id	sid	tid	token	lemma	pos
cana-511	1	1	communications	communication	NOUN
cana-511	1	2	on	on	ADP
cana-511	1	3	applied	apply	VERB
cana-511	1	4	nonlinear	nonlinear	ADJ
cana-511	1	5	analysis	analysis	NOUN
cana-511	1	6	issn	issn	NOUN
cana-511	1	7	:	:	PUNCT
cana-511	1	8	1074	1074	NUM
cana-511	1	9	-	-	PUNCT
cana-511	1	10	133x	133x	NUM
cana-511	1	11	vol	vol	NOUN
cana-511	1	12	31	31	NUM
cana-511	1	13	no	no	NOUN
cana-511	1	14	.	.	NOUN
cana-511	1	15	2	2	NUM
cana-511	1	16	(	(	PUNCT
cana-511	1	17	2024	2024	NUM
cana-511	1	18	)	)	PUNCT
cana-511	2	1	34	34	NUM
cana-511	2	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-511	2	3	coincidence	coincidence	NOUN
cana-511	2	4	point	point	NOUN
cana-511	2	5	results	result	NOUN
cana-511	2	6	for	for	ADP
cana-511	2	7	a	a	DET
cana-511	2	8	new	new	ADJ
cana-511	2	9	class	class	NOUN
cana-511	2	10	of	of	ADP
cana-511	2	11	fuzzy	fuzzy	ADJ
cana-511	2	12	contractive	contractive	ADJ
cana-511	2	13	mappings	mapping	NOUN
cana-511	2	14	prapoorna	prapoorna	PROPN
cana-511	2	15	manthena1	manthena1	PROPN
cana-511	2	16	,	,	PUNCT
cana-511	2	17	k	k	PROPN
cana-511	2	18	santosh	santosh	PROPN
cana-511	2	19	reddy2	reddy2	PROPN
cana-511	2	20	,	,	PUNCT
cana-511	2	21	ch	ch	PROPN
cana-511	2	22	shashi	shashi	PROPN
cana-511	2	23	kumar3	kumar3	PROPN
cana-511	2	24	,	,	PUNCT
cana-511	2	25	v	v	ADP
cana-511	2	26	lakshmi	lakshmi	PROPN
cana-511	2	27	narayana4	narayana4	NOUN
cana-511	2	28	,	,	PUNCT
cana-511	2	29	divvela	divvela	PROPN
cana-511	2	30	surendra5	surendra5	PROPN
cana-511	2	31	,	,	PUNCT
cana-511	2	32	n	n	PRON
cana-511	2	33	veerraju6	veerraju6	NOUN
cana-511	2	34	1department	1department	NUM
cana-511	2	35	of	of	ADP
cana-511	2	36	mathematics	mathematic	NOUN
cana-511	2	37	,	,	PUNCT
cana-511	2	38	tswrdcw	tswrdcw	VERB
cana-511	2	39	lb	lb	DET
cana-511	2	40	nagar	nagar	NOUN
cana-511	2	41	,	,	PUNCT
cana-511	2	42	hyderabad	hyderabad	PROPN
cana-511	2	43	,	,	PUNCT
cana-511	2	44	telangana	telangana	PROPN
cana-511	2	45	,	,	PUNCT
cana-511	2	46	india	india	PROPN
cana-511	2	47	email	email	NOUN
cana-511	2	48	:	:	PUNCT
cana-511	2	49	m.prapoorna@gmail.com	m.prapoorna@gmail.com	PROPN
cana-511	2	50	2	2	NUM
cana-511	2	51	assistant	assistant	NOUN
cana-511	2	52	professor	professor	NOUN
cana-511	2	53	department	department	PROPN
cana-511	2	54	of	of	ADP
cana-511	2	55	mathematics	mathematics	PROPN
cana-511	2	56	,	,	PUNCT
cana-511	2	57	vardhaman	vardhaman	NOUN
cana-511	2	58	college	college	NOUN
cana-511	2	59	of	of	ADP
cana-511	2	60	engineering	engineering	PROPN
cana-511	2	61	,	,	PUNCT
cana-511	2	62	hyderabad	hyderabad	PROPN
cana-511	2	63	,	,	PUNCT
cana-511	2	64	telangana	telangana	PROPN
cana-511	2	65	,	,	PUNCT
cana-511	2	66	india	india	PROPN
cana-511	2	67	email	email	NOUN
cana-511	2	68	:	:	PUNCT
cana-511	3	1	santureddyk@gmail.com	santureddyk@gmail.com	X
cana-511	4	1	3assistant	3assistant	NUM
cana-511	4	2	professor	professor	NOUN
cana-511	4	3	,	,	PUNCT
cana-511	4	4	department	department	NOUN
cana-511	4	5	of	of	ADP
cana-511	4	6	mathematics	mathematics	PROPN
cana-511	4	7	,	,	PUNCT
cana-511	4	8	vnr	vnr	PROPN
cana-511	4	9	vignana	vignana	PROPN
cana-511	4	10	jyothi	jyothi	PROPN
cana-511	4	11	institute	institute	PROPN
cana-511	4	12	of	of	ADP
cana-511	4	13	engineering	engineering	NOUN
cana-511	4	14	and	and	CCONJ
cana-511	4	15	technology	technology	NOUN
cana-511	4	16	,	,	PUNCT
cana-511	4	17	hyderabad	hyderabad	PROPN
cana-511	4	18	-500090	-500090	PROPN
cana-511	4	19	,	,	PUNCT
cana-511	4	20	telangana	telangana	PROPN
cana-511	4	21	,	,	PUNCT
cana-511	4	22	india.mailid	india.mailid	PROPN
cana-511	4	23	:	:	PUNCT
cana-511	4	24	skch17@gmail.com	skch17@gmail.com	PROPN
cana-511	4	25	.	.	PROPN
cana-511	4	26	4assistant	4assistant	NUM
cana-511	4	27	professor	professor	NOUN
cana-511	4	28	,	,	PUNCT
cana-511	4	29	department	department	NOUN
cana-511	4	30	of	of	ADP
cana-511	4	31	mathematics	mathematics	PROPN
cana-511	4	32	,	,	PUNCT
cana-511	4	33	vardhaman	vardhaman	NOUN
cana-511	4	34	college	college	NOUN
cana-511	4	35	of	of	ADP
cana-511	4	36	engineering	engineering	PROPN
cana-511	4	37	,	,	PUNCT
cana-511	4	38	hyderabad	hyderabad	PROPN
cana-511	4	39	.	.	PUNCT
cana-511	5	1	telangana	telangana	PROPN
cana-511	5	2	,	,	PUNCT
cana-511	5	3	india	india	PROPN
cana-511	5	4	.	.	PUNCT
cana-511	6	1	email.id	email.id	NUM
cana-511	6	2	:	:	PUNCT
cana-511	6	3	vlnarayana@vardhaman.org	vlnarayana@vardhaman.org	NUM
cana-511	6	4	,	,	PUNCT
cana-511	6	5	5assistant	5assistant	NUM
cana-511	6	6	professor	professor	NOUN
cana-511	6	7	,	,	PUNCT
cana-511	6	8	department	department	NOUN
cana-511	6	9	of	of	ADP
cana-511	6	10	english	english	PROPN
cana-511	6	11	,	,	PUNCT
cana-511	6	12	koneru	koneru	PROPN
cana-511	6	13	lakshmaiah	lakshmaiah	PROPN
cana-511	6	14	education	education	PROPN
cana-511	6	15	foundation	foundation	PROPN
cana-511	6	16	(	(	PUNCT
cana-511	6	17	kl	kl	PROPN
cana-511	6	18	deemed	deem	VERB
cana-511	6	19	to	to	PART
cana-511	6	20	be	be	AUX
cana-511	6	21	university	university	NOUN
cana-511	6	22	)	)	PUNCT
cana-511	6	23	vaddeswaram	vaddeswaram	PROPN
cana-511	6	24	,	,	PUNCT
cana-511	6	25	guntur	guntur	PROPN
cana-511	6	26	,	,	PUNCT
cana-511	6	27	andhra	andhra	PROPN
cana-511	6	28	pradesh	pradesh	PROPN
cana-511	6	29	,	,	PUNCT
cana-511	6	30	india	india	PROPN
cana-511	6	31	,	,	PUNCT
cana-511	6	32	pin	pin	PROPN
cana-511	6	33	code	code	NOUN
cana-511	6	34	:	:	PUNCT
cana-511	6	35	522502	522502	NUM
cana-511	6	36	email	email	NOUN
cana-511	6	37	:	:	PUNCT
cana-511	6	38	dsurendra@kluniversity.in	dsurendra@kluniversity.in	PROPN
cana-511	7	1	6assistant	6assistant	NUM
cana-511	7	2	professor	professor	NOUN
cana-511	7	3	,	,	PUNCT
cana-511	7	4	department	department	NOUN
cana-511	7	5	of	of	ADP
cana-511	7	6	engineering	engineering	NOUN
cana-511	7	7	mathematics	mathematic	NOUN
cana-511	7	8	,	,	PUNCT
cana-511	7	9	srkr	srkr	NOUN
cana-511	7	10	engineering	engineering	NOUN
cana-511	7	11	college	college	PROPN
cana-511	7	12	,	,	PUNCT
cana-511	7	13	bhimavaram	bhimavaram	PROPN
cana-511	7	14	,	,	PUNCT
cana-511	7	15	west	west	PROPN
cana-511	7	16	godavari	godavari	PROPN
cana-511	7	17	district	district	PROPN
cana-511	7	18	,	,	PUNCT
cana-511	7	19	andhra	andhra	PROPN
cana-511	7	20	pradesh	pradesh	PROPN
cana-511	7	21	,	,	PUNCT
cana-511	7	22	india	india	PROPN
cana-511	7	23	,	,	PUNCT
cana-511	7	24	pincode	pincode	ADJ
cana-511	7	25	:	:	PUNCT
cana-511	7	26	534204	534204	NUM
cana-511	7	27	email	email	NOUN
cana-511	7	28	:	:	PUNCT
cana-511	7	29	veerrajunalla@gmail.com	veerrajunalla@gmail.com	X
cana-511	7	30	article	article	NOUN
cana-511	7	31	history	history	NOUN
cana-511	7	32	:	:	PUNCT
cana-511	7	33	received	receive	VERB
cana-511	7	34	:	:	PUNCT
cana-511	7	35	22	22	NUM
cana-511	7	36	-	-	SYM
cana-511	7	37	01	01	NUM
cana-511	7	38	-	-	PUNCT
cana-511	7	39	2024	2024	NUM
cana-511	7	40	revised	revise	VERB
cana-511	7	41	:	:	PUNCT
cana-511	7	42	28	28	NUM
cana-511	7	43	-	-	SYM
cana-511	7	44	03	03	NUM
cana-511	7	45	-	-	PUNCT
cana-511	7	46	2024	2024	NUM
cana-511	7	47	accepted	accept	VERB
cana-511	7	48	:	:	PUNCT
cana-511	7	49	20	20	NUM
cana-511	7	50	-	-	PUNCT
cana-511	7	51	04	04	NUM
cana-511	7	52	-	-	PUNCT
cana-511	7	53	2024	2024	NUM
cana-511	7	54	abstract	abstract	NOUN
cana-511	7	55	:	:	PUNCT
cana-511	7	56	this	this	DET
cana-511	7	57	work	work	NOUN
cana-511	7	58	is	be	AUX
cana-511	7	59	mainly	mainly	ADV
cana-511	7	60	aimed	aim	VERB
cana-511	7	61	to	to	PART
cana-511	7	62	enhance	enhance	VERB
cana-511	7	63	the	the	DET
cana-511	7	64	concept	concept	NOUN
cana-511	7	65	of	of	ADP
cana-511	7	66	fuzzy	fuzzy	ADJ
cana-511	7	67	z	z	NOUN
cana-511	7	68	-contractive	-contractive	ADJ
cana-511	7	69	mapping	mapping	NOUN
cana-511	8	1	[	[	X
cana-511	8	2	11	11	NUM
cana-511	8	3	]	]	PUNCT
cana-511	8	4	by	by	AUX
cana-511	8	5	establish	establish	VERB
cana-511	8	6	a	a	DET
cana-511	8	7	different	different	ADJ
cana-511	8	8	contraction	contraction	NOUN
cana-511	8	9	called	call	VERB
cana-511	8	10	fuzzy	fuzzy	ADJ
cana-511	8	11	(	(	PUNCT
cana-511	8	12	)	)	PUNCT
cana-511	8	13	,	,	PUNCT
cana-511	8	14	gz	gz	PROPN
cana-511	8	15	.	.	PROPN
cana-511	8	16	contraction	contraction	PROPN
cana-511	8	17	.	.	PUNCT
cana-511	9	1	we	we	PRON
cana-511	9	2	obtain	obtain	VERB
cana-511	9	3	some	some	DET
cana-511	9	4	sufficient	sufficient	ADJ
cana-511	9	5	conditions	condition	NOUN
cana-511	9	6	for	for	ADP
cana-511	9	7	the	the	DET
cana-511	9	8	existence	existence	NOUN
cana-511	9	9	and	and	CCONJ
cana-511	9	10	uniqueness	uniqueness	NOUN
cana-511	9	11	of	of	ADP
cana-511	9	12	point	point	NOUN
cana-511	9	13	of	of	ADP
cana-511	9	14	coincidence	coincidence	NOUN
cana-511	9	15	o	o	NOUN
cana-511	9	16	f	f	X
cana-511	9	17	fuzzy	fuzzy	ADJ
cana-511	9	18	(	(	PUNCT
cana-511	9	19	)	)	PUNCT
cana-511	9	20	,	,	PUNCT
cana-511	9	21	gz	gz	PROPN
cana-511	9	22	.	.	PROPN
cana-511	9	23	contraction	contraction	NOUN
cana-511	9	24	mappings	mapping	NOUN
cana-511	9	25	in	in	ADP
cana-511	9	26	the	the	DET
cana-511	9	27	context	context	NOUN
cana-511	9	28	of	of	ADP
cana-511	9	29	fuzzy	fuzzy	ADJ
cana-511	9	30	metric	metric	ADJ
cana-511	9	31	spaces	space	NOUN
cana-511	9	32	and	and	CCONJ
cana-511	9	33	prove	prove	VERB
cana-511	9	34	some	some	DET
cana-511	9	35	intriguing	intriguing	ADJ
cana-511	9	36	results	result	NOUN
cana-511	9	37	.	.	PUNCT
cana-511	10	1	keywords	keyword	NOUN
cana-511	10	2	:	:	PUNCT
cana-511	10	3	fixed	fixed	ADJ
cana-511	10	4	point	point	NOUN
cana-511	10	5	,	,	PUNCT
cana-511	10	6	m	m	PROPN
cana-511	10	7	-completeness	-completeness	NOUN
cana-511	10	8	,	,	PUNCT
cana-511	10	9	fuzzy	fuzzy	ADJ
cana-511	10	10	metric	metric	ADJ
cana-511	10	11	space	space	NOUN
cana-511	10	12	,	,	PUNCT
cana-511	10	13	fuzzy	fuzzy	ADJ
cana-511	10	14	z	z	NOUN
cana-511	10	15	-	-	PUNCT
cana-511	10	16	contractive	contractive	ADJ
cana-511	10	17	mapping	mapping	NOUN
cana-511	10	18	.	.	PUNCT
cana-511	11	1	2010	2010	NUM
cana-511	11	2	m	m	VERB
cana-511	11	3	a	a	DET
cana-511	11	4	t	t	NOUN
cana-511	11	5	h	h	NOUN
cana-511	12	1	e	e	NOUN
cana-511	12	2	m	m	VERB
cana-511	12	3	a	a	DET
cana-511	12	4	t	t	X
cana-511	13	1	i	i	PRON
cana-511	13	2	c	c	NOUN
cana-511	13	3	s	s	PART
cana-511	13	4	subject	subject	ADJ
cana-511	13	5	classification	classification	NOUN
cana-511	13	6	:	:	PUNCT
cana-511	13	7	54h25	54h25	NUM
cana-511	13	8	;	;	PUNCT
cana-511	13	9	47h10	47h10	NUM
cana-511	13	10	1	1	X
cana-511	13	11	.	.	PUNCT
cana-511	13	12	introduction	introduction	NOUN
cana-511	13	13	in	in	ADP
cana-511	13	14	light	light	NOUN
cana-511	13	15	of	of	ADP
cana-511	13	16	its	its	PRON
cana-511	13	17	numerous	numerous	ADJ
cana-511	13	18	uses	use	NOUN
cana-511	13	19	across	across	ADP
cana-511	13	20	a	a	DET
cana-511	13	21	variety	variety	NOUN
cana-511	13	22	of	of	ADP
cana-511	13	23	fields	field	NOUN
cana-511	13	24	,	,	PUNCT
cana-511	13	25	the	the	DET
cana-511	13	26	analysis	analysis	NOUN
cana-511	13	27	of	of	ADP
cana-511	13	28	fixed	fix	VERB
cana-511	13	29	points	point	NOUN
cana-511	13	30	of	of	ADP
cana-511	13	31	mappings	mapping	NOUN
cana-511	13	32	following	follow	VERB
cana-511	13	33	contraction	contraction	NOUN
cana-511	13	34	conditions	condition	NOUN
cana-511	13	35	has	have	AUX
cana-511	13	36	become	become	VERB
cana-511	13	37	the	the	DET
cana-511	13	38	focus	focus	NOUN
cana-511	13	39	of	of	ADP
cana-511	13	40	numerous	numerous	ADJ
cana-511	13	41	research	research	NOUN
cana-511	13	42	initiatives	initiative	NOUN
cana-511	13	43	.	.	PUNCT
cana-511	14	1	regarding	regard	VERB
cana-511	14	2	this	this	PRON
cana-511	14	3	,	,	PUNCT
cana-511	14	4	the	the	DET
cana-511	14	5	classical	classical	ADJ
cana-511	14	6	findings	finding	NOUN
cana-511	14	7	of	of	ADP
cana-511	14	8	banach	banach	NOUN
cana-511	14	9	[	[	X
cana-511	14	10	1	1	NUM
cana-511	14	11	]	]	PUNCT
cana-511	14	12	and	and	CCONJ
cana-511	14	13	edelstien	edelstien	ADJ
cana-511	14	14	[	[	X
cana-511	14	15	2	2	NUM
cana-511	14	16	]	]	PUNCT
cana-511	14	17	have	have	AUX
cana-511	14	18	served	serve	VERB
cana-511	14	19	as	as	ADP
cana-511	14	20	the	the	DET
cana-511	14	21	inspiration	inspiration	NOUN
cana-511	14	22	for	for	ADP
cana-511	14	23	several	several	ADJ
cana-511	14	24	writers	writer	NOUN
cana-511	14	25	working	work	VERB
cana-511	14	26	in	in	ADP
cana-511	14	27	the	the	DET
cana-511	14	28	field	field	NOUN
cana-511	14	29	of	of	ADP
cana-511	14	30	metric	metric	ADJ
cana-511	14	31	fixed	fix	VERB
cana-511	14	32	-	-	PUNCT
cana-511	14	33	point	point	NOUN
cana-511	14	34	theory	theory	NOUN
cana-511	14	35	.	.	PUNCT
cana-511	15	1	grabiec	grabiec	PROPN
cana-511	16	1	[	[	X
cana-511	16	2	4	4	NUM
cana-511	16	3	]	]	PUNCT
cana-511	16	4	,	,	PUNCT
cana-511	16	5	who	who	PRON
cana-511	16	6	pioneered	pioneer	VERB
cana-511	16	7	the	the	DET
cana-511	16	8	introduction	introduction	NOUN
cana-511	16	9	of	of	ADP
cana-511	16	10	fixed	fix	VERB
cana-511	16	11	-	-	PUNCT
cana-511	16	12	point	point	NOUN
cana-511	16	13	theory	theory	NOUN
cana-511	16	14	in	in	ADP
cana-511	16	15	fuzzy	fuzzy	ADJ
cana-511	16	16	metric	metric	ADJ
cana-511	16	17	spaces	space	NOUN
cana-511	16	18	,	,	PUNCT
cana-511	16	19	extended	extend	VERB
cana-511	16	20	the	the	DET
cana-511	16	21	discoveries	discovery	NOUN
cana-511	16	22	of	of	ADP
cana-511	16	23	banach	banach	NOUN
cana-511	16	24	[	[	X
cana-511	16	25	1	1	X
cana-511	16	26	]	]	PUNCT
cana-511	16	27	and	and	CCONJ
cana-511	16	28	edelstein	edelstein	PROPN
cana-511	17	1	[	[	X
cana-511	17	2	2	2	NUM
cana-511	17	3	]	]	PUNCT
cana-511	17	4	in	in	ADP
cana-511	17	5	the	the	DET
cana-511	17	6	framework	framework	NOUN
cana-511	17	7	of	of	ADP
cana-511	17	8	fuzzy	fuzzy	ADJ
cana-511	17	9	metric	metric	ADJ
cana-511	17	10	spaces	space	NOUN
cana-511	17	11	in	in	ADP
cana-511	17	12	the	the	DET
cana-511	17	13	design	design	NOUN
cana-511	17	14	of	of	ADP
cana-511	17	15	communications	communication	NOUN
cana-511	17	16	on	on	ADP
cana-511	17	17	applied	apply	VERB
cana-511	17	18	nonlinear	nonlinear	ADJ
cana-511	17	19	analysis	analysis	NOUN
cana-511	17	20	issn	issn	NOUN
cana-511	17	21	:	:	PUNCT
cana-511	17	22	1074	1074	NUM
cana-511	17	23	-	-	PUNCT
cana-511	17	24	133x	133x	NUM
cana-511	17	25	vol	vol	NOUN
cana-511	17	26	31	31	NUM
cana-511	17	27	no	no	NOUN
cana-511	17	28	.	.	NOUN
cana-511	17	29	2	2	NUM
cana-511	17	30	(	(	PUNCT
cana-511	17	31	2024	2024	NUM
cana-511	17	32	)	)	PUNCT
cana-511	17	33	35	35	NUM
cana-511	17	34	https://internationalpubls.com	https://internationalpubls.com	X
cana-511	17	35	kramosil	kramosil	NOUN
cana-511	17	36	and	and	CCONJ
cana-511	17	37	michlek	michlek	ADJ
cana-511	18	1	[	[	X
cana-511	18	2	8	8	NUM
cana-511	18	3	]	]	PUNCT
cana-511	18	4	.	.	PUNCT
cana-511	19	1	the	the	DET
cana-511	19	2	fixed	fix	VERB
cana-511	19	3	-	-	PUNCT
cana-511	19	4	point	point	NOUN
cana-511	19	5	conclusion	conclusion	NOUN
cana-511	19	6	proposed	propose	VERB
cana-511	19	7	by	by	ADP
cana-511	19	8	grabiec	grabiec	PROPN
cana-511	19	9	in	in	ADP
cana-511	19	10	his	his	PRON
cana-511	19	11	work	work	NOUN
cana-511	19	12	[	[	X
cana-511	19	13	4	4	NUM
cana-511	19	14	]	]	PUNCT
cana-511	19	15	was	be	AUX
cana-511	19	16	based	base	VERB
cana-511	19	17	on	on	ADP
cana-511	19	18	the	the	DET
cana-511	19	19	notion	notion	NOUN
cana-511	19	20	of	of	ADP
cana-511	19	21	the	the	DET
cana-511	19	22	-completeness	-completeness	NOUN
cana-511	19	23	of	of	ADP
cana-511	19	24	fuzzy	fuzzy	ADJ
cana-511	19	25	metric	metric	ADJ
cana-511	19	26	spaces	space	NOUN
cana-511	19	27	,	,	PUNCT
cana-511	19	28	which	which	PRON
cana-511	19	29	george	george	NOUN
cana-511	19	30	and	and	CCONJ
cana-511	19	31	veeramani	veeramani	NOUN
cana-511	19	32	[	[	X
cana-511	19	33	3	3	NUM
cana-511	19	34	]	]	PUNCT
cana-511	19	35	weakened	weaken	VERB
cana-511	19	36	by	by	ADP
cana-511	19	37	introducing	introduce	VERB
cana-511	19	38	.	.	PUNCT
cana-511	20	1	many	many	ADJ
cana-511	20	2	authors	author	NOUN
cana-511	20	3	explored	explore	VERB
cana-511	20	4	and	and	CCONJ
cana-511	20	5	examined	examine	VERB
cana-511	20	6	various	various	ADJ
cana-511	20	7	contractions	contraction	NOUN
cana-511	20	8	in	in	ADP
cana-511	20	9	fuzzy	fuzzy	ADJ
cana-511	20	10	metric	metric	ADJ
cana-511	20	11	spaces	space	NOUN
cana-511	20	12	,	,	PUNCT
cana-511	20	13	and	and	CCONJ
cana-511	20	14	they	they	PRON
cana-511	20	15	came	come	VERB
cana-511	20	16	up	up	ADP
cana-511	20	17	with	with	ADP
cana-511	20	18	insightful	insightful	ADJ
cana-511	20	19	results	result	NOUN
cana-511	20	20	.	.	PUNCT
cana-511	21	1	(	(	PUNCT
cana-511	21	2	see	see	VERB
cana-511	21	3	[	[	X
cana-511	21	4	5	5	NUM
cana-511	21	5	]	]	PUNCT
cana-511	21	6	,	,	PUNCT
cana-511	21	7	[	[	X
cana-511	21	8	6	6	NUM
cana-511	21	9	]	]	PUNCT
cana-511	21	10	,	,	PUNCT
cana-511	21	11	[	[	X
cana-511	21	12	9	9	NUM
cana-511	21	13	]	]	PUNCT
cana-511	21	14	,	,	PUNCT
cana-511	21	15	[	[	X
cana-511	21	16	12	12	NUM
cana-511	21	17	]	]	PUNCT
cana-511	21	18	,	,	PUNCT
cana-511	21	19	[	[	X
cana-511	21	20	13	13	NUM
cana-511	21	21	]	]	NUM
cana-511	21	22	)	)	PUNCT
cana-511	21	23	.	.	PUNCT
cana-511	22	1	in	in	ADP
cana-511	22	2	order	order	NOUN
cana-511	22	3	to	to	PART
cana-511	22	4	integrate	integrate	VERB
cana-511	22	5	various	various	ADJ
cana-511	22	6	types	type	NOUN
cana-511	22	7	of	of	ADP
cana-511	22	8	fuzzy	fuzzy	ADJ
cana-511	22	9	contractive	contractive	ADJ
cana-511	22	10	mappings	mapping	NOUN
cana-511	22	11	,	,	PUNCT
cana-511	22	12	shukla	shukla	NOUN
cana-511	22	13	et	et	NOUN
cana-511	22	14	al	al	PROPN
cana-511	22	15	.	.	PUNCT
cana-511	23	1	[	[	X
cana-511	23	2	11	11	NUM
cana-511	23	3	]	]	PUNCT
cana-511	23	4	recently	recently	ADV
cana-511	23	5	introduced	introduce	VERB
cana-511	23	6	fuzzy	fuzzy	ADJ
cana-511	23	7	z	z	NOUN
cana-511	23	8	−	−	ADP
cana-511	23	9	contractive	contractive	ADJ
cana-511	23	10	mappings	mapping	NOUN
cana-511	23	11	.	.	PUNCT
cana-511	24	1	they	they	PRON
cana-511	24	2	demonstrated	demonstrate	VERB
cana-511	24	3	that	that	SCONJ
