id	sid	tid	token	lemma	pos
ejpam-6086	1	1	european	european	PROPN
ejpam-6086	1	2	journal	journal	PROPN
ejpam-6086	1	3	of	of	ADP
ejpam-6086	1	4	pure	pure	ADJ
ejpam-6086	1	5	and	and	CCONJ
ejpam-6086	1	6	applied	applied	ADJ
ejpam-6086	1	7	mathematics	mathematic	NOUN
ejpam-6086	1	8	2025	2025	NUM
ejpam-6086	1	9	,	,	PUNCT
ejpam-6086	1	10	vol	vol	NOUN
ejpam-6086	1	11	.	.	PROPN
ejpam-6086	1	12	18	18	NUM
ejpam-6086	1	13	,	,	PUNCT
ejpam-6086	1	14	issue	issue	NOUN
ejpam-6086	1	15	2	2	NUM
ejpam-6086	1	16	,	,	PUNCT
ejpam-6086	1	17	article	article	NOUN
ejpam-6086	1	18	number	number	NOUN
ejpam-6086	1	19	6086	6086	NUM
ejpam-6086	1	20	issn	issn	PROPN
ejpam-6086	1	21	1307	1307	NUM
ejpam-6086	1	22	-	-	SYM
ejpam-6086	1	23	5543	5543	NUM
ejpam-6086	1	24	–	–	PUNCT
ejpam-6086	1	25	ejpam.com	ejpam.com	X
ejpam-6086	1	26	published	publish	VERB
ejpam-6086	1	27	by	by	ADP
ejpam-6086	1	28	new	new	PROPN
ejpam-6086	1	29	york	york	PROPN
ejpam-6086	1	30	business	business	PROPN
ejpam-6086	1	31	global	global	PROPN
ejpam-6086	1	32	some	some	DET
ejpam-6086	1	33	fixed	fix	VERB
ejpam-6086	1	34	point	point	NOUN
ejpam-6086	1	35	theorems	theorem	NOUN
ejpam-6086	1	36	for	for	ADP
ejpam-6086	1	37	θ−	θ−	PROPN
ejpam-6086	1	38	ϕ-multivalued	ϕ-multivalue	VERB
ejpam-6086	1	39	contraction	contraction	NOUN
ejpam-6086	1	40	mappings	mapping	NOUN
ejpam-6086	1	41	in	in	ADP
ejpam-6086	1	42	rectangular	rectangular	ADJ
ejpam-6086	1	43	b	b	X
ejpam-6086	1	44	-	-	ADJ
ejpam-6086	1	45	metric	metric	ADJ
ejpam-6086	1	46	spaces	space	NOUN
ejpam-6086	1	47	hafida	hafida	PROPN
ejpam-6086	1	48	massit1	massit1	PROPN
ejpam-6086	1	49	,	,	PUNCT
ejpam-6086	1	50	mohamed	mohamed	PROPN
ejpam-6086	1	51	rossafi2	rossafi2	PROPN
ejpam-6086	1	52	,	,	PUNCT
ejpam-6086	1	53	zoran	zoran	PROPN
ejpam-6086	1	54	d.	d.	PROPN
ejpam-6086	1	55	mitrović3,∗	mitrović3,∗	PROPN
ejpam-6086	1	56	,	,	PUNCT
ejpam-6086	1	57	ahmad	ahmad	PROPN
ejpam-6086	1	58	aloqaily4	aloqaily4	PROPN
ejpam-6086	1	59	,	,	PUNCT
ejpam-6086	1	60	nabil	nabil	NOUN
ejpam-6086	1	61	mlaiki4	mlaiki4	NOUN
ejpam-6086	1	62	1	1	NUM
ejpam-6086	1	63	laboratory	laboratory	NOUN
ejpam-6086	1	64	analysis	analysis	NOUN
ejpam-6086	1	65	,	,	PUNCT
ejpam-6086	1	66	geometry	geometry	NOUN
ejpam-6086	1	67	and	and	CCONJ
ejpam-6086	1	68	applications	application	NOUN
ejpam-6086	1	69	,	,	PUNCT
ejpam-6086	1	70	university	university	NOUN
ejpam-6086	1	71	of	of	ADP
ejpam-6086	1	72	ibn	ibn	PROPN
ejpam-6086	1	73	tofail	tofail	NOUN
ejpam-6086	1	74	,	,	PUNCT
ejpam-6086	1	75	kenitra	kenitra	PROPN
ejpam-6086	1	76	,	,	PUNCT
ejpam-6086	1	77	morocco	morocco	PROPN
ejpam-6086	1	78	2	2	NUM
ejpam-6086	1	79	laboratory	laboratory	NOUN
ejpam-6086	1	80	analysis	analysis	NOUN
ejpam-6086	1	81	,	,	PUNCT
ejpam-6086	1	82	geometry	geometry	NOUN
ejpam-6086	1	83	and	and	CCONJ
ejpam-6086	1	84	applications	application	NOUN
ejpam-6086	1	85	,	,	PUNCT
ejpam-6086	1	86	higher	high	ADJ
ejpam-6086	1	87	school	school	NOUN
ejpam-6086	1	88	of	of	ADP
ejpam-6086	1	89	education	education	NOUN
ejpam-6086	1	90	and	and	CCONJ
ejpam-6086	1	91	training	training	NOUN
ejpam-6086	1	92	,	,	PUNCT
ejpam-6086	1	93	university	university	NOUN
ejpam-6086	1	94	of	of	ADP
ejpam-6086	1	95	ibn	ibn	PROPN
ejpam-6086	1	96	tofail	tofail	NOUN
ejpam-6086	1	97	,	,	PUNCT
ejpam-6086	1	98	kenitra	kenitra	PROPN
ejpam-6086	1	99	,	,	PUNCT
ejpam-6086	1	100	morocco	morocco	PROPN
ejpam-6086	1	101	3	3	NUM
ejpam-6086	1	102	faculty	faculty	NOUN
ejpam-6086	1	103	of	of	ADP
ejpam-6086	1	104	electrical	electrical	ADJ
ejpam-6086	1	105	engineering	engineering	NOUN
ejpam-6086	1	106	,	,	PUNCT
ejpam-6086	1	107	university	university	NOUN
ejpam-6086	1	108	of	of	ADP
ejpam-6086	1	109	banja	banja	PROPN
ejpam-6086	1	110	luka	luka	PROPN
ejpam-6086	1	111	,	,	PUNCT
ejpam-6086	1	112	patre	patre	NOUN
ejpam-6086	1	113	5	5	NUM
ejpam-6086	1	114	,	,	PUNCT
ejpam-6086	1	115	78000	78000	NUM
ejpam-6086	1	116	banja	banja	PROPN
ejpam-6086	1	117	luka	luka	PROPN
ejpam-6086	1	118	,	,	PUNCT
ejpam-6086	1	119	bosnia	bosnia	PROPN
ejpam-6086	1	120	and	and	CCONJ
ejpam-6086	1	121	herzegovina	herzegovina	PROPN
ejpam-6086	1	122	4	4	NUM
ejpam-6086	1	123	department	department	NOUN
ejpam-6086	1	124	of	of	ADP
ejpam-6086	1	125	mathematics	mathematic	NOUN
ejpam-6086	1	126	and	and	CCONJ
ejpam-6086	1	127	sciences	science	NOUN
ejpam-6086	1	128	,	,	PUNCT
ejpam-6086	1	129	prince	prince	PROPN
ejpam-6086	1	130	sultan	sultan	PROPN
ejpam-6086	1	131	university	university	PROPN
ejpam-6086	1	132	,	,	PUNCT
ejpam-6086	1	133	riyadh	riyadh	PROPN
ejpam-6086	1	134	11586	11586	NUM
ejpam-6086	1	135	,	,	PUNCT
ejpam-6086	1	136	saudi	saudi	PROPN
ejpam-6086	1	137	arabia	arabia	PROPN
ejpam-6086	1	138	abstract	abstract	NOUN
ejpam-6086	1	139	.	.	PUNCT
ejpam-6086	2	1	in	in	ADP
ejpam-6086	2	2	this	this	DET
ejpam-6086	2	3	paper	paper	NOUN
ejpam-6086	2	4	,	,	PUNCT
ejpam-6086	2	5	we	we	PRON
ejpam-6086	2	6	give	give	VERB
ejpam-6086	2	7	some	some	DET
ejpam-6086	2	8	fixed	fix	VERB
ejpam-6086	2	9	point	point	NOUN
ejpam-6086	2	10	theorems	theorem	NOUN
ejpam-6086	2	11	for	for	ADP
ejpam-6086	2	12	θ−ϕ−multivalued	θ−ϕ−multivalue	VERB
ejpam-6086	2	13	contractions	contraction	NOUN
ejpam-6086	2	14	in	in	ADP
ejpam-6086	2	15	α−complete	α−complete	NUM
ejpam-6086	2	16	rectangular	rectangular	ADJ
ejpam-6086	2	17	b−metric	b−metric	ADJ
ejpam-6086	2	18	spaces	space	NOUN
ejpam-6086	2	19	.	.	PUNCT
ejpam-6086	3	1	we	we	PRON
ejpam-6086	3	2	establish	establish	VERB
ejpam-6086	3	3	some	some	DET
ejpam-6086	3	4	fixed	fix	VERB
ejpam-6086	3	5	point	point	NOUN
ejpam-6086	3	6	theorems	theorem	NOUN
ejpam-6086	3	7	including	include	VERB
ejpam-6086	3	8	the	the	DET
ejpam-6086	3	9	α−admissible	α−admissible	PROPN
ejpam-6086	3	10	θ−ϕ−multivalued	θ−ϕ−multivalue	VERB
ejpam-6086	3	11	kannan	kannan	PROPN
ejpam-6086	3	12	type	type	NOUN
ejpam-6086	3	13	and	and	CCONJ
ejpam-6086	3	14	reich	reich	PROPN
ejpam-6086	3	15	type	type	NOUN
ejpam-6086	3	16	.	.	PUNCT
ejpam-6086	4	1	our	our	PRON
ejpam-6086	4	2	results	result	NOUN
ejpam-6086	4	3	improve	improve	VERB
ejpam-6086	4	4	and	and	CCONJ
ejpam-6086	4	5	generalize	generalize	VERB
ejpam-6086	4	6	some	some	DET
ejpam-6086	4	7	results	result	NOUN
ejpam-6086	4	8	from	from	ADP
ejpam-6086	4	9	the	the	DET
ejpam-6086	4	10	literature	literature	NOUN
ejpam-6086	4	11	.	.	PUNCT
ejpam-6086	5	1	2020	2020	NUM
ejpam-6086	5	2	mathematics	mathematics	PROPN
ejpam-6086	5	3	subject	subject	NOUN
ejpam-6086	5	4	classifications	classification	NOUN
ejpam-6086	5	5	:	:	PUNCT
ejpam-6086	5	6	41a58	41a58	NUM
ejpam-6086	5	7	,	,	PUNCT
ejpam-6086	5	8	42c15	42c15	NUM
ejpam-6086	5	9	,	,	PUNCT
ejpam-6086	5	10	46l05	46l05	NUM
ejpam-6086	5	11	key	key	ADJ
ejpam-6086	5	12	words	word	NOUN
ejpam-6086	5	13	and	and	CCONJ
ejpam-6086	5	14	phrases	phrase	NOUN
ejpam-6086	5	15	:	:	PUNCT
ejpam-6086	5	16	admissible	admissible	ADJ
ejpam-6086	5	17	mapping	mapping	NOUN
ejpam-6086	5	18	,	,	PUNCT
ejpam-6086	5	19	fixed	fix	VERB
ejpam-6086	5	20	point	point	NOUN
ejpam-6086	5	21	,	,	PUNCT
ejpam-6086	5	22	αcomplete	αcomplete	ADJ
ejpam-6086	5	23	spaces	space	NOUN
ejpam-6086	5	24	,	,	PUNCT
ejpam-6086	5	25	θ−ϕ−multivalued	θ−ϕ−multivalue	VERB
ejpam-6086	5	26	contraction	contraction	NOUN
ejpam-6086	5	27	,	,	PUNCT
ejpam-6086	5	28	rectangular	rectangular	ADJ
ejpam-6086	5	29	b−metric	b−metric	ADJ
ejpam-6086	5	30	spaces	space	NOUN
ejpam-6086	5	31	1	1	NUM
ejpam-6086	5	32	.	.	PUNCT
ejpam-6086	5	33	introduction	introduction	NOUN
ejpam-6086	5	34	and	and	CCONJ
ejpam-6086	5	35	preliminaries	preliminary	NOUN
ejpam-6086	5	36	many	many	ADJ
ejpam-6086	5	37	generalizations	generalization	NOUN
ejpam-6086	5	38	of	of	ADP
ejpam-6086	5	39	the	the	DET
ejpam-6086	5	40	concept	concept	NOUN
ejpam-6086	5	41	of	of	ADP
ejpam-6086	5	42	metric	metric	ADJ
ejpam-6086	5	43	spaces	space	NOUN
ejpam-6086	5	44	have	have	AUX
ejpam-6086	5	45	been	be	AUX
ejpam-6086	5	46	defined	define	VERB
ejpam-6086	5	47	and	and	CCONJ
ejpam-6086	5	48	some	some	DET
ejpam-6086	5	49	fixed	fix	VERB
ejpam-6086	5	50	theorems	theorem	NOUN
ejpam-6086	5	51	were	be	AUX
ejpam-6086	5	52	proven	prove	VERB
ejpam-6086	5	53	in	in	ADP
ejpam-6086	5	54	these	these	DET
ejpam-6086	5	55	spaces	space	NOUN
ejpam-6086	6	1	[	[	X
ejpam-6086	6	2	1–13	1–13	NOUN
ejpam-6086	6	3	]	]	PUNCT
ejpam-6086	6	4	.	.	PUNCT
ejpam-6086	7	1	particularly	particularly	ADV
ejpam-6086	7	2	,	,	PUNCT
ejpam-6086	7	3	b−metric	b−metric	ADJ
ejpam-6086	7	4	spaces	space	NOUN
ejpam-6086	7	5	were	be	AUX
ejpam-6086	7	6	introduced	introduce	VERB
ejpam-6086	7	7	by	by	ADP
ejpam-6086	7	8	bakhtin	bakhtin	NOUN
ejpam-6086	7	9	[	[	X
ejpam-6086	7	10	4	4	NUM
ejpam-6086	7	11	]	]	PUNCT
ejpam-6086	7	12	and	and	CCONJ
ejpam-6086	7	13	branciari	branciari	NOUN
ejpam-6086	8	1	[	[	X
ejpam-6086	8	2	5	5	X
ejpam-6086	8	3	]	]	PUNCT
ejpam-6086	8	4	introduced	introduce	VERB
ejpam-6086	8	5	generalized	generalized	ADJ
ejpam-6086	8	6	metric	metric	ADJ
ejpam-6086	8	7	spaces	space	NOUN
ejpam-6086	8	8	.	.	PUNCT
ejpam-6086	9	1	recently	recently	ADV
ejpam-6086	9	2	,	,	PUNCT
ejpam-6086	9	3	george	george	PROPN
ejpam-6086	9	4	et	et	PROPN
ejpam-6086	9	5	al	al	PROPN
ejpam-6086	9	6	[	[	X
ejpam-6086	9	7	7	7	X
ejpam-6086	9	8	]	]	PUNCT
ejpam-6086	9	9	announced	announce	VERB
ejpam-6086	9	10	the	the	DET
ejpam-6086	9	11	concept	concept	NOUN
ejpam-6086	9	12	of	of	ADP
ejpam-6086	9	13	rectangular	rectangular	ADJ
ejpam-6086	9	14	b−metric	b−metric	ADJ
ejpam-6086	9	15	spaces	space	NOUN
ejpam-6086	9	16	.	.	PUNCT
ejpam-6086	10	1	in	in	ADP
ejpam-6086	10	2	2017	2017	NUM
ejpam-6086	10	3	,	,	PUNCT
ejpam-6086	10	4	zheng	zheng	PROPN
ejpam-6086	10	5	et	et	PROPN
ejpam-6086	10	6	al	al	PROPN
ejpam-6086	11	1	[	[	X
ejpam-6086	11	2	14	14	NUM
ejpam-6086	11	3	]	]	PUNCT
ejpam-6086	11	4	established	establish	VERB
ejpam-6086	11	5	some	some	DET
ejpam-6086	11	6	fixed	fix	VERB
ejpam-6086	11	7	point	point	NOUN
ejpam-6086	11	8	results	result	NOUN
ejpam-6086	11	9	for	for	ADP
ejpam-6086	11	10	θ	θ	PROPN
ejpam-6086	11	11	−	−	PROPN
ejpam-6086	11	12	ϕ−contractions	ϕ−contraction	NOUN
ejpam-6086	11	13	in	in	ADP
ejpam-6086	11	14	complete	complete	ADJ
ejpam-6086	11	15	metric	metric	ADJ
ejpam-6086	11	16	spaces	space	NOUN
ejpam-6086	11	17	.	.	PUNCT
ejpam-6086	12	1	nadler	nadler	PROPN
ejpam-6086	13	1	[	[	X
ejpam-6086	13	2	15	15	NUM
ejpam-6086	13	3	]	]	PUNCT
ejpam-6086	13	4	extented	extente	VERB
ejpam-6086	13	5	the	the	DET
ejpam-6086	13	6	contraction	contraction	NOUN
ejpam-6086	13	7	principle	principle	NOUN
ejpam-6086	13	8	to	to	ADP
ejpam-6086	13	9	multivalued	multivalue	VERB
ejpam-6086	13	10	mappings	mapping	NOUN
ejpam-6086	13	11	.	.	PUNCT
ejpam-6086	14	1	in	in	ADP
ejpam-6086	14	2	this	this	DET
ejpam-6086	14	3	work	work	NOUN
ejpam-6086	14	4	,	,	PUNCT
ejpam-6086	14	5	we	we	PRON
ejpam-6086	14	6	introduce	introduce	VERB
ejpam-6086	14	7	a	a	DET
ejpam-6086	14	8	notion	notion	NOUN
ejpam-6086	14	9	of	of	ADP
ejpam-6086	14	10	θ	θ	PROPN
ejpam-6086	14	11	−	−	PROPN
ejpam-6086	14	12	ϕ−multivalued	ϕ−multivalued	PUNCT
ejpam-6086	14	13	contraction	contraction	NOUN
ejpam-6086	14	14	mappings	mapping	NOUN
ejpam-6086	14	15	in	in	ADP
ejpam-6086	14	16	rectangular	rectangular	ADJ
ejpam-6086	14	17	b−metric	b−metric	ADJ
ejpam-6086	14	18	spaces	space	NOUN
ejpam-6086	14	19	.	.	PUNCT
ejpam-6086	15	1	we	we	PRON
ejpam-6086	15	2	obtain	obtain	VERB
ejpam-6086	15	3	some	some	DET
ejpam-6086	15	4	fixed	fix	VERB
ejpam-6086	15	5	point	point	NOUN
ejpam-6086	15	6	theorems	theorem	NOUN
ejpam-6086	15	7	for	for	ADP
ejpam-6086	15	8	θ	θ	PROPN
ejpam-6086	15	9	−	−	PROPN
ejpam-6086	15	10	ϕ−multivalued	ϕ−multivalue	VERB
ejpam-6086	15	11	∗corresponding	∗corresponde	VERB
ejpam-6086	15	12	author	author	NOUN
ejpam-6086	15	13	.	.	PUNCT
ejpam-6086	16	1	doi	doi	NOUN
ejpam-6086	16	2	:	:	PUNCT
ejpam-6086	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6086	https://doi.org/10.29020/nybg.ejpam.v18i2.6086	ADJ
ejpam-6086	16	4	email	email	NOUN
ejpam-6086	16	5	addresses	address	NOUN
ejpam-6086	16	6	:	:	PUNCT
ejpam-6086	16	7	massithafida@yahoo.fr	massithafida@yahoo.fr	PROPN
ejpam-6086	16	8	(	(	PUNCT
ejpam-6086	16	9	h.	h.	PROPN
ejpam-6086	16	10	massit	massit	PROPN
ejpam-6086	16	11	)	)	PUNCT
ejpam-6086	16	12	,	,	PUNCT
ejpam-6086	16	13	mohamed.rossafi1@uit.ac.ma	mohamed.rossafi1@uit.ac.ma	PROPN
ejpam-6086	16	14	(	(	PUNCT
ejpam-6086	16	15	m.	m.	NOUN
ejpam-6086	16	16	rossafi	rossafi	NOUN
ejpam-6086	16	17	)	)	PUNCT
ejpam-6086	16	18	,	,	PUNCT
ejpam-6086	16	19	zoran.mitrovic@etf.unibl.org	zoran.mitrovic@etf.unibl.org	PROPN
ejpam-6086	16	20	(	(	PUNCT
ejpam-6086	16	21	z.	z.	PROPN
ejpam-6086	16	22	d.	d.	PROPN
ejpam-6086	16	23	mitrović	mitrović	PROPN
ejpam-6086	16	24	)	)	PUNCT
ejpam-6086	16	25	,	,	PUNCT
ejpam-6086	16	26	maloqaily@psu.edu.sa	maloqaily@psu.edu.sa	PROPN
ejpam-6086	16	27	(	(	PUNCT
ejpam-6086	16	28	a.	a.	NOUN
ejpam-6086	16	29	aloqaily	aloqaily	ADV
ejpam-6086	16	30	)	)	PUNCT
ejpam-6086	16	31	,	,	PUNCT
ejpam-6086	16	32	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-6086	16	33	(	(	PUNCT
ejpam-6086	16	34	n.	n.	PROPN
ejpam-6086	16	35	mlaiki	mlaiki	PROPN
ejpam-6086	16	36	)	)	PUNCT
ejpam-6086	16	37	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6086	17	1	1	1	NUM
ejpam-6086	17	2	copyright	copyright	NOUN
ejpam-6086	17	3	:	:	PUNCT
ejpam-6086	17	4	©	©	PROPN
ejpam-6086	17	5	2025	2025	NUM
ejpam-6086	17	6	the	the	DET
ejpam-6086	17	7	author(s	author(s	NOUN
ejpam-6086	17	8	)	)	PUNCT
ejpam-6086	17	9	.	.	PUNCT
ejpam-6086	18	1	(	(	PUNCT
ejpam-6086	18	2	cc	cc	NOUN
ejpam-6086	18	3	by	by	ADP
ejpam-6086	18	4	-	-	PUNCT
ejpam-6086	18	5	nc	nc	PROPN
ejpam-6086	18	6	4.0	4.0	NUM
ejpam-6086	18	7	)	)	PUNCT
ejpam-6086	18	8	h.	h.	NOUN
ejpam-6086	18	9	massit	massit	PROPN
ejpam-6086	18	10	et	et	PROPN
ejpam-6086	18	11	al	al	PROPN
ejpam-6086	18	12	.	.	PUNCT
ejpam-6086	18	13	/	/	SYM
ejpam-6086	18	14	eur	eur	PROPN
ejpam-6086	18	15	.	.	PUNCT
ejpam-6086	19	1	j.	j.	PROPN
ejpam-6086	19	2	pure	pure	PROPN
ejpam-6086	19	3	appl	appl	PROPN
ejpam-6086	19	4	.	.	PROPN
ejpam-6086	19	5	math	math	PROPN
ejpam-6086	19	6	,	,	PUNCT
ejpam-6086	19	7	18	18	NUM
ejpam-6086	19	8	(	(	PUNCT
ejpam-6086	19	9	2	2	NUM
ejpam-6086	19	10	)	)	PUNCT
ejpam-6086	19	11	(	(	PUNCT
ejpam-6086	19	12	2025	2025	NUM
ejpam-6086	19	13	)	)	PUNCT
ejpam-6086	19	14	,	,	PUNCT
ejpam-6086	19	15	6086	6086	NUM
ejpam-6086	19	16	2	2	NUM
ejpam-6086	19	17	of	of	ADP
ejpam-6086	19	18	19	19	NUM
ejpam-6086	19	19	contractions	contraction	NOUN
ejpam-6086	19	20	in	in	ADP
ejpam-6086	19	21	α−complete	α−complete	NUM
ejpam-6086	19	22	rectangular	rectangular	ADJ
ejpam-6086	19	23	b−metric	b−metric	ADJ
ejpam-6086	19	24	spaces	space	NOUN
ejpam-6086	19	25	.	.	PUNCT
ejpam-6086	20	1	we	we	PRON
ejpam-6086	20	2	establish	establish	VERB
ejpam-6086	20	3	some	some	DET
ejpam-6086	20	4	fixed	fix	VERB
ejpam-6086	20	5	point	point	NOUN
ejpam-6086	20	6	theorems	theorem	NOUN
ejpam-6086	20	7	including	include	VERB
ejpam-6086	20	8	the	the	DET
ejpam-6086	20	9	α−admissible	α−admissible	PROPN
ejpam-6086	20	10	θ−ϕ−multivalued	θ−ϕ−multivalue	VERB
ejpam-6086	20	11	kannan	kannan	PROPN
ejpam-6086	20	12	type	type	NOUN
ejpam-6086	21	1	[	[	X
ejpam-6086	21	2	16	16	NUM
ejpam-6086	21	3	]	]	PUNCT
ejpam-6086	21	4	and	and	CCONJ
ejpam-6086	21	5	reich	reich	PROPN
ejpam-6086	21	6	type	type	NOUN
ejpam-6086	22	1	[	[	X
ejpam-6086	22	2	17	17	NUM
ejpam-6086	22	3	]	]	PUNCT
ejpam-6086	22	4	in	in	ADP
ejpam-6086	22	5	rectangular	rectangular	ADJ
ejpam-6086	22	6	b−metric	b−metric	ADJ
ejpam-6086	22	7	spaces	space	NOUN
ejpam-6086	22	8	.	.	PUNCT
ejpam-6086	23	1	our	our	PRON
ejpam-6086	23	2	results	result	NOUN
ejpam-6086	23	3	improve	improve	VERB
ejpam-6086	23	4	and	and	CCONJ
ejpam-6086	23	5	generalize	generalize	VERB
ejpam-6086	23	6	some	some	DET
ejpam-6086	23	7	results	result	NOUN
ejpam-6086	23	8	from	from	ADP
ejpam-6086	23	9	the	the	DET
ejpam-6086	23	10	literature	literature	NOUN
ejpam-6086	23	11	.	.	PUNCT
ejpam-6086	24	1	we	we	PRON
ejpam-6086	24	2	believe	believe	VERB
ejpam-6086	24	3	that	that	SCONJ
ejpam-6086	24	4	our	our	PRON
ejpam-6086	24	5	paper	paper	NOUN
ejpam-6086	24	6	may	may	AUX
ejpam-6086	24	7	be	be	AUX
ejpam-6086	24	8	interesting	interesting	ADJ
ejpam-6086	24	9	to	to	ADP
ejpam-6086	24	10	researchers	researcher	NOUN
ejpam-6086	24	11	in	in	ADP
ejpam-6086	24	12	fixed	fix	VERB
ejpam-6086	24	13	point	point	NOUN
ejpam-6086	24	14	theory	theory	NOUN
ejpam-6086	24	15	,	,	PUNCT
ejpam-6086	24	16	because	because	SCONJ
ejpam-6086	24	17	using	use	VERB
ejpam-6086	24	18	the	the	DET
ejpam-6086	24	19	methods	method	NOUN
ejpam-6086	24	20	presented	present	VERB
ejpam-6086	24	21	in	in	ADP
ejpam-6086	24	22	this	this	DET
ejpam-6086	24	23	paper	paper	NOUN
ejpam-6086	24	24	,	,	PUNCT
ejpam-6086	24	25	at	at	ADP
ejpam-6086	24	26	the	the	DET
ejpam-6086	24	27	end	end	NOUN
ejpam-6086	24	28	we	we	PRON
ejpam-6086	24	29	give	give	VERB
ejpam-6086	24	30	several	several	ADJ
ejpam-6086	24	31	open	open	ADJ
ejpam-6086	24	32	problems	problem	NOUN
ejpam-6086	24	33	.	.	PUNCT
ejpam-6086	25	1	definition	definition	NOUN
ejpam-6086	25	2	1	1	NUM
ejpam-6086	25	3	.	.	PUNCT
ejpam-6086	26	1	[	[	X
ejpam-6086	26	2	13	13	NUM
ejpam-6086	26	3	]	]	PUNCT
ejpam-6086	26	4	let	let	VERB
ejpam-6086	26	5	u	u	PRON
ejpam-6086	26	6	be	be	AUX
ejpam-6086	26	7	a	a	DET
ejpam-6086	26	8	non	non	ADJ
ejpam-6086	26	9	-	-	ADJ
ejpam-6086	26	10	empty	empty	ADJ
ejpam-6086	26	11	set	set	NOUN
ejpam-6086	26	12	and	and	CCONJ
ejpam-6086	26	13	b	b	NOUN
ejpam-6086	26	14	≥	≥	NUM
ejpam-6086	26	15	1	1	NUM
ejpam-6086	26	16	.	.	PUNCT
ejpam-6086	26	17	suppose	suppose	VERB
ejpam-6086	26	18	that	that	SCONJ
ejpam-6086	26	19	the	the	DET
ejpam-6086	26	20	mapping	mapping	NOUN
ejpam-6086	26	21	d	d	NOUN
ejpam-6086	26	22	:	:	PUNCT
ejpam-6086	26	23	u	u	PRON
ejpam-6086	26	24	×	×	PROPN
ejpam-6086	26	25	u	u	X
ejpam-6086	26	26	→	→	PUNCT
ejpam-6086	26	27	[	[	X
ejpam-6086	26	28	0,+∞	0,+∞	NUM
ejpam-6086	26	29	)	)	PUNCT
ejpam-6086	26	30	satisfies	satisfie	NOUN
ejpam-6086	26	31	:	:	PUNCT
ejpam-6086	26	32	(	(	PUNCT
ejpam-6086	26	33	i	i	NOUN
ejpam-6086	26	34	)	)	PUNCT
ejpam-6086	26	35	d(x	d(x	PROPN
ejpam-6086	26	36	,	,	PUNCT
ejpam-6086	26	37	y	y	NOUN
ejpam-6086	26	38	)	)	PUNCT
ejpam-6086	27	1	=	=	SYM
ejpam-6086	27	2	0	0	PUNCT
ejpam-6086	28	1	if	if	SCONJ
ejpam-6086	28	2	and	and	CCONJ
ejpam-6086	28	3	only	only	ADV
ejpam-6086	28	4	if	if	SCONJ
ejpam-6086	28	5	x	x	X
ejpam-6086	28	6	=	=	SYM
ejpam-6086	28	7	y	y	PROPN
ejpam-6086	28	8	,	,	PUNCT
ejpam-6086	28	9	(	(	PUNCT
ejpam-6086	28	10	ii	ii	NOUN
ejpam-6086	28	11	)	)	PUNCT
ejpam-6086	28	12	d(x	d(x	PROPN
ejpam-6086	28	13	,	,	PUNCT
ejpam-6086	28	14	y	y	NOUN
ejpam-6086	28	15	)	)	PUNCT
ejpam-6086	28	16	=	=	SYM
ejpam-6086	28	17	d(y	d(y	NOUN
ejpam-6086	28	18	,	,	PUNCT
ejpam-6086	28	19	x	x	NOUN
ejpam-6086	28	20	)	)	PUNCT
ejpam-6086	28	21	for	for	ADP
ejpam-6086	28	22	all	all	DET
ejpam-6086	28	23	x	x	NOUN
ejpam-6086	28	24	,	,	PUNCT
ejpam-6086	28	25	y	y	PROPN
ejpam-6086	28	26	∈	∈	PROPN
ejpam-6086	28	27	u	u	PROPN
ejpam-6086	28	28	,	,	PUNCT
ejpam-6086	28	29	(	(	PUNCT
ejpam-6086	28	30	iii	iii	NOUN
ejpam-6086	28	31	)	)	PUNCT
ejpam-6086	28	32	d(x	d(x	PROPN
ejpam-6086	28	33	,	,	PUNCT
ejpam-6086	28	34	y	y	NOUN
ejpam-6086	28	35	)	)	PUNCT
ejpam-6086	28	36	≤	≤	NOUN
ejpam-6086	28	37	b[d(x	b[d(x	NOUN
ejpam-6086	28	38	,	,	PUNCT
ejpam-6086	28	39	u	u	NOUN
ejpam-6086	28	40	)	)	PUNCT
ejpam-6086	28	41	+	+	CCONJ
ejpam-6086	28	42	d(u	d(u	PROPN
ejpam-6086	28	43	,	,	PUNCT
ejpam-6086	28	44	v	v	NOUN
ejpam-6086	28	45	)	)	PUNCT
ejpam-6086	28	46	+	+	X
ejpam-6086	28	47	d(v	d(v	PROPN
ejpam-6086	28	48	,	,	PUNCT
ejpam-6086	28	49	y	y	NOUN
ejpam-6086	28	50	)	)	PUNCT
ejpam-6086	28	51	]	]	PUNCT
ejpam-6086	28	52	for	for	ADP
ejpam-6086	28	53	all	all	DET
ejpam-6086	28	54	x	x	NOUN
ejpam-6086	28	55	,	,	PUNCT
ejpam-6086	28	56	y	y	PROPN
ejpam-6086	28	57	∈	∈	PROPN
ejpam-6086	28	58	u	u	NOUN
ejpam-6086	28	59	and	and	CCONJ
ejpam-6086	28	60	for	for	ADP
ejpam-6086	28	61	all	all	DET
ejpam-6086	28	62	distinct	distinct	ADJ
ejpam-6086	28	63	points	point	NOUN
ejpam-6086	28	64	u	u	NOUN
ejpam-6086	28	65	,	,	PUNCT
ejpam-6086	28	66	v	v	PROPN
ejpam-6086	28	67	∈	∈	PROPN
ejpam-6086	28	68	u	u	NOUN
ejpam-6086	28	69	\	\	PROPN
ejpam-6086	28	70	{	{	PUNCT
ejpam-6086	28	71	x	x	NOUN
ejpam-6086	28	72	,	,	PUNCT
ejpam-6086	28	73	y	y	PROPN
ejpam-6086	28	74	}	}	PUNCT
ejpam-6086	28	75	.	.	PUNCT
ejpam-6086	29	1	then	then	ADV
ejpam-6086	29	2	(	(	PUNCT
ejpam-6086	29	3	u	u	NOUN
ejpam-6086	29	4	,	,	PUNCT
ejpam-6086	29	5	d	d	PROPN
ejpam-6086	29	6	)	)	PUNCT
ejpam-6086	29	7	is	be	AUX
ejpam-6086	29	8	called	call	VERB
ejpam-6086	29	9	a	a	DET
ejpam-6086	29	10	rectangular	rectangular	ADJ
ejpam-6086	29	11	b−metric	b−metric	ADJ
ejpam-6086	29	12	space	space	NOUN
ejpam-6086	29	13	with	with	ADP
ejpam-6086	29	14	coefficient	coefficient	PROPN
ejpam-6086	29	15	b.	b.	PROPN
ejpam-6086	29	16	lemma	lemma	PROPN
ejpam-6086	29	17	1	1	NUM
ejpam-6086	29	18	.	.	PUNCT
ejpam-6086	30	1	[	[	X
ejpam-6086	30	2	9	9	NUM
ejpam-6086	30	3	]	]	X
ejpam-6086	30	4	let	let	VERB
ejpam-6086	30	5	(	(	PUNCT
ejpam-6086	30	6	u	u	NOUN
ejpam-6086	30	7	,	,	PUNCT
ejpam-6086	30	8	d	d	PROPN
ejpam-6086	30	9	)	)	PUNCT
ejpam-6086	30	10	be	be	AUX
ejpam-6086	30	11	a	a	DET
ejpam-6086	30	12	rectangular	rectangular	ADJ
ejpam-6086	30	13	b−metric	b−metric	ADJ
ejpam-6086	30	14	space	space	NOUN
ejpam-6086	30	15	and	and	CCONJ
ejpam-6086	30	16	{	{	PUNCT
ejpam-6086	30	17	xn	xn	NOUN
ejpam-6086	30	18	}	}	PUNCT
ejpam-6086	30	19	be	be	AUX
ejpam-6086	30	20	a	a	DET
ejpam-6086	30	21	sequence	sequence	NOUN
ejpam-6086	30	22	in	in	ADP
ejpam-6086	30	23	u	u	NOUN
ejpam-6086	30	24	such	such	ADJ
ejpam-6086	30	25	that	that	SCONJ
ejpam-6086	30	26	lim	lim	PROPN
ejpam-6086	30	27	n→+∞	n→+∞	VERB
ejpam-6086	30	28	d(xn	d(xn	PROPN
ejpam-6086	30	29	,	,	PUNCT
ejpam-6086	30	30	xn+1	xn+1	NUM
ejpam-6086	30	31	)	)	PUNCT
ejpam-6086	31	1	=	=	VERB
ejpam-6086	31	2	lim	lim	PROPN
ejpam-6086	31	3	n→+∞	n→+∞	VERB
ejpam-6086	31	4	d(xn	d(xn	PROPN
ejpam-6086	31	5	,	,	PUNCT
ejpam-6086	31	6	xn+2	xn+2	NUM
ejpam-6086	31	7	)	)	PUNCT
ejpam-6086	31	8	=	=	SYM
ejpam-6086	32	1	0	0	X
ejpam-6086	32	2	.	.	PUNCT
ejpam-6086	33	1	if	if	SCONJ
ejpam-6086	33	2	{	{	PUNCT
ejpam-6086	33	3	xn	xn	X
ejpam-6086	33	4	}	}	PUNCT
ejpam-6086	33	5	is	be	AUX
ejpam-6086	33	6	not	not	PART
ejpam-6086	33	7	a	a	DET
ejpam-6086	33	8	cauchy	cauchy	ADJ
ejpam-6086	33	9	sequence	sequence	NOUN
ejpam-6086	33	10	then	then	ADV
ejpam-6086	33	11	there	there	PRON
ejpam-6086	33	12	exist	exist	VERB
ejpam-6086	33	13	ε	ε	PROPN
ejpam-6086	33	14	>	>	PUNCT
ejpam-6086	33	15	0	0	NUM
ejpam-6086	34	1	and	and	CCONJ
ejpam-6086	34	2	two	two	NUM
ejpam-6086	34	3	sequences	sequence	NOUN
ejpam-6086	34	4	{	{	PUNCT
ejpam-6086	34	5	mk	mk	PROPN
ejpam-6086	34	6	}	}	PUNCT
ejpam-6086	34	7	and	and	CCONJ
ejpam-6086	34	8	{	{	PUNCT
ejpam-6086	34	9	nk	nk	NOUN
ejpam-6086	34	10	}	}	PUNCT
ejpam-6086	34	11	of	of	ADP
ejpam-6086	34	12	positive	positive	ADJ
ejpam-6086	34	13	integers	integer	NOUN
ejpam-6086	34	14	such	such	ADJ
ejpam-6086	34	15	that	that	SCONJ
ejpam-6086	34	16	ε	ε	PROPN
ejpam-6086	34	17	≤	≤	PROPN
ejpam-6086	34	18	lim	lim	PROPN
ejpam-6086	34	19	k→+∞	k→+∞	PROPN
ejpam-6086	34	20	inf	inf	PROPN
ejpam-6086	34	21	d(xmk	d(xmk	PROPN
ejpam-6086	34	22	,	,	PUNCT
ejpam-6086	34	23	xnk	xnk	PROPN
ejpam-6086	34	24	)	)	PUNCT
ejpam-6086	34	25	≤	≤	PROPN
ejpam-6086	35	1	lim	lim	PROPN
ejpam-6086	35	2	k→+∞	k→+∞	PROPN
ejpam-6086	35	3	sup	sup	NOUN
ejpam-6086	35	4	d(xmk	d(xmk	NOUN
ejpam-6086	35	5	,	,	PUNCT
ejpam-6086	35	6	xnk	xnk	PROPN
ejpam-6086	35	7	)	)	PUNCT
ejpam-6086	35	8	≤	≤	PROPN
ejpam-6086	35	9	bε	bε	NOUN
ejpam-6086	35	10	,	,	PUNCT
ejpam-6086	35	11	ε	ε	PROPN
ejpam-6086	35	12	≤	≤	PROPN
ejpam-6086	35	13	lim	lim	PROPN
ejpam-6086	35	14	k→+∞	k→+∞	PROPN
ejpam-6086	35	15	inf	inf	PROPN
ejpam-6086	35	16	d(xmk	d(xmk	PROPN
ejpam-6086	35	17	,	,	PUNCT
ejpam-6086	35	18	xmk+1	xmk+1	X
ejpam-6086	35	19	)	)	PUNCT
ejpam-6086	35	20	≤	≤	NOUN
ejpam-6086	35	21	lim	lim	PROPN
ejpam-6086	35	22	k→+∞	k→+∞	PROPN
ejpam-6086	35	23	sup	sup	NOUN
ejpam-6086	35	24	d(xnk	d(xnk	NOUN
ejpam-6086	35	25	,	,	PUNCT
ejpam-6086	35	26	xmk+1	xmk+1	X
ejpam-6086	35	27	)	)	PUNCT
ejpam-6086	35	28	≤	≤	NUM
ejpam-6086	35	29	bε	bε	NOUN
ejpam-6086	35	30	,	,	PUNCT
ejpam-6086	35	31	ε	ε	PROPN
ejpam-6086	35	32	≤	≤	PROPN
ejpam-6086	35	33	lim	lim	PROPN
ejpam-6086	36	1	k→+∞	k→+∞	PROPN
ejpam-6086	36	2	inf	inf	PROPN
ejpam-6086	36	3	d(xmk	d(xmk	PROPN
ejpam-6086	36	4	,	,	PUNCT
ejpam-6086	36	5	xnk+1	xnk+1	PROPN
ejpam-6086	36	6	)	)	PUNCT
ejpam-6086	36	7	≤	≤	NOUN
ejpam-6086	37	1	lim	lim	PROPN
ejpam-6086	37	2	k→+∞	k→+∞	PROPN
ejpam-6086	37	3	sup	sup	NOUN
ejpam-6086	37	4	d(xmk	d(xmk	NOUN
ejpam-6086	37	5	,	,	PUNCT
ejpam-6086	37	6	xnk+1	xnk+1	X
ejpam-6086	37	7	)	)	PUNCT
ejpam-6086	37	8	≤	≤	NOUN
ejpam-6086	37	9	bε	bε	NOUN
ejpam-6086	37	10	,	,	PUNCT
ejpam-6086	37	11	ε	ε	PROPN
ejpam-6086	37	12	b	b	PROPN
ejpam-6086	37	13	≤	≤	PROPN
ejpam-6086	37	14	lim	lim	PROPN
ejpam-6086	37	15	k→+∞	k→+∞	PROPN
ejpam-6086	37	16	inf	inf	PROPN
ejpam-6086	37	17	d(xmk+1	d(xmk+1	PROPN
ejpam-6086	37	18	,	,	PUNCT
ejpam-6086	37	19	xnk+1	xnk+1	PROPN
ejpam-6086	37	20	)	)	PUNCT
ejpam-6086	37	21	≤	≤	NOUN
ejpam-6086	37	22	lim	lim	PROPN
ejpam-6086	37	23	k→+∞	k→+∞	PROPN
ejpam-6086	37	24	sup	sup	PROPN
ejpam-6086	37	25	d(xmk+1	d(xmk+1	NOUN
ejpam-6086	37	26	,	,	PUNCT
ejpam-6086	37	27	xnk+1	xnk+1	PROPN
ejpam-6086	37	28	)	)	PUNCT
ejpam-6086	38	1	≤	≤	NOUN
ejpam-6086	38	2	b2ε	b2ε	NOUN
ejpam-6086	38	3	.	.	PUNCT
ejpam-6086	39	1	zheng	zheng	PROPN
ejpam-6086	39	2	et	et	PROPN
ejpam-6086	39	3	al	al	PROPN
ejpam-6086	39	4	.	.	PUNCT
ejpam-6086	40	1	[	[	X
ejpam-6086	40	2	12	12	NUM
ejpam-6086	40	3	]	]	PUNCT
ejpam-6086	40	4	introduced	introduce	VERB
ejpam-6086	40	5	a	a	DET
ejpam-6086	40	6	new	new	ADJ
ejpam-6086	40	7	type	type	NOUN
ejpam-6086	40	8	of	of	ADP
ejpam-6086	40	9	contractions	contraction	NOUN
ejpam-6086	40	10	called	call	VERB
ejpam-6086	40	11	θ	θ	NOUN
ejpam-6086	40	12	−	−	PUNCT
ejpam-6086	40	13	ϕ−contractions	ϕ−contraction	NOUN
ejpam-6086	40	14	in	in	ADP
ejpam-6086	40	15	metric	metric	ADJ
ejpam-6086	40	16	spaces	space	NOUN
ejpam-6086	40	17	and	and	CCONJ
ejpam-6086	40	18	proved	prove	VERB
ejpam-6086	40	19	a	a	DET
ejpam-6086	40	20	new	new	ADJ
ejpam-6086	40	21	fixed	fix	VERB
ejpam-6086	40	22	point	point	NOUN
ejpam-6086	40	23	theorems	theorem	NOUN
ejpam-6086	40	24	for	for	ADP
ejpam-6086	40	25	such	such	ADJ
ejpam-6086	40	26	mapping	mapping	NOUN
ejpam-6086	40	27	.	.	PUNCT
ejpam-6086	41	1	definition	definition	NOUN
ejpam-6086	41	2	2	2	NUM
ejpam-6086	41	3	.	.	PUNCT
ejpam-6086	42	1	[	[	X
ejpam-6086	42	2	6	6	NUM
ejpam-6086	42	3	]	]	PUNCT
ejpam-6086	42	4	we	we	PRON
ejpam-6086	42	5	denote	denote	VERB
ejpam-6086	42	6	by	by	ADP
ejpam-6086	42	7	θ	θ	PROPN
ejpam-6086	42	8	the	the	DET
ejpam-6086	42	9	set	set	NOUN
ejpam-6086	42	10	of	of	ADP
ejpam-6086	42	11	functions	function	NOUN
ejpam-6086	42	12	θ	θ	PROPN
ejpam-6086	42	13	:	:	PUNCT
ejpam-6086	42	14	(	(	PUNCT
ejpam-6086	42	15	0,+∞	0,+∞	NUM
ejpam-6086	42	16	)	)	PUNCT
ejpam-6086	42	17	→	→	PUNCT
ejpam-6086	43	1	[	[	X
ejpam-6086	43	2	1,+∞	1,+∞	NUM
ejpam-6086	43	3	)	)	PUNCT
ejpam-6086	43	4	satisfying	satisfy	VERB
ejpam-6086	43	5	the	the	DET
ejpam-6086	43	6	following	follow	VERB
ejpam-6086	43	7	conditions	condition	NOUN
ejpam-6086	43	8	:	:	PUNCT
ejpam-6086	43	9	1	1	X
ejpam-6086	43	10	)	)	PUNCT
ejpam-6086	43	11	θ	θ	PROPN
ejpam-6086	43	12	is	be	AUX
ejpam-6086	43	13	increasing	increase	VERB
ejpam-6086	43	14	,	,	PUNCT
ejpam-6086	43	15	2	2	NUM
ejpam-6086	43	16	)	)	PUNCT
ejpam-6086	43	17	for	for	ADP
ejpam-6086	43	18	each	each	DET
ejpam-6086	43	19	sequence	sequence	NOUN
ejpam-6086	43	20	{	{	PUNCT
ejpam-6086	43	21	xn	xn	NOUN
ejpam-6086	43	22	}	}	PUNCT
ejpam-6086	43	23	∈	∈	PROPN
ejpam-6086	43	24	(	(	PUNCT
ejpam-6086	43	25	0,+∞	0,+∞	NUM
ejpam-6086	43	26	)	)	PUNCT
ejpam-6086	43	27	,	,	PUNCT
ejpam-6086	43	28	lim	lim	PROPN
ejpam-6086	43	29	n→+∞	n→+∞	VERB
ejpam-6086	43	30	θ(xn	θ(xn	ADV
ejpam-6086	43	31	)	)	PUNCT
ejpam-6086	43	32	=	=	SYM
ejpam-6086	43	33	1	1	NUM
ejpam-6086	43	34	if	if	SCONJ
ejpam-6086	43	35	and	and	CCONJ
ejpam-6086	43	36	only	only	ADV
ejpam-6086	43	37	if	if	SCONJ
ejpam-6086	43	38	lim	lim	PROPN
ejpam-6086	43	39	n→+∞	n→+∞	VERB
ejpam-6086	43	40	xn	xn	PUNCT
ejpam-6086	44	1	=	=	SYM
ejpam-6086	44	2	0	0	NUM
ejpam-6086	44	3	,	,	PUNCT
ejpam-6086	44	4	3	3	X
ejpam-6086	44	5	)	)	PUNCT
ejpam-6086	44	6	θ	θ	NOUN
ejpam-6086	44	7	is	be	AUX
ejpam-6086	44	8	continuous	continuous	ADJ
ejpam-6086	44	9	on	on	ADP
ejpam-6086	44	10	(	(	PUNCT
ejpam-6086	44	11	0,+∞	0,+∞	NUM
ejpam-6086	44	12	)	)	PUNCT
ejpam-6086	44	13	.	.	PUNCT
ejpam-6086	45	1	definition	definition	NOUN
ejpam-6086	45	2	3	3	NUM
ejpam-6086	45	3	.	.	PUNCT
ejpam-6086	46	1	[	[	X
ejpam-6086	46	2	13	13	NUM
ejpam-6086	46	3	]	]	PUNCT
ejpam-6086	46	4	we	we	PRON
ejpam-6086	46	5	denote	denote	VERB
ejpam-6086	46	6	by	by	ADP
ejpam-6086	46	7	φ	φ	PROPN
ejpam-6086	46	8	the	the	DET
ejpam-6086	46	9	set	set	NOUN
ejpam-6086	46	10	of	of	ADP
ejpam-6086	46	11	functions	function	NOUN
ejpam-6086	46	12	ϕ	ϕ	NOUN
ejpam-6086	46	13	:	:	PUNCT
ejpam-6086	47	1	[	[	X
ejpam-6086	47	2	1,+∞	1,+∞	NUM
ejpam-6086	47	3	)	)	PUNCT
ejpam-6086	47	4	→	→	PUNCT
ejpam-6086	48	1	[	[	X
ejpam-6086	48	2	1,+∞	1,+∞	NUM
ejpam-6086	48	3	)	)	PUNCT
ejpam-6086	48	4	satisfying	satisfy	VERB
ejpam-6086	48	5	the	the	DET
ejpam-6086	48	6	following	follow	VERB
ejpam-6086	48	7	conditions	condition	NOUN
ejpam-6086	48	8	:	:	PUNCT
ejpam-6086	48	9	h.	h.	PROPN
ejpam-6086	48	10	massit	massit	PROPN
ejpam-6086	48	11	et	et	PROPN
ejpam-6086	48	12	al	al	PROPN
ejpam-6086	48	13	.	.	PUNCT
ejpam-6086	48	14	/	/	SYM
ejpam-6086	48	15	eur	eur	PROPN
ejpam-6086	48	16	.	.	PUNCT
ejpam-6086	49	1	j.	j.	PROPN
ejpam-6086	49	2	pure	pure	PROPN
ejpam-6086	49	3	appl	appl	PROPN
ejpam-6086	49	4	.	.	PROPN
ejpam-6086	49	5	math	math	PROPN
ejpam-6086	49	6	,	,	PUNCT
ejpam-6086	49	7	18	18	NUM
ejpam-6086	49	8	(	(	PUNCT
ejpam-6086	49	9	2	2	NUM
ejpam-6086	49	10	)	)	PUNCT
ejpam-6086	49	11	(	(	PUNCT
ejpam-6086	49	12	2025	2025	NUM
ejpam-6086	49	13	)	)	PUNCT
