id	sid	tid	token	lemma	pos
cana-5359	1	1	communications	communication	NOUN
cana-5359	1	2	on	on	ADP
cana-5359	1	3	applied	apply	VERB
cana-5359	1	4	nonlinear	nonlinear	ADJ
cana-5359	1	5	analysis	analysis	NOUN
cana-5359	1	6	issn	issn	NOUN
cana-5359	1	7	:	:	PUNCT
cana-5359	1	8	1074	1074	NUM
cana-5359	1	9	-	-	PUNCT
cana-5359	1	10	133x	133x	NUM
cana-5359	1	11	vol	vol	VERB
cana-5359	1	12	32	32	NUM
cana-5359	1	13	no	no	NOUN
cana-5359	1	14	.	.	PUNCT
cana-5359	2	1	10s	10	NOUN
cana-5359	2	2	(	(	PUNCT
cana-5359	2	3	2025	2025	NUM
cana-5359	2	4	)	)	PUNCT
cana-5359	2	5	1909	1909	NUM
cana-5359	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	2	7	continuous	continuous	ADJ
cana-5359	2	8	and	and	CCONJ
cana-5359	2	9	irresolute	irresolute	ADJ
cana-5359	2	10	maps	map	NOUN
cana-5359	2	11	via	via	ADP
cana-5359	2	12	𝜹-open	𝜹-open	NOUN
cana-5359	2	13	sets	set	NOUN
cana-5359	2	14	in	in	ADP
cana-5359	2	15	fermatean	fermatean	ADJ
cana-5359	2	16	fuzzy	fuzzy	ADJ
cana-5359	2	17	topological	topological	ADJ
cana-5359	2	18	spaces	space	NOUN
cana-5359	2	19	and	and	CCONJ
cana-5359	2	20	application	application	NOUN
cana-5359	2	21	of	of	ADP
cana-5359	2	22	mcdm	mcdm	ADJ
cana-5359	2	23	techniques	technique	NOUN
cana-5359	2	24	a.	a.	NOUN
cana-5359	2	25	vadivel1	vadivel1	PROPN
cana-5359	2	26	,	,	PUNCT
cana-5359	3	1	v.	v.	CCONJ
cana-5359	3	2	sagunthaladevi2	sagunthaladevi2	PROPN
cana-5359	3	3	and	and	CCONJ
cana-5359	3	4	s.	s.	PROPN
cana-5359	3	5	priya3	priya3	PROPN
cana-5359	4	1	1pg	1pg	ADJ
cana-5359	4	2	and	and	CCONJ
cana-5359	4	3	research	research	NOUN
cana-5359	4	4	department	department	PROPN
cana-5359	4	5	of	of	ADP
cana-5359	4	6	mathematics	mathematic	NOUN
cana-5359	4	7	,	,	PUNCT
cana-5359	4	8	arignar	arignar	ADJ
cana-5359	4	9	anna	anna	PROPN
cana-5359	4	10	government	government	PROPN
cana-5359	4	11	arts	arts	PROPN
cana-5359	4	12	college	college	PROPN
cana-5359	4	13	,	,	PUNCT
cana-5359	4	14	namakkal	namakkal	NOUN
cana-5359	4	15	637	637	NUM
cana-5359	4	16	002	002	NUM
cana-5359	4	17	,	,	PUNCT
cana-5359	4	18	india	india	PROPN
cana-5359	4	19	.	.	PUNCT
cana-5359	5	1	avmaths@gmail.com	avmaths@gmail.com	PROPN
cana-5359	5	2	,	,	PUNCT
cana-5359	5	3	av12582@annamalaiuniversity.ac.in	av12582@annamalaiuniversity.ac.in	PROPN
cana-5359	5	4	3department	3department	NUM
cana-5359	5	5	of	of	ADP
cana-5359	5	6	mathematics	mathematic	NOUN
cana-5359	5	7	,	,	PUNCT
cana-5359	5	8	m.kumarasamy	m.kumarasamy	ADJ
cana-5359	5	9	college	college	NOUN
cana-5359	5	10	of	of	ADP
cana-5359	5	11	engineering	engineering	PROPN
cana-5359	5	12	,	,	PUNCT
cana-5359	5	13	karur	karur	PROPN
cana-5359	5	14	639	639	NUM
cana-5359	5	15	113	113	NUM
cana-5359	5	16	,	,	PUNCT
cana-5359	5	17	india	india	PROPN
cana-5359	5	18	.	.	PUNCT
cana-5359	6	1	sagunthala98v@gmail.com	sagunthala98v@gmail.com	PROPN
cana-5359	6	2	1,2,3department	1,2,3department	NUM
cana-5359	6	3	of	of	ADP
cana-5359	6	4	mathematics	mathematics	PROPN
cana-5359	6	5	,	,	PUNCT
cana-5359	6	6	annamalai	annamalai	PROPN
cana-5359	6	7	university	university	PROPN
cana-5359	6	8	,	,	PUNCT
cana-5359	6	9	annamalai	annamalai	PROPN
cana-5359	6	10	nagar	nagar	VERB
cana-5359	6	11	608	608	NUM
cana-5359	6	12	002	002	NUM
cana-5359	6	13	,	,	PUNCT
cana-5359	6	14	india	india	PROPN
cana-5359	6	15	.	.	PUNCT
cana-5359	7	1	pre9433@gmail.com	pre9433@gmail.com	X
cana-5359	8	1	corresponding	corresponding	ADJ
cana-5359	8	2	author	author	NOUN
cana-5359	8	3	:	:	PUNCT
cana-5359	8	4	s.	s.	PROPN
cana-5359	8	5	priya	priya	PROPN
cana-5359	8	6	and	and	CCONJ
cana-5359	8	7	v.	v.	ADP
cana-5359	8	8	sagunthaladevi	sagunthaladevi	ADJ
cana-5359	8	9	article	article	NOUN
cana-5359	8	10	history	history	NOUN
cana-5359	8	11	:	:	PUNCT
cana-5359	8	12	received	receive	VERB
cana-5359	8	13	:	:	PUNCT
cana-5359	8	14	12	12	NUM
cana-5359	8	15	-	-	SYM
cana-5359	8	16	01	01	NUM
cana-5359	8	17	-	-	PUNCT
cana-5359	8	18	2025	2025	NUM
cana-5359	8	19	revised	revise	VERB
cana-5359	8	20	:	:	PUNCT
cana-5359	8	21	15	15	NUM
cana-5359	8	22	-	-	NUM
cana-5359	8	23	02	02	NUM
cana-5359	8	24	-	-	PUNCT
cana-5359	8	25	2025	2025	NUM
cana-5359	8	26	accepted	accept	VERB
cana-5359	8	27	:	:	PUNCT
cana-5359	8	28	01	01	NUM
cana-5359	8	29	-	-	SYM
cana-5359	8	30	03	03	NUM
cana-5359	8	31	-	-	PUNCT
cana-5359	8	32	2025	2025	NUM
cana-5359	8	33	abstract	abstract	NOUN
cana-5359	8	34	:	:	PUNCT
cana-5359	8	35	in	in	ADP
cana-5359	8	36	this	this	DET
cana-5359	8	37	paper	paper	NOUN
cana-5359	8	38	,	,	PUNCT
cana-5359	8	39	we	we	PRON
cana-5359	8	40	develop	develop	VERB
cana-5359	8	41	the	the	DET
cana-5359	8	42	concept	concept	NOUN
cana-5359	8	43	of	of	ADP
cana-5359	8	44	fermatean	fermatean	ADJ
cana-5359	8	45	fuzzy	fuzzy	ADJ
cana-5359	8	46	(	(	PUNCT
cana-5359	8	47	resp	resp	NOUN
cana-5359	8	48	.	.	PUNCT
cana-5359	9	1	𝛿	𝛿	ADJ
cana-5359	9	2	,	,	PUNCT
cana-5359	9	3	𝛿𝒫	𝛿𝒫	NOUN
cana-5359	9	4	,	,	PUNCT
cana-5359	9	5	𝛿𝒮	𝛿𝒮	NOUN
cana-5359	9	6	,	,	PUNCT
cana-5359	9	7	𝛿𝛼	𝛿𝛼	NOUN
cana-5359	9	8	&	&	CCONJ
cana-5359	9	9	𝛿𝛽	𝛿𝛽	PROPN
cana-5359	9	10	or	or	CCONJ
cana-5359	9	11	𝑒∗)-continuity	𝑒∗)-continuity	NOUN
cana-5359	9	12	in	in	ADP
cana-5359	9	13	fermatean	fermatean	ADJ
cana-5359	9	14	fuzzy	fuzzy	ADJ
cana-5359	9	15	topological	topological	ADJ
cana-5359	9	16	spaces	space	NOUN
cana-5359	9	17	and	and	CCONJ
cana-5359	9	18	specialize	specialize	VERB
cana-5359	9	19	some	some	PRON
cana-5359	9	20	of	of	ADP
cana-5359	9	21	their	their	PRON
cana-5359	9	22	basic	basic	ADJ
cana-5359	9	23	properties	property	NOUN
cana-5359	9	24	with	with	ADP
cana-5359	9	25	examples	example	NOUN
cana-5359	9	26	.	.	PUNCT
cana-5359	10	1	also	also	ADV
cana-5359	10	2	,	,	PUNCT
cana-5359	10	3	we	we	PRON
cana-5359	10	4	discuss	discuss	VERB
cana-5359	10	5	about	about	ADP
cana-5359	10	6	properties	property	NOUN
cana-5359	10	7	and	and	CCONJ
cana-5359	10	8	characterization	characterization	NOUN
cana-5359	10	9	of	of	ADP
cana-5359	10	10	fermatean	fermatean	ADJ
cana-5359	10	11	fuzzy	fuzzy	ADJ
cana-5359	10	12	irresolute	irresolute	ADJ
cana-5359	10	13	maps	map	NOUN
cana-5359	10	14	and	and	CCONJ
cana-5359	10	15	application	application	NOUN
cana-5359	10	16	of	of	ADP
cana-5359	10	17	multiple	multiple	ADJ
cana-5359	10	18	criteria	criterion	NOUN
cana-5359	10	19	decision	decision	NOUN
cana-5359	10	20	making	making	NOUN
cana-5359	10	21	(	(	PUNCT
cana-5359	10	22	mcdm	mcdm	ADJ
cana-5359	10	23	)	)	PUNCT
cana-5359	10	24	techniques	technique	NOUN
cana-5359	10	25	to	to	ADP
cana-5359	10	26	the	the	DET
cana-5359	10	27	real	real	ADJ
cana-5359	10	28	-	-	PUNCT
cana-5359	10	29	world	world	NOUN
cana-5359	10	30	problem	problem	NOUN
cana-5359	10	31	using	use	VERB
cana-5359	10	32	a	a	DET
cana-5359	10	33	proposed	propose	VERB
cana-5359	10	34	entropy	entropy	NOUN
cana-5359	10	35	measure	measure	NOUN
cana-5359	10	36	in	in	ADP
cana-5359	10	37	fermatean	fermatean	ADJ
cana-5359	10	38	fuzzy	fuzzy	ADJ
cana-5359	10	39	topological	topological	ADJ
cana-5359	10	40	spaces	space	NOUN
cana-5359	10	41	.	.	PUNCT
cana-5359	11	1	keywords	keyword	NOUN
cana-5359	11	2	:	:	PUNCT
cana-5359	12	1	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	12	2	,	,	PUNCT
cana-5359	12	3	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	PRON
cana-5359	12	4	,	,	PUNCT
cana-5359	12	5	𝔉ℱ𝛿𝐼𝑟𝑟	𝔉ℱ𝛿𝐼𝑟𝑟	NOUN
cana-5359	12	6	and	and	CCONJ
cana-5359	12	7	fermatean	fermatean	ADJ
cana-5359	12	8	fuzzy	fuzzy	ADJ
cana-5359	12	9	entropy	entropy	NOUN
cana-5359	12	10	measure	measure	NOUN
cana-5359	12	11	.	.	PUNCT
cana-5359	13	1	ams	am	NOUN
cana-5359	13	2	(	(	PUNCT
cana-5359	13	3	2000	2000	NUM
cana-5359	13	4	)	)	PUNCT
cana-5359	13	5	subject	subject	ADJ
cana-5359	13	6	classification	classification	NOUN
cana-5359	13	7	:	:	PUNCT
cana-5359	13	8	03e72	03e72	NUM
cana-5359	13	9	,	,	PUNCT
cana-5359	13	10	54a40	54a40	NUM
cana-5359	13	11	,	,	PUNCT
cana-5359	13	12	94d05	94d05	NUM
cana-5359	13	13	1	1	NUM
cana-5359	13	14	introduction	introduction	NOUN
cana-5359	13	15	fuzzy	fuzzy	ADJ
cana-5359	13	16	sets	set	NOUN
cana-5359	13	17	were	be	AUX
cana-5359	13	18	introduced	introduce	VERB
cana-5359	13	19	zadeh	zadeh	PROPN
cana-5359	14	1	[	[	X
cana-5359	14	2	15	15	NUM
cana-5359	14	3	]	]	X
cana-5359	14	4	in	in	ADP
cana-5359	14	5	1965	1965	NUM
cana-5359	14	6	.	.	PUNCT
cana-5359	15	1	the	the	DET
cana-5359	15	2	fuzzy	fuzzy	ADJ
cana-5359	15	3	set	set	VERB
cana-5359	15	4	concept	concept	NOUN
cana-5359	15	5	was	be	AUX
cana-5359	15	6	the	the	DET
cana-5359	15	7	basis	basis	NOUN
cana-5359	15	8	of	of	ADP
cana-5359	15	9	mathematical	mathematical	ADJ
cana-5359	15	10	testing	testing	NOUN
cana-5359	15	11	of	of	ADP
cana-5359	15	12	the	the	DET
cana-5359	15	13	fuzzy	fuzzy	ADJ
cana-5359	15	14	concept	concept	NOUN
cana-5359	15	15	that	that	PRON
cana-5359	15	16	exists	exist	VERB
cana-5359	15	17	in	in	ADP
cana-5359	15	18	our	our	PRON
cana-5359	15	19	real	real	ADJ
cana-5359	15	20	world	world	NOUN
cana-5359	15	21	and	and	CCONJ
cana-5359	15	22	the	the	DET
cana-5359	15	23	formation	formation	NOUN
cana-5359	15	24	of	of	ADP
cana-5359	15	25	new	new	ADJ
cana-5359	15	26	branches	branch	NOUN
cana-5359	15	27	in	in	ADP
cana-5359	15	28	mathematics	mathematic	NOUN
cana-5359	15	29	.	.	PUNCT
cana-5359	16	1	the	the	DET
cana-5359	16	2	fuzzy	fuzzy	ADJ
cana-5359	16	3	set	set	VERB
cana-5359	16	4	concept	concept	NOUN
cana-5359	16	5	corresponding	correspond	VERB
cana-5359	16	6	to	to	ADP
cana-5359	16	7	unexplained	unexplained	ADJ
cana-5359	16	8	physical	physical	ADJ
cana-5359	16	9	situations	situation	NOUN
cana-5359	16	10	gives	give	VERB
cana-5359	16	11	useful	useful	ADJ
cana-5359	16	12	applications	application	NOUN
cana-5359	16	13	on	on	ADP
cana-5359	16	14	many	many	ADJ
cana-5359	16	15	topics	topic	NOUN
cana-5359	16	16	such	such	ADJ
cana-5359	16	17	as	as	ADP
cana-5359	16	18	statistics	statistic	NOUN
cana-5359	16	19	,	,	PUNCT
cana-5359	16	20	data	datum	NOUN
cana-5359	16	21	processing	processing	NOUN
cana-5359	16	22	and	and	CCONJ
cana-5359	16	23	linguistics	linguistic	NOUN
cana-5359	16	24	.	.	PUNCT
cana-5359	17	1	a	a	DET
cana-5359	17	2	lot	lot	NOUN
cana-5359	17	3	of	of	ADP
cana-5359	17	4	research	research	NOUN
cana-5359	17	5	has	have	AUX
cana-5359	17	6	been	be	AUX
cana-5359	17	7	done	do	VERB
cana-5359	17	8	on	on	ADP
cana-5359	17	9	this	this	DET
cana-5359	17	10	subject	subject	NOUN
cana-5359	17	11	since	since	SCONJ
cana-5359	17	12	1965	1965	NUM
cana-5359	17	13	.	.	PUNCT
cana-5359	18	1	in	in	ADP
cana-5359	18	2	1968	1968	NUM
cana-5359	18	3	,	,	PUNCT
cana-5359	18	4	chang	chang	PROPN
cana-5359	19	1	[	[	X
cana-5359	19	2	6	6	NUM
cana-5359	19	3	]	]	PUNCT
cana-5359	19	4	defined	define	VERB
cana-5359	19	5	the	the	DET
cana-5359	19	6	concept	concept	NOUN
cana-5359	19	7	of	of	ADP
cana-5359	19	8	fuzzy	fuzzy	ADJ
cana-5359	19	9	topological	topological	ADJ
cana-5359	19	10	space	space	NOUN
cana-5359	19	11	and	and	CCONJ
cana-5359	19	12	generalized	generalize	VERB
cana-5359	19	13	some	some	DET
cana-5359	19	14	basic	basic	ADJ
cana-5359	19	15	notions	notion	NOUN
cana-5359	19	16	of	of	ADP
cana-5359	19	17	topology	topology	NOUN
cana-5359	19	18	such	such	ADJ
cana-5359	19	19	as	as	ADP
cana-5359	19	20	open	open	ADJ
cana-5359	19	21	set	set	NOUN
cana-5359	19	22	,	,	PUNCT
cana-5359	19	23	closed	closed	ADJ
cana-5359	19	24	set	set	NOUN
cana-5359	19	25	,	,	PUNCT
cana-5359	19	26	continuity	continuity	NOUN
cana-5359	19	27	and	and	CCONJ
cana-5359	19	28	compactness	compactness	NOUN
cana-5359	19	29	to	to	ADP
cana-5359	19	30	fuzzy	fuzzy	ADJ
cana-5359	19	31	topological	topological	ADJ
cana-5359	19	32	spaces	space	NOUN
cana-5359	19	33	.	.	PUNCT
cana-5359	20	1	the	the	DET
cana-5359	20	2	idea	idea	NOUN
cana-5359	20	3	of	of	ADP
cana-5359	20	4	intuitionistic	intuitionistic	ADJ
cana-5359	20	5	fuzzy	fuzzy	ADJ
cana-5359	20	6	set	set	NOUN
cana-5359	20	7	was	be	AUX
cana-5359	20	8	first	first	ADV
cana-5359	20	9	published	publish	VERB
cana-5359	20	10	by	by	ADP
cana-5359	20	11	atanassov	atanassov	NOUN
cana-5359	21	1	[	[	X
cana-5359	21	2	1	1	NUM
cana-5359	21	3	]	]	PUNCT
cana-5359	21	4	and	and	CCONJ
cana-5359	21	5	many	many	ADJ
cana-5359	21	6	works	work	NOUN
cana-5359	21	7	by	by	ADP
cana-5359	21	8	the	the	DET
cana-5359	21	9	same	same	ADJ
cana-5359	21	10	author	author	NOUN
cana-5359	21	11	and	and	CCONJ
cana-5359	21	12	his	his	PRON
cana-5359	21	13	colleagues	colleague	NOUN
cana-5359	21	14	appeared	appear	VERB
cana-5359	21	15	in	in	ADP
cana-5359	21	16	the	the	DET
cana-5359	21	17	literature	literature	NOUN
cana-5359	21	18	[	[	X
cana-5359	21	19	2	2	NUM
cana-5359	21	20	,	,	PUNCT
cana-5359	21	21	5	5	NUM
cana-5359	21	22	]	]	PUNCT
cana-5359	21	23	.	.	PUNCT
cana-5359	22	1	coker	coker	NOUN
cana-5359	23	1	[	[	X
cana-5359	23	2	7	7	X
cana-5359	23	3	]	]	PUNCT
cana-5359	23	4	initiated	initiate	VERB
cana-5359	23	5	a	a	DET
cana-5359	23	6	study	study	NOUN
cana-5359	23	7	of	of	ADP
cana-5359	23	8	intuitionistic	intuitionistic	ADJ
cana-5359	23	9	fuzzy	fuzzy	ADJ
cana-5359	23	10	topological	topological	ADJ
cana-5359	23	11	spaces	space	NOUN
cana-5359	23	12	.	.	PUNCT
cana-5359	24	1	later	later	ADV
cana-5359	24	2	yager	yager	NOUN
cana-5359	25	1	[	[	X
cana-5359	25	2	13	13	NUM
cana-5359	25	3	]	]	PUNCT
cana-5359	25	4	launched	launch	VERB
cana-5359	25	5	a	a	DET
cana-5359	25	6	non	non	ADJ
cana-5359	25	7	standard	standard	ADJ
cana-5359	25	8	fuzzy	fuzzy	ADJ
cana-5359	25	9	set	set	NOUN
cana-5359	25	10	referred	refer	VERB
cana-5359	25	11	to	to	ADP
cana-5359	25	12	as	as	ADP
cana-5359	25	13	pythagorean	pythagorean	PROPN
cana-5359	25	14	fuzzy	fuzzy	ADJ
cana-5359	25	15	set	set	PROPN
cana-5359	25	16	.	.	PUNCT
cana-5359	26	1	olgun	olgun	PROPN
cana-5359	26	2	et	et	PROPN
cana-5359	26	3	al	al	PROPN
cana-5359	26	4	.	.	PROPN
cana-5359	26	5	,	,	PUNCT
cana-5359	27	1	[	[	X
cana-5359	27	2	9	9	NUM
cana-5359	27	3	]	]	PUNCT
cana-5359	27	4	defined	define	VERB
cana-5359	27	5	a	a	DET
cana-5359	27	6	pythagorean	pythagorean	ADJ
cana-5359	27	7	fuzzy	fuzzy	ADJ
cana-5359	27	8	topological	topological	ADJ
cana-5359	27	9	spaces	space	NOUN
cana-5359	27	10	.	.	PUNCT
cana-5359	28	1	fermatean	fermatean	ADJ
cana-5359	28	2	fuzzy	fuzzy	ADJ
cana-5359	28	3	sets	set	NOUN
cana-5359	28	4	proposed	propose	VERB
cana-5359	28	5	by	by	ADP
cana-5359	28	6	senapati	senapati	PROPN
cana-5359	28	7	and	and	CCONJ
cana-5359	28	8	yager	yager	NOUN
cana-5359	28	9	in	in	ADP
cana-5359	28	10	2020	2020	NUM
cana-5359	29	1	[	[	X
cana-5359	29	2	10	10	NUM
cana-5359	29	3	]	]	PUNCT
cana-5359	29	4	,	,	PUNCT
cana-5359	29	5	can	can	AUX
cana-5359	29	6	handle	handle	VERB
cana-5359	29	7	uncertain	uncertain	ADJ
cana-5359	29	8	information	information	NOUN
cana-5359	29	9	more	more	ADV
cana-5359	29	10	easily	easily	ADV
cana-5359	29	11	in	in	ADP
cana-5359	29	12	the	the	DET
cana-5359	29	13	process	process	NOUN
cana-5359	29	14	of	of	ADP
cana-5359	29	15	decision	decision	NOUN
cana-5359	29	16	making	making	NOUN
cana-5359	29	17	.	.	PUNCT
cana-5359	30	1	they	they	PRON
cana-5359	30	2	defined	define	VERB
cana-5359	30	3	basic	basic	ADJ
cana-5359	30	4	operations	operation	NOUN
cana-5359	30	5	over	over	ADP
cana-5359	30	6	the	the	DET
cana-5359	30	7	fermatean	fermatean	ADJ
cana-5359	30	8	fuzzy	fuzzy	ADJ
cana-5359	30	9	sets	set	NOUN
cana-5359	30	10	.	.	PUNCT
cana-5359	31	1	hariwan	hariwan	PROPN
cana-5359	31	2	z.	z.	PROPN
cana-5359	31	3	ibrahim	ibrahim	PROPN
cana-5359	31	4	defined	define	VERB
cana-5359	31	5	a	a	DET
cana-5359	31	6	fermatean	fermatean	ADJ
cana-5359	31	7	fuzzy	fuzzy	ADJ
cana-5359	31	8	topological	topological	ADJ
cana-5359	31	9	spaces	space	NOUN
cana-5359	31	10	and	and	CCONJ
cana-5359	31	11	the	the	DET
cana-5359	31	12	continuity	continuity	NOUN
cana-5359	31	13	of	of	ADP
cana-5359	31	14	a	a	DET
cana-5359	31	15	function	function	NOUN
cana-5359	31	16	defind	defind	NOUN
cana-5359	31	17	among	among	ADP
cana-5359	31	18	fermatean	fermatean	ADJ
cana-5359	31	19	fuzzy	fuzzy	ADJ
cana-5359	31	20	topological	topological	ADJ
cana-5359	31	21	spaces	space	NOUN
cana-5359	31	22	.	.	PUNCT
cana-5359	32	1	the	the	DET
cana-5359	32	2	aim	aim	NOUN
cana-5359	32	3	of	of	ADP
cana-5359	32	4	this	this	DET
cana-5359	32	5	paper	paper	NOUN
cana-5359	32	6	is	be	AUX
cana-5359	32	7	as	as	SCONJ
cana-5359	32	8	follows	follow	VERB
cana-5359	32	9	.	.	PUNCT
cana-5359	33	1	in	in	ADP
cana-5359	33	2	section	section	NOUN
cana-5359	33	3	2	2	NUM
cana-5359	33	4	,	,	PUNCT
cana-5359	33	5	some	some	DET
cana-5359	33	6	basic	basic	ADJ
cana-5359	33	7	definitions	definition	NOUN
cana-5359	33	8	of	of	ADP
cana-5359	33	9	𝑓𝑠	𝑓𝑠	NOUN
cana-5359	33	10	’s	’s	PART
cana-5359	33	11	,	,	PUNCT
cana-5359	33	12	𝑖𝑓𝑠	𝑖𝑓𝑠	PROPN
cana-5359	33	13	’s	’s	ADV
cana-5359	33	14	,	,	PUNCT
cana-5359	33	15	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5359	33	16	’s	’s	PART
cana-5359	33	17	and	and	CCONJ
cana-5359	33	18	fermatean	fermatean	ADJ
cana-5359	33	19	fuzzy	fuzzy	ADJ
cana-5359	33	20	sets	set	NOUN
cana-5359	33	21	are	be	AUX
cana-5359	33	22	briefly	briefly	ADV
cana-5359	33	23	reviewed	review	VERB
cana-5359	33	24	.	.	PUNCT
cana-5359	34	1	in	in	ADP
cana-5359	34	2	section	section	NOUN
cana-5359	34	3	3	3	NUM
cana-5359	34	4	and	and	CCONJ
cana-5359	34	5	4	4	NUM
cana-5359	34	6	,	,	PUNCT
cana-5359	34	7	we	we	PRON
cana-5359	34	8	develop	develop	VERB
cana-5359	34	9	the	the	DET
cana-5359	34	10	concept	concept	NOUN
cana-5359	34	11	of	of	ADP
cana-5359	34	12	some	some	DET
cana-5359	34	13	stronger	strong	ADJ
cana-5359	34	14	communications	communication	NOUN
cana-5359	34	15	on	on	ADP
cana-5359	34	16	applied	apply	VERB
cana-5359	34	17	nonlinear	nonlinear	ADJ
cana-5359	34	18	analysis	analysis	NOUN
cana-5359	34	19	issn	issn	NOUN
cana-5359	34	20	:	:	PUNCT
cana-5359	34	21	1074	1074	NUM
cana-5359	34	22	-	-	PUNCT
cana-5359	34	23	133x	133x	NUM
cana-5359	34	24	vol	vol	VERB
cana-5359	34	25	32	32	NUM
cana-5359	34	26	no	no	NOUN
cana-5359	34	27	.	.	PUNCT
cana-5359	35	1	10s	10	NOUN
cana-5359	35	2	(	(	PUNCT
cana-5359	35	3	2025	2025	NUM
cana-5359	35	4	)	)	PUNCT
cana-5359	35	5	1910	1910	NUM
cana-5359	35	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	35	7	and	and	CCONJ
cana-5359	35	8	weaker	weak	ADJ
cana-5359	35	9	forms	form	NOUN
cana-5359	35	10	of	of	ADP
cana-5359	35	11	fermatean	fermatean	ADJ
cana-5359	35	12	fuzzy	fuzzy	ADJ
cana-5359	35	13	continuous	continuous	ADJ
cana-5359	35	14	and	and	CCONJ
cana-5359	35	15	irresolute	irresolute	ADJ
cana-5359	35	16	maps	map	NOUN
cana-5359	35	17	in	in	ADP
cana-5359	35	18	fermatean	fermatean	ADJ
cana-5359	35	19	fuzzy	fuzzy	ADJ
cana-5359	35	20	topological	topological	ADJ
cana-5359	35	21	spaces	space	NOUN
cana-5359	35	22	and	and	CCONJ
cana-5359	35	23	also	also	ADV
cana-5359	35	24	specialized	specialize	VERB
cana-5359	35	25	some	some	PRON
cana-5359	35	26	of	of	ADP
cana-5359	35	27	their	their	PRON
cana-5359	35	28	basic	basic	ADJ
cana-5359	35	29	properties	property	NOUN
cana-5359	35	30	with	with	ADP
cana-5359	35	31	examples	example	NOUN
cana-5359	35	32	.	.	PUNCT
cana-5359	36	1	in	in	ADP
cana-5359	36	2	section	section	NOUN
cana-5359	36	3	5	5	NUM
cana-5359	36	4	,	,	PUNCT
cana-5359	36	5	entropy	entropy	NOUN
cana-5359	36	6	measure	measure	NOUN
cana-5359	36	7	was	be	AUX
cana-5359	36	8	introduced	introduce	VERB
cana-5359	36	9	by	by	ADP
cana-5359	36	10	zadeh	zadeh	PROPN
cana-5359	37	1	[	[	X
cana-5359	37	2	16	16	NUM
cana-5359	37	3	]	]	PUNCT
cana-5359	37	4	for	for	ADP
cana-5359	37	5	classical	classical	ADJ
cana-5359	37	6	fuzzy	fuzzy	ADJ
cana-5359	37	7	sets	set	NOUN
cana-5359	37	8	.	.	PUNCT
cana-5359	38	1	many	many	ADJ
cana-5359	38	2	authors	author	NOUN
cana-5359	38	3	developed	develop	VERB
cana-5359	38	4	and	and	CCONJ
cana-5359	38	5	created	create	VERB
cana-5359	38	6	for	for	ADP
cana-5359	38	7	their	their	PRON
cana-5359	38	8	version	version	NOUN
cana-5359	38	9	of	of	ADP
cana-5359	38	10	entropy	entropy	NOUN
cana-5359	38	11	measure	measure	NOUN
cana-5359	38	12	.	.	PUNCT
cana-5359	39	1	here	here	ADV
cana-5359	39	2	we	we	PRON
cana-5359	39	3	introduce	introduce	VERB
cana-5359	39	4	entropy	entropy	NOUN
cana-5359	39	5	measure	measure	NOUN
cana-5359	39	6	for	for	ADP
cana-5359	39	7	fermatean	fermatean	ADJ
cana-5359	39	8	fuzzy	fuzzy	ADJ
cana-5359	39	9	sets	set	NOUN
cana-5359	39	10	and	and	CCONJ
cana-5359	39	11	give	give	VERB
cana-5359	39	12	an	an	DET
cana-5359	39	13	example	example	NOUN
cana-5359	39	14	for	for	ADP
cana-5359	39	15	the	the	DET
cana-5359	39	16	decision	decision	NOUN
cana-5359	39	17	making	make	VERB
cana-5359	39	18	in	in	ADP
cana-5359	39	19	real	real	ADJ
cana-5359	39	20	life	life	NOUN
cana-5359	39	21	problem	problem	NOUN
cana-5359	39	22	.	.	PUNCT
cana-5359	40	1	the	the	DET
cana-5359	40	2	paper	paper	NOUN
cana-5359	40	3	is	be	AUX
cana-5359	40	4	concluded	conclude	VERB
cana-5359	40	5	in	in	ADP
cana-5359	40	6	section	section	NOUN
cana-5359	40	7	6	6	NUM
cana-5359	40	8	.	.	SYM
cana-5359	40	9	2	2	NUM
cana-5359	40	10	preliminaries	preliminary	NOUN
cana-5359	40	11	we	we	PRON
cana-5359	40	12	recall	recall	VERB
cana-5359	40	13	some	some	DET
cana-5359	40	14	basic	basic	ADJ
cana-5359	40	15	notions	notion	NOUN
cana-5359	40	16	of	of	ADP
cana-5359	40	17	fuzzy	fuzzy	ADJ
cana-5359	40	18	sets	set	NOUN
cana-5359	40	19	,	,	PUNCT
cana-5359	40	20	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-5359	40	21	’s	’s	PART
cana-5359	40	22	,	,	PUNCT
cana-5359	40	23	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-5359	40	24	’s	’s	NOUN
cana-5359	40	25	and	and	CCONJ
cana-5359	40	26	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	40	27	’s	’s	PART
cana-5359	40	28	.	.	PUNCT
cana-5359	41	1	definition	definition	NOUN
cana-5359	41	2	2.1	2.1	NUM
cana-5359	41	3	[	[	SYM
cana-5359	41	4	15	15	NUM
cana-5359	41	5	]	]	PUNCT
cana-5359	41	6	let	let	VERB
cana-5359	41	7	𝑋	𝑋	NOUN
cana-5359	41	8	be	be	AUX
cana-5359	41	9	a	a	DET
cana-5359	41	10	nonempty	nonempty	ADV
cana-5359	41	11	set	set	VERB
cana-5359	41	12	.	.	PUNCT
cana-5359	42	1	a	a	DET
cana-5359	42	2	fuzzy	fuzzy	ADJ
cana-5359	42	3	set	set	VERB
cana-5359	42	4	𝐴	𝐴	PROPN
cana-5359	42	5	in	in	ADP
cana-5359	42	6	𝑋	𝑋	PROPN
cana-5359	42	7	is	be	AUX
cana-5359	42	8	characterized	characterize	VERB
cana-5359	42	9	by	by	ADP
cana-5359	42	10	a	a	DET
cana-5359	42	11	membership	membership	NOUN
cana-5359	42	12	function	function	NOUN
cana-5359	42	13	𝜇𝐴	𝜇𝐴	ADP
cana-5359	42	14	:	:	PUNCT
cana-5359	42	15	𝑋	𝑋	PROPN
cana-5359	42	16	→	→	SYM
cana-5359	43	1	[	[	X
cana-5359	43	2	0,1	0,1	NUM
cana-5359	43	3	]	]	PUNCT
cana-5359	43	4	.	.	PUNCT
cana-5359	44	1	that	that	PRON
cana-5359	44	2	is	be	AUX
cana-5359	44	3	:	:	PUNCT
cana-5359	44	4	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	44	5	)	)	PUNCT
cana-5359	44	6	=	=	NOUN
cana-5359	44	7	{	{	PUNCT
cana-5359	45	1	1	1	NUM
cana-5359	45	2	,	,	PUNCT
cana-5359	45	3	if	if	SCONJ
cana-5359	45	4	𝑥	𝑥	PRON
cana-5359	45	5	∈	∈	PROPN
cana-5359	45	6	𝑋	𝑋	NOUN
cana-5359	45	7	0	0	NUM
cana-5359	45	8	,	,	PUNCT
cana-5359	45	9	if	if	SCONJ
cana-5359	45	10	𝑥	𝑥	PROPN
cana-5359	45	11	∉	∉	X
cana-5359	45	12	𝑋	𝑋	PROPN
cana-5359	45	13	(	(	PUNCT
cana-5359	45	14	0,1	0,1	NUM
cana-5359	45	15	)	)	PUNCT
cana-5359	45	16	if	if	SCONJ
cana-5359	45	17	𝑥	𝑥	NOUN
cana-5359	45	18	ispartlyin	ispartlyin	VERB
cana-5359	45	19	𝑋.	𝑋.	PROPN
cana-5359	45	20	alternatively	alternatively	ADV
cana-5359	45	21	,	,	PUNCT
cana-5359	45	22	a	a	DET
cana-5359	45	23	fuzzy	fuzzy	ADJ
cana-5359	45	24	set	set	VERB
cana-5359	45	25	𝐴	𝐴	PROPN
cana-5359	45	26	in	in	ADP
cana-5359	45	27	𝑋	𝑋	PROPN
cana-5359	45	28	is	be	AUX
cana-5359	45	29	an	an	DET
cana-5359	45	30	object	object	NOUN
cana-5359	45	31	having	have	VERB
cana-5359	45	32	the	the	DET
cana-5359	45	33	form	form	NOUN
cana-5359	45	34	𝐴	𝐴	NOUN
cana-5359	45	35	=	=	PUNCT
cana-5359	45	36	{	{	PUNCT
cana-5359	45	37	<	<	X
cana-5359	45	38	𝑥	𝑥	X
cana-5359	45	39	,	,	PUNCT
cana-5359	45	40	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	45	41	)	)	PUNCT
cana-5359	45	42	>	>	PUNCT
cana-5359	46	1	|𝑥	|𝑥	PROPN
cana-5359	46	2	∈	∈	PROPN
cana-5359	46	3	𝑋	𝑋	PROPN
cana-5359	46	4	}	}	PUNCT
cana-5359	46	5	or	or	CCONJ
cana-5359	46	6	𝐴	𝐴	PROPN
cana-5359	46	7	=	=	PUNCT
cana-5359	46	8	{	{	PUNCT
cana-5359	46	9	⟨	⟨	NOUN
cana-5359	46	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	46	11	)	)	PUNCT
cana-5359	46	12	𝑥	𝑥	DET
cana-5359	46	13	⟩	⟩	NOUN
cana-5359	46	14	|𝑥	|𝑥	NOUN
cana-5359	46	15	∈	∈	PROPN
cana-5359	46	16	𝑋	𝑋	PROPN
cana-5359	46	17	}	}	PUNCT
cana-5359	46	18	,	,	PUNCT
cana-5359	46	19	where	where	SCONJ
cana-5359	46	20	the	the	DET
cana-5359	46	21	function	function	NOUN
cana-5359	46	22	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-5359	46	23	):	):	PUNCT
cana-5359	46	24	𝑋	𝑋	PROPN
cana-5359	46	25	→	→	SYM
cana-5359	46	26	[	[	X
cana-5359	46	27	0,1	0,1	NUM
cana-5359	46	28	]	]	PUNCT
cana-5359	46	29	defines	define	VERB
cana-5359	46	30	the	the	DET
cana-5359	46	31	degree	degree	NOUN
cana-5359	46	32	of	of	ADP
cana-5359	46	33	membership	membership	NOUN
cana-5359	46	34	of	of	ADP
cana-5359	46	35	the	the	DET
cana-5359	46	36	element	element	NOUN
cana-5359	46	37	,	,	PUNCT
cana-5359	46	38	𝑥	𝑥	PROPN
cana-5359	46	39	∈	∈	PROPN
cana-5359	46	40	𝑋.	𝑋.	PROPN
cana-5359	46	41	the	the	PRON
cana-5359	46	42	closer	close	ADV
cana-5359	46	43	the	the	DET
cana-5359	46	44	membership	membership	NOUN
cana-5359	46	45	value	value	NOUN
cana-5359	46	46	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-5359	46	47	)	)	PUNCT
cana-5359	46	48	to	to	ADP
cana-5359	46	49	1	1	NUM
cana-5359	46	50	,	,	PUNCT
cana-5359	46	51	the	the	PRON
cana-5359	46	52	more	more	ADJ
cana-5359	46	53	𝑥	𝑥	NOUN
cana-5359	46	54	belongs	belong	VERB
cana-5359	46	55	to	to	ADP
cana-5359	46	56	𝐴	𝐴	PROPN
cana-5359	46	57	,	,	PUNCT
cana-5359	46	58	where	where	SCONJ
cana-5359	46	59	the	the	DET
cana-5359	46	60	grades	grade	NOUN
cana-5359	46	61	1	1	NUM
cana-5359	46	62	and	and	CCONJ
cana-5359	46	63	0	0	NUM
cana-5359	46	64	represent	represent	VERB
cana-5359	46	65	full	full	ADJ
cana-5359	46	66	membership	membership	NOUN
cana-5359	46	67	and	and	CCONJ
cana-5359	46	68	full	full	ADJ
cana-5359	46	69	nonmembership	nonmembership	NOUN
cana-5359	46	70	.	.	PUNCT
cana-5359	47	1	fuzzy	fuzzy	ADJ
cana-5359	47	2	set	set	NOUN
cana-5359	47	3	is	be	AUX
cana-5359	47	4	a	a	DET
cana-5359	47	5	collection	collection	NOUN
cana-5359	47	6	of	of	ADP
cana-5359	47	7	objects	object	NOUN
cana-5359	47	8	with	with	ADP
cana-5359	47	9	graded	grade	VERB
cana-5359	47	10	membership	membership	NOUN
cana-5359	47	11	,	,	PUNCT
cana-5359	47	12	that	that	ADV
cana-5359	47	13	is	is	ADV
cana-5359	47	14	,	,	PUNCT
cana-5359	47	15	having	have	VERB
cana-5359	47	16	degree	degree	NOUN
cana-5359	47	17	of	of	ADP
cana-5359	47	18	membership	membership	NOUN
cana-5359	47	19	.	.	PUNCT
cana-5359	48	1	fuzzy	fuzzy	ADJ
cana-5359	48	2	set	set	NOUN
cana-5359	48	3	is	be	AUX
cana-5359	48	4	an	an	DET
cana-5359	48	5	extension	extension	NOUN
cana-5359	48	6	of	of	ADP
cana-5359	48	7	the	the	DET
cana-5359	48	8	classical	classical	ADJ
cana-5359	48	9	notion	notion	NOUN
cana-5359	48	10	of	of	ADP
cana-5359	48	11	set	set	NOUN
cana-5359	48	12	.	.	PUNCT
cana-5359	49	1	in	in	ADP
cana-5359	49	2	classical	classical	ADJ
cana-5359	49	3	set	set	NOUN
cana-5359	49	4	theory	theory	NOUN
cana-5359	49	5	,	,	PUNCT
cana-5359	49	6	the	the	DET
cana-5359	49	7	membership	membership	NOUN
cana-5359	49	8	of	of	ADP
cana-5359	49	9	elements	element	NOUN
cana-5359	49	10	in	in	ADP
cana-5359	49	11	a	a	DET
cana-5359	49	12	set	set	NOUN
cana-5359	49	13	is	be	AUX
cana-5359	49	14	assessed	assess	VERB
cana-5359	49	15	in	in	ADP
cana-5359	49	16	a	a	DET
cana-5359	49	17	binary	binary	ADJ
cana-5359	49	18	terms	term	NOUN
cana-5359	49	19	according	accord	VERB
cana-5359	49	20	to	to	ADP
cana-5359	49	21	a	a	DET
cana-5359	49	22	bivalent	bivalent	ADJ
cana-5359	49	23	condition	condition	NOUN
cana-5359	49	24	;	;	PUNCT
cana-5359	49	25	an	an	DET
cana-5359	49	26	element	element	NOUN
cana-5359	49	27	either	either	CCONJ
cana-5359	49	28	belongs	belong	VERB
cana-5359	49	29	or	or	CCONJ
cana-5359	49	30	does	do	AUX
cana-5359	49	31	not	not	PART
cana-5359	49	32	belong	belong	VERB
cana-5359	49	33	to	to	ADP
cana-5359	49	34	the	the	DET
cana-5359	49	35	set	set	NOUN
cana-5359	49	36	.	.	PUNCT
cana-5359	50	1	classical	classical	ADJ
cana-5359	50	2	bivalent	bivalent	ADJ
cana-5359	50	3	sets	set	NOUN
cana-5359	50	4	are	be	AUX
cana-5359	50	5	in	in	ADP
cana-5359	50	6	fuzzy	fuzzy	ADJ
cana-5359	50	7	set	set	NOUN
cana-5359	50	8	theory	theory	NOUN
cana-5359	50	9	called	call	VERB
cana-5359	50	10	crisp	crisp	ADJ
cana-5359	50	11	sets	set	NOUN
cana-5359	50	12	.	.	PUNCT
cana-5359	51	1	fuzzy	fuzzy	ADJ
cana-5359	51	2	sets	set	NOUN
cana-5359	51	3	are	be	AUX
cana-5359	51	4	generalized	generalized	ADJ
cana-5359	51	5	classical	classical	ADJ
cana-5359	51	6	sets	set	NOUN
cana-5359	51	7	,	,	PUNCT
cana-5359	51	8	since	since	SCONJ
cana-5359	51	9	the	the	DET
cana-5359	51	10	indicator	indicator	NOUN
cana-5359	51	11	function	function	NOUN
cana-5359	51	12	of	of	ADP
cana-5359	51	13	classical	classical	ADJ
cana-5359	51	14	sets	set	NOUN
cana-5359	51	15	is	be	AUX
cana-5359	51	16	special	special	ADJ
cana-5359	51	17	cases	case	NOUN
cana-5359	51	18	of	of	ADP
cana-5359	51	19	the	the	DET
cana-5359	51	20	membership	membership	NOUN
cana-5359	51	21	functions	function	NOUN
cana-5359	51	22	of	of	ADP
cana-5359	51	23	fuzzy	fuzzy	ADJ
cana-5359	51	24	sets	set	NOUN
cana-5359	51	25	,	,	PUNCT
cana-5359	51	26	if	if	SCONJ
cana-5359	51	27	the	the	DET
cana-5359	51	28	latter	latter	ADJ
cana-5359	51	29	only	only	ADV
cana-5359	51	30	take	take	VERB
cana-5359	51	31	values	value	NOUN
cana-5359	51	32	0	0	NUM
cana-5359	51	33	or	or	CCONJ
cana-5359	51	34	1	1	NUM
cana-5359	51	35	.	.	X
cana-5359	51	36	fuzzy	fuzzy	ADJ
cana-5359	51	37	sets	set	NOUN
cana-5359	51	38	theory	theory	NOUN
cana-5359	51	39	permits	permit	VERB
cana-5359	51	40	the	the	DET
cana-5359	51	41	gradual	gradual	ADJ
cana-5359	51	42	assessment	assessment	NOUN
cana-5359	51	43	of	of	ADP
cana-5359	51	44	the	the	DET
cana-5359	51	45	membership	membership	NOUN
cana-5359	51	46	of	of	ADP
cana-5359	51	47	element	element	NOUN
cana-5359	51	48	in	in	ADP
cana-5359	51	49	a	a	DET
cana-5359	51	50	set	set	NOUN
cana-5359	51	51	;	;	PUNCT
cana-5359	51	52	this	this	PRON
cana-5359	51	53	is	be	AUX
cana-5359	51	54	described	describe	VERB
cana-5359	51	55	with	with	ADP
cana-5359	51	56	the	the	DET
cana-5359	51	57	aid	aid	NOUN
cana-5359	51	58	of	of	ADP
cana-5359	51	59	a	a	DET
cana-5359	51	60	membership	membership	NOUN
cana-5359	51	61	function	function	NOUN
cana-5359	51	62	valued	value	VERB
cana-5359	51	63	in	in	ADP
cana-5359	51	64	the	the	DET
cana-5359	51	65	real	real	ADJ
cana-5359	51	66	unit	unit	NOUN
cana-5359	51	67	interval	interval	NOUN
cana-5359	51	68	[	[	X
cana-5359	51	69	0,1	0,1	NUM
cana-5359	51	70	]	]	PUNCT
cana-5359	51	71	.	.	PUNCT
cana-5359	52	1	let	let	VERB
cana-5359	52	2	us	we	PRON
cana-5359	52	3	consider	consider	VERB
cana-5359	52	4	two	two	NUM
cana-5359	52	5	examples	example	NOUN
cana-5359	52	6	:	:	PUNCT
cana-5359	52	7	(	(	PUNCT
cana-5359	52	8	i	i	NOUN
cana-5359	52	9	)	)	PUNCT
cana-5359	52	10	all	all	DET
cana-5359	52	11	employees	employee	NOUN
cana-5359	52	12	of	of	ADP
cana-5359	52	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-5359	52	14	who	who	PRON
cana-5359	52	15	are	be	AUX
cana-5359	52	16	over	over	ADP
cana-5359	52	17	1.8𝑚	1.8𝑚	NUM
cana-5359	52	18	in	in	ADP
cana-5359	52	19	height	height	NOUN
cana-5359	52	20	;	;	PUNCT
cana-5359	52	21	(	(	PUNCT
cana-5359	52	22	ii	ii	NOUN
cana-5359	52	23	)	)	PUNCT
cana-5359	52	24	all	all	DET
cana-5359	52	25	employees	employee	NOUN
cana-5359	52	26	of	of	ADP
cana-5359	52	27	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-5359	52	28	who	who	PRON
cana-5359	52	29	are	be	AUX
cana-5359	52	30	tall	tall	ADJ
cana-5359	52	31	.	.	PUNCT
cana-5359	53	1	the	the	DET
cana-5359	53	2	first	first	ADJ
cana-5359	53	3	example	example	NOUN
cana-5359	53	4	is	be	AUX
cana-5359	53	5	a	a	DET
cana-5359	53	6	classical	classical	ADJ
cana-5359	53	7	set	set	NOUN
cana-5359	53	8	with	with	ADP
cana-5359	53	9	a	a	DET
cana-5359	53	10	universe	universe	NOUN
cana-5359	53	11	(	(	PUNCT
cana-5359	53	12	all	all	DET
cana-5359	53	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-5359	53	14	employees	employee	NOUN
cana-5359	53	15	)	)	PUNCT
cana-5359	53	16	and	and	CCONJ
cana-5359	53	17	a	a	DET
cana-5359	53	18	membership	membership	NOUN
cana-5359	53	19	rule	rule	NOUN
cana-5359	53	20	that	that	PRON
cana-5359	53	21	divides	divide	VERB
cana-5359	53	22	the	the	DET
cana-5359	53	23	universe	universe	NOUN
cana-5359	53	24	into	into	ADP
cana-5359	53	25	members	member	NOUN
cana-5359	53	26	(	(	PUNCT
cana-5359	53	27	those	those	PRON
cana-5359	53	28	over	over	ADP
cana-5359	53	29	1.8𝑚	1.8𝑚	NUM
cana-5359	53	30	)	)	PUNCT
cana-5359	53	31	and	and	CCONJ
cana-5359	53	32	nonmembers	nonmember	NOUN
cana-5359	53	33	.	.	PUNCT
cana-5359	54	1	the	the	DET
cana-5359	54	2	second	second	ADJ
cana-5359	54	3	example	example	NOUN
cana-5359	54	4	is	be	AUX
cana-5359	54	5	a	a	DET
cana-5359	54	6	fuzzy	fuzzy	ADJ
cana-5359	54	7	set	set	NOUN
cana-5359	54	8	,	,	PUNCT
cana-5359	54	9	because	because	SCONJ
cana-5359	54	10	some	some	DET
cana-5359	54	11	employees	employee	NOUN
cana-5359	54	12	are	be	AUX
cana-5359	54	13	definitely	definitely	ADV
cana-5359	54	14	in	in	ADP
cana-5359	54	15	the	the	DET
cana-5359	54	16	set	set	NOUN
cana-5359	54	17	and	and	CCONJ
cana-5359	54	18	some	some	PRON
cana-5359	54	19	are	be	AUX
cana-5359	54	20	definitely	definitely	ADV
cana-5359	54	21	not	not	PART
cana-5359	54	22	in	in	ADP
cana-5359	54	23	the	the	DET
cana-5359	54	24	set	set	NOUN
cana-5359	54	25	,	,	PUNCT
cana-5359	54	26	but	but	CCONJ
cana-5359	54	27	some	some	PRON
cana-5359	54	28	are	be	AUX
cana-5359	54	29	borderline	borderline	NOUN
cana-5359	54	30	.	.	PUNCT
cana-5359	55	1	this	this	DET
cana-5359	55	2	distinction	distinction	NOUN
cana-5359	55	3	between	between	ADP
cana-5359	55	4	the	the	DET
cana-5359	55	5	ins	in	NOUN
cana-5359	55	6	,	,	PUNCT
cana-5359	55	7	the	the	DET
cana-5359	55	8	outs	out	NOUN
cana-5359	55	9	,	,	PUNCT
cana-5359	55	10	and	and	CCONJ
cana-5359	55	11	the	the	DET
cana-5359	55	12	borderline	borderline	NOUN
cana-5359	55	13	is	be	AUX
cana-5359	55	14	made	make	VERB
cana-5359	55	15	more	more	ADV
cana-5359	55	16	exact	exact	ADJ
cana-5359	55	17	by	by	ADP
cana-5359	55	18	the	the	DET
cana-5359	55	19	membership	membership	NOUN
cana-5359	55	20	function	function	NOUN
cana-5359	55	21	,	,	PUNCT
cana-5359	55	22	𝜇.	𝜇.	ADV
cana-5359	55	23	if	if	SCONJ
cana-5359	55	24	we	we	PRON
cana-5359	55	25	return	return	VERB
cana-5359	55	26	to	to	ADP
cana-5359	55	27	our	our	PRON
cana-5359	55	28	second	second	ADJ
cana-5359	55	29	example	example	NOUN
cana-5359	55	30	and	and	CCONJ
cana-5359	55	31	let	let	VERB
cana-5359	55	32	𝐴	𝐴	PROPN
cana-5359	55	33	represent	represent	VERB
cana-5359	55	34	the	the	DET
cana-5359	55	35	fuzzy	fuzzy	ADJ
cana-5359	55	36	set	set	NOUN
cana-5359	55	37	of	of	ADP
cana-5359	55	38	all	all	DET
cana-5359	55	39	tall	tall	ADJ
cana-5359	55	40	employees	employee	NOUN
cana-5359	55	41	and	and	CCONJ
cana-5359	55	42	𝑥	𝑥	PROPN
cana-5359	55	43	represent	represent	VERB
cana-5359	55	44	a	a	DET
cana-5359	55	45	member	member	NOUN
cana-5359	55	46	of	of	ADP
cana-5359	55	47	the	the	DET
cana-5359	55	48	universe	universe	ADJ
cana-5359	55	49	𝑋	𝑋	NOUN
cana-5359	55	50	(	(	PUNCT
cana-5359	55	51	i.e.	i.e.	X
cana-5359	55	52	all	all	DET
cana-5359	55	53	employees	employee	NOUN
cana-5359	55	54	)	)	PUNCT
cana-5359	55	55	,	,	PUNCT
cana-5359	55	56	then	then	ADV
cana-5359	55	57	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	55	58	)	)	PUNCT
cana-5359	55	59	would	would	AUX
cana-5359	55	60	be	be	AUX
cana-5359	55	61	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	55	62	)	)	PUNCT
cana-5359	55	63	=	=	SYM
cana-5359	55	64	1	1	NUM
cana-5359	55	65	if	if	SCONJ
cana-5359	55	66	𝑥	𝑥	PRON
cana-5359	55	67	is	be	AUX
cana-5359	55	68	definitely	definitely	ADV
cana-5359	55	69	tall	tall	ADJ
cana-5359	55	70	or	or	CCONJ
cana-5359	55	71	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	55	72	)	)	PUNCT
cana-5359	55	73	=	=	SYM
cana-5359	55	74	0	0	PUNCT
cana-5359	56	1	if	if	SCONJ
cana-5359	56	2	𝑥	𝑥	PRON
cana-5359	56	3	is	be	AUX
cana-5359	56	4	definitely	definitely	ADV
cana-5359	56	5	not	not	PART
cana-5359	56	6	tall	tall	ADJ
cana-5359	56	7	or	or	CCONJ
cana-5359	56	8	0	0	NUM
cana-5359	56	9	<	<	X
cana-5359	56	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-5359	56	11	)	)	PUNCT
cana-5359	56	12	<	<	X
cana-5359	56	13	1	1	NUM
cana-5359	56	14	for	for	ADP
cana-5359	56	15	borderline	borderline	NOUN
cana-5359	56	16	cases	case	NOUN
cana-5359	56	17	.	.	PUNCT
cana-5359	57	1	definition	definition	NOUN
cana-5359	57	2	2.2	2.2	NUM
cana-5359	57	3	[	[	X
cana-5359	57	4	1	1	NUM
cana-5359	57	5	]	]	PUNCT
cana-5359	57	6	the	the	DET
cana-5359	57	7	intuitionistic	intuitionistic	ADJ
cana-5359	57	8	fuzzy	fuzzy	ADJ
cana-5359	57	9	sets	set	NOUN
cana-5359	57	10	are	be	AUX
cana-5359	57	11	defined	define	VERB
cana-5359	57	12	on	on	ADP
cana-5359	57	13	a	a	DET
cana-5359	57	14	non	non	ADJ
cana-5359	57	15	-	-	ADJ
cana-5359	57	16	empty	empty	ADJ
cana-5359	57	17	sets	set	NOUN
cana-5359	57	18	𝑋	𝑋	NOUN
cana-5359	57	19	as	as	ADP
cana-5359	57	20	objects	object	NOUN
cana-5359	57	21	having	have	VERB
cana-5359	57	22	the	the	DET
cana-5359	57	23	form	form	NOUN
cana-5359	57	24	𝐼	𝐼	ADV
cana-5359	57	25	=	=	PUNCT
cana-5359	57	26	{	{	PUNCT
cana-5359	57	27	〈	〈	X
cana-5359	57	28	𝑥	𝑥	PROPN
cana-5359	57	29	,	,	PUNCT
cana-5359	57	30	𝛼𝐼(𝑥	𝛼𝐼(𝑥	PROPN
cana-5359	57	31	)	)	PUNCT
cana-5359	57	32	,	,	PUNCT
cana-5359	57	33	𝛽𝐼(𝑥	𝛽𝐼(𝑥	PROPN
cana-5359	57	34	)	)	PUNCT
cana-5359	57	35	〉	〉	NOUN
cana-5359	57	36	:	:	PUNCT
cana-5359	57	37	𝑥	𝑥	PROPN
cana-5359	57	38	∈	∈	PROPN
cana-5359	57	39	𝑋	𝑋	PROPN
cana-5359	57	40	}	}	PUNCT
cana-5359	57	41	,	,	PUNCT
cana-5359	57	42	where	where	SCONJ
cana-5359	57	43	𝛼𝐼(𝑥	𝛼𝐼(𝑥	ADP
cana-5359	57	44	):	):	PUNCT
cana-5359	57	45	𝑋	𝑋	PROPN
cana-5359	57	46	→	→	SYM
cana-5359	58	1	[	[	X
cana-5359	58	2	0,1	0,1	NUM
cana-5359	58	3	]	]	PUNCT
cana-5359	58	4	and	and	CCONJ
cana-5359	58	5	𝛽𝐼(𝑥	𝛽𝐼(𝑥	PROPN
cana-5359	58	6	):	):	PUNCT
cana-5359	58	7	𝑋	𝑋	PROPN
cana-5359	58	8	→	→	SYM
cana-5359	58	9	[	[	X
cana-5359	58	10	0,1	0,1	NUM
cana-5359	58	11	]	]	PUNCT
cana-5359	58	12	denote	denote	VERB
cana-5359	58	13	the	the	DET
cana-5359	58	14	degree	degree	NOUN
cana-5359	58	15	of	of	ADP
cana-5359	58	16	memebership	memebership	NOUN
cana-5359	58	17	and	and	CCONJ
cana-5359	58	18	the	the	DET
cana-5359	58	19	degree	degree	NOUN
cana-5359	58	20	of	of	ADP
cana-5359	58	21	non	non	NOUN
cana-5359	58	22	-	-	NOUN
cana-5359	58	23	memebership	memebership	NOUN
cana-5359	58	24	of	of	ADP
cana-5359	58	25	each	each	DET
cana-5359	58	26	element	element	NOUN
cana-5359	58	27	𝑥	𝑥	PRON
cana-5359	58	28	∈	∈	PROPN
cana-5359	58	29	𝑋	𝑋	NOUN
cana-5359	58	30	to	to	ADP
cana-5359	58	31	the	the	DET
cana-5359	58	32	set	set	ADJ
cana-5359	58	33	𝐼	𝐼	PROPN
cana-5359	58	34	,	,	PUNCT
cana-5359	58	35	communications	communication	NOUN
cana-5359	58	36	on	on	ADP
cana-5359	58	37	applied	apply	VERB
cana-5359	58	38	nonlinear	nonlinear	ADJ
cana-5359	58	39	analysis	analysis	NOUN
cana-5359	58	40	issn	issn	NOUN
cana-5359	58	41	:	:	PUNCT
cana-5359	58	42	1074	1074	NUM
cana-5359	58	43	-	-	PUNCT
cana-5359	58	44	133x	133x	NUM
cana-5359	58	45	vol	vol	VERB
cana-5359	58	46	32	32	NUM
cana-5359	58	47	no	no	NOUN
cana-5359	58	48	.	.	PUNCT
cana-5359	59	1	10s	10	NOUN
cana-5359	59	2	(	(	PUNCT
cana-5359	59	3	2025	2025	NUM
cana-5359	59	4	)	)	PUNCT
cana-5359	59	5	1911	1911	NUM
cana-5359	59	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	59	7	respectively	respectively	ADV
cana-5359	59	8	,	,	PUNCT
cana-5359	59	9	and	and	CCONJ
cana-5359	59	10	0	0	NUM
cana-5359	59	11	≤	≤	NUM
cana-5359	59	12	𝛼𝐼(𝑥	𝛼𝐼(𝑥	ADP
cana-5359	59	13	)	)	PUNCT
cana-5359	59	14	+	+	CCONJ
cana-5359	59	15	𝛽𝐼(𝑥	𝛽𝐼(𝑥	PROPN
cana-5359	59	16	)	)	PUNCT
cana-5359	59	17	≤	≤	NOUN
cana-5359	59	18	1	1	NUM
cana-5359	59	19	,	,	PUNCT
cana-5359	59	20	for	for	ADP
cana-5359	59	21	all	all	DET
cana-5359	59	22	𝑥	𝑥	DET
cana-5359	59	23	∈	∈	PROPN
cana-5359	59	24	𝑋.	𝑋.	PROPN
cana-5359	59	25	definition	definition	NOUN
cana-5359	59	26	2.3	2.3	NUM
cana-5359	59	27	[	[	X
cana-5359	59	28	1	1	NUM
cana-5359	59	29	,	,	PUNCT
cana-5359	59	30	2	2	NUM
cana-5359	59	31	,	,	PUNCT
cana-5359	59	32	3	3	NUM
cana-5359	59	33	,	,	PUNCT
cana-5359	59	34	4	4	NUM
cana-5359	59	35	]	]	PUNCT
cana-5359	59	36	let	let	VERB
cana-5359	59	37	a	a	DET
cana-5359	59	38	nonempty	nonempty	ADV
cana-5359	59	39	set	set	VERB
cana-5359	59	40	𝑋	𝑋	NOUN
cana-5359	59	41	be	be	AUX
cana-5359	59	42	fixed	fix	VERB
cana-5359	59	43	.	.	PUNCT
cana-5359	60	1	an	an	DET
cana-5359	60	2	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-5359	60	3	𝐴	𝐴	PROPN
cana-5359	60	4	in	in	ADP
cana-5359	60	5	𝑋	𝑋	PROPN
cana-5359	60	6	is	be	AUX
cana-5359	60	7	an	an	DET
cana-5359	60	8	object	object	NOUN
cana-5359	60	9	having	have	VERB
cana-5359	60	10	the	the	DET
cana-5359	60	11	form	form	NOUN
cana-5359	60	12	:	:	PUNCT
cana-5359	60	13	𝐴	𝐴	PROPN
cana-5359	60	14	=	=	PUNCT
cana-5359	60	15	{	{	PUNCT
cana-5359	60	16	<	<	X
cana-5359	60	17	𝑥	𝑥	X
cana-5359	60	18	,	,	PUNCT
cana-5359	60	19	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	60	20	)	)	PUNCT
cana-5359	60	21	,	,	PUNCT
cana-5359	60	22	𝜆𝐴(𝑥	𝜆𝐴(𝑥	PROPN
cana-5359	60	23	)	)	PUNCT
cana-5359	60	24	>	>	PUNCT
cana-5359	61	1	|𝑥	|𝑥	PROPN
cana-5359	61	2	∈	∈	PROPN
cana-5359	61	3	𝑋	𝑋	PROPN
cana-5359	61	4	}	}	PUNCT
cana-5359	61	5	or	or	CCONJ
cana-5359	61	6	𝐴	𝐴	PROPN
cana-5359	61	7	=	=	PUNCT
cana-5359	61	8	{	{	PUNCT
cana-5359	61	9	⟨	⟨	NOUN
cana-5359	61	10	𝜇𝐴(𝑥),𝜆𝐴(𝑥	𝜇𝐴(𝑥),𝜆𝐴(𝑥	PUNCT
cana-5359	61	11	)	)	PUNCT
cana-5359	61	12	𝑥	𝑥	PRON
cana-5359	61	13	⟩	⟩	NOUN
cana-5359	61	14	|𝑥	|𝑥	NOUN
cana-5359	61	15	∈	∈	PROPN
cana-5359	61	16	𝑋	𝑋	PROPN
cana-5359	61	17	}	}	PUNCT
cana-5359	61	18	,	,	PUNCT
cana-5359	61	19	where	where	SCONJ
cana-5359	61	20	the	the	DET
cana-5359	61	21	functions	function	NOUN
cana-5359	61	22	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-5359	61	23	):	):	PUNCT
cana-5359	61	24	𝑋	𝑋	PROPN
cana-5359	61	25	→	→	SYM
cana-5359	61	26	[	[	X
cana-5359	61	27	0,1	0,1	NUM
cana-5359	61	28	]	]	PUNCT
cana-5359	61	29	and	and	CCONJ
cana-5359	61	30	𝜆𝐴(𝑥	𝜆𝐴(𝑥	NUM
cana-5359	61	31	):	):	PUNCT
cana-5359	61	32	𝑋	𝑋	PROPN
cana-5359	61	33	→	→	SYM
cana-5359	61	34	[	[	X
cana-5359	61	35	0,1	0,1	NUM
cana-5359	61	36	]	]	PUNCT
cana-5359	61	37	define	define	VERB
cana-5359	61	38	the	the	DET
cana-5359	61	39	degree	degree	NOUN
cana-5359	61	40	of	of	ADP
cana-5359	61	41	membership	membership	NOUN
cana-5359	61	42	and	and	CCONJ
cana-5359	61	43	the	the	DET
cana-5359	61	44	degree	degree	NOUN
cana-5359	61	45	of	of	ADP
cana-5359	61	46	nonmembership	nonmembership	NOUN
cana-5359	61	47	,	,	PUNCT
cana-5359	61	48	respectively	respectively	ADV
cana-5359	61	49	,	,	PUNCT
cana-5359	61	50	of	of	ADP
cana-5359	61	51	the	the	DET
