id	sid	tid	token	lemma	pos
cana-4135	1	1	communications	communication	NOUN
cana-4135	1	2	on	on	ADP
cana-4135	1	3	applied	apply	VERB
cana-4135	1	4	nonlinear	nonlinear	ADJ
cana-4135	1	5	analysis	analysis	NOUN
cana-4135	1	6	issn	issn	NOUN
cana-4135	1	7	:	:	PUNCT
cana-4135	1	8	1074	1074	NUM
cana-4135	1	9	-	-	PUNCT
cana-4135	1	10	133x	133x	NUM
cana-4135	1	11	vol	vol	NOUN
cana-4135	1	12	32	32	NUM
cana-4135	1	13	no	no	NOUN
cana-4135	1	14	.	.	PUNCT
cana-4135	2	1	9s	9s	NUM
cana-4135	2	2	(	(	PUNCT
cana-4135	2	3	2025	2025	NUM
cana-4135	2	4	)	)	PUNCT
cana-4135	2	5	1278	1278	NUM
cana-4135	2	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-4135	2	7	fixed	fix	VERB
cana-4135	2	8	point	point	NOUN
cana-4135	2	9	theorem	theorem	VERB
cana-4135	2	10	in	in	ADP
cana-4135	2	11	complete	complete	ADJ
cana-4135	2	12	multiplicative	multiplicative	ADJ
cana-4135	2	13	s	s	ADJ
cana-4135	2	14	-	-	ADJ
cana-4135	2	15	metric	metric	ADJ
cana-4135	2	16	space	space	NOUN
cana-4135	2	17	manjusha	manjusha	ADJ
cana-4135	2	18	p.	p.	NOUN
cana-4135	2	19	gandhi1	gandhi1	PROPN
cana-4135	2	20	,	,	PUNCT
cana-4135	2	21	anushree	anushree	ADJ
cana-4135	2	22	a.	a.	NOUN
cana-4135	2	23	aserkar2	aserkar2	PROPN
cana-4135	2	24	,	,	PUNCT
cana-4135	2	25	malabika	malabika	X
cana-4135	2	26	adak3	adak3	PROPN
cana-4135	2	27	,	,	PUNCT
cana-4135	2	28	nanda	nanda	PROPN
cana-4135	2	29	s.	s.	PROPN
cana-4135	2	30	thakre4	thakre4	PROPN
cana-4135	2	31	,	,	PUNCT
cana-4135	2	32	renuka	renuka	PROPN
cana-4135	2	33	nafdey5	nafdey5	PROPN
cana-4135	3	1	1associate	1associate	NUM
cana-4135	3	2	professor	professor	NOUN
cana-4135	3	3	,	,	PUNCT
cana-4135	3	4	department	department	NOUN
cana-4135	3	5	of	of	ADP
cana-4135	3	6	applied	apply	VERB
cana-4135	3	7	mathematics	mathematic	NOUN
cana-4135	3	8	and	and	CCONJ
cana-4135	3	9	humanities	humanity	NOUN
cana-4135	3	10	,	,	PUNCT
cana-4135	3	11	yeshwantrao	yeshwantrao	NOUN
cana-4135	3	12	chavan	chavan	PROPN
cana-4135	3	13	college	college	PROPN
cana-4135	3	14	of	of	ADP
cana-4135	3	15	engineering	engineering	PROPN
cana-4135	3	16	,	,	PUNCT
cana-4135	3	17	nagpur	nagpur	PROPN
cana-4135	3	18	,	,	PUNCT
cana-4135	3	19	441110	441110	NUM
cana-4135	3	20	,	,	PUNCT
cana-4135	3	21	india	india	PROPN
cana-4135	3	22	1manjusha_g2@rediffmail.com,2aserkar_aaa@rediffmail.com	1manjusha_g2@rediffmail.com,2aserkar_aaa@rediffmail.com	PROPN
cana-4135	3	23	2,3,4assistant	2,3,4assistant	NUM
cana-4135	3	24	professor	professor	NOUN
cana-4135	3	25	,	,	PUNCT
cana-4135	3	26	department	department	NOUN
cana-4135	3	27	of	of	ADP
cana-4135	3	28	applied	apply	VERB
cana-4135	3	29	mathematics	mathematic	NOUN
cana-4135	3	30	and	and	CCONJ
cana-4135	3	31	humanities	humanity	NOUN
cana-4135	3	32	,	,	PUNCT
cana-4135	3	33	yeshwantrao	yeshwantrao	NOUN
cana-4135	3	34	chavan	chavan	PROPN
cana-4135	3	35	college	college	PROPN
cana-4135	3	36	of	of	ADP
cana-4135	3	37	engineering	engineering	PROPN
cana-4135	3	38	,	,	PUNCT
cana-4135	3	39	nagpur	nagpur	PROPN
cana-4135	3	40	,	,	PUNCT
cana-4135	3	41	441110	441110	NUM
cana-4135	3	42	,	,	PUNCT
cana-4135	3	43	india	india	PROPN
cana-4135	3	44	5assistant	5assistant	NUM
cana-4135	3	45	professor	professor	NOUN
cana-4135	3	46	,	,	PUNCT
cana-4135	3	47	department	department	NOUN
cana-4135	3	48	of	of	ADP
cana-4135	3	49	physics	physics	PROPN
cana-4135	3	50	,	,	PUNCT
cana-4135	3	51	ramdeobaba	ramdeobaba	PROPN
cana-4135	3	52	university	university	PROPN
cana-4135	3	53	,	,	PUNCT
cana-4135	3	54	nagpur	nagpur	PROPN
cana-4135	3	55	,	,	PUNCT
cana-4135	3	56	india	india	PROPN
cana-4135	3	57	article	article	NOUN
cana-4135	3	58	history	history	NOUN
cana-4135	3	59	:	:	PUNCT
cana-4135	3	60	received	receive	VERB
cana-4135	3	61	:	:	PUNCT
cana-4135	3	62	12	12	NUM
cana-4135	3	63	-	-	SYM
cana-4135	3	64	01	01	NUM
cana-4135	3	65	-	-	PUNCT
cana-4135	3	66	2025	2025	NUM
cana-4135	3	67	revised	revise	VERB
cana-4135	3	68	:	:	PUNCT
cana-4135	3	69	15	15	NUM
cana-4135	3	70	-	-	NUM
cana-4135	3	71	02	02	NUM
cana-4135	3	72	-	-	PUNCT
cana-4135	3	73	2025	2025	NUM
cana-4135	3	74	accepted	accept	VERB
cana-4135	3	75	:	:	PUNCT
cana-4135	3	76	01	01	NUM
cana-4135	3	77	-	-	SYM
cana-4135	3	78	03	03	NUM
cana-4135	3	79	-	-	PUNCT
cana-4135	3	80	2025	2025	NUM
cana-4135	3	81	abstract	abstract	NOUN
cana-4135	3	82	:	:	PUNCT
cana-4135	3	83	the	the	DET
cana-4135	3	84	aim	aim	NOUN
cana-4135	3	85	of	of	ADP
cana-4135	3	86	this	this	DET
cana-4135	3	87	paper	paper	NOUN
cana-4135	3	88	to	to	PART
cana-4135	3	89	prove	prove	VERB
cana-4135	3	90	a	a	DET
cana-4135	3	91	unique	unique	ADJ
cana-4135	3	92	common	common	ADJ
cana-4135	3	93	fixed	fix	VERB
cana-4135	3	94	point	point	NOUN
cana-4135	3	95	theorem	theorem	NOUN
cana-4135	3	96	for	for	ADP
cana-4135	3	97	pair	pair	NOUN
cana-4135	3	98	of	of	ADP
cana-4135	3	99	noncontinuous	noncontinuous	ADJ
cana-4135	3	100	mappings	mapping	NOUN
cana-4135	3	101	in	in	ADP
cana-4135	3	102	multiplicative	multiplicative	PROPN
cana-4135	3	103	s	s	X
cana-4135	3	104	-metric	-metric	ADJ
cana-4135	3	105	space	space	NOUN
cana-4135	3	106	.	.	PUNCT
cana-4135	4	1	the	the	DET
cana-4135	4	2	authors	author	NOUN
cana-4135	4	3	have	have	AUX
cana-4135	4	4	introduced	introduce	VERB
cana-4135	4	5	a	a	DET
cana-4135	4	6	novel	novel	ADJ
cana-4135	4	7	contraction	contraction	NOUN
cana-4135	4	8	condition	condition	NOUN
cana-4135	4	9	to	to	PART
cana-4135	4	10	prove	prove	VERB
cana-4135	4	11	this	this	DET
cana-4135	4	12	result	result	NOUN
cana-4135	4	13	.	.	PUNCT
cana-4135	5	1	this	this	DET
cana-4135	5	2	theorem	theorem	NOUN
cana-4135	5	3	is	be	AUX
cana-4135	5	4	generalization	generalization	NOUN
cana-4135	5	5	,	,	PUNCT
cana-4135	5	6	improvement	improvement	NOUN
cana-4135	5	7	and	and	CCONJ
cana-4135	5	8	modification	modification	NOUN
cana-4135	5	9	of	of	ADP
cana-4135	5	10	existing	exist	VERB
cana-4135	5	11	results	result	NOUN
cana-4135	5	12	available	available	ADJ
cana-4135	5	13	in	in	ADP
cana-4135	5	14	the	the	DET
cana-4135	5	15	literature	literature	NOUN
cana-4135	5	16	.	.	PUNCT
cana-4135	6	1	an	an	DET
cana-4135	6	2	example	example	NOUN
cana-4135	6	3	has	have	AUX
cana-4135	6	4	been	be	AUX
cana-4135	6	5	given	give	VERB
cana-4135	6	6	to	to	PART
cana-4135	6	7	validate	validate	VERB
cana-4135	6	8	the	the	DET
cana-4135	6	9	result	result	NOUN
cana-4135	6	10	.	.	PUNCT
cana-4135	7	1	keywords	keyword	NOUN
cana-4135	7	2	:	:	PUNCT
cana-4135	7	3	fixed	fixed	ADJ
cana-4135	7	4	point	point	NOUN
cana-4135	7	5	,	,	PUNCT
cana-4135	7	6	multiplicative	multiplicative	ADJ
cana-4135	7	7	metric	metric	ADJ
cana-4135	7	8	space	space	NOUN
cana-4135	7	9	,	,	PUNCT
cana-4135	7	10	convergent	convergent	NOUN
cana-4135	7	11	,	,	PUNCT
cana-4135	7	12	mapping	mapping	NOUN
cana-4135	7	13	.	.	PUNCT
cana-4135	8	1	1	1	X
cana-4135	8	2	.	.	X
cana-4135	8	3	introduction	introduction	NOUN
cana-4135	8	4	the	the	DET
cana-4135	8	5	fixed	fix	VERB
cana-4135	8	6	point	point	NOUN
cana-4135	8	7	theory	theory	NOUN
cana-4135	8	8	has	have	AUX
cana-4135	8	9	started	start	VERB
cana-4135	8	10	in	in	ADP
cana-4135	8	11	1912	1912	NUM
cana-4135	8	12	.	.	PUNCT
cana-4135	9	1	it	it	PRON
cana-4135	9	2	has	have	VERB
cana-4135	9	3	three	three	NUM
cana-4135	9	4	main	main	ADJ
cana-4135	9	5	sections	section	NOUN
cana-4135	9	6	:	:	PUNCT
cana-4135	9	7	topological	topological	ADJ
cana-4135	9	8	fixed	fix	VERB
cana-4135	9	9	point	point	NOUN
cana-4135	9	10	theory	theory	NOUN
cana-4135	9	11	,	,	PUNCT
cana-4135	9	12	metric	metric	ADJ
cana-4135	9	13	fixed	fix	VERB
cana-4135	9	14	point	point	NOUN
cana-4135	9	15	theory	theory	NOUN
cana-4135	9	16	and	and	CCONJ
cana-4135	9	17	discrete	discrete	ADJ
cana-4135	9	18	fixed	fix	VERB
cana-4135	9	19	point	point	NOUN
cana-4135	9	20	theory	theory	NOUN
cana-4135	9	21	.	.	PUNCT
cana-4135	10	1	fréchet	fréchet	PROPN
cana-4135	11	1	[	[	X
cana-4135	11	2	1	1	X
cana-4135	11	3	]	]	PUNCT
cana-4135	11	4	introduced	introduce	VERB
cana-4135	11	5	metric	metric	ADJ
cana-4135	11	6	spaces	space	NOUN
cana-4135	11	7	in	in	ADP
cana-4135	11	8	the	the	DET
cana-4135	11	9	context	context	NOUN
cana-4135	11	10	of	of	ADP
cana-4135	11	11	functional	functional	ADJ
cana-4135	11	12	analysis	analysis	NOUN
cana-4135	11	13	.	.	PUNCT
cana-4135	12	1	further	far	ADV
cana-4135	12	2	many	many	ADJ
cana-4135	12	3	authors	author	NOUN
cana-4135	12	4	worked	work	VERB
cana-4135	12	5	on	on	ADP
cana-4135	12	6	it	it	PRON
cana-4135	12	7	and	and	CCONJ
cana-4135	12	8	initiated	initiate	VERB
cana-4135	12	9	various	various	ADJ
cana-4135	12	10	new	new	ADJ
cana-4135	12	11	spaces	space	NOUN
cana-4135	12	12	.	.	PUNCT
cana-4135	13	1	sedghi	sedghi	VERB
cana-4135	13	2	et	et	PROPN
cana-4135	13	3	al	al	PROPN
cana-4135	14	1	[	[	X
cana-4135	14	2	2	2	NUM
cana-4135	14	3	]	]	PUNCT
cana-4135	14	4	initiated	initiate	VERB
cana-4135	14	5	the	the	DET
cana-4135	14	6	concept	concept	NOUN
cana-4135	14	7	of	of	ADP
cana-4135	14	8	s	s	NOUN
cana-4135	14	9	-	-	ADJ
cana-4135	14	10	metric	metric	ADJ
cana-4135	14	11	space	space	NOUN
cana-4135	14	12	.	.	PUNCT
cana-4135	15	1	the	the	DET
cana-4135	15	2	authors	author	NOUN
cana-4135	15	3	[	[	X
cana-4135	15	4	3	3	NUM
cana-4135	15	5	]	]	PUNCT
cana-4135	15	6	,	,	PUNCT
cana-4135	15	7	[	[	X
cana-4135	15	8	4	4	NUM
cana-4135	15	9	]	]	PUNCT
cana-4135	15	10	,	,	PUNCT
cana-4135	15	11	[	[	X
cana-4135	15	12	5	5	NUM
cana-4135	15	13	]	]	PUNCT
cana-4135	15	14	,	,	PUNCT
cana-4135	15	15	[	[	X
cana-4135	15	16	6	6	NUM
cana-4135	15	17	]	]	PUNCT
cana-4135	15	18	,	,	PUNCT
cana-4135	15	19	[	[	X
cana-4135	15	20	7	7	NUM
cana-4135	15	21	]	]	PUNCT
cana-4135	15	22	,	,	PUNCT
cana-4135	15	23	[	[	X
cana-4135	15	24	8	8	NUM
cana-4135	15	25	]	]	PUNCT
cana-4135	15	26	,	,	PUNCT
cana-4135	15	27	[	[	X
cana-4135	15	28	9	9	NUM
cana-4135	15	29	]	]	PUNCT
cana-4135	15	30	,	,	PUNCT
cana-4135	15	31	[	[	X
cana-4135	15	32	10	10	NUM
cana-4135	15	33	]	]	PUNCT
cana-4135	15	34	have	have	AUX
cana-4135	15	35	extended	extend	VERB
cana-4135	15	36	the	the	DET
cana-4135	15	37	study	study	NOUN
cana-4135	15	38	of	of	ADP
cana-4135	15	39	s	s	NOUN
cana-4135	15	40	-	-	ADJ
cana-4135	15	41	metric	metric	ADJ
cana-4135	15	42	space	space	NOUN
cana-4135	15	43	.	.	PUNCT
cana-4135	16	1	ozavsar	ozavsar	VERB
cana-4135	16	2	et	et	PROPN
cana-4135	17	1	al	al	PROPN
cana-4135	18	1	[	[	X
cana-4135	18	2	11	11	NUM
cana-4135	18	3	]	]	PUNCT
cana-4135	18	4	showed	show	VERB
cana-4135	18	5	an	an	DET
cana-4135	18	6	equivalent	equivalent	NOUN
cana-4135	18	7	of	of	ADP
cana-4135	18	8	banach	banach	NOUN
cana-4135	18	9	contraction	contraction	NOUN
cana-4135	18	10	theorem	theorem	VERB
cana-4135	18	11	for	for	ADP
cana-4135	18	12	multiplicative	multiplicative	ADJ
cana-4135	18	13	metric	metric	ADJ
cana-4135	18	14	space	space	NOUN
cana-4135	18	15	.	.	PUNCT
cana-4135	19	1	the	the	DET
cana-4135	19	2	researchers	researcher	NOUN
cana-4135	19	3	kanchanapally	kanchanapally	ADV
cana-4135	19	4	et	et	X
cana-4135	19	5	al	al	PROPN
cana-4135	20	1	[	[	X
cana-4135	20	2	12	12	NUM
cana-4135	20	3	]	]	PUNCT
cana-4135	20	4	,	,	PUNCT
cana-4135	20	5	adewale	adewale	PROPN
cana-4135	20	6	et	et	PROPN
cana-4135	20	7	al	al	PROPN
cana-4135	21	1	[	[	X
cana-4135	21	2	13	13	NUM
cana-4135	21	3	]	]	PUNCT
cana-4135	21	4	and	and	CCONJ
cana-4135	21	5	terentius	terentius	NOUN
cana-4135	21	6	et	et	NOUN
cana-4135	21	7	al	al	PROPN
cana-4135	22	1	[	[	X
cana-4135	22	2	14	14	NUM
cana-4135	22	3	]	]	PUNCT
cana-4135	22	4	have	have	AUX
cana-4135	22	5	worked	work	VERB
cana-4135	22	6	on	on	ADP
cana-4135	22	7	recently	recently	ADV
cana-4135	22	8	developed	develop	VERB
cana-4135	22	9	multiplicative	multiplicative	ADJ
cana-4135	22	10	s	s	ADJ
cana-4135	22	11	-	-	ADJ
cana-4135	22	12	metric	metric	ADJ
cana-4135	22	13	space	space	NOUN
cana-4135	22	14	.	.	PUNCT
cana-4135	23	1	the	the	DET
cana-4135	23	2	authors	author	NOUN
cana-4135	23	3	are	be	AUX
cana-4135	23	4	motivated	motivated	ADJ
cana-4135	23	5	to	to	PART
cana-4135	23	6	work	work	VERB
cana-4135	23	7	on	on	ADP
cana-4135	23	8	multiplicative	multiplicative	ADJ
cana-4135	23	9	s	s	ADJ
cana-4135	23	10	-	-	ADJ
cana-4135	23	11	metric	metric	ADJ
cana-4135	23	12	space	space	NOUN
cana-4135	23	13	because	because	SCONJ
cana-4135	23	14	very	very	ADV
cana-4135	23	15	few	few	ADJ
cana-4135	23	16	researchers	researcher	NOUN
cana-4135	23	17	worked	work	VERB
cana-4135	23	18	in	in	ADP
cana-4135	23	19	this	this	DET
cana-4135	23	20	area	area	NOUN
cana-4135	23	21	.	.	PUNCT
cana-4135	24	1	the	the	DET
cana-4135	24	2	purpose	purpose	NOUN
cana-4135	24	3	of	of	ADP
cana-4135	24	4	the	the	DET
cana-4135	24	5	present	present	ADJ
cana-4135	24	6	study	study	NOUN
cana-4135	24	7	is	be	AUX
cana-4135	24	8	to	to	PART
cana-4135	24	9	establish	establish	VERB
cana-4135	24	10	a	a	DET
cana-4135	24	11	novel	novel	ADJ
cana-4135	24	12	theorem	theorem	NOUN
cana-4135	24	13	for	for	ADP
cana-4135	24	14	multiplicative	multiplicative	ADJ
cana-4135	24	15	s	s	ADJ
cana-4135	24	16	-	-	ADJ
cana-4135	24	17	metric	metric	ADJ
cana-4135	24	18	space	space	NOUN
cana-4135	24	19	.	.	PUNCT
cana-4135	25	1	we	we	PRON
cana-4135	25	2	have	have	AUX
cana-4135	25	3	presented	present	VERB
cana-4135	25	4	a	a	DET
cana-4135	25	5	distinguished	distinguished	ADJ
cana-4135	25	6	contraction	contraction	NOUN
cana-4135	25	7	condition	condition	NOUN
cana-4135	25	8	,	,	PUNCT
cana-4135	25	9	which	which	PRON
cana-4135	25	10	is	be	AUX
cana-4135	25	11	not	not	PART
cana-4135	25	12	available	available	ADJ
cana-4135	25	13	in	in	ADP
cana-4135	25	14	existing	exist	VERB
cana-4135	25	15	literature	literature	NOUN
cana-4135	25	16	.	.	PUNCT
cana-4135	26	1	also	also	ADV
cana-4135	26	2	proved	prove	VERB
cana-4135	26	3	two	two	NUM
cana-4135	26	4	new	new	ADJ
cana-4135	26	5	lemmas	lemma	NOUN
cana-4135	26	6	on	on	ADP
cana-4135	26	7	multiplicative	multiplicative	ADJ
cana-4135	26	8	s	s	ADJ
cana-4135	26	9	-	-	ADJ
cana-4135	26	10	metric	metric	ADJ
cana-4135	26	11	space	space	NOUN
cana-4135	26	12	.	.	PUNCT
cana-4135	27	1	2	2	X
cana-4135	27	2	.	.	X
cana-4135	27	3	preliminaries	preliminary	NOUN
cana-4135	27	4	the	the	DET
cana-4135	27	5	sequel	sequel	NOUN
cana-4135	27	6	include	include	VERB
cana-4135	27	7	the	the	DET
cana-4135	27	8	definitions	definition	NOUN
cana-4135	27	9	listed	list	VERB
cana-4135	27	10	below	below	ADP
cana-4135	27	11	:	:	PUNCT
cana-4135	27	12	definition	definition	NOUN
cana-4135	27	13	1.1[1	1.1[1	NUM
cana-4135	27	14	]	]	X
cana-4135	27	15	:	:	PUNCT
cana-4135	27	16	consider	consider	VERB
cana-4135	27	17	a	a	DET
cana-4135	27	18	non	non	ADJ
cana-4135	27	19	-	-	ADJ
cana-4135	27	20	empty	empty	ADJ
cana-4135	27	21	set	set	NOUN
cana-4135	27	22	m	m	PROPN
cana-4135	27	23	and	and	CCONJ
cana-4135	27	24	a	a	DET
cana-4135	27	25	function	function	NOUN
cana-4135	27	26	:	:	PUNCT
cana-4135	28	1	d	d	X
cana-4135	28	2	m	m	VERB
cana-4135	28	3	m	m	VERB
cana-4135	28	4	r	r	ADJ
cana-4135	28	5	→	→	PUNCT
cana-4135	28	6	such	such	ADJ
cana-4135	28	7	that	that	DET
cana-4135	28	8	mailto:1manjusha_g2@rediffmail.com,2aserkar_aaa@rediffmail.com	mailto:1manjusha_g2@rediffmail.com,2aserkar_aaa@rediffmail.com	PROPN
cana-4135	29	1	https://en.wikipedia.org/wiki/ren%c3%a9_maurice_fr%c3%a9chet	https://en.wikipedia.org/wiki/ren%c3%a9_maurice_fr%c3%a9chet	PROPN
cana-4135	29	2	https://en.wikipedia.org/wiki/functional_analysis	https://en.wikipedia.org/wiki/functional_analysis	NOUN
cana-4135	29	3	communications	communication	NOUN
cana-4135	29	4	on	on	ADP
cana-4135	29	5	applied	apply	VERB
cana-4135	29	6	nonlinear	nonlinear	ADJ
cana-4135	29	7	analysis	analysis	NOUN
cana-4135	29	8	issn	issn	NOUN
cana-4135	29	9	:	:	PUNCT
cana-4135	29	10	1074	1074	NUM
cana-4135	29	11	-	-	PUNCT
cana-4135	29	12	133x	133x	NUM
cana-4135	29	13	vol	vol	NOUN
cana-4135	29	14	32	32	NUM
cana-4135	29	15	no	no	NOUN
cana-4135	29	16	.	.	PUNCT
cana-4135	30	1	9s	9s	NUM
cana-4135	30	2	(	(	PUNCT
cana-4135	30	3	2025	2025	NUM
cana-4135	30	4	)	)	PUNCT
cana-4135	30	5	1279	1279	NUM
cana-4135	30	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4135	30	7	(	(	PUNCT
cana-4135	30	8	i	i	NOUN
cana-4135	30	9	)	)	PUNCT
cana-4135	30	10	(	(	PUNCT
cana-4135	30	11	)	)	PUNCT
cana-4135	30	12	,	,	PUNCT
cana-4135	30	13	0d	0d	X
cana-4135	31	1	h	h	VERB
cana-4135	32	1	i	i	PRON
cana-4135	32	2	=	=	PUNCT
cana-4135	32	3	for	for	ADP
cana-4135	32	4	all	all	PRON
cana-4135	32	5	,	,	PUNCT
cana-4135	32	6	h	h	NOUN
cana-4135	33	1	i	i	PRON
cana-4135	33	2	m	m	ADJ
cana-4135	33	3	:	:	PUNCT
cana-4135	33	4	(	(	PUNCT
cana-4135	33	5	)	)	PUNCT
cana-4135	33	6	,	,	PUNCT
cana-4135	33	7	0	0	PUNCT
cana-4135	34	1	d	d	NOUN
cana-4135	34	2	h	h	NOUN
cana-4135	35	1	i	i	PRON
cana-4135	35	2	=	=	PUNCT
cana-4135	36	1	if	if	SCONJ
cana-4135	36	2	and	and	CCONJ
cana-4135	36	3	only	only	ADV
cana-4135	36	4	if	if	SCONJ
cana-4135	36	5	h	h	PRON
cana-4135	36	6	i=	i=	PROPN
cana-4135	36	7	(	(	PUNCT
cana-4135	36	8	ii	ii	NOUN
cana-4135	36	9	)	)	PUNCT
cana-4135	36	10	(	(	PUNCT
cana-4135	36	11	)	)	PUNCT
cana-4135	36	12	(	(	PUNCT
cana-4135	36	13	)	)	PUNCT
cana-4135	36	14	,	,	PUNCT
cana-4135	36	15	,	,	PUNCT
cana-4135	36	16	d	d	NOUN
cana-4135	36	17	h	h	NOUN
cana-4135	37	1	i	i	PRON
cana-4135	38	1	d	d	VERB
cana-4135	38	2	i	i	PRON
cana-4135	38	3	h=	h=	VERB
cana-4135	38	4	for	for	ADP
cana-4135	38	5	all	all	PRON
cana-4135	38	6	,	,	PUNCT
cana-4135	38	7	h	h	NOUN
cana-4135	39	1	i	i	PRON
cana-4135	39	2	m	m	PROPN
cana-4135	39	3	(	(	PUNCT
cana-4135	39	4	iii	iii	NOUN
cana-4135	39	5	)	)	PUNCT
cana-4135	39	6	(	(	PUNCT
cana-4135	39	7	)	)	PUNCT
cana-4135	39	8	(	(	PUNCT
cana-4135	39	9	)	)	PUNCT
cana-4135	39	10	(	(	PUNCT
cana-4135	39	11	)	)	PUNCT
cana-4135	39	12	,	,	PUNCT
cana-4135	39	13	  	  	SPACE
cana-4135	39	14	,	,	PUNCT
cana-4135	39	15	,	,	PUNCT
cana-4135	39	16	d	d	NOUN
cana-4135	39	17	h	h	NOUN
cana-4135	40	1	i	i	NOUN
cana-4135	41	1	d	d	NOUN
cana-4135	41	2	h	h	NOUN
cana-4135	42	1	j	j	PROPN
cana-4135	42	2	d	d	X
cana-4135	42	3	j	j	PROPN
cana-4135	42	4	i	i	PROPN
cana-4135	42	5	+	+	X
cana-4135	42	6	for	for	ADP
cana-4135	42	7	all	all	PRON
cana-4135	42	8	,	,	PUNCT
cana-4135	42	9	h	h	NOUN
cana-4135	43	1	i	i	PRON
cana-4135	43	2	m	m	PROPN
cana-4135	43	3	.	.	PUNCT
cana-4135	44	1	here	here	ADV
cana-4135	44	2	d	d	X
cana-4135	44	3	is	be	AUX
cana-4135	44	4	named	name	VERB
cana-4135	44	5	as	as	ADV
cana-4135	44	6	metric	metric	ADJ
cana-4135	44	7	on	on	ADP
cana-4135	44	8	m	m	PROPN
cana-4135	44	9	,	,	PUNCT
cana-4135	44	10	and	and	CCONJ
cana-4135	44	11	(	(	PUNCT
cana-4135	44	12	)	)	PUNCT
cana-4135	44	13	,	,	PUNCT
cana-4135	44	14	m	m	PROPN
cana-4135	44	15	d	d	NOUN
cana-4135	44	16	is	be	AUX
cana-4135	44	17	metric	metric	ADJ
cana-4135	44	18	space	space	NOUN
cana-4135	44	19	.	.	PUNCT
cana-4135	45	1	definition	definition	NOUN
cana-4135	45	2	1.2[12	1.2[12	NUM
cana-4135	45	3	]	]	PUNCT
cana-4135	45	4	:	:	PUNCT
cana-4135	45	5	assume	assume	VERB
cana-4135	45	6	3	3	NUM
cana-4135	45	7	:	:	PUNCT
cana-4135	45	8	[	[	X
cana-4135	45	9	0	0	NUM
cana-4135	45	10	,	,	PUNCT
cana-4135	45	11	)	)	PUNCT
cana-4135	45	12	s	s	PART
cana-4135	45	13	m	m	VERB
cana-4135	45	14	→	→	SYM
cana-4135	45	15			NOUN
cana-4135	45	16	is	be	AUX
cana-4135	45	17	a	a	DET
cana-4135	45	18	function	function	NOUN
cana-4135	45	19	,	,	PUNCT
cana-4135	45	20	that	that	PRON
cana-4135	45	21	satisfy	satisfy	VERB
cana-4135	45	22	the	the	DET
cana-4135	45	23	constraints	constraint	NOUN
cana-4135	45	24	for	for	ADP
cana-4135	45	25	every	every	PRON
cana-4135	45	26	,	,	PUNCT
cana-4135	45	27	,	,	PUNCT
cana-4135	45	28	,	,	PUNCT
cana-4135	45	29	h	h	NOUN
cana-4135	46	1	i	i	PRON
cana-4135	46	2	j	j	PROPN
cana-4135	47	1	k	k	PROPN
cana-4135	47	2	m	m	PROPN
cana-4135	47	3	,	,	PUNCT
cana-4135	47	4	as	as	ADP
cana-4135	47	5	here	here	ADV
cana-4135	47	6	under	under	ADP
cana-4135	47	7	1	1	NUM
cana-4135	47	8	)	)	PUNCT
cana-4135	47	9	(	(	PUNCT
cana-4135	47	10	,	,	PUNCT
cana-4135	47	11	,	,	PUNCT
cana-4135	47	12	)	)	PUNCT
cana-4135	47	13	1s	1s	NUM
cana-4135	48	1	h	h	NOUN
cana-4135	49	1	i	i	NOUN
cana-4135	49	2	j	j	PROPN
cana-4135	50	1	=	=	PRON
cana-4135	50	2	,	,	PUNCT
cana-4135	50	3	iff	iff	PROPN
cana-4135	50	4	h	h	NOUN
cana-4135	50	5	i	i	PRON
cana-4135	50	6	j=	j=	VERB
cana-4135	50	7	=	=	PUNCT
cana-4135	50	8	.	.	PUNCT
cana-4135	51	1	2	2	X
cana-4135	51	2	)	)	PUNCT
cana-4135	51	3	(	(	PUNCT
cana-4135	51	4	,	,	PUNCT
cana-4135	51	5	,	,	PUNCT
cana-4135	51	6	)	)	PUNCT
cana-4135	51	7	(	(	PUNCT
cana-4135	51	8	,	,	PUNCT
cana-4135	51	9	,	,	PUNCT
cana-4135	51	10	)	)	PUNCT
cana-4135	51	11	(	(	PUNCT
cana-4135	51	12	,	,	PUNCT
cana-4135	51	13	,	,	PUNCT
cana-4135	51	14	)	)	PUNCT
cana-4135	51	15	(	(	PUNCT
cana-4135	51	16	,	,	PUNCT
cana-4135	51	17	,	,	PUNCT
cana-4135	51	18	)	)	PUNCT
cana-4135	51	19	s	s	PART
cana-4135	52	1	h	h	NOUN
cana-4135	53	1	i	i	PRON
cana-4135	53	2	j	j	PROPN
cana-4135	53	3	s	s	VERB
cana-4135	54	1	h	h	NOUN
cana-4135	55	1	h	h	NOUN
cana-4135	56	1	k	k	PROPN
cana-4135	56	2	s	s	VERB
cana-4135	57	1	i	i	PRON
cana-4135	58	1	i	i	PRON
cana-4135	58	2	k	k	PROPN
cana-4135	58	3	s	s	PROPN
cana-4135	58	4	j	j	PROPN
cana-4135	58	5	j	j	PROPN
cana-4135	58	6	k	k	PROPN
cana-4135	59	1	+	+	CCONJ
cana-4135	59	2	+	+	NUM
cana-4135	59	3	couple	couple	NOUN
cana-4135	59	4	(	(	PUNCT
cana-4135	59	5	,	,	PUNCT
cana-4135	59	6	)	)	PUNCT
cana-4135	59	7	m	m	VERB
cana-4135	59	8	s	s	VERB
cana-4135	59	9	is	be	AUX
cana-4135	59	10	named	name	VERB
cana-4135	59	11	as	as	ADP
cana-4135	59	12	s	s	NOUN
cana-4135	59	13	-metric	-metric	ADJ
cana-4135	59	14	space	space	NOUN
cana-4135	59	15	.	.	PUNCT
cana-4135	60	1	here	here	ADV
cana-4135	60	2	m	m	VERB
cana-4135	60	3	is	be	AUX
cana-4135	60	4	non	non	ADJ
cana-4135	60	5	-	-	ADJ
cana-4135	60	6	empty	empty	ADJ
cana-4135	60	7	set	set	NOUN
cana-4135	60	8	.	.	PUNCT
cana-4135	61	1	definition	definition	NOUN
cana-4135	61	2	1.3	1.3	NUM
cana-4135	62	1	[	[	X
cana-4135	62	2	12	12	NUM
cana-4135	62	3	]	]	X
cana-4135	62	4	:	:	PUNCT
cana-4135	62	5	let	let	VERB
cana-4135	62	6	m	m	PRON
cana-4135	62	7	be	be	AUX
cana-4135	62	8	a	a	DET
cana-4135	62	9	nonempty	nonempty	ADJ
cana-4135	62	10	set	set	VERB
cana-4135	62	11	.	.	PUNCT
cana-4135	63	1	then	then	ADV
cana-4135	63	2	the	the	DET
cana-4135	63	3	function	function	NOUN
cana-4135	63	4	3	3	NUM
cana-4135	63	5	:	:	PUNCT
cana-4135	63	6	[	[	X
cana-4135	63	7	0	0	NUM
cana-4135	63	8	,	,	PUNCT
cana-4135	63	9	)	)	PUNCT
cana-4135	63	10	s	s	PART
cana-4135	63	11	m	m	VERB
cana-4135	63	12	→	→	SYM
cana-4135	63	13			NOUN
cana-4135	63	14	is	be	AUX
cana-4135	63	15	named	name	VERB
cana-4135	63	16	as	as	ADP
cana-4135	63	17	multiplicative	multiplicative	ADJ
cana-4135	63	18	s	s	NOUN
cana-4135	63	19	-	-	ADJ
cana-4135	63	20	metric	metric	ADJ
cana-4135	63	21	on	on	ADP
cana-4135	63	22	m	m	PRON
cana-4135	63	23	,	,	PUNCT
cana-4135	63	24	if	if	SCONJ
cana-4135	63	25	and	and	CCONJ
cana-4135	63	26	only	only	ADV
cana-4135	63	27	if	if	SCONJ
cana-4135	63	28	,	,	PUNCT
cana-4135	63	29	the	the	DET