ejpam-6086	49	14	,	,	PUNCT
ejpam-6086	49	15	6086	6086	NUM
ejpam-6086	49	16	3	3	NUM
ejpam-6086	49	17	of	of	ADP
ejpam-6086	49	18	19	19	NUM
ejpam-6086	49	19	1	1	NUM
ejpam-6086	49	20	)	)	PUNCT
ejpam-6086	49	21	ϕ	ϕ	NOUN
ejpam-6086	49	22	is	be	AUX
ejpam-6086	49	23	nondecreasing	nondecrease	VERB
ejpam-6086	49	24	,	,	PUNCT
ejpam-6086	49	25	2	2	NUM
ejpam-6086	49	26	)	)	PUNCT
ejpam-6086	49	27	for	for	ADP
ejpam-6086	49	28	each	each	DET
ejpam-6086	49	29	λ	λ	PROPN
ejpam-6086	49	30	>	>	X
ejpam-6086	49	31	1	1	NUM
ejpam-6086	49	32	,	,	PUNCT
ejpam-6086	49	33	lim	lim	PROPN
ejpam-6086	49	34	n→+∞	n→+∞	VERB
ejpam-6086	49	35	ϕn(λ	ϕn(λ	X
ejpam-6086	49	36	)	)	PUNCT
ejpam-6086	49	37	=	=	SYM
ejpam-6086	50	1	1	1	NUM
ejpam-6086	50	2	,	,	PUNCT
ejpam-6086	50	3	3	3	X
ejpam-6086	50	4	)	)	PUNCT
ejpam-6086	50	5	ϕ	ϕ	NOUN
ejpam-6086	50	6	is	be	AUX
ejpam-6086	50	7	continuous	continuous	ADJ
ejpam-6086	50	8	on	on	ADP
ejpam-6086	50	9	[	[	X
ejpam-6086	50	10	1,+∞	1,+∞	NUM
ejpam-6086	50	11	)	)	PUNCT
ejpam-6086	50	12	.	.	PUNCT
ejpam-6086	51	1	lemma	lemma	PROPN
ejpam-6086	51	2	2	2	NUM
ejpam-6086	51	3	.	.	PUNCT
ejpam-6086	52	1	[	[	X
ejpam-6086	52	2	13	13	NUM
ejpam-6086	52	3	]	]	X
ejpam-6086	52	4	if	if	SCONJ
ejpam-6086	52	5	ϕ	ϕ	PROPN
ejpam-6086	52	6	∈	∈	PROPN
ejpam-6086	52	7	φ	φ	PROPN
ejpam-6086	52	8	,	,	PUNCT
ejpam-6086	52	9	then	then	ADV
ejpam-6086	52	10	ϕ(λ	ϕ(λ	X
ejpam-6086	52	11	)	)	PUNCT
ejpam-6086	53	1	<	<	X
ejpam-6086	53	2	λ	λ	X
ejpam-6086	53	3	for	for	ADP
ejpam-6086	53	4	all	all	DET
ejpam-6086	53	5	λ	λ	PROPN
ejpam-6086	53	6	∈	∈	PROPN
ejpam-6086	53	7	(	(	PUNCT
ejpam-6086	53	8	1,+∞	1,+∞	NUM
ejpam-6086	53	9	)	)	PUNCT
ejpam-6086	53	10	and	and	CCONJ
ejpam-6086	53	11	ϕ(1	ϕ(1	PROPN
ejpam-6086	53	12	)	)	PUNCT
ejpam-6086	53	13	=	=	SYM
ejpam-6086	54	1	1	1	X
ejpam-6086	54	2	.	.	X
ejpam-6086	54	3	definition	definition	NOUN
ejpam-6086	54	4	4	4	NUM
ejpam-6086	54	5	.	.	PUNCT
ejpam-6086	55	1	[	[	X
ejpam-6086	55	2	18	18	NUM
ejpam-6086	55	3	]	]	X
ejpam-6086	55	4	let	let	VERB
ejpam-6086	55	5	(	(	PUNCT
ejpam-6086	55	6	u	u	NOUN
ejpam-6086	55	7	,	,	PUNCT
ejpam-6086	55	8	d	d	PROPN
ejpam-6086	55	9	)	)	PUNCT
ejpam-6086	55	10	be	be	AUX
ejpam-6086	55	11	a	a	DET
ejpam-6086	55	12	rectangular	rectangular	ADJ
ejpam-6086	55	13	b−metric	b−metric	ADJ
ejpam-6086	55	14	space	space	NOUN
ejpam-6086	55	15	.	.	PUNCT
ejpam-6086	56	1	let	let	VERB
ejpam-6086	56	2	t	t	NOUN
ejpam-6086	56	3	:	:	PUNCT
ejpam-6086	56	4	u	u	PROPN
ejpam-6086	56	5	→	→	SYM
ejpam-6086	56	6	u	u	PROPN
ejpam-6086	56	7	and	and	CCONJ
ejpam-6086	56	8	α	α	NOUN
ejpam-6086	56	9	:	:	PUNCT
ejpam-6086	56	10	u	u	NOUN
ejpam-6086	56	11	×	×	PROPN
ejpam-6086	56	12	u	u	X
ejpam-6086	56	13	→	→	PUNCT
ejpam-6086	56	14	[	[	X
ejpam-6086	56	15	0,+∞	0,+∞	NUM
ejpam-6086	56	16	)	)	PUNCT
ejpam-6086	56	17	be	be	VERB
ejpam-6086	56	18	two	two	NUM
ejpam-6086	56	19	mappings	mapping	NOUN
ejpam-6086	56	20	.	.	PUNCT
ejpam-6086	57	1	a	a	DET
ejpam-6086	57	2	mapping	mapping	NOUN
ejpam-6086	57	3	t	t	NOUN
ejpam-6086	57	4	is	be	AUX
ejpam-6086	57	5	said	say	VERB
ejpam-6086	57	6	to	to	PART
ejpam-6086	57	7	be	be	AUX
ejpam-6086	57	8	α−admissible	α−admissible	ADJ
ejpam-6086	57	9	if	if	SCONJ
ejpam-6086	57	10	α(x	α(x	PROPN
ejpam-6086	57	11	,	,	PUNCT
ejpam-6086	57	12	y	y	PROPN
ejpam-6086	57	13	)	)	PUNCT
ejpam-6086	57	14	≥	≥	NOUN
ejpam-6086	57	15	1	1	NUM
ejpam-6086	57	16	implies	imply	VERB
ejpam-6086	57	17	α(tx	α(tx	PROPN
ejpam-6086	57	18	,	,	PUNCT
ejpam-6086	57	19	ty	ty	NOUN
ejpam-6086	57	20	)	)	PUNCT
ejpam-6086	57	21	≥	≥	NOUN
ejpam-6086	57	22	1	1	NUM
ejpam-6086	57	23	.	.	PUNCT
ejpam-6086	58	1	definition	definition	NOUN
ejpam-6086	58	2	5	5	NUM
ejpam-6086	58	3	.	.	PUNCT
ejpam-6086	59	1	[	[	X
ejpam-6086	59	2	19	19	NUM
ejpam-6086	59	3	]	]	PUNCT
ejpam-6086	59	4	let	let	VERB
ejpam-6086	59	5	t	t	NOUN
ejpam-6086	59	6	:	:	PUNCT
ejpam-6086	59	7	u	u	PROPN
ejpam-6086	59	8	→	→	SYM
ejpam-6086	59	9	u	u	PROPN
ejpam-6086	59	10	and	and	CCONJ
ejpam-6086	59	11	α	α	NOUN
ejpam-6086	59	12	:	:	PUNCT
ejpam-6086	59	13	u	u	NOUN
ejpam-6086	59	14	×u	×u	NUM
ejpam-6086	59	15	→	→	PUNCT
ejpam-6086	59	16	[	[	X
ejpam-6086	59	17	0,+∞	0,+∞	NUM
ejpam-6086	59	18	)	)	PUNCT
ejpam-6086	59	19	be	be	VERB
ejpam-6086	59	20	two	two	NUM
ejpam-6086	59	21	mappings	mapping	NOUN
ejpam-6086	59	22	such	such	ADJ
ejpam-6086	59	23	that	that	SCONJ
ejpam-6086	59	24	t	t	PROPN
ejpam-6086	59	25	is	be	AUX
ejpam-6086	59	26	α−admissible	α−admissible	PROPN
ejpam-6086	59	27	.	.	PUNCT
ejpam-6086	60	1	t	t	PROPN
ejpam-6086	60	2	is	be	AUX
ejpam-6086	60	3	said	say	VERB
ejpam-6086	60	4	to	to	PART
ejpam-6086	60	5	be	be	AUX
ejpam-6086	60	6	triangular	triangular	NOUN
ejpam-6086	60	7	α−admissible	α−admissible	ADJ
ejpam-6086	60	8	if	if	SCONJ
ejpam-6086	60	9	α(x	α(x	PROPN
ejpam-6086	60	10	,	,	PUNCT
ejpam-6086	60	11	y	y	PROPN
ejpam-6086	60	12	)	)	PUNCT
ejpam-6086	60	13	≥	≥	NOUN
ejpam-6086	60	14	1	1	NUM
ejpam-6086	60	15	and	and	CCONJ
ejpam-6086	60	16	α(y	α(y	NOUN
ejpam-6086	60	17	,	,	PUNCT
ejpam-6086	60	18	z	z	NOUN
ejpam-6086	60	19	)	)	PUNCT
ejpam-6086	60	20	≥	≥	NOUN
ejpam-6086	60	21	1	1	NUM
ejpam-6086	60	22	implies	imply	VERB
ejpam-6086	60	23	α(x	α(x	NOUN
ejpam-6086	60	24	,	,	PUNCT
ejpam-6086	60	25	z	z	NOUN
ejpam-6086	60	26	)	)	PUNCT
ejpam-6086	60	27	≥	≥	NOUN
ejpam-6086	60	28	1	1	NUM
ejpam-6086	60	29	.	.	PUNCT
ejpam-6086	61	1	definition	definition	NOUN
ejpam-6086	61	2	6	6	NUM
ejpam-6086	61	3	.	.	PUNCT
ejpam-6086	62	1	[	[	X
ejpam-6086	62	2	11	11	NUM
ejpam-6086	62	3	]	]	X
ejpam-6086	62	4	let	let	VERB
ejpam-6086	62	5	(	(	PUNCT
ejpam-6086	62	6	u	u	NOUN
ejpam-6086	62	7	,	,	PUNCT
ejpam-6086	62	8	d	d	PROPN
ejpam-6086	62	9	)	)	PUNCT
ejpam-6086	62	10	be	be	AUX
ejpam-6086	62	11	a	a	DET
ejpam-6086	62	12	rectangular	rectangular	ADJ
ejpam-6086	62	13	b−metric	b−metric	ADJ
ejpam-6086	62	14	space	space	NOUN
ejpam-6086	62	15	with	with	ADP
ejpam-6086	62	16	b	b	PROPN
ejpam-6086	62	17	>	>	SYM
ejpam-6086	62	18	1	1	NUM
ejpam-6086	62	19	and	and	CCONJ
ejpam-6086	62	20	t	t	PROPN
ejpam-6086	62	21	:	:	PUNCT
ejpam-6086	62	22	u	u	X
ejpam-6086	62	23	→	→	SYM
ejpam-6086	62	24	u	u	X
ejpam-6086	62	25	be	be	VERB
ejpam-6086	62	26	a	a	DET
ejpam-6086	62	27	mapping	mapping	NOUN
ejpam-6086	62	28	.	.	PUNCT
ejpam-6086	63	1	(	(	PUNCT
ejpam-6086	63	2	1	1	X
ejpam-6086	63	3	)	)	PUNCT
ejpam-6086	63	4	t	t	PROPN
ejpam-6086	63	5	is	be	AUX
ejpam-6086	63	6	called	call	VERB
ejpam-6086	63	7	θ	θ	NOUN
ejpam-6086	63	8	−	−	PROPN
ejpam-6086	64	1	ϕ−contraction	ϕ−contraction	NOUN
ejpam-6086	64	2	if	if	SCONJ
ejpam-6086	64	3	there	there	PRON
ejpam-6086	64	4	are	be	VERB
ejpam-6086	64	5	θ	θ	PROPN
ejpam-6086	64	6	∈	∈	PROPN
ejpam-6086	64	7	θ	θ	PROPN
ejpam-6086	64	8	and	and	CCONJ
ejpam-6086	64	9	ϕ	ϕ	PROPN
ejpam-6086	64	10	∈	∈	PROPN
ejpam-6086	64	11	φ	φ	NOUN
ejpam-6086	64	12	such	such	ADJ
ejpam-6086	64	13	that	that	SCONJ
ejpam-6086	64	14	d(tx	d(tx	PROPN
ejpam-6086	64	15	,	,	PUNCT
ejpam-6086	64	16	ty	ty	NOUN
ejpam-6086	64	17	)	)	PUNCT
ejpam-6086	64	18	>	>	X
ejpam-6086	64	19	0	0	NUM
ejpam-6086	64	20	implies	imply	VERB
ejpam-6086	64	21	θ[b2d(tx	θ[b2d(tx	PROPN
ejpam-6086	64	22	,	,	PUNCT
ejpam-6086	64	23	ty	ty	NOUN
ejpam-6086	64	24	)	)	PUNCT
ejpam-6086	64	25	]	]	PUNCT
ejpam-6086	65	1	≤	≤	NUM
ejpam-6086	65	2	ϕ[θ(m(x	ϕ[θ(m(x	PROPN
ejpam-6086	65	3	,	,	PUNCT
ejpam-6086	65	4	y	y	NOUN
ejpam-6086	65	5	)	)	PUNCT
ejpam-6086	65	6	)	)	PUNCT
ejpam-6086	66	1	]	]	PUNCT
ejpam-6086	66	2	,	,	PUNCT
ejpam-6086	66	3	(	(	PUNCT
ejpam-6086	66	4	1	1	X
ejpam-6086	66	5	)	)	PUNCT
ejpam-6086	66	6	where	where	SCONJ
ejpam-6086	66	7	m(x	m(x	PROPN
ejpam-6086	66	8	,	,	PUNCT
ejpam-6086	66	9	y	y	NOUN
ejpam-6086	66	10	)	)	PUNCT
ejpam-6086	66	11	=	=	PUNCT
ejpam-6086	66	12	max{d(x	max{d(x	PROPN
ejpam-6086	66	13	,	,	PUNCT
ejpam-6086	66	14	y	y	NOUN
ejpam-6086	66	15	)	)	PUNCT
ejpam-6086	66	16	,	,	PUNCT
ejpam-6086	66	17	d(x	d(x	PROPN
ejpam-6086	66	18	,	,	PUNCT
ejpam-6086	66	19	tx	tx	PROPN
ejpam-6086	66	20	)	)	PUNCT
ejpam-6086	66	21	,	,	PUNCT
ejpam-6086	66	22	d(y	d(y	PROPN
ejpam-6086	66	23	,	,	PUNCT
ejpam-6086	66	24	ty	ty	NOUN
ejpam-6086	66	25	)	)	PUNCT
ejpam-6086	66	26	,	,	PUNCT
ejpam-6086	66	27	d(y	d(y	PROPN
ejpam-6086	66	28	,	,	PUNCT
ejpam-6086	66	29	tx	tx	PROPN
ejpam-6086	66	30	)	)	PUNCT
ejpam-6086	66	31	}	}	PUNCT
ejpam-6086	66	32	.	.	PUNCT
ejpam-6086	67	1	(	(	PUNCT
ejpam-6086	67	2	2	2	X
ejpam-6086	67	3	)	)	PUNCT
ejpam-6086	67	4	t	t	PROPN
ejpam-6086	67	5	is	be	AUX
ejpam-6086	67	6	called	call	VERB
ejpam-6086	67	7	θ	θ	PROPN
ejpam-6086	67	8	−	−	PROPN
ejpam-6086	67	9	ϕ−	ϕ−	PROPN
ejpam-6086	67	10	kannan	kannan	PROPN
ejpam-6086	67	11	-	-	PUNCT
ejpam-6086	67	12	type	type	NOUN
ejpam-6086	67	13	contraction	contraction	NOUN
ejpam-6086	67	14	if	if	SCONJ
ejpam-6086	67	15	there	there	PRON
ejpam-6086	67	16	are	be	VERB
ejpam-6086	67	17	θ	θ	PROPN
ejpam-6086	67	18	∈	∈	PROPN
ejpam-6086	67	19	θ	θ	PROPN
ejpam-6086	67	20	and	and	CCONJ
ejpam-6086	67	21	ϕ	ϕ	PROPN
ejpam-6086	67	22	∈	∈	PROPN
ejpam-6086	67	23	φ	φ	NOUN
ejpam-6086	67	24	such	such	ADJ
ejpam-6086	67	25	that	that	SCONJ
ejpam-6086	67	26	d(tx	d(tx	PROPN
ejpam-6086	67	27	,	,	PUNCT
ejpam-6086	67	28	ty	ty	NOUN
ejpam-6086	67	29	)	)	PUNCT
ejpam-6086	67	30	>	>	X
ejpam-6086	67	31	0	0	NUM
ejpam-6086	67	32	implies	imply	VERB
ejpam-6086	67	33	θ[b2d(tx	θ[b2d(tx	PROPN
ejpam-6086	67	34	,	,	PUNCT
ejpam-6086	67	35	ty	ty	NOUN
ejpam-6086	67	36	)	)	PUNCT
ejpam-6086	67	37	]	]	PUNCT
ejpam-6086	68	1	≤	≤	NUM
ejpam-6086	68	2	ϕ	ϕ	X
ejpam-6086	68	3	[	[	PUNCT
ejpam-6086	68	4	θ	θ	X
ejpam-6086	68	5	(	(	PUNCT
ejpam-6086	68	6	d(x	d(x	PROPN
ejpam-6086	68	7	,	,	PUNCT
ejpam-6086	68	8	tx	tx	PROPN
ejpam-6086	68	9	)	)	PUNCT
ejpam-6086	68	10	+	+	CCONJ
ejpam-6086	68	11	d(y	d(y	PROPN
ejpam-6086	68	12	,	,	PUNCT
ejpam-6086	68	13	ty	ty	NOUN
ejpam-6086	68	14	)	)	PUNCT
ejpam-6086	68	15	2	2	NUM
ejpam-6086	68	16	)	)	PUNCT
ejpam-6086	68	17	]	]	PUNCT
ejpam-6086	68	18	.	.	PUNCT
ejpam-6086	69	1	(	(	PUNCT
ejpam-6086	69	2	2	2	X
ejpam-6086	69	3	)	)	PUNCT
ejpam-6086	69	4	(	(	PUNCT
ejpam-6086	69	5	3	3	X
ejpam-6086	69	6	)	)	PUNCT
ejpam-6086	69	7	t	t	PROPN
ejpam-6086	69	8	is	be	AUX
ejpam-6086	69	9	called	call	VERB
ejpam-6086	69	10	θ	θ	PROPN
ejpam-6086	69	11	−	−	NOUN
ejpam-6086	69	12	ϕ−reich	ϕ−reich	NOUN
ejpam-6086	69	13	-	-	PUNCT
ejpam-6086	69	14	type	type	NOUN
ejpam-6086	69	15	contraction	contraction	NOUN
ejpam-6086	69	16	if	if	SCONJ
ejpam-6086	69	17	there	there	PRON
ejpam-6086	69	18	are	be	VERB
ejpam-6086	69	19	θ	θ	PROPN
ejpam-6086	69	20	∈	∈	PROPN
ejpam-6086	69	21	θ	θ	PROPN
ejpam-6086	69	22	and	and	CCONJ
ejpam-6086	69	23	ϕ	ϕ	PROPN
ejpam-6086	69	24	∈	∈	PROPN
ejpam-6086	69	25	φ	φ	NOUN
ejpam-6086	69	26	such	such	ADJ
ejpam-6086	69	27	that	that	SCONJ
ejpam-6086	69	28	d(tx	d(tx	PROPN
ejpam-6086	69	29	,	,	PUNCT
ejpam-6086	69	30	ty	ty	NOUN
ejpam-6086	69	31	)	)	PUNCT
ejpam-6086	69	32	>	>	X
ejpam-6086	69	33	0	0	NUM
ejpam-6086	69	34	implies	imply	VERB
ejpam-6086	69	35	θ[b2d(tx	θ[b2d(tx	PROPN
ejpam-6086	69	36	,	,	PUNCT
ejpam-6086	69	37	ty	ty	NOUN
ejpam-6086	69	38	)	)	PUNCT
ejpam-6086	69	39	]	]	PUNCT
ejpam-6086	70	1	≤	≤	NUM
ejpam-6086	70	2	ϕ	ϕ	X
ejpam-6086	70	3	[	[	PUNCT
ejpam-6086	70	4	θ	θ	X
ejpam-6086	70	5	(	(	PUNCT
ejpam-6086	70	6	d(x	d(x	PROPN
ejpam-6086	70	7	,	,	PUNCT
ejpam-6086	70	8	y	y	NOUN
ejpam-6086	70	9	)	)	PUNCT
ejpam-6086	70	10	+	+	CCONJ
ejpam-6086	70	11	d(x	d(x	PROPN
ejpam-6086	70	12	,	,	PUNCT
ejpam-6086	70	13	tx	tx	PROPN
ejpam-6086	70	14	)	)	PUNCT
ejpam-6086	71	1	+	+	CCONJ
ejpam-6086	71	2	d(y	d(y	PROPN
ejpam-6086	71	3	,	,	PUNCT
ejpam-6086	71	4	ty	ty	NOUN
ejpam-6086	71	5	)	)	PUNCT
ejpam-6086	71	6	3	3	NUM
ejpam-6086	71	7	)	)	PUNCT
ejpam-6086	71	8	]	]	PUNCT
ejpam-6086	71	9	.	.	PUNCT
ejpam-6086	72	1	(	(	PUNCT
ejpam-6086	72	2	3	3	X
ejpam-6086	72	3	)	)	PUNCT
ejpam-6086	72	4	kari	kari	X
ejpam-6086	72	5	et	et	PROPN
ejpam-6086	72	6	al	al	PROPN
ejpam-6086	72	7	.	.	PUNCT
ejpam-6086	73	1	[	[	X
ejpam-6086	73	2	11	11	NUM
ejpam-6086	73	3	]	]	PUNCT
ejpam-6086	73	4	recently	recently	ADV
ejpam-6086	73	5	obtained	obtain	VERB
ejpam-6086	73	6	the	the	DET
ejpam-6086	73	7	following	following	ADJ
ejpam-6086	73	8	result	result	NOUN
ejpam-6086	73	9	.	.	PUNCT
ejpam-6086	74	1	theorem	theorem	NOUN
ejpam-6086	74	2	1	1	NUM
ejpam-6086	74	3	.	.	PUNCT
ejpam-6086	75	1	[	[	X
ejpam-6086	75	2	11	11	NUM
ejpam-6086	75	3	]	]	X
ejpam-6086	75	4	let	let	VERB
ejpam-6086	75	5	(	(	PUNCT
ejpam-6086	75	6	u	u	NOUN
ejpam-6086	75	7	,	,	PUNCT
ejpam-6086	75	8	d	d	PROPN
ejpam-6086	75	9	)	)	PUNCT
ejpam-6086	75	10	be	be	AUX
ejpam-6086	75	11	a	a	DET
ejpam-6086	75	12	complete	complete	ADJ
ejpam-6086	75	13	rectangular	rectangular	ADJ
ejpam-6086	75	14	b−metric	b−metric	ADJ
ejpam-6086	75	15	space	space	NOUN
ejpam-6086	75	16	and	and	CCONJ
ejpam-6086	75	17	t	t	NOUN
ejpam-6086	75	18	:	:	PUNCT
ejpam-6086	75	19	u	u	X
ejpam-6086	75	20	→	→	SYM
ejpam-6086	75	21	u	u	X
ejpam-6086	75	22	be	be	VERB
ejpam-6086	75	23	a	a	DET
ejpam-6086	75	24	θ	θ	NOUN
ejpam-6086	75	25	−	−	NOUN
ejpam-6086	76	1	ϕ−contraction	ϕ−contraction	NOUN
ejpam-6086	76	2	.	.	PUNCT
ejpam-6086	77	1	then	then	ADV
ejpam-6086	77	2	,	,	PUNCT
ejpam-6086	77	3	t	t	PROPN
ejpam-6086	77	4	has	have	VERB
ejpam-6086	77	5	a	a	DET
ejpam-6086	77	6	unique	unique	ADJ
ejpam-6086	77	7	fixed	fix	VERB
ejpam-6086	77	8	point	point	NOUN
ejpam-6086	77	9	.	.	PUNCT
ejpam-6086	78	1	in	in	ADP
ejpam-6086	78	2	2014	2014	NUM
ejpam-6086	78	3	,	,	PUNCT
ejpam-6086	78	4	hussain	hussain	PROPN
ejpam-6086	78	5	et	et	PROPN
ejpam-6086	78	6	al	al	PROPN
ejpam-6086	78	7	.	.	PUNCT
ejpam-6086	79	1	[	[	X
ejpam-6086	79	2	8	8	NUM
ejpam-6086	79	3	]	]	PUNCT
ejpam-6086	79	4	introduced	introduce	VERB
ejpam-6086	79	5	a	a	DET
ejpam-6086	79	6	notion	notion	NOUN
ejpam-6086	79	7	of	of	ADP
ejpam-6086	79	8	α−completeness	α−completeness	NUM
ejpam-6086	79	9	for	for	ADP
ejpam-6086	79	10	metric	metric	ADJ
ejpam-6086	79	11	spaces	space	NOUN
ejpam-6086	79	12	.	.	PUNCT
ejpam-6086	80	1	h.	h.	PROPN
ejpam-6086	80	2	massit	massit	PROPN
ejpam-6086	80	3	et	et	PROPN
ejpam-6086	80	4	al	al	PROPN
ejpam-6086	80	5	.	.	PUNCT
ejpam-6086	80	6	/	/	SYM
ejpam-6086	80	7	eur	eur	PROPN
ejpam-6086	80	8	.	.	PUNCT
ejpam-6086	81	1	j.	j.	PROPN
ejpam-6086	81	2	pure	pure	PROPN
ejpam-6086	81	3	appl	appl	PROPN
ejpam-6086	81	4	.	.	PROPN
ejpam-6086	81	5	math	math	PROPN
ejpam-6086	81	6	,	,	PUNCT
ejpam-6086	81	7	18	18	NUM
ejpam-6086	81	8	(	(	PUNCT
ejpam-6086	81	9	2	2	NUM
ejpam-6086	81	10	)	)	PUNCT
ejpam-6086	81	11	(	(	PUNCT
ejpam-6086	81	12	2025	2025	NUM
ejpam-6086	81	13	)	)	PUNCT
ejpam-6086	81	14	,	,	PUNCT
ejpam-6086	81	15	6086	6086	NUM
ejpam-6086	81	16	4	4	NUM
ejpam-6086	81	17	of	of	ADP
ejpam-6086	81	18	19	19	NUM
ejpam-6086	81	19	definition	definition	NOUN
ejpam-6086	81	20	7	7	NUM
ejpam-6086	81	21	.	.	PUNCT
ejpam-6086	82	1	[	[	X
ejpam-6086	82	2	8	8	NUM
ejpam-6086	82	3	]	]	X
ejpam-6086	82	4	let	let	VERB
ejpam-6086	82	5	(	(	PUNCT
ejpam-6086	82	6	u	u	NOUN
ejpam-6086	82	7	,	,	PUNCT
ejpam-6086	82	8	d	d	PROPN
ejpam-6086	82	9	)	)	PUNCT
ejpam-6086	82	10	be	be	AUX
ejpam-6086	82	11	a	a	DET
ejpam-6086	82	12	rectangular	rectangular	ADJ
ejpam-6086	82	13	b−metric	b−metric	ADJ
ejpam-6086	82	14	space	space	NOUN
ejpam-6086	82	15	and	and	CCONJ
ejpam-6086	82	16	α	α	NOUN
ejpam-6086	82	17	:	:	PUNCT
ejpam-6086	82	18	u	u	NOUN
ejpam-6086	82	19	×u	×u	NUM
ejpam-6086	82	20	→	→	PUNCT
ejpam-6086	82	21	[	[	X
ejpam-6086	82	22	0,+∞	0,+∞	NUM
ejpam-6086	82	23	[	[	PUNCT
ejpam-6086	82	24	be	be	AUX
ejpam-6086	82	25	a	a	DET
ejpam-6086	82	26	mapping	mapping	NOUN
ejpam-6086	82	27	.	.	PUNCT
ejpam-6086	83	1	the	the	DET
ejpam-6086	83	2	space	space	NOUN
ejpam-6086	83	3	u	u	NOUN
ejpam-6086	83	4	is	be	AUX
ejpam-6086	83	5	said	say	VERB
ejpam-6086	83	6	to	to	PART
ejpam-6086	83	7	be	be	AUX
ejpam-6086	83	8	α−complete	α−complete	NUM
ejpam-6086	83	9	,	,	PUNCT
ejpam-6086	83	10	if	if	SCONJ
ejpam-6086	83	11	every	every	DET
ejpam-6086	83	12	cauchy	cauchy	ADJ
ejpam-6086	83	13	sequence	sequence	NOUN
ejpam-6086	83	14	{	{	PUNCT
ejpam-6086	83	15	xn	xn	NUM
ejpam-6086	83	16	}	}	PUNCT
ejpam-6086	83	17	in	in	ADP
ejpam-6086	83	18	u	u	NOUN
ejpam-6086	83	19	with	with	ADP
ejpam-6086	83	20	α(xn	α(xn	PROPN
ejpam-6086	83	21	,	,	PUNCT
ejpam-6086	83	22	xn+1	xn+1	NUM
ejpam-6086	83	23	)	)	PUNCT
ejpam-6086	83	24	≥	≥	NOUN
ejpam-6086	83	25	1	1	NUM
ejpam-6086	83	26	for	for	ADP
ejpam-6086	83	27	all	all	PRON
ejpam-6086	83	28	n	n	PRON
ejpam-6086	83	29	∈	∈	PROPN
ejpam-6086	83	30	n	n	CCONJ
ejpam-6086	83	31	,	,	PUNCT
ejpam-6086	83	32	converges	converge	VERB
ejpam-6086	83	33	in	in	ADP
ejpam-6086	83	34	u	u	PROPN
ejpam-6086	83	35	.	.	PUNCT
ejpam-6086	84	1	remark	remark	PROPN
ejpam-6086	84	2	1	1	NUM
ejpam-6086	84	3	.	.	PUNCT
ejpam-6086	85	1	(	(	PUNCT
ejpam-6086	85	2	i	i	NOUN
ejpam-6086	85	3	)	)	PUNCT
ejpam-6086	85	4	in	in	ADP
ejpam-6086	85	5	this	this	DET
ejpam-6086	85	6	paper	paper	NOUN
ejpam-6086	85	7	,	,	PUNCT
ejpam-6086	85	8	using	use	VERB
ejpam-6086	85	9	definition	definition	NOUN
ejpam-6086	85	10	7	7	NUM
ejpam-6086	85	11	,	,	PUNCT
ejpam-6086	85	12	we	we	PRON
ejpam-6086	85	13	generalize	generalize	VERB
ejpam-6086	85	14	theorem	theorem	VERB
ejpam-6086	85	15	1	1	NUM
ejpam-6086	85	16	in	in	ADP
ejpam-6086	85	17	several	several	ADJ
ejpam-6086	85	18	directions	direction	NOUN
ejpam-6086	85	19	.	.	PUNCT
ejpam-6086	86	1	(	(	PUNCT
ejpam-6086	86	2	ii	ii	X
ejpam-6086	86	3	)	)	PUNCT
ejpam-6086	86	4	we	we	PRON
ejpam-6086	86	5	also	also	ADV
ejpam-6086	86	6	give	give	VERB
ejpam-6086	86	7	a	a	DET
ejpam-6086	86	8	generalized	generalized	ADJ
ejpam-6086	86	9	version	version	NOUN
ejpam-6086	86	10	of	of	ADP
ejpam-6086	86	11	definition	definition	NOUN
ejpam-6086	86	12	7	7	NUM
ejpam-6086	86	13	,	,	PUNCT
ejpam-6086	86	14	which	which	PRON
ejpam-6086	86	15	opens	open	VERB
ejpam-6086	86	16	up	up	ADP
ejpam-6086	86	17	new	new	ADJ
ejpam-6086	86	18	possibilities	possibility	NOUN
ejpam-6086	86	19	for	for	ADP
ejpam-6086	86	20	further	further	ADJ
ejpam-6086	86	21	research	research	NOUN
ejpam-6086	86	22	.	.	PUNCT
ejpam-6086	87	1	in	in	ADP
ejpam-6086	87	2	this	this	DET
ejpam-6086	87	3	section	section	NOUN
ejpam-6086	87	4	,	,	PUNCT
ejpam-6086	87	5	in	in	ADP
ejpam-6086	87	6	the	the	DET
ejpam-6086	87	7	end	end	NOUN
ejpam-6086	87	8	,	,	PUNCT
ejpam-6086	87	9	we	we	PRON
ejpam-6086	87	10	list	list	VERB
ejpam-6086	87	11	some	some	DET
ejpam-6086	87	12	concepts	concept	NOUN
ejpam-6086	87	13	regarding	regard	VERB
ejpam-6086	87	14	the	the	DET
ejpam-6086	87	15	multivalued	multivalued	ADJ
ejpam-6086	87	16	mapping	mapping	NOUN
ejpam-6086	87	17	.	.	PUNCT
ejpam-6086	88	1	let	let	VERB
ejpam-6086	88	2	(	(	PUNCT
ejpam-6086	88	3	u	u	NOUN
ejpam-6086	88	4	,	,	PUNCT
ejpam-6086	88	5	d	d	PROPN
ejpam-6086	88	6	)	)	PUNCT
ejpam-6086	88	7	be	be	AUX
ejpam-6086	88	8	a	a	DET
ejpam-6086	88	9	rectangular	rectangular	ADJ
ejpam-6086	88	10	b−metric	b−metric	ADJ
ejpam-6086	88	11	space	space	NOUN
ejpam-6086	88	12	,	,	PUNCT
ejpam-6086	88	13	we	we	PRON
ejpam-6086	88	14	will	will	AUX
ejpam-6086	88	15	denote	denote	VERB
ejpam-6086	88	16	by	by	ADP
ejpam-6086	88	17	cb(u	cb(u	NOUN
ejpam-6086	88	18	)	)	PUNCT
ejpam-6086	88	19	the	the	DET
ejpam-6086	88	20	set	set	NOUN
ejpam-6086	88	21	of	of	ADP
ejpam-6086	88	22	non	non	ADJ
ejpam-6086	88	23	-	-	ADJ
ejpam-6086	88	24	empty	empty	ADJ
ejpam-6086	88	25	bounded	bounded	ADJ
ejpam-6086	88	26	closed	closed	ADJ
ejpam-6086	88	27	subsets	subset	NOUN
ejpam-6086	88	28	of	of	ADP
ejpam-6086	88	29	u	u	PROPN
ejpam-6086	88	30	.	.	PUNCT
ejpam-6086	89	1	for	for	ADP
ejpam-6086	89	2	m	m	PROPN
ejpam-6086	89	3	,	,	PUNCT
ejpam-6086	89	4	n	n	PROPN
ejpam-6086	89	5	∈	∈	PROPN
ejpam-6086	89	6	cb(u	cb(u	X
ejpam-6086	89	7	)	)	PUNCT
ejpam-6086	90	1	and	and	CCONJ
ejpam-6086	90	2	x	x	X
ejpam-6086	90	3	∈	∈	PROPN
ejpam-6086	90	4	u	u	NOUN
ejpam-6086	90	5	,	,	PUNCT
ejpam-6086	90	6	we	we	PRON
ejpam-6086	90	7	define	define	VERB
ejpam-6086	90	8	d(x	d(x	PROPN
ejpam-6086	90	9	,	,	PUNCT
ejpam-6086	90	10	m	m	NOUN
ejpam-6086	90	11	)	)	PUNCT
ejpam-6086	90	12	=	=	SYM
ejpam-6086	90	13	inf	inf	NOUN
ejpam-6086	90	14	a∈m	a∈m	NOUN
ejpam-6086	90	15	d(x	d(x	PROPN
ejpam-6086	90	16	,	,	PUNCT
ejpam-6086	90	17	a	a	PRON
ejpam-6086	90	18	)	)	PUNCT
ejpam-6086	90	19	and	and	CCONJ
ejpam-6086	90	20	d(m	d(m	PROPN
ejpam-6086	90	21	,	,	PUNCT
ejpam-6086	90	22	n	n	CCONJ
ejpam-6086	90	23	)	)	PUNCT
ejpam-6086	90	24	=	=	NOUN
ejpam-6086	91	1	sup	sup	NOUN
ejpam-6086	91	2	a∈m	a∈m	VERB
ejpam-6086	91	3	d(a	d(a	PROPN
ejpam-6086	91	4	,	,	PUNCT
ejpam-6086	91	5	n	n	CCONJ
ejpam-6086	91	6	)	)	PUNCT
ejpam-6086	91	7	.	.	PUNCT
ejpam-6086	92	1	the	the	DET
ejpam-6086	92	2	mapping	mapping	NOUN
ejpam-6086	92	3	h	h	NOUN
ejpam-6086	92	4	:	:	PUNCT
ejpam-6086	92	5	cb(u)×	cb(u)×	X
ejpam-6086	92	6	cb(u	cb(u	X
ejpam-6086	92	7	)	)	PUNCT
ejpam-6086	92	8	→	→	PUNCT
ejpam-6086	93	1	[	[	X
ejpam-6086	93	2	0,+∞	0,+∞	NUM
ejpam-6086	93	3	)	)	PUNCT
ejpam-6086	93	4	,	,	PUNCT
ejpam-6086	93	5	given	give	VERB
ejpam-6086	93	6	by	by	ADP
ejpam-6086	93	7	h(m	h(m	PROPN
ejpam-6086	93	8	,	,	PUNCT
ejpam-6086	93	9	n	n	CCONJ
ejpam-6086	93	10	)	)	PUNCT
ejpam-6086	93	11	=	=	SYM
ejpam-6086	93	12	max	max	PROPN
ejpam-6086	93	13	{	{	PUNCT
ejpam-6086	93	14	sup	sup	NOUN
ejpam-6086	93	15	a∈m	a∈m	NOUN
ejpam-6086	93	16	d(a	d(a	PROPN
ejpam-6086	93	17	,	,	PUNCT
ejpam-6086	93	18	n	n	CCONJ
ejpam-6086	93	19	)	)	PUNCT
ejpam-6086	93	20	,	,	PUNCT
ejpam-6086	93	21	sup	sup	NOUN
ejpam-6086	93	22	b∈n	b∈n	VERB
ejpam-6086	93	23	d(b	d(b	PROPN
ejpam-6086	93	24	,	,	PUNCT
ejpam-6086	93	25	m	m	NOUN
ejpam-6086	93	26	)	)	PUNCT
ejpam-6086	93	27	}	}	PUNCT
ejpam-6086	93	28	,	,	PUNCT
ejpam-6086	93	29	is	be	AUX
ejpam-6086	93	30	the	the	DET
ejpam-6086	93	31	hausdorff	hausdorff	NOUN
ejpam-6086	93	32	distance	distance	NOUN
ejpam-6086	93	33	between	between	ADP
ejpam-6086	93	34	m	m	PROPN
ejpam-6086	93	35	and	and	CCONJ
ejpam-6086	93	36	n	n	PROPN
ejpam-6086	93	37	in	in	ADP
ejpam-6086	93	38	cb(u	cb(u	NOUN
ejpam-6086	93	39	)	)	PUNCT
ejpam-6086	93	40	.	.	PUNCT
ejpam-6086	94	1	we	we	PRON
ejpam-6086	94	2	define	define	VERB
ejpam-6086	94	3	b(u	b(u	PROPN
ejpam-6086	94	4	)	)	PUNCT
ejpam-6086	94	5	the	the	DET
ejpam-6086	94	6	set	set	NOUN
ejpam-6086	94	7	of	of	ADP
ejpam-6086	94	8	nonempty	nonempty	ADJ
ejpam-6086	94	9	compact	compact	ADJ
ejpam-6086	94	10	subsets	subset	NOUN
ejpam-6086	94	11	of	of	ADP
ejpam-6086	94	12	u	u	PROPN
ejpam-6086	94	13	.	.	PUNCT
ejpam-6086	95	1	a	a	DET
ejpam-6086	95	2	point	point	NOUN
ejpam-6086	95	3	x	x	VERB
ejpam-6086	95	4	is	be	AUX
ejpam-6086	95	5	said	say	VERB
ejpam-6086	95	6	to	to	PART
ejpam-6086	95	7	be	be	AUX
ejpam-6086	95	8	a	a	DET
ejpam-6086	95	9	fixed	fixed	ADJ
ejpam-6086	95	10	point	point	NOUN
ejpam-6086	95	11	of	of	ADP
ejpam-6086	95	12	multivalued	multivalue	VERB
ejpam-6086	95	13	mapping	mapping	NOUN
ejpam-6086	95	14	t	t	NOUN
ejpam-6086	95	15	:	:	PUNCT
ejpam-6086	95	16	u	u	SYM
ejpam-6086	95	17	→	→	SYM
ejpam-6086	95	18	cb(u	cb(u	X
ejpam-6086	95	19	)	)	PUNCT
ejpam-6086	95	20	provided	provide	VERB
ejpam-6086	95	21	x	x	PUNCT
ejpam-6086	95	22	∈	∈	PROPN
ejpam-6086	95	23	t	t	PROPN
ejpam-6086	95	24	(	(	PUNCT
ejpam-6086	95	25	x	x	NOUN
ejpam-6086	95	26	)	)	PUNCT
ejpam-6086	95	27	.	.	PUNCT
ejpam-6086	96	1	2	2	X
ejpam-6086	96	2	.	.	X
ejpam-6086	96	3	main	main	ADJ
ejpam-6086	96	4	result	result	NOUN
ejpam-6086	96	5	first	first	ADV
ejpam-6086	96	6	,	,	PUNCT
ejpam-6086	96	7	we	we	PRON
ejpam-6086	96	8	introduce	introduce	VERB
ejpam-6086	96	9	the	the	DET
ejpam-6086	96	10	concept	concept	NOUN
ejpam-6086	96	11	of	of	ADP
ejpam-6086	96	12	α−admissible	α−admissible	ADJ
ejpam-6086	96	13	θ	θ	X
ejpam-6086	96	14	−	−	X
ejpam-6086	96	15	ϕ−multivalued	ϕ−multivalued	PUNCT
ejpam-6086	96	16	contraction	contraction	NOUN
ejpam-6086	96	17	in	in	ADP
ejpam-6086	96	18	rectangular	rectangular	ADJ
ejpam-6086	96	19	b−metric	b−metric	ADJ
ejpam-6086	96	20	spaces	space	NOUN
ejpam-6086	96	21	.	.	PUNCT
ejpam-6086	97	1	definition	definition	NOUN
ejpam-6086	97	2	8	8	NUM
ejpam-6086	97	3	.	.	PUNCT
ejpam-6086	98	1	let	let	VERB
ejpam-6086	98	2	(	(	PUNCT
ejpam-6086	98	3	u	u	NOUN
ejpam-6086	98	4	,	,	PUNCT
ejpam-6086	98	5	d	d	PROPN
ejpam-6086	98	6	)	)	PUNCT
ejpam-6086	98	7	be	be	AUX
ejpam-6086	98	8	a	a	DET
ejpam-6086	98	9	rectangular	rectangular	ADJ
ejpam-6086	98	10	b−metric	b−metric	ADJ
ejpam-6086	98	11	space	space	NOUN
ejpam-6086	98	12	and	and	CCONJ
ejpam-6086	98	13	t	t	NOUN
ejpam-6086	98	14	:	:	PUNCT
ejpam-6086	98	15	u	u	PROPN
ejpam-6086	98	16	→	→	SYM
ejpam-6086	98	17	b(u	b(u	PROPN
ejpam-6086	98	18	)	)	PUNCT
ejpam-6086	98	19	be	be	AUX
ejpam-6086	98	20	a	a	DET
ejpam-6086	98	21	mapping	mapping	NOUN
ejpam-6086	98	22	and	and	CCONJ
ejpam-6086	98	23	w	w	PROPN
ejpam-6086	98	24	(	(	PUNCT
ejpam-6086	98	25	x	x	NOUN
ejpam-6086	98	26	,	,	PUNCT
ejpam-6086	98	27	y	y	NOUN
ejpam-6086	98	28	)	)	PUNCT
ejpam-6086	99	1	=	=	VERB
ejpam-6086	99	2	min{d(x	min{d(x	PROPN
ejpam-6086	99	3	,	,	PUNCT
ejpam-6086	99	4	tx	tx	PROPN
ejpam-6086	99	5	)	)	PUNCT
ejpam-6086	99	6	,	,	PUNCT
ejpam-6086	99	7	d(x	d(x	PROPN
ejpam-6086	99	8	,	,	PUNCT
ejpam-6086	99	9	ty	ty	NOUN
ejpam-6086	99	10	)	)	PUNCT
ejpam-6086	99	11	,	,	PUNCT
ejpam-6086	99	12	d(y	d(y	PROPN
ejpam-6086	99	13	,	,	PUNCT
ejpam-6086	99	14	ty	ty	NOUN
ejpam-6086	99	15	)	)	PUNCT
ejpam-6086	99	16	,	,	PUNCT
ejpam-6086	99	17	d(y	d(y	PROPN
ejpam-6086	99	18	,	,	PUNCT
ejpam-6086	99	19	tx	tx	PROPN
ejpam-6086	99	20	)	)	PUNCT
ejpam-6086	99	21	}	}	PUNCT
ejpam-6086	99	22	.	.	PUNCT
ejpam-6086	100	1	(	(	PUNCT
ejpam-6086	100	2	i	i	NOUN
ejpam-6086	100	3	)	)	PUNCT
ejpam-6086	100	4	t	t	PROPN
ejpam-6086	100	5	is	be	AUX
ejpam-6086	100	6	called	call	VERB
ejpam-6086	100	7	an	an	DET
ejpam-6086	100	8	α−admissible	α−admissible	ADJ
ejpam-6086	100	9	θ−multivalued	θ−multivalued	CCONJ
ejpam-6086	100	10	contraction	contraction	NOUN
ejpam-6086	100	11	if	if	SCONJ
ejpam-6086	100	12	exist	exist	VERB
ejpam-6086	100	13	θ	θ	PROPN
ejpam-6086	100	14	∈	∈	PROPN
ejpam-6086	100	15	θ	θ	PROPN
ejpam-6086	100	16	,	,	PUNCT
ejpam-6086	100	17	k	k	PROPN
ejpam-6086	100	18	≥	≥	X
ejpam-6086	100	19	0	0	NUM
ejpam-6086	100	20	and	and	CCONJ
ejpam-6086	100	21	s	s	PROPN
ejpam-6086	100	22	∈	∈	PROPN
ejpam-6086	100	23	(	(	PUNCT
ejpam-6086	100	24	0	0	NUM
ejpam-6086	100	25	,	,	PUNCT
ejpam-6086	100	26	1	1	NUM
ejpam-6086	100	27	)	)	PUNCT
ejpam-6086	100	28	such	such	ADJ
ejpam-6086	100	29	that	that	DET
ejpam-6086	100	30	h(tx	h(tx	PROPN
ejpam-6086	100	31	,	,	PUNCT
ejpam-6086	100	32	ty	ty	NOUN
ejpam-6086	100	33	)	)	PUNCT
ejpam-6086	100	34	>	>	SYM
ejpam-6086	100	35	0	0	NUM
ejpam-6086	100	36	implies	imply	VERB
ejpam-6086	100	37	θ[α(x	θ[α(x	NOUN
ejpam-6086	100	38	,	,	PUNCT
ejpam-6086	100	39	y)b3h(tx	y)b3h(tx	PROPN
ejpam-6086	100	40	,	,	PUNCT
ejpam-6086	100	41	ty	ty	NOUN
ejpam-6086	100	42	)	)	PUNCT
ejpam-6086	100	43	]	]	PUNCT
ejpam-6086	100	44	≤	≤	PROPN
ejpam-6086	101	1	θ[m(x	θ[m(x	PROPN
ejpam-6086	101	2	,	,	PUNCT
ejpam-6086	101	3	y)]s	y)]s	PROPN
ejpam-6086	101	4	+	+	ADJ
ejpam-6086	101	5	kw	kw	INTJ
ejpam-6086	101	6	(	(	PUNCT
ejpam-6086	101	7	x	x	PROPN
ejpam-6086	101	8	,	,	PUNCT
ejpam-6086	101	9	y	y	PROPN
ejpam-6086	101	10	)	)	PUNCT
ejpam-6086	101	11	,	,	PUNCT
ejpam-6086	101	12	(	(	PUNCT
ejpam-6086	101	13	4	4	X
ejpam-6086	101	14	)	)	PUNCT
ejpam-6086	101	15	for	for	ADP
ejpam-6086	101	16	all	all	DET
ejpam-6086	101	17	x	x	NOUN
ejpam-6086	101	18	,	,	PUNCT
ejpam-6086	101	19	y	y	PROPN
ejpam-6086	101	20	∈	∈	PROPN
ejpam-6086	101	21	u	u	PROPN
ejpam-6086	101	22	,	,	PUNCT
ejpam-6086	101	23	where	where	SCONJ
ejpam-6086	101	24	m(x	m(x	PROPN
ejpam-6086	101	25	,	,	PUNCT
ejpam-6086	101	26	y	y	NOUN
ejpam-6086	101	27	)	)	PUNCT
ejpam-6086	101	28	=	=	PUNCT
ejpam-6086	101	29	max{d(x	max{d(x	PROPN
ejpam-6086	101	30	,	,	PUNCT
ejpam-6086	101	31	y	y	NOUN
ejpam-6086	101	32	)	)	PUNCT
ejpam-6086	101	33	,	,	PUNCT
ejpam-6086	101	34	d(x	d(x	PROPN
ejpam-6086	101	35	,	,	PUNCT
ejpam-6086	101	36	tx	tx	PROPN
ejpam-6086	101	37	)	)	PUNCT
ejpam-6086	101	38	,	,	PUNCT
ejpam-6086	101	39	d(y	d(y	PROPN
ejpam-6086	101	40	,	,	PUNCT
ejpam-6086	101	41	ty	ty	NOUN
ejpam-6086	101	42	)	)	PUNCT
ejpam-6086	101	43	,	,	PUNCT
ejpam-6086	101	44	d(y	d(y	PROPN
ejpam-6086	101	45	,	,	PUNCT
ejpam-6086	101	46	tx	tx	PROPN
ejpam-6086	101	47	)	)	PUNCT
ejpam-6086	101	48	}	}	PUNCT
ejpam-6086	101	49	.	.	PUNCT
ejpam-6086	102	1	(	(	PUNCT
ejpam-6086	102	2	ii	ii	NOUN
ejpam-6086	102	3	)	)	PUNCT
ejpam-6086	102	4	t	t	PROPN
ejpam-6086	102	5	is	be	AUX
ejpam-6086	102	6	called	call	VERB
ejpam-6086	102	7	an	an	DET
ejpam-6086	102	8	α−admissible	α−admissible	ADV
ejpam-6086	102	9	θ−ϕ−multivalued	θ−ϕ−multivalue	VERB
ejpam-6086	102	10	contraction	contraction	NOUN
ejpam-6086	102	11	if	if	SCONJ
ejpam-6086	102	12	exist	exist	VERB
ejpam-6086	102	13	θ	θ	PROPN
ejpam-6086	102	14	∈	∈	PROPN
ejpam-6086	102	15	θ	θ	PROPN
ejpam-6086	102	16	and	and	CCONJ
ejpam-6086	102	17	k	k	PROPN
ejpam-6086	102	18	≥	≥	X
ejpam-6086	102	19	0	0	NUM
ejpam-6086	102	20	such	such	ADJ
ejpam-6086	102	21	that	that	DET
ejpam-6086	102	22	h(tx	h(tx	PROPN
ejpam-6086	102	23	,	,	PUNCT
ejpam-6086	102	24	ty	ty	NOUN
ejpam-6086	102	25	)	)	PUNCT
ejpam-6086	102	26	>	>	SYM
ejpam-6086	102	27	0	0	NUM
ejpam-6086	102	28	implies	imply	VERB
ejpam-6086	102	29	θ[α(x	θ[α(x	NOUN
ejpam-6086	102	30	,	,	PUNCT
ejpam-6086	102	31	y)b3h(tx	y)b3h(tx	PROPN
ejpam-6086	102	32	,	,	PUNCT
ejpam-6086	102	33	ty	ty	NOUN
ejpam-6086	102	34	)	)	PUNCT
ejpam-6086	102	35	]	]	PUNCT
ejpam-6086	102	36	≤	≤	NUM
ejpam-6086	102	37	ϕ[θ(m(x	ϕ[θ(m(x	PROPN
ejpam-6086	102	38	,	,	PUNCT
ejpam-6086	102	39	y	y	NOUN
ejpam-6086	102	40	)	)	PUNCT
ejpam-6086	102	41	)	)	PUNCT
ejpam-6086	102	42	]	]	PUNCT
ejpam-6086	103	1	+	+	ADV
ejpam-6086	103	2	kw	kw	INTJ
ejpam-6086	103	3	(	(	PUNCT
ejpam-6086	103	4	x	x	PROPN
ejpam-6086	103	5	,	,	PUNCT
ejpam-6086	103	6	y	y	PROPN
ejpam-6086	103	7	)	)	PUNCT
ejpam-6086	103	8	,	,	PUNCT
ejpam-6086	103	9	(	(	PUNCT
ejpam-6086	103	10	5	5	X
ejpam-6086	103	11	)	)	PUNCT
ejpam-6086	103	12	for	for	ADP
ejpam-6086	103	13	all	all	DET
ejpam-6086	103	14	x	x	NOUN
ejpam-6086	103	15	,	,	PUNCT
ejpam-6086	103	16	y	y	PROPN
ejpam-6086	103	17	∈	∈	PROPN
ejpam-6086	103	18	u	u	PROPN
ejpam-6086	103	19	,	,	PUNCT
ejpam-6086	103	20	where	where	SCONJ
ejpam-6086	103	21	m(x	m(x	PROPN
ejpam-6086	103	22	,	,	PUNCT
