id	sid	tid	token	lemma	pos
cana-5358	1	1	communications	communication	NOUN
cana-5358	1	2	on	on	ADP
cana-5358	1	3	applied	apply	VERB
cana-5358	1	4	nonlinear	nonlinear	ADJ
cana-5358	1	5	analysis	analysis	NOUN
cana-5358	1	6	issn	issn	NOUN
cana-5358	1	7	:	:	PUNCT
cana-5358	1	8	1074	1074	NUM
cana-5358	1	9	-	-	PUNCT
cana-5358	1	10	133x	133x	NUM
cana-5358	1	11	vol	vol	VERB
cana-5358	1	12	32	32	NUM
cana-5358	1	13	no	no	NOUN
cana-5358	1	14	.	.	PUNCT
cana-5358	2	1	10s	10	NOUN
cana-5358	2	2	(	(	PUNCT
cana-5358	2	3	2025	2025	NUM
cana-5358	2	4	)	)	PUNCT
cana-5358	2	5	1895	1895	NUM
cana-5358	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	2	7	homeomorphism	homeomorphism	PROPN
cana-5358	2	8	via	via	ADP
cana-5358	2	9	𝜹𝜷-open	𝜹𝜷-open	ADJ
cana-5358	2	10	sets	set	NOUN
cana-5358	2	11	in	in	ADP
cana-5358	2	12	fermatean	fermatean	ADJ
cana-5358	2	13	fuzzy	fuzzy	ADJ
cana-5358	2	14	topological	topological	ADJ
cana-5358	2	15	spaces	space	NOUN
cana-5358	2	16	and	and	CCONJ
cana-5358	2	17	application	application	NOUN
cana-5358	2	18	in	in	ADP
cana-5358	2	19	entropy	entropy	PROPN
cana-5358	2	20	measure	measure	PROPN
cana-5358	2	21	a.	a.	PROPN
cana-5358	2	22	vadivel1	vadivel1	PROPN
cana-5358	2	23	,	,	PUNCT
cana-5358	2	24	v.	v.	CCONJ
cana-5358	2	25	sagunthaladevi2	sagunthaladevi2	PROPN
cana-5358	2	26	and	and	CCONJ
cana-5358	2	27	s.	s.	PROPN
cana-5358	2	28	priya3	priya3	PROPN
cana-5358	3	1	1pg	1pg	ADJ
cana-5358	3	2	and	and	CCONJ
cana-5358	3	3	research	research	NOUN
cana-5358	3	4	department	department	PROPN
cana-5358	3	5	of	of	ADP
cana-5358	3	6	mathematics	mathematic	NOUN
cana-5358	3	7	,	,	PUNCT
cana-5358	3	8	arignar	arignar	ADJ
cana-5358	3	9	anna	anna	PROPN
cana-5358	3	10	government	government	PROPN
cana-5358	3	11	arts	arts	PROPN
cana-5358	3	12	college	college	PROPN
cana-5358	3	13	,	,	PUNCT
cana-5358	3	14	namakkal	namakkal	NOUN
cana-5358	3	15	637	637	NUM
cana-5358	3	16	002	002	NUM
cana-5358	3	17	,	,	PUNCT
cana-5358	3	18	india	india	PROPN
cana-5358	3	19	.	.	PUNCT
cana-5358	4	1	avmaths@gmail.com	avmaths@gmail.com	X
cana-5358	5	1	3department	3department	NUM
cana-5358	5	2	of	of	ADP
cana-5358	5	3	mathematics	mathematic	NOUN
cana-5358	5	4	,	,	PUNCT
cana-5358	5	5	m.kumarasamy	m.kumarasamy	ADJ
cana-5358	5	6	college	college	NOUN
cana-5358	5	7	of	of	ADP
cana-5358	5	8	engineering	engineering	PROPN
cana-5358	5	9	,	,	PUNCT
cana-5358	5	10	karur	karur	PROPN
cana-5358	5	11	639	639	NUM
cana-5358	5	12	113	113	NUM
cana-5358	5	13	,	,	PUNCT
cana-5358	5	14	india	india	PROPN
cana-5358	5	15	.	.	PUNCT
cana-5358	6	1	sagunthala98v@gmail.com	sagunthala98v@gmail.com	PROPN
cana-5358	6	2	1,2,3department	1,2,3department	NUM
cana-5358	6	3	of	of	ADP
cana-5358	6	4	mathematics	mathematics	PROPN
cana-5358	6	5	,	,	PUNCT
cana-5358	6	6	annamalai	annamalai	PROPN
cana-5358	6	7	university	university	PROPN
cana-5358	6	8	,	,	PUNCT
cana-5358	6	9	annamalai	annamalai	PROPN
cana-5358	6	10	nagar	nagar	VERB
cana-5358	6	11	608	608	NUM
cana-5358	6	12	002	002	NUM
cana-5358	6	13	,	,	PUNCT
cana-5358	6	14	india	india	PROPN
cana-5358	6	15	.	.	PUNCT
cana-5358	7	1	corresponding	correspond	VERB
cana-5358	7	2	author	author	NOUN
cana-5358	7	3	:	:	PUNCT
cana-5358	7	4	s.	s.	PROPN
cana-5358	7	5	priya	priya	PROPN
cana-5358	7	6	pre9433@gmail.com	pre9433@gmail.com	PROPN
cana-5358	8	1	article	article	NOUN
cana-5358	8	2	history	history	NOUN
cana-5358	8	3	:	:	PUNCT
cana-5358	8	4	received	receive	VERB
cana-5358	8	5	:	:	PUNCT
cana-5358	8	6	12	12	NUM
cana-5358	8	7	-	-	SYM
cana-5358	8	8	01	01	NUM
cana-5358	8	9	-	-	PUNCT
cana-5358	8	10	2025	2025	NUM
cana-5358	8	11	revised	revise	VERB
cana-5358	8	12	:	:	PUNCT
cana-5358	8	13	15	15	NUM
cana-5358	8	14	-	-	NUM
cana-5358	8	15	02	02	NUM
cana-5358	8	16	-	-	PUNCT
cana-5358	8	17	2025	2025	NUM
cana-5358	8	18	accepted	accept	VERB
cana-5358	8	19	:	:	PUNCT
cana-5358	8	20	01	01	NUM
cana-5358	8	21	-	-	SYM
cana-5358	8	22	03	03	NUM
cana-5358	8	23	-	-	PUNCT
cana-5358	8	24	2025	2025	NUM
cana-5358	8	25	abstract	abstract	NOUN
cana-5358	8	26	:	:	PUNCT
cana-5358	8	27	classical	classical	ADJ
cana-5358	8	28	set	set	NOUN
cana-5358	8	29	theory	theory	NOUN
cana-5358	8	30	failed	fail	VERB
cana-5358	8	31	to	to	PART
cana-5358	8	32	cover	cover	VERB
cana-5358	8	33	non	non	ADJ
cana-5358	8	34	-	-	ADJ
cana-5358	8	35	probabilistic	probabilistic	ADJ
cana-5358	8	36	uncertain	uncertain	ADJ
cana-5358	8	37	situations	situation	NOUN
cana-5358	8	38	in	in	ADP
cana-5358	8	39	to	to	ADP
cana-5358	8	40	the	the	DET
cana-5358	8	41	set	set	NOUN
cana-5358	8	42	format	format	NOUN
cana-5358	8	43	,	,	PUNCT
cana-5358	8	44	but	but	CCONJ
cana-5358	8	45	fuzzy	fuzzy	ADJ
cana-5358	8	46	set	set	NOUN
cana-5358	8	47	theory	theory	NOUN
cana-5358	8	48	can	can	AUX
cana-5358	8	49	do	do	VERB
cana-5358	8	50	this	this	DET
cana-5358	8	51	job	job	NOUN
cana-5358	8	52	perfectly	perfectly	ADV
cana-5358	8	53	with	with	ADP
cana-5358	8	54	the	the	DET
cana-5358	8	55	fuzzy	fuzzy	ADJ
cana-5358	8	56	number	number	NOUN
cana-5358	8	57	of	of	ADP
cana-5358	8	58	vagueness	vagueness	NOUN
cana-5358	8	59	of	of	ADP
cana-5358	8	60	non	non	ADJ
cana-5358	8	61	-	-	ADJ
cana-5358	8	62	probabilistic	probabilistic	ADJ
cana-5358	8	63	uncertainty	uncertainty	NOUN
cana-5358	8	64	.	.	PUNCT
cana-5358	9	1	topologist	topologist	PROPN
cana-5358	9	2	adopt	adopt	VERB
cana-5358	9	3	this	this	DET
cana-5358	9	4	fuzzy	fuzzy	ADJ
cana-5358	9	5	set	set	NOUN
cana-5358	9	6	and	and	CCONJ
cana-5358	9	7	fit	fit	ADJ
cana-5358	9	8	in	in	ADP
cana-5358	9	9	to	to	ADP
cana-5358	9	10	the	the	DET
cana-5358	9	11	topological	topological	ADJ
cana-5358	9	12	concepts	concept	NOUN
cana-5358	9	13	to	to	PART
cana-5358	9	14	extent	extent	VERB
cana-5358	9	15	and	and	CCONJ
cana-5358	9	16	apply	apply	VERB
cana-5358	9	17	their	their	PRON
cana-5358	9	18	innovations	innovation	NOUN
cana-5358	9	19	for	for	ADP
cana-5358	9	20	the	the	DET
cana-5358	9	21	needs	need	NOUN
cana-5358	9	22	and	and	CCONJ
cana-5358	9	23	growth	growth	NOUN
cana-5358	9	24	of	of	ADP
cana-5358	9	25	the	the	DET
cana-5358	9	26	humans	human	NOUN
cana-5358	9	27	.	.	PUNCT
cana-5358	10	1	even	even	ADV
cana-5358	10	2	though	though	SCONJ
cana-5358	10	3	the	the	DET
cana-5358	10	4	fuzzy	fuzzy	ADJ
cana-5358	10	5	concept	concept	NOUN
cana-5358	10	6	convert	convert	VERB
cana-5358	10	7	every	every	DET
cana-5358	10	8	situation	situation	NOUN
cana-5358	10	9	,	,	PUNCT
cana-5358	10	10	it	it	PRON
cana-5358	10	11	hire	hire	VERB
cana-5358	10	12	the	the	DET
cana-5358	10	13	concept	concept	NOUN
cana-5358	10	14	of	of	ADP
cana-5358	10	15	intuitionistic	intuitionistic	ADJ
cana-5358	10	16	fuzzy	fuzzy	ADJ
cana-5358	10	17	set	set	NOUN
cana-5358	10	18	to	to	PART
cana-5358	10	19	evident	evident	ADJ
cana-5358	10	20	the	the	DET
cana-5358	10	21	importance	importance	NOUN
cana-5358	10	22	of	of	ADP
cana-5358	10	23	non	non	ADJ
cana-5358	10	24	-	-	NOUN
cana-5358	10	25	membership	membership	NOUN
cana-5358	10	26	of	of	ADP
cana-5358	10	27	the	the	DET
cana-5358	10	28	situation	situation	NOUN
cana-5358	10	29	.	.	PUNCT
cana-5358	11	1	pythagorean	pythagorean	PROPN
cana-5358	11	2	fuzzy	fuzzy	ADJ
cana-5358	11	3	set	set	NOUN
cana-5358	11	4	is	be	AUX
cana-5358	11	5	one	one	NUM
cana-5358	11	6	of	of	ADP
cana-5358	11	7	by	by	ADP
cana-5358	11	8	membership	membership	NOUN
cana-5358	11	9	and	and	CCONJ
cana-5358	11	10	non	non	ADJ
cana-5358	11	11	-	-	NOUN
cana-5358	11	12	membership	membership	ADJ
cana-5358	11	13	,	,	PUNCT
cana-5358	11	14	more	more	ADV
cana-5358	11	15	forceful	forceful	ADJ
cana-5358	11	16	to	to	PART
cana-5358	11	17	seize	seize	VERB
cana-5358	11	18	indeterminacy	indeterminacy	NOUN
cana-5358	11	19	to	to	PART
cana-5358	11	20	cover	cover	VERB
cana-5358	11	21	the	the	DET
cana-5358	11	22	uncertain	uncertain	ADJ
cana-5358	11	23	situations	situation	NOUN
cana-5358	11	24	which	which	PRON
cana-5358	11	25	are	be	AUX
cana-5358	11	26	unable	unable	ADJ
cana-5358	11	27	to	to	PART
cana-5358	11	28	covered	cover	VERB
cana-5358	11	29	by	by	ADP
cana-5358	11	30	intuitionistic	intuitionistic	ADJ
cana-5358	11	31	fuzzy	fuzzy	ADJ
cana-5358	11	32	sets	set	NOUN
cana-5358	11	33	.	.	PUNCT
cana-5358	12	1	then	then	ADV
cana-5358	12	2	any	any	DET
cana-5358	12	3	intuitionistic	intuitionistic	ADJ
cana-5358	12	4	fuzzy	fuzzy	ADJ
cana-5358	12	5	subset	subset	NOUN
cana-5358	12	6	or	or	CCONJ
cana-5358	12	7	phythagorean	phythagorean	ADJ
cana-5358	12	8	fuzzy	fuzzy	ADJ
cana-5358	12	9	subset	subset	NOUN
cana-5358	12	10	of	of	ADP
cana-5358	12	11	a	a	DET
cana-5358	12	12	set	set	NOUN
cana-5358	12	13	can	can	AUX
cana-5358	12	14	be	be	AUX
cana-5358	12	15	considered	consider	VERB
cana-5358	12	16	as	as	SCONJ
cana-5358	12	17	fermatean	fermatean	ADJ
cana-5358	12	18	fuzzy	fuzzy	ADJ
cana-5358	12	19	subset	subset	NOUN
cana-5358	12	20	,	,	PUNCT
cana-5358	12	21	we	we	PRON
cana-5358	12	22	observe	observe	VERB
cana-5358	12	23	that	that	SCONJ
cana-5358	12	24	any	any	DET
cana-5358	12	25	intuitionstic	intuitionstic	ADJ
cana-5358	12	26	fuzzy	fuzzy	ADJ
cana-5358	12	27	topological	topological	ADJ
cana-5358	12	28	space	space	NOUN
cana-5358	12	29	or	or	CCONJ
cana-5358	12	30	phythagorean	phythagorean	ADJ
cana-5358	12	31	fuzzy	fuzzy	ADJ
cana-5358	12	32	topological	topological	ADJ
cana-5358	12	33	space	space	NOUN
cana-5358	12	34	is	be	AUX
cana-5358	12	35	a	a	DET
cana-5358	12	36	fermatean	fermatean	ADJ
cana-5358	12	37	fuzzy	fuzzy	ADJ
cana-5358	12	38	topological	topological	ADJ
cana-5358	12	39	space	space	NOUN
cana-5358	12	40	as	as	ADV
cana-5358	12	41	well	well	ADV
cana-5358	12	42	.	.	PUNCT
cana-5358	13	1	in	in	ADP
cana-5358	13	2	this	this	DET
cana-5358	13	3	paper	paper	NOUN
cana-5358	13	4	,	,	PUNCT
cana-5358	13	5	we	we	PRON
cana-5358	13	6	contribute	contribute	VERB
cana-5358	13	7	our	our	PRON
cana-5358	13	8	concept	concept	NOUN
cana-5358	13	9	of	of	ADP
cana-5358	13	10	𝛿	𝛿	PROPN
cana-5358	13	11	(	(	PUNCT
cana-5358	13	12	resp	resp	NOUN
cana-5358	13	13	.	.	PUNCT
cana-5358	14	1	𝛿𝑃	𝛿𝑃	PROPN
cana-5358	14	2	,	,	PUNCT
cana-5358	14	3	𝛿𝑆	𝛿𝑆	PROPN
cana-5358	14	4	,	,	PUNCT
cana-5358	14	5	𝛿𝛼	𝛿𝛼	PROPN
cana-5358	14	6	,	,	PUNCT
cana-5358	14	7	𝛿𝛽	𝛿𝛽	ADJ
cana-5358	14	8	)	)	PUNCT
cana-5358	14	9	-homeomorphism	-homeomorphism	NOUN
cana-5358	14	10	,	,	PUNCT
cana-5358	14	11	𝐶	𝐶	PROPN
cana-5358	14	12	-homeomorphism	-homeomorphism	PROPN
cana-5358	14	13	in	in	ADP
cana-5358	14	14	fermatean	fermatean	ADJ
cana-5358	14	15	fuzzy	fuzzy	ADJ
cana-5358	14	16	topological	topological	ADJ
cana-5358	14	17	spaces	space	NOUN
cana-5358	14	18	and	and	CCONJ
cana-5358	14	19	the	the	DET
cana-5358	14	20	properties	property	NOUN
cana-5358	14	21	for	for	ADP
cana-5358	14	22	the	the	DET
cana-5358	14	23	fermatean	fermatean	ADJ
cana-5358	14	24	field	field	NOUN
cana-5358	14	25	of	of	ADP
cana-5358	14	26	fuzzy	fuzzy	ADJ
cana-5358	14	27	topological	topological	ADJ
cana-5358	14	28	spaces	space	NOUN
cana-5358	14	29	.	.	PUNCT
cana-5358	15	1	to	to	PART
cana-5358	15	2	register	register	VERB
cana-5358	15	3	importance	importance	NOUN
cana-5358	15	4	of	of	ADP
cana-5358	15	5	fermatean	fermatean	ADJ
cana-5358	15	6	fuzzy	fuzzy	ADJ
cana-5358	15	7	sets	set	NOUN
cana-5358	15	8	we	we	PRON
cana-5358	15	9	applied	apply	VERB
cana-5358	15	10	a	a	DET
cana-5358	15	11	proposed	propose	VERB
cana-5358	15	12	entropy	entropy	NOUN
cana-5358	15	13	measure	measure	NOUN
cana-5358	15	14	for	for	ADP
cana-5358	15	15	multiple	multiple	ADJ
cana-5358	15	16	criteria	criterion	NOUN
cana-5358	15	17	decision	decision	NOUN
cana-5358	15	18	making	make	VERB
cana-5358	15	19	problem	problem	NOUN
cana-5358	15	20	.	.	PUNCT
cana-5358	16	1	keywords	keyword	NOUN
cana-5358	16	2	:	:	PUNCT
cana-5358	16	3	fermatean	fermatean	ADJ
cana-5358	16	4	fuzzy	fuzzy	ADJ
cana-5358	16	5	homeomorphism	homeomorphism	NOUN
cana-5358	16	6	,	,	PUNCT
cana-5358	16	7	fermatean	fermatean	ADJ
cana-5358	16	8	fuzzy	fuzzy	ADJ
cana-5358	16	9	𝐶	𝐶	PROPN
cana-5358	16	10	homeomorphism	homeomorphism	PROPN
cana-5358	16	11	,	,	PUNCT
cana-5358	16	12	entropy	entropy	NOUN
cana-5358	16	13	measure	measure	NOUN
cana-5358	16	14	.	.	PUNCT
cana-5358	17	1	ams	am	NOUN
cana-5358	17	2	(	(	PUNCT
cana-5358	17	3	2000	2000	NUM
cana-5358	17	4	)	)	PUNCT
cana-5358	17	5	subject	subject	ADJ
cana-5358	17	6	classification	classification	NOUN
cana-5358	17	7	:	:	PUNCT
cana-5358	17	8	06f35	06f35	NUM
cana-5358	17	9	,	,	PUNCT
cana-5358	17	10	03g10	03g10	NUM
cana-5358	17	11	,	,	PUNCT
cana-5358	17	12	03b52	03b52	NUM
cana-5358	17	13	.	.	PUNCT
cana-5358	18	1	1	1	NUM
cana-5358	18	2	introduction	introduction	NOUN
cana-5358	18	3	fuzzy	fuzzy	ADJ
cana-5358	18	4	sets	set	NOUN
cana-5358	18	5	were	be	AUX
cana-5358	18	6	introduced	introduce	VERB
cana-5358	18	7	zadeh	zadeh	PROPN
cana-5358	19	1	[	[	X
cana-5358	19	2	15	15	NUM
cana-5358	19	3	]	]	X
cana-5358	19	4	in	in	ADP
cana-5358	19	5	1965	1965	NUM
cana-5358	19	6	.	.	PUNCT
cana-5358	20	1	the	the	DET
cana-5358	20	2	fuzzy	fuzzy	ADJ
cana-5358	20	3	set	set	VERB
cana-5358	20	4	concept	concept	NOUN
cana-5358	20	5	was	be	AUX
cana-5358	20	6	the	the	DET
cana-5358	20	7	basis	basis	NOUN
cana-5358	20	8	of	of	ADP
cana-5358	20	9	mathematical	mathematical	ADJ
cana-5358	20	10	testing	testing	NOUN
cana-5358	20	11	of	of	ADP
cana-5358	20	12	the	the	DET
cana-5358	20	13	fuzzy	fuzzy	ADJ
cana-5358	20	14	concept	concept	NOUN
cana-5358	20	15	that	that	PRON
cana-5358	20	16	exists	exist	VERB
cana-5358	20	17	in	in	ADP
cana-5358	20	18	our	our	PRON
cana-5358	20	19	real	real	ADJ
cana-5358	20	20	world	world	NOUN
cana-5358	20	21	and	and	CCONJ
cana-5358	20	22	the	the	DET
cana-5358	20	23	formation	formation	NOUN
cana-5358	20	24	of	of	ADP
cana-5358	20	25	new	new	ADJ
cana-5358	20	26	branches	branch	NOUN
cana-5358	20	27	in	in	ADP
cana-5358	20	28	mathematics	mathematic	NOUN
cana-5358	20	29	.	.	PUNCT
cana-5358	21	1	the	the	DET
cana-5358	21	2	fuzzy	fuzzy	ADJ
cana-5358	21	3	set	set	VERB
cana-5358	21	4	concept	concept	NOUN
cana-5358	21	5	corresponding	correspond	VERB
cana-5358	21	6	to	to	ADP
cana-5358	21	7	unexplained	unexplained	ADJ
cana-5358	21	8	physical	physical	ADJ
cana-5358	21	9	situations	situation	NOUN
cana-5358	21	10	gives	give	VERB
cana-5358	21	11	useful	useful	ADJ
cana-5358	21	12	applications	application	NOUN
cana-5358	21	13	on	on	ADP
cana-5358	21	14	many	many	ADJ
cana-5358	21	15	topics	topic	NOUN
cana-5358	21	16	such	such	ADJ
cana-5358	21	17	as	as	ADP
cana-5358	21	18	statistics	statistic	NOUN
cana-5358	21	19	,	,	PUNCT
cana-5358	21	20	data	datum	NOUN
cana-5358	21	21	processing	processing	NOUN
cana-5358	21	22	and	and	CCONJ
cana-5358	21	23	linguistics	linguistic	NOUN
cana-5358	21	24	.	.	PUNCT
cana-5358	22	1	a	a	DET
cana-5358	22	2	lot	lot	NOUN
cana-5358	22	3	of	of	ADP
cana-5358	22	4	research	research	NOUN
cana-5358	22	5	has	have	AUX
cana-5358	22	6	been	be	AUX
cana-5358	22	7	done	do	VERB
cana-5358	22	8	on	on	ADP
cana-5358	22	9	this	this	DET
cana-5358	22	10	subject	subject	NOUN
cana-5358	22	11	since	since	SCONJ
cana-5358	22	12	1965	1965	NUM
cana-5358	22	13	.	.	PUNCT
cana-5358	23	1	in	in	ADP
cana-5358	23	2	1968	1968	NUM
cana-5358	23	3	,	,	PUNCT
cana-5358	23	4	chang	chang	PROPN
cana-5358	24	1	[	[	X
cana-5358	24	2	6	6	NUM
cana-5358	24	3	]	]	PUNCT
cana-5358	24	4	defined	define	VERB
cana-5358	24	5	the	the	DET
cana-5358	24	6	concept	concept	NOUN
cana-5358	24	7	of	of	ADP
cana-5358	24	8	fuzzy	fuzzy	ADJ
cana-5358	24	9	topological	topological	ADJ
cana-5358	24	10	space	space	NOUN
cana-5358	24	11	and	and	CCONJ
cana-5358	24	12	generalized	generalize	VERB
cana-5358	24	13	some	some	DET
cana-5358	24	14	basic	basic	ADJ
cana-5358	24	15	notions	notion	NOUN
cana-5358	24	16	of	of	ADP
cana-5358	24	17	topology	topology	NOUN
cana-5358	24	18	such	such	ADJ
cana-5358	24	19	as	as	ADP
cana-5358	24	20	open	open	ADJ
cana-5358	24	21	set	set	NOUN
cana-5358	24	22	,	,	PUNCT
cana-5358	24	23	closed	closed	ADJ
cana-5358	24	24	set	set	NOUN
cana-5358	24	25	,	,	PUNCT
cana-5358	24	26	continuity	continuity	NOUN
cana-5358	24	27	and	and	CCONJ
cana-5358	24	28	compactness	compactness	NOUN
cana-5358	24	29	to	to	ADP
cana-5358	24	30	fuzzy	fuzzy	ADJ
cana-5358	24	31	topological	topological	ADJ
cana-5358	24	32	spaces	space	NOUN
cana-5358	24	33	.	.	PUNCT
cana-5358	25	1	the	the	DET
cana-5358	25	2	idea	idea	NOUN
cana-5358	25	3	of	of	ADP
cana-5358	25	4	intuitionistic	intuitionistic	ADJ
cana-5358	25	5	fuzzy	fuzzy	ADJ
cana-5358	25	6	set	set	NOUN
cana-5358	25	7	was	be	AUX
cana-5358	25	8	first	first	ADV
cana-5358	25	9	published	publish	VERB
cana-5358	25	10	by	by	ADP
cana-5358	25	11	communications	communication	NOUN
cana-5358	25	12	on	on	ADP
cana-5358	25	13	applied	apply	VERB
cana-5358	25	14	nonlinear	nonlinear	ADJ
cana-5358	25	15	analysis	analysis	NOUN
cana-5358	25	16	issn	issn	NOUN
cana-5358	25	17	:	:	PUNCT
cana-5358	25	18	1074	1074	NUM
cana-5358	25	19	-	-	PUNCT
cana-5358	25	20	133x	133x	NUM
cana-5358	25	21	vol	vol	VERB
cana-5358	25	22	32	32	NUM
cana-5358	25	23	no	no	NOUN
cana-5358	25	24	.	.	PUNCT
cana-5358	26	1	10s	10	NOUN
cana-5358	26	2	(	(	PUNCT
cana-5358	26	3	2025	2025	NUM
cana-5358	26	4	)	)	PUNCT
cana-5358	26	5	1896	1896	NUM
cana-5358	26	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	26	7	atanassov	atanassov	NOUN
cana-5358	27	1	[	[	X
cana-5358	27	2	1	1	NUM
cana-5358	27	3	]	]	PUNCT
cana-5358	27	4	and	and	CCONJ
cana-5358	27	5	many	many	ADJ
cana-5358	27	6	works	work	NOUN
cana-5358	27	7	by	by	ADP
cana-5358	27	8	the	the	DET
cana-5358	27	9	same	same	ADJ
cana-5358	27	10	author	author	NOUN
cana-5358	27	11	and	and	CCONJ
cana-5358	27	12	his	his	PRON
cana-5358	27	13	colleagues	colleague	NOUN
cana-5358	27	14	appeared	appear	VERB
cana-5358	27	15	in	in	ADP
cana-5358	27	16	the	the	DET
cana-5358	27	17	literature	literature	NOUN
cana-5358	27	18	[	[	X
cana-5358	27	19	2	2	NUM
cana-5358	27	20	,	,	PUNCT
cana-5358	27	21	5	5	NUM
cana-5358	27	22	]	]	PUNCT
cana-5358	27	23	.	.	PUNCT
cana-5358	28	1	coker	coker	NOUN
cana-5358	29	1	[	[	X
cana-5358	29	2	7	7	X
cana-5358	29	3	]	]	PUNCT
cana-5358	29	4	initiated	initiate	VERB
cana-5358	29	5	a	a	DET
cana-5358	29	6	study	study	NOUN
cana-5358	29	7	of	of	ADP
cana-5358	29	8	intuitionistic	intuitionistic	ADJ
cana-5358	29	9	fuzzy	fuzzy	ADJ
cana-5358	29	10	topological	topological	ADJ
cana-5358	29	11	spaces	space	NOUN
cana-5358	29	12	.	.	PUNCT
cana-5358	30	1	later	later	ADV
cana-5358	30	2	yager	yager	NOUN
cana-5358	31	1	[	[	X
cana-5358	31	2	13	13	NUM
cana-5358	31	3	]	]	PUNCT
cana-5358	31	4	launched	launch	VERB
cana-5358	31	5	a	a	DET
cana-5358	31	6	non	non	ADJ
cana-5358	31	7	standard	standard	ADJ
cana-5358	31	8	fuzzy	fuzzy	ADJ
cana-5358	31	9	set	set	NOUN
cana-5358	31	10	referred	refer	VERB
cana-5358	31	11	to	to	ADP
cana-5358	31	12	as	as	ADP
cana-5358	31	13	phythagorean	phythagorean	ADJ
cana-5358	31	14	fuzzy	fuzzy	ADJ
cana-5358	31	15	set	set	NOUN
cana-5358	31	16	.	.	PUNCT
cana-5358	32	1	olgun	olgun	PROPN
cana-5358	32	2	et	et	PROPN
cana-5358	32	3	al	al	PROPN
cana-5358	32	4	.	.	PROPN
cana-5358	32	5	,	,	PUNCT
cana-5358	33	1	[	[	X
cana-5358	33	2	9	9	NUM
cana-5358	33	3	]	]	PUNCT
cana-5358	33	4	defined	define	VERB
cana-5358	33	5	a	a	DET
cana-5358	33	6	phythagorean	phythagorean	ADJ
cana-5358	33	7	fuzzy	fuzzy	ADJ
cana-5358	33	8	topological	topological	ADJ
cana-5358	33	9	spaces	space	NOUN
cana-5358	33	10	.	.	PUNCT
cana-5358	34	1	fermatean	fermatean	ADJ
cana-5358	34	2	fuzzy	fuzzy	ADJ
cana-5358	34	3	sets	set	NOUN
cana-5358	34	4	proposed	propose	VERB
cana-5358	34	5	by	by	ADP
cana-5358	34	6	senapati	senapati	PROPN
cana-5358	34	7	and	and	CCONJ
cana-5358	34	8	yager	yager	NOUN
cana-5358	34	9	in	in	ADP
cana-5358	34	10	2020	2020	NUM
cana-5358	35	1	[	[	X
cana-5358	35	2	10	10	NUM
cana-5358	35	3	]	]	PUNCT
cana-5358	35	4	,	,	PUNCT
cana-5358	35	5	can	can	AUX
cana-5358	35	6	handle	handle	VERB
cana-5358	35	7	uncertain	uncertain	ADJ
cana-5358	35	8	information	information	NOUN
cana-5358	35	9	more	more	ADV
cana-5358	35	10	easily	easily	ADV
cana-5358	35	11	in	in	ADP
cana-5358	35	12	the	the	DET
cana-5358	35	13	process	process	NOUN
cana-5358	35	14	of	of	ADP
cana-5358	35	15	decision	decision	NOUN
cana-5358	35	16	making	making	NOUN
cana-5358	35	17	.	.	PUNCT
cana-5358	36	1	they	they	PRON
cana-5358	36	2	defined	define	VERB
cana-5358	36	3	basic	basic	ADJ
cana-5358	36	4	operations	operation	NOUN
cana-5358	36	5	over	over	ADP
cana-5358	36	6	the	the	DET
cana-5358	36	7	fermatean	fermatean	ADJ
cana-5358	36	8	fuzzy	fuzzy	ADJ
cana-5358	36	9	sets	set	NOUN
cana-5358	36	10	.	.	PUNCT
cana-5358	37	1	hariwan	hariwan	PROPN
cana-5358	37	2	z.	z.	PROPN
cana-5358	37	3	ibrahim	ibrahim	PROPN
cana-5358	37	4	defined	define	VERB
cana-5358	37	5	a	a	DET
cana-5358	37	6	fermatean	fermatean	ADJ
cana-5358	37	7	fuzzy	fuzzy	ADJ
cana-5358	37	8	topological	topological	ADJ
cana-5358	37	9	spaces	space	NOUN
cana-5358	37	10	and	and	CCONJ
cana-5358	37	11	the	the	DET
cana-5358	37	12	continuity	continuity	NOUN
cana-5358	37	13	of	of	ADP
cana-5358	37	14	a	a	DET
cana-5358	37	15	function	function	NOUN
cana-5358	37	16	defind	defind	NOUN
cana-5358	37	17	among	among	ADP
cana-5358	37	18	fermatean	fermatean	ADJ
cana-5358	37	19	fuzzy	fuzzy	ADJ
cana-5358	37	20	topological	topological	ADJ
cana-5358	37	21	spaces	space	NOUN
cana-5358	37	22	.	.	PUNCT
cana-5358	38	1	the	the	DET
cana-5358	38	2	aim	aim	NOUN
cana-5358	38	3	of	of	ADP
cana-5358	38	4	this	this	DET
cana-5358	38	5	paper	paper	NOUN
cana-5358	38	6	is	be	AUX
cana-5358	38	7	as	as	SCONJ
cana-5358	38	8	follows	follow	VERB
cana-5358	38	9	.	.	PUNCT
cana-5358	39	1	in	in	ADP
cana-5358	39	2	section	section	NOUN
cana-5358	39	3	2	2	NUM
cana-5358	39	4	,	,	PUNCT
cana-5358	39	5	some	some	DET
cana-5358	39	6	basic	basic	ADJ
cana-5358	39	7	definitions	definition	NOUN
cana-5358	39	8	of	of	ADP
cana-5358	39	9	𝑓𝑠	𝑓𝑠	NOUN
cana-5358	39	10	’s	’s	PART
cana-5358	39	11	,	,	PUNCT
cana-5358	39	12	𝑖𝑓𝑠	𝑖𝑓𝑠	PROPN
cana-5358	39	13	’s	’s	ADV
cana-5358	39	14	,	,	PUNCT
cana-5358	39	15	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5358	39	16	’s	’s	PART
cana-5358	39	17	and	and	CCONJ
cana-5358	39	18	fermatean	fermatean	ADJ
cana-5358	39	19	fuzzy	fuzzy	ADJ
cana-5358	39	20	sets	set	NOUN
cana-5358	39	21	are	be	AUX
cana-5358	39	22	briefly	briefly	ADV
cana-5358	39	23	reviewed	review	VERB
cana-5358	39	24	.	.	PUNCT
cana-5358	40	1	in	in	ADP
cana-5358	40	2	section	section	NOUN
cana-5358	40	3	3	3	NUM
cana-5358	40	4	and	and	CCONJ
cana-5358	40	5	4	4	NUM
cana-5358	40	6	,	,	PUNCT
cana-5358	40	7	we	we	PRON
cana-5358	40	8	develop	develop	VERB
cana-5358	40	9	the	the	DET
cana-5358	40	10	concept	concept	NOUN
cana-5358	40	11	of	of	ADP
cana-5358	40	12	some	some	DET
cana-5358	40	13	stronger	strong	ADJ
cana-5358	40	14	and	and	CCONJ
cana-5358	40	15	weaker	weak	ADJ
cana-5358	40	16	forms	form	NOUN
cana-5358	40	17	of	of	ADP
cana-5358	40	18	fermatean	fermatean	ADJ
cana-5358	40	19	fuzzy	fuzzy	ADJ
cana-5358	40	20	𝛿𝛽	𝛿𝛽	PROPN
cana-5358	40	21	homeomorphism	homeomorphism	PROPN
cana-5358	40	22	and	and	CCONJ
cana-5358	40	23	𝐶-homeomorphism	𝐶-homeomorphism	PROPN
cana-5358	40	24	in	in	ADP
cana-5358	40	25	fermatean	fermatean	ADJ
cana-5358	40	26	fuzzy	fuzzy	ADJ
cana-5358	40	27	topological	topological	ADJ
cana-5358	40	28	spaces	space	NOUN
cana-5358	40	29	and	and	CCONJ
cana-5358	40	30	also	also	ADV
cana-5358	40	31	specialized	specialize	VERB
cana-5358	40	32	some	some	PRON
cana-5358	40	33	of	of	ADP
cana-5358	40	34	their	their	PRON
cana-5358	40	35	basic	basic	ADJ
cana-5358	40	36	properties	property	NOUN
cana-5358	40	37	with	with	ADP
cana-5358	40	38	examples	example	NOUN
cana-5358	40	39	.	.	PUNCT
cana-5358	41	1	entropy	entropy	PROPN
cana-5358	41	2	measure	measure	NOUN
cana-5358	41	3	was	be	AUX
cana-5358	41	4	introduced	introduce	VERB
cana-5358	41	5	by	by	ADP
cana-5358	41	6	zadeh	zadeh	PROPN
cana-5358	42	1	[	[	X
cana-5358	42	2	16	16	NUM
cana-5358	42	3	]	]	PUNCT
cana-5358	42	4	for	for	ADP
cana-5358	42	5	classical	classical	ADJ
cana-5358	42	6	fuzzy	fuzzy	ADJ
cana-5358	42	7	sets	set	NOUN
cana-5358	42	8	.	.	PUNCT
cana-5358	43	1	many	many	ADJ
cana-5358	43	2	authors	author	NOUN
cana-5358	43	3	developed	develop	VERB
cana-5358	43	4	and	and	CCONJ
cana-5358	43	5	created	create	VERB
cana-5358	43	6	for	for	ADP
cana-5358	43	7	their	their	PRON
cana-5358	43	8	version	version	NOUN
cana-5358	43	9	of	of	ADP
cana-5358	43	10	entropy	entropy	NOUN
cana-5358	43	11	measure	measure	NOUN
cana-5358	43	12	.	.	PUNCT
cana-5358	44	1	here	here	ADV
cana-5358	44	2	in	in	ADP
cana-5358	44	3	section	section	NOUN
cana-5358	44	4	5	5	NUM
cana-5358	44	5	,	,	PUNCT
cana-5358	44	6	we	we	PRON
cana-5358	44	7	introduce	introduce	VERB
cana-5358	44	8	entropy	entropy	NOUN
cana-5358	44	9	measure	measure	NOUN
cana-5358	44	10	for	for	ADP
cana-5358	44	11	fermatean	fermatean	ADJ
cana-5358	44	12	fuzzy	fuzzy	ADJ
cana-5358	44	13	sets	set	NOUN
cana-5358	44	14	and	and	CCONJ
cana-5358	44	15	give	give	VERB
cana-5358	44	16	an	an	DET
cana-5358	44	17	example	example	NOUN
cana-5358	44	18	for	for	ADP
cana-5358	44	19	the	the	DET
cana-5358	44	20	decision	decision	NOUN
cana-5358	44	21	making	make	VERB
cana-5358	44	22	in	in	ADP
cana-5358	44	23	real	real	ADJ
cana-5358	44	24	life	life	NOUN
cana-5358	44	25	problem	problem	NOUN
cana-5358	44	26	.	.	PUNCT
cana-5358	45	1	finally	finally	ADV
cana-5358	45	2	we	we	PRON
cana-5358	45	3	conclude	conclude	VERB
cana-5358	45	4	in	in	ADP
cana-5358	45	5	section	section	NOUN
cana-5358	45	6	6	6	NUM
cana-5358	45	7	.	.	SYM
cana-5358	45	8	2	2	NUM
cana-5358	45	9	preliminaries	preliminary	NOUN
cana-5358	45	10	we	we	PRON
cana-5358	45	11	recall	recall	VERB
cana-5358	45	12	some	some	DET
cana-5358	45	13	basic	basic	ADJ
cana-5358	45	14	notions	notion	NOUN
cana-5358	45	15	of	of	ADP
cana-5358	45	16	fuzzy	fuzzy	ADJ
cana-5358	45	17	sets	set	NOUN
cana-5358	45	18	,	,	PUNCT
cana-5358	45	19	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-5358	45	20	’s	’s	PART
cana-5358	45	21	,	,	PUNCT
cana-5358	45	22	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-5358	45	23	’s	’s	NOUN
cana-5358	45	24	and	and	CCONJ
cana-5358	45	25	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	45	26	’s	’s	PART
cana-5358	45	27	.	.	PUNCT
cana-5358	46	1	definition	definition	NOUN
cana-5358	46	2	2.1	2.1	NUM
cana-5358	46	3	[	[	SYM
cana-5358	46	4	15	15	NUM
cana-5358	46	5	]	]	PUNCT
cana-5358	46	6	let	let	VERB
cana-5358	46	7	𝑋	𝑋	NOUN
cana-5358	46	8	be	be	AUX
cana-5358	46	9	a	a	DET
cana-5358	46	10	nonempty	nonempty	ADV
cana-5358	46	11	set	set	VERB
cana-5358	46	12	.	.	PUNCT
cana-5358	47	1	a	a	DET
cana-5358	47	2	fuzzy	fuzzy	ADJ
cana-5358	47	3	set	set	VERB
cana-5358	47	4	𝐴	𝐴	PROPN
cana-5358	47	5	in	in	ADP
cana-5358	47	6	𝑋	𝑋	PROPN
cana-5358	47	7	is	be	AUX
cana-5358	47	8	characterized	characterize	VERB
cana-5358	47	9	by	by	ADP
cana-5358	47	10	a	a	DET
cana-5358	47	11	membership	membership	NOUN
cana-5358	47	12	function	function	NOUN
cana-5358	47	13	𝜇𝐴	𝜇𝐴	ADP
cana-5358	47	14	:	:	PUNCT
cana-5358	47	15	𝑋	𝑋	PROPN
cana-5358	47	16	→	→	SYM
cana-5358	48	1	[	[	X
cana-5358	48	2	0,1	0,1	NUM
cana-5358	48	3	]	]	PUNCT
cana-5358	48	4	.	.	PUNCT
cana-5358	49	1	that	that	PRON
cana-5358	49	2	is	be	AUX
cana-5358	49	3	:	:	PUNCT
cana-5358	49	4	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	49	5	)	)	PUNCT
cana-5358	49	6	=	=	NOUN
cana-5358	49	7	{	{	PUNCT
cana-5358	50	1	1	1	NUM
cana-5358	50	2	,	,	PUNCT
cana-5358	50	3	if	if	SCONJ
cana-5358	50	4	𝑥	𝑥	PRON
cana-5358	50	5	∈	∈	PROPN
cana-5358	50	6	𝑋	𝑋	NOUN
cana-5358	50	7	0	0	NUM
cana-5358	50	8	,	,	PUNCT
cana-5358	50	9	if	if	SCONJ
cana-5358	50	10	𝑥	𝑥	PROPN
cana-5358	50	11	∉	∉	X
cana-5358	50	12	𝑋	𝑋	PROPN
cana-5358	50	13	(	(	PUNCT
cana-5358	50	14	0,1	0,1	NUM
cana-5358	50	15	)	)	PUNCT
cana-5358	50	16	if	if	SCONJ
cana-5358	50	17	𝑥	𝑥	NOUN
cana-5358	50	18	ispartlyin	ispartlyin	VERB
cana-5358	50	19	𝑋.	𝑋.	PROPN
cana-5358	50	20	alternatively	alternatively	ADV
cana-5358	50	21	,	,	PUNCT
cana-5358	50	22	a	a	DET
cana-5358	50	23	fuzzy	fuzzy	ADJ
cana-5358	50	24	set	set	VERB
cana-5358	50	25	𝐴	𝐴	PROPN
cana-5358	50	26	in	in	ADP
cana-5358	50	27	𝑋	𝑋	PROPN
cana-5358	50	28	is	be	AUX
cana-5358	50	29	an	an	DET
cana-5358	50	30	object	object	NOUN
cana-5358	50	31	having	have	VERB
cana-5358	50	32	the	the	DET
cana-5358	50	33	form	form	NOUN
cana-5358	50	34	𝐴	𝐴	NOUN
cana-5358	50	35	=	=	PUNCT
cana-5358	50	36	{	{	PUNCT
cana-5358	50	37	<	<	X
cana-5358	50	38	𝑥	𝑥	X
cana-5358	50	39	,	,	PUNCT
cana-5358	50	40	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	50	41	)	)	PUNCT
cana-5358	50	42	>	>	PUNCT
cana-5358	51	1	|𝑥	|𝑥	PROPN
cana-5358	51	2	∈	∈	PROPN
cana-5358	51	3	𝑋	𝑋	PROPN
cana-5358	51	4	}	}	PUNCT
cana-5358	51	5	or	or	CCONJ
cana-5358	51	6	𝐴	𝐴	PROPN
cana-5358	51	7	=	=	PUNCT
cana-5358	51	8	{	{	PUNCT
cana-5358	51	9	⟨	⟨	NOUN
cana-5358	51	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	51	11	)	)	PUNCT
cana-5358	51	12	𝑥	𝑥	DET
cana-5358	51	13	⟩	⟩	NOUN
cana-5358	51	14	|𝑥	|𝑥	NOUN
cana-5358	51	15	∈	∈	PROPN
cana-5358	51	16	𝑋	𝑋	PROPN
cana-5358	51	17	}	}	PUNCT
cana-5358	51	18	,	,	PUNCT
cana-5358	51	19	where	where	SCONJ
cana-5358	51	20	the	the	DET
cana-5358	51	21	function	function	NOUN
cana-5358	51	22	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-5358	51	23	):	):	PUNCT
cana-5358	51	24	𝑋	𝑋	PROPN
cana-5358	51	25	→	→	SYM
cana-5358	51	26	[	[	X
cana-5358	51	27	0,1	0,1	NUM
cana-5358	51	28	]	]	PUNCT
cana-5358	51	29	defines	define	VERB
cana-5358	51	30	the	the	DET
cana-5358	51	31	degree	degree	NOUN
cana-5358	51	32	of	of	ADP
cana-5358	51	33	membership	membership	NOUN
cana-5358	51	34	of	of	ADP
cana-5358	51	35	the	the	DET
cana-5358	51	36	element	element	NOUN
cana-5358	51	37	,	,	PUNCT
cana-5358	51	38	𝑥	𝑥	PROPN
cana-5358	51	39	∈	∈	PROPN
cana-5358	51	40	𝑋.	𝑋.	PROPN
cana-5358	51	41	the	the	PRON
cana-5358	51	42	closer	close	ADV
cana-5358	51	43	the	the	DET
cana-5358	51	44	membership	membership	NOUN
cana-5358	51	45	value	value	NOUN
cana-5358	51	46	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-5358	51	47	)	)	PUNCT
cana-5358	51	48	to	to	ADP
cana-5358	51	49	1	1	NUM
cana-5358	51	50	,	,	PUNCT
cana-5358	51	51	the	the	PRON
cana-5358	51	52	more	more	ADJ
cana-5358	51	53	𝑥	𝑥	NOUN
cana-5358	51	54	belongs	belong	VERB
cana-5358	51	55	to	to	ADP
cana-5358	51	56	𝐴	𝐴	PROPN
cana-5358	51	57	,	,	PUNCT
cana-5358	51	58	where	where	SCONJ
cana-5358	51	59	the	the	DET
cana-5358	51	60	grades	grade	NOUN
cana-5358	51	61	1	1	NUM
cana-5358	51	62	and	and	CCONJ
cana-5358	51	63	0	0	NUM
cana-5358	51	64	represent	represent	VERB
cana-5358	51	65	full	full	ADJ
cana-5358	51	66	membership	membership	NOUN
cana-5358	51	67	and	and	CCONJ
cana-5358	51	68	full	full	ADJ
cana-5358	51	69	nonmembership	nonmembership	NOUN
cana-5358	51	70	.	.	PUNCT
cana-5358	52	1	fuzzy	fuzzy	ADJ
cana-5358	52	2	set	set	NOUN
cana-5358	52	3	is	be	AUX
cana-5358	52	4	a	a	DET
cana-5358	52	5	collection	collection	NOUN
cana-5358	52	6	of	of	ADP
cana-5358	52	7	objects	object	NOUN
cana-5358	52	8	with	with	ADP
cana-5358	52	9	graded	grade	VERB
cana-5358	52	10	membership	membership	NOUN
cana-5358	52	11	,	,	PUNCT
cana-5358	52	12	that	that	ADV
cana-5358	52	13	is	is	ADV
cana-5358	52	14	,	,	PUNCT
cana-5358	52	15	having	have	VERB
cana-5358	52	16	degree	degree	NOUN
cana-5358	52	17	of	of	ADP
cana-5358	52	18	membership	membership	NOUN
cana-5358	52	19	.	.	PUNCT
cana-5358	53	1	fuzzy	fuzzy	ADJ
cana-5358	53	2	set	set	NOUN
cana-5358	53	3	is	be	AUX
cana-5358	53	4	an	an	DET
cana-5358	53	5	extension	extension	NOUN
cana-5358	53	6	of	of	ADP
cana-5358	53	7	the	the	DET
cana-5358	53	8	classical	classical	ADJ
cana-5358	53	9	notion	notion	NOUN
cana-5358	53	10	of	of	ADP
cana-5358	53	11	set	set	NOUN
cana-5358	53	12	.	.	PUNCT
cana-5358	54	1	in	in	ADP
cana-5358	54	2	classical	classical	ADJ
cana-5358	54	3	set	set	NOUN
cana-5358	54	4	theory	theory	NOUN
cana-5358	54	5	,	,	PUNCT
cana-5358	54	6	the	the	DET
cana-5358	54	7	membership	membership	NOUN
cana-5358	54	8	of	of	ADP
cana-5358	54	9	elements	element	NOUN
cana-5358	54	10	in	in	ADP
cana-5358	54	11	a	a	DET
cana-5358	54	12	set	set	NOUN
cana-5358	54	13	is	be	AUX
cana-5358	54	14	assessed	assess	VERB
cana-5358	54	15	in	in	ADP
cana-5358	54	16	a	a	DET
cana-5358	54	17	binary	binary	ADJ
cana-5358	54	18	terms	term	NOUN
cana-5358	54	19	according	accord	VERB
cana-5358	54	20	to	to	ADP
cana-5358	54	21	a	a	DET
cana-5358	54	22	bivalent	bivalent	ADJ
cana-5358	54	23	condition	condition	NOUN
cana-5358	54	24	;	;	PUNCT
cana-5358	54	25	an	an	DET
cana-5358	54	26	element	element	NOUN
cana-5358	54	27	either	either	CCONJ
cana-5358	54	28	belongs	belong	VERB
cana-5358	54	29	or	or	CCONJ
cana-5358	54	30	does	do	AUX
cana-5358	54	31	not	not	PART
cana-5358	54	32	belong	belong	VERB
cana-5358	54	33	to	to	ADP
cana-5358	54	34	the	the	DET
cana-5358	54	35	set	set	NOUN
cana-5358	54	36	.	.	PUNCT
cana-5358	55	1	classical	classical	ADJ
cana-5358	55	2	bivalent	bivalent	ADJ
cana-5358	55	3	sets	set	NOUN
cana-5358	55	4	are	be	AUX
cana-5358	55	5	in	in	ADP
cana-5358	55	6	fuzzy	fuzzy	ADJ
cana-5358	55	7	set	set	NOUN
cana-5358	55	8	theory	theory	NOUN
cana-5358	55	9	called	call	VERB
cana-5358	55	10	crisp	crisp	ADJ
cana-5358	55	11	sets	set	NOUN
cana-5358	55	12	.	.	PUNCT
cana-5358	56	1	fuzzy	fuzzy	ADJ
cana-5358	56	2	sets	set	NOUN
cana-5358	56	3	are	be	AUX
cana-5358	56	4	generalized	generalized	ADJ
cana-5358	56	5	classical	classical	ADJ
cana-5358	56	6	sets	set	NOUN
cana-5358	56	7	,	,	PUNCT
cana-5358	56	8	since	since	SCONJ
cana-5358	56	9	the	the	DET
cana-5358	56	10	indicator	indicator	NOUN
cana-5358	56	11	function	function	NOUN
cana-5358	56	12	of	of	ADP
cana-5358	56	13	classical	classical	ADJ
cana-5358	56	14	sets	set	NOUN
cana-5358	56	15	is	be	AUX
cana-5358	56	16	special	special	ADJ
cana-5358	56	17	cases	case	NOUN
cana-5358	56	18	of	of	ADP
cana-5358	56	19	the	the	DET
cana-5358	56	20	membership	membership	NOUN
cana-5358	56	21	functions	function	NOUN
cana-5358	56	22	of	of	ADP
cana-5358	56	23	fuzzy	fuzzy	ADJ
cana-5358	56	24	sets	set	NOUN
cana-5358	56	25	,	,	PUNCT
cana-5358	56	26	if	if	SCONJ
cana-5358	56	27	the	the	DET
cana-5358	56	28	latter	latter	ADJ
cana-5358	56	29	only	only	ADV
cana-5358	56	30	take	take	VERB
cana-5358	56	31	values	value	NOUN
cana-5358	56	32	0	0	NUM
cana-5358	56	33	or	or	CCONJ
cana-5358	56	34	1	1	NUM
cana-5358	56	35	.	.	X
cana-5358	56	36	fuzzy	fuzzy	ADJ
cana-5358	56	37	sets	set	NOUN
cana-5358	56	38	theory	theory	NOUN
cana-5358	56	39	permits	permit	VERB
cana-5358	56	40	the	the	DET
cana-5358	56	41	gradual	gradual	ADJ
cana-5358	56	42	assessment	assessment	NOUN
cana-5358	56	43	of	of	ADP
cana-5358	56	44	the	the	DET
cana-5358	56	45	membership	membership	NOUN
cana-5358	56	46	of	of	ADP
cana-5358	56	47	element	element	NOUN
cana-5358	56	48	in	in	ADP
cana-5358	56	49	a	a	DET
cana-5358	56	50	set	set	NOUN
cana-5358	56	51	;	;	PUNCT
cana-5358	56	52	this	this	PRON
cana-5358	56	53	is	be	AUX
cana-5358	56	54	described	describe	VERB
cana-5358	56	55	with	with	ADP
cana-5358	56	56	the	the	DET
cana-5358	56	57	aid	aid	NOUN
cana-5358	56	58	of	of	ADP
cana-5358	56	59	a	a	DET
cana-5358	56	60	membership	membership	NOUN
cana-5358	56	61	function	function	NOUN
cana-5358	56	62	valued	value	VERB
cana-5358	56	63	in	in	ADP
cana-5358	56	64	the	the	DET
cana-5358	56	65	real	real	ADJ
cana-5358	56	66	unit	unit	NOUN
cana-5358	56	67	interval	interval	NOUN
cana-5358	56	68	[	[	X
cana-5358	56	69	0,1	0,1	NUM
cana-5358	56	70	]	]	PUNCT
cana-5358	56	71	.	.	PUNCT
cana-5358	57	1	let	let	VERB
cana-5358	57	2	us	we	PRON
cana-5358	57	3	consider	consider	VERB
cana-5358	57	4	two	two	NUM
cana-5358	57	5	examples	example	NOUN
cana-5358	57	6	:	:	PUNCT
cana-5358	57	7	(	(	PUNCT
cana-5358	57	8	i	i	NOUN
cana-5358	57	9	)	)	PUNCT
cana-5358	57	10	all	all	DET
cana-5358	57	11	employees	employee	NOUN
cana-5358	57	12	of	of	ADP
cana-5358	57	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-5358	57	14	who	who	PRON
cana-5358	57	15	are	be	AUX
cana-5358	57	16	over	over	ADP
cana-5358	57	17	1.8𝑚	1.8𝑚	NUM
cana-5358	57	18	in	in	ADP
cana-5358	57	19	height	height	NOUN
cana-5358	57	20	;	;	PUNCT
cana-5358	57	21	(	(	PUNCT
cana-5358	57	22	ii	ii	NOUN
cana-5358	57	23	)	)	PUNCT
cana-5358	57	24	all	all	DET
cana-5358	57	25	employees	employee	NOUN
cana-5358	57	26	of	of	ADP
cana-5358	57	27	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-5358	57	28	who	who	PRON
cana-5358	57	29	are	be	AUX
cana-5358	57	30	tall	tall	ADJ
cana-5358	57	31	.	.	PUNCT
cana-5358	58	1	the	the	DET
cana-5358	58	2	first	first	ADJ
cana-5358	58	3	example	example	NOUN
cana-5358	58	4	is	be	AUX
cana-5358	58	5	a	a	DET
cana-5358	58	6	classical	classical	ADJ
cana-5358	58	7	set	set	NOUN
cana-5358	58	8	with	with	ADP
cana-5358	58	9	a	a	DET
cana-5358	58	10	universe	universe	NOUN
cana-5358	58	11	(	(	PUNCT
cana-5358	58	12	all	all	DET
cana-5358	58	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-5358	58	14	employees	employee	NOUN
cana-5358	58	15	)	)	PUNCT
cana-5358	58	16	and	and	CCONJ
cana-5358	58	17	a	a	DET
cana-5358	58	18	membership	membership	NOUN
cana-5358	58	19	rule	rule	NOUN
cana-5358	58	20	that	that	PRON
cana-5358	58	21	divides	divide	VERB
cana-5358	58	22	the	the	DET
cana-5358	58	23	universe	universe	NOUN
cana-5358	58	24	into	into	ADP
cana-5358	58	25	members	member	NOUN