cana-511	24	4	this	this	DET
cana-511	24	5	new	new	ADJ
cana-511	24	6	type	type	NOUN
cana-511	24	7	is	be	AUX
cana-511	24	8	more	more	ADV
cana-511	24	9	thorough	thorough	ADJ
cana-511	24	10	than	than	ADP
cana-511	24	11	the	the	DET
cana-511	24	12	wellknown	wellknown	ADJ
cana-511	24	13	earlier	early	ADJ
cana-511	24	14	ones	one	NOUN
cana-511	24	15	and	and	CCONJ
cana-511	24	16	properly	properly	ADV
cana-511	24	17	incorporates	incorporate	VERB
cana-511	24	18	the	the	DET
cana-511	24	19	classes	class	NOUN
cana-511	24	20	that	that	PRON
cana-511	24	21	were	be	AUX
cana-511	24	22	proposed	propose	VERB
cana-511	24	23	by	by	ADP
cana-511	24	24	numerous	numerous	ADJ
cana-511	24	25	researchers	researcher	NOUN
cana-511	24	26	(	(	PUNCT
cana-511	24	27	[	[	X
cana-511	24	28	5	5	NUM
cana-511	24	29	]	]	PUNCT
cana-511	24	30	,	,	PUNCT
cana-511	25	1	[	[	X
cana-511	25	2	9	9	NUM
cana-511	25	3	]	]	PUNCT
cana-511	25	4	,	,	PUNCT
cana-511	25	5	[	[	X
cana-511	25	6	12	12	NUM
cana-511	25	7	]	]	PUNCT
cana-511	25	8	,	,	PUNCT
cana-511	25	9	and	and	CCONJ
cana-511	25	10	[	[	X
cana-511	25	11	13	13	NUM
cana-511	25	12	]	]	PUNCT
cana-511	25	13	)	)	PUNCT
cana-511	25	14	in	in	ADP
cana-511	25	15	fuzzy	fuzzy	ADJ
cana-511	25	16	metric	metric	ADJ
cana-511	25	17	spaces	space	NOUN
cana-511	25	18	in	in	ADP
cana-511	25	19	the	the	DET
cana-511	25	20	sense	sense	NOUN
cana-511	25	21	of	of	ADP
cana-511	25	22	george	george	NOUN
cana-511	25	23	and	and	CCONJ
cana-511	25	24	veeramani	veeramani	NOUN
cana-511	26	1	[	[	X
cana-511	26	2	3	3	NUM
cana-511	26	3	]	]	PUNCT
cana-511	26	4	.	.	PUNCT
cana-511	27	1	by	by	ADP
cana-511	27	2	expanding	expand	VERB
cana-511	27	3	on	on	ADP
cana-511	27	4	the	the	DET
cana-511	27	5	work	work	NOUN
cana-511	27	6	of	of	ADP
cana-511	27	7	shukla	shukla	NOUN
cana-511	27	8	et	et	PROPN
cana-511	27	9	al	al	PROPN
cana-511	27	10	.	.	PUNCT
cana-511	28	1	[	[	X
cana-511	28	2	11	11	NUM
cana-511	28	3	]	]	PUNCT
cana-511	28	4	,	,	PUNCT
cana-511	28	5	we	we	PRON
cana-511	28	6	introduce	introduce	VERB
cana-511	28	7	the	the	DET
cana-511	28	8	concept	concept	NOUN
cana-511	28	9	of	of	ADP
cana-511	28	10	fuzzy	fuzzy	ADJ
cana-511	28	11	(	(	PUNCT
cana-511	28	12	)	)	PUNCT
cana-511	28	13	,	,	PUNCT
cana-511	28	14	g	g	PROPN
cana-511	28	15	−z	−z	NOUN
cana-511	28	16	.	.	PUNCT
cana-511	29	1	contraction	contraction	NOUN
cana-511	29	2	in	in	ADP
cana-511	29	3	this	this	DET
cana-511	29	4	paper	paper	NOUN
cana-511	29	5	.	.	PUNCT
cana-511	30	1	in	in	ADP
cana-511	30	2	the	the	DET
cana-511	30	3	context	context	NOUN
cana-511	30	4	of	of	ADP
cana-511	30	5	fuzzy	fuzzy	ADJ
cana-511	30	6	metric	metric	ADJ
cana-511	30	7	spaces	space	NOUN
cana-511	30	8	,	,	PUNCT
cana-511	30	9	we	we	PRON
cana-511	30	10	also	also	ADV
cana-511	30	11	develop	develop	VERB
cana-511	30	12	certain	certain	ADJ
cana-511	30	13	discoveries	discovery	NOUN
cana-511	30	14	regarding	regard	VERB
cana-511	30	15	the	the	DET
cana-511	30	16	presence	presence	NOUN
cana-511	30	17	and	and	CCONJ
cana-511	30	18	uniqueness	uniqueness	NOUN
cana-511	30	19	of	of	ADP
cana-511	30	20	coincidence	coincidence	NOUN
cana-511	30	21	points	point	NOUN
cana-511	30	22	for	for	ADP
cana-511	30	23	such	such	ADJ
cana-511	30	24	contractions	contraction	NOUN
cana-511	30	25	.	.	PUNCT
cana-511	31	1	2	2	X
cana-511	31	2	.	.	X
cana-511	31	3	preliminaries	preliminary	NOUN
cana-511	31	4	let	let	VERB
cana-511	31	5	us	we	PRON
cana-511	31	6	recall	recall	VERB
cana-511	31	7	some	some	DET
cana-511	31	8	prefaces	preface	NOUN
cana-511	31	9	here	here	ADV
cana-511	31	10	:	:	PUNCT
cana-511	31	11	definition	definition	NOUN
cana-511	31	12	2.1	2.1	NUM
cana-511	31	13	.	.	PUNCT
cana-511	32	1	[	[	X
cana-511	32	2	10	10	NUM
cana-511	32	3	]	]	X
cana-511	32	4	a	a	DET
cana-511	32	5	continuous	continuous	ADJ
cana-511	32	6	t	t	NOUN
cana-511	32	7	-norm	-norm	NOUN
cana-511	32	8	is	be	AUX
cana-511	32	9	a	a	DET
cana-511	32	10	binary	binary	ADJ
cana-511	32	11	operation	operation	NOUN
cana-511	32	12			PROPN
cana-511	32	13			PUNCT
cana-511	32	14			ADJ
cana-511	32	15			PUNCT
cana-511	32	16			PROPN
cana-511	32	17			PROPN
cana-511	32	18	:	:	PUNCT
cana-511	32	19	0,1	0,1	NUM
cana-511	32	20	0,1	0,1	NUM
cana-511	32	21	0,1	0,1	NUM
cana-511	32	22			NOUN
cana-511	32	23	→	→	PUNCT
cana-511	32	24	which	which	PRON
cana-511	32	25	satisfies	satisfy	VERB
cana-511	32	26	the	the	DET
cana-511	32	27	following	follow	VERB
cana-511	32	28	conditions	condition	NOUN
cana-511	32	29			ADJ
cana-511	32	30			PROPN
cana-511	32	31	,	,	PUNCT
cana-511	32	32	,	,	PUNCT
cana-511	32	33	,	,	PUNCT
cana-511	32	34	0,1l	0,1l	NUM
cana-511	32	35	p	p	NOUN
cana-511	32	36	r	r	NOUN
cana-511	32	37	t	t	PROPN
cana-511	32	38			NOUN
cana-511	32	39	(	(	PUNCT
cana-511	32	40	1	1	NUM
cana-511	32	41	)	)	PUNCT
cana-511	32	42	1l	1l	NUM
cana-511	32	43	l	l	PROPN
cana-511	32	44	=	=	SYM
cana-511	32	45	(	(	PUNCT
cana-511	32	46	2	2	NUM
cana-511	32	47	)	)	PUNCT
cana-511	32	48	l	l	NOUN
cana-511	32	49	p	p	X
cana-511	32	50	p	p	X
cana-511	32	51	l	l	PROPN
cana-511	32	52	=	=	SYM
cana-511	32	53			PROPN
cana-511	32	54	(	(	PUNCT
cana-511	32	55	3	3	X
cana-511	32	56	)	)	PUNCT
cana-511	32	57	l	l	NOUN
cana-511	32	58	p	p	NOUN
cana-511	32	59	r	r	NOUN
cana-511	32	60	t	t	ADJ
cana-511	32	61			NOUN
cana-511	32	62			NUM
cana-511	32	63	whenever	whenever	SCONJ
cana-511	32	64	&	&	CCONJ
cana-511	32	65	l	l	NOUN
cana-511	32	66	r	r	NOUN
cana-511	32	67	p	p	PROPN
cana-511	32	68	t	t	NOUN
cana-511	32	69			NOUN
cana-511	32	70	(	(	PUNCT
cana-511	32	71	4	4	NUM
cana-511	32	72	)	)	PUNCT
cana-511	32	73	(	(	PUNCT
cana-511	32	74	)	)	PUNCT
cana-511	32	75	(	(	PUNCT
cana-511	32	76	)	)	PUNCT
cana-511	32	77	l	l	NOUN
cana-511	32	78	p	p	NOUN
cana-511	32	79	r	r	NOUN
cana-511	32	80	l	l	NOUN
cana-511	32	81	p	p	NOUN
cana-511	32	82	r	r	NOUN
cana-511	32	83			PROPN
cana-511	32	84	=	=	SYM
cana-511	32	85			PROPN
cana-511	32	86			PROPN
cana-511	32	87	definition	definition	NOUN
cana-511	32	88	2.2	2.2	NUM
cana-511	32	89	.	.	PUNCT
cana-511	33	1	[	[	X
cana-511	33	2	3	3	X
cana-511	33	3	]	]	PUNCT
cana-511	33	4	a	a	DET
cana-511	33	5	fuzzy	fuzzy	ADJ
cana-511	33	6	metric	metric	ADJ
cana-511	33	7	space	space	NOUN
cana-511	33	8	is	be	AUX
cana-511	33	9	a	a	DET
cana-511	33	10	3	3	NUM
cana-511	33	11	-	-	PUNCT
cana-511	33	12	tuple	tuple	NOUN
cana-511	33	13	(	(	PUNCT
cana-511	33	14	)	)	PUNCT
cana-511	33	15	,	,	PUNCT
cana-511	33	16	,	,	PUNCT
cana-511	33	17	x	x	X
cana-511	33	18	m	m	NUM
cana-511	33	19	where	where	SCONJ
cana-511	33	20	x	x	PRON
cana-511	33	21	is	be	AUX
cana-511	33	22	an	an	DET
cana-511	33	23	arbitrary	arbitrary	ADJ
cana-511	33	24	set	set	NOUN
cana-511	33	25	,	,	PUNCT
cana-511	33	26	is	be	AUX
cana-511	33	27	a	a	DET
cana-511	33	28	continuous	continuous	ADJ
cana-511	33	29	t	t	NOUN
cana-511	33	30	-norm	-norm	NOUN
cana-511	33	31	and	and	CCONJ
cana-511	33	32	m	m	PROPN
cana-511	33	33	is	be	AUX
cana-511	33	34	a	a	DET
cana-511	33	35	fuzzy	fuzzy	ADJ
cana-511	33	36	set	set	NOUN
cana-511	33	37	in	in	ADP
cana-511	33	38	(	(	PUNCT
cana-511	33	39	)	)	PUNCT
cana-511	33	40	0,x	0,x	PROPN
cana-511	33	41	x	x	NOUN
cana-511	33	42			PROPN
cana-511	33	43			PROPN
cana-511	33	44	,	,	PUNCT
cana-511	33	45	satisfying	satisfy	VERB
cana-511	33	46	the	the	DET
cana-511	33	47	following	follow	VERB
cana-511	33	48	conditions	condition	NOUN
cana-511	33	49	:	:	PUNCT
cana-511	33	50	(	(	PUNCT
cana-511	33	51	1	1	X
cana-511	33	52	)	)	PUNCT
cana-511	33	53	(	(	PUNCT
cana-511	33	54	)	)	PUNCT
cana-511	33	55	,	,	PUNCT
cana-511	33	56	,	,	PUNCT
cana-511	33	57	0a	0a	PROPN
cana-511	33	58	b	b	PROPN
cana-511	33	59	t	t	PROPN
cana-511	33	60	m	m	PROPN
cana-511	33	61	,	,	PUNCT
cana-511	33	62	(	(	PUNCT
cana-511	33	63	2	2	X
cana-511	33	64	)	)	PUNCT
cana-511	33	65	(	(	PUNCT
cana-511	33	66	)	)	PUNCT
cana-511	33	67	,	,	PUNCT
cana-511	33	68	,	,	PUNCT
cana-511	33	69	1	1	NUM
cana-511	33	70	,	,	PUNCT
cana-511	33	71	0a	0a	PROPN
cana-511	33	72	b	b	PROPN
cana-511	33	73	t	t	PROPN
cana-511	33	74	t	t	PROPN
cana-511	33	75	a	a	DET
cana-511	33	76	b=	b=	NOUN
cana-511	33	77			VERB
cana-511	33	78			PRON
cana-511	33	79			PUNCT
cana-511	34	1	=	=	ADJ
cana-511	34	2	m	m	PROPN
cana-511	34	3	,	,	PUNCT
cana-511	34	4	(	(	PUNCT
cana-511	34	5	3	3	X
cana-511	34	6	)	)	PUNCT
cana-511	34	7	(	(	PUNCT
cana-511	34	8	)	)	PUNCT
cana-511	34	9	(	(	PUNCT
cana-511	34	10	)	)	PUNCT
cana-511	34	11	,	,	PUNCT
cana-511	34	12	,	,	PUNCT
cana-511	34	13	,	,	PUNCT
cana-511	34	14	,	,	PUNCT
cana-511	34	15	a	a	DET
cana-511	34	16	b	b	PROPN
cana-511	34	17	t	t	PROPN
cana-511	34	18	b	b	PROPN
cana-511	34	19	a	a	DET
cana-511	34	20	t	t	PROPN
cana-511	34	21	=	=	PROPN
cana-511	34	22	m	m	NOUN
cana-511	34	23	m	m	VERB
cana-511	34	24	,	,	PUNCT
cana-511	34	25	(	(	PUNCT
cana-511	34	26	4	4	NUM
cana-511	34	27	)	)	PUNCT
cana-511	34	28	(	(	PUNCT
cana-511	34	29	)	)	PUNCT
cana-511	34	30	(	(	PUNCT
cana-511	34	31	)	)	PUNCT
cana-511	34	32	(	(	PUNCT
cana-511	34	33	)	)	PUNCT
cana-511	34	34	,	,	PUNCT
cana-511	34	35	,	,	PUNCT
cana-511	34	36	,	,	PUNCT
cana-511	34	37	,	,	PUNCT
cana-511	34	38	,	,	PUNCT
cana-511	34	39	,	,	PUNCT
cana-511	34	40	a	a	DET
cana-511	34	41	c	c	NOUN
cana-511	34	42	t	t	NOUN
cana-511	34	43	r	r	NOUN
cana-511	34	44	a	a	DET
cana-511	34	45	b	b	PROPN
cana-511	34	46	t	t	PROPN
cana-511	34	47	b	b	PROPN
cana-511	34	48	c	c	PROPN
cana-511	34	49	r+	r+	PUNCT
cana-511	34	50			NUM
cana-511	34	51	m	m	NUM
cana-511	34	52	m	m	VERB
cana-511	34	53	m	m	VERB
cana-511	34	54	,	,	PUNCT
cana-511	34	55	(	(	PUNCT
cana-511	34	56	5	5	NUM
cana-511	34	57	)	)	PUNCT
cana-511	34	58	(	(	PUNCT
cana-511	34	59	)	)	PUNCT
cana-511	34	60	(	(	PUNCT
cana-511	34	61	)	)	PUNCT
cana-511	34	62	(	(	PUNCT
cana-511	34	63			PROPN
cana-511	34	64	,	,	PUNCT
cana-511	34	65	,	,	PUNCT
cana-511	34	66	:	:	PUNCT
cana-511	34	67	0	0	NUM
cana-511	34	68	,	,	PUNCT
cana-511	34	69	0,1a	0,1a	NOUN
cana-511	34	70	b	b	X
cana-511	34	71			ADJ
cana-511	34	72			NOUN
cana-511	34	73	→m	→m	PUNCT
cana-511	34	74	is	be	AUX
cana-511	34	75	a	a	DET
cana-511	34	76	continuous	continuous	ADJ
cana-511	34	77	function	function	NOUN
cana-511	34	78	,	,	PUNCT
cana-511	34	79	,	,	PUNCT
cana-511	34	80	,	,	PUNCT
cana-511	34	81	&	&	CCONJ
cana-511	34	82	,	,	PUNCT
cana-511	34	83	0a	0a	PROPN
cana-511	34	84	b	b	X
cana-511	34	85	c	c	NOUN
cana-511	34	86	x	x	SYM
cana-511	34	87	t	t	PROPN
cana-511	34	88	r	r	PROPN
cana-511	34	89			NOUN
cana-511	34	90			VERB
cana-511	34	91	.	.	PUNCT
cana-511	35	1	lemma	lemma	PROPN
cana-511	35	2	2.3	2.3	NUM
cana-511	35	3	.	.	PUNCT
cana-511	36	1	[	[	X
cana-511	36	2	4	4	NUM
cana-511	36	3	]	]	X
cana-511	36	4	(	(	PUNCT
cana-511	36	5	)	)	PUNCT
cana-511	36	6	,	,	PUNCT
cana-511	36	7	,	,	PUNCT
cana-511	36	8	a	a	DET
cana-511	36	9	b	b	NOUN
cana-511	36	10	m	m	NOUN
cana-511	36	11	is	be	AUX
cana-511	36	12	nondecreasing	nondecrease	VERB
cana-511	36	13	,	,	PUNCT
cana-511	36	14	a	a	DET
cana-511	36	15	b	b	PROPN
cana-511	36	16	x	x	PROPN
cana-511	36	17			PROPN
cana-511	36	18	.	.	PUNCT
cana-511	37	1	definition	definition	NOUN
cana-511	37	2	2.4	2.4	NUM
cana-511	37	3	.	.	PUNCT
cana-511	38	1	[	[	X
cana-511	38	2	3	3	X
cana-511	38	3	]	]	X
cana-511	38	4	let	let	VERB
cana-511	38	5	(	(	PUNCT
cana-511	38	6	)	)	PUNCT
cana-511	38	7	,	,	PUNCT
cana-511	38	8	,	,	PUNCT
cana-511	38	9	x	x	X
cana-511	38	10	m	m	PRON
cana-511	38	11	be	be	AUX
cana-511	38	12	a	a	DET
cana-511	38	13	fuzzy	fuzzy	ADJ
cana-511	38	14	metric	metric	ADJ
cana-511	38	15	space	space	NOUN
cana-511	38	16	.	.	PUNCT
cana-511	39	1	a	a	DET
cana-511	39	2	sequence	sequence	NOUN
cana-511	39	3			NOUN
cana-511	39	4	qs	qs	NOUN
cana-511	39	5	in	in	ADP
cana-511	39	6	x	x	PRON
cana-511	39	7	is	be	AUX
cana-511	39	8	a	a	DET
cana-511	39	9	m	m	NOUN
cana-511	39	10	-cauchy	-cauchy	ADJ
cana-511	39	11	sequence	sequence	NOUN
cana-511	39	12	,	,	PUNCT
cana-511	39	13	if	if	SCONJ
cana-511	39	14	(	(	PUNCT
cana-511	39	15	)	)	PUNCT
cana-511	39	16	0,1	0,1	NUM
cana-511	39	17	&	&	CCONJ
cana-511	39	18	0,t	0,t	ADJ
cana-511	39	19			NOUN
cana-511	39	20			VERB
cana-511	39	21	there	there	PRON
cana-511	39	22	exists	exist	VERB
cana-511	39	23	0q	0q	X
cana-511	39	24	n	n	PROPN
cana-511	39	25	such	such	ADJ
cana-511	39	26	that	that	SCONJ
cana-511	39	27	(	(	PUNCT
cana-511	39	28	)	)	PUNCT
cana-511	39	29	0	0	NUM
cana-511	39	30	,	,	PUNCT
cana-511	39	31	,	,	PUNCT
cana-511	39	32	1	1	NUM
cana-511	39	33	,	,	PUNCT
cana-511	39	34	p	p	NOUN
cana-511	39	35	qs	qs	PROPN
cana-511	39	36	s	s	PROPN
cana-511	39	37	t	t	NOUN
cana-511	39	38	p	p	X
cana-511	39	39	q	q	PROPN
cana-511	39	40	−	−	PROPN
cana-511	39	41			NOUN
cana-511	39	42	m	m	NOUN
cana-511	39	43	.	.	PUNCT
cana-511	40	1	a	a	DET
cana-511	40	2	sequence	sequence	NOUN
cana-511	40	3			NOUN
cana-511	40	4	qs	qs	NOUN
cana-511	40	5	in	in	ADP
cana-511	40	6	x	x	SYM
cana-511	40	7	is	be	AUX
cana-511	40	8	convergent	convergent	ADJ
cana-511	40	9	to	to	ADP
cana-511	40	10	x	x	PROPN
cana-511	40	11	x	x	PROPN
cana-511	40	12	if	if	SCONJ
cana-511	40	13	(	(	PUNCT
cana-511	40	14	)	)	PUNCT
cana-511	40	15	l1	l1	PROPN
cana-511	40	16	m	m	PROPN
cana-511	40	17	,	,	PUNCT
cana-511	40	18	,	,	PUNCT
cana-511	40	19	i	i	PRON
cana-511	40	20	q	q	VERB
cana-511	41	1	q	q	X
cana-511	41	2	s	s	X
cana-511	41	3	x	x	X
cana-511	41	4	t	t	NOUN
cana-511	41	5	→	→	PUNCT
cana-511	41	6	=	=	NOUN
cana-511	41	7	m	m	VERB
cana-511	41	8	for	for	ADP
cana-511	41	9	each	each	DET
cana-511	41	10	0	0	NUM
cana-511	41	11	t	t	NOUN
cana-511	41	12			NOUN
cana-511	41	13	.	.	PUNCT
cana-511	42	1	if	if	SCONJ
cana-511	42	2	every	every	DET
cana-511	42	3	−m	−m	ADJ
cana-511	42	4	cauchy	cauchy	ADJ
cana-511	42	5	sequence	sequence	NOUN
cana-511	42	6	in	in	ADP
cana-511	42	7	x	x	PROPN
cana-511	42	8	is	be	AUX
cana-511	42	9	convergent	convergent	ADJ
cana-511	42	10	,	,	PUNCT
cana-511	42	11	then	then	ADV
cana-511	42	12	such	such	ADJ
cana-511	42	13	fuzzy	fuzzy	ADJ
cana-511	42	14	metric	metric	ADJ
cana-511	42	15	space	space	NOUN
cana-511	42	16	x	x	PRON
cana-511	42	17	is	be	AUX
cana-511	42	18	said	say	VERB
cana-511	42	19	to	to	PART
cana-511	42	20	be	be	AUX
cana-511	42	21	−m	−m	ADV
cana-511	42	22	complete	complete	ADJ
cana-511	42	23	.	.	PUNCT
cana-511	43	1			PROPN
cana-511	43	2	communications	communication	NOUN
cana-511	43	3	on	on	ADP
cana-511	43	4	applied	apply	VERB
cana-511	43	5	nonlinear	nonlinear	ADJ
cana-511	43	6	analysis	analysis	NOUN
cana-511	43	7	issn	issn	NOUN
cana-511	43	8	:	:	PUNCT
cana-511	43	9	1074	1074	NUM
cana-511	43	10	-	-	PUNCT
cana-511	43	11	133x	133x	NUM
cana-511	43	12	vol	vol	NOUN
cana-511	43	13	31	31	NUM
cana-511	43	14	no	no	NOUN
cana-511	43	15	.	.	NOUN
cana-511	43	16	2	2	NUM
cana-511	43	17	(	(	PUNCT
cana-511	43	18	2024	2024	NUM
cana-511	43	19	)	)	PUNCT
cana-511	43	20	36	36	NUM
cana-511	43	21	https://internationalpubls.com	https://internationalpubls.com	X
cana-511	43	22	definition	definition	NOUN
cana-511	43	23	2.5	2.5	NUM
cana-511	43	24	.	.	PUNCT
cana-511	44	1	[	[	X
cana-511	44	2	7	7	X
cana-511	44	3	]	]	PUNCT
cana-511	44	4	on	on	ADP
cana-511	44	5	a	a	DET
cana-511	44	6	fuzzy	fuzzy	ADJ
cana-511	44	7	metric	metric	ADJ
cana-511	44	8	space	space	NOUN
cana-511	44	9	(	(	PUNCT
cana-511	44	10	)	)	PUNCT
cana-511	44	11	,	,	PUNCT
cana-511	44	12	,	,	PUNCT
cana-511	44	13	x	x	X
cana-511	44	14	m	m	NUM
cana-511	44	15	,	,	PUNCT
cana-511	44	16	two	two	NUM
cana-511	44	17	self	self	NOUN
cana-511	44	18	-	-	PUNCT
cana-511	44	19	mappings	mapping	NOUN
cana-511	44	20	&	&	CCONJ
cana-511	44	21			X
cana-511	44	22			NOUN
cana-511	44	23	are	be	AUX
cana-511	44	24	said	say	VERB
cana-511	44	25	to	to	PART
cana-511	44	26	be	be	AUX
cana-511	44	27	compatible	compatible	ADJ
cana-511	44	28	if	if	SCONJ
cana-511	44	29	(	(	PUNCT
cana-511	44	30	)	)	PUNCT
cana-511	44	31	ll	ll	AUX
cana-511	44	32	,	,	PUNCT
cana-511	44	33	i	i	PRON
cana-511	44	34	m	m	VERB
cana-511	44	35	,	,	PUNCT
cana-511	44	36	q	q	PUNCT
cana-511	44	37	q	q	X
cana-511	44	38	qx	qx	PROPN
cana-511	44	39	x	x	PROPN
cana-511	44	40	t	t	NOUN
cana-511	44	41			X
cana-511	44	42	→	→	PUNCT
cana-511	44	43	=	=	NOUN
cana-511	44	44	m	m	VERB
cana-511	44	45	for	for	ADP
cana-511	44	46	each	each	DET
cana-511	44	47	0	0	NUM
cana-511	44	48	t	t	NOUN
cana-511	44	49			INTJ
cana-511	44	50	,	,	PUNCT
cana-511	44	51	whenever	whenever	SCONJ
cana-511	44	52			PROPN
cana-511	44	53	qx	qx	PROPN
cana-511	44	54	is	be	AUX
cana-511	44	55	a	a	DET
cana-511	44	56	sequence	sequence	NOUN
cana-511	44	57	in	in	ADP
cana-511	44	58	x	x	PROPN
cana-511	44	59	.1im	.1im	PROPN
cana-511	44	60	1imq	1imq	NUM
cana-511	45	1	q	q	NOUN
cana-511	45	2	q	q	X
cana-511	45	3	q	q	NOUN
cana-511	45	4	x	x	X
cana-511	45	5	x	x	SYM
cana-511	45	6	x	x	SYM
cana-511	45	7	x	x	PROPN
cana-511	45	8			NOUN
cana-511	45	9	→	→	PUNCT
cana-511	45	10	→	→	PUNCT
cana-511	45	11	=	=	NOUN
cana-511	45	12	=	=	SYM
cana-511	45	13			PROPN
cana-511	45	14	definition	definition	NOUN
cana-511	45	15	2.6	2.6	NUM
cana-511	45	16	.	.	PUNCT
cana-511	46	1	[	[	X
cana-511	46	2	7	7	X
cana-511	46	3	]	]	SYM
cana-511	46	4	two	two	NUM
cana-511	46	5	self	self	NOUN
cana-511	46	6	-	-	PUNCT
cana-511	46	7	maps	map	NOUN
cana-511	46	8	&	&	CCONJ
cana-511	46	9			X
cana-511	46	10			NOUN
cana-511	46	11	of	of	ADP
cana-511	46	12	a	a	DET
cana-511	46	13	fuzzy	fuzzy	ADJ
cana-511	46	14	metric	metric	ADJ
cana-511	46	15	space	space	NOUN
cana-511	46	16	(	(	PUNCT
cana-511	46	17	)	)	PUNCT
cana-511	46	18	,	,	PUNCT
cana-511	46	19	,	,	PUNCT
cana-511	46	20	x	x	X
cana-511	46	21	m	m	NUM
cana-511	46	22	are	be	AUX
cana-511	46	23	said	say	VERB
cana-511	46	24	to	to	PART
cana-511	46	25	be	be	AUX
cana-511	46	26	weakly	weakly	ADV
cana-511	46	27	compatible	compatible	ADJ
cana-511	46	28	if	if	SCONJ
cana-511	46	29	they	they	PRON
cana-511	46	30	commute	commute	VERB
cana-511	46	31	at	at	ADP
cana-511	46	32	their	their	PRON
cana-511	46	33	coincidence	coincidence	NOUN
cana-511	46	34	points	point	NOUN
cana-511	46	35	;	;	PUNCT
cana-511	46	36	x	x	SYM
cana-511	46	37	x	x	PROPN
cana-511	46	38	=	=	PROPN