ejpam-6086	103	23	y	y	NOUN
ejpam-6086	103	24	)	)	PUNCT
ejpam-6086	103	25	=	=	PUNCT
ejpam-6086	103	26	max{d(x	max{d(x	PROPN
ejpam-6086	103	27	,	,	PUNCT
ejpam-6086	103	28	y	y	NOUN
ejpam-6086	103	29	)	)	PUNCT
ejpam-6086	103	30	,	,	PUNCT
ejpam-6086	103	31	d(x	d(x	PROPN
ejpam-6086	103	32	,	,	PUNCT
ejpam-6086	103	33	tx	tx	PROPN
ejpam-6086	103	34	)	)	PUNCT
ejpam-6086	103	35	,	,	PUNCT
ejpam-6086	103	36	d(x	d(x	PROPN
ejpam-6086	103	37	,	,	PUNCT
ejpam-6086	103	38	ty	ty	NOUN
ejpam-6086	103	39	)	)	PUNCT
ejpam-6086	103	40	,	,	PUNCT
ejpam-6086	103	41	d(y	d(y	PROPN
ejpam-6086	103	42	,	,	PUNCT
ejpam-6086	103	43	tx	tx	PROPN
ejpam-6086	103	44	)	)	PUNCT
ejpam-6086	103	45	}	}	PUNCT
ejpam-6086	103	46	.	.	PUNCT
ejpam-6086	104	1	h.	h.	PROPN
ejpam-6086	104	2	massit	massit	PROPN
ejpam-6086	104	3	et	et	PROPN
ejpam-6086	104	4	al	al	PROPN
ejpam-6086	104	5	.	.	PUNCT
ejpam-6086	104	6	/	/	SYM
ejpam-6086	104	7	eur	eur	PROPN
ejpam-6086	104	8	.	.	PUNCT
ejpam-6086	105	1	j.	j.	PROPN
ejpam-6086	105	2	pure	pure	PROPN
ejpam-6086	105	3	appl	appl	PROPN
ejpam-6086	105	4	.	.	PROPN
ejpam-6086	105	5	math	math	PROPN
ejpam-6086	105	6	,	,	PUNCT
ejpam-6086	105	7	18	18	NUM
ejpam-6086	105	8	(	(	PUNCT
ejpam-6086	105	9	2	2	NUM
ejpam-6086	105	10	)	)	PUNCT
ejpam-6086	105	11	(	(	PUNCT
ejpam-6086	105	12	2025	2025	NUM
ejpam-6086	105	13	)	)	PUNCT
ejpam-6086	105	14	,	,	PUNCT
ejpam-6086	105	15	6086	6086	NUM
ejpam-6086	105	16	5	5	NUM
ejpam-6086	105	17	of	of	ADP
ejpam-6086	105	18	19	19	NUM
ejpam-6086	105	19	(	(	PUNCT
ejpam-6086	105	20	iii	iii	NOUN
ejpam-6086	105	21	)	)	PUNCT
ejpam-6086	105	22	t	t	PROPN
ejpam-6086	105	23	is	be	AUX
ejpam-6086	105	24	called	call	VERB
ejpam-6086	105	25	an	an	DET
ejpam-6086	105	26	α−admissible	α−admissible	ADJ
ejpam-6086	105	27	θ	θ	X
ejpam-6086	105	28	−	−	PROPN
ejpam-6086	105	29	ϕ−multivalued	ϕ−multivalued	PUNCT
ejpam-6086	105	30	kannan	kannan	PROPN
ejpam-6086	105	31	-	-	PUNCT
ejpam-6086	105	32	type	type	NOUN
ejpam-6086	105	33	if	if	SCONJ
ejpam-6086	105	34	there	there	PRON
ejpam-6086	105	35	are	be	VERB
ejpam-6086	105	36	θ	θ	PROPN
ejpam-6086	105	37	∈	∈	PROPN
ejpam-6086	105	38	θ	θ	PROPN
ejpam-6086	105	39	,	,	PUNCT
ejpam-6086	105	40	ϕ	ϕ	PROPN
ejpam-6086	105	41	∈	∈	PROPN
ejpam-6086	105	42	φ	φ	PROPN
ejpam-6086	105	43	and	and	CCONJ
ejpam-6086	105	44	k	k	PROPN
ejpam-6086	105	45	≥	≥	X
ejpam-6086	105	46	0	0	NUM
ejpam-6086	105	47	such	such	ADJ
ejpam-6086	105	48	that	that	DET
ejpam-6086	105	49	h(tx	h(tx	PROPN
ejpam-6086	105	50	,	,	PUNCT
ejpam-6086	105	51	ty	ty	NOUN
ejpam-6086	105	52	)	)	PUNCT
ejpam-6086	105	53	>	>	SYM
ejpam-6086	105	54	0	0	NUM
ejpam-6086	105	55	implies	imply	VERB
ejpam-6086	105	56	θ[α(x	θ[α(x	NOUN
ejpam-6086	105	57	,	,	PUNCT
ejpam-6086	105	58	y)b3h(tx	y)b3h(tx	PROPN
ejpam-6086	105	59	,	,	PUNCT
ejpam-6086	105	60	ty	ty	NOUN
ejpam-6086	105	61	)	)	PUNCT
ejpam-6086	105	62	]	]	PUNCT
ejpam-6086	106	1	≤	≤	NUM
ejpam-6086	106	2	ϕ	ϕ	X
ejpam-6086	106	3	[	[	PUNCT
ejpam-6086	106	4	θ	θ	X
ejpam-6086	106	5	(	(	PUNCT
ejpam-6086	106	6	d(x	d(x	PROPN
ejpam-6086	106	7	,	,	PUNCT
ejpam-6086	106	8	tx	tx	PROPN
ejpam-6086	106	9	)	)	PUNCT
ejpam-6086	106	10	+	+	CCONJ
ejpam-6086	106	11	d(y	d(y	PROPN
ejpam-6086	106	12	,	,	PUNCT
ejpam-6086	106	13	ty	ty	NOUN
ejpam-6086	106	14	)	)	PUNCT
ejpam-6086	106	15	2	2	NUM
ejpam-6086	106	16	)	)	PUNCT
ejpam-6086	106	17	]	]	PUNCT
ejpam-6086	107	1	+	+	ADV
ejpam-6086	107	2	kw	kw	INTJ
ejpam-6086	107	3	(	(	PUNCT
ejpam-6086	107	4	x	x	PROPN
ejpam-6086	107	5	,	,	PUNCT
ejpam-6086	107	6	y	y	PROPN
ejpam-6086	107	7	)	)	PUNCT
ejpam-6086	107	8	,	,	PUNCT
ejpam-6086	107	9	(	(	PUNCT
ejpam-6086	107	10	6	6	NUM
ejpam-6086	107	11	)	)	PUNCT
ejpam-6086	107	12	for	for	ADP
ejpam-6086	107	13	all	all	DET
ejpam-6086	107	14	x	x	NOUN
ejpam-6086	107	15	,	,	PUNCT
ejpam-6086	107	16	y	y	PROPN
ejpam-6086	107	17	∈	∈	PROPN
ejpam-6086	107	18	u	u	PROPN
ejpam-6086	107	19	.	.	PUNCT
ejpam-6086	108	1	(	(	PUNCT
ejpam-6086	108	2	iv	iv	X
ejpam-6086	108	3	)	)	PUNCT
ejpam-6086	108	4	t	t	PROPN
ejpam-6086	108	5	is	be	AUX
ejpam-6086	108	6	called	call	VERB
ejpam-6086	108	7	an	an	DET
ejpam-6086	108	8	α−admissible	α−admissible	ADJ
ejpam-6086	108	9	θ−	θ−	PROPN
ejpam-6086	108	10	ϕ−multivalued	ϕ−multivalued	PUNCT
ejpam-6086	108	11	reich	reich	NOUN
ejpam-6086	108	12	-	-	PUNCT
ejpam-6086	108	13	type	type	NOUN
ejpam-6086	108	14	if	if	SCONJ
ejpam-6086	108	15	exist	exist	VERB
ejpam-6086	108	16	θ	θ	PROPN
ejpam-6086	108	17	∈	∈	PROPN
ejpam-6086	108	18	θ	θ	PROPN
ejpam-6086	108	19	,	,	PUNCT
ejpam-6086	108	20	ϕ	ϕ	PROPN
ejpam-6086	108	21	∈	∈	PROPN
ejpam-6086	108	22	φ	φ	PROPN
ejpam-6086	108	23	and	and	CCONJ
ejpam-6086	108	24	k	k	PROPN
ejpam-6086	108	25	≥	≥	X
ejpam-6086	108	26	0	0	NUM
ejpam-6086	108	27	such	such	ADJ
ejpam-6086	108	28	that	that	DET
ejpam-6086	108	29	h(tx	h(tx	PROPN
ejpam-6086	108	30	,	,	PUNCT
ejpam-6086	108	31	ty	ty	NOUN
ejpam-6086	108	32	)	)	PUNCT
ejpam-6086	108	33	>	>	SYM
ejpam-6086	108	34	0	0	NUM
ejpam-6086	108	35	implies	imply	VERB
ejpam-6086	108	36	θ[α(x	θ[α(x	NOUN
ejpam-6086	108	37	,	,	PUNCT
ejpam-6086	108	38	y)b3h(tx	y)b3h(tx	PROPN
ejpam-6086	108	39	,	,	PUNCT
ejpam-6086	108	40	ty	ty	NOUN
ejpam-6086	108	41	)	)	PUNCT
ejpam-6086	108	42	]	]	PUNCT
ejpam-6086	109	1	≤	≤	NUM
ejpam-6086	109	2	ϕ	ϕ	X
ejpam-6086	109	3	[	[	PUNCT
ejpam-6086	109	4	θ	θ	X
ejpam-6086	109	5	(	(	PUNCT
ejpam-6086	109	6	d(x	d(x	PROPN
ejpam-6086	109	7	,	,	PUNCT
ejpam-6086	109	8	y	y	NOUN
ejpam-6086	109	9	)	)	PUNCT
ejpam-6086	109	10	+	+	CCONJ
ejpam-6086	109	11	d(x	d(x	PROPN
ejpam-6086	109	12	,	,	PUNCT
ejpam-6086	109	13	tx	tx	PROPN
ejpam-6086	109	14	)	)	PUNCT
ejpam-6086	110	1	+	+	CCONJ
ejpam-6086	110	2	d(y	d(y	PROPN
ejpam-6086	110	3	,	,	PUNCT
ejpam-6086	110	4	ty	ty	NOUN
ejpam-6086	110	5	)	)	PUNCT
ejpam-6086	110	6	3	3	NUM
ejpam-6086	110	7	)	)	PUNCT
ejpam-6086	110	8	]	]	PUNCT
ejpam-6086	111	1	+	+	ADV
ejpam-6086	111	2	kw	kw	INTJ
ejpam-6086	111	3	(	(	PUNCT
ejpam-6086	111	4	x	x	PROPN
ejpam-6086	111	5	,	,	PUNCT
ejpam-6086	111	6	y	y	PROPN
ejpam-6086	111	7	)	)	PUNCT
ejpam-6086	111	8	,	,	PUNCT
ejpam-6086	111	9	(	(	PUNCT
ejpam-6086	111	10	7	7	X
ejpam-6086	111	11	)	)	PUNCT
ejpam-6086	111	12	for	for	ADP
ejpam-6086	111	13	all	all	DET
ejpam-6086	111	14	x	x	NOUN
ejpam-6086	111	15	,	,	PUNCT
ejpam-6086	111	16	y	y	PROPN
ejpam-6086	111	17	∈	∈	PROPN
ejpam-6086	111	18	u	u	PROPN
ejpam-6086	111	19	.	.	PUNCT
ejpam-6086	112	1	(	(	PUNCT
ejpam-6086	112	2	v	v	NOUN
ejpam-6086	112	3	)	)	PUNCT
ejpam-6086	112	4	t	t	PROPN
ejpam-6086	112	5	is	be	AUX
ejpam-6086	112	6	called	call	VERB
ejpam-6086	112	7	α	α	DET
ejpam-6086	112	8	-	-	ADJ
ejpam-6086	112	9	continuous	continuous	ADJ
ejpam-6086	112	10	multivalued	multivalued	ADJ
ejpam-6086	112	11	mapping	mapping	NOUN
ejpam-6086	112	12	if	if	SCONJ
ejpam-6086	112	13	,	,	PUNCT
ejpam-6086	112	14	for	for	ADP
ejpam-6086	112	15	all	all	DET
ejpam-6086	112	16	sequences	sequence	NOUN
ejpam-6086	112	17	{	{	PUNCT
ejpam-6086	112	18	xn	xn	NUM
ejpam-6086	112	19	}	}	PUNCT
ejpam-6086	112	20	with	with	ADP
ejpam-6086	112	21	α(xn	α(xn	PROPN
ejpam-6086	112	22	,	,	PUNCT
ejpam-6086	112	23	xn+1	xn+1	NUM
ejpam-6086	112	24	)	)	PUNCT
ejpam-6086	112	25	≥	≥	NOUN
ejpam-6086	112	26	1	1	NUM
ejpam-6086	112	27	for	for	ADP
ejpam-6086	112	28	every	every	DET
ejpam-6086	112	29	n	n	PRON
ejpam-6086	112	30	∈	∈	PROPN
ejpam-6086	112	31	n	n	NOUN
ejpam-6086	112	32	and	and	CCONJ
ejpam-6086	112	33	limn→+∞	limn→+∞	PROPN
ejpam-6086	112	34	xn	xn	PUNCT
ejpam-6086	113	1	=	=	PUNCT
ejpam-6086	113	2	x	x	SYM
ejpam-6086	113	3	∈	∈	PROPN
ejpam-6086	113	4	u	u	NOUN
ejpam-6086	113	5	,	,	PUNCT
ejpam-6086	113	6	we	we	PRON
ejpam-6086	113	7	have	have	AUX
ejpam-6086	113	8	limn→+∞	limn→+∞	VERB
ejpam-6086	113	9	txn	txn	NOUN
ejpam-6086	113	10	=	=	SYM
ejpam-6086	113	11	tx	tx	VERB
ejpam-6086	113	12	so	so	SCONJ
ejpam-6086	113	13	that	that	PRON
ejpam-6086	113	14	limn→+∞	limn→+∞	VERB
ejpam-6086	113	15	d(xn	d(xn	PROPN
ejpam-6086	113	16	,	,	PUNCT
ejpam-6086	113	17	x	x	X
ejpam-6086	113	18	)	)	PUNCT
ejpam-6086	113	19	=	=	SYM
ejpam-6086	113	20	0	0	NUM
ejpam-6086	113	21	and	and	CCONJ
ejpam-6086	113	22	α(xn	α(xn	PROPN
ejpam-6086	113	23	,	,	PUNCT
ejpam-6086	113	24	xn+1	xn+1	NUM
ejpam-6086	113	25	)	)	PUNCT
ejpam-6086	113	26	≥	≥	NOUN
ejpam-6086	113	27	1	1	NUM
ejpam-6086	113	28	for	for	ADP
ejpam-6086	113	29	every	every	DET
ejpam-6086	113	30	n	n	PRON
ejpam-6086	113	31	∈	∈	PROPN
ejpam-6086	113	32	n	n	CCONJ
ejpam-6086	113	33	,	,	PUNCT
ejpam-6086	113	34	means	mean	VERB
ejpam-6086	113	35	that	that	SCONJ
ejpam-6086	113	36	limn→+∞h(txn	limn→+∞h(txn	NOUN
ejpam-6086	113	37	,	,	PUNCT
ejpam-6086	113	38	tx	tx	PROPN
ejpam-6086	113	39	)	)	PUNCT
ejpam-6086	114	1	=	=	SYM
ejpam-6086	114	2	0	0	X
ejpam-6086	114	3	.	.	PUNCT
ejpam-6086	114	4	theorem	theorem	NOUN
ejpam-6086	114	5	2	2	NUM
ejpam-6086	114	6	.	.	PUNCT
ejpam-6086	115	1	let	let	VERB
ejpam-6086	115	2	(	(	PUNCT
ejpam-6086	115	3	u	u	NOUN
ejpam-6086	115	4	,	,	PUNCT
ejpam-6086	115	5	d	d	PROPN
ejpam-6086	115	6	)	)	PUNCT
ejpam-6086	115	7	be	be	AUX
ejpam-6086	115	8	a	a	DET
ejpam-6086	115	9	rectangular	rectangular	ADJ
ejpam-6086	115	10	b−metric	b−metric	ADJ
ejpam-6086	115	11	space	space	NOUN
ejpam-6086	115	12	and	and	CCONJ
ejpam-6086	115	13	t	t	NOUN
ejpam-6086	115	14	:	:	PUNCT
ejpam-6086	115	15	u	u	PROPN
ejpam-6086	115	16	→	→	SYM
ejpam-6086	115	17	b(u	b(u	PROPN
ejpam-6086	115	18	)	)	PUNCT
ejpam-6086	115	19	be	be	VERB
ejpam-6086	115	20	an	an	DET
ejpam-6086	115	21	α−admissible	α−admissible	ADJ
ejpam-6086	115	22	θ−multivalued	θ−multivalued	CCONJ
ejpam-6086	115	23	contraction	contraction	NOUN
ejpam-6086	115	24	satisfying	satisfying	ADJ
ejpam-6086	115	25	:	:	PUNCT
ejpam-6086	115	26	(	(	PUNCT
ejpam-6086	115	27	i	i	NOUN
ejpam-6086	115	28	)	)	PUNCT
ejpam-6086	115	29	(	(	PUNCT
ejpam-6086	115	30	u	u	NOUN
ejpam-6086	115	31	,	,	PUNCT
ejpam-6086	115	32	d	d	PROPN
ejpam-6086	115	33	)	)	PUNCT
ejpam-6086	115	34	is	be	AUX
ejpam-6086	115	35	an	an	DET
ejpam-6086	115	36	α−complete	α−complete	NUM
ejpam-6086	115	37	metric	metric	ADJ
ejpam-6086	115	38	space	space	NOUN
ejpam-6086	115	39	,	,	PUNCT
ejpam-6086	115	40	(	(	PUNCT
ejpam-6086	115	41	ii	ii	NOUN
ejpam-6086	115	42	)	)	PUNCT
ejpam-6086	115	43	α(x0	α(x0	PROPN
ejpam-6086	115	44	,	,	PUNCT
ejpam-6086	115	45	x1	x1	PROPN
ejpam-6086	115	46	)	)	PUNCT
ejpam-6086	115	47	≥	≥	NOUN
ejpam-6086	115	48	1	1	NUM
ejpam-6086	115	49	for	for	ADP
ejpam-6086	115	50	x0	x0	PROPN
ejpam-6086	115	51	∈	∈	PROPN
ejpam-6086	115	52	u	u	NOUN
ejpam-6086	115	53	and	and	CCONJ
ejpam-6086	115	54	x1	x1	PROPN
ejpam-6086	115	55	∈	∈	PROPN
ejpam-6086	115	56	t	t	PROPN
ejpam-6086	115	57	(	(	PUNCT
ejpam-6086	115	58	u	u	NOUN
ejpam-6086	115	59	)	)	PUNCT
ejpam-6086	115	60	,	,	PUNCT
ejpam-6086	115	61	(	(	PUNCT
ejpam-6086	115	62	iii	iii	X
ejpam-6086	115	63	)	)	PUNCT
ejpam-6086	115	64	t	t	PROPN
ejpam-6086	115	65	is	be	AUX
ejpam-6086	115	66	triangular	triangular	NOUN
ejpam-6086	115	67	α−admissible	α−admissible	NOUN
ejpam-6086	115	68	,	,	PUNCT
ejpam-6086	115	69	(	(	PUNCT
ejpam-6086	115	70	iv	iv	X
ejpam-6086	115	71	)	)	PUNCT
ejpam-6086	115	72	t	t	PROPN
ejpam-6086	115	73	is	be	AUX
ejpam-6086	115	74	an	an	DET
ejpam-6086	115	75	α−continuous	α−continuous	ADJ
ejpam-6086	115	76	multivalued	multivalued	ADJ
ejpam-6086	115	77	mapping	mapping	NOUN
ejpam-6086	115	78	.	.	PUNCT
ejpam-6086	116	1	then	then	ADV
ejpam-6086	116	2	,	,	PUNCT
ejpam-6086	116	3	t	t	PROPN
ejpam-6086	116	4	has	have	VERB
ejpam-6086	116	5	a	a	DET
ejpam-6086	116	6	fixed	fix	VERB
ejpam-6086	116	7	point	point	NOUN
ejpam-6086	116	8	.	.	PUNCT
ejpam-6086	117	1	proof	proof	NOUN
ejpam-6086	117	2	.	.	PUNCT
ejpam-6086	118	1	let	let	VERB
ejpam-6086	118	2	{	{	PUNCT
ejpam-6086	118	3	xn	xn	VERB
ejpam-6086	118	4	}	}	PUNCT
ejpam-6086	118	5	be	be	AUX
ejpam-6086	118	6	a	a	DET
ejpam-6086	118	7	sequence	sequence	NOUN
ejpam-6086	118	8	in	in	ADP
ejpam-6086	118	9	u	u	PRON
ejpam-6086	118	10	such	such	ADJ
ejpam-6086	118	11	that	that	SCONJ
ejpam-6086	118	12	xn+1	xn+1	NUM
ejpam-6086	118	13	∈	∈	PROPN
ejpam-6086	118	14	txn	txn	NOUN
ejpam-6086	118	15	with	with	ADP
ejpam-6086	118	16	α(xn	α(xn	PROPN
ejpam-6086	118	17	,	,	PUNCT
ejpam-6086	118	18	xn+1	xn+1	NUM
ejpam-6086	118	19	)	)	PUNCT
ejpam-6086	118	20	≥	≥	NOUN
ejpam-6086	118	21	1	1	NUM
ejpam-6086	118	22	,	,	PUNCT
ejpam-6086	118	23	for	for	ADP
ejpam-6086	118	24	all	all	DET
ejpam-6086	118	25	k	k	PROPN
ejpam-6086	118	26	∈	∈	PROPN
ejpam-6086	118	27	n	n	PART
ejpam-6086	118	28	∪	∪	X
ejpam-6086	118	29	{	{	PUNCT
ejpam-6086	118	30	0	0	NUM
ejpam-6086	118	31	}	}	PUNCT
ejpam-6086	118	32	.	.	PUNCT
ejpam-6086	119	1	by	by	ADP
ejpam-6086	119	2	(	(	PUNCT
ejpam-6086	119	3	iv	iv	X
ejpam-6086	119	4	)	)	PUNCT
ejpam-6086	119	5	,	,	PUNCT
ejpam-6086	119	6	we	we	PRON
ejpam-6086	119	7	have	have	VERB
ejpam-6086	119	8	θ[h(txn−1	θ[h(txn−1	NOUN
ejpam-6086	119	9	,	,	PUNCT
ejpam-6086	119	10	txn	txn	NOUN
ejpam-6086	119	11	)	)	PUNCT
ejpam-6086	119	12	]	]	PUNCT
ejpam-6086	120	1	≤	≤	X
ejpam-6086	120	2	θ[b3h(txn−1	θ[b3h(txn−1	PROPN
ejpam-6086	120	3	,	,	PUNCT
ejpam-6086	120	4	txn	txn	NOUN
ejpam-6086	120	5	)	)	PUNCT
ejpam-6086	120	6	]	]	PUNCT
ejpam-6086	120	7	≤	≤	NUM
ejpam-6086	120	8	θ[α(xn−1	θ[α(xn−1	X
ejpam-6086	120	9	,	,	PUNCT
ejpam-6086	120	10	xn)b	xn)b	PROPN
ejpam-6086	120	11	3h(txn−1	3h(txn−1	NUM
ejpam-6086	120	12	,	,	PUNCT
ejpam-6086	120	13	txn	txn	NOUN
ejpam-6086	120	14	)	)	PUNCT
ejpam-6086	120	15	]	]	PUNCT
ejpam-6086	120	16	≤	≤	NUM
ejpam-6086	120	17	θ[m(xn−1	θ[m(xn−1	ADJ
ejpam-6086	120	18	,	,	PUNCT
ejpam-6086	120	19	xn	xn	PROPN
ejpam-6086	120	20	)	)	PUNCT
ejpam-6086	120	21	]	]	PUNCT
ejpam-6086	120	22	s	s	VERB
ejpam-6086	121	1	+	+	ADJ
ejpam-6086	121	2	kw	kw	INTJ
ejpam-6086	121	3	(	(	PUNCT
ejpam-6086	121	4	xn−1	xn−1	PROPN
ejpam-6086	121	5	,	,	PUNCT
ejpam-6086	121	6	xn	xn	PROPN
ejpam-6086	121	7	)	)	PUNCT
ejpam-6086	121	8	,	,	PUNCT
ejpam-6086	121	9	for	for	ADP
ejpam-6086	121	10	all	all	DET
ejpam-6086	121	11	n	n	DET
ejpam-6086	121	12	∈	∈	PROPN
ejpam-6086	121	13	n	n	CCONJ
ejpam-6086	121	14	,	,	PUNCT
ejpam-6086	121	15	where	where	SCONJ
ejpam-6086	121	16	m(xn−1	m(xn−1	NUM
ejpam-6086	121	17	,	,	PUNCT
ejpam-6086	121	18	xn	xn	NUM
ejpam-6086	121	19	)	)	PUNCT
ejpam-6086	121	20	=	=	SYM
ejpam-6086	121	21	max{d(xn−1	max{d(xn−1	ADJ
ejpam-6086	121	22	,	,	PUNCT
ejpam-6086	121	23	xn	xn	PROPN
ejpam-6086	121	24	)	)	PUNCT
ejpam-6086	121	25	,	,	PUNCT
ejpam-6086	121	26	d(xn−1	d(xn−1	PROPN
ejpam-6086	121	27	,	,	PUNCT
ejpam-6086	121	28	txn−1	txn−1	PROPN
ejpam-6086	121	29	)	)	PUNCT
ejpam-6086	121	30	,	,	PUNCT
ejpam-6086	121	31	d(xn	d(xn	PROPN
ejpam-6086	121	32	,	,	PUNCT
ejpam-6086	121	33	txn	txn	NOUN
ejpam-6086	121	34	)	)	PUNCT
ejpam-6086	121	35	,	,	PUNCT
ejpam-6086	121	36	d(xn	d(xn	PROPN
ejpam-6086	121	37	,	,	PUNCT
ejpam-6086	121	38	txn−1	txn−1	PROPN
ejpam-6086	121	39	)	)	PUNCT
ejpam-6086	121	40	}	}	PUNCT
ejpam-6086	121	41	=	=	SYM
ejpam-6086	121	42	max{d(xn−1	max{d(xn−1	ADJ
ejpam-6086	121	43	,	,	PUNCT
ejpam-6086	121	44	xn	xn	PROPN
ejpam-6086	121	45	)	)	PUNCT
ejpam-6086	121	46	,	,	PUNCT
ejpam-6086	121	47	d(xn	d(xn	PROPN
ejpam-6086	121	48	,	,	PUNCT
ejpam-6086	121	49	txn	txn	NOUN
ejpam-6086	121	50	)	)	PUNCT
ejpam-6086	121	51	}	}	PUNCT
ejpam-6086	121	52	h.	h.	NOUN
ejpam-6086	121	53	massit	massit	PROPN
ejpam-6086	121	54	et	et	PROPN
ejpam-6086	121	55	al	al	PROPN
ejpam-6086	121	56	.	.	PUNCT
ejpam-6086	121	57	/	/	SYM
ejpam-6086	121	58	eur	eur	PROPN
ejpam-6086	121	59	.	.	PUNCT
ejpam-6086	122	1	j.	j.	PROPN
ejpam-6086	122	2	pure	pure	PROPN
ejpam-6086	122	3	appl	appl	PROPN
ejpam-6086	122	4	.	.	PROPN
ejpam-6086	122	5	math	math	PROPN
ejpam-6086	122	6	,	,	PUNCT
ejpam-6086	122	7	18	18	NUM
ejpam-6086	122	8	(	(	PUNCT
ejpam-6086	122	9	2	2	NUM
ejpam-6086	122	10	)	)	PUNCT
ejpam-6086	122	11	(	(	PUNCT
ejpam-6086	122	12	2025	2025	NUM
ejpam-6086	122	13	)	)	PUNCT
ejpam-6086	122	14	,	,	PUNCT
ejpam-6086	122	15	6086	6086	NUM
ejpam-6086	122	16	6	6	NUM
ejpam-6086	122	17	of	of	ADP
ejpam-6086	122	18	19	19	NUM
ejpam-6086	122	19	and	and	CCONJ
ejpam-6086	122	20	w	w	PROPN
ejpam-6086	122	21	(	(	PUNCT
ejpam-6086	122	22	xn−1	xn−1	PROPN
ejpam-6086	122	23	,	,	PUNCT
ejpam-6086	122	24	xn	xn	PRON
ejpam-6086	122	25	)	)	PUNCT
ejpam-6086	122	26	=	=	SYM
ejpam-6086	122	27	min{d(xn−1	min{d(xn−1	PROPN
ejpam-6086	122	28	,	,	PUNCT
ejpam-6086	122	29	txn−1	txn−1	PROPN
ejpam-6086	122	30	)	)	PUNCT
ejpam-6086	122	31	,	,	PUNCT
ejpam-6086	122	32	d(xn	d(xn	PROPN
ejpam-6086	122	33	,	,	PUNCT
ejpam-6086	122	34	txn	txn	NOUN
ejpam-6086	122	35	)	)	PUNCT
ejpam-6086	122	36	,	,	PUNCT
ejpam-6086	122	37	d(txn−1	d(txn−1	PROPN
ejpam-6086	122	38	,	,	PUNCT
ejpam-6086	122	39	xn	xn	PROPN
ejpam-6086	122	40	)	)	PUNCT
ejpam-6086	122	41	,	,	PUNCT
ejpam-6086	122	42	d(xn−1	d(xn−1	PROPN
ejpam-6086	122	43	,	,	PUNCT
ejpam-6086	122	44	txn	txn	NOUN
ejpam-6086	122	45	)	)	PUNCT
ejpam-6086	122	46	}	}	PUNCT
ejpam-6086	122	47	=	=	SYM
ejpam-6086	122	48	min{d(xn−1	min{d(xn−1	PROPN
ejpam-6086	122	49	,	,	PUNCT
ejpam-6086	122	50	txn−1	txn−1	PROPN
ejpam-6086	122	51	)	)	PUNCT
ejpam-6086	122	52	,	,	PUNCT
ejpam-6086	122	53	d(xn	d(xn	PROPN
ejpam-6086	122	54	,	,	PUNCT
ejpam-6086	122	55	txn	txn	NOUN
ejpam-6086	122	56	)	)	PUNCT
ejpam-6086	122	57	,	,	PUNCT
ejpam-6086	122	58	0	0	NUM
ejpam-6086	122	59	,	,	PUNCT
ejpam-6086	122	60	d(xn−1	d(xn−1	PROPN
ejpam-6086	122	61	,	,	PUNCT
ejpam-6086	122	62	txn	txn	NOUN
ejpam-6086	122	63	)	)	PUNCT
ejpam-6086	122	64	}	}	PUNCT
ejpam-6086	122	65	=	=	PUNCT
ejpam-6086	123	1	0	0	X
ejpam-6086	123	2	.	.	PUNCT
ejpam-6086	124	1	if	if	SCONJ
ejpam-6086	124	2	m(xn−1	m(xn−1	NUM
ejpam-6086	124	3	,	,	PUNCT
ejpam-6086	124	4	xn	xn	NUM
ejpam-6086	124	5	)	)	PUNCT
ejpam-6086	125	1	=	=	PUNCT
ejpam-6086	126	1	d(xn	d(xn	X
ejpam-6086	126	2	,	,	PUNCT
ejpam-6086	126	3	txn	txn	NOUN
ejpam-6086	126	4	)	)	PUNCT
ejpam-6086	126	5	,	,	PUNCT
ejpam-6086	126	6	we	we	PRON
ejpam-6086	126	7	have	have	VERB
ejpam-6086	126	8	d(xn+1	d(xn+1	PROPN
ejpam-6086	126	9	,	,	PUNCT
ejpam-6086	126	10	xn	xn	PROPN
ejpam-6086	126	11	)	)	PUNCT
ejpam-6086	126	12	≤	≤	NUM
ejpam-6086	126	13	h(txn−1	h(txn−1	PROPN
ejpam-6086	126	14	,	,	PUNCT
ejpam-6086	126	15	txn	txn	NOUN
ejpam-6086	126	16	)	)	PUNCT
ejpam-6086	126	17	.	.	PUNCT
ejpam-6086	127	1	since	since	SCONJ
ejpam-6086	127	2	xn+1	xn+1	PROPN
ejpam-6086	127	3	∈	∈	PROPN
ejpam-6086	127	4	txn	txn	NOUN
ejpam-6086	127	5	this	this	PRON
ejpam-6086	127	6	implies	imply	VERB
ejpam-6086	127	7	that	that	SCONJ
ejpam-6086	127	8	d(xn	d(xn	ADJ
ejpam-6086	127	9	,	,	PUNCT
ejpam-6086	127	10	txn	txn	NOUN
ejpam-6086	127	11	)	)	PUNCT
ejpam-6086	127	12	≤	≤	NOUN
ejpam-6086	128	1	d(xn	d(xn	PROPN
ejpam-6086	128	2	,	,	PUNCT
ejpam-6086	128	3	xn+1	xn+1	NUM
ejpam-6086	128	4	)	)	PUNCT
ejpam-6086	128	5	.	.	PUNCT
ejpam-6086	129	1	now	now	ADV
ejpam-6086	129	2	,	,	PUNCT
ejpam-6086	129	3	we	we	PRON
ejpam-6086	129	4	obtain	obtain	VERB
ejpam-6086	129	5	θ(d(xn+1	θ(d(xn+1	ADJ
ejpam-6086	129	6	,	,	PUNCT
ejpam-6086	129	7	xn	xn	PROPN
ejpam-6086	129	8	)	)	PUNCT
ejpam-6086	129	9	)	)	PUNCT
ejpam-6086	130	1	≤	≤	NOUN
ejpam-6086	130	2	θ(h(txn−1	θ(h(txn−1	VERB
ejpam-6086	130	3	,	,	PUNCT
ejpam-6086	130	4	txn	txn	NOUN
ejpam-6086	130	5	)	)	PUNCT
ejpam-6086	130	6	)	)	PUNCT
ejpam-6086	131	1	≤	≤	NOUN
ejpam-6086	132	1	[	[	X
ejpam-6086	132	2	θ(m(xn−1	θ(m(xn−1	ADJ
ejpam-6086	132	3	,	,	PUNCT
ejpam-6086	132	4	xn	xn	NUM
ejpam-6086	132	5	)	)	PUNCT
ejpam-6086	132	6	)	)	PUNCT
ejpam-6086	132	7	]	]	PUNCT
ejpam-6086	133	1	s	s	VERB
ejpam-6086	133	2	+	+	NOUN
ejpam-6086	133	3	kn(xn−1	kn(xn−1	PROPN
ejpam-6086	133	4	,	,	PUNCT
ejpam-6086	133	5	xn	xn	NUM
ejpam-6086	133	6	)	)	PUNCT
ejpam-6086	133	7	≤	≤	NOUN
ejpam-6086	134	1	[	[	X
ejpam-6086	134	2	θ(m(xn−1	θ(m(xn−1	ADJ
ejpam-6086	134	3	,	,	PUNCT
ejpam-6086	134	4	xn	xn	NUM
ejpam-6086	134	5	)	)	PUNCT
ejpam-6086	134	6	)	)	PUNCT
ejpam-6086	134	7	]	]	PUNCT
ejpam-6086	135	1	s	s	VERB
ejpam-6086	135	2	<	<	X
ejpam-6086	135	3	θ(d(xn	θ(d(xn	X
ejpam-6086	135	4	,	,	PUNCT
ejpam-6086	135	5	txn	txn	NOUN
ejpam-6086	135	6	)	)	PUNCT
ejpam-6086	135	7	)	)	PUNCT
ejpam-6086	136	1	=	=	PUNCT
ejpam-6086	136	2	θ(d(xn	θ(d(xn	X
ejpam-6086	136	3	,	,	PUNCT
ejpam-6086	136	4	xn+1	xn+1	NUM
ejpam-6086	136	5	)	)	PUNCT
ejpam-6086	136	6	)	)	PUNCT
ejpam-6086	136	7	,	,	PUNCT
ejpam-6086	136	8	which	which	PRON
ejpam-6086	136	9	is	be	AUX
ejpam-6086	136	10	a	a	DET
ejpam-6086	136	11	contradiction	contradiction	NOUN
ejpam-6086	136	12	,	,	PUNCT
ejpam-6086	136	13	so	so	ADV
ejpam-6086	136	14	m(xn−1	m(xn−1	ADJ
ejpam-6086	136	15	,	,	PUNCT
ejpam-6086	136	16	xn	xn	X
ejpam-6086	136	17	)	)	PUNCT
ejpam-6086	136	18	=	=	SYM
ejpam-6086	136	19	d(xn−1	d(xn−1	NOUN
ejpam-6086	136	20	,	,	PUNCT
ejpam-6086	136	21	xn	xn	PRON
ejpam-6086	136	22	)	)	PUNCT
ejpam-6086	136	23	and	and	CCONJ
ejpam-6086	136	24	we	we	PRON
ejpam-6086	136	25	have	have	AUX
ejpam-6086	136	26	θ(d(xn+1	θ(d(xn+1	VERB
ejpam-6086	136	27	,	,	PUNCT
ejpam-6086	136	28	xn	xn	PROPN
ejpam-6086	136	29	)	)	PUNCT
ejpam-6086	136	30	)	)	PUNCT
ejpam-6086	137	1	≤	≤	NOUN
ejpam-6086	137	2	θ(h(txn−1	θ(h(txn−1	VERB
ejpam-6086	137	3	,	,	PUNCT
ejpam-6086	137	4	txn	txn	NOUN
ejpam-6086	137	5	)	)	PUNCT
ejpam-6086	137	6	)	)	PUNCT
ejpam-6086	138	1	≤	≤	NOUN
ejpam-6086	139	1	[	[	X
ejpam-6086	139	2	θ(m(xn−1	θ(m(xn−1	ADJ
ejpam-6086	139	3	,	,	PUNCT
ejpam-6086	139	4	xn	xn	NUM
ejpam-6086	139	5	)	)	PUNCT
ejpam-6086	139	6	)	)	PUNCT
ejpam-6086	139	7	]	]	PUNCT
ejpam-6086	140	1	s	s	VERB
ejpam-6086	140	2	+	+	NOUN
ejpam-6086	140	3	kn(xn−1	kn(xn−1	PROPN
ejpam-6086	140	4	,	,	PUNCT
ejpam-6086	140	5	xn	xn	NUM
ejpam-6086	140	6	)	)	PUNCT
ejpam-6086	140	7	≤	≤	NOUN
ejpam-6086	141	1	[	[	X
ejpam-6086	141	2	θ(m(xn−1	θ(m(xn−1	ADJ
ejpam-6086	141	3	,	,	PUNCT
ejpam-6086	141	4	xn	xn	NUM
ejpam-6086	141	5	)	)	PUNCT
ejpam-6086	141	6	)	)	PUNCT
ejpam-6086	141	7	]	]	PUNCT
ejpam-6086	142	1	s	s	X
ejpam-6086	142	2	=	=	X
ejpam-6086	143	1	[	[	X
ejpam-6086	143	2	θ(d(xn−1	θ(d(xn−1	PROPN
ejpam-6086	143	3	,	,	PUNCT
ejpam-6086	143	4	xn	xn	NUM
ejpam-6086	143	5	)	)	PUNCT
ejpam-6086	143	6	)	)	PUNCT
ejpam-6086	143	7	]	]	PUNCT
ejpam-6086	144	1	s	s	VERB
ejpam-6086	144	2	<	<	X
ejpam-6086	144	3	θ(d(xn−1	θ(d(xn−1	PROPN
ejpam-6086	144	4	,	,	PUNCT
ejpam-6086	144	5	xn	xn	NUM
ejpam-6086	144	6	)	)	PUNCT
ejpam-6086	144	7	)	)	PUNCT
ejpam-6086	144	8	.	.	PUNCT
ejpam-6086	145	1	by	by	ADP
ejpam-6086	145	2	the	the	DET
ejpam-6086	145	3	properties	property	NOUN
ejpam-6086	145	4	of	of	ADP
ejpam-6086	145	5	θ	θ	NOUN
ejpam-6086	145	6	we	we	PRON
ejpam-6086	145	7	have	have	VERB
ejpam-6086	145	8	,	,	PUNCT
ejpam-6086	145	9	d(xn	d(xn	PROPN
ejpam-6086	145	10	,	,	PUNCT
ejpam-6086	145	11	xn+1	xn+1	NUM
ejpam-6086	145	12	)	)	PUNCT
ejpam-6086	145	13	<	<	X
ejpam-6086	145	14	d(xn−1	d(xn−1	PROPN
ejpam-6086	145	15	,	,	PUNCT
ejpam-6086	145	16	xn	xn	PROPN
ejpam-6086	145	17	)	)	PUNCT
ejpam-6086	145	18	.	.	PUNCT
ejpam-6086	146	1	this	this	PRON
ejpam-6086	146	2	implies	imply	VERB
ejpam-6086	146	3	that	that	SCONJ
ejpam-6086	146	4	the	the	DET
ejpam-6086	146	5	sequence{d(xn	sequence{d(xn	NOUN
ejpam-6086	146	6	,	,	PUNCT
ejpam-6086	146	7	xn+1)}n	xn+1)}n	PROPN
ejpam-6086	146	8	is	be	AUX
ejpam-6086	146	9	strictly	strictly	ADV
ejpam-6086	146	10	decreasing	decrease	VERB
ejpam-6086	146	11	,	,	PUNCT
ejpam-6086	146	12	this	this	PRON
ejpam-6086	146	13	implies	imply	VERB
ejpam-6086	146	14	that	that	SCONJ
ejpam-6086	146	15	there	there	PRON
ejpam-6086	146	16	exists	exist	VERB
ejpam-6086	146	17	α	α	PROPN
ejpam-6086	146	18	>	>	X
ejpam-6086	146	19	0	0	NUM
ejpam-6086	146	20	such	such	ADJ
ejpam-6086	146	21	that	that	SCONJ
ejpam-6086	146	22	lim	lim	PROPN
ejpam-6086	146	23	n→+∞	n→+∞	VERB
ejpam-6086	146	24	d(xn	d(xn	PROPN
ejpam-6086	146	25	,	,	PUNCT
ejpam-6086	146	26	xn+1	xn+1	NUM
ejpam-6086	146	27	)	)	PUNCT
ejpam-6086	146	28	=	=	SYM
ejpam-6086	147	1	α	α	X
ejpam-6086	147	2	.	.	PUNCT
ejpam-6086	147	3	suppose	suppose	VERB
ejpam-6086	147	4	that	that	SCONJ
ejpam-6086	147	5	α	α	PROPN
ejpam-6086	147	6	>	>	X
ejpam-6086	147	7	0	0	NUM
ejpam-6086	147	8	,	,	PUNCT
ejpam-6086	147	9	we	we	PRON
ejpam-6086	147	10	can	can	AUX
ejpam-6086	147	11	conclude	conclude	VERB
ejpam-6086	147	12	that	that	SCONJ
ejpam-6086	147	13	d(xn	d(xn	PROPN
ejpam-6086	147	14	,	,	PUNCT
ejpam-6086	147	15	xn+1	xn+1	NUM
ejpam-6086	147	16	)	)	PUNCT
ejpam-6086	147	17	≥	≥	PROPN
ejpam-6086	147	18	α	α	NOUN
ejpam-6086	147	19	,	,	PUNCT
ejpam-6086	147	20	for	for	ADP
ejpam-6086	147	21	all	all	PRON
ejpam-6086	147	22	n	n	DET
ejpam-6086	147	23	∈	∈	PROPN
ejpam-6086	147	24	n.	n.	NOUN
ejpam-6086	147	25	we	we	PRON
ejpam-6086	147	26	get	get	AUX
ejpam-6086	147	27	θ(d(xn+1	θ(d(xn+1	VERB
ejpam-6086	147	28	,	,	PUNCT
ejpam-6086	147	29	xn	xn	PROPN
ejpam-6086	147	30	)	)	PUNCT
ejpam-6086	147	31	)	)	PUNCT
ejpam-6086	147	32	≤	≤	NOUN
ejpam-6086	148	1	[	[	X
ejpam-6086	148	2	θ(d(xn−1	θ(d(xn−1	PROPN
ejpam-6086	148	3	,	,	PUNCT
ejpam-6086	148	4	xn	xn	NUM
ejpam-6086	148	5	)	)	PUNCT
ejpam-6086	148	6	)	)	PUNCT
ejpam-6086	148	7	]	]	PUNCT
ejpam-6086	148	8	s	s	VERB
ejpam-6086	148	9	≤	≤	X
ejpam-6086	149	1	[	[	X
ejpam-6086	149	2	θ(d(xn−2	θ(d(xn−2	PROPN
ejpam-6086	149	3	,	,	PUNCT
ejpam-6086	149	4	xn−1	xn−1	PROPN
ejpam-6086	149	5	)	)	PUNCT
ejpam-6086	149	6	)	)	PUNCT
ejpam-6086	149	7	]	]	PUNCT
ejpam-6086	149	8	s2	s2	NOUN
ejpam-6086	149	9	...	...	PUNCT
ejpam-6086	149	10	≤	≤	NUM
ejpam-6086	150	1	[	[	X
ejpam-6086	150	2	θ(d(x0	θ(d(x0	NOUN
ejpam-6086	150	3	,	,	PUNCT
ejpam-6086	150	4	x1	x1	PROPN
ejpam-6086	150	5	)	)	PUNCT
ejpam-6086	150	6	)	)	PUNCT
ejpam-6086	150	7	]	]	PUNCT
ejpam-6086	150	8	sn	sn	INTJ
ejpam-6086	150	9	.	.	PUNCT
ejpam-6086	150	10	using	use	VERB
ejpam-6086	150	11	the	the	DET
ejpam-6086	150	12	property	property	NOUN
ejpam-6086	150	13	of	of	ADP
ejpam-6086	150	14	θ	θ	PROPN
ejpam-6086	150	15	,	,	PUNCT
ejpam-6086	150	16	we	we	PRON
ejpam-6086	150	17	obtain	obtain	VERB
ejpam-6086	150	18	1	1	NUM
ejpam-6086	150	19	<	<	X
ejpam-6086	150	20	θ(α	θ(α	NOUN
ejpam-6086	150	21	)	)	PUNCT
ejpam-6086	150	22	≤	≤	NOUN
ejpam-6086	151	1	[	[	X
ejpam-6086	151	2	θ(d(x0	θ(d(x0	NOUN
ejpam-6086	151	3	,	,	PUNCT
ejpam-6086	151	4	x1	x1	PROPN
ejpam-6086	151	5	)	)	PUNCT
ejpam-6086	151	6	)	)	PUNCT
ejpam-6086	151	7	]	]	PUNCT
ejpam-6086	152	1	sn	sn	INTJ
ejpam-6086	152	2	.	.	PUNCT
ejpam-6086	153	1	(	(	PUNCT
ejpam-6086	153	2	8)	8)	NUM
ejpam-6086	153	3	h.	h.	NOUN
ejpam-6086	153	4	massit	massit	PROPN
ejpam-6086	153	5	et	et	PROPN
ejpam-6086	153	6	al	al	PROPN
ejpam-6086	153	7	.	.	PUNCT
ejpam-6086	153	8	/	/	SYM
ejpam-6086	153	9	eur	eur	PROPN
ejpam-6086	153	10	.	.	PUNCT
ejpam-6086	154	1	j.	j.	PROPN
ejpam-6086	154	2	pure	pure	PROPN
ejpam-6086	154	3	appl	appl	PROPN
ejpam-6086	154	4	.	.	PROPN
ejpam-6086	154	5	math	math	PROPN
ejpam-6086	154	6	,	,	PUNCT
ejpam-6086	154	7	18	18	NUM
ejpam-6086	154	8	(	(	PUNCT
ejpam-6086	154	9	2	2	NUM
ejpam-6086	154	10	)	)	PUNCT
ejpam-6086	154	11	(	(	PUNCT
ejpam-6086	154	12	2025	2025	NUM
ejpam-6086	154	13	)	)	PUNCT
ejpam-6086	154	14	,	,	PUNCT
ejpam-6086	154	15	6086	6086	NUM
ejpam-6086	154	16	7	7	NUM
ejpam-6086	154	17	of	of	ADP
ejpam-6086	154	18	19	19	NUM
ejpam-6086	154	19	letting	let	VERB
ejpam-6086	154	20	n→	n→	ADV
ejpam-6086	154	21	+	+	ADJ
ejpam-6086	154	22	∞	∞	PROPN
ejpam-6086	154	23	in	in	ADP
ejpam-6086	154	24	(	(	PUNCT
ejpam-6086	154	25	8)	8)	NUM
ejpam-6086	154	26	,	,	PUNCT
ejpam-6086	154	27	we	we	PRON
ejpam-6086	154	28	get	get	VERB
ejpam-6086	154	29	1	1	NUM
ejpam-6086	154	30	<	<	X
ejpam-6086	154	31	θ(α	θ(α	NOUN
ejpam-6086	154	32	)	)	PUNCT
ejpam-6086	154	33	≤	≤	NOUN
ejpam-6086	154	34	1	1	NUM
ejpam-6086	154	35	.	.	PUNCT
ejpam-6086	155	1	this	this	DET
ejpam-6086	155	2	a	a	DET
ejpam-6086	155	3	contradiction	contradiction	NOUN
ejpam-6086	155	4	.	.	PUNCT
ejpam-6086	156	1	now	now	ADV
ejpam-6086	156	2	,	,	PUNCT
ejpam-6086	156	3	we	we	PRON
ejpam-6086	156	4	conclude	conclude	VERB
ejpam-6086	156	5	that	that	SCONJ
ejpam-6086	156	6	lim	lim	PROPN
ejpam-6086	156	7	n→+∞	n→+∞	VERB
ejpam-6086	156	8	d(xn	d(xn	PROPN
ejpam-6086	156	9	,	,	PUNCT
ejpam-6086	156	10	xn+1	xn+1	NUM
ejpam-6086	156	11	)	)	PUNCT
ejpam-6086	156	12	=	=	SYM
ejpam-6086	157	1	0	0	X
ejpam-6086	157	2	.	.	PUNCT
ejpam-6086	158	1	next	next	ADV
ejpam-6086	158	2	,	,	PUNCT
ejpam-6086	158	3	we	we	PRON
ejpam-6086	158	4	show	show	VERB
ejpam-6086	158	5	that	that	SCONJ
ejpam-6086	158	6	{	{	PUNCT
ejpam-6086	158	7	xn}n	xn}n	PROPN
ejpam-6086	158	8	is	be	AUX
ejpam-6086	158	9	a	a	DET
ejpam-6086	158	10	cauchy	cauchy	ADJ
ejpam-6086	158	11	sequence	sequence	NOUN
ejpam-6086	158	12	in	in	ADP
ejpam-6086	158	13	u	u	NOUN
ejpam-6086	158	14	,	,	PUNCT
ejpam-6086	158	15	there	there	PRON
ejpam-6086	158	16	exists	exist	VERB
ejpam-6086	158	17	an	an	DET
ejpam-6086	158	18	ε	ε	PROPN
ejpam-6086	158	19	>	>	X
ejpam-6086	158	20	0	0	PROPN
ejpam-6086	158	21	for	for	ADP
ejpam-6086	158	22	which	which	PRON
ejpam-6086	158	23	we	we	PRON
ejpam-6086	158	24	can	can	AUX
ejpam-6086	158	25	find	find	VERB
ejpam-6086	158	26	sequences	sequence	NOUN
ejpam-6086	158	27	of	of	ADP
ejpam-6086	158	28	positive	positive	ADJ
ejpam-6086	158	29	integers	integer	NOUN
ejpam-6086	158	30	{	{	PUNCT
ejpam-6086	158	31	xnk	xnk	PROPN
ejpam-6086	158	32	}	}	PUNCT
ejpam-6086	158	33	and	and	CCONJ
ejpam-6086	158	34	{	{	PUNCT
ejpam-6086	158	35	xmk	xmk	PROPN
ejpam-6086	158	36	}	}	PUNCT
ejpam-6086	158	37	of	of	ADP
ejpam-6086	158	38	{	{	PUNCT
ejpam-6086	158	39	xn	xn	NOUN
ejpam-6086	158	40	}	}	PUNCT
ejpam-6086	158	41	such	such	ADJ
ejpam-6086	158	42	that	that	SCONJ
ejpam-6086	158	43	,	,	PUNCT
ejpam-6086	158	44	for	for	ADP
ejpam-6086	158	45	all	all	DET
ejpam-6086	158	46	positive	positive	ADJ
ejpam-6086	158	47	integers	integer	NOUN
ejpam-6086	158	48	k	k	NOUN
ejpam-6086	158	49	,	,	PUNCT
ejpam-6086	158	50	nk	nk	PROPN
ejpam-6086	158	51	>	>	X
ejpam-6086	158	52	mk	mk	PROPN
ejpam-6086	158	53	>	>	X
ejpam-6086	158	54	k	k	PROPN
ejpam-6086	158	55	,	,	PUNCT
ejpam-6086	158	56	d(xmk	d(xmk	PROPN
ejpam-6086	158	57	,	,	PUNCT
ejpam-6086	158	58	xnk	xnk	PROPN
ejpam-6086	158	59	)	)	PUNCT
ejpam-6086	158	60	≥	≥	PROPN
ejpam-6086	158	61	ε	ε	PROPN
ejpam-6086	158	62	(	(	PUNCT
ejpam-6086	158	63	9	9	NUM
ejpam-6086	158	64	)	)	PUNCT
ejpam-6086	158	65	d(xmk	d(xmk	NOUN
ejpam-6086	158	66	,	,	PUNCT
ejpam-6086	158	67	xnk−1	xnk−1	PROPN