cana-5358	58	26	(	(	PUNCT
cana-5358	58	27	those	those	PRON
cana-5358	58	28	over	over	ADP
cana-5358	58	29	1.8𝑚	1.8𝑚	NUM
cana-5358	58	30	)	)	PUNCT
cana-5358	58	31	and	and	CCONJ
cana-5358	58	32	nonmembers	nonmember	NOUN
cana-5358	58	33	.	.	PUNCT
cana-5358	59	1	the	the	DET
cana-5358	59	2	second	second	ADJ
cana-5358	59	3	example	example	NOUN
cana-5358	59	4	is	be	AUX
cana-5358	59	5	a	a	DET
cana-5358	59	6	fuzzy	fuzzy	ADJ
cana-5358	59	7	set	set	NOUN
cana-5358	59	8	,	,	PUNCT
cana-5358	59	9	communications	communication	NOUN
cana-5358	59	10	on	on	ADP
cana-5358	59	11	applied	apply	VERB
cana-5358	59	12	nonlinear	nonlinear	ADJ
cana-5358	59	13	analysis	analysis	NOUN
cana-5358	59	14	issn	issn	NOUN
cana-5358	59	15	:	:	PUNCT
cana-5358	59	16	1074	1074	NUM
cana-5358	59	17	-	-	PUNCT
cana-5358	59	18	133x	133x	NUM
cana-5358	59	19	vol	vol	VERB
cana-5358	59	20	32	32	NUM
cana-5358	59	21	no	no	NOUN
cana-5358	59	22	.	.	PUNCT
cana-5358	60	1	10s	10	NOUN
cana-5358	60	2	(	(	PUNCT
cana-5358	60	3	2025	2025	NUM
cana-5358	60	4	)	)	PUNCT
cana-5358	60	5	1897	1897	NUM
cana-5358	60	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	60	7	because	because	SCONJ
cana-5358	60	8	some	some	DET
cana-5358	60	9	employees	employee	NOUN
cana-5358	60	10	are	be	AUX
cana-5358	60	11	definitely	definitely	ADV
cana-5358	60	12	in	in	ADP
cana-5358	60	13	the	the	DET
cana-5358	60	14	set	set	NOUN
cana-5358	60	15	and	and	CCONJ
cana-5358	60	16	some	some	PRON
cana-5358	60	17	are	be	AUX
cana-5358	60	18	definitely	definitely	ADV
cana-5358	60	19	not	not	PART
cana-5358	60	20	in	in	ADP
cana-5358	60	21	the	the	DET
cana-5358	60	22	set	set	NOUN
cana-5358	60	23	,	,	PUNCT
cana-5358	60	24	but	but	CCONJ
cana-5358	60	25	some	some	PRON
cana-5358	60	26	are	be	AUX
cana-5358	60	27	borderline	borderline	NOUN
cana-5358	60	28	.	.	PUNCT
cana-5358	61	1	this	this	DET
cana-5358	61	2	distinction	distinction	NOUN
cana-5358	61	3	between	between	ADP
cana-5358	61	4	the	the	DET
cana-5358	61	5	ins	in	NOUN
cana-5358	61	6	,	,	PUNCT
cana-5358	61	7	the	the	DET
cana-5358	61	8	outs	out	NOUN
cana-5358	61	9	,	,	PUNCT
cana-5358	61	10	and	and	CCONJ
cana-5358	61	11	the	the	DET
cana-5358	61	12	borderline	borderline	NOUN
cana-5358	61	13	is	be	AUX
cana-5358	61	14	made	make	VERB
cana-5358	61	15	more	more	ADV
cana-5358	61	16	exact	exact	ADJ
cana-5358	61	17	by	by	ADP
cana-5358	61	18	the	the	DET
cana-5358	61	19	membership	membership	NOUN
cana-5358	61	20	function	function	NOUN
cana-5358	61	21	,	,	PUNCT
cana-5358	61	22	𝜇.	𝜇.	ADV
cana-5358	61	23	if	if	SCONJ
cana-5358	61	24	we	we	PRON
cana-5358	61	25	return	return	VERB
cana-5358	61	26	to	to	ADP
cana-5358	61	27	our	our	PRON
cana-5358	61	28	second	second	ADJ
cana-5358	61	29	example	example	NOUN
cana-5358	61	30	and	and	CCONJ
cana-5358	61	31	let	let	VERB
cana-5358	61	32	𝐴	𝐴	PROPN
cana-5358	61	33	represent	represent	VERB
cana-5358	61	34	the	the	DET
cana-5358	61	35	fuzzy	fuzzy	ADJ
cana-5358	61	36	set	set	NOUN
cana-5358	61	37	of	of	ADP
cana-5358	61	38	all	all	DET
cana-5358	61	39	tall	tall	ADJ
cana-5358	61	40	employees	employee	NOUN
cana-5358	61	41	and	and	CCONJ
cana-5358	61	42	𝑥	𝑥	PROPN
cana-5358	61	43	represent	represent	VERB
cana-5358	61	44	a	a	DET
cana-5358	61	45	member	member	NOUN
cana-5358	61	46	of	of	ADP
cana-5358	61	47	the	the	DET
cana-5358	61	48	universe	universe	ADJ
cana-5358	61	49	𝑋	𝑋	NOUN
cana-5358	61	50	(	(	PUNCT
cana-5358	61	51	i.e.	i.e.	X
cana-5358	61	52	all	all	DET
cana-5358	61	53	employees	employee	NOUN
cana-5358	61	54	)	)	PUNCT
cana-5358	61	55	,	,	PUNCT
cana-5358	61	56	then	then	ADV
cana-5358	61	57	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	61	58	)	)	PUNCT
cana-5358	61	59	would	would	AUX
cana-5358	61	60	be	be	AUX
cana-5358	61	61	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	61	62	)	)	PUNCT
cana-5358	61	63	=	=	SYM
cana-5358	61	64	1	1	NUM
cana-5358	61	65	if	if	SCONJ
cana-5358	61	66	𝑥	𝑥	PRON
cana-5358	61	67	is	be	AUX
cana-5358	61	68	definitely	definitely	ADV
cana-5358	61	69	tall	tall	ADJ
cana-5358	61	70	or	or	CCONJ
cana-5358	61	71	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	61	72	)	)	PUNCT
cana-5358	61	73	=	=	SYM
cana-5358	61	74	0	0	PUNCT
cana-5358	62	1	if	if	SCONJ
cana-5358	62	2	𝑥	𝑥	PRON
cana-5358	62	3	is	be	AUX
cana-5358	62	4	definitely	definitely	ADV
cana-5358	62	5	not	not	PART
cana-5358	62	6	tall	tall	ADJ
cana-5358	62	7	or	or	CCONJ
cana-5358	62	8	0	0	NUM
cana-5358	62	9	<	<	X
cana-5358	62	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-5358	62	11	)	)	PUNCT
cana-5358	62	12	<	<	X
cana-5358	62	13	1	1	NUM
cana-5358	62	14	for	for	ADP
cana-5358	62	15	borderline	borderline	NOUN
cana-5358	62	16	cases	case	NOUN
cana-5358	62	17	.	.	PUNCT
cana-5358	63	1	definition	definition	NOUN
cana-5358	63	2	2.2	2.2	NUM
cana-5358	63	3	[	[	X
cana-5358	63	4	1	1	NUM
cana-5358	63	5	]	]	PUNCT
cana-5358	63	6	the	the	DET
cana-5358	63	7	intuitionistic	intuitionistic	ADJ
cana-5358	63	8	fuzzy	fuzzy	ADJ
cana-5358	63	9	sets	set	NOUN
cana-5358	63	10	are	be	AUX
cana-5358	63	11	defined	define	VERB
cana-5358	63	12	on	on	ADP
cana-5358	63	13	a	a	DET
cana-5358	63	14	non	non	ADJ
cana-5358	63	15	-	-	ADJ
cana-5358	63	16	empty	empty	ADJ
cana-5358	63	17	sets	set	NOUN
cana-5358	63	18	𝑋	𝑋	NOUN
cana-5358	63	19	as	as	ADP
cana-5358	63	20	objects	object	NOUN
cana-5358	63	21	having	have	VERB
cana-5358	63	22	the	the	DET
cana-5358	63	23	form	form	NOUN
cana-5358	63	24	𝐼	𝐼	ADV
cana-5358	63	25	=	=	PUNCT
cana-5358	63	26	{	{	PUNCT
cana-5358	63	27	〈	〈	X
cana-5358	63	28	𝑥	𝑥	PROPN
cana-5358	63	29	,	,	PUNCT
cana-5358	63	30	𝛼𝐼(𝑥	𝛼𝐼(𝑥	PROPN
cana-5358	63	31	)	)	PUNCT
cana-5358	63	32	,	,	PUNCT
cana-5358	63	33	𝛽𝐼(𝑥	𝛽𝐼(𝑥	PROPN
cana-5358	63	34	)	)	PUNCT
cana-5358	63	35	〉	〉	NOUN
cana-5358	63	36	:	:	PUNCT
cana-5358	63	37	𝑥	𝑥	PROPN
cana-5358	63	38	∈	∈	PROPN
cana-5358	63	39	𝑋	𝑋	PROPN
cana-5358	63	40	}	}	PUNCT
cana-5358	63	41	,	,	PUNCT
cana-5358	63	42	where	where	SCONJ
cana-5358	63	43	𝛼𝐼(𝑥	𝛼𝐼(𝑥	ADP
cana-5358	63	44	):	):	PUNCT
cana-5358	63	45	𝑋	𝑋	PROPN
cana-5358	63	46	→	→	SYM
cana-5358	64	1	[	[	X
cana-5358	64	2	0,1	0,1	NUM
cana-5358	64	3	]	]	PUNCT
cana-5358	64	4	and	and	CCONJ
cana-5358	64	5	𝛽𝐼(𝑥	𝛽𝐼(𝑥	PROPN
cana-5358	64	6	):	):	PUNCT
cana-5358	64	7	𝑋	𝑋	PROPN
cana-5358	64	8	→	→	SYM
cana-5358	64	9	[	[	X
cana-5358	64	10	0,1	0,1	NUM
cana-5358	64	11	]	]	PUNCT
cana-5358	64	12	denote	denote	VERB
cana-5358	64	13	the	the	DET
cana-5358	64	14	degree	degree	NOUN
cana-5358	64	15	of	of	ADP
cana-5358	64	16	memebership	memebership	NOUN
cana-5358	64	17	and	and	CCONJ
cana-5358	64	18	the	the	DET
cana-5358	64	19	degree	degree	NOUN
cana-5358	64	20	of	of	ADP
cana-5358	64	21	non	non	NOUN
cana-5358	64	22	-	-	NOUN
cana-5358	64	23	memebership	memebership	NOUN
cana-5358	64	24	of	of	ADP
cana-5358	64	25	each	each	DET
cana-5358	64	26	element	element	NOUN
cana-5358	64	27	𝑥	𝑥	PRON
cana-5358	64	28	∈	∈	PROPN
cana-5358	64	29	𝑋	𝑋	NOUN
cana-5358	64	30	to	to	ADP
cana-5358	64	31	the	the	DET
cana-5358	64	32	set	set	ADJ
cana-5358	64	33	𝐼	𝐼	PROPN
cana-5358	64	34	,	,	PUNCT
cana-5358	64	35	respectively	respectively	ADV
cana-5358	64	36	,	,	PUNCT
cana-5358	64	37	and	and	CCONJ
cana-5358	64	38	0	0	NUM
cana-5358	64	39	≤	≤	NUM
cana-5358	65	1	𝛼𝐼(𝑥	𝛼𝐼(𝑥	ADP
cana-5358	65	2	)	)	PUNCT
cana-5358	65	3	+	+	CCONJ
cana-5358	65	4	𝛽𝐼(𝑥	𝛽𝐼(𝑥	PROPN
cana-5358	65	5	)	)	PUNCT
cana-5358	65	6	≤	≤	NOUN
cana-5358	65	7	1	1	NUM
cana-5358	65	8	,	,	PUNCT
cana-5358	65	9	for	for	ADP
cana-5358	65	10	all	all	DET
cana-5358	65	11	𝑥	𝑥	DET
cana-5358	65	12	∈	∈	PROPN
cana-5358	65	13	𝑋.	𝑋.	PROPN
cana-5358	65	14	definition	definition	NOUN
cana-5358	65	15	2.3	2.3	NUM
cana-5358	65	16	[	[	X
cana-5358	65	17	1	1	NUM
cana-5358	65	18	,	,	PUNCT
cana-5358	65	19	2	2	NUM
cana-5358	65	20	,	,	PUNCT
cana-5358	65	21	3	3	NUM
cana-5358	65	22	,	,	PUNCT
cana-5358	65	23	4	4	NUM
cana-5358	65	24	]	]	PUNCT
cana-5358	65	25	let	let	VERB
cana-5358	65	26	a	a	DET
cana-5358	65	27	nonempty	nonempty	ADV
cana-5358	65	28	set	set	VERB
cana-5358	65	29	𝑋	𝑋	NOUN
cana-5358	65	30	be	be	AUX
cana-5358	65	31	fixed	fix	VERB
cana-5358	65	32	.	.	PUNCT
cana-5358	66	1	an	an	DET
cana-5358	66	2	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-5358	66	3	𝐴	𝐴	PROPN
cana-5358	66	4	in	in	ADP
cana-5358	66	5	𝑋	𝑋	PROPN
cana-5358	66	6	is	be	AUX
cana-5358	66	7	an	an	DET
cana-5358	66	8	object	object	NOUN
cana-5358	66	9	having	have	VERB
cana-5358	66	10	the	the	DET
cana-5358	66	11	form	form	NOUN
cana-5358	66	12	:	:	PUNCT
cana-5358	66	13	𝐴	𝐴	PROPN
cana-5358	66	14	=	=	PUNCT
cana-5358	66	15	{	{	PUNCT
cana-5358	66	16	<	<	X
cana-5358	66	17	𝑥	𝑥	X
cana-5358	66	18	,	,	PUNCT
cana-5358	66	19	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	66	20	)	)	PUNCT
cana-5358	66	21	,	,	PUNCT
cana-5358	66	22	𝜆𝐴(𝑥	𝜆𝐴(𝑥	PROPN
cana-5358	66	23	)	)	PUNCT
cana-5358	66	24	>	>	PUNCT
cana-5358	67	1	|𝑥	|𝑥	PROPN
cana-5358	67	2	∈	∈	PROPN
cana-5358	67	3	𝑋	𝑋	PROPN
cana-5358	67	4	}	}	PUNCT
cana-5358	67	5	or	or	CCONJ
cana-5358	67	6	𝐴	𝐴	PROPN
cana-5358	67	7	=	=	PUNCT
cana-5358	67	8	{	{	PUNCT
cana-5358	67	9	⟨	⟨	NOUN
cana-5358	67	10	𝜇𝐴(𝑥),𝜆𝐴(𝑥	𝜇𝐴(𝑥),𝜆𝐴(𝑥	PUNCT
cana-5358	67	11	)	)	PUNCT
cana-5358	67	12	𝑥	𝑥	PRON
cana-5358	67	13	⟩	⟩	NOUN
cana-5358	67	14	|𝑥	|𝑥	NOUN
cana-5358	67	15	∈	∈	PROPN
cana-5358	67	16	𝑋	𝑋	PROPN
cana-5358	67	17	}	}	PUNCT
cana-5358	67	18	,	,	PUNCT
cana-5358	67	19	where	where	SCONJ
cana-5358	67	20	the	the	DET
cana-5358	67	21	functions	function	NOUN
cana-5358	67	22	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-5358	67	23	):	):	PUNCT
cana-5358	67	24	𝑋	𝑋	PROPN
cana-5358	67	25	→	→	SYM
cana-5358	67	26	[	[	X
cana-5358	67	27	0,1	0,1	NUM
cana-5358	67	28	]	]	PUNCT
cana-5358	67	29	and	and	CCONJ
cana-5358	67	30	𝜆𝐴(𝑥	𝜆𝐴(𝑥	NUM
cana-5358	67	31	):	):	PUNCT
cana-5358	67	32	𝑋	𝑋	PROPN
cana-5358	67	33	→	→	SYM
cana-5358	67	34	[	[	X
cana-5358	67	35	0,1	0,1	NUM
cana-5358	67	36	]	]	PUNCT
cana-5358	67	37	define	define	VERB
cana-5358	67	38	the	the	DET
cana-5358	67	39	degree	degree	NOUN
cana-5358	67	40	of	of	ADP
cana-5358	67	41	membership	membership	NOUN
cana-5358	67	42	and	and	CCONJ
cana-5358	67	43	the	the	DET
cana-5358	67	44	degree	degree	NOUN
cana-5358	67	45	of	of	ADP
cana-5358	67	46	nonmembership	nonmembership	NOUN
cana-5358	67	47	,	,	PUNCT
cana-5358	67	48	respectively	respectively	ADV
cana-5358	67	49	,	,	PUNCT
cana-5358	67	50	of	of	ADP
cana-5358	67	51	the	the	DET
cana-5358	67	52	element	element	NOUN
cana-5358	67	53	𝑥	𝑥	PRON
cana-5358	67	54	∈	∈	PROPN
cana-5358	67	55	𝑋	𝑋	NOUN
cana-5358	67	56	to	to	ADP
cana-5358	67	57	𝐴	𝐴	PROPN
cana-5358	67	58	,	,	PUNCT
cana-5358	67	59	which	which	PRON
cana-5358	67	60	is	be	AUX
cana-5358	67	61	a	a	DET
cana-5358	67	62	subset	subset	NOUN
cana-5358	67	63	of	of	ADP
cana-5358	67	64	𝑋	𝑋	PROPN
cana-5358	67	65	,	,	PUNCT
cana-5358	67	66	and	and	CCONJ
cana-5358	67	67	for	for	ADP
cana-5358	67	68	every	every	DET
cana-5358	67	69	𝑥	𝑥	PRON
cana-5358	67	70	∈	∈	PROPN
cana-5358	67	71	𝑋	𝑋	NOUN
cana-5358	67	72	:	:	PUNCT
cana-5358	67	73	0	0	NUM
cana-5358	67	74	≤	≤	NUM
cana-5358	67	75	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	67	76	)	)	PUNCT
cana-5358	68	1	+	+	NUM
cana-5358	68	2	𝜆𝐴(𝑥	𝜆𝐴(𝑥	X
cana-5358	68	3	)	)	PUNCT
cana-5358	68	4	≤	≤	NUM
cana-5358	68	5	1	1	NUM
cana-5358	68	6	.	.	PUNCT
cana-5358	69	1	for	for	ADP
cana-5358	69	2	each	each	DET
cana-5358	69	3	𝐴	𝐴	PROPN
cana-5358	69	4	in	in	ADP
cana-5358	69	5	𝑋	𝑋	PROPN
cana-5358	69	6	:	:	PUNCT
cana-5358	69	7	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5358	69	8	)	)	PUNCT
cana-5358	69	9	=	=	SYM
cana-5358	69	10	1	1	NUM
cana-5358	69	11	−	−	NUM
cana-5358	69	12	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	69	13	)	)	PUNCT
cana-5358	69	14	−	−	PUNCT
cana-5358	69	15	𝜆𝐴(𝑥	𝜆𝐴(𝑥	NOUN
cana-5358	69	16	)	)	PUNCT
cana-5358	69	17	is	be	AUX
cana-5358	69	18	the	the	DET
cana-5358	69	19	intuitionistic	intuitionistic	ADJ
cana-5358	69	20	fuzzy	fuzzy	ADJ
cana-5358	69	21	set	set	VERB
cana-5358	69	22	index	index	NOUN
cana-5358	69	23	or	or	CCONJ
cana-5358	69	24	hesitation	hesitation	NOUN
cana-5358	69	25	margin	margin	NOUN
cana-5358	69	26	of	of	ADP
cana-5358	69	27	𝑥	𝑥	NOUN
cana-5358	69	28	in	in	ADP
cana-5358	69	29	𝑋.	𝑋.	PROPN
cana-5358	69	30	the	the	DET
cana-5358	69	31	hesitation	hesitation	NOUN
cana-5358	69	32	margin	margin	NOUN
cana-5358	69	33	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5358	69	34	)	)	PUNCT
cana-5358	69	35	is	be	AUX
cana-5358	69	36	the	the	DET
cana-5358	69	37	degree	degree	NOUN
cana-5358	69	38	of	of	ADP
cana-5358	69	39	nondeterminacy	nondeterminacy	NOUN
cana-5358	69	40	of	of	ADP
cana-5358	69	41	𝑥	𝑥	DET
cana-5358	69	42	∈	∈	PROPN
cana-5358	69	43	𝑋	𝑋	NOUN
cana-5358	69	44	to	to	ADP
cana-5358	69	45	the	the	DET
cana-5358	69	46	set	set	ADJ
cana-5358	69	47	𝐴	𝐴	PROPN
cana-5358	69	48	and	and	CCONJ
cana-5358	69	49	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5358	69	50	)	)	PUNCT
cana-5358	69	51	∈	∈	NOUN
cana-5358	70	1	[	[	X
cana-5358	70	2	0,1	0,1	NUM
cana-5358	70	3	]	]	PUNCT
cana-5358	70	4	.	.	PUNCT
cana-5358	71	1	the	the	DET
cana-5358	71	2	hesitation	hesitation	NOUN
cana-5358	71	3	margin	margin	NOUN
cana-5358	71	4	is	be	AUX
cana-5358	71	5	the	the	DET
cana-5358	71	6	function	function	NOUN
cana-5358	71	7	that	that	PRON
cana-5358	71	8	expresses	express	VERB
cana-5358	71	9	lack	lack	NOUN
cana-5358	71	10	of	of	ADP
cana-5358	71	11	knowledge	knowledge	NOUN
cana-5358	71	12	of	of	ADP
cana-5358	71	13	whether	whether	SCONJ
cana-5358	71	14	𝑥	𝑥	PRON
cana-5358	71	15	∈	∈	PROPN
cana-5358	71	16	𝑋	𝑋	NOUN
cana-5358	71	17	or	or	CCONJ
cana-5358	71	18	𝑥	𝑥	PROPN
cana-5358	71	19	∉	∉	PROPN
cana-5358	71	20	𝑋.	𝑋.	PROPN
cana-5358	71	21	thus	thus	ADV
cana-5358	71	22	:	:	PUNCT
cana-5358	71	23	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	71	24	)	)	PUNCT
cana-5358	71	25	+	+	CCONJ
cana-5358	71	26	𝜆𝐴(𝑥	𝜆𝐴(𝑥	X
cana-5358	71	27	)	)	PUNCT
cana-5358	71	28	+	+	NUM
cana-5358	71	29	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5358	71	30	)	)	PUNCT
cana-5358	71	31	=	=	SYM
cana-5358	71	32	1	1	X
cana-5358	71	33	.	.	PUNCT
cana-5358	71	34	example	example	NOUN
cana-5358	71	35	2.1	2.1	NUM
cana-5358	71	36	let	let	VERB
cana-5358	71	37	𝑋	𝑋	NOUN
cana-5358	71	38	=	=	SYM
cana-5358	71	39	{	{	PUNCT
cana-5358	71	40	𝑥	𝑥	PROPN
cana-5358	71	41	,	,	PUNCT
cana-5358	71	42	𝑦	𝑦	NOUN
cana-5358	71	43	,	,	PUNCT
cana-5358	71	44	𝑧	𝑧	PRON
cana-5358	71	45	}	}	PUNCT
cana-5358	71	46	be	be	AUX
cana-5358	71	47	a	a	DET
cana-5358	71	48	fixed	fix	VERB
cana-5358	71	49	universe	universe	NOUN
cana-5358	71	50	of	of	ADP
cana-5358	71	51	discourse	discourse	NOUN
cana-5358	71	52	and	and	CCONJ
cana-5358	71	53	𝐴	𝐴	PROPN
cana-5358	71	54	=	=	PUNCT
cana-5358	71	55	{	{	PUNCT
cana-5358	71	56	⟨	⟨	VERB
cana-5358	71	57	0.6,0.1	0.6,0.1	PROPN
cana-5358	71	58	𝑥	𝑥	DET
cana-5358	71	59	⟩	⟩	NOUN
cana-5358	71	60	,	,	PUNCT
cana-5358	71	61	⟨	⟨	VERB
cana-5358	71	62	0.8,0.1	0.8,0.1	PROPN
cana-5358	71	63	𝑦	𝑦	NOUN
cana-5358	71	64	⟩	⟩	NOUN
cana-5358	71	65	,	,	PUNCT
cana-5358	71	66	⟨	⟨	VERB
cana-5358	71	67	0.5,0.3	0.5,0.3	PROPN
cana-5358	71	68	𝑧	𝑧	DET
cana-5358	71	69	⟩	⟩	NOUN
cana-5358	71	70	}	}	PUNCT
cana-5358	71	71	,	,	PUNCT
cana-5358	71	72	be	be	AUX
cana-5358	71	73	the	the	DET
cana-5358	71	74	intuitionistic	intuitionistic	ADJ
cana-5358	71	75	fuzzy	fuzzy	ADJ
cana-5358	71	76	set	set	NOUN
cana-5358	71	77	in	in	ADP
cana-5358	71	78	𝑋.	𝑋.	PROPN
cana-5358	71	79	the	the	DET
cana-5358	71	80	hesitation	hesitation	NOUN
cana-5358	71	81	margins	margin	NOUN
cana-5358	71	82	of	of	ADP
cana-5358	71	83	the	the	DET
cana-5358	71	84	elements	element	NOUN
cana-5358	71	85	𝑥	𝑥	PROPN
cana-5358	71	86	,	,	PUNCT
cana-5358	71	87	𝑦	𝑦	NOUN
cana-5358	71	88	,	,	PUNCT
cana-5358	71	89	𝑧	𝑧	PUNCT
cana-5358	71	90	to	to	ADP
cana-5358	71	91	𝐴	𝐴	PROPN
cana-5358	71	92	are	be	AUX
cana-5358	71	93	as	as	SCONJ
cana-5358	71	94	follows	follow	VERB
cana-5358	71	95	:	:	PUNCT
cana-5358	71	96	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5358	71	97	)	)	PUNCT
cana-5358	71	98	=	=	SYM
cana-5358	71	99	0.3	0.3	NUM
cana-5358	71	100	,	,	PUNCT
cana-5358	71	101	𝜋𝐴(𝑦	𝜋𝐴(𝑦	PROPN
cana-5358	71	102	)	)	PUNCT
cana-5358	71	103	=	=	SYM
cana-5358	71	104	0.1	0.1	NUM
cana-5358	71	105	and	and	CCONJ
cana-5358	71	106	𝜋𝐴(𝑧	𝜋𝐴(𝑧	NUM
cana-5358	71	107	)	)	PUNCT
cana-5358	71	108	=	=	PUNCT
cana-5358	72	1	0.2	0.2	NUM
cana-5358	72	2	.	.	PUNCT
cana-5358	73	1	definition	definition	NOUN
cana-5358	73	2	2.4	2.4	NUM
cana-5358	73	3	[	[	SYM
cana-5358	73	4	12	12	NUM
cana-5358	73	5	,	,	PUNCT
cana-5358	73	6	13	13	NUM
cana-5358	73	7	,	,	PUNCT
cana-5358	73	8	14	14	NUM
cana-5358	73	9	]	]	PUNCT
cana-5358	73	10	let	let	VERB
cana-5358	73	11	𝑋	𝑋	NOUN
cana-5358	73	12	be	be	AUX
cana-5358	73	13	a	a	DET
cana-5358	73	14	universal	universal	ADJ
cana-5358	73	15	set	set	NOUN
cana-5358	73	16	.	.	PUNCT
cana-5358	74	1	then	then	ADV
cana-5358	74	2	,	,	PUNCT
cana-5358	74	3	a	a	DET
cana-5358	74	4	pythagorean	pythagorean	PROPN
cana-5358	74	5	fuzzy	fuzzy	ADJ
cana-5358	74	6	set	set	PROPN
cana-5358	74	7	𝐴	𝐴	PROPN
cana-5358	74	8	,	,	PUNCT
cana-5358	74	9	which	which	PRON
cana-5358	74	10	is	be	AUX
cana-5358	74	11	a	a	DET
cana-5358	74	12	set	set	NOUN
cana-5358	74	13	of	of	ADP
cana-5358	74	14	ordered	order	VERB
cana-5358	74	15	pairs	pair	NOUN
cana-5358	74	16	over	over	ADP
cana-5358	74	17	𝑋	𝑋	PROPN
cana-5358	74	18	,	,	PUNCT
cana-5358	74	19	is	be	AUX
cana-5358	74	20	defined	define	VERB
cana-5358	74	21	by	by	ADP
cana-5358	74	22	the	the	DET
cana-5358	74	23	following	following	NOUN
cana-5358	74	24	:	:	PUNCT
cana-5358	74	25	𝐴	𝐴	PROPN
cana-5358	74	26	=	=	PUNCT
cana-5358	74	27	{	{	PUNCT
cana-5358	74	28	<	<	X
cana-5358	74	29	𝑥	𝑥	X
cana-5358	74	30	,	,	PUNCT
cana-5358	74	31	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	74	32	)	)	PUNCT
cana-5358	74	33	,	,	PUNCT
cana-5358	74	34	𝜆𝐴(𝑥)|𝑥	𝜆𝐴(𝑥)|𝑥	NOUN
cana-5358	74	35	∈	∈	PROPN
cana-5358	74	36	𝑋	𝑋	PROPN
cana-5358	74	37	}	}	PUNCT
cana-5358	74	38	or	or	CCONJ
cana-5358	74	39	𝐴	𝐴	PROPN
cana-5358	74	40	=	=	PUNCT
cana-5358	74	41	{	{	PUNCT
cana-5358	74	42	⟨	⟨	NOUN
cana-5358	74	43	𝜇𝐴(𝑥),𝜆𝐴(𝑥	𝜇𝐴(𝑥),𝜆𝐴(𝑥	PUNCT
cana-5358	74	44	)	)	PUNCT
cana-5358	74	45	𝑥	𝑥	PRON
cana-5358	74	46	⟩	⟩	NOUN
cana-5358	74	47	|𝑥	|𝑥	NOUN
cana-5358	74	48	∈	∈	PROPN
cana-5358	74	49	𝑋	𝑋	PROPN
cana-5358	74	50	}	}	PUNCT
cana-5358	74	51	,	,	PUNCT
cana-5358	74	52	where	where	SCONJ
cana-5358	74	53	the	the	DET
cana-5358	74	54	functions	function	NOUN
cana-5358	74	55	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-5358	74	56	):	):	PUNCT
cana-5358	74	57	𝑋	𝑋	PROPN
cana-5358	74	58	→	→	SYM
cana-5358	74	59	[	[	X
cana-5358	74	60	0,1	0,1	NUM
cana-5358	74	61	]	]	PUNCT
cana-5358	74	62	and	and	CCONJ
cana-5358	74	63	𝜆𝐴(𝑥	𝜆𝐴(𝑥	NUM
cana-5358	74	64	):	):	PUNCT
cana-5358	74	65	𝑋	𝑋	PROPN
cana-5358	74	66	→	→	SYM
cana-5358	74	67	[	[	X
cana-5358	74	68	0,1	0,1	NUM
cana-5358	74	69	]	]	PUNCT
cana-5358	74	70	define	define	VERB
cana-5358	74	71	the	the	DET
cana-5358	74	72	degree	degree	NOUN
cana-5358	74	73	of	of	ADP
cana-5358	74	74	membership	membership	NOUN
cana-5358	74	75	and	and	CCONJ
cana-5358	74	76	the	the	DET
cana-5358	74	77	degree	degree	NOUN
cana-5358	74	78	of	of	ADP
cana-5358	74	79	nonmembership	nonmembership	NOUN
cana-5358	74	80	,	,	PUNCT
cana-5358	74	81	respectively	respectively	ADV
cana-5358	74	82	,	,	PUNCT
cana-5358	74	83	of	of	ADP
cana-5358	74	84	the	the	DET
cana-5358	74	85	element	element	NOUN
cana-5358	74	86	𝑥	𝑥	PRON
cana-5358	74	87	∈	∈	PROPN
cana-5358	74	88	𝑋	𝑋	NOUN
cana-5358	74	89	to	to	ADP
cana-5358	74	90	𝐴	𝐴	PROPN
cana-5358	74	91	,	,	PUNCT
cana-5358	74	92	which	which	PRON
cana-5358	74	93	is	be	AUX
cana-5358	74	94	a	a	DET
cana-5358	74	95	subset	subset	NOUN
cana-5358	74	96	of	of	ADP
cana-5358	74	97	𝑋	𝑋	PROPN
cana-5358	74	98	,	,	PUNCT
cana-5358	74	99	and	and	CCONJ
cana-5358	74	100	for	for	ADP
cana-5358	74	101	every	every	DET
cana-5358	74	102	𝑥	𝑥	DET
cana-5358	74	103	∈	∈	PROPN
cana-5358	74	104	𝑋	𝑋	NOUN
cana-5358	74	105	,	,	PUNCT
cana-5358	74	106	0	0	NUM
cana-5358	74	107	≤	≤	NOUN
cana-5358	74	108	(	(	PUNCT
cana-5358	74	109	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5358	74	110	+	+	CCONJ
cana-5358	74	111	(	(	PUNCT
cana-5358	74	112	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5358	74	113	≤	≤	NUM
cana-5358	74	114	1	1	NUM
cana-5358	74	115	.	.	PUNCT
cana-5358	75	1	supposing	suppose	VERB
cana-5358	75	2	(	(	PUNCT
cana-5358	75	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5358	75	4	+	+	CCONJ
cana-5358	75	5	(	(	PUNCT
cana-5358	75	6	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5358	75	7	≤	≤	NUM
cana-5358	75	8	1	1	NUM
cana-5358	75	9	,	,	PUNCT
cana-5358	75	10	then	then	ADV
cana-5358	75	11	there	there	PRON
cana-5358	75	12	is	be	VERB
cana-5358	75	13	a	a	DET
cana-5358	75	14	degree	degree	NOUN
cana-5358	75	15	of	of	ADP
cana-5358	75	16	indeterminacy	indeterminacy	NOUN
cana-5358	75	17	of	of	ADP
cana-5358	75	18	𝑥	𝑥	DET
cana-5358	75	19	∈	∈	PROPN
cana-5358	75	20	𝑋	𝑋	NOUN
cana-5358	75	21	to	to	ADP
cana-5358	75	22	𝐴	𝐴	PROPN
cana-5358	75	23	defined	define	VERB
cana-5358	75	24	by	by	ADP
cana-5358	75	25	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5358	75	26	)	)	PUNCT
cana-5358	75	27	=	=	PUNCT
cana-5358	76	1	√1	√1	ADV
cana-5358	76	2	−	−	PROPN
cana-5358	77	1	[	[	X
cana-5358	77	2	(	(	PUNCT
cana-5358	77	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5358	77	4	+	+	CCONJ
cana-5358	77	5	(	(	PUNCT
cana-5358	77	6	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5358	77	7	]	]	PUNCT
cana-5358	77	8	and	and	CCONJ
cana-5358	77	9	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5358	77	10	)	)	PUNCT
cana-5358	77	11	∈	∈	NOUN
cana-5358	78	1	[	[	X
cana-5358	78	2	0,1	0,1	NUM
cana-5358	78	3	]	]	PUNCT
cana-5358	78	4	.	.	PUNCT
cana-5358	79	1	in	in	ADP
cana-5358	79	2	what	what	PRON
cana-5358	79	3	follows	follow	VERB
cana-5358	79	4	,	,	PUNCT
cana-5358	79	5	(	(	PUNCT
cana-5358	79	6	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5358	79	7	+	+	CCONJ
cana-5358	79	8	(	(	PUNCT
cana-5358	79	9	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5358	79	10	+	+	CCONJ
cana-5358	79	11	(	(	PUNCT
cana-5358	79	12	𝜋𝐴(𝑥))2	𝜋𝐴(𝑥))2	NOUN
cana-5358	79	13	=	=	SYM
cana-5358	79	14	1	1	X
cana-5358	79	15	.	.	PUNCT
cana-5358	79	16	otherwise	otherwise	ADV
cana-5358	79	17	,	,	PUNCT
cana-5358	79	18	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5358	79	19	)	)	PUNCT
cana-5358	79	20	=	=	SYM
cana-5358	79	21	0	0	PUNCT
cana-5358	79	22	whenever	whenever	SCONJ
cana-5358	79	23	(	(	PUNCT
cana-5358	79	24	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5358	79	25	+	+	CCONJ
cana-5358	79	26	(	(	PUNCT
cana-5358	79	27	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5358	79	28	=	=	SYM
cana-5358	79	29	1	1	X
cana-5358	79	30	.	.	X
cana-5358	80	1	we	we	PRON
cana-5358	80	2	denote	denote	VERB
cana-5358	80	3	the	the	DET
cana-5358	80	4	set	set	NOUN
cana-5358	80	5	of	of	ADP
cana-5358	80	6	all	all	DET
cana-5358	80	7	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-5358	80	8	’s	’s	NOUN
cana-5358	80	9	over	over	ADP
cana-5358	80	10	𝑋	𝑋	PROPN
cana-5358	80	11	by	by	ADP
cana-5358	80	12	𝑝𝑓𝑠(𝑋	𝑝𝑓𝑠(𝑋	PROPN
cana-5358	80	13	)	)	PUNCT
cana-5358	80	14	.	.	PUNCT
cana-5358	81	1	definition	definition	NOUN
cana-5358	81	2	2.5	2.5	NUM
cana-5358	82	1	[	[	X
cana-5358	82	2	10	10	NUM
cana-5358	82	3	]	]	PUNCT
cana-5358	82	4	let	let	VERB
cana-5358	82	5	𝑋	𝑋	NOUN
cana-5358	82	6	be	be	AUX
cana-5358	82	7	a	a	DET
cana-5358	82	8	universe	universe	NOUN
cana-5358	82	9	of	of	ADP
cana-5358	82	10	discourse	discourse	NOUN
cana-5358	82	11	.	.	PUNCT
cana-5358	83	1	a	a	DET
cana-5358	83	2	fermatean	fermatean	ADJ
cana-5358	83	3	fuzzy	fuzzy	ADJ
cana-5358	83	4	set	set	NOUN
cana-5358	83	5	(	(	PUNCT
cana-5358	83	6	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	83	7	)	)	PUNCT
cana-5358	83	8	𝐹	𝐹	PROPN
cana-5358	83	9	in	in	ADP
cana-5358	83	10	𝑋	𝑋	PROPN
cana-5358	83	11	is	be	AUX
cana-5358	83	12	an	an	DET
cana-5358	83	13	object	object	NOUN
cana-5358	83	14	having	have	VERB
cana-5358	83	15	the	the	DET
cana-5358	83	16	form	form	NOUN
cana-5358	83	17	𝐹	𝐹	PROPN
cana-5358	83	18	=	=	PUNCT
cana-5358	83	19	{	{	PUNCT
cana-5358	83	20	<	<	X
cana-5358	83	21	𝑥	𝑥	X
cana-5358	83	22	,	,	PUNCT
cana-5358	83	23	𝛼𝐹(𝑥	𝛼𝐹(𝑥	NUM
cana-5358	83	24	)	)	PUNCT
cana-5358	83	25	,	,	PUNCT
cana-5358	83	26	𝛽𝐹(𝑥	𝛽𝐹(𝑥	PROPN
cana-5358	83	27	)	)	PUNCT
cana-5358	83	28	>	>	PUNCT
cana-5358	83	29	:	:	PUNCT
cana-5358	83	30	𝑥	𝑥	X
cana-5358	83	31	∈	∈	PROPN
cana-5358	83	32	𝑋	𝑋	PROPN
cana-5358	83	33	}	}	PUNCT
cana-5358	83	34	where	where	SCONJ
cana-5358	83	35	𝛼𝐹(𝑥	𝛼𝐹(𝑥	NUM
cana-5358	83	36	):	):	PUNCT
cana-5358	83	37	𝑋	𝑋	NOUN
cana-5358	83	38	→	→	SYM
cana-5358	83	39	[	[	X
cana-5358	83	40	0,1	0,1	NUM
cana-5358	83	41	]	]	PUNCT
cana-5358	83	42	and	and	CCONJ
cana-5358	83	43	𝛽𝐹(𝑥	𝛽𝐹(𝑥	NUM
cana-5358	83	44	):	):	PUNCT
cana-5358	83	45	𝑋	𝑋	PROPN
cana-5358	83	46	→	→	SYM
cana-5358	83	47	[	[	X
cana-5358	83	48	0,1	0,1	NUM
cana-5358	83	49	]	]	PUNCT
cana-5358	83	50	,	,	PUNCT
cana-5358	83	51	including	include	VERB
cana-5358	83	52	the	the	DET
cana-5358	83	53	condition	condition	NOUN
cana-5358	83	54	0	0	NUM
cana-5358	83	55	≤	≤	NOUN
cana-5358	83	56	(	(	PUNCT
cana-5358	83	57	𝛼𝐹(𝑥))3	𝛼𝐹(𝑥))3	PROPN
cana-5358	83	58	+	+	X
cana-5358	83	59	(	(	PUNCT
cana-5358	83	60	𝛽𝐹(𝑥))3	𝛽𝐹(𝑥))3	X
cana-5358	83	61	≤	≤	NUM
cana-5358	83	62	1	1	NUM
cana-5358	83	63	,	,	PUNCT
cana-5358	83	64	for	for	ADP
cana-5358	83	65	all	all	DET
cana-5358	83	66	𝑥	𝑥	DET
cana-5358	83	67	∈	∈	NOUN
cana-5358	83	68	𝑋.	𝑋.	NOUN
cana-5358	83	69	the	the	DET
cana-5358	83	70	numbers	number	NOUN
cana-5358	83	71	𝛼𝐹(𝑥	𝛼𝐹(𝑥	NUM
cana-5358	83	72	)	)	PUNCT
cana-5358	83	73	and	and	CCONJ
cana-5358	83	74	𝛽𝐹(𝑥	𝛽𝐹(𝑥	NUM
cana-5358	83	75	)	)	PUNCT
cana-5358	83	76	denote	denote	NOUN
cana-5358	83	77	,	,	PUNCT
cana-5358	83	78	respectively	respectively	ADV
cana-5358	83	79	,	,	PUNCT
cana-5358	83	80	the	the	DET
cana-5358	83	81	degree	degree	NOUN
cana-5358	83	82	of	of	ADP
cana-5358	83	83	memebership	memebership	NOUN
cana-5358	83	84	and	and	CCONJ
cana-5358	83	85	the	the	DET
cana-5358	83	86	degree	degree	NOUN
cana-5358	83	87	of	of	ADP
cana-5358	83	88	non	non	NOUN
cana-5358	83	89	-	-	NOUN
cana-5358	83	90	memebership	memebership	NOUN
cana-5358	83	91	of	of	ADP
cana-5358	83	92	the	the	DET
cana-5358	83	93	element	element	NOUN
cana-5358	83	94	𝑥	𝑥	PROPN
cana-5358	83	95	in	in	ADP
cana-5358	83	96	the	the	DET
cana-5358	83	97	set	set	NOUN
cana-5358	83	98	𝐹	𝐹	PROPN
cana-5358	83	99	.	.	PUNCT
cana-5358	84	1	for	for	ADP
cana-5358	84	2	any	any	DET
cana-5358	84	3	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	84	4	𝐹	𝐹	PROPN
cana-5358	84	5	and	and	CCONJ
cana-5358	84	6	𝑥	𝑥	DET
cana-5358	84	7	∈	∈	PROPN
cana-5358	84	8	𝑋	𝑋	NOUN
cana-5358	84	9	,	,	PUNCT
cana-5358	84	10	𝜋𝐹(𝑥	𝜋𝐹(𝑥	NUM
cana-5358	84	11	)	)	PUNCT
cana-5358	84	12	=	=	PUNCT
cana-5358	84	13	√1	√1	ADV
cana-5358	84	14	−	−	PROPN
cana-5358	85	1	[	[	X
cana-5358	85	2	(	(	PUNCT
cana-5358	85	3	𝛼𝐹(𝑥))3	𝛼𝐹(𝑥))3	PROPN
cana-5358	85	4	−	−	PROPN
cana-5358	85	5	(	(	PUNCT
cana-5358	85	6	𝛽𝐹(𝑥))3	𝛽𝐹(𝑥))3	X
cana-5358	85	7	]	]	PUNCT
cana-5358	85	8	3	3	NUM
cana-5358	85	9	is	be	AUX
cana-5358	85	10	identified	identify	VERB
cana-5358	85	11	as	as	ADP
cana-5358	85	12	the	the	DET
cana-5358	85	13	degree	degree	NOUN
cana-5358	85	14	of	of	ADP
cana-5358	85	15	interminancy	interminancy	NOUN
cana-5358	85	16	of	of	ADP
cana-5358	85	17	𝑥	𝑥	PRON
cana-5358	85	18	to	to	ADP
cana-5358	85	19	𝐹.	𝐹.	PROPN
cana-5358	85	20	in	in	ADP
cana-5358	85	21	the	the	DET
cana-5358	85	22	interest	interest	NOUN
cana-5358	85	23	of	of	ADP
cana-5358	85	24	simplicity	simplicity	NOUN
cana-5358	85	25	,	,	PUNCT
cana-5358	85	26	we	we	PRON
cana-5358	85	27	shall	shall	AUX
cana-5358	85	28	mention	mention	VERB
cana-5358	85	29	the	the	DET
cana-5358	85	30	symbol	symbol	NOUN
cana-5358	85	31	𝐹	𝐹	PROPN
cana-5358	85	32	=	=	PUNCT
cana-5358	85	33	(	(	PUNCT
cana-5358	85	34	𝛼𝐹	𝛼𝐹	NOUN
cana-5358	85	35	,	,	PUNCT
cana-5358	85	36	𝛽𝐹	𝛽𝐹	NOUN
cana-5358	85	37	)	)	PUNCT
cana-5358	85	38	for	for	ADP
cana-5358	85	39	the	the	DET
cana-5358	85	40	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	85	41	𝐹	𝐹	PROPN
cana-5358	85	42	=	=	PUNCT
cana-5358	85	43	{	{	PUNCT
cana-5358	85	44	<	<	X
cana-5358	85	45	𝑥	𝑥	X
cana-5358	85	46	,	,	PUNCT
cana-5358	85	47	𝛼𝐹(𝑥	𝛼𝐹(𝑥	NUM
cana-5358	85	48	)	)	PUNCT
cana-5358	85	49	,	,	PUNCT
cana-5358	85	50	𝛽𝐹(𝑥	𝛽𝐹(𝑥	PROPN
cana-5358	85	51	):	):	PUNCT
cana-5358	85	52	𝑥	𝑥	PROPN
cana-5358	85	53	∈	∈	PROPN
cana-5358	85	54	𝑋	𝑋	PROPN
cana-5358	85	55	}	}	PUNCT
cana-5358	85	56	.	.	PUNCT
cana-5358	86	1	communications	communication	NOUN
cana-5358	86	2	on	on	ADP
cana-5358	86	3	applied	apply	VERB
cana-5358	86	4	nonlinear	nonlinear	ADJ
cana-5358	86	5	analysis	analysis	NOUN
cana-5358	86	6	issn	issn	NOUN
cana-5358	86	7	:	:	PUNCT
cana-5358	86	8	1074	1074	NUM
cana-5358	86	9	-	-	PUNCT
cana-5358	86	10	133x	133x	NUM
cana-5358	86	11	vol	vol	VERB
cana-5358	86	12	32	32	NUM
cana-5358	86	13	no	no	NOUN
cana-5358	86	14	.	.	PUNCT
cana-5358	87	1	10s	10	NOUN
cana-5358	87	2	(	(	PUNCT
cana-5358	87	3	2025	2025	NUM
cana-5358	87	4	)	)	PUNCT
cana-5358	87	5	1898	1898	NUM
cana-5358	87	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	87	7	definition	definition	NOUN
cana-5358	87	8	2.6	2.6	NUM
cana-5358	87	9	[	[	SYM
cana-5358	87	10	10	10	NUM
cana-5358	87	11	]	]	PUNCT
cana-5358	87	12	let	let	VERB
cana-5358	87	13	𝐹	𝐹	PROPN
cana-5358	87	14	=	=	SYM
cana-5358	87	15	(	(	PUNCT
cana-5358	87	16	𝛼𝐹	𝛼𝐹	PROPN
cana-5358	87	17	,	,	PUNCT
cana-5358	87	18	𝛽𝐹	𝛽𝐹	NOUN
cana-5358	87	19	)	)	PUNCT
cana-5358	87	20	,	,	PUNCT
cana-5358	87	21	𝐹1	𝐹1	NOUN
cana-5358	87	22	=	=	SYM
cana-5358	87	23	(	(	PUNCT
cana-5358	87	24	𝛼𝐹1	𝛼𝐹1	PROPN
cana-5358	87	25	,	,	PUNCT
cana-5358	87	26	𝛽𝐹1	𝛽𝐹1	PROPN
cana-5358	87	27	)	)	PUNCT
cana-5358	87	28	and	and	CCONJ
cana-5358	87	29	𝐹2	𝐹2	NOUN
cana-5358	87	30	=	=	SYM
cana-5358	87	31	(	(	PUNCT
cana-5358	87	32	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5358	87	33	,	,	PUNCT
cana-5358	87	34	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5358	87	35	)	)	PUNCT
cana-5358	87	36	,	,	PUNCT
cana-5358	87	37	be	be	AUX
cana-5358	87	38	three	three	NUM
cana-5358	87	39	fermatean	fermatean	ADJ
cana-5358	87	40	fuzzy	fuzzy	ADJ
cana-5358	87	41	sets	set	NOUN
cana-5358	87	42	(	(	PUNCT
cana-5358	87	43	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	87	44	’s	’s	PART
cana-5358	87	45	)	)	PUNCT
cana-5358	87	46	,	,	PUNCT
cana-5358	87	47	then	then	ADV
cana-5358	87	48	their	their	PRON
cana-5358	87	49	operations	operation	NOUN
cana-5358	87	50	are	be	AUX
cana-5358	87	51	defined	define	VERB
cana-5358	87	52	as	as	SCONJ
cana-5358	87	53	follows	follow	VERB
cana-5358	87	54	:	:	PUNCT
cana-5358	88	1	[	[	X
cana-5358	88	2	(	(	PUNCT
cana-5358	88	3	i	i	NOUN
cana-5358	88	4	)	)	PUNCT
cana-5358	88	5	]	]	PUNCT
cana-5358	89	1	1	1	X
cana-5358	89	2	.	.	X
cana-5358	89	3	𝐹1	𝐹1	PROPN
cana-5358	89	4	∩	∩	PROPN
cana-5358	89	5	𝐹2	𝐹2	PROPN
cana-5358	89	6	=	=	PUNCT
cana-5358	89	7	(	(	PUNCT
cana-5358	89	8	𝑚𝑖𝑛{𝛼𝐹1	𝑚𝑖𝑛{𝛼𝐹1	VERB
cana-5358	89	9	,	,	PUNCT
cana-5358	89	10	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5358	89	11	}	}	PUNCT
cana-5358	89	12	,	,	PUNCT
cana-5358	89	13	𝑚𝑎𝑥{𝛽𝐹1	𝑚𝑎𝑥{𝛽𝐹1	NOUN
cana-5358	89	14	,	,	PUNCT
cana-5358	89	15	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5358	89	16	}	}	PUNCT
cana-5358	89	17	)	)	PUNCT
cana-5358	89	18	.	.	PUNCT
cana-5358	90	1	2	2	X
cana-5358	90	2	.	.	X
cana-5358	90	3	𝐹1	𝐹1	PROPN
cana-5358	90	4	∪	∪	PROPN
cana-5358	90	5	𝐹2	𝐹2	PROPN
cana-5358	90	6	=	=	SYM
cana-5358	90	7	(	(	PUNCT
cana-5358	90	8	𝑚𝑎𝑥{𝛼𝐹1	𝑚𝑎𝑥{𝛼𝐹1	ADV
cana-5358	90	9	,	,	PUNCT
cana-5358	90	10	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5358	90	11	}	}	PUNCT
cana-5358	90	12	,	,	PUNCT
cana-5358	90	13	𝑚𝑖𝑛{𝛽𝐹1	𝑚𝑖𝑛{𝛽𝐹1	NOUN
cana-5358	90	14	,	,	PUNCT
cana-5358	90	15	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5358	90	16	}	}	PUNCT
cana-5358	90	17	)	)	PUNCT
cana-5358	90	18	.	.	PUNCT
cana-5358	91	1	3	3	X
cana-5358	91	2	.	.	X
cana-5358	92	1	𝐹𝑐	𝐹𝑐	NOUN
cana-5358	92	2	=	=	PUNCT
cana-5358	92	3	(	(	PUNCT
cana-5358	92	4	𝛽𝐹	𝛽𝐹	PROPN
cana-5358	92	5	,	,	PUNCT
cana-5358	92	6	𝛼𝐹	𝛼𝐹	NUM
cana-5358	92	7	)	)	PUNCT
cana-5358	92	8	.	.	PUNCT
cana-5358	93	1	remark	remark	VERB
cana-5358	93	2	2.1	2.1	NUM
cana-5358	93	3	if	if	SCONJ
cana-5358	93	4	𝛼𝐹1	𝛼𝐹1	PROPN
cana-5358	93	5	=	=	SYM
cana-5358	93	6	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5358	93	7	and	and	CCONJ
cana-5358	93	8	𝛽𝐹1	𝛽𝐹1	PROPN
cana-5358	93	9	=	=	PUNCT
cana-5358	93	10	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5358	93	11	,	,	PUNCT
cana-5358	93	12	then	then	ADV
cana-5358	93	13	𝐹1	𝐹1	PROPN
cana-5358	93	14	=	=	X
cana-5358	93	15	𝐹2	𝐹2	PROPN
cana-5358	93	16	note	note	VERB
cana-5358	93	17	that	that	SCONJ
cana-5358	93	18	,	,	PUNCT
cana-5358	93	19	for	for	ADP
cana-5358	93	20	understanding	understand	VERB
cana-5358	93	21	the	the	DET
cana-5358	93	22	fermatean	fermatean	ADJ
cana-5358	93	23	fuzzy	fuzzy	NOUN
cana-5358	93	24	set	set	VERB
cana-5358	93	25	better	well	ADV
cana-5358	93	26	,	,	PUNCT
cana-5358	93	27	we	we	PRON
cana-5358	93	28	give	give	VERB
cana-5358	93	29	an	an	DET
cana-5358	93	30	instance	instance	NOUN
cana-5358	93	31	to	to	PART
cana-5358	93	32	illuminate	illuminate	VERB
cana-5358	93	33	the	the	DET
cana-5358	93	34	understandability	understandability	NOUN
cana-5358	93	35	of	of	ADP
cana-5358	93	36	the	the	DET
cana-5358	93	37	fermatean	fermatean	ADJ
cana-5358	93	38	fuzzy	fuzzy	ADJ
cana-5358	93	39	set	set	NOUN
cana-5358	93	40	.	.	PUNCT
cana-5358	94	1	the	the	DET
cana-5358	94	2	point	point	NOUN
cana-5358	94	3	when	when	SCONJ
cana-5358	94	4	someone	someone	PRON
cana-5358	94	5	needs	need	VERB
cana-5358	94	6	will	will	AUX
cana-5358	94	7	plan	plan	VERB
cana-5358	94	8	as	as	ADV
cana-5358	94	9	much	much	ADJ
cana-5358	94	10	craving	craving	NOUN
cana-5358	94	11	for	for	ADP
cana-5358	94	12	the	the	DET
cana-5358	94	13	level	level	NOUN
cana-5358	94	14	for	for	ADP
cana-5358	94	15	an	an	DET
cana-5358	94	16	alternative	alternative	ADJ
cana-5358	94	17	𝑠𝑖	𝑠𝑖	NOUN
cana-5358	94	18	on	on	ADP
cana-5358	94	19	a	a	DET
cana-5358	94	20	criterion	criterion	NOUN
cana-5358	94	21	𝐶𝑗	𝐶𝑗	PROPN
cana-5358	94	22	,	,	PUNCT
cana-5358	94	23	he	he	PRON
cana-5358	94	24	might	might	AUX
cana-5358	94	25	provide	provide	VERB
cana-5358	94	26	for	for	ADP
cana-5358	94	27	the	the	DET
cana-5358	94	28	degree	degree	NOUN
cana-5358	94	29	on	on	ADP
cana-5358	94	30	which	which	PRON
cana-5358	94	31	that	that	DET
cana-5358	94	32	alternative	alternative	ADJ
cana-5358	94	33	𝑠𝑖	𝑠𝑖	NOUN
cana-5358	94	34	fulfils	fulfil	VERB
cana-5358	94	35	those	those	DET
cana-5358	94	36	criteria	criterion	NOUN
cana-5358	94	37	𝐶𝑗	𝐶𝑗	PROPN
cana-5358	94	38	likewise	likewise	ADV
cana-5358	94	39	0.85	0.85	NUM
cana-5358	94	40	,	,	PUNCT
cana-5358	94	41	what	what	PRON
cana-5358	94	42	is	be	AUX
cana-5358	94	43	more	more	ADV
cana-5358	94	44	correspondingly	correspondingly	ADV
cana-5358	94	45	the	the	DET
cana-5358	94	46	elective	elective	ADJ
cana-5358	94	47	𝑠𝑖	𝑠𝑖	NOUN
cana-5358	94	48	dissatisfies	dissatisfie	NOUN
cana-5358	94	49	the	the	DET
cana-5358	94	50	criterion	criterion	NOUN
cana-5358	94	51	𝐶𝑗	𝐶𝑗	PROPN
cana-5358	94	52	similarly	similarly	ADV
cana-5358	94	53	as	as	ADP
cana-5358	94	54	0.65	0.65	NUM
cana-5358	94	55	.	.	PUNCT
cana-5358	95	1	we	we	PRON
cana-5358	95	2	can	can	AUX
cana-5358	95	3	definitely	definitely	ADV
cana-5358	95	4	get	get	VERB
cana-5358	95	5	0.85	0.85	NUM
cana-5358	95	6	+	+	CCONJ
cana-5358	95	7	0.65	0.65	NUM
cana-5358	95	8	=	=	SYM
cana-5358	95	9	1.5	1.5	NUM
cana-5358	95	10	>	>	SYM
cana-5358	95	11	1	1	NUM
cana-5358	95	12	,	,	PUNCT
cana-5358	95	13	and	and	CCONJ
cana-5358	95	14	,	,	PUNCT
cana-5358	95	15	therefore	therefore	ADV
cana-5358	95	16	,	,	PUNCT
cana-5358	95	17	it	it	PRON
cana-5358	95	18	does	do	AUX
cana-5358	95	19	not	not	PART
cana-5358	95	20	follow	follow	VERB
cana-5358	95	21	the	the	DET
cana-5358	95	22	condition	condition	NOUN
cana-5358	95	23	of	of	ADP
cana-5358	95	24	intuitionistic	intuitionistic	ADJ
cana-5358	95	25	fuzzy	fuzzy	ADJ
cana-5358	95	26	sets	set	NOUN
cana-5358	95	27	.	.	PUNCT
cana-5358	96	1	also	also	ADV
cana-5358	96	2	,	,	PUNCT
cana-5358	96	3	we	we	PRON
cana-5358	96	4	can	can	AUX
cana-5358	96	5	get	get	VERB
cana-5358	96	6	(	(	PUNCT
cana-5358	96	7	0.85)2	0.85)2	NOUN
cana-5358	96	8	+	+	CCONJ
cana-5358	96	9	(	(	PUNCT
cana-5358	96	10	0.65)2	0.65)2	NOUN
cana-5358	96	11	=	=	PUNCT
cana-5358	96	12	0.7225	0.7225	NUM
cana-5358	96	13	+	+	NUM
cana-5358	96	14	0.4225	0.4225	NUM
cana-5358	96	15	=	=	SYM
cana-5358	96	16	1.145	1.145	NUM
cana-5358	96	17	>	>	SYM
cana-5358	96	18	1	1	NUM
cana-5358	96	19	,	,	PUNCT
cana-5358	96	20	which	which	PRON
cana-5358	96	21	does	do	AUX
cana-5358	96	22	not	not	PART
cana-5358	96	23	obey	obey	VERB
cana-5358	96	24	the	the	DET
cana-5358	96	25	constraint	constraint	NOUN
cana-5358	96	26	condition	condition	NOUN
cana-5358	96	27	of	of	ADP
cana-5358	96	28	pythagorean	pythagorean	PROPN
cana-5358	96	29	fuzzy	fuzzy	ADJ
cana-5358	96	30	set	set	PROPN
cana-5358	96	31	.	.	PUNCT
cana-5358	97	1	however	however	ADV
cana-5358	97	2	,	,	PUNCT
cana-5358	97	3	we	we	PRON
cana-5358	97	4	can	can	AUX
cana-5358	97	5	get	get	VERB
cana-5358	97	6	(	(	PUNCT