cana-4135	63	30	constraints	constraint	NOUN
cana-4135	63	31	below	below	ADV
cana-4135	63	32	are	be	AUX
cana-4135	63	33	true	true	ADJ
cana-4135	63	34	for	for	ADP
cana-4135	63	35	all	all	PRON
cana-4135	63	36	,	,	PUNCT
cana-4135	63	37	,	,	PUNCT
cana-4135	63	38	,	,	PUNCT
cana-4135	63	39	h	h	NOUN
cana-4135	64	1	i	i	PRON
cana-4135	64	2	j	j	PROPN
cana-4135	65	1	k	k	PROPN
cana-4135	65	2	m	m	PROPN
cana-4135	65	3	(	(	PUNCT
cana-4135	65	4	i	i	NOUN
cana-4135	65	5	)	)	PUNCT
cana-4135	65	6	(	(	PUNCT
cana-4135	65	7	,	,	PUNCT
cana-4135	65	8	,	,	PUNCT
cana-4135	65	9	)	)	PUNCT
cana-4135	66	1	1s	1s	NUM
cana-4135	67	1	h	h	NOUN
cana-4135	68	1	i	i	PRON
cana-4135	68	2	j	j	PROPN
cana-4135	68	3			NUM
cana-4135	68	4	(	(	PUNCT
cana-4135	68	5	ii	ii	NOUN
cana-4135	68	6	)	)	PUNCT
cana-4135	68	7	(	(	PUNCT
cana-4135	68	8	,	,	PUNCT
cana-4135	68	9	,	,	PUNCT
cana-4135	68	10	)	)	PUNCT
cana-4135	68	11	1s	1s	NUM
cana-4135	69	1	h	h	NOUN
cana-4135	70	1	i	i	PRON
cana-4135	70	2	i	i	PRON
cana-4135	70	3	h	h	VERB
cana-4135	71	1	i	i	PRON
cana-4135	71	2	j=	j=	VERB
cana-4135	71	3			PUNCT
cana-4135	72	1	=	=	PUNCT
cana-4135	72	2	=	=	SYM
cana-4135	72	3	(	(	PUNCT
cana-4135	72	4	iii	iii	NOUN
cana-4135	72	5	)	)	PUNCT
cana-4135	72	6	(	(	PUNCT
cana-4135	72	7	,	,	PUNCT
cana-4135	72	8	,	,	PUNCT
cana-4135	72	9	)	)	PUNCT
cana-4135	72	10	(	(	PUNCT
cana-4135	72	11	,	,	PUNCT
cana-4135	72	12	,	,	PUNCT
cana-4135	72	13	)	)	PUNCT
cana-4135	72	14	(	(	PUNCT
cana-4135	72	15	,	,	PUNCT
cana-4135	72	16	,	,	PUNCT
cana-4135	72	17	)	)	PUNCT
cana-4135	72	18	(	(	PUNCT
cana-4135	72	19	,	,	PUNCT
cana-4135	72	20	,	,	PUNCT
cana-4135	72	21	)	)	PUNCT
cana-4135	72	22	s	s	PART
cana-4135	72	23	h	h	NOUN
cana-4135	73	1	i	i	PRON
cana-4135	73	2	j	j	PROPN
cana-4135	73	3	s	s	VERB
cana-4135	74	1	h	h	NOUN
cana-4135	75	1	h	h	NOUN
cana-4135	76	1	k	k	PROPN
cana-4135	76	2	s	s	VERB
cana-4135	77	1	i	i	PRON
cana-4135	78	1	i	i	PRON
cana-4135	78	2	k	k	PROPN
cana-4135	78	3	s	s	PROPN
cana-4135	79	1	j	j	PROPN
cana-4135	79	2	j	j	PROPN
cana-4135	79	3	k	k	PROPN
cana-4135	79	4	here	here	ADV
cana-4135	79	5	(	(	PUNCT
cana-4135	79	6	,	,	PUNCT
cana-4135	79	7	)	)	PUNCT
cana-4135	79	8	m	m	VERB
cana-4135	79	9	s	s	VERB
cana-4135	79	10	is	be	AUX
cana-4135	79	11	named	name	VERB
cana-4135	79	12	as	as	ADP
cana-4135	79	13	multiplicative	multiplicative	ADJ
cana-4135	79	14	s	s	ADJ
cana-4135	79	15	-	-	ADJ
cana-4135	79	16	metric	metric	ADJ
cana-4135	79	17	space	space	NOUN
cana-4135	79	18	.	.	PUNCT
cana-4135	80	1	definition	definition	NOUN
cana-4135	80	2	1.4	1.4	NUM
cana-4135	81	1	[	[	X
cana-4135	81	2	12	12	NUM
cana-4135	81	3	]	]	X
cana-4135	81	4	:	:	PUNCT
cana-4135	81	5	a	a	DET
cana-4135	81	6	sequence	sequence	NOUN
cana-4135	81	7	{	{	PUNCT
cana-4135	81	8	}	}	PUNCT
cana-4135	81	9	nh	nh	PROPN
cana-4135	81	10	in	in	ADP
cana-4135	81	11	multiplicative	multiplicative	ADJ
cana-4135	81	12	s	s	ADJ
cana-4135	81	13	-	-	ADJ
cana-4135	81	14	metric	metric	ADJ
cana-4135	81	15	space	space	NOUN
cana-4135	81	16	(	(	PUNCT
cana-4135	81	17	,	,	PUNCT
cana-4135	81	18	)	)	PUNCT
cana-4135	81	19	m	m	PROPN
cana-4135	81	20	s	s	NOUN
cana-4135	81	21	is	be	AUX
cana-4135	81	22	multiplicative	multiplicative	ADJ
cana-4135	81	23	sconverges	sconverge	NOUN
cana-4135	81	24	to	to	ADP
cana-4135	81	25	h	h	PROPN
cana-4135	81	26	m	m	PROPN
cana-4135	81	27	iff	iff	PROPN
cana-4135	81	28	for	for	ADP
cana-4135	81	29	every	every	DET
cana-4135	81	30	1	1	NUM
cana-4135	81	31			INTJ
cana-4135	81	32	,	,	PUNCT
cana-4135	81	33	there	there	PRON
cana-4135	81	34	exists	exist	VERB
cana-4135	81	35			PROPN
cana-4135	81	36	such	such	ADJ
cana-4135	81	37	that	that	PRON
cana-4135	81	38	(	(	PUNCT
cana-4135	81	39	,	,	PUNCT
cana-4135	81	40	,	,	PUNCT
cana-4135	81	41	)	)	PUNCT
cana-4135	81	42	n	n	X
cana-4135	82	1	ns	ns	NUM
cana-4135	82	2	h	h	NOUN
cana-4135	82	3	h	h	NOUN
cana-4135	82	4	h	h	PROPN
cana-4135	82	5			X
cana-4135	82	6	,	,	PUNCT
cana-4135	82	7	for	for	ADP
cana-4135	82	8	all	all	DET
cana-4135	82	9	n	n	PRON
cana-4135	82	10			NOUN
cana-4135	82	11	.	.	PUNCT
cana-4135	83	1	definition	definition	NOUN
cana-4135	83	2	1.5[12	1.5[12	NUM
cana-4135	83	3	]	]	PUNCT
cana-4135	83	4	:	:	PUNCT
cana-4135	83	5	the	the	DET
cana-4135	83	6	sequence	sequence	NOUN
cana-4135	83	7	{	{	PUNCT
cana-4135	83	8	}	}	PUNCT
cana-4135	83	9	nh	nh	X
cana-4135	83	10	of	of	ADP
cana-4135	83	11	multiplicative	multiplicative	ADJ
cana-4135	83	12	s	s	ADJ
cana-4135	83	13	-	-	ADJ
cana-4135	83	14	metric	metric	ADJ
cana-4135	83	15	space	space	NOUN
cana-4135	83	16	(	(	PUNCT
cana-4135	83	17	,	,	PUNCT
cana-4135	83	18	)	)	PUNCT
cana-4135	83	19	m	m	PROPN
cana-4135	83	20	s	s	PRON
cana-4135	83	21	,	,	PUNCT
cana-4135	83	22	is	be	AUX
cana-4135	83	23	known	know	VERB
cana-4135	83	24	as	as	ADP
cana-4135	83	25	multiplicative	multiplicative	ADJ
cana-4135	83	26	s	s	ADJ
cana-4135	83	27	-	-	ADJ
cana-4135	83	28	cauchy	cauchy	ADJ
cana-4135	83	29	sequence	sequence	NOUN
cana-4135	83	30	of	of	ADP
cana-4135	83	31	m	m	PROPN
cana-4135	83	32	if	if	SCONJ
cana-4135	84	1	and	and	CCONJ
cana-4135	84	2	only	only	ADV
cana-4135	84	3	if	if	SCONJ
cana-4135	84	4	,	,	PUNCT
cana-4135	84	5	for	for	ADP
cana-4135	84	6	every	every	DET
cana-4135	84	7	1	1	NUM
cana-4135	84	8			INTJ
cana-4135	84	9	,	,	PUNCT
cana-4135	84	10	there	there	PRON
cana-4135	84	11	occurs	occur	VERB
cana-4135	84	12	a	a	DET
cana-4135	84	13			PROPN
cana-4135	84	14	such	such	ADJ
cana-4135	84	15	that	that	PRON
cana-4135	84	16	(	(	PUNCT
cana-4135	84	17	,	,	PUNCT
cana-4135	84	18	,	,	PUNCT
cana-4135	84	19	)	)	PUNCT
cana-4135	84	20	n	n	CCONJ
cana-4135	84	21	n	n	PROPN
cana-4135	84	22	ms	ms	NOUN
cana-4135	84	23	h	h	PROPN
cana-4135	84	24	h	h	PROPN
cana-4135	84	25	h	h	PROPN
cana-4135	84	26			X
cana-4135	84	27	,	,	PUNCT
cana-4135	84	28	for	for	ADP
cana-4135	84	29	each	each	PRON
cana-4135	84	30	,	,	PUNCT
cana-4135	84	31	n	n	PRON
cana-4135	84	32	m	m	VERB
cana-4135	84	33			ADJ
cana-4135	84	34	.	.	PUNCT
cana-4135	85	1	definition	definition	NOUN
cana-4135	85	2	1.6	1.6	NUM
cana-4135	86	1	[	[	X
cana-4135	86	2	12	12	NUM
cana-4135	86	3	]	]	X
cana-4135	86	4	:	:	PUNCT
cana-4135	86	5	the	the	DET
cana-4135	86	6	multiplicative	multiplicative	ADJ
cana-4135	86	7	s	s	ADJ
cana-4135	86	8	-	-	ADJ
cana-4135	86	9	metric	metric	ADJ
cana-4135	86	10	space	space	NOUN
cana-4135	86	11	(	(	PUNCT
cana-4135	86	12	,	,	PUNCT
cana-4135	86	13	)	)	PUNCT
cana-4135	86	14	m	m	PROPN
cana-4135	86	15	s	s	NOUN
cana-4135	86	16	is	be	AUX
cana-4135	86	17	complete	complete	ADJ
cana-4135	86	18	iff	iff	PROPN
cana-4135	86	19	,	,	PUNCT
cana-4135	86	20	each	each	DET
cana-4135	86	21	multiplicative	multiplicative	ADJ
cana-4135	86	22	scauchy	scauchy	NOUN
cana-4135	86	23	sequence	sequence	NOUN
cana-4135	86	24	of	of	ADP
cana-4135	86	25	m	m	PROPN
cana-4135	86	26	is	be	AUX
cana-4135	86	27	multiplicative	multiplicative	ADJ
cana-4135	86	28	s	s	NOUN
cana-4135	86	29	-	-	NOUN
cana-4135	86	30	convergent	convergent	NOUN
cana-4135	86	31	of	of	ADP
cana-4135	86	32	m	m	PROPN
cana-4135	86	33	.	.	PUNCT
cana-4135	87	1	3	3	X
cana-4135	87	2	.	.	X
cana-4135	87	3	main	main	ADJ
cana-4135	87	4	result	result	NOUN
cana-4135	87	5	we	we	PRON
cana-4135	87	6	have	have	AUX
cana-4135	87	7	proved	prove	VERB
cana-4135	87	8	following	follow	VERB
cana-4135	87	9	two	two	NUM
cana-4135	87	10	lemmas	lemma	NOUN
cana-4135	87	11	,	,	PUNCT
cana-4135	87	12	which	which	PRON
cana-4135	87	13	are	be	AUX
cana-4135	87	14	required	require	VERB
cana-4135	87	15	to	to	PART
cana-4135	87	16	prove	prove	VERB
cana-4135	87	17	the	the	DET
cana-4135	87	18	theorems	theorem	NOUN
cana-4135	87	19	in	in	ADP
cana-4135	87	20	the	the	DET
cana-4135	87	21	present	present	ADJ
cana-4135	87	22	paper	paper	NOUN
cana-4135	87	23	.	.	PUNCT
cana-4135	88	1	lemma1	lemma1	PROPN
cana-4135	88	2	:	:	PUNCT
cana-4135	88	3	consider	consider	VERB
cana-4135	88	4	(	(	PUNCT
cana-4135	88	5	,	,	PUNCT
cana-4135	88	6	)	)	PUNCT
cana-4135	88	7	m	m	PROPN
cana-4135	88	8	s	s	NOUN
cana-4135	88	9	is	be	AUX
cana-4135	88	10	a	a	DET
cana-4135	88	11	multiplicative	multiplicative	ADJ
cana-4135	88	12	s	s	X
cana-4135	88	13	-metric	-metric	ADJ
cana-4135	88	14	space	space	NOUN
cana-4135	88	15	,	,	PUNCT
cana-4135	88	16	{	{	PUNCT
cana-4135	88	17	}	}	PUNCT
cana-4135	88	18	nh	nh	PROPN
cana-4135	88	19	and	and	CCONJ
cana-4135	88	20	{	{	PUNCT
cana-4135	88	21	}	}	PUNCT
cana-4135	88	22	ni	ni	PROPN
cana-4135	88	23	are	be	AUX
cana-4135	88	24	s	s	NOUN
cana-4135	88	25	convergent	convergent	NOUN
cana-4135	88	26	to	to	PART
cana-4135	88	27	,	,	PUNCT
cana-4135	88	28	h	h	VERB
cana-4135	88	29	i	i	PRON
cana-4135	88	30	respectively	respectively	ADV
cana-4135	88	31	.	.	PUNCT
cana-4135	89	1	then	then	ADV
cana-4135	89	2	,	,	PUNCT
cana-4135	89	3	we	we	PRON
cana-4135	89	4	have	have	VERB
cana-4135	89	5	limsup	limsup	NOUN
cana-4135	89	6	(	(	PUNCT
cana-4135	89	7	,	,	PUNCT
cana-4135	89	8	,	,	PUNCT
cana-4135	89	9	)	)	PUNCT
cana-4135	89	10	(	(	PUNCT
cana-4135	89	11	,	,	PUNCT
cana-4135	89	12	,	,	PUNCT
cana-4135	89	13	)	)	PUNCT
cana-4135	89	14	(	(	PUNCT
cana-4135	89	15	,	,	PUNCT
cana-4135	89	16	,	,	PUNCT
cana-4135	89	17	)	)	PUNCT
cana-4135	89	18	n	n	CCONJ
cana-4135	89	19	n	n	PROPN
cana-4135	89	20	n	n	NOUN
cana-4135	89	21	s	s	NOUN
cana-4135	89	22	h	h	NOUN
cana-4135	90	1	j	j	NOUN
cana-4135	91	1	i	i	PRON
cana-4135	91	2	s	s	VERB
cana-4135	91	3	j	j	PROPN
cana-4135	92	1	j	j	PROPN
cana-4135	92	2	h	h	PROPN
cana-4135	92	3	s	s	VERB
cana-4135	93	1	h	h	NOUN
cana-4135	93	2	h	h	NOUN
cana-4135	94	1	i	i	PRON
cana-4135	94	2	→	→	VERB
cana-4135	94	3			NOUN
cana-4135	94	4	.	.	PUNCT
cana-4135	95	1	communications	communication	NOUN
cana-4135	95	2	on	on	ADP
cana-4135	95	3	applied	apply	VERB
cana-4135	95	4	nonlinear	nonlinear	ADJ
cana-4135	95	5	analysis	analysis	NOUN
cana-4135	95	6	issn	issn	NOUN
cana-4135	95	7	:	:	PUNCT
cana-4135	95	8	1074	1074	NUM
cana-4135	95	9	-	-	PUNCT
cana-4135	95	10	133x	133x	NUM
cana-4135	95	11	vol	vol	NOUN
cana-4135	95	12	32	32	NUM
cana-4135	95	13	no	no	NOUN
cana-4135	95	14	.	.	PUNCT
cana-4135	96	1	9s	9s	NUM
cana-4135	96	2	(	(	PUNCT
cana-4135	96	3	2025	2025	NUM
cana-4135	96	4	)	)	PUNCT
cana-4135	96	5	1280	1280	NUM
cana-4135	97	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4135	97	2	proof	proof	NOUN
cana-4135	97	3	:	:	PUNCT
cana-4135	97	4	let	let	VERB
cana-4135	97	5	lim	lim	PROPN
cana-4135	97	6	,	,	PUNCT
cana-4135	97	7	limn	limn	PROPN
cana-4135	97	8	n	n	CCONJ
cana-4135	97	9	n	n	CCONJ
cana-4135	97	10	n	n	NOUN
cana-4135	97	11	h	h	NOUN
cana-4135	98	1	h	h	NOUN
cana-4135	99	1	i	i	PRON
cana-4135	99	2	i	i	PRON
cana-4135	99	3	→	→	VERB
cana-4135	99	4	→	→	PUNCT
cana-4135	99	5	=	=	NOUN
cana-4135	100	1	=	=	NOUN
cana-4135	100	2	.	.	PUNCT
cana-4135	101	1	then	then	ADV
cana-4135	101	2	for	for	ADP
cana-4135	101	3	each	each	PRON
cana-4135	101	4	0,	0,	NOUN
cana-4135	102	1			NOUN
cana-4135	102	2	there	there	PRON
cana-4135	102	3	exists	exist	VERB
cana-4135	102	4	natural	natural	ADJ
cana-4135	102	5	numbers	number	NOUN
cana-4135	102	6	1	1	NUM
cana-4135	102	7	2,n	2,n	NUM
cana-4135	102	8	n	n	NOUN
cana-4135	102	9	such	such	ADJ
cana-4135	102	10	that	that	PRON
cana-4135	102	11	for	for	ADP
cana-4135	102	12	every	every	DET
cana-4135	102	13	1n	1n	NUM
cana-4135	102	14	n	n	PROPN
cana-4135	102	15	,	,	PUNCT
cana-4135	102	16	(	(	PUNCT
cana-4135	102	17	,	,	PUNCT
cana-4135	102	18	,	,	PUNCT
cana-4135	102	19	)	)	PUNCT
cana-4135	102	20	2	2	NUM
cana-4135	102	21	n	n	SYM
cana-4135	102	22	ns	ns	NUM
cana-4135	102	23	h	h	NOUN
cana-4135	102	24	h	h	NOUN
cana-4135	102	25	h	h	PROPN
cana-4135	102	26			PROPN
cana-4135	102	27			PROPN
cana-4135	102	28	and	and	CCONJ
cana-4135	102	29	for	for	ADP
cana-4135	102	30	every	every	DET
cana-4135	102	31	2n	2n	NUM
cana-4135	102	32	n	n	PROPN
cana-4135	102	33	,	,	PUNCT
cana-4135	102	34	(	(	PUNCT
cana-4135	102	35	,	,	PUNCT
cana-4135	102	36	,	,	PUNCT
cana-4135	102	37	)	)	PUNCT
cana-4135	102	38	2	2	NUM
cana-4135	102	39	n	n	NUM
cana-4135	102	40	ns	ns	NOUN
cana-4135	103	1	i	i	PRON
cana-4135	103	2	i	i	PRON
cana-4135	104	1	i	i	PRON
cana-4135	104	2			PROPN
cana-4135	104	3			PROPN
cana-4135	104	4	.	.	PUNCT
cana-4135	105	1	if	if	SCONJ
cana-4135	105	2	1	1	NUM
cana-4135	105	3	2	2	NUM
cana-4135	105	4	0maximum	0maximum	NUM
cana-4135	105	5	{	{	PUNCT
cana-4135	105	6	,	,	PUNCT
cana-4135	105	7	}	}	PUNCT
cana-4135	105	8	n	n	CCONJ
cana-4135	105	9	n	n	CCONJ
cana-4135	105	10	n=	n=	ADJ
cana-4135	105	11	,	,	PUNCT
cana-4135	105	12	then	then	ADV
cana-4135	105	13	by	by	ADP
cana-4135	105	14	property	property	NOUN
cana-4135	105	15	of	of	ADP
cana-4135	105	16	multiplicative	multiplicative	ADJ
cana-4135	105	17	s	s	X
cana-4135	105	18	-metric	-metric	ADJ
cana-4135	105	19	space	space	NOUN
cana-4135	105	20	,	,	PUNCT
cana-4135	105	21	we	we	PRON
cana-4135	105	22	have	have	VERB
cana-4135	105	23	for	for	ADP
cana-4135	105	24	all	all	DET
cana-4135	105	25	0n	0n	NOUN
cana-4135	105	26	n	n	PROPN
cana-4135	105	27	(	(	PUNCT
cana-4135	105	28	,	,	PUNCT
cana-4135	105	29	,	,	PUNCT
cana-4135	105	30	)	)	PUNCT
cana-4135	105	31	(	(	PUNCT
cana-4135	105	32	,	,	PUNCT
cana-4135	105	33	,	,	PUNCT
cana-4135	105	34	)	)	PUNCT
cana-4135	105	35	(	(	PUNCT
cana-4135	105	36	,	,	PUNCT
cana-4135	105	37	,	,	PUNCT
cana-4135	105	38	)	)	PUNCT
cana-4135	105	39	(	(	PUNCT
cana-4135	105	40	,	,	PUNCT
cana-4135	105	41	,	,	PUNCT
cana-4135	105	42	)	)	PUNCT
cana-4135	105	43	n	n	CCONJ
cana-4135	105	44	n	n	CCONJ
cana-4135	105	45	n	n	CCONJ
cana-4135	105	46	n	n	CCONJ
cana-4135	105	47	n	n	CCONJ
cana-4135	105	48	ns	ns	NUM
cana-4135	105	49	h	h	NOUN
cana-4135	105	50	j	j	PROPN
cana-4135	106	1	i	i	PRON
cana-4135	106	2	s	s	VERB
cana-4135	107	1	h	h	NOUN
cana-4135	107	2	h	h	NOUN
cana-4135	107	3	h	h	PROPN
cana-4135	108	1	s	s	PART
cana-4135	109	1	j	j	PROPN
cana-4135	109	2	j	j	PROPN
cana-4135	109	3	h	h	PROPN
cana-4135	109	4	s	s	VERB
cana-4135	109	5	i	i	INTJ
cana-4135	110	1	i	i	PRON
cana-4135	110	2	h	h	VERB
cana-4135	110	3	2	2	NUM
cana-4135	110	4	(	(	PUNCT
cana-4135	110	5	,	,	PUNCT
cana-4135	110	6	,	,	PUNCT
cana-4135	110	7	)	)	PUNCT
cana-4135	110	8	(	(	PUNCT
cana-4135	110	9	,	,	PUNCT
cana-4135	110	10	,	,	PUNCT
cana-4135	110	11	)	)	PUNCT
cana-4135	110	12	(	(	PUNCT
cana-4135	110	13	,	,	PUNCT
cana-4135	110	14	,	,	PUNCT
cana-4135	110	15	)	)	PUNCT
cana-4135	110	16	(	(	PUNCT
cana-4135	110	17	,	,	PUNCT
cana-4135	110	18	,	,	PUNCT
cana-4135	110	19	)	)	PUNCT
cana-4135	110	20	n	n	CCONJ
cana-4135	110	21	n	n	CCONJ
cana-4135	110	22	n	n	CCONJ
cana-4135	110	23	ns	ns	NUM
cana-4135	110	24	h	h	NOUN
cana-4135	110	25	h	h	NOUN
cana-4135	110	26	h	h	PROPN
cana-4135	110	27	s	s	PART
cana-4135	111	1	j	j	PROPN
cana-4135	111	2	j	j	PROPN
cana-4135	111	3	h	h	PROPN
cana-4135	111	4	s	s	VERB
cana-4135	112	1	i	i	PRON
cana-4135	113	1	i	i	PRON
cana-4135	114	1	i	i	PRON
cana-4135	114	2	s	s	VERB
cana-4135	114	3	h	h	NOUN
cana-4135	114	4	h	h	PROPN
cana-4135	114	5	i	i	NOUN
cana-4135	114	6	take	take	VERB
cana-4135	114	7	upper	upper	ADJ
cana-4135	114	8	limit	limit	NOUN
cana-4135	114	9	n	n	PRON
cana-4135	114	10	→	→	PUNCT
cana-4135	114	11	.	.	PUNCT
cana-4135	115	1	2limsup	2limsup	NUM
cana-4135	115	2	(	(	PUNCT
cana-4135	115	3	,	,	PUNCT
cana-4135	115	4	,	,	PUNCT
cana-4135	115	5	)	)	PUNCT
cana-4135	115	6	(	(	PUNCT
cana-4135	115	7	,	,	PUNCT
cana-4135	115	8	,	,	PUNCT
cana-4135	115	9	)	)	PUNCT
cana-4135	115	10	(	(	PUNCT
cana-4135	115	11	,	,	PUNCT
cana-4135	115	12	,	,	PUNCT
cana-4135	115	13	)	)	PUNCT
cana-4135	115	14	(	(	PUNCT
cana-4135	115	15	,	,	PUNCT
cana-4135	115	16	,	,	PUNCT
cana-4135	115	17	)	)	PUNCT
cana-4135	115	18	(	(	PUNCT
cana-4135	115	19	,	,	PUNCT
cana-4135	115	20	,	,	PUNCT
cana-4135	115	21	)	)	PUNCT
cana-4135	115	22	(	(	PUNCT
cana-4135	115	23	,	,	PUNCT
cana-4135	115	24	,	,	PUNCT
cana-4135	115	25	)	)	PUNCT
cana-4135	115	26	(	(	PUNCT
cana-4135	115	27	,	,	PUNCT
cana-4135	115	28	,	,	PUNCT
cana-4135	115	29	)	)	PUNCT
cana-4135	115	30	n	n	CCONJ
cana-4135	115	31	n	n	PROPN
cana-4135	115	32	n	n	NOUN
cana-4135	115	33	s	s	NOUN
cana-4135	115	34	h	h	NOUN
cana-4135	116	1	j	j	NOUN
cana-4135	117	1	i	i	PRON
cana-4135	117	2	s	s	VERB
cana-4135	118	1	h	h	NOUN
cana-4135	118	2	h	h	NOUN
cana-4135	118	3	h	h	PROPN
cana-4135	119	1	s	s	PART
cana-4135	120	1	j	j	PROPN
cana-4135	120	2	j	j	PROPN
cana-4135	120	3	h	h	PROPN
cana-4135	120	4	s	s	VERB
cana-4135	121	1	i	i	PRON
cana-4135	122	1	i	i	PRON
cana-4135	123	1	i	i	PRON
cana-4135	123	2	s	s	VERB
cana-4135	123	3	h	h	NOUN
cana-4135	124	1	h	h	NOUN
cana-4135	125	1	i	i	PRON
cana-4135	125	2	s	s	VERB
cana-4135	125	3	j	j	PROPN
cana-4135	126	1	j	j	PROPN
cana-4135	126	2	h	h	PROPN
cana-4135	126	3	s	s	VERB
cana-4135	127	1	h	h	NOUN
cana-4135	127	2	h	h	NOUN
cana-4135	128	1	i	i	PRON
cana-4135	128	2	→	→	VERB
cana-4135	128	3			NUM
cana-4135	128	4	=	=	PUNCT
cana-4135	128	5	hence	hence	ADV
cana-4135	128	6	proved	prove	VERB
cana-4135	128	7	.	.	PUNCT
cana-4135	129	1	lemma	lemma	PROPN
cana-4135	129	2	2	2	NUM
cana-4135	129	3	:	:	PUNCT
cana-4135	129	4	consider	consider	VERB
cana-4135	129	5	(	(	PUNCT
cana-4135	129	6	,	,	PUNCT
cana-4135	129	7	)	)	PUNCT
cana-4135	129	8	m	m	PROPN
cana-4135	129	9	s	s	NOUN
cana-4135	129	10	is	be	AUX
cana-4135	129	11	a	a	DET
cana-4135	129	12	multiplicative	multiplicative	ADJ
cana-4135	129	13	s	s	X
cana-4135	129	14	-metric	-metric	ADJ
cana-4135	129	15	space	space	NOUN
cana-4135	129	16	,	,	PUNCT
cana-4135	129	17	then	then	ADV
cana-4135	129	18	(	(	PUNCT
cana-4135	129	19	,	,	PUNCT
cana-4135	129	20	,	,	PUNCT
cana-4135	129	21	)	)	PUNCT
cana-4135	129	22	(	(	PUNCT
cana-4135	129	23	,	,	PUNCT
cana-4135	129	24	,	,	PUNCT
cana-4135	129	25	)	)	PUNCT
cana-4135	129	26	s	s	PART
cana-4135	130	1	h	h	NOUN
cana-4135	130	2	h	h	NOUN
cana-4135	131	1	i	i	PRON
cana-4135	131	2	s	s	VERB
cana-4135	132	1	i	i	PRON
cana-4135	133	1	i	i	PRON
cana-4135	133	2	h=	h=	X
cana-4135	133	3	.	.	PUNCT
cana-4135	134	1	proof	proof	NOUN
cana-4135	134	2	:	:	PUNCT
cana-4135	134	3	by	by	ADP
cana-4135	134	4	property	property	NOUN
cana-4135	134	5	of	of	ADP
cana-4135	134	6	multiplicative	multiplicative	ADJ
cana-4135	134	7	s	s	X
cana-4135	134	8	-metric	-metric	ADJ
cana-4135	134	9	space	space	NOUN
cana-4135	134	10	(	(	PUNCT
cana-4135	134	11	,	,	PUNCT
cana-4135	134	12	,	,	PUNCT
cana-4135	134	13	)	)	PUNCT
cana-4135	134	14	(	(	PUNCT
cana-4135	134	15	,	,	PUNCT
cana-4135	134	16	,	,	PUNCT
cana-4135	134	17	)	)	PUNCT
cana-4135	134	18	(	(	PUNCT
cana-4135	134	19	,	,	PUNCT
cana-4135	134	20	,	,	PUNCT
cana-4135	134	21	)	)	PUNCT
cana-4135	134	22	(	(	PUNCT
cana-4135	134	23	,	,	PUNCT
cana-4135	134	24	,	,	PUNCT
cana-4135	134	25	)	)	PUNCT
cana-4135	134	26	s	s	PART
cana-4135	135	1	h	h	NOUN
cana-4135	135	2	h	h	NOUN
cana-4135	136	1	i	i	PRON
cana-4135	136	2	s	s	VERB
cana-4135	136	3	h	h	NOUN
cana-4135	137	1	h	h	NOUN
cana-4135	137	2	h	h	NOUN
cana-4135	137	3	s	s	VERB
cana-4135	138	1	h	h	NOUN
cana-4135	138	2	h	h	NOUN
cana-4135	138	3	h	h	NOUN
cana-4135	138	4	s	s	VERB
cana-4135	139	1	i	i	PRON
cana-4135	139	2	i	i	PRON
cana-4135	139	3	h	h	VERB
cana-4135	140	1	i.e.	i.e.	X
cana-4135	140	2	(	(	PUNCT
cana-4135	140	3	,	,	PUNCT
cana-4135	140	4	,	,	PUNCT
cana-4135	140	5	)	)	PUNCT
cana-4135	140	6	(	(	PUNCT
cana-4135	140	7	,	,	PUNCT
cana-4135	140	8	,	,	PUNCT
cana-4135	140	9	)	)	PUNCT
cana-4135	140	10	s	s	PART
cana-4135	141	1	h	h	NOUN
cana-4135	141	2	h	h	NOUN
cana-4135	142	1	i	i	PRON
cana-4135	142	2	s	s	VERB
cana-4135	143	1	i	i	PRON
cana-4135	144	1	i	i	PRON
cana-4135	144	2	h	h	VERB
cana-4135	144	3	now	now	ADV
cana-4135	144	4	,	,	PUNCT
cana-4135	144	5	(	(	PUNCT
cana-4135	144	6	,	,	PUNCT
cana-4135	144	7	,	,	PUNCT
cana-4135	144	8	)	)	PUNCT
cana-4135	144	9	(	(	PUNCT
cana-4135	144	10	,	,	PUNCT
cana-4135	144	11	,	,	PUNCT
cana-4135	144	12	)	)	PUNCT
cana-4135	144	13	(	(	PUNCT
cana-4135	144	14	,	,	PUNCT
cana-4135	144	15	,	,	PUNCT
cana-4135	144	16	)	)	PUNCT
cana-4135	144	17	(	(	PUNCT
cana-4135	144	18	,	,	PUNCT
cana-4135	145	1	,	,	PUNCT
cana-4135	145	2	)	)	PUNCT
cana-4135	145	3	s	s	VERB
cana-4135	145	4	i	i	PRON
cana-4135	146	1	i	i	PRON
cana-4135	146	2	h	h	VERB
cana-4135	146	3	s	s	VERB
cana-4135	147	1	i	i	PRON
cana-4135	148	1	i	i	PRON
cana-4135	149	1	i	i	PRON
cana-4135	149	2	s	s	VERB
cana-4135	150	1	i	i	PRON
cana-4135	151	1	i	i	PRON
cana-4135	152	1	i	i	PRON
cana-4135	152	2	s	s	VERB
cana-4135	152	3	h	h	NOUN
cana-4135	152	4	h	h	NOUN
cana-4135	152	5	i	i	NOUN
cana-4135	153	1	hence	hence	ADV
cana-4135	153	2	(	(	PUNCT
cana-4135	153	3	,	,	PUNCT
cana-4135	153	4	,	,	PUNCT
cana-4135	153	5	)	)	PUNCT
cana-4135	153	6	(	(	PUNCT
cana-4135	153	7	,	,	PUNCT
cana-4135	153	8	,	,	PUNCT
cana-4135	153	9	)	)	PUNCT
cana-4135	153	10	s	s	PART
cana-4135	154	1	h	h	NOUN
cana-4135	154	2	h	h	NOUN
cana-4135	155	1	i	i	PRON
cana-4135	155	2	s	s	VERB
cana-4135	156	1	i	i	PRON
cana-4135	157	1	i	i	PRON
cana-4135	157	2	h=	h=	PRON
cana-4135	157	3	.	.	PUNCT
cana-4135	158	1	[	[	X
cana-4135	158	2	13	13	NUM
cana-4135	158	3	]	]	PUNCT
cana-4135	158	4	has	have	AUX
cana-4135	158	5	proved	prove	VERB
cana-4135	158	6	the	the	DET
cana-4135	158	7	following	follow	VERB
cana-4135	158	8	theorems	theorem	NOUN
cana-4135	158	9	.	.	PUNCT
cana-4135	158	10	theorem	theorem	NOUN
cana-4135	158	11	1	1	NUM
cana-4135	158	12	.	.	PUNCT
cana-4135	159	1	[	[	X
cana-4135	159	2	13	13	NUM
cana-4135	159	3	]	]	PUNCT
cana-4135	159	4	let	let	VERB
cana-4135	159	5	(	(	PUNCT
cana-4135	159	6	,	,	PUNCT
cana-4135	159	7	)	)	PUNCT
cana-4135	159	8	m	m	VERB
cana-4135	159	9	s	s	AUX
cana-4135	159	10	be	be	AUX
cana-4135	159	11	a	a	DET
cana-4135	159	12	complete	complete	ADJ
cana-4135	159	13	s	s	NOUN
cana-4135	159	14	-	-	ADJ
cana-4135	159	15	multiplicative	multiplicative	ADJ
cana-4135	159	16	metric	metric	ADJ
cana-4135	159	17	space	space	NOUN
cana-4135	159	18	and	and	CCONJ
cana-4135	159	19	:	:	PUNCT
cana-4135	159	20	t	t	PROPN
cana-4135	159	21	m	m	PROPN
cana-4135	159	22	m→	m→	NOUN
cana-4135	159	23	a	a	DET
cana-4135	159	24	mapping	mapping	NOUN
cana-4135	159	25	for	for	ADP
cana-4135	159	26	which	which	PRON
cana-4135	159	27	there	there	PRON
cana-4135	159	28	exist	exist	VERB
cana-4135	159	29	the	the	DET
cana-4135	159	30	real	real	ADJ
cana-4135	159	31	number	number	NOUN
cana-4135	159	32	,	,	PUNCT
cana-4135	159	33			ADJ
cana-4135	159	34	satisfying	satisfying	NOUN
cana-4135	159	35	0	0	NUM
cana-4135	160	1	1	1	NUM
cana-4135	160	2			PROPN
cana-4135	160	3	such	such	ADJ
cana-4135	160	4	that	that	PRON
cana-4135	160	5	for	for	ADP
cana-4135	160	6	each	each	DET
cana-4135	160	7	pair	pair	NOUN
cana-4135	160	8	,	,	PUNCT
cana-4135	160	9	,	,	PUNCT
cana-4135	160	10	h	h	NOUN
cana-4135	161	1	i	i	PRON
cana-4135	161	2	j	j	PROPN
cana-4135	161	3	m	m	PROPN
cana-4135	161	4	(	(	PUNCT
cana-4135	161	5	,	,	PUNCT
cana-4135	161	6	,	,	PUNCT
cana-4135	161	7	)	)	PUNCT
cana-4135	162	1	[	[	PUNCT
cana-4135	162	2	(	(	PUNCT
cana-4135	162	3	,	,	PUNCT
cana-4135	162	4	,	,	PUNCT
cana-4135	162	5	)	)	PUNCT
cana-4135	162	6	]	]	X
cana-4135	162	7	s	s	X
