PUNCT
cana-2873	84	24	1074	1074	NUM
cana-2873	84	25	-	-	PUNCT
cana-2873	84	26	133x	133x	NUM
cana-2873	84	27	vol	vol	NOUN
cana-2873	84	28	32	32	NUM
cana-2873	84	29	no	no	NOUN
cana-2873	84	30	.	.	PUNCT
cana-2873	85	1	4s	4s	NUM
cana-2873	85	2	(	(	PUNCT
cana-2873	85	3	2025	2025	NUM
cana-2873	85	4	)	)	PUNCT
cana-2873	85	5	583	583	NUM
cana-2873	85	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	85	7	(	(	PUNCT
cana-2873	85	8	resp	resp	NOUN
cana-2873	85	9	.	.	PUNCT
cana-2873	86	1	q	q	X
cana-2873	86	2	-	-	PUNCT
cana-2873	86	3	nsso	nsso	ADJ
cana-2873	86	4	,	,	PUNCT
cana-2873	86	5	q	q	NOUN
cana-2873	86	6	-	-	PUNCT
cana-2873	86	7	nspo	nspo	NOUN
cana-2873	86	8	,	,	PUNCT
cana-2873	86	9	q	q	NOUN
cana-2873	86	10	-	-	PUNCT
cana-2873	86	11	nsbo	nsbo	PROPN
cana-2873	86	12	&	&	CCONJ
cana-2873	86	13	q	q	NOUN
cana-2873	86	14	-	-	PUNCT
cana-2873	86	15	nsβo	nsβo	ADJ
cana-2873	86	16	)	)	PUNCT
cana-2873	86	17	)	)	PUNCT
cana-2873	87	1	if	if	SCONJ
cana-2873	87	2	the	the	DET
cana-2873	87	3	inverse	inverse	ADJ
cana-2873	87	4	image	image	NOUN
cana-2873	87	5	of	of	ADP
cana-2873	87	6	every	every	DET
cana-2873	87	7	q	q	NOUN
cana-2873	87	8	-	-	PUNCT
cana-2873	87	9	nso	nso	NOUN
cana-2873	87	10	set	set	VERB
cana-2873	87	11	in	in	ADP
cana-2873	87	12	(	(	PUNCT
cana-2873	87	13	z1	z1	NOUN
cana-2873	87	14	,	,	PUNCT
cana-2873	87	15	γq	γq	ADP
cana-2873	87	16	)	)	PUNCT
cana-2873	87	17	is	be	AUX
cana-2873	87	18	a	a	DET
cana-2873	87	19	q	q	NOUN
cana-2873	87	20	-	-	PUNCT
cana-2873	87	21	nso	nso	NOUN
cana-2873	87	22	set	set	NOUN
cana-2873	87	23	(	(	PUNCT
cana-2873	87	24	resp	resp	NOUN
cana-2873	87	25	.	.	PUNCT
cana-2873	88	1	q	q	X
cana-2873	88	2	-	-	ADJ
cana-2873	88	3	nsso	nsso	ADJ
cana-2873	88	4	set	set	NOUN
cana-2873	88	5	,	,	PUNCT
cana-2873	88	6	q	q	NOUN
cana-2873	88	7	-	-	PUNCT
cana-2873	88	8	nspo	nspo	NOUN
cana-2873	88	9	set	set	NOUN
cana-2873	88	10	,	,	PUNCT
cana-2873	88	11	q	q	NOUN
cana-2873	88	12	-	-	PUNCT
cana-2873	88	13	nsbo	nsbo	NOUN
cana-2873	88	14	set	set	PROPN
cana-2873	88	15	&	&	CCONJ
cana-2873	88	16	q	q	NOUN
cana-2873	88	17	-	-	PUNCT
cana-2873	88	18	nsβo	nsβo	ADJ
cana-2873	88	19	set	set	NOUN
cana-2873	88	20	)	)	PUNCT
cana-2873	88	21	in	in	ADP
cana-2873	88	22	(	(	PUNCT
cana-2873	88	23	z2	z2	PROPN
cana-2873	88	24	,	,	PUNCT
cana-2873	88	25	σq	σq	NOUN
cana-2873	88	26	)	)	PUNCT
cana-2873	88	27	.	.	PUNCT
cana-2873	89	1	definition	definition	NOUN
cana-2873	89	2	2.12	2.12	NUM
cana-2873	89	3	.	.	PUNCT
cana-2873	90	1	let	let	VERB
cana-2873	90	2	(	(	PUNCT
cana-2873	90	3	z1	z1	VERB
cana-2873	90	4	,	,	PUNCT
cana-2873	90	5	γq	γq	NOUN
cana-2873	90	6	)	)	PUNCT
cana-2873	90	7	and	and	CCONJ
cana-2873	90	8	(	(	PUNCT
cana-2873	90	9	z2	z2	PROPN
cana-2873	90	10	,	,	PUNCT
cana-2873	90	11	σq	σq	NOUN
cana-2873	90	12	)	)	PUNCT
cana-2873	90	13	be	be	VERB
cana-2873	90	14	any	any	DET
cana-2873	90	15	two	two	NUM
cana-2873	90	16	q	q	NOUN
cana-2873	90	17	-	-	PUNCT
cana-2873	90	18	nsts	nst	NOUN
cana-2873	90	19	’s	’s	NOUN
cana-2873	90	20	.	.	PUNCT
cana-2873	91	1	a	a	DET
cana-2873	91	2	map	map	NOUN
cana-2873	91	3	k	k	X
cana-2873	91	4	:	:	PUNCT
cana-2873	91	5	(	(	PUNCT
cana-2873	91	6	z1	z1	VERB
cana-2873	91	7	,	,	PUNCT
cana-2873	91	8	γq	γq	ADP
cana-2873	91	9	)	)	PUNCT
cana-2873	91	10	→	→	SYM
cana-2873	91	11	(	(	PUNCT
cana-2873	91	12	z2	z2	PROPN
cana-2873	91	13	,	,	PUNCT
cana-2873	91	14	σq	σq	NOUN
cana-2873	91	15	)	)	PUNCT
cana-2873	91	16	is	be	AUX
cana-2873	91	17	said	say	VERB
cana-2873	91	18	to	to	PART
cana-2873	91	19	be	be	AUX
cana-2873	91	20	quadripartitioned	quadripartitione	VERB
cana-2873	91	21	neutrosophic	neutrosophic	ADJ
cana-2873	91	22	(	(	PUNCT
cana-2873	91	23	resp	resp	NOUN
cana-2873	91	24	.	.	PUNCT
cana-2873	92	1	semi	semi	ADJ
cana-2873	92	2	,	,	PUNCT
cana-2873	92	3	pre	pre	ADJ
cana-2873	92	4	,	,	PUNCT
cana-2873	92	5	b	b	PROPN
cana-2873	92	6	&	&	CCONJ
cana-2873	92	7	β	β	NOUN
cana-2873	92	8	)	)	PUNCT
cana-2873	92	9	closed	closed	ADJ
cana-2873	92	10	map	map	NOUN
cana-2873	92	11	(	(	PUNCT
cana-2873	92	12	briefly	briefly	ADV
cana-2873	92	13	,	,	PUNCT
cana-2873	92	14	q	q	NOUN
cana-2873	92	15	-	-	PUNCT
cana-2873	92	16	nsc	nsc	NOUN
cana-2873	92	17	(	(	PUNCT
cana-2873	92	18	resp	resp	NOUN
cana-2873	92	19	.	.	PUNCT
cana-2873	93	1	q	q	X
cana-2873	93	2	-	-	PUNCT
cana-2873	93	3	nssc	nssc	NOUN
cana-2873	93	4	,	,	PUNCT
cana-2873	93	5	q	q	NOUN
cana-2873	93	6	-	-	NOUN
cana-2873	93	7	nspc	nspc	NOUN
cana-2873	93	8	,	,	PUNCT
cana-2873	93	9	q	q	PROPN
cana-2873	93	10	-	-	PUNCT
cana-2873	93	11	nsbc	nsbc	PROPN
cana-2873	93	12	&	&	CCONJ
cana-2873	93	13	q	q	NOUN
cana-2873	93	14	-	-	PUNCT
cana-2873	93	15	nsβc	nsβc	VERB
cana-2873	93	16	)	)	PUNCT
cana-2873	93	17	)	)	PUNCT
cana-2873	94	1	if	if	SCONJ
cana-2873	94	2	the	the	DET
cana-2873	94	3	inverse	inverse	ADJ
cana-2873	94	4	image	image	NOUN
cana-2873	94	5	of	of	ADP
cana-2873	94	6	every	every	DET
cana-2873	94	7	q	q	ADJ
cana-2873	94	8	-	-	PUNCT
cana-2873	94	9	nsc	nsc	NOUN
cana-2873	94	10	set	set	NOUN
cana-2873	94	11	in	in	ADP
cana-2873	94	12	(	(	PUNCT
cana-2873	94	13	z1	z1	NOUN
cana-2873	94	14	,	,	PUNCT
cana-2873	94	15	γq	γq	ADP
cana-2873	94	16	)	)	PUNCT
cana-2873	94	17	is	be	AUX
cana-2873	94	18	a	a	DET
cana-2873	94	19	q	q	ADJ
cana-2873	94	20	-	-	PUNCT
cana-2873	94	21	nsc	nsc	NOUN
cana-2873	94	22	set	set	NOUN
cana-2873	94	23	(	(	PUNCT
cana-2873	94	24	resp	resp	NOUN
cana-2873	94	25	.	.	PUNCT
cana-2873	95	1	q	q	X
cana-2873	95	2	-	-	PUNCT
cana-2873	95	3	nssc	nssc	NOUN
cana-2873	95	4	set	set	NOUN
cana-2873	95	5	,	,	PUNCT
cana-2873	95	6	q	q	ADJ
cana-2873	95	7	-	-	PUNCT
cana-2873	95	8	nspc	nspc	NOUN
cana-2873	95	9	set	set	NOUN
cana-2873	95	10	,	,	PUNCT
cana-2873	95	11	q	q	ADJ
cana-2873	95	12	-	-	PUNCT
cana-2873	95	13	nsbc	nsbc	ADJ
cana-2873	95	14	set	set	PROPN
cana-2873	95	15	&	&	CCONJ
cana-2873	95	16	q	q	NOUN
cana-2873	95	17	-	-	PUNCT
cana-2873	95	18	nsβc	nsβc	NOUN
cana-2873	95	19	set	set	NOUN
cana-2873	95	20	)	)	PUNCT
cana-2873	95	21	in	in	ADP
cana-2873	95	22	(	(	PUNCT
cana-2873	95	23	z2	z2	PROPN
cana-2873	95	24	,	,	PUNCT
cana-2873	95	25	σq	σq	NOUN
cana-2873	95	26	)	)	PUNCT
cana-2873	95	27	.	.	PUNCT
cana-2873	96	1	definition	definition	NOUN
cana-2873	96	2	2.13	2.13	NUM
cana-2873	96	3	.	.	PUNCT
cana-2873	97	1	a	a	DET
cana-2873	97	2	bijection	bijection	NOUN
cana-2873	97	3	k	k	X
cana-2873	97	4	:	:	PUNCT
cana-2873	97	5	(	(	PUNCT
cana-2873	97	6	z1	z1	VERB
cana-2873	97	7	,	,	PUNCT
cana-2873	97	8	γq	γq	ADP
cana-2873	97	9	)	)	PUNCT
cana-2873	97	10	→	→	SYM
cana-2873	97	11	(	(	PUNCT
cana-2873	97	12	z2	z2	PROPN
cana-2873	97	13	,	,	PUNCT
cana-2873	97	14	σq	σq	NOUN
cana-2873	97	15	)	)	PUNCT
cana-2873	97	16	is	be	AUX
cana-2873	97	17	called	call	VERB
cana-2873	97	18	a	a	DET
cana-2873	97	19	(	(	PUNCT
cana-2873	97	20	i	i	NOUN
cana-2873	97	21	)	)	PUNCT
cana-2873	97	22	quadripartitioned	quadripartitione	VERB
cana-2873	97	23	neutrosophic	neutrosophic	PROPN
cana-2873	97	24	homeomorphism	homeomorphism	PROPN
cana-2873	97	25	(	(	PUNCT
cana-2873	97	26	briefly	briefly	ADV
cana-2873	97	27	q	q	X
cana-2873	97	28	-	-	PUNCT
cana-2873	97	29	nshom	nshom	ADJ
cana-2873	97	30	)	)	PUNCT
cana-2873	97	31	if	if	SCONJ
cana-2873	97	32	k	k	PROPN
cana-2873	97	33	and	and	CCONJ
cana-2873	97	34	k−1	k−1	PROPN
cana-2873	97	35	are	be	AUX
cana-2873	97	36	q	q	NOUN
cana-2873	97	37	-	-	PUNCT
cana-2873	97	38	nscts	nsct	NOUN
cana-2873	97	39	.	.	PUNCT
cana-2873	98	1	(	(	PUNCT
cana-2873	98	2	ii	ii	NOUN
cana-2873	98	3	)	)	PUNCT
cana-2873	98	4	quadripartitioned	quadripartitione	VERB
cana-2873	98	5	neutrosophic	neutrosophic	ADJ
cana-2873	98	6	β	β	PROPN
cana-2873	98	7	-	-	PUNCT
cana-2873	98	8	homeomorphism	homeomorphism	X
cana-2873	98	9	(	(	PUNCT
cana-2873	98	10	briefly	briefly	NOUN
cana-2873	98	11	q	q	NOUN
cana-2873	98	12	-	-	PUNCT
cana-2873	98	13	nsβhom	nsβhom	NOUN
cana-2873	98	14	)	)	PUNCT
cana-2873	98	15	if	if	SCONJ
cana-2873	98	16	k	k	PROPN
cana-2873	98	17	and	and	CCONJ
cana-2873	98	18	k−1	k−1	PROPN
cana-2873	98	19	are	be	AUX
cana-2873	98	20	qnsβcts	qnsβct	NOUN
cana-2873	98	21	.	.	PUNCT
cana-2873	99	1	definition	definition	NOUN
cana-2873	99	2	2.14	2.14	NUM
cana-2873	99	3	.	.	PUNCT
cana-2873	100	1	a	a	DET
cana-2873	100	2	bijection	bijection	NOUN
cana-2873	100	3	k	k	X
cana-2873	100	4	:	:	PUNCT
cana-2873	100	5	(	(	PUNCT
cana-2873	100	6	z1	z1	VERB
cana-2873	100	7	,	,	PUNCT
cana-2873	100	8	γq	γq	ADP
cana-2873	100	9	)	)	PUNCT
cana-2873	100	10	(	(	PUNCT
cana-2873	100	11	z2	z2	PROPN
cana-2873	100	12	,	,	PUNCT
cana-2873	100	13	σq	σq	NOUN
cana-2873	100	14	)	)	PUNCT
cana-2873	100	15	is	be	AUX
cana-2873	100	16	called	call	VERB
cana-2873	100	17	a	a	DET
cana-2873	100	18	quadripartitioned	quadripartitione	VERB
cana-2873	100	19	neutrosophic	neutrosophic	ADJ
cana-2873	100	20	βcompletely	βcompletely	ADV
cana-2873	100	21	homeomorphism	homeomorphism	X
cana-2873	100	22	(	(	PUNCT
cana-2873	100	23	briefly	briefly	ADV
cana-2873	100	24	,	,	PUNCT
cana-2873	100	25	q	q	NOUN
cana-2873	100	26	-	-	PUNCT
cana-2873	100	27	nsβchom	nsβchom	ADJ
cana-2873	100	28	)	)	PUNCT
cana-2873	100	29	if	if	SCONJ
cana-2873	100	30	k	k	PROPN
cana-2873	100	31	and	and	CCONJ
cana-2873	100	32	k−1	k−1	PROPN
cana-2873	100	33	are	be	AUX
cana-2873	100	34	q	q	ADJ
cana-2873	100	35	-	-	PUNCT
cana-2873	100	36	nsβirr	nsβirr	NOUN
cana-2873	100	37	mappings	mapping	NOUN
cana-2873	100	38	.	.	PUNCT
cana-2873	101	1	definition	definition	NOUN
cana-2873	101	2	2.15	2.15	NUM
cana-2873	101	3	.	.	PUNCT
cana-2873	102	1	a	a	DET
cana-2873	102	2	q	q	NOUN
cana-2873	102	3	-	-	PUNCT
cana-2873	102	4	nsts	nst	NOUN
cana-2873	102	5	(	(	PUNCT
cana-2873	102	6	z	z	NOUN
cana-2873	102	7	,	,	PUNCT
cana-2873	102	8	γq	γq	ADP
cana-2873	102	9	)	)	PUNCT
cana-2873	102	10	is	be	AUX
cana-2873	102	11	said	say	VERB
cana-2873	102	12	to	to	PART
cana-2873	102	13	be	be	AUX
cana-2873	102	14	a	a	DET
cana-2873	102	15	quadripartitioned	quadripartitione	VERB
cana-2873	102	16	neutrosophic	neutrosophic	ADJ
cana-2873	102	17	β	β	PROPN
cana-2873	102	18	½	½	NOUN
cana-2873	102	19	space	space	NOUN
cana-2873	102	20	(	(	PUNCT
cana-2873	102	21	briefly	briefly	ADV
cana-2873	102	22	,	,	PUNCT
cana-2873	102	23	q	q	PUNCT
cana-2873	102	24	-nsβt	-nsβt	NOUN
cana-2873	102	25	1/2	1/2	NUM
cana-2873	102	26	)	)	PUNCT
cana-2873	102	27	-space	-space	NOUN
cana-2873	102	28	if	if	SCONJ
cana-2873	102	29	every	every	DET
cana-2873	102	30	q	q	NOUN
cana-2873	102	31	-	-	PUNCT
cana-2873	102	32	nsβcs	nsβcs	NOUN
cana-2873	102	33	is	be	AUX
cana-2873	102	34	q	q	ADJ
cana-2873	102	35	-	-	PUNCT
cana-2873	102	36	nsc	nsc	NOUN
cana-2873	102	37	in	in	ADP
cana-2873	102	38	(	(	PUNCT
cana-2873	102	39	z	z	NOUN
cana-2873	102	40	,	,	PUNCT
cana-2873	102	41	γq	γq	ADP
cana-2873	102	42	)	)	PUNCT
cana-2873	102	43	.	.	PUNCT
cana-2873	103	1	3	3	NUM
cana-2873	103	2	quadripartitioned	quadripartitione	VERB
cana-2873	103	3	neutrosophic	neutrosophic	PROPN
cana-2873	103	4	contra	contra	PROPN
cana-2873	103	5	β	β	PROPN
cana-2873	103	6	-	-	ADJ
cana-2873	103	7	continuous	continuous	ADJ
cana-2873	103	8	maps	map	NOUN
cana-2873	103	9	in	in	ADP
cana-2873	103	10	this	this	DET
cana-2873	103	11	section	section	NOUN
cana-2873	103	12	,	,	PUNCT
cana-2873	103	13	quadripartitioned	quadripartitione	VERB
cana-2873	103	14	neutrosophic	neutrosophic	PROPN
cana-2873	103	15	contra	contra	PROPN
cana-2873	103	16	β	β	PROPN
cana-2873	103	17	-	-	ADJ
cana-2873	103	18	continuous	continuous	ADJ
cana-2873	103	19	maps	map	NOUN
cana-2873	103	20	are	be	AUX
cana-2873	103	21	introduced	introduce	VERB
cana-2873	103	22	and	and	CCONJ
cana-2873	103	23	some	some	PRON
cana-2873	103	24	of	of	ADP
cana-2873	103	25	its	its	PRON
cana-2873	103	26	properties	property	NOUN
cana-2873	103	27	are	be	AUX
cana-2873	103	28	discussed	discuss	VERB
cana-2873	103	29	.	.	PUNCT
cana-2873	104	1	definition	definition	NOUN
cana-2873	104	2	3.1	3.1	NUM
cana-2873	104	3	.	.	PUNCT
cana-2873	105	1	a	a	DET
cana-2873	105	2	mapping	mapping	NOUN
cana-2873	105	3	k	k	NOUN
cana-2873	105	4	:	:	PUNCT
cana-2873	105	5	(	(	PUNCT
cana-2873	105	6	z1	z1	VERB
cana-2873	105	7	,	,	PUNCT
cana-2873	105	8	γq	γq	ADP
cana-2873	105	9	)	)	PUNCT
cana-2873	105	10	→	→	SYM
cana-2873	105	11	(	(	PUNCT
cana-2873	105	12	z2	z2	PROPN
cana-2873	105	13	,	,	PUNCT
cana-2873	105	14	σq	σq	NOUN
cana-2873	105	15	)	)	PUNCT
cana-2873	105	16	is	be	AUX
cana-2873	105	17	said	say	VERB
cana-2873	105	18	to	to	PART
cana-2873	105	19	be	be	AUX
cana-2873	105	20	a	a	DET
cana-2873	105	21	quadripartitioned	quadripartitione	VERB
cana-2873	105	22	neutrosophic	neutrosophic	ADJ
cana-2873	105	23	contra	contra	PROPN
cana-2873	105	24	(	(	PUNCT
cana-2873	105	25	resp	resp	PROPN
cana-2873	105	26	.	.	PUNCT
cana-2873	106	1	semi	semi	ADJ
cana-2873	106	2	,	,	PUNCT
cana-2873	106	3	pre	pre	ADJ
cana-2873	106	4	,	,	PUNCT
cana-2873	106	5	b	b	PROPN
cana-2873	106	6	&	&	CCONJ
cana-2873	106	7	β	β	NOUN
cana-2873	106	8	)	)	PUNCT
cana-2873	106	9	continuous	continuous	ADJ
cana-2873	106	10	(	(	PUNCT
cana-2873	106	11	in	in	ADP
cana-2873	106	12	short	short	ADJ
cana-2873	106	13	,	,	PUNCT
cana-2873	106	14	q	q	NOUN
cana-2873	106	15	-	-	PUNCT
cana-2873	106	16	nsɕcts	nsɕct	NOUN
cana-2873	106	17	(	(	PUNCT
cana-2873	106	18	resp	resp	NOUN
cana-2873	106	19	.	.	PUNCT
cana-2873	107	1	q	q	X
cana-2873	107	2	-	-	PUNCT
cana-2873	107	3	ns	ns	ADJ
cana-2873	107	4	ɕscts	ɕsct	NOUN
cana-2873	107	5	,	,	PUNCT
cana-2873	107	6	q	q	NOUN
cana-2873	107	7	-	-	PUNCT
cana-2873	107	8	nsɕƿcts	nsɕƿct	NOUN
cana-2873	107	9	,	,	PUNCT
cana-2873	107	10	q	q	NOUN
cana-2873	107	11	-	-	PUNCT
cana-2873	107	12	nsɕbcts	nsɕbct	NOUN
cana-2873	107	13	&	&	CCONJ
cana-2873	107	14	q	q	NOUN
cana-2873	107	15	-	-	PUNCT
cana-2873	107	16	nsɕβcts	nsɕβct	NOUN
cana-2873	107	17	)	)	PUNCT
cana-2873	107	18	)	)	PUNCT
cana-2873	108	1	if	if	SCONJ
cana-2873	108	2	the	the	DET
cana-2873	108	3	inverse	inverse	ADJ
cana-2873	108	4	image	image	NOUN
cana-2873	108	5	of	of	ADP
cana-2873	108	6	each	each	DET
cana-2873	108	7	q	q	NOUN
cana-2873	108	8	-	-	PUNCT
cana-2873	108	9	nso	nso	NOUN
cana-2873	108	10	set	set	NOUN
cana-2873	108	11	of	of	ADP
cana-2873	108	12	(	(	PUNCT
cana-2873	108	13	z2	z2	PROPN
cana-2873	108	14	,	,	PUNCT
cana-2873	108	15	σq	σq	NOUN
cana-2873	108	16	)	)	PUNCT
cana-2873	108	17	is	be	AUX
cana-2873	108	18	q	q	ADJ
cana-2873	108	19	-	-	PUNCT
cana-2873	108	20	nsc	nsc	NOUN
cana-2873	108	21	(	(	PUNCT
cana-2873	108	22	resp	resp	PROPN
cana-2873	108	23	.	.	PUNCT
cana-2873	109	1	qns	qns	PROPN
cana-2873	109	2	sc	sc	PROPN
cana-2873	109	3	,	,	PUNCT
cana-2873	109	4	q	q	ADJ
cana-2873	109	5	-	-	PUNCT
cana-2873	109	6	ns	ns	ADJ
cana-2873	109	7	ρc	ρc	PROPN
cana-2873	109	8	,	,	PUNCT
cana-2873	109	9	q	q	PROPN
cana-2873	109	10	-	-	PUNCT
cana-2873	109	11	nsbc	nsbc	PROPN
cana-2873	109	12	&	&	CCONJ
cana-2873	109	13	q	q	NOUN
cana-2873	109	14	-	-	PUNCT
cana-2873	109	15	nsβc	nsβc	ADV
cana-2873	109	16	)	)	PUNCT
cana-2873	109	17	set	set	VERB
cana-2873	109	18	in	in	ADP
cana-2873	109	19	(	(	PUNCT
cana-2873	109	20	z1	z1	NOUN
cana-2873	109	21	,	,	PUNCT
cana-2873	109	22	γq	γq	ADP
cana-2873	109	23	)	)	PUNCT
cana-2873	109	24	.	.	PUNCT
cana-2873	110	1	example	example	NOUN
cana-2873	110	2	3.2	3.2	NUM
cana-2873	110	3	.	.	PUNCT
cana-2873	111	1	let	let	VERB
cana-2873	111	2	v	v	VERB
cana-2873	111	3	=	=	SYM
cana-2873	111	4	{	{	PUNCT
cana-2873	111	5	va	va	NOUN
cana-2873	111	6	,	,	PUNCT
cana-2873	111	7	vb	vb	NOUN
cana-2873	111	8	,	,	PUNCT
cana-2873	111	9	vc	vc	NOUN
cana-2873	111	10	}	}	PUNCT
cana-2873	111	11	=	=	SYM
cana-2873	111	12	w	w	NOUN
cana-2873	111	13	and	and	CCONJ
cana-2873	111	14	define	define	VERB
cana-2873	111	15	q	q	ADJ
cana-2873	111	16	-	-	PUNCT
cana-2873	111	17	nss	nss	NOUN
cana-2873	111	18	’s	’s	PART
cana-2873	111	19	v1	v1	NOUN
cana-2873	111	20	,	,	PUNCT
cana-2873	111	21	v2	v2	PROPN
cana-2873	111	22	&	&	CCONJ
cana-2873	111	23	v3	v3	PROPN
cana-2873	111	24	in	in	ADP
cana-2873	111	25	v	v	NOUN
cana-2873	111	26	and	and	CCONJ
cana-2873	111	27	w1	w1	NOUN
cana-2873	111	28	in	in	ADP
cana-2873	111	29	w	w	PROPN
cana-2873	111	30	are	be	AUX
cana-2873	111	31	v1	v1	NOUN
cana-2873	111	32	=	=	SYM
cana-2873	111	33	{	{	PUNCT
cana-2873	111	34	(	(	PUNCT
cana-2873	111	35	va	va	NOUN
cana-2873	111	36	,	,	PUNCT
cana-2873	111	37	0.2	0.2	NUM
cana-2873	111	38	,	,	PUNCT
cana-2873	111	39	0.5	0.5	NUM
cana-2873	111	40	,	,	PUNCT
cana-2873	111	41	0.5	0.5	NUM
cana-2873	111	42	,	,	PUNCT
cana-2873	111	43	0.8	0.8	NUM
cana-2873	111	44	)	)	PUNCT
cana-2873	111	45	,	,	PUNCT
cana-2873	111	46	(	(	PUNCT
cana-2873	111	47	vb	vb	NOUN
cana-2873	111	48	,	,	PUNCT
cana-2873	111	49	0.3	0.3	NUM
cana-2873	111	50	,	,	PUNCT
cana-2873	111	51	0.5	0.5	NUM
cana-2873	111	52	,	,	PUNCT
cana-2873	111	53	0.5	0.5	NUM
cana-2873	111	54	,	,	PUNCT
cana-2873	111	55	0.7	0.7	NUM
cana-2873	111	56	)	)	PUNCT
cana-2873	111	57	,	,	PUNCT
cana-2873	111	58	(	(	PUNCT
cana-2873	111	59	vc	vc	INTJ
cana-2873	111	60	,	,	PUNCT
cana-2873	111	61	0.4	0.4	NUM
cana-2873	111	62	,	,	PUNCT
cana-2873	111	63	0.5	0.5	NUM
cana-2873	111	64	,	,	PUNCT
cana-2873	111	65	0.5	0.5	NUM
cana-2873	111	66	,	,	PUNCT
cana-2873	111	67	0.6	0.6	NUM
cana-2873	111	68	)	)	PUNCT
cana-2873	111	69	}	}	PUNCT
cana-2873	111	70	,	,	PUNCT
cana-2873	111	71	v2	v2	PROPN
cana-2873	111	72	=	=	SYM
cana-2873	111	73	{	{	PUNCT
cana-2873	111	74	(	(	PUNCT
cana-2873	111	75	va	va	NOUN
cana-2873	111	76	,	,	PUNCT
cana-2873	111	77	0.1	0.1	NUM
cana-2873	111	78	,	,	PUNCT
cana-2873	111	79	0.5	0.5	NUM
cana-2873	111	80	,	,	PUNCT
cana-2873	111	81	0.5	0.5	NUM
cana-2873	111	82	,	,	PUNCT
cana-2873	111	83	0.9	0.9	NUM
cana-2873	111	84	)	)	PUNCT
cana-2873	111	85	,	,	PUNCT
cana-2873	111	86	(	(	PUNCT
cana-2873	111	87	vb	vb	NOUN
cana-2873	111	88	,	,	PUNCT
cana-2873	111	89	0.1	0.1	NUM
cana-2873	111	90	,	,	PUNCT
cana-2873	111	91	0.5	0.5	NUM
cana-2873	111	92	,	,	PUNCT
cana-2873	111	93	0.5	0.5	NUM
cana-2873	111	94	,	,	PUNCT
cana-2873	111	95	0.9	0.9	NUM
cana-2873	111	96	)	)	PUNCT
cana-2873	111	97	,	,	PUNCT
cana-2873	111	98	(	(	PUNCT
cana-2873	111	99	vc	vc	INTJ
cana-2873	111	100	,	,	PUNCT
cana-2873	111	101	0.4	0.4	NUM
cana-2873	111	102	,	,	PUNCT
cana-2873	111	103	0.5	0.5	NUM
cana-2873	111	104	,	,	PUNCT
cana-2873	111	105	0.5	0.5	NUM
cana-2873	111	106	,	,	PUNCT
cana-2873	111	107	0.6	0.6	NUM
cana-2873	111	108	)	)	PUNCT
cana-2873	111	109	}	}	PUNCT
cana-2873	111	110	,	,	PUNCT
cana-2873	111	111	v3	v3	PROPN
cana-2873	111	112	=	=	SYM
cana-2873	111	113	{	{	PUNCT
cana-2873	111	114	(	(	PUNCT
cana-2873	111	115	va	va	NOUN
cana-2873	111	116	,	,	PUNCT
cana-2873	111	117	0.2	0.2	NUM
cana-2873	111	118	,	,	PUNCT
cana-2873	111	119	0.5	0.5	NUM
cana-2873	111	120	,	,	PUNCT
cana-2873	111	121	0.5	0.5	NUM
cana-2873	111	122	,	,	PUNCT
cana-2873	111	123	0.8	0.8	NUM
cana-2873	111	124	)	)	PUNCT
cana-2873	111	125	,	,	PUNCT
cana-2873	111	126	(	(	PUNCT
cana-2873	111	127	vb	vb	NOUN
cana-2873	111	128	,	,	PUNCT
cana-2873	111	129	0.4	0.4	NUM
cana-2873	111	130	,	,	PUNCT
cana-2873	111	131	0.5	0.5	NUM
cana-2873	111	132	,	,	PUNCT
cana-2873	111	133	0.5	0.5	NUM
cana-2873	111	134	,	,	PUNCT
cana-2873	111	135	0.6	0.6	NUM
cana-2873	111	136	)	)	PUNCT
cana-2873	111	137	,	,	PUNCT
cana-2873	111	138	(	(	PUNCT
cana-2873	111	139	vc	vc	INTJ
cana-2873	111	140	,	,	PUNCT
cana-2873	111	141	0.4	0.4	NUM
cana-2873	111	142	,	,	PUNCT
cana-2873	111	143	0.5	0.5	NUM
cana-2873	111	144	,	,	PUNCT
cana-2873	111	145	0.5	0.5	NUM
cana-2873	111	146	,	,	PUNCT
cana-2873	111	147	0.6	0.6	NUM
cana-2873	111	148	)	)	PUNCT
cana-2873	111	149	}	}	PUNCT
cana-2873	111	150	,	,	PUNCT
cana-2873	111	151	w1	w1	NOUN
cana-2873	111	152	=	=	SYM
cana-2873	111	153	{	{	PUNCT
cana-2873	111	154	(	(	PUNCT
cana-2873	111	155	va	va	NOUN
cana-2873	111	156	,	,	PUNCT
cana-2873	111	157	0.2	0.2	NUM
cana-2873	111	158	,	,	PUNCT
cana-2873	111	159	0.5	0.5	NUM
cana-2873	111	160	,	,	PUNCT
cana-2873	111	161	0.5	0.5	NUM
cana-2873	111	162	,	,	PUNCT
cana-2873	111	163	0.8	0.8	NUM
cana-2873	111	164	)	)	PUNCT
cana-2873	111	165	,	,	PUNCT
cana-2873	111	166	(	(	PUNCT
cana-2873	111	167	vb	vb	NOUN
cana-2873	111	168	,	,	PUNCT
cana-2873	111	169	0.4	0.4	NUM
cana-2873	111	170	,	,	PUNCT
cana-2873	111	171	0.5	0.5	NUM
cana-2873	111	172	,	,	PUNCT
cana-2873	111	173	0.5	0.5	NUM
cana-2873	111	174	,	,	PUNCT
cana-2873	111	175	0.6	0.6	NUM
cana-2873	111	176	)	)	PUNCT
cana-2873	111	177	,	,	PUNCT
cana-2873	111	178	(	(	PUNCT
cana-2873	111	179	vc	vc	INTJ
cana-2873	111	180	,	,	PUNCT
cana-2873	111	181	0.4	0.4	NUM
cana-2873	111	182	,	,	PUNCT
cana-2873	111	183	0.5	0.5	NUM
cana-2873	111	184	,	,	PUNCT
cana-2873	111	185	0.5	0.5	NUM
cana-2873	111	186	,	,	PUNCT
cana-2873	111	187	0.6	0.6	NUM
cana-2873	111	188	)	)	PUNCT
cana-2873	111	189	}	}	PUNCT
cana-2873	111	190	.	.	PUNCT
cana-2873	112	1	then	then	ADV
cana-2873	112	2	we	we	PRON
cana-2873	112	3	have	have	VERB
cana-2873	112	4	γq	γq	ADP
cana-2873	112	5	=	=	NOUN
cana-2873	112	6	{	{	PUNCT
cana-2873	112	7	0qns	0qns	NOUN
cana-2873	112	8	,	,	PUNCT
cana-2873	112	9	v1	v1	PROPN
cana-2873	112	10	,	,	PUNCT
cana-2873	112	11	v2	v2	PROPN
cana-2873	112	12	,	,	PUNCT
cana-2873	112	13	1qns	1qns	NUM
cana-2873	112	14	}	}	PUNCT
cana-2873	112	15	and	and	CCONJ
cana-2873	112	16	σq	σq	NOUN
cana-2873	112	17	=	=	SYM
cana-2873	112	18	{	{	PUNCT
cana-2873	112	19	0qns	0qns	PROPN
cana-2873	112	20	,	,	PUNCT
cana-2873	112	21	w1	w1	NOUN
cana-2873	112	22	,	,	PUNCT
cana-2873	112	23	1qns	1qns	NUM
cana-2873	112	24	}	}	PUNCT
cana-2873	112	25	.	.	PUNCT
cana-2873	113	1	let	let	VERB
cana-2873	113	2	k	k	NOUN
cana-2873	113	3	:	:	PUNCT
cana-2873	113	4	(	(	PUNCT
cana-2873	113	5	v	v	NOUN
cana-2873	113	6	,	,	PUNCT
cana-2873	113	7	γq)(w	γq)(w	NOUN
cana-2873	113	8	,	,	PUNCT
cana-2873	113	9	σq	σq	NOUN
cana-2873	113	10	)	)	PUNCT
cana-2873	113	11	be	be	VERB
cana-2873	113	12	an	an	DET
cana-2873	113	13	identity	identity	NOUN
cana-2873	113	14	mapping	mapping	NOUN
cana-2873	113	15	,	,	PUNCT
cana-2873	113	16	then	then	ADV
cana-2873	113	17	k	k	PROPN
cana-2873	113	18	is	be	AUX
cana-2873	113	19	q	q	ADJ
cana-2873	113	20	-	-	PUNCT
cana-2873	113	21	nsɕβcts	nsɕβct	NOUN
cana-2873	113	22	function	function	NOUN
cana-2873	113	23	.	.	PUNCT
cana-2873	114	1	proposition	proposition	NOUN
cana-2873	114	2	3.3	3.3	NUM
cana-2873	114	3	.	.	PUNCT
cana-2873	115	1	a	a	DET
cana-2873	115	2	map	map	NOUN
cana-2873	115	3	k	k	X
cana-2873	115	4	:	:	PUNCT
cana-2873	115	5	(	(	PUNCT
cana-2873	115	6	z1	z1	VERB
cana-2873	115	7	,	,	PUNCT
cana-2873	115	8	γq	γq	ADP
cana-2873	115	9	)	)	PUNCT
cana-2873	115	10	(	(	PUNCT
cana-2873	115	11	z2	z2	PROPN
cana-2873	115	12	,	,	PUNCT
cana-2873	115	13	σq	σq	NOUN
cana-2873	115	14	)	)	PUNCT
cana-2873	115	15	,	,	PUNCT
cana-2873	115	16	then	then	ADV
cana-2873	115	17	the	the	DET
cana-2873	115	18	statements	statement	NOUN
cana-2873	115	19	are	be	AUX
cana-2873	115	20	hold	hold	NOUN
cana-2873	115	21	but	but	CCONJ
cana-2873	115	22	the	the	DET
cana-2873	115	23	converse	converse	NOUN
cana-2873	115	24	does	do	AUX
cana-2873	115	25	not	not	PART
cana-2873	115	26	true	true	ADJ
cana-2873	115	27	.	.	PUNCT
cana-2873	116	1	every	every	DET
cana-2873	116	2	(	(	PUNCT
cana-2873	116	3	i	i	NOUN
cana-2873	116	4	)	)	PUNCT
cana-2873	116	5	q	q	NOUN
cana-2873	116	6	-	-	PUNCT
cana-2873	116	7	nsɕcts	nsɕct	NOUN
cana-2873	116	8	is	be	AUX
cana-2873	116	9	a	a	DET
cana-2873	116	10	q	q	NOUN
cana-2873	116	11	-	-	PUNCT
cana-2873	116	12	nsɕscts	nsɕsct	NOUN
cana-2873	116	13	.	.	PUNCT
cana-2873	117	1	(	(	PUNCT
cana-2873	117	2	ii	ii	NOUN
cana-2873	117	3	)	)	PUNCT
cana-2873	117	4	q	q	NOUN
cana-2873	117	5	-	-	PUNCT
cana-2873	117	6	nsɕcts	nsɕct	NOUN
cana-2873	117	7	is	be	AUX
cana-2873	117	8	a	a	DET
cana-2873	117	9	q	q	NOUN
cana-2873	117	10	-	-	PUNCT
cana-2873	117	11	nsɕpcts	nsɕpct	NOUN
cana-2873	117	12	.	.	PUNCT
cana-2873	118	1	(	(	PUNCT
cana-2873	118	2	iii	iii	X
cana-2873	118	3	)	)	PUNCT
cana-2873	118	4	q	q	NOUN
cana-2873	118	5	-	-	PUNCT
cana-2873	118	6	nsɕscts	nsɕsct	NOUN
cana-2873	118	7	is	be	AUX
cana-2873	118	8	a	a	DET
cana-2873	118	9	q	q	NOUN
cana-2873	118	10	-	-	PUNCT
cana-2873	118	11	nsɕbcts	nsɕbct	NOUN
cana-2873	118	12	.	.	PUNCT
cana-2873	119	1	(	(	PUNCT
cana-2873	119	2	iv	iv	X
cana-2873	119	3	)	)	PUNCT
cana-2873	119	4	q	q	NOUN
cana-2873	119	5	-	-	PUNCT
cana-2873	119	6	nsɕpcts	nsɕpct	NOUN
cana-2873	119	7	is	be	AUX
cana-2873	119	8	a	a	DET
cana-2873	119	9	q	q	NOUN
cana-2873	119	10	-	-	PUNCT
cana-2873	119	11	nsɕbcts	nsɕbct	NOUN
cana-2873	119	12	.	.	PUNCT
cana-2873	120	1	communications	communication	NOUN
cana-2873	120	2	on	on	ADP
cana-2873	120	3	applied	apply	VERB
cana-2873	120	4	nonlinear	nonlinear	ADJ
cana-2873	120	5	analysis	analysis	NOUN
cana-2873	120	6	issn	issn	NOUN
cana-2873	120	7	:	:	PUNCT
cana-2873	120	8	1074	1074	NUM
cana-2873	120	9	-	-	PUNCT
cana-2873	120	10	133x	133x	NUM
cana-2873	120	11	vol	vol	NOUN
cana-2873	120	12	32	32	NUM
cana-2873	120	13	no	no	NOUN
cana-2873	120	14	.	.	PUNCT
cana-2873	121	1	4s	4s	NUM
cana-2873	121	2	(	(	PUNCT
cana-2873	121	3	2025	2025	NUM
cana-2873	121	4	)	)	PUNCT
cana-2873	121	5	584	584	NUM
cana-2873	121	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	121	7	(	(	PUNCT
cana-2873	121	8	v	v	NOUN
cana-2873	121	9	)	)	PUNCT
cana-2873	121	10	q	q	NOUN
cana-2873	121	11	-	-	PUNCT
cana-2873	121	12	nsɕbcts	nsɕbct	NOUN
cana-2873	121	13	is	be	AUX
cana-2873	121	14	a	a	DET
cana-2873	121	15	q	q	NOUN
cana-2873	121	16	-	-	PUNCT
cana-2873	121	17	nsɕβcts	nsɕβct	NOUN
cana-2873	121	18	.	.	PUNCT
cana-2873	122	1	proof	proof	NOUN
cana-2873	122	2	.	.	PUNCT
cana-2873	123	1	(	(	PUNCT
cana-2873	123	2	i	i	NOUN
cana-2873	123	3	)	)	PUNCT
cana-2873	123	4	let	let	VERB
cana-2873	123	5	η	η	X
cana-2873	123	6	be	be	AUX
cana-2873	123	7	a	a	DET
cana-2873	123	8	q	q	NOUN
cana-2873	123	9	-	-	PUNCT
cana-2873	123	10	nso	nso	NOUN
cana-2873	123	11	set	set	VERB
cana-2873	123	12	in	in	ADP
cana-2873	123	13	z2	z2	PROPN
cana-2873	123	14	.	.	PUNCT
cana-2873	124	1	since	since	SCONJ
cana-2873	124	2	k	k	PROPN
cana-2873	124	3	is	be	AUX
cana-2873	124	4	q	q	NOUN
cana-2873	124	5	-	-	PUNCT
cana-2873	124	6	nsɕcts	nsɕct	NOUN
cana-2873	124	7	,	,	PUNCT
cana-2873	124	8	k−1(η	k−1(η	PROPN
cana-2873	124	9	)	)	PUNCT
cana-2873	124	10	is	be	AUX
cana-2873	124	11	a	a	DET
cana-2873	124	12	q	q	ADJ
cana-2873	124	13	-	-	PUNCT
cana-2873	124	14	nsc	nsc	NOUN
cana-2873	124	15	set	set	NOUN
cana-2873	124	16	in	in	ADP
cana-2873	124	17	z1	z1	PROPN
cana-2873	124	18	.	.	PUNCT
cana-2873	125	1	since	since	SCONJ
cana-2873	125	2	every	every	DET
cana-2873	125	3	q	q	PROPN
cana-2873	125	4	-	-	PUNCT
cana-2873	125	5	nsc	nsc	NOUN
cana-2873	125	6	set	set	NOUN
cana-2873	125	7	is	be	AUX
cana-2873	125	8	a	a	DET
cana-2873	125	9	q	q	ADJ
cana-2873	125	10	-	-	PUNCT
cana-2873	125	11	nssc	nssc	NOUN
cana-2873	125	12	set	set	NOUN
cana-2873	125	13	,	,	PUNCT
cana-2873	125	14	k−1(η	k−1(η	PROPN
cana-2873	125	15	)	)	PUNCT
cana-2873	125	16	is	be	AUX
cana-2873	125	17	a	a	DET
cana-2873	125	18	q	q	NOUN
cana-2873	125	19	-	-	PUNCT
cana-2873	125	20	nssc	nssc	NOUN
cana-2873	125	21	set	set	NOUN
cana-2873	125	22	in	in	ADP
cana-2873	125	23	z1	z1	PROPN
cana-2873	125	24	.	.	PUNCT
cana-2873	126	1	hence	hence	ADV
cana-2873	126	2	k	k	PROPN
cana-2873	126	3	is	be	AUX
cana-2873	126	4	a	a	DET
cana-2873	126	5	q	q	NOUN
cana-2873	126	6	-	-	PUNCT
cana-2873	126	7	nsɕscts	nsɕsct	NOUN
cana-2873	126	8	.	.	PUNCT
cana-2873	127	1	(	(	PUNCT
cana-2873	127	2	ii	ii	NOUN
cana-2873	127	3	)	)	PUNCT
cana-2873	127	4	let	let	VERB
cana-2873	127	5	η	η	PROPN
cana-2873	127	6	be	be	AUX
cana-2873	127	7	a	a	DET
cana-2873	127	8	q	q	NOUN
cana-2873	127	9	-	-	PUNCT
cana-2873	127	10	nso	nso	NOUN
cana-2873	127	11	set	set	VERB
cana-2873	127	12	in	in	ADP
cana-2873	127	13	z2	z2	PROPN
cana-2873	127	14	.	.	PUNCT
cana-2873	128	1	since	since	SCONJ
cana-2873	128	2	k	k	PROPN
cana-2873	128	3	is	be	AUX
cana-2873	128	4	q	q	NOUN
cana-2873	128	5	-	-	PUNCT
cana-2873	128	6	nsɕcts	nsɕct	NOUN
cana-2873	128	7	,	,	PUNCT
cana-2873	128	8	k−1(η	k−1(η	PROPN
cana-2873	128	9	)	)	PUNCT
cana-2873	128	10	is	be	AUX
cana-2873	128	11	a	a	DET
cana-2873	128	12	q	q	ADJ
cana-2873	128	13	-	-	PUNCT
cana-2873	128	14	nsc	nsc	NOUN
cana-2873	128	15	set	set	NOUN
cana-2873	128	16	in	in	ADP
cana-2873	128	17	z1	z1	PROPN
cana-2873	128	18	.	.	PUNCT
cana-2873	129	1	since	since	SCONJ
cana-2873	129	2	every	every	DET
cana-2873	129	3	q	q	PROPN
cana-2873	129	4	-	-	PUNCT
cana-2873	129	5	nsc	nsc	NOUN
cana-2873	129	6	set	set	NOUN
cana-2873	129	7	is	be	AUX
cana-2873	129	8	a	a	DET
cana-2873	129	9	q	q	ADJ
cana-2873	129	10	-	-	PUNCT
cana-2873	129	11	nspc	nspc	NOUN
cana-2873	129	12	set	set	NOUN
cana-2873	129	13	,	,	PUNCT
cana-2873	129	14	k−1(η	k−1(η	PROPN
cana-2873	129	15	)	)	PUNCT
cana-2873	129	16	is	be	AUX
cana-2873	129	17	a	a	DET
cana-2873	129	18	q	q	ADJ
cana-2873	129	19	-	-	PUNCT
cana-2873	129	20	nspc	nspc	NOUN
cana-2873	129	21	set	set	NOUN
cana-2873	129	22	in	in	ADP
cana-2873	129	23	z1	z1	PROPN
cana-2873	129	24	.	.	PUNCT
cana-2873	130	1	hence	hence	ADV
cana-2873	130	2	k	k	PROPN
cana-2873	130	3	is	be	AUX
cana-2873	130	4	a	a	DET
cana-2873	130	5	q	q	NOUN
cana-2873	130	6	-	-	PUNCT
cana-2873	130	7	nscpcts	nscpct	NOUN
cana-2873	130	8	.	.	PUNCT
cana-2873	131	1	(	(	PUNCT
cana-2873	131	2	iii	iii	X
cana-2873	131	3	)	)	PUNCT
cana-2873	131	4	let	let	VERB
cana-2873	131	5	η	η	X
cana-2873	131	6	be	be	AUX
cana-2873	131	7	a	a	DET
cana-2873	131	8	q	q	NOUN
cana-2873	131	9	-	-	PUNCT
cana-2873	131	10	nso	nso	NOUN
cana-2873	131	11	set	set	VERB
cana-2873	131	12	in	in	ADP
cana-2873	131	13	z2	z2	PROPN
cana-2873	131	14	.	.	PUNCT
cana-2873	132	1	since	since	SCONJ
cana-2873	132	2	k	k	PROPN
cana-2873	132	3	is	be	AUX
cana-2873	132	4	q	q	NOUN
cana-2873	132	5	-	-	PUNCT
cana-2873	132	6	nsɕscts	nsɕsct	NOUN
cana-2873	132	7	,	,	PUNCT
cana-2873	132	8	k−1(η	k−1(η	PROPN
cana-2873	132	9	)	)	PUNCT
cana-2873	132	10	is	be	AUX
cana-2873	132	11	a	a	DET
cana-2873	132	12	q	q	NOUN
cana-2873	132	13	-	-	PUNCT
cana-2873	132	14	nssc	nssc	NOUN
cana-2873	132	15	set	set	NOUN
cana-2873	132	16	in	in	ADP
cana-2873	132	17	z1	z1	PROPN
cana-2873	132	18	.	.	PUNCT
cana-2873	133	1	since	since	SCONJ
cana-2873	133	2	every	every	DET
cana-2873	133	3	q	q	NOUN
cana-2873	133	4	-	-	PUNCT
cana-2873	133	5	nssc	nssc	NOUN
cana-2873	133	6	set	set	NOUN
cana-2873	133	7	is	be	AUX
cana-2873	133	8	a	a	DET
cana-2873	133	9	q	q	ADJ
cana-2873	133	10	-	-	PUNCT
cana-2873	133	11	nsbc	nsbc	ADJ
cana-2873	133	12	set	set	NOUN
cana-2873	133	13	,	,	PUNCT
cana-2873	133	14	k−1(η	k−1(η	PROPN
cana-2873	133	15	)	)	PUNCT
cana-2873	133	16	is	be	AUX
cana-2873	133	17	a	a	DET
cana-2873	133	18	q	q	ADJ
cana-2873	133	19	-	-	PUNCT
cana-2873	133	20	nsbc	nsbc	ADJ
cana-2873	133	21	set	set	NOUN
cana-2873	133	22	in	in	ADP
cana-2873	133	23	z1	z1	PROPN
cana-2873	133	24	.	.	PUNCT
cana-2873	134	1	hence	hence	ADV
cana-2873	134	2	k	k	PROPN
cana-2873	134	3	is	be	AUX
cana-2873	134	4	a	a	DET
cana-2873	134	5	q	q	NOUN
cana-2873	134	6	-	-	PUNCT
cana-2873	134	7	nscbcts	nscbct	NOUN
cana-2873	134	8	.	.	PUNCT
cana-2873	135	1	(	(	PUNCT
cana-2873	135	2	iv	iv	X
cana-2873	135	3	)	)	PUNCT
cana-2873	135	4	let	let	VERB
cana-2873	135	5	η	η	X
cana-2873	135	6	be	be	AUX
cana-2873	135	7	a	a	DET
cana-2873	135	8	q	q	NOUN
cana-2873	135	9	-	-	PUNCT
cana-2873	135	10	nso	nso	NOUN
cana-2873	135	11	set	set	VERB
cana-2873	135	12	in	in	ADP
cana-2873	135	13	z2	z2	PROPN
cana-2873	135	14	.	.	PUNCT
cana-2873	136	1	since	since	SCONJ
cana-2873	136	2	k	k	PROPN
cana-2873	136	3	is	be	AUX
cana-2873	136	4	q	q	NOUN
cana-2873	136	5	-	-	PUNCT
cana-2873	136	6	nsɕpcts	nsɕpct	NOUN
cana-2873	136	7	,	,	PUNCT
cana-2873	136	8	k−1(η	k−1(η	PROPN
cana-2873	136	9	)	)	PUNCT
cana-2873	136	10	is	be	AUX
cana-2873	136	11	a	a	DET
cana-2873	136	12	q	q	ADJ
cana-2873	136	13	-	-	PUNCT
cana-2873	136	14	nspc	nspc	NOUN
cana-2873	136	15	set	set	NOUN
cana-2873	136	16	in	in	ADP
cana-2873	136	17	z1	z1	PROPN
cana-2873	136	18	.	.	PUNCT
cana-2873	137	1	since	since	SCONJ
cana-2873	137	2	every	every	DET
cana-2873	137	3	q	q	NOUN
cana-2873	137	4	-	-	PUNCT
cana-2873	137	5	nspc	nspc	NOUN
cana-2873	137	6	set	set	NOUN
cana-2873	137	7	is	be	AUX
cana-2873	137	8	a	a	DET
cana-2873	137	9	q	q	ADJ
cana-2873	137	10	-	-	PUNCT
cana-2873	137	11	nsbc	nsbc	ADJ
cana-2873	137	12	set	set	NOUN
cana-2873	137	13	,	,	PUNCT
cana-2873	137	14	k−1(η	k−1(η	PROPN
cana-2873	137	15	)	)	PUNCT
cana-2873	137	16	is	be	AUX
cana-2873	137	17	a	a	DET
cana-2873	137	18	q	q	ADJ
cana-2873	137	19	-	-	PUNCT
cana-2873	137	20	nsbc	nsbc	ADJ
cana-2873	137	21	set	set	NOUN
cana-2873	137	22	in	in	ADP
cana-2873	137	23	z1	z1	PROPN
cana-2873	137	24	.	.	PUNCT
cana-2873	138	1	hence	hence	ADV
cana-2873	138	2	k	k	PROPN
cana-2873	138	3	is	be	AUX
cana-2873	138	4	a	a	DET
cana-2873	138	5	q	q	NOUN
cana-2873	138	6	-	-	PUNCT
cana-2873	138	7	nscbcts	nscbct	NOUN
cana-2873	138	8	.	.	PUNCT
cana-2873	139	1	(	(	PUNCT
cana-2873	139	2	v	v	NOUN
cana-2873	139	3	)	)	PUNCT
cana-2873	139	4	let	let	VERB
cana-2873	139	5	η	η	X
cana-2873	139	6	be	be	AUX
cana-2873	139	7	a	a	DET
cana-2873	139	8	q	q	NOUN
cana-2873	139	9	-	-	PUNCT
cana-2873	139	10	nso	nso	NOUN
cana-2873	139	11	set	set	VERB
cana-2873	139	12	in	in	ADP
cana-2873	139	13	z2	z2	PROPN
cana-2873	139	14	.	.	PUNCT
cana-2873	140	1	since	since	SCONJ
cana-2873	140	2	k	k	PROPN
cana-2873	140	3	is	be	AUX
cana-2873	140	4	q	q	NOUN
cana-2873	140	5	-	-	PUNCT
cana-2873	140	6	nsɕbcts	nsɕbct	NOUN
cana-2873	140	7	,	,	PUNCT
cana-2873	140	8	k−1(η	k−1(η	PROPN
cana-2873	140	9	)	)	PUNCT
cana-2873	140	10	is	be	AUX
cana-2873	140	11	a	a	DET
cana-2873	140	12	q	q	ADJ
cana-2873	140	13	-	-	PUNCT
cana-2873	140	14	nsbc	nsbc	ADJ
cana-2873	140	15	set	set	NOUN
cana-2873	140	16	in	in	ADP
cana-2873	140	17	z1	z1	PROPN
cana-2873	140	18	.	.	PUNCT
cana-2873	141	1	since	since	SCONJ
cana-2873	141	2	every	every	DET
cana-2873	141	3	q	q	ADJ
cana-2873	141	4	-	-	PUNCT
cana-2873	141	5	nsbc	nsbc	ADJ
cana-2873	141	6	set	set	NOUN
cana-2873	141	7	is	be	AUX
cana-2873	141	8	a	a	DET
cana-2873	141	9	q	q	ADJ
cana-2873	141	10	-	-	PUNCT
cana-2873	141	11	nsβc	nsβc	NOUN
cana-2873	141	12	set	set	NOUN
cana-2873	141	13	,	,	PUNCT
cana-2873	141	14	k−1(η	k−1(η	PROPN
cana-2873	141	15	)	)	PUNCT
cana-2873	141	16	is	be	AUX
cana-2873	141	17	a	a	DET
cana-2873	141	18	q	q	ADJ
cana-2873	141	19	-	-	PUNCT
cana-2873	141	20	nsβc	nsβc	NOUN
cana-2873	141	21	set	set	NOUN
cana-2873	141	22	in	in	ADP
cana-2873	141	23	z1	z1	PROPN
cana-2873	141	24	.	.	PUNCT
cana-2873	142	1	hence	hence	ADV
cana-2873	142	2	k	k	PROPN
cana-2873	142	3	is	be	AUX
cana-2873	142	4	a	a	DET
cana-2873	142	5	q	q	NOUN
cana-2873	142	6	-	-	PUNCT
cana-2873	142	7	nsɕβcts	nsɕβct	NOUN
cana-2873	142	8	.	.	PUNCT
cana-2873	143	1	figure	figure	NOUN
cana-2873	143	2	1	1	NUM
cana-2873	143	3	:	:	PUNCT
cana-2873	143	4	q	q	ADJ
cana-2873	143	5	-	-	PUNCT
cana-2873	143	6	nsɕβcts	nsɕβct	VERB
cana-2873	143	7	maps	map	NOUN
cana-2873	143	8	in	in	ADP
cana-2873	143	9	q	q	NOUN
cana-2873	143	10	-	-	PUNCT
cana-2873	143	11	nsts	nst	NOUN
cana-2873	143	12	example	example	NOUN
cana-2873	143	13	3.4	3.4	NUM
cana-2873	143	14	.	.	PUNCT
cana-2873	144	1	in	in	ADP
cana-2873	144	2	example	example	NOUN
cana-2873	144	3	3.2	3.2	NUM
cana-2873	144	4	,	,	PUNCT
cana-2873	144	5	k	k	PROPN
cana-2873	144	6	is	be	AUX
cana-2873	144	7	q	q	NOUN
cana-2873	144	8	-	-	PUNCT
cana-2873	144	9	nsɕbcts	nsɕbct	NOUN
cana-2873	144	10	but	but	CCONJ
cana-2873	144	11	not	not	PART
cana-2873	144	12	q	q	NOUN
cana-2873	144	13	-	-	PUNCT
cana-2873	144	14	nscpcts	nscpct	NOUN
cana-2873	144	15	,	,	PUNCT
cana-2873	144	16	the	the	DET
cana-2873	144	17	set	set	NOUN
cana-2873	144	18	k−1(w1	k−1(w1	PROPN
cana-2873	144	19	)	)	PUNCT
cana-2873	145	1	=	=	PROPN
cana-2873	145	2	v3	v3	PROPN
cana-2873	145	3	c	c	PROPN
cana-2873	145	4	is	be	AUX
cana-2873	145	5	a	a	DET
cana-2873	145	6	q	q	ADJ
cana-2873	145	7	-	-	PUNCT
cana-2873	145	8	nsbc	nsbc	ADJ
cana-2873	145	9	set	set	NOUN
cana-2873	145	10	but	but	CCONJ
cana-2873	145	11	not	not	PART
cana-2873	145	12	q	q	ADJ
cana-2873	145	13	-	-	PUNCT
cana-2873	145	14	nspc	nspc	NOUN
cana-2873	145	15	set	set	NOUN
cana-2873	145	16	.	.	PUNCT
cana-2873	146	1	example	example	NOUN
cana-2873	146	2	3.5	3.5	NUM
cana-2873	146	3	.	.	PUNCT
cana-2873	147	1	let	let	VERB
cana-2873	147	2	v	v	VERB
cana-2873	147	3	=	=	SYM
cana-2873	147	4	{	{	PUNCT
cana-2873	147	5	va	va	NOUN
cana-2873	147	6	,	,	PUNCT
cana-2873	147	7	vb	vb	NOUN
cana-2873	147	8	,	,	PUNCT
cana-2873	147	9	vc	vc	NOUN
cana-2873	147	10	}	}	PUNCT
cana-2873	147	11	=	=	SYM
cana-2873	147	12	w	w	NOUN
cana-2873	147	13	and	and	CCONJ
cana-2873	147	14	define	define	VERB
cana-2873	147	15	q	q	ADJ
cana-2873	147	16	-	-	PUNCT
cana-2873	147	17	nss	nss	NOUN
cana-2873	147	18	’s	’s	PART
cana-2873	147	19	v1	v1	NOUN
cana-2873	147	20	,	,	PUNCT
cana-2873	147	21	v2	v2	PROPN
cana-2873	147	22	,	,	PUNCT
cana-2873	147	23	v3	v3	PROPN
cana-2873	147	24	&	&	CCONJ
cana-2873	147	25	v4	v4	PROPN
cana-2873	147	26	in	in	ADP
cana-2873	147	27	v	v	NOUN
cana-2873	147	28	and	and	CCONJ
cana-2873	147	29	w1	w1	NOUN
cana-2873	147	30	in	in	ADP
cana-2873	147	31	w	w	PROPN
cana-2873	147	32	are	be	AUX
cana-2873	147	33	v1	v1	NOUN
cana-2873	147	34	=	=	SYM
cana-2873	147	35	{	{	PUNCT
cana-2873	147	36	(	(	PUNCT
cana-2873	147	37	va	va	NOUN
cana-2873	147	38	,	,	PUNCT
cana-2873	147	39	0.3	0.3	NUM
cana-2873	147	40	,	,	PUNCT
cana-2873	147	41	0.5	0.5	NUM
cana-2873	147	42	,	,	PUNCT
cana-2873	147	43	0.5	0.5	NUM
cana-2873	147	44	,	,	PUNCT
cana-2873	147	45	0.7	0.7	NUM
cana-2873	147	46	)	)	PUNCT
cana-2873	147	47	,	,	PUNCT
cana-2873	147	48	(	(	PUNCT
cana-2873	147	49	vb	vb	NOUN
cana-2873	147	50	,	,	PUNCT
cana-2873	147	51	0.5	0.5	NUM
cana-2873	147	52	,	,	PUNCT
cana-2873	147	53	0.5	0.5	NUM
cana-2873	147	54	,	,	PUNCT
cana-2873	147	55	0.5	0.5	NUM
cana-2873	147	56	,	,	PUNCT
cana-2873	147	57	0.5	0.5	NUM
cana-2873	147	58	)	)	PUNCT
cana-2873	147	59	,	,	PUNCT
cana-2873	147	60	(	(	PUNCT
cana-2873	147	61	vc	vc	INTJ
cana-2873	147	62	,	,	PUNCT
cana-2873	147	63	0.5	0.5	NUM
cana-2873	147	64	,	,	PUNCT
cana-2873	147	65	0.5	0.5	NUM
cana-2873	147	66	,	,	PUNCT
cana-2873	147	67	0.5	0.5	NUM
cana-2873	147	68	,	,	PUNCT
cana-2873	147	69	0.5	0.5	NUM
cana-2873	147	70	)	)	PUNCT
cana-2873	147	71	}	}	PUNCT
cana-2873	147	72	,	,	PUNCT
cana-2873	147	73	v2	v2	PROPN
cana-2873	147	74	=	=	SYM
cana-2873	147	75	{	{	PUNCT
cana-2873	147	76	(	(	PUNCT
cana-2873	147	77	va	va	NOUN
cana-2873	147	78	,	,	PUNCT
cana-2873	147	79	0.4	0.4	NUM
cana-2873	147	80	,	,	PUNCT
cana-2873	147	81	0.5	0.5	NUM
cana-2873	147	82	,	,	PUNCT
cana-2873	147	83	0.5	0.5	NUM
cana-2873	147	84	,	,	PUNCT
cana-2873	147	85	0.6	0.6	NUM
cana-2873	147	86	)	)	PUNCT
cana-2873	147	87	,	,	PUNCT
cana-2873	147	88	(	(	PUNCT
cana-2873	147	89	vb	vb	NOUN
cana-2873	147	90	,	,	PUNCT
cana-2873	147	91	0.2	0.2	NUM
cana-2873	147	92	,	,	PUNCT
cana-2873	147	93	0.5	0.5	NUM
cana-2873	147	94	,	,	PUNCT
cana-2873	147	95	0.5	0.5	NUM
cana-2873	147	96	,	,	PUNCT
cana-2873	147	97	0.8	0.8	NUM
cana-2873	147	98	)	)	PUNCT
cana-2873	147	99	,	,	PUNCT
cana-2873	147	100	(	(	PUNCT
cana-2873	147	101	vc	vc	INTJ
cana-2873	147	102	,	,	PUNCT
cana-2873	147	103	0.6	0.6	NUM
cana-2873	147	104	,	,	PUNCT
cana-2873	147	105	0.5	0.5	NUM
cana-2873	147	106	,	,	PUNCT
cana-2873	147	107	0.5	0.5	NUM
cana-2873	147	108	,	,	PUNCT
cana-2873	147	109	0.4	0.4	NUM
cana-2873	147	110	)	)	PUNCT
cana-2873	147	111	}	}	PUNCT
cana-2873	147	112	,	,	PUNCT
cana-2873	147	113	v3	v3	PROPN
cana-2873	147	114	=	=	SYM
cana-2873	147	115	{	{	PUNCT
cana-2873	147	116	(	(	PUNCT
cana-2873	147	117	va	va	NOUN
cana-2873	147	118	,	,	PUNCT
cana-2873	147	119	0.4	0.4	NUM
cana-2873	147	120	,	,	PUNCT
cana-2873	147	121	0.5	0.5	NUM
cana-2873	147	122	,	,	PUNCT
cana-2873	147	123	0.5	0.5	NUM
cana-2873	147	124	,	,	PUNCT
cana-2873	147	125	0.6	0.6	NUM
cana-2873	147	126	)	)	PUNCT
cana-2873	147	127	,	,	PUNCT
cana-2873	147	128	(	(	PUNCT
cana-2873	147	129	vb	vb	NOUN
cana-2873	147	130	,	,	PUNCT
cana-2873	147	131	0.5	0.5	NUM
cana-2873	147	132	,	,	PUNCT
cana-2873	147	133	0.5	0.5	NUM
cana-2873	147	134	,	,	PUNCT
cana-2873	147	135	0.5	0.5	NUM
cana-2873	147	136	,	,	PUNCT
cana-2873	147	137	0.5	0.5	NUM
cana-2873	147	138	)	)	PUNCT
cana-2873	147	139	,	,	PUNCT
cana-2873	147	140	(	(	PUNCT
cana-2873	147	141	vc	vc	INTJ
cana-2873	147	142	,	,	PUNCT
cana-2873	147	143	0.6	0.6	NUM
cana-2873	147	144	,	,	PUNCT
cana-2873	147	145	0.5	0.5	NUM
cana-2873	147	146	,	,	PUNCT
cana-2873	147	147	0.5	0.5	NUM
cana-2873	147	148	,	,	PUNCT
cana-2873	147	149	0.4	0.4	NUM
cana-2873	147	150	)	)	PUNCT
cana-2873	147	151	}	}	PUNCT
cana-2873	147	152	,	,	PUNCT
cana-2873	147	153	v4	v4	PROPN
cana-2873	147	154	=	=	SYM
cana-2873	147	155	{	{	PUNCT
cana-2873	147	156	(	(	PUNCT
cana-2873	147	157	va	va	NOUN
cana-2873	147	158	,	,	PUNCT
cana-2873	147	159	0.3	0.3	NUM
cana-2873	147	160	,	,	PUNCT
cana-2873	147	161	0.5	0.5	NUM
cana-2873	147	162	,	,	PUNCT
cana-2873	147	163	0.5	0.5	NUM
cana-2873	147	164	,	,	PUNCT
cana-2873	147	165	0.7	0.7	NUM
cana-2873	147	166	)	)	PUNCT
cana-2873	147	167	,	,	PUNCT
cana-2873	147	168	(	(	PUNCT
cana-2873	147	169	vb	vb	NOUN
cana-2873	147	170	,	,	PUNCT
cana-2873	147	171	0.5	0.5	NUM
cana-2873	147	172	,	,	PUNCT
cana-2873	147	173	0.5	0.5	NUM
cana-2873	147	174	,	,	PUNCT
cana-2873	147	175	0.5	0.5	NUM
cana-2873	147	176	,	,	PUNCT
cana-2873	147	177	0.5	0.5	NUM
cana-2873	147	178	)	)	PUNCT
cana-2873	147	179	,	,	PUNCT
cana-2873	147	180	(	(	PUNCT
cana-2873	147	181	vc	vc	INTJ
cana-2873	147	182	,	,	PUNCT
cana-2873	147	183	0.4	0.4	NUM
cana-2873	147	184	,	,	PUNCT
cana-2873	147	185	0.5	0.5	NUM
cana-2873	147	186	,	,	PUNCT
cana-2873	147	187	0.5	0.5	NUM
cana-2873	147	188	,	,	PUNCT
cana-2873	147	189	0.6	0.6	NUM
cana-2873	147	190	)	)	PUNCT
cana-2873	147	191	}	}	PUNCT
cana-2873	147	192	w1	w1	NOUN
cana-2873	147	193	=	=	SYM
cana-2873	147	194	{	{	PUNCT
cana-2873	147	195	(	(	PUNCT
cana-2873	147	196	va	va	NOUN
cana-2873	147	197	,	,	PUNCT
cana-2873	147	198	0.3	0.3	NUM
cana-2873	147	199	,	,	PUNCT
cana-2873	147	200	0.5	0.5	NUM
cana-2873	147	201	,	,	PUNCT
cana-2873	147	202	0.5	0.5	NUM
cana-2873	147	203	,	,	PUNCT
cana-2873	147	204	0.7	0.7	NUM
cana-2873	147	205	)	)	PUNCT
cana-2873	147	206	,	,	PUNCT
cana-2873	147	207	(	(	PUNCT
cana-2873	147	208	vb	vb	NOUN
cana-2873	147	209	,	,	PUNCT
cana-2873	147	210	0.5	0.5	NUM
cana-2873	147	211	,	,	PUNCT
cana-2873	147	212	0.5	0.5	NUM
cana-2873	147	213	,	,	PUNCT
cana-2873	147	214	0.5	0.5	NUM
cana-2873	147	215	,	,	PUNCT
cana-2873	147	216	0.5	0.5	NUM
cana-2873	147	217	)	)	PUNCT
cana-2873	147	218	,	,	PUNCT
cana-2873	147	219	(	(	PUNCT
cana-2873	147	220	vc	vc	INTJ
cana-2873	147	221	,	,	PUNCT