cana-5358	97	7	0.85)3	0.85)3	NOUN
cana-5358	97	8	+	+	CCONJ
cana-5358	97	9	(	(	PUNCT
cana-5358	97	10	0.65)3	0.65)3	NOUN
cana-5358	97	11	=	=	NOUN
cana-5358	97	12	0.614125	0.614125	NUM
cana-5358	97	13	+	+	NUM
cana-5358	97	14	0.274625	0.274625	NUM
cana-5358	97	15	=	=	PUNCT
cana-5358	97	16	0.88875	0.88875	NUM
cana-5358	97	17	≤	≤	NUM
cana-5358	97	18	1	1	NUM
cana-5358	97	19	,	,	PUNCT
cana-5358	97	20	which	which	PRON
cana-5358	97	21	is	be	AUX
cana-5358	97	22	good	good	ADJ
cana-5358	97	23	enough	enough	ADV
cana-5358	97	24	to	to	PART
cana-5358	97	25	apply	apply	VERB
cana-5358	97	26	the	the	DET
cana-5358	97	27	fermatean	fermatean	ADJ
cana-5358	97	28	fuzzy	fuzzy	NOUN
cana-5358	97	29	set	set	VERB
cana-5358	97	30	to	to	PART
cana-5358	97	31	control	control	VERB
cana-5358	97	32	it	it	PRON
cana-5358	97	33	[	[	X
cana-5358	97	34	10	10	NUM
cana-5358	97	35	]	]	PUNCT
cana-5358	97	36	.	.	PUNCT
cana-5358	98	1	throughout	throughout	ADP
cana-5358	98	2	this	this	DET
cana-5358	98	3	paper	paper	NOUN
cana-5358	98	4	,	,	PUNCT
cana-5358	98	5	we	we	PRON
cana-5358	98	6	use	use	VERB
cana-5358	98	7	the	the	DET
cana-5358	98	8	notation	notation	NOUN
cana-5358	98	9	1𝔉	1𝔉	NOUN
cana-5358	98	10	for	for	ADP
cana-5358	98	11	the	the	DET
cana-5358	98	12	fermatean	fermatean	ADJ
cana-5358	98	13	fuzzy	fuzzy	NOUN
cana-5358	98	14	subset	subset	NOUN
cana-5358	98	15	(	(	PUNCT
cana-5358	98	16	1,0	1,0	NUM
cana-5358	98	17	)	)	PUNCT
cana-5358	98	18	and	and	CCONJ
cana-5358	98	19	we	we	PRON
cana-5358	98	20	use	use	VERB
cana-5358	98	21	the	the	DET
cana-5358	98	22	notation	notation	NOUN
cana-5358	98	23	0𝔉	0𝔉	NOUN
cana-5358	98	24	for	for	ADP
cana-5358	98	25	the	the	DET
cana-5358	98	26	fermatean	fermatean	ADJ
cana-5358	98	27	fuzzy	fuzzy	ADJ
cana-5358	98	28	subset	subset	NOUN
cana-5358	98	29	(	(	PUNCT
cana-5358	98	30	0,1	0,1	NUM
cana-5358	98	31	)	)	PUNCT
cana-5358	98	32	,	,	PUNCT
cana-5358	98	33	that	that	ADV
cana-5358	98	34	is	is	ADV
cana-5358	98	35	,	,	PUNCT
cana-5358	98	36	𝛼1𝔉	𝛼1𝔉	NUM
cana-5358	98	37	=	=	SYM
cana-5358	98	38	1	1	NUM
cana-5358	98	39	,	,	PUNCT
cana-5358	98	40	𝛽1𝔉	𝛽1𝔉	X
cana-5358	98	41	=	=	SYM
cana-5358	98	42	0	0	NUM
cana-5358	98	43	,	,	PUNCT
cana-5358	98	44	𝛼0𝔉	𝛼0𝔉	NOUN
cana-5358	98	45	=	=	SYM
cana-5358	98	46	0	0	NUM
cana-5358	98	47	,	,	PUNCT
cana-5358	98	48	𝛽0𝔉	𝛽0𝔉	ADV
cana-5358	98	49	=	=	NOUN
cana-5358	98	50	1	1	X
cana-5358	98	51	.	.	PUNCT
cana-5358	98	52	a	a	DET
cana-5358	98	53	fermatean	fermatean	ADJ
cana-5358	98	54	fuzzy	fuzzy	NOUN
cana-5358	98	55	subset	subset	VERB
cana-5358	98	56	𝔉	𝔉	PROPN
cana-5358	98	57	of	of	ADP
cana-5358	98	58	a	a	DET
cana-5358	98	59	non	non	ADJ
cana-5358	98	60	-	-	ADJ
cana-5358	98	61	empty	empty	ADJ
cana-5358	98	62	set	set	ADJ
cana-5358	98	63	𝑋	𝑋	PROPN
cana-5358	98	64	is	be	AUX
cana-5358	98	65	a	a	DET
cana-5358	98	66	pair	pair	NOUN
cana-5358	98	67	(	(	PUNCT
cana-5358	98	68	𝛼𝔉	𝛼𝔉	NOUN
cana-5358	98	69	,	,	PUNCT
cana-5358	98	70	𝛽𝔉	𝛽𝔉	NOUN
cana-5358	98	71	)	)	PUNCT
cana-5358	98	72	of	of	ADP
cana-5358	98	73	a	a	DET
cana-5358	98	74	membership	membership	NOUN
cana-5358	98	75	function	function	NOUN
cana-5358	98	76	(	(	PUNCT
cana-5358	98	77	𝛼𝔉(𝑥	𝛼𝔉(𝑥	NUM
cana-5358	98	78	):	):	PUNCT
cana-5358	98	79	𝑋	𝑋	PROPN
cana-5358	98	80	→	→	SYM
cana-5358	98	81	[	[	X
cana-5358	98	82	0,1	0,1	NUM
cana-5358	98	83	]	]	PUNCT
cana-5358	98	84	and	and	CCONJ
cana-5358	98	85	a	a	DET
cana-5358	98	86	non	non	ADJ
cana-5358	98	87	-	-	ADJ
cana-5358	98	88	membership	membership	ADJ
cana-5358	98	89	function	function	NOUN
cana-5358	98	90	(	(	PUNCT
cana-5358	98	91	𝛽𝔉(𝑥	𝛽𝔉(𝑥	NUM
cana-5358	98	92	):	):	PUNCT
cana-5358	98	93	𝑋	𝑋	PROPN
cana-5358	98	94	→	→	SYM
cana-5358	99	1	[	[	X
cana-5358	99	2	0,1	0,1	NUM
cana-5358	99	3	]	]	PUNCT
cana-5358	99	4	with	with	ADP
cana-5358	99	5	(	(	PUNCT
cana-5358	99	6	𝛼𝔉(𝑥))3	𝛼𝔉(𝑥))3	PROPN
cana-5358	99	7	+	+	X
cana-5358	99	8	(	(	PUNCT
cana-5358	99	9	𝛽𝔉(𝑥))3	𝛽𝔉(𝑥))3	PROPN
cana-5358	99	10	=	=	SYM
cana-5358	99	11	(	(	PUNCT
cana-5358	99	12	𝛾𝔉(𝑥))3	𝛾𝔉(𝑥))3	NOUN
cana-5358	99	13	for	for	ADP
cana-5358	99	14	any	any	DET
cana-5358	99	15	𝑥	𝑥	PRON
cana-5358	99	16	∈	∈	NOUN
cana-5358	99	17	𝑋	𝑋	NOUN
cana-5358	99	18	where	where	SCONJ
cana-5358	99	19	𝛾𝔉(𝑥	𝛾𝔉(𝑥	NOUN
cana-5358	99	20	):	):	PUNCT
cana-5358	99	21	𝑋	𝑋	PROPN
cana-5358	99	22	→	→	SYM
cana-5358	99	23	[	[	X
cana-5358	99	24	0,1	0,1	NUM
cana-5358	99	25	]	]	PUNCT
cana-5358	99	26	is	be	AUX
cana-5358	99	27	a	a	DET
cana-5358	99	28	function	function	NOUN
cana-5358	99	29	which	which	PRON
cana-5358	99	30	is	be	AUX
cana-5358	99	31	called	call	VERB
cana-5358	99	32	the	the	DET
cana-5358	99	33	strength	strength	NOUN
cana-5358	99	34	of	of	ADP
cana-5358	99	35	commitment	commitment	NOUN
cana-5358	99	36	at	at	ADP
cana-5358	99	37	point	point	NOUN
cana-5358	99	38	𝑥.	𝑥.	DET
cana-5358	99	39	definition	definition	NOUN
cana-5358	99	40	2.7	2.7	NUM
cana-5358	99	41	[	[	SYM
cana-5358	99	42	8	8	NUM
cana-5358	99	43	]	]	PUNCT
cana-5358	99	44	let	let	VERB
cana-5358	99	45	𝑋	𝑋	NOUN
cana-5358	99	46	be	be	AUX
cana-5358	99	47	a	a	DET
cana-5358	99	48	non	non	X
cana-5358	99	49	empty	empty	ADJ
cana-5358	99	50	set	set	NOUN
cana-5358	99	51	and	and	CCONJ
cana-5358	99	52	𝜏	𝜏	NOUN
cana-5358	99	53	be	be	AUX
cana-5358	99	54	a	a	DET
cana-5358	99	55	family	family	NOUN
cana-5358	99	56	of	of	ADP
cana-5358	99	57	fermatean	fermatean	ADJ
cana-5358	99	58	fuzzy	fuzzy	ADJ
cana-5358	99	59	subsets	subset	NOUN
cana-5358	99	60	of	of	ADP
cana-5358	99	61	𝑋.	𝑋.	PROPN
cana-5358	99	62	if	if	SCONJ
cana-5358	99	63	1	1	NUM
cana-5358	99	64	.	.	X
cana-5358	99	65	1𝔉	1𝔉	NOUN
cana-5358	99	66	,	,	PUNCT
cana-5358	99	67	0𝔉	0𝔉	PROPN
cana-5358	99	68	∈	∈	PROPN
cana-5358	99	69	𝜏	𝜏	ADP
cana-5358	99	70	2	2	NUM
cana-5358	99	71	.	.	PUNCT
cana-5358	99	72	for	for	ADP
cana-5358	99	73	any	any	DET
cana-5358	99	74	𝐹1	𝐹1	NOUN
cana-5358	99	75	,	,	PUNCT
cana-5358	99	76	𝐹2	𝐹2	PROPN
cana-5358	99	77	∈	∈	PROPN
cana-5358	99	78	𝜏	𝜏	PROPN
cana-5358	99	79	,	,	PUNCT
cana-5358	99	80	we	we	PRON
cana-5358	99	81	have	have	VERB
cana-5358	99	82	𝐹1	𝐹1	PROPN
cana-5358	99	83	∩	∩	PROPN
cana-5358	99	84	𝐹2	𝐹2	PROPN
cana-5358	99	85	∈	∈	PROPN
cana-5358	99	86	𝜏	𝜏	PROPN
cana-5358	99	87	,	,	PUNCT
cana-5358	99	88	3	3	NUM
cana-5358	99	89	.	.	X
cana-5358	100	1	for	for	ADP
cana-5358	100	2	any	any	DET
cana-5358	100	3	{	{	PUNCT
cana-5358	100	4	𝐹𝑖}𝑖∈𝐼	𝐹𝑖}𝑖∈𝐼	X
cana-5358	100	5	⊂	⊂	SYM
cana-5358	100	6	𝜏	𝜏	NOUN
cana-5358	100	7	,	,	PUNCT
cana-5358	100	8	we	we	PRON
cana-5358	100	9	have	have	VERB
cana-5358	100	10	⋃𝑖∈𝐼	⋃𝑖∈𝐼	NOUN
cana-5358	100	11	𝐹𝑖	𝐹𝑖	PROPN
cana-5358	100	12	∈	∈	NOUN
cana-5358	100	13	𝜏	𝜏	NOUN
cana-5358	100	14	where	where	SCONJ
cana-5358	100	15	𝐼	𝐼	PROPN
cana-5358	100	16	is	be	AUX
cana-5358	100	17	an	an	DET
cana-5358	100	18	arbitrary	arbitrary	ADJ
cana-5358	100	19	index	index	NOUN
cana-5358	100	20	set	set	VERB
cana-5358	100	21	then	then	ADV
cana-5358	100	22	𝜏	𝜏	NOUN
cana-5358	100	23	is	be	AUX
cana-5358	100	24	called	call	VERB
cana-5358	100	25	a	a	DET
cana-5358	100	26	fermatean	fermatean	ADJ
cana-5358	100	27	fuzzy	fuzzy	ADJ
cana-5358	100	28	topology	topology	NOUN
cana-5358	100	29	on	on	ADP
cana-5358	100	30	𝑋.	𝑋.	PROPN
cana-5358	100	31	the	the	DET
cana-5358	100	32	pair	pair	NOUN
cana-5358	100	33	(	(	PUNCT
cana-5358	100	34	𝑋	𝑋	PROPN
cana-5358	100	35	,	,	PUNCT
cana-5358	100	36	𝜏	𝜏	NOUN
cana-5358	100	37	)	)	PUNCT
cana-5358	100	38	is	be	AUX
cana-5358	100	39	said	say	VERB
cana-5358	100	40	to	to	PART
cana-5358	100	41	be	be	AUX
cana-5358	100	42	a	a	DET
cana-5358	100	43	fermatean	fermatean	ADJ
cana-5358	100	44	fuzzy	fuzzy	ADJ
cana-5358	100	45	topological	topological	ADJ
cana-5358	100	46	space	space	NOUN
cana-5358	100	47	.	.	PUNCT
cana-5358	101	1	each	each	DET
cana-5358	101	2	member	member	NOUN
cana-5358	101	3	of	of	ADP
cana-5358	101	4	𝜏	𝜏	PROPN
cana-5358	101	5	is	be	AUX
cana-5358	101	6	called	call	VERB
cana-5358	101	7	an	an	DET
cana-5358	101	8	fermatean	fermatean	ADJ
cana-5358	101	9	fuzzy	fuzzy	ADJ
cana-5358	101	10	oprn	oprn	NOUN
cana-5358	101	11	set	set	VERB
cana-5358	101	12	.	.	PUNCT
cana-5358	102	1	the	the	DET
cana-5358	102	2	complement	complement	NOUN
cana-5358	102	3	of	of	ADP
cana-5358	102	4	an	an	DET
cana-5358	102	5	fermatean	fermatean	ADJ
cana-5358	102	6	fuzzy	fuzzy	ADJ
cana-5358	102	7	open	open	ADJ
cana-5358	102	8	set	set	NOUN
cana-5358	102	9	is	be	AUX
cana-5358	102	10	called	call	VERB
cana-5358	102	11	a	a	DET
cana-5358	102	12	fermatean	fermatean	ADJ
cana-5358	102	13	fuzzy	fuzzy	NOUN
cana-5358	102	14	closed	close	VERB
cana-5358	102	15	set	set	NOUN
cana-5358	102	16	.	.	PUNCT
cana-5358	103	1	remark	remark	VERB
cana-5358	103	2	2.2	2.2	NUM
cana-5358	104	1	[	[	SYM
cana-5358	104	2	8	8	NUM
cana-5358	104	3	]	]	PUNCT
cana-5358	104	4	as	as	SCONJ
cana-5358	104	5	any	any	DET
cana-5358	104	6	intuitionistic	intuitionistic	ADJ
cana-5358	104	7	fuzzy	fuzzy	ADJ
cana-5358	104	8	subset	subset	NOUN
cana-5358	104	9	or	or	CCONJ
cana-5358	104	10	phythagorean	phythagorean	ADJ
cana-5358	104	11	fuzzy	fuzzy	ADJ
cana-5358	104	12	subset	subset	NOUN
cana-5358	104	13	of	of	ADP
cana-5358	104	14	a	a	DET
cana-5358	104	15	set	set	NOUN
cana-5358	104	16	can	can	AUX
cana-5358	104	17	be	be	AUX
cana-5358	104	18	considered	consider	VERB
cana-5358	104	19	as	as	SCONJ
cana-5358	104	20	fermatean	fermatean	ADJ
cana-5358	104	21	fuzzy	fuzzy	ADJ
cana-5358	104	22	subset	subset	NOUN
cana-5358	104	23	,	,	PUNCT
cana-5358	104	24	we	we	PRON
cana-5358	104	25	observe	observe	VERB
cana-5358	104	26	that	that	SCONJ
cana-5358	104	27	any	any	DET
cana-5358	104	28	intuitionstic	intuitionstic	ADJ
cana-5358	104	29	fuzzy	fuzzy	ADJ
cana-5358	104	30	topological	topological	ADJ
cana-5358	104	31	space	space	NOUN
cana-5358	104	32	or	or	CCONJ
cana-5358	104	33	phythagorean	phythagorean	ADJ
cana-5358	104	34	fuzzy	fuzzy	ADJ
cana-5358	104	35	topological	topological	ADJ
cana-5358	104	36	space	space	NOUN
cana-5358	104	37	is	be	AUX
cana-5358	104	38	a	a	DET
cana-5358	104	39	fermatean	fermatean	ADJ
cana-5358	104	40	fuzzy	fuzzy	ADJ
cana-5358	104	41	topological	topological	ADJ
cana-5358	104	42	space	space	NOUN
cana-5358	104	43	as	as	ADV
cana-5358	104	44	well	well	ADV
cana-5358	104	45	.	.	PUNCT
cana-5358	105	1	on	on	ADP
cana-5358	105	2	the	the	DET
cana-5358	105	3	other	other	ADJ
cana-5358	105	4	hand	hand	NOUN
cana-5358	105	5	,	,	PUNCT
cana-5358	105	6	it	it	PRON
cana-5358	105	7	is	be	AUX
cana-5358	105	8	obvious	obvious	ADJ
cana-5358	105	9	that	that	SCONJ
cana-5358	105	10	a	a	DET
cana-5358	105	11	fermatean	fermatean	ADJ
cana-5358	105	12	fuzzy	fuzzy	ADJ
cana-5358	105	13	topological	topological	ADJ
cana-5358	105	14	space	space	NOUN
cana-5358	105	15	need	need	AUX
cana-5358	105	16	not	not	PART
cana-5358	105	17	be	be	AUX
cana-5358	105	18	intuitionistic	intuitionistic	ADJ
cana-5358	105	19	fuzzy	fuzzy	ADJ
cana-5358	105	20	topological	topological	ADJ
cana-5358	105	21	space	space	NOUN
cana-5358	105	22	and	and	CCONJ
cana-5358	105	23	phythagorean	phythagorean	ADJ
cana-5358	105	24	fuzzy	fuzzy	ADJ
cana-5358	105	25	topological	topological	ADJ
cana-5358	105	26	space	space	NOUN
cana-5358	105	27	.	.	PUNCT
cana-5358	106	1	even	even	ADV
cana-5358	106	2	an	an	DET
cana-5358	106	3	fermatean	fermatean	ADJ
cana-5358	106	4	fuzzy	fuzzy	ADJ
cana-5358	106	5	open	open	NOUN
cana-5358	106	6	set	set	VERB
cana-5358	106	7	maybe	maybe	ADV
cana-5358	106	8	neither	neither	CCONJ
cana-5358	106	9	an	an	DET
cana-5358	106	10	intuitionistic	intuitionistic	ADJ
cana-5358	106	11	fuzzy	fuzzy	ADJ
cana-5358	106	12	set	set	NOUN
cana-5358	106	13	nor	nor	CCONJ
cana-5358	106	14	phythagorean	phythagorean	ADJ
cana-5358	106	15	fuzzy	fuzzy	ADJ
cana-5358	106	16	set	set	NOUN
cana-5358	106	17	.	.	PUNCT
cana-5358	107	1	example	example	NOUN
cana-5358	107	2	2.2	2.2	NUM
cana-5358	108	1	[	[	SYM
cana-5358	108	2	8	8	NUM
cana-5358	108	3	]	]	PUNCT
cana-5358	108	4	let	let	VERB
cana-5358	108	5	𝑋	𝑋	PROPN
cana-5358	108	6	=	=	SYM
cana-5358	108	7	{	{	PUNCT
cana-5358	108	8	𝑐1	𝑐1	NOUN
cana-5358	108	9	,	,	PUNCT
cana-5358	108	10	𝑐2	𝑐2	NOUN
cana-5358	108	11	}	}	PUNCT
cana-5358	108	12	.	.	PUNCT
cana-5358	109	1	consider	consider	VERB
cana-5358	109	2	the	the	DET
cana-5358	109	3	following	follow	VERB
cana-5358	109	4	family	family	NOUN
cana-5358	109	5	fermatean	fermatean	NOUN
cana-5358	109	6	fuzzy	fuzzy	ADJ
cana-5358	109	7	subsets	subset	NOUN
cana-5358	109	8	𝜏	𝜏	X
cana-5358	109	9	=	=	PUNCT
cana-5358	109	10	{	{	PUNCT
cana-5358	109	11	1𝔉	1𝔉	NOUN
cana-5358	109	12	,	,	PUNCT
cana-5358	109	13	0𝔉	0𝔉	PROPN
cana-5358	109	14	,	,	PUNCT
cana-5358	109	15	𝐹1	𝐹1	PROPN
cana-5358	109	16	,	,	PUNCT
cana-5358	109	17	𝐹2	𝐹2	NOUN
cana-5358	109	18	}	}	PUNCT
cana-5358	109	19	where	where	SCONJ
cana-5358	109	20	communications	communication	NOUN
cana-5358	109	21	on	on	ADP
cana-5358	109	22	applied	apply	VERB
cana-5358	109	23	nonlinear	nonlinear	ADJ
cana-5358	109	24	analysis	analysis	NOUN
cana-5358	109	25	issn	issn	NOUN
cana-5358	109	26	:	:	PUNCT
cana-5358	109	27	1074	1074	NUM
cana-5358	109	28	-	-	PUNCT
cana-5358	109	29	133x	133x	NUM
cana-5358	109	30	vol	vol	VERB
cana-5358	109	31	32	32	NUM
cana-5358	109	32	no	no	NOUN
cana-5358	109	33	.	.	PUNCT
cana-5358	110	1	10s	10	NOUN
cana-5358	110	2	(	(	PUNCT
cana-5358	110	3	2025	2025	NUM
cana-5358	110	4	)	)	PUNCT
cana-5358	110	5	1899	1899	NUM
cana-5358	111	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	111	2	𝐹1	𝐹1	PROPN
cana-5358	111	3	=	=	PUNCT
cana-5358	111	4	{	{	PUNCT
cana-5358	111	5	〈	〈	NOUN
cana-5358	111	6	𝑐1	𝑐1	NOUN
cana-5358	111	7	,	,	PUNCT
cana-5358	111	8	𝛼𝐹1	𝛼𝐹1	PROPN
cana-5358	111	9	(	(	PUNCT
cana-5358	111	10	𝑐1	𝑐1	NOUN
cana-5358	111	11	)	)	PUNCT
cana-5358	111	12	=	=	SYM
cana-5358	111	13	0.4	0.4	NUM
cana-5358	111	14	,	,	PUNCT
cana-5358	111	15	𝛽𝐹1	𝛽𝐹1	PROPN
cana-5358	111	16	(	(	PUNCT
cana-5358	111	17	𝑐1	𝑐1	NOUN
cana-5358	111	18	)	)	PUNCT
cana-5358	111	19	=	=	SYM
cana-5358	111	20	0.6	0.6	NUM
cana-5358	111	21	〉	〉	NOUN
cana-5358	111	22	,	,	PUNCT
cana-5358	111	23	〈	〈	NOUN
cana-5358	111	24	𝑐2	𝑐2	NOUN
cana-5358	111	25	,	,	PUNCT
cana-5358	111	26	𝛼𝐹1	𝛼𝐹1	PROPN
cana-5358	111	27	(	(	PUNCT
cana-5358	111	28	𝑐2	𝑐2	NOUN
cana-5358	111	29	)	)	PUNCT
cana-5358	111	30	=	=	SYM
cana-5358	111	31	0.1	0.1	NUM
cana-5358	111	32	,	,	PUNCT
cana-5358	111	33	𝛽𝐹1	𝛽𝐹1	PROPN
cana-5358	111	34	(	(	PUNCT
cana-5358	111	35	𝑐2	𝑐2	NOUN
cana-5358	111	36	)	)	PUNCT
cana-5358	111	37	=	=	PUNCT
cana-5358	111	38	0.3	0.3	NUM
cana-5358	111	39	〉	〉	NOUN
cana-5358	111	40	}	}	PUNCT
cana-5358	111	41	and	and	CCONJ
cana-5358	111	42	𝐹2	𝐹2	NOUN
cana-5358	111	43	=	=	SYM
cana-5358	111	44	{	{	PUNCT
cana-5358	111	45	〈	〈	NOUN
cana-5358	111	46	𝑐1	𝑐1	NOUN
cana-5358	111	47	,	,	PUNCT
cana-5358	111	48	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5358	111	49	(	(	PUNCT
cana-5358	111	50	𝑐1	𝑐1	NOUN
cana-5358	111	51	)	)	PUNCT
cana-5358	111	52	=	=	SYM
cana-5358	111	53	0.9	0.9	NUM
cana-5358	111	54	,	,	PUNCT
cana-5358	111	55	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5358	111	56	(	(	PUNCT
cana-5358	111	57	𝑐1	𝑐1	NOUN
cana-5358	111	58	)	)	PUNCT
cana-5358	111	59	=	=	SYM
cana-5358	111	60	0.6	0.6	NUM
cana-5358	111	61	〉	〉	NOUN
cana-5358	111	62	,	,	PUNCT
cana-5358	111	63	〈	〈	NOUN
cana-5358	111	64	𝑐2	𝑐2	NOUN
cana-5358	111	65	,	,	PUNCT
cana-5358	111	66	𝛼𝐹2	𝛼𝐹2	PROPN
cana-5358	111	67	(	(	PUNCT
cana-5358	111	68	𝑐2	𝑐2	NOUN
cana-5358	111	69	)	)	PUNCT
cana-5358	111	70	=	=	SYM
cana-5358	111	71	0.2	0.2	NUM
cana-5358	111	72	,	,	PUNCT
cana-5358	111	73	𝛽𝐹2	𝛽𝐹2	PROPN
cana-5358	111	74	(	(	PUNCT
cana-5358	111	75	𝑐2	𝑐2	PROPN
cana-5358	111	76	)	)	PUNCT
cana-5358	111	77	=	=	PUNCT
cana-5358	111	78	0.3	0.3	NUM
cana-5358	111	79	〉	〉	NOUN
cana-5358	111	80	}	}	PUNCT
cana-5358	111	81	.	.	PUNCT
cana-5358	112	1	observe	observe	VERB
cana-5358	112	2	that	that	SCONJ
cana-5358	112	3	(	(	PUNCT
cana-5358	112	4	𝑋	𝑋	PROPN
cana-5358	112	5	,	,	PUNCT
cana-5358	112	6	𝜏	𝜏	NOUN
cana-5358	112	7	)	)	PUNCT
cana-5358	112	8	is	be	AUX
cana-5358	112	9	a	a	DET
cana-5358	112	10	fermatean	fermatean	ADJ
cana-5358	112	11	fuzzy	fuzzy	ADJ
cana-5358	112	12	topological	topological	ADJ
cana-5358	112	13	space	space	NOUN
cana-5358	112	14	but	but	CCONJ
cana-5358	112	15	(	(	PUNCT
cana-5358	112	16	𝑋	𝑋	PROPN
cana-5358	112	17	,	,	PUNCT
cana-5358	112	18	𝜏	𝜏	NOUN
cana-5358	112	19	)	)	PUNCT
cana-5358	112	20	is	be	AUX
cana-5358	112	21	neither	neither	CCONJ
cana-5358	112	22	intuitionistic	intuitionistic	ADJ
cana-5358	112	23	fuzzy	fuzzy	ADJ
cana-5358	112	24	topological	topological	ADJ
cana-5358	112	25	space	space	NOUN
cana-5358	112	26	nor	nor	CCONJ
cana-5358	112	27	phythagorean	phythagorean	ADJ
cana-5358	112	28	fuzzy	fuzzy	ADJ
cana-5358	112	29	topological	topological	ADJ
cana-5358	112	30	space	space	NOUN
cana-5358	112	31	.	.	PUNCT
cana-5358	113	1	definition	definition	NOUN
cana-5358	113	2	2.8	2.8	NUM
cana-5358	113	3	[	[	NOUN
cana-5358	113	4	8	8	NUM
cana-5358	113	5	]	]	X
cana-5358	113	6	let	let	NOUN
cana-5358	113	7	(	(	PUNCT
cana-5358	113	8	𝑋	𝑋	NOUN
cana-5358	113	9	,	,	PUNCT
cana-5358	113	10	𝜏	𝜏	NOUN
cana-5358	113	11	)	)	PUNCT
cana-5358	113	12	be	be	VERB
cana-5358	113	13	an	an	DET
cana-5358	113	14	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5358	113	15	and	and	CCONJ
cana-5358	113	16	𝐴	𝐴	PROPN
cana-5358	113	17	=	=	PUNCT
cana-5358	113	18	{	{	PUNCT
cana-5358	113	19	<	<	X
cana-5358	113	20	𝑎	𝑎	NOUN
cana-5358	113	21	,	,	PUNCT
cana-5358	113	22	𝛼𝐴(𝑎	𝛼𝐴(𝑎	NUM
cana-5358	113	23	)	)	PUNCT
cana-5358	113	24	,	,	PUNCT
cana-5358	113	25	𝛽𝐴(𝑎	𝛽𝐴(𝑎	NUM
cana-5358	113	26	)	)	PUNCT
cana-5358	113	27	>	>	X
cana-5358	113	28	|𝑎	|𝑎	PROPN
cana-5358	114	1	∈	∈	PROPN
cana-5358	114	2	𝑋	𝑋	PROPN
cana-5358	114	3	}	}	PUNCT
cana-5358	114	4	be	be	AUX
cana-5358	114	5	an	an	DET
cana-5358	114	6	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	114	7	in	in	ADP
cana-5358	114	8	𝑋.	𝑋.	PROPN
cana-5358	114	9	then	then	ADV
cana-5358	114	10	the	the	DET
cana-5358	114	11	fermatean	fermatean	ADJ
cana-5358	114	12	fuzzy	fuzzy	ADJ
cana-5358	114	13	interior	interior	NOUN
cana-5358	114	14	and	and	CCONJ
cana-5358	114	15	the	the	DET
cana-5358	114	16	fermatean	fermatean	ADJ
cana-5358	114	17	fuzzy	fuzzy	ADJ
cana-5358	114	18	closure	closure	NOUN
cana-5358	114	19	of	of	ADP
cana-5358	114	20	𝐴	𝐴	PROPN
cana-5358	114	21	are	be	AUX
cana-5358	114	22	denoted	denote	VERB
cana-5358	114	23	by	by	ADP
cana-5358	114	24	𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝐴	NOUN
cana-5358	114	25	)	)	PUNCT
cana-5358	114	26	and	and	CCONJ
cana-5358	114	27	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	PROPN
cana-5358	114	28	)	)	PUNCT
cana-5358	114	29	and	and	CCONJ
cana-5358	114	30	are	be	AUX
cana-5358	114	31	defined	define	VERB
cana-5358	114	32	as	as	SCONJ
cana-5358	114	33	follows	follow	VERB
cana-5358	114	34	:	:	PUNCT
cana-5358	114	35	𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝐴	NUM
cana-5358	114	36	)	)	PUNCT
cana-5358	114	37	=	=	NOUN
cana-5358	114	38	∪	∪	X
cana-5358	114	39	{	{	PUNCT
cana-5358	114	40	𝐺|𝐺	𝐺|𝐺	NOUN
cana-5358	114	41	𝑖𝑠𝑎	𝑖𝑠𝑎	NOUN
cana-5358	114	42	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5358	114	43	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5358	114	44	𝐺	𝐺	PROPN
cana-5358	114	45	⊆	⊆	NUM
cana-5358	114	46	𝐴	𝐴	PROPN
cana-5358	114	47	}	}	PUNCT
cana-5358	114	48	and	and	CCONJ
cana-5358	114	49	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	NOUN
cana-5358	114	50	)	)	PUNCT
cana-5358	115	1	=	=	NOUN
cana-5358	115	2	∩	∩	X
cana-5358	115	3	{	{	PUNCT
cana-5358	115	4	𝐾|𝐾	𝐾|𝐾	NOUN
cana-5358	115	5	𝑖𝑠𝑎	𝑖𝑠𝑎	NOUN
cana-5358	115	6	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	115	7	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-5358	115	8	𝐴	𝐴	PROPN
cana-5358	115	9	⊆	⊆	NUM
cana-5358	115	10	𝐾	𝐾	PROPN
cana-5358	115	11	}	}	PUNCT
cana-5358	115	12	.	.	PUNCT
cana-5358	116	1	also	also	ADV
cana-5358	116	2	,	,	PUNCT
cana-5358	116	3	it	it	PRON
cana-5358	116	4	can	can	AUX
cana-5358	116	5	be	be	AUX
cana-5358	116	6	established	establish	VERB
cana-5358	116	7	that	that	SCONJ
cana-5358	116	8	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	NOUN
cana-5358	116	9	)	)	PUNCT
cana-5358	116	10	is	be	AUX
cana-5358	116	11	an	an	DET
cana-5358	116	12	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	116	13	and	and	CCONJ
cana-5358	116	14	𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝐴	NUM
cana-5358	116	15	)	)	PUNCT
cana-5358	116	16	is	be	AUX
cana-5358	116	17	an	an	DET
cana-5358	116	18	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	NOUN
cana-5358	116	19	,	,	PUNCT
cana-5358	116	20	𝐴	𝐴	PROPN
cana-5358	116	21	is	be	AUX
cana-5358	116	22	an	an	DET
cana-5358	116	23	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	116	24	if	if	SCONJ
cana-5358	117	1	and	and	CCONJ
cana-5358	117	2	only	only	ADV
cana-5358	117	3	if	if	SCONJ
cana-5358	117	4	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	NOUN
cana-5358	117	5	)	)	PUNCT
cana-5358	117	6	=	=	SYM
cana-5358	117	7	𝐴	𝐴	PROPN
cana-5358	117	8	and	and	CCONJ
cana-5358	117	9	𝐴	𝐴	PROPN
cana-5358	117	10	is	be	AUX
cana-5358	117	11	an	an	DET
cana-5358	117	12	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5358	117	13	if	if	SCONJ
cana-5358	117	14	and	and	CCONJ
cana-5358	117	15	only	only	ADV
cana-5358	117	16	if	if	SCONJ
cana-5358	117	17	𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝐴	NUM
cana-5358	117	18	)	)	PUNCT
cana-5358	118	1	=	=	SYM
cana-5358	118	2	𝐴.	𝐴.	NOUN
cana-5358	118	3	we	we	PRON
cana-5358	118	4	say	say	VERB
cana-5358	118	5	that	that	SCONJ
cana-5358	118	6	𝐴	𝐴	PROPN
cana-5358	118	7	is	be	AUX
cana-5358	118	8	𝔉ℱ-dense	𝔉ℱ-dense	PROPN
cana-5358	118	9	if	if	SCONJ
cana-5358	118	10	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	PROPN
cana-5358	118	11	)	)	PUNCT
cana-5358	118	12	=	=	PUNCT
cana-5358	118	13	1𝔉.	1𝔉.	NUM
cana-5358	118	14	lemma	lemma	PROPN
cana-5358	118	15	2.1	2.1	NUM
cana-5358	118	16	[	[	NOUN
cana-5358	118	17	8	8	NUM
cana-5358	118	18	]	]	PUNCT
cana-5358	118	19	for	for	ADP
cana-5358	118	20	any	any	DET
cana-5358	118	21	fermatean	fermatean	ADJ
cana-5358	118	22	fuzzy	fuzzy	NOUN
cana-5358	118	23	set	set	VERB
cana-5358	118	24	𝐴	𝐴	PROPN
cana-5358	118	25	in	in	ADP
cana-5358	118	26	(	(	PUNCT
cana-5358	118	27	𝑋	𝑋	PROPN
cana-5358	118	28	,	,	PUNCT
cana-5358	118	29	𝜏	𝜏	NOUN
cana-5358	118	30	)	)	PUNCT
cana-5358	118	31	,	,	PUNCT
cana-5358	118	32	we	we	PRON
cana-5358	118	33	have	have	VERB
cana-5358	118	34	1𝔉	1𝔉	NOUN
cana-5358	118	35	−	−	PROPN
cana-5358	118	36	𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝐴	NUM
cana-5358	118	37	)	)	PUNCT
cana-5358	118	38	=	=	SYM
cana-5358	118	39	𝔉ℱ𝑐𝑙(1𝔉	𝔉ℱ𝑐𝑙(1𝔉	ADP
cana-5358	118	40	−	−	PROPN
cana-5358	118	41	𝐴	𝐴	PROPN
cana-5358	118	42	)	)	PUNCT
cana-5358	118	43	and	and	CCONJ
cana-5358	118	44	1𝔉	1𝔉	NOUN
cana-5358	118	45	−	−	PROPN
cana-5358	118	46	𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝐴	PROPN
cana-5358	118	47	)	)	PUNCT
cana-5358	118	48	=	=	PUNCT
cana-5358	118	49	𝔉ℱ𝑖𝑛𝑡(1𝔉	𝔉ℱ𝑖𝑛𝑡(1𝔉	PROPN
cana-5358	118	50	−	−	PROPN
cana-5358	118	51	𝐴	𝐴	PROPN
cana-5358	118	52	)	)	PUNCT
cana-5358	118	53	.	.	PUNCT
cana-5358	119	1	definition	definition	NOUN
cana-5358	119	2	2.9	2.9	NUM
cana-5358	120	1	[	[	X
cana-5358	120	2	11	11	NUM
cana-5358	120	3	]	]	X
cana-5358	120	4	let	let	VERB
cana-5358	120	5	(	(	PUNCT
cana-5358	120	6	𝑋	𝑋	NOUN
cana-5358	120	7	,	,	PUNCT
cana-5358	120	8	𝜏	𝜏	NOUN
cana-5358	120	9	)	)	PUNCT
cana-5358	120	10	be	be	VERB
cana-5358	120	11	an	an	DET
cana-5358	120	12	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5358	120	13	and	and	CCONJ
cana-5358	120	14	𝐴	𝐴	PROPN
cana-5358	120	15	be	be	VERB
cana-5358	120	16	an	an	DET
cana-5358	120	17	𝔉ℱ𝑠.	𝔉ℱ𝑠.	PROPN
cana-5358	120	18	then	then	ADV
cana-5358	120	19	𝐴	𝐴	PROPN
cana-5358	120	20	is	be	AUX
cana-5358	120	21	said	say	VERB
cana-5358	120	22	to	to	PART
cana-5358	120	23	be	be	AUX
cana-5358	120	24	an	an	DET
cana-5358	120	25	fermatean	fermatean	ADJ
cana-5358	120	26	fuzzy	fuzzy	NOUN
cana-5358	120	27	(	(	PUNCT
cana-5358	120	28	i	i	NOUN
cana-5358	120	29	)	)	PUNCT
cana-5358	120	30	regular	regular	ADJ
cana-5358	120	31	open	open	ADJ
cana-5358	120	32	set	set	NOUN
cana-5358	120	33	(	(	PUNCT
cana-5358	120	34	𝔉ℱ𝑟𝑜𝑠	𝔉ℱ𝑟𝑜𝑠	PROPN
cana-5358	120	35	in	in	ADP
cana-5358	120	36	short	short	ADJ
cana-5358	120	37	)	)	PUNCT
cana-5358	121	1	if	if	SCONJ
cana-5358	121	2	𝐴	𝐴	PROPN
cana-5358	121	3	=	=	PUNCT
cana-5358	121	4	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝑐𝑙(𝐴	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝑐𝑙(𝐴	PROPN
cana-5358	121	5	)	)	PUNCT
cana-5358	121	6	)	)	PUNCT
cana-5358	121	7	.	.	PUNCT
cana-5358	122	1	(	(	PUNCT
cana-5358	122	2	ii	ii	NOUN
cana-5358	122	3	)	)	PUNCT
cana-5358	122	4	regular	regular	ADJ
cana-5358	122	5	closed	close	VERB
cana-5358	122	6	set	set	NOUN
cana-5358	122	7	(	(	PUNCT
cana-5358	122	8	𝔉ℱ𝑟𝑐𝑠	𝔉ℱ𝑟𝑐𝑠	PROPN
cana-5358	122	9	in	in	ADP
cana-5358	122	10	short	short	ADJ
cana-5358	122	11	)	)	PUNCT
cana-5358	122	12	if	if	SCONJ
cana-5358	122	13	𝐴	𝐴	PROPN
cana-5358	122	14	=	=	SYM
cana-5358	122	15	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(𝐴	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(𝐴	NOUN
cana-5358	122	16	)	)	PUNCT
cana-5358	122	17	)	)	PUNCT
cana-5358	122	18	.	.	PUNCT
cana-5358	123	1	by	by	ADP
cana-5358	123	2	lemma	lemma	PROPN
cana-5358	123	3	2.1	2.1	NUM
cana-5358	123	4	,	,	PUNCT
cana-5358	123	5	it	it	PRON
cana-5358	123	6	follows	follow	VERB
cana-5358	123	7	that	that	SCONJ
cana-5358	123	8	𝐴	𝐴	PROPN
cana-5358	123	9	is	be	AUX
cana-5358	123	10	an	an	DET
cana-5358	123	11	𝔉ℱ𝑟𝑜𝑠	𝔉ℱ𝑟𝑜𝑠	PROPN
cana-5358	123	12	iff	iff	PROPN
cana-5358	123	13	𝐴̅	𝐴̅	PROPN
cana-5358	123	14	is	be	AUX
cana-5358	123	15	an	an	DET
cana-5358	123	16	𝔉ℱ𝑟𝑐𝑠.	𝔉ℱ𝑟𝑐𝑠.	ADJ
cana-5358	123	17	definition	definition	NOUN
cana-5358	123	18	2.10	2.10	NUM
cana-5358	123	19	[	[	X
cana-5358	123	20	11	11	NUM
cana-5358	123	21	]	]	X
cana-5358	123	22	let	let	VERB
cana-5358	123	23	(	(	PUNCT
cana-5358	123	24	𝑋	𝑋	NOUN
cana-5358	123	25	,	,	PUNCT
cana-5358	123	26	𝜏	𝜏	NOUN
cana-5358	123	27	)	)	PUNCT
cana-5358	123	28	be	be	VERB
cana-5358	123	29	an	an	DET
cana-5358	123	30	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5358	123	31	and	and	CCONJ
cana-5358	123	32	𝐴	𝐴	PROPN
cana-5358	123	33	=	=	PUNCT
cana-5358	123	34	{	{	PUNCT
cana-5358	123	35	<	<	X
cana-5358	123	36	𝑎	𝑎	NOUN
cana-5358	123	37	,	,	PUNCT
cana-5358	123	38	𝛼𝐴(𝑎	𝛼𝐴(𝑎	NUM
cana-5358	123	39	)	)	PUNCT
cana-5358	123	40	,	,	PUNCT
cana-5358	123	41	𝛽𝐴(𝑎	𝛽𝐴(𝑎	NUM
cana-5358	123	42	)	)	PUNCT
cana-5358	123	43	>	>	X
cana-5358	123	44	|𝑎	|𝑎	PROPN
cana-5358	124	1	∈	∈	PROPN
cana-5358	124	2	𝑋	𝑋	PROPN
cana-5358	124	3	}	}	PUNCT
cana-5358	124	4	be	be	AUX
cana-5358	124	5	an	an	DET
cana-5358	124	6	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	124	7	in	in	ADP
cana-5358	124	8	𝑋.	𝑋.	PROPN
cana-5358	124	9	then	then	ADV
cana-5358	124	10	the	the	DET
cana-5358	124	11	𝛿-interior	𝛿-interior	PROPN
cana-5358	124	12	and	and	CCONJ
cana-5358	124	13	the	the	DET
cana-5358	124	14	𝛿-closure	𝛿-closure	NOUN
cana-5358	124	15	of	of	ADP
cana-5358	124	16	𝐴	𝐴	PROPN
cana-5358	124	17	are	be	AUX
cana-5358	124	18	denoted	denote	VERB
cana-5358	124	19	by	by	ADP
cana-5358	124	20	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	NUM
cana-5358	124	21	)	)	PUNCT
cana-5358	124	22	and	and	CCONJ
cana-5358	124	23	𝔉ℱ𝛿𝑐𝑙(𝐴	𝔉ℱ𝛿𝑐𝑙(𝐴	NUM
cana-5358	124	24	)	)	PUNCT
cana-5358	124	25	and	and	CCONJ
cana-5358	124	26	are	be	AUX
cana-5358	124	27	defined	define	VERB
cana-5358	124	28	as	as	ADP
cana-5358	124	29	follows	follow	VERB
cana-5358	124	30	.	.	PUNCT
cana-5358	125	1	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	X
cana-5358	125	2	)	)	PUNCT
cana-5358	125	3	=	=	NOUN
cana-5358	125	4	∪	∪	X
cana-5358	125	5	{	{	PUNCT
cana-5358	125	6	𝐺|𝐺	𝐺|𝐺	PROPN
cana-5358	125	7	is	be	AUX
cana-5358	125	8	an	an	DET
cana-5358	125	9	𝔉ℱ𝑟𝑜𝑠	𝔉ℱ𝑟𝑜𝑠	PROPN
cana-5358	125	10	and	and	CCONJ
cana-5358	125	11	𝐺	𝐺	PROPN
cana-5358	125	12	⊆	⊆	NUM
cana-5358	125	13	𝐴	𝐴	PROPN
cana-5358	125	14	}	}	PUNCT
cana-5358	125	15	,	,	PUNCT
cana-5358	125	16	𝔉ℱ𝛿𝑐𝑙(𝐴	𝔉ℱ𝛿𝑐𝑙(𝐴	NOUN
cana-5358	125	17	)	)	PUNCT
cana-5358	125	18	=	=	NOUN
cana-5358	125	19	∩	∩	NOUN
cana-5358	125	20	{	{	PUNCT
cana-5358	125	21	𝐾|𝐾	𝐾|𝐾	NOUN
cana-5358	125	22	is	be	AUX
cana-5358	125	23	an	an	DET
cana-5358	125	24	𝔉ℱ𝑟𝑐𝑠	𝔉ℱ𝑟𝑐𝑠	PROPN
cana-5358	125	25	and	and	CCONJ
cana-5358	125	26	𝐴	𝐴	PROPN
cana-5358	125	27	⊆	⊆	NUM
cana-5358	125	28	𝐾	𝐾	PROPN
cana-5358	125	29	}	}	PUNCT
cana-5358	125	30	.	.	PUNCT
cana-5358	126	1	definition	definition	NOUN
cana-5358	126	2	2.11	2.11	NUM
cana-5358	126	3	[	[	X
cana-5358	126	4	11	11	NUM
cana-5358	126	5	]	]	X
cana-5358	126	6	let	let	VERB
cana-5358	126	7	(	(	PUNCT
cana-5358	126	8	𝑋	𝑋	NOUN
cana-5358	126	9	,	,	PUNCT
cana-5358	126	10	𝜏	𝜏	NOUN
cana-5358	126	11	)	)	PUNCT
cana-5358	126	12	be	be	VERB
cana-5358	126	13	an	an	DET
cana-5358	126	14	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5358	126	15	and	and	CCONJ
cana-5358	126	16	𝐴	𝐴	PROPN
cana-5358	126	17	=	=	PUNCT
cana-5358	126	18	{	{	PUNCT
cana-5358	126	19	<	<	X
cana-5358	126	20	𝑎	𝑎	NOUN
cana-5358	126	21	,	,	PUNCT
cana-5358	126	22	𝛼𝐴(𝑎	𝛼𝐴(𝑎	NUM
cana-5358	126	23	)	)	PUNCT
cana-5358	126	24	,	,	PUNCT
cana-5358	126	25	𝛽𝐴(𝑎	𝛽𝐴(𝑎	NUM
cana-5358	126	26	)	)	PUNCT
cana-5358	126	27	>	>	X
cana-5358	126	28	|𝑎	|𝑎	PROPN
cana-5358	127	1	∈	∈	PROPN
cana-5358	127	2	𝑋	𝑋	PROPN
cana-5358	127	3	}	}	PUNCT
cana-5358	127	4	be	be	AUX
cana-5358	127	5	an	an	DET
cana-5358	127	6	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	127	7	in	in	ADP
cana-5358	127	8	𝑋.	𝑋.	PROPN
cana-5358	127	9	a	a	DET
cana-5358	127	10	set	set	ADJ
cana-5358	127	11	𝐴	𝐴	PROPN
cana-5358	127	12	is	be	AUX
cana-5358	127	13	said	say	VERB
cana-5358	127	14	to	to	PART
cana-5358	127	15	be	be	AUX
cana-5358	127	16	𝔉ℱ	𝔉ℱ	PROPN
cana-5358	127	17	1	1	NUM
cana-5358	127	18	.	.	PUNCT
cana-5358	127	19	𝛿-open	𝛿-open	VERB
cana-5358	127	20	set	set	NOUN
cana-5358	127	21	(	(	PUNCT
cana-5358	127	22	briefly	briefly	ADV
cana-5358	127	23	,	,	PUNCT
cana-5358	127	24	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5358	127	25	)	)	PUNCT
cana-5358	128	1	if	if	SCONJ
cana-5358	128	2	𝐴	𝐴	PROPN
cana-5358	128	3	=	=	PUNCT
cana-5358	128	4	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	NUM
cana-5358	128	5	)	)	PUNCT
cana-5358	128	6	,	,	PUNCT
cana-5358	128	7	2	2	X
cana-5358	128	8	.	.	X
cana-5358	128	9	𝛿-pre	𝛿-pre	PROPN
cana-5358	128	10	open	open	ADJ
cana-5358	128	11	set	set	PROPN
cana-5358	128	12	(	(	PUNCT
cana-5358	128	13	briefly	briefly	ADV
cana-5358	128	14	,	,	PUNCT
cana-5358	128	15	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5358	128	16	)	)	PUNCT
cana-5358	128	17	if	if	SCONJ
cana-5358	128	18	𝐴	𝐴	PROPN
cana-5358	128	19	⊆	⊆	NUM
cana-5358	128	20	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝛿𝑐𝑙(𝐴	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝛿𝑐𝑙(𝐴	NOUN
cana-5358	128	21	)	)	PUNCT
cana-5358	128	22	)	)	PUNCT
cana-5358	128	23	.	.	PUNCT
cana-5358	129	1	3	3	X
cana-5358	129	2	.	.	X
cana-5358	129	3	𝛿-semi	𝛿-semi	PROPN
cana-5358	129	4	open	open	ADJ
cana-5358	129	5	set	set	NOUN
cana-5358	129	6	(	(	PUNCT
cana-5358	129	7	briefly	briefly	ADV
cana-5358	129	8	,	,	PUNCT
cana-5358	129	9	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5358	129	10	)	)	PUNCT
cana-5358	129	11	if	if	SCONJ
cana-5358	129	12	𝐴	𝐴	PROPN
cana-5358	129	13	⊆	⊆	NUM
cana-5358	129	14	𝔉ℱ𝑐𝑙(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	𝔉ℱ𝑐𝑙(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	NUM
cana-5358	129	15	)	)	PUNCT
cana-5358	129	16	)	)	PUNCT
cana-5358	129	17	.	.	PUNCT
cana-5358	130	1	4	4	X
cana-5358	130	2	.	.	X
cana-5358	130	3	𝛿	𝛿	DET
cana-5358	130	4	𝛼	𝛼	PRON
cana-5358	130	5	open	open	ADJ
cana-5358	130	6	set	set	NOUN
cana-5358	130	7	or	or	CCONJ
cana-5358	130	8	𝑎	𝑎	PRON
cana-5358	130	9	-open	-open	NOUN
cana-5358	130	10	set	set	NOUN
cana-5358	130	11	(	(	PUNCT
cana-5358	130	12	briefly	briefly	ADV
cana-5358	130	13	,	,	PUNCT
cana-5358	130	14	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5358	130	15	or	or	CCONJ
cana-5358	130	16	𝔉ℱ𝑎𝑜𝑠	𝔉ℱ𝑎𝑜𝑠	PROPN
cana-5358	130	17	)	)	PUNCT
cana-5358	131	1	if	if	SCONJ
cana-5358	131	2	𝐴	𝐴	PROPN
cana-5358	131	3	⊆	⊆	NUM
cana-5358	131	4	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝑐𝑙(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝑐𝑙(𝔉ℱ𝛿𝑖𝑛𝑡(𝐴	PROPN
cana-5358	131	5	)	)	PUNCT
cana-5358	131	6	)	)	PUNCT
cana-5358	131	7	)	)	PUNCT
cana-5358	131	8	.	.	PUNCT
cana-5358	132	1	5	5	X
cana-5358	132	2	.	.	X
cana-5358	132	3	𝛿	𝛿	DET
cana-5358	132	4	𝛽	𝛽	PROPN
cana-5358	132	5	open	open	ADJ
cana-5358	132	6	set	set	NOUN
cana-5358	132	7	or	or	CCONJ
cana-5358	132	8	𝑒∗	𝑒∗	PROPN
cana-5358	132	9	-open	-open	ADJ
cana-5358	132	10	set	set	NOUN
cana-5358	132	11	(	(	PUNCT
cana-5358	132	12	briefly	briefly	ADV
cana-5358	132	13	,	,	PUNCT
cana-5358	132	14	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5358	132	15	or	or	CCONJ
cana-5358	132	16	𝔉ℱ𝑒∗𝑜𝑠	𝔉ℱ𝑒∗𝑜𝑠	NOUN
cana-5358	132	17	)	)	PUNCT
cana-5358	132	18	if	if	SCONJ
cana-5358	132	19	𝐴	𝐴	PROPN
cana-5358	132	20	⊆	⊆	NUM
cana-5358	132	21	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝛿𝑐𝑙(𝐴	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(𝔉ℱ𝛿𝑐𝑙(𝐴	NOUN
cana-5358	132	22	)	)	PUNCT
cana-5358	132	23	)	)	PUNCT
cana-5358	132	24	)	)	PUNCT
cana-5358	132	25	.	.	PUNCT
cana-5358	133	1	6	6	X
cana-5358	133	2	.	.	X
cana-5358	134	1	𝛿	𝛿	ADJ
cana-5358	134	2	(	(	PUNCT
cana-5358	134	3	resp	resp	NOUN
cana-5358	134	4	.	.	PUNCT
cana-5358	135	1	𝛿	𝛿	PRON
cana-5358	135	2	-pre	-pre	NUM
cana-5358	135	3	,	,	PUNCT
cana-5358	135	4	𝛿	𝛿	ADJ
cana-5358	135	5	-semi	-semi	NOUN
cana-5358	135	6	,	,	PUNCT
cana-5358	135	7	𝛿	𝛿	PRON
cana-5358	135	8	𝛼	𝛼	NOUN
cana-5358	135	9	and	and	CCONJ
cana-5358	135	10	𝛿	𝛿	PRON
cana-5358	135	11	𝛽	𝛽	NOUN
cana-5358	135	12	)	)	PUNCT
cana-5358	135	13	dense	dense	ADJ
cana-5358	135	14	if	if	SCONJ
cana-5358	135	15	𝔉ℱ𝛿𝑐𝑙(𝐴	𝔉ℱ𝛿𝑐𝑙(𝐴	NOUN
cana-5358	135	16	)	)	PUNCT
cana-5358	135	17	(	(	PUNCT
cana-5358	135	18	resp	resp	NOUN
cana-5358	135	19	.	.	PUNCT
cana-5358	136	1	𝔉ℱ𝛿𝑝𝑐𝑙(𝐴	𝔉ℱ𝛿𝑝𝑐𝑙(𝐴	NOUN
cana-5358	136	2	)	)	PUNCT
cana-5358	136	3	,	,	PUNCT
cana-5358	136	4	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	PROPN
cana-5358	136	5	)	)	PUNCT
cana-5358	136	6	,	,	PUNCT
cana-5358	136	7	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	NOUN
cana-5358	136	8	)	)	PUNCT
cana-5358	136	9	and	and	CCONJ
cana-5358	136	10	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	VERB
cana-5358	136	11	)	)	PUNCT
cana-5358	136	12	)	)	PUNCT
cana-5358	137	1	=	=	PRON
cana-5358	137	2	1𝔉.	1𝔉.	NUM
cana-5358	137	3	the	the	DET
cana-5358	137	4	complement	complement	NOUN
cana-5358	137	5	of	of	ADP
cana-5358	137	6	an	an	DET
cana-5358	137	7	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5358	137	8	(	(	PUNCT
cana-5358	137	9	resp	resp	NOUN
cana-5358	137	10	.	.	PUNCT
cana-5358	138	1	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5358	138	2	,	,	PUNCT
cana-5358	138	3	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5358	138	4	,	,	PUNCT
cana-5358	138	5	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5358	138	6	and	and	CCONJ
cana-5358	138	7	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5358	138	8	)	)	PUNCT
cana-5358	138	9	is	be	AUX
cana-5358	138	10	called	call	VERB
cana-5358	138	11	an	an	DET
cana-5358	138	12	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5358	138	13	(	(	PUNCT
cana-5358	138	14	resp	resp	NOUN
cana-5358	138	15	.	.	PUNCT
cana-5358	139	1	𝔉ℱ𝛿𝒫	𝔉ℱ𝛿𝒫	NOUN
cana-5358	139	2	,	,	PUNCT
cana-5358	139	3	𝔉ℱ𝛿𝒮	𝔉ℱ𝛿𝒮	PROPN
cana-5358	139	4	,	,	PUNCT
cana-5358	139	5	𝔉ℱ𝛿𝛼	𝔉ℱ𝛿𝛼	ADJ
cana-5358	139	6	and	and	CCONJ
cana-5358	139	7	𝔉ℱ𝛿𝛽	𝔉ℱ𝛿𝛽	NOUN
cana-5358	139	8	)	)	PUNCT
cana-5358	139	9	closed	closed	ADJ
cana-5358	139	10	set	set	NOUN
cana-5358	139	11	(	(	PUNCT
cana-5358	139	12	briefly	briefly	ADV
cana-5358	139	13	,	,	PUNCT
cana-5358	139	14	𝔉ℱ𝛿𝑐𝑠	𝔉ℱ𝛿𝑐𝑠	PROPN
cana-5358	139	15	(	(	PUNCT
cana-5358	139	16	resp	resp	NOUN
cana-5358	139	17	.	.	PUNCT
cana-5358	140	1	𝔉ℱ𝛿𝒫𝑐𝑠	𝔉ℱ𝛿𝒫𝑐𝑠	NOUN
cana-5358	140	2	,	,	PUNCT
cana-5358	140	3	𝔉ℱ𝛿𝒮𝑐𝑠	𝔉ℱ𝛿𝒮𝑐𝑠	NUM
cana-5358	140	4	,	,	PUNCT
cana-5358	140	5	𝔉ℱ𝛿𝛼𝑐𝑠	𝔉ℱ𝛿𝛼𝑐𝑠	PROPN
cana-5358	140	6	and	and	CCONJ
cana-5358	140	7	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	140	8	)	)	PUNCT
cana-5358	140	9	)	)	PUNCT
cana-5358	140	10	in	in	ADP
cana-5358	140	11	𝑋.	𝑋.	PROPN
cana-5358	140	12	the	the	DET
cana-5358	140	13	family	family	NOUN
cana-5358	140	14	of	of	ADP
cana-5358	140	15	all	all	DET
cana-5358	140	16	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5358	140	17	(	(	PUNCT
cana-5358	140	18	resp	resp	NOUN
cana-5358	140	19	.	.	PUNCT
cana-5358	141	1	𝔉ℱ𝛿𝑐𝑠	𝔉ℱ𝛿𝑐𝑠	PROPN
cana-5358	141	2	,	,	PUNCT
cana-5358	141	3	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5358	141	4	,	,	PUNCT
cana-5358	141	5	𝔉ℱ𝛿𝒫𝑐𝑠	𝔉ℱ𝛿𝒫𝑐𝑠	NOUN
cana-5358	141	6	,	,	PUNCT
cana-5358	141	7	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5358	141	8	,	,	PUNCT
cana-5358	141	9	𝔉ℱ𝛿𝒮𝑐𝑠	𝔉ℱ𝛿𝒮𝑐𝑠	PROPN
cana-5358	141	10	,	,	PUNCT
cana-5358	141	11	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5358	141	12	,	,	PUNCT
cana-5358	141	13	𝔉ℱ𝛿𝛼𝑐𝑠	𝔉ℱ𝛿𝛼𝑐𝑠	PROPN
cana-5358	141	14	,	,	PUNCT
cana-5358	141	15	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5358	141	16	and	and	CCONJ
cana-5358	141	17	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	PROPN