cana-511	46	39	for	for	ADP
cana-511	46	40	some	some	PRON
cana-511	46	41	x	x	SYM
cana-511	46	42	x	x	PROPN
cana-511	46	43	implies	imply	VERB
cana-511	46	44	that	that	SCONJ
cana-511	46	45	x	x	SYM
cana-511	46	46	x	x	X
cana-511	46	47	=	=	PROPN
cana-511	46	48	.	.	PUNCT
cana-511	47	1	remark	remark	VERB
cana-511	47	2	2.7	2.7	NUM
cana-511	47	3	.	.	PUNCT
cana-511	48	1	let	let	VERB
cana-511	48	2	&	&	CCONJ
cana-511	48	3			PROPN
cana-511	48	4			NOUN
cana-511	48	5	be	be	AUX
cana-511	48	6	weakly	weakly	ADV
cana-511	48	7	compatible	compatible	ADJ
cana-511	48	8	s	s	X
cana-511	48	9	e	e	NOUN
cana-511	48	10	l	l	NOUN
cana-511	48	11	f	f	PROPN
cana-511	48	12	-maps	-map	NOUN
cana-511	48	13	of	of	ADP
cana-511	48	14	a	a	DET
cana-511	48	15	set	set	NOUN
cana-511	48	16	x	x	X
cana-511	48	17	.	.	PUNCT
cana-511	49	1	if	if	SCONJ
cana-511	49	2	&	&	CCONJ
cana-511	49	3			PROPN
cana-511	49	4			NOUN
cana-511	49	5	have	have	VERB
cana-511	49	6	a	a	DET
cana-511	49	7	unique	unique	ADJ
cana-511	49	8	point	point	NOUN
cana-511	49	9	of	of	ADP
cana-511	49	10	coincidence	coincidence	NOUN
cana-511	49	11	,	,	PUNCT
cana-511	49	12	w	w	PROPN
cana-511	49	13	x	x	SYM
cana-511	49	14	x	x	PROPN
cana-511	49	15	=	=	PROPN
cana-511	50	1	=	=	PUNCT
cana-511	50	2	then	then	ADV
cana-511	50	3	w	w	PROPN
cana-511	50	4	is	be	AUX
cana-511	50	5	the	the	DET
cana-511	50	6	unique	unique	ADJ
cana-511	50	7	common	common	ADJ
cana-511	50	8	fixed	fix	VERB
cana-511	50	9	point	point	NOUN
cana-511	50	10	of	of	ADP
cana-511	50	11	&	&	CCONJ
cana-511	50	12			X
cana-511	50	13			NOUN
cana-511	50	14	.	.	PUNCT
cana-511	51	1	definition	definition	NOUN
cana-511	51	2	2.8	2.8	NUM
cana-511	51	3	.	.	PUNCT
cana-511	52	1	[	[	X
cana-511	52	2	11	11	NUM
cana-511	52	3	]	]	PUNCT
cana-511	52	4	let	let	VERB
cana-511	52	5	the	the	DET
cana-511	52	6	family	family	NOUN
cana-511	52	7	of	of	ADP
cana-511	52	8	all	all	DET
cana-511	52	9	functions	function	NOUN
cana-511	52	10	(	(	PUNCT
cana-511	52	11			NOUN
cana-511	52	12	(	(	PUNCT
cana-511	52	13			NOUN
cana-511	52	14	:	:	PUNCT
cana-511	52	15	0	0	NUM
cana-511	52	16	,	,	PUNCT
cana-511	52	17	l	l	NOUN
cana-511	52	18	0	0	NUM
cana-511	52	19	,	,	PUNCT
cana-511	52	20	l	l	VERB
cana-511	52	21			NOUN
cana-511	52	22	→	→	SYM
cana-511	52	23	satisfying	satisfy	VERB
cana-511	52	24	,	,	PUNCT
cana-511	52	25	(	(	PUNCT
cana-511	52	26	)	)	PUNCT
cana-511	52	27	(	(	PUNCT
cana-511	52	28	)	)	PUNCT
cana-511	52	29	,	,	PUNCT
cana-511	52	30	,	,	PUNCT
cana-511	52	31	,	,	PUNCT
cana-511	52	32	0	0	NUM
cana-511	52	33	,	,	PUNCT
cana-511	52	34	lt	lt	DET
cana-511	52	35	r	r	NOUN
cana-511	52	36	r	r	NOUN
cana-511	52	37	t	t	NOUN
cana-511	52	38	r	r	NOUN
cana-511	52	39			PROPN
cana-511	52	40			PROPN
cana-511	52	41			PROPN
cana-511	52	42	be	be	AUX
cana-511	52	43	denoted	denote	VERB
cana-511	52	44	by	by	ADP
cana-511	52	45	z	z	PROPN
cana-511	52	46	.	.	PUNCT
cana-511	53	1	remark	remark	PROPN
cana-511	53	2	2	2	NUM
cana-511	53	3	.	.	PUNCT
cana-511	53	4	9	9	NUM
cana-511	53	5	.	.	PUNCT
cana-511	54	1	[	[	X
cana-511	54	2	11	11	NUM
cana-511	54	3	]	]	PUNCT
cana-511	54	4	from	from	ADP
cana-511	54	5	the	the	DET
cana-511	54	6	above	above	ADJ
cana-511	54	7	definition	definition	NOUN
cana-511	54	8	,	,	PUNCT
cana-511	54	9	we	we	PRON
cana-511	54	10	can	can	AUX
cana-511	54	11	see	see	VERB
cana-511	54	12	that	that	PRON
cana-511	54	13	,	,	PUNCT
cana-511	54	14	,	,	PUNCT
cana-511	54	15	0	0	NUM
cana-511	54	16	,	,	PUNCT
cana-511	54	17	l	l	NOUN
cana-511	54	18	.	.	PUNCT
cana-511	55	1	(	(	PUNCT
cana-511	55	2	)	)	PUNCT
cana-511	55	3	(	(	PUNCT
cana-511	55	4	)	)	PUNCT
cana-511	55	5	t	t	NOUN
cana-511	55	6	t	t	PROPN
cana-511	55	7	t	t	PROPN
cana-511	55	8	t	t	NOUN
cana-511	55	9			PROPN
cana-511	55	10			PROPN
cana-511	55	11			PROPN
cana-511	55	12	example	example	NOUN
cana-511	55	13	2.10	2.10	NUM
cana-511	55	14	.	.	PUNCT
cana-511	56	1	[	[	X
cana-511	56	2	11	11	NUM
cana-511	56	3	]	]	PUNCT
cana-511	56	4	consider	consider	VERB
cana-511	56	5	the	the	DET
cana-511	56	6	following	follow	VERB
cana-511	56	7	functions	function	NOUN
cana-511	56	8	(	(	PUNCT
cana-511	56	9			NOUN
cana-511	56	10	(	(	PUNCT
cana-511	56	11			NOUN
cana-511	56	12	:	:	PUNCT
cana-511	56	13	0	0	NUM
cana-511	56	14	,	,	PUNCT
cana-511	56	15	l	l	NOUN
cana-511	56	16	0	0	NUM
cana-511	56	17	,	,	PUNCT
cana-511	56	18	l	l	VERB
cana-511	56	19			NOUN
cana-511	56	20	→	→	SYM
cana-511	56	21	by	by	ADP
cana-511	56	22	:	:	PUNCT
cana-511	56	23	(	(	PUNCT
cana-511	56	24	1	1	X
cana-511	56	25	)	)	PUNCT
cana-511	56	26	(	(	PUNCT
cana-511	56	27	)	)	PUNCT
cana-511	56	28	(	(	PUNCT
cana-511	56	29	)	)	PUNCT
cana-511	56	30	,	,	PUNCT
cana-511	56	31	,	,	PUNCT
cana-511	56	32	p	p	PRON
cana-511	56	33	q	q	X
cana-511	56	34	q	q	VERB
cana-511	56	35	=	=	PROPN
cana-511	56	36	where	where	SCONJ
cana-511	56	37	(	(	PUNCT
cana-511	56	38			NOUN
cana-511	56	39	(	(	PUNCT
cana-511	56	40			NOUN
cana-511	56	41	:	:	PUNCT
cana-511	56	42	0	0	NUM
cana-511	56	43	,	,	PUNCT
cana-511	56	44	l	l	NOUN
cana-511	56	45	  	  	SPACE
cana-511	56	46	0	0	NUM
cana-511	56	47	,	,	PUNCT
cana-511	56	48	l	l	NOUN
cana-511	57	1	→	→	X
cana-511	57	2	is	be	AUX
cana-511	57	3	a	a	DET
cana-511	57	4	function	function	NOUN
cana-511	57	5	such	such	ADJ
cana-511	57	6	that	that	SCONJ
cana-511	57	7	(	(	PUNCT
cana-511	57	8	)	)	PUNCT
cana-511	57	9	,	,	PUNCT
cana-511	57	10	q	q	NOUN
cana-511	57	11	q	q	ADJ
cana-511	57	12	,	,	PUNCT
cana-511	57	13	0	0	NUM
cana-511	57	14	(	(	PUNCT
cana-511	57	15	)	)	PUNCT
cana-511	57	16	,	,	PUNCT
cana-511	57	17	1q	1q	NOUN
cana-511	57	18			NOUN
cana-511	57	19	(	(	PUNCT
cana-511	57	20	2	2	NUM
cana-511	57	21	)	)	PUNCT
cana-511	57	22	(	(	PUNCT
cana-511	57	23	)	)	PUNCT
cana-511	57	24	l	l	NOUN
cana-511	57	25	  	  	SPACE
cana-511	57	26	,	,	PUNCT
cana-511	57	27	      	      	SPACE
cana-511	57	28	,	,	PUNCT
cana-511	57	29	p	p	NOUN
cana-511	57	30	q	q	AUX
cana-511	57	31	p	p	X
cana-511	57	32	q	q	X
cana-511	57	33	p	p	NOUN
cana-511	57	34			NOUN
cana-511	57	35	=	=	PUNCT
cana-511	58	1	+	+	CCONJ
cana-511	58	2	+	+	CCONJ
cana-511	58	3	(	(	PUNCT
cana-511	58	4	3	3	NUM
cana-511	58	5	)	)	PUNCT
cana-511	58	6	(	(	PUNCT
cana-511	58	7	)	)	PUNCT
cana-511	58	8	,	,	PUNCT
cana-511	58	9	 	 	SPACE
cana-511	58	10	.	.	PUNCT
cana-511	59	1	q	q	X
cana-511	60	1	p	p	X
cana-511	60	2	q	q	X
cana-511	60	3	p	p	NOUN
cana-511	60	4			NOUN
cana-511	60	5	=	=	PUNCT
cana-511	61	1	then	then	ADV
cana-511	61	2	,	,	PUNCT
cana-511	61	3	in	in	ADP
cana-511	61	4	all	all	DET
cana-511	61	5	the	the	DET
cana-511	61	6	cases	case	NOUN
cana-511	61	7	  	  	SPACE
cana-511	61	8	.	.	PROPN
cana-511	61	9	z	z	NOUN
cana-511	61	10	definition	definition	NOUN
cana-511	61	11	2.11	2.11	NUM
cana-511	61	12	.	.	PUNCT
cana-511	62	1	[	[	X
cana-511	62	2	11	11	NUM
cana-511	62	3	]	]	PUNCT
cana-511	62	4	let	let	VERB
cana-511	62	5	:	:	PUNCT
cana-511	62	6	x	x	PROPN
cana-511	62	7	x	x	PROPN
cana-511	62	8	→	→	PUNCT
cana-511	62	9	be	be	AUX
cana-511	62	10	a	a	DET
cana-511	62	11	self	self	NOUN
cana-511	62	12	mapping	mapping	NOUN
cana-511	62	13	on	on	ADP
cana-511	62	14	a	a	DET
cana-511	62	15	fuzzy	fuzzy	ADJ
cana-511	62	16	metric	metric	ADJ
cana-511	62	17	space	space	NOUN
cana-511	62	18	(	(	PUNCT
cana-511	62	19	)	)	PUNCT
cana-511	62	20	,	,	PUNCT
cana-511	62	21	,	,	PUNCT
cana-511	62	22	.x	.x	PROPN
cana-511	62	23	m	m	NUM
cana-511	62	24	suppose	suppose	VERB
cana-511	62	25	,	,	PUNCT
cana-511	62	26	  	  	SPACE
cana-511	62	27			NOUN
cana-511	62	28	z	z	NOUN
cana-511	62	29	such	such	ADJ
cana-511	62	30	that	that	PRON
cana-511	62	31	,	,	PUNCT
cana-511	62	32	(	(	PUNCT
cana-511	62	33	)	)	PUNCT
cana-511	62	34	(	(	PUNCT
cana-511	62	35	)	)	PUNCT
cana-511	62	36	(	(	PUNCT
cana-511	62	37	)	)	PUNCT
cana-511	62	38	(	(	PUNCT
cana-511	62	39	)	)	PUNCT
cana-511	62	40	,	,	PUNCT
cana-511	62	41	,	,	PUNCT
cana-511	62	42	,	,	PUNCT
cana-511	62	43	,	,	PUNCT
cana-511	62	44	,	,	PUNCT
cana-511	62	45	,	,	PUNCT
cana-511	62	46	,	,	PUNCT
cana-511	62	47	   	   	SPACE
cana-511	62	48	x	x	VERB
cana-511	62	49	y	y	NOUN
cana-511	62	50	t	t	NOUN
cana-511	62	51	x	x	X
cana-511	62	52	y	y	NOUN
cana-511	62	53	t	t	NOUN
cana-511	62	54	x	x	X
cana-511	62	55	y	y	NOUN
cana-511	62	56	t	t	PROPN
cana-511	62	57			VERB
cana-511	62	58			NOUN
cana-511	62	59			VERB
cana-511	62	60	m	m	PROPN
cana-511	62	61	m	m	NOUN
cana-511	62	62	m	m	VERB
cana-511	62	63	(	(	PUNCT
cana-511	62	64	2.1	2.1	NUM
cana-511	62	65	)	)	PUNCT
cana-511	62	66	for	for	ADP
cana-511	62	67	all	all	PRON
cana-511	62	68	,	,	PUNCT
cana-511	62	69	,	,	PUNCT
cana-511	62	70	,	,	PUNCT
cana-511	62	71	0	0	X
cana-511	62	72	.	.	PUNCT
cana-511	62	73	 	 	SPACE
cana-511	63	1	x	x	X
cana-511	64	1	y	y	NOUN
cana-511	64	2	x	x	PUNCT
cana-511	64	3	x	x	SYM
cana-511	64	4	y	y	PRON
cana-511	64	5	t	t	NOUN
cana-511	64	6			PROPN
cana-511	64	7	=	=	PUNCT
cana-511	65	1			PROPN
cana-511	65	2	then	then	ADV
cana-511	65	3			VERB
cana-511	65	4	is	be	AUX
cana-511	65	5	called	call	VERB
cana-511	65	6	a	a	DET
cana-511	65	7	fuzzy	fuzzy	ADJ
cana-511	65	8	−z	−z	NOUN
cana-511	65	9	contractive	contractive	ADJ
cana-511	65	10	mapping	mapping	NOUN
cana-511	65	11	with	with	ADP
cana-511	65	12	respect	respect	NOUN
cana-511	65	13	to	to	ADP
cana-511	65	14	.	.	PROPN
cana-511	65	15	z	z	NOUN
cana-511	65	16	remark	remark	NOUN
cana-511	65	17	2.12	2.12	NUM
cana-511	65	18	.	.	PUNCT
cana-511	66	1	even	even	ADV
cana-511	66	2	in	in	ADP
cana-511	66	3	the	the	DET
cana-511	66	4	−m	−m	ADJ
cana-511	66	5	complete	complete	ADJ
cana-511	66	6	fuzzy	fuzzy	ADJ
cana-511	66	7	metric	metric	ADJ
cana-511	66	8	space	space	NOUN
cana-511	66	9	,	,	PUNCT
cana-511	66	10	a	a	DET
cana-511	66	11	fuzzy	fuzzy	ADJ
cana-511	66	12	−z	−z	NOUN
cana-511	66	13	contractive	contractive	ADJ
cana-511	66	14	mapping	mapping	NOUN
cana-511	66	15	may	may	AUX
cana-511	66	16	not	not	PART
cana-511	66	17	have	have	VERB
cana-511	66	18	a	a	DET
cana-511	66	19	fixed	fix	VERB
cana-511	66	20	point	point	NOUN
cana-511	66	21	.	.	PUNCT
cana-511	67	1	(	(	PUNCT
cana-511	67	2	see	see	VERB
cana-511	67	3	example	example	NOUN
cana-511	67	4	3.10	3.10	NUM
cana-511	67	5	.	.	PUNCT
cana-511	67	6	of	of	ADP
cana-511	67	7	[	[	X
cana-511	67	8	11	11	NUM
cana-511	67	9	]	]	PUNCT
cana-511	67	10	)	)	PUNCT
cana-511	67	11	s.	s.	PROPN
cana-511	67	12	shukla	shukla	PROPN
cana-511	67	13	et	et	PROPN
cana-511	67	14	al	al	PROPN
cana-511	67	15	.	.	PUNCT
cana-511	68	1	[	[	X
cana-511	68	2	11	11	NUM
cana-511	68	3	]	]	PUNCT
cana-511	68	4	considered	consider	VERB
cana-511	68	5	a	a	DET
cana-511	68	6	space	space	NOUN
cana-511	68	7	with	with	ADP
cana-511	68	8	the	the	DET
cana-511	68	9	additional	additional	ADJ
cana-511	68	10	characteristic	characteristic	NOUN
cana-511	68	11	listed	list	VERB
cana-511	68	12	below	below	ADV
cana-511	68	13	to	to	PART
cana-511	68	14	guarantee	guarantee	VERB
cana-511	68	15	the	the	DET
cana-511	68	16	existence	existence	NOUN
cana-511	68	17	of	of	ADP
cana-511	68	18	the	the	DET
cana-511	68	19	fixed	fix	VERB
cana-511	68	20	point	point	NOUN
cana-511	68	21	of	of	ADP
cana-511	68	22	a	a	DET
cana-511	68	23	fuzzy	fuzzy	ADJ
cana-511	68	24	−z	−z	NOUN
cana-511	68	25	contractive	contractive	ADJ
cana-511	68	26	mapping	mapping	NOUN
cana-511	68	27	.	.	PUNCT
cana-511	69	1	definition	definition	NOUN
cana-511	69	2	2.13	2.13	NUM
cana-511	69	3	.	.	PUNCT
cana-511	70	1	[	[	X
cana-511	70	2	11	11	NUM
cana-511	70	3	]	]	PUNCT
cana-511	70	4	let	let	VERB
cana-511	70	5	 	 	SPACE
cana-511	70	6	:	:	PUNCT
cana-511	70	7	       	       	SPACE
cana-511	70	8	x	x	SYM
cana-511	70	9	x	x	PROPN
cana-511	70	10	→	→	PUNCT
cana-511	70	11	be	be	AUX
cana-511	70	12	a	a	DET
cana-511	70	13	mapping	mapping	NOUN
cana-511	70	14	in	in	ADP
cana-511	70	15	a	a	DET
cana-511	70	16	fuzzy	fuzzy	ADJ
cana-511	70	17	metric	metric	ADJ
cana-511	70	18	space	space	NOUN
cana-511	70	19	(	(	PUNCT
cana-511	70	20	)	)	PUNCT
cana-511	70	21	,	,	PUNCT
cana-511	70	22	,	,	PUNCT
cana-511	70	23	 	 	SPACE
cana-511	70	24	x	x	SYM
cana-511	70	25	m	m	NUM
cana-511	70	26	and	and	CCONJ
cana-511	70	27	  	  	SPACE
cana-511	70	28	.	.	PROPN
cana-511	70	29	z	z	VERB
cana-511	70	30	then	then	ADV
cana-511	70	31	,	,	PUNCT
cana-511	70	32	we	we	PRON
cana-511	70	33	say	say	VERB
cana-511	70	34	that	that	SCONJ
cana-511	70	35	the	the	DET
cana-511	70	36	quadruple	quadruple	NOUN
cana-511	70	37	(	(	PUNCT
cana-511	70	38	)	)	PUNCT
cana-511	70	39	,	,	PUNCT
cana-511	70	40	,	,	PUNCT
cana-511	70	41	,	,	PUNCT
cana-511	70	42	x	x	PUNCT
cana-511	70	43			X
cana-511	70	44	m	m	PROPN
cana-511	70	45	has	have	VERB
cana-511	70	46	the	the	DET
cana-511	70	47	property	property	NOUN
cana-511	70	48	(	(	PUNCT
cana-511	70	49	)	)	PUNCT
cana-511	70	50	s	s	PART
cana-511	70	51	,	,	PUNCT
cana-511	70	52	if	if	SCONJ
cana-511	70	53	for	for	ADP
cana-511	70	54	any	any	DET
cana-511	70	55	picard	picard	NOUN
cana-511	70	56	sequence	sequence	NOUN
cana-511	70	57	{	{	PUNCT
cana-511	70	58	}	}	PUNCT
cana-511	70	59	qs	qs	NOUN
cana-511	70	60	with	with	ADP
cana-511	70	61	initial	initial	ADJ
cana-511	70	62	value	value	NOUN
cana-511	70	63	,	,	PUNCT
cana-511	70	64	.	.	PUNCT
cana-511	71	1	.	.	PUNCT
cana-511	72	1	,	,	PUNCT
cana-511	72	2	  	  	SPACE
cana-511	72	3	,	,	PUNCT
cana-511	72	4	q	q	PROPN
cana-511	73	1	qx	qx	INTJ
cana-511	73	2	x	x	INTJ
cana-511	74	1	i	i	NOUN
cana-511	74	2	e	e	X
cana-511	74	3	s	s	NOUN
cana-511	74	4	x	x	X
cana-511	74	5	q	q	X
cana-511	74	6	n	n	NOUN
cana-511	74	7	=	=	SYM
cana-511	74	8			VERB
cana-511	74	9			NOUN
cana-511	74	10	such	such	ADJ
cana-511	74	11	that	that	SCONJ
cana-511	74	12	l	l	PROPN
cana-511	74	13	1	1	NUM
cana-511	74	14	0	0	NUM
cana-511	74	15	(	(	PUNCT
cana-511	74	16	)	)	PUNCT
cana-511	74	17	(	(	PUNCT
cana-511	74	18	)	)	PUNCT
cana-511	74	19	inf	inf	PROPN
cana-511	74	20	,	,	PUNCT
cana-511	74	21	,	,	PUNCT
cana-511	74	22	inf	inf	PROPN
cana-511	74	23	,	,	PUNCT
cana-511	74	24	,	,	PUNCT
cana-511	74	25	    	    	SPACE
cana-511	74	26	,	,	PUNCT
cana-511	74	27	,	,	PUNCT
cana-511	74	28	q	q	PROPN
cana-511	74	29	p	p	X
cana-511	74	30	q	q	X
cana-511	74	31	p	p	X
cana-511	74	32	q	q	X
cana-511	74	33	q	q	X
cana-511	75	1	s	s	X
cana-511	75	2	s	s	X
cana-511	75	3	t	t	NOUN
cana-511	75	4	s	s	X
cana-511	75	5	s	s	PROPN
cana-511	75	6	t	t	PROPN
cana-511	75	7	q	q	PROPN
cana-511	75	8	n	n	PRON
cana-511	75	9	t+	t+	NOUN
cana-511	76	1	+	+	CCONJ
cana-511	77	1			PROPN
cana-511	77	2			PROPN
cana-511	77	3			PUNCT
cana-511	77	4			PROPN
cana-511	77	5	m	m	PROPN
cana-511	77	6	m	m	VERB
cana-511	77	7	p	p	NOUN
cana-511	77	8	p	p	NOUN
cana-511	77	9	implies	imply	VERB
cana-511	77	10	that	that	SCONJ
cana-511	77	11	1	1	NUM
cana-511	77	12	1	1	NUM
cana-511	77	13	.1	.1	NUM
cana-511	77	14	)	)	PUNCT
cana-511	77	15	,	,	PUNCT
cana-511	77	16	,	,	PUNCT
cana-511	77	17	i	i	PRON
cana-511	77	18	m	m	VERB
cana-511	77	19	(	(	PUNCT
cana-511	77	20	(	(	PUNCT
cana-511	77	21	)	)	PUNCT
cana-511	77	22	,	,	PUNCT
cana-511	77	23	,	,	PUNCT
cana-511	77	24	l	l	NOUN
cana-511	77	25	)	)	PUNCT
cana-511	77	26	,	,	PUNCT
cana-511	77	27	0(q	0(q	X
cana-511	77	28	q	q	NOUN
cana-511	78	1	p	p	X
cana-511	78	2	q	q	X
cana-511	78	3	p	p	X
cana-511	78	4	p	p	X
cana-511	78	5	q	q	PROPN
cana-511	78	6	inf	inf	PROPN
cana-511	78	7	s	s	PROPN
cana-511	78	8	s	s	PROPN
cana-511	78	9	t	t	NOUN
cana-511	78	10	s	s	PROPN
cana-511	78	11	s	s	PROPN
cana-511	78	12	t	t	NOUN
cana-511	78	13	t	t	NOUN
cana-511	79	1	+	+	X
cana-511	79	2	+	+	CCONJ
cana-511	79	3	→	→	SYM
cana-511	79	4			PROPN
cana-511	79	5	=	=	SYM
cana-511	79	6			NOUN
cana-511	79	7	m	m	PROPN
cana-511	79	8	m	m	PROPN
cana-511	79	9	(	(	PUNCT
cana-511	79	10	2.2	2.2	NUM
cana-511	79	11	)	)	PUNCT
cana-511	79	12	communications	communication	NOUN
cana-511	79	13	on	on	ADP
cana-511	79	14	applied	apply	VERB
cana-511	79	15	nonlinear	nonlinear	ADJ
cana-511	79	16	analysis	analysis	NOUN
cana-511	79	17	issn	issn	NOUN
cana-511	79	18	:	:	PUNCT
cana-511	79	19	1074	1074	NUM
cana-511	79	20	-	-	PUNCT
cana-511	79	21	133x	133x	NUM
cana-511	79	22	vol	vol	NOUN
cana-511	79	23	31	31	NUM
cana-511	79	24	no	no	NOUN
cana-511	79	25	.	.	NOUN
cana-511	79	26	2	2	NUM
cana-511	79	27	(	(	PUNCT
cana-511	79	28	2024	2024	NUM
cana-511	79	29	)	)	PUNCT
cana-511	79	30	37	37	NUM
cana-511	79	31	https://internationalpubls.com	https://internationalpubls.com	X
cana-511	79	32	theorem	theorem	VERB
cana-511	79	33	2.14	2.14	NUM
cana-511	79	34	.	.	PUNCT
cana-511	80	1	[	[	X
cana-511	80	2	11	11	NUM
cana-511	80	3	]	]	PUNCT
cana-511	80	4	let	let	VERB
cana-511	80	5	:	:	PUNCT
cana-511	80	6	     	     	SPACE
cana-511	80	7	x	x	SYM
cana-511	80	8	x	x	PROPN
cana-511	80	9	→	→	PUNCT
cana-511	80	10	be	be	AUX
cana-511	80	11	a	a	DET
cana-511	80	12	fuzzy	fuzzy	ADJ
cana-511	80	13	−z	−z	NOUN
cana-511	80	14	contraction	contraction	NOUN
cana-511	80	15	on	on	ADP
cana-511	80	16	an	an	DET
cana-511	80	17	−m	−m	ADJ
cana-511	80	18	complete	complete	ADJ
cana-511	80	19	fuzzy	fuzzy	ADJ
cana-511	80	20	metric	metric	ADJ
cana-511	80	21	space	space	NOUN
cana-511	80	22	,	,	PUNCT
cana-511	80	23	,	,	PUNCT
cana-511	80	24	.	.	PUNCT
cana-511	80	25	 	 	SPACE
cana-511	81	1	(	(	PUNCT
cana-511	81	2	)	)	PUNCT
cana-511	81	3	x	x	SYM
cana-511	81	4	m	m	NOUN
cana-511	81	5	if	if	SCONJ
cana-511	81	6	the	the	DET
cana-511	81	7	quadruple	quadruple	NOUN
cana-511	81	8	(	(	PUNCT
cana-511	81	9	)	)	PUNCT
cana-511	81	10	,	,	PUNCT
cana-511	81	11	,	,	PUNCT
cana-511	81	12	,	,	PUNCT
cana-511	81	13	x	x	PUNCT
cana-511	81	14			X
cana-511	81	15	m	m	PROPN
cana-511	81	16	has	have	VERB
cana-511	81	17	the	the	DET
cana-511	81	18	property	property	NOUN
cana-511	81	19	(	(	PUNCT
cana-511	81	20	)	)	PUNCT
cana-511	81	21	,	,	PUNCT
cana-511	81	22	s	s	AUX
cana-511	81	23	then	then	ADV
cana-511	81	24	f	f	PROPN
cana-511	81	25	has	have	VERB
cana-511	81	26	a	a	DET
cana-511	81	27	unique	unique	ADJ
cana-511	81	28	fixed	fix	VERB
cana-511	81	29	point	point	NOUN
cana-511	81	30	.z	.z	PUNCT
cana-511	82	1	x	x	PROPN
cana-511	82	2	3	3	NUM
cana-511	82	3	.	.	PUNCT
cana-511	82	4	main	main	ADJ
cana-511	82	5	results	result	NOUN