cana-2873	147	222	0.4	0.4	NUM
cana-2873	147	223	,	,	PUNCT
cana-2873	147	224	0.5	0.5	NUM
cana-2873	147	225	,	,	PUNCT
cana-2873	147	226	0.5	0.5	NUM
cana-2873	147	227	,	,	PUNCT
cana-2873	147	228	0.6	0.6	NUM
cana-2873	147	229	)	)	PUNCT
cana-2873	147	230	}	}	PUNCT
cana-2873	147	231	.	.	PUNCT
cana-2873	148	1	then	then	ADV
cana-2873	148	2	we	we	PRON
cana-2873	148	3	have	have	VERB
cana-2873	148	4	γq={0qns	γq={0qns	PROPN
cana-2873	148	5	,	,	PUNCT
cana-2873	148	6	v1	v1	PROPN
cana-2873	148	7	,	,	PUNCT
cana-2873	148	8	v2	v2	PROPN
cana-2873	148	9	,	,	PUNCT
cana-2873	148	10	v3	v3	PROPN
cana-2873	148	11	,	,	PUNCT
cana-2873	148	12	v1	v1	NOUN
cana-2873	148	13	∩	∩	ADJ
cana-2873	148	14	v2	v2	NOUN
cana-2873	148	15	,	,	PUNCT
cana-2873	148	16	1qns	1qns	NUM
cana-2873	148	17	}	}	PUNCT
cana-2873	148	18	and	and	CCONJ
cana-2873	148	19	σq	σq	PRON
cana-2873	148	20	=	=	NOUN
cana-2873	148	21	{	{	PUNCT
cana-2873	148	22	0qns	0qns	PROPN
cana-2873	148	23	,	,	PUNCT
cana-2873	148	24	w1	w1	NOUN
cana-2873	148	25	,	,	PUNCT
cana-2873	148	26	1qns	1qns	NUM
cana-2873	148	27	}	}	PUNCT
cana-2873	148	28	.	.	PUNCT
cana-2873	149	1	let	let	VERB
cana-2873	149	2	k	k	NOUN
cana-2873	149	3	:	:	PUNCT
cana-2873	149	4	(	(	PUNCT
cana-2873	149	5	z1	z1	VERB
cana-2873	149	6	,	,	PUNCT
cana-2873	149	7	γq	γq	NOUN
cana-2873	149	8	)	)	PUNCT
cana-2873	149	9	→(z2	→(z2	PROPN
cana-2873	149	10	,	,	PUNCT
cana-2873	149	11	σq	σq	NOUN
cana-2873	149	12	)	)	PUNCT
cana-2873	149	13	be	be	VERB
cana-2873	149	14	an	an	DET
cana-2873	149	15	identity	identity	NOUN
cana-2873	149	16	mapping	mapping	NOUN
cana-2873	149	17	,	,	PUNCT
cana-2873	149	18	then	then	ADV
cana-2873	149	19	k	k	PROPN
cana-2873	149	20	is	be	AUX
cana-2873	149	21	q	q	NOUN
cana-2873	149	22	-	-	PUNCT
cana-2873	149	23	nscbcts	nscbct	NOUN
cana-2873	149	24	but	but	CCONJ
cana-2873	149	25	not	not	PART
cana-2873	149	26	q	q	NOUN
cana-2873	149	27	-	-	PUNCT
cana-2873	149	28	nsɕscts	nsɕsct	NOUN
cana-2873	149	29	,	,	PUNCT
cana-2873	149	30	the	the	DET
cana-2873	149	31	set	set	NOUN
cana-2873	149	32	k−1(w1	k−1(w1	PROPN
cana-2873	149	33	)	)	PUNCT
cana-2873	149	34	=	=	PUNCT
cana-2873	150	1	v	v	ADP
cana-2873	150	2	c	c	NOUN
cana-2873	150	3	is	be	AUX
cana-2873	150	4	a	a	DET
cana-2873	150	5	q	q	ADJ
cana-2873	150	6	-	-	PUNCT
cana-2873	150	7	nsbc	nsbc	ADJ
cana-2873	150	8	set	set	NOUN
cana-2873	150	9	but	but	CCONJ
cana-2873	150	10	not	not	PART
cana-2873	150	11	q	q	ADJ
cana-2873	150	12	-	-	PUNCT
cana-2873	150	13	nssc	nssc	NOUN
cana-2873	150	14	set	set	NOUN
cana-2873	150	15	.	.	PUNCT
cana-2873	150	16	example	example	NOUN
cana-2873	151	1	3.6	3.6	NUM
cana-2873	151	2	.	.	PUNCT
cana-2873	152	1	let	let	VERB
cana-2873	152	2	v	v	VERB
cana-2873	152	3	=	=	SYM
cana-2873	152	4	{	{	PUNCT
cana-2873	152	5	va	va	NOUN
cana-2873	152	6	,	,	PUNCT
cana-2873	152	7	vb	vb	NOUN
cana-2873	152	8	}	}	PUNCT
cana-2873	152	9	=	=	SYM
cana-2873	152	10	w	w	NOUN
cana-2873	152	11	and	and	CCONJ
cana-2873	152	12	define	define	VERB
cana-2873	152	13	q	q	ADJ
cana-2873	152	14	-	-	PUNCT
cana-2873	152	15	nss	nss	NOUN
cana-2873	152	16	’s	’s	PART
cana-2873	152	17	v1	v1	PROPN
cana-2873	152	18	&	&	CCONJ
cana-2873	152	19	v2	v2	PROPN
cana-2873	152	20	in	in	ADP
cana-2873	152	21	v	v	NOUN
cana-2873	152	22	and	and	CCONJ
cana-2873	152	23	w1	w1	NOUN
cana-2873	152	24	in	in	ADP
cana-2873	152	25	w	w	PROPN
cana-2873	152	26	are	be	AUX
cana-2873	152	27	v1	v1	NOUN
cana-2873	152	28	=	=	SYM
cana-2873	152	29	{	{	PUNCT
cana-2873	152	30	(	(	PUNCT
cana-2873	152	31	va	va	NOUN
cana-2873	152	32	,	,	PUNCT
cana-2873	152	33	0.3	0.3	NUM
cana-2873	152	34	,	,	PUNCT
cana-2873	152	35	0.5	0.5	NUM
cana-2873	152	36	,	,	PUNCT
cana-2873	152	37	0.5	0.5	NUM
cana-2873	152	38	,	,	PUNCT
cana-2873	152	39	0.5	0.5	NUM
cana-2873	152	40	)	)	PUNCT
cana-2873	152	41	,	,	PUNCT
cana-2873	152	42	(	(	PUNCT
cana-2873	152	43	vb	vb	NOUN
cana-2873	152	44	,	,	PUNCT
cana-2873	152	45	0.2	0.2	NUM
cana-2873	152	46	,	,	PUNCT
cana-2873	152	47	0.5	0.5	NUM
cana-2873	152	48	,	,	PUNCT
cana-2873	152	49	0.5	0.5	NUM
cana-2873	152	50	,	,	PUNCT
cana-2873	152	51	0.5	0.5	NUM
cana-2873	152	52	)	)	PUNCT
cana-2873	152	53	}	}	PUNCT
cana-2873	152	54	,	,	PUNCT
cana-2873	152	55	v2	v2	PROPN
cana-2873	152	56	=	=	SYM
cana-2873	152	57	{	{	PUNCT
cana-2873	152	58	(	(	PUNCT
cana-2873	152	59	va	va	NOUN
cana-2873	152	60	,	,	PUNCT
cana-2873	152	61	0.3	0.3	NUM
cana-2873	152	62	,	,	PUNCT
cana-2873	152	63	0.5	0.5	NUM
cana-2873	152	64	,	,	PUNCT
cana-2873	152	65	0.5	0.5	NUM
cana-2873	152	66	,	,	PUNCT
cana-2873	152	67	0.7	0.7	NUM
cana-2873	152	68	)	)	PUNCT
cana-2873	152	69	,	,	PUNCT
cana-2873	152	70	(	(	PUNCT
cana-2873	152	71	vb	vb	NOUN
cana-2873	152	72	,	,	PUNCT
cana-2873	152	73	0.5	0.5	NUM
cana-2873	152	74	,	,	PUNCT
cana-2873	152	75	0.5	0.5	NUM
cana-2873	152	76	,	,	PUNCT
cana-2873	152	77	0.5	0.5	NUM
cana-2873	152	78	,	,	PUNCT
cana-2873	152	79	0.6	0.6	NUM
cana-2873	152	80	)	)	PUNCT
cana-2873	152	81	}	}	PUNCT
cana-2873	152	82	,	,	PUNCT
cana-2873	152	83	w1	w1	NOUN
cana-2873	152	84	=	=	SYM
cana-2873	152	85	{	{	PUNCT
cana-2873	152	86	(	(	PUNCT
cana-2873	152	87	va	va	NOUN
cana-2873	152	88	,	,	PUNCT
cana-2873	152	89	0.3	0.3	NUM
cana-2873	152	90	,	,	PUNCT
cana-2873	152	91	0.5	0.5	NUM
cana-2873	152	92	,	,	PUNCT
cana-2873	152	93	0.5	0.5	NUM
cana-2873	152	94	,	,	PUNCT
cana-2873	152	95	0.7	0.7	NUM
cana-2873	152	96	)	)	PUNCT
cana-2873	152	97	,	,	PUNCT
cana-2873	152	98	(	(	PUNCT
cana-2873	152	99	vb	vb	NOUN
cana-2873	152	100	,	,	PUNCT
cana-2873	152	101	0.5	0.5	NUM
cana-2873	152	102	,	,	PUNCT
cana-2873	152	103	0.5	0.5	NUM
cana-2873	152	104	,	,	PUNCT
cana-2873	152	105	0.5	0.5	NUM
cana-2873	152	106	,	,	PUNCT
cana-2873	152	107	0.6	0.6	NUM
cana-2873	152	108	)	)	PUNCT
cana-2873	152	109	}	}	PUNCT
cana-2873	152	110	.	.	PUNCT
cana-2873	153	1	communications	communication	NOUN
cana-2873	153	2	on	on	ADP
cana-2873	153	3	applied	apply	VERB
cana-2873	153	4	nonlinear	nonlinear	ADJ
cana-2873	153	5	analysis	analysis	NOUN
cana-2873	153	6	issn	issn	NOUN
cana-2873	153	7	:	:	PUNCT
cana-2873	153	8	1074	1074	NUM
cana-2873	153	9	-	-	PUNCT
cana-2873	153	10	133x	133x	NUM
cana-2873	153	11	vol	vol	NOUN
cana-2873	153	12	32	32	NUM
cana-2873	153	13	no	no	NOUN
cana-2873	153	14	.	.	PUNCT
cana-2873	154	1	4s	4s	NUM
cana-2873	154	2	(	(	PUNCT
cana-2873	154	3	2025	2025	NUM
cana-2873	154	4	)	)	PUNCT
cana-2873	154	5	585	585	NUM
cana-2873	154	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	154	7	then	then	ADV
cana-2873	154	8	we	we	PRON
cana-2873	154	9	have	have	VERB
cana-2873	154	10	γq	γq	ADP
cana-2873	154	11	=	=	SYM
cana-2873	154	12	{	{	PUNCT
cana-2873	154	13	0qns	0qns	PROPN
cana-2873	154	14	,	,	PUNCT
cana-2873	154	15	v1	v1	PROPN
cana-2873	154	16	,	,	PUNCT
cana-2873	154	17	1qns	1qns	NUM
cana-2873	154	18	}	}	PUNCT
cana-2873	154	19	and	and	CCONJ
cana-2873	154	20	σq	σq	NOUN
cana-2873	154	21	=	=	SYM
cana-2873	154	22	{	{	PUNCT
cana-2873	154	23	0qns	0qns	PROPN
cana-2873	154	24	,	,	PUNCT
cana-2873	154	25	w1	w1	NOUN
cana-2873	154	26	,	,	PUNCT
cana-2873	154	27	1qns	1qns	NUM
cana-2873	154	28	}	}	PUNCT
cana-2873	154	29	.	.	PUNCT
cana-2873	155	1	let	let	VERB
cana-2873	155	2	k	k	NOUN
cana-2873	155	3	:	:	PUNCT
cana-2873	155	4	(	(	PUNCT
cana-2873	155	5	z1	z1	NOUN
cana-2873	155	6	,	,	PUNCT
cana-2873	155	7	γq)(z2	γq)(z2	NOUN
cana-2873	155	8	,	,	PUNCT
cana-2873	155	9	σq	σq	NOUN
cana-2873	155	10	)	)	PUNCT
cana-2873	155	11	be	be	VERB
cana-2873	155	12	an	an	DET
cana-2873	155	13	identity	identity	NOUN
cana-2873	155	14	mapping	mapping	NOUN
cana-2873	155	15	,	,	PUNCT
cana-2873	155	16	then	then	ADV
cana-2873	155	17	k	k	PROPN
cana-2873	155	18	is	be	AUX
cana-2873	155	19	q	q	NOUN
cana-2873	155	20	-	-	PUNCT
cana-2873	155	21	nsɕβcts	nsɕβct	NOUN
cana-2873	155	22	but	but	CCONJ
cana-2873	155	23	not	not	PART
cana-2873	155	24	q	q	NOUN
cana-2873	155	25	-	-	PUNCT
cana-2873	155	26	nsɕbcts	nsɕbct	NOUN
cana-2873	155	27	,	,	PUNCT
cana-2873	155	28	the	the	DET
cana-2873	155	29	set	set	NOUN
cana-2873	155	30	k−1(w1	k−1(w1	PROPN
cana-2873	155	31	)	)	PUNCT
cana-2873	156	1	=	=	PUNCT
cana-2873	157	1	v2	v2	NOUN
cana-2873	157	2	c	c	NOUN
cana-2873	157	3	is	be	AUX
cana-2873	157	4	a	a	DET
cana-2873	157	5	qnsβc	qnsβc	PROPN
cana-2873	157	6	set	set	NOUN
cana-2873	157	7	but	but	CCONJ
cana-2873	157	8	not	not	PART
cana-2873	157	9	q	q	ADJ
cana-2873	157	10	-	-	PUNCT
cana-2873	157	11	nsbc	nsbc	ADJ
cana-2873	157	12	set	set	NOUN
cana-2873	157	13	.	.	PUNCT
cana-2873	158	1	theorem	theorem	VERB
cana-2873	158	2	3.7	3.7	NUM
cana-2873	158	3	.	.	PUNCT
cana-2873	159	1	a	a	DET
cana-2873	159	2	map	map	NOUN
cana-2873	159	3	k	k	X
cana-2873	159	4	:	:	PUNCT
cana-2873	159	5	(	(	PUNCT
cana-2873	159	6	z1	z1	VERB
cana-2873	159	7	,	,	PUNCT
cana-2873	159	8	γq	γq	NOUN
cana-2873	159	9	)	)	PUNCT
cana-2873	159	10	→(z2	→(z2	PROPN
cana-2873	159	11	,	,	PUNCT
cana-2873	159	12	σq	σq	NOUN
cana-2873	159	13	)	)	PUNCT
cana-2873	159	14	is	be	AUX
cana-2873	159	15	q	q	NOUN
cana-2873	159	16	-	-	PUNCT
cana-2873	159	17	nsɕβcts	nsɕβct	NOUN
cana-2873	159	18	iff	iff	VERB
cana-2873	159	19	the	the	DET
cana-2873	159	20	inverse	inverse	ADJ
cana-2873	159	21	image	image	NOUN
cana-2873	159	22	of	of	ADP
cana-2873	159	23	every	every	DET
cana-2873	159	24	qnscs	qnsc	NOUN
cana-2873	159	25	in	in	ADP
cana-2873	159	26	z2	z2	PROPN
cana-2873	159	27	is	be	AUX
cana-2873	159	28	q	q	NOUN
cana-2873	159	29	-	-	PUNCT
cana-2873	159	30	nsβos	nsβos	NOUN
cana-2873	159	31	in	in	ADP
cana-2873	159	32	z1	z1	PROPN
cana-2873	159	33	.	.	PUNCT
cana-2873	160	1	proof	proof	NOUN
cana-2873	160	2	.	.	PUNCT
cana-2873	161	1	consider	consider	VERB
cana-2873	161	2	a	a	DET
cana-2873	161	3	q	q	NOUN
cana-2873	161	4	-	-	PUNCT
cana-2873	161	5	nscs	nscs	ADJ
cana-2873	161	6	ψ̃	ψ̃	PROPN
cana-2873	161	7	in	in	ADP
cana-2873	161	8	z2	z2	PROPN
cana-2873	161	9	.	.	PUNCT
cana-2873	162	1	then	then	ADV
cana-2873	162	2	ψ̃c	ψ̃c	NOUN
cana-2873	162	3	is	be	AUX
cana-2873	162	4	q	q	NOUN
cana-2873	162	5	-	-	PUNCT
cana-2873	162	6	nsos	nsos	NOUN
cana-2873	162	7	in	in	ADP
cana-2873	162	8	z2	z2	PROPN
cana-2873	162	9	.	.	PUNCT
cana-2873	163	1	as	as	SCONJ
cana-2873	163	2	k	k	PROPN
cana-2873	163	3	is	be	AUX
cana-2873	163	4	q	q	NOUN
cana-2873	163	5	-	-	PUNCT
cana-2873	163	6	nsɕβcts	nsɕβct	NOUN
cana-2873	163	7	,	,	PUNCT
cana-2873	163	8	k−1(ψ̃c	k−1(ψ̃c	NOUN
cana-2873	163	9	)	)	PUNCT
cana-2873	163	10	is	be	AUX
cana-2873	163	11	q	q	ADJ
cana-2873	163	12	-	-	PUNCT
cana-2873	163	13	nsβcs	nsβcs	NOUN
cana-2873	163	14	in	in	ADP
cana-2873	163	15	z1	z1	PROPN
cana-2873	163	16	.	.	PUNCT
cana-2873	164	1	as	as	ADP
cana-2873	164	2	k−1(ψ̃c	k−1(ψ̃c	NOUN
cana-2873	164	3	)	)	PUNCT
cana-2873	164	4	=	=	SYM
cana-2873	164	5	(	(	PUNCT
cana-2873	164	6	k−1(ψ̃))c	k−1(ψ̃))c	PROPN
cana-2873	164	7	,	,	PUNCT
cana-2873	164	8	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	164	9	)	)	PUNCT
cana-2873	164	10	is	be	AUX
cana-2873	164	11	a	a	DET
cana-2873	164	12	q	q	NOUN
cana-2873	164	13	-	-	PUNCT
cana-2873	164	14	nsβos	nsβos	NOUN
cana-2873	164	15	in	in	ADP
cana-2873	164	16	z1	z1	PROPN
cana-2873	164	17	.	.	PUNCT
cana-2873	165	1	conversely	conversely	ADV
cana-2873	165	2	,	,	PUNCT
cana-2873	165	3	consider	consider	VERB
cana-2873	165	4	a	a	DET
cana-2873	165	5	q	q	NOUN
cana-2873	165	6	-	-	PUNCT
cana-2873	165	7	nscs	nscs	ADJ
cana-2873	165	8	ψ̃	ψ̃	PROPN
cana-2873	165	9	in	in	ADP
cana-2873	165	10	z2	z2	PROPN
cana-2873	165	11	.	.	PUNCT
cana-2873	166	1	so	so	ADV
cana-2873	166	2	ψ̃c	ψ̃c	PROPN
cana-2873	166	3	is	be	AUX
cana-2873	166	4	a	a	DET
cana-2873	166	5	q	q	NOUN
cana-2873	166	6	-	-	PUNCT
cana-2873	166	7	nsos	nsos	NOUN
cana-2873	166	8	in	in	ADP
cana-2873	166	9	z2	z2	PROPN
cana-2873	166	10	.	.	PUNCT
cana-2873	167	1	by	by	ADP
cana-2873	167	2	presumption	presumption	NOUN
cana-2873	167	3	,	,	PUNCT
cana-2873	167	4	k−1(ψ̃c	k−1(ψ̃c	NOUN
cana-2873	167	5	)	)	PUNCT
cana-2873	167	6	is	be	AUX
cana-2873	167	7	qnsβcs	qnsβcs	ADJ
cana-2873	167	8	in	in	ADP
cana-2873	167	9	z1	z1	PROPN
cana-2873	167	10	.	.	PUNCT
cana-2873	168	1	as	as	ADP
cana-2873	168	2	k−1(ψ̃c	k−1(ψ̃c	NOUN
cana-2873	168	3	)	)	PUNCT
cana-2873	168	4	=	=	SYM
cana-2873	169	1	(	(	PUNCT
cana-2873	169	2	k−1(ψ̃))c	k−1(ψ̃))c	PROPN
cana-2873	169	3	,	,	PUNCT
cana-2873	169	4	(	(	PUNCT
cana-2873	169	5	k−1(ψ̃))c	k−1(ψ̃))c	PROPN
cana-2873	169	6	is	be	AUX
cana-2873	169	7	a	a	DET
cana-2873	169	8	q	q	NOUN
cana-2873	169	9	-	-	PUNCT
cana-2873	169	10	nsβcs	nsβcs	NOUN
cana-2873	169	11	in	in	ADP
cana-2873	169	12	z1	z1	PROPN
cana-2873	169	13	.	.	PUNCT
cana-2873	170	1	hence	hence	ADV
cana-2873	170	2	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	170	3	)	)	PUNCT
cana-2873	170	4	is	be	AUX
cana-2873	170	5	a	a	DET
cana-2873	170	6	qnsβos	qnsβos	NOUN
cana-2873	170	7	in	in	ADP
cana-2873	170	8	z1	z1	PROPN
cana-2873	170	9	.	.	PUNCT
cana-2873	171	1	thus	thus	ADV
cana-2873	171	2	k	k	PROPN
cana-2873	171	3	is	be	AUX
cana-2873	171	4	q	q	NOUN
cana-2873	171	5	-	-	PUNCT
cana-2873	171	6	nsɕβcts	nsɕβct	NOUN
cana-2873	171	7	.	.	PUNCT
cana-2873	172	1	theorem	theorem	NOUN
cana-2873	172	2	3.8	3.8	NUM
cana-2873	172	3	.	.	PUNCT
cana-2873	173	1	let	let	VERB
cana-2873	173	2	k	k	NOUN
cana-2873	173	3	:	:	PUNCT
cana-2873	173	4	(	(	PUNCT
cana-2873	173	5	z1	z1	PROPN
cana-2873	173	6	,	,	PUNCT
cana-2873	173	7	γq)→(z2	γq)→(z2	NOUN
cana-2873	173	8	,	,	PUNCT
cana-2873	173	9	σq	σq	NOUN
cana-2873	173	10	)	)	PUNCT
cana-2873	173	11	be	be	VERB
cana-2873	173	12	q	q	NOUN
cana-2873	173	13	-	-	PUNCT
cana-2873	173	14	nscβcts	nscβct	NOUN
cana-2873	173	15	.	.	PUNCT
cana-2873	174	1	if	if	SCONJ
cana-2873	174	2	z1	z1	PROPN
cana-2873	174	3	is	be	AUX
cana-2873	174	4	a	a	DET
cana-2873	174	5	q	q	ADJ
cana-2873	174	6	-	-	PUNCT
cana-2873	174	7	nsβu1/2	nsβu1/2	ADJ
cana-2873	174	8	-space	-space	NOUN
cana-2873	174	9	,	,	PUNCT
cana-2873	174	10	then	then	ADV
cana-2873	174	11	k	k	PROPN
cana-2873	174	12	is	be	AUX
cana-2873	174	13	a	a	DET
cana-2873	174	14	q	q	NOUN
cana-2873	174	15	-	-	PUNCT
cana-2873	174	16	nsɕcts	nsɕct	NOUN
cana-2873	174	17	.	.	PUNCT
cana-2873	175	1	proof	proof	NOUN
cana-2873	175	2	.	.	PUNCT
cana-2873	176	1	consider	consider	VERB
cana-2873	176	2	a	a	DET
cana-2873	176	3	q	q	NOUN
cana-2873	176	4	-	-	PUNCT
cana-2873	176	5	nsos	nsos	ADJ
cana-2873	176	6	ψ̃	ψ̃	PROPN
cana-2873	176	7	in	in	ADP
cana-2873	176	8	z2	z2	PROPN
cana-2873	176	9	.	.	PUNCT
cana-2873	177	1	so	so	ADV
cana-2873	177	2	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	177	3	)	)	PUNCT
cana-2873	177	4	is	be	AUX
cana-2873	177	5	a	a	DET
cana-2873	177	6	q	q	NOUN
cana-2873	177	7	-	-	PUNCT
cana-2873	177	8	nsβcs	nsβcs	NOUN
cana-2873	177	9	in	in	ADP
cana-2873	177	10	z1	z1	PROPN
cana-2873	177	11	,	,	PUNCT
cana-2873	177	12	by	by	ADP
cana-2873	177	13	presumption	presumption	NOUN
cana-2873	177	14	.	.	PUNCT
cana-2873	178	1	as	as	SCONJ
cana-2873	178	2	z1	z1	PROPN
cana-2873	178	3	is	be	AUX
cana-2873	178	4	a	a	DET
cana-2873	178	5	qnsβu1/2	qnsβu1/2	ADJ
cana-2873	178	6	-space	-space	NOUN
cana-2873	178	7	,	,	PUNCT
cana-2873	178	8	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	178	9	)	)	PUNCT
cana-2873	178	10	is	be	AUX
cana-2873	178	11	a	a	DET
cana-2873	178	12	q	q	NOUN
cana-2873	178	13	-	-	PUNCT
cana-2873	178	14	nscs	nscs	NOUN
cana-2873	178	15	in	in	ADP
cana-2873	178	16	z1	z1	PROPN
cana-2873	178	17	.	.	PUNCT
cana-2873	179	1	thus	thus	ADV
cana-2873	179	2	k	k	PROPN
cana-2873	179	3	is	be	AUX
cana-2873	179	4	a	a	DET
cana-2873	179	5	q	q	NOUN
cana-2873	179	6	-	-	PUNCT
cana-2873	179	7	nsɕcts	nsɕct	NOUN
cana-2873	179	8	.	.	PUNCT
cana-2873	180	1	theorem	theorem	VERB
cana-2873	180	2	3.9	3.9	NUM
cana-2873	180	3	.	.	PUNCT
cana-2873	181	1	let	let	VERB
cana-2873	181	2	k	k	NOUN
cana-2873	181	3	:	:	PUNCT
cana-2873	181	4	(	(	PUNCT
cana-2873	181	5	z1	z1	VERB
cana-2873	181	6	,	,	PUNCT
cana-2873	181	7	γq	γq	ADP
cana-2873	181	8	)	)	PUNCT
cana-2873	181	9	→	→	SYM
cana-2873	181	10	(	(	PUNCT
cana-2873	181	11	z2	z2	PROPN
cana-2873	181	12	,	,	PUNCT
cana-2873	181	13	σq	σq	NOUN
cana-2873	181	14	)	)	PUNCT
cana-2873	181	15	be	be	VERB
cana-2873	181	16	a	a	DET
cana-2873	181	17	q	q	NOUN
cana-2873	181	18	-	-	PUNCT
cana-2873	181	19	nsɕβcts	nsɕβct	NOUN
cana-2873	181	20	map	map	NOUN
cana-2873	181	21	and	and	CCONJ
cana-2873	181	22	g	g	NOUN
cana-2873	181	23	:	:	PUNCT
cana-2873	181	24	(	(	PUNCT
cana-2873	181	25	z2	z2	NOUN
cana-2873	181	26	,	,	PUNCT
cana-2873	181	27	σq	σq	NOUN
cana-2873	181	28	)	)	PUNCT
cana-2873	181	29	→	→	SYM
cana-2873	181	30	(	(	PUNCT
cana-2873	181	31	z3	z3	PROPN
cana-2873	181	32	,	,	PUNCT
cana-2873	181	33	ρq	ρq	NUM
cana-2873	181	34	)	)	PUNCT
cana-2873	181	35	be	be	AUX
cana-2873	181	36	a	a	DET
cana-2873	181	37	q	q	NOUN
cana-2873	181	38	-	-	PUNCT
cana-2873	181	39	nscts	nsct	NOUN
cana-2873	181	40	,	,	PUNCT
cana-2873	182	1	then	then	ADV
cana-2873	182	2	g	g	PROPN
cana-2873	182	3	◦	◦	PROPN
cana-2873	182	4	k	k	X
cana-2873	182	5	:	:	PUNCT
cana-2873	182	6	(	(	PUNCT
cana-2873	182	7	z1	z1	VERB
cana-2873	182	8	,	,	PUNCT
cana-2873	182	9	γq	γq	ADP
cana-2873	182	10	)	)	PUNCT
cana-2873	182	11	→	→	SYM
cana-2873	182	12	(	(	PUNCT
cana-2873	182	13	z3	z3	PROPN
cana-2873	182	14	,	,	PUNCT
cana-2873	182	15	ρq	ρq	NUM
cana-2873	182	16	)	)	PUNCT
cana-2873	182	17	is	be	AUX
cana-2873	182	18	a	a	DET
cana-2873	182	19	q	q	NOUN
cana-2873	182	20	-	-	PUNCT
cana-2873	182	21	nsɕβcts	nsɕβct	NOUN
cana-2873	182	22	.	.	PUNCT
cana-2873	183	1	proof	proof	NOUN
cana-2873	183	2	.	.	PUNCT
cana-2873	184	1	let	let	VERB
cana-2873	184	2	ã	ã	PROPN
cana-2873	184	3	be	be	AUX
cana-2873	184	4	a	a	DET
cana-2873	184	5	q	q	NOUN
cana-2873	184	6	-	-	PUNCT
cana-2873	184	7	nsos	nsos	NOUN
cana-2873	184	8	in	in	ADP
cana-2873	184	9	z3	z3	PROPN
cana-2873	184	10	.	.	PUNCT
cana-2873	185	1	by	by	ADP
cana-2873	185	2	presumption	presumption	NOUN
cana-2873	185	3	,	,	PUNCT
cana-2873	185	4	g−1(ã	g−1(ã	X
cana-2873	185	5	)	)	PUNCT
cana-2873	185	6	is	be	AUX
cana-2873	185	7	a	a	DET
cana-2873	185	8	q	q	NOUN
cana-2873	185	9	-	-	PUNCT
cana-2873	185	10	nsos	nsos	NOUN
cana-2873	185	11	in	in	ADP
cana-2873	185	12	z2	z2	PROPN
cana-2873	185	13	.	.	PUNCT
cana-2873	186	1	as	as	SCONJ
cana-2873	186	2	k	k	PROPN
cana-2873	186	3	is	be	AUX
cana-2873	186	4	a	a	DET
cana-2873	186	5	q	q	ADJ
cana-2873	186	6	-	-	PUNCT
cana-2873	186	7	nsɕβcts	nsɕβct	NOUN
cana-2873	186	8	map	map	NOUN
cana-2873	186	9	,	,	PUNCT
cana-2873	186	10	k−1(g−1(ã	k−1(g−1(ã	PROPN
cana-2873	186	11	)	)	PUNCT
cana-2873	186	12	)	)	PUNCT
cana-2873	186	13	is	be	AUX
cana-2873	186	14	a	a	DET
cana-2873	186	15	q	q	NOUN
cana-2873	186	16	-	-	PUNCT
cana-2873	186	17	nsβcs	nsβcs	NOUN
cana-2873	186	18	in	in	ADP
cana-2873	186	19	z1	z1	PROPN
cana-2873	186	20	.	.	PUNCT
cana-2873	187	1	thus	thus	ADV
cana-2873	187	2	g	g	PROPN
cana-2873	187	3	◦	◦	NOUN
cana-2873	187	4	k	k	PROPN
cana-2873	187	5	is	be	AUX
cana-2873	187	6	a	a	DET
cana-2873	187	7	q	q	ADJ
cana-2873	187	8	-	-	PUNCT
cana-2873	187	9	nscβcts	nscβct	NOUN
cana-2873	187	10	map	map	NOUN
cana-2873	187	11	.	.	PUNCT
cana-2873	188	1	theorem	theorem	VERB
cana-2873	188	2	3.10	3.10	NUM
cana-2873	188	3	.	.	PUNCT
cana-2873	189	1	let	let	VERB
cana-2873	189	2	k	k	NOUN
cana-2873	189	3	:	:	PUNCT
cana-2873	189	4	(	(	PUNCT
cana-2873	189	5	z1	z1	VERB
cana-2873	189	6	,	,	PUNCT
cana-2873	189	7	γq	γq	ADP
cana-2873	189	8	)	)	PUNCT
cana-2873	189	9	(	(	PUNCT
cana-2873	189	10	z2	z2	PROPN
cana-2873	189	11	,	,	PUNCT
cana-2873	189	12	σq	σq	NOUN
cana-2873	189	13	)	)	PUNCT
cana-2873	189	14	be	be	VERB
cana-2873	189	15	a	a	DET
cana-2873	189	16	q	q	ADJ
cana-2873	189	17	-	-	PUNCT
cana-2873	189	18	nsɕβcts	nsɕβct	NOUN
cana-2873	189	19	map	map	NOUN
cana-2873	189	20	.	.	PUNCT
cana-2873	190	1	then	then	ADV
cana-2873	190	2	,	,	PUNCT
cana-2873	190	3	the	the	DET
cana-2873	190	4	succeeding	succeed	VERB
cana-2873	190	5	conditions	condition	NOUN
cana-2873	190	6	are	be	AUX
cana-2873	190	7	true	true	ADJ
cana-2873	190	8	.	.	PUNCT
cana-2873	191	1	(	(	PUNCT
cana-2873	191	2	i	i	NOUN
cana-2873	191	3	)	)	PUNCT
cana-2873	191	4	k(q	k(q	NOUN
cana-2873	191	5	-	-	PUNCT
cana-2873	191	6	nsβcl(ψ̃	nsβcl(ψ̃	PROPN
cana-2873	191	7	)	)	PUNCT
cana-2873	191	8	)	)	PUNCT
cana-2873	192	1	⊇	⊇	PROPN
cana-2873	192	2	q	q	PROPN
cana-2873	192	3	-	-	PUNCT
cana-2873	192	4	nsint(k(ψ̃	nsint(k(ψ̃	NUM
cana-2873	192	5	)	)	PUNCT
cana-2873	192	6	)	)	PUNCT
cana-2873	192	7	,	,	PUNCT
cana-2873	192	8	∀	∀	X
cana-2873	192	9	(	(	PUNCT
cana-2873	192	10	ψ̃	ψ̃	PROPN
cana-2873	192	11	)	)	PUNCT
cana-2873	192	12	in	in	ADP
cana-2873	192	13	z1	z1	PROPN
cana-2873	192	14	.	.	PUNCT
cana-2873	192	15	(	(	PUNCT
cana-2873	192	16	ii	ii	NOUN
cana-2873	192	17	)	)	PUNCT
cana-2873	192	18	q	q	NOUN
cana-2873	192	19	-	-	PUNCT
cana-2873	192	20	nsβcl(k−1(φ̃	nsβcl(k−1(φ̃	NUM
cana-2873	192	21	)	)	PUNCT
cana-2873	192	22	)	)	PUNCT
cana-2873	192	23	⊇	⊇	PROPN
cana-2873	192	24	k−1(q	k−1(q	PROPN
cana-2873	192	25	-	-	PUNCT
cana-2873	192	26	nsint(φ̃	nsint(φ̃	PROPN
cana-2873	192	27	)	)	PUNCT
cana-2873	192	28	)	)	PUNCT
cana-2873	192	29	,	,	PUNCT
cana-2873	192	30	∀	∀	X
cana-2873	192	31	(	(	PUNCT
cana-2873	192	32	φ̃	φ̃	PROPN
cana-2873	192	33	)	)	PUNCT
cana-2873	192	34	in	in	ADP
cana-2873	192	35	z2	z2	PROPN
cana-2873	192	36	.	.	PUNCT
cana-2873	193	1	proof	proof	NOUN
cana-2873	193	2	.	.	PUNCT
cana-2873	194	1	(	(	PUNCT
cana-2873	194	2	i	i	NOUN
cana-2873	194	3	)	)	PUNCT
cana-2873	194	4	as	as	ADP
cana-2873	194	5	q	q	NOUN
cana-2873	194	6	-	-	PUNCT
cana-2873	194	7	nsβcl(k(ψ̃	nsβcl(k(ψ̃	NOUN
cana-2873	194	8	)	)	PUNCT
cana-2873	194	9	)	)	PUNCT
cana-2873	194	10	is	be	AUX
cana-2873	194	11	a	a	DET
cana-2873	194	12	q	q	NOUN
cana-2873	194	13	-	-	PUNCT
cana-2873	194	14	nsβcs	nsβcs	NOUN
cana-2873	194	15	in	in	ADP
cana-2873	194	16	z2	z2	PROPN
cana-2873	194	17	and	and	CCONJ
cana-2873	194	18	k	k	PROPN
cana-2873	194	19	is	be	AUX
cana-2873	194	20	q	q	NOUN
cana-2873	194	21	-	-	PUNCT
cana-2873	194	22	nsɕβcts	nsɕβct	NOUN
cana-2873	194	23	,	,	PUNCT
cana-2873	194	24	k−1(q	k−1(q	ADV
cana-2873	194	25	-	-	PUNCT
cana-2873	194	26	nsβcl(k(ψ̃	nsβcl(k(ψ̃	NOUN
cana-2873	194	27	)	)	PUNCT
cana-2873	194	28	)	)	PUNCT
cana-2873	194	29	)	)	PUNCT
cana-2873	195	1	is	be	AUX
cana-2873	195	2	q	q	NOUN
cana-2873	195	3	-	-	PUNCT
cana-2873	195	4	nsβo	nsβo	ADJ
cana-2873	195	5	in	in	ADP
cana-2873	195	6	z1	z1	PROPN
cana-2873	195	7	.	.	PUNCT
cana-2873	196	1	now	now	ADV
cana-2873	196	2	,	,	PUNCT
cana-2873	196	3	as	as	ADP
cana-2873	196	4	(	(	PUNCT
cana-2873	196	5	ψ̃)⊇k−1(q	ψ̃)⊇k−1(q	ADV
cana-2873	196	6	-	-	PUNCT
cana-2873	196	7	nsint(k(ψ̃	nsint(k(ψ̃	NUM
cana-2873	196	8	)	)	PUNCT
cana-2873	196	9	)	)	PUNCT
cana-2873	196	10	)	)	PUNCT
cana-2873	196	11	,	,	PUNCT
cana-2873	196	12	q	q	X
cana-2873	196	13	-	-	PUNCT
cana-2873	196	14	nsβcl(ψ̃)⊇k−1(q	nsβcl(ψ̃)⊇k−1(q	NOUN
cana-2873	196	15	-	-	PUNCT
cana-2873	196	16	nsint(k(ψ̃	nsint(k(ψ̃	NOUN
cana-2873	196	17	)	)	PUNCT
cana-2873	196	18	)	)	PUNCT
cana-2873	196	19	)	)	PUNCT
cana-2873	196	20	.	.	PUNCT
cana-2873	197	1	therefore	therefore	ADV
cana-2873	197	2	,	,	PUNCT
cana-2873	197	3	k(q	k(q	PROPN
cana-2873	197	4	-	-	PUNCT
cana-2873	197	5	nsβcl(ψ̃	nsβcl(ψ̃	PROPN
cana-2873	197	6	)	)	PUNCT
cana-2873	197	7	)	)	PUNCT
cana-2873	198	1	q	q	X
cana-2873	198	2	-	-	PUNCT
cana-2873	198	3	nsint(k(ψ̃	nsint(k(ψ̃	NUM
cana-2873	198	4	)	)	PUNCT
cana-2873	198	5	)	)	PUNCT
cana-2873	198	6	.	.	PUNCT
cana-2873	199	1	(	(	PUNCT
cana-2873	199	2	ii	ii	NOUN
cana-2873	199	3	)	)	PUNCT
cana-2873	199	4	by	by	ADP
cana-2873	199	5	replacing	replace	VERB
cana-2873	199	6	(	(	PUNCT
cana-2873	199	7	ψ̃	ψ̃	PROPN
cana-2873	199	8	)	)	PUNCT
cana-2873	199	9	with	with	ADP
cana-2873	199	10	(	(	PUNCT
cana-2873	199	11	φ̃	φ̃	PROPN
cana-2873	199	12	)	)	PUNCT
cana-2873	199	13	in	in	ADP
cana-2873	199	14	(	(	PUNCT
cana-2873	199	15	i	i	NOUN
cana-2873	199	16	)	)	PUNCT
cana-2873	199	17	,	,	PUNCT
cana-2873	199	18	we	we	PRON
cana-2873	199	19	get	get	VERB
cana-2873	199	20	k(q	k(q	PROPN
cana-2873	199	21	-	-	PUNCT
cana-2873	199	22	nsβcl(k−1(φ̃)))⊇q	nsβcl(k−1(φ̃)))⊇q	PROPN
cana-2873	199	23	nsint(k(k−1(φ̃)))⊇qnsint(φ̃	nsint(k(k−1(φ̃)))⊇qnsint(φ̃	NOUN
cana-2873	199	24	)	)	PUNCT
cana-2873	199	25	.	.	PUNCT
cana-2873	200	1	hence	hence	ADV
cana-2873	200	2	,	,	PUNCT
cana-2873	200	3	q	q	NOUN
cana-2873	200	4	-	-	NOUN
cana-2873	200	5	nsβcl(k−1(φ̃	nsβcl(k−1(φ̃	NUM
cana-2873	200	6	)	)	PUNCT
cana-2873	200	7	)	)	PUNCT
cana-2873	200	8	⊇	⊇	PROPN
cana-2873	200	9	k−1(q	k−1(q	PROPN
cana-2873	200	10	-	-	PUNCT
cana-2873	200	11	nsint(φ̃	nsint(φ̃	PROPN
cana-2873	200	12	)	)	PUNCT
cana-2873	200	13	)	)	PUNCT
cana-2873	200	14	.	.	PUNCT
cana-2873	201	1	4	4	NUM
cana-2873	201	2	quadripartitioned	quadripartitione	VERB
cana-2873	201	3	neutrosophic	neutrosophic	PROPN
cana-2873	201	4	contra	contra	PROPN
cana-2873	201	5	β	β	PROPN
cana-2873	201	6	-	-	PUNCT
cana-2873	201	7	irresolute	irresolute	ADJ
cana-2873	201	8	maps	map	NOUN
cana-2873	201	9	the	the	DET
cana-2873	201	10	quadripartitioned	quadripartitione	VERB
cana-2873	201	11	neutrosophic	neutrosophic	PROPN
cana-2873	201	12	contra	contra	PROPN
cana-2873	201	13	β	β	PROPN
cana-2873	201	14	-	-	PUNCT
cana-2873	201	15	irresolute	irresolute	ADJ
cana-2873	201	16	maps	map	NOUN
cana-2873	201	17	are	be	AUX
cana-2873	201	18	introduced	introduce	VERB
cana-2873	201	19	and	and	CCONJ
cana-2873	201	20	some	some	PRON
cana-2873	201	21	of	of	ADP
cana-2873	201	22	its	its	PRON
cana-2873	201	23	properties	property	NOUN
cana-2873	201	24	are	be	AUX
cana-2873	201	25	discussed	discuss	VERB
cana-2873	201	26	in	in	ADP
cana-2873	201	27	this	this	DET
cana-2873	201	28	section	section	NOUN
cana-2873	201	29	.	.	PUNCT
cana-2873	202	1	communications	communication	NOUN
cana-2873	202	2	on	on	ADP
cana-2873	202	3	applied	apply	VERB
cana-2873	202	4	nonlinear	nonlinear	ADJ
cana-2873	202	5	analysis	analysis	NOUN
cana-2873	202	6	issn	issn	NOUN
cana-2873	202	7	:	:	PUNCT
cana-2873	202	8	1074	1074	NUM
cana-2873	202	9	-	-	PUNCT
cana-2873	202	10	133x	133x	NUM
cana-2873	202	11	vol	vol	NOUN
cana-2873	202	12	32	32	NUM
cana-2873	202	13	no	no	NOUN
cana-2873	202	14	.	.	PUNCT
cana-2873	203	1	4s	4s	NUM
cana-2873	203	2	(	(	PUNCT
cana-2873	203	3	2025	2025	NUM
cana-2873	203	4	)	)	PUNCT
cana-2873	203	5	586	586	NUM
cana-2873	203	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	203	7	definition	definition	NOUN
cana-2873	203	8	4.1	4.1	NUM
cana-2873	203	9	.	.	PUNCT
cana-2873	204	1	a	a	DET
cana-2873	204	2	map	map	NOUN
cana-2873	204	3	k	k	X
cana-2873	204	4	:	:	PUNCT
cana-2873	204	5	(	(	PUNCT
cana-2873	204	6	z1	z1	VERB
cana-2873	204	7	,	,	PUNCT
cana-2873	204	8	γq	γq	ADP
cana-2873	204	9	)	)	PUNCT
cana-2873	204	10	→	→	SYM
cana-2873	204	11	(	(	PUNCT
cana-2873	204	12	z2	z2	PROPN
cana-2873	204	13	,	,	PUNCT
cana-2873	204	14	σq	σq	NOUN
cana-2873	204	15	)	)	PUNCT
cana-2873	204	16	is	be	AUX
cana-2873	204	17	known	know	VERB
cana-2873	204	18	as	as	ADP
cana-2873	204	19	a	a	DET
cana-2873	204	20	quadripartitioned	quadripartitione	VERB
cana-2873	204	21	neutrosophic	neutrosophic	PROPN
cana-2873	204	22	contra	contra	PROPN
cana-2873	204	23	βirresolute	βirresolute	NOUN
cana-2873	204	24	(	(	PUNCT
cana-2873	204	25	in	in	ADP
cana-2873	204	26	short	short	ADJ
cana-2873	204	27	,	,	PUNCT
cana-2873	204	28	q	q	ADJ
cana-2873	204	29	-	-	PUNCT
cana-2873	204	30	nscβirr	nscβirr	ADJ
cana-2873	204	31	)	)	PUNCT
cana-2873	204	32	map	map	NOUN
cana-2873	204	33	if	if	SCONJ
cana-2873	204	34	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	204	35	)	)	PUNCT
cana-2873	204	36	is	be	AUX
cana-2873	204	37	a	a	DET
cana-2873	204	38	q	q	NOUN
cana-2873	204	39	-	-	PUNCT
cana-2873	204	40	nsβcs	nsβcs	NOUN
cana-2873	204	41	in	in	ADP
cana-2873	204	42	(	(	PUNCT
cana-2873	204	43	z1	z1	NOUN
cana-2873	204	44	,	,	PUNCT
cana-2873	204	45	γq	γq	ADP
cana-2873	204	46	)	)	PUNCT
cana-2873	204	47	for	for	ADP
cana-2873	204	48	each	each	DET
cana-2873	204	49	qnsβos	qnsβos	NOUN
cana-2873	204	50	ψ̃	ψ̃	PROPN
cana-2873	204	51	of	of	ADP
cana-2873	204	52	(	(	PUNCT
cana-2873	204	53	z2	z2	PROPN
cana-2873	204	54	,	,	PUNCT
cana-2873	204	55	σq	σq	NOUN
cana-2873	204	56	)	)	PUNCT
cana-2873	204	57	.	.	PUNCT
cana-2873	205	1	theorem	theorem	VERB
cana-2873	205	2	4.2	4.2	NUM
cana-2873	205	3	.	.	PUNCT
cana-2873	206	1	let	let	VERB
cana-2873	206	2	k	k	NOUN
cana-2873	206	3	:	:	PUNCT
cana-2873	206	4	(	(	PUNCT
cana-2873	206	5	z1	z1	VERB
cana-2873	206	6	,	,	PUNCT
cana-2873	206	7	γq)→	γq)→	X
cana-2873	206	8	(	(	PUNCT
cana-2873	206	9	z2	z2	PROPN
cana-2873	206	10	,	,	PUNCT
cana-2873	206	11	σq	σq	NOUN
cana-2873	206	12	)	)	PUNCT
cana-2873	206	13	be	be	VERB
cana-2873	206	14	a	a	DET
cana-2873	206	15	q	q	ADJ
cana-2873	206	16	-	-	PUNCT
cana-2873	206	17	nscβirr	nscβirr	ADJ
cana-2873	206	18	map	map	NOUN
cana-2873	206	19	.	.	PUNCT
cana-2873	207	1	then	then	ADV
cana-2873	207	2	k	k	PROPN
cana-2873	207	3	is	be	AUX
cana-2873	207	4	q	q	NOUN
cana-2873	207	5	-	-	PUNCT
cana-2873	207	6	nscβcts	nscβct	NOUN
cana-2873	207	7	.	.	PUNCT
cana-2873	208	1	but	but	CCONJ
cana-2873	208	2	the	the	DET
cana-2873	208	3	converse	converse	NOUN
cana-2873	208	4	need	need	AUX
cana-2873	208	5	not	not	PART
cana-2873	208	6	be	be	AUX
cana-2873	208	7	true	true	ADJ
cana-2873	208	8	.	.	PUNCT
cana-2873	209	1	proof	proof	NOUN
cana-2873	209	2	.	.	PUNCT
cana-2873	210	1	assume	assume	VERB
cana-2873	210	2	k	k	PROPN
cana-2873	210	3	is	be	AUX
cana-2873	210	4	a	a	DET
cana-2873	210	5	q	q	ADJ
cana-2873	210	6	-	-	PUNCT
cana-2873	210	7	nscβirr	nscβirr	ADJ
cana-2873	210	8	map	map	NOUN
cana-2873	210	9	.	.	PUNCT
cana-2873	211	1	consider	consider	VERB
cana-2873	211	2	a	a	DET
cana-2873	211	3	q	q	NOUN
cana-2873	211	4	-	-	PUNCT
cana-2873	211	5	nsos	nsos	ADJ
cana-2873	211	6	ψ̃	ψ̃	PROPN
cana-2873	211	7	in	in	ADP
cana-2873	211	8	z2	z2	PROPN
cana-2873	211	9	.	.	PUNCT
cana-2873	212	1	as	as	SCONJ
cana-2873	212	2	each	each	DET
cana-2873	212	3	q	q	NOUN
cana-2873	212	4	-	-	PUNCT
cana-2873	212	5	nsos	nsos	NOUN
cana-2873	212	6	is	be	AUX
cana-2873	212	7	a	a	DET
cana-2873	212	8	q	q	NOUN
cana-2873	212	9	-	-	PUNCT
cana-2873	212	10	nsβos	nsβos	NOUN
cana-2873	212	11	,	,	PUNCT
cana-2873	212	12	ψ̃	ψ̃	PROPN
cana-2873	212	13	is	be	AUX
cana-2873	212	14	a	a	DET
cana-2873	212	15	q	q	NOUN
cana-2873	212	16	-	-	PUNCT
cana-2873	212	17	nsβos	nsβos	NOUN
cana-2873	212	18	in	in	ADP
cana-2873	212	19	z2	z2	PROPN
cana-2873	212	20	.	.	PUNCT
cana-2873	213	1	by	by	ADP
cana-2873	213	2	presumption	presumption	NOUN
cana-2873	213	3	,	,	PUNCT
cana-2873	213	4	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	213	5	)	)	PUNCT
cana-2873	213	6	is	be	AUX
cana-2873	213	7	a	a	DET
cana-2873	213	8	q	q	NOUN
cana-2873	213	9	-	-	PUNCT
cana-2873	213	10	nsβcs	nsβcs	NOUN
cana-2873	213	11	in	in	ADP
cana-2873	213	12	z1	z1	PROPN
cana-2873	213	13	.	.	PUNCT
cana-2873	214	1	thus	thus	ADV
cana-2873	214	2	k	k	PROPN
cana-2873	214	3	is	be	AUX
cana-2873	214	4	a	a	DET
cana-2873	214	5	q	q	ADJ
cana-2873	214	6	-	-	PUNCT
cana-2873	214	7	nsɕβcts	nsɕβct	NOUN
cana-2873	214	8	map	map	NOUN
cana-2873	214	9	.	.	PUNCT
cana-2873	214	10	example	example	NOUN
cana-2873	215	1	4.3	4.3	NUM
cana-2873	215	2	.	.	PUNCT
cana-2873	216	1	let	let	VERB
cana-2873	216	2	v	v	VERB
cana-2873	216	3	=	=	SYM
cana-2873	216	4	{	{	PUNCT
cana-2873	216	5	va	va	NOUN
cana-2873	216	6	,	,	PUNCT
cana-2873	216	7	vb	vb	NOUN
cana-2873	216	8	,	,	PUNCT
cana-2873	216	9	vc	vc	NOUN
cana-2873	216	10	}	}	PUNCT
cana-2873	216	11	=	=	SYM
cana-2873	216	12	w	w	NOUN
cana-2873	216	13	and	and	CCONJ
cana-2873	216	14	define	define	VERB
cana-2873	216	15	q	q	ADJ
cana-2873	216	16	-	-	PUNCT
cana-2873	216	17	nss	nss	NOUN
cana-2873	216	18	’s	’s	PART
cana-2873	216	19	v1	v1	NOUN
cana-2873	216	20	,	,	PUNCT
cana-2873	216	21	v2	v2	PROPN
cana-2873	216	22	&	&	CCONJ
cana-2873	216	23	v3	v3	PROPN
cana-2873	216	24	in	in	ADP
cana-2873	216	25	v	v	NOUN
cana-2873	216	26	and	and	CCONJ
cana-2873	216	27	w1	w1	PROPN
cana-2873	216	28	&	&	CCONJ
cana-2873	216	29	w2	w2	PROPN
cana-2873	216	30	in	in	ADP
cana-2873	216	31	w	w	PROPN
cana-2873	216	32	are	be	AUX
cana-2873	216	33	v1	v1	NOUN
cana-2873	216	34	=	=	SYM
cana-2873	216	35	{	{	PUNCT
cana-2873	216	36	(	(	PUNCT
cana-2873	216	37	va	va	NOUN
cana-2873	216	38	,	,	PUNCT
cana-2873	216	39	0.2	0.2	NUM
cana-2873	216	40	,	,	PUNCT
cana-2873	216	41	0.5	0.5	NUM
cana-2873	216	42	,	,	PUNCT
cana-2873	216	43	0.5	0.5	NUM
cana-2873	216	44	,	,	PUNCT
cana-2873	216	45	0.8	0.8	NUM
cana-2873	216	46	)	)	PUNCT
cana-2873	216	47	,	,	PUNCT
cana-2873	216	48	(	(	PUNCT
cana-2873	216	49	vb	vb	NOUN
cana-2873	216	50	,	,	PUNCT
cana-2873	216	51	0.3	0.3	NUM
cana-2873	216	52	,	,	PUNCT
cana-2873	216	53	0.5	0.5	NUM
cana-2873	216	54	,	,	PUNCT
cana-2873	216	55	0.5	0.5	NUM
cana-2873	216	56	,	,	PUNCT
cana-2873	216	57	0.7	0.7	NUM
cana-2873	216	58	)	)	PUNCT
cana-2873	216	59	,	,	PUNCT
cana-2873	216	60	(	(	PUNCT
cana-2873	216	61	vc	vc	INTJ
cana-2873	216	62	,	,	PUNCT
cana-2873	216	63	0.4	0.4	NUM
cana-2873	216	64	,	,	PUNCT
cana-2873	216	65	0.5	0.5	NUM
cana-2873	216	66	,	,	PUNCT
cana-2873	216	67	0.5	0.5	NUM
cana-2873	216	68	,	,	PUNCT
cana-2873	216	69	0.6	0.6	NUM
cana-2873	216	70	)	)	PUNCT
cana-2873	216	71	}	}	PUNCT
cana-2873	216	72	,	,	PUNCT
cana-2873	216	73	v2	v2	PROPN
cana-2873	216	74	=	=	SYM
cana-2873	216	75	{	{	PUNCT
cana-2873	216	76	(	(	PUNCT
cana-2873	216	77	va	va	NOUN
cana-2873	216	78	,	,	PUNCT
cana-2873	216	79	0.1	0.1	NUM
cana-2873	216	80	,	,	PUNCT
cana-2873	216	81	0.5	0.5	NUM
cana-2873	216	82	,	,	PUNCT
cana-2873	216	83	0.5	0.5	NUM
cana-2873	216	84	,	,	PUNCT
cana-2873	216	85	0.9	0.9	NUM
cana-2873	216	86	)	)	PUNCT
cana-2873	216	87	,	,	PUNCT
cana-2873	216	88	(	(	PUNCT
cana-2873	216	89	vb	vb	NOUN
cana-2873	216	90	,	,	PUNCT
cana-2873	216	91	0.1	0.1	NUM
cana-2873	216	92	,	,	PUNCT
cana-2873	216	93	0.5	0.5	NUM
cana-2873	216	94	,	,	PUNCT
cana-2873	216	95	0.5	0.5	NUM
cana-2873	216	96	,	,	PUNCT
cana-2873	216	97	0.9	0.9	NUM
cana-2873	216	98	)	)	PUNCT
cana-2873	216	99	,	,	PUNCT
cana-2873	216	100	(	(	PUNCT
cana-2873	216	101	vc	vc	INTJ
cana-2873	216	102	,	,	PUNCT
cana-2873	216	103	0.4	0.4	NUM
cana-2873	216	104	,	,	PUNCT
cana-2873	216	105	0.5	0.5	NUM
cana-2873	216	106	,	,	PUNCT
cana-2873	216	107	0.5	0.5	NUM
cana-2873	216	108	,	,	PUNCT
cana-2873	216	109	0.6	0.6	NUM
cana-2873	216	110	)	)	PUNCT
cana-2873	216	111	}	}	PUNCT
cana-2873	216	112	,	,	PUNCT
cana-2873	216	113	v3	v3	PROPN
cana-2873	216	114	=	=	SYM
cana-2873	216	115	{	{	PUNCT
cana-2873	216	116	(	(	PUNCT
cana-2873	216	117	va	va	NOUN
cana-2873	216	118	,	,	PUNCT
cana-2873	216	119	0.2	0.2	NUM
cana-2873	216	120	,	,	PUNCT
cana-2873	216	121	0.5	0.5	NUM
cana-2873	216	122	,	,	PUNCT
cana-2873	216	123	0.5	0.5	NUM
cana-2873	216	124	,	,	PUNCT
cana-2873	216	125	0.8	0.8	NUM
cana-2873	216	126	)	)	PUNCT
cana-2873	216	127	,	,	PUNCT
cana-2873	216	128	(	(	PUNCT
cana-2873	216	129	vb	vb	NOUN
cana-2873	216	130	,	,	PUNCT
cana-2873	216	131	0.4	0.4	NUM
cana-2873	216	132	,	,	PUNCT
cana-2873	216	133	0.5	0.5	NUM
cana-2873	216	134	,	,	PUNCT
cana-2873	216	135	0.5	0.5	NUM
cana-2873	216	136	,	,	PUNCT
cana-2873	216	137	0.6	0.6	NUM
cana-2873	216	138	)	)	PUNCT
cana-2873	216	139	,	,	PUNCT
cana-2873	216	140	(	(	PUNCT
cana-2873	216	141	vc	vc	INTJ
cana-2873	216	142	,	,	PUNCT
cana-2873	216	143	0.4	0.4	NUM
cana-2873	216	144	,	,	PUNCT
cana-2873	216	145	0.5	0.5	NUM
cana-2873	216	146	,	,	PUNCT
cana-2873	216	147	0.5	0.5	NUM
cana-2873	216	148	,	,	PUNCT
cana-2873	216	149	0.6	0.6	NUM
cana-2873	216	150	)	)	PUNCT
cana-2873	216	151	}	}	PUNCT
cana-2873	216	152	,	,	PUNCT
cana-2873	216	153	w1	w1	NOUN
cana-2873	216	154	=	=	SYM
cana-2873	216	155	{	{	PUNCT
cana-2873	216	156	(	(	PUNCT
cana-2873	216	157	va	va	NOUN
cana-2873	216	158	,	,	PUNCT
cana-2873	216	159	0.1	0.1	NUM
cana-2873	216	160	,	,	PUNCT
cana-2873	216	161	0.5	0.5	NUM
cana-2873	216	162	,	,	PUNCT
cana-2873	216	163	0.5	0.5	NUM
cana-2873	216	164	,	,	PUNCT
cana-2873	216	165	0.9	0.9	NUM
cana-2873	216	166	)	)	PUNCT
cana-2873	216	167	,	,	PUNCT
cana-2873	216	168	(	(	PUNCT
cana-2873	216	169	vb	vb	NOUN
cana-2873	216	170	,	,	PUNCT
cana-2873	216	171	0.1	0.1	NUM
cana-2873	216	172	,	,	PUNCT
cana-2873	216	173	0.5	0.5	NUM
cana-2873	216	174	,	,	PUNCT
cana-2873	216	175	0.5	0.5	NUM
cana-2873	216	176	,	,	PUNCT
cana-2873	216	177	0.9	0.9	NUM
cana-2873	216	178	)	)	PUNCT
cana-2873	216	179	,	,	PUNCT
cana-2873	216	180	(	(	PUNCT
cana-2873	216	181	vc	vc	INTJ
cana-2873	216	182	,	,	PUNCT
cana-2873	216	183	0.4	0.4	NUM
cana-2873	216	184	,	,	PUNCT
cana-2873	216	185	0.5	0.5	NUM
cana-2873	216	186	,	,	PUNCT
cana-2873	216	187	0.5	0.5	NUM
cana-2873	216	188	,	,	PUNCT
cana-2873	216	189	0.6	0.6	NUM
cana-2873	216	190	)	)	PUNCT
cana-2873	216	191	}	}	PUNCT
cana-2873	216	192	,	,	PUNCT
cana-2873	216	193	w2	w2	NOUN
cana-2873	216	194	=	=	SYM
cana-2873	216	195	{	{	PUNCT
cana-2873	216	196	(	(	PUNCT
cana-2873	216	197	va	va	NOUN
cana-2873	216	198	,	,	PUNCT
cana-2873	216	199	0.1	0.1	NUM
cana-2873	216	200	,	,	PUNCT
cana-2873	216	201	0.5	0.5	NUM
cana-2873	216	202	,	,	PUNCT
cana-2873	216	203	0.5	0.5	NUM
cana-2873	216	204	,	,	PUNCT
cana-2873	216	205	0.9	0.9	NUM
cana-2873	216	206	)	)	PUNCT
cana-2873	216	207	,	,	PUNCT
cana-2873	216	208	(	(	PUNCT
cana-2873	216	209	vb	vb	NOUN
cana-2873	216	210	,	,	PUNCT
cana-2873	216	211	0.4	0.4	NUM
cana-2873	216	212	,	,	PUNCT
cana-2873	216	213	0.5	0.5	NUM
cana-2873	216	214	,	,	PUNCT
cana-2873	216	215	0.5	0.5	NUM
cana-2873	216	216	,	,	PUNCT
cana-2873	216	217	0.6	0.6	NUM
cana-2873	216	218	)	)	PUNCT
cana-2873	216	219	,	,	PUNCT
cana-2873	216	220	(	(	PUNCT
cana-2873	216	221	vc	vc	INTJ
cana-2873	216	222	,	,	PUNCT
cana-2873	216	223	0.5	0.5	NUM
cana-2873	216	224	,	,	PUNCT
cana-2873	216	225	0.5	0.5	NUM
cana-2873	216	226	,	,	PUNCT
cana-2873	216	227	0.5	0.5	NUM
cana-2873	216	228	,	,	PUNCT
cana-2873	216	229	0.5	0.5	NUM
cana-2873	216	230	)	)	PUNCT
cana-2873	216	231	}	}	PUNCT
cana-2873	216	232	.	.	PUNCT
cana-2873	217	1	then	then	ADV
cana-2873	217	2	we	we	PRON
cana-2873	217	3	have	have	VERB
cana-2873	217	4	γq	γq	ADP
cana-2873	217	5	=	=	NOUN
cana-2873	217	6	{	{	PUNCT
cana-2873	217	7	0qns	0qns	PROPN
cana-2873	217	8	,	,	PUNCT
cana-2873	217	9	v1	v1	PROPN
cana-2873	217	10	,	,	PUNCT
cana-2873	217	11	v2	v2	PROPN
cana-2873	217	12	,	,	PUNCT
cana-2873	217	13	1qns	1qns	NUM
cana-2873	217	14	}	}	PUNCT
cana-2873	217	15	and	and	CCONJ
cana-2873	217	16	σq	σq	PRON
cana-2873	217	17	=	=	NOUN
cana-2873	217	18	{	{	PUNCT
cana-2873	217	19	0qns	0qns	PROPN
cana-2873	217	20	,	,	PUNCT
cana-2873	217	21	w1	w1	NOUN
cana-2873	217	22	,	,	PUNCT
cana-2873	217	23	1qns	1qns	NUM
cana-2873	217	24	}	}	PUNCT
cana-2873	217	25	.	.	PUNCT
cana-2873	218	1	let	let	VERB
cana-2873	218	2	k	k	NOUN
cana-2873	218	3	:	:	PUNCT
cana-2873	218	4	(	(	PUNCT
cana-2873	218	5	z1	z1	PROPN
cana-2873	218	6	,	,	PUNCT
cana-2873	218	7	γq)→(z2	γq)→(z2	NOUN
cana-2873	218	8	,	,	PUNCT
cana-2873	218	9	σq	σq	NOUN
cana-2873	218	10	)	)	PUNCT
cana-2873	218	11	be	be	VERB
cana-2873	218	12	an	an	DET
cana-2873	218	13	identity	identity	NOUN
cana-2873	218	14	mapping	mapping	NOUN
cana-2873	218	15	,	,	PUNCT
cana-2873	218	16	then	then	ADV
cana-2873	218	17	k	k	PROPN
cana-2873	218	18	is	be	AUX
cana-2873	218	19	q	q	NOUN
cana-2873	218	20	-	-	PUNCT
cana-2873	218	21	nsɕβcts	nsɕβct	NOUN
cana-2873	218	22	but	but	CCONJ
cana-2873	218	23	not	not	PART
cana-2873	218	24	q	q	NOUN
cana-2873	218	25	-	-	PUNCT
cana-2873	218	26	nsɕβirr	nsɕβirr	ADJ
cana-2873	218	27	,	,	PUNCT
cana-2873	218	28	the	the	DET
cana-2873	218	29	set	set	NOUN
cana-2873	218	30	w2	w2	NOUN
cana-2873	218	31	is	be	AUX
cana-2873	218	32	a	a	DET
cana-2873	218	33	qnsβc	qnsβc	PROPN
cana-2873	218	34	set	set	VERB
cana-2873	218	35	in	in	ADP
cana-2873	218	36	w	w	PROPN
cana-2873	218	37	but	but	CCONJ
cana-2873	218	38	k−1(w2	k−1(w2	NOUN
cana-2873	218	39	)	)	PUNCT
cana-2873	218	40	is	be	AUX
cana-2873	218	41	not	not	PART
cana-2873	218	42	q	q	ADJ
cana-2873	218	43	-	-	PUNCT
cana-2873	218	44	nsβc	nsβc	VERB
cana-2873	218	45	set	set	NOUN
cana-2873	218	46	in	in	ADP
cana-2873	218	47	v	v	NUM
cana-2873	218	48	.	.	PUNCT
cana-2873	219	1	theorem	theorem	VERB
cana-2873	219	2	4.4	4.4	NUM
cana-2873	219	3	.	.	PUNCT
cana-2873	220	1	let	let	VERB
cana-2873	220	2	k	k	NOUN
cana-2873	220	3	:	:	PUNCT
cana-2873	220	4	(	(	PUNCT
cana-2873	220	5	z1	z1	PROPN
cana-2873	220	6	,	,	PUNCT
cana-2873	220	7	γq)→(z2	γq)→(z2	NOUN
cana-2873	220	8	,	,	PUNCT
cana-2873	220	9	σq	σq	NOUN
cana-2873	220	10	)	)	PUNCT
cana-2873	220	11	be	be	VERB
cana-2873	220	12	a	a	DET
cana-2873	220	13	q	q	NOUN
cana-2873	220	14	-	-	PUNCT
cana-2873	220	15	nsɕβirr	nsɕβirr	NOUN
cana-2873	220	16	.	.	PUNCT
cana-2873	221	1	if	if	SCONJ
cana-2873	221	2	z1	z1	PROPN
cana-2873	221	3	is	be	AUX
cana-2873	221	4	a	a	DET
cana-2873	221	5	q	q	ADJ
cana-2873	221	6	-	-	PUNCT
cana-2873	221	7	nsβu1/2	nsβu1/2	ADJ
cana-2873	221	8	-space	-space	NOUN
cana-2873	221	9	,	,	PUNCT
cana-2873	221	10	then	then	ADV
cana-2873	221	11	k	k	PROPN
cana-2873	221	12	is	be	AUX
cana-2873	221	13	a	a	DET
cana-2873	221	14	q	q	NOUN
cana-2873	221	15	-	-	PUNCT
cana-2873	221	16	nsɕcts	nsɕct	NOUN
cana-2873	221	17	map	map	NOUN
cana-2873	221	18	.	.	PUNCT
cana-2873	222	1	proof	proof	NOUN
cana-2873	222	2	.	.	PUNCT
cana-2873	223	1	consider	consider	VERB
cana-2873	223	2	a	a	DET
cana-2873	223	3	q	q	NOUN
cana-2873	223	4	-	-	PUNCT
cana-2873	223	5	nsos	nsos	ADJ
cana-2873	223	6	ψ̃	ψ̃	PROPN
cana-2873	223	7	in	in	ADP
cana-2873	223	8	z2	z2	PROPN
cana-2873	223	9	.	.	PUNCT
cana-2873	224	1	then	then	ADV
cana-2873	224	2	ψ̃	ψ̃	PROPN
cana-2873	224	3	is	be	AUX
cana-2873	224	4	a	a	DET
cana-2873	224	5	q	q	NOUN
cana-2873	224	6	-	-	PUNCT
cana-2873	224	7	nsβos	nsβos	NOUN
cana-2873	224	8	in	in	ADP
cana-2873	224	9	z2	z2	PROPN
cana-2873	224	10	.	.	PUNCT
cana-2873	225	1	hence	hence	ADV
cana-2873	225	2	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	225	3	)	)	PUNCT
cana-2873	225	4	is	be	AUX
cana-2873	225	5	a	a	DET
cana-2873	225	6	q	q	NOUN
cana-2873	225	7	-	-	PUNCT
cana-2873	225	8	nsβcs	nsβcs	NOUN
cana-2873	225	9	in	in	ADP
cana-2873	225	10	z1	z1	PROPN
cana-2873	225	11	.	.	PUNCT
cana-2873	226	1	as	as	SCONJ
cana-2873	226	2	z1	z1	PROPN
cana-2873	226	3	is	be	AUX
cana-2873	226	4	a	a	DET
cana-2873	226	5	q	q	ADJ
cana-2873	226	6	-	-	PUNCT
cana-2873	226	7	nsβu1/2	nsβu1/2	ADJ
cana-2873	226	8	-space	-space	NOUN
cana-2873	226	9	,	,	PUNCT
cana-2873	226	10	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	226	11	)	)	PUNCT
cana-2873	226	12	is	be	AUX
cana-2873	226	13	a	a	DET
cana-2873	226	14	q	q	NOUN
cana-2873	226	15	-	-	PUNCT
cana-2873	226	16	nscs	nscs	NOUN
cana-2873	226	17	in	in	ADP
cana-2873	226	18	z1	z1	PROPN
cana-2873	226	19	.	.	PUNCT
cana-2873	227	1	thus	thus	ADV
cana-2873	227	2	k	k	PROPN