cana-4135	162	8	th	th	X
cana-4135	162	9	ti	ti	NOUN
cana-4135	162	10	tj	tj	PROPN
cana-4135	162	11	s	s	PROPN
cana-4135	162	12	h	h	NOUN
cana-4135	162	13	h	h	NOUN
cana-4135	162	14	j	j	PROPN
cana-4135	162	15			X
cana-4135	162	16	(	(	PUNCT
cana-4135	162	17	2.1.1	2.1.1	NUM
cana-4135	162	18	)	)	PUNCT
cana-4135	162	19	then	then	ADV
cana-4135	162	20	,	,	PUNCT
cana-4135	162	21	t	t	PROPN
cana-4135	162	22	has	have	VERB
cana-4135	162	23	a	a	DET
cana-4135	162	24	unique	unique	ADJ
cana-4135	162	25	fixed	fix	VERB
cana-4135	162	26	point	point	NOUN
cana-4135	162	27	.	.	PUNCT
cana-4135	163	1	theorem	theorem	NOUN
cana-4135	163	2	2	2	NUM
cana-4135	163	3	.	.	PUNCT
cana-4135	164	1	[	[	X
cana-4135	164	2	13	13	NUM
cana-4135	164	3	]	]	PUNCT
cana-4135	164	4	assume	assume	VERB
cana-4135	164	5	(	(	PUNCT
cana-4135	164	6	,	,	PUNCT
cana-4135	164	7	)	)	PUNCT
cana-4135	164	8	m	m	PROPN
cana-4135	164	9	s	s	NOUN
cana-4135	164	10	is	be	AUX
cana-4135	164	11	a	a	DET
cana-4135	164	12	sequentially	sequentially	ADV
cana-4135	164	13	compact	compact	ADJ
cana-4135	164	14	s	s	NOUN
cana-4135	164	15	-	-	PUNCT
cana-4135	164	16	multiplicative	multiplicative	ADJ
cana-4135	164	17	metric	metric	ADJ
cana-4135	164	18	space	space	NOUN
cana-4135	164	19	and	and	CCONJ
cana-4135	164	20	:	:	PUNCT
cana-4135	164	21	f	f	PROPN
cana-4135	164	22	m	m	VERB
cana-4135	164	23	m→	m→	NOUN
cana-4135	164	24	fulfil	fulfil	VERB
cana-4135	164	25	the	the	DET
cana-4135	164	26	constraint	constraint	NOUN
cana-4135	164	27	(	(	PUNCT
cana-4135	164	28	,	,	PUNCT
cana-4135	164	29	,	,	PUNCT
cana-4135	164	30	)	)	PUNCT
cana-4135	165	1	[	[	PUNCT
cana-4135	165	2	(	(	PUNCT
cana-4135	165	3	,	,	PUNCT
cana-4135	165	4	,	,	PUNCT
cana-4135	165	5	)	)	PUNCT
cana-4135	165	6	]	]	X
cana-4135	165	7	s	s	X
cana-4135	165	8	fh	fh	PROPN
cana-4135	165	9	fi	fi	NOUN
cana-4135	166	1	fj	fj	PROPN
cana-4135	166	2	s	s	VERB
cana-4135	166	3	h	h	NOUN
cana-4135	167	1	i	i	PRON
cana-4135	167	2	j	j	NOUN
cana-4135	167	3	(	(	PUNCT
cana-4135	167	4	2.1.2	2.1.2	NUM
cana-4135	167	5	)	)	PUNCT
cana-4135	167	6	where	where	NOUN
cana-4135	167	7	:	:	PUNCT
cana-4135	168	1	[	[	X
cana-4135	168	2	0	0	NUM
cana-4135	168	3	,	,	PUNCT
cana-4135	168	4	∞	∞	PROPN
cana-4135	168	5	]	]	PUNCT
cana-4135	168	6	→	→	X
cana-4135	168	7	[	[	X
cana-4135	168	8	0,∞	0,∞	X
cana-4135	168	9	]	]	PUNCT
cana-4135	168	10	is	be	AUX
cana-4135	168	11	upper	upper	ADJ
cana-4135	168	12	semi	semi	ADJ
cana-4135	168	13	-	-	ADJ
cana-4135	168	14	continuous	continuous	ADJ
cana-4135	168	15	from	from	ADP
cana-4135	168	16	the	the	DET
cana-4135	168	17	right	right	NOUN
cana-4135	168	18	,	,	PUNCT
cana-4135	168	19	satisfying	satisfy	VERB
cana-4135	168	20			NOUN
cana-4135	168	21	(	(	PUNCT
cana-4135	168	22	t	t	PROPN
cana-4135	168	23	)	)	PUNCT
cana-4135	168	24	≥	≥	NOUN
cana-4135	168	25	t	t	PROPN
cana-4135	168	26	for	for	ADP
cana-4135	168	27	t	t	PROPN
cana-4135	168	28	>	>	X
cana-4135	168	29	0	0	PROPN
cana-4135	168	30	.	.	PUNCT
cana-4135	169	1	then	then	ADV
cana-4135	169	2	,	,	PUNCT
cana-4135	169	3	f	f	PROPN
cana-4135	169	4	has	have	VERB
cana-4135	169	5	a	a	DET
cana-4135	169	6	unique	unique	ADJ
cana-4135	169	7	fixed	fix	VERB
cana-4135	169	8	point	point	NOUN
cana-4135	169	9	.	.	PUNCT
cana-4135	170	1	we	we	PRON
cana-4135	170	2	have	have	AUX
cana-4135	170	3	generalized	generalize	VERB
cana-4135	170	4	above	above	ADP
cana-4135	170	5	theorems	theorem	NOUN
cana-4135	170	6	by	by	ADP
cana-4135	170	7	proving	prove	VERB
cana-4135	170	8	the	the	DET
cana-4135	170	9	following	following	ADJ
cana-4135	170	10	result	result	NOUN
cana-4135	170	11	for	for	ADP
cana-4135	170	12	pair	pair	NOUN
cana-4135	170	13	of	of	ADP
cana-4135	170	14	mappings	mapping	NOUN
cana-4135	170	15	which	which	PRON
cana-4135	170	16	satisfy	satisfy	VERB
cana-4135	170	17	a	a	DET
cana-4135	170	18	new	new	ADJ
cana-4135	170	19	contraction	contraction	NOUN
cana-4135	170	20	condition	condition	NOUN
cana-4135	170	21	.	.	PUNCT
cana-4135	171	1	communications	communication	NOUN
cana-4135	171	2	on	on	ADP
cana-4135	171	3	applied	apply	VERB
cana-4135	171	4	nonlinear	nonlinear	ADJ
cana-4135	171	5	analysis	analysis	NOUN
cana-4135	171	6	issn	issn	NOUN
cana-4135	171	7	:	:	PUNCT
cana-4135	171	8	1074	1074	NUM
cana-4135	171	9	-	-	PUNCT
cana-4135	171	10	133x	133x	NUM
cana-4135	171	11	vol	vol	NOUN
cana-4135	171	12	32	32	NUM
cana-4135	171	13	no	no	NOUN
cana-4135	171	14	.	.	PUNCT
cana-4135	172	1	9s	9s	NUM
cana-4135	172	2	(	(	PUNCT
cana-4135	172	3	2025	2025	NUM
cana-4135	172	4	)	)	PUNCT
cana-4135	172	5	1281	1281	NUM
cana-4135	172	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4135	172	7	theorem	theorem	VERB
cana-4135	172	8	2.1	2.1	NUM
cana-4135	172	9	:	:	PUNCT
cana-4135	172	10	consider	consider	VERB
cana-4135	172	11	a	a	DET
cana-4135	172	12	complete	complete	ADJ
cana-4135	172	13	multiplicative	multiplicative	ADJ
cana-4135	172	14	s	s	X
cana-4135	172	15	-metric	-metric	ADJ
cana-4135	172	16	space	space	NOUN
cana-4135	172	17	(	(	PUNCT
cana-4135	172	18	,	,	PUNCT
cana-4135	172	19	)	)	PUNCT
cana-4135	172	20	m	m	PROPN
cana-4135	172	21	s	s	PRON
cana-4135	172	22	.	.	PUNCT
cana-4135	173	1	assume	assume	VERB
cana-4135	173	2	:	:	PUNCT
cana-4135	173	3	[	[	X
cana-4135	173	4	1	1	NUM
cana-4135	173	5	,	,	PUNCT
cana-4135	173	6	)	)	PUNCT
cana-4135	174	1	[	[	X
cana-4135	174	2	1	1	NUM
cana-4135	174	3	,	,	PUNCT
cana-4135	174	4	)	)	PUNCT
cana-4135	174	5			NOUN
cana-4135	174	6			VERB
cana-4135	174	7	→	→	SYM
cana-4135	174	8			NOUN
cana-4135	174	9	,	,	PUNCT
cana-4135	174	10	an	an	DET
cana-4135	174	11	upper	upper	ADJ
cana-4135	174	12	semicontinuous	semicontinuous	NOUN
cana-4135	174	13	and	and	CCONJ
cana-4135	174	14	non	non	ADJ
cana-4135	174	15	-	-	ADJ
cana-4135	174	16	decreasing	decrease	VERB
cana-4135	174	17	function	function	NOUN
cana-4135	174	18	,	,	PUNCT
cana-4135	174	19	,	,	PUNCT
cana-4135	174	20	:	:	PUNCT
cana-4135	174	21	f	f	PROPN
cana-4135	174	22	g	g	PROPN
cana-4135	174	23	m	m	PROPN
cana-4135	174	24	m→	m→	NOUN
cana-4135	174	25	are	be	AUX
cana-4135	174	26	functions	function	NOUN
cana-4135	175	1	such	such	ADJ
cana-4135	175	2	that	that	SCONJ
cana-4135	175	3	(	(	PUNCT
cana-4135	175	4	1	1	NUM
cana-4135	175	5	)	)	PUNCT
cana-4135	175	6	(	(	PUNCT
cana-4135	175	7	)	)	PUNCT
cana-4135	175	8	(	(	PUNCT
cana-4135	175	9	)	)	PUNCT
cana-4135	175	10	f	f	X
cana-4135	175	11	m	m	VERB
cana-4135	175	12	g	g	PROPN
cana-4135	175	13	m	m	X
cana-4135	176	1	(	(	PUNCT
cana-4135	177	1	2	2	NUM
cana-4135	177	2	)	)	PUNCT
cana-4135	177	3	(	(	PUNCT
cana-4135	177	4	,	,	PUNCT
cana-4135	177	5	,	,	PUNCT
cana-4135	177	6	)	)	PUNCT
cana-4135	178	1	[	[	PUNCT
cana-4135	178	2	(	(	PUNCT
cana-4135	178	3	,	,	PUNCT
cana-4135	178	4	,	,	PUNCT
cana-4135	178	5	)	)	PUNCT
cana-4135	178	6	(	(	PUNCT
cana-4135	178	7	,	,	PUNCT
cana-4135	178	8	,	,	PUNCT
cana-4135	178	9	)	)	PUNCT
cana-4135	178	10	(	(	PUNCT
cana-4135	178	11	,	,	PUNCT
cana-4135	178	12	,	,	PUNCT
cana-4135	178	13	)	)	PUNCT
cana-4135	178	14	]	]	X
cana-4135	178	15	s	s	X
cana-4135	178	16	fh	fh	PROPN
cana-4135	178	17	fi	fi	NOUN
cana-4135	179	1	fj	fj	PROPN
cana-4135	179	2	s	s	PROPN
cana-4135	179	3	gh	gh	PROPN
cana-4135	179	4	gi	gi	PROPN
cana-4135	179	5	gj	gj	PROPN
cana-4135	179	6	s	s	PROPN
cana-4135	180	1	gj	gj	PROPN
cana-4135	180	2	fh	fh	PROPN
cana-4135	180	3	fi	fi	NOUN
cana-4135	180	4	s	s	PART
cana-4135	180	5	gj	gj	NOUN
cana-4135	180	6	fi	fi	NOUN
cana-4135	180	7	fj	fj	NOUN
cana-4135	180	8			X
cana-4135	180	9			PROPN
cana-4135	180	10			NOUN
cana-4135	180	11	(	(	PUNCT
cana-4135	180	12	2.1.3	2.1.3	NUM
cana-4135	180	13	)	)	PUNCT
cana-4135	180	14	for	for	ADP
cana-4135	180	15	all	all	PRON
cana-4135	180	16	,	,	PUNCT
cana-4135	180	17	,	,	PUNCT
cana-4135	180	18	h	h	NOUN
cana-4135	181	1	i	i	PRON
cana-4135	181	2	j	j	PROPN
cana-4135	181	3	m	m	PROPN
cana-4135	181	4	and	and	CCONJ
cana-4135	181	5	,	,	PUNCT
cana-4135	181	6	,	,	PUNCT
cana-4135	181	7	0	0	PROPN
cana-4135	181	8			PROPN
cana-4135	181	9			NUM
cana-4135	181	10			NUM
cana-4135	181	11	and	and	CCONJ
cana-4135	181	12	[	[	X
cana-4135	181	13	1	1	NUM
cana-4135	181	14	,	,	PUNCT
cana-4135	181	15	)	)	PUNCT
cana-4135	181	16			NOUN
cana-4135	181	17			NUM
cana-4135	181	18			NOUN
cana-4135	181	19	=	=	NOUN
cana-4135	181	20	+	+	CCONJ
cana-4135	181	21	+	+	CCONJ
cana-4135	181	22			NOUN
cana-4135	181	23			NOUN
cana-4135	181	24	then	then	ADV
cana-4135	181	25	f	f	PROPN
cana-4135	181	26	and	and	CCONJ
cana-4135	181	27	g	g	PROPN
cana-4135	181	28	possesses	possesse	NOUN
cana-4135	181	29	unique	unique	ADJ
cana-4135	181	30	common	common	ADJ
cana-4135	181	31	fixed	fix	VERB
cana-4135	181	32	point	point	NOUN
cana-4135	181	33	.	.	PUNCT
cana-4135	182	1	proof	proof	NOUN
cana-4135	182	2	:	:	PUNCT
cana-4135	182	3	step	step	NOUN
cana-4135	182	4	1	1	NUM
cana-4135	182	5	:	:	PUNCT
cana-4135	182	6	let	let	VERB
cana-4135	182	7	0h	0h	PROPN
cana-4135	182	8	m	m	PROPN
cana-4135	182	9	.	.	PUNCT
cana-4135	183	1	define	define	VERB
cana-4135	183	2	the	the	DET
cana-4135	183	3	sequence	sequence	NOUN
cana-4135	183	4	{	{	PUNCT
cana-4135	183	5	}	}	PUNCT
cana-4135	183	6	ni	ni	PROPN
cana-4135	183	7	as	as	ADP
cana-4135	183	8	1n	1n	PROPN
cana-4135	183	9	n	n	NUM
cana-4135	183	10	ni	ni	PROPN
cana-4135	183	11	fh	fh	PROPN
cana-4135	183	12	gh	gh	PROPN
cana-4135	184	1	+	+	PROPN
cana-4135	184	2	=	=	SYM
cana-4135	184	3	=	=	X
cana-4135	184	4	then	then	ADV
cana-4135	184	5	1	1	NUM
cana-4135	184	6	1	1	NUM
cana-4135	184	7	1	1	NUM
cana-4135	184	8	1	1	NUM
cana-4135	184	9	1	1	NUM
cana-4135	184	10	(	(	PUNCT
cana-4135	184	11	,	,	PUNCT
cana-4135	184	12	,	,	PUNCT
cana-4135	184	13	)	)	PUNCT
cana-4135	185	1	[	[	PUNCT
cana-4135	185	2	(	(	PUNCT
cana-4135	185	3	,	,	PUNCT
cana-4135	185	4	,	,	PUNCT
cana-4135	185	5	)	)	PUNCT
cana-4135	185	6	(	(	PUNCT
cana-4135	185	7	,	,	PUNCT
cana-4135	185	8	,	,	PUNCT
cana-4135	185	9	)	)	PUNCT
cana-4135	185	10	(	(	PUNCT
cana-4135	185	11	,	,	PUNCT
cana-4135	185	12	,	,	PUNCT
cana-4135	185	13	)	)	PUNCT
cana-4135	185	14	]	]	PUNCT
cana-4135	185	15	n	n	CCONJ
cana-4135	185	16	n	n	CCONJ
cana-4135	185	17	n	n	CCONJ
cana-4135	185	18	n	n	CCONJ
cana-4135	185	19	n	n	CCONJ
cana-4135	185	20	n	n	CCONJ
cana-4135	185	21	n	n	CCONJ
cana-4135	185	22	n	n	CCONJ
cana-4135	185	23	n	n	CCONJ
cana-4135	185	24	n	n	CCONJ
cana-4135	185	25	n	n	ADV
cana-4135	185	26	ns	ns	INTJ
cana-4135	186	1	i	i	PRON
cana-4135	186	2	i	i	PRON
cana-4135	187	1	i	i	PRON
cana-4135	187	2	s	s	VERB
cana-4135	187	3	gh	gh	PROPN
cana-4135	187	4	gh	gh	PROPN
cana-4135	187	5	gh	gh	PROPN
cana-4135	187	6	s	s	PROPN
cana-4135	187	7	gh	gh	PROPN
cana-4135	187	8	fh	fh	PROPN
cana-4135	187	9	fh	fh	PROPN
cana-4135	187	10	s	s	PROPN
cana-4135	187	11	gh	gh	PROPN
cana-4135	187	12	fh	fh	PROPN
cana-4135	187	13	fh	fh	PROPN
cana-4135	187	14			X
cana-4135	187	15			NOUN
cana-4135	187	16	+	+	NOUN
cana-4135	187	17	+	+	PUNCT
cana-4135	188	1	+	+	PUNCT
cana-4135	189	1	+	+	PUNCT
cana-4135	189	2	+	+	NOUN
cana-4135	189	3			NOUN
cana-4135	189	4	1	1	NUM
cana-4135	189	5	1	1	NUM
cana-4135	189	6	1	1	NUM
cana-4135	189	7	[	[	PUNCT
cana-4135	189	8	(	(	PUNCT
cana-4135	189	9	,	,	PUNCT
cana-4135	189	10	,	,	PUNCT
cana-4135	189	11	)	)	PUNCT
cana-4135	189	12	(	(	PUNCT
cana-4135	189	13	,	,	PUNCT
cana-4135	189	14	,	,	PUNCT
cana-4135	189	15	)	)	PUNCT
cana-4135	189	16	(	(	PUNCT
cana-4135	189	17	,	,	PUNCT
cana-4135	189	18	,	,	PUNCT
cana-4135	189	19	)	)	PUNCT
cana-4135	189	20	]	]	PUNCT
cana-4135	189	21	n	n	CCONJ
cana-4135	189	22	n	n	CCONJ
cana-4135	189	23	n	n	CCONJ
cana-4135	189	24	n	n	CCONJ
cana-4135	189	25	n	n	CCONJ
cana-4135	189	26	n	n	CCONJ
cana-4135	189	27	n	n	CCONJ
cana-4135	189	28	n	n	ADV
cana-4135	189	29	ns	ns	INTJ
cana-4135	190	1	i	i	PRON
cana-4135	190	2	i	i	INTJ
cana-4135	191	1	w	w	VERB
cana-4135	191	2	s	s	VERB
cana-4135	192	1	i	i	PRON
cana-4135	192	2	i	i	PRON
cana-4135	193	1	i	i	PRON
cana-4135	193	2	s	s	VERB
cana-4135	193	3	i	i	INTJ
cana-4135	194	1	i	i	PROPN
cana-4135	194	2	i	i	ADP
cana-4135	194	3			PROPN
cana-4135	194	4			NOUN
cana-4135	194	5	−	−	PROPN
cana-4135	194	6	−	−	PROPN
cana-4135	195	1	+	+	NOUN
cana-4135	195	2	=	=	SYM
cana-4135	195	3	1	1	NUM
cana-4135	195	4	1	1	NUM
cana-4135	195	5	1	1	NUM
cana-4135	195	6	1	1	NUM
cana-4135	195	7	(	(	PUNCT
cana-4135	195	8	,	,	PUNCT
cana-4135	195	9	,	,	PUNCT
cana-4135	195	10	)	)	PUNCT
cana-4135	195	11	[	[	PUNCT
cana-4135	195	12	(	(	PUNCT
cana-4135	195	13	,	,	PUNCT
cana-4135	195	14	,	,	PUNCT
cana-4135	195	15	)	)	PUNCT
cana-4135	195	16	(	(	PUNCT
cana-4135	195	17	,	,	PUNCT
cana-4135	195	18	,	,	PUNCT
cana-4135	195	19	)	)	PUNCT
cana-4135	195	20	]	]	PUNCT
cana-4135	195	21	n	n	CCONJ
cana-4135	195	22	n	n	CCONJ
cana-4135	195	23	n	n	CCONJ
cana-4135	195	24	n	n	CCONJ
cana-4135	195	25	n	n	CCONJ
cana-4135	195	26	n	n	CCONJ
cana-4135	195	27	n	n	CCONJ
cana-4135	195	28	n	n	ADV
cana-4135	195	29	ns	ns	INTJ
cana-4135	196	1	i	i	PRON
cana-4135	196	2	i	i	PRON
cana-4135	197	1	i	i	PRON
cana-4135	197	2	s	s	VERB
cana-4135	198	1	i	i	PRON
cana-4135	199	1	i	i	PRON
cana-4135	200	1	i	i	PRON
cana-4135	200	2	s	s	VERB
cana-4135	200	3	i	i	INTJ
cana-4135	201	1	i	i	PROPN
cana-4135	201	2	i	i	ADP
cana-4135	201	3			PROPN
cana-4135	201	4			NUM
cana-4135	201	5			NOUN
cana-4135	201	6	+	+	X
cana-4135	201	7	+	+	PUNCT
cana-4135	202	1	+	+	CCONJ
cana-4135	202	2	−	−	NOUN
cana-4135	202	3	−	−	PROPN
cana-4135	203	1	+	+	NOUN
cana-4135	203	2			NOUN
cana-4135	203	3			NOUN
cana-4135	203	4	1	1	NUM
cana-4135	203	5	1	1	NUM
cana-4135	203	6	1	1	NUM
cana-4135	203	7	(	(	PUNCT
cana-4135	203	8	,	,	PUNCT
cana-4135	203	9	,	,	PUNCT
cana-4135	203	10	)	)	PUNCT
cana-4135	203	11	(	(	PUNCT
cana-4135	203	12	,	,	PUNCT
cana-4135	203	13	,	,	PUNCT
cana-4135	203	14	)	)	PUNCT
cana-4135	203	15	n	n	CCONJ
cana-4135	203	16	n	n	CCONJ
cana-4135	203	17	n	n	CCONJ
cana-4135	203	18	n	n	CCONJ
cana-4135	203	19	n	n	ADV
cana-4135	203	20	ns	ns	INTJ
cana-4135	204	1	i	i	PRON
cana-4135	204	2	i	i	PRON
cana-4135	205	1	i	i	PRON
cana-4135	205	2	s	s	VERB
cana-4135	205	3	i	i	PRON
cana-4135	206	1	i	i	PRON
cana-4135	206	2	i	i	INTJ
cana-4135	206	3			NUM
cana-4135	206	4	−	−	NOUN
cana-4135	206	5	−	−	PROPN
cana-4135	207	1	+	+	ADJ
cana-4135	207	2			PROPN
cana-4135	207	3	1	1	NUM
cana-4135	207	4	1	1	NUM
cana-4135	207	5	1	1	NUM
cana-4135	207	6	1	1	NUM
cana-4135	207	7	1	1	NUM
cana-4135	207	8	(	(	PUNCT
cana-4135	207	9	,	,	PUNCT
cana-4135	207	10	,	,	PUNCT
cana-4135	207	11	)	)	PUNCT
cana-4135	207	12	(	(	PUNCT
cana-4135	207	13	,	,	PUNCT
cana-4135	207	14	,	,	PUNCT
cana-4135	207	15	)	)	PUNCT
cana-4135	207	16	(	(	PUNCT
cana-4135	207	17	,	,	PUNCT
cana-4135	207	18	,	,	PUNCT
cana-4135	207	19	)	)	PUNCT
cana-4135	207	20	n	n	CCONJ
cana-4135	207	21	n	n	CCONJ
cana-4135	207	22	n	n	CCONJ
cana-4135	207	23	n	n	CCONJ
cana-4135	207	24	n	n	CCONJ
cana-4135	207	25	n	n	CCONJ
cana-4135	207	26	n	n	CCONJ
cana-4135	207	27	n	n	ADV
cana-4135	208	1	ns	ns	INTJ
cana-4135	209	1	i	i	PRON
cana-4135	209	2	i	i	PRON
cana-4135	210	1	i	i	PRON
cana-4135	210	2	s	s	VERB
cana-4135	211	1	i	i	PRON
cana-4135	212	1	i	i	PRON
cana-4135	213	1	i	i	PRON
cana-4135	213	2	s	s	VERB
cana-4135	213	3	i	i	INTJ
cana-4135	214	1	i	i	PROPN
cana-4135	214	2	i	i	ADJ
cana-4135	214	3			PROPN
cana-4135	214	4			X
cana-4135	214	5			X
cana-4135	214	6	+	+	ADP
cana-4135	214	7	+	+	PROPN
cana-4135	215	1	+	+	CCONJ
cana-4135	215	2	−	−	NOUN
cana-4135	215	3	−	−	NOUN
cana-4135	215	4	−	−	PROPN
cana-4135	215	5	−	−	NUM
cana-4135	215	6			PROPN
cana-4135	215	7			PROPN
cana-4135	215	8	if	if	SCONJ
cana-4135	215	9	0	0	PROPN
cana-4135	215	10	+	+	PROPN
cana-4135	215	11	=	=	PRON
cana-4135	215	12	,	,	PUNCT
cana-4135	215	13	then	then	ADV
cana-4135	215	14	contradiction	contradiction	NOUN
cana-4135	215	15	arise	arise	VERB
cana-4135	215	16	.	.	PUNCT
cana-4135	216	1	0	0	PROPN
cana-4135	217	1			PROPN
cana-4135	218	1	+	+	CCONJ
cana-4135	218	2			INTJ
cana-4135	218	3	.	.	PUNCT
cana-4135	219	1	1	1	NUM
cana-4135	219	2	1	1	NUM
cana-4135	219	3	1	1	NUM
cana-4135	219	4	1	1	NUM
cana-4135	219	5	1	1	NUM
cana-4135	219	6	(	(	PUNCT
cana-4135	219	7	,	,	PUNCT
cana-4135	219	8	,	,	PUNCT
cana-4135	219	9	)	)	PUNCT
cana-4135	219	10	(	(	PUNCT
cana-4135	219	11	,	,	PUNCT
cana-4135	219	12	,	,	PUNCT
cana-4135	219	13	)	)	PUNCT
cana-4135	219	14	(	(	PUNCT
cana-4135	219	15	,	,	PUNCT
cana-4135	219	16	,	,	PUNCT
cana-4135	219	17	)	)	PUNCT
cana-4135	219	18	n	n	CCONJ
cana-4135	219	19	n	n	CCONJ
cana-4135	219	20	n	n	CCONJ
cana-4135	219	21	n	n	CCONJ
cana-4135	219	22	n	n	CCONJ
cana-4135	219	23	n	n	CCONJ
cana-4135	219	24	n	n	CCONJ
cana-4135	219	25	n	n	ADV
cana-4135	219	26	ns	ns	INTJ
cana-4135	220	1	i	i	PRON
cana-4135	220	2	i	i	PRON
cana-4135	221	1	i	i	PRON
cana-4135	221	2	s	s	VERB
cana-4135	222	1	i	i	PRON
cana-4135	223	1	i	i	PRON
cana-4135	224	1	i	i	PRON
cana-4135	224	2	s	s	VERB
cana-4135	224	3	i	i	INTJ
cana-4135	225	1	i	i	PROPN
cana-4135	225	2	i	i	ADJ
cana-4135	225	3			PROPN
cana-4135	225	4			X
cana-4135	225	5			X
cana-4135	225	6	+	+	ADP
cana-4135	225	7	+	+	PROPN
cana-4135	226	1	+	+	CCONJ
cana-4135	226	2	−	−	ADP
cana-4135	227	1	−	−	NOUN
cana-4135	227	2	−	−	PROPN
cana-4135	227	3	−	−	NOUN
cana-4135	227	4			PROPN
cana-4135	227	5	1	1	NUM
cana-4135	227	6	1	1	NUM
cana-4135	227	7	1	1	NUM
cana-4135	227	8	(	(	PUNCT
cana-4135	227	9	,	,	PUNCT
cana-4135	227	10	,	,	PUNCT
cana-4135	227	11	)	)	PUNCT
cana-4135	227	12	(	(	PUNCT
cana-4135	227	13	,	,	PUNCT
cana-4135	227	14	,	,	PUNCT
cana-4135	227	15	)	)	PUNCT
cana-4135	227	16	n	n	CCONJ
cana-4135	227	17	n	n	CCONJ
cana-4135	227	18	n	n	CCONJ
cana-4135	227	19	n	n	CCONJ
cana-4135	227	20	n	n	ADV
cana-4135	227	21	ns	ns	INTJ
cana-4135	228	1	i	i	PRON
cana-4135	228	2	i	i	PRON
cana-4135	229	1	i	i	PRON
cana-4135	229	2	s	s	VERB
cana-4135	230	1	i	i	PRON
cana-4135	231	1	i	i	PRON
cana-4135	231	2	i+	i+	VERB
cana-4135	231	3	−	−	DET
cana-4135	231	4	−	−	NOUN
cana-4135	231	5	similarly	similarly	ADV
cana-4135	231	6	,	,	PUNCT
cana-4135	231	7	we	we	PRON
cana-4135	231	8	can	can	AUX
cana-4135	231	9	show	show	VERB
cana-4135	231	10	that	that	SCONJ
cana-4135	231	11	1	1	NUM
cana-4135	231	12	1	1	NUM
cana-4135	231	13	2	2	NUM
cana-4135	231	14	2	2	NUM
cana-4135	231	15	1	1	NUM
cana-4135	231	16	(	(	PUNCT
cana-4135	231	17	,	,	PUNCT
cana-4135	231	18	,	,	PUNCT
cana-4135	231	19	)	)	PUNCT
cana-4135	231	20	(	(	PUNCT
cana-4135	231	21	,	,	PUNCT
cana-4135	231	22	,	,	PUNCT
cana-4135	231	23	)	)	PUNCT
cana-4135	231	24	n	n	CCONJ
cana-4135	231	25	n	n	CCONJ
cana-4135	231	26	n	n	CCONJ
cana-4135	231	27	n	n	CCONJ
cana-4135	231	28	n	n	ADV
cana-4135	231	29	ns	ns	INTJ
cana-4135	232	1	i	i	PRON
cana-4135	232	2	i	i	PRON
cana-4135	233	1	i	i	PRON
cana-4135	233	2	s	s	VERB
cana-4135	234	1	i	i	PRON
cana-4135	235	1	i	i	PRON
cana-4135	235	2	i−	i−	ADJ
cana-4135	235	3	−	−	PROPN
cana-4135	235	4	−	−	PROPN
cana-4135	236	1	−	−	NUM
cana-4135	236	2	−	−	NOUN
cana-4135	236	3	hence	hence	ADV
cana-4135	236	4	for	for	ADP
cana-4135	236	5	all	all	DET
cana-4135	236	6	natural	natural	ADJ
cana-4135	236	7	numbers	number	NOUN
cana-4135	236	8	n	n	CCONJ
cana-4135	236	9	1	1	NUM
cana-4135	236	10	1	1	NUM
cana-4135	236	11	1	1	NUM
cana-4135	236	12	(	(	PUNCT
cana-4135	236	13	,	,	PUNCT
cana-4135	236	14	,	,	PUNCT
cana-4135	236	15	)	)	PUNCT
cana-4135	236	16	(	(	PUNCT
cana-4135	236	17	,	,	PUNCT
cana-4135	236	18	,	,	PUNCT
cana-4135	236	19	)	)	PUNCT
cana-4135	236	20	n	n	CCONJ
cana-4135	236	21	n	n	CCONJ
cana-4135	236	22	n	n	CCONJ
cana-4135	236	23	n	n	CCONJ
cana-4135	236	24	n	n	ADV
cana-4135	237	1	ns	ns	INTJ
cana-4135	238	1	i	i	PRON
cana-4135	238	2	i	i	PRON
cana-4135	239	1	i	i	PRON
cana-4135	239	2	s	s	VERB
cana-4135	240	1	i	i	PRON
cana-4135	241	1	i	i	PRON
cana-4135	241	2	i+	i+	VERB
cana-4135	241	3	−	−	DET
cana-4135	241	4	−	−	NOUN
cana-4135	241	5	thus	thus	ADV
cana-4135	241	6	1	1	NUM
cana-4135	241	7	(	(	PUNCT
cana-4135	241	8	,	,	PUNCT
cana-4135	241	9	,	,	PUNCT
cana-4135	241	10	)	)	PUNCT
cana-4135	241	11	n	n	CCONJ
cana-4135	241	12	n	n	ADV
cana-4135	241	13	ns	ns	INTJ
cana-4135	242	1	i	i	PRON
cana-4135	242	2	i	i	PRON
cana-4135	243	1	i	i	PRON
cana-4135	243	2	+	+	CCONJ
cana-4135	243	3	converges	converge	VERB
cana-4135	243	4	to	to	ADP
cana-4135	243	5	some	some	DET
cana-4135	243	6	1c	1c	NOUN
cana-4135	243	7			NUM
cana-4135	243	8	.	.	PUNCT
cana-4135	244	1	assume	assume	VERB
cana-4135	244	2	1c	1c	NOUN
cana-4135	244	3			X
cana-4135	244	4	.	.	PUNCT
cana-4135	245	1	1	1	NUM
cana-4135	245	2	1	1	NUM
cana-4135	245	3	2lim	2lim	NUM
cana-4135	245	4	(	(	PUNCT
cana-4135	245	5	,	,	PUNCT
cana-4135	245	6	,	,	PUNCT
cana-4135	245	7	)	)	PUNCT
cana-4135	245	8	n	n	CCONJ
cana-4135	245	9	n	n	CCONJ
cana-4135	245	10	n	n	CCONJ
cana-4135	245	11	n	n	NOUN
cana-4135	245	12	c	c	NOUN
cana-4135	245	13	s	s	VERB
cana-4135	246	1	i	i	PRON
cana-4135	247	1	i	i	NOUN
cana-4135	247	2	i	i	VERB
cana-4135	247	3			NOUN
cana-4135	247	4	+	+	X
cana-4135	247	5	+	+	PUNCT
cana-4135	247	6	+	+	NUM
cana-4135	247	7	→	→	PUNCT
cana-4135	247	8	=	=	SYM
cana-4135	247	9	1	1	NUM
cana-4135	247	10	1	1	NUM
cana-4135	247	11	2	2	NUM
cana-4135	247	12	(	(	PUNCT
cana-4135	247	13	,	,	PUNCT
cana-4135	247	14	,	,	PUNCT
cana-4135	247	15	)	)	PUNCT
cana-4135	247	16	n	n	CCONJ
cana-4135	247	17	n	n	CCONJ
cana-4135	247	18	ns	ns	PROPN
cana-4135	247	19	fh	fh	PROPN
cana-4135	247	20	fh	fh	PROPN
cana-4135	247	21	fh	fh	NOUN
cana-4135	247	22	+	+	CCONJ
cana-4135	247	23	+	+	CCONJ
cana-4135	247	24	+	+	ADJ
cana-4135	247	25	=	=	SYM
cana-4135	247	26	1	1	NUM
cana-4135	247	27	1	1	NUM
cana-4135	247	28	2	2	NUM
cana-4135	247	29	2	2	NUM
cana-4135	247	30	1	1	NUM
cana-4135	247	31	1	1	NUM
cana-4135	247	32	2	2	NUM
cana-4135	247	33	1	1	NUM
cana-4135	247	34	2limsup	2limsup	NUM
cana-4135	247	35	[	[	PUNCT
cana-4135	247	36	(	(	PUNCT
cana-4135	247	37	,	,	PUNCT
cana-4135	247	38	,	,	PUNCT
cana-4135	247	39	)	)	PUNCT
cana-4135	247	40	(	(	PUNCT
cana-4135	247	41	,	,	PUNCT
cana-4135	247	42	,	,	PUNCT
cana-4135	247	43	)	)	PUNCT
cana-4135	247	44	(	(	PUNCT
cana-4135	247	45	,	,	PUNCT
cana-4135	247	46	,	,	PUNCT
cana-4135	247	47	)	)	PUNCT
cana-4135	247	48	]	]	PUNCT
cana-4135	247	49	n	n	CCONJ
cana-4135	247	50	n	n	CCONJ
cana-4135	247	51	n	n	CCONJ
cana-4135	247	52	n	n	CCONJ
cana-4135	247	53	n	n	CCONJ
cana-4135	247	54	n	n	CCONJ
cana-4135	247	55	n	n	CCONJ
cana-4135	247	56	n	n	CCONJ
cana-4135	247	57	n	n	CCONJ
cana-4135	247	58	n	n	PROPN
cana-4135	247	59	s	s	PROPN
cana-4135	247	60	gh	gh	PROPN
cana-4135	247	61	gh	gh	PROPN
cana-4135	247	62	gh	gh	PROPN
cana-4135	247	63	s	s	PROPN
cana-4135	247	64	gh	gh	PROPN
cana-4135	247	65	fh	fh	PROPN
cana-4135	247	66	fh	fh	PROPN
cana-4135	247	67	s	s	PROPN
cana-4135	247	68	gh	gh	PROPN
cana-4135	247	69	fh	fh	PROPN
cana-4135	247	70	fh	fh	NOUN
cana-4135	247	71			PROPN
cana-4135	247	72			NOUN
cana-4135	248	1	+	+	X
cana-4135	249	1	+	+	PUNCT
cana-4135	249	2	+	+	PUNCT
cana-4135	249	3	+	+	PUNCT
cana-4135	249	4	+	+	PUNCT
cana-4135	249	5	+	+	PUNCT
cana-4135	249	6	+	+	PUNCT
cana-4135	249	7	+	+	CCONJ
cana-4135	249	8	+	+	NUM
cana-4135	249	9	→	→	VERB
