id	sid	tid	token	lemma	pos
ejpam-5730	1	1	european	european	PROPN
ejpam-5730	1	2	journal	journal	PROPN
ejpam-5730	1	3	of	of	ADP
ejpam-5730	1	4	pure	pure	ADJ
ejpam-5730	1	5	and	and	CCONJ
ejpam-5730	1	6	applied	applied	ADJ
ejpam-5730	1	7	mathematics	mathematic	NOUN
ejpam-5730	1	8	2025	2025	NUM
ejpam-5730	1	9	,	,	PUNCT
ejpam-5730	1	10	vol	vol	NOUN
ejpam-5730	1	11	.	.	PROPN
ejpam-5730	1	12	18	18	NUM
ejpam-5730	1	13	,	,	PUNCT
ejpam-5730	1	14	issue	issue	NOUN
ejpam-5730	1	15	1	1	NUM
ejpam-5730	1	16	,	,	PUNCT
ejpam-5730	1	17	article	article	NOUN
ejpam-5730	1	18	number	number	NOUN
ejpam-5730	1	19	5730	5730	NUM
ejpam-5730	1	20	issn	issn	PROPN
ejpam-5730	1	21	1307	1307	NUM
ejpam-5730	1	22	-	-	SYM
ejpam-5730	1	23	5543	5543	NUM
ejpam-5730	1	24	–	–	PUNCT
ejpam-5730	1	25	ejpam.com	ejpam.com	X
ejpam-5730	1	26	published	publish	VERB
ejpam-5730	1	27	by	by	ADP
ejpam-5730	1	28	new	new	PROPN
ejpam-5730	1	29	york	york	PROPN
ejpam-5730	1	30	business	business	PROPN
ejpam-5730	1	31	global	global	ADJ
ejpam-5730	1	32	new	new	ADJ
ejpam-5730	1	33	proofs	proof	NOUN
ejpam-5730	1	34	of	of	ADP
ejpam-5730	1	35	fixed	fix	VERB
ejpam-5730	1	36	point	point	NOUN
ejpam-5730	1	37	theorems	theorem	NOUN
ejpam-5730	1	38	on	on	ADP
ejpam-5730	1	39	quasi	quasi	ADJ
ejpam-5730	1	40	-	-	ADJ
ejpam-5730	1	41	metric	metric	ADJ
ejpam-5730	1	42	spaces	space	NOUN
ejpam-5730	1	43	sehie	sehie	NOUN
ejpam-5730	1	44	park1,2	park1,2	PROPN
ejpam-5730	1	45	1	1	NUM
ejpam-5730	1	46	the	the	DET
ejpam-5730	1	47	national	national	PROPN
ejpam-5730	1	48	academy	academy	PROPN
ejpam-5730	1	49	of	of	ADP
ejpam-5730	1	50	sciences	sciences	PROPN
ejpam-5730	1	51	,	,	PUNCT
ejpam-5730	1	52	republic	republic	NOUN
ejpam-5730	1	53	of	of	ADP
ejpam-5730	1	54	korea	korea	PROPN
ejpam-5730	1	55	,	,	PUNCT
ejpam-5730	1	56	seoul	seoul	PROPN
ejpam-5730	1	57	06579	06579	NUM
ejpam-5730	1	58	2	2	NUM
ejpam-5730	1	59	department	department	NOUN
ejpam-5730	1	60	of	of	ADP
ejpam-5730	1	61	mathematical	mathematical	ADJ
ejpam-5730	1	62	sciences	sciences	PROPN
ejpam-5730	1	63	,	,	PUNCT
ejpam-5730	1	64	seoul	seoul	PROPN
ejpam-5730	1	65	national	national	PROPN
ejpam-5730	1	66	university	university	PROPN
ejpam-5730	1	67	,	,	PUNCT
ejpam-5730	1	68	seoul	seoul	PROPN
ejpam-5730	1	69	08826	08826	NUM
ejpam-5730	1	70	,	,	PUNCT
ejpam-5730	1	71	korea	korea	PROPN
ejpam-5730	1	72	abstract	abstract	NOUN
ejpam-5730	1	73	.	.	PUNCT
ejpam-5730	2	1	based	base	VERB
ejpam-5730	2	2	on	on	ADP
ejpam-5730	2	3	our	our	PRON
ejpam-5730	2	4	2023	2023	NUM
ejpam-5730	2	5	metatheorem	metatheorem	VERB
ejpam-5730	2	6	in	in	ADP
ejpam-5730	2	7	ordered	order	VERB
ejpam-5730	2	8	fixed	fix	VERB
ejpam-5730	2	9	point	point	NOUN
ejpam-5730	2	10	theory	theory	NOUN
ejpam-5730	2	11	,	,	PUNCT
ejpam-5730	2	12	we	we	PRON
ejpam-5730	2	13	give	give	VERB
ejpam-5730	2	14	very	very	ADV
ejpam-5730	2	15	simple	simple	ADJ
ejpam-5730	2	16	proofs	proof	NOUN
ejpam-5730	2	17	of	of	ADP
ejpam-5730	2	18	known	know	VERB
ejpam-5730	2	19	fixed	fix	VERB
ejpam-5730	2	20	point	point	NOUN
ejpam-5730	2	21	theorems	theorem	NOUN
ejpam-5730	2	22	for	for	ADP
ejpam-5730	2	23	various	various	ADJ
ejpam-5730	2	24	multimap	multimap	ADJ
ejpam-5730	2	25	classes	class	NOUN
ejpam-5730	2	26	on	on	ADP
ejpam-5730	2	27	quasi	quasi	ADJ
ejpam-5730	2	28	-	-	ADJ
ejpam-5730	2	29	metric	metric	ADJ
ejpam-5730	2	30	spaces	space	NOUN
ejpam-5730	2	31	.	.	PUNCT
ejpam-5730	3	1	such	such	ADJ
ejpam-5730	3	2	classes	class	NOUN
ejpam-5730	3	3	are	be	AUX
ejpam-5730	3	4	represented	represent	VERB
ejpam-5730	3	5	by	by	ADP
ejpam-5730	3	6	the	the	DET
ejpam-5730	3	7	banach	banach	NOUN
ejpam-5730	3	8	contractions	contraction	NOUN
ejpam-5730	3	9	,	,	PUNCT
ejpam-5730	3	10	the	the	DET
ejpam-5730	3	11	rus	rus	NOUN
ejpam-5730	3	12	-	-	PUNCT
ejpam-5730	3	13	hicks	hick	NOUN
ejpam-5730	3	14	-	-	PUNCT
ejpam-5730	3	15	rhoades	rhoade	NOUN
ejpam-5730	3	16	maps	map	NOUN
ejpam-5730	3	17	,	,	PUNCT
ejpam-5730	3	18	the	the	DET
ejpam-5730	3	19	nadler	nadler	NOUN
ejpam-5730	3	20	multimaps	multimap	NOUN
ejpam-5730	3	21	,	,	PUNCT
ejpam-5730	3	22	covitz	covitz	NOUN
ejpam-5730	3	23	-	-	PUNCT
ejpam-5730	3	24	nadler	nadler	NOUN
ejpam-5730	3	25	multimaps	multimap	NOUN
ejpam-5730	3	26	,	,	PUNCT
ejpam-5730	3	27	and	and	CCONJ
ejpam-5730	3	28	others	other	NOUN
ejpam-5730	3	29	.	.	PUNCT
ejpam-5730	4	1	consequently	consequently	ADV
ejpam-5730	4	2	,	,	PUNCT
ejpam-5730	4	3	we	we	PRON
ejpam-5730	4	4	obtain	obtain	VERB
ejpam-5730	4	5	simple	simple	ADJ
ejpam-5730	4	6	proofs	proof	NOUN
ejpam-5730	4	7	of	of	ADP
ejpam-5730	4	8	a	a	DET
ejpam-5730	4	9	large	large	ADJ
ejpam-5730	4	10	number	number	NOUN
ejpam-5730	4	11	of	of	ADP
ejpam-5730	4	12	known	know	VERB
ejpam-5730	4	13	theorems	theorem	NOUN
ejpam-5730	4	14	on	on	ADP
ejpam-5730	4	15	extremal	extremal	ADJ
ejpam-5730	4	16	elements	element	NOUN
ejpam-5730	4	17	,	,	PUNCT
ejpam-5730	4	18	fixed	fix	VERB
ejpam-5730	4	19	points	point	NOUN
ejpam-5730	4	20	,	,	PUNCT
ejpam-5730	4	21	stationary	stationary	ADJ
ejpam-5730	4	22	points	point	NOUN
ejpam-5730	4	23	for	for	ADP
ejpam-5730	4	24	several	several	ADJ
ejpam-5730	4	25	classes	class	NOUN
ejpam-5730	4	26	of	of	ADP
ejpam-5730	4	27	maps	map	NOUN
ejpam-5730	4	28	or	or	CCONJ
ejpam-5730	4	29	multimaps	multimap	NOUN
ejpam-5730	4	30	.	.	PUNCT
ejpam-5730	5	1	finally	finally	ADV
ejpam-5730	5	2	,	,	PUNCT
ejpam-5730	5	3	we	we	PRON
ejpam-5730	5	4	add	add	VERB
ejpam-5730	5	5	some	some	DET
ejpam-5730	5	6	known	know	VERB
ejpam-5730	5	7	theorems	theorem	NOUN
ejpam-5730	5	8	for	for	ADP
ejpam-5730	5	9	which	which	PRON
ejpam-5730	5	10	our	our	PRON
ejpam-5730	5	11	metatheorem	metatheorem	NOUN
ejpam-5730	5	12	does	do	AUX
ejpam-5730	5	13	not	not	PART
ejpam-5730	5	14	work	work	VERB
ejpam-5730	5	15	.	.	PUNCT
ejpam-5730	6	1	2020	2020	NUM
ejpam-5730	6	2	mathematics	mathematic	NOUN
ejpam-5730	6	3	subject	subject	NOUN
ejpam-5730	6	4	classifications	classification	NOUN
ejpam-5730	6	5	:	:	PUNCT
ejpam-5730	6	6	06a75	06a75	NUM
ejpam-5730	6	7	,	,	PUNCT
ejpam-5730	6	8	47h10	47h10	NUM
ejpam-5730	6	9	,	,	PUNCT
ejpam-5730	6	10	54e35	54e35	NUM
ejpam-5730	6	11	,	,	PUNCT
ejpam-5730	6	12	54h25	54h25	NUM
ejpam-5730	6	13	,	,	PUNCT
ejpam-5730	6	14	58e30	58e30	NUM
ejpam-5730	6	15	,	,	PUNCT
ejpam-5730	6	16	65k10	65k10	NUM
ejpam-5730	6	17	key	key	ADJ
ejpam-5730	6	18	words	word	NOUN
ejpam-5730	6	19	and	and	CCONJ
ejpam-5730	6	20	phrases	phrase	NOUN
ejpam-5730	6	21	:	:	PUNCT
ejpam-5730	6	22	fixed	fixed	ADJ
ejpam-5730	6	23	point	point	NOUN
ejpam-5730	6	24	,	,	PUNCT
ejpam-5730	6	25	quasi	quasi	ADJ
ejpam-5730	6	26	-	-	ADJ
ejpam-5730	6	27	metric	metric	ADJ
ejpam-5730	6	28	space	space	NOUN
ejpam-5730	6	29	,	,	PUNCT
ejpam-5730	6	30	banach	banach	NOUN
ejpam-5730	6	31	contraction	contraction	NOUN
ejpam-5730	6	32	,	,	PUNCT
ejpam-5730	6	33	rus	rus	NOUN
ejpam-5730	6	34	-	-	PUNCT
ejpam-5730	6	35	hicksrhoades	hicksrhoade	NOUN
ejpam-5730	6	36	map	map	NOUN
ejpam-5730	6	37	,	,	PUNCT
ejpam-5730	6	38	nadler	nadler	PROPN
ejpam-5730	6	39	multimap	multimap	PROPN
ejpam-5730	6	40	,	,	PUNCT
ejpam-5730	6	41	covitz	covitz	NOUN
ejpam-5730	6	42	-	-	PUNCT
ejpam-5730	6	43	nadler	nadler	NOUN
ejpam-5730	6	44	multimap	multimap	NOUN
ejpam-5730	6	45	,	,	PUNCT
ejpam-5730	6	46	extremal	extremal	ADJ
ejpam-5730	6	47	point	point	NOUN
ejpam-5730	6	48	,	,	PUNCT
ejpam-5730	6	49	stationary	stationary	ADJ
ejpam-5730	6	50	point	point	NOUN
ejpam-5730	6	51	1	1	NUM
ejpam-5730	6	52	.	.	PUNCT
ejpam-5730	7	1	introduction	introduction	NOUN
ejpam-5730	7	2	let	let	VERB
ejpam-5730	7	3	(	(	PUNCT
ejpam-5730	7	4	x	x	NOUN
ejpam-5730	7	5	,	,	PUNCT
ejpam-5730	7	6	d	d	NOUN
ejpam-5730	7	7	)	)	PUNCT
ejpam-5730	7	8	be	be	AUX
ejpam-5730	7	9	a	a	DET
ejpam-5730	7	10	metric	metric	ADJ
ejpam-5730	7	11	space	space	NOUN
ejpam-5730	7	12	.	.	PUNCT
ejpam-5730	8	1	a	a	DET
ejpam-5730	8	2	banach	banach	NOUN
ejpam-5730	8	3	contraction	contraction	NOUN
ejpam-5730	8	4	t	t	NOUN
ejpam-5730	8	5	:	:	PUNCT
ejpam-5730	8	6	x	x	X
ejpam-5730	8	7	→	→	PUNCT
ejpam-5730	8	8	x	x	X
ejpam-5730	8	9	is	be	AUX
ejpam-5730	8	10	a	a	DET
ejpam-5730	8	11	map	map	NOUN
ejpam-5730	8	12	such	such	ADJ
ejpam-5730	8	13	that	that	SCONJ
ejpam-5730	8	14	,	,	PUNCT
ejpam-5730	8	15	for	for	ADP
ejpam-5730	8	16	some	some	DET
ejpam-5730	8	17	r	r	NOUN
ejpam-5730	8	18	∈	∈	PROPN
ejpam-5730	8	19	(	(	PUNCT
ejpam-5730	8	20	0	0	NUM
ejpam-5730	8	21	,	,	PUNCT
ejpam-5730	8	22	1	1	NUM
ejpam-5730	8	23	)	)	PUNCT
ejpam-5730	8	24	,	,	PUNCT
ejpam-5730	8	25	d(tx	d(tx	PROPN
ejpam-5730	8	26	,	,	PUNCT
ejpam-5730	8	27	ty	ty	NOUN
ejpam-5730	8	28	)	)	PUNCT
ejpam-5730	8	29	≤	≤	NOUN
ejpam-5730	8	30	r	r	NOUN
ejpam-5730	8	31	d(x	d(x	PROPN
ejpam-5730	8	32	,	,	PUNCT
ejpam-5730	8	33	y	y	NOUN
ejpam-5730	8	34	)	)	PUNCT
ejpam-5730	8	35	∀	∀	PUNCT
ejpam-5730	9	1	x	x	NOUN
ejpam-5730	9	2	,	,	PUNCT
ejpam-5730	9	3	y	y	PROPN
ejpam-5730	9	4	∈	∈	PROPN
ejpam-5730	9	5	x.	x.	NOUN
ejpam-5730	9	6	there	there	PRON
ejpam-5730	9	7	have	have	AUX
ejpam-5730	9	8	been	be	AUX
ejpam-5730	9	9	appeared	appear	VERB
ejpam-5730	9	10	thousands	thousand	NOUN
ejpam-5730	9	11	of	of	ADP
ejpam-5730	9	12	articles	article	NOUN
ejpam-5730	9	13	related	relate	VERB
ejpam-5730	9	14	to	to	ADP
ejpam-5730	9	15	generalizations	generalization	NOUN
ejpam-5730	9	16	of	of	ADP
ejpam-5730	9	17	the	the	DET
ejpam-5730	9	18	banach	banach	NOUN
ejpam-5730	9	19	contraction	contraction	NOUN
ejpam-5730	9	20	.	.	PUNCT
ejpam-5730	10	1	recently	recently	ADV
ejpam-5730	10	2	,	,	PUNCT
ejpam-5730	10	3	we	we	PRON
ejpam-5730	10	4	introduced	introduce	VERB
ejpam-5730	10	5	the	the	DET
ejpam-5730	10	6	rus	rus	NOUN
ejpam-5730	10	7	-	-	PUNCT
ejpam-5730	10	8	hicks	hick	NOUN
ejpam-5730	10	9	-	-	PUNCT
ejpam-5730	10	10	rhoades	rhoade	NOUN
ejpam-5730	10	11	(	(	PUNCT
ejpam-5730	10	12	rhr	rhr	PROPN
ejpam-5730	10	13	)	)	PUNCT
ejpam-5730	10	14	map	map	NOUN
ejpam-5730	10	15	t	t	NOUN
ejpam-5730	10	16	:	:	PUNCT
ejpam-5730	10	17	x	x	X
ejpam-5730	10	18	→	→	SYM
ejpam-5730	10	19	x	x	SYM
ejpam-5730	10	20	for	for	ADP
ejpam-5730	10	21	some	some	DET
ejpam-5730	10	22	r	r	NOUN
ejpam-5730	10	23	∈	∈	PROPN
ejpam-5730	10	24	(	(	PUNCT
ejpam-5730	10	25	0	0	NUM
ejpam-5730	10	26	,	,	PUNCT
ejpam-5730	10	27	1	1	X
ejpam-5730	10	28	)	)	PUNCT
ejpam-5730	10	29	satisfying	satisfy	VERB
ejpam-5730	10	30	d(tx	d(tx	PROPN
ejpam-5730	10	31	,	,	PUNCT
ejpam-5730	10	32	t	t	PROPN
ejpam-5730	10	33	2x	2x	NUM
ejpam-5730	10	34	)	)	PUNCT
ejpam-5730	10	35	≤	≤	NUM
ejpam-5730	10	36	r	r	NOUN
ejpam-5730	10	37	d(x	d(x	NOUN
ejpam-5730	10	38	,	,	PUNCT
ejpam-5730	10	39	tx	tx	PROPN
ejpam-5730	10	40	)	)	PUNCT
ejpam-5730	10	41	∀	∀	X
ejpam-5730	10	42	x	x	X
ejpam-5730	11	1	∈	∈	NOUN
ejpam-5730	11	2	x.	x.	NOUN
ejpam-5730	11	3	we	we	PRON
ejpam-5730	11	4	found	find	VERB
ejpam-5730	11	5	that	that	SCONJ
ejpam-5730	11	6	the	the	DET
ejpam-5730	11	7	class	class	NOUN
ejpam-5730	11	8	of	of	ADP
ejpam-5730	11	9	the	the	DET
ejpam-5730	11	10	rus	rus	NOUN
ejpam-5730	11	11	-	-	PUNCT
ejpam-5730	11	12	hicks	hick	NOUN
ejpam-5730	11	13	-	-	PUNCT
ejpam-5730	11	14	rhoades	rhoade	NOUN
ejpam-5730	11	15	maps	map	NOUN
ejpam-5730	11	16	contains	contain	VERB
ejpam-5730	11	17	a	a	DET
ejpam-5730	11	18	large	large	ADJ
ejpam-5730	11	19	number	number	NOUN
ejpam-5730	11	20	of	of	ADP
ejpam-5730	11	21	maps	map	NOUN
ejpam-5730	11	22	including	include	VERB
ejpam-5730	11	23	banach	banach	NOUN
ejpam-5730	11	24	contractions	contraction	NOUN
ejpam-5730	11	25	.	.	PUNCT
ejpam-5730	12	1	see	see	VERB
ejpam-5730	12	2	our	our	PRON
ejpam-5730	12	3	recent	recent	ADJ
ejpam-5730	12	4	works	work	NOUN
ejpam-5730	12	5	[	[	X
ejpam-5730	12	6	33	33	NUM
ejpam-5730	12	7	]	]	PUNCT
ejpam-5730	12	8	,	,	PUNCT
ejpam-5730	12	9	[	[	X
ejpam-5730	12	10	35	35	NUM
ejpam-5730	12	11	]	]	PUNCT
ejpam-5730	12	12	,	,	PUNCT
ejpam-5730	12	13	[	[	X
ejpam-5730	12	14	39	39	NUM
ejpam-5730	12	15	]	]	PUNCT
ejpam-5730	12	16	.	.	PUNCT
ejpam-5730	13	1	moreover	moreover	ADV
ejpam-5730	13	2	,	,	PUNCT
ejpam-5730	13	3	we	we	PRON
ejpam-5730	13	4	found	find	VERB
ejpam-5730	13	5	that	that	SCONJ
ejpam-5730	13	6	the	the	DET
ejpam-5730	13	7	rhr	rhr	PROPN
ejpam-5730	13	8	maps	maps	PROPN
ejpam-5730	13	9	characterize	characterize	VERB
ejpam-5730	13	10	the	the	DET
ejpam-5730	13	11	metric	metric	ADJ
ejpam-5730	13	12	completeness	completeness	NOUN
ejpam-5730	13	13	.	.	PUNCT
ejpam-5730	14	1	see	see	VERB
ejpam-5730	14	2	[	[	X
ejpam-5730	14	3	39	39	NUM
ejpam-5730	14	4	]	]	PUNCT
ejpam-5730	14	5	,	,	PUNCT
ejpam-5730	14	6	[	[	X
ejpam-5730	14	7	40	40	NUM
ejpam-5730	14	8	]	]	PUNCT
ejpam-5730	14	9	.	.	PUNCT
ejpam-5730	15	1	in	in	ADP
ejpam-5730	15	2	our	our	PRON
ejpam-5730	15	3	previous	previous	ADJ
ejpam-5730	15	4	work	work	NOUN
ejpam-5730	15	5	[	[	X
ejpam-5730	15	6	40	40	NUM
ejpam-5730	15	7	]	]	PUNCT
ejpam-5730	15	8	,	,	PUNCT
ejpam-5730	15	9	we	we	PRON
ejpam-5730	15	10	classified	classify	VERB
ejpam-5730	15	11	known	know	VERB
ejpam-5730	15	12	fixed	fix	VERB
ejpam-5730	15	13	point	point	NOUN
ejpam-5730	15	14	theorems	theorem	NOUN
ejpam-5730	15	15	equivalent	equivalent	ADJ
ejpam-5730	15	16	to	to	ADP
ejpam-5730	15	17	quasimetric	quasimetric	ADJ
ejpam-5730	15	18	completeness	completeness	NOUN
ejpam-5730	15	19	based	base	VERB
ejpam-5730	15	20	on	on	ADP
ejpam-5730	15	21	our	our	PRON
ejpam-5730	15	22	2023	2023	NUM
ejpam-5730	15	23	metatheorem	metatheorem	VERB
ejpam-5730	15	24	in	in	ADP
ejpam-5730	15	25	ordered	order	VERB
ejpam-5730	15	26	fixed	fix	VERB
ejpam-5730	15	27	point	point	NOUN
ejpam-5730	15	28	theory	theory	NOUN
ejpam-5730	15	29	[	[	X
ejpam-5730	15	30	30	30	NUM
ejpam-5730	15	31	]	]	PUNCT
ejpam-5730	15	32	,	,	PUNCT
ejpam-5730	15	33	doi	doi	NOUN
ejpam-5730	15	34	:	:	PUNCT
ejpam-5730	15	35	https://doi.org/10.29020/nybg.ejpam.v18i1.5730	https://doi.org/10.29020/nybg.ejpam.v18i1.5730	NUM
ejpam-5730	15	36	email	email	NOUN
ejpam-5730	15	37	addresses	address	NOUN
ejpam-5730	15	38	:	:	PUNCT
ejpam-5730	15	39	park35@snu.ac.kr	park35@snu.ac.kr	PUNCT
ejpam-5730	15	40	,	,	PUNCT
ejpam-5730	15	41	sehiepark@gmail.com	sehiepark@gmail.com	X
ejpam-5730	15	42	(	(	PUNCT
ejpam-5730	15	43	s.	s.	PROPN
ejpam-5730	15	44	park	park	PROPN
ejpam-5730	15	45	)	)	PUNCT
ejpam-5730	15	46	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5730	16	1	1	1	NUM
ejpam-5730	16	2	copyright	copyright	NOUN
ejpam-5730	16	3	:	:	PUNCT
ejpam-5730	16	4	©	©	PROPN
ejpam-5730	16	5	2025	2025	NUM
ejpam-5730	16	6	the	the	DET
ejpam-5730	16	7	author(s	author(s	NOUN
ejpam-5730	16	8	)	)	PUNCT
ejpam-5730	16	9	.	.	PUNCT
ejpam-5730	17	1	(	(	PUNCT
ejpam-5730	17	2	cc	cc	NOUN
ejpam-5730	17	3	by	by	ADP
ejpam-5730	17	4	-	-	PUNCT
ejpam-5730	17	5	nc	nc	PROPN
ejpam-5730	17	6	4.0	4.0	NUM
ejpam-5730	17	7	)	)	PUNCT
ejpam-5730	17	8	s.	s.	PROPN
ejpam-5730	17	9	park	park	PROPN
ejpam-5730	17	10	/	/	SYM
ejpam-5730	17	11	eur	eur	PROPN
ejpam-5730	17	12	.	.	PUNCT
ejpam-5730	18	1	j.	j.	PROPN
ejpam-5730	18	2	pure	pure	PROPN
ejpam-5730	18	3	appl	appl	PROPN
ejpam-5730	18	4	.	.	PROPN
ejpam-5730	18	5	math	math	PROPN
ejpam-5730	18	6	,	,	PUNCT
ejpam-5730	18	7	18	18	NUM
ejpam-5730	18	8	(	(	PUNCT
ejpam-5730	18	9	1	1	NUM
ejpam-5730	18	10	)	)	PUNCT
ejpam-5730	18	11	(	(	PUNCT
ejpam-5730	18	12	2025	2025	NUM
ejpam-5730	18	13	)	)	PUNCT
ejpam-5730	18	14	,	,	PUNCT
ejpam-5730	18	15	5730	5730	NUM
ejpam-5730	18	16	2	2	NUM
ejpam-5730	18	17	of	of	ADP
ejpam-5730	18	18	21	21	NUM
ejpam-5730	19	1	[	[	X
ejpam-5730	19	2	31	31	NUM
ejpam-5730	19	3	]	]	PUNCT
ejpam-5730	19	4	,	,	PUNCT
ejpam-5730	19	5	[	[	X
ejpam-5730	19	6	32	32	NUM
ejpam-5730	19	7	]	]	PUNCT
ejpam-5730	19	8	.	.	PUNCT
ejpam-5730	20	1	in	in	ADP
ejpam-5730	20	2	the	the	DET
ejpam-5730	20	3	present	present	ADJ
ejpam-5730	20	4	paper	paper	NOUN
ejpam-5730	20	5	,	,	PUNCT
ejpam-5730	20	6	we	we	PRON
ejpam-5730	20	7	give	give	VERB
ejpam-5730	20	8	very	very	ADV
ejpam-5730	20	9	simple	simple	ADJ
ejpam-5730	20	10	proofs	proof	NOUN
ejpam-5730	20	11	of	of	ADP
ejpam-5730	20	12	fixed	fix	VERB
ejpam-5730	20	13	point	point	NOUN
ejpam-5730	20	14	theorems	theorem	NOUN
ejpam-5730	20	15	for	for	ADP
ejpam-5730	20	16	various	various	ADJ
ejpam-5730	20	17	multimap	multimap	ADJ
ejpam-5730	20	18	classes	class	NOUN
ejpam-5730	20	19	in	in	ADP
ejpam-5730	20	20	[	[	X
ejpam-5730	20	21	40	40	NUM
ejpam-5730	20	22	]	]	PUNCT
ejpam-5730	20	23	.	.	PUNCT
ejpam-5730	21	1	such	such	ADJ
ejpam-5730	21	2	classes	class	NOUN
ejpam-5730	21	3	are	be	AUX
ejpam-5730	21	4	represented	represent	VERB
ejpam-5730	21	5	by	by	ADP
ejpam-5730	21	6	the	the	DET
ejpam-5730	21	7	banach	banach	NOUN
ejpam-5730	21	8	contractions	contraction	NOUN
ejpam-5730	21	9	,	,	PUNCT
ejpam-5730	21	10	the	the	DET
ejpam-5730	21	11	rus	rus	NOUN
ejpam-5730	21	12	-	-	PUNCT
ejpam-5730	21	13	hicks	hick	NOUN
ejpam-5730	21	14	-	-	PUNCT
ejpam-5730	21	15	rhoades	rhoade	NOUN
ejpam-5730	21	16	maps	map	NOUN
ejpam-5730	21	17	,	,	PUNCT
ejpam-5730	21	18	the	the	DET
ejpam-5730	21	19	nadler	nadler	NOUN
ejpam-5730	21	20	multimaps	multimap	NOUN
ejpam-5730	21	21	,	,	PUNCT
ejpam-5730	21	22	covitz	covitz	NOUN
ejpam-5730	21	23	-	-	PUNCT
ejpam-5730	21	24	nadler	nadler	NOUN
ejpam-5730	21	25	multimaps	multimap	NOUN
ejpam-5730	21	26	,	,	PUNCT
ejpam-5730	21	27	and	and	CCONJ
ejpam-5730	21	28	others	other	NOUN
ejpam-5730	21	29	.	.	PUNCT
ejpam-5730	22	1	consequently	consequently	ADV
ejpam-5730	22	2	,	,	PUNCT
ejpam-5730	22	3	we	we	PRON
ejpam-5730	22	4	obtain	obtain	VERB
ejpam-5730	22	5	another	another	DET
ejpam-5730	22	6	large	large	ADJ
ejpam-5730	22	7	number	number	NOUN
ejpam-5730	22	8	of	of	ADP
ejpam-5730	22	9	new	new	ADJ
ejpam-5730	22	10	theorems	theorem	NOUN
ejpam-5730	22	11	on	on	ADP
ejpam-5730	22	12	extremal	extremal	ADJ
ejpam-5730	22	13	elements	element	NOUN
ejpam-5730	22	14	,	,	PUNCT
ejpam-5730	22	15	fixed	fix	VERB
ejpam-5730	22	16	points	point	NOUN
ejpam-5730	22	17	,	,	PUNCT
ejpam-5730	22	18	stationary	stationary	ADJ
ejpam-5730	22	19	points	point	NOUN
ejpam-5730	22	20	for	for	ADP
ejpam-5730	22	21	several	several	ADJ
ejpam-5730	22	22	classes	class	NOUN
ejpam-5730	22	23	of	of	ADP
ejpam-5730	22	24	maps	map	NOUN
ejpam-5730	22	25	or	or	CCONJ
ejpam-5730	22	26	multimaps	multimap	NOUN
ejpam-5730	22	27	.	.	PUNCT
ejpam-5730	23	1	the	the	DET
ejpam-5730	23	2	present	present	ADJ
ejpam-5730	23	3	paper	paper	NOUN
ejpam-5730	23	4	is	be	AUX
ejpam-5730	23	5	organized	organize	VERB
ejpam-5730	23	6	as	as	SCONJ
ejpam-5730	23	7	follows	follow	VERB
ejpam-5730	23	8	.	.	PUNCT
ejpam-5730	24	1	for	for	ADP
ejpam-5730	24	2	the	the	DET
ejpam-5730	24	3	preliminaries	preliminary	NOUN
ejpam-5730	24	4	,	,	PUNCT
ejpam-5730	24	5	we	we	PRON
ejpam-5730	24	6	follow	follow	VERB
ejpam-5730	24	7	[	[	X
ejpam-5730	24	8	16	16	NUM
ejpam-5730	24	9	]	]	PUNCT
ejpam-5730	24	10	,	,	PUNCT
ejpam-5730	24	11	[	[	X
ejpam-5730	24	12	34	34	NUM
ejpam-5730	24	13	]	]	PUNCT
ejpam-5730	24	14	,	,	PUNCT
ejpam-5730	24	15	[	[	X
ejpam-5730	24	16	40	40	NUM
ejpam-5730	24	17	]	]	PUNCT
ejpam-5730	24	18	.	.	PUNCT
ejpam-5730	25	1	in	in	ADP
ejpam-5730	25	2	section	section	NOUN
ejpam-5730	25	3	2	2	NUM
ejpam-5730	25	4	,	,	PUNCT
ejpam-5730	25	5	we	we	PRON
ejpam-5730	25	6	introduce	introduce	VERB
ejpam-5730	25	7	our	our	PRON
ejpam-5730	25	8	rus	rus	NOUN
ejpam-5730	25	9	-	-	PUNCT
ejpam-5730	25	10	hicks	hick	NOUN
ejpam-5730	25	11	-	-	PUNCT
ejpam-5730	25	12	rhoades	rhoade	NOUN
ejpam-5730	25	13	contraction	contraction	NOUN
ejpam-5730	25	14	principle	principle	NOUN
ejpam-5730	25	15	(	(	PUNCT
ejpam-5730	25	16	theorem	theorem	VERB
ejpam-5730	25	17	p	p	X
ejpam-5730	25	18	)	)	PUNCT
ejpam-5730	25	19	.	.	PUNCT
ejpam-5730	26	1	section	section	NOUN
ejpam-5730	26	2	3	3	NUM
ejpam-5730	26	3	devotes	devote	VERB
ejpam-5730	26	4	to	to	PART
ejpam-5730	26	5	derive	derive	VERB
ejpam-5730	26	6	theorem	theorem	ADJ
ejpam-5730	26	7	h	h	NOUN
ejpam-5730	26	8	which	which	PRON
ejpam-5730	26	9	is	be	AUX
ejpam-5730	26	10	equivalent	equivalent	ADJ
ejpam-5730	26	11	formulations	formulation	NOUN
ejpam-5730	26	12	of	of	ADP
ejpam-5730	26	13	the	the	DET
ejpam-5730	26	14	quasimetric	quasimetric	ADJ
ejpam-5730	26	15	completeness	completeness	NOUN
ejpam-5730	26	16	as	as	ADP
ejpam-5730	26	17	an	an	DET
ejpam-5730	26	18	application	application	NOUN
ejpam-5730	26	19	of	of	ADP
ejpam-5730	26	20	our	our	PRON
ejpam-5730	26	21	traditional	traditional	ADJ
ejpam-5730	26	22	metatheorem	metatheorem	VERB
ejpam-5730	26	23	and	and	CCONJ
ejpam-5730	26	24	theorem	theorem	ADJ
ejpam-5730	26	25	p.	p.	NOUN
ejpam-5730	26	26	let	let	VERB
ejpam-5730	26	27	{	{	PUNCT
ejpam-5730	26	28	0	0	NUM
ejpam-5730	26	29	}	}	PUNCT
ejpam-5730	26	30	denote	denote	VERB
ejpam-5730	26	31	the	the	DET
ejpam-5730	26	32	family	family	NOUN
ejpam-5730	26	33	of	of	ADP
ejpam-5730	26	34	theorems	theorem	NOUN
ejpam-5730	26	35	which	which	PRON
ejpam-5730	26	36	are	be	AUX
ejpam-5730	26	37	equivalent	equivalent	ADJ
ejpam-5730	26	38	to	to	ADP
ejpam-5730	26	39	the	the	DET
ejpam-5730	26	40	metric	metric	ADJ
ejpam-5730	26	41	completeness	completeness	NOUN
ejpam-5730	26	42	;	;	PUNCT
ejpam-5730	26	43	see	see	VERB
ejpam-5730	26	44	[	[	X
ejpam-5730	26	45	40	40	NUM
ejpam-5730	26	46	]	]	PUNCT
ejpam-5730	26	47	.	.	PUNCT
ejpam-5730	27	1	in	in	ADP
ejpam-5730	27	2	sections	section	NOUN
ejpam-5730	27	3	4	4	NUM
ejpam-5730	27	4	-	-	SYM
ejpam-5730	27	5	7	7	NUM
ejpam-5730	27	6	,	,	PUNCT
ejpam-5730	27	7	we	we	PRON
ejpam-5730	27	8	introduce	introduce	VERB
ejpam-5730	27	9	major	major	ADJ
ejpam-5730	27	10	results	result	NOUN
ejpam-5730	27	11	in	in	ADP
ejpam-5730	27	12	the	the	DET
ejpam-5730	27	13	subfamilies	subfamily	NOUN
ejpam-5730	27	14	{	{	PUNCT
ejpam-5730	27	15	α}-{ϵ	α}-{ϵ	NOUN
ejpam-5730	27	16	}	}	PUNCT
ejpam-5730	27	17	of	of	ADP
ejpam-5730	27	18	the	the	DET
ejpam-5730	27	19	family	family	NOUN
ejpam-5730	27	20	{	{	PUNCT
ejpam-5730	27	21	0	0	NUM
ejpam-5730	27	22	}	}	PUNCT
ejpam-5730	27	23	corresponding	correspond	VERB
ejpam-5730	27	24	to	to	ADP
ejpam-5730	27	25	each	each	DET
ejpam-5730	27	26	equivalent	equivalent	ADJ
ejpam-5730	27	27	formulation	formulation	NOUN
ejpam-5730	27	28	in	in	ADP
ejpam-5730	27	29	theorem	theorem	PROPN
ejpam-5730	27	30	h.	h.	PROPN
ejpam-5730	27	31	in	in	ADP
ejpam-5730	27	32	section	section	NOUN
ejpam-5730	27	33	8	8	NUM
ejpam-5730	27	34	,	,	PUNCT
ejpam-5730	27	35	we	we	PRON
ejpam-5730	27	36	give	give	VERB
ejpam-5730	27	37	a	a	DET
ejpam-5730	27	38	few	few	ADJ
ejpam-5730	27	39	example	example	NOUN
ejpam-5730	27	40	of	of	ADP
ejpam-5730	27	41	fixed	fix	VERB
ejpam-5730	27	42	point	point	NOUN
ejpam-5730	27	43	theorems	theorem	NOUN
ejpam-5730	27	44	which	which	PRON
ejpam-5730	27	45	can	can	AUX
ejpam-5730	27	46	not	not	PART
ejpam-5730	27	47	applicable	applicable	VERB
ejpam-5730	27	48	our	our	PRON
ejpam-5730	27	49	theorem	theorem	NOUN
ejpam-5730	27	50	h.	h.	PROPN
ejpam-5730	27	51	finally	finally	ADV
ejpam-5730	27	52	,	,	PUNCT
ejpam-5730	27	53	section	section	NOUN
ejpam-5730	27	54	9	9	NUM
ejpam-5730	27	55	is	be	AUX
ejpam-5730	27	56	for	for	ADP
ejpam-5730	27	57	epilogue	epilogue	NOUN
ejpam-5730	27	58	.	.	PUNCT
ejpam-5730	28	1	2	2	X
ejpam-5730	28	2	.	.	X
ejpam-5730	28	3	the	the	DET
ejpam-5730	28	4	rus	rus	PROPN
ejpam-5730	28	5	-	-	PUNCT
ejpam-5730	28	6	hicks	hick	NOUN
ejpam-5730	28	7	-	-	PUNCT
ejpam-5730	28	8	rhoades	rhoade	NOUN
ejpam-5730	28	9	contraction	contraction	NOUN
ejpam-5730	28	10	principle	principle	NOUN
ejpam-5730	28	11	for	for	ADP
ejpam-5730	28	12	quasi	quasi	ADJ
ejpam-5730	28	13	-	-	ADJ
ejpam-5730	28	14	metric	metric	ADJ
ejpam-5730	28	15	spaces	space	NOUN
ejpam-5730	28	16	,	,	PUNCT
ejpam-5730	28	17	the	the	DET
ejpam-5730	28	18	convergence	convergence	NOUN
ejpam-5730	28	19	of	of	ADP
ejpam-5730	28	20	a	a	DET
ejpam-5730	28	21	sequence	sequence	NOUN
ejpam-5730	28	22	,	,	PUNCT
ejpam-5730	28	23	cauchy	cauchy	NOUN
ejpam-5730	28	24	sequences	sequence	NOUN
ejpam-5730	28	25	,	,	PUNCT
ejpam-5730	28	26	completeness	completeness	NOUN
ejpam-5730	28	27	,	,	PUNCT
ejpam-5730	28	28	orbits	orbit	NOUN
ejpam-5730	28	29	,	,	PUNCT
ejpam-5730	28	30	and	and	CCONJ
ejpam-5730	28	31	orbital	orbital	ADJ
ejpam-5730	28	32	continuity	continuity	NOUN
ejpam-5730	28	33	are	be	AUX
ejpam-5730	28	34	routinely	routinely	ADV
ejpam-5730	28	35	defined	define	VERB
ejpam-5730	28	36	as	as	ADP
ejpam-5730	28	37	in	in	ADP
ejpam-5730	28	38	[	[	NOUN
ejpam-5730	28	39	16],[40	16],[40	NUM
ejpam-5730	28	40	]	]	PUNCT
ejpam-5730	28	41	.	.	PUNCT
ejpam-5730	29	1	the	the	DET
ejpam-5730	29	2	following	follow	VERB
ejpam-5730	29	3	rus	rus	PROPN
ejpam-5730	29	4	-	-	PUNCT
ejpam-5730	29	5	hicks	hick	NOUN
ejpam-5730	29	6	-	-	PUNCT
ejpam-5730	29	7	rhoades	rhoade	NOUN
ejpam-5730	29	8	(	(	PUNCT
ejpam-5730	29	9	rhr	rhr	PROPN
ejpam-5730	29	10	)	)	PUNCT
ejpam-5730	29	11	contraction	contraction	NOUN
ejpam-5730	29	12	principle	principle	NOUN
ejpam-5730	29	13	was	be	AUX
ejpam-5730	29	14	obtained	obtain	VERB
ejpam-5730	29	15	in	in	ADP
ejpam-5730	29	16	[	[	X
ejpam-5730	29	17	33	33	NUM
ejpam-5730	29	18	]	]	PUNCT
ejpam-5730	29	19	,	,	PUNCT
ejpam-5730	29	20	[	[	X
ejpam-5730	29	21	35	35	NUM
ejpam-5730	29	22	-	-	SYM
ejpam-5730	29	23	37	37	NUM
ejpam-5730	29	24	]	]	PUNCT
ejpam-5730	29	25	,	,	PUNCT
ejpam-5730	29	26	[	[	X
ejpam-5730	29	27	39	39	NUM
ejpam-5730	29	28	]	]	PUNCT
ejpam-5730	29	29	,	,	PUNCT
ejpam-5730	30	1	[	[	X
ejpam-5730	30	2	40	40	NUM
ejpam-5730	30	3	]	]	PUNCT
ejpam-5730	30	4	:	:	PUNCT
ejpam-5730	30	5	theorem	theorem	ADJ
ejpam-5730	30	6	p.	p.	NOUN
ejpam-5730	30	7	let	let	VERB
ejpam-5730	30	8	(	(	PUNCT
ejpam-5730	30	9	x	x	X
ejpam-5730	30	10	,	,	PUNCT
ejpam-5730	30	11	q	q	X
ejpam-5730	30	12	)	)	PUNCT
ejpam-5730	30	13	be	be	AUX
ejpam-5730	30	14	a	a	DET
ejpam-5730	30	15	quasi	quasi	ADJ
ejpam-5730	30	16	-	-	ADJ
ejpam-5730	30	17	metric	metric	ADJ
ejpam-5730	30	18	space	space	NOUN
ejpam-5730	30	19	and	and	CCONJ
ejpam-5730	30	20	let	let	VERB
ejpam-5730	30	21	t	t	NOUN
ejpam-5730	30	22	:	:	PUNCT
ejpam-5730	30	23	x	x	X
ejpam-5730	30	24	→	→	PUNCT
ejpam-5730	30	25	x	x	AUX
ejpam-5730	30	26	be	be	AUX
ejpam-5730	30	27	an	an	DET
ejpam-5730	30	28	rhr	rhr	NOUN
ejpam-5730	30	29	map	map	NOUN
ejpam-5730	30	30	;	;	PUNCT
ejpam-5730	30	31	that	that	PRON
ejpam-5730	30	32	is	is	ADV
ejpam-5730	30	33	,	,	PUNCT
ejpam-5730	30	34	q(t	q(t	PROPN
ejpam-5730	30	35	(	(	PUNCT
ejpam-5730	30	36	x	x	NOUN
ejpam-5730	30	37	)	)	PUNCT
ejpam-5730	30	38	,	,	PUNCT
ejpam-5730	30	39	t	t	PROPN
ejpam-5730	30	40	2(x	2(x	NUM
ejpam-5730	30	41	)	)	PUNCT
ejpam-5730	30	42	)	)	PUNCT
ejpam-5730	30	43	≤	≤	NUM
ejpam-5730	30	44	α	α	PROPN
ejpam-5730	30	45	q(x	q(x	PROPN
ejpam-5730	30	46	,	,	PUNCT
ejpam-5730	30	47	t	t	PROPN
ejpam-5730	30	48	(	(	PUNCT
ejpam-5730	30	49	x	x	NOUN
ejpam-5730	30	50	)	)	PUNCT
ejpam-5730	30	51	)	)	PUNCT
ejpam-5730	30	52	∀	∀	X
ejpam-5730	31	1	x	x	X
ejpam-5730	31	2	∈	∈	NOUN
ejpam-5730	31	3	x	x	X
ejpam-5730	31	4	,	,	PUNCT
ejpam-5730	31	5	(	(	PUNCT
ejpam-5730	31	6	p	p	NOUN
ejpam-5730	31	7	)	)	PUNCT
ejpam-5730	31	8	where	where	SCONJ
ejpam-5730	31	9	0	0	NUM
ejpam-5730	31	10	<	<	X
ejpam-5730	31	11	α	α	X
ejpam-5730	31	12	<	<	X
ejpam-5730	31	13	1	1	NUM
ejpam-5730	31	14	.	.	PUNCT
ejpam-5730	31	15	(	(	PUNCT
ejpam-5730	31	16	i	i	NOUN
ejpam-5730	31	17	)	)	PUNCT
ejpam-5730	31	18	if	if	SCONJ
ejpam-5730	31	19	x	x	PRON
ejpam-5730	31	20	is	be	AUX
ejpam-5730	31	21	t	t	NOUN
ejpam-5730	31	22	-orbitally	-orbitally	ADV
ejpam-5730	31	23	complete	complete	ADJ
ejpam-5730	31	24	,	,	PUNCT
ejpam-5730	31	25	then	then	ADV
ejpam-5730	31	26	,	,	PUNCT
ejpam-5730	31	27	for	for	ADP
ejpam-5730	31	28	each	each	DET
ejpam-5730	31	29	x	x	SYM
ejpam-5730	31	30	∈	∈	PROPN
ejpam-5730	31	31	x	x	X
ejpam-5730	31	32	,	,	PUNCT
ejpam-5730	31	33	there	there	PRON
ejpam-5730	31	34	exists	exist	VERB
ejpam-5730	31	35	a	a	DET
ejpam-5730	31	36	point	point	NOUN
ejpam-5730	31	37	x0	x0	PROPN
ejpam-5730	31	38	∈	∈	PROPN
ejpam-5730	31	39	x	x	PUNCT
ejpam-5730	31	40	such	such	ADJ
ejpam-5730	31	41	that	that	SCONJ
ejpam-5730	31	42	lim	lim	PROPN
ejpam-5730	31	43	n→∞	n→∞	X
ejpam-5730	31	44	tn(x	tn(x	PUNCT
ejpam-5730	31	45	)	)	PUNCT
ejpam-5730	32	1	=	=	SYM
ejpam-5730	32	2	x0	x0	PROPN
ejpam-5730	32	3	and	and	CCONJ
ejpam-5730	32	4	q(tn(x	q(tn(x	PROPN
ejpam-5730	32	5	)	)	PUNCT
ejpam-5730	32	6	,	,	PUNCT
ejpam-5730	32	7	x0	x0	PROPN
ejpam-5730	32	8	)	)	PUNCT
ejpam-5730	32	9	≤	≤	NUM
ejpam-5730	32	10	αn	αn	NOUN
ejpam-5730	32	11	1−	1−	NUM
ejpam-5730	32	12	α	α	PROPN
ejpam-5730	32	13	q(x	q(x	PROPN
ejpam-5730	32	14	,	,	PUNCT
ejpam-5730	32	15	t	t	PROPN
ejpam-5730	32	16	(	(	PUNCT
ejpam-5730	32	17	x	x	NOUN
ejpam-5730	32	18	)	)	PUNCT
ejpam-5730	32	19	)	)	PUNCT
ejpam-5730	32	20	,	,	PUNCT
ejpam-5730	32	21	n	n	NOUN
ejpam-5730	32	22	=	=	SYM
ejpam-5730	32	23	1	1	NUM
ejpam-5730	32	24	,	,	PUNCT
ejpam-5730	32	25	2	2	NUM
ejpam-5730	32	26	,	,	PUNCT
ejpam-5730	32	27	·	·	PUNCT
ejpam-5730	32	28	·	·	PUNCT
ejpam-5730	32	29	·	·	PUNCT
ejpam-5730	32	30	,	,	PUNCT
ejpam-5730	32	31	q(tn(x	q(tn(x	PROPN
ejpam-5730	32	32	)	)	PUNCT
ejpam-5730	32	33	,	,	PUNCT
ejpam-5730	32	34	x0	x0	PROPN
ejpam-5730	32	35	)	)	PUNCT
ejpam-5730	32	36	≤	≤	PUNCT
ejpam-5730	33	1	α	α	PRON
ejpam-5730	33	2	1−	1−	NUM
ejpam-5730	33	3	α	α	DET
ejpam-5730	33	4	q(tn−1(x	q(tn−1(x	NOUN
ejpam-5730	33	5	)	)	PUNCT
ejpam-5730	33	6	,	,	PUNCT
ejpam-5730	33	7	tn(x	tn(x	NOUN
ejpam-5730	33	8	)	)	PUNCT
ejpam-5730	33	9	)	)	PUNCT
ejpam-5730	33	10	,	,	PUNCT
ejpam-5730	33	11	n	n	NOUN
ejpam-5730	33	12	=	=	SYM
ejpam-5730	33	13	1	1	NUM
ejpam-5730	33	14	,	,	PUNCT
ejpam-5730	33	15	2	2	NUM
ejpam-5730	33	16	,	,	PUNCT
ejpam-5730	33	17	·	·	PUNCT
ejpam-5730	33	18	·	·	PUNCT
ejpam-5730	33	19	·	·	PUNCT
ejpam-5730	33	20	.	.	PUNCT
ejpam-5730	34	1	(	(	PUNCT
ejpam-5730	34	2	ii	ii	NOUN
ejpam-5730	34	3	)	)	PUNCT
ejpam-5730	34	4	x0	x0	PROPN
ejpam-5730	34	5	is	be	AUX
ejpam-5730	34	6	a	a	DET
ejpam-5730	34	7	fixed	fix	VERB
ejpam-5730	34	8	point	point	NOUN
ejpam-5730	34	9	of	of	ADP
ejpam-5730	34	10	t	t	PROPN
ejpam-5730	34	11	,	,	PUNCT
ejpam-5730	34	12	and	and	CCONJ
ejpam-5730	34	13	,	,	PUNCT
ejpam-5730	34	14	equivalently	equivalently	ADV
ejpam-5730	34	15	,	,	PUNCT
ejpam-5730	34	16	(	(	PUNCT
ejpam-5730	34	17	iii	iii	X
ejpam-5730	34	18	)	)	PUNCT
ejpam-5730	34	19	t	t	NOUN
ejpam-5730	34	20	:	:	PUNCT
ejpam-5730	34	21	x	x	X
ejpam-5730	34	22	→	→	PUNCT
ejpam-5730	34	23	x	x	X
ejpam-5730	34	24	is	be	AUX
ejpam-5730	34	25	orbitally	orbitally	ADV
ejpam-5730	34	26	continuous	continuous	ADJ
ejpam-5730	34	27	at	at	ADP
ejpam-5730	34	28	x0	x0	PROPN
ejpam-5730	34	29	∈	∈	PROPN
ejpam-5730	34	30	x.	x.	NOUN
ejpam-5730	34	31	let	let	VERB
ejpam-5730	34	32	f	f	NOUN
ejpam-5730	34	33	:	:	PUNCT
ejpam-5730	34	34	x	x	X
ejpam-5730	34	35	→	→	PUNCT
ejpam-5730	34	36	x	x	PUNCT
ejpam-5730	34	37	be	be	AUX
ejpam-5730	34	38	a	a	DET
ejpam-5730	34	39	(	(	PUNCT
ejpam-5730	34	40	banach	banach	NOUN
ejpam-5730	34	41	)	)	PUNCT
ejpam-5730	34	42	contraction	contraction	NOUN
ejpam-5730	34	43	of	of	ADP
ejpam-5730	34	44	a	a	DET
ejpam-5730	34	45	metric	metric	ADJ
ejpam-5730	34	46	space	space	NOUN
ejpam-5730	34	47	(	(	PUNCT
ejpam-5730	34	48	x	x	X
ejpam-5730	34	49	,	,	PUNCT
ejpam-5730	34	50	d	d	PROPN
ejpam-5730	34	51	)	)	PUNCT
ejpam-5730	34	52	,	,	PUNCT
ejpam-5730	34	53	that	that	ADV
ejpam-5730	34	54	is	is	ADV
ejpam-5730	34	55	,	,	PUNCT
ejpam-5730	34	56	there	there	PRON
ejpam-5730	34	57	exists	exist	VERB
ejpam-5730	34	58	r	r	NOUN
ejpam-5730	34	59	∈	∈	PROPN
ejpam-5730	34	60	(	(	PUNCT
ejpam-5730	34	61	0	0	NUM
ejpam-5730	34	62	,	,	PUNCT
ejpam-5730	34	63	1	1	NUM
ejpam-5730	34	64	)	)	PUNCT
ejpam-5730	34	65	such	such	ADJ
ejpam-5730	34	66	that	that	SCONJ
ejpam-5730	34	67	d(tx	d(tx	PROPN
ejpam-5730	34	68	,	,	PUNCT
ejpam-5730	34	69	ty	ty	NOUN
ejpam-5730	34	70	)	)	PUNCT
ejpam-5730	34	71	≤	≤	NOUN
ejpam-5730	34	72	r	r	NOUN
ejpam-5730	34	73	d(x	d(x	PROPN
ejpam-5730	34	74	,	,	PUNCT
ejpam-5730	34	75	y	y	NOUN
ejpam-5730	34	76	)	)	PUNCT
ejpam-5730	34	77	∀	∀	PUNCT
ejpam-5730	35	1	x	x	NOUN
ejpam-5730	35	2	,	,	PUNCT
ejpam-5730	35	3	y	y	PROPN
ejpam-5730	35	4	∈	∈	PROPN
ejpam-5730	35	5	x.	x.	NOUN
ejpam-5730	35	6	s.	s.	PROPN
ejpam-5730	35	7	park	park	PROPN
ejpam-5730	35	8	/	/	SYM
ejpam-5730	35	9	eur	eur	PROPN
ejpam-5730	35	10	.	.	PUNCT
ejpam-5730	36	1	j.	j.	PROPN
ejpam-5730	36	2	pure	pure	PROPN
ejpam-5730	36	3	appl	appl	PROPN
ejpam-5730	36	4	.	.	PROPN
ejpam-5730	36	5	math	math	PROPN
ejpam-5730	36	6	,	,	PUNCT
ejpam-5730	36	7	18	18	NUM
ejpam-5730	36	8	(	(	PUNCT
ejpam-5730	36	9	1	1	NUM
ejpam-5730	36	10	)	)	PUNCT
ejpam-5730	36	11	(	(	PUNCT
ejpam-5730	36	12	2025	2025	NUM
ejpam-5730	36	13	)	)	PUNCT
ejpam-5730	36	14	,	,	PUNCT
ejpam-5730	36	15	5730	5730	NUM
ejpam-5730	36	16	3	3	NUM
ejpam-5730	36	17	of	of	ADP
ejpam-5730	36	18	21	21	NUM
ejpam-5730	36	19	theorem	theorem	NOUN
ejpam-5730	36	20	p	p	NOUN
ejpam-5730	36	21	is	be	AUX
ejpam-5730	36	22	a	a	DET
ejpam-5730	36	23	far	far	ADV
ejpam-5730	36	24	-	-	PUNCT
ejpam-5730	36	25	reaching	reach	VERB
ejpam-5730	36	26	generalization	generalization	NOUN
ejpam-5730	36	27	of	of	ADP
ejpam-5730	36	28	the	the	DET
ejpam-5730	36	29	so	so	ADV
ejpam-5730	36	30	-	-	PUNCT
ejpam-5730	36	31	called	call	VERB
ejpam-5730	36	32	banach	banach	NOUN
ejpam-5730	36	33	contraction	contraction	NOUN
ejpam-5730	36	34	principle	principle	NOUN
ejpam-5730	36	35	originated	originate	VERB
ejpam-5730	36	36	from	from	ADP
ejpam-5730	36	37	banach	banach	NOUN
ejpam-5730	36	38	[	[	X
ejpam-5730	36	39	4	4	X
ejpam-5730	36	40	]	]	PUNCT
ejpam-5730	36	41	in	in	ADP
ejpam-5730	36	42	1922	1922	NUM
ejpam-5730	36	43	as	as	ADP
ejpam-5730	36	44	the	the	DET
ejpam-5730	36	45	following	following	NOUN
ejpam-5730	36	46	:	:	PUNCT
ejpam-5730	36	47	theorem	theorem	ADJ
ejpam-5730	36	48	.	.	PUNCT
ejpam-5730	37	1	(	(	PUNCT
ejpam-5730	37	2	banach	banach	NOUN
ejpam-5730	37	3	)	)	PUNCT
ejpam-5730	37	4	if	if	SCONJ
ejpam-5730	37	5	10	10	NUM
ejpam-5730	37	6	u(x	u(x	NOUN
ejpam-5730	37	7	)	)	PUNCT
ejpam-5730	37	8	be	be	VERB
ejpam-5730	37	9	a	a	DET
ejpam-5730	37	10	continuous	continuous	ADJ
ejpam-5730	37	11	operator	operator	NOUN
ejpam-5730	37	12	in	in	ADP
ejpam-5730	37	13	e	e	NOUN
ejpam-5730	37	14	,	,	PUNCT
ejpam-5730	37	15	the	the	DET
ejpam-5730	37	16	counter	counter	NOUN
ejpam-5730	37	17	-	-	NOUN
ejpam-5730	37	18	domain	domain	NOUN
ejpam-5730	37	19	of	of	ADP
ejpam-5730	37	20	u(x	u(x	NOUN
ejpam-5730	37	21	)	)	PUNCT
ejpam-5730	37	22	is	be	AUX
ejpam-5730	37	23	contained	contain	VERB
ejpam-5730	37	24	in	in	ADP
ejpam-5730	37	25	e1	e1	PROPN
ejpam-5730	37	26	.	.	PUNCT
ejpam-5730	38	1	20	20	NUM
ejpam-5730	38	2	there	there	PRON
ejpam-5730	38	3	exists	exist	VERB
ejpam-5730	38	4	a	a	DET
ejpam-5730	38	5	number	number	NOUN
ejpam-5730	38	6	0	0	NUM
ejpam-5730	38	7	<	<	X
ejpam-5730	38	8	m	m	X
ejpam-5730	38	9	<	<	X
ejpam-5730	38	10	1	1	NUM
ejpam-5730	38	11	which	which	PRON
ejpam-5730	38	12	implies	imply	VERB
ejpam-5730	38	13	,	,	PUNCT
ejpam-5730	38	14	for	for	ADP
ejpam-5730	38	15	every	every	DET
ejpam-5730	38	16	x	x	NOUN
ejpam-5730	38	17	′	′	NUM
ejpam-5730	38	18	and	and	CCONJ
ejpam-5730	38	19	x	x	PART
ejpam-5730	38	20	′′	′′	PROPN
ejpam-5730	38	21	,	,	PUNCT
ejpam-5730	38	22	the	the	DET
ejpam-5730	38	23	inequality	inequality	NOUN
ejpam-5730	38	24	||u(x	||u(x	VERB
ejpam-5730	38	25	′)−	′)−	PROPN
ejpam-5730	38	26	u(x	u(x	VERB
ejpam-5730	38	27	′′)||	′′)||	NUM
ejpam-5730	38	28	≤	≤	NUM
ejpam-5730	38	29	m.||x	m.||x	NOUN
ejpam-5730	38	30	′	′	NUM
ejpam-5730	38	31	−x	−x	NUM
ejpam-5730	38	32	′′||	′′||	NOUN
ejpam-5730	38	33	.	.	PUNCT
ejpam-5730	39	1	—	—	PUNCT
ejpam-5730	39	2	there	there	PRON
ejpam-5730	39	3	exists	exist	VERB
ejpam-5730	39	4	an	an	DET
ejpam-5730	39	5	element	element	NOUN
ejpam-5730	39	6	x	x	PUNCT
ejpam-5730	39	7	such	such	ADJ
ejpam-5730	39	8	that	that	SCONJ
ejpam-5730	39	9	x	x	NOUN