cana-2873	227	3	is	be	AUX
cana-2873	227	4	a	a	DET
cana-2873	227	5	q	q	NOUN
cana-2873	227	6	-	-	PUNCT
cana-2873	227	7	nsɕcts	nsɕct	NOUN
cana-2873	227	8	map	map	NOUN
cana-2873	227	9	.	.	PUNCT
cana-2873	228	1	theorem	theorem	VERB
cana-2873	228	2	4.5	4.5	NUM
cana-2873	228	3	.	.	PUNCT
cana-2873	229	1	let	let	VERB
cana-2873	229	2	k	k	NOUN
cana-2873	229	3	:	:	PUNCT
cana-2873	229	4	(	(	PUNCT
cana-2873	229	5	z1	z1	VERB
cana-2873	229	6	,	,	PUNCT
cana-2873	229	7	γq	γq	ADP
cana-2873	229	8	)	)	PUNCT
cana-2873	229	9	→	→	SYM
cana-2873	229	10	(	(	PUNCT
cana-2873	229	11	z2	z2	PROPN
cana-2873	229	12	,	,	PUNCT
cana-2873	229	13	σq	σq	NOUN
cana-2873	229	14	)	)	PUNCT
cana-2873	229	15	be	be	VERB
cana-2873	229	16	a	a	DET
cana-2873	229	17	q	q	ADJ
cana-2873	229	18	-	-	PUNCT
cana-2873	229	19	nscβirr	nscβirr	ADJ
cana-2873	229	20	map	map	NOUN
cana-2873	229	21	and	and	CCONJ
cana-2873	229	22	g	g	NOUN
cana-2873	229	23	:(	:(	PROPN
cana-2873	229	24	z2	z2	PROPN
cana-2873	229	25	,	,	PUNCT
cana-2873	229	26	σq	σq	NOUN
cana-2873	229	27	)	)	PUNCT
cana-2873	229	28	→	→	SYM
cana-2873	229	29	(	(	PUNCT
cana-2873	229	30	z3	z3	PROPN
cana-2873	229	31	,	,	PUNCT
cana-2873	229	32	ρq	ρq	NUM
cana-2873	229	33	)	)	PUNCT
cana-2873	229	34	be	be	AUX
cana-2873	229	35	q	q	ADJ
cana-2873	229	36	-	-	PUNCT
cana-2873	229	37	nsβcts	nsβct	NOUN
cana-2873	229	38	map	map	NOUN
cana-2873	229	39	.	.	PUNCT
cana-2873	230	1	then	then	ADV
cana-2873	230	2	g	g	PROPN
cana-2873	230	3	◦	◦	PROPN
cana-2873	230	4	k	k	X
cana-2873	230	5	:	:	PUNCT
cana-2873	230	6	(	(	PUNCT
cana-2873	230	7	z1	z1	VERB
cana-2873	230	8	,	,	PUNCT
cana-2873	230	9	γq	γq	ADP
cana-2873	230	10	)	)	PUNCT
cana-2873	230	11	→	→	SYM
cana-2873	230	12	(	(	PUNCT
cana-2873	230	13	z3	z3	PROPN
cana-2873	230	14	,	,	PUNCT
cana-2873	230	15	ρq	ρq	NUM
cana-2873	230	16	)	)	PUNCT
cana-2873	230	17	is	be	AUX
cana-2873	230	18	a	a	DET
cana-2873	230	19	q	q	ADJ
cana-2873	230	20	-	-	PUNCT
cana-2873	230	21	nsɕβcts	nsɕβct	NOUN
cana-2873	230	22	map	map	NOUN
cana-2873	230	23	.	.	PUNCT
cana-2873	231	1	proof	proof	NOUN
cana-2873	231	2	.	.	PUNCT
cana-2873	232	1	consider	consider	VERB
cana-2873	232	2	a	a	DET
cana-2873	232	3	q	q	ADJ
cana-2873	232	4	-	-	PUNCT
cana-2873	232	5	nsos	nsos	ADJ
cana-2873	232	6	ã	ã	PROPN
cana-2873	232	7	in	in	ADP
cana-2873	232	8	z3	z3	PROPN
cana-2873	232	9	.	.	PUNCT
cana-2873	233	1	then	then	ADV
cana-2873	233	2	g−1(ã	g−1(ã	X
cana-2873	233	3	)	)	PUNCT
cana-2873	233	4	is	be	AUX
cana-2873	233	5	a	a	DET
cana-2873	233	6	q	q	NOUN
cana-2873	233	7	-	-	PUNCT
cana-2873	233	8	nsβos	nsβos	NOUN
cana-2873	233	9	in	in	ADP
cana-2873	233	10	z2	z2	PROPN
cana-2873	233	11	.	.	PUNCT
cana-2873	234	1	as	as	SCONJ
cana-2873	234	2	k	k	PROPN
cana-2873	234	3	is	be	AUX
cana-2873	234	4	a	a	DET
cana-2873	234	5	q	q	NOUN
cana-2873	234	6	-	-	PUNCT
cana-2873	234	7	nsɕβirr	nsɕβirr	ADJ
cana-2873	234	8	,	,	PUNCT
cana-2873	234	9	k−1(g−1(ã	k−1(g−1(ã	PROPN
cana-2873	234	10	)	)	PUNCT
cana-2873	234	11	)	)	PUNCT
cana-2873	234	12	is	be	AUX
cana-2873	234	13	a	a	DET
cana-2873	234	14	q	q	NOUN
cana-2873	234	15	-	-	PUNCT
cana-2873	234	16	nsβcs	nsβcs	NOUN
cana-2873	234	17	in	in	ADP
cana-2873	234	18	z1	z1	PROPN
cana-2873	234	19	.	.	PUNCT
cana-2873	235	1	thus	thus	ADV
cana-2873	235	2	g	g	PROPN
cana-2873	235	3	◦	◦	NOUN
cana-2873	235	4	k	k	PROPN
cana-2873	235	5	is	be	AUX
cana-2873	235	6	a	a	DET
cana-2873	235	7	q	q	ADJ
cana-2873	235	8	-	-	PUNCT
cana-2873	235	9	nsɕβcts	nsɕβct	NOUN
cana-2873	235	10	map	map	NOUN
cana-2873	235	11	.	.	PUNCT
cana-2873	236	1	theorem	theorem	VERB
cana-2873	236	2	4.6	4.6	NUM
cana-2873	236	3	.	.	PUNCT
cana-2873	237	1	let	let	VERB
cana-2873	237	2	k	k	NOUN
cana-2873	237	3	:	:	PUNCT
cana-2873	237	4	(	(	PUNCT
cana-2873	237	5	z1	z1	VERB
cana-2873	237	6	,	,	PUNCT
cana-2873	237	7	γq	γq	ADP
cana-2873	237	8	)	)	PUNCT
cana-2873	237	9	→	→	SYM
cana-2873	237	10	(	(	PUNCT
cana-2873	237	11	z2	z2	PROPN
cana-2873	237	12	,	,	PUNCT
cana-2873	237	13	σq	σq	NOUN
cana-2873	237	14	)	)	PUNCT
cana-2873	237	15	and	and	CCONJ
cana-2873	237	16	g	g	NOUN
cana-2873	237	17	:	:	PUNCT
cana-2873	237	18	(	(	PUNCT
cana-2873	237	19	z2	z2	NOUN
cana-2873	237	20	,	,	PUNCT
cana-2873	237	21	σq	σq	NOUN
cana-2873	237	22	)	)	PUNCT
cana-2873	237	23	→	→	SYM
cana-2873	237	24	(	(	PUNCT
cana-2873	237	25	z3	z3	PROPN
cana-2873	237	26	,	,	PUNCT
cana-2873	237	27	ρq	ρq	NUM
cana-2873	237	28	)	)	PUNCT
cana-2873	237	29	be	be	AUX
cana-2873	237	30	mappings	mapping	NOUN
cana-2873	237	31	.	.	PUNCT
cana-2873	238	1	then	then	ADV
cana-2873	238	2	g	g	PROPN
cana-2873	238	3	◦	◦	PROPN
cana-2873	238	4	k	k	X
cana-2873	238	5	:	:	PUNCT
cana-2873	238	6	(	(	PUNCT
cana-2873	238	7	z1	z1	VERB
cana-2873	238	8	,	,	PUNCT
cana-2873	238	9	γq	γq	ADP
cana-2873	238	10	)	)	PUNCT
cana-2873	238	11	→	→	SYM
cana-2873	238	12	(	(	PUNCT
cana-2873	238	13	z3	z3	PROPN
cana-2873	238	14	,	,	PUNCT
cana-2873	238	15	ρq	ρq	NOUN
cana-2873	238	16	)	)	PUNCT
cana-2873	238	17	is	be	AUX
cana-2873	238	18	:	:	PUNCT
cana-2873	238	19	(	(	PUNCT
cana-2873	238	20	i	i	NOUN
cana-2873	238	21	)	)	PUNCT
cana-2873	238	22	q	q	X
cana-2873	238	23	-	-	PUNCT
cana-2873	238	24	nsɕβcts	nsɕβct	VERB
cana-2873	238	25	if	if	SCONJ
cana-2873	238	26	k	k	PROPN
cana-2873	238	27	is	be	AUX
cana-2873	238	28	q	q	ADJ
cana-2873	238	29	-	-	PUNCT
cana-2873	238	30	nsβirr	nsβirr	PROPN
cana-2873	238	31	and	and	CCONJ
cana-2873	238	32	g	g	PROPN
cana-2873	238	33	is	be	AUX
cana-2873	238	34	q	q	NOUN
cana-2873	238	35	-	-	PUNCT
cana-2873	238	36	nsɕβcts	nsɕβct	NOUN
cana-2873	238	37	.	.	PUNCT
cana-2873	239	1	(	(	PUNCT
cana-2873	239	2	ii	ii	NOUN
cana-2873	239	3	)	)	PUNCT
cana-2873	239	4	q	q	NOUN
cana-2873	239	5	-	-	PUNCT
cana-2873	239	6	nsɕβirr	nsɕβirr	ADJ
cana-2873	239	7	if	if	SCONJ
cana-2873	239	8	k	k	PROPN
cana-2873	239	9	is	be	AUX
cana-2873	239	10	q	q	ADJ
cana-2873	239	11	-	-	ADJ
cana-2873	239	12	nsɕβirr	nsɕβirr	ADJ
cana-2873	239	13	(	(	PUNCT
cana-2873	239	14	resp	resp	NOUN
cana-2873	239	15	.	.	PUNCT
cana-2873	240	1	q	q	X
cana-2873	240	2	-	-	PUNCT
cana-2873	240	3	nsβirr	nsβirr	NOUN
cana-2873	240	4	)	)	PUNCT
cana-2873	240	5	and	and	CCONJ
cana-2873	240	6	g	g	PROPN
cana-2873	240	7	is	be	AUX
cana-2873	240	8	q	q	ADJ
cana-2873	240	9	-	-	PUNCT
cana-2873	240	10	nsβirr	nsβirr	NOUN
cana-2873	240	11	(	(	PUNCT
cana-2873	240	12	resp.q	resp.q	NOUN
cana-2873	240	13	-	-	PUNCT
cana-2873	240	14	nsɕβirr	nsɕβirr	NOUN
cana-2873	240	15	)	)	PUNCT
cana-2873	240	16	.	.	PUNCT
cana-2873	241	1	proof	proof	NOUN
cana-2873	241	2	.	.	PUNCT
cana-2873	242	1	(	(	PUNCT
cana-2873	242	2	i	i	NOUN
cana-2873	242	3	)	)	PUNCT
cana-2873	242	4	let	let	VERB
cana-2873	242	5	ã	ã	PROPN
cana-2873	242	6	be	be	AUX
cana-2873	242	7	a	a	DET
cana-2873	242	8	q	q	NOUN
cana-2873	242	9	-	-	PUNCT
cana-2873	242	10	nsos	nsos	NOUN
cana-2873	242	11	in	in	ADP
cana-2873	242	12	z3	z3	PROPN
cana-2873	242	13	.	.	PUNCT
cana-2873	243	1	then	then	ADV
cana-2873	243	2	g−1(ã	g−1(ã	X
cana-2873	243	3	)	)	PUNCT
cana-2873	243	4	is	be	AUX
cana-2873	243	5	a	a	DET
cana-2873	243	6	q	q	NOUN
cana-2873	243	7	-	-	PUNCT
cana-2873	243	8	nsβcs	nsβcs	NOUN
cana-2873	243	9	in	in	ADP
cana-2873	243	10	z2	z2	PROPN
cana-2873	243	11	.	.	PUNCT
cana-2873	244	1	as	as	SCONJ
cana-2873	244	2	k	k	PROPN
cana-2873	244	3	is	be	AUX
cana-2873	244	4	a	a	DET
cana-2873	244	5	q	q	ADJ
cana-2873	244	6	-	-	PUNCT
cana-2873	244	7	nsβirr	nsβirr	NOUN
cana-2873	244	8	,	,	PUNCT
cana-2873	244	9	k−1(g−1(ã))is	k−1(g−1(ã))is	NOUN
cana-2873	244	10	a	a	DET
cana-2873	244	11	q	q	NOUN
cana-2873	244	12	-	-	PUNCT
cana-2873	244	13	nsβcs	nsβcs	NOUN
cana-2873	244	14	in	in	ADP
cana-2873	244	15	z1	z1	PROPN
cana-2873	244	16	.	.	PUNCT
cana-2873	245	1	thus	thus	ADV
cana-2873	245	2	g	g	PROPN
cana-2873	245	3	k	k	PROPN
cana-2873	245	4	is	be	AUX
cana-2873	245	5	a	a	DET
cana-2873	245	6	q	q	ADJ
cana-2873	245	7	-	-	PUNCT
cana-2873	245	8	nsɕβcts	nsɕβct	NOUN
cana-2873	245	9	map	map	NOUN
cana-2873	245	10	.	.	PUNCT
cana-2873	246	1	the	the	DET
cana-2873	246	2	other	other	ADJ
cana-2873	246	3	cases	case	NOUN
cana-2873	246	4	are	be	AUX
cana-2873	246	5	similar	similar	ADJ
cana-2873	246	6	.	.	PUNCT
cana-2873	247	1	communications	communication	NOUN
cana-2873	247	2	on	on	ADP
cana-2873	247	3	applied	apply	VERB
cana-2873	247	4	nonlinear	nonlinear	ADJ
cana-2873	247	5	analysis	analysis	NOUN
cana-2873	247	6	issn	issn	NOUN
cana-2873	247	7	:	:	PUNCT
cana-2873	247	8	1074	1074	NUM
cana-2873	247	9	-	-	PUNCT
cana-2873	247	10	133x	133x	NUM
cana-2873	247	11	vol	vol	NOUN
cana-2873	247	12	32	32	NUM
cana-2873	247	13	no	no	NOUN
cana-2873	247	14	.	.	PUNCT
cana-2873	248	1	4s	4s	NUM
cana-2873	248	2	(	(	PUNCT
cana-2873	248	3	2025	2025	NUM
cana-2873	248	4	)	)	PUNCT
cana-2873	248	5	587	587	NUM
cana-2873	248	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	248	7	theorem	theorem	VERB
cana-2873	248	8	4.7	4.7	NUM
cana-2873	248	9	.	.	PUNCT
cana-2873	249	1	let	let	VERB
cana-2873	249	2	k	k	NOUN
cana-2873	249	3	:	:	PUNCT
cana-2873	249	4	(	(	PUNCT
cana-2873	249	5	z1	z1	VERB
cana-2873	249	6	,	,	PUNCT
cana-2873	249	7	γq	γq	ADP
cana-2873	249	8	)	)	PUNCT
cana-2873	249	9	→	→	SYM
cana-2873	249	10	(	(	PUNCT
cana-2873	249	11	z2	z2	PROPN
cana-2873	249	12	,	,	PUNCT
cana-2873	249	13	σq	σq	NOUN
cana-2873	249	14	)	)	PUNCT
cana-2873	249	15	be	be	VERB
cana-2873	249	16	a	a	DET
cana-2873	249	17	mapping	mapping	NOUN
cana-2873	249	18	.	.	PUNCT
cana-2873	250	1	(	(	PUNCT
cana-2873	250	2	i	i	NOUN
cana-2873	250	3	)	)	PUNCT
cana-2873	250	4	if	if	SCONJ
cana-2873	250	5	(	(	PUNCT
cana-2873	250	6	z1	z1	NOUN
cana-2873	250	7	,	,	PUNCT
cana-2873	250	8	γq	γq	NOUN
cana-2873	250	9	)	)	PUNCT
cana-2873	250	10	is	be	AUX
cana-2873	250	11	q	q	ADJ
cana-2873	250	12	-	-	PUNCT
cana-2873	250	13	nsβu1/2	nsβu1/2	ADJ
cana-2873	250	14	-space	-space	NOUN
cana-2873	250	15	,	,	PUNCT
cana-2873	250	16	then	then	ADV
cana-2873	250	17	the	the	DET
cana-2873	250	18	concepts	concept	NOUN
cana-2873	250	19	of	of	ADP
cana-2873	250	20	q	q	NOUN
cana-2873	250	21	-	-	PUNCT
cana-2873	250	22	nsɕcts	nsɕct	NOUN
cana-2873	250	23	and	and	CCONJ
cana-2873	250	24	q	q	NOUN
cana-2873	250	25	-	-	PUNCT
cana-2873	250	26	nsɕβcts	nsɕβct	NOUN
cana-2873	250	27	are	be	AUX
cana-2873	250	28	equivalent	equivalent	ADJ
cana-2873	250	29	.	.	PUNCT
cana-2873	251	1	(	(	PUNCT
cana-2873	251	2	ii	ii	NOUN
cana-2873	251	3	)	)	PUNCT
cana-2873	251	4	if	if	SCONJ
cana-2873	251	5	(	(	PUNCT
cana-2873	251	6	z2	z2	NOUN
cana-2873	251	7	,	,	PUNCT
cana-2873	251	8	σq	σq	NOUN
cana-2873	251	9	)	)	PUNCT
cana-2873	251	10	is	be	AUX
cana-2873	251	11	q	q	ADJ
cana-2873	251	12	-	-	PUNCT
cana-2873	251	13	nsβu1/2	nsβu1/2	ADJ
cana-2873	251	14	-space	-space	NOUN
cana-2873	251	15	,	,	PUNCT
cana-2873	251	16	then	then	ADV
cana-2873	251	17	the	the	DET
cana-2873	251	18	concepts	concept	NOUN
cana-2873	251	19	of	of	ADP
cana-2873	251	20	q	q	NOUN
cana-2873	251	21	-	-	PUNCT
cana-2873	251	22	nsɕβcts	nsɕβct	NOUN
cana-2873	251	23	and	and	CCONJ
cana-2873	251	24	q	q	NOUN
cana-2873	251	25	-	-	PUNCT
cana-2873	251	26	nsɕβirr	nsɕβirr	NOUN
cana-2873	251	27	are	be	AUX
cana-2873	251	28	equivalent	equivalent	ADJ
cana-2873	251	29	.	.	PUNCT
cana-2873	252	1	(	(	PUNCT
cana-2873	252	2	iii	iii	X
cana-2873	252	3	)	)	PUNCT
cana-2873	252	4	if	if	SCONJ
cana-2873	252	5	(	(	PUNCT
cana-2873	252	6	z1	z1	NOUN
cana-2873	252	7	,	,	PUNCT
cana-2873	252	8	γq	γq	NOUN
cana-2873	252	9	)	)	PUNCT
cana-2873	252	10	and	and	CCONJ
cana-2873	252	11	(	(	PUNCT
cana-2873	252	12	z2	z2	PROPN
cana-2873	252	13	,	,	PUNCT
cana-2873	252	14	σq	σq	NOUN
cana-2873	252	15	)	)	PUNCT
cana-2873	252	16	are	be	AUX
cana-2873	252	17	q	q	ADJ
cana-2873	252	18	-	-	PUNCT
cana-2873	252	19	nsβu1/2	nsβu1/2	ADJ
cana-2873	252	20	-spaces	-space	NOUN
cana-2873	252	21	,	,	PUNCT
cana-2873	252	22	then	then	ADV
cana-2873	252	23	the	the	DET
cana-2873	252	24	concepts	concept	NOUN
cana-2873	252	25	of	of	ADP
cana-2873	252	26	q	q	NOUN
cana-2873	252	27	-	-	PUNCT
cana-2873	252	28	nsɕcts	nsɕct	NOUN
cana-2873	252	29	,	,	PUNCT
cana-2873	252	30	qnsɕβcts	qnsɕβct	VERB
cana-2873	252	31	andq	andq	PROPN
cana-2873	252	32	-	-	PUNCT
cana-2873	252	33	nsɕβirr	nsɕβirr	PROPN
cana-2873	252	34	are	be	AUX
cana-2873	252	35	equivalent	equivalent	ADJ
cana-2873	252	36	.	.	PUNCT
cana-2873	253	1	proof	proof	NOUN
cana-2873	253	2	.	.	PUNCT
cana-2873	254	1	(	(	PUNCT
cana-2873	254	2	i	i	NOUN
cana-2873	254	3	)	)	PUNCT
cana-2873	254	4	let	let	VERB
cana-2873	254	5	ψ̃	ψ̃	NOUN
cana-2873	254	6	be	be	AUX
cana-2873	254	7	a	a	DET
cana-2873	254	8	q	q	NOUN
cana-2873	254	9	-	-	PUNCT
cana-2873	254	10	nscs	nscs	NOUN
cana-2873	254	11	in	in	ADP
cana-2873	254	12	z2	z2	PROPN
cana-2873	254	13	.	.	PUNCT
cana-2873	255	1	then	then	ADV
cana-2873	255	2	g−1(ψ̃	g−1(ψ̃	NOUN
cana-2873	255	3	)	)	PUNCT
cana-2873	255	4	is	be	AUX
cana-2873	255	5	a	a	DET
cana-2873	255	6	q	q	NOUN
cana-2873	255	7	-	-	PUNCT
cana-2873	255	8	nsβos	nsβos	NOUN
cana-2873	255	9	in	in	ADP
cana-2873	255	10	z1	z1	PROPN
cana-2873	255	11	if	if	SCONJ
cana-2873	255	12	k	k	PROPN
cana-2873	255	13	is	be	AUX
cana-2873	255	14	q	q	NOUN
cana-2873	255	15	-	-	PUNCT
cana-2873	255	16	nsɕβcts	nsɕβct	NOUN
cana-2873	255	17	.	.	PUNCT
cana-2873	256	1	as	as	ADP
cana-2873	256	2	(	(	PUNCT
cana-2873	256	3	z1	z1	NOUN
cana-2873	256	4	,	,	PUNCT
cana-2873	256	5	γq	γq	ADP
cana-2873	256	6	)	)	PUNCT
cana-2873	256	7	is	be	AUX
cana-2873	256	8	a	a	DET
cana-2873	256	9	q	q	ADJ
cana-2873	256	10	-	-	PUNCT
cana-2873	256	11	nsβu	nsβu	NOUN
cana-2873	256	12	1/2	1/2	NUM
cana-2873	256	13	-space	-space	NOUN
cana-2873	256	14	,	,	PUNCT
cana-2873	256	15	g−1(ψ̃	g−1(ψ̃	NOUN
cana-2873	256	16	)	)	PUNCT
cana-2873	256	17	is	be	AUX
cana-2873	256	18	a	a	DET
cana-2873	256	19	q	q	NOUN
cana-2873	256	20	-	-	PUNCT
cana-2873	256	21	nsos	nsos	NOUN
cana-2873	256	22	in	in	ADP
cana-2873	256	23	z1	z1	PROPN
cana-2873	256	24	.	.	PUNCT
cana-2873	257	1	hence	hence	ADV
cana-2873	257	2	k	k	PROPN
cana-2873	257	3	is	be	AUX
cana-2873	257	4	also	also	ADV
cana-2873	257	5	q	q	ADJ
cana-2873	257	6	-	-	PUNCT
cana-2873	257	7	nsɕcts	nsɕct	NOUN
cana-2873	257	8	map	map	NOUN
cana-2873	257	9	.	.	PUNCT
cana-2873	258	1	the	the	DET
cana-2873	258	2	other	other	ADJ
cana-2873	258	3	cases	case	NOUN
cana-2873	258	4	are	be	AUX
cana-2873	258	5	similar	similar	ADJ
cana-2873	258	6	.	.	PUNCT
cana-2873	259	1	theorem	theorem	NOUN
cana-2873	259	2	4.8	4.8	NUM
cana-2873	259	3	.	.	PUNCT
cana-2873	260	1	let	let	VERB
cana-2873	260	2	k	k	NOUN
cana-2873	260	3	:	:	PUNCT
cana-2873	260	4	(	(	PUNCT
cana-2873	260	5	z1	z1	VERB
cana-2873	260	6	,	,	PUNCT
cana-2873	260	7	γq	γq	ADP
cana-2873	260	8	)	)	PUNCT
cana-2873	260	9	→	→	SYM
cana-2873	260	10	(	(	PUNCT
cana-2873	260	11	z2	z2	PROPN
cana-2873	260	12	,	,	PUNCT
cana-2873	260	13	σq	σq	NOUN
cana-2873	260	14	)	)	PUNCT
cana-2873	260	15	and	and	CCONJ
cana-2873	260	16	g	g	NOUN
cana-2873	260	17	:	:	PUNCT
cana-2873	260	18	(	(	PUNCT
cana-2873	260	19	z2	z2	NOUN
cana-2873	260	20	,	,	PUNCT
cana-2873	260	21	σq	σq	NOUN
cana-2873	260	22	)	)	PUNCT
cana-2873	260	23	→	→	SYM
cana-2873	260	24	(	(	PUNCT
cana-2873	260	25	z3	z3	PROPN
cana-2873	260	26	,	,	PUNCT
cana-2873	260	27	ρq	ρq	NUM
cana-2873	260	28	)	)	PUNCT
cana-2873	260	29	be	be	AUX
cana-2873	260	30	q	q	NOUN
cana-2873	260	31	-	-	PUNCT
cana-2873	260	32	nsɕβcts	nsɕβct	NOUN
cana-2873	260	33	mappings	mapping	NOUN
cana-2873	260	34	and	and	CCONJ
cana-2873	260	35	(	(	PUNCT
cana-2873	260	36	z2	z2	PROPN
cana-2873	260	37	,	,	PUNCT
cana-2873	260	38	σq	σq	NOUN
cana-2873	260	39	)	)	PUNCT
cana-2873	260	40	be	be	VERB
cana-2873	260	41	a	a	DET
cana-2873	260	42	q	q	ADJ
cana-2873	260	43	-	-	PUNCT
cana-2873	260	44	nsβu1/2	nsβu1/2	ADJ
cana-2873	260	45	-space	-space	NOUN
cana-2873	260	46	.	.	PUNCT
cana-2873	261	1	then	then	ADV
cana-2873	261	2	g	g	PROPN
cana-2873	261	3	◦	◦	PROPN
cana-2873	261	4	k	k	X
cana-2873	261	5	:	:	PUNCT
cana-2873	261	6	(	(	PUNCT
cana-2873	261	7	z1	z1	VERB
cana-2873	261	8	,	,	PUNCT
cana-2873	261	9	γq	γq	ADP
cana-2873	261	10	)	)	PUNCT
cana-2873	261	11	→	→	SYM
cana-2873	261	12	(	(	PUNCT
cana-2873	261	13	z3	z3	PROPN
cana-2873	261	14	,	,	PUNCT
cana-2873	261	15	ρq	ρq	NOUN
cana-2873	261	16	)	)	PUNCT
cana-2873	261	17	is	be	AUX
cana-2873	261	18	q	q	NOUN
cana-2873	261	19	-	-	PUNCT
cana-2873	261	20	nsβcts	nsβct	NOUN
cana-2873	261	21	.	.	PUNCT
cana-2873	262	1	proof	proof	NOUN
cana-2873	262	2	.	.	PUNCT
cana-2873	263	1	let	let	VERB
cana-2873	263	2	ã	ã	PROPN
cana-2873	263	3	be	be	AUX
cana-2873	263	4	a	a	DET
cana-2873	263	5	q	q	NOUN
cana-2873	263	6	-	-	PUNCT
cana-2873	263	7	nscs	nscs	NOUN
cana-2873	263	8	in	in	ADP
cana-2873	263	9	z3	z3	PROPN
cana-2873	263	10	.	.	PUNCT
cana-2873	264	1	then	then	ADV
cana-2873	264	2	g−1(ã	g−1(ã	X
cana-2873	264	3	)	)	PUNCT
cana-2873	264	4	is	be	AUX
cana-2873	264	5	a	a	DET
cana-2873	264	6	q	q	NOUN
cana-2873	264	7	-	-	PUNCT
cana-2873	264	8	nsβos	nsβos	NOUN
cana-2873	264	9	in	in	ADP
cana-2873	264	10	z2	z2	PROPN
cana-2873	264	11	,	,	PUNCT
cana-2873	264	12	since	since	SCONJ
cana-2873	264	13	g	g	PROPN
cana-2873	264	14	is	be	AUX
cana-2873	264	15	q	q	NOUN
cana-2873	264	16	-	-	PUNCT
cana-2873	264	17	nsɕβcts	nsɕβct	NOUN
cana-2873	264	18	.	.	PUNCT
cana-2873	265	1	as	as	SCONJ
cana-2873	265	2	(	(	PUNCT
cana-2873	265	3	z2	z2	NOUN
cana-2873	265	4	,	,	PUNCT
cana-2873	265	5	σq	σq	NOUN
cana-2873	265	6	)	)	PUNCT
cana-2873	265	7	is	be	AUX
cana-2873	265	8	a	a	DET
cana-2873	265	9	q	q	ADJ
cana-2873	265	10	-	-	PUNCT
cana-2873	265	11	nsβu1/2	nsβu1/2	ADJ
cana-2873	265	12	-space	-space	NOUN
cana-2873	265	13	,	,	PUNCT
cana-2873	265	14	g−1(ã	g−1(ã	X
cana-2873	265	15	)	)	PUNCT
cana-2873	265	16	is	be	AUX
cana-2873	265	17	a	a	DET
cana-2873	265	18	q	q	NOUN
cana-2873	265	19	-	-	PUNCT
cana-2873	265	20	nsos	nsos	NOUN
cana-2873	265	21	in	in	ADP
cana-2873	265	22	z2	z2	PROPN
cana-2873	265	23	.	.	PUNCT
cana-2873	266	1	then	then	ADV
cana-2873	266	2	,	,	PUNCT
cana-2873	266	3	k(g−1(ã	k(g−1(ã	PROPN
cana-2873	266	4	)	)	PUNCT
cana-2873	266	5	)	)	PUNCT
cana-2873	266	6	is	be	AUX
cana-2873	266	7	q	q	ADJ
cana-2873	266	8	-	-	NOUN
cana-2873	266	9	nsβcs	nsβcs	NOUN
cana-2873	266	10	in	in	ADP
cana-2873	266	11	z1	z1	PROPN
cana-2873	266	12	because	because	SCONJ
cana-2873	266	13	k	k	PROPN
cana-2873	266	14	is	be	AUX
cana-2873	266	15	q	q	NOUN
cana-2873	266	16	-	-	PUNCT
cana-2873	266	17	nsɕβcts	nsɕβct	NOUN
cana-2873	266	18	.	.	PUNCT
cana-2873	267	1	hence	hence	ADV
cana-2873	267	2	,	,	PUNCT
cana-2873	267	3	g	g	PROPN
cana-2873	267	4	◦	◦	NOUN
cana-2873	267	5	k	k	PROPN
cana-2873	267	6	is	be	AUX
cana-2873	267	7	a	a	DET
cana-2873	267	8	q	q	ADJ
cana-2873	267	9	-	-	PUNCT
cana-2873	267	10	nsβcts	nsβct	NOUN
cana-2873	267	11	map	map	NOUN
cana-2873	267	12	.	.	PUNCT
cana-2873	268	1	theorem	theorem	VERB
cana-2873	268	2	4.9	4.9	NUM
cana-2873	268	3	.	.	PUNCT
cana-2873	269	1	let	let	VERB
cana-2873	269	2	k	k	NOUN
cana-2873	269	3	:	:	PUNCT
cana-2873	269	4	(	(	PUNCT
cana-2873	269	5	z1	z1	VERB
cana-2873	269	6	,	,	PUNCT
cana-2873	269	7	γq	γq	ADP
cana-2873	269	8	)	)	PUNCT
cana-2873	269	9	→	→	SYM
cana-2873	269	10	(	(	PUNCT
cana-2873	269	11	z2	z2	PROPN
cana-2873	269	12	,	,	PUNCT
cana-2873	269	13	σq	σq	NOUN
cana-2873	269	14	)	)	PUNCT
cana-2873	269	15	be	be	VERB
cana-2873	269	16	a	a	DET
cana-2873	269	17	map	map	NOUN
cana-2873	269	18	from	from	ADP
cana-2873	269	19	a	a	DET
cana-2873	269	20	q	q	ADJ
cana-2873	269	21	-	-	PUNCT
cana-2873	269	22	nst	nst	NOUN
cana-2873	269	23	z1	z1	NOUN
cana-2873	269	24	into	into	ADP
cana-2873	269	25	a	a	DET
cana-2873	269	26	q	q	ADJ
cana-2873	269	27	-	-	PUNCT
cana-2873	269	28	nst	nst	NOUN
cana-2873	269	29	z2	z2	PROPN
cana-2873	269	30	.	.	PUNCT
cana-2873	270	1	if	if	SCONJ
cana-2873	270	2	z1	z1	PROPN
cana-2873	270	3	and	and	CCONJ
cana-2873	270	4	z2	z2	PROPN
cana-2873	270	5	are	be	AUX
cana-2873	270	6	q	q	ADJ
cana-2873	270	7	-	-	ADJ
cana-2873	270	8	nsβu	nsβu	NOUN
cana-2873	270	9	1/2	1/2	NUM
cana-2873	270	10	-spaces	-space	NOUN
cana-2873	270	11	,	,	PUNCT
cana-2873	270	12	then	then	ADV
cana-2873	270	13	the	the	DET
cana-2873	270	14	following	following	NOUN
cana-2873	270	15	are	be	AUX
cana-2873	270	16	equivalent	equivalent	ADJ
cana-2873	270	17	:	:	PUNCT
cana-2873	270	18	(	(	PUNCT
cana-2873	270	19	i	i	NOUN
cana-2873	270	20	)	)	PUNCT
cana-2873	271	1	k	k	PROPN
cana-2873	271	2	is	be	AUX
cana-2873	271	3	a	a	DET
cana-2873	271	4	q	q	ADJ
cana-2873	271	5	-	-	PUNCT
cana-2873	271	6	nsɕβirr	nsɕβirr	ADJ
cana-2873	271	7	map	map	NOUN
cana-2873	271	8	.	.	PUNCT
cana-2873	272	1	(	(	PUNCT
cana-2873	272	2	ii	ii	NOUN
cana-2873	272	3	)	)	PUNCT
cana-2873	272	4	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	272	5	)	)	PUNCT
cana-2873	272	6	is	be	AUX
cana-2873	272	7	a	a	DET
cana-2873	272	8	q	q	NOUN
cana-2873	272	9	-	-	PUNCT
cana-2873	272	10	nsβos	nsβos	NOUN
cana-2873	272	11	in	in	ADP
cana-2873	272	12	z1	z1	NOUN
cana-2873	272	13	for	for	ADP
cana-2873	272	14	every	every	DET
cana-2873	272	15	q	q	ADJ
cana-2873	272	16	-	-	PUNCT
cana-2873	272	17	nsβcs	nsβcs	NOUN
cana-2873	272	18	ψ̃	ψ̃	PROPN
cana-2873	272	19	in	in	ADP
cana-2873	272	20	z2	z2	PROPN
cana-2873	272	21	.	.	PUNCT
cana-2873	273	1	(	(	PUNCT
cana-2873	273	2	iii	iii	NOUN
cana-2873	273	3	)	)	PUNCT
cana-2873	273	4	q	q	NOUN
cana-2873	273	5	-	-	PUNCT
cana-2873	273	6	nscl(k−1(ψ̃	nscl(k−1(ψ̃	NOUN
cana-2873	273	7	)	)	PUNCT
cana-2873	273	8	)	)	PUNCT
cana-2873	274	1	⊇	⊇	PROPN
cana-2873	274	2	k−1(q	k−1(q	PROPN
cana-2873	274	3	-	-	PUNCT
cana-2873	274	4	nsint(ψ̃	nsint(ψ̃	NOUN
cana-2873	274	5	)	)	PUNCT
cana-2873	274	6	)	)	PUNCT
cana-2873	275	1	for	for	ADP
cana-2873	275	2	each	each	DET
cana-2873	275	3	q	q	ADJ
cana-2873	275	4	-	-	PUNCT
cana-2873	275	5	nss	nss	NOUN
cana-2873	275	6	ψ̃	ψ̃	PROPN
cana-2873	275	7	of	of	ADP
cana-2873	275	8	z2	z2	PROPN
cana-2873	275	9	.	.	PUNCT
cana-2873	276	1	proof	proof	NOUN
cana-2873	276	2	.	.	PUNCT
cana-2873	277	1	(	(	PUNCT
cana-2873	277	2	i	i	NOUN
cana-2873	277	3	)	)	PUNCT
cana-2873	277	4	→	→	SYM
cana-2873	277	5	(	(	PUNCT
cana-2873	277	6	ii	ii	NOUN
cana-2873	277	7	):	):	PUNCT
cana-2873	277	8	consider	consider	VERB
cana-2873	277	9	a	a	DET
cana-2873	277	10	q	q	ADJ
cana-2873	277	11	-	-	PUNCT
cana-2873	277	12	nsβcs	nsβcs	NOUN
cana-2873	277	13	ψ̃	ψ̃	PROPN
cana-2873	277	14	in	in	ADP
cana-2873	277	15	z2	z2	PROPN
cana-2873	277	16	.	.	PUNCT
cana-2873	278	1	so	so	ADV
cana-2873	278	2	ψ̃c	ψ̃c	PROPN
cana-2873	278	3	is	be	AUX
cana-2873	278	4	a	a	DET
cana-2873	278	5	q	q	NOUN
cana-2873	278	6	-	-	PUNCT
cana-2873	278	7	nsβos	nsβos	NOUN
cana-2873	278	8	in	in	ADP
cana-2873	278	9	z2	z2	PROPN
cana-2873	278	10	.	.	PUNCT
cana-2873	279	1	as	as	SCONJ
cana-2873	279	2	k	k	PROPN
cana-2873	279	3	is	be	AUX
cana-2873	279	4	q	q	ADJ
cana-2873	279	5	-	-	PUNCT
cana-2873	279	6	nsɕβirr	nsɕβirr	ADJ
cana-2873	279	7	,	,	PUNCT
cana-2873	279	8	k−1(ψ̃c)is	k−1(ψ̃c)is	VERB
cana-2873	279	9	a	a	DET
cana-2873	279	10	q	q	NOUN
cana-2873	279	11	-	-	PUNCT
cana-2873	279	12	nsβcs	nsβcs	NOUN
cana-2873	279	13	in	in	ADP
cana-2873	279	14	z1	z1	PROPN
cana-2873	279	15	.	.	PUNCT
cana-2873	280	1	we	we	PRON
cana-2873	280	2	know	know	VERB
cana-2873	280	3	that	that	SCONJ
cana-2873	280	4	,	,	PUNCT
cana-2873	280	5	k−1(ψ̃c	k−1(ψ̃c	NOUN
cana-2873	280	6	)	)	PUNCT
cana-2873	280	7	=	=	SYM
cana-2873	280	8	(	(	PUNCT
cana-2873	280	9	k−1(ψ̃))c	k−1(ψ̃))c	PROPN
cana-2873	280	10	.	.	PUNCT
cana-2873	281	1	thus	thus	ADV
cana-2873	281	2	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	281	3	)	)	PUNCT
cana-2873	281	4	is	be	AUX
cana-2873	281	5	a	a	DET
cana-2873	281	6	q	q	NOUN
cana-2873	281	7	-	-	PUNCT
cana-2873	281	8	nsβos	nsβos	NOUN
cana-2873	281	9	in	in	ADP
cana-2873	281	10	z1	z1	PROPN
cana-2873	281	11	.	.	PUNCT
cana-2873	282	1	(	(	PUNCT
cana-2873	282	2	ii	ii	NOUN
cana-2873	282	3	)	)	PUNCT
cana-2873	282	4	→	→	SYM
cana-2873	282	5	(	(	PUNCT
cana-2873	282	6	iii	iii	NOUN
cana-2873	282	7	):	):	PUNCT
cana-2873	282	8	consider	consider	VERB
cana-2873	282	9	a	a	DET
cana-2873	282	10	q	q	ADJ
cana-2873	282	11	-	-	PUNCT
cana-2873	282	12	nss	nss	NOUN
cana-2873	282	13	ψ̃	ψ̃	PROPN
cana-2873	282	14	in	in	ADP
cana-2873	282	15	z2	z2	PROPN
cana-2873	282	16	and	and	CCONJ
cana-2873	282	17	q	q	NOUN
cana-2873	282	18	-	-	ADJ
cana-2873	282	19	nsint(ψ̃)⊆	nsint(ψ̃)⊆	ADJ
cana-2873	282	20	(	(	PUNCT
cana-2873	282	21	ψ̃	ψ̃	PROPN
cana-2873	282	22	)	)	PUNCT
cana-2873	282	23	.	.	PUNCT
cana-2873	283	1	then	then	ADV
cana-2873	283	2	k−1(q	k−1(q	ADV
cana-2873	283	3	-	-	PUNCT
cana-2873	283	4	nsint(ψ̃))⊆	nsint(ψ̃))⊆	NOUN
cana-2873	283	5	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	283	6	)	)	PUNCT
cana-2873	283	7	.	.	PUNCT
cana-2873	284	1	as	as	ADP
cana-2873	284	2	q	q	NOUN
cana-2873	284	3	-	-	PUNCT
cana-2873	284	4	nsint(ψ̃	nsint(ψ̃	NOUN
cana-2873	284	5	)	)	PUNCT
cana-2873	284	6	is	be	AUX
cana-2873	284	7	a	a	DET
cana-2873	284	8	q	q	NOUN
cana-2873	284	9	-	-	PUNCT
cana-2873	284	10	nsos	nsos	NOUN
cana-2873	284	11	in	in	ADP
cana-2873	284	12	z2	z2	PROPN
cana-2873	284	13	,	,	PUNCT
cana-2873	284	14	q	q	NOUN
cana-2873	284	15	-	-	PUNCT
cana-2873	284	16	nsint(ψ̃	nsint(ψ̃	NOUN
cana-2873	284	17	)	)	PUNCT
cana-2873	284	18	is	be	AUX
cana-2873	284	19	a	a	DET
cana-2873	284	20	q	q	NOUN
cana-2873	284	21	-	-	PUNCT
cana-2873	284	22	nsβos	nsβos	NOUN
cana-2873	284	23	in	in	ADP
cana-2873	284	24	z2	z2	PROPN
cana-2873	284	25	.	.	PUNCT
cana-2873	285	1	therefore	therefore	ADV
cana-2873	285	2	(	(	PUNCT
cana-2873	285	3	qnsint(ψ̃))c	qnsint(ψ̃))c	PROPN
cana-2873	285	4	is	be	AUX
cana-2873	285	5	a	a	DET
cana-2873	285	6	q	q	NOUN
cana-2873	285	7	-	-	PUNCT
cana-2873	285	8	nsβcs	nsβcs	NOUN
cana-2873	285	9	in	in	ADP
cana-2873	285	10	z2	z2	PROPN
cana-2873	285	11	.	.	PUNCT
cana-2873	286	1	by	by	ADP
cana-2873	286	2	presumption	presumption	NOUN
cana-2873	286	3	,	,	PUNCT
cana-2873	286	4	k−1((q	k−1((q	NOUN
cana-2873	286	5	-	-	NOUN
cana-2873	286	6	nsint	nsint	NOUN
cana-2873	286	7	(	(	PUNCT
cana-2873	286	8	ψ̃))c	ψ̃))c	X
cana-2873	286	9	)	)	PUNCT
cana-2873	286	10	is	be	AUX
cana-2873	286	11	a	a	DET
cana-2873	286	12	q	q	NOUN
cana-2873	286	13	-	-	PUNCT
cana-2873	286	14	nsβos	nsβos	NOUN
cana-2873	286	15	in	in	ADP
cana-2873	286	16	z1	z1	PROPN
cana-2873	286	17	.	.	PUNCT
cana-2873	287	1	as	as	SCONJ
cana-2873	287	2	k−1((q	k−1((q	PROPN
cana-2873	287	3	-	-	PUNCT
cana-2873	287	4	nsint(ψ̃))c	nsint(ψ̃))c	NOUN
cana-2873	287	5	)	)	PUNCT
cana-2873	287	6	=	=	PUNCT
cana-2873	287	7	(	(	PUNCT
cana-2873	287	8	k−1(qnsint(ψ̃)))c	k−1(qnsint(ψ̃)))c	ADJ
cana-2873	287	9	,	,	PUNCT
cana-2873	287	10	k−1(q	k−1(q	ADJ
cana-2873	287	11	-	-	PUNCT
cana-2873	287	12	nsint(ψ̃	nsint(ψ̃	NOUN
cana-2873	287	13	)	)	PUNCT
cana-2873	287	14	)	)	PUNCT
cana-2873	287	15	is	be	AUX
cana-2873	287	16	a	a	DET
cana-2873	287	17	q	q	NOUN
cana-2873	287	18	-	-	PUNCT
cana-2873	287	19	nsβos	nsβos	NOUN
cana-2873	287	20	in	in	ADP
cana-2873	287	21	z1	z1	PROPN
cana-2873	287	22	.	.	PUNCT
cana-2873	288	1	as	as	SCONJ
cana-2873	288	2	z1	z1	PROPN
cana-2873	288	3	is	be	AUX
cana-2873	288	4	q	q	ADJ
cana-2873	288	5	-	-	PUNCT
cana-2873	288	6	nsβu1/2	nsβu1/2	ADJ
cana-2873	288	7	-space	-space	NOUN
cana-2873	288	8	,	,	PUNCT
cana-2873	288	9	k−1(q	k−1(q	PROPN
cana-2873	288	10	-	-	PUNCT
cana-2873	288	11	nsint(ψ̃	nsint(ψ̃	NOUN
cana-2873	288	12	)	)	PUNCT
cana-2873	288	13	)	)	PUNCT
cana-2873	288	14	is	be	AUX
cana-2873	288	15	a	a	DET
cana-2873	288	16	q	q	NOUN
cana-2873	288	17	-	-	PUNCT
cana-2873	288	18	nsos	nsos	NOUN
cana-2873	288	19	in	in	ADP
cana-2873	288	20	z1	z1	PROPN
cana-2873	288	21	.	.	PUNCT
cana-2873	289	1	thus	thus	ADV
cana-2873	289	2	,	,	PUNCT
cana-2873	289	3	q	q	PROPN
cana-2873	289	4	-	-	PUNCT
cana-2873	289	5	nscl(k−1(ψ̃))⊇	nscl(k−1(ψ̃))⊇	ADJ
cana-2873	289	6	q	q	ADJ
cana-2873	289	7	-	-	PUNCT
cana-2873	289	8	nscl(k−1(q	nscl(k−1(q	NUM
cana-2873	289	9	-	-	PUNCT
cana-2873	289	10	nsint(ψ̃	nsint(ψ̃	NOUN
cana-2873	289	11	)	)	PUNCT
cana-2873	289	12	)	)	PUNCT
cana-2873	289	13	)	)	PUNCT
cana-2873	290	1	=	=	SYM
cana-2873	290	2	k−1(q	k−1(q	ADJ
cana-2873	290	3	-	-	PUNCT
cana-2873	290	4	nsint(ψ̃	nsint(ψ̃	NOUN
cana-2873	290	5	)	)	PUNCT
cana-2873	290	6	)	)	PUNCT
cana-2873	290	7	.	.	PUNCT
cana-2873	291	1	that	that	PRON
cana-2873	291	2	is	be	AUX
cana-2873	291	3	q	q	ADJ
cana-2873	291	4	nscl(k−1(ψ̃	nscl(k−1(ψ̃	NOUN
cana-2873	291	5	)	)	PUNCT
cana-2873	291	6	)	)	PUNCT
cana-2873	291	7	⊇k−1(q	⊇k−1(q	ADJ
cana-2873	291	8	-	-	PUNCT
cana-2873	291	9	nsint(ψ̃	nsint(ψ̃	NOUN
cana-2873	291	10	)	)	PUNCT
cana-2873	291	11	)	)	PUNCT
cana-2873	291	12	.	.	PUNCT
cana-2873	292	1	(	(	PUNCT
cana-2873	292	2	iii	iii	NOUN
cana-2873	292	3	)	)	PUNCT
cana-2873	292	4	→	→	SYM
cana-2873	292	5	(	(	PUNCT
cana-2873	292	6	i	i	NOUN
cana-2873	292	7	):	):	PUNCT
cana-2873	292	8	consider	consider	VERB
cana-2873	292	9	a	a	DET
cana-2873	292	10	qin	qin	PROPN
cana-2873	292	11	z2	z2	PROPN
cana-2873	292	12	.	.	PUNCT
cana-2873	293	1	as	as	SCONJ
cana-2873	293	2	z2	z2	PROPN
cana-2873	293	3	is	be	AUX
cana-2873	293	4	q	q	ADJ
cana-2873	293	5	-	-	PUNCT
cana-2873	293	6	nsβu1/2	nsβu1/2	ADJ
cana-2873	293	7	space	space	NOUN
cana-2873	293	8	,	,	PUNCT
cana-2873	293	9	ψ̃	ψ̃	PROPN
cana-2873	293	10	is	be	AUX
cana-2873	293	11	a	a	DET
cana-2873	293	12	q	q	NOUN
cana-2873	293	13	-	-	PUNCT
cana-2873	293	14	nscs	nscs	ADJ
cana-2873	293	15	in	in	ADP
cana-2873	293	16	communications	communication	NOUN
cana-2873	293	17	on	on	ADP
cana-2873	293	18	applied	apply	VERB
cana-2873	293	19	nonlinear	nonlinear	ADJ
cana-2873	293	20	analysis	analysis	NOUN
cana-2873	293	21	issn	issn	NOUN
cana-2873	293	22	:	:	PUNCT
cana-2873	293	23	1074	1074	NUM
cana-2873	293	24	-	-	PUNCT
cana-2873	293	25	133x	133x	NUM
cana-2873	293	26	vol	vol	NOUN
cana-2873	293	27	32	32	NUM
cana-2873	293	28	no	no	NOUN
cana-2873	293	29	.	.	PUNCT
cana-2873	294	1	4s	4s	NUM
cana-2873	294	2	(	(	PUNCT
cana-2873	294	3	2025	2025	NUM
cana-2873	294	4	)	)	PUNCT
cana-2873	294	5	588	588	NUM
cana-2873	294	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	294	7	z2	z2	NOUN
cana-2873	294	8	and	and	CCONJ
cana-2873	294	9	q	q	ADJ
cana-2873	294	10	-nscl(ψ̃	-nscl(ψ̃	NOUN
cana-2873	294	11	)	)	PUNCT
cana-2873	294	12	=	=	SYM
cana-2873	294	13	(	(	PUNCT
cana-2873	294	14	ψ̃	ψ̃	PROPN
cana-2873	294	15	)	)	PUNCT
cana-2873	294	16	.	.	PUNCT
cana-2873	295	1	hence	hence	ADV
cana-2873	295	2	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	295	3	)	)	PUNCT
cana-2873	296	1	=	=	SYM
cana-2873	296	2	k−1(q	k−1(q	ADJ
cana-2873	296	3	-	-	PUNCT
cana-2873	296	4	nscl(ψ̃	nscl(ψ̃	NOUN
cana-2873	296	5	)	)	PUNCT
cana-2873	296	6	)	)	PUNCT
cana-2873	297	1	q	q	NOUN
cana-2873	297	2	-	-	PUNCT
cana-2873	297	3	nsint(k−1(ψ̃	nsint(k−1(ψ̃	NOUN
cana-2873	297	4	)	)	PUNCT
cana-2873	297	5	)	)	PUNCT
cana-2873	297	6	.	.	PUNCT
cana-2873	298	1	but	but	CCONJ
cana-2873	298	2	clearly	clearly	ADV
cana-2873	298	3	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	298	4	)	)	PUNCT
cana-2873	298	5	qnsint(k−1(ψ̃	qnsint(k−1(ψ̃	NOUN
cana-2873	298	6	)	)	PUNCT
cana-2873	298	7	)	)	PUNCT
cana-2873	298	8	.	.	PUNCT
cana-2873	299	1	therefore	therefore	ADV
cana-2873	299	2	q	q	NOUN
cana-2873	299	3	-	-	PUNCT
cana-2873	299	4	nsint(k−1(ψ̃	nsint(k−1(ψ̃	NOUN
cana-2873	299	5	)	)	PUNCT
cana-2873	299	6	)	)	PUNCT
cana-2873	300	1	=	=	SYM
cana-2873	300	2	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	300	3	)	)	PUNCT
cana-2873	300	4	.	.	PUNCT
cana-2873	301	1	so	so	ADV
cana-2873	301	2	,	,	PUNCT
cana-2873	301	3	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	301	4	)	)	PUNCT
cana-2873	301	5	is	be	AUX
cana-2873	301	6	a	a	DET
cana-2873	301	7	q	q	NOUN
cana-2873	301	8	-	-	PUNCT
cana-2873	301	9	nsos	nsos	NOUN
cana-2873	301	10	and	and	CCONJ
cana-2873	301	11	hence	hence	ADV
cana-2873	301	12	it	it	PRON
cana-2873	301	13	is	be	AUX
cana-2873	301	14	a	a	DET
cana-2873	301	15	qnsβos	qnsβos	NOUN
cana-2873	301	16	in	in	ADP
cana-2873	301	17	z1	z1	PROPN
cana-2873	301	18	.	.	PUNCT
cana-2873	302	1	thus	thus	ADV
cana-2873	302	2	k	k	PROPN
cana-2873	302	3	is	be	AUX
cana-2873	302	4	a	a	DET
cana-2873	302	5	q	q	ADJ
cana-2873	302	6	-	-	PUNCT
cana-2873	302	7	nsɕβirr	nsɕβirr	ADJ
cana-2873	302	8	map	map	NOUN
cana-2873	302	9	.	.	PUNCT
cana-2873	303	1	5	5	NUM
cana-2873	303	2	quadripartitioned	quadripartitione	VERB
cana-2873	303	3	neutrosophic	neutrosophic	PROPN
cana-2873	303	4	contra	contra	PROPN
cana-2873	303	5	β	β	PROPN
cana-2873	303	6	-	-	ADJ
cana-2873	303	7	open	open	ADJ
cana-2873	303	8	mapping	mapping	NOUN
cana-2873	303	9	the	the	DET
cana-2873	303	10	quadripartitioned	quadripartitione	VERB
cana-2873	303	11	neutrosophic	neutrosophic	PROPN
cana-2873	303	12	contra	contra	PROPN
cana-2873	303	13	β	β	PROPN
cana-2873	303	14	-	-	ADJ
cana-2873	303	15	open	open	ADJ
cana-2873	303	16	maps	map	NOUN
cana-2873	303	17	are	be	AUX
cana-2873	303	18	introduced	introduce	VERB
cana-2873	303	19	in	in	ADP
cana-2873	303	20	this	this	DET
cana-2873	303	21	section	section	NOUN
cana-2873	303	22	and	and	CCONJ
cana-2873	303	23	some	some	PRON
cana-2873	303	24	of	of	ADP
cana-2873	303	25	their	their	PRON
cana-2873	303	26	characteristics	characteristic	NOUN
cana-2873	303	27	are	be	AUX
cana-2873	303	28	analyzed	analyze	VERB
cana-2873	303	29	.	.	PUNCT
cana-2873	304	1	definition	definition	NOUN
cana-2873	304	2	5.1	5.1	NUM
cana-2873	304	3	.	.	PUNCT
cana-2873	305	1	a	a	DET
cana-2873	305	2	mapping	mapping	NOUN
cana-2873	305	3	k	k	NOUN
cana-2873	305	4	:	:	PUNCT
cana-2873	305	5	(	(	PUNCT
cana-2873	305	6	z1	z1	VERB
cana-2873	305	7	,	,	PUNCT
cana-2873	305	8	γq	γq	ADP
cana-2873	305	9	)	)	PUNCT
cana-2873	305	10	→	→	SYM
cana-2873	305	11	(	(	PUNCT
cana-2873	305	12	z2	z2	PROPN
cana-2873	305	13	,	,	PUNCT
cana-2873	305	14	σq	σq	NOUN
cana-2873	305	15	)	)	PUNCT
cana-2873	305	16	is	be	AUX
cana-2873	305	17	quadripartitioned	quadripartitione	VERB
cana-2873	305	18	neutrosophic	neutrosophic	PROPN
cana-2873	305	19	contra	contra	PROPN
cana-2873	305	20	(	(	PUNCT
cana-2873	305	21	resp	resp	PROPN
cana-2873	305	22	.	.	PUNCT
cana-2873	306	1	semi	semi	ADJ
cana-2873	306	2	,	,	PUNCT
cana-2873	306	3	pre	pre	ADJ
cana-2873	306	4	,	,	PUNCT
cana-2873	306	5	b	b	PROPN
cana-2873	306	6	&	&	CCONJ
cana-2873	306	7	β	β	NOUN
cana-2873	306	8	)	)	PUNCT
cana-2873	306	9	open	open	ADJ
cana-2873	306	10	(	(	PUNCT
cana-2873	306	11	in	in	ADP
cana-2873	306	12	short	short	ADJ
cana-2873	306	13	,	,	PUNCT
cana-2873	306	14	q	q	NOUN
cana-2873	306	15	-	-	PUNCT
cana-2873	306	16	nsɕo	nsɕo	PROPN
cana-2873	306	17	(	(	PUNCT
cana-2873	306	18	resp	resp	NOUN
cana-2873	306	19	.	.	PUNCT
cana-2873	307	1	q	q	X
cana-2873	307	2	-	-	PUNCT
cana-2873	307	3	nsɕso	nsɕso	NOUN
cana-2873	307	4	,	,	PUNCT
cana-2873	307	5	q	q	NOUN
cana-2873	307	6	-	-	PUNCT
cana-2873	307	7	nsɕpo	nsɕpo	ADJ
cana-2873	307	8	,	,	PUNCT
cana-2873	307	9	q	q	NOUN
cana-2873	307	10	-	-	PUNCT
cana-2873	307	11	nsɕbo	nsɕbo	NOUN
cana-2873	307	12	&	&	CCONJ
cana-2873	307	13	q	q	NOUN
cana-2873	307	14	-	-	PUNCT
cana-2873	307	15	nsɕβo	nsɕβo	NOUN
cana-2873	307	16	)	)	PUNCT
cana-2873	307	17	)	)	PUNCT
cana-2873	308	1	if	if	SCONJ
cana-2873	308	2	the	the	DET
cana-2873	308	3	image	image	NOUN
cana-2873	308	4	of	of	ADP
cana-2873	308	5	each	each	DET
cana-2873	308	6	q	q	NOUN
cana-2873	308	7	-	-	PUNCT
cana-2873	308	8	nso	nso	NOUN
cana-2873	308	9	set	set	NOUN
cana-2873	308	10	of	of	ADP
cana-2873	308	11	(	(	PUNCT
cana-2873	308	12	z1	z1	VERB
cana-2873	308	13	,	,	PUNCT
cana-2873	308	14	γq	γq	NOUN
cana-2873	308	15	)	)	PUNCT
cana-2873	308	16	is	be	AUX
cana-2873	308	17	q	q	ADJ
cana-2873	308	18	-	-	PUNCT
cana-2873	308	19	nsc	nsc	NOUN
cana-2873	308	20	(	(	PUNCT
cana-2873	308	21	resp	resp	NOUN
cana-2873	308	22	.	.	PUNCT
cana-2873	309	1	q	q	X
cana-2873	309	2	-	-	PUNCT
cana-2873	309	3	nssc	nssc	NOUN
cana-2873	309	4	,	,	PUNCT
cana-2873	309	5	q	q	NOUN
cana-2873	309	6	-	-	NOUN
cana-2873	309	7	nspc	nspc	NOUN
cana-2873	309	8	,	,	PUNCT
cana-2873	309	9	q	q	PROPN
cana-2873	309	10	-	-	PUNCT
cana-2873	309	11	nsbc	nsbc	PROPN
cana-2873	309	12	&	&	CCONJ
cana-2873	309	13	q	q	NOUN
cana-2873	309	14	-	-	PUNCT
cana-2873	309	15	nsβc	nsβc	ADV
cana-2873	309	16	)	)	PUNCT
cana-2873	309	17	set	set	VERB
cana-2873	309	18	in	in	ADP
cana-2873	309	19	(	(	PUNCT
cana-2873	309	20	z2	z2	PROPN
cana-2873	309	21	,	,	PUNCT
cana-2873	309	22	σq	σq	NOUN
cana-2873	309	23	)	)	PUNCT
cana-2873	309	24	.	.	PUNCT
cana-2873	310	1	proposition	proposition	NOUN
cana-2873	310	2	5.2	5.2	NUM
cana-2873	310	3	.	.	PUNCT
cana-2873	311	1	a	a	DET
cana-2873	311	2	map	map	NOUN
cana-2873	311	3	k	k	X
cana-2873	311	4	:	:	PUNCT
cana-2873	311	5	(	(	PUNCT
cana-2873	311	6	z1	z1	VERB
cana-2873	311	7	,	,	PUNCT
cana-2873	311	8	γq	γq	ADP
cana-2873	311	9	)	)	PUNCT
cana-2873	311	10	→	→	SYM
cana-2873	311	11	(	(	PUNCT
cana-2873	311	12	z2	z2	PROPN
cana-2873	311	13	,	,	PUNCT
cana-2873	311	14	σq	σq	NOUN
cana-2873	311	15	)	)	PUNCT
cana-2873	311	16	,	,	PUNCT
cana-2873	311	17	then	then	ADV
cana-2873	311	18	the	the	DET
cana-2873	311	19	statements	statement	NOUN
cana-2873	311	20	are	be	AUX
cana-2873	311	21	hold	hold	NOUN
cana-2873	311	22	but	but	CCONJ
cana-2873	311	23	the	the	DET
cana-2873	311	24	converse	converse	NOUN
cana-2873	311	25	does	do	AUX
cana-2873	311	26	not	not	PART
cana-2873	311	27	true	true	ADJ
cana-2873	311	28	.	.	PUNCT
cana-2873	312	1	every	every	DET
cana-2873	312	2	(	(	PUNCT
cana-2873	312	3	i	i	NOUN
cana-2873	312	4	)	)	PUNCT
cana-2873	312	5	q	q	X
cana-2873	312	6	-	-	PUNCT
cana-2873	312	7	nsɕo	nsɕo	PROPN
cana-2873	312	8	is	be	AUX
cana-2873	312	9	a	a	DET
cana-2873	312	10	q	q	NOUN
cana-2873	312	11	-	-	PUNCT
cana-2873	312	12	nsɕso	nsɕso	NOUN
cana-2873	312	13	.	.	PUNCT
cana-2873	313	1	(	(	PUNCT
cana-2873	313	2	ii	ii	NOUN
cana-2873	313	3	)	)	PUNCT
cana-2873	313	4	q	q	PROPN
cana-2873	313	5	-	-	PUNCT
cana-2873	313	6	nsɕo	nsɕo	PROPN
cana-2873	313	7	is	be	AUX
cana-2873	313	8	a	a	DET
cana-2873	313	9	q	q	ADJ
cana-2873	313	10	-	-	PUNCT
cana-2873	313	11	nsɕpo	nsɕpo	NOUN
cana-2873	313	12	.	.	PUNCT
cana-2873	314	1	(	(	PUNCT
cana-2873	314	2	iii	iii	NOUN
cana-2873	314	3	)	)	PUNCT
cana-2873	314	4	q	q	NOUN
cana-2873	314	5	-	-	PUNCT
cana-2873	314	6	nsɕso	nsɕso	NOUN
cana-2873	314	7	is	be	AUX
cana-2873	314	8	a	a	DET
cana-2873	314	9	q	q	NOUN
cana-2873	314	10	-	-	PUNCT
cana-2873	314	11	nsɕbo	nsɕbo	NOUN
cana-2873	314	12	.	.	PUNCT
cana-2873	315	1	(	(	PUNCT
cana-2873	315	2	iv	iv	X
cana-2873	315	3	)	)	PUNCT
cana-2873	315	4	q	q	ADJ
cana-2873	315	5	-	-	PUNCT
cana-2873	315	6	nsɕpo	nsɕpo	NOUN
cana-2873	315	7	is	be	AUX
cana-2873	315	8	a	a	DET
cana-2873	315	9	q	q	NOUN
cana-2873	315	10	-	-	PUNCT
cana-2873	315	11	nsɕbo	nsɕbo	NOUN
cana-2873	315	12	.	.	PUNCT
cana-2873	316	1	(	(	PUNCT
cana-2873	316	2	v	v	NOUN
cana-2873	316	3	)	)	PUNCT
cana-2873	316	4	q	q	NOUN
cana-2873	316	5	-	-	PUNCT
cana-2873	316	6	nsɕbo	nsɕbo	NOUN
cana-2873	316	7	is	be	AUX
cana-2873	316	8	a	a	DET
cana-2873	316	9	q	q	NOUN
cana-2873	316	10	-	-	PUNCT
cana-2873	316	11	nsɕβo	nsɕβo	NOUN
cana-2873	316	12	.	.	PUNCT
cana-2873	317	1	proof	proof	NOUN
cana-2873	317	2	.	.	PUNCT
cana-2873	318	1	(	(	PUNCT
cana-2873	318	2	i	i	NOUN
cana-2873	318	3	)	)	PUNCT
cana-2873	318	4	let	let	VERB
cana-2873	318	5	η	η	X
cana-2873	318	6	be	be	AUX
cana-2873	318	7	a	a	DET
cana-2873	318	8	q	q	NOUN
cana-2873	318	9	-	-	PUNCT
cana-2873	318	10	nso	nso	NOUN
cana-2873	318	11	set	set	VERB
cana-2873	318	12	in	in	ADP
cana-2873	318	13	z1	z1	PROPN
cana-2873	318	14	.	.	PUNCT
cana-2873	319	1	since	since	SCONJ
cana-2873	319	2	k	k	PROPN
cana-2873	319	3	is	be	AUX
cana-2873	319	4	q	q	NOUN
cana-2873	319	5	-	-	PUNCT
cana-2873	319	6	nsɕo	nsɕo	NOUN
cana-2873	319	7	,	,	PUNCT
cana-2873	319	8	k(η	k(η	PROPN
cana-2873	319	9	)	)	PUNCT
cana-2873	319	10	is	be	AUX
cana-2873	319	11	a	a	DET
cana-2873	319	12	q	q	ADJ
cana-2873	319	13	-	-	PUNCT
cana-2873	319	14	nsc	nsc	NOUN
cana-2873	319	15	set	set	NOUN
cana-2873	319	16	in	in	ADP
cana-2873	319	17	z2	z2	PROPN
cana-2873	319	18	.	.	PUNCT
cana-2873	320	1	since	since	SCONJ
cana-2873	320	2	every	every	DET
cana-2873	320	3	q	q	PROPN
cana-2873	320	4	-	-	PUNCT
cana-2873	320	5	nsc	nsc	NOUN
cana-2873	320	6	set	set	NOUN
cana-2873	320	7	is	be	AUX
cana-2873	320	8	a	a	DET
cana-2873	320	9	q	q	ADJ
cana-2873	320	10	-	-	PUNCT
cana-2873	320	11	nssc	nssc	NOUN
cana-2873	320	12	set	set	NOUN
cana-2873	320	13	,	,	PUNCT
cana-2873	320	14	k(η	k(η	PROPN
cana-2873	320	15	)	)	PUNCT
cana-2873	320	16	is	be	AUX
cana-2873	320	17	a	a	DET
cana-2873	320	18	q	q	NOUN
cana-2873	320	19	-	-	PUNCT
cana-2873	320	20	nssc	nssc	NOUN
cana-2873	320	21	set	set	NOUN
cana-2873	320	22	in	in	ADP
cana-2873	320	23	z2	z2	PROPN
cana-2873	320	24	.	.	PUNCT
cana-2873	321	1	hence	hence	ADV
cana-2873	321	2	k	k	PROPN
cana-2873	321	3	is	be	AUX
cana-2873	321	4	a	a	DET
cana-2873	321	5	q	q	NOUN
cana-2873	321	6	-	-	PUNCT
cana-2873	321	7	nsɕso	nsɕso	NOUN
cana-2873	321	8	.	.	PUNCT
cana-2873	322	1	(	(	PUNCT
cana-2873	322	2	ii	ii	NOUN
cana-2873	322	3	)	)	PUNCT
cana-2873	322	4	let	let	VERB
cana-2873	322	5	η	η	PROPN
cana-2873	322	6	be	be	AUX
cana-2873	322	7	a	a	DET
cana-2873	322	8	q	q	NOUN
cana-2873	322	9	-	-	PUNCT
cana-2873	322	10	nso	nso	NOUN
cana-2873	322	11	set	set	VERB
cana-2873	322	12	in	in	ADP
cana-2873	322	13	z1	z1	PROPN
cana-2873	322	14	.	.	PUNCT
cana-2873	323	1	since	since	SCONJ
cana-2873	323	2	k	k	PROPN
cana-2873	323	3	is	be	AUX
cana-2873	323	4	q	q	NOUN
cana-2873	323	5	-	-	PUNCT
cana-2873	323	6	nsɕo	nsɕo	NOUN
cana-2873	323	7	,	,	PUNCT
cana-2873	323	8	k(η	k(η	PROPN
cana-2873	323	9	)	)	PUNCT
cana-2873	323	10	is	be	AUX
cana-2873	323	11	a	a	DET
cana-2873	323	12	q	q	ADJ
cana-2873	323	13	-	-	PUNCT
cana-2873	323	14	nsc	nsc	NOUN
cana-2873	323	15	set	set	NOUN
cana-2873	323	16	in	in	ADP
cana-2873	323	17	z2	z2	PROPN
cana-2873	323	18	.	.	PUNCT
cana-2873	324	1	since	since	SCONJ
cana-2873	324	2	every	every	DET
cana-2873	324	3	q	q	PROPN
cana-2873	324	4	-	-	PUNCT
cana-2873	324	5	nsc	nsc	NOUN
cana-2873	324	6	set	set	NOUN
cana-2873	324	7	is	be	AUX
cana-2873	324	8	a	a	DET
cana-2873	324	9	q	q	ADJ
cana-2873	324	10	-	-	PUNCT
cana-2873	324	11	nspc	nspc	NOUN
cana-2873	324	12	set	set	NOUN
cana-2873	324	13	,	,	PUNCT
cana-2873	324	14	k(η	k(η	PROPN
cana-2873	324	15	)	)	PUNCT
cana-2873	324	16	is	be	AUX
cana-2873	324	17	a	a	DET
cana-2873	324	18	q	q	ADJ
cana-2873	324	19	-	-	PUNCT
cana-2873	324	20	nspc	nspc	NOUN
cana-2873	324	21	set	set	NOUN
cana-2873	324	22	in	in	ADP
cana-2873	324	23	z2	z2	PROPN
cana-2873	324	24	.	.	PUNCT
cana-2873	325	1	hence	hence	ADV
cana-2873	325	2	k	k	PROPN
cana-2873	325	3	is	be	AUX
cana-2873	325	4	a	a	DET
cana-2873	325	5	q	q	NOUN
cana-2873	325	6	-	-	PUNCT
cana-2873	325	7	nsɕpo	nsɕpo	NOUN
cana-2873	325	8	.	.	PUNCT
cana-2873	326	1	(	(	PUNCT
cana-2873	326	2	iii	iii	X
cana-2873	326	3	)	)	PUNCT
cana-2873	326	4	let	let	VERB