cana-511	82	6	definition	definition	NOUN
cana-511	82	7	3.1	3.1	NUM
cana-511	82	8	.	.	PUNCT
cana-511	83	1	let	let	VERB
cana-511	83	2	&	&	CCONJ
cana-511	83	3			VERB
cana-511	83	4			PROPN
cana-511	83	5	be	be	AUX
cana-511	83	6	two	two	NUM
cana-511	83	7	self	self	NOUN
cana-511	83	8	-	-	PUNCT
cana-511	83	9	mappings	mapping	NOUN
cana-511	83	10	on	on	ADP
cana-511	83	11	a	a	DET
cana-511	83	12	fuzzy	fuzzy	ADJ
cana-511	83	13	metric	metric	ADJ
cana-511	83	14	space	space	NOUN
cana-511	83	15	,	,	PUNCT
cana-511	83	16	,	,	PUNCT
cana-511	83	17	.	.	PUNCT
cana-511	83	18	 	 	SPACE
cana-511	84	1	(	(	PUNCT
cana-511	84	2	)	)	PUNCT
cana-511	84	3	x	x	SYM
cana-511	84	4	m	m	NUM
cana-511	84	5	then	then	ADV
cana-511	84	6			NOUN
cana-511	84	7	is	be	AUX
cana-511	84	8	called	call	VERB
cana-511	84	9	a	a	DET
cana-511	84	10	fuzzy	fuzzy	ADJ
cana-511	84	11	(	(	PUNCT
cana-511	84	12	)	)	PUNCT
cana-511	84	13	,	,	PUNCT
cana-511	84	14			NUM
cana-511	84	15	−z	−z	NOUN
cana-511	84	16	contraction	contraction	NOUN
cana-511	84	17	if	if	SCONJ
cana-511	84	18			NOUN
cana-511	84	19	z	z	NOUN
cana-511	84	20	such	such	ADJ
cana-511	84	21	that	that	PRON
cana-511	84	22	(	(	PUNCT
cana-511	84	23	)	)	PUNCT
cana-511	84	24	(	(	PUNCT
cana-511	84	25	)	)	PUNCT
cana-511	84	26	(	(	PUNCT
cana-511	84	27	)	)	PUNCT
cana-511	84	28	(	(	PUNCT
cana-511	84	29	)	)	PUNCT
cana-511	84	30	,	,	PUNCT
cana-511	84	31	,	,	PUNCT
cana-511	84	32	,	,	PUNCT
cana-511	84	33	,	,	PUNCT
cana-511	84	34	,	,	PUNCT
cana-511	84	35	,	,	PUNCT
cana-511	84	36	,	,	PUNCT
cana-511	84	37	x	x	VERB
cana-511	84	38	y	y	NOUN
cana-511	84	39	t	t	NOUN
cana-511	84	40	x	x	X
cana-511	84	41	y	y	NOUN
cana-511	84	42	t	t	NOUN
cana-511	84	43	x	x	X
cana-511	84	44	y	y	NOUN
cana-511	84	45	t	t	PROPN
cana-511	84	46			VERB
cana-511	84	47			NOUN
cana-511	84	48			VERB
cana-511	84	49			X
cana-511	84	50			PROPN
cana-511	84	51	m	m	ADJ
cana-511	84	52	m	m	VERB
cana-511	84	53	m	m	VERB
cana-511	84	54	(	(	PUNCT
cana-511	84	55	3.1	3.1	NUM
cana-511	84	56	)	)	PUNCT
cana-511	84	57	for	for	ADP
cana-511	84	58	all	all	PRON
cana-511	84	59	,	,	PUNCT
cana-511	84	60	,	,	PUNCT
cana-511	84	61	,	,	PUNCT
cana-511	84	62	0.x	0.x	NUM
cana-511	85	1	y	y	NOUN
cana-511	85	2	x	x	PUNCT
cana-511	86	1	x	x	PUNCT
cana-511	86	2	y	y	NOUN
cana-511	86	3	t	t	PROPN
cana-511	86	4			PROPN
cana-511	86	5			VERB
cana-511	86	6			INTJ
cana-511	86	7	remark	remark	VERB
cana-511	86	8	3.2	3.2	NUM
cana-511	86	9	.	.	PUNCT
cana-511	87	1	if	if	SCONJ
cana-511	87	2	  	  	SPACE
cana-511	87	3	i=	i=	PRON
cana-511	87	4	(	(	PUNCT
cana-511	87	5	identity	identity	NOUN
cana-511	87	6	mapping	mapping	NOUN
cana-511	87	7	)	)	PUNCT
cana-511	87	8	in	in	ADP
cana-511	87	9	(	(	PUNCT
cana-511	87	10	3.1	3.1	NUM
cana-511	87	11	)	)	PUNCT
cana-511	87	12	,	,	PUNCT
cana-511	87	13	then	then	ADV
cana-511	87	14	we	we	PRON
cana-511	87	15	get	get	VERB
cana-511	87	16	fuzzy	fuzzy	ADJ
cana-511	87	17	−z	−z	NOUN
cana-511	87	18	contraction	contraction	NOUN
cana-511	87	19	(	(	PUNCT
cana-511	87	20	definition	definition	NOUN
cana-511	87	21	2.11	2.11	NUM
cana-511	87	22	)	)	PUNCT
cana-511	87	23	.	.	PUNCT
cana-511	88	1	now	now	ADV
cana-511	88	2	,	,	PUNCT
cana-511	88	3	we	we	PRON
cana-511	88	4	state	state	VERB
cana-511	88	5	our	our	PRON
cana-511	88	6	result	result	NOUN
cana-511	88	7	for	for	ADP
cana-511	88	8	the	the	DET
cana-511	88	9	notion	notion	NOUN
cana-511	88	10	of	of	ADP
cana-511	88	11	fuzzy	fuzzy	ADJ
cana-511	88	12	(	(	PUNCT
cana-511	88	13	)	)	PUNCT
cana-511	88	14	,	,	PUNCT
cana-511	88	15			NUM
cana-511	88	16	−z	−z	NOUN
cana-511	88	17	contraction	contraction	NOUN
cana-511	88	18	.	.	PUNCT
cana-511	89	1	theorem	theorem	VERB
cana-511	89	2	3.3	3.3	NUM
cana-511	89	3	.	.	PUNCT
cana-511	90	1	let	let	VERB
cana-511	90	2	(	(	PUNCT
cana-511	90	3	,	,	PUNCT
cana-511	90	4	,	,	PUNCT
cana-511	90	5	)	)	PUNCT
cana-511	90	6	x	x	X
cana-511	90	7	m	m	PRON
cana-511	90	8	be	be	AUX
cana-511	90	9	a	a	DET
cana-511	90	10	fuzzy	fuzzy	ADJ
cana-511	90	11	metric	metric	ADJ
cana-511	90	12	space	space	NOUN
cana-511	90	13	and	and	CCONJ
cana-511	90	14	,	,	PUNCT
cana-511	90	15	:	:	PUNCT
cana-511	90	16	 	 	SPACE
cana-511	90	17	x	x	SYM
cana-511	90	18	x	x	PROPN
cana-511	90	19			PROPN
cana-511	90	20	→	→	PUNCT
cana-511	90	21	be	be	AUX
cana-511	90	22	self	self	NOUN
cana-511	90	23	-	-	PUNCT
cana-511	90	24	mappings	mapping	NOUN
cana-511	90	25	.	.	PUNCT
cana-511	91	1	let	let	VERB
cana-511	91	2			NOUN
cana-511	91	3	be	be	AUX
cana-511	91	4	a	a	DET
cana-511	91	5	fuzzy	fuzzy	ADJ
cana-511	91	6	(	(	PUNCT
cana-511	91	7	)	)	PUNCT
cana-511	91	8	,	,	PUNCT
cana-511	91	9			NUM
cana-511	91	10	−z	−z	NOUN
cana-511	91	11	contraction	contraction	NOUN
cana-511	91	12	and	and	CCONJ
cana-511	91	13	the	the	DET
cana-511	91	14	quadruple	quadruple	NOUN
cana-511	91	15	(	(	PUNCT
cana-511	91	16	)	)	PUNCT
cana-511	91	17	,	,	PUNCT
cana-511	91	18	,	,	PUNCT
cana-511	91	19	,	,	PUNCT
cana-511	91	20	x	x	PUNCT
cana-511	91	21			X
cana-511	91	22	m	m	PROPN
cana-511	91	23	has	have	VERB
cana-511	91	24	the	the	DET
cana-511	91	25	property	property	NOUN
cana-511	91	26	(	(	PUNCT
cana-511	91	27	)	)	PUNCT
cana-511	91	28	s	s	PART
cana-511	91	29	.	.	PUNCT
cana-511	92	1	also	also	ADV
cana-511	92	2	assume	assume	VERB
cana-511	92	3	that	that	SCONJ
cana-511	92	4	,	,	PUNCT
cana-511	92	5	at	at	ADV
cana-511	92	6	least	least	ADJ
cana-511	92	7	one	one	NUM
cana-511	92	8	of	of	ADP
cana-511	92	9	the	the	DET
cana-511	92	10	following	follow	VERB
cana-511	92	11	conditions	condition	NOUN
cana-511	92	12	hold	hold	VERB
cana-511	92	13	:	:	PUNCT
cana-511	92	14	(	(	PUNCT
cana-511	92	15	i	i	NOUN
cana-511	92	16	)	)	PUNCT
cana-511	92	17	(	(	PUNCT
cana-511	92	18	)	)	PUNCT
cana-511	92	19	(	(	PUNCT
cana-511	92	20	)	)	PUNCT
cana-511	92	21	   	   	SPACE
cana-511	93	1	x	x	PUNCT
cana-511	93	2	or	or	CCONJ
cana-511	93	3	x	x	NOUN
cana-511	94	1			PROPN
cana-511	94	2	is	be	AUX
cana-511	94	3	complete	complete	ADJ
cana-511	94	4	.	.	PUNCT
cana-511	95	1	(	(	PUNCT
cana-511	95	2	ii	ii	NOUN
cana-511	95	3	)	)	PUNCT
cana-511	95	4	x	x	X
cana-511	95	5	is	be	AUX
cana-511	95	6	complete	complete	ADJ
cana-511	95	7	,	,	PUNCT
cana-511	95	8			PROPN
cana-511	95	9	is	be	AUX
cana-511	95	10	continuous	continuous	ADJ
cana-511	95	11	and	and	CCONJ
cana-511	95	12	,	,	PUNCT
cana-511	95	13			VERB
cana-511	95	14			PRON
cana-511	95	15	are	be	AUX
cana-511	95	16	commuting	commute	VERB
cana-511	95	17	.	.	PUNCT
cana-511	96	1	(	(	PUNCT
cana-511	96	2	iii	iii	X
cana-511	96	3	)	)	PUNCT
cana-511	96	4	x	x	PRON
cana-511	96	5	is	be	AUX
cana-511	96	6	complete	complete	ADJ
cana-511	96	7	,	,	PUNCT
cana-511	96	8			PROPN
cana-511	96	9	is	be	AUX
cana-511	96	10	continuous	continuous	ADJ
cana-511	96	11	and	and	CCONJ
cana-511	96	12	,	,	PUNCT
cana-511	96	13			VERB
cana-511	96	14			PRON
cana-511	96	15	are	be	AUX
cana-511	96	16	compatible	compatible	ADJ
cana-511	96	17	.	.	PUNCT
cana-511	97	1	then	then	ADV
cana-511	97	2	&	&	CCONJ
cana-511	97	3			VERB
cana-511	97	4			PROPN
cana-511	97	5	have	have	VERB
cana-511	97	6	unique	unique	ADJ
cana-511	97	7	point	point	NOUN
cana-511	97	8	of	of	ADP
cana-511	97	9	coincidence	coincidence	NOUN
cana-511	97	10	.	.	PUNCT
cana-511	98	1	proof	proof	NOUN
cana-511	98	2	.	.	PUNCT
cana-511	99	1	firstly	firstly	ADV
cana-511	99	2	,	,	PUNCT
cana-511	99	3	we	we	PRON
cana-511	99	4	shall	shall	AUX
cana-511	99	5	show	show	VERB
cana-511	99	6	that	that	SCONJ
cana-511	99	7	the	the	DET
cana-511	99	8	point	point	NOUN
cana-511	99	9	of	of	ADP
cana-511	99	10	coincidence	coincidence	NOUN
cana-511	99	11	of	of	ADP
cana-511	99	12	&	&	CCONJ
cana-511	99	13			VERB
cana-511	99	14			PROPN
cana-511	99	15	,	,	PUNCT
cana-511	99	16	if	if	SCONJ
cana-511	99	17	exists	exist	NOUN
cana-511	99	18	is	be	AUX
cana-511	99	19	unique	unique	ADJ
cana-511	99	20	.	.	PUNCT
cana-511	100	1	let	let	VERB
cana-511	100	2	us	we	PRON
cana-511	100	3	suppose	suppose	VERB
cana-511	100	4	that	that	SCONJ
cana-511	100	5	1	1	NUM
cana-511	100	6	2	2	NUM
cana-511	100	7	 	 	SPACE
cana-511	100	8	&	&	CCONJ
cana-511	100	9	 	 	SPACE
cana-511	100	10	z	z	NOUN
cana-511	100	11	z	z	NOUN
cana-511	100	12	are	be	AUX
cana-511	100	13	distinct	distinct	ADJ
cana-511	100	14	points	point	NOUN
cana-511	100	15	of	of	ADP
cana-511	100	16	coincidence	coincidence	NOUN
cana-511	100	17	of	of	ADP
cana-511	100	18	&	&	CCONJ
cana-511	100	19			VERB
cana-511	100	20			PROPN
cana-511	100	21	which	which	PRON
cana-511	100	22	follows	follow	VERB
cana-511	100	23	that	that	SCONJ
cana-511	100	24	there	there	PRON
cana-511	100	25	exist	exist	VERB
cana-511	100	26	two	two	NUM
cana-511	100	27	points	point	NOUN
cana-511	100	28	(	(	PUNCT
cana-511	100	29	)	)	SYM
cana-511	100	30	1	1	NUM
cana-511	100	31	2	2	NUM
cana-511	100	32	1	1	NUM
cana-511	100	33	2	2	NUM
cana-511	100	34	 	 	SPACE
cana-511	100	35	&	&	CCONJ
cana-511	100	36	   	   	SPACE
cana-511	100	37	w	w	PROPN
cana-511	100	38	w	w	PROPN
cana-511	100	39	w	w	PROPN
cana-511	100	40	w=	w=	NOUN
cana-511	100	41	such	such	ADJ
cana-511	100	42	that	that	SCONJ
cana-511	100	43	1	1	NUM
cana-511	100	44	1	1	NUM
cana-511	100	45	1	1	NUM
cana-511	100	46	 	 	SPACE
cana-511	100	47	w	w	PROPN
cana-511	100	48	w	w	PROPN
cana-511	100	49	z	z	PROPN
cana-511	100	50	=	=	NOUN
cana-511	100	51	=	=	NOUN
cana-511	100	52	and	and	CCONJ
cana-511	100	53	2	2	NUM
cana-511	100	54	2	2	NUM
cana-511	100	55	2.w	2.w	NUM
cana-511	100	56	w	w	NOUN
cana-511	100	57	z	z	NOUN
cana-511	100	58	=	=	NOUN
cana-511	100	59	=	=	PUNCT
cana-511	100	60	in	in	ADP
cana-511	100	61	view	view	NOUN
cana-511	100	62	of	of	ADP
cana-511	100	63	(	(	PUNCT
cana-511	100	64	3.1	3.1	NUM
cana-511	100	65	)	)	PUNCT
cana-511	100	66	and	and	CCONJ
cana-511	100	67	the	the	DET
cana-511	100	68	property	property	NOUN
cana-511	100	69	of	of	ADP
cana-511	100	70	,	,	PUNCT
cana-511	100	71			VERB
cana-511	100	72	we	we	PRON
cana-511	100	73	obtain	obtain	VERB
cana-511	100	74	(	(	PUNCT
cana-511	100	75	)	)	PUNCT
cana-511	100	76	(	(	PUNCT
cana-511	100	77	)	)	PUNCT
cana-511	100	78	(	(	PUNCT
cana-511	100	79	)	)	PUNCT
cana-511	100	80	(	(	PUNCT
cana-511	100	81	)	)	PUNCT
cana-511	100	82	(	(	PUNCT
cana-511	100	83	)	)	SYM
cana-511	100	84	1	1	NUM
cana-511	100	85	2	2	NUM
cana-511	100	86	1	1	NUM
cana-511	100	87	2	2	NUM
cana-511	100	88	1	1	NUM
cana-511	100	89	2	2	NUM
cana-511	100	90	1	1	NUM
cana-511	100	91	2	2	NUM
cana-511	100	92	,	,	PUNCT
cana-511	100	93	,	,	PUNCT
cana-511	100	94	,	,	PUNCT
cana-511	100	95	,	,	PUNCT
cana-511	100	96	,	,	PUNCT
cana-511	100	97	,	,	PUNCT
cana-511	100	98	,	,	PUNCT
cana-511	100	99	,	,	PUNCT
cana-511	100	100	,	,	PUNCT
cana-511	100	101	z	z	NOUN
cana-511	100	102	z	z	NOUN
cana-511	101	1	t	t	PROPN
cana-511	101	2	w	w	PROPN
cana-511	101	3	w	w	PROPN
cana-511	101	4	t	t	PROPN
cana-511	101	5	w	w	PROPN
cana-511	101	6	w	w	PROPN
cana-511	101	7	t	t	PROPN
cana-511	101	8	w	w	PROPN
cana-511	101	9	w	w	PROPN
cana-511	101	10	t	t	NOUN
cana-511	101	11			VERB
cana-511	101	12			PROPN
cana-511	101	13			VERB
cana-511	101	14			X
cana-511	101	15			NUM
cana-511	101	16	=	=	NOUN
cana-511	101	17	m	m	NOUN
cana-511	101	18	m	m	VERB
cana-511	101	19	m	m	VERB
cana-511	101	20	m	m	VERB
cana-511	101	21	1	1	NUM
cana-511	101	22	2	2	NUM
cana-511	101	23	1	1	NUM
cana-511	101	24	2	2	NUM
cana-511	101	25	(	(	PUNCT
cana-511	101	26	)	)	PUNCT
cana-511	101	27	(	(	PUNCT
cana-511	101	28	)	)	PUNCT
cana-511	101	29	,	,	PUNCT
cana-511	101	30	,	,	PUNCT
cana-511	101	31	,	,	PUNCT
cana-511	101	32	,	,	PUNCT
cana-511	101	33	w	w	PROPN
cana-511	101	34	w	w	PROPN
cana-511	101	35	t	t	PROPN
cana-511	101	36	z	z	PROPN
cana-511	101	37	z	z	PROPN
cana-511	101	38	t	t	PRON
cana-511	102	1			PROPN
cana-511	103	1	=	=	PROPN
cana-511	103	2	m	m	VERB
cana-511	103	3	m	m	VERB
cana-511	103	4	(	(	PUNCT
cana-511	103	5	3.2	3.2	NUM
cana-511	103	6	)	)	PUNCT
cana-511	103	7	which	which	PRON
cana-511	103	8	is	be	AUX
cana-511	103	9	a	a	DET
cana-511	103	10	contradiction	contradiction	NOUN
cana-511	103	11	.	.	PUNCT
cana-511	104	1	let	let	VERB
cana-511	104	2	us	we	PRON
cana-511	104	3	consider	consider	VERB
cana-511	104	4	a	a	DET
cana-511	104	5	sequence	sequence	NOUN
cana-511	104	6	{	{	PUNCT
cana-511	104	7	 	 	SPACE
cana-511	104	8	}	}	PUNCT
cana-511	104	9	qy	qy	NOUN
cana-511	104	10	such	such	ADJ
cana-511	104	11	that	that	SCONJ
cana-511	104	12	1q	1q	NUM
cana-511	104	13	q	q	PROPN
cana-511	104	14	qy	qy	PROPN
cana-511	104	15	x	x	PROPN
cana-511	104	16	x	x	PROPN
cana-511	104	17			PROPN
cana-511	105	1	+	+	NOUN
cana-511	105	2	=	=	SYM
cana-511	105	3	=	=	SYM
cana-511	105	4	where	where	SCONJ
cana-511	105	5	{	{	PUNCT
cana-511	105	6	}	}	PUNCT
cana-511	105	7	0	0	NUM
cana-511	105	8	.q	.q	PROPN
cana-511	105	9	n	n	PROPN
cana-511	105	10	if	if	SCONJ
cana-511	105	11	0	0	NUM
cana-511	105	12	0	0	NUM
cana-511	105	13	1	1	NUM
cana-511	105	14	    	    	SPACE
cana-511	105	15	q	q	PROPN
cana-511	105	16	qy	qy	PROPN
cana-511	105	17	y	y	PROPN
cana-511	105	18	+	+	PROPN
cana-511	105	19	=	=	NOUN
cana-511	105	20	for	for	ADP
cana-511	105	21	any	any	DET
cana-511	105	22	0	0	NUM
cana-511	105	23	{	{	PUNCT
cana-511	105	24	    	    	SPACE
cana-511	105	25	}	}	PUNCT
cana-511	105	26	  	  	SPACE
cana-511	105	27	0	0	NUM
cana-511	105	28	,	,	PUNCT
cana-511	105	29	q	q	PROPN
cana-511	105	30	n	n	PROPN
cana-511	105	31			NOUN
cana-511	105	32	then	then	ADV
cana-511	105	33	0	0	NUM
cana-511	105	34	0	0	NUM
cana-511	105	35	0	0	NUM
cana-511	105	36	01	01	NUM
cana-511	105	37	l	l	NOUN
cana-511	105	38	  	  	SPACE
cana-511	105	39	1	1	NUM
cana-511	105	40	     	     	SPACE
cana-511	105	41	q	q	NOUN
cana-511	105	42	q	q	X
cana-511	105	43	q	q	X
cana-511	105	44	qx	qx	INTJ
cana-511	105	45	y	y	PROPN
cana-511	105	46	y	y	PROPN
cana-511	105	47	x	x	PROPN
cana-511	105	48	+	+	VERB
cana-511	105	49	+	+	PROPN
cana-511	105	50	=	=	SYM
cana-511	105	51	=	=	SYM
cana-511	106	1	+	+	PUNCT
cana-511	106	2	=	=	SYM
cana-511	106	3	which	which	PRON
cana-511	106	4	shows	show	VERB
cana-511	106	5	that	that	SCONJ
cana-511	106	6	&	&	CCONJ
cana-511	106	7			VERB
cana-511	106	8			PROPN
cana-511	106	9	have	have	VERB
cana-511	106	10	a	a	DET
cana-511	106	11	point	point	NOUN
cana-511	106	12	of	of	ADP
cana-511	106	13	coincidence	coincidence	NOUN
cana-511	106	14	.	.	PUNCT
cana-511	107	1	thus	thus	ADV
cana-511	107	2	,	,	PUNCT
cana-511	107	3	we	we	PRON
cana-511	107	4	assume	assume	VERB
cana-511	107	5	that	that	SCONJ
cana-511	107	6	1	1	NUM
cana-511	107	7	  	  	SPACE
cana-511	107	8	q	q	PROPN
cana-511	107	9	qy	qy	PROPN
cana-511	107	10	y	y	PROPN
cana-511	107	11	+	+	PROPN
cana-511	107	12	=	=	NOUN
cana-511	107	13	for	for	ADP
cana-511	107	14	all	all	DET
cana-511	107	15	    	    	SPACE
cana-511	107	16	0	0	NUM
cana-511	107	17	.	.	PUNCT
cana-511	107	18	{	{	PUNCT
cana-511	108	1	}	}	PUNCT
cana-511	108	2	q	q	PROPN
cana-511	108	3	n	n	PROPN
cana-511	108	4			NOUN
cana-511	108	5	consider	consider	VERB
cana-511	108	6	(	(	PUNCT
cana-511	108	7	)	)	PUNCT
cana-511	108	8	(	(	PUNCT
cana-511	108	9	)	)	PUNCT
cana-511	108	10	(	(	PUNCT
cana-511	108	11	)	)	PUNCT
cana-511	108	12	(	(	PUNCT
cana-511	108	13	)	)	PUNCT
cana-511	108	14	(	(	PUNCT
cana-511	108	15	)	)	PUNCT
cana-511	108	16	l	l	NOUN
cana-511	108	17	2	2	NUM
cana-511	108	18	l	l	NOUN
cana-511	108	19	2	2	NUM
cana-511	108	20	l	l	NOUN
cana-511	108	21	2	2	NUM
cana-511	108	22	1	1	NUM
cana-511	108	23	2	2	NUM
cana-511	108	24	,	,	PUNCT
cana-511	108	25	,	,	PUNCT
cana-511	108	26	,	,	PUNCT
cana-511	108	27	,	,	PUNCT
cana-511	108	28	,	,	PUNCT
cana-511	108	29	,	,	PUNCT
cana-511	108	30	,	,	PUNCT
cana-511	108	31	,	,	PUNCT
cana-511	108	32	,	,	PUNCT
cana-511	108	33	q	q	PRON
cana-511	108	34	q	q	X
cana-511	108	35	q	q	X
cana-511	108	36	q	q	X
cana-511	108	37	q	q	X
cana-511	108	38	q	q	X
cana-511	108	39	q	q	PROPN
cana-511	108	40	qy	qy	PROPN
cana-511	108	41	y	y	PROPN
cana-511	108	42	t	t	PROPN
cana-511	108	43	x	x	PUNCT
cana-511	109	1	x	x	X
cana-511	109	2	t	t	NOUN
cana-511	109	3	x	x	X
cana-511	109	4	x	x	X
cana-511	109	5	t	t	NOUN
cana-511	109	6	x	x	SYM
cana-511	109	7	x	x	SYM
cana-511	109	8	t	t	NOUN
cana-511	109	9			VERB
cana-511	109	10			NOUN
cana-511	109	11			VERB
cana-511	109	12			X
cana-511	109	13			PROPN
cana-511	109	14	+	+	PROPN
cana-511	110	1	+	+	CCONJ
cana-511	111	1	+	+	PUNCT
cana-511	112	1	+	+	PUNCT
cana-511	112	2	+	+	PUNCT
cana-511	112	3	+	+	PUNCT
cana-511	112	4	+	+	PUNCT
cana-511	112	5	+	+	ADJ
cana-511	112	6	=	=	AUX
cana-511	112	7	m	m	PROPN
cana-511	112	8	m	m	VERB
cana-511	112	9	m	m	VERB
cana-511	112	10	m	m	VERB
cana-511	112	11	1	1	NUM
cana-511	112	12	2	2	NUM
cana-511	112	13	)	)	PUNCT
cana-511	112	14	,	,	PUNCT
cana-511	112	15	(	(	PUNCT
cana-511	112	16	,	,	PUNCT
cana-511	112	17	q	q	PROPN
cana-511	112	18	qx	qx	PROPN
cana-511	112	19	x	x	PROPN
cana-511	112	20	t	t	PRON
cana-511	112	21	+	+	PROPN
cana-511	113	1	+	+	PROPN
cana-511	113	2			ADJ
cana-511	113	3	m	m	VERB
cana-511	113	4	(	(	PUNCT
cana-511	113	5	)	)	PUNCT
cana-511	113	6	l	l	NOUN
cana-511	113	7	,	,	PUNCT
cana-511	113	8	,	,	PUNCT
cana-511	113	9	 	 	SPACE
cana-511	113	10	q	q	PROPN
cana-511	113	11	qy	qy	PROPN
cana-511	113	12	y	y	PROPN
cana-511	113	13	t+=	t+=	PROPN
cana-511	113	14	m	m	PROPN
cana-511	113	15	(	(	PUNCT
cana-511	113	16	3.3	3.3	NUM
cana-511	113	17	)	)	PUNCT
cana-511	113	18	which	which	PRON
cana-511	113	19	gives	give	VERB
cana-511	113	20	(	(	PUNCT
cana-511	113	21	)	)	PUNCT
cana-511	113	22	(	(	PUNCT
cana-511	113	23	)	)	PUNCT
cana-511	113	24	l	l	NOUN
cana-511	113	25	l	l	NOUN
cana-511	113	26	2	2	NUM
cana-511	113	27	,	,	PUNCT
cana-511	113	28	,	,	PUNCT
cana-511	113	29	,	,	PUNCT
cana-511	113	30	,	,	PUNCT
cana-511	113	31	0.q	0.q	NUM
cana-511	113	32	q	q	X
cana-511	113	33	q	q	PROPN
cana-511	113	34	qy	qy	PROPN
cana-511	113	35	y	y	PROPN
cana-511	113	36	t	t	PROPN
cana-511	113	37	y	y	PROPN
cana-511	113	38	y	y	PROPN
cana-511	113	39	t	t	PROPN
cana-511	113	40	t+	t+	NOUN
cana-511	113	41	+	+	CCONJ
cana-511	113	42	+	+	ADJ
cana-511	113	43			PROPN
cana-511	113	44			VERB