ejpam-6086	158	68	)	)	PUNCT
ejpam-6086	158	69	<	<	X
ejpam-6086	158	70	ε	ε	PROPN
ejpam-6086	158	71	(	(	PUNCT
ejpam-6086	158	72	10	10	NUM
ejpam-6086	158	73	)	)	PUNCT
ejpam-6086	158	74	we	we	PRON
ejpam-6086	158	75	get	get	VERB
ejpam-6086	158	76	ε	ε	PROPN
ejpam-6086	158	77	≤	≤	PROPN
ejpam-6086	158	78	d(xmk	d(xmk	PROPN
ejpam-6086	158	79	,	,	PUNCT
ejpam-6086	158	80	xnk	xnk	PROPN
ejpam-6086	158	81	)	)	PUNCT
ejpam-6086	158	82	≤	≤	NUM
ejpam-6086	158	83	bd(xmk	bd(xmk	PROPN
ejpam-6086	158	84	,	,	PUNCT
ejpam-6086	158	85	xmk+1	xmk+1	X
ejpam-6086	158	86	)	)	PUNCT
ejpam-6086	159	1	+	+	CCONJ
ejpam-6086	159	2	bd(xmk+1	bd(xmk+1	NOUN
ejpam-6086	159	3	,	,	PUNCT
ejpam-6086	159	4	xnk+1	xnk+1	X
ejpam-6086	159	5	)	)	PUNCT
ejpam-6086	160	1	+	+	CCONJ
ejpam-6086	160	2	bd(xnk+1	bd(xnk+1	NOUN
ejpam-6086	160	3	,	,	PUNCT
ejpam-6086	160	4	xnk	xnk	PROPN
ejpam-6086	160	5	)	)	PUNCT
ejpam-6086	160	6	,	,	PUNCT
ejpam-6086	160	7	(	(	PUNCT
ejpam-6086	160	8	11	11	X
ejpam-6086	160	9	)	)	PUNCT
ejpam-6086	160	10	letting	let	VERB
ejpam-6086	160	11	k	k	X
ejpam-6086	160	12	→	→	PUNCT
ejpam-6086	160	13	+	+	PROPN
ejpam-6086	160	14	∞	∞	PROPN
ejpam-6086	160	15	,	,	PUNCT
ejpam-6086	160	16	we	we	PRON
ejpam-6086	160	17	get	get	VERB
ejpam-6086	160	18	ε	ε	PROPN
ejpam-6086	160	19	b	b	PROPN
ejpam-6086	160	20	lim	lim	PROPN
ejpam-6086	160	21	n→+∞	n→+∞	VERB
ejpam-6086	160	22	sup	sup	NOUN
ejpam-6086	160	23	d(xmk+1	d(xmk+1	NOUN
ejpam-6086	160	24	,	,	PUNCT
ejpam-6086	160	25	xnk+1	xnk+1	PROPN
ejpam-6086	160	26	)	)	PUNCT
ejpam-6086	160	27	(	(	PUNCT
ejpam-6086	160	28	12	12	NUM
ejpam-6086	160	29	)	)	PUNCT
ejpam-6086	160	30	and	and	CCONJ
ejpam-6086	160	31	lim	lim	PROPN
ejpam-6086	160	32	n→+∞	n→+∞	VERB
ejpam-6086	160	33	sup	sup	NOUN
ejpam-6086	160	34	d(xmk	d(xmk	NOUN
ejpam-6086	160	35	,	,	PUNCT
ejpam-6086	160	36	xnk	xnk	PROPN
ejpam-6086	160	37	)	)	PUNCT
ejpam-6086	160	38	≤	≤	NUM
ejpam-6086	160	39	bε	bε	NOUN
ejpam-6086	160	40	.	.	PUNCT
ejpam-6086	161	1	(	(	PUNCT
ejpam-6086	161	2	13	13	NUM
ejpam-6086	161	3	)	)	PUNCT
ejpam-6086	161	4	since	since	SCONJ
ejpam-6086	161	5	α(xmk	α(xmk	PROPN
ejpam-6086	161	6	,	,	PUNCT
ejpam-6086	161	7	xnk	xnk	PROPN
ejpam-6086	161	8	)	)	PUNCT
ejpam-6086	161	9	≥	≥	NOUN
ejpam-6086	161	10	1	1	NUM
ejpam-6086	161	11	,	,	PUNCT
ejpam-6086	161	12	we	we	PRON
ejpam-6086	161	13	have	have	VERB
ejpam-6086	161	14	m(xmk	m(xmk	NOUN
ejpam-6086	161	15	,	,	PUNCT
ejpam-6086	161	16	xnk	xnk	PROPN
ejpam-6086	161	17	)	)	PUNCT
ejpam-6086	162	1	=	=	SYM
ejpam-6086	162	2	max{d(xmk	max{d(xmk	NOUN
ejpam-6086	162	3	,	,	PUNCT
ejpam-6086	162	4	xnk	xnk	PROPN
ejpam-6086	162	5	)	)	PUNCT
ejpam-6086	162	6	,	,	PUNCT
ejpam-6086	162	7	d(xmk	d(xmk	PROPN
ejpam-6086	162	8	,	,	PUNCT
ejpam-6086	162	9	txmk	txmk	PROPN
ejpam-6086	162	10	)	)	PUNCT
ejpam-6086	162	11	,	,	PUNCT
ejpam-6086	162	12	d(xmk	d(xmk	PROPN
ejpam-6086	162	13	,	,	PUNCT
ejpam-6086	162	14	txmk	txmk	PROPN
ejpam-6086	162	15	)	)	PUNCT
ejpam-6086	162	16	,	,	PUNCT
ejpam-6086	162	17	d(xnk	d(xnk	PROPN
ejpam-6086	162	18	,	,	PUNCT
ejpam-6086	162	19	txmk	txmk	NOUN
ejpam-6086	162	20	)	)	PUNCT
ejpam-6086	162	21	}	}	PUNCT
ejpam-6086	163	1	≤	≤	NUM
ejpam-6086	163	2	max{d(xmk	max{d(xmk	NOUN
ejpam-6086	163	3	,	,	PUNCT
ejpam-6086	163	4	xnk	xnk	PROPN
ejpam-6086	163	5	)	)	PUNCT
ejpam-6086	163	6	,	,	PUNCT
ejpam-6086	163	7	d(xmk	d(xmk	PROPN
ejpam-6086	163	8	,	,	PUNCT
ejpam-6086	163	9	xmk+1	xmk+1	X
ejpam-6086	163	10	)	)	PUNCT
ejpam-6086	163	11	,	,	PUNCT
ejpam-6086	163	12	d(xmk	d(xmk	PROPN
ejpam-6086	163	13	,	,	PUNCT
ejpam-6086	163	14	xmk+1	xmk+1	PROPN
ejpam-6086	163	15	)	)	PUNCT
ejpam-6086	163	16	,	,	PUNCT
ejpam-6086	163	17	d(xnk	d(xnk	PROPN
ejpam-6086	163	18	,	,	PUNCT
ejpam-6086	163	19	xmk+1	xmk+1	X
ejpam-6086	163	20	)	)	PUNCT
ejpam-6086	163	21	}	}	PUNCT
ejpam-6086	163	22	=	=	SYM
ejpam-6086	163	23	max{d(xmk	max{d(xmk	NOUN
ejpam-6086	163	24	,	,	PUNCT
ejpam-6086	163	25	xnk	xnk	PROPN
ejpam-6086	163	26	)	)	PUNCT
ejpam-6086	163	27	,	,	PUNCT
ejpam-6086	163	28	d(xmk	d(xmk	PROPN
ejpam-6086	163	29	,	,	PUNCT
ejpam-6086	163	30	xmk+1	xmk+1	PROPN
ejpam-6086	163	31	)	)	PUNCT
ejpam-6086	163	32	,	,	PUNCT
ejpam-6086	163	33	d(xnk	d(xnk	PROPN
ejpam-6086	163	34	,	,	PUNCT
ejpam-6086	163	35	xmk+1	xmk+1	X
ejpam-6086	163	36	)	)	PUNCT
ejpam-6086	163	37	}	}	PUNCT
ejpam-6086	163	38	and	and	CCONJ
ejpam-6086	163	39	w	w	PROPN
ejpam-6086	163	40	(	(	PUNCT
ejpam-6086	163	41	xmk	xmk	PROPN
ejpam-6086	163	42	,	,	PUNCT
ejpam-6086	163	43	xnk	xnk	PROPN
ejpam-6086	163	44	)	)	PUNCT
ejpam-6086	164	1	=	=	SYM
ejpam-6086	164	2	min{d(xmk	min{d(xmk	NOUN
ejpam-6086	164	3	,	,	PUNCT
ejpam-6086	164	4	txmk	txmk	NOUN
ejpam-6086	164	5	)	)	PUNCT
ejpam-6086	164	6	,	,	PUNCT
ejpam-6086	164	7	d(xnk	d(xnk	PROPN
ejpam-6086	164	8	,	,	PUNCT
ejpam-6086	164	9	txnk	txnk	NOUN
ejpam-6086	164	10	)	)	PUNCT
ejpam-6086	164	11	,	,	PUNCT
ejpam-6086	164	12	d(txmk	d(txmk	INTJ
ejpam-6086	164	13	,	,	PUNCT
ejpam-6086	164	14	xnk	xnk	PROPN
ejpam-6086	164	15	)	)	PUNCT
ejpam-6086	164	16	,	,	PUNCT
ejpam-6086	164	17	d(xmk	d(xmk	PROPN
ejpam-6086	164	18	,	,	PUNCT
ejpam-6086	164	19	txnk	txnk	NOUN
ejpam-6086	164	20	)	)	PUNCT
ejpam-6086	164	21	}	}	PUNCT
ejpam-6086	164	22	≤	≤	NOUN
ejpam-6086	164	23	min{d(xmk	min{d(xmk	NOUN
ejpam-6086	164	24	,	,	PUNCT
ejpam-6086	164	25	xmk+1	xmk+1	X
ejpam-6086	164	26	)	)	PUNCT
ejpam-6086	164	27	,	,	PUNCT
ejpam-6086	164	28	d(xnk	d(xnk	PROPN
ejpam-6086	164	29	,	,	PUNCT
ejpam-6086	164	30	xnk+1	xnk+1	PROPN
ejpam-6086	164	31	)	)	PUNCT
ejpam-6086	164	32	,	,	PUNCT
ejpam-6086	164	33	d(xmk+1	d(xmk+1	VERB
ejpam-6086	164	34	,	,	PUNCT
ejpam-6086	164	35	xnk	xnk	PROPN
ejpam-6086	164	36	)	)	PUNCT
ejpam-6086	164	37	,	,	PUNCT
ejpam-6086	164	38	d(xmk	d(xmk	PROPN
ejpam-6086	164	39	,	,	PUNCT
ejpam-6086	164	40	xnk+1	xnk+1	PROPN
ejpam-6086	164	41	)	)	PUNCT
ejpam-6086	164	42	}	}	PUNCT
ejpam-6086	164	43	,	,	PUNCT
ejpam-6086	164	44	letting	let	VERB
ejpam-6086	164	45	n→	n→	ADV
ejpam-6086	164	46	+	+	PROPN
ejpam-6086	164	47	∞	∞	PROPN
ejpam-6086	164	48	,	,	PUNCT
ejpam-6086	164	49	we	we	PRON
ejpam-6086	164	50	obtain	obtain	VERB
ejpam-6086	164	51	lim	lim	PROPN
ejpam-6086	164	52	k→+∞	k→+∞	PROPN
ejpam-6086	164	53	m(xmk	m(xmk	PROPN
ejpam-6086	164	54	,	,	PUNCT
ejpam-6086	164	55	xnk	xnk	PROPN
ejpam-6086	164	56	)	)	PUNCT
ejpam-6086	164	57	≤	≤	PROPN
ejpam-6086	165	1	lim	lim	PROPN
ejpam-6086	165	2	k→+∞	k→+∞	PROPN
ejpam-6086	165	3	max{d(xmk	max{d(xmk	NOUN
ejpam-6086	165	4	,	,	PUNCT
ejpam-6086	165	5	xnk	xnk	PROPN
ejpam-6086	165	6	)	)	PUNCT
ejpam-6086	165	7	,	,	PUNCT
ejpam-6086	165	8	d(xmk	d(xmk	PROPN
ejpam-6086	165	9	,	,	PUNCT
ejpam-6086	165	10	xmk+1	xmk+1	PROPN
ejpam-6086	165	11	)	)	PUNCT
ejpam-6086	165	12	,	,	PUNCT
ejpam-6086	165	13	d(xnk	d(xnk	PROPN
ejpam-6086	165	14	,	,	PUNCT
ejpam-6086	165	15	xmk+1	xmk+1	X
ejpam-6086	165	16	)	)	PUNCT
ejpam-6086	165	17	}	}	PUNCT
ejpam-6086	165	18	≤	≤	NOUN
ejpam-6086	165	19	max{bε	max{bε	NOUN
ejpam-6086	165	20	,	,	PUNCT
ejpam-6086	165	21	0	0	NUM
ejpam-6086	165	22	,	,	PUNCT
ejpam-6086	165	23	b2ε	b2ε	ADJ
ejpam-6086	165	24	}	}	PUNCT
ejpam-6086	165	25	=	=	SYM
ejpam-6086	165	26	b2ε	b2ε	PROPN
ejpam-6086	165	27	and	and	CCONJ
ejpam-6086	165	28	lim	lim	PROPN
ejpam-6086	165	29	k→+∞	k→+∞	PROPN
ejpam-6086	165	30	w	w	PROPN
ejpam-6086	165	31	(	(	PUNCT
ejpam-6086	165	32	xmk	xmk	PROPN
ejpam-6086	165	33	,	,	PUNCT
ejpam-6086	165	34	xnk	xnk	PROPN
ejpam-6086	165	35	)	)	PUNCT
ejpam-6086	165	36	≤	≤	PROPN
ejpam-6086	166	1	lim	lim	PROPN
ejpam-6086	166	2	k→+∞	k→+∞	PROPN
ejpam-6086	166	3	min{d(xmk	min{d(xmk	PROPN
ejpam-6086	166	4	,	,	PUNCT
ejpam-6086	166	5	xnk	xnk	PROPN
ejpam-6086	166	6	)	)	PUNCT
ejpam-6086	166	7	,	,	PUNCT
ejpam-6086	166	8	d(xmk	d(xmk	PROPN
ejpam-6086	166	9	,	,	PUNCT
ejpam-6086	166	10	xmk+1	xmk+1	PROPN
ejpam-6086	166	11	)	)	PUNCT
ejpam-6086	166	12	,	,	PUNCT
ejpam-6086	166	13	d(xnk	d(xnk	PROPN
ejpam-6086	166	14	,	,	PUNCT
ejpam-6086	166	15	xmk+1	xmk+1	X
ejpam-6086	166	16	)	)	PUNCT
ejpam-6086	166	17	}	}	PUNCT
ejpam-6086	166	18	≤	≤	NOUN
ejpam-6086	166	19	min{bε	min{bε	NOUN
ejpam-6086	166	20	,	,	PUNCT
ejpam-6086	166	21	0	0	NUM
ejpam-6086	166	22	,	,	PUNCT
ejpam-6086	166	23	b2ε	b2ε	ADJ
ejpam-6086	166	24	}	}	PUNCT
ejpam-6086	166	25	h.	h.	NOUN
ejpam-6086	166	26	massit	massit	PROPN
ejpam-6086	166	27	et	et	PROPN
ejpam-6086	166	28	al	al	PROPN
ejpam-6086	166	29	.	.	PUNCT
ejpam-6086	166	30	/	/	SYM
ejpam-6086	166	31	eur	eur	PROPN
ejpam-6086	166	32	.	.	PUNCT
ejpam-6086	167	1	j.	j.	PROPN
ejpam-6086	167	2	pure	pure	PROPN
ejpam-6086	167	3	appl	appl	PROPN
ejpam-6086	167	4	.	.	PROPN
ejpam-6086	167	5	math	math	PROPN
ejpam-6086	167	6	,	,	PUNCT
ejpam-6086	167	7	18	18	NUM
ejpam-6086	167	8	(	(	PUNCT
ejpam-6086	167	9	2	2	NUM
ejpam-6086	167	10	)	)	PUNCT
ejpam-6086	167	11	(	(	PUNCT
ejpam-6086	167	12	2025	2025	NUM
ejpam-6086	167	13	)	)	PUNCT
ejpam-6086	167	14	,	,	PUNCT
ejpam-6086	167	15	6086	6086	NUM
ejpam-6086	167	16	8	8	NUM
ejpam-6086	167	17	of	of	ADP
ejpam-6086	167	18	19	19	NUM
ejpam-6086	167	19	=	=	SYM
ejpam-6086	167	20	0	0	NUM
ejpam-6086	167	21	.	.	PUNCT
ejpam-6086	168	1	so	so	ADV
ejpam-6086	168	2	,	,	PUNCT
ejpam-6086	168	3	we	we	PRON
ejpam-6086	168	4	have	have	AUX
ejpam-6086	168	5	θ[d(xmk+1	θ[d(xmk+1	VERB
ejpam-6086	168	6	,	,	PUNCT
ejpam-6086	168	7	xnk+1	xnk+1	PROPN
ejpam-6086	168	8	)	)	PUNCT
ejpam-6086	168	9	]	]	PUNCT
ejpam-6086	169	1	≤	≤	PROPN
ejpam-6086	169	2	θ[b3h(txmk	θ[b3h(txmk	ADV
ejpam-6086	169	3	,	,	PUNCT
ejpam-6086	169	4	txnk	txnk	NOUN
ejpam-6086	169	5	)	)	PUNCT
ejpam-6086	169	6	]	]	PUNCT
ejpam-6086	169	7	≤	≤	NUM
ejpam-6086	169	8	θ[α(xmk	θ[α(xmk	NOUN
ejpam-6086	169	9	,	,	PUNCT
ejpam-6086	169	10	xnk	xnk	PROPN
ejpam-6086	169	11	)	)	PUNCT
ejpam-6086	169	12	b3h(txmk	b3h(txmk	PROPN
ejpam-6086	169	13	,	,	PUNCT
ejpam-6086	169	14	txnk	txnk	VERB
ejpam-6086	169	15	)	)	PUNCT
ejpam-6086	169	16	]	]	PUNCT
ejpam-6086	170	1	≤	≤	X
ejpam-6086	171	1	[	[	X
ejpam-6086	171	2	θ(m(xmk	θ(m(xmk	X
ejpam-6086	171	3	,	,	PUNCT
ejpam-6086	171	4	xnk	xnk	PROPN
ejpam-6086	171	5	)	)	PUNCT
ejpam-6086	171	6	)	)	PUNCT
ejpam-6086	172	1	]	]	X
ejpam-6086	172	2	s	s	VERB
ejpam-6086	172	3	+	+	ADJ
ejpam-6086	172	4	kw	kw	INTJ
ejpam-6086	172	5	(	(	PUNCT
ejpam-6086	172	6	xmk	xmk	PROPN
ejpam-6086	172	7	,	,	PUNCT
ejpam-6086	172	8	xnk	xnk	PROPN
ejpam-6086	172	9	)	)	PUNCT
ejpam-6086	172	10	.	.	PUNCT
ejpam-6086	173	1	letting	let	VERB
ejpam-6086	173	2	k	k	PRON
ejpam-6086	173	3	→	→	PUNCT
ejpam-6086	173	4	+	+	PROPN
ejpam-6086	173	5	∞	∞	PROPN
ejpam-6086	173	6	,	,	PUNCT
ejpam-6086	173	7	we	we	PRON
ejpam-6086	173	8	obtain	obtain	VERB
ejpam-6086	173	9	θ(εb	θ(εb	NOUN
ejpam-6086	173	10	)	)	PUNCT
ejpam-6086	173	11	≤	≤	NOUN
ejpam-6086	173	12	θ[b3	θ[b3	SCONJ
ejpam-6086	173	13	lim	lim	PROPN
ejpam-6086	173	14	k→+∞	k→+∞	PROPN
ejpam-6086	173	15	d(xmk+1	d(xmk+1	VERB
ejpam-6086	173	16	,	,	PUNCT
ejpam-6086	173	17	xnk+1	xnk+1	PROPN
ejpam-6086	173	18	)	)	PUNCT
ejpam-6086	173	19	]	]	PUNCT
ejpam-6086	174	1	≤	≤	X
ejpam-6086	175	1	[	[	X
ejpam-6086	175	2	θ	θ	X
ejpam-6086	175	3	(	(	PUNCT
ejpam-6086	175	4	lim	lim	PROPN
ejpam-6086	175	5	k→+∞	k→+∞	PROPN
ejpam-6086	175	6	m(xmk	m(xmk	PROPN
ejpam-6086	175	7	,	,	PUNCT
ejpam-6086	175	8	xnk	xnk	PROPN
ejpam-6086	175	9	)	)	PUNCT
ejpam-6086	175	10	)	)	PUNCT
ejpam-6086	175	11	]	]	X
ejpam-6086	175	12	s	s	X
ejpam-6086	176	1	+	+	PROPN
ejpam-6086	176	2	k	k	PROPN
ejpam-6086	176	3	lim	lim	PROPN
ejpam-6086	176	4	k→+∞	k→+∞	PROPN
ejpam-6086	176	5	w	w	PROPN
ejpam-6086	176	6	(	(	PUNCT
ejpam-6086	176	7	xmk	xmk	PROPN
ejpam-6086	176	8	,	,	PUNCT
ejpam-6086	176	9	xnk	xnk	PROPN
ejpam-6086	176	10	)	)	PUNCT
ejpam-6086	177	1	=	=	PUNCT
ejpam-6086	178	1	[	[	X
ejpam-6086	178	2	θ	θ	X
ejpam-6086	178	3	(	(	PUNCT
ejpam-6086	178	4	lim	lim	PROPN
ejpam-6086	178	5	k→+∞	k→+∞	PROPN
ejpam-6086	178	6	m(xmk	m(xmk	PROPN
ejpam-6086	178	7	,	,	PUNCT
ejpam-6086	178	8	xnk	xnk	PROPN
ejpam-6086	178	9	)	)	PUNCT
ejpam-6086	178	10	)	)	PUNCT
ejpam-6086	179	1	]	]	X
ejpam-6086	179	2	s	s	VERB
ejpam-6086	179	3	≤	≤	X
ejpam-6086	180	1	[	[	X
ejpam-6086	180	2	θ(bε)]s	θ(bε)]s	X
ejpam-6086	180	3	<	<	X
ejpam-6086	180	4	θ(bε	θ(bε	PROPN
ejpam-6086	180	5	)	)	PUNCT
ejpam-6086	180	6	.	.	PUNCT
ejpam-6086	181	1	this	this	PRON
ejpam-6086	181	2	implies	imply	VERB
ejpam-6086	181	3	that	that	SCONJ
ejpam-6086	181	4	bε	bε	NOUN
ejpam-6086	181	5	<	<	X
ejpam-6086	181	6	bε	bε	NOUN
ejpam-6086	181	7	,	,	PUNCT
ejpam-6086	181	8	which	which	PRON
ejpam-6086	181	9	is	be	AUX
ejpam-6086	181	10	a	a	DET
ejpam-6086	181	11	contradiction	contradiction	NOUN
ejpam-6086	181	12	.	.	PUNCT
ejpam-6086	182	1	consequently	consequently	ADV
ejpam-6086	182	2	,	,	PUNCT
ejpam-6086	182	3	{	{	PUNCT
ejpam-6086	182	4	xn	xn	X
ejpam-6086	182	5	}	}	PUNCT
ejpam-6086	182	6	is	be	AUX
ejpam-6086	182	7	a	a	DET
ejpam-6086	182	8	cauchy	cauchy	ADJ
ejpam-6086	182	9	sequence	sequence	NOUN
ejpam-6086	182	10	in	in	ADP
ejpam-6086	182	11	u	u	PROPN
ejpam-6086	182	12	,	,	PUNCT
ejpam-6086	182	13	so	so	SCONJ
ejpam-6086	182	14	there	there	PRON
ejpam-6086	182	15	exists	exist	VERB
ejpam-6086	182	16	z	z	PROPN
ejpam-6086	182	17	∈	∈	PROPN
ejpam-6086	182	18	u	u	NOUN
ejpam-6086	182	19	such	such	ADJ
ejpam-6086	182	20	that	that	SCONJ
ejpam-6086	182	21	lim	lim	PROPN
ejpam-6086	182	22	n→+∞	n→+∞	VERB
ejpam-6086	182	23	d(xn	d(xn	PROPN
ejpam-6086	182	24	,	,	PUNCT
ejpam-6086	182	25	z	z	NOUN
ejpam-6086	182	26	)	)	PUNCT
ejpam-6086	182	27	=	=	SYM
ejpam-6086	183	1	0	0	X
ejpam-6086	183	2	.	.	PUNCT
ejpam-6086	184	1	since	since	SCONJ
ejpam-6086	184	2	t	t	PROPN
ejpam-6086	184	3	is	be	AUX
ejpam-6086	184	4	α−continuous	α−continuous	ADJ
ejpam-6086	184	5	multivalued	multivalued	ADJ
ejpam-6086	184	6	mapping	mapping	NOUN
ejpam-6086	184	7	,	,	PUNCT
ejpam-6086	184	8	we	we	PRON
ejpam-6086	184	9	have	have	VERB
ejpam-6086	184	10	lim	lim	PROPN
ejpam-6086	184	11	n→+∞	n→+∞	PROPN
ejpam-6086	184	12	h(txn	h(txn	PROPN
ejpam-6086	184	13	,	,	PUNCT
ejpam-6086	184	14	t	t	PROPN
ejpam-6086	184	15	z	z	PROPN
ejpam-6086	184	16	)	)	PUNCT
ejpam-6086	184	17	=	=	SYM
ejpam-6086	185	1	0	0	X
ejpam-6086	185	2	.	.	PUNCT
ejpam-6086	186	1	we	we	PRON
ejpam-6086	186	2	now	now	ADV
ejpam-6086	186	3	conclude	conclude	VERB
ejpam-6086	186	4	that	that	SCONJ
ejpam-6086	186	5	it	it	PRON
ejpam-6086	186	6	is	be	AUX
ejpam-6086	186	7	lim	lim	PROPN
ejpam-6086	186	8	n→+∞	n→+∞	PROPN
ejpam-6086	186	9	d(xn+1	d(xn+1	PROPN
ejpam-6086	186	10	,	,	PUNCT
ejpam-6086	186	11	t	t	PROPN
ejpam-6086	186	12	z	z	PROPN
ejpam-6086	186	13	)	)	PUNCT
ejpam-6086	186	14	≤	≤	NOUN
ejpam-6086	186	15	lim	lim	PROPN
ejpam-6086	186	16	n→+∞	n→+∞	PROPN
ejpam-6086	186	17	h(txn	h(txn	PROPN
ejpam-6086	186	18	,	,	PUNCT
ejpam-6086	186	19	t	t	PROPN
ejpam-6086	186	20	z	z	PROPN
ejpam-6086	186	21	)	)	PUNCT
ejpam-6086	186	22	=	=	SYM
ejpam-6086	187	1	0	0	X
ejpam-6086	187	2	.	.	PUNCT
ejpam-6086	188	1	therefore	therefore	ADV
ejpam-6086	188	2	,	,	PUNCT
ejpam-6086	188	3	z	z	PROPN
ejpam-6086	188	4	∈	∈	PROPN
ejpam-6086	188	5	tz	tz	NOUN
ejpam-6086	188	6	i.e.	i.e.	X
ejpam-6086	188	7	t	t	PROPN
ejpam-6086	188	8	has	have	VERB
ejpam-6086	188	9	a	a	DET
ejpam-6086	188	10	fixed	fix	VERB
ejpam-6086	188	11	point	point	NOUN
ejpam-6086	188	12	.	.	PUNCT
ejpam-6086	188	13	example	example	NOUN
ejpam-6086	189	1	1	1	NUM
ejpam-6086	189	2	.	.	PUNCT
ejpam-6086	189	3	let	let	VERB
ejpam-6086	189	4	u	u	PRON
ejpam-6086	189	5	=	=	PUNCT
ejpam-6086	190	1	[	[	X
ejpam-6086	190	2	−1	−1	NOUN
ejpam-6086	190	3	,	,	PUNCT
ejpam-6086	190	4	1	1	NUM
ejpam-6086	190	5	]	]	PUNCT
ejpam-6086	190	6	.	.	PUNCT
ejpam-6086	191	1	define	define	VERB
ejpam-6086	191	2	d	d	NOUN
ejpam-6086	191	3	:	:	PUNCT
ejpam-6086	191	4	u	u	PRON
ejpam-6086	191	5	×	×	PROPN
ejpam-6086	191	6	u	u	X
ejpam-6086	191	7	→	→	PUNCT
ejpam-6086	191	8	[	[	X
ejpam-6086	191	9	0,+∞	0,+∞	NUM
ejpam-6086	191	10	)	)	PUNCT
ejpam-6086	191	11	by	by	ADP
ejpam-6086	191	12	d(x	d(x	PROPN
ejpam-6086	191	13	,	,	PUNCT
ejpam-6086	191	14	y	y	NOUN
ejpam-6086	191	15	)	)	PUNCT
ejpam-6086	191	16	=	=	SYM
ejpam-6086	192	1	(	(	PUNCT
ejpam-6086	192	2	x	x	X
ejpam-6086	192	3	−	−	NOUN
ejpam-6086	192	4	y)2	y)2	NOUN
ejpam-6086	192	5	.	.	PUNCT
ejpam-6086	193	1	then	then	ADV
ejpam-6086	193	2	(	(	PUNCT
ejpam-6086	193	3	u	u	NOUN
ejpam-6086	193	4	,	,	PUNCT
ejpam-6086	193	5	d	d	PROPN
ejpam-6086	193	6	)	)	PUNCT
ejpam-6086	193	7	is	be	AUX
ejpam-6086	193	8	a	a	DET
ejpam-6086	193	9	rectangular	rectangular	ADJ
ejpam-6086	193	10	b−metric	b−metric	ADJ
ejpam-6086	193	11	space	space	NOUN
ejpam-6086	193	12	with	with	ADP
ejpam-6086	193	13	parameter	parameter	PROPN
ejpam-6086	193	14	b	b	PROPN
ejpam-6086	193	15	=	=	SYM
ejpam-6086	193	16	2	2	X
ejpam-6086	193	17	.	.	PUNCT
ejpam-6086	193	18	define	define	VERB
ejpam-6086	193	19	a	a	DET
ejpam-6086	193	20	mapping	mapping	NOUN
ejpam-6086	193	21	t	t	NOUN
ejpam-6086	193	22	:	:	PUNCT
ejpam-6086	193	23	u	u	PROPN
ejpam-6086	193	24	→	→	SYM
ejpam-6086	193	25	b(u	b(u	PROPN
ejpam-6086	193	26	)	)	PUNCT
ejpam-6086	193	27	by	by	ADP
ejpam-6086	193	28	tx	tx	PROPN
ejpam-6086	193	29	=	=	PUNCT
ejpam-6086	193	30	{	{	PUNCT
ejpam-6086	194	1	[	[	X
ejpam-6086	194	2	0	0	NUM
ejpam-6086	194	3	,	,	PUNCT
ejpam-6086	194	4	x4	x4	PROPN
ejpam-6086	194	5	]	]	X
ejpam-6086	194	6	,	,	PUNCT
ejpam-6086	194	7	if	if	SCONJ
ejpam-6086	194	8	x	x	X
ejpam-6086	194	9	,	,	PUNCT
ejpam-6086	194	10	y	y	PROPN
ejpam-6086	194	11	∈	∈	PROPN
ejpam-6086	195	1	[	[	X
ejpam-6086	195	2	0	0	NUM
ejpam-6086	195	3	,	,	PUNCT
ejpam-6086	195	4	14	14	NUM
ejpam-6086	195	5	]	]	PUNCT
ejpam-6086	196	1	[	[	X
ejpam-6086	196	2	x	x	X
ejpam-6086	196	3	,	,	PUNCT
ejpam-6086	196	4	x2	x2	PROPN
ejpam-6086	196	5	]	]	X
ejpam-6086	196	6	,	,	PUNCT
ejpam-6086	196	7	otherwise	otherwise	ADV
ejpam-6086	196	8	α(x	α(x	PROPN
ejpam-6086	196	9	,	,	PUNCT
ejpam-6086	196	10	y	y	PROPN
ejpam-6086	196	11	)	)	PUNCT
ejpam-6086	196	12	=	=	PUNCT
ejpam-6086	196	13			PROPN
ejpam-6086	196	14	1	1	NUM
ejpam-6086	196	15	,	,	PUNCT
ejpam-6086	196	16	if	if	SCONJ
ejpam-6086	196	17	x	x	NOUN
ejpam-6086	196	18	,	,	PUNCT
ejpam-6086	196	19	y	y	PROPN
ejpam-6086	196	20	∈	∈	PROPN
ejpam-6086	197	1	[	[	X
ejpam-6086	197	2	0	0	NUM
ejpam-6086	197	3	,	,	PUNCT
ejpam-6086	197	4	14	14	NUM
ejpam-6086	197	5	]	]	SYM
ejpam-6086	197	6	0	0	NUM
ejpam-6086	197	7	,	,	PUNCT
ejpam-6086	197	8	otherwise	otherwise	ADV
ejpam-6086	197	9	h.	h.	PROPN
ejpam-6086	197	10	massit	massit	PROPN
ejpam-6086	197	11	et	et	PROPN
ejpam-6086	197	12	al	al	PROPN
ejpam-6086	197	13	.	.	PUNCT
ejpam-6086	197	14	/	/	SYM
ejpam-6086	197	15	eur	eur	PROPN
ejpam-6086	197	16	.	.	PUNCT
ejpam-6086	198	1	j.	j.	PROPN
ejpam-6086	198	2	pure	pure	PROPN
ejpam-6086	198	3	appl	appl	PROPN
ejpam-6086	198	4	.	.	PROPN
ejpam-6086	198	5	math	math	PROPN
ejpam-6086	198	6	,	,	PUNCT
ejpam-6086	198	7	18	18	NUM
ejpam-6086	198	8	(	(	PUNCT
ejpam-6086	198	9	2	2	NUM
ejpam-6086	198	10	)	)	PUNCT
ejpam-6086	198	11	(	(	PUNCT
ejpam-6086	198	12	2025	2025	NUM
ejpam-6086	198	13	)	)	PUNCT
ejpam-6086	198	14	,	,	PUNCT
ejpam-6086	198	15	6086	6086	NUM
ejpam-6086	198	16	9	9	NUM
ejpam-6086	198	17	of	of	ADP
ejpam-6086	198	18	19	19	NUM
ejpam-6086	198	19	and	and	CCONJ
ejpam-6086	198	20	the	the	DET
ejpam-6086	198	21	function	function	NOUN
ejpam-6086	198	22	θ	θ	NOUN
ejpam-6086	198	23	:	:	PUNCT
ejpam-6086	199	1	[	[	X
ejpam-6086	199	2	0,+∞	0,+∞	NUM
ejpam-6086	199	3	)	)	PUNCT
ejpam-6086	199	4	→	→	PUNCT
ejpam-6086	200	1	[	[	X
ejpam-6086	200	2	1,+∞	1,+∞	NUM
ejpam-6086	200	3	)	)	PUNCT
ejpam-6086	200	4	by	by	ADP
ejpam-6086	200	5	θ(x	θ(x	PROPN
ejpam-6086	200	6	)	)	PUNCT
ejpam-6086	200	7	=	=	PUNCT
ejpam-6086	201	1	1+x	1+x	X
ejpam-6086	201	2	.	.	PUNCT
ejpam-6086	202	1	then	then	ADV
ejpam-6086	202	2	t	t	PROPN
ejpam-6086	202	3	is	be	AUX
ejpam-6086	202	4	triangular	triangular	NOUN
ejpam-6086	202	5	α−admissible	α−admissible	ADJ
ejpam-6086	202	6	and	and	CCONJ
ejpam-6086	202	7	h(tx	h(tx	NUM
ejpam-6086	202	8	,	,	PUNCT
ejpam-6086	202	9	ty	ty	INTJ
ejpam-6086	202	10	)	)	PUNCT
ejpam-6086	202	11	=	=	SYM
ejpam-6086	202	12	1	1	NUM
ejpam-6086	202	13	4(x−	4(x−	NUM
ejpam-6086	202	14	y)2	y)2	NOUN
ejpam-6086	202	15	.	.	PUNCT
ejpam-6086	203	1	case	case	NOUN
ejpam-6086	203	2	1	1	NUM
ejpam-6086	203	3	if	if	SCONJ
ejpam-6086	203	4	x	x	PROPN
ejpam-6086	203	5	,	,	PUNCT
ejpam-6086	203	6	y	y	PROPN
ejpam-6086	203	7	∈	∈	PROPN
ejpam-6086	204	1	[	[	X
ejpam-6086	204	2	0	0	NUM
ejpam-6086	204	3	,	,	PUNCT
ejpam-6086	204	4	14	14	NUM
ejpam-6086	204	5	]	]	PUNCT
ejpam-6086	204	6	we	we	PRON
ejpam-6086	204	7	have	have	VERB
ejpam-6086	204	8	α(x	α(x	PROPN
ejpam-6086	204	9	,	,	PUNCT
ejpam-6086	204	10	y	y	PROPN
ejpam-6086	204	11	)	)	PUNCT
ejpam-6086	204	12	≥	≥	NOUN
ejpam-6086	204	13	1	1	NUM
ejpam-6086	204	14	and	and	CCONJ
ejpam-6086	204	15	θ[α(x	θ[α(x	NOUN
ejpam-6086	204	16	,	,	PUNCT
ejpam-6086	204	17	y)b3h(tx	y)b3h(tx	PROPN
ejpam-6086	204	18	,	,	PUNCT
ejpam-6086	204	19	ty	ty	NOUN
ejpam-6086	204	20	)	)	PUNCT
ejpam-6086	204	21	]	]	PUNCT
ejpam-6086	204	22	≤	≤	NUM
ejpam-6086	204	23	1	1	NUM
ejpam-6086	204	24	2	2	NUM
ejpam-6086	204	25	(	(	PUNCT
ejpam-6086	204	26	x−	x−	PROPN
ejpam-6086	204	27	y)2	y)2	NOUN
ejpam-6086	204	28	+	+	CCONJ
ejpam-6086	204	29	1	1	NUM
ejpam-6086	204	30	≤	≤	NOUN
ejpam-6086	204	31	d(x	d(x	PROPN
ejpam-6086	204	32	,	,	PUNCT
ejpam-6086	204	33	y	y	NOUN
ejpam-6086	204	34	)	)	PUNCT
ejpam-6086	205	1	+	+	CCONJ
ejpam-6086	205	2	1	1	NUM
ejpam-6086	205	3	≤	≤	NOUN
ejpam-6086	205	4	θ[m(x	θ[m(x	PROPN
ejpam-6086	205	5	,	,	PUNCT
ejpam-6086	205	6	y	y	PROPN
ejpam-6086	205	7	)	)	PUNCT
ejpam-6086	205	8	]	]	PUNCT
ejpam-6086	206	1	+	+	ADV
ejpam-6086	206	2	kw	kw	INTJ
ejpam-6086	206	3	(	(	PUNCT
ejpam-6086	206	4	x	x	PROPN
ejpam-6086	206	5	,	,	PUNCT
ejpam-6086	206	6	y	y	PROPN
ejpam-6086	206	7	)	)	PUNCT
ejpam-6086	206	8	.	.	PUNCT
ejpam-6086	207	1	case	case	NOUN
ejpam-6086	207	2	2	2	NUM
ejpam-6086	207	3	if	if	SCONJ
ejpam-6086	207	4	x	x	PROPN
ejpam-6086	207	5	,	,	PUNCT
ejpam-6086	207	6	y	y	PROPN
ejpam-6086	207	7	∈	∈	PROPN
ejpam-6086	207	8	(	(	PUNCT
ejpam-6086	207	9	14	14	NUM
ejpam-6086	207	10	,	,	PUNCT
ejpam-6086	207	11	+	+	NOUN
ejpam-6086	207	12	∞	∞	NOUN
ejpam-6086	207	13	)	)	PUNCT
ejpam-6086	207	14	we	we	PRON
ejpam-6086	207	15	have	have	VERB
ejpam-6086	207	16	α(x	α(x	PROPN
ejpam-6086	207	17	,	,	PUNCT
ejpam-6086	207	18	y	y	PROPN
ejpam-6086	207	19	)	)	PUNCT
ejpam-6086	207	20	=	=	SYM
ejpam-6086	207	21	0	0	NUM
ejpam-6086	207	22	and	and	CCONJ
ejpam-6086	207	23	θ[α(x	θ[α(x	NOUN
ejpam-6086	207	24	,	,	PUNCT
ejpam-6086	207	25	y)b3h(tx	y)b3h(tx	PROPN
ejpam-6086	207	26	,	,	PUNCT
ejpam-6086	207	27	ty	ty	NOUN
ejpam-6086	207	28	)	)	PUNCT
ejpam-6086	207	29	]	]	PUNCT
ejpam-6086	208	1	=	=	PUNCT
ejpam-6086	208	2	θ(0	θ(0	PROPN
ejpam-6086	208	3	)	)	PUNCT
ejpam-6086	208	4	≤	≤	PROPN
ejpam-6086	208	5	θ((x−	θ((x−	PROPN
ejpam-6086	208	6	y)2	y)2	NOUN
ejpam-6086	208	7	)	)	PUNCT
ejpam-6086	208	8	≤	≤	NUM
ejpam-6086	208	9	d(x	d(x	NOUN
ejpam-6086	208	10	,	,	PUNCT
ejpam-6086	208	11	y	y	NOUN
ejpam-6086	208	12	)	)	PUNCT
ejpam-6086	208	13	+	+	CCONJ
ejpam-6086	208	14	1	1	NUM
ejpam-6086	208	15	≤	≤	NOUN
ejpam-6086	208	16	θ[m(x	θ[m(x	PROPN
ejpam-6086	208	17	,	,	PUNCT
ejpam-6086	208	18	y	y	PROPN
ejpam-6086	208	19	)	)	PUNCT
ejpam-6086	208	20	]	]	PUNCT
ejpam-6086	209	1	+	+	ADV
ejpam-6086	209	2	kw	kw	INTJ
ejpam-6086	209	3	(	(	PUNCT
ejpam-6086	209	4	x	x	PROPN
ejpam-6086	209	5	,	,	PUNCT
ejpam-6086	209	6	y	y	PROPN
ejpam-6086	209	7	)	)	PUNCT
ejpam-6086	209	8	.	.	PUNCT
ejpam-6086	210	1	then	then	ADV
ejpam-6086	210	2	,	,	PUNCT
ejpam-6086	210	3	t	t	PROPN
ejpam-6086	210	4	has	have	VERB
ejpam-6086	210	5	a	a	DET
ejpam-6086	210	6	fixed	fix	VERB
ejpam-6086	210	7	point	point	NOUN
ejpam-6086	210	8	.	.	PUNCT
ejpam-6086	211	1	theorem	theorem	NOUN
ejpam-6086	211	2	3	3	X
ejpam-6086	211	3	.	.	PUNCT
ejpam-6086	212	1	let	let	AUX
ejpam-6086	212	2	(	(	PUNCT
ejpam-6086	212	3	u	u	NOUN
ejpam-6086	212	4	,	,	PUNCT
ejpam-6086	212	5	d	d	PROPN
ejpam-6086	212	6	)	)	PUNCT
ejpam-6086	212	7	be	be	AUX
ejpam-6086	212	8	a	a	DET
ejpam-6086	212	9	complete	complete	ADJ
ejpam-6086	212	10	rectangular	rectangular	ADJ
ejpam-6086	212	11	b−metric	b−metric	ADJ
ejpam-6086	212	12	space	space	NOUN
ejpam-6086	212	13	and	and	CCONJ
ejpam-6086	212	14	t	t	NOUN
ejpam-6086	212	15	:	:	PUNCT
ejpam-6086	212	16	u	u	PROPN
ejpam-6086	212	17	→	→	SYM
ejpam-6086	212	18	b(u	b(u	PROPN
ejpam-6086	212	19	)	)	PUNCT
ejpam-6086	212	20	be	be	VERB
ejpam-6086	212	21	an	an	DET
ejpam-6086	212	22	α−admissible	α−admissible	ADJ
ejpam-6086	212	23	θ−multivalued	θ−multivalued	CCONJ
ejpam-6086	212	24	contraction	contraction	NOUN
ejpam-6086	212	25	satisfying	satisfying	ADJ
ejpam-6086	212	26	:	:	PUNCT
ejpam-6086	212	27	(	(	PUNCT
ejpam-6086	212	28	i	i	NOUN
ejpam-6086	212	29	)	)	PUNCT
ejpam-6086	212	30	(	(	PUNCT
ejpam-6086	212	31	u	u	NOUN
ejpam-6086	212	32	,	,	PUNCT
ejpam-6086	212	33	d	d	PROPN
ejpam-6086	212	34	)	)	PUNCT
ejpam-6086	212	35	is	be	AUX
ejpam-6086	212	36	an	an	DET
ejpam-6086	212	37	α−complete	α−complete	NUM
ejpam-6086	212	38	metric	metric	ADJ
ejpam-6086	212	39	space	space	NOUN
ejpam-6086	212	40	,	,	PUNCT
ejpam-6086	212	41	(	(	PUNCT
ejpam-6086	212	42	ii	ii	NOUN
ejpam-6086	212	43	)	)	PUNCT
ejpam-6086	212	44	α(x0	α(x0	PROPN
ejpam-6086	212	45	,	,	PUNCT
ejpam-6086	212	46	x1	x1	PROPN
ejpam-6086	212	47	)	)	PUNCT
ejpam-6086	212	48	≥	≥	NOUN
ejpam-6086	212	49	1	1	NUM
ejpam-6086	212	50	for	for	ADP
ejpam-6086	212	51	x0	x0	PROPN
ejpam-6086	212	52	∈	∈	PROPN
ejpam-6086	212	53	u	u	NOUN
ejpam-6086	212	54	and	and	CCONJ
ejpam-6086	212	55	x1	x1	PROPN
ejpam-6086	212	56	∈	∈	PROPN
ejpam-6086	212	57	t	t	PROPN
ejpam-6086	212	58	(	(	PUNCT
ejpam-6086	212	59	u	u	NOUN
ejpam-6086	212	60	)	)	PUNCT
ejpam-6086	212	61	,	,	PUNCT
ejpam-6086	212	62	(	(	PUNCT
ejpam-6086	212	63	iii	iii	X
ejpam-6086	212	64	)	)	PUNCT
ejpam-6086	212	65	t	t	PROPN
ejpam-6086	212	66	is	be	AUX
ejpam-6086	212	67	triangular	triangular	NOUN
ejpam-6086	212	68	α−admissible	α−admissible	NOUN
ejpam-6086	212	69	,	,	PUNCT
ejpam-6086	212	70	(	(	PUNCT
ejpam-6086	212	71	iv	iv	X
ejpam-6086	212	72	)	)	PUNCT
ejpam-6086	212	73	there	there	PRON
ejpam-6086	212	74	exists	exist	VERB
ejpam-6086	212	75	a	a	DET
ejpam-6086	212	76	sequence	sequence	NOUN
ejpam-6086	212	77	{	{	PUNCT
ejpam-6086	212	78	xn	xn	NUM
ejpam-6086	212	79	}	}	PUNCT
ejpam-6086	212	80	in	in	ADP
ejpam-6086	212	81	u	u	PRON
ejpam-6086	212	82	such	such	ADJ
ejpam-6086	212	83	that	that	SCONJ
ejpam-6086	212	84	α(xn	α(xn	NOUN
ejpam-6086	212	85	,	,	PUNCT
ejpam-6086	212	86	xn+1	xn+1	NUM
ejpam-6086	212	87	)	)	PUNCT
ejpam-6086	212	88	≥	≥	NOUN
ejpam-6086	212	89	1	1	NUM
ejpam-6086	212	90	for	for	ADP
ejpam-6086	212	91	all	all	PRON
ejpam-6086	212	92	n	n	PRON
ejpam-6086	212	93	∈	∈	NOUN
ejpam-6086	212	94	n	n	NOUN
ejpam-6086	212	95	∪	∪	X
ejpam-6086	212	96	{	{	PUNCT
ejpam-6086	212	97	0	0	NUM
ejpam-6086	212	98	}	}	PUNCT
ejpam-6086	212	99	and	and	CCONJ
ejpam-6086	212	100	lim	lim	PROPN
ejpam-6086	212	101	n→+∞	n→+∞	VERB
ejpam-6086	212	102	d(xn	d(xn	PROPN
ejpam-6086	212	103	,	,	PUNCT
ejpam-6086	212	104	z	z	NOUN
ejpam-6086	212	105	)	)	PUNCT
ejpam-6086	212	106	=	=	SYM
ejpam-6086	212	107	0	0	NUM
ejpam-6086	212	108	,	,	PUNCT
ejpam-6086	212	109	for	for	ADP
ejpam-6086	212	110	some	some	DET
ejpam-6086	212	111	z	z	NOUN
ejpam-6086	212	112	∈	∈	PROPN
ejpam-6086	212	113	u	u	NOUN
ejpam-6086	212	114	,	,	PUNCT
ejpam-6086	212	115	then	then	ADV
ejpam-6086	212	116	there	there	PRON
ejpam-6086	212	117	exists	exist	VERB
ejpam-6086	212	118	a	a	DET
ejpam-6086	212	119	subsequence	subsequence	NOUN
ejpam-6086	212	120	{	{	PUNCT
ejpam-6086	212	121	xn(k	xn(k	NUM
ejpam-6086	212	122	)	)	PUNCT
ejpam-6086	212	123	}	}	PUNCT
ejpam-6086	212	124	of	of	ADP
ejpam-6086	212	125	{	{	PUNCT
ejpam-6086	212	126	xn	xn	NOUN
ejpam-6086	212	127	}	}	PUNCT
ejpam-6086	212	128	such	such	ADJ
ejpam-6086	212	129	that	that	SCONJ
ejpam-6086	212	130	α(xn(k	α(xn(k	PROPN
ejpam-6086	212	131	)	)	PUNCT
ejpam-6086	212	132	,	,	PUNCT
ejpam-6086	212	133	z	z	NOUN
ejpam-6086	212	134	)	)	PUNCT
ejpam-6086	212	135	≥	≥	NOUN
ejpam-6086	212	136	1	1	NUM
ejpam-6086	212	137	,	,	PUNCT
ejpam-6086	212	138	for	for	ADP
ejpam-6086	212	139	all	all	DET
ejpam-6086	212	140	k	k	PROPN
ejpam-6086	212	141	∈	∈	PROPN
ejpam-6086	212	142	n	n	PART
ejpam-6086	212	143	∪	∪	X
ejpam-6086	212	144	{	{	PUNCT
ejpam-6086	212	145	0	0	NUM
ejpam-6086	212	146	}	}	PUNCT
ejpam-6086	212	147	.	.	PUNCT
ejpam-6086	213	1	then	then	ADV
ejpam-6086	213	2	,	,	PUNCT
ejpam-6086	213	3	t	t	PROPN
ejpam-6086	213	4	has	have	VERB
ejpam-6086	213	5	a	a	DET
ejpam-6086	213	6	fixed	fix	VERB
ejpam-6086	213	7	point	point	NOUN
ejpam-6086	213	8	.	.	PUNCT
ejpam-6086	214	1	proof	proof	NOUN
ejpam-6086	214	2	.	.	PUNCT
ejpam-6086	215	1	let	let	VERB
ejpam-6086	215	2	{	{	PUNCT
ejpam-6086	215	3	xn	xn	VERB
ejpam-6086	215	4	}	}	PUNCT
ejpam-6086	215	5	be	be	AUX
ejpam-6086	215	6	a	a	DET
ejpam-6086	215	7	sequence	sequence	NOUN
ejpam-6086	215	8	in	in	ADP
ejpam-6086	215	9	u	u	PRON
ejpam-6086	215	10	such	such	ADJ
ejpam-6086	215	11	that	that	SCONJ
ejpam-6086	215	12	xn+1	xn+1	NUM
ejpam-6086	215	13	∈	∈	PROPN
ejpam-6086	215	14	txn	txn	NOUN
ejpam-6086	215	15	with	with	ADP
ejpam-6086	215	16	α(xn	α(xn	PROPN
ejpam-6086	215	17	,	,	PUNCT
ejpam-6086	215	18	xn+1	xn+1	NUM
ejpam-6086	215	19	)	)	PUNCT
ejpam-6086	215	20	≥	≥	NOUN
ejpam-6086	215	21	1	1	NUM
ejpam-6086	215	22	,	,	PUNCT
ejpam-6086	215	23	for	for	ADP
ejpam-6086	215	24	all	all	DET
ejpam-6086	215	25	n	n	PRON
ejpam-6086	215	26	∈	∈	NOUN
ejpam-6086	215	27	n	n	NOUN
ejpam-6086	215	28	∪	∪	X
ejpam-6086	215	29	{	{	PUNCT
ejpam-6086	215	30	0	0	NUM
ejpam-6086	215	31	}	}	PUNCT
ejpam-6086	215	32	and	and	CCONJ
ejpam-6086	215	33	xn	xn	PROPN
ejpam-6086	215	34	→	→	SYM
ejpam-6086	215	35	z	z	NOUN
ejpam-6086	215	36	∈	∈	PROPN
ejpam-6086	215	37	u	u	NOUN
ejpam-6086	215	38	.	.	PUNCT
ejpam-6086	216	1	by	by	ADP
ejpam-6086	216	2	(	(	PUNCT
ejpam-6086	216	3	iv	iv	X
ejpam-6086	216	4	)	)	PUNCT
ejpam-6086	216	5	,	,	PUNCT
ejpam-6086	216	6	we	we	PRON
ejpam-6086	216	7	show	show	VERB
ejpam-6086	216	8	that	that	SCONJ
ejpam-6086	216	9	z	z	PROPN
ejpam-6086	216	10	∈	∈	PROPN
ejpam-6086	216	11	tz	tz	PROPN
ejpam-6086	216	12	.	.	PROPN
ejpam-6086	216	13	suppose	suppose	VERB
ejpam-6086	216	14	that	that	SCONJ
ejpam-6086	216	15	z	z	PROPN
ejpam-6086	216	16	̸∈	̸∈	PROPN
ejpam-6086	216	17	tz	tz	PROPN