cana-5359	61	52	element	element	NOUN
cana-5359	61	53	𝑥	𝑥	PRON
cana-5359	61	54	∈	∈	PROPN
cana-5359	61	55	𝑋	𝑋	NOUN
cana-5359	61	56	to	to	ADP
cana-5359	61	57	𝐴	𝐴	PROPN
cana-5359	61	58	,	,	PUNCT
cana-5359	61	59	which	which	PRON
cana-5359	61	60	is	be	AUX
cana-5359	61	61	a	a	DET
cana-5359	61	62	subset	subset	NOUN
cana-5359	61	63	of	of	ADP
cana-5359	61	64	𝑋	𝑋	PROPN
cana-5359	61	65	,	,	PUNCT
cana-5359	61	66	and	and	CCONJ
cana-5359	61	67	for	for	ADP
cana-5359	61	68	every	every	DET
cana-5359	61	69	𝑥	𝑥	PRON
cana-5359	61	70	∈	∈	PROPN
cana-5359	61	71	𝑋	𝑋	NOUN
cana-5359	61	72	:	:	PUNCT
cana-5359	61	73	0	0	NUM
cana-5359	61	74	≤	≤	NUM
cana-5359	61	75	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	61	76	)	)	PUNCT
cana-5359	62	1	+	+	NUM
cana-5359	62	2	𝜆𝐴(𝑥	𝜆𝐴(𝑥	X
cana-5359	62	3	)	)	PUNCT
cana-5359	62	4	≤	≤	NUM
cana-5359	62	5	1	1	NUM
cana-5359	62	6	.	.	PUNCT
cana-5359	63	1	for	for	ADP
cana-5359	63	2	each	each	DET
cana-5359	63	3	𝐴	𝐴	PROPN
cana-5359	63	4	in	in	ADP
cana-5359	63	5	𝑋	𝑋	PROPN
cana-5359	63	6	:	:	PUNCT
cana-5359	63	7	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5359	63	8	)	)	PUNCT
cana-5359	63	9	=	=	SYM
cana-5359	63	10	1	1	NUM
cana-5359	63	11	−	−	NUM
cana-5359	63	12	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	63	13	)	)	PUNCT
cana-5359	63	14	−	−	PUNCT
cana-5359	63	15	𝜆𝐴(𝑥	𝜆𝐴(𝑥	NOUN
cana-5359	63	16	)	)	PUNCT
cana-5359	63	17	is	be	AUX
cana-5359	63	18	the	the	DET
cana-5359	63	19	intuitionistic	intuitionistic	ADJ
cana-5359	63	20	fuzzy	fuzzy	ADJ
cana-5359	63	21	set	set	VERB
cana-5359	63	22	index	index	NOUN
cana-5359	63	23	or	or	CCONJ
cana-5359	63	24	hesitation	hesitation	NOUN
cana-5359	63	25	margin	margin	NOUN
cana-5359	63	26	of	of	ADP
cana-5359	63	27	𝑥	𝑥	NOUN
cana-5359	63	28	in	in	ADP
cana-5359	63	29	𝑋.	𝑋.	PROPN
cana-5359	63	30	the	the	DET
cana-5359	63	31	hesitation	hesitation	NOUN
cana-5359	63	32	margin	margin	NOUN
cana-5359	63	33	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5359	63	34	)	)	PUNCT
cana-5359	63	35	is	be	AUX
cana-5359	63	36	the	the	DET
cana-5359	63	37	degree	degree	NOUN
cana-5359	63	38	of	of	ADP
cana-5359	63	39	nondeterminacy	nondeterminacy	NOUN
cana-5359	63	40	of	of	ADP
cana-5359	63	41	𝑥	𝑥	DET
cana-5359	63	42	∈	∈	PROPN
cana-5359	63	43	𝑋	𝑋	NOUN
cana-5359	63	44	to	to	ADP
cana-5359	63	45	the	the	DET
cana-5359	63	46	set	set	ADJ
cana-5359	63	47	𝐴	𝐴	PROPN
cana-5359	63	48	and	and	CCONJ
cana-5359	63	49	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5359	63	50	)	)	PUNCT
cana-5359	63	51	∈	∈	NOUN
cana-5359	64	1	[	[	X
cana-5359	64	2	0,1	0,1	NUM
cana-5359	64	3	]	]	PUNCT
cana-5359	64	4	.	.	PUNCT
cana-5359	65	1	the	the	DET
cana-5359	65	2	hesitation	hesitation	NOUN
cana-5359	65	3	margin	margin	NOUN
cana-5359	65	4	is	be	AUX
cana-5359	65	5	the	the	DET
cana-5359	65	6	function	function	NOUN
cana-5359	65	7	that	that	PRON
cana-5359	65	8	expresses	express	VERB
cana-5359	65	9	lack	lack	NOUN
cana-5359	65	10	of	of	ADP
cana-5359	65	11	knowledge	knowledge	NOUN
cana-5359	65	12	of	of	ADP
cana-5359	65	13	whether	whether	SCONJ
cana-5359	65	14	𝑥	𝑥	PRON
cana-5359	65	15	∈	∈	PROPN
cana-5359	65	16	𝑋	𝑋	NOUN
cana-5359	65	17	or	or	CCONJ
cana-5359	65	18	𝑥	𝑥	PROPN
cana-5359	65	19	∉	∉	PROPN
cana-5359	65	20	𝑋.	𝑋.	PROPN
cana-5359	65	21	thus	thus	ADV
cana-5359	65	22	:	:	PUNCT
cana-5359	65	23	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	65	24	)	)	PUNCT
cana-5359	65	25	+	+	CCONJ
cana-5359	65	26	𝜆𝐴(𝑥	𝜆𝐴(𝑥	X
cana-5359	65	27	)	)	PUNCT
cana-5359	65	28	+	+	NUM
cana-5359	65	29	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5359	65	30	)	)	PUNCT
cana-5359	65	31	=	=	SYM
cana-5359	65	32	1	1	X
cana-5359	65	33	.	.	PUNCT
cana-5359	65	34	example	example	NOUN
cana-5359	65	35	2.1	2.1	NUM
cana-5359	65	36	let	let	VERB
cana-5359	65	37	𝑋	𝑋	NOUN
cana-5359	65	38	=	=	SYM
cana-5359	65	39	{	{	PUNCT
cana-5359	65	40	𝑥	𝑥	PROPN
cana-5359	65	41	,	,	PUNCT
cana-5359	65	42	𝑦	𝑦	NOUN
cana-5359	65	43	,	,	PUNCT
cana-5359	65	44	𝑧	𝑧	PRON
cana-5359	65	45	}	}	PUNCT
cana-5359	65	46	be	be	AUX
cana-5359	65	47	a	a	DET
cana-5359	65	48	fixed	fix	VERB
cana-5359	65	49	universe	universe	NOUN
cana-5359	65	50	of	of	ADP
cana-5359	65	51	discourse	discourse	NOUN
cana-5359	65	52	and	and	CCONJ
cana-5359	65	53	𝐴	𝐴	PROPN
cana-5359	65	54	=	=	PUNCT
cana-5359	65	55	{	{	PUNCT
cana-5359	65	56	⟨	⟨	VERB
cana-5359	65	57	0.6,0.1	0.6,0.1	PROPN
cana-5359	65	58	𝑥	𝑥	DET
cana-5359	65	59	⟩	⟩	NOUN
cana-5359	65	60	,	,	PUNCT
cana-5359	65	61	⟨	⟨	VERB
cana-5359	65	62	0.8,0.1	0.8,0.1	PROPN
cana-5359	65	63	𝑦	𝑦	NOUN
cana-5359	65	64	⟩	⟩	NOUN
cana-5359	65	65	,	,	PUNCT
cana-5359	65	66	⟨	⟨	VERB
cana-5359	65	67	0.5,0.3	0.5,0.3	PROPN
cana-5359	65	68	𝑧	𝑧	DET
cana-5359	65	69	⟩	⟩	NOUN
cana-5359	65	70	}	}	PUNCT
cana-5359	65	71	,	,	PUNCT
cana-5359	65	72	be	be	AUX
cana-5359	65	73	the	the	DET
cana-5359	65	74	intuitionistic	intuitionistic	ADJ
cana-5359	65	75	fuzzy	fuzzy	ADJ
cana-5359	65	76	set	set	NOUN
cana-5359	65	77	in	in	ADP
cana-5359	65	78	𝑋.	𝑋.	PROPN
cana-5359	65	79	the	the	DET
cana-5359	65	80	hesitation	hesitation	NOUN
cana-5359	65	81	margins	margin	NOUN
cana-5359	65	82	of	of	ADP
cana-5359	65	83	the	the	DET
cana-5359	65	84	elements	element	NOUN
cana-5359	65	85	𝑥	𝑥	PROPN
cana-5359	65	86	,	,	PUNCT
cana-5359	65	87	𝑦	𝑦	NOUN
cana-5359	65	88	,	,	PUNCT
cana-5359	65	89	𝑧	𝑧	PUNCT
cana-5359	65	90	to	to	ADP
cana-5359	65	91	𝐴	𝐴	PROPN
cana-5359	65	92	are	be	AUX
cana-5359	65	93	as	as	SCONJ
cana-5359	65	94	follows	follow	VERB
cana-5359	65	95	:	:	PUNCT
cana-5359	65	96	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5359	65	97	)	)	PUNCT
cana-5359	65	98	=	=	SYM
cana-5359	65	99	0.3	0.3	NUM
cana-5359	65	100	,	,	PUNCT
cana-5359	65	101	𝜋𝐴(𝑦	𝜋𝐴(𝑦	PROPN
cana-5359	65	102	)	)	PUNCT
cana-5359	65	103	=	=	SYM
cana-5359	65	104	0.1	0.1	NUM
cana-5359	65	105	and	and	CCONJ
cana-5359	65	106	𝜋𝐴(𝑧	𝜋𝐴(𝑧	NUM
cana-5359	65	107	)	)	PUNCT
cana-5359	65	108	=	=	PUNCT
cana-5359	66	1	0.2	0.2	NUM
cana-5359	66	2	.	.	PUNCT
cana-5359	67	1	definition	definition	NOUN
cana-5359	67	2	2.4	2.4	NUM
cana-5359	67	3	[	[	SYM
cana-5359	67	4	12	12	NUM
cana-5359	67	5	,	,	PUNCT
cana-5359	67	6	13	13	NUM
cana-5359	67	7	,	,	PUNCT
cana-5359	67	8	14	14	NUM
cana-5359	67	9	]	]	PUNCT
cana-5359	67	10	let	let	VERB
cana-5359	67	11	𝑋	𝑋	NOUN
cana-5359	67	12	be	be	AUX
cana-5359	67	13	a	a	DET
cana-5359	67	14	universal	universal	ADJ
cana-5359	67	15	set	set	NOUN
cana-5359	67	16	.	.	PUNCT
cana-5359	68	1	then	then	ADV
cana-5359	68	2	,	,	PUNCT
cana-5359	68	3	a	a	DET
cana-5359	68	4	pythagorean	pythagorean	PROPN
cana-5359	68	5	fuzzy	fuzzy	ADJ
cana-5359	68	6	set	set	PROPN
cana-5359	68	7	𝐴	𝐴	PROPN
cana-5359	68	8	,	,	PUNCT
cana-5359	68	9	which	which	PRON
cana-5359	68	10	is	be	AUX
cana-5359	68	11	a	a	DET
cana-5359	68	12	set	set	NOUN
cana-5359	68	13	of	of	ADP
cana-5359	68	14	ordered	order	VERB
cana-5359	68	15	pairs	pair	NOUN
cana-5359	68	16	over	over	ADP
cana-5359	68	17	𝑋	𝑋	PROPN
cana-5359	68	18	,	,	PUNCT
cana-5359	68	19	is	be	AUX
cana-5359	68	20	defined	define	VERB
cana-5359	68	21	by	by	ADP
cana-5359	68	22	the	the	DET
cana-5359	68	23	following	following	NOUN
cana-5359	68	24	:	:	PUNCT
cana-5359	68	25	𝐴	𝐴	PROPN
cana-5359	68	26	=	=	PUNCT
cana-5359	68	27	{	{	PUNCT
cana-5359	68	28	<	<	X
cana-5359	68	29	𝑥	𝑥	X
cana-5359	68	30	,	,	PUNCT
cana-5359	68	31	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5359	68	32	)	)	PUNCT
cana-5359	68	33	,	,	PUNCT
cana-5359	68	34	𝜆𝐴(𝑥)|𝑥	𝜆𝐴(𝑥)|𝑥	NOUN
cana-5359	68	35	∈	∈	PROPN
cana-5359	68	36	𝑋	𝑋	PROPN
cana-5359	68	37	}	}	PUNCT
cana-5359	68	38	or	or	CCONJ
cana-5359	68	39	𝐴	𝐴	PROPN
cana-5359	68	40	=	=	PUNCT
cana-5359	68	41	{	{	PUNCT
cana-5359	68	42	⟨	⟨	NOUN
cana-5359	68	43	𝜇𝐴(𝑥),𝜆𝐴(𝑥	𝜇𝐴(𝑥),𝜆𝐴(𝑥	PUNCT
cana-5359	68	44	)	)	PUNCT
cana-5359	68	45	𝑥	𝑥	PRON
cana-5359	68	46	⟩	⟩	NOUN
cana-5359	68	47	|𝑥	|𝑥	NOUN
cana-5359	68	48	∈	∈	PROPN
cana-5359	68	49	𝑋	𝑋	PROPN
cana-5359	68	50	}	}	PUNCT
cana-5359	68	51	,	,	PUNCT
cana-5359	68	52	where	where	SCONJ
cana-5359	68	53	the	the	DET
cana-5359	68	54	functions	function	NOUN
cana-5359	68	55	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-5359	68	56	):	):	PUNCT
cana-5359	68	57	𝑋	𝑋	PROPN
cana-5359	68	58	→	→	SYM
cana-5359	68	59	[	[	X
cana-5359	68	60	0,1	0,1	NUM
cana-5359	68	61	]	]	PUNCT
cana-5359	68	62	and	and	CCONJ
cana-5359	68	63	𝜆𝐴(𝑥	𝜆𝐴(𝑥	NUM
cana-5359	68	64	):	):	PUNCT
cana-5359	68	65	𝑋	𝑋	PROPN
cana-5359	68	66	→	→	SYM
cana-5359	68	67	[	[	X
cana-5359	68	68	0,1	0,1	NUM
cana-5359	68	69	]	]	PUNCT
cana-5359	68	70	define	define	VERB
cana-5359	68	71	the	the	DET
cana-5359	68	72	degree	degree	NOUN
cana-5359	68	73	of	of	ADP
cana-5359	68	74	membership	membership	NOUN
cana-5359	68	75	and	and	CCONJ
cana-5359	68	76	the	the	DET
cana-5359	68	77	degree	degree	NOUN
cana-5359	68	78	of	of	ADP
cana-5359	68	79	nonmembership	nonmembership	NOUN
cana-5359	68	80	,	,	PUNCT
cana-5359	68	81	respectively	respectively	ADV
cana-5359	68	82	,	,	PUNCT
cana-5359	68	83	of	of	ADP
cana-5359	68	84	the	the	DET
cana-5359	68	85	element	element	NOUN
cana-5359	68	86	𝑥	𝑥	PRON
cana-5359	68	87	∈	∈	PROPN
cana-5359	68	88	𝑋	𝑋	NOUN
cana-5359	68	89	to	to	ADP
cana-5359	68	90	𝐴	𝐴	PROPN
cana-5359	68	91	,	,	PUNCT
cana-5359	68	92	which	which	PRON
cana-5359	68	93	is	be	AUX
cana-5359	68	94	a	a	DET
cana-5359	68	95	subset	subset	NOUN
cana-5359	68	96	of	of	ADP
cana-5359	68	97	𝑋	𝑋	PROPN
cana-5359	68	98	,	,	PUNCT
cana-5359	68	99	and	and	CCONJ
cana-5359	68	100	for	for	ADP
cana-5359	68	101	every	every	DET
cana-5359	68	102	𝑥	𝑥	DET
cana-5359	68	103	∈	∈	PROPN
cana-5359	68	104	𝑋	𝑋	NOUN
cana-5359	68	105	,	,	PUNCT
cana-5359	68	106	0	0	NUM
cana-5359	68	107	≤	≤	NOUN
cana-5359	68	108	(	(	PUNCT
cana-5359	68	109	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5359	68	110	+	+	CCONJ
cana-5359	68	111	(	(	PUNCT
cana-5359	68	112	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5359	68	113	≤	≤	NUM
cana-5359	68	114	1	1	NUM
cana-5359	68	115	.	.	PUNCT
cana-5359	69	1	supposing	suppose	VERB
cana-5359	69	2	(	(	PUNCT
cana-5359	69	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5359	69	4	+	+	CCONJ
cana-5359	69	5	(	(	PUNCT
cana-5359	69	6	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5359	69	7	≤	≤	NUM
cana-5359	69	8	1	1	NUM
cana-5359	69	9	,	,	PUNCT
cana-5359	69	10	then	then	ADV
cana-5359	69	11	there	there	PRON
cana-5359	69	12	is	be	VERB
cana-5359	69	13	a	a	DET
cana-5359	69	14	degree	degree	NOUN
cana-5359	69	15	of	of	ADP
cana-5359	69	16	indeterminacy	indeterminacy	NOUN
cana-5359	69	17	of	of	ADP
cana-5359	69	18	𝑥	𝑥	DET
cana-5359	69	19	∈	∈	PROPN
cana-5359	69	20	𝑋	𝑋	NOUN
cana-5359	69	21	to	to	ADP
cana-5359	69	22	𝐴	𝐴	PROPN
cana-5359	69	23	defined	define	VERB
cana-5359	69	24	by	by	ADP
cana-5359	69	25	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5359	69	26	)	)	PUNCT
cana-5359	69	27	=	=	PUNCT
cana-5359	70	1	√1	√1	ADV
cana-5359	70	2	−	−	PROPN
cana-5359	71	1	[	[	X
cana-5359	71	2	(	(	PUNCT
cana-5359	71	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5359	71	4	+	+	CCONJ
cana-5359	71	5	(	(	PUNCT
cana-5359	71	6	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5359	71	7	]	]	PUNCT
cana-5359	71	8	and	and	CCONJ
cana-5359	71	9	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5359	71	10	)	)	PUNCT
cana-5359	71	11	∈	∈	NOUN
cana-5359	72	1	[	[	X
cana-5359	72	2	0,1	0,1	NUM
cana-5359	72	3	]	]	PUNCT
cana-5359	72	4	.	.	PUNCT
cana-5359	73	1	in	in	ADP
cana-5359	73	2	what	what	PRON
cana-5359	73	3	follows	follow	VERB
cana-5359	73	4	,	,	PUNCT
cana-5359	73	5	(	(	PUNCT
cana-5359	73	6	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5359	73	7	+	+	CCONJ
cana-5359	73	8	(	(	PUNCT
cana-5359	73	9	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5359	73	10	+	+	CCONJ
cana-5359	73	11	(	(	PUNCT
cana-5359	73	12	𝜋𝐴(𝑥))2	𝜋𝐴(𝑥))2	NOUN
cana-5359	73	13	=	=	SYM
cana-5359	73	14	1	1	X
cana-5359	73	15	.	.	PUNCT
cana-5359	73	16	otherwise	otherwise	ADV
cana-5359	73	17	,	,	PUNCT
cana-5359	73	18	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5359	73	19	)	)	PUNCT
cana-5359	73	20	=	=	SYM
cana-5359	73	21	0	0	PUNCT
cana-5359	73	22	whenever	whenever	SCONJ
cana-5359	73	23	(	(	PUNCT
cana-5359	73	24	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5359	73	25	+	+	CCONJ
cana-5359	73	26	(	(	PUNCT
cana-5359	73	27	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5359	73	28	=	=	SYM
cana-5359	73	29	1	1	X
cana-5359	73	30	.	.	X
cana-5359	74	1	we	we	PRON
cana-5359	74	2	denote	denote	VERB
cana-5359	74	3	the	the	DET
cana-5359	74	4	set	set	NOUN
cana-5359	74	5	of	of	ADP
cana-5359	74	6	all	all	DET
cana-5359	74	7	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-5359	74	8	’s	’s	NOUN
cana-5359	74	9	over	over	ADP
cana-5359	74	10	𝑋	𝑋	PROPN
cana-5359	74	11	by	by	ADP
cana-5359	74	12	𝑝𝑓𝑠(𝑋	𝑝𝑓𝑠(𝑋	PROPN
cana-5359	74	13	)	)	PUNCT
cana-5359	74	14	.	.	PUNCT
cana-5359	75	1	definition	definition	NOUN
cana-5359	75	2	2.5	2.5	NUM
cana-5359	76	1	[	[	X
cana-5359	76	2	10	10	NUM
cana-5359	76	3	]	]	PUNCT
cana-5359	76	4	let	let	VERB
cana-5359	76	5	𝑋	𝑋	NOUN
cana-5359	76	6	be	be	AUX
cana-5359	76	7	a	a	DET
cana-5359	76	8	universe	universe	NOUN
cana-5359	76	9	of	of	ADP
cana-5359	76	10	discourse	discourse	NOUN
cana-5359	76	11	.	.	PUNCT
cana-5359	77	1	a	a	DET
cana-5359	77	2	fermatean	fermatean	ADJ
cana-5359	77	3	fuzzy	fuzzy	ADJ
cana-5359	77	4	set	set	NOUN
cana-5359	77	5	(	(	PUNCT
cana-5359	77	6	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	77	7	)	)	PUNCT
cana-5359	77	8	𝐹	𝐹	PROPN
cana-5359	77	9	in	in	ADP
cana-5359	77	10	𝑋	𝑋	PROPN
cana-5359	77	11	is	be	AUX
cana-5359	77	12	an	an	DET
cana-5359	77	13	object	object	NOUN
cana-5359	77	14	having	have	VERB
cana-5359	77	15	the	the	DET
cana-5359	77	16	form	form	NOUN
cana-5359	77	17	𝐹	𝐹	PROPN
cana-5359	77	18	=	=	PUNCT
cana-5359	77	19	{	{	PUNCT
cana-5359	77	20	<	<	X
cana-5359	77	21	𝑥	𝑥	X
cana-5359	77	22	,	,	PUNCT
cana-5359	77	23	𝛼𝐹(𝑥	𝛼𝐹(𝑥	NUM
cana-5359	77	24	)	)	PUNCT
cana-5359	77	25	,	,	PUNCT
cana-5359	77	26	𝛽𝐹(𝑥	𝛽𝐹(𝑥	PROPN
cana-5359	77	27	)	)	PUNCT
cana-5359	77	28	>	>	PUNCT
cana-5359	77	29	:	:	PUNCT
cana-5359	77	30	𝑥	𝑥	X
cana-5359	77	31	∈	∈	PROPN
cana-5359	77	32	𝑋	𝑋	PROPN
cana-5359	77	33	}	}	PUNCT
cana-5359	77	34	where	where	SCONJ
cana-5359	77	35	𝛼𝐹(𝑥	𝛼𝐹(𝑥	NUM
cana-5359	77	36	):	):	PUNCT
cana-5359	77	37	𝑋	𝑋	NOUN
cana-5359	77	38	→	→	SYM
cana-5359	77	39	[	[	X
cana-5359	77	40	0,1	0,1	NUM
cana-5359	77	41	]	]	PUNCT
cana-5359	77	42	and	and	CCONJ
cana-5359	77	43	𝛽𝐹(𝑥	𝛽𝐹(𝑥	NUM
cana-5359	77	44	):	):	PUNCT
cana-5359	77	45	𝑋	𝑋	PROPN
cana-5359	77	46	→	→	SYM
cana-5359	77	47	[	[	X
cana-5359	77	48	0,1	0,1	NUM
cana-5359	77	49	]	]	PUNCT
cana-5359	77	50	,	,	PUNCT
cana-5359	77	51	including	include	VERB
cana-5359	77	52	the	the	DET
cana-5359	77	53	condition	condition	NOUN
cana-5359	77	54	0	0	NUM
cana-5359	77	55	≤	≤	NOUN
cana-5359	77	56	(	(	PUNCT
cana-5359	77	57	𝛼𝐹(𝑥))3	𝛼𝐹(𝑥))3	PROPN
cana-5359	77	58	+	+	X
cana-5359	77	59	(	(	PUNCT
cana-5359	77	60	𝛽𝐹(𝑥))3	𝛽𝐹(𝑥))3	X
cana-5359	77	61	≤	≤	NUM
cana-5359	77	62	1	1	NUM
cana-5359	77	63	,	,	PUNCT
cana-5359	77	64	for	for	ADP
cana-5359	77	65	all	all	DET
cana-5359	77	66	𝑥	𝑥	DET
cana-5359	77	67	∈	∈	NOUN
cana-5359	77	68	𝑋.	𝑋.	NOUN
cana-5359	77	69	the	the	DET
cana-5359	77	70	numbers	number	NOUN
cana-5359	77	71	𝛼𝐹(𝑥	𝛼𝐹(𝑥	NUM
cana-5359	77	72	)	)	PUNCT
cana-5359	77	73	and	and	CCONJ
cana-5359	77	74	𝛽𝐹(𝑥	𝛽𝐹(𝑥	NUM
cana-5359	77	75	)	)	PUNCT
cana-5359	77	76	denote	denote	NOUN
cana-5359	77	77	,	,	PUNCT
cana-5359	77	78	respectively	respectively	ADV
cana-5359	77	79	,	,	PUNCT
cana-5359	77	80	the	the	DET
cana-5359	77	81	degree	degree	NOUN
cana-5359	77	82	of	of	ADP
cana-5359	77	83	memebership	memebership	NOUN
cana-5359	77	84	and	and	CCONJ
cana-5359	77	85	the	the	DET
cana-5359	77	86	degree	degree	NOUN
cana-5359	77	87	of	of	ADP
cana-5359	77	88	non	non	NOUN
cana-5359	77	89	-	-	NOUN
cana-5359	77	90	memebership	memebership	NOUN
cana-5359	77	91	of	of	ADP
cana-5359	77	92	the	the	DET
cana-5359	77	93	element	element	NOUN
cana-5359	77	94	𝑥	𝑥	PROPN
cana-5359	77	95	in	in	ADP
cana-5359	77	96	the	the	DET
cana-5359	77	97	set	set	NOUN
cana-5359	77	98	𝐹	𝐹	PROPN
cana-5359	77	99	.	.	PUNCT
cana-5359	78	1	for	for	ADP
cana-5359	78	2	any	any	DET
cana-5359	78	3	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	78	4	𝐹	𝐹	PROPN
cana-5359	78	5	and	and	CCONJ
cana-5359	78	6	𝑥	𝑥	DET
cana-5359	78	7	∈	∈	PROPN
cana-5359	78	8	𝑋	𝑋	NOUN
cana-5359	78	9	,	,	PUNCT
cana-5359	78	10	𝜋𝐹(𝑥	𝜋𝐹(𝑥	NUM
cana-5359	78	11	)	)	PUNCT
cana-5359	78	12	=	=	PUNCT
cana-5359	78	13	√1	√1	ADV
cana-5359	78	14	−	−	PROPN
cana-5359	79	1	[	[	X
cana-5359	79	2	(	(	PUNCT
cana-5359	79	3	𝛼𝐹(𝑥))3	𝛼𝐹(𝑥))3	PROPN
cana-5359	79	4	−	−	PROPN
cana-5359	79	5	(	(	PUNCT
cana-5359	79	6	𝛽𝐹(𝑥))3]3	𝛽𝐹(𝑥))3]3	NOUN
cana-5359	79	7	is	be	AUX
cana-5359	79	8	identified	identify	VERB
cana-5359	79	9	as	as	ADP
cana-5359	79	10	the	the	DET
cana-5359	79	11	degree	degree	NOUN
cana-5359	79	12	of	of	ADP
cana-5359	79	13	interminancy	interminancy	NOUN
cana-5359	79	14	of	of	ADP
cana-5359	79	15	𝑥	𝑥	PRON
cana-5359	79	16	to	to	ADP
cana-5359	79	17	𝐹.	𝐹.	PROPN
cana-5359	79	18	in	in	ADP
cana-5359	79	19	the	the	DET
cana-5359	79	20	interest	interest	NOUN
cana-5359	79	21	of	of	ADP
cana-5359	79	22	simplicity	simplicity	NOUN
cana-5359	79	23	,	,	PUNCT
cana-5359	79	24	we	we	PRON
cana-5359	79	25	shall	shall	AUX
cana-5359	79	26	mention	mention	VERB
cana-5359	79	27	the	the	DET
cana-5359	79	28	symbol	symbol	NOUN
cana-5359	79	29	𝐹	𝐹	PROPN
cana-5359	79	30	=	=	PUNCT
cana-5359	79	31	(	(	PUNCT
cana-5359	79	32	𝛼𝐹	𝛼𝐹	NOUN
cana-5359	79	33	,	,	PUNCT
cana-5359	79	34	𝛽𝐹	𝛽𝐹	NOUN
cana-5359	79	35	)	)	PUNCT
cana-5359	79	36	for	for	ADP
cana-5359	79	37	the	the	DET
cana-5359	79	38	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	79	39	𝐹	𝐹	PROPN
cana-5359	79	40	=	=	PUNCT
cana-5359	79	41	{	{	PUNCT
cana-5359	79	42	<	<	X
cana-5359	79	43	𝑥	𝑥	X
cana-5359	79	44	,	,	PUNCT
cana-5359	79	45	𝛼𝐹(𝑥	𝛼𝐹(𝑥	NUM
cana-5359	79	46	)	)	PUNCT
cana-5359	79	47	,	,	PUNCT
cana-5359	79	48	𝛽𝐹(𝑥	𝛽𝐹(𝑥	PROPN
cana-5359	79	49	):	):	PUNCT
cana-5359	79	50	𝑥	𝑥	PROPN
cana-5359	79	51	∈	∈	PROPN
cana-5359	79	52	𝑋	𝑋	PROPN
cana-5359	79	53	}	}	PUNCT
cana-5359	79	54	.	.	PUNCT
cana-5359	80	1	definition	definition	NOUN
cana-5359	80	2	2.6	2.6	NUM
cana-5359	80	3	[	[	SYM
cana-5359	80	4	10	10	NUM
cana-5359	80	5	]	]	PUNCT
cana-5359	80	6	let	let	VERB
cana-5359	80	7	𝐹	𝐹	PROPN
cana-5359	80	8	=	=	SYM
cana-5359	80	9	(	(	PUNCT
cana-5359	80	10	𝛼𝐹	𝛼𝐹	PROPN
cana-5359	80	11	,	,	PUNCT
cana-5359	80	12	𝛽𝐹	𝛽𝐹	NOUN
cana-5359	80	13	)	)	PUNCT
cana-5359	80	14	,	,	PUNCT
cana-5359	80	15	𝐹1	𝐹1	NOUN
cana-5359	80	16	=	=	SYM
cana-5359	80	17	(	(	PUNCT
cana-5359	80	18	𝛼𝐹1	𝛼𝐹1	PROPN
cana-5359	80	19	,	,	PUNCT
cana-5359	80	20	𝛽𝐹1	𝛽𝐹1	PROPN
cana-5359	80	21	)	)	PUNCT
cana-5359	80	22	and	and	CCONJ
cana-5359	80	23	𝐹2	𝐹2	NOUN
cana-5359	80	24	=	=	SYM
cana-5359	80	25	(	(	PUNCT
cana-5359	80	26	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5359	80	27	,	,	PUNCT
cana-5359	80	28	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5359	80	29	)	)	PUNCT
cana-5359	80	30	,	,	PUNCT
cana-5359	80	31	be	be	AUX
cana-5359	80	32	three	three	NUM
cana-5359	80	33	fermatean	fermatean	ADJ
cana-5359	80	34	fuzzy	fuzzy	ADJ
cana-5359	80	35	sets	set	NOUN
cana-5359	80	36	(	(	PUNCT
cana-5359	80	37	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	80	38	’s	’s	PART
cana-5359	80	39	)	)	PUNCT
cana-5359	80	40	,	,	PUNCT
cana-5359	80	41	then	then	ADV
cana-5359	80	42	their	their	PRON
cana-5359	80	43	operations	operation	NOUN
cana-5359	80	44	are	be	AUX
cana-5359	80	45	defined	define	VERB
cana-5359	80	46	as	as	SCONJ
cana-5359	80	47	follows	follow	VERB
cana-5359	80	48	:	:	PUNCT
cana-5359	80	49	1	1	NUM
cana-5359	80	50	.	.	NUM
cana-5359	80	51	𝐹1	𝐹1	PROPN
cana-5359	80	52	∩	∩	PROPN
cana-5359	80	53	𝐹2	𝐹2	PROPN
cana-5359	80	54	=	=	PUNCT
cana-5359	80	55	(	(	PUNCT
cana-5359	80	56	𝑚𝑖𝑛{𝛼𝐹1	𝑚𝑖𝑛{𝛼𝐹1	VERB
cana-5359	80	57	,	,	PUNCT
cana-5359	80	58	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5359	80	59	}	}	PUNCT
cana-5359	80	60	,	,	PUNCT
cana-5359	80	61	𝑚𝑎𝑥{𝛽𝐹1	𝑚𝑎𝑥{𝛽𝐹1	NOUN
cana-5359	80	62	,	,	PUNCT
cana-5359	80	63	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5359	80	64	}	}	PUNCT
cana-5359	80	65	)	)	PUNCT
cana-5359	80	66	.	.	PUNCT
cana-5359	81	1	2	2	X
cana-5359	81	2	.	.	X
cana-5359	81	3	𝐹1	𝐹1	PROPN
cana-5359	81	4	∪	∪	PROPN
cana-5359	81	5	𝐹2	𝐹2	PROPN
cana-5359	81	6	=	=	SYM
cana-5359	81	7	(	(	PUNCT
cana-5359	81	8	𝑚𝑎𝑥{𝛼𝐹1	𝑚𝑎𝑥{𝛼𝐹1	ADV
cana-5359	81	9	,	,	PUNCT
cana-5359	81	10	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5359	81	11	}	}	PUNCT
cana-5359	81	12	,	,	PUNCT
cana-5359	81	13	𝑚𝑖𝑛{𝛽𝐹1	𝑚𝑖𝑛{𝛽𝐹1	NOUN
cana-5359	81	14	,	,	PUNCT
cana-5359	81	15	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5359	81	16	}	}	PUNCT
cana-5359	81	17	)	)	PUNCT
cana-5359	81	18	.	.	PUNCT
cana-5359	82	1	3	3	X
cana-5359	82	2	.	.	X
cana-5359	83	1	𝐹𝑐	𝐹𝑐	NOUN
cana-5359	83	2	=	=	PUNCT
cana-5359	83	3	(	(	PUNCT
cana-5359	83	4	𝛽𝐹	𝛽𝐹	PROPN
cana-5359	83	5	,	,	PUNCT
cana-5359	83	6	𝛼𝐹	𝛼𝐹	NUM
cana-5359	83	7	)	)	PUNCT
cana-5359	83	8	.	.	PUNCT
cana-5359	84	1	remark	remark	VERB
cana-5359	84	2	2.1	2.1	NUM
cana-5359	84	3	if	if	SCONJ
cana-5359	84	4	𝛼𝐹1	𝛼𝐹1	PROPN
cana-5359	84	5	=	=	SYM
cana-5359	84	6	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5359	84	7	and	and	CCONJ
cana-5359	84	8	𝛽𝐹1	𝛽𝐹1	PROPN
cana-5359	84	9	=	=	PUNCT
cana-5359	84	10	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5359	84	11	,	,	PUNCT
cana-5359	84	12	then	then	ADV
cana-5359	84	13	𝐹1	𝐹1	PROPN
cana-5359	84	14	=	=	X
cana-5359	84	15	𝐹2	𝐹2	PROPN
cana-5359	84	16	note	note	VERB
cana-5359	84	17	that	that	SCONJ
cana-5359	84	18	,	,	PUNCT
cana-5359	84	19	for	for	ADP
cana-5359	84	20	understanding	understand	VERB
cana-5359	84	21	the	the	DET
cana-5359	84	22	fermatean	fermatean	ADJ
cana-5359	84	23	fuzzy	fuzzy	NOUN
cana-5359	84	24	set	set	VERB
cana-5359	84	25	better	well	ADV
cana-5359	84	26	,	,	PUNCT
cana-5359	84	27	we	we	PRON
cana-5359	84	28	give	give	VERB
cana-5359	84	29	an	an	DET
cana-5359	84	30	instance	instance	NOUN
cana-5359	84	31	to	to	PART
cana-5359	84	32	illuminate	illuminate	VERB
cana-5359	84	33	the	the	DET
cana-5359	84	34	communications	communication	NOUN
cana-5359	84	35	on	on	ADP
cana-5359	84	36	applied	apply	VERB
cana-5359	84	37	nonlinear	nonlinear	ADJ
cana-5359	84	38	analysis	analysis	NOUN
cana-5359	84	39	issn	issn	NOUN
cana-5359	84	40	:	:	PUNCT
cana-5359	84	41	1074	1074	NUM
cana-5359	84	42	-	-	PUNCT
cana-5359	84	43	133x	133x	NUM
cana-5359	84	44	vol	vol	VERB
cana-5359	84	45	32	32	NUM
cana-5359	84	46	no	no	NOUN
cana-5359	84	47	.	.	PUNCT
cana-5359	85	1	10s	10	NOUN
cana-5359	85	2	(	(	PUNCT
cana-5359	85	3	2025	2025	NUM
cana-5359	85	4	)	)	PUNCT
cana-5359	85	5	1912	1912	NUM
cana-5359	85	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	85	7	understandability	understandability	NOUN
cana-5359	85	8	of	of	ADP
cana-5359	85	9	the	the	DET
cana-5359	85	10	fermatean	fermatean	ADJ
cana-5359	85	11	fuzzy	fuzzy	ADJ
cana-5359	85	12	set	set	NOUN
cana-5359	85	13	.	.	PUNCT
cana-5359	86	1	the	the	DET
cana-5359	86	2	point	point	NOUN
cana-5359	86	3	when	when	SCONJ
cana-5359	86	4	someone	someone	PRON
cana-5359	86	5	needs	need	VERB
cana-5359	86	6	will	will	AUX
cana-5359	86	7	plan	plan	VERB
cana-5359	86	8	as	as	ADV
cana-5359	86	9	much	much	ADJ
cana-5359	86	10	craving	craving	NOUN
cana-5359	86	11	for	for	ADP
cana-5359	86	12	the	the	DET
cana-5359	86	13	level	level	NOUN
cana-5359	86	14	for	for	ADP
cana-5359	86	15	an	an	DET
cana-5359	86	16	alternative	alternative	ADJ
cana-5359	86	17	𝑠𝑖	𝑠𝑖	NOUN
cana-5359	86	18	on	on	ADP
cana-5359	86	19	a	a	DET
cana-5359	86	20	criterion	criterion	NOUN
cana-5359	86	21	𝐶𝑗	𝐶𝑗	PROPN
cana-5359	86	22	,	,	PUNCT
cana-5359	86	23	he	he	PRON
cana-5359	86	24	might	might	AUX
cana-5359	86	25	provide	provide	VERB
cana-5359	86	26	for	for	ADP
cana-5359	86	27	the	the	DET
cana-5359	86	28	degree	degree	NOUN
cana-5359	86	29	on	on	ADP
cana-5359	86	30	which	which	PRON
cana-5359	86	31	that	that	DET
cana-5359	86	32	alternative	alternative	ADJ
cana-5359	86	33	𝑠𝑖	𝑠𝑖	NOUN
cana-5359	86	34	fulfils	fulfil	VERB
cana-5359	86	35	those	those	DET
cana-5359	86	36	criteria	criterion	NOUN
cana-5359	86	37	𝐶𝑗	𝐶𝑗	PROPN
cana-5359	86	38	likewise	likewise	ADV
cana-5359	86	39	0.85	0.85	NUM
cana-5359	86	40	,	,	PUNCT
cana-5359	86	41	what	what	PRON
cana-5359	86	42	is	be	AUX
cana-5359	86	43	more	more	ADV
cana-5359	86	44	correspondingly	correspondingly	ADV
cana-5359	86	45	the	the	DET
cana-5359	86	46	elective	elective	ADJ
cana-5359	86	47	𝑠𝑖	𝑠𝑖	NOUN
cana-5359	86	48	dissatisfies	dissatisfie	NOUN
cana-5359	86	49	the	the	DET
cana-5359	86	50	criterion	criterion	NOUN
cana-5359	86	51	𝐶𝑗	𝐶𝑗	PROPN
cana-5359	86	52	similarly	similarly	ADV
cana-5359	86	53	as	as	ADP
cana-5359	86	54	0.65	0.65	NUM
cana-5359	86	55	.	.	PUNCT
cana-5359	87	1	we	we	PRON
cana-5359	87	2	can	can	AUX
cana-5359	87	3	definitely	definitely	ADV
cana-5359	87	4	get	get	VERB
cana-5359	87	5	0.85	0.85	NUM
cana-5359	87	6	+	+	CCONJ
cana-5359	87	7	0.65	0.65	NUM
cana-5359	87	8	=	=	SYM
cana-5359	87	9	1.5	1.5	NUM
cana-5359	87	10	>	>	SYM
cana-5359	87	11	1	1	NUM
cana-5359	87	12	,	,	PUNCT
cana-5359	87	13	and	and	CCONJ
cana-5359	87	14	therefore	therefore	ADV
cana-5359	87	15	,	,	PUNCT
cana-5359	87	16	it	it	PRON
cana-5359	87	17	does	do	AUX
cana-5359	87	18	not	not	PART
cana-5359	87	19	follow	follow	VERB
cana-5359	87	20	the	the	DET
cana-5359	87	21	condition	condition	NOUN
cana-5359	87	22	of	of	ADP
cana-5359	87	23	intuitionistic	intuitionistic	ADJ
cana-5359	87	24	fuzzy	fuzzy	ADJ
cana-5359	87	25	sets	set	NOUN
cana-5359	87	26	.	.	PUNCT
cana-5359	88	1	also	also	ADV
cana-5359	88	2	,	,	PUNCT
cana-5359	88	3	we	we	PRON
cana-5359	88	4	can	can	AUX
cana-5359	88	5	get	get	VERB
cana-5359	88	6	(	(	PUNCT
cana-5359	88	7	0.85)2	0.85)2	NOUN
cana-5359	88	8	+	+	CCONJ
cana-5359	88	9	(	(	PUNCT
cana-5359	88	10	0.65)2	0.65)2	NOUN
cana-5359	88	11	=	=	PUNCT
cana-5359	88	12	0.7225	0.7225	NUM
cana-5359	88	13	+	+	NUM
cana-5359	88	14	0.4225	0.4225	NUM
cana-5359	88	15	=	=	SYM
cana-5359	88	16	1.145	1.145	NUM
cana-5359	88	17	>	>	SYM
cana-5359	88	18	1	1	NUM
cana-5359	88	19	,	,	PUNCT
cana-5359	88	20	which	which	PRON
cana-5359	88	21	does	do	AUX
cana-5359	88	22	not	not	PART
cana-5359	88	23	obey	obey	VERB
cana-5359	88	24	the	the	DET
cana-5359	88	25	constraint	constraint	NOUN
cana-5359	88	26	condition	condition	NOUN
cana-5359	88	27	of	of	ADP
cana-5359	88	28	pythagorean	pythagorean	PROPN
cana-5359	88	29	fuzzy	fuzzy	ADJ
cana-5359	88	30	set	set	PROPN
cana-5359	88	31	.	.	PUNCT
cana-5359	89	1	however	however	ADV
cana-5359	89	2	,	,	PUNCT
cana-5359	89	3	we	we	PRON
cana-5359	89	4	can	can	AUX
cana-5359	89	5	get	get	VERB
cana-5359	89	6	(	(	PUNCT
cana-5359	89	7	0.85)3	0.85)3	NOUN
cana-5359	89	8	+	+	CCONJ
cana-5359	89	9	(	(	PUNCT
cana-5359	89	10	0.65)3	0.65)3	NOUN
cana-5359	89	11	=	=	NOUN
cana-5359	89	12	0.614125	0.614125	NUM
cana-5359	89	13	+	+	NUM
cana-5359	89	14	0.274625	0.274625	NUM
cana-5359	89	15	=	=	PUNCT
cana-5359	89	16	0.88875	0.88875	NUM
cana-5359	89	17	≤	≤	NUM
cana-5359	89	18	1	1	NUM
cana-5359	89	19	,	,	PUNCT
cana-5359	89	20	which	which	PRON
cana-5359	89	21	is	be	AUX
cana-5359	89	22	good	good	ADJ
cana-5359	89	23	enough	enough	ADV
cana-5359	89	24	to	to	PART
cana-5359	89	25	apply	apply	VERB
cana-5359	89	26	the	the	DET
cana-5359	89	27	fermatean	fermatean	ADJ
cana-5359	89	28	fuzzy	fuzzy	NOUN
cana-5359	89	29	set	set	VERB
cana-5359	89	30	to	to	PART
cana-5359	89	31	control	control	VERB
cana-5359	89	32	it	it	PRON
cana-5359	89	33	[	[	X
cana-5359	89	34	10	10	NUM
cana-5359	89	35	]	]	PUNCT
cana-5359	89	36	.	.	PUNCT
cana-5359	90	1	throughout	throughout	ADP
cana-5359	90	2	this	this	DET
cana-5359	90	3	paper	paper	NOUN
cana-5359	90	4	,	,	PUNCT
cana-5359	90	5	we	we	PRON
cana-5359	90	6	use	use	VERB
cana-5359	90	7	the	the	DET
cana-5359	90	8	notation	notation	NOUN
cana-5359	90	9	1𝔉	1𝔉	NOUN
cana-5359	90	10	for	for	ADP
cana-5359	90	11	the	the	DET
cana-5359	90	12	fermatean	fermatean	ADJ
cana-5359	90	13	fuzzy	fuzzy	NOUN
cana-5359	90	14	subset	subset	NOUN
cana-5359	90	15	(	(	PUNCT
cana-5359	90	16	1,0	1,0	NUM
cana-5359	90	17	)	)	PUNCT
cana-5359	90	18	and	and	CCONJ
cana-5359	90	19	we	we	PRON
cana-5359	90	20	use	use	VERB
cana-5359	90	21	the	the	DET
cana-5359	90	22	notation	notation	NOUN
cana-5359	90	23	0𝔉	0𝔉	NOUN
cana-5359	90	24	for	for	ADP
cana-5359	90	25	the	the	DET
cana-5359	90	26	fermatean	fermatean	ADJ
cana-5359	90	27	fuzzy	fuzzy	ADJ
cana-5359	90	28	subset	subset	NOUN
cana-5359	90	29	(	(	PUNCT
cana-5359	90	30	0,1	0,1	NUM
cana-5359	90	31	)	)	PUNCT
cana-5359	90	32	,	,	PUNCT
cana-5359	90	33	that	that	ADV
cana-5359	90	34	is	is	ADV
cana-5359	90	35	,	,	PUNCT
cana-5359	90	36	𝛼1𝔉	𝛼1𝔉	NUM
cana-5359	90	37	=	=	SYM
cana-5359	90	38	1	1	NUM
cana-5359	90	39	,	,	PUNCT
cana-5359	90	40	𝛽1𝔉	𝛽1𝔉	X
cana-5359	90	41	=	=	SYM
cana-5359	90	42	0	0	NUM
cana-5359	90	43	,	,	PUNCT
cana-5359	90	44	𝛼0𝔉	𝛼0𝔉	NOUN
cana-5359	90	45	=	=	SYM
cana-5359	90	46	0	0	NUM
cana-5359	90	47	,	,	PUNCT
cana-5359	90	48	𝛽0𝔉	𝛽0𝔉	ADV
cana-5359	90	49	=	=	NOUN
cana-5359	90	50	1	1	X
cana-5359	90	51	.	.	PUNCT
cana-5359	90	52	a	a	DET
cana-5359	90	53	fermatean	fermatean	ADJ
cana-5359	90	54	fuzzy	fuzzy	NOUN
cana-5359	90	55	subset	subset	VERB
cana-5359	90	56	𝔉	𝔉	PROPN
cana-5359	90	57	of	of	ADP
cana-5359	90	58	a	a	DET
cana-5359	90	59	non	non	ADJ
cana-5359	90	60	-	-	ADJ
cana-5359	90	61	empty	empty	ADJ
cana-5359	90	62	set	set	ADJ
cana-5359	90	63	𝑋	𝑋	PROPN
cana-5359	90	64	is	be	AUX
cana-5359	90	65	a	a	DET
cana-5359	90	66	pair	pair	NOUN
cana-5359	90	67	(	(	PUNCT
cana-5359	90	68	𝛼𝔉	𝛼𝔉	NOUN
cana-5359	90	69	,	,	PUNCT
cana-5359	90	70	𝛽𝔉	𝛽𝔉	NOUN
cana-5359	90	71	)	)	PUNCT
cana-5359	90	72	of	of	ADP
cana-5359	90	73	a	a	DET
cana-5359	90	74	membership	membership	NOUN
cana-5359	90	75	function	function	NOUN
cana-5359	90	76	(	(	PUNCT
cana-5359	90	77	𝛼𝔉(𝑥	𝛼𝔉(𝑥	NUM
cana-5359	90	78	):	):	PUNCT
cana-5359	90	79	𝑋	𝑋	PROPN
cana-5359	90	80	→	→	SYM
cana-5359	90	81	[	[	X
cana-5359	90	82	0,1	0,1	NUM
cana-5359	90	83	]	]	PUNCT
cana-5359	90	84	and	and	CCONJ
cana-5359	90	85	a	a	DET
cana-5359	90	86	non	non	ADJ
cana-5359	90	87	-	-	ADJ
cana-5359	90	88	membership	membership	ADJ
cana-5359	90	89	function	function	NOUN
cana-5359	90	90	(	(	PUNCT
cana-5359	90	91	𝛽𝔉(𝑥	𝛽𝔉(𝑥	NUM
cana-5359	90	92	):	):	PUNCT
cana-5359	90	93	𝑋	𝑋	PROPN
cana-5359	90	94	→	→	SYM
cana-5359	91	1	[	[	X
cana-5359	91	2	0,1	0,1	NUM
cana-5359	91	3	]	]	PUNCT
cana-5359	91	4	with	with	ADP
cana-5359	91	5	(	(	PUNCT
cana-5359	91	6	𝛼𝔉(𝑥))3	𝛼𝔉(𝑥))3	PROPN
cana-5359	91	7	+	+	X
cana-5359	91	8	(	(	PUNCT
cana-5359	91	9	𝛽𝔉(𝑥))3	𝛽𝔉(𝑥))3	PROPN
cana-5359	91	10	=	=	SYM
cana-5359	91	11	(	(	PUNCT
cana-5359	91	12	𝛾𝔉(𝑥))3	𝛾𝔉(𝑥))3	NOUN
cana-5359	91	13	for	for	ADP
cana-5359	91	14	any	any	DET
cana-5359	91	15	𝑥	𝑥	PRON
cana-5359	91	16	∈	∈	NOUN
cana-5359	91	17	𝑋	𝑋	NOUN
cana-5359	91	18	where	where	SCONJ
cana-5359	91	19	𝛾𝔉(𝑥	𝛾𝔉(𝑥	NOUN
cana-5359	91	20	):	):	PUNCT
cana-5359	91	21	𝑋	𝑋	PROPN
cana-5359	91	22	→	→	SYM
cana-5359	91	23	[	[	X
cana-5359	91	24	0,1	0,1	NUM
cana-5359	91	25	]	]	PUNCT
cana-5359	91	26	is	be	AUX
cana-5359	91	27	a	a	DET
cana-5359	91	28	function	function	NOUN
cana-5359	91	29	which	which	PRON
cana-5359	91	30	is	be	AUX
cana-5359	91	31	called	call	VERB
cana-5359	91	32	the	the	DET
cana-5359	91	33	strength	strength	NOUN
cana-5359	91	34	of	of	ADP
cana-5359	91	35	commitment	commitment	NOUN
cana-5359	91	36	at	at	ADP
cana-5359	91	37	point	point	NOUN
cana-5359	91	38	𝑥.	𝑥.	DET
cana-5359	91	39	definition	definition	NOUN
cana-5359	91	40	2.7	2.7	NUM
cana-5359	91	41	[	[	SYM
cana-5359	91	42	8	8	NUM
cana-5359	91	43	]	]	PUNCT
cana-5359	91	44	let	let	VERB
cana-5359	91	45	𝑋	𝑋	NOUN
cana-5359	91	46	be	be	AUX
cana-5359	91	47	a	a	DET
cana-5359	91	48	non	non	X
cana-5359	91	49	empty	empty	ADJ
cana-5359	91	50	set	set	NOUN
cana-5359	91	51	and	and	CCONJ
cana-5359	91	52	𝜏	𝜏	NOUN
cana-5359	91	53	be	be	AUX
cana-5359	91	54	a	a	DET
cana-5359	91	55	family	family	NOUN
cana-5359	91	56	of	of	ADP
cana-5359	91	57	fermatean	fermatean	ADJ
cana-5359	91	58	fuzzy	fuzzy	ADJ
cana-5359	91	59	subsets	subset	NOUN
cana-5359	91	60	of	of	ADP
cana-5359	91	61	𝑋.	𝑋.	PROPN
cana-5359	91	62	if	if	SCONJ
cana-5359	91	63	1	1	NUM
cana-5359	91	64	.	.	X
cana-5359	91	65	1𝔉	1𝔉	NOUN
cana-5359	91	66	,	,	PUNCT
cana-5359	91	67	0𝔉	0𝔉	PROPN
cana-5359	91	68	∈	∈	PROPN
cana-5359	91	69	𝜏	𝜏	ADP
cana-5359	91	70	2	2	NUM
cana-5359	91	71	.	.	PUNCT
cana-5359	91	72	for	for	ADP
cana-5359	91	73	any	any	DET
cana-5359	91	74	𝐹1	𝐹1	NOUN
cana-5359	91	75	,	,	PUNCT
cana-5359	91	76	𝐹2	𝐹2	PROPN
cana-5359	91	77	∈	∈	PROPN
cana-5359	91	78	𝜏	𝜏	PROPN
cana-5359	91	79	,	,	PUNCT
cana-5359	91	80	we	we	PRON
cana-5359	91	81	have	have	VERB
cana-5359	91	82	𝐹1	𝐹1	PROPN
cana-5359	91	83	∩	∩	PROPN
cana-5359	91	84	𝐹2	𝐹2	PROPN
cana-5359	91	85	∈	∈	PROPN
cana-5359	91	86	𝜏	𝜏	PROPN
cana-5359	91	87	,	,	PUNCT
cana-5359	91	88	3	3	NUM
cana-5359	91	89	.	.	X
cana-5359	92	1	for	for	ADP
cana-5359	92	2	any	any	DET
cana-5359	92	3	{	{	PUNCT
cana-5359	92	4	𝐹𝑖}𝑖∈𝐼	𝐹𝑖}𝑖∈𝐼	X
cana-5359	92	5	⊂	⊂	SYM
cana-5359	92	6	𝜏	𝜏	NOUN
cana-5359	92	7	,	,	PUNCT
cana-5359	92	8	we	we	PRON
cana-5359	92	9	have	have	VERB
cana-5359	92	10	⋃𝑖∈𝐼	⋃𝑖∈𝐼	NOUN
cana-5359	92	11	𝐹𝑖	𝐹𝑖	PROPN
cana-5359	92	12	∈	∈	NOUN
cana-5359	92	13	𝜏	𝜏	NOUN
cana-5359	92	14	where	where	SCONJ
cana-5359	92	15	𝐼	𝐼	PROPN
cana-5359	92	16	is	be	AUX
cana-5359	92	17	an	an	DET
cana-5359	92	18	arbitrary	arbitrary	ADJ
cana-5359	92	19	index	index	NOUN
cana-5359	92	20	set	set	VERB
cana-5359	92	21	then	then	ADV
cana-5359	92	22	𝜏	𝜏	NOUN
cana-5359	92	23	is	be	AUX
cana-5359	92	24	called	call	VERB
cana-5359	92	25	a	a	DET
cana-5359	92	26	fermatean	fermatean	ADJ
cana-5359	92	27	fuzzy	fuzzy	ADJ
cana-5359	92	28	topology	topology	NOUN
cana-5359	92	29	on	on	ADP
cana-5359	92	30	𝑋.	𝑋.	PROPN
cana-5359	92	31	the	the	DET
cana-5359	92	32	pair	pair	NOUN
cana-5359	92	33	(	(	PUNCT
cana-5359	92	34	𝑋	𝑋	PROPN
cana-5359	92	35	,	,	PUNCT
cana-5359	92	36	𝜏	𝜏	NOUN
cana-5359	92	37	)	)	PUNCT
cana-5359	92	38	is	be	AUX
cana-5359	92	39	said	say	VERB
cana-5359	92	40	to	to	PART
cana-5359	92	41	be	be	AUX
cana-5359	92	42	a	a	DET
cana-5359	92	43	fermatean	fermatean	ADJ
cana-5359	92	44	fuzzy	fuzzy	ADJ
cana-5359	92	45	topological	topological	ADJ
cana-5359	92	46	space	space	NOUN
cana-5359	92	47	.	.	PUNCT
cana-5359	93	1	each	each	DET
cana-5359	93	2	member	member	NOUN
cana-5359	93	3	of	of	ADP
cana-5359	93	4	𝜏	𝜏	PROPN
cana-5359	93	5	is	be	AUX
cana-5359	93	6	called	call	VERB
cana-5359	93	7	an	an	DET
cana-5359	93	8	fermatean	fermatean	ADJ
cana-5359	93	9	fuzzy	fuzzy	ADJ
cana-5359	93	10	oprn	oprn	NOUN
cana-5359	93	11	set	set	VERB
cana-5359	93	12	.	.	PUNCT
cana-5359	94	1	the	the	DET
cana-5359	94	2	complement	complement	NOUN
cana-5359	94	3	of	of	ADP
cana-5359	94	4	an	an	DET
cana-5359	94	5	fermatean	fermatean	ADJ
cana-5359	94	6	fuzzy	fuzzy	ADJ
cana-5359	94	7	open	open	ADJ
cana-5359	94	8	set	set	NOUN
cana-5359	94	9	is	be	AUX
cana-5359	94	10	called	call	VERB
cana-5359	94	11	a	a	DET
cana-5359	94	12	fermatean	fermatean	ADJ
cana-5359	94	13	fuzzy	fuzzy	NOUN
cana-5359	94	14	closed	close	VERB
cana-5359	94	15	set	set	NOUN
cana-5359	94	16	.	.	PUNCT
cana-5359	95	1	remark	remark	VERB
cana-5359	95	2	2.2	2.2	NUM
cana-5359	96	1	[	[	SYM
cana-5359	96	2	8	8	NUM
cana-5359	96	3	]	]	PUNCT
cana-5359	96	4	as	as	ADP
cana-5359	96	5	any	any	DET
cana-5359	96	6	intuitionistic	intuitionistic	ADJ
cana-5359	96	7	fuzzy	fuzzy	ADJ
cana-5359	96	8	subset	subset	NOUN
cana-5359	96	9	or	or	CCONJ
cana-5359	96	10	pythagorean	pythagorean	PROPN
cana-5359	96	11	fuzzy	fuzzy	ADJ
cana-5359	96	12	subset	subset	NOUN
cana-5359	96	13	of	of	ADP
cana-5359	96	14	a	a	DET
cana-5359	96	15	set	set	NOUN
cana-5359	96	16	can	can	AUX
cana-5359	96	17	be	be	AUX
cana-5359	96	18	considered	consider	VERB
cana-5359	96	19	as	as	SCONJ
cana-5359	96	20	fermatean	fermatean	ADJ
cana-5359	96	21	fuzzy	fuzzy	ADJ
cana-5359	96	22	subset	subset	NOUN
cana-5359	96	23	,	,	PUNCT
cana-5359	96	24	we	we	PRON
cana-5359	96	25	observe	observe	VERB
cana-5359	96	26	that	that	SCONJ
cana-5359	96	27	any	any	DET
cana-5359	96	28	intuitionstic	intuitionstic	ADJ
cana-5359	96	29	fuzzy	fuzzy	ADJ
cana-5359	96	30	topological	topological	ADJ
cana-5359	96	31	space	space	NOUN
cana-5359	96	32	or	or	CCONJ
cana-5359	96	33	pythagorean	pythagorean	PROPN
cana-5359	96	34	fuzzy	fuzzy	ADJ
cana-5359	96	35	topological	topological	ADJ
cana-5359	96	36	space	space	NOUN
cana-5359	96	37	is	be	AUX
cana-5359	96	38	a	a	DET
cana-5359	96	39	fermatean	fermatean	ADJ
cana-5359	96	40	fuzzy	fuzzy	ADJ
cana-5359	96	41	topological	topological	ADJ
cana-5359	96	42	space	space	NOUN
cana-5359	96	43	as	as	ADV
cana-5359	96	44	well	well	ADV
cana-5359	96	45	.	.	PUNCT
cana-5359	97	1	on	on	ADP
cana-5359	97	2	the	the	DET
cana-5359	97	3	other	other	ADJ
cana-5359	97	4	hand	hand	NOUN
cana-5359	97	5	,	,	PUNCT
cana-5359	97	6	it	it	PRON
cana-5359	97	7	is	be	AUX
cana-5359	97	8	obvious	obvious	ADJ
cana-5359	97	9	that	that	SCONJ
cana-5359	97	10	a	a	DET
cana-5359	97	11	fermatean	fermatean	ADJ
cana-5359	97	12	fuzzy	fuzzy	ADJ
cana-5359	97	13	topological	topological	ADJ
cana-5359	97	14	space	space	NOUN
cana-5359	97	15	need	need	AUX
cana-5359	97	16	not	not	PART
cana-5359	97	17	be	be	AUX
cana-5359	97	18	intuitionistic	intuitionistic	ADJ
cana-5359	97	19	fuzzy	fuzzy	ADJ
cana-5359	97	20	topological	topological	ADJ
cana-5359	97	21	space	space	NOUN
cana-5359	97	22	and	and	CCONJ
cana-5359	97	23	pythagorean	pythagorean	PROPN
cana-5359	97	24	fuzzy	fuzzy	ADJ
cana-5359	97	25	topological	topological	ADJ
cana-5359	97	26	space	space	NOUN
cana-5359	97	27	.	.	PUNCT
cana-5359	98	1	even	even	ADV
cana-5359	98	2	an	an	DET
cana-5359	98	3	fermatean	fermatean	ADJ
cana-5359	98	4	fuzzy	fuzzy	ADJ
cana-5359	98	5	open	open	NOUN
cana-5359	98	6	set	set	VERB
cana-5359	98	7	maybe	maybe	ADV
cana-5359	98	8	neither	neither	CCONJ
cana-5359	98	9	an	an	DET
cana-5359	98	10	intuitionistic	intuitionistic	ADJ
cana-5359	98	11	fuzzy	fuzzy	ADJ
cana-5359	98	12	set	set	NOUN
cana-5359	98	13	nor	nor	CCONJ
cana-5359	98	14	pythagorean	pythagorean	PROPN
cana-5359	98	15	fuzzy	fuzzy	ADJ
cana-5359	98	16	set	set	NOUN
cana-5359	98	17	.	.	PUNCT
cana-5359	99	1	example	example	NOUN
cana-5359	99	2	2.2	2.2	NUM
cana-5359	100	1	[	[	SYM
cana-5359	100	2	8	8	NUM
cana-5359	100	3	]	]	PUNCT
cana-5359	100	4	let	let	VERB
cana-5359	100	5	𝑋	𝑋	PROPN
cana-5359	100	6	=	=	SYM
cana-5359	100	7	{	{	PUNCT
cana-5359	100	8	𝑐1	𝑐1	NOUN
cana-5359	100	9	,	,	PUNCT
cana-5359	100	10	𝑐2	𝑐2	NOUN
cana-5359	100	11	}	}	PUNCT
cana-5359	100	12	.	.	PUNCT
cana-5359	101	1	consider	consider	VERB
cana-5359	101	2	the	the	DET
cana-5359	101	3	following	follow	VERB
cana-5359	101	4	family	family	NOUN
cana-5359	101	5	fermatean	fermatean	NOUN
cana-5359	101	6	fuzzy	fuzzy	ADJ
cana-5359	101	7	subsets	subset	NOUN
cana-5359	101	8	𝜏	𝜏	X
cana-5359	101	9	=	=	PUNCT
cana-5359	101	10	{	{	PUNCT
cana-5359	101	11	1𝔉	1𝔉	NOUN
cana-5359	101	12	,	,	PUNCT
cana-5359	101	13	0𝔉	0𝔉	PROPN
cana-5359	101	14	,	,	PUNCT
cana-5359	101	15	𝐹1	𝐹1	PROPN
cana-5359	101	16	,	,	PUNCT
cana-5359	101	17	𝐹2	𝐹2	NOUN
cana-5359	101	18	}	}	PUNCT
cana-5359	101	19	where	where	SCONJ
cana-5359	101	20	𝐹1	𝐹1	PROPN
cana-5359	101	21	=	=	SYM
cana-5359	101	22	{	{	PUNCT
cana-5359	101	23	〈	〈	NOUN
cana-5359	101	24	𝑐1	𝑐1	NOUN
cana-5359	101	25	,	,	PUNCT
cana-5359	101	26	𝛼𝐹1	𝛼𝐹1	PROPN
cana-5359	101	27	(	(	PUNCT
cana-5359	101	28	𝑐1	𝑐1	NOUN
cana-5359	101	29	)	)	PUNCT
cana-5359	101	30	=	=	SYM
cana-5359	101	31	0.4	0.4	NUM
cana-5359	101	32	,	,	PUNCT
cana-5359	101	33	𝛽𝐹1	𝛽𝐹1	PROPN
cana-5359	101	34	(	(	PUNCT
cana-5359	101	35	𝑐1	𝑐1	NOUN
cana-5359	101	36	)	)	PUNCT
cana-5359	101	37	=	=	SYM
cana-5359	101	38	0.6	0.6	NUM
cana-5359	101	39	〉	〉	NOUN
cana-5359	101	40	,	,	PUNCT
cana-5359	101	41	〈	〈	NOUN
cana-5359	101	42	𝑐2	𝑐2	NOUN
cana-5359	101	43	,	,	PUNCT
cana-5359	101	44	𝛼𝐹1	𝛼𝐹1	PROPN
cana-5359	101	45	(	(	PUNCT
cana-5359	101	46	𝑐2	𝑐2	NOUN
cana-5359	101	47	)	)	PUNCT
cana-5359	101	48	=	=	SYM
cana-5359	101	49	0.1	0.1	NUM
cana-5359	101	50	,	,	PUNCT
cana-5359	101	51	𝛽𝐹1	𝛽𝐹1	PROPN
cana-5359	101	52	(	(	PUNCT
cana-5359	101	53	𝑐2	𝑐2	NOUN
cana-5359	101	54	)	)	PUNCT
cana-5359	101	55	=	=	PUNCT
cana-5359	101	56	0.3	0.3	NUM
cana-5359	101	57	〉	〉	NOUN
cana-5359	101	58	}	}	PUNCT
cana-5359	101	59	and	and	CCONJ
cana-5359	101	60	𝐹2	𝐹2	NOUN
cana-5359	101	61	=	=	SYM
cana-5359	101	62	{	{	PUNCT
cana-5359	101	63	〈	〈	NOUN
cana-5359	101	64	𝑐1	𝑐1	NOUN
cana-5359	101	65	,	,	PUNCT
cana-5359	101	66	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5359	101	67	(	(	PUNCT
cana-5359	101	68	𝑐1	𝑐1	NOUN
cana-5359	101	69	)	)	PUNCT
cana-5359	101	70	=	=	SYM
cana-5359	101	71	0.9	0.9	NUM
cana-5359	101	72	,	,	PUNCT
cana-5359	101	73	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5359	101	74	(	(	PUNCT
cana-5359	101	75	𝑐1	𝑐1	NOUN
cana-5359	101	76	)	)	PUNCT
cana-5359	101	77	=	=	SYM
cana-5359	101	78	0.6	0.6	NUM
cana-5359	101	79	〉	〉	NOUN
cana-5359	101	80	,	,	PUNCT
cana-5359	101	81	〈	〈	NOUN
cana-5359	101	82	𝑐2	𝑐2	NOUN
cana-5359	101	83	,	,	PUNCT
cana-5359	101	84	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5359	101	85	(	(	PUNCT
cana-5359	101	86	𝑐2	𝑐2	NOUN
cana-5359	101	87	)	)	PUNCT
cana-5359	101	88	=	=	SYM
cana-5359	101	89	0.2	0.2	NUM
cana-5359	101	90	,	,	PUNCT
cana-5359	101	91	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5359	101	92	(	(	PUNCT
cana-5359	101	93	𝑐2	𝑐2	PROPN
cana-5359	101	94	)	)	PUNCT
cana-5359	101	95	=	=	PUNCT
cana-5359	101	96	0.3	0.3	NUM
cana-5359	101	97	〉	〉	NOUN
cana-5359	101	98	}	}	PUNCT
cana-5359	101	99	.	.	PUNCT
cana-5359	102	1	observe	observe	VERB
cana-5359	102	2	that	that	SCONJ
cana-5359	102	3	(	(	PUNCT
cana-5359	102	4	x	x	X
cana-5359	102	5	,	,	PUNCT
cana-5359	102	6	τ	τ	X
cana-5359	102	7	)	)	PUNCT
cana-5359	102	8	is	be	AUX
cana-5359	102	9	a	a	DET
cana-5359	102	10	fermatean	fermatean	ADJ
cana-5359	102	11	fuzzy	fuzzy	ADJ
cana-5359	102	12	topological	topological	ADJ
cana-5359	102	13	space	space	NOUN
cana-5359	102	14	but	but	CCONJ
cana-5359	102	15	(	(	PUNCT
cana-5359	102	16	x	x	X
cana-5359	102	17	,	,	PUNCT
cana-5359	102	18	τ	τ	X
cana-5359	102	19	)	)	PUNCT
cana-5359	102	20	is	be	AUX
cana-5359	102	21	neither	neither	CCONJ
cana-5359	102	22	intuitionistic	intuitionistic	ADJ
cana-5359	102	23	fuzzy	fuzzy	ADJ
cana-5359	102	24	topological	topological	ADJ
cana-5359	102	25	space	space	NOUN
cana-5359	102	26	nor	nor	CCONJ
cana-5359	102	27	pythagorean	pythagorean	VERB
cana-5359	102	28	fuzzy	fuzzy	ADJ
cana-5359	102	29	topological	topological	ADJ
cana-5359	102	30	space	space	NOUN
cana-5359	102	31	.	.	PUNCT
cana-5359	103	1	definition	definition	NOUN
cana-5359	103	2	2.8	2.8	NUM
cana-5359	103	3	[	[	NOUN
cana-5359	103	4	8	8	NUM
cana-5359	103	5	]	]	X
cana-5359	103	6	let	let	NOUN
cana-5359	103	7	(	(	PUNCT
cana-5359	103	8	𝑋	𝑋	NOUN
cana-5359	103	9	,	,	PUNCT
cana-5359	103	10	𝜏	𝜏	NOUN
cana-5359	103	11	)	)	PUNCT
cana-5359	103	12	be	be	VERB
cana-5359	103	13	an	an	DET
cana-5359	103	14	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	103	15	and	and	CCONJ