cana-5358	141	18	)	)	PUNCT
cana-5358	141	19	of	of	ADP
cana-5358	141	20	𝑋	𝑋	PROPN
cana-5358	141	21	is	be	AUX
cana-5358	141	22	denoted	denote	VERB
cana-5358	141	23	by	by	ADP
cana-5358	141	24	𝔉ℱ𝛿𝑂𝑆(𝑋	𝔉ℱ𝛿𝑂𝑆(𝑋	NOUN
cana-5358	141	25	)	)	PUNCT
cana-5358	141	26	(	(	PUNCT
cana-5358	141	27	resp	resp	NOUN
cana-5358	141	28	.	.	PUNCT
cana-5358	142	1	𝔉ℱ𝛿𝐶𝑆(𝑋	𝔉ℱ𝛿𝐶𝑆(𝑋	PROPN
cana-5358	142	2	)	)	PUNCT
cana-5358	142	3	,	,	PUNCT
cana-5358	142	4	𝔉ℱ𝛿𝒫𝑂𝑆(𝑋	𝔉ℱ𝛿𝒫𝑂𝑆(𝑋	NOUN
cana-5358	142	5	)	)	PUNCT
cana-5358	143	1	,	,	PUNCT
cana-5358	143	2	communications	communication	NOUN
cana-5358	143	3	on	on	ADP
cana-5358	143	4	applied	apply	VERB
cana-5358	143	5	nonlinear	nonlinear	ADJ
cana-5358	143	6	analysis	analysis	NOUN
cana-5358	143	7	issn	issn	NOUN
cana-5358	143	8	:	:	PUNCT
cana-5358	143	9	1074	1074	NUM
cana-5358	143	10	-	-	PUNCT
cana-5358	143	11	133x	133x	NUM
cana-5358	143	12	vol	vol	VERB
cana-5358	143	13	32	32	NUM
cana-5358	143	14	no	no	NOUN
cana-5358	143	15	.	.	PUNCT
cana-5358	144	1	10s	10	NOUN
cana-5358	144	2	(	(	PUNCT
cana-5358	144	3	2025	2025	NUM
cana-5358	144	4	)	)	PUNCT
cana-5358	144	5	1900	1900	NUM
cana-5358	144	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	144	7	𝔉ℱ𝛿𝒫𝐶𝑆(𝑋	𝔉ℱ𝛿𝒫𝐶𝑆(𝑋	PROPN
cana-5358	144	8	)	)	PUNCT
cana-5358	144	9	,	,	PUNCT
cana-5358	144	10	𝔉ℱ𝛿𝒮𝑂𝑆(𝑋	𝔉ℱ𝛿𝒮𝑂𝑆(𝑋	PROPN
cana-5358	144	11	)	)	PUNCT
cana-5358	144	12	,	,	PUNCT
cana-5358	144	13	𝔉ℱ𝛿𝒮𝐶𝑆(𝑋	𝔉ℱ𝛿𝒮𝐶𝑆(𝑋	PROPN
cana-5358	144	14	)	)	PUNCT
cana-5358	144	15	,	,	PUNCT
cana-5358	144	16	𝔉ℱ𝛿𝛼𝑂𝑆(𝑋	𝔉ℱ𝛿𝛼𝑂𝑆(𝑋	NOUN
cana-5358	144	17	)	)	PUNCT
cana-5358	144	18	,	,	PUNCT
cana-5358	144	19	𝔉ℱ𝛿𝛼𝐶𝑆(𝑋	𝔉ℱ𝛿𝛼𝐶𝑆(𝑋	NOUN
cana-5358	144	20	)	)	PUNCT
cana-5358	144	21	,	,	PUNCT
cana-5358	144	22	𝔉ℱ𝛿𝛽𝑂𝑆(𝑋	𝔉ℱ𝛿𝛽𝑂𝑆(𝑋	PROPN
cana-5358	144	23	)	)	PUNCT
cana-5358	144	24	and	and	CCONJ
cana-5358	144	25	𝔉ℱ𝛿𝛽𝐶𝑆(𝑋	𝔉ℱ𝛿𝛽𝐶𝑆(𝑋	NOUN
cana-5358	144	26	)	)	PUNCT
cana-5358	144	27	)	)	PUNCT
cana-5358	144	28	.	.	PUNCT
cana-5358	145	1	definition	definition	NOUN
cana-5358	145	2	2.12	2.12	NUM
cana-5358	145	3	[	[	X
cana-5358	145	4	11	11	NUM
cana-5358	145	5	]	]	X
cana-5358	145	6	let	let	VERB
cana-5358	145	7	(	(	PUNCT
cana-5358	145	8	𝑋	𝑋	NOUN
cana-5358	145	9	,	,	PUNCT
cana-5358	145	10	𝜏	𝜏	NOUN
cana-5358	145	11	)	)	PUNCT
cana-5358	145	12	be	be	VERB
cana-5358	145	13	an	an	DET
cana-5358	145	14	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5358	145	15	and	and	CCONJ
cana-5358	145	16	𝐴	𝐴	PROPN
cana-5358	145	17	=	=	PUNCT
cana-5358	145	18	{	{	PUNCT
cana-5358	145	19	<	<	X
cana-5358	145	20	𝑎	𝑎	NOUN
cana-5358	145	21	,	,	PUNCT
cana-5358	145	22	𝛼𝐴(𝑎	𝛼𝐴(𝑎	NUM
cana-5358	145	23	)	)	PUNCT
cana-5358	145	24	,	,	PUNCT
cana-5358	145	25	𝛽𝐴(𝑎	𝛽𝐴(𝑎	NUM
cana-5358	145	26	)	)	PUNCT
cana-5358	145	27	>	>	X
cana-5358	145	28	|𝑎	|𝑎	PROPN
cana-5358	146	1	∈	∈	PROPN
cana-5358	146	2	𝑋	𝑋	PROPN
cana-5358	146	3	}	}	PUNCT
cana-5358	146	4	be	be	AUX
cana-5358	146	5	an	an	DET
cana-5358	146	6	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	146	7	in	in	ADP
cana-5358	146	8	𝑋	𝑋	PROPN
cana-5358	146	9	.	.	PUNCT
cana-5358	147	1	then	then	ADV
cana-5358	147	2	the	the	DET
cana-5358	147	3	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5358	147	4	-pre	-pre	PUNCT
cana-5358	147	5	(	(	PUNCT
cana-5358	147	6	resp	resp	NOUN
cana-5358	147	7	.	.	PUNCT
cana-5358	148	1	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5358	148	2	-semi	-semi	PROPN
cana-5358	148	3	,	,	PUNCT
cana-5358	148	4	𝔉ℱ𝛿𝛼	𝔉ℱ𝛿𝛼	ADJ
cana-5358	148	5	and	and	CCONJ
cana-5358	148	6	𝔉ℱ𝛿𝛽	𝔉ℱ𝛿𝛽	ADJ
cana-5358	148	7	)	)	PUNCT
cana-5358	148	8	-interior	-interior	NOUN
cana-5358	148	9	and	and	CCONJ
cana-5358	148	10	the	the	DET
cana-5358	148	11	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5358	148	12	-pre	-pre	PUNCT
cana-5358	148	13	(	(	PUNCT
cana-5358	148	14	resp	resp	NOUN
cana-5358	148	15	.	.	PUNCT
cana-5358	149	1	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5358	149	2	-semi	-semi	PROPN
cana-5358	149	3	,	,	PUNCT
cana-5358	149	4	𝔉ℱ𝛿𝛼	𝔉ℱ𝛿𝛼	ADJ
cana-5358	149	5	and	and	CCONJ
cana-5358	149	6	𝔉ℱ𝛿𝛽	𝔉ℱ𝛿𝛽	ADJ
cana-5358	149	7	)	)	PUNCT
cana-5358	149	8	-closure	-closure	NOUN
cana-5358	149	9	of	of	ADP
cana-5358	149	10	𝐴	𝐴	PROPN
cana-5358	149	11	are	be	AUX
cana-5358	149	12	denoted	denote	VERB
cana-5358	149	13	by	by	ADP
cana-5358	149	14	𝔉ℱ𝛿𝒫𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝒫𝑖𝑛𝑡(𝐴	NOUN
cana-5358	149	15	)	)	PUNCT
cana-5358	149	16	(	(	PUNCT
cana-5358	149	17	resp	resp	NOUN
cana-5358	149	18	.	.	PUNCT
cana-5358	150	1	𝔉ℱ𝛿𝒮𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝒮𝑖𝑛𝑡(𝐴	ADV
cana-5358	150	2	)	)	PUNCT
cana-5358	150	3	,	,	PUNCT
cana-5358	150	4	𝔉ℱ𝛿𝛼𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝛼𝑖𝑛𝑡(𝐴	NUM
cana-5358	150	5	)	)	PUNCT
cana-5358	150	6	and	and	CCONJ
cana-5358	150	7	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(𝐴	NOUN
cana-5358	150	8	)	)	PUNCT
cana-5358	150	9	)	)	PUNCT
cana-5358	150	10	and	and	CCONJ
cana-5358	150	11	the	the	DET
cana-5358	150	12	𝔉ℱ𝛿𝒫𝑐𝑙(𝐴	𝔉ℱ𝛿𝒫𝑐𝑙(𝐴	PROPN
cana-5358	150	13	)	)	PUNCT
cana-5358	150	14	(	(	PUNCT
cana-5358	150	15	resp	resp	NOUN
cana-5358	150	16	.	.	PUNCT
cana-5358	151	1	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	NOUN
cana-5358	151	2	)	)	PUNCT
cana-5358	151	3	,	,	PUNCT
cana-5358	151	4	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	NOUN
cana-5358	151	5	)	)	PUNCT
cana-5358	151	6	and	and	CCONJ
cana-5358	151	7	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	VERB
cana-5358	151	8	)	)	PUNCT
cana-5358	151	9	)	)	PUNCT
cana-5358	152	1	and	and	CCONJ
cana-5358	152	2	are	be	AUX
cana-5358	152	3	defined	define	VERB
cana-5358	152	4	as	as	SCONJ
cana-5358	152	5	follows	follow	VERB
cana-5358	152	6	:	:	PUNCT
cana-5358	152	7	𝔉ℱ𝛿𝒫𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝒫𝑖𝑛𝑡(𝐴	X
cana-5358	152	8	)	)	PUNCT
cana-5358	152	9	(	(	PUNCT
cana-5358	152	10	resp	resp	NOUN
cana-5358	152	11	.	.	PUNCT
cana-5358	153	1	𝔉ℱ𝛿𝒮𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝒮𝑖𝑛𝑡(𝐴	X
cana-5358	153	2	)	)	PUNCT
cana-5358	153	3	,	,	PUNCT
cana-5358	153	4	𝔉ℱ𝛿𝛼𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝛼𝑖𝑛𝑡(𝐴	NOUN
cana-5358	153	5	)	)	PUNCT
cana-5358	153	6	and	and	CCONJ
cana-5358	153	7	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(𝐴	𝔉ℱ𝛿𝛽𝑖𝑛𝑡(𝐴	NOUN
cana-5358	153	8	)	)	PUNCT
cana-5358	153	9	)	)	PUNCT
cana-5358	154	1	=	=	SYM
cana-5358	154	2	∪	∪	X
cana-5358	154	3	{	{	PUNCT
cana-5358	154	4	𝐺|𝐺	𝐺|𝐺	NOUN
cana-5358	154	5	in	in	ADP
cana-5358	154	6	a	a	DET
cana-5358	154	7	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5358	154	8	(	(	PUNCT
cana-5358	154	9	resp	resp	PROPN
cana-5358	154	10	.	.	PUNCT
cana-5358	155	1	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5358	155	2	,	,	PUNCT
cana-5358	155	3	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5358	155	4	and	and	CCONJ
cana-5358	155	5	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5358	155	6	)	)	PUNCT
cana-5358	155	7	and	and	CCONJ
cana-5358	155	8	𝐺	𝐺	PROPN
cana-5358	155	9	⊆	⊆	NUM
cana-5358	155	10	𝐴	𝐴	PROPN
cana-5358	155	11	}	}	PUNCT
cana-5358	155	12	and	and	CCONJ
cana-5358	155	13	𝔉ℱ𝛿𝒫𝑐𝑙(𝐴	𝔉ℱ𝛿𝒫𝑐𝑙(𝐴	NUM
cana-5358	155	14	)	)	PUNCT
cana-5358	155	15	(	(	PUNCT
cana-5358	155	16	resp	resp	NOUN
cana-5358	155	17	.	.	PUNCT
cana-5358	156	1	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	𝔉ℱ𝛿𝒮𝑐𝑙(𝐴	NOUN
cana-5358	156	2	)	)	PUNCT
cana-5358	156	3	,	,	PUNCT
cana-5358	156	4	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	𝔉ℱ𝛿𝛼𝑐𝑙(𝐴	NOUN
cana-5358	156	5	)	)	PUNCT
cana-5358	156	6	and	and	CCONJ
cana-5358	156	7	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	𝔉ℱ𝛿𝛽𝑐𝑙(𝐴	VERB
cana-5358	156	8	)	)	PUNCT
cana-5358	156	9	)	)	PUNCT
cana-5358	157	1	=	=	NOUN
cana-5358	157	2	∩	∩	NOUN
cana-5358	157	3	{	{	PUNCT
cana-5358	157	4	𝐾|𝐾	𝐾|𝐾	NOUN
cana-5358	157	5	is	be	AUX
cana-5358	157	6	an	an	DET
cana-5358	157	7	𝔉ℱ𝛿𝒫𝑐𝑠	𝔉ℱ𝛿𝒫𝑐𝑠	NOUN
cana-5358	157	8	(	(	PUNCT
cana-5358	157	9	resp	resp	NOUN
cana-5358	157	10	.	.	PUNCT
cana-5358	158	1	𝔉ℱ𝛿𝒮𝑐𝑠	𝔉ℱ𝛿𝒮𝑐𝑠	PROPN
cana-5358	158	2	,	,	PUNCT
cana-5358	158	3	𝔉ℱ𝛿𝛼𝑐𝑠	𝔉ℱ𝛿𝛼𝑐𝑠	PROPN
cana-5358	158	4	,	,	PUNCT
cana-5358	158	5	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	158	6	)	)	PUNCT
cana-5358	158	7	and	and	CCONJ
cana-5358	158	8	𝐴	𝐴	PROPN
cana-5358	158	9	⊆	⊆	NUM
cana-5358	158	10	𝐾	𝐾	PROPN
cana-5358	158	11	}	}	PUNCT
cana-5358	158	12	.	.	PUNCT
cana-5358	159	1	3	3	NUM
cana-5358	159	2	fermatean	fermatean	NOUN
cana-5358	159	3	fuzzy	fuzzy	ADJ
cana-5358	159	4	𝜹𝜷-homeomorphism	𝜹𝜷-homeomorphism	NOUN
cana-5358	159	5	in	in	ADP
cana-5358	159	6	this	this	DET
cana-5358	159	7	section	section	NOUN
cana-5358	159	8	,	,	PUNCT
cana-5358	159	9	we	we	PRON
cana-5358	159	10	introduce	introduce	VERB
cana-5358	159	11	fermatean	fermatean	NOUN
cana-5358	159	12	fuzzy	fuzzy	ADJ
cana-5358	159	13	𝛿	𝛿	ADJ
cana-5358	159	14	(	(	PUNCT
cana-5358	159	15	resp	resp	NOUN
cana-5358	159	16	.	.	PUNCT
cana-5358	160	1	𝛿	𝛿	DET
cana-5358	160	2	pre	pre	NOUN
cana-5358	160	3	,	,	PUNCT
cana-5358	160	4	𝛿	𝛿	ADJ
cana-5358	160	5	semi	semi	ADJ
cana-5358	160	6	,	,	PUNCT
cana-5358	160	7	𝛿𝛼	𝛿𝛼	NOUN
cana-5358	160	8	and	and	CCONJ
cana-5358	160	9	𝛿𝛽)-homeomorphism	𝛿𝛽)-homeomorphism	NOUN
cana-5358	160	10	and	and	CCONJ
cana-5358	160	11	discuss	discuss	VERB
cana-5358	160	12	some	some	PRON
cana-5358	160	13	of	of	ADP
cana-5358	160	14	their	their	PRON
cana-5358	160	15	properties	property	NOUN
cana-5358	160	16	.	.	PUNCT
cana-5358	161	1	definition	definition	NOUN
cana-5358	161	2	3.1	3.1	NUM
cana-5358	161	3	let	let	NOUN
cana-5358	161	4	(	(	PUNCT
cana-5358	161	5	𝑋1	𝑋1	PROPN
cana-5358	161	6	,	,	PUNCT
cana-5358	161	7	𝜏1	𝜏1	NOUN
cana-5358	161	8	)	)	PUNCT
cana-5358	161	9	and	and	CCONJ
cana-5358	161	10	(	(	PUNCT
cana-5358	161	11	𝑋2	𝑋2	PROPN
cana-5358	161	12	,	,	PUNCT
cana-5358	161	13	𝜏2	𝜏2	PROPN
cana-5358	161	14	)	)	PUNCT
cana-5358	161	15	be	be	VERB
cana-5358	161	16	two	two	NUM
cana-5358	161	17	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5358	161	18	’s	’s	NOUN
cana-5358	161	19	.	.	PUNCT
cana-5358	162	1	then	then	ADV
cana-5358	162	2	a	a	DET
cana-5358	162	3	function	function	NOUN
cana-5358	162	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	162	5	:	:	PUNCT
cana-5358	162	6	(	(	PUNCT
cana-5358	162	7	𝑋1	𝑋1	PROPN
cana-5358	162	8	,	,	PUNCT
cana-5358	162	9	𝜏1	𝜏1	NOUN
cana-5358	162	10	)	)	PUNCT
cana-5358	162	11	→	→	SYM
cana-5358	162	12	(	(	PUNCT
cana-5358	162	13	𝑋2	𝑋2	PROPN
cana-5358	162	14	,	,	PUNCT
cana-5358	162	15	𝜏2	𝜏2	PROPN
cana-5358	162	16	)	)	PUNCT
cana-5358	162	17	is	be	AUX
cana-5358	162	18	said	say	VERB
cana-5358	162	19	to	to	PART
cana-5358	162	20	be	be	AUX
cana-5358	162	21	a	a	DET
cana-5358	162	22	fermatean	fermatean	ADJ
cana-5358	162	23	fuzzy	fuzzy	ADJ
cana-5358	162	24	𝛿	𝛿	ADJ
cana-5358	162	25	(	(	PUNCT
cana-5358	162	26	resp	resp	NOUN
cana-5358	162	27	.	.	PUNCT
cana-5358	163	1	𝛿	𝛿	DET
cana-5358	163	2	pre	pre	NOUN
cana-5358	163	3	,	,	PUNCT
cana-5358	163	4	𝛿	𝛿	ADJ
cana-5358	163	5	semi	semi	ADJ
cana-5358	163	6	,	,	PUNCT
cana-5358	163	7	𝛿𝛼	𝛿𝛼	ADP
cana-5358	163	8	and	and	CCONJ
cana-5358	163	9	𝛿𝛽	𝛿𝛽	ADJ
cana-5358	163	10	)	)	PUNCT
cana-5358	163	11	continuous	continuous	ADJ
cana-5358	163	12	(	(	PUNCT
cana-5358	163	13	briefly	briefly	ADV
cana-5358	163	14	,	,	PUNCT
cana-5358	163	15	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	PUNCT
cana-5358	163	16	(	(	PUNCT
cana-5358	163	17	resp	resp	NOUN
cana-5358	163	18	.	.	PUNCT
cana-5358	164	1	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5358	164	2	,	,	PUNCT
cana-5358	164	3	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	PROPN
cana-5358	164	4	,	,	PUNCT
cana-5358	164	5	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5358	164	6	and	and	CCONJ
cana-5358	164	7	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	NOUN
cana-5358	164	8	)	)	PUNCT
cana-5358	164	9	)	)	PUNCT
cana-5358	164	10	function	function	VERB
cana-5358	164	11	if	if	SCONJ
cana-5358	164	12	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	164	13	−1(𝐺	−1(𝐺	VERB
cana-5358	164	14	)	)	PUNCT
cana-5358	164	15	is	be	AUX
cana-5358	164	16	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5358	164	17	(	(	PUNCT
cana-5358	164	18	resp	resp	NOUN
cana-5358	164	19	.	.	PUNCT
cana-5358	165	1	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	PROPN
cana-5358	165	2	,	,	PUNCT
cana-5358	165	3	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	NUM
cana-5358	165	4	,	,	PUNCT
cana-5358	165	5	𝔉ℱ𝛿𝛼𝑜	𝔉ℱ𝛿𝛼𝑜	PROPN
cana-5358	165	6	&	&	CCONJ
cana-5358	165	7	𝔉ℱ𝛿𝛽𝑜	𝔉ℱ𝛿𝛽𝑜	PROPN
cana-5358	165	8	)	)	PUNCT
cana-5358	165	9	set	set	VERB
cana-5358	165	10	in	in	ADP
cana-5358	165	11	𝑋1	𝑋1	NOUN
cana-5358	165	12	for	for	ADP
cana-5358	165	13	all	all	DET
cana-5358	165	14	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5358	165	15	set	set	VERB
cana-5358	165	16	𝐺	𝐺	PROPN
cana-5358	165	17	in	in	ADP
cana-5358	165	18	𝑋2	𝑋2	PROPN
cana-5358	165	19	.	.	PUNCT
cana-5358	166	1	definition	definition	NOUN
cana-5358	166	2	3.2	3.2	NUM
cana-5358	166	3	let	let	VERB
cana-5358	166	4	(	(	PUNCT
cana-5358	166	5	𝑋1	𝑋1	PROPN
cana-5358	166	6	,	,	PUNCT
cana-5358	166	7	𝜏1	𝜏1	NOUN
cana-5358	166	8	)	)	PUNCT
cana-5358	166	9	&	&	CCONJ
cana-5358	166	10	(	(	PUNCT
cana-5358	166	11	𝑋2	𝑋2	PROPN
cana-5358	166	12	,	,	PUNCT
cana-5358	166	13	𝜏2	𝜏2	PROPN
cana-5358	166	14	)	)	PUNCT
cana-5358	166	15	be	be	VERB
cana-5358	166	16	a	a	DET
cana-5358	166	17	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5358	166	18	’s	’s	NOUN
cana-5358	166	19	.	.	PUNCT
cana-5358	167	1	a	a	DET
cana-5358	167	2	mapping	mapping	NOUN
cana-5358	167	3	ℎ𝑃	ℎ𝑃	NOUN
cana-5358	167	4	:	:	PUNCT
cana-5358	167	5	(	(	PUNCT
cana-5358	167	6	𝑋1	𝑋1	PROPN
cana-5358	167	7	,	,	PUNCT
cana-5358	167	8	𝜏1	𝜏1	NOUN
cana-5358	167	9	)	)	PUNCT
cana-5358	167	10	→	→	SYM
cana-5358	167	11	(	(	PUNCT
cana-5358	167	12	𝑋2	𝑋2	PROPN
cana-5358	167	13	,	,	PUNCT
cana-5358	167	14	𝜏2	𝜏2	PROPN
cana-5358	167	15	)	)	PUNCT
cana-5358	167	16	is	be	AUX
cana-5358	167	17	said	say	VERB
cana-5358	167	18	to	to	PART
cana-5358	167	19	be	be	AUX
cana-5358	167	20	a	a	DET
cana-5358	167	21	fermatean	fermatean	ADJ
cana-5358	167	22	fuzzy	fuzzy	ADJ
cana-5358	167	23	(	(	PUNCT
cana-5358	167	24	resp	resp	NOUN
cana-5358	167	25	.	.	PUNCT
cana-5358	168	1	𝛿	𝛿	ADJ
cana-5358	168	2	,	,	PUNCT
cana-5358	168	3	𝛿𝒫	𝛿𝒫	NOUN
cana-5358	168	4	,	,	PUNCT
cana-5358	168	5	𝛿𝒮	𝛿𝒮	NOUN
cana-5358	168	6	,	,	PUNCT
cana-5358	168	7	𝛿𝛼	𝛿𝛼	NOUN
cana-5358	168	8	&	&	CCONJ
cana-5358	168	9	𝛿𝛽	𝛿𝛽	PROPN
cana-5358	168	10	or	or	CCONJ
cana-5358	168	11	𝑒∗)open	𝑒∗)open	PROPN
cana-5358	168	12	map	map	NOUN
cana-5358	168	13	(	(	PUNCT
cana-5358	168	14	briefly	briefly	ADV
cana-5358	168	15	,	,	PUNCT
cana-5358	168	16	𝔉ℱ𝑂	𝔉ℱ𝑂	PROPN
cana-5358	168	17	(	(	PUNCT
cana-5358	168	18	resp	resp	NOUN
cana-5358	168	19	.	.	PUNCT
cana-5358	169	1	𝔉ℱ𝛿𝑂	𝔉ℱ𝛿𝑂	PROPN
cana-5358	169	2	,	,	PUNCT
cana-5358	169	3	𝔉ℱ𝛿𝒫𝑂	𝔉ℱ𝛿𝒫𝑂	ADJ
cana-5358	169	4	,	,	PUNCT
cana-5358	169	5	𝔉ℱ𝛿𝒮𝑂	𝔉ℱ𝛿𝒮𝑂	NOUN
cana-5358	169	6	,	,	PUNCT
cana-5358	169	7	𝔉ℱ𝛿𝛼𝑂	𝔉ℱ𝛿𝛼𝑂	NOUN
cana-5358	169	8	,	,	PUNCT
cana-5358	169	9	&	&	CCONJ
cana-5358	169	10	𝔉ℱ𝛿𝛽𝑂	𝔉ℱ𝛿𝛽𝑂	PROPN
cana-5358	169	11	or	or	CCONJ
cana-5358	169	12	𝔉ℱ𝑒∗𝑂	𝔉ℱ𝑒∗𝑂	PROPN
cana-5358	169	13	)	)	PUNCT
cana-5358	169	14	)	)	PUNCT
cana-5358	170	1	if	if	SCONJ
cana-5358	170	2	the	the	DET
cana-5358	170	3	image	image	NOUN
cana-5358	170	4	of	of	ADP
cana-5358	170	5	every	every	DET
cana-5358	170	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5358	170	7	in	in	ADP
cana-5358	170	8	𝑋1	𝑋1	PROPN
cana-5358	170	9	is	be	AUX
cana-5358	170	10	a	a	DET
cana-5358	170	11	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5358	170	12	(	(	PUNCT
cana-5358	170	13	resp	resp	NOUN
cana-5358	170	14	.	.	PUNCT
cana-5358	171	1	𝔉ℱ𝛿𝑜𝑠	𝔉ℱ𝛿𝑜𝑠	PROPN
cana-5358	171	2	,	,	PUNCT
cana-5358	171	3	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5358	171	4	,	,	PUNCT
cana-5358	171	5	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5358	171	6	,	,	PUNCT
cana-5358	171	7	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5358	171	8	&	&	CCONJ
cana-5358	171	9	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5358	171	10	or	or	CCONJ
cana-5358	171	11	𝔉ℱ𝑒∗𝑜𝑠	𝔉ℱ𝑒∗𝑜𝑠	NOUN
cana-5358	171	12	)	)	PUNCT
cana-5358	171	13	in	in	ADP
cana-5358	171	14	𝑋2	𝑋2	PROPN
cana-5358	171	15	.	.	PUNCT
cana-5358	172	1	definition	definition	NOUN
cana-5358	172	2	3.3	3.3	NUM
cana-5358	172	3	a	a	DET
cana-5358	172	4	bijection	bijection	ADJ
cana-5358	172	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	172	6	:	:	PUNCT
cana-5358	172	7	(	(	PUNCT
cana-5358	172	8	𝑋1	𝑋1	PROPN
cana-5358	172	9	,	,	PUNCT
cana-5358	172	10	𝜏1	𝜏1	NOUN
cana-5358	172	11	)	)	PUNCT
cana-5358	172	12	→	→	SYM
cana-5358	172	13	(	(	PUNCT
cana-5358	172	14	𝑋2	𝑋2	PROPN
cana-5358	172	15	,	,	PUNCT
cana-5358	172	16	𝜏2	𝜏2	PROPN
cana-5358	172	17	)	)	PUNCT
cana-5358	172	18	is	be	AUX
cana-5358	172	19	called	call	VERB
cana-5358	172	20	a	a	DET
cana-5358	172	21	fermatean	fermatean	ADJ
cana-5358	172	22	fuzzy	fuzzy	NOUN
cana-5358	172	23	(	(	PUNCT
cana-5358	172	24	resp	resp	NOUN
cana-5358	172	25	.	.	PUNCT
cana-5358	173	1	𝛿	𝛿	ADJ
cana-5358	173	2	,	,	PUNCT
cana-5358	173	3	𝛿𝛼	𝛿𝛼	NOUN
cana-5358	173	4	,	,	PUNCT
cana-5358	173	5	𝛿𝒮	𝛿𝒮	NOUN
cana-5358	173	6	,	,	PUNCT
cana-5358	173	7	𝛿𝒫	𝛿𝒫	NOUN
cana-5358	173	8	&	&	CCONJ
cana-5358	173	9	𝛿𝛽	𝛿𝛽	VERB
cana-5358	173	10	or	or	CCONJ
cana-5358	173	11	𝑒∗	𝑒∗	PROPN
cana-5358	173	12	)	)	PUNCT
cana-5358	173	13	-homeomorphism	-homeomorphism	NOUN
cana-5358	173	14	(	(	PUNCT
cana-5358	173	15	briefly	briefly	ADV
cana-5358	173	16	,	,	PUNCT
cana-5358	173	17	𝔉ℱ𝐻𝑜𝑚	𝔉ℱ𝐻𝑜𝑚	PROPN
cana-5358	173	18	(	(	PUNCT
cana-5358	173	19	resp	resp	NOUN
cana-5358	173	20	.	.	PUNCT
cana-5358	173	21	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	PROPN
cana-5358	173	22	,	,	PUNCT
cana-5358	173	23	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	ADJ
cana-5358	173	24	,	,	PUNCT
cana-5358	173	25	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	ADJ
cana-5358	173	26	,	,	PUNCT
cana-5358	173	27	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	PROPN
cana-5358	173	28	&	&	CCONJ
cana-5358	173	29	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	ADJ
cana-5358	173	30	or	or	CCONJ
cana-5358	173	31	𝔉ℱ𝑒∗𝐻𝑜𝑚	𝔉ℱ𝑒∗𝐻𝑜𝑚	NUM
cana-5358	173	32	)	)	PUNCT
cana-5358	173	33	)	)	PUNCT
cana-5358	174	1	if	if	SCONJ
cana-5358	174	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	174	3	and	and	CCONJ
cana-5358	174	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	174	5	−1	−1	VERB
cana-5358	174	6	are	be	AUX
cana-5358	174	7	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	PROPN
cana-5358	174	8	(	(	PUNCT
cana-5358	174	9	resp	resp	NOUN
cana-5358	174	10	.	.	PUNCT
cana-5358	175	1	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	NOUN
cana-5358	175	2	,	,	PUNCT
cana-5358	175	3	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5358	175	4	,	,	PUNCT
cana-5358	175	5	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5358	175	6	,	,	PUNCT
cana-5358	175	7	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5358	175	8	&	&	CCONJ
cana-5358	175	9	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5358	175	10	or	or	CCONJ
cana-5358	175	11	𝔉ℱ𝑒∗𝐶𝑡𝑠	𝔉ℱ𝑒∗𝐶𝑡𝑠	NOUN
cana-5358	175	12	)	)	PUNCT
cana-5358	175	13	mappings	mapping	NOUN
cana-5358	175	14	.	.	PUNCT
cana-5358	176	1	theorem	theorem	VERB
cana-5358	176	2	3.1	3.1	NUM
cana-5358	176	3	let	let	NOUN
cana-5358	176	4	(	(	PUNCT
cana-5358	176	5	𝑋1	𝑋1	PROPN
cana-5358	176	6	,	,	PUNCT
cana-5358	176	7	𝜏1	𝜏1	NOUN
cana-5358	176	8	)	)	PUNCT
cana-5358	176	9	&	&	CCONJ
cana-5358	176	10	(	(	PUNCT
cana-5358	176	11	𝑋2	𝑋2	PROPN
cana-5358	176	12	,	,	PUNCT
cana-5358	176	13	𝜏2	𝜏2	PROPN
cana-5358	176	14	)	)	PUNCT
cana-5358	176	15	be	be	VERB
cana-5358	176	16	a	a	DET
cana-5358	176	17	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5358	176	18	’s	’s	PART
cana-5358	176	19	.	.	PUNCT
cana-5358	177	1	let	let	VERB
cana-5358	177	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	177	3	:	:	PUNCT
cana-5358	177	4	(	(	PUNCT
cana-5358	177	5	𝑋1	𝑋1	PROPN
cana-5358	177	6	,	,	PUNCT
cana-5358	177	7	𝜏1	𝜏1	NOUN
cana-5358	177	8	)	)	PUNCT
cana-5358	177	9	→	→	SYM
cana-5358	177	10	(	(	PUNCT
cana-5358	177	11	𝑋2	𝑋2	PROPN
cana-5358	177	12	,	,	PUNCT
cana-5358	177	13	𝜏2	𝜏2	PROPN
cana-5358	177	14	)	)	PUNCT
cana-5358	177	15	be	be	VERB
cana-5358	177	16	a	a	DET
cana-5358	177	17	mapping	mapping	NOUN
cana-5358	177	18	.	.	PUNCT
cana-5358	178	1	then	then	ADV
cana-5358	178	2	the	the	DET
cana-5358	178	3	following	following	ADJ
cana-5358	178	4	statements	statement	NOUN
cana-5358	178	5	are	be	AUX
cana-5358	178	6	hold	hold	NOUN
cana-5358	178	7	for	for	ADP
cana-5358	178	8	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5358	178	9	,	,	PUNCT
cana-5358	178	10	but	but	CCONJ
cana-5358	178	11	not	not	PART
cana-5358	178	12	conversely	conversely	ADV
cana-5358	178	13	.	.	PUNCT
cana-5358	179	1	(	(	PUNCT
cana-5358	179	2	i	i	NOUN
cana-5358	179	3	)	)	PUNCT
cana-5358	179	4	every	every	DET
cana-5358	179	5	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	NOUN
cana-5358	179	6	is	be	AUX
cana-5358	179	7	a	a	DET
cana-5358	179	8	𝔉ℱ𝐻𝑜𝑚.	𝔉ℱ𝐻𝑜𝑚.	PROPN
cana-5358	179	9	(	(	PUNCT
cana-5358	179	10	ii	ii	NOUN
cana-5358	179	11	)	)	PUNCT
cana-5358	179	12	every	every	DET
cana-5358	179	13	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	NOUN
cana-5358	179	14	is	be	AUX
cana-5358	179	15	a	a	DET
cana-5358	179	16	𝔉ℱ𝛿𝒮𝐻𝑜𝑚.	𝔉ℱ𝛿𝒮𝐻𝑜𝑚.	PROPN
cana-5358	179	17	(	(	PUNCT
cana-5358	179	18	iii	iii	NOUN
cana-5358	179	19	)	)	PUNCT
cana-5358	179	20	every	every	DET
cana-5358	179	21	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	NOUN
cana-5358	179	22	is	be	AUX
cana-5358	179	23	a	a	DET
cana-5358	179	24	𝔉ℱ𝛿𝒫𝐻𝑜𝑚.	𝔉ℱ𝛿𝒫𝐻𝑜𝑚.	PROPN
cana-5358	179	25	(	(	PUNCT
cana-5358	179	26	iv	iv	X
cana-5358	179	27	)	)	PUNCT
cana-5358	179	28	every	every	DET
cana-5358	179	29	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	NOUN
cana-5358	179	30	is	be	AUX
cana-5358	179	31	a	a	DET
cana-5358	179	32	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	ADJ
cana-5358	179	33	(	(	PUNCT
cana-5358	179	34	v	v	NOUN
cana-5358	179	35	)	)	PUNCT
cana-5358	179	36	every	every	DET
cana-5358	179	37	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	NOUN
cana-5358	179	38	is	be	AUX
cana-5358	179	39	a	a	DET
cana-5358	179	40	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	ADJ
cana-5358	179	41	(	(	PUNCT
cana-5358	179	42	vi	vi	NOUN
cana-5358	179	43	)	)	PUNCT
cana-5358	179	44	every	every	DET
cana-5358	179	45	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	ADJ
cana-5358	179	46	is	be	AUX
cana-5358	179	47	a	a	DET
cana-5358	179	48	𝔉ℱ𝛿𝒮𝐻𝑜𝑚.	𝔉ℱ𝛿𝒮𝐻𝑜𝑚.	PROPN
cana-5358	179	49	(	(	PUNCT
cana-5358	179	50	vii	vii	PROPN
cana-5358	179	51	)	)	PUNCT
cana-5358	179	52	every	every	DET
cana-5358	179	53	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	ADJ
cana-5358	179	54	is	be	AUX
cana-5358	179	55	a	a	DET
cana-5358	179	56	𝔉ℱ𝛿𝒫𝐻𝑜𝑚.	𝔉ℱ𝛿𝒫𝐻𝑜𝑚.	PROPN
cana-5358	179	57	communications	communication	NOUN
cana-5358	179	58	on	on	ADP
cana-5358	179	59	applied	apply	VERB
cana-5358	179	60	nonlinear	nonlinear	ADJ
cana-5358	179	61	analysis	analysis	NOUN
cana-5358	179	62	issn	issn	NOUN
cana-5358	179	63	:	:	PUNCT
cana-5358	179	64	1074	1074	NUM
cana-5358	179	65	-	-	PUNCT
cana-5358	179	66	133x	133x	NUM
cana-5358	179	67	vol	vol	VERB
cana-5358	179	68	32	32	NUM
cana-5358	179	69	no	no	NOUN
cana-5358	179	70	.	.	PUNCT
cana-5358	180	1	10s	10	NOUN
cana-5358	180	2	(	(	PUNCT
cana-5358	180	3	2025	2025	NUM
cana-5358	180	4	)	)	PUNCT
cana-5358	180	5	1901	1901	NUM
cana-5358	180	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	180	7	proof	proof	NOUN
cana-5358	180	8	.	.	PUNCT
cana-5358	181	1	(	(	PUNCT
cana-5358	181	2	i	i	NOUN
cana-5358	181	3	)	)	PUNCT
cana-5358	181	4	let	let	VERB
cana-5358	181	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	6	be	be	AUX
cana-5358	181	7	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	NOUN
cana-5358	181	8	,	,	PUNCT
cana-5358	181	9	then	then	ADV
cana-5358	181	10	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	11	and	and	CCONJ
cana-5358	181	12	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	13	−1	−1	VERB
cana-5358	181	14	are	be	AUX
cana-5358	181	15	𝔉ℱ𝛿𝐶𝑡𝑠.	𝔉ℱ𝛿𝐶𝑡𝑠.	X
cana-5358	181	16	but	but	CCONJ
cana-5358	181	17	every	every	DET
cana-5358	181	18	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	NUM
cana-5358	181	19	function	function	NOUN
cana-5358	181	20	is	be	AUX
cana-5358	181	21	𝔉ℱ𝐶𝑡𝑠.	𝔉ℱ𝐶𝑡𝑠.	PROPN
cana-5358	181	22	hence	hence	ADV
cana-5358	181	23	,	,	PUNCT
cana-5358	181	24	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	25	and	and	CCONJ
cana-5358	181	26	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	27	−1	−1	VERB
cana-5358	181	28	are	be	AUX
cana-5358	181	29	𝔉ℱ𝐶𝑡𝑠.	𝔉ℱ𝐶𝑡𝑠.	PROPN
cana-5358	181	30	therefore	therefore	ADV
cana-5358	181	31	,	,	PUNCT
cana-5358	181	32	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	33	is	be	AUX
cana-5358	181	34	a	a	DET
cana-5358	181	35	𝔉ℱ𝐻𝑜𝑚.	𝔉ℱ𝐻𝑜𝑚.	PROPN
cana-5358	181	36	(	(	PUNCT
cana-5358	181	37	ii	ii	NOUN
cana-5358	181	38	)	)	PUNCT
cana-5358	181	39	let	let	VERB
cana-5358	181	40	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	41	be	be	AUX
cana-5358	181	42	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	NOUN
cana-5358	181	43	,	,	PUNCT
cana-5358	181	44	then	then	ADV
cana-5358	181	45	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	46	and	and	CCONJ
cana-5358	181	47	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	48	−1	−1	VERB
cana-5358	181	49	are	be	AUX
cana-5358	181	50	𝔉ℱ𝛿𝐶𝑡𝑠.	𝔉ℱ𝛿𝐶𝑡𝑠.	X
cana-5358	181	51	but	but	CCONJ
cana-5358	181	52	every	every	DET
cana-5358	181	53	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	NUM
cana-5358	181	54	function	function	NOUN
cana-5358	181	55	is	be	AUX
cana-5358	181	56	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	NUM
cana-5358	181	57	hence	hence	ADV
cana-5358	181	58	,	,	PUNCT
cana-5358	181	59	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	60	and	and	CCONJ
cana-5358	181	61	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	62	−1	−1	VERB
cana-5358	181	63	are	be	AUX
cana-5358	181	64	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	NUM
cana-5358	181	65	therefore	therefore	ADV
cana-5358	181	66	,	,	PUNCT
cana-5358	181	67	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	68	is	be	AUX
cana-5358	181	69	a	a	DET
cana-5358	181	70	𝔉ℱ𝛿𝒮𝐻𝑜𝑚.	𝔉ℱ𝛿𝒮𝐻𝑜𝑚.	PROPN
cana-5358	181	71	(	(	PUNCT
cana-5358	181	72	iii	iii	NOUN
cana-5358	181	73	)	)	PUNCT
cana-5358	181	74	let	let	VERB
cana-5358	181	75	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	76	be	be	AUX
cana-5358	181	77	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	NOUN
cana-5358	181	78	,	,	PUNCT
cana-5358	181	79	then	then	ADV
cana-5358	181	80	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	81	and	and	CCONJ
cana-5358	181	82	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	83	−1	−1	VERB
cana-5358	181	84	are	be	AUX
cana-5358	181	85	𝔉ℱ𝛿𝐶𝑡𝑠.	𝔉ℱ𝛿𝐶𝑡𝑠.	X
cana-5358	181	86	but	but	CCONJ
cana-5358	181	87	every	every	DET
cana-5358	181	88	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	NUM
cana-5358	181	89	function	function	NOUN
cana-5358	181	90	is	be	AUX
cana-5358	181	91	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	NOUN
cana-5358	181	92	hence	hence	ADV
cana-5358	181	93	,	,	PUNCT
cana-5358	181	94	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	95	and	and	CCONJ
cana-5358	181	96	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	97	−1	−1	VERB
cana-5358	181	98	are	be	AUX
cana-5358	181	99	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	PROPN
cana-5358	181	100	therefore	therefore	ADV
cana-5358	181	101	,	,	PUNCT
cana-5358	181	102	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	103	is	be	AUX
cana-5358	181	104	a	a	DET
cana-5358	181	105	𝔉ℱ𝛿𝒫𝐻𝑜𝑚.	𝔉ℱ𝛿𝒫𝐻𝑜𝑚.	PROPN
cana-5358	181	106	(	(	PUNCT
cana-5358	181	107	iv	iv	X
cana-5358	181	108	)	)	PUNCT
cana-5358	181	109	let	let	VERB
cana-5358	181	110	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	111	be	be	AUX
cana-5358	181	112	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	ADJ
cana-5358	181	113	,	,	PUNCT
cana-5358	181	114	then	then	ADV
cana-5358	181	115	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	116	and	and	CCONJ
cana-5358	181	117	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	181	118	−1	−1	VERB
cana-5358	181	119	are	be	AUX
cana-5358	181	120	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	PRON
cana-5358	181	121	.	.	PUNCT
cana-5358	182	1	but	but	CCONJ
cana-5358	182	2	every	every	DET
cana-5358	182	3	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5358	182	4	function	function	NOUN
cana-5358	182	5	is	be	AUX
cana-5358	182	6	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	X
cana-5358	182	7	hence	hence	ADV
cana-5358	182	8	,	,	PUNCT
cana-5358	182	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	182	10	and	and	CCONJ
cana-5358	182	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	182	12	−1	−1	VERB
cana-5358	182	13	are	be	AUX
cana-5358	182	14	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	VERB
cana-5358	182	15	therefore	therefore	ADV
cana-5358	182	16	,	,	PUNCT
cana-5358	182	17	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	182	18	is	be	AUX
cana-5358	182	19	a	a	DET
cana-5358	182	20	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	ADJ
cana-5358	182	21	(	(	PUNCT
cana-5358	182	22	v	v	NOUN
cana-5358	182	23	)	)	PUNCT
cana-5358	182	24	let	let	VERB
cana-5358	182	25	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	182	26	be	be	AUX
cana-5358	182	27	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	NOUN
cana-5358	182	28	,	,	PUNCT
cana-5358	182	29	then	then	ADV
cana-5358	182	30	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	182	31	and	and	CCONJ
cana-5358	182	32	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	182	33	−1	−1	VERB
cana-5358	182	34	are	be	AUX
cana-5358	182	35	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	PRON
cana-5358	182	36	.	.	PUNCT
cana-5358	183	1	but	but	CCONJ
cana-5358	183	2	every	every	DET
cana-5358	183	3	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	NOUN
cana-5358	183	4	function	function	NOUN
cana-5358	183	5	is	be	AUX
cana-5358	183	6	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	VERB
cana-5358	183	7	hence	hence	ADV
cana-5358	183	8	,	,	PUNCT
cana-5358	183	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	183	10	and	and	CCONJ
cana-5358	183	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	183	12	−1	−1	VERB
cana-5358	183	13	are	be	AUX
cana-5358	183	14	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	VERB
cana-5358	183	15	therefore	therefore	ADV
cana-5358	183	16	,	,	PUNCT
cana-5358	183	17	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	183	18	is	be	AUX
cana-5358	183	19	a	a	DET
cana-5358	183	20	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	ADJ
cana-5358	183	21	(	(	PUNCT
cana-5358	183	22	vi	vi	X
cana-5358	183	23	)	)	PUNCT
cana-5358	183	24	let	let	VERB
cana-5358	183	25	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	183	26	be	be	AUX
cana-5358	183	27	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	ADJ
cana-5358	183	28	,	,	PUNCT
cana-5358	183	29	then	then	ADV
cana-5358	183	30	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	183	31	and	and	CCONJ
cana-5358	183	32	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	183	33	−1	−1	VERB
cana-5358	183	34	are	be	AUX
cana-5358	183	35	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	ADJ
cana-5358	183	36	.	.	PUNCT
cana-5358	184	1	but	but	CCONJ
cana-5358	184	2	every	every	DET
cana-5358	184	3	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5358	184	4	function	function	NOUN
cana-5358	184	5	is	be	AUX
cana-5358	184	6	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	NUM
cana-5358	184	7	hence	hence	ADV
cana-5358	184	8	,	,	PUNCT
cana-5358	184	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	184	10	and	and	CCONJ
cana-5358	184	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	184	12	−1	−1	VERB
cana-5358	184	13	are	be	AUX
cana-5358	184	14	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	𝔉ℱ𝛿𝒮𝐶𝑡𝑠.	NUM
cana-5358	184	15	therefore	therefore	ADV
cana-5358	184	16	,	,	PUNCT
cana-5358	184	17	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	184	18	is	be	AUX
cana-5358	184	19	a	a	DET
cana-5358	184	20	𝔉ℱ𝛿𝒮𝐻𝑜𝑚.	𝔉ℱ𝛿𝒮𝐻𝑜𝑚.	PROPN
cana-5358	184	21	(	(	PUNCT
cana-5358	184	22	vii	vii	PROPN
cana-5358	184	23	)	)	PUNCT
cana-5358	184	24	let	let	VERB
cana-5358	184	25	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	184	26	be	be	AUX
cana-5358	184	27	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	ADJ
cana-5358	184	28	,	,	PUNCT
cana-5358	184	29	then	then	ADV
cana-5358	184	30	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	184	31	and	and	CCONJ
cana-5358	184	32	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	184	33	−1	−1	VERB
cana-5358	184	34	are	be	AUX
cana-5358	184	35	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	ADJ
cana-5358	184	36	.	.	PUNCT
cana-5358	185	1	but	but	CCONJ
cana-5358	185	2	every	every	DET
cana-5358	185	3	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5358	185	4	function	function	NOUN
cana-5358	185	5	is	be	AUX
cana-5358	185	6	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	NOUN
cana-5358	185	7	hence	hence	ADV
cana-5358	185	8	,	,	PUNCT
cana-5358	185	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	185	10	and	and	CCONJ
cana-5358	185	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	185	12	−1	−1	VERB
cana-5358	185	13	are	be	AUX
cana-5358	185	14	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	𝔉ℱ𝛿𝒫𝐶𝑡𝑠.	PROPN
cana-5358	185	15	therefore	therefore	ADV
cana-5358	185	16	,	,	PUNCT
cana-5358	185	17	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	185	18	is	be	AUX
cana-5358	185	19	a	a	DET
cana-5358	185	20	𝔉ℱ𝛿𝒫𝐻𝑜𝑚.	𝔉ℱ𝛿𝒫𝐻𝑜𝑚.	PROPN
cana-5358	185	21	example	example	NOUN
cana-5358	185	22	3.1	3.1	NUM
cana-5358	185	23	let	let	VERB
cana-5358	185	24	𝑋1	𝑋1	NOUN
cana-5358	185	25	=	=	SYM
cana-5358	185	26	𝑋2	𝑋2	VERB
cana-5358	185	27	=	=	SYM
cana-5358	185	28	𝑋	𝑋	NOUN
cana-5358	185	29	=	=	PUNCT
cana-5358	185	30	{	{	PUNCT
cana-5358	185	31	𝑎	𝑎	NOUN
cana-5358	185	32	,	,	PUNCT
cana-5358	185	33	𝑏	𝑏	NOUN
cana-5358	185	34	}	}	PUNCT
cana-5358	185	35	and	and	CCONJ
cana-5358	185	36	the	the	DET
cana-5358	185	37	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	185	38	’s	’s	PART
cana-5358	185	39	𝐴1	𝐴1	PROPN
cana-5358	185	40	,	,	PUNCT
cana-5358	185	41	𝐴2	𝐴2	PROPN
cana-5358	185	42	,	,	PUNCT
cana-5358	185	43	𝐴3	𝐴3	PROPN
cana-5358	185	44	and	and	CCONJ
cana-5358	185	45	𝐴4	𝐴4	PROPN
cana-5358	185	46	are	be	AUX
cana-5358	185	47	defined	define	VERB
cana-5358	185	48	as	as	ADP
cana-5358	185	49	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5358	185	50	(	(	PUNCT
cana-5358	185	51	𝑎	𝑎	NOUN
cana-5358	185	52	)	)	PUNCT
cana-5358	185	53	=	=	SYM
cana-5358	185	54	0.2	0.2	NUM
cana-5358	185	55	,	,	PUNCT
cana-5358	185	56	𝛽𝐴1	𝛽𝐴1	X
cana-5358	185	57	(	(	PUNCT
cana-5358	185	58	𝑎	𝑎	NOUN
cana-5358	185	59	)	)	PUNCT
cana-5358	185	60	=	=	SYM
cana-5358	185	61	0.8	0.8	NUM
cana-5358	185	62	,	,	PUNCT
cana-5358	185	63	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5358	185	64	(	(	PUNCT
cana-5358	185	65	𝑏	𝑏	NOUN
cana-5358	185	66	)	)	PUNCT
cana-5358	185	67	=	=	SYM
cana-5358	185	68	0.4	0.4	NUM
cana-5358	185	69	,	,	PUNCT
cana-5358	185	70	𝛽𝐴1	𝛽𝐴1	PROPN
cana-5358	185	71	(	(	PUNCT
cana-5358	185	72	𝑏	𝑏	NOUN
cana-5358	185	73	)	)	PUNCT
cana-5358	185	74	=	=	SYM
cana-5358	185	75	0.6	0.6	NUM
cana-5358	185	76	;	;	PUNCT
cana-5358	185	77	𝛼𝐴2	𝛼𝐴2	NUM
cana-5358	185	78	(	(	PUNCT
cana-5358	185	79	𝑎	𝑎	NOUN
cana-5358	185	80	)	)	PUNCT
cana-5358	185	81	=	=	SYM
cana-5358	185	82	0.1	0.1	NUM
cana-5358	185	83	,	,	PUNCT
cana-5358	185	84	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5358	185	85	(	(	PUNCT
cana-5358	185	86	𝑎	𝑎	NOUN
cana-5358	185	87	)	)	PUNCT
cana-5358	185	88	=	=	SYM
cana-5358	185	89	0.9	0.9	NUM
cana-5358	185	90	,	,	PUNCT
cana-5358	185	91	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5358	185	92	(	(	PUNCT
cana-5358	185	93	𝑏	𝑏	NOUN
cana-5358	185	94	)	)	PUNCT
cana-5358	185	95	=	=	SYM
cana-5358	185	96	0.3	0.3	NUM
cana-5358	185	97	,	,	PUNCT
cana-5358	185	98	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5358	185	99	(	(	PUNCT
cana-5358	185	100	𝑏	𝑏	NOUN
cana-5358	185	101	)	)	PUNCT
cana-5358	185	102	=	=	SYM
cana-5358	185	103	0.7	0.7	NUM
cana-5358	185	104	;	;	PUNCT
cana-5358	185	105	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5358	185	106	(	(	PUNCT
cana-5358	185	107	𝑎	𝑎	NOUN
cana-5358	185	108	)	)	PUNCT
cana-5358	185	109	=	=	SYM
cana-5358	185	110	0.9	0.9	NUM
cana-5358	185	111	,	,	PUNCT
cana-5358	185	112	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5358	185	113	(	(	PUNCT
cana-5358	185	114	𝑎	𝑎	NOUN
cana-5358	185	115	)	)	PUNCT
cana-5358	185	116	=	=	SYM
cana-5358	185	117	0.1	0.1	NUM
cana-5358	185	118	,	,	PUNCT
cana-5358	185	119	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5358	185	120	(	(	PUNCT
cana-5358	185	121	𝑏	𝑏	NOUN
cana-5358	185	122	)	)	PUNCT
cana-5358	185	123	=	=	SYM