cana-2873	326	5	η	η	X
cana-2873	326	6	be	be	AUX
cana-2873	326	7	a	a	DET
cana-2873	326	8	q	q	NOUN
cana-2873	326	9	-	-	PUNCT
cana-2873	326	10	nso	nso	NOUN
cana-2873	326	11	set	set	VERB
cana-2873	326	12	in	in	ADP
cana-2873	326	13	z1	z1	PROPN
cana-2873	326	14	.	.	PUNCT
cana-2873	327	1	since	since	SCONJ
cana-2873	327	2	k	k	PROPN
cana-2873	327	3	is	be	AUX
cana-2873	327	4	q	q	NOUN
cana-2873	327	5	-	-	PUNCT
cana-2873	327	6	nsɕso	nsɕso	NOUN
cana-2873	327	7	,	,	PUNCT
cana-2873	327	8	k(η	k(η	PROPN
cana-2873	327	9	)	)	PUNCT
cana-2873	327	10	is	be	AUX
cana-2873	327	11	a	a	DET
cana-2873	327	12	q	q	ADJ
cana-2873	327	13	-	-	PUNCT
cana-2873	327	14	ns	ns	ADJ
cana-2873	327	15	sc	sc	PROPN
cana-2873	327	16	set	set	NOUN
cana-2873	327	17	in	in	ADP
cana-2873	327	18	z2	z2	PROPN
cana-2873	327	19	.	.	PUNCT
cana-2873	328	1	since	since	SCONJ
cana-2873	328	2	every	every	DET
cana-2873	328	3	q	q	ADJ
cana-2873	328	4	-	-	PUNCT
cana-2873	328	5	ns	ns	ADJ
cana-2873	328	6	sc	sc	PROPN
cana-2873	328	7	set	set	NOUN
cana-2873	328	8	is	be	AUX
cana-2873	328	9	a	a	DET
cana-2873	328	10	q	q	ADJ
cana-2873	328	11	-	-	PUNCT
cana-2873	328	12	nsbc	nsbc	ADJ
cana-2873	328	13	set	set	NOUN
cana-2873	328	14	,	,	PUNCT
cana-2873	328	15	k(η	k(η	PROPN
cana-2873	328	16	)	)	PUNCT
cana-2873	328	17	is	be	AUX
cana-2873	328	18	a	a	DET
cana-2873	328	19	q	q	ADJ
cana-2873	328	20	-	-	PUNCT
cana-2873	328	21	nsbc	nsbc	ADJ
cana-2873	328	22	set	set	NOUN
cana-2873	328	23	in	in	ADP
cana-2873	328	24	z2	z2	PROPN
cana-2873	328	25	.	.	PUNCT
cana-2873	329	1	hence	hence	ADV
cana-2873	329	2	k	k	PROPN
cana-2873	329	3	is	be	AUX
cana-2873	329	4	a	a	DET
cana-2873	329	5	q	q	NOUN
cana-2873	329	6	-	-	PUNCT
cana-2873	329	7	nsɕbo	nsɕbo	NOUN
cana-2873	329	8	.	.	PUNCT
cana-2873	330	1	(	(	PUNCT
cana-2873	330	2	iv	iv	X
cana-2873	330	3	)	)	PUNCT
cana-2873	330	4	let	let	VERB
cana-2873	330	5	η	η	X
cana-2873	330	6	be	be	AUX
cana-2873	330	7	a	a	DET
cana-2873	330	8	q	q	NOUN
cana-2873	330	9	-	-	PUNCT
cana-2873	330	10	nso	nso	NOUN
cana-2873	330	11	set	set	VERB
cana-2873	330	12	in	in	ADP
cana-2873	330	13	z1	z1	PROPN
cana-2873	330	14	.	.	PUNCT
cana-2873	331	1	since	since	SCONJ
cana-2873	331	2	k	k	PROPN
cana-2873	331	3	is	be	AUX
cana-2873	331	4	q	q	NOUN
cana-2873	331	5	-	-	PUNCT
cana-2873	331	6	nsɕ	nsɕ	NOUN
cana-2873	331	7	ρo	ρo	NOUN
cana-2873	331	8	,	,	PUNCT
cana-2873	331	9	k(η	k(η	PROPN
cana-2873	331	10	)	)	PUNCT
cana-2873	331	11	is	be	AUX
cana-2873	331	12	a	a	DET
cana-2873	331	13	q	q	NOUN
cana-2873	331	14	-	-	PUNCT
cana-2873	331	15	ns	ns	ADJ
cana-2873	331	16	ρc	ρc	AUX
cana-2873	331	17	set	set	VERB
cana-2873	331	18	in	in	ADP
cana-2873	331	19	z2	z2	PROPN
cana-2873	331	20	.	.	PUNCT
cana-2873	332	1	since	since	SCONJ
cana-2873	332	2	every	every	DET
cana-2873	332	3	q	q	PROPN
cana-2873	332	4	-	-	PUNCT
cana-2873	332	5	ns	ns	ADJ
cana-2873	332	6	bc	bc	PROPN
cana-2873	332	7	set	set	NOUN
cana-2873	332	8	is	be	AUX
cana-2873	332	9	a	a	DET
cana-2873	332	10	q	q	ADJ
cana-2873	332	11	-	-	PUNCT
cana-2873	332	12	nsbc	nsbc	ADJ
cana-2873	332	13	set	set	NOUN
cana-2873	332	14	,	,	PUNCT
cana-2873	332	15	k(η	k(η	PROPN
cana-2873	332	16	)	)	PUNCT
cana-2873	332	17	is	be	AUX
cana-2873	332	18	a	a	DET
cana-2873	332	19	q	q	ADJ
cana-2873	332	20	-	-	PUNCT
cana-2873	332	21	nsbc	nsbc	ADJ
cana-2873	332	22	set	set	NOUN
cana-2873	332	23	in	in	ADP
cana-2873	332	24	z2	z2	PROPN
cana-2873	332	25	.	.	PUNCT
cana-2873	333	1	hence	hence	ADV
cana-2873	333	2	k	k	PROPN
cana-2873	333	3	is	be	AUX
cana-2873	333	4	a	a	DET
cana-2873	333	5	q	q	NOUN
cana-2873	333	6	-	-	PUNCT
cana-2873	333	7	nsɕbo	nsɕbo	NOUN
cana-2873	333	8	.	.	PUNCT
cana-2873	334	1	(	(	PUNCT
cana-2873	334	2	v	v	NOUN
cana-2873	334	3	)	)	PUNCT
cana-2873	334	4	let	let	VERB
cana-2873	334	5	η	η	X
cana-2873	334	6	be	be	AUX
cana-2873	334	7	a	a	DET
cana-2873	334	8	q	q	NOUN
cana-2873	334	9	-	-	PUNCT
cana-2873	334	10	nso	nso	NOUN
cana-2873	334	11	set	set	VERB
cana-2873	334	12	in	in	ADP
cana-2873	334	13	z1	z1	PROPN
cana-2873	334	14	.	.	PUNCT
cana-2873	335	1	since	since	SCONJ
cana-2873	335	2	k	k	PROPN
cana-2873	335	3	is	be	AUX
cana-2873	335	4	q	q	NOUN
cana-2873	335	5	-	-	PUNCT
cana-2873	335	6	nsɕbo	nsɕbo	NOUN
cana-2873	335	7	,	,	PUNCT
cana-2873	335	8	k(η	k(η	PROPN
cana-2873	335	9	)	)	PUNCT
cana-2873	335	10	is	be	AUX
cana-2873	335	11	a	a	DET
cana-2873	335	12	q	q	ADJ
cana-2873	335	13	-	-	PUNCT
cana-2873	335	14	nsbc	nsbc	ADJ
cana-2873	335	15	set	set	NOUN
cana-2873	335	16	in	in	ADP
cana-2873	335	17	z2	z2	PROPN
cana-2873	335	18	.	.	PUNCT
cana-2873	336	1	since	since	SCONJ
cana-2873	336	2	every	every	DET
cana-2873	336	3	qnsbc	qnsbc	NOUN
cana-2873	336	4	set	set	NOUN
cana-2873	336	5	is	be	AUX
cana-2873	336	6	a	a	DET
cana-2873	336	7	q	q	ADJ
cana-2873	336	8	-	-	PUNCT
cana-2873	336	9	nsβc	nsβc	NOUN
cana-2873	336	10	set	set	NOUN
cana-2873	336	11	,	,	PUNCT
cana-2873	336	12	k(η	k(η	PROPN
cana-2873	336	13	)	)	PUNCT
cana-2873	336	14	is	be	AUX
cana-2873	336	15	a	a	DET
cana-2873	336	16	q	q	ADJ
cana-2873	336	17	-	-	PUNCT
cana-2873	336	18	nsβc	nsβc	NOUN
cana-2873	336	19	set	set	NOUN
cana-2873	336	20	in	in	ADP
cana-2873	336	21	z2	z2	PROPN
cana-2873	336	22	.	.	PUNCT
cana-2873	337	1	hence	hence	ADV
cana-2873	337	2	k	k	PROPN
cana-2873	337	3	is	be	AUX
cana-2873	337	4	a	a	DET
cana-2873	337	5	q	q	NOUN
cana-2873	337	6	-	-	PUNCT
cana-2873	337	7	nsɕβo	nsɕβo	NOUN
cana-2873	337	8	.	.	PUNCT
cana-2873	337	9	example	example	NOUN
cana-2873	338	1	5.3	5.3	NUM
cana-2873	338	2	.	.	PUNCT
cana-2873	339	1	let	let	VERB
cana-2873	339	2	v	v	VERB
cana-2873	339	3	=	=	SYM
cana-2873	339	4	{	{	PUNCT
cana-2873	339	5	va	va	NOUN
cana-2873	339	6	,	,	PUNCT
cana-2873	339	7	vb	vb	NOUN
cana-2873	339	8	,	,	PUNCT
cana-2873	339	9	vc	vc	NOUN
cana-2873	339	10	}	}	PUNCT
cana-2873	339	11	=	=	SYM
cana-2873	339	12	w	w	NOUN
cana-2873	339	13	and	and	CCONJ
cana-2873	339	14	define	define	VERB
cana-2873	339	15	q	q	ADJ
cana-2873	339	16	-	-	PUNCT
cana-2873	339	17	nss	nss	NOUN
cana-2873	339	18	’s	’s	PART
cana-2873	339	19	v1	v1	NOUN
cana-2873	339	20	in	in	ADP
cana-2873	339	21	v	v	NOUN
cana-2873	339	22	and	and	CCONJ
cana-2873	339	23	w1	w1	NOUN
cana-2873	339	24	,	,	PUNCT
cana-2873	339	25	w2	w2	PROPN
cana-2873	339	26	&	&	CCONJ
cana-2873	339	27	w3	w3	PROPN
cana-2873	339	28	in	in	ADP
cana-2873	339	29	w	w	PROPN
cana-2873	339	30	are	be	AUX
cana-2873	339	31	v1	v1	NOUN
cana-2873	339	32	=	=	SYM
cana-2873	339	33	{	{	PUNCT
cana-2873	339	34	(	(	PUNCT
cana-2873	339	35	va	va	NOUN
cana-2873	339	36	,	,	PUNCT
cana-2873	339	37	0.2	0.2	NUM
cana-2873	339	38	,	,	PUNCT
cana-2873	339	39	0.5	0.5	NUM
cana-2873	339	40	,	,	PUNCT
cana-2873	339	41	0.5	0.5	NUM
cana-2873	339	42	,	,	PUNCT
cana-2873	339	43	0.8	0.8	NUM
cana-2873	339	44	)	)	PUNCT
cana-2873	339	45	,	,	PUNCT
cana-2873	339	46	(	(	PUNCT
cana-2873	339	47	vb	vb	NOUN
cana-2873	339	48	,	,	PUNCT
cana-2873	339	49	0.4	0.4	NUM
cana-2873	339	50	,	,	PUNCT
cana-2873	339	51	0.5	0.5	NUM
cana-2873	339	52	,	,	PUNCT
cana-2873	339	53	0.5	0.5	NUM
cana-2873	339	54	,	,	PUNCT
cana-2873	339	55	0.6	0.6	NUM
cana-2873	339	56	)	)	PUNCT
cana-2873	339	57	,	,	PUNCT
cana-2873	339	58	(	(	PUNCT
cana-2873	339	59	vc	vc	INTJ
cana-2873	339	60	,	,	PUNCT
cana-2873	339	61	0.4	0.4	NUM
cana-2873	339	62	,	,	PUNCT
cana-2873	339	63	0.5	0.5	NUM
cana-2873	339	64	,	,	PUNCT
cana-2873	339	65	0.5	0.5	NUM
cana-2873	339	66	,	,	PUNCT
cana-2873	339	67	0.6	0.6	NUM
cana-2873	339	68	)	)	PUNCT
cana-2873	339	69	}	}	PUNCT
cana-2873	339	70	,	,	PUNCT
cana-2873	339	71	w1	w1	NOUN
cana-2873	339	72	=	=	SYM
cana-2873	339	73	{	{	PUNCT
cana-2873	339	74	(	(	PUNCT
cana-2873	339	75	va	va	NOUN
cana-2873	339	76	,	,	PUNCT
cana-2873	339	77	0.2	0.2	NUM
cana-2873	339	78	,	,	PUNCT
cana-2873	339	79	0.5	0.5	NUM
cana-2873	339	80	,	,	PUNCT
cana-2873	339	81	0.5	0.5	NUM
cana-2873	339	82	,	,	PUNCT
cana-2873	339	83	0.8	0.8	NUM
cana-2873	339	84	)	)	PUNCT
cana-2873	339	85	,	,	PUNCT
cana-2873	339	86	(	(	PUNCT
cana-2873	339	87	vb	vb	NOUN
cana-2873	339	88	,	,	PUNCT
cana-2873	339	89	0.3	0.3	NUM
cana-2873	339	90	,	,	PUNCT
cana-2873	339	91	0.5	0.5	NUM
cana-2873	339	92	,	,	PUNCT
cana-2873	339	93	0.5	0.5	NUM
cana-2873	339	94	,	,	PUNCT
cana-2873	339	95	0.7	0.7	NUM
cana-2873	339	96	)	)	PUNCT
cana-2873	339	97	,	,	PUNCT
cana-2873	339	98	(	(	PUNCT
cana-2873	339	99	vc	vc	INTJ
cana-2873	339	100	,	,	PUNCT
cana-2873	339	101	0.4	0.4	NUM
cana-2873	339	102	,	,	PUNCT
cana-2873	339	103	0.5	0.5	NUM
cana-2873	339	104	,	,	PUNCT
cana-2873	339	105	0.5	0.5	NUM
cana-2873	339	106	,	,	PUNCT
cana-2873	339	107	0.6	0.6	NUM
cana-2873	339	108	)	)	PUNCT
cana-2873	339	109	}	}	PUNCT
cana-2873	339	110	,	,	PUNCT
cana-2873	339	111	w2	w2	NOUN
cana-2873	339	112	=	=	SYM
cana-2873	339	113	{	{	PUNCT
cana-2873	339	114	(	(	PUNCT
cana-2873	339	115	va	va	NOUN
cana-2873	339	116	,	,	PUNCT
cana-2873	339	117	0.1	0.1	NUM
cana-2873	339	118	,	,	PUNCT
cana-2873	339	119	0.5	0.5	NUM
cana-2873	339	120	,	,	PUNCT
cana-2873	339	121	0.5	0.5	NUM
cana-2873	339	122	,	,	PUNCT
cana-2873	339	123	0.9	0.9	NUM
cana-2873	339	124	)	)	PUNCT
cana-2873	339	125	,	,	PUNCT
cana-2873	339	126	(	(	PUNCT
cana-2873	339	127	vb	vb	NOUN
cana-2873	339	128	,	,	PUNCT
cana-2873	339	129	0.1	0.1	NUM
cana-2873	339	130	,	,	PUNCT
cana-2873	339	131	0.5	0.5	NUM
cana-2873	339	132	,	,	PUNCT
cana-2873	339	133	0.5	0.5	NUM
cana-2873	339	134	,	,	PUNCT
cana-2873	339	135	0.9	0.9	NUM
cana-2873	339	136	)	)	PUNCT
cana-2873	339	137	,	,	PUNCT
cana-2873	339	138	(	(	PUNCT
cana-2873	339	139	vc	vc	INTJ
cana-2873	339	140	,	,	PUNCT
cana-2873	339	141	0.4	0.4	NUM
cana-2873	339	142	,	,	PUNCT
cana-2873	339	143	0.5	0.5	NUM
cana-2873	339	144	,	,	PUNCT
cana-2873	339	145	0.5	0.5	NUM
cana-2873	339	146	,	,	PUNCT
cana-2873	339	147	0.6	0.6	NUM
cana-2873	339	148	)	)	PUNCT
cana-2873	339	149	}	}	PUNCT
cana-2873	339	150	,	,	PUNCT
cana-2873	339	151	w3	w3	PROPN
cana-2873	339	152	=	=	SYM
cana-2873	339	153	{	{	PUNCT
cana-2873	339	154	(	(	PUNCT
cana-2873	339	155	va	va	NOUN
cana-2873	339	156	,	,	PUNCT
cana-2873	339	157	0.2	0.2	NUM
cana-2873	339	158	,	,	PUNCT
cana-2873	339	159	0.5	0.5	NUM
cana-2873	339	160	,	,	PUNCT
cana-2873	339	161	0.5	0.5	NUM
cana-2873	339	162	,	,	PUNCT
cana-2873	339	163	0.8	0.8	NUM
cana-2873	339	164	)	)	PUNCT
cana-2873	339	165	,	,	PUNCT
cana-2873	339	166	(	(	PUNCT
cana-2873	339	167	vb	vb	NOUN
cana-2873	339	168	,	,	PUNCT
cana-2873	339	169	0.4	0.4	NUM
cana-2873	339	170	,	,	PUNCT
cana-2873	339	171	0.5	0.5	NUM
cana-2873	339	172	,	,	PUNCT
cana-2873	339	173	0.5	0.5	NUM
cana-2873	339	174	,	,	PUNCT
cana-2873	339	175	0.6	0.6	NUM
cana-2873	339	176	)	)	PUNCT
cana-2873	339	177	,	,	PUNCT
cana-2873	339	178	(	(	PUNCT
cana-2873	339	179	vc	vc	INTJ
cana-2873	339	180	,	,	PUNCT
cana-2873	339	181	0.4	0.4	NUM
cana-2873	339	182	,	,	PUNCT
cana-2873	339	183	0.5	0.5	NUM
cana-2873	339	184	,	,	PUNCT
cana-2873	339	185	0.5	0.5	NUM
cana-2873	339	186	,	,	PUNCT
cana-2873	339	187	0.6	0.6	NUM
cana-2873	339	188	)	)	PUNCT
cana-2873	339	189	}	}	PUNCT
cana-2873	339	190	.	.	PUNCT
cana-2873	340	1	communications	communication	NOUN
cana-2873	340	2	on	on	ADP
cana-2873	340	3	applied	apply	VERB
cana-2873	340	4	nonlinear	nonlinear	ADJ
cana-2873	340	5	analysis	analysis	NOUN
cana-2873	340	6	issn	issn	NOUN
cana-2873	340	7	:	:	PUNCT
cana-2873	340	8	1074	1074	NUM
cana-2873	340	9	-	-	PUNCT
cana-2873	340	10	133x	133x	NUM
cana-2873	340	11	vol	vol	NOUN
cana-2873	340	12	32	32	NUM
cana-2873	340	13	no	no	NOUN
cana-2873	340	14	.	.	PUNCT
cana-2873	341	1	4s	4s	NUM
cana-2873	341	2	(	(	PUNCT
cana-2873	341	3	2025	2025	NUM
cana-2873	341	4	)	)	PUNCT
cana-2873	341	5	589	589	NUM
cana-2873	341	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	341	7	3	3	NUM
cana-2873	341	8	then	then	ADV
cana-2873	341	9	we	we	PRON
cana-2873	341	10	have	have	VERB
cana-2873	341	11	γq	γq	ADP
cana-2873	341	12	=	=	SYM
cana-2873	341	13	{	{	PUNCT
cana-2873	341	14	0qns	0qns	PROPN
cana-2873	341	15	,	,	PUNCT
cana-2873	341	16	v1	v1	PROPN
cana-2873	341	17	,	,	PUNCT
cana-2873	341	18	1qns	1qns	NUM
cana-2873	341	19	}	}	PUNCT
cana-2873	341	20	and	and	CCONJ
cana-2873	341	21	σq	σq	NOUN
cana-2873	341	22	=	=	SYM
cana-2873	341	23	{	{	PUNCT
cana-2873	341	24	0qns	0qns	PROPN
cana-2873	341	25	,	,	PUNCT
cana-2873	341	26	w1	w1	NOUN
cana-2873	341	27	,	,	PUNCT
cana-2873	341	28	w2	w2	NOUN
cana-2873	341	29	,	,	PUNCT
cana-2873	341	30	1qns	1qns	NUM
cana-2873	341	31	}	}	PUNCT
cana-2873	341	32	.	.	PUNCT
cana-2873	342	1	let	let	VERB
cana-2873	342	2	k	k	NOUN
cana-2873	342	3	:	:	PUNCT
cana-2873	342	4	(	(	PUNCT
cana-2873	342	5	z1	z1	VERB
cana-2873	342	6	,	,	PUNCT
cana-2873	342	7	γq	γq	ADP
cana-2873	342	8	)	)	PUNCT
cana-2873	342	9	→	→	SYM
cana-2873	342	10	(	(	PUNCT
cana-2873	342	11	z2	z2	PROPN
cana-2873	342	12	,	,	PUNCT
cana-2873	342	13	σq	σq	NOUN
cana-2873	342	14	)	)	PUNCT
cana-2873	342	15	be	be	VERB
cana-2873	342	16	an	an	DET
cana-2873	342	17	identity	identity	NOUN
cana-2873	342	18	mapping	mapping	NOUN
cana-2873	342	19	,	,	PUNCT
cana-2873	342	20	then	then	ADV
cana-2873	342	21	k	k	PROPN
cana-2873	342	22	is	be	AUX
cana-2873	342	23	q	q	ADJ
cana-2873	342	24	-	-	PUNCT
cana-2873	342	25	nscbo	nscbo	NOUN
cana-2873	342	26	but	but	CCONJ
cana-2873	342	27	not	not	PART
cana-2873	342	28	q	q	NOUN
cana-2873	342	29	-	-	PUNCT
cana-2873	342	30	nscpo	nscpo	ADJ
cana-2873	342	31	,	,	PUNCT
cana-2873	342	32	the	the	DET
cana-2873	342	33	set	set	NOUN
cana-2873	342	34	k(v1	k(v1	NOUN
cana-2873	342	35	)	)	PUNCT
cana-2873	343	1	=	=	SYM
cana-2873	343	2	wc	wc	PROPN
cana-2873	343	3	is	be	AUX
cana-2873	343	4	a	a	DET
cana-2873	343	5	q	q	ADJ
cana-2873	343	6	-	-	PUNCT
cana-2873	343	7	nsbc	nsbc	ADJ
cana-2873	343	8	set	set	NOUN
cana-2873	343	9	but	but	CCONJ
cana-2873	343	10	not	not	PART
cana-2873	343	11	q	q	ADJ
cana-2873	343	12	-	-	PUNCT
cana-2873	343	13	nspc	nspc	NOUN
cana-2873	343	14	set	set	NOUN
cana-2873	343	15	.	.	PUNCT
cana-2873	343	16	example	example	NOUN
cana-2873	344	1	5.4	5.4	NUM
cana-2873	344	2	.	.	PUNCT
cana-2873	345	1	let	let	VERB
cana-2873	345	2	v	v	VERB
cana-2873	345	3	=	=	SYM
cana-2873	345	4	{	{	PUNCT
cana-2873	345	5	va	va	NOUN
cana-2873	345	6	,	,	PUNCT
cana-2873	345	7	vb	vb	NOUN
cana-2873	345	8	,	,	PUNCT
cana-2873	345	9	vc	vc	NOUN
cana-2873	345	10	}	}	PUNCT
cana-2873	345	11	=	=	SYM
cana-2873	345	12	w	w	NOUN
cana-2873	345	13	and	and	CCONJ
cana-2873	345	14	define	define	VERB
cana-2873	345	15	q	q	ADJ
cana-2873	345	16	-	-	PUNCT
cana-2873	345	17	nss	nss	NOUN
cana-2873	345	18	’s	’s	PART
cana-2873	345	19	v1	v1	NOUN
cana-2873	345	20	in	in	ADP
cana-2873	345	21	v	v	NOUN
cana-2873	345	22	and	and	CCONJ
cana-2873	345	23	w1	w1	NOUN
cana-2873	345	24	,	,	PUNCT
cana-2873	345	25	w2	w2	NOUN
cana-2873	345	26	,	,	PUNCT
cana-2873	345	27	w3	w3	PROPN
cana-2873	345	28	&	&	CCONJ
cana-2873	345	29	w4	w4	PROPN
cana-2873	345	30	in	in	ADP
cana-2873	345	31	w	w	PROPN
cana-2873	345	32	are	be	AUX
cana-2873	345	33	v1	v1	NOUN
cana-2873	345	34	=	=	SYM
cana-2873	345	35	{	{	PUNCT
cana-2873	345	36	(	(	PUNCT
cana-2873	345	37	va	va	NOUN
cana-2873	345	38	,	,	PUNCT
cana-2873	345	39	0.3	0.3	NUM
cana-2873	345	40	,	,	PUNCT
cana-2873	345	41	0.5	0.5	NUM
cana-2873	345	42	,	,	PUNCT
cana-2873	345	43	0.5	0.5	NUM
cana-2873	345	44	,	,	PUNCT
cana-2873	345	45	0.7	0.7	NUM
cana-2873	345	46	)	)	PUNCT
cana-2873	345	47	,	,	PUNCT
cana-2873	345	48	(	(	PUNCT
cana-2873	345	49	vb	vb	NOUN
cana-2873	345	50	,	,	PUNCT
cana-2873	345	51	0.5	0.5	NUM
cana-2873	345	52	,	,	PUNCT
cana-2873	345	53	0.5	0.5	NUM
cana-2873	345	54	,	,	PUNCT
cana-2873	345	55	0.5	0.5	NUM
cana-2873	345	56	,	,	PUNCT
cana-2873	345	57	0.5	0.5	NUM
cana-2873	345	58	)	)	PUNCT
cana-2873	345	59	,	,	PUNCT
cana-2873	345	60	(	(	PUNCT
cana-2873	345	61	vc	vc	INTJ
cana-2873	345	62	,	,	PUNCT
cana-2873	345	63	0.4	0.4	NUM
cana-2873	345	64	,	,	PUNCT
cana-2873	345	65	0.5	0.5	NUM
cana-2873	345	66	,	,	PUNCT
cana-2873	345	67	0.5	0.5	NUM
cana-2873	345	68	,	,	PUNCT
cana-2873	345	69	0.6	0.6	NUM
cana-2873	345	70	)	)	PUNCT
cana-2873	345	71	}	}	PUNCT
cana-2873	345	72	,	,	PUNCT
cana-2873	345	73	w1	w1	NOUN
cana-2873	345	74	=	=	SYM
cana-2873	345	75	{	{	PUNCT
cana-2873	345	76	(	(	PUNCT
cana-2873	345	77	va	va	NOUN
cana-2873	345	78	,	,	PUNCT
cana-2873	345	79	0.3	0.3	NUM
cana-2873	345	80	,	,	PUNCT
cana-2873	345	81	0.5	0.5	NUM
cana-2873	345	82	,	,	PUNCT
cana-2873	345	83	0.5	0.5	NUM
cana-2873	345	84	,	,	PUNCT
cana-2873	345	85	0.7	0.7	NUM
cana-2873	345	86	)	)	PUNCT
cana-2873	345	87	,	,	PUNCT
cana-2873	345	88	(	(	PUNCT
cana-2873	345	89	vb	vb	NOUN
cana-2873	345	90	,	,	PUNCT
cana-2873	345	91	0.5	0.5	NUM
cana-2873	345	92	,	,	PUNCT
cana-2873	345	93	0.5	0.5	NUM
cana-2873	345	94	,	,	PUNCT
cana-2873	345	95	0.5	0.5	NUM
cana-2873	345	96	,	,	PUNCT
cana-2873	345	97	0.5	0.5	NUM
cana-2873	345	98	)	)	PUNCT
cana-2873	345	99	,	,	PUNCT
cana-2873	345	100	(	(	PUNCT
cana-2873	345	101	vc	vc	INTJ
cana-2873	345	102	,	,	PUNCT
cana-2873	345	103	0.5	0.5	NUM
cana-2873	345	104	,	,	PUNCT
cana-2873	345	105	0.5	0.5	NUM
cana-2873	345	106	,	,	PUNCT
cana-2873	345	107	0.5	0.5	NUM
cana-2873	345	108	,	,	PUNCT
cana-2873	345	109	0.5	0.5	NUM
cana-2873	345	110	)	)	PUNCT
cana-2873	345	111	}	}	PUNCT
cana-2873	345	112	,	,	PUNCT
cana-2873	345	113	w2	w2	NOUN
cana-2873	345	114	=	=	SYM
cana-2873	345	115	{	{	PUNCT
cana-2873	345	116	(	(	PUNCT
cana-2873	345	117	va	va	NOUN
cana-2873	345	118	,	,	PUNCT
cana-2873	345	119	0.4	0.4	NUM
cana-2873	345	120	,	,	PUNCT
cana-2873	345	121	0.5	0.5	NUM
cana-2873	345	122	,	,	PUNCT
cana-2873	345	123	0.5	0.5	NUM
cana-2873	345	124	,	,	PUNCT
cana-2873	345	125	0.6	0.6	NUM
cana-2873	345	126	)	)	PUNCT
cana-2873	345	127	,	,	PUNCT
cana-2873	345	128	(	(	PUNCT
cana-2873	345	129	vb	vb	NOUN
cana-2873	345	130	,	,	PUNCT
cana-2873	345	131	0.2	0.2	NUM
cana-2873	345	132	,	,	PUNCT
cana-2873	345	133	0.5	0.5	NUM
cana-2873	345	134	,	,	PUNCT
cana-2873	345	135	0.5	0.5	NUM
cana-2873	345	136	,	,	PUNCT
cana-2873	345	137	0.8	0.8	NUM
cana-2873	345	138	)	)	PUNCT
cana-2873	345	139	,	,	PUNCT
cana-2873	345	140	(	(	PUNCT
cana-2873	345	141	vc	vc	INTJ
cana-2873	345	142	,	,	PUNCT
cana-2873	345	143	0.6	0.6	NUM
cana-2873	345	144	,	,	PUNCT
cana-2873	345	145	0.5	0.5	NUM
cana-2873	345	146	,	,	PUNCT
cana-2873	345	147	0.5	0.5	NUM
cana-2873	345	148	,	,	PUNCT
cana-2873	345	149	0.4	0.4	NUM
cana-2873	345	150	)	)	PUNCT
cana-2873	345	151	}	}	PUNCT
cana-2873	345	152	,	,	PUNCT
cana-2873	345	153	w3	w3	PROPN
cana-2873	345	154	=	=	SYM
cana-2873	345	155	{	{	PUNCT
cana-2873	345	156	(	(	PUNCT
cana-2873	345	157	va	va	NOUN
cana-2873	345	158	,	,	PUNCT
cana-2873	345	159	0.4	0.4	NUM
cana-2873	345	160	,	,	PUNCT
cana-2873	345	161	0.5	0.5	NUM
cana-2873	345	162	,	,	PUNCT
cana-2873	345	163	0.5	0.5	NUM
cana-2873	345	164	,	,	PUNCT
cana-2873	345	165	0.6	0.6	NUM
cana-2873	345	166	)	)	PUNCT
cana-2873	345	167	,	,	PUNCT
cana-2873	345	168	(	(	PUNCT
cana-2873	345	169	vb	vb	NOUN
cana-2873	345	170	,	,	PUNCT
cana-2873	345	171	0.5	0.5	NUM
cana-2873	345	172	,	,	PUNCT
cana-2873	345	173	0.5	0.5	NUM
cana-2873	345	174	,	,	PUNCT
cana-2873	345	175	0.5	0.5	NUM
cana-2873	345	176	,	,	PUNCT
cana-2873	345	177	0.5	0.5	NUM
cana-2873	345	178	)	)	PUNCT
cana-2873	345	179	,	,	PUNCT
cana-2873	345	180	(	(	PUNCT
cana-2873	345	181	vc	vc	INTJ
cana-2873	345	182	,	,	PUNCT
cana-2873	345	183	0.6	0.6	NUM
cana-2873	345	184	,	,	PUNCT
cana-2873	345	185	0.5	0.5	NUM
cana-2873	345	186	,	,	PUNCT
cana-2873	345	187	0.5	0.5	NUM
cana-2873	345	188	,	,	PUNCT
cana-2873	345	189	0.4	0.4	NUM
cana-2873	345	190	)	)	PUNCT
cana-2873	345	191	}	}	PUNCT
cana-2873	345	192	,	,	PUNCT
cana-2873	345	193	w4	w4	NOUN
cana-2873	345	194	=	=	SYM
cana-2873	345	195	{	{	PUNCT
cana-2873	345	196	(	(	PUNCT
cana-2873	345	197	va	va	NOUN
cana-2873	345	198	,	,	PUNCT
cana-2873	345	199	0.3	0.3	NUM
cana-2873	345	200	,	,	PUNCT
cana-2873	345	201	0.5	0.5	NUM
cana-2873	345	202	,	,	PUNCT
cana-2873	345	203	0.5	0.5	NUM
cana-2873	345	204	,	,	PUNCT
cana-2873	345	205	0.7	0.7	NUM
cana-2873	345	206	)	)	PUNCT
cana-2873	345	207	,	,	PUNCT
cana-2873	345	208	(	(	PUNCT
cana-2873	345	209	vb	vb	NOUN
cana-2873	345	210	,	,	PUNCT
cana-2873	345	211	0.5	0.5	NUM
cana-2873	345	212	,	,	PUNCT
cana-2873	345	213	0.5	0.5	NUM
cana-2873	345	214	,	,	PUNCT
cana-2873	345	215	0.5	0.5	NUM
cana-2873	345	216	,	,	PUNCT
cana-2873	345	217	0.5	0.5	NUM
cana-2873	345	218	)	)	PUNCT
cana-2873	345	219	,	,	PUNCT
cana-2873	345	220	(	(	PUNCT
cana-2873	345	221	vc	vc	INTJ
cana-2873	345	222	,	,	PUNCT
cana-2873	345	223	0.4	0.4	NUM
cana-2873	345	224	,	,	PUNCT
cana-2873	345	225	0.5	0.5	NUM
cana-2873	345	226	,	,	PUNCT
cana-2873	345	227	0.5	0.5	NUM
cana-2873	345	228	,	,	PUNCT
cana-2873	345	229	0.6	0.6	NUM
cana-2873	345	230	)	)	PUNCT
cana-2873	345	231	}	}	PUNCT
cana-2873	345	232	.	.	PUNCT
cana-2873	346	1	then	then	ADV
cana-2873	346	2	we	we	PRON
cana-2873	346	3	have	have	VERB
cana-2873	346	4	γ	γ	NOUN
cana-2873	346	5	=	=	PRON
cana-2873	346	6	{	{	PUNCT
cana-2873	346	7	0qns	0qns	PROPN
cana-2873	346	8	,	,	PUNCT
cana-2873	346	9	v1	v1	PROPN
cana-2873	346	10	,	,	PUNCT
cana-2873	346	11	1qns	1qns	NUM
cana-2873	346	12	}	}	PUNCT
cana-2873	346	13	and	and	CCONJ
cana-2873	346	14	σq=	σq=	PROPN
cana-2873	346	15	0qns	0qns	PROPN
cana-2873	346	16	,	,	PUNCT
cana-2873	346	17	w1	w1	NOUN
cana-2873	346	18	,	,	PUNCT
cana-2873	346	19	w2	w2	NOUN
cana-2873	346	20	,	,	PUNCT
cana-2873	346	21	w3	w3	PROPN
cana-2873	346	22	,	,	PUNCT
cana-2873	346	23	w1∩w2	w1∩w2	PROPN
cana-2873	346	24	,	,	PUNCT
cana-2873	346	25	1qns	1qns	NUM
cana-2873	346	26	}	}	PUNCT
cana-2873	346	27	.	.	PUNCT
cana-2873	347	1	let	let	VERB
cana-2873	347	2	k	k	NOUN
cana-2873	347	3	:	:	PUNCT
cana-2873	347	4	(	(	PUNCT
cana-2873	347	5	z1	z1	VERB
cana-2873	347	6	,	,	PUNCT
cana-2873	347	7	γq	γq	NOUN
cana-2873	347	8	)	)	PUNCT
cana-2873	347	9	→(z2	→(z2	PROPN
cana-2873	347	10	,	,	PUNCT
cana-2873	347	11	σq	σq	NOUN
cana-2873	347	12	)	)	PUNCT
cana-2873	347	13	be	be	VERB
cana-2873	347	14	an	an	DET
cana-2873	347	15	identity	identity	NOUN
cana-2873	347	16	mapping	mapping	NOUN
cana-2873	347	17	,	,	PUNCT
cana-2873	347	18	then	then	ADV
cana-2873	347	19	k	k	PROPN
cana-2873	347	20	is	be	AUX
cana-2873	347	21	q	q	NOUN
cana-2873	347	22	-	-	PUNCT
cana-2873	347	23	nsɕbo	nsɕbo	NOUN
cana-2873	347	24	but	but	CCONJ
cana-2873	347	25	not	not	PART
cana-2873	347	26	q	q	NOUN
cana-2873	347	27	-	-	PUNCT
cana-2873	347	28	nsɕso	nsɕso	NOUN
cana-2873	347	29	,	,	PUNCT
cana-2873	347	30	the	the	DET
cana-2873	347	31	set	set	NOUN
cana-2873	347	32	k(v1	k(v1	NOUN
cana-2873	347	33	)	)	PUNCT
cana-2873	348	1	=	=	PUNCT
cana-2873	348	2	w3c	w3c	PROPN
cana-2873	348	3	is	be	AUX
cana-2873	348	4	a	a	DET
cana-2873	348	5	q	q	ADJ
cana-2873	348	6	-	-	PUNCT
cana-2873	348	7	nsbc	nsbc	ADJ
cana-2873	348	8	set	set	NOUN
cana-2873	348	9	but	but	CCONJ
cana-2873	348	10	not	not	PART
cana-2873	348	11	q	q	ADJ
cana-2873	348	12	-	-	PUNCT
cana-2873	348	13	nssc	nssc	NOUN
cana-2873	348	14	set	set	NOUN
cana-2873	348	15	.	.	PUNCT
cana-2873	349	1	example	example	NOUN
cana-2873	349	2	5.5	5.5	NUM
cana-2873	349	3	.	.	PUNCT
cana-2873	350	1	let	let	VERB
cana-2873	350	2	v	v	VERB
cana-2873	350	3	=	=	SYM
cana-2873	350	4	{	{	PUNCT
cana-2873	350	5	va	va	NOUN
cana-2873	350	6	,	,	PUNCT
cana-2873	350	7	vb	vb	NOUN
cana-2873	350	8	}	}	PUNCT
cana-2873	350	9	=	=	SYM
cana-2873	350	10	w	w	NOUN
cana-2873	350	11	and	and	CCONJ
cana-2873	350	12	define	define	VERB
cana-2873	350	13	q	q	ADJ
cana-2873	350	14	-	-	PUNCT
cana-2873	350	15	nss	nss	NOUN
cana-2873	350	16	’s	’s	PART
cana-2873	350	17	v1	v1	NOUN
cana-2873	350	18	in	in	ADP
cana-2873	350	19	v	v	NOUN
cana-2873	350	20	and	and	CCONJ
cana-2873	350	21	w1	w1	PROPN
cana-2873	350	22	&	&	CCONJ
cana-2873	350	23	w2	w2	PROPN
cana-2873	350	24	in	in	ADP
cana-2873	350	25	w	w	PROPN
cana-2873	350	26	are	be	AUX
cana-2873	350	27	v1	v1	NOUN
cana-2873	350	28	=	=	SYM
cana-2873	350	29	{	{	PUNCT
cana-2873	350	30	(	(	PUNCT
cana-2873	350	31	va	va	NOUN
cana-2873	350	32	,	,	PUNCT
cana-2873	350	33	0.3	0.3	NUM
cana-2873	350	34	,	,	PUNCT
cana-2873	350	35	0.5	0.5	NUM
cana-2873	350	36	,	,	PUNCT
cana-2873	350	37	0.5	0.5	NUM
cana-2873	350	38	,	,	PUNCT
cana-2873	350	39	0.7	0.7	NUM
cana-2873	350	40	)	)	PUNCT
cana-2873	350	41	,	,	PUNCT
cana-2873	350	42	(	(	PUNCT
cana-2873	350	43	vb	vb	NOUN
cana-2873	350	44	,	,	PUNCT
cana-2873	350	45	0.5	0.5	NUM
cana-2873	350	46	,	,	PUNCT
cana-2873	350	47	0.5	0.5	NUM
cana-2873	350	48	,	,	PUNCT
cana-2873	350	49	0.5	0.5	NUM
cana-2873	350	50	,	,	PUNCT
cana-2873	350	51	0.6	0.6	NUM
cana-2873	350	52	)	)	PUNCT
cana-2873	350	53	}	}	PUNCT
cana-2873	350	54	,	,	PUNCT
cana-2873	350	55	w1	w1	NOUN
cana-2873	350	56	=	=	SYM
cana-2873	350	57	{	{	PUNCT
cana-2873	350	58	(	(	PUNCT
cana-2873	350	59	va	va	NOUN
cana-2873	350	60	,	,	PUNCT
cana-2873	350	61	0.3	0.3	NUM
cana-2873	350	62	,	,	PUNCT
cana-2873	350	63	0.5	0.5	NUM
cana-2873	350	64	,	,	PUNCT
cana-2873	350	65	0.5	0.5	NUM
cana-2873	350	66	,	,	PUNCT
cana-2873	350	67	0.5	0.5	NUM
cana-2873	350	68	)	)	PUNCT
cana-2873	350	69	,	,	PUNCT
cana-2873	350	70	(	(	PUNCT
cana-2873	350	71	vb	vb	NOUN
cana-2873	350	72	,	,	PUNCT
cana-2873	350	73	0.2	0.2	NUM
cana-2873	350	74	,	,	PUNCT
cana-2873	350	75	0.5	0.5	NUM
cana-2873	350	76	,	,	PUNCT
cana-2873	350	77	0.5	0.5	NUM
cana-2873	350	78	,	,	PUNCT
cana-2873	350	79	0.5	0.5	NUM
cana-2873	350	80	)	)	PUNCT
cana-2873	350	81	}	}	PUNCT
cana-2873	350	82	,	,	PUNCT
cana-2873	350	83	w2	w2	NOUN
cana-2873	350	84	=	=	SYM
cana-2873	350	85	{	{	PUNCT
cana-2873	350	86	(	(	PUNCT
cana-2873	350	87	va	va	NOUN
cana-2873	350	88	,	,	PUNCT
cana-2873	350	89	0.3	0.3	NUM
cana-2873	350	90	,	,	PUNCT
cana-2873	350	91	0.5	0.5	NUM
cana-2873	350	92	,	,	PUNCT
cana-2873	350	93	0.5	0.5	NUM
cana-2873	350	94	,	,	PUNCT
cana-2873	350	95	0.7	0.7	NUM
cana-2873	350	96	)	)	PUNCT
cana-2873	350	97	,	,	PUNCT
cana-2873	350	98	(	(	PUNCT
cana-2873	350	99	vb	vb	NOUN
cana-2873	350	100	,	,	PUNCT
cana-2873	350	101	0.5	0.5	NUM
cana-2873	350	102	,	,	PUNCT
cana-2873	350	103	0.5	0.5	NUM
cana-2873	350	104	,	,	PUNCT
cana-2873	350	105	0.5	0.5	NUM
cana-2873	350	106	,	,	PUNCT
cana-2873	350	107	0.6	0.6	NUM
cana-2873	350	108	)	)	PUNCT
cana-2873	350	109	}	}	PUNCT
cana-2873	350	110	.	.	PUNCT
cana-2873	351	1	then	then	ADV
cana-2873	351	2	we	we	PRON
cana-2873	351	3	have	have	VERB
cana-2873	351	4	γq={0qns	γq={0qns	PROPN
cana-2873	351	5	,	,	PUNCT
cana-2873	351	6	v1	v1	PROPN
cana-2873	351	7	,	,	PUNCT
cana-2873	351	8	1qns	1qns	PROPN
cana-2873	351	9	and	and	CCONJ
cana-2873	351	10	σq	σq	PRON
cana-2873	351	11	=	=	NOUN
cana-2873	351	12	{	{	PUNCT
cana-2873	351	13	0qns	0qns	PROPN
cana-2873	351	14	,	,	PUNCT
cana-2873	351	15	w1	w1	NOUN
cana-2873	351	16	,	,	PUNCT
cana-2873	351	17	1qns}.let	1qns}.let	NUM
cana-2873	351	18	k	k	NOUN
cana-2873	351	19	:	:	PUNCT
cana-2873	351	20	(	(	PUNCT
cana-2873	351	21	z1	z1	VERB
cana-2873	351	22	,	,	PUNCT
cana-2873	351	23	γq	γq	ADP
cana-2873	351	24	)	)	PUNCT
cana-2873	351	25	→	→	SYM
cana-2873	351	26	(	(	PUNCT
cana-2873	351	27	z2	z2	PROPN
cana-2873	351	28	,	,	PUNCT
cana-2873	351	29	σq	σq	NOUN
cana-2873	351	30	)	)	PUNCT
cana-2873	351	31	be	be	VERB
cana-2873	351	32	an	an	DET
cana-2873	351	33	identity	identity	NOUN
cana-2873	351	34	mapping	mapping	NOUN
cana-2873	351	35	,	,	PUNCT
cana-2873	351	36	then	then	ADV
cana-2873	351	37	k	k	PROPN
cana-2873	351	38	is	be	AUX
cana-2873	351	39	q	q	NOUN
cana-2873	351	40	-	-	PUNCT
cana-2873	351	41	nsɕβo	nsɕβo	NOUN
cana-2873	351	42	but	but	CCONJ
cana-2873	351	43	not	not	PART
cana-2873	351	44	q	q	NOUN
cana-2873	351	45	-	-	PUNCT
cana-2873	351	46	nsɕbo	nsɕbo	NOUN
cana-2873	351	47	,	,	PUNCT
cana-2873	351	48	the	the	DET
cana-2873	351	49	set	set	NOUN
cana-2873	351	50	k(v1	k(v1	NOUN
cana-2873	351	51	)	)	PUNCT
cana-2873	352	1	=	=	SYM
cana-2873	352	2	wc	wc	PROPN
cana-2873	352	3	is	be	AUX
cana-2873	352	4	a	a	DET
cana-2873	352	5	qnsβc	qnsβc	PROPN
cana-2873	352	6	set	set	NOUN
cana-2873	352	7	but	but	CCONJ
cana-2873	352	8	not	not	PART
cana-2873	352	9	q	q	ADJ
cana-2873	352	10	-	-	PUNCT
cana-2873	352	11	nsbc	nsbc	ADJ
cana-2873	352	12	set	set	NOUN
cana-2873	352	13	.	.	PUNCT
cana-2873	353	1	figure	figure	NOUN
cana-2873	353	2	2	2	NUM
cana-2873	353	3	:	:	PUNCT
cana-2873	353	4	q	q	ADJ
cana-2873	353	5	-	-	PUNCT
cana-2873	353	6	nscβo	nscβo	ADV
cana-2873	353	7	maps	map	NOUN
cana-2873	353	8	in	in	ADP
cana-2873	353	9	q	q	ADJ
cana-2873	353	10	-	-	PUNCT
cana-2873	353	11	nsts	nst	NOUN
cana-2873	353	12	theorem	theorem	VERB
cana-2873	353	13	5.6	5.6	NUM
cana-2873	353	14	.	.	PUNCT
cana-2873	354	1	a	a	DET
cana-2873	354	2	mapping	mapping	NOUN
cana-2873	354	3	k	k	NOUN
cana-2873	354	4	:	:	PUNCT
cana-2873	354	5	(	(	PUNCT
cana-2873	354	6	z1	z1	VERB
cana-2873	354	7	,	,	PUNCT
cana-2873	354	8	γq	γq	ADP
cana-2873	354	9	)	)	PUNCT
cana-2873	354	10	→	→	SYM
cana-2873	354	11	(	(	PUNCT
cana-2873	354	12	z2	z2	PROPN
cana-2873	354	13	,	,	PUNCT
cana-2873	354	14	σq	σq	NOUN
cana-2873	354	15	)	)	PUNCT
cana-2873	354	16	is	be	AUX
cana-2873	354	17	q	q	NOUN
cana-2873	354	18	-	-	PUNCT
cana-2873	354	19	nscβo	nscβo	ADV
cana-2873	354	20	iff	iff	NOUN
cana-2873	354	21	for	for	ADP
cana-2873	354	22	every	every	DET
cana-2873	354	23	q	q	NOUN
cana-2873	354	24	-	-	PUNCT
cana-2873	354	25	nss	nss	NOUN
cana-2873	354	26	(	(	PUNCT
cana-2873	354	27	ψ̃	ψ̃	PROPN
cana-2873	354	28	)	)	PUNCT
cana-2873	354	29	of	of	ADP
cana-2873	354	30	(	(	PUNCT
cana-2873	354	31	z1	z1	NOUN
cana-2873	354	32	,	,	PUNCT
cana-2873	354	33	γq	γq	ADP
cana-2873	354	34	)	)	PUNCT
cana-2873	354	35	,	,	PUNCT
cana-2873	354	36	k(q	k(q	PROPN
cana-2873	354	37	-	-	PUNCT
cana-2873	354	38	nsint(ψ̃	nsint(ψ̃	PROPN
cana-2873	354	39	)	)	PUNCT
cana-2873	354	40	)	)	PUNCT
cana-2873	355	1	⊇	⊇	PROPN
cana-2873	355	2	q	q	NOUN
cana-2873	355	3	-	-	PUNCT
cana-2873	355	4	nsβcl(k(ψ̃	nsβcl(k(ψ̃	NOUN
cana-2873	355	5	)	)	PUNCT
cana-2873	355	6	)	)	PUNCT
cana-2873	355	7	.	.	PUNCT
cana-2873	356	1	proof	proof	NOUN
cana-2873	356	2	.	.	PUNCT
cana-2873	357	1	necessity	necessity	NOUN
cana-2873	357	2	:	:	PUNCT
cana-2873	357	3	assume	assume	VERB
cana-2873	357	4	k	k	PROPN
cana-2873	357	5	is	be	AUX
cana-2873	357	6	a	a	DET
cana-2873	357	7	q	q	ADJ
cana-2873	357	8	-	-	PUNCT
cana-2873	357	9	nsɕβo	nsɕβo	NOUN
cana-2873	357	10	mapping	mapping	NOUN
cana-2873	357	11	and	and	CCONJ
cana-2873	357	12	(	(	PUNCT
cana-2873	357	13	ψ̃	ψ̃	PROPN
cana-2873	357	14	)	)	PUNCT
cana-2873	357	15	is	be	AUX
cana-2873	357	16	a	a	DET
cana-2873	357	17	q	q	NOUN
cana-2873	357	18	-	-	PUNCT
cana-2873	357	19	nsos	nsos	NOUN
cana-2873	357	20	in	in	ADP
cana-2873	357	21	(	(	PUNCT
cana-2873	357	22	z1	z1	NOUN
cana-2873	357	23	,	,	PUNCT
cana-2873	357	24	γq	γq	ADP
cana-2873	357	25	)	)	PUNCT
cana-2873	357	26	.	.	PUNCT
cana-2873	358	1	now	now	ADV
cana-2873	358	2	,	,	PUNCT
cana-2873	358	3	qnsint(ψ̃	qnsint(ψ̃	PROPN
cana-2873	358	4	)	)	PUNCT
cana-2873	359	1	⊆	⊆	NUM
cana-2873	359	2	(	(	PUNCT
cana-2873	359	3	ψ̃	ψ̃	PROPN
cana-2873	359	4	)	)	PUNCT
cana-2873	359	5	implies	imply	VERB
cana-2873	359	6	k(q	k(q	PROPN
cana-2873	359	7	-	-	PUNCT
cana-2873	359	8	nsint(ψ̃	nsint(ψ̃	PROPN
cana-2873	359	9	)	)	PUNCT
cana-2873	359	10	)	)	PUNCT
cana-2873	360	1	⊆	⊆	NUM
cana-2873	360	2	k(ψ̃	k(ψ̃	NOUN
cana-2873	360	3	)	)	PUNCT
cana-2873	360	4	.	.	PUNCT
cana-2873	361	1	since	since	SCONJ
cana-2873	361	2	k	k	PROPN
cana-2873	361	3	is	be	AUX
cana-2873	361	4	a	a	DET
cana-2873	361	5	q	q	ADJ
cana-2873	361	6	-	-	PUNCT
cana-2873	361	7	nsɕβo	nsɕβo	NOUN
cana-2873	361	8	mapping	mapping	NOUN
cana-2873	361	9	,	,	PUNCT
cana-2873	361	10	k(qnsint(ψ̃	k(qnsint(ψ̃	NOUN
cana-2873	361	11	)	)	PUNCT
cana-2873	361	12	)	)	PUNCT
cana-2873	361	13	is	be	AUX
cana-2873	361	14	q	q	ADJ
cana-2873	361	15	-	-	NOUN
cana-2873	361	16	nsβcs	nsβcs	NOUN
cana-2873	361	17	in	in	ADP
cana-2873	361	18	(	(	PUNCT
cana-2873	361	19	z2	z2	PROPN
cana-2873	361	20	,	,	PUNCT
cana-2873	361	21	σq	σq	NOUN
cana-2873	361	22	)	)	PUNCT
cana-2873	361	23	such	such	ADJ
cana-2873	361	24	that	that	SCONJ
cana-2873	361	25	k(q	k(q	PROPN
cana-2873	361	26	-	-	PUNCT
cana-2873	361	27	nsint(ψ̃	nsint(ψ̃	PROPN
cana-2873	361	28	)	)	PUNCT
cana-2873	361	29	)	)	PUNCT
cana-2873	361	30	⊇	⊇	PROPN
cana-2873	361	31	k(ψ̃	k(ψ̃	PROPN
cana-2873	361	32	)	)	PUNCT
cana-2873	361	33	.	.	PUNCT
cana-2873	362	1	therefore	therefore	ADV
cana-2873	362	2	k(q	k(q	PROPN
cana-2873	362	3	-	-	PUNCT
cana-2873	362	4	nsint(ψ̃	nsint(ψ̃	PROPN
cana-2873	362	5	)	)	PUNCT
cana-2873	362	6	)	)	PUNCT
cana-2873	362	7	⊇	⊇	PROPN
cana-2873	362	8	q	q	NOUN
cana-2873	362	9	-	-	PUNCT
cana-2873	362	10	nsβcl(k(ψ̃	nsβcl(k(ψ̃	NOUN
cana-2873	362	11	)	)	PUNCT
cana-2873	362	12	)	)	PUNCT
cana-2873	362	13	.	.	PUNCT
cana-2873	363	1	communications	communication	NOUN
cana-2873	363	2	on	on	ADP
cana-2873	363	3	applied	apply	VERB
cana-2873	363	4	nonlinear	nonlinear	ADJ
cana-2873	363	5	analysis	analysis	NOUN
cana-2873	363	6	issn	issn	NOUN
cana-2873	363	7	:	:	PUNCT
cana-2873	363	8	1074	1074	NUM
cana-2873	363	9	-	-	PUNCT
cana-2873	363	10	133x	133x	NUM
cana-2873	363	11	vol	vol	NOUN
cana-2873	363	12	32	32	NUM
cana-2873	363	13	no	no	NOUN
cana-2873	363	14	.	.	PUNCT
cana-2873	364	1	4s	4s	NUM
cana-2873	364	2	(	(	PUNCT
cana-2873	364	3	2025	2025	NUM
cana-2873	364	4	)	)	PUNCT
cana-2873	364	5	590	590	NUM
cana-2873	364	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	364	7	sufficiency	sufficiency	NOUN
cana-2873	364	8	:	:	PUNCT
cana-2873	364	9	assume	assume	VERB
cana-2873	364	10	(	(	PUNCT
cana-2873	364	11	ψ̃	ψ̃	PROPN
cana-2873	364	12	)	)	PUNCT
cana-2873	364	13	is	be	AUX
cana-2873	364	14	a	a	DET
cana-2873	364	15	q	q	NOUN
cana-2873	364	16	-	-	PUNCT
cana-2873	364	17	nsos	nsos	NOUN
cana-2873	364	18	of	of	ADP
cana-2873	364	19	(	(	PUNCT
cana-2873	364	20	z1	z1	VERB
cana-2873	364	21	,	,	PUNCT
cana-2873	364	22	γq	γq	ADP
cana-2873	364	23	)	)	PUNCT
cana-2873	364	24	.	.	PUNCT
cana-2873	365	1	then	then	ADV
cana-2873	365	2	we	we	PRON
cana-2873	365	3	have	have	VERB
cana-2873	365	4	k(ψ̃	k(ψ̃	NOUN
cana-2873	365	5	)	)	PUNCT
cana-2873	366	1	=	=	SYM
cana-2873	366	2	k(q	k(q	PROPN
cana-2873	366	3	-	-	PUNCT
cana-2873	366	4	nsint(ψ̃	nsint(ψ̃	PROPN
cana-2873	366	5	)	)	PUNCT
cana-2873	366	6	)	)	PUNCT
cana-2873	367	1	⊇	⊇	PROPN
cana-2873	367	2	qnsβcl(k(ψ̃	qnsβcl(k(ψ̃	PROPN
cana-2873	367	3	)	)	PUNCT
cana-2873	367	4	)	)	PUNCT
cana-2873	367	5	.	.	PUNCT
cana-2873	368	1	but	but	CCONJ
cana-2873	368	2	q	q	X
cana-2873	368	3	-	-	PUNCT
cana-2873	368	4	nsβcl(k(ψ̃	nsβcl(k(ψ̃	NOUN
cana-2873	368	5	)	)	PUNCT
cana-2873	368	6	)	)	PUNCT
cana-2873	369	1	⊇k(ψ̃	⊇k(ψ̃	NOUN
cana-2873	369	2	)	)	PUNCT
cana-2873	369	3	.	.	PUNCT
cana-2873	370	1	so	so	ADV
cana-2873	370	2	,	,	PUNCT
cana-2873	370	3	k(ψ̃	k(ψ̃	NOUN
cana-2873	370	4	)	)	PUNCT
cana-2873	370	5	=	=	SYM
cana-2873	371	1	q	q	NOUN
cana-2873	371	2	-	-	PUNCT
cana-2873	371	3	nsβcl(ψ̃	nsβcl(ψ̃	NOUN
cana-2873	371	4	)	)	PUNCT
cana-2873	371	5	which	which	PRON
cana-2873	371	6	implies	imply	VERB
cana-2873	371	7	k(ψ̃	k(ψ̃	PROPN
cana-2873	371	8	)	)	PUNCT
cana-2873	371	9	is	be	AUX
cana-2873	371	10	a	a	DET
cana-2873	371	11	q	q	NOUN
cana-2873	371	12	-	-	PUNCT
cana-2873	371	13	nsβcs	nsβcs	NOUN
cana-2873	371	14	of	of	ADP
cana-2873	371	15	(	(	PUNCT
cana-2873	371	16	z2	z2	PROPN
cana-2873	371	17	,	,	PUNCT
cana-2873	371	18	σq	σq	NOUN
cana-2873	371	19	)	)	PUNCT
cana-2873	371	20	and	and	CCONJ
cana-2873	371	21	hence	hence	ADV
cana-2873	371	22	k	k	PROPN
cana-2873	371	23	is	be	AUX
cana-2873	371	24	a	a	DET
cana-2873	371	25	q	q	NOUN
cana-2873	371	26	-	-	PUNCT
cana-2873	371	27	nscβo	nscβo	ADV
cana-2873	371	28	.	.	PUNCT
cana-2873	372	1	theorem	theorem	VERB
cana-2873	372	2	5.7	5.7	NUM
cana-2873	372	3	.	.	PUNCT
cana-2873	373	1	if	if	SCONJ
cana-2873	373	2	k	k	X
cana-2873	373	3	:	:	PUNCT
cana-2873	373	4	(	(	PUNCT
cana-2873	373	5	z1	z1	VERB
cana-2873	373	6	,	,	PUNCT
cana-2873	373	7	γq	γq	ADP
cana-2873	373	8	)	)	PUNCT
cana-2873	373	9	→	→	SYM
cana-2873	373	10	(	(	PUNCT
cana-2873	373	11	z2	z2	PROPN
cana-2873	373	12	,	,	PUNCT
cana-2873	373	13	σq	σq	NOUN
cana-2873	373	14	)	)	PUNCT
cana-2873	373	15	is	be	AUX
cana-2873	373	16	a	a	DET
cana-2873	373	17	q	q	ADJ
cana-2873	373	18	-	-	PUNCT
cana-2873	373	19	nsɕβo	nsɕβo	NOUN
cana-2873	373	20	mapping	mapping	NOUN
cana-2873	373	21	,	,	PUNCT
cana-2873	373	22	then	then	ADV
cana-2873	373	23	q	q	NOUN
cana-2873	373	24	-	-	PUNCT
cana-2873	373	25	nsint(k−1(ψ̃	nsint(k−1(ψ̃	NOUN
cana-2873	373	26	)	)	PUNCT
cana-2873	373	27	)	)	PUNCT
cana-2873	374	1	⊆	⊆	NUM
cana-2873	374	2	k−1(q	k−1(q	ADV
cana-2873	374	3	-	-	PUNCT
cana-2873	374	4	nsβcl(ψ̃	nsβcl(ψ̃	NOUN
cana-2873	374	5	)	)	PUNCT
cana-2873	374	6	)	)	PUNCT
cana-2873	374	7	for	for	ADP
cana-2873	374	8	every	every	DET
cana-2873	374	9	q	q	NOUN
cana-2873	374	10	-	-	PUNCT
cana-2873	374	11	nss	nss	NOUN
cana-2873	374	12	(	(	PUNCT
cana-2873	374	13	ψ̃	ψ̃	PROPN
cana-2873	374	14	)	)	PUNCT
cana-2873	374	15	of	of	ADP
cana-2873	374	16	(	(	PUNCT
cana-2873	374	17	z2	z2	PROPN
cana-2873	374	18	,	,	PUNCT
cana-2873	374	19	σq	σq	NOUN
cana-2873	374	20	)	)	PUNCT
cana-2873	374	21	.	.	PUNCT
cana-2873	375	1	proof	proof	NOUN
cana-2873	375	2	.	.	PUNCT
cana-2873	376	1	consider	consider	VERB
cana-2873	376	2	a	a	DET
cana-2873	376	3	q	q	NOUN
cana-2873	376	4	-	-	PUNCT
cana-2873	376	5	nss	nss	NOUN
cana-2873	376	6	(	(	PUNCT
cana-2873	376	7	ψ̃	ψ̃	PROPN
cana-2873	376	8	)	)	PUNCT
cana-2873	376	9	in	in	ADP
cana-2873	376	10	(	(	PUNCT
cana-2873	376	11	z2	z2	PROPN
cana-2873	376	12	,	,	PUNCT
cana-2873	376	13	σq	σq	NOUN
cana-2873	376	14	)	)	PUNCT
cana-2873	376	15	.	.	PUNCT
cana-2873	377	1	we	we	PRON
cana-2873	377	2	know	know	VERB
cana-2873	377	3	that	that	SCONJ
cana-2873	377	4	q	q	NOUN
cana-2873	377	5	-	-	PUNCT
cana-2873	377	6	nsint(k−1(ψ̃	nsint(k−1(ψ̃	NOUN
cana-2873	377	7	)	)	PUNCT
cana-2873	377	8	)	)	PUNCT
cana-2873	377	9	is	be	AUX
cana-2873	377	10	a	a	DET
cana-2873	377	11	q	q	NOUN
cana-2873	377	12	-	-	PUNCT
cana-2873	377	13	nsos	nsos	NOUN
cana-2873	377	14	in	in	ADP
cana-2873	377	15	(	(	PUNCT
cana-2873	377	16	z1	z1	NOUN
cana-2873	377	17	,	,	PUNCT
cana-2873	377	18	γq	γq	ADP
cana-2873	377	19	)	)	PUNCT
cana-2873	377	20	.	.	PUNCT
cana-2873	378	1	since	since	SCONJ
cana-2873	378	2	k	k	PROPN
cana-2873	378	3	is	be	AUX
cana-2873	378	4	q	q	NOUN
cana-2873	378	5	-	-	PUNCT
cana-2873	378	6	nsβo	nsβo	ADJ
cana-2873	378	7	,	,	PUNCT
cana-2873	378	8	k(q	k(q	NOUN
cana-2873	378	9	-	-	PUNCT
cana-2873	378	10	nsint(k−1(ψ̃	nsint(k−1(ψ̃	NOUN
cana-2873	378	11	)	)	PUNCT
cana-2873	378	12	)	)	PUNCT
cana-2873	378	13	)	)	PUNCT
cana-2873	378	14	is	be	AUX
cana-2873	378	15	q	q	ADJ
cana-2873	378	16	-	-	NOUN
cana-2873	378	17	nsβcs	nsβcs	NOUN
cana-2873	378	18	in	in	ADP
cana-2873	378	19	(	(	PUNCT
cana-2873	378	20	z2	z2	PROPN
cana-2873	378	21	,	,	PUNCT
cana-2873	378	22	σq	σq	NOUN
cana-2873	378	23	)	)	PUNCT
cana-2873	378	24	and	and	CCONJ
cana-2873	378	25	hence	hence	ADV
cana-2873	378	26	k(qnsint(k−1(ψ̃)))⊆	k(qnsint(k−1(ψ̃)))⊆	VERB
cana-2873	378	27	qnsβcl(k(k−1(ψ̃	qnsβcl(k(k−1(ψ̃	NOUN
cana-2873	378	28	)	)	PUNCT
cana-2873	378	29	)	)	PUNCT
cana-2873	378	30	)	)	PUNCT
cana-2873	379	1	⊆	⊆	NUM
cana-2873	379	2	q	q	NOUN
cana-2873	379	3	-	-	PUNCT
cana-2873	379	4	nsβcl(ψ̃	nsβcl(ψ̃	NOUN
cana-2873	379	5	)	)	PUNCT
cana-2873	379	6	.	.	PUNCT
cana-2873	380	1	thus	thus	ADV
cana-2873	380	2	q	q	X
cana-2873	380	3	-	-	PUNCT
cana-2873	380	4	nsint(k−1(ψ̃	nsint(k−1(ψ̃	NOUN
cana-2873	380	5	)	)	PUNCT
cana-2873	380	6	)	)	PUNCT
cana-2873	381	1	⊆	⊆	NUM
cana-2873	381	2	k−1(qnsβcl(ψ̃	k−1(qnsβcl(ψ̃	NOUN
cana-2873	381	3	)	)	PUNCT
cana-2873	381	4	)	)	PUNCT
cana-2873	381	5	.	.	PUNCT
cana-2873	382	1	theorem	theorem	VERB
cana-2873	382	2	5.8	5.8	NUM
cana-2873	382	3	.	.	PUNCT
cana-2873	383	1	a	a	DET
cana-2873	383	2	mapping	mapping	NOUN
cana-2873	383	3	k	k	NOUN
cana-2873	383	4	:	:	PUNCT
cana-2873	383	5	(	(	PUNCT
cana-2873	383	6	z1	z1	VERB
cana-2873	383	7	,	,	PUNCT
cana-2873	383	8	γq	γq	ADP
cana-2873	383	9	)	)	PUNCT
cana-2873	383	10	→	→	SYM
cana-2873	383	11	(	(	PUNCT
cana-2873	383	12	z2	z2	PROPN
cana-2873	383	13	,	,	PUNCT
cana-2873	383	14	σq	σq	NOUN
cana-2873	383	15	)	)	PUNCT
cana-2873	383	16	is	be	AUX
cana-2873	383	17	q	q	NOUN
cana-2873	383	18	-	-	PUNCT
cana-2873	383	19	nscβo	nscβo	ADV
cana-2873	383	20	iff	iff	NOUN
cana-2873	383	21	for	for	ADP
cana-2873	383	22	each	each	DET
cana-2873	383	23	q	q	ADJ
cana-2873	383	24	-	-	PUNCT
cana-2873	383	25	nss	nss	NOUN
cana-2873	383	26	ψ̃	ψ̃	PROPN
cana-2873	383	27	of	of	ADP
cana-2873	383	28	(	(	PUNCT
cana-2873	383	29	z2	z2	PROPN
cana-2873	383	30	,	,	PUNCT
cana-2873	383	31	σq	σq	NOUN
cana-2873	383	32	)	)	PUNCT
cana-2873	383	33	and	and	CCONJ
cana-2873	383	34	for	for	ADP
cana-2873	383	35	each	each	DET
cana-2873	383	36	q	q	NOUN
cana-2873	383	37	-	-	PUNCT
cana-2873	383	38	nsos	nsos	NOUN
cana-2873	383	39	(	(	PUNCT
cana-2873	383	40	ψ̃	ψ̃	PROPN
cana-2873	383	41	)	)	PUNCT
cana-2873	383	42	of	of	ADP
cana-2873	383	43	(	(	PUNCT
cana-2873	383	44	z1	z1	NOUN
cana-2873	383	45	,	,	PUNCT
cana-2873	383	46	γq	γq	AUX
cana-2873	383	47	)	)	PUNCT
cana-2873	383	48	containing	contain	VERB
cana-2873	383	49	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	383	50	)	)	PUNCT
cana-2873	383	51	,	,	PUNCT
cana-2873	383	52	there	there	PRON
cana-2873	383	53	is	be	VERB
cana-2873	383	54	a	a	DET
cana-2873	383	55	q	q	ADJ
cana-2873	383	56	-	-	PUNCT
cana-2873	383	57	nsβos	nsβos	NOUN
cana-2873	383	58	ã	ã	PROPN
cana-2873	383	59	of	of	ADP
cana-2873	383	60	(	(	PUNCT
cana-2873	383	61	z2	z2	PROPN
cana-2873	383	62	,	,	PUNCT
cana-2873	383	63	σq	σq	NOUN
cana-2873	383	64	)	)	PUNCT
cana-2873	383	65	such	such	ADJ
cana-2873	383	66	that	that	SCONJ
cana-2873	383	67	(	(	PUNCT
cana-2873	383	68	ψ̃	ψ̃	PROPN
cana-2873	383	69	)	)	PUNCT
cana-2873	383	70	⊆	⊆	NUM
cana-2873	383	71	(	(	PUNCT
cana-2873	383	72	ã	ã	PROPN
cana-2873	383	73	)	)	PUNCT
cana-2873	383	74	and	and	CCONJ
cana-2873	383	75	k−1(ã	k−1(ã	NOUN
cana-2873	383	76	)	)	PUNCT
cana-2873	383	77	⊆	⊆	NUM
cana-2873	383	78	(	(	PUNCT
cana-2873	383	79	ψ̃	ψ̃	PROPN
cana-2873	383	80	)	)	PUNCT
cana-2873	383	81	.	.	PUNCT
cana-2873	384	1	proof	proof	NOUN
cana-2873	384	2	.	.	PUNCT
cana-2873	385	1	necessity	necessity	NOUN
cana-2873	385	2	:	:	PUNCT
cana-2873	385	3	let	let	VERB
cana-2873	385	4	k	k	PRON
cana-2873	385	5	be	be	AUX
cana-2873	385	6	a	a	DET
cana-2873	385	7	q	q	ADJ
cana-2873	385	8	-	-	PUNCT
cana-2873	385	9	nsɕβo	nsɕβo	NOUN
cana-2873	385	10	mapping	mapping	NOUN
cana-2873	385	11	.	.	PUNCT
cana-2873	386	1	consider	consider	VERB
cana-2873	386	2	a	a	DET
cana-2873	386	3	q	q	NOUN
cana-2873	386	4	-	-	PUNCT
cana-2873	386	5	nscs	nscs	ADJ
cana-2873	386	6	ψ̃	ψ̃	PROPN
cana-2873	386	7	in	in	ADP
cana-2873	386	8	(	(	PUNCT
cana-2873	386	9	z2	z2	PROPN
cana-2873	386	10	,	,	PUNCT
cana-2873	386	11	σq	σq	NOUN