cana-5359	103	16	𝐴	𝐴	PROPN
cana-5359	103	17	=	=	PUNCT
cana-5359	103	18	{	{	PUNCT
cana-5359	103	19	<	<	X
cana-5359	103	20	𝑎	𝑎	NOUN
cana-5359	103	21	,	,	PUNCT
cana-5359	103	22	𝛼𝐴(𝑎	𝛼𝐴(𝑎	NUM
cana-5359	103	23	)	)	PUNCT
cana-5359	103	24	,	,	PUNCT
cana-5359	103	25	𝛽𝐴(𝑎	𝛽𝐴(𝑎	NUM
cana-5359	103	26	)	)	PUNCT
cana-5359	103	27	>	>	X
cana-5359	103	28	|𝑎	|𝑎	PROPN
cana-5359	104	1	∈	∈	PROPN
cana-5359	104	2	𝑋	𝑋	PROPN
cana-5359	104	3	}	}	PUNCT
cana-5359	104	4	be	be	AUX
cana-5359	104	5	an	an	DET
cana-5359	104	6	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	104	7	in	in	ADP
cana-5359	104	8	𝑋.	𝑋.	PROPN
cana-5359	104	9	then	then	ADV
cana-5359	104	10	the	the	DET
cana-5359	104	11	fermatean	fermatean	ADJ
cana-5359	104	12	fuzzy	fuzzy	ADJ
cana-5359	104	13	interior	interior	NOUN
cana-5359	104	14	and	and	CCONJ
cana-5359	104	15	the	the	DET
cana-5359	104	16	fermatean	fermatean	ADJ
cana-5359	104	17	fuzzy	fuzzy	ADJ
cana-5359	104	18	closure	closure	NOUN
cana-5359	104	19	of	of	ADP
cana-5359	104	20	𝐴	𝐴	PROPN
cana-5359	104	21	are	be	AUX
cana-5359	104	22	denoted	denote	VERB
cana-5359	104	23	by	by	ADP
cana-5359	104	24	𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝐴	NOUN
cana-5359	104	25	)	)	PUNCT
cana-5359	104	26	and	and	CCONJ
cana-5359	104	27	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	PROPN
cana-5359	104	28	)	)	PUNCT
cana-5359	104	29	and	and	CCONJ
cana-5359	104	30	are	be	AUX
cana-5359	104	31	defined	define	VERB
cana-5359	104	32	as	as	SCONJ
cana-5359	104	33	follows	follow	VERB
cana-5359	104	34	:	:	PUNCT
cana-5359	104	35	communications	communication	NOUN
cana-5359	104	36	on	on	ADP
cana-5359	104	37	applied	apply	VERB
cana-5359	104	38	nonlinear	nonlinear	ADJ
cana-5359	104	39	analysis	analysis	NOUN
cana-5359	104	40	issn	issn	NOUN
cana-5359	104	41	:	:	PUNCT
cana-5359	104	42	1074	1074	NUM
cana-5359	104	43	-	-	PUNCT
cana-5359	104	44	133x	133x	NUM
cana-5359	104	45	vol	vol	VERB
cana-5359	104	46	32	32	NUM
cana-5359	104	47	no	no	NOUN
cana-5359	104	48	.	.	PUNCT
cana-5359	105	1	10s	10	NOUN
cana-5359	105	2	(	(	PUNCT
cana-5359	105	3	2025	2025	NUM
cana-5359	105	4	)	)	PUNCT
cana-5359	105	5	1913	1913	NUM
cana-5359	105	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	105	7	𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝐴	NUM
cana-5359	105	8	)	)	PUNCT
cana-5359	105	9	=	=	SYM
cana-5359	105	10	∪	∪	X
cana-5359	105	11	{	{	PUNCT
cana-5359	105	12	𝐺|𝐺	𝐺|𝐺	NOUN
cana-5359	105	13	𝑖𝑠𝑎	𝑖𝑠𝑎	NOUN
cana-5359	105	14	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	105	15	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5359	105	16	𝐺	𝐺	PROPN
cana-5359	105	17	⊆	⊆	NUM
cana-5359	105	18	𝐴	𝐴	PROPN
cana-5359	105	19	}	}	PUNCT
cana-5359	105	20	and	and	CCONJ
cana-5359	105	21	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	NOUN
cana-5359	105	22	)	)	PUNCT
cana-5359	106	1	=	=	NOUN
cana-5359	106	2	∩	∩	X
cana-5359	106	3	{	{	PUNCT
cana-5359	106	4	𝐾|𝐾	𝐾|𝐾	NOUN
cana-5359	106	5	𝑖𝑠𝑎	𝑖𝑠𝑎	NOUN
cana-5359	106	6	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5359	106	7	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-5359	106	8	𝐴	𝐴	PROPN
cana-5359	106	9	⊆	⊆	NUM
cana-5359	106	10	𝐾	𝐾	PROPN
cana-5359	106	11	}	}	PUNCT
cana-5359	106	12	.	.	PUNCT
cana-5359	107	1	also	also	ADV
cana-5359	107	2	,	,	PUNCT
cana-5359	107	3	it	it	PRON
cana-5359	107	4	can	can	AUX
cana-5359	107	5	be	be	AUX
cana-5359	107	6	established	establish	VERB
cana-5359	107	7	that	that	SCONJ
cana-5359	107	8	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	NOUN
cana-5359	107	9	)	)	PUNCT
cana-5359	107	10	is	be	AUX
cana-5359	107	11	an	an	DET
cana-5359	107	12	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5359	107	13	and	and	CCONJ
cana-5359	107	14	𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝐴	NUM
cana-5359	107	15	)	)	PUNCT
cana-5359	107	16	is	be	AUX
cana-5359	107	17	an	an	DET
cana-5359	107	18	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	NOUN
cana-5359	107	19	,	,	PUNCT
cana-5359	107	20	𝐴	𝐴	PROPN
cana-5359	107	21	is	be	AUX
cana-5359	107	22	an	an	DET
cana-5359	107	23	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5359	107	24	if	if	SCONJ
cana-5359	108	1	and	and	CCONJ
cana-5359	108	2	only	only	ADV
cana-5359	108	3	if	if	SCONJ
cana-5359	108	4	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	NOUN
cana-5359	108	5	)	)	PUNCT
cana-5359	108	6	=	=	SYM
cana-5359	108	7	𝐴	𝐴	PROPN
cana-5359	108	8	and	and	CCONJ
cana-5359	108	9	𝐴	𝐴	PROPN
cana-5359	108	10	is	be	AUX
cana-5359	108	11	an	an	DET
cana-5359	108	12	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	108	13	if	if	SCONJ
cana-5359	108	14	and	and	CCONJ
cana-5359	108	15	only	only	ADV
cana-5359	108	16	if	if	SCONJ
cana-5359	108	17	𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝐴	NUM
cana-5359	108	18	)	)	PUNCT
cana-5359	109	1	=	=	SYM
cana-5359	109	2	𝐴.	𝐴.	NOUN
cana-5359	109	3	we	we	PRON
cana-5359	109	4	say	say	VERB
cana-5359	109	5	that	that	SCONJ
cana-5359	109	6	𝐴	𝐴	PROPN
cana-5359	109	7	is	be	AUX
cana-5359	109	8	𝔉ℱ-dense	𝔉ℱ-dense	PROPN
cana-5359	109	9	if	if	SCONJ
cana-5359	109	10	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	PROPN
cana-5359	109	11	)	)	PUNCT
cana-5359	109	12	=	=	PUNCT
cana-5359	109	13	1𝔉.	1𝔉.	NUM
cana-5359	109	14	lemma	lemma	PROPN
cana-5359	109	15	2.1	2.1	NUM
cana-5359	109	16	[	[	NOUN
cana-5359	109	17	8	8	NUM
cana-5359	109	18	]	]	PUNCT
cana-5359	109	19	for	for	ADP
cana-5359	109	20	any	any	DET
cana-5359	109	21	fermatean	fermatean	ADJ
cana-5359	109	22	fuzzy	fuzzy	NOUN
cana-5359	109	23	set	set	VERB
cana-5359	109	24	𝐴	𝐴	PROPN
cana-5359	109	25	in	in	ADP
cana-5359	109	26	(	(	PUNCT
cana-5359	109	27	𝑋	𝑋	PROPN
cana-5359	109	28	,	,	PUNCT
cana-5359	109	29	𝜏	𝜏	NOUN
cana-5359	109	30	)	)	PUNCT
cana-5359	109	31	,	,	PUNCT
cana-5359	109	32	we	we	PRON
cana-5359	109	33	have	have	VERB
cana-5359	109	34	1𝔉	1𝔉	NOUN
cana-5359	109	35	−	−	PROPN
cana-5359	109	36	𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝐴	NUM
cana-5359	109	37	)	)	PUNCT
cana-5359	109	38	=	=	SYM
cana-5359	109	39	𝔉ℱ𝑐𝑙(1𝔉	𝔉ℱ𝑐𝑙(1𝔉	ADP
cana-5359	109	40	−	−	PROPN
cana-5359	109	41	𝐴	𝐴	PROPN
cana-5359	109	42	)	)	PUNCT
cana-5359	109	43	and	and	CCONJ
cana-5359	109	44	1𝔉	1𝔉	NOUN
cana-5359	109	45	−	−	PROPN
cana-5359	109	46	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	PROPN
cana-5359	109	47	)	)	PUNCT
cana-5359	109	48	=	=	PUNCT
cana-5359	109	49	𝔉ℱ𝑖𝑛𝑡(1𝔉	𝔉ℱ𝑖𝑛𝑡(1𝔉	PROPN
cana-5359	109	50	−	−	PROPN
cana-5359	109	51	𝐴	𝐴	PROPN
cana-5359	109	52	)	)	PUNCT
cana-5359	109	53	.	.	PUNCT
cana-5359	110	1	definition	definition	NOUN
cana-5359	110	2	2.9	2.9	NUM
cana-5359	111	1	[	[	X
cana-5359	111	2	11	11	NUM
cana-5359	111	3	]	]	X
cana-5359	111	4	let	let	VERB
cana-5359	111	5	(	(	PUNCT
cana-5359	111	6	𝑋	𝑋	NOUN
cana-5359	111	7	,	,	PUNCT
cana-5359	111	8	𝜏	𝜏	NOUN
cana-5359	111	9	)	)	PUNCT
cana-5359	111	10	be	be	VERB
cana-5359	111	11	an	an	DET
cana-5359	111	12	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	111	13	and	and	CCONJ
cana-5359	111	14	𝐴	𝐴	PROPN
cana-5359	111	15	be	be	VERB
cana-5359	111	16	an	an	DET
cana-5359	111	17	𝔉ℱ𝑠.	𝔉ℱ𝑠.	PROPN
cana-5359	111	18	then	then	ADV
cana-5359	111	19	𝐴	𝐴	PROPN
cana-5359	111	20	is	be	AUX
cana-5359	111	21	said	say	VERB
cana-5359	111	22	to	to	PART
cana-5359	111	23	be	be	AUX
cana-5359	111	24	an	an	DET
cana-5359	111	25	fermatean	fermatean	ADJ
cana-5359	111	26	fuzzy	fuzzy	NOUN
cana-5359	111	27	(	(	PUNCT
cana-5359	111	28	i	i	NOUN
cana-5359	111	29	)	)	PUNCT
cana-5359	111	30	regular	regular	ADJ
cana-5359	111	31	open	open	ADJ
cana-5359	111	32	set	set	NOUN
cana-5359	111	33	(	(	PUNCT
cana-5359	111	34	𝔉ℱ𝑟𝑜𝑠	𝔉ℱ𝑟𝑜𝑠	PROPN
cana-5359	111	35	in	in	ADP
cana-5359	111	36	short	short	ADJ
cana-5359	111	37	)	)	PUNCT
cana-5359	112	1	if	if	SCONJ
cana-5359	112	2	𝐴	𝐴	PROPN
cana-5359	112	3	=	=	PUNCT
cana-5359	112	4	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝑐𝑙(𝐴	PROPN
cana-5359	112	5	)	)	PUNCT
cana-5359	112	6	)	)	PUNCT
cana-5359	112	7	.	.	PUNCT
cana-5359	113	1	(	(	PUNCT
cana-5359	113	2	ii	ii	NOUN
cana-5359	113	3	)	)	PUNCT
cana-5359	113	4	regular	regular	ADJ
cana-5359	113	5	closed	close	VERB
cana-5359	113	6	set	set	NOUN
cana-5359	113	7	(	(	PUNCT
cana-5359	113	8	𝔉ℱ𝑟𝑐𝑠	𝔉ℱ𝑟𝑐𝑠	PROPN
cana-5359	113	9	in	in	ADP
cana-5359	113	10	short	short	ADJ
cana-5359	113	11	)	)	PUNCT
cana-5359	113	12	if	if	SCONJ
cana-5359	113	13	𝐴	𝐴	PROPN
cana-5359	113	14	=	=	SYM
cana-5359	113	15	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(𝐴	NOUN
cana-5359	113	16	)	)	PUNCT
cana-5359	113	17	)	)	PUNCT
cana-5359	113	18	.	.	PUNCT
cana-5359	114	1	by	by	ADP
cana-5359	114	2	lemma	lemma	PROPN
cana-5359	114	3	2.1	2.1	NUM
cana-5359	114	4	,	,	PUNCT
cana-5359	114	5	it	it	PRON
cana-5359	114	6	follows	follow	VERB
cana-5359	114	7	that	that	SCONJ
cana-5359	114	8	𝐴	𝐴	PROPN
cana-5359	114	9	is	be	AUX
cana-5359	114	10	an	an	DET
cana-5359	114	11	𝔉ℱ𝑟𝑜𝑠	𝔉ℱ𝑟𝑜𝑠	PROPN
cana-5359	114	12	iff	iff	PROPN
cana-5359	114	13	𝐴̅	𝐴̅	PROPN
cana-5359	114	14	is	be	AUX
cana-5359	114	15	an	an	DET
cana-5359	114	16	𝔉ℱ𝑟𝑐𝑠.	𝔉ℱ𝑟𝑐𝑠.	ADJ
cana-5359	114	17	definition	definition	NOUN
cana-5359	114	18	2.10	2.10	NUM
cana-5359	114	19	[	[	X
cana-5359	114	20	11	11	NUM
cana-5359	114	21	]	]	X
cana-5359	114	22	let	let	VERB
cana-5359	114	23	(	(	PUNCT
cana-5359	114	24	𝑋	𝑋	NOUN
cana-5359	114	25	,	,	PUNCT
cana-5359	114	26	𝜏	𝜏	NOUN
cana-5359	114	27	)	)	PUNCT
cana-5359	114	28	be	be	VERB
cana-5359	114	29	an	an	DET
cana-5359	114	30	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	114	31	and	and	CCONJ
cana-5359	114	32	𝐴	𝐴	PROPN
cana-5359	114	33	=	=	PUNCT
cana-5359	114	34	{	{	PUNCT
cana-5359	114	35	<	<	X
cana-5359	114	36	𝑎	𝑎	NOUN
cana-5359	114	37	,	,	PUNCT
cana-5359	114	38	𝛼𝐴(𝑎	𝛼𝐴(𝑎	NUM
cana-5359	114	39	)	)	PUNCT
cana-5359	114	40	,	,	PUNCT
cana-5359	114	41	𝛽𝐴(𝑎	𝛽𝐴(𝑎	NUM
cana-5359	114	42	)	)	PUNCT
cana-5359	114	43	>	>	X
cana-5359	114	44	|𝑎	|𝑎	PROPN
cana-5359	115	1	∈	∈	PROPN
cana-5359	115	2	𝑋	𝑋	PROPN
cana-5359	115	3	}	}	PUNCT
cana-5359	115	4	be	be	AUX
cana-5359	115	5	an	an	DET
cana-5359	115	6	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	115	7	in	in	ADP
cana-5359	115	8	𝑋.	𝑋.	PROPN
cana-5359	115	9	then	then	ADV
cana-5359	115	10	the	the	DET
cana-5359	115	11	𝛿-interior	𝛿-interior	PROPN
cana-5359	115	12	and	and	CCONJ
cana-5359	115	13	the	the	DET
cana-5359	115	14	𝛿-closure	𝛿-closure	NOUN
cana-5359	115	15	of	of	ADP
cana-5359	115	16	𝐴	𝐴	PROPN
cana-5359	115	17	are	be	AUX
cana-5359	115	18	denoted	denote	VERB
cana-5359	115	19	by	by	ADP
cana-5359	115	20	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	NUM
cana-5359	115	21	)	)	PUNCT
cana-5359	115	22	and	and	CCONJ
cana-5359	115	23	𝔉ℱ𝛿𝑐𝑙(𝐴	𝔉ℱ𝛿𝑐𝑙(𝐴	NUM
cana-5359	115	24	)	)	PUNCT
cana-5359	115	25	and	and	CCONJ
cana-5359	115	26	are	be	AUX
cana-5359	115	27	defined	define	VERB
cana-5359	115	28	as	as	ADP
cana-5359	115	29	follows	follow	VERB
cana-5359	115	30	.	.	PUNCT
cana-5359	116	1	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	X
cana-5359	116	2	)	)	PUNCT
cana-5359	116	3	=	=	NOUN
cana-5359	116	4	∪	∪	X
cana-5359	116	5	{	{	PUNCT
cana-5359	116	6	𝐺|𝐺	𝐺|𝐺	PROPN
cana-5359	116	7	is	be	AUX
cana-5359	116	8	an	an	DET
cana-5359	116	9	𝔉ℱ𝑟𝑜𝑠	𝔉ℱ𝑟𝑜𝑠	PROPN
cana-5359	116	10	and	and	CCONJ
cana-5359	116	11	𝐺	𝐺	PROPN
cana-5359	116	12	⊆	⊆	NUM
cana-5359	116	13	𝐴	𝐴	PROPN
cana-5359	116	14	}	}	PUNCT
cana-5359	116	15	,	,	PUNCT
cana-5359	116	16	𝔉ℱ𝛿𝑐𝑙(𝐴	𝔉ℱ𝛿𝑐𝑙(𝐴	NOUN
cana-5359	116	17	)	)	PUNCT
cana-5359	116	18	=	=	NOUN
cana-5359	116	19	∩	∩	NOUN
cana-5359	116	20	{	{	PUNCT
cana-5359	116	21	𝐾|𝐾	𝐾|𝐾	NOUN
cana-5359	116	22	is	be	AUX
cana-5359	116	23	an	an	DET
cana-5359	116	24	𝔉ℱ𝑟𝑐𝑠	𝔉ℱ𝑟𝑐𝑠	PROPN
cana-5359	116	25	and	and	CCONJ
cana-5359	116	26	𝐴	𝐴	PROPN
cana-5359	116	27	⊆	⊆	NUM
cana-5359	116	28	𝐾	𝐾	PROPN
cana-5359	116	29	}	}	PUNCT
cana-5359	116	30	.	.	PUNCT
cana-5359	117	1	definition	definition	NOUN
cana-5359	117	2	2.11	2.11	NUM
cana-5359	117	3	[	[	X
cana-5359	117	4	11	11	NUM
cana-5359	117	5	]	]	X
cana-5359	117	6	let	let	VERB
cana-5359	117	7	(	(	PUNCT
cana-5359	117	8	𝑋	𝑋	NOUN
cana-5359	117	9	,	,	PUNCT
cana-5359	117	10	𝜏	𝜏	NOUN
cana-5359	117	11	)	)	PUNCT
cana-5359	117	12	be	be	VERB
cana-5359	117	13	an	an	DET
cana-5359	117	14	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	117	15	and	and	CCONJ
cana-5359	117	16	𝐴	𝐴	PROPN
cana-5359	117	17	=	=	PUNCT
cana-5359	117	18	{	{	PUNCT
cana-5359	117	19	<	<	X
cana-5359	117	20	𝑎	𝑎	NOUN
cana-5359	117	21	,	,	PUNCT
cana-5359	117	22	𝛼𝐴(𝑎	𝛼𝐴(𝑎	NUM
cana-5359	117	23	)	)	PUNCT
cana-5359	117	24	,	,	PUNCT
cana-5359	117	25	𝛽𝐴(𝑎	𝛽𝐴(𝑎	NUM
cana-5359	117	26	)	)	PUNCT
cana-5359	117	27	>	>	X
cana-5359	117	28	|𝑎	|𝑎	PROPN
cana-5359	118	1	∈	∈	PROPN
cana-5359	118	2	𝑋	𝑋	PROPN
cana-5359	118	3	}	}	PUNCT
cana-5359	118	4	be	be	AUX
cana-5359	118	5	an	an	DET
cana-5359	118	6	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	118	7	in	in	ADP
cana-5359	118	8	𝑋.	𝑋.	PROPN
cana-5359	118	9	a	a	DET
cana-5359	118	10	set	set	ADJ
cana-5359	118	11	𝐴	𝐴	PROPN
cana-5359	118	12	is	be	AUX
cana-5359	118	13	said	say	VERB
cana-5359	118	14	to	to	PART
cana-5359	118	15	be	be	AUX
cana-5359	118	16	𝔉ℱ	𝔉ℱ	PROPN
cana-5359	118	17	1	1	NUM
cana-5359	118	18	.	.	PUNCT
cana-5359	118	19	𝛿-open	𝛿-open	VERB
cana-5359	118	20	set	set	NOUN
cana-5359	118	21	(	(	PUNCT
cana-5359	118	22	briefly	briefly	ADV
cana-5359	118	23	,	,	PUNCT
cana-5359	118	24	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	118	25	)	)	PUNCT
cana-5359	119	1	if	if	SCONJ
cana-5359	119	2	𝐴	𝐴	PROPN
cana-5359	119	3	=	=	PUNCT
cana-5359	119	4	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	NUM
cana-5359	119	5	)	)	PUNCT
cana-5359	119	6	,	,	PUNCT
cana-5359	119	7	2	2	X
cana-5359	119	8	.	.	X
cana-5359	119	9	𝛿-pre	𝛿-pre	PROPN
cana-5359	119	10	open	open	ADJ
cana-5359	119	11	set	set	PROPN
cana-5359	119	12	(	(	PUNCT
cana-5359	119	13	briefly	briefly	ADV
cana-5359	119	14	,	,	PUNCT
cana-5359	119	15	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	119	16	)	)	PUNCT
cana-5359	119	17	if	if	SCONJ
cana-5359	119	18	𝐴	𝐴	PROPN
cana-5359	119	19	⊆	⊆	NUM
cana-5359	119	20	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝛿𝑐𝑙(𝐴	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝛿𝑐𝑙(𝐴	NOUN
cana-5359	119	21	)	)	PUNCT
cana-5359	119	22	)	)	PUNCT
cana-5359	119	23	.	.	PUNCT
cana-5359	120	1	3	3	X
cana-5359	120	2	.	.	X
cana-5359	120	3	𝛿-semi	𝛿-semi	PROPN
cana-5359	120	4	open	open	ADJ
cana-5359	120	5	set	set	NOUN
cana-5359	120	6	(	(	PUNCT
cana-5359	120	7	briefly	briefly	ADV
cana-5359	120	8	,	,	PUNCT
cana-5359	120	9	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	120	10	)	)	PUNCT
cana-5359	120	11	if	if	SCONJ
cana-5359	120	12	𝐴	𝐴	PROPN
cana-5359	120	13	⊆	⊆	NUM
cana-5359	120	14	𝔉ℱ𝑐𝑙(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	𝔉ℱ𝑐𝑙(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	NUM
cana-5359	120	15	)	)	PUNCT
cana-5359	120	16	)	)	PUNCT
cana-5359	120	17	.	.	PUNCT
cana-5359	121	1	4	4	X
cana-5359	121	2	.	.	X
cana-5359	121	3	𝛿	𝛿	DET
cana-5359	121	4	𝛼	𝛼	PRON
cana-5359	121	5	open	open	ADJ
cana-5359	121	6	set	set	NOUN
cana-5359	121	7	or	or	CCONJ
cana-5359	121	8	𝑎	𝑎	PRON
cana-5359	121	9	-open	-open	NOUN
cana-5359	121	10	set	set	NOUN
cana-5359	121	11	(	(	PUNCT
cana-5359	121	12	briefly	briefly	ADV
cana-5359	121	13	,	,	PUNCT
cana-5359	121	14	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	121	15	or	or	CCONJ
cana-5359	121	16	𝔉ℱ𝑎𝑜𝑠	𝔉ℱ𝑎𝑜𝑠	PROPN
cana-5359	121	17	)	)	PUNCT
cana-5359	122	1	if	if	SCONJ
cana-5359	122	2	𝐴	𝐴	PROPN
cana-5359	122	3	⊆	⊆	NUM
cana-5359	122	4	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝑐𝑙(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝑐𝑙(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	PROPN
cana-5359	122	5	)	)	PUNCT
cana-5359	122	6	)	)	PUNCT
cana-5359	122	7	)	)	PUNCT
cana-5359	122	8	.	.	PUNCT
cana-5359	123	1	5	5	X
cana-5359	123	2	.	.	X
cana-5359	123	3	𝛿	𝛿	DET
cana-5359	123	4	𝛽	𝛽	PROPN
cana-5359	123	5	open	open	ADJ
cana-5359	123	6	set	set	NOUN
cana-5359	123	7	or	or	CCONJ
cana-5359	123	8	𝑒∗	𝑒∗	PROPN
cana-5359	123	9	-open	-open	ADJ
cana-5359	123	10	set	set	NOUN
cana-5359	123	11	(	(	PUNCT
cana-5359	123	12	briefly	briefly	ADV
cana-5359	123	13	,	,	PUNCT
cana-5359	123	14	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	123	15	or	or	CCONJ
cana-5359	123	16	𝔉ℱ𝑒∗𝑜𝑠	𝔉ℱ𝑒∗𝑜𝑠	NOUN
cana-5359	123	17	)	)	PUNCT
cana-5359	123	18	if	if	SCONJ
cana-5359	123	19	𝐴	𝐴	PROPN
cana-5359	123	20	⊆	⊆	NUM
cana-5359	123	21	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝛿𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝛿𝑐𝑙(𝐴	NOUN
cana-5359	123	22	)	)	PUNCT
cana-5359	123	23	)	)	PUNCT
cana-5359	123	24	)	)	PUNCT
cana-5359	123	25	.	.	PUNCT
cana-5359	124	1	6	6	X
cana-5359	124	2	.	.	X
cana-5359	125	1	𝛿	𝛿	ADJ
cana-5359	125	2	(	(	PUNCT
cana-5359	125	3	resp	resp	NOUN
cana-5359	125	4	.	.	PUNCT
cana-5359	126	1	𝛿	𝛿	PRON
cana-5359	126	2	-pre	-pre	NUM
cana-5359	126	3	,	,	PUNCT
cana-5359	126	4	𝛿	𝛿	ADJ
cana-5359	126	5	-semi	-semi	NOUN
cana-5359	126	6	,	,	PUNCT
cana-5359	126	7	𝛿	𝛿	PRON
cana-5359	126	8	𝛼	𝛼	NOUN
cana-5359	126	9	and	and	CCONJ
cana-5359	126	10	𝛿	𝛿	PRON
cana-5359	126	11	𝛽	𝛽	NOUN
cana-5359	126	12	)	)	PUNCT
cana-5359	126	13	dense	dense	ADJ
cana-5359	126	14	if	if	SCONJ
cana-5359	126	15	𝔉ℱ𝛿𝑐𝑙(𝐴	𝔉ℱ𝛿𝑐𝑙(𝐴	NOUN
cana-5359	126	16	)	)	PUNCT
cana-5359	126	17	(	(	PUNCT
cana-5359	126	18	resp	resp	NOUN
cana-5359	126	19	.	.	PUNCT
cana-5359	127	1	𝔉ℱ𝛿𝑝𝑐𝑙(𝐴	𝔉ℱ𝛿𝑝𝑐𝑙(𝐴	NOUN
cana-5359	127	2	)	)	PUNCT
cana-5359	127	3	,	,	PUNCT
cana-5359	127	4	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	PROPN
cana-5359	127	5	)	)	PUNCT
cana-5359	127	6	,	,	PUNCT
cana-5359	127	7	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	NOUN
cana-5359	127	8	)	)	PUNCT
cana-5359	127	9	and	and	CCONJ
cana-5359	127	10	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	VERB
cana-5359	127	11	)	)	PUNCT
cana-5359	127	12	)	)	PUNCT
cana-5359	128	1	=	=	PRON
cana-5359	128	2	1𝔉.	1𝔉.	NUM
cana-5359	128	3	the	the	DET
cana-5359	128	4	complement	complement	NOUN
cana-5359	128	5	of	of	ADP
cana-5359	128	6	an	an	DET
cana-5359	128	7	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	128	8	(	(	PUNCT
cana-5359	128	9	resp	resp	NOUN
cana-5359	128	10	.	.	PUNCT
cana-5359	129	1	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	129	2	,	,	PUNCT
cana-5359	129	3	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	129	4	,	,	PUNCT
cana-5359	129	5	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	129	6	and	and	CCONJ
cana-5359	129	7	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	129	8	)	)	PUNCT
cana-5359	129	9	is	be	AUX
cana-5359	129	10	called	call	VERB
cana-5359	129	11	an	an	DET
cana-5359	129	12	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5359	129	13	(	(	PUNCT
cana-5359	129	14	resp	resp	NOUN
cana-5359	129	15	.	.	PUNCT
cana-5359	130	1	𝔉ℱ𝛿𝒫	𝔉ℱ𝛿𝒫	NOUN
cana-5359	130	2	,	,	PUNCT
cana-5359	130	3	𝔉ℱ𝛿𝒮	𝔉ℱ𝛿𝒮	PROPN
cana-5359	130	4	,	,	PUNCT
cana-5359	130	5	𝔉ℱ𝛿𝛼	𝔉ℱ𝛿𝛼	ADJ
cana-5359	130	6	and	and	CCONJ
cana-5359	130	7	𝔉ℱ𝛿𝛽	𝔉ℱ𝛿𝛽	NOUN
cana-5359	130	8	)	)	PUNCT
cana-5359	130	9	closed	closed	ADJ
cana-5359	130	10	set	set	NOUN
cana-5359	130	11	(	(	PUNCT
cana-5359	130	12	briefly	briefly	ADV
cana-5359	130	13	,	,	PUNCT
cana-5359	130	14	𝔉ℱ𝛿𝑐𝑠	𝔉ℱ𝛿𝑐𝑠	PROPN
cana-5359	130	15	(	(	PUNCT
cana-5359	130	16	resp	resp	NOUN
cana-5359	130	17	.	.	PUNCT
cana-5359	131	1	𝔉ℱ𝛿𝒫𝑐𝑠	𝔉ℱ𝛿𝒫𝑐𝑠	NOUN
cana-5359	131	2	,	,	PUNCT
cana-5359	131	3	𝔉ℱ𝛿𝒮𝑐𝑠	𝔉ℱ𝛿𝒮𝑐𝑠	NUM
cana-5359	131	4	,	,	PUNCT
cana-5359	131	5	𝔉ℱ𝛿𝛼𝑐𝑠	𝔉ℱ𝛿𝛼𝑐𝑠	PROPN
cana-5359	131	6	and	and	CCONJ
cana-5359	131	7	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5359	131	8	)	)	PUNCT
cana-5359	131	9	)	)	PUNCT
cana-5359	131	10	in	in	ADP
cana-5359	131	11	𝑋.	𝑋.	PROPN
cana-5359	131	12	the	the	DET
cana-5359	131	13	family	family	NOUN
cana-5359	131	14	of	of	ADP
cana-5359	131	15	all	all	DET
cana-5359	131	16	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	131	17	(	(	PUNCT
cana-5359	131	18	resp	resp	NOUN
cana-5359	131	19	.	.	PUNCT
cana-5359	132	1	𝔉ℱ𝛿𝑐𝑠	𝔉ℱ𝛿𝑐𝑠	PROPN
cana-5359	132	2	,	,	PUNCT
cana-5359	132	3	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	132	4	,	,	PUNCT
cana-5359	132	5	𝔉ℱ𝛿𝒫𝑐𝑠	𝔉ℱ𝛿𝒫𝑐𝑠	NOUN
cana-5359	132	6	,	,	PUNCT
cana-5359	132	7	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	132	8	,	,	PUNCT
cana-5359	132	9	𝔉ℱ𝛿𝒮𝑐𝑠	𝔉ℱ𝛿𝒮𝑐𝑠	PROPN
cana-5359	132	10	,	,	PUNCT
cana-5359	132	11	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	132	12	,	,	PUNCT
cana-5359	132	13	𝔉ℱ𝛿𝛼𝑐𝑠	𝔉ℱ𝛿𝛼𝑐𝑠	PROPN
cana-5359	132	14	,	,	PUNCT
cana-5359	132	15	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	132	16	and	and	CCONJ
cana-5359	132	17	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	PROPN
cana-5359	132	18	)	)	PUNCT
cana-5359	132	19	of	of	ADP
cana-5359	132	20	𝑋	𝑋	PROPN
cana-5359	132	21	is	be	AUX
cana-5359	132	22	denoted	denote	VERB
cana-5359	132	23	by	by	ADP
cana-5359	132	24	𝔉ℱ𝛿𝑂𝑆(𝑋	𝔉ℱ𝛿𝑂𝑆(𝑋	NOUN
cana-5359	132	25	)	)	PUNCT
cana-5359	132	26	,	,	PUNCT
cana-5359	132	27	(	(	PUNCT
cana-5359	132	28	resp	resp	NOUN
cana-5359	132	29	.	.	PUNCT
cana-5359	133	1	𝔉ℱ𝛿𝐶𝑆(𝑋	𝔉ℱ𝛿𝐶𝑆(𝑋	PROPN
cana-5359	133	2	)	)	PUNCT
cana-5359	133	3	,	,	PUNCT
cana-5359	133	4	𝔉ℱ𝛿𝒫𝑂𝑆(𝑋	𝔉ℱ𝛿𝒫𝑂𝑆(𝑋	PROPN
cana-5359	133	5	)	)	PUNCT
cana-5359	133	6	,	,	PUNCT
cana-5359	133	7	𝔉ℱ𝛿𝒫𝐶𝑆(𝑋	𝔉ℱ𝛿𝒫𝐶𝑆(𝑋	PROPN
cana-5359	133	8	)	)	PUNCT
cana-5359	133	9	,	,	PUNCT
cana-5359	133	10	𝔉ℱ𝛿𝒮𝑂𝑆(𝑋	𝔉ℱ𝛿𝒮𝑂𝑆(𝑋	PROPN
cana-5359	133	11	)	)	PUNCT
cana-5359	133	12	,	,	PUNCT
cana-5359	133	13	𝔉ℱ𝛿𝒮𝐶𝑆(𝑋	𝔉ℱ𝛿𝒮𝐶𝑆(𝑋	PROPN
cana-5359	133	14	)	)	PUNCT
cana-5359	133	15	,	,	PUNCT
cana-5359	133	16	𝔉ℱ𝛿𝛼𝑂𝑆(𝑋	𝔉ℱ𝛿𝛼𝑂𝑆(𝑋	NOUN
cana-5359	133	17	)	)	PUNCT
cana-5359	133	18	,	,	PUNCT
cana-5359	133	19	𝔉ℱ𝛿𝛼𝐶𝑆(𝑋	𝔉ℱ𝛿𝛼𝐶𝑆(𝑋	NOUN
cana-5359	133	20	)	)	PUNCT
cana-5359	133	21	,	,	PUNCT
cana-5359	133	22	𝔉ℱ𝛿𝛽𝑂𝑆(𝑋	𝔉ℱ𝛿𝛽𝑂𝑆(𝑋	PROPN
cana-5359	133	23	)	)	PUNCT
cana-5359	133	24	and	and	CCONJ
cana-5359	133	25	𝔉ℱ𝛿𝛽𝐶𝑆(𝑋	𝔉ℱ𝛿𝛽𝐶𝑆(𝑋	NOUN
cana-5359	133	26	)	)	PUNCT
cana-5359	133	27	)	)	PUNCT
cana-5359	133	28	.	.	PUNCT
cana-5359	134	1	definition	definition	NOUN
cana-5359	134	2	2.12	2.12	NUM
cana-5359	134	3	[	[	X
cana-5359	134	4	11	11	NUM
cana-5359	134	5	]	]	X
cana-5359	134	6	let	let	VERB
cana-5359	134	7	(	(	PUNCT
cana-5359	134	8	𝑋	𝑋	NOUN
cana-5359	134	9	,	,	PUNCT
cana-5359	134	10	𝜏	𝜏	NOUN
cana-5359	134	11	)	)	PUNCT
cana-5359	134	12	be	be	VERB
cana-5359	134	13	an	an	DET
cana-5359	134	14	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	134	15	and	and	CCONJ
cana-5359	134	16	𝐴	𝐴	PROPN
cana-5359	134	17	=	=	PUNCT
cana-5359	134	18	{	{	PUNCT
cana-5359	134	19	<	<	X
cana-5359	134	20	𝑎	𝑎	NOUN
cana-5359	134	21	,	,	PUNCT
cana-5359	134	22	𝛼𝐴(𝑎	𝛼𝐴(𝑎	NUM
cana-5359	134	23	)	)	PUNCT
cana-5359	134	24	,	,	PUNCT
cana-5359	134	25	𝛽𝐴(𝑎	𝛽𝐴(𝑎	NUM
cana-5359	134	26	)	)	PUNCT
cana-5359	134	27	>	>	X
cana-5359	134	28	|𝑎	|𝑎	PROPN
cana-5359	135	1	∈	∈	PROPN
cana-5359	135	2	𝑋	𝑋	PROPN
cana-5359	135	3	}	}	PUNCT
cana-5359	135	4	be	be	AUX
cana-5359	135	5	an	an	DET
cana-5359	135	6	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	135	7	in	in	ADP
cana-5359	135	8	𝑋	𝑋	PROPN
cana-5359	135	9	.	.	PUNCT
cana-5359	136	1	then	then	ADV
cana-5359	136	2	the	the	DET
cana-5359	136	3	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5359	136	4	-pre	-pre	PUNCT
cana-5359	136	5	(	(	PUNCT
cana-5359	136	6	resp	resp	NOUN
cana-5359	136	7	.	.	PUNCT
cana-5359	137	1	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5359	137	2	-semi	-semi	PROPN
cana-5359	137	3	,	,	PUNCT
cana-5359	137	4	𝔉ℱ𝛿𝛼	𝔉ℱ𝛿𝛼	ADJ
cana-5359	137	5	and	and	CCONJ
cana-5359	137	6	𝔉ℱ𝛿𝛽	𝔉ℱ𝛿𝛽	ADJ
cana-5359	137	7	)	)	PUNCT
cana-5359	137	8	-interior	-interior	NOUN
cana-5359	137	9	and	and	CCONJ
cana-5359	137	10	the	the	DET
cana-5359	137	11	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5359	137	12	-pre	-pre	PUNCT
cana-5359	137	13	(	(	PUNCT
cana-5359	137	14	resp	resp	NOUN
cana-5359	137	15	.	.	PUNCT
cana-5359	138	1	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5359	138	2	-semi	-semi	PROPN
cana-5359	138	3	,	,	PUNCT
cana-5359	138	4	𝔉ℱ𝛿𝛼	𝔉ℱ𝛿𝛼	ADJ
cana-5359	138	5	and	and	CCONJ
cana-5359	138	6	𝔉ℱ𝛿𝛽	𝔉ℱ𝛿𝛽	ADJ
cana-5359	138	7	)	)	PUNCT
cana-5359	138	8	-closure	-closure	NOUN
cana-5359	138	9	of	of	ADP
cana-5359	138	10	𝐴	𝐴	PROPN
cana-5359	138	11	are	be	AUX
cana-5359	138	12	denoted	denote	VERB
cana-5359	138	13	by	by	ADP
cana-5359	138	14	𝔉ℱ𝛿𝒫𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝒫𝑖𝑛𝑡(𝐴	NOUN
cana-5359	138	15	)	)	PUNCT
cana-5359	138	16	(	(	PUNCT
cana-5359	138	17	resp	resp	NOUN
cana-5359	138	18	.	.	PUNCT
cana-5359	139	1	𝔉ℱ𝛿𝒮𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝒮𝑖𝑛𝑡(𝐴	ADV
cana-5359	139	2	)	)	PUNCT
cana-5359	139	3	,	,	PUNCT
cana-5359	139	4	𝔉ℱ𝛿𝛼𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝛼𝑖𝑛𝑡(𝐴	NUM
cana-5359	139	5	)	)	PUNCT
cana-5359	139	6	and	and	CCONJ
cana-5359	139	7	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(𝐴	NOUN
cana-5359	139	8	)	)	PUNCT
cana-5359	139	9	)	)	PUNCT
cana-5359	139	10	and	and	CCONJ
cana-5359	139	11	the	the	DET
cana-5359	139	12	𝔉ℱ𝛿𝒫𝑐𝑙(𝐴	𝔉ℱ𝛿𝒫𝑐𝑙(𝐴	PROPN
cana-5359	139	13	)	)	PUNCT
cana-5359	139	14	(	(	PUNCT
cana-5359	139	15	resp	resp	NOUN
cana-5359	139	16	.	.	PUNCT
cana-5359	140	1	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	NOUN
cana-5359	140	2	)	)	PUNCT
cana-5359	140	3	,	,	PUNCT
cana-5359	140	4	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	NOUN
cana-5359	140	5	)	)	PUNCT
cana-5359	140	6	and	and	CCONJ
cana-5359	140	7	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	VERB
cana-5359	140	8	)	)	PUNCT
cana-5359	140	9	)	)	PUNCT
cana-5359	141	1	and	and	CCONJ
cana-5359	141	2	are	be	AUX
cana-5359	141	3	defined	define	VERB
cana-5359	141	4	as	as	SCONJ
cana-5359	141	5	follows	follow	VERB
cana-5359	141	6	:	:	PUNCT
cana-5359	141	7	communications	communication	NOUN
cana-5359	141	8	on	on	ADP
cana-5359	141	9	applied	apply	VERB
cana-5359	141	10	nonlinear	nonlinear	ADJ
cana-5359	141	11	analysis	analysis	NOUN
cana-5359	141	12	issn	issn	NOUN
cana-5359	141	13	:	:	PUNCT
cana-5359	141	14	1074	1074	NUM
cana-5359	141	15	-	-	PUNCT
cana-5359	141	16	133x	133x	NUM
cana-5359	141	17	vol	vol	VERB
cana-5359	141	18	32	32	NUM
cana-5359	141	19	no	no	NOUN
cana-5359	141	20	.	.	PUNCT
cana-5359	142	1	10s	10	NOUN
cana-5359	142	2	(	(	PUNCT
cana-5359	142	3	2025	2025	NUM
cana-5359	142	4	)	)	PUNCT
cana-5359	142	5	1914	1914	NUM
cana-5359	142	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	142	7	𝔉ℱ𝛿𝒫𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝒫𝑖𝑛𝑡(𝐴	NOUN
cana-5359	142	8	)	)	PUNCT
cana-5359	142	9	(	(	PUNCT
cana-5359	142	10	resp	resp	NOUN
cana-5359	142	11	.	.	PUNCT
cana-5359	143	1	𝔉ℱ𝛿𝒮𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝒮𝑖𝑛𝑡(𝐴	X
cana-5359	143	2	)	)	PUNCT
cana-5359	143	3	,	,	PUNCT
cana-5359	143	4	𝔉ℱ𝛿𝛼𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝛼𝑖𝑛𝑡(𝐴	NOUN
cana-5359	143	5	)	)	PUNCT
cana-5359	143	6	and	and	CCONJ
cana-5359	143	7	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(𝐴	NOUN
cana-5359	143	8	)	)	PUNCT
cana-5359	143	9	)	)	PUNCT
cana-5359	144	1	=	=	SYM
cana-5359	144	2	∪	∪	X
cana-5359	144	3	{	{	PUNCT
cana-5359	144	4	𝐺|𝐺	𝐺|𝐺	NOUN
cana-5359	144	5	in	in	ADP
cana-5359	144	6	a	a	DET
cana-5359	144	7	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	144	8	(	(	PUNCT
cana-5359	144	9	resp	resp	PROPN
cana-5359	144	10	.	.	PUNCT
cana-5359	145	1	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	145	2	,	,	PUNCT
cana-5359	145	3	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	145	4	and	and	CCONJ
cana-5359	145	5	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	145	6	)	)	PUNCT
cana-5359	145	7	and	and	CCONJ
cana-5359	145	8	𝐺	𝐺	PROPN
cana-5359	145	9	⊆	⊆	NUM
cana-5359	145	10	𝐴	𝐴	PROPN
cana-5359	145	11	}	}	PUNCT
cana-5359	145	12	and	and	CCONJ
cana-5359	145	13	𝔉ℱ𝛿𝒫𝑐𝑙(𝐴	𝔉ℱ𝛿𝒫𝑐𝑙(𝐴	NUM
cana-5359	145	14	)	)	PUNCT
cana-5359	145	15	(	(	PUNCT
cana-5359	145	16	resp	resp	NOUN
cana-5359	145	17	.	.	PUNCT
cana-5359	146	1	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	NOUN
cana-5359	146	2	)	)	PUNCT
cana-5359	146	3	,	,	PUNCT
cana-5359	146	4	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	NOUN
cana-5359	146	5	)	)	PUNCT
cana-5359	146	6	and	and	CCONJ
cana-5359	146	7	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	VERB
cana-5359	146	8	)	)	PUNCT
cana-5359	146	9	)	)	PUNCT
cana-5359	147	1	=	=	NOUN
cana-5359	147	2	∩	∩	NOUN
cana-5359	147	3	{	{	PUNCT
cana-5359	147	4	𝐾|𝐾	𝐾|𝐾	NOUN
cana-5359	147	5	is	be	AUX
cana-5359	147	6	an	an	DET
cana-5359	147	7	𝔉ℱ𝛿𝒫𝑐𝑠	𝔉ℱ𝛿𝒫𝑐𝑠	NOUN
cana-5359	147	8	(	(	PUNCT
cana-5359	147	9	resp	resp	NOUN
cana-5359	147	10	.	.	PUNCT
cana-5359	148	1	𝔉ℱ𝛿𝒮𝑐𝑠	𝔉ℱ𝛿𝒮𝑐𝑠	PROPN
cana-5359	148	2	,	,	PUNCT
cana-5359	148	3	𝔉ℱ𝛿𝛼𝑐𝑠	𝔉ℱ𝛿𝛼𝑐𝑠	PROPN
cana-5359	148	4	,	,	PUNCT
cana-5359	148	5	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5359	148	6	)	)	PUNCT
cana-5359	148	7	and	and	CCONJ
cana-5359	148	8	𝐴	𝐴	PROPN
cana-5359	148	9	⊆	⊆	NUM
cana-5359	148	10	𝐾	𝐾	PROPN
cana-5359	148	11	}	}	PUNCT
cana-5359	148	12	.	.	PUNCT
cana-5359	149	1	3	3	NUM
cana-5359	149	2	fermatean	fermatean	NOUN
cana-5359	149	3	fuzzy	fuzzy	ADJ
cana-5359	149	4	𝜹	𝜹	X
cana-5359	149	5	(	(	PUNCT
cana-5359	149	6	resp	resp	NOUN
cana-5359	149	7	.	.	PUNCT
cana-5359	150	1	𝜹	𝜹	X
cana-5359	150	2	pre	pre	ADJ
cana-5359	150	3	,	,	PUNCT
cana-5359	150	4	𝜹	𝜹	X
cana-5359	150	5	semi	semi	ADV
cana-5359	150	6	,	,	PUNCT
cana-5359	150	7	𝜹𝜶	𝜹𝜶	VERB
cana-5359	150	8	and	and	CCONJ
cana-5359	150	9	𝜹𝜷)-continuous	𝜹𝜷)-continuous	ADJ
cana-5359	150	10	mappings	mapping	NOUN
cana-5359	150	11	in	in	ADP
cana-5359	150	12	this	this	DET
cana-5359	150	13	section	section	NOUN
cana-5359	150	14	,	,	PUNCT
cana-5359	150	15	we	we	PRON
cana-5359	150	16	introduce	introduce	VERB
cana-5359	150	17	fermatean	fermatean	NOUN
cana-5359	150	18	fuzzy	fuzzy	ADJ
cana-5359	150	19	𝛿	𝛿	ADJ
cana-5359	150	20	(	(	PUNCT
cana-5359	150	21	resp	resp	NOUN
cana-5359	150	22	.	.	PUNCT
cana-5359	151	1	𝛿	𝛿	DET
cana-5359	151	2	pre	pre	NOUN
cana-5359	151	3	,	,	PUNCT
cana-5359	151	4	𝛿	𝛿	ADJ
cana-5359	151	5	semi	semi	ADJ
cana-5359	151	6	,	,	PUNCT
cana-5359	151	7	𝛿𝛼	𝛿𝛼	NOUN
cana-5359	151	8	and	and	CCONJ
cana-5359	151	9	𝛿𝛽)-continuous	𝛿𝛽)-continuous	ADJ
cana-5359	151	10	mappings	mapping	NOUN
cana-5359	151	11	and	and	CCONJ
cana-5359	151	12	discuss	discuss	VERB
cana-5359	151	13	some	some	PRON
cana-5359	151	14	of	of	ADP
cana-5359	151	15	their	their	PRON
cana-5359	151	16	properties	property	NOUN
cana-5359	151	17	.	.	PUNCT
cana-5359	152	1	definition	definition	NOUN
cana-5359	152	2	3.1	3.1	NUM
cana-5359	152	3	let	let	NOUN
cana-5359	152	4	(	(	PUNCT
cana-5359	152	5	𝑋1	𝑋1	PROPN
cana-5359	152	6	,	,	PUNCT
cana-5359	152	7	𝜏1	𝜏1	NOUN
cana-5359	152	8	)	)	PUNCT
cana-5359	152	9	and	and	CCONJ
cana-5359	152	10	(	(	PUNCT
cana-5359	152	11	𝑋2	𝑋2	PROPN
cana-5359	152	12	,	,	PUNCT
cana-5359	152	13	𝜏2	𝜏2	PROPN
cana-5359	152	14	)	)	PUNCT
cana-5359	152	15	be	be	VERB
cana-5359	152	16	two	two	NUM
cana-5359	152	17	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	152	18	’s	’s	NOUN
cana-5359	152	19	.	.	PUNCT
cana-5359	153	1	then	then	ADV
cana-5359	153	2	a	a	DET
cana-5359	153	3	function	function	NOUN
cana-5359	153	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	153	5	:	:	PUNCT
cana-5359	153	6	(	(	PUNCT
cana-5359	153	7	𝑋1	𝑋1	PROPN
cana-5359	153	8	,	,	PUNCT
cana-5359	153	9	𝜏1	𝜏1	NOUN
cana-5359	153	10	)	)	PUNCT
cana-5359	153	11	→	→	SYM
cana-5359	153	12	(	(	PUNCT
cana-5359	153	13	𝑋2	𝑋2	PROPN
cana-5359	153	14	,	,	PUNCT
cana-5359	153	15	𝜏2	𝜏2	PROPN
cana-5359	153	16	)	)	PUNCT
cana-5359	153	17	is	be	AUX
cana-5359	153	18	said	say	VERB
cana-5359	153	19	to	to	PART
cana-5359	153	20	be	be	AUX
cana-5359	153	21	a	a	DET
cana-5359	153	22	fermatean	fermatean	ADJ
cana-5359	153	23	fuzzy	fuzzy	ADJ
cana-5359	153	24	𝛿	𝛿	ADJ
cana-5359	153	25	(	(	PUNCT
cana-5359	153	26	resp	resp	NOUN
cana-5359	153	27	.	.	PUNCT
cana-5359	154	1	𝛿	𝛿	DET
cana-5359	154	2	pre	pre	NOUN
cana-5359	154	3	,	,	PUNCT
cana-5359	154	4	𝛿	𝛿	ADJ
cana-5359	154	5	semi	semi	ADJ
cana-5359	154	6	,	,	PUNCT
cana-5359	154	7	𝛿𝛼	𝛿𝛼	ADP
cana-5359	154	8	and	and	CCONJ
cana-5359	154	9	𝛿𝛽	𝛿𝛽	ADJ
cana-5359	154	10	)	)	PUNCT
cana-5359	154	11	continuous	continuous	ADJ
cana-5359	154	12	(	(	PUNCT
cana-5359	154	13	briefly	briefly	ADV
cana-5359	154	14	,	,	PUNCT
cana-5359	154	15	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	PUNCT
cana-5359	154	16	(	(	PUNCT
cana-5359	154	17	resp	resp	NOUN
cana-5359	154	18	.	.	PUNCT
cana-5359	155	1	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5359	155	2	,	,	PUNCT
cana-5359	155	3	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	PROPN
cana-5359	155	4	,	,	PUNCT
cana-5359	155	5	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5359	155	6	and	and	CCONJ
cana-5359	155	7	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	NOUN
cana-5359	155	8	)	)	PUNCT
cana-5359	155	9	)	)	PUNCT
cana-5359	155	10	function	function	VERB
cana-5359	155	11	if	if	SCONJ
cana-5359	155	12	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	155	13	−1(𝐺	−1(𝐺	VERB
cana-5359	155	14	)	)	PUNCT
cana-5359	155	15	is	be	AUX
cana-5359	155	16	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	155	17	(	(	PUNCT
cana-5359	155	18	resp	resp	NOUN
cana-5359	155	19	.	.	PUNCT
cana-5359	156	1	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	PROPN
cana-5359	156	2	,	,	PUNCT
cana-5359	156	3	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	NUM
cana-5359	156	4	,	,	PUNCT
cana-5359	156	5	𝔉ℱ𝛿𝛼𝑜	𝔉ℱ𝛿𝛼𝑜	PROPN
cana-5359	156	6	&	&	CCONJ
cana-5359	156	7	𝔉ℱ𝛿𝛽𝑜	𝔉ℱ𝛿𝛽𝑜	PROPN
cana-5359	156	8	)	)	PUNCT
cana-5359	156	9	set	set	VERB
cana-5359	156	10	in	in	ADP
cana-5359	156	11	𝑋1	𝑋1	NOUN
cana-5359	156	12	for	for	ADP
cana-5359	156	13	all	all	DET
cana-5359	156	14	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	156	15	set	set	VERB
cana-5359	156	16	𝐺	𝐺	PROPN
cana-5359	156	17	in	in	ADP
cana-5359	156	18	𝑋2	𝑋2	PROPN
cana-5359	156	19	.	.	PUNCT
cana-5359	157	1	lemma	lemma	PROPN
cana-5359	157	2	3.1	3.1	NUM
cana-5359	157	3	let	let	VERB
cana-5359	157	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	157	5	:	:	PUNCT
cana-5359	157	6	(	(	PUNCT
cana-5359	157	7	𝑋1	𝑋1	PROPN
cana-5359	157	8	,	,	PUNCT
cana-5359	157	9	𝜏1	𝜏1	NOUN
cana-5359	157	10	)	)	PUNCT
cana-5359	157	11	→	→	SYM
cana-5359	157	12	(	(	PUNCT
cana-5359	157	13	𝑋2	𝑋2	PROPN
cana-5359	157	14	,	,	PUNCT
cana-5359	157	15	𝜏2	𝜏2	PROPN
cana-5359	157	16	)	)	PUNCT
cana-5359	157	17	be	be	VERB
cana-5359	157	18	a	a	DET
cana-5359	157	19	function	function	NOUN
cana-5359	157	20	.	.	PUNCT
cana-5359	158	1	then	then	ADV
cana-5359	158	2	the	the	DET
cana-5359	158	3	following	follow	VERB
cana-5359	158	4	statements	statement	NOUN
cana-5359	158	5	hold	hold	VERB
cana-5359	158	6	.	.	PUNCT
cana-5359	159	1	1	1	X
cana-5359	159	2	.	.	X
cana-5359	159	3	if	if	SCONJ
cana-5359	159	4	𝑆	𝑆	PROPN
cana-5359	159	5	and	and	CCONJ
cana-5359	159	6	𝑇	𝑇	PROPN
cana-5359	159	7	are	be	AUX
cana-5359	159	8	𝔉𝑓𝑠	𝔉𝑓𝑠	PROPN
cana-5359	159	9	’s	’s	NOUN
cana-5359	159	10	of	of	ADP
cana-5359	159	11	𝑋1	𝑋1	NOUN
cana-5359	159	12	such	such	ADJ
cana-5359	159	13	that	that	SCONJ
cana-5359	159	14	𝑆	𝑆	PROPN
cana-5359	159	15	⊆	⊆	NUM
cana-5359	159	16	𝑇	𝑇	PROPN
cana-5359	159	17	,	,	PUNCT
cana-5359	159	18	then	then	ADV
cana-5359	159	19	ℎ𝔉(𝑆	ℎ𝔉(𝑆	NOUN
cana-5359	159	20	)	)	PUNCT
cana-5359	159	21	⊆	⊆	NUM
cana-5359	159	22	ℎ𝔉(𝑇	ℎ𝔉(𝑇	NUM
cana-5359	159	23	)	)	PUNCT
cana-5359	159	24	.	.	PUNCT
cana-5359	160	1	2	2	X
cana-5359	160	2	.	.	X
cana-5359	160	3	if	if	SCONJ
cana-5359	160	4	𝑆	𝑆	PROPN
cana-5359	160	5	and	and	CCONJ
cana-5359	160	6	𝑇	𝑇	PROPN
cana-5359	160	7	are	be	AUX
cana-5359	160	8	𝔉𝑓𝑠	𝔉𝑓𝑠	PROPN
cana-5359	160	9	’s	’s	NOUN
cana-5359	160	10	of	of	ADP
cana-5359	160	11	𝑋2	𝑋2	VERB
cana-5359	160	12	such	such	ADJ
cana-5359	160	13	that	that	SCONJ
cana-5359	160	14	𝑆	𝑆	PROPN
cana-5359	160	15	⊆	⊆	NUM
cana-5359	160	16	𝑇	𝑇	PROPN
cana-5359	160	17	,	,	PUNCT
cana-5359	160	18	then	then	ADV
cana-5359	160	19	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	160	20	−1(𝑆	−1(𝑆	PART
cana-5359	160	21	)	)	PUNCT
cana-5359	160	22	⊆	⊆	NUM
cana-5359	160	23	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	160	24	−1(𝑇	−1(𝑇	VERB
cana-5359	160	25	)	)	PUNCT
cana-5359	160	26	.	.	PUNCT
cana-5359	161	1	lemma	lemma	PROPN
cana-5359	161	2	3.2	3.2	NUM
cana-5359	161	3	let	let	VERB
cana-5359	161	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	161	5	:	:	PUNCT
cana-5359	161	6	(	(	PUNCT
cana-5359	161	7	𝑋1	𝑋1	PROPN
cana-5359	161	8	,	,	PUNCT
cana-5359	161	9	𝜏1	𝜏1	NOUN
cana-5359	161	10	)	)	PUNCT
cana-5359	161	11	→	→	SYM
cana-5359	161	12	(	(	PUNCT
cana-5359	161	13	𝑋2	𝑋2	PROPN
cana-5359	161	14	,	,	PUNCT
cana-5359	161	15	𝜏2	𝜏2	PROPN
cana-5359	161	16	)	)	PUNCT
cana-5359	161	17	be	be	VERB
cana-5359	161	18	a	a	DET
cana-5359	161	19	function	function	NOUN
cana-5359	161	20	.	.	PUNCT
cana-5359	162	1	if	if	SCONJ
cana-5359	162	2	𝑆	𝑆	PROPN
cana-5359	162	3	is	be	AUX
cana-5359	162	4	a	a	DET
cana-5359	162	5	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	162	6	of	of	ADP
cana-5359	162	7	𝑋1	𝑋1	PROPN
cana-5359	162	8	and	and	CCONJ
cana-5359	162	9	𝑇	𝑇	PROPN
cana-5359	162	10	is	be	AUX
cana-5359	162	11	a	a	DET
cana-5359	162	12	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	162	13	of	of	ADP
cana-5359	162	14	𝑋2	𝑋2	PROPN
cana-5359	162	15	.	.	PUNCT
cana-5359	163	1	then	then	ADV
cana-5359	163	2	1	1	X
cana-5359	163	3	.	.	X
cana-5359	163	4	ℎ𝔉(ℎ𝔉	ℎ𝔉(ℎ𝔉	PROPN
cana-5359	163	5	−1(𝑆	−1(𝑆	ADJ
cana-5359	163	6	)	)	PUNCT
cana-5359	163	7	)	)	PUNCT
cana-5359	164	1	⊆	⊆	NUM
cana-5359	164	2	𝑆	𝑆	PROPN
cana-5359	164	3	2	2	NUM
cana-5359	164	4	.	.	PUNCT
cana-5359	164	5	ℎ𝔉(ℎ𝔉	ℎ𝔉(ℎ𝔉	PROPN
cana-5359	164	6	−1(𝑆	−1(𝑆	ADJ
cana-5359	164	7	)	)	PUNCT
cana-5359	164	8	)	)	PUNCT
cana-5359	165	1	=	=	SYM
cana-5359	165	2	𝑆	𝑆	PROPN
cana-5359	165	3	⇔	⇔	PROPN
cana-5359	165	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	165	5	is	be	AUX
cana-5359	165	6	surjective	surjective	ADJ
cana-5359	165	7	.	.	PUNCT
cana-5359	166	1	3	3	X
cana-5359	166	2	.	.	X
cana-5359	166	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	166	4	−1(ℎ𝔉(𝑆	−1(ℎ𝔉(𝑆	ADJ
cana-5359	166	5	)	)	PUNCT
cana-5359	166	6	)	)	PUNCT
cana-5359	166	7	⊇	⊇	PROPN
cana-5359	166	8	𝑆	𝑆	PROPN
cana-5359	166	9	4	4	NUM
cana-5359	166	10	.	.	PUNCT
cana-5359	167	1	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	167	2	−1(ℎ𝔉(𝑆	−1(ℎ𝔉(𝑆	NOUN
cana-5359	167	3	)	)	PUNCT
cana-5359	167	4	)	)	PUNCT
cana-5359	168	1	=	=	PUNCT
cana-5359	168	2	𝑆	𝑆	PROPN
cana-5359	168	3	whenever	whenever	SCONJ
cana-5359	168	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	168	5	is	be	AUX
cana-5359	168	6	injective	injective	ADJ
cana-5359	168	7	.	.	PUNCT
cana-5359	169	1	theorem	theorem	VERB
cana-5359	169	2	3.1	3.1	NUM
cana-5359	169	3	let	let	NOUN
cana-5359	169	4	(	(	PUNCT
cana-5359	169	5	𝑋1	𝑋1	PROPN
cana-5359	169	6	,	,	PUNCT
cana-5359	169	7	𝜏1	𝜏1	NOUN
cana-5359	169	8	)	)	PUNCT
cana-5359	169	9	and	and	CCONJ
cana-5359	169	10	(	(	PUNCT
cana-5359	169	11	𝑋2	𝑋2	PROPN
cana-5359	169	12	,	,	PUNCT
cana-5359	169	13	𝜏2	𝜏2	PROPN
cana-5359	169	14	)	)	PUNCT
cana-5359	169	15	be	be	AUX
cana-5359	169	16	two	two	NUM
cana-5359	169	17	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	169	18	’s	’s	PART
cana-5359	169	19	and	and	CCONJ
cana-5359	169	20	let	let	VERB
cana-5359	169	21	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	169	22	:	:	PUNCT
cana-5359	169	23	(	(	PUNCT
cana-5359	169	24	𝑋1	𝑋1	PROPN
cana-5359	169	25	,	,	PUNCT
cana-5359	169	26	𝜏1	𝜏1	NOUN
cana-5359	169	27	)	)	PUNCT
cana-5359	169	28	→	→	SYM
cana-5359	169	29	(	(	PUNCT
cana-5359	169	30	𝑋2	𝑋2	PROPN
cana-5359	169	31	,	,	PUNCT
cana-5359	169	32	𝜏2	𝜏2	PROPN
cana-5359	169	33	)	)	PUNCT
cana-5359	169	34	,	,	PUNCT
cana-5359	169	35	then	then	ADV
cana-5359	169	36	(	(	PUNCT
cana-5359	169	37	i	i	NOUN
cana-5359	169	38	)	)	PUNCT
cana-5359	169	39	every	every	DET
cana-5359	169	40	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	NOUN
cana-5359	169	41	is	be	AUX
cana-5359	169	42	a	a	DET
cana-5359	169	43	𝔉ℱ𝐶𝑡𝑠.	𝔉ℱ𝐶𝑡𝑠.	PROPN
cana-5359	169	44	(	(	PUNCT
cana-5359	169	45	ii	ii	NOUN
cana-5359	169	46	)	)	PUNCT
cana-5359	169	47	every	every	PRON
cana-5359	169	48	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	NOUN
cana-5359	169	49	is	be	AUX
cana-5359	169	50	a	a	DET
cana-5359	169	51	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	PROPN
cana-5359	169	52	(	(	PUNCT
cana-5359	169	53	iii	iii	NOUN
cana-5359	169	54	)	)	PUNCT
cana-5359	169	55	every	every	DET
cana-5359	169	56	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	NOUN
cana-5359	169	57	is	be	AUX
cana-5359	169	58	a	a	DET
cana-5359	169	59	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	NUM
cana-5359	169	60	(	(	PUNCT
cana-5359	169	61	iv	iv	X
cana-5359	169	62	)	)	PUNCT
cana-5359	169	63	every	every	DET
cana-5359	169	64	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5359	169	65	is	be	AUX
cana-5359	169	66	a	a	DET
cana-5359	169	67	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	PROPN
cana-5359	169	68	(	(	PUNCT
cana-5359	169	69	v	v	NOUN
cana-5359	169	70	)	)	PUNCT
cana-5359	169	71	every	every	DET
cana-5359	169	72	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	NOUN
cana-5359	169	73	is	be	AUX
cana-5359	169	74	a	a	DET
cana-5359	169	75	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	PROPN
cana-5359	169	76	(	(	PUNCT
cana-5359	169	77	vi	vi	NOUN
cana-5359	169	78	)	)	PUNCT
cana-5359	169	79	every	every	DET
cana-5359	169	80	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5359	169	81	is	be	AUX
cana-5359	169	82	a	a	DET
cana-5359	169	83	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	PROPN
cana-5359	169	84	(	(	PUNCT
cana-5359	169	85	vii	vii	PROPN
cana-5359	169	86	)	)	PUNCT
cana-5359	169	87	every	every	DET
cana-5359	169	88	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5359	169	89	is	be	AUX
cana-5359	169	90	a	a	DET
cana-5359	169	91	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	NUM
cana-5359	169	92	but	but	CCONJ
cana-5359	169	93	not	not	PART
cana-5359	169	94	converse	converse	NOUN
cana-5359	169	95	.	.	PUNCT
cana-5359	170	1	proof	proof	NOUN
cana-5359	170	2	.	.	PUNCT
cana-5359	171	1	(	(	PUNCT
cana-5359	171	2	i	i	NOUN
cana-5359	171	3	)	)	PUNCT
cana-5359	171	4	let	let	VERB
cana-5359	171	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	171	6	:	:	PUNCT
cana-5359	171	7	(	(	PUNCT
cana-5359	171	8	𝑋1	𝑋1	PROPN
cana-5359	171	9	,	,	PUNCT
cana-5359	171	10	𝜏1	𝜏1	NOUN
cana-5359	171	11	)	)	PUNCT
cana-5359	171	12	→	→	SYM
cana-5359	171	13	(	(	PUNCT
cana-5359	171	14	𝑋2	𝑋2	PROPN
cana-5359	171	15	,	,	PUNCT
cana-5359	171	16	𝜏2	𝜏2	PROPN
cana-5359	171	17	)	)	PUNCT
cana-5359	171	18	be	be	VERB
cana-5359	171	19	a	a	DET
cana-5359	171	20	𝔉ℱ𝛿𝐶𝑡𝑠.	𝔉ℱ𝛿𝐶𝑡𝑠.	PUNCT
cana-5359	171	21	let	let	VERB
cana-5359	171	22	𝑆	𝑆	PROPN
cana-5359	171	23	be	be	AUX
cana-5359	171	24	a	a	DET
cana-5359	171	25	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	171	26	set	set	VERB
cana-5359	171	27	in	in	ADP
cana-5359	171	28	(	(	PUNCT
cana-5359	171	29	𝑋2	𝑋2	ADJ
cana-5359	171	30	,	,	PUNCT
cana-5359	171	31	𝜏2	𝜏2	PROPN