cana-5358	185	124	0.7	0.7	NUM
cana-5358	185	125	,	,	PUNCT
cana-5358	185	126	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5358	185	127	(	(	PUNCT
cana-5358	185	128	𝑏	𝑏	NOUN
cana-5358	185	129	)	)	PUNCT
cana-5358	185	130	=	=	SYM
cana-5358	185	131	0.7	0.7	NUM
cana-5358	185	132	;	;	PUNCT
cana-5358	185	133	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5358	185	134	(	(	PUNCT
cana-5358	185	135	𝑎	𝑎	NOUN
cana-5358	185	136	)	)	PUNCT
cana-5358	185	137	=	=	SYM
cana-5358	185	138	0.2	0.2	NUM
cana-5358	185	139	,	,	PUNCT
cana-5358	185	140	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5358	185	141	(	(	PUNCT
cana-5358	185	142	𝑎	𝑎	NOUN
cana-5358	185	143	)	)	PUNCT
cana-5358	185	144	=	=	SYM
cana-5358	185	145	0.8	0.8	NUM
cana-5358	185	146	,	,	PUNCT
cana-5358	185	147	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5358	185	148	(	(	PUNCT
cana-5358	185	149	𝑏	𝑏	NOUN
cana-5358	185	150	)	)	PUNCT
cana-5358	185	151	=	=	SYM
cana-5358	185	152	0.3	0.3	NUM
cana-5358	185	153	,	,	PUNCT
cana-5358	185	154	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5358	185	155	(	(	PUNCT
cana-5358	185	156	𝑏	𝑏	NOUN
cana-5358	185	157	)	)	PUNCT
cana-5358	185	158	=	=	SYM
cana-5358	185	159	0.7	0.7	NUM
cana-5358	185	160	;	;	PUNCT
cana-5358	185	161	let	let	VERB
cana-5358	185	162	𝜏1	𝜏1	NOUN
cana-5358	185	163	=	=	SYM
cana-5358	185	164	𝜏2	𝜏2	NOUN
cana-5358	185	165	=	=	SYM
cana-5358	185	166	𝜏	𝜏	PROPN
cana-5358	185	167	=	=	PUNCT
cana-5358	185	168	{	{	PUNCT
cana-5358	185	169	0𝔉	0𝔉	PROPN
cana-5358	185	170	,	,	PUNCT
cana-5358	185	171	1𝔉	1𝔉	NOUN
cana-5358	185	172	,	,	PUNCT
cana-5358	185	173	𝐴1	𝐴1	PROPN
cana-5358	185	174	,	,	PUNCT
cana-5358	185	175	𝐴2	𝐴2	PROPN
cana-5358	185	176	,	,	PUNCT
cana-5358	185	177	𝐴3	𝐴3	PROPN
cana-5358	185	178	,	,	PUNCT
cana-5358	185	179	𝐴4	𝐴4	PROPN
cana-5358	185	180	}	}	PUNCT
cana-5358	185	181	be	be	AUX
cana-5358	185	182	a	a	DET
cana-5358	185	183	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5358	185	184	on	on	ADP
cana-5358	185	185	𝑋	𝑋	NOUN
cana-5358	185	186	and	and	CCONJ
cana-5358	185	187	let	let	VERB
cana-5358	185	188	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	185	189	:	:	PUNCT
cana-5358	185	190	(	(	PUNCT
cana-5358	185	191	𝑋1	𝑋1	PROPN
cana-5358	185	192	,	,	PUNCT
cana-5358	185	193	𝜏1	𝜏1	NOUN
cana-5358	185	194	)	)	PUNCT
cana-5358	185	195	→	→	SYM
cana-5358	185	196	(	(	PUNCT
cana-5358	185	197	𝑋2	𝑋2	PROPN
cana-5358	185	198	,	,	PUNCT
cana-5358	185	199	𝜏2	𝜏2	PROPN
cana-5358	185	200	)	)	PUNCT
cana-5358	185	201	be	be	VERB
cana-5358	185	202	an	an	DET
cana-5358	185	203	identity	identity	NOUN
cana-5358	185	204	function	function	NOUN
cana-5358	185	205	,	,	PUNCT
cana-5358	185	206	then	then	ADV
cana-5358	185	207	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	185	208	is	be	AUX
cana-5358	185	209	𝔉ℱ𝐻𝑜𝑚	𝔉ℱ𝐻𝑜𝑚	NOUN
cana-5358	185	210	(	(	PUNCT
cana-5358	185	211	resp	resp	NOUN
cana-5358	185	212	.	.	PUNCT
cana-5358	186	1	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	ADJ
cana-5358	186	2	,	,	PUNCT
cana-5358	186	3	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	NOUN
cana-5358	186	4	and	and	CCONJ
cana-5358	186	5	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	NOUN
cana-5358	186	6	)	)	PUNCT
cana-5358	186	7	but	but	CCONJ
cana-5358	186	8	not	not	PART
cana-5358	186	9	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	NOUN
cana-5358	186	10	(	(	PUNCT
cana-5358	186	11	resp	resp	NOUN
cana-5358	186	12	.	.	PUNCT
cana-5358	186	13	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	NUM
cana-5358	186	14	,	,	PUNCT
cana-5358	186	15	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	X
cana-5358	186	16	and	and	CCONJ
cana-5358	186	17	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	ADJ
cana-5358	186	18	)	)	PUNCT
cana-5358	186	19	.	.	PUNCT
cana-5358	187	1	since	since	SCONJ
cana-5358	187	2	,	,	PUNCT
cana-5358	187	3	𝐴4	𝐴4	PROPN
cana-5358	187	4	is	be	AUX
cana-5358	187	5	a	a	DET
cana-5358	187	6	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5358	187	7	set	set	VERB
cana-5358	187	8	in	in	ADP
cana-5358	187	9	𝑋2	𝑋2	ADJ
cana-5358	187	10	but	but	CCONJ
cana-5358	187	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	187	12	−1(𝐴4	−1(𝐴4	ADJ
cana-5358	187	13	)	)	PUNCT
cana-5358	188	1	=	=	PUNCT
cana-5358	188	2	𝐴4	𝐴4	PROPN
cana-5358	188	3	is	be	AUX
cana-5358	188	4	not	not	PART
cana-5358	188	5	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5358	188	6	(	(	PUNCT
cana-5358	188	7	resp	resp	NOUN
cana-5358	188	8	.	.	PUNCT
cana-5358	189	1	𝔉ℱ𝛿𝒮𝑜	𝔉ℱ𝛿𝒮𝑜	NUM
cana-5358	189	2	,	,	PUNCT
cana-5358	189	3	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5358	189	4	and	and	CCONJ
cana-5358	189	5	𝔉ℱ𝛿𝛼𝑜	𝔉ℱ𝛿𝛼𝑜	PROPN
cana-5358	189	6	)	)	PUNCT
cana-5358	189	7	set	set	VERB
cana-5358	189	8	in	in	ADP
cana-5358	189	9	𝑋1	𝑋1	PROPN
cana-5358	189	10	.	.	PUNCT
cana-5358	190	1	example	example	NOUN
cana-5358	190	2	3.2	3.2	NUM
cana-5358	190	3	let	let	VERB
cana-5358	190	4	𝑋1	𝑋1	NOUN
cana-5358	190	5	=	=	SYM
cana-5358	190	6	𝑋2	𝑋2	VERB
cana-5358	190	7	=	=	SYM
cana-5358	190	8	𝑋	𝑋	NOUN
cana-5358	190	9	=	=	PUNCT
cana-5358	190	10	{	{	PUNCT
cana-5358	190	11	𝑎	𝑎	NOUN
cana-5358	190	12	,	,	PUNCT
cana-5358	190	13	𝑏	𝑏	NOUN
cana-5358	190	14	}	}	PUNCT
cana-5358	190	15	and	and	CCONJ
cana-5358	190	16	the	the	DET
cana-5358	190	17	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	190	18	’s	’s	PART
cana-5358	190	19	𝐴1	𝐴1	PROPN
cana-5358	190	20	,	,	PUNCT
cana-5358	190	21	𝐴2	𝐴2	PROPN
cana-5358	190	22	,	,	PUNCT
cana-5358	190	23	𝐴3	𝐴3	PROPN
cana-5358	190	24	and	and	CCONJ
cana-5358	190	25	𝐴4	𝐴4	PROPN
cana-5358	190	26	are	be	AUX
cana-5358	190	27	defined	define	VERB
cana-5358	190	28	as	as	ADP
cana-5358	190	29	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5358	190	30	(	(	PUNCT
cana-5358	190	31	𝑎	𝑎	NOUN
cana-5358	190	32	)	)	PUNCT
cana-5358	190	33	=	=	SYM
cana-5358	190	34	0.4	0.4	NUM
cana-5358	190	35	,	,	PUNCT
cana-5358	190	36	𝛽𝐴1	𝛽𝐴1	X
cana-5358	190	37	(	(	PUNCT
cana-5358	190	38	𝑎	𝑎	NOUN
cana-5358	190	39	)	)	PUNCT
cana-5358	190	40	=	=	SYM
cana-5358	190	41	0.6	0.6	NUM
cana-5358	190	42	,	,	PUNCT
cana-5358	190	43	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5358	190	44	(	(	PUNCT
cana-5358	190	45	𝑏	𝑏	NOUN
cana-5358	190	46	)	)	PUNCT
cana-5358	190	47	=	=	SYM
cana-5358	190	48	0.5	0.5	NUM
cana-5358	190	49	,	,	PUNCT
cana-5358	190	50	𝛽𝐴1	𝛽𝐴1	X
cana-5358	190	51	(	(	PUNCT
cana-5358	190	52	𝑏	𝑏	NOUN
cana-5358	190	53	)	)	PUNCT
cana-5358	191	1	=	=	NOUN
cana-5358	191	2	0.5	0.5	NUM
cana-5358	191	3	;	;	PUNCT
cana-5358	191	4	𝛼𝐴2	𝛼𝐴2	NUM
cana-5358	191	5	(	(	PUNCT
cana-5358	191	6	𝑎	𝑎	NOUN
cana-5358	191	7	)	)	PUNCT
cana-5358	191	8	=	=	SYM
cana-5358	191	9	0.6	0.6	NUM
cana-5358	191	10	,	,	PUNCT
cana-5358	191	11	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5358	191	12	(	(	PUNCT
cana-5358	191	13	𝑎	𝑎	NOUN
cana-5358	191	14	)	)	PUNCT
cana-5358	191	15	=	=	SYM
cana-5358	191	16	0.4	0.4	NUM
cana-5358	191	17	,	,	PUNCT
cana-5358	191	18	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5358	191	19	(	(	PUNCT
cana-5358	191	20	𝑏	𝑏	NOUN
cana-5358	191	21	)	)	PUNCT
cana-5358	191	22	=	=	SYM
cana-5358	191	23	0.6	0.6	NUM
cana-5358	191	24	,	,	PUNCT
cana-5358	191	25	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5358	191	26	(	(	PUNCT
cana-5358	191	27	𝑏	𝑏	NOUN
cana-5358	191	28	)	)	PUNCT
cana-5358	191	29	=	=	SYM
cana-5358	191	30	0.4	0.4	NUM
cana-5358	191	31	;	;	PUNCT
cana-5358	191	32	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5358	191	33	(	(	PUNCT
cana-5358	191	34	𝑎	𝑎	NOUN
cana-5358	191	35	)	)	PUNCT
cana-5358	191	36	=	=	SYM
cana-5358	191	37	0.7	0.7	NUM
cana-5358	191	38	,	,	PUNCT
cana-5358	191	39	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5358	191	40	(	(	PUNCT
cana-5358	191	41	𝑎	𝑎	NOUN
cana-5358	191	42	)	)	PUNCT
cana-5358	191	43	=	=	SYM
cana-5358	191	44	0.3	0.3	NUM
cana-5358	191	45	,	,	PUNCT
cana-5358	191	46	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5358	191	47	(	(	PUNCT
cana-5358	191	48	𝑏	𝑏	NOUN
cana-5358	191	49	)	)	PUNCT
cana-5358	191	50	=	=	SYM
cana-5358	191	51	0.6	0.6	NUM
cana-5358	191	52	,	,	PUNCT
cana-5358	191	53	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5358	191	54	(	(	PUNCT
cana-5358	191	55	𝑏	𝑏	NOUN
cana-5358	191	56	)	)	PUNCT
cana-5358	191	57	=	=	SYM
cana-5358	191	58	0.4	0.4	NUM
cana-5358	191	59	;	;	PUNCT
cana-5358	191	60	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5358	191	61	(	(	PUNCT
cana-5358	191	62	𝑎	𝑎	NOUN
cana-5358	191	63	)	)	PUNCT
cana-5358	191	64	=	=	SYM
cana-5358	191	65	0.4	0.4	NUM
cana-5358	191	66	,	,	PUNCT
cana-5358	191	67	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5358	191	68	(	(	PUNCT
cana-5358	191	69	𝑎	𝑎	NOUN
cana-5358	191	70	)	)	PUNCT
cana-5358	191	71	=	=	SYM
cana-5358	191	72	0.6	0.6	NUM
cana-5358	191	73	,	,	PUNCT
cana-5358	191	74	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5358	191	75	(	(	PUNCT
cana-5358	191	76	𝑏	𝑏	NOUN
cana-5358	191	77	)	)	PUNCT
cana-5358	191	78	=	=	SYM
cana-5358	191	79	0.4	0.4	NUM
cana-5358	191	80	,	,	PUNCT
cana-5358	191	81	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5358	191	82	(	(	PUNCT
cana-5358	191	83	𝑏	𝑏	NOUN
cana-5358	191	84	)	)	PUNCT
cana-5358	191	85	=	=	SYM
cana-5358	191	86	0.6	0.6	NUM
cana-5358	191	87	;	;	PUNCT
cana-5358	191	88	let	let	VERB
cana-5358	191	89	𝜏1	𝜏1	NOUN
cana-5358	191	90	=	=	SYM
cana-5358	191	91	𝜏2	𝜏2	NOUN
cana-5358	191	92	=	=	SYM
cana-5358	191	93	𝜏	𝜏	PROPN
cana-5358	191	94	=	=	PUNCT
cana-5358	191	95	{	{	PUNCT
cana-5358	191	96	0𝔉	0𝔉	PROPN
cana-5358	191	97	,	,	PUNCT
cana-5358	191	98	1𝔉	1𝔉	NOUN
cana-5358	191	99	,	,	PUNCT
cana-5358	191	100	𝐴1	𝐴1	PROPN
cana-5358	191	101	,	,	PUNCT
cana-5358	191	102	𝐴2	𝐴2	PROPN
cana-5358	191	103	,	,	PUNCT
cana-5358	191	104	𝐴3	𝐴3	PROPN
cana-5358	191	105	,	,	PUNCT
cana-5358	191	106	𝐴4	𝐴4	PROPN
cana-5358	191	107	}	}	PUNCT
cana-5358	191	108	be	be	AUX
cana-5358	191	109	a	a	DET
cana-5358	191	110	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5358	191	111	on	on	ADP
cana-5358	191	112	𝑋	𝑋	NOUN
cana-5358	191	113	and	and	CCONJ
cana-5358	191	114	let	let	VERB
cana-5358	191	115	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	191	116	:	:	PUNCT
cana-5358	191	117	(	(	PUNCT
cana-5358	191	118	𝑋1	𝑋1	PROPN
cana-5358	191	119	,	,	PUNCT
cana-5358	191	120	𝜏1	𝜏1	NOUN
cana-5358	191	121	)	)	PUNCT
cana-5358	191	122	→	→	SYM
cana-5358	191	123	(	(	PUNCT
cana-5358	191	124	𝑋2	𝑋2	PROPN
cana-5358	191	125	,	,	PUNCT
cana-5358	191	126	𝜏2	𝜏2	PROPN
cana-5358	191	127	)	)	PUNCT
cana-5358	191	128	be	be	VERB
cana-5358	191	129	an	an	DET
cana-5358	191	130	identity	identity	NOUN
cana-5358	191	131	function	function	NOUN
cana-5358	191	132	,	,	PUNCT
cana-5358	191	133	then	then	ADV
cana-5358	191	134	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	191	135	is	be	AUX
cana-5358	191	136	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	ADJ
cana-5358	191	137	but	but	CCONJ
cana-5358	191	138	not	not	PART
cana-5358	191	139	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	PROPN
cana-5358	191	140	.	.	PUNCT
cana-5358	192	1	since	since	SCONJ
cana-5358	192	2	,	,	PUNCT
cana-5358	192	3	𝐴3	𝐴3	PROPN
cana-5358	192	4	is	be	AUX
cana-5358	192	5	a	a	DET
cana-5358	192	6	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5358	192	7	set	set	VERB
cana-5358	192	8	in	in	ADP
cana-5358	192	9	𝑋2	𝑋2	ADJ
cana-5358	192	10	but	but	CCONJ
cana-5358	192	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	192	12	−1(𝐴3	−1(𝐴3	NOUN
cana-5358	192	13	)	)	PUNCT
cana-5358	193	1	=	=	PRON
cana-5358	193	2	𝐴3	𝐴3	PROPN
cana-5358	193	3	is	be	AUX
cana-5358	193	4	not	not	PART
cana-5358	193	5	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5358	193	6	set	set	VERB
cana-5358	193	7	in	in	ADP
cana-5358	193	8	𝑋1	𝑋1	PROPN
cana-5358	193	9	.	.	PUNCT
cana-5358	194	1	communications	communication	NOUN
cana-5358	194	2	on	on	ADP
cana-5358	194	3	applied	apply	VERB
cana-5358	194	4	nonlinear	nonlinear	ADJ
cana-5358	194	5	analysis	analysis	NOUN
cana-5358	194	6	issn	issn	NOUN
cana-5358	194	7	:	:	PUNCT
cana-5358	194	8	1074	1074	NUM
cana-5358	194	9	-	-	PUNCT
cana-5358	194	10	133x	133x	NUM
cana-5358	194	11	vol	vol	VERB
cana-5358	194	12	32	32	NUM
cana-5358	194	13	no	no	NOUN
cana-5358	194	14	.	.	PUNCT
cana-5358	195	1	10s	10	NOUN
cana-5358	195	2	(	(	PUNCT
cana-5358	195	3	2025	2025	NUM
cana-5358	195	4	)	)	PUNCT
cana-5358	195	5	1902	1902	NUM
cana-5358	196	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	196	2	example	example	NOUN
cana-5358	196	3	3.3	3.3	NUM
cana-5358	196	4	let	let	VERB
cana-5358	196	5	𝑋1	𝑋1	NOUN
cana-5358	196	6	=	=	SYM
cana-5358	196	7	𝑋2	𝑋2	VERB
cana-5358	196	8	=	=	SYM
cana-5358	196	9	𝑋	𝑋	NOUN
cana-5358	196	10	=	=	PUNCT
cana-5358	196	11	{	{	PUNCT
cana-5358	196	12	𝑎	𝑎	NOUN
cana-5358	196	13	,	,	PUNCT
cana-5358	196	14	𝑏	𝑏	NOUN
cana-5358	196	15	}	}	PUNCT
cana-5358	196	16	and	and	CCONJ
cana-5358	196	17	the	the	DET
cana-5358	196	18	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	196	19	’s	’s	PART
cana-5358	196	20	𝐴1	𝐴1	PROPN
cana-5358	196	21	,	,	PUNCT
cana-5358	196	22	𝐴2	𝐴2	PROPN
cana-5358	196	23	,	,	PUNCT
cana-5358	196	24	𝐵1	𝐵1	NOUN
cana-5358	196	25	and	and	CCONJ
cana-5358	196	26	𝐵2	𝐵2	NOUN
cana-5358	196	27	are	be	AUX
cana-5358	196	28	defined	define	VERB
cana-5358	196	29	as	as	ADP
cana-5358	196	30	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5358	196	31	(	(	PUNCT
cana-5358	196	32	𝑎	𝑎	NOUN
cana-5358	196	33	)	)	PUNCT
cana-5358	196	34	=	=	SYM
cana-5358	196	35	0.2	0.2	NUM
cana-5358	196	36	,	,	PUNCT
cana-5358	196	37	𝛽𝐴1	𝛽𝐴1	X
cana-5358	196	38	(	(	PUNCT
cana-5358	196	39	𝑎	𝑎	NOUN
cana-5358	196	40	)	)	PUNCT
cana-5358	196	41	=	=	SYM
cana-5358	196	42	0.7	0.7	NUM
cana-5358	196	43	,	,	PUNCT
cana-5358	196	44	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5358	196	45	(	(	PUNCT
cana-5358	196	46	𝑏	𝑏	NOUN
cana-5358	196	47	)	)	PUNCT
cana-5358	196	48	=	=	SYM
cana-5358	196	49	0.1	0.1	NUM
cana-5358	196	50	,	,	PUNCT
cana-5358	196	51	𝛽𝐴1	𝛽𝐴1	X
cana-5358	196	52	(	(	PUNCT
cana-5358	196	53	𝑏	𝑏	NOUN
cana-5358	196	54	)	)	PUNCT
cana-5358	196	55	=	=	SYM
cana-5358	196	56	0.8	0.8	NUM
cana-5358	196	57	;	;	PUNCT
cana-5358	196	58	𝛼𝐴2	𝛼𝐴2	NUM
cana-5358	196	59	(	(	PUNCT
cana-5358	196	60	𝑎	𝑎	NOUN
cana-5358	196	61	)	)	PUNCT
cana-5358	196	62	=	=	SYM
cana-5358	196	63	0.3	0.3	NUM
cana-5358	196	64	,	,	PUNCT
cana-5358	196	65	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5358	196	66	(	(	PUNCT
cana-5358	196	67	𝑎	𝑎	NOUN
cana-5358	196	68	)	)	PUNCT
cana-5358	196	69	=	=	SYM
cana-5358	196	70	0.6	0.6	NUM
cana-5358	196	71	,	,	PUNCT
cana-5358	196	72	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5358	196	73	(	(	PUNCT
cana-5358	196	74	𝑏	𝑏	NOUN
cana-5358	196	75	)	)	PUNCT
cana-5358	196	76	=	=	SYM
cana-5358	196	77	0.4	0.4	NUM
cana-5358	196	78	,	,	PUNCT
cana-5358	196	79	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5358	196	80	(	(	PUNCT
cana-5358	196	81	𝑏	𝑏	NOUN
cana-5358	196	82	)	)	PUNCT
cana-5358	196	83	=	=	SYM
cana-5358	196	84	0.5	0.5	NUM
cana-5358	196	85	;	;	PUNCT
cana-5358	196	86	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5358	196	87	(	(	PUNCT
cana-5358	196	88	𝑎	𝑎	NOUN
cana-5358	196	89	)	)	PUNCT
cana-5358	196	90	=	=	SYM
cana-5358	196	91	0.1	0.1	NUM
cana-5358	196	92	,	,	PUNCT
cana-5358	196	93	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5358	196	94	(	(	PUNCT
cana-5358	196	95	𝑎	𝑎	NOUN
cana-5358	196	96	)	)	PUNCT
cana-5358	196	97	=	=	SYM
cana-5358	196	98	0.9	0.9	NUM
cana-5358	196	99	,	,	PUNCT
cana-5358	196	100	𝛼𝐵1	𝛼𝐵1	PROPN
cana-5358	196	101	(	(	PUNCT
cana-5358	196	102	𝑏	𝑏	NOUN
cana-5358	196	103	)	)	PUNCT
cana-5358	196	104	=	=	SYM
cana-5358	196	105	0.2	0.2	NUM
cana-5358	196	106	,	,	PUNCT
cana-5358	196	107	𝛽𝐵1	𝛽𝐵1	PROPN
cana-5358	196	108	(	(	PUNCT
cana-5358	196	109	𝑏	𝑏	NOUN
cana-5358	196	110	)	)	PUNCT
cana-5358	196	111	=	=	SYM
cana-5358	196	112	0.9	0.9	NUM
cana-5358	196	113	;	;	PUNCT
cana-5358	196	114	𝛼𝐵2	𝛼𝐵2	NUM
cana-5358	196	115	(	(	PUNCT
cana-5358	196	116	𝑎	𝑎	NOUN
cana-5358	196	117	)	)	PUNCT
cana-5358	196	118	=	=	SYM
cana-5358	196	119	0.2	0.2	NUM
cana-5358	196	120	,	,	PUNCT
cana-5358	196	121	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5358	196	122	(	(	PUNCT
cana-5358	196	123	𝑎	𝑎	NOUN
cana-5358	196	124	)	)	PUNCT
cana-5358	196	125	=	=	SYM
cana-5358	196	126	0.3	0.3	NUM
cana-5358	196	127	,	,	PUNCT
cana-5358	196	128	𝛼𝐵2	𝛼𝐵2	NUM
cana-5358	196	129	(	(	PUNCT
cana-5358	196	130	𝑏	𝑏	NOUN
cana-5358	196	131	)	)	PUNCT
cana-5358	196	132	=	=	SYM
cana-5358	196	133	0.4	0.4	NUM
cana-5358	196	134	,	,	PUNCT
cana-5358	196	135	𝛽𝐵2	𝛽𝐵2	PROPN
cana-5358	196	136	(	(	PUNCT
cana-5358	196	137	𝑏	𝑏	NOUN
cana-5358	196	138	)	)	PUNCT
cana-5358	196	139	=	=	SYM
cana-5358	196	140	0.7	0.7	NUM
cana-5358	196	141	;	;	PUNCT
cana-5358	196	142	let	let	VERB
cana-5358	196	143	𝜏1	𝜏1	NOUN
cana-5358	196	144	=	=	PUNCT
cana-5358	196	145	{	{	PUNCT
cana-5358	196	146	0𝔉	0𝔉	PROPN
cana-5358	196	147	,	,	PUNCT
cana-5358	196	148	1𝔉	1𝔉	NOUN
cana-5358	196	149	,	,	PUNCT
cana-5358	196	150	𝐴1	𝐴1	PROPN
cana-5358	196	151	,	,	PUNCT
cana-5358	196	152	𝐴2	𝐴2	PROPN
cana-5358	196	153	}	}	PUNCT
cana-5358	196	154	and	and	CCONJ
cana-5358	196	155	𝜏2	𝜏2	PROPN
cana-5358	196	156	=	=	SYM
cana-5358	196	157	{	{	PUNCT
cana-5358	196	158	0𝔉	0𝔉	PROPN
cana-5358	196	159	,	,	PUNCT
cana-5358	196	160	1𝔉	1𝔉	NOUN
cana-5358	196	161	,	,	PUNCT
cana-5358	196	162	𝐵1	𝐵1	PROPN
cana-5358	196	163	,	,	PUNCT
cana-5358	196	164	𝐵2	𝐵2	NOUN
cana-5358	196	165	}	}	PUNCT
cana-5358	196	166	are	be	AUX
cana-5358	196	167	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5358	196	168	’s	’s	NOUN
cana-5358	196	169	on	on	ADP
cana-5358	196	170	𝑋	𝑋	PROPN
cana-5358	196	171	and	and	CCONJ
cana-5358	196	172	let	let	VERB
cana-5358	196	173	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	196	174	:	:	PUNCT
cana-5358	196	175	(	(	PUNCT
cana-5358	196	176	𝑋1	𝑋1	PROPN
cana-5358	196	177	,	,	PUNCT
cana-5358	196	178	𝜏1	𝜏1	NOUN
cana-5358	196	179	)	)	PUNCT
cana-5358	196	180	→	→	SYM
cana-5358	196	181	(	(	PUNCT
cana-5358	196	182	𝑋2	𝑋2	PROPN
cana-5358	196	183	,	,	PUNCT
cana-5358	196	184	𝜏2	𝜏2	PROPN
cana-5358	196	185	)	)	PUNCT
cana-5358	196	186	be	be	VERB
cana-5358	196	187	an	an	DET
cana-5358	196	188	identity	identity	NOUN
cana-5358	196	189	function	function	NOUN
cana-5358	196	190	,	,	PUNCT
cana-5358	196	191	then	then	ADV
cana-5358	196	192	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	196	193	is	be	AUX
cana-5358	196	194	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	ADJ
cana-5358	196	195	but	but	CCONJ
cana-5358	196	196	not	not	PART
cana-5358	196	197	𝔉ℱ𝛿𝒫𝐻𝑜𝑚.	𝔉ℱ𝛿𝒫𝐻𝑜𝑚.	NUM
cana-5358	196	198	since	since	ADV
cana-5358	196	199	,	,	PUNCT
cana-5358	196	200	𝐴2	𝐴2	PROPN
cana-5358	196	201	is	be	AUX
cana-5358	196	202	a	a	DET
cana-5358	196	203	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5358	196	204	set	set	VERB
cana-5358	196	205	in	in	ADP
cana-5358	196	206	𝑋2	𝑋2	ADJ
cana-5358	196	207	but	but	CCONJ
cana-5358	196	208	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	196	209	−1(𝐴2	−1(𝐴2	NOUN
cana-5358	196	210	)	)	PUNCT
cana-5358	197	1	=	=	SYM
cana-5358	197	2	𝐴2	𝐴2	PROPN
cana-5358	197	3	is	be	AUX
cana-5358	197	4	not	not	PART
cana-5358	197	5	𝔉ℱ𝛿𝒫𝑜	𝔉ℱ𝛿𝒫𝑜	NOUN
cana-5358	197	6	set	set	VERB
cana-5358	197	7	in	in	ADP
cana-5358	197	8	𝑋1	𝑋1	PROPN
cana-5358	197	9	.	.	PUNCT
cana-5358	198	1	theorem	theorem	ADJ
cana-5358	198	2	3.2	3.2	NUM
cana-5358	198	3	let	let	VERB
cana-5358	198	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	198	5	:	:	PUNCT
cana-5358	198	6	(	(	PUNCT
cana-5358	198	7	𝑋1	𝑋1	PROPN
cana-5358	198	8	,	,	PUNCT
cana-5358	198	9	𝜏1	𝜏1	NOUN
cana-5358	198	10	)	)	PUNCT
cana-5358	198	11	→	→	SYM
cana-5358	198	12	(	(	PUNCT
cana-5358	198	13	𝑋2	𝑋2	PROPN
cana-5358	198	14	,	,	PUNCT
cana-5358	198	15	𝜏2	𝜏2	PROPN
cana-5358	198	16	)	)	PUNCT
cana-5358	198	17	be	be	VERB
cana-5358	198	18	a	a	DET
cana-5358	198	19	bijective	bijective	ADJ
cana-5358	198	20	mapping	mapping	NOUN
cana-5358	198	21	.	.	PUNCT
cana-5358	199	1	if	if	SCONJ
cana-5358	199	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	199	3	is	be	AUX
cana-5358	199	4	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	PUNCT
cana-5358	199	5	(	(	PUNCT
cana-5358	199	6	resp	resp	NOUN
cana-5358	199	7	.	.	PUNCT
cana-5358	200	1	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	NOUN
cana-5358	200	2	,	,	PUNCT
cana-5358	200	3	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5358	200	4	,	,	PUNCT
cana-5358	200	5	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	NUM
cana-5358	200	6	,	,	PUNCT
cana-5358	200	7	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5358	200	8	&	&	CCONJ
cana-5358	200	9	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5358	200	10	)	)	PUNCT
cana-5358	200	11	,	,	PUNCT
cana-5358	200	12	then	then	ADV
cana-5358	200	13	the	the	DET
cana-5358	200	14	followings	following	NOUN
cana-5358	200	15	statements	statement	NOUN
cana-5358	200	16	are	be	AUX
cana-5358	200	17	equivalent	equivalent	ADJ
cana-5358	200	18	:	:	PUNCT
cana-5358	200	19	(	(	PUNCT
cana-5358	200	20	i	i	NOUN
cana-5358	200	21	)	)	PUNCT
cana-5358	200	22	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	200	23	is	be	AUX
cana-5358	200	24	a	a	DET
cana-5358	200	25	𝔉ℱ𝐶	𝔉ℱ𝐶	NOUN
cana-5358	200	26	(	(	PUNCT
cana-5358	200	27	resp	resp	NOUN
cana-5358	200	28	.	.	PUNCT
cana-5358	201	1	𝔉ℱ𝛿𝐶	𝔉ℱ𝛿𝐶	PROPN
cana-5358	201	2	,	,	PUNCT
cana-5358	201	3	𝔉ℱ𝛿𝛼𝐶	𝔉ℱ𝛿𝛼𝐶	NOUN
cana-5358	201	4	,	,	PUNCT
cana-5358	201	5	𝔉ℱ𝛿𝒮𝐶	𝔉ℱ𝛿𝒮𝐶	PROPN
cana-5358	201	6	,	,	PUNCT
cana-5358	201	7	𝔉ℱ𝛿𝒫𝐶	𝔉ℱ𝛿𝒫𝐶	PROPN
cana-5358	201	8	&	&	CCONJ
cana-5358	201	9	𝔉ℱ𝛿𝛽𝐶	𝔉ℱ𝛿𝛽𝐶	PROPN
cana-5358	201	10	or	or	CCONJ
cana-5358	201	11	𝔉ℱ𝑒∗𝐶	𝔉ℱ𝑒∗𝐶	ADJ
cana-5358	201	12	)	)	PUNCT
cana-5358	201	13	mapping	mapping	NOUN
cana-5358	201	14	.	.	PUNCT
cana-5358	202	1	(	(	PUNCT
cana-5358	202	2	ii	ii	X
cana-5358	202	3	)	)	PUNCT
cana-5358	202	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	202	5	is	be	AUX
cana-5358	202	6	a	a	DET
cana-5358	202	7	𝔉ℱ𝑂	𝔉ℱ𝑂	PROPN
cana-5358	202	8	(	(	PUNCT
cana-5358	202	9	resp	resp	NOUN
cana-5358	202	10	.	.	PUNCT
cana-5358	203	1	𝔉ℱ𝛿𝑂	𝔉ℱ𝛿𝑂	PROPN
cana-5358	203	2	,	,	PUNCT
cana-5358	203	3	𝔉ℱ𝛿𝛼𝑂	𝔉ℱ𝛿𝛼𝑂	PROPN
cana-5358	203	4	,	,	PUNCT
cana-5358	203	5	𝔉ℱ𝛿𝒮𝑂	𝔉ℱ𝛿𝒮𝑂	NOUN
cana-5358	203	6	,	,	PUNCT
cana-5358	203	7	𝔉ℱ𝛿𝒫𝑂	𝔉ℱ𝛿𝒫𝑂	PROPN
cana-5358	203	8	&	&	CCONJ
cana-5358	203	9	𝔉ℱ𝛿𝛽𝑂	𝔉ℱ𝛿𝛽𝑂	PROPN
cana-5358	203	10	or	or	CCONJ
cana-5358	203	11	𝔉ℱ𝑒∗𝐶	𝔉ℱ𝑒∗𝐶	ADJ
cana-5358	203	12	)	)	PUNCT
cana-5358	203	13	mapping	mapping	NOUN
cana-5358	203	14	.	.	PUNCT
cana-5358	204	1	(	(	PUNCT
cana-5358	204	2	iii	iii	X
cana-5358	204	3	)	)	PUNCT
cana-5358	204	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	204	5	−1	−1	VERB
cana-5358	204	6	is	be	AUX
cana-5358	204	7	a	a	DET
cana-5358	204	8	𝔉ℱ𝐻𝑜𝑚	𝔉ℱ𝐻𝑜𝑚	PROPN
cana-5358	204	9	(	(	PUNCT
cana-5358	204	10	resp	resp	NOUN
cana-5358	204	11	.	.	PUNCT
cana-5358	205	1	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	PROPN
cana-5358	205	2	,	,	PUNCT
cana-5358	205	3	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	ADJ
cana-5358	205	4	,	,	PUNCT
cana-5358	205	5	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	ADJ
cana-5358	205	6	,	,	PUNCT
cana-5358	205	7	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	ADJ
cana-5358	205	8	&	&	CCONJ
cana-5358	205	9	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	ADJ
cana-5358	205	10	or	or	CCONJ
cana-5358	205	11	𝔉ℱ𝑒∗𝐻𝑜𝑚	𝔉ℱ𝑒∗𝐻𝑜𝑚	NOUN
cana-5358	205	12	)	)	PUNCT
cana-5358	205	13	.	.	PUNCT
cana-5358	206	1	proof	proof	NOUN
cana-5358	206	2	.	.	PUNCT
cana-5358	207	1	(	(	PUNCT
cana-5358	207	2	i	i	NOUN
cana-5358	207	3	)	)	PUNCT
cana-5358	207	4	⇒	⇒	PROPN
cana-5358	207	5	(	(	PUNCT
cana-5358	207	6	ii	ii	PROPN
cana-5358	207	7	)	)	PUNCT
cana-5358	207	8	:	:	PUNCT
cana-5358	207	9	assume	assume	VERB
cana-5358	207	10	that	that	SCONJ
cana-5358	207	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	207	12	is	be	AUX
cana-5358	207	13	a	a	DET
cana-5358	207	14	bijective	bijective	ADJ
cana-5358	207	15	mapping	mapping	NOUN
cana-5358	207	16	and	and	CCONJ
cana-5358	207	17	a	a	DET
cana-5358	207	18	𝔉ℱ𝛿𝛽𝐶	𝔉ℱ𝛿𝛽𝐶	NOUN
cana-5358	207	19	mapping	mapping	NOUN
cana-5358	207	20	.	.	PUNCT
cana-5358	208	1	hence	hence	ADV
cana-5358	208	2	,	,	PUNCT
cana-5358	208	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	208	4	−1	−1	VERB
cana-5358	208	5	is	be	AUX
cana-5358	208	6	a	a	DET
cana-5358	208	7	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5358	208	8	mapping	mapping	NOUN
cana-5358	208	9	.	.	PUNCT
cana-5358	209	1	we	we	PRON
cana-5358	209	2	know	know	VERB
cana-5358	209	3	that	that	SCONJ
cana-5358	209	4	each	each	DET
cana-5358	209	5	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5358	209	6	in	in	ADP
cana-5358	209	7	(	(	PUNCT
cana-5358	209	8	𝑋1	𝑋1	PROPN
cana-5358	209	9	,	,	PUNCT
cana-5358	209	10	𝜏1	𝜏1	NOUN
cana-5358	209	11	)	)	PUNCT
cana-5358	209	12	is	be	AUX
cana-5358	209	13	a	a	DET
cana-5358	209	14	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5358	209	15	in	in	ADP
cana-5358	209	16	(	(	PUNCT
cana-5358	209	17	𝑋2	𝑋2	ADJ
cana-5358	209	18	,	,	PUNCT
cana-5358	209	19	𝜏2	𝜏2	PROPN
cana-5358	209	20	)	)	PUNCT
cana-5358	209	21	.	.	PUNCT
cana-5358	210	1	hence	hence	ADV
cana-5358	210	2	,	,	PUNCT
cana-5358	210	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	210	4	is	be	AUX
cana-5358	210	5	a	a	DET
cana-5358	210	6	𝔉ℱ𝛿𝛽𝑂	𝔉ℱ𝛿𝛽𝑂	PROPN
cana-5358	210	7	mapping	mapping	NOUN
cana-5358	210	8	.	.	PUNCT
cana-5358	211	1	(	(	PUNCT
cana-5358	211	2	ii	ii	NOUN
cana-5358	211	3	)	)	PUNCT
cana-5358	211	4	⇒	⇒	NOUN
cana-5358	211	5	(	(	PUNCT
cana-5358	211	6	iii	iii	NOUN
cana-5358	211	7	)	)	PUNCT
cana-5358	211	8	:	:	PUNCT
cana-5358	211	9	let	let	VERB
cana-5358	211	10	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	211	11	be	be	AUX
cana-5358	211	12	a	a	DET
cana-5358	211	13	bijective	bijective	ADJ
cana-5358	211	14	and	and	CCONJ
cana-5358	211	15	𝔉ℱ𝛿𝛽𝑂	𝔉ℱ𝛿𝛽𝑂	PROPN
cana-5358	211	16	mapping	mapping	NOUN
cana-5358	211	17	.	.	PUNCT
cana-5358	212	1	further	far	ADV
cana-5358	212	2	,	,	PUNCT
cana-5358	212	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	212	4	−1	−1	VERB
cana-5358	212	5	is	be	AUX
cana-5358	212	6	a	a	DET
cana-5358	212	7	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5358	212	8	mapping	mapping	NOUN
cana-5358	212	9	.	.	PUNCT
cana-5358	213	1	hence	hence	ADV
cana-5358	213	2	,	,	PUNCT
cana-5358	213	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	213	4	and	and	CCONJ
cana-5358	213	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	213	6	−1	−1	VERB
cana-5358	213	7	are	be	AUX
cana-5358	213	8	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	VERB
cana-5358	213	9	therefore	therefore	ADV
cana-5358	213	10	,	,	PUNCT
cana-5358	213	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	213	12	is	be	AUX
cana-5358	213	13	a	a	DET
cana-5358	213	14	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	ADJ
cana-5358	213	15	(	(	PUNCT
cana-5358	213	16	iii	iii	NOUN
cana-5358	213	17	)	)	PUNCT
cana-5358	213	18	⇒	⇒	NOUN
cana-5358	213	19	(	(	PUNCT
cana-5358	213	20	i	i	NOUN
cana-5358	213	21	):	):	PUNCT
cana-5358	213	22	let	let	VERB
cana-5358	213	23	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	213	24	be	be	AUX
cana-5358	213	25	a	a	DET
cana-5358	213	26	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	ADJ
cana-5358	213	27	.	.	PUNCT
cana-5358	214	1	then	then	ADV
cana-5358	214	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	214	3	and	and	CCONJ
cana-5358	214	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	214	5	−1	−1	VERB
cana-5358	214	6	are	be	AUX
cana-5358	214	7	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5358	214	8	.	.	PUNCT
cana-5358	215	1	since	since	SCONJ
cana-5358	215	2	each	each	DET
cana-5358	215	3	𝔉ℱ𝛿𝑐𝑠	𝔉ℱ𝛿𝑐𝑠	PROPN
cana-5358	215	4	in	in	ADP
cana-5358	215	5	(	(	PUNCT
cana-5358	215	6	𝑋1	𝑋1	PROPN
cana-5358	215	7	,	,	PUNCT
cana-5358	215	8	𝜏1	𝜏1	NOUN
cana-5358	215	9	)	)	PUNCT
cana-5358	215	10	is	be	AUX
cana-5358	215	11	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	215	12	in	in	ADP
cana-5358	215	13	(	(	PUNCT
cana-5358	215	14	𝑋1	𝑋1	PROPN
cana-5358	215	15	,	,	PUNCT
cana-5358	215	16	𝜏1	𝜏1	NOUN
cana-5358	215	17	)	)	PUNCT
cana-5358	215	18	is	be	AUX
cana-5358	215	19	a	a	DET
cana-5358	215	20	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	215	21	in	in	ADP
cana-5358	215	22	(	(	PUNCT
cana-5358	215	23	𝑋2	𝑋2	ADJ
cana-5358	215	24	,	,	PUNCT
cana-5358	215	25	𝜏2	𝜏2	PROPN
cana-5358	215	26	)	)	PUNCT
cana-5358	215	27	,	,	PUNCT
cana-5358	215	28	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	215	29	is	be	AUX
cana-5358	215	30	a	a	DET
cana-5358	215	31	𝔉ℱ𝛿𝛽𝐶	𝔉ℱ𝛿𝛽𝐶	NOUN
cana-5358	215	32	mapping	mapping	NOUN
cana-5358	215	33	.	.	PUNCT
cana-5358	216	1	the	the	DET
cana-5358	216	2	proof	proof	NOUN
cana-5358	216	3	of	of	ADP
cana-5358	216	4	other	other	ADJ
cana-5358	216	5	cases	case	NOUN
cana-5358	216	6	are	be	AUX
cana-5358	216	7	similar	similar	ADJ
cana-5358	216	8	.	.	PUNCT
cana-5358	217	1	definition	definition	NOUN
cana-5358	217	2	3.4	3.4	NUM
cana-5358	217	3	a	a	DET
cana-5358	217	4	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5358	217	5	(	(	PUNCT
cana-5358	217	6	𝑋	𝑋	PROPN
cana-5358	217	7	,	,	PUNCT
cana-5358	217	8	𝜏	𝜏	NOUN
cana-5358	217	9	)	)	PUNCT
cana-5358	217	10	is	be	AUX
cana-5358	217	11	said	say	VERB
cana-5358	217	12	to	to	PART
cana-5358	217	13	be	be	AUX
cana-5358	217	14	a	a	DET
cana-5358	217	15	fermatean	fermatean	ADJ
cana-5358	217	16	fuzzy	fuzzy	ADJ
cana-5358	217	17	𝛼𝑇1	𝛼𝑇1	PROPN
cana-5358	217	18	2	2	NUM
cana-5358	217	19	(	(	PUNCT
cana-5358	217	20	resp	resp	NOUN
cana-5358	217	21	.	.	PUNCT
cana-5358	218	1	𝛿𝒮𝑇1	𝛿𝒮𝑇1	PROPN
cana-5358	218	2	2	2	NUM
cana-5358	218	3	,	,	PUNCT
cana-5358	218	4	𝛿𝒫𝑇1	𝛿𝒫𝑇1	NOUN
cana-5358	218	5	2	2	NUM
cana-5358	218	6	and	and	CCONJ
cana-5358	218	7	𝛿𝛽𝑇1	𝛿𝛽𝑇1	NOUN
cana-5358	218	8	2	2	NUM
cana-5358	218	9	)	)	PUNCT
cana-5358	218	10	(	(	PUNCT
cana-5358	218	11	briefly	briefly	ADV
cana-5358	218	12	,	,	PUNCT
cana-5358	218	13	𝔉ℱ𝛿𝛼𝑇1	𝔉ℱ𝛿𝛼𝑇1	PROPN
cana-5358	218	14	2	2	NUM
cana-5358	218	15	(	(	PUNCT
cana-5358	218	16	resp	resp	NOUN
cana-5358	218	17	.	.	PUNCT
cana-5358	219	1	𝔉ℱ𝛿𝒮𝑇1	𝔉ℱ𝛿𝒮𝑇1	PROPN
cana-5358	219	2	2	2	NUM
cana-5358	219	3	,	,	PUNCT
cana-5358	219	4	𝔉ℱ𝛿𝒫𝑇1	𝔉ℱ𝛿𝒫𝑇1	ADV
cana-5358	219	5	2	2	NUM
cana-5358	219	6	and	and	CCONJ
cana-5358	219	7	𝔉ℱ𝛿𝛽𝑇1	𝔉ℱ𝛿𝛽𝑇1	PROPN
cana-5358	219	8	2	2	NUM
cana-5358	219	9	)	)	PUNCT
cana-5358	219	10	)	)	PUNCT
cana-5358	219	11	-space	-space	NOUN
cana-5358	219	12	if	if	SCONJ
cana-5358	219	13	every	every	DET
cana-5358	219	14	𝔉ℱ𝛿𝛼𝑐𝑠	𝔉ℱ𝛿𝛼𝑐𝑠	PROPN
cana-5358	219	15	(	(	PUNCT
cana-5358	219	16	resp	resp	NOUN
cana-5358	219	17	.	.	PUNCT
cana-5358	220	1	𝔉ℱ𝛿𝒮𝑐𝑠	𝔉ℱ𝛿𝒮𝑐𝑠	PROPN
cana-5358	220	2	,	,	PUNCT
cana-5358	220	3	𝔉ℱ𝛿𝒫𝑐𝑠	𝔉ℱ𝛿𝒫𝑐𝑠	NOUN
cana-5358	220	4	,	,	PUNCT
cana-5358	220	5	and	and	CCONJ
cana-5358	220	6	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	220	7	)	)	PUNCT
cana-5358	220	8	is	be	AUX
cana-5358	220	9	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	220	10	in	in	ADP
cana-5358	220	11	(	(	PUNCT
cana-5358	220	12	𝑋	𝑋	PROPN
cana-5358	220	13	,	,	PUNCT
cana-5358	220	14	𝜏	𝜏	NOUN
cana-5358	220	15	)	)	PUNCT
cana-5358	220	16	.	.	PUNCT
cana-5358	221	1	theorem	theorem	VERB
cana-5358	221	2	3.3	3.3	NUM
cana-5358	221	3	let	let	VERB
cana-5358	221	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	221	5	:	:	PUNCT
cana-5358	221	6	(	(	PUNCT
cana-5358	221	7	𝑋1	𝑋1	PROPN
cana-5358	221	8	,	,	PUNCT
cana-5358	221	9	𝜏1	𝜏1	NOUN
cana-5358	221	10	)	)	PUNCT
cana-5358	221	11	→	→	SYM
cana-5358	221	12	(	(	PUNCT
cana-5358	221	13	𝑋2	𝑋2	PROPN
cana-5358	221	14	,	,	PUNCT
cana-5358	221	15	𝜏2	𝜏2	PROPN
cana-5358	221	16	)	)	PUNCT
cana-5358	221	17	be	be	VERB
cana-5358	221	18	a	a	DET
cana-5358	221	19	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	ADJ
cana-5358	221	20	(	(	PUNCT
cana-5358	221	21	resp	resp	NOUN
cana-5358	221	22	.	.	PUNCT
cana-5358	221	23	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	NUM
cana-5358	221	24	,	,	PUNCT
cana-5358	221	25	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	PROPN
cana-5358	221	26	&	&	CCONJ
cana-5358	221	27	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	ADJ
cana-5358	221	28	or	or	CCONJ
cana-5358	221	29	𝔉ℱ𝑒∗𝐻𝑜𝑚	𝔉ℱ𝑒∗𝐻𝑜𝑚	NUM
cana-5358	221	30	)	)	PUNCT
cana-5358	221	31	.	.	PUNCT
cana-5358	222	1	then	then	ADV
cana-5358	222	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	222	3	is	be	AUX
cana-5358	222	4	a	a	DET
cana-5358	222	5	𝔉ℱ𝐻𝑜𝑚	𝔉ℱ𝐻𝑜𝑚	NOUN
cana-5358	222	6	if	if	SCONJ
cana-5358	222	7	(	(	PUNCT
cana-5358	222	8	𝑋1	𝑋1	PROPN
cana-5358	222	9	,	,	PUNCT
cana-5358	222	10	𝜏1	𝜏1	NOUN
cana-5358	222	11	)	)	PUNCT
cana-5358	222	12	and	and	CCONJ
cana-5358	222	13	(	(	PUNCT
cana-5358	222	14	𝑋2	𝑋2	PROPN
cana-5358	222	15	,	,	PUNCT
cana-5358	222	16	𝜏2	𝜏2	PROPN
cana-5358	222	17	)	)	PUNCT
cana-5358	222	18	are	be	AUX
cana-5358	222	19	𝔉ℱ𝛿𝛼𝑇1	𝔉ℱ𝛿𝛼𝑇1	PROPN
cana-5358	222	20	2	2	NUM
cana-5358	222	21	(	(	PUNCT
cana-5358	222	22	resp	resp	NOUN
cana-5358	222	23	.	.	PUNCT
cana-5358	223	1	𝔉ℱ𝛿𝒮𝑇1	𝔉ℱ𝛿𝒮𝑇1	PROPN
cana-5358	223	2	2	2	NUM
cana-5358	223	3	,	,	PUNCT
cana-5358	223	4	𝔉ℱ𝛿𝒫𝑇1	𝔉ℱ𝛿𝒫𝑇1	ADV
cana-5358	223	5	2	2	NUM
cana-5358	223	6	and	and	CCONJ
cana-5358	223	7	𝔉ℱ𝛿𝛽𝑇1	𝔉ℱ𝛿𝛽𝑇1	PROPN
cana-5358	223	8	2	2	NUM
cana-5358	223	9	)	)	PUNCT
cana-5358	223	10	-space	-space	NOUN
cana-5358	223	11	.	.	PUNCT
cana-5358	224	1	proof	proof	NOUN
cana-5358	224	2	.	.	PUNCT
cana-5358	225	1	assume	assume	VERB
cana-5358	225	2	that	that	SCONJ
cana-5358	225	3	𝐾	𝐾	PROPN
cana-5358	225	4	is	be	AUX
cana-5358	225	5	a	a	DET
cana-5358	225	6	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	225	7	in	in	ADP
cana-5358	225	8	(	(	PUNCT
cana-5358	225	9	𝑋2	𝑋2	ADJ
cana-5358	225	10	,	,	PUNCT
cana-5358	225	11	𝜏2	𝜏2	PROPN
cana-5358	225	12	)	)	PUNCT
cana-5358	225	13	.	.	PUNCT
cana-5358	226	1	then	then	ADV
cana-5358	226	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	226	3	−1(𝐾	−1(𝐾	NOUN
cana-5358	226	4	)	)	PUNCT
cana-5358	226	5	is	be	AUX
cana-5358	226	6	a	a	DET
cana-5358	226	7	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	226	8	in	in	ADP
cana-5358	226	9	(	(	PUNCT
cana-5358	226	10	𝑋1	𝑋1	PROPN
cana-5358	226	11	,	,	PUNCT
cana-5358	226	12	𝜏1	𝜏1	NOUN
cana-5358	226	13	)	)	PUNCT
cana-5358	226	14	.	.	PUNCT
cana-5358	227	1	since	since	SCONJ
cana-5358	227	2	(	(	PUNCT
cana-5358	227	3	𝑋1	𝑋1	PROPN
cana-5358	227	4	,	,	PUNCT
cana-5358	227	5	𝜏1	𝜏1	NOUN
cana-5358	227	6	)	)	PUNCT
cana-5358	227	7	is	be	AUX
cana-5358	227	8	a	a	DET
cana-5358	227	9	𝔉ℱ𝛿𝛽𝑇1	𝔉ℱ𝛿𝛽𝑇1	NOUN
cana-5358	227	10	2	2	NUM
cana-5358	227	11	-space	-space	NOUN
cana-5358	227	12	,	,	PUNCT
cana-5358	227	13	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	227	14	−1(𝐾	−1(𝐾	NOUN
cana-5358	227	15	)	)	PUNCT
cana-5358	227	16	is	be	AUX
cana-5358	227	17	a	a	DET
cana-5358	227	18	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	227	19	in	in	ADP
cana-5358	227	20	(	(	PUNCT
cana-5358	227	21	𝑋1	𝑋1	PROPN
cana-5358	227	22	,	,	PUNCT
cana-5358	227	23	𝜏1	𝜏1	NOUN
cana-5358	227	24	)	)	PUNCT
cana-5358	227	25	.	.	PUNCT
cana-5358	228	1	therefore	therefore	ADV
cana-5358	228	2	,	,	PUNCT
cana-5358	228	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	228	4	is	be	AUX
cana-5358	228	5	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	NOUN
cana-5358	228	6	.	.	PUNCT
cana-5358	229	1	by	by	ADP
cana-5358	229	2	hypothesis	hypothesis	NOUN
cana-5358	229	3	,	,	PUNCT
cana-5358	229	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	229	5	−1	−1	VERB
cana-5358	229	6	is	be	AUX
cana-5358	229	7	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	𝔉ℱ𝛿𝛽𝐶𝑡𝑠.	NOUN
cana-5358	229	8	let	let	VERB
cana-5358	229	9	𝐿	𝐿	PROPN
cana-5358	229	10	be	be	AUX
cana-5358	229	11	a	a	DET
cana-5358	229	12	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	229	13	in	in	ADP
cana-5358	229	14	(	(	PUNCT
cana-5358	229	15	𝑋1	𝑋1	PROPN
cana-5358	229	16	,	,	PUNCT
cana-5358	229	17	𝜏1	𝜏1	NOUN
cana-5358	229	18	)	)	PUNCT
cana-5358	229	19	.	.	PUNCT
cana-5358	230	1	then	then	ADV
cana-5358	230	2	,	,	PUNCT
cana-5358	230	3	(	(	PUNCT
cana-5358	230	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	230	5	−1)−1(𝐿	−1)−1(𝐿	NOUN
cana-5358	230	6	)	)	PUNCT
cana-5358	230	7	=	=	PUNCT
cana-5358	230	8	ℎ𝔉(𝐿	ℎ𝔉(𝐿	NOUN
cana-5358	230	9	)	)	PUNCT
cana-5358	230	10	is	be	AUX
cana-5358	230	11	a	a	DET
cana-5358	230	12	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	230	13	communications	communication	NOUN
cana-5358	230	14	on	on	ADP
cana-5358	230	15	applied	apply	VERB
cana-5358	230	16	nonlinear	nonlinear	ADJ
cana-5358	230	17	analysis	analysis	NOUN
cana-5358	230	18	issn	issn	NOUN
cana-5358	230	19	:	:	PUNCT
cana-5358	230	20	1074	1074	NUM
cana-5358	230	21	-	-	PUNCT
cana-5358	230	22	133x	133x	NUM
cana-5358	230	23	vol	vol	VERB
cana-5358	230	24	32	32	NUM
cana-5358	230	25	no	no	NOUN
cana-5358	230	26	.	.	PUNCT
cana-5358	231	1	10s	10	NOUN
cana-5358	231	2	(	(	PUNCT
cana-5358	231	3	2025	2025	NUM
cana-5358	231	4	)	)	PUNCT
cana-5358	231	5	1903	1903	NUM
cana-5358	231	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	231	7	in	in	ADP
cana-5358	231	8	(	(	PUNCT
cana-5358	231	9	𝑋2	𝑋2	ADJ
cana-5358	231	10	,	,	PUNCT
cana-5358	231	11	𝜏2	𝜏2	PROPN
cana-5358	231	12	)	)	PUNCT
cana-5358	231	13	,	,	PUNCT