cana-2873	386	12	)	)	PUNCT
cana-2873	386	13	and	and	CCONJ
cana-2873	386	14	a	a	DET
cana-2873	386	15	q	q	NOUN
cana-2873	386	16	-	-	PUNCT
cana-2873	386	17	nsos	nsos	NOUN
cana-2873	386	18	(	(	PUNCT
cana-2873	386	19	ψ̃	ψ̃	PROPN
cana-2873	386	20	)	)	PUNCT
cana-2873	386	21	in	in	ADP
cana-2873	386	22	(	(	PUNCT
cana-2873	386	23	z1	z1	NOUN
cana-2873	386	24	,	,	PUNCT
cana-2873	386	25	γq	γq	ADP
cana-2873	386	26	)	)	PUNCT
cana-2873	386	27	such	such	ADJ
cana-2873	386	28	that	that	SCONJ
cana-2873	386	29	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	386	30	)	)	PUNCT
cana-2873	386	31	⊆	⊆	NUM
cana-2873	386	32	(	(	PUNCT
cana-2873	386	33	ψ̃	ψ̃	PROPN
cana-2873	386	34	)	)	PUNCT
cana-2873	386	35	.	.	PUNCT
cana-2873	387	1	then	then	ADV
cana-2873	387	2	(	(	PUNCT
cana-2873	387	3	ã	ã	PROPN
cana-2873	387	4	)	)	PUNCT
cana-2873	387	5	=	=	PUNCT
cana-2873	387	6	(	(	PUNCT
cana-2873	387	7	k(ψ̃)c)c	k(ψ̃)c)c	PROPN
cana-2873	387	8	is	be	AUX
cana-2873	387	9	q	q	NOUN
cana-2873	387	10	-	-	PUNCT
cana-2873	387	11	nsβos	nsβos	NOUN
cana-2873	387	12	of	of	ADP
cana-2873	387	13	(	(	PUNCT
cana-2873	387	14	z2	z2	PROPN
cana-2873	387	15	,	,	PUNCT
cana-2873	387	16	σq	σq	NOUN
cana-2873	387	17	)	)	PUNCT
cana-2873	387	18	such	such	ADJ
cana-2873	387	19	that	that	SCONJ
cana-2873	387	20	k−1(ã	k−1(ã	NOUN
cana-2873	387	21	)	)	PUNCT
cana-2873	387	22	⊆	⊆	NUM
cana-2873	387	23	(	(	PUNCT
cana-2873	387	24	ψ̃	ψ̃	PROPN
cana-2873	387	25	)	)	PUNCT
cana-2873	387	26	.	.	PUNCT
cana-2873	388	1	sufficiency	sufficiency	NOUN
cana-2873	388	2	:	:	PUNCT
cana-2873	388	3	assume	assume	VERB
cana-2873	388	4	(	(	PUNCT
cana-2873	388	5	ψ̃	ψ̃	PROPN
cana-2873	388	6	)	)	PUNCT
cana-2873	388	7	is	be	AUX
cana-2873	388	8	a	a	DET
cana-2873	388	9	q	q	NOUN
cana-2873	388	10	-	-	PUNCT
cana-2873	388	11	nsos	nsos	NOUN
cana-2873	388	12	of	of	ADP
cana-2873	388	13	(	(	PUNCT
cana-2873	388	14	z1	z1	VERB
cana-2873	388	15	,	,	PUNCT
cana-2873	388	16	γq	γq	ADP
cana-2873	388	17	)	)	PUNCT
cana-2873	388	18	.	.	PUNCT
cana-2873	389	1	so	so	ADV
cana-2873	389	2	k−1((k(ψ̃))c	k−1((k(ψ̃))c	PROPN
cana-2873	389	3	)	)	PUNCT
cana-2873	390	1	⊆	⊆	NUM
cana-2873	390	2	(	(	PUNCT
cana-2873	390	3	ψ̃)c	ψ̃)c	PROPN
cana-2873	390	4	and	and	CCONJ
cana-2873	390	5	(	(	PUNCT
cana-2873	390	6	ψ̃)c	ψ̃)c	PROPN
cana-2873	390	7	is	be	AUX
cana-2873	390	8	qnscs	qnsc	NOUN
cana-2873	390	9	in	in	ADP
cana-2873	390	10	(	(	PUNCT
cana-2873	390	11	z1	z1	NOUN
cana-2873	390	12	,	,	PUNCT
cana-2873	390	13	γq	γq	ADP
cana-2873	390	14	)	)	PUNCT
cana-2873	390	15	.	.	PUNCT
cana-2873	391	1	by	by	ADP
cana-2873	391	2	presumption	presumption	NOUN
cana-2873	391	3	,	,	PUNCT
cana-2873	391	4	there	there	PRON
cana-2873	391	5	is	be	VERB
cana-2873	391	6	a	a	DET
cana-2873	391	7	q	q	ADJ
cana-2873	391	8	-	-	PUNCT
cana-2873	391	9	nsβos	nsβos	NOUN
cana-2873	391	10	ã	ã	PROPN
cana-2873	391	11	of	of	ADP
cana-2873	391	12	(	(	PUNCT
cana-2873	391	13	z2	z2	PROPN
cana-2873	391	14	,	,	PUNCT
cana-2873	391	15	σq	σq	NOUN
cana-2873	391	16	)	)	PUNCT
cana-2873	391	17	such	such	ADJ
cana-2873	391	18	that	that	PRON
cana-2873	391	19	(	(	PUNCT
cana-2873	391	20	k(ψ̃))c⊆(ã	k(ψ̃))c⊆(ã	NOUN
cana-2873	391	21	)	)	PUNCT
cana-2873	391	22	and	and	CCONJ
cana-2873	391	23	k−1(ã)⊆(ψ̃)c	k−1(ã)⊆(ψ̃)c	ADJ
cana-2873	391	24	.	.	PUNCT
cana-2873	392	1	therefore	therefore	ADV
cana-2873	392	2	(	(	PUNCT
cana-2873	392	3	ψ̃)⊆(k−1(ã))c	ψ̃)⊆(k−1(ã))c	ADJ
cana-2873	392	4	.hence	.hence	PROPN
cana-2873	392	5	(	(	PUNCT
cana-2873	392	6	ã)c⊆k(ψ̃)⊆	ã)c⊆k(ψ̃)⊆	ADJ
cana-2873	392	7	k((k−1(ã))c	k((k−1(ã))c	NOUN
cana-2873	392	8	)	)	PUNCT
cana-2873	392	9	⊆(ã)c	⊆(ã)c	NOUN
cana-2873	392	10	which	which	PRON
cana-2873	392	11	implies	imply	VERB
cana-2873	392	12	k(ψ̃	k(ψ̃	NOUN
cana-2873	392	13	)	)	PUNCT
cana-2873	392	14	=	=	SYM
cana-2873	393	1	(	(	PUNCT
cana-2873	393	2	ã)c.as	ã)c.as	X
cana-2873	393	3	(	(	PUNCT
cana-2873	393	4	ã)c	ã)c	PROPN
cana-2873	393	5	is	be	AUX
cana-2873	393	6	q	q	ADJ
cana-2873	393	7	-	-	PUNCT
cana-2873	393	8	nsβcs	nsβcs	NOUN
cana-2873	393	9	of	of	ADP
cana-2873	393	10	(	(	PUNCT
cana-2873	393	11	z2	z2	PROPN
cana-2873	393	12	,	,	PUNCT
cana-2873	393	13	σq	σq	NOUN
cana-2873	393	14	)	)	PUNCT
cana-2873	393	15	,	,	PUNCT
cana-2873	393	16	k(ψ̃	k(ψ̃	PROPN
cana-2873	393	17	)	)	PUNCT
cana-2873	393	18	is	be	AUX
cana-2873	393	19	q	q	ADJ
cana-2873	393	20	-	-	NOUN
cana-2873	393	21	nsβcs	nsβcs	NOUN
cana-2873	393	22	in	in	ADP
cana-2873	393	23	(	(	PUNCT
cana-2873	393	24	z2	z2	PROPN
cana-2873	393	25	,	,	PUNCT
cana-2873	393	26	σq	σq	NOUN
cana-2873	393	27	)	)	PUNCT
cana-2873	393	28	and	and	CCONJ
cana-2873	393	29	hence	hence	ADV
cana-2873	393	30	k	k	PROPN
cana-2873	393	31	is	be	AUX
cana-2873	393	32	q	q	ADJ
cana-2873	393	33	-	-	PUNCT
cana-2873	393	34	nscβo	nscβo	ADJ
cana-2873	393	35	mapping	mapping	NOUN
cana-2873	393	36	.	.	PUNCT
cana-2873	394	1	theorem	theorem	VERB
cana-2873	394	2	5.9	5.9	NUM
cana-2873	394	3	.	.	PUNCT
cana-2873	395	1	a	a	DET
cana-2873	395	2	mapping	mapping	NOUN
cana-2873	395	3	k	k	NOUN
cana-2873	395	4	:	:	PUNCT
cana-2873	395	5	(	(	PUNCT
cana-2873	395	6	z1	z1	VERB
cana-2873	395	7	,	,	PUNCT
cana-2873	395	8	γq	γq	ADP
cana-2873	395	9	)	)	PUNCT
cana-2873	395	10	→	→	SYM
cana-2873	395	11	(	(	PUNCT
cana-2873	395	12	z2	z2	PROPN
cana-2873	395	13	,	,	PUNCT
cana-2873	395	14	σq	σq	NOUN
cana-2873	395	15	)	)	PUNCT
cana-2873	395	16	is	be	AUX
cana-2873	395	17	q	q	NOUN
cana-2873	395	18	-	-	PUNCT
cana-2873	395	19	nscβo	nscβo	ADV
cana-2873	395	20	iff	iff	PROPN
cana-2873	395	21	k−1(q	k−1(q	PROPN
cana-2873	395	22	-	-	PUNCT
cana-2873	395	23	nsβcl(ψ̃	nsβcl(ψ̃	NOUN
cana-2873	395	24	)	)	PUNCT
cana-2873	395	25	)	)	PUNCT
cana-2873	395	26	⊇	⊇	NOUN
cana-2873	395	27	qnsint(k−1(ψ̃	qnsint(k−1(ψ̃	NOUN
cana-2873	395	28	)	)	PUNCT
cana-2873	395	29	)	)	PUNCT
cana-2873	395	30	for	for	ADP
cana-2873	395	31	every	every	DET
cana-2873	395	32	q	q	ADJ
cana-2873	395	33	-	-	PUNCT
cana-2873	395	34	nss	nss	NOUN
cana-2873	395	35	ψ̃	ψ̃	PROPN
cana-2873	395	36	of	of	ADP
cana-2873	395	37	(	(	PUNCT
cana-2873	395	38	z2	z2	PROPN
cana-2873	395	39	,	,	PUNCT
cana-2873	395	40	σq	σq	NOUN
cana-2873	395	41	)	)	PUNCT
cana-2873	395	42	.	.	PUNCT
cana-2873	396	1	proof	proof	NOUN
cana-2873	396	2	.	.	PUNCT
cana-2873	397	1	necessity	necessity	NOUN
cana-2873	397	2	:	:	PUNCT
cana-2873	397	3	let	let	VERB
cana-2873	397	4	k	k	PRON
cana-2873	397	5	be	be	AUX
cana-2873	397	6	a	a	DET
cana-2873	397	7	q	q	ADJ
cana-2873	397	8	-	-	PUNCT
cana-2873	397	9	nscβo	nscβo	ADJ
cana-2873	397	10	mapping	mapping	NOUN
cana-2873	397	11	.	.	PUNCT
cana-2873	398	1	for	for	ADP
cana-2873	398	2	any	any	DET
cana-2873	398	3	q	q	ADJ
cana-2873	398	4	-	-	PUNCT
cana-2873	398	5	nss	nss	NOUN
cana-2873	398	6	ψ̃	ψ̃	PROPN
cana-2873	398	7	of	of	ADP
cana-2873	398	8	(	(	PUNCT
cana-2873	398	9	z2	z2	PROPN
cana-2873	398	10	,	,	PUNCT
cana-2873	398	11	σq	σq	NOUN
cana-2873	398	12	)	)	PUNCT
cana-2873	398	13	,	,	PUNCT
cana-2873	398	14	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	398	15	)	)	PUNCT
cana-2873	398	16	⊆	⊆	NUM
cana-2873	398	17	q	q	NOUN
cana-2873	398	18	-	-	PUNCT
cana-2873	398	19	nscl(k−1(ψ̃	nscl(k−1(ψ̃	NOUN
cana-2873	398	20	)	)	PUNCT
cana-2873	398	21	)	)	PUNCT
cana-2873	398	22	.	.	PUNCT
cana-2873	399	1	therefore	therefore	ADV
cana-2873	399	2	by	by	ADP
cana-2873	399	3	theorem	theorem	NOUN
cana-2873	399	4	5.8	5.8	NUM
cana-2873	399	5	,	,	PUNCT
cana-2873	399	6	there	there	PRON
cana-2873	399	7	exists	exist	VERB
cana-2873	399	8	a	a	DET
cana-2873	399	9	q	q	NOUN
cana-2873	399	10	-	-	PUNCT
cana-2873	399	11	nsβos	nsβos	NOUN
cana-2873	399	12	(	(	PUNCT
cana-2873	399	13	ψ̃	ψ̃	PROPN
cana-2873	399	14	)	)	PUNCT
cana-2873	399	15	in	in	ADP
cana-2873	399	16	(	(	PUNCT
cana-2873	399	17	z2	z2	PROPN
cana-2873	399	18	,	,	PUNCT
cana-2873	399	19	σq	σq	NOUN
cana-2873	399	20	)	)	PUNCT
cana-2873	399	21	∋	∋	NOUN
cana-2873	399	22	(	(	PUNCT
cana-2873	399	23	ψ̃	ψ̃	PROPN
cana-2873	399	24	)	)	PUNCT
cana-2873	399	25	⊇	⊇	NOUN
cana-2873	399	26	(	(	PUNCT
cana-2873	399	27	ψ̃	ψ̃	PROPN
cana-2873	399	28	)	)	PUNCT
cana-2873	399	29	&	&	CCONJ
cana-2873	399	30	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	399	31	)	)	PUNCT
cana-2873	399	32	⊇q	⊇q	NOUN
cana-2873	399	33	-	-	PUNCT
cana-2873	399	34	nsint(k−1(ψ̃	nsint(k−1(ψ̃	NOUN
cana-2873	399	35	)	)	PUNCT
cana-2873	399	36	)	)	PUNCT
cana-2873	399	37	.	.	PUNCT
cana-2873	400	1	hence	hence	ADV
cana-2873	400	2	k−1(q	k−1(q	ADV
cana-2873	400	3	-	-	PUNCT
cana-2873	400	4	nsβcl(ψ̃	nsβcl(ψ̃	NOUN
cana-2873	400	5	)	)	PUNCT
cana-2873	400	6	)	)	PUNCT
cana-2873	400	7	⊇	⊇	ADJ
cana-2873	400	8	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	400	9	)	)	PUNCT
cana-2873	400	10	⊇	⊇	NOUN
cana-2873	400	11	q	q	NOUN
cana-2873	400	12	-	-	PUNCT
cana-2873	400	13	nsint(k−1(ψ̃	nsint(k−1(ψ̃	NOUN
cana-2873	400	14	)	)	PUNCT
cana-2873	400	15	)	)	PUNCT
cana-2873	400	16	.	.	PUNCT
cana-2873	401	1	sufficiency	sufficiency	NOUN
cana-2873	401	2	:	:	PUNCT
cana-2873	401	3	let	let	VERB
cana-2873	401	4	ψ̃	ψ̃	NOUN
cana-2873	401	5	be	be	AUX
cana-2873	401	6	a	a	DET
cana-2873	401	7	q	q	NOUN
cana-2873	401	8	-	-	PUNCT
cana-2873	401	9	nss	nss	NOUN
cana-2873	401	10	in	in	ADP
cana-2873	401	11	(	(	PUNCT
cana-2873	401	12	z2	z2	PROPN
cana-2873	401	13	,	,	PUNCT
cana-2873	401	14	σq	σq	NOUN
cana-2873	401	15	)	)	PUNCT
cana-2873	401	16	and	and	CCONJ
cana-2873	401	17	(	(	PUNCT
cana-2873	401	18	ψ̃	ψ̃	PROPN
cana-2873	401	19	)	)	PUNCT
cana-2873	401	20	be	be	VERB
cana-2873	401	21	a	a	DET
cana-2873	401	22	q	q	NOUN
cana-2873	401	23	-	-	PUNCT
cana-2873	401	24	nscs	nscs	NOUN
cana-2873	401	25	of	of	ADP
cana-2873	401	26	(	(	PUNCT
cana-2873	401	27	z1	z1	VERB
cana-2873	401	28	,	,	PUNCT
cana-2873	401	29	γq	γq	ADP
cana-2873	401	30	)	)	PUNCT
cana-2873	401	31	containing	contain	VERB
cana-2873	401	32	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	401	33	)	)	PUNCT
cana-2873	401	34	.	.	PUNCT
cana-2873	402	1	put	put	NOUN
cana-2873	402	2	(	(	PUNCT
cana-2873	402	3	ã	ã	PROPN
cana-2873	402	4	)	)	PUNCT
cana-2873	402	5	=	=	SYM
cana-2873	403	1	q	q	NOUN
cana-2873	403	2	-	-	PUNCT
cana-2873	403	3	nscl(ψ̃	nscl(ψ̃	NOUN
cana-2873	403	4	)	)	PUNCT
cana-2873	403	5	,	,	PUNCT
cana-2873	403	6	then	then	ADV
cana-2873	403	7	(	(	PUNCT
cana-2873	403	8	ψ̃)⊆(ã	ψ̃)⊆(ã	NOUN
cana-2873	403	9	)	)	PUNCT
cana-2873	403	10	and	and	CCONJ
cana-2873	403	11	ã	ã	PROPN
cana-2873	403	12	is	be	AUX
cana-2873	403	13	q	q	NOUN
cana-2873	403	14	-	-	PUNCT
cana-2873	403	15	nsβc	nsβc	NOUN
cana-2873	403	16	and	and	CCONJ
cana-2873	403	17	k−1(ã	k−1(ã	NOUN
cana-2873	403	18	)	)	PUNCT
cana-2873	403	19	⊆qnsint(k−1(ψ̃	⊆qnsint(k−1(ψ̃	NOUN
cana-2873	403	20	)	)	PUNCT
cana-2873	403	21	)	)	PUNCT
cana-2873	404	1	⊆(ψ̃	⊆(ψ̃	PROPN
cana-2873	404	2	)	)	PUNCT
cana-2873	404	3	.	.	PUNCT
cana-2873	405	1	thus	thus	ADV
cana-2873	405	2	by	by	ADP
cana-2873	405	3	theorem	theorem	NOUN
cana-2873	405	4	5.8	5.8	NUM
cana-2873	405	5	,	,	PUNCT
cana-2873	405	6	k	k	PROPN
cana-2873	405	7	is	be	AUX
cana-2873	405	8	q	q	ADJ
cana-2873	405	9	-	-	ADJ
cana-2873	405	10	q	q	ADJ
cana-2873	405	11	-	-	PUNCT
cana-2873	405	12	nsɕβo	nsɕβo	NOUN
cana-2873	405	13	mapping	mapping	NOUN
cana-2873	405	14	.	.	PUNCT
cana-2873	406	1	theorem	theorem	VERB
cana-2873	406	2	5.10	5.10	NUM
cana-2873	406	3	.	.	PUNCT
cana-2873	407	1	if	if	SCONJ
cana-2873	407	2	k	k	X
cana-2873	407	3	:	:	PUNCT
cana-2873	407	4	(	(	PUNCT
cana-2873	407	5	z1	z1	VERB
cana-2873	407	6	,	,	PUNCT
cana-2873	407	7	γq	γq	ADP
cana-2873	407	8	)	)	PUNCT
cana-2873	407	9	→	→	SYM
cana-2873	407	10	(	(	PUNCT
cana-2873	407	11	z2	z2	PROPN
cana-2873	407	12	,	,	PUNCT
cana-2873	407	13	σq	σq	NOUN
cana-2873	407	14	)	)	PUNCT
cana-2873	407	15	and	and	CCONJ
cana-2873	407	16	g	g	NOUN
cana-2873	407	17	:	:	PUNCT
cana-2873	407	18	(	(	PUNCT
cana-2873	407	19	z2	z2	NOUN
cana-2873	407	20	,	,	PUNCT
cana-2873	407	21	σq	σq	NOUN
cana-2873	407	22	)	)	PUNCT
cana-2873	407	23	→	→	SYM
cana-2873	407	24	(	(	PUNCT
cana-2873	407	25	z3	z3	PROPN
cana-2873	407	26	,	,	PUNCT
cana-2873	407	27	ρq	ρq	NUM
cana-2873	407	28	)	)	PUNCT
cana-2873	407	29	be	be	AUX
cana-2873	407	30	two	two	NUM
cana-2873	407	31	quadripartitioned	quadripartitione	VERB
cana-2873	407	32	neutrosophic	neutrosophic	ADJ
cana-2873	407	33	mappings	mapping	NOUN
cana-2873	407	34	and	and	CCONJ
cana-2873	407	35	g	g	ADP
cana-2873	407	36	◦	◦	NOUN
cana-2873	407	37	k	k	X
cana-2873	407	38	:	:	PUNCT
cana-2873	407	39	(	(	PUNCT
cana-2873	407	40	z1	z1	VERB
cana-2873	407	41	,	,	PUNCT
cana-2873	407	42	γq	γq	ADP
cana-2873	407	43	)	)	PUNCT
cana-2873	407	44	→	→	SYM
cana-2873	407	45	(	(	PUNCT
cana-2873	407	46	z3	z3	PROPN
cana-2873	407	47	,	,	PUNCT
cana-2873	407	48	ρq	ρq	NOUN
cana-2873	407	49	)	)	PUNCT
cana-2873	407	50	is	be	AUX
cana-2873	407	51	q	q	NOUN
cana-2873	407	52	-	-	PUNCT
cana-2873	407	53	nsɕβo	nsɕβo	NOUN
cana-2873	407	54	.	.	PUNCT
cana-2873	408	1	if	if	SCONJ
cana-2873	408	2	g	g	NOUN
cana-2873	408	3	:	:	PUNCT
cana-2873	408	4	(	(	PUNCT
cana-2873	408	5	z2	z2	NOUN
cana-2873	408	6	,	,	PUNCT
cana-2873	408	7	σq	σq	NOUN
cana-2873	408	8	)	)	PUNCT
cana-2873	408	9	→	→	SYM
cana-2873	408	10	(	(	PUNCT
cana-2873	408	11	z3	z3	PROPN
cana-2873	408	12	,	,	PUNCT
cana-2873	408	13	ρq	ρq	NOUN
cana-2873	408	14	)	)	PUNCT
cana-2873	408	15	is	be	AUX
cana-2873	408	16	q	q	NOUN
cana-2873	408	17	-	-	PUNCT
cana-2873	408	18	nsɕβirr	nsɕβirr	ADJ
cana-2873	408	19	,	,	PUNCT
cana-2873	408	20	then	then	ADV
cana-2873	408	21	k	k	X
cana-2873	408	22	:	:	PUNCT
cana-2873	408	23	(	(	PUNCT
cana-2873	408	24	z1	z1	VERB
cana-2873	408	25	,	,	PUNCT
cana-2873	408	26	γq	γq	ADP
cana-2873	408	27	)	)	PUNCT
cana-2873	408	28	→	→	SYM
cana-2873	408	29	(	(	PUNCT
cana-2873	408	30	z2	z2	PROPN
cana-2873	408	31	,	,	PUNCT
cana-2873	408	32	σq	σq	NOUN
cana-2873	408	33	)	)	PUNCT
cana-2873	408	34	is	be	AUX
cana-2873	408	35	q	q	ADJ
cana-2873	408	36	-	-	PUNCT
cana-2873	408	37	nsɕβo	nsɕβo	NOUN
cana-2873	408	38	mapping	mapping	NOUN
cana-2873	408	39	.	.	PUNCT
cana-2873	409	1	communications	communication	NOUN
cana-2873	409	2	on	on	ADP
cana-2873	409	3	applied	apply	VERB
cana-2873	409	4	nonlinear	nonlinear	ADJ
cana-2873	409	5	analysis	analysis	NOUN
cana-2873	409	6	issn	issn	NOUN
cana-2873	409	7	:	:	PUNCT
cana-2873	409	8	1074	1074	NUM
cana-2873	409	9	-	-	PUNCT
cana-2873	409	10	133x	133x	NUM
cana-2873	409	11	vol	vol	NOUN
cana-2873	409	12	32	32	NUM
cana-2873	409	13	no	no	NOUN
cana-2873	409	14	.	.	PUNCT
cana-2873	410	1	4s	4s	NUM
cana-2873	410	2	(	(	PUNCT
cana-2873	410	3	2025	2025	NUM
cana-2873	410	4	)	)	PUNCT
cana-2873	410	5	591	591	NUM
cana-2873	410	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	410	7	proof	proof	NOUN
cana-2873	410	8	.	.	PUNCT
cana-2873	411	1	let	let	VERB
cana-2873	411	2	(	(	PUNCT
cana-2873	411	3	ψ̃	ψ̃	PROPN
cana-2873	411	4	)	)	PUNCT
cana-2873	411	5	be	be	VERB
cana-2873	411	6	a	a	DET
cana-2873	411	7	q	q	NOUN
cana-2873	411	8	-	-	PUNCT
cana-2873	411	9	nsos	nsos	NOUN
cana-2873	411	10	in	in	ADP
cana-2873	411	11	(	(	PUNCT
cana-2873	411	12	z1	z1	NOUN
cana-2873	411	13	,	,	PUNCT
cana-2873	411	14	γq	γq	ADP
cana-2873	411	15	)	)	PUNCT
cana-2873	411	16	.	.	PUNCT
cana-2873	412	1	then	then	ADV
cana-2873	412	2	g	g	ADP
cana-2873	412	3	◦	◦	NOUN
cana-2873	412	4	k(ψ̃	k(ψ̃	NOUN
cana-2873	412	5	)	)	PUNCT
cana-2873	412	6	is	be	AUX
cana-2873	412	7	q	q	ADJ
cana-2873	412	8	-	-	PUNCT
cana-2873	412	9	nsβcs	nsβcs	NOUN
cana-2873	412	10	of	of	ADP
cana-2873	412	11	(	(	PUNCT
cana-2873	412	12	z3	z3	PROPN
cana-2873	412	13	,	,	PUNCT
cana-2873	412	14	ρq	ρq	NOUN
cana-2873	412	15	)	)	PUNCT
cana-2873	412	16	because	because	SCONJ
cana-2873	412	17	g	g	PROPN
cana-2873	412	18	◦	◦	NOUN
cana-2873	412	19	k	k	PROPN
cana-2873	412	20	is	be	AUX
cana-2873	412	21	qnsɕβo	qnsɕβo	ADJ
cana-2873	412	22	mapping	mapping	NOUN
cana-2873	412	23	.	.	PUNCT
cana-2873	413	1	as	as	SCONJ
cana-2873	413	2	g	g	PROPN
cana-2873	413	3	is	be	AUX
cana-2873	413	4	q	q	ADJ
cana-2873	413	5	-	-	ADJ
cana-2873	413	6	nscβirr	nscβirr	ADJ
cana-2873	413	7	and	and	CCONJ
cana-2873	413	8	g	g	PROPN
cana-2873	413	9	k(ψ̃	k(ψ̃	PROPN
cana-2873	413	10	)	)	PUNCT
cana-2873	413	11	is	be	AUX
cana-2873	413	12	q	q	ADJ
cana-2873	413	13	-	-	PUNCT
cana-2873	413	14	nsβcs	nsβcs	NOUN
cana-2873	413	15	of	of	ADP
cana-2873	413	16	(	(	PUNCT
cana-2873	413	17	z3	z3	PROPN
cana-2873	413	18	,	,	PUNCT
cana-2873	413	19	ρq	ρq	NOUN
cana-2873	413	20	)	)	PUNCT
cana-2873	413	21	,	,	PUNCT
cana-2873	413	22	g−1(g	g−1(g	PROPN
cana-2873	413	23	∘	∘	PROPN
cana-2873	413	24	k(ψ̃	k(ψ̃	PROPN
cana-2873	413	25	)	)	PUNCT
cana-2873	413	26	)	)	PUNCT
cana-2873	414	1	=	=	SYM
cana-2873	414	2	k(ψ̃	k(ψ̃	NOUN
cana-2873	414	3	)	)	PUNCT
cana-2873	414	4	is	be	AUX
cana-2873	414	5	q	q	NOUN
cana-2873	414	6	-	-	PUNCT
cana-2873	414	7	nsβos	nsβos	NOUN
cana-2873	414	8	in	in	ADP
cana-2873	414	9	(	(	PUNCT
cana-2873	414	10	z2	z2	PROPN
cana-2873	414	11	,	,	PUNCT
cana-2873	414	12	σq	σq	NOUN
cana-2873	414	13	)	)	PUNCT
cana-2873	414	14	.	.	PUNCT
cana-2873	415	1	hence	hence	ADV
cana-2873	415	2	k	k	PROPN
cana-2873	415	3	is	be	AUX
cana-2873	415	4	q	q	ADJ
cana-2873	415	5	-	-	PUNCT
cana-2873	415	6	nsɕβo	nsɕβo	NOUN
cana-2873	415	7	mapping	mapping	NOUN
cana-2873	415	8	.	.	PUNCT
cana-2873	416	1	theorem	theorem	VERB
cana-2873	416	2	5.11	5.11	NUM
cana-2873	416	3	.	.	PUNCT
cana-2873	417	1	if	if	SCONJ
cana-2873	417	2	k	k	X
cana-2873	417	3	:	:	PUNCT
cana-2873	417	4	(	(	PUNCT
cana-2873	417	5	z1	z1	VERB
cana-2873	417	6	,	,	PUNCT
cana-2873	417	7	γq	γq	ADP
cana-2873	417	8	)	)	PUNCT
cana-2873	417	9	→	→	SYM
cana-2873	417	10	(	(	PUNCT
cana-2873	417	11	z2	z2	PROPN
cana-2873	417	12	,	,	PUNCT
cana-2873	417	13	σq	σq	NOUN
cana-2873	417	14	)	)	PUNCT
cana-2873	417	15	is	be	AUX
cana-2873	417	16	q	q	NOUN
cana-2873	417	17	-	-	PUNCT
cana-2873	417	18	nso	nso	NOUN
cana-2873	417	19	&	&	CCONJ
cana-2873	417	20	g	g	PROPN
cana-2873	417	21	:	:	PUNCT
cana-2873	417	22	(	(	PUNCT
cana-2873	417	23	z2	z2	NOUN
cana-2873	417	24	,	,	PUNCT
cana-2873	417	25	σq	σq	NOUN
cana-2873	417	26	)	)	PUNCT
cana-2873	417	27	→	→	SYM
cana-2873	417	28	(	(	PUNCT
cana-2873	417	29	z3	z3	PROPN
cana-2873	417	30	,	,	PUNCT
cana-2873	417	31	ρq	ρq	NOUN
cana-2873	417	32	)	)	PUNCT
cana-2873	417	33	is	be	AUX
cana-2873	417	34	q	q	ADJ
cana-2873	417	35	-	-	PUNCT
cana-2873	417	36	nsɕβo	nsɕβo	NOUN
cana-2873	417	37	mappings	mapping	NOUN
cana-2873	417	38	,	,	PUNCT
cana-2873	417	39	then	then	ADV
cana-2873	417	40	g	g	PROPN
cana-2873	417	41	◦	◦	PROPN
cana-2873	417	42	k	k	X
cana-2873	417	43	:	:	PUNCT
cana-2873	417	44	(	(	PUNCT
cana-2873	417	45	z1	z1	VERB
cana-2873	417	46	,	,	PUNCT
cana-2873	417	47	γq	γq	ADP
cana-2873	417	48	)	)	PUNCT
cana-2873	417	49	→	→	SYM
cana-2873	417	50	(	(	PUNCT
cana-2873	417	51	z3	z3	PROPN
cana-2873	417	52	,	,	PUNCT
cana-2873	417	53	ρq	ρq	NOUN
cana-2873	417	54	)	)	PUNCT
cana-2873	417	55	is	be	AUX
cana-2873	417	56	q	q	NOUN
cana-2873	417	57	-	-	PUNCT
cana-2873	417	58	nsɕβo	nsɕβo	NOUN
cana-2873	417	59	.	.	PUNCT
cana-2873	418	1	proof	proof	NOUN
cana-2873	418	2	.	.	PUNCT
cana-2873	419	1	let	let	VERB
cana-2873	419	2	(	(	PUNCT
cana-2873	419	3	ψ̃	ψ̃	PROPN
cana-2873	419	4	)	)	PUNCT
cana-2873	419	5	be	be	VERB
cana-2873	419	6	a	a	DET
cana-2873	419	7	q	q	NOUN
cana-2873	419	8	-	-	PUNCT
cana-2873	419	9	nsos	nsos	NOUN
cana-2873	419	10	in	in	ADP
cana-2873	419	11	(	(	PUNCT
cana-2873	419	12	z1	z1	NOUN
cana-2873	419	13	,	,	PUNCT
cana-2873	419	14	γq	γq	ADP
cana-2873	419	15	)	)	PUNCT
cana-2873	419	16	.	.	PUNCT
cana-2873	420	1	then	then	ADV
cana-2873	420	2	k(ψ̃	k(ψ̃	PROPN
cana-2873	420	3	)	)	PUNCT
cana-2873	420	4	is	be	AUX
cana-2873	420	5	a	a	DET
cana-2873	420	6	q	q	NOUN
cana-2873	420	7	-	-	PUNCT
cana-2873	420	8	nsos	nsos	NOUN
cana-2873	420	9	of	of	ADP
cana-2873	420	10	(	(	PUNCT
cana-2873	420	11	z2	z2	PROPN
cana-2873	420	12	,	,	PUNCT
cana-2873	420	13	σq	σq	NOUN
cana-2873	420	14	)	)	PUNCT
cana-2873	420	15	because	because	SCONJ
cana-2873	420	16	k	k	PROPN
cana-2873	420	17	is	be	AUX
cana-2873	420	18	a	a	DET
cana-2873	420	19	qnso	qnso	NOUN
cana-2873	420	20	mapping	mapping	NOUN
cana-2873	420	21	.	.	PUNCT
cana-2873	421	1	as	as	SCONJ
cana-2873	421	2	g	g	PROPN
cana-2873	421	3	is	be	AUX
cana-2873	421	4	q	q	NOUN
cana-2873	421	5	-	-	PUNCT
cana-2873	421	6	nsɕβo	nsɕβo	NOUN
cana-2873	421	7	,	,	PUNCT
cana-2873	421	8	g(k(ψ̃	g(k(ψ̃	NOUN
cana-2873	421	9	)	)	PUNCT
cana-2873	421	10	)	)	PUNCT
cana-2873	422	1	=	=	PRON
cana-2873	422	2	(	(	PUNCT
cana-2873	422	3	g∘	g∘	PROPN
cana-2873	422	4	k)(ψ̃	k)(ψ̃	PROPN
cana-2873	422	5	)	)	PUNCT
cana-2873	422	6	is	be	AUX
cana-2873	422	7	a	a	DET
cana-2873	422	8	q	q	NOUN
cana-2873	422	9	-	-	PUNCT
cana-2873	422	10	nsβcs	nsβcs	NOUN
cana-2873	422	11	of	of	ADP
cana-2873	422	12	(	(	PUNCT
cana-2873	422	13	z3	z3	PROPN
cana-2873	422	14	,	,	PUNCT
cana-2873	422	15	ρq	ρq	NOUN
cana-2873	422	16	)	)	PUNCT
cana-2873	422	17	.	.	PUNCT
cana-2873	423	1	thus	thus	ADV
cana-2873	423	2	g	g	PROPN
cana-2873	423	3	k	k	PROPN
cana-2873	423	4	is	be	AUX
cana-2873	423	5	q	q	ADJ
cana-2873	423	6	-	-	PUNCT
cana-2873	423	7	nsɕβo	nsɕβo	NOUN
cana-2873	423	8	mapping	mapping	NOUN
cana-2873	423	9	.	.	PUNCT
cana-2873	424	1	6	6	NUM
cana-2873	424	2	quadripartitioned	quadripartitione	VERB
cana-2873	424	3	neutrosophic	neutrosophic	PROPN
cana-2873	424	4	contra	contra	PROPN
cana-2873	424	5	β	β	PROPN
cana-2873	424	6	-	-	PUNCT
cana-2873	424	7	closed	closed	ADJ
cana-2873	424	8	mapping	mapping	NOUN
cana-2873	424	9	in	in	ADP
cana-2873	424	10	this	this	DET
cana-2873	424	11	section	section	NOUN
cana-2873	424	12	,	,	PUNCT
cana-2873	424	13	quadripartitioned	quadripartitione	VERB
cana-2873	424	14	neutrosophic	neutrosophic	PROPN
cana-2873	424	15	contra	contra	PROPN
cana-2873	424	16	β	β	PROPN
cana-2873	424	17	-	-	PUNCT
cana-2873	424	18	closed	closed	ADJ
cana-2873	424	19	maps	map	NOUN
cana-2873	424	20	are	be	AUX
cana-2873	424	21	introduced	introduce	VERB
cana-2873	424	22	and	and	CCONJ
cana-2873	424	23	some	some	PRON
cana-2873	424	24	of	of	ADP
cana-2873	424	25	its	its	PRON
cana-2873	424	26	properties	property	NOUN
cana-2873	424	27	are	be	AUX
cana-2873	424	28	discussed	discuss	VERB
cana-2873	424	29	.	.	PUNCT
cana-2873	425	1	definition	definition	NOUN
cana-2873	425	2	6.1	6.1	NUM
cana-2873	425	3	.	.	PUNCT
cana-2873	426	1	a	a	DET
cana-2873	426	2	mapping	mapping	NOUN
cana-2873	426	3	k	k	NOUN
cana-2873	426	4	:	:	PUNCT
cana-2873	426	5	(	(	PUNCT
cana-2873	426	6	z1	z1	VERB
cana-2873	426	7	,	,	PUNCT
cana-2873	426	8	γq	γq	ADP
cana-2873	426	9	)	)	PUNCT
cana-2873	426	10	→	→	SYM
cana-2873	426	11	(	(	PUNCT
cana-2873	426	12	z2	z2	PROPN
cana-2873	426	13	,	,	PUNCT
cana-2873	426	14	σq	σq	NOUN
cana-2873	426	15	)	)	PUNCT
cana-2873	426	16	is	be	AUX
cana-2873	426	17	quadripartitioned	quadripartitione	VERB
cana-2873	426	18	neutrosophic	neutrosophic	PROPN
cana-2873	426	19	contra	contra	PROPN
cana-2873	426	20	(	(	PUNCT
cana-2873	426	21	resp	resp	PROPN
cana-2873	426	22	.	.	PUNCT
cana-2873	427	1	semi	semi	ADJ
cana-2873	427	2	,	,	PUNCT
cana-2873	427	3	pre	pre	ADJ
cana-2873	427	4	,	,	PUNCT
cana-2873	427	5	b	b	PROPN
cana-2873	427	6	&	&	CCONJ
cana-2873	427	7	β	β	NOUN
cana-2873	427	8	)	)	PUNCT
cana-2873	427	9	closed	close	VERB
cana-2873	427	10	(	(	PUNCT
cana-2873	427	11	in	in	ADP
cana-2873	427	12	short	short	ADJ
cana-2873	427	13	,	,	PUNCT
cana-2873	427	14	q	q	NOUN
cana-2873	427	15	-	-	PUNCT
cana-2873	427	16	nscc	nscc	ADJ
cana-2873	427	17	(	(	PUNCT
cana-2873	427	18	resp	resp	NOUN
cana-2873	427	19	.	.	PUNCT
cana-2873	428	1	q	q	X
cana-2873	428	2	-	-	PUNCT
cana-2873	428	3	nscsc	nscsc	NOUN
cana-2873	428	4	,	,	PUNCT
cana-2873	428	5	q	q	NOUN
cana-2873	428	6	-	-	PUNCT
cana-2873	428	7	nscpc	nscpc	ADJ
cana-2873	428	8	,	,	PUNCT
cana-2873	428	9	q	q	NOUN
cana-2873	428	10	-	-	PUNCT
cana-2873	428	11	nscbc	nscbc	PROPN
cana-2873	428	12	&	&	CCONJ
cana-2873	428	13	q	q	NOUN
cana-2873	428	14	-	-	PUNCT
cana-2873	428	15	nscβc	nscβc	NOUN
cana-2873	428	16	)	)	PUNCT
cana-2873	428	17	)	)	PUNCT
cana-2873	429	1	if	if	SCONJ
cana-2873	429	2	the	the	DET
cana-2873	429	3	image	image	NOUN
cana-2873	429	4	of	of	ADP
cana-2873	429	5	each	each	DET
cana-2873	429	6	q	q	ADJ
cana-2873	429	7	-	-	PUNCT
cana-2873	429	8	nsc	nsc	NOUN
cana-2873	429	9	set	set	NOUN
cana-2873	429	10	of	of	ADP
cana-2873	429	11	(	(	PUNCT
cana-2873	429	12	z1	z1	NOUN
cana-2873	429	13	,	,	PUNCT
cana-2873	429	14	γq	γq	NOUN
cana-2873	429	15	)	)	PUNCT
cana-2873	429	16	is	be	AUX
cana-2873	429	17	q	q	NOUN
cana-2873	429	18	-	-	PUNCT
cana-2873	429	19	nso	nso	NOUN
cana-2873	429	20	(	(	PUNCT
cana-2873	429	21	resp	resp	NOUN
cana-2873	429	22	.	.	PUNCT
cana-2873	430	1	q	q	X
cana-2873	430	2	-	-	PUNCT
cana-2873	430	3	nsso	nsso	ADJ
cana-2873	430	4	,	,	PUNCT
cana-2873	430	5	q	q	NOUN
cana-2873	430	6	-	-	PUNCT
cana-2873	430	7	nspo	nspo	NOUN
cana-2873	430	8	,	,	PUNCT
cana-2873	430	9	q	q	NOUN
cana-2873	430	10	-	-	PUNCT
cana-2873	430	11	nsbo	nsbo	PROPN
cana-2873	430	12	&	&	CCONJ
cana-2873	430	13	q	q	NOUN
cana-2873	430	14	-	-	PUNCT
cana-2873	430	15	nsβo	nsβo	ADJ
cana-2873	430	16	)	)	PUNCT
cana-2873	430	17	set	set	VERB
cana-2873	430	18	in	in	ADP
cana-2873	430	19	(	(	PUNCT
cana-2873	430	20	z2	z2	PROPN
cana-2873	430	21	,	,	PUNCT
cana-2873	430	22	σq	σq	NOUN
cana-2873	430	23	)	)	PUNCT
cana-2873	430	24	.	.	PUNCT
cana-2873	431	1	proposition	proposition	NOUN
cana-2873	431	2	6.2	6.2	NUM
cana-2873	431	3	.	.	PUNCT
cana-2873	432	1	a	a	DET
cana-2873	432	2	map	map	NOUN
cana-2873	432	3	k	k	X
cana-2873	432	4	:	:	PUNCT
cana-2873	432	5	(	(	PUNCT
cana-2873	432	6	z1	z1	VERB
cana-2873	432	7	,	,	PUNCT
cana-2873	432	8	γq	γq	ADP
cana-2873	432	9	)	)	PUNCT
cana-2873	432	10	→	→	SYM
cana-2873	432	11	(	(	PUNCT
cana-2873	432	12	z2	z2	PROPN
cana-2873	432	13	,	,	PUNCT
cana-2873	432	14	σq	σq	NOUN
cana-2873	432	15	)	)	PUNCT
cana-2873	432	16	,	,	PUNCT
cana-2873	432	17	then	then	ADV
cana-2873	432	18	the	the	DET
cana-2873	432	19	statements	statement	NOUN
cana-2873	432	20	are	be	AUX
cana-2873	432	21	hold	hold	NOUN
cana-2873	432	22	but	but	CCONJ
cana-2873	432	23	the	the	DET
cana-2873	432	24	converse	converse	NOUN
cana-2873	432	25	does	do	AUX
cana-2873	432	26	not	not	PART
cana-2873	432	27	true	true	ADJ
cana-2873	432	28	.	.	PUNCT
cana-2873	433	1	every	every	DET
cana-2873	433	2	(	(	PUNCT
cana-2873	433	3	i	i	NOUN
cana-2873	433	4	)	)	PUNCT
cana-2873	433	5	q	q	NOUN
cana-2873	433	6	-	-	PUNCT
cana-2873	433	7	nsɕc	nsɕc	ADJ
cana-2873	433	8	is	be	AUX
cana-2873	433	9	a	a	DET
cana-2873	433	10	q	q	NOUN
cana-2873	433	11	-	-	PUNCT
cana-2873	433	12	nsɕsc	nsɕsc	NOUN
cana-2873	433	13	.	.	PUNCT
cana-2873	434	1	(	(	PUNCT
cana-2873	434	2	ii	ii	NOUN
cana-2873	434	3	)	)	PUNCT
cana-2873	434	4	q	q	NOUN
cana-2873	434	5	-	-	PUNCT
cana-2873	434	6	nsɕc	nsɕc	ADJ
cana-2873	434	7	is	be	AUX
cana-2873	434	8	a	a	DET
cana-2873	434	9	q	q	NOUN
cana-2873	434	10	-	-	NOUN
cana-2873	434	11	nsɕpc	nsɕpc	NOUN
cana-2873	434	12	.	.	PUNCT
cana-2873	435	1	(	(	PUNCT
cana-2873	435	2	iii	iii	NOUN
cana-2873	435	3	)	)	PUNCT
cana-2873	435	4	q	q	NOUN
cana-2873	435	5	-	-	PUNCT
cana-2873	435	6	nsɕsc	nsɕsc	NOUN
cana-2873	435	7	is	be	AUX
cana-2873	435	8	a	a	DET
cana-2873	435	9	q	q	NOUN
cana-2873	435	10	-	-	PUNCT
cana-2873	435	11	nsɕbc	nsɕbc	NOUN
cana-2873	435	12	.	.	PUNCT
cana-2873	436	1	(	(	PUNCT
cana-2873	436	2	iv	iv	X
cana-2873	436	3	)	)	PUNCT
cana-2873	436	4	q	q	ADJ
cana-2873	436	5	-	-	PUNCT
cana-2873	436	6	nsɕpc	nsɕpc	NOUN
cana-2873	436	7	is	be	AUX
cana-2873	436	8	a	a	DET
cana-2873	436	9	q	q	NOUN
cana-2873	436	10	-	-	PUNCT
cana-2873	436	11	nsɕbc	nsɕbc	NOUN
cana-2873	436	12	.	.	PUNCT
cana-2873	437	1	(	(	PUNCT
cana-2873	437	2	v	v	NOUN
cana-2873	437	3	)	)	PUNCT
cana-2873	437	4	q	q	NOUN
cana-2873	437	5	-	-	PUNCT
cana-2873	437	6	nsɕbc	nsɕbc	NOUN
cana-2873	437	7	is	be	AUX
cana-2873	437	8	a	a	DET
cana-2873	437	9	q	q	NOUN
cana-2873	437	10	-	-	PUNCT
cana-2873	437	11	nsɕβc	nsɕβc	NOUN
cana-2873	437	12	.	.	PUNCT
cana-2873	438	1	proof	proof	NOUN
cana-2873	438	2	.	.	PUNCT
cana-2873	439	1	(	(	PUNCT
cana-2873	439	2	i	i	NOUN
cana-2873	439	3	)	)	PUNCT
cana-2873	439	4	let	let	VERB
cana-2873	439	5	η	η	X
cana-2873	439	6	be	be	AUX
cana-2873	439	7	a	a	DET
cana-2873	439	8	q	q	ADJ
cana-2873	439	9	-	-	PUNCT
cana-2873	439	10	nsc	nsc	NOUN
cana-2873	439	11	set	set	NOUN
cana-2873	439	12	in	in	ADP
cana-2873	439	13	z1	z1	PROPN
cana-2873	439	14	.	.	PUNCT
cana-2873	440	1	since	since	SCONJ
cana-2873	440	2	k	k	PROPN
cana-2873	440	3	is	be	AUX
cana-2873	440	4	q	q	ADJ
cana-2873	440	5	-	-	PUNCT
cana-2873	440	6	nsɕc	nsɕc	ADJ
cana-2873	440	7	,	,	PUNCT
cana-2873	440	8	k(η	k(η	PROPN
cana-2873	440	9	)	)	PUNCT
cana-2873	440	10	is	be	AUX
cana-2873	440	11	a	a	DET
cana-2873	440	12	q	q	NOUN
cana-2873	440	13	-	-	PUNCT
cana-2873	440	14	nso	nso	NOUN
cana-2873	440	15	set	set	VERB
cana-2873	440	16	in	in	ADP
cana-2873	440	17	z2	z2	PROPN
cana-2873	440	18	.	.	PUNCT
cana-2873	441	1	since	since	SCONJ
cana-2873	441	2	every	every	DET
cana-2873	441	3	q	q	NOUN
cana-2873	441	4	-	-	PUNCT
cana-2873	441	5	nsoset	nsoset	NOUN
cana-2873	441	6	is	be	AUX
cana-2873	441	7	a	a	DET
cana-2873	441	8	q	q	ADJ
cana-2873	441	9	-	-	PUNCT
cana-2873	441	10	nsso	nsso	ADJ
cana-2873	441	11	set	set	NOUN
cana-2873	441	12	,	,	PUNCT
cana-2873	441	13	k(η	k(η	PROPN
cana-2873	441	14	)	)	PUNCT
cana-2873	441	15	is	be	AUX
cana-2873	441	16	a	a	DET
cana-2873	441	17	q	q	ADJ
cana-2873	441	18	-	-	PUNCT
cana-2873	441	19	nsso	nsso	ADJ
cana-2873	441	20	set	set	NOUN
cana-2873	441	21	in	in	ADP
cana-2873	441	22	z2	z2	PROPN
cana-2873	441	23	.	.	PUNCT
cana-2873	442	1	hence	hence	ADV
cana-2873	442	2	k	k	PROPN
cana-2873	442	3	is	be	AUX
cana-2873	442	4	a	a	DET
cana-2873	442	5	q	q	NOUN
cana-2873	442	6	-	-	PUNCT
cana-2873	442	7	nsɕsc	nsɕsc	NOUN
cana-2873	442	8	.	.	PUNCT
cana-2873	443	1	(	(	PUNCT
cana-2873	443	2	ii	ii	NOUN
cana-2873	443	3	)	)	PUNCT
cana-2873	443	4	let	let	VERB
cana-2873	443	5	η	η	PROPN
cana-2873	443	6	be	be	AUX
cana-2873	443	7	a	a	DET
cana-2873	443	8	q	q	ADJ
cana-2873	443	9	-	-	PUNCT
cana-2873	443	10	nsc	nsc	NOUN
cana-2873	443	11	set	set	NOUN
cana-2873	443	12	in	in	ADP
cana-2873	443	13	z1	z1	PROPN
cana-2873	443	14	.	.	PUNCT
cana-2873	444	1	since	since	SCONJ
cana-2873	444	2	k	k	PROPN
cana-2873	444	3	is	be	AUX
cana-2873	444	4	q	q	ADJ
cana-2873	444	5	-	-	PUNCT
cana-2873	444	6	nsɕc	nsɕc	ADJ
cana-2873	444	7	,	,	PUNCT
cana-2873	444	8	k(η	k(η	PROPN
cana-2873	444	9	)	)	PUNCT
cana-2873	444	10	is	be	AUX
cana-2873	444	11	a	a	DET
cana-2873	444	12	q	q	NOUN
cana-2873	444	13	-	-	PUNCT
cana-2873	444	14	nso	nso	NOUN
cana-2873	444	15	set	set	VERB
cana-2873	444	16	in	in	ADP
cana-2873	444	17	z2	z2	PROPN
cana-2873	444	18	.	.	PUNCT
cana-2873	445	1	since	since	SCONJ
cana-2873	445	2	every	every	PRON
cana-2873	445	3	q	q	NOUN
cana-2873	445	4	-	-	PUNCT
cana-2873	445	5	ns	ns	ADJ
cana-2873	445	6	ρo	ρo	ADP
cana-2873	445	7	set	set	NOUN
cana-2873	445	8	is	be	AUX
cana-2873	445	9	a	a	DET
cana-2873	445	10	q	q	NOUN
cana-2873	445	11	-	-	PUNCT
cana-2873	445	12	nspo	nspo	NOUN
cana-2873	445	13	set	set	NOUN
cana-2873	445	14	,	,	PUNCT
cana-2873	445	15	k(η	k(η	PROPN
cana-2873	445	16	)	)	PUNCT
cana-2873	445	17	is	be	AUX
cana-2873	445	18	a	a	DET
cana-2873	445	19	q	q	NOUN
cana-2873	445	20	-	-	PUNCT
cana-2873	445	21	nspo	nspo	NOUN
cana-2873	445	22	set	set	VERB
cana-2873	445	23	in	in	ADP
cana-2873	445	24	z2	z2	PROPN
cana-2873	445	25	.	.	PUNCT
cana-2873	446	1	hence	hence	ADV
cana-2873	446	2	k	k	PROPN
cana-2873	446	3	is	be	AUX
cana-2873	446	4	a	a	DET
cana-2873	446	5	q	q	NOUN
cana-2873	446	6	-	-	NOUN
cana-2873	446	7	nsɕpc	nsɕpc	NOUN
cana-2873	446	8	.	.	PUNCT
cana-2873	447	1	(	(	PUNCT
cana-2873	447	2	iii	iii	X
cana-2873	447	3	)	)	PUNCT
cana-2873	447	4	let	let	VERB
cana-2873	447	5	η	η	X
cana-2873	447	6	be	be	AUX
cana-2873	447	7	a	a	DET
cana-2873	447	8	q	q	ADJ
cana-2873	447	9	-	-	PUNCT
cana-2873	447	10	nsc	nsc	NOUN
cana-2873	447	11	set	set	NOUN
cana-2873	447	12	in	in	ADP
cana-2873	447	13	z1	z1	PROPN
cana-2873	447	14	.	.	PUNCT
cana-2873	448	1	since	since	SCONJ
cana-2873	448	2	k	k	PROPN
cana-2873	448	3	is	be	AUX
cana-2873	448	4	q	q	ADJ
cana-2873	448	5	-	-	PUNCT
cana-2873	448	6	nsɕc	nsɕc	ADJ
cana-2873	448	7	,	,	PUNCT
cana-2873	448	8	k(η	k(η	PROPN
cana-2873	448	9	)	)	PUNCT
cana-2873	448	10	is	be	AUX
cana-2873	448	11	a	a	DET
cana-2873	448	12	q	q	NOUN
cana-2873	448	13	-	-	PUNCT
cana-2873	448	14	nsѕo	nsѕo	NOUN
cana-2873	448	15	set	set	VERB
cana-2873	448	16	in	in	ADP
cana-2873	448	17	z2	z2	PROPN
cana-2873	448	18	.	.	PUNCT
cana-2873	449	1	since	since	SCONJ
cana-2873	449	2	every	every	DET
cana-2873	449	3	qns	qns	PROPN
cana-2873	449	4	ѕo	ѕo	ADP
cana-2873	449	5	set	set	NOUN
cana-2873	449	6	is	be	AUX
cana-2873	449	7	a	a	DET
cana-2873	449	8	q	q	ADJ
cana-2873	449	9	-	-	PUNCT
cana-2873	449	10	nsbo	nsbo	NOUN
cana-2873	449	11	set	set	NOUN
cana-2873	449	12	,	,	PUNCT
cana-2873	449	13	k(η	k(η	PROPN
cana-2873	449	14	)	)	PUNCT
cana-2873	449	15	is	be	AUX
cana-2873	449	16	a	a	DET
cana-2873	449	17	q	q	NOUN
cana-2873	449	18	-	-	PUNCT
cana-2873	449	19	nsbo	nsbo	NOUN
cana-2873	449	20	set	set	VERB
cana-2873	449	21	in	in	ADP
cana-2873	449	22	z2	z2	PROPN
cana-2873	449	23	.	.	PUNCT
cana-2873	450	1	hence	hence	ADV
cana-2873	450	2	k	k	PROPN
cana-2873	450	3	is	be	AUX
cana-2873	450	4	a	a	DET
cana-2873	450	5	q	q	NOUN
cana-2873	450	6	-	-	PUNCT
cana-2873	450	7	nsɕbc	nsɕbc	NOUN
cana-2873	450	8	.	.	PUNCT
cana-2873	451	1	(	(	PUNCT
cana-2873	451	2	iv	iv	X
cana-2873	451	3	)	)	PUNCT
cana-2873	451	4	let	let	VERB
cana-2873	451	5	η	η	X
cana-2873	451	6	be	be	AUX
cana-2873	451	7	a	a	DET
cana-2873	451	8	q	q	ADJ
cana-2873	451	9	-	-	PUNCT
cana-2873	451	10	nsc	nsc	NOUN
cana-2873	451	11	set	set	NOUN
cana-2873	451	12	in	in	ADP
cana-2873	451	13	z1	z1	PROPN
cana-2873	451	14	.	.	PUNCT
cana-2873	452	1	since	since	SCONJ
cana-2873	452	2	k	k	PROPN
cana-2873	452	3	is	be	AUX
cana-2873	452	4	q	q	ADJ
cana-2873	452	5	-	-	PUNCT
cana-2873	452	6	nsɕc	nsɕc	ADJ
cana-2873	452	7	,	,	PUNCT
cana-2873	452	8	k(η	k(η	PROPN
cana-2873	452	9	)	)	PUNCT
cana-2873	452	10	is	be	AUX
cana-2873	452	11	a	a	DET
cana-2873	452	12	q	q	NOUN
cana-2873	452	13	-	-	PUNCT
cana-2873	452	14	nsb	nsb	NOUN
cana-2873	452	15	o	o	NOUN
cana-2873	452	16	set	set	NOUN
cana-2873	452	17	in	in	ADP
cana-2873	452	18	z2	z2	PROPN
cana-2873	452	19	.	.	PUNCT
cana-2873	453	1	since	since	SCONJ
cana-2873	453	2	every	every	DET
cana-2873	453	3	qnsρo	qnsρo	NOUN
cana-2873	453	4	set	set	VERB
cana-2873	453	5	is	be	AUX
cana-2873	453	6	a	a	DET
cana-2873	453	7	q	q	ADJ
cana-2873	453	8	-	-	PUNCT
cana-2873	453	9	nsbo	nsbo	NOUN
cana-2873	453	10	set	set	NOUN
cana-2873	453	11	,	,	PUNCT
cana-2873	453	12	k(η	k(η	PROPN
cana-2873	453	13	)	)	PUNCT
cana-2873	453	14	is	be	AUX
cana-2873	453	15	a	a	DET
cana-2873	453	16	q	q	NOUN
cana-2873	453	17	-	-	PUNCT
cana-2873	453	18	nsbo	nsbo	NOUN
cana-2873	453	19	set	set	VERB
cana-2873	453	20	in	in	ADP
cana-2873	453	21	z2	z2	PROPN
cana-2873	453	22	.	.	PUNCT
cana-2873	454	1	hence	hence	ADV
cana-2873	454	2	k	k	PROPN
cana-2873	454	3	is	be	AUX
cana-2873	454	4	a	a	DET
cana-2873	454	5	q	q	NOUN
cana-2873	454	6	-	-	PUNCT
cana-2873	454	7	nscbc	nscbc	NOUN
cana-2873	454	8	.	.	PUNCT
cana-2873	455	1	(	(	PUNCT
cana-2873	455	2	v	v	NOUN
cana-2873	455	3	)	)	PUNCT
cana-2873	455	4	let	let	VERB
cana-2873	455	5	η	η	X
cana-2873	455	6	be	be	AUX
cana-2873	455	7	a	a	DET
cana-2873	455	8	q	q	ADJ
cana-2873	455	9	-	-	PUNCT
cana-2873	455	10	nsc	nsc	NOUN
cana-2873	455	11	set	set	NOUN
cana-2873	455	12	in	in	ADP
cana-2873	455	13	z1	z1	PROPN
cana-2873	455	14	.	.	PUNCT
cana-2873	456	1	since	since	SCONJ
cana-2873	456	2	k	k	PROPN
cana-2873	456	3	is	be	AUX
cana-2873	456	4	q	q	ADJ
cana-2873	456	5	-	-	PUNCT
cana-2873	456	6	nsɕbc	nsɕbc	ADJ
cana-2873	456	7	,	,	PUNCT
cana-2873	456	8	k(η	k(η	PROPN
cana-2873	456	9	)	)	PUNCT
cana-2873	456	10	is	be	AUX
cana-2873	456	11	a	a	DET
cana-2873	456	12	q	q	NOUN
cana-2873	456	13	-	-	PUNCT
cana-2873	456	14	nsbo	nsbo	NOUN
cana-2873	456	15	set	set	VERB
cana-2873	456	16	in	in	ADP
cana-2873	456	17	z2	z2	PROPN
cana-2873	456	18	.	.	PUNCT
cana-2873	457	1	since	since	SCONJ
cana-2873	457	2	every	every	DET
cana-2873	457	3	qnsbo	qnsbo	NOUN
cana-2873	457	4	set	set	VERB
cana-2873	457	5	is	be	AUX
cana-2873	457	6	a	a	DET
cana-2873	457	7	q	q	NOUN
cana-2873	457	8	-	-	PUNCT
cana-2873	457	9	nsβo	nsβo	ADJ
cana-2873	457	10	set	set	NOUN
cana-2873	457	11	,	,	PUNCT
cana-2873	457	12	k(η	k(η	PROPN
cana-2873	457	13	)	)	PUNCT
cana-2873	457	14	is	be	AUX
cana-2873	457	15	a	a	DET
cana-2873	457	16	q	q	NOUN
cana-2873	457	17	-	-	PUNCT
cana-2873	457	18	nsβo	nsβo	ADJ
cana-2873	457	19	set	set	NOUN
cana-2873	457	20	in	in	ADP
cana-2873	457	21	z2	z2	PROPN
cana-2873	457	22	.	.	PUNCT
cana-2873	458	1	hence	hence	ADV
cana-2873	458	2	k	k	PROPN
cana-2873	458	3	is	be	AUX
cana-2873	458	4	a	a	DET
cana-2873	458	5	q	q	NOUN
cana-2873	458	6	-	-	PUNCT
cana-2873	458	7	nsɕβc	nsɕβc	NOUN
cana-2873	458	8	.	.	PUNCT
cana-2873	458	9	example	example	NOUN
cana-2873	459	1	6.3	6.3	NUM
cana-2873	459	2	.	.	PUNCT
cana-2873	460	1	in	in	ADP
cana-2873	460	2	example	example	NOUN
cana-2873	460	3	5.3	5.3	NUM
cana-2873	460	4	,	,	PUNCT
cana-2873	460	5	k	k	PROPN
cana-2873	460	6	is	be	AUX
cana-2873	460	7	q	q	NOUN
cana-2873	460	8	-	-	PUNCT
cana-2873	460	9	nsɕbc	nsɕbc	ADJ
cana-2873	460	10	but	but	CCONJ
cana-2873	460	11	not	not	PART
cana-2873	460	12	q	q	ADJ
cana-2873	460	13	-	-	NOUN
cana-2873	460	14	nsɕpc	nsɕpc	NOUN
cana-2873	460	15	.	.	PUNCT
cana-2873	460	16	example	example	NOUN
cana-2873	461	1	6.4	6.4	NUM
cana-2873	461	2	.	.	PUNCT
cana-2873	462	1	in	in	ADP
cana-2873	462	2	example	example	NOUN
cana-2873	462	3	5.4	5.4	NUM
cana-2873	462	4	,	,	PUNCT
cana-2873	462	5	k	k	PROPN
cana-2873	462	6	is	be	AUX
cana-2873	462	7	q	q	NOUN
cana-2873	462	8	-	-	PUNCT
cana-2873	462	9	nsɕbc	nsɕbc	ADJ
cana-2873	462	10	but	but	CCONJ
cana-2873	462	11	not	not	PART
cana-2873	462	12	q	q	NOUN
cana-2873	462	13	-	-	PUNCT
cana-2873	462	14	nsɕsc	nsɕsc	NOUN
cana-2873	462	15	.	.	PUNCT
cana-2873	463	1	communications	communication	NOUN
cana-2873	463	2	on	on	ADP
cana-2873	463	3	applied	apply	VERB
cana-2873	463	4	nonlinear	nonlinear	ADJ
cana-2873	463	5	analysis	analysis	NOUN
cana-2873	463	6	issn	issn	NOUN
cana-2873	463	7	:	:	PUNCT
cana-2873	463	8	1074	1074	NUM
cana-2873	463	9	-	-	PUNCT
cana-2873	463	10	133x	133x	NUM
cana-2873	463	11	vol	vol	NOUN
cana-2873	463	12	32	32	NUM
cana-2873	463	13	no	no	NOUN
cana-2873	463	14	.	.	PUNCT
cana-2873	464	1	4s	4s	NUM
cana-2873	464	2	(	(	PUNCT
cana-2873	464	3	2025	2025	NUM
cana-2873	464	4	)	)	PUNCT
cana-2873	464	5	592	592	NUM
cana-2873	464	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	464	7	example	example	NOUN
cana-2873	464	8	6.5	6.5	NUM
cana-2873	464	9	.	.	PUNCT
cana-2873	465	1	in	in	ADP
cana-2873	465	2	example	example	NOUN
cana-2873	465	3	5.5	5.5	NUM
cana-2873	465	4	,	,	PUNCT
cana-2873	465	5	k	k	PROPN
cana-2873	465	6	is	be	AUX
cana-2873	465	7	q	q	NOUN
cana-2873	465	8	-	-	PUNCT
cana-2873	465	9	nsɕβc	nsɕβc	NOUN
cana-2873	465	10	but	but	CCONJ
cana-2873	465	11	not	not	PART
cana-2873	465	12	q	q	ADJ
cana-2873	465	13	-	-	PUNCT
cana-2873	465	14	nsɕbc	nsɕbc	ADJ
cana-2873	465	15	.	.	PUNCT
cana-2873	466	1	figure	figure	VERB
cana-2873	466	2	3	3	NUM
cana-2873	466	3	:	:	PUNCT
cana-2873	466	4	q	q	ADJ
cana-2873	466	5	-	-	PUNCT
cana-2873	466	6	nsɕβc	nsɕβc	ADJ
cana-2873	466	7	maps	map	NOUN
cana-2873	466	8	in	in	ADP
cana-2873	466	9	q	q	ADJ
cana-2873	466	10	-	-	PUNCT
cana-2873	466	11	nsts	nst	NOUN
cana-2873	466	12	theorem	theorem	VERB
cana-2873	466	13	6.6	6.6	NUM
cana-2873	466	14	.	.	PUNCT
cana-2873	467	1	a	a	DET
cana-2873	467	2	mapping	mapping	NOUN
cana-2873	467	3	k	k	NOUN
cana-2873	467	4	:	:	PUNCT
cana-2873	467	5	(	(	PUNCT
cana-2873	467	6	z1	z1	VERB
cana-2873	467	7	,	,	PUNCT
cana-2873	467	8	γq	γq	ADP
cana-2873	467	9	)	)	PUNCT
cana-2873	467	10	→	→	SYM
cana-2873	467	11	(	(	PUNCT
cana-2873	467	12	z2	z2	PROPN
cana-2873	467	13	,	,	PUNCT
cana-2873	467	14	σq	σq	NOUN
cana-2873	467	15	)	)	PUNCT
cana-2873	467	16	is	be	AUX
cana-2873	467	17	q	q	ADJ
cana-2873	467	18	-	-	PUNCT
cana-2873	467	19	nsɕβc	nsɕβc	ADJ
cana-2873	467	20	iff	iff	NOUN
cana-2873	467	21	for	for	ADP
cana-2873	467	22	each	each	DET
cana-2873	467	23	q	q	ADJ
cana-2873	467	24	-	-	PUNCT
cana-2873	467	25	nss	nss	NOUN
cana-2873	467	26	ψ̃	ψ̃	PROPN
cana-2873	467	27	of	of	ADP
cana-2873	467	28	(	(	PUNCT
cana-2873	467	29	z2	z2	PROPN
cana-2873	467	30	,	,	PUNCT
cana-2873	467	31	σq	σq	NOUN
cana-2873	467	32	)	)	PUNCT
cana-2873	467	33	and	and	CCONJ
cana-2873	467	34	for	for	ADP
cana-2873	467	35	each	each	DET
cana-2873	467	36	q	q	NOUN
cana-2873	467	37	-	-	PUNCT
cana-2873	467	38	nscs	nscs	ADJ
cana-2873	467	39	(	(	PUNCT
cana-2873	467	40	ψ̃	ψ̃	PROPN
cana-2873	467	41	)	)	PUNCT
cana-2873	467	42	of	of	ADP
cana-2873	467	43	(	(	PUNCT
cana-2873	467	44	z1	z1	NOUN
cana-2873	467	45	,	,	PUNCT
cana-2873	467	46	γq	γq	ADP
cana-2873	467	47	)	)	PUNCT
cana-2873	467	48	containing	contain	VERB
cana-2873	467	49	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	467	50	)	)	PUNCT
cana-2873	467	51	,	,	PUNCT
cana-2873	467	52	there	there	PRON
cana-2873	467	53	is	be	VERB
cana-2873	467	54	a	a	DET
cana-2873	467	55	q	q	ADJ
cana-2873	467	56	-	-	PUNCT
cana-2873	467	57	nsβcs	nsβcs	NOUN
cana-2873	467	58	ã	ã	PROPN
cana-2873	467	59	of	of	ADP
cana-2873	467	60	(	(	PUNCT
cana-2873	467	61	z2	z2	PROPN
cana-2873	467	62	,	,	PUNCT
cana-2873	467	63	σq	σq	NOUN
cana-2873	467	64	)	)	PUNCT
cana-2873	467	65	such	such	ADJ
cana-2873	467	66	that	that	SCONJ
cana-2873	467	67	(	(	PUNCT
cana-2873	467	68	ψ̃	ψ̃	PROPN
cana-2873	467	69	)	)	PUNCT
cana-2873	467	70	⊆	⊆	NUM
cana-2873	467	71	(	(	PUNCT
cana-2873	467	72	ã	ã	PROPN
cana-2873	467	73	)	)	PUNCT
cana-2873	467	74	and	and	CCONJ
cana-2873	467	75	k−1(ã	k−1(ã	NOUN
cana-2873	467	76	)	)	PUNCT
cana-2873	467	77	⊆	⊆	NUM
cana-2873	467	78	(	(	PUNCT
cana-2873	467	79	ψ̃	ψ̃	PROPN
cana-2873	467	80	)	)	PUNCT
cana-2873	467	81	.	.	PUNCT
cana-2873	468	1	proof	proof	NOUN
cana-2873	468	2	.	.	PUNCT
cana-2873	469	1	necessity	necessity	NOUN
cana-2873	469	2	:	:	PUNCT
cana-2873	469	3	let	let	VERB
cana-2873	469	4	k	k	PRON
cana-2873	469	5	be	be	AUX
cana-2873	469	6	a	a	DET
cana-2873	469	7	q	q	ADJ
cana-2873	469	8	-	-	PUNCT
cana-2873	469	9	nscβc	nscβc	NOUN
cana-2873	469	10	mapping	mapping	NOUN
cana-2873	469	11	.	.	PUNCT
cana-2873	470	1	consider	consider	VERB
cana-2873	470	2	a	a	DET
cana-2873	470	3	q	q	NOUN
cana-2873	470	4	-	-	PUNCT
cana-2873	470	5	nsos	nsos	ADJ
cana-2873	470	6	ψ̃	ψ̃	PROPN
cana-2873	470	7	in	in	ADP
cana-2873	470	8	(	(	PUNCT
cana-2873	470	9	z2	z2	PROPN
cana-2873	470	10	,	,	PUNCT
cana-2873	470	11	σq	σq	NOUN