cana-5359	171	32	)	)	PUNCT
cana-5359	171	33	.	.	PUNCT
cana-5359	172	1	then	then	ADV
cana-5359	172	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	172	3	−1(𝑆	−1(𝑆	PART
cana-5359	172	4	)	)	PUNCT
cana-5359	172	5	is	be	AUX
cana-5359	172	6	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	172	7	set	set	VERB
cana-5359	172	8	in	in	ADP
cana-5359	172	9	(	(	PUNCT
cana-5359	172	10	𝑋1	𝑋1	PROPN
cana-5359	172	11	,	,	PUNCT
cana-5359	172	12	𝜏1	𝜏1	NOUN
cana-5359	172	13	)	)	PUNCT
cana-5359	172	14	.	.	PUNCT
cana-5359	173	1	since	since	SCONJ
cana-5359	173	2	every	every	DET
cana-5359	173	3	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	173	4	set	set	VERB
cana-5359	173	5	is	be	AUX
cana-5359	173	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	173	7	,	,	PUNCT
cana-5359	173	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	173	9	−1(𝑆	−1(𝑆	PART
cana-5359	173	10	)	)	PUNCT
cana-5359	173	11	is	be	AUX
cana-5359	173	12	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	173	13	set	set	VERB
cana-5359	173	14	in	in	ADP
cana-5359	173	15	(	(	PUNCT
cana-5359	173	16	𝑋1	𝑋1	PROPN
cana-5359	173	17	,	,	PUNCT
cana-5359	173	18	𝜏1	𝜏1	NOUN
cana-5359	173	19	)	)	PUNCT
cana-5359	173	20	.	.	PUNCT
cana-5359	174	1	hence	hence	ADV
cana-5359	174	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	174	3	is	be	AUX
cana-5359	174	4	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	NOUN
cana-5359	174	5	function	function	NOUN
cana-5359	174	6	.	.	PUNCT
cana-5359	175	1	communications	communication	NOUN
cana-5359	175	2	on	on	ADP
cana-5359	175	3	applied	apply	VERB
cana-5359	175	4	nonlinear	nonlinear	ADJ
cana-5359	175	5	analysis	analysis	NOUN
cana-5359	175	6	issn	issn	NOUN
cana-5359	175	7	:	:	PUNCT
cana-5359	175	8	1074	1074	NUM
cana-5359	175	9	-	-	PUNCT
cana-5359	175	10	133x	133x	NUM
cana-5359	175	11	vol	vol	VERB
cana-5359	175	12	32	32	NUM
cana-5359	175	13	no	no	NOUN
cana-5359	175	14	.	.	PUNCT
cana-5359	176	1	10s	10	NOUN
cana-5359	176	2	(	(	PUNCT
cana-5359	176	3	2025	2025	NUM
cana-5359	176	4	)	)	PUNCT
cana-5359	176	5	1915	1915	NUM
cana-5359	177	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	177	2	(	(	PUNCT
cana-5359	177	3	ii	ii	NOUN
cana-5359	177	4	)	)	PUNCT
cana-5359	177	5	let	let	VERB
cana-5359	177	6	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	177	7	:	:	PUNCT
cana-5359	177	8	(	(	PUNCT
cana-5359	177	9	𝑋1	𝑋1	PROPN
cana-5359	177	10	,	,	PUNCT
cana-5359	177	11	𝜏1	𝜏1	NOUN
cana-5359	177	12	)	)	PUNCT
cana-5359	177	13	→	→	SYM
cana-5359	177	14	(	(	PUNCT
cana-5359	177	15	𝑋2	𝑋2	PROPN
cana-5359	177	16	,	,	PUNCT
cana-5359	177	17	𝜏2	𝜏2	PROPN
cana-5359	177	18	)	)	PUNCT
cana-5359	177	19	be	be	VERB
cana-5359	177	20	a	a	DET
cana-5359	177	21	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	NOUN
cana-5359	177	22	.	.	PUNCT
cana-5359	178	1	let	let	VERB
cana-5359	178	2	𝑆	𝑆	PROPN
cana-5359	178	3	be	be	AUX
cana-5359	178	4	a	a	DET
cana-5359	178	5	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	178	6	set	set	VERB
cana-5359	178	7	in	in	ADP
cana-5359	178	8	(	(	PUNCT
cana-5359	178	9	𝑋2	𝑋2	ADJ
cana-5359	178	10	,	,	PUNCT
cana-5359	178	11	𝜏2	𝜏2	PROPN
cana-5359	178	12	)	)	PUNCT
cana-5359	178	13	.	.	PUNCT
cana-5359	179	1	then	then	ADV
cana-5359	179	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	179	3	−1(𝑆	−1(𝑆	PART
cana-5359	179	4	)	)	PUNCT
cana-5359	179	5	is	be	AUX
cana-5359	179	6	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	179	7	set	set	VERB
cana-5359	179	8	in	in	ADP
cana-5359	179	9	(	(	PUNCT
cana-5359	179	10	𝑋1	𝑋1	PROPN
cana-5359	179	11	,	,	PUNCT
cana-5359	179	12	𝜏1	𝜏1	NOUN
cana-5359	179	13	)	)	PUNCT
cana-5359	179	14	.	.	PUNCT
cana-5359	180	1	since	since	SCONJ
cana-5359	180	2	every	every	DET
cana-5359	180	3	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	180	4	set	set	VERB
cana-5359	180	5	is	be	AUX
cana-5359	180	6	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	180	7	,	,	PUNCT
cana-5359	180	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	180	9	−1(𝑆	−1(𝑆	PART
cana-5359	180	10	)	)	PUNCT
cana-5359	180	11	is	be	AUX
cana-5359	180	12	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	NOUN
cana-5359	180	13	set	set	VERB
cana-5359	180	14	in	in	ADP
cana-5359	180	15	(	(	PUNCT
cana-5359	180	16	𝑋1	𝑋1	PROPN
cana-5359	180	17	,	,	PUNCT
cana-5359	180	18	𝜏1	𝜏1	NOUN
cana-5359	180	19	)	)	PUNCT
cana-5359	180	20	.	.	PUNCT
cana-5359	181	1	hence	hence	ADV
cana-5359	181	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	181	3	is	be	AUX
cana-5359	181	4	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	NOUN
cana-5359	181	5	function	function	NOUN
cana-5359	181	6	.	.	PUNCT
cana-5359	182	1	(	(	PUNCT
cana-5359	182	2	iii	iii	X
cana-5359	182	3	)	)	PUNCT
cana-5359	182	4	let	let	VERB
cana-5359	182	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	182	6	:	:	PUNCT
cana-5359	182	7	(	(	PUNCT
cana-5359	182	8	𝑋1	𝑋1	PROPN
cana-5359	182	9	,	,	PUNCT
cana-5359	182	10	𝜏1	𝜏1	NOUN
cana-5359	182	11	)	)	PUNCT
cana-5359	182	12	→	→	SYM
cana-5359	182	13	(	(	PUNCT
cana-5359	182	14	𝑋2	𝑋2	PROPN
cana-5359	182	15	,	,	PUNCT
cana-5359	182	16	𝜏2	𝜏2	PROPN
cana-5359	182	17	)	)	PUNCT
cana-5359	182	18	be	be	VERB
cana-5359	182	19	a	a	DET
cana-5359	182	20	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	NOUN
cana-5359	182	21	.	.	PUNCT
cana-5359	183	1	let	let	VERB
cana-5359	183	2	𝑆	𝑆	PROPN
cana-5359	183	3	be	be	AUX
cana-5359	183	4	a	a	DET
cana-5359	183	5	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	183	6	set	set	VERB
cana-5359	183	7	in	in	ADP
cana-5359	183	8	(	(	PUNCT
cana-5359	183	9	𝑋2	𝑋2	ADJ
cana-5359	183	10	,	,	PUNCT
cana-5359	183	11	𝜏2	𝜏2	PROPN
cana-5359	183	12	)	)	PUNCT
cana-5359	183	13	.	.	PUNCT
cana-5359	184	1	then	then	ADV
cana-5359	184	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	184	3	−1(𝑆	−1(𝑆	PART
cana-5359	184	4	)	)	PUNCT
cana-5359	184	5	is	be	AUX
cana-5359	184	6	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	184	7	set	set	VERB
cana-5359	184	8	in	in	ADP
cana-5359	184	9	(	(	PUNCT
cana-5359	184	10	𝑋1	𝑋1	PROPN
cana-5359	184	11	,	,	PUNCT
cana-5359	184	12	𝜏1	𝜏1	NOUN
cana-5359	184	13	)	)	PUNCT
cana-5359	184	14	.	.	PUNCT
cana-5359	185	1	since	since	SCONJ
cana-5359	185	2	every	every	DET
cana-5359	185	3	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	185	4	set	set	VERB
cana-5359	185	5	is	be	AUX
cana-5359	185	6	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	NOUN
cana-5359	185	7	,	,	PUNCT
cana-5359	185	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	185	9	−1(𝑆	−1(𝑆	PART
cana-5359	185	10	)	)	PUNCT
cana-5359	185	11	is	be	AUX
cana-5359	185	12	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	NUM
cana-5359	185	13	set	set	NOUN
cana-5359	185	14	in	in	ADP
cana-5359	185	15	(	(	PUNCT
cana-5359	185	16	𝑋1	𝑋1	PROPN
cana-5359	185	17	,	,	PUNCT
cana-5359	185	18	𝜏1	𝜏1	NOUN
cana-5359	185	19	)	)	PUNCT
cana-5359	185	20	.	.	PUNCT
cana-5359	186	1	hence	hence	ADV
cana-5359	186	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	186	3	is	be	AUX
cana-5359	186	4	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	PRON
cana-5359	186	5	function	function	NOUN
cana-5359	186	6	.	.	PUNCT
cana-5359	187	1	(	(	PUNCT
cana-5359	187	2	iv	iv	X
cana-5359	187	3	)	)	PUNCT
cana-5359	187	4	let	let	VERB
cana-5359	187	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	187	6	:	:	PUNCT
cana-5359	187	7	(	(	PUNCT
cana-5359	187	8	𝑋1	𝑋1	PROPN
cana-5359	187	9	,	,	PUNCT
cana-5359	187	10	𝜏1	𝜏1	NOUN
cana-5359	187	11	)	)	PUNCT
cana-5359	187	12	→	→	SYM
cana-5359	187	13	(	(	PUNCT
cana-5359	187	14	𝑋2	𝑋2	PROPN
cana-5359	187	15	,	,	PUNCT
cana-5359	187	16	𝜏2	𝜏2	PROPN
cana-5359	187	17	)	)	PUNCT
cana-5359	187	18	be	be	VERB
cana-5359	187	19	a	a	DET
cana-5359	187	20	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	NUM
cana-5359	187	21	let	let	VERB
cana-5359	187	22	𝑆	𝑆	PROPN
cana-5359	187	23	be	be	AUX
cana-5359	187	24	a	a	DET
cana-5359	187	25	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	187	26	set	set	VERB
cana-5359	187	27	in	in	ADP
cana-5359	187	28	(	(	PUNCT
cana-5359	187	29	𝑋2	𝑋2	ADJ
cana-5359	187	30	,	,	PUNCT
cana-5359	187	31	𝜏2	𝜏2	PROPN
cana-5359	187	32	)	)	PUNCT
cana-5359	187	33	.	.	PUNCT
cana-5359	188	1	then	then	ADV
cana-5359	188	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	188	3	−1(𝑆	−1(𝑆	PART
cana-5359	188	4	)	)	PUNCT
cana-5359	188	5	is	be	AUX
cana-5359	188	6	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	NUM
cana-5359	188	7	set	set	NOUN
cana-5359	188	8	in	in	ADP
cana-5359	188	9	(	(	PUNCT
cana-5359	188	10	𝑋1	𝑋1	PROPN
cana-5359	188	11	,	,	PUNCT
cana-5359	188	12	𝜏1	𝜏1	NOUN
cana-5359	188	13	)	)	PUNCT
cana-5359	188	14	.	.	PUNCT
cana-5359	189	1	since	since	SCONJ
cana-5359	189	2	every	every	DET
cana-5359	189	3	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	NOUN
cana-5359	189	4	set	set	NOUN
cana-5359	189	5	is	be	AUX
cana-5359	189	6	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	189	7	,	,	PUNCT
cana-5359	189	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	189	9	−1(𝑆	−1(𝑆	PART
cana-5359	189	10	)	)	PUNCT
cana-5359	189	11	is	be	AUX
cana-5359	190	1	𝔉ℱ𝛿𝛽𝑜	𝔉ℱ𝛿𝛽𝑜	PROPN
cana-5359	190	2	set	set	VERB
cana-5359	190	3	in	in	ADP
cana-5359	190	4	(	(	PUNCT
cana-5359	190	5	𝑋1	𝑋1	PROPN
cana-5359	190	6	,	,	PUNCT
cana-5359	190	7	𝜏1	𝜏1	NOUN
cana-5359	190	8	)	)	PUNCT
cana-5359	190	9	.	.	PUNCT
cana-5359	191	1	hence	hence	ADV
cana-5359	191	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	191	3	is	be	AUX
cana-5359	191	4	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	191	5	function	function	NOUN
cana-5359	191	6	.	.	PUNCT
cana-5359	192	1	(	(	PUNCT
cana-5359	192	2	v	v	NOUN
cana-5359	192	3	)	)	PUNCT
cana-5359	192	4	let	let	VERB
cana-5359	192	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	192	6	:	:	PUNCT
cana-5359	192	7	(	(	PUNCT
cana-5359	192	8	𝑋1	𝑋1	PROPN
cana-5359	192	9	,	,	PUNCT
cana-5359	192	10	𝜏1	𝜏1	NOUN
cana-5359	192	11	)	)	PUNCT
cana-5359	192	12	→	→	SYM
cana-5359	192	13	(	(	PUNCT
cana-5359	192	14	𝑋2	𝑋2	PROPN
cana-5359	192	15	,	,	PUNCT
cana-5359	192	16	𝜏2	𝜏2	PROPN
cana-5359	192	17	)	)	PUNCT
cana-5359	192	18	be	be	VERB
cana-5359	192	19	a	a	DET
cana-5359	192	20	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	NOUN
cana-5359	192	21	let	let	VERB
cana-5359	192	22	𝑆	𝑆	PROPN
cana-5359	192	23	be	be	AUX
cana-5359	192	24	a	a	DET
cana-5359	192	25	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	192	26	set	set	VERB
cana-5359	192	27	in	in	ADP
cana-5359	192	28	(	(	PUNCT
cana-5359	192	29	𝑋2	𝑋2	ADJ
cana-5359	192	30	,	,	PUNCT
cana-5359	192	31	𝜏2	𝜏2	PROPN
cana-5359	192	32	)	)	PUNCT
cana-5359	192	33	.	.	PUNCT
cana-5359	193	1	then	then	ADV
cana-5359	193	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	193	3	−1(𝑆	−1(𝑆	PART
cana-5359	193	4	)	)	PUNCT
cana-5359	193	5	is	be	AUX
cana-5359	193	6	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	NOUN
cana-5359	193	7	set	set	VERB
cana-5359	193	8	in	in	ADP
cana-5359	193	9	(	(	PUNCT
cana-5359	193	10	𝑋1	𝑋1	PROPN
cana-5359	193	11	,	,	PUNCT
cana-5359	193	12	𝜏1	𝜏1	NOUN
cana-5359	193	13	)	)	PUNCT
cana-5359	193	14	.	.	PUNCT
cana-5359	194	1	since	since	SCONJ
cana-5359	194	2	every	every	DET
cana-5359	194	3	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	NOUN
cana-5359	194	4	set	set	VERB
cana-5359	194	5	is	be	AUX
cana-5359	194	6	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	194	7	,	,	PUNCT
cana-5359	194	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	194	9	−1(𝑆	−1(𝑆	PART
cana-5359	194	10	)	)	PUNCT
cana-5359	194	11	is	be	AUX
cana-5359	194	12	𝔉ℱ𝛿𝛽𝑜	𝔉ℱ𝛿𝛽𝑜	PROPN
cana-5359	194	13	set	set	VERB
cana-5359	194	14	in	in	ADP
cana-5359	194	15	(	(	PUNCT
cana-5359	194	16	𝑋1	𝑋1	PROPN
cana-5359	194	17	,	,	PUNCT
cana-5359	194	18	𝜏1	𝜏1	NOUN
cana-5359	194	19	)	)	PUNCT
cana-5359	194	20	.	.	PUNCT
cana-5359	195	1	hence	hence	ADV
cana-5359	195	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	195	3	is	be	AUX
cana-5359	195	4	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	195	5	function	function	NOUN
cana-5359	195	6	.	.	PUNCT
cana-5359	196	1	(	(	PUNCT
cana-5359	196	2	vi	vi	X
cana-5359	196	3	)	)	PUNCT
cana-5359	196	4	let	let	VERB
cana-5359	196	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	196	6	:	:	PUNCT
cana-5359	196	7	(	(	PUNCT
cana-5359	196	8	𝑋1	𝑋1	PROPN
cana-5359	196	9	,	,	PUNCT
cana-5359	196	10	𝜏1	𝜏1	NOUN
cana-5359	196	11	)	)	PUNCT
cana-5359	196	12	→	→	SYM
cana-5359	196	13	(	(	PUNCT
cana-5359	196	14	𝑋2	𝑋2	PROPN
cana-5359	196	15	,	,	PUNCT
cana-5359	196	16	𝜏2	𝜏2	PROPN
cana-5359	196	17	)	)	PUNCT
cana-5359	196	18	be	be	VERB
cana-5359	196	19	a	a	DET
cana-5359	196	20	𝔉ℱ𝛿𝛼𝐶𝑡𝑠.	𝔉ℱ𝛿𝛼𝐶𝑡𝑠.	PRON
cana-5359	196	21	let	let	VERB
cana-5359	196	22	𝑆	𝑆	PROPN
cana-5359	196	23	be	be	AUX
cana-5359	196	24	a	a	DET
cana-5359	196	25	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	196	26	set	set	VERB
cana-5359	196	27	in	in	ADP
cana-5359	196	28	(	(	PUNCT
cana-5359	196	29	𝑋2	𝑋2	ADJ
cana-5359	196	30	,	,	PUNCT
cana-5359	196	31	𝜏2	𝜏2	PROPN
cana-5359	196	32	)	)	PUNCT
cana-5359	196	33	.	.	PUNCT
cana-5359	197	1	then	then	ADV
cana-5359	197	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	197	3	−1(𝑆	−1(𝑆	PART
cana-5359	197	4	)	)	PUNCT
cana-5359	197	5	is	be	AUX
cana-5359	197	6	𝔉ℱ𝛿𝛼𝑜	𝔉ℱ𝛿𝛼𝑜	PROPN
cana-5359	197	7	set	set	VERB
cana-5359	197	8	in	in	ADP
cana-5359	197	9	(	(	PUNCT
cana-5359	197	10	𝑋1	𝑋1	PROPN
cana-5359	197	11	,	,	PUNCT
cana-5359	197	12	𝜏1	𝜏1	NOUN
cana-5359	197	13	)	)	PUNCT
cana-5359	197	14	.	.	PUNCT
cana-5359	198	1	since	since	SCONJ
cana-5359	198	2	every	every	DET
cana-5359	198	3	𝔉ℱ𝛿𝛼𝑜	𝔉ℱ𝛿𝛼𝑜	PROPN
cana-5359	198	4	set	set	VERB
cana-5359	198	5	is	be	AUX
cana-5359	198	6	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	198	7	,	,	PUNCT
cana-5359	198	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	198	9	−1(𝑆	−1(𝑆	PART
cana-5359	198	10	)	)	PUNCT
cana-5359	198	11	is	be	AUX
cana-5359	198	12	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	NOUN
cana-5359	198	13	set	set	VERB
cana-5359	198	14	in	in	ADP
cana-5359	198	15	(	(	PUNCT
cana-5359	198	16	𝑋1	𝑋1	PROPN
cana-5359	198	17	,	,	PUNCT
cana-5359	198	18	𝜏1	𝜏1	NOUN
cana-5359	198	19	)	)	PUNCT
cana-5359	198	20	.	.	PUNCT
cana-5359	199	1	hence	hence	ADV
cana-5359	199	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	199	3	is	be	AUX
cana-5359	199	4	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	NOUN
cana-5359	199	5	function	function	NOUN
cana-5359	199	6	.	.	PUNCT
cana-5359	200	1	(	(	PUNCT
cana-5359	200	2	vii	vii	PROPN
cana-5359	200	3	)	)	PUNCT
cana-5359	200	4	let	let	VERB
cana-5359	200	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	200	6	:	:	PUNCT
cana-5359	200	7	(	(	PUNCT
cana-5359	200	8	𝑋1	𝑋1	PROPN
cana-5359	200	9	,	,	PUNCT
cana-5359	200	10	𝜏1	𝜏1	NOUN
cana-5359	200	11	)	)	PUNCT
cana-5359	200	12	→	→	SYM
cana-5359	200	13	(	(	PUNCT
cana-5359	200	14	𝑋2	𝑋2	PROPN
cana-5359	200	15	,	,	PUNCT
cana-5359	200	16	𝜏2	𝜏2	PROPN
cana-5359	200	17	)	)	PUNCT
cana-5359	200	18	be	be	VERB
cana-5359	200	19	a	a	DET
cana-5359	200	20	𝔉ℱ𝛿𝛼𝐶𝑡𝑠.	𝔉ℱ𝛿𝛼𝐶𝑡𝑠.	PRON
cana-5359	200	21	let	let	VERB
cana-5359	200	22	𝑆	𝑆	PROPN
cana-5359	200	23	be	be	AUX
cana-5359	200	24	a	a	DET
cana-5359	200	25	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	200	26	set	set	VERB
cana-5359	200	27	in	in	ADP
cana-5359	200	28	(	(	PUNCT
cana-5359	200	29	𝑋2	𝑋2	ADJ
cana-5359	200	30	,	,	PUNCT
cana-5359	200	31	𝜏2	𝜏2	PROPN
cana-5359	200	32	)	)	PUNCT
cana-5359	200	33	.	.	PUNCT
cana-5359	201	1	then	then	ADV
cana-5359	201	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	201	3	−1(𝑆	−1(𝑆	PART
cana-5359	201	4	)	)	PUNCT
cana-5359	201	5	is	be	AUX
cana-5359	201	6	𝔉ℱ𝛿𝛼𝑜	𝔉ℱ𝛿𝛼𝑜	PROPN
cana-5359	201	7	set	set	VERB
cana-5359	201	8	in	in	ADP
cana-5359	201	9	(	(	PUNCT
cana-5359	201	10	𝑋1	𝑋1	PROPN
cana-5359	201	11	,	,	PUNCT
cana-5359	201	12	𝜏1	𝜏1	NOUN
cana-5359	201	13	)	)	PUNCT
cana-5359	201	14	.	.	PUNCT
cana-5359	202	1	since	since	SCONJ
cana-5359	202	2	every	every	DET
cana-5359	202	3	𝔉ℱ𝛿𝛼𝑜	𝔉ℱ𝛿𝛼𝑜	PROPN
cana-5359	202	4	set	set	VERB
cana-5359	202	5	is	be	AUX
cana-5359	202	6	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	202	7	,	,	PUNCT
cana-5359	202	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	202	9	−1(𝑆	−1(𝑆	PART
cana-5359	202	10	)	)	PUNCT
cana-5359	202	11	is	be	AUX
cana-5359	202	12	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	NUM
cana-5359	202	13	set	set	NOUN
cana-5359	202	14	in	in	ADP
cana-5359	202	15	(	(	PUNCT
cana-5359	202	16	𝑋1	𝑋1	PROPN
cana-5359	202	17	,	,	PUNCT
cana-5359	202	18	𝜏1	𝜏1	NOUN
cana-5359	202	19	)	)	PUNCT
cana-5359	202	20	.	.	PUNCT
cana-5359	203	1	hence	hence	ADV
cana-5359	203	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	203	3	is	be	AUX
cana-5359	203	4	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5359	203	5	function	function	NOUN
cana-5359	203	6	.	.	PUNCT
cana-5359	204	1	remark	remark	VERB
cana-5359	204	2	3.1	3.1	NUM
cana-5359	204	3	the	the	DET
cana-5359	204	4	following	follow	VERB
cana-5359	204	5	figure	figure	NOUN
cana-5359	204	6	shows	show	VERB
cana-5359	204	7	the	the	DET
cana-5359	204	8	relations	relation	NOUN
cana-5359	204	9	among	among	ADP
cana-5359	204	10	the	the	DET
cana-5359	204	11	different	different	ADJ
cana-5359	204	12	types	type	NOUN
cana-5359	204	13	of	of	ADP
cana-5359	204	14	fermatean	fermatean	ADJ
cana-5359	204	15	fuzzy	fuzzy	ADJ
cana-5359	204	16	δ	δ	PROPN
cana-5359	204	17	continuous	continuous	ADJ
cana-5359	204	18	mappings	mapping	NOUN
cana-5359	204	19	that	that	PRON
cana-5359	204	20	were	be	AUX
cana-5359	204	21	studied	study	VERB
cana-5359	204	22	in	in	ADP
cana-5359	204	23	this	this	DET
cana-5359	204	24	section	section	NOUN
cana-5359	204	25	.	.	PUNCT
cana-5359	205	1	figure	figure	NOUN
cana-5359	205	2	:	:	PUNCT
cana-5359	205	3	𝕱𝓕𝜹𝑪𝒕𝒔	𝕱𝓕𝜹𝑪𝒕𝒔	X
cana-5359	205	4	mappings	mapping	NOUN
cana-5359	205	5	in	in	ADP
cana-5359	205	6	𝕱𝓕𝒕𝒔	𝕱𝓕𝒕𝒔	PROPN
cana-5359	205	7	example	example	NOUN
cana-5359	205	8	3.1	3.1	NUM
cana-5359	205	9	let	let	VERB
cana-5359	205	10	𝑋1	𝑋1	NOUN
cana-5359	205	11	=	=	SYM
cana-5359	205	12	𝑋2	𝑋2	VERB
cana-5359	205	13	=	=	SYM
cana-5359	205	14	𝑋	𝑋	NOUN
cana-5359	205	15	=	=	PUNCT
cana-5359	205	16	{	{	PUNCT
cana-5359	205	17	𝑎	𝑎	NOUN
cana-5359	205	18	,	,	PUNCT
cana-5359	205	19	𝑏	𝑏	NOUN
cana-5359	205	20	}	}	PUNCT
cana-5359	205	21	and	and	CCONJ
cana-5359	205	22	the	the	DET
cana-5359	205	23	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	205	24	’s	’s	PART
cana-5359	205	25	𝐴1	𝐴1	PROPN
cana-5359	205	26	and	and	CCONJ
cana-5359	205	27	𝐴2	𝐴2	PROPN
cana-5359	205	28	are	be	AUX
cana-5359	205	29	defined	define	VERB
cana-5359	205	30	as	as	ADP
cana-5359	205	31	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	205	32	(	(	PUNCT
cana-5359	205	33	𝑎	𝑎	NOUN
cana-5359	205	34	)	)	PUNCT
cana-5359	205	35	=	=	SYM
cana-5359	205	36	0.4	0.4	NUM
cana-5359	205	37	,	,	PUNCT
cana-5359	205	38	𝛽𝐴1	𝛽𝐴1	X
cana-5359	205	39	(	(	PUNCT
cana-5359	205	40	𝑎	𝑎	NOUN
cana-5359	205	41	)	)	PUNCT
cana-5359	205	42	=	=	SYM
cana-5359	205	43	0.1	0.1	NUM
cana-5359	205	44	,	,	PUNCT
cana-5359	205	45	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	205	46	(	(	PUNCT
cana-5359	205	47	𝑏	𝑏	NOUN
cana-5359	205	48	)	)	PUNCT
cana-5359	205	49	=	=	SYM
cana-5359	205	50	0.6	0.6	NUM
cana-5359	205	51	,	,	PUNCT
cana-5359	205	52	𝛽𝐴1	𝛽𝐴1	PROPN
cana-5359	205	53	(	(	PUNCT
cana-5359	205	54	𝑏	𝑏	NOUN
cana-5359	205	55	)	)	PUNCT
cana-5359	205	56	=	=	SYM
cana-5359	205	57	0.3	0.3	NUM
cana-5359	205	58	;	;	PUNCT
cana-5359	205	59	𝛼𝐴2	𝛼𝐴2	NUM
cana-5359	205	60	(	(	PUNCT
cana-5359	205	61	𝑎	𝑎	NOUN
cana-5359	205	62	)	)	PUNCT
cana-5359	205	63	=	=	SYM
cana-5359	205	64	0.9	0.9	NUM
cana-5359	205	65	,	,	PUNCT
cana-5359	205	66	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	205	67	(	(	PUNCT
cana-5359	205	68	𝑎	𝑎	NOUN
cana-5359	205	69	)	)	PUNCT
cana-5359	205	70	=	=	SYM
cana-5359	205	71	0.2	0.2	NUM
cana-5359	205	72	,	,	PUNCT
cana-5359	205	73	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5359	205	74	(	(	PUNCT
cana-5359	205	75	𝑏	𝑏	NOUN
cana-5359	205	76	)	)	PUNCT
cana-5359	205	77	=	=	SYM
cana-5359	205	78	0.6	0.6	NUM
cana-5359	205	79	,	,	PUNCT
cana-5359	205	80	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	205	81	(	(	PUNCT
cana-5359	205	82	𝑏	𝑏	NOUN
cana-5359	205	83	)	)	PUNCT
cana-5359	205	84	=	=	SYM
cana-5359	205	85	0.3	0.3	NUM
cana-5359	205	86	;	;	PUNCT
cana-5359	205	87	let	let	VERB
cana-5359	205	88	𝜏1	𝜏1	NOUN
cana-5359	205	89	=	=	SYM
cana-5359	205	90	𝜏2	𝜏2	NOUN
cana-5359	205	91	=	=	SYM
cana-5359	205	92	𝜏	𝜏	PROPN
cana-5359	205	93	=	=	PUNCT
cana-5359	205	94	{	{	PUNCT
cana-5359	205	95	0𝔉	0𝔉	PROPN
cana-5359	205	96	,	,	PUNCT
cana-5359	205	97	1𝔉	1𝔉	NOUN
cana-5359	205	98	,	,	PUNCT
cana-5359	205	99	𝐴1	𝐴1	PROPN
cana-5359	205	100	,	,	PUNCT
cana-5359	205	101	𝐴2	𝐴2	PROPN
cana-5359	205	102	}	}	PUNCT
cana-5359	205	103	be	be	VERB
cana-5359	205	104	a	a	DET
cana-5359	205	105	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	205	106	on	on	ADP
cana-5359	205	107	𝑋	𝑋	NOUN
cana-5359	205	108	and	and	CCONJ
cana-5359	205	109	let	let	VERB
cana-5359	205	110	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	205	111	:	:	PUNCT
cana-5359	205	112	(	(	PUNCT
cana-5359	205	113	𝑋1	𝑋1	PROPN
cana-5359	205	114	,	,	PUNCT
cana-5359	205	115	𝜏1	𝜏1	NOUN
cana-5359	205	116	)	)	PUNCT
cana-5359	205	117	→	→	SYM
cana-5359	205	118	(	(	PUNCT
cana-5359	205	119	𝑋2	𝑋2	PROPN
cana-5359	205	120	,	,	PUNCT
cana-5359	205	121	𝜏2	𝜏2	PROPN
cana-5359	205	122	)	)	PUNCT
cana-5359	205	123	be	be	VERB
cana-5359	205	124	an	an	DET
cana-5359	205	125	identity	identity	NOUN
cana-5359	205	126	function	function	NOUN
cana-5359	205	127	,	,	PUNCT
cana-5359	205	128	then	then	ADV
cana-5359	205	129	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	205	130	is	be	AUX
cana-5359	205	131	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	PUNCT
cana-5359	205	132	(	(	PUNCT
cana-5359	205	133	resp	resp	NOUN
cana-5359	205	134	.	.	PUNCT
cana-5359	206	1	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5359	206	2	)	)	PUNCT
cana-5359	206	3	but	but	CCONJ
cana-5359	206	4	not	not	PART
cana-5359	206	5	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	PUNCT
cana-5359	206	6	(	(	PUNCT
cana-5359	206	7	resp	resp	NOUN
cana-5359	206	8	.	.	PUNCT
cana-5359	206	9	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5359	206	10	)	)	PUNCT
cana-5359	206	11	.	.	PUNCT
cana-5359	207	1	since	since	SCONJ
cana-5359	207	2	,	,	PUNCT
cana-5359	207	3	𝐴2	𝐴2	PROPN
cana-5359	207	4	is	be	AUX
cana-5359	207	5	a	a	DET
cana-5359	207	6	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	207	7	set	set	VERB
cana-5359	207	8	in	in	ADP
cana-5359	207	9	𝑋2	𝑋2	ADJ
cana-5359	207	10	but	but	CCONJ
cana-5359	207	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	207	12	−1(𝐴2	−1(𝐴2	NOUN
cana-5359	207	13	)	)	PUNCT
cana-5359	208	1	=	=	SYM
cana-5359	208	2	𝐴2	𝐴2	NOUN
cana-5359	208	3	is	be	AUX
cana-5359	208	4	not	not	PART
cana-5359	208	5	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	208	6	(	(	PUNCT
cana-5359	208	7	resp	resp	NOUN
cana-5359	208	8	.	.	PUNCT
cana-5359	209	1	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	NOUN
cana-5359	209	2	)	)	PUNCT
cana-5359	210	1	set	set	VERB
cana-5359	210	2	in	in	ADP
cana-5359	210	3	𝑋1	𝑋1	PROPN
cana-5359	210	4	.	.	PUNCT
cana-5359	211	1	communications	communication	NOUN
cana-5359	211	2	on	on	ADP
cana-5359	211	3	applied	apply	VERB
cana-5359	211	4	nonlinear	nonlinear	ADJ
cana-5359	211	5	analysis	analysis	NOUN
cana-5359	211	6	issn	issn	NOUN
cana-5359	211	7	:	:	PUNCT
cana-5359	211	8	1074	1074	NUM
cana-5359	211	9	-	-	PUNCT
cana-5359	211	10	133x	133x	NUM
cana-5359	211	11	vol	vol	VERB
cana-5359	211	12	32	32	NUM
cana-5359	211	13	no	no	NOUN
cana-5359	211	14	.	.	PUNCT
cana-5359	212	1	10s	10	NOUN
cana-5359	212	2	(	(	PUNCT
cana-5359	212	3	2025	2025	NUM
cana-5359	212	4	)	)	PUNCT
cana-5359	212	5	1916	1916	NUM
cana-5359	212	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	212	7	example	example	NOUN
cana-5359	212	8	3.2	3.2	NUM
cana-5359	212	9	let	let	VERB
cana-5359	212	10	𝑋1	𝑋1	NOUN
cana-5359	212	11	=	=	SYM
cana-5359	212	12	𝑋2	𝑋2	VERB
cana-5359	212	13	=	=	SYM
cana-5359	212	14	𝑋	𝑋	NOUN
cana-5359	212	15	=	=	PUNCT
cana-5359	212	16	{	{	PUNCT
cana-5359	212	17	𝑎	𝑎	NOUN
cana-5359	212	18	,	,	PUNCT
cana-5359	212	19	𝑏	𝑏	NOUN
cana-5359	212	20	}	}	PUNCT
cana-5359	212	21	and	and	CCONJ
cana-5359	212	22	the	the	DET
cana-5359	212	23	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	212	24	’s	’s	PART
cana-5359	212	25	𝐴1	𝐴1	PROPN
cana-5359	212	26	,	,	PUNCT
cana-5359	212	27	𝐴2	𝐴2	PROPN
cana-5359	212	28	and	and	CCONJ
cana-5359	212	29	𝐴3	𝐴3	PROPN
cana-5359	212	30	are	be	AUX
cana-5359	212	31	defined	define	VERB
cana-5359	212	32	as	as	ADP
cana-5359	212	33	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	212	34	(	(	PUNCT
cana-5359	212	35	𝑎	𝑎	NOUN
cana-5359	212	36	)	)	PUNCT
cana-5359	212	37	=	=	SYM
cana-5359	212	38	0.2	0.2	NUM
cana-5359	212	39	,	,	PUNCT
cana-5359	212	40	𝛽𝐴1	𝛽𝐴1	X
cana-5359	212	41	(	(	PUNCT
cana-5359	212	42	𝑎	𝑎	NOUN
cana-5359	212	43	)	)	PUNCT
cana-5359	212	44	=	=	SYM
cana-5359	212	45	0.8	0.8	NUM
cana-5359	212	46	,	,	PUNCT
cana-5359	212	47	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	212	48	(	(	PUNCT
cana-5359	212	49	𝑏	𝑏	NOUN
cana-5359	212	50	)	)	PUNCT
cana-5359	212	51	=	=	SYM
cana-5359	212	52	0.3	0.3	NUM
cana-5359	212	53	,	,	PUNCT
cana-5359	212	54	𝛽𝐴1	𝛽𝐴1	PROPN
cana-5359	212	55	(	(	PUNCT
cana-5359	212	56	𝑏	𝑏	NOUN
cana-5359	212	57	)	)	PUNCT
cana-5359	212	58	=	=	SYM
cana-5359	212	59	0.7	0.7	NUM
cana-5359	212	60	;	;	PUNCT
cana-5359	212	61	𝛼𝐴2	𝛼𝐴2	NUM
cana-5359	212	62	(	(	PUNCT
cana-5359	212	63	𝑎	𝑎	NOUN
cana-5359	212	64	)	)	PUNCT
cana-5359	212	65	=	=	SYM
cana-5359	212	66	0.1	0.1	NUM
cana-5359	212	67	,	,	PUNCT
cana-5359	212	68	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	212	69	(	(	PUNCT
cana-5359	212	70	𝑎	𝑎	NOUN
cana-5359	212	71	)	)	PUNCT
cana-5359	212	72	=	=	SYM
cana-5359	212	73	0.9	0.9	NUM
cana-5359	212	74	,	,	PUNCT
cana-5359	212	75	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5359	212	76	(	(	PUNCT
cana-5359	212	77	𝑏	𝑏	NOUN
cana-5359	212	78	)	)	PUNCT
cana-5359	212	79	=	=	SYM
cana-5359	212	80	0.1	0.1	NUM
cana-5359	212	81	,	,	PUNCT
cana-5359	212	82	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	212	83	(	(	PUNCT
cana-5359	212	84	𝑏	𝑏	NOUN
cana-5359	212	85	)	)	PUNCT
cana-5359	212	86	=	=	SYM
cana-5359	212	87	0.9	0.9	NUM
cana-5359	212	88	;	;	PUNCT
cana-5359	212	89	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	212	90	(	(	PUNCT
cana-5359	212	91	𝑎	𝑎	NOUN
cana-5359	212	92	)	)	PUNCT
cana-5359	212	93	=	=	SYM
cana-5359	212	94	0.2	0.2	NUM
cana-5359	212	95	,	,	PUNCT
cana-5359	212	96	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	212	97	(	(	PUNCT
cana-5359	212	98	𝑎	𝑎	NOUN
cana-5359	212	99	)	)	PUNCT
cana-5359	212	100	=	=	SYM
cana-5359	212	101	0.8	0.8	NUM
cana-5359	212	102	,	,	PUNCT
cana-5359	212	103	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	212	104	(	(	PUNCT
cana-5359	212	105	𝑏	𝑏	NOUN
cana-5359	212	106	)	)	PUNCT
cana-5359	212	107	=	=	SYM
cana-5359	212	108	0.4	0.4	NUM
cana-5359	212	109	,	,	PUNCT
cana-5359	212	110	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	212	111	(	(	PUNCT
cana-5359	212	112	𝑏	𝑏	NOUN
cana-5359	212	113	)	)	PUNCT
cana-5359	212	114	=	=	SYM
cana-5359	212	115	0.6	0.6	NUM
cana-5359	212	116	;	;	PUNCT
cana-5359	212	117	let	let	VERB
cana-5359	212	118	𝜏1	𝜏1	NOUN
cana-5359	212	119	=	=	SYM
cana-5359	212	120	𝜏2	𝜏2	NOUN
cana-5359	212	121	=	=	SYM
cana-5359	212	122	𝜏	𝜏	PROPN
cana-5359	212	123	=	=	PUNCT
cana-5359	212	124	{	{	PUNCT
cana-5359	212	125	0𝔉	0𝔉	PROPN
cana-5359	212	126	,	,	PUNCT
cana-5359	212	127	1𝔉	1𝔉	NOUN
cana-5359	212	128	,	,	PUNCT
cana-5359	212	129	𝐴1	𝐴1	PROPN
cana-5359	212	130	,	,	PUNCT
cana-5359	212	131	𝐴2	𝐴2	PROPN
cana-5359	212	132	,	,	PUNCT
cana-5359	212	133	𝐴3	𝐴3	PROPN
cana-5359	212	134	}	}	PUNCT
cana-5359	212	135	be	be	VERB
cana-5359	212	136	a	a	DET
cana-5359	212	137	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	212	138	on	on	ADP
cana-5359	212	139	𝑋	𝑋	NOUN
cana-5359	212	140	and	and	CCONJ
cana-5359	212	141	let	let	VERB
cana-5359	212	142	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	212	143	:	:	PUNCT
cana-5359	212	144	(	(	PUNCT
cana-5359	212	145	𝑋1	𝑋1	PROPN
cana-5359	212	146	,	,	PUNCT
cana-5359	212	147	𝜏1	𝜏1	NOUN
cana-5359	212	148	)	)	PUNCT
cana-5359	212	149	→	→	SYM
cana-5359	212	150	(	(	PUNCT
cana-5359	212	151	𝑋2	𝑋2	PROPN
cana-5359	212	152	,	,	PUNCT
cana-5359	212	153	𝜏2	𝜏2	PROPN
cana-5359	212	154	)	)	PUNCT
cana-5359	212	155	be	be	VERB
cana-5359	212	156	an	an	DET
cana-5359	212	157	identity	identity	NOUN
cana-5359	212	158	function	function	NOUN
cana-5359	212	159	,	,	PUNCT
cana-5359	212	160	then	then	ADV
cana-5359	212	161	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	212	162	is	be	AUX
cana-5359	212	163	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5359	212	164	(	(	PUNCT
cana-5359	212	165	resp	resp	PROPN
cana-5359	212	166	.	.	PUNCT
cana-5359	212	167	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5359	212	168	)	)	PUNCT
cana-5359	212	169	but	but	CCONJ
cana-5359	212	170	not	not	PART
cana-5359	212	171	𝔉ℱ𝛿𝐶𝑡𝑠.	𝔉ℱ𝛿𝐶𝑡𝑠.	PUNCT
cana-5359	212	172	since	since	ADV
cana-5359	212	173	,	,	PUNCT
cana-5359	212	174	𝐴1	𝐴1	PROPN
cana-5359	212	175	is	be	AUX
cana-5359	212	176	a	a	DET
cana-5359	212	177	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	212	178	set	set	VERB
cana-5359	212	179	in	in	ADP
cana-5359	212	180	𝑋2	𝑋2	ADJ
cana-5359	212	181	but	but	CCONJ
cana-5359	212	182	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	212	183	−1(𝐴1	−1(𝐴1	VERB
cana-5359	212	184	)	)	PUNCT
cana-5359	212	185	=	=	SYM
cana-5359	213	1	𝐴1	𝐴1	PROPN
cana-5359	213	2	is	be	AUX
cana-5359	213	3	not	not	PART
cana-5359	213	4	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	213	5	set	set	VERB
cana-5359	213	6	in	in	ADP
cana-5359	213	7	𝑋1	𝑋1	PROPN
cana-5359	213	8	.	.	PUNCT
cana-5359	214	1	example	example	NOUN
cana-5359	214	2	3.3	3.3	NUM
cana-5359	214	3	let	let	VERB
cana-5359	214	4	𝑋1	𝑋1	NOUN
cana-5359	214	5	=	=	SYM
cana-5359	214	6	𝑋2	𝑋2	VERB
cana-5359	214	7	=	=	SYM
cana-5359	214	8	𝑋	𝑋	NOUN
cana-5359	214	9	=	=	PUNCT
cana-5359	214	10	{	{	PUNCT
cana-5359	214	11	𝑎	𝑎	NOUN
cana-5359	214	12	,	,	PUNCT
cana-5359	214	13	𝑏	𝑏	NOUN
cana-5359	214	14	}	}	PUNCT
cana-5359	214	15	and	and	CCONJ
cana-5359	214	16	the	the	DET
cana-5359	214	17	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	214	18	’s	’s	PART
cana-5359	214	19	𝐴1	𝐴1	PROPN
cana-5359	214	20	,	,	PUNCT
cana-5359	214	21	𝐴2	𝐴2	PROPN
cana-5359	214	22	and	and	CCONJ
cana-5359	214	23	𝐴3	𝐴3	PROPN
cana-5359	214	24	are	be	AUX
cana-5359	214	25	defined	define	VERB
cana-5359	214	26	as	as	ADP
cana-5359	214	27	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	214	28	(	(	PUNCT
cana-5359	214	29	𝑎	𝑎	NOUN
cana-5359	214	30	)	)	PUNCT
cana-5359	214	31	=	=	SYM
cana-5359	214	32	0.2	0.2	NUM
cana-5359	214	33	,	,	PUNCT
cana-5359	214	34	𝛽𝐴1	𝛽𝐴1	X
cana-5359	214	35	(	(	PUNCT
cana-5359	214	36	𝑎	𝑎	NOUN
cana-5359	214	37	)	)	PUNCT
cana-5359	214	38	=	=	SYM
cana-5359	214	39	0.6	0.6	NUM
cana-5359	214	40	,	,	PUNCT
cana-5359	214	41	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	214	42	(	(	PUNCT
cana-5359	214	43	𝑏	𝑏	NOUN
cana-5359	214	44	)	)	PUNCT
cana-5359	214	45	=	=	SYM
cana-5359	214	46	0.3	0.3	NUM
cana-5359	214	47	,	,	PUNCT
cana-5359	214	48	𝛽𝐴1	𝛽𝐴1	PROPN
cana-5359	214	49	(	(	PUNCT
cana-5359	214	50	𝑏	𝑏	NOUN
cana-5359	214	51	)	)	PUNCT
cana-5359	215	1	=	=	NOUN
cana-5359	215	2	0.5	0.5	NUM
cana-5359	215	3	;	;	PUNCT
cana-5359	215	4	𝛼𝐴2	𝛼𝐴2	NUM
cana-5359	215	5	(	(	PUNCT
cana-5359	215	6	𝑎	𝑎	NOUN
cana-5359	215	7	)	)	PUNCT
cana-5359	215	8	=	=	SYM
cana-5359	215	9	0.6	0.6	NUM
cana-5359	215	10	,	,	PUNCT
cana-5359	215	11	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	215	12	(	(	PUNCT
cana-5359	215	13	𝑎	𝑎	NOUN
cana-5359	215	14	)	)	PUNCT
cana-5359	215	15	=	=	SYM
cana-5359	215	16	0.2	0.2	NUM
cana-5359	215	17	,	,	PUNCT
cana-5359	215	18	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5359	215	19	(	(	PUNCT
cana-5359	215	20	𝑏	𝑏	NOUN
cana-5359	215	21	)	)	PUNCT
cana-5359	215	22	=	=	SYM
cana-5359	215	23	0.5	0.5	NUM
cana-5359	215	24	,	,	PUNCT
cana-5359	215	25	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	215	26	(	(	PUNCT
cana-5359	215	27	𝑏	𝑏	NOUN
cana-5359	215	28	)	)	PUNCT
cana-5359	215	29	=	=	SYM
cana-5359	215	30	0.3	0.3	NUM
cana-5359	215	31	;	;	PUNCT
cana-5359	215	32	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	215	33	(	(	PUNCT
cana-5359	215	34	𝑎	𝑎	NOUN
cana-5359	215	35	)	)	PUNCT
cana-5359	215	36	=	=	SYM
cana-5359	215	37	0.6	0.6	NUM
cana-5359	215	38	,	,	PUNCT
cana-5359	215	39	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	215	40	(	(	PUNCT
cana-5359	215	41	𝑎	𝑎	NOUN
cana-5359	215	42	)	)	PUNCT
cana-5359	215	43	=	=	SYM
cana-5359	215	44	0.6	0.6	NUM
cana-5359	215	45	,	,	PUNCT
cana-5359	215	46	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	215	47	(	(	PUNCT
cana-5359	215	48	𝑏	𝑏	NOUN
cana-5359	215	49	)	)	PUNCT
cana-5359	215	50	=	=	SYM
cana-5359	215	51	0.5	0.5	NUM
cana-5359	215	52	,	,	PUNCT
cana-5359	215	53	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	215	54	(	(	PUNCT
cana-5359	215	55	𝑏	𝑏	NOUN
cana-5359	215	56	)	)	PUNCT
cana-5359	216	1	=	=	NOUN
cana-5359	216	2	0.5	0.5	NUM
cana-5359	216	3	;	;	PUNCT
cana-5359	216	4	let	let	VERB
cana-5359	216	5	𝜏1	𝜏1	NOUN
cana-5359	216	6	=	=	SYM
cana-5359	216	7	𝜏2	𝜏2	NOUN
cana-5359	216	8	=	=	SYM
cana-5359	216	9	𝜏	𝜏	PROPN
cana-5359	216	10	=	=	PUNCT
cana-5359	216	11	{	{	PUNCT
cana-5359	216	12	0𝔉	0𝔉	PROPN
cana-5359	216	13	,	,	PUNCT
cana-5359	216	14	1𝔉	1𝔉	NOUN
cana-5359	216	15	,	,	PUNCT
cana-5359	216	16	𝐴1	𝐴1	PROPN
cana-5359	216	17	,	,	PUNCT
cana-5359	216	18	𝐴2	𝐴2	PROPN
cana-5359	216	19	,	,	PUNCT
cana-5359	216	20	𝐴3	𝐴3	PROPN
cana-5359	216	21	}	}	PUNCT
cana-5359	216	22	be	be	VERB
cana-5359	216	23	a	a	DET
cana-5359	216	24	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	216	25	on	on	ADP
cana-5359	216	26	𝑋	𝑋	NOUN
cana-5359	216	27	and	and	CCONJ
cana-5359	216	28	let	let	VERB
cana-5359	216	29	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	216	30	:	:	PUNCT
cana-5359	216	31	(	(	PUNCT
cana-5359	216	32	𝑋1	𝑋1	PROPN
cana-5359	216	33	,	,	PUNCT
cana-5359	216	34	𝜏1	𝜏1	NOUN
cana-5359	216	35	)	)	PUNCT
cana-5359	216	36	→	→	SYM
cana-5359	216	37	(	(	PUNCT
cana-5359	216	38	𝑋2	𝑋2	PROPN
cana-5359	216	39	,	,	PUNCT
cana-5359	216	40	𝜏2	𝜏2	PROPN
cana-5359	216	41	)	)	PUNCT
cana-5359	216	42	be	be	VERB
cana-5359	216	43	an	an	DET
cana-5359	216	44	identity	identity	NOUN
cana-5359	216	45	function	function	NOUN
cana-5359	216	46	,	,	PUNCT
cana-5359	216	47	then	then	ADV
cana-5359	216	48	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	216	49	is	be	AUX
cana-5359	216	50	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5359	216	51	(	(	PUNCT
cana-5359	216	52	resp	resp	PROPN
cana-5359	216	53	.	.	PUNCT
cana-5359	216	54	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5359	216	55	)	)	PUNCT
cana-5359	216	56	but	but	CCONJ
cana-5359	216	57	not	not	PART
cana-5359	216	58	𝔉ℱ𝛼𝐶𝑡𝑠.	𝔉ℱ𝛼𝐶𝑡𝑠.	PUNCT
cana-5359	216	59	since	since	SCONJ
cana-5359	216	60	,	,	PUNCT
cana-5359	216	61	𝐴3	𝐴3	PROPN
cana-5359	216	62	is	be	AUX
cana-5359	216	63	a	a	DET
cana-5359	216	64	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	216	65	set	set	VERB
cana-5359	216	66	in	in	ADP
cana-5359	216	67	𝑋2	𝑋2	ADJ
cana-5359	216	68	but	but	CCONJ
cana-5359	216	69	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	216	70	−1(𝐴3	−1(𝐴3	NOUN
cana-5359	216	71	)	)	PUNCT
cana-5359	217	1	=	=	PRON
cana-5359	217	2	𝐴3	𝐴3	PROPN
cana-5359	217	3	is	be	AUX
cana-5359	217	4	not	not	PART
cana-5359	217	5	𝔉ℱ𝛼𝑜	𝔉ℱ𝛼𝑜	PROPN
cana-5359	217	6	set	set	VERB
cana-5359	217	7	in	in	ADP
cana-5359	217	8	𝑋1	𝑋1	PROPN
cana-5359	217	9	.	.	PUNCT
cana-5359	218	1	example	example	NOUN
cana-5359	218	2	3.4	3.4	NUM
cana-5359	218	3	let	let	VERB
cana-5359	218	4	𝑋1	𝑋1	NOUN
cana-5359	218	5	=	=	SYM
cana-5359	218	6	𝑋2	𝑋2	VERB
cana-5359	218	7	=	=	SYM
cana-5359	218	8	𝑋	𝑋	NOUN
cana-5359	218	9	=	=	PUNCT
cana-5359	218	10	{	{	PUNCT
cana-5359	218	11	𝑎	𝑎	NOUN
cana-5359	218	12	,	,	PUNCT
cana-5359	218	13	𝑏	𝑏	NOUN
cana-5359	218	14	}	}	PUNCT
cana-5359	218	15	and	and	CCONJ
cana-5359	218	16	the	the	DET
cana-5359	218	17	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	218	18	’s	’s	PART
cana-5359	218	19	𝐴1	𝐴1	PROPN
cana-5359	218	20	,	,	PUNCT
cana-5359	218	21	𝐴2	𝐴2	PROPN
cana-5359	218	22	,	,	PUNCT
cana-5359	218	23	𝐴3	𝐴3	PROPN
cana-5359	218	24	,	,	PUNCT
cana-5359	218	25	𝐴4	𝐴4	PROPN
cana-5359	218	26	,	,	PUNCT
cana-5359	218	27	𝐵1	𝐵1	PROPN
cana-5359	218	28	,	,	PUNCT
cana-5359	218	29	𝐵2	𝐵2	NOUN
cana-5359	218	30	,	,	PUNCT
cana-5359	218	31	𝐵3	𝐵3	NOUN
cana-5359	218	32	and	and	CCONJ
cana-5359	218	33	𝐵4	𝐵4	NOUN
cana-5359	218	34	are	be	AUX
cana-5359	218	35	defined	define	VERB
cana-5359	218	36	as	as	ADP
cana-5359	218	37	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	218	38	(	(	PUNCT
cana-5359	218	39	𝑎	𝑎	NOUN
cana-5359	218	40	)	)	PUNCT
cana-5359	218	41	=	=	SYM
cana-5359	218	42	0.4	0.4	NUM
cana-5359	218	43	,	,	PUNCT
cana-5359	218	44	𝛽𝐴1	𝛽𝐴1	X
cana-5359	218	45	(	(	PUNCT
cana-5359	218	46	𝑎	𝑎	NOUN
cana-5359	218	47	)	)	PUNCT
cana-5359	218	48	=	=	SYM
cana-5359	218	49	0.6	0.6	NUM
cana-5359	218	50	,	,	PUNCT
cana-5359	218	51	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	218	52	(	(	PUNCT
cana-5359	218	53	𝑏	𝑏	NOUN
cana-5359	218	54	)	)	PUNCT
cana-5359	218	55	=	=	SYM
cana-5359	218	56	0.5	0.5	NUM
cana-5359	218	57	,	,	PUNCT
cana-5359	218	58	𝛽𝐴1	𝛽𝐴1	X
cana-5359	218	59	(	(	PUNCT
cana-5359	218	60	𝑏	𝑏	NOUN
cana-5359	218	61	)	)	PUNCT
cana-5359	219	1	=	=	NOUN
cana-5359	219	2	0.5	0.5	NUM
cana-5359	219	3	;	;	PUNCT
cana-5359	219	4	𝛼𝐴2	𝛼𝐴2	NUM
cana-5359	219	5	(	(	PUNCT
cana-5359	219	6	𝑎	𝑎	NOUN
cana-5359	219	7	)	)	PUNCT
cana-5359	219	8	=	=	SYM
cana-5359	219	9	0.6	0.6	NUM
cana-5359	219	10	,	,	PUNCT
cana-5359	219	11	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	219	12	(	(	PUNCT
cana-5359	219	13	𝑎	𝑎	NOUN
cana-5359	219	14	)	)	PUNCT
cana-5359	219	15	=	=	SYM
cana-5359	219	16	0.4	0.4	NUM
cana-5359	219	17	,	,	PUNCT
cana-5359	219	18	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5359	219	19	(	(	PUNCT
cana-5359	219	20	𝑏	𝑏	NOUN
cana-5359	219	21	)	)	PUNCT
cana-5359	219	22	=	=	SYM
cana-5359	219	23	0.6	0.6	NUM
cana-5359	219	24	,	,	PUNCT
cana-5359	219	25	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	219	26	(	(	PUNCT
cana-5359	219	27	𝑏	𝑏	NOUN
cana-5359	219	28	)	)	PUNCT
cana-5359	219	29	=	=	SYM
cana-5359	219	30	0.4	0.4	NUM
cana-5359	219	31	;	;	PUNCT
cana-5359	219	32	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	219	33	(	(	PUNCT
cana-5359	219	34	𝑎	𝑎	NOUN
cana-5359	219	35	)	)	PUNCT
cana-5359	219	36	=	=	SYM
cana-5359	219	37	0.7	0.7	NUM
cana-5359	219	38	,	,	PUNCT
cana-5359	219	39	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	219	40	(	(	PUNCT
cana-5359	219	41	𝑎	𝑎	NOUN
cana-5359	219	42	)	)	PUNCT
cana-5359	219	43	=	=	SYM
cana-5359	219	44	0.3	0.3	NUM
cana-5359	219	45	,	,	PUNCT
cana-5359	219	46	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	219	47	(	(	PUNCT
cana-5359	219	48	𝑏	𝑏	NOUN
cana-5359	219	49	)	)	PUNCT
cana-5359	219	50	=	=	SYM
cana-5359	219	51	0.6	0.6	NUM
cana-5359	219	52	,	,	PUNCT
cana-5359	219	53	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	219	54	(	(	PUNCT
cana-5359	219	55	𝑏	𝑏	NOUN
cana-5359	219	56	)	)	PUNCT
cana-5359	219	57	=	=	SYM
cana-5359	219	58	0.4	0.4	NUM
cana-5359	219	59	;	;	PUNCT
cana-5359	219	60	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5359	219	61	(	(	PUNCT
cana-5359	219	62	𝑎	𝑎	NOUN
cana-5359	219	63	)	)	PUNCT
cana-5359	219	64	=	=	SYM
cana-5359	219	65	0.4	0.4	NUM
cana-5359	219	66	,	,	PUNCT
cana-5359	219	67	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5359	219	68	(	(	PUNCT
cana-5359	219	69	𝑎	𝑎	NOUN
cana-5359	219	70	)	)	PUNCT
cana-5359	219	71	=	=	SYM
cana-5359	219	72	0.6	0.6	NUM
cana-5359	219	73	,	,	PUNCT
cana-5359	219	74	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5359	219	75	(	(	PUNCT
cana-5359	219	76	𝑏	𝑏	NOUN
cana-5359	219	77	)	)	PUNCT
cana-5359	219	78	=	=	SYM
cana-5359	219	79	0.4	0.4	NUM
cana-5359	219	80	,	,	PUNCT
cana-5359	219	81	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5359	219	82	(	(	PUNCT
cana-5359	219	83	𝑏	𝑏	NOUN
cana-5359	219	84	)	)	PUNCT
cana-5359	219	85	=	=	SYM
cana-5359	219	86	0.6	0.6	NUM
cana-5359	219	87	;	;	PUNCT
cana-5359	219	88	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5359	219	89	(	(	PUNCT
cana-5359	219	90	𝑎	𝑎	NOUN
cana-5359	219	91	)	)	PUNCT
cana-5359	219	92	=	=	SYM
cana-5359	219	93	0.2	0.2	NUM
cana-5359	219	94	,	,	PUNCT
cana-5359	219	95	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5359	219	96	(	(	PUNCT
cana-5359	219	97	𝑎	𝑎	NOUN
cana-5359	219	98	)	)	PUNCT
cana-5359	219	99	=	=	SYM
cana-5359	219	100	0.8	0.8	NUM
cana-5359	219	101	,	,	PUNCT
cana-5359	219	102	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5359	219	103	(	(	PUNCT
cana-5359	219	104	𝑏	𝑏	NOUN
cana-5359	219	105	)	)	PUNCT
cana-5359	219	106	=	=	SYM
cana-5359	219	107	0.4	0.4	NUM
cana-5359	219	108	,	,	PUNCT
cana-5359	219	109	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5359	219	110	(	(	PUNCT
cana-5359	219	111	𝑏	𝑏	NOUN
cana-5359	219	112	)	)	PUNCT
cana-5359	219	113	=	=	SYM
cana-5359	219	114	0.6	0.6	NUM
cana-5359	219	115	;	;	PUNCT
cana-5359	219	116	𝛼𝐵2	𝛼𝐵2	NUM
cana-5359	219	117	(	(	PUNCT
cana-5359	219	118	𝑎	𝑎	NOUN
cana-5359	219	119	)	)	PUNCT
cana-5359	219	120	=	=	SYM
cana-5359	219	121	0.1	0.1	NUM
cana-5359	219	122	,	,	PUNCT
cana-5359	219	123	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5359	219	124	(	(	PUNCT
cana-5359	219	125	𝑎	𝑎	NOUN
cana-5359	219	126	)	)	PUNCT
cana-5359	219	127	=	=	SYM
cana-5359	219	128	0.9	0.9	NUM
cana-5359	219	129	,	,	PUNCT
cana-5359	219	130	𝛼𝐵2	𝛼𝐵2	NUM
cana-5359	219	131	(	(	PUNCT
cana-5359	219	132	𝑏	𝑏	NOUN
cana-5359	219	133	)	)	PUNCT
cana-5359	219	134	=	=	SYM
cana-5359	219	135	0.3	0.3	NUM
cana-5359	219	136	,	,	PUNCT
cana-5359	219	137	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5359	219	138	(	(	PUNCT
cana-5359	219	139	𝑏	𝑏	NOUN
cana-5359	219	140	)	)	PUNCT
cana-5359	219	141	=	=	SYM
cana-5359	219	142	0.7	0.7	NUM
cana-5359	219	143	;	;	PUNCT
cana-5359	219	144	𝛼𝐵3	𝛼𝐵3	PROPN
cana-5359	219	145	(	(	PUNCT
cana-5359	219	146	𝑎	𝑎	NOUN
cana-5359	219	147	)	)	PUNCT
cana-5359	219	148	=	=	SYM
cana-5359	219	149	0.9	0.9	NUM
cana-5359	219	150	,	,	PUNCT
cana-5359	219	151	𝛽𝐵3	𝛽𝐵3	PROPN
cana-5359	219	152	(	(	PUNCT
cana-5359	219	153	𝑎	𝑎	NOUN
cana-5359	219	154	)	)	PUNCT
cana-5359	219	155	=	=	SYM
cana-5359	219	156	0.1	0.1	NUM
cana-5359	219	157	,	,	PUNCT
cana-5359	219	158	𝛼𝐵3	𝛼𝐵3	PROPN
cana-5359	219	159	(	(	PUNCT
cana-5359	219	160	𝑏	𝑏	NOUN
cana-5359	219	161	)	)	PUNCT
cana-5359	219	162	=	=	SYM
cana-5359	219	163	0.7	0.7	NUM
cana-5359	219	164	,	,	PUNCT
cana-5359	219	165	𝛽𝐵3	𝛽𝐵3	PROPN