ejpam-5730	39	10	=	=	SYM
ejpam-5730	39	11	u(x	u(x	PROPN
ejpam-5730	39	12	)	)	PUNCT
ejpam-5730	39	13	.	.	PUNCT
ejpam-5730	40	1	here	here	ADV
ejpam-5730	40	2	e	e	X
ejpam-5730	40	3	and	and	CCONJ
ejpam-5730	40	4	e1	e1	PROPN
ejpam-5730	40	5	is	be	AUX
ejpam-5730	40	6	a	a	DET
ejpam-5730	40	7	normed	normed	ADJ
ejpam-5730	40	8	space	space	NOUN
ejpam-5730	40	9	and	and	CCONJ
ejpam-5730	40	10	its	its	PRON
ejpam-5730	40	11	complete	complete	ADJ
ejpam-5730	40	12	subset	subset	NOUN
ejpam-5730	40	13	,	,	PUNCT
ejpam-5730	40	14	resp	resp	NOUN
ejpam-5730	40	15	.	.	PUNCT
ejpam-5730	41	1	3	3	X
ejpam-5730	41	2	.	.	X
ejpam-5730	41	3	a	a	DET
ejpam-5730	41	4	form	form	NOUN
ejpam-5730	41	5	of	of	ADP
ejpam-5730	41	6	our	our	PRON
ejpam-5730	41	7	new	new	ADJ
ejpam-5730	41	8	2023	2023	NUM
ejpam-5730	41	9	metatheorem	metatheorem	VERB
ejpam-5730	41	10	let	let	VERB
ejpam-5730	41	11	(	(	PUNCT
ejpam-5730	41	12	x	x	NOUN
ejpam-5730	41	13	,	,	PUNCT
ejpam-5730	41	14	q	q	X
ejpam-5730	41	15	)	)	PUNCT
ejpam-5730	41	16	be	be	AUX
ejpam-5730	41	17	a	a	DET
ejpam-5730	41	18	quasi	quasi	ADJ
ejpam-5730	41	19	-	-	ADJ
ejpam-5730	41	20	metric	metric	ADJ
ejpam-5730	41	21	space	space	NOUN
ejpam-5730	41	22	and	and	CCONJ
ejpam-5730	41	23	cl(x	cl(x	PROPN
ejpam-5730	41	24	)	)	PUNCT
ejpam-5730	41	25	denote	denote	VERB
ejpam-5730	41	26	the	the	DET
ejpam-5730	41	27	family	family	NOUN
ejpam-5730	41	28	of	of	ADP
ejpam-5730	41	29	all	all	DET
ejpam-5730	41	30	nonempty	nonempty	ADV
ejpam-5730	41	31	closed	close	VERB
ejpam-5730	41	32	subsets	subset	NOUN
ejpam-5730	41	33	of	of	ADP
ejpam-5730	41	34	x	x	PUNCT
ejpam-5730	41	35	(	(	PUNCT
ejpam-5730	41	36	not	not	PART
ejpam-5730	41	37	necessarily	necessarily	ADV
ejpam-5730	41	38	bounded	bound	VERB
ejpam-5730	41	39	)	)	PUNCT
ejpam-5730	41	40	.	.	PUNCT
ejpam-5730	42	1	for	for	ADP
ejpam-5730	42	2	a	a	DET
ejpam-5730	42	3	,	,	PUNCT
ejpam-5730	42	4	b	b	PROPN
ejpam-5730	42	5	∈	∈	NOUN
ejpam-5730	42	6	cl(x	cl(x	NOUN
ejpam-5730	42	7	)	)	PUNCT
ejpam-5730	42	8	,	,	PUNCT
ejpam-5730	42	9	set	set	VERB
ejpam-5730	42	10	h(a	h(a	PROPN
ejpam-5730	42	11	,	,	PUNCT
ejpam-5730	42	12	b	b	NOUN
ejpam-5730	42	13	)	)	PUNCT
ejpam-5730	42	14	=	=	SYM
ejpam-5730	42	15	max{sup{q(a	max{sup{q(a	NOUN
ejpam-5730	42	16	,	,	PUNCT
ejpam-5730	42	17	b	b	NOUN
ejpam-5730	42	18	)	)	PUNCT
ejpam-5730	42	19	:	:	PUNCT
ejpam-5730	42	20	a	a	DET
ejpam-5730	42	21	∈	∈	PROPN
ejpam-5730	42	22	a	a	PRON
ejpam-5730	42	23	}	}	PUNCT
ejpam-5730	42	24	,	,	PUNCT
ejpam-5730	42	25	sup{q(b	sup{q(b	NOUN
ejpam-5730	42	26	,	,	PUNCT
ejpam-5730	42	27	a	a	PRON
ejpam-5730	42	28	)	)	PUNCT
ejpam-5730	42	29	:	:	PUNCT
ejpam-5730	42	30	b	b	X
ejpam-5730	42	31	∈	∈	ADJ
ejpam-5730	42	32	b	b	NOUN
ejpam-5730	42	33	}	}	PUNCT
ejpam-5730	42	34	}	}	PUNCT
ejpam-5730	42	35	,	,	PUNCT
ejpam-5730	42	36	where	where	SCONJ
ejpam-5730	42	37	q(a	q(a	NOUN
ejpam-5730	42	38	,	,	PUNCT
ejpam-5730	42	39	b	b	NOUN
ejpam-5730	42	40	)	)	PUNCT
ejpam-5730	43	1	=	=	SYM
ejpam-5730	43	2	inf{q(a	inf{q(a	NOUN
ejpam-5730	43	3	,	,	PUNCT
ejpam-5730	43	4	b	b	NOUN
ejpam-5730	43	5	)	)	PUNCT
ejpam-5730	43	6	:	:	PUNCT
ejpam-5730	44	1	b	b	X
ejpam-5730	44	2	∈	∈	PROPN
ejpam-5730	44	3	b	b	NOUN
ejpam-5730	44	4	}	}	PUNCT
ejpam-5730	44	5	.	.	PUNCT
ejpam-5730	45	1	then	then	ADV
ejpam-5730	45	2	h	h	PROPN
ejpam-5730	45	3	is	be	AUX
ejpam-5730	45	4	called	call	VERB
ejpam-5730	45	5	a	a	DET
ejpam-5730	45	6	generalized	generalized	ADJ
ejpam-5730	45	7	hausdorff	hausdorff	NOUN
ejpam-5730	45	8	distance	distance	NOUN
ejpam-5730	45	9	and	and	CCONJ
ejpam-5730	45	10	it	it	PRON
ejpam-5730	45	11	may	may	AUX
ejpam-5730	45	12	have	have	VERB
ejpam-5730	45	13	infinite	infinite	ADJ
ejpam-5730	45	14	values	value	NOUN
ejpam-5730	45	15	.	.	PUNCT
ejpam-5730	46	1	recently	recently	ADV
ejpam-5730	46	2	,	,	PUNCT
ejpam-5730	46	3	as	as	ADP
ejpam-5730	46	4	a	a	DET
ejpam-5730	46	5	basis	basis	NOUN
ejpam-5730	46	6	of	of	ADP
ejpam-5730	46	7	ordered	order	VERB
ejpam-5730	46	8	fixed	fix	VERB
ejpam-5730	46	9	point	point	NOUN
ejpam-5730	46	10	theory	theory	NOUN
ejpam-5730	46	11	[	[	X
ejpam-5730	46	12	30	30	NUM
ejpam-5730	46	13	]	]	PUNCT
ejpam-5730	46	14	,	,	PUNCT
ejpam-5730	46	15	we	we	PRON
ejpam-5730	46	16	obtained	obtain	VERB
ejpam-5730	46	17	the	the	DET
ejpam-5730	46	18	2023	2023	NUM
ejpam-5730	46	19	metatheorem	metatheorem	VERB
ejpam-5730	46	20	and	and	CCONJ
ejpam-5730	46	21	theorem	theorem	ADJ
ejpam-5730	46	22	h	h	PROPN
ejpam-5730	46	23	including	include	VERB
ejpam-5730	46	24	nadler	nadler	PROPN
ejpam-5730	46	25	’s	’s	PART
ejpam-5730	46	26	fixed	fix	VERB
ejpam-5730	46	27	point	point	NOUN
ejpam-5730	46	28	theorem	theorem	VERB
ejpam-5730	46	29	[	[	X
ejpam-5730	46	30	28	28	NUM
ejpam-5730	46	31	]	]	PUNCT
ejpam-5730	46	32	in	in	ADP
ejpam-5730	46	33	1969	1969	NUM
ejpam-5730	46	34	and	and	CCONJ
ejpam-5730	46	35	its	its	PRON
ejpam-5730	46	36	extended	extended	ADJ
ejpam-5730	46	37	version	version	NOUN
ejpam-5730	46	38	by	by	ADP
ejpam-5730	46	39	covitz	covitz	NOUN
ejpam-5730	46	40	-	-	PUNCT
ejpam-5730	46	41	nadler	nadler	NOUN
ejpam-5730	46	42	[	[	X
ejpam-5730	46	43	9	9	NUM
ejpam-5730	46	44	]	]	PUNCT
ejpam-5730	46	45	in	in	ADP
ejpam-5730	46	46	1970	1970	NUM
ejpam-5730	46	47	.	.	PUNCT
ejpam-5730	47	1	theorem	theorem	PROPN
ejpam-5730	47	2	h.	h.	PROPN
ejpam-5730	48	1	(	(	PUNCT
ejpam-5730	48	2	[	[	X
ejpam-5730	48	3	36],[38],[39	36],[38],[39	NUM
ejpam-5730	48	4	]	]	PUNCT
ejpam-5730	48	5	)	)	PUNCT
ejpam-5730	48	6	let	let	VERB
ejpam-5730	48	7	(	(	PUNCT
ejpam-5730	48	8	x	x	NOUN
ejpam-5730	48	9	,	,	PUNCT
ejpam-5730	48	10	q	q	X
ejpam-5730	48	11	)	)	PUNCT
ejpam-5730	48	12	be	be	AUX
ejpam-5730	48	13	a	a	DET
ejpam-5730	48	14	quasi	quasi	ADJ
ejpam-5730	48	15	-	-	ADJ
ejpam-5730	48	16	metric	metric	ADJ
ejpam-5730	48	17	space	space	NOUN
ejpam-5730	48	18	and	and	CCONJ
ejpam-5730	48	19	0	0	NUM
ejpam-5730	48	20	<	<	X
ejpam-5730	48	21	r	r	X
ejpam-5730	48	22	<	<	X
ejpam-5730	48	23	1	1	NUM
ejpam-5730	48	24	.	.	PUNCT
ejpam-5730	49	1	then	then	ADV
ejpam-5730	49	2	the	the	DET
ejpam-5730	49	3	following	follow	VERB
ejpam-5730	49	4	equivalent	equivalent	ADJ
ejpam-5730	49	5	statements	statement	NOUN
ejpam-5730	49	6	hold	hold	VERB
ejpam-5730	49	7	:	:	PUNCT
ejpam-5730	49	8	(	(	PUNCT
ejpam-5730	49	9	0	0	NUM
ejpam-5730	49	10	)	)	PUNCT
ejpam-5730	49	11	(	(	PUNCT
ejpam-5730	49	12	x	x	X
ejpam-5730	49	13	,	,	PUNCT
ejpam-5730	49	14	q	q	X
ejpam-5730	49	15	)	)	PUNCT
ejpam-5730	49	16	is	be	AUX
ejpam-5730	49	17	complete	complete	ADJ
ejpam-5730	49	18	.	.	PUNCT
ejpam-5730	50	1	(	(	PUNCT
ejpam-5730	50	2	α	α	X
ejpam-5730	50	3	)	)	PUNCT
ejpam-5730	50	4	for	for	ADP
ejpam-5730	50	5	a	a	DET
ejpam-5730	50	6	multimap	multimap	NOUN
ejpam-5730	50	7	t	t	NOUN
ejpam-5730	50	8	:	:	PUNCT
ejpam-5730	50	9	x	x	X
ejpam-5730	50	10	→	→	SYM
ejpam-5730	50	11	cl(x	cl(x	NOUN
ejpam-5730	50	12	)	)	PUNCT
ejpam-5730	50	13	,	,	PUNCT
ejpam-5730	50	14	there	there	PRON
ejpam-5730	50	15	exists	exist	VERB
ejpam-5730	50	16	an	an	DET
ejpam-5730	50	17	element	element	NOUN
ejpam-5730	50	18	v	v	ADP
ejpam-5730	50	19	∈	∈	PROPN
ejpam-5730	50	20	x	x	PUNCT
ejpam-5730	50	21	such	such	ADJ
ejpam-5730	50	22	that	that	PRON
ejpam-5730	50	23	h(tv	h(tv	PROPN
ejpam-5730	50	24	,	,	PUNCT
ejpam-5730	50	25	tw	tw	PROPN
ejpam-5730	50	26	)	)	PUNCT
ejpam-5730	50	27	>	>	PUNCT
ejpam-5730	51	1	r	r	PROPN
ejpam-5730	51	2	q(v	q(v	PROPN
ejpam-5730	51	3	,	,	PUNCT
ejpam-5730	51	4	w	w	NOUN
ejpam-5730	51	5	)	)	PUNCT
ejpam-5730	51	6	for	for	ADP
ejpam-5730	51	7	any	any	DET
ejpam-5730	51	8	w	w	PROPN
ejpam-5730	51	9	∈	∈	PROPN
ejpam-5730	51	10	x\{v	x\{v	PROPN
ejpam-5730	51	11	}	}	PUNCT
ejpam-5730	51	12	.	.	PUNCT
ejpam-5730	52	1	(	(	PUNCT
ejpam-5730	52	2	β	β	X
ejpam-5730	52	3	)	)	PUNCT
ejpam-5730	52	4	if	if	SCONJ
ejpam-5730	52	5	f	f	PROPN
ejpam-5730	52	6	is	be	AUX
ejpam-5730	52	7	a	a	DET
ejpam-5730	52	8	family	family	NOUN
ejpam-5730	52	9	of	of	ADP
ejpam-5730	52	10	maps	map	NOUN
ejpam-5730	52	11	f	f	X
ejpam-5730	52	12	:	:	PUNCT
ejpam-5730	52	13	x	x	X
ejpam-5730	53	1	→	→	PUNCT
ejpam-5730	53	2	x	x	X
ejpam-5730	53	3	such	such	ADJ
ejpam-5730	53	4	that	that	SCONJ
ejpam-5730	53	5	,	,	PUNCT
ejpam-5730	53	6	for	for	ADP
ejpam-5730	53	7	any	any	DET
ejpam-5730	53	8	x	x	SYM
ejpam-5730	53	9	∈	∈	PROPN
ejpam-5730	53	10	x\{fx	x\{fx	PROPN
ejpam-5730	53	11	}	}	PUNCT
ejpam-5730	53	12	,	,	PUNCT
ejpam-5730	53	13	there	there	PRON
ejpam-5730	53	14	exists	exist	VERB
ejpam-5730	53	15	a	a	DET
ejpam-5730	53	16	y	y	PROPN
ejpam-5730	53	17	∈	∈	PROPN
ejpam-5730	53	18	x\{x	x\{x	PROPN
ejpam-5730	53	19	}	}	PUNCT
ejpam-5730	53	20	satisfying	satisfy	VERB
ejpam-5730	53	21	q(fx	q(fx	ADP
ejpam-5730	53	22	,	,	PUNCT
ejpam-5730	53	23	fy	fy	NOUN
ejpam-5730	53	24	)	)	PUNCT
ejpam-5730	53	25	≤	≤	NOUN
ejpam-5730	53	26	r	r	NOUN
ejpam-5730	53	27	q(x	q(x	PROPN
ejpam-5730	53	28	,	,	PUNCT
ejpam-5730	53	29	y	y	PROPN
ejpam-5730	53	30	)	)	PUNCT
ejpam-5730	53	31	,	,	PUNCT
ejpam-5730	53	32	then	then	ADV
ejpam-5730	53	33	f	f	PROPN
ejpam-5730	53	34	has	have	VERB
ejpam-5730	53	35	a	a	DET
ejpam-5730	53	36	common	common	ADJ
ejpam-5730	53	37	fixed	fix	VERB
ejpam-5730	53	38	element	element	NOUN
ejpam-5730	53	39	v	v	ADP
ejpam-5730	53	40	∈	∈	PROPN
ejpam-5730	53	41	x	x	NOUN
ejpam-5730	53	42	,	,	PUNCT
ejpam-5730	53	43	that	that	ADV
ejpam-5730	53	44	is	is	ADV
ejpam-5730	53	45	,	,	PUNCT
ejpam-5730	53	46	v	v	X
ejpam-5730	53	47	=	=	SYM
ejpam-5730	53	48	fv	fv	NOUN
ejpam-5730	53	49	for	for	ADP
ejpam-5730	53	50	all	all	DET
ejpam-5730	53	51	f	f	PROPN
ejpam-5730	53	52	∈	∈	PROPN
ejpam-5730	53	53	f.	f.	PROPN
ejpam-5730	53	54	(	(	PUNCT
ejpam-5730	53	55	γ	γ	PROPN
ejpam-5730	53	56	)	)	PUNCT
ejpam-5730	53	57	if	if	SCONJ
ejpam-5730	53	58	f	f	PROPN
ejpam-5730	53	59	is	be	AUX
ejpam-5730	53	60	a	a	DET
ejpam-5730	53	61	family	family	NOUN
ejpam-5730	53	62	of	of	ADP
ejpam-5730	53	63	maps	map	NOUN
ejpam-5730	53	64	f	f	X
ejpam-5730	53	65	:	:	PUNCT
ejpam-5730	53	66	x	x	X
ejpam-5730	53	67	→	→	SYM
ejpam-5730	53	68	x	x	SYM
ejpam-5730	53	69	satisfying	satisfy	VERB
ejpam-5730	53	70	q(fx	q(fx	NOUN
ejpam-5730	53	71	,	,	PUNCT
ejpam-5730	53	72	f2x	f2x	X
ejpam-5730	53	73	)	)	PUNCT
ejpam-5730	53	74	≤	≤	NUM
ejpam-5730	53	75	r	r	NOUN
ejpam-5730	53	76	q(x	q(x	PROPN
ejpam-5730	53	77	,	,	PUNCT
ejpam-5730	53	78	fx	fx	PROPN
ejpam-5730	53	79	)	)	PUNCT
ejpam-5730	53	80	for	for	ADP
ejpam-5730	53	81	all	all	DET
ejpam-5730	53	82	x	x	SYM
ejpam-5730	53	83	∈	∈	PROPN
ejpam-5730	53	84	x\{fx	x\{fx	PROPN
ejpam-5730	53	85	}	}	PUNCT
ejpam-5730	53	86	,	,	PUNCT
ejpam-5730	53	87	then	then	ADV
ejpam-5730	53	88	f	f	PROPN
ejpam-5730	53	89	has	have	VERB
ejpam-5730	53	90	a	a	DET
ejpam-5730	53	91	common	common	ADJ
ejpam-5730	53	92	fixed	fix	VERB
ejpam-5730	53	93	element	element	NOUN
ejpam-5730	53	94	v	v	ADP
ejpam-5730	53	95	∈	∈	PROPN
ejpam-5730	53	96	a	a	PRON
ejpam-5730	53	97	,	,	PUNCT
ejpam-5730	53	98	that	that	ADV
ejpam-5730	53	99	is	is	ADV
ejpam-5730	53	100	,	,	PUNCT
ejpam-5730	53	101	v	v	X
ejpam-5730	53	102	=	=	SYM
ejpam-5730	53	103	fv	fv	NOUN
ejpam-5730	53	104	for	for	ADP
ejpam-5730	53	105	all	all	DET
ejpam-5730	53	106	f	f	PROPN
ejpam-5730	53	107	∈	∈	PROPN
ejpam-5730	53	108	f.	f.	PROPN
ejpam-5730	53	109	(	(	PUNCT
ejpam-5730	53	110	δ	δ	PROPN
ejpam-5730	53	111	)	)	PUNCT
ejpam-5730	53	112	let	let	VERB
ejpam-5730	53	113	f	f	PRON
ejpam-5730	53	114	be	be	AUX
ejpam-5730	53	115	a	a	DET
ejpam-5730	53	116	family	family	NOUN
ejpam-5730	53	117	of	of	ADP
ejpam-5730	53	118	multimaps	multimap	NOUN
ejpam-5730	53	119	t	t	PROPN
ejpam-5730	53	120	:	:	PUNCT
ejpam-5730	53	121	x	x	X
ejpam-5730	53	122	→	→	SYM
ejpam-5730	53	123	cl(x	cl(x	NOUN
ejpam-5730	53	124	)	)	PUNCT
ejpam-5730	53	125	such	such	ADJ
ejpam-5730	53	126	that	that	SCONJ
ejpam-5730	53	127	,	,	PUNCT
ejpam-5730	53	128	for	for	ADP
ejpam-5730	53	129	any	any	DET
ejpam-5730	53	130	x	x	SYM
ejpam-5730	53	131	∈	∈	PROPN
ejpam-5730	53	132	x\tx	x\tx	NOUN
ejpam-5730	53	133	,	,	PUNCT
ejpam-5730	53	134	there	there	PRON
ejpam-5730	53	135	exists	exist	VERB
ejpam-5730	53	136	y	y	PROPN
ejpam-5730	53	137	∈	∈	PROPN
ejpam-5730	53	138	x\{x	x\{x	PROPN
ejpam-5730	53	139	}	}	PUNCT
ejpam-5730	53	140	satisfying	satisfy	VERB
ejpam-5730	53	141	h(tx	h(tx	PROPN
ejpam-5730	53	142	,	,	PUNCT
ejpam-5730	53	143	ty	ty	NOUN
ejpam-5730	53	144	)	)	PUNCT
ejpam-5730	53	145	≤	≤	NOUN
ejpam-5730	53	146	r	r	NOUN
ejpam-5730	53	147	q(x	q(x	PROPN
ejpam-5730	53	148	,	,	PUNCT
ejpam-5730	53	149	y	y	NOUN
ejpam-5730	53	150	)	)	PUNCT
ejpam-5730	53	151	.	.	PUNCT
ejpam-5730	54	1	then	then	ADV
ejpam-5730	54	2	f	f	PROPN
ejpam-5730	54	3	has	have	VERB
ejpam-5730	54	4	a	a	DET
ejpam-5730	54	5	common	common	ADJ
ejpam-5730	54	6	fixed	fix	VERB
ejpam-5730	54	7	element	element	NOUN
ejpam-5730	54	8	v	v	ADP
ejpam-5730	54	9	∈	∈	PROPN
ejpam-5730	54	10	x	x	NOUN
ejpam-5730	54	11	,	,	PUNCT
ejpam-5730	54	12	that	that	ADV
ejpam-5730	54	13	is	is	ADV
ejpam-5730	54	14	,	,	PUNCT
ejpam-5730	54	15	v	v	PROPN
ejpam-5730	54	16	∈	∈	PROPN
ejpam-5730	54	17	tv	tv	NOUN
ejpam-5730	54	18	for	for	ADP
ejpam-5730	54	19	all	all	DET
ejpam-5730	54	20	t	t	PROPN
ejpam-5730	54	21	∈	∈	PROPN
ejpam-5730	54	22	f.	f.	PROPN
ejpam-5730	54	23	(	(	PUNCT
ejpam-5730	54	24	ϵ	ϵ	X
ejpam-5730	54	25	)	)	PUNCT
ejpam-5730	54	26	if	if	SCONJ
ejpam-5730	54	27	f	f	PROPN
ejpam-5730	54	28	is	be	AUX
ejpam-5730	54	29	a	a	DET
ejpam-5730	54	30	family	family	NOUN
ejpam-5730	54	31	of	of	ADP
ejpam-5730	54	32	multimaps	multimap	NOUN
ejpam-5730	54	33	t	t	PROPN
ejpam-5730	54	34	:	:	PUNCT
ejpam-5730	54	35	x	x	X
ejpam-5730	54	36	→	→	SYM
ejpam-5730	54	37	cl(x	cl(x	X
ejpam-5730	54	38	)	)	PUNCT
ejpam-5730	54	39	satisfying	satisfy	VERB
ejpam-5730	54	40	h(tx	h(tx	PROPN
ejpam-5730	54	41	,	,	PUNCT
ejpam-5730	54	42	ty	ty	NOUN
ejpam-5730	54	43	)	)	PUNCT
ejpam-5730	54	44	≤	≤	NOUN
ejpam-5730	54	45	r	r	NOUN
ejpam-5730	54	46	q(x	q(x	PROPN
ejpam-5730	54	47	,	,	PUNCT
ejpam-5730	54	48	y	y	NOUN
ejpam-5730	54	49	)	)	PUNCT
ejpam-5730	54	50	for	for	ADP
ejpam-5730	54	51	all	all	PRON
ejpam-5730	54	52	x	x	SYM
ejpam-5730	54	53	∈	∈	PROPN
ejpam-5730	54	54	x	x	X
ejpam-5730	54	55	and	and	CCONJ
ejpam-5730	54	56	any	any	DET
ejpam-5730	54	57	y	y	PROPN
ejpam-5730	54	58	∈	∈	PROPN
ejpam-5730	54	59	tx\{x	tx\{x	NUM
ejpam-5730	54	60	}	}	PUNCT
ejpam-5730	54	61	,	,	PUNCT
ejpam-5730	54	62	then	then	ADV
ejpam-5730	54	63	f	f	PROPN
ejpam-5730	54	64	has	have	VERB
ejpam-5730	54	65	a	a	DET
ejpam-5730	54	66	common	common	ADJ
ejpam-5730	54	67	stationary	stationary	ADJ
ejpam-5730	54	68	element	element	NOUN
ejpam-5730	54	69	v	v	ADP
ejpam-5730	54	70	∈	∈	PROPN
ejpam-5730	54	71	x	x	NOUN
ejpam-5730	54	72	,	,	PUNCT
ejpam-5730	54	73	that	that	ADV
ejpam-5730	54	74	is	is	ADV
ejpam-5730	54	75	,	,	PUNCT
ejpam-5730	54	76	{	{	PUNCT
ejpam-5730	54	77	v	v	NOUN
ejpam-5730	54	78	}	}	PUNCT
ejpam-5730	54	79	=	=	SYM
ejpam-5730	54	80	tv	tv	NOUN
ejpam-5730	54	81	for	for	ADP
ejpam-5730	54	82	all	all	DET
ejpam-5730	54	83	t	t	PROPN
ejpam-5730	54	84	∈	∈	PROPN
ejpam-5730	54	85	f.	f.	PROPN
ejpam-5730	54	86	s.	s.	PROPN
ejpam-5730	54	87	park	park	PROPN
ejpam-5730	54	88	/	/	SYM
ejpam-5730	54	89	eur	eur	PROPN
ejpam-5730	54	90	.	.	PUNCT
ejpam-5730	55	1	j.	j.	PROPN
ejpam-5730	55	2	pure	pure	PROPN
ejpam-5730	55	3	appl	appl	PROPN
ejpam-5730	55	4	.	.	PROPN
ejpam-5730	55	5	math	math	PROPN
ejpam-5730	55	6	,	,	PUNCT
ejpam-5730	55	7	18	18	NUM
ejpam-5730	55	8	(	(	PUNCT
ejpam-5730	55	9	1	1	NUM
ejpam-5730	55	10	)	)	PUNCT
ejpam-5730	55	11	(	(	PUNCT
ejpam-5730	55	12	2025	2025	NUM
ejpam-5730	55	13	)	)	PUNCT
ejpam-5730	55	14	,	,	PUNCT
ejpam-5730	55	15	5730	5730	NUM
ejpam-5730	55	16	4	4	NUM
ejpam-5730	55	17	of	of	ADP
ejpam-5730	55	18	21	21	NUM
ejpam-5730	55	19	(	(	PUNCT
ejpam-5730	55	20	η	η	NOUN
ejpam-5730	55	21	)	)	PUNCT
ejpam-5730	55	22	if	if	SCONJ
ejpam-5730	55	23	y	y	PROPN
ejpam-5730	55	24	is	be	AUX
ejpam-5730	55	25	a	a	DET
ejpam-5730	55	26	subset	subset	NOUN
ejpam-5730	55	27	of	of	ADP
ejpam-5730	55	28	x	x	SYM
ejpam-5730	55	29	such	such	ADJ
ejpam-5730	55	30	that	that	PRON
ejpam-5730	55	31	for	for	ADP
ejpam-5730	55	32	each	each	DET
ejpam-5730	55	33	x	x	SYM
ejpam-5730	55	34	∈	∈	PROPN
ejpam-5730	55	35	x\y	x\y	X
ejpam-5730	56	1	there	there	PRON
ejpam-5730	56	2	exists	exist	VERB
ejpam-5730	56	3	a	a	DET
ejpam-5730	56	4	z	z	NOUN
ejpam-5730	56	5	∈	∈	PROPN
ejpam-5730	56	6	x\{x	x\{x	X
ejpam-5730	56	7	}	}	PUNCT
ejpam-5730	56	8	satisfying	satisfy	VERB
ejpam-5730	56	9	h(tx	h(tx	PROPN
ejpam-5730	56	10	,	,	PUNCT
ejpam-5730	56	11	tz	tz	NOUN
ejpam-5730	56	12	)	)	PUNCT
ejpam-5730	56	13	≤	≤	NOUN
ejpam-5730	56	14	r	r	NOUN
ejpam-5730	56	15	q(x	q(x	PROPN
ejpam-5730	56	16	,	,	PUNCT
ejpam-5730	56	17	z	z	NOUN
ejpam-5730	56	18	)	)	PUNCT
ejpam-5730	56	19	for	for	ADP
ejpam-5730	56	20	a	a	DET
ejpam-5730	56	21	t	t	NOUN
ejpam-5730	56	22	:	:	PUNCT
ejpam-5730	56	23	x	x	X
ejpam-5730	56	24	→	→	SYM
ejpam-5730	56	25	cl(x	cl(x	NOUN
ejpam-5730	56	26	)	)	PUNCT
ejpam-5730	56	27	,	,	PUNCT
ejpam-5730	56	28	then	then	ADV
ejpam-5730	56	29	there	there	PRON
ejpam-5730	56	30	exists	exist	VERB
ejpam-5730	56	31	a	a	DET
ejpam-5730	56	32	v	v	NOUN
ejpam-5730	56	33	∈	∈	NOUN
ejpam-5730	56	34	x	x	SYM
ejpam-5730	56	35	∩	∩	ADJ
ejpam-5730	56	36	y	y	PROPN
ejpam-5730	56	37	=	=	SYM
ejpam-5730	56	38	y	y	PROPN
ejpam-5730	56	39	.	.	PUNCT
ejpam-5730	57	1	proof	proof	NOUN
ejpam-5730	57	2	.	.	PUNCT
ejpam-5730	58	1	the	the	DET
ejpam-5730	58	2	equivalency	equivalency	NOUN
ejpam-5730	58	3	(	(	PUNCT
ejpam-5730	58	4	α)−	α)−	PROPN
ejpam-5730	58	5	(	(	PUNCT
ejpam-5730	58	6	η	η	X
ejpam-5730	58	7	)	)	PUNCT
ejpam-5730	58	8	follows	follow	VERB
ejpam-5730	58	9	from	from	ADP
ejpam-5730	58	10	our	our	PRON
ejpam-5730	58	11	2023	2023	NUM
ejpam-5730	58	12	metatheorem	metatheorem	VERB
ejpam-5730	58	13	in	in	ADP
ejpam-5730	58	14	[	[	X
ejpam-5730	58	15	30]-[32	30]-[32	PROPN
ejpam-5730	58	16	]	]	X
ejpam-5730	58	17	.	.	PUNCT
ejpam-5730	59	1	when	when	SCONJ
ejpam-5730	59	2	f	f	PROPN
ejpam-5730	59	3	is	be	AUX
ejpam-5730	59	4	a	a	DET
ejpam-5730	59	5	singleton	singleton	NOUN
ejpam-5730	59	6	,	,	PUNCT
ejpam-5730	59	7	(	(	PUNCT
ejpam-5730	59	8	β)-(ϵ	β)-(ϵ	X
ejpam-5730	59	9	)	)	PUNCT
ejpam-5730	59	10	are	be	AUX
ejpam-5730	59	11	denoted	denote	VERB
ejpam-5730	59	12	by	by	ADP
ejpam-5730	59	13	(	(	PUNCT
ejpam-5730	59	14	β1)-(ϵ1	β1)-(ϵ1	NUM
ejpam-5730	59	15	)	)	PUNCT
ejpam-5730	59	16	,	,	PUNCT
ejpam-5730	59	17	respectively	respectively	ADV
ejpam-5730	59	18	,	,	PUNCT
ejpam-5730	59	19	they	they	PRON
ejpam-5730	59	20	are	be	AUX
ejpam-5730	59	21	also	also	ADV
ejpam-5730	59	22	logically	logically	ADV
ejpam-5730	59	23	equivalent	equivalent	ADJ
ejpam-5730	59	24	to	to	ADP
ejpam-5730	59	25	(	(	PUNCT
ejpam-5730	59	26	α)-(η	α)-(η	PROPN
ejpam-5730	59	27	)	)	PUNCT
ejpam-5730	59	28	.	.	PUNCT
ejpam-5730	60	1	note	note	VERB
ejpam-5730	60	2	that	that	SCONJ
ejpam-5730	60	3	(	(	PUNCT
ejpam-5730	60	4	α	α	X
ejpam-5730	60	5	)	)	PUNCT
ejpam-5730	60	6	=	=	NOUN
ejpam-5730	60	7	⇒	⇒	NOUN
ejpam-5730	60	8	(	(	PUNCT
ejpam-5730	60	9	γ1	γ1	PROPN
ejpam-5730	60	10	)	)	PUNCT
ejpam-5730	60	11	follows	follow	VERB
ejpam-5730	60	12	from	from	ADP
ejpam-5730	60	13	theorem	theorem	ADJ
ejpam-5730	60	14	p	p	PROPN
ejpam-5730	60	15	for	for	ADP
ejpam-5730	60	16	quasi	quasi	ADJ
ejpam-5730	60	17	-	-	ADJ
ejpam-5730	60	18	metric	metric	ADJ
ejpam-5730	60	19	spaces	space	NOUN
ejpam-5730	60	20	.	.	PUNCT
ejpam-5730	61	1	the	the	DET
ejpam-5730	61	2	equivalency	equivalency	NOUN
ejpam-5730	61	3	of	of	ADP
ejpam-5730	61	4	(	(	PUNCT
ejpam-5730	61	5	0	0	NUM
ejpam-5730	61	6	)	)	PUNCT
ejpam-5730	61	7	and	and	CCONJ
ejpam-5730	61	8	(	(	PUNCT
ejpam-5730	61	9	γ1	γ1	PROPN
ejpam-5730	61	10	)	)	PUNCT
ejpam-5730	61	11	is	be	AUX
ejpam-5730	61	12	given	give	VERB
ejpam-5730	61	13	in	in	ADP
ejpam-5730	61	14	[	[	X
ejpam-5730	61	15	36	36	NUM
ejpam-5730	61	16	]	]	PUNCT
ejpam-5730	61	17	,	,	PUNCT
ejpam-5730	61	18	[	[	X
ejpam-5730	61	19	39	39	NUM
ejpam-5730	61	20	]	]	PUNCT
ejpam-5730	61	21	.	.	PUNCT
ejpam-5730	62	1	then	then	ADV
ejpam-5730	62	2	theorem	theorem	VERB
ejpam-5730	62	3	h	h	NOUN
ejpam-5730	62	4	holds	hold	VERB
ejpam-5730	62	5	.	.	PUNCT
ejpam-5730	63	1	□	□	PUNCT
ejpam-5730	63	2	remark	remark	NOUN
ejpam-5730	63	3	3.1	3.1	NUM
ejpam-5730	63	4	.	.	PUNCT
ejpam-5730	64	1	(	(	PUNCT
ejpam-5730	64	2	1	1	NUM
ejpam-5730	64	3	)	)	PUNCT
ejpam-5730	64	4	(	(	PUNCT
ejpam-5730	64	5	α	α	X
ejpam-5730	64	6	)	)	PUNCT
ejpam-5730	64	7	=	=	NOUN
ejpam-5730	64	8	⇒	⇒	NOUN
ejpam-5730	64	9	(	(	PUNCT
ejpam-5730	64	10	β1	β1	PROPN
ejpam-5730	64	11	)	)	PUNCT
ejpam-5730	64	12	implies	imply	VERB
ejpam-5730	64	13	the	the	DET
ejpam-5730	64	14	banach	banach	NOUN
ejpam-5730	64	15	contraction	contraction	NOUN
ejpam-5730	64	16	principle	principle	NOUN
ejpam-5730	64	17	,	,	PUNCT
ejpam-5730	64	18	which	which	PRON
ejpam-5730	64	19	does	do	AUX
ejpam-5730	64	20	not	not	PART
ejpam-5730	64	21	characterize	characterize	VERB
ejpam-5730	64	22	the	the	DET
ejpam-5730	64	23	metric	metric	ADJ
ejpam-5730	64	24	completeness	completeness	NOUN
ejpam-5730	64	25	.	.	PUNCT
ejpam-5730	65	1	(	(	PUNCT
ejpam-5730	65	2	2	2	X
ejpam-5730	65	3	)	)	PUNCT
ejpam-5730	65	4	moreover	moreover	ADV
ejpam-5730	65	5	,	,	PUNCT
ejpam-5730	65	6	(	(	PUNCT
ejpam-5730	65	7	α	α	X
ejpam-5730	65	8	)	)	PUNCT
ejpam-5730	65	9	=	=	NOUN
ejpam-5730	65	10	⇒	⇒	NOUN
ejpam-5730	65	11	(	(	PUNCT
ejpam-5730	65	12	δ1	δ1	NOUN
ejpam-5730	65	13	)	)	PUNCT
ejpam-5730	65	14	and	and	CCONJ
ejpam-5730	65	15	(	(	PUNCT
ejpam-5730	65	16	α	α	NOUN
ejpam-5730	65	17	)	)	PUNCT
ejpam-5730	65	18	=	=	NOUN
ejpam-5730	65	19	⇒	⇒	NOUN
ejpam-5730	65	20	(	(	PUNCT
ejpam-5730	65	21	ϵ1	ϵ1	ADJ
ejpam-5730	65	22	)	)	PUNCT
ejpam-5730	65	23	extend	extend	VERB
ejpam-5730	65	24	the	the	DET
ejpam-5730	65	25	well	well	ADV
ejpam-5730	65	26	-	-	PUNCT
ejpam-5730	65	27	known	know	VERB
ejpam-5730	65	28	fixed	fix	VERB
ejpam-5730	65	29	point	point	NOUN
ejpam-5730	65	30	theorems	theorem	NOUN
ejpam-5730	65	31	of	of	ADP
ejpam-5730	65	32	nadler	nadler	NOUN
ejpam-5730	66	1	[	[	X
ejpam-5730	66	2	28	28	NUM
ejpam-5730	66	3	]	]	PUNCT
ejpam-5730	66	4	and	and	CCONJ
ejpam-5730	66	5	covitz	covitz	NOUN
ejpam-5730	66	6	-	-	PUNCT
ejpam-5730	66	7	nadler	nadler	NOUN
ejpam-5730	66	8	[	[	X
ejpam-5730	66	9	9	9	NUM
ejpam-5730	66	10	]	]	PUNCT
ejpam-5730	66	11	.	.	PUNCT
ejpam-5730	67	1	the	the	DET
ejpam-5730	67	2	following	follow	VERB
ejpam-5730	67	3	(	(	PUNCT
ejpam-5730	67	4	α	α	NOUN
ejpam-5730	67	5	)	)	PUNCT
ejpam-5730	67	6	=	=	NOUN
ejpam-5730	67	7	⇒	⇒	NOUN
ejpam-5730	67	8	(	(	PUNCT
ejpam-5730	67	9	γ1	γ1	PROPN
ejpam-5730	67	10	)	)	PUNCT
ejpam-5730	67	11	of	of	ADP
ejpam-5730	67	12	theorem	theorem	ADJ
ejpam-5730	67	13	h	h	NOUN
ejpam-5730	67	14	also	also	ADV
ejpam-5730	67	15	follows	follow	VERB
ejpam-5730	67	16	from	from	ADP
ejpam-5730	67	17	theorem	theorem	ADJ
ejpam-5730	67	18	p.	p.	NOUN
ejpam-5730	67	19	it	it	PRON
ejpam-5730	67	20	is	be	AUX
ejpam-5730	67	21	the	the	DET
ejpam-5730	67	22	basis	basis	NOUN
ejpam-5730	67	23	in	in	ADP
ejpam-5730	67	24	the	the	DET
ejpam-5730	67	25	present	present	ADJ
ejpam-5730	67	26	article	article	NOUN
ejpam-5730	67	27	and	and	CCONJ
ejpam-5730	67	28	will	will	AUX
ejpam-5730	67	29	be	be	AUX
ejpam-5730	67	30	called	call	VERB
ejpam-5730	67	31	the	the	DET
ejpam-5730	67	32	rhr	rhr	PROPN
ejpam-5730	67	33	theorem	theorem	PROPN
ejpam-5730	67	34	,	,	PUNCT
ejpam-5730	67	35	which	which	PRON
ejpam-5730	67	36	characterizes	characterize	VERB
ejpam-5730	67	37	the	the	DET
ejpam-5730	67	38	metric	metric	ADJ
ejpam-5730	67	39	completeness	completeness	NOUN
ejpam-5730	67	40	.	.	PUNCT
ejpam-5730	68	1	theorem	theorem	ADJ
ejpam-5730	68	2	h(γ1	h(γ1	NOUN
ejpam-5730	68	3	)	)	PUNCT
ejpam-5730	68	4	.	.	PUNCT
ejpam-5730	69	1	let	let	AUX
ejpam-5730	69	2	(	(	PUNCT
ejpam-5730	69	3	x	x	NOUN
ejpam-5730	69	4	,	,	PUNCT
ejpam-5730	69	5	δ	δ	PROPN
ejpam-5730	69	6	)	)	PUNCT
ejpam-5730	69	7	be	be	VERB
ejpam-5730	69	8	a	a	DET
ejpam-5730	69	9	complete	complete	ADJ
ejpam-5730	69	10	quasi	quasi	ADJ
ejpam-5730	69	11	-	-	ADJ
ejpam-5730	69	12	metric	metric	ADJ
ejpam-5730	69	13	space	space	NOUN
ejpam-5730	69	14	and	and	CCONJ
ejpam-5730	69	15	0	0	NUM
ejpam-5730	69	16	<	<	X
ejpam-5730	69	17	r	r	X
ejpam-5730	69	18	<	<	X
ejpam-5730	69	19	1	1	NUM
ejpam-5730	69	20	.	.	PUNCT
ejpam-5730	69	21	(	(	PUNCT
ejpam-5730	69	22	γ1	γ1	PROPN
ejpam-5730	69	23	)	)	PUNCT
ejpam-5730	69	24	if	if	SCONJ
ejpam-5730	69	25	a	a	DET
ejpam-5730	69	26	map	map	NOUN
ejpam-5730	69	27	f	f	X
ejpam-5730	70	1	:	:	PUNCT
ejpam-5730	70	2	x	x	X
ejpam-5730	70	3	→	→	SYM
ejpam-5730	70	4	x	x	SYM
ejpam-5730	70	5	satisfies	satisfie	NOUN
ejpam-5730	70	6	δ(fx	δ(fx	ADV
ejpam-5730	70	7	,	,	PUNCT
ejpam-5730	70	8	f2x	f2x	X
ejpam-5730	70	9	)	)	PUNCT
ejpam-5730	70	10	≤	≤	NUM
ejpam-5730	70	11	r	r	NOUN
ejpam-5730	70	12	δ(x	δ(x	PROPN
ejpam-5730	70	13	,	,	PUNCT
ejpam-5730	70	14	fx	fx	NOUN
ejpam-5730	70	15	)	)	PUNCT
ejpam-5730	70	16	for	for	ADP
ejpam-5730	70	17	all	all	DET
ejpam-5730	70	18	x	x	SYM
ejpam-5730	70	19	∈	∈	PROPN
ejpam-5730	70	20	x\{fx	x\{fx	PROPN
ejpam-5730	70	21	}	}	PUNCT
ejpam-5730	70	22	,	,	PUNCT
ejpam-5730	70	23	then	then	ADV
ejpam-5730	70	24	f	f	PROPN
ejpam-5730	70	25	has	have	VERB
ejpam-5730	70	26	a	a	DET
ejpam-5730	70	27	fixed	fix	VERB
ejpam-5730	70	28	element	element	NOUN
ejpam-5730	70	29	v	v	ADP
ejpam-5730	70	30	∈	∈	PROPN
ejpam-5730	70	31	x	x	NOUN
ejpam-5730	70	32	,	,	PUNCT
ejpam-5730	70	33	that	that	ADV
ejpam-5730	70	34	is	is	ADV
ejpam-5730	70	35	,	,	PUNCT
ejpam-5730	70	36	v	v	NOUN
ejpam-5730	70	37	=	=	SYM
ejpam-5730	70	38	fv	fv	X
ejpam-5730	70	39	.	.	PUNCT
ejpam-5730	70	40	consequently	consequently	ADV
ejpam-5730	70	41	,	,	PUNCT
ejpam-5730	70	42	this	this	PRON
ejpam-5730	70	43	is	be	AUX
ejpam-5730	70	44	a	a	DET
ejpam-5730	70	45	close	close	ADJ
ejpam-5730	70	46	relative	relative	NOUN
ejpam-5730	70	47	of	of	ADP
ejpam-5730	70	48	theorems	theorem	NOUN
ejpam-5730	70	49	of	of	ADP
ejpam-5730	70	50	rus	rus	NOUN
ejpam-5730	70	51	[	[	PUNCT
ejpam-5730	70	52	48	48	NUM
ejpam-5730	70	53	]	]	PUNCT
ejpam-5730	70	54	and	and	CCONJ
ejpam-5730	70	55	hicks	hicks	PROPN
ejpam-5730	70	56	-	-	PUNCT
ejpam-5730	70	57	rhoades	rhoade	NOUN
ejpam-5730	70	58	[	[	X
ejpam-5730	70	59	14	14	NUM
ejpam-5730	70	60	]	]	PUNCT
ejpam-5730	70	61	.	.	PUNCT
ejpam-5730	71	1	this	this	PRON
ejpam-5730	71	2	is	be	AUX
ejpam-5730	71	3	rather	rather	ADV
ejpam-5730	71	4	surprising	surprising	ADJ
ejpam-5730	71	5	and	and	CCONJ
ejpam-5730	71	6	they	they	PRON
ejpam-5730	71	7	are	be	AUX
ejpam-5730	71	8	all	all	ADV
ejpam-5730	71	9	close	close	ADJ
ejpam-5730	71	10	relatives	relative	NOUN
ejpam-5730	71	11	of	of	ADP
ejpam-5730	71	12	the	the	DET
ejpam-5730	71	13	banach	banach	NOUN
ejpam-5730	71	14	contraction	contraction	NOUN
ejpam-5730	71	15	principle	principle	NOUN
ejpam-5730	71	16	;	;	PUNCT
ejpam-5730	71	17	see	see	VERB
ejpam-5730	71	18	[	[	X
ejpam-5730	71	19	4	4	NUM
ejpam-5730	71	20	]	]	PUNCT
ejpam-5730	71	21	.	.	PUNCT
ejpam-5730	72	1	4	4	X
ejpam-5730	72	2	.	.	X
ejpam-5730	72	3	the	the	DET
ejpam-5730	72	4	subfamily	subfamily	ADV
ejpam-5730	72	5	{	{	PUNCT
ejpam-5730	72	6	α	α	NOUN
ejpam-5730	72	7	}	}	PUNCT
ejpam-5730	72	8	based	base	VERB
ejpam-5730	72	9	on	on	ADP
ejpam-5730	72	10	our	our	PRON
ejpam-5730	72	11	2023	2023	NUM
ejpam-5730	72	12	metatheorem	metatheorem	ADJ
ejpam-5730	72	13	[	[	X
ejpam-5730	72	14	30	30	NUM
ejpam-5730	72	15	]	]	PUNCT
ejpam-5730	72	16	and	and	CCONJ
ejpam-5730	72	17	theorem	theorem	ADJ
ejpam-5730	72	18	h	h	NOUN
ejpam-5730	72	19	,	,	PUNCT
ejpam-5730	72	20	we	we	PRON
ejpam-5730	72	21	obtained	obtain	VERB
ejpam-5730	72	22	the	the	DET
ejpam-5730	72	23	following	following	NOUN
ejpam-5730	72	24	in	in	ADP
ejpam-5730	72	25	[	[	X
ejpam-5730	72	26	38	38	NUM
ejpam-5730	72	27	]	]	PUNCT
ejpam-5730	72	28	,	,	PUNCT
ejpam-5730	72	29	[	[	X
ejpam-5730	72	30	39	39	NUM
ejpam-5730	72	31	]	]	PUNCT
ejpam-5730	72	32	:	:	PUNCT
ejpam-5730	72	33	theorem	theorem	ADJ
ejpam-5730	72	34	h(α	h(α	ADV
ejpam-5730	72	35	)	)	PUNCT
ejpam-5730	72	36	.	.	PUNCT
ejpam-5730	73	1	let	let	VERB
ejpam-5730	73	2	(	(	PUNCT
ejpam-5730	73	3	x	x	X
ejpam-5730	73	4	,	,	PUNCT
ejpam-5730	73	5	q	q	X
ejpam-5730	73	6	)	)	PUNCT
ejpam-5730	73	7	be	be	AUX
ejpam-5730	73	8	a	a	DET
ejpam-5730	73	9	quasi	quasi	ADJ
ejpam-5730	73	10	-	-	ADJ
ejpam-5730	73	11	metric	metric	ADJ
ejpam-5730	73	12	space	space	NOUN
ejpam-5730	73	13	and	and	CCONJ
ejpam-5730	73	14	0	0	NUM
ejpam-5730	73	15	<	<	X
ejpam-5730	73	16	r	r	X
ejpam-5730	73	17	<	<	X
ejpam-5730	73	18	1	1	NUM
ejpam-5730	73	19	.	.	PUNCT
ejpam-5730	74	1	then	then	ADV
ejpam-5730	74	2	the	the	DET
ejpam-5730	74	3	following	following	ADJ
ejpam-5730	74	4	statements	statement	NOUN
ejpam-5730	74	5	are	be	AUX
ejpam-5730	74	6	equivalent	equivalent	ADJ
ejpam-5730	74	7	:	:	PUNCT
ejpam-5730	74	8	(	(	PUNCT
ejpam-5730	74	9	0	0	NUM
ejpam-5730	74	10	)	)	PUNCT
ejpam-5730	74	11	(	(	PUNCT
ejpam-5730	74	12	x	x	X
ejpam-5730	74	13	,	,	PUNCT
ejpam-5730	74	14	q	q	X
ejpam-5730	74	15	)	)	PUNCT
ejpam-5730	74	16	is	be	AUX
ejpam-5730	74	17	complete	complete	ADJ
ejpam-5730	74	18	.	.	PUNCT
ejpam-5730	75	1	(	(	PUNCT
ejpam-5730	75	2	α1	α1	PROPN
ejpam-5730	75	3	)	)	PUNCT
ejpam-5730	75	4	for	for	ADP
ejpam-5730	75	5	a	a	DET
ejpam-5730	75	6	map	map	NOUN
ejpam-5730	76	1	f	f	NOUN
ejpam-5730	76	2	:	:	PUNCT
ejpam-5730	76	3	x	x	X
ejpam-5730	76	4	→	→	SYM
ejpam-5730	76	5	x	x	X
ejpam-5730	76	6	,	,	PUNCT
ejpam-5730	76	7	there	there	PRON
ejpam-5730	76	8	exists	exist	VERB
ejpam-5730	76	9	an	an	DET
ejpam-5730	76	10	element	element	NOUN
ejpam-5730	76	11	v	v	ADP
ejpam-5730	76	12	∈	∈	PROPN
ejpam-5730	76	13	x	x	PUNCT
ejpam-5730	76	14	such	such	ADJ
ejpam-5730	76	15	that	that	DET
ejpam-5730	76	16	q(fv	q(fv	PROPN
ejpam-5730	76	17	,	,	PUNCT
ejpam-5730	76	18	fw	fw	ADJ
ejpam-5730	76	19	)	)	PUNCT
ejpam-5730	76	20	>	>	PUNCT
ejpam-5730	76	21	r	r	PROPN
ejpam-5730	76	22	q(v	q(v	PROPN
ejpam-5730	76	23	,	,	PUNCT
ejpam-5730	76	24	w	w	NOUN
ejpam-5730	76	25	)	)	PUNCT
ejpam-5730	76	26	for	for	ADP
ejpam-5730	76	27	any	any	DET
ejpam-5730	76	28	w	w	PROPN
ejpam-5730	76	29	∈	∈	PROPN
ejpam-5730	76	30	x\{v	x\{v	PROPN
ejpam-5730	76	31	}	}	PUNCT
ejpam-5730	76	32	.	.	PUNCT
ejpam-5730	77	1	(	(	PUNCT
ejpam-5730	77	2	α	α	X
ejpam-5730	77	3	)	)	PUNCT
ejpam-5730	77	4	for	for	ADP
ejpam-5730	77	5	a	a	DET
ejpam-5730	77	6	multimap	multimap	NOUN
ejpam-5730	77	7	t	t	NOUN
ejpam-5730	77	8	:	:	PUNCT
ejpam-5730	77	9	x	x	X
ejpam-5730	77	10	→	→	SYM
ejpam-5730	77	11	cl(x	cl(x	NOUN
ejpam-5730	77	12	)	)	PUNCT
ejpam-5730	77	13	,	,	PUNCT
ejpam-5730	77	14	there	there	PRON
ejpam-5730	77	15	exists	exist	VERB
ejpam-5730	77	16	an	an	DET
ejpam-5730	77	17	element	element	NOUN
ejpam-5730	77	18	v	v	ADP
ejpam-5730	77	19	∈	∈	PROPN
ejpam-5730	77	20	x	x	PUNCT
ejpam-5730	77	21	such	such	ADJ
ejpam-5730	77	22	that	that	PRON
ejpam-5730	77	23	h(tv	h(tv	PROPN
ejpam-5730	77	24	,	,	PUNCT
ejpam-5730	77	25	tw	tw	PROPN
ejpam-5730	77	26	)	)	PUNCT
ejpam-5730	77	27	>	>	PUNCT
ejpam-5730	78	1	r	r	PROPN
ejpam-5730	78	2	q(v	q(v	PROPN
ejpam-5730	78	3	,	,	PUNCT
ejpam-5730	78	4	w	w	NOUN
ejpam-5730	78	5	)	)	PUNCT
ejpam-5730	78	6	for	for	ADP
ejpam-5730	78	7	any	any	DET
ejpam-5730	78	8	w	w	PROPN
ejpam-5730	78	9	∈	∈	PROPN
ejpam-5730	78	10	x\{v	x\{v	PROPN
ejpam-5730	78	11	}	}	PUNCT
ejpam-5730	78	12	.	.	PUNCT
ejpam-5730	79	1	if	if	SCONJ
ejpam-5730	79	2	x	x	PRON
ejpam-5730	79	3	is	be	AUX
ejpam-5730	79	4	t	t	NOUN
ejpam-5730	79	5	-orbitally	-orbitally	ADV
ejpam-5730	79	6	complete	complete	ADJ
ejpam-5730	79	7	,	,	PUNCT
ejpam-5730	79	8	then	then	ADV
ejpam-5730	79	9	(	(	PUNCT
ejpam-5730	79	10	α	α	NOUN
ejpam-5730	79	11	)	)	PUNCT
ejpam-5730	79	12	holds	hold	VERB
ejpam-5730	79	13	;	;	PUNCT
ejpam-5730	79	14	see	see	VERB
ejpam-5730	79	15	[	[	X
ejpam-5730	79	16	40	40	NUM
ejpam-5730	79	17	]	]	PUNCT
ejpam-5730	79	18	.	.	PUNCT
ejpam-5730	80	1	5	5	X
ejpam-5730	80	2	.	.	X
ejpam-5730	80	3	the	the	DET
ejpam-5730	80	4	subfamily	subfamily	ADV
ejpam-5730	80	5	{	{	PUNCT
ejpam-5730	80	6	β	β	NOUN
ejpam-5730	80	7	}	}	PUNCT
ejpam-5730	80	8	of	of	ADP
ejpam-5730	80	9	the	the	DET
ejpam-5730	80	10	extended	extended	ADJ
ejpam-5730	80	11	banach	banach	NOUN
ejpam-5730	80	12	type	type	NOUN
ejpam-5730	80	13	theorem	theorem	VERB
ejpam-5730	80	14	h(β	h(β	NOUN
ejpam-5730	80	15	)	)	PUNCT
ejpam-5730	80	16	.	.	PUNCT
ejpam-5730	81	1	let	let	VERB
ejpam-5730	81	2	(	(	PUNCT
ejpam-5730	81	3	x	x	X
ejpam-5730	81	4	,	,	PUNCT
ejpam-5730	81	5	q	q	X
ejpam-5730	81	6	)	)	PUNCT
ejpam-5730	81	7	be	be	AUX
ejpam-5730	81	8	a	a	DET
ejpam-5730	81	9	quasi	quasi	ADJ
ejpam-5730	81	10	-	-	ADJ
ejpam-5730	81	11	metric	metric	ADJ
ejpam-5730	81	12	space	space	NOUN
ejpam-5730	81	13	and	and	CCONJ
ejpam-5730	81	14	0	0	NUM
ejpam-5730	81	15	<	<	X
ejpam-5730	81	16	r	r	X
ejpam-5730	81	17	<	<	X
ejpam-5730	81	18	1	1	NUM
ejpam-5730	81	19	.	.	PUNCT
ejpam-5730	82	1	then	then	ADV
ejpam-5730	82	2	the	the	DET
ejpam-5730	82	3	following	following	ADJ
ejpam-5730	82	4	statements	statement	NOUN
ejpam-5730	82	5	are	be	AUX
ejpam-5730	82	6	equivalent	equivalent	ADJ
ejpam-5730	82	7	:	:	PUNCT
ejpam-5730	82	8	s.	s.	PROPN
ejpam-5730	82	9	park	park	PROPN
ejpam-5730	82	10	/	/	SYM
ejpam-5730	82	11	eur	eur	PROPN
ejpam-5730	82	12	.	.	PUNCT
ejpam-5730	83	1	j.	j.	PROPN
ejpam-5730	83	2	pure	pure	PROPN
ejpam-5730	83	3	appl	appl	PROPN
ejpam-5730	83	4	.	.	PROPN
ejpam-5730	83	5	math	math	PROPN
ejpam-5730	83	6	,	,	PUNCT
ejpam-5730	83	7	18	18	NUM
ejpam-5730	83	8	(	(	PUNCT
ejpam-5730	83	9	1	1	NUM
ejpam-5730	83	10	)	)	PUNCT
ejpam-5730	83	11	(	(	PUNCT
ejpam-5730	83	12	2025	2025	NUM
ejpam-5730	83	13	)	)	PUNCT
ejpam-5730	83	14	,	,	PUNCT
ejpam-5730	83	15	5730	5730	NUM
ejpam-5730	83	16	5	5	NUM
ejpam-5730	83	17	of	of	ADP
ejpam-5730	83	18	21	21	NUM
ejpam-5730	83	19	(	(	PUNCT
ejpam-5730	83	20	0	0	NUM
ejpam-5730	83	21	)	)	PUNCT
ejpam-5730	83	22	(	(	PUNCT
ejpam-5730	83	23	x	x	X
ejpam-5730	83	24	,	,	PUNCT
ejpam-5730	83	25	q	q	X
ejpam-5730	83	26	)	)	PUNCT
ejpam-5730	83	27	is	be	AUX
ejpam-5730	83	28	complete	complete	ADJ
ejpam-5730	83	29	.	.	PUNCT
ejpam-5730	84	1	(	(	PUNCT
ejpam-5730	84	2	β	β	X
ejpam-5730	84	3	)	)	PUNCT
ejpam-5730	84	4	if	if	SCONJ
ejpam-5730	84	5	f	f	PROPN
ejpam-5730	84	6	is	be	AUX
ejpam-5730	84	7	a	a	DET
ejpam-5730	84	8	family	family	NOUN
ejpam-5730	84	9	of	of	ADP
ejpam-5730	84	10	maps	map	NOUN
ejpam-5730	84	11	f	f	X
ejpam-5730	84	12	:	:	PUNCT
ejpam-5730	84	13	x	x	X
ejpam-5730	85	1	→	→	PUNCT
ejpam-5730	85	2	x	x	X
ejpam-5730	85	3	such	such	ADJ
ejpam-5730	85	4	that	that	SCONJ
ejpam-5730	85	5	,	,	PUNCT
ejpam-5730	85	6	for	for	ADP
ejpam-5730	85	7	any	any	DET
ejpam-5730	85	8	x	x	SYM
ejpam-5730	85	9	∈	∈	PROPN
ejpam-5730	85	10	x\{fx	x\{fx	PROPN
ejpam-5730	85	11	}	}	PUNCT
ejpam-5730	85	12	,	,	PUNCT
ejpam-5730	85	13	there	there	PRON
ejpam-5730	85	14	exists	exist	VERB
ejpam-5730	85	15	a	a	DET
ejpam-5730	85	16	y	y	PROPN
ejpam-5730	85	17	∈	∈	PROPN
ejpam-5730	85	18	x\{x	x\{x	PROPN
ejpam-5730	85	19	}	}	PUNCT
ejpam-5730	85	20	satisfying	satisfy	VERB
ejpam-5730	85	21	q(fx	q(fx	ADP
ejpam-5730	85	22	,	,	PUNCT
ejpam-5730	85	23	fy	fy	PROPN
ejpam-5730	85	24	)	)	PUNCT
ejpam-5730	85	25	≤	≤	NOUN
ejpam-5730	85	26	α	α	PROPN
ejpam-5730	85	27	q(x	q(x	PROPN
ejpam-5730	85	28	,	,	PUNCT
ejpam-5730	85	29	y	y	PROPN
ejpam-5730	85	30	)	)	PUNCT
ejpam-5730	85	31	,	,	PUNCT
ejpam-5730	85	32	then	then	ADV
ejpam-5730	85	33	f	f	PROPN
ejpam-5730	85	34	has	have	VERB
ejpam-5730	85	35	a	a	DET
ejpam-5730	85	36	common	common	ADJ
ejpam-5730	85	37	fixed	fix	VERB
ejpam-5730	85	38	element	element	NOUN
ejpam-5730	85	39	v	v	ADP
ejpam-5730	85	40	∈	∈	PROPN
ejpam-5730	85	41	x	x	NOUN
ejpam-5730	85	42	,	,	PUNCT
ejpam-5730	85	43	that	that	ADV
ejpam-5730	85	44	is	is	ADV
ejpam-5730	85	45	,	,	PUNCT
ejpam-5730	85	46	v	v	X