cana-511	113	45	m	m	PROPN
cana-511	113	46	m	m	VERB
cana-511	113	47	if	if	SCONJ
cana-511	113	48	 	 	SPACE
cana-511	113	49	q	q	PROPN
cana-511	114	1	py	py	INTJ
cana-511	114	2	y=	y=	X
cana-511	114	3	for	for	ADP
cana-511	114	4	some	some	PRON
cana-511	114	5	,	,	PUNCT
cana-511	114	6	qp	qp	VERB
cana-511	114	7	then	then	ADV
cana-511	114	8	we	we	PRON
cana-511	114	9	have	have	VERB
cana-511	114	10	l	l	NOUN
cana-511	114	11	l	l	NOUN
cana-511	114	12	l	l	X
cana-511	114	13	l	l	NOUN
cana-511	114	14	      	      	SPACE
cana-511	114	15	.q	.q	PROPN
cana-511	115	1	q	q	PROPN
cana-511	116	1	p	p	X
cana-511	116	2	py	py	X
cana-511	116	3	x	x	PUNCT
cana-511	116	4	x	x	PROPN
cana-511	116	5	y	y	PROPN
cana-511	116	6	+	+	VERB
cana-511	116	7	+	+	PROPN
cana-511	117	1	+	+	PUNCT
cana-511	117	2	+	+	ADJ
cana-511	117	3	=	=	SYM
cana-511	117	4	=	=	SYM
cana-511	117	5	=	=	NOUN
cana-511	117	6	communications	communication	NOUN
cana-511	117	7	on	on	ADP
cana-511	117	8	applied	apply	VERB
cana-511	117	9	nonlinear	nonlinear	ADJ
cana-511	117	10	analysis	analysis	NOUN
cana-511	117	11	issn	issn	NOUN
cana-511	117	12	:	:	PUNCT
cana-511	117	13	1074	1074	NUM
cana-511	117	14	-	-	PUNCT
cana-511	117	15	133x	133x	NUM
cana-511	117	16	vol	vol	NOUN
cana-511	117	17	31	31	NUM
cana-511	117	18	no	no	NOUN
cana-511	117	19	.	.	NOUN
cana-511	117	20	2	2	NUM
cana-511	117	21	(	(	PUNCT
cana-511	117	22	2024	2024	NUM
cana-511	117	23	)	)	PUNCT
cana-511	117	24	38	38	NUM
cana-511	117	25	https://internationalpubls.com	https://internationalpubls.com	X
cana-511	117	26	now	now	ADV
cana-511	117	27	using	use	VERB
cana-511	117	28	(	(	PUNCT
cana-511	117	29	3.1	3.1	NUM
cana-511	117	30	)	)	PUNCT
cana-511	117	31	and	and	CCONJ
cana-511	117	32	(	(	PUNCT
cana-511	117	33	3.3	3.3	NUM
cana-511	117	34	)	)	PUNCT
cana-511	117	35	,	,	PUNCT
cana-511	117	36	one	one	PRON
cana-511	117	37	can	can	AUX
cana-511	117	38	get	get	VERB
cana-511	117	39	(	(	PUNCT
cana-511	117	40	)	)	PUNCT
cana-511	117	41	(	(	PUNCT
cana-511	117	42	)	)	PUNCT
cana-511	117	43	(	(	PUNCT
cana-511	117	44	)	)	PUNCT
cana-511	117	45	l	l	NOUN
cana-511	117	46	l	l	NOUN
cana-511	117	47	l	l	NOUN
cana-511	117	48	,	,	PUNCT
cana-511	117	49	,	,	PUNCT
cana-511	117	50	,	,	PUNCT
cana-511	117	51	,	,	PUNCT
cana-511	117	52	,	,	PUNCT
cana-511	117	53	,	,	PUNCT
cana-511	117	54	,	,	PUNCT
cana-511	117	55	0	0	X
cana-511	117	56	.	.	PUNCT
cana-511	117	57	(	(	PUNCT
cana-511	117	58	)	)	PUNCT
cana-511	117	59	q	q	NOUN
cana-511	117	60	q	q	X
cana-511	118	1	p	p	X
cana-511	118	2	p	p	X
cana-511	118	3	q	q	PROPN
cana-511	118	4	qy	qy	PROPN
cana-511	118	5	y	y	PROPN
cana-511	118	6	t	t	PROPN
cana-511	118	7	y	y	PROPN
cana-511	118	8	y	y	PROPN
cana-511	118	9	t	t	PROPN
cana-511	118	10	y	y	PROPN
cana-511	118	11	y	y	PROPN
cana-511	118	12	t	t	PROPN
cana-511	118	13	t+	t+	NOUN
cana-511	118	14	+	+	CCONJ
cana-511	118	15	+	+	ADJ
cana-511	118	16			PROPN
cana-511	118	17	=	=	PUNCT
cana-511	119	1			X
cana-511	119	2	m	m	PROPN
cana-511	119	3	m	m	VERB
cana-511	119	4	m	m	VERB
cana-511	119	5	m	m	VERB
cana-511	119	6	which	which	PRON
cana-511	119	7	is	be	AUX
cana-511	119	8	a	a	DET
cana-511	119	9	contradiction	contradiction	NOUN
cana-511	119	10	.	.	PUNCT
cana-511	120	1	thus	thus	ADV
cana-511	120	2	,	,	PUNCT
cana-511	120	3	we	we	PRON
cana-511	120	4	assume	assume	VERB
cana-511	120	5	that	that	SCONJ
cana-511	120	6	 	 	SPACE
cana-511	120	7	q	q	X
cana-511	120	8	py	py	INTJ
cana-511	120	9	y=	y=	X
cana-511	120	10	for	for	ADP
cana-511	120	11	all	all	DET
cana-511	120	12	distinct	distinct	ADJ
cana-511	120	13	,	,	PUNCT
cana-511	120	14	.q	.q	PROPN
cana-511	120	15	np	np	X
cana-511	121	1	now	now	ADV
cana-511	121	2	we	we	PRON
cana-511	121	3	prove	prove	VERB
cana-511	121	4	{	{	PUNCT
cana-511	121	5	}	}	PUNCT
cana-511	121	6	qy	qy	NOUN
cana-511	121	7	is	be	AUX
cana-511	121	8	a	a	DET
cana-511	121	9	cauchy	cauchy	ADJ
cana-511	121	10	sequence	sequence	NOUN
cana-511	121	11	:	:	PUNCT
cana-511	121	12	for	for	ADP
cana-511	121	13	0,t	0,t	PROPN
cana-511	121	14			INTJ
cana-511	121	15	let	let	VERB
cana-511	121	16	us	we	PRON
cana-511	121	17	suppose	suppose	VERB
cana-511	121	18	that	that	SCONJ
cana-511	121	19	(	(	PUNCT
cana-511	121	20	)	)	PUNCT
cana-511	121	21	,	,	PUNCT
cana-511	121	22	(	(	PUNCT
cana-511	121	23	)	)	PUNCT
cana-511	121	24	.,q	.,q	PUNCT
cana-511	122	1	p	p	X
cana-511	122	2	p	p	X
cana-511	122	3	p	p	X
cana-511	122	4	q	q	X
cana-511	122	5	a	a	DET
cana-511	122	6	t	t	NOUN
cana-511	122	7	inf	inf	NOUN
cana-511	122	8	y	y	PROPN
cana-511	122	9	y	y	PROPN
cana-511	122	10	t	t	PROPN
cana-511	122	11			X
cana-511	122	12	=	=	PUNCT
cana-511	122	13	m	m	AUX
cana-511	122	14	consider	consider	VERB
cana-511	122	15	(	(	PUNCT
cana-511	122	16	)	)	PUNCT
cana-511	122	17	l	l	NOUN
cana-511	122	18	l	l	NOUN
cana-511	122	19	l	l	X
cana-511	122	20	l	l	NOUN
cana-511	122	21	(	(	PUNCT
cana-511	122	22	)	)	PUNCT
cana-511	122	23	,	,	PUNCT
cana-511	122	24	,	,	PUNCT
cana-511	122	25	,	,	PUNCT
cana-511	122	26	,	,	PUNCT
cana-511	122	27	q	q	PROPN
cana-511	122	28	p	p	X
cana-511	122	29	q	q	X
cana-511	122	30	py	py	INTJ
cana-511	122	31	y	y	PROPN
cana-511	122	32	t	t	PROPN
cana-511	122	33	x	x	PUNCT
cana-511	122	34	x	x	X
cana-511	122	35	t	t	NOUN
cana-511	122	36	+	+	VERB
cana-511	122	37	+	+	CCONJ
cana-511	123	1	+	+	PUNCT
cana-511	123	2	+	+	NOUN
cana-511	123	3	=	=	NOUN
cana-511	123	4	m	m	VERB
cana-511	123	5	m	m	VERB
cana-511	123	6	(	(	PUNCT
cana-511	124	1	)	)	PUNCT
cana-511	124	2	(	(	PUNCT
cana-511	124	3	)	)	PUNCT
cana-511	124	4	(	(	PUNCT
cana-511	124	5	)	)	PUNCT
cana-511	124	6	l	l	NOUN
cana-511	124	7	l	l	NOUN
cana-511	124	8	l	l	NOUN
cana-511	124	9	l	l	NOUN
cana-511	124	10	,	,	PUNCT
cana-511	124	11	,	,	PUNCT
cana-511	124	12	,	,	PUNCT
cana-511	124	13	,	,	PUNCT
cana-511	124	14	,	,	PUNCT
cana-511	124	15	q	q	X
cana-511	125	1	p	p	X
cana-511	125	2	q	q	X
cana-511	125	3	px	px	X
cana-511	125	4	x	x	X
cana-511	125	5	t	t	NOUN
cana-511	125	6	x	x	PUNCT
cana-511	125	7	x	x	X
cana-511	125	8	t	t	NOUN
cana-511	125	9			VERB
cana-511	125	10			X
cana-511	125	11			PROPN
cana-511	125	12	+	+	PROPN
cana-511	126	1	+	+	CCONJ
cana-511	127	1	+	+	PUNCT
cana-511	128	1	+	+	NOUN
cana-511	128	2			X
cana-511	128	3	m	m	VERB
cana-511	128	4	m	m	VERB
cana-511	128	5	(	(	PUNCT
cana-511	128	6	)	)	PUNCT
cana-511	128	7	l	l	NOUN
cana-511	128	8	l	l	NOUN
cana-511	128	9	,	,	PUNCT
cana-511	128	10	,	,	PUNCT
cana-511	128	11	,	,	PUNCT
cana-511	128	12	,	,	PUNCT
cana-511	128	13	,	,	PUNCT
cana-511	128	14	0	0	X
cana-511	128	15	.	.	PUNCT
cana-511	128	16	(	(	PUNCT
cana-511	128	17	)	)	PUNCT
cana-511	128	18	q	q	PROPN
cana-511	129	1	p	p	X
cana-511	129	2	q	q	X
cana-511	129	3	px	px	X
cana-511	129	4	x	x	PROPN
cana-511	129	5	t	t	PROPN
cana-511	129	6	y	y	PROPN
cana-511	129	7	y	y	PROPN
cana-511	129	8	t	t	PROPN
cana-511	129	9	t	t	PRON
cana-511	129	10	+	+	PROPN
cana-511	130	1	+	+	PROPN
cana-511	130	2			X
cana-511	130	3	=	=	PUNCT
cana-511	130	4			PROPN
cana-511	130	5	m	m	PROPN
cana-511	130	6	m	m	PROPN
cana-511	130	7	(	(	PUNCT
cana-511	130	8	3.4	3.4	NUM
cana-511	130	9	)	)	PUNCT
cana-511	130	10	thus	thus	ADV
cana-511	130	11	,	,	PUNCT
cana-511	130	12	(	(	PUNCT
cana-511	130	13	)	)	PUNCT
cana-511	130	14	(	(	PUNCT
cana-511	130	15	)	)	PUNCT
cana-511	130	16	l	l	NOUN
cana-511	130	17	l	l	NOUN
cana-511	130	18	,	,	PUNCT
cana-511	130	19	.	.	PUNCT
cana-511	130	20	,	,	PUNCT
cana-511	130	21	,	,	PUNCT
cana-511	130	22	,	,	PUNCT
cana-511	130	23	,	,	PUNCT
cana-511	130	24	q	q	PROPN
cana-511	130	25	p	p	X
cana-511	130	26	q	q	X
cana-511	130	27	py	py	INTJ
cana-511	130	28	y	y	PROPN
cana-511	130	29	t	t	PROPN
cana-511	130	30	y	y	PROPN
cana-511	130	31	y	y	PROPN
cana-511	130	32	qt	qt	PROPN
cana-511	130	33	p+	p+	PROPN
cana-511	130	34	+	+	X
cana-511	131	1			PROPN
cana-511	131	2	m	m	AUX
cana-511	131	3	m	m	AUX
cana-511	131	4	taking	take	VERB
cana-511	131	5	infimum	infimum	ADV
cana-511	131	6	over	over	ADP
cana-511	131	7	all	all	PRON
cana-511	131	8	(	(	PUNCT
cana-511	131	9	)	)	PUNCT
cana-511	131	10	qp	qp	ADJ
cana-511	131	11	in	in	ADP
cana-511	131	12	the	the	DET
cana-511	131	13	above	above	ADJ
cana-511	131	14	inequality	inequality	NOUN
cana-511	131	15	,	,	PUNCT
cana-511	131	16	we	we	PRON
cana-511	131	17	get	get	VERB
cana-511	131	18	(	(	PUNCT
cana-511	131	19	)	)	PUNCT
cana-511	131	20	l	l	NOUN
cana-511	131	21	l	l	NOUN
cana-511	131	22	)	)	PUNCT
cana-511	131	23	inf	inf	NOUN
cana-511	131	24	,	,	PUNCT
cana-511	131	25	,	,	PUNCT
cana-511	131	26	 	 	SPACE
cana-511	131	27	inf	inf	NOUN
cana-511	131	28	,	,	PUNCT
cana-511	131	29	,	,	PUNCT
cana-511	131	30	(	(	PUNCT
cana-511	131	31	q	q	X
cana-511	131	32	p	p	X
cana-511	131	33	q	q	X
cana-511	131	34	p	p	X
cana-511	131	35	p	p	X
cana-511	131	36	q	q	X
cana-511	131	37	p	p	X
cana-511	131	38	q	q	X
cana-511	131	39	y	y	PROPN
cana-511	131	40	y	y	PROPN
cana-511	131	41	t	t	PROPN
cana-511	132	1	y	y	PROPN
cana-511	132	2	y	y	PROPN
cana-511	132	3	t+	t+	PUNCT
cana-511	132	4	+	+	CCONJ
cana-511	132	5			INTJ
cana-511	132	6			VERB
cana-511	132	7	m	m	PROPN
cana-511	132	8	m	m	VERB
cana-511	132	9	(	(	PUNCT
cana-511	132	10	)	)	PUNCT
cana-511	132	11	(	(	PUNCT
cana-511	132	12	)	)	PUNCT
cana-511	132	13	l.	l.	PROPN
cana-511	132	14	.	.	PUNCT
cana-511	133	1	,	,	PUNCT
cana-511	133	2	      	      	SPACE
cana-511	133	3	.,q	.,q	PUNCT
cana-511	134	1	qi	qi	PROPN
cana-511	134	2	e	e	PROPN
cana-511	134	3	a	a	PROPN
cana-511	134	4	t	t	NOUN
cana-511	134	5	a	a	DET
cana-511	134	6	t	t	PROPN
cana-511	134	7	q	q	X
cana-511	134	8	n+	n+	PROPN
cana-511	134	9			VERB
cana-511	134	10			NOUN
cana-511	134	11	thus	thus	ADV
cana-511	134	12	,	,	PUNCT
cana-511	134	13	(	(	PUNCT
cana-511	134	14	)	)	PUNCT
cana-511	134	15			PROPN
cana-511	134	16	qa	qa	PROPN
cana-511	134	17	t	t	NOUN
cana-511	134	18	is	be	AUX
cana-511	134	19	monotonic	monotonic	ADJ
cana-511	134	20	and	and	CCONJ
cana-511	134	21	bounded	bound	VERB
cana-511	134	22	for	for	ADP
cana-511	134	23	each	each	DET
cana-511	134	24	0.t	0.t	NUM
cana-511	135	1			INTJ
cana-511	135	2	we	we	PRON
cana-511	135	3	prove	prove	VERB
cana-511	135	4	(	(	PUNCT
cana-511	135	5	)	)	PUNCT
cana-511	136	1	0lim	0lim	NUM
cana-511	137	1	l	l	NOUN
cana-511	137	2	,	,	PUNCT
cana-511	137	3	q	q	NOUN
cana-511	137	4	q	q	NOUN
cana-511	137	5	a	a	DET
cana-511	137	6	t	t	NOUN
cana-511	137	7	t	t	NOUN
cana-511	137	8	→	→	PUNCT
cana-511	137	9	=	=	NOUN
cana-511	137	10			VERB
cana-511	137	11			PROPN
cana-511	137	12	.	.	PUNCT
cana-511	138	1	on	on	ADP
cana-511	138	2	the	the	DET
cana-511	138	3	contrary	contrary	NOUN
cana-511	138	4	,	,	PUNCT
cana-511	138	5	let	let	VERB
cana-511	138	6	us	we	PRON
cana-511	138	7	suppose	suppose	VERB
cana-511	138	8	that	that	SCONJ
cana-511	138	9			NUM
cana-511	138	10	some	some	DET
cana-511	138	11	0	0	NUM
cana-511	138	12	t	t	NOUN
cana-511	138	13	,	,	PUNCT
cana-511	138	14	where	where	SCONJ
cana-511	138	15	00	00	NUM
cana-511	138	16	t	t	PROPN
cana-511	139	1	t	t	PROPN
cana-511	139	2			PROPN
cana-511	139	3	such	such	ADJ
cana-511	139	4	that	that	PRON
cana-511	139	5	(	(	PUNCT
cana-511	139	6	)	)	PUNCT
cana-511	139	7	(	(	PUNCT
cana-511	139	8	)	)	PUNCT
cana-511	139	9	0	0	X
cana-511	140	1	0lim	0lim	NUM
cana-511	141	1	l.q	l.q	VERB
cana-511	141	2	q	q	NOUN
cana-511	141	3	a	a	PROPN
cana-511	141	4	t	t	NOUN
cana-511	141	5	a	a	DET
cana-511	141	6	t	t	NOUN
cana-511	141	7	→	→	PUNCT
cana-511	142	1	=	=	NOUN
cana-511	142	2			PROPN
cana-511	142	3	for	for	ADP
cana-511	142	4	such	such	ADJ
cana-511	142	5	0	0	NUM
cana-511	142	6	t	t	NOUN
cana-511	142	7	,	,	PUNCT
cana-511	142	8	using	use	VERB
cana-511	142	9	the	the	DET
cana-511	142	10	fact	fact	NOUN
cana-511	142	11	that	that	SCONJ
cana-511	142	12	the	the	DET
cana-511	142	13	quadruple	quadruple	NOUN
cana-511	142	14	(	(	PUNCT
cana-511	142	15	)	)	PUNCT
cana-511	142	16	,	,	PUNCT
cana-511	142	17	,	,	PUNCT
cana-511	142	18	,	,	PUNCT
cana-511	142	19	x	x	PUNCT
cana-511	142	20			VERB
cana-511	142	21	m	m	NOUN
cana-511	142	22	have	have	VERB
cana-511	142	23	the	the	DET
cana-511	142	24	property	property	NOUN
cana-511	142	25	(	(	PUNCT
cana-511	142	26	)	)	PUNCT
cana-511	142	27	s	s	PART
cana-511	142	28	(	(	PUNCT
cana-511	142	29	)	)	PUNCT
cana-511	142	30	(	(	PUNCT
cana-511	142	31	)	)	PUNCT
cana-511	142	32	since	since	SCONJ
cana-511	142	33	  	  	SPACE
cana-511	142	34	,	,	PUNCT
cana-511	142	35	q	q	PROPN
cana-511	142	36	qy	qy	NOUN
cana-511	142	37	q	q	NOUN
cana-511	142	38	x=	x=	PROPN
cana-511	143	1	=	=	PUNCT
cana-511	143	2	we	we	PRON
cana-511	143	3	obtain	obtain	VERB
cana-511	143	4	(	(	PUNCT
cana-511	143	5	)	)	PUNCT
cana-511	143	6	(	(	PUNCT
cana-511	143	7	)	)	PUNCT
cana-511	143	8	(	(	PUNCT
cana-511	143	9	)	)	PUNCT
cana-511	143	10	l	l	NOUN
cana-511	143	11	l	l	NOUN
cana-511	143	12	0	0	NUM
cana-511	143	13	0liminf	0liminf	NUM
cana-511	143	14	,	,	PUNCT
cana-511	143	15	,	,	PUNCT
cana-511	143	16	,	,	PUNCT
cana-511	143	17	,	,	PUNCT
cana-511	143	18	,	,	PUNCT
cana-511	143	19	l	l	NOUN
cana-511	143	20	 	 	SPACE
cana-511	143	21	q	q	PROPN
cana-511	143	22	p	p	X
cana-511	143	23	q	q	X
cana-511	143	24	p	p	X
cana-511	143	25	q	q	X
cana-511	143	26	p	p	X
cana-511	143	27	q	q	X
cana-511	143	28	y	y	PROPN
cana-511	144	1	y	y	PROPN
cana-511	145	1	t	t	PROPN
cana-511	146	1	y	y	PROPN
cana-511	146	2	y	y	PROPN
cana-511	146	3	t	t	VERB
cana-511	146	4	+	+	CCONJ
cana-511	147	1	+	+	CCONJ
cana-511	147	2	→	→	NOUN
cana-511	147	3			VERB
cana-511	147	4	=	=	NOUN
cana-511	147	5	m	m	VERB
cana-511	147	6	m	m	VERB
cana-511	147	7	(	(	PUNCT
cana-511	147	8	)	)	PUNCT
cana-511	147	9	  	  	SPACE
cana-511	147	10	3.5	3.5	NUM
cana-511	147	11	(	(	PUNCT
cana-511	147	12	)	)	PUNCT
cana-511	147	13	(	(	PUNCT
cana-511	147	14	)	)	PUNCT
cana-511	147	15	(	(	PUNCT
cana-511	147	16	)	)	PUNCT
cana-511	147	17	(	(	PUNCT
cana-511	147	18	)	)	PUNCT
cana-511	147	19	(	(	PUNCT
cana-511	147	20	)	)	PUNCT
cana-511	147	21	l	l	NOUN
cana-511	147	22	l	l	NOUN
cana-511	147	23	0	0	PUNCT
cana-511	147	24	l	l	NOUN
cana-511	147	25	l	l	NOUN
cana-511	147	26	0	0	PUNCT
cana-511	147	27	l	l	NOUN
cana-511	147	28	l	l	NOUN
cana-511	147	29	0	0	PUNCT
cana-511	147	30	0inf	0inf	NOUN
cana-511	147	31	,	,	PUNCT
cana-511	147	32	,	,	PUNCT
cana-511	147	33	 	 	SPACE
cana-511	147	34	inf	inf	NOUN
cana-511	147	35	,	,	PUNCT
cana-511	147	36	  	  	SPACE
cana-511	147	37	,	,	PUNCT
cana-511	147	38	  	  	SPACE
cana-511	147	39	,	,	PUNCT
cana-511	147	40	,	,	PUNCT
cana-511	147	41	,	,	PUNCT
cana-511	147	42	,	,	PUNCT
cana-511	147	43	,	,	PUNCT
cana-511	147	44	q	q	PROPN
cana-511	147	45	p	p	X
cana-511	147	46	q	q	X
cana-511	147	47	p	p	X
cana-511	147	48	q	q	X
cana-511	147	49	p	p	X
cana-511	147	50	p	p	X
cana-511	147	51	q	q	NOUN
cana-511	147	52	q	q	X
cana-511	147	53	p	p	X
cana-511	147	54	p	p	X
cana-511	147	55	q	q	X
cana-511	147	56	p	p	X
cana-511	147	57	q	q	X
cana-511	147	58	y	y	PROPN
cana-511	147	59	y	y	PROPN
cana-511	147	60	t	t	PROPN
cana-511	147	61	x	x	PUNCT
cana-511	148	1	x	x	X
cana-511	148	2	t	t	NOUN
cana-511	148	3	x	x	PUNCT
cana-511	148	4	x	x	SYM
cana-511	148	5	t	t	PROPN
cana-511	148	6	y	y	PROPN
cana-511	148	7	y	y	PROPN
cana-511	148	8	t	t	NOUN
cana-511	148	9			VERB
cana-511	148	10			VERB
cana-511	148	11			PRON
cana-511	148	12			ADV
cana-511	148	13	+	+	VERB
cana-511	148	14	+	+	PUNCT
cana-511	149	1	+	+	PUNCT
cana-511	149	2	+	+	PUNCT
cana-511	149	3	+	+	CCONJ
cana-511	149	4	+	+	CCONJ
cana-511	149	5			PROPN
cana-511	149	6			PROPN
cana-511	149	7			PROPN
cana-511	149	8			PROPN
cana-511	149	9	mm	mm	PROPN
cana-511	149	10	m	m	VERB
cana-511	149	11	m	m	VERB
cana-511	149	12	(	(	PUNCT
cana-511	149	13	)	)	PUNCT
cana-511	149	14	(	(	PUNCT
cana-511	149	15	)	)	PUNCT
cana-511	149	16	(	(	PUNCT
cana-511	149	17	)	)	PUNCT
cana-511	149	18	(	(	PUNCT
cana-511	149	19	)	)	PUNCT
cana-511	149	20	(	(	PUNCT
cana-511	149	21	)	)	PUNCT
cana-511	149	22	l	l	NOUN
cana-511	149	23	l	l	NOUN
cana-511	149	24	0	0	PUNCT
cana-511	149	25	l	l	NOUN
cana-511	149	26	l	l	NOUN
cana-511	149	27	0	0	NUM
cana-511	149	28	0	0	SYM
cana-511	149	29	0	0	NUM
cana-511	149	30	  	  	SPACE
cana-511	149	31	inf	inf	NOUN
cana-511	149	32	,	,	PUNCT
cana-511	149	33	,	,	PUNCT
cana-511	149	34	  	  	SPACE
cana-511	149	35	inf	inf	NOUN
cana-511	149	36	,	,	PUNCT
cana-511	149	37	,	,	PUNCT
cana-511	149	38	,	,	PUNCT
cana-511	149	39	,	,	PUNCT
cana-511	149	40	,	,	PUNCT
cana-511	149	41	 	 	SPACE
cana-511	149	42	inf	inf	NOUN
cana-511	149	43	,	,	PUNCT
cana-511	149	44	,	,	PUNCT
cana-511	149	45	q	q	PROPN
cana-511	149	46	p	p	X
cana-511	149	47	q	q	X
cana-511	149	48	p	p	X
cana-511	149	49	q	q	X
cana-511	149	50	p	p	NOUN
cana-511	149	51	q	q	X
cana-511	149	52	p	p	X
cana-511	149	53	p	p	X
cana-511	149	54	q	q	X
cana-511	149	55	p	p	X
cana-511	149	56	q	q	X
cana-511	149	57	p	p	X
cana-511	149	58	q	q	X
cana-511	149	59	y	y	PROPN
cana-511	149	60	y	y	PROPN
cana-511	149	61	t	t	PROPN
cana-511	150	1	y	y	PROPN
cana-511	150	2	y	y	PROPN
cana-511	150	3	t	t	PROPN
cana-511	150	4	y	y	PROPN
cana-511	150	5	y	y	PROPN
cana-511	150	6	t	t	PROPN
cana-511	150	7	y	y	PROPN
cana-511	150	8	y	y	PROPN
cana-511	150	9	t+	t+	PROPN
cana-511	150	10	+	+	CCONJ
cana-511	150	11	+	+	PUNCT
cana-511	150	12	+	+	CCONJ
cana-511	150	13			PROPN
cana-511	150	14			PROPN
cana-511	151	1			PROPN
cana-511	151	2			PROPN
cana-511	151	3			PROPN
cana-511	152	1	mmm	mmm	PROPN
cana-511	152	2	m	m	PROPN
cana-511	152	3	(	(	PUNCT
cana-511	152	4	)	)	PUNCT
cana-511	152	5	(	(	PUNCT
cana-511	152	6	)	)	PUNCT
cana-511	152	7	(	(	PUNCT
cana-511	152	8	)	)	PUNCT
cana-511	152	9	(	(	PUNCT
cana-511	152	10	)	)	PUNCT
cana-511	152	11	l	l	NOUN
cana-511	152	12	0	0	NUM
cana-511	152	13	l	l	NOUN
cana-511	152	14	l	l	NOUN
cana-511	152	15	0	0	NUM
cana-511	152	16	0	0	NUM
cana-511	152	17	0	0	NUM
cana-511	152	18	.	.	PUNCT
cana-511	152	19	.	.	PUNCT
cana-511	152	20	,	,	PUNCT
cana-511	152	21	  	  	SPACE
cana-511	152	22	inf	inf	NOUN
cana-511	152	23	,	,	PUNCT
cana-511	152	24	,	,	PUNCT
cana-511	152	25	,	,	PUNCT
cana-511	152	26	,	,	PUNCT
cana-511	152	27	)	)	PUNCT
cana-511	152	28	 	 	SPACE