cana-2873	470	12	)	)	PUNCT
cana-2873	470	13	and	and	CCONJ
cana-2873	470	14	a	a	DET
cana-2873	470	15	qnscs	qnscs	NOUN
cana-2873	470	16	in	in	ADP
cana-2873	470	17	(	(	PUNCT
cana-2873	470	18	z1	z1	NOUN
cana-2873	470	19	,	,	PUNCT
cana-2873	470	20	γq	γq	ADP
cana-2873	470	21	)	)	PUNCT
cana-2873	471	1	such	such	ADJ
cana-2873	471	2	that	that	SCONJ
cana-2873	471	3	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	471	4	)	)	PUNCT
cana-2873	471	5	⊆	⊆	NUM
cana-2873	471	6	(	(	PUNCT
cana-2873	471	7	ψ̃	ψ̃	PROPN
cana-2873	471	8	)	)	PUNCT
cana-2873	471	9	.then	.then	X
cana-2873	471	10	(	(	PUNCT
cana-2873	471	11	ψ̃	ψ̃	PROPN
cana-2873	471	12	)	)	PUNCT
cana-2873	471	13	=	=	SYM
cana-2873	471	14	1qnk−1((ψ̃)c	1qnk−1((ψ̃)c	NUM
cana-2873	471	15	)	)	PUNCT
cana-2873	471	16	is	be	AUX
cana-2873	471	17	q	q	ADJ
cana-2873	471	18	-	-	PUNCT
cana-2873	471	19	nsβcs	nsβcs	NOUN
cana-2873	471	20	of	of	ADP
cana-2873	471	21	(	(	PUNCT
cana-2873	471	22	z2	z2	PROPN
cana-2873	471	23	,	,	PUNCT
cana-2873	471	24	σq	σq	NOUN
cana-2873	471	25	)	)	PUNCT
cana-2873	471	26	such	such	ADJ
cana-2873	471	27	that	that	DET
cana-2873	471	28	sufficiency	sufficiency	NOUN
cana-2873	471	29	:	:	PUNCT
cana-2873	471	30	assume	assume	VERB
cana-2873	471	31	(	(	PUNCT
cana-2873	471	32	ψ̃	ψ̃	PROPN
cana-2873	471	33	)	)	PUNCT
cana-2873	471	34	is	be	AUX
cana-2873	471	35	a	a	DET
cana-2873	471	36	q	q	NOUN
cana-2873	471	37	-	-	PUNCT
cana-2873	471	38	nscs	nscs	NOUN
cana-2873	471	39	of	of	ADP
cana-2873	471	40	(	(	PUNCT
cana-2873	471	41	z1	z1	VERB
cana-2873	471	42	,	,	PUNCT
cana-2873	471	43	γq	γq	ADP
cana-2873	471	44	)	)	PUNCT
cana-2873	471	45	.	.	PUNCT
cana-2873	472	1	then	then	ADV
cana-2873	472	2	(	(	PUNCT
cana-2873	472	3	k(ψ̃))c	k(ψ̃))c	PROPN
cana-2873	472	4	is	be	AUX
cana-2873	472	5	a	a	DET
cana-2873	472	6	q	q	NOUN
cana-2873	472	7	-	-	PUNCT
cana-2873	472	8	nss	nss	NOUN
cana-2873	472	9	of	of	ADP
cana-2873	472	10	(	(	PUNCT
cana-2873	472	11	z2	z2	PROPN
cana-2873	472	12	,	,	PUNCT
cana-2873	472	13	σq	σq	NOUN
cana-2873	472	14	)	)	PUNCT
cana-2873	472	15	and	and	CCONJ
cana-2873	472	16	(	(	PUNCT
cana-2873	472	17	ψ̃)c	ψ̃)c	PROPN
cana-2873	472	18	isq	isq	PROPN
cana-2873	472	19	-	-	PUNCT
cana-2873	472	20	nsos	nsos	NOUN
cana-2873	472	21	in	in	ADP
cana-2873	472	22	(	(	PUNCT
cana-2873	472	23	z1	z1	NOUN
cana-2873	472	24	,	,	PUNCT
cana-2873	472	25	γq	γq	ADP
cana-2873	472	26	)	)	PUNCT
cana-2873	472	27	such	such	ADJ
cana-2873	472	28	that	that	DET
cana-2873	472	29	k−1((k(ψ̃))c)⊆(ψ̃)c	k−1((k(ψ̃))c)⊆(ψ̃)c	PROPN
cana-2873	472	30	.	.	PUNCT
cana-2873	473	1	by	by	ADP
cana-2873	473	2	presumption	presumption	NOUN
cana-2873	473	3	,	,	PUNCT
cana-2873	473	4	there	there	PRON
cana-2873	473	5	is	be	VERB
cana-2873	473	6	a	a	DET
cana-2873	473	7	q	q	ADJ
cana-2873	473	8	-	-	PUNCT
cana-2873	473	9	nsβcs	nsβcs	NOUN
cana-2873	473	10	ã	ã	PROPN
cana-2873	473	11	of	of	ADP
cana-2873	473	12	(	(	PUNCT
cana-2873	473	13	z2	z2	PROPN
cana-2873	473	14	,	,	PUNCT
cana-2873	473	15	σq	σq	NOUN
cana-2873	473	16	)	)	PUNCT
cana-2873	473	17	such	such	ADJ
cana-2873	473	18	that	that	PRON
cana-2873	473	19	(	(	PUNCT
cana-2873	473	20	k(ψ̃))c⊆(ψ̃	k(ψ̃))c⊆(ψ̃	NOUN
cana-2873	473	21	)	)	PUNCT
cana-2873	473	22	and	and	CCONJ
cana-2873	473	23	k−1(ψ̃)⊆(ψ̃)c	k−1(ψ̃)⊆(ψ̃)c	NOUN
cana-2873	473	24	.	.	PUNCT
cana-2873	474	1	therefore	therefore	ADV
cana-2873	474	2	(	(	PUNCT
cana-2873	474	3	ψ̃)⊆(k−1(ψ̃))c	ψ̃)⊆(k−1(ψ̃))c	PROPN
cana-2873	474	4	.	.	PUNCT
cana-2873	475	1	hence	hence	ADV
cana-2873	475	2	(	(	PUNCT
cana-2873	475	3	ψ̃)c⊆k(ψ̃	ψ̃)c⊆k(ψ̃	PROPN
cana-2873	475	4	)	)	PUNCT
cana-2873	475	5	k⊆((k−1(ψ̃))c)⊆(ψ̃)c	k⊆((k−1(ψ̃))c)⊆(ψ̃)c	NOUN
cana-2873	475	6	which	which	PRON
cana-2873	475	7	implies	imply	VERB
cana-2873	475	8	k(ψ̃	k(ψ̃	NOUN
cana-2873	475	9	)	)	PUNCT
cana-2873	476	1	=	=	PUNCT
cana-2873	476	2	(	(	PUNCT
cana-2873	476	3	ψ̃)c	ψ̃)c	PROPN
cana-2873	476	4	.	.	PUNCT
cana-2873	477	1	as	as	SCONJ
cana-2873	477	2	(	(	PUNCT
cana-2873	477	3	ψ̃)c	ψ̃)c	PROPN
cana-2873	477	4	is	be	AUX
cana-2873	477	5	q	q	NOUN
cana-2873	477	6	-	-	PUNCT
cana-2873	477	7	nsβos	nsβos	NOUN
cana-2873	477	8	of	of	ADP
cana-2873	477	9	(	(	PUNCT
cana-2873	477	10	z2	z2	PROPN
cana-2873	477	11	,	,	PUNCT
cana-2873	477	12	σq	σq	NOUN
cana-2873	477	13	)	)	PUNCT
cana-2873	477	14	,	,	PUNCT
cana-2873	477	15	k(ψ̃	k(ψ̃	PROPN
cana-2873	477	16	)	)	PUNCT
cana-2873	477	17	is	be	AUX
cana-2873	477	18	q	q	NOUN
cana-2873	477	19	-	-	PUNCT
cana-2873	477	20	nsβo	nsβo	ADJ
cana-2873	477	21	in	in	ADP
cana-2873	477	22	(	(	PUNCT
cana-2873	477	23	z2	z2	PROPN
cana-2873	477	24	,	,	PUNCT
cana-2873	477	25	σq	σq	NOUN
cana-2873	477	26	)	)	PUNCT
cana-2873	477	27	and	and	CCONJ
cana-2873	477	28	hence	hence	ADV
cana-2873	477	29	k	k	PROPN
cana-2873	477	30	is	be	AUX
cana-2873	477	31	q	q	ADJ
cana-2873	477	32	-	-	PUNCT
cana-2873	477	33	nsɕβc	nsɕβc	ADJ
cana-2873	477	34	mapping	mapping	NOUN
cana-2873	477	35	.	.	PUNCT
cana-2873	478	1	theorem	theorem	VERB
cana-2873	478	2	6.7	6.7	NUM
cana-2873	478	3	.	.	PUNCT
cana-2873	479	1	if	if	SCONJ
cana-2873	479	2	k	k	X
cana-2873	479	3	:	:	PUNCT
cana-2873	479	4	(	(	PUNCT
cana-2873	479	5	z1	z1	VERB
cana-2873	479	6	,	,	PUNCT
cana-2873	479	7	γq	γq	ADP
cana-2873	479	8	)	)	PUNCT
cana-2873	479	9	→	→	SYM
cana-2873	479	10	(	(	PUNCT
cana-2873	479	11	z2	z2	PROPN
cana-2873	479	12	,	,	PUNCT
cana-2873	479	13	σq	σq	NOUN
cana-2873	479	14	)	)	PUNCT
cana-2873	479	15	is	be	AUX
cana-2873	479	16	q	q	ADJ
cana-2873	479	17	-	-	PUNCT
cana-2873	479	18	nsc	nsc	NOUN
cana-2873	479	19	and	and	CCONJ
cana-2873	479	20	g	g	PROPN
cana-2873	479	21	:	:	PUNCT
cana-2873	479	22	(	(	PUNCT
cana-2873	479	23	z2	z2	NOUN
cana-2873	479	24	,	,	PUNCT
cana-2873	479	25	σq	σq	NOUN
cana-2873	479	26	)	)	PUNCT
cana-2873	479	27	→	→	SYM
cana-2873	479	28	(	(	PUNCT
cana-2873	479	29	z3	z3	PROPN
cana-2873	479	30	,	,	PUNCT
cana-2873	479	31	ρq	ρq	NOUN
cana-2873	479	32	)	)	PUNCT
cana-2873	479	33	is	be	AUX
cana-2873	479	34	q	q	NOUN
cana-2873	479	35	-	-	PUNCT
cana-2873	479	36	nsɕβc	nsɕβc	NOUN
cana-2873	479	37	.	.	PUNCT
cana-2873	480	1	then	then	ADV
cana-2873	480	2	g	g	PROPN
cana-2873	480	3	◦	◦	PROPN
cana-2873	480	4	k	k	X
cana-2873	480	5	:	:	PUNCT
cana-2873	480	6	(	(	PUNCT
cana-2873	480	7	z1	z1	VERB
cana-2873	480	8	,	,	PUNCT
cana-2873	480	9	γq	γq	ADP
cana-2873	480	10	)	)	PUNCT
cana-2873	480	11	→	→	SYM
cana-2873	480	12	(	(	PUNCT
cana-2873	480	13	z3	z3	PROPN
cana-2873	480	14	,	,	PUNCT
cana-2873	480	15	ρq	ρq	NOUN
cana-2873	480	16	)	)	PUNCT
cana-2873	480	17	is	be	AUX
cana-2873	480	18	q	q	NOUN
cana-2873	480	19	-	-	PUNCT
cana-2873	480	20	nsɕβc	nsɕβc	NOUN
cana-2873	480	21	.	.	PUNCT
cana-2873	481	1	proof	proof	NOUN
cana-2873	481	2	.	.	PUNCT
cana-2873	482	1	let	let	VERB
cana-2873	482	2	(	(	PUNCT
cana-2873	482	3	ψ̃	ψ̃	PROPN
cana-2873	482	4	)	)	PUNCT
cana-2873	482	5	be	be	VERB
cana-2873	482	6	a	a	DET
cana-2873	482	7	q	q	NOUN
cana-2873	482	8	-	-	PUNCT
cana-2873	482	9	nscs	nscs	ADJ
cana-2873	482	10	in	in	ADP
cana-2873	482	11	(	(	PUNCT
cana-2873	482	12	z1	z1	NOUN
cana-2873	482	13	,	,	PUNCT
cana-2873	482	14	γq	γq	ADP
cana-2873	482	15	)	)	PUNCT
cana-2873	482	16	.	.	PUNCT
cana-2873	483	1	as	as	SCONJ
cana-2873	483	2	k	k	PROPN
cana-2873	483	3	is	be	AUX
cana-2873	483	4	q	q	ADJ
cana-2873	483	5	-	-	PUNCT
cana-2873	483	6	nsc	nsc	NOUN
cana-2873	483	7	mapping	mapping	NOUN
cana-2873	483	8	,	,	PUNCT
cana-2873	483	9	k(ψ̃	k(ψ̃	PROPN
cana-2873	483	10	)	)	PUNCT
cana-2873	483	11	is	be	AUX
cana-2873	483	12	q	q	NOUN
cana-2873	483	13	-	-	PUNCT
cana-2873	483	14	nscs	nscs	ADJ
cana-2873	483	15	in	in	ADP
cana-2873	483	16	(	(	PUNCT
cana-2873	483	17	z2	z2	PROPN
cana-2873	483	18	,	,	PUNCT
cana-2873	483	19	σq	σq	NOUN
cana-2873	483	20	)	)	PUNCT
cana-2873	483	21	.	.	PUNCT
cana-2873	484	1	as	as	SCONJ
cana-2873	484	2	g	g	PROPN
cana-2873	484	3	is	be	AUX
cana-2873	484	4	qnscβc	qnscβc	ADJ
cana-2873	484	5	mapping	mapping	NOUN
cana-2873	484	6	,	,	PUNCT
cana-2873	484	7	(	(	PUNCT
cana-2873	484	8	g	g	NOUN
cana-2873	484	9	◦	◦	NOUN
cana-2873	484	10	k)(ψ̃	k)(ψ̃	NOUN
cana-2873	484	11	)	)	PUNCT
cana-2873	484	12	=	=	SYM
cana-2873	484	13	g(k(ψ̃	g(k(ψ̃	NOUN
cana-2873	484	14	)	)	PUNCT
cana-2873	484	15	)	)	PUNCT
cana-2873	484	16	is	be	AUX
cana-2873	484	17	q	q	NOUN
cana-2873	484	18	-	-	PUNCT
cana-2873	484	19	nsβos	nsβos	NOUN
cana-2873	484	20	in	in	ADP
cana-2873	484	21	(	(	PUNCT
cana-2873	484	22	z3	z3	PROPN
cana-2873	484	23	,	,	PUNCT
cana-2873	484	24	ρq	ρq	NOUN
cana-2873	484	25	)	)	PUNCT
cana-2873	484	26	.	.	PUNCT
cana-2873	485	1	hence	hence	ADV
cana-2873	485	2	g	g	PROPN
cana-2873	485	3	◦	◦	NOUN
cana-2873	485	4	k	k	PROPN
cana-2873	485	5	is	be	AUX
cana-2873	485	6	qnsɕβc	qnsɕβc	PROPN
cana-2873	485	7	mapping	mapping	NOUN
cana-2873	485	8	.	.	PUNCT
cana-2873	486	1	theorem	theorem	VERB
cana-2873	486	2	6.8	6.8	NUM
cana-2873	486	3	.	.	PUNCT
cana-2873	487	1	if	if	SCONJ
cana-2873	487	2	k	k	X
cana-2873	487	3	:	:	PUNCT
cana-2873	487	4	(	(	PUNCT
cana-2873	487	5	z1	z1	VERB
cana-2873	487	6	,	,	PUNCT
cana-2873	487	7	γq	γq	ADP
cana-2873	487	8	)	)	PUNCT
cana-2873	487	9	→	→	SYM
cana-2873	487	10	(	(	PUNCT
cana-2873	487	11	z2	z2	PROPN
cana-2873	487	12	,	,	PUNCT
cana-2873	487	13	σq	σq	NOUN
cana-2873	487	14	)	)	PUNCT
cana-2873	487	15	is	be	AUX
cana-2873	487	16	q	q	ADJ
cana-2873	487	17	-	-	PUNCT
cana-2873	487	18	nscβc	nscβc	NOUN
cana-2873	487	19	map	map	NOUN
cana-2873	487	20	,	,	PUNCT
cana-2873	487	21	then	then	ADV
cana-2873	487	22	q	q	NOUN
cana-2873	487	23	-	-	PUNCT
cana-2873	487	24	nsβint(k(ψ̃	nsβint(k(ψ̃	NOUN
cana-2873	487	25	)	)	PUNCT
cana-2873	487	26	)	)	PUNCT
cana-2873	487	27	⊇	⊇	PROPN
cana-2873	487	28	k(qnsint(ψ̃	k(qnsint(ψ̃	NOUN
cana-2873	487	29	)	)	PUNCT
cana-2873	487	30	)	)	PUNCT
cana-2873	487	31	.	.	PUNCT
cana-2873	488	1	proof	proof	NOUN
cana-2873	488	2	.	.	PUNCT
cana-2873	489	1	the	the	DET
cana-2873	489	2	proof	proof	NOUN
cana-2873	489	3	is	be	AUX
cana-2873	489	4	obvious	obvious	ADJ
cana-2873	489	5	from	from	ADP
cana-2873	489	6	definition	definition	NOUN
cana-2873	489	7	2.7	2.7	NUM
cana-2873	489	8	and	and	CCONJ
cana-2873	489	9	definition	definition	NOUN
cana-2873	489	10	6.1	6.1	NUM
cana-2873	489	11	.	.	PUNCT
cana-2873	490	1	theorem	theorem	VERB
cana-2873	490	2	6.9	6.9	NUM
cana-2873	490	3	.	.	PUNCT
cana-2873	491	1	let	let	VERB
cana-2873	491	2	k	k	NOUN
cana-2873	491	3	:	:	PUNCT
cana-2873	491	4	(	(	PUNCT
cana-2873	491	5	z1	z1	VERB
cana-2873	491	6	,	,	PUNCT
cana-2873	491	7	γq	γq	ADP
cana-2873	491	8	)	)	PUNCT
cana-2873	491	9	→	→	SYM
cana-2873	491	10	(	(	PUNCT
cana-2873	491	11	z2	z2	PROPN
cana-2873	491	12	,	,	PUNCT
cana-2873	491	13	σq	σq	NOUN
cana-2873	491	14	)	)	PUNCT
cana-2873	491	15	and	and	CCONJ
cana-2873	491	16	g	g	NOUN
cana-2873	491	17	:	:	PUNCT
cana-2873	491	18	(	(	PUNCT
cana-2873	491	19	z2	z2	NOUN
cana-2873	491	20	,	,	PUNCT
cana-2873	491	21	σq	σq	NOUN
cana-2873	491	22	)	)	PUNCT
cana-2873	491	23	→	→	SYM
cana-2873	491	24	(	(	PUNCT
cana-2873	491	25	z3	z3	PROPN
cana-2873	491	26	,	,	PUNCT
cana-2873	491	27	ρq	ρq	NUM
cana-2873	491	28	)	)	PUNCT
cana-2873	491	29	be	be	AUX
cana-2873	491	30	q	q	ADJ
cana-2873	491	31	-	-	PUNCT
cana-2873	491	32	nsɕβc	nsɕβc	NOUN
cana-2873	491	33	mappings	mapping	NOUN
cana-2873	491	34	.	.	PUNCT
cana-2873	492	1	if	if	SCONJ
cana-2873	492	2	every	every	DET
cana-2873	492	3	q	q	NOUN
cana-2873	492	4	-	-	PUNCT
cana-2873	492	5	nsβos	nsβos	NOUN
cana-2873	492	6	of	of	ADP
cana-2873	492	7	(	(	PUNCT
cana-2873	492	8	z2	z2	PROPN
cana-2873	492	9	,	,	PUNCT
cana-2873	492	10	σq	σq	NOUN
cana-2873	492	11	)	)	PUNCT
cana-2873	492	12	is	be	AUX
cana-2873	492	13	q	q	NOUN
cana-2873	492	14	-	-	PUNCT
cana-2873	492	15	nsos	nsos	ADJ
cana-2873	492	16	,	,	PUNCT
cana-2873	492	17	then	then	ADV
cana-2873	492	18	g	g	PROPN
cana-2873	492	19	◦	◦	PROPN
cana-2873	492	20	k	k	X
cana-2873	492	21	:	:	PUNCT
cana-2873	492	22	(	(	PUNCT
cana-2873	492	23	z1	z1	VERB
cana-2873	492	24	,	,	PUNCT
cana-2873	492	25	γq	γq	ADP
cana-2873	492	26	)	)	PUNCT
cana-2873	492	27	→	→	SYM
cana-2873	492	28	(	(	PUNCT
cana-2873	492	29	z3	z3	PROPN
cana-2873	492	30	,	,	PUNCT
cana-2873	492	31	ρq	ρq	NOUN
cana-2873	492	32	)	)	PUNCT
cana-2873	492	33	is	be	AUX
cana-2873	492	34	q	q	NOUN
cana-2873	492	35	-	-	PUNCT
cana-2873	492	36	nsβc	nsβc	ADJ
cana-2873	492	37	.	.	PUNCT
cana-2873	493	1	proof	proof	NOUN
cana-2873	493	2	.	.	PUNCT
cana-2873	494	1	let	let	VERB
cana-2873	494	2	(	(	PUNCT
cana-2873	494	3	ψ̃	ψ̃	PROPN
cana-2873	494	4	)	)	PUNCT
cana-2873	494	5	be	be	VERB
cana-2873	494	6	a	a	DET
cana-2873	494	7	q	q	NOUN
cana-2873	494	8	-	-	PUNCT
cana-2873	494	9	nscs	nscs	ADJ
cana-2873	494	10	in	in	ADP
cana-2873	494	11	(	(	PUNCT
cana-2873	494	12	z1	z1	NOUN
cana-2873	494	13	,	,	PUNCT
cana-2873	494	14	γq	γq	ADP
cana-2873	494	15	)	)	PUNCT
cana-2873	494	16	.	.	PUNCT
cana-2873	495	1	as	as	SCONJ
cana-2873	495	2	k	k	PROPN
cana-2873	495	3	is	be	AUX
cana-2873	495	4	q	q	ADJ
cana-2873	495	5	-	-	PUNCT
cana-2873	495	6	nsɕβc	nsɕβc	ADJ
cana-2873	495	7	mapping	mapping	NOUN
cana-2873	495	8	,	,	PUNCT
cana-2873	495	9	k(ψ̃	k(ψ̃	PROPN
cana-2873	495	10	)	)	PUNCT
cana-2873	495	11	is	be	AUX
cana-2873	495	12	q	q	NOUN
cana-2873	495	13	-	-	PUNCT
cana-2873	495	14	nsβos	nsβos	NOUN
cana-2873	495	15	in	in	ADP
cana-2873	495	16	(	(	PUNCT
cana-2873	495	17	z2	z2	PROPN
cana-2873	495	18	,	,	PUNCT
cana-2873	495	19	σq	σq	NOUN
cana-2873	495	20	)	)	PUNCT
cana-2873	495	21	.	.	PUNCT
cana-2873	496	1	by	by	ADP
cana-2873	496	2	presumption	presumption	NOUN
cana-2873	496	3	,	,	PUNCT
cana-2873	496	4	k(ψ̃	k(ψ̃	NOUN
cana-2873	496	5	)	)	PUNCT
cana-2873	496	6	is	be	AUX
cana-2873	496	7	q	q	NOUN
cana-2873	496	8	-	-	PUNCT
cana-2873	496	9	nsos	nsos	NOUN
cana-2873	496	10	of	of	ADP
cana-2873	496	11	(	(	PUNCT
cana-2873	496	12	z2	z2	PROPN
cana-2873	496	13	,	,	PUNCT
cana-2873	496	14	σq	σq	NOUN
cana-2873	496	15	)	)	PUNCT
cana-2873	496	16	.	.	PUNCT
cana-2873	497	1	as	as	SCONJ
cana-2873	497	2	g	g	PROPN
cana-2873	497	3	is	be	AUX
cana-2873	497	4	q	q	ADJ
cana-2873	497	5	-	-	PUNCT
cana-2873	497	6	nsɕβc	nsɕβc	ADJ
cana-2873	497	7	mapping	mapping	NOUN
cana-2873	497	8	,	,	PUNCT
cana-2873	497	9	g(k(ψ̃	g(k(ψ̃	NOUN
cana-2873	497	10	)	)	PUNCT
cana-2873	497	11	)	)	PUNCT
cana-2873	498	1	=	=	PRON
cana-2873	498	2	(	(	PUNCT
cana-2873	498	3	g	g	ADP
cana-2873	498	4	◦	◦	NOUN
cana-2873	498	5	k)(ψ̃	k)(ψ̃	NOUN
cana-2873	498	6	)	)	PUNCT
cana-2873	498	7	is	be	AUX
cana-2873	498	8	q	q	ADJ
cana-2873	498	9	-	-	NOUN
cana-2873	498	10	nsβcs	nsβcs	NOUN
cana-2873	498	11	in	in	ADP
cana-2873	498	12	(	(	PUNCT
cana-2873	498	13	z3	z3	PROPN
cana-2873	498	14	,	,	PUNCT
cana-2873	498	15	ρq	ρq	NOUN
cana-2873	498	16	)	)	PUNCT
cana-2873	498	17	.	.	PUNCT
cana-2873	499	1	hence	hence	ADV
cana-2873	499	2	g	g	PROPN
cana-2873	499	3	◦	◦	NOUN
cana-2873	499	4	k	k	PROPN
cana-2873	499	5	is	be	AUX
cana-2873	499	6	q	q	ADJ
cana-2873	499	7	-	-	PUNCT
cana-2873	499	8	nsβc	nsβc	ADJ
cana-2873	499	9	mapping	mapping	NOUN
cana-2873	499	10	.	.	PUNCT
cana-2873	500	1	theorem	theorem	VERB
cana-2873	500	2	6.10	6.10	NUM
cana-2873	500	3	.	.	PUNCT
cana-2873	501	1	consider	consider	VERB
cana-2873	501	2	a	a	DET
cana-2873	501	3	bijective	bijective	ADJ
cana-2873	501	4	mapping	mapping	NOUN
cana-2873	501	5	k	k	NOUN
cana-2873	501	6	:	:	PUNCT
cana-2873	501	7	(	(	PUNCT
cana-2873	501	8	z1	z1	VERB
cana-2873	501	9	,	,	PUNCT
cana-2873	501	10	γq	γq	ADP
cana-2873	501	11	)	)	PUNCT
cana-2873	501	12	→	→	SYM
cana-2873	501	13	(	(	PUNCT
cana-2873	501	14	z2	z2	PROPN
cana-2873	501	15	,	,	PUNCT
cana-2873	501	16	σq	σq	NOUN
cana-2873	501	17	)	)	PUNCT
cana-2873	501	18	.	.	PUNCT
cana-2873	502	1	then	then	ADV
cana-2873	502	2	the	the	DET
cana-2873	502	3	following	follow	VERB
cana-2873	502	4	statements	statement	NOUN
cana-2873	502	5	are	be	AUX
cana-2873	502	6	equivalent	equivalent	ADJ
cana-2873	502	7	:	:	PUNCT
cana-2873	502	8	communications	communication	NOUN
cana-2873	502	9	on	on	ADP
cana-2873	502	10	applied	apply	VERB
cana-2873	502	11	nonlinear	nonlinear	ADJ
cana-2873	502	12	analysis	analysis	NOUN
cana-2873	502	13	issn	issn	NOUN
cana-2873	502	14	:	:	PUNCT
cana-2873	502	15	1074	1074	NUM
cana-2873	502	16	-	-	PUNCT
cana-2873	502	17	133x	133x	NUM
cana-2873	502	18	vol	vol	NOUN
cana-2873	502	19	32	32	NUM
cana-2873	502	20	no	no	NOUN
cana-2873	502	21	.	.	PUNCT
cana-2873	503	1	4s	4s	NUM
cana-2873	503	2	(	(	PUNCT
cana-2873	503	3	2025	2025	NUM
cana-2873	503	4	)	)	PUNCT
cana-2873	503	5	593	593	NUM
cana-2873	503	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	503	7	(	(	PUNCT
cana-2873	503	8	i	i	NOUN
cana-2873	503	9	)	)	PUNCT
cana-2873	504	1	k	k	PROPN
cana-2873	504	2	is	be	AUX
cana-2873	504	3	a	a	DET
cana-2873	504	4	q	q	ADJ
cana-2873	504	5	-	-	PUNCT
cana-2873	504	6	nsɕβo	nsɕβo	NOUN
cana-2873	504	7	mapping	mapping	NOUN
cana-2873	504	8	.	.	PUNCT
cana-2873	505	1	(	(	PUNCT
cana-2873	505	2	ii	ii	X
cana-2873	505	3	)	)	PUNCT
cana-2873	505	4	k	k	PROPN
cana-2873	505	5	is	be	AUX
cana-2873	505	6	a	a	DET
cana-2873	505	7	q	q	ADJ
cana-2873	505	8	-	-	PUNCT
cana-2873	505	9	nsɕβc	nsɕβc	ADJ
cana-2873	505	10	mapping	mapping	NOUN
cana-2873	505	11	.	.	PUNCT
cana-2873	506	1	(	(	PUNCT
cana-2873	506	2	iii	iii	X
cana-2873	506	3	)	)	PUNCT
cana-2873	506	4	k−1	k−1	PROPN
cana-2873	506	5	is	be	AUX
cana-2873	506	6	q	q	ADJ
cana-2873	506	7	-	-	PUNCT
cana-2873	506	8	nsβcts	nsβct	NOUN
cana-2873	506	9	mapping	mapping	NOUN
cana-2873	506	10	.	.	PUNCT
cana-2873	507	1	proof	proof	NOUN
cana-2873	507	2	.	.	PUNCT
cana-2873	508	1	(	(	PUNCT
cana-2873	508	2	i	i	NOUN
cana-2873	508	3	)	)	PUNCT
cana-2873	508	4	⇒	⇒	PROPN
cana-2873	508	5	(	(	PUNCT
cana-2873	508	6	ii	ii	PROPN
cana-2873	508	7	):	):	PUNCT
cana-2873	508	8	assume	assume	VERB
cana-2873	508	9	k	k	PROPN
cana-2873	508	10	is	be	AUX
cana-2873	508	11	a	a	DET
cana-2873	508	12	q	q	ADJ
cana-2873	508	13	-	-	PUNCT
cana-2873	508	14	nsɕβo	nsɕβo	NOUN
cana-2873	508	15	mapping	mapping	NOUN
cana-2873	508	16	.	.	PUNCT
cana-2873	509	1	if	if	SCONJ
cana-2873	509	2	q	q	NOUN
cana-2873	509	3	-	-	PUNCT
cana-2873	509	4	nsos	nsos	NOUN
cana-2873	509	5	(	(	PUNCT
cana-2873	509	6	ψ̃	ψ̃	PROPN
cana-2873	509	7	)	)	PUNCT
cana-2873	509	8	in	in	ADP
cana-2873	509	9	(	(	PUNCT
cana-2873	509	10	z1	z1	NOUN
cana-2873	509	11	,	,	PUNCT
cana-2873	509	12	γq	γq	ADP
cana-2873	509	13	)	)	PUNCT
cana-2873	509	14	,	,	PUNCT
cana-2873	509	15	by	by	ADP
cana-2873	509	16	presumption	presumption	NOUN
cana-2873	509	17	k(ψ̃	k(ψ̃	PROPN
cana-2873	509	18	)	)	PUNCT
cana-2873	509	19	is	be	AUX
cana-2873	509	20	a	a	DET
cana-2873	509	21	q	q	NOUN
cana-2873	509	22	-	-	PUNCT
cana-2873	509	23	nsβcs	nsβcs	NOUN
cana-2873	509	24	in	in	ADP
cana-2873	509	25	(	(	PUNCT
cana-2873	509	26	z2	z2	PROPN
cana-2873	509	27	,	,	PUNCT
cana-2873	509	28	σq	σq	NOUN
cana-2873	509	29	)	)	PUNCT
cana-2873	509	30	.	.	PUNCT
cana-2873	510	1	but	but	CCONJ
cana-2873	510	2	now	now	ADV
cana-2873	510	3	,	,	PUNCT
cana-2873	510	4	(	(	PUNCT
cana-2873	510	5	ψ̃	ψ̃	PROPN
cana-2873	510	6	)	)	PUNCT
cana-2873	510	7	is	be	AUX
cana-2873	510	8	q	q	NOUN
cana-2873	510	9	-	-	PUNCT
cana-2873	510	10	nscs	nscs	ADJ
cana-2873	510	11	in	in	ADP
cana-2873	510	12	(	(	PUNCT
cana-2873	510	13	z1	z1	NOUN
cana-2873	510	14	,	,	PUNCT
cana-2873	510	15	γq	γq	ADP
cana-2873	510	16	)	)	PUNCT
cana-2873	510	17	.	.	PUNCT
cana-2873	511	1	so	so	ADV
cana-2873	511	2	,	,	PUNCT
cana-2873	511	3	1qns	1qns	PROPN
cana-2873	511	4	−	−	PROPN
cana-2873	511	5	(	(	PUNCT
cana-2873	511	6	ψ̃	ψ̃	PROPN
cana-2873	511	7	)	)	PUNCT
cana-2873	511	8	is	be	AUX
cana-2873	511	9	a	a	DET
cana-2873	511	10	qnsos	qnsos	NOUN
cana-2873	511	11	in	in	ADP
cana-2873	511	12	(	(	PUNCT
cana-2873	511	13	z1	z1	NOUN
cana-2873	511	14	,	,	PUNCT
cana-2873	511	15	γq	γq	ADP
cana-2873	511	16	)	)	PUNCT
cana-2873	511	17	.	.	PUNCT
cana-2873	512	1	by	by	ADP
cana-2873	512	2	assumption	assumption	NOUN
cana-2873	512	3	,	,	PUNCT
cana-2873	512	4	k(1qns	k(1qns	PROPN
cana-2873	512	5	(	(	PUNCT
cana-2873	512	6	ψ̃	ψ̃	PROPN
cana-2873	512	7	)	)	PUNCT
cana-2873	512	8	)	)	PUNCT
cana-2873	512	9	is	be	AUX
cana-2873	512	10	a	a	DET
cana-2873	512	11	q	q	NOUN
cana-2873	512	12	-	-	PUNCT
cana-2873	512	13	nsβcs	nsβcs	NOUN
cana-2873	512	14	in	in	ADP
cana-2873	512	15	(	(	PUNCT
cana-2873	512	16	z2	z2	PROPN
cana-2873	512	17	,	,	PUNCT
cana-2873	512	18	σq	σq	NOUN
cana-2873	512	19	)	)	PUNCT
cana-2873	512	20	.	.	PUNCT
cana-2873	513	1	hence	hence	ADV
cana-2873	513	2	,	,	PUNCT
cana-2873	513	3	1qns	1qns	PROPN
cana-2873	513	4	k(1qns	k(1qns	PROPN
cana-2873	513	5	(	(	PUNCT
cana-2873	513	6	ψ̃	ψ̃	PROPN
cana-2873	513	7	)	)	PUNCT
cana-2873	513	8	)	)	PUNCT
cana-2873	513	9	is	be	AUX
cana-2873	513	10	a	a	DET
cana-2873	513	11	q	q	NOUN
cana-2873	513	12	-	-	PUNCT
cana-2873	513	13	nsβos	nsβos	NOUN
cana-2873	513	14	in	in	ADP
cana-2873	513	15	(	(	PUNCT
cana-2873	513	16	z2	z2	PROPN
cana-2873	513	17	,	,	PUNCT
cana-2873	513	18	σq	σq	NOUN
cana-2873	513	19	)	)	PUNCT
cana-2873	513	20	.	.	PUNCT
cana-2873	514	1	thus	thus	ADV
cana-2873	514	2	,	,	PUNCT
cana-2873	514	3	k	k	PROPN
cana-2873	514	4	is	be	AUX
cana-2873	514	5	a	a	DET
cana-2873	514	6	q	q	ADJ
cana-2873	514	7	-	-	PUNCT
cana-2873	514	8	nsɕβc	nsɕβc	ADJ
cana-2873	514	9	mapping	mapping	NOUN
cana-2873	514	10	.	.	PUNCT
cana-2873	515	1	(	(	PUNCT
cana-2873	515	2	ii	ii	NOUN
cana-2873	515	3	)	)	PUNCT
cana-2873	515	4	⇒	⇒	NOUN
cana-2873	515	5	(	(	PUNCT
cana-2873	515	6	iii	iii	NOUN
cana-2873	515	7	):	):	PUNCT
cana-2873	515	8	consider	consider	VERB
cana-2873	515	9	a	a	DET
cana-2873	515	10	q	q	NOUN
cana-2873	515	11	-	-	PUNCT
cana-2873	515	12	nscs	nscs	ADJ
cana-2873	515	13	(	(	PUNCT
cana-2873	515	14	ψ̃	ψ̃	PROPN
cana-2873	515	15	)	)	PUNCT
cana-2873	515	16	in	in	ADP
cana-2873	515	17	(	(	PUNCT
cana-2873	515	18	z1	z1	NOUN
cana-2873	515	19	,	,	PUNCT
cana-2873	515	20	γq	γq	ADP
cana-2873	515	21	)	)	PUNCT
cana-2873	515	22	.	.	PUNCT
cana-2873	516	1	by	by	ADP
cana-2873	516	2	assumption	assumption	NOUN
cana-2873	516	3	,	,	PUNCT
cana-2873	516	4	k(ψ̃	k(ψ̃	NOUN
cana-2873	516	5	)	)	PUNCT
cana-2873	516	6	is	be	AUX
cana-2873	516	7	a	a	DET
cana-2873	516	8	q	q	NOUN
cana-2873	516	9	-	-	PUNCT
cana-2873	516	10	nsβos	nsβos	NOUN
cana-2873	516	11	in	in	ADP
cana-2873	516	12	(	(	PUNCT
cana-2873	516	13	z2	z2	PROPN
cana-2873	516	14	,	,	PUNCT
cana-2873	516	15	σq	σq	NOUN
cana-2873	516	16	)	)	PUNCT
cana-2873	516	17	.	.	PUNCT
cana-2873	517	1	hence	hence	ADV
cana-2873	517	2	,	,	PUNCT
cana-2873	517	3	k(ψ̃	k(ψ̃	NOUN
cana-2873	517	4	)	)	PUNCT
cana-2873	517	5	=	=	SYM
cana-2873	517	6	(	(	PUNCT
cana-2873	517	7	k−1)−1(ψ̃	k−1)−1(ψ̃	PROPN
cana-2873	517	8	)	)	PUNCT
cana-2873	517	9	.	.	PUNCT
cana-2873	518	1	so	so	ADV
cana-2873	518	2	k−1	k−1	PROPN
cana-2873	518	3	is	be	AUX
cana-2873	518	4	a	a	DET
cana-2873	518	5	q	q	NOUN
cana-2873	518	6	-	-	PUNCT
cana-2873	518	7	nsβos	nsβos	NOUN
cana-2873	518	8	in	in	ADP
cana-2873	518	9	(	(	PUNCT
cana-2873	518	10	z2	z2	PROPN
cana-2873	518	11	,	,	PUNCT
cana-2873	518	12	σq	σq	NOUN
cana-2873	518	13	)	)	PUNCT
cana-2873	518	14	.	.	PUNCT
cana-2873	519	1	thus	thus	ADV
cana-2873	519	2	,	,	PUNCT
cana-2873	519	3	k−1	k−1	PROPN
cana-2873	519	4	is	be	AUX
cana-2873	519	5	q	q	NOUN
cana-2873	519	6	-	-	PUNCT
cana-2873	519	7	nsβcts	nsβct	NOUN
cana-2873	519	8	.	.	PUNCT
cana-2873	520	1	(	(	PUNCT
cana-2873	520	2	iii	iii	X
cana-2873	520	3	)	)	PUNCT
cana-2873	520	4	⇒	⇒	NOUN
cana-2873	520	5	(	(	PUNCT
cana-2873	520	6	i	i	NOUN
cana-2873	520	7	):	):	PUNCT
cana-2873	520	8	consider	consider	VERB
cana-2873	520	9	a	a	DET
cana-2873	520	10	q	q	NOUN
cana-2873	520	11	-	-	PUNCT
cana-2873	520	12	nsos	nsos	NOUN
cana-2873	520	13	(	(	PUNCT
cana-2873	520	14	ψ̃	ψ̃	PROPN
cana-2873	520	15	)	)	PUNCT
cana-2873	520	16	in	in	ADP
cana-2873	520	17	(	(	PUNCT
cana-2873	520	18	z1	z1	NOUN
cana-2873	520	19	,	,	PUNCT
cana-2873	520	20	γq	γq	ADP
cana-2873	520	21	)	)	PUNCT
cana-2873	520	22	.	.	PUNCT
cana-2873	521	1	by	by	ADP
cana-2873	521	2	assumption	assumption	NOUN
cana-2873	521	3	,	,	PUNCT
cana-2873	521	4	(	(	PUNCT
cana-2873	521	5	k−1)−1(ψ̃	k−1)−1(ψ̃	NOUN
cana-2873	521	6	)	)	PUNCT
cana-2873	521	7	=	=	SYM
cana-2873	521	8	k(ψ̃	k(ψ̃	NOUN
cana-2873	521	9	)	)	PUNCT
cana-2873	521	10	is	be	AUX
cana-2873	521	11	a	a	DET
cana-2873	521	12	q	q	ADJ
cana-2873	521	13	-	-	PUNCT
cana-2873	521	14	nscβo	nscβo	ADJ
cana-2873	521	15	mapping	mapping	NOUN
cana-2873	521	16	.	.	PUNCT
cana-2873	522	1	7	7	NUM
cana-2873	522	2	quadripartitioned	quadripartitione	VERB
cana-2873	522	3	neutrosophic	neutrosophic	PROPN
cana-2873	522	4	contra	contra	PROPN
cana-2873	522	5	β	β	PROPN
cana-2873	522	6	-	-	PUNCT
cana-2873	522	7	homeomorphism	homeomorphism	PROPN
cana-2873	522	8	in	in	ADP
cana-2873	522	9	this	this	DET
cana-2873	522	10	section	section	NOUN
cana-2873	522	11	,	,	PUNCT
cana-2873	522	12	the	the	DET
cana-2873	522	13	concept	concept	NOUN
cana-2873	522	14	of	of	ADP
cana-2873	522	15	quadripartitioned	quadripartitione	VERB
cana-2873	522	16	neutrosophic	neutrosophic	PROPN
cana-2873	522	17	contra	contra	PROPN
cana-2873	522	18	β	β	PROPN
cana-2873	522	19	-	-	PUNCT
cana-2873	522	20	homeomorphism	homeomorphism	PROPN
cana-2873	522	21	is	be	AUX
cana-2873	522	22	introduced	introduce	VERB
cana-2873	522	23	and	and	CCONJ
cana-2873	522	24	its	its	PRON
cana-2873	522	25	properties	property	NOUN
cana-2873	522	26	are	be	AUX
cana-2873	522	27	discussed	discuss	VERB
cana-2873	522	28	.	.	PUNCT
cana-2873	523	1	definition	definition	NOUN
cana-2873	523	2	7.1	7.1	NUM
cana-2873	523	3	.	.	PUNCT
cana-2873	524	1	a	a	DET
cana-2873	524	2	bijection	bijection	NOUN
cana-2873	524	3	k	k	X
cana-2873	524	4	:	:	PUNCT
cana-2873	524	5	(	(	PUNCT
cana-2873	524	6	z1	z1	VERB
cana-2873	524	7	,	,	PUNCT
cana-2873	524	8	γq	γq	ADP
cana-2873	524	9	)	)	PUNCT
cana-2873	524	10	→	→	SYM
cana-2873	524	11	(	(	PUNCT
cana-2873	524	12	z2	z2	PROPN
cana-2873	524	13	,	,	PUNCT
cana-2873	524	14	σq	σq	NOUN
cana-2873	524	15	)	)	PUNCT
cana-2873	524	16	is	be	AUX
cana-2873	524	17	called	call	VERB
cana-2873	524	18	a	a	DET
cana-2873	524	19	(	(	PUNCT
cana-2873	524	20	i	i	NOUN
cana-2873	524	21	)	)	PUNCT
cana-2873	524	22	quadripartitioned	quadripartitione	VERB
cana-2873	524	23	neutrosophic	neutrosophic	PROPN
cana-2873	524	24	contra	contra	PROPN
cana-2873	524	25	homeomorphism	homeomorphism	PROPN
cana-2873	524	26	(	(	PUNCT
cana-2873	524	27	briefly	briefly	ADV
cana-2873	524	28	q	q	NOUN
cana-2873	524	29	-	-	PUNCT
cana-2873	524	30	nschom	nschom	NOUN
cana-2873	524	31	)	)	PUNCT
cana-2873	524	32	if	if	SCONJ
cana-2873	524	33	k	k	PROPN
cana-2873	524	34	and	and	CCONJ
cana-2873	524	35	k−1	k−1	PROPN
cana-2873	524	36	are	be	AUX
cana-2873	524	37	qnsccts	qnscct	NOUN
cana-2873	524	38	mapping	mapping	NOUN
cana-2873	524	39	.	.	PUNCT
cana-2873	525	1	(	(	PUNCT
cana-2873	525	2	ii	ii	NOUN
cana-2873	525	3	)	)	PUNCT
cana-2873	525	4	quadripartitioned	quadripartitione	VERB
cana-2873	525	5	neutrosophic	neutrosophic	PROPN
cana-2873	525	6	contra	contra	PROPN
cana-2873	525	7	β	β	PROPN
cana-2873	525	8	-	-	PUNCT
cana-2873	525	9	homeomorphism	homeomorphism	X
cana-2873	525	10	(	(	PUNCT
cana-2873	525	11	briefly	briefly	NOUN
cana-2873	525	12	q	q	X
cana-2873	525	13	-	-	PUNCT
cana-2873	525	14	nscβhom	nscβhom	ADJ
cana-2873	525	15	)	)	PUNCT
cana-2873	525	16	if	if	SCONJ
cana-2873	525	17	k	k	PROPN
cana-2873	525	18	and	and	CCONJ
cana-2873	525	19	k−1	k−1	PROPN
cana-2873	525	20	are	be	AUX
cana-2873	525	21	qnscβcts	qnscβct	NOUN
cana-2873	525	22	mapping	mapping	NOUN
cana-2873	525	23	.	.	PUNCT
cana-2873	526	1	theorem	theorem	VERB
cana-2873	526	2	7.2	7.2	NUM
cana-2873	526	3	.	.	PUNCT
cana-2873	527	1	each	each	DET
cana-2873	527	2	q	q	NOUN
cana-2873	527	3	-	-	PUNCT
cana-2873	527	4	nsɕhom	nsɕhom	ADV
cana-2873	527	5	is	be	AUX
cana-2873	527	6	a	a	DET
cana-2873	527	7	q	q	NOUN
cana-2873	527	8	-	-	PUNCT
cana-2873	527	9	nsɕβhom	nsɕβhom	ADJ
cana-2873	527	10	.	.	PUNCT
cana-2873	528	1	but	but	CCONJ
cana-2873	528	2	the	the	DET
cana-2873	528	3	converse	converse	NOUN
cana-2873	528	4	not	not	PART
cana-2873	528	5	true	true	ADJ
cana-2873	528	6	.	.	PUNCT
cana-2873	529	1	proof	proof	NOUN
cana-2873	529	2	.	.	PUNCT
cana-2873	530	1	assume	assume	VERB
cana-2873	530	2	k	k	PROPN
cana-2873	530	3	is	be	AUX
cana-2873	530	4	q	q	NOUN
cana-2873	530	5	-	-	NOUN
cana-2873	530	6	nsɕhom	nsɕhom	NOUN
cana-2873	530	7	.	.	PUNCT
cana-2873	531	1	then	then	ADV
cana-2873	531	2	k	k	PROPN
cana-2873	531	3	and	and	CCONJ
cana-2873	531	4	k−1	k−1	PROPN
cana-2873	531	5	are	be	AUX
cana-2873	531	6	q	q	NOUN
cana-2873	531	7	-	-	PUNCT
cana-2873	531	8	nsɕcts	nsɕct	NOUN
cana-2873	531	9	.	.	PUNCT
cana-2873	532	1	we	we	PRON
cana-2873	532	2	know	know	VERB
cana-2873	532	3	that	that	SCONJ
cana-2873	532	4	each	each	DET
cana-2873	532	5	q	q	NOUN
cana-2873	532	6	-	-	PUNCT
cana-2873	532	7	nsɕcts	nsɕct	NOUN
cana-2873	532	8	function	function	NOUN
cana-2873	532	9	is	be	AUX
cana-2873	532	10	q	q	NOUN
cana-2873	532	11	-	-	PUNCT
cana-2873	532	12	nsɕβcts	nsɕβct	NOUN
cana-2873	532	13	.	.	PUNCT
cana-2873	533	1	so	so	ADV
cana-2873	533	2	,	,	PUNCT
cana-2873	533	3	k	k	PROPN
cana-2873	533	4	and	and	CCONJ
cana-2873	533	5	k−1	k−1	PROPN
cana-2873	533	6	are	be	AUX
cana-2873	533	7	q	q	NOUN
cana-2873	533	8	-	-	PUNCT
cana-2873	533	9	nsɕβcts	nsɕβct	NOUN
cana-2873	533	10	.	.	PUNCT
cana-2873	534	1	thus	thus	ADV
cana-2873	534	2	,	,	PUNCT
cana-2873	534	3	k	k	PROPN
cana-2873	534	4	is	be	AUX
cana-2873	534	5	a	a	DET
cana-2873	534	6	q	q	NOUN
cana-2873	534	7	-	-	PUNCT
cana-2873	534	8	nsɕβhom	nsɕβhom	ADJ
cana-2873	534	9	.	.	PUNCT
cana-2873	535	1	example	example	NOUN
cana-2873	535	2	7.3	7.3	NUM
cana-2873	535	3	.	.	PUNCT
cana-2873	536	1	let	let	VERB
cana-2873	536	2	v	v	VERB
cana-2873	536	3	=	=	PUNCT
cana-2873	536	4	{	{	PUNCT
cana-2873	536	5	a	a	PRON
cana-2873	536	6	,	,	PUNCT
cana-2873	536	7	b	b	NOUN
cana-2873	536	8	,	,	PUNCT
cana-2873	536	9	c	c	NOUN
cana-2873	536	10	}	}	PUNCT
cana-2873	536	11	=	=	SYM
cana-2873	536	12	w	w	NOUN
cana-2873	536	13	and	and	CCONJ
cana-2873	536	14	define	define	VERB
cana-2873	536	15	q	q	ADJ
cana-2873	536	16	-	-	PUNCT
cana-2873	536	17	nss	nss	NOUN
cana-2873	536	18	’s	’s	PART
cana-2873	536	19	v1	v1	NOUN
cana-2873	536	20	,	,	PUNCT
cana-2873	536	21	v2	v2	PROPN
cana-2873	536	22	&	&	CCONJ
cana-2873	536	23	v3	v3	PROPN
cana-2873	536	24	in	in	ADP
cana-2873	536	25	v	v	NOUN
cana-2873	536	26	and	and	CCONJ
cana-2873	536	27	w1	w1	NOUN
cana-2873	536	28	in	in	ADP
cana-2873	536	29	w	w	PROPN
cana-2873	536	30	are	be	AUX
cana-2873	536	31	v1	v1	NOUN
cana-2873	536	32	=	=	SYM
cana-2873	536	33	{	{	PUNCT
cana-2873	536	34	(	(	PUNCT
cana-2873	536	35	a	a	PRON
cana-2873	536	36	,	,	PUNCT
cana-2873	536	37	0.2	0.2	NUM
cana-2873	536	38	,	,	PUNCT
cana-2873	536	39	0.5	0.5	NUM
cana-2873	536	40	,	,	PUNCT
cana-2873	536	41	0.5	0.5	NUM
cana-2873	536	42	,	,	PUNCT
cana-2873	536	43	0.8	0.8	NUM
cana-2873	536	44	)	)	PUNCT
cana-2873	536	45	,	,	PUNCT
cana-2873	536	46	(	(	PUNCT
cana-2873	536	47	b	b	X
cana-2873	536	48	,	,	PUNCT
cana-2873	536	49	0.3	0.3	NUM
cana-2873	536	50	,	,	PUNCT
cana-2873	536	51	0.5	0.5	NUM
cana-2873	536	52	,	,	PUNCT
cana-2873	536	53	0.5	0.5	NUM
cana-2873	536	54	,	,	PUNCT
cana-2873	536	55	0.7	0.7	NUM
cana-2873	536	56	)	)	PUNCT
cana-2873	536	57	,	,	PUNCT
cana-2873	536	58	(	(	PUNCT
cana-2873	536	59	c	c	X
cana-2873	536	60	,	,	PUNCT
cana-2873	536	61	0.4	0.4	NUM
cana-2873	536	62	,	,	PUNCT
cana-2873	536	63	0.5	0.5	NUM
cana-2873	536	64	,	,	PUNCT
cana-2873	536	65	0.5	0.5	NUM
cana-2873	536	66	,	,	PUNCT
cana-2873	536	67	0.6	0.6	NUM
cana-2873	536	68	)	)	PUNCT
cana-2873	536	69	}	}	PUNCT
cana-2873	536	70	,	,	PUNCT
cana-2873	536	71	v2	v2	PROPN
cana-2873	536	72	=	=	SYM
cana-2873	536	73	{	{	PUNCT
cana-2873	536	74	(	(	PUNCT
cana-2873	536	75	a	a	PRON
cana-2873	536	76	,	,	PUNCT
cana-2873	536	77	0.1	0.1	NUM
cana-2873	536	78	,	,	PUNCT
cana-2873	536	79	0.5	0.5	NUM
cana-2873	536	80	,	,	PUNCT
cana-2873	536	81	0.5	0.5	NUM
cana-2873	536	82	,	,	PUNCT
cana-2873	536	83	0.9	0.9	NUM
cana-2873	536	84	)	)	PUNCT
cana-2873	536	85	,	,	PUNCT
cana-2873	536	86	(	(	PUNCT
cana-2873	536	87	b	b	NOUN
cana-2873	536	88	,	,	PUNCT
cana-2873	536	89	0.1	0.1	NUM
cana-2873	536	90	,	,	PUNCT
cana-2873	536	91	0.5	0.5	NUM
cana-2873	536	92	,	,	PUNCT
cana-2873	536	93	0.5	0.5	NUM
cana-2873	536	94	,	,	PUNCT
cana-2873	536	95	0.9	0.9	NUM
cana-2873	536	96	)	)	PUNCT
cana-2873	536	97	,	,	PUNCT
cana-2873	536	98	(	(	PUNCT
cana-2873	536	99	c	c	X
cana-2873	536	100	,	,	PUNCT
cana-2873	536	101	0.4	0.4	NUM
cana-2873	536	102	,	,	PUNCT
cana-2873	536	103	0.5	0.5	NUM
cana-2873	536	104	,	,	PUNCT
cana-2873	536	105	0.5	0.5	NUM
cana-2873	536	106	,	,	PUNCT
cana-2873	536	107	0.6	0.6	NUM
cana-2873	536	108	)	)	PUNCT
cana-2873	536	109	}	}	PUNCT
cana-2873	536	110	,	,	PUNCT
cana-2873	536	111	v3	v3	PROPN
cana-2873	536	112	=	=	SYM
cana-2873	536	113	{	{	PUNCT
cana-2873	536	114	(	(	PUNCT
cana-2873	536	115	a	a	PRON
cana-2873	536	116	,	,	PUNCT
cana-2873	536	117	0.2	0.2	NUM
cana-2873	536	118	,	,	PUNCT
cana-2873	536	119	0.5	0.5	NUM
cana-2873	536	120	,	,	PUNCT
cana-2873	536	121	0.5	0.5	NUM
cana-2873	536	122	,	,	PUNCT
cana-2873	536	123	0.8	0.8	NUM
cana-2873	536	124	)	)	PUNCT
cana-2873	536	125	,	,	PUNCT
cana-2873	536	126	(	(	PUNCT
cana-2873	536	127	b	b	X
cana-2873	536	128	,	,	PUNCT
cana-2873	536	129	0.4	0.4	NUM
cana-2873	536	130	,	,	PUNCT
cana-2873	536	131	0.5	0.5	NUM
cana-2873	536	132	,	,	PUNCT
cana-2873	536	133	0.5	0.5	NUM
cana-2873	536	134	,	,	PUNCT
cana-2873	536	135	0.6	0.6	NUM
cana-2873	536	136	)	)	PUNCT
cana-2873	536	137	,	,	PUNCT
cana-2873	536	138	(	(	PUNCT
cana-2873	536	139	c	c	X
cana-2873	536	140	,	,	PUNCT
cana-2873	536	141	0.4	0.4	NUM
cana-2873	536	142	,	,	PUNCT
cana-2873	536	143	0.5	0.5	NUM
cana-2873	536	144	,	,	PUNCT
cana-2873	536	145	0.5	0.5	NUM
cana-2873	536	146	,	,	PUNCT
cana-2873	536	147	0.6	0.6	NUM
cana-2873	536	148	)	)	PUNCT
cana-2873	536	149	}	}	PUNCT
cana-2873	536	150	,	,	PUNCT
cana-2873	536	151	w1	w1	NOUN
cana-2873	536	152	=	=	SYM
cana-2873	536	153	{	{	PUNCT
cana-2873	536	154	(	(	PUNCT
cana-2873	536	155	a	a	PRON
cana-2873	536	156	,	,	PUNCT
cana-2873	536	157	0.2	0.2	NUM
cana-2873	536	158	,	,	PUNCT
cana-2873	536	159	0.5	0.5	NUM
cana-2873	536	160	,	,	PUNCT
cana-2873	536	161	0.5	0.5	NUM
cana-2873	536	162	,	,	PUNCT
cana-2873	536	163	0.8	0.8	NUM
cana-2873	536	164	)	)	PUNCT
cana-2873	536	165	,	,	PUNCT
cana-2873	536	166	(	(	PUNCT
cana-2873	536	167	b	b	X
cana-2873	536	168	,	,	PUNCT
cana-2873	536	169	0.4	0.4	NUM
cana-2873	536	170	,	,	PUNCT
cana-2873	536	171	0.5	0.5	NUM
cana-2873	536	172	,	,	PUNCT
cana-2873	536	173	0.5	0.5	NUM
cana-2873	536	174	,	,	PUNCT
cana-2873	536	175	0.6	0.6	NUM
cana-2873	536	176	)	)	PUNCT
cana-2873	536	177	,	,	PUNCT
cana-2873	536	178	(	(	PUNCT
cana-2873	536	179	c	c	X
cana-2873	536	180	,	,	PUNCT
cana-2873	536	181	0.4	0.4	NUM
cana-2873	536	182	,	,	PUNCT
cana-2873	536	183	0.5	0.5	NUM
cana-2873	536	184	,	,	PUNCT
cana-2873	536	185	0.5	0.5	NUM
cana-2873	536	186	,	,	PUNCT
cana-2873	536	187	0.6	0.6	NUM
cana-2873	536	188	)	)	PUNCT
cana-2873	536	189	}	}	PUNCT
cana-2873	536	190	.	.	PUNCT
cana-2873	537	1	then	then	ADV
cana-2873	537	2	we	we	PRON
cana-2873	537	3	have	have	VERB
cana-2873	537	4	γq	γq	ADP
cana-2873	537	5	=	=	SYM
cana-2873	537	6	{	{	PUNCT
cana-2873	537	7	0qns	0qns	PROPN
cana-2873	537	8	,	,	PUNCT
cana-2873	537	9	v1	v1	PROPN
cana-2873	537	10	,	,	PUNCT
cana-2873	537	11	v2	v2	PROPN
cana-2873	537	12	,	,	PUNCT
cana-2873	537	13	1qns	1qns	NUM
cana-2873	537	14	}	}	PUNCT
cana-2873	537	15	and	and	CCONJ
cana-2873	537	16	σq	σq	NOUN
cana-2873	537	17	=	=	SYM
cana-2873	537	18	{	{	PUNCT
cana-2873	537	19	0qns	0qns	PROPN
cana-2873	537	20	,	,	PUNCT
cana-2873	537	21	w1	w1	NOUN
cana-2873	537	22	,	,	PUNCT
cana-2873	537	23	1qns	1qns	NUM
cana-2873	537	24	}	}	PUNCT
cana-2873	537	25	.	.	PUNCT
cana-2873	538	1	let	let	VERB
cana-2873	538	2	k	k	NOUN
cana-2873	538	3	:	:	PUNCT
cana-2873	538	4	(	(	PUNCT
cana-2873	538	5	z1	z1	VERB
cana-2873	538	6	,	,	PUNCT
cana-2873	538	7	γq	γq	ADP
cana-2873	538	8	)	)	PUNCT
cana-2873	538	9	→	→	SYM
cana-2873	538	10	(	(	PUNCT
cana-2873	538	11	z2	z2	PROPN
cana-2873	538	12	,	,	PUNCT
cana-2873	538	13	σq	σq	NOUN
cana-2873	538	14	)	)	PUNCT
cana-2873	538	15	be	be	VERB
cana-2873	538	16	an	an	DET
cana-2873	538	17	identity	identity	NOUN
cana-2873	538	18	mapping	mapping	NOUN
cana-2873	538	19	,	,	PUNCT
cana-2873	538	20	then	then	ADV
cana-2873	538	21	k	k	PROPN
cana-2873	538	22	is	be	AUX
cana-2873	538	23	q	q	NOUN
cana-2873	538	24	-	-	PUNCT
cana-2873	538	25	nshom	nshom	ADJ
cana-2873	538	26	but	but	CCONJ
cana-2873	538	27	not	not	PART
cana-2873	538	28	q	q	NOUN
cana-2873	538	29	-	-	PUNCT
cana-2873	538	30	nsɕhom	nsɕhom	NOUN
cana-2873	538	31	.	.	PUNCT
cana-2873	539	1	theorem	theorem	NOUN
cana-2873	539	2	7.4	7.4	NUM
cana-2873	539	3	.	.	PUNCT
cana-2873	540	1	consider	consider	VERB
cana-2873	540	2	a	a	DET
cana-2873	540	3	bijective	bijective	ADJ
cana-2873	540	4	mapping	mapping	NOUN
cana-2873	540	5	k	k	NOUN
cana-2873	540	6	:	:	PUNCT
cana-2873	540	7	(	(	PUNCT
cana-2873	540	8	z1	z1	VERB
cana-2873	540	9	,	,	PUNCT
cana-2873	540	10	γq	γq	ADP
cana-2873	540	11	)	)	PUNCT
cana-2873	540	12	→(z2,σq	→(z2,σq	NOUN
cana-2873	540	13	)	)	PUNCT
cana-2873	540	14	.	.	PUNCT
cana-2873	541	1	the	the	DET
cana-2873	541	2	followings	following	NOUN
cana-2873	541	3	statements	statement	NOUN
cana-2873	541	4	are	be	AUX
cana-2873	541	5	equivalent	equivalent	ADJ
cana-2873	541	6	if	if	SCONJ
cana-2873	541	7	k	k	PROPN
cana-2873	541	8	is	be	AUX
cana-2873	541	9	q	q	NOUN
cana-2873	541	10	-	-	PUNCT
cana-2873	541	11	nsɕβcts	nsɕβct	NOUN
cana-2873	541	12	.	.	PUNCT
cana-2873	542	1	(	(	PUNCT
cana-2873	542	2	i	i	NOUN
cana-2873	542	3	)	)	PUNCT
cana-2873	543	1	k	k	PROPN
cana-2873	543	2	is	be	AUX
cana-2873	543	3	a	a	DET
cana-2873	543	4	q	q	ADJ
cana-2873	543	5	-	-	PUNCT
cana-2873	543	6	nsɕβc	nsɕβc	ADJ
cana-2873	543	7	mapping	mapping	NOUN
cana-2873	543	8	.	.	PUNCT
cana-2873	544	1	communications	communication	NOUN
cana-2873	544	2	on	on	ADP
cana-2873	544	3	applied	apply	VERB
cana-2873	544	4	nonlinear	nonlinear	ADJ
cana-2873	544	5	analysis	analysis	NOUN
cana-2873	544	6	issn	issn	NOUN
cana-2873	544	7	:	:	PUNCT
cana-2873	544	8	1074	1074	NUM
cana-2873	544	9	-	-	PUNCT
cana-2873	544	10	133x	133x	NUM
cana-2873	544	11	vol	vol	NOUN
cana-2873	544	12	32	32	NUM
cana-2873	544	13	no	no	NOUN
cana-2873	544	14	.	.	PUNCT
cana-2873	545	1	4s	4s	NUM
cana-2873	545	2	(	(	PUNCT
cana-2873	545	3	2025	2025	NUM
cana-2873	545	4	)	)	PUNCT
cana-2873	545	5	594	594	NUM
cana-2873	545	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	545	7	(	(	PUNCT
cana-2873	545	8	ii	ii	NOUN
cana-2873	545	9	)	)	PUNCT
cana-2873	546	1	k	k	PROPN
cana-2873	546	2	is	be	AUX
cana-2873	546	3	a	a	DET
cana-2873	546	4	q	q	ADJ
cana-2873	546	5	-	-	PUNCT
cana-2873	546	6	nsɕβo	nsɕβo	NOUN
cana-2873	546	7	mapping	mapping	NOUN
cana-2873	546	8	.	.	PUNCT
cana-2873	547	1	(	(	PUNCT
cana-2873	547	2	iii	iii	X
cana-2873	547	3	)	)	PUNCT
cana-2873	547	4	k	k	NOUN
cana-2873	547	5	is	be	AUX
cana-2873	547	6	a	a	DET
cana-2873	547	7	q	q	NOUN
cana-2873	547	8	-	-	PUNCT
cana-2873	547	9	nsɕβhom	nsɕβhom	ADJ
cana-2873	547	10	.	.	PUNCT
cana-2873	548	1	proof	proof	NOUN
cana-2873	548	2	.	.	PUNCT
cana-2873	549	1	(	(	PUNCT
cana-2873	549	2	i)⇒(ii	i)⇒(ii	ADV
cana-2873	549	3	)	)	PUNCT
cana-2873	549	4	:	:	PUNCT
cana-2873	549	5	let	let	VERB
cana-2873	549	6	k	k	PRON
cana-2873	549	7	be	be	AUX
cana-2873	549	8	a	a	DET
cana-2873	549	9	bijective	bijective	ADJ
cana-2873	549	10	mapping	mapping	NOUN
cana-2873	549	11	and	and	CCONJ
cana-2873	549	12	a	a	DET
cana-2873	549	13	q	q	ADJ
cana-2873	549	14	-	-	PUNCT
cana-2873	549	15	nsɕβc	nsɕβc	ADJ
cana-2873	549	16	mapping	mapping	NOUN
cana-2873	549	17	.	.	PUNCT
cana-2873	550	1	therefore	therefore	ADV
cana-2873	550	2	,	,	PUNCT
cana-2873	550	3	k−1	k−1	PROPN
cana-2873	550	4	is	be	AUX
cana-2873	550	5	a	a	DET
cana-2873	550	6	qnsɕβcts	qnsɕβct	NOUN
cana-2873	550	7	mapping	mapping	NOUN
cana-2873	550	8	.	.	PUNCT
cana-2873	551	1	as	as	SCONJ
cana-2873	551	2	each	each	DET
cana-2873	551	3	q	q	NOUN
cana-2873	551	4	-	-	PUNCT
cana-2873	551	5	nsos	nsos	NOUN
cana-2873	551	6	in	in	ADP
cana-2873	551	7	(	(	PUNCT
cana-2873	551	8	z1	z1	NOUN
cana-2873	551	9	,	,	PUNCT
cana-2873	551	10	γq	γq	ADP
cana-2873	551	11	)	)	PUNCT
cana-2873	551	12	is	be	AUX
cana-2873	551	13	a	a	DET
cana-2873	551	14	q	q	NOUN
cana-2873	551	15	-	-	PUNCT
cana-2873	551	16	nsβcs	nsβcs	NOUN
cana-2873	551	17	in	in	ADP
cana-2873	551	18	(	(	PUNCT
cana-2873	551	19	z2	z2	PROPN
cana-2873	551	20	,	,	PUNCT
cana-2873	551	21	σq	σq	NOUN
cana-2873	551	22	)	)	PUNCT
cana-2873	551	23	,	,	PUNCT
cana-2873	551	24	k	k	PROPN
cana-2873	551	25	is	be	AUX
cana-2873	551	26	a	a	DET
cana-2873	551	27	q	q	ADJ
cana-2873	551	28	-	-	PUNCT
cana-2873	551	29	nsɕβo	nsɕβo	NOUN
cana-2873	551	30	mapping	mapping	NOUN
cana-2873	551	31	.	.	PUNCT
cana-2873	552	1	(	(	PUNCT
cana-2873	552	2	ii	ii	NOUN
cana-2873	552	3	)	)	PUNCT
cana-2873	552	4	⇒	⇒	NOUN
cana-2873	552	5	(	(	PUNCT
cana-2873	552	6	iii	iii	NOUN
cana-2873	552	7	)	)	PUNCT
cana-2873	552	8	:	:	PUNCT
cana-2873	552	9	assume	assume	VERB
cana-2873	552	10	k	k	PROPN
cana-2873	552	11	is	be	AUX
cana-2873	552	12	a	a	DET
cana-2873	552	13	bijective	bijective	ADJ
cana-2873	552	14	and	and	CCONJ
cana-2873	552	15	q	q	ADJ
cana-2873	552	16	-	-	PUNCT
cana-2873	552	17	nsɕβo	nsɕβo	NOUN
cana-2873	552	18	mapping	mapping	NOUN
cana-2873	552	19	.	.	PUNCT
cana-2873	553	1	also	also	ADV
cana-2873	553	2	,	,	PUNCT
cana-2873	553	3	k−1	k−1	PROPN
cana-2873	553	4	is	be	AUX
cana-2873	553	5	a	a	DET
cana-2873	553	6	q	q	ADJ
cana-2873	553	7	-	-	PUNCT
cana-2873	553	8	nscβcts	nscβct	NOUN
cana-2873	553	9	mapping	mapping	NOUN
cana-2873	553	10	.	.	PUNCT
cana-2873	554	1	therefore	therefore	ADV
cana-2873	554	2	,	,	PUNCT
cana-2873	554	3	k	k	PROPN
cana-2873	554	4	and	and	CCONJ
cana-2873	554	5	k−1	k−1	PROPN
cana-2873	554	6	are	be	AUX
cana-2873	554	7	q	q	NOUN
cana-2873	554	8	-	-	PUNCT
cana-2873	554	9	nsɕβcts	nsɕβct	NOUN
cana-2873	554	10	.	.	PUNCT
cana-2873	555	1	thus	thus	ADV
cana-2873	555	2	,	,	PUNCT
cana-2873	555	3	k	k	PROPN
cana-2873	555	4	is	be	AUX
cana-2873	555	5	a	a	DET
cana-2873	555	6	q	q	NOUN
cana-2873	555	7	-	-	PUNCT
cana-2873	555	8	nsɕβhom	nsɕβhom	ADJ
cana-2873	555	9	.	.	PUNCT
cana-2873	556	1	(	(	PUNCT
cana-2873	556	2	iii	iii	X
cana-2873	556	3	)	)	PUNCT
cana-2873	556	4	⇒	⇒	NOUN
cana-2873	556	5	(	(	PUNCT
cana-2873	556	6	i	i	NOUN
cana-2873	556	7	):	):	PUNCT
cana-2873	556	8	assume	assume	VERB
cana-2873	556	9	k	k	PROPN
cana-2873	556	10	is	be	AUX
cana-2873	556	11	a	a	DET
cana-2873	556	12	q	q	NOUN
cana-2873	556	13	-	-	PUNCT
cana-2873	556	14	nsɕβhom	nsɕβhom	ADJ
cana-2873	556	15	.	.	PUNCT
cana-2873	557	1	so	so	ADV