ejpam-5730	85	47	=	=	SYM
ejpam-5730	85	48	fv	fv	NOUN
ejpam-5730	85	49	for	for	ADP
ejpam-5730	85	50	all	all	DET
ejpam-5730	85	51	f	f	PROPN
ejpam-5730	85	52	∈	∈	PROPN
ejpam-5730	85	53	f.	f.	PROPN
ejpam-5730	85	54	in	in	ADP
ejpam-5730	85	55	this	this	DET
ejpam-5730	85	56	section	section	NOUN
ejpam-5730	85	57	,	,	PUNCT
ejpam-5730	85	58	we	we	PRON
ejpam-5730	85	59	want	want	VERB
ejpam-5730	85	60	to	to	PART
ejpam-5730	85	61	collect	collect	VERB
ejpam-5730	85	62	certain	certain	ADJ
ejpam-5730	85	63	extensions	extension	NOUN
ejpam-5730	85	64	of	of	ADP
ejpam-5730	85	65	the	the	DET
ejpam-5730	85	66	banach	banach	NOUN
ejpam-5730	85	67	contraction	contraction	NOUN
ejpam-5730	85	68	satisfying	satisfy	VERB
ejpam-5730	85	69	theorem	theorem	NOUN
ejpam-5730	85	70	h(β	h(β	NOUN
ejpam-5730	85	71	)	)	PUNCT
ejpam-5730	85	72	.	.	PUNCT
ejpam-5730	86	1	there	there	PRON
ejpam-5730	86	2	are	be	VERB
ejpam-5730	86	3	a	a	DET
ejpam-5730	86	4	huge	huge	ADJ
ejpam-5730	86	5	number	number	NOUN
ejpam-5730	86	6	of	of	ADP
ejpam-5730	86	7	extensions	extension	NOUN
ejpam-5730	86	8	of	of	ADP
ejpam-5730	86	9	the	the	DET
ejpam-5730	86	10	banach	banach	NOUN
ejpam-5730	86	11	contraction	contraction	NOUN
ejpam-5730	86	12	principle	principle	NOUN
ejpam-5730	86	13	,	,	PUNCT
ejpam-5730	86	14	however	however	ADV
ejpam-5730	86	15	,	,	PUNCT
ejpam-5730	86	16	we	we	PRON
ejpam-5730	86	17	have	have	AUX
ejpam-5730	86	18	known	know	VERB
ejpam-5730	86	19	only	only	ADV
ejpam-5730	86	20	one	one	NUM
ejpam-5730	86	21	example	example	NOUN
ejpam-5730	86	22	of	of	ADP
ejpam-5730	86	23	the	the	DET
ejpam-5730	86	24	family	family	NOUN
ejpam-5730	86	25	{	{	PUNCT
ejpam-5730	86	26	β	β	NOUN
ejpam-5730	86	27	}	}	PUNCT
ejpam-5730	86	28	.	.	PUNCT
ejpam-5730	87	1	recall	recall	VERB
ejpam-5730	87	2	that	that	SCONJ
ejpam-5730	87	3	the	the	DET
ejpam-5730	87	4	banach	banach	NOUN
ejpam-5730	87	5	contraction	contraction	NOUN
ejpam-5730	87	6	principle	principle	NOUN
ejpam-5730	87	7	follows	follow	VERB
ejpam-5730	87	8	from	from	ADP
ejpam-5730	87	9	theorem	theorem	ADJ
ejpam-5730	87	10	h(β	h(β	NOUN
ejpam-5730	87	11	)	)	PUNCT
ejpam-5730	87	12	.	.	PUNCT
ejpam-5730	88	1	the	the	DET
ejpam-5730	88	2	origin	origin	NOUN
ejpam-5730	88	3	of	of	ADP
ejpam-5730	88	4	the	the	DET
ejpam-5730	88	5	subfamily	subfamily	ADV
ejpam-5730	88	6	{	{	PUNCT
ejpam-5730	88	7	β	β	NOUN
ejpam-5730	88	8	}	}	PUNCT
ejpam-5730	88	9	is	be	AUX
ejpam-5730	88	10	banach	banach	ADV
ejpam-5730	88	11	’s	’s	ADV
ejpam-5730	88	12	theorem	theorem	NOUN
ejpam-5730	88	13	[	[	X
ejpam-5730	88	14	4	4	NUM
ejpam-5730	88	15	]	]	PUNCT
ejpam-5730	88	16	in	in	ADP
ejpam-5730	88	17	1922	1922	NUM
ejpam-5730	88	18	.	.	PUNCT
ejpam-5730	89	1	6	6	NUM
ejpam-5730	89	2	.	.	X
ejpam-5730	90	1	the	the	DET
ejpam-5730	90	2	subfamily	subfamily	ADV
ejpam-5730	90	3	{	{	PUNCT
ejpam-5730	90	4	γ	γ	X
ejpam-5730	90	5	}	}	PUNCT
ejpam-5730	90	6	of	of	ADP
ejpam-5730	90	7	the	the	DET
ejpam-5730	90	8	rus	rus	NOUN
ejpam-5730	90	9	-	-	PUNCT
ejpam-5730	90	10	hicks	hick	NOUN
ejpam-5730	90	11	-	-	PUNCT
ejpam-5730	90	12	rhoades	rhoade	NOUN
ejpam-5730	90	13	type	type	VERB
ejpam-5730	90	14	the	the	DET
ejpam-5730	90	15	following	follow	VERB
ejpam-5730	90	16	originates	originate	NOUN
ejpam-5730	90	17	in	in	ADP
ejpam-5730	90	18	[	[	X
ejpam-5730	90	19	35],[36	35],[36	NOUN
ejpam-5730	90	20	]	]	PUNCT
ejpam-5730	90	21	:	:	PUNCT
ejpam-5730	90	22	theorem	theorem	VERB
ejpam-5730	90	23	h(γ	h(γ	PROPN
ejpam-5730	90	24	)	)	PUNCT
ejpam-5730	90	25	.	.	PUNCT
ejpam-5730	91	1	let	let	VERB
ejpam-5730	91	2	(	(	PUNCT
ejpam-5730	91	3	x	x	X
ejpam-5730	91	4	,	,	PUNCT
ejpam-5730	91	5	q	q	X
ejpam-5730	91	6	)	)	PUNCT
ejpam-5730	91	7	be	be	AUX
ejpam-5730	91	8	a	a	DET
ejpam-5730	91	9	quasi	quasi	ADJ
ejpam-5730	91	10	-	-	ADJ
ejpam-5730	91	11	metric	metric	ADJ
ejpam-5730	91	12	space	space	NOUN
ejpam-5730	91	13	and	and	CCONJ
ejpam-5730	91	14	0	0	NUM
ejpam-5730	91	15	<	<	X
ejpam-5730	91	16	r	r	X
ejpam-5730	91	17	<	<	X
ejpam-5730	91	18	1	1	NUM
ejpam-5730	91	19	.	.	PUNCT
ejpam-5730	92	1	then	then	ADV
ejpam-5730	92	2	the	the	DET
ejpam-5730	92	3	following	following	ADJ
ejpam-5730	92	4	statements	statement	NOUN
ejpam-5730	92	5	are	be	AUX
ejpam-5730	92	6	equivalent	equivalent	ADJ
ejpam-5730	92	7	:	:	PUNCT
ejpam-5730	92	8	(	(	PUNCT
ejpam-5730	92	9	0	0	NUM
ejpam-5730	92	10	)	)	PUNCT
ejpam-5730	92	11	(	(	PUNCT
ejpam-5730	92	12	x	x	X
ejpam-5730	92	13	,	,	PUNCT
ejpam-5730	92	14	q	q	X
ejpam-5730	92	15	)	)	PUNCT
ejpam-5730	92	16	is	be	AUX
ejpam-5730	92	17	complete	complete	ADJ
ejpam-5730	92	18	.	.	PUNCT
ejpam-5730	93	1	(	(	PUNCT
ejpam-5730	93	2	γ	γ	X
ejpam-5730	93	3	)	)	PUNCT
ejpam-5730	93	4	if	if	SCONJ
ejpam-5730	93	5	f	f	PROPN
ejpam-5730	93	6	is	be	AUX
ejpam-5730	93	7	a	a	DET
ejpam-5730	93	8	family	family	NOUN
ejpam-5730	93	9	of	of	ADP
ejpam-5730	93	10	maps	map	NOUN
ejpam-5730	93	11	f	f	X
ejpam-5730	93	12	:	:	PUNCT
ejpam-5730	93	13	x	x	X
ejpam-5730	93	14	→	→	SYM
ejpam-5730	93	15	x	x	SYM
ejpam-5730	93	16	satisfying	satisfy	VERB
ejpam-5730	93	17	q(fx	q(fx	NOUN
ejpam-5730	93	18	,	,	PUNCT
ejpam-5730	93	19	f2x	f2x	X
ejpam-5730	93	20	)	)	PUNCT
ejpam-5730	93	21	≤	≤	NUM
ejpam-5730	93	22	α	α	PROPN
ejpam-5730	93	23	q(x	q(x	PROPN
ejpam-5730	93	24	,	,	PUNCT
ejpam-5730	93	25	fx	fx	PROPN
ejpam-5730	93	26	)	)	PUNCT
ejpam-5730	93	27	for	for	ADP
ejpam-5730	93	28	all	all	DET
ejpam-5730	93	29	x	x	SYM
ejpam-5730	93	30	∈	∈	PROPN
ejpam-5730	93	31	x\{fx	x\{fx	PROPN
ejpam-5730	93	32	}	}	PUNCT
ejpam-5730	93	33	,	,	PUNCT
ejpam-5730	93	34	then	then	ADV
ejpam-5730	93	35	f	f	PROPN
ejpam-5730	93	36	has	have	VERB
ejpam-5730	93	37	a	a	DET
ejpam-5730	93	38	common	common	ADJ
ejpam-5730	93	39	fixed	fix	VERB
ejpam-5730	93	40	element	element	NOUN
ejpam-5730	93	41	v	v	ADP
ejpam-5730	93	42	∈	∈	PROPN
ejpam-5730	93	43	x	x	NOUN
ejpam-5730	93	44	,	,	PUNCT
ejpam-5730	93	45	that	that	ADV
ejpam-5730	93	46	is	is	ADV
ejpam-5730	93	47	,	,	PUNCT
ejpam-5730	93	48	v	v	X
ejpam-5730	93	49	=	=	SYM
ejpam-5730	93	50	fv	fv	NOUN
ejpam-5730	93	51	for	for	ADP
ejpam-5730	93	52	all	all	DET
ejpam-5730	93	53	f	f	PROPN
ejpam-5730	93	54	∈	∈	PROPN
ejpam-5730	93	55	f.	f.	PROPN
ejpam-5730	93	56	note	note	VERB
ejpam-5730	93	57	that	that	SCONJ
ejpam-5730	93	58	the	the	DET
ejpam-5730	93	59	f	f	PROPN
ejpam-5730	93	60	-orbital	-orbital	PROPN
ejpam-5730	93	61	completeness	completeness	NOUN
ejpam-5730	93	62	of	of	ADP
ejpam-5730	93	63	(	(	PUNCT
ejpam-5730	93	64	x	x	NOUN
ejpam-5730	93	65	,	,	PUNCT
ejpam-5730	93	66	q	q	NOUN
ejpam-5730	93	67	)	)	PUNCT
ejpam-5730	93	68	for	for	ADP
ejpam-5730	93	69	any	any	DET
ejpam-5730	93	70	rhr	rhr	PROPN
ejpam-5730	93	71	map	map	NOUN
ejpam-5730	94	1	f	f	X
ejpam-5730	94	2	:	:	PUNCT
ejpam-5730	94	3	x	x	SYM
ejpam-5730	94	4	→	→	SYM
ejpam-5730	94	5	x	x	X
ejpam-5730	94	6	in	in	ADP
ejpam-5730	94	7	f	f	PROPN
ejpam-5730	94	8	implies	imply	VERB
ejpam-5730	94	9	(	(	PUNCT
ejpam-5730	94	10	γ	γ	X
ejpam-5730	94	11	)	)	PUNCT
ejpam-5730	94	12	.	.	PUNCT
ejpam-5730	95	1	such	such	ADJ
ejpam-5730	95	2	map	map	NOUN
ejpam-5730	95	3	is	be	AUX
ejpam-5730	95	4	traditionally	traditionally	ADV
ejpam-5730	95	5	called	call	VERB
ejpam-5730	95	6	as	as	ADP
ejpam-5730	95	7	graphic	graphic	ADJ
ejpam-5730	95	8	contraction	contraction	NOUN
ejpam-5730	95	9	,	,	PUNCT
ejpam-5730	95	10	iterative	iterative	NOUN
ejpam-5730	95	11	contraction	contraction	NOUN
ejpam-5730	95	12	,	,	PUNCT
ejpam-5730	95	13	weakly	weakly	ADJ
ejpam-5730	95	14	contraction	contraction	NOUN
ejpam-5730	95	15	,	,	PUNCT
ejpam-5730	95	16	banach	banach	NOUN
ejpam-5730	95	17	mapping	mapping	NOUN
ejpam-5730	95	18	,	,	PUNCT
ejpam-5730	95	19	.	.	PUNCT
ejpam-5730	95	20	.	.	PUNCT
ejpam-5730	96	1	.	.	PUNCT
ejpam-5730	97	1	.	.	PUNCT
ejpam-5730	98	1	we	we	PRON
ejpam-5730	98	2	prefer	prefer	VERB
ejpam-5730	98	3	to	to	PART
ejpam-5730	98	4	call	call	VERB
ejpam-5730	98	5	it	it	PRON
ejpam-5730	98	6	a	a	DET
ejpam-5730	98	7	weak	weak	ADJ
ejpam-5730	98	8	contraction	contraction	NOUN
ejpam-5730	98	9	.	.	PUNCT
ejpam-5730	99	1	many	many	ADJ
ejpam-5730	99	2	generalizations	generalization	NOUN
ejpam-5730	99	3	of	of	ADP
ejpam-5730	99	4	the	the	DET
ejpam-5730	99	5	banach	banach	NOUN
ejpam-5730	99	6	principle	principle	NOUN
ejpam-5730	99	7	are	be	AUX
ejpam-5730	99	8	of	of	ADP
ejpam-5730	99	9	the	the	DET
ejpam-5730	99	10	rus	rus	NOUN
ejpam-5730	99	11	-	-	PUNCT
ejpam-5730	99	12	hicks	hick	NOUN
ejpam-5730	99	13	-	-	PUNCT
ejpam-5730	99	14	rhoades	rhoade	NOUN
ejpam-5730	99	15	type	type	NOUN
ejpam-5730	99	16	;	;	PUNCT
ejpam-5730	99	17	see	see	VERB
ejpam-5730	99	18	[	[	X
ejpam-5730	99	19	40	40	NUM
ejpam-5730	99	20	]	]	PUNCT
ejpam-5730	99	21	.	.	PUNCT
ejpam-5730	100	1	rhoades	rhoade	NOUN
ejpam-5730	100	2	[	[	X
ejpam-5730	100	3	46	46	NUM
ejpam-5730	100	4	]	]	PUNCT
ejpam-5730	100	5	in	in	ADP
ejpam-5730	100	6	1978	1978	NUM
ejpam-5730	100	7	noted	note	VERB
ejpam-5730	100	8	that	that	SCONJ
ejpam-5730	100	9	the	the	DET
ejpam-5730	100	10	analogues	analogue	NOUN
ejpam-5730	100	11	of	of	ADP
ejpam-5730	100	12	most	most	ADJ
ejpam-5730	100	13	of	of	ADP
ejpam-5730	100	14	the	the	DET
ejpam-5730	100	15	conditions	condition	NOUN
ejpam-5730	100	16	in	in	ADP
ejpam-5730	100	17	his	his	PRON
ejpam-5730	100	18	wellknown	wellknown	ADJ
ejpam-5730	100	19	list	list	NOUN
ejpam-5730	100	20	[	[	X
ejpam-5730	100	21	45	45	NUM
ejpam-5730	100	22	]	]	PUNCT
ejpam-5730	100	23	could	could	AUX
ejpam-5730	100	24	be	be	AUX
ejpam-5730	100	25	extended	extend	VERB
ejpam-5730	100	26	to	to	ADP
ejpam-5730	100	27	the	the	DET
ejpam-5730	100	28	rhr	rhr	PROPN
ejpam-5730	100	29	type	type	NOUN
ejpam-5730	100	30	of	of	ADP
ejpam-5730	100	31	contractive	contractive	ADJ
ejpam-5730	100	32	definitions	definition	NOUN
ejpam-5730	100	33	;	;	PUNCT
ejpam-5730	100	34	see	see	VERB
ejpam-5730	100	35	also	also	ADV
ejpam-5730	100	36	[	[	X
ejpam-5730	100	37	41	41	NUM
ejpam-5730	100	38	]	]	PUNCT
ejpam-5730	100	39	.	.	PUNCT
ejpam-5730	101	1	in	in	ADP
ejpam-5730	101	2	this	this	DET
ejpam-5730	101	3	section	section	NOUN
ejpam-5730	101	4	,	,	PUNCT
ejpam-5730	101	5	we	we	PRON
ejpam-5730	101	6	list	list	VERB
ejpam-5730	101	7	some	some	DET
ejpam-5730	101	8	typical	typical	ADJ
ejpam-5730	101	9	old	old	ADJ
ejpam-5730	101	10	and	and	CCONJ
ejpam-5730	101	11	new	new	ADJ
ejpam-5730	101	12	examples	example	NOUN
ejpam-5730	101	13	of	of	ADP
ejpam-5730	101	14	theorem	theorem	ADJ
ejpam-5730	101	15	h(γ	h(γ	PROPN
ejpam-5730	101	16	)	)	PUNCT
ejpam-5730	101	17	.	.	PUNCT
ejpam-5730	102	1	most	most	ADJ
ejpam-5730	102	2	of	of	ADP
ejpam-5730	102	3	examples	example	NOUN
ejpam-5730	102	4	hold	hold	VERB
ejpam-5730	102	5	for	for	ADP
ejpam-5730	102	6	quasi	quasi	ADJ
ejpam-5730	102	7	-	-	ADJ
ejpam-5730	102	8	metric	metric	ADJ
ejpam-5730	102	9	spaces	space	NOUN
ejpam-5730	102	10	,	,	PUNCT
ejpam-5730	102	11	but	but	CCONJ
ejpam-5730	102	12	we	we	PRON
ejpam-5730	102	13	state	state	VERB
ejpam-5730	102	14	their	their	PRON
ejpam-5730	102	15	original	original	ADJ
ejpam-5730	102	16	forms	form	NOUN
ejpam-5730	102	17	.	.	PUNCT
ejpam-5730	103	1	kannan	kannan	PROPN
ejpam-5730	103	2	[	[	X
ejpam-5730	103	3	17	17	NUM
ejpam-5730	103	4	]	]	PUNCT
ejpam-5730	103	5	in	in	ADP
ejpam-5730	103	6	1969	1969	NUM
ejpam-5730	103	7	recall	recall	VERB
ejpam-5730	103	8	the	the	DET
ejpam-5730	103	9	following	following	NOUN
ejpam-5730	103	10	:	:	PUNCT
ejpam-5730	103	11	theorem	theorem	VERB
ejpam-5730	103	12	6.1	6.1	NUM
ejpam-5730	103	13	.	.	PUNCT
ejpam-5730	104	1	(	(	PUNCT
ejpam-5730	104	2	kannan	kannan	PROPN
ejpam-5730	104	3	)	)	PUNCT
ejpam-5730	104	4	let	let	VERB
ejpam-5730	104	5	(	(	PUNCT
ejpam-5730	104	6	x	x	NOUN
ejpam-5730	104	7	,	,	PUNCT
ejpam-5730	104	8	d	d	NOUN
ejpam-5730	104	9	)	)	PUNCT
ejpam-5730	104	10	be	be	AUX
ejpam-5730	104	11	a	a	DET
ejpam-5730	104	12	complete	complete	ADJ
ejpam-5730	104	13	metric	metric	ADJ
ejpam-5730	104	14	spaces	space	NOUN
ejpam-5730	104	15	and	and	CCONJ
ejpam-5730	104	16	t	t	NOUN
ejpam-5730	104	17	:	:	PUNCT
ejpam-5730	104	18	x	x	X
ejpam-5730	104	19	→	→	PUNCT
ejpam-5730	104	20	x	x	PUNCT
ejpam-5730	104	21	be	be	AUX
ejpam-5730	104	22	a	a	DET
ejpam-5730	104	23	kannan	kannan	PROPN
ejpam-5730	104	24	contraction	contraction	PROPN
ejpam-5730	104	25	mapping	mapping	NOUN
ejpam-5730	104	26	,	,	PUNCT
ejpam-5730	104	27	i.e.	i.e.	X
ejpam-5730	104	28	,	,	PUNCT
ejpam-5730	104	29	d(tx	d(tx	PROPN
ejpam-5730	104	30	,	,	PUNCT
ejpam-5730	104	31	ty	ty	NOUN
ejpam-5730	104	32	)	)	PUNCT
ejpam-5730	104	33	≤	≤	NOUN
ejpam-5730	104	34	λ[d(x	λ[d(x	PUNCT
ejpam-5730	104	35	,	,	PUNCT
ejpam-5730	104	36	tx	tx	PROPN
ejpam-5730	104	37	)	)	PUNCT
ejpam-5730	105	1	+	+	CCONJ
ejpam-5730	105	2	d(y	d(y	PROPN
ejpam-5730	105	3	,	,	PUNCT
ejpam-5730	105	4	ty	ty	NOUN
ejpam-5730	105	5	)	)	PUNCT
ejpam-5730	105	6	]	]	PUNCT
ejpam-5730	105	7	∀	∀	PUNCT
ejpam-5730	105	8	x	x	NOUN
ejpam-5730	105	9	,	,	PUNCT
ejpam-5730	105	10	y	y	PROPN
ejpam-5730	105	11	∈	∈	PROPN
ejpam-5730	106	1	x	x	NOUN
ejpam-5730	106	2	,	,	PUNCT
ejpam-5730	106	3	where	where	SCONJ
ejpam-5730	106	4	λ	λ	PROPN
ejpam-5730	106	5	∈	∈	PROPN
ejpam-5730	107	1	[	[	X
ejpam-5730	107	2	0	0	NUM
ejpam-5730	107	3	,	,	PUNCT
ejpam-5730	107	4	1/2	1/2	NUM
ejpam-5730	107	5	)	)	PUNCT
ejpam-5730	107	6	.	.	PUNCT
ejpam-5730	108	1	then	then	ADV
ejpam-5730	108	2	t	t	PROPN
ejpam-5730	108	3	has	have	VERB
ejpam-5730	108	4	a	a	DET
ejpam-5730	108	5	unique	unique	ADJ
ejpam-5730	108	6	fixed	fix	VERB
ejpam-5730	108	7	point	point	NOUN
ejpam-5730	108	8	.	.	PUNCT
ejpam-5730	109	1	comment	comment	NOUN
ejpam-5730	109	2	:	:	PUNCT
ejpam-5730	109	3	this	this	PRON
ejpam-5730	109	4	is	be	AUX
ejpam-5730	109	5	a	a	DET
ejpam-5730	109	6	simple	simple	ADJ
ejpam-5730	109	7	consequence	consequence	NOUN
ejpam-5730	109	8	of	of	ADP
ejpam-5730	109	9	theorem	theorem	NOUN
ejpam-5730	109	10	p	p	PROPN
ejpam-5730	109	11	for	for	ADP
ejpam-5730	109	12	quasi	quasi	ADJ
ejpam-5730	109	13	-	-	ADJ
ejpam-5730	109	14	metric	metric	ADJ
ejpam-5730	109	15	spaces	space	NOUN
ejpam-5730	109	16	.	.	PUNCT
ejpam-5730	110	1	in	in	ADP
ejpam-5730	110	2	fact	fact	NOUN
ejpam-5730	110	3	,	,	PUNCT
ejpam-5730	110	4	for	for	ADP
ejpam-5730	110	5	y	y	PROPN
ejpam-5730	110	6	=	=	SYM
ejpam-5730	110	7	tx	tx	PROPN
ejpam-5730	110	8	,	,	PUNCT
ejpam-5730	110	9	we	we	PRON
ejpam-5730	110	10	have	have	VERB
ejpam-5730	110	11	d(tx	d(tx	PROPN
ejpam-5730	110	12	,	,	PUNCT
ejpam-5730	110	13	t	t	NOUN
ejpam-5730	110	14	2x	2x	NUM
ejpam-5730	110	15	)	)	PUNCT
ejpam-5730	110	16	≤	≤	NUM
ejpam-5730	111	1	λ	λ	PROPN
ejpam-5730	111	2	1−	1−	NUM
ejpam-5730	111	3	λ	λ	NOUN
ejpam-5730	111	4	d(x	d(x	PROPN
ejpam-5730	111	5	,	,	PUNCT
ejpam-5730	111	6	tx	tx	PROPN
ejpam-5730	111	7	)	)	PUNCT
ejpam-5730	111	8	and	and	CCONJ
ejpam-5730	111	9	0	0	NUM
ejpam-5730	111	10	≤	≤	NUM
ejpam-5730	111	11	λ	λ	NOUN
ejpam-5730	111	12	1−	1−	NUM
ejpam-5730	111	13	λ	λ	X
ejpam-5730	111	14	<	<	X
ejpam-5730	111	15	1	1	NUM
ejpam-5730	111	16	.	.	PUNCT
ejpam-5730	112	1	s.	s.	PROPN
ejpam-5730	112	2	park	park	PROPN
ejpam-5730	112	3	/	/	SYM
ejpam-5730	112	4	eur	eur	PROPN
ejpam-5730	112	5	.	.	PUNCT
ejpam-5730	113	1	j.	j.	PROPN
ejpam-5730	113	2	pure	pure	PROPN
ejpam-5730	113	3	appl	appl	PROPN
ejpam-5730	113	4	.	.	PROPN
ejpam-5730	113	5	math	math	PROPN
ejpam-5730	113	6	,	,	PUNCT
ejpam-5730	113	7	18	18	NUM
ejpam-5730	113	8	(	(	PUNCT
ejpam-5730	113	9	1	1	NUM
ejpam-5730	113	10	)	)	PUNCT
ejpam-5730	113	11	(	(	PUNCT
ejpam-5730	113	12	2025	2025	NUM
ejpam-5730	113	13	)	)	PUNCT
ejpam-5730	113	14	,	,	PUNCT
ejpam-5730	113	15	5730	5730	NUM
ejpam-5730	113	16	6	6	NUM
ejpam-5730	113	17	of	of	ADP
ejpam-5730	113	18	21	21	NUM
ejpam-5730	113	19	kannan	kannan	PROPN
ejpam-5730	113	20	’s	’s	PART
ejpam-5730	113	21	example	example	NOUN
ejpam-5730	113	22	does	do	AUX
ejpam-5730	113	23	not	not	PART
ejpam-5730	113	24	require	require	VERB
ejpam-5730	113	25	the	the	DET
ejpam-5730	113	26	continuity	continuity	NOUN
ejpam-5730	113	27	of	of	ADP
ejpam-5730	113	28	the	the	DET
ejpam-5730	113	29	map	map	NOUN
ejpam-5730	113	30	at	at	ADP
ejpam-5730	113	31	every	every	DET
ejpam-5730	113	32	point	point	NOUN
ejpam-5730	113	33	,	,	PUNCT
ejpam-5730	113	34	although	although	SCONJ
ejpam-5730	113	35	maps	map	NOUN
ejpam-5730	113	36	satisfying	satisfy	VERB
ejpam-5730	113	37	his	his	PRON
ejpam-5730	113	38	condition	condition	NOUN
ejpam-5730	113	39	are	be	AUX
ejpam-5730	113	40	continuous	continuous	ADJ
ejpam-5730	113	41	at	at	ADP
ejpam-5730	113	42	fixed	fix	VERB
ejpam-5730	113	43	points	point	NOUN
ejpam-5730	113	44	;	;	PUNCT
ejpam-5730	113	45	see	see	VERB
ejpam-5730	113	46	theorem	theorem	VERB
ejpam-5730	113	47	p(ii	p(ii	NOUN
ejpam-5730	113	48	)	)	PUNCT
ejpam-5730	113	49	.	.	PUNCT
ejpam-5730	114	1	reich	reich	PROPN
ejpam-5730	115	1	[	[	X
ejpam-5730	115	2	44	44	NUM
ejpam-5730	115	3	]	]	PUNCT
ejpam-5730	115	4	in	in	ADP
ejpam-5730	115	5	1971	1971	NUM
ejpam-5730	115	6	the	the	DET
ejpam-5730	115	7	following	follow	VERB
ejpam-5730	115	8	theorem	theorem	NOUN
ejpam-5730	115	9	proved	prove	VERB
ejpam-5730	115	10	by	by	ADP
ejpam-5730	115	11	reich	reich	PROPN
ejpam-5730	115	12	generalizes	generalize	VERB
ejpam-5730	115	13	banach	banach	ADV
ejpam-5730	115	14	’s	’s	PART
ejpam-5730	115	15	fixed	fix	VERB
ejpam-5730	115	16	point	point	NOUN
ejpam-5730	115	17	theorem	theorem	NOUN
ejpam-5730	115	18	and	and	CCONJ
ejpam-5730	115	19	kannan	kannan	PROPN
ejpam-5730	115	20	’s	’s	PART
ejpam-5730	115	21	fixed	fix	VERB
ejpam-5730	115	22	point	point	NOUN
ejpam-5730	115	23	theorem	theorem	VERB
ejpam-5730	115	24	.	.	PUNCT
ejpam-5730	115	25	theorem	theorem	VERB
ejpam-5730	115	26	6.2	6.2	NUM
ejpam-5730	115	27	.	.	PUNCT
ejpam-5730	116	1	(	(	PUNCT
ejpam-5730	116	2	reich	reich	NOUN
ejpam-5730	116	3	)	)	PUNCT
ejpam-5730	116	4	let	let	VERB
ejpam-5730	116	5	f	f	PRON
ejpam-5730	116	6	be	be	AUX
ejpam-5730	116	7	a	a	DET
ejpam-5730	116	8	selfmap	selfmap	NOUN
ejpam-5730	116	9	on	on	ADP
ejpam-5730	116	10	a	a	DET
ejpam-5730	116	11	complete	complete	ADJ
ejpam-5730	116	12	metric	metric	ADJ
ejpam-5730	116	13	space	space	NOUN
ejpam-5730	116	14	(	(	PUNCT
ejpam-5730	116	15	x	x	X
ejpam-5730	116	16	,	,	PUNCT
ejpam-5730	116	17	d	d	NOUN
ejpam-5730	116	18	)	)	PUNCT
ejpam-5730	116	19	.	.	PUNCT
ejpam-5730	117	1	if	if	SCONJ
ejpam-5730	117	2	there	there	PRON
ejpam-5730	117	3	exist	exist	VERB
ejpam-5730	117	4	constants	constant	NOUN
ejpam-5730	117	5	a	a	DET
ejpam-5730	117	6	,	,	PUNCT
ejpam-5730	117	7	b	b	NOUN
ejpam-5730	117	8	,	,	PUNCT
ejpam-5730	117	9	c	c	PROPN
ejpam-5730	117	10	∈	∈	PROPN
ejpam-5730	118	1	[	[	X
ejpam-5730	118	2	0	0	NUM
ejpam-5730	118	3	,	,	PUNCT
ejpam-5730	118	4	1	1	NUM
ejpam-5730	118	5	)	)	PUNCT
ejpam-5730	118	6	with	with	ADP
ejpam-5730	118	7	a+	a+	X
ejpam-5730	118	8	b+	b+	X
ejpam-5730	118	9	c	c	X
ejpam-5730	118	10	<	<	X
ejpam-5730	118	11	1	1	NUM
ejpam-5730	118	12	such	such	ADJ
ejpam-5730	118	13	that	that	SCONJ
ejpam-5730	118	14	d(fx	d(fx	NOUN
ejpam-5730	118	15	,	,	PUNCT
ejpam-5730	118	16	fy	fy	NOUN
ejpam-5730	118	17	)	)	PUNCT
ejpam-5730	118	18	≤	≤	NOUN
ejpam-5730	118	19	ad(x	ad(x	ADV
ejpam-5730	118	20	,	,	PUNCT
ejpam-5730	118	21	fx	fx	PROPN
ejpam-5730	118	22	)	)	PUNCT
ejpam-5730	118	23	+	+	CCONJ
ejpam-5730	118	24	bd(y	bd(y	PROPN
ejpam-5730	118	25	,	,	PUNCT
ejpam-5730	118	26	fy	fy	PROPN
ejpam-5730	118	27	)	)	PUNCT
ejpam-5730	118	28	)	)	PUNCT
ejpam-5730	118	29	+	+	CCONJ
ejpam-5730	118	30	cd(x	cd(x	X
ejpam-5730	118	31	,	,	PUNCT
ejpam-5730	118	32	y	y	NOUN
ejpam-5730	118	33	)	)	PUNCT
ejpam-5730	118	34	∀	∀	PUNCT
ejpam-5730	119	1	x	x	NOUN
ejpam-5730	119	2	,	,	PUNCT
ejpam-5730	119	3	y	y	PROPN
ejpam-5730	119	4	∈	∈	PROPN
ejpam-5730	119	5	x	x	X
ejpam-5730	119	6	,	,	PUNCT
ejpam-5730	119	7	then	then	ADV
ejpam-5730	119	8	f	f	PROPN
ejpam-5730	119	9	has	have	VERB
ejpam-5730	119	10	a	a	DET
ejpam-5730	119	11	unique	unique	ADJ
ejpam-5730	119	12	fixed	fix	VERB
ejpam-5730	119	13	point	point	NOUN
ejpam-5730	119	14	.	.	PUNCT
ejpam-5730	120	1	comment	comment	NOUN
ejpam-5730	120	2	:	:	PUNCT
ejpam-5730	120	3	note	note	VERB
ejpam-5730	120	4	that	that	SCONJ
ejpam-5730	120	5	f	f	PROPN
ejpam-5730	120	6	is	be	AUX
ejpam-5730	120	7	an	an	DET
ejpam-5730	120	8	rhr	rhr	NOUN
ejpam-5730	120	9	map	map	NOUN
ejpam-5730	120	10	and	and	CCONJ
ejpam-5730	120	11	that	that	SCONJ
ejpam-5730	120	12	theorems	theorem	VERB
ejpam-5730	120	13	p	p	NOUN
ejpam-5730	120	14	and	and	CCONJ
ejpam-5730	120	15	h(γ1	h(γ1	NOUN
ejpam-5730	120	16	)	)	PUNCT
ejpam-5730	120	17	are	be	AUX
ejpam-5730	120	18	applicable	applicable	ADJ
ejpam-5730	120	19	to	to	ADP
ejpam-5730	120	20	f	f	PROPN
ejpam-5730	120	21	.	.	PUNCT
ejpam-5730	121	1	the	the	DET
ejpam-5730	121	2	uniqueness	uniqueness	NOUN
ejpam-5730	121	3	follows	follow	VERB
ejpam-5730	121	4	from	from	ADP
ejpam-5730	121	5	the	the	DET
ejpam-5730	121	6	contractive	contractive	ADJ
ejpam-5730	121	7	condition	condition	NOUN
ejpam-5730	121	8	.	.	PUNCT
ejpam-5730	122	1	rus	rus	PROPN
ejpam-5730	122	2	,	,	PUNCT
ejpam-5730	122	3	reich	reich	PROPN
ejpam-5730	122	4	,	,	PUNCT
ejpam-5730	122	5	ćirić	ćirić	VERB
ejpam-5730	122	6	in	in	ADP
ejpam-5730	122	7	1971	1971	NUM
ejpam-5730	122	8	-	-	SYM
ejpam-5730	122	9	2001	2001	NUM
ejpam-5730	122	10	the	the	DET
ejpam-5730	122	11	following	follow	VERB
ejpam-5730	122	12	theorem	theorem	NOUN
ejpam-5730	122	13	was	be	AUX
ejpam-5730	122	14	proved	prove	VERB
ejpam-5730	122	15	by	by	ADP
ejpam-5730	122	16	reich	reich	PROPN
ejpam-5730	122	17	,	,	PUNCT
ejpam-5730	122	18	rus	rus	NOUN
ejpam-5730	122	19	and	and	CCONJ
ejpam-5730	122	20	ćirić	ćirić	NOUN
ejpam-5730	122	21	independently	independently	ADV
ejpam-5730	122	22	to	to	PART
ejpam-5730	122	23	combine	combine	VERB
ejpam-5730	122	24	and	and	CCONJ
ejpam-5730	122	25	improve	improve	VERB
ejpam-5730	122	26	both	both	DET
ejpam-5730	122	27	banach	banach	NOUN
ejpam-5730	122	28	and	and	CCONJ
ejpam-5730	122	29	kannan	kannan	PROPN
ejpam-5730	122	30	fixed	fix	VERB
ejpam-5730	122	31	point	point	NOUN
ejpam-5730	122	32	theorems	theorem	NOUN
ejpam-5730	122	33	.	.	PUNCT
ejpam-5730	123	1	theorem	theorem	VERB
ejpam-5730	123	2	6.3	6.3	NUM
ejpam-5730	123	3	.	.	PUNCT
ejpam-5730	124	1	(	(	PUNCT
ejpam-5730	124	2	rus	rus	NOUN
ejpam-5730	124	3	-	-	PUNCT
ejpam-5730	124	4	reich	reich	NOUN
ejpam-5730	124	5	-	-	PUNCT
ejpam-5730	124	6	ćirić	ćirić	NOUN
ejpam-5730	124	7	)	)	PUNCT
ejpam-5730	125	1	let	let	VERB
ejpam-5730	125	2	(	(	PUNCT
ejpam-5730	125	3	x	x	NOUN
ejpam-5730	125	4	,	,	PUNCT
ejpam-5730	125	5	d	d	NOUN
ejpam-5730	125	6	)	)	PUNCT
ejpam-5730	125	7	be	be	AUX
ejpam-5730	125	8	a	a	DET
ejpam-5730	125	9	complete	complete	ADJ
ejpam-5730	125	10	metric	metric	ADJ
ejpam-5730	125	11	spaces	space	NOUN
ejpam-5730	125	12	and	and	CCONJ
ejpam-5730	125	13	t	t	NOUN
ejpam-5730	125	14	:	:	PUNCT
ejpam-5730	125	15	x	x	X
ejpam-5730	125	16	→	→	PUNCT
ejpam-5730	125	17	x	x	PUNCT
ejpam-5730	125	18	be	be	AUX
ejpam-5730	125	19	a	a	DET
ejpam-5730	125	20	rus	rus	PROPN
ejpam-5730	125	21	-	-	PUNCT
ejpam-5730	125	22	reich	reich	NOUN
ejpam-5730	125	23	-	-	PUNCT
ejpam-5730	125	24	ćirić	ćirić	PROPN
ejpam-5730	125	25	contraction	contraction	NOUN
ejpam-5730	125	26	mapping	mapping	NOUN
ejpam-5730	125	27	,	,	PUNCT
ejpam-5730	125	28	i.e.	i.e.	X
ejpam-5730	125	29	,	,	PUNCT
ejpam-5730	125	30	d(tx	d(tx	PROPN
ejpam-5730	125	31	,	,	PUNCT
ejpam-5730	125	32	ty	ty	NOUN
ejpam-5730	125	33	)	)	PUNCT
ejpam-5730	125	34	≤	≤	NOUN
ejpam-5730	125	35	λ[d(x	λ[d(x	PROPN
ejpam-5730	125	36	,	,	PUNCT
ejpam-5730	125	37	y	y	NOUN
ejpam-5730	125	38	)	)	PUNCT
ejpam-5730	126	1	+	+	CCONJ
ejpam-5730	126	2	d(x	d(x	PROPN
ejpam-5730	126	3	,	,	PUNCT
ejpam-5730	126	4	tx	tx	PROPN
ejpam-5730	126	5	)	)	PUNCT
ejpam-5730	127	1	+	+	CCONJ
ejpam-5730	127	2	d(y	d(y	PROPN
ejpam-5730	127	3	,	,	PUNCT
ejpam-5730	127	4	ty	ty	NOUN
ejpam-5730	127	5	)	)	PUNCT
ejpam-5730	127	6	]	]	PUNCT
ejpam-5730	127	7	for	for	ADP
ejpam-5730	127	8	all	all	DET
ejpam-5730	127	9	x	x	NOUN
ejpam-5730	127	10	,	,	PUNCT
ejpam-5730	127	11	y	y	PROPN
ejpam-5730	127	12	∈	∈	PROPN
ejpam-5730	127	13	x	x	NOUN
ejpam-5730	127	14	,	,	PUNCT
ejpam-5730	127	15	where	where	SCONJ
ejpam-5730	127	16	λ	λ	PROPN
ejpam-5730	127	17	∈	∈	PROPN
ejpam-5730	128	1	[	[	X
ejpam-5730	128	2	0	0	NUM
ejpam-5730	128	3	,	,	PUNCT
ejpam-5730	128	4	1/3	1/3	NUM
ejpam-5730	128	5	)	)	PUNCT
ejpam-5730	128	6	.	.	PUNCT
ejpam-5730	129	1	then	then	ADV
ejpam-5730	129	2	t	t	PROPN
ejpam-5730	129	3	has	have	VERB
ejpam-5730	129	4	a	a	DET
ejpam-5730	129	5	unique	unique	ADJ
ejpam-5730	129	6	fixed	fix	VERB
ejpam-5730	129	7	point	point	NOUN
ejpam-5730	129	8	.	.	PUNCT
ejpam-5730	130	1	comment	comment	NOUN
ejpam-5730	130	2	:	:	PUNCT
ejpam-5730	130	3	this	this	PRON
ejpam-5730	130	4	is	be	AUX
ejpam-5730	130	5	a	a	DET
ejpam-5730	130	6	simple	simple	ADJ
ejpam-5730	130	7	consequence	consequence	NOUN
ejpam-5730	130	8	of	of	ADP
ejpam-5730	130	9	the	the	DET
ejpam-5730	130	10	rhr	rhr	PROPN
ejpam-5730	130	11	theorem	theorem	NOUN
ejpam-5730	130	12	for	for	ADP
ejpam-5730	130	13	quasi	quasi	ADJ
ejpam-5730	130	14	-	-	ADJ
ejpam-5730	130	15	metric	metric	ADJ
ejpam-5730	130	16	spaces	space	NOUN
ejpam-5730	130	17	.	.	PUNCT
ejpam-5730	131	1	in	in	ADP
ejpam-5730	131	2	fact	fact	NOUN
ejpam-5730	131	3	,	,	PUNCT
ejpam-5730	131	4	for	for	ADP
ejpam-5730	131	5	y	y	PROPN
ejpam-5730	131	6	=	=	SYM
ejpam-5730	131	7	tx	tx	PROPN
ejpam-5730	131	8	,	,	PUNCT
ejpam-5730	131	9	we	we	PRON
ejpam-5730	131	10	have	have	VERB
ejpam-5730	131	11	d(tx	d(tx	PROPN
ejpam-5730	131	12	,	,	PUNCT
ejpam-5730	131	13	t	t	NOUN
ejpam-5730	131	14	2x	2x	NUM
ejpam-5730	131	15	)	)	PUNCT
ejpam-5730	131	16	≤	≤	NOUN
ejpam-5730	132	1	2λ	2λ	NOUN
ejpam-5730	132	2	1−	1−	NUM
ejpam-5730	132	3	λ	λ	NOUN
ejpam-5730	132	4	d(x	d(x	PROPN
ejpam-5730	132	5	,	,	PUNCT
ejpam-5730	132	6	tx	tx	PROPN
ejpam-5730	132	7	)	)	PUNCT
ejpam-5730	132	8	and	and	CCONJ
ejpam-5730	132	9	0	0	NUM
ejpam-5730	132	10	≤	≤	NOUN
ejpam-5730	132	11	2λ	2λ	NOUN
ejpam-5730	132	12	1−	1−	NUM
ejpam-5730	132	13	λ	λ	X
ejpam-5730	132	14	<	<	X
ejpam-5730	132	15	1	1	NUM
ejpam-5730	132	16	.	.	PUNCT
ejpam-5730	133	1	therefore	therefore	ADV
ejpam-5730	133	2	,	,	PUNCT
ejpam-5730	133	3	theorems	theorems	PROPN
ejpam-5730	133	4	p	p	NOUN
ejpam-5730	133	5	and	and	CCONJ
ejpam-5730	133	6	h(γ1	h(γ1	NOUN
ejpam-5730	133	7	)	)	PUNCT
ejpam-5730	133	8	are	be	AUX
ejpam-5730	133	9	applicable	applicable	ADJ
ejpam-5730	133	10	to	to	ADP
ejpam-5730	133	11	t	t	PROPN
ejpam-5730	133	12	.	.	PUNCT
ejpam-5730	134	1	ćirić	ćirić	VERB
ejpam-5730	135	1	[	[	X
ejpam-5730	135	2	6	6	NUM
ejpam-5730	135	3	]	]	PUNCT
ejpam-5730	135	4	in	in	ADP
ejpam-5730	135	5	1974	1974	NUM
ejpam-5730	135	6	theorem	theorem	VERB
ejpam-5730	135	7	6.4	6.4	NUM
ejpam-5730	135	8	.	.	PUNCT
ejpam-5730	136	1	(	(	PUNCT
ejpam-5730	136	2	ćirić	ćirić	NOUN
ejpam-5730	136	3	)	)	PUNCT
ejpam-5730	136	4	let	let	VERB
ejpam-5730	136	5	(	(	PUNCT
ejpam-5730	136	6	m	m	NOUN
ejpam-5730	136	7	,	,	PUNCT
ejpam-5730	136	8	d	d	NOUN
ejpam-5730	136	9	)	)	PUNCT
ejpam-5730	136	10	be	be	AUX
ejpam-5730	136	11	a	a	DET
ejpam-5730	136	12	quasi	quasi	ADJ
ejpam-5730	136	13	-	-	ADJ
ejpam-5730	136	14	metric	metric	ADJ
ejpam-5730	136	15	space	space	NOUN
ejpam-5730	136	16	,	,	PUNCT
ejpam-5730	136	17	and	and	CCONJ
ejpam-5730	136	18	let	let	VERB
ejpam-5730	136	19	t	t	NOUN
ejpam-5730	136	20	:	:	PUNCT
ejpam-5730	136	21	m	m	VERB
ejpam-5730	136	22	→	→	PUNCT
ejpam-5730	136	23	m	m	AUX
ejpam-5730	136	24	be	be	AUX
ejpam-5730	136	25	a	a	DET
ejpam-5730	136	26	given	give	VERB
ejpam-5730	136	27	mapping	mapping	NOUN
ejpam-5730	136	28	.	.	PUNCT
ejpam-5730	137	1	suppose	suppose	VERB
ejpam-5730	137	2	that	that	SCONJ
ejpam-5730	137	3	the	the	DET
ejpam-5730	137	4	following	follow	VERB
ejpam-5730	137	5	conditions	condition	NOUN
ejpam-5730	137	6	are	be	AUX
ejpam-5730	137	7	satisfied	satisfied	ADJ
ejpam-5730	137	8	:	:	PUNCT
ejpam-5730	137	9	(	(	PUNCT
ejpam-5730	137	10	i	i	NOUN
ejpam-5730	137	11	)	)	PUNCT
ejpam-5730	137	12	t	t	PROPN
ejpam-5730	137	13	is	be	AUX
ejpam-5730	137	14	orbitally	orbitally	ADV
ejpam-5730	137	15	continuous	continuous	ADJ
ejpam-5730	137	16	on	on	ADP
ejpam-5730	137	17	m	m	PRON
ejpam-5730	137	18	;	;	PUNCT
ejpam-5730	137	19	(	(	PUNCT
ejpam-5730	137	20	ii	ii	NOUN
ejpam-5730	137	21	)	)	PUNCT
ejpam-5730	137	22	(	(	PUNCT
ejpam-5730	137	23	m	m	PROPN
ejpam-5730	137	24	,	,	PUNCT
ejpam-5730	137	25	d	d	NOUN
ejpam-5730	137	26	)	)	PUNCT
ejpam-5730	137	27	is	be	AUX
ejpam-5730	137	28	t	t	NOUN
ejpam-5730	137	29	-	-	PUNCT
ejpam-5730	137	30	orbitally	orbitally	ADV
ejpam-5730	137	31	complete	complete	ADJ
ejpam-5730	137	32	;	;	PUNCT
ejpam-5730	137	33	(	(	PUNCT
ejpam-5730	137	34	iii	iii	X
ejpam-5730	137	35	)	)	PUNCT
ejpam-5730	137	36	there	there	PRON
ejpam-5730	137	37	exists	exist	VERB
ejpam-5730	137	38	a	a	DET
ejpam-5730	137	39	constant	constant	ADJ
ejpam-5730	137	40	q	q	NOUN
ejpam-5730	137	41	∈	∈	PROPN
ejpam-5730	137	42	(	(	PUNCT
ejpam-5730	137	43	0	0	NUM
ejpam-5730	137	44	,	,	PUNCT
ejpam-5730	137	45	1	1	NUM
ejpam-5730	137	46	)	)	PUNCT
ejpam-5730	137	47	such	such	ADJ
ejpam-5730	137	48	that	that	SCONJ
ejpam-5730	137	49	min{d(tx	min{d(tx	PROPN
ejpam-5730	137	50	,	,	PUNCT
ejpam-5730	137	51	ty	ty	NOUN
ejpam-5730	137	52	)	)	PUNCT
ejpam-5730	137	53	,	,	PUNCT
ejpam-5730	137	54	d(x	d(x	PROPN
ejpam-5730	137	55	,	,	PUNCT
ejpam-5730	137	56	tx	tx	PROPN
ejpam-5730	137	57	)	)	PUNCT
ejpam-5730	137	58	,	,	PUNCT
ejpam-5730	137	59	d(y	d(y	PROPN
ejpam-5730	137	60	,	,	PUNCT
ejpam-5730	137	61	ty	ty	NOUN
ejpam-5730	137	62	)	)	PUNCT
ejpam-5730	137	63	}	}	PUNCT
ejpam-5730	137	64	−min{d(x	−min{d(x	PROPN
ejpam-5730	137	65	,	,	PUNCT
ejpam-5730	137	66	ty	ty	NOUN
ejpam-5730	137	67	)	)	PUNCT
ejpam-5730	137	68	,	,	PUNCT
ejpam-5730	137	69	d(y	d(y	PROPN
ejpam-5730	137	70	,	,	PUNCT
ejpam-5730	137	71	tx	tx	PROPN
ejpam-5730	137	72	)	)	PUNCT
ejpam-5730	137	73	}	}	PUNCT
ejpam-5730	137	74	≤	≤	NUM
ejpam-5730	137	75	q	q	ADJ
ejpam-5730	137	76	d(x	d(x	PROPN
ejpam-5730	137	77	,	,	PUNCT
ejpam-5730	137	78	y	y	NOUN
ejpam-5730	137	79	)	)	PUNCT
ejpam-5730	137	80	,	,	PUNCT
ejpam-5730	137	81	∀	∀	X
ejpam-5730	137	82	x	x	NOUN
ejpam-5730	137	83	,	,	PUNCT
ejpam-5730	137	84	y	y	PROPN
ejpam-5730	137	85	∈	∈	PROPN
ejpam-5730	137	86	m.	m.	NOUN
ejpam-5730	137	87	then	then	ADV
ejpam-5730	137	88	,	,	PUNCT
ejpam-5730	137	89	for	for	ADP
ejpam-5730	137	90	every	every	DET
ejpam-5730	137	91	x	x	SYM
ejpam-5730	137	92	∈	∈	PROPN
ejpam-5730	137	93	m	m	NOUN
ejpam-5730	137	94	,	,	PUNCT
ejpam-5730	137	95	the	the	DET
ejpam-5730	137	96	picard	picard	NOUN
ejpam-5730	137	97	sequence	sequence	NOUN
ejpam-5730	137	98	{	{	PUNCT
ejpam-5730	137	99	tnx	tnx	NOUN
ejpam-5730	137	100	}	}	PUNCT
ejpam-5730	137	101	converges	converge	NOUN
ejpam-5730	137	102	to	to	ADP
ejpam-5730	137	103	a	a	DET
ejpam-5730	137	104	fixed	fix	VERB
ejpam-5730	137	105	point	point	NOUN
ejpam-5730	137	106	of	of	ADP
ejpam-5730	137	107	t.	t.	PROPN
ejpam-5730	137	108	s.	s.	PROPN
ejpam-5730	137	109	park	park	PROPN
ejpam-5730	137	110	/	/	SYM
ejpam-5730	137	111	eur	eur	PROPN
ejpam-5730	137	112	.	.	PUNCT
ejpam-5730	138	1	j.	j.	PROPN
ejpam-5730	138	2	pure	pure	PROPN
ejpam-5730	138	3	appl	appl	PROPN
ejpam-5730	138	4	.	.	PROPN
ejpam-5730	138	5	math	math	PROPN
ejpam-5730	138	6	,	,	PUNCT
ejpam-5730	138	7	18	18	NUM
ejpam-5730	138	8	(	(	PUNCT
ejpam-5730	138	9	1	1	NUM
ejpam-5730	138	10	)	)	PUNCT
ejpam-5730	138	11	(	(	PUNCT
ejpam-5730	138	12	2025	2025	NUM
ejpam-5730	138	13	)	)	PUNCT
ejpam-5730	138	14	,	,	PUNCT
ejpam-5730	138	15	5730	5730	NUM
ejpam-5730	138	16	7	7	NUM
ejpam-5730	138	17	of	of	ADP
ejpam-5730	138	18	21	21	NUM
ejpam-5730	138	19	comment	comment	NOUN
ejpam-5730	138	20	:	:	PUNCT
ejpam-5730	139	1	for	for	ADP
ejpam-5730	139	2	y	y	PROPN
ejpam-5730	139	3	=	=	SYM
ejpam-5730	139	4	tx	tx	PROPN
ejpam-5730	139	5	,	,	PUNCT
ejpam-5730	139	6	we	we	PRON
ejpam-5730	139	7	can	can	AUX
ejpam-5730	139	8	consider	consider	VERB
ejpam-5730	139	9	the	the	DET
ejpam-5730	139	10	following	follow	VERB
ejpam-5730	139	11	:	:	PUNCT
ejpam-5730	139	12	min{d(tx	min{d(tx	PROPN
ejpam-5730	139	13	,	,	PUNCT
ejpam-5730	139	14	t	t	PROPN
ejpam-5730	139	15	2x	2x	NUM
ejpam-5730	139	16	)	)	PUNCT
ejpam-5730	139	17	,	,	PUNCT
ejpam-5730	139	18	d(x	d(x	PROPN
ejpam-5730	139	19	,	,	PUNCT
ejpam-5730	139	20	tx	tx	PROPN
ejpam-5730	139	21	)	)	PUNCT
ejpam-5730	139	22	,	,	PUNCT
ejpam-5730	139	23	d(tx	d(tx	PROPN
ejpam-5730	139	24	,	,	PUNCT
ejpam-5730	139	25	t	t	NOUN
ejpam-5730	139	26	2x	2x	NUM
ejpam-5730	139	27	)	)	PUNCT
ejpam-5730	139	28	}	}	PUNCT
ejpam-5730	139	29	−min{d(x	−min{d(x	PROPN
ejpam-5730	139	30	,	,	PUNCT
ejpam-5730	139	31	t	t	PROPN
ejpam-5730	139	32	2x	2x	NUM
ejpam-5730	139	33	)	)	PUNCT
ejpam-5730	139	34	,	,	PUNCT
ejpam-5730	139	35	d(tx	d(tx	PROPN
ejpam-5730	139	36	,	,	PUNCT
ejpam-5730	139	37	tx	tx	PROPN
ejpam-5730	139	38	)	)	PUNCT
ejpam-5730	139	39	}	}	PUNCT
ejpam-5730	139	40	≤	≤	NUM
ejpam-5730	139	41	q	q	ADJ
ejpam-5730	139	42	d(x	d(x	PROPN
ejpam-5730	139	43	,	,	PUNCT
ejpam-5730	139	44	tx	tx	PROPN
ejpam-5730	139	45	)	)	PUNCT
ejpam-5730	139	46	for	for	ADP
ejpam-5730	139	47	all	all	DET
ejpam-5730	139	48	x	x	NOUN
ejpam-5730	139	49	,	,	PUNCT
ejpam-5730	139	50	y	y	PROPN
ejpam-5730	139	51	=	=	PUNCT
ejpam-5730	139	52	tx	tx	PROPN
ejpam-5730	139	53	∈	∈	PROPN
ejpam-5730	139	54	m	m	NOUN
ejpam-5730	139	55	.	.	PUNCT
ejpam-5730	140	1	case	case	NOUN
ejpam-5730	140	2	1	1	NUM
ejpam-5730	140	3	:	:	PUNCT
ejpam-5730	140	4	if	if	SCONJ
ejpam-5730	140	5	d(tx	d(tx	PROPN
ejpam-5730	140	6	,	,	PUNCT
ejpam-5730	140	7	t	t	NOUN
ejpam-5730	140	8	2x	2x	NUM
ejpam-5730	140	9	)	)	PUNCT
ejpam-5730	141	1	≤	≤	NOUN
ejpam-5730	141	2	d(x	d(x	NOUN
ejpam-5730	141	3	,	,	PUNCT
ejpam-5730	141	4	tx	tx	PROPN
ejpam-5730	141	5	)	)	PUNCT
ejpam-5730	141	6	,	,	PUNCT
ejpam-5730	141	7	then	then	ADV
ejpam-5730	141	8	d(tx	d(tx	PROPN
ejpam-5730	141	9	,	,	PUNCT
ejpam-5730	141	10	t	t	PROPN
ejpam-5730	141	11	2x	2x	NUM
ejpam-5730	141	12	)	)	PUNCT
ejpam-5730	141	13	≤	≤	NUM
ejpam-5730	141	14	q	q	PUNCT
ejpam-5730	141	15	d(x	d(x	PROPN
ejpam-5730	141	16	,	,	PUNCT
ejpam-5730	141	17	tx	tx	PROPN
ejpam-5730	141	18	)	)	PUNCT
ejpam-5730	141	19	,	,	PUNCT
ejpam-5730	141	20	possible	possible	ADJ
ejpam-5730	141	21	.	.	PUNCT
ejpam-5730	142	1	case	case	NOUN
ejpam-5730	142	2	2	2	NUM
ejpam-5730	142	3	:	:	PUNCT
ejpam-5730	142	4	if	if	SCONJ
ejpam-5730	142	5	d(tx	d(tx	PROPN
ejpam-5730	142	6	,	,	PUNCT
ejpam-5730	142	7	t	t	PROPN
ejpam-5730	142	8	2x	2x	NUM
ejpam-5730	142	9	)	)	PUNCT
ejpam-5730	142	10	≥	≥	NOUN
ejpam-5730	142	11	d(x	d(x	PROPN
ejpam-5730	142	12	,	,	PUNCT
ejpam-5730	142	13	tx	tx	PROPN
ejpam-5730	142	14	)	)	PUNCT
ejpam-5730	142	15	,	,	PUNCT
ejpam-5730	142	16	then	then	ADV
ejpam-5730	142	17	d(x	d(x	PROPN
ejpam-5730	142	18	,	,	PUNCT
ejpam-5730	142	19	tx	tx	PROPN
ejpam-5730	142	20	)	)	PUNCT
ejpam-5730	142	21	≤	≤	NUM
ejpam-5730	142	22	q	q	PUNCT
ejpam-5730	142	23	d(x	d(x	PROPN
ejpam-5730	142	24	,	,	PUNCT
ejpam-5730	142	25	tx	tx	PROPN
ejpam-5730	142	26	)	)	PUNCT
ejpam-5730	142	27	implies	imply	VERB
ejpam-5730	142	28	x	x	PROPN
ejpam-5730	142	29	=	=	SYM
ejpam-5730	142	30	tx	tx	PROPN
ejpam-5730	142	31	.	.	PUNCT
ejpam-5730	143	1	in	in	ADP
ejpam-5730	143	2	any	any	DET
ejpam-5730	143	3	case	case	NOUN
ejpam-5730	143	4	,	,	PUNCT
ejpam-5730	143	5	theorems	theorem	NOUN
ejpam-5730	143	6	p	p	NOUN
ejpam-5730	143	7	and	and	CCONJ
ejpam-5730	143	8	h(γ1	h(γ1	NOUN
ejpam-5730	143	9	)	)	PUNCT
ejpam-5730	143	10	are	be	AUX
ejpam-5730	143	11	applicable	applicable	ADJ
ejpam-5730	143	12	to	to	ADP
ejpam-5730	143	13	t	t	PROPN
ejpam-5730	143	14	.	.	PUNCT
ejpam-5730	144	1	dass	dass	PROPN
ejpam-5730	144	2	and	and	CCONJ
ejpam-5730	144	3	gupta	gupta	PROPN
ejpam-5730	144	4	[	[	X
ejpam-5730	144	5	10	10	NUM
ejpam-5730	144	6	]	]	PUNCT