ejpam-6086	216	18	,	,	PUNCT
ejpam-6086	216	19	we	we	PRON
ejpam-6086	216	20	have	have	VERB
ejpam-6086	216	21	lim	lim	PROPN
ejpam-6086	216	22	n→+∞	n→+∞	PROPN
ejpam-6086	216	23	d(txn	d(txn	PROPN
ejpam-6086	216	24	,	,	PUNCT
ejpam-6086	216	25	z	z	NOUN
ejpam-6086	216	26	)	)	PUNCT
ejpam-6086	216	27	=	=	SYM
ejpam-6086	216	28	0	0	NUM
ejpam-6086	216	29	and	and	CCONJ
ejpam-6086	216	30	1	1	NUM
ejpam-6086	216	31	b2	b2	NOUN
ejpam-6086	216	32	d(z	d(z	PROPN
ejpam-6086	216	33	,	,	PUNCT
ejpam-6086	216	34	tz	tz	NOUN
ejpam-6086	216	35	)	)	PUNCT
ejpam-6086	216	36	≤	≤	NOUN
ejpam-6086	216	37	lim	lim	PROPN
ejpam-6086	216	38	n→+∞	n→+∞	PROPN
ejpam-6086	216	39	infh(txn	infh(txn	PROPN
ejpam-6086	216	40	,	,	PUNCT
ejpam-6086	216	41	t	t	PROPN
ejpam-6086	216	42	z	z	PROPN
ejpam-6086	216	43	)	)	PUNCT
ejpam-6086	216	44	≤	≤	NOUN
ejpam-6086	216	45	lim	lim	PROPN
ejpam-6086	216	46	n→+∞	n→+∞	PROPN
ejpam-6086	216	47	suph(txn	suph(txn	PROPN
ejpam-6086	216	48	,	,	PUNCT
ejpam-6086	216	49	t	t	PROPN
ejpam-6086	216	50	z	z	PROPN
ejpam-6086	216	51	)	)	PUNCT
ejpam-6086	216	52	≤	≤	PROPN
ejpam-6086	216	53	b2d(z	b2d(z	PROPN
ejpam-6086	216	54	,	,	PUNCT
ejpam-6086	216	55	tz	tz	PROPN
ejpam-6086	216	56	)	)	PUNCT
ejpam-6086	216	57	.	.	PUNCT
ejpam-6086	217	1	h.	h.	PROPN
ejpam-6086	217	2	massit	massit	PROPN
ejpam-6086	217	3	et	et	PROPN
ejpam-6086	217	4	al	al	PROPN
ejpam-6086	217	5	.	.	PUNCT
ejpam-6086	217	6	/	/	SYM
ejpam-6086	217	7	eur	eur	PROPN
ejpam-6086	217	8	.	.	PUNCT
ejpam-6086	218	1	j.	j.	PROPN
ejpam-6086	218	2	pure	pure	PROPN
ejpam-6086	218	3	appl	appl	PROPN
ejpam-6086	218	4	.	.	PROPN
ejpam-6086	218	5	math	math	PROPN
ejpam-6086	218	6	,	,	PUNCT
ejpam-6086	218	7	18	18	NUM
ejpam-6086	218	8	(	(	PUNCT
ejpam-6086	218	9	2	2	NUM
ejpam-6086	218	10	)	)	PUNCT
ejpam-6086	218	11	(	(	PUNCT
ejpam-6086	218	12	2025	2025	NUM
ejpam-6086	218	13	)	)	PUNCT
ejpam-6086	218	14	,	,	PUNCT
ejpam-6086	218	15	6086	6086	NUM
ejpam-6086	218	16	10	10	NUM
ejpam-6086	218	17	of	of	ADP
ejpam-6086	218	18	19	19	NUM
ejpam-6086	219	1	so	so	ADV
ejpam-6086	219	2	,	,	PUNCT
ejpam-6086	219	3	we	we	PRON
ejpam-6086	219	4	have	have	VERB
ejpam-6086	219	5	θ[b3h(txn	θ[b3h(txn	PROPN
ejpam-6086	219	6	,	,	PUNCT
ejpam-6086	219	7	t	t	PROPN
ejpam-6086	219	8	z	z	PROPN
ejpam-6086	219	9	)	)	PUNCT
ejpam-6086	219	10	]	]	PUNCT
ejpam-6086	220	1	≤	≤	NUM
ejpam-6086	220	2	θ[α(xn	θ[α(xn	NOUN
ejpam-6086	220	3	,	,	PUNCT
ejpam-6086	220	4	z)b	z)b	X
ejpam-6086	220	5	3h(txn	3h(txn	NUM
ejpam-6086	220	6	,	,	PUNCT
ejpam-6086	220	7	t	t	PROPN
ejpam-6086	220	8	z	z	PROPN
ejpam-6086	220	9	)	)	PUNCT
ejpam-6086	220	10	]	]	PUNCT
ejpam-6086	220	11	≤	≤	NUM
ejpam-6086	220	12	θ[m(xn	θ[m(xn	NOUN
ejpam-6086	220	13	,	,	PUNCT
ejpam-6086	220	14	z	z	NOUN
ejpam-6086	220	15	)	)	PUNCT
ejpam-6086	220	16	]	]	PUNCT
ejpam-6086	220	17	s	s	VERB
ejpam-6086	221	1	+	+	ADJ
ejpam-6086	221	2	kw	kw	INTJ
ejpam-6086	221	3	(	(	PUNCT
ejpam-6086	221	4	xn	xn	PROPN
ejpam-6086	221	5	,	,	PUNCT
ejpam-6086	221	6	z	z	NOUN
ejpam-6086	221	7	)	)	PUNCT
ejpam-6086	221	8	for	for	ADP
ejpam-6086	221	9	all	all	PRON
ejpam-6086	221	10	n	n	PRON
ejpam-6086	221	11	∈	∈	PROPN
ejpam-6086	221	12	n	n	CCONJ
ejpam-6086	221	13	,	,	PUNCT
ejpam-6086	221	14	where	where	SCONJ
ejpam-6086	221	15	m(xn	m(xn	NOUN
ejpam-6086	221	16	,	,	PUNCT
ejpam-6086	221	17	z	z	NOUN
ejpam-6086	221	18	)	)	PUNCT
ejpam-6086	221	19	=	=	SYM
ejpam-6086	221	20	max{d(xn	max{d(xn	PROPN
ejpam-6086	221	21	,	,	PUNCT
ejpam-6086	221	22	z	z	NOUN
ejpam-6086	221	23	)	)	PUNCT
ejpam-6086	221	24	,	,	PUNCT
ejpam-6086	221	25	d(xn	d(xn	PROPN
ejpam-6086	221	26	,	,	PUNCT
ejpam-6086	221	27	txn	txn	NOUN
ejpam-6086	221	28	)	)	PUNCT
ejpam-6086	221	29	,	,	PUNCT
ejpam-6086	221	30	d(z	d(z	PROPN
ejpam-6086	221	31	,	,	PUNCT
ejpam-6086	221	32	tz	tz	PROPN
ejpam-6086	221	33	)	)	PUNCT
ejpam-6086	221	34	,	,	PUNCT
ejpam-6086	221	35	d(z	d(z	PROPN
ejpam-6086	221	36	,	,	PUNCT
ejpam-6086	221	37	txn	txn	NOUN
ejpam-6086	221	38	)	)	PUNCT
ejpam-6086	221	39	}	}	PUNCT
ejpam-6086	221	40	and	and	CCONJ
ejpam-6086	221	41	w	w	PROPN
ejpam-6086	221	42	(	(	PUNCT
ejpam-6086	221	43	xn	xn	PROPN
ejpam-6086	221	44	,	,	PUNCT
ejpam-6086	221	45	z	z	NOUN
ejpam-6086	221	46	)	)	PUNCT
ejpam-6086	221	47	=	=	SYM
ejpam-6086	222	1	min{d(xn	min{d(xn	X
ejpam-6086	222	2	,	,	PUNCT
ejpam-6086	222	3	txn	txn	NOUN
ejpam-6086	222	4	)	)	PUNCT
ejpam-6086	222	5	,	,	PUNCT
ejpam-6086	222	6	d(z	d(z	PROPN
ejpam-6086	222	7	,	,	PUNCT
ejpam-6086	222	8	tz	tz	PROPN
ejpam-6086	222	9	)	)	PUNCT
ejpam-6086	222	10	,	,	PUNCT
ejpam-6086	222	11	d(txn	d(txn	PROPN
ejpam-6086	222	12	,	,	PUNCT
ejpam-6086	222	13	z	z	NOUN
ejpam-6086	222	14	)	)	PUNCT
ejpam-6086	222	15	,	,	PUNCT
ejpam-6086	222	16	d(xn	d(xn	PROPN
ejpam-6086	222	17	,	,	PUNCT
ejpam-6086	222	18	t	t	PROPN
ejpam-6086	222	19	z	z	PROPN
ejpam-6086	222	20	)	)	PUNCT
ejpam-6086	222	21	}	}	PUNCT
ejpam-6086	222	22	.	.	PUNCT
ejpam-6086	223	1	letting	let	VERB
ejpam-6086	223	2	n→	n→	ADV
ejpam-6086	223	3	+	+	SYM
ejpam-6086	223	4	∞	∞	NUM
ejpam-6086	223	5	we	we	PRON
ejpam-6086	223	6	obtain	obtain	VERB
ejpam-6086	223	7	lim	lim	PROPN
ejpam-6086	223	8	n→+∞	n→+∞	PROPN
ejpam-6086	223	9	supm(xn	supm(xn	PROPN
ejpam-6086	223	10	,	,	PUNCT
ejpam-6086	223	11	z	z	NOUN
ejpam-6086	223	12	)	)	PUNCT
ejpam-6086	224	1	=	=	SYM
ejpam-6086	224	2	lim	lim	PROPN
ejpam-6086	224	3	n→+∞	n→+∞	PROPN
ejpam-6086	224	4	supmax{d(xn	supmax{d(xn	PROPN
ejpam-6086	224	5	,	,	PUNCT
ejpam-6086	224	6	z	z	NOUN
ejpam-6086	224	7	)	)	PUNCT
ejpam-6086	224	8	,	,	PUNCT
ejpam-6086	224	9	d(xn	d(xn	PROPN
ejpam-6086	224	10	,	,	PUNCT
ejpam-6086	224	11	txn	txn	NOUN
ejpam-6086	224	12	)	)	PUNCT
ejpam-6086	224	13	,	,	PUNCT
ejpam-6086	224	14	d(z	d(z	PROPN
ejpam-6086	224	15	,	,	PUNCT
ejpam-6086	224	16	tz	tz	PROPN
ejpam-6086	224	17	)	)	PUNCT
ejpam-6086	224	18	,	,	PUNCT
ejpam-6086	224	19	d(z	d(z	PROPN
ejpam-6086	224	20	,	,	PUNCT
ejpam-6086	224	21	txn	txn	NOUN
ejpam-6086	224	22	)	)	PUNCT
ejpam-6086	224	23	}	}	PUNCT
ejpam-6086	224	24	≤	≤	NUM
ejpam-6086	224	25	lim	lim	PROPN
ejpam-6086	224	26	n→+∞	n→+∞	PROPN
ejpam-6086	224	27	supmax{d(xn	supmax{d(xn	PROPN
ejpam-6086	224	28	,	,	PUNCT
ejpam-6086	224	29	z	z	NOUN
ejpam-6086	224	30	)	)	PUNCT
ejpam-6086	224	31	,	,	PUNCT
ejpam-6086	224	32	d(xn	d(xn	PROPN
ejpam-6086	224	33	,	,	PUNCT
ejpam-6086	224	34	xn+1	xn+1	NUM
ejpam-6086	224	35	)	)	PUNCT
ejpam-6086	224	36	,	,	PUNCT
ejpam-6086	224	37	d(z	d(z	PROPN
ejpam-6086	224	38	,	,	PUNCT
ejpam-6086	224	39	tz	tz	PROPN
ejpam-6086	224	40	)	)	PUNCT
ejpam-6086	224	41	,	,	PUNCT
ejpam-6086	224	42	d(z	d(z	PROPN
ejpam-6086	224	43	,	,	PUNCT
ejpam-6086	224	44	xn+1	xn+1	NUM
ejpam-6086	224	45	)	)	PUNCT
ejpam-6086	224	46	}	}	PUNCT
ejpam-6086	224	47	≤	≤	NUM
ejpam-6086	224	48	d(z	d(z	PROPN
ejpam-6086	224	49	,	,	PUNCT
ejpam-6086	224	50	tz	tz	PROPN
ejpam-6086	224	51	)	)	PUNCT
ejpam-6086	224	52	and	and	CCONJ
ejpam-6086	224	53	lim	lim	PROPN
ejpam-6086	224	54	n→+∞	n→+∞	PROPN
ejpam-6086	224	55	supw	supw	PROPN
ejpam-6086	224	56	(	(	PUNCT
ejpam-6086	224	57	xn	xn	PROPN
ejpam-6086	224	58	,	,	PUNCT
ejpam-6086	224	59	z	z	NOUN
ejpam-6086	224	60	)	)	PUNCT
ejpam-6086	225	1	=	=	SYM
ejpam-6086	225	2	lim	lim	PROPN
ejpam-6086	225	3	n→+∞	n→+∞	PROPN
ejpam-6086	225	4	supmin{d(xn	supmin{d(xn	PROPN
ejpam-6086	225	5	,	,	PUNCT
ejpam-6086	225	6	txn	txn	NOUN
ejpam-6086	225	7	)	)	PUNCT
ejpam-6086	225	8	,	,	PUNCT
ejpam-6086	225	9	d(z	d(z	PROPN
ejpam-6086	225	10	,	,	PUNCT
ejpam-6086	225	11	tz	tz	PROPN
ejpam-6086	225	12	)	)	PUNCT
ejpam-6086	225	13	,	,	PUNCT
ejpam-6086	225	14	d(txn	d(txn	PROPN
ejpam-6086	225	15	,	,	PUNCT
ejpam-6086	225	16	z	z	NOUN
ejpam-6086	225	17	)	)	PUNCT
ejpam-6086	225	18	,	,	PUNCT
ejpam-6086	225	19	d(xn	d(xn	PROPN
ejpam-6086	225	20	,	,	PUNCT
ejpam-6086	225	21	t	t	PROPN
ejpam-6086	225	22	z	z	PROPN
ejpam-6086	225	23	)	)	PUNCT
ejpam-6086	225	24	}	}	PUNCT
ejpam-6086	225	25	≤	≤	NUM
ejpam-6086	225	26	lim	lim	PROPN
ejpam-6086	225	27	n→+∞	n→+∞	PROPN
ejpam-6086	225	28	supmin{d(xn	supmin{d(xn	PROPN
ejpam-6086	225	29	,	,	PUNCT
ejpam-6086	225	30	xn+1	xn+1	NUM
ejpam-6086	225	31	)	)	PUNCT
ejpam-6086	225	32	,	,	PUNCT
ejpam-6086	225	33	d(z	d(z	PROPN
ejpam-6086	225	34	,	,	PUNCT
ejpam-6086	225	35	tz	tz	NOUN
ejpam-6086	225	36	)	)	PUNCT
ejpam-6086	225	37	,	,	PUNCT
ejpam-6086	225	38	d(xn+1	d(xn+1	PROPN
ejpam-6086	225	39	,	,	PUNCT
ejpam-6086	225	40	z	z	NOUN
ejpam-6086	225	41	)	)	PUNCT
ejpam-6086	225	42	,	,	PUNCT
ejpam-6086	225	43	d(xn	d(xn	PROPN
ejpam-6086	225	44	,	,	PUNCT
ejpam-6086	225	45	t	t	PROPN
ejpam-6086	225	46	z	z	PROPN
ejpam-6086	225	47	)	)	PUNCT
ejpam-6086	225	48	}	}	PUNCT
ejpam-6086	225	49	=	=	SYM
ejpam-6086	225	50	0	0	X
ejpam-6086	225	51	.	.	PUNCT
ejpam-6086	226	1	then	then	ADV
ejpam-6086	226	2	,	,	PUNCT
ejpam-6086	226	3	θ(bd(z	θ(bd(z	PROPN
ejpam-6086	226	4	,	,	PUNCT
ejpam-6086	226	5	tz	tz	NOUN
ejpam-6086	226	6	)	)	PUNCT
ejpam-6086	226	7	)	)	PUNCT
ejpam-6086	226	8	≤	≤	NOUN
ejpam-6086	226	9	θ[b3	θ[b3	ADP
ejpam-6086	226	10	lim	lim	PROPN
ejpam-6086	226	11	n→+∞	n→+∞	PROPN
ejpam-6086	226	12	h(txn	h(txn	PROPN
ejpam-6086	226	13	,	,	PUNCT
ejpam-6086	226	14	t	t	PROPN
ejpam-6086	226	15	z	z	PROPN
ejpam-6086	226	16	)	)	PUNCT
ejpam-6086	226	17	]	]	PUNCT
ejpam-6086	227	1	lim	lim	PROPN
ejpam-6086	227	2	n→+∞	n→+∞	PROPN
ejpam-6086	227	3	θ[b3h(txn	θ[b3h(txn	PROPN
ejpam-6086	227	4	,	,	PUNCT
ejpam-6086	227	5	t	t	PROPN
ejpam-6086	227	6	z	z	PROPN
ejpam-6086	227	7	)	)	PUNCT
ejpam-6086	227	8	]	]	PUNCT
ejpam-6086	227	9	≤	≤	NUM
ejpam-6086	227	10	lim	lim	PROPN
ejpam-6086	227	11	n→+∞	n→+∞	VERB
ejpam-6086	227	12	θ[α(xn	θ[α(xn	NOUN
ejpam-6086	227	13	,	,	PUNCT
ejpam-6086	227	14	z)b	z)b	X
ejpam-6086	227	15	3h(txn	3h(txn	NUM
ejpam-6086	227	16	,	,	PUNCT
ejpam-6086	227	17	t	t	PROPN
ejpam-6086	227	18	z	z	PROPN
ejpam-6086	227	19	)	)	PUNCT
ejpam-6086	227	20	]	]	PUNCT
ejpam-6086	227	21	≤	≤	NUM
ejpam-6086	227	22	θ	θ	PROPN
ejpam-6086	227	23	[	[	PUNCT
ejpam-6086	227	24	lim	lim	PROPN
ejpam-6086	227	25	n→+∞	n→+∞	VERB
ejpam-6086	227	26	m(xn	m(xn	PROPN
ejpam-6086	227	27	,	,	PUNCT
ejpam-6086	227	28	z	z	NOUN
ejpam-6086	227	29	)	)	PUNCT
ejpam-6086	227	30	]	]	PUNCT
ejpam-6086	228	1	s	s	VERB
ejpam-6086	229	1	+	+	PROPN
ejpam-6086	229	2	k	k	PROPN
ejpam-6086	229	3	lim	lim	PROPN
ejpam-6086	229	4	n→+∞	n→+∞	PROPN
ejpam-6086	229	5	w	w	PROPN
ejpam-6086	229	6	(	(	PUNCT
ejpam-6086	229	7	xn	xn	PROPN
ejpam-6086	229	8	,	,	PUNCT
ejpam-6086	229	9	z	z	NOUN
ejpam-6086	229	10	)	)	PUNCT
ejpam-6086	229	11	≤	≤	NOUN
ejpam-6086	230	1	[	[	X
ejpam-6086	230	2	θ(d(z	θ(d(z	NOUN
ejpam-6086	230	3	,	,	PUNCT
ejpam-6086	230	4	tz))]s	tz))]s	ADV
ejpam-6086	230	5	<	<	X
ejpam-6086	230	6	θ(d(z	θ(d(z	PROPN
ejpam-6086	230	7	,	,	PUNCT
ejpam-6086	230	8	tz	tz	NOUN
ejpam-6086	230	9	)	)	PUNCT
ejpam-6086	230	10	)	)	PUNCT
ejpam-6086	230	11	.	.	PUNCT
ejpam-6086	231	1	this	this	PRON
ejpam-6086	231	2	implies	imply	VERB
ejpam-6086	231	3	that	that	SCONJ
ejpam-6086	231	4	bd(z	bd(z	X
ejpam-6086	231	5	,	,	PUNCT
ejpam-6086	231	6	tz	tz	PROPN
ejpam-6086	231	7	)	)	PUNCT
ejpam-6086	231	8	<	<	X
ejpam-6086	231	9	d(z	d(z	PROPN
ejpam-6086	231	10	,	,	PUNCT
ejpam-6086	231	11	tz	tz	PROPN
ejpam-6086	231	12	)	)	PUNCT
ejpam-6086	231	13	,	,	PUNCT
ejpam-6086	231	14	this	this	DET
ejpam-6086	231	15	a	a	DET
ejpam-6086	231	16	contradiction	contradiction	NOUN
ejpam-6086	231	17	,	,	PUNCT
ejpam-6086	231	18	so	so	SCONJ
ejpam-6086	231	19	z	z	PROPN
ejpam-6086	231	20	∈	∈	PROPN
ejpam-6086	231	21	tz	tz	PROPN
ejpam-6086	231	22	.	.	PUNCT
ejpam-6086	231	23	corollary	corollary	ADJ
ejpam-6086	231	24	1	1	NUM
ejpam-6086	231	25	.	.	PUNCT
ejpam-6086	232	1	let	let	VERB
ejpam-6086	232	2	(	(	PUNCT
ejpam-6086	232	3	u	u	NOUN
ejpam-6086	232	4	,	,	PUNCT
ejpam-6086	232	5	d	d	PROPN
ejpam-6086	232	6	)	)	PUNCT
ejpam-6086	232	7	be	be	AUX
ejpam-6086	232	8	a	a	DET
ejpam-6086	232	9	complete	complete	ADJ
ejpam-6086	232	10	rectangular	rectangular	ADJ
ejpam-6086	232	11	b−metric	b−metric	ADJ
ejpam-6086	232	12	space	space	NOUN
ejpam-6086	232	13	and	and	CCONJ
ejpam-6086	232	14	t	t	NOUN
ejpam-6086	232	15	:	:	PUNCT
ejpam-6086	232	16	u	u	PROPN
ejpam-6086	232	17	→	→	SYM
ejpam-6086	232	18	b(u	b(u	PROPN
ejpam-6086	232	19	)	)	PUNCT
ejpam-6086	232	20	be	be	AUX
ejpam-6086	232	21	a	a	DET
ejpam-6086	232	22	mapping	mapping	NOUN
ejpam-6086	232	23	.	.	PUNCT
ejpam-6086	233	1	if	if	SCONJ
ejpam-6086	233	2	exist	exist	VERB
ejpam-6086	233	3	θ	θ	PROPN
ejpam-6086	233	4	∈	∈	PROPN
ejpam-6086	233	5	θ	θ	PROPN
ejpam-6086	233	6	and	and	CCONJ
ejpam-6086	233	7	s	s	PROPN
ejpam-6086	233	8	∈	∈	PROPN
ejpam-6086	233	9	(	(	PUNCT
ejpam-6086	233	10	0	0	NUM
ejpam-6086	233	11	,	,	PUNCT
ejpam-6086	233	12	1	1	NUM
ejpam-6086	233	13	)	)	PUNCT
ejpam-6086	233	14	such	such	ADJ
ejpam-6086	233	15	that	that	DET
ejpam-6086	233	16	h(tx	h(tx	PROPN
ejpam-6086	233	17	,	,	PUNCT
ejpam-6086	233	18	ty	ty	NOUN
ejpam-6086	233	19	)	)	PUNCT
ejpam-6086	233	20	>	>	SYM
ejpam-6086	233	21	0	0	NUM
ejpam-6086	233	22	implies	imply	VERB
ejpam-6086	233	23	θ[b3h(tx	θ[b3h(tx	PROPN
ejpam-6086	233	24	,	,	PUNCT
ejpam-6086	233	25	ty	ty	NOUN
ejpam-6086	233	26	)	)	PUNCT
ejpam-6086	233	27	]	]	PUNCT
ejpam-6086	234	1	≤	≤	NOUN
ejpam-6086	235	1	[	[	X
ejpam-6086	235	2	θ(d(x	θ(d(x	NOUN
ejpam-6086	235	3	,	,	PUNCT
ejpam-6086	235	4	y))]s	y))]s	PROPN
ejpam-6086	235	5	for	for	ADP
ejpam-6086	235	6	all	all	DET
ejpam-6086	235	7	x	x	NOUN
ejpam-6086	235	8	,	,	PUNCT
ejpam-6086	235	9	y	y	PROPN
ejpam-6086	235	10	∈	∈	PROPN
ejpam-6086	235	11	u	u	PROPN
ejpam-6086	235	12	,	,	PUNCT
ejpam-6086	235	13	then	then	ADV
ejpam-6086	235	14	,	,	PUNCT
ejpam-6086	235	15	t	t	PROPN
ejpam-6086	235	16	has	have	VERB
ejpam-6086	235	17	a	a	DET
ejpam-6086	235	18	fixed	fix	VERB
ejpam-6086	235	19	point	point	NOUN
ejpam-6086	235	20	.	.	PUNCT
ejpam-6086	236	1	h.	h.	PROPN
ejpam-6086	236	2	massit	massit	PROPN
ejpam-6086	236	3	et	et	PROPN
ejpam-6086	236	4	al	al	PROPN
ejpam-6086	236	5	.	.	PUNCT
ejpam-6086	236	6	/	/	SYM
ejpam-6086	236	7	eur	eur	PROPN
ejpam-6086	236	8	.	.	PUNCT
ejpam-6086	237	1	j.	j.	PROPN
ejpam-6086	237	2	pure	pure	PROPN
ejpam-6086	237	3	appl	appl	PROPN
ejpam-6086	237	4	.	.	PROPN
ejpam-6086	237	5	math	math	PROPN
ejpam-6086	237	6	,	,	PUNCT
ejpam-6086	237	7	18	18	NUM
ejpam-6086	237	8	(	(	PUNCT
ejpam-6086	237	9	2	2	NUM
ejpam-6086	237	10	)	)	PUNCT
ejpam-6086	237	11	(	(	PUNCT
ejpam-6086	237	12	2025	2025	NUM
ejpam-6086	237	13	)	)	PUNCT
ejpam-6086	237	14	,	,	PUNCT
ejpam-6086	237	15	6086	6086	NUM
ejpam-6086	237	16	11	11	NUM
ejpam-6086	237	17	of	of	ADP
ejpam-6086	237	18	19	19	NUM
ejpam-6086	237	19	theorem	theorem	NOUN
ejpam-6086	237	20	4	4	NUM
ejpam-6086	237	21	.	.	PUNCT
ejpam-6086	238	1	let	let	AUX
ejpam-6086	238	2	(	(	PUNCT
ejpam-6086	238	3	u	u	NOUN
ejpam-6086	238	4	,	,	PUNCT
ejpam-6086	238	5	d	d	PROPN
ejpam-6086	238	6	)	)	PUNCT
ejpam-6086	238	7	be	be	AUX
ejpam-6086	238	8	a	a	DET
ejpam-6086	238	9	complete	complete	ADJ
ejpam-6086	238	10	rectangular	rectangular	ADJ
ejpam-6086	238	11	b−metric	b−metric	ADJ
ejpam-6086	238	12	space	space	NOUN
ejpam-6086	238	13	and	and	CCONJ
ejpam-6086	238	14	t	t	NOUN
ejpam-6086	238	15	:	:	PUNCT
ejpam-6086	238	16	u	u	PROPN
ejpam-6086	238	17	→	→	SYM
ejpam-6086	238	18	b(u	b(u	PROPN
ejpam-6086	238	19	)	)	PUNCT
ejpam-6086	238	20	be	be	VERB
ejpam-6086	238	21	an	an	DET
ejpam-6086	238	22	α−admissible	α−admissible	ADJ
ejpam-6086	238	23	θ	θ	X
ejpam-6086	238	24	−	−	NOUN
ejpam-6086	238	25	ϕ−multivalued	ϕ−multivalued	PUNCT
ejpam-6086	238	26	contraction	contraction	NOUN
ejpam-6086	238	27	satisfying	satisfying	ADJ
ejpam-6086	238	28	:	:	PUNCT
ejpam-6086	238	29	(	(	PUNCT
ejpam-6086	238	30	i	i	NOUN
ejpam-6086	238	31	)	)	PUNCT
ejpam-6086	238	32	(	(	PUNCT
ejpam-6086	238	33	u	u	NOUN
ejpam-6086	238	34	,	,	PUNCT
ejpam-6086	238	35	d	d	PROPN
ejpam-6086	238	36	)	)	PUNCT
ejpam-6086	238	37	is	be	AUX
ejpam-6086	238	38	an	an	DET
ejpam-6086	238	39	α−complete	α−complete	NUM
ejpam-6086	238	40	metric	metric	ADJ
ejpam-6086	238	41	space	space	NOUN
ejpam-6086	238	42	,	,	PUNCT
ejpam-6086	238	43	(	(	PUNCT
ejpam-6086	238	44	ii	ii	NOUN
ejpam-6086	238	45	)	)	PUNCT
ejpam-6086	238	46	α(x0	α(x0	PROPN
ejpam-6086	238	47	,	,	PUNCT
ejpam-6086	238	48	x1	x1	PROPN
ejpam-6086	238	49	)	)	PUNCT
ejpam-6086	238	50	≥	≥	NOUN
ejpam-6086	238	51	1	1	NUM
ejpam-6086	238	52	for	for	ADP
ejpam-6086	238	53	x0	x0	PROPN
ejpam-6086	238	54	∈	∈	PROPN
ejpam-6086	238	55	u	u	NOUN
ejpam-6086	238	56	and	and	CCONJ
ejpam-6086	238	57	x1	x1	PROPN
ejpam-6086	238	58	∈	∈	PROPN
ejpam-6086	238	59	t	t	PROPN
ejpam-6086	238	60	(	(	PUNCT
ejpam-6086	238	61	u	u	NOUN
ejpam-6086	238	62	)	)	PUNCT
ejpam-6086	238	63	,	,	PUNCT
ejpam-6086	238	64	(	(	PUNCT
ejpam-6086	238	65	iii	iii	X
ejpam-6086	238	66	)	)	PUNCT
ejpam-6086	238	67	t	t	PROPN
ejpam-6086	238	68	is	be	AUX
ejpam-6086	238	69	triangular	triangular	NOUN
ejpam-6086	238	70	α−admissible	α−admissible	NOUN
ejpam-6086	238	71	.	.	PUNCT
ejpam-6086	239	1	(	(	PUNCT
ejpam-6086	239	2	iv	iv	X
ejpam-6086	239	3	)	)	PUNCT
ejpam-6086	239	4	t	t	PROPN
ejpam-6086	239	5	is	be	AUX
ejpam-6086	239	6	an	an	DET
ejpam-6086	239	7	α−continuous	α−continuous	ADJ
ejpam-6086	239	8	multivalued	multivalued	ADJ
ejpam-6086	239	9	mapping	mapping	NOUN
ejpam-6086	239	10	.	.	PUNCT
ejpam-6086	240	1	then	then	ADV
ejpam-6086	240	2	,	,	PUNCT
ejpam-6086	240	3	t	t	PROPN
ejpam-6086	240	4	has	have	VERB
ejpam-6086	240	5	a	a	DET
ejpam-6086	240	6	fixed	fix	VERB
ejpam-6086	240	7	point	point	NOUN
ejpam-6086	240	8	.	.	PUNCT
ejpam-6086	241	1	proof	proof	NOUN
ejpam-6086	241	2	.	.	PUNCT
ejpam-6086	242	1	let	let	VERB
ejpam-6086	242	2	{	{	PUNCT
ejpam-6086	242	3	xn	xn	VERB
ejpam-6086	242	4	}	}	PUNCT
ejpam-6086	242	5	be	be	AUX
ejpam-6086	242	6	a	a	DET
ejpam-6086	242	7	sequence	sequence	NOUN
ejpam-6086	242	8	in	in	ADP
ejpam-6086	242	9	u	u	PRON
ejpam-6086	242	10	such	such	ADJ
ejpam-6086	242	11	that	that	SCONJ
ejpam-6086	242	12	xn+1	xn+1	NUM
ejpam-6086	242	13	∈	∈	PROPN
ejpam-6086	242	14	txn	txn	NOUN
ejpam-6086	242	15	with	with	ADP
ejpam-6086	242	16	α(xn	α(xn	PROPN
ejpam-6086	242	17	,	,	PUNCT
ejpam-6086	242	18	xn+1	xn+1	NUM
ejpam-6086	242	19	)	)	PUNCT
ejpam-6086	242	20	≥	≥	NOUN
ejpam-6086	242	21	1	1	NUM
ejpam-6086	242	22	,	,	PUNCT
ejpam-6086	242	23	by	by	ADP
ejpam-6086	242	24	(	(	PUNCT
ejpam-6086	242	25	iv	iv	X
ejpam-6086	242	26	)	)	PUNCT
ejpam-6086	242	27	,	,	PUNCT
ejpam-6086	242	28	we	we	PRON
ejpam-6086	242	29	have	have	VERB
ejpam-6086	242	30	θ[h(txn−1	θ[h(txn−1	NOUN
ejpam-6086	242	31	,	,	PUNCT
ejpam-6086	242	32	txn	txn	NOUN
ejpam-6086	242	33	)	)	PUNCT
ejpam-6086	242	34	]	]	PUNCT
ejpam-6086	243	1	≤	≤	X
ejpam-6086	243	2	θ[b3h(txn−1	θ[b3h(txn−1	PROPN
ejpam-6086	243	3	,	,	PUNCT
ejpam-6086	243	4	txn	txn	NOUN
ejpam-6086	243	5	)	)	PUNCT
ejpam-6086	243	6	]	]	PUNCT
ejpam-6086	243	7	≤	≤	NUM
ejpam-6086	243	8	θ[α(xn−1	θ[α(xn−1	X
ejpam-6086	243	9	,	,	PUNCT
ejpam-6086	243	10	xn)b	xn)b	PROPN
ejpam-6086	243	11	3h(txn−1	3h(txn−1	NUM
ejpam-6086	243	12	,	,	PUNCT
ejpam-6086	243	13	txn	txn	NOUN
ejpam-6086	243	14	)	)	PUNCT
ejpam-6086	243	15	]	]	PUNCT
ejpam-6086	243	16	≤	≤	NUM
ejpam-6086	243	17	ϕ[θ(m(xn−1	ϕ[θ(m(xn−1	PROPN
ejpam-6086	243	18	,	,	PUNCT
ejpam-6086	243	19	xn	xn	PROPN
ejpam-6086	243	20	)	)	PUNCT
ejpam-6086	243	21	)	)	PUNCT
ejpam-6086	243	22	]	]	PUNCT
ejpam-6086	244	1	+	+	ADV
ejpam-6086	244	2	kw	kw	INTJ
ejpam-6086	244	3	(	(	PUNCT
ejpam-6086	244	4	xn−1	xn−1	PROPN
ejpam-6086	244	5	,	,	PUNCT
ejpam-6086	244	6	xn	xn	PROPN
ejpam-6086	244	7	)	)	PUNCT
ejpam-6086	244	8	∀n	∀n	NUM
ejpam-6086	244	9	∈	∈	PROPN
ejpam-6086	244	10	n	n	X
ejpam-6086	244	11	where	where	SCONJ
ejpam-6086	244	12	m(xn−1	m(xn−1	NUM
ejpam-6086	244	13	,	,	PUNCT
ejpam-6086	244	14	xn	xn	NUM
ejpam-6086	244	15	)	)	PUNCT
ejpam-6086	244	16	=	=	SYM
ejpam-6086	244	17	max{d(xn−1	max{d(xn−1	ADJ
ejpam-6086	244	18	,	,	PUNCT
ejpam-6086	244	19	xn	xn	PROPN
ejpam-6086	244	20	)	)	PUNCT
ejpam-6086	244	21	,	,	PUNCT
ejpam-6086	244	22	d(xn−1	d(xn−1	PROPN
ejpam-6086	244	23	,	,	PUNCT
ejpam-6086	244	24	txn−1	txn−1	PROPN
ejpam-6086	244	25	)	)	PUNCT
ejpam-6086	244	26	,	,	PUNCT
ejpam-6086	244	27	d(xn	d(xn	PROPN
ejpam-6086	244	28	,	,	PUNCT
ejpam-6086	244	29	txn	txn	NOUN
ejpam-6086	244	30	)	)	PUNCT
ejpam-6086	244	31	,	,	PUNCT
ejpam-6086	244	32	d(xn	d(xn	PROPN
ejpam-6086	244	33	,	,	PUNCT
ejpam-6086	244	34	txn−1	txn−1	PROPN
ejpam-6086	244	35	)	)	PUNCT
ejpam-6086	244	36	}	}	PUNCT
ejpam-6086	244	37	=	=	SYM
ejpam-6086	244	38	max{d(xn−1	max{d(xn−1	ADJ
ejpam-6086	244	39	,	,	PUNCT
ejpam-6086	244	40	xn	xn	PROPN
ejpam-6086	244	41	)	)	PUNCT
ejpam-6086	244	42	,	,	PUNCT
ejpam-6086	244	43	d(xn	d(xn	PROPN
ejpam-6086	244	44	,	,	PUNCT
ejpam-6086	244	45	txn	txn	NOUN
ejpam-6086	244	46	)	)	PUNCT
ejpam-6086	244	47	}	}	PUNCT
ejpam-6086	244	48	and	and	CCONJ
ejpam-6086	244	49	w	w	PROPN
ejpam-6086	244	50	(	(	PUNCT
ejpam-6086	244	51	xn−1	xn−1	PROPN
ejpam-6086	244	52	,	,	PUNCT
ejpam-6086	244	53	xn	xn	PRON
ejpam-6086	244	54	)	)	PUNCT
ejpam-6086	244	55	=	=	SYM
ejpam-6086	244	56	min{d(xn−1	min{d(xn−1	PROPN
ejpam-6086	244	57	,	,	PUNCT
ejpam-6086	244	58	txn−1	txn−1	PROPN
ejpam-6086	244	59	)	)	PUNCT
ejpam-6086	244	60	,	,	PUNCT
ejpam-6086	244	61	d(xn	d(xn	PROPN
ejpam-6086	244	62	,	,	PUNCT
ejpam-6086	244	63	txn	txn	NOUN
ejpam-6086	244	64	)	)	PUNCT
ejpam-6086	244	65	,	,	PUNCT
ejpam-6086	244	66	d(txn−1	d(txn−1	PROPN
ejpam-6086	244	67	,	,	PUNCT
ejpam-6086	244	68	xn	xn	PROPN
ejpam-6086	244	69	)	)	PUNCT
ejpam-6086	244	70	,	,	PUNCT
ejpam-6086	244	71	d(xn−1	d(xn−1	PROPN
ejpam-6086	244	72	,	,	PUNCT
ejpam-6086	244	73	txn	txn	NOUN
ejpam-6086	244	74	)	)	PUNCT
ejpam-6086	244	75	}	}	PUNCT
ejpam-6086	244	76	=	=	SYM
ejpam-6086	244	77	min{d(xn−1	min{d(xn−1	PROPN
ejpam-6086	244	78	,	,	PUNCT
ejpam-6086	244	79	txn−1	txn−1	PROPN
ejpam-6086	244	80	)	)	PUNCT
ejpam-6086	244	81	,	,	PUNCT
ejpam-6086	244	82	d(xn	d(xn	PROPN
ejpam-6086	244	83	,	,	PUNCT
ejpam-6086	244	84	txn	txn	NOUN
ejpam-6086	244	85	)	)	PUNCT
ejpam-6086	244	86	,	,	PUNCT
ejpam-6086	244	87	0	0	NUM
ejpam-6086	244	88	,	,	PUNCT
ejpam-6086	244	89	d(xn−1	d(xn−1	PROPN
ejpam-6086	244	90	,	,	PUNCT
ejpam-6086	244	91	txn	txn	NOUN
ejpam-6086	244	92	)	)	PUNCT
ejpam-6086	244	93	}	}	PUNCT
ejpam-6086	244	94	=	=	PUNCT
ejpam-6086	244	95	0	0	X
ejpam-6086	244	96	.	.	PUNCT
ejpam-6086	245	1	if	if	SCONJ
ejpam-6086	245	2	m(xn−1	m(xn−1	NUM
ejpam-6086	245	3	,	,	PUNCT
ejpam-6086	245	4	xn	xn	NUM
ejpam-6086	245	5	)	)	PUNCT
ejpam-6086	246	1	=	=	PUNCT
ejpam-6086	247	1	d(xn	d(xn	X
ejpam-6086	247	2	,	,	PUNCT
ejpam-6086	247	3	txn	txn	NOUN
ejpam-6086	247	4	)	)	PUNCT
ejpam-6086	247	5	,	,	PUNCT
ejpam-6086	247	6	we	we	PRON
ejpam-6086	247	7	have	have	VERB
ejpam-6086	247	8	d(xn+1	d(xn+1	PROPN
ejpam-6086	247	9	,	,	PUNCT
ejpam-6086	247	10	xn	xn	PROPN
ejpam-6086	247	11	)	)	PUNCT
ejpam-6086	247	12	≤	≤	NUM
ejpam-6086	247	13	h(txn−1	h(txn−1	PROPN
ejpam-6086	247	14	,	,	PUNCT
ejpam-6086	247	15	txn	txn	NOUN
ejpam-6086	247	16	)	)	PUNCT
ejpam-6086	247	17	.	.	PUNCT
ejpam-6086	248	1	since	since	SCONJ
ejpam-6086	248	2	xn+1	xn+1	PROPN
ejpam-6086	248	3	∈	∈	PROPN
ejpam-6086	248	4	txn	txn	NOUN
ejpam-6086	248	5	we	we	PRON
ejpam-6086	248	6	have	have	VERB
ejpam-6086	248	7	d(xn	d(xn	PROPN
ejpam-6086	248	8	,	,	PUNCT
ejpam-6086	248	9	txn	txn	NOUN
ejpam-6086	248	10	)	)	PUNCT
ejpam-6086	248	11	≤	≤	NOUN
ejpam-6086	249	1	d(xn	d(xn	PROPN
ejpam-6086	249	2	,	,	PUNCT
ejpam-6086	249	3	xn+1	xn+1	NUM
ejpam-6086	249	4	)	)	PUNCT
ejpam-6086	249	5	.	.	PUNCT
ejpam-6086	250	1	now	now	ADV
ejpam-6086	250	2	,	,	PUNCT
ejpam-6086	250	3	we	we	PRON
ejpam-6086	250	4	obtain	obtain	VERB
ejpam-6086	250	5	θ(d(xn+1	θ(d(xn+1	ADJ
ejpam-6086	250	6	,	,	PUNCT
ejpam-6086	250	7	xn	xn	PROPN
ejpam-6086	250	8	)	)	PUNCT
ejpam-6086	250	9	)	)	PUNCT
ejpam-6086	251	1	≤	≤	NOUN
ejpam-6086	251	2	θ(h(txn−1	θ(h(txn−1	VERB
ejpam-6086	251	3	,	,	PUNCT
ejpam-6086	251	4	txn	txn	NOUN
ejpam-6086	251	5	)	)	PUNCT
ejpam-6086	251	6	)	)	PUNCT
ejpam-6086	252	1	≤	≤	NOUN
ejpam-6086	252	2	ϕ[θ(m(xn−1	ϕ[θ(m(xn−1	NUM
ejpam-6086	252	3	,	,	PUNCT
ejpam-6086	252	4	xn	xn	PROPN
ejpam-6086	252	5	)	)	PUNCT
ejpam-6086	252	6	)	)	PUNCT
ejpam-6086	252	7	]	]	PUNCT
ejpam-6086	253	1	+	+	PUNCT
ejpam-6086	253	2	kn(xn−1	kn(xn−1	X
ejpam-6086	253	3	,	,	PUNCT
ejpam-6086	253	4	xn	xn	NUM
ejpam-6086	253	5	)	)	PUNCT
ejpam-6086	253	6	≤	≤	NOUN
ejpam-6086	253	7	ϕ[θ(m(xn−1	ϕ[θ(m(xn−1	PROPN
ejpam-6086	253	8	,	,	PUNCT
ejpam-6086	253	9	xn	xn	PROPN
ejpam-6086	253	10	)	)	PUNCT
ejpam-6086	253	11	)	)	PUNCT
ejpam-6086	253	12	]	]	PUNCT
ejpam-6086	253	13	<	<	X
ejpam-6086	253	14	ϕ[θ(d(xn	ϕ[θ(d(xn	PROPN
ejpam-6086	253	15	,	,	PUNCT
ejpam-6086	253	16	txn	txn	NOUN
ejpam-6086	253	17	)	)	PUNCT
ejpam-6086	253	18	)	)	PUNCT
ejpam-6086	253	19	]	]	PUNCT
ejpam-6086	253	20	<	<	X
ejpam-6086	253	21	θ(d(xn	θ(d(xn	X
ejpam-6086	253	22	,	,	PUNCT
ejpam-6086	253	23	txn	txn	NOUN
ejpam-6086	253	24	)	)	PUNCT
ejpam-6086	253	25	)	)	PUNCT
ejpam-6086	253	26	,	,	PUNCT
ejpam-6086	253	27	which	which	PRON
ejpam-6086	253	28	is	be	AUX
ejpam-6086	253	29	a	a	DET
ejpam-6086	253	30	contradiction	contradiction	NOUN
ejpam-6086	253	31	,	,	PUNCT
ejpam-6086	253	32	so	so	ADV
ejpam-6086	253	33	,	,	PUNCT
ejpam-6086	253	34	m(xn−1	m(xn−1	NUM
ejpam-6086	253	35	,	,	PUNCT
ejpam-6086	253	36	xn	xn	NUM
ejpam-6086	253	37	)	)	PUNCT
ejpam-6086	253	38	=	=	SYM
ejpam-6086	253	39	d(xn−1	d(xn−1	NOUN
ejpam-6086	253	40	,	,	PUNCT
ejpam-6086	253	41	xn	xn	PRON
ejpam-6086	253	42	)	)	PUNCT
ejpam-6086	253	43	and	and	CCONJ
ejpam-6086	253	44	θ(d(xn+1	θ(d(xn+1	VERB
ejpam-6086	253	45	,	,	PUNCT
ejpam-6086	253	46	xn	xn	PROPN
ejpam-6086	253	47	)	)	PUNCT
ejpam-6086	253	48	)	)	PUNCT
ejpam-6086	253	49	≤	≤	NUM
ejpam-6086	254	1	ϕ[θ(d(xn−1	ϕ[θ(d(xn−1	PROPN
ejpam-6086	254	2	,	,	PUNCT
ejpam-6086	254	3	xn	xn	PROPN
ejpam-6086	254	4	)	)	PUNCT
ejpam-6086	254	5	)	)	PUNCT
ejpam-6086	254	6	]	]	PUNCT
ejpam-6086	255	1	<	<	X
ejpam-6086	255	2	θ(d(xn−1	θ(d(xn−1	PROPN
ejpam-6086	255	3	,	,	PUNCT
ejpam-6086	255	4	xn	xn	NUM
ejpam-6086	255	5	)	)	PUNCT
ejpam-6086	255	6	)	)	PUNCT
ejpam-6086	255	7	.	.	PUNCT
ejpam-6086	256	1	h.	h.	PROPN
ejpam-6086	256	2	massit	massit	PROPN
ejpam-6086	256	3	et	et	PROPN
ejpam-6086	256	4	al	al	PROPN
ejpam-6086	256	5	.	.	PUNCT
ejpam-6086	256	6	/	/	SYM
ejpam-6086	256	7	eur	eur	PROPN
ejpam-6086	256	8	.	.	PUNCT
ejpam-6086	257	1	j.	j.	PROPN
ejpam-6086	257	2	pure	pure	PROPN
ejpam-6086	257	3	appl	appl	PROPN
ejpam-6086	257	4	.	.	PROPN
ejpam-6086	257	5	math	math	PROPN
ejpam-6086	257	6	,	,	PUNCT
ejpam-6086	257	7	18	18	NUM
ejpam-6086	257	8	(	(	PUNCT
ejpam-6086	257	9	2	2	NUM
ejpam-6086	257	10	)	)	PUNCT
ejpam-6086	257	11	(	(	PUNCT
ejpam-6086	257	12	2025	2025	NUM
ejpam-6086	257	13	)	)	PUNCT
ejpam-6086	257	14	,	,	PUNCT
ejpam-6086	257	15	6086	6086	NUM
ejpam-6086	257	16	12	12	NUM
ejpam-6086	257	17	of	of	ADP
ejpam-6086	257	18	19	19	NUM
ejpam-6086	257	19	by	by	ADP
ejpam-6086	257	20	the	the	DET
ejpam-6086	257	21	properties	property	NOUN
ejpam-6086	257	22	of	of	ADP
ejpam-6086	257	23	θ	θ	NOUN
ejpam-6086	257	24	we	we	PRON
ejpam-6086	257	25	have	have	VERB
ejpam-6086	257	26	,	,	PUNCT
ejpam-6086	257	27	d(xn	d(xn	PROPN
ejpam-6086	257	28	,	,	PUNCT
ejpam-6086	257	29	xn+1	xn+1	NUM
ejpam-6086	257	30	)	)	PUNCT
ejpam-6086	257	31	<	<	X
ejpam-6086	257	32	d(xn−1	d(xn−1	PROPN
ejpam-6086	257	33	,	,	PUNCT
ejpam-6086	257	34	xn	xn	PROPN
ejpam-6086	257	35	)	)	PUNCT
ejpam-6086	257	36	.	.	PUNCT
ejpam-6086	258	1	this	this	PRON
ejpam-6086	258	2	implies	imply	VERB
ejpam-6086	258	3	that	that	SCONJ
ejpam-6086	258	4	the	the	DET
ejpam-6086	258	5	sequence	sequence	NOUN
ejpam-6086	258	6	{	{	PUNCT
ejpam-6086	258	7	d(xn	d(xn	PROPN
ejpam-6086	258	8	,	,	PUNCT
ejpam-6086	258	9	xn+1)}n	xn+1)}n	PROPN
ejpam-6086	258	10	is	be	AUX
ejpam-6086	258	11	strictly	strictly	ADV
ejpam-6086	258	12	decreasing	decrease	VERB
ejpam-6086	258	13	,	,	PUNCT
ejpam-6086	258	14	this	this	PRON
ejpam-6086	258	15	implies	imply	VERB
ejpam-6086	258	16	that	that	SCONJ
ejpam-6086	258	17	there	there	PRON
ejpam-6086	258	18	exists	exist	VERB
ejpam-6086	258	19	α	α	PROPN
ejpam-6086	258	20	>	>	X
ejpam-6086	258	21	0	0	NUM
ejpam-6086	258	22	such	such	ADJ
ejpam-6086	258	23	that	that	SCONJ
ejpam-6086	258	24	lim	lim	PROPN
ejpam-6086	258	25	n→+∞	n→+∞	VERB
ejpam-6086	258	26	d(xn	d(xn	PROPN
ejpam-6086	258	27	,	,	PUNCT
ejpam-6086	258	28	xn+1	xn+1	NUM
ejpam-6086	258	29	)	)	PUNCT
ejpam-6086	258	30	=	=	SYM
ejpam-6086	259	1	α	α	X
ejpam-6086	259	2	.	.	PUNCT
ejpam-6086	259	3	suppose	suppose	VERB
ejpam-6086	259	4	that	that	SCONJ
ejpam-6086	259	5	α	α	PROPN
ejpam-6086	259	6	>	>	X
ejpam-6086	259	7	0	0	NUM
ejpam-6086	259	8	,	,	PUNCT
ejpam-6086	259	9	we	we	PRON
ejpam-6086	259	10	can	can	AUX
ejpam-6086	259	11	conclude	conclude	VERB
ejpam-6086	259	12	that	that	SCONJ
ejpam-6086	259	13	d(xn	d(xn	PROPN
ejpam-6086	259	14	,	,	PUNCT
ejpam-6086	259	15	xn+1	xn+1	NUM
ejpam-6086	259	16	)	)	PUNCT
ejpam-6086	259	17	≥	≥	PROPN
ejpam-6086	259	18	α	α	NOUN
ejpam-6086	259	19	,	,	PUNCT
ejpam-6086	259	20	for	for	ADP
ejpam-6086	259	21	all	all	PRON
ejpam-6086	259	22	n	n	DET
ejpam-6086	259	23	∈	∈	PROPN
ejpam-6086	259	24	n.	n.	NOUN
ejpam-6086	259	25	we	we	PRON
ejpam-6086	259	26	get	get	AUX
ejpam-6086	259	27	θ(d(xn+1	θ(d(xn+1	VERB
ejpam-6086	259	28	,	,	PUNCT
ejpam-6086	259	29	xn	xn	PROPN
ejpam-6086	259	30	)	)	PUNCT
ejpam-6086	259	31	)	)	PUNCT
ejpam-6086	259	32	≤	≤	NUM
ejpam-6086	260	1	ϕ[θ(d(xn−1	ϕ[θ(d(xn−1	PROPN
ejpam-6086	260	2	,	,	PUNCT
ejpam-6086	260	3	xn	xn	PROPN
ejpam-6086	260	4	)	)	PUNCT
ejpam-6086	260	5	)	)	PUNCT
ejpam-6086	260	6	]	]	PUNCT
ejpam-6086	261	1	≤	≤	PROPN
ejpam-6086	261	2	ϕ2[θ(d(xn−2	ϕ2[θ(d(xn−2	PROPN
ejpam-6086	261	3	,	,	PUNCT
ejpam-6086	261	4	xn−1	xn−1	PROPN
ejpam-6086	261	5	)	)	PUNCT
ejpam-6086	261	6	)	)	PUNCT
ejpam-6086	261	7	]	]	PUNCT
ejpam-6086	261	8	...	...	PUNCT
ejpam-6086	262	1	≤	≤	NUM
ejpam-6086	262	2	ϕn[θ(d(x0	ϕn[θ(d(x0	ADV
ejpam-6086	262	3	,	,	PUNCT
ejpam-6086	262	4	x1	x1	PROPN
ejpam-6086	262	5	)	)	PUNCT
ejpam-6086	262	6	)	)	PUNCT
ejpam-6086	262	7	]	]	PUNCT
ejpam-6086	262	8	.	.	PUNCT
ejpam-6086	263	1	using	use	VERB
ejpam-6086	263	2	the	the	DET
ejpam-6086	263	3	property	property	NOUN
ejpam-6086	263	4	of	of	ADP
ejpam-6086	263	5	θ	θ	PROPN
ejpam-6086	263	6	,	,	PUNCT
ejpam-6086	263	7	we	we	PRON
ejpam-6086	263	8	get	get	VERB
ejpam-6086	263	9	1	1	NUM