cana-5358	231	14	by	by	ADP
cana-5358	231	15	presumption	presumption	NOUN
cana-5358	231	16	.	.	PUNCT
cana-5358	232	1	since	since	SCONJ
cana-5358	232	2	(	(	PUNCT
cana-5358	232	3	𝑋2	𝑋2	ADJ
cana-5358	232	4	,	,	PUNCT
cana-5358	232	5	𝜏2	𝜏2	PROPN
cana-5358	232	6	)	)	PUNCT
cana-5358	232	7	is	be	AUX
cana-5358	232	8	a	a	DET
cana-5358	232	9	𝔉ℱ𝛿𝛽𝑇1	𝔉ℱ𝛿𝛽𝑇1	NOUN
cana-5358	232	10	2	2	NUM
cana-5358	232	11	-space	-space	NOUN
cana-5358	232	12	,	,	PUNCT
cana-5358	232	13	ℎ𝔉(𝐿	ℎ𝔉(𝐿	NOUN
cana-5358	232	14	)	)	PUNCT
cana-5358	232	15	is	be	AUX
cana-5358	232	16	a	a	DET
cana-5358	232	17	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	232	18	in	in	ADP
cana-5358	232	19	(	(	PUNCT
cana-5358	232	20	𝑋2	𝑋2	ADJ
cana-5358	232	21	,	,	PUNCT
cana-5358	232	22	𝜏2	𝜏2	PROPN
cana-5358	232	23	)	)	PUNCT
cana-5358	232	24	.	.	PUNCT
cana-5358	233	1	hence	hence	ADV
cana-5358	233	2	,	,	PUNCT
cana-5358	233	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	233	4	−1	−1	NOUN
cana-5358	233	5	is	be	AUX
cana-5358	233	6	𝔉ℱ𝐶𝑡𝑠.	𝔉ℱ𝐶𝑡𝑠.	PROPN
cana-5358	233	7	hence	hence	ADV
cana-5358	233	8	,	,	PUNCT
cana-5358	233	9	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	233	10	is	be	AUX
cana-5358	233	11	a	a	DET
cana-5358	233	12	𝔉ℱ𝐻𝑜𝑚.	𝔉ℱ𝐻𝑜𝑚.	ADJ
cana-5358	233	13	proof	proof	NOUN
cana-5358	233	14	of	of	ADP
cana-5358	233	15	other	other	ADJ
cana-5358	233	16	cases	case	NOUN
cana-5358	233	17	are	be	AUX
cana-5358	233	18	similar	similar	ADJ
cana-5358	233	19	.	.	PUNCT
cana-5358	234	1	theorem	theorem	VERB
cana-5358	234	2	3.4	3.4	NUM
cana-5358	234	3	let	let	VERB
cana-5358	234	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	234	5	:	:	PUNCT
cana-5358	234	6	(	(	PUNCT
cana-5358	234	7	𝑋1	𝑋1	PROPN
cana-5358	234	8	,	,	PUNCT
cana-5358	234	9	𝜏1	𝜏1	NOUN
cana-5358	234	10	)	)	PUNCT
cana-5358	234	11	→	→	SYM
cana-5358	234	12	(	(	PUNCT
cana-5358	234	13	𝑋2	𝑋2	PROPN
cana-5358	234	14	,	,	PUNCT
cana-5358	234	15	𝜏2	𝜏2	PROPN
cana-5358	234	16	)	)	PUNCT
cana-5358	234	17	be	be	VERB
cana-5358	234	18	a	a	DET
cana-5358	234	19	mapping	mapping	NOUN
cana-5358	234	20	.	.	PUNCT
cana-5358	235	1	then	then	ADV
cana-5358	235	2	the	the	DET
cana-5358	235	3	following	follow	VERB
cana-5358	235	4	are	be	AUX
cana-5358	235	5	equivalent	equivalent	ADJ
cana-5358	235	6	if	if	SCONJ
cana-5358	235	7	(	(	PUNCT
cana-5358	235	8	𝑋2	𝑋2	ADJ
cana-5358	235	9	,	,	PUNCT
cana-5358	235	10	𝜏2	𝜏2	PROPN
cana-5358	235	11	)	)	PUNCT
cana-5358	235	12	is	be	AUX
cana-5358	235	13	a	a	DET
cana-5358	235	14	𝔉ℱ𝛿𝛼𝑇1	𝔉ℱ𝛿𝛼𝑇1	PROPN
cana-5358	235	15	2	2	NUM
cana-5358	235	16	(	(	PUNCT
cana-5358	235	17	resp	resp	NOUN
cana-5358	235	18	.	.	PUNCT
cana-5358	236	1	𝔉ℱ𝛿𝒮𝑇1	𝔉ℱ𝛿𝒮𝑇1	PROPN
cana-5358	236	2	2	2	NUM
cana-5358	236	3	,	,	PUNCT
cana-5358	236	4	𝔉ℱ𝛿𝒫𝑇1	𝔉ℱ𝛿𝒫𝑇1	ADV
cana-5358	236	5	2	2	NUM
cana-5358	236	6	and	and	CCONJ
cana-5358	236	7	𝔉ℱ𝛿𝛽𝑇1	𝔉ℱ𝛿𝛽𝑇1	PROPN
cana-5358	236	8	2	2	NUM
cana-5358	236	9	)	)	PUNCT
cana-5358	236	10	-space	-space	NOUN
cana-5358	236	11	:	:	PUNCT
cana-5358	236	12	(	(	PUNCT
cana-5358	236	13	i	i	NOUN
cana-5358	236	14	)	)	PUNCT
cana-5358	236	15	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	236	16	is	be	AUX
cana-5358	236	17	𝔉ℱ𝛿𝛼𝐶	𝔉ℱ𝛿𝛼𝐶	NOUN
cana-5358	236	18	(	(	PUNCT
cana-5358	236	19	resp	resp	NOUN
cana-5358	236	20	.	.	PUNCT
cana-5358	237	1	𝔉ℱ𝛿𝒮𝐶	𝔉ℱ𝛿𝒮𝐶	SYM
cana-5358	237	2	,	,	PUNCT
cana-5358	237	3	𝔉ℱ𝛿𝒫𝐶	𝔉ℱ𝛿𝒫𝐶	PROPN
cana-5358	237	4	and	and	CCONJ
cana-5358	237	5	𝔉ℱ𝛿𝛽𝐶	𝔉ℱ𝛿𝛽𝐶	NOUN
cana-5358	237	6	)	)	PUNCT
cana-5358	237	7	mapping	mapping	NOUN
cana-5358	237	8	.	.	PUNCT
cana-5358	238	1	(	(	PUNCT
cana-5358	238	2	ii	ii	NOUN
cana-5358	238	3	)	)	PUNCT
cana-5358	238	4	if	if	SCONJ
cana-5358	238	5	𝐾	𝐾	PROPN
cana-5358	238	6	is	be	AUX
cana-5358	238	7	a	a	DET
cana-5358	238	8	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5358	238	9	in	in	ADP
cana-5358	238	10	(	(	PUNCT
cana-5358	238	11	𝑋1	𝑋1	PROPN
cana-5358	238	12	,	,	PUNCT
cana-5358	238	13	𝜏1	𝜏1	NOUN
cana-5358	238	14	)	)	PUNCT
cana-5358	238	15	,	,	PUNCT
cana-5358	238	16	then	then	ADV
cana-5358	238	17	ℎ𝔉(𝑋1	ℎ𝔉(𝑋1	PROPN
cana-5358	238	18	,	,	PUNCT
cana-5358	238	19	𝜏1	𝜏1	NOUN
cana-5358	238	20	)	)	PUNCT
cana-5358	238	21	is	be	AUX
cana-5358	238	22	𝔉ℱ𝛿𝛼𝑜𝑠	𝔉ℱ𝛿𝛼𝑜𝑠	PROPN
cana-5358	238	23	(	(	PUNCT
cana-5358	238	24	resp	resp	PROPN
cana-5358	238	25	.	.	PUNCT
cana-5358	239	1	𝔉ℱ𝛿𝒮𝑜𝑠	𝔉ℱ𝛿𝒮𝑜𝑠	PROPN
cana-5358	239	2	,	,	PUNCT
cana-5358	239	3	𝔉ℱ𝛿𝒫𝑜𝑠	𝔉ℱ𝛿𝒫𝑜𝑠	PROPN
cana-5358	239	4	and	and	CCONJ
cana-5358	239	5	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5358	239	6	)	)	PUNCT
cana-5358	239	7	in	in	ADP
cana-5358	239	8	(	(	PUNCT
cana-5358	239	9	𝑋2	𝑋2	ADJ
cana-5358	239	10	,	,	PUNCT
cana-5358	239	11	𝜏2	𝜏2	PROPN
cana-5358	239	12	)	)	PUNCT
cana-5358	239	13	.	.	PUNCT
cana-5358	240	1	(	(	PUNCT
cana-5358	240	2	iii	iii	X
cana-5358	240	3	)	)	PUNCT
cana-5358	240	4	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾	PROPN
cana-5358	240	5	)	)	PUNCT
cana-5358	240	6	)	)	PUNCT
cana-5358	241	1	⊆	⊆	NUM
cana-5358	241	2	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(ℎ𝔉(𝐾	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(ℎ𝔉(𝐾	NOUN
cana-5358	241	3	)	)	PUNCT
cana-5358	241	4	)	)	PUNCT
cana-5358	241	5	)	)	PUNCT
cana-5358	241	6	for	for	ADP
cana-5358	241	7	every	every	DET
cana-5358	241	8	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	241	9	𝐾	𝐾	PROPN
cana-5358	241	10	in	in	ADP
cana-5358	241	11	(	(	PUNCT
cana-5358	241	12	𝑋1	𝑋1	PROPN
cana-5358	241	13	,	,	PUNCT
cana-5358	241	14	𝜏1	𝜏1	NOUN
cana-5358	241	15	)	)	PUNCT
cana-5358	241	16	.	.	PUNCT
cana-5358	242	1	proof	proof	NOUN
cana-5358	242	2	.	.	PUNCT
cana-5358	243	1	(	(	PUNCT
cana-5358	243	2	i	i	NOUN
cana-5358	243	3	)	)	PUNCT
cana-5358	243	4	⇒	⇒	PROPN
cana-5358	243	5	(	(	PUNCT
cana-5358	243	6	ii	ii	NOUN
cana-5358	243	7	):	):	PUNCT
cana-5358	243	8	obvious	obvious	ADJ
cana-5358	243	9	.	.	PUNCT
cana-5358	244	1	(	(	PUNCT
cana-5358	244	2	ii	ii	NOUN
cana-5358	244	3	)	)	PUNCT
cana-5358	244	4	⇒	⇒	NOUN
cana-5358	244	5	(	(	PUNCT
cana-5358	244	6	iii	iii	NOUN
cana-5358	244	7	):	):	PUNCT
cana-5358	244	8	let	let	VERB
cana-5358	244	9	𝐾	𝐾	PRON
cana-5358	244	10	be	be	AUX
cana-5358	244	11	a	a	DET
cana-5358	244	12	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	244	13	in	in	ADP
cana-5358	244	14	(	(	PUNCT
cana-5358	244	15	𝑋1	𝑋1	PROPN
cana-5358	244	16	,	,	PUNCT
cana-5358	244	17	𝜏1	𝜏1	NOUN
cana-5358	244	18	)	)	PUNCT
cana-5358	244	19	.	.	PUNCT
cana-5358	245	1	then	then	ADV
cana-5358	245	2	,	,	PUNCT
cana-5358	245	3	𝔉ℱ𝑖𝑛𝑡(𝐾	𝔉ℱ𝑖𝑛𝑡(𝐾	PROPN
cana-5358	245	4	)	)	PUNCT
cana-5358	245	5	is	be	AUX
cana-5358	245	6	a	a	DET
cana-5358	245	7	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5358	245	8	in	in	ADP
cana-5358	245	9	(	(	PUNCT
cana-5358	245	10	𝑋1	𝑋1	PROPN
cana-5358	245	11	,	,	PUNCT
cana-5358	245	12	𝜏1	𝜏1	NOUN
cana-5358	245	13	)	)	PUNCT
cana-5358	245	14	.	.	PUNCT
cana-5358	246	1	then	then	ADV
cana-5358	246	2	,	,	PUNCT
cana-5358	246	3	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾	PROPN
cana-5358	246	4	)	)	PUNCT
cana-5358	246	5	is	be	AUX
cana-5358	246	6	a	a	DET
cana-5358	246	7	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5358	246	8	in	in	ADP
cana-5358	246	9	(	(	PUNCT
cana-5358	246	10	𝑋2	𝑋2	ADJ
cana-5358	246	11	,	,	PUNCT
cana-5358	246	12	𝜏2	𝜏2	PROPN
cana-5358	246	13	)	)	PUNCT
cana-5358	246	14	.	.	PUNCT
cana-5358	247	1	since	since	SCONJ
cana-5358	247	2	(	(	PUNCT
cana-5358	247	3	𝑋2	𝑋2	ADJ
cana-5358	247	4	,	,	PUNCT
cana-5358	247	5	𝜏2	𝜏2	PROPN
cana-5358	247	6	)	)	PUNCT
cana-5358	247	7	is	be	AUX
cana-5358	247	8	a	a	DET
cana-5358	247	9	𝔉ℱ𝛿𝛽𝑇1	𝔉ℱ𝛿𝛽𝑇1	NOUN
cana-5358	247	10	2	2	NUM
cana-5358	247	11	-space	-space	NOUN
cana-5358	247	12	,	,	PUNCT
cana-5358	247	13	so	so	ADV
cana-5358	247	14	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾	PROPN
cana-5358	247	15	)	)	PUNCT
cana-5358	247	16	)	)	PUNCT
cana-5358	247	17	is	be	AUX
cana-5358	247	18	a𝔉ℱ𝑜𝑠	a𝔉ℱ𝑜𝑠	ADJ
cana-5358	247	19	in	in	ADP
cana-5358	247	20	(	(	PUNCT
cana-5358	247	21	𝑋2	𝑋2	ADJ
cana-5358	247	22	,	,	PUNCT
cana-5358	247	23	𝜏2	𝜏2	PROPN
cana-5358	247	24	)	)	PUNCT
cana-5358	247	25	.	.	PUNCT
cana-5358	248	1	therefore	therefore	ADV
cana-5358	248	2	,	,	PUNCT
cana-5358	248	3	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾	PROPN
cana-5358	248	4	)	)	PUNCT
cana-5358	248	5	)	)	PUNCT
cana-5358	249	1	=	=	PUNCT
cana-5358	249	2	𝔉ℱ𝑖𝑛𝑡	𝔉ℱ𝑖𝑛𝑡	PROPN
cana-5358	249	3	(	(	PUNCT
cana-5358	249	4	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾	PROPN
cana-5358	249	5	)	)	PUNCT
cana-5358	249	6	)	)	PUNCT
cana-5358	249	7	)	)	PUNCT
cana-5358	250	1	⊆	⊆	NUM
cana-5358	250	2	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(ℎ𝔉(𝐾	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(ℎ𝔉(𝐾	NOUN
cana-5358	250	3	)	)	PUNCT
cana-5358	250	4	)	)	PUNCT
cana-5358	250	5	)	)	PUNCT
cana-5358	250	6	.	.	PUNCT
cana-5358	251	1	(	(	PUNCT
cana-5358	251	2	iii	iii	X
cana-5358	251	3	)	)	PUNCT
cana-5358	251	4	⇒	⇒	NOUN
cana-5358	251	5	(	(	PUNCT
cana-5358	251	6	i	i	NOUN
cana-5358	251	7	):	):	PUNCT
cana-5358	251	8	let	let	VERB
cana-5358	251	9	𝐾	𝐾	PRON
cana-5358	251	10	be	be	AUX
cana-5358	251	11	a	a	DET
cana-5358	251	12	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	251	13	in	in	ADP
cana-5358	251	14	(	(	PUNCT
cana-5358	251	15	𝑋1	𝑋1	PROPN
cana-5358	251	16	,	,	PUNCT
cana-5358	251	17	𝜏1	𝜏1	NOUN
cana-5358	251	18	)	)	PUNCT
cana-5358	251	19	.	.	PUNCT
cana-5358	252	1	then	then	ADV
cana-5358	252	2	,	,	PUNCT
cana-5358	252	3	𝐾𝑐	𝐾𝑐	VERB
cana-5358	252	4	is	be	AUX
cana-5358	252	5	a	a	DET
cana-5358	252	6	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5358	252	7	in	in	ADP
cana-5358	252	8	(	(	PUNCT
cana-5358	252	9	𝑋1	𝑋1	PROPN
cana-5358	252	10	,	,	PUNCT
cana-5358	252	11	𝜏1	𝜏1	NOUN
cana-5358	252	12	)	)	PUNCT
cana-5358	252	13	.	.	PUNCT
cana-5358	253	1	from	from	ADP
cana-5358	253	2	,	,	PUNCT
cana-5358	253	3	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾)𝑐	ℎ𝔉(𝔉ℱ𝑖𝑛𝑡(𝐾)𝑐	PROPN
cana-5358	253	4	)	)	PUNCT
cana-5358	253	5	⊆	⊆	NUM
cana-5358	253	6	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(ℎ𝔉(𝐾)𝑐	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(ℎ𝔉(𝐾)𝑐	NOUN
cana-5358	253	7	)	)	PUNCT
cana-5358	253	8	)	)	PUNCT
cana-5358	253	9	,	,	PUNCT
cana-5358	253	10	ℎ𝔉((𝐾)𝑐	ℎ𝔉((𝐾)𝑐	PROPN
cana-5358	253	11	)	)	PUNCT
cana-5358	253	12	⊆	⊆	NUM
cana-5358	253	13	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(ℎ𝔉(𝐾)𝑐	𝔉ℱ𝑐𝑙(𝔉ℱ𝑖𝑛𝑡(ℎ𝔉(𝐾)𝑐	NOUN
cana-5358	253	14	)	)	PUNCT
cana-5358	253	15	)	)	PUNCT
cana-5358	253	16	.	.	PUNCT
cana-5358	254	1	therefore	therefore	ADV
cana-5358	254	2	,	,	PUNCT
cana-5358	254	3	ℎ𝔉((𝐾)𝑐	ℎ𝔉((𝐾)𝑐	PROPN
cana-5358	254	4	)	)	PUNCT
cana-5358	254	5	is	be	AUX
cana-5358	254	6	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5358	254	7	in	in	ADP
cana-5358	254	8	(	(	PUNCT
cana-5358	254	9	𝑋2	𝑋2	ADJ
cana-5358	254	10	,	,	PUNCT
cana-5358	254	11	𝜏2	𝜏2	PROPN
cana-5358	254	12	)	)	PUNCT
cana-5358	254	13	.	.	PUNCT
cana-5358	255	1	therefore	therefore	ADV
cana-5358	255	2	,	,	PUNCT
cana-5358	255	3	ℎ𝔉(𝐾	ℎ𝔉(𝐾	ADV
cana-5358	255	4	)	)	PUNCT
cana-5358	255	5	is	be	AUX
cana-5358	255	6	a	a	DET
cana-5358	255	7	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	255	8	in	in	ADP
cana-5358	255	9	(	(	PUNCT
cana-5358	255	10	𝑋1	𝑋1	PROPN
cana-5358	255	11	,	,	PUNCT
cana-5358	255	12	𝜏1	𝜏1	NOUN
cana-5358	255	13	)	)	PUNCT
cana-5358	255	14	.	.	PUNCT
cana-5358	256	1	hence	hence	ADV
cana-5358	256	2	,	,	PUNCT
cana-5358	256	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	256	4	is	be	AUX
cana-5358	256	5	a	a	DET
cana-5358	256	6	𝔉ℱ𝐶	𝔉ℱ𝐶	NOUN
cana-5358	256	7	mapping	mapping	NOUN
cana-5358	256	8	.	.	PUNCT
cana-5358	257	1	the	the	DET
cana-5358	257	2	proof	proof	NOUN
cana-5358	257	3	of	of	ADP
cana-5358	257	4	other	other	ADJ
cana-5358	257	5	cases	case	NOUN
cana-5358	257	6	are	be	AUX
cana-5358	257	7	similar	similar	ADJ
cana-5358	257	8	.	.	PUNCT
cana-5358	258	1	theorem	theorem	VERB
cana-5358	258	2	3.5	3.5	NUM
cana-5358	258	3	let	let	VERB
cana-5358	258	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	258	5	:	:	PUNCT
cana-5358	258	6	(	(	PUNCT
cana-5358	258	7	𝑋1	𝑋1	PROPN
cana-5358	258	8	,	,	PUNCT
cana-5358	258	9	𝜏1	𝜏1	NOUN
cana-5358	258	10	)	)	PUNCT
cana-5358	258	11	→	→	SYM
cana-5358	258	12	(	(	PUNCT
cana-5358	258	13	𝑋2	𝑋2	PROPN
cana-5358	258	14	,	,	PUNCT
cana-5358	258	15	𝜏2	𝜏2	PROPN
cana-5358	258	16	)	)	PUNCT
cana-5358	258	17	and	and	CCONJ
cana-5358	258	18	𝑔𝔉	𝑔𝔉	NOUN
cana-5358	258	19	:	:	PUNCT
cana-5358	258	20	(	(	PUNCT
cana-5358	258	21	𝑋2	𝑋2	ADJ
cana-5358	258	22	,	,	PUNCT
cana-5358	258	23	𝜏2	𝜏2	PROPN
cana-5358	258	24	)	)	PUNCT
cana-5358	258	25	→	→	SYM
cana-5358	258	26	(	(	PUNCT
cana-5358	258	27	𝑋3	𝑋3	NOUN
cana-5358	258	28	,	,	PUNCT
cana-5358	258	29	𝜏3	𝜏3	NOUN
cana-5358	258	30	)	)	PUNCT
cana-5358	258	31	be	be	VERB
cana-5358	258	32	𝔉ℱ𝛿𝛼𝐶	𝔉ℱ𝛿𝛼𝐶	NOUN
cana-5358	258	33	(	(	PUNCT
cana-5358	258	34	resp	resp	NOUN
cana-5358	258	35	.	.	PUNCT
cana-5358	259	1	𝔉ℱ𝛿𝒮𝐶	𝔉ℱ𝛿𝒮𝐶	NUM
cana-5358	259	2	,	,	PUNCT
cana-5358	259	3	𝔉ℱ𝛿𝒫𝐶	𝔉ℱ𝛿𝒫𝐶	PROPN
cana-5358	259	4	and	and	CCONJ
cana-5358	259	5	𝔉ℱ𝛿𝛽𝐶	𝔉ℱ𝛿𝛽𝐶	NOUN
cana-5358	259	6	)	)	PUNCT
cana-5358	259	7	,	,	PUNCT
cana-5358	259	8	where	where	SCONJ
cana-5358	259	9	(	(	PUNCT
cana-5358	259	10	𝑋1	𝑋1	PROPN
cana-5358	259	11	,	,	PUNCT
cana-5358	259	12	𝜏1	𝜏1	NOUN
cana-5358	259	13	)	)	PUNCT
cana-5358	259	14	and	and	CCONJ
cana-5358	259	15	(	(	PUNCT
cana-5358	259	16	𝑋3	𝑋3	NOUN
cana-5358	259	17	,	,	PUNCT
cana-5358	259	18	𝜏3	𝜏3	NOUN
cana-5358	259	19	)	)	PUNCT
cana-5358	259	20	are	be	AUX
cana-5358	259	21	two	two	NUM
cana-5358	259	22	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5358	259	23	’s	’s	PART
cana-5358	259	24	and	and	CCONJ
cana-5358	259	25	(	(	PUNCT
cana-5358	259	26	𝑋2	𝑋2	PROPN
cana-5358	259	27	,	,	PUNCT
cana-5358	259	28	𝜏2	𝜏2	PROPN
cana-5358	259	29	)	)	PUNCT
cana-5358	259	30	a	a	DET
cana-5358	259	31	𝔉ℱ𝛿𝑇1	𝔉ℱ𝛿𝑇1	NUM
cana-5358	259	32	2	2	NUM
cana-5358	259	33	(	(	PUNCT
cana-5358	259	34	resp	resp	NOUN
cana-5358	259	35	.	.	PUNCT
cana-5358	260	1	𝔉ℱ𝛿𝛼𝑇1	𝔉ℱ𝛿𝛼𝑇1	PROPN
cana-5358	260	2	2	2	NUM
cana-5358	260	3	,	,	PUNCT
cana-5358	260	4	𝔉ℱ𝛿𝒮𝑇1	𝔉ℱ𝛿𝒮𝑇1	PROPN
cana-5358	260	5	2	2	NUM
cana-5358	260	6	,	,	PUNCT
cana-5358	260	7	𝔉ℱ𝛿𝒫𝑇1	𝔉ℱ𝛿𝒫𝑇1	ADV
cana-5358	260	8	2	2	NUM
cana-5358	260	9	and	and	CCONJ
cana-5358	260	10	𝔉ℱ𝛿𝛽𝑇1	𝔉ℱ𝛿𝛽𝑇1	PROPN
cana-5358	260	11	2	2	NUM
cana-5358	260	12	)	)	PUNCT
cana-5358	260	13	-space	-space	NOUN
cana-5358	260	14	,	,	PUNCT
cana-5358	260	15	then	then	ADV
cana-5358	260	16	the	the	DET
cana-5358	260	17	composition	composition	NOUN
cana-5358	260	18	𝑔𝔉	𝑔𝔉	NOUN
cana-5358	260	19	∘	∘	VERB
cana-5358	260	20	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	260	21	is	be	AUX
cana-5358	260	22	𝔉ℱ𝛿𝛼𝐶	𝔉ℱ𝛿𝛼𝐶	NOUN
cana-5358	260	23	(	(	PUNCT
cana-5358	260	24	resp	resp	NOUN
cana-5358	260	25	.	.	PUNCT
cana-5358	261	1	𝔉ℱ𝛿𝒮𝐶	𝔉ℱ𝛿𝒮𝐶	SYM
cana-5358	261	2	,	,	PUNCT
cana-5358	261	3	𝔉ℱ𝛿𝒫𝐶	𝔉ℱ𝛿𝒫𝐶	PROPN
cana-5358	261	4	and	and	CCONJ
cana-5358	261	5	𝔉ℱ𝛿𝛽𝐶	𝔉ℱ𝛿𝛽𝐶	NOUN
cana-5358	261	6	)	)	PUNCT
cana-5358	261	7	.	.	PUNCT
cana-5358	262	1	proof	proof	NOUN
cana-5358	262	2	.	.	PUNCT
cana-5358	263	1	let	let	VERB
cana-5358	263	2	𝐾	𝐾	PRON
cana-5358	263	3	be	be	AUX
cana-5358	263	4	a	a	DET
cana-5358	263	5	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	263	6	in	in	ADP
cana-5358	263	7	(	(	PUNCT
cana-5358	263	8	𝑋1	𝑋1	PROPN
cana-5358	263	9	,	,	PUNCT
cana-5358	263	10	𝜏1	𝜏1	NOUN
cana-5358	263	11	)	)	PUNCT
cana-5358	263	12	.	.	PUNCT
cana-5358	264	1	since	since	SCONJ
cana-5358	264	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	264	3	is	be	AUX
cana-5358	264	4	𝔉ℱ𝛿𝛽𝐶	𝔉ℱ𝛿𝛽𝐶	NOUN
cana-5358	264	5	and	and	CCONJ
cana-5358	264	6	ℎ𝔉(𝐾	ℎ𝔉(𝐾	CCONJ
cana-5358	264	7	)	)	PUNCT
cana-5358	264	8	is	be	AUX
cana-5358	264	9	a	a	DET
cana-5358	264	10	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	264	11	in	in	ADP
cana-5358	264	12	(	(	PUNCT
cana-5358	264	13	𝑋2	𝑋2	ADJ
cana-5358	264	14	,	,	PUNCT
cana-5358	264	15	𝜏2	𝜏2	PROPN
cana-5358	264	16	)	)	PUNCT
cana-5358	264	17	,	,	PUNCT
cana-5358	264	18	by	by	ADP
cana-5358	264	19	assumption	assumption	NOUN
cana-5358	264	20	,	,	PUNCT
cana-5358	264	21	ℎ𝔉(𝐾	ℎ𝔉(𝐾	X
cana-5358	264	22	)	)	PUNCT
cana-5358	264	23	is	be	AUX
cana-5358	264	24	a	a	DET
cana-5358	264	25	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	264	26	in	in	ADP
cana-5358	264	27	(	(	PUNCT
cana-5358	264	28	𝑋2	𝑋2	ADJ
cana-5358	264	29	,	,	PUNCT
cana-5358	264	30	𝜏2	𝜏2	PROPN
cana-5358	264	31	)	)	PUNCT
cana-5358	264	32	.	.	PUNCT
cana-5358	265	1	since	since	SCONJ
cana-5358	265	2	𝑔𝔉	𝑔𝔉	PROPN
cana-5358	265	3	is	be	AUX
cana-5358	265	4	𝔉ℱ𝛿𝛽𝐶	𝔉ℱ𝛿𝛽𝐶	PROPN
cana-5358	265	5	,	,	PUNCT
cana-5358	265	6	then	then	ADV
cana-5358	265	7	𝑔𝔉(ℎ𝔉(𝐾	𝑔𝔉(ℎ𝔉(𝐾	NOUN
cana-5358	265	8	)	)	PUNCT
cana-5358	265	9	)	)	PUNCT
cana-5358	265	10	is	be	AUX
cana-5358	265	11	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	ADV
cana-5358	265	12	in	in	ADP
cana-5358	265	13	(	(	PUNCT
cana-5358	265	14	𝑋3	𝑋3	NOUN
cana-5358	265	15	,	,	PUNCT
cana-5358	265	16	𝜏3	𝜏3	NOUN
cana-5358	265	17	)	)	PUNCT
cana-5358	265	18	and	and	CCONJ
cana-5358	265	19	𝑔𝔉(ℎ𝔉(𝐾	𝑔𝔉(ℎ𝔉(𝐾	NOUN
cana-5358	265	20	)	)	PUNCT
cana-5358	265	21	)	)	PUNCT
cana-5358	266	1	=	=	PUNCT
cana-5358	266	2	(	(	PUNCT
cana-5358	266	3	𝑔𝔉	𝑔𝔉	PROPN
cana-5358	266	4	∘	∘	PROPN
cana-5358	266	5	ℎ𝔉)(𝐾	ℎ𝔉)(𝐾	ADJ
cana-5358	266	6	)	)	PUNCT
cana-5358	266	7	.	.	PUNCT
cana-5358	267	1	therefore	therefore	ADV
cana-5358	267	2	,	,	PUNCT
cana-5358	267	3	𝑔𝔉	𝑔𝔉	PROPN
cana-5358	267	4	∘	∘	ADJ
cana-5358	267	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	267	6	is	be	AUX
cana-5358	267	7	𝔉ℱ𝛿𝛽𝐶.	𝔉ℱ𝛿𝛽𝐶.	NOUN
cana-5358	267	8	theorem	theorem	VERB
cana-5358	267	9	3.6	3.6	NUM
cana-5358	267	10	let	let	VERB
cana-5358	267	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	267	12	:	:	PUNCT
cana-5358	267	13	(	(	PUNCT
cana-5358	267	14	𝑋1	𝑋1	PROPN
cana-5358	267	15	,	,	PUNCT
cana-5358	267	16	𝜏1	𝜏1	NOUN
cana-5358	267	17	)	)	PUNCT
cana-5358	267	18	→	→	SYM
cana-5358	267	19	(	(	PUNCT
cana-5358	267	20	𝑋2	𝑋2	PROPN
cana-5358	267	21	,	,	PUNCT
cana-5358	267	22	𝜏2	𝜏2	PROPN
cana-5358	267	23	)	)	PUNCT
cana-5358	267	24	and	and	CCONJ
cana-5358	267	25	𝑔𝔉	𝑔𝔉	NOUN
cana-5358	267	26	:	:	PUNCT
cana-5358	267	27	(	(	PUNCT
cana-5358	267	28	𝑋2	𝑋2	ADJ
cana-5358	267	29	,	,	PUNCT
cana-5358	267	30	𝜏2	𝜏2	PROPN
cana-5358	267	31	)	)	PUNCT
cana-5358	267	32	→	→	SYM
cana-5358	267	33	(	(	PUNCT
cana-5358	267	34	𝑋3	𝑋3	NOUN
cana-5358	267	35	,	,	PUNCT
cana-5358	267	36	𝜏3	𝜏3	NOUN
cana-5358	267	37	)	)	PUNCT
cana-5358	267	38	be	be	VERB
cana-5358	267	39	two	two	NUM
cana-5358	267	40	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	NOUN
cana-5358	267	41	’s	’s	ADV
cana-5358	267	42	,	,	PUNCT
cana-5358	267	43	then	then	ADV
cana-5358	267	44	the	the	DET
cana-5358	267	45	following	follow	VERB
cana-5358	267	46	hold	hold	NOUN
cana-5358	267	47	:	:	PUNCT
cana-5358	267	48	(	(	PUNCT
cana-5358	267	49	i	i	NOUN
cana-5358	267	50	)	)	PUNCT
cana-5358	267	51	if	if	SCONJ
cana-5358	267	52	𝑔𝔉	𝑔𝔉	PROPN
cana-5358	267	53	∘	∘	VERB
cana-5358	267	54	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	267	55	is	be	AUX
cana-5358	267	56	𝔉ℱ𝛿𝑂	𝔉ℱ𝛿𝑂	PROPN
cana-5358	267	57	(	(	PUNCT
cana-5358	267	58	resp	resp	NOUN
cana-5358	267	59	.	.	PUNCT
cana-5358	268	1	𝔉ℱ𝛿𝛼𝑂	𝔉ℱ𝛿𝛼𝑂	ADP
cana-5358	268	2	,	,	PUNCT
cana-5358	268	3	𝔉ℱ𝛿𝒮𝑂	𝔉ℱ𝛿𝒮𝑂	NUM
cana-5358	268	4	,	,	PUNCT
cana-5358	268	5	𝔉ℱ𝛿𝒫𝑂	𝔉ℱ𝛿𝒫𝑂	PROPN
cana-5358	268	6	and	and	CCONJ
cana-5358	268	7	𝔉ℱ𝛿𝛽𝑂	𝔉ℱ𝛿𝛽𝑂	PROPN
cana-5358	268	8	)	)	PUNCT
cana-5358	268	9	and	and	CCONJ
cana-5358	268	10	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	268	11	is	be	AUX
cana-5358	268	12	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	PROPN
cana-5358	268	13	,	,	PUNCT
cana-5358	268	14	then	then	ADV
cana-5358	268	15	𝑔𝔉	𝑔𝔉	PROPN
cana-5358	268	16	is	be	AUX
cana-5358	268	17	𝔉ℱ𝛿𝑂	𝔉ℱ𝛿𝑂	PROPN
cana-5358	268	18	(	(	PUNCT
cana-5358	268	19	resp	resp	NOUN
cana-5358	268	20	.	.	PUNCT
cana-5358	269	1	𝔉ℱ𝛿𝛼𝑂	𝔉ℱ𝛿𝛼𝑂	ADP
cana-5358	269	2	,	,	PUNCT
cana-5358	269	3	𝔉ℱ𝛿𝒮𝑂	𝔉ℱ𝛿𝒮𝑂	NOUN
cana-5358	269	4	,	,	PUNCT
cana-5358	269	5	𝔉ℱ𝛿𝒫𝑂	𝔉ℱ𝛿𝒫𝑂	X
cana-5358	269	6	and	and	CCONJ
cana-5358	269	7	𝔉ℱ𝛿𝛽𝑂	𝔉ℱ𝛿𝛽𝑂	NOUN
cana-5358	269	8	)	)	PUNCT
cana-5358	269	9	.	.	PUNCT
cana-5358	270	1	(	(	PUNCT
cana-5358	270	2	ii	ii	NOUN
cana-5358	270	3	)	)	PUNCT
cana-5358	270	4	if	if	SCONJ
cana-5358	270	5	𝑔𝔉	𝑔𝔉	PROPN
cana-5358	270	6	∘	∘	VERB
cana-5358	270	7	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	270	8	is	be	AUX
cana-5358	270	9	𝔉ℱ𝑂	𝔉ℱ𝑂	PROPN
cana-5358	270	10	and	and	CCONJ
cana-5358	270	11	𝑔𝔉	𝑔𝔉	PROPN
cana-5358	270	12	is	be	AUX
cana-5358	270	13	𝔉ℱ𝛿𝐶𝑡𝑠	𝔉ℱ𝛿𝐶𝑡𝑠	PRON
cana-5358	270	14	(	(	PUNCT
cana-5358	270	15	resp	resp	NOUN
cana-5358	270	16	.	.	PUNCT
cana-5358	271	1	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	𝔉ℱ𝛿𝛼𝐶𝑡𝑠	PROPN
cana-5358	271	2	,	,	PUNCT
cana-5358	271	3	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	𝔉ℱ𝛿𝒮𝐶𝑡𝑠	PROPN
cana-5358	271	4	,	,	PUNCT
cana-5358	271	5	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	𝔉ℱ𝛿𝒫𝐶𝑡𝑠	X
cana-5358	271	6	and	and	CCONJ
cana-5358	271	7	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5358	271	8	)	)	PUNCT
cana-5358	271	9	,	,	PUNCT
cana-5358	271	10	then	then	ADV
cana-5358	271	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	271	12	is	be	AUX
cana-5358	271	13	𝔉ℱ𝛿𝑂	𝔉ℱ𝛿𝑂	PROPN
cana-5358	271	14	(	(	PUNCT
cana-5358	271	15	resp	resp	NOUN
cana-5358	271	16	.	.	PUNCT
cana-5358	272	1	𝔉ℱ𝛿𝛼𝑂	𝔉ℱ𝛿𝛼𝑂	ADP
cana-5358	272	2	,	,	PUNCT
cana-5358	272	3	𝔉ℱ𝛿𝒮𝑂	𝔉ℱ𝛿𝒮𝑂	NOUN
cana-5358	272	4	,	,	PUNCT
cana-5358	272	5	𝔉ℱ𝛿𝒫𝑂	𝔉ℱ𝛿𝒫𝑂	X
cana-5358	272	6	and	and	CCONJ
cana-5358	272	7	𝔉ℱ𝛿𝛽𝑂	𝔉ℱ𝛿𝛽𝑂	NOUN
cana-5358	272	8	)	)	PUNCT
cana-5358	272	9	.	.	PUNCT
cana-5358	273	1	proof	proof	NOUN
cana-5358	273	2	.	.	PUNCT
cana-5358	274	1	(	(	PUNCT
cana-5358	274	2	i	i	NOUN
cana-5358	274	3	)	)	PUNCT
cana-5358	274	4	let	let	VERB
cana-5358	274	5	𝐾	𝐾	PRON
cana-5358	274	6	be	be	AUX
cana-5358	274	7	a	a	DET
cana-5358	274	8	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5358	274	9	in	in	ADP
cana-5358	274	10	(	(	PUNCT
cana-5358	274	11	𝑋2	𝑋2	ADJ
cana-5358	274	12	,	,	PUNCT
cana-5358	274	13	𝜏2	𝜏2	PROPN
cana-5358	274	14	)	)	PUNCT
cana-5358	274	15	.	.	PUNCT
cana-5358	275	1	as	as	SCONJ
cana-5358	275	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	275	3	is	be	AUX
cana-5358	275	4	𝔉ℱ𝐶𝑡𝑠	𝔉ℱ𝐶𝑡𝑠	NOUN
cana-5358	275	5	mapping	mapping	NOUN
cana-5358	275	6	,	,	PUNCT
cana-5358	275	7	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	275	8	−1(𝐾	−1(𝐾	NOUN
cana-5358	275	9	)	)	PUNCT
cana-5358	275	10	is	be	AUX
cana-5358	275	11	𝔉ℱ𝑜𝑠	𝔉ℱ𝑜𝑠	PROPN
cana-5358	275	12	in	in	ADP
cana-5358	275	13	(	(	PUNCT
cana-5358	275	14	𝑋1	𝑋1	PROPN
cana-5358	275	15	,	,	PUNCT
cana-5358	275	16	𝜏1	𝜏1	NOUN
cana-5358	275	17	)	)	PUNCT
cana-5358	275	18	.	.	PUNCT
cana-5358	276	1	as	as	SCONJ
cana-5358	276	2	𝑔𝔉	𝑔𝔉	PROPN
cana-5358	276	3	∘	∘	NOUN
cana-5358	276	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	276	5	is	be	AUX
cana-5358	276	6	𝔉ℱ𝛿𝛽𝑂	𝔉ℱ𝛿𝛽𝑂	PROPN
cana-5358	276	7	mapping	mapping	NOUN
cana-5358	276	8	,	,	PUNCT
cana-5358	276	9	(	(	PUNCT
cana-5358	276	10	𝑔𝔉	𝑔𝔉	NOUN
cana-5358	276	11	∘	∘	NOUN
cana-5358	276	12	ℎ𝔉)(ℎ𝔉	ℎ𝔉)(ℎ𝔉	NOUN
cana-5358	276	13	−1(𝐾	−1(𝐾	NOUN
cana-5358	276	14	)	)	PUNCT
cana-5358	276	15	)	)	PUNCT
cana-5358	277	1	=	=	PUNCT
cana-5358	277	2	𝑔𝔉(ℎ𝔉(ℎ𝔉	𝑔𝔉(ℎ𝔉(ℎ𝔉	DET
cana-5358	277	3	−1(𝐾	−1(𝐾	NOUN
cana-5358	277	4	)	)	PUNCT
cana-5358	277	5	)	)	PUNCT
cana-5358	277	6	)	)	PUNCT
cana-5358	278	1	=	=	PUNCT
cana-5358	278	2	𝑔𝔉(𝐾	𝑔𝔉(𝐾	NOUN
cana-5358	278	3	)	)	PUNCT
cana-5358	278	4	is	be	AUX
cana-5358	278	5	𝔉ℱ𝛿𝛽𝑜𝑠	𝔉ℱ𝛿𝛽𝑜𝑠	PROPN
cana-5358	278	6	in	in	ADP
cana-5358	278	7	communications	communication	NOUN
cana-5358	278	8	on	on	ADP
cana-5358	278	9	applied	apply	VERB
cana-5358	278	10	nonlinear	nonlinear	ADJ
cana-5358	278	11	analysis	analysis	NOUN
cana-5358	278	12	issn	issn	NOUN
cana-5358	278	13	:	:	PUNCT
cana-5358	278	14	1074	1074	NUM
cana-5358	278	15	-	-	PUNCT
cana-5358	278	16	133x	133x	NUM
cana-5358	278	17	vol	vol	VERB
cana-5358	278	18	32	32	NUM
cana-5358	278	19	no	no	NOUN
cana-5358	278	20	.	.	PUNCT
cana-5358	279	1	10s	10	NOUN
cana-5358	279	2	(	(	PUNCT
cana-5358	279	3	2025	2025	NUM
cana-5358	279	4	)	)	PUNCT
cana-5358	279	5	1904	1904	NUM
cana-5358	279	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	279	7	(	(	PUNCT
cana-5358	279	8	𝑋3	𝑋3	NOUN
cana-5358	279	9	,	,	PUNCT
cana-5358	279	10	𝜏3	𝜏3	NOUN
cana-5358	279	11	)	)	PUNCT
cana-5358	279	12	.	.	PUNCT
cana-5358	280	1	thus	thus	ADV
cana-5358	280	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	280	3	is	be	AUX
cana-5358	280	4	𝔉ℱ𝛿𝛽𝑂	𝔉ℱ𝛿𝛽𝑂	PROPN
cana-5358	280	5	mapping	mapping	NOUN
cana-5358	280	6	.	.	PUNCT
cana-5358	281	1	the	the	DET
cana-5358	281	2	other	other	ADJ
cana-5358	281	3	case	case	NOUN
cana-5358	281	4	is	be	AUX
cana-5358	281	5	similar	similar	ADJ
cana-5358	281	6	.	.	PUNCT
cana-5358	282	1	4	4	NUM
cana-5358	282	2	fermatean	fermatean	NOUN
cana-5358	282	3	fuzzy	fuzzy	ADJ
cana-5358	282	4	𝜹𝜷-𝑪	𝜹𝜷-𝑪	PROPN
cana-5358	282	5	homeomorphism	homeomorphism	PROPN
cana-5358	282	6	definition	definition	VERB
cana-5358	282	7	4.1	4.1	NUM
cana-5358	282	8	a	a	DET
cana-5358	282	9	bijection	bijection	ADJ
cana-5358	282	10	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	282	11	:	:	PUNCT
cana-5358	282	12	(	(	PUNCT
cana-5358	282	13	𝑋1	𝑋1	PROPN
cana-5358	282	14	,	,	PUNCT
cana-5358	282	15	𝜏1	𝜏1	NOUN
cana-5358	282	16	)	)	PUNCT
cana-5358	282	17	→	→	SYM
cana-5358	282	18	(	(	PUNCT
cana-5358	282	19	𝑋2	𝑋2	PROPN
cana-5358	282	20	,	,	PUNCT
cana-5358	282	21	𝜏2	𝜏2	PROPN
cana-5358	282	22	)	)	PUNCT
cana-5358	282	23	is	be	AUX
cana-5358	282	24	called	call	VERB
cana-5358	282	25	a	a	DET
cana-5358	282	26	fermatean	fermatean	ADJ
cana-5358	282	27	fuzzy	fuzzy	NOUN
cana-5358	282	28	(	(	PUNCT
cana-5358	282	29	resp	resp	NOUN
cana-5358	282	30	.	.	PUNCT
cana-5358	283	1	𝛿	𝛿	ADJ
cana-5358	283	2	,	,	PUNCT
cana-5358	283	3	𝛿𝛼	𝛿𝛼	NOUN
cana-5358	283	4	,	,	PUNCT
cana-5358	283	5	𝛿𝒮	𝛿𝒮	NOUN
cana-5358	283	6	,	,	PUNCT
cana-5358	283	7	𝛿𝒫	𝛿𝒫	NOUN
cana-5358	283	8	&	&	CCONJ
cana-5358	283	9	𝛿𝛽	𝛿𝛽	VERB
cana-5358	283	10	or	or	CCONJ
cana-5358	283	11	𝑒∗	𝑒∗	PROPN
cana-5358	283	12	)	)	PUNCT
cana-5358	283	13	𝐶	𝐶	PROPN
cana-5358	283	14	homeomorphism	homeomorphism	X
cana-5358	283	15	(	(	PUNCT
cana-5358	283	16	briefly	briefly	ADV
cana-5358	283	17	,	,	PUNCT
cana-5358	283	18	𝔉ℱ𝐶𝐻𝑜𝑚	𝔉ℱ𝐶𝐻𝑜𝑚	PROPN
cana-5358	283	19	(	(	PUNCT
cana-5358	283	20	resp	resp	NOUN
cana-5358	283	21	.	.	PUNCT
cana-5358	284	1	𝔉ℱ𝛿𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝐶𝐻𝑜𝑚	PROPN
cana-5358	284	2	,	,	PUNCT
cana-5358	284	3	𝔉ℱ𝛿𝛼𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐶𝐻𝑜𝑚	NOUN
cana-5358	284	4	,	,	PUNCT
cana-5358	284	5	𝔉ℱ𝛿𝒮𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐶𝐻𝑜𝑚	NOUN
cana-5358	284	6	,	,	PUNCT
cana-5358	284	7	𝔉ℱ𝛿𝒫𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐶𝐻𝑜𝑚	NUM
cana-5358	284	8	&	&	CCONJ
cana-5358	284	9	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	NOUN
cana-5358	284	10	or	or	CCONJ
cana-5358	284	11	𝔉ℱ𝑒∗𝐶𝐻𝑜𝑚	𝔉ℱ𝑒∗𝐶𝐻𝑜𝑚	NUM
cana-5358	284	12	)	)	PUNCT
cana-5358	284	13	)	)	PUNCT
cana-5358	285	1	if	if	SCONJ
cana-5358	285	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	285	3	and	and	CCONJ
cana-5358	285	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	285	5	−1	−1	VERB
cana-5358	285	6	are	be	AUX
cana-5358	285	7	𝔉ℱ𝐼𝑟𝑟	𝔉ℱ𝐼𝑟𝑟	ADJ
cana-5358	285	8	(	(	PUNCT
cana-5358	285	9	resp	resp	NOUN
cana-5358	285	10	.	.	PUNCT
cana-5358	286	1	𝔉ℱ𝛿𝐼𝑟𝑟	𝔉ℱ𝛿𝐼𝑟𝑟	PROPN
cana-5358	286	2	,	,	PUNCT
cana-5358	286	3	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	𝔉ℱ𝛿𝛼𝐼𝑟𝑟	NOUN
cana-5358	286	4	,	,	PUNCT
cana-5358	286	5	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	𝔉ℱ𝛿𝒮𝐼𝑟𝑟	NOUN
cana-5358	286	6	,	,	PUNCT
cana-5358	286	7	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	𝔉ℱ𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5358	286	8	&	&	CCONJ
cana-5358	286	9	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5358	286	10	or	or	CCONJ
cana-5358	286	11	𝔉ℱ𝑒∗𝐼𝑟𝑟	𝔉ℱ𝑒∗𝐼𝑟𝑟	ADJ
cana-5358	286	12	)	)	PUNCT
cana-5358	286	13	mappings	mapping	NOUN
cana-5358	286	14	.	.	PUNCT
cana-5358	287	1	theorem	theorem	VERB
cana-5358	287	2	4.1	4.1	NUM
cana-5358	287	3	each	each	DET
cana-5358	287	4	𝔉ℱ𝐻𝑜𝑚	𝔉ℱ𝐻𝑜𝑚	PROPN
cana-5358	287	5	(	(	PUNCT
cana-5358	287	6	resp	resp	NOUN
cana-5358	287	7	.	.	PUNCT
cana-5358	287	8	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	PROPN
cana-5358	287	9	,	,	PUNCT
cana-5358	287	10	𝔉ℱ𝛿𝛼𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐶𝐻𝑜𝑚	NOUN
cana-5358	287	11	,	,	PUNCT
cana-5358	287	12	𝔉ℱ𝛿𝒮𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐶𝐻𝑜𝑚	NOUN
cana-5358	287	13	,	,	PUNCT
cana-5358	287	14	𝔉ℱ𝛿𝒫𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐶𝐻𝑜𝑚	NUM
cana-5358	287	15	&	&	CCONJ
cana-5358	287	16	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	PROPN
cana-5358	287	17	or	or	CCONJ
cana-5358	287	18	𝔉ℱ𝑒∗𝐶𝐻𝑜𝑚	𝔉ℱ𝑒∗𝐶𝐻𝑜𝑚	NUM
cana-5358	287	19	)	)	PUNCT
cana-5358	287	20	is	be	AUX
cana-5358	287	21	a	a	DET
cana-5358	287	22	𝔉ℱ𝐶𝐻𝑜𝑚	𝔉ℱ𝐶𝐻𝑜𝑚	PROPN
cana-5358	287	23	(	(	PUNCT
cana-5358	287	24	resp	resp	NOUN
cana-5358	287	25	.	.	PUNCT
cana-5358	288	1	𝔉ℱ𝛿𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝐶𝐻𝑜𝑚	PROPN
cana-5358	288	2	,	,	PUNCT
cana-5358	288	3	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐻𝑜𝑚	ADJ
cana-5358	288	4	,	,	PUNCT
cana-5358	288	5	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐻𝑜𝑚	ADJ
cana-5358	288	6	,	,	PUNCT
cana-5358	288	7	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐻𝑜𝑚	PROPN
cana-5358	288	8	&	&	CCONJ
cana-5358	288	9	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	ADJ
cana-5358	288	10	or	or	CCONJ
cana-5358	288	11	𝔉ℱ𝑒∗𝐻𝑜𝑚	𝔉ℱ𝑒∗𝐻𝑜𝑚	NUM
cana-5358	288	12	)	)	PUNCT
cana-5358	288	13	.	.	PUNCT
cana-5358	289	1	but	but	CCONJ
cana-5358	289	2	not	not	PART
cana-5358	289	3	conversely	conversely	ADV
cana-5358	289	4	.	.	PUNCT
cana-5358	290	1	proof	proof	NOUN
cana-5358	290	2	.	.	PUNCT
cana-5358	291	1	let	let	VERB
cana-5358	291	2	us	we	PRON
cana-5358	291	3	assume	assume	VERB
cana-5358	291	4	that	that	SCONJ
cana-5358	291	5	𝐾	𝐾	PROPN
cana-5358	291	6	be	be	VERB
cana-5358	291	7	a	a	DET
cana-5358	291	8	𝔉ℱ𝛿𝑐𝑠	𝔉ℱ𝛿𝑐𝑠	PROPN
cana-5358	291	9	in	in	ADP
cana-5358	291	10	(	(	PUNCT
cana-5358	291	11	𝑋2	𝑋2	ADJ
cana-5358	291	12	,	,	PUNCT
cana-5358	291	13	𝜏2	𝜏2	PROPN
cana-5358	291	14	)	)	PUNCT
cana-5358	291	15	is	be	AUX
cana-5358	291	16	𝔉ℱ𝑐𝑠.	𝔉ℱ𝑐𝑠.	NUM
cana-5358	291	17	this	this	PRON
cana-5358	291	18	shows	show	VERB
cana-5358	291	19	that	that	SCONJ
cana-5358	291	20	𝐾	𝐾	PROPN
cana-5358	291	21	is	be	AUX
cana-5358	291	22	a	a	DET
cana-5358	291	23	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	291	24	in	in	ADP
cana-5358	291	25	(	(	PUNCT
cana-5358	291	26	𝑋2	𝑋2	ADJ
cana-5358	291	27	,	,	PUNCT
cana-5358	291	28	𝜏2	𝜏2	PROPN
cana-5358	291	29	)	)	PUNCT
cana-5358	291	30	.	.	PUNCT
cana-5358	292	1	by	by	ADP
cana-5358	292	2	assumption	assumption	NOUN
cana-5358	292	3	,	,	PUNCT
cana-5358	292	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	292	5	−1(𝐾	−1(𝐾	NOUN
cana-5358	292	6	)	)	PUNCT
cana-5358	292	7	is	be	AUX
cana-5358	292	8	a	a	DET
cana-5358	292	9	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	292	10	in	in	ADP
cana-5358	292	11	(	(	PUNCT
cana-5358	292	12	𝑋1	𝑋1	PROPN
cana-5358	292	13	,	,	PUNCT
cana-5358	292	14	𝜏1	𝜏1	NOUN
cana-5358	292	15	)	)	PUNCT
cana-5358	292	16	.	.	PUNCT
cana-5358	293	1	hence	hence	ADV
cana-5358	293	2	,	,	PUNCT
cana-5358	293	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	293	4	is	be	AUX
cana-5358	293	5	a	a	DET
cana-5358	293	6	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5358	293	7	mapping	mapping	NOUN
cana-5358	293	8	.	.	PUNCT
cana-5358	294	1	hence	hence	ADV
cana-5358	294	2	,	,	PUNCT
cana-5358	294	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	294	4	and	and	CCONJ
cana-5358	294	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	294	6	−1	−1	VERB
cana-5358	294	7	are	be	AUX
cana-5358	294	8	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	𝔉ℱ𝛿𝛽𝐶𝑡𝑠	ADJ
cana-5358	294	9	mappings	mapping	NOUN
cana-5358	294	10	.	.	PUNCT
cana-5358	295	1	hence	hence	ADV
cana-5358	295	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	295	3	is	be	AUX
cana-5358	295	4	a	a	DET
cana-5358	295	5	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	𝔉ℱ𝛿𝛽𝐻𝑜𝑚.	NOUN
cana-5358	295	6	the	the	DET
cana-5358	295	7	proof	proof	NOUN
cana-5358	295	8	of	of	ADP
cana-5358	295	9	other	other	ADJ
cana-5358	295	10	cases	case	NOUN
cana-5358	295	11	are	be	AUX
cana-5358	295	12	similar	similar	ADJ
cana-5358	295	13	.	.	PUNCT
cana-5358	296	1	example	example	NOUN
cana-5358	296	2	4.1	4.1	NUM
cana-5358	296	3	let	let	VERB
cana-5358	296	4	𝑋1	𝑋1	NOUN
cana-5358	296	5	=	=	SYM
cana-5358	296	6	𝑋2	𝑋2	VERB
cana-5358	296	7	=	=	SYM
cana-5358	296	8	𝑋	𝑋	NOUN
cana-5358	296	9	=	=	PUNCT
cana-5358	296	10	{	{	PUNCT
cana-5358	296	11	𝑎	𝑎	NOUN
cana-5358	296	12	,	,	PUNCT
cana-5358	296	13	𝑏	𝑏	NOUN
cana-5358	296	14	}	}	PUNCT
cana-5358	296	15	and	and	CCONJ
cana-5358	296	16	the	the	DET
cana-5358	296	17	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	296	18	’s	’s	PART
cana-5358	296	19	𝐴1	𝐴1	PROPN
cana-5358	296	20	,	,	PUNCT
cana-5358	296	21	𝐴2	𝐴2	PROPN
cana-5358	296	22	,	,	PUNCT
cana-5358	296	23	𝐴3	𝐴3	PROPN
cana-5358	296	24	and	and	CCONJ
cana-5358	296	25	𝐴4	𝐴4	PROPN
cana-5358	296	26	are	be	AUX
cana-5358	296	27	defined	define	VERB
cana-5358	296	28	as	as	ADP
cana-5358	296	29	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5358	296	30	(	(	PUNCT
cana-5358	296	31	𝑎	𝑎	NOUN
cana-5358	296	32	)	)	PUNCT
cana-5358	296	33	=	=	SYM
cana-5358	296	34	0.2	0.2	NUM
cana-5358	296	35	,	,	PUNCT
cana-5358	296	36	𝛽𝐴1	𝛽𝐴1	X
cana-5358	296	37	(	(	PUNCT
cana-5358	296	38	𝑎	𝑎	NOUN
cana-5358	296	39	)	)	PUNCT
cana-5358	296	40	=	=	SYM
cana-5358	296	41	0.8	0.8	NUM
cana-5358	296	42	,	,	PUNCT
cana-5358	296	43	𝛼𝐴1	𝛼𝐴1	PROPN
cana-5358	296	44	(	(	PUNCT
cana-5358	296	45	𝑏	𝑏	NOUN
cana-5358	296	46	)	)	PUNCT
cana-5358	296	47	=	=	SYM
cana-5358	296	48	0.4	0.4	NUM
cana-5358	296	49	,	,	PUNCT
cana-5358	296	50	𝛽𝐴1	𝛽𝐴1	PROPN
cana-5358	296	51	(	(	PUNCT
cana-5358	296	52	𝑏	𝑏	NOUN
cana-5358	296	53	)	)	PUNCT
cana-5358	296	54	=	=	SYM
cana-5358	296	55	0.6	0.6	NUM
cana-5358	296	56	;	;	PUNCT
cana-5358	296	57	𝛼𝐴2	𝛼𝐴2	NUM
cana-5358	296	58	(	(	PUNCT
cana-5358	296	59	𝑎	𝑎	NOUN
cana-5358	296	60	)	)	PUNCT
cana-5358	296	61	=	=	SYM
cana-5358	296	62	0.1	0.1	NUM
cana-5358	296	63	,	,	PUNCT
cana-5358	296	64	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5358	296	65	(	(	PUNCT
cana-5358	296	66	𝑎	𝑎	NOUN
cana-5358	296	67	)	)	PUNCT
cana-5358	296	68	=	=	SYM
cana-5358	296	69	0.9	0.9	NUM
cana-5358	296	70	,	,	PUNCT
cana-5358	296	71	𝛼𝐴2	𝛼𝐴2	PROPN
cana-5358	296	72	(	(	PUNCT
cana-5358	296	73	𝑏	𝑏	NOUN
cana-5358	296	74	)	)	PUNCT
cana-5358	296	75	=	=	SYM
cana-5358	296	76	0.3	0.3	NUM
cana-5358	296	77	,	,	PUNCT
cana-5358	296	78	𝛽𝐴2	𝛽𝐴2	PROPN
cana-5358	296	79	(	(	PUNCT
cana-5358	296	80	𝑏	𝑏	NOUN
cana-5358	296	81	)	)	PUNCT
cana-5358	296	82	=	=	SYM
cana-5358	296	83	0.7	0.7	NUM
cana-5358	296	84	;	;	PUNCT
cana-5358	296	85	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5358	296	86	(	(	PUNCT
cana-5358	296	87	𝑎	𝑎	NOUN
cana-5358	296	88	)	)	PUNCT
cana-5358	296	89	=	=	SYM
cana-5358	296	90	0.9	0.9	NUM
cana-5358	296	91	,	,	PUNCT
cana-5358	296	92	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5358	296	93	(	(	PUNCT
cana-5358	296	94	𝑎	𝑎	NOUN
cana-5358	296	95	)	)	PUNCT
cana-5358	296	96	=	=	SYM
cana-5358	296	97	0.1	0.1	NUM
cana-5358	296	98	,	,	PUNCT
cana-5358	296	99	𝛼𝐴3	𝛼𝐴3	PROPN
cana-5358	296	100	(	(	PUNCT
cana-5358	296	101	𝑏	𝑏	NOUN
cana-5358	296	102	)	)	PUNCT
cana-5358	296	103	=	=	SYM
cana-5358	296	104	0.7	0.7	NUM
cana-5358	296	105	,	,	PUNCT
cana-5358	296	106	𝛽𝐴3	𝛽𝐴3	PROPN
cana-5358	296	107	(	(	PUNCT
cana-5358	296	108	𝑏	𝑏	NOUN
cana-5358	296	109	)	)	PUNCT
cana-5358	296	110	=	=	SYM
cana-5358	296	111	0.3	0.3	NUM
cana-5358	296	112	;	;	PUNCT
cana-5358	296	113	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5358	296	114	(	(	PUNCT
cana-5358	296	115	𝑎	𝑎	NOUN
cana-5358	296	116	)	)	PUNCT
cana-5358	296	117	=	=	SYM
cana-5358	296	118	0.2	0.2	NUM
cana-5358	296	119	,	,	PUNCT
cana-5358	296	120	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5358	296	121	(	(	PUNCT
cana-5358	296	122	𝑎	𝑎	NOUN
cana-5358	296	123	)	)	PUNCT
cana-5358	296	124	=	=	SYM
cana-5358	296	125	0.8	0.8	NUM
cana-5358	296	126	,	,	PUNCT
cana-5358	296	127	𝛼𝐴4	𝛼𝐴4	PROPN
cana-5358	296	128	(	(	PUNCT
cana-5358	296	129	𝑏	𝑏	NOUN
cana-5358	296	130	)	)	PUNCT
cana-5358	296	131	=	=	SYM
cana-5358	296	132	0.3	0.3	NUM
cana-5358	296	133	,	,	PUNCT
cana-5358	296	134	𝛽𝐴4	𝛽𝐴4	PROPN
cana-5358	296	135	(	(	PUNCT
cana-5358	296	136	𝑏	𝑏	NOUN
cana-5358	296	137	)	)	PUNCT
cana-5358	296	138	=	=	SYM
cana-5358	296	139	0.7	0.7	NUM
cana-5358	296	140	;	;	PUNCT
cana-5358	296	141	let	let	VERB
cana-5358	296	142	𝜏1	𝜏1	NOUN
cana-5358	296	143	=	=	PUNCT
cana-5358	296	144	{	{	PUNCT
cana-5358	296	145	0𝔉	0𝔉	PROPN
cana-5358	296	146	,	,	PUNCT
cana-5358	296	147	1𝔉	1𝔉	NOUN
cana-5358	296	148	,	,	PUNCT
cana-5358	296	149	𝐴1	𝐴1	PROPN
cana-5358	296	150	,	,	PUNCT
cana-5358	296	151	𝐴2	𝐴2	PROPN
cana-5358	296	152	,	,	PUNCT
cana-5358	296	153	𝐴3	𝐴3	PROPN
cana-5358	296	154	,	,	PUNCT
cana-5358	296	155	𝐴4	𝐴4	PROPN
cana-5358	296	156	}	}	PUNCT
cana-5358	296	157	,	,	PUNCT
cana-5358	296	158	𝜏2	𝜏2	PROPN
cana-5358	296	159	=	=	SYM