ejpam-5730	144	7	in	in	ADP
ejpam-5730	144	8	1975	1975	NUM
ejpam-5730	144	9	theorem	theorem	VERB
ejpam-5730	144	10	6.5	6.5	NUM
ejpam-5730	144	11	.	.	PUNCT
ejpam-5730	145	1	(	(	PUNCT
ejpam-5730	145	2	dass	dass	PROPN
ejpam-5730	145	3	-	-	PUNCT
ejpam-5730	145	4	gupta	gupta	PROPN
ejpam-5730	145	5	)	)	PUNCT
ejpam-5730	145	6	let	let	VERB
ejpam-5730	145	7	(	(	PUNCT
ejpam-5730	145	8	x	x	NOUN
ejpam-5730	145	9	,	,	PUNCT
ejpam-5730	145	10	d	d	NOUN
ejpam-5730	145	11	)	)	PUNCT
ejpam-5730	145	12	be	be	AUX
ejpam-5730	145	13	a	a	DET
ejpam-5730	145	14	complete	complete	ADJ
ejpam-5730	145	15	metric	metric	ADJ
ejpam-5730	145	16	space	space	NOUN
ejpam-5730	145	17	and	and	CCONJ
ejpam-5730	145	18	t	t	NOUN
ejpam-5730	145	19	:	:	PUNCT
ejpam-5730	145	20	x	x	X
ejpam-5730	145	21	→	→	PUNCT
ejpam-5730	145	22	x	x	PUNCT
ejpam-5730	145	23	be	be	AUX
ejpam-5730	145	24	a	a	DET
ejpam-5730	145	25	mapping	mapping	NOUN
ejpam-5730	145	26	.	.	PUNCT
ejpam-5730	146	1	if	if	SCONJ
ejpam-5730	146	2	there	there	PRON
ejpam-5730	146	3	exist	exist	VERB
ejpam-5730	146	4	k1	k1	NOUN
ejpam-5730	146	5	,	,	PUNCT
ejpam-5730	146	6	k2	k2	PROPN
ejpam-5730	146	7	∈	∈	PROPN
ejpam-5730	147	1	[	[	X
ejpam-5730	147	2	0	0	NUM
ejpam-5730	147	3	,	,	PUNCT
ejpam-5730	147	4	1	1	NUM
ejpam-5730	147	5	)	)	PUNCT
ejpam-5730	147	6	,	,	PUNCT
ejpam-5730	147	7	with	with	ADP
ejpam-5730	147	8	k1	k1	NOUN
ejpam-5730	147	9	+	+	CCONJ
ejpam-5730	147	10	k2	k2	X
ejpam-5730	147	11	<	<	X
ejpam-5730	147	12	1	1	NUM
ejpam-5730	147	13	such	such	ADJ
ejpam-5730	147	14	that	that	SCONJ
ejpam-5730	147	15	d(tx	d(tx	PROPN
ejpam-5730	147	16	,	,	PUNCT
ejpam-5730	147	17	ty	ty	NOUN
ejpam-5730	147	18	)	)	PUNCT
ejpam-5730	147	19	≤	≤	NOUN
ejpam-5730	147	20	k1	k1	X
ejpam-5730	147	21	·	·	PUNCT
ejpam-5730	147	22	d(y	d(y	NOUN
ejpam-5730	147	23	,	,	PUNCT
ejpam-5730	147	24	ty	ty	NOUN
ejpam-5730	147	25	)	)	PUNCT
ejpam-5730	147	26	1	1	NUM
ejpam-5730	147	27	+	+	CCONJ
ejpam-5730	147	28	d(x	d(x	PROPN
ejpam-5730	147	29	,	,	PUNCT
ejpam-5730	147	30	tx	tx	PROPN
ejpam-5730	147	31	)	)	PUNCT
ejpam-5730	147	32	1	1	NUM
ejpam-5730	147	33	+	+	CCONJ
ejpam-5730	147	34	d(x	d(x	PROPN
ejpam-5730	147	35	,	,	PUNCT
ejpam-5730	147	36	y	y	NOUN
ejpam-5730	147	37	)	)	PUNCT
ejpam-5730	147	38	+	+	CCONJ
ejpam-5730	147	39	k2	k2	X
ejpam-5730	147	40	·	·	PUNCT
ejpam-5730	147	41	d(x	d(x	PROPN
ejpam-5730	147	42	,	,	PUNCT
ejpam-5730	147	43	y	y	NOUN
ejpam-5730	147	44	)	)	PUNCT
ejpam-5730	147	45	,	,	PUNCT
ejpam-5730	147	46	for	for	ADP
ejpam-5730	147	47	all	all	DET
ejpam-5730	147	48	x	x	NOUN
ejpam-5730	147	49	,	,	PUNCT
ejpam-5730	147	50	y	y	PROPN
ejpam-5730	147	51	∈	∈	PROPN
ejpam-5730	147	52	x	x	X
ejpam-5730	147	53	,	,	PUNCT
ejpam-5730	147	54	then	then	ADV
ejpam-5730	147	55	t	t	PROPN
ejpam-5730	147	56	has	have	VERB
ejpam-5730	147	57	a	a	DET
ejpam-5730	147	58	unique	unique	ADJ
ejpam-5730	147	59	fixed	fix	VERB
ejpam-5730	147	60	point	point	NOUN
ejpam-5730	147	61	u	u	NOUN
ejpam-5730	147	62	∈	∈	PROPN
ejpam-5730	147	63	x	x	X
ejpam-5730	147	64	and	and	CCONJ
ejpam-5730	147	65	the	the	DET
ejpam-5730	147	66	sequence	sequence	NOUN
ejpam-5730	147	67	{	{	PUNCT
ejpam-5730	147	68	tnx	tnx	NOUN
ejpam-5730	147	69	}	}	PUNCT
ejpam-5730	147	70	converges	converge	NOUN
ejpam-5730	147	71	to	to	ADP
ejpam-5730	147	72	the	the	DET
ejpam-5730	147	73	fixed	fixed	ADJ
ejpam-5730	147	74	point	point	NOUN
ejpam-5730	147	75	u	u	NOUN
ejpam-5730	147	76	for	for	ADP
ejpam-5730	147	77	all	all	DET
ejpam-5730	147	78	x	x	SYM
ejpam-5730	147	79	∈	∈	NOUN
ejpam-5730	147	80	x.	x.	NOUN
ejpam-5730	147	81	comment	comment	NOUN
ejpam-5730	147	82	:	:	PUNCT
ejpam-5730	147	83	note	note	VERB
ejpam-5730	147	84	that	that	SCONJ
ejpam-5730	147	85	t	t	PROPN
ejpam-5730	147	86	is	be	AUX
ejpam-5730	147	87	an	an	DET
ejpam-5730	147	88	rhr	rhr	NOUN
ejpam-5730	147	89	map	map	NOUN
ejpam-5730	147	90	and	and	CCONJ
ejpam-5730	147	91	can	can	AUX
ejpam-5730	147	92	be	be	AUX
ejpam-5730	147	93	applied	apply	VERB
ejpam-5730	147	94	theorems	theorem	NOUN
ejpam-5730	147	95	p	p	NOUN
ejpam-5730	147	96	and	and	CCONJ
ejpam-5730	147	97	h(γ1	h(γ1	NOUN
ejpam-5730	147	98	)	)	PUNCT
ejpam-5730	147	99	.	.	PUNCT
ejpam-5730	148	1	the	the	DET
ejpam-5730	148	2	uniqueness	uniqueness	NOUN
ejpam-5730	148	3	follows	follow	VERB
ejpam-5730	148	4	from	from	ADP
ejpam-5730	148	5	the	the	DET
ejpam-5730	148	6	contractive	contractive	ADJ
ejpam-5730	148	7	condition	condition	NOUN
ejpam-5730	148	8	.	.	PUNCT
ejpam-5730	149	1	ran	ran	NOUN
ejpam-5730	149	2	and	and	CCONJ
ejpam-5730	149	3	reurings	reuring	NOUN
ejpam-5730	150	1	[	[	X
ejpam-5730	150	2	43	43	NUM
ejpam-5730	150	3	]	]	PUNCT
ejpam-5730	150	4	in	in	ADP
ejpam-5730	150	5	2004	2004	NUM
ejpam-5730	150	6	in	in	ADP
ejpam-5730	150	7	this	this	DET
ejpam-5730	150	8	paper	paper	NOUN
ejpam-5730	150	9	,	,	PUNCT
ejpam-5730	150	10	the	the	DET
ejpam-5730	150	11	following	follow	VERB
ejpam-5730	150	12	fixed	fix	VERB
ejpam-5730	150	13	point	point	NOUN
ejpam-5730	150	14	theorem	theorem	VERB
ejpam-5730	150	15	in	in	ADP
ejpam-5730	150	16	a	a	DET
ejpam-5730	150	17	partially	partially	ADV
ejpam-5730	150	18	ordered	order	VERB
ejpam-5730	150	19	metric	metric	ADJ
ejpam-5730	150	20	space	space	NOUN
ejpam-5730	150	21	is	be	AUX
ejpam-5730	150	22	proved	prove	VERB
ejpam-5730	150	23	:	:	PUNCT
ejpam-5730	150	24	theorem	theorem	VERB
ejpam-5730	150	25	6.6	6.6	NUM
ejpam-5730	150	26	.	.	PUNCT
ejpam-5730	151	1	(	(	PUNCT
ejpam-5730	151	2	ran	ran	NOUN
ejpam-5730	151	3	-	-	PUNCT
ejpam-5730	151	4	reurings	reuring	NOUN
ejpam-5730	151	5	)	)	PUNCT
ejpam-5730	151	6	let	let	VERB
ejpam-5730	151	7	(	(	PUNCT
ejpam-5730	151	8	m,≤	m,≤	X
ejpam-5730	151	9	)	)	PUNCT
ejpam-5730	151	10	be	be	VERB
ejpam-5730	151	11	an	an	DET
ejpam-5730	151	12	ordered	order	VERB
ejpam-5730	151	13	set	set	NOUN
ejpam-5730	151	14	and	and	CCONJ
ejpam-5730	151	15	d	d	NOUN
ejpam-5730	151	16	be	be	AUX
ejpam-5730	151	17	a	a	DET
ejpam-5730	151	18	metric	metric	NOUN
ejpam-5730	151	19	on	on	ADP
ejpam-5730	151	20	m	m	PRON
ejpam-5730	151	21	such	such	ADJ
ejpam-5730	151	22	that	that	SCONJ
ejpam-5730	151	23	(	(	PUNCT
ejpam-5730	151	24	m	m	NOUN
ejpam-5730	151	25	,	,	PUNCT
ejpam-5730	151	26	d	d	NOUN
ejpam-5730	151	27	)	)	PUNCT
ejpam-5730	151	28	is	be	AUX
ejpam-5730	151	29	a	a	DET
ejpam-5730	151	30	complete	complete	ADJ
ejpam-5730	151	31	metric	metric	ADJ
ejpam-5730	151	32	space	space	NOUN
ejpam-5730	151	33	.	.	PUNCT
ejpam-5730	152	1	let	let	VERB
ejpam-5730	152	2	u	u	PRON
ejpam-5730	152	3	:	:	PUNCT
ejpam-5730	152	4	m	m	VERB
ejpam-5730	152	5	→	→	NOUN
ejpam-5730	152	6	m	m	AUX
ejpam-5730	152	7	be	be	AUX
ejpam-5730	152	8	a	a	DET
ejpam-5730	152	9	nondecreasing	nondecrease	VERB
ejpam-5730	152	10	mapping	mapping	NOUN
ejpam-5730	152	11	,	,	PUNCT
ejpam-5730	152	12	i.e.	i.e.	X
ejpam-5730	152	13	ux	ux	ADV
ejpam-5730	152	14	≤	≤	ADV
ejpam-5730	152	15	uy	uy	ADP
ejpam-5730	152	16	,	,	PUNCT
ejpam-5730	152	17	for	for	ADP
ejpam-5730	152	18	every	every	DET
ejpam-5730	152	19	x	x	NOUN
ejpam-5730	152	20	,	,	PUNCT
ejpam-5730	152	21	y	y	PROPN
ejpam-5730	152	22	∈	∈	PROPN
ejpam-5730	152	23	m	m	VERB
ejpam-5730	152	24	with	with	ADP
ejpam-5730	152	25	x	x	SYM
ejpam-5730	152	26	≤	≤	PROPN
ejpam-5730	152	27	y.	y.	NOUN
ejpam-5730	152	28	suppose	suppose	VERB
ejpam-5730	152	29	that	that	SCONJ
ejpam-5730	152	30	there	there	PRON
ejpam-5730	152	31	exists	exist	VERB
ejpam-5730	152	32	x0	x0	PROPN
ejpam-5730	152	33	∈	∈	PROPN
ejpam-5730	152	34	m	m	VERB
ejpam-5730	152	35	with	with	ADP
ejpam-5730	152	36	x0	x0	PROPN
ejpam-5730	152	37	≤	≤	PROPN
ejpam-5730	152	38	ux0	ux0	NOUN
ejpam-5730	152	39	and	and	CCONJ
ejpam-5730	152	40	l	l	NOUN
ejpam-5730	152	41	∈	∈	PROPN
ejpam-5730	153	1	[	[	X
ejpam-5730	153	2	0	0	NUM
ejpam-5730	153	3	,	,	PUNCT
ejpam-5730	153	4	1	1	NUM
ejpam-5730	153	5	)	)	PUNCT
ejpam-5730	153	6	such	such	ADJ
ejpam-5730	153	7	that	that	SCONJ
ejpam-5730	153	8	d(ux	d(ux	NOUN
ejpam-5730	153	9	,	,	PUNCT
ejpam-5730	153	10	uy	uy	NOUN
ejpam-5730	153	11	)	)	PUNCT
ejpam-5730	153	12	≤	≤	NOUN
ejpam-5730	153	13	ld(x	ld(x	PUNCT
ejpam-5730	153	14	,	,	PUNCT
ejpam-5730	153	15	y	y	NOUN
ejpam-5730	153	16	)	)	PUNCT
ejpam-5730	153	17	∀	∀	PUNCT
ejpam-5730	154	1	x	x	NOUN
ejpam-5730	154	2	,	,	PUNCT
ejpam-5730	154	3	y	y	PROPN
ejpam-5730	154	4	∈	∈	PROPN
ejpam-5730	154	5	m	m	VERB
ejpam-5730	154	6	with	with	ADP
ejpam-5730	154	7	x	x	SYM
ejpam-5730	154	8	≤	≤	X
ejpam-5730	154	9	y.	y.	NOUN
ejpam-5730	154	10	if	if	SCONJ
ejpam-5730	154	11	u	u	NOUN
ejpam-5730	154	12	is	be	AUX
ejpam-5730	154	13	continuous	continuous	ADJ
ejpam-5730	154	14	,	,	PUNCT
ejpam-5730	154	15	then	then	ADV
ejpam-5730	154	16	it	it	PRON
ejpam-5730	154	17	has	have	VERB
ejpam-5730	154	18	a	a	DET
ejpam-5730	154	19	fixed	fix	VERB
ejpam-5730	154	20	point	point	NOUN
ejpam-5730	154	21	in	in	ADP
ejpam-5730	154	22	m.	m.	NOUN
ejpam-5730	154	23	comment	comment	NOUN
ejpam-5730	154	24	:	:	PUNCT
ejpam-5730	154	25	note	note	VERB
ejpam-5730	154	26	that	that	SCONJ
ejpam-5730	154	27	u	u	NOUN
ejpam-5730	154	28	is	be	AUX
ejpam-5730	154	29	an	an	DET
ejpam-5730	154	30	rhr	rhr	NOUN
ejpam-5730	154	31	map	map	NOUN
ejpam-5730	154	32	and	and	CCONJ
ejpam-5730	154	33	can	can	AUX
ejpam-5730	154	34	be	be	AUX
ejpam-5730	154	35	applied	apply	VERB
ejpam-5730	154	36	theorems	theorem	NOUN
ejpam-5730	154	37	p	p	NOUN
ejpam-5730	154	38	and	and	CCONJ
ejpam-5730	154	39	h(γ1	h(γ1	NOUN
ejpam-5730	154	40	)	)	PUNCT
ejpam-5730	154	41	.	.	PUNCT
ejpam-5730	155	1	suzuki	suzuki	PROPN
ejpam-5730	156	1	[	[	X
ejpam-5730	156	2	49	49	NUM
ejpam-5730	156	3	]	]	PUNCT
ejpam-5730	156	4	in	in	ADP
ejpam-5730	156	5	2008	2008	NUM
ejpam-5730	156	6	suzuki	suzuki	NOUN
ejpam-5730	156	7	generalized	generalize	VERB
ejpam-5730	156	8	the	the	DET
ejpam-5730	156	9	banach	banach	NOUN
ejpam-5730	156	10	contraction	contraction	NOUN
ejpam-5730	156	11	principle	principle	NOUN
ejpam-5730	156	12	as	as	SCONJ
ejpam-5730	156	13	follows	follow	VERB
ejpam-5730	156	14	:	:	PUNCT
ejpam-5730	156	15	theorem	theorem	NOUN
ejpam-5730	156	16	6.7	6.7	NUM
ejpam-5730	156	17	.	.	PUNCT
ejpam-5730	157	1	(	(	PUNCT
ejpam-5730	157	2	suzuki	suzuki	X
ejpam-5730	157	3	)	)	PUNCT
ejpam-5730	157	4	let	let	AUX
ejpam-5730	157	5	(	(	PUNCT
ejpam-5730	157	6	x	x	NOUN
ejpam-5730	157	7	,	,	PUNCT
ejpam-5730	157	8	d	d	NOUN
ejpam-5730	157	9	)	)	PUNCT
ejpam-5730	157	10	be	be	AUX
ejpam-5730	157	11	a	a	DET
ejpam-5730	157	12	complete	complete	ADJ
ejpam-5730	157	13	metric	metric	ADJ
ejpam-5730	157	14	space	space	NOUN
ejpam-5730	157	15	and	and	CCONJ
ejpam-5730	157	16	t	t	PROPN
ejpam-5730	157	17	be	be	AUX
ejpam-5730	157	18	a	a	DET
ejpam-5730	157	19	mapping	mapping	NOUN
ejpam-5730	157	20	on	on	ADP
ejpam-5730	157	21	x.	x.	NOUN
ejpam-5730	157	22	define	define	VERB
ejpam-5730	157	23	a	a	DET
ejpam-5730	157	24	nonincreasing	nonincrease	VERB
ejpam-5730	157	25	function	function	NOUN
ejpam-5730	157	26	θ	θ	NOUN
ejpam-5730	157	27	from	from	ADP
ejpam-5730	157	28	[	[	X
ejpam-5730	157	29	0	0	NUM
ejpam-5730	157	30	,	,	PUNCT
ejpam-5730	157	31	1	1	NUM
ejpam-5730	157	32	)	)	PUNCT
ejpam-5730	157	33	onto	onto	ADP
ejpam-5730	157	34	(	(	PUNCT
ejpam-5730	157	35	1/2	1/2	NUM
ejpam-5730	157	36	,	,	PUNCT
ejpam-5730	157	37	1	1	NUM
ejpam-5730	157	38	]	]	PUNCT
ejpam-5730	157	39	by	by	ADP
ejpam-5730	157	40	θ(r	θ(r	NOUN
ejpam-5730	157	41	)	)	PUNCT
ejpam-5730	158	1	=	=	SYM
ejpam-5730	158	2			NOUN
ejpam-5730	158	3	1	1	NUM
ejpam-5730	158	4	if	if	SCONJ
ejpam-5730	158	5	0	0	NUM
ejpam-5730	158	6	≤	≤	NUM
ejpam-5730	158	7	r	r	NOUN
ejpam-5730	158	8	≤	≤	NUM
ejpam-5730	158	9	(	(	PUNCT
ejpam-5730	158	10	√	√	NUM
ejpam-5730	158	11	5−	5−	NUM
ejpam-5730	158	12	1)/2	1)/2	NUM
ejpam-5730	158	13	,	,	PUNCT
ejpam-5730	158	14	(	(	PUNCT
ejpam-5730	158	15	1−	1−	NUM
ejpam-5730	158	16	r)r−2	r)r−2	NOUN
ejpam-5730	158	17	if	if	SCONJ
ejpam-5730	158	18	(	(	PUNCT
ejpam-5730	158	19	√	√	NUM
ejpam-5730	158	20	5−	5−	NUM
ejpam-5730	158	21	1)/2	1)/2	NUM
ejpam-5730	158	22	≤	≤	NUM
ejpam-5730	158	23	r	r	NOUN
ejpam-5730	158	24	≤	≤	NUM
ejpam-5730	158	25	2−1/2	2−1/2	NUM
ejpam-5730	158	26	,	,	PUNCT
ejpam-5730	158	27	(	(	PUNCT
ejpam-5730	158	28	1	1	NUM
ejpam-5730	158	29	+	+	NOUN
ejpam-5730	158	30	r)−1	r)−1	NOUN
ejpam-5730	158	31	if	if	SCONJ
ejpam-5730	158	32	2−1/2	2−1/2	NUM
ejpam-5730	158	33	≤	≤	NOUN
ejpam-5730	158	34	r	r	NOUN
ejpam-5730	158	35	<	<	X
ejpam-5730	158	36	1	1	NUM
ejpam-5730	158	37	.	.	PUNCT
ejpam-5730	158	38	(	(	PUNCT
ejpam-5730	158	39	1	1	X
ejpam-5730	158	40	)	)	PUNCT
ejpam-5730	158	41	s.	s.	PROPN
ejpam-5730	158	42	park	park	PROPN
ejpam-5730	158	43	/	/	SYM
ejpam-5730	158	44	eur	eur	PROPN
ejpam-5730	158	45	.	.	PUNCT
ejpam-5730	159	1	j.	j.	PROPN
ejpam-5730	159	2	pure	pure	PROPN
ejpam-5730	159	3	appl	appl	PROPN
ejpam-5730	159	4	.	.	PROPN
ejpam-5730	159	5	math	math	PROPN
ejpam-5730	159	6	,	,	PUNCT
ejpam-5730	159	7	18	18	NUM
ejpam-5730	159	8	(	(	PUNCT
ejpam-5730	159	9	1	1	NUM
ejpam-5730	159	10	)	)	PUNCT
ejpam-5730	159	11	(	(	PUNCT
ejpam-5730	159	12	2025	2025	NUM
ejpam-5730	159	13	)	)	PUNCT
ejpam-5730	159	14	,	,	PUNCT
ejpam-5730	159	15	5730	5730	NUM
ejpam-5730	159	16	8	8	NUM
ejpam-5730	159	17	of	of	ADP
ejpam-5730	159	18	21	21	NUM
ejpam-5730	159	19	assume	assume	VERB
ejpam-5730	159	20	there	there	PRON
ejpam-5730	159	21	exists	exist	VERB
ejpam-5730	159	22	r	r	NOUN
ejpam-5730	159	23	∈	∈	PROPN
ejpam-5730	160	1	[	[	X
ejpam-5730	160	2	0	0	NUM
ejpam-5730	160	3	,	,	PUNCT
ejpam-5730	160	4	1	1	NUM
ejpam-5730	160	5	)	)	PUNCT
ejpam-5730	160	6	such	such	ADJ
ejpam-5730	160	7	that	that	DET
ejpam-5730	160	8	θ(r)d(x	θ(r)d(x	NOUN
ejpam-5730	160	9	,	,	PUNCT
ejpam-5730	160	10	tx	tx	PROPN
ejpam-5730	160	11	)	)	PUNCT
ejpam-5730	160	12	≤	≤	NOUN
ejpam-5730	160	13	d(x	d(x	PROPN
ejpam-5730	160	14	,	,	PUNCT
ejpam-5730	160	15	y	y	NOUN
ejpam-5730	160	16	)	)	PUNCT
ejpam-5730	161	1	=	=	VERB
ejpam-5730	161	2	⇒	⇒	NOUN
ejpam-5730	161	3	d(tx	d(tx	PROPN
ejpam-5730	161	4	,	,	PUNCT
ejpam-5730	161	5	ty	ty	NOUN
ejpam-5730	161	6	)	)	PUNCT
ejpam-5730	161	7	≤	≤	NOUN
ejpam-5730	162	1	r	r	NOUN
ejpam-5730	162	2	d(x	d(x	PROPN
ejpam-5730	162	3	,	,	PUNCT
ejpam-5730	162	4	y	y	NOUN
ejpam-5730	162	5	)	)	PUNCT
ejpam-5730	162	6	for	for	ADP
ejpam-5730	162	7	all	all	DET
ejpam-5730	162	8	x	x	NOUN
ejpam-5730	162	9	,	,	PUNCT
ejpam-5730	162	10	y	y	PROPN
ejpam-5730	162	11	∈	∈	PROPN
ejpam-5730	162	12	x.	x.	NOUN
ejpam-5730	163	1	then	then	ADV
ejpam-5730	163	2	there	there	PRON
ejpam-5730	163	3	exists	exist	VERB
ejpam-5730	163	4	a	a	DET
ejpam-5730	163	5	unique	unique	ADJ
ejpam-5730	163	6	fixed	fix	VERB
ejpam-5730	163	7	point	point	NOUN
ejpam-5730	163	8	z	z	PROPN
ejpam-5730	163	9	of	of	ADP
ejpam-5730	163	10	t.	t.	PROPN
ejpam-5730	163	11	moreover	moreover	PROPN
ejpam-5730	163	12	limn	limn	PROPN
ejpam-5730	163	13	t	t	PROPN
ejpam-5730	163	14	nx	nx	PROPN
ejpam-5730	164	1	=	=	PROPN
ejpam-5730	164	2	z	z	PROPN
ejpam-5730	164	3	for	for	ADP
ejpam-5730	164	4	all	all	DET
ejpam-5730	164	5	x	x	SYM
ejpam-5730	164	6	∈	∈	NOUN
ejpam-5730	164	7	x.	x.	NOUN
ejpam-5730	164	8	comment	comment	NOUN
ejpam-5730	164	9	:	:	PUNCT
ejpam-5730	164	10	note	note	VERB
ejpam-5730	164	11	that	that	SCONJ
ejpam-5730	164	12	t	t	PROPN
ejpam-5730	164	13	is	be	AUX
ejpam-5730	164	14	an	an	DET
ejpam-5730	164	15	rhr	rhr	NOUN
ejpam-5730	164	16	map	map	NOUN
ejpam-5730	164	17	and	and	CCONJ
ejpam-5730	164	18	theorems	theorem	NOUN
ejpam-5730	164	19	p	p	NOUN
ejpam-5730	164	20	or	or	CCONJ
ejpam-5730	164	21	h(γ1	h(γ1	NOUN
ejpam-5730	164	22	)	)	PUNCT
ejpam-5730	164	23	can	can	AUX
ejpam-5730	164	24	be	be	AUX
ejpam-5730	164	25	applied	apply	VERB
ejpam-5730	164	26	.	.	PUNCT
ejpam-5730	165	1	now	now	ADV
ejpam-5730	165	2	it	it	PRON
ejpam-5730	165	3	suffices	suffice	VERB
ejpam-5730	165	4	to	to	PART
ejpam-5730	165	5	show	show	VERB
ejpam-5730	165	6	the	the	DET
ejpam-5730	165	7	uniqueness	uniqueness	NOUN
ejpam-5730	165	8	of	of	ADP
ejpam-5730	165	9	the	the	DET
ejpam-5730	165	10	fixed	fix	VERB
ejpam-5730	165	11	point	point	NOUN
ejpam-5730	165	12	z.	z.	PROPN
ejpam-5730	166	1	if	if	SCONJ
ejpam-5730	166	2	w	w	PROPN
ejpam-5730	166	3	∈	∈	PROPN
ejpam-5730	166	4	x	x	PUNCT
ejpam-5730	166	5	is	be	AUX
ejpam-5730	166	6	a	a	DET
ejpam-5730	166	7	fixed	fix	VERB
ejpam-5730	166	8	point	point	NOUN
ejpam-5730	166	9	,	,	PUNCT
ejpam-5730	166	10	then	then	ADV
ejpam-5730	166	11	θ(r)d(z	θ(r)d(z	NOUN
ejpam-5730	166	12	,	,	PUNCT
ejpam-5730	166	13	tz	tz	NOUN
ejpam-5730	166	14	)	)	PUNCT
ejpam-5730	166	15	≤	≤	NOUN
ejpam-5730	166	16	d(z	d(z	PROPN
ejpam-5730	166	17	,	,	PUNCT
ejpam-5730	166	18	w	w	NOUN
ejpam-5730	166	19	)	)	PUNCT
ejpam-5730	167	1	=	=	NOUN
ejpam-5730	167	2	⇒	⇒	NOUN
ejpam-5730	167	3	d(tz	d(tz	PROPN
ejpam-5730	167	4	,	,	PUNCT
ejpam-5730	167	5	tw	tw	NOUN
ejpam-5730	167	6	)	)	PUNCT
ejpam-5730	167	7	≤	≤	NUM
ejpam-5730	167	8	r	r	NOUN
ejpam-5730	167	9	d(z	d(z	PROPN
ejpam-5730	167	10	,	,	PUNCT
ejpam-5730	167	11	w	w	NOUN
ejpam-5730	167	12	)	)	PUNCT
ejpam-5730	167	13	.	.	PUNCT
ejpam-5730	168	1	hence	hence	ADV
ejpam-5730	168	2	d(z	d(z	PROPN
ejpam-5730	168	3	,	,	PUNCT
ejpam-5730	168	4	w	w	NOUN
ejpam-5730	168	5	)	)	PUNCT
ejpam-5730	168	6	=	=	SYM
ejpam-5730	168	7	d(tz	d(tz	NOUN
ejpam-5730	168	8	,	,	PUNCT
ejpam-5730	168	9	tw	tw	NOUN
ejpam-5730	168	10	)	)	PUNCT
ejpam-5730	168	11	≤	≤	NUM
ejpam-5730	168	12	r	r	NOUN
ejpam-5730	168	13	d(z	d(z	PROPN
ejpam-5730	168	14	,	,	PUNCT
ejpam-5730	168	15	w	w	NOUN
ejpam-5730	168	16	)	)	PUNCT
ejpam-5730	168	17	and	and	CCONJ
ejpam-5730	168	18	consequently	consequently	ADV
ejpam-5730	168	19	d(z	d(z	PROPN
ejpam-5730	168	20	,	,	PUNCT
ejpam-5730	168	21	w	w	NOUN
ejpam-5730	168	22	)	)	PUNCT
ejpam-5730	168	23	=	=	SYM
ejpam-5730	168	24	0	0	X
ejpam-5730	168	25	.	.	PUNCT
ejpam-5730	169	1	this	this	PRON
ejpam-5730	169	2	is	be	AUX
ejpam-5730	169	3	a	a	DET
ejpam-5730	169	4	simple	simple	ADJ
ejpam-5730	169	5	proof	proof	NOUN
ejpam-5730	169	6	of	of	ADP
ejpam-5730	169	7	theorem	theorem	NOUN
ejpam-5730	169	8	6.7	6.7	NUM
ejpam-5730	169	9	.	.	PUNCT
ejpam-5730	170	1	there	there	PRON
ejpam-5730	170	2	have	have	AUX
ejpam-5730	170	3	been	be	AUX
ejpam-5730	170	4	appeared	appear	VERB
ejpam-5730	170	5	a	a	DET
ejpam-5730	170	6	large	large	ADJ
ejpam-5730	170	7	number	number	NOUN
ejpam-5730	170	8	of	of	ADP
ejpam-5730	170	9	variants	variant	NOUN
ejpam-5730	170	10	of	of	ADP
ejpam-5730	170	11	suzuki	suzuki	PROPN
ejpam-5730	170	12	’s	’s	PART
ejpam-5730	170	13	theorem	theorem	VERB
ejpam-5730	170	14	.	.	PUNCT
ejpam-5730	171	1	many	many	ADJ
ejpam-5730	171	2	of	of	ADP
ejpam-5730	171	3	them	they	PRON
ejpam-5730	171	4	can	can	AUX
ejpam-5730	171	5	be	be	AUX
ejpam-5730	171	6	improved	improve	VERB
ejpam-5730	171	7	by	by	ADP
ejpam-5730	171	8	easy	easy	ADJ
ejpam-5730	171	9	proofs	proof	NOUN
ejpam-5730	171	10	as	as	SCONJ
ejpam-5730	171	11	shown	show	VERB
ejpam-5730	171	12	as	as	ADP
ejpam-5730	171	13	above	above	ADV
ejpam-5730	171	14	;	;	PUNCT
ejpam-5730	171	15	see	see	VERB
ejpam-5730	171	16	[	[	X
ejpam-5730	171	17	38	38	NUM
ejpam-5730	171	18	]	]	PUNCT
ejpam-5730	171	19	.	.	PUNCT
ejpam-5730	172	1	in	in	ADP
ejpam-5730	172	2	order	order	NOUN
ejpam-5730	172	3	to	to	PART
ejpam-5730	172	4	show	show	VERB
ejpam-5730	172	5	uselessness	uselessness	NOUN
ejpam-5730	172	6	of	of	ADP
ejpam-5730	172	7	theorems	theorem	NOUN
ejpam-5730	172	8	2	2	NUM
ejpam-5730	172	9	and	and	CCONJ
ejpam-5730	172	10	3	3	NUM
ejpam-5730	172	11	in	in	ADP
ejpam-5730	172	12	[	[	X
ejpam-5730	172	13	49	49	NUM
ejpam-5730	172	14	]	]	PUNCT
ejpam-5730	172	15	and	and	CCONJ
ejpam-5730	172	16	other	other	ADJ
ejpam-5730	172	17	works	work	NOUN
ejpam-5730	172	18	of	of	ADP
ejpam-5730	172	19	suzuki	suzuki	PROPN
ejpam-5730	172	20	,	,	PUNCT
ejpam-5730	172	21	let	let	VERB
ejpam-5730	172	22	us	we	PRON
ejpam-5730	172	23	consider	consider	VERB
ejpam-5730	172	24	any	any	DET
ejpam-5730	172	25	function	function	NOUN
ejpam-5730	172	26	θ′	θ′	NOUN
ejpam-5730	172	27	:	:	PUNCT
ejpam-5730	173	1	[	[	X
ejpam-5730	173	2	0,+∞	0,+∞	NUM
ejpam-5730	173	3	)	)	PUNCT
ejpam-5730	173	4	→	→	PUNCT
ejpam-5730	174	1	[	[	X
ejpam-5730	174	2	0	0	NUM
ejpam-5730	174	3	,	,	PUNCT
ejpam-5730	174	4	1	1	NUM
ejpam-5730	174	5	]	]	NUM
ejpam-5730	174	6	:	:	PUNCT
ejpam-5730	174	7	theorem	theorem	NOUN
ejpam-5730	174	8	6.8	6.8	NUM
ejpam-5730	174	9	.	.	PUNCT
ejpam-5730	175	1	(	(	PUNCT
ejpam-5730	175	2	park	park	NOUN
ejpam-5730	175	3	)	)	PUNCT
ejpam-5730	175	4	replace	replace	VERB
ejpam-5730	175	5	the	the	DET
ejpam-5730	175	6	function	function	NOUN
ejpam-5730	175	7	θ	θ	PROPN
ejpam-5730	175	8	in	in	ADP
ejpam-5730	175	9	theorem	theorem	NOUN
ejpam-5730	175	10	6.7	6.7	NUM
ejpam-5730	175	11	by	by	ADP
ejpam-5730	175	12	θ′.	θ′.	NOUN
ejpam-5730	175	13	then	then	ADV
ejpam-5730	175	14	the	the	DET
ejpam-5730	175	15	conclusion	conclusion	NOUN
ejpam-5730	175	16	of	of	ADP
ejpam-5730	175	17	theorem	theorem	ADJ
ejpam-5730	175	18	6.7	6.7	NUM
ejpam-5730	175	19	holds	hold	NOUN
ejpam-5730	175	20	.	.	PUNCT
ejpam-5730	176	1	proof	proof	NOUN
ejpam-5730	176	2	.	.	PUNCT
ejpam-5730	177	1	note	note	VERB
ejpam-5730	177	2	that	that	SCONJ
ejpam-5730	177	3	,	,	PUNCT
ejpam-5730	177	4	by	by	ADP
ejpam-5730	177	5	putting	put	VERB
ejpam-5730	177	6	y	y	PROPN
ejpam-5730	177	7	=	=	SYM
ejpam-5730	177	8	tx	tx	PROPN
ejpam-5730	177	9	,	,	PUNCT
ejpam-5730	177	10	t	t	PROPN
ejpam-5730	177	11	becomes	become	VERB
ejpam-5730	177	12	an	an	DET
ejpam-5730	177	13	rhr	rhr	NOUN
ejpam-5730	177	14	map	map	NOUN
ejpam-5730	177	15	.	.	PUNCT
ejpam-5730	178	1	then	then	ADV
ejpam-5730	178	2	by	by	ADP
ejpam-5730	178	3	theorems	theorem	NOUN
ejpam-5730	178	4	p	p	NOUN
ejpam-5730	178	5	or	or	CCONJ
ejpam-5730	178	6	h(γ1	h(γ1	NOUN
ejpam-5730	178	7	)	)	PUNCT
ejpam-5730	178	8	,	,	PUNCT
ejpam-5730	178	9	t	t	PROPN
ejpam-5730	178	10	has	have	VERB
ejpam-5730	178	11	a	a	DET
ejpam-5730	178	12	fixed	fix	VERB
ejpam-5730	178	13	point	point	NOUN
ejpam-5730	178	14	and	and	CCONJ
ejpam-5730	178	15	its	its	PRON
ejpam-5730	178	16	uniqueness	uniqueness	NOUN
ejpam-5730	178	17	follows	follow	VERB
ejpam-5730	178	18	as	as	ADP
ejpam-5730	178	19	in	in	ADP
ejpam-5730	178	20	our	our	PRON
ejpam-5730	178	21	proof	proof	NOUN
ejpam-5730	178	22	of	of	ADP
ejpam-5730	178	23	theorem	theorem	NOUN
ejpam-5730	178	24	6.7	6.7	NUM
ejpam-5730	178	25	in	in	ADP
ejpam-5730	178	26	[	[	X
ejpam-5730	178	27	36	36	NUM
ejpam-5730	178	28	]	]	PUNCT
ejpam-5730	178	29	.	.	PUNCT
ejpam-5730	179	1	□	□	PUNCT
ejpam-5730	179	2	altun	altun	NOUN
ejpam-5730	179	3	and	and	CCONJ
ejpam-5730	179	4	erduran	erduran	VERB
ejpam-5730	180	1	[	[	X
ejpam-5730	180	2	1	1	X
ejpam-5730	180	3	]	]	PUNCT
ejpam-5730	180	4	in	in	ADP
ejpam-5730	180	5	2011	2011	NUM
ejpam-5730	180	6	the	the	DET
ejpam-5730	180	7	authors	author	NOUN
ejpam-5730	180	8	present	present	VERB
ejpam-5730	180	9	a	a	DET
ejpam-5730	180	10	fixed	fix	VERB
ejpam-5730	180	11	-	-	PUNCT
ejpam-5730	180	12	point	point	NOUN
ejpam-5730	180	13	theorem	theorem	NOUN
ejpam-5730	180	14	for	for	ADP
ejpam-5730	180	15	a	a	DET
ejpam-5730	180	16	single	single	ADV
ejpam-5730	180	17	-	-	PUNCT
ejpam-5730	180	18	valued	value	VERB
ejpam-5730	180	19	map	map	NOUN
ejpam-5730	180	20	in	in	ADP
ejpam-5730	180	21	a	a	DET
ejpam-5730	180	22	complete	complete	ADJ
ejpam-5730	180	23	metric	metric	ADJ
ejpam-5730	180	24	space	space	NOUN
ejpam-5730	180	25	using	use	VERB
ejpam-5730	180	26	implicit	implicit	ADJ
ejpam-5730	180	27	relation	relation	NOUN
ejpam-5730	180	28	,	,	PUNCT
ejpam-5730	180	29	which	which	PRON
ejpam-5730	180	30	is	be	AUX
ejpam-5730	180	31	a	a	DET
ejpam-5730	180	32	generalization	generalization	NOUN
ejpam-5730	180	33	of	of	ADP
ejpam-5730	180	34	several	several	ADJ
ejpam-5730	180	35	previously	previously	ADV
ejpam-5730	180	36	stated	state	VERB
ejpam-5730	180	37	results	result	NOUN
ejpam-5730	180	38	including	include	VERB
ejpam-5730	180	39	that	that	PRON
ejpam-5730	180	40	of	of	ADP
ejpam-5730	180	41	suzuki	suzuki	PROPN
ejpam-5730	180	42	[	[	X
ejpam-5730	180	43	49	49	NUM
ejpam-5730	180	44	]	]	PUNCT
ejpam-5730	180	45	.	.	PUNCT
ejpam-5730	181	1	the	the	DET
ejpam-5730	181	2	aim	aim	NOUN
ejpam-5730	181	3	of	of	ADP
ejpam-5730	181	4	[	[	X
ejpam-5730	181	5	1	1	X
ejpam-5730	181	6	]	]	PUNCT
ejpam-5730	181	7	is	be	AUX
ejpam-5730	181	8	to	to	PART
ejpam-5730	181	9	generalize	generalize	VERB
ejpam-5730	181	10	the	the	DET
ejpam-5730	181	11	above	above	ADJ
ejpam-5730	181	12	results	result	NOUN
ejpam-5730	181	13	using	use	VERB
ejpam-5730	181	14	the	the	DET
ejpam-5730	181	15	implicit	implicit	ADJ
ejpam-5730	181	16	relation	relation	NOUN
ejpam-5730	181	17	technique	technique	NOUN
ejpam-5730	181	18	in	in	ADP
ejpam-5730	181	19	such	such	DET
ejpam-5730	181	20	a	a	DET
ejpam-5730	181	21	way	way	NOUN
ejpam-5730	181	22	that	that	PRON
ejpam-5730	181	23	f	f	X
ejpam-5730	181	24	(	(	PUNCT
ejpam-5730	181	25	d(tx	d(tx	PROPN
ejpam-5730	181	26	,	,	PUNCT
ejpam-5730	181	27	ty	ty	NOUN
ejpam-5730	181	28	)	)	PUNCT
ejpam-5730	181	29	,	,	PUNCT
ejpam-5730	181	30	d(x	d(x	PROPN
ejpam-5730	181	31	,	,	PUNCT
ejpam-5730	181	32	y	y	NOUN
ejpam-5730	181	33	)	)	PUNCT
ejpam-5730	181	34	,	,	PUNCT
ejpam-5730	181	35	d(x	d(x	PROPN
ejpam-5730	181	36	,	,	PUNCT
ejpam-5730	181	37	tx	tx	PROPN
ejpam-5730	181	38	)	)	PUNCT
ejpam-5730	181	39	,	,	PUNCT
ejpam-5730	181	40	d(y	d(y	PROPN
ejpam-5730	181	41	,	,	PUNCT
ejpam-5730	181	42	ty	ty	NOUN
ejpam-5730	181	43	)	)	PUNCT
ejpam-5730	181	44	,	,	PUNCT
ejpam-5730	181	45	d(x	d(x	PROPN
ejpam-5730	181	46	,	,	PUNCT
ejpam-5730	181	47	ty	ty	NOUN
ejpam-5730	181	48	)	)	PUNCT
ejpam-5730	181	49	,	,	PUNCT
ejpam-5730	181	50	d(y	d(y	PROPN
ejpam-5730	181	51	,	,	PUNCT
ejpam-5730	181	52	tx	tx	PROPN
ejpam-5730	181	53	)	)	PUNCT
ejpam-5730	181	54	≤	≤	NOUN
ejpam-5730	181	55	0	0	NUM
ejpam-5730	181	56	,	,	PUNCT
ejpam-5730	181	57	for	for	ADP
ejpam-5730	181	58	x	x	X
ejpam-5730	181	59	,	,	PUNCT
ejpam-5730	181	60	y	y	PROPN
ejpam-5730	181	61	∈	∈	PROPN
ejpam-5730	182	1	x	x	NOUN
ejpam-5730	182	2	,	,	PUNCT
ejpam-5730	182	3	where	where	SCONJ
ejpam-5730	182	4	f	f	NOUN
ejpam-5730	182	5	:	:	PUNCT
ejpam-5730	183	1	[	[	X
ejpam-5730	183	2	0,∞)6	0,∞)6	NUM
ejpam-5730	183	3	→	→	SYM
ejpam-5730	183	4	r	r	NOUN
ejpam-5730	183	5	is	be	AUX
ejpam-5730	183	6	a	a	DET
ejpam-5730	183	7	function	function	NOUN
ejpam-5730	183	8	as	as	SCONJ
ejpam-5730	183	9	given	give	VERB
ejpam-5730	183	10	in	in	ADP
ejpam-5730	183	11	section	section	NOUN
ejpam-5730	183	12	2	2	NUM
ejpam-5730	183	13	in	in	ADP
ejpam-5730	183	14	[	[	X
ejpam-5730	183	15	1	1	NUM
ejpam-5730	183	16	]	]	PUNCT
ejpam-5730	183	17	with	with	ADP
ejpam-5730	183	18	5	5	NUM
ejpam-5730	183	19	examples	example	NOUN
ejpam-5730	183	20	.	.	PUNCT
ejpam-5730	184	1	theorem	theorem	NOUN
ejpam-5730	184	2	6.9	6.9	NUM
ejpam-5730	184	3	.	.	PUNCT
ejpam-5730	185	1	(	(	PUNCT
ejpam-5730	185	2	altun	altun	NOUN
ejpam-5730	185	3	-	-	PUNCT
ejpam-5730	185	4	erduran	erduran	ADJ
ejpam-5730	185	5	)	)	PUNCT
ejpam-5730	185	6	let	let	AUX
ejpam-5730	185	7	(	(	PUNCT
ejpam-5730	185	8	x	x	NOUN
ejpam-5730	185	9	,	,	PUNCT
ejpam-5730	185	10	d	d	NOUN
ejpam-5730	185	11	)	)	PUNCT
ejpam-5730	185	12	be	be	AUX
ejpam-5730	185	13	a	a	DET
ejpam-5730	185	14	complete	complete	ADJ
ejpam-5730	185	15	metric	metric	ADJ
ejpam-5730	185	16	space	space	NOUN
ejpam-5730	185	17	,	,	PUNCT
ejpam-5730	185	18	and	and	CCONJ
ejpam-5730	185	19	let	let	VERB
ejpam-5730	185	20	t	t	PROPN
ejpam-5730	185	21	be	be	AUX
ejpam-5730	185	22	a	a	DET
ejpam-5730	185	23	mapping	mapping	NOUN
ejpam-5730	185	24	on	on	ADP
ejpam-5730	185	25	x.	x.	NOUN
ejpam-5730	185	26	define	define	VERB
ejpam-5730	185	27	a	a	DET
ejpam-5730	185	28	nonincreasing	nonincrease	VERB
ejpam-5730	185	29	function	function	NOUN
ejpam-5730	185	30	θ	θ	NOUN
ejpam-5730	185	31	:	:	PUNCT
ejpam-5730	186	1	[	[	X
ejpam-5730	186	2	0	0	NUM
ejpam-5730	186	3	,	,	PUNCT
ejpam-5730	186	4	1	1	NUM
ejpam-5730	186	5	)	)	PUNCT
ejpam-5730	186	6	→	→	SYM
ejpam-5730	186	7	(	(	PUNCT
ejpam-5730	186	8	1/2	1/2	NUM
ejpam-5730	186	9	,	,	PUNCT
ejpam-5730	186	10	1	1	NUM
ejpam-5730	186	11	]	]	PUNCT
ejpam-5730	186	12	as	as	ADP
ejpam-5730	186	13	in	in	ADP
ejpam-5730	186	14	suzuki	suzuki	NOUN
ejpam-5730	186	15	[	[	X
ejpam-5730	186	16	49	49	NUM
ejpam-5730	186	17	]	]	PUNCT
ejpam-5730	186	18	.	.	PUNCT
ejpam-5730	187	1	assume	assume	VERB
ejpam-5730	187	2	that	that	SCONJ
ejpam-5730	187	3	there	there	PRON
ejpam-5730	187	4	exists	exist	VERB
ejpam-5730	187	5	an	an	DET
ejpam-5730	187	6	f	f	NOUN
ejpam-5730	187	7	as	as	ADP
ejpam-5730	187	8	above	above	ADV
ejpam-5730	187	9	,	,	PUNCT
ejpam-5730	187	10	such	such	ADJ
ejpam-5730	187	11	that	that	DET
ejpam-5730	187	12	θ(r)d(x	θ(r)d(x	NOUN
ejpam-5730	187	13	,	,	PUNCT
ejpam-5730	187	14	tx	tx	PROPN
ejpam-5730	187	15	)	)	PUNCT
ejpam-5730	187	16	≤	≤	NOUN
ejpam-5730	187	17	d(x	d(x	PROPN
ejpam-5730	187	18	,	,	PUNCT
ejpam-5730	187	19	y	y	NOUN
ejpam-5730	187	20	)	)	PUNCT
ejpam-5730	187	21	implies	imply	VERB
ejpam-5730	187	22	f	f	X
ejpam-5730	187	23	(	(	PUNCT
ejpam-5730	187	24	d(tx	d(tx	PROPN
ejpam-5730	187	25	,	,	PUNCT
ejpam-5730	187	26	ty	ty	NOUN
ejpam-5730	187	27	)	)	PUNCT
ejpam-5730	187	28	,	,	PUNCT
ejpam-5730	187	29	d(x	d(x	PROPN
ejpam-5730	187	30	,	,	PUNCT
ejpam-5730	187	31	y	y	NOUN
ejpam-5730	187	32	)	)	PUNCT
ejpam-5730	187	33	,	,	PUNCT
ejpam-5730	187	34	d(x	d(x	PROPN
ejpam-5730	187	35	,	,	PUNCT
ejpam-5730	187	36	tx	tx	PROPN
ejpam-5730	187	37	)	)	PUNCT
ejpam-5730	187	38	,	,	PUNCT
ejpam-5730	187	39	d(y	d(y	PROPN
ejpam-5730	187	40	,	,	PUNCT
ejpam-5730	187	41	ty	ty	NOUN
ejpam-5730	187	42	)	)	PUNCT
ejpam-5730	187	43	,	,	PUNCT
ejpam-5730	187	44	d(x	d(x	PROPN
ejpam-5730	187	45	,	,	PUNCT
ejpam-5730	187	46	ty	ty	NOUN
ejpam-5730	187	47	)	)	PUNCT
ejpam-5730	187	48	,	,	PUNCT
ejpam-5730	187	49	d(y	d(y	PROPN
ejpam-5730	187	50	,	,	PUNCT
ejpam-5730	187	51	tx	tx	PROPN
ejpam-5730	187	52	)	)	PUNCT
ejpam-5730	187	53	≤	≤	NOUN
ejpam-5730	187	54	0	0	NUM
ejpam-5730	187	55	,	,	PUNCT
ejpam-5730	187	56	for	for	ADP
ejpam-5730	187	57	all	all	DET
ejpam-5730	187	58	x	x	NOUN
ejpam-5730	187	59	,	,	PUNCT
ejpam-5730	187	60	y	y	PROPN
ejpam-5730	187	61	∈	∈	PROPN
ejpam-5730	187	62	x	x	X
ejpam-5730	187	63	,	,	PUNCT
ejpam-5730	187	64	then	then	ADV
ejpam-5730	187	65	t	t	PROPN
ejpam-5730	187	66	has	have	VERB
ejpam-5730	187	67	a	a	DET
ejpam-5730	187	68	unique	unique	ADJ
ejpam-5730	187	69	fixed	fix	VERB
ejpam-5730	187	70	-	-	PUNCT
ejpam-5730	187	71	point	point	NOUN
ejpam-5730	187	72	z	z	NOUN
ejpam-5730	187	73	and	and	CCONJ
ejpam-5730	187	74	limn	limn	PROPN
ejpam-5730	187	75	t	t	PROPN
ejpam-5730	187	76	nx	nx	PROPN
ejpam-5730	188	1	=	=	X
ejpam-5730	188	2	z	z	NOUN
ejpam-5730	188	3	holds	hold	VERB
ejpam-5730	188	4	for	for	ADP
ejpam-5730	188	5	every	every	DET
ejpam-5730	188	6	x	x	SYM
ejpam-5730	188	7	∈	∈	PROPN
ejpam-5730	188	8	x.	x.	NOUN
ejpam-5730	188	9	s.	s.	PROPN
ejpam-5730	188	10	park	park	PROPN
ejpam-5730	188	11	/	/	SYM
ejpam-5730	188	12	eur	eur	PROPN
ejpam-5730	188	13	.	.	PUNCT
ejpam-5730	189	1	j.	j.	PROPN
ejpam-5730	189	2	pure	pure	PROPN
ejpam-5730	189	3	appl	appl	PROPN
ejpam-5730	189	4	.	.	PROPN
ejpam-5730	189	5	math	math	PROPN
ejpam-5730	189	6	,	,	PUNCT
ejpam-5730	189	7	18	18	NUM
ejpam-5730	189	8	(	(	PUNCT
ejpam-5730	189	9	1	1	NUM
ejpam-5730	189	10	)	)	PUNCT
ejpam-5730	189	11	(	(	PUNCT
ejpam-5730	189	12	2025	2025	NUM
ejpam-5730	189	13	)	)	PUNCT
ejpam-5730	189	14	,	,	PUNCT
ejpam-5730	189	15	5730	5730	NUM
ejpam-5730	189	16	9	9	NUM
ejpam-5730	189	17	of	of	ADP
ejpam-5730	189	18	21	21	NUM
ejpam-5730	189	19	comment	comment	NOUN
ejpam-5730	189	20	:	:	PUNCT
ejpam-5730	189	21	in	in	ADP
ejpam-5730	189	22	the	the	DET
ejpam-5730	189	23	proof	proof	NOUN
ejpam-5730	189	24	,	,	PUNCT
ejpam-5730	189	25	the	the	DET
ejpam-5730	189	26	authors	author	NOUN
ejpam-5730	189	27	showed	show	VERB
ejpam-5730	189	28	that	that	SCONJ
ejpam-5730	189	29	d(tx	d(tx	PROPN
ejpam-5730	189	30	,	,	PUNCT
ejpam-5730	189	31	t	t	NOUN
ejpam-5730	189	32	2x	2x	NUM
ejpam-5730	189	33	)	)	PUNCT
ejpam-5730	189	34	≤	≤	NUM
ejpam-5730	189	35	r	r	NOUN
ejpam-5730	189	36	d(x	d(x	NOUN
ejpam-5730	189	37	,	,	PUNCT
ejpam-5730	189	38	tx	tx	PROPN
ejpam-5730	189	39	)	)	PUNCT
ejpam-5730	189	40	for	for	ADP
ejpam-5730	189	41	all	all	PRON
ejpam-5730	189	42	x	x	SYM
ejpam-5730	189	43	∈	∈	PROPN
ejpam-5730	189	44	x	x	NOUN
ejpam-5730	189	45	,	,	PUNCT
ejpam-5730	189	46	that	that	ADV
ejpam-5730	189	47	is	is	ADV
ejpam-5730	189	48	,	,	PUNCT
ejpam-5730	189	49	t	t	PROPN
ejpam-5730	189	50	is	be	AUX
ejpam-5730	189	51	an	an	DET
ejpam-5730	189	52	rhr	rhr	NOUN
ejpam-5730	189	53	map	map	NOUN
ejpam-5730	189	54	.	.	PUNCT
ejpam-5730	190	1	hence	hence	ADV
ejpam-5730	190	2	t	t	PROPN
ejpam-5730	190	3	has	have	VERB
ejpam-5730	190	4	a	a	DET
ejpam-5730	190	5	fixed	fix	VERB
ejpam-5730	190	6	point	point	NOUN
ejpam-5730	190	7	by	by	ADP
ejpam-5730	190	8	theorems	theorem	NOUN
ejpam-5730	190	9	p	p	NOUN
ejpam-5730	190	10	and	and	CCONJ
ejpam-5730	190	11	h(γ1	h(γ1	NOUN
ejpam-5730	190	12	)	)	PUNCT
ejpam-5730	190	13	and	and	CCONJ
ejpam-5730	190	14	its	its	PRON
ejpam-5730	190	15	uniqueness	uniqueness	NOUN
ejpam-5730	190	16	follows	follow	VERB
ejpam-5730	190	17	from	from	ADP
ejpam-5730	190	18	properties	property	NOUN
ejpam-5730	190	19	of	of	ADP
ejpam-5730	190	20	f	f	PROPN
ejpam-5730	190	21	.	.	PUNCT
ejpam-5730	191	1	khojasteh	khojasteh	PROPN
ejpam-5730	191	2	,	,	PUNCT
ejpam-5730	191	3	abbas	abbas	PROPN
ejpam-5730	191	4	,	,	PUNCT
ejpam-5730	191	5	costache	costache	NOUN
ejpam-5730	192	1	[	[	X
ejpam-5730	192	2	25	25	NUM
ejpam-5730	192	3	]	]	PUNCT
ejpam-5730	192	4	in	in	ADP
ejpam-5730	192	5	2014	2014	NUM
ejpam-5730	192	6	theorem	theorem	VERB
ejpam-5730	192	7	6.10	6.10	NUM
ejpam-5730	192	8	.	.	PUNCT
ejpam-5730	193	1	(	(	PUNCT
ejpam-5730	193	2	khojasteh	khojasteh	PROPN
ejpam-5730	193	3	et	et	PROPN
ejpam-5730	193	4	al	al	PROPN
ejpam-5730	193	5	.	.	PROPN
ejpam-5730	193	6	)	)	PUNCT
ejpam-5730	194	1	let	let	VERB
ejpam-5730	194	2	(	(	PUNCT
ejpam-5730	194	3	x	x	NOUN
ejpam-5730	194	4	,	,	PUNCT
ejpam-5730	194	5	d	d	NOUN
ejpam-5730	194	6	)	)	PUNCT
ejpam-5730	194	7	be	be	AUX
ejpam-5730	194	8	a	a	DET
ejpam-5730	194	9	complete	complete	ADJ
ejpam-5730	194	10	metric	metric	ADJ
ejpam-5730	194	11	space	space	NOUN
ejpam-5730	194	12	and	and	CCONJ
ejpam-5730	194	13	let	let	VERB
ejpam-5730	194	14	t	t	PROPN
ejpam-5730	194	15	be	be	AUX
ejpam-5730	194	16	a	a	DET
ejpam-5730	194	17	mapping	mapping	NOUN
ejpam-5730	194	18	from	from	ADP
ejpam-5730	194	19	x	x	NOUN
ejpam-5730	194	20	into	into	ADP
ejpam-5730	194	21	itself	itself	PRON
ejpam-5730	194	22	.	.	PUNCT
ejpam-5730	195	1	suppose	suppose	VERB
ejpam-5730	195	2	that	that	SCONJ
ejpam-5730	195	3	t	t	PROPN
ejpam-5730	195	4	satisfies	satisfy	VERB
ejpam-5730	195	5	the	the	DET
ejpam-5730	195	6	following	follow	VERB
ejpam-5730	195	7	condition	condition	NOUN
ejpam-5730	195	8	:	:	PUNCT
ejpam-5730	195	9	d(tx	d(tx	PROPN
ejpam-5730	195	10	,	,	PUNCT
ejpam-5730	195	11	ty	ty	NOUN
ejpam-5730	195	12	)	)	PUNCT
ejpam-5730	195	13	≤	≤	NOUN
ejpam-5730	195	14	d(x	d(x	NOUN
ejpam-5730	195	15	,	,	PUNCT
ejpam-5730	195	16	ty	ty	INTJ
ejpam-5730	195	17	)	)	PUNCT
ejpam-5730	196	1	+	+	CCONJ
ejpam-5730	196	2	d(y	d(y	PROPN
ejpam-5730	196	3	,	,	PUNCT
ejpam-5730	196	4	tx	tx	PROPN
ejpam-5730	196	5	)	)	PUNCT
ejpam-5730	196	6	d(x	d(x	PROPN
ejpam-5730	196	7	,	,	PUNCT
ejpam-5730	196	8	tx	tx	PROPN
ejpam-5730	196	9	)	)	PUNCT
ejpam-5730	197	1	+	+	CCONJ
ejpam-5730	197	2	d(y	d(y	PROPN
ejpam-5730	197	3	,	,	PUNCT
ejpam-5730	197	4	ty	ty	INTJ
ejpam-5730	197	5	)	)	PUNCT
ejpam-5730	197	6	+	+	CCONJ
ejpam-5730	197	7	1	1	NUM
ejpam-5730	197	8	d(x	d(x	PROPN
ejpam-5730	197	9	,	,	PUNCT
ejpam-5730	197	10	y	y	NOUN
ejpam-5730	197	11	)	)	PUNCT
ejpam-5730	197	12	for	for	ADP
ejpam-5730	197	13	all	all	DET
ejpam-5730	197	14	x	x	NOUN