cana-4135	249	10			NUM
cana-4135	249	11	1	1	NUM
cana-4135	249	12	1	1	NUM
cana-4135	249	13	1	1	NUM
cana-4135	249	14	1	1	NUM
cana-4135	249	15	1	1	NUM
cana-4135	249	16	1	1	NUM
cana-4135	249	17	2lim	2lim	NUM
cana-4135	249	18	[	[	PUNCT
cana-4135	249	19	(	(	PUNCT
cana-4135	249	20	,	,	PUNCT
cana-4135	249	21	,	,	PUNCT
cana-4135	249	22	)	)	PUNCT
cana-4135	249	23	(	(	PUNCT
cana-4135	249	24	,	,	PUNCT
cana-4135	249	25	,	,	PUNCT
cana-4135	249	26	)	)	PUNCT
cana-4135	249	27	(	(	PUNCT
cana-4135	249	28	,	,	PUNCT
cana-4135	249	29	,	,	PUNCT
cana-4135	249	30	)	)	PUNCT
cana-4135	249	31	]	]	PUNCT
cana-4135	249	32	n	n	CCONJ
cana-4135	249	33	n	n	CCONJ
cana-4135	249	34	n	n	CCONJ
cana-4135	249	35	n	n	CCONJ
cana-4135	249	36	n	n	CCONJ
cana-4135	249	37	n	n	CCONJ
cana-4135	249	38	n	n	CCONJ
cana-4135	249	39	n	n	CCONJ
cana-4135	249	40	n	n	CCONJ
cana-4135	249	41	n	n	NOUN
cana-4135	249	42	s	s	VERB
cana-4135	250	1	i	i	PRON
cana-4135	250	2	i	i	PRON
cana-4135	251	1	i	i	PRON
cana-4135	251	2	s	s	VERB
cana-4135	252	1	i	i	PRON
cana-4135	253	1	i	i	PRON
cana-4135	254	1	i	i	PRON
cana-4135	254	2	s	s	VERB
cana-4135	254	3	i	i	INTJ
cana-4135	255	1	i	i	PROPN
cana-4135	255	2	i	i	ADP
cana-4135	255	3			PROPN
cana-4135	255	4			NOUN
cana-4135	255	5	+	+	X
cana-4135	256	1	+	+	PUNCT
cana-4135	256	2	+	+	PUNCT
cana-4135	256	3	+	+	PUNCT
cana-4135	256	4	+	+	PUNCT
cana-4135	256	5	+	+	CCONJ
cana-4135	256	6	+	+	NUM
cana-4135	256	7	→	→	NOUN
cana-4135	256	8	=	=	NOUN
cana-4135	256	9	communications	communication	NOUN
cana-4135	256	10	on	on	ADP
cana-4135	256	11	applied	apply	VERB
cana-4135	256	12	nonlinear	nonlinear	ADJ
cana-4135	256	13	analysis	analysis	NOUN
cana-4135	256	14	issn	issn	NOUN
cana-4135	256	15	:	:	PUNCT
cana-4135	256	16	1074	1074	NUM
cana-4135	256	17	-	-	PUNCT
cana-4135	256	18	133x	133x	NUM
cana-4135	256	19	vol	vol	NOUN
cana-4135	256	20	32	32	NUM
cana-4135	256	21	no	no	NOUN
cana-4135	256	22	.	.	PUNCT
cana-4135	257	1	9s	9s	NUM
cana-4135	257	2	(	(	PUNCT
cana-4135	257	3	2025	2025	NUM
cana-4135	257	4	)	)	PUNCT
cana-4135	257	5	1282	1282	NUM
cana-4135	257	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4135	257	7	1	1	NUM
cana-4135	257	8	1	1	NUM
cana-4135	257	9	1	1	NUM
cana-4135	257	10	2lim	2lim	NUM
cana-4135	257	11	[	[	PUNCT
cana-4135	257	12	(	(	PUNCT
cana-4135	257	13	,	,	PUNCT
cana-4135	257	14	,	,	PUNCT
cana-4135	257	15	)	)	PUNCT
cana-4135	257	16	(	(	PUNCT
cana-4135	257	17	,	,	PUNCT
cana-4135	257	18	,	,	PUNCT
cana-4135	257	19	)	)	PUNCT
cana-4135	257	20	]	]	PUNCT
cana-4135	257	21	n	n	CCONJ
cana-4135	257	22	n	n	CCONJ
cana-4135	257	23	n	n	CCONJ
cana-4135	257	24	n	n	CCONJ
cana-4135	257	25	n	n	CCONJ
cana-4135	257	26	n	n	CCONJ
cana-4135	257	27	n	n	NOUN
cana-4135	257	28	s	s	VERB
cana-4135	258	1	i	i	PRON
cana-4135	258	2	i	i	PRON
cana-4135	259	1	i	i	PRON
cana-4135	259	2	s	s	VERB
cana-4135	260	1	i	i	PRON
cana-4135	261	1	i	i	INTJ
cana-4135	262	1	i	i	INTJ
cana-4135	262	2	c	c	VERB
cana-4135	262	3	c	c	NOUN
cana-4135	262	4	c	c	NOUN
cana-4135	262	5			NUM
cana-4135	262	6			NOUN
cana-4135	262	7			ADP
cana-4135	262	8			NUM
cana-4135	262	9			PROPN
cana-4135	262	10			NUM
cana-4135	262	11			X
cana-4135	263	1	+	+	X
cana-4135	264	1	+	+	PUNCT
cana-4135	264	2	+	+	PUNCT
cana-4135	264	3	+	+	PUNCT
cana-4135	264	4	+	+	PUNCT
cana-4135	264	5	+	+	CCONJ
cana-4135	264	6	+	+	NUM
cana-4135	264	7	→	→	NOUN
cana-4135	264	8	=	=	NOUN
cana-4135	264	9			NOUN
cana-4135	264	10			PROPN
cana-4135	264	11	=	=	PUNCT
cana-4135	264	12	which	which	PRON
cana-4135	264	13	is	be	AUX
cana-4135	264	14	a	a	DET
cana-4135	264	15	contradiction	contradiction	NOUN
cana-4135	264	16	1c	1c	NUM
cana-4135	264	17	=	=	SYM
cana-4135	264	18	1	1	NUM
cana-4135	264	19	1lim	1lim	NUM
cana-4135	264	20	(	(	PUNCT
cana-4135	264	21	,	,	PUNCT
cana-4135	264	22	,	,	PUNCT
cana-4135	264	23	)	)	PUNCT
cana-4135	264	24	1	1	NUM
cana-4135	264	25	lim	lim	NOUN
cana-4135	264	26	(	(	PUNCT
cana-4135	264	27	,	,	PUNCT
cana-4135	264	28	,	,	PUNCT
cana-4135	264	29	)	)	PUNCT
cana-4135	264	30	1n	1n	NUM
cana-4135	264	31	n	n	CCONJ
cana-4135	264	32	n	n	CCONJ
cana-4135	264	33	n	n	CCONJ
cana-4135	264	34	n	n	CCONJ
cana-4135	264	35	n	n	CCONJ
cana-4135	264	36	n	n	CCONJ
cana-4135	264	37	n	n	NOUN
cana-4135	264	38	s	s	VERB
cana-4135	265	1	i	i	PRON
cana-4135	265	2	i	i	PRON
cana-4135	266	1	i	i	PRON
cana-4135	266	2	s	s	VERB
cana-4135	266	3	i	i	INTJ
cana-4135	267	1	i	i	PROPN
cana-4135	267	2	i	i	VERB
cana-4135	267	3	+	+	CCONJ
cana-4135	267	4	+	+	CCONJ
cana-4135	267	5	→	→	NUM
cana-4135	267	6	→	→	PUNCT
cana-4135	267	7			NOUN
cana-4135	267	8	=	=	PUNCT
cana-4135	267	9			NOUN
cana-4135	268	1	=	=	X
cana-4135	268	2	.	.	PUNCT
cana-4135	269	1	(	(	PUNCT
cana-4135	269	2	2.1.4	2.1.4	NUM
cana-4135	269	3	)	)	PUNCT
cana-4135	269	4	step	step	NOUN
cana-4135	269	5	2	2	NUM
cana-4135	269	6	:	:	PUNCT
cana-4135	269	7	to	to	PART
cana-4135	269	8	show	show	VERB
cana-4135	269	9	that	that	SCONJ
cana-4135	269	10	{	{	PUNCT
cana-4135	269	11	}	}	PUNCT
cana-4135	269	12	ni	ni	PROPN
cana-4135	269	13	is	be	AUX
cana-4135	269	14	cauchy	cauchy	ADJ
cana-4135	269	15	sequence	sequence	NOUN
cana-4135	269	16	.	.	PUNCT
cana-4135	270	1	if	if	SCONJ
cana-4135	270	2	{	{	PUNCT
cana-4135	270	3	}	}	PUNCT
cana-4135	270	4	ni	ni	PROPN
cana-4135	270	5	is	be	AUX
cana-4135	270	6	not	not	PART
cana-4135	270	7	cauchy	cauchy	ADJ
cana-4135	270	8	sequence	sequence	NOUN
cana-4135	270	9	,	,	PUNCT
cana-4135	270	10	there	there	PRON
cana-4135	270	11	exists	exist	VERB
cana-4135	270	12	0	0	X
cana-4135	270	13			INTJ
cana-4135	270	14	,	,	PUNCT
cana-4135	270	15	then	then	ADV
cana-4135	270	16	one	one	PRON
cana-4135	270	17	can	can	AUX
cana-4135	270	18	find	find	VERB
cana-4135	270	19	sub	sub	NOUN
cana-4135	270	20	-	-	NOUN
cana-4135	270	21	sequences	sequence	NOUN
cana-4135	270	22	(	(	PUNCT
cana-4135	270	23	)	)	PUNCT
cana-4135	270	24	{	{	PUNCT
cana-4135	270	25	}	}	PUNCT
cana-4135	270	26	m	m	VERB
cana-4135	270	27	li	li	NOUN
cana-4135	270	28	and	and	CCONJ
cana-4135	270	29	(	(	PUNCT
cana-4135	270	30	)	)	PUNCT
cana-4135	270	31	{	{	PUNCT
cana-4135	270	32	}	}	PUNCT
cana-4135	271	1	n	n	DET
cana-4135	271	2	li	li	NOUN
cana-4135	271	3	of	of	ADP
cana-4135	271	4	{	{	PUNCT
cana-4135	271	5	}	}	PUNCT
cana-4135	271	6	ni	ni	PROPN
cana-4135	271	7	and	and	CCONJ
cana-4135	271	8	increasing	increase	VERB
cana-4135	271	9	sequences	sequence	NOUN
cana-4135	271	10	of	of	ADP
cana-4135	271	11	integers	integer	NOUN
cana-4135	271	12	{	{	PUNCT
cana-4135	271	13	}	}	PUNCT
cana-4135	271	14	lm	lm	INTJ
cana-4135	271	15	and	and	CCONJ
cana-4135	271	16	{	{	PUNCT
cana-4135	271	17	}	}	PUNCT
cana-4135	271	18	ln	ln	NOUN
cana-4135	271	19	such	such	ADJ
cana-4135	271	20	that	that	SCONJ
cana-4135	271	21	{	{	PUNCT
cana-4135	271	22	}	}	PUNCT
cana-4135	271	23	ln	ln	ADV
cana-4135	271	24	is	be	AUX
cana-4135	271	25	the	the	DET
cana-4135	271	26	smallest	small	ADJ
cana-4135	271	27	index	index	NOUN
cana-4135	271	28	such	such	ADJ
cana-4135	271	29	that	that	PRON
cana-4135	271	30	(	(	PUNCT
cana-4135	271	31	)	)	PUNCT
cana-4135	271	32	(	(	PUNCT
cana-4135	271	33	)	)	PUNCT
cana-4135	271	34	(	(	PUNCT
cana-4135	271	35	)	)	PUNCT
cana-4135	271	36	(	(	PUNCT
cana-4135	271	37	)	)	PUNCT
cana-4135	271	38	(	(	PUNCT
cana-4135	271	39	)	)	PUNCT
cana-4135	271	40	,	,	PUNCT
cana-4135	271	41	(	(	PUNCT
cana-4135	271	42	,	,	PUNCT
cana-4135	271	43	,	,	PUNCT
cana-4135	271	44	)	)	PUNCT
cana-4135	271	45	m	m	VERB
cana-4135	271	46	l	l	NOUN
cana-4135	271	47	m	m	VERB
cana-4135	271	48	l	l	NOUN
cana-4135	271	49	n	n	CCONJ
cana-4135	271	50	ln	ln	ADJ
cana-4135	271	51	l	l	NOUN
cana-4135	271	52	m	m	PROPN
cana-4135	271	53	l	l	NOUN
cana-4135	271	54	l	l	NOUN
cana-4135	271	55	s	s	VERB
cana-4135	271	56	i	i	PRON
cana-4135	272	1	i	i	PRON
cana-4135	272	2	i	i	VERB
cana-4135	272	3			NOUN
cana-4135	272	4			X
cana-4135	272	5			NUM
cana-4135	272	6	.then	.then	PUNCT
cana-4135	272	7	(	(	PUNCT
cana-4135	272	8	)	)	PUNCT
cana-4135	272	9	(	(	PUNCT
cana-4135	272	10	)	)	PUNCT
cana-4135	272	11	(	(	PUNCT
cana-4135	272	12	)	)	PUNCT
cana-4135	272	13	1	1	NUM
cana-4135	272	14	(	(	PUNCT
cana-4135	272	15	,	,	PUNCT
cana-4135	272	16	,	,	PUNCT
cana-4135	272	17	)	)	PUNCT
cana-4135	272	18	m	m	VERB
cana-4135	272	19	l	l	NOUN
cana-4135	272	20	m	m	VERB
cana-4135	272	21	l	l	NOUN
cana-4135	272	22	n	n	ADV
cana-4135	273	1	ls	ls	INTJ
cana-4135	274	1	i	i	PRON
cana-4135	275	1	i	i	PROPN
cana-4135	275	2	i	i	VERB
cana-4135	275	3	−	−	NOUN
cana-4135	275	4			PROPN
cana-4135	275	5	(	(	PUNCT
cana-4135	275	6	2.1.5	2.1.5	NUM
cana-4135	275	7	)	)	PUNCT
cana-4135	275	8	now	now	ADV
cana-4135	275	9	(	(	PUNCT
cana-4135	275	10	)	)	PUNCT
cana-4135	275	11	(	(	PUNCT
cana-4135	275	12	)	)	PUNCT
cana-4135	275	13	(	(	PUNCT
cana-4135	275	14	)	)	PUNCT
cana-4135	275	15	(	(	PUNCT
cana-4135	275	16	,	,	PUNCT
cana-4135	275	17	,	,	PUNCT
cana-4135	275	18	)	)	PUNCT
cana-4135	275	19	m	m	VERB
cana-4135	275	20	l	l	NOUN
cana-4135	275	21	m	m	VERB
cana-4135	275	22	l	l	NOUN
cana-4135	275	23	n	n	ADV
cana-4135	276	1	ls	ls	INTJ
cana-4135	277	1	i	i	PRON
cana-4135	277	2	i	i	PROPN
cana-4135	277	3	i	i	VERB
cana-4135	277	4			PROPN
cana-4135	277	5	(	(	PUNCT
cana-4135	277	6	)	)	PUNCT
cana-4135	277	7	(	(	PUNCT
cana-4135	277	8	)	)	PUNCT
cana-4135	277	9	(	(	PUNCT
cana-4135	277	10	)	)	PUNCT
cana-4135	277	11	(	(	PUNCT
cana-4135	277	12	,	,	PUNCT
cana-4135	277	13	,	,	PUNCT
cana-4135	277	14	)	)	PUNCT
cana-4135	277	15	n	n	CCONJ
cana-4135	277	16	l	l	NOUN
cana-4135	277	17	n	n	ADP
cana-4135	277	18	l	l	NOUN
cana-4135	277	19	m	m	VERB
cana-4135	277	20	ls	ls	INTJ
cana-4135	278	1	i	i	PRON
cana-4135	279	1	i	i	PROPN
cana-4135	279	2	i	i	NUM
cana-4135	279	3	--by	--by	ADJ
cana-4135	279	4	lemma	lemma	PROPN
cana-4135	279	5	2	2	NUM
cana-4135	279	6	2	2	NUM
cana-4135	279	7	(	(	PUNCT
cana-4135	279	8	)	)	PUNCT
cana-4135	279	9	(	(	PUNCT
cana-4135	279	10	)	)	PUNCT
cana-4135	279	11	(	(	PUNCT
cana-4135	279	12	)	)	PUNCT
cana-4135	279	13	1	1	NUM
cana-4135	279	14	(	(	PUNCT
cana-4135	279	15	)	)	PUNCT
cana-4135	279	16	(	(	PUNCT
cana-4135	279	17	)	)	PUNCT
cana-4135	279	18	(	(	PUNCT
cana-4135	279	19	)	)	PUNCT
cana-4135	279	20	1	1	NUM
cana-4135	279	21	(	(	PUNCT
cana-4135	279	22	,	,	PUNCT
cana-4135	279	23	,	,	PUNCT
cana-4135	279	24	)	)	PUNCT
cana-4135	279	25	(	(	PUNCT
cana-4135	279	26	,	,	PUNCT
cana-4135	279	27	,	,	PUNCT
cana-4135	279	28	)	)	PUNCT
cana-4135	279	29	n	n	CCONJ
cana-4135	279	30	l	l	NOUN
cana-4135	279	31	n	n	ADP
cana-4135	279	32	l	l	NOUN
cana-4135	279	33	n	n	CCONJ
cana-4135	279	34	l	l	NOUN
cana-4135	279	35	m	m	VERB
cana-4135	279	36	l	l	NOUN
cana-4135	279	37	m	m	VERB
cana-4135	279	38	l	l	NOUN
cana-4135	279	39	n	n	ADV
cana-4135	279	40	ls	ls	INTJ
cana-4135	280	1	i	i	PRON
cana-4135	280	2	i	i	PRON
cana-4135	281	1	i	i	PRON
cana-4135	281	2	s	s	VERB
cana-4135	281	3	i	i	INTJ
cana-4135	282	1	i	i	NOUN
cana-4135	282	2	i	i	VERB
cana-4135	282	3			NOUN
cana-4135	282	4	−	−	NOUN
cana-4135	282	5	−	−	NOUN
cana-4135	282	6	--by	--by	ADJ
cana-4135	282	7	property	property	NOUN
cana-4135	282	8	of	of	ADP
cana-4135	282	9	s	s	NOUN
cana-4135	282	10	-metric	-metric	ADJ
cana-4135	282	11	space	space	NOUN
cana-4135	282	12	.	.	PUNCT
cana-4135	283	1	2	2	NUM
cana-4135	283	2	(	(	PUNCT
cana-4135	283	3	)	)	PUNCT
cana-4135	283	4	(	(	PUNCT
cana-4135	283	5	)	)	PUNCT
cana-4135	283	6	(	(	PUNCT
cana-4135	283	7	)	)	PUNCT
cana-4135	283	8	1	1	NUM
cana-4135	283	9	(	(	PUNCT
cana-4135	283	10	,	,	PUNCT
cana-4135	283	11	,	,	PUNCT
cana-4135	283	12	)	)	PUNCT
cana-4135	283	13	n	n	CCONJ
cana-4135	283	14	l	l	NOUN
cana-4135	283	15	n	n	ADP
cana-4135	283	16	l	l	NOUN
cana-4135	283	17	n	n	CCONJ
cana-4135	284	1	ls	ls	INTJ
cana-4135	284	2	i	i	PRON
cana-4135	284	3	i	i	PRON
cana-4135	284	4	i	i	VERB
cana-4135	284	5	−	−	NOUN
cana-4135	284	6	=	=	SYM
cana-4135	284	7	(	(	PUNCT
cana-4135	284	8	)	)	PUNCT
cana-4135	284	9	(	(	PUNCT
cana-4135	284	10	)	)	PUNCT
cana-4135	284	11	(	(	PUNCT
cana-4135	284	12	)	)	PUNCT
cana-4135	284	13	(	(	PUNCT
cana-4135	284	14	,	,	PUNCT
cana-4135	284	15	,	,	PUNCT
cana-4135	284	16	)	)	PUNCT
cana-4135	284	17	m	m	VERB
cana-4135	284	18	l	l	NOUN
cana-4135	284	19	m	m	VERB
cana-4135	284	20	l	l	NOUN
cana-4135	284	21	n	n	ADV
cana-4135	285	1	ls	ls	INTJ
cana-4135	286	1	i	i	PRON
cana-4135	286	2	i	i	PROPN
cana-4135	286	3	i	i	VERB
cana-4135	286	4			VERB
cana-4135	286	5			PROPN
cana-4135	286	6	--using	--using	PROPN
cana-4135	286	7	(	(	PUNCT
cana-4135	286	8	2.1.4	2.1.4	NUM
cana-4135	286	9	)	)	PUNCT
cana-4135	286	10	which	which	PRON
cana-4135	286	11	is	be	AUX
cana-4135	286	12	a	a	DET
cana-4135	286	13	contradiction	contradiction	NOUN
cana-4135	286	14	(	(	PUNCT
cana-4135	286	15	)	)	PUNCT
cana-4135	286	16	(	(	PUNCT
cana-4135	286	17	)	)	PUNCT
cana-4135	286	18	(	(	PUNCT
cana-4135	286	19	)	)	PUNCT
cana-4135	286	20	lim	lim	PROPN
cana-4135	286	21	(	(	PUNCT
cana-4135	286	22	,	,	PUNCT
cana-4135	286	23	,	,	PUNCT
cana-4135	286	24	)	)	PUNCT
cana-4135	286	25	m	m	VERB
cana-4135	286	26	l	l	NOUN
cana-4135	286	27	m	m	VERB
cana-4135	286	28	l	l	NOUN
cana-4135	286	29	n	n	NOUN
cana-4135	286	30	l	l	NOUN
cana-4135	286	31	k	k	NOUN
cana-4135	287	1	s	s	X
cana-4135	287	2	i	i	INTJ
cana-4135	287	3	i	i	PROPN
cana-4135	287	4	i	i	NUM
cana-4135	287	5			NOUN
cana-4135	287	6	→	→	PUNCT
cana-4135	287	7			PROPN
cana-4135	287	8	=	=	PUNCT
cana-4135	287	9	.	.	PUNCT
cana-4135	288	1	(	(	PUNCT
cana-4135	288	2	2.1.6	2.1.6	X
cana-4135	288	3	)	)	PUNCT
cana-4135	288	4	then	then	ADV
cana-4135	288	5	(	(	PUNCT
cana-4135	288	6	)	)	PUNCT
cana-4135	288	7	(	(	PUNCT
cana-4135	288	8	)	)	PUNCT
cana-4135	288	9	(	(	PUNCT
cana-4135	288	10	)	)	PUNCT
cana-4135	288	11	(	(	PUNCT
cana-4135	288	12	,	,	PUNCT
cana-4135	288	13	,	,	PUNCT
cana-4135	288	14	)	)	PUNCT
cana-4135	288	15	m	m	VERB
cana-4135	288	16	l	l	NOUN
cana-4135	288	17	m	m	VERB
cana-4135	288	18	l	l	NOUN
cana-4135	289	1	n	n	ADV
cana-4135	289	2	ls	ls	INTJ
cana-4135	290	1	i	i	INTJ
cana-4135	290	2	i	i	PROPN
cana-4135	290	3	i	i	VERB
cana-4135	290	4	2	2	NUM
cana-4135	290	5	(	(	PUNCT
cana-4135	290	6	)	)	PUNCT
cana-4135	290	7	(	(	PUNCT
cana-4135	290	8	)	)	PUNCT
cana-4135	290	9	(	(	PUNCT
cana-4135	290	10	)	)	PUNCT
cana-4135	290	11	1	1	NUM
cana-4135	290	12	(	(	PUNCT
cana-4135	290	13	)	)	PUNCT
cana-4135	290	14	(	(	PUNCT
cana-4135	290	15	)	)	PUNCT
cana-4135	290	16	(	(	PUNCT
cana-4135	290	17	)	)	PUNCT
cana-4135	290	18	1	1	NUM
cana-4135	290	19	(	(	PUNCT
cana-4135	290	20	,	,	PUNCT
cana-4135	290	21	,	,	PUNCT
cana-4135	290	22	)	)	PUNCT
cana-4135	290	23	(	(	PUNCT
cana-4135	290	24	,	,	PUNCT
cana-4135	290	25	,	,	PUNCT
cana-4135	290	26	)	)	PUNCT
cana-4135	290	27	m	m	VERB
cana-4135	290	28	l	l	NOUN
cana-4135	290	29	m	m	VERB
cana-4135	290	30	l	l	NOUN
cana-4135	290	31	m	m	VERB
cana-4135	290	32	l	l	NOUN
cana-4135	290	33	n	n	ADP
cana-4135	290	34	l	l	NOUN
cana-4135	290	35	n	n	ADP
cana-4135	290	36	l	l	NOUN
cana-4135	290	37	m	m	VERB
cana-4135	291	1	ls	ls	INTJ
cana-4135	291	2	i	i	PRON
cana-4135	292	1	i	i	PRON
cana-4135	293	1	i	i	PRON
cana-4135	293	2	s	s	VERB
cana-4135	293	3	i	i	INTJ
cana-4135	294	1	i	i	NOUN
cana-4135	294	2	i	i	VERB
cana-4135	294	3			NOUN
cana-4135	294	4	−	−	NOUN
cana-4135	294	5	−	−	NOUN
cana-4135	294	6	2	2	NUM
cana-4135	294	7	2	2	NUM
cana-4135	294	8	(	(	PUNCT
cana-4135	294	9	)	)	PUNCT
cana-4135	294	10	(	(	PUNCT
cana-4135	294	11	)	)	PUNCT
cana-4135	294	12	(	(	PUNCT
cana-4135	294	13	)	)	PUNCT
cana-4135	294	14	1	1	NUM
cana-4135	294	15	(	(	PUNCT
cana-4135	294	16	)	)	PUNCT
cana-4135	294	17	)	)	PUNCT
cana-4135	294	18	(	(	PUNCT
cana-4135	294	19	)	)	PUNCT
cana-4135	294	20	1	1	NUM
cana-4135	294	21	(	(	PUNCT
cana-4135	294	22	)	)	PUNCT
cana-4135	294	23	1	1	NUM
cana-4135	294	24	(	(	PUNCT
cana-4135	294	25	)	)	PUNCT
cana-4135	294	26	1	1	NUM
cana-4135	294	27	(	(	PUNCT
cana-4135	294	28	)	)	PUNCT
cana-4135	294	29	1	1	NUM
cana-4135	294	30	(	(	PUNCT
cana-4135	294	31	,	,	PUNCT
cana-4135	294	32	,	,	PUNCT
cana-4135	294	33	)	)	PUNCT
cana-4135	294	34	(	(	PUNCT
cana-4135	294	35	,	,	PUNCT
cana-4135	294	36	,	,	PUNCT
cana-4135	294	37	)	)	PUNCT
cana-4135	294	38	(	(	PUNCT
cana-4135	294	39	,	,	PUNCT
cana-4135	294	40	,	,	PUNCT
cana-4135	294	41	)	)	PUNCT
cana-4135	294	42	m	m	VERB
cana-4135	294	43	l	l	NOUN
cana-4135	294	44	m	m	VERB
cana-4135	294	45	l	l	NOUN
cana-4135	294	46	m	m	VERB
cana-4135	294	47	l	l	NOUN
cana-4135	294	48	n	n	NUM
cana-4135	294	49	l	l	NOUN
cana-4135	294	50	nl	nl	NOUN
cana-4135	294	51	n	n	PROPN
cana-4135	294	52	l	l	NOUN
cana-4135	294	53	m	m	VERB
cana-4135	294	54	l	l	NOUN
cana-4135	294	55	m	m	VERB
cana-4135	294	56	l	l	NOUN
cana-4135	294	57	n	n	ADV
cana-4135	295	1	ls	ls	INTJ
cana-4135	296	1	i	i	PRON
cana-4135	296	2	i	i	PRON
cana-4135	297	1	i	i	PRON
cana-4135	297	2	s	s	VERB
cana-4135	298	1	i	i	PRON
cana-4135	299	1	i	i	PRON
cana-4135	300	1	i	i	PRON
cana-4135	300	2	s	s	VERB
cana-4135	300	3	i	i	INTJ
cana-4135	301	1	i	i	NOUN
cana-4135	301	2	i	i	VERB
cana-4135	301	3			NOUN
cana-4135	301	4			NOUN
cana-4135	301	5	−	−	ADP
cana-4135	301	6	−	−	NOUN
cana-4135	302	1	−	−	PROPN
cana-4135	302	2	−	−	NOUN
cana-4135	303	1	−	−	NOUN
cana-4135	303	2	(	(	PUNCT
cana-4135	303	3	2.1.7	2.1.7	NUM
cana-4135	303	4	)	)	PUNCT
cana-4135	303	5	also	also	ADV
cana-4135	303	6	2	2	NUM
cana-4135	303	7	(	(	PUNCT
cana-4135	303	8	)	)	PUNCT
cana-4135	303	9	1	1	NUM
cana-4135	303	10	(	(	PUNCT
cana-4135	303	11	)	)	PUNCT
cana-4135	303	12	1	1	NUM
cana-4135	303	13	(	(	PUNCT
cana-4135	303	14	)	)	PUNCT
cana-4135	303	15	(	(	PUNCT
cana-4135	303	16	)	)	PUNCT
cana-4135	303	17	1	1	NUM
cana-4135	303	18	(	(	PUNCT
cana-4135	303	19	)	)	PUNCT
cana-4135	303	20	1	1	NUM
cana-4135	303	21	(	(	PUNCT
cana-4135	303	22	)	)	PUNCT
cana-4135	303	23	(	(	PUNCT
cana-4135	303	24	,	,	PUNCT
cana-4135	303	25	,	,	PUNCT
cana-4135	303	26	)	)	PUNCT
cana-4135	303	27	(	(	PUNCT
cana-4135	303	28	,	,	PUNCT
cana-4135	303	29	,	,	PUNCT
cana-4135	303	30	)	)	PUNCT
cana-4135	303	31	m	m	VERB
cana-4135	303	32	l	l	NOUN
cana-4135	303	33	m	m	VERB
cana-4135	303	34	l	l	NOUN
cana-4135	303	35	m	m	VERB
cana-4135	303	36	l	l	NOUN
cana-4135	303	37	n	n	ADP
cana-4135	303	38	l	l	NOUN
cana-4135	303	39	n	n	ADP
cana-4135	303	40	l	l	NOUN
cana-4135	303	41	m	m	VERB
cana-4135	303	42	ls	ls	INTJ
cana-4135	304	1	i	i	PRON
cana-4135	304	2	i	i	PRON
cana-4135	305	1	i	i	PRON
cana-4135	305	2	s	s	VERB
cana-4135	305	3	i	i	INTJ
cana-4135	306	1	i	i	NOUN
cana-4135	306	2	i	i	VERB
cana-4135	306	3			NOUN
cana-4135	306	4	−	−	NOUN
cana-4135	307	1	−	−	NOUN
cana-4135	307	2	−	−	NOUN
cana-4135	308	1	−	−	NOUN
cana-4135	308	2	2	2	NUM
cana-4135	308	3	(	(	PUNCT
cana-4135	308	4	)	)	PUNCT
cana-4135	308	5	1	1	NUM
cana-4135	308	6	(	(	PUNCT
cana-4135	308	7	)	)	PUNCT
cana-4135	308	8	1	1	NUM
cana-4135	308	9	(	(	PUNCT
cana-4135	308	10	)	)	PUNCT
cana-4135	308	11	(	(	PUNCT
cana-4135	308	12	)	)	PUNCT
cana-4135	308	13	(	(	PUNCT
cana-4135	308	14	)	)	PUNCT
cana-4135	308	15	(	(	PUNCT
cana-4135	308	16	)	)	PUNCT
cana-4135	308	17	1	1	NUM
cana-4135	308	18	(	(	PUNCT
cana-4135	308	19	,	,	PUNCT
cana-4135	308	20	,	,	PUNCT
cana-4135	308	21	)	)	PUNCT
cana-4135	308	22	(	(	PUNCT
cana-4135	308	23	,	,	PUNCT
cana-4135	308	24	,	,	PUNCT
cana-4135	308	25	)	)	PUNCT
cana-4135	308	26	m	m	VERB
cana-4135	308	27	l	l	NOUN
cana-4135	308	28	m	m	VERB
cana-4135	308	29	l	l	NOUN
cana-4135	308	30	m	m	VERB
cana-4135	308	31	l	l	NOUN
cana-4135	308	32	m	m	VERB
cana-4135	308	33	l	l	NOUN
cana-4135	308	34	m	m	VERB
cana-4135	308	35	l	l	NOUN
cana-4135	308	36	n	n	ADV
cana-4135	308	37	ls	ls	INTJ
cana-4135	309	1	i	i	PRON
cana-4135	309	2	i	i	PRON
cana-4135	310	1	i	i	PRON
cana-4135	310	2	s	s	VERB
cana-4135	310	3	i	i	INTJ
cana-4135	311	1	i	i	NOUN
cana-4135	311	2	i	i	VERB
cana-4135	311	3			NOUN
cana-4135	311	4	−	−	NOUN
cana-4135	311	5	−	−	NOUN
cana-4135	311	6	−=	−=	NOUN
cana-4135	311	7	,	,	PUNCT
cana-4135	311	8	using	use	VERB
cana-4135	311	9	lemma	lemma	PROPN
cana-4135	311	10	2	2	NUM
cana-4135	311	11	(	(	PUNCT
cana-4135	311	12	2.1.8	2.1.8	PROPN
cana-4135	311	13	)	)	PUNCT
cana-4135	311	14	letting	let	VERB
cana-4135	311	15	l	l	NOUN
cana-4135	311	16	→	→	PUNCT
cana-4135	311	17	in	in	ADP
cana-4135	311	18	(	(	PUNCT
cana-4135	311	19	2.1.8	2.1.8	NUM
cana-4135	311	20	)	)	PUNCT
cana-4135	311	21	and	and	CCONJ
cana-4135	311	22	using	use	VERB
cana-4135	311	23	(	(	PUNCT
cana-4135	311	24	2.1.4	2.1.4	NUM
cana-4135	311	25	)	)	PUNCT
cana-4135	311	26	,	,	PUNCT
cana-4135	311	27	(	(	PUNCT
cana-4135	311	28	2.1.5	2.1.5	NUM
cana-4135	311	29	)	)	PUNCT
cana-4135	311	30	,	,	PUNCT
cana-4135	311	31	(	(	PUNCT
cana-4135	311	32	2.1.6),(2.1.7	2.1.6),(2.1.7	ADV
cana-4135	311	33	)	)	PUNCT
cana-4135	311	34	(	(	PUNCT
cana-4135	311	35	)	)	PUNCT
cana-4135	311	36	1	1	NUM
cana-4135	311	37	(	(	PUNCT
cana-4135	311	38	)	)	PUNCT
cana-4135	311	39	1	1	NUM
cana-4135	311	40	(	(	PUNCT
cana-4135	311	41	)	)	PUNCT
cana-4135	311	42	1	1	NUM
cana-4135	311	43	(	(	PUNCT
cana-4135	311	44	,	,	PUNCT
cana-4135	311	45	,	,	PUNCT
cana-4135	311	46	)	)	PUNCT
cana-4135	311	47	m	m	VERB
cana-4135	311	48	l	l	NOUN
cana-4135	311	49	m	m	VERB
cana-4135	311	50	l	l	NOUN
cana-4135	312	1	n	n	ADV
cana-4135	312	2	ls	ls	INTJ
cana-4135	313	1	i	i	INTJ
cana-4135	313	2	i	i	PRON
cana-4135	313	3	i	i	VERB
cana-4135	313	4	−	−	NUM
cana-4135	313	5	−	−	NOUN
cana-4135	313	6	−	−	PROPN
cana-4135	313	7	communications	communication	NOUN
cana-4135	313	8	on	on	ADP
cana-4135	313	9	applied	apply	VERB
cana-4135	313	10	nonlinear	nonlinear	ADJ
cana-4135	313	11	analysis	analysis	NOUN
cana-4135	313	12	issn	issn	NOUN
cana-4135	313	13	:	:	PUNCT
cana-4135	313	14	1074	1074	NUM
cana-4135	313	15	-	-	PUNCT
cana-4135	313	16	133x	133x	NUM
cana-4135	313	17	vol	vol	NOUN
cana-4135	313	18	32	32	NUM
cana-4135	313	19	no	no	NOUN
cana-4135	313	20	.	.	PUNCT
cana-4135	314	1	9s	9s	NUM
cana-4135	314	2	(	(	PUNCT
cana-4135	314	3	2025	2025	NUM
cana-4135	314	4	)	)	PUNCT
cana-4135	314	5	1283	1283	NUM
cana-4135	314	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4135	314	7	(	(	PUNCT
cana-4135	314	8	)	)	PUNCT
cana-4135	314	9	1	1	NUM
cana-4135	314	10	(	(	PUNCT
cana-4135	314	11	)	)	PUNCT
cana-4135	314	12	1	1	NUM
cana-4135	314	13	(	(	PUNCT
cana-4135	314	14	)	)	PUNCT
cana-4135	314	15	1lim	1lim	NUM
cana-4135	314	16	(	(	PUNCT
cana-4135	314	17	,	,	PUNCT
cana-4135	314	18	,	,	PUNCT
cana-4135	314	19	)	)	PUNCT
cana-4135	314	20	m	m	VERB
cana-4135	314	21	l	l	NOUN
cana-4135	314	22	m	m	VERB
cana-4135	314	23	l	l	NOUN
cana-4135	314	24	n	n	NOUN
cana-4135	314	25	l	l	NOUN
cana-4135	315	1	k	k	NOUN
cana-4135	315	2	s	s	X
cana-4135	316	1	i	i	INTJ
cana-4135	317	1	i	i	PROPN
cana-4135	317	2	i	i	VERB
cana-4135	317	3	−	−	NOUN
cana-4135	317	4	−	−	NOUN
cana-4135	317	5	−	−	NOUN
cana-4135	317	6	→	→	PUNCT
cana-4135	317	7	=	=	SYM
cana-4135	317	8	(	(	PUNCT
cana-4135	317	9	2.1.9	2.1.9	NUM
cana-4135	317	10	)	)	PUNCT
cana-4135	317	11	now	now	ADV
cana-4135	317	12	,	,	PUNCT
cana-4135	317	13	again	again	ADV
cana-4135	317	14	(	(	PUNCT
cana-4135	317	15	)	)	PUNCT
cana-4135	317	16	(	(	PUNCT