ejpam-6086	263	10	<	<	X
ejpam-6086	263	11	θ(α	θ(α	NOUN
ejpam-6086	263	12	)	)	PUNCT
ejpam-6086	263	13	≤	≤	NOUN
ejpam-6086	263	14	ϕn[θ(d(x0	ϕn[θ(d(x0	ADP
ejpam-6086	263	15	,	,	PUNCT
ejpam-6086	263	16	x1	x1	PROPN
ejpam-6086	263	17	)	)	PUNCT
ejpam-6086	263	18	)	)	PUNCT
ejpam-6086	263	19	]	]	PUNCT
ejpam-6086	263	20	.	.	PUNCT
ejpam-6086	264	1	(	(	PUNCT
ejpam-6086	264	2	14	14	X
ejpam-6086	264	3	)	)	PUNCT
ejpam-6086	264	4	letting	let	VERB
ejpam-6086	264	5	n→	n→	ADV
ejpam-6086	264	6	+	+	ADJ
ejpam-6086	264	7	∞	∞	PROPN
ejpam-6086	264	8	in	in	ADP
ejpam-6086	264	9	(	(	PUNCT
ejpam-6086	264	10	14	14	NUM
ejpam-6086	264	11	)	)	PUNCT
ejpam-6086	264	12	,	,	PUNCT
ejpam-6086	264	13	we	we	PRON
ejpam-6086	264	14	get	get	VERB
ejpam-6086	264	15	1	1	NUM
ejpam-6086	264	16	<	<	X
ejpam-6086	264	17	θ(α	θ(α	NOUN
ejpam-6086	264	18	)	)	PUNCT
ejpam-6086	264	19	≤	≤	NOUN
ejpam-6086	264	20	1	1	NUM
ejpam-6086	264	21	.	.	PUNCT
ejpam-6086	265	1	this	this	DET
ejpam-6086	265	2	a	a	DET
ejpam-6086	265	3	contradiction	contradiction	NOUN
ejpam-6086	265	4	,	,	PUNCT
ejpam-6086	265	5	so	so	SCONJ
ejpam-6086	265	6	we	we	PRON
ejpam-6086	265	7	obtain	obtain	VERB
ejpam-6086	265	8	lim	lim	NOUN
ejpam-6086	265	9	n→+∞	n→+∞	VERB
ejpam-6086	265	10	d(xn	d(xn	PROPN
ejpam-6086	265	11	,	,	PUNCT
ejpam-6086	265	12	xn+1	xn+1	NUM
ejpam-6086	265	13	)	)	PUNCT
ejpam-6086	265	14	=	=	SYM
ejpam-6086	266	1	0	0	X
ejpam-6086	266	2	.	.	PUNCT
ejpam-6086	267	1	next	next	ADV
ejpam-6086	267	2	,	,	PUNCT
ejpam-6086	267	3	we	we	PRON
ejpam-6086	267	4	show	show	VERB
ejpam-6086	267	5	that	that	SCONJ
ejpam-6086	267	6	{	{	PUNCT
ejpam-6086	267	7	xn}n	xn}n	PROPN
ejpam-6086	267	8	is	be	AUX
ejpam-6086	267	9	a	a	DET
ejpam-6086	267	10	cauchy	cauchy	ADJ
ejpam-6086	267	11	sequence	sequence	NOUN
ejpam-6086	267	12	in	in	ADP
ejpam-6086	267	13	u	u	NOUN
ejpam-6086	267	14	,	,	PUNCT
ejpam-6086	267	15	there	there	PRON
ejpam-6086	267	16	exists	exist	VERB
ejpam-6086	267	17	an	an	DET
ejpam-6086	267	18	ε	ε	PROPN
ejpam-6086	267	19	>	>	X
ejpam-6086	267	20	0	0	PROPN
ejpam-6086	267	21	for	for	ADP
ejpam-6086	267	22	which	which	PRON
ejpam-6086	267	23	we	we	PRON
ejpam-6086	267	24	can	can	AUX
ejpam-6086	267	25	find	find	VERB
ejpam-6086	267	26	sequences	sequence	NOUN
ejpam-6086	267	27	of	of	ADP
ejpam-6086	267	28	positive	positive	ADJ
ejpam-6086	267	29	integers	integer	NOUN
ejpam-6086	267	30	{	{	PUNCT
ejpam-6086	267	31	xnk	xnk	PROPN
ejpam-6086	267	32	}	}	PUNCT
ejpam-6086	267	33	and	and	CCONJ
ejpam-6086	267	34	{	{	PUNCT
ejpam-6086	267	35	xmk	xmk	PROPN
ejpam-6086	267	36	}	}	PUNCT
ejpam-6086	267	37	of	of	ADP
ejpam-6086	267	38	{	{	PUNCT
ejpam-6086	267	39	xn	xn	NOUN
ejpam-6086	267	40	}	}	PUNCT
ejpam-6086	267	41	such	such	ADJ
ejpam-6086	267	42	that	that	SCONJ
ejpam-6086	267	43	,	,	PUNCT
ejpam-6086	267	44	for	for	ADP
ejpam-6086	267	45	all	all	DET
ejpam-6086	267	46	positive	positive	ADJ
ejpam-6086	267	47	integers	integer	NOUN
ejpam-6086	267	48	k	k	NOUN
ejpam-6086	267	49	,	,	PUNCT
ejpam-6086	267	50	nk	nk	PROPN
ejpam-6086	267	51	>	>	X
ejpam-6086	267	52	mk	mk	PROPN
ejpam-6086	267	53	>	>	X
ejpam-6086	267	54	k	k	PROPN
ejpam-6086	267	55	,	,	PUNCT
ejpam-6086	267	56	d(xmk	d(xmk	PROPN
ejpam-6086	267	57	,	,	PUNCT
ejpam-6086	267	58	xnk	xnk	PROPN
ejpam-6086	267	59	)	)	PUNCT
ejpam-6086	267	60	≥	≥	PROPN
ejpam-6086	267	61	ε	ε	PROPN
ejpam-6086	267	62	(	(	PUNCT
ejpam-6086	267	63	15	15	NUM
ejpam-6086	267	64	)	)	PUNCT
ejpam-6086	267	65	d(xmk	d(xmk	NOUN
ejpam-6086	267	66	,	,	PUNCT
ejpam-6086	267	67	xnk−1	xnk−1	PROPN
ejpam-6086	267	68	)	)	PUNCT
ejpam-6086	267	69	<	<	X
ejpam-6086	267	70	ε	ε	PROPN
ejpam-6086	267	71	(	(	PUNCT
ejpam-6086	267	72	16	16	NUM
ejpam-6086	267	73	)	)	PUNCT
ejpam-6086	267	74	we	we	PRON
ejpam-6086	267	75	get	get	VERB
ejpam-6086	267	76	ε	ε	PROPN
ejpam-6086	267	77	≤	≤	PROPN
ejpam-6086	267	78	d(xmk	d(xmk	PROPN
ejpam-6086	267	79	,	,	PUNCT
ejpam-6086	267	80	xnk	xnk	PROPN
ejpam-6086	267	81	)	)	PUNCT
ejpam-6086	267	82	≤	≤	NUM
ejpam-6086	267	83	bd(xmk	bd(xmk	PROPN
ejpam-6086	267	84	,	,	PUNCT
ejpam-6086	267	85	xmk+1	xmk+1	X
ejpam-6086	267	86	)	)	PUNCT
ejpam-6086	268	1	+	+	CCONJ
ejpam-6086	268	2	bd(xmk+1	bd(xmk+1	NOUN
ejpam-6086	268	3	,	,	PUNCT
ejpam-6086	268	4	xnk+1	xnk+1	X
ejpam-6086	268	5	)	)	PUNCT
ejpam-6086	269	1	+	+	CCONJ
ejpam-6086	269	2	bd(xnk+1	bd(xnk+1	NOUN
ejpam-6086	269	3	,	,	PUNCT
ejpam-6086	269	4	xnk	xnk	PROPN
ejpam-6086	269	5	)	)	PUNCT
ejpam-6086	269	6	(	(	PUNCT
ejpam-6086	269	7	17	17	X
ejpam-6086	269	8	)	)	PUNCT
ejpam-6086	269	9	letting	let	VERB
ejpam-6086	269	10	k	k	X
ejpam-6086	269	11	→	→	PUNCT
ejpam-6086	269	12	+	+	PROPN
ejpam-6086	269	13	∞	∞	PROPN
ejpam-6086	269	14	,	,	PUNCT
ejpam-6086	269	15	we	we	PRON
ejpam-6086	269	16	get	get	VERB
ejpam-6086	269	17	ε	ε	PROPN
ejpam-6086	269	18	b	b	PROPN
ejpam-6086	269	19	lim	lim	PROPN
ejpam-6086	269	20	n→+∞	n→+∞	VERB
ejpam-6086	269	21	sup	sup	NOUN
ejpam-6086	269	22	d(xmk+1	d(xmk+1	NOUN
ejpam-6086	269	23	,	,	PUNCT
ejpam-6086	269	24	xnk+1	xnk+1	PROPN
ejpam-6086	269	25	)	)	PUNCT
ejpam-6086	269	26	(	(	PUNCT
ejpam-6086	269	27	18	18	NUM
ejpam-6086	269	28	)	)	PUNCT
ejpam-6086	269	29	and	and	CCONJ
ejpam-6086	269	30	lim	lim	PROPN
ejpam-6086	269	31	n→+∞	n→+∞	VERB
ejpam-6086	269	32	sup	sup	NOUN
ejpam-6086	269	33	d(xmk	d(xmk	NOUN
ejpam-6086	269	34	,	,	PUNCT
ejpam-6086	269	35	xnk	xnk	PROPN
ejpam-6086	269	36	)	)	PUNCT
ejpam-6086	269	37	≤	≤	NUM
ejpam-6086	269	38	bε	bε	NOUN
ejpam-6086	269	39	.	.	PUNCT
ejpam-6086	270	1	(	(	PUNCT
ejpam-6086	270	2	19	19	NUM
ejpam-6086	270	3	)	)	PUNCT
ejpam-6086	270	4	since	since	SCONJ
ejpam-6086	270	5	α(xmk	α(xmk	PROPN
ejpam-6086	270	6	,	,	PUNCT
ejpam-6086	270	7	xnk	xnk	PROPN
ejpam-6086	270	8	)	)	PUNCT
ejpam-6086	270	9	≥	≥	NOUN
ejpam-6086	270	10	1	1	NUM
ejpam-6086	270	11	,	,	PUNCT
ejpam-6086	270	12	we	we	PRON
ejpam-6086	270	13	have	have	VERB
ejpam-6086	270	14	m(xmk	m(xmk	NOUN
ejpam-6086	270	15	,	,	PUNCT
ejpam-6086	270	16	xnk	xnk	PROPN
ejpam-6086	270	17	)	)	PUNCT
ejpam-6086	271	1	=	=	SYM
ejpam-6086	271	2	max{d(xmk	max{d(xmk	NOUN
ejpam-6086	271	3	,	,	PUNCT
ejpam-6086	271	4	xnk	xnk	PROPN
ejpam-6086	271	5	)	)	PUNCT
ejpam-6086	271	6	,	,	PUNCT
ejpam-6086	271	7	d(xmk	d(xmk	PROPN
ejpam-6086	271	8	,	,	PUNCT
ejpam-6086	271	9	txmk	txmk	PROPN
ejpam-6086	271	10	)	)	PUNCT
ejpam-6086	271	11	,	,	PUNCT
ejpam-6086	271	12	d(xmk	d(xmk	PROPN
ejpam-6086	271	13	,	,	PUNCT
ejpam-6086	271	14	txmk	txmk	PROPN
ejpam-6086	271	15	)	)	PUNCT
ejpam-6086	271	16	,	,	PUNCT
ejpam-6086	271	17	d(xnk	d(xnk	PROPN
ejpam-6086	271	18	,	,	PUNCT
ejpam-6086	271	19	txmk	txmk	NOUN
ejpam-6086	271	20	)	)	PUNCT
ejpam-6086	271	21	}	}	PUNCT
ejpam-6086	272	1	≤	≤	NUM
ejpam-6086	272	2	max{d(xmk	max{d(xmk	NOUN
ejpam-6086	272	3	,	,	PUNCT
ejpam-6086	272	4	xnk	xnk	PROPN
ejpam-6086	272	5	)	)	PUNCT
ejpam-6086	272	6	,	,	PUNCT
ejpam-6086	272	7	d(xmk	d(xmk	PROPN
ejpam-6086	272	8	,	,	PUNCT
ejpam-6086	272	9	xmk+1	xmk+1	X
ejpam-6086	272	10	)	)	PUNCT
ejpam-6086	272	11	,	,	PUNCT
ejpam-6086	272	12	d(xmk	d(xmk	PROPN
ejpam-6086	272	13	,	,	PUNCT
ejpam-6086	272	14	xmk+1	xmk+1	PROPN
ejpam-6086	272	15	)	)	PUNCT
ejpam-6086	272	16	,	,	PUNCT
ejpam-6086	272	17	d(xnk	d(xnk	PROPN
ejpam-6086	272	18	,	,	PUNCT
ejpam-6086	272	19	xmk+1	xmk+1	X
ejpam-6086	272	20	)	)	PUNCT
ejpam-6086	272	21	}	}	PUNCT
ejpam-6086	272	22	=	=	SYM
ejpam-6086	272	23	max{d(xmk	max{d(xmk	NOUN
ejpam-6086	272	24	,	,	PUNCT
ejpam-6086	272	25	xnk	xnk	PROPN
ejpam-6086	272	26	)	)	PUNCT
ejpam-6086	272	27	,	,	PUNCT
ejpam-6086	272	28	d(xmk	d(xmk	PROPN
ejpam-6086	272	29	,	,	PUNCT
ejpam-6086	272	30	xmk+1	xmk+1	PROPN
ejpam-6086	272	31	)	)	PUNCT
ejpam-6086	272	32	,	,	PUNCT
ejpam-6086	272	33	d(xnk	d(xnk	PROPN
ejpam-6086	272	34	,	,	PUNCT
ejpam-6086	272	35	xmk+1	xmk+1	X
ejpam-6086	272	36	)	)	PUNCT
ejpam-6086	272	37	}	}	PUNCT
ejpam-6086	272	38	h.	h.	NOUN
ejpam-6086	272	39	massit	massit	PROPN
ejpam-6086	272	40	et	et	PROPN
ejpam-6086	272	41	al	al	PROPN
ejpam-6086	272	42	.	.	PUNCT
ejpam-6086	272	43	/	/	SYM
ejpam-6086	272	44	eur	eur	PROPN
ejpam-6086	272	45	.	.	PUNCT
ejpam-6086	273	1	j.	j.	PROPN
ejpam-6086	273	2	pure	pure	PROPN
ejpam-6086	273	3	appl	appl	PROPN
ejpam-6086	273	4	.	.	PROPN
ejpam-6086	273	5	math	math	PROPN
ejpam-6086	273	6	,	,	PUNCT
ejpam-6086	273	7	18	18	NUM
ejpam-6086	273	8	(	(	PUNCT
ejpam-6086	273	9	2	2	NUM
ejpam-6086	273	10	)	)	PUNCT
ejpam-6086	273	11	(	(	PUNCT
ejpam-6086	273	12	2025	2025	NUM
ejpam-6086	273	13	)	)	PUNCT
ejpam-6086	273	14	,	,	PUNCT
ejpam-6086	273	15	6086	6086	NUM
ejpam-6086	273	16	13	13	NUM
ejpam-6086	273	17	of	of	ADP
ejpam-6086	273	18	19	19	NUM
ejpam-6086	273	19	and	and	CCONJ
ejpam-6086	273	20	w	w	PROPN
ejpam-6086	273	21	(	(	PUNCT
ejpam-6086	273	22	xmk	xmk	PROPN
ejpam-6086	273	23	,	,	PUNCT
ejpam-6086	273	24	xnk	xnk	PROPN
ejpam-6086	273	25	)	)	PUNCT
ejpam-6086	274	1	=	=	SYM
ejpam-6086	274	2	min{d(xmk	min{d(xmk	NOUN
ejpam-6086	274	3	,	,	PUNCT
ejpam-6086	274	4	txmk	txmk	NOUN
ejpam-6086	274	5	)	)	PUNCT
ejpam-6086	274	6	,	,	PUNCT
ejpam-6086	274	7	d(xnk	d(xnk	PROPN
ejpam-6086	274	8	,	,	PUNCT
ejpam-6086	274	9	txnk	txnk	NOUN
ejpam-6086	274	10	)	)	PUNCT
ejpam-6086	274	11	,	,	PUNCT
ejpam-6086	274	12	d(txmk	d(txmk	INTJ
ejpam-6086	274	13	,	,	PUNCT
ejpam-6086	274	14	xnk	xnk	PROPN
ejpam-6086	274	15	)	)	PUNCT
ejpam-6086	274	16	,	,	PUNCT
ejpam-6086	274	17	d(xmk	d(xmk	PROPN
ejpam-6086	274	18	,	,	PUNCT
ejpam-6086	274	19	txnk	txnk	NOUN
ejpam-6086	274	20	)	)	PUNCT
ejpam-6086	274	21	}	}	PUNCT
ejpam-6086	274	22	≤	≤	NOUN
ejpam-6086	274	23	min{d(xmk	min{d(xmk	NOUN
ejpam-6086	274	24	,	,	PUNCT
ejpam-6086	274	25	xmk+1	xmk+1	X
ejpam-6086	274	26	)	)	PUNCT
ejpam-6086	274	27	,	,	PUNCT
ejpam-6086	274	28	d(xnk	d(xnk	PROPN
ejpam-6086	274	29	,	,	PUNCT
ejpam-6086	274	30	xnk+1	xnk+1	PROPN
ejpam-6086	274	31	)	)	PUNCT
ejpam-6086	274	32	,	,	PUNCT
ejpam-6086	274	33	d(xmk+1	d(xmk+1	VERB
ejpam-6086	274	34	,	,	PUNCT
ejpam-6086	274	35	xnk	xnk	PROPN
ejpam-6086	274	36	)	)	PUNCT
ejpam-6086	274	37	;	;	PUNCT
ejpam-6086	274	38	d(xmk	d(xmk	PROPN
ejpam-6086	274	39	,	,	PUNCT
ejpam-6086	274	40	xnk+1	xnk+1	PROPN
ejpam-6086	274	41	)	)	PUNCT
ejpam-6086	274	42	}	}	PUNCT
ejpam-6086	274	43	letting	let	VERB
ejpam-6086	274	44	n→	n→	ADV
ejpam-6086	274	45	+	+	SCONJ
ejpam-6086	274	46	∞	∞	NUM
ejpam-6086	274	47	we	we	PRON
ejpam-6086	274	48	obtain	obtain	VERB
ejpam-6086	274	49	lim	lim	PROPN
ejpam-6086	274	50	k→+∞	k→+∞	PROPN
ejpam-6086	274	51	m(xmk	m(xmk	PROPN
ejpam-6086	274	52	,	,	PUNCT
ejpam-6086	274	53	xnk	xnk	PROPN
ejpam-6086	274	54	)	)	PUNCT
ejpam-6086	275	1	≤	≤	PROPN
ejpam-6086	276	1	lim	lim	PROPN
ejpam-6086	276	2	k→+∞	k→+∞	PROPN
ejpam-6086	276	3	max{d(xmk	max{d(xmk	NOUN
ejpam-6086	276	4	,	,	PUNCT
ejpam-6086	276	5	xnk	xnk	PROPN
ejpam-6086	276	6	)	)	PUNCT
ejpam-6086	276	7	,	,	PUNCT
ejpam-6086	276	8	d(xmk	d(xmk	PROPN
ejpam-6086	276	9	,	,	PUNCT
ejpam-6086	276	10	xmk+1	xmk+1	PROPN
ejpam-6086	276	11	)	)	PUNCT
ejpam-6086	276	12	,	,	PUNCT
ejpam-6086	276	13	d(xnk	d(xnk	PROPN
ejpam-6086	276	14	,	,	PUNCT
ejpam-6086	276	15	xmk+1	xmk+1	X
ejpam-6086	276	16	)	)	PUNCT
ejpam-6086	276	17	}	}	PUNCT
ejpam-6086	276	18	≤	≤	NOUN
ejpam-6086	276	19	max{bε	max{bε	NOUN
ejpam-6086	276	20	,	,	PUNCT
ejpam-6086	276	21	0	0	NUM
ejpam-6086	276	22	,	,	PUNCT
ejpam-6086	276	23	b2ε	b2ε	ADJ
ejpam-6086	276	24	}	}	PUNCT
ejpam-6086	276	25	=	=	SYM
ejpam-6086	276	26	b2ε	b2ε	NOUN
ejpam-6086	276	27	.	.	PUNCT
ejpam-6086	277	1	now	now	ADV
ejpam-6086	277	2	,	,	PUNCT
ejpam-6086	277	3	we	we	PRON
ejpam-6086	277	4	obtain	obtain	VERB
ejpam-6086	277	5	lim	lim	PROPN
ejpam-6086	277	6	k→+∞	k→+∞	PROPN
ejpam-6086	277	7	w	w	PROPN
ejpam-6086	277	8	(	(	PUNCT
ejpam-6086	277	9	xmk	xmk	PROPN
ejpam-6086	277	10	,	,	PUNCT
ejpam-6086	277	11	xnk	xnk	PROPN
ejpam-6086	277	12	)	)	PUNCT
ejpam-6086	277	13	≤	≤	PROPN
ejpam-6086	278	1	lim	lim	PROPN
ejpam-6086	278	2	k→+∞	k→+∞	PROPN
ejpam-6086	278	3	min{d(xmk	min{d(xmk	PROPN
ejpam-6086	278	4	,	,	PUNCT
ejpam-6086	278	5	xnk	xnk	PROPN
ejpam-6086	278	6	)	)	PUNCT
ejpam-6086	278	7	,	,	PUNCT
ejpam-6086	278	8	d(xmk	d(xmk	PROPN
ejpam-6086	278	9	,	,	PUNCT
ejpam-6086	278	10	xmk+1	xmk+1	PROPN
ejpam-6086	278	11	)	)	PUNCT
ejpam-6086	278	12	,	,	PUNCT
ejpam-6086	278	13	d(xnk	d(xnk	PROPN
ejpam-6086	278	14	,	,	PUNCT
ejpam-6086	278	15	xmk+1	xmk+1	X
ejpam-6086	278	16	)	)	PUNCT
ejpam-6086	278	17	}	}	PUNCT
ejpam-6086	278	18	≤	≤	NOUN
ejpam-6086	278	19	min{bε	min{bε	NOUN
ejpam-6086	278	20	,	,	PUNCT
ejpam-6086	278	21	0	0	NUM
ejpam-6086	278	22	,	,	PUNCT
ejpam-6086	278	23	b2ε	b2ε	ADJ
ejpam-6086	278	24	}	}	PUNCT
ejpam-6086	278	25	=	=	SYM
ejpam-6086	278	26	0	0	X
ejpam-6086	278	27	.	.	PUNCT
ejpam-6086	279	1	so	so	ADV
ejpam-6086	279	2	,	,	PUNCT
ejpam-6086	279	3	we	we	PRON
ejpam-6086	279	4	have	have	AUX
ejpam-6086	279	5	θ[d(xmk+1	θ[d(xmk+1	VERB
ejpam-6086	279	6	,	,	PUNCT
ejpam-6086	279	7	xnk+1	xnk+1	PROPN
ejpam-6086	279	8	)	)	PUNCT
ejpam-6086	279	9	]	]	PUNCT
ejpam-6086	280	1	≤	≤	PROPN
ejpam-6086	280	2	θ[b3h(txmk	θ[b3h(txmk	ADV
ejpam-6086	280	3	,	,	PUNCT
ejpam-6086	280	4	txnk	txnk	NOUN
ejpam-6086	280	5	)	)	PUNCT
ejpam-6086	280	6	]	]	PUNCT
ejpam-6086	280	7	≤	≤	NUM
ejpam-6086	280	8	θ[α(xmk	θ[α(xmk	NOUN
ejpam-6086	280	9	,	,	PUNCT
ejpam-6086	280	10	xnk	xnk	PROPN
ejpam-6086	280	11	)	)	PUNCT
ejpam-6086	280	12	b3h(txmk	b3h(txmk	PROPN
ejpam-6086	280	13	,	,	PUNCT
ejpam-6086	280	14	txnk	txnk	VERB
ejpam-6086	280	15	)	)	PUNCT
ejpam-6086	280	16	]	]	PUNCT
ejpam-6086	281	1	≤	≤	PROPN
ejpam-6086	281	2	ϕ[θ(m(xmk	ϕ[θ(m(xmk	PUNCT
ejpam-6086	281	3	,	,	PUNCT
ejpam-6086	281	4	xnk	xnk	PROPN
ejpam-6086	281	5	)	)	PUNCT
ejpam-6086	281	6	)	)	PUNCT
ejpam-6086	281	7	]	]	PUNCT
ejpam-6086	282	1	+	+	ADV
ejpam-6086	282	2	kw	kw	INTJ
ejpam-6086	282	3	(	(	PUNCT
ejpam-6086	282	4	xmk	xmk	PROPN
ejpam-6086	282	5	,	,	PUNCT
ejpam-6086	282	6	xnk	xnk	PROPN
ejpam-6086	282	7	)	)	PUNCT
ejpam-6086	282	8	.	.	PUNCT
ejpam-6086	283	1	letting	let	VERB
ejpam-6086	283	2	k	k	PRON
ejpam-6086	283	3	→	→	PUNCT
ejpam-6086	283	4	+	+	PROPN
ejpam-6086	283	5	∞	∞	PROPN
ejpam-6086	283	6	,	,	PUNCT
ejpam-6086	283	7	we	we	PRON
ejpam-6086	283	8	obtain	obtain	VERB
ejpam-6086	283	9	θ(εb	θ(εb	NOUN
ejpam-6086	283	10	)	)	PUNCT
ejpam-6086	283	11	≤	≤	NOUN
ejpam-6086	283	12	θ[b3	θ[b3	SCONJ
ejpam-6086	283	13	lim	lim	PROPN
ejpam-6086	283	14	k→+∞	k→+∞	PROPN
ejpam-6086	283	15	d(xmk+1	d(xmk+1	VERB
ejpam-6086	283	16	,	,	PUNCT
ejpam-6086	283	17	xnk+1	xnk+1	PROPN
ejpam-6086	283	18	)	)	PUNCT
ejpam-6086	283	19	]	]	PUNCT
ejpam-6086	284	1	≤	≤	NUM
ejpam-6086	284	2	ϕ[θ	ϕ[θ	PROPN
ejpam-6086	284	3	(	(	PUNCT
ejpam-6086	284	4	lim	lim	PROPN
ejpam-6086	284	5	k→+∞	k→+∞	PROPN
ejpam-6086	284	6	m(xmk	m(xmk	PROPN
ejpam-6086	284	7	,	,	PUNCT
ejpam-6086	284	8	xnk	xnk	PROPN
ejpam-6086	284	9	)	)	PUNCT
ejpam-6086	284	10	)	)	PUNCT
ejpam-6086	284	11	]	]	PUNCT
ejpam-6086	285	1	+	+	ADP
ejpam-6086	285	2	k	k	PROPN
ejpam-6086	285	3	lim	lim	PROPN
ejpam-6086	285	4	k→+∞	k→+∞	PROPN
ejpam-6086	285	5	w	w	PROPN
ejpam-6086	285	6	(	(	PUNCT
ejpam-6086	285	7	xmk	xmk	PROPN
ejpam-6086	285	8	,	,	PUNCT
ejpam-6086	285	9	xnk	xnk	PROPN
ejpam-6086	285	10	)	)	PUNCT
ejpam-6086	286	1	=	=	PUNCT
ejpam-6086	286	2	ϕ[θ	ϕ[θ	PROPN
ejpam-6086	286	3	(	(	PUNCT
ejpam-6086	286	4	lim	lim	PROPN
ejpam-6086	286	5	k→+∞	k→+∞	PROPN
ejpam-6086	286	6	m(xmk	m(xmk	PROPN
ejpam-6086	286	7	,	,	PUNCT
ejpam-6086	286	8	xnk	xnk	PROPN
ejpam-6086	286	9	)	)	PUNCT
ejpam-6086	286	10	)	)	PUNCT
ejpam-6086	286	11	]	]	PUNCT
ejpam-6086	286	12	≤	≤	NUM
ejpam-6086	286	13	ϕ[θ(bε	ϕ[θ(bε	NOUN
ejpam-6086	286	14	)	)	PUNCT
ejpam-6086	286	15	]	]	PUNCT
ejpam-6086	286	16	.	.	PUNCT
ejpam-6086	287	1	by	by	ADP
ejpam-6086	287	2	lemma	lemma	PROPN
ejpam-6086	287	3	2	2	NUM
ejpam-6086	287	4	we	we	PRON
ejpam-6086	287	5	have	have	VERB
ejpam-6086	287	6	θ(bε	θ(bε	NOUN
ejpam-6086	287	7	)	)	PUNCT
ejpam-6086	287	8	≤	≤	NUM
ejpam-6086	287	9	ϕ[θ(bε	ϕ[θ(bε	NOUN
ejpam-6086	287	10	)	)	PUNCT
ejpam-6086	287	11	]	]	PUNCT
ejpam-6086	288	1	<	<	X
ejpam-6086	288	2	θ(bε	θ(bε	PROPN
ejpam-6086	288	3	)	)	PUNCT
ejpam-6086	288	4	.	.	PUNCT
ejpam-6086	289	1	this	this	PRON
ejpam-6086	289	2	implies	imply	VERB
ejpam-6086	289	3	that	that	SCONJ
ejpam-6086	289	4	bε	bε	NOUN
ejpam-6086	289	5	<	<	X
ejpam-6086	289	6	bε	bε	NOUN
ejpam-6086	289	7	,	,	PUNCT
ejpam-6086	289	8	which	which	PRON
ejpam-6086	289	9	is	be	AUX
ejpam-6086	289	10	a	a	DET
ejpam-6086	289	11	contradiction	contradiction	NOUN
ejpam-6086	289	12	.	.	PUNCT
ejpam-6086	290	1	consequently	consequently	ADV
ejpam-6086	290	2	,	,	PUNCT
ejpam-6086	290	3	{	{	PUNCT
ejpam-6086	290	4	xn	xn	X
ejpam-6086	290	5	}	}	PUNCT
ejpam-6086	290	6	is	be	AUX
ejpam-6086	290	7	a	a	DET
ejpam-6086	290	8	cauchy	cauchy	ADJ
ejpam-6086	290	9	sequence	sequence	NOUN
ejpam-6086	290	10	in	in	ADP
ejpam-6086	290	11	u	u	PROPN
ejpam-6086	290	12	.	.	PUNCT
ejpam-6086	291	1	therefore	therefore	ADV
ejpam-6086	291	2	,	,	PUNCT
ejpam-6086	291	3	there	there	PRON
ejpam-6086	291	4	exists	exist	VERB
ejpam-6086	291	5	z	z	PROPN
ejpam-6086	291	6	∈	∈	PROPN
ejpam-6086	291	7	u	u	NOUN
ejpam-6086	291	8	such	such	ADJ
ejpam-6086	291	9	that	that	SCONJ
ejpam-6086	291	10	lim	lim	PROPN
ejpam-6086	291	11	n→+∞	n→+∞	VERB
ejpam-6086	291	12	d(xn	d(xn	PROPN
ejpam-6086	291	13	,	,	PUNCT
ejpam-6086	291	14	z	z	NOUN
ejpam-6086	291	15	)	)	PUNCT
ejpam-6086	291	16	=	=	SYM
ejpam-6086	291	17	0	0	X
ejpam-6086	291	18	.	.	PUNCT
ejpam-6086	292	1	h.	h.	PROPN
ejpam-6086	292	2	massit	massit	PROPN
ejpam-6086	292	3	et	et	PROPN
ejpam-6086	292	4	al	al	PROPN
ejpam-6086	292	5	.	.	PUNCT
ejpam-6086	292	6	/	/	SYM
ejpam-6086	292	7	eur	eur	PROPN
ejpam-6086	292	8	.	.	PUNCT
ejpam-6086	293	1	j.	j.	PROPN
ejpam-6086	293	2	pure	pure	PROPN
ejpam-6086	293	3	appl	appl	PROPN
ejpam-6086	293	4	.	.	PROPN
ejpam-6086	293	5	math	math	PROPN
ejpam-6086	293	6	,	,	PUNCT
ejpam-6086	293	7	18	18	NUM
ejpam-6086	293	8	(	(	PUNCT
ejpam-6086	293	9	2	2	NUM
ejpam-6086	293	10	)	)	PUNCT
ejpam-6086	293	11	(	(	PUNCT
ejpam-6086	293	12	2025	2025	NUM
ejpam-6086	293	13	)	)	PUNCT
ejpam-6086	293	14	,	,	PUNCT
ejpam-6086	293	15	6086	6086	NUM
ejpam-6086	293	16	14	14	NUM
ejpam-6086	293	17	of	of	ADP
ejpam-6086	293	18	19	19	NUM
ejpam-6086	293	19	since	since	SCONJ
ejpam-6086	293	20	t	t	PROPN
ejpam-6086	293	21	is	be	AUX
ejpam-6086	293	22	α−continuous	α−continuous	ADJ
ejpam-6086	293	23	multivalued	multivalued	ADJ
ejpam-6086	293	24	mapping	mapping	NOUN
ejpam-6086	293	25	,	,	PUNCT
ejpam-6086	293	26	we	we	PRON
ejpam-6086	293	27	have	have	VERB
ejpam-6086	293	28	lim	lim	PROPN
ejpam-6086	293	29	n→+∞	n→+∞	PROPN
ejpam-6086	293	30	h(txn	h(txn	PROPN
ejpam-6086	293	31	,	,	PUNCT
ejpam-6086	293	32	t	t	PROPN
ejpam-6086	293	33	z	z	PROPN
ejpam-6086	293	34	)	)	PUNCT
ejpam-6086	293	35	=	=	SYM
ejpam-6086	294	1	0	0	X
ejpam-6086	294	2	.	.	PUNCT
ejpam-6086	295	1	now	now	ADV
ejpam-6086	295	2	,	,	PUNCT
ejpam-6086	295	3	we	we	PRON
ejpam-6086	295	4	obtain	obtain	VERB
ejpam-6086	295	5	,	,	PUNCT
ejpam-6086	295	6	lim	lim	PROPN
ejpam-6086	295	7	n→+∞	n→+∞	PROPN
ejpam-6086	295	8	d(xn+1	d(xn+1	PROPN
ejpam-6086	295	9	,	,	PUNCT
ejpam-6086	295	10	t	t	PROPN
ejpam-6086	295	11	z	z	PROPN
ejpam-6086	295	12	)	)	PUNCT
ejpam-6086	295	13	≤	≤	NOUN
ejpam-6086	295	14	lim	lim	PROPN
ejpam-6086	295	15	n→+∞	n→+∞	PROPN
ejpam-6086	295	16	h(txn	h(txn	PROPN
ejpam-6086	295	17	,	,	PUNCT
ejpam-6086	295	18	t	t	PROPN
ejpam-6086	295	19	z	z	PROPN
ejpam-6086	295	20	)	)	PUNCT
ejpam-6086	296	1	=	=	SYM
ejpam-6086	296	2	0	0	X
ejpam-6086	296	3	.	.	PUNCT
ejpam-6086	297	1	therefore	therefore	ADV
ejpam-6086	297	2	,	,	PUNCT
ejpam-6086	297	3	z	z	PROPN
ejpam-6086	297	4	∈	∈	PROPN
ejpam-6086	297	5	tz	tz	NOUN
ejpam-6086	297	6	i.e.	i.e.	X
ejpam-6086	297	7	t	t	PROPN
ejpam-6086	297	8	has	have	VERB
ejpam-6086	297	9	a	a	DET
ejpam-6086	297	10	fixed	fix	VERB
ejpam-6086	297	11	point	point	NOUN
ejpam-6086	297	12	.	.	PUNCT
ejpam-6086	297	13	example	example	NOUN
ejpam-6086	298	1	2	2	NUM
ejpam-6086	298	2	.	.	PUNCT
ejpam-6086	298	3	let	let	VERB
ejpam-6086	298	4	u	u	NOUN
ejpam-6086	298	5	=	=	NOUN
ejpam-6086	298	6	a	a	PRON
ejpam-6086	298	7	∪b	∪b	NOUN
ejpam-6086	298	8	,	,	PUNCT
ejpam-6086	298	9	where	where	SCONJ
ejpam-6086	298	10	a	a	DET
ejpam-6086	298	11	=	=	X
ejpam-6086	298	12	{	{	PUNCT
ejpam-6086	298	13	0	0	NUM
ejpam-6086	298	14	,	,	PUNCT
ejpam-6086	298	15	12	12	NUM
ejpam-6086	298	16	,	,	PUNCT
ejpam-6086	298	17	1	1	NUM
ejpam-6086	298	18	3	3	NUM
ejpam-6086	298	19	,	,	PUNCT
ejpam-6086	298	20	1	1	NUM
ejpam-6086	298	21	4	4	NUM
ejpam-6086	298	22	}	}	PUNCT
ejpam-6086	298	23	and	and	CCONJ
ejpam-6086	298	24	b	b	X
ejpam-6086	298	25	=	=	SYM
ejpam-6086	299	1	[	[	X
ejpam-6086	299	2	1	1	NUM
ejpam-6086	299	3	,	,	PUNCT
ejpam-6086	299	4	2	2	NUM
ejpam-6086	299	5	]	]	PUNCT
ejpam-6086	299	6	.	.	PUNCT
ejpam-6086	300	1	define	define	VERB
ejpam-6086	300	2	d	d	NOUN
ejpam-6086	300	3	:	:	PUNCT
ejpam-6086	300	4	u	u	PRON
ejpam-6086	300	5	×	×	PROPN
ejpam-6086	300	6	u	u	X
ejpam-6086	300	7	→	→	PUNCT
ejpam-6086	300	8	[	[	X
ejpam-6086	300	9	0,+∞	0,+∞	NUM
ejpam-6086	300	10	)	)	PUNCT
ejpam-6086	300	11	by	by	ADP
ejpam-6086	300	12	d	d	PROPN
ejpam-6086	300	13	(	(	PUNCT
ejpam-6086	300	14	0	0	NUM
ejpam-6086	300	15	,	,	PUNCT
ejpam-6086	300	16	1	1	NUM
ejpam-6086	300	17	2	2	NUM
ejpam-6086	300	18	)	)	PUNCT
ejpam-6086	300	19	=	=	SYM
ejpam-6086	301	1	d	d	X
ejpam-6086	301	2	(	(	PUNCT
ejpam-6086	301	3	1	1	NUM
ejpam-6086	301	4	2	2	NUM
ejpam-6086	301	5	,	,	PUNCT
ejpam-6086	301	6	1	1	NUM
ejpam-6086	301	7	3	3	NUM
ejpam-6086	301	8	)	)	PUNCT
ejpam-6086	301	9	=	=	SYM
ejpam-6086	301	10	0.16	0.16	NUM
ejpam-6086	301	11	,	,	PUNCT
ejpam-6086	301	12	d	d	X
ejpam-6086	301	13	(	(	PUNCT
ejpam-6086	301	14	0	0	NUM
ejpam-6086	301	15	,	,	PUNCT
ejpam-6086	301	16	1	1	NUM
ejpam-6086	301	17	3	3	NUM
ejpam-6086	301	18	)	)	PUNCT
ejpam-6086	301	19	=	=	SYM
ejpam-6086	302	1	d	d	X
ejpam-6086	302	2	(	(	PUNCT
ejpam-6086	302	3	1	1	NUM
ejpam-6086	302	4	3	3	NUM
ejpam-6086	302	5	,	,	PUNCT
ejpam-6086	302	6	1	1	NUM
ejpam-6086	302	7	4	4	NUM
ejpam-6086	302	8	)	)	PUNCT
ejpam-6086	302	9	=	=	NOUN
ejpam-6086	302	10	0.04	0.04	NUM
ejpam-6086	302	11	,	,	PUNCT
ejpam-6086	302	12	d	d	X
ejpam-6086	302	13	(	(	PUNCT
ejpam-6086	302	14	0	0	NUM
ejpam-6086	302	15	,	,	PUNCT
ejpam-6086	302	16	1	1	NUM
ejpam-6086	302	17	4	4	NUM
ejpam-6086	302	18	)	)	PUNCT
ejpam-6086	302	19	d	d	NOUN
ejpam-6086	302	20	(	(	PUNCT
ejpam-6086	302	21	1	1	NUM
ejpam-6086	302	22	2	2	NUM
ejpam-6086	302	23	,	,	PUNCT
ejpam-6086	302	24	1	1	NUM
ejpam-6086	302	25	4	4	NUM
ejpam-6086	302	26	)	)	PUNCT
ejpam-6086	302	27	=	=	SYM
ejpam-6086	302	28	0.25	0.25	NUM
ejpam-6086	302	29	,	,	PUNCT
ejpam-6086	302	30	d	d	X
ejpam-6086	302	31	(	(	PUNCT
ejpam-6086	302	32	x	x	NOUN
ejpam-6086	302	33	,	,	PUNCT
ejpam-6086	302	34	y	y	NOUN
ejpam-6086	302	35	)	)	PUNCT
ejpam-6086	302	36	=	=	SYM
ejpam-6086	302	37	(	(	PUNCT
ejpam-6086	302	38	x−	x−	PROPN
ejpam-6086	302	39	y)2	y)2	NOUN
ejpam-6086	302	40	,	,	PUNCT
ejpam-6086	302	41	for	for	ADP
ejpam-6086	302	42	x	x	X
ejpam-6086	302	43	,	,	PUNCT
ejpam-6086	302	44	y	y	PROPN
ejpam-6086	302	45	∈	∈	PROPN
ejpam-6086	303	1	[	[	X
ejpam-6086	303	2	1	1	NUM
ejpam-6086	303	3	,	,	PUNCT
ejpam-6086	303	4	2	2	NUM
ejpam-6086	303	5	]	]	PUNCT
ejpam-6086	303	6	.	.	PUNCT
ejpam-6086	304	1	then	then	ADV
ejpam-6086	304	2	(	(	PUNCT
ejpam-6086	304	3	u	u	NOUN
ejpam-6086	304	4	,	,	PUNCT
ejpam-6086	304	5	d	d	PROPN
ejpam-6086	304	6	)	)	PUNCT
ejpam-6086	304	7	is	be	AUX
ejpam-6086	304	8	a	a	DET
ejpam-6086	304	9	rectangular	rectangular	ADJ
ejpam-6086	304	10	b−metric	b−metric	ADJ
ejpam-6086	304	11	space	space	NOUN
ejpam-6086	304	12	with	with	ADP
ejpam-6086	304	13	parameter	parameter	PROPN
ejpam-6086	304	14	b	b	PROPN
ejpam-6086	304	15	=	=	SYM
ejpam-6086	304	16	3	3	X
ejpam-6086	304	17	.	.	PUNCT
ejpam-6086	305	1	let	let	VERB
ejpam-6086	305	2	t	t	NOUN
ejpam-6086	305	3	:	:	PUNCT
ejpam-6086	305	4	u	u	PROPN
ejpam-6086	305	5	→	→	SYM
ejpam-6086	305	6	b(u	b(u	PROPN
ejpam-6086	305	7	)	)	PUNCT
ejpam-6086	305	8	defined	define	VERB
ejpam-6086	305	9	by	by	ADP
ejpam-6086	305	10	tx	tx	PROPN
ejpam-6086	305	11	=	=	PUNCT
ejpam-6086	305	12	{	{	PUNCT
ejpam-6086	305	13	a	a	X
ejpam-6086	305	14	,	,	PUNCT
ejpam-6086	305	15	if	if	SCONJ
ejpam-6086	305	16	x	x	SYM
ejpam-6086	305	17	∈	∈	PROPN
ejpam-6086	305	18	a	a	X
ejpam-6086	305	19	[	[	PUNCT
ejpam-6086	305	20	0	0	NUM
ejpam-6086	305	21	,	,	PUNCT
ejpam-6086	305	22	x2	x2	PROPN
ejpam-6086	305	23	]	]	PUNCT
ejpam-6086	305	24	,	,	PUNCT
ejpam-6086	305	25	if	if	SCONJ
ejpam-6086	305	26	x	x	PUNCT
ejpam-6086	305	27	∈	∈	PROPN
ejpam-6086	305	28	b	b	PROPN
ejpam-6086	305	29	,	,	PUNCT
ejpam-6086	305	30	and	and	CCONJ
ejpam-6086	305	31	α(x	α(x	PROPN
ejpam-6086	305	32	,	,	PUNCT
ejpam-6086	305	33	y	y	PROPN
ejpam-6086	305	34	)	)	PUNCT
ejpam-6086	306	1	=	=	PRON
ejpam-6086	306	2	{	{	PUNCT
ejpam-6086	306	3	1	1	NUM
ejpam-6086	306	4	if	if	SCONJ
ejpam-6086	306	5	x	x	PROPN
ejpam-6086	306	6	,	,	PUNCT
ejpam-6086	306	7	y	y	PROPN
ejpam-6086	306	8	∈	∈	PROPN
ejpam-6086	306	9	[	[	PUNCT
ejpam-6086	306	10	0	0	NUM
ejpam-6086	306	11	,	,	PUNCT
ejpam-6086	306	12	14	14	NUM
ejpam-6086	306	13	]	]	PUNCT
ejpam-6086	306	14	.	.	PUNCT
ejpam-6086	307	1	0	0	NUM
ejpam-6086	307	2	,	,	PUNCT
ejpam-6086	307	3	otherwise	otherwise	ADV
ejpam-6086	307	4	and	and	CCONJ
ejpam-6086	307	5	the	the	DET
ejpam-6086	307	6	functions	function	NOUN
ejpam-6086	307	7	θ	θ	X
ejpam-6086	307	8	:	:	PUNCT
ejpam-6086	308	1	[	[	X
ejpam-6086	308	2	0,+∞	0,+∞	NUM
ejpam-6086	308	3	)	)	PUNCT
ejpam-6086	308	4	→	→	PUNCT
ejpam-6086	309	1	[	[	X
ejpam-6086	309	2	1,+∞	1,+∞	NUM
ejpam-6086	309	3	)	)	PUNCT
ejpam-6086	309	4	defined	define	VERB
ejpam-6086	309	5	by	by	ADP
ejpam-6086	309	6	θ(z	θ(z	NOUN
ejpam-6086	309	7	)	)	PUNCT
ejpam-6086	309	8	=	=	SYM
ejpam-6086	310	1	1	1	NUM
ejpam-6086	310	2	+	+	CCONJ
ejpam-6086	310	3	z	z	NOUN
ejpam-6086	310	4	and	and	CCONJ
ejpam-6086	310	5	ϕ	ϕ	NOUN
ejpam-6086	310	6	:	:	PUNCT
ejpam-6086	311	1	[	[	X
ejpam-6086	311	2	1,+∞	1,+∞	NUM
ejpam-6086	311	3	)	)	PUNCT
ejpam-6086	311	4	→	→	PUNCT
ejpam-6086	312	1	[	[	X
ejpam-6086	312	2	1,+∞	1,+∞	NUM
ejpam-6086	312	3	)	)	PUNCT
ejpam-6086	312	4	defined	define	VERB
ejpam-6086	312	5	by	by	ADP
ejpam-6086	312	6	ϕ(z	ϕ(z	NOUN
ejpam-6086	312	7	)	)	PUNCT
ejpam-6086	312	8	=	=	SYM
ejpam-6086	313	1	1	1	NUM
ejpam-6086	313	2	+	+	NUM
ejpam-6086	313	3	z	z	NOUN
ejpam-6086	313	4	2	2	NUM
ejpam-6086	313	5	.	.	PUNCT
ejpam-6086	314	1	then	then	ADV
ejpam-6086	314	2	a	a	DET
ejpam-6086	314	3	mapping	mapping	NOUN
ejpam-6086	314	4	t	t	NOUN
ejpam-6086	314	5	is	be	AUX
ejpam-6086	314	6	triangular	triangular	NOUN
ejpam-6086	314	7	α−admissible	α−admissible	ADJ
ejpam-6086	314	8	and	and	CCONJ
ejpam-6086	314	9	h(tx	h(tx	NUM
ejpam-6086	314	10	,	,	PUNCT
ejpam-6086	314	11	ty	ty	INTJ
ejpam-6086	314	12	)	)	PUNCT
ejpam-6086	314	13	=	=	SYM
ejpam-6086	314	14	1	1	NUM
ejpam-6086	314	15	4	4	NUM
ejpam-6086	314	16	(	(	PUNCT
ejpam-6086	314	17	x−	x−	PROPN
ejpam-6086	314	18	y)2	y)2	NOUN
ejpam-6086	314	19	.	.	PUNCT
ejpam-6086	315	1	corollary	corollary	ADJ
ejpam-6086	315	2	2	2	NUM
ejpam-6086	315	3	.	.	PUNCT
ejpam-6086	316	1	let	let	VERB
ejpam-6086	316	2	(	(	PUNCT
ejpam-6086	316	3	u	u	NOUN
ejpam-6086	316	4	,	,	PUNCT
ejpam-6086	316	5	d	d	PROPN
ejpam-6086	316	6	)	)	PUNCT
ejpam-6086	316	7	be	be	AUX
ejpam-6086	316	8	a	a	DET
ejpam-6086	316	9	complete	complete	ADJ
ejpam-6086	316	10	rectangular	rectangular	ADJ
ejpam-6086	316	11	b−metric	b−metric	ADJ
ejpam-6086	316	12	space	space	NOUN
ejpam-6086	316	13	and	and	CCONJ
ejpam-6086	316	14	t	t	NOUN
ejpam-6086	316	15	:	:	PUNCT
ejpam-6086	316	16	u	u	PROPN
ejpam-6086	316	17	→	→	SYM
ejpam-6086	316	18	b(u	b(u	PROPN
ejpam-6086	316	19	)	)	PUNCT
ejpam-6086	316	20	be	be	AUX
ejpam-6086	316	21	a	a	DET
ejpam-6086	316	22	mapping	mapping	NOUN
ejpam-6086	316	23	.	.	PUNCT
ejpam-6086	317	1	if	if	SCONJ
ejpam-6086	317	2	θ	θ	PROPN
ejpam-6086	317	3	∈	∈	PROPN
ejpam-6086	317	4	θ	θ	PROPN
ejpam-6086	317	5	and	and	CCONJ
ejpam-6086	317	6	ϕ	ϕ	PROPN
ejpam-6086	317	7	∈	∈	PROPN
ejpam-6086	317	8	φ	φ	INTJ
ejpam-6086	317	9	we	we	PRON
ejpam-6086	317	10	have	have	VERB
ejpam-6086	317	11	h(tx	h(tx	NUM
ejpam-6086	317	12	,	,	PUNCT
ejpam-6086	317	13	ty	ty	INTJ
ejpam-6086	317	14	)	)	PUNCT
ejpam-6086	317	15	>	>	SYM
ejpam-6086	317	16	0	0	NUM
ejpam-6086	317	17	implies	imply	VERB
ejpam-6086	317	18	θ[b3h(tx	θ[b3h(tx	PROPN
ejpam-6086	317	19	,	,	PUNCT
ejpam-6086	317	20	ty	ty	NOUN
ejpam-6086	317	21	)	)	PUNCT
ejpam-6086	317	22	]	]	PUNCT
ejpam-6086	317	23	≤	≤	NUM
ejpam-6086	317	24	ϕ[θ(m(x	ϕ[θ(m(x	PROPN
ejpam-6086	317	25	,	,	PUNCT
ejpam-6086	317	26	y	y	NOUN
ejpam-6086	317	27	)	)	PUNCT
ejpam-6086	317	28	)	)	PUNCT
ejpam-6086	317	29	]	]	PUNCT
ejpam-6086	317	30	,	,	PUNCT
ejpam-6086	317	31	for	for	ADP
ejpam-6086	317	32	all	all	DET
ejpam-6086	317	33	x	x	NOUN
ejpam-6086	317	34	,	,	PUNCT
ejpam-6086	317	35	y	y	PROPN
ejpam-6086	317	36	∈	∈	PROPN
ejpam-6086	317	37	u	u	PROPN
ejpam-6086	317	38	,	,	PUNCT
ejpam-6086	317	39	where	where	SCONJ
ejpam-6086	317	40	m(x	m(x	PROPN
ejpam-6086	317	41	,	,	PUNCT
ejpam-6086	317	42	y	y	NOUN
ejpam-6086	317	43	)	)	PUNCT
ejpam-6086	317	44	=	=	PUNCT
ejpam-6086	317	45	max{d(x	max{d(x	PROPN
ejpam-6086	317	46	,	,	PUNCT
ejpam-6086	317	47	y	y	NOUN
ejpam-6086	317	48	)	)	PUNCT
ejpam-6086	317	49	,	,	PUNCT
ejpam-6086	317	50	d(x	d(x	PROPN
ejpam-6086	317	51	,	,	PUNCT
ejpam-6086	317	52	tx	tx	PROPN
ejpam-6086	317	53	)	)	PUNCT
ejpam-6086	317	54	,	,	PUNCT
ejpam-6086	317	55	d(x	d(x	PROPN
ejpam-6086	317	56	,	,	PUNCT
ejpam-6086	317	57	ty	ty	NOUN
ejpam-6086	317	58	)	)	PUNCT
ejpam-6086	317	59	,	,	PUNCT
ejpam-6086	317	60	d(y	d(y	PROPN
ejpam-6086	317	61	,	,	PUNCT
ejpam-6086	317	62	tx	tx	PROPN
ejpam-6086	317	63	)	)	PUNCT
ejpam-6086	317	64	}	}	PUNCT
ejpam-6086	317	65	.	.	PUNCT
ejpam-6086	318	1	then	then	ADV
ejpam-6086	318	2	,	,	PUNCT
ejpam-6086	318	3	t	t	PROPN
ejpam-6086	318	4	has	have	VERB
ejpam-6086	318	5	a	a	DET
ejpam-6086	318	6	fixed	fix	VERB
ejpam-6086	318	7	point	point	NOUN
ejpam-6086	318	8	.	.	PUNCT
ejpam-6086	319	1	h.	h.	PROPN
ejpam-6086	319	2	massit	massit	PROPN
ejpam-6086	319	3	et	et	PROPN
ejpam-6086	319	4	al	al	PROPN
ejpam-6086	319	5	.	.	PUNCT
ejpam-6086	319	6	/	/	SYM
ejpam-6086	319	7	eur	eur	PROPN
ejpam-6086	319	8	.	.	PUNCT
ejpam-6086	320	1	j.	j.	PROPN
ejpam-6086	320	2	pure	pure	PROPN
ejpam-6086	320	3	appl	appl	PROPN