ejpam-5730	197	15	,	,	PUNCT
ejpam-5730	197	16	y	y	PROPN
ejpam-5730	197	17	∈	∈	PROPN
ejpam-5730	197	18	x.	x.	NOUN
ejpam-5730	197	19	then	then	ADV
ejpam-5730	197	20	(	(	PUNCT
ejpam-5730	197	21	a	a	X
ejpam-5730	197	22	)	)	PUNCT
ejpam-5730	197	23	t	t	PROPN
ejpam-5730	197	24	has	have	VERB
ejpam-5730	197	25	at	at	ADV
ejpam-5730	197	26	least	least	ADV
ejpam-5730	197	27	one	one	NUM
ejpam-5730	197	28	fixed	fix	VERB
ejpam-5730	197	29	point	point	NOUN
ejpam-5730	197	30	ẋ	ẋ	PROPN
ejpam-5730	198	1	∈	∈	PROPN
ejpam-5730	199	1	x	x	X
ejpam-5730	199	2	,	,	PUNCT
ejpam-5730	199	3	(	(	PUNCT
ejpam-5730	199	4	b	b	NOUN
ejpam-5730	199	5	)	)	PUNCT
ejpam-5730	199	6	{	{	PUNCT
ejpam-5730	199	7	tnx	tnx	NOUN
ejpam-5730	199	8	}	}	PUNCT
ejpam-5730	199	9	converges	converge	NOUN
ejpam-5730	199	10	to	to	ADP
ejpam-5730	199	11	a	a	DET
ejpam-5730	199	12	fixed	fix	VERB
ejpam-5730	199	13	point	point	NOUN
ejpam-5730	199	14	,	,	PUNCT
ejpam-5730	199	15	for	for	ADP
ejpam-5730	199	16	all	all	DET
ejpam-5730	199	17	x	x	SYM
ejpam-5730	199	18	∈	∈	PROPN
ejpam-5730	199	19	x	x	X
ejpam-5730	199	20	;	;	PUNCT
ejpam-5730	199	21	(	(	PUNCT
ejpam-5730	199	22	c	c	X
ejpam-5730	199	23	)	)	PUNCT
ejpam-5730	200	1	if	if	SCONJ
ejpam-5730	200	2	ẋ	ẋ	PROPN
ejpam-5730	200	3	and	and	CCONJ
ejpam-5730	200	4	ẏ	ẏ	PRON
ejpam-5730	200	5	are	be	AUX
ejpam-5730	200	6	distinct	distinct	ADJ
ejpam-5730	200	7	fixed	fix	VERB
ejpam-5730	200	8	points	point	NOUN
ejpam-5730	200	9	of	of	ADP
ejpam-5730	200	10	t	t	PROPN
ejpam-5730	200	11	,	,	PUNCT
ejpam-5730	200	12	then	then	ADV
ejpam-5730	200	13	d(ẋ	d(ẋ	PROPN
ejpam-5730	200	14	,	,	PUNCT
ejpam-5730	200	15	ẏ	ẏ	NOUN
ejpam-5730	200	16	)	)	PUNCT
ejpam-5730	200	17	≤	≤	NUM
ejpam-5730	200	18	1/2	1/2	NUM
ejpam-5730	200	19	.	.	PUNCT
ejpam-5730	201	1	comment	comment	NOUN
ejpam-5730	201	2	:	:	PUNCT
ejpam-5730	201	3	note	note	VERB
ejpam-5730	201	4	that	that	SCONJ
ejpam-5730	201	5	t	t	PROPN
ejpam-5730	201	6	is	be	AUX
ejpam-5730	201	7	an	an	DET
ejpam-5730	201	8	rhr	rhr	NOUN
ejpam-5730	201	9	map	map	NOUN
ejpam-5730	201	10	and	and	CCONJ
ejpam-5730	201	11	can	can	AUX
ejpam-5730	201	12	be	be	AUX
ejpam-5730	201	13	applicable	applicable	ADJ
ejpam-5730	201	14	theorems	theorem	NOUN
ejpam-5730	201	15	p	p	NOUN
ejpam-5730	201	16	and	and	CCONJ
ejpam-5730	201	17	h(γ1	h(γ1	NOUN
ejpam-5730	201	18	)	)	PUNCT
ejpam-5730	201	19	.	.	PUNCT
ejpam-5730	202	1	the	the	DET
ejpam-5730	202	2	(	(	PUNCT
ejpam-5730	202	3	c	c	NOUN
ejpam-5730	202	4	)	)	PUNCT
ejpam-5730	202	5	follows	follow	VERB
ejpam-5730	202	6	from	from	ADP
ejpam-5730	202	7	the	the	DET
ejpam-5730	202	8	contractive	contractive	ADJ
ejpam-5730	202	9	condition	condition	NOUN
ejpam-5730	202	10	.	.	PUNCT
ejpam-5730	203	1	karapinar	karapinar	NOUN
ejpam-5730	203	2	[	[	X
ejpam-5730	203	3	18	18	NUM
ejpam-5730	203	4	]	]	PUNCT
ejpam-5730	203	5	in	in	ADP
ejpam-5730	203	6	2018	2018	NUM
ejpam-5730	203	7	we	we	PRON
ejpam-5730	203	8	start	start	VERB
ejpam-5730	203	9	our	our	PRON
ejpam-5730	203	10	results	result	NOUN
ejpam-5730	203	11	by	by	ADP
ejpam-5730	203	12	the	the	DET
ejpam-5730	203	13	generalization	generalization	NOUN
ejpam-5730	203	14	of	of	ADP
ejpam-5730	203	15	the	the	DET
ejpam-5730	203	16	definition	definition	NOUN
ejpam-5730	203	17	of	of	ADP
ejpam-5730	203	18	kannan	kannan	PROPN
ejpam-5730	203	19	type	type	NOUN
ejpam-5730	203	20	contraction	contraction	NOUN
ejpam-5730	203	21	via	via	ADP
ejpam-5730	203	22	interpolation	interpolation	NOUN
ejpam-5730	203	23	notion	notion	NOUN
ejpam-5730	203	24	,	,	PUNCT
ejpam-5730	203	25	as	as	SCONJ
ejpam-5730	203	26	follows	follow	VERB
ejpam-5730	203	27	:	:	PUNCT
ejpam-5730	203	28	definition	definition	NOUN
ejpam-5730	203	29	6.11	6.11	NUM
ejpam-5730	203	30	.	.	PUNCT
ejpam-5730	204	1	let	let	VERB
ejpam-5730	204	2	(	(	PUNCT
ejpam-5730	204	3	x	x	NOUN
ejpam-5730	204	4	,	,	PUNCT
ejpam-5730	204	5	d	d	NOUN
ejpam-5730	204	6	)	)	PUNCT
ejpam-5730	204	7	be	be	AUX
ejpam-5730	204	8	a	a	DET
ejpam-5730	204	9	metric	metric	ADJ
ejpam-5730	204	10	space	space	NOUN
ejpam-5730	204	11	.	.	PUNCT
ejpam-5730	205	1	we	we	PRON
ejpam-5730	205	2	say	say	VERB
ejpam-5730	205	3	that	that	SCONJ
ejpam-5730	205	4	the	the	DET
ejpam-5730	205	5	self	self	NOUN
ejpam-5730	205	6	-	-	PUNCT
ejpam-5730	205	7	mapping	mapping	NOUN
ejpam-5730	205	8	t	t	NOUN
ejpam-5730	205	9	:	:	PUNCT
ejpam-5730	205	10	x	x	X
ejpam-5730	205	11	→	→	PUNCT
ejpam-5730	205	12	x	x	X
ejpam-5730	205	13	is	be	AUX
ejpam-5730	205	14	an	an	DET
ejpam-5730	205	15	interpolative	interpolative	ADJ
ejpam-5730	205	16	kannan	kannan	PROPN
ejpam-5730	205	17	type	type	NOUN
ejpam-5730	205	18	contraction	contraction	NOUN
ejpam-5730	205	19	,	,	PUNCT
ejpam-5730	205	20	if	if	SCONJ
ejpam-5730	205	21	there	there	PRON
ejpam-5730	205	22	exist	exist	VERB
ejpam-5730	205	23	a	a	DET
ejpam-5730	205	24	constant	constant	ADJ
ejpam-5730	205	25	λ	λ	X
ejpam-5730	205	26	∈	∈	PROPN
ejpam-5730	206	1	[	[	X
ejpam-5730	206	2	0	0	NUM
ejpam-5730	206	3	,	,	PUNCT
ejpam-5730	206	4	1	1	NUM
ejpam-5730	206	5	)	)	PUNCT
ejpam-5730	206	6	and	and	CCONJ
ejpam-5730	206	7	α	α	PRON
ejpam-5730	206	8	∈	∈	PROPN
ejpam-5730	206	9	(	(	PUNCT
ejpam-5730	206	10	0	0	NUM
ejpam-5730	206	11	,	,	PUNCT
ejpam-5730	206	12	1	1	NUM
ejpam-5730	206	13	)	)	PUNCT
ejpam-5730	207	1	such	such	ADJ
ejpam-5730	207	2	that	that	SCONJ
ejpam-5730	207	3	d(tx	d(tx	PROPN
ejpam-5730	207	4	,	,	PUNCT
ejpam-5730	207	5	ty	ty	NOUN
ejpam-5730	207	6	)	)	PUNCT
ejpam-5730	207	7	≤	≤	NOUN
ejpam-5730	207	8	λ[d(x	λ[d(x	ADP
ejpam-5730	207	9	,	,	PUNCT
ejpam-5730	207	10	tx)]α	tx)]α	NOUN
ejpam-5730	207	11	·	·	PUNCT
ejpam-5730	208	1	[	[	X
ejpam-5730	208	2	d(y	d(y	NOUN
ejpam-5730	208	3	,	,	PUNCT
ejpam-5730	208	4	ty)]1−α	ty)]1−α	NOUN
ejpam-5730	208	5	for	for	ADP
ejpam-5730	208	6	all	all	DET
ejpam-5730	208	7	x	x	NOUN
ejpam-5730	208	8	,	,	PUNCT
ejpam-5730	208	9	y	y	PROPN
ejpam-5730	208	10	∈	∈	PROPN
ejpam-5730	208	11	x	x	PUNCT
ejpam-5730	208	12	with	with	ADP
ejpam-5730	208	13	x	x	PROPN
ejpam-5730	208	14	̸=	̸=	PROPN
ejpam-5730	208	15	tx	tx	PROPN
ejpam-5730	208	16	.	.	PUNCT
ejpam-5730	208	17	theorem	theorem	VERB
ejpam-5730	208	18	6.12	6.12	NUM
ejpam-5730	208	19	.	.	PUNCT
ejpam-5730	209	1	(	(	PUNCT
ejpam-5730	209	2	karapinar	karapinar	NOUN
ejpam-5730	209	3	)	)	PUNCT
ejpam-5730	209	4	let	let	VERB
ejpam-5730	209	5	(	(	PUNCT
ejpam-5730	209	6	x	x	NOUN
ejpam-5730	209	7	,	,	PUNCT
ejpam-5730	209	8	d	d	NOUN
ejpam-5730	209	9	)	)	PUNCT
ejpam-5730	209	10	be	be	AUX
ejpam-5730	209	11	a	a	DET
ejpam-5730	209	12	complete	complete	ADJ
ejpam-5730	209	13	metric	metric	ADJ
ejpam-5730	209	14	space	space	NOUN
ejpam-5730	209	15	and	and	CCONJ
ejpam-5730	209	16	t	t	PROPN
ejpam-5730	209	17	be	be	AUX
ejpam-5730	209	18	an	an	DET
ejpam-5730	209	19	interpolative	interpolative	ADJ
ejpam-5730	209	20	kannan	kannan	PROPN
ejpam-5730	209	21	type	type	NOUN
ejpam-5730	209	22	contraction	contraction	NOUN
ejpam-5730	209	23	.	.	PUNCT
ejpam-5730	210	1	then	then	ADV
ejpam-5730	210	2	t	t	PROPN
ejpam-5730	210	3	has	have	VERB
ejpam-5730	210	4	a	a	DET
ejpam-5730	210	5	unique	unique	ADJ
ejpam-5730	210	6	fixed	fix	VERB
ejpam-5730	210	7	point	point	NOUN
ejpam-5730	210	8	in	in	ADP
ejpam-5730	210	9	x.	x.	PROPN
ejpam-5730	210	10	comment	comment	NOUN
ejpam-5730	210	11	:	:	PUNCT
ejpam-5730	210	12	later	later	ADV
ejpam-5730	210	13	,	,	PUNCT
ejpam-5730	210	14	the	the	DET
ejpam-5730	210	15	author	author	NOUN
ejpam-5730	210	16	withdraw	withdraw	VERB
ejpam-5730	210	17	the	the	DET
ejpam-5730	210	18	uniqueness	uniqueness	NOUN
ejpam-5730	210	19	of	of	ADP
ejpam-5730	210	20	fixed	fix	VERB
ejpam-5730	210	21	point	point	NOUN
ejpam-5730	210	22	.	.	PUNCT
ejpam-5730	211	1	for	for	ADP
ejpam-5730	211	2	y	y	PROPN
ejpam-5730	211	3	=	=	SYM
ejpam-5730	211	4	tx	tx	PROPN
ejpam-5730	211	5	,	,	PUNCT
ejpam-5730	211	6	we	we	PRON
ejpam-5730	211	7	have	have	VERB
ejpam-5730	211	8	d(tx	d(tx	PROPN
ejpam-5730	211	9	,	,	PUNCT
ejpam-5730	211	10	t	t	NOUN
ejpam-5730	211	11	2x	2x	NUM
ejpam-5730	211	12	)	)	PUNCT
ejpam-5730	211	13	≤	≤	NOUN
ejpam-5730	212	1	λ[d(x	λ[d(x	ADP
ejpam-5730	212	2	,	,	PUNCT
ejpam-5730	212	3	tx)]α	tx)]α	NOUN
ejpam-5730	212	4	·	·	PUNCT
ejpam-5730	213	1	[	[	X
ejpam-5730	213	2	d(tx	d(tx	X
ejpam-5730	213	3	,	,	PUNCT
ejpam-5730	213	4	t	t	PROPN
ejpam-5730	213	5	2x)]1−α	2x)]1−α	NUM
ejpam-5730	213	6	=	=	AUX
ejpam-5730	213	7	⇒	⇒	NOUN
ejpam-5730	213	8	[	[	X
ejpam-5730	213	9	d(tx	d(tx	PROPN
ejpam-5730	213	10	,	,	PUNCT
ejpam-5730	213	11	t	t	NOUN
ejpam-5730	213	12	2x)]α	2x)]α	NUM
ejpam-5730	213	13	≤	≤	NUM
ejpam-5730	213	14	λ[d(x	λ[d(x	ADP
ejpam-5730	213	15	,	,	PUNCT
ejpam-5730	213	16	tx)]α	tx)]α	ADP
ejpam-5730	213	17	=	=	X
ejpam-5730	213	18	⇒	⇒	NOUN
ejpam-5730	213	19	d(tx	d(tx	PROPN
ejpam-5730	213	20	,	,	PUNCT
ejpam-5730	213	21	t	t	PROPN
ejpam-5730	213	22	2x	2x	NUM
ejpam-5730	213	23	)	)	PUNCT
ejpam-5730	213	24	≤	≤	NOUN
ejpam-5730	213	25	λ1	λ1	VERB
ejpam-5730	213	26	/	/	SYM
ejpam-5730	213	27	αd(x	αd(x	NUM
ejpam-5730	213	28	,	,	PUNCT
ejpam-5730	213	29	tx	tx	PROPN
ejpam-5730	213	30	)	)	PUNCT
ejpam-5730	213	31	with	with	ADP
ejpam-5730	213	32	0	0	NUM
ejpam-5730	213	33	<	<	X
ejpam-5730	213	34	λ1	λ1	PROPN
ejpam-5730	213	35	/	/	SYM
ejpam-5730	213	36	α	α	NOUN
ejpam-5730	213	37	<	<	X
ejpam-5730	213	38	1	1	NUM
ejpam-5730	213	39	.	.	PUNCT
ejpam-5730	214	1	therefore	therefore	ADV
ejpam-5730	214	2	,	,	PUNCT
ejpam-5730	214	3	t	t	PROPN
ejpam-5730	214	4	is	be	AUX
ejpam-5730	214	5	an	an	DET
ejpam-5730	214	6	rhr	rhr	NOUN
ejpam-5730	214	7	map	map	NOUN
ejpam-5730	214	8	for	for	ADP
ejpam-5730	214	9	which	which	PRON
ejpam-5730	214	10	theorems	theorem	NOUN
ejpam-5730	214	11	p	p	NOUN
ejpam-5730	214	12	and	and	CCONJ
ejpam-5730	214	13	h(γ1	h(γ1	NOUN
ejpam-5730	214	14	)	)	PUNCT
ejpam-5730	214	15	can	can	AUX
ejpam-5730	214	16	be	be	AUX
ejpam-5730	214	17	applicable	applicable	ADJ
ejpam-5730	214	18	.	.	PUNCT
ejpam-5730	215	1	hence	hence	ADV
ejpam-5730	215	2	theorem	theorem	VERB
ejpam-5730	215	3	6.12	6.12	NUM
ejpam-5730	215	4	can	can	AUX
ejpam-5730	215	5	be	be	AUX
ejpam-5730	215	6	stated	state	VERB
ejpam-5730	215	7	for	for	ADP
ejpam-5730	215	8	t	t	PROPN
ejpam-5730	215	9	-orbitally	-orbitally	PROPN
ejpam-5730	215	10	complete	complete	ADJ
ejpam-5730	215	11	quasi	quasi	ADJ
ejpam-5730	215	12	-	-	ADJ
ejpam-5730	215	13	metric	metric	ADJ
ejpam-5730	215	14	spaces	space	NOUN
ejpam-5730	215	15	.	.	PUNCT
ejpam-5730	216	1	karapinar	karapinar	NOUN
ejpam-5730	216	2	,	,	PUNCT
ejpam-5730	216	3	agarwal	agarwal	PROPN
ejpam-5730	216	4	,	,	PUNCT
ejpam-5730	216	5	and	and	CCONJ
ejpam-5730	216	6	aydi	aydi	VERB
ejpam-5730	216	7	[	[	X
ejpam-5730	216	8	23	23	NUM
ejpam-5730	216	9	]	]	PUNCT
ejpam-5730	216	10	in	in	ADP
ejpam-5730	216	11	2018	2018	NUM
ejpam-5730	216	12	as	as	ADP
ejpam-5730	216	13	a	a	DET
ejpam-5730	216	14	correction	correction	NOUN
ejpam-5730	216	15	of	of	ADP
ejpam-5730	216	16	theorem	theorem	ADJ
ejpam-5730	216	17	6.12	6.12	NUM
ejpam-5730	216	18	of	of	ADP
ejpam-5730	216	19	the	the	DET
ejpam-5730	216	20	previous	previous	ADJ
ejpam-5730	216	21	paper	paper	NOUN
ejpam-5730	216	22	,	,	PUNCT
ejpam-5730	216	23	the	the	DET
ejpam-5730	216	24	authors	author	NOUN
ejpam-5730	216	25	stated	state	VERB
ejpam-5730	216	26	:	:	PUNCT
ejpam-5730	216	27	s.	s.	PROPN
ejpam-5730	216	28	park	park	PROPN
ejpam-5730	216	29	/	/	SYM
ejpam-5730	216	30	eur	eur	PROPN
ejpam-5730	216	31	.	.	PUNCT
ejpam-5730	217	1	j.	j.	PROPN
ejpam-5730	217	2	pure	pure	PROPN
ejpam-5730	217	3	appl	appl	PROPN
ejpam-5730	217	4	.	.	PROPN
ejpam-5730	217	5	math	math	PROPN
ejpam-5730	217	6	,	,	PUNCT
ejpam-5730	217	7	18	18	NUM
ejpam-5730	217	8	(	(	PUNCT
ejpam-5730	217	9	1	1	NUM
ejpam-5730	217	10	)	)	PUNCT
ejpam-5730	217	11	(	(	PUNCT
ejpam-5730	217	12	2025	2025	NUM
ejpam-5730	217	13	)	)	PUNCT
ejpam-5730	217	14	,	,	PUNCT
ejpam-5730	217	15	5730	5730	NUM
ejpam-5730	217	16	10	10	NUM
ejpam-5730	217	17	of	of	ADP
ejpam-5730	217	18	21	21	NUM
ejpam-5730	217	19	theorem	theorem	NOUN
ejpam-5730	217	20	6.13	6.13	NUM
ejpam-5730	217	21	.	.	PUNCT
ejpam-5730	218	1	(	(	PUNCT
ejpam-5730	218	2	karapinar	karapinar	VERB
ejpam-5730	218	3	et	et	PROPN
ejpam-5730	218	4	al	al	PROPN
ejpam-5730	218	5	.	.	PUNCT
ejpam-5730	218	6	)	)	PUNCT
ejpam-5730	219	1	let	let	VERB
ejpam-5730	219	2	(	(	PUNCT
ejpam-5730	219	3	x	x	NOUN
ejpam-5730	219	4	,	,	PUNCT
ejpam-5730	219	5	ρ	ρ	PROPN
ejpam-5730	219	6	)	)	PUNCT
ejpam-5730	219	7	be	be	AUX
ejpam-5730	219	8	a	a	DET
ejpam-5730	219	9	complete	complete	ADJ
ejpam-5730	219	10	metric	metric	ADJ
ejpam-5730	219	11	space	space	NOUN
ejpam-5730	219	12	.	.	PUNCT
ejpam-5730	220	1	a	a	DET
ejpam-5730	220	2	self	self	NOUN
ejpam-5730	220	3	-	-	PUNCT
ejpam-5730	220	4	mapping	mapping	NOUN
ejpam-5730	220	5	t	t	NOUN
ejpam-5730	220	6	:	:	PUNCT
ejpam-5730	220	7	x	x	X
ejpam-5730	220	8	→	→	PUNCT
ejpam-5730	220	9	x	x	PART
ejpam-5730	220	10	possesses	possess	VERB
ejpam-5730	220	11	a	a	DET
ejpam-5730	220	12	fixed	fix	VERB
ejpam-5730	220	13	point	point	NOUN
ejpam-5730	220	14	in	in	ADP
ejpam-5730	220	15	x	x	NOUN
ejpam-5730	220	16	,	,	PUNCT
ejpam-5730	220	17	if	if	SCONJ
ejpam-5730	220	18	there	there	PRON
ejpam-5730	220	19	exist	exist	VERB
ejpam-5730	220	20	constants	constant	NOUN
ejpam-5730	220	21	λ	λ	X
ejpam-5730	220	22	∈	∈	PROPN
ejpam-5730	221	1	[	[	X
ejpam-5730	221	2	0	0	NUM
ejpam-5730	221	3	,	,	PUNCT
ejpam-5730	221	4	1	1	NUM
ejpam-5730	221	5	)	)	PUNCT
ejpam-5730	221	6	and	and	CCONJ
ejpam-5730	221	7	α	α	PRON
ejpam-5730	221	8	∈	∈	PROPN
ejpam-5730	221	9	(	(	PUNCT
ejpam-5730	221	10	0	0	NUM
ejpam-5730	221	11	,	,	PUNCT
ejpam-5730	221	12	1	1	NUM
ejpam-5730	221	13	)	)	PUNCT
ejpam-5730	222	1	such	such	ADJ
ejpam-5730	222	2	that	that	SCONJ
ejpam-5730	222	3	ρ(tζ	ρ(tζ	NUM
ejpam-5730	222	4	,	,	PUNCT
ejpam-5730	222	5	tη	tη	NOUN
ejpam-5730	222	6	)	)	PUNCT
ejpam-5730	222	7	≤	≤	NOUN
ejpam-5730	222	8	λ[ρ(ζ	λ[ρ(ζ	ADJ
ejpam-5730	222	9	,	,	PUNCT
ejpam-5730	222	10	t	t	PROPN
ejpam-5730	222	11	ζ)]α	ζ)]α	X
ejpam-5730	222	12	·	·	PUNCT
ejpam-5730	223	1	[	[	X
ejpam-5730	223	2	ρ(η	ρ(η	PROPN
ejpam-5730	223	3	,	,	PUNCT
ejpam-5730	223	4	tη)]1−α	tη)]1−α	NOUN
ejpam-5730	223	5	for	for	ADP
ejpam-5730	223	6	all	all	DET
ejpam-5730	223	7	ζ	ζ	NOUN
ejpam-5730	223	8	,	,	PUNCT
ejpam-5730	223	9	η	η	PROPN
ejpam-5730	223	10	∈	∈	PROPN
ejpam-5730	223	11	x\fix(t	x\fix(t	X
ejpam-5730	223	12	)	)	PUNCT
ejpam-5730	223	13	.	.	PUNCT
ejpam-5730	224	1	notice	notice	VERB
ejpam-5730	224	2	that	that	SCONJ
ejpam-5730	224	3	several	several	ADJ
ejpam-5730	224	4	variations	variation	NOUN
ejpam-5730	224	5	of	of	ADP
ejpam-5730	224	6	reich	reich	NOUN
ejpam-5730	224	7	contractions	contraction	NOUN
ejpam-5730	224	8	(	(	PUNCT
ejpam-5730	224	9	in	in	ADP
ejpam-5730	224	10	theorem	theorem	NOUN
ejpam-5730	224	11	3	3	NUM
ejpam-5730	224	12	in	in	ADP
ejpam-5730	224	13	[	[	X
ejpam-5730	224	14	23	23	NUM
ejpam-5730	224	15	]	]	PUNCT
ejpam-5730	224	16	)	)	PUNCT
ejpam-5730	224	17	can	can	AUX
ejpam-5730	224	18	be	be	AUX
ejpam-5730	224	19	stated	state	VERB
ejpam-5730	224	20	.	.	PUNCT
ejpam-5730	225	1	we	we	PRON
ejpam-5730	225	2	may	may	AUX
ejpam-5730	225	3	state	state	VERB
ejpam-5730	225	4	the	the	DET
ejpam-5730	225	5	following	following	NOUN
ejpam-5730	225	6	:	:	PUNCT
ejpam-5730	225	7	ρ(tζ	ρ(tζ	NUM
ejpam-5730	225	8	,	,	PUNCT
ejpam-5730	225	9	tη	tη	NOUN
ejpam-5730	225	10	)	)	PUNCT
ejpam-5730	225	11	≤	≤	NOUN
ejpam-5730	225	12	aρ(ζ	aρ(ζ	X
ejpam-5730	225	13	,	,	PUNCT
ejpam-5730	225	14	η	η	NOUN
ejpam-5730	225	15	)	)	PUNCT
ejpam-5730	225	16	+	+	CCONJ
ejpam-5730	225	17	bρ(ζ	bρ(ζ	NUM
ejpam-5730	225	18	,	,	PUNCT
ejpam-5730	225	19	t	t	PROPN
ejpam-5730	225	20	ζ	ζ	NOUN
ejpam-5730	225	21	)	)	PUNCT
ejpam-5730	225	22	+	+	CCONJ
ejpam-5730	225	23	cρ(η	cρ(η	NOUN
ejpam-5730	225	24	,	,	PUNCT
ejpam-5730	225	25	tη	tη	NOUN
ejpam-5730	225	26	)	)	PUNCT
ejpam-5730	225	27	,	,	PUNCT
ejpam-5730	225	28	where	where	SCONJ
ejpam-5730	225	29	a	a	DET
ejpam-5730	225	30	,	,	PUNCT
ejpam-5730	225	31	b	b	NOUN
ejpam-5730	225	32	,	,	PUNCT
ejpam-5730	225	33	c	c	PROPN
ejpam-5730	225	34	∈	∈	PROPN
ejpam-5730	225	35	(	(	PUNCT
ejpam-5730	225	36	0,∞	0,∞	NOUN
ejpam-5730	225	37	)	)	PUNCT
ejpam-5730	225	38	such	such	ADJ
ejpam-5730	225	39	that	that	SCONJ
ejpam-5730	225	40	0	0	NUM
ejpam-5730	225	41	≤	≤	NOUN
ejpam-5730	225	42	a+	a+	PUNCT
ejpam-5730	225	43	b+	b+	X
ejpam-5730	225	44	c	c	X
ejpam-5730	225	45	<	<	X
ejpam-5730	225	46	1	1	NUM
ejpam-5730	225	47	.	.	PUNCT
ejpam-5730	226	1	in	in	ADP
ejpam-5730	226	2	[	[	X
ejpam-5730	226	3	23	23	NUM
ejpam-5730	226	4	]	]	PUNCT
ejpam-5730	226	5	,	,	PUNCT
ejpam-5730	226	6	the	the	DET
ejpam-5730	226	7	authors	author	NOUN
ejpam-5730	226	8	investigate	investigate	VERB
ejpam-5730	226	9	the	the	DET
ejpam-5730	226	10	validity	validity	NOUN
ejpam-5730	226	11	of	of	ADP
ejpam-5730	226	12	the	the	DET
ejpam-5730	226	13	interpolation	interpolation	NOUN
ejpam-5730	226	14	approach	approach	NOUN
ejpam-5730	226	15	for	for	ADP
ejpam-5730	226	16	reich	reich	PROPN
ejpam-5730	226	17	contractions	contraction	NOUN
ejpam-5730	226	18	in	in	ADP
ejpam-5730	226	19	the	the	DET
ejpam-5730	226	20	context	context	NOUN
ejpam-5730	226	21	of	of	ADP
ejpam-5730	226	22	partial	partial	ADJ
ejpam-5730	226	23	metric	metric	ADJ
ejpam-5730	226	24	spaces	space	NOUN
ejpam-5730	226	25	that	that	PRON
ejpam-5730	226	26	was	be	AUX
ejpam-5730	226	27	introduced	introduce	VERB
ejpam-5730	226	28	by	by	ADP
ejpam-5730	226	29	matthews	matthews	PROPN
ejpam-5730	226	30	.	.	PUNCT
ejpam-5730	227	1	comment	comment	NOUN
ejpam-5730	227	2	:	:	PUNCT
ejpam-5730	228	1	we	we	PRON
ejpam-5730	228	2	have	have	VERB
ejpam-5730	228	3	two	two	NUM
ejpam-5730	228	4	examples	example	NOUN
ejpam-5730	228	5	of	of	ADP
ejpam-5730	228	6	rhr	rhr	PROPN
ejpam-5730	228	7	maps	map	NOUN
ejpam-5730	228	8	in	in	ADP
ejpam-5730	228	9	[	[	X
ejpam-5730	228	10	23	23	NUM
ejpam-5730	228	11	]	]	PUNCT
ejpam-5730	228	12	as	as	SCONJ
ejpam-5730	228	13	follows	follow	VERB
ejpam-5730	228	14	:	:	PUNCT
ejpam-5730	228	15	for	for	ADP
ejpam-5730	228	16	the	the	DET
ejpam-5730	228	17	reich	reich	NOUN
ejpam-5730	228	18	-	-	PUNCT
ejpam-5730	228	19	rus	rus	NOUN
ejpam-5730	228	20	-	-	ADJ
ejpam-5730	228	21	ćirić	ćirić	NOUN
ejpam-5730	228	22	contraction	contraction	NOUN
ejpam-5730	228	23	,	,	PUNCT
ejpam-5730	228	24	by	by	ADP
ejpam-5730	228	25	putting	put	VERB
ejpam-5730	228	26	η	η	PROPN
ejpam-5730	228	27	=	=	PROPN
ejpam-5730	228	28	tζ	tζ	PROPN
ejpam-5730	228	29	,	,	PUNCT
ejpam-5730	228	30	we	we	PRON
ejpam-5730	228	31	have	have	VERB
ejpam-5730	228	32	ρ(tζ	ρ(tζ	NOUN
ejpam-5730	228	33	,	,	PUNCT
ejpam-5730	228	34	t	t	NOUN
ejpam-5730	228	35	2ζ	2ζ	NUM
ejpam-5730	228	36	)	)	PUNCT
ejpam-5730	228	37	≤	≤	NUM
ejpam-5730	228	38	2λ	2λ	PROPN
ejpam-5730	228	39	ρ(ζ	ρ(ζ	NOUN
ejpam-5730	228	40	,	,	PUNCT
ejpam-5730	228	41	t	t	NOUN
ejpam-5730	228	42	ζ	ζ	NOUN
ejpam-5730	228	43	)	)	PUNCT
ejpam-5730	228	44	+	+	NUM
ejpam-5730	228	45	λ	λ	NOUN
ejpam-5730	228	46	ρ(tζ	ρ(tζ	NUM
ejpam-5730	228	47	,	,	PUNCT
ejpam-5730	228	48	t	t	NOUN
ejpam-5730	228	49	2ζ	2ζ	NUM
ejpam-5730	228	50	)	)	PUNCT
ejpam-5730	229	1	=	=	SYM
ejpam-5730	229	2	⇒	⇒	NOUN
ejpam-5730	229	3	ρ(tζ	ρ(tζ	NUM
ejpam-5730	229	4	,	,	PUNCT
ejpam-5730	229	5	t	t	NOUN
ejpam-5730	229	6	2ζ	2ζ	NUM
ejpam-5730	229	7	)	)	PUNCT
ejpam-5730	229	8	≤	≤	NUM
ejpam-5730	229	9	2λ	2λ	NOUN
ejpam-5730	229	10	1−	1−	NUM
ejpam-5730	229	11	λ	λ	PROPN
ejpam-5730	229	12	ρ(ζ	ρ(ζ	PROPN
ejpam-5730	229	13	,	,	PUNCT
ejpam-5730	229	14	t	t	NOUN
ejpam-5730	229	15	ζ	ζ	NOUN
ejpam-5730	229	16	)	)	PUNCT
ejpam-5730	229	17	,	,	PUNCT
ejpam-5730	229	18	λ	λ	PROPN
ejpam-5730	229	19	∈	∈	PROPN
ejpam-5730	230	1	[	[	X
ejpam-5730	230	2	0	0	NUM
ejpam-5730	230	3	,	,	PUNCT
ejpam-5730	230	4	1/2	1/2	NUM
ejpam-5730	230	5	)	)	PUNCT
ejpam-5730	230	6	.	.	PUNCT
ejpam-5730	231	1	for	for	ADP
ejpam-5730	231	2	the	the	DET
ejpam-5730	231	3	variation	variation	NOUN
ejpam-5730	231	4	of	of	ADP
ejpam-5730	231	5	the	the	DET
ejpam-5730	231	6	reich	reich	PROPN
ejpam-5730	231	7	contraction	contraction	NOUN
ejpam-5730	231	8	,	,	PUNCT
ejpam-5730	231	9	by	by	ADP
ejpam-5730	231	10	putting	put	VERB
ejpam-5730	231	11	η	η	PROPN
ejpam-5730	231	12	=	=	PROPN
ejpam-5730	231	13	tζ	tζ	PROPN
ejpam-5730	231	14	,	,	PUNCT
ejpam-5730	231	15	we	we	PRON
ejpam-5730	231	16	have	have	VERB
ejpam-5730	231	17	ρ(tζ	ρ(tζ	NOUN
ejpam-5730	231	18	,	,	PUNCT
ejpam-5730	231	19	t	t	NOUN
ejpam-5730	231	20	2ζ	2ζ	NUM
ejpam-5730	231	21	)	)	PUNCT
ejpam-5730	231	22	≤	≤	NOUN
ejpam-5730	231	23	(	(	PUNCT
ejpam-5730	231	24	a+b)ρ(ζ	a+b)ρ(ζ	PROPN
ejpam-5730	231	25	,	,	PUNCT
ejpam-5730	231	26	t	t	PROPN
ejpam-5730	231	27	ζ)+c	ζ)+c	NUM
ejpam-5730	231	28	ρ(tζ	ρ(tζ	NUM
ejpam-5730	231	29	,	,	PUNCT
ejpam-5730	231	30	t	t	NOUN
ejpam-5730	231	31	2ζ	2ζ	NUM
ejpam-5730	231	32	)	)	PUNCT
ejpam-5730	232	1	=	=	SYM
ejpam-5730	232	2	⇒	⇒	NOUN
ejpam-5730	232	3	ρ(tζ	ρ(tζ	NUM
ejpam-5730	232	4	,	,	PUNCT
ejpam-5730	232	5	t	t	NOUN
ejpam-5730	232	6	2ζ	2ζ	NUM
ejpam-5730	232	7	)	)	PUNCT
ejpam-5730	232	8	≤	≤	NOUN
ejpam-5730	232	9	a+	a+	PUNCT
ejpam-5730	232	10	b	b	NOUN
ejpam-5730	232	11	1−	1−	NUM
ejpam-5730	232	12	c	c	NOUN
ejpam-5730	232	13	ρ(ζ	ρ(ζ	NOUN
ejpam-5730	232	14	,	,	PUNCT
ejpam-5730	232	15	t	t	NOUN
ejpam-5730	232	16	ζ	ζ	NOUN
ejpam-5730	232	17	)	)	PUNCT
ejpam-5730	232	18	,	,	PUNCT
ejpam-5730	232	19	0	0	PUNCT
ejpam-5730	232	20	<	<	X
ejpam-5730	232	21	a+	a+	X
ejpam-5730	232	22	b	b	PROPN
ejpam-5730	232	23	1−	1−	NUM
ejpam-5730	232	24	c	c	NOUN
ejpam-5730	232	25	<	<	X
ejpam-5730	232	26	1	1	NUM
ejpam-5730	232	27	.	.	PUNCT
ejpam-5730	232	28	therefore	therefore	ADV
ejpam-5730	232	29	,	,	PUNCT
ejpam-5730	232	30	theorems	theorems	PROPN
ejpam-5730	232	31	p	p	NOUN
ejpam-5730	232	32	and	and	CCONJ
ejpam-5730	232	33	h(γ1	h(γ1	NOUN
ejpam-5730	232	34	)	)	PUNCT
ejpam-5730	232	35	can	can	AUX
ejpam-5730	232	36	be	be	AUX
ejpam-5730	232	37	applied	apply	VERB
ejpam-5730	232	38	to	to	ADP
ejpam-5730	232	39	such	such	ADJ
ejpam-5730	232	40	two	two	NUM
ejpam-5730	232	41	examples	example	NOUN
ejpam-5730	232	42	for	for	ADP
ejpam-5730	232	43	t	t	PROPN
ejpam-5730	232	44	-orbitally	-orbitally	PROPN
ejpam-5730	232	45	complete	complete	ADJ
ejpam-5730	232	46	quasi	quasi	ADJ
ejpam-5730	232	47	-	-	ADJ
ejpam-5730	232	48	metric	metric	ADJ
ejpam-5730	232	49	spaces	space	NOUN
ejpam-5730	232	50	.	.	PUNCT
ejpam-5730	233	1	karapinar	karapinar	NOUN
ejpam-5730	233	2	,	,	PUNCT
ejpam-5730	233	3	alqahtani	alqahtani	ADJ
ejpam-5730	233	4	,	,	PUNCT
ejpam-5730	233	5	and	and	CCONJ
ejpam-5730	233	6	aydi	aydi	VERB
ejpam-5730	233	7	[	[	X
ejpam-5730	233	8	24	24	NUM
ejpam-5730	233	9	]	]	PUNCT
ejpam-5730	233	10	in	in	ADP
ejpam-5730	233	11	2018	2018	NUM
ejpam-5730	233	12	by	by	ADP
ejpam-5730	233	13	using	use	VERB
ejpam-5730	233	14	an	an	DET
ejpam-5730	233	15	interpolative	interpolative	ADJ
ejpam-5730	233	16	approach	approach	NOUN
ejpam-5730	233	17	,	,	PUNCT
ejpam-5730	233	18	the	the	DET
ejpam-5730	233	19	authors	author	NOUN
ejpam-5730	233	20	recognize	recognize	VERB
ejpam-5730	233	21	the	the	DET
ejpam-5730	233	22	hardy	hardy	ADJ
ejpam-5730	233	23	-	-	PUNCT
ejpam-5730	233	24	rogers	rogers	NOUN
ejpam-5730	233	25	fixed	fix	VERB
ejpam-5730	233	26	point	point	NOUN
ejpam-5730	233	27	theorem	theorem	VERB
ejpam-5730	233	28	in	in	ADP
ejpam-5730	233	29	the	the	DET
ejpam-5730	233	30	class	class	NOUN
ejpam-5730	233	31	of	of	ADP
ejpam-5730	233	32	metric	metric	ADJ
ejpam-5730	233	33	spaces	space	NOUN
ejpam-5730	233	34	.	.	PUNCT
ejpam-5730	234	1	the	the	DET
ejpam-5730	234	2	obtained	obtain	VERB
ejpam-5730	234	3	result	result	NOUN
ejpam-5730	234	4	is	be	AUX
ejpam-5730	234	5	supported	support	VERB
ejpam-5730	234	6	by	by	ADP
ejpam-5730	234	7	some	some	DET
ejpam-5730	234	8	examples	example	NOUN
ejpam-5730	234	9	.	.	PUNCT
ejpam-5730	235	1	they	they	PRON
ejpam-5730	235	2	also	also	ADV
ejpam-5730	235	3	give	give	VERB
ejpam-5730	235	4	the	the	DET
ejpam-5730	235	5	partial	partial	ADJ
ejpam-5730	235	6	metric	metric	ADJ
ejpam-5730	235	7	case	case	NOUN
ejpam-5730	235	8	,	,	PUNCT
ejpam-5730	235	9	according	accord	VERB
ejpam-5730	235	10	to	to	ADP
ejpam-5730	235	11	their	their	PRON
ejpam-5730	235	12	result	result	NOUN
ejpam-5730	235	13	.	.	PUNCT
ejpam-5730	236	1	a	a	DET
ejpam-5730	236	2	generalization	generalization	NOUN
ejpam-5730	236	3	of	of	ADP
ejpam-5730	236	4	the	the	DET
ejpam-5730	236	5	banach	banach	NOUN
ejpam-5730	236	6	contraction	contraction	NOUN
ejpam-5730	236	7	principle	principle	NOUN
ejpam-5730	236	8	is	be	AUX
ejpam-5730	236	9	due	due	ADJ
ejpam-5730	236	10	to	to	ADP
ejpam-5730	236	11	hardy	hardy	ADJ
ejpam-5730	236	12	-	-	PUNCT
ejpam-5730	236	13	rogers	roger	NOUN
ejpam-5730	236	14	as	as	SCONJ
ejpam-5730	236	15	follows	follow	VERB
ejpam-5730	236	16	;	;	PUNCT
ejpam-5730	236	17	see	see	VERB
ejpam-5730	236	18	[	[	X
ejpam-5730	236	19	13	13	NUM
ejpam-5730	236	20	]	]	PUNCT
ejpam-5730	236	21	.	.	PUNCT
ejpam-5730	237	1	theorem	theorem	VERB
ejpam-5730	237	2	6.14	6.14	NUM
ejpam-5730	237	3	.	.	PUNCT
ejpam-5730	238	1	(	(	PUNCT
ejpam-5730	238	2	karapinar	karapinar	VERB
ejpam-5730	238	3	et	et	PROPN
ejpam-5730	238	4	al	al	PROPN
ejpam-5730	238	5	.	.	PUNCT
ejpam-5730	238	6	)	)	PUNCT
ejpam-5730	239	1	let	let	VERB
ejpam-5730	239	2	(	(	PUNCT
ejpam-5730	239	3	x	x	NOUN
ejpam-5730	239	4	,	,	PUNCT
ejpam-5730	239	5	d	d	NOUN
ejpam-5730	239	6	)	)	PUNCT
ejpam-5730	239	7	be	be	AUX
ejpam-5730	239	8	a	a	DET
ejpam-5730	239	9	complete	complete	ADJ
ejpam-5730	239	10	metric	metric	ADJ
ejpam-5730	239	11	space	space	NOUN
ejpam-5730	239	12	.	.	PUNCT
ejpam-5730	240	1	let	let	VERB
ejpam-5730	240	2	t	t	NOUN
ejpam-5730	240	3	:	:	PUNCT
ejpam-5730	240	4	x	x	X
ejpam-5730	240	5	→	→	PUNCT
ejpam-5730	240	6	x	x	PUNCT
ejpam-5730	240	7	be	be	AUX
ejpam-5730	240	8	a	a	DET
ejpam-5730	240	9	given	give	VERB
ejpam-5730	240	10	mapping	mapping	NOUN
ejpam-5730	240	11	such	such	ADJ
ejpam-5730	240	12	that	that	PRON
ejpam-5730	240	13	d(tθ	d(tθ	PROPN
ejpam-5730	240	14	,	,	PUNCT
ejpam-5730	240	15	tϑ	tϑ	NOUN
ejpam-5730	240	16	)	)	PUNCT
ejpam-5730	240	17	≤	≤	NOUN
ejpam-5730	240	18	αd(θ	αd(θ	NUM
ejpam-5730	240	19	,	,	PUNCT
ejpam-5730	240	20	ϑ	ϑ	X
ejpam-5730	240	21	)	)	PUNCT
ejpam-5730	240	22	+	+	NUM
ejpam-5730	240	23	βd(θ	βd(θ	NUM
ejpam-5730	240	24	,	,	PUNCT
ejpam-5730	240	25	tθ	tθ	NOUN
ejpam-5730	240	26	)	)	PUNCT
ejpam-5730	240	27	+	+	NUM
ejpam-5730	240	28	γd(ϑ	γd(ϑ	NUM
ejpam-5730	240	29	,	,	PUNCT
ejpam-5730	240	30	tϑ	tϑ	PRON
ejpam-5730	240	31	)	)	PUNCT
ejpam-5730	241	1	+	+	CCONJ
ejpam-5730	241	2	δ	δ	PROPN
ejpam-5730	241	3	2	2	NUM
ejpam-5730	241	4	[	[	X
ejpam-5730	241	5	d(θ	d(θ	PROPN
ejpam-5730	241	6	,	,	PUNCT
ejpam-5730	241	7	tϑ	tϑ	PRON
ejpam-5730	241	8	)	)	PUNCT
ejpam-5730	242	1	+	+	CCONJ
ejpam-5730	242	2	d(ϑ	d(ϑ	VERB
ejpam-5730	242	3	,	,	PUNCT
ejpam-5730	242	4	tθ	tθ	NOUN
ejpam-5730	242	5	)	)	PUNCT
ejpam-5730	242	6	]	]	PUNCT
ejpam-5730	242	7	,	,	PUNCT
ejpam-5730	242	8	for	for	ADP
ejpam-5730	242	9	all	all	DET
ejpam-5730	242	10	θ	θ	PROPN
ejpam-5730	242	11	,	,	PUNCT
ejpam-5730	242	12	ϑ	ϑ	X
ejpam-5730	242	13	∈	∈	X
ejpam-5730	242	14	x	x	SYM
ejpam-5730	242	15	,	,	PUNCT
ejpam-5730	242	16	where	where	SCONJ
ejpam-5730	242	17	α	α	X
ejpam-5730	242	18	,	,	PUNCT
ejpam-5730	242	19	β	β	X
ejpam-5730	242	20	,	,	PUNCT
ejpam-5730	242	21	γ	γ	PROPN
ejpam-5730	242	22	,	,	PUNCT
ejpam-5730	242	23	δ	δ	PROPN
ejpam-5730	242	24	are	be	AUX
ejpam-5730	242	25	non	non	ADJ
ejpam-5730	242	26	-	-	ADJ
ejpam-5730	242	27	negative	negative	ADJ
ejpam-5730	242	28	reals	real	NOUN
ejpam-5730	242	29	such	such	ADJ
ejpam-5730	242	30	that	that	SCONJ
ejpam-5730	242	31	α+	α+	X
ejpam-5730	242	32	β	β	X
ejpam-5730	242	33	+	+	X
ejpam-5730	242	34	γ	γ	PROPN
ejpam-5730	242	35	+	+	PROPN
ejpam-5730	242	36	δ	δ	PROPN
ejpam-5730	242	37	<	<	X
ejpam-5730	242	38	1	1	NUM
ejpam-5730	242	39	.	.	PUNCT
ejpam-5730	243	1	then	then	ADV
ejpam-5730	243	2	t	t	PROPN
ejpam-5730	243	3	has	have	VERB
ejpam-5730	243	4	a	a	DET
ejpam-5730	243	5	unique	unique	ADJ
ejpam-5730	243	6	fixed	fix	VERB
ejpam-5730	243	7	point	point	NOUN
ejpam-5730	243	8	in	in	ADP
ejpam-5730	243	9	x.	x.	NOUN
ejpam-5730	243	10	in	in	ADP
ejpam-5730	243	11	[	[	X
ejpam-5730	243	12	24	24	NUM
ejpam-5730	243	13	]	]	PUNCT
ejpam-5730	243	14	,	,	PUNCT
ejpam-5730	243	15	the	the	DET
ejpam-5730	243	16	authors	author	NOUN
ejpam-5730	243	17	introduce	introduce	VERB
ejpam-5730	243	18	the	the	DET
ejpam-5730	243	19	concept	concept	NOUN
ejpam-5730	243	20	of	of	ADP
ejpam-5730	243	21	interpolative	interpolative	ADJ
ejpam-5730	243	22	hardy	hardy	ADJ
ejpam-5730	243	23	-	-	PUNCT
ejpam-5730	243	24	rogers	rogers	NOUN
ejpam-5730	243	25	type	type	NOUN
ejpam-5730	243	26	contractions	contraction	NOUN
ejpam-5730	243	27	,	,	PUNCT
ejpam-5730	243	28	and	and	CCONJ
ejpam-5730	243	29	provide	provide	VERB
ejpam-5730	243	30	some	some	DET
ejpam-5730	243	31	examples	example	NOUN
ejpam-5730	243	32	illustrating	illustrate	VERB
ejpam-5730	243	33	the	the	DET
ejpam-5730	243	34	obtained	obtain	VERB
ejpam-5730	243	35	result	result	NOUN
ejpam-5730	243	36	.	.	PUNCT
ejpam-5730	244	1	they	they	PRON
ejpam-5730	244	2	also	also	ADV
ejpam-5730	244	3	extend	extend	VERB
ejpam-5730	244	4	their	their	PRON
ejpam-5730	244	5	obtained	obtain	VERB
ejpam-5730	244	6	result	result	NOUN
ejpam-5730	244	7	to	to	ADP
ejpam-5730	244	8	partial	partial	ADJ
ejpam-5730	244	9	metric	metric	ADJ
ejpam-5730	244	10	spaces	space	NOUN
ejpam-5730	244	11	.	.	PUNCT
ejpam-5730	245	1	s.	s.	PROPN
ejpam-5730	245	2	park	park	PROPN
ejpam-5730	245	3	/	/	SYM
ejpam-5730	245	4	eur	eur	PROPN
ejpam-5730	245	5	.	.	PUNCT
ejpam-5730	246	1	j.	j.	PROPN
ejpam-5730	246	2	pure	pure	PROPN
ejpam-5730	246	3	appl	appl	PROPN
ejpam-5730	246	4	.	.	PROPN
ejpam-5730	246	5	math	math	PROPN
ejpam-5730	246	6	,	,	PUNCT
ejpam-5730	246	7	18	18	NUM
ejpam-5730	246	8	(	(	PUNCT
ejpam-5730	246	9	1	1	NUM
ejpam-5730	246	10	)	)	PUNCT
ejpam-5730	246	11	(	(	PUNCT
ejpam-5730	246	12	2025	2025	NUM
ejpam-5730	246	13	)	)	PUNCT
ejpam-5730	246	14	,	,	PUNCT
ejpam-5730	246	15	5730	5730	NUM
ejpam-5730	246	16	11	11	NUM
ejpam-5730	246	17	of	of	ADP
ejpam-5730	246	18	21	21	NUM
ejpam-5730	246	19	definition	definition	NOUN
ejpam-5730	246	20	6.15	6.15	NUM
ejpam-5730	246	21	.	.	PUNCT
ejpam-5730	247	1	let	let	VERB
ejpam-5730	247	2	(	(	PUNCT
ejpam-5730	247	3	x	x	NOUN
ejpam-5730	247	4	,	,	PUNCT
ejpam-5730	247	5	d	d	NOUN
ejpam-5730	247	6	)	)	PUNCT
ejpam-5730	247	7	be	be	AUX
ejpam-5730	247	8	a	a	DET
ejpam-5730	247	9	metric	metric	ADJ
ejpam-5730	247	10	space	space	NOUN
ejpam-5730	247	11	.	.	PUNCT
ejpam-5730	248	1	we	we	PRON
ejpam-5730	248	2	say	say	VERB
ejpam-5730	248	3	that	that	SCONJ
ejpam-5730	248	4	the	the	DET
ejpam-5730	248	5	self	self	NOUN
ejpam-5730	248	6	-	-	PUNCT
ejpam-5730	248	7	mapping	mapping	NOUN
ejpam-5730	248	8	t	t	NOUN
ejpam-5730	248	9	:	:	PUNCT
ejpam-5730	248	10	x	x	X
ejpam-5730	248	11	→	→	PUNCT
ejpam-5730	248	12	x	x	X
ejpam-5730	248	13	is	be	AUX
ejpam-5730	248	14	an	an	DET
ejpam-5730	248	15	interpolative	interpolative	ADJ
ejpam-5730	248	16	hardy	hardy	ADJ
ejpam-5730	248	17	-	-	PUNCT
ejpam-5730	248	18	rogers	rogers	NOUN
ejpam-5730	248	19	type	type	NOUN
ejpam-5730	248	20	contraction	contraction	NOUN
ejpam-5730	248	21	if	if	SCONJ
ejpam-5730	248	22	there	there	PRON
ejpam-5730	248	23	exists	exist	VERB
ejpam-5730	248	24	λ	λ	X
ejpam-5730	248	25	∈	∈	PROPN
ejpam-5730	249	1	[	[	X
ejpam-5730	249	2	0	0	NUM
ejpam-5730	249	3	,	,	PUNCT
ejpam-5730	249	4	1	1	NUM
ejpam-5730	249	5	)	)	PUNCT
ejpam-5730	249	6	and	and	CCONJ
ejpam-5730	249	7	α	α	NOUN
ejpam-5730	249	8	,	,	PUNCT
ejpam-5730	249	9	β	β	X
ejpam-5730	249	10	,	,	PUNCT
ejpam-5730	249	11	γ	γ	PROPN
ejpam-5730	249	12	∈	∈	PROPN
ejpam-5730	249	13	(	(	PUNCT
ejpam-5730	249	14	0	0	NUM
ejpam-5730	249	15	,	,	PUNCT
ejpam-5730	249	16	1	1	NUM
ejpam-5730	249	17	)	)	PUNCT
ejpam-5730	249	18	with	with	ADP
ejpam-5730	249	19	α+	α+	PRON
ejpam-5730	249	20	β	β	NOUN
ejpam-5730	249	21	+	+	X
ejpam-5730	249	22	γ	γ	X
ejpam-5730	249	23	<	<	X
ejpam-5730	249	24	1	1	NUM
ejpam-5730	249	25	,	,	PUNCT
ejpam-5730	249	26	such	such	ADJ
ejpam-5730	249	27	that	that	SCONJ
ejpam-5730	249	28	d(tθ	d(tθ	PROPN
ejpam-5730	249	29	,	,	PUNCT
ejpam-5730	249	30	tϑ	tϑ	NOUN
ejpam-5730	249	31	)	)	PUNCT
ejpam-5730	249	32	≤	≤	NOUN
ejpam-5730	249	33	λ[d(θ	λ[d(θ	PROPN
ejpam-5730	249	34	,	,	PUNCT
ejpam-5730	249	35	ϑ)]β	ϑ)]β	VERB
ejpam-5730	249	36	·	·	PUNCT
ejpam-5730	250	1	[	[	X
ejpam-5730	250	2	d(θ	d(θ	PROPN
ejpam-5730	250	3	,	,	PUNCT
ejpam-5730	250	4	tθ)]α	tθ)]α	X
ejpam-5730	250	5	·	·	PUNCT
ejpam-5730	251	1	[	[	X
ejpam-5730	251	2	d(ϑ	d(ϑ	NOUN
ejpam-5730	251	3	,	,	PUNCT
ejpam-5730	251	4	tϑ)]γ	tϑ)]γ	NOUN
ejpam-5730	251	5	·	·	PUNCT
ejpam-5730	252	1	[	[	X
ejpam-5730	252	2	1	1	NUM
ejpam-5730	252	3	2	2	NUM
ejpam-5730	252	4	(	(	PUNCT
ejpam-5730	252	5	d(θ	d(θ	PROPN
ejpam-5730	252	6	,	,	PUNCT
ejpam-5730	252	7	tϑ	tϑ	PRON
ejpam-5730	252	8	)	)	PUNCT
ejpam-5730	253	1	+	+	CCONJ
ejpam-5730	253	2	d(ϑ	d(ϑ	PROPN
ejpam-5730	253	3	,	,	PUNCT
ejpam-5730	253	4	tθ))]1−α−β−γ	tθ))]1−α−β−γ	NOUN
ejpam-5730	253	5	for	for	ADP
ejpam-5730	253	6	all	all	DET
ejpam-5730	253	7	θ	θ	PROPN
ejpam-5730	253	8	,	,	PUNCT
ejpam-5730	253	9	ϑ	ϑ	X
ejpam-5730	253	10	∈	∈	NOUN
ejpam-5730	253	11	x\fix(t	x\fix(t	X
ejpam-5730	253	12	)	)	PUNCT
ejpam-5730	253	13	.	.	PUNCT
ejpam-5730	254	1	theorem	theorem	VERB
ejpam-5730	254	2	6.16	6.16	NUM
ejpam-5730	254	3	.	.	PUNCT
ejpam-5730	255	1	(	(	PUNCT
ejpam-5730	255	2	karapinar	karapinar	VERB
ejpam-5730	255	3	et	et	PROPN
ejpam-5730	255	4	al	al	PROPN
ejpam-5730	255	5	.	.	PUNCT
ejpam-5730	255	6	)	)	PUNCT
ejpam-5730	256	1	let	let	VERB
ejpam-5730	256	2	(	(	PUNCT
ejpam-5730	256	3	x	x	NOUN
ejpam-5730	256	4	,	,	PUNCT
ejpam-5730	256	5	d	d	NOUN
ejpam-5730	256	6	)	)	PUNCT
ejpam-5730	256	7	be	be	AUX
ejpam-5730	256	8	a	a	DET
ejpam-5730	256	9	complete	complete	ADJ
ejpam-5730	256	10	metric	metric	ADJ
ejpam-5730	256	11	space	space	NOUN
ejpam-5730	256	12	and	and	CCONJ
ejpam-5730	256	13	t	t	PROPN
ejpam-5730	256	14	be	be	AUX
ejpam-5730	256	15	an	an	DET
ejpam-5730	256	16	interpolative	interpolative	ADJ
ejpam-5730	256	17	hardy	hardy	ADJ
ejpam-5730	256	18	-	-	PUNCT
ejpam-5730	256	19	rogers	rogers	NOUN
ejpam-5730	256	20	type	type	NOUN
ejpam-5730	256	21	contraction	contraction	NOUN
ejpam-5730	256	22	.	.	PUNCT
ejpam-5730	257	1	then	then	ADV
ejpam-5730	257	2	,	,	PUNCT
ejpam-5730	257	3	t	t	PROPN
ejpam-5730	257	4	has	have	VERB
ejpam-5730	257	5	a	a	DET
ejpam-5730	257	6	fixed	fix	VERB
ejpam-5730	257	7	point	point	NOUN
ejpam-5730	257	8	in	in	ADP
ejpam-5730	257	9	x.	x.	PROPN
ejpam-5730	257	10	comment	comment	NOUN
ejpam-5730	257	11	:	:	PUNCT
ejpam-5730	257	12	the	the	DET
ejpam-5730	257	13	map	map	NOUN
ejpam-5730	257	14	in	in	ADP
ejpam-5730	257	15	theorem	theorem	NOUN
ejpam-5730	257	16	6.16	6.16	NUM
ejpam-5730	257	17	is	be	AUX
ejpam-5730	257	18	an	an	DET
ejpam-5730	257	19	rhr	rhr	NOUN
ejpam-5730	257	20	map	map	NOUN
ejpam-5730	257	21	by	by	ADP
ejpam-5730	257	22	putting	put	VERB
ejpam-5730	257	23	ϑ	ϑ	X
ejpam-5730	257	24	=	=	X
ejpam-5730	257	25	tθ	tθ	NOUN
ejpam-5730	257	26	.	.	PUNCT
ejpam-5730	258	1	in	in	ADP
ejpam-5730	258	2	fact	fact	NOUN
ejpam-5730	258	3	,	,	PUNCT
ejpam-5730	258	4	we	we	PRON
ejpam-5730	258	5	have	have	AUX
ejpam-5730	258	6	d(tθ	d(tθ	VERB
ejpam-5730	258	7	,	,	PUNCT
ejpam-5730	258	8	t	t	NOUN
ejpam-5730	258	9	2θ	2θ	NUM
ejpam-5730	258	10	)	)	PUNCT
ejpam-5730	258	11	≤	≤	NOUN
ejpam-5730	258	12	(	(	PUNCT
ejpam-5730	258	13	α+	α+	X
ejpam-5730	258	14	β)d(θ	β)d(θ	NOUN
ejpam-5730	258	15	,	,	PUNCT
ejpam-5730	258	16	tθ	tθ	NOUN
ejpam-5730	258	17	)	)	PUNCT
ejpam-5730	259	1	+	+	CCONJ
ejpam-5730	259	2	δ	δ	PROPN
ejpam-5730	259	3	2	2	NUM
ejpam-5730	259	4	[	[	X
ejpam-5730	259	5	d(θ	d(θ	NOUN
ejpam-5730	259	6	,	,	PUNCT
ejpam-5730	259	7	tθ	tθ	NOUN