cana-511	153	1	(	(	PUNCT
cana-511	153	2	,	,	PUNCT
cana-511	153	3	q	q	NOUN
cana-511	153	4	q	q	X
cana-511	153	5	p	p	X
cana-511	153	6	q	q	X
cana-511	153	7	p	p	X
cana-511	153	8	q	q	X
cana-511	153	9	p	p	X
cana-511	153	10	q	q	X
cana-511	154	1	i	i	NOUN
cana-511	154	2	e	e	PROPN
cana-511	154	3	a	a	DET
cana-511	154	4	t	t	X
cana-511	155	1	y	y	PROPN
cana-511	155	2	y	y	PROPN
cana-511	155	3	t	t	PROPN
cana-511	155	4	y	y	PROPN
cana-511	155	5	y	y	PROPN
cana-511	155	6	t	t	PROPN
cana-511	155	7	a	a	DET
cana-511	155	8	t+	t+	PROPN
cana-511	155	9	+	+	CCONJ
cana-511	155	10	+	+	CCONJ
cana-511	155	11			ADJ
cana-511	155	12			PROPN
cana-511	155	13	mm	mm	PROPN
cana-511	155	14	letting	let	VERB
cana-511	155	15	   	   	SPACE
cana-511	155	16	q→	q→	NOUN
cana-511	155	17	in	in	ADP
cana-511	155	18	the	the	DET
cana-511	155	19	above	above	ADJ
cana-511	155	20	inequality	inequality	NOUN
cana-511	155	21	and	and	CCONJ
cana-511	155	22	using	use	VERB
cana-511	155	23	(	(	PUNCT
cana-511	155	24	3.5	3.5	NUM
cana-511	155	25	)	)	PUNCT
cana-511	155	26	,	,	PUNCT
cana-511	155	27	we	we	PRON
cana-511	155	28	get	get	VERB
cana-511	155	29	(	(	PUNCT
cana-511	155	30	)	)	PUNCT
cana-511	155	31	0	0	PUNCT
cana-511	156	1	la	la	PROPN
cana-511	156	2	t	t	PROPN
cana-511	156	3	=	=	PUNCT
cana-511	156	4	which	which	PRON
cana-511	156	5	is	be	AUX
cana-511	156	6	a	a	DET
cana-511	156	7	contradiction	contradiction	NOUN
cana-511	156	8	to	to	ADP
cana-511	156	9	our	our	PRON
cana-511	156	10	assumption	assumption	NOUN
cana-511	156	11	.	.	PUNCT
cana-511	157	1	thus	thus	ADV
cana-511	157	2	,	,	PUNCT
cana-511	157	3	1iminf	1iminf	NUM
cana-511	157	4	,	,	PUNCT
cana-511	157	5	,	,	PUNCT
cana-511	157	6	l	l	NOUN
cana-511	157	7	,	,	PUNCT
cana-511	157	8	0	0	NUM
cana-511	157	9	.	.	PUNCT
cana-511	157	10	(	(	PUNCT
cana-511	157	11	)	)	PUNCT
cana-511	157	12	q	q	PROPN
cana-511	158	1	p	p	X
cana-511	158	2	q	q	X
cana-511	158	3	p	p	X
cana-511	158	4	q	q	X
cana-511	158	5	y	y	PROPN
cana-511	158	6	y	y	PROPN
cana-511	158	7	t	t	PROPN
cana-511	158	8	t	t	PROPN
cana-511	158	9	→	→	PUNCT
cana-511	158	10			PRON
cana-511	158	11	=	=	PUNCT
cana-511	158	12			ADJ
cana-511	158	13	m	m	PROPN
cana-511	158	14	hence	hence	ADV
cana-511	158	15	from	from	ADP
cana-511	158	16	the	the	DET
cana-511	158	17	definition	definition	NOUN
cana-511	158	18	of	of	ADP
cana-511	158	19	,	,	PUNCT
cana-511	158	20	qa	qa	PROPN
cana-511	158	21	we	we	PRON
cana-511	158	22	get	get	VERB
cana-511	158	23	,	,	PUNCT
cana-511	158	24	1im	1im	ADJ
cana-511	158	25	,	,	PUNCT
cana-511	158	26	,	,	PUNCT
cana-511	158	27	l	l	NOUN
cana-511	158	28	,	,	PUNCT
cana-511	158	29	0	0	NUM
cana-511	158	30	.	.	PUNCT
cana-511	158	31	 	 	SPACE
cana-511	158	32	(	(	PUNCT
cana-511	158	33	)	)	PUNCT
cana-511	158	34	q	q	PROPN
cana-511	159	1	p	p	X
cana-511	159	2	p	p	X
cana-511	159	3	q	q	X
cana-511	159	4	y	y	PROPN
cana-511	159	5	y	y	PROPN
cana-511	159	6	t	t	PROPN
cana-511	159	7	t	t	PROPN
cana-511	159	8	→	→	PUNCT
cana-511	159	9	=	=	NOUN
cana-511	160	1			VERB
cana-511	160	2	m	m	PROPN
cana-511	160	3	(	(	PUNCT
cana-511	160	4	3.6	3.6	NUM
cana-511	160	5	)	)	PUNCT
cana-511	160	6	which	which	PRON
cana-511	160	7	shows	show	VERB
cana-511	160	8	{	{	PUNCT
cana-511	160	9	 	 	SPACE
cana-511	160	10	}	}	PUNCT
cana-511	160	11	qy	qy	NOUN
cana-511	160	12	is	be	AUX
cana-511	160	13	an	an	DET
cana-511	160	14	−m	−m	ADJ
cana-511	160	15	cauchy	cauchy	ADJ
cana-511	160	16	sequence	sequence	NOUN
cana-511	160	17	.	.	PUNCT
cana-511	161	1	suppose	suppose	VERB
cana-511	161	2	that	that	SCONJ
cana-511	161	3	(	(	PUNCT
cana-511	161	4	i	i	NOUN
cana-511	161	5	)	)	PUNCT
cana-511	161	6	holds	hold	VERB
cana-511	161	7	:	:	PUNCT
cana-511	161	8	(	(	PUNCT
cana-511	161	9	)	)	PUNCT
cana-511	161	10	.	.	PUNCT
cana-511	162	1	.	.	PUNCT
cana-511	162	2	,	,	PUNCT
cana-511	162	3	 	 	SPACE
cana-511	162	4	i	i	PRON
cana-511	162	5	e	e	PROPN
cana-511	162	6	x	x	PROPN
cana-511	162	7	is	be	AUX
cana-511	162	8	complete	complete	ADJ
cana-511	162	9	.	.	PUNCT
cana-511	163	1	communications	communication	NOUN
cana-511	163	2	on	on	ADP
cana-511	163	3	applied	apply	VERB
cana-511	163	4	nonlinear	nonlinear	ADJ
cana-511	163	5	analysis	analysis	NOUN
cana-511	163	6	issn	issn	NOUN
cana-511	163	7	:	:	PUNCT
cana-511	163	8	1074	1074	NUM
cana-511	163	9	-	-	PUNCT
cana-511	163	10	133x	133x	NUM
cana-511	163	11	vol	vol	NOUN
cana-511	163	12	31	31	NUM
cana-511	163	13	no	no	NOUN
cana-511	163	14	.	.	NOUN
cana-511	163	15	2	2	NUM
cana-511	163	16	(	(	PUNCT
cana-511	163	17	2024	2024	NUM
cana-511	163	18	)	)	PUNCT
cana-511	163	19	39	39	NUM
cana-511	163	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-511	163	21	then	then	ADV
cana-511	163	22	since	since	SCONJ
cana-511	163	23	{	{	PUNCT
cana-511	163	24	 	 	SPACE
cana-511	163	25	}	}	PUNCT
cana-511	163	26	qy	qy	NOUN
cana-511	163	27	is	be	AUX
cana-511	163	28	in	in	ADP
cana-511	163	29	(	(	PUNCT
cana-511	163	30	)	)	PUNCT
cana-511	163	31	,	,	PUNCT
cana-511	163	32	 	 	SPACE
cana-511	163	33	x	x	VERB
cana-511	164	1	it	it	PRON
cana-511	164	2	has	have	VERB
cana-511	164	3	a	a	DET
cana-511	164	4	limit	limit	NOUN
cana-511	164	5	in	in	ADP
cana-511	164	6	(	(	PUNCT
cana-511	164	7	)	)	PUNCT
cana-511	164	8	.x	.x	PUNCT
cana-511	164	9	let	let	VERB
cana-511	164	10	    	    	SPACE
cana-511	164	11	.	.	PUNCT
cana-511	165	1	.	.	PUNCT
cana-511	165	2	,	,	PUNCT
cana-511	165	3	   	   	SPACE
cana-511	165	4	q	q	PROPN
cana-511	166	1	qy	qy	NOUN
cana-511	166	2	u	u	NOUN
cana-511	166	3	i	i	NOUN
cana-511	166	4	e	e	VERB
cana-511	166	5	x	x	X
cana-511	166	6	u	u	ADJ
cana-511	166	7			NUM
cana-511	166	8	→	→	PROPN
cana-511	166	9	→	→	PUNCT
cana-511	166	10	as	as	ADP
cana-511	166	11	 	 	SPACE
cana-511	166	12	q→	q→	NOUN
cana-511	166	13	for	for	ADP
cana-511	166	14	.	.	PUNCT
cana-511	166	15	 	 	SPACE
cana-511	167	1	u	u	PRON
cana-511	167	2	x	x	PROPN
cana-511	167	3	now	now	ADV
cana-511	167	4	,	,	PUNCT
cana-511	167	5	we	we	PRON
cana-511	167	6	shall	shall	AUX
cana-511	167	7	prove	prove	VERB
cana-511	167	8	that	that	SCONJ
cana-511	167	9	u	u	NOUN
cana-511	167	10	is	be	AUX
cana-511	167	11	the	the	DET
cana-511	167	12	coincidence	coincidence	NOUN
cana-511	167	13	point	point	NOUN
cana-511	167	14	of	of	ADP
cana-511	167	15	and	and	CCONJ
cana-511	167	16	.	.	PUNCT
cana-511	167	17	.	.	PUNCT
cana-511	167	18	,	,	PUNCT
cana-511	167	19	.i	.i	X
cana-511	168	1	e	e	X
cana-511	168	2	u	u	PROPN
cana-511	168	3	u	u	VERB
cana-511	168	4			PROPN
cana-511	168	5			VERB
cana-511	168	6	=	=	NOUN
cana-511	168	7	it	it	PRON
cana-511	168	8	is	be	AUX
cana-511	168	9	clear	clear	ADJ
cana-511	168	10	that	that	SCONJ
cana-511	168	11	,	,	PUNCT
cana-511	168	12	we	we	PRON
cana-511	168	13	can	can	AUX
cana-511	168	14	suppose	suppose	VERB
cana-511	168	15	,	,	PUNCT
cana-511	168	16	qy	qy	PROPN
cana-511	168	17	u	u	PROPN
cana-511	168	18	u	u	ADJ
cana-511	168	19			PROPN
cana-511	168	20	for	for	ADP
cana-511	168	21	all	all	DET
cana-511	168	22	}	}	PUNCT
cana-511	168	23	0{n	0{n	NUM
cana-511	168	24	n	n	PROPN
cana-511	168	25	.	.	PUNCT
cana-511	169	1	in	in	ADP
cana-511	169	2	view	view	NOUN
cana-511	169	3	of	of	ADP
cana-511	169	4	(	(	PUNCT
cana-511	169	5	3.1	3.1	NUM
cana-511	169	6	)	)	PUNCT
cana-511	169	7	and	and	CCONJ
cana-511	169	8	the	the	DET
cana-511	169	9	property	property	NOUN
cana-511	169	10	of	of	ADP
cana-511	169	11	,	,	PUNCT
cana-511	169	12			AUX
cana-511	169	13	we	we	PRON
cana-511	169	14	have	have	VERB
cana-511	169	15	(	(	PUNCT
cana-511	169	16	)	)	PUNCT
cana-511	169	17	(	(	PUNCT
cana-511	169	18	)	)	PUNCT
cana-511	169	19	(	(	PUNCT
cana-511	169	20	)	)	PUNCT
cana-511	169	21	(	(	PUNCT
cana-511	169	22	)	)	PUNCT
cana-511	169	23	,	,	PUNCT
cana-511	169	24	,	,	PUNCT
cana-511	169	25	,	,	PUNCT
cana-511	169	26	,	,	PUNCT
cana-511	169	27	,	,	PUNCT
cana-511	169	28	,	,	PUNCT
cana-511	169	29	,	,	PUNCT
cana-511	169	30	,	,	PUNCT
cana-511	169	31	,	,	PUNCT
cana-511	169	32	(	(	PUNCT
cana-511	169	33	)	)	PUNCT
cana-511	169	34	q	q	NOUN
cana-511	169	35	q	q	X
cana-511	169	36	q	q	X
cana-511	169	37	qx	qx	INTJ
cana-511	169	38	u	u	NOUN
cana-511	169	39	t	t	NOUN
cana-511	169	40	x	x	PUNCT
cana-511	169	41	u	u	NOUN
cana-511	169	42	t	t	PROPN
cana-511	169	43	x	x	PUNCT
cana-511	169	44	u	u	NOUN
cana-511	169	45	t	t	PROPN
cana-511	169	46	x	x	PUNCT
cana-511	169	47	u	u	NOUN
cana-511	169	48	t	t	NOUN
cana-511	169	49			PROPN
cana-511	169	50			NOUN
cana-511	169	51			VERB
cana-511	169	52			VERB
cana-511	169	53			PRON
cana-511	169	54			ADV
cana-511	170	1			NUM
cana-511	170	2	m	m	PROPN
cana-511	170	3	mm	mm	INTJ
cana-511	170	4	m	m	AUX
cana-511	170	5	letting	let	VERB
cana-511	170	6	 	 	SPACE
cana-511	170	7	q→	q→	NOUN
cana-511	170	8	in	in	ADP
cana-511	170	9	the	the	DET
cana-511	170	10	above	above	ADJ
cana-511	170	11	inequality	inequality	NOUN
cana-511	170	12	and	and	CCONJ
cana-511	170	13	considering	consider	VERB
cana-511	170	14	the	the	DET
cana-511	170	15	extremities	extremity	NOUN
cana-511	170	16	gives	give	VERB
cana-511	170	17	(	(	PUNCT
cana-511	170	18	)	)	PUNCT
cana-511	170	19	(	(	PUNCT
cana-511	170	20	)	)	PUNCT
cana-511	170	21	(	(	PUNCT
cana-511	170	22	)	)	PUNCT
cana-511	170	23	,	,	PUNCT
cana-511	170	24	,	,	PUNCT
cana-511	170	25	1	1	NUM
cana-511	170	26	  	  	SPACE
cana-511	170	27	i	i	PRON
cana-511	170	28	m	m	VERB
cana-511	170	29	,	,	PUNCT
cana-511	170	30	,	,	PUNCT
cana-511	170	31	l	l	PROPN
cana-511	170	32	1im	1im	NOUN
cana-511	170	33	,	,	PUNCT
cana-511	170	34	,	,	PUNCT
cana-511	170	35	.n	.n	PROPN
cana-511	170	36	q	q	X
cana-511	171	1	q	q	X
cana-511	171	2	q	q	X
cana-511	171	3	u	u	X
cana-511	171	4	u	u	NOUN
cana-511	171	5	t	t	NOUN
cana-511	171	6	x	x	X
cana-511	171	7	u	u	NOUN
cana-511	171	8	t	t	PROPN
cana-511	171	9	x	x	PUNCT
cana-511	171	10	u	u	NOUN
cana-511	171	11	t	t	NOUN
cana-511	171	12			PROPN
cana-511	171	13			VERB
cana-511	171	14			X
cana-511	171	15			X
cana-511	171	16			X
cana-511	171	17	→	→	PUNCT
cana-511	171	18	→	→	NUM
cana-511	171	19			NOUN
cana-511	171	20			NOUN
cana-511	172	1	m	m	PROPN
cana-511	172	2	m	m	VERB
cana-511	172	3	m	m	VERB
cana-511	172	4	thus	thus	ADV
cana-511	172	5	,	,	PUNCT
cana-511	172	6	as	as	ADP
cana-511	172	7	 	 	SPACE
cana-511	172	8	qx	qx	PROPN
cana-511	172	9	u	u	NOUN
cana-511	172	10	q	q	ADJ
cana-511	172	11	→	→	NUM
cana-511	172	12	→	→	PUNCT
cana-511	172	13	which	which	PRON
cana-511	172	14	implies	imply	VERB
cana-511	172	15	as	as	ADP
cana-511	172	16	q	q	PROPN
cana-511	172	17	.qy	.qy	PUNCT
cana-511	173	1	ku→	ku→	ADJ
cana-511	173	2	→	→	PUNCT
cana-511	173	3	since	since	SCONJ
cana-511	173	4	limit	limit	NOUN
cana-511	173	5	is	be	AUX
cana-511	173	6	unique	unique	ADJ
cana-511	173	7	,	,	PUNCT
cana-511	173	8	we	we	PRON
cana-511	173	9	obtain	obtain	VERB
cana-511	173	10	.u	.u	ADJ
cana-511	173	11	u	u	ADJ
cana-511	173	12	=	=	NOUN
cana-511	173	13	hence	hence	ADV
cana-511	173	14	,	,	PUNCT
cana-511	173	15	u	u	NOUN
cana-511	173	16	u	u	ADJ
cana-511	173	17	=	=	NOUN
cana-511	173	18	is	be	AUX
cana-511	173	19	a	a	DET
cana-511	173	20	(	(	PUNCT
cana-511	173	21	unique	unique	ADJ
cana-511	173	22	)	)	PUNCT
cana-511	173	23	point	point	NOUN
cana-511	173	24	of	of	ADP
cana-511	173	25	coincidence	coincidence	NOUN
cana-511	173	26	of	of	ADP
cana-511	173	27	&	&	CCONJ
cana-511	173	28			VERB
cana-511	173	29			PROPN
cana-511	173	30	.	.	PUNCT
cana-511	174	1	similarly	similarly	ADV
cana-511	174	2	,	,	PUNCT
cana-511	174	3	we	we	PRON
cana-511	174	4	can	can	AUX
cana-511	174	5	show	show	VERB
cana-511	174	6	that	that	SCONJ
cana-511	174	7	u	u	PROPN
cana-511	174	8	u	u	ADJ
cana-511	174	9	=	=	NOUN
cana-511	174	10	is	be	AUX
cana-511	174	11	a	a	DET
cana-511	174	12	(	(	PUNCT
cana-511	174	13	unique	unique	ADJ
cana-511	174	14	)	)	PUNCT
cana-511	174	15	point	point	NOUN
cana-511	174	16	of	of	ADP
cana-511	174	17	coincidence	coincidence	NOUN
cana-511	174	18	of	of	ADP
cana-511	174	19	&	&	CCONJ
cana-511	174	20			VERB
cana-511	174	21			PROPN
cana-511	174	22	when	when	SCONJ
cana-511	174	23	(	(	PUNCT
cana-511	174	24	)	)	PUNCT
cana-511	174	25	x	x	PROPN
cana-511	174	26	is	be	AUX
cana-511	174	27	complete	complete	ADJ
cana-511	174	28	.	.	PUNCT
cana-511	175	1	suppose	suppose	VERB
cana-511	175	2	that	that	SCONJ
cana-511	175	3	(	(	PUNCT
cana-511	175	4	ii	ii	NOUN
cana-511	175	5	)	)	PUNCT
cana-511	175	6	holds	hold	VERB
cana-511	175	7	:	:	PUNCT
cana-511	175	8	since	since	SCONJ
cana-511	175	9	x	x	PRON
cana-511	175	10	is	be	AUX
cana-511	175	11	complete	complete	ADJ
cana-511	175	12	,	,	PUNCT
cana-511	175	13	there	there	PRON
cana-511	175	14	exists	exist	VERB
cana-511	175	15	   	   	SPACE
cana-511	175	16	u	u	PROPN
cana-511	175	17	x	x	PROPN
cana-511	175	18	such	such	ADJ
cana-511	175	19	that	that	SCONJ
cana-511	175	20	         	         	SPACE
cana-511	175	21	as	as	ADP
cana-511	175	22	q	q	PROPN
cana-511	175	23	  	  	SPACE
cana-511	175	24	.q	.q	PROPN
cana-511	175	25	qy	qy	PROPN
cana-511	175	26	u	u	PROPN
cana-511	175	27	x	x	PROPN
cana-511	175	28	u→	u→	PROPN
cana-511	175	29			NOUN
cana-511	175	30	→	→	PUNCT
cana-511	175	31	→	→	PUNCT
cana-511	175	32	since	since	SCONJ
cana-511	175	33			PRON
cana-511	175	34	is	be	AUX
cana-511	175	35	continuous	continuous	ADJ
cana-511	175	36	,	,	PUNCT
cana-511	175	37	we	we	PRON
cana-511	175	38	have	have	VERB
cana-511	175	39	2	2	NUM
cana-511	175	40	as	as	ADP
cana-511	175	41	.qx	.qx	PUNCT
cana-511	175	42	q	q	PROPN
cana-511	175	43	→	→	PROPN
cana-511	175	44	→	→	PUNCT
cana-511	175	45	in	in	ADP
cana-511	175	46	view	view	NOUN
cana-511	175	47	of	of	ADP
cana-511	175	48	(	(	PUNCT
cana-511	175	49	3.1	3.1	NUM
cana-511	175	50	)	)	PUNCT
cana-511	175	51	and	and	CCONJ
cana-511	175	52	the	the	DET
cana-511	175	53	property	property	NOUN
cana-511	175	54	of	of	ADP
cana-511	175	55	,	,	PUNCT
cana-511	175	56			AUX
cana-511	175	57	we	we	PRON
cana-511	175	58	have	have	VERB
cana-511	175	59	(	(	PUNCT
cana-511	175	60	)	)	PUNCT
cana-511	175	61	(	(	PUNCT
cana-511	175	62	)	)	PUNCT
cana-511	175	63	(	(	PUNCT
cana-511	175	64	)	)	PUNCT
cana-511	175	65	(	(	PUNCT
cana-511	175	66	)	)	PUNCT
cana-511	175	67	(	(	PUNCT
cana-511	175	68	)	)	PUNCT
cana-511	175	69	(	(	PUNCT
cana-511	175	70	)	)	PUNCT
cana-511	175	71	(	(	PUNCT
cana-511	175	72	)	)	PUNCT
cana-511	175	73	(	(	PUNCT
cana-511	175	74	)	)	PUNCT
cana-511	175	75	(	(	PUNCT
cana-511	175	76	)	)	PUNCT
cana-511	175	77	,	,	PUNCT
cana-511	175	78	,	,	PUNCT
cana-511	175	79	,	,	PUNCT
cana-511	175	80	,	,	PUNCT
cana-511	175	81	,	,	PUNCT
cana-511	175	82	,	,	PUNCT
cana-511	175	83	,	,	PUNCT
cana-511	175	84	,	,	PUNCT
cana-511	175	85	,	,	PUNCT
cana-511	175	86	q	q	PRON
cana-511	175	87	q	q	X
cana-511	175	88	q	q	X
cana-511	175	89	qx	qx	INTJ
cana-511	175	90	u	u	NOUN
cana-511	175	91	t	t	NOUN
cana-511	175	92	x	x	PUNCT
cana-511	175	93	u	u	NOUN
cana-511	175	94	t	t	PROPN
cana-511	175	95	x	x	PUNCT
cana-511	175	96	u	u	NOUN
cana-511	175	97	t	t	PROPN
cana-511	175	98	x	x	PUNCT
cana-511	175	99	u	u	NOUN
cana-511	175	100	t	t	NOUN
cana-511	175	101			PRON
cana-511	175	102			VERB
cana-511	175	103			PRON
cana-511	175	104			VERB
cana-511	175	105			PRON
cana-511	175	106			NUM
cana-511	175	107			NUM
cana-511	175	108			NUM
cana-511	175	109			VERB
cana-511	175	110			NUM
cana-511	175	111			NOUN
cana-511	175	112	m	m	PROPN
cana-511	175	113	m	m	VERB
cana-511	175	114	m	m	AUX
cana-511	175	115	m	m	AUX
cana-511	175	116	letting	let	VERB
cana-511	175	117	 	 	SPACE
cana-511	175	118	q→	q→	NOUN
cana-511	175	119	in	in	ADP
cana-511	175	120	the	the	DET
cana-511	175	121	above	above	ADJ
cana-511	175	122	inequality	inequality	NOUN
cana-511	175	123	and	and	CCONJ
cana-511	175	124	considering	consider	VERB
cana-511	175	125	the	the	DET
cana-511	175	126	extremities	extremity	NOUN
cana-511	175	127	gives	give	VERB
cana-511	175	128	(	(	PUNCT
cana-511	175	129	)	)	PUNCT
cana-511	175	130	(	(	PUNCT
cana-511	175	131	)	)	PUNCT
cana-511	175	132	(	(	PUNCT
cana-511	175	133	)	)	PUNCT
cana-511	175	134	(	(	PUNCT
cana-511	175	135	)	)	PUNCT
cana-511	175	136	,	,	PUNCT
cana-511	175	137	,	,	PUNCT
cana-511	175	138	1	1	NUM
cana-511	175	139	  	  	SPACE
cana-511	175	140	i	i	PRON
cana-511	175	141	m	m	VERB
cana-511	175	142	,	,	PUNCT
cana-511	175	143	,	,	PUNCT
cana-511	175	144	1im	1im	ADJ
cana-511	175	145	,	,	PUNCT
cana-511	175	146	,	,	PUNCT
cana-511	175	147	 	 	SPACE
cana-511	175	148	l	l	NOUN
cana-511	175	149	1im	1im	ADJ
cana-511	175	150	,	,	PUNCT
cana-511	175	151	,	,	PUNCT
cana-511	175	152	.q	.q	PROPN
cana-511	175	153	q	q	PROPN
cana-511	176	1	n	n	PRON
cana-511	176	2	q	q	NOUN
cana-511	176	3	q	q	X
cana-511	176	4	q	q	X
cana-511	176	5	u	u	X
cana-511	176	6	u	u	NOUN
cana-511	176	7	t	t	NOUN
cana-511	176	8	x	x	X
cana-511	176	9	u	u	NOUN
cana-511	176	10	t	t	PROPN
cana-511	176	11	x	x	PUNCT
cana-511	176	12	u	u	NOUN
cana-511	176	13	t	t	PROPN
cana-511	176	14	x	x	PUNCT
cana-511	176	15	u	u	NOUN
cana-511	176	16	t	t	VERB
cana-511	176	17			PRON
cana-511	176	18			NUM
cana-511	176	19			PUNCT
cana-511	176	20			PROPN
cana-511	176	21			ADJ
cana-511	176	22			NOUN
cana-511	176	23			ADJ
cana-511	176	24	→	→	PUNCT
cana-511	176	25	→	→	NUM
cana-511	176	26	→	→	NUM
cana-511	177	1			NUM
cana-511	177	2	=	=	SYM
cana-511	177	3			NOUN
cana-511	178	1	m	m	NOUN
cana-511	178	2	mm	mm	INTJ
cana-511	178	3	m	m	VERB
cana-511	178	4	thus	thus	ADV
cana-511	178	5	,	,	PUNCT
cana-511	178	6	as	as	ADP
cana-511	178	7	q	q	PROPN
cana-511	178	8	.	.	PUNCT
cana-511	178	9	 	 	SPACE
cana-511	179	1	qx	qx	PROPN
cana-511	179	2	u	u	PROPN
cana-511	179	3	→	→	X
cana-511	179	4	→	→	PUNCT
cana-511	179	5	but	but	CCONJ
cana-511	179	6	from	from	ADP
cana-511	179	7	the	the	DET
cana-511	179	8	definition	definition	NOUN
cana-511	179	9	of	of	ADP
cana-511	179	10	,	,	PUNCT
cana-511	179	11	qy	qy	NOUN
cana-511	179	12	we	we	PRON
cana-511	179	13	get	get	VERB
cana-511	179	14	2	2	NUM
cana-511	179	15	l	l	NOUN
cana-511	179	16	l	l	NOUN
cana-511	179	17	 	 	SPACE
cana-511	179	18	q	q	NOUN
cana-511	180	1	q	q	X
cana-511	180	2	qx	qx	INTJ
cana-511	180	3	x	x	INTJ
cana-511	180	4	x	x	PROPN