cana-5358	296	160	{	{	PUNCT
cana-5358	296	161	0𝔉	0𝔉	PROPN
cana-5358	296	162	,	,	PUNCT
cana-5358	296	163	1𝔉	1𝔉	NOUN
cana-5358	296	164	,	,	PUNCT
cana-5358	296	165	𝐴1	𝐴1	PROPN
cana-5358	296	166	,	,	PUNCT
cana-5358	296	167	𝐴2	𝐴2	PROPN
cana-5358	296	168	,	,	PUNCT
cana-5358	296	169	𝐴3	𝐴3	PROPN
cana-5358	296	170	}	}	PUNCT
cana-5358	296	171	be	be	VERB
cana-5358	296	172	a	a	DET
cana-5358	296	173	𝔉ℱ𝑡𝑠	𝔉ℱ𝑡𝑠	PROPN
cana-5358	296	174	on	on	ADP
cana-5358	296	175	𝑋1	𝑋1	PROPN
cana-5358	296	176	and	and	CCONJ
cana-5358	296	177	𝑋2	𝑋2	VERB
cana-5358	296	178	;	;	PUNCT
cana-5358	296	179	and	and	CCONJ
cana-5358	296	180	let	let	VERB
cana-5358	296	181	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	296	182	:	:	PUNCT
cana-5358	296	183	(	(	PUNCT
cana-5358	296	184	𝑋1	𝑋1	PROPN
cana-5358	296	185	,	,	PUNCT
cana-5358	296	186	𝜏1	𝜏1	NOUN
cana-5358	296	187	)	)	PUNCT
cana-5358	296	188	→	→	SYM
cana-5358	296	189	(	(	PUNCT
cana-5358	296	190	𝑋2	𝑋2	PROPN
cana-5358	296	191	,	,	PUNCT
cana-5358	296	192	𝜏2	𝜏2	PROPN
cana-5358	296	193	)	)	PUNCT
cana-5358	296	194	be	be	VERB
cana-5358	296	195	an	an	DET
cana-5358	296	196	identity	identity	NOUN
cana-5358	296	197	function	function	NOUN
cana-5358	296	198	,	,	PUNCT
cana-5358	296	199	then	then	ADV
cana-5358	296	200	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	296	201	is	be	AUX
cana-5358	296	202	𝔉ℱ𝐶𝐻𝑜𝑚	𝔉ℱ𝐶𝐻𝑜𝑚	PROPN
cana-5358	296	203	(	(	PUNCT
cana-5358	296	204	resp	resp	NOUN
cana-5358	296	205	.	.	PUNCT
cana-5358	297	1	𝔉ℱ𝛿𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝐶𝐻𝑜𝑚	NUM
cana-5358	297	2	)	)	PUNCT
cana-5358	298	1	but	but	CCONJ
cana-5358	298	2	not	not	PART
cana-5358	298	3	𝔉ℱ𝐻𝑜𝑚	𝔉ℱ𝐻𝑜𝑚	PROPN
cana-5358	298	4	(	(	PUNCT
cana-5358	298	5	resp	resp	NOUN
cana-5358	298	6	.	.	PUNCT
cana-5358	299	1	𝔉ℱ𝛿𝐻𝑜𝑚	𝔉ℱ𝛿𝐻𝑜𝑚	PROPN
cana-5358	299	2	)	)	PUNCT
cana-5358	299	3	.	.	PUNCT
cana-5358	300	1	since	since	SCONJ
cana-5358	300	2	,	,	PUNCT
cana-5358	300	3	𝐴4	𝐴4	PROPN
cana-5358	300	4	is	be	AUX
cana-5358	300	5	a	a	DET
cana-5358	300	6	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5358	300	7	set	set	VERB
cana-5358	300	8	in	in	ADP
cana-5358	300	9	𝑋1	𝑋1	PROPN
cana-5358	300	10	but	but	CCONJ
cana-5358	300	11	(	(	PUNCT
cana-5358	300	12	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	300	13	−1)−1(𝐴4	−1)−1(𝐴4	PRON
cana-5358	300	14	)	)	PUNCT
cana-5358	300	15	=	=	NOUN
cana-5358	301	1	𝐴4	𝐴4	PROPN
cana-5358	301	2	is	be	AUX
cana-5358	301	3	not	not	PART
cana-5358	301	4	𝔉ℱ𝑜	𝔉ℱ𝑜	NOUN
cana-5358	301	5	(	(	PUNCT
cana-5358	301	6	resp	resp	NOUN
cana-5358	301	7	.	.	PUNCT
cana-5358	302	1	𝔉ℱ𝛿𝑜	𝔉ℱ𝛿𝑜	PROPN
cana-5358	302	2	)	)	PUNCT
cana-5358	303	1	set	set	VERB
cana-5358	303	2	in	in	ADP
cana-5358	303	3	𝑋2	𝑋2	PROPN
cana-5358	303	4	.	.	PUNCT
cana-5358	304	1	theorem	theorem	VERB
cana-5358	304	2	4.2	4.2	NUM
cana-5358	304	3	if	if	SCONJ
cana-5358	304	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	304	5	:	:	PUNCT
cana-5358	304	6	(	(	PUNCT
cana-5358	304	7	𝑋1	𝑋1	PROPN
cana-5358	304	8	,	,	PUNCT
cana-5358	304	9	𝜏1	𝜏1	NOUN
cana-5358	304	10	)	)	PUNCT
cana-5358	304	11	→	→	SYM
cana-5358	304	12	(	(	PUNCT
cana-5358	304	13	𝑋2	𝑋2	PROPN
cana-5358	304	14	,	,	PUNCT
cana-5358	304	15	𝜏2	𝜏2	PROPN
cana-5358	304	16	)	)	PUNCT
cana-5358	304	17	is	be	AUX
cana-5358	304	18	a	a	DET
cana-5358	304	19	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	NOUN
cana-5358	304	20	,	,	PUNCT
cana-5358	304	21	then	then	ADV
cana-5358	304	22	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5358	304	23	−1(𝐾	−1(𝐾	NOUN
cana-5358	304	24	)	)	PUNCT
cana-5358	304	25	)	)	PUNCT
cana-5358	305	1	⊆	⊆	NUM
cana-5358	305	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	305	3	−1(𝔉ℱ𝑐𝑙(𝐾	−1(𝔉ℱ𝑐𝑙(𝐾	NOUN
cana-5358	305	4	)	)	PUNCT
cana-5358	305	5	)	)	PUNCT
cana-5358	305	6	for	for	ADP
cana-5358	305	7	each	each	DET
cana-5358	305	8	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	305	9	𝐾	𝐾	PROPN
cana-5358	305	10	in	in	ADP
cana-5358	305	11	(	(	PUNCT
cana-5358	305	12	𝑋2	𝑋2	ADJ
cana-5358	305	13	,	,	PUNCT
cana-5358	305	14	𝜏2	𝜏2	PROPN
cana-5358	305	15	)	)	PUNCT
cana-5358	305	16	.	.	PUNCT
cana-5358	306	1	proof	proof	NOUN
cana-5358	306	2	.	.	PUNCT
cana-5358	307	1	let	let	VERB
cana-5358	307	2	𝐾	𝐾	PRON
cana-5358	307	3	be	be	AUX
cana-5358	307	4	a	a	DET
cana-5358	307	5	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	307	6	in	in	ADP
cana-5358	307	7	(	(	PUNCT
cana-5358	307	8	𝑋2	𝑋2	ADJ
cana-5358	307	9	,	,	PUNCT
cana-5358	307	10	𝜏2	𝜏2	PROPN
cana-5358	307	11	)	)	PUNCT
cana-5358	307	12	.	.	PUNCT
cana-5358	308	1	then	then	ADV
cana-5358	308	2	,	,	PUNCT
cana-5358	308	3	𝔉ℱ𝑐𝑙(𝐾	𝔉ℱ𝑐𝑙(𝐾	PROPN
cana-5358	308	4	)	)	PUNCT
cana-5358	308	5	is	be	AUX
cana-5358	308	6	a	a	DET
cana-5358	308	7	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	308	8	in	in	ADP
cana-5358	308	9	(	(	PUNCT
cana-5358	308	10	𝑋2	𝑋2	ADJ
cana-5358	308	11	,	,	PUNCT
cana-5358	308	12	𝜏2	𝜏2	PROPN
cana-5358	308	13	)	)	PUNCT
cana-5358	308	14	,	,	PUNCT
cana-5358	308	15	and	and	CCONJ
cana-5358	308	16	every	every	DET
cana-5358	308	17	𝔉ℱ𝑐𝑠	𝔉ℱ𝑐𝑠	PROPN
cana-5358	308	18	is	be	AUX
cana-5358	308	19	a	a	DET
cana-5358	308	20	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	308	21	in	in	ADP
cana-5358	308	22	(	(	PUNCT
cana-5358	308	23	𝑋2	𝑋2	ADJ
cana-5358	308	24	,	,	PUNCT
cana-5358	308	25	𝜏2	𝜏2	PROPN
cana-5358	308	26	)	)	PUNCT
cana-5358	308	27	.	.	PUNCT
cana-5358	309	1	assume	assume	VERB
cana-5358	309	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	309	3	is	be	AUX
cana-5358	309	4	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5358	309	5	and	and	CCONJ
cana-5358	309	6	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	309	7	−1(𝔉ℱ𝑐𝑙(𝐾	−1(𝔉ℱ𝑐𝑙(𝐾	NOUN
cana-5358	309	8	)	)	PUNCT
cana-5358	309	9	)	)	PUNCT
cana-5358	310	1	is	be	AUX
cana-5358	310	2	a	a	DET
cana-5358	310	3	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	310	4	in	in	ADP
cana-5358	310	5	(	(	PUNCT
cana-5358	310	6	𝑋1	𝑋1	PROPN
cana-5358	310	7	,	,	PUNCT
cana-5358	310	8	𝜏1	𝜏1	NOUN
cana-5358	310	9	)	)	PUNCT
cana-5358	310	10	.	.	PUNCT
cana-5358	311	1	then	then	ADV
cana-5358	311	2	,	,	PUNCT
cana-5358	311	3	𝔉ℱ𝑐𝑙(ℎ𝔉	𝔉ℱ𝑐𝑙(ℎ𝔉	NOUN
cana-5358	311	4	−1(𝔉ℱ𝑐𝑙(𝐾	−1(𝔉ℱ𝑐𝑙(𝐾	PROPN
cana-5358	311	5	)	)	PUNCT
cana-5358	311	6	)	)	PUNCT
cana-5358	311	7	)	)	PUNCT
cana-5358	312	1	=	=	PRON
cana-5358	312	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	312	3	−1(𝔉ℱ𝑐𝑙(𝐾	−1(𝔉ℱ𝑐𝑙(𝐾	NOUN
cana-5358	312	4	)	)	PUNCT
cana-5358	312	5	)	)	PUNCT
cana-5358	312	6	.	.	PUNCT
cana-5358	313	1	here	here	ADV
cana-5358	313	2	,	,	PUNCT
cana-5358	313	3	𝔉ℱ𝛿𝛽𝑐𝑙	𝔉ℱ𝛿𝛽𝑐𝑙	PROPN
cana-5358	313	4	(	(	PUNCT
cana-5358	313	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	313	6	−1(𝐾	−1(𝐾	NOUN
cana-5358	313	7	)	)	PUNCT
cana-5358	313	8	)	)	PUNCT
cana-5358	314	1	⊆	⊆	X
cana-5358	314	2	𝔉ℱ𝛿𝛽𝑐𝑙	𝔉ℱ𝛿𝛽𝑐𝑙	PROPN
cana-5358	314	3	(	(	PUNCT
cana-5358	314	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	314	5	−1(𝔉ℱ𝑐𝑙(𝐾	−1(𝔉ℱ𝑐𝑙(𝐾	NOUN
cana-5358	314	6	)	)	PUNCT
cana-5358	314	7	)	)	PUNCT
cana-5358	314	8	)	)	PUNCT
cana-5358	315	1	=	=	PRON
cana-5358	315	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	315	3	−1(𝔉ℱ𝑐𝑙(𝐾	−1(𝔉ℱ𝑐𝑙(𝐾	NOUN
cana-5358	315	4	)	)	PUNCT
cana-5358	315	5	)	)	PUNCT
cana-5358	315	6	.	.	PUNCT
cana-5358	316	1	therefore	therefore	ADV
cana-5358	316	2	,	,	PUNCT
cana-5358	316	3	𝔉ℱ𝛿𝛽𝑐𝑙	𝔉ℱ𝛿𝛽𝑐𝑙	PROPN
cana-5358	316	4	(	(	PUNCT
cana-5358	316	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	316	6	−1(𝐾	−1(𝐾	NOUN
cana-5358	316	7	)	)	PUNCT
cana-5358	316	8	)	)	PUNCT
cana-5358	316	9	⊆	⊆	NUM
cana-5358	316	10	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	316	11	−1(𝔉ℱ𝑐𝑙(𝐾	−1(𝔉ℱ𝑐𝑙(𝐾	NOUN
cana-5358	316	12	)	)	PUNCT
cana-5358	316	13	)	)	PUNCT
cana-5358	316	14	for	for	ADP
cana-5358	316	15	every	every	DET
cana-5358	316	16	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	316	17	𝐾	𝐾	PROPN
cana-5358	316	18	in	in	ADP
cana-5358	316	19	(	(	PUNCT
cana-5358	316	20	𝑋2	𝑋2	ADJ
cana-5358	316	21	,	,	PUNCT
cana-5358	316	22	𝜏2	𝜏2	PROPN
cana-5358	316	23	)	)	PUNCT
cana-5358	316	24	.	.	PUNCT
cana-5358	317	1	theorem	theorem	VERB
cana-5358	317	2	4.3	4.3	NUM
cana-5358	317	3	let	let	VERB
cana-5358	317	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	317	5	:	:	PUNCT
cana-5358	317	6	(	(	PUNCT
cana-5358	317	7	𝑋1	𝑋1	PROPN
cana-5358	317	8	,	,	PUNCT
cana-5358	317	9	𝜏1	𝜏1	NOUN
cana-5358	317	10	)	)	PUNCT
cana-5358	317	11	→	→	SYM
cana-5358	317	12	(	(	PUNCT
cana-5358	317	13	𝑋2	𝑋2	PROPN
cana-5358	317	14	,	,	PUNCT
cana-5358	317	15	𝜏2	𝜏2	PROPN
cana-5358	317	16	)	)	PUNCT
cana-5358	317	17	be	be	VERB
cana-5358	317	18	a	a	DET
cana-5358	317	19	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	NOUN
cana-5358	317	20	.	.	PUNCT
cana-5358	318	1	then	then	ADV
cana-5358	318	2	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5358	318	3	−1(𝐾	−1(𝐾	NOUN
cana-5358	318	4	)	)	PUNCT
cana-5358	318	5	)	)	PUNCT
cana-5358	319	1	=	=	PUNCT
cana-5358	319	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	319	3	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5358	319	4	)	)	PUNCT
cana-5358	319	5	)	)	PUNCT
cana-5358	319	6	for	for	ADP
cana-5358	319	7	each	each	DET
cana-5358	319	8	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	319	9	𝐾	𝐾	PROPN
cana-5358	319	10	in	in	ADP
cana-5358	319	11	(	(	PUNCT
cana-5358	319	12	𝑋2	𝑋2	ADJ
cana-5358	319	13	,	,	PUNCT
cana-5358	319	14	𝜏2	𝜏2	PROPN
cana-5358	319	15	)	)	PUNCT
cana-5358	319	16	.	.	PUNCT
cana-5358	320	1	communications	communication	NOUN
cana-5358	320	2	on	on	ADP
cana-5358	320	3	applied	apply	VERB
cana-5358	320	4	nonlinear	nonlinear	ADJ
cana-5358	320	5	analysis	analysis	NOUN
cana-5358	320	6	issn	issn	NOUN
cana-5358	320	7	:	:	PUNCT
cana-5358	320	8	1074	1074	NUM
cana-5358	320	9	-	-	PUNCT
cana-5358	320	10	133x	133x	NUM
cana-5358	320	11	vol	vol	VERB
cana-5358	320	12	32	32	NUM
cana-5358	320	13	no	no	NOUN
cana-5358	320	14	.	.	PUNCT
cana-5358	321	1	10s	10	NOUN
cana-5358	321	2	(	(	PUNCT
cana-5358	321	3	2025	2025	NUM
cana-5358	321	4	)	)	PUNCT
cana-5358	321	5	1905	1905	NUM
cana-5358	321	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	321	7	proof	proof	NOUN
cana-5358	321	8	.	.	PUNCT
cana-5358	322	1	since	since	SCONJ
cana-5358	322	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	322	3	is	be	AUX
cana-5358	322	4	a	a	DET
cana-5358	322	5	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	NOUN
cana-5358	322	6	,	,	PUNCT
cana-5358	322	7	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	322	8	is	be	AUX
cana-5358	322	9	a	a	DET
cana-5358	322	10	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5358	322	11	mapping	mapping	NOUN
cana-5358	322	12	.	.	PUNCT
cana-5358	323	1	let	let	VERB
cana-5358	323	2	𝐾	𝐾	PRON
cana-5358	323	3	be	be	AUX
cana-5358	323	4	a	a	DET
cana-5358	323	5	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	323	6	in	in	ADP
cana-5358	323	7	(	(	PUNCT
cana-5358	323	8	𝑋2	𝑋2	ADJ
cana-5358	323	9	,	,	PUNCT
cana-5358	323	10	𝜏2	𝜏2	PROPN
cana-5358	323	11	)	)	PUNCT
cana-5358	323	12	.	.	PUNCT
cana-5358	324	1	clearly	clearly	ADV
cana-5358	324	2	,	,	PUNCT
cana-5358	324	3	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5358	324	4	)	)	PUNCT
cana-5358	324	5	is	be	AUX
cana-5358	324	6	a	a	DET
cana-5358	324	7	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	324	8	in	in	ADP
cana-5358	324	9	(	(	PUNCT
cana-5358	324	10	𝑋2	𝑋2	ADJ
cana-5358	324	11	,	,	PUNCT
cana-5358	324	12	𝜏2	𝜏2	PROPN
cana-5358	324	13	)	)	PUNCT
cana-5358	324	14	.	.	PUNCT
cana-5358	325	1	then	then	ADV
cana-5358	325	2	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5358	325	3	)	)	PUNCT
cana-5358	325	4	is	be	AUX
cana-5358	325	5	a	a	DET
cana-5358	325	6	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	325	7	in	in	ADP
cana-5358	325	8	(	(	PUNCT
cana-5358	325	9	𝑋2	𝑋2	ADJ
cana-5358	325	10	,	,	PUNCT
cana-5358	325	11	𝜏2	𝜏2	PROPN
cana-5358	325	12	)	)	PUNCT
cana-5358	325	13	.	.	PUNCT
cana-5358	326	1	since	since	SCONJ
cana-5358	326	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	326	3	−1(𝐾	−1(𝐾	NOUN
cana-5358	326	4	)	)	PUNCT
cana-5358	326	5	⊆	⊆	NUM
cana-5358	326	6	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	326	7	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	NOUN
cana-5358	326	8	)	)	PUNCT
cana-5358	326	9	)	)	PUNCT
cana-5358	327	1	,	,	PUNCT
cana-5358	327	2	then	then	ADV
cana-5358	327	3	𝔉ℱ𝛿𝛽𝑐𝑙	𝔉ℱ𝛿𝛽𝑐𝑙	PROPN
cana-5358	327	4	(	(	PUNCT
cana-5358	327	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	327	6	−1(𝐾	−1(𝐾	NOUN
cana-5358	327	7	)	)	PUNCT
cana-5358	327	8	)	)	PUNCT
cana-5358	328	1	⊆	⊆	X
cana-5358	328	2	𝔉ℱ𝛿𝛽𝑐𝑙	𝔉ℱ𝛿𝛽𝑐𝑙	PROPN
cana-5358	328	3	(	(	PUNCT
cana-5358	328	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	328	5	−1	−1	NOUN
cana-5358	328	6	(	(	PUNCT
cana-5358	328	7	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5358	328	8	)	)	PUNCT
cana-5358	328	9	)	)	PUNCT
cana-5358	328	10	)	)	PUNCT
cana-5358	329	1	=	=	PUNCT
cana-5358	329	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	329	3	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5358	329	4	)	)	PUNCT
cana-5358	329	5	)	)	PUNCT
cana-5358	329	6	.	.	PUNCT
cana-5358	330	1	therefore	therefore	ADV
cana-5358	330	2	,	,	PUNCT
cana-5358	330	3	𝔉ℱ	𝔉ℱ	PROPN
cana-5358	330	4	𝛿𝛽𝑐𝑙(ℎ𝔉	𝛿𝛽𝑐𝑙(ℎ𝔉	DET
cana-5358	330	5	−1(𝐾	−1(𝐾	NOUN
cana-5358	330	6	)	)	PUNCT
cana-5358	330	7	)	)	PUNCT
cana-5358	331	1	⊆	⊆	NUM
cana-5358	331	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	331	3	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	NOUN
cana-5358	331	4	)	)	PUNCT
cana-5358	331	5	)	)	PUNCT
cana-5358	331	6	.	.	PUNCT
cana-5358	332	1	let	let	VERB
cana-5358	332	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	332	3	be	be	AUX
cana-5358	332	4	a	a	DET
cana-5358	332	5	𝔉ℱ𝛿𝛽𝐶	𝔉ℱ𝛿𝛽𝐶	NOUN
cana-5358	332	6	𝐻𝑜𝑚.	𝐻𝑜𝑚.	PROPN
cana-5358	332	7	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	332	8	−1	−1	NOUN
cana-5358	332	9	is	be	AUX
cana-5358	332	10	a	a	DET
cana-5358	332	11	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5358	332	12	mapping	mapping	NOUN
cana-5358	332	13	.	.	PUNCT
cana-5358	333	1	let	let	VERB
cana-5358	333	2	us	we	PRON
cana-5358	333	3	consider	consider	VERB
cana-5358	333	4	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	333	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	333	6	−1(𝐾	−1(𝐾	NOUN
cana-5358	333	7	)	)	PUNCT
cana-5358	333	8	in	in	ADP
cana-5358	333	9	(	(	PUNCT
cana-5358	333	10	𝑋1	𝑋1	PROPN
cana-5358	333	11	,	,	PUNCT
cana-5358	333	12	𝜏1	𝜏1	NOUN
cana-5358	333	13	)	)	PUNCT
cana-5358	333	14	,	,	PUNCT
cana-5358	333	15	which	which	PRON
cana-5358	333	16	implies	imply	VERB
cana-5358	333	17	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5358	333	18	−1(𝐾	−1(𝐾	NOUN
cana-5358	333	19	)	)	PUNCT
cana-5358	333	20	)	)	PUNCT
cana-5358	333	21	is	be	AUX
cana-5358	333	22	a	a	DET
cana-5358	333	23	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	333	24	in	in	ADP
cana-5358	333	25	(	(	PUNCT
cana-5358	333	26	𝑋1	𝑋1	PROPN
cana-5358	333	27	,	,	PUNCT
cana-5358	333	28	𝜏1	𝜏1	NOUN
cana-5358	333	29	)	)	PUNCT
cana-5358	333	30	.	.	PUNCT
cana-5358	334	1	hence	hence	ADV
cana-5358	334	2	,	,	PUNCT
cana-5358	334	3	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5358	334	4	−1(𝐾	−1(𝐾	NOUN
cana-5358	334	5	)	)	PUNCT
cana-5358	334	6	)	)	PUNCT
cana-5358	334	7	is	be	AUX
cana-5358	334	8	a	a	DET
cana-5358	334	9	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	334	10	in	in	ADP
cana-5358	334	11	(	(	PUNCT
cana-5358	334	12	𝑋1	𝑋1	PROPN
cana-5358	334	13	,	,	PUNCT
cana-5358	334	14	𝜏1	𝜏1	NOUN
cana-5358	334	15	)	)	PUNCT
cana-5358	334	16	.	.	PUNCT
cana-5358	335	1	this	this	PRON
cana-5358	335	2	implies	imply	VERB
cana-5358	335	3	that	that	SCONJ
cana-5358	335	4	(	(	PUNCT
cana-5358	335	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	335	6	−1)−1(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	−1)−1(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	X
cana-5358	335	7	−1(𝐾	−1(𝐾	NOUN
cana-5358	335	8	)	)	PUNCT
cana-5358	335	9	)	)	PUNCT
cana-5358	335	10	)	)	PUNCT
cana-5358	336	1	=	=	SYM
cana-5358	336	2	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NOUN
cana-5358	336	3	−1(𝐾	−1(𝐾	NOUN
cana-5358	336	4	)	)	PUNCT
cana-5358	336	5	)	)	PUNCT
cana-5358	336	6	)	)	PUNCT
cana-5358	336	7	is	be	AUX
cana-5358	336	8	a	a	DET
cana-5358	336	9	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	336	10	in	in	ADP
cana-5358	336	11	(	(	PUNCT
cana-5358	336	12	𝑋2	𝑋2	ADJ
cana-5358	336	13	,	,	PUNCT
cana-5358	336	14	𝜏2	𝜏2	PROPN
cana-5358	336	15	)	)	PUNCT
cana-5358	336	16	.	.	PUNCT
cana-5358	337	1	this	this	PRON
cana-5358	337	2	proves	prove	VERB
cana-5358	337	3	𝐾	𝐾	PROPN
cana-5358	337	4	=	=	SYM
cana-5358	337	5	(	(	PUNCT
cana-5358	337	6	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	337	7	−1)−1(ℎ𝔉	−1)−1(ℎ𝔉	NOUN
cana-5358	337	8	−1(𝐾	−1(𝐾	NOUN
cana-5358	337	9	)	)	PUNCT
cana-5358	337	10	)	)	PUNCT
cana-5358	338	1	⊆	⊆	NUM
cana-5358	338	2	(	(	PUNCT
cana-5358	338	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	338	4	−1)−1(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	−1)−1(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	X
cana-5358	338	5	−1(𝐾	−1(𝐾	NOUN
cana-5358	338	6	)	)	PUNCT
cana-5358	338	7	)	)	PUNCT
cana-5358	338	8	)	)	PUNCT
cana-5358	339	1	=	=	SYM
cana-5358	339	2	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NOUN
cana-5358	339	3	−1(𝐾	−1(𝐾	NOUN
cana-5358	339	4	)	)	PUNCT
cana-5358	339	5	)	)	PUNCT
cana-5358	339	6	)	)	PUNCT
cana-5358	339	7	.	.	PUNCT
cana-5358	340	1	therefore	therefore	ADV
cana-5358	340	2	,	,	PUNCT
cana-5358	340	3	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5358	340	4	)	)	PUNCT
cana-5358	340	5	⊆	⊆	NUM
cana-5358	340	6	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝑝(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝑝(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NOUN
cana-5358	340	7	−1(𝐾	−1(𝐾	NOUN
cana-5358	340	8	)	)	PUNCT
cana-5358	340	9	)	)	PUNCT
cana-5358	340	10	)	)	PUNCT
cana-5358	340	11	)	)	PUNCT
cana-5358	340	12	=	=	SYM
cana-5358	340	13	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NOUN
cana-5358	340	14	−1(𝐾	−1(𝐾	NOUN
cana-5358	340	15	)	)	PUNCT
cana-5358	340	16	)	)	PUNCT
cana-5358	340	17	)	)	PUNCT
cana-5358	340	18	.	.	PUNCT
cana-5358	341	1	since	since	SCONJ
cana-5358	341	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	341	3	−1	−1	NOUN
cana-5358	341	4	is	be	AUX
cana-5358	341	5	a	a	DET
cana-5358	341	6	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5358	341	7	mapping	mapping	NOUN
cana-5358	341	8	.	.	PUNCT
cana-5358	342	1	hence	hence	ADV
cana-5358	342	2	,	,	PUNCT
cana-5358	342	3	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	342	4	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5358	342	5	)	)	PUNCT
cana-5358	342	6	)	)	PUNCT
cana-5358	343	1	⊆	⊆	NUM
cana-5358	343	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	343	3	−1(ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	−1(ℎ𝔉(𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	X
cana-5358	343	4	−1(𝐾	−1(𝐾	NOUN
cana-5358	343	5	)	)	PUNCT
cana-5358	343	6	)	)	PUNCT
cana-5358	343	7	)	)	PUNCT
cana-5358	343	8	)	)	PUNCT
cana-5358	344	1	=	=	PUNCT
cana-5358	345	1	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5358	345	2	−1(𝐾	−1(𝐾	NOUN
cana-5358	345	3	)	)	PUNCT
cana-5358	345	4	)	)	PUNCT
cana-5358	345	5	.	.	PUNCT
cana-5358	346	1	that	that	PRON
cana-5358	346	2	is	be	AUX
cana-5358	346	3	,	,	PUNCT
cana-5358	346	4	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	346	5	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5358	346	6	)	)	PUNCT
cana-5358	346	7	)	)	PUNCT
cana-5358	347	1	⊆	⊆	X
cana-5358	347	2	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5358	347	3	−1(𝐾	−1(𝐾	NOUN
cana-5358	347	4	)	)	PUNCT
cana-5358	347	5	)	)	PUNCT
cana-5358	347	6	.	.	PUNCT
cana-5358	348	1	hence	hence	ADV
cana-5358	348	2	,	,	PUNCT
cana-5358	348	3	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	𝔉ℱ𝛿𝛽𝑐𝑙(ℎ𝔉	NUM
cana-5358	348	4	−1(𝐾	−1(𝐾	NOUN
cana-5358	348	5	)	)	PUNCT
cana-5358	348	6	)	)	PUNCT
cana-5358	349	1	=	=	PUNCT
cana-5358	349	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	349	3	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	−1(𝔉ℱ𝛿𝛽𝑐𝑙(𝐾	PROPN
cana-5358	349	4	)	)	PUNCT
cana-5358	349	5	)	)	PUNCT
cana-5358	349	6	.	.	PUNCT
cana-5358	350	1	remark	remark	VERB
cana-5358	350	2	4.1	4.1	NUM
cana-5358	350	3	theorems	theorem	NOUN
cana-5358	350	4	4.2	4.2	NUM
cana-5358	350	5	and	and	CCONJ
cana-5358	350	6	4.3	4.3	NUM
cana-5358	350	7	are	be	AUX
cana-5358	350	8	also	also	ADV
cana-5358	350	9	true	true	ADJ
cana-5358	350	10	if	if	SCONJ
cana-5358	350	11	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	350	12	is	be	AUX
cana-5358	350	13	a	a	DET
cana-5358	350	14	𝔉ℱ𝐶𝐻𝑜𝑚	𝔉ℱ𝐶𝐻𝑜𝑚	PROPN
cana-5358	350	15	(	(	PUNCT
cana-5358	350	16	resp	resp	NOUN
cana-5358	350	17	.	.	PUNCT
cana-5358	350	18	𝔉ℱ𝛿𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝐶𝐻𝑜𝑚	PROPN
cana-5358	350	19	,	,	PUNCT
cana-5358	350	20	𝔉ℱ𝛿𝛼𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐶𝐻𝑜𝑚	PROPN
cana-5358	350	21	,	,	PUNCT
cana-5358	350	22	𝔉ℱ𝛿𝒮𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐶𝐻𝑜𝑚	PROPN
cana-5358	350	23	&	&	CCONJ
cana-5358	350	24	𝔉ℱ𝛿𝒫𝐶𝐻𝑜𝑚.	𝔉ℱ𝛿𝒫𝐶𝐻𝑜𝑚.	PROPN
cana-5358	350	25	)	)	PUNCT
cana-5358	350	26	theorem	theorem	VERB
cana-5358	350	27	4.4	4.4	NUM
cana-5358	350	28	if	if	SCONJ
cana-5358	350	29	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	350	30	:	:	PUNCT
cana-5358	350	31	(	(	PUNCT
cana-5358	350	32	𝑋1	𝑋1	PROPN
cana-5358	350	33	,	,	PUNCT
cana-5358	350	34	𝜏1	𝜏1	NOUN
cana-5358	350	35	)	)	PUNCT
cana-5358	350	36	→	→	SYM
cana-5358	350	37	(	(	PUNCT
cana-5358	350	38	𝑋2	𝑋2	PROPN
cana-5358	350	39	,	,	PUNCT
cana-5358	350	40	𝜏2	𝜏2	PROPN
cana-5358	350	41	)	)	PUNCT
cana-5358	350	42	and	and	CCONJ
cana-5358	350	43	𝑔𝔉	𝑔𝔉	NOUN
cana-5358	350	44	:	:	PUNCT
cana-5358	350	45	(	(	PUNCT
cana-5358	350	46	𝑋2	𝑋2	ADJ
cana-5358	350	47	,	,	PUNCT
cana-5358	350	48	𝜏2	𝜏2	PROPN
cana-5358	350	49	)	)	PUNCT
cana-5358	350	50	→	→	SYM
cana-5358	350	51	(	(	PUNCT
cana-5358	350	52	𝑋3	𝑋3	NOUN
cana-5358	350	53	,	,	PUNCT
cana-5358	350	54	𝜏3	𝜏3	NOUN
cana-5358	350	55	)	)	PUNCT
cana-5358	350	56	are	be	AUX
cana-5358	350	57	𝔉ℱ𝐶𝐻𝑜𝑚	𝔉ℱ𝐶𝐻𝑜𝑚	PROPN
cana-5358	350	58	(	(	PUNCT
cana-5358	350	59	resp	resp	NOUN
cana-5358	350	60	.	.	PUNCT
cana-5358	351	1	𝔉ℱ𝛿	𝔉ℱ𝛿	NOUN
cana-5358	351	2	𝐶𝐻𝑜𝑚	𝐶𝐻𝑜𝑚	PROPN
cana-5358	351	3	,	,	PUNCT
cana-5358	351	4	𝔉ℱ𝛿𝛼𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐶𝐻𝑜𝑚	NOUN
cana-5358	351	5	,	,	PUNCT
cana-5358	351	6	𝔉ℱ𝛿𝒮𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐶𝐻𝑜𝑚	PROPN
cana-5358	351	7	,	,	PUNCT
cana-5358	351	8	𝔉ℱ𝛿𝒫𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐶𝐻𝑜𝑚	NUM
cana-5358	351	9	&	&	CCONJ
cana-5358	351	10	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	PROPN
cana-5358	351	11	or	or	CCONJ
cana-5358	351	12	𝔉ℱ𝑒∗𝐶𝐻𝑜𝑚	𝔉ℱ𝑒∗𝐶𝐻𝑜𝑚	NUM
cana-5358	351	13	)	)	PUNCT
cana-5358	351	14	’s	’s	ADV
cana-5358	351	15	,	,	PUNCT
cana-5358	351	16	then	then	ADV
cana-5358	351	17	𝑔𝔉	𝑔𝔉	PROPN
cana-5358	351	18	∘	∘	ADJ
cana-5358	351	19	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	351	20	is	be	AUX
cana-5358	351	21	a	a	DET
cana-5358	351	22	𝔉ℱ𝐶𝐻𝑜𝑚	𝔉ℱ𝐶𝐻𝑜𝑚	PROPN
cana-5358	351	23	(	(	PUNCT
cana-5358	351	24	resp	resp	NOUN
cana-5358	351	25	.	.	PUNCT
cana-5358	352	1	𝔉ℱ𝛿𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝐶𝐻𝑜𝑚	PROPN
cana-5358	352	2	,	,	PUNCT
cana-5358	352	3	𝔉ℱ𝛿𝛼𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛼𝐶𝐻𝑜𝑚	NOUN
cana-5358	352	4	,	,	PUNCT
cana-5358	352	5	𝔉ℱ𝛿𝒮𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝒮𝐶𝐻𝑜𝑚	NOUN
cana-5358	352	6	,	,	PUNCT
cana-5358	352	7	𝔉ℱ𝛿𝒫𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝒫𝐶𝐻𝑜𝑚	NUM
cana-5358	352	8	&	&	CCONJ
cana-5358	352	9	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	NOUN
cana-5358	352	10	or	or	CCONJ
cana-5358	352	11	𝔉ℱ𝑒∗𝐶𝐻𝑜𝑚	𝔉ℱ𝑒∗𝐶𝐻𝑜𝑚	NUM
cana-5358	352	12	)	)	PUNCT
cana-5358	352	13	.	.	PUNCT
cana-5358	353	1	proof	proof	NOUN
cana-5358	353	2	.	.	PUNCT
cana-5358	354	1	let	let	VERB
cana-5358	354	2	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	354	3	and	and	CCONJ
cana-5358	354	4	𝑔𝔉	𝑔𝔉	AUX
cana-5358	354	5	be	be	AUX
cana-5358	354	6	two	two	NUM
cana-5358	354	7	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	NOUN
cana-5358	354	8	’s	’s	PART
cana-5358	354	9	.	.	PUNCT
cana-5358	355	1	assume	assume	VERB
cana-5358	355	2	𝐾	𝐾	PROPN
cana-5358	355	3	is	be	AUX
cana-5358	355	4	a	a	DET
cana-5358	355	5	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	355	6	in	in	ADP
cana-5358	355	7	(	(	PUNCT
cana-5358	355	8	𝑋3	𝑋3	NOUN
cana-5358	355	9	,	,	PUNCT
cana-5358	355	10	𝜏3	𝜏3	NOUN
cana-5358	355	11	)	)	PUNCT
cana-5358	355	12	.	.	PUNCT
cana-5358	356	1	then	then	ADV
cana-5358	356	2	,	,	PUNCT
cana-5358	356	3	𝑔𝔉	𝑔𝔉	NOUN
cana-5358	356	4	−1(𝐾	−1(𝐾	NOUN
cana-5358	356	5	)	)	PUNCT
cana-5358	356	6	is	be	AUX
cana-5358	356	7	a	a	DET
cana-5358	356	8	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	356	9	in	in	ADP
cana-5358	356	10	(	(	PUNCT
cana-5358	356	11	𝑋2	𝑋2	ADJ
cana-5358	356	12	,	,	PUNCT
cana-5358	356	13	𝜏2	𝜏2	PROPN
cana-5358	356	14	)	)	PUNCT
cana-5358	356	15	.	.	PUNCT
cana-5358	357	1	then	then	ADV
cana-5358	357	2	,	,	PUNCT
cana-5358	357	3	by	by	ADP
cana-5358	357	4	hypothesis	hypothesis	NOUN
cana-5358	357	5	,	,	PUNCT
cana-5358	357	6	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	357	7	−1(𝑔𝔉	−1(𝑔𝔉	CCONJ
cana-5358	357	8	−1(𝐾	−1(𝐾	NOUN
cana-5358	357	9	)	)	PUNCT
cana-5358	357	10	)	)	PUNCT
cana-5358	357	11	is	be	AUX
cana-5358	357	12	a	a	DET
cana-5358	357	13	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	357	14	in	in	ADP
cana-5358	357	15	(	(	PUNCT
cana-5358	357	16	𝑋1	𝑋1	PROPN
cana-5358	357	17	,	,	PUNCT
cana-5358	357	18	𝜏1	𝜏1	NOUN
cana-5358	357	19	)	)	PUNCT
cana-5358	357	20	.	.	PUNCT
cana-5358	358	1	hence	hence	ADV
cana-5358	358	2	,	,	PUNCT
cana-5358	358	3	𝑔𝔉	𝑔𝔉	NOUN
cana-5358	358	4	∘	∘	ADJ
cana-5358	358	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	358	6	is	be	AUX
cana-5358	358	7	a	a	DET
cana-5358	358	8	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5358	358	9	mapping	mapping	NOUN
cana-5358	358	10	.	.	PUNCT
cana-5358	359	1	now	now	ADV
cana-5358	359	2	,	,	PUNCT
cana-5358	359	3	let	let	VERB
cana-5358	359	4	𝐾	𝐾	PRON
cana-5358	359	5	be	be	AUX
cana-5358	359	6	a	a	DET
cana-5358	359	7	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	359	8	in	in	ADP
cana-5358	359	9	(	(	PUNCT
cana-5358	359	10	𝑋1	𝑋1	PROPN
cana-5358	359	11	,	,	PUNCT
cana-5358	359	12	𝜏1	𝜏1	NOUN
cana-5358	359	13	)	)	PUNCT
cana-5358	359	14	.	.	PUNCT
cana-5358	360	1	then	then	ADV
cana-5358	360	2	,	,	PUNCT
cana-5358	360	3	by	by	ADP
cana-5358	360	4	presumption	presumption	NOUN
cana-5358	360	5	,	,	PUNCT
cana-5358	360	6	ℎ𝔉(𝐾	ℎ𝔉(𝐾	X
cana-5358	360	7	)	)	PUNCT
cana-5358	360	8	is	be	AUX
cana-5358	360	9	a	a	DET
cana-5358	360	10	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	360	11	in	in	ADP
cana-5358	360	12	(	(	PUNCT
cana-5358	360	13	𝑋2	𝑋2	ADJ
cana-5358	360	14	,	,	PUNCT
cana-5358	360	15	𝜏2	𝜏2	PROPN
cana-5358	360	16	)	)	PUNCT
cana-5358	360	17	.	.	PUNCT
cana-5358	361	1	then	then	ADV
cana-5358	361	2	,	,	PUNCT
cana-5358	361	3	by	by	ADP
cana-5358	361	4	hypothesis	hypothesis	NOUN
cana-5358	361	5	,	,	PUNCT
cana-5358	361	6	𝑔𝔉(ℎ𝔉(𝐾	𝑔𝔉(ℎ𝔉(𝐾	PROPN
cana-5358	361	7	)	)	PUNCT
cana-5358	361	8	)	)	PUNCT
cana-5358	361	9	is	be	AUX
cana-5358	361	10	a	a	DET
cana-5358	361	11	𝔉ℱ𝛿𝛽𝑐𝑠	𝔉ℱ𝛿𝛽𝑐𝑠	NOUN
cana-5358	361	12	in	in	ADP
cana-5358	361	13	(	(	PUNCT
cana-5358	361	14	𝑋3	𝑋3	NOUN
cana-5358	361	15	,	,	PUNCT
cana-5358	361	16	𝜏3	𝜏3	NOUN
cana-5358	361	17	)	)	PUNCT
cana-5358	361	18	.	.	PUNCT
cana-5358	362	1	this	this	PRON
cana-5358	362	2	implies	imply	VERB
cana-5358	362	3	that	that	SCONJ
cana-5358	362	4	𝑔𝔉	𝑔𝔉	AUX
cana-5358	362	5	∘	∘	ADJ
cana-5358	362	6	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	362	7	is	be	AUX
cana-5358	362	8	a	a	DET
cana-5358	362	9	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	𝔉ℱ𝛿𝛽𝐼𝑟𝑟	ADJ
cana-5358	362	10	mapping	mapping	NOUN
cana-5358	362	11	.	.	PUNCT
cana-5358	363	1	hence	hence	ADV
cana-5358	363	2	,	,	PUNCT
cana-5358	363	3	𝑔𝔉	𝑔𝔉	NOUN
cana-5358	363	4	∘	∘	ADJ
cana-5358	363	5	ℎ𝔉	ℎ𝔉	NOUN
cana-5358	363	6	is	be	AUX
cana-5358	363	7	a	a	DET
cana-5358	363	8	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚.	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚.	NOUN
cana-5358	363	9	the	the	DET
cana-5358	363	10	proof	proof	NOUN
cana-5358	363	11	of	of	ADP
cana-5358	363	12	other	other	ADJ
cana-5358	363	13	cases	case	NOUN
cana-5358	363	14	are	be	AUX
cana-5358	363	15	similar	similar	ADJ
cana-5358	363	16	.	.	PUNCT
cana-5358	364	1	5	5	NUM
cana-5358	364	2	application	application	NOUN
cana-5358	364	3	entropy	entropy	NOUN
cana-5358	364	4	as	as	ADP
cana-5358	364	5	a	a	DET
cana-5358	364	6	measure	measure	NOUN
cana-5358	364	7	of	of	ADP
cana-5358	364	8	fuzziness	fuzziness	NOUN
cana-5358	364	9	was	be	AUX
cana-5358	364	10	first	first	ADV
cana-5358	364	11	proposed	propose	VERB
cana-5358	364	12	by	by	ADP
cana-5358	364	13	zadeh	zadeh	PROPN
cana-5358	365	1	[	[	X
cana-5358	365	2	16	16	NUM
cana-5358	365	3	]	]	PUNCT
cana-5358	365	4	.	.	PUNCT
cana-5358	366	1	later	later	ADV
cana-5358	366	2	many	many	ADJ
cana-5358	366	3	mathematicians	mathematician	NOUN
cana-5358	366	4	defined	define	VERB
cana-5358	366	5	several	several	ADJ
cana-5358	366	6	entropy	entropy	NOUN
cana-5358	366	7	measures	measure	NOUN
cana-5358	366	8	.	.	PUNCT
cana-5358	367	1	in	in	ADP
cana-5358	367	2	this	this	DET
cana-5358	367	3	section	section	NOUN
cana-5358	367	4	,	,	PUNCT
cana-5358	367	5	we	we	PRON
cana-5358	367	6	focus	focus	VERB
cana-5358	367	7	on	on	ADP
cana-5358	367	8	defining	define	VERB
cana-5358	367	9	an	an	DET
cana-5358	367	10	entropy	entropy	NOUN
cana-5358	367	11	measure	measure	NOUN
cana-5358	367	12	for	for	ADP
cana-5358	367	13	𝔉𝑓𝑠	𝔉𝑓𝑠	PROPN
cana-5358	367	14	that	that	PRON
cana-5358	367	15	connects	connect	VERB
cana-5358	367	16	the	the	DET
cana-5358	367	17	degree	degree	NOUN
cana-5358	367	18	of	of	ADP
cana-5358	367	19	membership	membership	NOUN
cana-5358	367	20	and	and	CCONJ
cana-5358	367	21	non	non	ADJ
cana-5358	367	22	-	-	NOUN
cana-5358	367	23	membership	membership	NOUN
cana-5358	367	24	.	.	PUNCT
cana-5358	368	1	as	as	ADP
cana-5358	368	2	an	an	DET
cana-5358	368	3	example	example	NOUN
cana-5358	368	4	,	,	PUNCT
cana-5358	368	5	we	we	PRON
cana-5358	368	6	have	have	AUX
cana-5358	368	7	applied	apply	VERB
cana-5358	368	8	the	the	DET
cana-5358	368	9	proposed	propose	VERB
cana-5358	368	10	entropy	entropy	NOUN
cana-5358	368	11	measure	measure	NOUN
cana-5358	368	12	in	in	ADP
cana-5358	368	13	the	the	DET
cana-5358	368	14	field	field	NOUN
cana-5358	368	15	of	of	ADP
cana-5358	368	16	decision	decision	NOUN
cana-5358	368	17	making	making	NOUN
cana-5358	368	18	.	.	PUNCT
cana-5358	369	1	definition	definition	NOUN
cana-5358	369	2	5.1	5.1	NUM
cana-5358	369	3	let	let	VERB
cana-5358	369	4	𝐴	𝐴	PROPN
cana-5358	369	5	=	=	PUNCT
cana-5358	369	6	{	{	PUNCT
cana-5358	369	7	<	<	X
cana-5358	369	8	𝑥	𝑥	X
cana-5358	369	9	,	,	PUNCT
cana-5358	369	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5358	369	11	)	)	PUNCT
cana-5358	369	12	,	,	PUNCT
cana-5358	369	13	𝜆𝐴(𝑥)|𝑥	𝜆𝐴(𝑥)|𝑥	NOUN
cana-5358	369	14	∈	∈	PROPN
cana-5358	369	15	𝑋	𝑋	PROPN
cana-5358	369	16	}	}	PUNCT
cana-5358	369	17	be	be	AUX
cana-5358	369	18	a	a	DET
cana-5358	369	19	𝔉𝑓𝑠	𝔉𝑓𝑠	PROPN
cana-5358	369	20	in	in	ADP
cana-5358	369	21	𝑈.	𝑈.	PROPN
cana-5358	369	22	the	the	DET
cana-5358	369	23	new	new	ADJ
cana-5358	369	24	entropy	entropy	NOUN
cana-5358	369	25	measure	measure	NOUN
cana-5358	369	26	for	for	ADP
cana-5358	369	27	𝐴	𝐴	PROPN
cana-5358	369	28	denoted	denote	VERB
cana-5358	369	29	by	by	ADP
cana-5358	369	30	휀𝔉𝑓𝑠(𝐴	휀𝔉𝑓𝑠(𝐴	NOUN
cana-5358	369	31	)	)	PUNCT
cana-5358	369	32	,	,	PUNCT
cana-5358	369	33	is	be	AUX
cana-5358	369	34	a	a	DET
cana-5358	369	35	function	function	NOUN
cana-5358	369	36	,	,	PUNCT
cana-5358	369	37	휀𝔉𝑓𝑠	휀𝔉𝑓𝑠	PROPN
cana-5358	369	38	:	:	PUNCT
cana-5358	369	39	𝜏𝔉𝑓𝑠(𝑈	𝜏𝔉𝑓𝑠(𝑈	PROPN
cana-5358	369	40	)	)	PUNCT
cana-5358	369	41	→	→	PUNCT
cana-5358	370	1	[	[	X
cana-5358	370	2	0,1	0,1	NUM
cana-5358	370	3	]	]	PUNCT
cana-5358	370	4	and	and	CCONJ
cana-5358	370	5	is	be	AUX
cana-5358	370	6	defined	define	VERB
cana-5358	370	7	as	as	ADP
cana-5358	370	8	휀𝔉𝑓𝑠(𝐴	휀𝔉𝑓𝑠(𝐴	X
cana-5358	370	9	)	)	PUNCT
cana-5358	370	10	=	=	SYM
cana-5358	371	1	1	1	NUM
cana-5358	371	2	−	−	NUM
cana-5358	371	3	1	1	NUM
cana-5358	371	4	𝑛	𝑛	PRON
cana-5358	371	5	∑𝑛	∑𝑛	PROPN
cana-5358	371	6	𝑖=1	𝑖=1	PROPN
cana-5358	371	7	(	(	PUNCT
cana-5358	371	8	𝜇𝐴	𝜇𝐴	ADP
cana-5358	371	9	−	−	PROPN
cana-5358	371	10	𝜆𝐴)2	𝜆𝐴)2	NUM
cana-5358	371	11	;	;	PUNCT
cana-5358	371	12	𝑓𝑜𝑟𝑒𝑣𝑒𝑟𝑦`𝑥𝑖	𝑓𝑜𝑟𝑒𝑣𝑒𝑟𝑦`𝑥𝑖	NUM
cana-5358	371	13	∈	∈	PROPN
cana-5358	371	14	𝐴	𝐴	PROPN
cana-5358	371	15	,	,	PUNCT
cana-5358	371	16	where	where	SCONJ
cana-5358	371	17	𝜏𝔉𝑓𝑠(𝑈	𝜏𝔉𝑓𝑠(𝑈	NOUN
cana-5358	371	18	)	)	PUNCT
cana-5358	371	19	denote	denote	VERB
cana-5358	371	20	the	the	DET
cana-5358	371	21	family	family	NOUN
cana-5358	371	22	of	of	ADP
cana-5358	371	23	all	all	DET
cana-5358	371	24	𝔉𝑓𝑠	𝔉𝑓𝑠	PROPN
cana-5358	371	25	’s	’s	NOUN
cana-5358	371	26	on	on	ADP
cana-5358	371	27	𝑈.	𝑈.	PROPN
cana-5358	371	28	example	example	NOUN
cana-5358	371	29	5.1	5.1	NUM
cana-5358	371	30	assume	assume	VERB
cana-5358	371	31	that	that	SCONJ
cana-5358	371	32	a	a	DET
cana-5358	371	33	certain	certain	ADJ
cana-5358	371	34	institution	institution	NOUN
cana-5358	371	35	wants	want	VERB
cana-5358	371	36	to	to	PART
cana-5358	371	37	assign	assign	VERB
cana-5358	371	38	a	a	DET
cana-5358	371	39	permanent	permanent	ADJ
cana-5358	371	40	faculty	faculty	NOUN
cana-5358	371	41	member	member	NOUN
cana-5358	371	42	from	from	ADP
cana-5358	371	43	the	the	DET
cana-5358	371	44	set	set	NOUN
cana-5358	371	45	of	of	ADP
cana-5358	371	46	candidates	candidate	NOUN
cana-5358	371	47	{	{	PUNCT
cana-5358	371	48	𝑃1	𝑃1	NOUN
cana-5358	371	49	,	,	PUNCT
cana-5358	371	50	𝑃2	𝑃2	PROPN
cana-5358	371	51	,	,	PUNCT
cana-5358	371	52	𝑃3	𝑃3	NOUN
cana-5358	371	53	,	,	PUNCT
cana-5358	371	54	𝑃4	𝑃4	NOUN
cana-5358	371	55	,	,	PUNCT
cana-5358	371	56	𝑃5	𝑃5	NOUN
cana-5358	371	57	}	}	PUNCT
cana-5358	371	58	.	.	PUNCT
cana-5358	372	1	for	for	ADP
cana-5358	372	2	this	this	PRON
cana-5358	372	3	,	,	PUNCT
cana-5358	372	4	the	the	DET
cana-5358	372	5	institution	institution	NOUN
cana-5358	372	6	authorities	authority	NOUN
cana-5358	372	7	consider	consider	VERB
cana-5358	372	8	the	the	DET
cana-5358	372	9	following	follow	VERB
cana-5358	372	10	four	four	NUM
cana-5358	372	11	criteria	criterion	NOUN
cana-5358	372	12	𝐶	𝐶	PROPN
cana-5358	372	13	=	=	PRON
cana-5358	372	14	{	{	PUNCT
cana-5358	372	15	𝐶𝑖	𝐶𝑖	PROPN
cana-5358	372	16	:	:	PUNCT
cana-5358	372	17	𝑖	𝑖	NOUN
cana-5358	372	18	=	=	NOUN
cana-5358	372	19	1,2,3,4	1,2,3,4	NUM
cana-5358	372	20	}	}	PUNCT
cana-5358	372	21	,	,	PUNCT
cana-5358	372	22	where	where	SCONJ
cana-5358	372	23	:	:	PUNCT
cana-5358	372	24	•	•	NOUN
cana-5358	372	25	𝐶1	𝐶1	NOUN
cana-5358	372	26	represents	represent	VERB
cana-5358	372	27	the	the	DET
cana-5358	372	28	number	number	NOUN
cana-5358	372	29	of	of	ADP
cana-5358	372	30	research	research	NOUN
cana-5358	372	31	publications	publication	NOUN
cana-5358	372	32	,	,	PUNCT
cana-5358	372	33	conferences	conference	NOUN
cana-5358	372	34	and	and	CCONJ
cana-5358	372	35	𝐹𝐷𝑃	𝐹𝐷𝑃	PROPN
cana-5358	372	36	participated	participate	VERB
cana-5358	372	37	,	,	PUNCT
cana-5358	372	38	•	•	NUM
cana-5358	372	39	𝐶2	𝐶2	X
cana-5358	372	40	represents	represent	VERB
cana-5358	372	41	the	the	DET
cana-5358	372	42	teaching	teaching	NOUN
cana-5358	372	43	experience	experience	NOUN
cana-5358	372	44	,	,	PUNCT
cana-5358	372	45	•	•	DET
cana-5358	372	46	𝐶3	𝐶3	NOUN
cana-5358	372	47	represents	represent	VERB
cana-5358	372	48	the	the	DET
cana-5358	372	49	communications	communication	NOUN
cana-5358	372	50	on	on	ADP
cana-5358	372	51	applied	apply	VERB
cana-5358	372	52	nonlinear	nonlinear	ADJ
cana-5358	372	53	analysis	analysis	NOUN
cana-5358	372	54	issn	issn	NOUN
cana-5358	372	55	:	:	PUNCT
cana-5358	372	56	1074	1074	NUM
cana-5358	372	57	-	-	PUNCT
cana-5358	372	58	133x	133x	NUM
cana-5358	372	59	vol	vol	VERB
cana-5358	372	60	32	32	NUM
cana-5358	372	61	no	no	NOUN
cana-5358	372	62	.	.	PUNCT
cana-5358	373	1	10s	10	NOUN
cana-5358	373	2	(	(	PUNCT
cana-5358	373	3	2025	2025	NUM
cana-5358	373	4	)	)	PUNCT
cana-5358	373	5	1906	1906	NUM
cana-5358	373	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	373	7	regularity	regularity	NOUN
cana-5358	373	8	and	and	CCONJ
cana-5358	373	9	punctuality	punctuality	NOUN
cana-5358	373	10	,	,	PUNCT
cana-5358	373	11	•	•	NUM
cana-5358	373	12	𝐶4	𝐶4	NOUN
cana-5358	373	13	represents	represent	VERB
cana-5358	373	14	the	the	DET
cana-5358	373	15	behavior	behavior	NOUN
cana-5358	373	16	with	with	ADP
cana-5358	373	17	students	student	NOUN
cana-5358	373	18	through	through	ADP
cana-5358	373	19	the	the	DET
cana-5358	373	20	class	class	NOUN
cana-5358	373	21	.	.	PUNCT
cana-5358	374	1	after	after	ADP
cana-5358	374	2	a	a	DET
cana-5358	374	3	deep	deep	ADJ
cana-5358	374	4	discussion	discussion	NOUN
cana-5358	374	5	,	,	PUNCT
cana-5358	374	6	a	a	DET
cana-5358	374	7	committee	committee	NOUN
cana-5358	374	8	(	(	PUNCT