ejpam-5730	259	8	)	)	PUNCT
ejpam-5730	259	9	+	+	CCONJ
ejpam-5730	259	10	d(tθ	d(tθ	PROPN
ejpam-5730	259	11	,	,	PUNCT
ejpam-5730	259	12	t	t	NOUN
ejpam-5730	259	13	2θ	2θ	NUM
ejpam-5730	259	14	)	)	PUNCT
ejpam-5730	259	15	]	]	PUNCT
ejpam-5730	260	1	=	=	X
ejpam-5730	260	2	⇒	⇒	NOUN
ejpam-5730	260	3	(	(	PUNCT
ejpam-5730	260	4	1−	1−	NUM
ejpam-5730	260	5	γ	γ	PROPN
ejpam-5730	260	6	−	−	PROPN
ejpam-5730	260	7	δ/2)d(tθ	δ/2)d(tθ	PROPN
ejpam-5730	260	8	,	,	PUNCT
ejpam-5730	260	9	t	t	NOUN
ejpam-5730	260	10	2θ	2θ	NUM
ejpam-5730	260	11	)	)	PUNCT
ejpam-5730	260	12	≤	≤	NOUN
ejpam-5730	260	13	(	(	PUNCT
ejpam-5730	260	14	α+	α+	X
ejpam-5730	260	15	β	β	X
ejpam-5730	260	16	+	+	SYM
ejpam-5730	260	17	δ/2)d(θ	δ/2)d(θ	ADJ
ejpam-5730	260	18	,	,	PUNCT
ejpam-5730	260	19	tθ	tθ	NOUN
ejpam-5730	260	20	)	)	PUNCT
ejpam-5730	260	21	,	,	PUNCT
ejpam-5730	260	22	where	where	SCONJ
ejpam-5730	260	23	α+	α+	PRON
ejpam-5730	260	24	β	β	X
ejpam-5730	260	25	+	+	CCONJ
ejpam-5730	260	26	δ/2	δ/2	X
ejpam-5730	260	27	<	<	X
ejpam-5730	260	28	1−	1−	NUM
ejpam-5730	260	29	γ	γ	NOUN
ejpam-5730	260	30	−	−	PROPN
ejpam-5730	260	31	δ/2	δ/2	NUM
ejpam-5730	260	32	.	.	PUNCT
ejpam-5730	261	1	for	for	ADP
ejpam-5730	261	2	an	an	DET
ejpam-5730	261	3	interpolative	interpolative	ADJ
ejpam-5730	261	4	hardy	hardy	ADJ
ejpam-5730	261	5	-	-	PUNCT
ejpam-5730	261	6	roger	roger	NOUN
ejpam-5730	261	7	contraction	contraction	NOUN
ejpam-5730	261	8	,	,	PUNCT
ejpam-5730	261	9	by	by	ADP
ejpam-5730	261	10	putting	put	VERB
ejpam-5730	261	11	ϑ	ϑ	X
ejpam-5730	261	12	=	=	X
ejpam-5730	261	13	tθ	tθ	NOUN
ejpam-5730	261	14	,	,	PUNCT
ejpam-5730	261	15	we	we	PRON
ejpam-5730	261	16	have	have	AUX
ejpam-5730	261	17	d(tθ	d(tθ	VERB
ejpam-5730	261	18	,	,	PUNCT
ejpam-5730	261	19	t	t	NOUN
ejpam-5730	261	20	2θ	2θ	NUM
ejpam-5730	261	21	)	)	PUNCT
ejpam-5730	261	22	≤	≤	NOUN
ejpam-5730	261	23	λ[d(θ	λ[d(θ	NUM
ejpam-5730	261	24	,	,	PUNCT
ejpam-5730	261	25	tθ)]α+β	tθ)]α+β	PROPN
ejpam-5730	261	26	·	·	PUNCT
ejpam-5730	262	1	[	[	X
ejpam-5730	262	2	d(tθ	d(tθ	ADP
ejpam-5730	262	3	,	,	PUNCT
ejpam-5730	262	4	t	t	PROPN
ejpam-5730	262	5	2θ)]γ	2θ)]γ	NOUN
ejpam-5730	262	6	·	·	PUNCT
ejpam-5730	263	1	[	[	X
ejpam-5730	263	2	max{d(θ	max{d(θ	PROPN
ejpam-5730	263	3	,	,	PUNCT
ejpam-5730	263	4	tθ	tθ	NOUN
ejpam-5730	263	5	)	)	PUNCT
ejpam-5730	263	6	,	,	PUNCT
ejpam-5730	263	7	d(tθ	d(tθ	PROPN
ejpam-5730	263	8	,	,	PUNCT
ejpam-5730	263	9	t	t	PROPN
ejpam-5730	263	10	2θ)}]1−α−β−γ	2θ)}]1−α−β−γ	NOUN
ejpam-5730	263	11	=	=	AUX
ejpam-5730	263	12	⇒	⇒	NOUN
ejpam-5730	263	13	d(tθ	d(tθ	PROPN
ejpam-5730	263	14	,	,	PUNCT
ejpam-5730	263	15	t	t	NOUN
ejpam-5730	263	16	2θ)1−γ	2θ)1−γ	NUM
ejpam-5730	263	17	≤	≤	NUM
ejpam-5730	263	18	λ[d(θ	λ[d(θ	NUM
ejpam-5730	263	19	,	,	PUNCT
ejpam-5730	263	20	tθ)]α+β+1−α−β−γ	tθ)]α+β+1−α−β−γ	PROPN
ejpam-5730	263	21	or	or	CCONJ
ejpam-5730	263	22	[	[	X
ejpam-5730	263	23	d(tθ	d(tθ	PROPN
ejpam-5730	263	24	,	,	PUNCT
ejpam-5730	263	25	t	t	PROPN
ejpam-5730	263	26	2θ)]1−γ	2θ)]1−γ	NUM
ejpam-5730	263	27	≤	≤	NUM
ejpam-5730	263	28	λ[d(θ	λ[d(θ	PROPN
ejpam-5730	263	29	,	,	PUNCT
ejpam-5730	263	30	tθ)]α+β	tθ)]α+β	PROPN
ejpam-5730	263	31	·	·	PUNCT
ejpam-5730	264	1	[	[	X
ejpam-5730	264	2	d(tθ	d(tθ	ADP
ejpam-5730	264	3	,	,	PUNCT
ejpam-5730	264	4	t	t	PROPN
ejpam-5730	264	5	2θ)]1−α−β−γ	2θ)]1−α−β−γ	NUM
ejpam-5730	265	1	=	=	AUX
ejpam-5730	265	2	⇒	⇒	NOUN
ejpam-5730	265	3	d(tθ	d(tθ	PROPN
ejpam-5730	265	4	,	,	PUNCT
ejpam-5730	265	5	t	t	NOUN
ejpam-5730	265	6	2θ)1−γ	2θ)1−γ	NUM
ejpam-5730	265	7	≤	≤	NUM
ejpam-5730	265	8	λ[d(θ	λ[d(θ	PROPN
ejpam-5730	265	9	,	,	PUNCT
ejpam-5730	265	10	tθ)]1−γ	tθ)]1−γ	NOUN
ejpam-5730	265	11	or	or	CCONJ
ejpam-5730	265	12	d(tθ	d(tθ	PROPN
ejpam-5730	265	13	,	,	PUNCT
ejpam-5730	265	14	t	t	PROPN
ejpam-5730	265	15	2θ)α+β	2θ)α+β	NUM
ejpam-5730	265	16	≤	≤	PUNCT
ejpam-5730	265	17	λ[d(θ	λ[d(θ	PROPN
ejpam-5730	265	18	,	,	PUNCT
ejpam-5730	265	19	tθ)]α+β	tθ)]α+β	PROPN
ejpam-5730	265	20	=	=	AUX
ejpam-5730	265	21	⇒	⇒	NOUN
ejpam-5730	265	22	d(tθ	d(tθ	PROPN
ejpam-5730	265	23	,	,	PUNCT
ejpam-5730	265	24	t	t	NOUN
ejpam-5730	265	25	2θ	2θ	NUM
ejpam-5730	265	26	)	)	PUNCT
ejpam-5730	265	27	≤	≤	NOUN
ejpam-5730	266	1	λpd(θ	λpd(θ	PROPN
ejpam-5730	266	2	,	,	PUNCT
ejpam-5730	266	3	tθ	tθ	NOUN
ejpam-5730	266	4	)	)	PUNCT
ejpam-5730	266	5	or	or	CCONJ
ejpam-5730	266	6	d(tθ	d(tθ	PROPN
ejpam-5730	266	7	,	,	PUNCT
ejpam-5730	266	8	t	t	NOUN
ejpam-5730	266	9	2θ	2θ	NUM
ejpam-5730	266	10	)	)	PUNCT
ejpam-5730	267	1	≤	≤	NUM
ejpam-5730	267	2	λqd(θ	λqd(θ	PROPN
ejpam-5730	267	3	,	,	PUNCT
ejpam-5730	267	4	tθ	tθ	NOUN
ejpam-5730	267	5	)	)	PUNCT
ejpam-5730	267	6	.	.	PUNCT
ejpam-5730	268	1	note	note	VERB
ejpam-5730	268	2	that	that	SCONJ
ejpam-5730	268	3	0	0	PUNCT
ejpam-5730	268	4	<	<	X
ejpam-5730	268	5	λp	λp	X
ejpam-5730	269	1	:	:	PUNCT
ejpam-5730	269	2	=	=	SYM
ejpam-5730	269	3	λ	λ	X
ejpam-5730	269	4	1	1	NUM
ejpam-5730	269	5	1−γ	1−γ	NUM
ejpam-5730	269	6	<	<	X
ejpam-5730	269	7	1	1	NUM
ejpam-5730	269	8	and	and	CCONJ
ejpam-5730	269	9	0	0	NUM
ejpam-5730	269	10	<	<	X
ejpam-5730	269	11	λq	λq	INTJ
ejpam-5730	269	12	:	:	PUNCT
ejpam-5730	269	13	=	=	SYM
ejpam-5730	269	14	λ	λ	X
ejpam-5730	269	15	1	1	NUM
ejpam-5730	269	16	α+β	α+β	PROPN
ejpam-5730	269	17	<	<	X
ejpam-5730	269	18	1	1	NUM
ejpam-5730	269	19	.	.	PUNCT
ejpam-5730	269	20	consequently	consequently	ADV
ejpam-5730	269	21	,	,	PUNCT
ejpam-5730	269	22	theorems	theorems	PROPN
ejpam-5730	269	23	p	p	NOUN
ejpam-5730	269	24	and	and	CCONJ
ejpam-5730	269	25	h(γ1	h(γ1	NOUN
ejpam-5730	269	26	)	)	PUNCT
ejpam-5730	269	27	can	can	AUX
ejpam-5730	269	28	be	be	AUX
ejpam-5730	269	29	applied	apply	VERB
ejpam-5730	269	30	to	to	ADP
ejpam-5730	269	31	such	such	ADJ
ejpam-5730	269	32	two	two	NUM
ejpam-5730	269	33	examples	example	NOUN
ejpam-5730	269	34	on	on	ADP
ejpam-5730	269	35	t	t	PROPN
ejpam-5730	269	36	orbitally	orbitally	ADV
ejpam-5730	269	37	complete	complete	VERB
ejpam-5730	269	38	quasi	quasi	ADJ
ejpam-5730	269	39	-	-	ADJ
ejpam-5730	269	40	metric	metric	ADJ
ejpam-5730	269	41	spaces	space	NOUN
ejpam-5730	269	42	.	.	PUNCT
ejpam-5730	270	1	karapinar	karapinar	VERB
ejpam-5730	271	1	[	[	X
ejpam-5730	271	2	19	19	NUM
ejpam-5730	271	3	]	]	PUNCT
ejpam-5730	271	4	in	in	ADP
ejpam-5730	271	5	2019	2019	NUM
ejpam-5730	271	6	the	the	DET
ejpam-5730	271	7	author	author	NOUN
ejpam-5730	271	8	collect	collect	VERB
ejpam-5730	271	9	and	and	CCONJ
ejpam-5730	271	10	combine	combine	VERB
ejpam-5730	271	11	several	several	ADJ
ejpam-5730	271	12	non	non	ADJ
ejpam-5730	271	13	-	-	ADJ
ejpam-5730	271	14	unique	unique	ADJ
ejpam-5730	271	15	fixed	fix	VERB
ejpam-5730	271	16	point	point	NOUN
ejpam-5730	271	17	results	result	NOUN
ejpam-5730	271	18	in	in	ADP
ejpam-5730	271	19	the	the	DET
ejpam-5730	271	20	context	context	NOUN
ejpam-5730	271	21	of	of	ADP
ejpam-5730	271	22	several	several	ADJ
ejpam-5730	271	23	distinct	distinct	ADJ
ejpam-5730	271	24	abstract	abstract	ADJ
ejpam-5730	271	25	spaces	space	NOUN
ejpam-5730	271	26	.	.	PUNCT
ejpam-5730	272	1	the	the	DET
ejpam-5730	272	2	main	main	ADJ
ejpam-5730	272	3	goal	goal	NOUN
ejpam-5730	272	4	is	be	AUX
ejpam-5730	272	5	to	to	PART
ejpam-5730	272	6	give	give	VERB
ejpam-5730	272	7	a	a	DET
ejpam-5730	272	8	brief	brief	ADJ
ejpam-5730	272	9	background	background	NOUN
ejpam-5730	272	10	on	on	ADP
ejpam-5730	272	11	the	the	DET
ejpam-5730	272	12	topic	topic	NOUN
ejpam-5730	272	13	as	as	ADV
ejpam-5730	272	14	well	well	ADV
ejpam-5730	272	15	as	as	ADP
ejpam-5730	272	16	the	the	PRON
ejpam-5730	272	17	to	to	PART
ejpam-5730	272	18	underline	underline	VERB
ejpam-5730	272	19	the	the	DET
ejpam-5730	272	20	importance	importance	NOUN
ejpam-5730	272	21	of	of	ADP
ejpam-5730	272	22	the	the	DET
ejpam-5730	272	23	non	non	ADJ
ejpam-5730	272	24	-	-	ADJ
ejpam-5730	272	25	unique	unique	ADJ
ejpam-5730	272	26	fixed	fix	VERB
ejpam-5730	272	27	points	point	NOUN
ejpam-5730	272	28	.	.	PUNCT
ejpam-5730	273	1	by	by	ADP
ejpam-5730	273	2	using	use	VERB
ejpam-5730	273	3	the	the	DET
ejpam-5730	273	4	auxiliary	auxiliary	ADJ
ejpam-5730	273	5	functions	function	NOUN
ejpam-5730	273	6	,	,	PUNCT
ejpam-5730	273	7	some	some	PRON
ejpam-5730	273	8	of	of	ADP
ejpam-5730	273	9	the	the	DET
ejpam-5730	273	10	given	give	VERB
ejpam-5730	273	11	results	result	NOUN
ejpam-5730	273	12	are	be	AUX
ejpam-5730	273	13	reformulated	reformulate	VERB
ejpam-5730	273	14	in	in	ADP
ejpam-5730	273	15	a	a	DET
ejpam-5730	273	16	more	more	ADV
ejpam-5730	273	17	general	general	ADJ
ejpam-5730	273	18	form	form	NOUN
ejpam-5730	273	19	to	to	PART
ejpam-5730	273	20	cover	cover	VERB
ejpam-5730	273	21	the	the	DET
ejpam-5730	273	22	existing	exist	VERB
ejpam-5730	273	23	results	result	NOUN
ejpam-5730	273	24	on	on	ADP
ejpam-5730	273	25	the	the	DET
ejpam-5730	273	26	topic	topic	NOUN
ejpam-5730	273	27	in	in	ADP
ejpam-5730	273	28	the	the	DET
ejpam-5730	273	29	literature	literature	NOUN
ejpam-5730	273	30	.	.	PUNCT
ejpam-5730	274	1	given	give	VERB
ejpam-5730	274	2	nonunique	nonunique	ADJ
ejpam-5730	274	3	fixed	fix	VERB
ejpam-5730	274	4	point	point	NOUN
ejpam-5730	274	5	theorems	theorem	NOUN
ejpam-5730	274	6	are	be	AUX
ejpam-5730	274	7	due	due	ADJ
ejpam-5730	274	8	to	to	ADP
ejpam-5730	274	9	ćirić	ćirić	PROPN
ejpam-5730	274	10	(	(	PUNCT
ejpam-5730	274	11	1974	1974	NUM
ejpam-5730	274	12	)	)	PUNCT
ejpam-5730	274	13	,	,	PUNCT
ejpam-5730	274	14	achari	achari	X
ejpam-5730	274	15	(	(	PUNCT
ejpam-5730	274	16	1976	1976	NUM
ejpam-5730	274	17	)	)	PUNCT
ejpam-5730	274	18	,	,	PUNCT
ejpam-5730	274	19	pachpatte	pachpatte	NOUN
ejpam-5730	274	20	(	(	PUNCT
ejpam-5730	274	21	1979	1979	NUM
ejpam-5730	274	22	)	)	PUNCT
ejpam-5730	274	23	,	,	PUNCT
ejpam-5730	274	24	ćirić-jotić	ćirić-jotić	PROPN
ejpam-5730	274	25	(	(	PUNCT
ejpam-5730	274	26	1998	1998	NUM
ejpam-5730	274	27	)	)	PUNCT
ejpam-5730	274	28	,	,	PUNCT
ejpam-5730	274	29	and	and	CCONJ
ejpam-5730	274	30	karapinar	karapinar	VERB
ejpam-5730	274	31	[	[	X
ejpam-5730	274	32	19	19	NUM
ejpam-5730	274	33	]	]	PUNCT
ejpam-5730	274	34	in	in	ADP
ejpam-5730	274	35	2019	2019	NUM
ejpam-5730	274	36	.	.	PUNCT
ejpam-5730	275	1	for	for	ADP
ejpam-5730	275	2	example	example	NOUN
ejpam-5730	275	3	,	,	PUNCT
ejpam-5730	275	4	theorem	theorem	VERB
ejpam-5730	275	5	6.17	6.17	NUM
ejpam-5730	275	6	.	.	PUNCT
ejpam-5730	276	1	(	(	PUNCT
ejpam-5730	276	2	karapinar	karapinar	PROPN
ejpam-5730	276	3	)	)	PUNCT
ejpam-5730	276	4	let	let	VERB
ejpam-5730	276	5	t	t	NOUN
ejpam-5730	276	6	:	:	PUNCT
ejpam-5730	276	7	x	x	X
ejpam-5730	276	8	→	→	PUNCT
ejpam-5730	276	9	x	x	PUNCT
ejpam-5730	276	10	be	be	AUX
ejpam-5730	276	11	an	an	DET
ejpam-5730	276	12	orbitally	orbitally	ADV
ejpam-5730	276	13	continuous	continuous	ADJ
ejpam-5730	276	14	self	self	NOUN
ejpam-5730	276	15	-	-	PUNCT
ejpam-5730	276	16	map	map	NOUN
ejpam-5730	276	17	on	on	ADP
ejpam-5730	276	18	the	the	DET
ejpam-5730	276	19	t	t	PROPN
ejpam-5730	276	20	-orbitally	-orbitally	PROPN
ejpam-5730	276	21	complete	complete	ADJ
ejpam-5730	276	22	metric	metric	ADJ
ejpam-5730	276	23	space	space	NOUN
ejpam-5730	276	24	(	(	PUNCT
ejpam-5730	276	25	x	x	X
ejpam-5730	276	26	,	,	PUNCT
ejpam-5730	276	27	d	d	NOUN
ejpam-5730	276	28	)	)	PUNCT
ejpam-5730	276	29	.	.	PUNCT
ejpam-5730	277	1	suppose	suppose	VERB
ejpam-5730	277	2	there	there	PRON
ejpam-5730	277	3	exist	exist	VERB
ejpam-5730	277	4	real	real	ADJ
ejpam-5730	277	5	numbers	number	NOUN
ejpam-5730	277	6	a1	a1	PROPN
ejpam-5730	277	7	,	,	PUNCT
ejpam-5730	277	8	a2	a2	PROPN
ejpam-5730	277	9	,	,	PUNCT
ejpam-5730	277	10	a3	a3	NOUN
ejpam-5730	277	11	,	,	PUNCT
ejpam-5730	277	12	a4	a4	PROPN
ejpam-5730	277	13	,	,	PUNCT
ejpam-5730	277	14	a5	a5	PROPN
ejpam-5730	277	15	and	and	CCONJ
ejpam-5730	277	16	a	a	DET
ejpam-5730	277	17	self	self	NOUN
ejpam-5730	277	18	mapping	mapping	NOUN
ejpam-5730	277	19	t	t	NOUN
ejpam-5730	277	20	:	:	PUNCT
ejpam-5730	277	21	x	x	X
ejpam-5730	277	22	→	→	PUNCT
ejpam-5730	277	23	x	x	X
ejpam-5730	277	24	which	which	PRON
ejpam-5730	277	25	satisfies	satisfy	VERB
ejpam-5730	277	26	e(x	e(x	NUM
ejpam-5730	277	27	,	,	PUNCT
ejpam-5730	277	28	y	y	NOUN
ejpam-5730	277	29	)	)	PUNCT
ejpam-5730	277	30	≤	≤	NOUN
ejpam-5730	277	31	a4d(x	a4d(x	PROPN
ejpam-5730	277	32	,	,	PUNCT
ejpam-5730	277	33	y	y	NOUN
ejpam-5730	277	34	)	)	PUNCT
ejpam-5730	278	1	+	+	CCONJ
ejpam-5730	278	2	a5d(x	a5d(x	NOUN
ejpam-5730	278	3	,	,	PUNCT
ejpam-5730	278	4	t	t	PROPN
ejpam-5730	278	5	2x	2x	NUM
ejpam-5730	278	6	)	)	PUNCT
ejpam-5730	278	7	,	,	PUNCT
ejpam-5730	278	8	where	where	SCONJ
ejpam-5730	278	9	e(x	e(x	NUM
ejpam-5730	278	10	,	,	PUNCT
ejpam-5730	278	11	y	y	NOUN
ejpam-5730	278	12	)	)	PUNCT
ejpam-5730	278	13	:	:	PUNCT
ejpam-5730	278	14	=	=	SYM
ejpam-5730	278	15	a1d(tx	a1d(tx	VERB
ejpam-5730	278	16	,	,	PUNCT
ejpam-5730	278	17	ty	ty	NOUN
ejpam-5730	278	18	)	)	PUNCT
ejpam-5730	278	19	+	+	CCONJ
ejpam-5730	278	20	a2[d(x	a2[d(x	ADJ
ejpam-5730	278	21	,	,	PUNCT
ejpam-5730	278	22	tx	tx	PROPN
ejpam-5730	278	23	)	)	PUNCT
ejpam-5730	279	1	+	+	CCONJ
ejpam-5730	279	2	d(y	d(y	PROPN
ejpam-5730	279	3	,	,	PUNCT
ejpam-5730	279	4	ty	ty	NOUN
ejpam-5730	279	5	)	)	PUNCT
ejpam-5730	279	6	]	]	PUNCT
ejpam-5730	280	1	+	+	CCONJ
ejpam-5730	280	2	a3[d(y	a3[d(y	PROPN
ejpam-5730	280	3	,	,	PUNCT
ejpam-5730	280	4	tx	tx	PROPN
ejpam-5730	280	5	)	)	PUNCT
ejpam-5730	281	1	+	+	CCONJ
ejpam-5730	281	2	d(x	d(x	PROPN
ejpam-5730	281	3	,	,	PUNCT
ejpam-5730	281	4	ty	ty	NOUN
ejpam-5730	281	5	)	)	PUNCT
ejpam-5730	281	6	]	]	PUNCT
ejpam-5730	281	7	,	,	PUNCT
ejpam-5730	281	8	s.	s.	PROPN
ejpam-5730	281	9	park	park	PROPN
ejpam-5730	281	10	/	/	SYM
ejpam-5730	281	11	eur	eur	PROPN
ejpam-5730	281	12	.	.	PUNCT
ejpam-5730	282	1	j.	j.	PROPN
ejpam-5730	282	2	pure	pure	PROPN
ejpam-5730	282	3	appl	appl	PROPN
ejpam-5730	282	4	.	.	PROPN
ejpam-5730	282	5	math	math	PROPN
ejpam-5730	282	6	,	,	PUNCT
ejpam-5730	282	7	18	18	NUM
ejpam-5730	282	8	(	(	PUNCT
ejpam-5730	282	9	1	1	NUM
ejpam-5730	282	10	)	)	PUNCT
ejpam-5730	282	11	(	(	PUNCT
ejpam-5730	282	12	2025	2025	NUM
ejpam-5730	282	13	)	)	PUNCT
ejpam-5730	282	14	,	,	PUNCT
ejpam-5730	282	15	5730	5730	NUM
ejpam-5730	282	16	12	12	NUM
ejpam-5730	282	17	of	of	ADP
ejpam-5730	282	18	21	21	NUM
ejpam-5730	282	19	for	for	ADP
ejpam-5730	282	20	all	all	DET
ejpam-5730	282	21	x	x	NOUN
ejpam-5730	282	22	,	,	PUNCT
ejpam-5730	282	23	y	y	PROPN
ejpam-5730	282	24	∈	∈	PROPN
ejpam-5730	282	25	x.	x.	NOUN
ejpam-5730	283	1	then	then	ADV
ejpam-5730	283	2	,	,	PUNCT
ejpam-5730	283	3	t	t	PROPN
ejpam-5730	283	4	has	have	VERB
ejpam-5730	283	5	at	at	ADV
ejpam-5730	283	6	least	least	ADV
ejpam-5730	283	7	one	one	NUM
ejpam-5730	283	8	fixed	fix	VERB
ejpam-5730	283	9	point	point	NOUN
ejpam-5730	283	10	.	.	PUNCT
ejpam-5730	284	1	comment	comment	NOUN
ejpam-5730	284	2	:	:	PUNCT
ejpam-5730	284	3	here	here	ADV
ejpam-5730	284	4	{	{	PUNCT
ejpam-5730	284	5	ai}5i=1	ai}5i=1	PROPN
ejpam-5730	284	6	are	be	AUX
ejpam-5730	284	7	chosen	choose	VERB
ejpam-5730	284	8	to	to	PART
ejpam-5730	284	9	hold	hold	VERB
ejpam-5730	284	10	the	the	DET
ejpam-5730	284	11	rhr	rhr	PROPN
ejpam-5730	284	12	condition	condition	NOUN
ejpam-5730	284	13	d(tx	d(tx	PROPN
ejpam-5730	284	14	,	,	PUNCT
ejpam-5730	284	15	t	t	PROPN
ejpam-5730	284	16	2x	2x	NUM
ejpam-5730	284	17	)	)	PUNCT
ejpam-5730	285	1	≤	≤	NUM
ejpam-5730	285	2	r	r	NOUN
ejpam-5730	285	3	d(x	d(x	NOUN
ejpam-5730	285	4	,	,	PUNCT
ejpam-5730	285	5	tx	tx	PROPN
ejpam-5730	285	6	)	)	PUNCT
ejpam-5730	285	7	with	with	ADP
ejpam-5730	285	8	r	r	NOUN
ejpam-5730	285	9	∈	∈	PROPN
ejpam-5730	286	1	[	[	X
ejpam-5730	286	2	0	0	NUM
ejpam-5730	286	3	,	,	PUNCT
ejpam-5730	286	4	1	1	NUM
ejpam-5730	286	5	)	)	PUNCT
ejpam-5730	286	6	for	for	ADP
ejpam-5730	286	7	all	all	DET
ejpam-5730	286	8	x	x	SYM
ejpam-5730	286	9	∈	∈	PROPN
ejpam-5730	286	10	x.	x.	NOUN
ejpam-5730	286	11	note	note	NOUN
ejpam-5730	286	12	that	that	SCONJ
ejpam-5730	286	13	theorem	theorem	VERB
ejpam-5730	286	14	6.17	6.17	NUM
ejpam-5730	286	15	holds	hold	NOUN
ejpam-5730	286	16	for	for	ADP
ejpam-5730	286	17	quasi	quasi	ADJ
ejpam-5730	286	18	-	-	ADJ
ejpam-5730	286	19	metric	metric	ADJ
ejpam-5730	286	20	spaces	space	NOUN
ejpam-5730	286	21	,	,	PUNCT
ejpam-5730	286	22	and	and	CCONJ
ejpam-5730	286	23	theorems	theorem	NOUN
ejpam-5730	286	24	p	p	NOUN
ejpam-5730	286	25	and	and	CCONJ
ejpam-5730	286	26	h(γ1	h(γ1	NOUN
ejpam-5730	286	27	)	)	PUNCT
ejpam-5730	286	28	can	can	AUX
ejpam-5730	286	29	be	be	AUX
ejpam-5730	286	30	applied	apply	VERB
ejpam-5730	286	31	.	.	PUNCT
ejpam-5730	287	1	for	for	ADP
ejpam-5730	287	2	some	some	DET
ejpam-5730	287	3	related	relate	VERB
ejpam-5730	287	4	results	result	NOUN
ejpam-5730	287	5	,	,	PUNCT
ejpam-5730	287	6	see	see	VERB
ejpam-5730	287	7	[	[	X
ejpam-5730	287	8	20	20	NUM
ejpam-5730	287	9	]	]	PUNCT
ejpam-5730	287	10	,	,	PUNCT
ejpam-5730	287	11	[	[	X
ejpam-5730	287	12	21	21	NUM
ejpam-5730	287	13	]	]	PUNCT
ejpam-5730	287	14	.	.	PUNCT
ejpam-5730	288	1	miñana	miñana	PROPN
ejpam-5730	288	2	and	and	CCONJ
ejpam-5730	288	3	valero	valero	PROPN
ejpam-5730	289	1	[	[	X
ejpam-5730	289	2	27	27	NUM
ejpam-5730	289	3	]	]	PUNCT
ejpam-5730	289	4	in	in	ADP
ejpam-5730	289	5	2019	2019	NUM
ejpam-5730	289	6	many	many	ADJ
ejpam-5730	289	7	g	g	NOUN
ejpam-5730	289	8	-	-	PUNCT
ejpam-5730	289	9	metric	metric	ADJ
ejpam-5730	289	10	fixed	fix	VERB
ejpam-5730	289	11	point	point	NOUN
ejpam-5730	289	12	results	result	NOUN
ejpam-5730	289	13	can	can	AUX
ejpam-5730	289	14	be	be	AUX
ejpam-5730	289	15	retrieved	retrieve	VERB
ejpam-5730	289	16	from	from	ADP
ejpam-5730	289	17	classical	classical	ADJ
ejpam-5730	289	18	ones	one	NOUN
ejpam-5730	289	19	given	give	VERB
ejpam-5730	289	20	in	in	ADP
ejpam-5730	289	21	the	the	DET
ejpam-5730	289	22	(	(	PUNCT
ejpam-5730	289	23	quasi-)metric	quasi-)metric	ADJ
ejpam-5730	289	24	framework	framework	NOUN
ejpam-5730	289	25	.	.	PUNCT
ejpam-5730	290	1	indeed	indeed	ADV
ejpam-5730	290	2	,	,	PUNCT
ejpam-5730	290	3	many	many	ADJ
ejpam-5730	290	4	g	g	NOUN
ejpam-5730	290	5	-	-	PUNCT
ejpam-5730	290	6	contractive	contractive	ADJ
ejpam-5730	290	7	conditions	condition	NOUN
ejpam-5730	290	8	can	can	AUX
ejpam-5730	290	9	be	be	AUX
ejpam-5730	290	10	reduced	reduce	VERB
ejpam-5730	290	11	to	to	ADP
ejpam-5730	290	12	a	a	DET
ejpam-5730	290	13	quasi	quasi	ADJ
ejpam-5730	290	14	-	-	ADJ
ejpam-5730	290	15	metric	metric	ADJ
ejpam-5730	290	16	counterpart	counterpart	NOUN
ejpam-5730	290	17	assumed	assume	VERB
ejpam-5730	290	18	in	in	ADP
ejpam-5730	290	19	the	the	DET
ejpam-5730	290	20	statement	statement	NOUN
ejpam-5730	290	21	of	of	ADP
ejpam-5730	290	22	celebrated	celebrated	ADJ
ejpam-5730	290	23	fixed	fix	VERB
ejpam-5730	290	24	point	point	NOUN
ejpam-5730	290	25	results	result	NOUN
ejpam-5730	290	26	.	.	PUNCT
ejpam-5730	291	1	in	in	ADP
ejpam-5730	291	2	this	this	DET
ejpam-5730	291	3	paper	paper	NOUN
ejpam-5730	291	4	,	,	PUNCT
ejpam-5730	291	5	we	we	PRON
ejpam-5730	291	6	show	show	VERB
ejpam-5730	291	7	that	that	SCONJ
ejpam-5730	291	8	the	the	DET
ejpam-5730	291	9	existence	existence	NOUN
ejpam-5730	291	10	of	of	ADP
ejpam-5730	291	11	fixed	fix	VERB
ejpam-5730	291	12	points	point	NOUN
ejpam-5730	291	13	for	for	ADP
ejpam-5730	291	14	the	the	DET
ejpam-5730	291	15	most	most	ADJ
ejpam-5730	291	16	part	part	NOUN
ejpam-5730	291	17	in	in	ADP
ejpam-5730	291	18	the	the	DET
ejpam-5730	291	19	aforesaid	aforesaid	NOUN
ejpam-5730	291	20	g	g	NOUN
ejpam-5730	291	21	-	-	PUNCT
ejpam-5730	291	22	metric	metric	ADJ
ejpam-5730	291	23	fixed	fix	VERB
ejpam-5730	291	24	point	point	NOUN
ejpam-5730	291	25	results	result	NOUN
ejpam-5730	291	26	is	be	AUX
ejpam-5730	291	27	guaranteed	guarantee	VERB
ejpam-5730	291	28	by	by	ADP
ejpam-5730	291	29	a	a	DET
ejpam-5730	291	30	very	very	ADV
ejpam-5730	291	31	general	general	ADJ
ejpam-5730	291	32	celebrated	celebrate	VERB
ejpam-5730	291	33	result	result	NOUN
ejpam-5730	291	34	by	by	ADP
ejpam-5730	291	35	park	park	NOUN
ejpam-5730	291	36	,	,	PUNCT
ejpam-5730	291	37	even	even	ADV
ejpam-5730	291	38	when	when	SCONJ
ejpam-5730	291	39	the	the	DET
ejpam-5730	291	40	g	g	NOUN
ejpam-5730	291	41	-	-	PUNCT
ejpam-5730	291	42	contractive	contractive	ADJ
ejpam-5730	291	43	condition	condition	NOUN
ejpam-5730	291	44	is	be	AUX
ejpam-5730	291	45	reduced	reduce	VERB
ejpam-5730	291	46	to	to	ADP
ejpam-5730	291	47	a	a	DET
ejpam-5730	291	48	quasi	quasi	ADJ
ejpam-5730	291	49	-	-	ADJ
ejpam-5730	291	50	metric	metric	ADJ
ejpam-5730	291	51	one	one	NOUN
ejpam-5730	291	52	which	which	PRON
ejpam-5730	291	53	is	be	AUX
ejpam-5730	291	54	not	not	PART
ejpam-5730	291	55	considered	consider	VERB
ejpam-5730	291	56	as	as	ADP
ejpam-5730	291	57	a	a	DET
ejpam-5730	291	58	contractive	contractive	ADJ
ejpam-5730	291	59	condition	condition	NOUN
ejpam-5730	291	60	in	in	ADP
ejpam-5730	291	61	any	any	DET
ejpam-5730	291	62	celebrated	celebrated	ADJ
ejpam-5730	291	63	fixed	fix	VERB
ejpam-5730	291	64	point	point	NOUN
ejpam-5730	291	65	result	result	NOUN
ejpam-5730	291	66	.	.	PUNCT
ejpam-5730	292	1	moreover	moreover	ADV
ejpam-5730	292	2	,	,	PUNCT
ejpam-5730	292	3	in	in	ADP
ejpam-5730	292	4	all	all	DET
ejpam-5730	292	5	those	those	DET
ejpam-5730	292	6	cases	case	NOUN
ejpam-5730	292	7	in	in	ADP
ejpam-5730	292	8	which	which	PRON
ejpam-5730	292	9	a	a	DET
ejpam-5730	292	10	quasi	quasi	ADJ
ejpam-5730	292	11	-	-	ADJ
ejpam-5730	292	12	metric	metric	ADJ
ejpam-5730	292	13	contractivity	contractivity	NOUN
ejpam-5730	292	14	can	can	AUX
ejpam-5730	292	15	be	be	AUX
ejpam-5730	292	16	raised	raise	VERB
ejpam-5730	292	17	,	,	PUNCT
ejpam-5730	292	18	we	we	PRON
ejpam-5730	292	19	show	show	VERB
ejpam-5730	292	20	that	that	SCONJ
ejpam-5730	292	21	the	the	DET
ejpam-5730	292	22	uniqueness	uniqueness	NOUN
ejpam-5730	292	23	of	of	ADP
ejpam-5730	292	24	the	the	DET
ejpam-5730	292	25	fixed	fix	VERB
ejpam-5730	292	26	point	point	NOUN
ejpam-5730	292	27	is	be	AUX
ejpam-5730	292	28	also	also	ADV
ejpam-5730	292	29	derived	derive	VERB
ejpam-5730	292	30	from	from	ADP
ejpam-5730	292	31	it	it	PRON
ejpam-5730	292	32	.	.	PUNCT
ejpam-5730	292	33	·	·	PUNCT
ejpam-5730	292	34	·	·	PUNCT
ejpam-5730	293	1	·	·	PUNCT
ejpam-5730	294	1	we	we	PRON
ejpam-5730	294	2	are	be	AUX
ejpam-5730	294	3	able	able	ADJ
ejpam-5730	294	4	to	to	PART
ejpam-5730	294	5	show	show	VERB
ejpam-5730	294	6	that	that	SCONJ
ejpam-5730	294	7	most	most	ADJ
ejpam-5730	294	8	fixed	fix	VERB
ejpam-5730	294	9	point	point	NOUN
ejpam-5730	294	10	results	result	NOUN
ejpam-5730	294	11	obtained	obtain	VERB
ejpam-5730	294	12	in	in	ADP
ejpam-5730	294	13	g	g	NOUN
ejpam-5730	294	14	-	-	PUNCT
ejpam-5730	294	15	metric	metric	ADJ
ejpam-5730	294	16	spaces	space	NOUN
ejpam-5730	294	17	can	can	AUX
ejpam-5730	294	18	be	be	AUX
ejpam-5730	294	19	deduced	deduce	VERB
ejpam-5730	294	20	from	from	ADP
ejpam-5730	294	21	a	a	DET
ejpam-5730	294	22	fixed	fix	VERB
ejpam-5730	294	23	point	point	NOUN
ejpam-5730	294	24	result	result	NOUN
ejpam-5730	294	25	stated	state	VERB
ejpam-5730	294	26	in	in	ADP
ejpam-5730	294	27	quasi	quasi	ADJ
ejpam-5730	294	28	-	-	ADJ
ejpam-5730	294	29	metric	metric	ADJ
ejpam-5730	294	30	spaces	space	NOUN
ejpam-5730	294	31	obtained	obtain	VERB
ejpam-5730	294	32	by	by	ADP
ejpam-5730	294	33	park	park	NOUN
ejpam-5730	294	34	in	in	ADP
ejpam-5730	294	35	[	[	X
ejpam-5730	294	36	29	29	NUM
ejpam-5730	294	37	]	]	PUNCT
ejpam-5730	294	38	.	.	PUNCT
ejpam-5730	295	1	to	to	ADP
ejpam-5730	295	2	this	this	DET
ejpam-5730	295	3	end	end	NOUN
ejpam-5730	295	4	,	,	PUNCT
ejpam-5730	295	5	let	let	VERB
ejpam-5730	295	6	us	we	PRON
ejpam-5730	295	7	recall	recall	VERB
ejpam-5730	295	8	such	such	DET
ejpam-5730	295	9	a	a	DET
ejpam-5730	295	10	result	result	NOUN
ejpam-5730	295	11	.	.	PUNCT
ejpam-5730	296	1	theorem	theorem	NOUN
ejpam-5730	296	2	6.18	6.18	NUM
ejpam-5730	296	3	.	.	PUNCT
ejpam-5730	297	1	(	(	PUNCT
ejpam-5730	297	2	miñana	miñana	PROPN
ejpam-5730	297	3	-	-	PUNCT
ejpam-5730	297	4	valero	valero	NOUN
ejpam-5730	297	5	)	)	PUNCT
ejpam-5730	297	6	let	let	VERB
ejpam-5730	297	7	(	(	PUNCT
ejpam-5730	297	8	x	x	NOUN
ejpam-5730	297	9	,	,	PUNCT
ejpam-5730	297	10	τ	τ	X
ejpam-5730	297	11	)	)	PUNCT
ejpam-5730	297	12	be	be	VERB
ejpam-5730	297	13	a	a	DET
ejpam-5730	297	14	topological	topological	ADJ
ejpam-5730	297	15	space	space	NOUN
ejpam-5730	297	16	,	,	PUNCT
ejpam-5730	297	17	let	let	VERB
ejpam-5730	297	18	d	d	NOUN
ejpam-5730	297	19	:	:	PUNCT
ejpam-5730	297	20	x×x	x×x	PROPN
ejpam-5730	297	21	→	→	PUNCT
ejpam-5730	298	1	[	[	X
ejpam-5730	298	2	0	0	NUM
ejpam-5730	298	3	,	,	PUNCT
ejpam-5730	298	4	!	!	PUNCT
ejpam-5730	298	5	‘	'	PUNCT
ejpam-5730	298	6	ä	ä	PRON
ejpam-5730	298	7	[	[	PUNCT
ejpam-5730	298	8	be	be	AUX
ejpam-5730	298	9	a	a	DET
ejpam-5730	298	10	continuous	continuous	ADJ
ejpam-5730	298	11	map	map	NOUN
ejpam-5730	298	12	,	,	PUNCT
ejpam-5730	298	13	such	such	ADJ
ejpam-5730	298	14	that	that	SCONJ
ejpam-5730	298	15	d(x	d(x	PROPN
ejpam-5730	298	16	,	,	PUNCT
ejpam-5730	298	17	y	y	NOUN
ejpam-5730	298	18	)	)	PUNCT
ejpam-5730	299	1	=	=	SYM
ejpam-5730	299	2	0	0	NUM
ejpam-5730	299	3	⇐	⇐	ADJ
ejpam-5730	299	4	⇒	⇒	NOUN
ejpam-5730	299	5	x	x	PUNCT
ejpam-5730	299	6	=	=	SYM
ejpam-5730	299	7	y	y	PROPN
ejpam-5730	299	8	,	,	PUNCT
ejpam-5730	299	9	and	and	CCONJ
ejpam-5730	299	10	let	let	VERB
ejpam-5730	299	11	f	f	PRON
ejpam-5730	299	12	:	:	PUNCT
ejpam-5730	299	13	x	x	X
ejpam-5730	299	14	→	→	PUNCT
ejpam-5730	299	15	x	x	PUNCT
ejpam-5730	299	16	be	be	AUX
ejpam-5730	299	17	a	a	DET
ejpam-5730	299	18	map	map	NOUN
ejpam-5730	299	19	.	.	PUNCT
ejpam-5730	299	20	suppose	suppose	VERB
ejpam-5730	299	21	that	that	SCONJ
ejpam-5730	299	22	there	there	PRON
ejpam-5730	299	23	exist	exist	VERB
ejpam-5730	299	24	x	x	NOUN
ejpam-5730	299	25	,	,	PUNCT
ejpam-5730	299	26	x0	x0	PROPN
ejpam-5730	299	27	∈	∈	PROPN
ejpam-5730	300	1	x	x	NOUN
ejpam-5730	300	2	,	,	PUNCT
ejpam-5730	300	3	such	such	ADJ
ejpam-5730	300	4	that	that	SCONJ
ejpam-5730	300	5	the	the	DET
ejpam-5730	300	6	following	follow	VERB
ejpam-5730	300	7	conditions	condition	NOUN
ejpam-5730	300	8	hold	hold	VERB
ejpam-5730	300	9	:	:	PUNCT
ejpam-5730	300	10	1	1	X
ejpam-5730	300	11	.	.	X
ejpam-5730	300	12	limn→∞	limn→∞	PROPN
ejpam-5730	300	13	d(fn(x0	d(fn(x0	PROPN
ejpam-5730	300	14	)	)	PUNCT
ejpam-5730	300	15	,	,	PUNCT
ejpam-5730	300	16	f	f	PROPN
ejpam-5730	300	17	n+1(x0	n+1(x0	ADV
ejpam-5730	300	18	)	)	PUNCT
ejpam-5730	300	19	)	)	PUNCT
ejpam-5730	301	1	=	=	PUNCT
ejpam-5730	301	2	0	0	NUM
ejpam-5730	301	3	;	;	PUNCT
ejpam-5730	301	4	2	2	NUM
ejpam-5730	301	5	.	.	PUNCT
ejpam-5730	301	6	(	(	PUNCT
ejpam-5730	301	7	fn(x0))n∈n	fn(x0))n∈n	X
ejpam-5730	301	8	converges	converge	NOUN
ejpam-5730	301	9	to	to	ADP
ejpam-5730	301	10	x	x	PUNCT
ejpam-5730	301	11	with	with	ADP
ejpam-5730	301	12	respect	respect	NOUN
ejpam-5730	301	13	to	to	ADP
ejpam-5730	301	14	τ	τ	PROPN
ejpam-5730	301	15	;	;	PUNCT
ejpam-5730	301	16	3	3	X
ejpam-5730	301	17	.	.	X
ejpam-5730	301	18	f	f	PROPN
ejpam-5730	301	19	is	be	AUX
ejpam-5730	301	20	orbitally	orbitally	ADV
ejpam-5730	301	21	continuous	continuous	ADJ
ejpam-5730	301	22	at	at	ADP
ejpam-5730	301	23	x	x	SYM
ejpam-5730	301	24	with	with	ADP
ejpam-5730	301	25	respect	respect	NOUN
ejpam-5730	301	26	to	to	ADP
ejpam-5730	301	27	τ	τ	PROPN
ejpam-5730	301	28	.	.	PUNCT
ejpam-5730	302	1	then	then	ADV
ejpam-5730	302	2	x	x	X
ejpam-5730	302	3	∈	∈	PROPN
ejpam-5730	302	4	fix(f	fix(f	PROPN
ejpam-5730	302	5	)	)	PUNCT
ejpam-5730	302	6	=	=	PRON
ejpam-5730	302	7	{	{	PUNCT
ejpam-5730	302	8	y	y	PROPN
ejpam-5730	302	9	∈	∈	PROPN
ejpam-5730	302	10	x	x	X
ejpam-5730	302	11	:	:	PUNCT
ejpam-5730	302	12	f(y	f(y	NOUN
ejpam-5730	302	13	)	)	PUNCT
ejpam-5730	302	14	=	=	SYM
ejpam-5730	303	1	y	y	PROPN
ejpam-5730	303	2	}	}	PUNCT
ejpam-5730	303	3	.	.	PUNCT
ejpam-5730	304	1	it	it	PRON
ejpam-5730	304	2	must	must	AUX
ejpam-5730	304	3	be	be	AUX
ejpam-5730	304	4	stressed	stress	VERB
ejpam-5730	304	5	that	that	SCONJ
ejpam-5730	304	6	park	park	NOUN
ejpam-5730	304	7	’s	’s	PART
ejpam-5730	304	8	original	original	ADJ
ejpam-5730	304	9	version	version	NOUN
ejpam-5730	304	10	of	of	ADP
ejpam-5730	304	11	the	the	DET
ejpam-5730	304	12	preceding	precede	VERB
ejpam-5730	304	13	result	result	NOUN
ejpam-5730	304	14	was	be	AUX
ejpam-5730	304	15	stated	state	VERB
ejpam-5730	304	16	for	for	ADP
ejpam-5730	304	17	lower	low	ADJ
ejpam-5730	304	18	semicontinuous	semicontinuous	ADJ
ejpam-5730	304	19	mappings	mapping	NOUN
ejpam-5730	304	20	d.	d.	PROPN
ejpam-5730	304	21	however	however	ADV
ejpam-5730	304	22	,	,	PUNCT
ejpam-5730	304	23	we	we	PRON
ejpam-5730	304	24	have	have	AUX
ejpam-5730	304	25	focused	focus	VERB
ejpam-5730	304	26	our	our	PRON
ejpam-5730	304	27	attention	attention	NOUN
ejpam-5730	304	28	on	on	ADP
ejpam-5730	304	29	continuous	continuous	ADJ
ejpam-5730	304	30	ones	one	NOUN
ejpam-5730	304	31	,	,	PUNCT
ejpam-5730	304	32	because	because	SCONJ
ejpam-5730	304	33	it	it	PRON
ejpam-5730	304	34	is	be	AUX
ejpam-5730	304	35	enough	enough	ADJ
ejpam-5730	304	36	for	for	ADP
ejpam-5730	304	37	our	our	PRON
ejpam-5730	304	38	announced	announced	ADJ
ejpam-5730	304	39	purpose	purpose	NOUN
ejpam-5730	304	40	.	.	PUNCT
ejpam-5730	305	1	corollary	corollary	ADJ
ejpam-5730	305	2	6.19	6.19	NUM
ejpam-5730	305	3	.	.	PUNCT
ejpam-5730	306	1	(	(	PUNCT
ejpam-5730	306	2	miñana	miñana	PROPN
ejpam-5730	306	3	-	-	PUNCT
ejpam-5730	306	4	valero	valero	NOUN
ejpam-5730	306	5	)	)	PUNCT
ejpam-5730	306	6	let	let	VERB
ejpam-5730	306	7	(	(	PUNCT
ejpam-5730	306	8	x	x	NOUN
ejpam-5730	306	9	,	,	PUNCT
ejpam-5730	306	10	g	g	NOUN
ejpam-5730	306	11	)	)	PUNCT
ejpam-5730	306	12	be	be	AUX
ejpam-5730	306	13	a	a	DET
ejpam-5730	306	14	g	g	NOUN
ejpam-5730	306	15	-	-	PUNCT
ejpam-5730	306	16	metric	metric	ADJ
ejpam-5730	306	17	space	space	NOUN
ejpam-5730	306	18	and	and	CCONJ
ejpam-5730	306	19	let	let	VERB
ejpam-5730	306	20	f	f	NOUN
ejpam-5730	306	21	:	:	PUNCT
ejpam-5730	306	22	x	x	X
ejpam-5730	306	23	→	→	PUNCT
ejpam-5730	306	24	x	x	PUNCT
ejpam-5730	306	25	be	be	AUX
ejpam-5730	306	26	a	a	DET
ejpam-5730	306	27	mapping	mapping	NOUN
ejpam-5730	306	28	.	.	PUNCT
ejpam-5730	307	1	suppose	suppose	VERB
ejpam-5730	307	2	that	that	SCONJ
ejpam-5730	307	3	there	there	PRON
ejpam-5730	307	4	exist	exist	VERB
ejpam-5730	307	5	x	x	NOUN
ejpam-5730	307	6	,	,	PUNCT
ejpam-5730	307	7	x0	x0	PROPN
ejpam-5730	307	8	∈	∈	PROPN
ejpam-5730	308	1	x	x	NOUN
ejpam-5730	308	2	,	,	PUNCT
ejpam-5730	308	3	such	such	ADJ
ejpam-5730	308	4	that	that	SCONJ
ejpam-5730	308	5	the	the	DET
ejpam-5730	308	6	following	follow	VERB
ejpam-5730	308	7	conditions	condition	NOUN
ejpam-5730	308	8	hold	hold	VERB
ejpam-5730	308	9	:	:	PUNCT
ejpam-5730	308	10	1	1	X
ejpam-5730	308	11	.	.	X
ejpam-5730	309	1	limn→∞	limn→∞	PROPN
ejpam-5730	309	2	dg(f	dg(f	X
ejpam-5730	309	3	n(x0	n(x0	NOUN
ejpam-5730	309	4	)	)	PUNCT
ejpam-5730	309	5	,	,	PUNCT
ejpam-5730	309	6	f	f	PROPN
ejpam-5730	309	7	n+1(x0	n+1(x0	ADV
ejpam-5730	309	8	)	)	PUNCT
ejpam-5730	309	9	)	)	PUNCT
ejpam-5730	310	1	=	=	PUNCT
ejpam-5730	310	2	0	0	NUM
ejpam-5730	310	3	;	;	PUNCT
ejpam-5730	310	4	2	2	NUM
ejpam-5730	310	5	.	.	PUNCT
ejpam-5730	310	6	(	(	PUNCT
ejpam-5730	310	7	fn(x0))n∈n	fn(x0))n∈n	X
ejpam-5730	310	8	converges	converge	NOUN
ejpam-5730	310	9	to	to	ADP
ejpam-5730	310	10	x	x	PUNCT
ejpam-5730	310	11	with	with	ADP
ejpam-5730	310	12	respect	respect	NOUN
ejpam-5730	310	13	to	to	ADP
ejpam-5730	310	14	τdg	τdg	NOUN
ejpam-5730	310	15	;	;	PUNCT
ejpam-5730	310	16	3	3	X
ejpam-5730	310	17	.	.	X
ejpam-5730	310	18	f	f	PROPN
ejpam-5730	310	19	is	be	AUX
ejpam-5730	310	20	orbitally	orbitally	ADV
ejpam-5730	310	21	continuous	continuous	ADJ
ejpam-5730	310	22	at	at	ADP
ejpam-5730	310	23	x	x	SYM
ejpam-5730	310	24	with	with	ADP
ejpam-5730	310	25	respect	respect	NOUN
ejpam-5730	310	26	to	to	ADP
ejpam-5730	310	27	τdg	τdg	PROPN
ejpam-5730	310	28	.	.	PUNCT
ejpam-5730	311	1	then	then	ADV
ejpam-5730	311	2	x	x	X
ejpam-5730	311	3	=	=	SYM
ejpam-5730	311	4	f(x	f(x	PROPN
ejpam-5730	311	5	)	)	PUNCT
ejpam-5730	311	6	.	.	PUNCT
ejpam-5730	312	1	moreover	moreover	ADV
ejpam-5730	312	2	,	,	PUNCT
ejpam-5730	312	3	the	the	DET
ejpam-5730	312	4	authors	author	NOUN
ejpam-5730	312	5	have	have	AUX
ejpam-5730	312	6	shown	show	VERB
ejpam-5730	312	7	that	that	SCONJ
ejpam-5730	312	8	the	the	DET
ejpam-5730	312	9	existence	existence	NOUN
ejpam-5730	312	10	of	of	ADP
ejpam-5730	312	11	fixed	fix	VERB
ejpam-5730	312	12	points	point	NOUN
ejpam-5730	312	13	in	in	ADP
ejpam-5730	312	14	many	many	ADJ
ejpam-5730	312	15	of	of	ADP
ejpam-5730	312	16	the	the	DET
ejpam-5730	312	17	aforesaid	aforesaid	NOUN
ejpam-5730	312	18	g	g	NOUN
ejpam-5730	312	19	-	-	PUNCT
ejpam-5730	312	20	metric	metric	ADJ
ejpam-5730	312	21	fixed	fix	VERB
ejpam-5730	312	22	point	point	NOUN
ejpam-5730	312	23	results	result	NOUN
ejpam-5730	312	24	is	be	AUX
ejpam-5730	312	25	a	a	DET
ejpam-5730	312	26	consequence	consequence	NOUN
ejpam-5730	312	27	of	of	ADP
ejpam-5730	312	28	park	park	NOUN
ejpam-5730	312	29	’s	’s	PART
ejpam-5730	312	30	celebrated	celebrate	VERB
ejpam-5730	312	31	result	result	NOUN
ejpam-5730	312	32	,	,	PUNCT
ejpam-5730	312	33	even	even	ADV
ejpam-5730	312	34	when	when	SCONJ
ejpam-5730	312	35	the	the	DET
ejpam-5730	312	36	g	g	NOUN
ejpam-5730	312	37	-	-	PUNCT
ejpam-5730	312	38	contractive	contractive	ADJ
ejpam-5730	312	39	condition	condition	NOUN
ejpam-5730	312	40	is	be	AUX
ejpam-5730	312	41	reduced	reduce	VERB
ejpam-5730	312	42	to	to	ADP
ejpam-5730	312	43	a	a	DET
ejpam-5730	312	44	quasi	quasi	ADJ
ejpam-5730	312	45	-	-	ADJ
ejpam-5730	312	46	metric	metric	ADJ
ejpam-5730	312	47	one	one	NOUN
ejpam-5730	312	48	that	that	PRON
ejpam-5730	312	49	is	be	AUX
ejpam-5730	312	50	not	not	PART
ejpam-5730	312	51	considered	consider	VERB
ejpam-5730	312	52	as	as	ADP
ejpam-5730	312	53	a	a	DET
ejpam-5730	312	54	contractive	contractive	ADJ
ejpam-5730	312	55	condition	condition	NOUN
ejpam-5730	312	56	in	in	ADP
ejpam-5730	312	57	the	the	DET
ejpam-5730	312	58	statement	statement	NOUN
ejpam-5730	312	59	of	of	ADP
ejpam-5730	312	60	any	any	DET
ejpam-5730	312	61	known	know	VERB
ejpam-5730	312	62	fixed	fix	VERB
ejpam-5730	312	63	point	point	NOUN
ejpam-5730	312	64	result	result	NOUN
ejpam-5730	312	65	.	.	PUNCT
ejpam-5730	313	1	s.	s.	PROPN
ejpam-5730	313	2	park	park	PROPN
ejpam-5730	313	3	/	/	SYM
ejpam-5730	313	4	eur	eur	PROPN
ejpam-5730	313	5	.	.	PUNCT
ejpam-5730	314	1	j.	j.	PROPN
ejpam-5730	314	2	pure	pure	PROPN
ejpam-5730	314	3	appl	appl	PROPN
ejpam-5730	314	4	.	.	PROPN
ejpam-5730	314	5	math	math	PROPN
ejpam-5730	314	6	,	,	PUNCT
ejpam-5730	314	7	18	18	NUM
ejpam-5730	314	8	(	(	PUNCT
ejpam-5730	314	9	1	1	NUM
ejpam-5730	314	10	)	)	PUNCT
ejpam-5730	314	11	(	(	PUNCT
ejpam-5730	314	12	2025	2025	NUM
ejpam-5730	314	13	)	)	PUNCT
ejpam-5730	314	14	,	,	PUNCT
ejpam-5730	314	15	5730	5730	NUM
ejpam-5730	314	16	13	13	NUM
ejpam-5730	314	17	of	of	ADP
ejpam-5730	314	18	21	21	NUM
ejpam-5730	314	19	aouine	aouine	ADJ
ejpam-5730	314	20	and	and	CCONJ
ejpam-5730	314	21	aliouche	aliouche	NOUN
ejpam-5730	315	1	[	[	X
ejpam-5730	315	2	3	3	X
ejpam-5730	315	3	]	]	PUNCT
ejpam-5730	315	4	in	in	ADP
ejpam-5730	315	5	2021	2021	NUM
ejpam-5730	315	6	abstract	abstract	NOUN
ejpam-5730	315	7	:	:	PUNCT
ejpam-5730	315	8	we	we	PRON
ejpam-5730	315	9	prove	prove	VERB
ejpam-5730	315	10	unique	unique	ADJ
ejpam-5730	315	11	fixed	fix	VERB
ejpam-5730	315	12	point	point	NOUN
ejpam-5730	315	13	theorems	theorem	NOUN
ejpam-5730	315	14	for	for	ADP
ejpam-5730	315	15	a	a	DET
ejpam-5730	315	16	self	self	NOUN
ejpam-5730	315	17	-	-	PUNCT
ejpam-5730	315	18	mapping	mapping	NOUN
ejpam-5730	315	19	in	in	ADP
ejpam-5730	315	20	complete	complete	ADJ
ejpam-5730	315	21	metric	metric	ADJ
ejpam-5730	315	22	spaces	space	NOUN
ejpam-5730	315	23	and	and	CCONJ
ejpam-5730	315	24	that	that	SCONJ