ejpam-6086	320	4	.	.	PROPN
ejpam-6086	320	5	math	math	PROPN
ejpam-6086	320	6	,	,	PUNCT
ejpam-6086	320	7	18	18	NUM
ejpam-6086	320	8	(	(	PUNCT
ejpam-6086	320	9	2	2	NUM
ejpam-6086	320	10	)	)	PUNCT
ejpam-6086	320	11	(	(	PUNCT
ejpam-6086	320	12	2025	2025	NUM
ejpam-6086	320	13	)	)	PUNCT
ejpam-6086	320	14	,	,	PUNCT
ejpam-6086	320	15	6086	6086	NUM
ejpam-6086	320	16	15	15	NUM
ejpam-6086	320	17	of	of	ADP
ejpam-6086	320	18	19	19	NUM
ejpam-6086	320	19	theorem	theorem	NOUN
ejpam-6086	320	20	5	5	NUM
ejpam-6086	320	21	.	.	PUNCT
ejpam-6086	321	1	let	let	AUX
ejpam-6086	321	2	(	(	PUNCT
ejpam-6086	321	3	u	u	NOUN
ejpam-6086	321	4	,	,	PUNCT
ejpam-6086	321	5	d	d	PROPN
ejpam-6086	321	6	)	)	PUNCT
ejpam-6086	321	7	be	be	AUX
ejpam-6086	321	8	a	a	DET
ejpam-6086	321	9	complete	complete	ADJ
ejpam-6086	321	10	rectangular	rectangular	ADJ
ejpam-6086	321	11	b−metric	b−metric	ADJ
ejpam-6086	321	12	space	space	NOUN
ejpam-6086	321	13	and	and	CCONJ
ejpam-6086	321	14	t	t	NOUN
ejpam-6086	321	15	:	:	PUNCT
ejpam-6086	321	16	u	u	PROPN
ejpam-6086	321	17	→	→	SYM
ejpam-6086	321	18	b(u	b(u	PROPN
ejpam-6086	321	19	)	)	PUNCT
ejpam-6086	321	20	be	be	VERB
ejpam-6086	321	21	an	an	DET
ejpam-6086	321	22	α−admissible	α−admissible	ADJ
ejpam-6086	321	23	θ	θ	X
ejpam-6086	321	24	−	−	NOUN
ejpam-6086	321	25	ϕ−multivalued	ϕ−multivalued	PUNCT
ejpam-6086	321	26	contraction	contraction	NOUN
ejpam-6086	321	27	satisfying	satisfy	VERB
ejpam-6086	321	28	(	(	PUNCT
ejpam-6086	321	29	i	i	NOUN
ejpam-6086	321	30	)	)	PUNCT
ejpam-6086	321	31	(	(	PUNCT
ejpam-6086	321	32	u	u	NOUN
ejpam-6086	321	33	,	,	PUNCT
ejpam-6086	321	34	d	d	PROPN
ejpam-6086	321	35	)	)	PUNCT
ejpam-6086	321	36	is	be	AUX
ejpam-6086	321	37	an	an	DET
ejpam-6086	321	38	α−complete	α−complete	NUM
ejpam-6086	321	39	metric	metric	ADJ
ejpam-6086	321	40	space	space	NOUN
ejpam-6086	321	41	(	(	PUNCT
ejpam-6086	321	42	ii	ii	NOUN
ejpam-6086	321	43	)	)	PUNCT
ejpam-6086	321	44	α(x0	α(x0	PROPN
ejpam-6086	321	45	,	,	PUNCT
ejpam-6086	321	46	x1	x1	PROPN
ejpam-6086	321	47	)	)	PUNCT
ejpam-6086	321	48	≥	≥	NOUN
ejpam-6086	321	49	1	1	NUM
ejpam-6086	321	50	for	for	ADP
ejpam-6086	321	51	x0	x0	PROPN
ejpam-6086	321	52	∈	∈	PROPN
ejpam-6086	321	53	u	u	NOUN
ejpam-6086	321	54	and	and	CCONJ
ejpam-6086	321	55	x1	x1	PROPN
ejpam-6086	321	56	∈	∈	PROPN
ejpam-6086	321	57	t	t	PROPN
ejpam-6086	321	58	(	(	PUNCT
ejpam-6086	321	59	u	u	NOUN
ejpam-6086	321	60	)	)	PUNCT
ejpam-6086	321	61	(	(	PUNCT
ejpam-6086	321	62	iii	iii	X
ejpam-6086	321	63	)	)	PUNCT
ejpam-6086	321	64	t	t	PROPN
ejpam-6086	321	65	is	be	AUX
ejpam-6086	321	66	triangular	triangular	NOUN
ejpam-6086	321	67	α−admissible	α−admissible	NOUN
ejpam-6086	321	68	.	.	PUNCT
ejpam-6086	322	1	(	(	PUNCT
ejpam-6086	322	2	iv	iv	X
ejpam-6086	322	3	)	)	PUNCT
ejpam-6086	322	4	exist	exist	VERB
ejpam-6086	322	5	{	{	PUNCT
ejpam-6086	322	6	xn	xn	X
ejpam-6086	322	7	}	}	PUNCT
ejpam-6086	322	8	is	be	AUX
ejpam-6086	322	9	a	a	DET
ejpam-6086	322	10	sequence	sequence	NOUN
ejpam-6086	322	11	in	in	ADP
ejpam-6086	322	12	u	u	PRON
ejpam-6086	322	13	such	such	ADJ
ejpam-6086	322	14	that	that	SCONJ
ejpam-6086	322	15	α(xn	α(xn	NOUN
ejpam-6086	322	16	,	,	PUNCT
ejpam-6086	322	17	xn+1	xn+1	NUM
ejpam-6086	322	18	)	)	PUNCT
ejpam-6086	322	19	≥	≥	NOUN
ejpam-6086	322	20	1	1	NUM
ejpam-6086	322	21	for	for	ADP
ejpam-6086	322	22	all	all	PRON
ejpam-6086	322	23	n	n	PRON
ejpam-6086	322	24	∈	∈	NOUN
ejpam-6086	322	25	n	n	NOUN
ejpam-6086	322	26	∪	∪	X
ejpam-6086	322	27	{	{	PUNCT
ejpam-6086	322	28	0	0	NUM
ejpam-6086	322	29	}	}	PUNCT
ejpam-6086	322	30	and	and	CCONJ
ejpam-6086	322	31	lim	lim	PROPN
ejpam-6086	322	32	n→+∞	n→+∞	VERB
ejpam-6086	322	33	d(xn	d(xn	PROPN
ejpam-6086	322	34	,	,	PUNCT
ejpam-6086	322	35	z	z	NOUN
ejpam-6086	322	36	)	)	PUNCT
ejpam-6086	322	37	=	=	SYM
ejpam-6086	322	38	0	0	NUM
ejpam-6086	322	39	,	,	PUNCT
ejpam-6086	322	40	for	for	ADP
ejpam-6086	322	41	some	some	DET
ejpam-6086	322	42	z	z	NOUN
ejpam-6086	322	43	∈	∈	NOUN
ejpam-6086	322	44	u	u	NOUN
ejpam-6086	322	45	then	then	ADV
ejpam-6086	322	46	there	there	PRON
ejpam-6086	322	47	exists	exist	VERB
ejpam-6086	322	48	a	a	DET
ejpam-6086	322	49	subsequence	subsequence	NOUN
ejpam-6086	322	50	{	{	PUNCT
ejpam-6086	322	51	xn(k	xn(k	NUM
ejpam-6086	322	52	)	)	PUNCT
ejpam-6086	322	53	}	}	PUNCT
ejpam-6086	322	54	of	of	ADP
ejpam-6086	322	55	{	{	PUNCT
ejpam-6086	322	56	xn	xn	NOUN
ejpam-6086	322	57	}	}	PUNCT
ejpam-6086	322	58	such	such	ADJ
ejpam-6086	322	59	that	that	SCONJ
ejpam-6086	322	60	α(xn(k	α(xn(k	PROPN
ejpam-6086	322	61	)	)	PUNCT
ejpam-6086	322	62	,	,	PUNCT
ejpam-6086	322	63	z	z	X
ejpam-6086	322	64	)	)	PUNCT
ejpam-6086	322	65	≥	≥	NOUN
ejpam-6086	322	66	1	1	NUM
ejpam-6086	322	67	for	for	ADP
ejpam-6086	322	68	all	all	DET
ejpam-6086	322	69	k	k	PROPN
ejpam-6086	322	70	∈	∈	PROPN
ejpam-6086	322	71	n	n	PART
ejpam-6086	322	72	∪	∪	X
ejpam-6086	322	73	{	{	PUNCT
ejpam-6086	322	74	0	0	NUM
ejpam-6086	322	75	}	}	PUNCT
ejpam-6086	322	76	.	.	PUNCT
ejpam-6086	323	1	then	then	ADV
ejpam-6086	323	2	,	,	PUNCT
ejpam-6086	323	3	t	t	PROPN
ejpam-6086	323	4	has	have	VERB
ejpam-6086	323	5	a	a	DET
ejpam-6086	323	6	fixed	fix	VERB
ejpam-6086	323	7	point	point	NOUN
ejpam-6086	323	8	.	.	PUNCT
ejpam-6086	324	1	proof	proof	NOUN
ejpam-6086	324	2	.	.	PUNCT
ejpam-6086	325	1	let	let	VERB
ejpam-6086	325	2	{	{	PUNCT
ejpam-6086	325	3	xn	xn	VERB
ejpam-6086	325	4	}	}	PUNCT
ejpam-6086	325	5	be	be	AUX
ejpam-6086	325	6	a	a	DET
ejpam-6086	325	7	sequence	sequence	NOUN
ejpam-6086	325	8	in	in	ADP
ejpam-6086	325	9	u	u	PRON
ejpam-6086	325	10	such	such	ADJ
ejpam-6086	325	11	that	that	SCONJ
ejpam-6086	325	12	xn+1	xn+1	NUM
ejpam-6086	325	13	∈	∈	PROPN
ejpam-6086	325	14	txn	txn	NOUN
ejpam-6086	325	15	with	with	ADP
ejpam-6086	325	16	α(xn	α(xn	PROPN
ejpam-6086	325	17	,	,	PUNCT
ejpam-6086	325	18	xn+1	xn+1	NUM
ejpam-6086	325	19	)	)	PUNCT
ejpam-6086	325	20	≥	≥	NOUN
ejpam-6086	325	21	1	1	NUM
ejpam-6086	325	22	,	,	PUNCT
ejpam-6086	325	23	for	for	ADP
ejpam-6086	325	24	all	all	DET
ejpam-6086	325	25	n	n	PRON
ejpam-6086	325	26	∈	∈	NOUN
ejpam-6086	325	27	n	n	NOUN
ejpam-6086	325	28	∪	∪	X
ejpam-6086	325	29	{	{	PUNCT
ejpam-6086	325	30	0	0	NUM
ejpam-6086	325	31	}	}	PUNCT
ejpam-6086	325	32	and	and	CCONJ
ejpam-6086	325	33	xn	xn	PROPN
ejpam-6086	325	34	→	→	SYM
ejpam-6086	325	35	z	z	NOUN
ejpam-6086	325	36	∈	∈	PROPN
ejpam-6086	325	37	u	u	NOUN
ejpam-6086	325	38	.	.	PUNCT
ejpam-6086	326	1	by	by	ADP
ejpam-6086	326	2	(	(	PUNCT
ejpam-6086	326	3	iv	iv	X
ejpam-6086	326	4	)	)	PUNCT
ejpam-6086	326	5	,	,	PUNCT
ejpam-6086	326	6	we	we	PRON
ejpam-6086	326	7	show	show	VERB
ejpam-6086	326	8	that	that	SCONJ
ejpam-6086	326	9	z	z	PROPN
ejpam-6086	326	10	∈	∈	PROPN
ejpam-6086	326	11	tz	tz	PROPN
ejpam-6086	326	12	.	.	PROPN
ejpam-6086	326	13	suppose	suppose	VERB
ejpam-6086	326	14	that	that	SCONJ
ejpam-6086	326	15	z	z	PROPN
ejpam-6086	326	16	̸∈	̸∈	PROPN
ejpam-6086	326	17	tz	tz	PROPN
ejpam-6086	326	18	,	,	PUNCT
ejpam-6086	326	19	we	we	PRON
ejpam-6086	326	20	have	have	VERB
ejpam-6086	326	21	lim	lim	PROPN
ejpam-6086	326	22	n→+∞	n→+∞	PROPN
ejpam-6086	326	23	d(txn	d(txn	PROPN
ejpam-6086	326	24	,	,	PUNCT
ejpam-6086	326	25	z	z	NOUN
ejpam-6086	326	26	)	)	PUNCT
ejpam-6086	326	27	=	=	SYM
ejpam-6086	326	28	0	0	NUM
ejpam-6086	326	29	and	and	CCONJ
ejpam-6086	326	30	1	1	NUM
ejpam-6086	326	31	b2	b2	NOUN
ejpam-6086	326	32	d(z	d(z	PROPN
ejpam-6086	326	33	,	,	PUNCT
ejpam-6086	326	34	tz	tz	NOUN
ejpam-6086	326	35	)	)	PUNCT
ejpam-6086	326	36	≤	≤	NOUN
ejpam-6086	326	37	lim	lim	PROPN
ejpam-6086	326	38	n→+∞	n→+∞	PROPN
ejpam-6086	326	39	infh(txn	infh(txn	PROPN
ejpam-6086	326	40	,	,	PUNCT
ejpam-6086	326	41	t	t	PROPN
ejpam-6086	326	42	z	z	PROPN
ejpam-6086	326	43	)	)	PUNCT
ejpam-6086	326	44	≤	≤	NOUN
ejpam-6086	326	45	lim	lim	PROPN
ejpam-6086	326	46	n→+∞	n→+∞	PROPN
ejpam-6086	326	47	suph(txn	suph(txn	PROPN
ejpam-6086	326	48	,	,	PUNCT
ejpam-6086	326	49	t	t	PROPN
ejpam-6086	326	50	z	z	PROPN
ejpam-6086	326	51	)	)	PUNCT
ejpam-6086	326	52	≤	≤	PROPN
ejpam-6086	326	53	b2d(z	b2d(z	PROPN
ejpam-6086	326	54	,	,	PUNCT
ejpam-6086	326	55	tz	tz	PROPN
ejpam-6086	326	56	)	)	PUNCT
ejpam-6086	326	57	.	.	PUNCT
ejpam-6086	327	1	so	so	ADV
ejpam-6086	327	2	,	,	PUNCT
ejpam-6086	327	3	we	we	PRON
ejpam-6086	327	4	have	have	VERB
ejpam-6086	327	5	θ[b3h(txn	θ[b3h(txn	PROPN
ejpam-6086	327	6	,	,	PUNCT
ejpam-6086	327	7	t	t	PROPN
ejpam-6086	327	8	z	z	PROPN
ejpam-6086	327	9	)	)	PUNCT
ejpam-6086	327	10	]	]	PUNCT
ejpam-6086	328	1	≤	≤	NUM
ejpam-6086	328	2	θ[α(xn	θ[α(xn	NOUN
ejpam-6086	328	3	,	,	PUNCT
ejpam-6086	328	4	z)b	z)b	X
ejpam-6086	328	5	3h(txn	3h(txn	NUM
ejpam-6086	328	6	,	,	PUNCT
ejpam-6086	328	7	t	t	PROPN
ejpam-6086	328	8	z	z	PROPN
ejpam-6086	328	9	)	)	PUNCT
ejpam-6086	328	10	]	]	PUNCT
ejpam-6086	328	11	≤	≤	PROPN
ejpam-6086	329	1	ϕθ[m(xn	ϕθ[m(xn	PROPN
ejpam-6086	329	2	,	,	PUNCT
ejpam-6086	329	3	z	z	NOUN
ejpam-6086	329	4	)	)	PUNCT
ejpam-6086	329	5	]	]	PUNCT
ejpam-6086	330	1	+	+	ADV
ejpam-6086	330	2	kw	kw	INTJ
ejpam-6086	330	3	(	(	PUNCT
ejpam-6086	330	4	xn	xn	PROPN
ejpam-6086	330	5	,	,	PUNCT
ejpam-6086	330	6	z	z	NOUN
ejpam-6086	330	7	)	)	PUNCT
ejpam-6086	330	8	for	for	ADP
ejpam-6086	330	9	all	all	PRON
ejpam-6086	330	10	n	n	PRON
ejpam-6086	330	11	∈	∈	PROPN
ejpam-6086	330	12	n	n	CCONJ
ejpam-6086	330	13	,	,	PUNCT
ejpam-6086	330	14	where	where	SCONJ
ejpam-6086	330	15	m(xn	m(xn	NOUN
ejpam-6086	330	16	,	,	PUNCT
ejpam-6086	330	17	z	z	NOUN
ejpam-6086	330	18	)	)	PUNCT
ejpam-6086	330	19	=	=	SYM
ejpam-6086	330	20	max{d(xn	max{d(xn	PROPN
ejpam-6086	330	21	,	,	PUNCT
ejpam-6086	330	22	z	z	NOUN
ejpam-6086	330	23	)	)	PUNCT
ejpam-6086	330	24	,	,	PUNCT
ejpam-6086	330	25	d(xn	d(xn	PROPN
ejpam-6086	330	26	,	,	PUNCT
ejpam-6086	330	27	txn	txn	NOUN
ejpam-6086	330	28	)	)	PUNCT
ejpam-6086	330	29	,	,	PUNCT
ejpam-6086	330	30	d(z	d(z	PROPN
ejpam-6086	330	31	,	,	PUNCT
ejpam-6086	330	32	tz	tz	PROPN
ejpam-6086	330	33	)	)	PUNCT
ejpam-6086	330	34	,	,	PUNCT
ejpam-6086	330	35	d(z	d(z	PROPN
ejpam-6086	330	36	,	,	PUNCT
ejpam-6086	330	37	txn	txn	NOUN
ejpam-6086	330	38	)	)	PUNCT
ejpam-6086	330	39	}	}	PUNCT
ejpam-6086	330	40	and	and	CCONJ
ejpam-6086	330	41	w	w	PROPN
ejpam-6086	330	42	(	(	PUNCT
ejpam-6086	330	43	xn	xn	PROPN
ejpam-6086	330	44	,	,	PUNCT
ejpam-6086	330	45	z	z	NOUN
ejpam-6086	330	46	)	)	PUNCT
ejpam-6086	330	47	=	=	SYM
ejpam-6086	330	48	min{d(xn	min{d(xn	X
ejpam-6086	330	49	,	,	PUNCT
ejpam-6086	330	50	txn	txn	NOUN
ejpam-6086	330	51	)	)	PUNCT
ejpam-6086	330	52	,	,	PUNCT
ejpam-6086	330	53	d(z	d(z	PROPN
ejpam-6086	330	54	,	,	PUNCT
ejpam-6086	330	55	tz	tz	PROPN
ejpam-6086	330	56	)	)	PUNCT
ejpam-6086	330	57	,	,	PUNCT
ejpam-6086	330	58	d(txn	d(txn	PROPN
ejpam-6086	330	59	,	,	PUNCT
ejpam-6086	330	60	z	z	NOUN
ejpam-6086	330	61	)	)	PUNCT
ejpam-6086	330	62	,	,	PUNCT
ejpam-6086	330	63	d(xn	d(xn	PROPN
ejpam-6086	330	64	,	,	PUNCT
ejpam-6086	330	65	t	t	PROPN
ejpam-6086	330	66	z	z	PROPN
ejpam-6086	330	67	)	)	PUNCT
ejpam-6086	330	68	}	}	PUNCT
ejpam-6086	330	69	.	.	PUNCT
ejpam-6086	331	1	letting	let	VERB
ejpam-6086	331	2	n→	n→	ADV
ejpam-6086	331	3	+	+	SYM
ejpam-6086	331	4	∞	∞	NUM
ejpam-6086	331	5	we	we	PRON
ejpam-6086	331	6	obtain	obtain	VERB
ejpam-6086	331	7	lim	lim	PROPN
ejpam-6086	331	8	n→+∞	n→+∞	PROPN
ejpam-6086	331	9	supm(xn	supm(xn	PROPN
ejpam-6086	331	10	,	,	PUNCT
ejpam-6086	331	11	z	z	NOUN
ejpam-6086	331	12	)	)	PUNCT
ejpam-6086	332	1	=	=	SYM
ejpam-6086	332	2	lim	lim	PROPN
ejpam-6086	332	3	n→+∞	n→+∞	PROPN
ejpam-6086	332	4	supmax{d(xn	supmax{d(xn	PROPN
ejpam-6086	332	5	,	,	PUNCT
ejpam-6086	332	6	z	z	NOUN
ejpam-6086	332	7	)	)	PUNCT
ejpam-6086	332	8	,	,	PUNCT
ejpam-6086	332	9	d(xn	d(xn	PROPN
ejpam-6086	332	10	,	,	PUNCT
ejpam-6086	332	11	txn	txn	NOUN
ejpam-6086	332	12	)	)	PUNCT
ejpam-6086	332	13	,	,	PUNCT
ejpam-6086	332	14	d(z	d(z	PROPN
ejpam-6086	332	15	,	,	PUNCT
ejpam-6086	332	16	tz	tz	PROPN
ejpam-6086	332	17	)	)	PUNCT
ejpam-6086	332	18	,	,	PUNCT
ejpam-6086	332	19	d(z	d(z	PROPN
ejpam-6086	332	20	,	,	PUNCT
ejpam-6086	332	21	txn	txn	NOUN
ejpam-6086	332	22	)	)	PUNCT
ejpam-6086	332	23	}	}	PUNCT
ejpam-6086	332	24	≤	≤	NUM
ejpam-6086	332	25	lim	lim	PROPN
ejpam-6086	332	26	n→+∞	n→+∞	PROPN
ejpam-6086	332	27	supmax{d(xn	supmax{d(xn	PROPN
ejpam-6086	332	28	,	,	PUNCT
ejpam-6086	332	29	z	z	NOUN
ejpam-6086	332	30	)	)	PUNCT
ejpam-6086	332	31	,	,	PUNCT
ejpam-6086	332	32	d(xn	d(xn	PROPN
ejpam-6086	332	33	,	,	PUNCT
ejpam-6086	332	34	xn+1	xn+1	NUM
ejpam-6086	332	35	)	)	PUNCT
ejpam-6086	332	36	,	,	PUNCT
ejpam-6086	332	37	d(z	d(z	PROPN
ejpam-6086	332	38	,	,	PUNCT
ejpam-6086	332	39	tz	tz	PROPN
ejpam-6086	332	40	)	)	PUNCT
ejpam-6086	332	41	,	,	PUNCT
ejpam-6086	332	42	d(z	d(z	PROPN
ejpam-6086	332	43	,	,	PUNCT
ejpam-6086	332	44	xn+1	xn+1	NUM
ejpam-6086	332	45	)	)	PUNCT
ejpam-6086	332	46	}	}	PUNCT
ejpam-6086	332	47	h.	h.	NOUN
ejpam-6086	332	48	massit	massit	PROPN
ejpam-6086	332	49	et	et	PROPN
ejpam-6086	332	50	al	al	PROPN
ejpam-6086	332	51	.	.	PUNCT
ejpam-6086	332	52	/	/	SYM
ejpam-6086	332	53	eur	eur	PROPN
ejpam-6086	332	54	.	.	PUNCT
ejpam-6086	333	1	j.	j.	PROPN
ejpam-6086	333	2	pure	pure	PROPN
ejpam-6086	333	3	appl	appl	PROPN
ejpam-6086	333	4	.	.	PROPN
ejpam-6086	333	5	math	math	PROPN
ejpam-6086	333	6	,	,	PUNCT
ejpam-6086	333	7	18	18	NUM
ejpam-6086	333	8	(	(	PUNCT
ejpam-6086	333	9	2	2	NUM
ejpam-6086	333	10	)	)	PUNCT
ejpam-6086	333	11	(	(	PUNCT
ejpam-6086	333	12	2025	2025	NUM
ejpam-6086	333	13	)	)	PUNCT
ejpam-6086	333	14	,	,	PUNCT
ejpam-6086	333	15	6086	6086	NUM
ejpam-6086	333	16	16	16	NUM
ejpam-6086	333	17	of	of	ADP
ejpam-6086	333	18	19	19	NUM
ejpam-6086	333	19	≤	≤	NUM
ejpam-6086	333	20	d(z	d(z	PROPN
ejpam-6086	333	21	,	,	PUNCT
ejpam-6086	333	22	tz	tz	PROPN
ejpam-6086	333	23	)	)	PUNCT
ejpam-6086	333	24	and	and	CCONJ
ejpam-6086	333	25	lim	lim	PROPN
ejpam-6086	333	26	n→+∞	n→+∞	PROPN
ejpam-6086	333	27	supw	supw	PROPN
ejpam-6086	333	28	(	(	PUNCT
ejpam-6086	333	29	xn	xn	PROPN
ejpam-6086	333	30	,	,	PUNCT
ejpam-6086	333	31	z	z	NOUN
ejpam-6086	333	32	)	)	PUNCT
ejpam-6086	334	1	=	=	SYM
ejpam-6086	334	2	lim	lim	PROPN
ejpam-6086	334	3	n→+∞	n→+∞	PROPN
ejpam-6086	334	4	supmin{d(xn	supmin{d(xn	PROPN
ejpam-6086	334	5	,	,	PUNCT
ejpam-6086	334	6	txn	txn	NOUN
ejpam-6086	334	7	)	)	PUNCT
ejpam-6086	334	8	,	,	PUNCT
ejpam-6086	334	9	d(z	d(z	PROPN
ejpam-6086	334	10	,	,	PUNCT
ejpam-6086	334	11	tz	tz	PROPN
ejpam-6086	334	12	)	)	PUNCT
ejpam-6086	334	13	,	,	PUNCT
ejpam-6086	334	14	d(txn	d(txn	PROPN
ejpam-6086	334	15	,	,	PUNCT
ejpam-6086	334	16	z	z	NOUN
ejpam-6086	334	17	)	)	PUNCT
ejpam-6086	334	18	,	,	PUNCT
ejpam-6086	334	19	d(xn	d(xn	PROPN
ejpam-6086	334	20	,	,	PUNCT
ejpam-6086	334	21	t	t	PROPN
ejpam-6086	334	22	z	z	PROPN
ejpam-6086	334	23	)	)	PUNCT
ejpam-6086	334	24	}	}	PUNCT
ejpam-6086	334	25	≤	≤	NUM
ejpam-6086	334	26	lim	lim	PROPN
ejpam-6086	334	27	n→+∞	n→+∞	PROPN
ejpam-6086	334	28	supmin{d(xn	supmin{d(xn	PROPN
ejpam-6086	334	29	,	,	PUNCT
ejpam-6086	334	30	xn+1	xn+1	NUM
ejpam-6086	334	31	)	)	PUNCT
ejpam-6086	334	32	,	,	PUNCT
ejpam-6086	334	33	d(z	d(z	PROPN
ejpam-6086	334	34	,	,	PUNCT
ejpam-6086	334	35	tz	tz	NOUN
ejpam-6086	334	36	)	)	PUNCT
ejpam-6086	334	37	,	,	PUNCT
ejpam-6086	334	38	d(xn+1	d(xn+1	PROPN
ejpam-6086	334	39	,	,	PUNCT
ejpam-6086	334	40	z	z	NOUN
ejpam-6086	334	41	)	)	PUNCT
ejpam-6086	334	42	,	,	PUNCT
ejpam-6086	334	43	d(xn	d(xn	PROPN
ejpam-6086	334	44	,	,	PUNCT
ejpam-6086	334	45	t	t	PROPN
ejpam-6086	334	46	z	z	PROPN
ejpam-6086	334	47	)	)	PUNCT
ejpam-6086	334	48	}	}	PUNCT
ejpam-6086	334	49	=	=	SYM
ejpam-6086	334	50	0	0	X
ejpam-6086	334	51	.	.	PUNCT
ejpam-6086	335	1	now	now	ADV
ejpam-6086	335	2	,	,	PUNCT
ejpam-6086	335	3	we	we	PRON
ejpam-6086	335	4	obtain	obtain	VERB
ejpam-6086	335	5	θ(bd(z	θ(bd(z	PROPN
ejpam-6086	335	6	,	,	PUNCT
ejpam-6086	335	7	tz	tz	NOUN
ejpam-6086	335	8	)	)	PUNCT
ejpam-6086	335	9	)	)	PUNCT
ejpam-6086	335	10	≤	≤	NOUN
ejpam-6086	335	11	θ[b3	θ[b3	ADP
ejpam-6086	335	12	lim	lim	PROPN
ejpam-6086	335	13	n→+∞	n→+∞	PROPN
ejpam-6086	335	14	h(txn	h(txn	PROPN
ejpam-6086	335	15	,	,	PUNCT
ejpam-6086	335	16	t	t	PROPN
ejpam-6086	335	17	z	z	PROPN
ejpam-6086	335	18	)	)	PUNCT
ejpam-6086	335	19	]	]	PUNCT
ejpam-6086	336	1	≤	≤	NUM
ejpam-6086	336	2	lim	lim	PROPN
ejpam-6086	336	3	n→+∞	n→+∞	PROPN
ejpam-6086	336	4	θ[b3h(txn	θ[b3h(txn	PROPN
ejpam-6086	336	5	,	,	PUNCT
ejpam-6086	336	6	t	t	PROPN
ejpam-6086	336	7	z	z	PROPN
ejpam-6086	336	8	)	)	PUNCT
ejpam-6086	336	9	]	]	PUNCT
ejpam-6086	336	10	≤	≤	NUM
ejpam-6086	336	11	lim	lim	PROPN
ejpam-6086	336	12	n→+∞	n→+∞	VERB
ejpam-6086	336	13	θ[α(xn	θ[α(xn	NOUN
ejpam-6086	336	14	,	,	PUNCT
ejpam-6086	336	15	z)b	z)b	X
ejpam-6086	336	16	3h(txn	3h(txn	NUM
ejpam-6086	336	17	,	,	PUNCT
ejpam-6086	336	18	t	t	PROPN
ejpam-6086	336	19	z	z	PROPN
ejpam-6086	336	20	)	)	PUNCT
ejpam-6086	336	21	]	]	PUNCT
ejpam-6086	337	1	≤	≤	PROPN
ejpam-6086	337	2	ϕ(θ	ϕ(θ	PROPN
ejpam-6086	337	3	[	[	PUNCT
ejpam-6086	337	4	lim	lim	PROPN
ejpam-6086	337	5	n→+∞	n→+∞	VERB
ejpam-6086	337	6	m(xn	m(xn	PROPN
ejpam-6086	337	7	,	,	PUNCT
ejpam-6086	337	8	z	z	NOUN
ejpam-6086	337	9	)	)	PUNCT
ejpam-6086	337	10	]	]	PUNCT
ejpam-6086	337	11	)	)	PUNCT
ejpam-6086	338	1	+	+	ADP
ejpam-6086	338	2	k	k	PROPN
ejpam-6086	338	3	lim	lim	PROPN
ejpam-6086	338	4	n→+∞	n→+∞	PROPN
ejpam-6086	338	5	w	w	PROPN
ejpam-6086	338	6	(	(	PUNCT
ejpam-6086	338	7	xn	xn	PROPN
ejpam-6086	338	8	,	,	PUNCT
ejpam-6086	338	9	z	z	NOUN
ejpam-6086	338	10	)	)	PUNCT
ejpam-6086	338	11	≤	≤	NOUN
ejpam-6086	338	12	ϕ[θ(d(z	ϕ[θ(d(z	PROPN
ejpam-6086	338	13	,	,	PUNCT
ejpam-6086	338	14	tz	tz	NOUN
ejpam-6086	338	15	)	)	PUNCT
ejpam-6086	338	16	)	)	PUNCT
ejpam-6086	338	17	]	]	PUNCT
ejpam-6086	339	1	<	<	X
ejpam-6086	339	2	θ(d(z	θ(d(z	PROPN
ejpam-6086	339	3	,	,	PUNCT
ejpam-6086	339	4	tz	tz	NOUN
ejpam-6086	339	5	)	)	PUNCT
ejpam-6086	339	6	)	)	PUNCT
ejpam-6086	339	7	.	.	PUNCT
ejpam-6086	340	1	this	this	PRON
ejpam-6086	340	2	implies	imply	VERB
ejpam-6086	340	3	that	that	SCONJ
ejpam-6086	340	4	bd(z	bd(z	X
ejpam-6086	340	5	,	,	PUNCT
ejpam-6086	340	6	tz	tz	PROPN
ejpam-6086	340	7	)	)	PUNCT
ejpam-6086	340	8	<	<	X
ejpam-6086	340	9	d(z	d(z	PROPN
ejpam-6086	340	10	,	,	PUNCT
ejpam-6086	340	11	tz	tz	PROPN
ejpam-6086	340	12	)	)	PUNCT
ejpam-6086	340	13	,	,	PUNCT
ejpam-6086	340	14	this	this	DET
ejpam-6086	340	15	a	a	DET
ejpam-6086	340	16	contradiction	contradiction	NOUN
ejpam-6086	340	17	,	,	PUNCT
ejpam-6086	340	18	then	then	ADV
ejpam-6086	340	19	z	z	PROPN
ejpam-6086	340	20	∈	∈	PROPN
ejpam-6086	340	21	tz	tz	NOUN
ejpam-6086	340	22	.	.	PUNCT
ejpam-6086	341	1	the	the	DET
ejpam-6086	341	2	following	follow	VERB
ejpam-6086	341	3	corollaries	corollary	NOUN
ejpam-6086	341	4	are	be	AUX
ejpam-6086	341	5	immediate	immediate	ADJ
ejpam-6086	341	6	results	result	NOUN
ejpam-6086	341	7	of	of	ADP
ejpam-6086	341	8	theorem	theorem	ADJ
ejpam-6086	341	9	4	4	NUM
ejpam-6086	341	10	and	and	CCONJ
ejpam-6086	341	11	theorem	theorem	VERB
ejpam-6086	341	12	5	5	NUM
ejpam-6086	341	13	.	.	PUNCT
ejpam-6086	341	14	corollary	corollary	ADJ
ejpam-6086	341	15	3	3	NUM
ejpam-6086	341	16	.	.	PUNCT
ejpam-6086	342	1	let	let	AUX
ejpam-6086	342	2	(	(	PUNCT
ejpam-6086	342	3	u	u	NOUN
ejpam-6086	342	4	,	,	PUNCT
ejpam-6086	342	5	d	d	PROPN
ejpam-6086	342	6	)	)	PUNCT
ejpam-6086	342	7	be	be	AUX
ejpam-6086	342	8	a	a	DET
ejpam-6086	342	9	complete	complete	ADJ
ejpam-6086	342	10	rectangular	rectangular	ADJ
ejpam-6086	342	11	b−metric	b−metric	ADJ
ejpam-6086	342	12	space	space	NOUN
ejpam-6086	342	13	and	and	CCONJ
ejpam-6086	342	14	t	t	NOUN
ejpam-6086	342	15	:	:	PUNCT
ejpam-6086	342	16	u	u	PROPN
ejpam-6086	342	17	→	→	SYM
ejpam-6086	342	18	b(u	b(u	PROPN
ejpam-6086	342	19	)	)	PUNCT
ejpam-6086	342	20	be	be	VERB
ejpam-6086	342	21	an	an	DET
ejpam-6086	342	22	α−admissible	α−admissible	ADJ
ejpam-6086	342	23	θ	θ	X
ejpam-6086	342	24	−	−	PROPN
ejpam-6086	342	25	ϕ−multivalued	ϕ−multivalued	PUNCT
ejpam-6086	342	26	contraction	contraction	PROPN
ejpam-6086	342	27	kannan	kannan	PROPN
ejpam-6086	342	28	type	type	NOUN
ejpam-6086	342	29	satisfying	satisfying	ADJ
ejpam-6086	342	30	:	:	PUNCT
ejpam-6086	342	31	(	(	PUNCT
ejpam-6086	342	32	i	i	NOUN
ejpam-6086	342	33	)	)	PUNCT
ejpam-6086	342	34	(	(	PUNCT
ejpam-6086	342	35	u	u	NOUN
ejpam-6086	342	36	,	,	PUNCT
ejpam-6086	342	37	d	d	PROPN
ejpam-6086	342	38	)	)	PUNCT
ejpam-6086	342	39	is	be	AUX
ejpam-6086	342	40	an	an	DET
ejpam-6086	342	41	α−complete	α−complete	NUM
ejpam-6086	342	42	metric	metric	ADJ
ejpam-6086	342	43	space	space	NOUN
ejpam-6086	342	44	,	,	PUNCT
ejpam-6086	342	45	(	(	PUNCT
ejpam-6086	342	46	ii	ii	NOUN
ejpam-6086	342	47	)	)	PUNCT
ejpam-6086	342	48	α(x0	α(x0	PROPN
ejpam-6086	342	49	,	,	PUNCT
ejpam-6086	342	50	x1	x1	PROPN
ejpam-6086	342	51	)	)	PUNCT
ejpam-6086	342	52	≥	≥	NOUN
ejpam-6086	342	53	1	1	NUM
ejpam-6086	342	54	for	for	ADP
ejpam-6086	342	55	x0	x0	PROPN
ejpam-6086	342	56	∈	∈	PROPN
ejpam-6086	342	57	u	u	NOUN
ejpam-6086	342	58	and	and	CCONJ
ejpam-6086	342	59	x1	x1	PROPN
ejpam-6086	342	60	∈	∈	PROPN
ejpam-6086	342	61	t	t	PROPN
ejpam-6086	342	62	(	(	PUNCT
ejpam-6086	342	63	u	u	NOUN
ejpam-6086	342	64	)	)	PUNCT
ejpam-6086	342	65	,	,	PUNCT
ejpam-6086	342	66	(	(	PUNCT
ejpam-6086	342	67	iii	iii	X
ejpam-6086	342	68	)	)	PUNCT
ejpam-6086	342	69	t	t	PROPN
ejpam-6086	342	70	is	be	AUX
ejpam-6086	342	71	triangular	triangular	NOUN
ejpam-6086	342	72	α−admissible	α−admissible	NOUN
ejpam-6086	342	73	,	,	PUNCT
ejpam-6086	342	74	(	(	PUNCT
ejpam-6086	342	75	iv	iv	X
ejpam-6086	342	76	)	)	PUNCT
ejpam-6086	342	77	t	t	PROPN
ejpam-6086	342	78	is	be	AUX
ejpam-6086	342	79	an	an	DET
ejpam-6086	342	80	α−continuous	α−continuous	ADJ
ejpam-6086	342	81	multivalued	multivalued	ADJ
ejpam-6086	342	82	mapping	mapping	NOUN
ejpam-6086	342	83	or	or	CCONJ
ejpam-6086	342	84	exists	exist	VERB
ejpam-6086	342	85	a	a	DET
ejpam-6086	342	86	sequence	sequence	NOUN
ejpam-6086	342	87	{	{	PUNCT
ejpam-6086	342	88	xn	xn	NUM
ejpam-6086	342	89	}	}	PUNCT
ejpam-6086	342	90	in	in	ADP
ejpam-6086	342	91	u	u	PRON
ejpam-6086	342	92	such	such	ADJ
ejpam-6086	342	93	that	that	SCONJ
ejpam-6086	342	94	α(xn	α(xn	NOUN
ejpam-6086	342	95	,	,	PUNCT
ejpam-6086	342	96	xn+1	xn+1	NUM
ejpam-6086	342	97	)	)	PUNCT
ejpam-6086	342	98	≥	≥	NOUN
ejpam-6086	342	99	1	1	NUM
ejpam-6086	342	100	for	for	ADP
ejpam-6086	342	101	all	all	DET
ejpam-6086	342	102	n	n	PRON
ejpam-6086	342	103	∈	∈	PROPN
ejpam-6086	342	104	n∪{0	n∪{0	NOUN
ejpam-6086	342	105	}	}	PUNCT
ejpam-6086	342	106	and	and	CCONJ
ejpam-6086	342	107	lim	lim	PROPN
ejpam-6086	342	108	n→+∞	n→+∞	VERB
ejpam-6086	342	109	d(xn	d(xn	PROPN
ejpam-6086	342	110	,	,	PUNCT
ejpam-6086	342	111	z	z	NOUN
ejpam-6086	342	112	)	)	PUNCT
ejpam-6086	342	113	=	=	SYM
ejpam-6086	342	114	0	0	NUM
ejpam-6086	342	115	,	,	PUNCT
ejpam-6086	342	116	for	for	ADP
ejpam-6086	342	117	some	some	DET
ejpam-6086	342	118	z	z	NOUN
ejpam-6086	342	119	∈	∈	NOUN
ejpam-6086	342	120	u	u	NOUN
ejpam-6086	342	121	then	then	ADV
ejpam-6086	342	122	there	there	PRON
ejpam-6086	342	123	exists	exist	VERB
ejpam-6086	342	124	a	a	DET
ejpam-6086	342	125	subsequence	subsequence	NOUN
ejpam-6086	342	126	{	{	PUNCT
ejpam-6086	342	127	xn(k	xn(k	NUM
ejpam-6086	342	128	)	)	PUNCT
ejpam-6086	342	129	}	}	PUNCT
ejpam-6086	342	130	of	of	ADP
ejpam-6086	342	131	{	{	PUNCT
ejpam-6086	342	132	xn	xn	NOUN
ejpam-6086	342	133	}	}	PUNCT
ejpam-6086	342	134	such	such	ADJ
ejpam-6086	342	135	that	that	SCONJ
ejpam-6086	342	136	α(xn(k	α(xn(k	PROPN
ejpam-6086	342	137	)	)	PUNCT
ejpam-6086	342	138	,	,	PUNCT
ejpam-6086	342	139	z	z	X
ejpam-6086	342	140	)	)	PUNCT
ejpam-6086	342	141	≥	≥	NOUN
ejpam-6086	342	142	1	1	NUM
ejpam-6086	342	143	for	for	ADP
ejpam-6086	342	144	all	all	DET
ejpam-6086	342	145	k	k	PROPN
ejpam-6086	342	146	∈	∈	PROPN
ejpam-6086	342	147	n	n	PART
ejpam-6086	342	148	∪	∪	X
ejpam-6086	342	149	{	{	PUNCT
ejpam-6086	342	150	0	0	NUM
ejpam-6086	342	151	}	}	PUNCT
ejpam-6086	342	152	.	.	PUNCT
ejpam-6086	343	1	then	then	ADV
ejpam-6086	343	2	,	,	PUNCT
ejpam-6086	343	3	t	t	PROPN
ejpam-6086	343	4	has	have	VERB
ejpam-6086	343	5	a	a	DET
ejpam-6086	343	6	fixed	fix	VERB
ejpam-6086	343	7	point	point	NOUN
ejpam-6086	343	8	.	.	PUNCT
ejpam-6086	344	1	corollary	corollary	ADJ
ejpam-6086	344	2	4	4	NUM
ejpam-6086	344	3	.	.	PUNCT
ejpam-6086	345	1	let	let	VERB
ejpam-6086	345	2	(	(	PUNCT
ejpam-6086	345	3	u	u	NOUN
ejpam-6086	345	4	,	,	PUNCT
ejpam-6086	345	5	d	d	PROPN
ejpam-6086	345	6	)	)	PUNCT
ejpam-6086	345	7	be	be	AUX
ejpam-6086	345	8	a	a	DET
ejpam-6086	345	9	complete	complete	ADJ
ejpam-6086	345	10	rectangular	rectangular	ADJ
ejpam-6086	345	11	b−metric	b−metric	ADJ
ejpam-6086	345	12	space	space	NOUN
ejpam-6086	345	13	and	and	CCONJ
ejpam-6086	345	14	t	t	NOUN
ejpam-6086	345	15	:	:	PUNCT
ejpam-6086	345	16	u	u	PROPN
ejpam-6086	345	17	→	→	SYM
ejpam-6086	345	18	b(u	b(u	PROPN
ejpam-6086	345	19	)	)	PUNCT
ejpam-6086	345	20	be	be	VERB
ejpam-6086	345	21	an	an	DET
ejpam-6086	345	22	α−admissible	α−admissible	ADJ
ejpam-6086	345	23	θ	θ	X
ejpam-6086	345	24	−	−	PROPN
ejpam-6086	345	25	ϕ−multivalued	ϕ−multivalued	PROPN
ejpam-6086	345	26	contraction	contraction	NOUN
ejpam-6086	345	27	reich	reich	NOUN
ejpam-6086	345	28	-	-	PUNCT
ejpam-6086	345	29	type	type	NOUN
ejpam-6086	345	30	satisfying	satisfying	NOUN
ejpam-6086	345	31	:	:	PUNCT
ejpam-6086	345	32	(	(	PUNCT
ejpam-6086	345	33	i	i	NOUN
ejpam-6086	345	34	)	)	PUNCT
ejpam-6086	345	35	(	(	PUNCT
ejpam-6086	345	36	u	u	NOUN
ejpam-6086	345	37	,	,	PUNCT
ejpam-6086	345	38	d	d	PROPN
ejpam-6086	345	39	)	)	PUNCT
ejpam-6086	345	40	is	be	AUX
ejpam-6086	345	41	an	an	DET
ejpam-6086	345	42	α−complete	α−complete	NUM
ejpam-6086	345	43	metric	metric	ADJ
ejpam-6086	345	44	space	space	NOUN
ejpam-6086	345	45	,	,	PUNCT
ejpam-6086	346	1	h.	h.	PROPN
ejpam-6086	346	2	massit	massit	PROPN
ejpam-6086	346	3	et	et	PROPN
ejpam-6086	346	4	al	al	PROPN
ejpam-6086	346	5	.	.	PUNCT
ejpam-6086	346	6	/	/	SYM
ejpam-6086	346	7	eur	eur	PROPN
ejpam-6086	346	8	.	.	PUNCT
ejpam-6086	347	1	j.	j.	PROPN
ejpam-6086	347	2	pure	pure	PROPN
ejpam-6086	347	3	appl	appl	PROPN
ejpam-6086	347	4	.	.	PROPN
ejpam-6086	347	5	math	math	PROPN
ejpam-6086	347	6	,	,	PUNCT
ejpam-6086	347	7	18	18	NUM
ejpam-6086	347	8	(	(	PUNCT
ejpam-6086	347	9	2	2	NUM
ejpam-6086	347	10	)	)	PUNCT
ejpam-6086	347	11	(	(	PUNCT
ejpam-6086	347	12	2025	2025	NUM
ejpam-6086	347	13	)	)	PUNCT
ejpam-6086	347	14	,	,	PUNCT
ejpam-6086	347	15	6086	6086	NUM
ejpam-6086	347	16	17	17	NUM
ejpam-6086	347	17	of	of	ADP
ejpam-6086	347	18	19	19	NUM
ejpam-6086	347	19	(	(	PUNCT
ejpam-6086	347	20	ii	ii	NOUN
ejpam-6086	347	21	)	)	PUNCT
ejpam-6086	347	22	α(x0	α(x0	PROPN
ejpam-6086	347	23	,	,	PUNCT
ejpam-6086	347	24	x1	x1	PROPN
ejpam-6086	347	25	)	)	PUNCT
ejpam-6086	347	26	≥	≥	NOUN
ejpam-6086	347	27	1	1	NUM
ejpam-6086	347	28	for	for	ADP
ejpam-6086	347	29	x0	x0	PROPN
ejpam-6086	347	30	∈	∈	PROPN
ejpam-6086	347	31	u	u	NOUN
ejpam-6086	347	32	and	and	CCONJ
ejpam-6086	347	33	x1	x1	PROPN
ejpam-6086	347	34	∈	∈	PROPN
ejpam-6086	347	35	t	t	PROPN
ejpam-6086	347	36	(	(	PUNCT
ejpam-6086	347	37	u	u	NOUN
ejpam-6086	347	38	)	)	PUNCT
ejpam-6086	347	39	,	,	PUNCT
ejpam-6086	347	40	(	(	PUNCT
ejpam-6086	347	41	iii	iii	X
ejpam-6086	347	42	)	)	PUNCT
ejpam-6086	347	43	t	t	PROPN
ejpam-6086	347	44	is	be	AUX
ejpam-6086	347	45	triangular	triangular	NOUN
ejpam-6086	347	46	α−admissible	α−admissible	NOUN
ejpam-6086	347	47	,	,	PUNCT
ejpam-6086	347	48	(	(	PUNCT
ejpam-6086	347	49	iv	iv	X
ejpam-6086	347	50	)	)	PUNCT
ejpam-6086	347	51	there	there	PRON
ejpam-6086	347	52	exists	exist	VERB
ejpam-6086	347	53	{	{	PUNCT
ejpam-6086	347	54	xn	xn	PUNCT
ejpam-6086	347	55	}	}	PUNCT
ejpam-6086	347	56	is	be	AUX
ejpam-6086	347	57	a	a	DET
ejpam-6086	347	58	sequence	sequence	NOUN
ejpam-6086	347	59	in	in	ADP
ejpam-6086	347	60	u	u	PRON
ejpam-6086	347	61	such	such	ADJ
ejpam-6086	347	62	that	that	SCONJ
ejpam-6086	347	63	α(xn	α(xn	NOUN
ejpam-6086	347	64	,	,	PUNCT
ejpam-6086	347	65	xn+1	xn+1	NUM
ejpam-6086	347	66	)	)	PUNCT
ejpam-6086	347	67	≥	≥	NOUN
ejpam-6086	347	68	1	1	NUM
ejpam-6086	347	69	for	for	ADP
ejpam-6086	347	70	all	all	PRON
ejpam-6086	347	71	n	n	PRON
ejpam-6086	347	72	∈	∈	NOUN
ejpam-6086	347	73	n	n	NOUN
ejpam-6086	347	74	∪	∪	X
ejpam-6086	347	75	{	{	PUNCT
ejpam-6086	347	76	0	0	NUM
ejpam-6086	347	77	}	}	PUNCT
ejpam-6086	347	78	and	and	CCONJ
ejpam-6086	347	79	lim	lim	PROPN
ejpam-6086	347	80	n→+∞	n→+∞	VERB
ejpam-6086	347	81	d(xn	d(xn	PROPN
ejpam-6086	347	82	,	,	PUNCT
ejpam-6086	347	83	z	z	NOUN
ejpam-6086	347	84	)	)	PUNCT
ejpam-6086	347	85	=	=	SYM
ejpam-6086	347	86	0	0	NUM
ejpam-6086	347	87	,	,	PUNCT
ejpam-6086	347	88	then	then	ADV
ejpam-6086	347	89	there	there	PRON
ejpam-6086	347	90	exists	exist	VERB
ejpam-6086	347	91	a	a	DET
ejpam-6086	347	92	subsequence	subsequence	NOUN
ejpam-6086	347	93	{	{	PUNCT
ejpam-6086	347	94	xn(k	xn(k	NUM
ejpam-6086	347	95	)	)	PUNCT
ejpam-6086	347	96	}	}	PUNCT
ejpam-6086	347	97	of	of	ADP
ejpam-6086	347	98	{	{	PUNCT
ejpam-6086	347	99	xn	xn	NOUN
ejpam-6086	347	100	}	}	PUNCT
ejpam-6086	347	101	such	such	ADJ
ejpam-6086	347	102	that	that	SCONJ
ejpam-6086	347	103	α(xn(k	α(xn(k	PROPN
ejpam-6086	347	104	)	)	PUNCT
ejpam-6086	347	105	,	,	PUNCT
ejpam-6086	347	106	z	z	X
ejpam-6086	347	107	)	)	PUNCT
ejpam-6086	347	108	≥	≥	NOUN
ejpam-6086	347	109	1	1	NUM
ejpam-6086	347	110	for	for	ADP
ejpam-6086	347	111	all	all	DET
ejpam-6086	347	112	k	k	PROPN
ejpam-6086	347	113	∈	∈	PROPN
ejpam-6086	347	114	n	n	PART
ejpam-6086	347	115	∪	∪	X
ejpam-6086	347	116	{	{	PUNCT
ejpam-6086	347	117	0	0	NUM
ejpam-6086	347	118	}	}	PUNCT
ejpam-6086	347	119	.	.	PUNCT
ejpam-6086	348	1	then	then	ADV
ejpam-6086	348	2	,	,	PUNCT
ejpam-6086	348	3	t	t	PROPN
ejpam-6086	348	4	has	have	VERB
ejpam-6086	348	5	a	a	DET
ejpam-6086	348	6	fixed	fix	VERB
ejpam-6086	348	7	point	point	NOUN
ejpam-6086	348	8	.	.	PUNCT
ejpam-6086	349	1	conclusion	conclusion	NOUN
ejpam-6086	349	2	we	we	PRON
ejpam-6086	349	3	obtain	obtain	VERB
ejpam-6086	349	4	some	some	DET
ejpam-6086	349	5	fixed	fix	VERB
ejpam-6086	349	6	point	point	NOUN
ejpam-6086	349	7	theorems	theorem	NOUN
ejpam-6086	349	8	for	for	ADP
ejpam-6086	349	9	θ−ϕ−multivalued	θ−ϕ−multivalue	VERB
ejpam-6086	349	10	contractions	contraction	NOUN
ejpam-6086	349	11	in	in	ADP