cana-511	181	1			PROPN
cana-511	181	2	+	+	PROPN
cana-511	182	1	+	+	PROPN
cana-511	182	2	=	=	SYM
cana-511	182	3	=	=	PUNCT
cana-511	182	4	from	from	ADP
cana-511	182	5	which	which	PRON
cana-511	182	6	the	the	DET
cana-511	182	7	result	result	NOUN
cana-511	182	8	follows	follow	VERB
cana-511	182	9	.	.	PUNCT
cana-511	183	1	.,i	.,i	PUNCT
cana-511	184	1	e	e	X
cana-511	184	2	u	u	PROPN
cana-511	184	3	u	u	PROPN
cana-511	184	4	=	=	NOUN
cana-511	184	5	is	be	AUX
cana-511	184	6	a	a	DET
cana-511	184	7	(	(	PUNCT
cana-511	184	8	unique	unique	ADJ
cana-511	184	9	)	)	PUNCT
cana-511	184	10	point	point	NOUN
cana-511	184	11	of	of	ADP
cana-511	184	12	coincidence	coincidence	NOUN
cana-511	184	13	of	of	ADP
cana-511	184	14	&	&	CCONJ
cana-511	184	15	.	.	PROPN
cana-511	185	1			PROPN
cana-511	185	2	suppose	suppose	VERB
cana-511	185	3	that	that	SCONJ
cana-511	185	4	(	(	PUNCT
cana-511	185	5	iii	iii	NOUN
cana-511	185	6	)	)	PUNCT
cana-511	185	7	holds	hold	VERB
cana-511	185	8	:	:	PUNCT
cana-511	185	9	since	since	SCONJ
cana-511	185	10	x	x	PRON
cana-511	185	11	is	be	AUX
cana-511	185	12	complete	complete	ADJ
cana-511	185	13	,	,	PUNCT
cana-511	185	14	there	there	PRON
cana-511	185	15	exists	exist	VERB
cana-511	185	16	 	 	SPACE
cana-511	185	17	u	u	PRON
cana-511	185	18	x	x	PROPN
cana-511	185	19	such	such	ADJ
cana-511	185	20	that	that	SCONJ
cana-511	185	21	          	          	SPACE
cana-511	185	22	as	as	ADP
cana-511	185	23	  	  	SPACE
cana-511	185	24	.	.	PUNCT
cana-511	185	25	 	 	SPACE
cana-511	186	1	q	q	PROPN
cana-511	186	2	qy	qy	PROPN
cana-511	186	3	u	u	NOUN
cana-511	186	4	x	x	X
cana-511	186	5	u	u	NOUN
cana-511	186	6	q→	q→	VERB
cana-511	186	7			NOUN
cana-511	186	8	→	→	SYM
cana-511	186	9	→	→	PUNCT
cana-511	186	10	since	since	SCONJ
cana-511	186	11			ADJ
cana-511	186	12	is	be	AUX
cana-511	186	13	continuous	continuous	ADJ
cana-511	186	14	,	,	PUNCT
cana-511	186	15	we	we	PRON
cana-511	186	16	have	have	VERB
cana-511	186	17	as	as	ADP
cana-511	186	18	q	q	PROPN
cana-511	186	19	.qx	.qx	PUNCT
cana-511	186	20	u	u	PROPN
cana-511	187	1	→	→	PROPN
cana-511	187	2	→	→	PUNCT
cana-511	187	3	in	in	ADP
cana-511	187	4	view	view	NOUN
cana-511	187	5	of	of	ADP
cana-511	187	6	(	(	PUNCT
cana-511	187	7	3.1	3.1	NUM
cana-511	187	8	)	)	PUNCT
cana-511	187	9	and	and	CCONJ
cana-511	187	10	the	the	DET
cana-511	187	11	property	property	NOUN
cana-511	187	12	of	of	ADP
cana-511	187	13			NOUN
cana-511	187	14	and	and	CCONJ
cana-511	187	15	2	2	NUM
cana-511	187	16	l	l	NOUN
cana-511	187	17	l	l	NOUN
cana-511	187	18	  	  	SPACE
cana-511	187	19	,	,	PUNCT
cana-511	187	20	q	q	X
cana-511	187	21	q	q	X
cana-511	187	22	qx	qx	INTJ
cana-511	187	23	x	x	INTJ
cana-511	187	24	x	x	PROPN
cana-511	188	1			PROPN
cana-511	188	2	+	+	PROPN
cana-511	189	1	+	+	PROPN
cana-511	189	2	=	=	SYM
cana-511	189	3	=	=	PRON
cana-511	189	4	we	we	PRON
cana-511	189	5	have	have	VERB
cana-511	189	6	(	(	PUNCT
cana-511	189	7	)	)	PUNCT
cana-511	189	8	(	(	PUNCT
cana-511	189	9	)	)	PUNCT
cana-511	189	10	(	(	PUNCT
cana-511	189	11	)	)	PUNCT
cana-511	189	12	(	(	PUNCT
cana-511	189	13	)	)	PUNCT
cana-511	189	14	(	(	PUNCT
cana-511	189	15	)	)	PUNCT
cana-511	189	16	(	(	PUNCT
cana-511	189	17	)	)	PUNCT
cana-511	189	18	(	(	PUNCT
cana-511	189	19	)	)	PUNCT
cana-511	189	20	(	(	PUNCT
cana-511	189	21	)	)	PUNCT
cana-511	189	22	(	(	PUNCT
cana-511	189	23	)	)	PUNCT
cana-511	189	24	(	(	PUNCT
cana-511	189	25	)	)	PUNCT
cana-511	189	26	l	l	NOUN
cana-511	189	27	,	,	PUNCT
cana-511	189	28	,	,	PUNCT
cana-511	189	29	,	,	PUNCT
cana-511	189	30	,	,	PUNCT
cana-511	189	31	,	,	PUNCT
cana-511	189	32	,	,	PUNCT
cana-511	189	33	,	,	PUNCT
cana-511	189	34	,	,	PUNCT
cana-511	189	35	,	,	PUNCT
cana-511	189	36	,	,	PUNCT
cana-511	189	37	,	,	PUNCT
cana-511	189	38	q	q	PRON
cana-511	189	39	q	q	X
cana-511	189	40	q	q	X
cana-511	189	41	q	q	X
cana-511	189	42	qx	qx	INTJ
cana-511	189	43	u	u	NOUN
cana-511	189	44	t	t	NOUN
cana-511	189	45	x	x	PUNCT
cana-511	189	46	u	u	NOUN
cana-511	189	47	t	t	PROPN
cana-511	189	48	x	x	PUNCT
cana-511	189	49	u	u	NOUN
cana-511	189	50	t	t	PROPN
cana-511	189	51	x	x	PUNCT
cana-511	189	52	u	u	NOUN
cana-511	189	53	t	t	PROPN
cana-511	189	54	x	x	PUNCT
cana-511	189	55	u	u	NOUN
cana-511	189	56	t	t	NOUN
cana-511	189	57			NOUN
cana-511	189	58			NOUN
cana-511	189	59			PROPN
cana-511	189	60			VERB
cana-511	189	61			PRON
cana-511	189	62			NUM
cana-511	189	63			PRON
cana-511	189	64			NUM
cana-511	189	65			NUM
cana-511	189	66			NOUN
cana-511	189	67			PROPN
cana-511	189	68	−	−	NOUN
cana-511	189	69	=	=	SYM
cana-511	189	70			PROPN
cana-511	190	1	m	m	INTJ
cana-511	190	2	m	m	VERB
cana-511	190	3	m	m	VERB
cana-511	190	4	m	m	AUX
cana-511	190	5	m	m	AUX
cana-511	190	6	letting	let	VERB
cana-511	190	7	 	 	SPACE
cana-511	190	8	q→	q→	NOUN
cana-511	190	9	in	in	ADP
cana-511	190	10	the	the	DET
cana-511	190	11	above	above	ADJ
cana-511	190	12	inequality	inequality	NOUN
cana-511	190	13	and	and	CCONJ
cana-511	190	14	considering	consider	VERB
cana-511	190	15	the	the	DET
cana-511	190	16	extremities	extremity	NOUN
cana-511	190	17	gives	give	VERB
cana-511	190	18	(	(	PUNCT
cana-511	190	19	)	)	PUNCT
cana-511	190	20	(	(	PUNCT
cana-511	190	21	)	)	PUNCT
cana-511	190	22	(	(	PUNCT
cana-511	190	23	)	)	PUNCT
cana-511	190	24	,	,	PUNCT
cana-511	190	25	,	,	PUNCT
cana-511	190	26	1	1	NUM
cana-511	190	27	  	  	SPACE
cana-511	190	28	i	i	PRON
cana-511	190	29	m	m	VERB
cana-511	190	30	,	,	PUNCT
cana-511	190	31	,	,	PUNCT
cana-511	190	32	 	 	SPACE
cana-511	190	33	l	l	NOUN
cana-511	190	34	1im	1im	ADJ
cana-511	190	35	,	,	PUNCT
cana-511	190	36	,	,	PUNCT
cana-511	190	37	.q	.q	PROPN
cana-511	190	38	q	q	PROPN
cana-511	191	1	q	q	X
cana-511	191	2	q	q	X
cana-511	191	3	u	u	X
cana-511	191	4	u	u	NOUN
cana-511	191	5	t	t	NOUN
cana-511	191	6	x	x	X
cana-511	191	7	u	u	NOUN
cana-511	191	8	t	t	PROPN
cana-511	191	9	x	x	PUNCT
cana-511	191	10	u	u	NOUN
cana-511	191	11	t	t	NOUN
cana-511	191	12			PRON
cana-511	191	13			NUM
cana-511	191	14			PUNCT
cana-511	191	15			PROPN
cana-511	191	16			PROPN
cana-511	191	17	→	→	PUNCT
cana-511	191	18	→	→	NUM
cana-511	191	19			NOUN
cana-511	191	20			NOUN
cana-511	192	1	m	m	PROPN
cana-511	192	2	m	m	VERB
cana-511	192	3	m	m	VERB
cana-511	192	4	thus	thus	ADV
cana-511	192	5	as	as	SCONJ
cana-511	192	6	q	q	NOUN
cana-511	192	7	.qx	.qx	PUNCT
cana-511	192	8	u	u	PROPN
cana-511	192	9	→	→	X
cana-511	192	10	→	→	PUNCT
cana-511	192	11	since	since	ADV
cana-511	192	12	,	,	PUNCT
cana-511	192	13			VERB
cana-511	192	14			PRON
cana-511	192	15	are	be	AUX
cana-511	192	16	compatible	compatible	ADJ
cana-511	192	17	,	,	PUNCT
cana-511	192	18	we	we	PRON
cana-511	192	19	have	have	VERB
cana-511	192	20	(	(	PUNCT
cana-511	192	21	)	)	PUNCT
cana-511	192	22	1im	1im	ADJ
cana-511	192	23	,	,	PUNCT
cana-511	192	24	,	,	PUNCT
cana-511	192	25	l	l	NOUN
cana-511	192	26	,	,	PUNCT
cana-511	192	27	0.q	0.q	PRON
cana-511	192	28	q	q	NOUN
cana-511	193	1	q	q	X
cana-511	194	1	x	x	X
cana-511	194	2	x	x	SYM
cana-511	194	3	t	t	PROPN
cana-511	194	4	t	t	PROPN
cana-511	194	5			PROPN
cana-511	194	6	→	→	PUNCT
cana-511	194	7	=	=	NOUN
cana-511	195	1	m	m	NOUN
cana-511	195	2	consider	consider	VERB
cana-511	195	3	(	(	PUNCT
cana-511	195	4	)	)	PUNCT
cana-511	195	5	,	,	PUNCT
cana-511	195	6	,	,	PUNCT
cana-511	195	7	,	,	PUNCT
cana-511	195	8	,	,	PUNCT
cana-511	195	9	      	      	SPACE
cana-511	195	10	,	,	PUNCT
cana-511	195	11	,	,	PUNCT
cana-511	195	12	      	      	SPACE
cana-511	195	13	,	,	PUNCT
cana-511	195	14	,	,	PUNCT
cana-511	195	15	    	    	SPACE
cana-511	195	16	3	3	NUM
cana-511	195	17	3	3	NUM
cana-511	195	18	3	3	NUM
cana-511	195	19	q	q	NOUN
cana-511	195	20	n	n	ADP
cana-511	195	21	q	q	NOUN
cana-511	195	22	q	q	NOUN
cana-511	195	23	t	t	PROPN
cana-511	195	24	t	t	PROPN
cana-511	195	25	t	t	X
cana-511	195	26	u	u	X
cana-511	195	27	u	u	NOUN
cana-511	195	28	t	t	X
cana-511	195	29	u	u	NOUN
cana-511	195	30	x	x	NOUN
cana-511	195	31	x	x	PUNCT
cana-511	195	32	x	x	SYM
cana-511	195	33	x	x	SYM
cana-511	195	34	u	u	ADJ
cana-511	195	35			PROPN
cana-511	195	36			VERB
cana-511	195	37			PROPN
cana-511	195	38			NUM
cana-511	195	39			NUM
cana-511	195	40			PROPN
cana-511	195	41			PROPN
cana-511	195	42			NOUN
cana-511	195	43			NOUN
cana-511	195	44			NOUN
cana-511	195	45			PROPN
cana-511	195	46			NOUN
cana-511	195	47			PROPN
cana-511	195	48			NUM
cana-511	195	49			NUM
cana-511	196	1			PRON
cana-511	196	2			PROPN
cana-511	197	1			PROPN
cana-511	198	1			INTJ
cana-511	199	1			PROPN
cana-511	199	2			PROPN
cana-511	200	1			ADJ
cana-511	200	2			PROPN
cana-511	200	3			PROPN
cana-511	200	4			NOUN
cana-511	200	5			PROPN
cana-511	200	6			NOUN
cana-511	200	7	m	m	VERB
cana-511	200	8	m	m	VERB
cana-511	200	9	m	m	VERB
cana-511	200	10	m	m	NOUN
cana-511	200	11	communications	communication	NOUN
cana-511	200	12	on	on	ADP
cana-511	200	13	applied	apply	VERB
cana-511	200	14	nonlinear	nonlinear	ADJ
cana-511	200	15	analysis	analysis	NOUN
cana-511	200	16	issn	issn	NOUN
cana-511	200	17	:	:	PUNCT
cana-511	200	18	1074	1074	NUM
cana-511	200	19	-	-	PUNCT
cana-511	200	20	133x	133x	NUM
cana-511	200	21	vol	vol	NOUN
cana-511	200	22	31	31	NUM
cana-511	200	23	no	no	NOUN
cana-511	200	24	.	.	NOUN
cana-511	200	25	2	2	NUM
cana-511	200	26	(	(	PUNCT
cana-511	200	27	2024	2024	NUM
cana-511	200	28	)	)	PUNCT
cana-511	200	29	40	40	NUM
cana-511	200	30	https://internationalpubls.com	https://internationalpubls.com	X
cana-511	201	1	letting	let	VERB
cana-511	201	2	   	   	SPACE
cana-511	201	3	q→	q→	NOUN
cana-511	201	4	in	in	ADP
cana-511	201	5	the	the	DET
cana-511	201	6	above	above	ADJ
cana-511	201	7	inequality	inequality	NOUN
cana-511	201	8	gives	give	VERB
cana-511	201	9	u	u	PRON
cana-511	201	10	u	u	ADJ
cana-511	201	11	=	=	NOUN
cana-511	201	12	thus	thus	ADV
cana-511	201	13	showing	show	VERB
cana-511	201	14	that	that	SCONJ
cana-511	201	15	u	u	PROPN
cana-511	201	16	u	u	ADJ
cana-511	201	17	=	=	NOUN
cana-511	201	18	is	be	AUX
cana-511	201	19	a	a	DET
cana-511	201	20	(	(	PUNCT
cana-511	201	21	unique	unique	ADJ
cana-511	201	22	)	)	PUNCT
cana-511	201	23	point	point	NOUN
cana-511	201	24	of	of	ADP
cana-511	201	25	coincidence	coincidence	NOUN
cana-511	201	26	of	of	ADP
cana-511	201	27	&	&	CCONJ
cana-511	201	28	.	.	VERB
cana-511	201	29			PRON
cana-511	201	30	hence	hence	ADV
cana-511	201	31	,	,	PUNCT
cana-511	201	32	the	the	DET
cana-511	201	33	result	result	NOUN
cana-511	201	34	is	be	AUX
cana-511	201	35	proved	prove	VERB
cana-511	201	36	for	for	ADP
cana-511	201	37	all	all	DET
cana-511	201	38	three	three	NUM
cana-511	201	39	cases	case	NOUN
cana-511	201	40	(	(	PUNCT
cana-511	201	41	i	i	NOUN
cana-511	201	42	)	)	PUNCT
cana-511	201	43	,	,	PUNCT
cana-511	201	44	(	(	PUNCT
cana-511	201	45	ii	ii	NOUN
cana-511	201	46	)	)	PUNCT
cana-511	201	47	and	and	CCONJ
cana-511	201	48	(	(	PUNCT
cana-511	201	49	iii	iii	NOUN
cana-511	201	50	)	)	PUNCT
cana-511	201	51	,	,	PUNCT
cana-511	201	52	i.e.	i.e.	X
cana-511	201	53	,	,	PUNCT
cana-511	201	54	the	the	DET
cana-511	201	55	mappings	mapping	NOUN
cana-511	201	56	&	&	CCONJ
cana-511	201	57			VERB
cana-511	201	58			PROPN
cana-511	201	59	have	have	VERB
cana-511	201	60	a	a	DET
cana-511	201	61	unique	unique	ADJ
cana-511	201	62	point	point	NOUN
cana-511	201	63	of	of	ADP
cana-511	201	64	coincidence	coincidence	NOUN
cana-511	201	65	.	.	PUNCT
cana-511	202	1	theorem	theorem	VERB
cana-511	202	2	3.4	3.4	NUM
cana-511	202	3	.	.	PUNCT
cana-511	203	1	besides	besides	SCONJ
cana-511	203	2	the	the	DET
cana-511	203	3	hypotheses	hypothesis	NOUN
cana-511	203	4	of	of	ADP
cana-511	203	5	theorem	theorem	ADJ
cana-511	203	6	3.3	3.3	NUM
cana-511	203	7	,	,	PUNCT
cana-511	203	8	if	if	SCONJ
cana-511	203	9	&	&	CCONJ
cana-511	203	10			VERB
cana-511	203	11			PROPN
cana-511	203	12	are	be	AUX
cana-511	203	13	weakly	weakly	ADV
cana-511	203	14	compatible	compatible	ADJ
cana-511	203	15	,	,	PUNCT
cana-511	203	16	then	then	ADV
cana-511	203	17	they	they	PRON
cana-511	203	18	have	have	VERB
cana-511	203	19	a	a	DET
cana-511	203	20	unique	unique	ADJ
cana-511	203	21	common	common	ADJ
cana-511	203	22	fixed	fix	VERB
cana-511	203	23	point	point	NOUN
cana-511	203	24	in	in	ADP
cana-511	203	25	.x	.x	NOUN
cana-511	203	26	proof	proof	NOUN
cana-511	203	27	.	.	PUNCT
cana-511	204	1	using	use	VERB
cana-511	204	2	theorem	theorem	ADJ
cana-511	204	3	3.3	3.3	NUM
cana-511	204	4	,	,	PUNCT
cana-511	204	5	&	&	CCONJ
cana-511	204	6			VERB
cana-511	204	7			PROPN
cana-511	204	8	have	have	VERB
cana-511	204	9	unique	unique	ADJ
cana-511	204	10	point	point	NOUN
cana-511	204	11	of	of	ADP
cana-511	204	12	coincidence	coincidence	NOUN
cana-511	204	13	.	.	PUNCT
cana-511	205	1	further	far	ADV
cana-511	205	2	,	,	PUNCT
cana-511	205	3	if	if	SCONJ
cana-511	205	4	&	&	CCONJ
cana-511	205	5			VERB
cana-511	205	6			PROPN
cana-511	205	7	are	be	AUX
cana-511	205	8	weakly	weakly	ADV
cana-511	205	9	compatible	compatible	ADJ
cana-511	205	10	,	,	PUNCT
cana-511	205	11	then	then	ADV
cana-511	205	12	according	accord	VERB
cana-511	205	13	to	to	ADP
cana-511	205	14	remark	remark	NOUN
cana-511	205	15	2.7	2.7	NUM
cana-511	205	16	,	,	PUNCT
cana-511	205	17	they	they	PRON
cana-511	205	18	have	have	VERB
cana-511	205	19	a	a	DET
cana-511	205	20	unique	unique	ADJ
cana-511	205	21	common	common	ADJ
cana-511	205	22	fixed	fix	VERB
cana-511	205	23	point	point	NOUN
cana-511	205	24	in	in	ADP
cana-511	205	25	.x	.x	PROPN
cana-511	205	26	example	example	NOUN
cana-511	206	1	3.5	3.5	NUM
cana-511	206	2	.	.	PUNCT
cana-511	207	1	let	let	VERB
cana-511	208	1	l	l	NOUN
cana-511	208	2	[	[	PUNCT
cana-511	208	3	]	]	X
cana-511	208	4	0,x	0,x	NOUN
cana-511	208	5	=	=	X
cana-511	209	1	and	and	CCONJ
cana-511	209	2	m	m	AUX
cana-511	209	3	be	be	VERB
cana-511	209	4	the	the	DET
cana-511	209	5	fuzzy	fuzzy	ADJ
cana-511	209	6	set	set	NOUN
cana-511	209	7	on	on	ADP
cana-511	209	8	(	(	PUNCT
cana-511	209	9	)	)	PUNCT
cana-511	209	10	0,x	0,x	PROPN
cana-511	209	11	x	x	PROPN
cana-511	209	12			PROPN
cana-511	209	13			PROPN
cana-511	209	14	defined	define	VERB
cana-511	209	15	by	by	ADP
cana-511	209	16	(	(	PUNCT
cana-511	209	17	)	)	PUNCT
cana-511	209	18	,	,	PUNCT
cana-511	209	19	,	,	PUNCT
cana-511	209	20	     	     	SPACE
cana-511	209	21	t	t	NOUN
cana-511	209	22	x	x	X
cana-511	209	23	y	y	PROPN
cana-511	209	24	t	t	PROPN
cana-511	209	25	t	t	NOUN
cana-511	209	26	x	x	PUNCT
cana-511	209	27	y	y	PROPN
cana-511	209	28	=	=	PUNCT
cana-511	210	1	+	+	NUM
cana-511	210	2	−	−	PROPN
cana-511	210	3	m	m	NOUN
cana-511	210	4	and	and	CCONJ
cana-511	210	5			PROPN
cana-511	210	6	is	be	AUX
cana-511	210	7	minimum	minimum	ADJ
cana-511	210	8	norm	norm	NOUN
cana-511	210	9	.	.	PUNCT
cana-511	211	1	then	then	ADV
cana-511	211	2	,	,	PUNCT
cana-511	211	3	(	(	PUNCT
cana-511	211	4	)	)	PUNCT
cana-511	211	5	,	,	PUNCT
cana-511	211	6	,	,	PUNCT
cana-511	211	7	x	x	PRON
cana-511	211	8	m	m	NOUN
cana-511	211	9	is	be	AUX
cana-511	211	10	an	an	DET
cana-511	211	11	complete	complete	ADJ
cana-511	211	12	fuzzy	fuzzy	ADJ
cana-511	211	13	metric	metric	ADJ
cana-511	211	14	space	space	NOUN
cana-511	211	15	.	.	PUNCT
cana-511	212	1	let	let	VERB
cana-511	212	2	{	{	PUNCT
cana-511	212	3	}	}	PUNCT
cana-511	212	4	qx	qx	INTJ
cana-511	212	5	be	be	AUX
cana-511	212	6	a	a	DET
cana-511	212	7	sequence	sequence	NOUN
cana-511	212	8	given	give	VERB
cana-511	212	9	by	by	ADP
cana-511	212	10	  	  	SPACE
cana-511	212	11	.q	.q	PROPN
cana-511	213	1	n	n	PRON
cana-511	213	2			NOUN
cana-511	213	3	consider	consider	VERB
cana-511	213	4	the	the	DET
cana-511	213	5	function	function	NOUN
cana-511	213	6	(	(	PUNCT
cana-511	213	7			NOUN
cana-511	213	8	(	(	PUNCT
cana-511	213	9			NOUN
cana-511	213	10	:	:	PUNCT
cana-511	213	11	0	0	NUM
cana-511	213	12	,	,	PUNCT
cana-511	213	13	l	l	NOUN
cana-511	213	14	0	0	NUM
cana-511	213	15	,	,	PUNCT
cana-511	213	16	l	l	NOUN
cana-511	213	17	 	 	SPACE
cana-511	213	18			VERB
cana-511	213	19			NOUN
cana-511	213	20	→	→	SYM
cana-511	213	21	by	by	ADP
cana-511	213	22	(	(	PUNCT
cana-511	213	23	)	)	PUNCT
cana-511	213	24	,	,	PUNCT
cana-511	213	25	s	s	PROPN
cana-511	213	26	s	s	PROPN
cana-511	213	27	t	t	NOUN
cana-511	213	28	t	t	NOUN
cana-511	213	29			NOUN
cana-511	213	30	=	=	SYM
cana-511	213	31	(	(	PUNCT
cana-511	213	32			PROPN
cana-511	213	33	,	,	PUNCT
cana-511	213	34	  	  	SPACE
cana-511	213	35	0	0	NUM
cana-511	213	36	,	,	PUNCT
cana-511	213	37	l	l	NOUN
cana-511	213	38	.t	.t	PROPN
cana-511	214	1	s	s	PROPN
cana-511	214	2			NOUN
cana-511	214	3	let	let	VERB
cana-511	214	4	,	,	PUNCT
cana-511	214	5			VERB
cana-511	214	6			PRON
cana-511	214	7	be	be	AUX
cana-511	214	8	given	give	VERB
cana-511	214	9	by	by	ADP
cana-511	214	10	l	l	PROPN
cana-511	214	11	0	0	NUM
cana-511	214	12	0	0	NUM
cana-511	214	13	,	,	PUNCT
cana-511	214	14	4	4	NUM
cana-511	214	15	7	7	NUM
cana-511	214	16	1	1	NUM
cana-511	214	17	l	l	NOUN
cana-511	214	18	,	,	PUNCT
cana-511	214	19	20	20	NUM
cana-511	214	20	4	4	NUM
cana-511	214	21	2	2	NUM
cana-511	214	22	4	4	NUM
cana-511	214	23	l	l	NOUN
cana-511	214	24	,	,	PUNCT
cana-511	214	25	l	l	NOUN
cana-511	214	26	25	25	NUM
cana-511	214	27	2	2	NUM
cana-511	214	28	if	if	SCONJ
cana-511	214	29	x	x	NOUN
cana-511	214	30	x	x	X
cana-511	214	31	if	if	SCONJ
cana-511	214	32	x	x	SYM
cana-511	214	33	if	if	SCONJ
cana-511	214	34	x	x	PRON
cana-511	214	35			VERB
cana-511	214	36			ADV
cana-511	214	37			PROPN
cana-511	214	38			NOUN
cana-511	214	39			NOUN
cana-511	214	40			X
cana-511	214	41			NOUN
cana-511	214	42			NOUN
cana-511	214	43			NOUN
cana-511	214	44			NUM
cana-511	214	45			NOUN
cana-511	214	46			NOUN
cana-511	214	47	=	=	PUNCT
cana-511	214	48			PROPN
cana-511	214	49			PROPN
cana-511	214	50			PROPN
cana-511	215	1			ADV
cana-511	215	2			PROPN
cana-511	215	3			NUM
cana-511	215	4			PROPN
cana-511	215	5			NOUN
cana-511	215	6			NOUN
cana-511	215	7			X
cana-511	215	8			PROPN
cana-511	215	9			NOUN
cana-511	215	10			NOUN
cana-511	215	11	and	and	CCONJ
cana-511	215	12	l	l	PROPN
cana-511	215	13	0	0	NUM