cana-2873	557	2	,	,	PUNCT
cana-2873	557	3	k	k	PROPN
cana-2873	557	4	and	and	CCONJ
cana-2873	557	5	k−1	k−1	PROPN
cana-2873	557	6	are	be	AUX
cana-2873	557	7	q	q	NOUN
cana-2873	557	8	-	-	PUNCT
cana-2873	557	9	nsɕβcts	nsɕβct	NOUN
cana-2873	557	10	.	.	PUNCT
cana-2873	558	1	as	as	SCONJ
cana-2873	558	2	every	every	PRON
cana-2873	558	3	q	q	NOUN
cana-2873	558	4	nscs	nscs	ADJ
cana-2873	558	5	in	in	ADP
cana-2873	558	6	(	(	PUNCT
cana-2873	558	7	z1	z1	NOUN
cana-2873	558	8	,	,	PUNCT
cana-2873	558	9	γq	γq	ADP
cana-2873	558	10	)	)	PUNCT
cana-2873	558	11	is	be	AUX
cana-2873	558	12	a	a	DET
cana-2873	558	13	q	q	NOUN
cana-2873	558	14	-	-	PUNCT
cana-2873	558	15	nsβos	nsβos	NOUN
cana-2873	558	16	in	in	ADP
cana-2873	558	17	(	(	PUNCT
cana-2873	558	18	z2	z2	PROPN
cana-2873	558	19	,	,	PUNCT
cana-2873	558	20	σq	σq	NOUN
cana-2873	558	21	)	)	PUNCT
cana-2873	558	22	,	,	PUNCT
cana-2873	558	23	k	k	PROPN
cana-2873	558	24	is	be	AUX
cana-2873	558	25	a	a	DET
cana-2873	558	26	q	q	ADJ
cana-2873	558	27	-	-	PUNCT
cana-2873	558	28	nsɕβc	nsɕβc	ADJ
cana-2873	558	29	mapping	mapping	NOUN
cana-2873	558	30	.	.	PUNCT
cana-2873	559	1	theorem	theorem	VERB
cana-2873	559	2	7.5	7.5	NUM
cana-2873	559	3	.	.	PUNCT
cana-2873	560	1	let	let	VERB
cana-2873	560	2	k	k	NOUN
cana-2873	560	3	:	:	PUNCT
cana-2873	560	4	(	(	PUNCT
cana-2873	560	5	z1	z1	VERB
cana-2873	560	6	,	,	PUNCT
cana-2873	560	7	γq	γq	ADP
cana-2873	560	8	)	)	PUNCT
cana-2873	560	9	(	(	PUNCT
cana-2873	560	10	z2	z2	PROPN
cana-2873	560	11	,	,	PUNCT
cana-2873	560	12	σq	σq	NOUN
cana-2873	560	13	)	)	PUNCT
cana-2873	560	14	be	be	VERB
cana-2873	560	15	a	a	DET
cana-2873	560	16	q	q	NOUN
cana-2873	560	17	-	-	PUNCT
cana-2873	560	18	nsɕβhom	nsɕβhom	ADJ
cana-2873	560	19	.	.	PUNCT
cana-2873	561	1	if	if	SCONJ
cana-2873	561	2	(	(	PUNCT
cana-2873	561	3	z1	z1	NOUN
cana-2873	561	4	,	,	PUNCT
cana-2873	561	5	γq	γq	NOUN
cana-2873	561	6	)	)	PUNCT
cana-2873	561	7	and	and	CCONJ
cana-2873	561	8	(	(	PUNCT
cana-2873	561	9	z2	z2	PROPN
cana-2873	561	10	,	,	PUNCT
cana-2873	561	11	σq	σq	NOUN
cana-2873	561	12	)	)	PUNCT
cana-2873	561	13	are	be	AUX
cana-2873	561	14	qnsβt	qnsβt	NOUN
cana-2873	561	15	1	1	NUM
cana-2873	561	16	spaces	space	NOUN
cana-2873	561	17	,	,	PUNCT
cana-2873	561	18	then	then	ADV
cana-2873	561	19	k	k	PROPN
cana-2873	561	20	is	be	AUX
cana-2873	561	21	a	a	DET
cana-2873	561	22	q	q	NOUN
cana-2873	561	23	-	-	NOUN
cana-2873	561	24	nsɕhom	nsɕhom	NOUN
cana-2873	561	25	.	.	PUNCT
cana-2873	562	1	proof	proof	NOUN
cana-2873	562	2	.	.	PUNCT
cana-2873	563	1	consider	consider	VERB
cana-2873	563	2	a	a	DET
cana-2873	563	3	q	q	NOUN
cana-2873	563	4	-	-	PUNCT
cana-2873	563	5	nscs	nscs	ADJ
cana-2873	563	6	ψ̃	ψ̃	PROPN
cana-2873	563	7	in	in	ADP
cana-2873	563	8	(	(	PUNCT
cana-2873	563	9	z2	z2	PROPN
cana-2873	563	10	,	,	PUNCT
cana-2873	563	11	σq	σq	NOUN
cana-2873	563	12	)	)	PUNCT
cana-2873	563	13	.	.	PUNCT
cana-2873	564	1	so	so	ADV
cana-2873	564	2	,	,	PUNCT
cana-2873	564	3	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	564	4	)	)	PUNCT
cana-2873	564	5	is	be	AUX
cana-2873	564	6	a	a	DET
cana-2873	564	7	q	q	NOUN
cana-2873	564	8	-	-	PUNCT
cana-2873	564	9	nsβos	nsβos	NOUN
cana-2873	564	10	in	in	ADP
cana-2873	564	11	(	(	PUNCT
cana-2873	564	12	z1	z1	NOUN
cana-2873	564	13	,	,	PUNCT
cana-2873	564	14	γq	γq	ADP
cana-2873	564	15	)	)	PUNCT
cana-2873	564	16	.	.	PUNCT
cana-2873	565	1	as	as	SCONJ
cana-2873	565	2	(	(	PUNCT
cana-2873	565	3	z1	z1	NOUN
cana-2873	565	4	,	,	PUNCT
cana-2873	565	5	γq	γq	ADP
cana-2873	565	6	)	)	PUNCT
cana-2873	565	7	is	be	AUX
cana-2873	565	8	a	a	DET
cana-2873	565	9	q	q	ADJ
cana-2873	565	10	-	-	PUNCT
cana-2873	565	11	nsβt1/2	nsβt1/2	ADJ
cana-2873	565	12	-space	-space	NOUN
cana-2873	565	13	,	,	PUNCT
cana-2873	565	14	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	565	15	)	)	PUNCT
cana-2873	565	16	is	be	AUX
cana-2873	565	17	a	a	DET
cana-2873	565	18	q	q	NOUN
cana-2873	565	19	-	-	PUNCT
cana-2873	565	20	nsos	nsos	NOUN
cana-2873	565	21	in	in	ADP
cana-2873	565	22	(	(	PUNCT
cana-2873	565	23	z1	z1	NOUN
cana-2873	565	24	,	,	PUNCT
cana-2873	565	25	γq	γq	ADP
cana-2873	565	26	)	)	PUNCT
cana-2873	565	27	.	.	PUNCT
cana-2873	566	1	therefore	therefore	ADV
cana-2873	566	2	,	,	PUNCT
cana-2873	566	3	k	k	PROPN
cana-2873	566	4	is	be	AUX
cana-2873	566	5	q	q	NOUN
cana-2873	566	6	-	-	PUNCT
cana-2873	566	7	nsɕcts	nsɕct	NOUN
cana-2873	566	8	.	.	PUNCT
cana-2873	567	1	by	by	ADP
cana-2873	567	2	hypothesis	hypothesis	NOUN
cana-2873	567	3	,	,	PUNCT
cana-2873	567	4	k−1	k−1	PROPN
cana-2873	567	5	is	be	AUX
cana-2873	567	6	q	q	NOUN
cana-2873	567	7	-	-	PUNCT
cana-2873	567	8	nsɕβcts	nsɕβct	NOUN
cana-2873	567	9	.	.	PUNCT
cana-2873	568	1	let	let	VERB
cana-2873	568	2	(	(	PUNCT
cana-2873	568	3	ψ̃	ψ̃	PROPN
cana-2873	568	4	)	)	PUNCT
cana-2873	568	5	be	be	VERB
cana-2873	568	6	a	a	DET
cana-2873	568	7	q	q	NOUN
cana-2873	568	8	-	-	PUNCT
cana-2873	568	9	nscs	nscs	ADJ
cana-2873	568	10	in	in	ADP
cana-2873	568	11	(	(	PUNCT
cana-2873	568	12	z1	z1	NOUN
cana-2873	568	13	,	,	PUNCT
cana-2873	568	14	γq	γq	ADP
cana-2873	568	15	)	)	PUNCT
cana-2873	568	16	.	.	PUNCT
cana-2873	569	1	then	then	ADV
cana-2873	569	2	,	,	PUNCT
cana-2873	569	3	k(ψ̃	k(ψ̃	PROPN
cana-2873	569	4	)	)	PUNCT
cana-2873	569	5	is	be	AUX
cana-2873	569	6	a	a	DET
cana-2873	569	7	q	q	NOUN
cana-2873	569	8	-	-	PUNCT
cana-2873	569	9	nsβos	nsβos	NOUN
cana-2873	569	10	in	in	ADP
cana-2873	569	11	(	(	PUNCT
cana-2873	569	12	z2	z2	PROPN
cana-2873	569	13	,	,	PUNCT
cana-2873	569	14	σq	σq	NOUN
cana-2873	569	15	)	)	PUNCT
cana-2873	569	16	,	,	PUNCT
cana-2873	569	17	by	by	ADP
cana-2873	569	18	presumption	presumption	NOUN
cana-2873	569	19	.	.	PUNCT
cana-2873	570	1	since	since	SCONJ
cana-2873	570	2	(	(	PUNCT
cana-2873	570	3	z2	z2	PROPN
cana-2873	570	4	,	,	PUNCT
cana-2873	570	5	σq	σq	NOUN
cana-2873	570	6	)	)	PUNCT
cana-2873	570	7	is	be	AUX
cana-2873	570	8	a	a	DET
cana-2873	570	9	q	q	ADJ
cana-2873	570	10	-	-	PUNCT
cana-2873	570	11	nsβt1/2	nsβt1/2	ADJ
cana-2873	570	12	-space	-space	NOUN
cana-2873	570	13	,	,	PUNCT
cana-2873	570	14	k(ψ̃	k(ψ̃	NOUN
cana-2873	570	15	)	)	PUNCT
cana-2873	570	16	is	be	AUX
cana-2873	570	17	a	a	DET
cana-2873	570	18	q	q	NOUN
cana-2873	570	19	-	-	PUNCT
cana-2873	570	20	nsos	nsos	NOUN
cana-2873	570	21	in	in	ADP
cana-2873	570	22	(	(	PUNCT
cana-2873	570	23	z2	z2	PROPN
cana-2873	570	24	,	,	PUNCT
cana-2873	570	25	σq	σq	NOUN
cana-2873	570	26	)	)	PUNCT
cana-2873	570	27	.	.	PUNCT
cana-2873	571	1	therefore	therefore	ADV
cana-2873	571	2	,	,	PUNCT
cana-2873	571	3	k−1	k−1	PROPN
cana-2873	571	4	is	be	AUX
cana-2873	571	5	q	q	NOUN
cana-2873	571	6	-	-	PUNCT
cana-2873	571	7	nsɕcts	nsɕct	NOUN
cana-2873	571	8	.	.	PUNCT
cana-2873	572	1	thus	thus	ADV
cana-2873	572	2	,	,	PUNCT
cana-2873	572	3	k	k	PROPN
cana-2873	572	4	is	be	AUX
cana-2873	572	5	a	a	DET
cana-2873	572	6	q	q	NOUN
cana-2873	572	7	-	-	NOUN
cana-2873	572	8	nsɕhom	nsɕhom	NOUN
cana-2873	572	9	.	.	PUNCT
cana-2873	573	1	theorem	theorem	NOUN
cana-2873	573	2	7.6	7.6	NUM
cana-2873	573	3	.	.	PUNCT
cana-2873	574	1	let	let	VERB
cana-2873	574	2	k	k	NOUN
cana-2873	574	3	:	:	PUNCT
cana-2873	574	4	(	(	PUNCT
cana-2873	574	5	z1	z1	VERB
cana-2873	574	6	,	,	PUNCT
cana-2873	574	7	γq)→	γq)→	X
cana-2873	574	8	(	(	PUNCT
cana-2873	574	9	z2	z2	PROPN
cana-2873	574	10	,	,	PUNCT
cana-2873	574	11	σq	σq	NOUN
cana-2873	574	12	)	)	PUNCT
cana-2873	574	13	be	be	VERB
cana-2873	574	14	a	a	DET
cana-2873	574	15	q	q	NOUN
cana-2873	574	16	-	-	NOUN
cana-2873	574	17	nsts	nst	NOUN
cana-2873	574	18	.	.	PUNCT
cana-2873	575	1	if	if	SCONJ
cana-2873	575	2	(	(	PUNCT
cana-2873	575	3	z2	z2	NOUN
cana-2873	575	4	,	,	PUNCT
cana-2873	575	5	σq	σq	NOUN
cana-2873	575	6	)	)	PUNCT
cana-2873	575	7	is	be	AUX
cana-2873	575	8	a	a	DET
cana-2873	575	9	q	q	ADJ
cana-2873	575	10	-	-	PUNCT
cana-2873	575	11	nsβt1/2	nsβt1/2	ADJ
cana-2873	575	12	-space	-space	NOUN
cana-2873	575	13	,	,	PUNCT
cana-2873	575	14	then	then	ADV
cana-2873	575	15	the	the	DET
cana-2873	575	16	following	following	NOUN
cana-2873	575	17	are	be	AUX
cana-2873	575	18	equivalent	equivalent	ADJ
cana-2873	575	19	:	:	PUNCT
cana-2873	575	20	(	(	PUNCT
cana-2873	575	21	i	i	NOUN
cana-2873	575	22	)	)	PUNCT
cana-2873	576	1	k	k	PROPN
cana-2873	576	2	is	be	AUX
cana-2873	576	3	q	q	ADJ
cana-2873	576	4	-	-	PUNCT
cana-2873	576	5	nsɕβc	nsɕβc	ADJ
cana-2873	576	6	mapping	mapping	NOUN
cana-2873	576	7	.	.	PUNCT
cana-2873	577	1	(	(	PUNCT
cana-2873	577	2	ii	ii	NOUN
cana-2873	577	3	)	)	PUNCT
cana-2873	577	4	if	if	SCONJ
cana-2873	577	5	(	(	PUNCT
cana-2873	577	6	ψ̃	ψ̃	PROPN
cana-2873	577	7	)	)	PUNCT
cana-2873	577	8	is	be	AUX
cana-2873	577	9	a	a	DET
cana-2873	577	10	q	q	NOUN
cana-2873	577	11	-	-	PUNCT
cana-2873	577	12	nsos	nsos	NOUN
cana-2873	577	13	in	in	ADP
cana-2873	577	14	(	(	PUNCT
cana-2873	577	15	z1	z1	NOUN
cana-2873	577	16	,	,	PUNCT
cana-2873	577	17	γq	γq	ADP
cana-2873	577	18	)	)	PUNCT
cana-2873	577	19	,	,	PUNCT
cana-2873	577	20	then	then	ADV
cana-2873	577	21	k(ψ̃	k(ψ̃	PROPN
cana-2873	577	22	)	)	PUNCT
cana-2873	577	23	is	be	AUX
cana-2873	577	24	q	q	ADJ
cana-2873	577	25	-	-	NOUN
cana-2873	577	26	nsβcs	nsβcs	NOUN
cana-2873	577	27	in	in	ADP
cana-2873	577	28	(	(	PUNCT
cana-2873	577	29	z2	z2	PROPN
cana-2873	577	30	,	,	PUNCT
cana-2873	577	31	σq	σq	NOUN
cana-2873	577	32	)	)	PUNCT
cana-2873	577	33	.	.	PUNCT
cana-2873	578	1	(	(	PUNCT
cana-2873	578	2	iii	iii	X
cana-2873	578	3	)	)	PUNCT
cana-2873	578	4	k(q	k(q	PROPN
cana-2873	578	5	-	-	PUNCT
cana-2873	578	6	nsint(ψ̃	nsint(ψ̃	PROPN
cana-2873	578	7	)	)	PUNCT
cana-2873	578	8	)	)	PUNCT
cana-2873	579	1	⊆	⊆	X
cana-2873	579	2	q	q	X
cana-2873	579	3	-	-	PUNCT
cana-2873	579	4	nscl	nscl	NOUN
cana-2873	579	5	(	(	PUNCT
cana-2873	579	6	q	q	NOUN
cana-2873	579	7	-	-	PUNCT
cana-2873	579	8	nsint(k(ψ̃	nsint(k(ψ̃	NUM
cana-2873	579	9	)	)	PUNCT
cana-2873	579	10	)	)	PUNCT
cana-2873	579	11	)	)	PUNCT
cana-2873	579	12	for	for	ADP
cana-2873	579	13	every	every	DET
cana-2873	579	14	q	q	NOUN
cana-2873	579	15	-	-	PUNCT
cana-2873	579	16	nss	nss	NOUN
cana-2873	579	17	(	(	PUNCT
cana-2873	579	18	ψ̃	ψ̃	PROPN
cana-2873	579	19	)	)	PUNCT
cana-2873	579	20	in	in	ADP
cana-2873	579	21	(	(	PUNCT
cana-2873	579	22	z1	z1	NOUN
cana-2873	579	23	,	,	PUNCT
cana-2873	579	24	γq	γq	ADP
cana-2873	579	25	)	)	PUNCT
cana-2873	579	26	.	.	PUNCT
cana-2873	580	1	proof	proof	NOUN
cana-2873	580	2	.	.	PUNCT
cana-2873	581	1	(	(	PUNCT
cana-2873	581	2	i	i	NOUN
cana-2873	581	3	)	)	PUNCT
cana-2873	581	4	⇒	⇒	PROPN
cana-2873	581	5	(	(	PUNCT
cana-2873	581	6	ii	ii	NOUN
cana-2873	581	7	):	):	PUNCT
cana-2873	581	8	obvious	obvious	ADJ
cana-2873	581	9	.	.	PUNCT
cana-2873	582	1	(	(	PUNCT
cana-2873	582	2	ii)⇒	ii)⇒	X
cana-2873	582	3	(	(	PUNCT
cana-2873	582	4	iii	iii	NOUN
cana-2873	582	5	):	):	PUNCT
cana-2873	582	6	consider	consider	VERB
cana-2873	582	7	a	a	DET
cana-2873	582	8	q	q	NOUN
cana-2873	582	9	-	-	PUNCT
cana-2873	582	10	nss	nss	NOUN
cana-2873	582	11	(	(	PUNCT
cana-2873	582	12	ψ	ψ	NOUN
cana-2873	582	13	)	)	PUNCT
cana-2873	582	14	in	in	ADP
cana-2873	582	15	(	(	PUNCT
cana-2873	582	16	z1	z1	NOUN
cana-2873	582	17	,	,	PUNCT
cana-2873	582	18	γq	γq	ADP
cana-2873	582	19	)	)	PUNCT
cana-2873	582	20	.	.	PUNCT
cana-2873	583	1	we	we	PRON
cana-2873	583	2	know	know	VERB
cana-2873	583	3	that	that	SCONJ
cana-2873	583	4	,	,	PUNCT
cana-2873	583	5	q	q	NOUN
cana-2873	583	6	-	-	PUNCT
cana-2873	583	7	nsint(ψ	nsint(ψ	NOUN
cana-2873	583	8	)	)	PUNCT
cana-2873	583	9	is	be	AUX
cana-2873	583	10	a	a	DET
cana-2873	583	11	q	q	NOUN
cana-2873	583	12	-	-	PUNCT
cana-2873	583	13	nsos	nsos	NOUN
cana-2873	583	14	in	in	ADP
cana-2873	583	15	(	(	PUNCT
cana-2873	583	16	z1	z1	NOUN
cana-2873	583	17	,	,	PUNCT
cana-2873	583	18	γq	γq	ADP
cana-2873	583	19	)	)	PUNCT
cana-2873	583	20	.	.	PUNCT
cana-2873	584	1	then	then	ADV
cana-2873	584	2	,	,	PUNCT
cana-2873	584	3	k(q	k(q	PROPN
cana-2873	584	4	-	-	PUNCT
cana-2873	584	5	nsint(ψ̃	nsint(ψ̃	PROPN
cana-2873	584	6	)	)	PUNCT
cana-2873	584	7	)	)	PUNCT
cana-2873	584	8	is	be	AUX
cana-2873	584	9	a	a	DET
cana-2873	584	10	q	q	NOUN
cana-2873	584	11	-	-	PUNCT
cana-2873	584	12	nsβcs	nsβcs	NOUN
cana-2873	584	13	in	in	ADP
cana-2873	584	14	(	(	PUNCT
cana-2873	584	15	z2	z2	PROPN
cana-2873	584	16	,	,	PUNCT
cana-2873	584	17	σq	σq	NOUN
cana-2873	584	18	)	)	PUNCT
cana-2873	584	19	.	.	PUNCT
cana-2873	585	1	since	since	SCONJ
cana-2873	585	2	(	(	PUNCT
cana-2873	585	3	z2	z2	PROPN
cana-2873	585	4	,	,	PUNCT
cana-2873	585	5	σq	σq	NOUN
cana-2873	585	6	)	)	PUNCT
cana-2873	585	7	is	be	AUX
cana-2873	585	8	a	a	DET
cana-2873	585	9	q	q	ADJ
cana-2873	585	10	-	-	PUNCT
cana-2873	585	11	nsβt1/2	nsβt1/2	ADJ
cana-2873	585	12	-space	-space	NOUN
cana-2873	585	13	,	,	PUNCT
cana-2873	585	14	k(qnsint(ψ̃	k(qnsint(ψ̃	NOUN
cana-2873	585	15	)	)	PUNCT
cana-2873	585	16	)	)	PUNCT
cana-2873	586	1	is	be	AUX
cana-2873	586	2	a	a	DET
cana-2873	586	3	q	q	NOUN
cana-2873	586	4	-	-	PUNCT
cana-2873	586	5	nscs	nscs	ADJ
cana-2873	586	6	in	in	ADP
cana-2873	586	7	(	(	PUNCT
cana-2873	586	8	z2	z2	PROPN
cana-2873	586	9	,	,	PUNCT
cana-2873	586	10	σq	σq	NOUN
cana-2873	586	11	)	)	PUNCT
cana-2873	586	12	.	.	PUNCT
cana-2873	587	1	therefore	therefore	ADV
cana-2873	587	2	,	,	PUNCT
cana-2873	587	3	k(q	k(q	PROPN
cana-2873	587	4	-	-	PUNCT
cana-2873	587	5	nsint(ψ̃	nsint(ψ̃	PROPN
cana-2873	587	6	)	)	PUNCT
cana-2873	587	7	)	)	PUNCT
cana-2873	588	1	=	=	SYM
cana-2873	588	2	q	q	X
cana-2873	588	3	-	-	PUNCT
cana-2873	588	4	nscl(k(q	nscl(k(q	NOUN
cana-2873	588	5	-	-	PUNCT
cana-2873	588	6	nsint(ψ̃	nsint(ψ̃	NOUN
cana-2873	588	7	)	)	PUNCT
cana-2873	588	8	)	)	PUNCT
cana-2873	588	9	)	)	PUNCT
cana-2873	589	1	⊆	⊆	X
cana-2873	589	2	q	q	NOUN
cana-2873	589	3	-	-	PUNCT
cana-2873	589	4	nscl(q	nscl(q	ADP
cana-2873	589	5	-	-	PUNCT
cana-2873	589	6	nsint(k(ψ̃	nsint(k(ψ̃	NOUN
cana-2873	589	7	)	)	PUNCT
cana-2873	589	8	)	)	PUNCT
cana-2873	589	9	)	)	PUNCT
cana-2873	589	10	.	.	PUNCT
cana-2873	590	1	(	(	PUNCT
cana-2873	590	2	iii)⇒	iii)⇒	PROPN
cana-2873	590	3	(	(	PUNCT
cana-2873	590	4	i	i	NOUN
cana-2873	590	5	):	):	PUNCT
cana-2873	590	6	let	let	VERB
cana-2873	590	7	(	(	PUNCT
cana-2873	590	8	ψ̃	ψ̃	PROPN
cana-2873	590	9	)	)	PUNCT
cana-2873	590	10	be	be	VERB
cana-2873	590	11	a	a	DET
cana-2873	590	12	q	q	NOUN
cana-2873	590	13	-	-	PUNCT
cana-2873	590	14	nscs	nscs	ADJ
cana-2873	590	15	in	in	ADP
cana-2873	590	16	(	(	PUNCT
cana-2873	590	17	z1	z1	NOUN
cana-2873	590	18	,	,	PUNCT
cana-2873	590	19	γq	γq	ADP
cana-2873	590	20	)	)	PUNCT
cana-2873	590	21	.	.	PUNCT
cana-2873	591	1	then	then	ADV
cana-2873	591	2	,	,	PUNCT
cana-2873	591	3	(	(	PUNCT
cana-2873	591	4	ψ̃)c	ψ̃)c	PROPN
cana-2873	591	5	is	be	AUX
cana-2873	591	6	a	a	DET
cana-2873	591	7	q	q	NOUN
cana-2873	591	8	-	-	PUNCT
cana-2873	591	9	nsos	nsos	NOUN
cana-2873	591	10	in	in	ADP
cana-2873	591	11	(	(	PUNCT
cana-2873	591	12	z1	z1	NOUN
cana-2873	591	13	,	,	PUNCT
cana-2873	591	14	γq	γq	ADP
cana-2873	591	15	)	)	PUNCT
cana-2873	591	16	.	.	PUNCT
cana-2873	592	1	as	as	ADP
cana-2873	592	2	k(qnsint(ψ̃)c	k(qnsint(ψ̃)c	NUM
cana-2873	592	3	)	)	PUNCT
cana-2873	592	4	⊆	⊆	NUM
cana-2873	592	5	q	q	PROPN
cana-2873	592	6	-	-	PUNCT
cana-2873	592	7	nscl(q	nscl(q	ADP
cana-2873	592	8	-	-	PUNCT
cana-2873	592	9	nsint(k(ψ̃)c	nsint(k(ψ̃)c	NUM
cana-2873	592	10	)	)	PUNCT
cana-2873	592	11	)	)	PUNCT
cana-2873	592	12	,	,	PUNCT
cana-2873	592	13	we	we	PRON
cana-2873	592	14	get	get	VERB
cana-2873	592	15	k((ψ̃)c)⊆	k((ψ̃)c)⊆	PROPN
cana-2873	592	16	q	q	PROPN
cana-2873	592	17	-	-	PUNCT
cana-2873	592	18	nscl(q	nscl(q	ADP
cana-2873	592	19	-	-	PUNCT
cana-2873	592	20	nsint(k(ψ̃)c	nsint(k(ψ̃)c	NUM
cana-2873	592	21	)	)	PUNCT
cana-2873	592	22	)	)	PUNCT
cana-2873	592	23	.	.	PUNCT
cana-2873	593	1	therefore	therefore	ADV
cana-2873	593	2	,	,	PUNCT
cana-2873	593	3	k((ψ̃)c	k((ψ̃)c	PROPN
cana-2873	593	4	)	)	PUNCT
cana-2873	593	5	is	be	AUX
cana-2873	593	6	q	q	ADJ
cana-2873	593	7	-	-	NOUN
cana-2873	593	8	nsβcs	nsβcs	NOUN
cana-2873	593	9	in	in	ADP
cana-2873	593	10	(	(	PUNCT
cana-2873	593	11	z2	z2	PROPN
cana-2873	593	12	,	,	PUNCT
cana-2873	593	13	σq	σq	NOUN
cana-2873	593	14	)	)	PUNCT
cana-2873	593	15	.	.	PUNCT
cana-2873	594	1	thus	thus	ADV
cana-2873	594	2	,	,	PUNCT
cana-2873	594	3	k(ψ̃	k(ψ̃	PROPN
cana-2873	594	4	)	)	PUNCT
cana-2873	594	5	is	be	AUX
cana-2873	594	6	a	a	DET
cana-2873	594	7	q	q	NOUN
cana-2873	594	8	-	-	PUNCT
cana-2873	594	9	nsβos	nsβos	NOUN
cana-2873	594	10	in	in	ADP
cana-2873	594	11	(	(	PUNCT
cana-2873	594	12	z1	z1	NOUN
cana-2873	594	13	,	,	PUNCT
cana-2873	594	14	γq	γq	ADP
cana-2873	594	15	)	)	PUNCT
cana-2873	594	16	.	.	PUNCT
cana-2873	595	1	hence	hence	ADV
cana-2873	595	2	,	,	PUNCT
cana-2873	595	3	k	k	PROPN
cana-2873	595	4	is	be	AUX
cana-2873	595	5	a	a	DET
cana-2873	595	6	q	q	ADJ
cana-2873	595	7	-	-	PUNCT
cana-2873	595	8	nscβc	nscβc	ADJ
cana-2873	595	9	mapping	mapping	NOUN
cana-2873	595	10	.	.	PUNCT
cana-2873	596	1	theorem	theorem	VERB
cana-2873	596	2	7.7	7.7	NUM
cana-2873	596	3	.	.	PUNCT
cana-2873	597	1	let	let	VERB
cana-2873	597	2	k	k	NOUN
cana-2873	597	3	:	:	PUNCT
cana-2873	597	4	(	(	PUNCT
cana-2873	597	5	z1	z1	VERB
cana-2873	597	6	,	,	PUNCT
cana-2873	597	7	γq	γq	ADP
cana-2873	597	8	)	)	PUNCT
cana-2873	597	9	→	→	SYM
cana-2873	597	10	(	(	PUNCT
cana-2873	597	11	z2	z2	PROPN
cana-2873	597	12	,	,	PUNCT
cana-2873	597	13	σq	σq	NOUN
cana-2873	597	14	)	)	PUNCT
cana-2873	597	15	and	and	CCONJ
cana-2873	597	16	g	g	NOUN
cana-2873	597	17	:	:	PUNCT
cana-2873	597	18	(	(	PUNCT
cana-2873	597	19	z2	z2	NOUN
cana-2873	597	20	,	,	PUNCT
cana-2873	597	21	σq	σq	NOUN
cana-2873	597	22	)	)	PUNCT
cana-2873	597	23	→	→	SYM
cana-2873	597	24	(	(	PUNCT
cana-2873	597	25	z3	z3	PROPN
cana-2873	597	26	,	,	PUNCT
cana-2873	597	27	ρq	ρq	NUM
cana-2873	597	28	)	)	PUNCT
cana-2873	597	29	be	be	AUX
cana-2873	597	30	q	q	ADJ
cana-2873	597	31	-	-	PUNCT
cana-2873	597	32	nsɕβc	nsɕβc	ADJ
cana-2873	597	33	,	,	PUNCT
cana-2873	598	1	where	where	SCONJ
cana-2873	598	2	(	(	PUNCT
cana-2873	598	3	z1	z1	NOUN
cana-2873	598	4	,	,	PUNCT
cana-2873	598	5	γq)and	γq)and	PROPN
cana-2873	598	6	(	(	PUNCT
cana-2873	598	7	z3	z3	PROPN
cana-2873	598	8	,	,	PUNCT
cana-2873	598	9	ρq	ρq	NUM
cana-2873	598	10	)	)	PUNCT
cana-2873	598	11	are	be	AUX
cana-2873	598	12	two	two	NUM
cana-2873	598	13	q	q	NOUN
cana-2873	598	14	-	-	PUNCT
cana-2873	598	15	nsts	nst	NOUN
cana-2873	598	16	’s	’s	PART
cana-2873	598	17	and	and	CCONJ
cana-2873	598	18	(	(	PUNCT
cana-2873	598	19	z2	z2	PROPN
cana-2873	598	20	,	,	PUNCT
cana-2873	598	21	σq	σq	NOUN
cana-2873	598	22	)	)	PUNCT
cana-2873	598	23	a	a	DET
cana-2873	598	24	q	q	ADJ
cana-2873	598	25	-	-	PUNCT
cana-2873	598	26	nsβt1/2	nsβt1/2	NOUN
cana-2873	598	27	-	-	PUNCT
cana-2873	598	28	space	space	NOUN
cana-2873	598	29	,	,	PUNCT
cana-2873	598	30	then	then	ADV
cana-2873	598	31	the	the	DET
cana-2873	598	32	composition	composition	NOUN
cana-2873	598	33	g∘	g∘	PROPN
cana-2873	598	34	k	k	PROPN
cana-2873	598	35	is	be	AUX
cana-2873	598	36	q	q	NOUN
cana-2873	598	37	-	-	PUNCT
cana-2873	598	38	nsβc	nsβc	ADJ
cana-2873	598	39	.	.	PUNCT
cana-2873	599	1	communications	communication	NOUN
cana-2873	599	2	on	on	ADP
cana-2873	599	3	applied	apply	VERB
cana-2873	599	4	nonlinear	nonlinear	ADJ
cana-2873	599	5	analysis	analysis	NOUN
cana-2873	599	6	issn	issn	NOUN
cana-2873	599	7	:	:	PUNCT
cana-2873	599	8	1074	1074	NUM
cana-2873	599	9	-	-	PUNCT
cana-2873	599	10	133x	133x	NUM
cana-2873	599	11	vol	vol	NOUN
cana-2873	599	12	32	32	NUM
cana-2873	599	13	no	no	NOUN
cana-2873	599	14	.	.	PUNCT
cana-2873	600	1	4s	4s	NUM
cana-2873	600	2	(	(	PUNCT
cana-2873	600	3	2025	2025	NUM
cana-2873	600	4	)	)	PUNCT
cana-2873	600	5	595	595	NUM
cana-2873	600	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	600	7	proof	proof	NOUN
cana-2873	600	8	.	.	PUNCT
cana-2873	601	1	consider	consider	VERB
cana-2873	601	2	a	a	DET
cana-2873	601	3	q	q	NOUN
cana-2873	601	4	-	-	PUNCT
cana-2873	601	5	nscs	nscs	ADJ
cana-2873	601	6	(	(	PUNCT
cana-2873	601	7	ψ̃	ψ̃	PROPN
cana-2873	601	8	)	)	PUNCT
cana-2873	601	9	in	in	ADP
cana-2873	601	10	(	(	PUNCT
cana-2873	601	11	z1	z1	NOUN
cana-2873	601	12	,	,	PUNCT
cana-2873	601	13	γq	γq	ADP
cana-2873	601	14	)	)	PUNCT
cana-2873	601	15	.	.	PUNCT
cana-2873	602	1	as	as	SCONJ
cana-2873	602	2	k	k	PROPN
cana-2873	602	3	is	be	AUX
cana-2873	602	4	q	q	ADJ
cana-2873	602	5	-	-	PUNCT
cana-2873	602	6	nsɕβc	nsɕβc	NOUN
cana-2873	602	7	and	and	CCONJ
cana-2873	602	8	k(ψ̃	k(ψ̃	NOUN
cana-2873	602	9	)	)	PUNCT
cana-2873	602	10	is	be	AUX
cana-2873	602	11	a	a	DET
cana-2873	602	12	q	q	NOUN
cana-2873	602	13	-	-	PUNCT
cana-2873	602	14	nsβos	nsβos	NOUN
cana-2873	602	15	in	in	ADP
cana-2873	602	16	(	(	PUNCT
cana-2873	602	17	z2	z2	PROPN
cana-2873	602	18	,	,	PUNCT
cana-2873	602	19	σq	σq	NOUN
cana-2873	602	20	)	)	PUNCT
cana-2873	602	21	,	,	PUNCT
cana-2873	602	22	by	by	ADP
cana-2873	602	23	assumption	assumption	NOUN
cana-2873	602	24	,	,	PUNCT
cana-2873	602	25	k(ψ̃	k(ψ̃	NOUN
cana-2873	602	26	)	)	PUNCT
cana-2873	602	27	is	be	AUX
cana-2873	602	28	a	a	DET
cana-2873	602	29	q	q	NOUN
cana-2873	602	30	-	-	PUNCT
cana-2873	602	31	nsos	nsos	NOUN
cana-2873	602	32	in	in	ADP
cana-2873	602	33	(	(	PUNCT
cana-2873	602	34	z2	z2	PROPN
cana-2873	602	35	,	,	PUNCT
cana-2873	602	36	σq	σq	NOUN
cana-2873	602	37	)	)	PUNCT
cana-2873	602	38	.	.	PUNCT
cana-2873	603	1	since	since	SCONJ
cana-2873	603	2	g	g	PROPN
cana-2873	603	3	is	be	AUX
cana-2873	603	4	q	q	NOUN
cana-2873	603	5	-	-	PUNCT
cana-2873	603	6	nsɕβc	nsɕβc	ADJ
cana-2873	603	7	,	,	PUNCT
cana-2873	603	8	then	then	ADV
cana-2873	603	9	g(k(ψ̃	g(k(ψ̃	NOUN
cana-2873	603	10	)	)	PUNCT
cana-2873	603	11	)	)	PUNCT
cana-2873	603	12	is	be	AUX
cana-2873	603	13	qnsβcs	qnsβcs	ADV
cana-2873	603	14	in	in	ADP
cana-2873	603	15	(	(	PUNCT
cana-2873	603	16	z3	z3	PROPN
cana-2873	603	17	,	,	PUNCT
cana-2873	603	18	ρq	ρq	NOUN
cana-2873	603	19	)	)	PUNCT
cana-2873	603	20	and	and	CCONJ
cana-2873	603	21	g(k(ψ̃	g(k(ψ̃	NOUN
cana-2873	603	22	)	)	PUNCT
cana-2873	603	23	)	)	PUNCT
cana-2873	604	1	=	=	PRON
cana-2873	604	2	(	(	PUNCT
cana-2873	604	3	g	g	NOUN
cana-2873	604	4	◦	◦	NOUN
cana-2873	604	5	k)(ψ̃	k)(ψ̃	NOUN
cana-2873	604	6	)	)	PUNCT
cana-2873	604	7	.	.	PUNCT
cana-2873	605	1	thus	thus	ADV
cana-2873	605	2	,	,	PUNCT
cana-2873	605	3	g	g	PROPN
cana-2873	605	4	◦	◦	NOUN
cana-2873	605	5	k	k	PROPN
cana-2873	605	6	is	be	AUX
cana-2873	605	7	q	q	NOUN
cana-2873	605	8	-	-	PUNCT
cana-2873	605	9	nsβc	nsβc	ADJ
cana-2873	605	10	.	.	PUNCT
cana-2873	606	1	theorem	theorem	VERB
cana-2873	606	2	7.8	7.8	NUM
cana-2873	606	3	.	.	PUNCT
cana-2873	607	1	let	let	VERB
cana-2873	607	2	k	k	NOUN
cana-2873	607	3	:	:	PUNCT
cana-2873	607	4	(	(	PUNCT
cana-2873	607	5	z1	z1	VERB
cana-2873	607	6	,	,	PUNCT
cana-2873	607	7	γq	γq	ADP
cana-2873	607	8	)	)	PUNCT
cana-2873	607	9	→	→	SYM
cana-2873	607	10	(	(	PUNCT
cana-2873	607	11	z2	z2	PROPN
cana-2873	607	12	,	,	PUNCT
cana-2873	607	13	σq	σq	NOUN
cana-2873	607	14	)	)	PUNCT
cana-2873	607	15	and	and	CCONJ
cana-2873	607	16	g	g	PROPN
cana-2873	607	17	:(	:(	PROPN
cana-2873	607	18	z2	z2	PROPN
cana-2873	607	19	,	,	PUNCT
cana-2873	607	20	σq	σq	NOUN
cana-2873	607	21	)	)	PUNCT
cana-2873	607	22	→	→	SYM
cana-2873	607	23	(	(	PUNCT
cana-2873	607	24	z3	z3	PROPN
cana-2873	607	25	,	,	PUNCT
cana-2873	607	26	ρq	ρq	NUM
cana-2873	607	27	)	)	PUNCT
cana-2873	607	28	be	be	AUX
cana-2873	607	29	two	two	NUM
cana-2873	607	30	q	q	NOUN
cana-2873	607	31	-	-	PUNCT
cana-2873	607	32	nsts	nst	NOUN
cana-2873	607	33	’s	’s	PART
cana-2873	607	34	,	,	PUNCT
cana-2873	607	35	then	then	ADV
cana-2873	607	36	the	the	DET
cana-2873	607	37	following	follow	VERB
cana-2873	607	38	hold	hold	NOUN
cana-2873	607	39	:	:	PUNCT
cana-2873	607	40	(	(	PUNCT
cana-2873	607	41	i	i	NOUN
cana-2873	607	42	)	)	PUNCT
cana-2873	607	43	if	if	SCONJ
cana-2873	607	44	g	g	PROPN
cana-2873	607	45	◦	◦	NOUN
cana-2873	607	46	k	k	PROPN
cana-2873	607	47	is	be	AUX
cana-2873	607	48	q	q	ADJ
cana-2873	607	49	-	-	PUNCT
cana-2873	607	50	nsɕβo	nsɕβo	NOUN
cana-2873	607	51	and	and	CCONJ
cana-2873	607	52	k	k	PROPN
cana-2873	607	53	is	be	AUX
cana-2873	607	54	q	q	NOUN
cana-2873	607	55	-	-	PUNCT
cana-2873	607	56	nscts	nsct	NOUN
cana-2873	607	57	,	,	PUNCT
cana-2873	607	58	then	then	ADV
cana-2873	607	59	g	g	PROPN
cana-2873	607	60	is	be	AUX
cana-2873	607	61	q	q	NOUN
cana-2873	607	62	-	-	PUNCT
cana-2873	607	63	nsɕβo	nsɕβo	NOUN
cana-2873	607	64	.	.	PUNCT
cana-2873	608	1	(	(	PUNCT
cana-2873	608	2	ii	ii	NOUN
cana-2873	608	3	)	)	PUNCT
cana-2873	608	4	if	if	SCONJ
cana-2873	608	5	g	g	PROPN
cana-2873	608	6	◦	◦	NOUN
cana-2873	608	7	k	k	PROPN
cana-2873	608	8	is	be	AUX
cana-2873	608	9	q	q	NOUN
cana-2873	608	10	-	-	PUNCT
cana-2873	608	11	nso	nso	NOUN
cana-2873	608	12	and	and	CCONJ
cana-2873	608	13	g	g	PROPN
cana-2873	608	14	is	be	AUX
cana-2873	608	15	q	q	NOUN
cana-2873	608	16	-	-	PUNCT
cana-2873	608	17	nsɕβcts	nsɕβct	NOUN
cana-2873	608	18	,	,	PUNCT
cana-2873	608	19	then	then	ADV
cana-2873	608	20	k	k	PROPN
cana-2873	608	21	is	be	AUX
cana-2873	608	22	q	q	NOUN
cana-2873	608	23	-	-	PUNCT
cana-2873	608	24	nsɕβo	nsɕβo	NOUN
cana-2873	608	25	.	.	PUNCT
cana-2873	609	1	proof	proof	NOUN
cana-2873	609	2	.	.	PUNCT
cana-2873	610	1	the	the	DET
cana-2873	610	2	proof	proof	NOUN
cana-2873	610	3	is	be	AUX
cana-2873	610	4	obvious	obvious	ADJ
cana-2873	610	5	from	from	ADP
cana-2873	610	6	definition	definition	NOUN
cana-2873	610	7	3.1	3.1	NUM
cana-2873	610	8	and	and	CCONJ
cana-2873	610	9	definition	definition	NOUN
cana-2873	610	10	5.1	5.1	NUM
cana-2873	610	11	.	.	NOUN
cana-2873	610	12	8	8	NUM
cana-2873	610	13	quadripartitioned	quadripartitione	VERB
cana-2873	610	14	neutrosophic	neutrosophic	PROPN
cana-2873	610	15	contra	contra	PROPN
cana-2873	610	16	β	β	PROPN
cana-2873	610	17	-	-	PROPN
cana-2873	610	18	c	c	VERB
cana-2873	610	19	homeomorphism	homeomorphism	NOUN
cana-2873	610	20	the	the	DET
cana-2873	610	21	quadripartitioned	quadripartitioned	PROPN
cana-2873	610	22	neutrosophic	neutrosophic	PROPN
cana-2873	610	23	contra	contra	PROPN
cana-2873	610	24	β	β	PROPN
cana-2873	610	25	-	-	PROPN
cana-2873	610	26	c	c	ADJ
cana-2873	610	27	homeomorphism	homeomorphism	NOUN
cana-2873	610	28	is	be	AUX
cana-2873	610	29	introduced	introduce	VERB
cana-2873	610	30	in	in	ADP
cana-2873	610	31	this	this	DET
cana-2873	610	32	section	section	NOUN
cana-2873	610	33	and	and	CCONJ
cana-2873	610	34	some	some	PRON
cana-2873	610	35	of	of	ADP
cana-2873	610	36	its	its	PRON
cana-2873	610	37	properties	property	NOUN
cana-2873	610	38	are	be	AUX
cana-2873	610	39	analyzed	analyze	VERB
cana-2873	610	40	.	.	PUNCT
cana-2873	611	1	definition	definition	NOUN
cana-2873	611	2	8.1	8.1	NUM
cana-2873	611	3	.	.	PUNCT
cana-2873	612	1	a	a	DET
cana-2873	612	2	bijection	bijection	NOUN
cana-2873	612	3	k	k	X
cana-2873	612	4	:	:	PUNCT
cana-2873	612	5	(	(	PUNCT
cana-2873	612	6	z1	z1	VERB
cana-2873	612	7	,	,	PUNCT
cana-2873	612	8	γq	γq	ADP
cana-2873	612	9	)	)	PUNCT
cana-2873	612	10	→	→	SYM
cana-2873	612	11	(	(	PUNCT
cana-2873	612	12	z2	z2	PROPN
cana-2873	612	13	,	,	PUNCT
cana-2873	612	14	σq	σq	NOUN
cana-2873	612	15	)	)	PUNCT
cana-2873	612	16	is	be	AUX
cana-2873	612	17	called	call	VERB
cana-2873	612	18	a	a	DET
cana-2873	612	19	quadripartitioned	quadripartitione	VERB
cana-2873	612	20	neutrosophic	neutrosophic	PROPN
cana-2873	612	21	contra	contra	PROPN
cana-2873	612	22	β	β	PROPN
cana-2873	612	23	completely	completely	ADV
cana-2873	612	24	homeomorphism	homeomorphism	X
cana-2873	612	25	(	(	PUNCT
cana-2873	612	26	briefly	briefly	ADV
cana-2873	612	27	,	,	PUNCT
cana-2873	612	28	q	q	NOUN
cana-2873	612	29	-	-	NOUN
cana-2873	612	30	nsɕβchom	nsɕβchom	NOUN
cana-2873	612	31	)	)	PUNCT
cana-2873	612	32	if	if	SCONJ
cana-2873	612	33	k	k	PROPN
cana-2873	612	34	and	and	CCONJ
cana-2873	612	35	k−1	k−1	PROPN
cana-2873	612	36	are	be	AUX
cana-2873	612	37	q	q	ADJ
cana-2873	612	38	-	-	PUNCT
cana-2873	612	39	nsɕβirr	nsɕβirr	ADJ
cana-2873	612	40	mappings	mapping	NOUN
cana-2873	612	41	.	.	PUNCT
cana-2873	613	1	theorem	theorem	VERB
cana-2873	613	2	8.2	8.2	NUM
cana-2873	613	3	.	.	PUNCT
cana-2873	614	1	each	each	DET
cana-2873	614	2	q	q	NOUN
cana-2873	614	3	-	-	PUNCT
cana-2873	614	4	nsɕβchom	nsɕβchom	NOUN
cana-2873	614	5	is	be	AUX
cana-2873	614	6	a	a	DET
cana-2873	614	7	q	q	NOUN
cana-2873	614	8	-	-	PUNCT
cana-2873	614	9	nsɕβhom	nsɕβhom	ADJ
cana-2873	614	10	.	.	PUNCT
cana-2873	615	1	but	but	CCONJ
cana-2873	615	2	not	not	PART
cana-2873	615	3	conversely	conversely	ADV
cana-2873	615	4	.	.	PUNCT
cana-2873	616	1	proof	proof	NOUN
cana-2873	616	2	.	.	PUNCT
cana-2873	617	1	consider	consider	VERB
cana-2873	617	2	a	a	DET
cana-2873	617	3	q	q	NOUN
cana-2873	617	4	-	-	PUNCT
cana-2873	617	5	nsos	nsos	ADJ
cana-2873	617	6	ψ̃	ψ̃	PROPN
cana-2873	617	7	in	in	ADP
cana-2873	617	8	(	(	PUNCT
cana-2873	617	9	z2	z2	PROPN
cana-2873	617	10	,	,	PUNCT
cana-2873	617	11	σq	σq	NOUN
cana-2873	617	12	)	)	PUNCT
cana-2873	617	13	.	.	PUNCT
cana-2873	618	1	then	then	ADV
cana-2873	618	2	ψ̃	ψ̃	PROPN
cana-2873	618	3	is	be	AUX
cana-2873	618	4	a	a	DET
cana-2873	618	5	q	q	NOUN
cana-2873	618	6	-	-	PUNCT
cana-2873	618	7	nsβos	nsβos	NOUN
cana-2873	618	8	in	in	ADP
cana-2873	618	9	(	(	PUNCT
cana-2873	618	10	z2	z2	PROPN
cana-2873	618	11	,	,	PUNCT
cana-2873	618	12	σq	σq	NOUN
cana-2873	618	13	)	)	PUNCT
cana-2873	618	14	.	.	PUNCT
cana-2873	619	1	by	by	ADP
cana-2873	619	2	presumption	presumption	NOUN
cana-2873	619	3	,	,	PUNCT
cana-2873	619	4	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	619	5	)	)	PUNCT
cana-2873	619	6	is	be	AUX
cana-2873	619	7	a	a	DET
cana-2873	619	8	q	q	NOUN
cana-2873	619	9	-	-	PUNCT
cana-2873	619	10	nsβcs	nsβcs	NOUN
cana-2873	619	11	in	in	ADP
cana-2873	619	12	(	(	PUNCT
cana-2873	619	13	z1	z1	NOUN
cana-2873	619	14	,	,	PUNCT
cana-2873	619	15	γq	γq	ADP
cana-2873	619	16	)	)	PUNCT
cana-2873	619	17	.	.	PUNCT
cana-2873	620	1	therefore	therefore	ADV
cana-2873	620	2	,	,	PUNCT
cana-2873	620	3	k	k	PROPN
cana-2873	620	4	is	be	AUX
cana-2873	620	5	a	a	DET
cana-2873	620	6	q	q	NOUN
cana-2873	620	7	-	-	PUNCT
cana-2873	620	8	nsɕβcts	nsɕβct	VERB
cana-2873	620	9	mapping	mapping	NOUN
cana-2873	620	10	.	.	PUNCT
cana-2873	621	1	so	so	ADV
cana-2873	621	2	,	,	PUNCT
cana-2873	621	3	k	k	PROPN
cana-2873	621	4	and	and	CCONJ
cana-2873	621	5	k−1	k−1	PROPN
cana-2873	621	6	are	be	AUX
cana-2873	621	7	qnsɕβcts	qnsɕβct	NOUN
cana-2873	621	8	mappings	mapping	NOUN
cana-2873	621	9	.	.	PUNCT
cana-2873	622	1	thus	thus	ADV
cana-2873	622	2	,	,	PUNCT
cana-2873	622	3	k	k	PROPN
cana-2873	622	4	is	be	AUX
cana-2873	622	5	a	a	DET
cana-2873	622	6	q	q	NOUN
cana-2873	622	7	-	-	PUNCT
cana-2873	622	8	nsɕβhom	nsɕβhom	ADJ
cana-2873	622	9	.	.	PUNCT
cana-2873	622	10	example	example	NOUN
cana-2873	622	11	8.3	8.3	NUM
cana-2873	622	12	.	.	PUNCT
cana-2873	623	1	let	let	VERB
cana-2873	623	2	v	v	VERB
cana-2873	623	3	=	=	PUNCT
cana-2873	623	4	{	{	PUNCT
cana-2873	623	5	a	a	PRON
cana-2873	623	6	,	,	PUNCT
cana-2873	623	7	b	b	NOUN
cana-2873	623	8	,	,	PUNCT
cana-2873	623	9	c	c	NOUN
cana-2873	623	10	}	}	PUNCT
cana-2873	623	11	=	=	SYM
cana-2873	623	12	w	w	NOUN
cana-2873	623	13	and	and	CCONJ
cana-2873	623	14	define	define	VERB
cana-2873	623	15	q	q	ADJ
cana-2873	623	16	-	-	PUNCT
cana-2873	623	17	nss	nss	NOUN
cana-2873	623	18	’s	’s	PART
cana-2873	623	19	v1	v1	PROPN
cana-2873	623	20	&	&	CCONJ
cana-2873	623	21	v2	v2	PROPN
cana-2873	623	22	in	in	ADP
cana-2873	623	23	v	v	NOUN
cana-2873	623	24	and	and	CCONJ
cana-2873	623	25	w1	w1	NOUN
cana-2873	623	26	in	in	ADP
cana-2873	623	27	w	w	PROPN
cana-2873	623	28	are	be	AUX
cana-2873	623	29	v1	v1	NOUN
cana-2873	623	30	=	=	SYM
cana-2873	623	31	{	{	PUNCT
cana-2873	623	32	(	(	PUNCT
cana-2873	623	33	a	a	PRON
cana-2873	623	34	,	,	PUNCT
cana-2873	623	35	0.2	0.2	NUM
cana-2873	623	36	,	,	PUNCT
cana-2873	623	37	0.5	0.5	NUM
cana-2873	623	38	,	,	PUNCT
cana-2873	623	39	0.5	0.5	NUM
cana-2873	623	40	,	,	PUNCT
cana-2873	623	41	0.8	0.8	NUM
cana-2873	623	42	)	)	PUNCT
cana-2873	623	43	,	,	PUNCT
cana-2873	623	44	(	(	PUNCT
cana-2873	623	45	b	b	X
cana-2873	623	46	,	,	PUNCT
cana-2873	623	47	0.3	0.3	NUM
cana-2873	623	48	,	,	PUNCT
cana-2873	623	49	0.5	0.5	NUM
cana-2873	623	50	,	,	PUNCT
cana-2873	623	51	0.5	0.5	NUM
cana-2873	623	52	,	,	PUNCT
cana-2873	623	53	0.7	0.7	NUM
cana-2873	623	54	)	)	PUNCT
cana-2873	623	55	,	,	PUNCT
cana-2873	623	56	(	(	PUNCT
cana-2873	623	57	c	c	X
cana-2873	623	58	,	,	PUNCT
cana-2873	623	59	0.4	0.4	NUM
cana-2873	623	60	,	,	PUNCT
cana-2873	623	61	0.5	0.5	NUM
cana-2873	623	62	,	,	PUNCT
cana-2873	623	63	0.5	0.5	NUM
cana-2873	623	64	,	,	PUNCT
cana-2873	623	65	0.6	0.6	NUM
cana-2873	623	66	)	)	PUNCT
cana-2873	623	67	}	}	PUNCT
cana-2873	623	68	,	,	PUNCT
cana-2873	623	69	v2	v2	PROPN
cana-2873	623	70	=	=	SYM
cana-2873	623	71	{	{	PUNCT
cana-2873	623	72	(	(	PUNCT
cana-2873	623	73	a	a	PRON
cana-2873	623	74	,	,	PUNCT
cana-2873	623	75	0.1	0.1	NUM
cana-2873	623	76	,	,	PUNCT
cana-2873	623	77	0.5	0.5	NUM
cana-2873	623	78	,	,	PUNCT
cana-2873	623	79	0.5	0.5	NUM
cana-2873	623	80	,	,	PUNCT
cana-2873	623	81	0.9	0.9	NUM
cana-2873	623	82	)	)	PUNCT
cana-2873	623	83	,	,	PUNCT
cana-2873	623	84	(	(	PUNCT
cana-2873	623	85	b	b	NOUN
cana-2873	623	86	,	,	PUNCT
cana-2873	623	87	0.1	0.1	NUM
cana-2873	623	88	,	,	PUNCT
cana-2873	623	89	0.5	0.5	NUM
cana-2873	623	90	,	,	PUNCT
cana-2873	623	91	0.5	0.5	NUM
cana-2873	623	92	,	,	PUNCT
cana-2873	623	93	0.9	0.9	NUM
cana-2873	623	94	)	)	PUNCT
cana-2873	623	95	,	,	PUNCT
cana-2873	623	96	(	(	PUNCT
cana-2873	623	97	c	c	X
cana-2873	623	98	,	,	PUNCT
cana-2873	623	99	0.4	0.4	NUM
cana-2873	623	100	,	,	PUNCT
cana-2873	623	101	0.5	0.5	NUM
cana-2873	623	102	,	,	PUNCT
cana-2873	623	103	0.5	0.5	NUM
cana-2873	623	104	,	,	PUNCT
cana-2873	623	105	0.6	0.6	NUM
cana-2873	623	106	)	)	PUNCT
cana-2873	623	107	}	}	PUNCT
cana-2873	623	108	,	,	PUNCT
cana-2873	623	109	w1	w1	NOUN
cana-2873	623	110	=	=	SYM
cana-2873	623	111	{	{	PUNCT
cana-2873	623	112	(	(	PUNCT
cana-2873	623	113	a	a	PRON
cana-2873	623	114	,	,	PUNCT
cana-2873	623	115	0.4	0.4	NUM
cana-2873	623	116	,	,	PUNCT
cana-2873	623	117	0.5	0.5	NUM
cana-2873	623	118	,	,	PUNCT
cana-2873	623	119	0.5	0.5	NUM
cana-2873	623	120	,	,	PUNCT
cana-2873	623	121	0.6	0.6	NUM
cana-2873	623	122	)	)	PUNCT
cana-2873	623	123	,	,	PUNCT
cana-2873	623	124	(	(	PUNCT
cana-2873	623	125	b	b	X
cana-2873	623	126	,	,	PUNCT
cana-2873	623	127	0.3	0.3	NUM
cana-2873	623	128	,	,	PUNCT
cana-2873	623	129	0.5	0.5	NUM
cana-2873	623	130	,	,	PUNCT
cana-2873	623	131	0.5	0.5	NUM
cana-2873	623	132	,	,	PUNCT
cana-2873	623	133	0.7	0.7	NUM
cana-2873	623	134	)	)	PUNCT
cana-2873	623	135	,	,	PUNCT
cana-2873	623	136	(	(	PUNCT
cana-2873	623	137	c	c	X
cana-2873	623	138	,	,	PUNCT
cana-2873	623	139	0.2	0.2	NUM
cana-2873	623	140	,	,	PUNCT
cana-2873	623	141	0.5	0.5	NUM
cana-2873	623	142	,	,	PUNCT
cana-2873	623	143	0.5	0.5	NUM
cana-2873	623	144	,	,	PUNCT
cana-2873	623	145	0.8	0.8	NUM
cana-2873	623	146	)	)	PUNCT
cana-2873	623	147	}	}	PUNCT
cana-2873	623	148	.	.	PUNCT
cana-2873	624	1	then	then	ADV
cana-2873	624	2	we	we	PRON
cana-2873	624	3	have	have	VERB
cana-2873	624	4	γq	γq	ADP
cana-2873	624	5	=	=	SYM
cana-2873	624	6	{	{	PUNCT
cana-2873	624	7	0qns	0qns	PROPN
cana-2873	624	8	,	,	PUNCT
cana-2873	624	9	v1	v1	PROPN
cana-2873	624	10	,	,	PUNCT
cana-2873	624	11	v2	v2	PROPN
cana-2873	624	12	,	,	PUNCT
cana-2873	624	13	1qns	1qns	NUM
cana-2873	624	14	}	}	PUNCT
cana-2873	624	15	and	and	CCONJ
cana-2873	624	16	σq	σq	NOUN
cana-2873	624	17	=	=	SYM
cana-2873	624	18	{	{	PUNCT
cana-2873	624	19	0qns	0qns	PROPN
cana-2873	624	20	,	,	PUNCT
cana-2873	624	21	w1	w1	NOUN
cana-2873	624	22	,	,	PUNCT
cana-2873	624	23	1qns	1qns	NUM
cana-2873	624	24	}	}	PUNCT
cana-2873	624	25	.	.	PUNCT
cana-2873	625	1	let	let	VERB
cana-2873	625	2	k	k	NOUN
cana-2873	625	3	:	:	PUNCT
cana-2873	625	4	(	(	PUNCT
cana-2873	625	5	z1	z1	VERB
cana-2873	625	6	,	,	PUNCT
cana-2873	625	7	γq	γq	ADP
cana-2873	625	8	)	)	PUNCT
cana-2873	625	9	(	(	PUNCT
cana-2873	625	10	z2	z2	PROPN
cana-2873	625	11	,	,	PUNCT
cana-2873	625	12	σq	σq	NOUN
cana-2873	625	13	)	)	PUNCT
cana-2873	625	14	be	be	VERB
cana-2873	625	15	a	a	DET
cana-2873	625	16	mapping	mapping	NOUN
cana-2873	625	17	,	,	PUNCT
cana-2873	625	18	defined	define	VERB
cana-2873	625	19	as	as	ADP
cana-2873	625	20	k(a	k(a	NOUN
cana-2873	625	21	)	)	PUNCT
cana-2873	626	1	=	=	SYM
cana-2873	626	2	c	c	X
cana-2873	626	3	,	,	PUNCT
cana-2873	626	4	k(b	k(b	PROPN
cana-2873	626	5	)	)	PUNCT
cana-2873	626	6	=	=	SYM
cana-2873	626	7	b	b	PROPN
cana-2873	626	8	&	&	CCONJ
cana-2873	626	9	k(c	k(c	PROPN
cana-2873	626	10	)	)	PUNCT
cana-2873	626	11	=	=	SYM
cana-2873	627	1	a	a	PRON
cana-2873	627	2	,	,	PUNCT
cana-2873	627	3	then	then	ADV
cana-2873	627	4	k	k	PROPN
cana-2873	627	5	is	be	AUX
cana-2873	627	6	q	q	ADJ
cana-2873	627	7	-	-	ADJ
cana-2873	627	8	nsɕβhom	nsɕβhom	ADJ
cana-2873	627	9	but	but	CCONJ
cana-2873	627	10	not	not	PART
cana-2873	627	11	q	q	NOUN
cana-2873	627	12	-	-	NOUN
cana-2873	627	13	nsɕβchom	nsɕβchom	NOUN
cana-2873	627	14	.	.	PUNCT
cana-2873	628	1	theorem	theorem	NOUN
cana-2873	628	2	8.4	8.4	NUM
cana-2873	628	3	.	.	PUNCT
cana-2873	629	1	if	if	SCONJ
cana-2873	629	2	k	k	X
cana-2873	629	3	:	:	PUNCT
cana-2873	629	4	(	(	PUNCT
cana-2873	629	5	z1	z1	VERB
cana-2873	629	6	,	,	PUNCT
cana-2873	629	7	γq	γq	ADP
cana-2873	629	8	)	)	PUNCT
cana-2873	629	9	→	→	SYM
cana-2873	629	10	(	(	PUNCT
cana-2873	629	11	z2	z2	PROPN
cana-2873	629	12	,	,	PUNCT
cana-2873	629	13	σq	σq	NOUN
cana-2873	629	14	)	)	PUNCT
cana-2873	629	15	is	be	AUX
cana-2873	629	16	a	a	DET
cana-2873	629	17	q	q	NOUN
cana-2873	629	18	-	-	PUNCT
cana-2873	629	19	nsɕβchom	nsɕβchom	NOUN
cana-2873	629	20	,	,	PUNCT
cana-2873	629	21	then	then	ADV
cana-2873	629	22	q	q	NOUN
cana-2873	629	23	-	-	PUNCT
cana-2873	629	24	nsβint(k−1(ψ̃	nsβint(k−1(ψ̃	NOUN
cana-2873	629	25	)	)	PUNCT
cana-2873	629	26	)	)	PUNCT
cana-2873	630	1	⊆	⊆	NUM
cana-2873	630	2	k−1(q	k−1(q	ADV
cana-2873	630	3	-	-	PUNCT
cana-2873	630	4	nscl(ψ̃	nscl(ψ̃	NOUN
cana-2873	630	5	)	)	PUNCT
cana-2873	630	6	)	)	PUNCT
cana-2873	630	7	for	for	ADP
cana-2873	630	8	every	every	DET
cana-2873	630	9	q	q	ADJ
cana-2873	630	10	-	-	PUNCT
cana-2873	630	11	nss	nss	NOUN
cana-2873	630	12	ψ̃	ψ̃	PROPN
cana-2873	630	13	in	in	ADP
cana-2873	630	14	(	(	PUNCT
cana-2873	630	15	z2	z2	PROPN
cana-2873	630	16	,	,	PUNCT
cana-2873	630	17	σq	σq	NOUN
cana-2873	630	18	)	)	PUNCT
cana-2873	630	19	.	.	PUNCT
cana-2873	631	1	proof	proof	NOUN
cana-2873	631	2	.	.	PUNCT
cana-2873	632	1	consider	consider	VERB
cana-2873	632	2	a	a	DET
cana-2873	632	3	q	q	ADJ
cana-2873	632	4	-	-	PUNCT
cana-2873	632	5	nss	nss	NOUN
cana-2873	632	6	ψ̃	ψ̃	PROPN
cana-2873	632	7	in	in	ADP
cana-2873	632	8	(	(	PUNCT
cana-2873	632	9	z2	z2	PROPN
cana-2873	632	10	,	,	PUNCT
cana-2873	632	11	σq	σq	NOUN
cana-2873	632	12	)	)	PUNCT
cana-2873	632	13	.	.	PUNCT
cana-2873	633	1	since	since	SCONJ
cana-2873	633	2	,	,	PUNCT
cana-2873	633	3	q	q	NOUN
cana-2873	633	4	-	-	PUNCT
cana-2873	633	5	nscl(ψ̃	nscl(ψ̃	NOUN
cana-2873	633	6	)	)	PUNCT
cana-2873	633	7	is	be	AUX
cana-2873	633	8	a	a	DET
cana-2873	633	9	q	q	NOUN
cana-2873	633	10	-	-	PUNCT
cana-2873	633	11	nscs	nscs	ADJ
cana-2873	633	12	in	in	ADP
cana-2873	633	13	(	(	PUNCT
cana-2873	633	14	z2	z2	PROPN
cana-2873	633	15	,	,	PUNCT
cana-2873	633	16	σq	σq	NOUN
cana-2873	633	17	)	)	PUNCT
cana-2873	633	18	and	and	CCONJ
cana-2873	633	19	every	every	DET
cana-2873	633	20	q	q	NOUN
cana-2873	633	21	-	-	PUNCT
cana-2873	633	22	nscs	nscs	NOUN
cana-2873	633	23	is	be	AUX
cana-2873	633	24	a	a	DET
cana-2873	633	25	q	q	NOUN
cana-2873	633	26	-	-	PUNCT
cana-2873	633	27	nsβcs	nsβcs	NOUN
cana-2873	633	28	in	in	ADP
cana-2873	633	29	(	(	PUNCT
cana-2873	633	30	z2	z2	PROPN
cana-2873	633	31	,	,	PUNCT
cana-2873	633	32	σq	σq	NOUN
cana-2873	633	33	)	)	PUNCT
cana-2873	633	34	.	.	PUNCT
cana-2873	634	1	as	as	SCONJ
cana-2873	634	2	k	k	PROPN
cana-2873	634	3	is	be	AUX
cana-2873	634	4	q	q	ADJ
cana-2873	634	5	-	-	ADJ
cana-2873	634	6	nsɕβirr	nsɕβirr	ADJ
cana-2873	634	7	,	,	PUNCT
cana-2873	634	8	k−1(q	k−1(q	PROPN
cana-2873	634	9	-	-	PUNCT
cana-2873	634	10	nscl(ψ̃	nscl(ψ̃	NOUN
cana-2873	634	11	)	)	PUNCT
cana-2873	634	12	)	)	PUNCT
cana-2873	634	13	is	be	AUX
cana-2873	634	14	a	a	DET
cana-2873	634	15	q	q	NOUN
cana-2873	634	16	-	-	PUNCT
cana-2873	634	17	nsβos	nsβos	NOUN
cana-2873	634	18	in	in	ADP
cana-2873	634	19	(	(	PUNCT
cana-2873	634	20	z1	z1	NOUN
cana-2873	634	21	,	,	PUNCT
cana-2873	634	22	γq	γq	ADP
cana-2873	634	23	)	)	PUNCT
cana-2873	634	24	.	.	PUNCT
cana-2873	635	1	then	then	ADV
cana-2873	635	2	,	,	PUNCT
cana-2873	635	3	q	q	ADJ
cana-2873	635	4	-	-	PUNCT
cana-2873	635	5	nsint(k−1(q	nsint(k−1(q	NUM
cana-2873	635	6	-	-	PUNCT
cana-2873	635	7	nscl(ψ̃	nscl(ψ̃	NOUN
cana-2873	635	8	)	)	PUNCT
cana-2873	635	9	)	)	PUNCT
cana-2873	635	10	)	)	PUNCT
cana-2873	636	1	=	=	SYM
cana-2873	636	2	k−1(q	k−1(q	ADJ
cana-2873	636	3	-	-	PUNCT
cana-2873	636	4	nscl(ψ̃	nscl(ψ̃	NOUN
cana-2873	636	5	)	)	PUNCT
cana-2873	636	6	)	)	PUNCT
cana-2873	636	7	.	.	PUNCT
cana-2873	637	1	here	here	ADV
cana-2873	637	2	,	,	PUNCT
cana-2873	637	3	q	q	NOUN
cana-2873	637	4	-	-	PUNCT
cana-2873	637	5	nsβint(k−1(ψ̃	nsβint(k−1(ψ̃	NOUN
cana-2873	637	6	)	)	PUNCT
cana-2873	637	7	)	)	PUNCT
cana-2873	638	1	⊆	⊆	NUM
cana-2873	638	2	q	q	NOUN
cana-2873	638	3	-	-	PUNCT
cana-2873	638	4	nsβint(k−1(q	nsβint(k−1(q	NOUN
cana-2873	638	5	-	-	PUNCT
cana-2873	638	6	nscl(ψ̃)))=	nscl(ψ̃)))=	NOUN
cana-2873	638	7	k−1(q	k−1(q	ADJ
cana-2873	638	8	-	-	PUNCT
cana-2873	638	9	nscl(ψ̃	nscl(ψ̃	NOUN
cana-2873	638	10	)	)	PUNCT
cana-2873	638	11	)	)	PUNCT
cana-2873	638	12	.	.	PUNCT
cana-2873	639	1	therefore	therefore	ADV
cana-2873	639	2	,	,	PUNCT
cana-2873	639	3	q	q	NOUN
cana-2873	639	4	-	-	NOUN
cana-2873	639	5	nsβint(k−1(ψ̃	nsβint(k−1(ψ̃	NOUN
cana-2873	639	6	)	)	PUNCT
cana-2873	639	7	)	)	PUNCT
cana-2873	640	1	⊆	⊆	NUM
cana-2873	640	2	k−1(qnscl(ψ̃	k−1(qnscl(ψ̃	NOUN
cana-2873	640	3	)	)	PUNCT
cana-2873	640	4	)	)	PUNCT
cana-2873	640	5	for	for	ADP
cana-2873	640	6	every	every	DET
cana-2873	640	7	q	q	ADJ
cana-2873	640	8	-	-	PUNCT
cana-2873	640	9	nss	nss	NOUN
cana-2873	640	10	ψ̃	ψ̃	PROPN
cana-2873	640	11	in	in	ADP
cana-2873	640	12	(	(	PUNCT
cana-2873	640	13	z2	z2	PROPN
cana-2873	640	14	,	,	PUNCT
cana-2873	640	15	σq	σq	NOUN
cana-2873	640	16	)	)	PUNCT
cana-2873	640	17	.	.	PUNCT
cana-2873	641	1	theorem	theorem	VERB
cana-2873	641	2	8.5	8.5	NUM
cana-2873	641	3	.	.	PUNCT
cana-2873	642	1	let	let	VERB
cana-2873	642	2	k	k	NOUN
cana-2873	642	3	:	:	PUNCT
cana-2873	642	4	(	(	PUNCT
cana-2873	642	5	z1	z1	VERB
cana-2873	642	6	,	,	PUNCT
cana-2873	642	7	γq	γq	ADP
cana-2873	642	8	)	)	PUNCT