cana-4135	317	17	)	)	PUNCT
cana-4135	317	18	(	(	PUNCT
cana-4135	317	19	)	)	PUNCT
cana-4135	317	20	(	(	PUNCT
cana-4135	317	21	,	,	PUNCT
cana-4135	317	22	,	,	PUNCT
cana-4135	317	23	)	)	PUNCT
cana-4135	317	24	m	m	VERB
cana-4135	317	25	l	l	NOUN
cana-4135	317	26	m	m	VERB
cana-4135	317	27	l	l	NOUN
cana-4135	317	28	n	n	ADV
cana-4135	318	1	ls	ls	INTJ
cana-4135	318	2	i	i	PRON
cana-4135	318	3	i	i	PRON
cana-4135	318	4	i	i	NOUN
cana-4135	318	5	=	=	INTJ
cana-4135	318	6	(	(	PUNCT
cana-4135	318	7	)	)	PUNCT
cana-4135	318	8	(	(	PUNCT
cana-4135	318	9	)	)	PUNCT
cana-4135	318	10	(	(	PUNCT
cana-4135	318	11	)	)	PUNCT
cana-4135	318	12	(	(	PUNCT
cana-4135	318	13	(	(	PUNCT
cana-4135	318	14	)	)	PUNCT
cana-4135	318	15	,	,	PUNCT
cana-4135	318	16	(	(	PUNCT
cana-4135	318	17	)	)	PUNCT
cana-4135	318	18	,	,	PUNCT
cana-4135	318	19	(	(	PUNCT
cana-4135	318	20	)	)	PUNCT
cana-4135	318	21	)	)	PUNCT
cana-4135	319	1	m	m	VERB
cana-4135	319	2	l	l	NOUN
cana-4135	319	3	m	m	VERB
cana-4135	319	4	l	l	NOUN
cana-4135	319	5	n	n	CCONJ
cana-4135	320	1	ls	ls	INTJ
cana-4135	320	2	f	f	PROPN
cana-4135	320	3	h	h	NOUN
cana-4135	321	1	f	f	NOUN
cana-4135	321	2	h	h	NOUN
cana-4135	321	3	f	f	NOUN
cana-4135	321	4	h=	h=	NOUN
cana-4135	321	5	(	(	PUNCT
cana-4135	321	6	)	)	PUNCT
cana-4135	321	7	(	(	PUNCT
cana-4135	321	8	)	)	PUNCT
cana-4135	321	9	(	(	PUNCT
cana-4135	321	10	)	)	PUNCT
cana-4135	321	11	(	(	PUNCT
cana-4135	321	12	)	)	PUNCT
cana-4135	321	13	(	(	PUNCT
cana-4135	321	14	)	)	PUNCT
cana-4135	321	15	(	(	PUNCT
cana-4135	321	16	)	)	PUNCT
cana-4135	321	17	(	(	PUNCT
cana-4135	321	18	)	)	PUNCT
cana-4135	321	19	(	(	PUNCT
cana-4135	321	20	)	)	PUNCT
cana-4135	321	21	(	(	PUNCT
cana-4135	321	22	)	)	PUNCT
cana-4135	321	23	[	[	PUNCT
cana-4135	321	24	(	(	PUNCT
cana-4135	321	25	(	(	PUNCT
cana-4135	321	26	)	)	PUNCT
cana-4135	321	27	,	,	PUNCT
cana-4135	321	28	(	(	PUNCT
cana-4135	321	29	)	)	PUNCT
cana-4135	321	30	,	,	PUNCT
cana-4135	321	31	(	(	PUNCT
cana-4135	321	32	)	)	PUNCT
cana-4135	321	33	)	)	PUNCT
cana-4135	322	1	(	(	PUNCT
cana-4135	322	2	(	(	PUNCT
cana-4135	322	3	)	)	PUNCT
cana-4135	322	4	,	,	PUNCT
cana-4135	322	5	(	(	PUNCT
cana-4135	322	6	)	)	PUNCT
cana-4135	322	7	,	,	PUNCT
cana-4135	322	8	(	(	PUNCT
cana-4135	322	9	)	)	PUNCT
cana-4135	322	10	)	)	PUNCT
cana-4135	322	11	(	(	PUNCT
cana-4135	322	12	(	(	PUNCT
cana-4135	322	13	)	)	PUNCT
cana-4135	322	14	,	,	PUNCT
cana-4135	322	15	(	(	PUNCT
cana-4135	322	16	)	)	PUNCT
cana-4135	322	17	,	,	PUNCT
cana-4135	322	18	(	(	PUNCT
cana-4135	322	19	)	)	PUNCT
cana-4135	322	20	)	)	PUNCT
cana-4135	323	1	]	]	PUNCT
cana-4135	323	2	m	m	VERB
cana-4135	323	3	l	l	NOUN
cana-4135	323	4	m	m	VERB
cana-4135	323	5	l	l	NOUN
cana-4135	323	6	n	n	ADP
cana-4135	323	7	l	l	NOUN
cana-4135	323	8	n	n	CCONJ
cana-4135	323	9	l	l	NOUN
cana-4135	323	10	m	m	VERB
cana-4135	323	11	l	l	NOUN
cana-4135	323	12	n	n	ADP
cana-4135	323	13	l	l	NOUN
cana-4135	323	14	n	n	CCONJ
cana-4135	323	15	l	l	NOUN
cana-4135	323	16	m	m	VERB
cana-4135	323	17	l	l	NOUN
cana-4135	323	18	n	n	NOUN
cana-4135	323	19	ls	ls	ADJ
cana-4135	323	20	g	g	PROPN
cana-4135	323	21	h	h	NOUN
cana-4135	323	22	g	g	NOUN
cana-4135	323	23	h	h	NOUN
cana-4135	323	24	g	g	PROPN
cana-4135	323	25	h	h	PROPN
cana-4135	323	26	s	s	PROPN
cana-4135	323	27	g	g	NOUN
cana-4135	323	28	h	h	NOUN
cana-4135	323	29	f	f	NOUN
cana-4135	323	30	h	h	NOUN
cana-4135	324	1	f	f	PROPN
cana-4135	324	2	h	h	NOUN
cana-4135	324	3	s	s	VERB
cana-4135	325	1	g	g	NOUN
cana-4135	325	2	h	h	NOUN
cana-4135	326	1	f	f	NOUN
cana-4135	326	2	h	h	NOUN
cana-4135	327	1	f	f	PROPN
cana-4135	327	2	h	h	PROPN
cana-4135	327	3			PROPN
cana-4135	327	4			NOUN
cana-4135	327	5	(	(	PUNCT
cana-4135	327	6	)	)	PUNCT
cana-4135	327	7	1	1	NUM
cana-4135	327	8	(	(	PUNCT
cana-4135	327	9	)	)	PUNCT
cana-4135	327	10	1	1	NUM
cana-4135	327	11	(	(	PUNCT
cana-4135	327	12	)	)	PUNCT
cana-4135	327	13	1	1	NUM
cana-4135	327	14	(	(	PUNCT
cana-4135	327	15	)	)	PUNCT
cana-4135	327	16	1	1	NUM
cana-4135	327	17	(	(	PUNCT
cana-4135	327	18	)	)	PUNCT
cana-4135	327	19	(	(	PUNCT
cana-4135	327	20	)	)	PUNCT
cana-4135	327	21	(	(	PUNCT
cana-4135	327	22	)	)	PUNCT
cana-4135	327	23	1	1	NUM
cana-4135	327	24	(	(	PUNCT
cana-4135	327	25	)	)	PUNCT
cana-4135	327	26	(	(	PUNCT
cana-4135	327	27	)	)	PUNCT
cana-4135	327	28	[	[	PUNCT
cana-4135	327	29	(	(	PUNCT
cana-4135	327	30	,	,	PUNCT
cana-4135	327	31	,	,	PUNCT
cana-4135	327	32	)	)	PUNCT
cana-4135	327	33	(	(	PUNCT
cana-4135	327	34	,	,	PUNCT
cana-4135	327	35	,	,	PUNCT
cana-4135	327	36	)	)	PUNCT
cana-4135	327	37	(	(	PUNCT
cana-4135	327	38	,	,	PUNCT
cana-4135	327	39	,	,	PUNCT
cana-4135	327	40	)	)	PUNCT
cana-4135	327	41	m	m	VERB
cana-4135	327	42	l	l	NOUN
cana-4135	327	43	m	m	VERB
cana-4135	327	44	l	l	NOUN
cana-4135	327	45	n	n	ADP
cana-4135	327	46	l	l	NOUN
cana-4135	327	47	n	n	CCONJ
cana-4135	327	48	l	l	NOUN
cana-4135	327	49	m	m	VERB
cana-4135	327	50	l	l	NOUN
cana-4135	327	51	m	m	VERB
cana-4135	327	52	l	l	NOUN
cana-4135	327	53	n	n	NUM
cana-4135	327	54	l	l	NOUN
cana-4135	327	55	m	m	VERB
cana-4135	327	56	l	l	NOUN
cana-4135	327	57	n	n	ADV
cana-4135	328	1	ls	ls	INTJ
cana-4135	329	1	i	i	PRON
cana-4135	329	2	i	i	PRON
cana-4135	330	1	i	i	PRON
cana-4135	330	2	s	s	VERB
cana-4135	331	1	i	i	PRON
cana-4135	332	1	i	i	PRON
cana-4135	333	1	i	i	PRON
cana-4135	333	2	s	s	VERB
cana-4135	333	3	i	i	INTJ
cana-4135	334	1	i	i	PROPN
cana-4135	334	2	i	i	ADP
cana-4135	334	3			PROPN
cana-4135	334	4			NOUN
cana-4135	334	5	−	−	PROPN
cana-4135	334	6	−	−	PROPN
cana-4135	334	7	−	−	PROPN
cana-4135	334	8	−	−	PROPN
cana-4135	334	9	−=	−=	NOUN
cana-4135	334	10	(	(	PUNCT
cana-4135	334	11	)	)	PUNCT
cana-4135	334	12	1	1	NUM
cana-4135	334	13	(	(	PUNCT
cana-4135	334	14	)	)	PUNCT
cana-4135	334	15	1	1	NUM
cana-4135	334	16	(	(	PUNCT
cana-4135	334	17	)	)	PUNCT
cana-4135	334	18	1	1	NUM
cana-4135	334	19	(	(	PUNCT
cana-4135	334	20	)	)	PUNCT
cana-4135	334	21	(	(	PUNCT
cana-4135	334	22	)	)	PUNCT
cana-4135	334	23	(	(	PUNCT
cana-4135	334	24	)	)	PUNCT
cana-4135	334	25	1	1	NUM
cana-4135	334	26	(	(	PUNCT
cana-4135	334	27	)	)	PUNCT
cana-4135	334	28	1	1	NUM
cana-4135	334	29	(	(	PUNCT
cana-4135	334	30	)	)	PUNCT
cana-4135	334	31	(	(	PUNCT
cana-4135	334	32	)	)	PUNCT
cana-4135	334	33	(	(	PUNCT
cana-4135	334	34	,	,	PUNCT
cana-4135	334	35	,	,	PUNCT
cana-4135	334	36	)	)	PUNCT
cana-4135	334	37	(	(	PUNCT
cana-4135	334	38	,	,	PUNCT
cana-4135	334	39	,	,	PUNCT
cana-4135	334	40	)	)	PUNCT
cana-4135	334	41	(	(	PUNCT
cana-4135	334	42	,	,	PUNCT
cana-4135	334	43	,	,	PUNCT
cana-4135	334	44	)	)	PUNCT
cana-4135	334	45	m	m	VERB
cana-4135	334	46	l	l	NOUN
cana-4135	334	47	m	m	VERB
cana-4135	334	48	l	l	NOUN
cana-4135	334	49	n	n	NUM
cana-4135	334	50	l	l	NOUN
cana-4135	334	51	m	m	VERB
cana-4135	334	52	l	l	NOUN
cana-4135	334	53	m	m	VERB
cana-4135	334	54	l	l	NOUN
cana-4135	334	55	n	n	ADP
cana-4135	334	56	l	l	NOUN
cana-4135	334	57	n	n	CCONJ
cana-4135	334	58	l	l	NOUN
cana-4135	334	59	m	m	VERB
cana-4135	334	60	l	l	NOUN
cana-4135	334	61	n	n	ADV
cana-4135	335	1	ls	ls	INTJ
cana-4135	336	1	i	i	PRON
cana-4135	336	2	i	i	PRON
cana-4135	337	1	i	i	PRON
cana-4135	337	2	s	s	VERB
cana-4135	338	1	i	i	PRON
cana-4135	339	1	i	i	PRON
cana-4135	340	1	i	i	PRON
cana-4135	340	2	s	s	VERB
cana-4135	340	3	i	i	INTJ
cana-4135	341	1	i	i	PROPN
cana-4135	341	2	i	i	ADP
cana-4135	341	3			PROPN
cana-4135	341	4			NUM
cana-4135	341	5	−	−	PROPN
cana-4135	341	6	−	−	NOUN
cana-4135	341	7	−	−	NOUN
cana-4135	341	8	−	−	NOUN
cana-4135	341	9	−	−	NOUN
cana-4135	341	10	(	(	PUNCT
cana-4135	341	11	2.1.10	2.1.10	NUM
cana-4135	341	12	)	)	PUNCT
cana-4135	341	13	letting	let	VERB
cana-4135	341	14	l	l	NOUN
cana-4135	341	15	→	→	PUNCT
cana-4135	341	16	in	in	ADP
cana-4135	341	17	(	(	PUNCT
cana-4135	341	18	2.1.10	2.1.10	NUM
cana-4135	341	19	)	)	PUNCT
cana-4135	341	20	and	and	CCONJ
cana-4135	341	21	using	use	VERB
cana-4135	341	22	(	(	PUNCT
cana-4135	341	23	2.1.5	2.1.5	NUM
cana-4135	341	24	)	)	PUNCT
cana-4135	341	25	,	,	PUNCT
cana-4135	341	26	(	(	PUNCT
cana-4135	341	27	2.1.9	2.1.9	NUM
cana-4135	341	28	)	)	PUNCT
cana-4135	341	29	and	and	CCONJ
cana-4135	341	30	lemma	lemma	PROPN
cana-4135	341	31	1,we	1,we	NUM
cana-4135	341	32	have	have	VERB
cana-4135	341	33			PROPN
cana-4135	341	34			X
cana-4135	341	35	,	,	PUNCT
cana-4135	341	36	which	which	PRON
cana-4135	341	37	is	be	AUX
cana-4135	341	38	a	a	DET
cana-4135	341	39	contradiction	contradiction	NOUN
cana-4135	341	40	.	.	PUNCT
cana-4135	342	1	this	this	PRON
cana-4135	342	2	indicates	indicate	VERB
cana-4135	342	3	that	that	SCONJ
cana-4135	342	4	{	{	PUNCT
cana-4135	342	5	}	}	PUNCT
cana-4135	342	6	ni	ni	PROPN
cana-4135	342	7	is	be	AUX
cana-4135	342	8	a	a	DET
cana-4135	342	9	cauchy	cauchy	ADJ
cana-4135	342	10	sequence	sequence	NOUN
cana-4135	342	11	in	in	ADP
cana-4135	342	12	complete	complete	ADJ
cana-4135	342	13	multiplicative	multiplicative	PROPN
cana-4135	342	14	s	s	X
cana-4135	342	15	metric	metric	ADJ
cana-4135	342	16	space	space	NOUN
cana-4135	342	17	(	(	PUNCT
cana-4135	342	18	,	,	PUNCT
cana-4135	342	19	)	)	PUNCT
cana-4135	342	20	m	m	PROPN
cana-4135	342	21	s	s	NOUN
cana-4135	342	22	.	.	PUNCT
cana-4135	343	1	step	step	NOUN
cana-4135	343	2	3	3	NUM
cana-4135	343	3	:	:	PUNCT
cana-4135	343	4	to	to	PART
cana-4135	343	5	show	show	VERB
cana-4135	343	6	that	that	SCONJ
cana-4135	343	7	f	f	PROPN
cana-4135	343	8	and	and	CCONJ
cana-4135	343	9	g	g	PROPN
cana-4135	343	10	have	have	VERB
cana-4135	343	11	common	common	ADJ
cana-4135	343	12	fixed	fix	VERB
cana-4135	343	13	point	point	NOUN
cana-4135	343	14	.	.	PUNCT
cana-4135	344	1	consider	consider	VERB
cana-4135	344	2	1lim	1lim	NUM
cana-4135	344	3	limn	limn	NOUN
cana-4135	344	4	n	n	CCONJ
cana-4135	344	5	n	n	PROPN
cana-4135	344	6	n	n	PROPN
cana-4135	344	7	fh	fh	PROPN
cana-4135	344	8	gh	gh	PROPN
cana-4135	344	9	p+	p+	PROPN
cana-4135	344	10	→	→	PRON
cana-4135	344	11	→	→	PUNCT
cana-4135	344	12	=	=	NOUN
cana-4135	345	1	=	=	NOUN
cana-4135	345	2	.	.	PUNCT
cana-4135	346	1	let	let	VERB
cana-4135	346	2	gu	gu	NOUN
cana-4135	346	3	p=	p=	VERB
cana-4135	346	4	.	.	PUNCT
cana-4135	347	1	now	now	ADV
cana-4135	347	2	(	(	PUNCT
cana-4135	347	3	,	,	PUNCT
cana-4135	347	4	,	,	PUNCT
cana-4135	347	5	)	)	PUNCT
cana-4135	347	6	[	[	PUNCT
cana-4135	347	7	(	(	PUNCT
cana-4135	347	8	,	,	PUNCT
cana-4135	347	9	,	,	PUNCT
cana-4135	347	10	)	)	PUNCT
cana-4135	347	11	(	(	PUNCT
cana-4135	347	12	,	,	PUNCT
cana-4135	347	13	,	,	PUNCT
cana-4135	347	14	)	)	PUNCT
cana-4135	347	15	(	(	PUNCT
cana-4135	347	16	,	,	PUNCT
cana-4135	347	17	,	,	PUNCT
cana-4135	347	18	)	)	PUNCT
cana-4135	347	19	]	]	PUNCT
cana-4135	347	20	n	n	CCONJ
cana-4135	347	21	n	n	CCONJ
cana-4135	347	22	n	n	CCONJ
cana-4135	347	23	n	n	CCONJ
cana-4135	347	24	ns	ns	NUM
cana-4135	347	25	fu	fu	PROPN
cana-4135	347	26	fu	fu	PROPN
cana-4135	347	27	fh	fh	PROPN
cana-4135	347	28	s	s	PROPN
cana-4135	347	29	gu	gu	NOUN
cana-4135	347	30	gu	gu	PROPN
cana-4135	347	31	gh	gh	PROPN
cana-4135	347	32	s	s	PROPN
cana-4135	347	33	gh	gh	PROPN
cana-4135	347	34	fu	fu	PROPN
cana-4135	347	35	fu	fu	PROPN
cana-4135	347	36	s	s	PROPN
cana-4135	347	37	gh	gh	PROPN
cana-4135	347	38	fu	fu	PROPN
cana-4135	347	39	fh	fh	PROPN
cana-4135	347	40			X
cana-4135	347	41			PROPN
cana-4135	347	42			NOUN
cana-4135	347	43	1	1	NUM
cana-4135	347	44	1	1	NUM
cana-4135	347	45	1	1	NUM
cana-4135	347	46	sup	sup	NOUN
cana-4135	347	47	lim	lim	PROPN
cana-4135	347	48	(	(	PUNCT
cana-4135	347	49	,	,	PUNCT
cana-4135	347	50	,	,	PUNCT
cana-4135	347	51	)	)	PUNCT
cana-4135	347	52	[	[	PUNCT
cana-4135	347	53	(	(	PUNCT
cana-4135	347	54	,	,	PUNCT
cana-4135	347	55	,	,	PUNCT
cana-4135	347	56	)	)	PUNCT
cana-4135	347	57	(	(	PUNCT
cana-4135	347	58	,	,	PUNCT
cana-4135	347	59	,	,	PUNCT
cana-4135	347	60	)	)	PUNCT
cana-4135	347	61	(	(	PUNCT
cana-4135	347	62	,	,	PUNCT
cana-4135	347	63	,	,	PUNCT
cana-4135	347	64	)	)	PUNCT
cana-4135	347	65	]	]	PUNCT
cana-4135	347	66	n	n	CCONJ
cana-4135	347	67	n	n	CCONJ
cana-4135	347	68	n	n	CCONJ
cana-4135	347	69	n	n	CCONJ
cana-4135	347	70	n	n	CCONJ
cana-4135	347	71	n	n	NOUN
cana-4135	347	72	s	s	NOUN
cana-4135	347	73	fu	fu	NOUN
cana-4135	347	74	fu	fu	NOUN
cana-4135	348	1	i	i	PRON
cana-4135	348	2	s	s	PROPN
cana-4135	348	3	gu	gu	NOUN
cana-4135	349	1	gu	gu	NOUN
cana-4135	350	1	i	i	PRON
cana-4135	350	2	s	s	VERB
cana-4135	351	1	i	i	NOUN
cana-4135	351	2	fu	fu	NOUN
cana-4135	351	3	fu	fu	PROPN
cana-4135	352	1	s	s	VERB
cana-4135	353	1	i	i	NOUN
cana-4135	353	2	fu	fu	PROPN
cana-4135	353	3	i	i	NUM
cana-4135	353	4			NUM
cana-4135	353	5			PROPN
cana-4135	353	6			NOUN
cana-4135	353	7	−	−	PROPN
cana-4135	353	8	−	−	PROPN
cana-4135	353	9	−	−	PROPN
cana-4135	353	10	→	→	PUNCT
cana-4135	353	11			NOUN
cana-4135	353	12			NUM
cana-4135	353	13	sup	sup	NOUN
cana-4135	353	14	lim	lim	PROPN
cana-4135	353	15	(	(	PUNCT
cana-4135	353	16	,	,	PUNCT
cana-4135	353	17	,	,	PUNCT
cana-4135	353	18	)	)	PUNCT
cana-4135	353	19	[	[	PUNCT
cana-4135	353	20	(	(	PUNCT
cana-4135	353	21	,	,	PUNCT
cana-4135	353	22	,	,	PUNCT
cana-4135	353	23	)	)	PUNCT
cana-4135	353	24	(	(	PUNCT
cana-4135	353	25	,	,	PUNCT
cana-4135	353	26	,	,	PUNCT
cana-4135	353	27	)	)	PUNCT
cana-4135	353	28	(	(	PUNCT
cana-4135	353	29	,	,	PUNCT
cana-4135	353	30	,	,	PUNCT
cana-4135	353	31	)	)	PUNCT
cana-4135	353	32	]	]	PUNCT
cana-4135	354	1	n	n	DET
cana-4135	354	2	s	s	PROPN
cana-4135	354	3	fu	fu	NOUN
cana-4135	354	4	fu	fu	NOUN
cana-4135	354	5	p	p	PROPN
cana-4135	354	6	s	s	PROPN
cana-4135	354	7	gu	gu	NOUN
cana-4135	354	8	gu	gu	NOUN
cana-4135	354	9	p	p	PROPN
cana-4135	354	10	s	s	PROPN
cana-4135	354	11	p	p	PROPN
cana-4135	354	12	fu	fu	NOUN
cana-4135	354	13	fu	fu	NOUN
cana-4135	354	14	s	s	PART
cana-4135	354	15	p	p	X
cana-4135	354	16	fu	fu	ADJ
cana-4135	354	17	p	p	NUM
cana-4135	354	18			NOUN
cana-4135	354	19			PROPN
cana-4135	354	20			NOUN
cana-4135	354	21	→	→	PUNCT
cana-4135	354	22			NOUN
cana-4135	354	23			NOUN
cana-4135	354	24	[	[	PUNCT
cana-4135	354	25	(	(	PUNCT
cana-4135	354	26	,	,	PUNCT
cana-4135	354	27	,	,	PUNCT
cana-4135	354	28	)	)	PUNCT
cana-4135	354	29	(	(	PUNCT
cana-4135	354	30	,	,	PUNCT
cana-4135	354	31	,	,	PUNCT
cana-4135	354	32	)	)	PUNCT
cana-4135	354	33	(	(	PUNCT
cana-4135	354	34	,	,	PUNCT
cana-4135	354	35	,	,	PUNCT
cana-4135	354	36	)	)	PUNCT
cana-4135	354	37	(	(	PUNCT
cana-4135	354	38	,	,	PUNCT
cana-4135	354	39	,	,	PUNCT
cana-4135	354	40	)	)	PUNCT
cana-4135	354	41	(	(	PUNCT
cana-4135	354	42	,	,	PUNCT
cana-4135	354	43	,	,	PUNCT
cana-4135	354	44	)	)	PUNCT
cana-4135	354	45	]	]	X
cana-4135	354	46	s	s	X
cana-4135	354	47	p	p	X
cana-4135	354	48	p	p	X
cana-4135	354	49	p	p	X
cana-4135	354	50	s	s	PROPN
cana-4135	354	51	fu	fu	NOUN
cana-4135	354	52	fu	fu	NOUN
cana-4135	354	53	p	p	PROPN
cana-4135	355	1	s	s	AUX
cana-4135	355	2	p	p	X
cana-4135	355	3	p	p	X
cana-4135	355	4	p	p	X
cana-4135	355	5	s	s	PROPN
cana-4135	355	6	fu	fu	NOUN
cana-4135	355	7	fu	fu	NOUN
cana-4135	355	8	p	p	PROPN
cana-4135	355	9	s	s	PROPN
cana-4135	355	10	p	p	X
cana-4135	355	11	p	p	PROPN
cana-4135	355	12	p	p	PROPN
cana-4135	355	13			PROPN
cana-4135	355	14			NUM
cana-4135	355	15			ADP
cana-4135	355	16			NOUN
cana-4135	355	17	[	[	PUNCT
cana-4135	355	18	(	(	PUNCT
cana-4135	355	19	,	,	PUNCT
cana-4135	355	20	,	,	PUNCT
cana-4135	355	21	)	)	PUNCT
cana-4135	355	22	]	]	PUNCT
cana-4135	355	23	(	(	PUNCT
cana-4135	355	24	,	,	PUNCT
cana-4135	355	25	,	,	PUNCT
cana-4135	355	26	)	)	PUNCT
cana-4135	355	27	s	s	PROPN
cana-4135	355	28	fu	fu	NOUN
cana-4135	355	29	fu	fu	PROPN
cana-4135	355	30	p	p	PROPN
cana-4135	355	31	s	s	PROPN
cana-4135	355	32	fu	fu	NOUN
cana-4135	355	33	fu	fu	NOUN
cana-4135	355	34	p	p	PROPN
cana-4135	355	35			NUM
cana-4135	355	36			PROPN
cana-4135	355	37			NOUN
cana-4135	355	38	+	+	X
cana-4135	355	39	+	+	PROPN
cana-4135	355	40	=	=	ADJ
cana-4135	355	41			PROPN
cana-4135	355	42	(	(	PUNCT
cana-4135	355	43	,	,	PUNCT
cana-4135	355	44	,	,	PUNCT
cana-4135	355	45	)	)	PUNCT
cana-4135	355	46	]	]	PUNCT
cana-4135	356	1	1s	1s	NUM
cana-4135	356	2	fu	fu	NOUN
cana-4135	356	3	fu	fu	NOUN
cana-4135	356	4	p	p	PROPN
cana-4135	356	5			PROPN
cana-4135	356	6	,	,	PUNCT
cana-4135	356	7	which	which	PRON
cana-4135	356	8	is	be	AUX
cana-4135	356	9	a	a	DET
cana-4135	356	10	contradiction	contradiction	NOUN
cana-4135	356	11	.	.	PUNCT
cana-4135	357	1	fu	fu	NOUN
cana-4135	357	2	p	p	PROPN
cana-4135	357	3	=	=	PUNCT
cana-4135	357	4	.	.	PUNCT
cana-4135	358	1	hence	hence	ADV
cana-4135	358	2	gu	gu	VERB
cana-4135	358	3	p	p	PROPN
cana-4135	358	4	fu	fu	PROPN
cana-4135	358	5	p=	p=	PROPN
cana-4135	358	6			NOUN
cana-4135	359	1	=	=	NOUN
cana-4135	359	2	gu	gu	NOUN
cana-4135	359	3	u	u	NOUN
cana-4135	359	4	fu	fu	NOUN
cana-4135	359	5	u	u	PROPN
cana-4135	359	6	=	=	PUNCT
cana-4135	359	7			NOUN
cana-4135	360	1	=	=	NOUN
cana-4135	360	2	hence	hence	ADV
cana-4135	360	3	if	if	SCONJ
cana-4135	360	4	g	g	PROPN
cana-4135	360	5	has	have	AUX
cana-4135	360	6	fixed	fix	VERB
cana-4135	360	7	point	point	NOUN
cana-4135	360	8	u	u	PROPN
cana-4135	360	9	then	then	ADV
cana-4135	360	10	f	f	PROPN
cana-4135	360	11	will	will	AUX
cana-4135	360	12	also	also	ADV
cana-4135	360	13	have	have	AUX
cana-4135	360	14	fixed	fix	VERB
cana-4135	360	15	point	point	NOUN
cana-4135	360	16	u	u	NOUN
cana-4135	360	17	.i.e	.i.e	PRON
cana-4135	360	18	.	.	PUNCT
cana-4135	361	1	f	f	PROPN
cana-4135	361	2	and	and	CCONJ
cana-4135	361	3	g	g	PROPN
cana-4135	361	4	have	have	VERB
cana-4135	361	5	common	common	ADJ
cana-4135	361	6	fixed	fix	VERB
cana-4135	361	7	point	point	NOUN
cana-4135	361	8	.	.	PUNCT
cana-4135	362	1	step	step	NOUN
cana-4135	362	2	4	4	NUM
cana-4135	362	3	:	:	PUNCT
cana-4135	362	4	to	to	PART
cana-4135	362	5	prove	prove	VERB
cana-4135	362	6	that	that	SCONJ
cana-4135	362	7	f	f	PROPN
cana-4135	362	8	and	and	CCONJ
cana-4135	362	9	g	g	PROPN
cana-4135	362	10	have	have	AUX
cana-4135	362	11	fixed	fix	VERB
cana-4135	362	12	point	point	NOUN
cana-4135	362	13	communications	communication	NOUN
cana-4135	362	14	on	on	ADP
cana-4135	362	15	applied	apply	VERB
cana-4135	362	16	nonlinear	nonlinear	ADJ
cana-4135	362	17	analysis	analysis	NOUN
cana-4135	362	18	issn	issn	NOUN
cana-4135	362	19	:	:	PUNCT
cana-4135	362	20	1074	1074	NUM
cana-4135	362	21	-	-	PUNCT
cana-4135	362	22	133x	133x	NUM
cana-4135	362	23	vol	vol	NOUN
cana-4135	362	24	32	32	NUM
cana-4135	363	1	no	no	NOUN
cana-4135	363	2	.	.	PUNCT
cana-4135	364	1	9s	9s	NUM
cana-4135	364	2	(	(	PUNCT
cana-4135	364	3	2025	2025	NUM
cana-4135	364	4	)	)	PUNCT
cana-4135	364	5	1284	1284	NUM
cana-4135	364	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4135	364	7	since	since	SCONJ
cana-4135	364	8	(	(	PUNCT
cana-4135	364	9	,	,	PUNCT
cana-4135	364	10	)	)	PUNCT
cana-4135	364	11	m	m	PROPN
cana-4135	364	12	s	s	NOUN
cana-4135	364	13	is	be	AUX
cana-4135	364	14	complete	complete	ADJ
cana-4135	364	15	multiplicative	multiplicative	ADJ
cana-4135	364	16	metric	metric	ADJ
cana-4135	364	17	space	space	NOUN
cana-4135	364	18	,	,	PUNCT
cana-4135	364	19	there	there	PRON
cana-4135	364	20	existsu	existsu	VERB
cana-4135	364	21	m	m	PROPN
cana-4135	364	22	,	,	PUNCT
cana-4135	364	23	such	such	ADJ
cana-4135	364	24	that	that	SCONJ
cana-4135	364	25	(	(	PUNCT
cana-4135	364	26	,	,	PUNCT
cana-4135	364	27	,	,	PUNCT
cana-4135	364	28	)	)	PUNCT
cana-4135	364	29	]	]	PUNCT
cana-4135	365	1	1ns	1ns	X
cana-4135	365	2	u	u	X
cana-4135	365	3	u	u	NOUN
cana-4135	366	1	i	i	PRON
cana-4135	366	2	=	=	PUNCT
cana-4135	366	3	.	.	PUNCT
cana-4135	367	1	assume	assume	VERB
cana-4135	367	2	(	(	PUNCT
cana-4135	367	3	,	,	PUNCT
cana-4135	367	4	,	,	PUNCT
cana-4135	367	5	(	(	PUNCT
cana-4135	367	6	)	)	PUNCT
cana-4135	367	7	)	)	PUNCT
cana-4135	368	1	1s	1	VERB
cana-4135	368	2	u	u	NOUN
cana-4135	368	3	u	u	NOUN
cana-4135	368	4	f	f	PROPN
cana-4135	368	5	u	u	NOUN
cana-4135	368	6			INTJ
cana-4135	368	7	.	.	PUNCT
cana-4135	369	1	then	then	ADV
cana-4135	369	2	1	1	NUM
cana-4135	369	3	1	1	NUM
cana-4135	369	4	1	1	NUM
cana-4135	369	5	1	1	NUM
cana-4135	369	6	(	(	PUNCT
cana-4135	369	7	,	,	PUNCT
cana-4135	369	8	,	,	PUNCT
cana-4135	369	9	(	(	PUNCT
cana-4135	369	10	)	)	PUNCT
cana-4135	369	11	)	)	PUNCT
cana-4135	369	12	(	(	PUNCT
cana-4135	369	13	,	,	PUNCT
cana-4135	369	14	,	,	PUNCT
cana-4135	369	15	)	)	PUNCT
cana-4135	369	16	n	n	CCONJ
cana-4135	369	17	n	n	CCONJ
cana-4135	369	18	n	n	ADV
cana-4135	369	19	ns	ns	INTJ
cana-4135	370	1	i	i	INTJ
cana-4135	370	2	i	i	PRON
cana-4135	371	1	f	f	PROPN
cana-4135	371	2	u	u	PROPN
cana-4135	371	3	s	s	PROPN
cana-4135	371	4	fh	fh	PROPN
cana-4135	371	5	fh	fh	PROPN
cana-4135	371	6	fu	fu	PROPN
cana-4135	371	7	+	+	PUNCT
cana-4135	372	1	+	+	PUNCT
cana-4135	372	2	+	+	PUNCT
cana-4135	372	3	+	+	ADJ
cana-4135	372	4	=	=	SYM
cana-4135	372	5	1	1	NUM
cana-4135	372	6	1	1	NUM
cana-4135	372	7	1	1	NUM
cana-4135	372	8	1	1	NUM
cana-4135	372	9	1	1	NUM
cana-4135	372	10	[	[	PUNCT
cana-4135	372	11	(	(	PUNCT
cana-4135	372	12	,	,	PUNCT
cana-4135	372	13	,	,	PUNCT
cana-4135	372	14	)	)	PUNCT
cana-4135	372	15	(	(	PUNCT
cana-4135	372	16	,	,	PUNCT
cana-4135	372	17	,	,	PUNCT
cana-4135	372	18	)	)	PUNCT
cana-4135	372	19	(	(	PUNCT
cana-4135	372	20	,	,	PUNCT
cana-4135	372	21	,	,	PUNCT
cana-4135	372	22	)	)	PUNCT
cana-4135	372	23	n	n	CCONJ
cana-4135	372	24	n	n	CCONJ
cana-4135	372	25	n	n	CCONJ
cana-4135	372	26	n	n	CCONJ
cana-4135	372	27	ns	ns	PROPN
cana-4135	373	1	gh	gh	PROPN
cana-4135	373	2	gh	gh	PROPN
cana-4135	373	3	gu	gu	PROPN
cana-4135	373	4	s	s	PROPN
cana-4135	373	5	gu	gu	PROPN
cana-4135	373	6	fh	fh	PROPN
cana-4135	373	7	fh	fh	PROPN
cana-4135	373	8	s	s	PROPN
cana-4135	374	1	gu	gu	PROPN
cana-4135	374	2	fh	fh	PROPN
cana-4135	374	3	fu	fu	PROPN
cana-4135	375	1			NOUN
cana-4135	375	2			NOUN
cana-4135	376	1	+	+	X
cana-4135	377	1	+	+	PUNCT
cana-4135	377	2	+	+	PUNCT
cana-4135	377	3	+	+	PUNCT
cana-4135	377	4	+	+	NOUN
cana-4135	377	5			NOUN
cana-4135	377	6	1	1	NUM
cana-4135	377	7	1	1	NUM
cana-4135	377	8	1	1	NUM
cana-4135	377	9	sup	sup	NOUN
cana-4135	377	10	lim	lim	NOUN
cana-4135	377	11	[	[	PUNCT
cana-4135	377	12	(	(	PUNCT
cana-4135	377	13	,	,	PUNCT
cana-4135	377	14	,	,	PUNCT
cana-4135	377	15	)	)	PUNCT
cana-4135	377	16	(	(	PUNCT
cana-4135	377	17	,	,	PUNCT
cana-4135	377	18	,	,	PUNCT
cana-4135	377	19	)	)	PUNCT
cana-4135	377	20	(	(	PUNCT
cana-4135	377	21	,	,	PUNCT
cana-4135	377	22	,	,	PUNCT
cana-4135	377	23	)	)	PUNCT
cana-4135	377	24	n	n	CCONJ
cana-4135	377	25	n	n	CCONJ
cana-4135	377	26	n	n	CCONJ
cana-4135	377	27	n	n	CCONJ
cana-4135	377	28	n	n	CCONJ
cana-4135	377	29	n	n	NOUN
cana-4135	377	30	s	s	VERB
cana-4135	378	1	i	i	PRON
cana-4135	379	1	i	i	PRON
cana-4135	379	2	gu	gu	VERB
cana-4135	379	3	s	s	PRON
cana-4135	380	1	gu	gu	NOUN
cana-4135	381	1	i	i	PRON
cana-4135	382	1	i	i	PRON
cana-4135	382	2	s	s	VERB
cana-4135	382	3	gu	gu	NOUN
cana-4135	383	1	i	i	PRON
cana-4135	383	2	fu	fu	VERB
cana-4135	383	3			NOUN
cana-4135	383	4			NOUN
cana-4135	383	5	+	+	CCONJ
cana-4135	384	1	+	+	PUNCT
cana-4135	384	2	+	+	NUM
cana-4135	384	3	→	→	PUNCT