ejpam-5730	315	25	the	the	DET
ejpam-5730	315	26	fixed	fix	VERB
ejpam-5730	315	27	point	point	NOUN
ejpam-5730	315	28	problem	problem	NOUN
ejpam-5730	315	29	is	be	AUX
ejpam-5730	315	30	well	well	ADV
ejpam-5730	315	31	-	-	PUNCT
ejpam-5730	315	32	posed	pose	VERB
ejpam-5730	315	33	.	.	PUNCT
ejpam-5730	316	1	examples	example	NOUN
ejpam-5730	316	2	are	be	AUX
ejpam-5730	316	3	provided	provide	VERB
ejpam-5730	316	4	to	to	PART
ejpam-5730	316	5	illustrate	illustrate	VERB
ejpam-5730	316	6	the	the	DET
ejpam-5730	316	7	validity	validity	NOUN
ejpam-5730	316	8	of	of	ADP
ejpam-5730	316	9	our	our	PRON
ejpam-5730	316	10	results	result	NOUN
ejpam-5730	316	11	and	and	CCONJ
ejpam-5730	316	12	we	we	PRON
ejpam-5730	316	13	give	give	VERB
ejpam-5730	316	14	some	some	DET
ejpam-5730	316	15	remarks	remark	NOUN
ejpam-5730	316	16	about	about	ADP
ejpam-5730	316	17	three	three	NUM
ejpam-5730	316	18	papers	paper	NOUN
ejpam-5730	316	19	.	.	PUNCT
ejpam-5730	317	1	·	·	PUNCT
ejpam-5730	317	2	·	·	PUNCT
ejpam-5730	317	3	·	·	PUNCT
ejpam-5730	317	4	afterwards	afterwards	ADV
ejpam-5730	317	5	,	,	PUNCT
ejpam-5730	317	6	we	we	PRON
ejpam-5730	317	7	apply	apply	VERB
ejpam-5730	317	8	our	our	PRON
ejpam-5730	317	9	result	result	NOUN
ejpam-5730	317	10	to	to	PART
ejpam-5730	317	11	study	study	VERB
ejpam-5730	317	12	the	the	DET
ejpam-5730	317	13	possibility	possibility	NOUN
ejpam-5730	317	14	of	of	ADP
ejpam-5730	317	15	optimally	optimally	ADV
ejpam-5730	317	16	controlling	control	VERB
ejpam-5730	317	17	the	the	DET
ejpam-5730	317	18	solution	solution	NOUN
ejpam-5730	317	19	of	of	ADP
ejpam-5730	317	20	an	an	DET
ejpam-5730	317	21	ordinary	ordinary	ADJ
ejpam-5730	317	22	di¡×erential	di¡×erential	ADJ
ejpam-5730	317	23	equation	equation	NOUN
ejpam-5730	317	24	via	via	ADP
ejpam-5730	317	25	dynamic	dynamic	ADJ
ejpam-5730	317	26	programming	programming	NOUN
ejpam-5730	317	27	.	.	PUNCT
ejpam-5730	318	1	definition	definition	NOUN
ejpam-5730	318	2	6.20	6.20	NUM
ejpam-5730	318	3	.	.	PUNCT
ejpam-5730	319	1	(	(	PUNCT
ejpam-5730	319	2	reich	reich	NOUN
ejpam-5730	319	3	-	-	PUNCT
ejpam-5730	319	4	zaslavski	zaslavski	PROPN
ejpam-5730	319	5	)	)	PUNCT
ejpam-5730	319	6	let	let	VERB
ejpam-5730	319	7	(	(	PUNCT
ejpam-5730	319	8	x	x	NOUN
ejpam-5730	319	9	,	,	PUNCT
ejpam-5730	319	10	d	d	NOUN
ejpam-5730	319	11	)	)	PUNCT
ejpam-5730	319	12	be	be	AUX
ejpam-5730	319	13	a	a	DET
ejpam-5730	319	14	metric	metric	ADJ
ejpam-5730	319	15	space	space	NOUN
ejpam-5730	319	16	and	and	CCONJ
ejpam-5730	319	17	t	t	NOUN
ejpam-5730	319	18	:	:	PUNCT
ejpam-5730	319	19	x	x	X
ejpam-5730	320	1	→	→	PUNCT
ejpam-5730	320	2	x	x	X
ejpam-5730	320	3	a	a	DET
ejpam-5730	320	4	mapping	mapping	NOUN
ejpam-5730	320	5	.	.	PUNCT
ejpam-5730	321	1	the	the	DET
ejpam-5730	321	2	fixed	fix	VERB
ejpam-5730	321	3	point	point	NOUN
ejpam-5730	321	4	problem	problem	NOUN
ejpam-5730	321	5	of	of	ADP
ejpam-5730	321	6	t	t	PROPN
ejpam-5730	321	7	is	be	AUX
ejpam-5730	321	8	said	say	VERB
ejpam-5730	321	9	to	to	PART
ejpam-5730	321	10	be	be	AUX
ejpam-5730	321	11	well	well	ADV
ejpam-5730	321	12	-	-	PUNCT
ejpam-5730	321	13	posed	pose	VERB
ejpam-5730	321	14	if	if	SCONJ
ejpam-5730	321	15	i	i	PRON
ejpam-5730	321	16	)	)	PUNCT
ejpam-5730	321	17	t	t	PROPN
ejpam-5730	321	18	has	have	VERB
ejpam-5730	321	19	a	a	DET
ejpam-5730	321	20	unique	unique	ADJ
ejpam-5730	321	21	fixed	fix	VERB
ejpam-5730	321	22	point	point	NOUN
ejpam-5730	321	23	z	z	PROPN
ejpam-5730	321	24	in	in	ADP
ejpam-5730	321	25	x	x	PROPN
ejpam-5730	321	26	,	,	PUNCT
ejpam-5730	321	27	ii	ii	NOUN
ejpam-5730	321	28	)	)	PUNCT
ejpam-5730	321	29	for	for	ADP
ejpam-5730	321	30	any	any	DET
ejpam-5730	321	31	sequence	sequence	NOUN
ejpam-5730	321	32	{	{	PUNCT
ejpam-5730	321	33	yn	yn	NOUN
ejpam-5730	321	34	}	}	PUNCT
ejpam-5730	321	35	inx	inx	VERB
ejpam-5730	321	36	such	such	ADJ
ejpam-5730	321	37	that	that	SCONJ
ejpam-5730	321	38	limn→∞	limn→∞	PROPN
ejpam-5730	321	39	d(tyn	d(tyn	PROPN
ejpam-5730	321	40	,	,	PUNCT
ejpam-5730	321	41	yn	yn	PROPN
ejpam-5730	321	42	)	)	PUNCT
ejpam-5730	322	1	=	=	SYM
ejpam-5730	322	2	0	0	NUM
ejpam-5730	322	3	,	,	PUNCT
ejpam-5730	322	4	we	we	PRON
ejpam-5730	322	5	have	have	VERB
ejpam-5730	322	6	limn→∞	limn→∞	PRON
ejpam-5730	322	7	d(yn	d(yn	NOUN
ejpam-5730	322	8	,	,	PUNCT
ejpam-5730	322	9	z	z	NOUN
ejpam-5730	322	10	)	)	PUNCT
ejpam-5730	322	11	=	=	SYM
ejpam-5730	322	12	0	0	X
ejpam-5730	322	13	.	.	PUNCT
ejpam-5730	322	14	theorem	theorem	VERB
ejpam-5730	322	15	6.21	6.21	NUM
ejpam-5730	322	16	.	.	PUNCT
ejpam-5730	323	1	(	(	PUNCT
ejpam-5730	323	2	aouine	aouine	NOUN
ejpam-5730	323	3	-	-	PUNCT
ejpam-5730	323	4	aliouche	aliouche	NOUN
ejpam-5730	323	5	)	)	PUNCT
ejpam-5730	324	1	let	let	VERB
ejpam-5730	324	2	(	(	PUNCT
ejpam-5730	324	3	x	x	NOUN
ejpam-5730	324	4	,	,	PUNCT
ejpam-5730	324	5	d	d	NOUN
ejpam-5730	324	6	)	)	PUNCT
ejpam-5730	324	7	be	be	AUX
ejpam-5730	324	8	a	a	DET
ejpam-5730	324	9	complete	complete	ADJ
ejpam-5730	324	10	metric	metric	ADJ
ejpam-5730	324	11	space	space	NOUN
ejpam-5730	324	12	and	and	CCONJ
ejpam-5730	324	13	t	t	X
ejpam-5730	324	14	a	a	DET
ejpam-5730	324	15	mapping	mapping	NOUN
ejpam-5730	324	16	from	from	ADP
ejpam-5730	324	17	x	x	PUNCT
ejpam-5730	324	18	into	into	ADP
ejpam-5730	324	19	itself	itself	PRON
ejpam-5730	324	20	satisfying	satisfy	VERB
ejpam-5730	324	21	the	the	DET
ejpam-5730	324	22	following	follow	VERB
ejpam-5730	324	23	condition	condition	NOUN
ejpam-5730	324	24	d(tx	d(tx	PROPN
ejpam-5730	324	25	,	,	PUNCT
ejpam-5730	324	26	ty	ty	NOUN
ejpam-5730	324	27	)	)	PUNCT
ejpam-5730	324	28	≤	≤	NOUN
ejpam-5730	324	29	d(x	d(x	NOUN
ejpam-5730	324	30	,	,	PUNCT
ejpam-5730	324	31	ty	ty	INTJ
ejpam-5730	324	32	)	)	PUNCT
ejpam-5730	325	1	+	+	CCONJ
ejpam-5730	325	2	d(y	d(y	PROPN
ejpam-5730	325	3	,	,	PUNCT
ejpam-5730	325	4	tx	tx	PROPN
ejpam-5730	325	5	)	)	PUNCT
ejpam-5730	325	6	d(x	d(x	PROPN
ejpam-5730	325	7	,	,	PUNCT
ejpam-5730	325	8	tx	tx	PROPN
ejpam-5730	325	9	)	)	PUNCT
ejpam-5730	326	1	+	+	CCONJ
ejpam-5730	326	2	d(y	d(y	PROPN
ejpam-5730	326	3	,	,	PUNCT
ejpam-5730	326	4	ty	ty	INTJ
ejpam-5730	326	5	)	)	PUNCT
ejpam-5730	326	6	+	+	CCONJ
ejpam-5730	326	7	1	1	NUM
ejpam-5730	326	8	max{d(x	max{d(x	NOUN
ejpam-5730	326	9	,	,	PUNCT
ejpam-5730	326	10	tx	tx	PROPN
ejpam-5730	326	11	)	)	PUNCT
ejpam-5730	326	12	,	,	PUNCT
ejpam-5730	326	13	d(y	d(y	PROPN
ejpam-5730	326	14	,	,	PUNCT
ejpam-5730	326	15	ty	ty	NOUN
ejpam-5730	326	16	)	)	PUNCT
ejpam-5730	326	17	}	}	PUNCT
ejpam-5730	326	18	for	for	ADP
ejpam-5730	326	19	all	all	DET
ejpam-5730	326	20	x	x	NOUN
ejpam-5730	326	21	,	,	PUNCT
ejpam-5730	326	22	y	y	PROPN
ejpam-5730	326	23	∈	∈	PROPN
ejpam-5730	326	24	x.	x.	NOUN
ejpam-5730	326	25	then	then	ADV
ejpam-5730	326	26	a	a	X
ejpam-5730	326	27	)	)	PUNCT
ejpam-5730	326	28	t	t	PROPN
ejpam-5730	326	29	has	have	VERB
ejpam-5730	326	30	a	a	DET
ejpam-5730	326	31	unique	unique	ADJ
ejpam-5730	326	32	fixed	fix	VERB
ejpam-5730	326	33	point	point	NOUN
ejpam-5730	326	34	z	z	PROPN
ejpam-5730	326	35	∈	∈	PROPN
ejpam-5730	326	36	x	x	SYM
ejpam-5730	326	37	,	,	PUNCT
ejpam-5730	326	38	b	b	X
ejpam-5730	326	39	)	)	PUNCT
ejpam-5730	326	40	the	the	DET
ejpam-5730	326	41	fixed	fix	VERB
ejpam-5730	326	42	point	point	NOUN
ejpam-5730	326	43	problem	problem	NOUN
ejpam-5730	326	44	of	of	ADP
ejpam-5730	326	45	t	t	PROPN
ejpam-5730	326	46	is	be	AUX
ejpam-5730	326	47	well	well	ADV
ejpam-5730	326	48	-	-	PUNCT
ejpam-5730	326	49	posed	pose	VERB
ejpam-5730	326	50	,	,	PUNCT
ejpam-5730	326	51	and	and	CCONJ
ejpam-5730	326	52	c	c	X
ejpam-5730	326	53	)	)	PUNCT
ejpam-5730	326	54	t	t	PROPN
ejpam-5730	326	55	is	be	AUX
ejpam-5730	326	56	continuous	continuous	ADJ
ejpam-5730	326	57	at	at	ADP
ejpam-5730	326	58	z.	z.	PROPN
ejpam-5730	326	59	comment	comment	PROPN
ejpam-5730	326	60	:	:	PUNCT
ejpam-5730	326	61	for	for	ADP
ejpam-5730	326	62	y	y	PROPN
ejpam-5730	326	63	=	=	SYM
ejpam-5730	326	64	tx	tx	PROPN
ejpam-5730	326	65	,	,	PUNCT
ejpam-5730	326	66	d(x	d(x	PROPN
ejpam-5730	326	67	,	,	PUNCT
ejpam-5730	326	68	ty	ty	INTJ
ejpam-5730	326	69	)	)	PUNCT
ejpam-5730	327	1	+	+	CCONJ
ejpam-5730	327	2	d(y	d(y	PROPN
ejpam-5730	327	3	,	,	PUNCT
ejpam-5730	327	4	tx	tx	PROPN
ejpam-5730	327	5	)	)	PUNCT
ejpam-5730	327	6	d(x	d(x	PROPN
ejpam-5730	327	7	,	,	PUNCT
ejpam-5730	327	8	tx	tx	PROPN
ejpam-5730	327	9	)	)	PUNCT
ejpam-5730	328	1	+	+	CCONJ
ejpam-5730	328	2	d(y	d(y	PROPN
ejpam-5730	328	3	,	,	PUNCT
ejpam-5730	328	4	ty	ty	INTJ
ejpam-5730	328	5	)	)	PUNCT
ejpam-5730	328	6	+	+	CCONJ
ejpam-5730	328	7	1	1	NUM
ejpam-5730	328	8	<	<	SYM
ejpam-5730	328	9	1	1	NUM
ejpam-5730	328	10	and	and	CCONJ
ejpam-5730	328	11	hence	hence	ADV
ejpam-5730	328	12	max{d(x	max{d(x	PROPN
ejpam-5730	328	13	,	,	PUNCT
ejpam-5730	328	14	tx	tx	PROPN
ejpam-5730	328	15	)	)	PUNCT
ejpam-5730	328	16	,	,	PUNCT
ejpam-5730	328	17	d(y	d(y	PROPN
ejpam-5730	328	18	,	,	PUNCT
ejpam-5730	328	19	ty	ty	NOUN
ejpam-5730	328	20	)	)	PUNCT
ejpam-5730	328	21	}	}	PUNCT
ejpam-5730	329	1	=	=	SYM
ejpam-5730	329	2	d(x	d(x	PROPN
ejpam-5730	329	3	,	,	PUNCT
ejpam-5730	329	4	tx	tx	PROPN
ejpam-5730	329	5	)	)	PUNCT
ejpam-5730	329	6	.	.	PUNCT
ejpam-5730	330	1	therefore	therefore	ADV
ejpam-5730	330	2	t	t	PROPN
ejpam-5730	330	3	is	be	AUX
ejpam-5730	330	4	an	an	DET
ejpam-5730	330	5	rhr	rhr	NOUN
ejpam-5730	330	6	map	map	NOUN
ejpam-5730	330	7	and	and	CCONJ
ejpam-5730	330	8	applicable	applicable	ADJ
ejpam-5730	330	9	theorems	theorem	NOUN
ejpam-5730	330	10	p	p	NOUN
ejpam-5730	330	11	and	and	CCONJ
ejpam-5730	330	12	h(γ1	h(γ1	NOUN
ejpam-5730	330	13	)	)	PUNCT
ejpam-5730	330	14	.	.	PUNCT
ejpam-5730	331	1	aouine	aouine	ADJ
ejpam-5730	332	1	[	[	X
ejpam-5730	332	2	2	2	X
ejpam-5730	332	3	]	]	PUNCT
ejpam-5730	332	4	in	in	ADP
ejpam-5730	332	5	2022	2022	NUM
ejpam-5730	332	6	in	in	ADP
ejpam-5730	332	7	[	[	X
ejpam-5730	332	8	2	2	NUM
ejpam-5730	332	9	]	]	PUNCT
ejpam-5730	332	10	,	,	PUNCT
ejpam-5730	332	11	aouine	aouine	PROPN
ejpam-5730	332	12	prove	prove	VERB
ejpam-5730	332	13	a	a	DET
ejpam-5730	332	14	fixed	fix	VERB
ejpam-5730	332	15	point	point	NOUN
ejpam-5730	332	16	theorem	theorem	NOUN
ejpam-5730	332	17	for	for	ADP
ejpam-5730	332	18	p	p	NOUN
ejpam-5730	332	19	-	-	PUNCT
ejpam-5730	332	20	contraction	contraction	NOUN
ejpam-5730	332	21	mappings	mapping	NOUN
ejpam-5730	332	22	in	in	ADP
ejpam-5730	332	23	partially	partially	ADV
ejpam-5730	332	24	ordered	order	VERB
ejpam-5730	332	25	metric	metric	ADJ
ejpam-5730	332	26	spaces	space	NOUN
ejpam-5730	332	27	.	.	PUNCT
ejpam-5730	333	1	as	as	ADP
ejpam-5730	333	2	an	an	DET
ejpam-5730	333	3	application	application	NOUN
ejpam-5730	333	4	,	,	PUNCT
ejpam-5730	333	5	aouine	aouine	PROPN
ejpam-5730	333	6	investigate	investigate	VERB
ejpam-5730	333	7	the	the	DET
ejpam-5730	333	8	possibility	possibility	NOUN
ejpam-5730	333	9	of	of	ADP
ejpam-5730	333	10	optimally	optimally	ADV
ejpam-5730	333	11	controlling	control	VERB
ejpam-5730	333	12	the	the	DET
ejpam-5730	333	13	solution	solution	NOUN
ejpam-5730	333	14	of	of	ADP
ejpam-5730	333	15	the	the	DET
ejpam-5730	333	16	ordinary	ordinary	ADJ
ejpam-5730	333	17	differential	differential	ADJ
ejpam-5730	333	18	equations	equation	NOUN
ejpam-5730	333	19	.	.	PUNCT
ejpam-5730	334	1	definition	definition	NOUN
ejpam-5730	334	2	6.22	6.22	NUM
ejpam-5730	334	3	.	.	PUNCT
ejpam-5730	335	1	let	let	AUX
ejpam-5730	335	2	(	(	PUNCT
ejpam-5730	335	3	x	x	NOUN
ejpam-5730	335	4	,	,	PUNCT
ejpam-5730	335	5	d	d	NOUN
ejpam-5730	335	6	)	)	PUNCT
ejpam-5730	335	7	be	be	AUX
ejpam-5730	335	8	a	a	DET
ejpam-5730	335	9	metric	metric	ADJ
ejpam-5730	335	10	space	space	NOUN
ejpam-5730	335	11	.	.	PUNCT
ejpam-5730	336	1	a	a	DET
ejpam-5730	336	2	mapping	mapping	NOUN
ejpam-5730	336	3	t	t	NOUN
ejpam-5730	336	4	:	:	PUNCT
ejpam-5730	336	5	y	y	PROPN
ejpam-5730	336	6	⊂	⊂	PROPN
ejpam-5730	336	7	x	x	PUNCT
ejpam-5730	336	8	→	→	PUNCT
ejpam-5730	336	9	x	x	X
ejpam-5730	336	10	is	be	AUX
ejpam-5730	336	11	said	say	VERB
ejpam-5730	336	12	to	to	PART
ejpam-5730	336	13	be	be	AUX
ejpam-5730	336	14	a	a	DET
ejpam-5730	336	15	metric	metric	ADJ
ejpam-5730	336	16	p	p	NOUN
ejpam-5730	336	17	-	-	PUNCT
ejpam-5730	336	18	contraction	contraction	NOUN
ejpam-5730	336	19	(	(	PUNCT
ejpam-5730	336	20	or	or	CCONJ
ejpam-5730	336	21	simply	simply	ADV
ejpam-5730	336	22	p	p	ADJ
ejpam-5730	336	23	-	-	PUNCT
ejpam-5730	336	24	contraction	contraction	NOUN
ejpam-5730	336	25	)	)	PUNCT
ejpam-5730	336	26	mapping	mapping	NOUN
ejpam-5730	336	27	if	if	SCONJ
ejpam-5730	336	28	y	y	PROPN
ejpam-5730	336	29	is	be	AUX
ejpam-5730	336	30	t	t	PROPN
ejpam-5730	336	31	-invariant	-invariant	ADJ
ejpam-5730	336	32	and	and	CCONJ
ejpam-5730	336	33	it	it	PRON
ejpam-5730	336	34	satisfies	satisfy	VERB
ejpam-5730	336	35	the	the	DET
ejpam-5730	336	36	following	follow	VERB
ejpam-5730	336	37	inequality	inequality	NOUN
ejpam-5730	336	38	:	:	PUNCT
ejpam-5730	336	39	d(t	d(t	PROPN
ejpam-5730	336	40	(	(	PUNCT
ejpam-5730	336	41	x	x	NOUN
ejpam-5730	336	42	)	)	PUNCT
ejpam-5730	336	43	,	,	PUNCT
ejpam-5730	336	44	t	t	PROPN
ejpam-5730	336	45	2(x	2(x	NUM
ejpam-5730	336	46	)	)	PUNCT
ejpam-5730	336	47	)	)	PUNCT
ejpam-5730	336	48	≤	≤	NUM
ejpam-5730	336	49	p(x)d(x	p(x)d(x	NOUN
ejpam-5730	336	50	,	,	PUNCT
ejpam-5730	336	51	t	t	PROPN
ejpam-5730	336	52	(	(	PUNCT
ejpam-5730	336	53	x	x	NOUN
ejpam-5730	336	54	)	)	PUNCT
ejpam-5730	336	55	)	)	PUNCT
ejpam-5730	336	56	∀	∀	X
ejpam-5730	337	1	x	x	X
ejpam-5730	337	2	∈	∈	NOUN
ejpam-5730	337	3	y	y	PROPN
ejpam-5730	337	4	,	,	PUNCT
ejpam-5730	337	5	where	where	SCONJ
ejpam-5730	337	6	p	p	NOUN
ejpam-5730	337	7	:	:	PUNCT
ejpam-5730	337	8	y	y	PROPN
ejpam-5730	337	9	→	→	PUNCT
ejpam-5730	338	1	[	[	X
ejpam-5730	338	2	0	0	NUM
ejpam-5730	338	3	,	,	PUNCT
ejpam-5730	338	4	1	1	NUM
ejpam-5730	338	5	]	]	PUNCT
ejpam-5730	338	6	is	be	AUX
ejpam-5730	338	7	a	a	DET
ejpam-5730	338	8	function	function	NOUN
ejpam-5730	338	9	such	such	ADJ
ejpam-5730	338	10	that	that	DET
ejpam-5730	338	11	p(x	p(x	NOUN
ejpam-5730	338	12	)	)	PUNCT
ejpam-5730	338	13	<	<	X
ejpam-5730	338	14	1	1	NUM
ejpam-5730	338	15	for	for	ADP
ejpam-5730	338	16	all	all	DET
ejpam-5730	338	17	x	x	SYM
ejpam-5730	338	18	∈	∈	PROPN
ejpam-5730	338	19	y	y	PROPN
ejpam-5730	338	20	and	and	CCONJ
ejpam-5730	338	21	supx∈y	supx∈y	NOUN
ejpam-5730	338	22	p(tx	p(tx	NUM
ejpam-5730	338	23	)	)	PUNCT
ejpam-5730	338	24	=	=	SYM
ejpam-5730	339	1	á	á	NOUN
ejpam-5730	339	2	<	<	X
ejpam-5730	339	3	1	1	NUM
ejpam-5730	339	4	.	.	PUNCT
ejpam-5730	340	1	further	far	ADV
ejpam-5730	340	2	,	,	PUNCT
ejpam-5730	340	3	if	if	SCONJ
ejpam-5730	340	4	⋂∞	⋂∞	NOUN
ejpam-5730	340	5	n=0	n=0	NUM
ejpam-5730	340	6	t	t	NOUN
ejpam-5730	340	7	n(y	n(y	PROPN
ejpam-5730	340	8	)	)	PUNCT
ejpam-5730	340	9	is	be	AUX
ejpam-5730	340	10	a	a	DET
ejpam-5730	340	11	singleton	singleton	NOUN
ejpam-5730	340	12	set	set	NOUN
ejpam-5730	340	13	,	,	PUNCT
ejpam-5730	340	14	where	where	SCONJ
ejpam-5730	340	15	tn(y	tn(y	PUNCT
ejpam-5730	340	16	)	)	PUNCT
ejpam-5730	341	1	=	=	SYM
ejpam-5730	341	2	t	t	PROPN
ejpam-5730	341	3	(	(	PUNCT
ejpam-5730	341	4	tn−1(y	tn−1(y	ADJ
ejpam-5730	341	5	)	)	PUNCT
ejpam-5730	341	6	)	)	PUNCT
ejpam-5730	341	7	for	for	ADP
ejpam-5730	341	8	each	each	DET
ejpam-5730	341	9	n	n	PRON
ejpam-5730	341	10	∈	∈	PROPN
ejpam-5730	341	11	n	n	NOUN
ejpam-5730	341	12	and	and	CCONJ
ejpam-5730	341	13	t	t	NOUN
ejpam-5730	341	14	0(y	0(y	NUM
ejpam-5730	341	15	)	)	PUNCT
ejpam-5730	342	1	=	=	SYM
ejpam-5730	342	2	y	y	PROPN
ejpam-5730	342	3	,	,	PUNCT
ejpam-5730	342	4	then	then	ADV
ejpam-5730	342	5	t	t	PROPN
ejpam-5730	342	6	is	be	AUX
ejpam-5730	342	7	said	say	VERB
ejpam-5730	342	8	to	to	PART
ejpam-5730	342	9	be	be	AUX
ejpam-5730	342	10	a	a	DET
ejpam-5730	342	11	strong	strong	ADJ
ejpam-5730	342	12	p	p	NOUN
ejpam-5730	342	13	-	-	PUNCT
ejpam-5730	342	14	contraction	contraction	NOUN
ejpam-5730	342	15	.	.	PUNCT
ejpam-5730	343	1	s.	s.	PROPN
ejpam-5730	343	2	park	park	PROPN
ejpam-5730	343	3	/	/	SYM
ejpam-5730	343	4	eur	eur	PROPN
ejpam-5730	343	5	.	.	PUNCT
ejpam-5730	344	1	j.	j.	PROPN
ejpam-5730	344	2	pure	pure	PROPN
ejpam-5730	344	3	appl	appl	PROPN
ejpam-5730	344	4	.	.	PROPN
ejpam-5730	344	5	math	math	PROPN
ejpam-5730	344	6	,	,	PUNCT
ejpam-5730	344	7	18	18	NUM
ejpam-5730	344	8	(	(	PUNCT
ejpam-5730	344	9	1	1	NUM
ejpam-5730	344	10	)	)	PUNCT
ejpam-5730	344	11	(	(	PUNCT
ejpam-5730	344	12	2025	2025	NUM
ejpam-5730	344	13	)	)	PUNCT
ejpam-5730	344	14	,	,	PUNCT
ejpam-5730	344	15	5730	5730	NUM
ejpam-5730	344	16	14	14	NUM
ejpam-5730	344	17	of	of	ADP
ejpam-5730	344	18	21	21	NUM
ejpam-5730	344	19	comment	comment	NOUN
ejpam-5730	344	20	:	:	PUNCT
ejpam-5730	344	21	note	note	VERB
ejpam-5730	344	22	that	that	SCONJ
ejpam-5730	344	23	t	t	PROPN
ejpam-5730	344	24	is	be	AUX
ejpam-5730	344	25	an	an	DET
ejpam-5730	344	26	rhr	rhr	PROPN
ejpam-5730	344	27	map	map	NOUN
ejpam-5730	344	28	.	.	PUNCT
ejpam-5730	345	1	romaguera	romaguera	NOUN
ejpam-5730	346	1	[	[	X
ejpam-5730	346	2	47	47	NUM
ejpam-5730	346	3	]	]	PUNCT
ejpam-5730	346	4	in	in	ADP
ejpam-5730	346	5	2022	2022	NUM
ejpam-5730	346	6	the	the	DET
ejpam-5730	346	7	author	author	NOUN
ejpam-5730	346	8	stated	state	VERB
ejpam-5730	346	9	:	:	PUNCT
ejpam-5730	346	10	the	the	DET
ejpam-5730	346	11	above	above	ADJ
ejpam-5730	346	12	theorem	theorem	NOUN
ejpam-5730	346	13	suggests	suggest	VERB
ejpam-5730	346	14	the	the	DET
ejpam-5730	346	15	following	follow	VERB
ejpam-5730	346	16	natural	natural	ADJ
ejpam-5730	346	17	question	question	NOUN
ejpam-5730	346	18	(	(	PUNCT
ejpam-5730	346	19	see	see	VERB
ejpam-5730	346	20	section	section	NOUN
ejpam-5730	346	21	2	2	NUM
ejpam-5730	346	22	for	for	ADP
ejpam-5730	346	23	notation	notation	NOUN
ejpam-5730	346	24	and	and	CCONJ
ejpam-5730	346	25	concepts	concept	NOUN
ejpam-5730	346	26	)	)	PUNCT
ejpam-5730	346	27	.	.	PUNCT
ejpam-5730	347	1	question	question	NOUN
ejpam-5730	347	2	.	.	PUNCT
ejpam-5730	348	1	let	let	VERB
ejpam-5730	348	2	f	f	PRON
ejpam-5730	348	3	be	be	AUX
ejpam-5730	348	4	a	a	DET
ejpam-5730	348	5	self	self	NOUN
ejpam-5730	348	6	map	map	NOUN
ejpam-5730	348	7	of	of	ADP
ejpam-5730	348	8	a	a	DET
ejpam-5730	348	9	bicomplete	bicomplete	ADJ
ejpam-5730	348	10	(	(	PUNCT
ejpam-5730	348	11	or	or	CCONJ
ejpam-5730	348	12	at	at	ADP
ejpam-5730	348	13	least	least	ADJ
ejpam-5730	348	14	,	,	PUNCT
ejpam-5730	348	15	smyth	smyth	PROPN
ejpam-5730	348	16	complete	complete	ADJ
ejpam-5730	348	17	)	)	PUNCT
ejpam-5730	348	18	quasi	quasi	ADJ
ejpam-5730	348	19	-	-	ADJ
ejpam-5730	348	20	metric	metric	ADJ
ejpam-5730	348	21	space	space	NOUN
ejpam-5730	348	22	(	(	PUNCT
ejpam-5730	348	23	x	x	X
ejpam-5730	348	24	,	,	PUNCT
ejpam-5730	348	25	d	d	NOUN
ejpam-5730	348	26	)	)	PUNCT
ejpam-5730	348	27	and	and	CCONJ
ejpam-5730	348	28	let	let	VERB
ejpam-5730	348	29	c	c	PROPN
ejpam-5730	348	30	∈	∈	PROPN
ejpam-5730	348	31	(	(	PUNCT
ejpam-5730	348	32	0	0	NUM
ejpam-5730	348	33	,	,	PUNCT
ejpam-5730	348	34	1	1	NUM
ejpam-5730	348	35	)	)	PUNCT
ejpam-5730	348	36	be	be	AUX
ejpam-5730	348	37	a	a	DET
ejpam-5730	348	38	constant	constant	ADJ
ejpam-5730	348	39	,	,	PUNCT
ejpam-5730	348	40	such	such	ADJ
ejpam-5730	348	41	that	that	PRON
ejpam-5730	348	42	for	for	ADP
ejpam-5730	348	43	every	every	DET
ejpam-5730	348	44	x	x	NOUN
ejpam-5730	348	45	,	,	PUNCT
ejpam-5730	348	46	y	y	PROPN
ejpam-5730	348	47	∈	∈	PROPN
ejpam-5730	349	1	x	x	PRON
ejpam-5730	349	2	,	,	PUNCT
ejpam-5730	349	3	the	the	DET
ejpam-5730	349	4	following	follow	VERB
ejpam-5730	349	5	contraction	contraction	NOUN
ejpam-5730	349	6	condition	condition	NOUN
ejpam-5730	349	7	holds	hold	VERB
ejpam-5730	349	8	:	:	PUNCT
ejpam-5730	349	9	d(x	d(x	NOUN
ejpam-5730	349	10	,	,	PUNCT
ejpam-5730	349	11	fx	fx	NOUN
ejpam-5730	349	12	)	)	PUNCT
ejpam-5730	349	13	≤	≤	NOUN
ejpam-5730	349	14	2d(x	2d(x	NUM
ejpam-5730	349	15	,	,	PUNCT
ejpam-5730	349	16	y	y	NOUN
ejpam-5730	349	17	)	)	PUNCT
ejpam-5730	350	1	=	=	NOUN
ejpam-5730	350	2	⇒	⇒	NOUN
ejpam-5730	350	3	d(fx	d(fx	PROPN
ejpam-5730	350	4	,	,	PUNCT
ejpam-5730	350	5	fy	fy	NOUN
ejpam-5730	350	6	)	)	PUNCT
ejpam-5730	350	7	≤	≤	NOUN
ejpam-5730	350	8	c	c	ADP
ejpam-5730	350	9	d(x	d(x	PROPN
ejpam-5730	350	10	,	,	PUNCT
ejpam-5730	350	11	y	y	NOUN
ejpam-5730	350	12	)	)	PUNCT
ejpam-5730	350	13	.	.	PUNCT
ejpam-5730	351	1	under	under	ADP
ejpam-5730	351	2	the	the	DET
ejpam-5730	351	3	above	above	ADJ
ejpam-5730	351	4	assumptions	assumption	NOUN
ejpam-5730	351	5	,	,	PUNCT
ejpam-5730	351	6	does	do	AUX
ejpam-5730	351	7	f	f	PROPN
ejpam-5730	351	8	admit	admit	VERB
ejpam-5730	351	9	a	a	DET
ejpam-5730	351	10	fixed	fix	VERB
ejpam-5730	351	11	point	point	NOUN
ejpam-5730	351	12	?	?	PUNCT
ejpam-5730	352	1	in	in	ADP
ejpam-5730	352	2	section	section	NOUN
ejpam-5730	352	3	3	3	NUM
ejpam-5730	352	4	,	,	PUNCT
ejpam-5730	352	5	the	the	DET
ejpam-5730	352	6	author	author	NOUN
ejpam-5730	352	7	gives	give	VERB
ejpam-5730	352	8	an	an	DET
ejpam-5730	352	9	example	example	NOUN
ejpam-5730	352	10	showing	show	VERB
ejpam-5730	352	11	that	that	SCONJ
ejpam-5730	352	12	this	this	DET
ejpam-5730	352	13	question	question	NOUN
ejpam-5730	352	14	has	have	VERB
ejpam-5730	352	15	a	a	DET
ejpam-5730	352	16	negative	negative	ADJ
ejpam-5730	352	17	answer	answer	NOUN
ejpam-5730	352	18	in	in	ADP
ejpam-5730	352	19	the	the	DET
ejpam-5730	352	20	general	general	ADJ
ejpam-5730	352	21	quasi	quasi	ADJ
ejpam-5730	352	22	-	-	ADJ
ejpam-5730	352	23	metric	metric	ADJ
ejpam-5730	352	24	context	context	NOUN
ejpam-5730	352	25	.	.	PUNCT
ejpam-5730	353	1	comment	comment	NOUN
ejpam-5730	353	2	:	:	PUNCT
ejpam-5730	353	3	note	note	VERB
ejpam-5730	353	4	that	that	SCONJ
ejpam-5730	353	5	f	f	PROPN
ejpam-5730	353	6	is	be	AUX
ejpam-5730	353	7	an	an	DET
ejpam-5730	353	8	rhr	rhr	PROPN
ejpam-5730	353	9	map	map	NOUN
ejpam-5730	353	10	.	.	PUNCT
ejpam-5730	354	1	petrov	petrov	PROPN
ejpam-5730	355	1	[	[	X
ejpam-5730	355	2	42	42	NUM
ejpam-5730	355	3	]	]	PUNCT
ejpam-5730	355	4	in	in	ADP
ejpam-5730	355	5	2023	2023	NUM
ejpam-5730	355	6	petrov	petrov	PROPN
ejpam-5730	355	7	defined	define	VERB
ejpam-5730	355	8	generalized	generalized	ADJ
ejpam-5730	355	9	kannan	kannan	PROPN
ejpam-5730	355	10	type	type	NOUN
ejpam-5730	355	11	maps	map	NOUN
ejpam-5730	355	12	and	and	CCONJ
ejpam-5730	355	13	obtained	obtain	VERB
ejpam-5730	355	14	:	:	PUNCT
ejpam-5730	355	15	proposition	proposition	NOUN
ejpam-5730	355	16	6.23	6.23	NUM
ejpam-5730	355	17	.	.	PUNCT
ejpam-5730	356	1	(	(	PUNCT
ejpam-5730	356	2	petrov	petrov	PROPN
ejpam-5730	356	3	)	)	PUNCT
ejpam-5730	356	4	let	let	VERB
ejpam-5730	356	5	(	(	PUNCT
ejpam-5730	356	6	x	x	NOUN
ejpam-5730	356	7	,	,	PUNCT
ejpam-5730	356	8	d	d	NOUN
ejpam-5730	356	9	)	)	PUNCT
ejpam-5730	356	10	be	be	AUX
ejpam-5730	356	11	a	a	DET
ejpam-5730	356	12	metric	metric	ADJ
ejpam-5730	356	13	space	space	NOUN
ejpam-5730	356	14	and	and	CCONJ
ejpam-5730	356	15	let	let	VERB
ejpam-5730	356	16	t	t	NOUN
ejpam-5730	356	17	:	:	PUNCT
ejpam-5730	356	18	x	x	X
ejpam-5730	356	19	→	→	PUNCT
ejpam-5730	356	20	x	x	PUNCT
ejpam-5730	356	21	be	be	AUX
ejpam-5730	356	22	a	a	DET
ejpam-5730	356	23	generalized	generalize	VERB
ejpam-5730	356	24	kannan	kannan	PROPN
ejpam-5730	356	25	type	type	NOUN
ejpam-5730	356	26	metric	metric	ADJ
ejpam-5730	356	27	with	with	ADP
ejpam-5730	356	28	some	some	DET
ejpam-5730	356	29	λ	λ	PROPN
ejpam-5730	356	30	∈	∈	PROPN
ejpam-5730	357	1	[	[	X
ejpam-5730	357	2	0	0	NUM
ejpam-5730	357	3	,	,	PUNCT
ejpam-5730	357	4	2/3	2/3	NUM
ejpam-5730	357	5	)	)	PUNCT
ejpam-5730	357	6	.	.	PUNCT
ejpam-5730	358	1	if	if	SCONJ
ejpam-5730	358	2	x	x	PRON
ejpam-5730	358	3	is	be	AUX
ejpam-5730	358	4	an	an	DET
ejpam-5730	358	5	accumulation	accumulation	NOUN
ejpam-5730	358	6	point	point	NOUN
ejpam-5730	358	7	of	of	ADP
ejpam-5730	358	8	x	x	PUNCT
ejpam-5730	358	9	and	and	CCONJ
ejpam-5730	358	10	t	t	PROPN
ejpam-5730	358	11	is	be	AUX
ejpam-5730	358	12	continuous	continuous	ADJ
ejpam-5730	358	13	at	at	ADP
ejpam-5730	358	14	x	x	X
ejpam-5730	358	15	,	,	PUNCT
ejpam-5730	358	16	then	then	ADV
ejpam-5730	358	17	the	the	DET
ejpam-5730	358	18	inequality	inequality	NOUN
ejpam-5730	358	19	d(tx	d(tx	PROPN
ejpam-5730	358	20	,	,	PUNCT
ejpam-5730	358	21	ty	ty	NOUN
ejpam-5730	358	22	)	)	PUNCT
ejpam-5730	358	23	≤	≤	NOUN
ejpam-5730	358	24	λ[d(x	λ[d(x	PUNCT
ejpam-5730	358	25	,	,	PUNCT
ejpam-5730	358	26	tx	tx	PROPN
ejpam-5730	358	27	)	)	PUNCT
ejpam-5730	359	1	+	+	CCONJ
ejpam-5730	359	2	d(y	d(y	NOUN
ejpam-5730	359	3	,	,	PUNCT
ejpam-5730	359	4	ty)/2	ty)/2	PROPN
ejpam-5730	359	5	]	]	PUNCT
ejpam-5730	359	6	holds	hold	VERB
ejpam-5730	359	7	for	for	ADP
ejpam-5730	359	8	all	all	DET
ejpam-5730	359	9	points	point	NOUN
ejpam-5730	359	10	y	y	PROPN
ejpam-5730	359	11	∈	∈	PROPN
ejpam-5730	359	12	x.	x.	NOUN
ejpam-5730	359	13	theorem	theorem	VERB
ejpam-5730	359	14	6.24	6.24	NUM
ejpam-5730	359	15	.	.	PUNCT
ejpam-5730	360	1	(	(	PUNCT
ejpam-5730	360	2	petrov	petrov	PROPN
ejpam-5730	360	3	)	)	PUNCT
ejpam-5730	360	4	let	let	VERB
ejpam-5730	360	5	(	(	PUNCT
ejpam-5730	360	6	x	x	NOUN
ejpam-5730	360	7	,	,	PUNCT
ejpam-5730	360	8	d	d	PROPN
ejpam-5730	360	9	)	)	PUNCT
ejpam-5730	360	10	,	,	PUNCT
ejpam-5730	360	11	|x|	|x|	PROPN
ejpam-5730	360	12	>	>	X
ejpam-5730	360	13	3	3	NUM
ejpam-5730	360	14	,	,	PUNCT
ejpam-5730	360	15	be	be	AUX
ejpam-5730	360	16	a	a	DET
ejpam-5730	360	17	complete	complete	ADJ
ejpam-5730	360	18	metric	metric	ADJ
ejpam-5730	360	19	space	space	NOUN
ejpam-5730	360	20	and	and	CCONJ
ejpam-5730	360	21	let	let	VERB
ejpam-5730	360	22	the	the	DET
ejpam-5730	360	23	mapping	mapping	NOUN
ejpam-5730	360	24	t	t	NOUN
ejpam-5730	360	25	:	:	PUNCT
ejpam-5730	360	26	x	x	X
ejpam-5730	360	27	→	→	PUNCT
ejpam-5730	360	28	x	x	PUNCT
ejpam-5730	360	29	satisfy	satisfy	VERB
ejpam-5730	360	30	the	the	DET
ejpam-5730	360	31	following	follow	VERB
ejpam-5730	360	32	two	two	NUM
ejpam-5730	360	33	conditions	condition	NOUN
ejpam-5730	360	34	:	:	PUNCT
ejpam-5730	360	35	(	(	PUNCT
ejpam-5730	360	36	i	i	NOUN
ejpam-5730	360	37	)	)	PUNCT
ejpam-5730	360	38	t	t	PROPN
ejpam-5730	360	39	(	(	PUNCT
ejpam-5730	360	40	t	t	PROPN
ejpam-5730	360	41	(	(	PUNCT
ejpam-5730	360	42	x	x	NOUN
ejpam-5730	360	43	)	)	PUNCT
ejpam-5730	360	44	)	)	PUNCT
ejpam-5730	361	1	̸=	̸=	PROPN
ejpam-5730	361	2	x	x	PUNCT
ejpam-5730	361	3	for	for	ADP
ejpam-5730	361	4	all	all	DET
ejpam-5730	361	5	x	x	SYM
ejpam-5730	361	6	∈	∈	NOUN
ejpam-5730	361	7	x	x	PUNCT
ejpam-5730	361	8	such	such	ADJ
ejpam-5730	361	9	that	that	SCONJ
ejpam-5730	361	10	tx	tx	PROPN
ejpam-5730	361	11	̸=	̸=	PROPN
ejpam-5730	361	12	x.	x.	NOUN
ejpam-5730	361	13	(	(	PUNCT
ejpam-5730	361	14	ii	ii	PROPN
ejpam-5730	361	15	)	)	PUNCT
ejpam-5730	361	16	t	t	PROPN
ejpam-5730	361	17	is	be	AUX
ejpam-5730	361	18	a	a	DET
ejpam-5730	361	19	generalized	generalized	ADJ
ejpam-5730	361	20	kannan	kannan	NOUN
ejpam-5730	361	21	-	-	PUNCT
ejpam-5730	361	22	type	type	NOUN
ejpam-5730	361	23	mapping	mapping	NOUN
ejpam-5730	361	24	on	on	ADP
ejpam-5730	361	25	x.	x.	NOUN
ejpam-5730	361	26	then	then	ADV
ejpam-5730	361	27	t	t	PROPN
ejpam-5730	361	28	has	have	VERB
ejpam-5730	361	29	a	a	DET
ejpam-5730	361	30	fixed	fix	VERB
ejpam-5730	361	31	point	point	NOUN
ejpam-5730	361	32	.	.	PUNCT
ejpam-5730	362	1	the	the	DET
ejpam-5730	362	2	number	number	NOUN
ejpam-5730	362	3	of	of	ADP
ejpam-5730	362	4	fixed	fix	VERB
ejpam-5730	362	5	points	point	NOUN
ejpam-5730	362	6	is	be	AUX
ejpam-5730	362	7	at	at	ADP
ejpam-5730	362	8	most	most	ADV
ejpam-5730	362	9	two	two	NUM
ejpam-5730	362	10	.	.	PUNCT
ejpam-5730	363	1	comment	comment	NOUN
ejpam-5730	363	2	:	:	PUNCT
ejpam-5730	363	3	for	for	ADP
ejpam-5730	363	4	any	any	DET
ejpam-5730	363	5	point	point	NOUN
ejpam-5730	363	6	x	x	X
ejpam-5730	363	7	∈	∈	NOUN
ejpam-5730	363	8	x	x	NOUN
ejpam-5730	363	9	,	,	PUNCT
ejpam-5730	363	10	the	the	DET
ejpam-5730	363	11	inequality	inequality	NOUN
ejpam-5730	363	12	in	in	ADP
ejpam-5730	363	13	proposition	proposition	NOUN
ejpam-5730	363	14	6.22	6.22	NUM
ejpam-5730	363	15	for	for	ADP
ejpam-5730	363	16	y	y	PROPN
ejpam-5730	363	17	=	=	PUNCT
ejpam-5730	363	18	tx	tx	PROPN
ejpam-5730	363	19	implies	imply	VERB
ejpam-5730	363	20	(	(	PUNCT
ejpam-5730	363	21	1−	1−	NUM
ejpam-5730	363	22	λ	λ	NOUN
ejpam-5730	363	23	2	2	NUM
ejpam-5730	363	24	)	)	PUNCT
ejpam-5730	363	25	d(tx	d(tx	PROPN
ejpam-5730	363	26	,	,	PUNCT
ejpam-5730	363	27	t	t	NOUN
ejpam-5730	363	28	2x	2x	NUM
ejpam-5730	363	29	)	)	PUNCT
ejpam-5730	363	30	≤	≤	NUM
ejpam-5730	364	1	λ	λ	NOUN
ejpam-5730	364	2	d(x	d(x	PROPN
ejpam-5730	364	3	,	,	PUNCT
ejpam-5730	364	4	tx	tx	PROPN
ejpam-5730	364	5	)	)	PUNCT
ejpam-5730	364	6	or	or	CCONJ
ejpam-5730	364	7	d(tx	d(tx	PROPN
ejpam-5730	364	8	,	,	PUNCT
ejpam-5730	364	9	t	t	NOUN
ejpam-5730	364	10	2	2	NUM
ejpam-5730	364	11	)	)	PUNCT
ejpam-5730	364	12	≤	≤	NOUN
ejpam-5730	364	13	αd(x	αd(x	PUNCT
ejpam-5730	364	14	,	,	PUNCT
ejpam-5730	364	15	tx	tx	PROPN
ejpam-5730	364	16	)	)	PUNCT
ejpam-5730	364	17	where	where	SCONJ
ejpam-5730	364	18	α	α	NOUN
ejpam-5730	364	19	=	=	SYM
ejpam-5730	364	20	λ	λ	X
ejpam-5730	364	21	2−	2−	NUM
ejpam-5730	364	22	λ	λ	NOUN
ejpam-5730	364	23	∈	∈	PROPN
ejpam-5730	365	1	[	[	X
ejpam-5730	365	2	0	0	NUM
ejpam-5730	365	3	,	,	PUNCT
ejpam-5730	365	4	1	1	NUM
ejpam-5730	365	5	)	)	PUNCT
ejpam-5730	365	6	.	.	PUNCT
ejpam-5730	366	1	hence	hence	ADV
ejpam-5730	366	2	,	,	PUNCT
ejpam-5730	366	3	t	t	PROPN
ejpam-5730	366	4	is	be	AUX
ejpam-5730	366	5	an	an	DET
ejpam-5730	366	6	rhr	rhr	NOUN
ejpam-5730	366	7	map	map	NOUN
ejpam-5730	366	8	and	and	CCONJ
ejpam-5730	366	9	has	have	VERB
ejpam-5730	366	10	a	a	DET
ejpam-5730	366	11	fixed	fix	VERB
ejpam-5730	366	12	point	point	NOUN
ejpam-5730	366	13	by	by	ADP
ejpam-5730	366	14	theorems	theorem	NOUN
ejpam-5730	366	15	p	p	NOUN
ejpam-5730	366	16	and	and	CCONJ
ejpam-5730	366	17	h(γ1	h(γ1	NOUN
ejpam-5730	366	18	)	)	PUNCT
ejpam-5730	366	19	.	.	PUNCT
ejpam-5730	367	1	suppose	suppose	VERB
ejpam-5730	367	2	that	that	SCONJ
ejpam-5730	367	3	there	there	PRON
ejpam-5730	367	4	exists	exist	VERB
ejpam-5730	367	5	at	at	ADP
ejpam-5730	367	6	least	least	ADV
ejpam-5730	367	7	three	three	NUM
ejpam-5730	367	8	pairwise	pairwise	NOUN
ejpam-5730	367	9	distinct	distinct	ADJ
ejpam-5730	367	10	fixed	fix	VERB
ejpam-5730	367	11	points	point	NOUN
ejpam-5730	367	12	x	x	NOUN
ejpam-5730	367	13	,	,	PUNCT
ejpam-5730	367	14	y	y	PROPN
ejpam-5730	367	15	and	and	CCONJ
ejpam-5730	367	16	z.	z.	PROPN
ejpam-5730	367	17	then	then	ADV
ejpam-5730	367	18	tx	tx	VERB
ejpam-5730	368	1	=	=	PUNCT
ejpam-5730	368	2	x	x	X
ejpam-5730	368	3	,	,	PUNCT
ejpam-5730	368	4	ty	ty	INTJ
ejpam-5730	368	5	=	=	SYM
ejpam-5730	368	6	y	y	PROPN
ejpam-5730	368	7	and	and	CCONJ
ejpam-5730	368	8	tz	tz	PROPN
ejpam-5730	368	9	=	=	SYM
ejpam-5730	368	10	z	z	PROPN
ejpam-5730	368	11	,	,	PUNCT
ejpam-5730	368	12	which	which	PRON
ejpam-5730	368	13	contradicts	contradict	VERB
ejpam-5730	368	14	to	to	ADP
ejpam-5730	368	15	the	the	DET
ejpam-5730	368	16	definition	definition	NOUN
ejpam-5730	368	17	of	of	ADP
ejpam-5730	368	18	generalized	generalized	ADJ
ejpam-5730	368	19	kannan	kannan	PROPN
ejpam-5730	368	20	-	-	PUNCT
ejpam-5730	368	21	type	type	NOUN
ejpam-5730	368	22	map	map	NOUN
ejpam-5730	368	23	.	.	PUNCT
ejpam-5730	369	1	anyway	anyway	ADV
ejpam-5730	369	2	,	,	PUNCT
ejpam-5730	369	3	the	the	DET
ejpam-5730	369	4	concept	concept	NOUN
ejpam-5730	369	5	of	of	ADP
ejpam-5730	369	6	generalized	generalized	ADJ
ejpam-5730	369	7	kannan	kannan	PROPN
ejpam-5730	369	8	-	-	PUNCT
ejpam-5730	369	9	type	type	NOUN
ejpam-5730	369	10	maps	map	NOUN
ejpam-5730	369	11	can	can	AUX
ejpam-5730	369	12	be	be	AUX
ejpam-5730	369	13	replaced	replace	VERB
ejpam-5730	369	14	by	by	ADP
ejpam-5730	369	15	rhr	rhr	PROPN
ejpam-5730	369	16	maps	map	NOUN
ejpam-5730	369	17	.	.	PUNCT
ejpam-5730	370	1	s.	s.	PROPN
ejpam-5730	370	2	park	park	PROPN
ejpam-5730	370	3	/	/	SYM
ejpam-5730	370	4	eur	eur	PROPN
ejpam-5730	370	5	.	.	PUNCT
ejpam-5730	371	1	j.	j.	PROPN
ejpam-5730	371	2	pure	pure	PROPN
ejpam-5730	371	3	appl	appl	PROPN
ejpam-5730	371	4	.	.	PROPN
ejpam-5730	371	5	math	math	PROPN
ejpam-5730	371	6	,	,	PUNCT
ejpam-5730	371	7	18	18	NUM
ejpam-5730	371	8	(	(	PUNCT
ejpam-5730	371	9	1	1	NUM
ejpam-5730	371	10	)	)	PUNCT
ejpam-5730	371	11	(	(	PUNCT
ejpam-5730	371	12	2025	2025	NUM
ejpam-5730	371	13	)	)	PUNCT
ejpam-5730	371	14	,	,	PUNCT
ejpam-5730	371	15	5730	5730	NUM
ejpam-5730	371	16	15	15	NUM
ejpam-5730	371	17	of	of	ADP
ejpam-5730	371	18	21	21	NUM
ejpam-5730	371	19	7	7	NUM
ejpam-5730	371	20	.	.	PUNCT
ejpam-5730	372	1	the	the	DET
ejpam-5730	372	2	subfamilies	subfamily	NOUN
ejpam-5730	372	3	{	{	PUNCT
ejpam-5730	372	4	δ	δ	X
ejpam-5730	372	5	}	}	PUNCT
ejpam-5730	372	6	and	and	CCONJ
ejpam-5730	372	7	{	{	PUNCT
ejpam-5730	372	8	ϵ	ϵ	NOUN
ejpam-5730	372	9	}	}	PUNCT
ejpam-5730	372	10	of	of	ADP
ejpam-5730	372	11	the	the	DET
ejpam-5730	372	12	covitz	covitz	PROPN
ejpam-5730	372	13	-	-	PUNCT
ejpam-5730	372	14	nadler	nadler	NOUN
ejpam-5730	372	15	type	type	NOUN
ejpam-5730	372	16	theorem	theorem	VERB
ejpam-5730	372	17	h((δ)-(ϵ	h((δ)-(ϵ	NOUN
ejpam-5730	372	18	)	)	PUNCT
ejpam-5730	372	19	generalize	generalize	VERB
ejpam-5730	372	20	the	the	DET
ejpam-5730	372	21	celebrated	celebrated	ADJ
ejpam-5730	372	22	multi	multi	ADJ
ejpam-5730	372	23	-	-	ADJ
ejpam-5730	372	24	valued	value	VERB
ejpam-5730	372	25	versions	version	NOUN
ejpam-5730	372	26	of	of	ADP
ejpam-5730	372	27	the	the	DET
ejpam-5730	372	28	banach	banach	NOUN
ejpam-5730	372	29	contractions	contraction	NOUN
ejpam-5730	372	30	due	due	ADJ
ejpam-5730	372	31	to	to	ADP
ejpam-5730	372	32	nadler	nadler	NOUN
ejpam-5730	372	33	and	and	CCONJ
ejpam-5730	372	34	covitz	covitz	PROPN
ejpam-5730	372	35	-	-	PUNCT
ejpam-5730	372	36	nadler	nadler	NOUN
ejpam-5730	372	37	.	.	PUNCT
ejpam-5730	373	1	moreover	moreover	ADV
ejpam-5730	373	2	,	,	PUNCT
ejpam-5730	373	3	theorem	theorem	ADJ
ejpam-5730	373	4	h	h	NOUN
ejpam-5730	373	5	gives	give	VERB
ejpam-5730	373	6	a	a	DET
ejpam-5730	373	7	unified	unified	ADJ
ejpam-5730	373	8	elementary	elementary	ADJ
ejpam-5730	373	9	proof	proof	NOUN
ejpam-5730	373	10	of	of	ADP
ejpam-5730	373	11	them	they	PRON
ejpam-5730	373	12	.	.	PUNCT
ejpam-5730	374	1	nadler	nadler	PROPN
ejpam-5730	375	1	[	[	X
ejpam-5730	375	2	28	28	NUM
ejpam-5730	375	3	]	]	PUNCT
ejpam-5730	375	4	in	in	ADP
ejpam-5730	375	5	1969	1969	NUM
ejpam-5730	375	6	some	some	DET
ejpam-5730	375	7	fixed	fix	VERB
ejpam-5730	375	8	point	point	NOUN
ejpam-5730	375	9	theorems	theorem	NOUN
ejpam-5730	375	10	for	for	ADP
ejpam-5730	375	11	multi	multi	ADJ
ejpam-5730	375	12	-	-	ADJ
ejpam-5730	375	13	valued	value	VERB
ejpam-5730	375	14	contraction	contraction	NOUN
ejpam-5730	375	15	mappings	mapping	NOUN
ejpam-5730	375	16	(	(	PUNCT
ejpam-5730	375	17	m.v.c.m	m.v.c.m	X
ejpam-5730	375	18	.	.	PUNCT
ejpam-5730	375	19	)	)	PUNCT
ejpam-5730	375	20	are	be	AUX
ejpam-5730	375	21	proved	prove	VERB
ejpam-5730	375	22	,	,	PUNCT
ejpam-5730	375	23	as	as	ADV
ejpam-5730	375	24	well	well	ADV
ejpam-5730	375	25	as	as	ADP
ejpam-5730	375	26	a	a	DET
ejpam-5730	375	27	theorem	theorem	NOUN
ejpam-5730	375	28	on	on	ADP
ejpam-5730	375	29	the	the	DET
ejpam-5730	375	30	behaviour	behaviour	NOUN
ejpam-5730	375	31	of	of	ADP
ejpam-5730	375	32	fixed	fix	VERB
ejpam-5730	375	33	points	point	NOUN
ejpam-5730	375	34	as	as	SCONJ
ejpam-5730	375	35	the	the	DET
ejpam-5730	375	36	mappings	mapping	NOUN
ejpam-5730	375	37	vary	vary	VERB
ejpam-5730	375	38	.	.	PUNCT
ejpam-5730	376	1	theorem	theorem	VERB
ejpam-5730	376	2	7.1	7.1	NUM
ejpam-5730	376	3	.	.	PUNCT
ejpam-5730	377	1	(	(	PUNCT
ejpam-5730	377	2	nadler	nadler	PROPN
ejpam-5730	377	3	)	)	PUNCT
ejpam-5730	377	4	let	let	VERB
ejpam-5730	377	5	(	(	PUNCT
ejpam-5730	377	6	x	x	NOUN
ejpam-5730	377	7	,	,	PUNCT
ejpam-5730	377	8	d	d	NOUN
ejpam-5730	377	9	)	)	PUNCT