cana-2873	642	9	→	→	SYM
cana-2873	642	10	(	(	PUNCT
cana-2873	642	11	z2	z2	PROPN
cana-2873	642	12	,	,	PUNCT
cana-2873	642	13	σq	σq	NOUN
cana-2873	642	14	)	)	PUNCT
cana-2873	642	15	be	be	VERB
cana-2873	642	16	a	a	DET
cana-2873	642	17	q	q	NOUN
cana-2873	642	18	-	-	ADJ
cana-2873	642	19	nsβchom	nsβchom	PRON
cana-2873	642	20	.	.	PUNCT
cana-2873	643	1	then	then	ADV
cana-2873	643	2	q	q	NOUN
cana-2873	643	3	-	-	PUNCT
cana-2873	643	4	nsβint(k−1(ψ̃	nsβint(k−1(ψ̃	NOUN
cana-2873	643	5	)	)	PUNCT
cana-2873	643	6	)	)	PUNCT
cana-2873	644	1	⊆	⊆	NUM
cana-2873	644	2	k−1(q	k−1(q	ADV
cana-2873	644	3	-	-	PUNCT
cana-2873	644	4	nsβcl(ψ̃	nsβcl(ψ̃	NOUN
cana-2873	644	5	)	)	PUNCT
cana-2873	644	6	)	)	PUNCT
cana-2873	644	7	for	for	ADP
cana-2873	644	8	every	every	DET
cana-2873	644	9	q	q	ADJ
cana-2873	644	10	-	-	PUNCT
cana-2873	644	11	nss	nss	NOUN
cana-2873	644	12	ψ̃	ψ̃	PROPN
cana-2873	644	13	in	in	ADP
cana-2873	644	14	(	(	PUNCT
cana-2873	644	15	z2	z2	PROPN
cana-2873	644	16	,	,	PUNCT
cana-2873	644	17	σq	σq	NOUN
cana-2873	644	18	)	)	PUNCT
cana-2873	644	19	.	.	PUNCT
cana-2873	645	1	communications	communication	NOUN
cana-2873	645	2	on	on	ADP
cana-2873	645	3	applied	apply	VERB
cana-2873	645	4	nonlinear	nonlinear	ADJ
cana-2873	645	5	analysis	analysis	NOUN
cana-2873	645	6	issn	issn	NOUN
cana-2873	645	7	:	:	PUNCT
cana-2873	645	8	1074	1074	NUM
cana-2873	645	9	-	-	PUNCT
cana-2873	645	10	133x	133x	NUM
cana-2873	645	11	vol	vol	NOUN
cana-2873	645	12	32	32	NUM
cana-2873	645	13	no	no	NOUN
cana-2873	645	14	.	.	PUNCT
cana-2873	646	1	4s	4s	NUM
cana-2873	646	2	(	(	PUNCT
cana-2873	646	3	2025	2025	NUM
cana-2873	646	4	)	)	PUNCT
cana-2873	646	5	596	596	NUM
cana-2873	646	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	646	7	proof	proof	NOUN
cana-2873	646	8	.	.	PUNCT
cana-2873	647	1	as	as	SCONJ
cana-2873	647	2	k	k	PROPN
cana-2873	647	3	is	be	AUX
cana-2873	647	4	a	a	DET
cana-2873	647	5	q	q	NOUN
cana-2873	647	6	-	-	PUNCT
cana-2873	647	7	nscβchom	nscβchom	ADJ
cana-2873	647	8	,	,	PUNCT
cana-2873	647	9	k	k	PROPN
cana-2873	647	10	is	be	AUX
cana-2873	647	11	a	a	DET
cana-2873	647	12	q	q	ADJ
cana-2873	647	13	-	-	ADJ
cana-2873	647	14	nscβirr	nscβirr	ADJ
cana-2873	647	15	mapping	mapping	NOUN
cana-2873	647	16	.	.	PUNCT
cana-2873	648	1	consider	consider	VERB
cana-2873	648	2	a	a	DET
cana-2873	648	3	q	q	ADJ
cana-2873	648	4	-	-	PUNCT
cana-2873	648	5	nss	nss	NOUN
cana-2873	648	6	ψ̃	ψ̃	PROPN
cana-2873	648	7	in	in	ADP
cana-2873	648	8	(	(	PUNCT
cana-2873	648	9	z2	z2	PROPN
cana-2873	648	10	,	,	PUNCT
cana-2873	648	11	σq	σq	NOUN
cana-2873	648	12	)	)	PUNCT
cana-2873	648	13	.	.	PUNCT
cana-2873	649	1	it	it	PRON
cana-2873	649	2	is	be	AUX
cana-2873	649	3	obvious	obvious	ADJ
cana-2873	649	4	that	that	SCONJ
cana-2873	649	5	,	,	PUNCT
cana-2873	649	6	q	q	NOUN
cana-2873	649	7	-	-	PUNCT
cana-2873	649	8	nsβcl(ψ̃	nsβcl(ψ̃	NOUN
cana-2873	649	9	)	)	PUNCT
cana-2873	649	10	is	be	AUX
cana-2873	649	11	a	a	DET
cana-2873	649	12	q	q	NOUN
cana-2873	649	13	-	-	PUNCT
cana-2873	649	14	nsβcs	nsβcs	NOUN
cana-2873	649	15	in	in	ADP
cana-2873	649	16	(	(	PUNCT
cana-2873	649	17	z2	z2	PROPN
cana-2873	649	18	,	,	PUNCT
cana-2873	649	19	σq	σq	NOUN
cana-2873	649	20	)	)	PUNCT
cana-2873	649	21	.	.	PUNCT
cana-2873	650	1	as	as	ADP
cana-2873	650	2	k−1(ψ̃	k−1(ψ̃	NOUN
cana-2873	650	3	)	)	PUNCT
cana-2873	650	4	⊆	⊆	NUM
cana-2873	650	5	k−1(q	k−1(q	ADJ
cana-2873	650	6	-	-	PUNCT
cana-2873	650	7	nsβcl(ψ̃	nsβcl(ψ̃	NOUN
cana-2873	650	8	)	)	PUNCT
cana-2873	650	9	)	)	PUNCT
cana-2873	650	10	,	,	PUNCT
cana-2873	650	11	we	we	PRON
cana-2873	650	12	have	have	AUX
cana-2873	650	13	q−nsβint(k−1(ψ̃	q−nsβint(k−1(ψ̃	VERB
cana-2873	650	14	)	)	PUNCT
cana-2873	650	15	)	)	PUNCT
cana-2873	651	1	⊆	⊆	NUM
cana-2873	651	2	q−nsβint(k−1(q−nsβcl(ψ̃	q−nsβint(k−1(q−nsβcl(ψ̃	NOUN
cana-2873	651	3	)	)	PUNCT
cana-2873	651	4	)	)	PUNCT
cana-2873	651	5	)	)	PUNCT
cana-2873	652	1	⊆	⊆	NUM
cana-2873	652	2	k−1(q−nsβcl(ψ̃	k−1(q−nsβcl(ψ̃	NOUN
cana-2873	652	3	)	)	PUNCT
cana-2873	652	4	)	)	PUNCT
cana-2873	652	5	.	.	PUNCT
cana-2873	653	1	⇒q	⇒q	NUM
cana-2873	653	2	-	-	PUNCT
cana-2873	653	3	nsβint(k−1(ψ̃))⊆k−1(nsβcl(ψ̃	nsβint(k−1(ψ̃))⊆k−1(nsβcl(ψ̃	NOUN
cana-2873	653	4	)	)	PUNCT
cana-2873	653	5	)	)	PUNCT
cana-2873	653	6	.	.	PUNCT
cana-2873	654	1	theorem	theorem	VERB
cana-2873	654	2	8.6	8.6	NUM
cana-2873	654	3	.	.	PUNCT
cana-2873	655	1	if	if	SCONJ
cana-2873	655	2	k	k	X
cana-2873	655	3	:	:	PUNCT
cana-2873	655	4	(	(	PUNCT
cana-2873	655	5	z1	z1	VERB
cana-2873	655	6	,	,	PUNCT
cana-2873	655	7	γq	γq	ADP
cana-2873	655	8	)	)	PUNCT
cana-2873	655	9	→	→	SYM
cana-2873	655	10	(	(	PUNCT
cana-2873	655	11	z2	z2	PROPN
cana-2873	655	12	,	,	PUNCT
cana-2873	655	13	σq	σq	NOUN
cana-2873	655	14	)	)	PUNCT
cana-2873	655	15	and	and	CCONJ
cana-2873	655	16	g	g	NOUN
cana-2873	655	17	:	:	PUNCT
cana-2873	655	18	(	(	PUNCT
cana-2873	655	19	z2	z2	NOUN
cana-2873	655	20	,	,	PUNCT
cana-2873	655	21	σq	σq	NOUN
cana-2873	655	22	)	)	PUNCT
cana-2873	655	23	→	→	SYM
cana-2873	655	24	(	(	PUNCT
cana-2873	655	25	z3	z3	PROPN
cana-2873	655	26	,	,	PUNCT
cana-2873	655	27	ρq	ρq	NOUN
cana-2873	655	28	)	)	PUNCT
cana-2873	655	29	are	be	AUX
cana-2873	655	30	q	q	ADJ
cana-2873	655	31	-	-	PUNCT
cana-2873	655	32	nsɕβchom	nsɕβchom	NOUN
cana-2873	655	33	’s	’s	NOUN
cana-2873	655	34	,	,	PUNCT
cana-2873	655	35	then	then	ADV
cana-2873	655	36	g∘k	g∘k	PROPN
cana-2873	655	37	is	be	AUX
cana-2873	655	38	a	a	DET
cana-2873	655	39	q	q	NOUN
cana-2873	655	40	-	-	ADJ
cana-2873	655	41	nsβchom	nsβchom	ADJ
cana-2873	655	42	.	.	PUNCT
cana-2873	656	1	proof	proof	NOUN
cana-2873	656	2	.	.	PUNCT
cana-2873	657	1	assume	assume	VERB
cana-2873	657	2	that	that	SCONJ
cana-2873	657	3	k	k	PROPN
cana-2873	657	4	and	and	CCONJ
cana-2873	657	5	g	g	PROPN
cana-2873	657	6	are	be	AUX
cana-2873	657	7	two	two	NUM
cana-2873	657	8	q	q	ADJ
cana-2873	657	9	-	-	PUNCT
cana-2873	657	10	nsɕβchom	nsɕβchom	NOUN
cana-2873	657	11	’s	’s	PART
cana-2873	657	12	.	.	PUNCT
cana-2873	658	1	let	let	VERB
cana-2873	658	2	ψ̃	ψ̃	NOUN
cana-2873	658	3	be	be	AUX
cana-2873	658	4	a	a	DET
cana-2873	658	5	q	q	NOUN
cana-2873	658	6	-	-	PUNCT
cana-2873	658	7	nsβcs	nsβcs	NOUN
cana-2873	658	8	in	in	ADP
cana-2873	658	9	(	(	PUNCT
cana-2873	658	10	z3	z3	PROPN
cana-2873	658	11	,	,	PUNCT
cana-2873	658	12	ρq	ρq	NOUN
cana-2873	658	13	)	)	PUNCT
cana-2873	658	14	.	.	PUNCT
cana-2873	659	1	then	then	ADV
cana-2873	659	2	,	,	PUNCT
cana-2873	659	3	g−1(ψ̃	g−1(ψ̃	NOUN
cana-2873	659	4	)	)	PUNCT
cana-2873	659	5	is	be	AUX
cana-2873	659	6	a	a	DET
cana-2873	659	7	q	q	NOUN
cana-2873	659	8	-	-	PUNCT
cana-2873	659	9	nsβos	nsβos	NOUN
cana-2873	659	10	in	in	ADP
cana-2873	659	11	(	(	PUNCT
cana-2873	659	12	z2	z2	PROPN
cana-2873	659	13	,	,	PUNCT
cana-2873	659	14	σq	σq	NOUN
cana-2873	659	15	)	)	PUNCT
cana-2873	659	16	.	.	PUNCT
cana-2873	660	1	by	by	ADP
cana-2873	660	2	presumption	presumption	NOUN
cana-2873	660	3	,	,	PUNCT
cana-2873	660	4	k−1(g−1(ψ̃	k−1(g−1(ψ̃	NOUN
cana-2873	660	5	)	)	PUNCT
cana-2873	660	6	)	)	PUNCT
cana-2873	660	7	is	be	AUX
cana-2873	660	8	a	a	DET
cana-2873	660	9	q	q	NOUN
cana-2873	660	10	-	-	PUNCT
cana-2873	660	11	nsβcs	nsβcs	NOUN
cana-2873	660	12	in	in	ADP
cana-2873	660	13	(	(	PUNCT
cana-2873	660	14	z1	z1	NOUN
cana-2873	660	15	,	,	PUNCT
cana-2873	660	16	γq	γq	ADP
cana-2873	660	17	)	)	PUNCT
cana-2873	660	18	.	.	PUNCT
cana-2873	661	1	therefore	therefore	ADV
cana-2873	661	2	,	,	PUNCT
cana-2873	661	3	(	(	PUNCT
cana-2873	661	4	g	g	NOUN
cana-2873	661	5	◦	◦	NOUN
cana-2873	661	6	k)−1	k)−1	NOUN
cana-2873	661	7	is	be	AUX
cana-2873	661	8	a	a	DET
cana-2873	661	9	q	q	ADJ
cana-2873	661	10	-	-	PUNCT
cana-2873	661	11	nsβirr	nsβirr	NOUN
cana-2873	661	12	mapping	mapping	NOUN
cana-2873	661	13	.	.	PUNCT
cana-2873	662	1	assume	assume	VERB
cana-2873	662	2	(	(	PUNCT
cana-2873	662	3	ψ̃	ψ̃	PROPN
cana-2873	662	4	)	)	PUNCT
cana-2873	662	5	is	be	AUX
cana-2873	662	6	a	a	DET
cana-2873	662	7	q	q	NOUN
cana-2873	662	8	-	-	PUNCT
cana-2873	662	9	nsβcs	nsβcs	NOUN
cana-2873	662	10	in	in	ADP
cana-2873	662	11	(	(	PUNCT
cana-2873	662	12	z1	z1	NOUN
cana-2873	662	13	,	,	PUNCT
cana-2873	662	14	γq	γq	ADP
cana-2873	662	15	)	)	PUNCT
cana-2873	662	16	.	.	PUNCT
cana-2873	663	1	then	then	ADV
cana-2873	663	2	,	,	PUNCT
cana-2873	663	3	by	by	ADP
cana-2873	663	4	hypothesis	hypothesis	NOUN
cana-2873	663	5	,	,	PUNCT
cana-2873	663	6	k(g	k(g	PROPN
cana-2873	663	7	)	)	PUNCT
cana-2873	663	8	is	be	AUX
cana-2873	663	9	a	a	DET
cana-2873	663	10	q	q	NOUN
cana-2873	663	11	-	-	PUNCT
cana-2873	663	12	nsβos	nsβos	NOUN
cana-2873	663	13	in	in	ADP
cana-2873	663	14	(	(	PUNCT
cana-2873	663	15	z2	z2	PROPN
cana-2873	663	16	,	,	PUNCT
cana-2873	663	17	σq	σq	NOUN
cana-2873	663	18	)	)	PUNCT
cana-2873	663	19	.	.	PUNCT
cana-2873	664	1	hence	hence	ADV
cana-2873	664	2	,	,	PUNCT
cana-2873	664	3	g(k(ψ̃	g(k(ψ̃	NOUN
cana-2873	664	4	)	)	PUNCT
cana-2873	664	5	)	)	PUNCT
cana-2873	664	6	is	be	AUX
cana-2873	664	7	a	a	DET
cana-2873	664	8	q	q	NOUN
cana-2873	664	9	-	-	PUNCT
cana-2873	664	10	nsβcs	nsβcs	NOUN
cana-2873	664	11	in	in	ADP
cana-2873	664	12	(	(	PUNCT
cana-2873	664	13	z3	z3	PROPN
cana-2873	664	14	,	,	PUNCT
cana-2873	664	15	ρq	ρq	NOUN
cana-2873	664	16	)	)	PUNCT
cana-2873	664	17	.	.	PUNCT
cana-2873	665	1	this	this	PRON
cana-2873	665	2	implies	imply	VERB
cana-2873	665	3	that	that	SCONJ
cana-2873	665	4	g	g	PROPN
cana-2873	665	5	◦	◦	NOUN
cana-2873	665	6	k	k	PROPN
cana-2873	665	7	is	be	AUX
cana-2873	665	8	a	a	DET
cana-2873	665	9	q	q	ADJ
cana-2873	665	10	-	-	PUNCT
cana-2873	665	11	nsβirr	nsβirr	NOUN
cana-2873	665	12	mapping	mapping	NOUN
cana-2873	665	13	.	.	PUNCT
cana-2873	666	1	thus	thus	ADV
cana-2873	666	2	,	,	PUNCT
cana-2873	666	3	g	g	PROPN
cana-2873	666	4	◦	◦	NOUN
cana-2873	666	5	k	k	PROPN
cana-2873	666	6	is	be	AUX
cana-2873	666	7	a	a	DET
cana-2873	666	8	q	q	NOUN
cana-2873	666	9	-	-	ADJ
cana-2873	666	10	nsβchom	nsβchom	ADJ
cana-2873	666	11	.	.	PUNCT
cana-2873	667	1	9	9	NUM
cana-2873	667	2	conclusions	conclusion	NOUN
cana-2873	667	3	in	in	ADP
cana-2873	667	4	this	this	DET
cana-2873	667	5	paper	paper	NOUN
cana-2873	667	6	,	,	PUNCT
cana-2873	667	7	the	the	DET
cana-2873	667	8	new	new	ADJ
cana-2873	667	9	concept	concept	NOUN
cana-2873	667	10	of	of	ADP
cana-2873	667	11	a	a	DET
cana-2873	667	12	quadripartitioned	quadripartitione	VERB
cana-2873	667	13	neutrosophic	neutrosophic	PROPN
cana-2873	667	14	contra	contra	PROPN
cana-2873	667	15	β	β	PROPN
cana-2873	667	16	-	-	ADJ
cana-2873	667	17	continuous	continuous	ADJ
cana-2873	667	18	mappings	mapping	NOUN
cana-2873	667	19	,	,	PUNCT
cana-2873	667	20	quadripartitioned	quadripartitione	VERB
cana-2873	667	21	neutrosophic	neutrosophic	PROPN
cana-2873	667	22	contra	contra	PROPN
cana-2873	667	23	β	β	PROPN
cana-2873	667	24	-	-	ADJ
cana-2873	667	25	open	open	ADJ
cana-2873	667	26	mappings	mapping	NOUN
cana-2873	667	27	,	,	PUNCT
cana-2873	667	28	a	a	DET
cana-2873	667	29	quadripartitioned	quadripartitione	VERB
cana-2873	667	30	neutrosophic	neutrosophic	PROPN
cana-2873	667	31	contra	contra	PROPN
cana-2873	667	32	βclosed	βclose	VERB
cana-2873	667	33	mappings	mapping	NOUN
cana-2873	667	34	,	,	PUNCT
cana-2873	667	35	a	a	DET
cana-2873	667	36	quadripartitioned	quadripartitione	VERB
cana-2873	667	37	neutrosophic	neutrosophic	PROPN
cana-2873	667	38	contra	contra	PROPN
cana-2873	667	39	β	β	PROPN
cana-2873	667	40	-	-	PUNCT
cana-2873	667	41	homeomorphism	homeomorphism	PROPN
cana-2873	667	42	,	,	PUNCT
cana-2873	667	43	a	a	DET
cana-2873	667	44	quadripartitioned	quadripartitione	VERB
cana-2873	667	45	neutrosophic	neutrosophic	PROPN
cana-2873	667	46	contra	contra	PROPN
cana-2873	667	47	β	β	X
cana-2873	667	48	-	-	PUNCT
cana-2873	667	49	completely	completely	ADV
cana-2873	667	50	homeomorphism	homeomorphism	NOUN
cana-2873	667	51	in	in	ADP
cana-2873	667	52	q	q	NOUN
cana-2873	667	53	-	-	NOUN
cana-2873	667	54	nsts	nst	NOUN
cana-2873	667	55	are	be	AUX
cana-2873	667	56	discussed	discuss	VERB
cana-2873	667	57	and	and	CCONJ
cana-2873	667	58	also	also	ADV
cana-2873	667	59	derived	derive	VERB
cana-2873	667	60	some	some	PRON
cana-2873	667	61	of	of	ADP
cana-2873	667	62	their	their	PRON
cana-2873	667	63	related	relate	VERB
cana-2873	667	64	attributes	attribute	NOUN
cana-2873	667	65	.	.	PUNCT
cana-2873	668	1	in	in	ADP
cana-2873	668	2	future	future	NOUN
cana-2873	668	3	,	,	PUNCT
cana-2873	668	4	we	we	PRON
cana-2873	668	5	can	can	AUX
cana-2873	668	6	carry	carry	VERB
cana-2873	668	7	out	out	ADP
cana-2873	668	8	the	the	DET
cana-2873	668	9	further	further	ADJ
cana-2873	668	10	research	research	NOUN
cana-2873	668	11	on	on	ADP
cana-2873	668	12	a	a	DET
cana-2873	668	13	quadripartitioned	quadripartitione	VERB
cana-2873	668	14	neutrosophic	neutrosophic	ADJ
cana-2873	668	15	β	β	NOUN
cana-2873	668	16	-	-	NOUN
cana-2873	668	17	compactness	compactness	NOUN
cana-2873	668	18	,	,	PUNCT
cana-2873	668	19	a	a	DET
cana-2873	668	20	quadripartitioned	quadripartitione	VERB
cana-2873	668	21	neutrosophic	neutrosophic	ADJ
cana-2873	668	22	β	β	NOUN
cana-2873	668	23	-	-	NOUN
cana-2873	668	24	connectedness	connectedness	NOUN
cana-2873	668	25	and	and	CCONJ
cana-2873	668	26	a	a	DET
cana-2873	668	27	quadripartitioned	quadripartitione	VERB
cana-2873	668	28	neutrosophic	neutrosophic	ADJ
cana-2873	668	29	β	β	NOUN
cana-2873	668	30	-	-	ADJ
cana-2873	668	31	regular	regular	ADJ
cana-2873	668	32	and	and	CCONJ
cana-2873	668	33	normal	normal	ADJ
cana-2873	668	34	spaces	space	NOUN
cana-2873	668	35	in	in	ADP
cana-2873	668	36	q	q	NOUN
cana-2873	668	37	-	-	NOUN
cana-2873	668	38	nsts	nst	NOUN
cana-2873	668	39	.	.	PUNCT
cana-2873	669	1	references	reference	NOUN
cana-2873	669	2	[	[	X
cana-2873	669	3	1	1	NUM
cana-2873	669	4	]	]	PUNCT
cana-2873	669	5	k.	k.	PROPN
cana-2873	669	6	atanassov	atanassov	PROPN
cana-2873	669	7	,	,	PUNCT
cana-2873	669	8	intuitionistic	intuitionistic	ADJ
cana-2873	669	9	fuzzy	fuzzy	ADJ
cana-2873	669	10	sets	set	NOUN
cana-2873	669	11	,	,	PUNCT
cana-2873	669	12	fuzzy	fuzzy	ADJ
cana-2873	669	13	sets	set	NOUN
cana-2873	669	14	and	and	CCONJ
cana-2873	669	15	systems	system	NOUN
cana-2873	669	16	,	,	PUNCT
cana-2873	669	17	20	20	NUM
cana-2873	669	18	(	(	PUNCT
cana-2873	669	19	1986	1986	NUM
cana-2873	669	20	)	)	PUNCT
cana-2873	669	21	,	,	PUNCT
cana-2873	669	22	87	87	NUM
cana-2873	669	23	-	-	SYM
cana-2873	669	24	96	96	NUM
cana-2873	669	25	.	.	PUNCT
cana-2873	670	1	[	[	X
cana-2873	670	2	2	2	NUM
cana-2873	670	3	]	]	PUNCT
cana-2873	670	4	.	.	PUNCT
cana-2873	671	1	c.	c.	PROPN
cana-2873	671	2	l.	l.	PROPN
cana-2873	671	3	chang	chang	PROPN
cana-2873	671	4	,	,	PUNCT
cana-2873	671	5	fuzzy	fuzzy	ADJ
cana-2873	671	6	topological	topological	ADJ
cana-2873	671	7	spaces	space	NOUN
cana-2873	671	8	,	,	PUNCT
cana-2873	671	9	j.	j.	PROPN
cana-2873	671	10	math	math	PROPN
cana-2873	671	11	.	.	PUNCT
cana-2873	672	1	anal	anal	PROPN
cana-2873	672	2	.	.	PUNCT
cana-2873	673	1	appl	appl	PROPN
cana-2873	673	2	.	.	PROPN
cana-2873	673	3	,	,	PUNCT
cana-2873	673	4	24	24	NUM
cana-2873	673	5	(	(	PUNCT
cana-2873	673	6	1968	1968	NUM
cana-2873	673	7	)	)	PUNCT
cana-2873	673	8	,	,	PUNCT
cana-2873	673	9	182	182	NUM
cana-2873	673	10	-	-	SYM
cana-2873	673	11	190	190	NUM
cana-2873	673	12	.	.	PUNCT
cana-2873	674	1	[	[	X
cana-2873	674	2	3	3	X
cana-2873	674	3	]	]	X
cana-2873	674	4	r.	r.	PROPN
cana-2873	674	5	chatterjee	chatterjee	PROPN
cana-2873	674	6	,	,	PUNCT
cana-2873	674	7	p.	p.	PROPN
cana-2873	674	8	majumdar	majumdar	PROPN
cana-2873	674	9	and	and	CCONJ
cana-2873	674	10	s.	s.	PROPN
cana-2873	674	11	k.	k.	PROPN
cana-2873	674	12	samanta	samanta	PROPN
cana-2873	674	13	,	,	PUNCT
cana-2873	674	14	on	on	ADP
cana-2873	674	15	some	some	DET
cana-2873	674	16	similarity	similarity	NOUN
cana-2873	674	17	measures	measure	NOUN
cana-2873	674	18	and	and	CCONJ
cana-2873	674	19	entropy	entropy	NOUN
cana-2873	674	20	on	on	ADP
cana-2873	674	21	quadripartitioned	quadripartitione	VERB
cana-2873	674	22	single	single	ADJ
cana-2873	674	23	valued	value	VERB
cana-2873	674	24	neutrosophic	neutrosophic	ADJ
cana-2873	674	25	sets	set	NOUN
cana-2873	674	26	,	,	PUNCT
cana-2873	674	27	journal	journal	NOUN
cana-2873	674	28	of	of	ADP
cana-2873	674	29	intelligent	intelligent	ADJ
cana-2873	674	30	&	&	CCONJ
cana-2873	674	31	fuzzy	fuzzy	ADJ
cana-2873	674	32	systems	system	NOUN
cana-2873	674	33	,	,	PUNCT
cana-2873	674	34	30	30	NUM
cana-2873	674	35	(	(	PUNCT
cana-2873	674	36	4	4	NUM
cana-2873	674	37	)	)	PUNCT
cana-2873	674	38	(	(	PUNCT
cana-2873	674	39	2016	2016	NUM
cana-2873	674	40	)	)	PUNCT
cana-2873	674	41	,	,	PUNCT
cana-2873	674	42	2475	2475	NUM
cana-2873	674	43	-	-	SYM
cana-2873	674	44	2485	2485	NUM
cana-2873	674	45	.	.	PUNCT
cana-2873	675	1	[	[	X
cana-2873	675	2	4	4	X
cana-2873	675	3	]	]	X
cana-2873	675	4	d.	d.	PROPN
cana-2873	675	5	coker	coker	PROPN
cana-2873	675	6	,	,	PUNCT
cana-2873	675	7	an	an	DET
cana-2873	675	8	introduction	introduction	NOUN
cana-2873	675	9	to	to	ADP
cana-2873	675	10	intuitionistic	intuitionistic	ADJ
cana-2873	675	11	fuzzy	fuzzy	ADJ
cana-2873	675	12	topological	topological	ADJ
cana-2873	675	13	spaces	space	NOUN
cana-2873	675	14	,	,	PUNCT
cana-2873	675	15	fuzzy	fuzzy	ADJ
cana-2873	675	16	sets	set	NOUN
cana-2873	675	17	and	and	CCONJ
cana-2873	675	18	systems	system	NOUN
cana-2873	675	19	,	,	PUNCT
cana-2873	675	20	88	88	NUM
cana-2873	675	21	(	(	PUNCT
cana-2873	675	22	1997	1997	NUM
cana-2873	675	23	)	)	PUNCT
cana-2873	675	24	,	,	PUNCT
cana-2873	675	25	81	81	NUM
cana-2873	675	26	-	-	SYM
cana-2873	675	27	89	89	NUM
cana-2873	675	28	.	.	PUNCT
cana-2873	676	1	[	[	X
cana-2873	676	2	5	5	X
cana-2873	676	3	]	]	PUNCT
cana-2873	676	4	s.	s.	PROPN
cana-2873	676	5	das	das	PROPN
cana-2873	676	6	,	,	PUNCT
cana-2873	676	7	r.	r.	PROPN
cana-2873	676	8	das	das	PROPN
cana-2873	676	9	and	and	CCONJ
cana-2873	676	10	c.	c.	PROPN
cana-2873	676	11	granados	granados	PROPN
cana-2873	676	12	,	,	PUNCT
cana-2873	676	13	topology	topology	NOUN
cana-2873	676	14	on	on	ADP
cana-2873	676	15	quadripartitioned	quadripartitione	VERB
cana-2873	676	16	neutrosophic	neutrosophic	ADJ
cana-2873	676	17	sets	set	NOUN
cana-2873	676	18	,	,	PUNCT
cana-2873	676	19	neutrosophic	neutrosophic	ADJ
cana-2873	676	20	sets	set	NOUN
cana-2873	676	21	and	and	CCONJ
cana-2873	676	22	systems	system	NOUN
cana-2873	676	23	,	,	PUNCT
cana-2873	676	24	45	45	NUM
cana-2873	676	25	(	(	PUNCT
cana-2873	676	26	2021	2021	NUM
cana-2873	676	27	)	)	PUNCT
cana-2873	676	28	,	,	PUNCT
cana-2873	676	29	54	54	NUM
cana-2873	676	30	-	-	SYM
cana-2873	676	31	61	61	NUM
cana-2873	676	32	.	.	PUNCT
cana-2873	677	1	[	[	X
cana-2873	677	2	6	6	NUM
cana-2873	677	3	]	]	PUNCT
cana-2873	677	4	s.	s.	PROPN
cana-2873	677	5	das	das	PROPN
cana-2873	677	6	and	and	CCONJ
cana-2873	677	7	s.	s.	PROPN
cana-2873	677	8	pramanik	pramanik	PROPN
cana-2873	677	9	,	,	PUNCT
cana-2873	677	10	generalized	generalize	VERB
cana-2873	677	11	neutrosophic	neutrosophic	ADJ
cana-2873	677	12	b	b	X
cana-2873	677	13	-	-	PUNCT
cana-2873	677	14	open	open	ADJ
cana-2873	677	15	sets	set	NOUN
cana-2873	677	16	in	in	ADP
cana-2873	677	17	neutrosophic	neutrosophic	ADJ
cana-2873	677	18	topological	topological	ADJ
cana-2873	677	19	space	space	NOUN
cana-2873	677	20	,	,	PUNCT
cana-2873	677	21	neutrosophic	neutrosophic	ADJ
cana-2873	677	22	sets	set	NOUN
cana-2873	677	23	and	and	CCONJ
cana-2873	677	24	systems	system	NOUN
cana-2873	677	25	,	,	PUNCT
cana-2873	677	26	35	35	NUM
cana-2873	677	27	(	(	PUNCT
cana-2873	677	28	2020	2020	NUM
cana-2873	677	29	)	)	PUNCT
cana-2873	677	30	,	,	PUNCT
cana-2873	677	31	522	522	NUM
cana-2873	677	32	-	-	SYM
cana-2873	677	33	530	530	NUM
cana-2873	677	34	.	.	PUNCT
cana-2873	678	1	[	[	X
cana-2873	678	2	7	7	X
cana-2873	678	3	]	]	X
cana-2873	678	4	s.	s.	PROPN
cana-2873	678	5	das	das	PROPN
cana-2873	678	6	and	and	CCONJ
cana-2873	678	7	s.	s.	PROPN
cana-2873	678	8	pramanik	pramanik	PROPN
cana-2873	678	9	,	,	PUNCT
cana-2873	678	10	neutrosophic	neutrosophic	ADJ
cana-2873	678	11	φ	φ	VERB
cana-2873	678	12	-	-	ADJ
cana-2873	678	13	open	open	ADJ
cana-2873	678	14	sets	set	NOUN
cana-2873	678	15	and	and	CCONJ
cana-2873	678	16	neutrosophic	neutrosophic	ADJ
cana-2873	678	17	φ	φ	VERB
cana-2873	678	18	-	-	ADJ
cana-2873	678	19	continuous	continuous	ADJ
cana-2873	678	20	functions	function	NOUN
cana-2873	678	21	,	,	PUNCT
cana-2873	678	22	neutrosophic	neutrosophic	ADJ
cana-2873	678	23	sets	set	NOUN
cana-2873	678	24	and	and	CCONJ
cana-2873	678	25	systems	system	NOUN
cana-2873	678	26	,	,	PUNCT
cana-2873	678	27	38	38	NUM
cana-2873	678	28	(	(	PUNCT
cana-2873	678	29	2020	2020	NUM
cana-2873	678	30	)	)	PUNCT
cana-2873	678	31	,	,	PUNCT
cana-2873	678	32	355	355	NUM
cana-2873	678	33	-	-	SYM
cana-2873	678	34	367	367	NUM
cana-2873	678	35	.	.	PUNCT
cana-2873	679	1	[	[	X
cana-2873	679	2	8	8	NUM
cana-2873	679	3	]	]	X
cana-2873	679	4	e.	e.	PROPN
cana-2873	679	5	ebenanjar	ebenanjar	PROPN
cana-2873	679	6	,	,	PUNCT
cana-2873	679	7	j.	j.	PROPN
cana-2873	679	8	immaculate	immaculate	PROPN
cana-2873	679	9	and	and	CCONJ
cana-2873	679	10	c.	c.	PROPN
cana-2873	679	11	b.	b.	PROPN
cana-2873	679	12	wilfred	wilfred	PROPN
cana-2873	679	13	,	,	PUNCT
cana-2873	679	14	on	on	ADP
cana-2873	679	15	neutrosophic	neutrosophic	ADJ
cana-2873	679	16	b	b	X
cana-2873	679	17	-	-	PUNCT
cana-2873	679	18	open	open	ADJ
cana-2873	679	19	sets	set	NOUN
cana-2873	679	20	in	in	ADP
cana-2873	679	21	neutrosophic	neutrosophic	ADJ
cana-2873	679	22	topological	topological	ADJ
cana-2873	679	23	space	space	NOUN
cana-2873	679	24	,	,	PUNCT
cana-2873	679	25	journal	journal	NOUN
cana-2873	679	26	of	of	ADP
cana-2873	679	27	physics	physics	PROPN
cana-2873	679	28	conference	conference	NOUN
cana-2873	679	29	series	series	NOUN
cana-2873	679	30	,	,	PUNCT
cana-2873	679	31	1139	1139	NUM
cana-2873	679	32	(	(	PUNCT
cana-2873	679	33	1	1	NUM
cana-2873	679	34	)	)	PUNCT
cana-2873	679	35	(	(	PUNCT
cana-2873	679	36	2018	2018	NUM
cana-2873	679	37	)	)	PUNCT
cana-2873	679	38	,	,	PUNCT
cana-2873	679	39	012062	012062	NUM
cana-2873	679	40	.	.	PUNCT
cana-2873	680	1	[	[	X
cana-2873	680	2	9	9	NUM
cana-2873	680	3	]	]	PUNCT
cana-2873	680	4	p.	p.	NOUN
cana-2873	680	5	iswarya	iswarya	PROPN
cana-2873	680	6	and	and	CCONJ
cana-2873	680	7	k.	k.	PROPN
cana-2873	680	8	bageerathi	bageerathi	PROPN
cana-2873	680	9	,	,	PUNCT
cana-2873	680	10	on	on	ADP
cana-2873	680	11	neutrosophic	neutrosophic	ADJ
cana-2873	680	12	semi	semi	ADJ
cana-2873	680	13	-	-	ADJ
cana-2873	680	14	open	open	ADJ
cana-2873	680	15	sets	set	NOUN
cana-2873	680	16	in	in	ADP
cana-2873	680	17	neutrosophic	neutrosophic	ADJ
cana-2873	680	18	topological	topological	ADJ
cana-2873	680	19	spaces	space	NOUN
cana-2873	680	20	,	,	PUNCT
cana-2873	680	21	international	international	ADJ
cana-2873	680	22	journal	journal	NOUN
cana-2873	680	23	of	of	ADP
cana-2873	680	24	mathematical	mathematical	ADJ
cana-2873	680	25	trends	trend	NOUN
cana-2873	680	26	and	and	CCONJ
cana-2873	680	27	technology	technology	NOUN
cana-2873	680	28	,	,	PUNCT
cana-2873	680	29	37	37	NUM
cana-2873	680	30	(	(	PUNCT
cana-2873	680	31	3	3	NUM
cana-2873	680	32	)	)	PUNCT
cana-2873	680	33	(	(	PUNCT
cana-2873	680	34	2016	2016	NUM
cana-2873	680	35	)	)	PUNCT
cana-2873	680	36	,	,	PUNCT
cana-2873	680	37	214	214	NUM
cana-2873	680	38	-	-	SYM
cana-2873	680	39	223	223	NUM
cana-2873	680	40	.	.	PUNCT
cana-2873	681	1	[	[	X
cana-2873	681	2	10	10	NUM
cana-2873	681	3	]	]	X
cana-2873	681	4	c.	c.	PROPN
cana-2873	681	5	maheswari	maheswari	PROPN
cana-2873	681	6	,	,	PUNCT
cana-2873	681	7	m.	m.	NOUN
cana-2873	681	8	sathyabama	sathyabama	PROPN
cana-2873	681	9	and	and	CCONJ
cana-2873	681	10	s.	s.	PROPN
cana-2873	681	11	chandrasekar	chandrasekar	PROPN
cana-2873	681	12	,	,	PUNCT
cana-2873	681	13	neutrosophic	neutrosophic	ADJ
cana-2873	681	14	generalized	generalized	ADJ
cana-2873	681	15	b	b	X
cana-2873	681	16	-	-	PUNCT
cana-2873	681	17	closed	closed	ADJ
cana-2873	681	18	sets	set	NOUN
cana-2873	681	19	in	in	ADP
cana-2873	681	20	neutrosophic	neutrosophic	ADJ
cana-2873	681	21	topological	topological	ADJ
cana-2873	681	22	spaces	space	NOUN
cana-2873	681	23	,	,	PUNCT
cana-2873	681	24	journal	journal	NOUN
cana-2873	681	25	of	of	ADP
cana-2873	681	26	physics	physics	PROPN
cana-2873	681	27	conference	conference	NOUN
cana-2873	681	28	series	series	NOUN
cana-2873	681	29	,	,	PUNCT
cana-2873	681	30	1139	1139	NUM
cana-2873	681	31	(	(	PUNCT
cana-2873	681	32	1	1	NUM
cana-2873	681	33	)	)	PUNCT
cana-2873	681	34	(	(	PUNCT
cana-2873	681	35	2018	2018	NUM
cana-2873	681	36	)	)	PUNCT
cana-2873	681	37	,	,	PUNCT
cana-2873	681	38	012065	012065	NUM
cana-2873	681	39	.	.	PUNCT
cana-2873	682	1	[	[	X
cana-2873	682	2	11	11	NUM
cana-2873	682	3	]	]	PUNCT
cana-2873	682	4	i.	i.	PROPN
cana-2873	682	5	mohammed	mohammed	PROPN
cana-2873	682	6	ali	ali	PROPN
cana-2873	682	7	jaffer	jaffer	PROPN
cana-2873	682	8	and	and	CCONJ
cana-2873	682	9	k.	k.	PROPN
cana-2873	682	10	ramesh	ramesh	PROPN
cana-2873	682	11	,	,	PUNCT
cana-2873	682	12	neutrosophic	neutrosophic	PROPN
cana-2873	682	13	generalized	generalize	VERB
cana-2873	682	14	pre	pre	X
cana-2873	682	15	regular	regular	ADJ
cana-2873	682	16	closed	closed	ADJ
cana-2873	682	17	sets	set	NOUN
cana-2873	682	18	,	,	PUNCT
cana-2873	682	19	neutrosophic	neutrosophic	ADJ
cana-2873	682	20	sets	set	NOUN
cana-2873	682	21	and	and	CCONJ
cana-2873	682	22	communications	communication	NOUN
cana-2873	682	23	on	on	ADP
cana-2873	682	24	applied	apply	VERB
cana-2873	682	25	nonlinear	nonlinear	ADJ
cana-2873	682	26	analysis	analysis	NOUN
cana-2873	682	27	issn	issn	NOUN
cana-2873	682	28	:	:	PUNCT
cana-2873	682	29	1074	1074	NUM
cana-2873	682	30	-	-	PUNCT
cana-2873	682	31	133x	133x	NUM
cana-2873	682	32	vol	vol	NOUN
cana-2873	682	33	32	32	NUM
cana-2873	682	34	no	no	NOUN
cana-2873	682	35	.	.	PUNCT
cana-2873	683	1	4s	4s	NUM
cana-2873	683	2	(	(	PUNCT
cana-2873	683	3	2025	2025	NUM
cana-2873	683	4	)	)	PUNCT
cana-2873	683	5	597	597	NUM
cana-2873	683	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2873	683	7	system	system	NOUN
cana-2873	683	8	,	,	PUNCT
cana-2873	683	9	30	30	NUM
cana-2873	683	10	(	(	PUNCT
cana-2873	683	11	2019	2019	NUM
cana-2873	683	12	)	)	PUNCT
cana-2873	683	13	,	,	PUNCT
cana-2873	683	14	171	171	NUM
cana-2873	683	15	-	-	SYM
cana-2873	683	16	181	181	NUM
cana-2873	683	17	.	.	PUNCT
cana-2873	684	1	[	[	X
cana-2873	684	2	12	12	NUM
cana-2873	684	3	]	]	PUNCT
cana-2873	684	4	a.	a.	NOUN
cana-2873	684	5	pushpalatha	pushpalatha	PROPN
cana-2873	684	6	and	and	CCONJ
cana-2873	684	7	t.	t.	PROPN
cana-2873	684	8	nandhini	nandhini	PROPN
cana-2873	684	9	,	,	PUNCT
cana-2873	684	10	generalized	generalize	VERB
cana-2873	684	11	closed	close	VERB
cana-2873	684	12	sets	set	NOUN
cana-2873	684	13	via	via	ADP
cana-2873	684	14	neutrosophic	neutrosophic	ADJ
cana-2873	684	15	topological	topological	ADJ
cana-2873	684	16	spaces	space	NOUN
cana-2873	684	17	,	,	PUNCT
cana-2873	684	18	malaya	malaya	PROPN
cana-2873	684	19	journal	journal	PROPN
cana-2873	684	20	of	of	ADP
cana-2873	684	21	matematik	matematik	PROPN
cana-2873	684	22	,	,	PUNCT
cana-2873	684	23	7	7	NUM
cana-2873	684	24	(	(	PUNCT
cana-2873	684	25	1	1	NUM
cana-2873	684	26	)	)	PUNCT
cana-2873	684	27	(	(	PUNCT
cana-2873	684	28	2019	2019	NUM
cana-2873	684	29	)	)	PUNCT
cana-2873	684	30	,	,	PUNCT
cana-2873	684	31	50	50	NUM
cana-2873	684	32	-	-	SYM
cana-2873	684	33	54	54	NUM
cana-2873	684	34	.	.	PUNCT
cana-2873	685	1	[	[	X
cana-2873	685	2	13	13	NUM
cana-2873	685	3	]	]	X
cana-2873	685	4	v.	v.	PROPN
cana-2873	685	5	v.	v.	ADP
cana-2873	685	6	rao	rao	PROPN
cana-2873	685	7	and	and	CCONJ
cana-2873	685	8	r.	r.	PROPN
cana-2873	685	9	srinivasa	srinivasa	PROPN
cana-2873	685	10	,	,	PUNCT
cana-2873	685	11	neutrosophic	neutrosophic	ADJ
cana-2873	685	12	pre	pre	ADJ
cana-2873	685	13	-	-	ADJ
cana-2873	685	14	open	open	ADJ
cana-2873	685	15	sets	set	NOUN
cana-2873	685	16	and	and	CCONJ
cana-2873	685	17	pre	pre	ADJ
cana-2873	685	18	-	-	ADJ
cana-2873	685	19	closed	closed	ADJ
cana-2873	685	20	sets	set	NOUN
cana-2873	685	21	in	in	ADP
cana-2873	685	22	neutrosophic	neutrosophic	ADJ
cana-2873	685	23	topology	topology	NOUN
cana-2873	685	24	,	,	PUNCT
cana-2873	685	25	international	international	ADJ
cana-2873	685	26	journal	journal	NOUN
cana-2873	685	27	of	of	ADP
cana-2873	685	28	chemtech	chemtech	PROPN
cana-2873	685	29	research	research	NOUN
cana-2873	685	30	,	,	PUNCT
cana-2873	685	31	10	10	NUM
cana-2873	685	32	(	(	PUNCT
cana-2873	685	33	10	10	NUM
cana-2873	685	34	)	)	PUNCT
cana-2873	685	35	(	(	PUNCT
cana-2873	685	36	2017	2017	NUM
cana-2873	685	37	)	)	PUNCT
cana-2873	685	38	,	,	PUNCT
cana-2873	685	39	449	449	NUM
cana-2873	685	40	-	-	SYM
cana-2873	685	41	458	458	NUM
cana-2873	685	42	.	.	PUNCT
cana-2873	686	1	[	[	X
cana-2873	686	2	14	14	NUM
cana-2873	686	3	]	]	PUNCT
cana-2873	686	4	a.	a.	NOUN
cana-2873	686	5	a.	a.	NOUN
cana-2873	686	6	salama	salama	PROPN
cana-2873	686	7	and	and	CCONJ
cana-2873	686	8	s.	s.	PROPN
cana-2873	686	9	a.	a.	PROPN
cana-2873	686	10	alblowi	alblowi	PROPN
cana-2873	686	11	,	,	PUNCT
cana-2873	686	12	neutrosophic	neutrosophic	ADJ
cana-2873	686	13	set	set	NOUN
cana-2873	686	14	and	and	CCONJ
cana-2873	686	15	neutrosophic	neutrosophic	ADJ
cana-2873	686	16	topological	topological	ADJ
cana-2873	686	17	spaces	space	NOUN
cana-2873	686	18	,	,	PUNCT
cana-2873	686	19	iosr	iosr	ADJ
cana-2873	686	20	journal	journal	NOUN
cana-2873	686	21	of	of	ADP
cana-2873	686	22	mathematics	mathematic	NOUN
cana-2873	686	23	,	,	PUNCT
cana-2873	686	24	3	3	NUM
cana-2873	686	25	(	(	PUNCT
cana-2873	686	26	4	4	NUM
cana-2873	686	27	)	)	PUNCT
cana-2873	686	28	(	(	PUNCT
cana-2873	686	29	2012	2012	NUM
cana-2873	686	30	)	)	PUNCT
cana-2873	686	31	,	,	PUNCT
cana-2873	686	32	31	31	NUM
cana-2873	686	33	-	-	SYM
cana-2873	686	34	35	35	NUM
cana-2873	686	35	.	.	PUNCT
cana-2873	687	1	[	[	X
cana-2873	687	2	15	15	NUM
cana-2873	687	3	]	]	PUNCT
cana-2873	687	4	a.	a.	NOUN
cana-2873	687	5	a.	a.	NOUN
cana-2873	687	6	salama	salama	PROPN
cana-2873	687	7	and	and	CCONJ
cana-2873	687	8	f.	f.	PROPN
cana-2873	687	9	smarandache	smarandache	PROPN
cana-2873	687	10	,	,	PUNCT
cana-2873	687	11	neutrosophic	neutrosophic	ADJ
cana-2873	687	12	crisp	crisp	ADJ
cana-2873	687	13	set	set	NOUN
cana-2873	687	14	theory	theory	NOUN
cana-2873	687	15	,	,	PUNCT
cana-2873	687	16	educational	educational	ADJ
cana-2873	687	17	publisher	publisher	NOUN
cana-2873	687	18	,	,	PUNCT
cana-2873	687	19	columbus	columbus	PROPN
cana-2873	687	20	,	,	PUNCT
cana-2873	687	21	ohio	ohio	PROPN
cana-2873	687	22	,	,	PUNCT
cana-2873	687	23	usa	usa	PROPN
cana-2873	687	24	,	,	PUNCT
cana-2873	687	25	2015	2015	NUM
cana-2873	687	26	.	.	PUNCT
cana-2873	688	1	[	[	X
cana-2873	688	2	16	16	NUM
cana-2873	688	3	]	]	X
cana-2873	688	4	f.	f.	PROPN
cana-2873	688	5	smarandache	smarandache	PROPN
cana-2873	688	6	,	,	PUNCT
cana-2873	688	7	a	a	DET
cana-2873	688	8	unifying	unifying	ADJ
cana-2873	688	9	field	field	NOUN
cana-2873	688	10	in	in	ADP
cana-2873	688	11	logics	logic	NOUN
cana-2873	688	12	:	:	PUNCT
cana-2873	688	13	neutrosophic	neutrosophic	ADJ
cana-2873	688	14	logic	logic	NOUN
cana-2873	688	15	.	.	PUNCT
cana-2873	689	1	neutrosophy	neutrosophy	NOUN
cana-2873	689	2	,	,	PUNCT
cana-2873	689	3	neutrosophic	neutrosophic	ADJ
cana-2873	689	4	set	set	NOUN
cana-2873	689	5	,	,	PUNCT
cana-2873	689	6	neutrosophic	neutrosophic	ADJ
cana-2873	689	7	probability	probability	NOUN
cana-2873	689	8	,	,	PUNCT
cana-2873	689	9	american	american	ADJ
cana-2873	689	10	research	research	PROPN
cana-2873	689	11	press	press	PROPN
cana-2873	689	12	,	,	PUNCT
cana-2873	689	13	rehoboth	rehoboth	PROPN
cana-2873	689	14	,	,	PUNCT
cana-2873	689	15	nm	nm	PROPN
cana-2873	689	16	,	,	PUNCT
cana-2873	689	17	(	(	PUNCT
cana-2873	689	18	1999	1999	NUM
cana-2873	689	19	)	)	PUNCT
cana-2873	689	20	.	.	PUNCT
cana-2873	690	1	[	[	X
cana-2873	690	2	17	17	NUM
cana-2873	690	3	]	]	X
cana-2873	690	4	f.	f.	PROPN
cana-2873	690	5	smarandache	smarandache	PROPN
cana-2873	690	6	,	,	PUNCT
cana-2873	690	7	neutrosophy	neutrosophy	NOUN
cana-2873	690	8	and	and	CCONJ
cana-2873	690	9	neutrosophic	neutrosophic	ADJ
cana-2873	690	10	logic	logic	NOUN
cana-2873	690	11	,	,	PUNCT
cana-2873	690	12	first	first	ADJ
cana-2873	690	13	international	international	ADJ
cana-2873	690	14	conference	conference	NOUN
cana-2873	690	15	on	on	ADP
cana-2873	690	16	neutrosophy	neutrosophy	NOUN
cana-2873	690	17	,	,	PUNCT
cana-2873	690	18	neutrosophic	neutrosophic	ADJ
cana-2873	690	19	logic	logic	NOUN
cana-2873	690	20	,	,	PUNCT
cana-2873	690	21	set	set	NOUN
cana-2873	690	22	,	,	PUNCT
cana-2873	690	23	probability	probability	NOUN
cana-2873	690	24	,	,	PUNCT
cana-2873	690	25	and	and	CCONJ
cana-2873	690	26	statistics	statistic	NOUN
cana-2873	690	27	,	,	PUNCT
cana-2873	690	28	university	university	NOUN
cana-2873	690	29	of	of	ADP
cana-2873	690	30	new	new	PROPN
cana-2873	690	31	mexico	mexico	PROPN
cana-2873	690	32	,	,	PUNCT
cana-2873	690	33	gallup	gallup	PROPN
cana-2873	690	34	,	,	PUNCT
cana-2873	690	35	nm	nm	PROPN
cana-2873	690	36	87301	87301	NUM
cana-2873	690	37	,	,	PUNCT
cana-2873	690	38	usa	usa	PROPN
cana-2873	690	39	(	(	PUNCT
cana-2873	690	40	2002	2002	NUM
cana-2873	690	41	)	)	PUNCT
cana-2873	690	42	.	.	PUNCT
cana-2873	691	1	[	[	X
cana-2873	691	2	18	18	NUM
cana-2873	691	3	]	]	PUNCT
cana-2873	691	4	a.	a.	NOUN
cana-2873	691	5	vadivel	vadivel	NOUN
cana-2873	691	6	and	and	CCONJ
cana-2873	691	7	c.	c.	PROPN
cana-2873	691	8	john	john	PROPN
cana-2873	691	9	sundar	sundar	PROPN
cana-2873	691	10	,	,	PUNCT
cana-2873	691	11	γ	γ	X
cana-2873	691	12	-	-	ADJ
cana-2873	691	13	open	open	ADJ
cana-2873	691	14	sets	set	NOUN
cana-2873	691	15	in	in	ADP
cana-2873	691	16	nnc	nnc	PROPN
cana-2873	691	17	-	-	PUNCT
cana-2873	691	18	topological	topological	ADJ
cana-2873	691	19	spaces	space	NOUN
cana-2873	691	20	,	,	PUNCT
cana-2873	691	21	advances	advance	NOUN
cana-2873	691	22	in	in	ADP
cana-2873	691	23	mathematics	mathematic	NOUN
cana-2873	691	24	:	:	PUNCT
cana-2873	691	25	scientific	scientific	ADJ
cana-2873	691	26	journal	journal	NOUN
cana-2873	691	27	,	,	PUNCT
cana-2873	691	28	9	9	NUM
cana-2873	691	29	(	(	PUNCT
cana-2873	691	30	4	4	NUM
cana-2873	691	31	)	)	PUNCT
cana-2873	691	32	(	(	PUNCT
cana-2873	691	33	2020	2020	NUM
cana-2873	691	34	)	)	PUNCT
cana-2873	691	35	,	,	PUNCT
cana-2873	691	36	2197	2197	NUM
cana-2873	691	37	-	-	SYM
cana-2873	691	38	2202	2202	NUM
cana-2873	691	39	.	.	PUNCT
cana-2873	692	1	[	[	X
cana-2873	692	2	19	19	NUM
cana-2873	692	3	]	]	PUNCT
cana-2873	692	4	a.	a.	NOUN
cana-2873	692	5	vadivel	vadivel	NOUN
cana-2873	692	6	and	and	CCONJ
cana-2873	692	7	c.	c.	PROPN
cana-2873	692	8	john	john	PROPN
cana-2873	692	9	sundar	sundar	PROPN
cana-2873	692	10	,	,	PUNCT
cana-2873	692	11	nncβ	nncβ	NOUN
cana-2873	692	12	-	-	PUNCT
cana-2873	692	13	open	open	ADJ
cana-2873	692	14	sets	set	NOUN
cana-2873	692	15	,	,	PUNCT
cana-2873	692	16	advances	advance	NOUN
cana-2873	692	17	in	in	ADP
cana-2873	692	18	mathematics	mathematic	NOUN
cana-2873	692	19	:	:	PUNCT
cana-2873	692	20	scientific	scientific	ADJ
cana-2873	692	21	journal	journal	NOUN
cana-2873	692	22	,	,	PUNCT
cana-2873	692	23	9	9	NUM
cana-2873	692	24	(	(	PUNCT
cana-2873	692	25	4	4	NUM
cana-2873	692	26	)	)	PUNCT
cana-2873	692	27	(	(	PUNCT
cana-2873	692	28	2020	2020	NUM
cana-2873	692	29	)	)	PUNCT
cana-2873	692	30	,	,	PUNCT
cana-2873	692	31	22032207	22032207	NUM
cana-2873	692	32	.	.	PUNCT
cana-2873	693	1	[	[	X
cana-2873	693	2	20	20	NUM
cana-2873	693	3	]	]	PUNCT
cana-2873	693	4	a.	a.	NOUN
cana-2873	693	5	vadivel	vadivel	NOUN
cana-2873	693	6	and	and	CCONJ
cana-2873	693	7	c.	c.	PROPN
cana-2873	693	8	john	john	PROPN
cana-2873	693	9	sundar	sundar	PROPN
cana-2873	693	10	,	,	PUNCT
cana-2873	693	11	on	on	ADP
cana-2873	693	12	almost	almost	ADV
cana-2873	693	13	γ	γ	ADJ
cana-2873	693	14	-	-	ADJ
cana-2873	693	15	continuous	continuous	ADJ
cana-2873	693	16	functions	function	NOUN
cana-2873	693	17	in	in	ADP
cana-2873	693	18	n	n	CCONJ
cana-2873	693	19	-	-	PUNCT
cana-2873	693	20	neutrosophic	neutrosophic	ADJ
cana-2873	693	21	crisp	crisp	ADJ
cana-2873	693	22	topological	topological	ADJ
cana-2873	693	23	spaces	space	NOUN
cana-2873	693	24	,	,	PUNCT
cana-2873	693	25	palestine	palestine	PROPN
cana-2873	693	26	journal	journal	PROPN
cana-2873	693	27	of	of	ADP
cana-2873	693	28	mathematics	mathematic	NOUN
cana-2873	693	29	,	,	PUNCT
cana-2873	693	30	11	11	NUM
cana-2873	693	31	(	(	PUNCT
cana-2873	693	32	3	3	NUM
cana-2873	693	33	)	)	PUNCT
cana-2873	693	34	(	(	PUNCT
cana-2873	693	35	2022	2022	NUM
cana-2873	693	36	)	)	PUNCT
cana-2873	693	37	,	,	PUNCT
cana-2873	693	38	424	424	NUM
cana-2873	693	39	-	-	SYM
cana-2873	693	40	432	432	NUM
cana-2873	693	41	.	.	PUNCT
cana-2873	694	1	[	[	X
cana-2873	694	2	21	21	NUM
cana-2873	694	3	]	]	PUNCT
cana-2873	694	4	a.	a.	NOUN
cana-2873	694	5	vadivel	vadivel	NOUN
cana-2873	694	6	and	and	CCONJ
cana-2873	694	7	c.	c.	PROPN
cana-2873	694	8	john	john	PROPN
cana-2873	694	9	sundar	sundar	PROPN
cana-2873	694	10	,	,	PUNCT
cana-2873	694	11	nncγ	nncγ	NOUN
cana-2873	694	12	maps	map	NOUN
cana-2873	694	13	in	in	ADP
cana-2873	694	14	nnc	nnc	PROPN
cana-2873	694	15	-	-	PUNCT
cana-2873	694	16	topological	topological	ADJ
cana-2873	694	17	spaces	space	NOUN
cana-2873	694	18	,	,	PUNCT
cana-2873	694	19	international	international	ADJ
cana-2873	694	20	journal	journal	NOUN
cana-2873	694	21	of	of	ADP
cana-2873	694	22	neutrosophic	neutrosophic	ADJ
cana-2873	694	23	science	science	NOUN
cana-2873	694	24	,	,	PUNCT
cana-2873	694	25	18	18	NUM
cana-2873	694	26	(	(	PUNCT
cana-2873	694	27	3	3	NUM
cana-2873	694	28	)	)	PUNCT
cana-2873	694	29	(	(	PUNCT
cana-2873	694	30	2022	2022	NUM
cana-2873	694	31	)	)	PUNCT
cana-2873	694	32	,	,	PUNCT
cana-2873	694	33	30	30	NUM
cana-2873	694	34	-	-	SYM
cana-2873	694	35	40	40	NUM
cana-2873	694	36	.	.	PUNCT
cana-2873	695	1	[	[	X
cana-2873	695	2	22	22	NUM
cana-2873	695	3	]	]	PUNCT
cana-2873	695	4	a.	a.	NOUN
cana-2873	695	5	vadivel	vadivel	NOUN
cana-2873	695	6	and	and	CCONJ
cana-2873	695	7	c.	c.	PROPN
cana-2873	695	8	john	john	PROPN
cana-2873	695	9	sundar	sundar	PROPN
cana-2873	695	10	,	,	PUNCT
cana-2873	695	11	on	on	ADP
cana-2873	695	12	almost	almost	ADV
cana-2873	695	13	γ	γ	ADJ
cana-2873	695	14	-	-	ADJ
cana-2873	695	15	continuous	continuous	ADJ
cana-2873	695	16	functions	function	NOUN
cana-2873	695	17	in	in	ADP
cana-2873	695	18	n	n	CCONJ
cana-2873	695	19	-	-	PUNCT
cana-2873	695	20	neutrosophic	neutrosophic	ADJ
cana-2873	695	21	crisp	crisp	ADJ
cana-2873	695	22	topological	topological	ADJ
cana-2873	695	23	spaces	space	NOUN
cana-2873	695	24	,	,	PUNCT
cana-2873	695	25	palestine	palestine	PROPN
cana-2873	695	26	journal	journal	PROPN
cana-2873	695	27	of	of	ADP
cana-2873	695	28	mathematics	mathematic	NOUN
cana-2873	695	29	,	,	PUNCT
cana-2873	695	30	11	11	NUM
cana-2873	695	31	(	(	PUNCT
cana-2873	695	32	3	3	NUM
cana-2873	695	33	)	)	PUNCT
cana-2873	695	34	(	(	PUNCT
cana-2873	695	35	2022	2022	NUM
cana-2873	695	36	)	)	PUNCT
cana-2873	695	37	,	,	PUNCT
cana-2873	695	38	424	424	NUM
cana-2873	695	39	-	-	SYM
cana-2873	695	40	432	432	NUM
cana-2873	695	41	.	.	PUNCT
cana-2873	696	1	[	[	X
cana-2873	696	2	23	23	NUM
cana-2873	696	3	]	]	PUNCT
cana-2873	696	4	a.	a.	NOUN
cana-2873	696	5	vadivel	vadivel	NOUN
cana-2873	696	6	and	and	CCONJ
cana-2873	696	7	c.	c.	PROPN
cana-2873	696	8	john	john	PROPN
cana-2873	696	9	sundar	sundar	PROPN
cana-2873	696	10	,	,	PUNCT
cana-2873	696	11	(	(	PUNCT
cana-2873	696	12	r1957	r1957	NOUN
cana-2873	696	13	)	)	PUNCT
cana-2873	696	14	some	some	DET
cana-2873	696	15	types	type	NOUN
cana-2873	696	16	of	of	ADP
cana-2873	696	17	continuous	continuous	ADJ
cana-2873	696	18	function	function	NOUN
cana-2873	696	19	via	via	ADP
cana-2873	696	20	n	n	CCONJ
cana-2873	696	21	-neutrosophic	-neutrosophic	ADJ
cana-2873	696	22	crisp	crisp	ADJ
cana-2873	696	23	topological	topological	ADJ
cana-2873	696	24	spaces	space	NOUN
cana-2873	696	25	,	,	PUNCT
cana-2873	696	26	applications	application	NOUN
cana-2873	696	27	and	and	CCONJ
cana-2873	696	28	applied	apply	VERB
cana-2873	696	29	mathematics	mathematic	NOUN
cana-2873	696	30	:	:	PUNCT
cana-2873	696	31	an	an	DET
cana-2873	696	32	international	international	ADJ
cana-2873	696	33	journal	journal	NOUN
cana-2873	696	34	(	(	PUNCT
cana-2873	696	35	aam	aam	PROPN
cana-2873	696	36	)	)	PUNCT
cana-2873	696	37	,	,	PUNCT
cana-2873	696	38	18	18	NUM
cana-2873	696	39	(	(	PUNCT
cana-2873	696	40	1	1	NUM
cana-2873	696	41	)	)	PUNCT
cana-2873	696	42	(	(	PUNCT
cana-2873	696	43	2023	2023	NUM
cana-2873	696	44	)	)	PUNCT
cana-2873	696	45	,	,	PUNCT
cana-2873	696	46	article	article	NOUN
cana-2873	696	47	12	12	NUM
cana-2873	696	48	.	.	PUNCT
cana-2873	697	1	[	[	X
cana-2873	697	2	24	24	NUM
cana-2873	697	3	]	]	PUNCT
cana-2873	697	4	a.	a.	NOUN
cana-2873	697	5	vadivel	vadivel	NOUN
cana-2873	697	6	,	,	PUNCT
cana-2873	697	7	c.	c.	PROPN
cana-2873	697	8	john	john	PROPN
cana-2873	697	9	sundar	sundar	PROPN
cana-2873	697	10	and	and	CCONJ
cana-2873	697	11	p.	p.	PROPN
cana-2873	697	12	thangaraja	thangaraja	PROPN
cana-2873	697	13	,	,	PUNCT
cana-2873	697	14	nncβ	nncβ	ADJ
cana-2873	697	15	-	-	PUNCT
cana-2873	697	16	continuous	continuous	ADJ
cana-2873	697	17	maps	map	NOUN
cana-2873	697	18	,	,	PUNCT
cana-2873	697	19	south	south	PROPN
cana-2873	697	20	east	east	PROPN
cana-2873	697	21	asian	asian	PROPN
cana-2873	697	22	journal	journal	NOUN
cana-2873	697	23	of	of	ADP
cana-2873	697	24	mathematics	mathematics	PROPN
cana-2873	697	25	and	and	CCONJ
cana-2873	697	26	mathematical	mathematical	ADJ
cana-2873	697	27	sciences	science	NOUN
cana-2873	697	28	,	,	PUNCT
cana-2873	697	29	18	18	NUM
cana-2873	697	30	(	(	PUNCT
cana-2873	697	31	2	2	NUM
cana-2873	697	32	)	)	PUNCT
cana-2873	697	33	(	(	PUNCT
cana-2873	697	34	2022	2022	NUM
cana-2873	697	35	)	)	PUNCT
cana-2873	697	36	,	,	PUNCT
cana-2873	697	37	275	275	NUM
cana-2873	697	38	-	-	SYM
cana-2873	697	39	288	288	NUM
cana-2873	697	40	.	.	PUNCT
cana-2873	698	1	[	[	X
cana-2873	698	2	25	25	NUM
cana-2873	698	3	]	]	PUNCT
cana-2873	698	4	l.	l.	PROPN
cana-2873	698	5	a.	a.	PROPN
cana-2873	698	6	zadeh	zadeh	PROPN
cana-2873	698	7	,	,	PUNCT
cana-2873	698	8	fuzzy	fuzzy	ADJ
cana-2873	698	9	sets	set	NOUN
cana-2873	698	10	,	,	PUNCT
cana-2873	698	11	information	information	NOUN
cana-2873	698	12	and	and	CCONJ
cana-2873	698	13	control	control	NOUN
cana-2873	698	14	,	,	PUNCT
cana-2873	698	15	8	8	NUM
cana-2873	698	16	(	(	PUNCT
cana-2873	698	17	1965	1965	NUM
cana-2873	698	18	)	)	PUNCT