cana-5358	374	9	forms	form	NOUN
cana-5358	374	10	by	by	ADP
cana-5358	374	11	the	the	DET
cana-5358	374	12	institution	institution	NOUN
cana-5358	374	13	authorities	authority	NOUN
cana-5358	374	14	)	)	PUNCT
cana-5358	374	15	proposed	propose	VERB
cana-5358	374	16	a	a	DET
cana-5358	374	17	performance	performance	NOUN
cana-5358	374	18	of	of	ADP
cana-5358	374	19	these	these	DET
cana-5358	374	20	candidates	candidate	NOUN
cana-5358	374	21	environment	environment	NOUN
cana-5358	374	22	as	as	SCONJ
cana-5358	374	23	given	give	VERB
cana-5358	374	24	in	in	ADP
cana-5358	374	25	table	table	NOUN
cana-5358	374	26	.	.	PUNCT
cana-5358	375	1	every	every	DET
cana-5358	375	2	ordered	order	VERB
cana-5358	375	3	pair	pair	NOUN
cana-5358	375	4	given	give	VERB
cana-5358	375	5	in	in	ADP
cana-5358	375	6	table	table	NOUN
cana-5358	375	7	represents	represent	VERB
cana-5358	375	8	the	the	DET
cana-5358	375	9	membership	membership	NOUN
cana-5358	375	10	and	and	CCONJ
cana-5358	375	11	non	non	ADJ
cana-5358	375	12	-	-	ADJ
cana-5358	375	13	membership	membership	ADJ
cana-5358	375	14	degrees	degree	NOUN
cana-5358	375	15	of	of	ADP
cana-5358	375	16	a	a	DET
cana-5358	375	17	candidate	candidate	NOUN
cana-5358	375	18	corresponding	correspond	VERB
cana-5358	375	19	criteria	criterion	NOUN
cana-5358	375	20	(	(	PUNCT
cana-5358	375	21	or	or	CCONJ
cana-5358	375	22	attribute	attribute	NOUN
cana-5358	375	23	)	)	PUNCT
cana-5358	375	24	.	.	PUNCT
cana-5358	376	1	assume	assume	VERB
cana-5358	376	2	that	that	SCONJ
cana-5358	376	3	the	the	DET
cana-5358	376	4	proposed	propose	VERB
cana-5358	376	5	approach	approach	NOUN
cana-5358	376	6	for	for	ADP
cana-5358	376	7	accessing	access	VERB
cana-5358	376	8	the	the	DET
cana-5358	376	9	best	good	ADJ
cana-5358	376	10	candidate	candidate	NOUN
cana-5358	376	11	with	with	ADP
cana-5358	376	12	appreciation	appreciation	NOUN
cana-5358	376	13	to	to	ADP
cana-5358	376	14	every	every	DET
cana-5358	376	15	criterion	criterion	NOUN
cana-5358	376	16	provided	provide	VERB
cana-5358	376	17	the	the	DET
cana-5358	376	18	committee	committee	NOUN
cana-5358	376	19	.	.	PUNCT
cana-5358	377	1	then	then	ADV
cana-5358	377	2	,	,	PUNCT
cana-5358	377	3	we	we	PRON
cana-5358	377	4	compute	compute	VERB
cana-5358	377	5	the	the	DET
cana-5358	377	6	entropy	entropy	NOUN
cana-5358	377	7	measure	measure	NOUN
cana-5358	377	8	for	for	SCONJ
cana-5358	377	9	each	each	DET
cana-5358	377	10	candidate	candidate	NOUN
cana-5358	377	11	to	to	PART
cana-5358	377	12	decide	decide	VERB
cana-5358	377	13	who	who	PRON
cana-5358	377	14	is	be	AUX
cana-5358	377	15	the	the	DET
cana-5358	377	16	optimal	optimal	ADJ
cana-5358	377	17	candidate(s	candidate(s	PROPN
cana-5358	377	18	)	)	PUNCT
cana-5358	377	19	.	.	PUNCT
cana-5358	378	1	table	table	NOUN
cana-5358	378	2	1	1	NUM
cana-5358	378	3	.	.	PUNCT
cana-5358	378	4	selection	selection	NOUN
cana-5358	378	5	criteria	criterion	NOUN
cana-5358	378	6	for	for	ADP
cana-5358	378	7	the	the	DET
cana-5358	378	8	candidates	candidate	NOUN
cana-5358	378	9	.	.	PUNCT
cana-5358	379	1	person	person	NOUN
cana-5358	379	2	1	1	NUM
cana-5358	379	3	(	(	PUNCT
cana-5358	379	4	p1	p1	NOUN
cana-5358	379	5	)	)	PUNCT
cana-5358	379	6	person	person	NOUN
cana-5358	379	7	2	2	NUM
cana-5358	379	8	(	(	PUNCT
cana-5358	379	9	p2	p2	NOUN
cana-5358	379	10	)	)	PUNCT
cana-5358	379	11	person	person	NOUN
cana-5358	379	12	3	3	NUM
cana-5358	379	13	(	(	PUNCT
cana-5358	379	14	p3	p3	NOUN
cana-5358	379	15	)	)	PUNCT
cana-5358	379	16	person	person	NOUN
cana-5358	379	17	4	4	NUM
cana-5358	379	18	(	(	PUNCT
cana-5358	379	19	p4	p4	ADJ
cana-5358	379	20	)	)	PUNCT
cana-5358	379	21	person	person	NOUN
cana-5358	379	22	5	5	NUM
cana-5358	379	23	(	(	PUNCT
cana-5358	379	24	p5	p5	PROPN
cana-5358	379	25	)	)	PUNCT
cana-5358	379	26	(	(	PUNCT
cana-5358	379	27	c1	c1	NOUN
cana-5358	379	28	)	)	PUNCT
cana-5358	379	29	<	<	X
cana-5358	379	30	𝐶1	𝐶1	PROPN
cana-5358	379	31	,	,	PUNCT
cana-5358	379	32	𝑃1	𝑃1	NOUN
cana-5358	379	33	;	;	PUNCT
cana-5358	379	34	0.3,0.7	0.3,0.7	NUM
cana-5358	379	35	>	>	PUNCT
cana-5358	379	36	<	<	X
cana-5358	379	37	𝐶1	𝐶1	PROPN
cana-5358	379	38	,	,	PUNCT
cana-5358	379	39	𝑃2	𝑃2	NOUN
cana-5358	379	40	;	;	PUNCT
cana-5358	379	41	0.7,0.2	0.7,0.2	PROPN
cana-5358	379	42	>	>	X
cana-5358	379	43	<	<	X
cana-5358	379	44	𝐶1	𝐶1	PROPN
cana-5358	379	45	,	,	PUNCT
cana-5358	379	46	𝑃3	𝑃3	NOUN
cana-5358	379	47	;	;	PUNCT
cana-5358	379	48	0.2,0.3	0.2,0.3	PROPN
cana-5358	379	49	>	>	X
cana-5358	379	50	<	<	X
cana-5358	379	51	𝐶1	𝐶1	PROPN
cana-5358	379	52	,	,	PUNCT
cana-5358	379	53	𝑃4	𝑃4	NOUN
cana-5358	379	54	;	;	PUNCT
cana-5358	380	1	0.3,0.4	0.3,0.4	NUM
cana-5358	380	2	>	>	X
cana-5358	380	3	<	<	X
cana-5358	380	4	𝐶1	𝐶1	PROPN
cana-5358	380	5	,	,	PUNCT
cana-5358	380	6	𝑃5	𝑃5	NOUN
cana-5358	380	7	;	;	PUNCT
cana-5358	380	8	0.1,0.3	0.1,0.3	PROPN
cana-5358	380	9	>	>	X
cana-5358	380	10	(	(	PUNCT
cana-5358	380	11	c2	c2	PROPN
cana-5358	380	12	)	)	PUNCT
cana-5358	380	13	<	<	X
cana-5358	380	14	𝐶2	𝐶2	PROPN
cana-5358	380	15	,	,	PUNCT
cana-5358	380	16	𝑃1	𝑃1	NOUN
cana-5358	380	17	;	;	PUNCT
cana-5358	380	18	0.7,0.6	0.7,0.6	NUM
cana-5358	380	19	>	>	X
cana-5358	380	20	<	<	X
cana-5358	380	21	𝐶2	𝐶2	PROPN
cana-5358	380	22	,	,	PUNCT
cana-5358	380	23	𝑃2	𝑃2	PROPN
cana-5358	380	24	;	;	PUNCT
cana-5358	380	25	0.7,0.1	0.7,0.1	PROPN
cana-5358	380	26	>	>	X
cana-5358	380	27	<	<	X
cana-5358	380	28	𝐶2	𝐶2	PROPN
cana-5358	380	29	,	,	PUNCT
cana-5358	380	30	𝑃3	𝑃3	NOUN
cana-5358	380	31	;	;	PUNCT
cana-5358	380	32	0.7,0.5	0.7,0.5	NUM
cana-5358	380	33	>	>	X
cana-5358	380	34	<	<	X
cana-5358	380	35	𝐶2	𝐶2	PROPN
cana-5358	380	36	,	,	PUNCT
cana-5358	380	37	𝑃4	𝑃4	PROPN
cana-5358	380	38	;	;	PUNCT
cana-5358	380	39	0.3,0.4	0.3,0.4	NUM
cana-5358	380	40	>	>	X
cana-5358	380	41	<	<	X
cana-5358	380	42	𝐶2	𝐶2	PROPN
cana-5358	380	43	,	,	PUNCT
cana-5358	380	44	𝑃5	𝑃5	NOUN
cana-5358	380	45	;	;	PUNCT
cana-5358	380	46	0.2,0.7	0.2,0.7	PROPN
cana-5358	380	47	>	>	X
cana-5358	380	48	(	(	PUNCT
cana-5358	380	49	c3	c3	PROPN
cana-5358	380	50	)	)	PUNCT
cana-5358	380	51	<	<	X
cana-5358	380	52	𝐶3	𝐶3	PROPN
cana-5358	380	53	,	,	PUNCT
cana-5358	380	54	𝑃1	𝑃1	NOUN
cana-5358	380	55	;	;	PUNCT
cana-5358	380	56	0.3,0.2	0.3,0.2	PROPN
cana-5358	380	57	>	>	X
cana-5358	380	58	<	<	X
cana-5358	380	59	𝐶3	𝐶3	PROPN
cana-5358	380	60	,	,	PUNCT
cana-5358	380	61	𝑃2	𝑃2	PROPN
cana-5358	380	62	;	;	PUNCT
cana-5358	380	63	0.2,0.4	0.2,0.4	NUM
cana-5358	380	64	>	>	X
cana-5358	380	65	<	<	X
cana-5358	380	66	𝐶3	𝐶3	PROPN
cana-5358	380	67	,	,	PUNCT
cana-5358	380	68	𝑃3	𝑃3	NOUN
cana-5358	380	69	;	;	PUNCT
cana-5358	380	70	0.9,0.2	0.9,0.2	X
cana-5358	380	71	>	>	X
cana-5358	380	72	<	<	X
cana-5358	380	73	𝐶3	𝐶3	PROPN
cana-5358	380	74	,	,	PUNCT
cana-5358	380	75	𝑃4	𝑃4	PROPN
cana-5358	380	76	;	;	PUNCT
cana-5358	380	77	0.2,0.5	0.2,0.5	NUM
cana-5358	380	78	>	>	X
cana-5358	380	79	<	<	X
cana-5358	380	80	𝐶3	𝐶3	PROPN
cana-5358	380	81	,	,	PUNCT
cana-5358	380	82	𝑃5	𝑃5	NOUN
cana-5358	380	83	;	;	PUNCT
cana-5358	380	84	0.6,0.2	0.6,0.2	PROPN
cana-5358	380	85	>	>	X
cana-5358	380	86	(	(	PUNCT
cana-5358	380	87	c4	c4	NOUN
cana-5358	380	88	)	)	PUNCT
cana-5358	380	89	<	<	X
cana-5358	380	90	𝐶4	𝐶4	PROPN
cana-5358	380	91	,	,	PUNCT
cana-5358	380	92	𝑃1	𝑃1	NOUN
cana-5358	380	93	;	;	PUNCT
cana-5358	380	94	0.1,0.7	0.1,0.7	X
cana-5358	380	95	>	>	X
cana-5358	380	96	<	<	X
cana-5358	380	97	𝐶4	𝐶4	PROPN
cana-5358	380	98	,	,	PUNCT
cana-5358	380	99	𝑃2	𝑃2	NOUN
cana-5358	380	100	;	;	PUNCT
cana-5358	380	101	0.3,0.3	0.3,0.3	PROPN
cana-5358	380	102	>	>	X
cana-5358	380	103	<	<	X
cana-5358	380	104	𝐶4	𝐶4	PROPN
cana-5358	380	105	,	,	PUNCT
cana-5358	380	106	𝑃3	𝑃3	NOUN
cana-5358	380	107	;	;	PUNCT
cana-5358	380	108	0.1,0.3	0.1,0.3	PROPN
cana-5358	380	109	>	>	X
cana-5358	380	110	<	<	X
cana-5358	380	111	𝐶4	𝐶4	PROPN
cana-5358	380	112	,	,	PUNCT
cana-5358	380	113	𝑃4	𝑃4	NOUN
cana-5358	380	114	;	;	PUNCT
cana-5358	380	115	0.5,0.1	0.5,0.1	X
cana-5358	380	116	>	>	X
cana-5358	380	117	<	<	X
cana-5358	380	118	𝐶4	𝐶4	NOUN
cana-5358	380	119	,	,	PUNCT
cana-5358	380	120	𝑃5	𝑃5	NOUN
cana-5358	380	121	;	;	PUNCT
cana-5358	380	122	0.1,0.9	0.1,0.9	NUM
cana-5358	380	123	>	>	PUNCT
cana-5358	380	124	clearly	clearly	ADV
cana-5358	380	125	,	,	PUNCT
cana-5358	380	126	all	all	DET
cana-5358	380	127	values	value	NOUN
cana-5358	380	128	in	in	ADP
cana-5358	380	129	the	the	DET
cana-5358	380	130	table	table	NOUN
cana-5358	380	131	1	1	NUM
cana-5358	380	132	are	be	AUX
cana-5358	380	133	𝔉ℱ𝑠	𝔉ℱ𝑠	NOUN
cana-5358	380	134	’s	’s	NOUN
cana-5358	380	135	.	.	PUNCT
cana-5358	381	1	now	now	ADV
cana-5358	381	2	we	we	PRON
cana-5358	381	3	calculate	calculate	VERB
cana-5358	381	4	the	the	DET
cana-5358	381	5	휀𝔉ℱ𝑠	휀𝔉ℱ𝑠	PROPN
cana-5358	381	6	of	of	ADP
cana-5358	381	7	each	each	DET
cana-5358	381	8	value	value	NOUN
cana-5358	381	9	.	.	PUNCT
cana-5358	382	1	table	table	NOUN
cana-5358	382	2	2	2	NUM
cana-5358	382	3	.	.	PUNCT
cana-5358	382	4	entropy	entropy	PROPN
cana-5358	382	5	measure	measure	NOUN
cana-5358	382	6	of	of	ADP
cana-5358	382	7	each	each	DET
cana-5358	382	8	candidate	candidate	NOUN
cana-5358	382	9	based	base	VERB
cana-5358	382	10	on	on	ADP
cana-5358	382	11	their	their	PRON
cana-5358	382	12	criteria	criterion	NOUN
cana-5358	382	13	.	.	PUNCT
cana-5358	383	1	person	person	NOUN
cana-5358	383	2	1	1	NUM
cana-5358	383	3	(	(	PUNCT
cana-5358	383	4	p1	p1	NOUN
cana-5358	383	5	)	)	PUNCT
cana-5358	383	6	person	person	NOUN
cana-5358	383	7	2	2	NUM
cana-5358	383	8	(	(	PUNCT
cana-5358	383	9	p2	p2	NOUN
cana-5358	383	10	)	)	PUNCT
cana-5358	383	11	person	person	NOUN
cana-5358	383	12	3	3	NUM
cana-5358	383	13	(	(	PUNCT
cana-5358	383	14	p3	p3	NOUN
cana-5358	383	15	)	)	PUNCT
cana-5358	383	16	person	person	NOUN
cana-5358	383	17	4	4	NUM
cana-5358	383	18	(	(	PUNCT
cana-5358	383	19	p4	p4	ADJ
cana-5358	383	20	)	)	PUNCT
cana-5358	383	21	person	person	NOUN
cana-5358	383	22	5	5	NUM
cana-5358	383	23	(	(	PUNCT
cana-5358	383	24	p5	p5	PROPN
cana-5358	383	25	)	)	PUNCT
cana-5358	383	26	(	(	PUNCT
cana-5358	383	27	c1	c1	PROPN
cana-5358	383	28	)	)	PUNCT
cana-5358	383	29	0.84	0.84	NUM
cana-5358	383	30	0.75	0.75	NUM
cana-5358	383	31	0.99	0.99	NUM
cana-5358	383	32	0.99	0.99	NUM
cana-5358	383	33	0.96	0.96	NUM
cana-5358	383	34	(	(	PUNCT
cana-5358	383	35	c2	c2	PROPN
cana-5358	383	36	)	)	PUNCT
cana-5358	383	37	0.99	0.99	NUM
cana-5358	383	38	0.64	0.64	NUM
cana-5358	383	39	0.96	0.96	NUM
cana-5358	383	40	0.99	0.99	NUM
cana-5358	383	41	0.75	0.75	NUM
cana-5358	383	42	(	(	PUNCT
cana-5358	383	43	c3	c3	NOUN
cana-5358	383	44	)	)	PUNCT
cana-5358	383	45	0.99	0.99	NUM
cana-5358	383	46	0.96	0.96	NUM
cana-5358	383	47	0.51	0.51	NUM
cana-5358	383	48	0.91	0.91	NUM
cana-5358	383	49	0.84	0.84	NUM
cana-5358	383	50	(	(	PUNCT
cana-5358	383	51	c4	c4	NOUN
cana-5358	383	52	)	)	PUNCT
cana-5358	383	53	0.64	0.64	NUM
cana-5358	383	54	1.0	1.0	NUM
cana-5358	383	55	0.96	0.96	NUM
cana-5358	383	56	0.84	0.84	NUM
cana-5358	383	57	0.36	0.36	NUM
cana-5358	383	58	from	from	ADP
cana-5358	383	59	table	table	NOUN
cana-5358	383	60	2	2	NUM
cana-5358	383	61	,	,	PUNCT
cana-5358	383	62	it	it	PRON
cana-5358	383	63	is	be	AUX
cana-5358	383	64	clear	clear	ADJ
cana-5358	383	65	that	that	SCONJ
cana-5358	383	66	,	,	PUNCT
cana-5358	383	67	휀𝔉ℱ𝑠(𝐶1	휀𝔉ℱ𝑠(𝐶1	ADJ
cana-5358	383	68	,	,	PUNCT
cana-5358	383	69	𝑃2	𝑃2	PROPN
cana-5358	383	70	)	)	PUNCT
cana-5358	383	71	<	<	X
cana-5358	383	72	휀𝔉ℱ𝑠(𝐶1	휀𝔉ℱ𝑠(𝐶1	PROPN
cana-5358	383	73	,	,	PUNCT
cana-5358	383	74	𝑃1	𝑃1	NOUN
cana-5358	383	75	)	)	PUNCT
cana-5358	383	76	<	<	X
cana-5358	383	77	휀𝔉ℱ𝑠(𝐶1	휀𝔉ℱ𝑠(𝐶1	VERB
cana-5358	383	78	,	,	PUNCT
cana-5358	383	79	𝑃5	𝑃5	NOUN
cana-5358	383	80	)	)	PUNCT
cana-5358	383	81	<	<	X
cana-5358	383	82	휀𝔉ℱ𝑠(𝐶1	휀𝔉ℱ𝑠(𝐶1	VERB
cana-5358	383	83	,	,	PUNCT
cana-5358	383	84	𝑃3	𝑃3	NOUN
cana-5358	383	85	)	)	PUNCT
cana-5358	383	86	≤	≤	NOUN
cana-5358	383	87	휀𝔉ℱ𝑠(𝐶1	휀𝔉ℱ𝑠(𝐶1	VERB
cana-5358	383	88	,	,	PUNCT
cana-5358	383	89	𝑃4	𝑃4	NOUN
cana-5358	383	90	)	)	PUNCT
cana-5358	383	91	similarly	similarly	ADV
cana-5358	383	92	휀𝔉ℱ𝑠(𝐶2	휀𝔉ℱ𝑠(𝐶2	PROPN
cana-5358	383	93	,	,	PUNCT
cana-5358	383	94	𝑃2	𝑃2	PROPN
cana-5358	383	95	)	)	PUNCT
cana-5358	383	96	<	<	X
cana-5358	383	97	휀𝔉ℱ𝑠(𝐶2	휀𝔉ℱ𝑠(𝐶2	PROPN
cana-5358	383	98	,	,	PUNCT
cana-5358	383	99	𝑃5	𝑃5	NOUN
cana-5358	383	100	)	)	PUNCT
cana-5358	383	101	<	<	X
cana-5358	384	1	휀𝔉ℱ𝑠(𝐶2	휀𝔉ℱ𝑠(𝐶2	PROPN
cana-5358	384	2	,	,	PUNCT
cana-5358	384	3	𝑃3	𝑃3	NOUN
cana-5358	384	4	)	)	PUNCT
cana-5358	384	5	<	<	X
cana-5358	384	6	휀𝔉ℱ𝑠(𝐶2	휀𝔉ℱ𝑠(𝐶2	PROPN
cana-5358	384	7	,	,	PUNCT
cana-5358	384	8	𝑃1	𝑃1	NOUN
cana-5358	384	9	)	)	PUNCT
cana-5358	384	10	≤	≤	NUM
cana-5358	384	11	휀𝔉ℱ𝑠(𝐶2	휀𝔉ℱ𝑠(𝐶2	PROPN
cana-5358	384	12	,	,	PUNCT
cana-5358	384	13	𝑃4	𝑃4	PROPN
cana-5358	384	14	)	)	PUNCT
cana-5358	384	15	휀𝔉ℱ𝑠(𝐶3	휀𝔉ℱ𝑠(𝐶3	ADV
cana-5358	384	16	,	,	PUNCT
cana-5358	384	17	𝑃3	𝑃3	NOUN
cana-5358	384	18	)	)	PUNCT
cana-5358	384	19	<	<	X
cana-5358	384	20	휀𝔉ℱ𝑠(𝐶3	휀𝔉ℱ𝑠(𝐶3	NOUN
cana-5358	384	21	,	,	PUNCT
cana-5358	384	22	𝑃5	𝑃5	NOUN
cana-5358	384	23	)	)	PUNCT
cana-5358	384	24	<	<	X
cana-5358	384	25	휀𝔉ℱ𝑠(𝐶3	휀𝔉ℱ𝑠(𝐶3	NOUN
cana-5358	384	26	,	,	PUNCT
cana-5358	384	27	𝑃4	𝑃4	PROPN
cana-5358	384	28	)	)	PUNCT
cana-5358	384	29	<	<	X
cana-5358	384	30	휀𝔉ℱ𝑠(𝐶3	휀𝔉ℱ𝑠(𝐶3	PROPN
cana-5358	384	31	,	,	PUNCT
cana-5358	384	32	𝑃2	𝑃2	PROPN
cana-5358	384	33	)	)	PUNCT
cana-5358	384	34	≤	≤	NOUN
cana-5358	384	35	휀𝔉ℱ𝑠(𝐶3	휀𝔉ℱ𝑠(𝐶3	ADV
cana-5358	384	36	,	,	PUNCT
cana-5358	384	37	𝑃1	𝑃1	NOUN
cana-5358	384	38	)	)	PUNCT
cana-5358	384	39	휀𝔉ℱ𝑠(𝐶4	휀𝔉ℱ𝑠(𝐶4	NOUN
cana-5358	384	40	,	,	PUNCT
cana-5358	384	41	𝑃5	𝑃5	NOUN
cana-5358	384	42	)	)	PUNCT
cana-5358	384	43	<	<	X
cana-5358	384	44	휀𝔉ℱ𝑠(𝐶4	휀𝔉ℱ𝑠(𝐶4	PROPN
cana-5358	384	45	,	,	PUNCT
cana-5358	384	46	𝑃1	𝑃1	NOUN
cana-5358	384	47	)	)	PUNCT
cana-5358	384	48	<	<	X
cana-5358	384	49	휀𝔉ℱ𝑠(𝐶4	휀𝔉ℱ𝑠(𝐶4	PROPN
cana-5358	384	50	,	,	PUNCT
cana-5358	384	51	𝑃4	𝑃4	PROPN
cana-5358	384	52	)	)	PUNCT
cana-5358	384	53	<	<	X
cana-5358	384	54	휀𝔉ℱ𝑠(𝐶4	휀𝔉ℱ𝑠(𝐶4	PROPN
cana-5358	384	55	,	,	PUNCT
cana-5358	384	56	𝑃3	𝑃3	NOUN
cana-5358	384	57	)	)	PUNCT
cana-5358	384	58	≤	≤	NUM
cana-5358	384	59	휀𝔉ℱ𝑠(𝐶4	휀𝔉ℱ𝑠(𝐶4	NOUN
cana-5358	384	60	,	,	PUNCT
cana-5358	384	61	𝑃2	𝑃2	PROPN
cana-5358	384	62	)	)	PUNCT
cana-5358	384	63	communications	communication	NOUN
cana-5358	384	64	on	on	ADP
cana-5358	384	65	applied	apply	VERB
cana-5358	384	66	nonlinear	nonlinear	ADJ
cana-5358	384	67	analysis	analysis	NOUN
cana-5358	384	68	issn	issn	NOUN
cana-5358	384	69	:	:	PUNCT
cana-5358	384	70	1074	1074	NUM
cana-5358	384	71	-	-	PUNCT
cana-5358	384	72	133x	133x	NUM
cana-5358	384	73	vol	vol	VERB
cana-5358	384	74	32	32	NUM
cana-5358	384	75	no	no	NOUN
cana-5358	384	76	.	.	PUNCT
cana-5358	385	1	10s	10	NOUN
cana-5358	385	2	(	(	PUNCT
cana-5358	385	3	2025	2025	NUM
cana-5358	385	4	)	)	PUNCT
cana-5358	385	5	1907	1907	NUM
cana-5358	385	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	386	1	it	it	PRON
cana-5358	386	2	is	be	AUX
cana-5358	386	3	clear	clear	ADJ
cana-5358	386	4	that	that	SCONJ
cana-5358	386	5	based	base	VERB
cana-5358	386	6	on	on	ADP
cana-5358	386	7	the	the	DET
cana-5358	386	8	criteria	criterion	NOUN
cana-5358	386	9	1	1	NUM
cana-5358	386	10	and	and	CCONJ
cana-5358	386	11	2	2	NUM
cana-5358	386	12	,	,	PUNCT
cana-5358	386	13	person	person	NOUN
cana-5358	386	14	2	2	NUM
cana-5358	386	15	be	be	AUX
cana-5358	386	16	the	the	DET
cana-5358	386	17	selection	selection	NOUN
cana-5358	386	18	for	for	ADP
cana-5358	386	19	the	the	DET
cana-5358	386	20	permanent	permanent	ADJ
cana-5358	386	21	post	post	NOUN
cana-5358	386	22	,	,	PUNCT
cana-5358	386	23	criteria	criterion	NOUN
cana-5358	386	24	3	3	NUM
cana-5358	386	25	,	,	PUNCT
cana-5358	386	26	person	person	NOUN
cana-5358	386	27	3	3	NUM
cana-5358	386	28	be	be	AUX
cana-5358	386	29	the	the	DET
cana-5358	386	30	selection	selection	NOUN
cana-5358	386	31	for	for	ADP
cana-5358	386	32	the	the	DET
cana-5358	386	33	permanent	permanent	ADJ
cana-5358	386	34	post	post	NOUN
cana-5358	386	35	,	,	PUNCT
cana-5358	386	36	criteria	criterion	NOUN
cana-5358	386	37	4	4	NUM
cana-5358	386	38	,	,	PUNCT
cana-5358	386	39	person	person	NOUN
cana-5358	386	40	5	5	NUM
cana-5358	386	41	be	be	AUX
cana-5358	386	42	the	the	DET
cana-5358	386	43	selection	selection	NOUN
cana-5358	386	44	for	for	ADP
cana-5358	386	45	the	the	DET
cana-5358	386	46	permanent	permanent	ADJ
cana-5358	386	47	post	post	NOUN
cana-5358	386	48	.	.	PROPN
cana-5358	387	1	6	6	NUM
cana-5358	387	2	conclusion	conclusion	NOUN
cana-5358	387	3	fuzzy	fuzzy	ADJ
cana-5358	387	4	topological	topological	ADJ
cana-5358	387	5	spaces	space	NOUN
cana-5358	387	6	are	be	AUX
cana-5358	387	7	the	the	DET
cana-5358	387	8	classical	classical	ADJ
cana-5358	387	9	topological	topological	ADJ
cana-5358	387	10	spaces	space	NOUN
cana-5358	387	11	which	which	PRON
cana-5358	387	12	characterises	characterise	VERB
cana-5358	387	13	the	the	DET
cana-5358	387	14	membership	membership	NOUN
cana-5358	387	15	values	value	NOUN
cana-5358	387	16	alone	alone	ADV
cana-5358	387	17	.	.	PUNCT
cana-5358	388	1	intuitionistic	intuitionistic	ADJ
cana-5358	388	2	fuzzy	fuzzy	ADJ
cana-5358	388	3	topological	topological	ADJ
cana-5358	388	4	spaces	space	NOUN
cana-5358	388	5	portates	portate	VERB
cana-5358	388	6	the	the	DET
cana-5358	388	7	membership	membership	NOUN
cana-5358	388	8	as	as	ADV
cana-5358	388	9	well	well	ADV
cana-5358	388	10	as	as	ADP
cana-5358	388	11	the	the	DET
cana-5358	388	12	non	non	ADJ
cana-5358	388	13	-	-	ADJ
cana-5358	388	14	membership	membership	ADJ
cana-5358	388	15	values	value	NOUN
cana-5358	388	16	.	.	PUNCT
cana-5358	389	1	pythagorean	pythagorean	PROPN
cana-5358	389	2	fuzzy	fuzzy	ADJ
cana-5358	389	3	topological	topological	PROPN
cana-5358	389	4	spaces	space	NOUN
cana-5358	389	5	extent	extent	VERB
cana-5358	389	6	its	its	PRON
cana-5358	389	7	arm	arm	NOUN
cana-5358	389	8	to	to	PART
cana-5358	389	9	cover	cover	VERB
cana-5358	389	10	the	the	DET
cana-5358	389	11	missed	miss	VERB
cana-5358	389	12	ones	one	NOUN
cana-5358	389	13	of	of	ADP
cana-5358	389	14	the	the	DET
cana-5358	389	15	intuitionistic	intuitionistic	ADJ
cana-5358	389	16	fuzzy	fuzzy	ADJ
cana-5358	389	17	topological	topological	ADJ
cana-5358	389	18	spaces	space	NOUN
cana-5358	389	19	.	.	PUNCT
cana-5358	390	1	fermatean	fermatean	ADJ
cana-5358	390	2	fuzzy	fuzzy	ADJ
cana-5358	390	3	topological	topological	ADJ
cana-5358	390	4	spaces	space	NOUN
cana-5358	390	5	shorten	shorten	VERB
cana-5358	390	6	the	the	DET
cana-5358	390	7	pythagorean	pythagorean	ADJ
cana-5358	390	8	fuzzy	fuzzy	ADJ
cana-5358	390	9	sets	set	NOUN
cana-5358	390	10	of	of	ADP
cana-5358	390	11	any	any	DET
cana-5358	390	12	cardinality	cardinality	NOUN
cana-5358	390	13	in	in	ADP
cana-5358	390	14	to	to	ADP
cana-5358	390	15	a	a	DET
cana-5358	390	16	tiny	tiny	ADJ
cana-5358	390	17	set	set	NOUN
cana-5358	390	18	which	which	PRON
cana-5358	390	19	represents	represent	VERB
cana-5358	390	20	the	the	DET
cana-5358	390	21	same	same	ADJ
cana-5358	390	22	in	in	ADP
cana-5358	390	23	nano	nano	NOUN
cana-5358	390	24	approximation	approximation	NOUN
cana-5358	390	25	with	with	ADP
cana-5358	390	26	boundary	boundary	ADJ
cana-5358	390	27	space	space	NOUN
cana-5358	390	28	.	.	PUNCT
cana-5358	391	1	our	our	PRON
cana-5358	391	2	contribution	contribution	NOUN
cana-5358	391	3	to	to	ADP
cana-5358	391	4	this	this	DET
cana-5358	391	5	area	area	NOUN
cana-5358	391	6	is	be	AUX
cana-5358	391	7	the	the	DET
cana-5358	391	8	concepts	concept	NOUN
cana-5358	391	9	of	of	ADP
cana-5358	391	10	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐻𝑜𝑚	ADJ
cana-5358	391	11	,	,	PUNCT
cana-5358	391	12	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	𝔉ℱ𝛿𝛽𝐶𝐻𝑜𝑚	ADJ
cana-5358	391	13	and	and	CCONJ
cana-5358	391	14	𝔉ℱ𝛿𝛽𝑇1	𝔉ℱ𝛿𝛽𝑇1	PROPN
cana-5358	391	15	2	2	NUM
cana-5358	391	16	-space	-space	NOUN
cana-5358	391	17	and	and	CCONJ
cana-5358	391	18	derived	derive	VERB
cana-5358	391	19	some	some	PRON
cana-5358	391	20	of	of	ADP
cana-5358	391	21	its	its	PRON
cana-5358	391	22	related	related	ADJ
cana-5358	391	23	characteristics	characteristic	NOUN
cana-5358	391	24	.	.	PUNCT
cana-5358	392	1	finally	finally	ADV
cana-5358	392	2	applied	apply	VERB
cana-5358	392	3	a	a	DET
cana-5358	392	4	entropy	entropy	NOUN
cana-5358	392	5	measure	measure	NOUN
cana-5358	392	6	to	to	ADP
cana-5358	392	7	the	the	DET
cana-5358	392	8	multiple	multiple	ADJ
cana-5358	392	9	criteria	criterion	NOUN
cana-5358	392	10	decision	decision	NOUN
cana-5358	392	11	making	make	VERB
cana-5358	392	12	with	with	ADP
cana-5358	392	13	the	the	DET
cana-5358	392	14	help	help	NOUN
cana-5358	392	15	of	of	ADP
cana-5358	392	16	fermatean	fermatean	ADJ
cana-5358	392	17	fuzzy	fuzzy	ADJ
cana-5358	392	18	sets	set	NOUN
cana-5358	392	19	.	.	PUNCT
cana-5358	393	1	in	in	ADP
cana-5358	393	2	future	future	NOUN
cana-5358	393	3	we	we	PRON
cana-5358	393	4	will	will	AUX
cana-5358	393	5	employee	employee	VERB
cana-5358	393	6	some	some	DET
cana-5358	393	7	entropy	entropy	NOUN
cana-5358	393	8	or	or	CCONJ
cana-5358	393	9	any	any	DET
cana-5358	393	10	other	other	ADJ
cana-5358	393	11	measures	measure	NOUN
cana-5358	393	12	for	for	ADP
cana-5358	393	13	comparing	compare	VERB
cana-5358	393	14	in	in	ADP
cana-5358	393	15	decision	decision	NOUN
cana-5358	393	16	making	make	VERB
cana-5358	393	17	to	to	ADP
cana-5358	393	18	the	the	DET
cana-5358	393	19	field	field	NOUN
cana-5358	393	20	of	of	ADP
cana-5358	393	21	medical	medical	ADJ
cana-5358	393	22	diagnosis	diagnosis	NOUN
cana-5358	393	23	and	and	CCONJ
cana-5358	393	24	teaching	teaching	NOUN
cana-5358	393	25	learning	learning	NOUN
cana-5358	393	26	process	process	NOUN
cana-5358	393	27	.	.	PUNCT
cana-5358	394	1	we	we	PRON
cana-5358	394	2	also	also	ADV
cana-5358	394	3	takeup	takeup	VERB
cana-5358	394	4	this	this	DET
cana-5358	394	5	idea	idea	NOUN
cana-5358	394	6	into	into	ADP
cana-5358	394	7	the	the	DET
cana-5358	394	8	diverse	diverse	ADJ
cana-5358	394	9	fuzzy	fuzzy	ADJ
cana-5358	394	10	environment	environment	NOUN
cana-5358	394	11	for	for	ADP
cana-5358	394	12	real	real	ADJ
cana-5358	394	13	world	world	NOUN
cana-5358	394	14	application	application	NOUN
cana-5358	394	15	purpose	purpose	NOUN
cana-5358	394	16	.	.	PUNCT
cana-5358	395	1	references	reference	NOUN
cana-5358	395	2	[	[	X
cana-5358	395	3	1	1	NUM
cana-5358	395	4	]	]	PUNCT
cana-5358	395	5	k.	k.	PROPN
cana-5358	395	6	t.	t.	PROPN
cana-5358	395	7	atanassov	atanassov	PROPN
cana-5358	395	8	(	(	PUNCT
cana-5358	395	9	1983	1983	NUM
cana-5358	395	10	)	)	PUNCT
cana-5358	395	11	,	,	PUNCT
cana-5358	395	12	intuitionistic	intuitionistic	ADJ
cana-5358	395	13	fuzzy	fuzzy	ADJ
cana-5358	395	14	sets	set	NOUN
cana-5358	395	15	,	,	PUNCT
cana-5358	395	16	vii	vii	PROPN
cana-5358	395	17	itkrâ€	itkrâ€	PROPN
cana-5358	395	18	™	™	PROPN
cana-5358	395	19	s	s	PART
cana-5358	395	20	session	session	NOUN
cana-5358	395	21	,	,	PUNCT
cana-5358	395	22	sofia	sofia	PROPN
cana-5358	395	23	.	.	PUNCT
cana-5358	396	1	[	[	X
cana-5358	396	2	2	2	X
cana-5358	396	3	]	]	PUNCT
cana-5358	396	4	k.	k.	PROPN
cana-5358	396	5	t.	t.	PROPN
cana-5358	396	6	atanassov	atanassov	PROPN
cana-5358	396	7	(	(	PUNCT
cana-5358	396	8	1986	1986	NUM
cana-5358	396	9	)	)	PUNCT
cana-5358	396	10	,	,	PUNCT
cana-5358	396	11	intuitionistic	intuitionistic	ADJ
cana-5358	396	12	fuzzy	fuzzy	ADJ
cana-5358	396	13	sets	set	NOUN
cana-5358	396	14	,	,	PUNCT
cana-5358	396	15	fuzzy	fuzzy	ADJ
cana-5358	396	16	sets	set	NOUN
cana-5358	396	17	syst	syst	NOUN
cana-5358	396	18	.	.	PUNCT
cana-5358	397	1	20	20	NUM
cana-5358	397	2	,	,	PUNCT
cana-5358	397	3	87	87	NUM
cana-5358	397	4	-	-	SYM
cana-5358	397	5	96	96	NUM
cana-5358	397	6	.	.	PUNCT
cana-5358	398	1	[	[	X
cana-5358	398	2	3	3	X
cana-5358	398	3	]	]	PUNCT
cana-5358	398	4	k.	k.	PROPN
cana-5358	398	5	t.	t.	PROPN
cana-5358	398	6	atanassov	atanassov	PROPN
cana-5358	398	7	(	(	PUNCT
cana-5358	398	8	1999	1999	NUM
cana-5358	398	9	)	)	PUNCT
cana-5358	398	10	,	,	PUNCT
cana-5358	398	11	intuitionistic	intuitionistic	ADJ
cana-5358	398	12	fuzzy	fuzzy	ADJ
cana-5358	398	13	sets	set	NOUN
cana-5358	398	14	:	:	PUNCT
cana-5358	398	15	theory	theory	NOUN
cana-5358	398	16	and	and	CCONJ
cana-5358	398	17	applications	application	NOUN
cana-5358	398	18	,	,	PUNCT
cana-5358	398	19	physica	physica	NOUN
cana-5358	398	20	,	,	PUNCT
cana-5358	398	21	heidelberg	heidelberg	NOUN
cana-5358	398	22	.	.	PUNCT
cana-5358	399	1	[	[	X
cana-5358	399	2	4	4	X
cana-5358	399	3	]	]	PUNCT
cana-5358	399	4	k.	k.	PROPN
cana-5358	399	5	t.	t.	PROPN
cana-5358	399	6	atanassov	atanassov	PROPN
cana-5358	399	7	(	(	PUNCT
cana-5358	399	8	2012	2012	NUM
cana-5358	399	9	)	)	PUNCT
cana-5358	399	10	,	,	PUNCT
cana-5358	399	11	on	on	ADP
cana-5358	399	12	intuitionistic	intuitionistic	ADJ
cana-5358	399	13	fuzzy	fuzzy	ADJ
cana-5358	399	14	sets	set	NOUN
cana-5358	399	15	theory	theory	NOUN
cana-5358	399	16	,	,	PUNCT
cana-5358	399	17	springer	springer	NOUN
cana-5358	399	18	,	,	PUNCT
cana-5358	399	19	berlin	berlin	PROPN
cana-5358	399	20	.	.	PUNCT
cana-5358	400	1	[	[	X
cana-5358	400	2	5	5	X
cana-5358	400	3	]	]	PUNCT
cana-5358	400	4	k.	k.	PROPN
cana-5358	400	5	atanassov	atanassov	PROPN
cana-5358	400	6	(	(	PUNCT
cana-5358	400	7	2016	2016	NUM
cana-5358	400	8	)	)	PUNCT
cana-5358	400	9	,	,	PUNCT
cana-5358	400	10	review	review	NOUN
cana-5358	400	11	and	and	CCONJ
cana-5358	400	12	new	new	ADJ
cana-5358	400	13	results	result	NOUN
cana-5358	400	14	on	on	ADP
cana-5358	400	15	intuitionistic	intuitionistic	ADJ
cana-5358	400	16	fuzzy	fuzzy	ADJ
cana-5358	400	17	sets	set	NOUN
cana-5358	400	18	,	,	PUNCT
cana-5358	400	19	international	international	ADJ
cana-5358	400	20	journal	journal	NOUN
cana-5358	400	21	bioautomation	bioautomation	NOUN
cana-5358	400	22	.	.	PUNCT
cana-5358	401	1	20	20	NUM
cana-5358	401	2	,	,	PUNCT
cana-5358	401	3	s17	s17	NOUN
cana-5358	401	4	-	-	PUNCT
cana-5358	401	5	s26	s26	NOUN
cana-5358	401	6	.	.	PUNCT
cana-5358	402	1	on	on	ADP
cana-5358	402	2	fuzzy	fuzzy	ADJ
cana-5358	402	3	systems	system	NOUN
cana-5358	402	4	(	(	PUNCT
cana-5358	402	5	fuzz	fuzz	NOUN
cana-5358	402	6	-	-	PUNCT
cana-5358	402	7	ieee	ieee	NOUN
cana-5358	402	8	)	)	PUNCT
cana-5358	402	9	,	,	PUNCT
cana-5358	402	10	298	298	NUM
cana-5358	402	11	-	-	SYM
cana-5358	402	12	305	305	NUM
cana-5358	402	13	.	.	PUNCT
cana-5358	403	1	[	[	X
cana-5358	403	2	6	6	NUM
cana-5358	403	3	]	]	PUNCT
cana-5358	403	4	c.	c.	PROPN
cana-5358	403	5	l	l	PROPN
cana-5358	403	6	chang	chang	PROPN
cana-5358	403	7	(	(	PUNCT
cana-5358	403	8	1968	1968	NUM
cana-5358	403	9	)	)	PUNCT
cana-5358	403	10	,	,	PUNCT
cana-5358	403	11	fuzzy	fuzzy	ADJ
cana-5358	403	12	topological	topological	ADJ
cana-5358	403	13	spaces	space	NOUN
cana-5358	403	14	,	,	PUNCT
cana-5358	403	15	j.	j.	PROPN
cana-5358	403	16	math	math	PROPN
cana-5358	403	17	.	.	PUNCT
cana-5358	404	1	anal	anal	PROPN
cana-5358	404	2	.	.	PUNCT
cana-5358	405	1	appl	appl	PROPN
cana-5358	405	2	.	.	PROPN
cana-5358	405	3	,	,	PUNCT
cana-5358	405	4	24	24	NUM
cana-5358	405	5	,	,	PUNCT
cana-5358	405	6	182	182	NUM
cana-5358	405	7	-	-	SYM
cana-5358	405	8	190	190	NUM
cana-5358	405	9	.	.	PUNCT
cana-5358	406	1	[	[	X
cana-5358	406	2	7	7	X
cana-5358	406	3	]	]	X
cana-5358	406	4	d.	d.	PROPN
cana-5358	406	5	coker	coker	NOUN
cana-5358	406	6	(	(	PUNCT
cana-5358	406	7	1997	1997	NUM
cana-5358	406	8	)	)	PUNCT
cana-5358	406	9	,	,	PUNCT
cana-5358	406	10	an	an	DET
cana-5358	406	11	introduction	introduction	NOUN
cana-5358	406	12	to	to	ADP
cana-5358	406	13	intuitionistic	intuitionistic	ADJ
cana-5358	406	14	fuzzy	fuzzy	ADJ
cana-5358	406	15	topological	topological	ADJ
cana-5358	406	16	spaces	space	NOUN
cana-5358	406	17	,	,	PUNCT
cana-5358	406	18	fuzzy	fuzzy	ADJ
cana-5358	406	19	sets	set	NOUN
cana-5358	406	20	and	and	CCONJ
cana-5358	406	21	systems	system	NOUN
cana-5358	406	22	,	,	PUNCT
cana-5358	406	23	88	88	NUM
cana-5358	406	24	,	,	PUNCT
cana-5358	406	25	81	81	NUM
cana-5358	406	26	-	-	SYM
cana-5358	406	27	89	89	NUM
cana-5358	406	28	.	.	PUNCT
cana-5358	407	1	[	[	X
cana-5358	407	2	8	8	X
cana-5358	407	3	]	]	X
cana-5358	407	4	hariwan	hariwan	X
cana-5358	407	5	z.	z.	PROPN
cana-5358	407	6	ibrahim	ibrahim	PROPN
cana-5358	407	7	(	(	PUNCT
cana-5358	407	8	2022	2022	NUM
cana-5358	407	9	)	)	PUNCT
cana-5358	407	10	,	,	PUNCT
cana-5358	407	11	fermatean	fermatean	NOUN
cana-5358	407	12	fuzzy	fuzzy	ADJ
cana-5358	407	13	topological	topological	ADJ
cana-5358	407	14	spaces	space	NOUN
cana-5358	407	15	,	,	PUNCT
cana-5358	407	16	j.	j.	PROPN
cana-5358	407	17	appl	appl	PROPN
cana-5358	407	18	.	.	PROPN
cana-5358	407	19	math	math	PROPN
cana-5358	407	20	.	.	PUNCT
cana-5358	408	1	and	and	CCONJ
cana-5358	409	1	informatics	informatic	NOUN
cana-5358	409	2	.	.	PUNCT
cana-5358	410	1	40	40	NUM
cana-5358	410	2	,	,	PUNCT
cana-5358	410	3	85	85	NUM
cana-5358	410	4	-	-	SYM
cana-5358	410	5	98	98	NUM
cana-5358	410	6	.	.	PUNCT
cana-5358	411	1	[	[	X
cana-5358	411	2	9	9	NUM
cana-5358	411	3	]	]	X
cana-5358	411	4	murat	murat	NOUN
cana-5358	411	5	olgun	olgun	PROPN
cana-5358	411	6	,	,	PUNCT
cana-5358	411	7	mehmet	mehmet	PROPN
cana-5358	411	8	unver	unver	PROPN
cana-5358	411	9	and	and	CCONJ
cana-5358	411	10	seyhmus	seyhmus	VERB
cana-5358	411	11	yardimci	yardimci	PROPN
cana-5358	411	12	(	(	PUNCT
cana-5358	411	13	2019	2019	NUM
cana-5358	411	14	)	)	PUNCT
cana-5358	411	15	,	,	PUNCT
cana-5358	411	16	pythagorean	pythagorean	PROPN
cana-5358	411	17	fuzzy	fuzzy	ADJ
cana-5358	411	18	topological	topological	ADJ
cana-5358	411	19	spaces	space	NOUN
cana-5358	411	20	,	,	PUNCT
cana-5358	411	21	complex	complex	ADJ
cana-5358	411	22	&	&	CCONJ
cana-5358	411	23	intelligent	intelligent	ADJ
cana-5358	411	24	systems	system	NOUN
cana-5358	411	25	.	.	PUNCT
cana-5358	412	1	https://doi.org/10.1007/s40747-019-0095-2	https://doi.org/10.1007/s40747-019-0095-2	NUM
cana-5358	412	2	.	.	PUNCT
cana-5358	413	1	[	[	X
cana-5358	413	2	10	10	NUM
cana-5358	413	3	]	]	PUNCT
cana-5358	413	4	t.senapati	t.senapati	NOUN
cana-5358	413	5	and	and	CCONJ
cana-5358	413	6	r.r.yager	r.r.yager	NOUN
cana-5358	413	7	(	(	PUNCT
cana-5358	413	8	2020	2020	NUM
cana-5358	413	9	)	)	PUNCT
cana-5358	413	10	,	,	PUNCT
cana-5358	413	11	fermatean	fermatean	ADJ
cana-5358	413	12	fuzzy	fuzzy	ADJ
cana-5358	413	13	sets	set	NOUN
cana-5358	413	14	,	,	PUNCT
cana-5358	413	15	journal	journal	NOUN
cana-5358	413	16	of	of	ADP
cana-5358	413	17	ambient	ambient	ADJ
cana-5358	413	18	intelligence	intelligence	NOUN
cana-5358	413	19	and	and	CCONJ
cana-5358	413	20	humanized	humanize	VERB
cana-5358	413	21	computing	compute	VERB
cana-5358	413	22	11	11	NUM
cana-5358	413	23	,	,	PUNCT
cana-5358	413	24	663	663	NUM
cana-5358	413	25	-	-	SYM
cana-5358	413	26	674	674	NUM
cana-5358	413	27	.	.	PUNCT
cana-5358	414	1	[	[	X
cana-5358	414	2	11	11	NUM
cana-5358	414	3	]	]	PUNCT
cana-5358	414	4	a.	a.	NOUN
cana-5358	414	5	vadivel	vadivel	NOUN
cana-5358	414	6	,	,	PUNCT
cana-5358	414	7	v.	v.	ADP
cana-5358	414	8	sagunthaladevi	sagunthaladevi	NOUN
cana-5358	414	9	and	and	CCONJ
cana-5358	414	10	s.	s.	PROPN
cana-5358	414	11	priya	priya	PROPN
cana-5358	414	12	(	(	PUNCT
cana-5358	414	13	2025	2025	NUM
cana-5358	414	14	)	)	PUNCT
cana-5358	414	15	,	,	PUNCT
cana-5358	414	16	more	more	ADJ
cana-5358	414	17	on	on	ADP
cana-5358	414	18	open	open	ADJ
cana-5358	414	19	sets	set	NOUN
cana-5358	414	20	in	in	ADP
cana-5358	414	21	fermatean	fermatean	ADJ
cana-5358	414	22	fuzzy	fuzzy	ADJ
cana-5358	414	23	topological	topological	ADJ
cana-5358	414	24	spaces	space	NOUN
cana-5358	414	25	and	and	CCONJ
cana-5358	414	26	its	its	PRON
cana-5358	414	27	application	application	NOUN
cana-5358	414	28	,	,	PUNCT
cana-5358	414	29	accepted	accept	VERB
cana-5358	414	30	in	in	ADP
cana-5358	414	31	j.	j.	PROPN
cana-5358	414	32	appl	appl	PROPN
cana-5358	414	33	.	.	PROPN
cana-5358	414	34	math	math	PROPN
cana-5358	414	35	.	.	PUNCT
cana-5358	414	36	&	&	CCONJ
cana-5358	414	37	informatics	informatics	PROPN
cana-5358	414	38	.	.	PUNCT
cana-5358	415	1	[	[	X
cana-5358	415	2	12	12	NUM
cana-5358	415	3	]	]	PUNCT
cana-5358	415	4	r.	r.	PROPN
cana-5358	415	5	r.	r.	PROPN
cana-5358	415	6	yager	yager	PROPN
cana-5358	415	7	(	(	PUNCT
cana-5358	415	8	2013	2013	NUM
cana-5358	415	9	)	)	PUNCT
cana-5358	415	10	,	,	PUNCT
cana-5358	415	11	pythagorean	pythagorean	PROPN
cana-5358	415	12	membership	membership	NOUN
cana-5358	415	13	grades	grade	NOUN
cana-5358	415	14	in	in	ADP
cana-5358	415	15	multicriteria	multicriteria	PROPN
cana-5358	415	16	decision	decision	NOUN
cana-5358	415	17	making	making	NOUN
cana-5358	415	18	,	,	PUNCT
cana-5358	415	19	in	in	ADP
cana-5358	415	20	:	:	PUNCT
cana-5358	415	21	technical	technical	ADJ
cana-5358	415	22	report	report	NOUN
cana-5358	415	23	𝑀𝐼𝐼-3301	𝑀𝐼𝐼-3301	PROPN
cana-5358	415	24	.	.	PUNCT
cana-5358	416	1	machine	machine	NOUN
cana-5358	416	2	intelligence	intelligence	PROPN
cana-5358	416	3	institute	institute	PROPN
cana-5358	416	4	,	,	PUNCT
cana-5358	416	5	iona	iona	PROPN
cana-5358	416	6	college	college	PROPN
cana-5358	416	7	,	,	PUNCT
cana-5358	416	8	new	new	ADJ
cana-5358	416	9	rochelle	rochelle	NOUN
cana-5358	416	10	.	.	PUNCT
cana-5358	417	1	communications	communication	NOUN
cana-5358	417	2	on	on	ADP
cana-5358	417	3	applied	apply	VERB
cana-5358	417	4	nonlinear	nonlinear	ADJ
cana-5358	417	5	analysis	analysis	NOUN
cana-5358	417	6	issn	issn	NOUN
cana-5358	417	7	:	:	PUNCT
cana-5358	417	8	1074	1074	NUM
cana-5358	417	9	-	-	PUNCT
cana-5358	417	10	133x	133x	NUM
cana-5358	417	11	vol	vol	VERB
cana-5358	417	12	32	32	NUM
cana-5358	417	13	no	no	NOUN
cana-5358	417	14	.	.	PUNCT
cana-5358	418	1	10s	10	NOUN
cana-5358	418	2	(	(	PUNCT
cana-5358	418	3	2025	2025	NUM
cana-5358	418	4	)	)	PUNCT
cana-5358	418	5	1908	1908	NUM
cana-5358	418	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5358	419	1	[	[	X
cana-5358	419	2	13	13	NUM
cana-5358	419	3	]	]	PUNCT
cana-5358	419	4	r.	r.	PROPN
cana-5358	419	5	r.	r.	PROPN
cana-5358	419	6	yager	yager	PROPN
cana-5358	419	7	(	(	PUNCT
cana-5358	419	8	2013	2013	NUM
cana-5358	419	9	)	)	PUNCT
cana-5358	419	10	,	,	PUNCT
cana-5358	419	11	pythagorean	pythagorean	PROPN
cana-5358	419	12	fuzzy	fuzzy	ADJ
cana-5358	419	13	subsets	subset	NOUN
cana-5358	419	14	,	,	PUNCT
cana-5358	419	15	in	in	ADP
cana-5358	419	16	:	:	PUNCT
cana-5358	419	17	proceedings	proceeding	NOUN
cana-5358	419	18	of	of	ADP
cana-5358	419	19	the	the	DET
cana-5358	419	20	joint	joint	ADJ
cana-5358	419	21	𝐼𝐹𝑆𝐴	𝐼𝐹𝑆𝐴	PROPN
cana-5358	419	22	world	world	PROPN
cana-5358	419	23	congress	congress	PROPN
cana-5358	419	24	𝑁𝐴𝐹𝐼𝑃𝑆	𝑁𝐴𝐹𝐼𝑃𝑆	PROPN
cana-5358	419	25	annual	annual	ADJ
cana-5358	419	26	meeting	meeting	NOUN
cana-5358	419	27	,	,	PUNCT
cana-5358	419	28	57	57	NUM
cana-5358	419	29	-	-	SYM
cana-5358	419	30	61	61	NUM
cana-5358	419	31	.	.	PUNCT
cana-5358	420	1	[	[	X
cana-5358	420	2	14	14	NUM
cana-5358	420	3	]	]	X
cana-5358	420	4	r.	r.	PROPN
cana-5358	420	5	r.	r.	PROPN
cana-5358	420	6	yager	yager	PROPN
cana-5358	420	7	(	(	PUNCT
cana-5358	420	8	2014	2014	NUM
cana-5358	420	9	)	)	PUNCT
cana-5358	420	10	,	,	PUNCT
cana-5358	420	11	pythagorean	pythagorean	PROPN
cana-5358	420	12	membership	membership	NOUN
cana-5358	420	13	grades	grade	NOUN
cana-5358	420	14	in	in	ADP
cana-5358	420	15	multicriteria	multicriteria	PROPN
cana-5358	420	16	decision	decision	NOUN
cana-5358	420	17	making	making	NOUN
cana-5358	420	18	,	,	PUNCT
cana-5358	420	19	𝐼𝐸𝐸𝐸	𝐼𝐸𝐸𝐸	PROPN
cana-5358	420	20	trans	trans	PROPN
cana-5358	420	21	fuzzy	fuzzy	PROPN
cana-5358	420	22	syst	syst	PROPN
cana-5358	420	23	.	.	PUNCT
cana-5358	421	1	22	22	NUM
cana-5358	421	2	(	(	PUNCT
cana-5358	421	3	4	4	NUM
cana-5358	421	4	)	)	PUNCT
cana-5358	421	5	,	,	PUNCT
cana-5358	421	6	958	958	NUM
cana-5358	421	7	-	-	SYM
cana-5358	421	8	965	965	NUM
cana-5358	421	9	.	.	PUNCT
cana-5358	422	1	[	[	X
cana-5358	422	2	15	15	NUM
cana-5358	422	3	]	]	X
cana-5358	422	4	l.	l.	PROPN
cana-5358	422	5	a.	a.	PROPN
cana-5358	422	6	zadeh	zadeh	PROPN
cana-5358	422	7	(	(	PUNCT
cana-5358	422	8	1965	1965	NUM
cana-5358	422	9	)	)	PUNCT
cana-5358	422	10	,	,	PUNCT
cana-5358	422	11	fuzzy	fuzzy	ADJ
cana-5358	422	12	sets	set	NOUN
cana-5358	422	13	,	,	PUNCT
cana-5358	422	14	inf	inf	PROPN
cana-5358	422	15	.	.	PROPN
cana-5358	422	16	control	control	PROPN
cana-5358	422	17	,	,	PUNCT
cana-5358	422	18	8	8	NUM
cana-5358	422	19	,	,	PUNCT
cana-5358	422	20	338	338	NUM
cana-5358	422	21	-	-	SYM
cana-5358	422	22	353	353	NUM
cana-5358	422	23	.	.	PUNCT
cana-5358	423	1	[	[	X
cana-5358	423	2	16	16	NUM
cana-5358	423	3	]	]	X
cana-5358	423	4	l.	l.	PROPN
cana-5358	423	5	a.	a.	PROPN
cana-5358	423	6	zadeh	zadeh	PROPN
cana-5358	423	7	(	(	PUNCT
cana-5358	423	8	1965	1965	NUM
cana-5358	423	9	)	)	PUNCT
cana-5358	423	10	,	,	PUNCT
cana-5358	423	11	fuzzy	fuzzy	ADJ
cana-5358	423	12	sets	set	NOUN
cana-5358	423	13	and	and	CCONJ
cana-5358	423	14	systems	system	NOUN
cana-5358	423	15	,	,	PUNCT
cana-5358	423	16	in	in	ADP
cana-5358	423	17	:	:	PUNCT
cana-5358	423	18	proc.symp	proc.symp	NOUN
cana-5358	423	19	.	.	PUNCT
cana-5358	423	20	onsystems	onsystem	NOUN
cana-5358	423	21	theory	theory	NOUN
cana-5358	423	22	,	,	PUNCT
cana-5358	423	23	polytechnic	polytechnic	PROPN
cana-5358	423	24	institute	institute	PROPN
cana-5358	423	25	of	of	ADP
cana-5358	423	26	brooklyn	brooklyn	PROPN
cana-5358	423	27	,	,	PUNCT
cana-5358	423	28	new	new	PROPN
cana-5358	423	29	york	york	PROPN
cana-5358	423	30	.	.	PUNCT