cana-4135	384	4	=	=	SYM
cana-4135	384	5	(	(	PUNCT
cana-4135	384	6	,	,	PUNCT
cana-4135	384	7	,	,	PUNCT
cana-4135	384	8	)	)	PUNCT
cana-4135	385	1	[	[	PUNCT
cana-4135	385	2	(	(	PUNCT
cana-4135	385	3	,	,	PUNCT
cana-4135	385	4	,	,	PUNCT
cana-4135	385	5	)	)	PUNCT
cana-4135	385	6	(	(	PUNCT
cana-4135	385	7	,	,	PUNCT
cana-4135	385	8	,	,	PUNCT
cana-4135	385	9	)	)	PUNCT
cana-4135	385	10	(	(	PUNCT
cana-4135	385	11	,	,	PUNCT
cana-4135	385	12	,	,	PUNCT
cana-4135	385	13	)	)	PUNCT
cana-4135	385	14	s	s	PART
cana-4135	385	15	u	u	NOUN
cana-4135	385	16	u	u	X
cana-4135	385	17	fu	fu	NOUN
cana-4135	385	18	s	s	PART
cana-4135	385	19	u	u	NOUN
cana-4135	385	20	u	u	NOUN
cana-4135	385	21	gu	gu	X
cana-4135	385	22	s	s	PROPN
cana-4135	385	23	gu	gu	NOUN
cana-4135	385	24	u	u	NOUN
cana-4135	385	25	u	u	NOUN
cana-4135	385	26	s	s	PROPN
cana-4135	385	27	gu	gu	NOUN
cana-4135	385	28	u	u	PROPN
cana-4135	385	29	fu	fu	PROPN
cana-4135	385	30			NUM
cana-4135	385	31			PROPN
cana-4135	385	32			NOUN
cana-4135	385	33	[	[	PUNCT
cana-4135	385	34	(	(	PUNCT
cana-4135	385	35	,	,	PUNCT
cana-4135	385	36	,	,	PUNCT
cana-4135	385	37	)	)	PUNCT
cana-4135	385	38	(	(	PUNCT
cana-4135	385	39	,	,	PUNCT
cana-4135	385	40	,	,	PUNCT
cana-4135	385	41	)	)	PUNCT
cana-4135	385	42	(	(	PUNCT
cana-4135	385	43	,	,	PUNCT
cana-4135	385	44	,	,	PUNCT
cana-4135	385	45	)	)	PUNCT
cana-4135	386	1	]	]	X
cana-4135	386	2	s	s	VERB
cana-4135	386	3	u	u	X
cana-4135	386	4	u	u	NOUN
cana-4135	386	5	fu	fu	NOUN
cana-4135	387	1	s	s	PART
cana-4135	387	2	fu	fu	NOUN
cana-4135	387	3	u	u	PROPN
cana-4135	387	4	u	u	NOUN
cana-4135	387	5	s	s	PROPN
cana-4135	387	6	fu	fu	NOUN
cana-4135	387	7	u	u	NOUN
cana-4135	387	8	fu	fu	NOUN
cana-4135	387	9			PROPN
cana-4135	387	10	=	=	PUNCT
cana-4135	387	11	gu	gu	NOUN
cana-4135	387	12	fu	fu	PUNCT
cana-4135	387	13	=	=	PUNCT
cana-4135	387	14	[	[	PUNCT
cana-4135	387	15	(	(	PUNCT
cana-4135	387	16	,	,	PUNCT
cana-4135	387	17	,	,	PUNCT
cana-4135	387	18	)	)	PUNCT
cana-4135	387	19	(	(	PUNCT
cana-4135	387	20	,	,	PUNCT
cana-4135	387	21	,	,	PUNCT
cana-4135	387	22	)	)	PUNCT
cana-4135	387	23	(	(	PUNCT
cana-4135	387	24	,	,	PUNCT
cana-4135	387	25	,	,	PUNCT
cana-4135	387	26	)	)	PUNCT
cana-4135	387	27	(	(	PUNCT
cana-4135	387	28	,	,	PUNCT
cana-4135	387	29	,	,	PUNCT
cana-4135	387	30	)	)	PUNCT
cana-4135	387	31	(	(	PUNCT
cana-4135	387	32	,	,	PUNCT
cana-4135	387	33	,	,	PUNCT
cana-4135	387	34	)	)	PUNCT
cana-4135	387	35	]	]	X
cana-4135	387	36	s	s	VERB
cana-4135	387	37	u	u	X
cana-4135	387	38	u	u	NOUN
cana-4135	387	39	fu	fu	NOUN
cana-4135	387	40	s	s	PART
cana-4135	387	41	fu	fu	NOUN
cana-4135	387	42	u	u	PROPN
cana-4135	387	43	u	u	PROPN
cana-4135	387	44	s	s	PROPN
cana-4135	387	45	fu	fu	PROPN
cana-4135	387	46	fu	fu	PROPN
cana-4135	387	47	fu	fu	PROPN
cana-4135	387	48	s	s	PART
cana-4135	387	49	u	u	NOUN
cana-4135	387	50	u	u	NOUN
cana-4135	387	51	fu	fu	NOUN
cana-4135	387	52	s	s	PROPN
cana-4135	387	53	fu	fu	PROPN
cana-4135	387	54	fu	fu	PROPN
cana-4135	387	55	fu	fu	VERB
cana-4135	387	56			PROPN
cana-4135	387	57			NUM
cana-4135	387	58			NUM
cana-4135	387	59	=	=	PUNCT
cana-4135	387	60	,	,	PUNCT
cana-4135	387	61	using	use	VERB
cana-4135	387	62	lemma	lemma	PROPN
cana-4135	387	63	2	2	NUM
cana-4135	387	64	and	and	CCONJ
cana-4135	387	65	triangular	triangular	NOUN
cana-4135	387	66	inequality	inequality	NOUN
cana-4135	387	67	of	of	ADP
cana-4135	387	68	multiplicative	multiplicative	PROPN
cana-4135	387	69	s	s	X
cana-4135	387	70	metric	metric	ADJ
cana-4135	387	71	space	space	NOUN
cana-4135	387	72	.	.	PUNCT
cana-4135	388	1	(	(	PUNCT
cana-4135	388	2	,	,	PUNCT
cana-4135	388	3	,	,	PUNCT
cana-4135	388	4	)	)	PUNCT
cana-4135	389	1	[	[	PUNCT
cana-4135	389	2	(	(	PUNCT
cana-4135	389	3	,	,	PUNCT
cana-4135	389	4	,	,	PUNCT
cana-4135	389	5	)	)	PUNCT
cana-4135	389	6	]	]	PUNCT
cana-4135	389	7	(	(	PUNCT
cana-4135	389	8	,	,	PUNCT
cana-4135	389	9	,	,	PUNCT
cana-4135	389	10	)	)	PUNCT
cana-4135	389	11	s	s	PART
cana-4135	389	12	u	u	NOUN
cana-4135	389	13	u	u	X
cana-4135	389	14	fu	fu	NOUN
cana-4135	389	15	s	s	PART
cana-4135	389	16	u	u	NOUN
cana-4135	389	17	u	u	NOUN
cana-4135	389	18	fu	fu	NOUN
cana-4135	389	19	s	s	PART
cana-4135	389	20	u	u	NOUN
cana-4135	389	21	u	u	NOUN
cana-4135	389	22	fu	fu	PROPN
cana-4135	389	23			X
cana-4135	389	24			PROPN
cana-4135	389	25			NUM
cana-4135	389	26			X
cana-4135	389	27	+	+	X
cana-4135	390	1	+	+	ADJ
cana-4135	390	2			NOUN
cana-4135	390	3			PROPN
cana-4135	390	4	which	which	PRON
cana-4135	390	5	is	be	AUX
cana-4135	390	6	a	a	DET
cana-4135	390	7	contradiction	contradiction	NOUN
cana-4135	390	8	fu	fu	NOUN
cana-4135	390	9	u	u	NOUN
cana-4135	390	10	=	=	SYM
cana-4135	390	11	i.e.	i.e.	X
cana-4135	390	12	u	u	NOUN
cana-4135	390	13	is	be	AUX
cana-4135	390	14	fixed	fix	VERB
cana-4135	390	15	point	point	NOUN
cana-4135	390	16	of	of	ADP
cana-4135	390	17	f	f	PROPN
cana-4135	390	18	,	,	PUNCT
cana-4135	390	19	which	which	PRON
cana-4135	390	20	implies	imply	VERB
cana-4135	390	21	gu	gu	NOUN
cana-4135	390	22	u=	u=	ADV
cana-4135	390	23	,	,	PUNCT
cana-4135	390	24	using	use	VERB
cana-4135	390	25	step3	step3	PROPN
cana-4135	390	26	.	.	PUNCT
cana-4135	391	1	step	step	NOUN
cana-4135	391	2	5	5	NUM
cana-4135	391	3	:	:	PUNCT
cana-4135	391	4	to	to	PART
cana-4135	391	5	prove	prove	VERB
cana-4135	391	6	uniqueness	uniqueness	NOUN
cana-4135	391	7	of	of	ADP
cana-4135	391	8	fixed	fix	VERB
cana-4135	391	9	point	point	NOUN
cana-4135	391	10	.	.	PUNCT
cana-4135	392	1	let	let	VERB
cana-4135	392	2	u	u	PRON
cana-4135	392	3	and	and	CCONJ
cana-4135	392	4	v	v	NOUN
cana-4135	392	5	be	be	AUX
cana-4135	392	6	two	two	NUM
cana-4135	392	7	distinct	distinct	ADJ
cana-4135	392	8	common	common	ADJ
cana-4135	392	9	fixed	fix	VERB
cana-4135	392	10	point	point	NOUN
cana-4135	392	11	of	of	ADP
cana-4135	392	12	f	f	PROPN
cana-4135	392	13	and	and	CCONJ
cana-4135	392	14	g	g	PROPN
cana-4135	392	15	.	.	PUNCT
cana-4135	393	1	i.	i.	PROPN
cana-4135	393	2	e.	e.	PROPN
cana-4135	393	3	fu	fu	PROPN
cana-4135	393	4	gu	gu	PROPN
cana-4135	393	5	u=	u=	ADV
cana-4135	393	6	=	=	PUNCT
cana-4135	393	7	and	and	CCONJ
cana-4135	393	8	fv	fv	X
cana-4135	393	9	gv	gv	VERB
cana-4135	393	10	v=	v=	INTJ
cana-4135	393	11	=	=	PUNCT
cana-4135	393	12	.	.	PUNCT
cana-4135	394	1	now	now	ADV
cana-4135	394	2	(	(	PUNCT
cana-4135	394	3	,	,	PUNCT
cana-4135	394	4	,	,	PUNCT
cana-4135	394	5	)	)	PUNCT
cana-4135	394	6	(	(	PUNCT
cana-4135	394	7	,	,	PUNCT
cana-4135	394	8	,	,	PUNCT
cana-4135	394	9	)	)	PUNCT
cana-4135	394	10	s	s	PART
cana-4135	394	11	u	u	NOUN
cana-4135	394	12	u	u	NOUN
cana-4135	394	13	v	v	NOUN
cana-4135	394	14	s	s	NOUN
cana-4135	394	15	fu	fu	NOUN
cana-4135	394	16	fu	fu	NOUN
cana-4135	394	17	fv	fv	NOUN
cana-4135	394	18	=	=	NOUN
cana-4135	394	19	[	[	PUNCT
cana-4135	394	20	(	(	PUNCT
cana-4135	394	21	,	,	PUNCT
cana-4135	394	22	,	,	PUNCT
cana-4135	394	23	)	)	PUNCT
cana-4135	394	24	(	(	PUNCT
cana-4135	394	25	,	,	PUNCT
cana-4135	394	26	,	,	PUNCT
cana-4135	394	27	)	)	PUNCT
cana-4135	394	28	(	(	PUNCT
cana-4135	394	29	,	,	PUNCT
cana-4135	394	30	,	,	PUNCT
cana-4135	394	31	)	)	PUNCT
cana-4135	394	32	]	]	X
cana-4135	394	33	s	s	X
cana-4135	394	34	gu	gu	NOUN
cana-4135	394	35	gu	gu	NOUN
cana-4135	394	36	gv	gv	NOUN
cana-4135	394	37	s	s	PART
cana-4135	394	38	gv	gv	PROPN
cana-4135	394	39	fu	fu	PROPN
cana-4135	394	40	fu	fu	PROPN
cana-4135	394	41	s	s	PART
cana-4135	394	42	gv	gv	PROPN
cana-4135	394	43	fu	fu	PROPN
cana-4135	394	44	fv	fv	PROPN
cana-4135	394	45			PROPN
cana-4135	394	46			NOUN
cana-4135	394	47	[	[	PUNCT
cana-4135	394	48	(	(	PUNCT
cana-4135	394	49	,	,	PUNCT
cana-4135	394	50	,	,	PUNCT
cana-4135	394	51	)	)	PUNCT
cana-4135	394	52	(	(	PUNCT
cana-4135	394	53	,	,	PUNCT
cana-4135	394	54	,	,	PUNCT
cana-4135	394	55	)	)	PUNCT
cana-4135	394	56	(	(	PUNCT
cana-4135	394	57	,	,	PUNCT
cana-4135	394	58	,	,	PUNCT
cana-4135	394	59	)	)	PUNCT
cana-4135	394	60	]	]	X
cana-4135	394	61	s	s	VERB
cana-4135	394	62	u	u	X
cana-4135	394	63	u	u	NOUN
cana-4135	394	64	v	v	ADP
cana-4135	394	65	s	s	X
cana-4135	394	66	v	v	NUM
cana-4135	394	67	u	u	NOUN
cana-4135	394	68	u	u	NOUN
cana-4135	394	69	s	s	NOUN
cana-4135	394	70	v	v	NUM
cana-4135	394	71	u	u	NOUN
cana-4135	394	72	v	v	ADP
cana-4135	394	73			PROPN
cana-4135	394	74	=	=	PUNCT
cana-4135	394	75	[	[	PUNCT
cana-4135	394	76	(	(	PUNCT
cana-4135	394	77	,	,	PUNCT
cana-4135	394	78	,	,	PUNCT
cana-4135	394	79	)	)	PUNCT
cana-4135	394	80	(	(	PUNCT
cana-4135	394	81	,	,	PUNCT
cana-4135	394	82	,	,	PUNCT
cana-4135	394	83	)	)	PUNCT
cana-4135	394	84	(	(	PUNCT
cana-4135	394	85	,	,	PUNCT
cana-4135	394	86	,	,	PUNCT
cana-4135	394	87	)	)	PUNCT
cana-4135	394	88	(	(	PUNCT
cana-4135	394	89	,	,	PUNCT
cana-4135	394	90	,	,	PUNCT
cana-4135	394	91	)	)	PUNCT
cana-4135	394	92	(	(	PUNCT
cana-4135	394	93	,	,	PUNCT
cana-4135	394	94	,	,	PUNCT
cana-4135	394	95	)	)	PUNCT
cana-4135	394	96	]	]	X
cana-4135	394	97	s	s	VERB
cana-4135	394	98	u	u	X
cana-4135	394	99	u	u	NOUN
cana-4135	394	100	v	v	ADP
cana-4135	394	101	s	s	X
cana-4135	394	102	u	u	NOUN
cana-4135	394	103	u	u	NOUN
cana-4135	394	104	v	v	ADP
cana-4135	394	105	s	s	PROPN
cana-4135	394	106	v	v	NOUN
cana-4135	394	107	v	v	ADP
cana-4135	394	108	v	v	NOUN
cana-4135	394	109	s	s	X
cana-4135	394	110	u	u	NOUN
cana-4135	394	111	u	u	NOUN
cana-4135	394	112	v	v	ADP
cana-4135	394	113	s	s	PROPN
cana-4135	394	114	v	v	NOUN
cana-4135	394	115	v	v	NOUN
cana-4135	394	116	v	v	ADP
cana-4135	394	117			PROPN
cana-4135	394	118			NUM
cana-4135	394	119			ADP
cana-4135	394	120			ADV
cana-4135	394	121	,	,	PUNCT
cana-4135	394	122	using	use	VERB
cana-4135	394	123	lemma	lemma	PROPN
cana-4135	394	124	2	2	NUM
cana-4135	394	125	and	and	CCONJ
cana-4135	394	126	property	property	NOUN
cana-4135	394	127	of	of	ADP
cana-4135	394	128	multiplicative	multiplicative	ADJ
cana-4135	394	129	s	s	X
cana-4135	394	130	-metric	-metric	ADJ
cana-4135	394	131	space	space	NOUN
cana-4135	394	132	.	.	PUNCT
cana-4135	395	1	thus	thus	ADV
cana-4135	395	2	(	(	PUNCT
cana-4135	395	3	,	,	PUNCT
cana-4135	395	4	,	,	PUNCT
cana-4135	395	5	)	)	PUNCT
cana-4135	395	6	(	(	PUNCT
cana-4135	395	7	,	,	PUNCT
cana-4135	395	8	,	,	PUNCT
cana-4135	395	9	)	)	PUNCT
cana-4135	395	10	(	(	PUNCT
cana-4135	395	11	,	,	PUNCT
cana-4135	395	12	,	,	PUNCT
cana-4135	395	13	)	)	PUNCT
cana-4135	395	14	1s	1	VERB
cana-4135	395	15	u	u	NOUN
cana-4135	395	16	u	u	NOUN
cana-4135	395	17	v	v	ADP
cana-4135	395	18	s	s	X
cana-4135	395	19	u	u	NOUN
cana-4135	395	20	u	u	NOUN
cana-4135	395	21	v	v	ADP
cana-4135	395	22	s	s	X
cana-4135	395	23	u	u	NOUN
cana-4135	395	24	u	u	NOUN
cana-4135	395	25	v	v	ADP
cana-4135	395	26			PROPN
cana-4135	395	27			NUM
cana-4135	395	28			NUM
cana-4135	396	1			NOUN
cana-4135	396	2	+	+	NOUN
cana-4135	397	1	+	+	PUNCT
cana-4135	397	2	+	+	ADJ
cana-4135	397	3			PROPN
cana-4135	397	4			NOUN
cana-4135	397	5			PROPN
cana-4135	397	6	which	which	PRON
cana-4135	397	7	is	be	AUX
cana-4135	397	8	a	a	DET
cana-4135	397	9	contradiction	contradiction	NOUN
cana-4135	397	10	u	u	NOUN
cana-4135	397	11	v	v	NOUN
cana-4135	397	12	=	=	PUNCT
cana-4135	397	13	.	.	PUNCT
cana-4135	398	1	hence	hence	ADV
cana-4135	398	2	f	f	PROPN
cana-4135	398	3	and	and	CCONJ
cana-4135	398	4	g	g	PROPN
cana-4135	398	5	have	have	VERB
cana-4135	398	6	unique	unique	ADJ
cana-4135	398	7	common	common	ADJ
cana-4135	398	8	fixed	fix	VERB
cana-4135	398	9	point	point	NOUN
cana-4135	398	10	.	.	PUNCT
cana-4135	399	1	example	example	NOUN
cana-4135	399	2	:	:	PUNCT
cana-4135	399	3	let	let	VERB
cana-4135	399	4	m	m	PRON
cana-4135	399	5	r=	r=	ADJ
cana-4135	399	6	and	and	CCONJ
cana-4135	399	7	s	s	VERB
cana-4135	399	8	is	be	AUX
cana-4135	399	9	multiplicative	multiplicative	ADJ
cana-4135	399	10	s	s	X
cana-4135	399	11	-metric	-metric	ADJ
cana-4135	399	12	space	space	NOUN
cana-4135	399	13	on	on	ADP
cana-4135	399	14	m	m	PROPN
cana-4135	399	15	,	,	PUNCT
cana-4135	399	16	defined	define	VERB
cana-4135	399	17	by	by	ADP
cana-4135	399	18	2	2	NUM
cana-4135	399	19	(	(	PUNCT
cana-4135	399	20	,	,	PUNCT
cana-4135	399	21	,	,	PUNCT
cana-4135	399	22	)	)	PUNCT
cana-4135	399	23	,	,	PUNCT
cana-4135	399	24	1	1	NUM
cana-4135	399	25	h	h	NOUN
cana-4135	400	1	i	i	PRON
cana-4135	400	2	j	j	PROPN
cana-4135	401	1	s	s	VERB
cana-4135	401	2	h	h	NOUN
cana-4135	402	1	i	i	PRON
cana-4135	402	2	j	j	PROPN
cana-4135	403	1	a	a	DET
cana-4135	403	2	a	a	X
cana-4135	403	3	+	+	NOUN
cana-4135	403	4	−	−	NOUN
cana-4135	403	5	=	=	SYM
cana-4135	403	6			INTJ
cana-4135	403	7	.	.	PUNCT
cana-4135	404	1	then	then	ADV
cana-4135	404	2	(	(	PUNCT
cana-4135	404	3	i	i	NOUN
cana-4135	404	4	)	)	PUNCT
cana-4135	404	5	(	(	PUNCT
cana-4135	404	6	,	,	PUNCT
cana-4135	404	7	,	,	PUNCT
cana-4135	404	8	)	)	PUNCT
cana-4135	404	9	1s	1s	NUM
cana-4135	405	1	h	h	NOUN
cana-4135	406	1	i	i	PRON
cana-4135	406	2	j	j	PROPN
cana-4135	406	3			NUM
cana-4135	406	4	(	(	PUNCT
cana-4135	406	5	ii	ii	NOUN
cana-4135	406	6	)	)	PUNCT
cana-4135	406	7	(	(	PUNCT
cana-4135	406	8	,	,	PUNCT
cana-4135	406	9	,	,	PUNCT
cana-4135	406	10	)	)	PUNCT
cana-4135	406	11	1s	1s	NUM
cana-4135	407	1	h	h	NOUN
cana-4135	408	1	i	i	NOUN
cana-4135	408	2	j	j	PROPN
cana-4135	409	1	=	=	PUNCT
cana-4135	409	2	,	,	PUNCT
cana-4135	409	3	when	when	SCONJ
cana-4135	409	4	h	h	NOUN
cana-4135	409	5	i	i	PRON
cana-4135	409	6	j=	j=	VERB
cana-4135	409	7	=	=	PUNCT
cana-4135	409	8	.	.	PUNCT
cana-4135	410	1	communications	communication	NOUN
cana-4135	410	2	on	on	ADP
cana-4135	410	3	applied	apply	VERB
cana-4135	410	4	nonlinear	nonlinear	ADJ
cana-4135	410	5	analysis	analysis	NOUN
cana-4135	410	6	issn	issn	NOUN
cana-4135	410	7	:	:	PUNCT
cana-4135	410	8	1074	1074	NUM
cana-4135	410	9	-	-	PUNCT
cana-4135	410	10	133x	133x	NUM
cana-4135	410	11	vol	vol	NOUN
cana-4135	410	12	32	32	NUM
cana-4135	410	13	no	no	NOUN
cana-4135	410	14	.	.	PUNCT
cana-4135	411	1	9s	9s	NUM
cana-4135	411	2	(	(	PUNCT
cana-4135	411	3	2025	2025	NUM
cana-4135	411	4	)	)	PUNCT
cana-4135	411	5	1285	1285	NUM
cana-4135	411	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4135	411	7	now	now	ADV
cana-4135	411	8	2	2	NUM
cana-4135	411	9	2	2	NUM
cana-4135	411	10	2	2	NUM
cana-4135	411	11	2	2	NUM
cana-4135	411	12	{	{	PUNCT
cana-4135	411	13	}	}	PUNCT
cana-4135	411	14	(	(	PUNCT
cana-4135	411	15	,	,	PUNCT
cana-4135	411	16	,	,	PUNCT
cana-4135	411	17	)	)	PUNCT
cana-4135	411	18	(	(	PUNCT
cana-4135	411	19	,	,	PUNCT
cana-4135	411	20	,	,	PUNCT
cana-4135	411	21	)	)	PUNCT
cana-4135	411	22	(	(	PUNCT
cana-4135	411	23	,	,	PUNCT
cana-4135	411	24	,	,	PUNCT
cana-4135	411	25	)	)	PUNCT
cana-4135	412	1	h	h	NOUN
cana-4135	412	2	h	h	NOUN
cana-4135	412	3	u	u	INTJ
cana-4135	413	1	i	i	PRON
cana-4135	413	2	i	i	PRON
cana-4135	413	3	u	u	VERB
cana-4135	413	4	j	j	PROPN
cana-4135	413	5	j	j	X
cana-4135	413	6	u	u	PROPN
cana-4135	413	7	h	h	NOUN
cana-4135	413	8	u	u	NOUN
cana-4135	413	9	i	i	NOUN
cana-4135	413	10	u	u	VERB
cana-4135	413	11	j	j	PROPN
cana-4135	413	12	u	u	NOUN
cana-4135	413	13	s	s	PROPN
cana-4135	413	14	h	h	NOUN
cana-4135	413	15	h	h	NOUN
cana-4135	414	1	u	u	NOUN
cana-4135	414	2	s	s	VERB
cana-4135	414	3	i	i	PRON
cana-4135	415	1	i	i	PRON
cana-4135	415	2	u	u	NOUN
cana-4135	415	3	s	s	PROPN
cana-4135	415	4	j	j	PROPN
cana-4135	415	5	j	j	PROPN
cana-4135	415	6	u	u	PROPN
cana-4135	415	7	a	a	DET
cana-4135	415	8	a	a	DET
cana-4135	415	9	a	a	DET
cana-4135	415	10	a	a	DET
cana-4135	415	11	+	+	NOUN
cana-4135	415	12	−	−	NOUN
cana-4135	415	13	+	+	CCONJ
cana-4135	415	14	−	−	PROPN
cana-4135	416	1	+	+	CCONJ
cana-4135	416	2	−	−	PROPN
cana-4135	416	3	−	−	PROPN
cana-4135	417	1	+	+	CCONJ
cana-4135	417	2	−	−	PROPN
cana-4135	418	1	+	+	CCONJ
cana-4135	418	2	−	−	PROPN
cana-4135	419	1	=	=	SYM
cana-4135	419	2	=	=	PUNCT
cana-4135	419	3	also	also	ADV
cana-4135	419	4	2	2	NUM
cana-4135	419	5	(	(	PUNCT
cana-4135	419	6	)	)	PUNCT
cana-4135	419	7	(	(	PUNCT
cana-4135	419	8	)	)	PUNCT
cana-4135	419	9	2	2	NUM
cana-4135	419	10	(	(	PUNCT
cana-4135	419	11	)	)	PUNCT
cana-4135	419	12	(	(	PUNCT
cana-4135	419	13	,	,	PUNCT
cana-4135	419	14	,	,	PUNCT
cana-4135	419	15	)	)	PUNCT
cana-4135	419	16	h	h	NOUN
cana-4135	420	1	i	i	PRON
cana-4135	420	2	j	j	NOUN
cana-4135	421	1	h	h	NOUN
cana-4135	422	1	u	u	VERB
cana-4135	423	1	i	i	PRON
cana-4135	423	2	u	u	VERB
cana-4135	423	3	j	j	PROPN
cana-4135	423	4	u	u	NOUN
cana-4135	423	5	s	s	VERB
cana-4135	423	6	h	h	NOUN
cana-4135	424	1	i	i	PRON
cana-4135	424	2	j	j	PROPN
cana-4135	425	1	a	a	DET
cana-4135	425	2	a	a	X
cana-4135	425	3	+	+	NOUN
cana-4135	425	4	−	−	ADP
cana-4135	425	5	−	−	PROPN
cana-4135	426	1	+	+	CCONJ
cana-4135	426	2	−	−	PROPN
cana-4135	426	3	−	−	NOUN
cana-4135	427	1	−	−	PROPN
cana-4135	428	1	=	=	SYM
cana-4135	428	2	=	=	PUNCT
cana-4135	428	3	obviously	obviously	ADV
cana-4135	428	4	(	(	PUNCT
cana-4135	428	5	,	,	PUNCT
cana-4135	428	6	,	,	PUNCT
cana-4135	428	7	)	)	PUNCT
cana-4135	428	8	(	(	PUNCT
cana-4135	428	9	,	,	PUNCT
cana-4135	428	10	,	,	PUNCT
cana-4135	428	11	)	)	PUNCT
cana-4135	428	12	(	(	PUNCT
cana-4135	428	13	,	,	PUNCT
cana-4135	428	14	,	,	PUNCT
cana-4135	428	15	)	)	PUNCT
cana-4135	428	16	(	(	PUNCT
cana-4135	428	17	,	,	PUNCT
cana-4135	428	18	,	,	PUNCT
cana-4135	428	19	)	)	PUNCT
cana-4135	428	20	s	s	PART
cana-4135	428	21	h	h	NOUN
cana-4135	429	1	i	i	PRON
cana-4135	429	2	j	j	PROPN
cana-4135	430	1	s	s	VERB
cana-4135	430	2	h	h	NOUN
cana-4135	431	1	h	h	NOUN
cana-4135	432	1	u	u	NOUN
cana-4135	432	2	s	s	VERB
cana-4135	432	3	i	i	PRON
cana-4135	433	1	i	i	PRON
cana-4135	433	2	u	u	NOUN
cana-4135	433	3	s	s	PROPN
cana-4135	433	4	j	j	PROPN
cana-4135	433	5	j	j	PROPN
cana-4135	433	6	u	u	NOUN
cana-4135	433	7	hence	hence	ADV
cana-4135	433	8	all	all	DET
cana-4135	433	9	three	three	NUM
cana-4135	433	10	conditions	condition	NOUN
cana-4135	433	11	of	of	ADP
cana-4135	433	12	multiplicative	multiplicative	ADJ
cana-4135	433	13	s	s	X
cana-4135	433	14	-metric	-metric	ADJ
cana-4135	433	15	space	space	NOUN
cana-4135	433	16	are	be	AUX
cana-4135	433	17	fulfilled	fulfil	VERB
cana-4135	433	18	.	.	PUNCT
cana-4135	434	1	now	now	ADV
cana-4135	434	2	assume	assume	VERB
cana-4135	434	3	,	,	PUNCT
cana-4135	434	4	:	:	PUNCT
cana-4135	434	5	f	f	PROPN
cana-4135	435	1	g	g	PROPN
cana-4135	435	2	m	m	VERB
cana-4135	435	3	m→	m→	PRON
cana-4135	435	4	defined	define	VERB
cana-4135	435	5	by	by	ADP
cana-4135	435	6	1	1	NUM
cana-4135	435	7	2	2	NUM
cana-4135	435	8	(	(	PUNCT
cana-4135	435	9	)	)	PUNCT
cana-4135	435	10	,	,	PUNCT
cana-4135	435	11	(	(	PUNCT
cana-4135	435	12	)	)	PUNCT
cana-4135	435	13	5	5	NUM
cana-4135	435	14	4	4	NUM
cana-4135	435	15	,	,	PUNCT
cana-4135	435	16	(	(	PUNCT
cana-4135	435	17	)	)	PUNCT
cana-4135	435	18	,	,	PUNCT
cana-4135	435	19	,	,	PUNCT
cana-4135	435	20	2	2	NUM
cana-4135	435	21	7	7	NUM
cana-4135	435	22	6	6	NUM
cana-4135	435	23	3	3	NUM
cana-4135	435	24	h	h	NOUN
cana-4135	435	25	t	t	NOUN
cana-4135	436	1	f	f	NOUN
cana-4135	436	2	h	h	NOUN
cana-4135	436	3	g	g	PROPN
cana-4135	436	4	h	h	PROPN
cana-4135	436	5	h	h	PROPN
cana-4135	436	6	t	t	NOUN
cana-4135	436	7			NOUN
cana-4135	436	8			NOUN
cana-4135	436	9			NOUN
cana-4135	436	10			X
cana-4135	436	11			PROPN
cana-4135	436	12			NUM
cana-4135	436	13	+	+	PUNCT
cana-4135	437	1	=	=	SYM
cana-4135	437	2	=	=	PUNCT
cana-4135	437	3	−	−	NOUN
cana-4135	437	4	=	=	SYM
cana-4135	438	1	=	=	PUNCT
cana-4135	438	2	=	=	PUNCT
cana-4135	438	3	=	=	SYM
cana-4135	438	4	.	.	PUNCT
cana-4135	438	5	l.h.s	l.h.s	NOUN
cana-4135	438	6	.	.	PUNCT
cana-4135	439	1	=	=	NOUN
cana-4135	439	2	3	3	NUM
cana-4135	439	3	2	2	NUM
cana-4135	439	4	3	3	NUM
cana-4135	439	5	5	5	NUM
cana-4135	439	6	(	(	PUNCT
cana-4135	439	7	(	(	PUNCT
cana-4135	439	8	2	2	NUM
cana-4135	439	9	)	)	PUNCT
cana-4135	439	10	,	,	PUNCT
cana-4135	439	11	(	(	PUNCT
cana-4135	439	12	3	3	NUM
cana-4135	439	13	)	)	PUNCT
cana-4135	439	14	,	,	PUNCT
cana-4135	439	15	(	(	PUNCT
cana-4135	439	16	4	4	NUM
cana-4135	439	17	)	)	PUNCT
cana-4135	439	18	)	)	PUNCT
cana-4135	439	19	,	,	PUNCT
cana-4135	439	20	2	2	X
cana-4135	439	21	,	,	PUNCT
cana-4135	439	22	2	2	NUM
cana-4135	439	23	2	2	NUM
cana-4135	439	24	s	s	NOUN
cana-4135	439	25	f	f	NOUN
cana-4135	440	1	f	f	PROPN
cana-4135	440	2	f	f	PROPN
cana-4135	440	3	s	s	PROPN
cana-4135	440	4	a	a	DET
cana-4135	440	5			NOUN
cana-4135	440	6			NOUN
cana-4135	440	7			NOUN
cana-4135	440	8	−	−	NOUN
cana-4135	440	9			NOUN
cana-4135	440	10	=	=	PUNCT
cana-4135	441	1	=	=	SYM
cana-4135	441	2			PROPN
cana-4135	441	3			PROPN
cana-4135	441	4			PROPN
cana-4135	441	5			NOUN
cana-4135	441	6	r.h.s	r.h.s	VERB
cana-4135	441	7	.	.	PUNCT
cana-4135	442	1	=	=	PUNCT
cana-4135	443	1	[	[	PUNCT
cana-4135	443	2	(	(	PUNCT
cana-4135	443	3	(	(	PUNCT
cana-4135	443	4	2	2	NUM
cana-4135	443	5	)	)	PUNCT
cana-4135	443	6	,	,	PUNCT
cana-4135	443	7	(	(	PUNCT
cana-4135	443	8	3	3	NUM
cana-4135	443	9	)	)	PUNCT
cana-4135	443	10	,	,	PUNCT
cana-4135	443	11	(	(	PUNCT
cana-4135	443	12	4	4	NUM
cana-4135	443	13	)	)	PUNCT
cana-4135	443	14	)	)	PUNCT
cana-4135	443	15	(	(	PUNCT
cana-4135	443	16	(	(	PUNCT
cana-4135	443	17	4	4	NUM
cana-4135	443	18	)	)	PUNCT
cana-4135	443	19	,	,	PUNCT
cana-4135	443	20	(	(	PUNCT
cana-4135	443	21	2	2	NUM
cana-4135	443	22	)	)	PUNCT
cana-4135	443	23	,	,	PUNCT
cana-4135	443	24	(	(	PUNCT
cana-4135	443	25	3	3	NUM
cana-4135	443	26	)	)	PUNCT
cana-4135	443	27	)	)	PUNCT
cana-4135	443	28	(	(	PUNCT
cana-4135	443	29	(	(	PUNCT
cana-4135	443	30	4	4	NUM
cana-4135	443	31	)	)	PUNCT
cana-4135	443	32	,	,	PUNCT
cana-4135	443	33	(	(	PUNCT
cana-4135	443	34	3	3	NUM
cana-4135	443	35	)	)	PUNCT
cana-4135	443	36	,	,	PUNCT
cana-4135	443	37	(	(	PUNCT
cana-4135	443	38	4))]s	4))]s	PRON
cana-4135	443	39	g	g	VERB
cana-4135	444	1	g	g	PROPN
cana-4135	444	2	g	g	PROPN
cana-4135	444	3	s	s	PROPN
cana-4135	444	4	g	g	PROPN
cana-4135	444	5	f	f	PROPN
cana-4135	444	6	f	f	PROPN
cana-4135	444	7	s	s	PROPN
cana-4135	444	8	g	g	PROPN
cana-4135	444	9	f	f	PROPN
cana-4135	444	10	f	f	PROPN
cana-4135	444	11			PROPN
cana-4135	444	12			NOUN
cana-4135	444	13	101	101	NUM
cana-4135	444	14	12	12	NUM
cana-4135	444	15	1	1	NUM
cana-4135	444	16	3	3	NUM
cana-4135	444	17	5	5	NUM
cana-4135	444	18	1	1	NUM
cana-4135	444	19	[	[	PUNCT
cana-4135	444	20	(	(	PUNCT
cana-4135	444	21	6,11,16	6,11,16	NUM
cana-4135	444	22	)	)	PUNCT
cana-4135	444	23	(	(	PUNCT
cana-4135	444	24	16	16	NUM
cana-4135	444	25	,	,	PUNCT
cana-4135	444	26	,	,	PUNCT
cana-4135	444	27	2	2	X
cana-4135	444	28	)	)	PUNCT
cana-4135	444	29	(	(	PUNCT
cana-4135	444	30	16,2	16,2	NUM
cana-4135	444	31	,	,	PUNCT
cana-4135	444	32	)	)	PUNCT
cana-4135	444	33	]	]	PUNCT
cana-4135	444	34	7	7	NUM
cana-4135	444	35	2	2	NUM
cana-4135	444	36	2	2	NUM
cana-4135	444	37	7	7	NUM
cana-4135	444	38	s	s	NOUN
cana-4135	444	39	s	s	NOUN
cana-4135	444	40	s	s	X
cana-4135	444	41	a	a	DET
cana-4135	444	42			NOUN
cana-4135	444	43			NOUN
cana-4135	444	44			PROPN
cana-4135	444	45			ADV
cana-4135	444	46	=	=	PUNCT
cana-4135	444	47	thus	thus	ADV
cana-4135	444	48	contraction	contraction	NOUN
cana-4135	444	49	condition	condition	NOUN