cana-511	215	14	,	,	PUNCT
cana-511	215	15	3	3	NUM
cana-511	215	16	4	4	NUM
cana-511	215	17	2	2	NUM
cana-511	215	18	1	1	NUM
cana-511	215	19	l	l	NOUN
cana-511	215	20	,	,	PUNCT
cana-511	215	21	5	5	NUM
cana-511	215	22	4	4	NUM
cana-511	215	23	2	2	NUM
cana-511	215	24	2	2	NUM
cana-511	215	25	l	l	NOUN
cana-511	215	26	,	,	PUNCT
cana-511	215	27	l	l	NOUN
cana-511	215	28	3	3	NUM
cana-511	215	29	2	2	NUM
cana-511	215	30	x	x	NOUN
cana-511	215	31	if	if	SCONJ
cana-511	215	32	x	x	X
cana-511	215	33	x	x	X
cana-511	215	34	if	if	SCONJ
cana-511	215	35	x	x	PART
cana-511	215	36	if	if	SCONJ
cana-511	215	37	x	x	PROPN
cana-511	215	38			NOUN
cana-511	215	39			ADP
cana-511	216	1			PROPN
cana-511	216	2			NOUN
cana-511	216	3			NOUN
cana-511	216	4			X
cana-511	216	5			NOUN
cana-511	216	6			NOUN
cana-511	216	7			NOUN
cana-511	216	8			NUM
cana-511	216	9			NOUN
cana-511	216	10			NOUN
cana-511	216	11	=	=	PUNCT
cana-511	216	12			PROPN
cana-511	216	13			PROPN
cana-511	216	14			PROPN
cana-511	217	1			ADV
cana-511	217	2			PROPN
cana-511	217	3			NUM
cana-511	217	4			PROPN
cana-511	217	5			NOUN
cana-511	217	6			NOUN
cana-511	217	7			X
cana-511	217	8			NOUN
cana-511	217	9			NOUN
cana-511	217	10			PROPN
cana-511	217	11	then	then	ADV
cana-511	217	12			VERB
cana-511	217	13	z	z	X
cana-511	217	14	and	and	CCONJ
cana-511	217	15	the	the	DET
cana-511	217	16	quadruple	quadruple	NOUN
cana-511	217	17	(	(	PUNCT
cana-511	217	18	)	)	PUNCT
cana-511	217	19	,	,	PUNCT
cana-511	217	20	,	,	PUNCT
cana-511	217	21	,	,	PUNCT
cana-511	217	22	x	x	PUNCT
cana-511	217	23			X
cana-511	217	24	m	m	PROPN
cana-511	217	25	has	have	VERB
cana-511	217	26	the	the	DET
cana-511	217	27	property	property	NOUN
cana-511	217	28	(	(	PUNCT
cana-511	217	29	)	)	PUNCT
cana-511	217	30	.	.	PUNCT
cana-511	217	31	 	 	SPACE
cana-511	218	1	s	s	VERB
cana-511	218	2	furthermore	furthermore	ADV
cana-511	218	3	,	,	PUNCT
cana-511	218	4	the	the	DET
cana-511	218	5	mapping	mapping	NOUN
cana-511	218	6			VERB
cana-511	218	7	is	be	AUX
cana-511	218	8	a	a	DET
cana-511	218	9	fuzzy	fuzzy	ADJ
cana-511	218	10	(	(	PUNCT
cana-511	218	11	)	)	PUNCT
cana-511	218	12	,	,	PUNCT
cana-511	218	13			NUM
cana-511	218	14	−z	−z	VERB
cana-511	218	15	contractive	contractive	ADJ
cana-511	218	16	mapping	mapping	NOUN
cana-511	218	17	with	with	ADP
cana-511	218	18	respect	respect	NOUN
cana-511	218	19	to	to	ADP
cana-511	218	20	the	the	DET
cana-511	218	21	function	function	NOUN
cana-511	218	22	.	.	PUNCT
cana-511	219	1	thus	thus	ADV
cana-511	219	2	,	,	PUNCT
cana-511	219	3	all	all	DET
cana-511	219	4	the	the	DET
cana-511	219	5	conditions	condition	NOUN
cana-511	219	6	of	of	ADP
cana-511	219	7	theorem	theorem	NOUN
cana-511	219	8	(	(	PUNCT
cana-511	219	9	3.4	3.4	NUM
cana-511	219	10	)	)	PUNCT
cana-511	219	11	are	be	AUX
cana-511	219	12	satisfied	satisfied	ADJ
cana-511	219	13	i.e.	i.e.	ADV
cana-511	219	14	,	,	PUNCT
cana-511	219	15	the	the	DET
cana-511	219	16	mappings	mapping	NOUN
cana-511	219	17	and	and	VERB
cana-511	219	18			PRON
cana-511	219	19	have	have	VERB
cana-511	219	20	a	a	DET
cana-511	219	21	coincidence	coincidence	NOUN
cana-511	219	22	point	point	NOUN
cana-511	219	23	0.x	0.x	NUM
cana-511	220	1	=	=	PUNCT
cana-511	221	1	on	on	ADP
cana-511	221	2	the	the	DET
cana-511	221	3	other	other	ADJ
cana-511	221	4	word	word	NOUN
cana-511	221	5	,	,	PUNCT
cana-511	221	6	they	they	PRON
cana-511	221	7	have	have	VERB
cana-511	221	8	a	a	DET
cana-511	221	9	unique	unique	ADJ
cana-511	221	10	common	common	ADJ
cana-511	221	11	fixed	fix	VERB
cana-511	221	12	point	point	NOUN
cana-511	221	13	i.e.	i.e.	X
cana-511	221	14	,	,	PUNCT
cana-511	221	15	at	at	ADP
cana-511	221	16	0.x	0.x	NUM
cana-511	221	17	=	=	NOUN
cana-511	222	1	references	reference	NOUN
cana-511	222	2	[	[	X
cana-511	222	3	1	1	NUM
cana-511	222	4	]	]	PUNCT
cana-511	222	5	banach	banach	NOUN
cana-511	222	6	,	,	PUNCT
cana-511	222	7	s.	s.	PROPN
cana-511	222	8	(	(	PUNCT
cana-511	222	9	1922	1922	NUM
cana-511	222	10	)	)	PUNCT
cana-511	222	11	,	,	PUNCT
cana-511	222	12	sur	sur	PROPN
cana-511	222	13	les	les	X
cana-511	222	14	opérations	opération	NOUN
cana-511	222	15	dans	dan	NOUN
cana-511	222	16	les	les	X
cana-511	222	17	ensembles	ensemble	NOUN
cana-511	222	18	abstraits	abstrait	NOUN
cana-511	222	19	et	et	PROPN
cana-511	222	20	leur	leur	X
cana-511	222	21	application	application	PROPN
cana-511	222	22	aux	aux	PROPN
cana-511	222	23	équations	équations	PROPN
cana-511	222	24	intégrales	intégrale	NOUN
cana-511	222	25	,	,	PUNCT
cana-511	222	26	fundamenta	fundamenta	PROPN
cana-511	222	27	mathematicae	mathematicae	PROPN
cana-511	222	28	,	,	PUNCT
cana-511	222	29	3(1	3(1	NUM
cana-511	222	30	)	)	PUNCT
cana-511	222	31	,	,	PUNCT
cana-511	222	32	133	133	NUM
cana-511	222	33	181	181	NUM
cana-511	222	34	.	.	PUNCT
cana-511	223	1	[	[	X
cana-511	223	2	2	2	NUM
cana-511	223	3	]	]	X
cana-511	223	4	edelstein	edelstein	PROPN
cana-511	223	5	,	,	PUNCT
cana-511	223	6	m.	m.	NOUN
cana-511	223	7	(	(	PUNCT
cana-511	223	8	1962	1962	NUM
cana-511	223	9	)	)	PUNCT
cana-511	223	10	,	,	PUNCT
cana-511	223	11	on	on	ADP
cana-511	223	12	fixed	fixed	ADJ
cana-511	223	13	and	and	CCONJ
cana-511	223	14	periodic	periodic	ADJ
cana-511	223	15	points	point	NOUN
cana-511	223	16	under	under	ADP
cana-511	223	17	contractive	contractive	ADJ
cana-511	223	18	mappings	mapping	NOUN
cana-511	223	19	,	,	PUNCT
cana-511	223	20	j.lond	j.lond	ADJ
cana-511	223	21	.	.	PUNCT
cana-511	223	22	math	math	NOUN
cana-511	223	23	.	.	PUNCT
cana-511	224	1	soc	soc	PROPN
cana-511	224	2	.	.	PUNCT
cana-511	224	3	,	,	PUNCT
cana-511	224	4	37	37	NUM
cana-511	224	5	,	,	PUNCT
cana-511	224	6	74	74	NUM
cana-511	224	7	79	79	NUM
cana-511	224	8	.	.	PUNCT
cana-511	225	1	[	[	X
cana-511	225	2	3	3	NUM
cana-511	225	3	]	]	X
cana-511	225	4	george	george	PROPN
cana-511	225	5	,	,	PUNCT
cana-511	225	6	a.	a.	NOUN
cana-511	225	7	,	,	PUNCT
cana-511	225	8	veeramani	veeramani	PROPN
cana-511	225	9	,	,	PUNCT
cana-511	225	10	p.	p.	NOUN
cana-511	225	11	(	(	PUNCT
cana-511	225	12	1994	1994	NUM
cana-511	225	13	)	)	PUNCT
cana-511	225	14	,	,	PUNCT
cana-511	225	15	on	on	ADP
cana-511	225	16	some	some	DET
cana-511	225	17	results	result	NOUN
cana-511	225	18	in	in	ADP
cana-511	225	19	fuzzy	fuzzy	ADJ
cana-511	225	20	metric	metric	ADJ
cana-511	225	21	spaces	space	NOUN
cana-511	225	22	,	,	PUNCT
cana-511	225	23	fuzzy	fuzzy	ADJ
cana-511	225	24	sets	set	VERB
cana-511	225	25	syst	syst	PROPN
cana-511	225	26	.	.	PUNCT
cana-511	226	1	,	,	PUNCT
cana-511	226	2	64	64	NUM
cana-511	226	3	,	,	PUNCT
cana-511	226	4	395	395	NUM
cana-511	226	5	399	399	NUM
cana-511	226	6	.	.	PUNCT
cana-511	227	1	[	[	X
cana-511	227	2	4	4	NUM
cana-511	227	3	]	]	X
cana-511	227	4	grabiec	grabiec	PROPN
cana-511	227	5	,	,	PUNCT
cana-511	227	6	m.	m.	NOUN
cana-511	227	7	(	(	PUNCT
cana-511	227	8	1988	1988	NUM
cana-511	227	9	)	)	PUNCT
cana-511	227	10	,	,	PUNCT
cana-511	227	11	fixed	fix	VERB
cana-511	227	12	points	point	NOUN
cana-511	227	13	in	in	ADP
cana-511	227	14	fuzzy	fuzzy	ADJ
cana-511	227	15	metric	metric	ADJ
cana-511	227	16	spaces	space	NOUN
cana-511	227	17	,	,	PUNCT
cana-511	227	18	fuzzy	fuzzy	ADJ
cana-511	227	19	sets	set	NOUN
cana-511	227	20	and	and	CCONJ
cana-511	227	21	systems	system	NOUN
cana-511	227	22	,	,	PUNCT
cana-511	227	23	27(3	27(3	NUM
cana-511	227	24	)	)	PUNCT
cana-511	227	25	,	,	PUNCT
cana-511	227	26	385	385	NUM
cana-511	227	27	389	389	NUM
cana-511	227	28	.	.	PUNCT
cana-511	228	1	[	[	X
cana-511	228	2	5	5	NUM
cana-511	228	3	]	]	X
cana-511	228	4	gregori	gregori	X
cana-511	228	5	,	,	PUNCT
cana-511	228	6	v.	v.	ADV
cana-511	228	7	,	,	PUNCT
cana-511	228	8	sapena	sapena	NOUN
cana-511	228	9	,	,	PUNCT
cana-511	228	10	a.	a.	NOUN
cana-511	228	11	(	(	PUNCT
cana-511	228	12	2002	2002	NUM
cana-511	228	13	)	)	PUNCT
cana-511	228	14	,	,	PUNCT
cana-511	228	15	on	on	ADP
cana-511	228	16	fixed	fix	VERB
cana-511	228	17	-	-	PUNCT
cana-511	228	18	point	point	NOUN
cana-511	228	19	theorems	theorem	NOUN
cana-511	228	20	in	in	ADP
cana-511	228	21	fuzzy	fuzzy	ADJ
cana-511	228	22	metric	metric	ADJ
cana-511	228	23	spaces	space	NOUN
cana-511	228	24	,	,	PUNCT
cana-511	228	25	fuzzy	fuzzy	ADJ
cana-511	228	26	sets	set	VERB
cana-511	228	27	syst	syst	PROPN
cana-511	228	28	.	.	PUNCT
cana-511	228	29	,	,	PUNCT
cana-511	228	30	125	125	NUM
cana-511	228	31	,	,	PUNCT
cana-511	228	32	245	245	NUM
cana-511	228	33	252	252	NUM
cana-511	228	34	.	.	PUNCT
cana-511	229	1	[	[	X
cana-511	229	2	6	6	NUM
cana-511	229	3	]	]	X
cana-511	229	4	gregori	gregori	X
cana-511	229	5	,	,	PUNCT
cana-511	229	6	v	v	NOUN
cana-511	229	7	.	.	PUNCT
cana-511	229	8	,	,	PUNCT
cana-511	229	9	minana	minana	PROPN
cana-511	229	10	,	,	PUNCT
cana-511	229	11	j.-j	j.-j	PROPN
cana-511	229	12	.	.	PUNCT
cana-511	229	13	(	(	PUNCT
cana-511	229	14	2014	2014	NUM
cana-511	229	15	)	)	PUNCT
cana-511	229	16	,	,	PUNCT
cana-511	229	17	so	so	SCONJ
cana-511	229	18	me	i	PRON
cana-511	229	19	remarks	remark	VERB
cana-511	229	20	on	on	ADP
cana-511	229	21	fuzzy	fuzzy	ADJ
cana-511	229	22	contractive	contractive	ADJ
cana-511	229	23	mappings	mapping	NOUN
cana-511	229	24	,	,	PUNCT
cana-511	229	25	fuzzy	fuzzy	ADJ
cana-511	229	26	se	se	PROPN
cana-511	229	27	t	t	PROPN
cana-511	229	28	s	s	PROPN
cana-511	229	29	syst	syst	PROPN
cana-511	229	30	.	.	PUNCT
cana-511	229	31	,	,	PUNCT
cana-511	229	32	2	2	NUM
cana-511	229	33	5	5	NUM
cana-511	229	34	1	1	NUM
cana-511	229	35	,	,	PUNCT
cana-511	229	36	1	1	NUM
cana-511	229	37	0	0	NUM
cana-511	229	38	1	1	NUM
cana-511	229	39	103	103	NUM
cana-511	229	40	.	.	PUNCT
cana-511	230	1	[	[	X
cana-511	230	2	7	7	NUM
cana-511	230	3	]	]	X
cana-511	230	4	jain	jain	PROPN
cana-511	230	5	,	,	PUNCT
cana-511	230	6	s.	s.	PROPN
cana-511	230	7	,	,	PUNCT
cana-511	230	8	singh	singh	PROPN
cana-511	230	9	,	,	PUNCT
cana-511	230	10	b.	b.	PROPN
cana-511	230	11	(	(	PUNCT
cana-511	230	12	2005	2005	NUM
cana-511	230	13	)	)	PUNCT
cana-511	230	14	,	,	PUNCT
cana-511	230	15	semi	semi	ADJ
cana-511	230	16	compatibility	compatibility	NOUN
cana-511	230	17	and	and	CCONJ
cana-511	230	18	fixed	fix	VERB
cana-511	230	19	point	point	NOUN
cana-511	230	20	theorems	theorem	NOUN
cana-511	230	21	in	in	ADP
cana-511	230	22	fuzzy	fuzzy	ADJ
cana-511	230	23	metric	metric	ADJ
cana-511	230	24	space	space	NOUN
cana-511	230	25	using	use	VERB
cana-511	230	26	implicit	implicit	ADJ
cana-511	230	27	relation	relation	NOUN
cana-511	230	28	,	,	PUNCT
cana-511	230	29	int	int	NOUN
cana-511	230	30	.	.	PUNCT
cana-511	231	1	j.	j.	PROPN
cana-511	231	2	math	math	PROPN
cana-511	231	3	.	.	PUNCT
cana-511	232	1	math	math	NOUN
cana-511	232	2	.	.	PUNCT
cana-511	233	1	sci	sci	PROPN
cana-511	233	2	.	.	PROPN
cana-511	233	3	2005:16	2005:16	NUM
cana-511	233	4	,	,	PUNCT
cana-511	233	5	2617	2617	NUM
cana-511	233	6	2629	2629	NUM
cana-511	233	7	.	.	PUNCT
cana-511	234	1	[	[	X
cana-511	234	2	8	8	NUM
cana-511	234	3	]	]	X
cana-511	234	4	kramosil	kramosil	NOUN
cana-511	234	5	,	,	PUNCT
cana-511	234	6	i.	i.	NOUN
cana-511	234	7	,	,	PUNCT
cana-511	234	8	michalek	michalek	NOUN
cana-511	234	9	,	,	PUNCT
cana-511	234	10	j	j	PROPN
cana-511	234	11	.	.	PUNCT
cana-511	235	1	(	(	PUNCT
cana-511	235	2	1975	1975	NUM
cana-511	235	3	)	)	PUNCT
cana-511	235	4	,	,	PUNCT
cana-511	235	5	fuzzy	fuzzy	ADJ
cana-511	235	6	metric	metric	ADJ
cana-511	235	7	and	and	CCONJ
cana-511	235	8	statistical	statistical	ADJ
cana-511	235	9	metric	metric	ADJ
cana-511	235	10	spaces	space	NOUN
cana-511	235	11	,	,	PUNCT
cana-511	235	12	kybernetika,11	kybernetika,11	NOUN
cana-511	235	13	,	,	PUNCT
cana-511	235	14	336	336	NUM
cana-511	235	15	344	344	NUM
cana-511	235	16	.	.	PUNCT
cana-511	236	1	[	[	X
cana-511	236	2	9	9	NUM
cana-511	236	3	]	]	SYM
cana-511	236	4	mihet	mihet	PROPN
cana-511	236	5	,	,	PUNCT
cana-511	236	6	d.	d.	PROPN
cana-511	236	7	(	(	PUNCT
cana-511	236	8	2008	2008	NUM
cana-511	236	9	)	)	PUNCT
cana-511	236	10	,	,	PUNCT
cana-511	236	11	fuzzy	fuzzy	ADJ
cana-511	236	12	ψ	ψ	ADJ
cana-511	236	13	-	-	ADJ
cana-511	236	14	contractive	contractive	ADJ
cana-511	236	15	mappings	mapping	NOUN
cana-511	236	16	in	in	ADP
cana-511	236	17	non	non	ADJ
cana-511	236	18	-	-	ADJ
cana-511	236	19	archimedean	archimedean	ADJ
cana-511	236	20	fuzzy	fuzzy	ADJ
cana-511	236	21	metric	metric	ADJ
cana-511	236	22	spaces	space	NOUN
cana-511	236	23	,	,	PUNCT
cana-511	236	24	fuzzy	fuzzy	ADJ
cana-511	236	25	sets	set	VERB
cana-511	236	26	syst	syst	PROPN
cana-511	236	27	.	.	PUNCT
cana-511	236	28	,	,	PUNCT
cana-511	236	29	159	159	NUM
cana-511	236	30	,	,	PUNCT
cana-511	236	31	739	739	NUM
cana-511	236	32	744	744	NUM
cana-511	236	33	.	.	PUNCT
cana-511	237	1	[	[	X
cana-511	237	2	10	10	NUM
cana-511	237	3	]	]	X
cana-511	237	4	schweizer	schweizer	PROPN
cana-511	237	5	,	,	PUNCT
cana-511	237	6	b.	b.	PROPN
cana-511	237	7	,	,	PUNCT
cana-511	237	8	sklar	sklar	PROPN
cana-511	237	9	,	,	PUNCT
cana-511	237	10	a.	a.	NOUN
cana-511	237	11	(	(	PUNCT
cana-511	237	12	1960	1960	NUM
cana-511	237	13	)	)	PUNCT
cana-511	237	14	,	,	PUNCT
cana-511	237	15	statistical	statistical	ADJ
cana-511	237	16	metric	metric	ADJ
cana-511	237	17	spaces	space	NOUN
cana-511	237	18	,	,	PUNCT
cana-511	237	19	pacific	pacific	PROPN
cana-511	237	20	j.	j.	PROPN
cana-511	237	21	math	math	PROPN
cana-511	237	22	.	.	PUNCT
cana-511	237	23	,	,	PUNCT
cana-511	237	24	10(1	10(1	NUM
cana-511	237	25	)	)	PUNCT
cana-511	237	26	,	,	PUNCT
cana-511	237	27	385	385	NUM
cana-511	237	28	389	389	NUM
cana-511	237	29	.	.	PUNCT
cana-511	237	30	communications	communication	NOUN
cana-511	237	31	on	on	ADP
cana-511	237	32	applied	apply	VERB
cana-511	237	33	nonlinear	nonlinear	ADJ
cana-511	237	34	analysis	analysis	NOUN
cana-511	237	35	issn	issn	NOUN
cana-511	237	36	:	:	PUNCT
cana-511	237	37	1074	1074	NUM
cana-511	237	38	-	-	PUNCT
cana-511	237	39	133x	133x	NUM
cana-511	237	40	vol	vol	NOUN
cana-511	237	41	31	31	NUM
cana-511	237	42	no	no	NOUN
cana-511	237	43	.	.	NOUN
cana-511	237	44	2	2	NUM
cana-511	237	45	(	(	PUNCT
cana-511	237	46	2024	2024	NUM
cana-511	237	47	)	)	PUNCT
cana-511	237	48	41	41	NUM
cana-511	237	49	https://internationalpubls.com	https://internationalpubls.com	X
cana-511	238	1	[	[	X
cana-511	238	2	11	11	NUM
cana-511	238	3	]	]	PUNCT
cana-511	238	4	shukla	shukla	NOUN
cana-511	238	5	,	,	PUNCT
cana-511	238	6	s.	s.	PROPN
cana-511	238	7	,	,	PUNCT
cana-511	238	8	gopal	gopal	PROPN
cana-511	238	9	,	,	PUNCT
cana-511	238	10	d.	d.	PROPN
cana-511	238	11	,	,	PUNCT
cana-511	238	12	sintunavarat	sintunavarat	PROPN
cana-511	238	13	,	,	PUNCT
cana-511	238	14	w.	w.	PROPN
cana-511	238	15	(	(	PUNCT
cana-511	238	16	2018	2018	NUM
cana-511	238	17	)	)	PUNCT
cana-511	238	18	,	,	PUNCT
cana-511	238	19	a	a	DET
cana-511	238	20	new	new	ADJ
cana-511	238	21	class	class	NOUN
cana-511	239	1	o	o	NOUN
cana-511	239	2	f	f	X
cana-511	239	3	fuzzy	fuzzy	ADJ
cana-511	239	4	contractive	contractive	ADJ
cana-511	239	5	mappings	mapping	NOUN
cana-511	239	6	and	and	CCONJ
cana-511	239	7	f	f	NOUN
cana-511	240	1	i	i	NOUN
cana-511	240	2	x	x	PUNCT
cana-511	240	3	e	e	NOUN
cana-511	241	1	d	d	NOUN
cana-511	241	2	p	p	X
cana-511	241	3	o	o	X
cana-511	241	4	i	i	PRON
cana-511	241	5	n	n	NOUN
cana-511	241	6	t	t	NOUN
cana-511	241	7	theorems	theorem	NOUN
cana-511	241	8	,	,	PUNCT
cana-511	241	9	fuzzy	fuzzy	ADJ
cana-511	241	10	sets	set	NOUN
cana-511	241	11	and	and	CCONJ
cana-511	241	12	systems	system	NOUN
cana-511	241	13	(	(	PUNCT
cana-511	241	14	in	in	ADP
cana-511	241	15	press	press	NOUN
cana-511	241	16	)	)	PUNCT
cana-511	241	17	.	.	PUNCT
cana-511	242	1	[	[	X
cana-511	242	2	12	12	NUM
cana-511	242	3	]	]	PUNCT
cana-511	242	4	tirado	tirado	NOUN
cana-511	242	5	,	,	PUNCT
cana-511	242	6	p.	p.	NOUN
cana-511	242	7	(	(	PUNCT
cana-511	242	8	2012	2012	NUM
cana-511	242	9	)	)	PUNCT
cana-511	242	10	,	,	PUNCT
cana-511	243	1	c	c	NOUN
cana-511	243	2	o	o	PROPN
cana-511	244	1	n	n	ADP
cana-511	244	2	t	t	NOUN
cana-511	244	3	r	r	NOUN
cana-511	244	4	a	a	DET
cana-511	244	5	c	c	NOUN
cana-511	244	6	t	t	NOUN
cana-511	245	1	i	i	PRON
cana-511	245	2	o	o	VERB
cana-511	245	3	n	n	PRON
cana-511	245	4	mappings	mapping	NOUN
cana-511	245	5	in	in	ADP
cana-511	245	6	fuzzy	fuzzy	ADJ
cana-511	245	7	quasi	quasi	ADJ
cana-511	245	8	-	-	ADJ
cana-511	245	9	metric	metric	ADJ
cana-511	245	10	spaces	space	NOUN
cana-511	245	11	a	a	DET
cana-511	245	12	n	n	NOUN
cana-511	245	13	d	d	NOUN
cana-511	245	14	[	[	X
cana-511	245	15	0	0	NUM
cana-511	245	16	,	,	PUNCT
cana-511	245	17	1	1	NUM
cana-511	245	18	]	]	X
cana-511	245	19	fuzzy	fuzzy	ADJ
cana-511	245	20	posets	poset	NOUN
cana-511	245	21	,	,	PUNCT
cana-511	245	22	f	f	PROPN
cana-511	245	23	i	i	NOUN
cana-511	245	24	x	x	PUNCT
cana-511	246	1	e	e	NOUN
cana-511	246	2	d	d	NOUN
cana-511	246	3	p	p	X
cana-511	246	4	o	o	X
cana-511	247	1	i	i	PRON
cana-511	247	2	n	n	NOUN
cana-511	247	3	t	t	PROPN
cana-511	247	4	theory	theory	NOUN
cana-511	247	5	,	,	PUNCT
cana-511	247	6	13(1	13(1	NUM
cana-511	247	7	)	)	PUNCT
cana-511	247	8	,	,	PUNCT
cana-511	247	9	273	273	NUM
cana-511	247	10	283	283	NUM
cana-511	247	11	.	.	PUNCT
cana-511	248	1	[	[	X
cana-511	248	2	13	13	NUM
cana-511	248	3	]	]	X
cana-511	248	4	d.	d.	PROPN
cana-511	248	5	wardowski	wardowski	PROPN
cana-511	248	6	(	(	PUNCT
cana-511	248	7	2013	2013	NUM
cana-511	248	8	)	)	PUNCT
cana-511	248	9	,	,	PUNCT
cana-511	248	10	fuzzy	fuzzy	ADJ
cana-511	248	11	contractive	contractive	ADJ
cana-511	248	12	mappings	mapping	NOUN
cana-511	248	13	and	and	CCONJ
cana-511	248	14	fixed	fix	VERB
cana-511	248	15	points	point	NOUN
cana-511	248	16	in	in	ADP
cana-511	248	17	fuzzy	fuzzy	ADJ
cana-511	248	18	metric	metric	ADJ
cana-511	248	19	spaces	space	NOUN
cana-511	248	20	,	,	PUNCT
cana-511	248	21	fuzzy	fuzzy	ADJ
cana-511	248	22	sets	set	VERB
cana-511	248	23	syst	syst	PROPN
cana-511	248	24	.	.	PUNCT
cana-511	248	25	,	,	PUNCT
cana-511	248	26	222	222	NUM
cana-511	248	27	,	,	PUNCT
cana-511	248	28	108	108	NUM
cana-511	248	29	114	114	NUM
cana-511	248	30	.	.	PUNCT