cana-5359	219	166	(	(	PUNCT
cana-5359	219	167	𝑏	𝑏	NOUN
cana-5359	219	168	)	)	PUNCT
cana-5359	219	169	=	=	SYM
cana-5359	219	170	0.3	0.3	NUM
cana-5359	219	171	;	;	PUNCT
cana-5359	219	172	𝛼𝐵4	𝛼𝐵4	PROPN
cana-5359	219	173	(	(	PUNCT
cana-5359	219	174	𝑎	𝑎	NOUN
cana-5359	219	175	)	)	PUNCT
cana-5359	219	176	=	=	SYM
cana-5359	219	177	0.2	0.2	NUM
cana-5359	219	178	,	,	PUNCT
cana-5359	219	179	𝛽𝐵4	𝛽𝐵4	PROPN
cana-5359	219	180	(	(	PUNCT
cana-5359	219	181	𝑎	𝑎	NOUN
cana-5359	219	182	)	)	PUNCT
cana-5359	219	183	=	=	SYM
cana-5359	219	184	0.8	0.8	NUM
cana-5359	219	185	,	,	PUNCT
cana-5359	219	186	𝛼𝐵4	𝛼𝐵4	PROPN
cana-5359	219	187	(	(	PUNCT
cana-5359	219	188	𝑏	𝑏	NOUN
cana-5359	219	189	)	)	PUNCT
cana-5359	219	190	=	=	SYM
cana-5359	219	191	0.3	0.3	NUM
cana-5359	219	192	,	,	PUNCT
cana-5359	219	193	𝛽𝐵4	𝛽𝐵4	PROPN
cana-5359	219	194	(	(	PUNCT
cana-5359	219	195	𝑏	𝑏	NOUN
cana-5359	219	196	)	)	PUNCT
cana-5359	219	197	=	=	SYM
cana-5359	219	198	0.7	0.7	NUM
cana-5359	219	199	;	;	PUNCT
cana-5359	219	200	let	let	VERB
cana-5359	219	201	𝜏1	𝜏1	NOUN
cana-5359	219	202	=	=	PUNCT
cana-5359	219	203	{	{	PUNCT
cana-5359	219	204	0𝔉	0𝔉	PROPN
cana-5359	219	205	,	,	PUNCT
cana-5359	219	206	1𝔉	1𝔉	NOUN
cana-5359	219	207	,	,	PUNCT
cana-5359	219	208	𝐴1	𝐴1	PROPN
cana-5359	219	209	,	,	PUNCT
cana-5359	219	210	𝐴2	𝐴2	PROPN
cana-5359	219	211	,	,	PUNCT
cana-5359	219	212	𝐴3	𝐴3	PROPN
cana-5359	219	213	,	,	PUNCT
cana-5359	219	214	𝐴4	𝐴4	PROPN
cana-5359	219	215	}	}	PUNCT
cana-5359	219	216	and	and	CCONJ
cana-5359	219	217	𝜏2	𝜏2	PROPN
cana-5359	219	218	=	=	SYM
cana-5359	219	219	{	{	PUNCT
cana-5359	219	220	0𝔉	0𝔉	PROPN
cana-5359	219	221	,	,	PUNCT
cana-5359	219	222	1𝔉	1𝔉	NOUN
cana-5359	219	223	,	,	PUNCT
cana-5359	219	224	𝐵1	𝐵1	PROPN
cana-5359	219	225	,	,	PUNCT
cana-5359	219	226	𝐵2	𝐵2	NOUN
cana-5359	219	227	,	,	PUNCT
cana-5359	219	228	𝐵3	𝐵3	PROPN
cana-5359	219	229	,	,	PUNCT
cana-5359	219	230	𝐵4	𝐵4	NOUN
cana-5359	219	231	}	}	PUNCT
cana-5359	219	232	are	be	AUX
cana-5359	219	233	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	219	234	’s	’s	ADV
cana-5359	219	235	on	on	ADP
cana-5359	219	236	𝑋	𝑋	PROPN
cana-5359	219	237	and	and	CCONJ
cana-5359	219	238	let	let	VERB
cana-5359	219	239	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	219	240	:	:	PUNCT
cana-5359	219	241	(	(	PUNCT
cana-5359	219	242	𝑋1	𝑋1	PROPN
cana-5359	219	243	,	,	PUNCT
cana-5359	219	244	𝜏1	𝜏1	NOUN
cana-5359	219	245	)	)	PUNCT
cana-5359	219	246	→	→	SYM
cana-5359	219	247	(	(	PUNCT
cana-5359	219	248	𝑋2	𝑋2	PROPN
cana-5359	219	249	,	,	PUNCT
cana-5359	219	250	𝜏2	𝜏2	PROPN
cana-5359	219	251	)	)	PUNCT
cana-5359	219	252	be	be	VERB
cana-5359	219	253	an	an	DET
cana-5359	219	254	identity	identity	NOUN
cana-5359	219	255	function	function	NOUN
cana-5359	219	256	,	,	PUNCT
cana-5359	219	257	then	then	ADV
cana-5359	219	258	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	219	259	is	be	AUX
cana-5359	219	260	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	219	261	but	but	CCONJ
cana-5359	219	262	not	not	PART
cana-5359	219	263	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	NOUN
cana-5359	219	264	since	since	SCONJ
cana-5359	219	265	,	,	PUNCT
cana-5359	219	266	𝐵4	𝐵4	PROPN
cana-5359	219	267	is	be	AUX
cana-5359	219	268	a	a	DET
cana-5359	219	269	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	219	270	set	set	VERB
cana-5359	219	271	in	in	ADP
cana-5359	219	272	𝑋2	𝑋2	ADJ
cana-5359	219	273	but	but	CCONJ
cana-5359	219	274	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	219	275	−1(𝐵4	−1(𝐵4	VERB
cana-5359	219	276	)	)	PUNCT
cana-5359	220	1	=	=	NOUN
cana-5359	220	2	𝐵4	𝐵4	NOUN
cana-5359	220	3	is	be	AUX
cana-5359	220	4	not	not	PART
cana-5359	220	5	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	NOUN
cana-5359	220	6	set	set	VERB
cana-5359	220	7	in	in	ADP
cana-5359	220	8	𝑋1	𝑋1	PROPN
cana-5359	220	9	.	.	PUNCT
cana-5359	221	1	theorem	theorem	ADJ
cana-5359	221	2	3.2	3.2	NUM
cana-5359	221	3	let	let	VERB
cana-5359	221	4	(	(	PUNCT
cana-5359	221	5	𝑋1	𝑋1	PROPN
cana-5359	221	6	,	,	PUNCT
cana-5359	221	7	𝜏1	𝜏1	NOUN
cana-5359	221	8	)	)	PUNCT
cana-5359	221	9	&	&	CCONJ
cana-5359	221	10	(	(	PUNCT
cana-5359	221	11	𝑋2	𝑋2	PROPN
cana-5359	221	12	,	,	PUNCT
cana-5359	221	13	𝜏2	𝜏2	PROPN
cana-5359	221	14	)	)	PUNCT
cana-5359	221	15	be	be	AUX
cana-5359	221	16	a	a	DET
cana-5359	221	17	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	221	18	’s	’s	NOUN
cana-5359	221	19	.	.	PUNCT
cana-5359	222	1	a	a	DET
cana-5359	222	2	mapping	mapping	NOUN
cana-5359	222	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	222	4	:	:	PUNCT
cana-5359	222	5	(	(	PUNCT
cana-5359	222	6	𝑋1	𝑋1	PROPN
cana-5359	222	7	,	,	PUNCT
cana-5359	222	8	𝜏1	𝜏1	NOUN
cana-5359	222	9	)	)	PUNCT
cana-5359	222	10	→	→	SYM
cana-5359	222	11	(	(	PUNCT
cana-5359	222	12	𝑋2	𝑋2	PROPN
cana-5359	222	13	,	,	PUNCT
cana-5359	222	14	𝜏2	𝜏2	PROPN
cana-5359	222	15	)	)	PUNCT
cana-5359	222	16	satisfies	satisfy	VERB
cana-5359	222	17	the	the	DET
cana-5359	222	18	following	follow	VERB
cana-5359	222	19	conditions	condition	NOUN
cana-5359	222	20	are	be	AUX
cana-5359	222	21	equivalent	equivalent	ADJ
cana-5359	222	22	.	.	PUNCT
cana-5359	223	1	1	1	X
cana-5359	223	2	.	.	X
cana-5359	223	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	223	4	is	be	AUX
cana-5359	223	5	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	NOUN
cana-5359	223	6	2	2	NUM
cana-5359	223	7	.	.	PUNCT
cana-5359	224	1	the	the	DET
cana-5359	224	2	inverse	inverse	ADJ
cana-5359	224	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	224	4	−1(𝐾	−1(𝐾	NOUN
cana-5359	224	5	)	)	PUNCT
cana-5359	224	6	of	of	ADP
cana-5359	224	7	all	all	PRON
cana-5359	224	8	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5359	224	9	set	set	VERB
cana-5359	224	10	𝐾	𝐾	PROPN
cana-5359	224	11	in	in	ADP
cana-5359	224	12	𝑋2	𝑋2	ADV
cana-5359	224	13	is	be	AUX
cana-5359	224	14	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	PROPN
cana-5359	224	15	in	in	ADP
cana-5359	224	16	𝑋1	𝑋1	PROPN
cana-5359	224	17	.	.	PUNCT
cana-5359	225	1	communications	communication	NOUN
cana-5359	225	2	on	on	ADP
cana-5359	225	3	applied	apply	VERB
cana-5359	225	4	nonlinear	nonlinear	ADJ
cana-5359	225	5	analysis	analysis	NOUN
cana-5359	225	6	issn	issn	NOUN
cana-5359	225	7	:	:	PUNCT
cana-5359	225	8	1074	1074	NUM
cana-5359	225	9	-	-	PUNCT
cana-5359	225	10	133x	133x	NUM
cana-5359	225	11	vol	vol	VERB
cana-5359	225	12	32	32	NUM
cana-5359	225	13	no	no	NOUN
cana-5359	225	14	.	.	PUNCT
cana-5359	226	1	10s	10	NOUN
cana-5359	226	2	(	(	PUNCT
cana-5359	226	3	2025	2025	NUM
cana-5359	226	4	)	)	PUNCT
cana-5359	226	5	1917	1917	NUM
cana-5359	227	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	227	2	proof	proof	NOUN
cana-5359	227	3	.	.	PUNCT
cana-5359	228	1	the	the	DET
cana-5359	228	2	proof	proof	NOUN
cana-5359	228	3	is	be	AUX
cana-5359	228	4	directly	directly	ADV
cana-5359	228	5	,	,	PUNCT
cana-5359	228	6	from	from	ADP
cana-5359	228	7	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	228	8	−1(𝐾	−1(𝐾	NOUN
cana-5359	228	9	)	)	PUNCT
cana-5359	229	1	=	=	SYM
cana-5359	229	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	229	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	229	4	)	)	PUNCT
cana-5359	229	5	for	for	ADP
cana-5359	229	6	all	all	DET
cana-5359	229	7	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5359	229	8	𝐾	𝐾	PROPN
cana-5359	229	9	of	of	ADP
cana-5359	229	10	𝑋2	𝑋2	PROPN
cana-5359	229	11	.	.	PUNCT
cana-5359	230	1	theorem	theorem	VERB
cana-5359	230	2	3.3	3.3	NUM
cana-5359	230	3	let	let	NOUN
cana-5359	230	4	(	(	PUNCT
cana-5359	230	5	𝑋1	𝑋1	PROPN
cana-5359	230	6	,	,	PUNCT
cana-5359	230	7	𝜏1	𝜏1	NOUN
cana-5359	230	8	)	)	PUNCT
cana-5359	230	9	&	&	CCONJ
cana-5359	230	10	(	(	PUNCT
cana-5359	230	11	𝑋2	𝑋2	PROPN
cana-5359	230	12	,	,	PUNCT
cana-5359	230	13	𝜏2	𝜏2	PROPN
cana-5359	230	14	)	)	PUNCT
cana-5359	230	15	be	be	VERB
cana-5359	230	16	a	a	DET
cana-5359	230	17	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	230	18	’s	’s	NOUN
cana-5359	230	19	.	.	PUNCT
cana-5359	231	1	a	a	DET
cana-5359	231	2	mapping	mapping	NOUN
cana-5359	231	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	231	4	:	:	PUNCT
cana-5359	231	5	(	(	PUNCT
cana-5359	231	6	𝑋1	𝑋1	PROPN
cana-5359	231	7	,	,	PUNCT
cana-5359	231	8	𝜏1	𝜏1	NOUN
cana-5359	231	9	)	)	PUNCT
cana-5359	231	10	→	→	SYM
cana-5359	231	11	(	(	PUNCT
cana-5359	231	12	𝑋2	𝑋2	PROPN
cana-5359	231	13	,	,	PUNCT
cana-5359	231	14	𝜏2	𝜏2	PROPN
cana-5359	231	15	)	)	PUNCT
cana-5359	231	16	satisfies	satisfy	VERB
cana-5359	231	17	the	the	DET
cana-5359	231	18	following	follow	VERB
cana-5359	231	19	conditions	condition	NOUN
cana-5359	231	20	are	be	AUX
cana-5359	231	21	hold	hold	ADJ
cana-5359	231	22	.	.	PUNCT
cana-5359	232	1	(	(	PUNCT
cana-5359	232	2	i	i	NOUN
cana-5359	232	3	)	)	PUNCT
cana-5359	232	4	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(𝐿	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(𝐿	NOUN
cana-5359	232	5	)	)	PUNCT
cana-5359	232	6	)	)	PUNCT
cana-5359	233	1	⊆	⊆	NUM
cana-5359	233	2	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	PROPN
cana-5359	233	3	)	)	PUNCT
cana-5359	233	4	)	)	PUNCT
cana-5359	233	5	,	,	PUNCT
cana-5359	233	6	for	for	ADP
cana-5359	233	7	all	all	DET
cana-5359	233	8	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5359	233	9	𝐿	𝐿	PROPN
cana-5359	233	10	in	in	ADP
cana-5359	233	11	𝑋1	𝑋1	PROPN
cana-5359	233	12	.	.	PUNCT
cana-5359	234	1	(	(	PUNCT
cana-5359	234	2	ii	ii	NOUN
cana-5359	234	3	)	)	PUNCT
cana-5359	234	4	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5359	234	5	−1(𝐾	−1(𝐾	NOUN
cana-5359	234	6	)	)	PUNCT
cana-5359	234	7	)	)	PUNCT
cana-5359	235	1	⊆	⊆	NUM
cana-5359	235	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	235	3	−1(𝔉ℱ𝛿𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝑐𝑙(𝐾	NOUN
cana-5359	235	4	)	)	PUNCT
cana-5359	235	5	)	)	PUNCT
cana-5359	235	6	,	,	PUNCT
cana-5359	235	7	for	for	ADP
cana-5359	235	8	all	all	DET
cana-5359	235	9	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5359	235	10	𝐾	𝐾	PROPN
cana-5359	235	11	in	in	ADP
cana-5359	235	12	𝑋2	𝑋2	ADJ
cana-5359	235	13	.	.	PUNCT
cana-5359	236	1	proof	proof	NOUN
cana-5359	236	2	.	.	PUNCT
cana-5359	237	1	(	(	PUNCT
cana-5359	237	2	i	i	NOUN
cana-5359	237	3	)	)	PUNCT
cana-5359	237	4	since	since	SCONJ
cana-5359	237	5	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	PROPN
cana-5359	237	6	)	)	PUNCT
cana-5359	237	7	)	)	PUNCT
cana-5359	237	8	is	be	AUX
cana-5359	237	9	a	a	DET
cana-5359	237	10	𝔉ℱ𝛿𝑐𝑠	𝔉ℱ𝛿𝑐𝑠	PROPN
cana-5359	237	11	in	in	ADP
cana-5359	237	12	𝑋2	𝑋2	ADJ
cana-5359	237	13	and	and	CCONJ
cana-5359	237	14	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	237	15	is	be	AUX
cana-5359	237	16	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	237	17	,	,	PUNCT
cana-5359	237	18	then	then	ADV
cana-5359	237	19	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	238	1	−1(𝔉ℱ𝛿𝑐𝑙	−1(𝔉ℱ𝛿𝑐𝑙	ADV
cana-5359	238	2	(	(	PUNCT
cana-5359	238	3	ℎ𝔉(𝐿	ℎ𝔉(𝐿	NOUN
cana-5359	238	4	)	)	PUNCT
cana-5359	238	5	)	)	PUNCT
cana-5359	238	6	)	)	PUNCT
cana-5359	238	7	is	be	AUX
cana-5359	238	8	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5359	238	9	in	in	ADP
cana-5359	238	10	𝑋1	𝑋1	PROPN
cana-5359	238	11	.	.	PUNCT
cana-5359	239	1	now	now	ADV
cana-5359	239	2	,	,	PUNCT
cana-5359	239	3	since	since	SCONJ
cana-5359	239	4	𝐿	𝐿	PROPN
cana-5359	239	5	⊆	⊆	NUM
cana-5359	239	6	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	239	7	−1(𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	−1(𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	NUM
cana-5359	239	8	)	)	PUNCT
cana-5359	239	9	)	)	PUNCT
cana-5359	239	10	)	)	PUNCT
cana-5359	239	11	,	,	PUNCT
cana-5359	239	12	𝔉ℱ𝛿𝛽𝑐𝑙(𝐿	𝔉ℱ𝛿𝛽𝑐𝑙(𝐿	X
cana-5359	239	13	)	)	PUNCT
cana-5359	239	14	⊆	⊆	NUM
cana-5359	239	15	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	239	16	−1(𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	−1(𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	NUM
cana-5359	239	17	)	)	PUNCT
cana-5359	239	18	)	)	PUNCT
cana-5359	239	19	)	)	PUNCT
cana-5359	239	20	.	.	PUNCT
cana-5359	240	1	therefore	therefore	ADV
cana-5359	240	2	,	,	PUNCT
cana-5359	240	3	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(𝐿	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(𝐿	NOUN
cana-5359	240	4	)	)	PUNCT
cana-5359	240	5	)	)	PUNCT
cana-5359	240	6	⊆	⊆	NUM
cana-5359	240	7	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	PROPN
cana-5359	240	8	)	)	PUNCT
cana-5359	240	9	)	)	PUNCT
cana-5359	240	10	.	.	PUNCT
cana-5359	241	1	(	(	PUNCT
cana-5359	241	2	ii	ii	NOUN
cana-5359	241	3	)	)	PUNCT
cana-5359	241	4	by	by	ADP
cana-5359	241	5	replacing	replace	VERB
cana-5359	241	6	𝐿	𝐿	PROPN
cana-5359	241	7	with	with	ADP
cana-5359	241	8	𝐾	𝐾	PROPN
cana-5359	241	9	in	in	ADP
cana-5359	241	10	(	(	PUNCT
cana-5359	241	11	i	i	NOUN
cana-5359	241	12	)	)	PUNCT
cana-5359	241	13	,	,	PUNCT
cana-5359	241	14	we	we	PRON
cana-5359	241	15	obtain	obtain	VERB
cana-5359	241	16	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NOUN
cana-5359	241	17	−1(𝐾	−1(𝐾	NOUN
cana-5359	241	18	)	)	PUNCT
cana-5359	241	19	)	)	PUNCT
cana-5359	241	20	)	)	PUNCT
cana-5359	242	1	⊆	⊆	NUM
cana-5359	242	2	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉	NUM
cana-5359	242	3	(	(	PUNCT
cana-5359	242	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	242	5	−1(𝐾	−1(𝐾	NOUN
cana-5359	242	6	)	)	PUNCT
cana-5359	242	7	)	)	PUNCT
cana-5359	242	8	)	)	PUNCT
cana-5359	243	1	⊆	⊆	NUM
cana-5359	243	2	𝔉ℱ𝛿𝑐𝑙(𝐾	𝔉ℱ𝛿𝑐𝑙(𝐾	NUM
cana-5359	243	3	)	)	PUNCT
cana-5359	243	4	.	.	PUNCT
cana-5359	244	1	hence	hence	ADV
cana-5359	244	2	,	,	PUNCT
cana-5359	244	3	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5359	244	4	−1(𝐾	−1(𝐾	NOUN
cana-5359	244	5	)	)	PUNCT
cana-5359	244	6	)	)	PUNCT
cana-5359	245	1	⊆	⊆	NUM
cana-5359	245	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	245	3	−1(𝔉ℱ𝛿𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝑐𝑙(𝐾	NOUN
cana-5359	245	4	)	)	PUNCT
cana-5359	245	5	)	)	PUNCT
cana-5359	245	6	.	.	PUNCT
cana-5359	245	7	remark	remark	PROPN
cana-5359	245	8	3.2	3.2	NUM
cana-5359	245	9	let	let	VERB
cana-5359	245	10	(	(	PUNCT
cana-5359	245	11	𝑋1	𝑋1	PROPN
cana-5359	245	12	,	,	PUNCT
cana-5359	245	13	𝜏1	𝜏1	NOUN
cana-5359	245	14	)	)	PUNCT
cana-5359	245	15	&	&	CCONJ
cana-5359	245	16	(	(	PUNCT
cana-5359	245	17	𝑋2	𝑋2	PROPN
cana-5359	245	18	,	,	PUNCT
cana-5359	245	19	𝜏2	𝜏2	PROPN
cana-5359	245	20	)	)	PUNCT
cana-5359	245	21	be	be	VERB
cana-5359	245	22	a	a	DET
cana-5359	245	23	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	245	24	’s	’s	PART
cana-5359	245	25	.	.	PUNCT
cana-5359	246	1	let	let	VERB
cana-5359	246	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	246	3	:	:	PUNCT
cana-5359	246	4	(	(	PUNCT
cana-5359	246	5	𝑋1	𝑋1	PROPN
cana-5359	246	6	,	,	PUNCT
cana-5359	246	7	𝜏1	𝜏1	NOUN
cana-5359	246	8	)	)	PUNCT
cana-5359	246	9	→	→	SYM
cana-5359	246	10	(	(	PUNCT
cana-5359	246	11	𝑋2	𝑋2	PROPN
cana-5359	246	12	,	,	PUNCT
cana-5359	246	13	𝜏2	𝜏2	PROPN
cana-5359	246	14	)	)	PUNCT
cana-5359	246	15	be	be	VERB
cana-5359	246	16	a	a	DET
cana-5359	246	17	mapping	mapping	NOUN
cana-5359	246	18	.	.	PUNCT
cana-5359	247	1	if	if	SCONJ
cana-5359	247	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	247	3	is	be	AUX
cana-5359	247	4	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	247	5	,	,	PUNCT
cana-5359	247	6	then	then	ADV
cana-5359	247	7	1	1	NUM
cana-5359	247	8	.	.	PUNCT
cana-5359	247	9	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(𝐿	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(𝐿	NOUN
cana-5359	247	10	)	)	PUNCT
cana-5359	247	11	)	)	PUNCT
cana-5359	247	12	is	be	AUX
cana-5359	247	13	not	not	PART
cana-5359	247	14	necessarily	necessarily	ADV
cana-5359	247	15	equal	equal	ADJ
cana-5359	247	16	to	to	ADP
cana-5359	247	17	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐿	PROPN
cana-5359	247	18	)	)	PUNCT
cana-5359	247	19	)	)	PUNCT
cana-5359	247	20	where	where	SCONJ
cana-5359	247	21	𝐿	𝐿	PROPN
cana-5359	247	22	∈	∈	PROPN
cana-5359	247	23	𝑋1	𝑋1	NOUN
cana-5359	247	24	.	.	PUNCT
cana-5359	248	1	2	2	NUM
cana-5359	248	2	.	.	X
cana-5359	248	3	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5359	248	4	−1(𝐾	−1(𝐾	NOUN
cana-5359	248	5	)	)	PUNCT
cana-5359	248	6	)	)	PUNCT
cana-5359	248	7	is	be	AUX
cana-5359	248	8	not	not	PART
cana-5359	248	9	necessarily	necessarily	ADV
cana-5359	248	10	equal	equal	ADJ
cana-5359	248	11	to	to	ADP
cana-5359	248	12	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	248	13	−1(𝔉ℱ𝛿𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝑐𝑙(𝐾	NOUN
cana-5359	248	14	)	)	PUNCT
cana-5359	248	15	)	)	PUNCT
cana-5359	248	16	where	where	SCONJ
cana-5359	248	17	𝐾	𝐾	PROPN
cana-5359	248	18	∈	∈	PROPN
cana-5359	248	19	𝑋2	𝑋2	VERB
cana-5359	248	20	.	.	PUNCT
cana-5359	249	1	example	example	NOUN
cana-5359	249	2	3.5	3.5	NUM
cana-5359	249	3	let	let	VERB
cana-5359	249	4	𝑋1	𝑋1	NOUN
cana-5359	249	5	=	=	SYM
cana-5359	249	6	𝑋2	𝑋2	VERB
cana-5359	249	7	=	=	SYM
cana-5359	249	8	𝑋	𝑋	NOUN
cana-5359	249	9	=	=	PUNCT
cana-5359	249	10	{	{	PUNCT
cana-5359	249	11	𝑎	𝑎	NOUN
cana-5359	249	12	,	,	PUNCT
cana-5359	249	13	𝑏	𝑏	NOUN
cana-5359	249	14	}	}	PUNCT
cana-5359	249	15	and	and	CCONJ
cana-5359	249	16	the	the	DET
cana-5359	249	17	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	249	18	’s	’s	PART
cana-5359	249	19	𝐴1	𝐴1	PROPN
cana-5359	249	20	,	,	PUNCT
cana-5359	249	21	𝐴2	𝐴2	PROPN
cana-5359	249	22	,	,	PUNCT
cana-5359	249	23	𝐴3	𝐴3	PROPN
cana-5359	249	24	,	,	PUNCT
cana-5359	249	25	𝐴4	𝐴4	PROPN
cana-5359	249	26	,	,	PUNCT
cana-5359	249	27	𝐵1	𝐵1	PROPN
cana-5359	249	28	,	,	PUNCT
cana-5359	249	29	𝐵2	𝐵2	NOUN
cana-5359	249	30	,	,	PUNCT
cana-5359	249	31	𝐵3	𝐵3	NOUN
cana-5359	249	32	and	and	CCONJ
cana-5359	249	33	𝐵4	𝐵4	NOUN
cana-5359	249	34	are	be	AUX
cana-5359	249	35	defined	define	VERB
cana-5359	249	36	as	as	ADP
cana-5359	249	37	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	249	38	(	(	PUNCT
cana-5359	249	39	𝑎	𝑎	NOUN
cana-5359	249	40	)	)	PUNCT
cana-5359	249	41	=	=	SYM
cana-5359	249	42	0.4	0.4	NUM
cana-5359	249	43	,	,	PUNCT
cana-5359	249	44	𝛽𝐴1	𝛽𝐴1	X
cana-5359	249	45	(	(	PUNCT
cana-5359	249	46	𝑎	𝑎	NOUN
cana-5359	249	47	)	)	PUNCT
cana-5359	249	48	=	=	SYM
cana-5359	249	49	0.6	0.6	NUM
cana-5359	249	50	,	,	PUNCT
cana-5359	249	51	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	249	52	(	(	PUNCT
cana-5359	249	53	𝑏	𝑏	NOUN
cana-5359	249	54	)	)	PUNCT
cana-5359	249	55	=	=	SYM
cana-5359	249	56	0.5	0.5	NUM
cana-5359	249	57	,	,	PUNCT
cana-5359	249	58	𝛽𝐴1	𝛽𝐴1	X
cana-5359	249	59	(	(	PUNCT
cana-5359	249	60	𝑏	𝑏	NOUN
cana-5359	249	61	)	)	PUNCT
cana-5359	250	1	=	=	NOUN
cana-5359	250	2	0.5	0.5	NUM
cana-5359	250	3	;	;	PUNCT
cana-5359	250	4	𝛼𝐴2	𝛼𝐴2	NUM
cana-5359	250	5	(	(	PUNCT
cana-5359	250	6	𝑎	𝑎	NOUN
cana-5359	250	7	)	)	PUNCT
cana-5359	250	8	=	=	SYM
cana-5359	250	9	0.6	0.6	NUM
cana-5359	250	10	,	,	PUNCT
cana-5359	250	11	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	250	12	(	(	PUNCT
cana-5359	250	13	𝑎	𝑎	NOUN
cana-5359	250	14	)	)	PUNCT
cana-5359	250	15	=	=	SYM
cana-5359	250	16	0.4	0.4	NUM
cana-5359	250	17	,	,	PUNCT
cana-5359	250	18	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5359	250	19	(	(	PUNCT
cana-5359	250	20	𝑏	𝑏	NOUN
cana-5359	250	21	)	)	PUNCT
cana-5359	250	22	=	=	SYM
cana-5359	250	23	0.6	0.6	NUM
cana-5359	250	24	,	,	PUNCT
cana-5359	250	25	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	250	26	(	(	PUNCT
cana-5359	250	27	𝑏	𝑏	NOUN
cana-5359	250	28	)	)	PUNCT
cana-5359	250	29	=	=	SYM
cana-5359	250	30	0.4	0.4	NUM
cana-5359	250	31	;	;	PUNCT
cana-5359	250	32	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	250	33	(	(	PUNCT
cana-5359	250	34	𝑎	𝑎	NOUN
cana-5359	250	35	)	)	PUNCT
cana-5359	250	36	=	=	SYM
cana-5359	250	37	0.7	0.7	NUM
cana-5359	250	38	,	,	PUNCT
cana-5359	250	39	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	250	40	(	(	PUNCT
cana-5359	250	41	𝑎	𝑎	NOUN
cana-5359	250	42	)	)	PUNCT
cana-5359	250	43	=	=	SYM
cana-5359	250	44	0.3	0.3	NUM
cana-5359	250	45	,	,	PUNCT
cana-5359	250	46	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	250	47	(	(	PUNCT
cana-5359	250	48	𝑏	𝑏	NOUN
cana-5359	250	49	)	)	PUNCT
cana-5359	250	50	=	=	SYM
cana-5359	250	51	0.6	0.6	NUM
cana-5359	250	52	,	,	PUNCT
cana-5359	250	53	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	250	54	(	(	PUNCT
cana-5359	250	55	𝑏	𝑏	NOUN
cana-5359	250	56	)	)	PUNCT
cana-5359	250	57	=	=	SYM
cana-5359	250	58	0.4	0.4	NUM
cana-5359	250	59	;	;	PUNCT
cana-5359	250	60	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5359	250	61	(	(	PUNCT
cana-5359	250	62	𝑎	𝑎	NOUN
cana-5359	250	63	)	)	PUNCT
cana-5359	250	64	=	=	SYM
cana-5359	250	65	0.4	0.4	NUM
cana-5359	250	66	,	,	PUNCT
cana-5359	250	67	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5359	250	68	(	(	PUNCT
cana-5359	250	69	𝑎	𝑎	NOUN
cana-5359	250	70	)	)	PUNCT
cana-5359	250	71	=	=	SYM
cana-5359	250	72	0.6	0.6	NUM
cana-5359	250	73	,	,	PUNCT
cana-5359	250	74	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5359	250	75	(	(	PUNCT
cana-5359	250	76	𝑏	𝑏	NOUN
cana-5359	250	77	)	)	PUNCT
cana-5359	250	78	=	=	SYM
cana-5359	250	79	0.4	0.4	NUM
cana-5359	250	80	,	,	PUNCT
cana-5359	250	81	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5359	250	82	(	(	PUNCT
cana-5359	250	83	𝑏	𝑏	NOUN
cana-5359	250	84	)	)	PUNCT
cana-5359	250	85	=	=	SYM
cana-5359	250	86	0.6	0.6	NUM
cana-5359	250	87	;	;	PUNCT
cana-5359	250	88	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5359	250	89	(	(	PUNCT
cana-5359	250	90	𝑎	𝑎	NOUN
cana-5359	250	91	)	)	PUNCT
cana-5359	250	92	=	=	SYM
cana-5359	250	93	0.2	0.2	NUM
cana-5359	250	94	,	,	PUNCT
cana-5359	250	95	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5359	250	96	(	(	PUNCT
cana-5359	250	97	𝑎	𝑎	NOUN
cana-5359	250	98	)	)	PUNCT
cana-5359	250	99	=	=	SYM
cana-5359	250	100	0.8	0.8	NUM
cana-5359	250	101	,	,	PUNCT
cana-5359	250	102	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5359	250	103	(	(	PUNCT
cana-5359	250	104	𝑏	𝑏	NOUN
cana-5359	250	105	)	)	PUNCT
cana-5359	250	106	=	=	SYM
cana-5359	250	107	0.4	0.4	NUM
cana-5359	250	108	,	,	PUNCT
cana-5359	250	109	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5359	250	110	(	(	PUNCT
cana-5359	250	111	𝑏	𝑏	NOUN
cana-5359	250	112	)	)	PUNCT
cana-5359	250	113	=	=	SYM
cana-5359	250	114	0.6	0.6	NUM
cana-5359	250	115	;	;	PUNCT
cana-5359	250	116	𝛼𝐵2	𝛼𝐵2	NUM
cana-5359	250	117	(	(	PUNCT
cana-5359	250	118	𝑎	𝑎	NOUN
cana-5359	250	119	)	)	PUNCT
cana-5359	250	120	=	=	SYM
cana-5359	250	121	0.1	0.1	NUM
cana-5359	250	122	,	,	PUNCT
cana-5359	250	123	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5359	250	124	(	(	PUNCT
cana-5359	250	125	𝑎	𝑎	NOUN
cana-5359	250	126	)	)	PUNCT
cana-5359	250	127	=	=	SYM
cana-5359	250	128	0.9	0.9	NUM
cana-5359	250	129	,	,	PUNCT
cana-5359	250	130	𝛼𝐵2	𝛼𝐵2	NUM
cana-5359	250	131	(	(	PUNCT
cana-5359	250	132	𝑏	𝑏	NOUN
cana-5359	250	133	)	)	PUNCT
cana-5359	250	134	=	=	SYM
cana-5359	250	135	0.3	0.3	NUM
cana-5359	250	136	,	,	PUNCT
cana-5359	250	137	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5359	250	138	(	(	PUNCT
cana-5359	250	139	𝑏	𝑏	NOUN
cana-5359	250	140	)	)	PUNCT
cana-5359	250	141	=	=	SYM
cana-5359	250	142	0.7	0.7	NUM
cana-5359	250	143	;	;	PUNCT
cana-5359	250	144	𝛼𝐵3	𝛼𝐵3	PROPN
cana-5359	250	145	(	(	PUNCT
cana-5359	250	146	𝑎	𝑎	NOUN
cana-5359	250	147	)	)	PUNCT
cana-5359	250	148	=	=	SYM
cana-5359	250	149	0.9	0.9	NUM
cana-5359	250	150	,	,	PUNCT
cana-5359	250	151	𝛽𝐵3	𝛽𝐵3	PROPN
cana-5359	250	152	(	(	PUNCT
cana-5359	250	153	𝑎	𝑎	NOUN
cana-5359	250	154	)	)	PUNCT
cana-5359	250	155	=	=	SYM
cana-5359	250	156	0.1	0.1	NUM
cana-5359	250	157	,	,	PUNCT
cana-5359	250	158	𝛼𝐵3	𝛼𝐵3	PROPN
cana-5359	250	159	(	(	PUNCT
cana-5359	250	160	𝑏	𝑏	NOUN
cana-5359	250	161	)	)	PUNCT
cana-5359	250	162	=	=	SYM
cana-5359	250	163	0.7	0.7	NUM
cana-5359	250	164	,	,	PUNCT
cana-5359	250	165	𝛽𝐵3	𝛽𝐵3	PROPN
cana-5359	250	166	(	(	PUNCT
cana-5359	250	167	𝑏	𝑏	NOUN
cana-5359	250	168	)	)	PUNCT
cana-5359	250	169	=	=	SYM
cana-5359	250	170	0.3	0.3	NUM
cana-5359	250	171	;	;	PUNCT
cana-5359	250	172	𝛼𝐵4	𝛼𝐵4	PROPN
cana-5359	250	173	(	(	PUNCT
cana-5359	250	174	𝑎	𝑎	NOUN
cana-5359	250	175	)	)	PUNCT
cana-5359	250	176	=	=	SYM
cana-5359	250	177	0.2	0.2	NUM
cana-5359	250	178	,	,	PUNCT
cana-5359	250	179	𝛽𝐵4	𝛽𝐵4	PROPN
cana-5359	250	180	(	(	PUNCT
cana-5359	250	181	𝑎	𝑎	NOUN
cana-5359	250	182	)	)	PUNCT
cana-5359	250	183	=	=	SYM
cana-5359	250	184	0.8	0.8	NUM
cana-5359	250	185	,	,	PUNCT
cana-5359	250	186	𝛼𝐵4	𝛼𝐵4	PROPN
cana-5359	250	187	(	(	PUNCT
cana-5359	250	188	𝑏	𝑏	NOUN
cana-5359	250	189	)	)	PUNCT
cana-5359	250	190	=	=	SYM
cana-5359	250	191	0.3	0.3	NUM
cana-5359	250	192	,	,	PUNCT
cana-5359	250	193	𝛽𝐵4	𝛽𝐵4	PROPN
cana-5359	250	194	(	(	PUNCT
cana-5359	250	195	𝑏	𝑏	NOUN
cana-5359	250	196	)	)	PUNCT
cana-5359	250	197	=	=	SYM
cana-5359	250	198	0.7	0.7	NUM
cana-5359	250	199	;	;	PUNCT
cana-5359	250	200	let	let	VERB
cana-5359	250	201	𝜏1	𝜏1	NOUN
cana-5359	250	202	=	=	PUNCT
cana-5359	250	203	{	{	PUNCT
cana-5359	250	204	0𝔉	0𝔉	PROPN
cana-5359	250	205	,	,	PUNCT
cana-5359	250	206	1𝔉	1𝔉	NOUN
cana-5359	250	207	,	,	PUNCT
cana-5359	250	208	𝐵1	𝐵1	PROPN
cana-5359	250	209	,	,	PUNCT
cana-5359	250	210	𝐵2	𝐵2	NOUN
cana-5359	250	211	,	,	PUNCT
cana-5359	250	212	𝐵3	𝐵3	PROPN
cana-5359	250	213	,	,	PUNCT
cana-5359	250	214	𝐵4	𝐵4	NOUN
cana-5359	250	215	}	}	PUNCT
cana-5359	250	216	and	and	CCONJ
cana-5359	250	217	𝜏2	𝜏2	PROPN
cana-5359	250	218	=	=	SYM
cana-5359	250	219	{	{	PUNCT
cana-5359	250	220	0𝔉	0𝔉	PROPN
cana-5359	250	221	,	,	PUNCT
cana-5359	250	222	1𝔉	1𝔉	NOUN
cana-5359	250	223	,	,	PUNCT
cana-5359	250	224	𝐴1	𝐴1	PROPN
cana-5359	250	225	,	,	PUNCT
cana-5359	250	226	𝐴2	𝐴2	PROPN
cana-5359	250	227	,	,	PUNCT
cana-5359	250	228	𝐴3	𝐴3	PROPN
cana-5359	250	229	,	,	PUNCT
cana-5359	250	230	𝐴4	𝐴4	PROPN
cana-5359	250	231	}	}	PUNCT
cana-5359	250	232	are	be	AUX
cana-5359	250	233	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	250	234	’s	’s	NOUN
cana-5359	250	235	on	on	ADP
cana-5359	250	236	𝑋	𝑋	PROPN
cana-5359	250	237	and	and	CCONJ
cana-5359	250	238	let	let	VERB
cana-5359	250	239	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	250	240	:	:	PUNCT
cana-5359	250	241	(	(	PUNCT
cana-5359	250	242	𝑋1	𝑋1	PROPN
cana-5359	250	243	,	,	PUNCT
cana-5359	250	244	𝜏1	𝜏1	NOUN
cana-5359	250	245	)	)	PUNCT
cana-5359	250	246	→	→	SYM
cana-5359	250	247	(	(	PUNCT
cana-5359	250	248	𝑋2	𝑋2	PROPN
cana-5359	250	249	,	,	PUNCT
cana-5359	250	250	𝜏2	𝜏2	PROPN
cana-5359	250	251	)	)	PUNCT
cana-5359	250	252	be	be	VERB
cana-5359	250	253	an	an	DET
cana-5359	250	254	identity	identity	NOUN
cana-5359	250	255	function	function	NOUN
cana-5359	250	256	,	,	PUNCT
cana-5359	250	257	then	then	ADV
cana-5359	250	258	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	250	259	is	be	AUX
cana-5359	250	260	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	250	261	,	,	PUNCT
cana-5359	250	262	[	[	X
cana-5359	250	263	(	(	PUNCT
cana-5359	250	264	i	i	NOUN
cana-5359	250	265	)	)	PUNCT
cana-5359	250	266	]	]	PUNCT
cana-5359	251	1	1	1	X
cana-5359	251	2	.	.	X
cana-5359	251	3	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(𝐴1	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(𝐴1	NOUN
cana-5359	251	4	)	)	PUNCT
cana-5359	251	5	)	)	PUNCT
cana-5359	252	1	=	=	SYM
cana-5359	252	2	𝐴1	𝐴1	PROPN
cana-5359	252	3	.	.	PUNCT
cana-5359	253	1	but	but	CCONJ
cana-5359	253	2	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐴1	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐴1	NOUN
cana-5359	253	3	)	)	PUNCT
cana-5359	253	4	)	)	PUNCT
cana-5359	254	1	=	=	SYM
cana-5359	254	2	𝐴1	𝐴1	PROPN
cana-5359	254	3	𝑐	𝑐	NOUN
cana-5359	254	4	.	.	PUNCT
cana-5359	255	1	thus	thus	ADV
cana-5359	255	2	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(𝐴1	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(𝐴1	ADJ
cana-5359	255	3	)	)	PUNCT
cana-5359	255	4	)	)	PUNCT
cana-5359	256	1	≠	≠	PROPN
cana-5359	256	2	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐴1	𝔉ℱ𝛿𝑐𝑙(ℎ𝔉(𝐴1	NOUN
cana-5359	256	3	)	)	PUNCT
cana-5359	256	4	)	)	PUNCT
cana-5359	256	5	.	.	PUNCT
cana-5359	257	1	2	2	X
cana-5359	257	2	.	.	X
cana-5359	257	3	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5359	257	4	−1(𝐴1	−1(𝐴1	NOUN
cana-5359	257	5	)	)	PUNCT
cana-5359	257	6	)	)	PUNCT
cana-5359	258	1	=	=	SYM
cana-5359	258	2	𝐴1	𝐴1	PROPN
cana-5359	258	3	.	.	PUNCT
cana-5359	259	1	but	but	CCONJ
cana-5359	259	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	259	3	−1(𝔉ℱ𝛿𝑐𝑙(𝐴1	−1(𝔉ℱ𝛿𝑐𝑙(𝐴1	NOUN
cana-5359	259	4	)	)	PUNCT
cana-5359	259	5	)	)	PUNCT
cana-5359	260	1	=	=	SYM
cana-5359	260	2	𝐴1	𝐴1	PROPN
cana-5359	260	3	𝑐	𝑐	NOUN
cana-5359	260	4	.	.	PUNCT
cana-5359	261	1	thus	thus	ADV
cana-5359	261	2	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5359	261	3	−1(𝐴1	−1(𝐴1	NOUN
cana-5359	261	4	)	)	PUNCT
cana-5359	261	5	)	)	PUNCT
cana-5359	262	1	≠	≠	PROPN
cana-5359	262	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	262	3	−1(𝔉ℱ𝛿𝑐𝑙(𝐴1	−1(𝔉ℱ𝛿𝑐𝑙(𝐴1	NOUN
cana-5359	262	4	)	)	PUNCT
cana-5359	262	5	)	)	PUNCT
cana-5359	262	6	.	.	PUNCT
cana-5359	263	1	communications	communication	NOUN
cana-5359	263	2	on	on	ADP
cana-5359	263	3	applied	apply	VERB
cana-5359	263	4	nonlinear	nonlinear	ADJ
cana-5359	263	5	analysis	analysis	NOUN
cana-5359	263	6	issn	issn	NOUN
cana-5359	263	7	:	:	PUNCT
cana-5359	263	8	1074	1074	NUM
cana-5359	263	9	-	-	PUNCT
cana-5359	263	10	133x	133x	NUM
cana-5359	263	11	vol	vol	VERB
cana-5359	263	12	32	32	NUM
cana-5359	263	13	no	no	NOUN
cana-5359	263	14	.	.	PUNCT
cana-5359	264	1	10s	10	NOUN
cana-5359	264	2	(	(	PUNCT
cana-5359	264	3	2025	2025	NUM
cana-5359	264	4	)	)	PUNCT
cana-5359	264	5	1918	1918	NUM
cana-5359	264	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	264	7	theorem	theorem	VERB
cana-5359	264	8	3.4	3.4	NUM
cana-5359	264	9	let	let	NOUN
cana-5359	264	10	(	(	PUNCT
cana-5359	264	11	𝑋1	𝑋1	PROPN
cana-5359	264	12	,	,	PUNCT
cana-5359	264	13	𝜏1	𝜏1	NOUN
cana-5359	264	14	)	)	PUNCT
cana-5359	264	15	&	&	CCONJ
cana-5359	264	16	(	(	PUNCT
cana-5359	264	17	𝑋2	𝑋2	PROPN
cana-5359	264	18	,	,	PUNCT
cana-5359	264	19	𝜏2	𝜏2	PROPN
cana-5359	264	20	)	)	PUNCT
cana-5359	264	21	be	be	VERB
cana-5359	264	22	a	a	DET
cana-5359	264	23	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	264	24	’s	’s	PART
cana-5359	264	25	.	.	PUNCT
cana-5359	265	1	let	let	VERB
cana-5359	265	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	265	3	:	:	PUNCT
cana-5359	265	4	(	(	PUNCT
cana-5359	265	5	𝑋1	𝑋1	PROPN
cana-5359	265	6	,	,	PUNCT
cana-5359	265	7	𝜏1	𝜏1	NOUN
cana-5359	265	8	)	)	PUNCT
cana-5359	265	9	→	→	SYM
cana-5359	265	10	(	(	PUNCT
cana-5359	265	11	𝑋2	𝑋2	PROPN
cana-5359	265	12	,	,	PUNCT
cana-5359	265	13	𝜏2	𝜏2	PROPN
cana-5359	265	14	)	)	PUNCT
cana-5359	265	15	be	be	VERB
cana-5359	265	16	a	a	DET
cana-5359	265	17	mapping	mapping	NOUN
cana-5359	265	18	.	.	PUNCT
cana-5359	266	1	if	if	SCONJ
cana-5359	266	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	266	3	is	be	AUX
cana-5359	266	4	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	266	5	,	,	PUNCT
cana-5359	266	6	then	then	ADV
cana-5359	266	7	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	266	8	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	VERB
cana-5359	266	9	)	)	PUNCT
cana-5359	266	10	)	)	PUNCT
cana-5359	267	1	⊆	⊆	NUM
cana-5359	267	2	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	267	3	−1(𝐿	−1(𝐿	NOUN
cana-5359	267	4	)	)	PUNCT
cana-5359	267	5	)	)	PUNCT
cana-5359	267	6	,	,	PUNCT
cana-5359	267	7	for	for	ADP
cana-5359	267	8	all	all	DET
cana-5359	267	9	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	267	10	𝐿	𝐿	PROPN
cana-5359	267	11	in	in	ADP
cana-5359	267	12	𝑋2	𝑋2	ADJ
cana-5359	267	13	.	.	PUNCT
cana-5359	268	1	proof	proof	NOUN
cana-5359	268	2	.	.	PUNCT
cana-5359	269	1	if	if	SCONJ
cana-5359	269	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	269	3	is	be	AUX
cana-5359	269	4	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	269	5	and	and	CCONJ
cana-5359	269	6	𝐿	𝐿	PROPN
cana-5359	269	7	⊆	⊆	PROPN
cana-5359	269	8	𝑋2	𝑋2	ADJ
cana-5359	269	9	.	.	PUNCT
cana-5359	270	1	𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	NOUN
cana-5359	270	2	)	)	PUNCT
cana-5359	270	3	is	be	AUX
cana-5359	270	4	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	270	5	in	in	ADP
cana-5359	270	6	𝑋2	𝑋2	ADJ
cana-5359	270	7	and	and	CCONJ
cana-5359	270	8	hence	hence	ADV
cana-5359	270	9	,	,	PUNCT
cana-5359	270	10	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	270	11	−1(𝔉ℱ𝛿	−1(𝔉ℱ𝛿	X
cana-5359	270	12	𝑖𝑛𝑡(𝐿	𝑖𝑛𝑡(𝐿	NUM
cana-5359	270	13	)	)	PUNCT
cana-5359	270	14	)	)	PUNCT
cana-5359	270	15	is	be	AUX
cana-5359	270	16	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	270	17	in	in	ADP
cana-5359	270	18	𝑋1	𝑋1	PROPN
cana-5359	270	19	.	.	PUNCT
cana-5359	271	1	therefore	therefore	ADV
cana-5359	271	2	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	271	3	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	NOUN
cana-5359	271	4	)	)	PUNCT
cana-5359	271	5	)	)	PUNCT
cana-5359	271	6	)	)	PUNCT
cana-5359	272	1	=	=	SYM
cana-5359	272	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	272	3	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	VERB
cana-5359	272	4	)	)	PUNCT
cana-5359	272	5	)	)	PUNCT
cana-5359	272	6	.	.	PUNCT
cana-5359	273	1	also	also	ADV
cana-5359	273	2	,	,	PUNCT
cana-5359	273	3	𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	NOUN
cana-5359	273	4	)	)	PUNCT
cana-5359	273	5	⊆	⊆	NUM
cana-5359	273	6	𝐿	𝐿	PROPN
cana-5359	273	7	,	,	PUNCT
cana-5359	273	8	implies	imply	VERB
cana-5359	273	9	that	that	SCONJ
cana-5359	273	10	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	273	11	−1(𝔉ℱ	−1(𝔉ℱ	ADJ
cana-5359	273	12	𝛿𝑖𝑛𝑡(𝐿	𝛿𝑖𝑛𝑡(𝐿	NOUN
cana-5359	273	13	)	)	PUNCT
cana-5359	273	14	)	)	PUNCT
cana-5359	274	1	⊆	⊆	NUM
cana-5359	274	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	274	3	−1(𝐿	−1(𝐿	NOUN
cana-5359	274	4	)	)	PUNCT
cana-5359	274	5	.	.	PUNCT
cana-5359	275	1	therefore	therefore	ADV
cana-5359	275	2	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	275	3	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	NOUN
cana-5359	275	4	)	)	PUNCT
cana-5359	275	5	)	)	PUNCT
cana-5359	275	6	)	)	PUNCT
cana-5359	276	1	⊆	⊆	NUM
cana-5359	276	2	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	276	3	−1(𝐿	−1(𝐿	NOUN
cana-5359	276	4	)	)	PUNCT
cana-5359	276	5	)	)	PUNCT
cana-5359	276	6	.	.	PUNCT
cana-5359	277	1	that	that	PRON
cana-5359	277	2	is	be	AUX
cana-5359	277	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	277	4	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	ADJ
cana-5359	277	5	)	)	PUNCT
cana-5359	277	6	)	)	PUNCT
cana-5359	278	1	⊆	⊆	X
cana-5359	278	2	𝔉ℱ𝛿𝛽𝑖𝑛𝑡	𝔉ℱ𝛿𝛽𝑖𝑛𝑡	NOUN
cana-5359	278	3	(	(	PUNCT
cana-5359	278	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	278	5	−1(𝐿	−1(𝐿	NOUN
cana-5359	278	6	)	)	PUNCT
cana-5359	278	7	)	)	PUNCT
cana-5359	278	8	.	.	PUNCT
cana-5359	279	1	conversely	conversely	ADV
cana-5359	279	2	,	,	PUNCT
cana-5359	279	3	let	let	VERB
cana-5359	279	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	279	5	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	VERB
cana-5359	279	6	)	)	PUNCT
cana-5359	279	7	)	)	PUNCT
cana-5359	280	1	⊆	⊆	NUM
cana-5359	280	2	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	280	3	−1(𝐿	−1(𝐿	NOUN
cana-5359	280	4	)	)	PUNCT
cana-5359	280	5	)	)	PUNCT
cana-5359	280	6	for	for	ADP
cana-5359	280	7	all	all	DET
cana-5359	280	8	subset	subset	ADJ
cana-5359	280	9	𝐿	𝐿	PROPN
cana-5359	280	10	of	of	ADP
cana-5359	280	11	𝑋2	𝑋2	PROPN
cana-5359	280	12	.	.	PUNCT
cana-5359	281	1	if	if	SCONJ
cana-5359	281	2	𝐿	𝐿	PROPN
cana-5359	281	3	is	be	AUX
cana-5359	281	4	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	281	5	in	in	ADP
cana-5359	281	6	𝑋2	𝑋2	PROPN
cana-5359	281	7	,	,	PUNCT
cana-5359	281	8	then	then	ADV
cana-5359	281	9	𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	VERB
cana-5359	281	10	)	)	PUNCT
cana-5359	281	11	=	=	SYM
cana-5359	281	12	𝐿	𝐿	PROPN
cana-5359	281	13	.	.	PUNCT
cana-5359	282	1	by	by	ADP
cana-5359	282	2	assumption	assumption	NOUN
cana-5359	282	3	,	,	PUNCT
cana-5359	282	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	282	5	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐿	VERB
cana-5359	282	6	)	)	PUNCT
cana-5359	282	7	)	)	PUNCT
cana-5359	283	1	⊆	⊆	NUM
cana-5359	283	2	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	283	3	−1(𝐿	−1(𝐿	NOUN
cana-5359	283	4	)	)	PUNCT
cana-5359	283	5	)	)	PUNCT
cana-5359	283	6	.	.	PUNCT
cana-5359	284	1	thus	thus	ADV
cana-5359	284	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	284	3	−1(𝐿	−1(𝐿	NOUN
cana-5359	284	4	)	)	PUNCT
cana-5359	284	5	⊆	⊆	NUM
cana-5359	284	6	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	284	7	−1(𝐿	−1(𝐿	NOUN
cana-5359	284	8	)	)	PUNCT
cana-5359	284	9	)	)	PUNCT
cana-5359	284	10	.	.	PUNCT
cana-5359	285	1	but	but	CCONJ
cana-5359	285	2	𝔉ℱ𝛿𝛽𝑖𝑛𝑡	𝔉ℱ𝛿𝛽𝑖𝑛𝑡	NOUN
cana-5359	285	3	(	(	PUNCT
cana-5359	285	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	285	5	−1(𝐿	−1(𝐿	NOUN
cana-5359	285	6	)	)	PUNCT
cana-5359	285	7	)	)	PUNCT
cana-5359	285	8	⊆	⊆	NUM
cana-5359	285	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	285	10	−1(𝐿	−1(𝐿	NOUN
cana-5359	285	11	)	)	PUNCT
cana-5359	285	12	.	.	PUNCT
cana-5359	286	1	therefore	therefore	ADV
cana-5359	286	2	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	286	3	−1(𝐿	−1(𝐿	NOUN
cana-5359	286	4	)	)	PUNCT
cana-5359	286	5	)	)	PUNCT
cana-5359	287	1	=	=	PRON
cana-5359	287	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	287	3	−1(𝐿	−1(𝐿	NOUN
cana-5359	287	4	)	)	PUNCT
cana-5359	287	5	.	.	PUNCT
cana-5359	288	1	that	that	PRON
cana-5359	288	2	is	be	AUX
cana-5359	288	3	,	,	PUNCT
cana-5359	288	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	288	5	−1(𝐿	−1(𝐿	NOUN
cana-5359	288	6	)	)	PUNCT
cana-5359	288	7	is	be	AUX
cana-5359	288	8	𝔉ℱ𝛿𝛽𝑜	𝔉ℱ𝛿𝛽𝑜	PROPN
cana-5359	288	9	in	in	ADP
cana-5359	288	10	𝑋1	𝑋1	PROPN
cana-5359	288	11	,	,	PUNCT
cana-5359	288	12	for	for	ADP
cana-5359	288	13	all	all	DET
cana-5359	288	14	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	288	15	𝐿	𝐿	PROPN
cana-5359	288	16	in	in	ADP
cana-5359	288	17	𝑋2	𝑋2	PROPN
cana-5359	288	18	.	.	PUNCT
cana-5359	289	1	therefore	therefore	ADV
cana-5359	289	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	289	3	is	be	AUX
cana-5359	289	4	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	289	5	in	in	ADP
cana-5359	289	6	𝑋1	𝑋1	PROPN
cana-5359	289	7	.	.	PUNCT
cana-5359	290	1	remark	remark	VERB
cana-5359	290	2	3.3	3.3	NUM
cana-5359	290	3	let	let	VERB
cana-5359	290	4	(	(	PUNCT
cana-5359	290	5	𝑋1	𝑋1	PROPN
cana-5359	290	6	,	,	PUNCT
cana-5359	290	7	𝜏1	𝜏1	NOUN
cana-5359	290	8	)	)	PUNCT
cana-5359	290	9	&	&	CCONJ
cana-5359	290	10	(	(	PUNCT
cana-5359	290	11	𝑋2	𝑋2	PROPN
cana-5359	290	12	,	,	PUNCT
cana-5359	290	13	𝜏2	𝜏2	PROPN
cana-5359	290	14	)	)	PUNCT
cana-5359	291	1	be	be	VERB
cana-5359	291	2	a	a	DET
cana-5359	291	3	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	291	4	’s	’s	PART
cana-5359	291	5	.	.	PUNCT
cana-5359	292	1	let	let	VERB
cana-5359	292	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	292	3	:	:	PUNCT
cana-5359	292	4	(	(	PUNCT
cana-5359	292	5	𝑋1	𝑋1	PROPN
cana-5359	292	6	,	,	PUNCT
cana-5359	292	7	𝜏1	𝜏1	NOUN
cana-5359	292	8	)	)	PUNCT
cana-5359	292	9	→	→	SYM
cana-5359	292	10	(	(	PUNCT
cana-5359	292	11	𝑋2	𝑋2	PROPN
cana-5359	292	12	,	,	PUNCT
cana-5359	292	13	𝜏2	𝜏2	PROPN
cana-5359	292	14	)	)	PUNCT
cana-5359	292	15	be	be	VERB
cana-5359	292	16	a	a	DET
cana-5359	292	17	mapping	mapping	NOUN
cana-5359	292	18	.	.	PUNCT
cana-5359	293	1	if	if	SCONJ
cana-5359	293	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	293	3	is	be	AUX
cana-5359	293	4	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	293	5	,	,	PUNCT
cana-5359	293	6	then	then	ADV
cana-5359	293	7	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	293	8	−1(𝐾	−1(𝐾	NOUN
cana-5359	293	9	)	)	PUNCT
cana-5359	293	10	)	)	PUNCT
cana-5359	293	11	is	be	AUX
cana-5359	293	12	not	not	PART
cana-5359	293	13	necessarily	necessarily	ADV
cana-5359	293	14	equal	equal	ADJ
cana-5359	293	15	to	to	ADP
cana-5359	293	16	h𝔉	h𝔉	NOUN
cana-5359	293	17	−1(𝔉ℱδint(k	−1(𝔉ℱδint(k	ADJ
cana-5359	293	18	)	)	PUNCT
cana-5359	293	19	)	)	PUNCT
cana-5359	293	20	where	where	SCONJ
cana-5359	293	21	k	k	PROPN
cana-5359	293	22	∈	∈	PROPN
cana-5359	293	23	x2	x2	PROPN
cana-5359	293	24	.	.	PUNCT
cana-5359	293	25	example	example	NOUN
cana-5359	293	26	3.6	3.6	NUM
cana-5359	293	27	in	in	ADP
cana-5359	293	28	example	example	NOUN
cana-5359	293	29	3.5	3.5	NUM
cana-5359	293	30	,	,	PUNCT
cana-5359	293	31	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	293	32	is	be	AUX
cana-5359	293	33	a	a	DET
cana-5359	293	34	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	NOUN
cana-5359	293	35	.then	.then	PUNCT
cana-5359	293	36	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	293	37	−1(𝐴1	−1(𝐴1	NOUN
cana-5359	293	38	)	)	PUNCT
cana-5359	293	39	)	)	PUNCT
cana-5359	294	1	=	=	SYM
cana-5359	294	2	𝐴1	𝐴1	PROPN
cana-5359	294	3	.	.	PUNCT
cana-5359	295	1	but	but	CCONJ
cana-5359	295	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	295	3	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴1	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴1	NOUN
cana-5359	295	4	)	)	PUNCT
cana-5359	295	5	)	)	PUNCT
cana-5359	296	1	=	=	SYM
cana-5359	296	2	𝐴1	𝐴1	PROPN
cana-5359	296	3	𝑐.	𝑐.	VERB
cana-5359	296	4	thus	thus	ADV
cana-5359	296	5	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(ℎ𝔉	NUM
cana-5359	296	6	−1(𝐴1	−1(𝐴1	NOUN
cana-5359	296	7	)	)	PUNCT
cana-5359	296	8	)	)	PUNCT
cana-5359	297	1	≠	≠	PROPN
cana-5359	297	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	297	3	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴1	−1(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴1	NOUN
cana-5359	297	4	)	)	PUNCT
cana-5359	297	5	)	)	PUNCT
cana-5359	297	6	.	.	PUNCT
cana-5359	298	1	remark	remark	VERB
cana-5359	298	2	3.4	3.4	NUM
cana-5359	298	3	theorems	theorem	NOUN
cana-5359	298	4	3.2	3.2	NUM
cana-5359	298	5	,	,	PUNCT
cana-5359	298	6	3.3	3.3	NUM
cana-5359	298	7	,	,	PUNCT
cana-5359	298	8	3.4	3.4	NUM
cana-5359	298	9	and	and	CCONJ
cana-5359	298	10	remarks	remark	NOUN
cana-5359	298	11	3.2	3.2	NUM
cana-5359	298	12	,	,	PUNCT
cana-5359	298	13	3.3	3.3	NUM
cana-5359	298	14	are	be	AUX
cana-5359	298	15	true	true	ADJ
cana-5359	298	16	for	for	ADP
cana-5359	298	17	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	298	18	,	,	PUNCT
cana-5359	298	19	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	NOUN
cana-5359	298	20	and	and	CCONJ
cana-5359	298	21	𝔉ℱ𝛿𝛼𝑜𝑠.	𝔉ℱ𝛿𝛼𝑜𝑠.	NOUN
cana-5359	298	22	4	4	NUM
cana-5359	298	23	fermatean	fermatean	NOUN
cana-5359	298	24	fuzzy	fuzzy	ADJ
cana-5359	298	25	𝜹	𝜹	X
cana-5359	298	26	(	(	PUNCT
cana-5359	298	27	resp	resp	NOUN
cana-5359	298	28	.	.	PUNCT
cana-5359	299	1	𝜹	𝜹	X
cana-5359	299	2	pre	pre	ADJ
cana-5359	299	3	,	,	PUNCT
cana-5359	299	4	𝜹	𝜹	X