cana-4135	444	50	is	be	AUX
cana-4135	444	51	satisfied	satisfied	ADJ
cana-4135	444	52	.	.	PUNCT
cana-4135	445	1	also	also	ADV
cana-4135	445	2	(	(	PUNCT
cana-4135	445	3	1	1	X
cana-4135	445	4	)	)	PUNCT
cana-4135	445	5	(	(	PUNCT
cana-4135	445	6	1	1	X
cana-4135	445	7	)	)	PUNCT
cana-4135	445	8	1f	1f	NOUN
cana-4135	445	9	g=	g=	NOUN
cana-4135	445	10	=	=	PUNCT
cana-4135	445	11	.	.	PUNCT
cana-4135	446	1	corollary	corollary	ADJ
cana-4135	446	2	1	1	NUM
cana-4135	446	3	:	:	PUNCT
cana-4135	446	4	consider	consider	VERB
cana-4135	446	5	a	a	DET
cana-4135	446	6	complete	complete	ADJ
cana-4135	446	7	multiplicative	multiplicative	ADJ
cana-4135	446	8	s	s	X
cana-4135	446	9	-metric	-metric	ADJ
cana-4135	446	10	space	space	NOUN
cana-4135	446	11	(	(	PUNCT
cana-4135	446	12	,	,	PUNCT
cana-4135	446	13	)	)	PUNCT
cana-4135	446	14	m	m	PROPN
cana-4135	446	15	s	s	PRON
cana-4135	446	16	.	.	PUNCT
cana-4135	447	1	assume	assume	VERB
cana-4135	447	2	:	:	PUNCT
cana-4135	447	3	[	[	X
cana-4135	447	4	1	1	NUM
cana-4135	447	5	,	,	PUNCT
cana-4135	447	6	)	)	PUNCT
cana-4135	448	1	[	[	X
cana-4135	448	2	1	1	NUM
cana-4135	448	3	,	,	PUNCT
cana-4135	448	4	)	)	PUNCT
cana-4135	448	5			NOUN
cana-4135	448	6			VERB
cana-4135	448	7	→	→	SYM
cana-4135	448	8			NOUN
cana-4135	448	9	,	,	PUNCT
cana-4135	448	10	an	an	DET
cana-4135	448	11	upper	upper	ADJ
cana-4135	448	12	semicontinuous	semicontinuous	NOUN
cana-4135	448	13	and	and	CCONJ
cana-4135	448	14	non	non	ADJ
cana-4135	448	15	-	-	ADJ
cana-4135	448	16	decreasing	decrease	VERB
cana-4135	448	17	function	function	NOUN
cana-4135	448	18	.	.	PUNCT
cana-4135	449	1	let	let	VERB
cana-4135	449	2	:	:	PUNCT
cana-4135	449	3	f	f	PROPN
cana-4135	449	4	m	m	VERB
cana-4135	449	5	m→	m→	NOUN
cana-4135	449	6	be	be	AUX
cana-4135	449	7	function	function	NOUN
cana-4135	450	1	such	such	ADJ
cana-4135	450	2	that	that	SCONJ
cana-4135	450	3	(	(	PUNCT
cana-4135	450	4	1	1	NUM
cana-4135	450	5	)	)	PUNCT
cana-4135	450	6	(	(	PUNCT
cana-4135	450	7	)	)	PUNCT
cana-4135	450	8	f	f	X
cana-4135	450	9	m	m	VERB
cana-4135	450	10	m	m	NOUN
cana-4135	450	11	(	(	PUNCT
cana-4135	450	12	2	2	NUM
cana-4135	450	13	)	)	PUNCT
cana-4135	450	14	(	(	PUNCT
cana-4135	450	15	,	,	PUNCT
cana-4135	450	16	,	,	PUNCT
cana-4135	450	17	)	)	PUNCT
cana-4135	450	18	[	[	PUNCT
cana-4135	450	19	(	(	PUNCT
cana-4135	450	20	,	,	PUNCT
cana-4135	450	21	,	,	PUNCT
cana-4135	450	22	)	)	PUNCT
cana-4135	450	23	(	(	PUNCT
cana-4135	450	24	,	,	PUNCT
cana-4135	450	25	,	,	PUNCT
cana-4135	450	26	)	)	PUNCT
cana-4135	450	27	(	(	PUNCT
cana-4135	450	28	,	,	PUNCT
cana-4135	450	29	,	,	PUNCT
cana-4135	450	30	)	)	PUNCT
cana-4135	450	31	]	]	X
cana-4135	450	32	s	s	X
cana-4135	450	33	fh	fh	PROPN
cana-4135	450	34	fi	fi	NOUN
cana-4135	450	35	fj	fj	PROPN
cana-4135	450	36	s	s	VERB
cana-4135	450	37	h	h	NOUN
cana-4135	451	1	i	i	INTJ
cana-4135	451	2	j	j	PROPN
cana-4135	451	3	s	s	PROPN
cana-4135	451	4	j	j	PROPN
cana-4135	451	5	fh	fh	PROPN
cana-4135	451	6	fi	fi	PROPN
cana-4135	451	7	s	s	PART
cana-4135	451	8	j	j	PROPN
cana-4135	451	9	fi	fi	NOUN
cana-4135	451	10	fj	fj	NOUN
cana-4135	451	11			X
cana-4135	451	12			PROPN
cana-4135	451	13			NOUN
cana-4135	451	14	for	for	ADP
cana-4135	451	15	all	all	PRON
cana-4135	451	16	,	,	PUNCT
cana-4135	451	17	,	,	PUNCT
cana-4135	451	18	h	h	NOUN
cana-4135	452	1	i	i	PRON
cana-4135	452	2	j	j	PROPN
cana-4135	452	3	m	m	PROPN
cana-4135	452	4	and	and	CCONJ
cana-4135	452	5	,	,	PUNCT
cana-4135	452	6	,	,	PUNCT
cana-4135	452	7	0	0	PROPN
cana-4135	452	8			PROPN
cana-4135	452	9			NUM
cana-4135	452	10			NUM
cana-4135	452	11	and	and	CCONJ
cana-4135	452	12	[	[	X
cana-4135	452	13	1	1	NUM
cana-4135	452	14	,	,	PUNCT
cana-4135	452	15	)	)	PUNCT
cana-4135	452	16			NOUN
cana-4135	452	17			NUM
cana-4135	452	18			NOUN
cana-4135	452	19	=	=	NOUN
cana-4135	452	20	+	+	CCONJ
cana-4135	452	21	+	+	CCONJ
cana-4135	452	22			NOUN
cana-4135	452	23			NOUN
cana-4135	452	24	then	then	ADV
cana-4135	452	25	f	f	PROPN
cana-4135	452	26	possesses	possess	VERB
cana-4135	452	27	unique	unique	ADJ
cana-4135	452	28	fixed	fix	VERB
cana-4135	452	29	point	point	NOUN
cana-4135	452	30	.	.	PUNCT
cana-4135	453	1	remark	remark	NOUN
cana-4135	453	2	1	1	NUM
cana-4135	453	3	:	:	PUNCT
cana-4135	453	4	if	if	SCONJ
cana-4135	453	5	we	we	PRON
cana-4135	453	6	put	put	VERB
cana-4135	453	7	1	1	NUM
cana-4135	453	8	,	,	PUNCT
cana-4135	453	9	0	0	NUM
cana-4135	453	10	,	,	PUNCT
cana-4135	453	11	0	0	PROPN
cana-4135	453	12			NOUN
cana-4135	453	13	=	=	NOUN
cana-4135	454	1	=	=	PUNCT
cana-4135	454	2	=	=	PUNCT
cana-4135	454	3	in	in	ADP
cana-4135	454	4	corollary	corollary	ADJ
cana-4135	454	5	1	1	NUM
cana-4135	454	6	,	,	PUNCT
cana-4135	454	7	we	we	PRON
cana-4135	454	8	get	get	AUX
cana-4135	454	9	theorem	theorem	VERB
cana-4135	454	10	1[13	1[13	NUM
cana-4135	454	11	]	]	PUNCT
cana-4135	454	12	corollary	corollary	NOUN
cana-4135	454	13	2	2	NUM
cana-4135	454	14	:	:	PUNCT
cana-4135	454	15	consider	consider	VERB
cana-4135	454	16	a	a	DET
cana-4135	454	17	complete	complete	ADJ
cana-4135	454	18	multiplicative	multiplicative	ADJ
cana-4135	454	19	s	s	X
cana-4135	454	20	-metric	-metric	ADJ
cana-4135	454	21	space	space	NOUN
cana-4135	454	22	(	(	PUNCT
cana-4135	454	23	,	,	PUNCT
cana-4135	454	24	)	)	PUNCT
cana-4135	454	25	m	m	PROPN
cana-4135	454	26	s	s	PRON
cana-4135	454	27	.	.	PUNCT
cana-4135	455	1	assume	assume	VERB
cana-4135	455	2	:	:	PUNCT
cana-4135	455	3	[	[	X
cana-4135	455	4	1	1	NUM
cana-4135	455	5	,	,	PUNCT
cana-4135	455	6	)	)	PUNCT
cana-4135	456	1	[	[	X
cana-4135	456	2	1	1	NUM
cana-4135	456	3	,	,	PUNCT
cana-4135	456	4	)	)	PUNCT
cana-4135	456	5			NOUN
cana-4135	456	6			VERB
cana-4135	456	7	→	→	SYM
cana-4135	456	8			NOUN
cana-4135	456	9	,	,	PUNCT
cana-4135	456	10	an	an	DET
cana-4135	456	11	upper	upper	ADJ
cana-4135	456	12	semicontinuous	semicontinuous	NOUN
cana-4135	456	13	and	and	CCONJ
cana-4135	456	14	non	non	ADJ
cana-4135	456	15	-	-	ADJ
cana-4135	456	16	decreasing	decrease	VERB
cana-4135	456	17	function	function	NOUN
cana-4135	456	18	.	.	PUNCT
cana-4135	457	1	let	let	VERB
cana-4135	457	2	,	,	PUNCT
cana-4135	457	3	:	:	PUNCT
cana-4135	457	4	f	f	PROPN
cana-4135	457	5	g	g	PROPN
cana-4135	457	6	m	m	VERB
cana-4135	457	7	m→	m→	NOUN
cana-4135	457	8	be	be	AUX
cana-4135	457	9	functions	function	NOUN
cana-4135	458	1	such	such	ADJ
cana-4135	458	2	that	that	SCONJ
cana-4135	458	3	(	(	PUNCT
cana-4135	458	4	1	1	NUM
cana-4135	458	5	)	)	PUNCT
cana-4135	458	6	(	(	PUNCT
cana-4135	458	7	)	)	PUNCT
cana-4135	458	8	(	(	PUNCT
cana-4135	458	9	)	)	PUNCT
cana-4135	458	10	f	f	X
cana-4135	458	11	m	m	VERB
cana-4135	458	12	g	g	PROPN
cana-4135	458	13	m	m	X
cana-4135	459	1	(	(	PUNCT
cana-4135	460	1	2	2	NUM
cana-4135	460	2	)	)	PUNCT
cana-4135	460	3	(	(	PUNCT
cana-4135	460	4	,	,	PUNCT
cana-4135	460	5	,	,	PUNCT
cana-4135	460	6	)	)	PUNCT
cana-4135	461	1	[	[	PUNCT
cana-4135	461	2	(	(	PUNCT
cana-4135	461	3	,	,	PUNCT
cana-4135	461	4	,	,	PUNCT
cana-4135	461	5	)	)	PUNCT
cana-4135	461	6	(	(	PUNCT
cana-4135	461	7	,	,	PUNCT
cana-4135	461	8	,	,	PUNCT
cana-4135	461	9	)	)	PUNCT
cana-4135	461	10	(	(	PUNCT
cana-4135	461	11	,	,	PUNCT
cana-4135	461	12	,	,	PUNCT
cana-4135	461	13	)	)	PUNCT
cana-4135	461	14	]	]	X
cana-4135	461	15	p	p	X
cana-4135	462	1	p	p	X
cana-4135	462	2	p	p	X
cana-4135	462	3	q	q	X
cana-4135	462	4	q	q	X
cana-4135	462	5	q	q	X
cana-4135	462	6	q	q	X
cana-4135	462	7	p	p	X
cana-4135	462	8	p	p	X
cana-4135	462	9	q	q	X
cana-4135	462	10	p	p	NOUN
cana-4135	462	11	ps	ps	PROPN
cana-4135	462	12	f	f	PROPN
cana-4135	462	13	h	h	NOUN
cana-4135	463	1	f	f	PROPN
cana-4135	464	1	i	i	PRON
cana-4135	464	2	f	f	PROPN
cana-4135	464	3	j	j	PROPN
cana-4135	464	4	s	s	PROPN
cana-4135	464	5	g	g	NOUN
cana-4135	464	6	h	h	NOUN
cana-4135	464	7	g	g	NOUN
cana-4135	465	1	i	i	PRON
cana-4135	465	2	g	g	PROPN
cana-4135	466	1	j	j	PROPN
cana-4135	466	2	s	s	PROPN
cana-4135	466	3	g	g	PROPN
cana-4135	466	4	j	j	PROPN
cana-4135	467	1	f	f	X
cana-4135	468	1	i	i	PRON
cana-4135	468	2	f	f	PROPN
cana-4135	469	1	k	k	PROPN
cana-4135	469	2	s	s	PROPN
cana-4135	469	3	g	g	PROPN
cana-4135	470	1	j	j	PROPN
cana-4135	470	2	f	f	INTJ
cana-4135	471	1	i	i	PRON
cana-4135	471	2	f	f	PROPN
cana-4135	471	3	j	j	INTJ
cana-4135	471	4			X
cana-4135	471	5			PROPN
cana-4135	471	6			NOUN
cana-4135	471	7	for	for	ADP
cana-4135	471	8	all	all	PRON
cana-4135	471	9	,	,	PUNCT
cana-4135	471	10	,	,	PUNCT
cana-4135	471	11	h	h	NOUN
cana-4135	472	1	i	i	PRON
cana-4135	472	2	j	j	PROPN
cana-4135	472	3	m	m	INTJ
cana-4135	472	4	,	,	PUNCT
cana-4135	472	5	,	,	PUNCT
cana-4135	472	6	,	,	PUNCT
cana-4135	472	7	0	0	PROPN
cana-4135	472	8			PROPN
cana-4135	472	9			NUM
cana-4135	472	10			NUM
cana-4135	472	11	and	and	CCONJ
cana-4135	472	12	[	[	X
cana-4135	472	13	1	1	NUM
cana-4135	472	14	,	,	PUNCT
cana-4135	472	15	)	)	PUNCT
cana-4135	472	16			NOUN
cana-4135	472	17			NUM
cana-4135	472	18			NOUN
cana-4135	472	19	=	=	NOUN
cana-4135	472	20	+	+	CCONJ
cana-4135	472	21	+	+	CCONJ
cana-4135	472	22			NOUN
cana-4135	472	23			NOUN
cana-4135	472	24	,	,	PUNCT
cana-4135	472	25	,	,	PUNCT
cana-4135	472	26	p	p	X
cana-4135	472	27	q	q	PROPN
cana-4135	472	28	n	n	PROPN
cana-4135	472	29	then	then	ADV
cana-4135	472	30	f	f	PROPN
cana-4135	472	31	and	and	CCONJ
cana-4135	472	32	g	g	PROPN
cana-4135	472	33	have	have	VERB
cana-4135	472	34	unique	unique	ADJ
cana-4135	472	35	common	common	ADJ
cana-4135	472	36	fixed	fix	VERB
cana-4135	472	37	point	point	NOUN
cana-4135	472	38	.	.	PUNCT
cana-4135	473	1	proof	proof	NOUN
cana-4135	473	2	:	:	PUNCT
cana-4135	473	3	from	from	ADP
cana-4135	473	4	theorem	theorem	ADJ
cana-4135	473	5	2.1	2.1	NUM
cana-4135	473	6	,	,	PUNCT
cana-4135	473	7	pf	pf	PROPN
cana-4135	473	8	and	and	CCONJ
cana-4135	473	9	qg	qg	PROPN
cana-4135	473	10	will	will	AUX
cana-4135	473	11	have	have	VERB
cana-4135	473	12	unique	unique	ADJ
cana-4135	473	13	common	common	ADJ
cana-4135	473	14	fixed	fix	VERB
cana-4135	473	15	pointu	pointu	NOUN
cana-4135	473	16	.	.	PUNCT
cana-4135	474	1	now	now	ADV
cana-4135	474	2	1	1	NUM
cana-4135	474	3	(	(	PUNCT
cana-4135	474	4	)	)	PUNCT
cana-4135	474	5	[	[	PUNCT
cana-4135	474	6	(	(	PUNCT
cana-4135	474	7	)	)	PUNCT
cana-4135	474	8	]	]	PUNCT
cana-4135	474	9	(	(	PUNCT
cana-4135	474	10	)	)	PUNCT
cana-4135	474	11	[	[	PUNCT
cana-4135	474	12	(	(	PUNCT
cana-4135	474	13	)	)	PUNCT
cana-4135	474	14	]	]	X
cana-4135	474	15	p	p	X
cana-4135	474	16	p	p	X
cana-4135	474	17	pf	pf	PROPN
cana-4135	474	18	u	u	NOUN
cana-4135	474	19	f	f	PROPN
cana-4135	474	20	f	f	PROPN
cana-4135	474	21	u	u	NOUN
cana-4135	474	22	f	f	PROPN
cana-4135	474	23	u	u	X
cana-4135	474	24	f	f	PROPN
cana-4135	474	25	f	f	X
cana-4135	474	26	u+=	u+=	PROPN
cana-4135	474	27	=	=	SYM
cana-4135	474	28	=	=	SYM
cana-4135	474	29	and	and	CCONJ
cana-4135	474	30	1	1	NUM
cana-4135	474	31	(	(	PUNCT
cana-4135	474	32	)	)	PUNCT
cana-4135	474	33	[	[	PUNCT
cana-4135	474	34	(	(	PUNCT
cana-4135	474	35	)	)	PUNCT
cana-4135	474	36	]	]	PUNCT
cana-4135	474	37	(	(	PUNCT
cana-4135	474	38	)	)	PUNCT
cana-4135	474	39	[	[	PUNCT
cana-4135	474	40	(	(	PUNCT
cana-4135	474	41	)	)	PUNCT
cana-4135	474	42	]	]	X
cana-4135	474	43	q	q	X
cana-4135	474	44	q	q	X
cana-4135	474	45	qg	qg	PROPN
cana-4135	474	46	u	u	NOUN
cana-4135	474	47	g	g	PROPN
cana-4135	474	48	g	g	PROPN
cana-4135	474	49	u	u	NOUN
cana-4135	474	50	g	g	PROPN
cana-4135	474	51	u	u	NOUN
cana-4135	474	52	g	g	NOUN
cana-4135	474	53	g	g	NOUN
cana-4135	474	54	u+=	u+=	PROPN
cana-4135	474	55	=	=	SYM
cana-4135	474	56	=	=	PUNCT
cana-4135	474	57	.	.	PUNCT
cana-4135	475	1	communications	communication	NOUN
cana-4135	475	2	on	on	ADP
cana-4135	475	3	applied	apply	VERB
cana-4135	475	4	nonlinear	nonlinear	ADJ
cana-4135	475	5	analysis	analysis	NOUN
cana-4135	475	6	issn	issn	NOUN
cana-4135	475	7	:	:	PUNCT
cana-4135	475	8	1074	1074	NUM
cana-4135	475	9	-	-	PUNCT
cana-4135	475	10	133x	133x	NUM
cana-4135	475	11	vol	vol	NOUN
cana-4135	475	12	32	32	NUM
cana-4135	475	13	no	no	NOUN
cana-4135	475	14	.	.	PUNCT
cana-4135	476	1	9s	9s	NUM
cana-4135	476	2	(	(	PUNCT
cana-4135	476	3	2025	2025	NUM
cana-4135	476	4	)	)	PUNCT
cana-4135	476	5	1286	1286	NUM
cana-4135	476	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4135	476	7	thus	thus	ADV
cana-4135	476	8	(	(	PUNCT
cana-4135	476	9	)	)	PUNCT
cana-4135	476	10	f	f	PROPN
cana-4135	476	11	u	u	NOUN
cana-4135	476	12	and	and	CCONJ
cana-4135	476	13	(	(	PUNCT
cana-4135	476	14	)	)	PUNCT
cana-4135	476	15	g	g	NOUN
cana-4135	476	16	u	u	NOUN
cana-4135	476	17	are	be	AUX
cana-4135	476	18	also	also	ADV
cana-4135	476	19	fixed	fix	VERB
cana-4135	476	20	point	point	NOUN
cana-4135	476	21	of	of	ADP
cana-4135	476	22	pf	pf	PROPN
cana-4135	476	23	and	and	CCONJ
cana-4135	476	24	qg	qg	PROPN
cana-4135	476	25	respectively	respectively	ADV
cana-4135	476	26	.	.	PUNCT
cana-4135	477	1	due	due	ADP
cana-4135	477	2	to	to	ADP
cana-4135	477	3	the	the	DET
cana-4135	477	4	uniqueness	uniqueness	NOUN
cana-4135	477	5	of	of	ADP
cana-4135	477	6	fixed	fix	VERB
cana-4135	477	7	point	point	NOUN
cana-4135	477	8	(	(	PUNCT
cana-4135	477	9	)	)	PUNCT
cana-4135	477	10	(	(	PUNCT
cana-4135	477	11	)	)	PUNCT
cana-4135	477	12	f	f	X
cana-4135	477	13	u	u	NOUN
cana-4135	477	14	g	g	PROPN
cana-4135	477	15	u	u	NOUN
cana-4135	477	16	u=	u=	ADV
cana-4135	477	17	=	=	PUNCT
cana-4135	477	18	.i.e	.i.e	X
cana-4135	477	19	.	.	PUNCT
cana-4135	478	1	f	f	PROPN
cana-4135	478	2	and	and	CCONJ
cana-4135	478	3	g	g	PROPN
cana-4135	478	4	have	have	VERB
cana-4135	478	5	unique	unique	ADJ
cana-4135	478	6	common	common	ADJ
cana-4135	478	7	fixed	fix	VERB
cana-4135	478	8	point	point	NOUN
cana-4135	478	9	.	.	PUNCT
cana-4135	479	1	corollary	corollary	ADJ
cana-4135	479	2	3	3	NUM
cana-4135	479	3	:	:	PUNCT
cana-4135	479	4	consider	consider	VERB
cana-4135	479	5	a	a	DET
cana-4135	479	6	complete	complete	ADJ
cana-4135	479	7	multiplicative	multiplicative	ADJ
cana-4135	479	8	s	s	X
cana-4135	479	9	-metric	-metric	ADJ
cana-4135	479	10	space	space	NOUN
cana-4135	479	11	(	(	PUNCT
cana-4135	479	12	,	,	PUNCT
cana-4135	479	13	)	)	PUNCT
cana-4135	479	14	m	m	PROPN
cana-4135	479	15	s	s	PRON
cana-4135	479	16	.	.	PUNCT
cana-4135	480	1	assume	assume	VERB
cana-4135	480	2	:	:	PUNCT
cana-4135	480	3	[	[	X
cana-4135	480	4	1	1	NUM
cana-4135	480	5	,	,	PUNCT
cana-4135	480	6	)	)	PUNCT
cana-4135	481	1	[	[	X
cana-4135	481	2	1	1	NUM
cana-4135	481	3	,	,	PUNCT
cana-4135	481	4	)	)	PUNCT
cana-4135	481	5			NOUN
cana-4135	481	6			VERB
cana-4135	481	7	→	→	SYM
cana-4135	481	8			NOUN
cana-4135	481	9	,	,	PUNCT
cana-4135	481	10	an	an	DET
cana-4135	481	11	upper	upper	ADJ
cana-4135	481	12	semicontinuous	semicontinuous	NOUN
cana-4135	481	13	and	and	CCONJ
cana-4135	481	14	non	non	ADJ
cana-4135	481	15	-	-	ADJ
cana-4135	481	16	decreasing	decrease	VERB
cana-4135	481	17	function	function	NOUN
cana-4135	481	18	.	.	PUNCT
cana-4135	482	1	let	let	VERB
cana-4135	482	2	,	,	PUNCT
cana-4135	482	3	:	:	PUNCT
cana-4135	482	4	f	f	PROPN
cana-4135	482	5	g	g	PROPN
cana-4135	482	6	m	m	VERB
cana-4135	482	7	m→	m→	NOUN
cana-4135	482	8	be	be	AUX
cana-4135	482	9	functions	function	NOUN
cana-4135	483	1	such	such	ADJ
cana-4135	483	2	that	that	SCONJ
cana-4135	483	3	(	(	PUNCT
cana-4135	483	4	1	1	NUM
cana-4135	483	5	)	)	PUNCT
cana-4135	483	6	(	(	PUNCT
cana-4135	483	7	)	)	PUNCT
cana-4135	483	8	(	(	PUNCT
cana-4135	483	9	)	)	PUNCT
cana-4135	483	10	f	f	X
cana-4135	483	11	m	m	VERB
cana-4135	483	12	g	g	PROPN
cana-4135	483	13	m	m	X
cana-4135	484	1	(	(	PUNCT
cana-4135	485	1	2	2	NUM
cana-4135	485	2	)	)	PUNCT
cana-4135	485	3	(	(	PUNCT
cana-4135	485	4	,	,	PUNCT
cana-4135	485	5	,	,	PUNCT
cana-4135	485	6	)	)	PUNCT
cana-4135	486	1	[	[	PUNCT
cana-4135	486	2	(	(	PUNCT
cana-4135	486	3	,	,	PUNCT
cana-4135	486	4	,	,	PUNCT
cana-4135	486	5	)	)	PUNCT
cana-4135	486	6	(	(	PUNCT
cana-4135	486	7	,	,	PUNCT
cana-4135	486	8	,	,	PUNCT
cana-4135	486	9	)	)	PUNCT
cana-4135	486	10	(	(	PUNCT
cana-4135	486	11	,	,	PUNCT
cana-4135	486	12	,	,	PUNCT
cana-4135	486	13	)	)	PUNCT
cana-4135	486	14	]	]	X
cana-4135	486	15	s	s	X
cana-4135	486	16	fh	fh	PROPN
cana-4135	486	17	fi	fi	NOUN
cana-4135	487	1	fj	fj	PROPN
cana-4135	487	2	s	s	PROPN
cana-4135	487	3	gh	gh	PROPN
cana-4135	487	4	gi	gi	PROPN
cana-4135	487	5	gj	gj	PROPN
cana-4135	487	6	s	s	PROPN
cana-4135	487	7	gj	gj	PROPN
cana-4135	487	8	fh	fh	PROPN
cana-4135	487	9	fi	fi	NOUN
cana-4135	487	10	s	s	PART
cana-4135	487	11	gj	gj	NOUN
cana-4135	487	12	fi	fi	NOUN
cana-4135	487	13	fj	fj	NOUN
cana-4135	487	14			X
cana-4135	487	15			PROPN
cana-4135	487	16			NUM
cana-4135	487	17			PROPN
cana-4135	487	18	for	for	ADP
cana-4135	487	19	all	all	PRON
cana-4135	487	20	,	,	PUNCT
cana-4135	487	21	,	,	PUNCT
cana-4135	487	22	h	h	NOUN
cana-4135	487	23	i	i	PRON
cana-4135	487	24	j	j	PROPN
cana-4135	487	25	m	m	INTJ
cana-4135	487	26	,	,	PUNCT
cana-4135	487	27	,	,	PUNCT
cana-4135	487	28	,	,	PUNCT
cana-4135	487	29	0	0	PROPN
cana-4135	487	30			PROPN
cana-4135	487	31			NUM
cana-4135	487	32			NUM
cana-4135	487	33	and	and	CCONJ
cana-4135	487	34	[	[	X
cana-4135	487	35	1	1	NUM
cana-4135	487	36	,	,	PUNCT
cana-4135	487	37	)	)	PUNCT
cana-4135	487	38			NOUN
cana-4135	487	39			NUM
cana-4135	487	40			NOUN
cana-4135	487	41	=	=	NOUN
cana-4135	487	42	+	+	CCONJ
cana-4135	487	43	+	+	CCONJ
cana-4135	487	44			NOUN
cana-4135	487	45			NOUN
cana-4135	487	46	,	,	PUNCT
cana-4135	487	47	[	[	X
cana-4135	487	48	0,1)l	0,1)l	X
cana-4135	487	49	then	then	ADV
cana-4135	487	50	f	f	PROPN
cana-4135	487	51	and	and	CCONJ
cana-4135	487	52	g	g	PROPN
cana-4135	487	53	possesses	possesse	NOUN
cana-4135	487	54	unique	unique	ADJ
cana-4135	487	55	common	common	ADJ
cana-4135	487	56	fixed	fix	VERB
cana-4135	487	57	point	point	NOUN
cana-4135	487	58	.	.	PUNCT
cana-4135	488	1	proof	proof	NOUN
cana-4135	488	2	:	:	PUNCT
cana-4135	488	3	put	put	VERB
cana-4135	488	4	(	(	PUNCT
cana-4135	488	5	)	)	PUNCT
cana-4135	488	6	t	t	NOUN
cana-4135	488	7	t	t	NOUN
cana-4135	489	1	=	=	PUNCT
cana-4135	489	2	in	in	ADP
cana-4135	489	3	theorem	theorem	NOUN
cana-4135	489	4	2.1	2.1	NUM
cana-4135	489	5	,	,	PUNCT
cana-4135	489	6	one	one	PRON
cana-4135	489	7	can	can	AUX
cana-4135	489	8	get	get	AUX
cana-4135	489	9	desired	desire	VERB
cana-4135	489	10	result	result	NOUN
cana-4135	489	11	.	.	PUNCT
cana-4135	490	1	remark	remark	NOUN
cana-4135	490	2	2	2	NUM
cana-4135	490	3	:	:	PUNCT
cana-4135	490	4	if	if	SCONJ
cana-4135	490	5	we	we	PRON
cana-4135	490	6	put	put	VERB
cana-4135	490	7	1	1	NUM
cana-4135	490	8	,	,	PUNCT
cana-4135	490	9	0	0	NUM
cana-4135	490	10	,	,	PUNCT
cana-4135	490	11	0	0	PROPN
cana-4135	490	12			NOUN
cana-4135	490	13	=	=	NOUN
cana-4135	490	14	=	=	PUNCT
cana-4135	490	15	=	=	PUNCT
cana-4135	490	16	and	and	CCONJ
cana-4135	490	17	consider	consider	VERB
cana-4135	490	18	g	g	NOUN
cana-4135	490	19	as	as	ADP
cana-4135	490	20	identity	identity	NOUN
cana-4135	490	21	mapping	mapping	NOUN
cana-4135	490	22	,	,	PUNCT
cana-4135	490	23	then	then	ADV
cana-4135	490	24	we	we	PRON
cana-4135	490	25	get	get	AUX
cana-4135	490	26	theorem	theorem	VERB
cana-4135	490	27	2[13	2[13	NUM
cana-4135	490	28	]	]	PUNCT
cana-4135	490	29	.	.	PUNCT
cana-4135	491	1	corollary	corollary	ADJ
cana-4135	491	2	4	4	NUM
cana-4135	491	3	:	:	PUNCT
cana-4135	491	4	let	let	VERB
cana-4135	491	5	(	(	PUNCT
cana-4135	491	6	,	,	PUNCT
cana-4135	491	7	)	)	PUNCT
cana-4135	491	8	m	m	VERB
cana-4135	491	9	s	s	AUX
cana-4135	491	10	be	be	AUX
cana-4135	491	11	a	a	DET
cana-4135	491	12	complete	complete	ADJ
cana-4135	491	13	multiplicative	multiplicative	ADJ
cana-4135	491	14	s	s	X
cana-4135	491	15	-metric	-metric	ADJ
cana-4135	491	16	space	space	NOUN
cana-4135	491	17	.	.	PUNCT
cana-4135	492	1	assume	assume	VERB
cana-4135	492	2	:	:	PUNCT
cana-4135	492	3	[	[	X
cana-4135	492	4	1	1	NUM
cana-4135	492	5	,	,	PUNCT
cana-4135	492	6	)	)	PUNCT
cana-4135	493	1	[	[	X
cana-4135	493	2	1	1	NUM
cana-4135	493	3	,	,	PUNCT
cana-4135	493	4	)	)	PUNCT
cana-4135	493	5			NOUN
cana-4135	493	6			VERB
cana-4135	493	7	→	→	SYM
cana-4135	493	8			NOUN
cana-4135	493	9	,	,	PUNCT
cana-4135	493	10	an	an	DET
cana-4135	493	11	upper	upper	ADJ
cana-4135	493	12	semicontinuous	semicontinuous	NOUN
cana-4135	493	13	and	and	CCONJ
cana-4135	493	14	non	non	ADJ
cana-4135	493	15	-	-	ADJ
cana-4135	493	16	decreasing	decrease	VERB
cana-4135	493	17	function	function	NOUN
cana-4135	493	18	.	.	PUNCT
cana-4135	494	1	let	let	VERB
cana-4135	494	2	,	,	PUNCT
cana-4135	494	3	:	:	PUNCT
cana-4135	494	4	f	f	PROPN
cana-4135	494	5	g	g	PROPN
cana-4135	494	6	m	m	VERB
cana-4135	494	7	m→	m→	NOUN
cana-4135	494	8	be	be	AUX
cana-4135	494	9	functions	function	NOUN
cana-4135	494	10	such	such	ADJ
cana-4135	494	11	that	that	PRON
cana-4135	494	12	,	,	PUNCT
cana-4135	494	13	(	(	PUNCT
cana-4135	494	14	1	1	X
cana-4135	494	15	)	)	PUNCT
cana-4135	494	16	(	(	PUNCT
cana-4135	494	17	)	)	PUNCT
cana-4135	494	18	(	(	PUNCT
cana-4135	494	19	)	)	PUNCT
cana-4135	494	20	f	f	X
cana-4135	494	21	m	m	VERB
cana-4135	494	22	g	g	PROPN
cana-4135	494	23	m	m	X
cana-4135	494	24	(	(	PUNCT
cana-4135	494	25	2	2	NUM
cana-4135	494	26	)	)	PUNCT
cana-4135	494	27	(	(	PUNCT
cana-4135	494	28	i	i	NOUN
cana-4135	494	29	)	)	PUNCT
cana-4135	494	30	(	(	PUNCT
cana-4135	494	31	,	,	PUNCT
cana-4135	494	32	,	,	PUNCT
cana-4135	494	33	)	)	PUNCT
cana-4135	495	1	[	[	PUNCT
cana-4135	495	2	(	(	PUNCT
cana-4135	495	3	,	,	PUNCT
cana-4135	495	4	,	,	PUNCT
cana-4135	495	5	)	)	PUNCT
cana-4135	495	6	]	]	X
cana-4135	495	7	s	s	X
cana-4135	495	8	fh	fh	PROPN
cana-4135	495	9	fi	fi	NOUN
cana-4135	496	1	fj	fj	PROPN
cana-4135	496	2	s	s	PROPN
cana-4135	496	3	gh	gh	PROPN
cana-4135	496	4	gi	gi	PROPN
cana-4135	496	5	gj	gj	PROPN
cana-4135	496	6	(	(	PUNCT
cana-4135	496	7	ii	ii	PROPN
cana-4135	496	8	)	)	PUNCT
cana-4135	496	9	(	(	PUNCT
cana-4135	496	10	,	,	PUNCT
cana-4135	496	11	,	,	PUNCT
cana-4135	496	12	)	)	PUNCT
cana-4135	496	13	[	[	PUNCT
cana-4135	496	14	(	(	PUNCT
cana-4135	496	15	,	,	PUNCT
cana-4135	496	16	,	,	PUNCT
cana-4135	496	17	)	)	PUNCT
cana-4135	496	18	]	]	X
cana-4135	496	19	s	s	X
cana-4135	496	20	fh	fh	PROPN
cana-4135	496	21	fi	fi	NOUN
cana-4135	496	22	fj	fj	PROPN
cana-4135	496	23	s	s	PROPN
cana-4135	496	24	gj	gj	PROPN
cana-4135	496	25	fi	fi	NOUN
cana-4135	496	26	fh	fh	PROPN
cana-4135	496	27	(	(	PUNCT
cana-4135	496	28	iii	iii	NOUN
cana-4135	496	29	)	)	PUNCT
cana-4135	496	30	(	(	PUNCT
cana-4135	496	31	,	,	PUNCT
cana-4135	496	32	,	,	PUNCT
cana-4135	496	33	)	)	PUNCT
cana-4135	496	34	[	[	PUNCT
cana-4135	496	35	(	(	PUNCT
cana-4135	496	36	,	,	PUNCT
cana-4135	496	37	,	,	PUNCT
cana-4135	496	38	)	)	PUNCT
cana-4135	496	39	]	]	X
cana-4135	496	40	s	s	X
cana-4135	496	41	fh	fh	PROPN
cana-4135	496	42	fi	fi	NOUN
cana-4135	496	43	fj	fj	PROPN
cana-4135	496	44	s	s	PROPN
cana-4135	496	45	gj	gj	PROPN
cana-4135	496	46	fi	fi	NOUN
cana-4135	496	47	fj	fj	PROPN
cana-4135	496	48	,	,	PUNCT
cana-4135	496	49	for	for	ADP
cana-4135	496	50	all	all	PRON
cana-4135	496	51	,	,	PUNCT
cana-4135	496	52	,	,	PUNCT