ejpam-6086	349	12	α−complete	α−complete	NUM
ejpam-6086	349	13	rectangular	rectangular	ADJ
ejpam-6086	349	14	b−metric	b−metric	ADJ
ejpam-6086	349	15	spaces	space	NOUN
ejpam-6086	349	16	.	.	PUNCT
ejpam-6086	350	1	we	we	PRON
ejpam-6086	350	2	establish	establish	VERB
ejpam-6086	350	3	some	some	DET
ejpam-6086	350	4	fixed	fix	VERB
ejpam-6086	350	5	point	point	NOUN
ejpam-6086	350	6	theorems	theorem	NOUN
ejpam-6086	350	7	including	include	VERB
ejpam-6086	350	8	the	the	DET
ejpam-6086	350	9	α−admissible	α−admissible	X
ejpam-6086	350	10	θ	θ	X
ejpam-6086	350	11	−	−	PROPN
ejpam-6086	350	12	ϕ−multivalued	ϕ−multivalued	SCONJ
ejpam-6086	350	13	kannan	kannan	PROPN
ejpam-6086	350	14	type	type	NOUN
ejpam-6086	350	15	and	and	CCONJ
ejpam-6086	350	16	reich	reich	PROPN
ejpam-6086	350	17	type	type	NOUN
ejpam-6086	350	18	.	.	PUNCT
ejpam-6086	351	1	our	our	PRON
ejpam-6086	351	2	results	result	NOUN
ejpam-6086	351	3	improve	improve	VERB
ejpam-6086	351	4	and	and	CCONJ
ejpam-6086	351	5	generalize	generalize	VERB
ejpam-6086	351	6	some	some	DET
ejpam-6086	351	7	results	result	NOUN
ejpam-6086	351	8	from	from	ADP
ejpam-6086	351	9	the	the	DET
ejpam-6086	351	10	literature	literature	NOUN
ejpam-6086	351	11	.	.	PUNCT
ejpam-6086	352	1	we	we	PRON
ejpam-6086	352	2	believe	believe	VERB
ejpam-6086	352	3	that	that	SCONJ
ejpam-6086	352	4	our	our	PRON
ejpam-6086	352	5	paper	paper	NOUN
ejpam-6086	352	6	may	may	AUX
ejpam-6086	352	7	be	be	AUX
ejpam-6086	352	8	interesting	interesting	ADJ
ejpam-6086	352	9	to	to	ADP
ejpam-6086	352	10	researchers	researcher	NOUN
ejpam-6086	352	11	in	in	ADP
ejpam-6086	352	12	fixed	fix	VERB
ejpam-6086	352	13	point	point	NOUN
ejpam-6086	352	14	theory	theory	NOUN
ejpam-6086	352	15	,	,	PUNCT
ejpam-6086	352	16	because	because	SCONJ
ejpam-6086	352	17	using	use	VERB
ejpam-6086	352	18	the	the	DET
ejpam-6086	352	19	methods	method	NOUN
ejpam-6086	352	20	presented	present	VERB
ejpam-6086	352	21	in	in	ADP
ejpam-6086	352	22	this	this	DET
ejpam-6086	352	23	paper	paper	NOUN
ejpam-6086	352	24	,	,	PUNCT
ejpam-6086	352	25	the	the	DET
ejpam-6086	352	26	following	follow	VERB
ejpam-6086	352	27	problems	problem	NOUN
ejpam-6086	352	28	remain	remain	VERB
ejpam-6086	352	29	open	open	ADJ
ejpam-6086	352	30	:	:	PUNCT
ejpam-6086	352	31	1	1	X
ejpam-6086	352	32	.	.	X
ejpam-6086	352	33	prove	prove	VERB
ejpam-6086	352	34	the	the	DET
ejpam-6086	352	35	hardy	hardy	ADJ
ejpam-6086	352	36	-	-	PUNCT
ejpam-6086	352	37	rogers	roger	NOUN
ejpam-6086	352	38	result	result	NOUN
ejpam-6086	352	39	for	for	ADP
ejpam-6086	352	40	θ	θ	PROPN
ejpam-6086	352	41	−	−	PROPN
ejpam-6086	352	42	ϕ-multivalued	ϕ-multivalue	VERB
ejpam-6086	352	43	contractions	contraction	NOUN
ejpam-6086	352	44	in	in	ADP
ejpam-6086	352	45	α	α	NOUN
ejpam-6086	352	46	-	-	ADJ
ejpam-6086	352	47	complete	complete	ADJ
ejpam-6086	352	48	rectangular	rectangular	ADJ
ejpam-6086	352	49	b	b	X
ejpam-6086	352	50	-	-	ADJ
ejpam-6086	352	51	metric	metric	ADJ
ejpam-6086	352	52	spaces	space	NOUN
ejpam-6086	352	53	.	.	PUNCT
ejpam-6086	353	1	2	2	X
ejpam-6086	353	2	.	.	X
ejpam-6086	353	3	prove	prove	VERB
ejpam-6086	353	4	the	the	DET
ejpam-6086	353	5	ćirić	ćirić	PROPN
ejpam-6086	353	6	result	result	NOUN
ejpam-6086	353	7	for	for	ADP
ejpam-6086	353	8	θ	θ	PROPN
ejpam-6086	353	9	−	−	PROPN
ejpam-6086	353	10	ϕ-multivalued	ϕ-multivalue	VERB
ejpam-6086	353	11	contractions	contraction	NOUN
ejpam-6086	353	12	in	in	ADP
ejpam-6086	353	13	α	α	NOUN
ejpam-6086	353	14	-	-	ADJ
ejpam-6086	353	15	complete	complete	ADJ
ejpam-6086	353	16	rectangular	rectangular	ADJ
ejpam-6086	353	17	b	b	X
ejpam-6086	353	18	-	-	ADJ
ejpam-6086	353	19	metric	metric	ADJ
ejpam-6086	353	20	spaces	space	NOUN
ejpam-6086	353	21	.	.	PUNCT
ejpam-6086	354	1	of	of	ADP
ejpam-6086	354	2	course	course	NOUN
ejpam-6086	354	3	,	,	PUNCT
ejpam-6086	354	4	other	other	ADJ
ejpam-6086	354	5	questions	question	NOUN
ejpam-6086	354	6	such	such	ADJ
ejpam-6086	354	7	as	as	ADP
ejpam-6086	354	8	kirk	kirk	PROPN
ejpam-6086	354	9	theorem	theorem	PROPN
ejpam-6086	354	10	of	of	ADP
ejpam-6086	354	11	fixed	fix	VERB
ejpam-6086	354	12	point	point	NOUN
ejpam-6086	354	13	,	,	PUNCT
ejpam-6086	354	14	suzuki	suzuki	PROPN
ejpam-6086	354	15	fixed	fix	VERB
ejpam-6086	354	16	point	point	NOUN
ejpam-6086	354	17	theorem	theorem	VERB
ejpam-6086	354	18	,	,	PUNCT
ejpam-6086	354	19	etc	etc	X
ejpam-6086	354	20	.	.	X
ejpam-6086	354	21	acknowledgements	acknowledgement	VERB
ejpam-6086	354	22	the	the	DET
ejpam-6086	354	23	authors	author	NOUN
ejpam-6086	354	24	a.	a.	VERB
ejpam-6086	354	25	aloqaily	aloqaily	ADV
ejpam-6086	354	26	,	,	PUNCT
ejpam-6086	354	27	and	and	CCONJ
ejpam-6086	354	28	n.	n.	PROPN
ejpam-6086	354	29	mlaiki	mlaiki	PROPN
ejpam-6086	354	30	would	would	AUX
ejpam-6086	354	31	like	like	VERB
ejpam-6086	354	32	to	to	PART
ejpam-6086	354	33	thank	thank	VERB
ejpam-6086	354	34	prince	prince	PROPN
ejpam-6086	354	35	sultan	sultan	PROPN
ejpam-6086	354	36	university	university	PROPN
ejpam-6086	354	37	for	for	ADP
ejpam-6086	354	38	paying	pay	VERB
ejpam-6086	354	39	the	the	DET
ejpam-6086	354	40	publication	publication	NOUN
ejpam-6086	354	41	fees	fee	NOUN
ejpam-6086	354	42	for	for	ADP
ejpam-6086	354	43	this	this	DET
ejpam-6086	354	44	work	work	NOUN
ejpam-6086	354	45	through	through	ADP
ejpam-6086	354	46	tas	ta	NOUN
ejpam-6086	354	47	lab	lab	PROPN
ejpam-6086	354	48	.	.	PUNCT
ejpam-6086	355	1	author	author	NOUN
ejpam-6086	355	2	contributions	contribution	NOUN
ejpam-6086	355	3	all	all	DET
ejpam-6086	355	4	authors	author	NOUN
ejpam-6086	355	5	have	have	AUX
ejpam-6086	355	6	read	read	VERB
ejpam-6086	355	7	and	and	CCONJ
ejpam-6086	355	8	agreed	agree	VERB
ejpam-6086	355	9	to	to	ADP
ejpam-6086	355	10	the	the	DET
ejpam-6086	355	11	published	publish	VERB
ejpam-6086	355	12	version	version	NOUN
ejpam-6086	355	13	of	of	ADP
ejpam-6086	355	14	the	the	DET
ejpam-6086	355	15	manuscript	manuscript	NOUN
ejpam-6086	355	16	.	.	PUNCT
ejpam-6086	356	1	data	datum	NOUN
ejpam-6086	356	2	availability	availability	NOUN
ejpam-6086	356	3	not	not	PART
ejpam-6086	356	4	applicable	applicable	ADJ
ejpam-6086	356	5	.	.	PUNCT
ejpam-6086	357	1	conflicts	conflict	NOUN
ejpam-6086	357	2	of	of	ADP
ejpam-6086	357	3	interest	interest	NOUN
ejpam-6086	357	4	the	the	DET
ejpam-6086	357	5	authors	author	NOUN
ejpam-6086	357	6	declare	declare	VERB
ejpam-6086	357	7	no	no	DET
ejpam-6086	357	8	conflict	conflict	NOUN
ejpam-6086	357	9	of	of	ADP
ejpam-6086	357	10	interest	interest	NOUN
ejpam-6086	357	11	.	.	PUNCT
ejpam-6086	358	1	h.	h.	PROPN
ejpam-6086	358	2	massit	massit	PROPN
ejpam-6086	358	3	et	et	PROPN
ejpam-6086	358	4	al	al	PROPN
ejpam-6086	358	5	.	.	PUNCT
ejpam-6086	358	6	/	/	SYM
ejpam-6086	358	7	eur	eur	PROPN
ejpam-6086	358	8	.	.	PUNCT
ejpam-6086	359	1	j.	j.	PROPN
ejpam-6086	359	2	pure	pure	PROPN
ejpam-6086	359	3	appl	appl	PROPN
ejpam-6086	359	4	.	.	PROPN
ejpam-6086	359	5	math	math	PROPN
ejpam-6086	359	6	,	,	PUNCT
ejpam-6086	359	7	18	18	NUM
ejpam-6086	359	8	(	(	PUNCT
ejpam-6086	359	9	2	2	NUM
ejpam-6086	359	10	)	)	PUNCT
ejpam-6086	359	11	(	(	PUNCT
ejpam-6086	359	12	2025	2025	NUM
ejpam-6086	359	13	)	)	PUNCT
ejpam-6086	359	14	,	,	PUNCT
ejpam-6086	359	15	6086	6086	NUM
ejpam-6086	359	16	18	18	NUM
ejpam-6086	359	17	of	of	ADP
ejpam-6086	359	18	19	19	NUM
ejpam-6086	359	19	references	reference	NOUN
ejpam-6086	359	20	[	[	X
ejpam-6086	359	21	1	1	NUM
ejpam-6086	359	22	]	]	PUNCT
ejpam-6086	359	23	w.	w.	PROPN
ejpam-6086	359	24	shatanawi	shatanawi	PROPN
ejpam-6086	359	25	and	and	CCONJ
ejpam-6086	359	26	t.	t.	PROPN
ejpam-6086	359	27	a.	a.	PROPN
ejpam-6086	359	28	m.	m.	PROPN
ejpam-6086	359	29	shatnawi	shatnawi	PROPN
ejpam-6086	359	30	.	.	PUNCT
ejpam-6086	360	1	new	new	ADJ
ejpam-6086	360	2	fixed	fix	VERB
ejpam-6086	360	3	point	point	NOUN
ejpam-6086	360	4	results	result	NOUN
ejpam-6086	360	5	in	in	ADP
ejpam-6086	360	6	controlled	control	VERB
ejpam-6086	360	7	metric	metric	ADJ
ejpam-6086	360	8	type	type	NOUN
ejpam-6086	360	9	spaces	space	NOUN
ejpam-6086	360	10	based	base	VERB
ejpam-6086	360	11	on	on	ADP
ejpam-6086	360	12	new	new	ADJ
ejpam-6086	360	13	contractive	contractive	ADJ
ejpam-6086	360	14	conditions	condition	NOUN
ejpam-6086	360	15	.	.	PUNCT
ejpam-6086	361	1	aims	aim	VERB
ejpam-6086	361	2	mathematics	mathematic	NOUN
ejpam-6086	361	3	,	,	PUNCT
ejpam-6086	361	4	8(4):9314–9330	8(4):9314–9330	NUM
ejpam-6086	361	5	,	,	PUNCT
ejpam-6086	361	6	2023	2023	NUM
ejpam-6086	361	7	.	.	PUNCT
ejpam-6086	362	1	[	[	X
ejpam-6086	362	2	2	2	NUM
ejpam-6086	362	3	]	]	PUNCT
ejpam-6086	362	4	a.-z	a.-z	PROPN
ejpam-6086	362	5	.	.	PUNCT
ejpam-6086	363	1	rezazgui	rezazgui	PROPN
ejpam-6086	363	2	,	,	PUNCT
ejpam-6086	363	3	a.	a.	NOUN
ejpam-6086	363	4	a.	a.	NOUN
ejpam-6086	363	5	tallafha	tallafha	PROPN
ejpam-6086	363	6	,	,	PUNCT
ejpam-6086	363	7	and	and	CCONJ
ejpam-6086	363	8	w.	w.	PROPN
ejpam-6086	363	9	shatanawi	shatanawi	PROPN
ejpam-6086	363	10	.	.	PUNCT
ejpam-6086	364	1	common	common	ADJ
ejpam-6086	364	2	fixed	fix	VERB
ejpam-6086	364	3	point	point	NOUN
ejpam-6086	364	4	results	result	NOUN
ejpam-6086	364	5	via	via	ADP
ejpam-6086	364	6	aν	aν	NOUN
ejpam-6086	364	7	−	−	X
ejpam-6086	365	1	α	α	NUM
ejpam-6086	365	2	-	-	PUNCT
ejpam-6086	365	3	contractions	contraction	NOUN
ejpam-6086	365	4	with	with	ADP
ejpam-6086	365	5	a	a	DET
ejpam-6086	365	6	pair	pair	NOUN
ejpam-6086	365	7	and	and	CCONJ
ejpam-6086	365	8	two	two	NUM
ejpam-6086	365	9	pairs	pair	NOUN
ejpam-6086	365	10	of	of	ADP
ejpam-6086	365	11	self	self	NOUN
ejpam-6086	365	12	-	-	PUNCT
ejpam-6086	365	13	mappings	mapping	NOUN
ejpam-6086	365	14	in	in	ADP
ejpam-6086	365	15	the	the	DET
ejpam-6086	365	16	frame	frame	NOUN
ejpam-6086	365	17	of	of	ADP
ejpam-6086	365	18	an	an	DET
ejpam-6086	365	19	extended	extend	VERB
ejpam-6086	365	20	quasi	quasi	ADJ
ejpam-6086	365	21	b	b	NOUN
ejpam-6086	365	22	-	-	PUNCT
ejpam-6086	365	23	metric	metric	ADJ
ejpam-6086	365	24	space	space	NOUN
ejpam-6086	365	25	.	.	PUNCT
ejpam-6086	366	1	aims	aim	VERB
ejpam-6086	366	2	mathematics	mathematic	NOUN
ejpam-6086	366	3	,	,	PUNCT
ejpam-6086	366	4	8(3):7225–7241	8(3):7225–7241	NUM
ejpam-6086	366	5	,	,	PUNCT
ejpam-6086	366	6	2023	2023	NUM
ejpam-6086	366	7	.	.	PUNCT
ejpam-6086	367	1	[	[	X
ejpam-6086	367	2	3	3	NUM
ejpam-6086	367	3	]	]	X
ejpam-6086	367	4	m.	m.	NOUN
ejpam-6086	367	5	joshi	joshi	PROPN
ejpam-6086	367	6	,	,	PUNCT
ejpam-6086	367	7	a.	a.	PROPN
ejpam-6086	367	8	tomar	tomar	PROPN
ejpam-6086	367	9	,	,	PUNCT
ejpam-6086	367	10	and	and	CCONJ
ejpam-6086	367	11	t.	t.	NOUN
ejpam-6086	367	12	abdeljawad	abdeljawad	NOUN
ejpam-6086	367	13	.	.	PUNCT
ejpam-6086	368	1	on	on	ADP
ejpam-6086	368	2	fixed	fix	VERB
ejpam-6086	368	3	points	point	NOUN
ejpam-6086	368	4	,	,	PUNCT
ejpam-6086	368	5	their	their	PRON
ejpam-6086	368	6	geometry	geometry	NOUN
ejpam-6086	368	7	and	and	CCONJ
ejpam-6086	368	8	application	application	NOUN
ejpam-6086	368	9	to	to	ADP
ejpam-6086	368	10	satellite	satellite	NOUN
ejpam-6086	368	11	web	web	NOUN
ejpam-6086	368	12	coupling	coupling	NOUN
ejpam-6086	368	13	problem	problem	NOUN
ejpam-6086	368	14	in	in	ADP
ejpam-6086	368	15	s	s	NOUN
ejpam-6086	368	16	-	-	ADJ
ejpam-6086	368	17	metric	metric	ADJ
ejpam-6086	368	18	spaces	space	NOUN
ejpam-6086	368	19	.	.	PUNCT
ejpam-6086	369	1	aims	aim	VERB
ejpam-6086	369	2	mathematics	mathematics	PROPN
ejpam-6086	369	3	,	,	PUNCT
ejpam-6086	369	4	8(2):4407–4441	8(2):4407–4441	NOUN
ejpam-6086	369	5	,	,	PUNCT
ejpam-6086	369	6	2023	2023	NUM
ejpam-6086	369	7	.	.	PUNCT
ejpam-6086	370	1	[	[	X
ejpam-6086	370	2	4	4	NUM
ejpam-6086	370	3	]	]	X
ejpam-6086	370	4	i.	i.	PROPN
ejpam-6086	370	5	a.	a.	PROPN
ejpam-6086	370	6	bakhtin	bakhtin	PROPN
ejpam-6086	370	7	.	.	PUNCT
ejpam-6086	371	1	the	the	DET
ejpam-6086	371	2	contraction	contraction	NOUN
ejpam-6086	371	3	mapping	map	VERB
ejpam-6086	371	4	principle	principle	NOUN
ejpam-6086	371	5	in	in	ADP
ejpam-6086	371	6	quasi	quasi	ADJ
ejpam-6086	371	7	-	-	ADJ
ejpam-6086	371	8	metric	metric	ADJ
ejpam-6086	371	9	spaces	space	NOUN
ejpam-6086	371	10	.	.	PUNCT
ejpam-6086	372	1	functional	functional	ADJ
ejpam-6086	372	2	analysis	analysis	NOUN
ejpam-6086	372	3	,	,	PUNCT
ejpam-6086	372	4	ulyanovsk	ulyanovsk	VERB
ejpam-6086	372	5	state	state	PROPN
ejpam-6086	372	6	pedagogical	pedagogical	PROPN
ejpam-6086	372	7	institute	institute	PROPN
ejpam-6086	372	8	,	,	PUNCT
ejpam-6086	372	9	30:26–37	30:26–37	PROPN
ejpam-6086	372	10	,	,	PUNCT
ejpam-6086	372	11	1989	1989	NUM
ejpam-6086	372	12	.	.	PUNCT
ejpam-6086	373	1	[	[	X
ejpam-6086	373	2	5	5	NUM
ejpam-6086	373	3	]	]	PUNCT
ejpam-6086	373	4	a.	a.	NOUN
ejpam-6086	373	5	branciari	branciari	PROPN
ejpam-6086	373	6	.	.	PUNCT
ejpam-6086	374	1	a	a	DET
ejpam-6086	374	2	fixed	fix	VERB
ejpam-6086	374	3	point	point	NOUN
ejpam-6086	374	4	theorem	theorem	NOUN
ejpam-6086	374	5	of	of	ADP
ejpam-6086	374	6	banach	banach	NOUN
ejpam-6086	374	7	-	-	PUNCT
ejpam-6086	374	8	caccioppoli	caccioppoli	NOUN
ejpam-6086	374	9	type	type	NOUN
ejpam-6086	374	10	on	on	ADP
ejpam-6086	374	11	a	a	DET
ejpam-6086	374	12	class	class	NOUN
ejpam-6086	374	13	of	of	ADP
ejpam-6086	374	14	generalized	generalized	ADJ
ejpam-6086	374	15	metric	metric	ADJ
ejpam-6086	374	16	spaces	space	NOUN
ejpam-6086	374	17	.	.	PUNCT
ejpam-6086	375	1	publicationes	publicatione	NOUN
ejpam-6086	375	2	mathematicae	mathematicae	PROPN
ejpam-6086	375	3	debrecen	debrecen	PROPN
ejpam-6086	375	4	,	,	PUNCT
ejpam-6086	375	5	57(1	57(1	PROPN
ejpam-6086	375	6	-	-	PUNCT
ejpam-6086	375	7	2):31–37	2):31–37	NUM
ejpam-6086	375	8	,	,	PUNCT
ejpam-6086	375	9	2000	2000	NUM
ejpam-6086	375	10	.	.	PUNCT
ejpam-6086	376	1	[	[	X
ejpam-6086	376	2	6	6	NUM
ejpam-6086	376	3	]	]	PUNCT
ejpam-6086	376	4	p.	p.	NOUN
ejpam-6086	376	5	das	das	PROPN
ejpam-6086	376	6	.	.	PUNCT
ejpam-6086	377	1	a	a	DET
ejpam-6086	377	2	fixed	fix	VERB
ejpam-6086	377	3	point	point	NOUN
ejpam-6086	377	4	theorem	theorem	VERB
ejpam-6086	377	5	on	on	ADP
ejpam-6086	377	6	a	a	DET
ejpam-6086	377	7	class	class	NOUN
ejpam-6086	377	8	of	of	ADP
ejpam-6086	377	9	generalized	generalized	ADJ
ejpam-6086	377	10	metric	metric	ADJ
ejpam-6086	377	11	spaces	space	NOUN
ejpam-6086	377	12	.	.	PUNCT
ejpam-6086	378	1	korean	korean	ADJ
ejpam-6086	378	2	journal	journal	PROPN
ejpam-6086	378	3	of	of	ADP
ejpam-6086	378	4	mathematical	mathematical	ADJ
ejpam-6086	378	5	sciences	science	NOUN
ejpam-6086	378	6	,	,	PUNCT
ejpam-6086	378	7	9:29–33	9:29–33	NUM
ejpam-6086	378	8	,	,	PUNCT
ejpam-6086	378	9	2002	2002	NUM
ejpam-6086	378	10	.	.	PUNCT
ejpam-6086	379	1	[	[	X
ejpam-6086	379	2	7	7	X
ejpam-6086	379	3	]	]	X
ejpam-6086	379	4	r.	r.	PROPN
ejpam-6086	379	5	george	george	PROPN
ejpam-6086	379	6	,	,	PUNCT
ejpam-6086	379	7	s.	s.	PROPN
ejpam-6086	379	8	radenović	radenović	PROPN
ejpam-6086	379	9	,	,	PUNCT
ejpam-6086	379	10	k.	k.	PROPN
ejpam-6086	380	1	p.	p.	PROPN
ejpam-6086	380	2	reshma	reshma	PROPN
ejpam-6086	380	3	,	,	PUNCT
ejpam-6086	380	4	and	and	CCONJ
ejpam-6086	380	5	s.	s.	PROPN
ejpam-6086	380	6	shukla	shukla	PROPN
ejpam-6086	380	7	.	.	PUNCT
ejpam-6086	381	1	rectangular	rectangular	ADJ
ejpam-6086	381	2	b	b	X
ejpam-6086	381	3	-	-	PUNCT
ejpam-6086	381	4	metric	metric	ADJ
ejpam-6086	381	5	space	space	NOUN
ejpam-6086	381	6	and	and	CCONJ
ejpam-6086	381	7	contraction	contraction	NOUN
ejpam-6086	381	8	principles	principle	NOUN
ejpam-6086	381	9	.	.	PUNCT
ejpam-6086	382	1	journal	journal	PROPN
ejpam-6086	382	2	of	of	ADP
ejpam-6086	382	3	nonlinear	nonlinear	PROPN
ejpam-6086	382	4	sciences	sciences	PROPN
ejpam-6086	382	5	and	and	CCONJ
ejpam-6086	382	6	applications	application	NOUN
ejpam-6086	382	7	,	,	PUNCT
ejpam-6086	382	8	8(6):1005–1013	8(6):1005–1013	NUM
ejpam-6086	382	9	,	,	PUNCT
ejpam-6086	382	10	2015	2015	NUM
ejpam-6086	382	11	.	.	PUNCT
ejpam-6086	383	1	[	[	X
ejpam-6086	383	2	8	8	NUM
ejpam-6086	383	3	]	]	X
ejpam-6086	383	4	n.	n.	PROPN
ejpam-6086	383	5	hussain	hussain	PROPN
ejpam-6086	383	6	,	,	PUNCT
ejpam-6086	383	7	m.	m.	NOUN
ejpam-6086	383	8	a.	a.	NOUN
ejpam-6086	383	9	kutbi	kutbi	PROPN
ejpam-6086	383	10	,	,	PUNCT
ejpam-6086	383	11	and	and	CCONJ
ejpam-6086	383	12	p.	p.	PROPN
ejpam-6086	383	13	salimi	salimi	PROPN
ejpam-6086	383	14	.	.	PUNCT
ejpam-6086	384	1	fixed	fix	VERB
ejpam-6086	384	2	point	point	NOUN
ejpam-6086	384	3	theory	theory	NOUN
ejpam-6086	384	4	in	in	ADP
ejpam-6086	384	5	α	α	NOUN
ejpam-6086	384	6	-	-	ADJ
ejpam-6086	384	7	complete	complete	ADJ
ejpam-6086	384	8	metric	metric	ADJ
ejpam-6086	384	9	spaces	space	NOUN
ejpam-6086	384	10	with	with	ADP
ejpam-6086	384	11	applications	application	NOUN
ejpam-6086	384	12	.	.	PUNCT
ejpam-6086	385	1	abstract	abstract	ADJ
ejpam-6086	385	2	and	and	CCONJ
ejpam-6086	385	3	applied	apply	VERB
ejpam-6086	385	4	analysis	analysis	NOUN
ejpam-6086	385	5	,	,	PUNCT
ejpam-6086	385	6	2014:280817	2014:280817	NUM
ejpam-6086	385	7	,	,	PUNCT
ejpam-6086	385	8	2014	2014	NUM
ejpam-6086	385	9	.	.	PUNCT
ejpam-6086	386	1	[	[	X
ejpam-6086	386	2	9	9	NUM
ejpam-6086	386	3	]	]	PUNCT
ejpam-6086	386	4	a.	a.	NOUN
ejpam-6086	386	5	kari	kari	PROPN
ejpam-6086	386	6	,	,	PUNCT
ejpam-6086	386	7	m.	m.	NOUN
ejpam-6086	386	8	rossafi	rossafi	PROPN
ejpam-6086	386	9	,	,	PUNCT
ejpam-6086	386	10	e.	e.	PROPN
ejpam-6086	386	11	marhani	marhani	PROPN
ejpam-6086	386	12	,	,	PUNCT
ejpam-6086	386	13	and	and	CCONJ
ejpam-6086	386	14	m.	m.	PROPN
ejpam-6086	386	15	aamari	aamari	PROPN
ejpam-6086	386	16	.	.	PUNCT
ejpam-6086	387	1	θ−ϕ-contraction	θ−ϕ-contraction	NOUN
ejpam-6086	387	2	on	on	ADP
ejpam-6086	387	3	(	(	PUNCT
ejpam-6086	387	4	α	α	X
ejpam-6086	387	5	,	,	PUNCT
ejpam-6086	387	6	η)-complete	η)-complete	PUNCT
ejpam-6086	387	7	rectangular	rectangular	ADJ
ejpam-6086	387	8	b	b	X
ejpam-6086	387	9	-	-	ADJ
ejpam-6086	387	10	metric	metric	ADJ
ejpam-6086	387	11	spaces	space	NOUN
ejpam-6086	387	12	.	.	PUNCT
ejpam-6086	388	1	international	international	ADJ
ejpam-6086	388	2	journal	journal	PROPN
ejpam-6086	388	3	of	of	ADP
ejpam-6086	388	4	mathematics	mathematics	PROPN
ejpam-6086	388	5	and	and	CCONJ
ejpam-6086	388	6	mathematical	mathematical	ADJ
ejpam-6086	388	7	sciences	science	NOUN
ejpam-6086	388	8	,	,	PUNCT
ejpam-6086	388	9	2020:8846324	2020:8846324	NUM
ejpam-6086	388	10	,	,	PUNCT
ejpam-6086	388	11	2020	2020	NUM
ejpam-6086	388	12	.	.	PUNCT
ejpam-6086	389	1	[	[	X
ejpam-6086	389	2	10	10	NUM
ejpam-6086	389	3	]	]	X
ejpam-6086	389	4	m.	m.	NOUN
ejpam-6086	389	5	a.	a.	NOUN
ejpam-6086	389	6	kutbi	kutbi	PROPN
ejpam-6086	389	7	and	and	CCONJ
ejpam-6086	389	8	w.	w.	PROPN
ejpam-6086	389	9	sintunavarat	sintunavarat	PROPN
ejpam-6086	389	10	.	.	PUNCT
ejpam-6086	390	1	on	on	ADP
ejpam-6086	390	2	new	new	ADJ
ejpam-6086	390	3	fixed	fix	VERB
ejpam-6086	390	4	point	point	NOUN
ejpam-6086	390	5	results	result	NOUN
ejpam-6086	390	6	for	for	ADP
ejpam-6086	390	7	(	(	PUNCT
ejpam-6086	390	8	α	α	X
ejpam-6086	390	9	,	,	PUNCT
ejpam-6086	390	10	ψ	ψ	NOUN
ejpam-6086	390	11	,	,	PUNCT
ejpam-6086	390	12	ζ)-contractive	ζ)-contractive	VERB
ejpam-6086	390	13	multivalued	multivalue	VERB
ejpam-6086	390	14	mappings	mapping	NOUN
ejpam-6086	390	15	on	on	ADP
ejpam-6086	390	16	α	α	NOUN
ejpam-6086	390	17	-	-	ADJ
ejpam-6086	390	18	complete	complete	ADJ
ejpam-6086	390	19	metric	metric	ADJ
ejpam-6086	390	20	spaces	space	NOUN
ejpam-6086	390	21	and	and	CCONJ
ejpam-6086	390	22	their	their	PRON
ejpam-6086	390	23	consequences	consequence	NOUN
ejpam-6086	390	24	.	.	PUNCT
ejpam-6086	391	1	fixed	fix	VERB
ejpam-6086	391	2	point	point	NOUN
ejpam-6086	391	3	theory	theory	NOUN
ejpam-6086	391	4	and	and	CCONJ
ejpam-6086	391	5	applications	application	NOUN
ejpam-6086	391	6	,	,	PUNCT
ejpam-6086	391	7	2015:2	2015:2	NOUN
ejpam-6086	391	8	,	,	PUNCT
ejpam-6086	391	9	2015	2015	NUM
ejpam-6086	391	10	.	.	PUNCT
ejpam-6086	392	1	[	[	X
ejpam-6086	392	2	11	11	NUM
ejpam-6086	392	3	]	]	PUNCT
ejpam-6086	392	4	a.	a.	NOUN
ejpam-6086	392	5	kari	kari	PROPN
ejpam-6086	392	6	,	,	PUNCT
ejpam-6086	392	7	m.	m.	NOUN
ejpam-6086	392	8	rossafi	rossafi	PROPN
ejpam-6086	392	9	,	,	PUNCT
ejpam-6086	392	10	e.	e.	PROPN
ejpam-6086	392	11	marhani	marhani	PROPN
ejpam-6086	392	12	,	,	PUNCT
ejpam-6086	392	13	and	and	CCONJ
ejpam-6086	392	14	m.	m.	NOUN
ejpam-6086	392	15	aamari	aamari	PROPN
ejpam-6086	392	16	.	.	PUNCT
ejpam-6086	393	1	θ	θ	PROPN
ejpam-6086	393	2	−	−	PROPN
ejpam-6086	393	3	ϕ-contraction	ϕ-contraction	NOUN
ejpam-6086	393	4	on	on	ADP
ejpam-6086	393	5	rectangular	rectangular	ADJ
ejpam-6086	393	6	b	b	NOUN
ejpam-6086	393	7	-	-	ADJ
ejpam-6086	393	8	metric	metric	ADJ
ejpam-6086	393	9	spaces	space	NOUN
ejpam-6086	393	10	.	.	PUNCT
ejpam-6086	394	1	international	international	ADJ
ejpam-6086	394	2	journal	journal	PROPN
ejpam-6086	394	3	of	of	ADP
ejpam-6086	394	4	mathematics	mathematics	PROPN
ejpam-6086	394	5	and	and	CCONJ
ejpam-6086	394	6	mathematical	mathematical	ADJ
ejpam-6086	394	7	sciences	science	NOUN
ejpam-6086	394	8	,	,	PUNCT
ejpam-6086	394	9	2020:8817616	2020:8817616	NUM
ejpam-6086	394	10	,	,	PUNCT
ejpam-6086	394	11	2020	2020	NUM
ejpam-6086	394	12	.	.	PUNCT
ejpam-6086	395	1	[	[	X
ejpam-6086	395	2	12	12	NUM
ejpam-6086	395	3	]	]	PUNCT
ejpam-6086	395	4	z.	z.	PROPN
ejpam-6086	395	5	ma	ma	PROPN
ejpam-6086	395	6	,	,	PUNCT
ejpam-6086	395	7	a.	a.	NOUN
ejpam-6086	395	8	asif	asif	PROPN
ejpam-6086	395	9	,	,	PUNCT
ejpam-6086	395	10	h.	h.	PROPN
ejpam-6086	395	11	aydi	aydi	PROPN
ejpam-6086	395	12	,	,	PUNCT
ejpam-6086	395	13	s.	s.	PROPN
ejpam-6086	395	14	u.	u.	PROPN
ejpam-6086	395	15	khan	khan	PROPN
ejpam-6086	395	16	,	,	PUNCT
ejpam-6086	395	17	and	and	CCONJ
ejpam-6086	395	18	m.	m.	PROPN
ejpam-6086	395	19	arshad	arshad	PROPN
ejpam-6086	395	20	.	.	PROPN
ejpam-6086	396	1	analysis	analysis	NOUN
ejpam-6086	396	2	of	of	ADP
ejpam-6086	396	3	f	f	NOUN
ejpam-6086	396	4	-	-	PUNCT
ejpam-6086	396	5	contractions	contraction	NOUN
ejpam-6086	396	6	in	in	ADP
ejpam-6086	396	7	function	function	NOUN
ejpam-6086	396	8	weighted	weight	VERB
ejpam-6086	396	9	metric	metric	ADJ
ejpam-6086	396	10	spaces	space	NOUN
ejpam-6086	396	11	with	with	ADP
ejpam-6086	396	12	an	an	DET
ejpam-6086	396	13	application	application	NOUN
ejpam-6086	396	14	.	.	PUNCT
ejpam-6086	397	1	open	open	ADJ
ejpam-6086	397	2	mathematics	mathematic	NOUN
ejpam-6086	397	3	,	,	PUNCT
ejpam-6086	397	4	18(1):582	18(1):582	NUM
ejpam-6086	397	5	–	–	PUNCT
ejpam-6086	397	6	594	594	NUM
ejpam-6086	397	7	,	,	PUNCT
ejpam-6086	397	8	2020	2020	NUM
ejpam-6086	397	9	.	.	PUNCT
ejpam-6086	398	1	[	[	X
ejpam-6086	398	2	13	13	NUM
ejpam-6086	398	3	]	]	PUNCT
ejpam-6086	398	4	j.	j.	PROPN
ejpam-6086	398	5	r.	r.	PROPN
ejpam-6086	398	6	roshan	roshan	PROPN
ejpam-6086	398	7	,	,	PUNCT
ejpam-6086	398	8	v.	v.	CCONJ
ejpam-6086	398	9	parvaneh	parvaneh	PROPN
ejpam-6086	398	10	,	,	PUNCT
ejpam-6086	398	11	z.	z.	PROPN
ejpam-6086	398	12	kadelburg	kadelburg	PROPN
ejpam-6086	398	13	,	,	PUNCT
ejpam-6086	398	14	and	and	CCONJ
ejpam-6086	398	15	n.	n.	PROPN
ejpam-6086	398	16	hussain	hussain	PROPN
ejpam-6086	398	17	.	.	PUNCT
ejpam-6086	399	1	new	new	ADJ
ejpam-6086	399	2	fixed	fix	VERB
ejpam-6086	399	3	point	point	NOUN
ejpam-6086	399	4	results	result	NOUN
ejpam-6086	399	5	in	in	ADP
ejpam-6086	399	6	b	b	NOUN
ejpam-6086	399	7	-	-	ADJ
ejpam-6086	399	8	rectangular	rectangular	ADJ
ejpam-6086	399	9	metric	metric	ADJ
ejpam-6086	399	10	spaces	space	NOUN
ejpam-6086	399	11	.	.	PUNCT
ejpam-6086	400	1	nonlinear	nonlinear	ADJ
ejpam-6086	400	2	analysis	analysis	NOUN
ejpam-6086	400	3	:	:	PUNCT
ejpam-6086	400	4	modelling	modelling	NOUN
ejpam-6086	400	5	and	and	CCONJ
ejpam-6086	400	6	control	control	NOUN
ejpam-6086	400	7	,	,	PUNCT
ejpam-6086	400	8	21(5):614	21(5):614	NUM
ejpam-6086	400	9	–	–	PUNCT
ejpam-6086	400	10	634	634	NUM
ejpam-6086	400	11	,	,	PUNCT
ejpam-6086	400	12	2016	2016	NUM
ejpam-6086	400	13	.	.	PUNCT
ejpam-6086	401	1	[	[	X
ejpam-6086	401	2	14	14	NUM
ejpam-6086	401	3	]	]	X
ejpam-6086	401	4	d.	d.	PROPN
ejpam-6086	401	5	w.	w.	PROPN
ejpam-6086	401	6	zheng	zheng	PROPN
ejpam-6086	401	7	,	,	PUNCT
ejpam-6086	401	8	z.	z.	PROPN
ejpam-6086	401	9	y.	y.	PROPN
ejpam-6086	401	10	cai	cai	PROPN
ejpam-6086	401	11	,	,	PUNCT
ejpam-6086	401	12	and	and	CCONJ
ejpam-6086	401	13	p.	p.	PROPN
ejpam-6086	401	14	wang	wang	PROPN
ejpam-6086	401	15	.	.	PUNCT
ejpam-6086	402	1	new	new	ADJ
ejpam-6086	402	2	fixed	fix	VERB
ejpam-6086	402	3	point	point	NOUN
ejpam-6086	402	4	theorems	theorem	NOUN
ejpam-6086	402	5	for	for	ADP
ejpam-6086	402	6	θ	θ	PROPN
ejpam-6086	402	7	−	−	PROPN
ejpam-6086	402	8	ϕcontraction	ϕcontraction	NOUN
ejpam-6086	402	9	in	in	ADP
ejpam-6086	402	10	complete	complete	ADJ
ejpam-6086	402	11	metric	metric	ADJ
ejpam-6086	402	12	spaces	space	NOUN
ejpam-6086	402	13	.	.	PUNCT
ejpam-6086	403	1	journal	journal	PROPN
ejpam-6086	403	2	of	of	ADP
ejpam-6086	403	3	nonlinear	nonlinear	PROPN
ejpam-6086	403	4	sciences	sciences	PROPN
ejpam-6086	403	5	and	and	CCONJ
ejpam-6086	403	6	applications	application	NOUN
ejpam-6086	403	7	,	,	PUNCT
ejpam-6086	403	8	10(5):2662–2670	10(5):2662–2670	NUM
ejpam-6086	403	9	,	,	PUNCT
ejpam-6086	403	10	2017	2017	NUM
ejpam-6086	403	11	.	.	PUNCT
ejpam-6086	404	1	[	[	X
ejpam-6086	404	2	15	15	NUM
ejpam-6086	404	3	]	]	X
ejpam-6086	404	4	s.	s.	PROPN
ejpam-6086	404	5	b.	b.	PROPN
ejpam-6086	404	6	nadler	nadler	PROPN
ejpam-6086	404	7	.	.	PUNCT
ejpam-6086	404	8	multivalued	multivalue	VERB
ejpam-6086	404	9	contraction	contraction	NOUN
ejpam-6086	404	10	mappings	mapping	NOUN
ejpam-6086	404	11	.	.	PUNCT
ejpam-6086	405	1	pacific	pacific	PROPN
ejpam-6086	405	2	journal	journal	PROPN
ejpam-6086	405	3	of	of	ADP
ejpam-6086	405	4	mathematics	mathematic	NOUN
ejpam-6086	405	5	,	,	PUNCT
ejpam-6086	405	6	30(2):475–488	30(2):475–488	PROPN
ejpam-6086	405	7	,	,	PUNCT
ejpam-6086	405	8	1969	1969	NUM
ejpam-6086	405	9	.	.	PUNCT
ejpam-6086	406	1	[	[	X
ejpam-6086	406	2	16	16	NUM
ejpam-6086	406	3	]	]	PUNCT
ejpam-6086	406	4	r.	r.	PROPN
ejpam-6086	406	5	kannan	kannan	PROPN
ejpam-6086	406	6	.	.	PUNCT
ejpam-6086	407	1	some	some	DET
ejpam-6086	407	2	results	result	NOUN
ejpam-6086	407	3	on	on	ADP
ejpam-6086	407	4	fixed	fixed	ADJ
ejpam-6086	407	5	points	point	NOUN
ejpam-6086	407	6	—	—	PUNCT
ejpam-6086	407	7	ii	ii	NOUN
ejpam-6086	407	8	.	.	PUNCT
ejpam-6086	408	1	the	the	DET
ejpam-6086	408	2	american	american	PROPN
ejpam-6086	408	3	mathematical	mathematical	PROPN
ejpam-6086	408	4	monthly	monthly	ADV
ejpam-6086	408	5	,	,	PUNCT
ejpam-6086	408	6	h.	h.	PROPN
ejpam-6086	408	7	massit	massit	PROPN
ejpam-6086	408	8	et	et	PROPN
ejpam-6086	408	9	al	al	PROPN
ejpam-6086	408	10	.	.	PUNCT
ejpam-6086	408	11	/	/	SYM
ejpam-6086	408	12	eur	eur	PROPN
ejpam-6086	408	13	.	.	PUNCT
ejpam-6086	409	1	j.	j.	PROPN
ejpam-6086	409	2	pure	pure	PROPN
ejpam-6086	409	3	appl	appl	PROPN
ejpam-6086	409	4	.	.	PROPN
ejpam-6086	409	5	math	math	PROPN
ejpam-6086	409	6	,	,	PUNCT
ejpam-6086	409	7	18	18	NUM
ejpam-6086	409	8	(	(	PUNCT
ejpam-6086	409	9	2	2	NUM
ejpam-6086	409	10	)	)	PUNCT
ejpam-6086	409	11	(	(	PUNCT
ejpam-6086	409	12	2025	2025	NUM
ejpam-6086	409	13	)	)	PUNCT
ejpam-6086	409	14	,	,	PUNCT
ejpam-6086	409	15	6086	6086	NUM
ejpam-6086	409	16	19	19	NUM
ejpam-6086	409	17	of	of	ADP
ejpam-6086	409	18	19	19	NUM
ejpam-6086	409	19	76(4):405–408	76(4):405–408	NUM
ejpam-6086	409	20	,	,	PUNCT
ejpam-6086	409	21	1969	1969	NUM
ejpam-6086	409	22	.	.	PUNCT
ejpam-6086	410	1	[	[	X
ejpam-6086	410	2	17	17	NUM
ejpam-6086	410	3	]	]	X
ejpam-6086	410	4	s.	s.	PROPN
ejpam-6086	410	5	reich	reich	PROPN
ejpam-6086	410	6	.	.	PUNCT
ejpam-6086	411	1	some	some	DET
ejpam-6086	411	2	remarks	remark	NOUN
ejpam-6086	411	3	concerning	concern	VERB
ejpam-6086	411	4	contraction	contraction	NOUN
ejpam-6086	411	5	mappings	mapping	NOUN
ejpam-6086	411	6	.	.	PUNCT
ejpam-6086	412	1	canadian	canadian	ADJ
ejpam-6086	412	2	mathematical	mathematical	ADJ
ejpam-6086	412	3	bulletin	bulletin	NOUN
ejpam-6086	412	4	,	,	PUNCT
ejpam-6086	412	5	14(2):121–124	14(2):121–124	NUM
ejpam-6086	412	6	,	,	PUNCT
ejpam-6086	412	7	1971	1971	NUM
ejpam-6086	412	8	.	.	PUNCT
ejpam-6086	413	1	[	[	X
ejpam-6086	413	2	18	18	NUM
ejpam-6086	413	3	]	]	X
ejpam-6086	413	4	b.	b.	NOUN
ejpam-6086	413	5	mohammadi	mohammadi	PROPN
ejpam-6086	413	6	,	,	PUNCT
ejpam-6086	413	7	s.	s.	PROPN
ejpam-6086	413	8	rezapour	rezapour	PROPN
ejpam-6086	413	9	,	,	PUNCT
ejpam-6086	413	10	and	and	CCONJ
ejpam-6086	413	11	n.	n.	PROPN
ejpam-6086	413	12	shahzad	shahzad	PROPN
ejpam-6086	413	13	.	.	PUNCT
ejpam-6086	414	1	some	some	DET
ejpam-6086	414	2	results	result	NOUN
ejpam-6086	414	3	on	on	ADP
ejpam-6086	414	4	fixed	fix	VERB
ejpam-6086	414	5	points	point	NOUN
ejpam-6086	414	6	of	of	ADP
ejpam-6086	414	7	α−ψciric	α−ψciric	ADP
ejpam-6086	414	8	generalized	generalized	ADJ
ejpam-6086	414	9	multifunctions	multifunction	NOUN
ejpam-6086	414	10	.	.	PUNCT
ejpam-6086	415	1	fixed	fix	VERB
ejpam-6086	415	2	point	point	NOUN
ejpam-6086	415	3	theory	theory	NOUN
ejpam-6086	415	4	and	and	CCONJ
ejpam-6086	415	5	applications	application	NOUN
ejpam-6086	415	6	,	,	PUNCT
ejpam-6086	415	7	2013:24	2013:24	NUM
ejpam-6086	415	8	,	,	PUNCT
ejpam-6086	415	9	2013	2013	NUM
ejpam-6086	415	10	.	.	PUNCT
ejpam-6086	416	1	[	[	X
ejpam-6086	416	2	19	19	NUM
ejpam-6086	416	3	]	]	X
ejpam-6086	416	4	d.	d.	PROPN
ejpam-6086	416	5	k.	k.	PROPN
ejpam-6086	416	6	patel	patel	PROPN
ejpam-6086	416	7	.	.	PUNCT
ejpam-6086	417	1	fixed	fix	VERB
ejpam-6086	417	2	points	point	NOUN
ejpam-6086	417	3	of	of	ADP
ejpam-6086	417	4	multivalued	multivalued	ADJ
ejpam-6086	417	5	contractions	contraction	NOUN
ejpam-6086	417	6	via	via	ADP
ejpam-6086	417	7	generalized	generalized	ADJ
ejpam-6086	417	8	class	class	NOUN
ejpam-6086	417	9	of	of	ADP
ejpam-6086	417	10	simulation	simulation	NOUN
ejpam-6086	417	11	functions	function	NOUN
ejpam-6086	417	12	.	.	PUNCT
ejpam-6086	418	1	boletim	boletim	PROPN
ejpam-6086	418	2	da	da	PROPN
ejpam-6086	418	3	sociedade	sociedade	PROPN
ejpam-6086	418	4	paranaense	paranaense	PROPN
ejpam-6086	418	5	de	de	PROPN
ejpam-6086	418	6	matemática	matemática	PROPN
ejpam-6086	418	7	,	,	PUNCT
ejpam-6086	418	8	38(3):161–179	38(3):161–179	PROPN
ejpam-6086	418	9	,	,	PUNCT
ejpam-6086	418	10	2020	2020	NUM
ejpam-6086	418	11	.	.	PUNCT