cana-5359	299	5	semi	semi	ADV
cana-5359	299	6	,	,	PUNCT
cana-5359	299	7	𝜹𝜶	𝜹𝜶	VERB
cana-5359	299	8	and	and	CCONJ
cana-5359	299	9	𝜹𝜷)-irresolute	𝜹𝜷)-irresolute	ADJ
cana-5359	299	10	maps	map	NOUN
cana-5359	299	11	in	in	ADP
cana-5359	299	12	this	this	DET
cana-5359	299	13	section	section	NOUN
cana-5359	299	14	,	,	PUNCT
cana-5359	299	15	we	we	PRON
cana-5359	299	16	introduce	introduce	VERB
cana-5359	299	17	the	the	DET
cana-5359	299	18	concept	concept	NOUN
cana-5359	299	19	of	of	ADP
cana-5359	299	20	fermatean	fermatean	ADJ
cana-5359	299	21	fuzzy	fuzzy	ADJ
cana-5359	299	22	irresoluteness	irresoluteness	NOUN
cana-5359	299	23	called	call	VERB
cana-5359	299	24	fermatean	fermatean	NOUN
cana-5359	299	25	fuzzy	fuzzy	ADJ
cana-5359	299	26	(	(	PUNCT
cana-5359	299	27	resp	resp	NOUN
cana-5359	299	28	.	.	PUNCT
cana-5359	300	1	𝛿	𝛿	ADJ
cana-5359	300	2	,	,	PUNCT
cana-5359	300	3	𝛿𝒫	𝛿𝒫	NOUN
cana-5359	300	4	,	,	PUNCT
cana-5359	300	5	𝛿𝒮	𝛿𝒮	NOUN
cana-5359	300	6	,	,	PUNCT
cana-5359	300	7	𝛿𝛼	𝛿𝛼	NOUN
cana-5359	300	8	and	and	CCONJ
cana-5359	300	9	𝛿𝛽	𝛿𝛽	ADJ
cana-5359	300	10	)	)	PUNCT
cana-5359	300	11	-irresolute	-irresolute	ADJ
cana-5359	300	12	maps	map	NOUN
cana-5359	300	13	by	by	ADP
cana-5359	300	14	using	use	VERB
cana-5359	300	15	𝔉ℱ𝒮𝑜𝑠	𝔉ℱ𝒮𝑜𝑠	PROPN
cana-5359	300	16	(	(	PUNCT
cana-5359	300	17	resp	resp	NOUN
cana-5359	300	18	.	.	PUNCT
cana-5359	301	1	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	301	2	,	,	PUNCT
cana-5359	301	3	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	301	4	,	,	PUNCT
cana-5359	301	5	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	301	6	,	,	PUNCT
cana-5359	301	7	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	301	8	and	and	CCONJ
cana-5359	301	9	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	301	10	)	)	PUNCT
cana-5359	301	11	’s	’	VERB
cana-5359	301	12	and	and	CCONJ
cana-5359	301	13	study	study	VERB
cana-5359	301	14	some	some	PRON
cana-5359	301	15	of	of	ADP
cana-5359	301	16	their	their	PRON
cana-5359	301	17	basic	basic	ADJ
cana-5359	301	18	properties	property	NOUN
cana-5359	301	19	.	.	PUNCT
cana-5359	302	1	this	this	DET
cana-5359	302	2	definition	definition	NOUN
cana-5359	302	3	enables	enable	VERB
cana-5359	302	4	us	we	PRON
cana-5359	302	5	to	to	PART
cana-5359	302	6	obtain	obtain	VERB
cana-5359	302	7	conditions	condition	NOUN
cana-5359	302	8	under	under	ADP
cana-5359	302	9	which	which	PRON
cana-5359	302	10	maps	map	NOUN
cana-5359	302	11	and	and	CCONJ
cana-5359	302	12	inverse	inverse	NOUN
cana-5359	302	13	maps	map	NOUN
cana-5359	302	14	preserve	preserve	VERB
cana-5359	302	15	respective	respective	ADJ
cana-5359	302	16	open	open	ADJ
cana-5359	302	17	sets	set	NOUN
cana-5359	302	18	.	.	PUNCT
cana-5359	303	1	definition	definition	NOUN
cana-5359	303	2	4.1	4.1	NUM
cana-5359	303	3	a	a	DET
cana-5359	303	4	map	map	NOUN
cana-5359	303	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	303	6	:	:	PUNCT
cana-5359	303	7	(	(	PUNCT
cana-5359	303	8	𝑋1	𝑋1	PROPN
cana-5359	303	9	,	,	PUNCT
cana-5359	303	10	𝜏1	𝜏1	NOUN
cana-5359	303	11	)	)	PUNCT
cana-5359	303	12	→	→	SYM
cana-5359	303	13	(	(	PUNCT
cana-5359	303	14	𝑋2	𝑋2	PROPN
cana-5359	303	15	,	,	PUNCT
cana-5359	303	16	𝜏2	𝜏2	PROPN
cana-5359	303	17	)	)	PUNCT
cana-5359	303	18	is	be	AUX
cana-5359	303	19	said	say	VERB
cana-5359	303	20	to	to	PART
cana-5359	303	21	be	be	AUX
cana-5359	303	22	fermatean	fermatean	ADJ
cana-5359	303	23	fuzzy	fuzzy	ADJ
cana-5359	303	24	(	(	PUNCT
cana-5359	303	25	resp	resp	NOUN
cana-5359	303	26	.	.	PUNCT
cana-5359	304	1	𝛿	𝛿	ADJ
cana-5359	304	2	,	,	PUNCT
cana-5359	304	3	𝛿𝒫	𝛿𝒫	NOUN
cana-5359	304	4	,	,	PUNCT
cana-5359	304	5	𝛿𝒮	𝛿𝒮	NOUN
cana-5359	304	6	,	,	PUNCT
cana-5359	304	7	𝛿𝛼	𝛿𝛼	NOUN
cana-5359	304	8	and	and	CCONJ
cana-5359	304	9	𝛿𝛽	𝛿𝛽	ADJ
cana-5359	304	10	)	)	PUNCT
cana-5359	304	11	-irresolute	-irresolute	NOUN
cana-5359	304	12	(	(	PUNCT
cana-5359	304	13	in	in	ADP
cana-5359	304	14	short	short	ADJ
cana-5359	304	15	,	,	PUNCT
cana-5359	304	16	𝔉ℱ𝐼𝑟𝑟	𝔉ℱ𝐼𝑟𝑟	ADJ
cana-5359	304	17	(	(	PUNCT
cana-5359	304	18	resp	resp	NOUN
cana-5359	304	19	.	.	PUNCT
cana-5359	304	20	𝔉ℱ𝛿𝐼𝑟𝑟	𝔉ℱ𝛿𝐼𝑟𝑟	NOUN
cana-5359	304	21	,	,	PUNCT
cana-5359	304	22	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5359	304	23	,	,	PUNCT
cana-5359	304	24	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	NOUN
cana-5359	304	25	,	,	PUNCT
cana-5359	304	26	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	NOUN
cana-5359	304	27	and	and	CCONJ
cana-5359	304	28	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	NOUN
cana-5359	304	29	)	)	PUNCT
cana-5359	304	30	)	)	PUNCT
cana-5359	304	31	map	map	VERB
cana-5359	304	32	if	if	SCONJ
cana-5359	304	33	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	304	34	−1(𝐾	−1(𝐾	NOUN
cana-5359	304	35	)	)	PUNCT
cana-5359	304	36	is	be	AUX
cana-5359	304	37	a	a	DET
cana-5359	304	38	𝔉ℱ𝒮𝑜𝑠	𝔉ℱ𝒮𝑜𝑠	PROPN
cana-5359	304	39	(	(	PUNCT
cana-5359	304	40	resp	resp	NOUN
cana-5359	304	41	.	.	PUNCT
cana-5359	305	1	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	305	2	,	,	PUNCT
cana-5359	305	3	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	305	4	,	,	PUNCT
cana-5359	305	5	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	305	6	,	,	PUNCT
cana-5359	305	7	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	305	8	and	and	CCONJ
cana-5359	305	9	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	305	10	)	)	PUNCT
cana-5359	305	11	in	in	ADP
cana-5359	305	12	(	(	PUNCT
cana-5359	305	13	𝑋1	𝑋1	PROPN
cana-5359	305	14	,	,	PUNCT
cana-5359	305	15	𝜏1	𝜏1	NOUN
cana-5359	305	16	)	)	PUNCT
cana-5359	305	17	for	for	ADP
cana-5359	305	18	each	each	DET
cana-5359	305	19	𝔉ℱ𝒮𝑜𝑠	𝔉ℱ𝒮𝑜𝑠	PROPN
cana-5359	305	20	(	(	PUNCT
cana-5359	305	21	resp	resp	NOUN
cana-5359	305	22	.	.	PUNCT
cana-5359	306	1	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	306	2	,	,	PUNCT
cana-5359	306	3	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	306	4	,	,	PUNCT
cana-5359	306	5	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	306	6	,	,	PUNCT
cana-5359	306	7	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	306	8	and	and	CCONJ
cana-5359	306	9	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	306	10	)	)	PUNCT
cana-5359	306	11	𝐾	𝐾	PROPN
cana-5359	306	12	of	of	ADP
cana-5359	306	13	(	(	PUNCT
cana-5359	306	14	𝑋2	𝑋2	PROPN
cana-5359	306	15	,	,	PUNCT
cana-5359	306	16	𝜏2	𝜏2	PROPN
cana-5359	306	17	)	)	PUNCT
cana-5359	306	18	.	.	PUNCT
cana-5359	307	1	theorem	theorem	VERB
cana-5359	307	2	4.1	4.1	NUM
cana-5359	307	3	let	let	NOUN
cana-5359	307	4	(	(	PUNCT
cana-5359	307	5	𝑋1	𝑋1	PROPN
cana-5359	307	6	,	,	PUNCT
cana-5359	307	7	𝜏1	𝜏1	NOUN
cana-5359	307	8	)	)	PUNCT
cana-5359	307	9	&	&	CCONJ
cana-5359	307	10	(	(	PUNCT
cana-5359	307	11	𝑋2	𝑋2	PROPN
cana-5359	307	12	,	,	PUNCT
cana-5359	307	13	𝜏2	𝜏2	PROPN
cana-5359	307	14	)	)	PUNCT
cana-5359	307	15	be	be	AUX
cana-5359	307	16	a	a	DET
cana-5359	307	17	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	307	18	’s	’s	PART
cana-5359	307	19	.	.	PUNCT
cana-5359	308	1	let	let	VERB
cana-5359	308	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	308	3	:	:	PUNCT
cana-5359	308	4	(	(	PUNCT
cana-5359	308	5	𝑋1	𝑋1	PROPN
cana-5359	308	6	,	,	PUNCT
cana-5359	308	7	𝜏1	𝜏1	NOUN
cana-5359	308	8	)	)	PUNCT
cana-5359	308	9	→	→	SYM
cana-5359	308	10	(	(	PUNCT
cana-5359	308	11	𝑋2	𝑋2	PROPN
cana-5359	308	12	,	,	PUNCT
cana-5359	308	13	𝜏2	𝜏2	PROPN
cana-5359	308	14	)	)	PUNCT
cana-5359	308	15	be	be	VERB
cana-5359	308	16	a	a	DET
cana-5359	308	17	mapping	mapping	NOUN
cana-5359	308	18	.	.	PUNCT
cana-5359	309	1	then	then	ADV
cana-5359	309	2	the	the	DET
cana-5359	309	3	following	following	ADJ
cana-5359	309	4	statements	statement	NOUN
cana-5359	309	5	are	be	AUX
cana-5359	309	6	hold	hold	NOUN
cana-5359	309	7	for	for	ADP
cana-5359	309	8	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	309	9	,	,	PUNCT
cana-5359	309	10	but	but	CCONJ
cana-5359	309	11	not	not	PART
cana-5359	309	12	conversely	conversely	ADV
cana-5359	309	13	.	.	PUNCT
cana-5359	310	1	(	(	PUNCT
cana-5359	310	2	i	i	NOUN
cana-5359	310	3	)	)	PUNCT
cana-5359	310	4	every	every	DET
cana-5359	310	5	𝔉ℱ𝐼𝑟𝑟	𝔉ℱ𝐼𝑟𝑟	ADJ
cana-5359	310	6	map	map	NOUN
cana-5359	310	7	is	be	AUX
cana-5359	310	8	a	a	DET
cana-5359	310	9	𝔉ℱ𝒮𝐶𝑡𝑠.	𝔉ℱ𝒮𝐶𝑡𝑠.	NOUN
cana-5359	310	10	(	(	PUNCT
cana-5359	310	11	ii	ii	NOUN
cana-5359	310	12	)	)	PUNCT
cana-5359	310	13	every	every	DET
cana-5359	310	14	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	NOUN
cana-5359	310	15	map	map	NOUN
cana-5359	310	16	is	be	AUX
cana-5359	310	17	a	a	DET
cana-5359	310	18	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	NUM
cana-5359	310	19	(	(	PUNCT
cana-5359	310	20	iii	iii	NOUN
cana-5359	310	21	)	)	PUNCT
cana-5359	310	22	every	every	DET
cana-5359	310	23	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5359	310	24	map	map	NOUN
cana-5359	310	25	is	be	AUX
cana-5359	310	26	a	a	DET
cana-5359	310	27	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	PROPN
cana-5359	310	28	(	(	PUNCT
cana-5359	310	29	iv	iv	X
cana-5359	310	30	)	)	PUNCT
cana-5359	310	31	every	every	DET
cana-5359	310	32	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5359	310	33	map	map	NOUN
cana-5359	310	34	is	be	AUX
cana-5359	310	35	a	a	DET
cana-5359	310	36	𝔉ℱ𝛿𝛼𝐶𝑡𝑠.	𝔉ℱ𝛿𝛼𝐶𝑡𝑠.	PROPN
cana-5359	310	37	(	(	PUNCT
cana-5359	310	38	v	v	NOUN
cana-5359	310	39	)	)	PUNCT
cana-5359	310	40	every	every	DET
cana-5359	310	41	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5359	310	42	map	map	NOUN
cana-5359	310	43	is	be	AUX
cana-5359	310	44	a	a	DET
cana-5359	310	45	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	NOUN
cana-5359	310	46	proof	proof	NOUN
cana-5359	310	47	.	.	PUNCT
cana-5359	311	1	(	(	PUNCT
cana-5359	311	2	i	i	NOUN
cana-5359	311	3	)	)	PUNCT
cana-5359	311	4	consider	consider	VERB
cana-5359	311	5	a	a	DET
cana-5359	311	6	𝔉ℱ𝐼𝑟𝑟	𝔉ℱ𝐼𝑟𝑟	ADJ
cana-5359	311	7	map	map	NOUN
cana-5359	311	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	311	9	and	and	CCONJ
cana-5359	311	10	a	a	DET
cana-5359	311	11	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	311	12	𝐾	𝐾	PROPN
cana-5359	311	13	in	in	ADP
cana-5359	311	14	𝑋2	𝑋2	ADJ
cana-5359	311	15	.	.	PUNCT
cana-5359	312	1	as	as	SCONJ
cana-5359	312	2	each	each	DET
cana-5359	312	3	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	312	4	is	be	AUX
cana-5359	312	5	a	a	DET
cana-5359	312	6	𝔉ℱ𝒮𝑜𝑠	𝔉ℱ𝒮𝑜𝑠	PROPN
cana-5359	312	7	,	,	PUNCT
cana-5359	312	8	𝐾	𝐾	PROPN
cana-5359	312	9	is	be	AUX
cana-5359	312	10	a	a	DET
cana-5359	312	11	communications	communication	NOUN
cana-5359	312	12	on	on	ADP
cana-5359	312	13	applied	apply	VERB
cana-5359	312	14	nonlinear	nonlinear	ADJ
cana-5359	312	15	analysis	analysis	NOUN
cana-5359	312	16	issn	issn	NOUN
cana-5359	312	17	:	:	PUNCT
cana-5359	312	18	1074	1074	NUM
cana-5359	312	19	-	-	PUNCT
cana-5359	312	20	133x	133x	NUM
cana-5359	312	21	vol	vol	VERB
cana-5359	312	22	32	32	NUM
cana-5359	312	23	no	no	NOUN
cana-5359	312	24	.	.	PUNCT
cana-5359	313	1	10s	10	NOUN
cana-5359	313	2	(	(	PUNCT
cana-5359	313	3	2025	2025	NUM
cana-5359	313	4	)	)	PUNCT
cana-5359	313	5	1919	1919	NUM
cana-5359	313	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	313	7	𝔉ℱ𝒮𝑜𝑠	𝔉ℱ𝒮𝑜𝑠	PROPN
cana-5359	313	8	in	in	ADP
cana-5359	313	9	𝑋2	𝑋2	PROPN
cana-5359	313	10	.	.	PUNCT
cana-5359	314	1	by	by	ADP
cana-5359	314	2	presumption	presumption	NOUN
cana-5359	314	3	,	,	PUNCT
cana-5359	314	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	314	5	−1(𝐾	−1(𝐾	NOUN
cana-5359	314	6	)	)	PUNCT
cana-5359	314	7	is	be	AUX
cana-5359	314	8	a	a	DET
cana-5359	314	9	𝔉ℱ𝒮𝑜𝑠	𝔉ℱ𝒮𝑜𝑠	PROPN
cana-5359	314	10	in	in	ADP
cana-5359	314	11	𝑋1	𝑋1	PROPN
cana-5359	314	12	.	.	PUNCT
cana-5359	315	1	thus	thus	ADV
cana-5359	315	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	315	3	is	be	AUX
cana-5359	315	4	a	a	DET
cana-5359	315	5	𝔉ℱ𝒮𝐶𝑡𝑠	𝔉ℱ𝒮𝐶𝑡𝑠	PROPN
cana-5359	315	6	map	map	NOUN
cana-5359	315	7	.	.	PUNCT
cana-5359	316	1	(	(	PUNCT
cana-5359	316	2	ii	ii	NOUN
cana-5359	316	3	)	)	PUNCT
cana-5359	316	4	consider	consider	VERB
cana-5359	316	5	a	a	PRON
cana-5359	316	6	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	NOUN
cana-5359	316	7	map	map	VERB
cana-5359	316	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	316	9	and	and	CCONJ
cana-5359	316	10	a	a	DET
cana-5359	316	11	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	316	12	𝐾	𝐾	PROPN
cana-5359	316	13	in	in	ADP
cana-5359	316	14	𝑋2	𝑋2	PROPN
cana-5359	316	15	.	.	PUNCT
cana-5359	317	1	as	as	SCONJ
cana-5359	317	2	each	each	DET
cana-5359	317	3	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	317	4	is	be	AUX
cana-5359	317	5	a	a	DET
cana-5359	317	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	317	7	and	and	CCONJ
cana-5359	317	8	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	NOUN
cana-5359	317	9	,	,	PUNCT
cana-5359	317	10	𝐾	𝐾	PROPN
cana-5359	317	11	is	be	AUX
cana-5359	317	12	a	a	DET
cana-5359	317	13	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	317	14	and	and	CCONJ
cana-5359	317	15	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	317	16	in	in	ADP
cana-5359	317	17	𝑋2	𝑋2	PROPN
cana-5359	317	18	.	.	PUNCT
cana-5359	318	1	by	by	ADP
cana-5359	318	2	presumption	presumption	NOUN
cana-5359	318	3	,	,	PUNCT
cana-5359	318	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	318	5	−1(𝐾	−1(𝐾	NOUN
cana-5359	318	6	)	)	PUNCT
cana-5359	318	7	is	be	AUX
cana-5359	318	8	a	a	DET
cana-5359	318	9	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	318	10	in	in	ADP
cana-5359	318	11	𝑋1	𝑋1	PROPN
cana-5359	318	12	.	.	PUNCT
cana-5359	319	1	thus	thus	ADV
cana-5359	319	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	319	3	is	be	AUX
cana-5359	319	4	a	a	DET
cana-5359	319	5	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5359	319	6	map	map	NOUN
cana-5359	319	7	.	.	PUNCT
cana-5359	320	1	(	(	PUNCT
cana-5359	320	2	iii	iii	X
cana-5359	320	3	)	)	PUNCT
cana-5359	320	4	consider	consider	VERB
cana-5359	320	5	a	a	PRON
cana-5359	320	6	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	NOUN
cana-5359	320	7	map	map	VERB
cana-5359	320	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	320	9	and	and	CCONJ
cana-5359	320	10	a	a	DET
cana-5359	320	11	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	320	12	𝐾	𝐾	PROPN
cana-5359	320	13	in	in	SCONJ
cana-5359	320	14	𝑋2	𝑋2	PROPN
cana-5359	320	15	.	.	PUNCT
cana-5359	321	1	as	as	SCONJ
cana-5359	321	2	each	each	DET
cana-5359	321	3	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	321	4	is	be	AUX
cana-5359	321	5	a	a	DET
cana-5359	321	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	321	7	and	and	CCONJ
cana-5359	321	8	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	321	9	,	,	PUNCT
cana-5359	321	10	𝐾	𝐾	PROPN
cana-5359	321	11	is	be	AUX
cana-5359	321	12	a	a	DET
cana-5359	321	13	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	321	14	and	and	CCONJ
cana-5359	321	15	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	321	16	in	in	ADP
cana-5359	321	17	𝑋2	𝑋2	PROPN
cana-5359	321	18	.	.	PUNCT
cana-5359	322	1	by	by	ADP
cana-5359	322	2	presumption	presumption	NOUN
cana-5359	322	3	,	,	PUNCT
cana-5359	322	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	322	5	−1(𝐾	−1(𝐾	NOUN
cana-5359	322	6	)	)	PUNCT
cana-5359	322	7	is	be	AUX
cana-5359	322	8	a	a	DET
cana-5359	322	9	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	322	10	in	in	ADP
cana-5359	322	11	𝑋1	𝑋1	PROPN
cana-5359	322	12	.	.	PUNCT
cana-5359	323	1	thus	thus	ADV
cana-5359	323	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	323	3	is	be	AUX
cana-5359	323	4	a	a	DET
cana-5359	323	5	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	NOUN
cana-5359	323	6	map	map	NOUN
cana-5359	323	7	.	.	PUNCT
cana-5359	324	1	(	(	PUNCT
cana-5359	324	2	iv	iv	X
cana-5359	324	3	)	)	PUNCT
cana-5359	324	4	consider	consider	VERB
cana-5359	324	5	a	a	DET
cana-5359	324	6	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5359	324	7	map	map	NOUN
cana-5359	324	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	324	9	and	and	CCONJ
cana-5359	324	10	a	a	DET
cana-5359	324	11	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	324	12	𝐾	𝐾	PROPN
cana-5359	324	13	in	in	SCONJ
cana-5359	324	14	𝑋2	𝑋2	PROPN
cana-5359	324	15	.	.	PUNCT
cana-5359	325	1	as	as	SCONJ
cana-5359	325	2	each	each	DET
cana-5359	325	3	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	325	4	is	be	AUX
cana-5359	325	5	a	a	DET
cana-5359	325	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	325	7	and	and	CCONJ
cana-5359	325	8	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	325	9	,	,	PUNCT
cana-5359	325	10	𝐾	𝐾	PROPN
cana-5359	325	11	is	be	AUX
cana-5359	325	12	a	a	DET
cana-5359	325	13	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	325	14	and	and	CCONJ
cana-5359	325	15	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	325	16	in	in	ADP
cana-5359	325	17	𝑋2	𝑋2	PROPN
cana-5359	325	18	.	.	PUNCT
cana-5359	326	1	by	by	ADP
cana-5359	326	2	presumption	presumption	NOUN
cana-5359	326	3	,	,	PUNCT
cana-5359	326	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	326	5	−1(𝐾	−1(𝐾	NOUN
cana-5359	326	6	)	)	PUNCT
cana-5359	326	7	is	be	AUX
cana-5359	326	8	a	a	DET
cana-5359	326	9	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	326	10	in	in	ADP
cana-5359	326	11	𝑋1	𝑋1	PROPN
cana-5359	326	12	.	.	PUNCT
cana-5359	327	1	thus	thus	ADV
cana-5359	327	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	327	3	is	be	AUX
cana-5359	327	4	a	a	DET
cana-5359	327	5	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	ADJ
cana-5359	327	6	map	map	NOUN
cana-5359	327	7	.	.	PUNCT
cana-5359	328	1	(	(	PUNCT
cana-5359	328	2	v	v	NOUN
cana-5359	328	3	)	)	PUNCT
cana-5359	328	4	consider	consider	VERB
cana-5359	328	5	a	a	DET
cana-5359	328	6	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	NOUN
cana-5359	328	7	map	map	NOUN
cana-5359	328	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	328	9	and	and	CCONJ
cana-5359	328	10	a	a	DET
cana-5359	328	11	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	328	12	𝐾	𝐾	PROPN
cana-5359	328	13	in	in	ADP
cana-5359	328	14	𝑋2	𝑋2	PROPN
cana-5359	328	15	.	.	PUNCT
cana-5359	329	1	as	as	SCONJ
cana-5359	329	2	each	each	DET
cana-5359	329	3	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	329	4	is	be	AUX
cana-5359	329	5	a	a	DET
cana-5359	329	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	329	7	and	and	CCONJ
cana-5359	329	8	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	329	9	,	,	PUNCT
cana-5359	329	10	𝐾	𝐾	PROPN
cana-5359	329	11	is	be	AUX
cana-5359	329	12	a	a	DET
cana-5359	329	13	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	329	14	and	and	CCONJ
cana-5359	329	15	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	329	16	in	in	ADP
cana-5359	329	17	𝑋2	𝑋2	PROPN
cana-5359	329	18	.	.	PUNCT
cana-5359	330	1	by	by	ADP
cana-5359	330	2	presumption	presumption	NOUN
cana-5359	330	3	,	,	PUNCT
cana-5359	330	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	330	5	−1(𝐾	−1(𝐾	NOUN
cana-5359	330	6	)	)	PUNCT
cana-5359	330	7	is	be	AUX
cana-5359	330	8	a	a	DET
cana-5359	330	9	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	330	10	in	in	ADP
cana-5359	330	11	𝑋1	𝑋1	PROPN
cana-5359	330	12	.	.	PUNCT
cana-5359	331	1	thus	thus	ADV
cana-5359	331	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	331	3	is	be	AUX
cana-5359	331	4	a	a	DET
cana-5359	331	5	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	331	6	map	map	NOUN
cana-5359	331	7	.	.	PUNCT
cana-5359	332	1	example	example	NOUN
cana-5359	332	2	4.1	4.1	NUM
cana-5359	332	3	let	let	VERB
cana-5359	332	4	𝑋1	𝑋1	NOUN
cana-5359	332	5	=	=	SYM
cana-5359	332	6	𝑋2	𝑋2	VERB
cana-5359	332	7	=	=	SYM
cana-5359	332	8	𝑋	𝑋	NOUN
cana-5359	332	9	=	=	PUNCT
cana-5359	332	10	{	{	PUNCT
cana-5359	332	11	𝑎	𝑎	NOUN
cana-5359	332	12	,	,	PUNCT
cana-5359	332	13	𝑏	𝑏	NOUN
cana-5359	332	14	}	}	PUNCT
cana-5359	332	15	and	and	CCONJ
cana-5359	332	16	the	the	DET
cana-5359	332	17	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	332	18	’s	’s	PART
cana-5359	332	19	𝐴1	𝐴1	PROPN
cana-5359	332	20	,	,	PUNCT
cana-5359	332	21	𝐴2	𝐴2	PROPN
cana-5359	332	22	,	,	PUNCT
cana-5359	332	23	𝐵1	𝐵1	NOUN
cana-5359	332	24	and	and	CCONJ
cana-5359	332	25	𝐵2	𝐵2	NOUN
cana-5359	332	26	are	be	AUX
cana-5359	332	27	defined	define	VERB
cana-5359	332	28	as	as	ADP
cana-5359	332	29	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	332	30	(	(	PUNCT
cana-5359	332	31	𝑎	𝑎	NOUN
cana-5359	332	32	)	)	PUNCT
cana-5359	332	33	=	=	SYM
cana-5359	332	34	0.2	0.2	NUM
cana-5359	332	35	,	,	PUNCT
cana-5359	332	36	𝛽𝐴1	𝛽𝐴1	X
cana-5359	332	37	(	(	PUNCT
cana-5359	332	38	𝑎	𝑎	NOUN
cana-5359	332	39	)	)	PUNCT
cana-5359	332	40	=	=	SYM
cana-5359	332	41	0.7	0.7	NUM
cana-5359	332	42	,	,	PUNCT
cana-5359	332	43	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	332	44	(	(	PUNCT
cana-5359	332	45	𝑏	𝑏	NOUN
cana-5359	332	46	)	)	PUNCT
cana-5359	332	47	=	=	SYM
cana-5359	332	48	0.1	0.1	NUM
cana-5359	332	49	,	,	PUNCT
cana-5359	332	50	𝛽𝐴1	𝛽𝐴1	X
cana-5359	332	51	(	(	PUNCT
cana-5359	332	52	𝑏	𝑏	NOUN
cana-5359	332	53	)	)	PUNCT
cana-5359	332	54	=	=	SYM
cana-5359	332	55	0.8	0.8	NUM
cana-5359	332	56	;	;	PUNCT
cana-5359	332	57	𝛼𝐴2	𝛼𝐴2	NUM
cana-5359	332	58	(	(	PUNCT
cana-5359	332	59	𝑎	𝑎	NOUN
cana-5359	332	60	)	)	PUNCT
cana-5359	332	61	=	=	SYM
cana-5359	332	62	0.3	0.3	NUM
cana-5359	332	63	,	,	PUNCT
cana-5359	332	64	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	332	65	(	(	PUNCT
cana-5359	332	66	𝑎	𝑎	NOUN
cana-5359	332	67	)	)	PUNCT
cana-5359	332	68	=	=	SYM
cana-5359	332	69	0.6	0.6	NUM
cana-5359	332	70	,	,	PUNCT
cana-5359	332	71	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5359	332	72	(	(	PUNCT
cana-5359	332	73	𝑏	𝑏	NOUN
cana-5359	332	74	)	)	PUNCT
cana-5359	332	75	=	=	SYM
cana-5359	332	76	0.4	0.4	NUM
cana-5359	332	77	,	,	PUNCT
cana-5359	332	78	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	332	79	(	(	PUNCT
cana-5359	332	80	𝑏	𝑏	NOUN
cana-5359	332	81	)	)	PUNCT
cana-5359	332	82	=	=	SYM
cana-5359	332	83	0.5	0.5	NUM
cana-5359	332	84	;	;	PUNCT
cana-5359	332	85	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5359	332	86	(	(	PUNCT
cana-5359	332	87	𝑎	𝑎	NOUN
cana-5359	332	88	)	)	PUNCT
cana-5359	332	89	=	=	SYM
cana-5359	332	90	0.1	0.1	NUM
cana-5359	332	91	,	,	PUNCT
cana-5359	332	92	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5359	332	93	(	(	PUNCT
cana-5359	332	94	𝑎	𝑎	NOUN
cana-5359	332	95	)	)	PUNCT
cana-5359	332	96	=	=	SYM
cana-5359	332	97	0.9	0.9	NUM
cana-5359	332	98	,	,	PUNCT
cana-5359	332	99	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5359	332	100	(	(	PUNCT
cana-5359	332	101	𝑏	𝑏	NOUN
cana-5359	332	102	)	)	PUNCT
cana-5359	332	103	=	=	SYM
cana-5359	332	104	0.2	0.2	NUM
cana-5359	332	105	,	,	PUNCT
cana-5359	332	106	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5359	332	107	(	(	PUNCT
cana-5359	332	108	𝑏	𝑏	NOUN
cana-5359	332	109	)	)	PUNCT
cana-5359	332	110	=	=	SYM
cana-5359	332	111	0.9	0.9	NUM
cana-5359	332	112	;	;	PUNCT
cana-5359	332	113	𝛼𝐵2	𝛼𝐵2	NUM
cana-5359	332	114	(	(	PUNCT
cana-5359	332	115	𝑎	𝑎	NOUN
cana-5359	332	116	)	)	PUNCT
cana-5359	332	117	=	=	SYM
cana-5359	332	118	0.2	0.2	NUM
cana-5359	332	119	,	,	PUNCT
cana-5359	332	120	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5359	332	121	(	(	PUNCT
cana-5359	332	122	𝑎	𝑎	NOUN
cana-5359	332	123	)	)	PUNCT
cana-5359	332	124	=	=	SYM
cana-5359	332	125	0.3	0.3	NUM
cana-5359	332	126	,	,	PUNCT
cana-5359	332	127	𝛼𝐵2	𝛼𝐵2	NUM
cana-5359	332	128	(	(	PUNCT
cana-5359	332	129	𝑏	𝑏	NOUN
cana-5359	332	130	)	)	PUNCT
cana-5359	332	131	=	=	SYM
cana-5359	332	132	0.4	0.4	NUM
cana-5359	332	133	,	,	PUNCT
cana-5359	332	134	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5359	332	135	(	(	PUNCT
cana-5359	332	136	𝑏	𝑏	NOUN
cana-5359	332	137	)	)	PUNCT
cana-5359	332	138	=	=	SYM
cana-5359	332	139	0.7	0.7	NUM
cana-5359	332	140	;	;	PUNCT
cana-5359	332	141	let	let	VERB
cana-5359	332	142	𝜏1	𝜏1	NOUN
cana-5359	332	143	=	=	PUNCT
cana-5359	332	144	{	{	PUNCT
cana-5359	332	145	0𝔉	0𝔉	PROPN
cana-5359	332	146	,	,	PUNCT
cana-5359	332	147	1𝔉	1𝔉	NOUN
cana-5359	332	148	,	,	PUNCT
cana-5359	332	149	𝐴1	𝐴1	PROPN
cana-5359	332	150	,	,	PUNCT
cana-5359	332	151	𝐴2	𝐴2	PROPN
cana-5359	332	152	}	}	PUNCT
cana-5359	332	153	and	and	CCONJ
cana-5359	332	154	𝜏2	𝜏2	PROPN
cana-5359	332	155	=	=	SYM
cana-5359	332	156	{	{	PUNCT
cana-5359	332	157	0𝔉	0𝔉	PROPN
cana-5359	332	158	,	,	PUNCT
cana-5359	332	159	1𝔉	1𝔉	NOUN
cana-5359	332	160	,	,	PUNCT
cana-5359	332	161	𝐵1	𝐵1	PROPN
cana-5359	332	162	,	,	PUNCT
cana-5359	332	163	𝐵2	𝐵2	NOUN
cana-5359	332	164	}	}	PUNCT
cana-5359	332	165	are	be	AUX
cana-5359	332	166	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5359	332	167	’s	’s	NOUN
cana-5359	332	168	on	on	ADP
cana-5359	332	169	𝑋	𝑋	PROPN
cana-5359	332	170	and	and	CCONJ
cana-5359	332	171	let	let	VERB
cana-5359	332	172	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	332	173	:	:	PUNCT
cana-5359	332	174	(	(	PUNCT
cana-5359	332	175	𝑋1	𝑋1	PROPN
cana-5359	332	176	,	,	PUNCT
cana-5359	332	177	𝜏1	𝜏1	NOUN
cana-5359	332	178	)	)	PUNCT
cana-5359	332	179	→	→	SYM
cana-5359	332	180	(	(	PUNCT
cana-5359	332	181	𝑋2	𝑋2	PROPN
cana-5359	332	182	,	,	PUNCT
cana-5359	332	183	𝜏2	𝜏2	PROPN
cana-5359	332	184	)	)	PUNCT
cana-5359	332	185	be	be	VERB
cana-5359	332	186	an	an	DET
cana-5359	332	187	identity	identity	NOUN
cana-5359	332	188	function	function	NOUN
cana-5359	332	189	,	,	PUNCT
cana-5359	332	190	then	then	ADV
cana-5359	332	191	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	332	192	is	be	AUX
cana-5359	332	193	𝔉ℱ𝒮𝐶𝑡𝑠	𝔉ℱ𝒮𝐶𝑡𝑠	PROPN
cana-5359	332	194	(	(	PUNCT
cana-5359	332	195	resp	resp	NOUN
cana-5359	332	196	.	.	PUNCT
cana-5359	332	197	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5359	332	198	)	)	PUNCT
cana-5359	332	199	but	but	CCONJ
cana-5359	332	200	not	not	PART
cana-5359	332	201	𝔉ℱ𝐼𝑟𝑟	𝔉ℱ𝐼𝑟𝑟	ADJ
cana-5359	332	202	(	(	PUNCT
cana-5359	332	203	resp	resp	NOUN
cana-5359	332	204	.	.	PUNCT
cana-5359	332	205	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5359	332	206	)	)	PUNCT
cana-5359	332	207	.	.	PUNCT
cana-5359	333	1	since	since	ADV
cana-5359	333	2	,	,	PUNCT
cana-5359	333	3	𝐴2	𝐴2	PROPN
cana-5359	333	4	𝑐	𝑐	PROPN
cana-5359	333	5	is	be	AUX
cana-5359	333	6	a	a	DET
cana-5359	333	7	𝔉ℱ𝒮𝑜	𝔉ℱ𝒮𝑜	NOUN
cana-5359	333	8	(	(	PUNCT
cana-5359	333	9	resp	resp	NOUN
cana-5359	333	10	.	.	PUNCT
cana-5359	334	1	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	NOUN
cana-5359	334	2	)	)	PUNCT
cana-5359	334	3	set	set	VERB
cana-5359	334	4	in	in	ADP
cana-5359	334	5	𝑋2	𝑋2	ADV
cana-5359	334	6	but	but	CCONJ
cana-5359	334	7	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	334	8	−1(𝐴2	−1(𝐴2	VERB
cana-5359	334	9	𝑐	𝑐	NOUN
cana-5359	334	10	)	)	PUNCT
cana-5359	334	11	=	=	PUNCT
cana-5359	335	1	𝐴2	𝐴2	PROPN
cana-5359	335	2	𝑐	𝑐	PROPN
cana-5359	335	3	is	be	AUX
cana-5359	335	4	not	not	PART
cana-5359	335	5	𝔉ℱ𝒮𝑜	𝔉ℱ𝒮𝑜	NOUN
cana-5359	335	6	(	(	PUNCT
cana-5359	335	7	resp	resp	NOUN
cana-5359	335	8	.	.	PUNCT
cana-5359	336	1	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	NOUN
cana-5359	336	2	)	)	PUNCT
cana-5359	337	1	set	set	VERB
cana-5359	337	2	in	in	ADP
cana-5359	337	3	𝑋1	𝑋1	PROPN
cana-5359	337	4	.	.	PUNCT
cana-5359	338	1	example	example	NOUN
cana-5359	338	2	4.2	4.2	NUM
cana-5359	338	3	let	let	VERB
cana-5359	338	4	𝑋1	𝑋1	NOUN
cana-5359	338	5	=	=	SYM
cana-5359	338	6	𝑋2	𝑋2	VERB
cana-5359	338	7	=	=	SYM
cana-5359	338	8	𝑋	𝑋	NOUN
cana-5359	338	9	=	=	PUNCT
cana-5359	338	10	{	{	PUNCT
cana-5359	338	11	𝑎	𝑎	NOUN
cana-5359	338	12	,	,	PUNCT
cana-5359	338	13	𝑏	𝑏	NOUN
cana-5359	338	14	}	}	PUNCT
cana-5359	338	15	and	and	CCONJ
cana-5359	338	16	the	the	DET
cana-5359	338	17	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	338	18	’s	’s	PART
cana-5359	338	19	𝐴1	𝐴1	PROPN
cana-5359	338	20	,	,	PUNCT
cana-5359	338	21	𝐴2	𝐴2	PROPN
cana-5359	338	22	,	,	PUNCT
cana-5359	338	23	𝐴3	𝐴3	PROPN
cana-5359	338	24	,	,	PUNCT
cana-5359	338	25	𝐴4	𝐴4	PROPN
cana-5359	338	26	,	,	PUNCT
cana-5359	338	27	𝐵1	𝐵1	PROPN
cana-5359	338	28	,	,	PUNCT
cana-5359	338	29	𝐵2	𝐵2	NOUN
cana-5359	338	30	,	,	PUNCT
cana-5359	338	31	𝐵3	𝐵3	NOUN
cana-5359	338	32	and	and	CCONJ
cana-5359	338	33	𝐵4	𝐵4	NOUN
cana-5359	338	34	are	be	AUX
cana-5359	338	35	defined	define	VERB
cana-5359	338	36	as	as	ADP
cana-5359	338	37	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	338	38	(	(	PUNCT
cana-5359	338	39	𝑎	𝑎	NOUN
cana-5359	338	40	)	)	PUNCT
cana-5359	338	41	=	=	SYM
cana-5359	338	42	0.4	0.4	NUM
cana-5359	338	43	,	,	PUNCT
cana-5359	338	44	𝛽𝐴1	𝛽𝐴1	X
cana-5359	338	45	(	(	PUNCT
cana-5359	338	46	𝑎	𝑎	NOUN
cana-5359	338	47	)	)	PUNCT
cana-5359	338	48	=	=	SYM
cana-5359	338	49	0.6	0.6	NUM
cana-5359	338	50	,	,	PUNCT
cana-5359	338	51	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	338	52	(	(	PUNCT
cana-5359	338	53	𝑏	𝑏	NOUN
cana-5359	338	54	)	)	PUNCT
cana-5359	338	55	=	=	SYM
cana-5359	338	56	0.5	0.5	NUM
cana-5359	338	57	,	,	PUNCT
cana-5359	338	58	𝛽𝐴1	𝛽𝐴1	X
cana-5359	338	59	(	(	PUNCT
cana-5359	338	60	𝑏	𝑏	NOUN
cana-5359	338	61	)	)	PUNCT
cana-5359	339	1	=	=	NOUN
cana-5359	339	2	0.5	0.5	NUM
cana-5359	339	3	;	;	PUNCT
cana-5359	339	4	𝛼𝐴2	𝛼𝐴2	NUM
cana-5359	339	5	(	(	PUNCT
cana-5359	339	6	𝑎	𝑎	NOUN
cana-5359	339	7	)	)	PUNCT
cana-5359	339	8	=	=	SYM
cana-5359	339	9	0.6	0.6	NUM
cana-5359	339	10	,	,	PUNCT
cana-5359	339	11	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	339	12	(	(	PUNCT
cana-5359	339	13	𝑎	𝑎	NOUN
cana-5359	339	14	)	)	PUNCT
cana-5359	339	15	=	=	SYM
cana-5359	339	16	0.4	0.4	NUM
cana-5359	339	17	,	,	PUNCT
cana-5359	339	18	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5359	339	19	(	(	PUNCT
cana-5359	339	20	𝑏	𝑏	NOUN
cana-5359	339	21	)	)	PUNCT
cana-5359	339	22	=	=	SYM
cana-5359	339	23	0.6	0.6	NUM
cana-5359	339	24	,	,	PUNCT
cana-5359	339	25	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	339	26	(	(	PUNCT
cana-5359	339	27	𝑏	𝑏	NOUN
cana-5359	339	28	)	)	PUNCT
cana-5359	339	29	=	=	SYM
cana-5359	339	30	0.4	0.4	NUM
cana-5359	339	31	;	;	PUNCT
cana-5359	339	32	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	339	33	(	(	PUNCT
cana-5359	339	34	𝑎	𝑎	NOUN
cana-5359	339	35	)	)	PUNCT
cana-5359	339	36	=	=	SYM
cana-5359	339	37	0.7	0.7	NUM
cana-5359	339	38	,	,	PUNCT
cana-5359	339	39	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	339	40	(	(	PUNCT
cana-5359	339	41	𝑎	𝑎	NOUN
cana-5359	339	42	)	)	PUNCT
cana-5359	339	43	=	=	SYM
cana-5359	339	44	0.3	0.3	NUM
cana-5359	339	45	,	,	PUNCT
cana-5359	339	46	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	339	47	(	(	PUNCT
cana-5359	339	48	𝑏	𝑏	NOUN
cana-5359	339	49	)	)	PUNCT
cana-5359	339	50	=	=	SYM
cana-5359	339	51	0.6	0.6	NUM
cana-5359	339	52	,	,	PUNCT
cana-5359	339	53	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	339	54	(	(	PUNCT
cana-5359	339	55	𝑏	𝑏	NOUN
cana-5359	339	56	)	)	PUNCT
cana-5359	339	57	=	=	SYM
cana-5359	339	58	0.4	0.4	NUM
cana-5359	339	59	;	;	PUNCT
cana-5359	339	60	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5359	339	61	(	(	PUNCT
cana-5359	339	62	𝑎	𝑎	NOUN
cana-5359	339	63	)	)	PUNCT
cana-5359	339	64	=	=	SYM
cana-5359	339	65	0.4	0.4	NUM
cana-5359	339	66	,	,	PUNCT
cana-5359	339	67	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5359	339	68	(	(	PUNCT
cana-5359	339	69	𝑎	𝑎	NOUN
cana-5359	339	70	)	)	PUNCT
cana-5359	339	71	=	=	SYM
cana-5359	339	72	0.6	0.6	NUM
cana-5359	339	73	,	,	PUNCT
cana-5359	339	74	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5359	339	75	(	(	PUNCT
cana-5359	339	76	𝑏	𝑏	NOUN
cana-5359	339	77	)	)	PUNCT
cana-5359	339	78	=	=	SYM
cana-5359	339	79	0.4	0.4	NUM
cana-5359	339	80	,	,	PUNCT
cana-5359	339	81	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5359	339	82	(	(	PUNCT
cana-5359	339	83	𝑏	𝑏	NOUN
cana-5359	339	84	)	)	PUNCT
cana-5359	339	85	=	=	SYM
cana-5359	339	86	0.6	0.6	NUM
cana-5359	339	87	;	;	PUNCT
cana-5359	339	88	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5359	339	89	(	(	PUNCT
cana-5359	339	90	𝑎	𝑎	NOUN
cana-5359	339	91	)	)	PUNCT
cana-5359	339	92	=	=	SYM
cana-5359	339	93	0.2	0.2	NUM
cana-5359	339	94	,	,	PUNCT
cana-5359	339	95	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5359	339	96	(	(	PUNCT
cana-5359	339	97	𝑎	𝑎	NOUN
cana-5359	339	98	)	)	PUNCT
cana-5359	339	99	=	=	SYM
cana-5359	339	100	0.8	0.8	NUM
cana-5359	339	101	,	,	PUNCT
cana-5359	339	102	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5359	339	103	(	(	PUNCT
cana-5359	339	104	𝑏	𝑏	NOUN
cana-5359	339	105	)	)	PUNCT
cana-5359	339	106	=	=	SYM
cana-5359	339	107	0.4	0.4	NUM
cana-5359	339	108	,	,	PUNCT
cana-5359	339	109	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5359	339	110	(	(	PUNCT
cana-5359	339	111	𝑏	𝑏	NOUN
cana-5359	339	112	)	)	PUNCT
cana-5359	339	113	=	=	SYM
cana-5359	339	114	0.6	0.6	NUM
cana-5359	339	115	;	;	PUNCT
cana-5359	339	116	𝛼𝐵2	𝛼𝐵2	NUM
cana-5359	339	117	(	(	PUNCT
cana-5359	339	118	𝑎	𝑎	NOUN
cana-5359	339	119	)	)	PUNCT
cana-5359	339	120	=	=	SYM
cana-5359	339	121	0.1	0.1	NUM
cana-5359	339	122	,	,	PUNCT
cana-5359	339	123	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5359	339	124	(	(	PUNCT
cana-5359	339	125	𝑎	𝑎	NOUN
cana-5359	339	126	)	)	PUNCT
cana-5359	339	127	=	=	SYM
cana-5359	339	128	0.9	0.9	NUM
cana-5359	339	129	,	,	PUNCT
cana-5359	339	130	𝛼𝐵2	𝛼𝐵2	NUM
cana-5359	339	131	(	(	PUNCT
cana-5359	339	132	𝑏	𝑏	NOUN
cana-5359	339	133	)	)	PUNCT
cana-5359	339	134	=	=	SYM
cana-5359	339	135	0.3	0.3	NUM
cana-5359	339	136	,	,	PUNCT
cana-5359	339	137	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5359	339	138	(	(	PUNCT
cana-5359	339	139	𝑏	𝑏	NOUN
cana-5359	339	140	)	)	PUNCT
cana-5359	339	141	=	=	SYM
cana-5359	339	142	0.7	0.7	NUM
cana-5359	339	143	;	;	PUNCT
cana-5359	339	144	𝛼𝐵3	𝛼𝐵3	PROPN
cana-5359	339	145	(	(	PUNCT
cana-5359	339	146	𝑎	𝑎	NOUN
cana-5359	339	147	)	)	PUNCT
cana-5359	339	148	=	=	SYM
cana-5359	339	149	0.9	0.9	NUM
cana-5359	339	150	,	,	PUNCT
cana-5359	339	151	𝛽𝐵3	𝛽𝐵3	PROPN
cana-5359	339	152	(	(	PUNCT
cana-5359	339	153	𝑎	𝑎	NOUN
cana-5359	339	154	)	)	PUNCT
cana-5359	339	155	=	=	SYM
cana-5359	339	156	0.1	0.1	NUM
cana-5359	339	157	,	,	PUNCT
cana-5359	339	158	𝛼𝐵3	𝛼𝐵3	PROPN
cana-5359	339	159	(	(	PUNCT
cana-5359	339	160	𝑏	𝑏	NOUN
cana-5359	339	161	)	)	PUNCT
cana-5359	339	162	=	=	SYM
cana-5359	339	163	0.7	0.7	NUM
cana-5359	339	164	,	,	PUNCT
cana-5359	339	165	𝛽𝐵3	𝛽𝐵3	PROPN
cana-5359	339	166	(	(	PUNCT
cana-5359	339	167	𝑏	𝑏	NOUN
cana-5359	339	168	)	)	PUNCT
cana-5359	339	169	=	=	SYM
cana-5359	339	170	0.3	0.3	NUM
cana-5359	339	171	;	;	PUNCT
cana-5359	339	172	𝛼𝐵4	𝛼𝐵4	PROPN
cana-5359	339	173	(	(	PUNCT
cana-5359	339	174	𝑎	𝑎	NOUN
cana-5359	339	175	)	)	PUNCT
cana-5359	339	176	=	=	SYM
cana-5359	339	177	0.2	0.2	NUM
cana-5359	339	178	,	,	PUNCT
cana-5359	339	179	𝛽𝐵4	𝛽𝐵4	PROPN
cana-5359	339	180	(	(	PUNCT
cana-5359	339	181	𝑎	𝑎	NOUN
cana-5359	339	182	)	)	PUNCT
cana-5359	339	183	=	=	SYM
cana-5359	339	184	0.8	0.8	NUM
cana-5359	339	185	,	,	PUNCT
cana-5359	339	186	𝛼𝐵4	𝛼𝐵4	PROPN
cana-5359	339	187	(	(	PUNCT
cana-5359	339	188	𝑏	𝑏	NOUN
cana-5359	339	189	)	)	PUNCT
cana-5359	339	190	=	=	SYM
cana-5359	339	191	0.3	0.3	NUM
cana-5359	339	192	,	,	PUNCT
cana-5359	339	193	𝛽𝐵4	𝛽𝐵4	PROPN
cana-5359	339	194	(	(	PUNCT
cana-5359	339	195	𝑏	𝑏	NOUN
cana-5359	339	196	)	)	PUNCT
cana-5359	339	197	=	=	SYM
cana-5359	339	198	0.7	0.7	NUM
cana-5359	339	199	;	;	PUNCT
cana-5359	339	200	communications	communication	NOUN
cana-5359	339	201	on	on	ADP
cana-5359	339	202	applied	apply	VERB
cana-5359	339	203	nonlinear	nonlinear	ADJ
cana-5359	339	204	analysis	analysis	NOUN
cana-5359	339	205	issn	issn	NOUN
cana-5359	339	206	:	:	PUNCT
cana-5359	339	207	1074	1074	NUM
cana-5359	339	208	-	-	PUNCT
cana-5359	339	209	133x	133x	NUM
cana-5359	339	210	vol	vol	VERB
cana-5359	339	211	32	32	NUM
cana-5359	339	212	no	no	NOUN
cana-5359	339	213	.	.	PUNCT
cana-5359	340	1	10s	10	NOUN
cana-5359	340	2	(	(	PUNCT
cana-5359	340	3	2025	2025	NUM
cana-5359	340	4	)	)	PUNCT
cana-5359	340	5	1920	1920	NUM
cana-5359	340	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	340	7	let	let	VERB
cana-5359	340	8	𝜏1	𝜏1	NOUN
cana-5359	340	9	=	=	PUNCT
cana-5359	340	10	{	{	PUNCT
cana-5359	340	11	0𝔉	0𝔉	PROPN
cana-5359	340	12	,	,	PUNCT
cana-5359	340	13	1𝔉	1𝔉	NOUN
cana-5359	340	14	,	,	PUNCT
cana-5359	340	15	𝐴1	𝐴1	PROPN
cana-5359	340	16	,	,	PUNCT
cana-5359	340	17	𝐴2	𝐴2	PROPN
cana-5359	340	18	,	,	PUNCT
cana-5359	340	19	𝐴3	𝐴3	PROPN
cana-5359	340	20	,	,	PUNCT
cana-5359	340	21	𝐴4	𝐴4	PROPN
cana-5359	340	22	}	}	PUNCT
cana-5359	340	23	and	and	CCONJ
cana-5359	340	24	𝜏2	𝜏2	PROPN
cana-5359	340	25	=	=	SYM
cana-5359	340	26	{	{	PUNCT
cana-5359	340	27	0𝔉	0𝔉	PROPN
cana-5359	340	28	,	,	PUNCT
cana-5359	340	29	1𝔉	1𝔉	NOUN
cana-5359	340	30	,	,	PUNCT
cana-5359	340	31	𝐵1	𝐵1	PROPN
cana-5359	340	32	,	,	PUNCT
cana-5359	340	33	𝐵2	𝐵2	NOUN
cana-5359	340	34	,	,	PUNCT
cana-5359	340	35	𝐵3	𝐵3	PROPN
cana-5359	340	36	,	,	PUNCT
cana-5359	340	37	𝐵4	𝐵4	NOUN
cana-5359	340	38	}	}	PUNCT
cana-5359	340	39	are	be	AUX
cana-5359	340	40	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	340	41	’s	’s	ADV
cana-5359	340	42	on	on	ADP
cana-5359	340	43	𝑋	𝑋	PROPN
cana-5359	340	44	and	and	CCONJ
cana-5359	340	45	let	let	VERB
cana-5359	340	46	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	340	47	:	:	PUNCT
cana-5359	340	48	(	(	PUNCT
cana-5359	340	49	𝑋1	𝑋1	PROPN
cana-5359	340	50	,	,	PUNCT
cana-5359	340	51	𝜏1	𝜏1	NOUN
cana-5359	340	52	)	)	PUNCT
cana-5359	340	53	→	→	SYM
cana-5359	340	54	(	(	PUNCT
cana-5359	340	55	𝑋2	𝑋2	PROPN
cana-5359	340	56	,	,	PUNCT
cana-5359	340	57	𝜏2	𝜏2	PROPN
cana-5359	340	58	)	)	PUNCT
cana-5359	340	59	be	be	VERB
cana-5359	340	60	an	an	DET
cana-5359	340	61	identity	identity	NOUN
cana-5359	340	62	function	function	NOUN
cana-5359	340	63	,	,	PUNCT
cana-5359	340	64	then	then	ADV
cana-5359	340	65	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	340	66	is	be	AUX
cana-5359	340	67	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5359	340	68	but	but	CCONJ
cana-5359	340	69	not	not	PART
cana-5359	340	70	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	PRON
cana-5359	340	71	.	.	PUNCT
cana-5359	341	1	since	since	ADV
cana-5359	341	2	,	,	PUNCT
cana-5359	341	3	𝐴4	𝐴4	PROPN
cana-5359	341	4	is	be	AUX
cana-5359	341	5	a	a	DET
cana-5359	341	6	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	ADJ
cana-5359	341	7	set	set	NOUN
cana-5359	341	8	in	in	ADP
cana-5359	341	9	𝑋2	𝑋2	ADJ
cana-5359	341	10	but	but	CCONJ
cana-5359	341	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	341	12	−1(𝐴4	−1(𝐴4	ADJ
cana-5359	341	13	)	)	PUNCT
cana-5359	342	1	=	=	PUNCT
cana-5359	342	2	𝐴4	𝐴4	PROPN
cana-5359	342	3	is	be	AUX
cana-5359	342	4	not	not	PART
cana-5359	342	5	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	NOUN
cana-5359	342	6	set	set	NOUN
cana-5359	342	7	in	in	ADP
cana-5359	342	8	𝑋1	𝑋1	PROPN
cana-5359	342	9	.	.	PUNCT
cana-5359	343	1	example	example	NOUN
cana-5359	343	2	4.3	4.3	NUM
cana-5359	343	3	let	let	VERB
cana-5359	343	4	𝑋1	𝑋1	NOUN
cana-5359	343	5	=	=	SYM
cana-5359	343	6	𝑋2	𝑋2	VERB
cana-5359	343	7	=	=	SYM
cana-5359	343	8	𝑋	𝑋	NOUN
cana-5359	343	9	=	=	PUNCT
cana-5359	343	10	{	{	PUNCT
cana-5359	343	11	𝑎	𝑎	NOUN
cana-5359	343	12	,	,	PUNCT
cana-5359	343	13	𝑏	𝑏	NOUN
cana-5359	343	14	}	}	PUNCT
cana-5359	343	15	and	and	CCONJ
cana-5359	343	16	the	the	DET
cana-5359	343	17	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	343	18	’s	’s	PART
cana-5359	343	19	𝐴1	𝐴1	PROPN
cana-5359	343	20	,	,	PUNCT
cana-5359	343	21	𝐴2	𝐴2	PROPN
cana-5359	343	22	,	,	PUNCT
cana-5359	343	23	𝐴3	𝐴3	PROPN
cana-5359	343	24	,	,	PUNCT
cana-5359	343	25	𝐴4	𝐴4	PROPN
cana-5359	343	26	,	,	PUNCT
cana-5359	343	27	and	and	CCONJ
cana-5359	343	28	𝐴5	𝐴5	NOUN
cana-5359	343	29	are	be	AUX
cana-5359	343	30	defined	define	VERB
cana-5359	343	31	as	as	ADP
cana-5359	343	32	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	343	33	(	(	PUNCT
cana-5359	343	34	𝑎	𝑎	NOUN
cana-5359	343	35	)	)	PUNCT
cana-5359	343	36	=	=	SYM
cana-5359	343	37	0.2	0.2	NUM
cana-5359	343	38	,	,	PUNCT
cana-5359	343	39	𝛽𝐴1	𝛽𝐴1	X
cana-5359	343	40	(	(	PUNCT
cana-5359	343	41	𝑎	𝑎	NOUN
cana-5359	343	42	)	)	PUNCT
cana-5359	343	43	=	=	SYM
cana-5359	343	44	0.8	0.8	NUM
cana-5359	343	45	,	,	PUNCT
cana-5359	343	46	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	343	47	(	(	PUNCT
cana-5359	343	48	𝑏	𝑏	NOUN
cana-5359	343	49	)	)	PUNCT
cana-5359	343	50	=	=	SYM
cana-5359	343	51	0.4	0.4	NUM
cana-5359	343	52	,	,	PUNCT
cana-5359	343	53	𝛽𝐴1	𝛽𝐴1	PROPN
cana-5359	343	54	(	(	PUNCT
cana-5359	343	55	𝑏	𝑏	NOUN
cana-5359	343	56	)	)	PUNCT
cana-5359	343	57	=	=	SYM
cana-5359	343	58	0.6	0.6	NUM
cana-5359	343	59	;	;	PUNCT
cana-5359	343	60	𝛼𝐴2	𝛼𝐴2	NUM
cana-5359	343	61	(	(	PUNCT
cana-5359	343	62	𝑎	𝑎	NOUN
cana-5359	343	63	)	)	PUNCT
cana-5359	343	64	=	=	SYM
cana-5359	343	65	0.1	0.1	NUM
cana-5359	343	66	,	,	PUNCT
cana-5359	343	67	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	343	68	(	(	PUNCT
cana-5359	343	69	𝑎	𝑎	NOUN
cana-5359	343	70	)	)	PUNCT
cana-5359	343	71	=	=	SYM
cana-5359	343	72	0.9	0.9	NUM
cana-5359	343	73	,	,	PUNCT
cana-5359	343	74	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5359	343	75	(	(	PUNCT
cana-5359	343	76	𝑏	𝑏	NOUN
cana-5359	343	77	)	)	PUNCT
cana-5359	344	1	=	=	SYM
cana-5359	344	2	0.3	0.3	NUM
cana-5359	344	3	,	,	PUNCT
cana-5359	344	4	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	344	5	(	(	PUNCT
cana-5359	344	6	𝑏	𝑏	NOUN
cana-5359	344	7	)	)	PUNCT
cana-5359	344	8	=	=	SYM
cana-5359	344	9	0.3	0.3	NUM
cana-5359	344	10	;	;	PUNCT
cana-5359	344	11	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	344	12	(	(	PUNCT
cana-5359	344	13	𝑎	𝑎	NOUN
cana-5359	344	14	)	)	PUNCT
cana-5359	344	15	=	=	SYM
cana-5359	344	16	0.9	0.9	NUM
cana-5359	344	17	,	,	PUNCT
cana-5359	344	18	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	344	19	(	(	PUNCT
cana-5359	344	20	𝑎	𝑎	NOUN
cana-5359	344	21	)	)	PUNCT
cana-5359	344	22	=	=	SYM
cana-5359	344	23	0.1	0.1	NUM
cana-5359	344	24	,	,	PUNCT
cana-5359	344	25	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	344	26	(	(	PUNCT
cana-5359	344	27	𝑏	𝑏	NOUN
cana-5359	344	28	)	)	PUNCT
cana-5359	344	29	=	=	SYM
cana-5359	344	30	0.7	0.7	NUM
cana-5359	344	31	,	,	PUNCT
cana-5359	344	32	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	344	33	(	(	PUNCT
cana-5359	344	34	𝑏	𝑏	NOUN
cana-5359	344	35	)	)	PUNCT
cana-5359	344	36	=	=	SYM
cana-5359	344	37	0.3	0.3	NUM
cana-5359	344	38	;	;	PUNCT
cana-5359	344	39	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5359	344	40	(	(	PUNCT
cana-5359	344	41	𝑎	𝑎	NOUN
cana-5359	344	42	)	)	PUNCT
cana-5359	344	43	=	=	SYM
cana-5359	344	44	0.2	0.2	NUM
cana-5359	344	45	,	,	PUNCT
cana-5359	344	46	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5359	344	47	(	(	PUNCT
cana-5359	344	48	𝑎	𝑎	NOUN
cana-5359	344	49	)	)	PUNCT
cana-5359	344	50	=	=	SYM
cana-5359	344	51	0.8	0.8	NUM
cana-5359	344	52	,	,	PUNCT
cana-5359	344	53	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5359	344	54	(	(	PUNCT
cana-5359	344	55	𝑏	𝑏	NOUN
cana-5359	344	56	)	)	PUNCT