cana-4135	496	53	h	h	NOUN
cana-4135	497	1	i	i	PRON
cana-4135	497	2	j	j	PROPN
cana-4135	498	1	m	m	PROPN
cana-4135	498	2	then	then	ADV
cana-4135	498	3	f	f	PROPN
cana-4135	498	4	and	and	CCONJ
cana-4135	498	5	g	g	PROPN
cana-4135	498	6	have	have	VERB
cana-4135	498	7	unique	unique	ADJ
cana-4135	498	8	common	common	ADJ
cana-4135	498	9	fixed	fix	VERB
cana-4135	498	10	point	point	NOUN
cana-4135	498	11	.	.	PUNCT
cana-4135	499	1	proof	proof	NOUN
cana-4135	499	2	:	:	PUNCT
cana-4135	499	3	the	the	DET
cana-4135	499	4	result	result	NOUN
cana-4135	499	5	can	can	AUX
cana-4135	499	6	be	be	AUX
cana-4135	499	7	proved	prove	VERB
cana-4135	499	8	easily	easily	ADV
cana-4135	499	9	by	by	ADP
cana-4135	499	10	substituting	substitute	VERB
cana-4135	499	11	the	the	DET
cana-4135	499	12	following	follow	VERB
cana-4135	499	13	values	value	NOUN
cana-4135	499	14	in	in	ADP
cana-4135	499	15	condition	condition	NOUN
cana-4135	499	16	(	(	PUNCT
cana-4135	499	17	2.1.3	2.1.3	NUM
cana-4135	499	18	)	)	PUNCT
cana-4135	499	19	of	of	ADP
cana-4135	499	20	theorem	theorem	NOUN
cana-4135	499	21	2.1	2.1	NUM
cana-4135	499	22	.	.	PUNCT
cana-4135	500	1	(	(	PUNCT
cana-4135	500	2	i	i	NOUN
cana-4135	500	3	)	)	PUNCT
cana-4135	500	4	1	1	NUM
cana-4135	500	5	,	,	PUNCT
cana-4135	500	6	0	0	PROPN
cana-4135	500	7			PROPN
cana-4135	500	8	=	=	NOUN
cana-4135	500	9	=	=	PUNCT
cana-4135	500	10	=	=	SYM
cana-4135	500	11	(	(	PUNCT
cana-4135	500	12	ii	ii	NOUN
cana-4135	500	13	)	)	PUNCT
cana-4135	500	14	0	0	NUM
cana-4135	500	15	,	,	PUNCT
cana-4135	500	16	1	1	PROPN
cana-4135	500	17			NUM
cana-4135	500	18	=	=	NOUN
cana-4135	501	1	=	=	SYM
cana-4135	501	2	=	=	SYM
cana-4135	501	3	(	(	PUNCT
cana-4135	501	4	iii	iii	NOUN
cana-4135	501	5	)	)	PUNCT
cana-4135	501	6	0	0	NUM
cana-4135	501	7	,	,	PUNCT
cana-4135	501	8	1	1	PROPN
cana-4135	501	9			PROPN
cana-4135	501	10	=	=	NOUN
cana-4135	501	11	=	=	PUNCT
cana-4135	502	1	=	=	PUNCT
cana-4135	502	2	corollary	corollary	ADJ
cana-4135	502	3	5	5	NUM
cana-4135	502	4	:	:	PUNCT
cana-4135	502	5	consider	consider	VERB
cana-4135	502	6	a	a	DET
cana-4135	502	7	complete	complete	ADJ
cana-4135	502	8	multiplicative	multiplicative	ADJ
cana-4135	502	9	s	s	X
cana-4135	502	10	-metric	-metric	ADJ
cana-4135	502	11	space	space	NOUN
cana-4135	502	12	(	(	PUNCT
cana-4135	502	13	,	,	PUNCT
cana-4135	502	14	)	)	PUNCT
cana-4135	502	15	m	m	PROPN
cana-4135	502	16	s	s	PRON
cana-4135	502	17	.	.	PUNCT
cana-4135	503	1	assume	assume	VERB
cana-4135	503	2	:	:	PUNCT
cana-4135	503	3	[	[	X
cana-4135	503	4	1	1	NUM
cana-4135	503	5	,	,	PUNCT
cana-4135	503	6	)	)	PUNCT
cana-4135	504	1	[	[	X
cana-4135	504	2	1	1	NUM
cana-4135	504	3	,	,	PUNCT
cana-4135	504	4	)	)	PUNCT
cana-4135	504	5			NOUN
cana-4135	504	6			VERB
cana-4135	504	7	→	→	SYM
cana-4135	504	8			NOUN
cana-4135	504	9	,	,	PUNCT
cana-4135	504	10	an	an	DET
cana-4135	504	11	upper	upper	ADJ
cana-4135	504	12	semicontinuous	semicontinuous	NOUN
cana-4135	504	13	and	and	CCONJ
cana-4135	504	14	non	non	ADJ
cana-4135	504	15	-	-	ADJ
cana-4135	504	16	decreasing	decrease	VERB
cana-4135	504	17	function	function	NOUN
cana-4135	504	18	.	.	PUNCT
cana-4135	505	1	let	let	VERB
cana-4135	505	2	,	,	PUNCT
cana-4135	505	3	:	:	PUNCT
cana-4135	505	4	f	f	PROPN
cana-4135	505	5	g	g	PROPN
cana-4135	505	6	m	m	VERB
cana-4135	505	7	m→	m→	NOUN
cana-4135	505	8	be	be	AUX
cana-4135	505	9	functions	function	NOUN
cana-4135	506	1	such	such	ADJ
cana-4135	506	2	that	that	SCONJ
cana-4135	506	3	(	(	PUNCT
cana-4135	506	4	1	1	NUM
cana-4135	506	5	)	)	PUNCT
cana-4135	506	6	(	(	PUNCT
cana-4135	506	7	)	)	PUNCT
cana-4135	506	8	(	(	PUNCT
cana-4135	506	9	)	)	PUNCT
cana-4135	506	10	f	f	X
cana-4135	506	11	m	m	VERB
cana-4135	506	12	g	g	PROPN
cana-4135	506	13	m	m	X
cana-4135	507	1	(	(	PUNCT
cana-4135	508	1	2	2	NUM
cana-4135	508	2	)	)	PUNCT
cana-4135	508	3	(	(	PUNCT
cana-4135	508	4	i	i	NOUN
cana-4135	508	5	)	)	PUNCT
cana-4135	508	6	2	2	NUM
cana-4135	508	7	(	(	PUNCT
cana-4135	508	8	,	,	PUNCT
cana-4135	508	9	,	,	PUNCT
cana-4135	508	10	)	)	PUNCT
cana-4135	508	11	(	(	PUNCT
cana-4135	508	12	,	,	PUNCT
cana-4135	508	13	,	,	PUNCT
cana-4135	508	14	)	)	PUNCT
cana-4135	508	15	(	(	PUNCT
cana-4135	508	16	,	,	PUNCT
cana-4135	508	17	,	,	PUNCT
cana-4135	508	18	)	)	PUNCT
cana-4135	508	19	s	s	PART
cana-4135	508	20	fh	fh	PROPN
cana-4135	508	21	fi	fi	NOUN
cana-4135	509	1	fj	fj	PROPN
cana-4135	509	2	s	s	PROPN
cana-4135	509	3	gh	gh	PROPN
cana-4135	509	4	gi	gi	PROPN
cana-4135	509	5	gj	gj	PROPN
cana-4135	509	6	s	s	PROPN
cana-4135	509	7	gj	gj	PROPN
cana-4135	509	8	fh	fh	PROPN
cana-4135	509	9	fi	fi	NOUN
cana-4135	509	10	(	(	PUNCT
cana-4135	509	11	ii	ii	NOUN
cana-4135	509	12	)	)	PUNCT
cana-4135	509	13	2	2	NUM
cana-4135	509	14	(	(	PUNCT
cana-4135	509	15	,	,	PUNCT
cana-4135	509	16	,	,	PUNCT
cana-4135	509	17	)	)	PUNCT
cana-4135	509	18	(	(	PUNCT
cana-4135	509	19	,	,	PUNCT
cana-4135	509	20	,	,	PUNCT
cana-4135	509	21	)	)	PUNCT
cana-4135	509	22	(	(	PUNCT
cana-4135	509	23	,	,	PUNCT
cana-4135	509	24	,	,	PUNCT
cana-4135	509	25	)	)	PUNCT
cana-4135	509	26	s	s	PART
cana-4135	509	27	fh	fh	PROPN
cana-4135	509	28	fi	fi	NOUN
cana-4135	510	1	fj	fj	PROPN
cana-4135	510	2	s	s	PROPN
cana-4135	510	3	gh	gh	PROPN
cana-4135	510	4	gi	gi	PROPN
cana-4135	510	5	gj	gj	PROPN
cana-4135	510	6	s	s	PROPN
cana-4135	510	7	gj	gj	PROPN
cana-4135	510	8	fi	fi	NOUN
cana-4135	510	9	fj	fj	X
cana-4135	510	10	(	(	PUNCT
cana-4135	510	11	iii	iii	NOUN
cana-4135	510	12	)	)	PUNCT
cana-4135	510	13	2	2	NUM
cana-4135	510	14	(	(	PUNCT
cana-4135	510	15	,	,	PUNCT
cana-4135	510	16	,	,	PUNCT
cana-4135	510	17	)	)	PUNCT
cana-4135	510	18	(	(	PUNCT
cana-4135	510	19	,	,	PUNCT
cana-4135	510	20	,	,	PUNCT
cana-4135	510	21	)	)	PUNCT
cana-4135	510	22	(	(	PUNCT
cana-4135	510	23	,	,	PUNCT
cana-4135	510	24	,	,	PUNCT
cana-4135	510	25	)	)	PUNCT
cana-4135	510	26	s	s	PART
cana-4135	510	27	fh	fh	PROPN
cana-4135	510	28	fi	fi	NOUN
cana-4135	510	29	fj	fj	PROPN
cana-4135	510	30	s	s	PROPN
cana-4135	510	31	gj	gj	PROPN
cana-4135	510	32	fh	fh	PROPN
cana-4135	510	33	fi	fi	PROPN
cana-4135	510	34	s	s	PART
cana-4135	510	35	gj	gj	PROPN
cana-4135	510	36	fi	fi	NOUN
cana-4135	510	37	fj	fj	NOUN
cana-4135	510	38	,	,	PUNCT
cana-4135	510	39	for	for	ADP
cana-4135	510	40	all	all	PRON
cana-4135	510	41	,	,	PUNCT
cana-4135	510	42	,	,	PUNCT
cana-4135	510	43	h	h	PROPN
cana-4135	511	1	k	k	PROPN
cana-4135	512	1	j	j	PROPN
cana-4135	513	1	x	x	PROPN
cana-4135	513	2	then	then	ADV
cana-4135	513	3	f	f	PROPN
cana-4135	513	4	and	and	CCONJ
cana-4135	513	5	g	g	PROPN
cana-4135	513	6	have	have	VERB
cana-4135	513	7	unique	unique	ADJ
cana-4135	513	8	common	common	ADJ
cana-4135	513	9	fixed	fix	VERB
cana-4135	513	10	point	point	NOUN
cana-4135	513	11	.	.	PUNCT
cana-4135	514	1	communications	communication	NOUN
cana-4135	514	2	on	on	ADP
cana-4135	514	3	applied	apply	VERB
cana-4135	514	4	nonlinear	nonlinear	ADJ
cana-4135	514	5	analysis	analysis	NOUN
cana-4135	514	6	issn	issn	NOUN
cana-4135	514	7	:	:	PUNCT
cana-4135	514	8	1074	1074	NUM
cana-4135	514	9	-	-	PUNCT
cana-4135	514	10	133x	133x	NUM
cana-4135	514	11	vol	vol	NOUN
cana-4135	514	12	32	32	NUM
cana-4135	514	13	no	no	NOUN
cana-4135	514	14	.	.	PUNCT
cana-4135	515	1	9s	9s	NUM
cana-4135	515	2	(	(	PUNCT
cana-4135	515	3	2025	2025	NUM
cana-4135	515	4	)	)	PUNCT
cana-4135	515	5	1287	1287	NUM
cana-4135	516	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4135	516	2	proof	proof	NOUN
cana-4135	516	3	:	:	PUNCT
cana-4135	516	4	the	the	DET
cana-4135	516	5	result	result	NOUN
cana-4135	516	6	can	can	AUX
cana-4135	516	7	be	be	AUX
cana-4135	516	8	proved	prove	VERB
cana-4135	516	9	easily	easily	ADV
cana-4135	516	10	by	by	ADP
cana-4135	516	11	substituting	substitute	VERB
cana-4135	516	12	the	the	DET
cana-4135	516	13	following	follow	VERB
cana-4135	516	14	values	value	NOUN
cana-4135	516	15	in	in	ADP
cana-4135	516	16	condition	condition	NOUN
cana-4135	516	17	(	(	PUNCT
cana-4135	516	18	2.1.3	2.1.3	NUM
cana-4135	516	19	)	)	PUNCT
cana-4135	516	20	of	of	ADP
cana-4135	516	21	theorem	theorem	NOUN
cana-4135	516	22	2.1	2.1	NUM
cana-4135	516	23	.	.	PUNCT
cana-4135	517	1	(	(	PUNCT
cana-4135	517	2	i	i	NOUN
cana-4135	517	3	)	)	PUNCT
cana-4135	517	4	1	1	NUM
cana-4135	517	5	,	,	PUNCT
cana-4135	517	6	1	1	NUM
cana-4135	517	7	,	,	PUNCT
cana-4135	517	8	0	0	PROPN
cana-4135	517	9			NOUN
cana-4135	517	10	=	=	NOUN
cana-4135	517	11	=	=	PUNCT
cana-4135	517	12	=	=	SYM
cana-4135	517	13	(	(	PUNCT
cana-4135	517	14	ii	ii	NOUN
cana-4135	517	15	)	)	PUNCT
cana-4135	517	16	1	1	NUM
cana-4135	517	17	,	,	PUNCT
cana-4135	517	18	0	0	PROPN
cana-4135	517	19			NUM
cana-4135	517	20	=	=	NOUN
cana-4135	518	1	=	=	SYM
cana-4135	518	2	=	=	SYM
cana-4135	518	3	(	(	PUNCT
cana-4135	518	4	iii	iii	NOUN
cana-4135	518	5	)	)	PUNCT
cana-4135	518	6	0	0	NUM
cana-4135	518	7	,	,	PUNCT
cana-4135	518	8	1	1	PROPN
cana-4135	518	9			PROPN
cana-4135	518	10	=	=	NOUN
cana-4135	518	11	=	=	PUNCT
cana-4135	519	1	=	=	PUNCT
cana-4135	519	2	corollary	corollary	NOUN
cana-4135	519	3	6	6	NUM
cana-4135	519	4	:	:	PUNCT
cana-4135	519	5	consider	consider	VERB
cana-4135	519	6	a	a	DET
cana-4135	519	7	complete	complete	ADJ
cana-4135	519	8	multiplicative	multiplicative	ADJ
cana-4135	519	9	s	s	X
cana-4135	519	10	-metric	-metric	ADJ
cana-4135	519	11	space	space	NOUN
cana-4135	519	12	(	(	PUNCT
cana-4135	519	13	,	,	PUNCT
cana-4135	519	14	)	)	PUNCT
cana-4135	519	15	m	m	PROPN
cana-4135	519	16	s	s	PRON
cana-4135	519	17	.	.	PUNCT
cana-4135	520	1	assume	assume	VERB
cana-4135	520	2	:	:	PUNCT
cana-4135	520	3	[	[	X
cana-4135	520	4	1	1	NUM
cana-4135	520	5	,	,	PUNCT
cana-4135	520	6	)	)	PUNCT
cana-4135	521	1	[	[	X
cana-4135	521	2	1	1	NUM
cana-4135	521	3	,	,	PUNCT
cana-4135	521	4	)	)	PUNCT
cana-4135	521	5			NOUN
cana-4135	521	6			VERB
cana-4135	521	7	→	→	SYM
cana-4135	521	8			NOUN
cana-4135	521	9	,	,	PUNCT
cana-4135	521	10	an	an	DET
cana-4135	521	11	upper	upper	ADJ
cana-4135	521	12	semicontinuous	semicontinuous	NOUN
cana-4135	521	13	and	and	CCONJ
cana-4135	521	14	non	non	ADJ
cana-4135	521	15	-	-	ADJ
cana-4135	521	16	decreasing	decrease	VERB
cana-4135	521	17	function	function	NOUN
cana-4135	521	18	.	.	PUNCT
cana-4135	522	1	let	let	VERB
cana-4135	522	2	,	,	PUNCT
cana-4135	522	3	:	:	PUNCT
cana-4135	522	4	f	f	PROPN
cana-4135	522	5	g	g	PROPN
cana-4135	522	6	m	m	VERB
cana-4135	522	7	m→	m→	NOUN
cana-4135	522	8	be	be	AUX
cana-4135	522	9	functions	function	NOUN
cana-4135	522	10	such	such	ADJ
cana-4135	522	11	that	that	SCONJ
cana-4135	522	12	(	(	PUNCT
cana-4135	522	13	1	1	NUM
cana-4135	522	14	)	)	PUNCT
cana-4135	522	15	(	(	PUNCT
cana-4135	522	16	)	)	PUNCT
cana-4135	522	17	(	(	PUNCT
cana-4135	522	18	)	)	PUNCT
cana-4135	522	19	f	f	X
cana-4135	522	20	m	m	VERB
cana-4135	522	21	g	g	PROPN
cana-4135	522	22	m	m	X
cana-4135	522	23	(	(	PUNCT
cana-4135	522	24	2	2	NUM
cana-4135	522	25	)	)	PUNCT
cana-4135	522	26	3	3	NUM
cana-4135	522	27	(	(	PUNCT
cana-4135	522	28	,	,	PUNCT
cana-4135	522	29	,	,	PUNCT
cana-4135	522	30	)	)	PUNCT
cana-4135	522	31	[	[	PUNCT
cana-4135	522	32	(	(	PUNCT
cana-4135	522	33	,	,	PUNCT
cana-4135	522	34	,	,	PUNCT
cana-4135	522	35	)	)	PUNCT
cana-4135	522	36	(	(	PUNCT
cana-4135	522	37	,	,	PUNCT
cana-4135	522	38	,	,	PUNCT
cana-4135	522	39	)	)	PUNCT
cana-4135	522	40	(	(	PUNCT
cana-4135	522	41	,	,	PUNCT
cana-4135	522	42	,	,	PUNCT
cana-4135	522	43	)	)	PUNCT
cana-4135	522	44	]	]	X
cana-4135	522	45	s	s	X
cana-4135	522	46	fh	fh	PROPN
cana-4135	522	47	fi	fi	NOUN
cana-4135	523	1	fj	fj	PROPN
cana-4135	523	2	s	s	PROPN
cana-4135	523	3	gh	gh	PROPN
cana-4135	523	4	gi	gi	PROPN
cana-4135	523	5	gj	gj	PROPN
cana-4135	523	6	s	s	PROPN
cana-4135	523	7	gj	gj	PROPN
cana-4135	523	8	fh	fh	PROPN
cana-4135	523	9	fi	fi	NOUN
cana-4135	523	10	s	s	PART
cana-4135	523	11	gj	gj	NOUN
cana-4135	523	12	fi	fi	NOUN
cana-4135	523	13	fj	fj	PROPN
cana-4135	523	14	,	,	PUNCT
cana-4135	523	15	for	for	ADP
cana-4135	523	16	all	all	PRON
cana-4135	523	17	,	,	PUNCT
cana-4135	523	18	,	,	PUNCT
cana-4135	523	19	x	x	PUNCT
cana-4135	523	20	y	y	PROPN
cana-4135	523	21	z	z	PROPN
cana-4135	523	22	m	m	PROPN
cana-4135	523	23	.	.	PUNCT
cana-4135	524	1	then	then	ADV
cana-4135	524	2	f	f	PROPN
cana-4135	524	3	and	and	CCONJ
cana-4135	524	4	g	g	PROPN
cana-4135	524	5	have	have	VERB
cana-4135	524	6	unique	unique	ADJ
cana-4135	524	7	common	common	ADJ
cana-4135	524	8	fixed	fix	VERB
cana-4135	524	9	point	point	NOUN
cana-4135	524	10	.	.	PUNCT
cana-4135	525	1	proof	proof	NOUN
cana-4135	525	2	:	:	PUNCT
cana-4135	525	3	put	put	VERB
cana-4135	525	4	1	1	PROPN
cana-4135	525	5			NOUN
cana-4135	525	6	=	=	NOUN
cana-4135	525	7	=	=	PUNCT
cana-4135	526	1	=	=	PUNCT
cana-4135	526	2	in	in	ADP
cana-4135	526	3	condition	condition	NOUN
cana-4135	526	4	(	(	PUNCT
cana-4135	526	5	2.1.3	2.1.3	NUM
cana-4135	526	6	)	)	PUNCT
cana-4135	526	7	of	of	ADP
cana-4135	526	8	theorem	theorem	NOUN
cana-4135	526	9	2.1	2.1	NUM
cana-4135	526	10	,	,	PUNCT
cana-4135	526	11	we	we	PRON
cana-4135	526	12	will	will	AUX
cana-4135	526	13	get	get	VERB
cana-4135	526	14	the	the	DET
cana-4135	526	15	desired	desire	VERB
cana-4135	526	16	result	result	NOUN
cana-4135	526	17	.	.	PUNCT
cana-4135	527	1	discussion	discussion	NOUN
cana-4135	527	2	:	:	PUNCT
cana-4135	527	3	a	a	DET
cana-4135	527	4	fixed	fix	VERB
cana-4135	527	5	-	-	PUNCT
cana-4135	527	6	point	point	NOUN
cana-4135	527	7	theorem	theorem	NOUN
cana-4135	527	8	has	have	AUX
cana-4135	527	9	been	be	AUX
cana-4135	527	10	formulated	formulate	VERB
cana-4135	527	11	for	for	ADP
cana-4135	527	12	a	a	DET
cana-4135	527	13	novel	novel	ADJ
cana-4135	527	14	category	category	NOUN
cana-4135	527	15	of	of	ADP
cana-4135	527	16	contractive	contractive	ADJ
cana-4135	527	17	condition	condition	NOUN
cana-4135	527	18	for	for	ADP
cana-4135	527	19	pair	pair	NOUN
cana-4135	527	20	of	of	ADP
cana-4135	527	21	mappings	mapping	NOUN
cana-4135	527	22	within	within	ADP
cana-4135	527	23	multiplicative	multiplicative	ADJ
cana-4135	527	24	s	s	ADJ
cana-4135	527	25	-	-	ADJ
cana-4135	527	26	metric	metric	ADJ
cana-4135	527	27	space	space	NOUN
cana-4135	527	28	.	.	PUNCT
cana-4135	528	1	it	it	PRON
cana-4135	528	2	has	have	AUX
cana-4135	528	3	proven	prove	VERB
cana-4135	528	4	that	that	SCONJ
cana-4135	528	5	this	this	DET
cana-4135	528	6	theorem	theorem	NOUN
cana-4135	528	7	is	be	AUX
cana-4135	528	8	generalization	generalization	NOUN
cana-4135	528	9	of	of	ADP
cana-4135	528	10	results	result	NOUN
cana-4135	528	11	in	in	ADP
cana-4135	528	12	existing	exist	VERB
cana-4135	528	13	literature	literature	NOUN
cana-4135	528	14	.	.	PUNCT
cana-4135	529	1	the	the	DET
cana-4135	529	2	various	various	ADJ
cana-4135	529	3	corollaries	corollary	NOUN
cana-4135	529	4	are	be	AUX
cana-4135	529	5	also	also	ADV
cana-4135	529	6	discussed	discuss	VERB
cana-4135	529	7	.	.	PUNCT
cana-4135	530	1	references	reference	NOUN
cana-4135	530	2	[	[	X
cana-4135	530	3	1	1	NUM
cana-4135	530	4	]	]	PUNCT
cana-4135	530	5	m.	m.	NOUN
cana-4135	530	6	fréchet	fréchet	PROPN
cana-4135	530	7	,	,	PUNCT
cana-4135	530	8	sur	sur	PROPN
cana-4135	530	9	quelques	quelques	PROPN
cana-4135	530	10	points	point	NOUN
cana-4135	530	11	du	du	PROPN
cana-4135	530	12	calcul	calcul	PROPN
cana-4135	530	13	fonctionnel	fonctionnel	PROPN
cana-4135	530	14	,	,	PUNCT
cana-4135	530	15	rendiconti	rendiconti	ADJ
cana-4135	530	16	del	del	PROPN
cana-4135	530	17	circolo	circolo	PROPN
cana-4135	530	18	matematicom	matematicom	PROPN
cana-4135	530	19	di	di	X
cana-4135	530	20	palermo	palermo	PROPN
cana-4135	530	21	.	.	PUNCT
cana-4135	531	1	22	22	NUM
cana-4135	531	2	(	(	PUNCT
cana-4135	531	3	1	1	NUM
cana-4135	531	4	)	)	PUNCT
cana-4135	531	5	,	,	PUNCT
cana-4135	531	6	december	december	PROPN
cana-4135	531	7	1906	1906	NUM
cana-4135	531	8	,	,	PUNCT
cana-4135	531	9	1–72	1–72	PROPN
cana-4135	531	10	.	.	PUNCT
cana-4135	532	1	doi:10.1007	doi:10.1007	PROPN
cana-4135	532	2	/	/	SYM
cana-4135	532	3	bf03018603	bf03018603	PROPN
cana-4135	532	4	.	.	PUNCT
cana-4135	533	1	s2cid	s2cid	PROPN
cana-4135	533	2	123251660	123251660	NUM
cana-4135	533	3	.	.	PUNCT
cana-4135	534	1	[	[	X
cana-4135	534	2	2	2	NUM
cana-4135	534	3	]	]	PUNCT
cana-4135	534	4	s.sedghi	s.sedghi	PROPN
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cana-4135	534	6	n.	n.	PROPN
cana-4135	534	7	shobe	shobe	PROPN
cana-4135	534	8	,	,	PUNCT
cana-4135	534	9	a.	a.	PROPN
cana-4135	534	10	aliouche	aliouche	PROPN
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cana-4135	534	17	theorem	theorem	VERB
cana-4135	534	18	in	in	ADP
cana-4135	534	19	smetric	smetric	ADJ
cana-4135	534	20	spaces	space	NOUN
cana-4135	534	21	.	.	PUNCT
cana-4135	535	1	mat	mat	NOUN
cana-4135	535	2	.	.	PUNCT
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cana-4135	535	4	.	.	PUNCT
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cana-4135	536	2	,	,	PUNCT
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cana-4135	536	4	,	,	PUNCT
cana-4135	536	5	258–266	258–266	NUM
cana-4135	536	6	.	.	PUNCT
cana-4135	537	1	[	[	X
cana-4135	537	2	3	3	X
cana-4135	537	3	]	]	X
cana-4135	537	4	v.	v.	ADP
cana-4135	537	5	singh	singh	PROPN
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cana-4135	537	8	singh	singh	PROPN
cana-4135	537	9	,	,	PUNCT
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cana-4135	537	11	point	point	NOUN
cana-4135	537	12	theorems	theorem	NOUN
cana-4135	537	13	in	in	ADP
cana-4135	537	14	a	a	DET
cana-4135	537	15	generalized	generalized	ADJ
cana-4135	537	16	s	s	ADJ
cana-4135	537	17	-	-	ADJ
cana-4135	537	18	metric	metric	ADJ
cana-4135	537	19	space	space	NOUN
cana-4135	537	20	,	,	PUNCT
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cana-4135	537	22	in	in	ADP
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cana-4135	537	24	:	:	PUNCT
cana-4135	537	25	scientific	scientific	ADJ
cana-4135	537	26	journal	journal	NOUN
cana-4135	537	27	10	10	NUM
cana-4135	537	28	,	,	PUNCT
cana-4135	537	29	no.3	no.3	VERB
cana-4135	537	30	,	,	PUNCT
cana-4135	537	31	2021	2021	NUM
cana-4135	537	32	,	,	PUNCT
cana-4135	537	33	12371248,doi.org/10.37418	12371248,doi.org/10.37418	NUM
cana-4135	537	34	/	/	SYM
cana-4135	537	35	amsj.10.3.12	amsj.10.3.12	PROPN
cana-4135	537	36	.	.	PUNCT
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cana-4135	538	2	4	4	X
cana-4135	538	3	]	]	X
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cana-4135	538	6	,	,	PUNCT
cana-4135	538	7	k.	k.	PROPN
cana-4135	538	8	r.	r.	PROPN
cana-4135	538	9	devi	devi	PROPN
cana-4135	538	10	and	and	CCONJ
cana-4135	538	11	j.	j.	PROPN
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cana-4135	538	36	,	,	PUNCT
cana-4135	538	37	vol	vol	NOUN
cana-4135	538	38	.	.	PROPN
cana-4135	538	39	8	8	NUM
cana-4135	538	40	,	,	PUNCT
cana-4135	538	41	no	no	INTJ
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cana-4135	538	43	2	2	NUM
cana-4135	538	44	,	,	PUNCT
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cana-4135	538	46	,	,	PUNCT
cana-4135	538	47	363	363	NUM
cana-4135	538	48	-	-	SYM
cana-4135	538	49	368	368	NUM
cana-4135	538	50	,	,	PUNCT
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cana-4135	538	52	.	.	PUNCT
cana-4135	539	1	[	[	X
cana-4135	539	2	5	5	X
cana-4135	539	3	]	]	PUNCT
cana-4135	539	4	k.	k.	PROPN
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cana-4135	539	12	common	common	ADJ
cana-4135	539	13	fixed	fix	VERB
cana-4135	539	14	point	point	NOUN
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cana-4135	539	16	in	in	ADP
cana-4135	539	17	s	s	NOUN
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cana-4135	539	20	space	space	NOUN
cana-4135	539	21	,	,	PUNCT
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cana-4135	539	25	10(1	10(1	NUM
cana-4135	539	26	)	)	PUNCT
cana-4135	539	27	,	,	PUNCT
cana-4135	539	28	2022	2022	NUM
cana-4135	539	29	,	,	PUNCT
cana-4135	539	30	160	160	NUM
cana-4135	539	31	-	-	SYM
cana-4135	539	32	165	165	NUM
cana-4135	539	33	,	,	PUNCT
cana-4135	539	34	doi	doi	NOUN
cana-4135	539	35	:	:	PUNCT
cana-4135	539	36	10.13189	10.13189	NUM
cana-4135	539	37	/	/	SYM
cana-4135	539	38	ms.2022.100114	ms.2022.100114	NOUN
cana-4135	539	39	.	.	PUNCT
cana-4135	540	1	[	[	X
cana-4135	540	2	6	6	NUM
cana-4135	540	3	]	]	PUNCT
cana-4135	540	4	t.	t.	PROPN
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cana-4135	540	13	,	,	PUNCT
cana-4135	540	14	m.	m.	PROPN
cana-4135	540	15	r.	r.	PROPN
cana-4135	540	16	singh	singh	PROPN
cana-4135	540	17	,	,	PUNCT
cana-4135	540	18	common	common	ADJ
cana-4135	540	19	fixed	fix	VERB
cana-4135	540	20	point	point	NOUN
cana-4135	540	21	theorems	theorem	NOUN
cana-4135	540	22	for	for	ADP
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cana-4135	540	24	selfmappings	selfmapping	NOUN
cana-4135	540	25	on	on	ADP
cana-4135	540	26	s	s	NOUN
cana-4135	540	27	-	-	ADJ
cana-4135	540	28	metric	metric	ADJ
cana-4135	540	29	spaces	space	NOUN
cana-4135	540	30	,	,	PUNCT
cana-4135	540	31	international	international	ADJ
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cana-4135	540	34	analysis	analysis	NOUN
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cana-4135	540	36	applications	application	NOUN
cana-4135	540	37	volume	volume	NOUN
cana-4135	540	38	19	19	NUM
cana-4135	540	39	,	,	PUNCT
cana-4135	540	40	number	number	NOUN
cana-4135	540	41	5	5	NUM
cana-4135	540	42	,	,	PUNCT
cana-4135	540	43	2021	2021	NUM
cana-4135	540	44	,	,	PUNCT
cana-4135	540	45	794	794	NUM
cana-4135	540	46	-	-	SYM
cana-4135	540	47	811	811	NUM
cana-4135	540	48	,	,	PUNCT
cana-4135	540	49	doi	doi	NOUN
cana-4135	540	50	:	:	PUNCT
cana-4135	540	51	10.28924/2291	10.28924/2291	NUM
cana-4135	540	52	-	-	PUNCT
cana-4135	540	53	8639	8639	NUM
cana-4135	540	54	-	-	PUNCT
cana-4135	540	55	19	19	NUM
cana-4135	540	56	-	-	PUNCT
cana-4135	540	57	2021	2021	NUM
cana-4135	540	58	-	-	SYM
cana-4135	540	59	794	794	NUM
cana-4135	540	60	.	.	PUNCT
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cana-4135	541	2	7	7	NUM
cana-4135	541	3	]	]	SYM
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cana-4135	541	5	,	,	PUNCT
cana-4135	541	6	n.v	n.v	PROPN
cana-4135	541	7	.	.	NOUN
cana-4135	541	8	dung	dung	NOUN
cana-4135	541	9	,	,	PUNCT
cana-4135	541	10	fixed	fix	VERB
cana-4135	541	11	point	point	NOUN
cana-4135	541	12	theorems	theorem	NOUN
cana-4135	541	13	on	on	ADP
cana-4135	541	14	s	s	NOUN
cana-4135	541	15	-	-	ADJ
cana-4135	541	16	metric	metric	ADJ
cana-4135	541	17	space	space	NOUN
cana-4135	541	18	.	.	PUNCT
cana-4135	542	1	matematicki	matematicki	NOUN
cana-4135	542	2	vesnik	vesnik	PROPN
cana-4135	542	3	,	,	PUNCT
cana-4135	542	4	255	255	NUM
cana-4135	542	5	2014	2014	NUM
cana-4135	542	6	,	,	PUNCT
cana-4135	542	7	113	113	NUM
cana-4135	542	8	-	-	SYM
cana-4135	542	9	124	124	NUM
cana-4135	542	10	.	.	PUNCT
cana-4135	543	1	[	[	X
cana-4135	543	2	8	8	X
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