cana-5359	344	57	=	=	SYM
cana-5359	344	58	0.3	0.3	NUM
cana-5359	344	59	,	,	PUNCT
cana-5359	344	60	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5359	344	61	(	(	PUNCT
cana-5359	344	62	𝑏	𝑏	NOUN
cana-5359	344	63	)	)	PUNCT
cana-5359	344	64	=	=	SYM
cana-5359	344	65	0.7	0.7	NUM
cana-5359	344	66	;	;	PUNCT
cana-5359	344	67	𝛼𝐴5	𝛼𝐴5	PROPN
cana-5359	344	68	(	(	PUNCT
cana-5359	344	69	𝑎	𝑎	NOUN
cana-5359	344	70	)	)	PUNCT
cana-5359	344	71	=	=	SYM
cana-5359	344	72	0.6	0.6	NUM
cana-5359	344	73	,	,	PUNCT
cana-5359	344	74	𝛽𝐴5	𝛽𝐴5	PROPN
cana-5359	344	75	(	(	PUNCT
cana-5359	344	76	𝑎	𝑎	NOUN
cana-5359	344	77	)	)	PUNCT
cana-5359	344	78	=	=	SYM
cana-5359	344	79	0.4	0.4	NUM
cana-5359	344	80	,	,	PUNCT
cana-5359	344	81	𝛼𝐴5	𝛼𝐴5	PROPN
cana-5359	344	82	(	(	PUNCT
cana-5359	344	83	𝑏	𝑏	NOUN
cana-5359	344	84	)	)	PUNCT
cana-5359	344	85	=	=	SYM
cana-5359	344	86	0.6	0.6	NUM
cana-5359	344	87	,	,	PUNCT
cana-5359	344	88	𝛽𝐴5	𝛽𝐴5	PROPN
cana-5359	344	89	(	(	PUNCT
cana-5359	344	90	𝑏	𝑏	NOUN
cana-5359	344	91	)	)	PUNCT
cana-5359	344	92	=	=	SYM
cana-5359	344	93	0.4	0.4	NUM
cana-5359	344	94	;	;	PUNCT
cana-5359	344	95	let	let	VERB
cana-5359	344	96	𝜏1	𝜏1	NOUN
cana-5359	344	97	=	=	PUNCT
cana-5359	344	98	{	{	PUNCT
cana-5359	344	99	0𝔉	0𝔉	PROPN
cana-5359	344	100	,	,	PUNCT
cana-5359	344	101	1𝔉	1𝔉	NOUN
cana-5359	344	102	,	,	PUNCT
cana-5359	344	103	𝐴1	𝐴1	PROPN
cana-5359	344	104	,	,	PUNCT
cana-5359	344	105	𝐴2	𝐴2	PROPN
cana-5359	344	106	,	,	PUNCT
cana-5359	344	107	𝐴3	𝐴3	PROPN
cana-5359	344	108	,	,	PUNCT
cana-5359	344	109	𝐴4	𝐴4	PROPN
cana-5359	344	110	}	}	PUNCT
cana-5359	344	111	and	and	CCONJ
cana-5359	344	112	𝜏2	𝜏2	PROPN
cana-5359	344	113	=	=	SYM
cana-5359	344	114	{	{	PUNCT
cana-5359	344	115	0𝔉	0𝔉	PROPN
cana-5359	344	116	,	,	PUNCT
cana-5359	344	117	1𝔉	1𝔉	NOUN
cana-5359	344	118	,	,	PUNCT
cana-5359	344	119	𝐴1	𝐴1	PROPN
cana-5359	344	120	,	,	PUNCT
cana-5359	344	121	𝐴2	𝐴2	PROPN
cana-5359	344	122	,	,	PUNCT
cana-5359	344	123	𝐴3	𝐴3	PROPN
cana-5359	344	124	}	}	PUNCT
cana-5359	344	125	are	be	AUX
cana-5359	344	126	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	344	127	’s	’s	ADV
cana-5359	344	128	on	on	ADP
cana-5359	344	129	𝑋	𝑋	PROPN
cana-5359	344	130	and	and	CCONJ
cana-5359	344	131	let	let	VERB
cana-5359	344	132	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	344	133	:	:	PUNCT
cana-5359	344	134	(	(	PUNCT
cana-5359	344	135	𝑋1	𝑋1	PROPN
cana-5359	344	136	,	,	PUNCT
cana-5359	344	137	𝜏1	𝜏1	NOUN
cana-5359	344	138	)	)	PUNCT
cana-5359	344	139	→	→	SYM
cana-5359	344	140	(	(	PUNCT
cana-5359	344	141	𝑋2	𝑋2	PROPN
cana-5359	344	142	,	,	PUNCT
cana-5359	344	143	𝜏2	𝜏2	PROPN
cana-5359	344	144	)	)	PUNCT
cana-5359	344	145	be	be	VERB
cana-5359	344	146	an	an	DET
cana-5359	344	147	identity	identity	NOUN
cana-5359	344	148	function	function	NOUN
cana-5359	344	149	,	,	PUNCT
cana-5359	344	150	then	then	ADV
cana-5359	344	151	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	344	152	is	be	AUX
cana-5359	344	153	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	ADJ
cana-5359	344	154	but	but	CCONJ
cana-5359	344	155	not	not	PART
cana-5359	344	156	𝔉ℱ𝛿𝛼𝐼𝑟𝑟.	𝔉ℱ𝛿𝛼𝐼𝑟𝑟.	NOUN
cana-5359	344	157	since	since	ADV
cana-5359	344	158	,	,	PUNCT
cana-5359	344	159	𝐴5	𝐴5	PROPN
cana-5359	344	160	is	be	AUX
cana-5359	344	161	a	a	DET
cana-5359	344	162	𝔉ℱ𝛿𝛼𝑜	𝔉ℱ𝛿𝛼𝑜	PROPN
cana-5359	344	163	set	set	VERB
cana-5359	344	164	in	in	ADP
cana-5359	344	165	𝑋2	𝑋2	ADJ
cana-5359	344	166	but	but	CCONJ
cana-5359	344	167	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	344	168	−1(𝐴5	−1(𝐴5	ADJ
cana-5359	344	169	)	)	PUNCT
cana-5359	345	1	=	=	PUNCT
cana-5359	345	2	𝐴5	𝐴5	NOUN
cana-5359	345	3	is	be	AUX
cana-5359	345	4	not	not	PART
cana-5359	345	5	𝔉ℱ𝛿𝛼𝑜	𝔉ℱ𝛿𝛼𝑜	PROPN
cana-5359	345	6	set	set	VERB
cana-5359	345	7	in	in	ADP
cana-5359	345	8	𝑋1	𝑋1	PROPN
cana-5359	345	9	.	.	PUNCT
cana-5359	346	1	example	example	NOUN
cana-5359	346	2	4.4	4.4	NUM
cana-5359	346	3	let	let	VERB
cana-5359	346	4	𝑋1	𝑋1	NOUN
cana-5359	346	5	=	=	SYM
cana-5359	346	6	𝑋2	𝑋2	VERB
cana-5359	346	7	=	=	SYM
cana-5359	346	8	𝑋	𝑋	NOUN
cana-5359	346	9	=	=	PUNCT
cana-5359	346	10	{	{	PUNCT
cana-5359	346	11	𝑎	𝑎	NOUN
cana-5359	346	12	,	,	PUNCT
cana-5359	346	13	𝑏	𝑏	NOUN
cana-5359	346	14	}	}	PUNCT
cana-5359	346	15	and	and	CCONJ
cana-5359	346	16	the	the	DET
cana-5359	346	17	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	346	18	’s	’s	PART
cana-5359	346	19	𝐴1	𝐴1	PROPN
cana-5359	346	20	,	,	PUNCT
cana-5359	346	21	𝐴2	𝐴2	PROPN
cana-5359	346	22	,	,	PUNCT
cana-5359	346	23	𝐴3	𝐴3	PROPN
cana-5359	346	24	,	,	PUNCT
cana-5359	346	25	𝐴4	𝐴4	PROPN
cana-5359	346	26	,	,	PUNCT
cana-5359	346	27	𝐵1	𝐵1	PROPN
cana-5359	346	28	,	,	PUNCT
cana-5359	346	29	𝐵2	𝐵2	NOUN
cana-5359	346	30	,	,	PUNCT
cana-5359	346	31	𝐵3	𝐵3	NOUN
cana-5359	346	32	and	and	CCONJ
cana-5359	346	33	𝐵4	𝐵4	NOUN
cana-5359	346	34	are	be	AUX
cana-5359	346	35	defined	define	VERB
cana-5359	346	36	as	as	ADP
cana-5359	346	37	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	346	38	(	(	PUNCT
cana-5359	346	39	𝑎	𝑎	NOUN
cana-5359	346	40	)	)	PUNCT
cana-5359	346	41	=	=	SYM
cana-5359	346	42	0.2	0.2	NUM
cana-5359	346	43	,	,	PUNCT
cana-5359	346	44	𝛽𝐴1	𝛽𝐴1	X
cana-5359	346	45	(	(	PUNCT
cana-5359	346	46	𝑎	𝑎	NOUN
cana-5359	346	47	)	)	PUNCT
cana-5359	347	1	=	=	SYM
cana-5359	347	2	0.8	0.8	NUM
cana-5359	347	3	,	,	PUNCT
cana-5359	347	4	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5359	347	5	(	(	PUNCT
cana-5359	347	6	𝑏	𝑏	NOUN
cana-5359	347	7	)	)	PUNCT
cana-5359	347	8	=	=	SYM
cana-5359	347	9	0.4	0.4	NUM
cana-5359	347	10	,	,	PUNCT
cana-5359	347	11	𝛽𝐴1	𝛽𝐴1	PROPN
cana-5359	347	12	(	(	PUNCT
cana-5359	347	13	𝑏	𝑏	NOUN
cana-5359	347	14	)	)	PUNCT
cana-5359	347	15	=	=	SYM
cana-5359	347	16	0.6	0.6	NUM
cana-5359	347	17	;	;	PUNCT
cana-5359	347	18	𝛼𝐴2	𝛼𝐴2	NUM
cana-5359	347	19	(	(	PUNCT
cana-5359	347	20	𝑎	𝑎	NOUN
cana-5359	347	21	)	)	PUNCT
cana-5359	347	22	=	=	SYM
cana-5359	347	23	0.1	0.1	NUM
cana-5359	347	24	,	,	PUNCT
cana-5359	347	25	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	347	26	(	(	PUNCT
cana-5359	347	27	𝑎	𝑎	NOUN
cana-5359	347	28	)	)	PUNCT
cana-5359	347	29	=	=	SYM
cana-5359	347	30	0.9	0.9	NUM
cana-5359	347	31	,	,	PUNCT
cana-5359	347	32	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5359	347	33	(	(	PUNCT
cana-5359	347	34	𝑏	𝑏	NOUN
cana-5359	347	35	)	)	PUNCT
cana-5359	347	36	=	=	SYM
cana-5359	347	37	0.3	0.3	NUM
cana-5359	347	38	,	,	PUNCT
cana-5359	347	39	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5359	347	40	(	(	PUNCT
cana-5359	347	41	𝑏	𝑏	NOUN
cana-5359	347	42	)	)	PUNCT
cana-5359	347	43	=	=	SYM
cana-5359	347	44	0.7	0.7	NUM
cana-5359	347	45	;	;	PUNCT
cana-5359	347	46	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	347	47	(	(	PUNCT
cana-5359	347	48	𝑎	𝑎	NOUN
cana-5359	347	49	)	)	PUNCT
cana-5359	347	50	=	=	SYM
cana-5359	347	51	0.9	0.9	NUM
cana-5359	347	52	,	,	PUNCT
cana-5359	347	53	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	347	54	(	(	PUNCT
cana-5359	347	55	𝑎	𝑎	NOUN
cana-5359	347	56	)	)	PUNCT
cana-5359	347	57	=	=	SYM
cana-5359	347	58	0.1	0.1	NUM
cana-5359	347	59	,	,	PUNCT
cana-5359	347	60	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5359	347	61	(	(	PUNCT
cana-5359	347	62	𝑏	𝑏	NOUN
cana-5359	347	63	)	)	PUNCT
cana-5359	347	64	=	=	SYM
cana-5359	347	65	0.7	0.7	NUM
cana-5359	347	66	,	,	PUNCT
cana-5359	347	67	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5359	347	68	(	(	PUNCT
cana-5359	347	69	𝑏	𝑏	NOUN
cana-5359	347	70	)	)	PUNCT
cana-5359	347	71	=	=	SYM
cana-5359	347	72	0.3	0.3	NUM
cana-5359	347	73	;	;	PUNCT
cana-5359	347	74	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5359	347	75	(	(	PUNCT
cana-5359	347	76	𝑎	𝑎	NOUN
cana-5359	347	77	)	)	PUNCT
cana-5359	347	78	=	=	SYM
cana-5359	347	79	0.2	0.2	NUM
cana-5359	347	80	,	,	PUNCT
cana-5359	347	81	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5359	347	82	(	(	PUNCT
cana-5359	347	83	𝑎	𝑎	NOUN
cana-5359	347	84	)	)	PUNCT
cana-5359	347	85	=	=	SYM
cana-5359	347	86	0.8	0.8	NUM
cana-5359	347	87	,	,	PUNCT
cana-5359	347	88	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5359	347	89	(	(	PUNCT
cana-5359	347	90	𝑏	𝑏	NOUN
cana-5359	347	91	)	)	PUNCT
cana-5359	347	92	=	=	SYM
cana-5359	347	93	0.3	0.3	NUM
cana-5359	347	94	,	,	PUNCT
cana-5359	347	95	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5359	347	96	(	(	PUNCT
cana-5359	347	97	𝑏	𝑏	NOUN
cana-5359	347	98	)	)	PUNCT
cana-5359	347	99	=	=	SYM
cana-5359	347	100	0.7	0.7	NUM
cana-5359	347	101	;	;	PUNCT
cana-5359	347	102	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5359	347	103	(	(	PUNCT
cana-5359	347	104	𝑎	𝑎	NOUN
cana-5359	347	105	)	)	PUNCT
cana-5359	347	106	=	=	SYM
cana-5359	347	107	0.4	0.4	NUM
cana-5359	347	108	,	,	PUNCT
cana-5359	347	109	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5359	347	110	(	(	PUNCT
cana-5359	347	111	𝑎	𝑎	NOUN
cana-5359	347	112	)	)	PUNCT
cana-5359	347	113	=	=	SYM
cana-5359	347	114	0.6	0.6	NUM
cana-5359	347	115	,	,	PUNCT
cana-5359	347	116	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5359	347	117	(	(	PUNCT
cana-5359	347	118	𝑏	𝑏	NOUN
cana-5359	347	119	)	)	PUNCT
cana-5359	347	120	=	=	SYM
cana-5359	347	121	0.5	0.5	NUM
cana-5359	347	122	,	,	PUNCT
cana-5359	347	123	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5359	347	124	(	(	PUNCT
cana-5359	347	125	𝑏	𝑏	NOUN
cana-5359	347	126	)	)	PUNCT
cana-5359	347	127	=	=	SYM
cana-5359	347	128	0.5	0.5	NUM
cana-5359	347	129	;	;	PUNCT
cana-5359	347	130	𝛼𝐵2	𝛼𝐵2	NUM
cana-5359	347	131	(	(	PUNCT
cana-5359	347	132	𝑎	𝑎	NOUN
cana-5359	347	133	)	)	PUNCT
cana-5359	347	134	=	=	SYM
cana-5359	347	135	0.6	0.6	NUM
cana-5359	347	136	,	,	PUNCT
cana-5359	347	137	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5359	347	138	(	(	PUNCT
cana-5359	347	139	𝑎	𝑎	NOUN
cana-5359	347	140	)	)	PUNCT
cana-5359	347	141	=	=	SYM
cana-5359	347	142	0.4	0.4	NUM
cana-5359	347	143	,	,	PUNCT
cana-5359	347	144	𝛼𝐵2	𝛼𝐵2	NUM
cana-5359	347	145	(	(	PUNCT
cana-5359	347	146	𝑏	𝑏	NOUN
cana-5359	347	147	)	)	PUNCT
cana-5359	347	148	=	=	SYM
cana-5359	347	149	0.6	0.6	NUM
cana-5359	347	150	,	,	PUNCT
cana-5359	347	151	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5359	347	152	(	(	PUNCT
cana-5359	347	153	𝑏	𝑏	NOUN
cana-5359	347	154	)	)	PUNCT
cana-5359	347	155	=	=	SYM
cana-5359	347	156	0.4	0.4	NUM
cana-5359	347	157	;	;	PUNCT
cana-5359	347	158	𝛼𝐵3	𝛼𝐵3	PROPN
cana-5359	347	159	(	(	PUNCT
cana-5359	347	160	𝑎	𝑎	NOUN
cana-5359	347	161	)	)	PUNCT
cana-5359	347	162	=	=	SYM
cana-5359	347	163	0.7	0.7	NUM
cana-5359	347	164	,	,	PUNCT
cana-5359	347	165	𝛽𝐵3	𝛽𝐵3	PROPN
cana-5359	347	166	(	(	PUNCT
cana-5359	347	167	𝑎	𝑎	NOUN
cana-5359	347	168	)	)	PUNCT
cana-5359	347	169	=	=	SYM
cana-5359	347	170	0.3	0.3	NUM
cana-5359	347	171	,	,	PUNCT
cana-5359	347	172	𝛼𝐵3	𝛼𝐵3	PROPN
cana-5359	347	173	(	(	PUNCT
cana-5359	347	174	𝑏	𝑏	NOUN
cana-5359	347	175	)	)	PUNCT
cana-5359	347	176	=	=	SYM
cana-5359	347	177	0.6	0.6	NUM
cana-5359	347	178	,	,	PUNCT
cana-5359	347	179	𝛽𝐵3	𝛽𝐵3	PROPN
cana-5359	347	180	(	(	PUNCT
cana-5359	347	181	𝑏	𝑏	NOUN
cana-5359	347	182	)	)	PUNCT
cana-5359	347	183	=	=	NUM
cana-5359	347	184	0.4	0.4	NUM
cana-5359	347	185	;	;	PUNCT
cana-5359	347	186	𝛼𝐵4	𝛼𝐵4	PROPN
cana-5359	347	187	(	(	PUNCT
cana-5359	347	188	𝑎	𝑎	NOUN
cana-5359	347	189	)	)	PUNCT
cana-5359	347	190	=	=	SYM
cana-5359	347	191	0.4	0.4	NUM
cana-5359	347	192	,	,	PUNCT
cana-5359	347	193	𝛽𝐵4	𝛽𝐵4	PROPN
cana-5359	347	194	(	(	PUNCT
cana-5359	347	195	𝑎	𝑎	NOUN
cana-5359	347	196	)	)	PUNCT
cana-5359	347	197	=	=	SYM
cana-5359	347	198	0.6	0.6	NUM
cana-5359	347	199	,	,	PUNCT
cana-5359	347	200	𝛼𝐵4	𝛼𝐵4	PROPN
cana-5359	347	201	(	(	PUNCT
cana-5359	347	202	𝑏	𝑏	NOUN
cana-5359	347	203	)	)	PUNCT
cana-5359	347	204	=	=	SYM
cana-5359	347	205	0.4	0.4	NUM
cana-5359	347	206	,	,	PUNCT
cana-5359	347	207	𝛽𝐵4	𝛽𝐵4	PROPN
cana-5359	347	208	(	(	PUNCT
cana-5359	347	209	𝑏	𝑏	NOUN
cana-5359	347	210	)	)	PUNCT
cana-5359	347	211	=	=	SYM
cana-5359	347	212	0.6	0.6	NUM
cana-5359	347	213	;	;	PUNCT
cana-5359	347	214	let	let	VERB
cana-5359	347	215	𝜏1	𝜏1	NOUN
cana-5359	347	216	=	=	PRON
cana-5359	347	217	{	{	PUNCT
cana-5359	347	218	0𝔉	0𝔉	PROPN
cana-5359	347	219	,	,	PUNCT
cana-5359	347	220	1𝔉	1𝔉	NOUN
cana-5359	347	221	,	,	PUNCT
cana-5359	347	222	𝐴1	𝐴1	PROPN
cana-5359	347	223	,	,	PUNCT
cana-5359	347	224	𝐴2	𝐴2	PROPN
cana-5359	347	225	,	,	PUNCT
cana-5359	347	226	𝐴3	𝐴3	PROPN
cana-5359	347	227	,	,	PUNCT
cana-5359	347	228	𝐴4	𝐴4	PROPN
cana-5359	347	229	}	}	PUNCT
cana-5359	347	230	and	and	CCONJ
cana-5359	347	231	𝜏2	𝜏2	PROPN
cana-5359	347	232	=	=	SYM
cana-5359	347	233	{	{	PUNCT
cana-5359	347	234	0𝔉	0𝔉	PROPN
cana-5359	347	235	,	,	PUNCT
cana-5359	347	236	1𝔉	1𝔉	NOUN
cana-5359	347	237	,	,	PUNCT
cana-5359	347	238	𝐵1	𝐵1	PROPN
cana-5359	347	239	,	,	PUNCT
cana-5359	347	240	𝐵2	𝐵2	NOUN
cana-5359	347	241	,	,	PUNCT
cana-5359	347	242	𝐵3	𝐵3	PROPN
cana-5359	347	243	,	,	PUNCT
cana-5359	347	244	𝐵4	𝐵4	NOUN
cana-5359	347	245	}	}	PUNCT
cana-5359	347	246	are	be	AUX
cana-5359	347	247	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	347	248	’s	’s	ADV
cana-5359	347	249	on	on	ADP
cana-5359	347	250	𝑋	𝑋	PROPN
cana-5359	347	251	and	and	CCONJ
cana-5359	347	252	let	let	VERB
cana-5359	347	253	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	347	254	:	:	PUNCT
cana-5359	347	255	(	(	PUNCT
cana-5359	347	256	𝑋1	𝑋1	PROPN
cana-5359	347	257	,	,	PUNCT
cana-5359	347	258	𝜏1	𝜏1	NOUN
cana-5359	347	259	)	)	PUNCT
cana-5359	347	260	→	→	SYM
cana-5359	347	261	(	(	PUNCT
cana-5359	347	262	𝑋2	𝑋2	PROPN
cana-5359	347	263	,	,	PUNCT
cana-5359	347	264	𝜏2	𝜏2	PROPN
cana-5359	347	265	)	)	PUNCT
cana-5359	347	266	be	be	VERB
cana-5359	347	267	an	an	DET
cana-5359	347	268	identity	identity	NOUN
cana-5359	347	269	function	function	NOUN
cana-5359	347	270	,	,	PUNCT
cana-5359	347	271	then	then	ADV
cana-5359	347	272	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	347	273	is	be	AUX
cana-5359	347	274	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	347	275	but	but	CCONJ
cana-5359	347	276	not	not	PART
cana-5359	347	277	𝔉ℱ𝛿𝛽𝐼𝑟𝑟.	𝔉ℱ𝛿𝛽𝐼𝑟𝑟.	ADJ
cana-5359	347	278	since	since	ADV
cana-5359	347	279	,	,	PUNCT
cana-5359	347	280	𝐴4	𝐴4	PROPN
cana-5359	347	281	𝑐	𝑐	PROPN
cana-5359	347	282	is	be	AUX
cana-5359	347	283	a	a	DET
cana-5359	347	284	𝔉ℱ𝛿𝛽𝑜	𝔉ℱ𝛿𝛽𝑜	PROPN
cana-5359	347	285	set	set	NOUN
cana-5359	347	286	in	in	ADP
cana-5359	347	287	𝑋2	𝑋2	ADV
cana-5359	347	288	but	but	CCONJ
cana-5359	347	289	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	347	290	−1(𝐴4	−1(𝐴4	ADJ
cana-5359	347	291	𝑐	𝑐	NOUN
cana-5359	347	292	)	)	PUNCT
cana-5359	347	293	=	=	VERB
cana-5359	348	1	𝐴4	𝐴4	PROPN
cana-5359	348	2	𝑐	𝑐	NOUN
cana-5359	348	3	is	be	AUX
cana-5359	348	4	not	not	PART
cana-5359	348	5	𝔉ℱ𝛿𝛽𝑜	𝔉ℱ𝛿𝛽𝑜	PROPN
cana-5359	348	6	set	set	NOUN
cana-5359	348	7	in	in	ADP
cana-5359	348	8	𝑋1	𝑋1	PROPN
cana-5359	348	9	.	.	PUNCT
cana-5359	349	1	definition	definition	NOUN
cana-5359	349	2	4.2	4.2	NUM
cana-5359	349	3	a	a	DET
cana-5359	349	4	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	349	5	(	(	PUNCT
cana-5359	349	6	𝑋1	𝑋1	PROPN
cana-5359	349	7	,	,	PUNCT
cana-5359	349	8	𝜏1	𝜏1	NOUN
cana-5359	349	9	)	)	PUNCT
cana-5359	349	10	is	be	AUX
cana-5359	349	11	known	know	VERB
cana-5359	349	12	as	as	ADP
cana-5359	349	13	a	a	DET
cana-5359	349	14	fermatean	fermatean	ADJ
cana-5359	349	15	fuzzy	fuzzy	ADJ
cana-5359	349	16	𝛿𝒮𝑈1	𝛿𝒮𝑈1	NOUN
cana-5359	349	17	2	2	NUM
cana-5359	349	18	(	(	PUNCT
cana-5359	349	19	resp	resp	NOUN
cana-5359	349	20	.	.	PUNCT
cana-5359	350	1	𝛿𝒫𝑈1	𝛿𝒫𝑈1	NOUN
cana-5359	350	2	2	2	NUM
cana-5359	350	3	,	,	PUNCT
cana-5359	350	4	𝛿𝛼𝑈1	𝛿𝛼𝑈1	NOUN
cana-5359	350	5	2	2	NUM
cana-5359	350	6	and	and	CCONJ
cana-5359	350	7	𝛿𝛽𝑈1	𝛿𝛽𝑈1	NOUN
cana-5359	350	8	2	2	NUM
cana-5359	350	9	)	)	PUNCT
cana-5359	350	10	(	(	PUNCT
cana-5359	350	11	in	in	ADP
cana-5359	350	12	short	short	ADJ
cana-5359	350	13	,	,	PUNCT
cana-5359	350	14	𝔉ℱ𝛿𝒮𝑈1	𝔉ℱ𝛿𝒮𝑈1	PROPN
cana-5359	350	15	2	2	NUM
cana-5359	350	16	(	(	PUNCT
cana-5359	350	17	resp	resp	NOUN
cana-5359	350	18	.	.	PUNCT
cana-5359	351	1	𝔉ℱ𝛿𝒫𝑈1	𝔉ℱ𝛿𝒫𝑈1	VERB
cana-5359	351	2	2	2	NUM
cana-5359	351	3	,	,	PUNCT
cana-5359	351	4	𝔉ℱ𝛿𝛼𝑈1	𝔉ℱ𝛿𝛼𝑈1	NOUN
cana-5359	351	5	2	2	NUM
cana-5359	351	6	and	and	CCONJ
cana-5359	351	7	𝔉ℱ𝛿𝛽𝑈1	𝔉ℱ𝛿𝛽𝑈1	ADP
cana-5359	351	8	2	2	NUM
cana-5359	351	9	)	)	PUNCT
cana-5359	351	10	)	)	PUNCT
cana-5359	351	11	-space	-space	NOUN
cana-5359	351	12	,	,	PUNCT
cana-5359	351	13	if	if	SCONJ
cana-5359	351	14	each	each	DET
cana-5359	351	15	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	351	16	(	(	PUNCT
cana-5359	351	17	resp	resp	PROPN
cana-5359	351	18	.	.	PUNCT
cana-5359	352	1	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	352	2	,	,	PUNCT
cana-5359	352	3	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	352	4	and	and	CCONJ
cana-5359	352	5	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	352	6	)	)	PUNCT
cana-5359	352	7	in	in	ADP
cana-5359	352	8	𝑋	𝑋	PROPN
cana-5359	352	9	is	be	AUX
cana-5359	352	10	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	352	11	in	in	ADP
cana-5359	352	12	𝑋1	𝑋1	PROPN
cana-5359	352	13	.	.	PUNCT
cana-5359	353	1	theorem	theorem	VERB
cana-5359	353	2	4.2	4.2	NUM
cana-5359	353	3	let	let	VERB
cana-5359	353	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	353	5	:	:	PUNCT
cana-5359	353	6	(	(	PUNCT
cana-5359	353	7	𝑋1	𝑋1	PROPN
cana-5359	353	8	,	,	PUNCT
cana-5359	353	9	𝜏1	𝜏1	NOUN
cana-5359	353	10	)	)	PUNCT
cana-5359	353	11	→	→	SYM
cana-5359	353	12	(	(	PUNCT
cana-5359	353	13	𝑋2	𝑋2	PROPN
cana-5359	353	14	,	,	PUNCT
cana-5359	353	15	𝜏2	𝜏2	PROPN
cana-5359	353	16	)	)	PUNCT
cana-5359	353	17	be	be	VERB
cana-5359	353	18	a	a	DET
cana-5359	353	19	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	NOUN
cana-5359	353	20	(	(	PUNCT
cana-5359	353	21	resp	resp	PROPN
cana-5359	353	22	.	.	PUNCT
cana-5359	354	1	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5359	354	2	,	,	PUNCT
cana-5359	354	3	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	NOUN
cana-5359	354	4	and	and	CCONJ
cana-5359	354	5	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5359	354	6	)	)	PUNCT
cana-5359	354	7	map	map	NOUN
cana-5359	354	8	.	.	PUNCT
cana-5359	355	1	then	then	ADV
cana-5359	355	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	355	3	is	be	AUX
cana-5359	355	4	a	a	DET
cana-5359	355	5	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	NOUN
cana-5359	355	6	map	map	NOUN
cana-5359	355	7	if	if	SCONJ
cana-5359	355	8	𝑋	𝑋	PROPN
cana-5359	355	9	is	be	AUX
cana-5359	355	10	a	a	DET
cana-5359	355	11	𝔉ℱ𝛿𝒮𝑈1	𝔉ℱ𝛿𝒮𝑈1	PROPN
cana-5359	355	12	2	2	NUM
cana-5359	355	13	(	(	PUNCT
cana-5359	355	14	resp	resp	NOUN
cana-5359	355	15	.	.	PUNCT
cana-5359	356	1	𝔉ℱ𝛿𝒫𝑈1	𝔉ℱ𝛿𝒫𝑈1	VERB
cana-5359	356	2	2	2	NUM
cana-5359	356	3	,	,	PUNCT
cana-5359	356	4	𝔉ℱ𝛿𝛼𝑈1	𝔉ℱ𝛿𝛼𝑈1	NOUN
cana-5359	356	5	2	2	NUM
cana-5359	356	6	and	and	CCONJ
cana-5359	356	7	communications	communication	NOUN
cana-5359	356	8	on	on	ADP
cana-5359	356	9	applied	apply	VERB
cana-5359	356	10	nonlinear	nonlinear	ADJ
cana-5359	356	11	analysis	analysis	NOUN
cana-5359	356	12	issn	issn	NOUN
cana-5359	356	13	:	:	PUNCT
cana-5359	356	14	1074	1074	NUM
cana-5359	356	15	-	-	PUNCT
cana-5359	356	16	133x	133x	NUM
cana-5359	356	17	vol	vol	VERB
cana-5359	356	18	32	32	NUM
cana-5359	356	19	no	no	NOUN
cana-5359	356	20	.	.	PUNCT
cana-5359	357	1	10s	10	NOUN
cana-5359	357	2	(	(	PUNCT
cana-5359	357	3	2025	2025	NUM
cana-5359	357	4	)	)	PUNCT
cana-5359	357	5	1921	1921	NUM
cana-5359	357	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	357	7	𝔉ℱ𝛿𝛽𝑈1	𝔉ℱ𝛿𝛽𝑈1	ADP
cana-5359	357	8	2	2	NUM
cana-5359	357	9	)	)	PUNCT
cana-5359	357	10	-space	-space	NOUN
cana-5359	357	11	.	.	PUNCT
cana-5359	358	1	proof	proof	NOUN
cana-5359	358	2	.	.	PUNCT
cana-5359	359	1	(	(	PUNCT
cana-5359	359	2	i	i	NOUN
cana-5359	359	3	)	)	PUNCT
cana-5359	359	4	consider	consider	VERB
cana-5359	359	5	a	a	DET
cana-5359	359	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	359	7	𝐾	𝐾	PROPN
cana-5359	359	8	in	in	ADP
cana-5359	359	9	𝑋2	𝑋2	PROPN
cana-5359	359	10	.	.	PUNCT
cana-5359	360	1	then	then	ADV
cana-5359	360	2	𝐾	𝐾	PROPN
cana-5359	360	3	is	be	AUX
cana-5359	360	4	a	a	DET
cana-5359	360	5	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	360	6	in	in	ADP
cana-5359	360	7	𝑋2	𝑋2	PROPN
cana-5359	360	8	.	.	PUNCT
cana-5359	361	1	therefore	therefore	ADV
cana-5359	361	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	361	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	361	4	)	)	PUNCT
cana-5359	361	5	is	be	AUX
cana-5359	361	6	a	a	DET
cana-5359	361	7	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5359	361	8	in	in	ADP
cana-5359	361	9	𝑋1	𝑋1	PROPN
cana-5359	361	10	.	.	PUNCT
cana-5359	362	1	since	since	SCONJ
cana-5359	362	2	𝑋1	𝑋1	PROPN
cana-5359	362	3	is	be	AUX
cana-5359	362	4	a	a	DET
cana-5359	362	5	𝔉ℱ𝛿𝒮𝑈1	𝔉ℱ𝛿𝒮𝑈1	PROPN
cana-5359	362	6	2	2	NUM
cana-5359	362	7	-space	-space	NOUN
cana-5359	362	8	,	,	PUNCT
cana-5359	362	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	362	10	−1(𝐾	−1(𝐾	NOUN
cana-5359	362	11	)	)	PUNCT
cana-5359	362	12	is	be	AUX
cana-5359	362	13	a	a	DET
cana-5359	362	14	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	362	15	in	in	ADP
cana-5359	362	16	𝑋1	𝑋1	PROPN
cana-5359	362	17	.	.	PUNCT
cana-5359	363	1	hence	hence	ADV
cana-5359	363	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	363	3	is	be	AUX
cana-5359	363	4	a	a	DET
cana-5359	363	5	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	PUNCT
cana-5359	363	6	map	map	NOUN
cana-5359	363	7	.	.	PUNCT
cana-5359	364	1	(	(	PUNCT
cana-5359	364	2	ii	ii	NOUN
cana-5359	364	3	)	)	PUNCT
cana-5359	364	4	consider	consider	VERB
cana-5359	364	5	a	a	DET
cana-5359	364	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	364	7	𝐾	𝐾	PROPN
cana-5359	364	8	in	in	ADP
cana-5359	364	9	𝑋2	𝑋2	PROPN
cana-5359	364	10	.	.	PUNCT
cana-5359	365	1	then	then	ADV
cana-5359	365	2	𝐾	𝐾	PROPN
cana-5359	365	3	is	be	AUX
cana-5359	365	4	a	a	DET
cana-5359	365	5	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	365	6	in	in	ADP
cana-5359	365	7	𝑋2	𝑋2	PROPN
cana-5359	365	8	.	.	PUNCT
cana-5359	366	1	therefore	therefore	ADV
cana-5359	366	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	366	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	366	4	)	)	PUNCT
cana-5359	366	5	is	be	AUX
cana-5359	366	6	a	a	DET
cana-5359	366	7	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	366	8	in	in	ADP
cana-5359	366	9	𝑋1	𝑋1	PROPN
cana-5359	366	10	.	.	PUNCT
cana-5359	367	1	since	since	SCONJ
cana-5359	367	2	𝑋	𝑋	PROPN
cana-5359	367	3	is	be	AUX
cana-5359	367	4	a	a	DET
cana-5359	367	5	𝔉ℱ𝛿𝒫𝑈1	𝔉ℱ𝛿𝒫𝑈1	NOUN
cana-5359	367	6	2	2	NUM
cana-5359	367	7	-space	-space	NOUN
cana-5359	367	8	,	,	PUNCT
cana-5359	367	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	367	10	−1(𝐾	−1(𝐾	NOUN
cana-5359	367	11	)	)	PUNCT
cana-5359	367	12	is	be	AUX
cana-5359	367	13	a	a	DET
cana-5359	367	14	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	367	15	in	in	ADP
cana-5359	367	16	𝑋1	𝑋1	PROPN
cana-5359	367	17	.	.	PUNCT
cana-5359	368	1	hence	hence	ADV
cana-5359	368	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	368	3	is	be	AUX
cana-5359	368	4	a	a	DET
cana-5359	368	5	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	PUNCT
cana-5359	368	6	map	map	NOUN
cana-5359	368	7	.	.	PUNCT
cana-5359	369	1	(	(	PUNCT
cana-5359	369	2	iii	iii	X
cana-5359	369	3	)	)	PUNCT
cana-5359	369	4	consider	consider	VERB
cana-5359	369	5	a	a	DET
cana-5359	369	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	369	7	𝐾	𝐾	PROPN
cana-5359	369	8	in	in	ADP
cana-5359	369	9	𝑋2	𝑋2	PROPN
cana-5359	369	10	.	.	PUNCT
cana-5359	370	1	then	then	ADV
cana-5359	370	2	𝐾	𝐾	PROPN
cana-5359	370	3	is	be	AUX
cana-5359	370	4	a	a	DET
cana-5359	370	5	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	370	6	in	in	ADP
cana-5359	370	7	𝑋2	𝑋2	PROPN
cana-5359	370	8	.	.	PUNCT
cana-5359	371	1	therefore	therefore	ADV
cana-5359	371	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	371	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	371	4	)	)	PUNCT
cana-5359	371	5	is	be	AUX
cana-5359	371	6	a	a	DET
cana-5359	371	7	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5359	371	8	in	in	ADP
cana-5359	371	9	𝑋1	𝑋1	PROPN
cana-5359	371	10	.	.	PUNCT
cana-5359	372	1	since	since	SCONJ
cana-5359	372	2	𝑋1	𝑋1	PROPN
cana-5359	372	3	is	be	AUX
cana-5359	372	4	a	a	DET
cana-5359	372	5	𝔉ℱ𝛿𝛼𝑈1	𝔉ℱ𝛿𝛼𝑈1	NOUN
cana-5359	372	6	2	2	NUM
cana-5359	372	7	-space	-space	NOUN
cana-5359	372	8	,	,	PUNCT
cana-5359	372	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	372	10	−1(𝐾	−1(𝐾	NOUN
cana-5359	372	11	)	)	PUNCT
cana-5359	372	12	is	be	AUX
cana-5359	372	13	a	a	DET
cana-5359	372	14	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	372	15	in	in	ADP
cana-5359	372	16	𝑋1	𝑋1	PROPN
cana-5359	372	17	.	.	PUNCT
cana-5359	373	1	hence	hence	ADV
cana-5359	373	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	373	3	is	be	AUX
cana-5359	373	4	a	a	DET
cana-5359	373	5	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	PUNCT
cana-5359	373	6	map	map	NOUN
cana-5359	373	7	.	.	PUNCT
cana-5359	374	1	(	(	PUNCT
cana-5359	374	2	iv	iv	X
cana-5359	374	3	)	)	PUNCT
cana-5359	374	4	consider	consider	VERB
cana-5359	374	5	a	a	DET
cana-5359	374	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	374	7	𝐾	𝐾	PROPN
cana-5359	374	8	in	in	ADP
cana-5359	374	9	𝑋2	𝑋2	PROPN
cana-5359	374	10	.	.	PUNCT
cana-5359	375	1	then	then	ADV
cana-5359	375	2	𝐾	𝐾	PROPN
cana-5359	375	3	is	be	AUX
cana-5359	375	4	a	a	DET
cana-5359	375	5	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	375	6	in	in	ADP
cana-5359	375	7	𝑋2	𝑋2	PROPN
cana-5359	375	8	.	.	PUNCT
cana-5359	376	1	therefore	therefore	ADV
cana-5359	376	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	376	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	376	4	)	)	PUNCT
cana-5359	376	5	is	be	AUX
cana-5359	376	6	a	a	DET
cana-5359	376	7	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	376	8	in	in	ADP
cana-5359	376	9	𝑋1	𝑋1	PROPN
cana-5359	376	10	.	.	PUNCT
cana-5359	377	1	since	since	SCONJ
cana-5359	377	2	𝑋1	𝑋1	PROPN
cana-5359	377	3	is	be	AUX
cana-5359	377	4	a	a	DET
cana-5359	377	5	𝔉ℱ𝛿𝛽𝑈1	𝔉ℱ𝛿𝛽𝑈1	PROPN
cana-5359	377	6	2	2	NUM
cana-5359	377	7	-space	-space	NOUN
cana-5359	377	8	,	,	PUNCT
cana-5359	377	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	377	10	−1(𝐾	−1(𝐾	NOUN
cana-5359	377	11	)	)	PUNCT
cana-5359	377	12	is	be	AUX
cana-5359	377	13	a	a	DET
cana-5359	377	14	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	377	15	in	in	ADP
cana-5359	377	16	𝑋1	𝑋1	PROPN
cana-5359	377	17	.	.	PUNCT
cana-5359	378	1	hence	hence	ADV
cana-5359	378	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	378	3	is	be	AUX
cana-5359	378	4	a	a	DET
cana-5359	378	5	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	PUNCT
cana-5359	378	6	map	map	NOUN
cana-5359	378	7	.	.	PUNCT
cana-5359	379	1	theorem	theorem	VERB
cana-5359	379	2	4.3	4.3	NUM
cana-5359	379	3	let	let	VERB
cana-5359	379	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	379	5	:	:	PUNCT
cana-5359	379	6	(	(	PUNCT
cana-5359	379	7	𝑋1	𝑋1	PROPN
cana-5359	379	8	,	,	PUNCT
cana-5359	379	9	𝜏1	𝜏1	NOUN
cana-5359	379	10	)	)	PUNCT
cana-5359	379	11	→	→	SYM
cana-5359	379	12	(	(	PUNCT
cana-5359	379	13	𝑋2	𝑋2	PROPN
cana-5359	379	14	,	,	PUNCT
cana-5359	379	15	𝜏2	𝜏2	PROPN
cana-5359	379	16	)	)	PUNCT
cana-5359	379	17	and	and	CCONJ
cana-5359	379	18	𝑔𝔉	𝑔𝔉	NOUN
cana-5359	379	19	:	:	PUNCT
cana-5359	379	20	(	(	PUNCT
cana-5359	379	21	𝑋2	𝑋2	ADJ
cana-5359	379	22	,	,	PUNCT
cana-5359	379	23	𝜏2	𝜏2	PROPN
cana-5359	379	24	)	)	PUNCT
cana-5359	379	25	→	→	SYM
cana-5359	379	26	(	(	PUNCT
cana-5359	379	27	𝑋3	𝑋3	NOUN
cana-5359	379	28	,	,	PUNCT
cana-5359	379	29	𝜏3	𝜏3	NOUN
cana-5359	379	30	)	)	PUNCT
cana-5359	379	31	be	be	VERB
cana-5359	379	32	𝔉ℱ𝛿𝐼𝑟𝑟	𝔉ℱ𝛿𝐼𝑟𝑟	NOUN
cana-5359	379	33	(	(	PUNCT
cana-5359	379	34	resp	resp	NOUN
cana-5359	379	35	.	.	PUNCT
cana-5359	380	1	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	NOUN
cana-5359	380	2	,	,	PUNCT
cana-5359	380	3	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5359	380	4	,	,	PUNCT
cana-5359	380	5	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	NOUN
cana-5359	380	6	and	and	CCONJ
cana-5359	380	7	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5359	380	8	)	)	PUNCT
cana-5359	380	9	maps	map	NOUN
cana-5359	380	10	,	,	PUNCT
cana-5359	380	11	then	then	ADV
cana-5359	380	12	𝑔𝔉	𝑔𝔉	VERB
cana-5359	380	13	∘	∘	VERB
cana-5359	380	14	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	380	15	:	:	PUNCT
cana-5359	380	16	(	(	PUNCT
cana-5359	380	17	𝑋1	𝑋1	PROPN
cana-5359	380	18	,	,	PUNCT
cana-5359	380	19	𝜏1	𝜏1	NOUN
cana-5359	380	20	)	)	PUNCT
cana-5359	380	21	→	→	SYM
cana-5359	380	22	(	(	PUNCT
cana-5359	380	23	𝑋3	𝑋3	NOUN
cana-5359	380	24	,	,	PUNCT
cana-5359	380	25	𝜏3	𝜏3	NOUN
cana-5359	380	26	)	)	PUNCT
cana-5359	380	27	is	be	AUX
cana-5359	380	28	a	a	DET
cana-5359	380	29	𝔉ℱ𝛿𝐼𝑟𝑟	𝔉ℱ𝛿𝐼𝑟𝑟	NOUN
cana-5359	380	30	(	(	PUNCT
cana-5359	380	31	resp	resp	NOUN
cana-5359	380	32	.	.	PUNCT
cana-5359	381	1	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	NOUN
cana-5359	381	2	,	,	PUNCT
cana-5359	381	3	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5359	381	4	,	,	PUNCT
cana-5359	381	5	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	NOUN
cana-5359	381	6	and	and	CCONJ
cana-5359	381	7	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5359	381	8	)	)	PUNCT
cana-5359	381	9	map	map	NOUN
cana-5359	381	10	.	.	PUNCT
cana-5359	382	1	proof	proof	NOUN
cana-5359	382	2	.	.	PUNCT
cana-5359	383	1	consider	consider	VERB
cana-5359	383	2	a	a	DET
cana-5359	383	3	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	383	4	𝐾	𝐾	PROPN
cana-5359	383	5	in	in	ADP
cana-5359	383	6	𝑋3	𝑋3	NOUN
cana-5359	383	7	.	.	PUNCT
cana-5359	384	1	so	so	ADV
cana-5359	384	2	𝑔𝔉	𝑔𝔉	PROPN
cana-5359	384	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	384	4	)	)	PUNCT
cana-5359	384	5	is	be	AUX
cana-5359	384	6	a	a	DET
cana-5359	384	7	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	384	8	in	in	ADP
cana-5359	384	9	𝑋2	𝑋2	PROPN
cana-5359	384	10	.	.	PUNCT
cana-5359	385	1	as	as	SCONJ
cana-5359	385	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	385	3	is	be	AUX
cana-5359	385	4	a	a	DET
cana-5359	385	5	𝔉ℱ𝛿𝐼𝑟𝑟	𝔉ℱ𝛿𝐼𝑟𝑟	NOUN
cana-5359	385	6	map	map	NOUN
cana-5359	385	7	,	,	PUNCT
cana-5359	385	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	385	9	−1(𝑔𝔉	−1(𝑔𝔉	CCONJ
cana-5359	385	10	−1(𝐾	−1(𝐾	NOUN
cana-5359	385	11	)	)	PUNCT
cana-5359	385	12	)	)	PUNCT
cana-5359	385	13	is	be	AUX
cana-5359	385	14	a	a	DET
cana-5359	385	15	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	385	16	in	in	ADP
cana-5359	385	17	𝑋1	𝑋1	PROPN
cana-5359	385	18	.	.	PUNCT
cana-5359	386	1	thus	thus	ADV
cana-5359	386	2	𝑔𝔉	𝑔𝔉	VERB
cana-5359	386	3	∘	∘	ADJ
cana-5359	386	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	386	5	is	be	AUX
cana-5359	386	6	a	a	DET
cana-5359	386	7	𝔉ℱ𝛿𝐼𝑟𝑟	𝔉ℱ𝛿𝐼𝑟𝑟	NOUN
cana-5359	386	8	map	map	NOUN
cana-5359	386	9	.	.	PUNCT
cana-5359	387	1	the	the	DET
cana-5359	387	2	other	other	ADJ
cana-5359	387	3	cases	case	NOUN
cana-5359	387	4	are	be	AUX
cana-5359	387	5	similar	similar	ADJ
cana-5359	387	6	.	.	PUNCT
cana-5359	388	1	theorem	theorem	VERB
cana-5359	388	2	4.4	4.4	NUM
cana-5359	388	3	consider	consider	VERB
cana-5359	388	4	a	a	DET
cana-5359	388	5	𝔉ℱ𝛿𝐼𝑟𝑟	𝔉ℱ𝛿𝐼𝑟𝑟	NOUN
cana-5359	388	6	(	(	PUNCT
cana-5359	388	7	resp	resp	NOUN
cana-5359	388	8	.	.	PUNCT
cana-5359	389	1	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	NOUN
cana-5359	389	2	,	,	PUNCT
cana-5359	389	3	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5359	389	4	,	,	PUNCT
cana-5359	389	5	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	NOUN
cana-5359	389	6	and	and	CCONJ
cana-5359	389	7	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	NOUN
cana-5359	389	8	)	)	PUNCT
cana-5359	389	9	map	map	NOUN
cana-5359	389	10	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	389	11	:	:	PUNCT
cana-5359	389	12	(	(	PUNCT
cana-5359	389	13	𝑋1	𝑋1	PROPN
cana-5359	389	14	,	,	PUNCT
cana-5359	389	15	𝜏1	𝜏1	NOUN
cana-5359	389	16	)	)	PUNCT
cana-5359	389	17	→	→	SYM
cana-5359	389	18	(	(	PUNCT
cana-5359	389	19	𝑋2	𝑋2	PROPN
cana-5359	389	20	,	,	PUNCT
cana-5359	389	21	𝜏2	𝜏2	PROPN
cana-5359	389	22	)	)	PUNCT
cana-5359	389	23	and	and	CCONJ
cana-5359	389	24	a	a	DET
cana-5359	389	25	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	PUNCT
cana-5359	389	26	(	(	PUNCT
cana-5359	389	27	resp	resp	NOUN
cana-5359	389	28	.	.	PUNCT
cana-5359	390	1	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	X
cana-5359	390	2	,	,	PUNCT
cana-5359	390	3	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	NOUN
cana-5359	390	4	,	,	PUNCT
cana-5359	390	5	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5359	390	6	and	and	CCONJ
cana-5359	390	7	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	390	8	)	)	PUNCT
cana-5359	390	9	map	map	NOUN
cana-5359	390	10	𝑔𝔉	𝑔𝔉	NOUN
cana-5359	390	11	:	:	PUNCT
cana-5359	390	12	(	(	PUNCT
cana-5359	390	13	𝑋2	𝑋2	ADJ
cana-5359	390	14	,	,	PUNCT
cana-5359	390	15	𝜏2	𝜏2	PROPN
cana-5359	390	16	)	)	PUNCT
cana-5359	390	17	→	→	SYM
cana-5359	390	18	(	(	PUNCT
cana-5359	390	19	𝑋3	𝑋3	NOUN
cana-5359	390	20	,	,	PUNCT
cana-5359	390	21	𝜏3	𝜏3	NOUN
cana-5359	390	22	)	)	PUNCT
cana-5359	390	23	.	.	PUNCT
cana-5359	391	1	then	then	ADV
cana-5359	391	2	𝑔𝔉	𝑔𝔉	VERB
cana-5359	391	3	∘	∘	ADJ
cana-5359	391	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	391	5	:	:	PUNCT
cana-5359	391	6	(	(	PUNCT
cana-5359	391	7	𝑋1	𝑋1	PROPN
cana-5359	391	8	,	,	PUNCT
cana-5359	391	9	𝜏1	𝜏1	NOUN
cana-5359	391	10	)	)	PUNCT
cana-5359	391	11	→	→	SYM
cana-5359	391	12	(	(	PUNCT
cana-5359	391	13	𝑋3	𝑋3	NOUN
cana-5359	391	14	,	,	PUNCT
cana-5359	391	15	𝜏3	𝜏3	NOUN
cana-5359	391	16	)	)	PUNCT
cana-5359	391	17	is	be	AUX
cana-5359	391	18	a	a	DET
cana-5359	391	19	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	ADJ
cana-5359	391	20	(	(	PUNCT
cana-5359	391	21	resp	resp	NOUN
cana-5359	391	22	.	.	PUNCT
cana-5359	392	1	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	PROPN
cana-5359	392	2	,	,	PUNCT
cana-5359	392	3	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5359	392	4	,	,	PUNCT
cana-5359	392	5	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5359	392	6	and	and	CCONJ
cana-5359	392	7	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5359	392	8	)	)	PUNCT
cana-5359	392	9	map	map	NOUN
cana-5359	392	10	.	.	PUNCT
cana-5359	393	1	proof	proof	NOUN
cana-5359	393	2	.	.	PUNCT
cana-5359	394	1	consider	consider	VERB
cana-5359	394	2	a	a	DET
cana-5359	394	3	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5359	394	4	𝐾	𝐾	PROPN
cana-5359	394	5	in	in	ADP
cana-5359	394	6	𝑋3	𝑋3	NOUN
cana-5359	394	7	.	.	PUNCT
cana-5359	395	1	so	so	ADV
cana-5359	395	2	𝑔𝔉	𝑔𝔉	PROPN
cana-5359	395	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	395	4	)	)	PUNCT
cana-5359	395	5	is	be	AUX
cana-5359	395	6	a	a	DET
cana-5359	395	7	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	395	8	in	in	ADP
cana-5359	395	9	𝑋2	𝑋2	PROPN
cana-5359	395	10	.	.	PUNCT
cana-5359	396	1	as	as	SCONJ
cana-5359	396	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	396	3	is	be	AUX
cana-5359	396	4	a	a	DET
cana-5359	396	5	𝔉ℱ𝛿𝐼𝑟𝑟	𝔉ℱ𝛿𝐼𝑟𝑟	NOUN
cana-5359	396	6	map	map	NOUN
cana-5359	396	7	,	,	PUNCT
cana-5359	396	8	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	396	9	−1(𝑔𝔉	−1(𝑔𝔉	CCONJ
cana-5359	396	10	−1(𝑈	−1(𝑈	NOUN
cana-5359	396	11	)	)	PUNCT
cana-5359	396	12	)	)	PUNCT
cana-5359	396	13	is	be	AUX
cana-5359	396	14	a	a	DET
cana-5359	396	15	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	396	16	in	in	ADP
cana-5359	396	17	𝑋1	𝑋1	PROPN
cana-5359	396	18	.	.	PUNCT
cana-5359	397	1	thus	thus	ADV
cana-5359	397	2	𝑔𝔉	𝑔𝔉	VERB
cana-5359	397	3	∘	∘	ADJ
cana-5359	397	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	397	5	is	be	AUX
cana-5359	397	6	a	a	DET
cana-5359	397	7	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	PUNCT
cana-5359	397	8	map	map	NOUN
cana-5359	397	9	.	.	PUNCT
cana-5359	398	1	the	the	DET
cana-5359	398	2	other	other	ADJ
cana-5359	398	3	cases	case	NOUN
cana-5359	398	4	are	be	AUX
cana-5359	398	5	similar	similar	ADJ
cana-5359	398	6	.	.	PUNCT
cana-5359	399	1	theorem	theorem	VERB
cana-5359	399	2	4.5	4.5	NUM
cana-5359	399	3	consider	consider	VERB
cana-5359	399	4	a	a	DET
cana-5359	399	5	map	map	NOUN
cana-5359	399	6	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	399	7	:	:	PUNCT
cana-5359	399	8	(	(	PUNCT
cana-5359	399	9	𝑋1	𝑋1	PROPN
cana-5359	399	10	,	,	PUNCT
cana-5359	399	11	𝜏1	𝜏1	NOUN
cana-5359	399	12	)	)	PUNCT
cana-5359	399	13	→	→	SYM
cana-5359	399	14	(	(	PUNCT
cana-5359	399	15	𝑋2	𝑋2	PROPN
cana-5359	399	16	,	,	PUNCT
cana-5359	399	17	𝜏2	𝜏2	PROPN
cana-5359	399	18	)	)	PUNCT
cana-5359	399	19	from	from	ADP
cana-5359	399	20	a	a	DET
cana-5359	399	21	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	399	22	𝑋1	𝑋1	NOUN
cana-5359	399	23	into	into	ADP
cana-5359	399	24	a	a	DET
cana-5359	399	25	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5359	399	26	𝑋2	𝑋2	VERB
cana-5359	399	27	.	.	PUNCT
cana-5359	400	1	the	the	DET
cana-5359	400	2	following	follow	VERB
cana-5359	400	3	are	be	AUX
cana-5359	400	4	equivalent	equivalent	ADJ
cana-5359	400	5	if	if	SCONJ
cana-5359	400	6	𝑋1	𝑋1	PROPN
cana-5359	400	7	and	and	CCONJ
cana-5359	400	8	𝑋2	𝑋2	VERB
cana-5359	400	9	are	be	AUX
cana-5359	400	10	𝔉ℱ𝛿𝛽𝑈1	𝔉ℱ𝛿𝛽𝑈1	ADP
cana-5359	400	11	2	2	NUM
cana-5359	400	12	-spaces	-space	NOUN
cana-5359	400	13	.	.	PUNCT
cana-5359	401	1	(	(	PUNCT
cana-5359	401	2	i	i	NOUN
cana-5359	401	3	)	)	PUNCT
cana-5359	401	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	401	5	is	be	AUX
cana-5359	401	6	a	a	DET
cana-5359	401	7	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5359	401	8	map	map	NOUN
cana-5359	401	9	.	.	PUNCT
cana-5359	402	1	(	(	PUNCT
cana-5359	402	2	ii	ii	X
cana-5359	402	3	)	)	PUNCT
cana-5359	402	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	402	5	−1(𝐾	−1(𝐾	NOUN
cana-5359	402	6	)	)	PUNCT
cana-5359	402	7	is	be	AUX
cana-5359	402	8	a	a	DET
cana-5359	402	9	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5359	402	10	in	in	ADP
cana-5359	402	11	𝑋1	𝑋1	NOUN
cana-5359	402	12	for	for	ADP
cana-5359	402	13	every	every	DET
cana-5359	402	14	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	PROPN
cana-5359	402	15	𝐾	𝐾	PROPN
cana-5359	402	16	in	in	ADP
cana-5359	402	17	𝑋2	𝑋2	ADJ
cana-5359	402	18	.	.	PUNCT
cana-5359	403	1	(	(	PUNCT
cana-5359	403	2	iii	iii	X
cana-5359	403	3	)	)	PUNCT
cana-5359	403	4	𝔉ℱ𝑐𝑙(ℎ𝔉	𝔉ℱ𝑐𝑙(ℎ𝔉	NOUN
cana-5359	403	5	−1(𝐾	−1(𝐾	NOUN
cana-5359	403	6	)	)	PUNCT
cana-5359	403	7	)	)	PUNCT
cana-5359	404	1	⊆	⊆	NUM
cana-5359	404	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	404	3	−1(𝔉ℱ𝑐𝑙(𝐾	−1(𝔉ℱ𝑐𝑙(𝐾	NOUN
cana-5359	404	4	)	)	PUNCT
cana-5359	404	5	)	)	PUNCT
cana-5359	404	6	for	for	ADP
cana-5359	404	7	every	every	DET
cana-5359	404	8	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	404	9	𝐾	𝐾	PROPN
cana-5359	404	10	of	of	ADP
cana-5359	404	11	𝑋2	𝑋2	PROPN
cana-5359	404	12	.	.	PUNCT
cana-5359	405	1	proof	proof	NOUN
cana-5359	405	2	.	.	PUNCT
cana-5359	406	1	(	(	PUNCT
cana-5359	406	2	i	i	NOUN
cana-5359	406	3	)	)	PUNCT
cana-5359	406	4	→	→	SYM
cana-5359	406	5	(	(	PUNCT
cana-5359	406	6	ii	ii	NOUN
cana-5359	406	7	):	):	PUNCT
cana-5359	406	8	consider	consider	VERB
cana-5359	406	9	a	a	DET
cana-5359	406	10	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	PROPN
cana-5359	406	11	𝐾	𝐾	PROPN
cana-5359	406	12	in	in	ADP
cana-5359	406	13	𝑋2	𝑋2	ADJ
cana-5359	406	14	.	.	PUNCT
cana-5359	407	1	it	it	PRON
cana-5359	407	2	follows	follow	VERB
cana-5359	407	3	𝐾𝑐	𝐾𝑐	PROPN
cana-5359	407	4	is	be	AUX
cana-5359	407	5	a	a	DET
cana-5359	407	6	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	407	7	in	in	ADP
cana-5359	407	8	𝑋2	𝑋2	PROPN
cana-5359	407	9	.	.	PUNCT
cana-5359	408	1	as	as	SCONJ
cana-5359	408	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	408	3	is	be	AUX
cana-5359	408	4	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5359	408	5	,	,	PUNCT
cana-5359	408	6	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	408	7	−1((𝐾)𝑐	−1((𝐾)𝑐	PROPN
cana-5359	408	8	)	)	PUNCT
cana-5359	408	9	is	be	AUX
cana-5359	408	10	a	a	DET
cana-5359	408	11	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5359	408	12	in	in	ADP
cana-5359	408	13	𝑋1	𝑋1	PROPN
cana-5359	408	14	.	.	PUNCT
cana-5359	409	1	we	we	PRON
cana-5359	409	2	know	know	VERB
cana-5359	409	3	that	that	SCONJ
cana-5359	409	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	409	5	−1((𝐾)𝑐	−1((𝐾)𝑐	PROPN
cana-5359	409	6	)	)	PUNCT
cana-5359	409	7	=	=	SYM
cana-5359	409	8	(	(	PUNCT
cana-5359	409	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	409	10	−1(𝐾	−1(𝐾	NOUN
cana-5359	409	11	)	)	PUNCT
cana-5359	409	12	)	)	PUNCT
cana-5359	410	1	𝑐	𝑐	NOUN
cana-5359	410	2	.	.	PUNCT
cana-5359	411	1	hence	hence	ADV
cana-5359	411	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	411	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	411	4	)	)	PUNCT
cana-5359	411	5	is	be	AUX
cana-5359	411	6	a	a	DET
cana-5359	411	7	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5359	411	8	in	in	ADP
cana-5359	411	9	𝑋1	𝑋1	PROPN
cana-5359	411	10	.	.	PUNCT
cana-5359	412	1	(	(	PUNCT
cana-5359	412	2	ii	ii	NOUN
cana-5359	412	3	)	)	PUNCT
cana-5359	412	4	→	→	SYM
cana-5359	412	5	(	(	PUNCT
cana-5359	412	6	iii	iii	NOUN
cana-5359	412	7	):	):	PUNCT
cana-5359	412	8	consider	consider	VERB
cana-5359	412	9	a	a	DET
cana-5359	412	10	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	412	11	𝐾	𝐾	PROPN
cana-5359	412	12	in	in	ADP
cana-5359	412	13	𝑋2	𝑋2	ADJ
cana-5359	412	14	and	and	CCONJ
cana-5359	412	15	𝐾	𝐾	PROPN
cana-5359	412	16	⊆	⊆	NUM
cana-5359	412	17	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	NOUN
cana-5359	412	18	)	)	PUNCT
cana-5359	412	19	.	.	PUNCT
cana-5359	413	1	then	then	ADV
cana-5359	413	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	413	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	413	4	)	)	PUNCT
cana-5359	413	5	⊆	⊆	NUM
cana-5359	413	6	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	413	7	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	NOUN
cana-5359	413	8	)	)	PUNCT
cana-5359	413	9	)	)	PUNCT
cana-5359	413	10	.	.	PUNCT
cana-5359	414	1	since	since	SCONJ
cana-5359	414	2	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	NOUN
cana-5359	414	3	)	)	PUNCT
cana-5359	414	4	)	)	PUNCT
cana-5359	414	5	is	be	AUX
cana-5359	414	6	a	a	DET
cana-5359	414	7	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5359	414	8	in	in	ADP
cana-5359	414	9	𝑋2	𝑋2	ADJ
cana-5359	414	10	.	.	PUNCT
cana-5359	415	1	by	by	ADP
cana-5359	415	2	presumption	presumption	NOUN
cana-5359	415	3	,	,	PUNCT
cana-5359	415	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	415	5	−1((𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1((𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	NOUN
cana-5359	415	6	)	)	PUNCT
cana-5359	415	7	)	)	PUNCT
cana-5359	415	8	)	)	PUNCT
cana-5359	415	9	is	be	AUX
cana-5359	415	10	a	a	DET
cana-5359	415	11	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5359	415	12	in	in	ADP
cana-5359	415	13	𝑋1	𝑋1	PROPN
cana-5359	415	14	.	.	PUNCT
cana-5359	416	1	communications	communication	NOUN
cana-5359	416	2	on	on	ADP
cana-5359	416	3	applied	apply	VERB
cana-5359	416	4	nonlinear	nonlinear	ADJ
cana-5359	416	5	analysis	analysis	NOUN
cana-5359	416	6	issn	issn	NOUN
cana-5359	416	7	:	:	PUNCT
cana-5359	416	8	1074	1074	NUM
cana-5359	416	9	-	-	PUNCT
cana-5359	416	10	133x	133x	NUM
cana-5359	416	11	vol	vol	VERB
cana-5359	416	12	32	32	NUM
cana-5359	416	13	no	no	NOUN
cana-5359	416	14	.	.	PUNCT
cana-5359	417	1	10s	10	NOUN
cana-5359	417	2	(	(	PUNCT
cana-5359	417	3	2025	2025	NUM
cana-5359	417	4	)	)	PUNCT
cana-5359	417	5	1922	1922	NUM
cana-5359	417	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	417	7	also	also	ADV
cana-5359	417	8	,	,	PUNCT
cana-5359	417	9	as	as	SCONJ
cana-5359	417	10	𝑋1	𝑋1	PROPN
cana-5359	417	11	is	be	AUX
cana-5359	417	12	𝔉ℱ𝛿𝛽𝑈1	𝔉ℱ𝛿𝛽𝑈1	ADP
cana-5359	417	13	2	2	NUM
cana-5359	417	14	-space	-space	NOUN
cana-5359	417	15	,	,	PUNCT
cana-5359	417	16	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	417	17	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5359	417	18	)	)	PUNCT
cana-5359	417	19	)	)	PUNCT
cana-5359	417	20	is	be	AUX
cana-5359	417	21	a	a	DET
cana-5359	417	22	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5359	417	23	in	in	ADP
cana-5359	417	24	𝑋1	𝑋1	PROPN
cana-5359	417	25	.	.	PUNCT
cana-5359	418	1	(	(	PUNCT
cana-5359	418	2	iii	iii	NOUN
cana-5359	418	3	)	)	PUNCT
cana-5359	418	4	→	→	SYM
cana-5359	418	5	(	(	PUNCT
cana-5359	418	6	i	i	NOUN
cana-5359	418	7	):	):	PUNCT
cana-5359	418	8	consider	consider	VERB
cana-5359	418	9	a	a	DET
cana-5359	418	10	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	PROPN
cana-5359	418	11	𝐾	𝐾	PROPN
cana-5359	418	12	in	in	ADP
cana-5359	418	13	𝑋2	𝑋2	ADJ
cana-5359	418	14	.	.	PUNCT
cana-5359	419	1	as	as	ADP
cana-5359	419	2	𝑋2	𝑋2	ADJ
cana-5359	419	3	is	be	AUX
cana-5359	419	4	𝔉ℱ𝛿𝛽𝑈1	𝔉ℱ𝛿𝛽𝑈1	ADP
cana-5359	419	5	2	2	NUM
cana-5359	419	6	-space	-space	NOUN
cana-5359	419	7	,	,	PUNCT
cana-5359	419	8	𝐾	𝐾	PROPN
cana-5359	419	9	is	be	AUX
cana-5359	419	10	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5359	419	11	in	in	ADP
cana-5359	419	12	𝑋2	𝑋2	PROPN
cana-5359	419	13	and	and	CCONJ
cana-5359	419	14	𝔉ℱ𝑐𝑙(𝐾	𝔉ℱ𝑐𝑙(𝐾	PROPN
cana-5359	419	15	)	)	PUNCT
cana-5359	419	16	=	=	SYM
cana-5359	419	17	𝐾	𝐾	PROPN
cana-5359	419	18	.	.	PUNCT
cana-5359	420	1	thus	thus	ADV
cana-5359	420	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	420	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	420	4	)	)	PUNCT
cana-5359	421	1	=	=	SYM
cana-5359	421	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	421	3	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5359	421	4	)	)	PUNCT
cana-5359	421	5	)	)	PUNCT
cana-5359	422	1	⊇	⊇	PROPN
cana-5359	422	2	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5359	422	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	422	4	)	)	PUNCT
cana-5359	422	5	)	)	PUNCT
cana-5359	423	1	=	=	PUNCT
cana-5359	423	2	𝔉ℱ𝑐𝑙(ℎ𝔉	𝔉ℱ𝑐𝑙(ℎ𝔉	NOUN
cana-5359	423	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	423	4	)	)	PUNCT
cana-5359	423	5	)	)	PUNCT
cana-5359	423	6	.	.	PUNCT
cana-5359	424	1	but	but	CCONJ
cana-5359	424	2	clearly	clearly	ADV
cana-5359	424	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	424	4	−1(𝐾	−1(𝐾	NOUN
cana-5359	424	5	)	)	PUNCT
cana-5359	424	6	⊆	⊆	NUM
cana-5359	424	7	𝔉ℱ𝑐𝑙(ℎ𝔉	𝔉ℱ𝑐𝑙(ℎ𝔉	NOUN
cana-5359	424	8	−1(𝐾	−1(𝐾	NOUN
cana-5359	424	9	)	)	PUNCT
cana-5359	424	10	)	)	PUNCT
cana-5359	424	11	.	.	PUNCT
cana-5359	425	1	therefore	therefore	ADV
cana-5359	425	2	𝔉ℱ𝑐𝑙(ℎ𝔉	𝔉ℱ𝑐𝑙(ℎ𝔉	NOUN
cana-5359	425	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	425	4	)	)	PUNCT
cana-5359	425	5	)	)	PUNCT
cana-5359	426	1	=	=	SYM
cana-5359	426	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	426	3	−1(𝐾	−1(𝐾	NOUN
cana-5359	426	4	)	)	PUNCT
cana-5359	426	5	.	.	PUNCT
cana-5359	427	1	it	it	PRON
cana-5359	427	2	follows	follow	VERB
cana-5359	427	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	427	4	−1(𝐾	−1(𝐾	NOUN
cana-5359	427	5	)	)	PUNCT
cana-5359	427	6	is	be	AUX
cana-5359	427	7	a	a	DET
cana-5359	427	8	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5359	428	1	and	and	CCONJ
cana-5359	428	2	so	so	ADV
cana-5359	428	3	it	it	PRON
cana-5359	428	4	is	be	AUX
cana-5359	428	5	a	a	DET
cana-5359	428	6	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5359	428	7	in	in	ADP
cana-5359	428	8	𝑋1	𝑋1	PROPN
cana-5359	428	9	.	.	PUNCT
cana-5359	429	1	hence	hence	ADV
cana-5359	429	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5359	429	3	is	be	AUX
cana-5359	429	4	𝔉ℱ𝛿𝛽𝑖𝑟𝑟	𝔉ℱ𝛿𝛽𝑖𝑟𝑟	PROPN
cana-5359	429	5	map	map	NOUN
cana-5359	429	6	.	.	PUNCT
cana-5359	430	1	the	the	DET
cana-5359	430	2	proof	proof	NOUN
cana-5359	430	3	is	be	AUX
cana-5359	430	4	similar	similar	ADJ
cana-5359	430	5	for	for	ADP
cana-5359	430	6	other	other	ADJ
cana-5359	430	7	cases	case	NOUN
cana-5359	430	8	of	of	ADP
cana-5359	430	9	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5359	430	10	,	,	PUNCT
cana-5359	430	11	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5359	430	12	,	,	PUNCT
cana-5359	430	13	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	NOUN
cana-5359	430	14	and	and	CCONJ
cana-5359	430	15	𝔉ℱ𝛿𝛼𝑜𝑠.	𝔉ℱ𝛿𝛼𝑜𝑠.	NOUN
cana-5359	430	16	5	5	NUM
cana-5359	430	17	application	application	NOUN
cana-5359	430	18	entropy	entropy	NOUN
cana-5359	430	19	as	as	ADP
cana-5359	430	20	a	a	DET
cana-5359	430	21	measure	measure	NOUN
cana-5359	430	22	of	of	ADP
cana-5359	430	23	fuzziness	fuzziness	NOUN
cana-5359	430	24	was	be	AUX
cana-5359	430	25	first	first	ADV
cana-5359	430	26	proposed	propose	VERB
cana-5359	430	27	by	by	ADP
cana-5359	430	28	zadeh	zadeh	PROPN
cana-5359	431	1	[	[	X
cana-5359	431	2	16	16	NUM
cana-5359	431	3	]	]	PUNCT
cana-5359	431	4	.	.	PUNCT
cana-5359	432	1	later	later	ADV
cana-5359	432	2	many	many	ADJ
cana-5359	432	3	mathematicians	mathematician	NOUN
cana-5359	432	4	defined	define	VERB
cana-5359	432	5	several	several	ADJ
cana-5359	432	6	entropy	entropy	NOUN
cana-5359	432	7	measures	measure	NOUN
cana-5359	432	8	.	.	PUNCT
cana-5359	433	1	in	in	ADP
cana-5359	433	2	this	this	DET
cana-5359	433	3	section	section	NOUN
cana-5359	433	4	,	,	PUNCT
cana-5359	433	5	we	we	PRON
cana-5359	433	6	focus	focus	VERB
cana-5359	433	7	on	on	ADP
cana-5359	433	8	defining	define	VERB
cana-5359	433	9	an	an	DET
cana-5359	433	10	entropy	entropy	NOUN
cana-5359	433	11	measure	measure	NOUN
cana-5359	433	12	for	for	ADP
cana-5359	433	13	𝔉𝑓𝑠	𝔉𝑓𝑠	PROPN
cana-5359	433	14	that	that	PRON
cana-5359	433	15	connects	connect	VERB
cana-5359	433	16	the	the	DET
cana-5359	433	17	degree	degree	NOUN
cana-5359	433	18	of	of	ADP
cana-5359	433	19	membership	membership	NOUN
cana-5359	433	20	and	and	CCONJ
cana-5359	433	21	non	non	ADJ
cana-5359	433	22	-	-	NOUN
cana-5359	433	23	membership	membership	NOUN
cana-5359	433	24	.	.	PUNCT
cana-5359	434	1	as	as	ADP
cana-5359	434	2	an	an	DET
cana-5359	434	3	example	example	NOUN
cana-5359	434	4	,	,	PUNCT
cana-5359	434	5	we	we	PRON
cana-5359	434	6	have	have	AUX
cana-5359	434	7	applied	apply	VERB
cana-5359	434	8	the	the	DET
cana-5359	434	9	proposed	propose	VERB
cana-5359	434	10	entropy	entropy	NOUN
cana-5359	434	11	measure	measure	NOUN
cana-5359	434	12	in	in	ADP
cana-5359	434	13	the	the	DET
cana-5359	434	14	field	field	NOUN
cana-5359	434	15	of	of	ADP
cana-5359	434	16	decision	decision	NOUN
cana-5359	434	17	making	making	NOUN
cana-5359	434	18	.	.	PUNCT
cana-5359	435	1	definition	definition	NOUN
cana-5359	435	2	5.1	5.1	NUM
cana-5359	435	3	let	let	VERB
cana-5359	435	4	𝐴	𝐴	PROPN
cana-5359	435	5	=	=	PUNCT
cana-5359	435	6	{	{	PUNCT
cana-5359	435	7	<	<	X
cana-5359	435	8	𝑥	𝑥	X
cana-5359	435	9	,	,	PUNCT
cana-5359	435	10	𝛼𝐴(𝑥	𝛼𝐴(𝑥	NUM
cana-5359	435	11	)	)	PUNCT
cana-5359	435	12	,	,	PUNCT
cana-5359	435	13	𝛽𝐴(𝑥)|𝑥	𝛽𝐴(𝑥)|𝑥	PROPN
cana-5359	435	14	∈	∈	PROPN
cana-5359	435	15	𝑋	𝑋	PROPN
cana-5359	435	16	}	}	PUNCT
cana-5359	435	17	be	be	AUX
cana-5359	435	18	a	a	DET
cana-5359	435	19	𝔉𝑓𝑠	𝔉𝑓𝑠	PROPN
cana-5359	435	20	in	in	ADP
cana-5359	435	21	𝑈.	𝑈.	PROPN
cana-5359	435	22	the	the	DET
cana-5359	435	23	new	new	ADJ
cana-5359	435	24	entropy	entropy	NOUN
cana-5359	435	25	measure	measure	NOUN
cana-5359	435	26	for	for	ADP
cana-5359	435	27	𝐴	𝐴	PROPN
cana-5359	435	28	denoted	denote	VERB
cana-5359	435	29	by	by	ADP
cana-5359	435	30	휀𝔉𝑓𝑠(𝐴	휀𝔉𝑓𝑠(𝐴	NOUN
cana-5359	435	31	)	)	PUNCT
cana-5359	435	32	,	,	PUNCT
cana-5359	435	33	is	be	AUX
cana-5359	435	34	a	a	DET
cana-5359	435	35	function	function	NOUN
cana-5359	435	36	,	,	PUNCT
cana-5359	435	37	휀𝔉𝑓𝑠	휀𝔉𝑓𝑠	PROPN
cana-5359	435	38	:	:	PUNCT
cana-5359	435	39	𝜏𝔉𝑓𝑠(𝑈	𝜏𝔉𝑓𝑠(𝑈	PROPN
cana-5359	435	40	)	)	PUNCT
cana-5359	435	41	→	→	PUNCT
cana-5359	436	1	[	[	X
cana-5359	436	2	0,1	0,1	NUM
cana-5359	436	3	]	]	PUNCT
cana-5359	436	4	and	and	CCONJ
cana-5359	436	5	is	be	AUX
cana-5359	436	6	defined	define	VERB
cana-5359	436	7	as	as	ADP
cana-5359	436	8	휀𝔉𝑓𝑠(𝐴	휀𝔉𝑓𝑠(𝐴	X
cana-5359	436	9	)	)	PUNCT
cana-5359	436	10	=	=	SYM
cana-5359	437	1	1	1	NUM
cana-5359	437	2	−	−	NUM
cana-5359	437	3	1	1	NUM
cana-5359	437	4	𝑛	𝑛	PRON
cana-5359	437	5	∑𝑛	∑𝑛	PROPN
cana-5359	437	6	𝑖=1	𝑖=1	PROPN
cana-5359	437	7	(	(	PUNCT
cana-5359	437	8	𝛼𝐴	𝛼𝐴	ADV
cana-5359	437	9	−	−	NOUN
cana-5359	437	10	𝛽𝐴)2	𝛽𝐴)2	NOUN
cana-5359	437	11	;	;	PUNCT
cana-5359	437	12	𝑓𝑜𝑟𝑒𝑣𝑒𝑟𝑦`𝑥𝑖	𝑓𝑜𝑟𝑒𝑣𝑒𝑟𝑦`𝑥𝑖	NUM
cana-5359	437	13	∈	∈	PROPN
cana-5359	437	14	𝐴	𝐴	PROPN
cana-5359	437	15	,	,	PUNCT
cana-5359	437	16	where	where	SCONJ
cana-5359	437	17	𝜏𝔉𝑓𝑠(𝑈	𝜏𝔉𝑓𝑠(𝑈	NOUN
cana-5359	437	18	)	)	PUNCT
cana-5359	437	19	denote	denote	VERB
cana-5359	437	20	the	the	DET
cana-5359	437	21	family	family	NOUN
cana-5359	437	22	of	of	ADP
cana-5359	437	23	all	all	DET
cana-5359	437	24	𝔉𝑓𝑠	𝔉𝑓𝑠	PROPN
cana-5359	437	25	’s	’s	NOUN
cana-5359	437	26	on	on	ADP
cana-5359	437	27	𝑈.	𝑈.	PROPN
cana-5359	437	28	example	example	NOUN
cana-5359	437	29	5.1	5.1	NUM
cana-5359	437	30	consider	consider	VERB
cana-5359	437	31	an	an	DET
cana-5359	437	32	example	example	NOUN
cana-5359	437	33	of	of	ADP
cana-5359	437	34	a	a	DET
cana-5359	437	35	shopping	shopping	NOUN
cana-5359	437	36	experience	experience	NOUN
cana-5359	437	37	with	with	ADP
cana-5359	437	38	different	different	ADJ
cana-5359	437	39	items	item	NOUN
cana-5359	437	40	.	.	PUNCT
cana-5359	438	1	the	the	DET
cana-5359	438	2	pandemic	pandemic	ADJ
cana-5359	438	3	situation	situation	NOUN
cana-5359	438	4	of	of	ADP
cana-5359	438	5	covid-19	covid-19	PROPN
cana-5359	438	6	has	have	AUX
cana-5359	438	7	broadened	broaden	VERB
cana-5359	438	8	the	the	DET
cana-5359	438	9	doorstep	doorstep	NOUN
cana-5359	438	10	of	of	ADP
cana-5359	438	11	our	our	PRON
cana-5359	438	12	shopping	shopping	NOUN
cana-5359	438	13	experience	experience	NOUN
cana-5359	438	14	.	.	PUNCT
cana-5359	439	1	nowadays	nowadays	ADV
cana-5359	439	2	we	we	PRON
cana-5359	439	3	depend	depend	VERB
cana-5359	439	4	on	on	ADP
cana-5359	439	5	different	different	ADJ
cana-5359	439	6	methods	method	NOUN
cana-5359	439	7	of	of	ADP
cana-5359	439	8	shopping	shopping	NOUN
cana-5359	439	9	like	like	ADP
cana-5359	439	10	online	online	ADV
cana-5359	439	11	(	(	PUNCT
cana-5359	439	12	purchasing	purchase	VERB
cana-5359	439	13	through	through	ADP
cana-5359	439	14	internet	internet	NOUN
cana-5359	439	15	,	,	PUNCT
cana-5359	439	16	often	often	ADV
cana-5359	439	17	through	through	ADP
cana-5359	439	18	the	the	DET
cana-5359	439	19	websites	website	NOUN
cana-5359	439	20	or	or	CCONJ
cana-5359	439	21	apps	app	NOUN
cana-5359	439	22	)	)	PUNCT
cana-5359	439	23	,	,	PUNCT
cana-5359	439	24	in	in	ADP
cana-5359	439	25	-	-	PUNCT
cana-5359	439	26	store	store	NOUN
cana-5359	439	27	(	(	PUNCT
cana-5359	439	28	visiting	visit	VERB
cana-5359	439	29	physically	physically	ADV
cana-5359	439	30	)	)	PUNCT
cana-5359	439	31	,	,	PUNCT
cana-5359	439	32	mobile	mobile	NOUN
cana-5359	439	33	(	(	PUNCT
cana-5359	439	34	using	use	VERB
cana-5359	439	35	mobile	mobile	NOUN
cana-5359	439	36	to	to	PART
cana-5359	439	37	browse	browse	VERB
cana-5359	439	38	and	and	CCONJ
cana-5359	439	39	purchase	purchase	VERB
cana-5359	439	40	)	)	PUNCT
cana-5359	439	41	shopping	shopping	NOUN
cana-5359	439	42	.	.	PUNCT
cana-5359	440	1	based	base	VERB
cana-5359	440	2	on	on	ADP
cana-5359	440	3	the	the	DET
cana-5359	440	4	reviews	review	NOUN
cana-5359	440	5	and	and	CCONJ
cana-5359	440	6	ratings	rating	NOUN
cana-5359	440	7	,	,	PUNCT
cana-5359	440	8	we	we	PRON
cana-5359	440	9	will	will	AUX
cana-5359	440	10	find	find	VERB
cana-5359	440	11	out	out	ADP
cana-5359	440	12	the	the	DET
cana-5359	440	13	most	most	ADV
cana-5359	440	14	reliable	reliable	ADJ
cana-5359	440	15	method	method	NOUN
cana-5359	440	16	of	of	ADP
cana-5359	440	17	shopping	shop	VERB
cana-5359	440	18	for	for	ADP
cana-5359	440	19	a	a	DET
cana-5359	440	20	specific	specific	ADJ
cana-5359	440	21	item	item	NOUN
cana-5359	440	22	using	use	VERB
cana-5359	440	23	the	the	DET
cana-5359	440	24	fermatean	fermatean	ADJ
cana-5359	440	25	fuzzy	fuzzy	ADJ
cana-5359	440	26	entropy	entropy	NOUN
cana-5359	440	27	measure	measure	NOUN
cana-5359	440	28	.	.	PUNCT
cana-5359	441	1	table	table	NOUN
cana-5359	441	2	1	1	NUM
cana-5359	441	3	.	.	PUNCT
cana-5359	442	1	ratings	rating	NOUN
cana-5359	442	2	of	of	ADP
cana-5359	442	3	products	product	NOUN
cana-5359	442	4	based	base	VERB
cana-5359	442	5	on	on	ADP
cana-5359	442	6	the	the	DET
cana-5359	442	7	different	different	ADJ
cana-5359	442	8	shopping	shopping	NOUN
cana-5359	442	9	ways	way	NOUN
cana-5359	442	10	.	.	PUNCT
cana-5359	443	1	gadgets	gadget	NOUN
cana-5359	443	2	(	(	PUNCT
cana-5359	443	3	a	a	X
cana-5359	443	4	)	)	PUNCT
cana-5359	443	5	gold	gold	NOUN
cana-5359	443	6	jewellery	jewellery	NOUN
cana-5359	443	7	(	(	PUNCT
cana-5359	443	8	b	b	NOUN
cana-5359	443	9	)	)	PUNCT
cana-5359	443	10	food	food	NOUN
cana-5359	443	11	products(c	products(c	NOUN
cana-5359	443	12	)	)	PUNCT
cana-5359	443	13	cloths	cloth	NOUN
cana-5359	443	14	(	(	PUNCT
cana-5359	443	15	d	d	NOUN
cana-5359	443	16	)	)	PUNCT
cana-5359	443	17	online	online	ADV
cana-5359	443	18	(	(	PUNCT
cana-5359	443	19	1	1	NUM
cana-5359	443	20	)	)	PUNCT
cana-5359	443	21	<	<	X
cana-5359	443	22	1	1	NUM
cana-5359	443	23	,	,	PUNCT
cana-5359	443	24	𝑎	𝑎	NOUN
cana-5359	443	25	;	;	PUNCT
cana-5359	443	26	0.6,0.3	0.6,0.3	PROPN
cana-5359	443	27	>	>	X
cana-5359	443	28	<	<	X
cana-5359	443	29	1	1	NUM
cana-5359	443	30	,	,	PUNCT
cana-5359	443	31	𝑏	𝑏	NOUN
cana-5359	443	32	;	;	PUNCT
cana-5359	443	33	0.8,0.7	0.8,0.7	PROPN
cana-5359	443	34	>	>	X
cana-5359	443	35	<	<	X
cana-5359	443	36	1	1	NUM
cana-5359	443	37	,	,	PUNCT
cana-5359	443	38	𝑐	𝑐	NOUN
cana-5359	443	39	;	;	PUNCT
cana-5359	443	40	0.7,0.3	0.7,0.3	PROPN
cana-5359	443	41	>	>	X
cana-5359	443	42	<	<	X
cana-5359	443	43	1	1	NUM
cana-5359	443	44	,	,	PUNCT
cana-5359	443	45	𝑑	𝑑	NOUN
cana-5359	443	46	;	;	PUNCT
cana-5359	443	47	0.5,0.3	0.5,0.3	PROPN
cana-5359	443	48	>	>	PUNCT
cana-5359	443	49	in	in	ADP
cana-5359	443	50	-	-	PUNCT
cana-5359	443	51	store	store	NOUN
cana-5359	443	52	(	(	PUNCT
cana-5359	443	53	2	2	NUM
cana-5359	443	54	)	)	PUNCT
cana-5359	443	55	<	<	X
cana-5359	443	56	2	2	NUM
cana-5359	443	57	,	,	PUNCT
cana-5359	443	58	𝑎	𝑎	NOUN
cana-5359	443	59	;	;	PUNCT
cana-5359	443	60	0.9,0.4	0.9,0.4	NUM
cana-5359	443	61	>	>	X
cana-5359	443	62	<	<	X
cana-5359	443	63	2	2	NUM
cana-5359	443	64	,	,	PUNCT
cana-5359	443	65	𝑏	𝑏	NOUN
cana-5359	443	66	;	;	PUNCT
cana-5359	443	67	0.4,0.7	0.4,0.7	PROPN
cana-5359	443	68	>	>	X
cana-5359	443	69	<	<	X
cana-5359	443	70	2	2	NUM
cana-5359	443	71	,	,	PUNCT
cana-5359	443	72	𝑐	𝑐	NOUN
cana-5359	443	73	;	;	PUNCT
cana-5359	443	74	0.7,0.8	0.7,0.8	PROPN
cana-5359	443	75	>	>	X
cana-5359	443	76	<	<	X
cana-5359	443	77	2	2	NUM
cana-5359	443	78	,	,	PUNCT
cana-5359	443	79	𝑑	𝑑	NOUN
cana-5359	443	80	;	;	PUNCT
cana-5359	443	81	0.2,0.8	0.2,0.8	PROPN
cana-5359	443	82	>	>	X
cana-5359	443	83	mobile	mobile	NOUN
cana-5359	443	84	(	(	PUNCT
cana-5359	443	85	3	3	NUM
cana-5359	443	86	)	)	PUNCT
cana-5359	443	87	<	<	X
cana-5359	443	88	3	3	NUM
cana-5359	443	89	,	,	PUNCT
cana-5359	443	90	𝑎	𝑎	NOUN
cana-5359	443	91	;	;	PUNCT
cana-5359	443	92	0.6,0.8	0.6,0.8	X
cana-5359	443	93	>	>	PUNCT
cana-5359	443	94	<	<	X
cana-5359	443	95	3	3	NUM
cana-5359	443	96	,	,	PUNCT
cana-5359	443	97	𝑏	𝑏	NOUN
cana-5359	443	98	;	;	PUNCT
cana-5359	443	99	0.2,0.1	0.2,0.1	PROPN
cana-5359	443	100	>	>	X
cana-5359	443	101	<	<	X
cana-5359	443	102	3	3	NUM
cana-5359	443	103	,	,	PUNCT
cana-5359	443	104	𝑐	𝑐	NOUN
cana-5359	443	105	;	;	PUNCT
cana-5359	443	106	0.9,0.2	0.9,0.2	X
cana-5359	443	107	>	>	X
cana-5359	443	108	<	<	X
cana-5359	443	109	3	3	NUM
cana-5359	443	110	,	,	PUNCT
cana-5359	443	111	𝑑	𝑑	NOUN
cana-5359	443	112	;	;	PUNCT
cana-5359	443	113	0.1,0.5	0.1,0.5	PROPN
cana-5359	443	114	>	>	X
cana-5359	443	115	clearly	clearly	ADV
cana-5359	443	116	,	,	PUNCT
cana-5359	443	117	all	all	DET
cana-5359	443	118	values	value	NOUN
cana-5359	443	119	in	in	ADP
cana-5359	443	120	the	the	DET
cana-5359	443	121	table	table	NOUN
cana-5359	443	122	1	1	NUM
cana-5359	443	123	are	be	AUX
cana-5359	443	124	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5359	443	125	’s	’s	NOUN
cana-5359	443	126	.	.	PUNCT
cana-5359	444	1	now	now	ADV
cana-5359	444	2	we	we	PRON
cana-5359	444	3	calculate	calculate	VERB
cana-5359	444	4	the	the	DET
cana-5359	444	5	휀𝔉ℱ𝑠	휀𝔉ℱ𝑠	PROPN
cana-5359	444	6	of	of	ADP
cana-5359	444	7	each	each	DET
cana-5359	444	8	value	value	NOUN
cana-5359	444	9	.	.	PUNCT
cana-5359	445	1	table	table	NOUN
cana-5359	445	2	2	2	NUM
cana-5359	445	3	.	.	PUNCT
cana-5359	445	4	entropy	entropy	PROPN
cana-5359	445	5	measure	measure	NOUN
cana-5359	445	6	of	of	ADP
cana-5359	445	7	each	each	DET
cana-5359	445	8	shopping	shopping	NOUN
cana-5359	445	9	for	for	ADP
cana-5359	445	10	the	the	DET
cana-5359	445	11	different	different	ADJ
cana-5359	445	12	purchase	purchase	NOUN
cana-5359	445	13	.	.	PUNCT
cana-5359	446	1	gadgets	gadget	NOUN
cana-5359	446	2	(	(	PUNCT
cana-5359	446	3	a	a	X
cana-5359	446	4	)	)	PUNCT
cana-5359	446	5	gold	gold	NOUN
cana-5359	446	6	jewellery	jewellery	NOUN
cana-5359	446	7	(	(	PUNCT
cana-5359	446	8	b	b	NOUN
cana-5359	446	9	)	)	PUNCT
cana-5359	446	10	food	food	NOUN
cana-5359	446	11	products(c	products(c	NOUN
cana-5359	446	12	)	)	PUNCT
cana-5359	446	13	cloths	cloth	NOUN
cana-5359	446	14	(	(	PUNCT
cana-5359	446	15	d	d	NOUN
cana-5359	446	16	)	)	PUNCT
cana-5359	446	17	online	online	ADV
cana-5359	446	18	(	(	PUNCT
cana-5359	446	19	1	1	NUM
cana-5359	446	20	)	)	PUNCT
cana-5359	446	21	0.91	0.91	NUM
cana-5359	446	22	0.99	0.99	NUM
cana-5359	446	23	0.84	0.84	NUM
cana-5359	446	24	0.96	0.96	NUM
cana-5359	446	25	in	in	ADP
cana-5359	446	26	-	-	PUNCT
cana-5359	446	27	store	store	NOUN
cana-5359	446	28	(	(	PUNCT
cana-5359	446	29	2	2	NUM
cana-5359	446	30	)	)	PUNCT
cana-5359	446	31	0.75	0.75	NUM
cana-5359	446	32	0.91	0.91	NUM
cana-5359	446	33	0.99	0.99	NUM
cana-5359	446	34	0.64	0.64	NUM
cana-5359	446	35	mobile	mobile	NOUN
cana-5359	446	36	(	(	PUNCT
cana-5359	446	37	3	3	NUM
cana-5359	446	38	)	)	PUNCT
cana-5359	446	39	0.96	0.96	NUM
cana-5359	446	40	0.99	0.99	NUM
cana-5359	446	41	0.51	0.51	NUM
cana-5359	446	42	0.84	0.84	NUM
cana-5359	446	43	communications	communication	NOUN
cana-5359	446	44	on	on	ADP
cana-5359	446	45	applied	apply	VERB
cana-5359	446	46	nonlinear	nonlinear	ADJ
cana-5359	446	47	analysis	analysis	NOUN
cana-5359	446	48	issn	issn	NOUN
cana-5359	446	49	:	:	PUNCT
cana-5359	446	50	1074	1074	NUM
cana-5359	446	51	-	-	PUNCT
cana-5359	446	52	133x	133x	NUM
cana-5359	446	53	vol	vol	VERB
cana-5359	446	54	32	32	NUM
cana-5359	446	55	no	no	NOUN
cana-5359	446	56	.	.	PUNCT
cana-5359	447	1	10s	10	NOUN
cana-5359	447	2	(	(	PUNCT
cana-5359	447	3	2025	2025	NUM
cana-5359	447	4	)	)	PUNCT
cana-5359	447	5	1923	1923	NUM
cana-5359	447	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	447	7	from	from	ADP
cana-5359	447	8	table	table	NOUN
cana-5359	447	9	2	2	NUM
cana-5359	447	10	,	,	PUNCT
cana-5359	447	11	it	it	PRON
cana-5359	447	12	is	be	AUX
cana-5359	447	13	clear	clear	ADJ
cana-5359	447	14	that	that	SCONJ
cana-5359	447	15	휀𝔉ℱ𝑠(1	휀𝔉ℱ𝑠(1	NOUN
cana-5359	447	16	,	,	PUNCT
cana-5359	447	17	𝑐	𝑐	NOUN
cana-5359	447	18	)	)	PUNCT
cana-5359	447	19	<	<	X
cana-5359	447	20	휀𝔉ℱ𝑠(1	휀𝔉ℱ𝑠(1	NOUN
cana-5359	447	21	,	,	PUNCT
cana-5359	447	22	𝑎	𝑎	NOUN
cana-5359	447	23	)	)	PUNCT
cana-5359	447	24	<	<	X
cana-5359	447	25	휀𝔉ℱ𝑠(1	휀𝔉ℱ𝑠(1	NOUN
cana-5359	447	26	,	,	PUNCT
cana-5359	447	27	𝑑	𝑑	NOUN
cana-5359	447	28	)	)	PUNCT
cana-5359	447	29	≤	≤	NOUN
cana-5359	447	30	휀𝔉ℱ𝑠(1	휀𝔉ℱ𝑠(1	NOUN
cana-5359	447	31	,	,	PUNCT
cana-5359	447	32	𝑏	𝑏	NOUN
cana-5359	447	33	)	)	PUNCT
cana-5359	447	34	similarly	similarly	ADV
cana-5359	447	35	휀𝔉ℱ𝑠(2	휀𝔉ℱ𝑠(2	PROPN
cana-5359	447	36	,	,	PUNCT
cana-5359	447	37	𝑐	𝑐	NOUN
cana-5359	447	38	)	)	PUNCT
cana-5359	447	39	<	<	X
cana-5359	447	40	휀𝔉ℱ𝑠(2	휀𝔉ℱ𝑠(2	PROPN
cana-5359	447	41	,	,	PUNCT
cana-5359	447	42	𝑏	𝑏	NOUN
cana-5359	447	43	)	)	PUNCT
cana-5359	447	44	≤	≤	NOUN
cana-5359	447	45	<	<	X
cana-5359	447	46	휀𝔉ℱ𝑠(2	휀𝔉ℱ𝑠(2	PROPN
cana-5359	447	47	,	,	PUNCT
cana-5359	447	48	𝑎	𝑎	NOUN
cana-5359	447	49	)	)	PUNCT
cana-5359	447	50	<	<	X
cana-5359	447	51	휀𝔉ℱ𝑠(2	휀𝔉ℱ𝑠(2	PROPN
cana-5359	447	52	,	,	PUNCT
cana-5359	447	53	𝑑	𝑑	NOUN
cana-5359	447	54	)	)	PUNCT
cana-5359	447	55	휀𝔉ℱ𝑠(3	휀𝔉ℱ𝑠(3	PROPN
cana-5359	447	56	,	,	PUNCT
cana-5359	447	57	𝑏	𝑏	NOUN
cana-5359	447	58	)	)	PUNCT
cana-5359	447	59	<	<	X
cana-5359	447	60	휀𝔉ℱ𝑠(3	휀𝔉ℱ𝑠(3	PROPN
cana-5359	447	61	,	,	PUNCT
cana-5359	447	62	𝑎	𝑎	NOUN
cana-5359	447	63	)	)	PUNCT
cana-5359	447	64	≤	≤	NOUN
cana-5359	447	65	휀𝔉ℱ𝑠(3	휀𝔉ℱ𝑠(3	PROPN
cana-5359	447	66	,	,	PUNCT
cana-5359	447	67	𝑑	𝑑	NOUN
cana-5359	447	68	)	)	PUNCT
cana-5359	447	69	≤	≤	NOUN
cana-5359	447	70	휀𝔉ℱ𝑠(3	휀𝔉ℱ𝑠(3	PROPN
cana-5359	447	71	,	,	PUNCT
cana-5359	447	72	𝑐	𝑐	PROPN
cana-5359	447	73	)	)	PUNCT
cana-5359	447	74	it	it	PRON
cana-5359	447	75	is	be	AUX
cana-5359	447	76	clear	clear	ADJ
cana-5359	447	77	that	that	SCONJ
cana-5359	447	78	people	people	NOUN
cana-5359	447	79	are	be	AUX
cana-5359	447	80	most	most	ADV
cana-5359	447	81	like	like	ADJ
cana-5359	447	82	to	to	PART
cana-5359	447	83	shop	shop	VERB
cana-5359	447	84	the	the	DET
cana-5359	447	85	online	online	ADJ
cana-5359	447	86	and	and	CCONJ
cana-5359	447	87	mobile	mobile	ADJ
cana-5359	447	88	shopping	shopping	NOUN
cana-5359	447	89	for	for	ADP
cana-5359	447	90	food	food	NOUN
cana-5359	447	91	products	product	NOUN
cana-5359	447	92	and	and	CCONJ
cana-5359	447	93	in	in	ADP
cana-5359	447	94	-	-	PUNCT
cana-5359	447	95	store	store	NOUN
cana-5359	447	96	shopping	shopping	NOUN
cana-5359	447	97	was	be	AUX
cana-5359	447	98	buy	buy	VERB
cana-5359	447	99	a	a	DET
cana-5359	447	100	cloths	cloth	NOUN
cana-5359	447	101	.	.	PUNCT
cana-5359	448	1	6	6	NUM
cana-5359	448	2	conclusion	conclusion	NOUN
cana-5359	448	3	in	in	ADP
cana-5359	448	4	this	this	DET
cana-5359	448	5	paper	paper	NOUN
cana-5359	448	6	,	,	PUNCT
cana-5359	448	7	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	PUNCT
cana-5359	448	8	,	,	PUNCT
cana-5359	448	9	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	PROPN
cana-5359	448	10	,	,	PUNCT
cana-5359	448	11	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5359	448	12	,	,	PUNCT
cana-5359	448	13	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	X
cana-5359	448	14	,	,	PUNCT
cana-5359	448	15	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5359	448	16	,	,	PUNCT
cana-5359	448	17	and	and	CCONJ
cana-5359	448	18	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5359	448	19	respective	respective	ADJ
cana-5359	448	20	irresolute	irresolute	ADJ
cana-5359	448	21	map	map	NOUN
cana-5359	448	22	is	be	AUX
cana-5359	448	23	defined	define	VERB
cana-5359	448	24	using	use	VERB
cana-5359	448	25	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5359	448	26	,	,	PUNCT
cana-5359	448	27	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	NUM
cana-5359	448	28	,	,	PUNCT
cana-5359	448	29	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	NOUN
cana-5359	448	30	,	,	PUNCT
cana-5359	448	31	𝔉ℱ𝛿𝛼𝑜	𝔉ℱ𝛿𝛼𝑜	PROPN
cana-5359	448	32	and	and	CCONJ
cana-5359	448	33	𝔉ℱ𝛿𝛽𝑜	𝔉ℱ𝛿𝛽𝑜	PROPN
cana-5359	448	34	set	set	NOUN
cana-5359	448	35	and	and	CCONJ
cana-5359	448	36	its	its	PRON
cana-5359	448	37	properties	property	NOUN
cana-5359	448	38	are	be	AUX
cana-5359	448	39	analyzed	analyze	VERB
cana-5359	448	40	with	with	ADP
cana-5359	448	41	the	the	DET
cana-5359	448	42	examples	example	NOUN
cana-5359	448	43	.	.	PUNCT
cana-5359	449	1	then	then	ADV
cana-5359	449	2	fermatean	fermatean	VERB
cana-5359	449	3	fuzzy	fuzzy	ADJ
cana-5359	449	4	continuous	continuous	ADJ
cana-5359	449	5	maps	map	NOUN
cana-5359	449	6	are	be	AUX
cana-5359	449	7	compared	compare	VERB
cana-5359	449	8	with	with	ADP
cana-5359	449	9	other	other	ADJ
cana-5359	449	10	generalized	generalized	ADJ
cana-5359	449	11	fermatean	fermatean	NOUN
cana-5359	449	12	fuzzy	fuzzy	ADJ
cana-5359	449	13	continuous	continuous	ADJ
cana-5359	449	14	maps	map	NOUN
cana-5359	449	15	.	.	PUNCT
cana-5359	450	1	also	also	ADV
cana-5359	450	2	we	we	PRON
cana-5359	450	3	extended	extend	VERB
cana-5359	450	4	the	the	DET
cana-5359	450	5	concept	concept	NOUN
cana-5359	450	6	of	of	ADP
cana-5359	450	7	fermatean	fermatean	ADJ
cana-5359	450	8	fuzzy	fuzzy	ADJ
cana-5359	450	9	irresolute	irresolute	ADJ
cana-5359	450	10	maps	map	NOUN
cana-5359	450	11	in	in	ADP
cana-5359	450	12	fermatean	fermatean	ADJ
cana-5359	450	13	fuzzy	fuzzy	ADJ
cana-5359	450	14	topological	topological	ADJ
cana-5359	450	15	spaces	space	NOUN
cana-5359	450	16	using	use	VERB
cana-5359	450	17	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5359	450	18	sets	set	NOUN
cana-5359	450	19	.	.	PUNCT
cana-5359	451	1	some	some	DET
cana-5359	451	2	examples	example	NOUN
cana-5359	451	3	and	and	CCONJ
cana-5359	451	4	basic	basic	ADJ
cana-5359	451	5	relationships	relationship	NOUN
cana-5359	451	6	between	between	ADP
cana-5359	451	7	the	the	DET
cana-5359	451	8	mappings	mapping	NOUN
cana-5359	451	9	were	be	AUX
cana-5359	451	10	also	also	ADV
cana-5359	451	11	discussed	discuss	VERB
cana-5359	451	12	.	.	PUNCT
cana-5359	452	1	in	in	ADP
cana-5359	452	2	future	future	NOUN
cana-5359	452	3	,	,	PUNCT
cana-5359	452	4	these	these	PRON
cana-5359	452	5	can	can	AUX
cana-5359	452	6	be	be	AUX
cana-5359	452	7	extended	extend	VERB
cana-5359	452	8	to	to	ADP
cana-5359	452	9	fermatean	fermatean	VERB
cana-5359	452	10	fuzzy	fuzzy	ADJ
cana-5359	452	11	open	open	ADJ
cana-5359	452	12	,	,	PUNCT
cana-5359	452	13	closed	closed	ADJ
cana-5359	452	14	,	,	PUNCT
cana-5359	452	15	homeomorphism	homeomorphism	PROPN
cana-5359	452	16	and	and	CCONJ
cana-5359	452	17	contra	contra	PROPN
cana-5359	452	18	maps	map	NOUN
cana-5359	452	19	.	.	PUNCT
cana-5359	453	1	application	application	NOUN
cana-5359	453	2	for	for	ADP
cana-5359	453	3	mcdm	mcdm	ADJ
cana-5359	453	4	to	to	ADP
cana-5359	453	5	the	the	DET
cana-5359	453	6	real	real	ADJ
cana-5359	453	7	world	world	NOUN
cana-5359	453	8	problem	problem	NOUN
cana-5359	453	9	was	be	AUX
cana-5359	453	10	solved	solve	VERB
cana-5359	453	11	with	with	ADP
cana-5359	453	12	the	the	DET
cana-5359	453	13	proposed	propose	VERB
cana-5359	453	14	entropy	entropy	NOUN
cana-5359	453	15	measure	measure	NOUN
cana-5359	453	16	.	.	PUNCT
cana-5359	454	1	in	in	ADP
cana-5359	454	2	future	future	NOUN
cana-5359	454	3	,	,	PUNCT
cana-5359	454	4	mcdm	mcdm	ADJ
cana-5359	454	5	to	to	ADP
cana-5359	454	6	the	the	DET
cana-5359	454	7	real	real	ADJ
cana-5359	454	8	world	world	NOUN
cana-5359	454	9	problem	problem	NOUN
cana-5359	454	10	can	can	AUX
cana-5359	454	11	be	be	AUX
cana-5359	454	12	developed	develop	VERB
cana-5359	454	13	to	to	ADP
cana-5359	454	14	the	the	DET
cana-5359	454	15	𝔉ℱ𝑡𝑠.	𝔉ℱ𝑡𝑠.	ADJ
cana-5359	454	16	references	reference	NOUN
cana-5359	454	17	[	[	X
cana-5359	454	18	1	1	NUM
cana-5359	454	19	]	]	PUNCT
cana-5359	454	20	k.	k.	PROPN
cana-5359	454	21	t.	t.	PROPN
cana-5359	454	22	atanassov	atanassov	PROPN
cana-5359	454	23	(	(	PUNCT
cana-5359	454	24	1983	1983	NUM
cana-5359	454	25	)	)	PUNCT
cana-5359	454	26	,	,	PUNCT
cana-5359	454	27	intuitionistic	intuitionistic	ADJ
cana-5359	454	28	fuzzy	fuzzy	ADJ
cana-5359	454	29	sets	set	NOUN
cana-5359	454	30	,	,	PUNCT
cana-5359	454	31	vii	vii	PROPN
cana-5359	454	32	itkrâ€	itkrâ€	PROPN
cana-5359	454	33	™	™	PROPN
cana-5359	454	34	s	s	PART
cana-5359	454	35	session	session	NOUN
cana-5359	454	36	,	,	PUNCT
cana-5359	454	37	sofia	sofia	PROPN
cana-5359	454	38	.	.	PUNCT
cana-5359	455	1	[	[	X
cana-5359	455	2	2	2	X
cana-5359	455	3	]	]	PUNCT
cana-5359	455	4	k.	k.	PROPN
cana-5359	455	5	t.	t.	PROPN
cana-5359	455	6	atanassov	atanassov	PROPN
cana-5359	455	7	(	(	PUNCT
cana-5359	455	8	1986	1986	NUM
cana-5359	455	9	)	)	PUNCT
cana-5359	455	10	,	,	PUNCT
cana-5359	455	11	intuitionistic	intuitionistic	ADJ
cana-5359	455	12	fuzzy	fuzzy	ADJ
cana-5359	455	13	sets	set	NOUN
cana-5359	455	14	,	,	PUNCT
cana-5359	455	15	fuzzy	fuzzy	ADJ
cana-5359	455	16	sets	set	NOUN
cana-5359	455	17	syst	syst	NOUN
cana-5359	455	18	.	.	PUNCT
cana-5359	456	1	20	20	NUM
cana-5359	456	2	,	,	PUNCT
cana-5359	456	3	87	87	NUM
cana-5359	456	4	-	-	SYM
cana-5359	456	5	96	96	NUM
cana-5359	456	6	.	.	PUNCT
cana-5359	457	1	[	[	X
cana-5359	457	2	3	3	X
cana-5359	457	3	]	]	PUNCT
cana-5359	457	4	k.	k.	PROPN
cana-5359	457	5	t.	t.	PROPN
cana-5359	457	6	atanassov	atanassov	PROPN
cana-5359	457	7	(	(	PUNCT
cana-5359	457	8	1999	1999	NUM
cana-5359	457	9	)	)	PUNCT
cana-5359	457	10	,	,	PUNCT
cana-5359	457	11	intuitionistic	intuitionistic	ADJ
cana-5359	457	12	fuzzy	fuzzy	ADJ
cana-5359	457	13	sets	set	NOUN
cana-5359	457	14	:	:	PUNCT
cana-5359	457	15	theory	theory	NOUN
cana-5359	457	16	and	and	CCONJ
cana-5359	457	17	applications	application	NOUN
cana-5359	457	18	,	,	PUNCT
cana-5359	457	19	physica	physica	NOUN
cana-5359	457	20	,	,	PUNCT
cana-5359	457	21	heidelberg	heidelberg	NOUN
cana-5359	457	22	.	.	PUNCT
cana-5359	458	1	[	[	X
cana-5359	458	2	4	4	X
cana-5359	458	3	]	]	PUNCT
cana-5359	458	4	k.	k.	PROPN
cana-5359	458	5	t.	t.	PROPN
cana-5359	458	6	atanassov	atanassov	PROPN
cana-5359	458	7	(	(	PUNCT
cana-5359	458	8	2012	2012	NUM
cana-5359	458	9	)	)	PUNCT
cana-5359	458	10	,	,	PUNCT
cana-5359	458	11	on	on	ADP
cana-5359	458	12	intuitionistic	intuitionistic	ADJ
cana-5359	458	13	fuzzy	fuzzy	ADJ
cana-5359	458	14	sets	set	NOUN
cana-5359	458	15	theory	theory	NOUN
cana-5359	458	16	,	,	PUNCT
cana-5359	458	17	springer	springer	NOUN
cana-5359	458	18	,	,	PUNCT
cana-5359	458	19	berlin	berlin	PROPN
cana-5359	458	20	.	.	PUNCT
cana-5359	459	1	[	[	X
cana-5359	459	2	5	5	X
cana-5359	459	3	]	]	PUNCT
cana-5359	459	4	k.	k.	PROPN
cana-5359	459	5	atanassov	atanassov	PROPN
cana-5359	459	6	(	(	PUNCT
cana-5359	459	7	2016	2016	NUM
cana-5359	459	8	)	)	PUNCT
cana-5359	459	9	,	,	PUNCT
cana-5359	459	10	review	review	NOUN
cana-5359	459	11	and	and	CCONJ
cana-5359	459	12	new	new	ADJ
cana-5359	459	13	results	result	NOUN
cana-5359	459	14	on	on	ADP
cana-5359	459	15	intuitionistic	intuitionistic	ADJ
cana-5359	459	16	fuzzy	fuzzy	ADJ
cana-5359	459	17	sets	set	NOUN
cana-5359	459	18	,	,	PUNCT
cana-5359	459	19	international	international	ADJ
cana-5359	459	20	journal	journal	NOUN
cana-5359	459	21	bioautomation	bioautomation	NOUN
cana-5359	459	22	.	.	PUNCT
cana-5359	460	1	20	20	NUM
cana-5359	460	2	,	,	PUNCT
cana-5359	460	3	s17	s17	NOUN
cana-5359	460	4	-	-	PUNCT
cana-5359	460	5	s26	s26	NOUN
cana-5359	460	6	.	.	PUNCT
cana-5359	461	1	on	on	ADP
cana-5359	461	2	fuzzy	fuzzy	ADJ
cana-5359	461	3	systems	system	NOUN
cana-5359	461	4	(	(	PUNCT
cana-5359	461	5	fuzz	fuzz	NOUN
cana-5359	461	6	-	-	PUNCT
cana-5359	461	7	ieee	ieee	NOUN
cana-5359	461	8	)	)	PUNCT
cana-5359	461	9	,	,	PUNCT
cana-5359	461	10	298	298	NUM
cana-5359	461	11	-	-	SYM
cana-5359	461	12	305	305	NUM
cana-5359	461	13	.	.	PUNCT
cana-5359	462	1	[	[	X
cana-5359	462	2	6	6	NUM
cana-5359	462	3	]	]	PUNCT
cana-5359	462	4	c.	c.	PROPN
cana-5359	462	5	l	l	PROPN
cana-5359	462	6	chang	chang	PROPN
cana-5359	462	7	(	(	PUNCT
cana-5359	462	8	1968	1968	NUM
cana-5359	462	9	)	)	PUNCT
cana-5359	462	10	,	,	PUNCT
cana-5359	462	11	fuzzy	fuzzy	ADJ
cana-5359	462	12	topological	topological	ADJ
cana-5359	462	13	spaces	space	NOUN
cana-5359	462	14	,	,	PUNCT
cana-5359	462	15	j.	j.	PROPN
cana-5359	462	16	math	math	PROPN
cana-5359	462	17	.	.	PUNCT
cana-5359	463	1	anal	anal	PROPN
cana-5359	463	2	.	.	PUNCT
cana-5359	464	1	appl	appl	PROPN
cana-5359	464	2	.	.	PROPN
cana-5359	464	3	,	,	PUNCT
cana-5359	464	4	24	24	NUM
cana-5359	464	5	,	,	PUNCT
cana-5359	464	6	182	182	NUM
cana-5359	464	7	-	-	SYM
cana-5359	464	8	190	190	NUM
cana-5359	464	9	.	.	PUNCT
cana-5359	465	1	[	[	X
cana-5359	465	2	7	7	X
cana-5359	465	3	]	]	X
cana-5359	465	4	d.	d.	PROPN
cana-5359	465	5	coker	coker	NOUN
cana-5359	465	6	(	(	PUNCT
cana-5359	465	7	1997	1997	NUM
cana-5359	465	8	)	)	PUNCT
cana-5359	465	9	,	,	PUNCT
cana-5359	465	10	an	an	DET
cana-5359	465	11	introduction	introduction	NOUN
cana-5359	465	12	to	to	ADP
cana-5359	465	13	intuitionistic	intuitionistic	ADJ
cana-5359	465	14	fuzzy	fuzzy	ADJ
cana-5359	465	15	topological	topological	ADJ
cana-5359	465	16	spaces	space	NOUN
cana-5359	465	17	,	,	PUNCT
cana-5359	465	18	fuzzy	fuzzy	ADJ
cana-5359	465	19	sets	set	NOUN
cana-5359	465	20	and	and	CCONJ
cana-5359	465	21	systems	system	NOUN
cana-5359	465	22	,	,	PUNCT
cana-5359	465	23	88	88	NUM
cana-5359	465	24	,	,	PUNCT
cana-5359	465	25	81	81	NUM
cana-5359	465	26	-	-	SYM
cana-5359	465	27	89	89	NUM
cana-5359	465	28	.	.	PUNCT
cana-5359	466	1	[	[	X
cana-5359	466	2	8	8	X
cana-5359	466	3	]	]	X
cana-5359	466	4	hariwan	hariwan	X
cana-5359	466	5	z.	z.	PROPN
cana-5359	466	6	ibrahim	ibrahim	PROPN
cana-5359	466	7	(	(	PUNCT
cana-5359	466	8	2022	2022	NUM
cana-5359	466	9	)	)	PUNCT
cana-5359	466	10	,	,	PUNCT
cana-5359	466	11	fermatean	fermatean	NOUN
cana-5359	466	12	fuzzy	fuzzy	ADJ
cana-5359	466	13	topological	topological	ADJ
cana-5359	466	14	spaces	space	NOUN
cana-5359	466	15	,	,	PUNCT
cana-5359	466	16	j.	j.	PROPN
cana-5359	466	17	appl	appl	PROPN
cana-5359	466	18	.	.	PROPN
cana-5359	466	19	math	math	PROPN
cana-5359	466	20	.	.	PUNCT
cana-5359	467	1	and	and	CCONJ
cana-5359	468	1	informatics	informatic	NOUN
cana-5359	468	2	.	.	PUNCT
cana-5359	469	1	40	40	NUM
cana-5359	469	2	,	,	PUNCT
cana-5359	469	3	85	85	NUM
cana-5359	469	4	-	-	SYM
cana-5359	469	5	98	98	NUM
cana-5359	469	6	.	.	PUNCT
cana-5359	470	1	[	[	X
cana-5359	470	2	9	9	NUM
cana-5359	470	3	]	]	X
cana-5359	470	4	murat	murat	NOUN
cana-5359	470	5	olgun	olgun	PROPN
cana-5359	470	6	,	,	PUNCT
cana-5359	470	7	mehmet	mehmet	PROPN
cana-5359	470	8	unver	unver	PROPN
cana-5359	470	9	and	and	CCONJ
cana-5359	470	10	seyhmus	seyhmus	VERB
cana-5359	470	11	yardimci	yardimci	PROPN
cana-5359	470	12	(	(	PUNCT
cana-5359	470	13	2019	2019	NUM
cana-5359	470	14	)	)	PUNCT
cana-5359	470	15	,	,	PUNCT
cana-5359	470	16	pythagorean	pythagorean	PROPN
cana-5359	470	17	fuzzy	fuzzy	ADJ
cana-5359	470	18	topological	topological	ADJ
cana-5359	470	19	spaces	space	NOUN
cana-5359	470	20	,	,	PUNCT
cana-5359	470	21	complex	complex	ADJ
cana-5359	470	22	&	&	CCONJ
cana-5359	470	23	intelligent	intelligent	ADJ
cana-5359	470	24	systems	system	NOUN
cana-5359	470	25	.	.	PUNCT
cana-5359	471	1	https://doi.org/10.1007/s40747-019-0095-2	https://doi.org/10.1007/s40747-019-0095-2	NUM
cana-5359	471	2	.	.	PUNCT
cana-5359	472	1	[	[	X
cana-5359	472	2	10	10	NUM
cana-5359	472	3	]	]	PUNCT
cana-5359	472	4	t.senapati	t.senapati	NOUN
cana-5359	472	5	and	and	CCONJ
cana-5359	472	6	r.r.yager	r.r.yager	NOUN
cana-5359	472	7	(	(	PUNCT
cana-5359	472	8	2020	2020	NUM
cana-5359	472	9	)	)	PUNCT
cana-5359	472	10	,	,	PUNCT
cana-5359	472	11	fermatean	fermatean	ADJ
cana-5359	472	12	fuzzy	fuzzy	ADJ
cana-5359	472	13	sets	set	NOUN
cana-5359	472	14	,	,	PUNCT
cana-5359	472	15	journal	journal	NOUN
cana-5359	472	16	of	of	ADP
cana-5359	472	17	ambient	ambient	ADJ
cana-5359	472	18	intelligence	intelligence	NOUN
cana-5359	472	19	and	and	CCONJ
cana-5359	472	20	humanized	humanize	VERB
cana-5359	472	21	computing	compute	VERB
cana-5359	472	22	11	11	NUM
cana-5359	472	23	,	,	PUNCT
cana-5359	472	24	663	663	NUM
cana-5359	472	25	-	-	SYM
cana-5359	472	26	674	674	NUM
cana-5359	472	27	.	.	PUNCT
cana-5359	473	1	[	[	X
cana-5359	473	2	11	11	NUM
cana-5359	473	3	]	]	PUNCT
cana-5359	473	4	a.	a.	NOUN
cana-5359	473	5	vadivel	vadivel	NOUN
cana-5359	473	6	,	,	PUNCT
cana-5359	473	7	v.	v.	ADP
cana-5359	473	8	sagunthaladevi	sagunthaladevi	NOUN
cana-5359	473	9	and	and	CCONJ
cana-5359	473	10	s.	s.	PROPN
cana-5359	473	11	priya	priya	PROPN
cana-5359	473	12	(	(	PUNCT
cana-5359	473	13	2025	2025	NUM
cana-5359	473	14	)	)	PUNCT
cana-5359	473	15	,	,	PUNCT
cana-5359	473	16	more	more	ADJ
cana-5359	473	17	on	on	ADP
cana-5359	473	18	open	open	ADJ
cana-5359	473	19	sets	set	NOUN
cana-5359	473	20	in	in	ADP
cana-5359	473	21	fermatean	fermatean	ADJ
cana-5359	473	22	fuzzy	fuzzy	ADJ
cana-5359	473	23	topological	topological	ADJ
cana-5359	473	24	spaces	space	NOUN
cana-5359	473	25	and	and	CCONJ
cana-5359	473	26	its	its	PRON
cana-5359	473	27	application	application	NOUN
cana-5359	473	28	,	,	PUNCT
cana-5359	473	29	accepted	accept	VERB
cana-5359	473	30	in	in	ADP
cana-5359	473	31	j.	j.	PROPN
cana-5359	473	32	appl	appl	PROPN
cana-5359	473	33	.	.	PROPN
cana-5359	473	34	math	math	PROPN
cana-5359	473	35	.	.	PUNCT
cana-5359	473	36	&	&	CCONJ
cana-5359	473	37	informatics	informatics	PROPN
cana-5359	473	38	.	.	PUNCT
cana-5359	474	1	communications	communication	NOUN
cana-5359	474	2	on	on	ADP
cana-5359	474	3	applied	apply	VERB
cana-5359	474	4	nonlinear	nonlinear	ADJ
cana-5359	474	5	analysis	analysis	NOUN
cana-5359	474	6	issn	issn	NOUN
cana-5359	474	7	:	:	PUNCT
cana-5359	474	8	1074	1074	NUM
cana-5359	474	9	-	-	PUNCT
cana-5359	474	10	133x	133x	NUM
cana-5359	474	11	vol	vol	VERB
cana-5359	474	12	32	32	NUM
cana-5359	474	13	no	no	NOUN
cana-5359	474	14	.	.	PUNCT
cana-5359	475	1	10s	10	NOUN
cana-5359	475	2	(	(	PUNCT
cana-5359	475	3	2025	2025	NUM
cana-5359	475	4	)	)	PUNCT
cana-5359	475	5	1924	1924	NUM
cana-5359	475	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5359	476	1	[	[	X
cana-5359	476	2	12	12	NUM
cana-5359	476	3	]	]	PUNCT
cana-5359	476	4	r.	r.	PROPN
cana-5359	476	5	r.	r.	PROPN
cana-5359	476	6	yager	yager	PROPN
cana-5359	476	7	(	(	PUNCT
cana-5359	476	8	2013	2013	NUM
cana-5359	476	9	)	)	PUNCT
cana-5359	476	10	,	,	PUNCT
cana-5359	476	11	pythagorean	pythagorean	PROPN
cana-5359	476	12	membership	membership	NOUN
cana-5359	476	13	grades	grade	NOUN
cana-5359	476	14	in	in	ADP
cana-5359	476	15	multicriteria	multicriteria	PROPN
cana-5359	476	16	decision	decision	NOUN
cana-5359	476	17	making	making	NOUN
cana-5359	476	18	,	,	PUNCT
cana-5359	476	19	in	in	ADP
cana-5359	476	20	:	:	PUNCT
cana-5359	476	21	technical	technical	ADJ
cana-5359	476	22	report	report	NOUN
cana-5359	476	23	𝑀𝐼𝐼-3301	𝑀𝐼𝐼-3301	PROPN
cana-5359	476	24	.	.	PUNCT
cana-5359	477	1	machine	machine	NOUN
cana-5359	477	2	intelligence	intelligence	PROPN
cana-5359	477	3	institute	institute	PROPN
cana-5359	477	4	,	,	PUNCT
cana-5359	477	5	iona	iona	PROPN
cana-5359	477	6	college	college	PROPN
cana-5359	477	7	,	,	PUNCT
cana-5359	477	8	new	new	ADJ
cana-5359	477	9	rochelle	rochelle	NOUN
cana-5359	477	10	.	.	PUNCT
cana-5359	478	1	[	[	X
cana-5359	478	2	13	13	NUM
cana-5359	478	3	]	]	PUNCT
cana-5359	478	4	r.	r.	PROPN
cana-5359	478	5	r.	r.	PROPN
cana-5359	478	6	yager	yager	PROPN
cana-5359	478	7	(	(	PUNCT
cana-5359	478	8	2013	2013	NUM
cana-5359	478	9	)	)	PUNCT
cana-5359	478	10	,	,	PUNCT
cana-5359	478	11	pythagorean	pythagorean	PROPN
cana-5359	478	12	fuzzy	fuzzy	ADJ
cana-5359	478	13	subsets	subset	NOUN
cana-5359	478	14	,	,	PUNCT
cana-5359	478	15	in	in	ADP
cana-5359	478	16	:	:	PUNCT
cana-5359	478	17	proceedings	proceeding	NOUN
cana-5359	478	18	of	of	ADP
cana-5359	478	19	the	the	DET
cana-5359	478	20	joint	joint	ADJ
cana-5359	478	21	𝐼𝐹𝑆𝐴	𝐼𝐹𝑆𝐴	PROPN
cana-5359	478	22	world	world	PROPN
cana-5359	478	23	congress	congress	PROPN
cana-5359	478	24	𝑁𝐴𝐹𝐼𝑃𝑆	𝑁𝐴𝐹𝐼𝑃𝑆	PROPN
cana-5359	478	25	annual	annual	ADJ
cana-5359	478	26	meeting	meeting	NOUN
cana-5359	478	27	,	,	PUNCT
cana-5359	478	28	57	57	NUM
cana-5359	478	29	-	-	SYM
cana-5359	478	30	61	61	NUM
cana-5359	478	31	.	.	PUNCT
cana-5359	479	1	[	[	X
cana-5359	479	2	14	14	NUM
cana-5359	479	3	]	]	X
cana-5359	479	4	r.	r.	PROPN
cana-5359	479	5	r.	r.	PROPN
cana-5359	479	6	yager	yager	PROPN
cana-5359	479	7	(	(	PUNCT
cana-5359	479	8	2014	2014	NUM
cana-5359	479	9	)	)	PUNCT
cana-5359	479	10	,	,	PUNCT
cana-5359	479	11	pythagorean	pythagorean	PROPN
cana-5359	479	12	membership	membership	NOUN
cana-5359	479	13	grades	grade	NOUN
cana-5359	479	14	in	in	ADP
cana-5359	479	15	multicriteria	multicriteria	PROPN
cana-5359	479	16	decision	decision	NOUN
cana-5359	479	17	making	making	NOUN
cana-5359	479	18	,	,	PUNCT
cana-5359	479	19	𝐼𝐸𝐸𝐸	𝐼𝐸𝐸𝐸	PROPN
cana-5359	479	20	trans	trans	PROPN
cana-5359	479	21	fuzzy	fuzzy	PROPN
cana-5359	479	22	syst	syst	PROPN
cana-5359	479	23	.	.	PUNCT
cana-5359	480	1	22	22	NUM
cana-5359	480	2	(	(	PUNCT
cana-5359	480	3	4	4	NUM
cana-5359	480	4	)	)	PUNCT
cana-5359	480	5	,	,	PUNCT
cana-5359	480	6	958	958	NUM
cana-5359	480	7	-	-	SYM
cana-5359	480	8	965	965	NUM
cana-5359	480	9	.	.	PUNCT
cana-5359	481	1	[	[	X
cana-5359	481	2	15	15	NUM
cana-5359	481	3	]	]	X
cana-5359	481	4	l.	l.	PROPN
cana-5359	481	5	a.	a.	PROPN
cana-5359	481	6	zadeh	zadeh	PROPN
cana-5359	481	7	(	(	PUNCT
cana-5359	481	8	1965	1965	NUM
cana-5359	481	9	)	)	PUNCT
cana-5359	481	10	,	,	PUNCT
cana-5359	481	11	fuzzy	fuzzy	ADJ
cana-5359	481	12	sets	set	NOUN
cana-5359	481	13	,	,	PUNCT
cana-5359	481	14	inf	inf	PROPN
cana-5359	481	15	.	.	PROPN
cana-5359	481	16	control	control	PROPN
cana-5359	481	17	,	,	PUNCT
cana-5359	481	18	8	8	NUM
cana-5359	481	19	,	,	PUNCT
cana-5359	481	20	338	338	NUM
cana-5359	481	21	-	-	SYM
cana-5359	481	22	353	353	NUM
cana-5359	481	23	.	.	PUNCT
cana-5359	482	1	[	[	X
cana-5359	482	2	16	16	NUM
cana-5359	482	3	]	]	X
cana-5359	482	4	l.	l.	PROPN
cana-5359	482	5	a.	a.	PROPN
cana-5359	482	6	zadeh	zadeh	PROPN
cana-5359	482	7	(	(	PUNCT
cana-5359	482	8	1965	1965	NUM
cana-5359	482	9	)	)	PUNCT
cana-5359	482	10	,	,	PUNCT
cana-5359	482	11	fuzzy	fuzzy	ADJ
cana-5359	482	12	sets	set	NOUN
cana-5359	482	13	and	and	CCONJ
cana-5359	482	14	systems	system	NOUN
cana-5359	482	15	,	,	PUNCT
cana-5359	482	16	in	in	ADP
cana-5359	482	17	:	:	PUNCT
cana-5359	482	18	proc	proc	NOUN
cana-5359	482	19	.	.	PUNCT
cana-5359	483	1	symp	symp	PROPN
cana-5359	483	2	.	.	PUNCT
cana-5359	484	1	on	on	ADP
cana-5359	484	2	systems	system	NOUN
cana-5359	484	3	theory	theory	NOUN
cana-5359	484	4	,	,	PUNCT
cana-5359	484	5	polytechnic	polytechnic	PROPN
cana-5359	484	6	institute	institute	PROPN
cana-5359	484	7	of	of	ADP
cana-5359	484	8	brooklyn	brooklyn	PROPN
cana-5359	484	9	,	,	PUNCT
cana-5359	484	10	new	new	PROPN
cana-5359	484	11	york	york	PROPN
cana-5359	484	12	.	.	PUNCT