ejpam-5730	377	10	be	be	AUX
ejpam-5730	377	11	a	a	DET
ejpam-5730	377	12	complete	complete	ADJ
ejpam-5730	377	13	metric	metric	ADJ
ejpam-5730	377	14	space	space	NOUN
ejpam-5730	377	15	.	.	PUNCT
ejpam-5730	378	1	if	if	SCONJ
ejpam-5730	378	2	f	f	PROPN
ejpam-5730	378	3	:	:	PUNCT
ejpam-5730	378	4	x	x	X
ejpam-5730	378	5	→	→	SYM
ejpam-5730	378	6	bc(x	bc(x	NOUN
ejpam-5730	378	7	)	)	PUNCT
ejpam-5730	378	8	is	be	AUX
ejpam-5730	378	9	a	a	DET
ejpam-5730	378	10	m.v.c.m	m.v.c.m	PROPN
ejpam-5730	378	11	.	.	PROPN
ejpam-5730	378	12	,	,	PUNCT
ejpam-5730	378	13	then	then	ADV
ejpam-5730	378	14	f	f	PROPN
ejpam-5730	378	15	has	have	VERB
ejpam-5730	378	16	a	a	DET
ejpam-5730	378	17	fixed	fix	VERB
ejpam-5730	378	18	point	point	NOUN
ejpam-5730	378	19	.	.	PUNCT
ejpam-5730	379	1	5	5	X
ejpam-5730	379	2	.	.	PUNCT
ejpam-5730	379	3	added	add	VERB
ejpam-5730	379	4	in	in	ADP
ejpam-5730	379	5	proof	proof	NOUN
ejpam-5730	379	6	.	.	PUNCT
ejpam-5730	380	1	in	in	ADP
ejpam-5730	380	2	a	a	DET
ejpam-5730	380	3	forthcoming	forthcoming	ADJ
ejpam-5730	380	4	paper	paper	NOUN
ejpam-5730	380	5	with	with	ADP
ejpam-5730	380	6	professor	professor	NOUN
ejpam-5730	380	7	covitz	covitz	NOUN
ejpam-5730	380	8	on	on	ADP
ejpam-5730	380	9	multi	multi	ADJ
ejpam-5730	380	10	-	-	ADJ
ejpam-5730	380	11	valued	value	VERB
ejpam-5730	380	12	contraction	contraction	NOUN
ejpam-5730	380	13	mappings	mapping	NOUN
ejpam-5730	380	14	in	in	ADP
ejpam-5730	380	15	generalized	generalized	ADJ
ejpam-5730	380	16	metric	metric	ADJ
ejpam-5730	380	17	spaces	space	NOUN
ejpam-5730	380	18	the	the	DET
ejpam-5730	380	19	author	author	NOUN
ejpam-5730	380	20	has	have	AUX
ejpam-5730	380	21	extended	extend	VERB
ejpam-5730	380	22	theorems	theorem	NOUN
ejpam-5730	380	23	5	5	NUM
ejpam-5730	380	24	and	and	CCONJ
ejpam-5730	380	25	6	6	NUM
ejpam-5730	380	26	of	of	ADP
ejpam-5730	380	27	this	this	DET
ejpam-5730	380	28	paper	paper	NOUN
ejpam-5730	380	29	to	to	PART
ejpam-5730	380	30	mappings	mapping	NOUN
ejpam-5730	380	31	into	into	ADP
ejpam-5730	380	32	cl(x	cl(x	NOUN
ejpam-5730	380	33	)	)	PUNCT
ejpam-5730	380	34	=	=	PRON
ejpam-5730	380	35	{	{	PUNCT
ejpam-5730	380	36	c	c	NOUN
ejpam-5730	380	37	:	:	PUNCT
ejpam-5730	380	38	c	c	NOUN
ejpam-5730	380	39	is	be	AUX
ejpam-5730	380	40	a	a	DET
ejpam-5730	380	41	nonempty	nonempty	ADJ
ejpam-5730	380	42	closed	close	VERB
ejpam-5730	380	43	subset	subset	NOUN
ejpam-5730	380	44	of	of	ADP
ejpam-5730	380	45	x	x	NOUN
ejpam-5730	380	46	}	}	PUNCT
ejpam-5730	380	47	with	with	ADP
ejpam-5730	380	48	the	the	DET
ejpam-5730	380	49	generalized	generalize	VERB
ejpam-5730	380	50	hausdorff	hausdorff	NOUN
ejpam-5730	380	51	distance	distance	NOUN
ejpam-5730	380	52	.	.	PUNCT
ejpam-5730	381	1	these	these	DET
ejpam-5730	381	2	results	result	NOUN
ejpam-5730	381	3	give	give	VERB
ejpam-5730	381	4	an	an	DET
ejpam-5730	381	5	affirmative	affirmative	ADJ
ejpam-5730	381	6	answer	answer	NOUN
ejpam-5730	381	7	to	to	ADP
ejpam-5730	381	8	problems	problem	NOUN
ejpam-5730	381	9	posed	pose	VERB
ejpam-5730	381	10	in	in	ADP
ejpam-5730	381	11	this	this	DET
ejpam-5730	381	12	remark	remark	NOUN
ejpam-5730	381	13	and	and	CCONJ
ejpam-5730	381	14	show	show	VERB
ejpam-5730	381	15	that	that	SCONJ
ejpam-5730	381	16	even	even	ADV
ejpam-5730	381	17	boundedness	boundedness	NOUN
ejpam-5730	381	18	of	of	ADP
ejpam-5730	381	19	point	point	NOUN
ejpam-5730	381	20	images	image	NOUN
ejpam-5730	381	21	is	be	AUX
ejpam-5730	381	22	not	not	PART
ejpam-5730	381	23	necessary	necessary	ADJ
ejpam-5730	381	24	.	.	PUNCT
ejpam-5730	382	1	comment	comment	NOUN
ejpam-5730	382	2	:	:	PUNCT
ejpam-5730	382	3	nadler	nadler	PROPN
ejpam-5730	382	4	’s	’s	NOUN
ejpam-5730	382	5	and	and	CCONJ
ejpam-5730	382	6	covitz	covitz	PROPN
ejpam-5730	382	7	-	-	PUNCT
ejpam-5730	382	8	nadler	nadler	PROPN
ejpam-5730	382	9	’s	’s	PART
ejpam-5730	382	10	fixed	fix	VERB
ejpam-5730	382	11	point	point	NOUN
ejpam-5730	382	12	theorems	theorem	NOUN
ejpam-5730	382	13	are	be	AUX
ejpam-5730	382	14	consequences	consequence	NOUN
ejpam-5730	382	15	of	of	ADP
ejpam-5730	382	16	theorem	theorem	ADJ
ejpam-5730	382	17	h(δ	h(δ	NOUN
ejpam-5730	382	18	)	)	PUNCT
ejpam-5730	382	19	with	with	ADP
ejpam-5730	382	20	simple	simple	ADJ
ejpam-5730	382	21	elementary	elementary	ADJ
ejpam-5730	382	22	proofs	proof	NOUN
ejpam-5730	382	23	.	.	PUNCT
ejpam-5730	383	1	in	in	ADP
ejpam-5730	383	2	fact	fact	NOUN
ejpam-5730	383	3	,	,	PUNCT
ejpam-5730	383	4	theorems	theorems	PROPN
ejpam-5730	383	5	h(δ)–(ϵ	h(δ)–(ϵ	NOUN
ejpam-5730	383	6	)	)	PUNCT
ejpam-5730	383	7	are	be	AUX
ejpam-5730	383	8	new	new	ADJ
ejpam-5730	383	9	theorems	theorem	NOUN
ejpam-5730	383	10	.	.	PUNCT
ejpam-5730	384	1	fierro	fierro	PROPN
ejpam-5730	384	2	and	and	CCONJ
ejpam-5730	384	3	pizarro	pizarro	PROPN
ejpam-5730	385	1	[	[	X
ejpam-5730	385	2	12	12	NUM
ejpam-5730	385	3	]	]	PUNCT
ejpam-5730	385	4	in	in	ADP
ejpam-5730	385	5	2023	2023	NUM
ejpam-5730	385	6	from	from	ADP
ejpam-5730	385	7	text	text	NOUN
ejpam-5730	385	8	:	:	PUNCT
ejpam-5730	385	9	in	in	ADP
ejpam-5730	385	10	this	this	DET
ejpam-5730	385	11	note	note	NOUN
ejpam-5730	385	12	,	,	PUNCT
ejpam-5730	385	13	we	we	PRON
ejpam-5730	385	14	prove	prove	VERB
ejpam-5730	385	15	a	a	DET
ejpam-5730	385	16	fixed	fix	VERB
ejpam-5730	385	17	point	point	NOUN
ejpam-5730	385	18	existence	existence	NOUN
ejpam-5730	385	19	theorem	theorem	VERB
ejpam-5730	385	20	for	for	ADP
ejpam-5730	385	21	set	set	NOUN
ejpam-5730	385	22	-	-	PUNCT
ejpam-5730	385	23	valued	value	VERB
ejpam-5730	385	24	functions	function	NOUN
ejpam-5730	385	25	by	by	ADP
ejpam-5730	385	26	extending	extend	VERB
ejpam-5730	385	27	the	the	DET
ejpam-5730	385	28	usual	usual	ADJ
ejpam-5730	385	29	banach	banach	NOUN
ejpam-5730	385	30	orbital	orbital	ADJ
ejpam-5730	385	31	condition	condition	NOUN
ejpam-5730	385	32	concept	concept	NOUN
ejpam-5730	385	33	for	for	ADP
ejpam-5730	385	34	single	single	ADJ
ejpam-5730	385	35	valued	value	VERB
ejpam-5730	385	36	mappings	mapping	NOUN
ejpam-5730	385	37	.	.	PUNCT
ejpam-5730	386	1	as	as	SCONJ
ejpam-5730	386	2	we	we	PRON
ejpam-5730	386	3	show	show	VERB
ejpam-5730	386	4	,	,	PUNCT
ejpam-5730	386	5	this	this	DET
ejpam-5730	386	6	result	result	NOUN
ejpam-5730	386	7	applies	apply	VERB
ejpam-5730	386	8	to	to	ADP
ejpam-5730	386	9	various	various	ADJ
ejpam-5730	386	10	types	type	NOUN
ejpam-5730	386	11	of	of	ADP
ejpam-5730	386	12	set	set	NOUN
ejpam-5730	386	13	-	-	PUNCT
ejpam-5730	386	14	valued	value	VERB
ejpam-5730	386	15	contractions	contraction	NOUN
ejpam-5730	386	16	existing	exist	VERB
ejpam-5730	386	17	in	in	ADP
ejpam-5730	386	18	the	the	DET
ejpam-5730	386	19	literature	literature	NOUN
ejpam-5730	386	20	.	.	PUNCT
ejpam-5730	387	1	given	give	VERB
ejpam-5730	387	2	a	a	DET
ejpam-5730	387	3	multimap	multimap	ADJ
ejpam-5730	387	4	t	t	NOUN
ejpam-5730	387	5	:	:	PUNCT
ejpam-5730	387	6	x	x	X
ejpam-5730	387	7	→	→	SYM
ejpam-5730	387	8	bc(x	bc(x	NOUN
ejpam-5730	387	9	)	)	PUNCT
ejpam-5730	387	10	,	,	PUNCT
ejpam-5730	387	11	x0	x0	PROPN
ejpam-5730	387	12	∈	∈	PROPN
ejpam-5730	387	13	x	x	X
ejpam-5730	387	14	,	,	PUNCT
ejpam-5730	387	15	and	and	CCONJ
ejpam-5730	387	16	k	k	PROPN
ejpam-5730	387	17	∈	∈	PROPN
ejpam-5730	387	18	[	[	X
ejpam-5730	387	19	0	0	NUM
ejpam-5730	387	20	,	,	PUNCT
ejpam-5730	387	21	1	1	NUM
ejpam-5730	387	22	)	)	PUNCT
ejpam-5730	387	23	,	,	PUNCT
ejpam-5730	387	24	we	we	PRON
ejpam-5730	387	25	say	say	VERB
ejpam-5730	387	26	t	t	PROPN
ejpam-5730	387	27	satisfies	satisfy	VERB
ejpam-5730	387	28	the	the	DET
ejpam-5730	387	29	multivalued	multivalued	ADJ
ejpam-5730	387	30	banach	banach	NOUN
ejpam-5730	387	31	orbital	orbital	ADJ
ejpam-5730	387	32	(	(	PUNCT
ejpam-5730	387	33	mbo	mbo	NOUN
ejpam-5730	387	34	)	)	PUNCT
ejpam-5730	387	35	condition	condition	NOUN
ejpam-5730	387	36	at	at	ADP
ejpam-5730	387	37	x0	x0	PROPN
ejpam-5730	387	38	with	with	ADP
ejpam-5730	387	39	constant	constant	ADJ
ejpam-5730	387	40	k	k	NOUN
ejpam-5730	387	41	,	,	PUNCT
ejpam-5730	387	42	whenever	whenever	SCONJ
ejpam-5730	387	43	for	for	ADP
ejpam-5730	387	44	all	all	DET
ejpam-5730	387	45	x	x	SYM
ejpam-5730	387	46	∈	∈	PROPN
ejpam-5730	387	47	o(x0	o(x0	NOUN
ejpam-5730	387	48	,	,	PUNCT
ejpam-5730	387	49	t	t	PROPN
ejpam-5730	387	50	)	)	PUNCT
ejpam-5730	387	51	,	,	PUNCT
ejpam-5730	387	52	infy∈tx	infy∈tx	PROPN
ejpam-5730	388	1	d(y	d(y	PROPN
ejpam-5730	388	2	,	,	PUNCT
ejpam-5730	388	3	ty	ty	NOUN
ejpam-5730	388	4	)	)	PUNCT
ejpam-5730	388	5	≤	≤	NOUN
ejpam-5730	389	1	k	k	PROPN
ejpam-5730	389	2	d(x	d(x	PROPN
ejpam-5730	389	3	,	,	PUNCT
ejpam-5730	389	4	tx	tx	PROPN
ejpam-5730	389	5	)	)	PUNCT
ejpam-5730	389	6	,	,	PUNCT
ejpam-5730	389	7	and	and	CCONJ
ejpam-5730	389	8	that	that	SCONJ
ejpam-5730	389	9	,	,	PUNCT
ejpam-5730	389	10	t	t	PROPN
ejpam-5730	389	11	satisfies	satisfy	VERB
ejpam-5730	389	12	the	the	DET
ejpam-5730	389	13	strong	strong	ADJ
ejpam-5730	389	14	multivalued	multivalued	ADJ
ejpam-5730	389	15	banach	banach	NOUN
ejpam-5730	389	16	orbital	orbital	ADJ
ejpam-5730	389	17	(	(	PUNCT
ejpam-5730	389	18	smbo	smbo	ADJ
ejpam-5730	389	19	)	)	PUNCT
ejpam-5730	389	20	condition	condition	NOUN
ejpam-5730	389	21	at	at	ADP
ejpam-5730	389	22	x0	x0	PROPN
ejpam-5730	389	23	with	with	ADP
ejpam-5730	389	24	constant	constant	ADJ
ejpam-5730	389	25	k	k	NOUN
ejpam-5730	389	26	,	,	PUNCT
ejpam-5730	389	27	whenever	whenever	SCONJ
ejpam-5730	389	28	for	for	ADP
ejpam-5730	389	29	all	all	DET
ejpam-5730	389	30	x	x	SYM
ejpam-5730	389	31	∈	∈	PROPN
ejpam-5730	389	32	o(x0	o(x0	NOUN
ejpam-5730	389	33	,	,	PUNCT
ejpam-5730	389	34	t	t	PROPN
ejpam-5730	389	35	)	)	PUNCT
ejpam-5730	389	36	,	,	PUNCT
ejpam-5730	389	37	supy∈tx	supy∈tx	PROPN
ejpam-5730	390	1	d(y	d(y	PROPN
ejpam-5730	390	2	,	,	PUNCT
ejpam-5730	390	3	ty	ty	NOUN
ejpam-5730	390	4	)	)	PUNCT
ejpam-5730	390	5	≤	≤	NOUN
ejpam-5730	391	1	k	k	PROPN
ejpam-5730	391	2	d(x	d(x	PROPN
ejpam-5730	391	3	,	,	PUNCT
ejpam-5730	391	4	tx	tx	PROPN
ejpam-5730	391	5	)	)	PUNCT
ejpam-5730	391	6	.	.	PUNCT
ejpam-5730	392	1	theorem	theorem	VERB
ejpam-5730	392	2	7.2	7.2	NUM
ejpam-5730	392	3	.	.	PUNCT
ejpam-5730	393	1	(	(	PUNCT
ejpam-5730	393	2	fierro	fierro	ADJ
ejpam-5730	393	3	-	-	PUNCT
ejpam-5730	393	4	pizarro	pizarro	PROPN
ejpam-5730	393	5	)	)	PUNCT
ejpam-5730	393	6	let	let	AUX
ejpam-5730	393	7	t	t	NOUN
ejpam-5730	393	8	:	:	PUNCT
ejpam-5730	393	9	x	x	X
ejpam-5730	393	10	→	→	SYM
ejpam-5730	393	11	bc(x	bc(x	NOUN
ejpam-5730	393	12	)	)	PUNCT
ejpam-5730	393	13	be	be	AUX
ejpam-5730	393	14	a	a	DET
ejpam-5730	393	15	set	set	NOUN
ejpam-5730	393	16	-	-	PUNCT
ejpam-5730	393	17	valued	value	VERB
ejpam-5730	393	18	mapping	mapping	NOUN
ejpam-5730	393	19	satisfying	satisfy	VERB
ejpam-5730	393	20	the	the	DET
ejpam-5730	393	21	mbo	mbo	NOUN
ejpam-5730	393	22	condition	condition	NOUN
ejpam-5730	393	23	at	at	ADP
ejpam-5730	393	24	x0	x0	PROPN
ejpam-5730	393	25	∈	∈	PROPN
ejpam-5730	393	26	x	x	PUNCT
ejpam-5730	393	27	with	with	ADP
ejpam-5730	393	28	constant	constant	ADJ
ejpam-5730	393	29	k.	k.	PROPN
ejpam-5730	393	30	then	then	ADV
ejpam-5730	393	31	,	,	PUNCT
ejpam-5730	393	32	there	there	PRON
ejpam-5730	393	33	exist	exist	VERB
ejpam-5730	393	34	x∗	x∗	PROPN
ejpam-5730	393	35	∈	∈	PROPN
ejpam-5730	393	36	x	x	X
ejpam-5730	393	37	and	and	CCONJ
ejpam-5730	393	38	a	a	DET
ejpam-5730	393	39	sequence	sequence	NOUN
ejpam-5730	393	40	{	{	PUNCT
ejpam-5730	393	41	xn}n∈n	xn}n∈n	PUNCT
ejpam-5730	393	42	converging	converge	VERB
ejpam-5730	393	43	to	to	ADP
ejpam-5730	393	44	x∗	x∗	PROPN
ejpam-5730	393	45	such	such	ADJ
ejpam-5730	393	46	that	that	SCONJ
ejpam-5730	393	47	,	,	PUNCT
ejpam-5730	393	48	for	for	ADP
ejpam-5730	393	49	all	all	PRON
ejpam-5730	393	50	n	n	PRON
ejpam-5730	393	51	∈	∈	PROPN
ejpam-5730	393	52	n	n	CCONJ
ejpam-5730	393	53	,	,	PUNCT
ejpam-5730	393	54	xn+1	xn+1	PROPN
ejpam-5730	393	55	∈	∈	PROPN
ejpam-5730	393	56	txn	txn	NOUN
ejpam-5730	393	57	,	,	PUNCT
ejpam-5730	393	58	and	and	CCONJ
ejpam-5730	393	59	the	the	DET
ejpam-5730	393	60	following	follow	VERB
ejpam-5730	393	61	two	two	NUM
ejpam-5730	393	62	conditions	condition	NOUN
ejpam-5730	393	63	hold	hold	VERB
ejpam-5730	393	64	:	:	PUNCT
ejpam-5730	393	65	(	(	PUNCT
ejpam-5730	393	66	i	i	NOUN
ejpam-5730	393	67	)	)	PUNCT
ejpam-5730	394	1	d(xn	d(xn	PROPN
ejpam-5730	394	2	,	,	PUNCT
ejpam-5730	394	3	txn	txn	NOUN
ejpam-5730	394	4	)	)	PUNCT
ejpam-5730	394	5	≤	≤	NOUN
ejpam-5730	395	1	d(xn	d(xn	PROPN
ejpam-5730	395	2	,	,	PUNCT
ejpam-5730	395	3	xn+1	xn+1	NUM
ejpam-5730	395	4	)	)	PUNCT
ejpam-5730	395	5	≤	≤	NUM
ejpam-5730	395	6	kn	kn	PROPN
ejpam-5730	395	7	d(x0	d(x0	PROPN
ejpam-5730	395	8	,	,	PUNCT
ejpam-5730	395	9	tx0	tx0	PROPN
ejpam-5730	395	10	)	)	PUNCT
ejpam-5730	395	11	and	and	CCONJ
ejpam-5730	395	12	(	(	PUNCT
ejpam-5730	395	13	ii	ii	NOUN
ejpam-5730	395	14	)	)	PUNCT
ejpam-5730	395	15	d(x∗	d(x∗	NOUN
ejpam-5730	395	16	,	,	PUNCT
ejpam-5730	395	17	txn	txn	NOUN
ejpam-5730	395	18	)	)	PUNCT
ejpam-5730	395	19	≤	≤	NOUN
ejpam-5730	395	20	{	{	PUNCT
ejpam-5730	395	21	kn+1/(1−	kn+1/(1−	ADJ
ejpam-5730	395	22	k)}d(x0	k)}d(x0	NOUN
ejpam-5730	395	23	,	,	PUNCT
ejpam-5730	395	24	tx0	tx0	NOUN
ejpam-5730	395	25	)	)	PUNCT
ejpam-5730	395	26	for	for	ADP
ejpam-5730	395	27	all	all	PRON
ejpam-5730	395	28	n	n	DET
ejpam-5730	395	29	∈	∈	PROPN
ejpam-5730	395	30	n.	n.	NOUN
ejpam-5730	395	31	moreover	moreover	ADV
ejpam-5730	395	32	,	,	PUNCT
ejpam-5730	395	33	the	the	DET
ejpam-5730	395	34	following	follow	VERB
ejpam-5730	395	35	conditions	condition	NOUN
ejpam-5730	395	36	are	be	AUX
ejpam-5730	395	37	equivalent	equivalent	ADJ
ejpam-5730	395	38	:	:	PUNCT
ejpam-5730	395	39	(	(	PUNCT
ejpam-5730	395	40	iii	iii	X
ejpam-5730	395	41	)	)	PUNCT
ejpam-5730	395	42	x∗	x∗	PROPN
ejpam-5730	395	43	∈	∈	PROPN
ejpam-5730	395	44	tx∗	tx∗	PROPN
ejpam-5730	395	45	,	,	PUNCT
ejpam-5730	395	46	(	(	PUNCT
ejpam-5730	395	47	iv	iv	X
ejpam-5730	395	48	)	)	PUNCT
ejpam-5730	395	49	gt	gt	PROPN
ejpam-5730	395	50	is	be	AUX
ejpam-5730	395	51	(	(	PUNCT
ejpam-5730	395	52	x0	x0	PROPN
ejpam-5730	395	53	,	,	PUNCT
ejpam-5730	395	54	t	t	NOUN
ejpam-5730	395	55	)	)	PUNCT
ejpam-5730	395	56	-orbitally	-orbitally	ADV
ejpam-5730	395	57	lower	low	ADJ
ejpam-5730	395	58	semicontinuous	semicontinuous	ADJ
ejpam-5730	395	59	at	at	ADP
ejpam-5730	395	60	x∗	x∗	PROPN
ejpam-5730	395	61	,	,	PUNCT
ejpam-5730	395	62	and	and	CCONJ
ejpam-5730	395	63	(	(	PUNCT
ejpam-5730	395	64	v	v	NOUN
ejpam-5730	395	65	)	)	PUNCT
ejpam-5730	395	66	the	the	DET
ejpam-5730	395	67	function	function	NOUN
ejpam-5730	395	68	h	h	NOUN
ejpam-5730	395	69	:	:	PUNCT
ejpam-5730	395	70	x	x	X
ejpam-5730	395	71	→	→	SYM
ejpam-5730	395	72	r	r	NOUN
ejpam-5730	395	73	,	,	PUNCT
ejpam-5730	395	74	defined	define	VERB
ejpam-5730	395	75	by	by	ADP
ejpam-5730	395	76	h(x	h(x	PROPN
ejpam-5730	395	77	)	)	PUNCT
ejpam-5730	396	1	=	=	SYM
ejpam-5730	396	2	d(x	d(x	PROPN
ejpam-5730	396	3	,	,	PUNCT
ejpam-5730	396	4	tx	tx	PROPN
ejpam-5730	396	5	)	)	PUNCT
ejpam-5730	396	6	,	,	PUNCT
ejpam-5730	396	7	is	be	AUX
ejpam-5730	396	8	lower	low	ADJ
ejpam-5730	396	9	semicontinuous	semicontinuous	ADJ
ejpam-5730	396	10	at	at	ADP
ejpam-5730	396	11	x∗.	x∗.	PROPN
ejpam-5730	396	12	s.	s.	PROPN
ejpam-5730	396	13	park	park	PROPN
ejpam-5730	396	14	/	/	SYM
ejpam-5730	396	15	eur	eur	PROPN
ejpam-5730	396	16	.	.	PUNCT
ejpam-5730	397	1	j.	j.	PROPN
ejpam-5730	397	2	pure	pure	PROPN
ejpam-5730	397	3	appl	appl	PROPN
ejpam-5730	397	4	.	.	PROPN
ejpam-5730	397	5	math	math	PROPN
ejpam-5730	397	6	,	,	PUNCT
ejpam-5730	397	7	18	18	NUM
ejpam-5730	397	8	(	(	PUNCT
ejpam-5730	397	9	1	1	NUM
ejpam-5730	397	10	)	)	PUNCT
ejpam-5730	397	11	(	(	PUNCT
ejpam-5730	397	12	2025	2025	NUM
ejpam-5730	397	13	)	)	PUNCT
ejpam-5730	397	14	,	,	PUNCT
ejpam-5730	397	15	5730	5730	NUM
ejpam-5730	397	16	16	16	NUM
ejpam-5730	397	17	of	of	ADP
ejpam-5730	397	18	21	21	NUM
ejpam-5730	397	19	comment	comment	NOUN
ejpam-5730	397	20	:	:	PUNCT
ejpam-5730	397	21	the	the	DET
ejpam-5730	397	22	authors	author	NOUN
ejpam-5730	397	23	only	only	ADV
ejpam-5730	397	24	claimed	claim	VERB
ejpam-5730	397	25	the	the	DET
ejpam-5730	397	26	equivalency	equivalency	NOUN
ejpam-5730	397	27	of	of	ADP
ejpam-5730	397	28	(	(	PUNCT
ejpam-5730	397	29	iii)-(v	iii)-(v	PROPN
ejpam-5730	397	30	)	)	PUNCT
ejpam-5730	397	31	.	.	PUNCT
ejpam-5730	398	1	in	in	ADP
ejpam-5730	398	2	the	the	DET
ejpam-5730	398	3	present	present	ADJ
ejpam-5730	398	4	article	article	NOUN
ejpam-5730	398	5	,	,	PUNCT
ejpam-5730	398	6	we	we	PRON
ejpam-5730	398	7	showed	show	VERB
ejpam-5730	398	8	that	that	SCONJ
ejpam-5730	398	9	(	(	PUNCT
ejpam-5730	398	10	iii)-(v	iii)-(v	PROPN
ejpam-5730	398	11	)	)	PUNCT
ejpam-5730	398	12	actually	actually	ADV
ejpam-5730	398	13	hold	hold	VERB
ejpam-5730	398	14	when	when	SCONJ
ejpam-5730	398	15	x	x	PRON
ejpam-5730	398	16	is	be	AUX
ejpam-5730	398	17	t	t	NOUN
ejpam-5730	398	18	-orbitally	-orbitally	ADV
ejpam-5730	398	19	complete	complete	ADJ
ejpam-5730	398	20	quasi	quasi	ADJ
ejpam-5730	398	21	-	-	ADJ
ejpam-5730	398	22	metric	metric	ADJ
ejpam-5730	398	23	space	space	NOUN
ejpam-5730	398	24	.	.	PUNCT
ejpam-5730	399	1	8	8	X
ejpam-5730	399	2	.	.	PUNCT
ejpam-5730	399	3	theorems	theorem	NOUN
ejpam-5730	399	4	not	not	PART
ejpam-5730	399	5	belonging	belong	VERB
ejpam-5730	399	6	any	any	PRON
ejpam-5730	399	7	of	of	ADP
ejpam-5730	399	8	the	the	DET
ejpam-5730	399	9	above	above	ADJ
ejpam-5730	399	10	families	family	NOUN
ejpam-5730	399	11	there	there	PRON
ejpam-5730	399	12	are	be	VERB
ejpam-5730	399	13	relatively	relatively	ADV
ejpam-5730	399	14	small	small	ADJ
ejpam-5730	399	15	number	number	NOUN
ejpam-5730	399	16	of	of	ADP
ejpam-5730	399	17	theorems	theorem	NOUN
ejpam-5730	399	18	which	which	PRON
ejpam-5730	399	19	does	do	AUX
ejpam-5730	399	20	not	not	PART
ejpam-5730	399	21	belong	belong	VERB
ejpam-5730	399	22	to	to	ADP
ejpam-5730	399	23	any	any	PRON
ejpam-5730	399	24	of	of	ADP
ejpam-5730	399	25	the	the	DET
ejpam-5730	399	26	families	family	NOUN
ejpam-5730	399	27	{	{	PUNCT
ejpam-5730	399	28	α	α	NOUN
ejpam-5730	399	29	}	}	PUNCT
ejpam-5730	399	30	−	−	PROPN
ejpam-5730	399	31	{	{	PUNCT
ejpam-5730	399	32	ϵ	ϵ	NOUN
ejpam-5730	399	33	}	}	PUNCT
ejpam-5730	399	34	.	.	PUNCT
ejpam-5730	400	1	we	we	PRON
ejpam-5730	400	2	give	give	VERB
ejpam-5730	400	3	only	only	ADV
ejpam-5730	400	4	a	a	DET
ejpam-5730	400	5	few	few	ADJ
ejpam-5730	400	6	example	example	NOUN
ejpam-5730	400	7	of	of	ADP
ejpam-5730	400	8	such	such	ADJ
ejpam-5730	400	9	theorems	theorem	NOUN
ejpam-5730	400	10	.	.	PUNCT
ejpam-5730	401	1	ćirić	ćirić	NOUN
ejpam-5730	402	1	[	[	X
ejpam-5730	402	2	7	7	X
ejpam-5730	402	3	]	]	PUNCT
ejpam-5730	402	4	in	in	ADP
ejpam-5730	402	5	1974	1974	NUM
ejpam-5730	402	6	ćirić	ćirić	NOUN
ejpam-5730	402	7	proved	prove	VERB
ejpam-5730	402	8	a	a	DET
ejpam-5730	402	9	celebrated	celebrated	ADJ
ejpam-5730	402	10	fixed	fix	VERB
ejpam-5730	402	11	point	point	NOUN
ejpam-5730	402	12	theorem	theorem	NOUN
ejpam-5730	402	13	as	as	SCONJ
ejpam-5730	402	14	follows	follow	VERB
ejpam-5730	402	15	:	:	PUNCT
ejpam-5730	402	16	theorem	theorem	NOUN
ejpam-5730	402	17	8.1	8.1	NUM
ejpam-5730	402	18	.	.	PUNCT
ejpam-5730	403	1	(	(	PUNCT
ejpam-5730	403	2	ćirić	ćirić	NOUN
ejpam-5730	403	3	)	)	PUNCT
ejpam-5730	403	4	let	let	VERB
ejpam-5730	403	5	t	t	NOUN
ejpam-5730	403	6	be	be	AUX
ejpam-5730	403	7	a	a	DET
ejpam-5730	403	8	self	self	NOUN
ejpam-5730	403	9	map	map	NOUN
ejpam-5730	403	10	of	of	ADP
ejpam-5730	403	11	a	a	DET
ejpam-5730	403	12	complete	complete	ADJ
ejpam-5730	403	13	metric	metric	ADJ
ejpam-5730	403	14	space	space	NOUN
ejpam-5730	403	15	(	(	PUNCT
ejpam-5730	403	16	x	x	X
ejpam-5730	403	17	,	,	PUNCT
ejpam-5730	403	18	d	d	NOUN
ejpam-5730	403	19	)	)	PUNCT
ejpam-5730	403	20	.	.	PUNCT
ejpam-5730	404	1	if	if	SCONJ
ejpam-5730	404	2	there	there	PRON
ejpam-5730	404	3	is	be	VERB
ejpam-5730	404	4	a	a	DET
ejpam-5730	404	5	constant	constant	ADJ
ejpam-5730	404	6	α	α	NOUN
ejpam-5730	404	7	∈	∈	PROPN
ejpam-5730	404	8	(	(	PUNCT
ejpam-5730	404	9	0	0	NUM
ejpam-5730	404	10	,	,	PUNCT
ejpam-5730	404	11	1	1	NUM
ejpam-5730	404	12	)	)	PUNCT
ejpam-5730	404	13	such	such	ADJ
ejpam-5730	404	14	that	that	SCONJ
ejpam-5730	404	15	d(tx	d(tx	PROPN
ejpam-5730	404	16	,	,	PUNCT
ejpam-5730	404	17	ty	ty	NOUN
ejpam-5730	404	18	)	)	PUNCT
ejpam-5730	404	19	≤	≤	NOUN
ejpam-5730	404	20	αmax{d(x	αmax{d(x	NOUN
ejpam-5730	404	21	,	,	PUNCT
ejpam-5730	404	22	y	y	NOUN
ejpam-5730	404	23	)	)	PUNCT
ejpam-5730	404	24	,	,	PUNCT
ejpam-5730	404	25	d(x	d(x	PROPN
ejpam-5730	404	26	,	,	PUNCT
ejpam-5730	404	27	tx	tx	PROPN
ejpam-5730	404	28	)	)	PUNCT
ejpam-5730	404	29	,	,	PUNCT
ejpam-5730	404	30	d(y	d(y	PROPN
ejpam-5730	404	31	,	,	PUNCT
ejpam-5730	404	32	ty	ty	NOUN
ejpam-5730	404	33	)	)	PUNCT
ejpam-5730	404	34	,	,	PUNCT
ejpam-5730	404	35	d(x	d(x	PROPN
ejpam-5730	404	36	,	,	PUNCT
ejpam-5730	404	37	ty	ty	NOUN
ejpam-5730	404	38	)	)	PUNCT
ejpam-5730	404	39	,	,	PUNCT
ejpam-5730	404	40	d(y	d(y	PROPN
ejpam-5730	404	41	,	,	PUNCT
ejpam-5730	404	42	tx	tx	PROPN
ejpam-5730	404	43	)	)	PUNCT
ejpam-5730	404	44	}	}	PUNCT
ejpam-5730	404	45	,	,	PUNCT
ejpam-5730	404	46	for	for	ADP
ejpam-5730	404	47	all	all	DET
ejpam-5730	404	48	x	x	NOUN
ejpam-5730	404	49	,	,	PUNCT
ejpam-5730	404	50	y	y	PROPN
ejpam-5730	404	51	∈	∈	PROPN
ejpam-5730	404	52	x	x	X
ejpam-5730	404	53	,	,	PUNCT
ejpam-5730	404	54	then	then	ADV
ejpam-5730	404	55	t	t	PROPN
ejpam-5730	404	56	has	have	VERB
ejpam-5730	404	57	a	a	DET
ejpam-5730	404	58	unique	unique	ADJ
ejpam-5730	404	59	point	point	NOUN
ejpam-5730	404	60	z	z	NOUN
ejpam-5730	404	61	∈	∈	PROPN
ejpam-5730	404	62	x	x	X
ejpam-5730	404	63	and	and	CCONJ
ejpam-5730	404	64	d(z	d(z	PROPN
ejpam-5730	404	65	,	,	PUNCT
ejpam-5730	404	66	tnx0	tnx0	PROPN
ejpam-5730	404	67	)	)	PUNCT
ejpam-5730	404	68	→	→	SYM
ejpam-5730	404	69	0	0	NUM
ejpam-5730	404	70	as	as	ADP
ejpam-5730	404	71	n	n	NUM
ejpam-5730	404	72	→	→	SYM
ejpam-5730	404	73	∞	∞	PROPN
ejpam-5730	404	74	,	,	PUNCT
ejpam-5730	404	75	for	for	ADP
ejpam-5730	404	76	all	all	DET
ejpam-5730	404	77	x0	x0	PROPN
ejpam-5730	404	78	∈	∈	PROPN
ejpam-5730	404	79	x.	x.	NOUN
ejpam-5730	404	80	this	this	DET
ejpam-5730	404	81	theorem	theorem	NOUN
ejpam-5730	404	82	is	be	AUX
ejpam-5730	404	83	not	not	PART
ejpam-5730	404	84	in	in	ADP
ejpam-5730	404	85	{	{	PUNCT
ejpam-5730	404	86	β	β	NOUN
ejpam-5730	404	87	}	}	PUNCT
ejpam-5730	404	88	.	.	PUNCT
ejpam-5730	405	1	bogin	bogin	NOUN
ejpam-5730	406	1	[	[	X
ejpam-5730	406	2	5	5	X
ejpam-5730	406	3	]	]	PUNCT
ejpam-5730	406	4	in	in	ADP
ejpam-5730	406	5	1976	1976	NUM
ejpam-5730	406	6	theorem	theorem	VERB
ejpam-5730	406	7	8.2	8.2	NUM
ejpam-5730	406	8	.	.	PUNCT
ejpam-5730	407	1	(	(	PUNCT
ejpam-5730	407	2	bogin	bogin	NOUN
ejpam-5730	407	3	)	)	PUNCT
ejpam-5730	407	4	let	let	VERB
ejpam-5730	407	5	(	(	PUNCT
ejpam-5730	407	6	x	x	NOUN
ejpam-5730	407	7	,	,	PUNCT
ejpam-5730	407	8	d	d	NOUN
ejpam-5730	407	9	)	)	PUNCT
ejpam-5730	407	10	be	be	AUX
ejpam-5730	407	11	a	a	DET
ejpam-5730	407	12	complete	complete	ADJ
ejpam-5730	407	13	metric	metric	ADJ
ejpam-5730	407	14	space	space	NOUN
ejpam-5730	407	15	and	and	CCONJ
ejpam-5730	407	16	f	f	NOUN
ejpam-5730	407	17	:	:	PUNCT
ejpam-5730	407	18	x	x	X
ejpam-5730	407	19	→	→	SYM
ejpam-5730	407	20	x	x	X
ejpam-5730	407	21	a	a	DET
ejpam-5730	407	22	mapping	mapping	NOUN
ejpam-5730	407	23	satisfying	satisfy	VERB
ejpam-5730	407	24	for	for	ADP
ejpam-5730	407	25	each	each	DET
ejpam-5730	407	26	x	x	NOUN
ejpam-5730	407	27	,	,	PUNCT
ejpam-5730	407	28	y	y	PROPN
ejpam-5730	407	29	∈	∈	PROPN
ejpam-5730	408	1	x	x	X
ejpam-5730	408	2	:	:	PUNCT
ejpam-5730	408	3	d(fx	d(fx	PROPN
ejpam-5730	408	4	,	,	PUNCT
ejpam-5730	408	5	fy	fy	NOUN
ejpam-5730	408	6	)	)	PUNCT
ejpam-5730	408	7	≤	≤	NOUN
ejpam-5730	408	8	ad(x	ad(x	PUNCT
ejpam-5730	408	9	,	,	PUNCT
ejpam-5730	408	10	y	y	PROPN
ejpam-5730	408	11	)	)	PUNCT
ejpam-5730	409	1	+	+	CCONJ
ejpam-5730	409	2	b[d(x	b[d(x	NOUN
ejpam-5730	409	3	,	,	PUNCT
ejpam-5730	409	4	fx	fx	NOUN
ejpam-5730	409	5	)	)	PUNCT
ejpam-5730	409	6	+	+	CCONJ
ejpam-5730	409	7	d(y	d(y	PROPN
ejpam-5730	409	8	,	,	PUNCT
ejpam-5730	409	9	fy	fy	PROPN
ejpam-5730	409	10	)	)	PUNCT
ejpam-5730	409	11	]	]	PUNCT
ejpam-5730	410	1	+	+	CCONJ
ejpam-5730	410	2	c[d(x	c[d(x	NOUN
ejpam-5730	410	3	,	,	PUNCT
ejpam-5730	410	4	fy	fy	PROPN
ejpam-5730	410	5	)	)	PUNCT
ejpam-5730	411	1	+	+	CCONJ
ejpam-5730	411	2	d(y	d(y	PROPN
ejpam-5730	411	3	,	,	PUNCT
ejpam-5730	411	4	fx	fx	PROPN
ejpam-5730	411	5	)	)	PUNCT
ejpam-5730	411	6	]	]	PUNCT
ejpam-5730	411	7	where	where	SCONJ
ejpam-5730	411	8	a	a	DET
ejpam-5730	411	9	,	,	PUNCT
ejpam-5730	411	10	b	b	NOUN
ejpam-5730	411	11	,	,	PUNCT
ejpam-5730	411	12	c	c	NOUN
ejpam-5730	411	13	>	>	X
ejpam-5730	411	14	0	0	PUNCT
ejpam-5730	412	1	and	and	CCONJ
ejpam-5730	412	2	a+	a+	PUNCT
ejpam-5730	412	3	2b+	2b+	NUM
ejpam-5730	412	4	2c	2c	NUM
ejpam-5730	412	5	=	=	SYM
ejpam-5730	412	6	1	1	X
ejpam-5730	412	7	.	.	PUNCT
ejpam-5730	413	1	then	then	ADV
ejpam-5730	413	2	f	f	PROPN
ejpam-5730	413	3	has	have	VERB
ejpam-5730	413	4	a	a	DET
ejpam-5730	413	5	unique	unique	ADJ
ejpam-5730	413	6	fixed	fix	VERB
ejpam-5730	413	7	point	point	NOUN
ejpam-5730	413	8	in	in	ADP
ejpam-5730	413	9	x.	x.	PROPN
ejpam-5730	413	10	note	note	VERB
ejpam-5730	413	11	that	that	SCONJ
ejpam-5730	413	12	f	f	PROPN
ejpam-5730	413	13	is	be	AUX
ejpam-5730	413	14	not	not	PART
ejpam-5730	413	15	an	an	DET
ejpam-5730	413	16	rhr	rhr	NOUN
ejpam-5730	413	17	map	map	NOUN
ejpam-5730	413	18	.	.	PUNCT
ejpam-5730	414	1	jaggi	jaggi	NOUN
ejpam-5730	414	2	[	[	X
ejpam-5730	414	3	15	15	NUM
ejpam-5730	414	4	]	]	PUNCT
ejpam-5730	414	5	in	in	ADP
ejpam-5730	414	6	1977	1977	NUM
ejpam-5730	414	7	consider	consider	VERB
ejpam-5730	414	8	the	the	DET
ejpam-5730	414	9	following	following	NOUN
ejpam-5730	414	10	:	:	PUNCT
ejpam-5730	414	11	theorem	theorem	VERB
ejpam-5730	414	12	8.3	8.3	NUM
ejpam-5730	414	13	.	.	PUNCT
ejpam-5730	415	1	(	(	PUNCT
ejpam-5730	415	2	jaggi	jaggi	NOUN
ejpam-5730	415	3	)	)	PUNCT
ejpam-5730	415	4	let	let	VERB
ejpam-5730	415	5	(	(	PUNCT
ejpam-5730	415	6	x	x	NOUN
ejpam-5730	415	7	,	,	PUNCT
ejpam-5730	415	8	d	d	NOUN
ejpam-5730	415	9	)	)	PUNCT
ejpam-5730	415	10	be	be	AUX
ejpam-5730	415	11	a	a	DET
ejpam-5730	415	12	complete	complete	ADJ
ejpam-5730	415	13	metric	metric	ADJ
ejpam-5730	415	14	space	space	NOUN
ejpam-5730	415	15	and	and	CCONJ
ejpam-5730	415	16	t	t	NOUN
ejpam-5730	415	17	:	:	PUNCT
ejpam-5730	415	18	x	x	X
ejpam-5730	415	19	→	→	PUNCT
ejpam-5730	415	20	x	x	PUNCT
ejpam-5730	415	21	be	be	AUX
ejpam-5730	415	22	a	a	DET
ejpam-5730	415	23	continuous	continuous	ADJ
ejpam-5730	415	24	mapping	mapping	NOUN
ejpam-5730	415	25	.	.	PUNCT
ejpam-5730	416	1	if	if	SCONJ
ejpam-5730	416	2	there	there	PRON
ejpam-5730	416	3	exist	exist	VERB
ejpam-5730	416	4	k1	k1	NOUN
ejpam-5730	416	5	,	,	PUNCT
ejpam-5730	416	6	k2	k2	PROPN
ejpam-5730	416	7	∈	∈	PROPN
ejpam-5730	417	1	[	[	X
ejpam-5730	417	2	0	0	NUM
ejpam-5730	417	3	,	,	PUNCT
ejpam-5730	417	4	1	1	NUM
ejpam-5730	417	5	)	)	PUNCT
ejpam-5730	417	6	,	,	PUNCT
ejpam-5730	417	7	with	with	ADP
ejpam-5730	417	8	k1	k1	NOUN
ejpam-5730	417	9	+	+	CCONJ
ejpam-5730	417	10	k2	k2	X
ejpam-5730	417	11	<	<	X
ejpam-5730	417	12	1	1	NUM
ejpam-5730	417	13	such	such	ADJ
ejpam-5730	417	14	that	that	SCONJ
ejpam-5730	417	15	d(tx	d(tx	PROPN
ejpam-5730	417	16	,	,	PUNCT
ejpam-5730	417	17	ty	ty	NOUN
ejpam-5730	417	18	)	)	PUNCT
ejpam-5730	417	19	≤	≤	NOUN
ejpam-5730	417	20	k1	k1	X
ejpam-5730	417	21	·	·	PUNCT
ejpam-5730	417	22	d(x	d(x	NOUN
ejpam-5730	417	23	,	,	PUNCT
ejpam-5730	417	24	tx	tx	PROPN
ejpam-5730	417	25	)	)	PUNCT
ejpam-5730	417	26	d(y	d(y	PROPN
ejpam-5730	417	27	,	,	PUNCT
ejpam-5730	417	28	ty	ty	NOUN
ejpam-5730	417	29	)	)	PUNCT
ejpam-5730	417	30	d(x	d(x	PROPN
ejpam-5730	417	31	,	,	PUNCT
ejpam-5730	417	32	y	y	NOUN
ejpam-5730	417	33	)	)	PUNCT
ejpam-5730	417	34	+	+	CCONJ
ejpam-5730	417	35	k2	k2	X
ejpam-5730	417	36	·	·	PUNCT
ejpam-5730	417	37	d(x	d(x	PROPN
ejpam-5730	417	38	,	,	PUNCT
ejpam-5730	417	39	y	y	NOUN
ejpam-5730	417	40	)	)	PUNCT
ejpam-5730	417	41	for	for	ADP
ejpam-5730	417	42	all	all	DET
ejpam-5730	417	43	distinct	distinct	ADJ
ejpam-5730	417	44	x	x	NOUN
ejpam-5730	417	45	,	,	PUNCT
ejpam-5730	417	46	y	y	PROPN
ejpam-5730	417	47	∈	∈	PROPN
ejpam-5730	417	48	x	x	X
ejpam-5730	417	49	,	,	PUNCT
ejpam-5730	417	50	then	then	ADV
ejpam-5730	417	51	t	t	PROPN
ejpam-5730	417	52	possesses	possess	VERB
ejpam-5730	417	53	a	a	DET
ejpam-5730	417	54	unique	unique	ADJ
ejpam-5730	417	55	fixed	fix	VERB
ejpam-5730	417	56	point	point	NOUN
ejpam-5730	417	57	in	in	ADP
ejpam-5730	417	58	x.	x.	NOUN
ejpam-5730	417	59	comment	comment	NOUN
ejpam-5730	417	60	:	:	PUNCT
ejpam-5730	417	61	for	for	ADP
ejpam-5730	417	62	y	y	PROPN
ejpam-5730	417	63	=	=	SYM
ejpam-5730	417	64	tx	tx	PROPN
ejpam-5730	417	65	,	,	PUNCT
ejpam-5730	417	66	we	we	PRON
ejpam-5730	417	67	have	have	VERB
ejpam-5730	417	68	the	the	DET
ejpam-5730	417	69	following	follow	VERB
ejpam-5730	417	70	d(tx	d(tx	PROPN
ejpam-5730	417	71	,	,	PUNCT
ejpam-5730	417	72	t	t	NOUN
ejpam-5730	417	73	2x	2x	NUM
ejpam-5730	417	74	)	)	PUNCT
ejpam-5730	417	75	≤	≤	NOUN
ejpam-5730	417	76	k1	k1	X
ejpam-5730	417	77	·	·	PUNCT
ejpam-5730	417	78	d(x	d(x	NOUN
ejpam-5730	417	79	,	,	PUNCT
ejpam-5730	417	80	tx	tx	PROPN
ejpam-5730	417	81	)	)	PUNCT
ejpam-5730	417	82	d(tx	d(tx	PROPN
ejpam-5730	417	83	,	,	PUNCT
ejpam-5730	417	84	t	t	NOUN
ejpam-5730	417	85	2x	2x	NUM
ejpam-5730	417	86	)	)	PUNCT
ejpam-5730	417	87	d(x	d(x	NOUN
ejpam-5730	417	88	,	,	PUNCT
ejpam-5730	417	89	tx	tx	PROPN
ejpam-5730	417	90	)	)	PUNCT
ejpam-5730	418	1	+	+	CCONJ
ejpam-5730	418	2	k2	k2	X
ejpam-5730	418	3	·	·	PUNCT
ejpam-5730	418	4	d(x	d(x	PROPN
ejpam-5730	418	5	,	,	PUNCT
ejpam-5730	418	6	tx	tx	PROPN
ejpam-5730	418	7	)	)	PUNCT
ejpam-5730	418	8	,	,	PUNCT
ejpam-5730	418	9	s.	s.	PROPN
ejpam-5730	418	10	park	park	PROPN
ejpam-5730	418	11	/	/	SYM
ejpam-5730	418	12	eur	eur	PROPN
ejpam-5730	418	13	.	.	PUNCT
ejpam-5730	419	1	j.	j.	PROPN
ejpam-5730	419	2	pure	pure	PROPN
ejpam-5730	419	3	appl	appl	PROPN
ejpam-5730	419	4	.	.	PROPN
ejpam-5730	419	5	math	math	PROPN
ejpam-5730	419	6	,	,	PUNCT
ejpam-5730	419	7	18	18	NUM
ejpam-5730	419	8	(	(	PUNCT
ejpam-5730	419	9	1	1	NUM
ejpam-5730	419	10	)	)	PUNCT
ejpam-5730	419	11	(	(	PUNCT
ejpam-5730	419	12	2025	2025	NUM
ejpam-5730	419	13	)	)	PUNCT
ejpam-5730	419	14	,	,	PUNCT
ejpam-5730	419	15	5730	5730	NUM
ejpam-5730	419	16	17	17	NUM
ejpam-5730	419	17	of	of	ADP
ejpam-5730	419	18	21	21	NUM
ejpam-5730	419	19	which	which	PRON
ejpam-5730	419	20	implies	imply	VERB
ejpam-5730	419	21	d(tx	d(tx	PROPN
ejpam-5730	419	22	,	,	PUNCT
ejpam-5730	419	23	t	t	NOUN
ejpam-5730	419	24	2x	2x	NUM
ejpam-5730	419	25	)	)	PUNCT
ejpam-5730	419	26	≤	≤	NOUN
ejpam-5730	419	27	(	(	PUNCT
ejpam-5730	419	28	k1+k2)d(x	k1+k2)d(x	NOUN
ejpam-5730	419	29	,	,	PUNCT
ejpam-5730	419	30	tx	tx	PROPN
ejpam-5730	419	31	)	)	PUNCT
ejpam-5730	419	32	whenever	whenever	SCONJ
ejpam-5730	419	33	d(x	d(x	PROPN
ejpam-5730	419	34	,	,	PUNCT
ejpam-5730	419	35	tx	tx	PROPN
ejpam-5730	419	36	)	)	PUNCT
ejpam-5730	419	37	≤	≤	NOUN
ejpam-5730	420	1	d(tx	d(tx	PROPN
ejpam-5730	420	2	,	,	PUNCT
ejpam-5730	420	3	t	t	NOUN
ejpam-5730	420	4	2x	2x	NUM
ejpam-5730	420	5	)	)	PUNCT
ejpam-5730	420	6	.	.	PUNCT
ejpam-5730	421	1	this	this	PRON
ejpam-5730	421	2	leads	lead	VERB
ejpam-5730	421	3	a	a	DET
ejpam-5730	421	4	contradiction	contradiction	NOUN
ejpam-5730	421	5	.	.	PUNCT
ejpam-5730	422	1	hence	hence	ADV
ejpam-5730	422	2	we	we	PRON
ejpam-5730	422	3	have	have	VERB
ejpam-5730	422	4	to	to	PART
ejpam-5730	422	5	assume	assume	VERB
ejpam-5730	422	6	d(tx	d(tx	PROPN
ejpam-5730	422	7	,	,	PUNCT
ejpam-5730	422	8	t	t	NOUN
ejpam-5730	422	9	2x	2x	NUM
ejpam-5730	422	10	)	)	PUNCT
ejpam-5730	422	11	<	<	X
ejpam-5730	422	12	d(x	d(x	PROPN
ejpam-5730	422	13	,	,	PUNCT
ejpam-5730	422	14	tx	tx	PROPN
ejpam-5730	422	15	)	)	PUNCT
ejpam-5730	422	16	for	for	ADP
ejpam-5730	422	17	all	all	PRON
ejpam-5730	422	18	x	x	SYM
ejpam-5730	422	19	∈	∈	NOUN
ejpam-5730	422	20	x.	x.	NOUN
ejpam-5730	422	21	therefore	therefore	ADV
ejpam-5730	422	22	t	t	PROPN
ejpam-5730	422	23	can	can	AUX
ejpam-5730	422	24	not	not	PART
ejpam-5730	422	25	have	have	VERB
ejpam-5730	422	26	a	a	DET
ejpam-5730	422	27	fixed	fix	VERB
ejpam-5730	422	28	point	point	NOUN
ejpam-5730	422	29	.	.	PUNCT
ejpam-5730	423	1	ćirić	ćirić	VERB
ejpam-5730	424	1	[	[	X
ejpam-5730	424	2	8	8	NUM
ejpam-5730	424	3	]	]	PUNCT
ejpam-5730	424	4	in	in	ADP
ejpam-5730	424	5	1993	1993	NUM
ejpam-5730	424	6	theorem	theorem	VERB
ejpam-5730	424	7	8.4	8.4	NUM
ejpam-5730	424	8	.	.	PUNCT
ejpam-5730	425	1	(	(	PUNCT
ejpam-5730	425	2	ćirić	ćirić	NOUN
ejpam-5730	425	3	)	)	PUNCT
ejpam-5730	425	4	let	let	VERB
ejpam-5730	425	5	k	k	PRON
ejpam-5730	425	6	be	be	AUX
ejpam-5730	425	7	a	a	DET
ejpam-5730	425	8	closed	closed	ADJ
ejpam-5730	425	9	convex	convex	NOUN
ejpam-5730	425	10	subset	subset	NOUN
ejpam-5730	425	11	of	of	ADP
ejpam-5730	425	12	a	a	DET
ejpam-5730	425	13	complete	complete	ADJ
ejpam-5730	425	14	convex	convex	NOUN
ejpam-5730	425	15	metric	metric	ADJ
ejpam-5730	425	16	space	space	NOUN
ejpam-5730	425	17	x	x	PUNCT
ejpam-5730	425	18	and	and	CCONJ
ejpam-5730	425	19	t	t	PROPN
ejpam-5730	425	20	:	:	PUNCT
ejpam-5730	426	1	k	k	X
ejpam-5730	426	2	→	→	PUNCT
ejpam-5730	426	3	k	k	X
ejpam-5730	426	4	a	a	DET
ejpam-5730	426	5	mapping	mapping	NOUN
ejpam-5730	426	6	satisfying	satisfy	VERB
ejpam-5730	426	7	d(tx	d(tx	PROPN
ejpam-5730	426	8	,	,	PUNCT
ejpam-5730	426	9	ty	ty	NOUN
ejpam-5730	426	10	)	)	PUNCT
ejpam-5730	426	11	≤	≤	NOUN
ejpam-5730	426	12	a	a	DET
ejpam-5730	426	13	d(x	d(x	PROPN
ejpam-5730	426	14	,	,	PUNCT
ejpam-5730	426	15	y	y	NOUN
ejpam-5730	426	16	)	)	PUNCT
ejpam-5730	427	1	+	+	CCONJ
ejpam-5730	427	2	(	(	PUNCT
ejpam-5730	427	3	1−	1−	NUM
ejpam-5730	427	4	a)max{d(x	a)max{d(x	NOUN
ejpam-5730	427	5	,	,	PUNCT
ejpam-5730	427	6	tx	tx	PROPN
ejpam-5730	427	7	)	)	PUNCT
ejpam-5730	427	8	,	,	PUNCT
ejpam-5730	427	9	d(y	d(y	PROPN
ejpam-5730	427	10	,	,	PUNCT
ejpam-5730	427	11	ty	ty	NOUN
ejpam-5730	427	12	)	)	PUNCT
ejpam-5730	427	13	,	,	PUNCT
ejpam-5730	427	14	b	b	X
ejpam-5730	428	1	[	[	X
ejpam-5730	428	2	d(x	d(x	PROPN
ejpam-5730	428	3	,	,	PUNCT
ejpam-5730	428	4	ty	ty	INTJ
ejpam-5730	428	5	)	)	PUNCT
ejpam-5730	428	6	+	+	CCONJ
ejpam-5730	428	7	d(y	d(y	PROPN
ejpam-5730	428	8	,	,	PUNCT
ejpam-5730	428	9	tx	tx	PROPN
ejpam-5730	428	10	)	)	PUNCT
ejpam-5730	428	11	]	]	PUNCT
ejpam-5730	428	12	}	}	PUNCT
ejpam-5730	428	13	for	for	ADP
ejpam-5730	428	14	all	all	DET
ejpam-5730	428	15	x	x	NOUN
ejpam-5730	428	16	,	,	PUNCT
ejpam-5730	428	17	y	y	PROPN
ejpam-5730	428	18	∈	∈	PROPN
ejpam-5730	428	19	k	k	NOUN
ejpam-5730	428	20	,	,	PUNCT
ejpam-5730	428	21	where	where	SCONJ
ejpam-5730	428	22	0	0	PUNCT
ejpam-5730	428	23	<	<	X
ejpam-5730	428	24	a	a	DET
ejpam-5730	428	25	<	<	X
ejpam-5730	428	26	1	1	NUM
ejpam-5730	428	27	and	and	CCONJ
ejpam-5730	428	28	b	b	NOUN
ejpam-5730	428	29	≤	≤	ADV
ejpam-5730	428	30	1	1	NUM
ejpam-5730	428	31	2	2	NUM
ejpam-5730	428	32	−	−	NUM
ejpam-5730	428	33	1−a2	1−a2	NUM
ejpam-5730	428	34	10	10	NUM
ejpam-5730	428	35	+	+	SYM
ejpam-5730	428	36	6a2	6a2	NUM
ejpam-5730	428	37	.	.	PUNCT
ejpam-5730	429	1	then	then	ADV
ejpam-5730	429	2	t	t	PROPN
ejpam-5730	429	3	has	have	VERB
ejpam-5730	429	4	a	a	DET
ejpam-5730	429	5	unique	unique	ADJ
ejpam-5730	429	6	fixed	fix	VERB
ejpam-5730	429	7	point	point	NOUN
ejpam-5730	429	8	.	.	PUNCT
ejpam-5730	430	1	note	note	VERB
ejpam-5730	430	2	that	that	SCONJ
ejpam-5730	430	3	t	t	PROPN
ejpam-5730	430	4	is	be	AUX
ejpam-5730	430	5	not	not	PART
ejpam-5730	430	6	an	an	DET
ejpam-5730	430	7	rhr	rhr	NOUN
ejpam-5730	430	8	map	map	NOUN
ejpam-5730	430	9	.	.	PUNCT
ejpam-5730	431	1	feng	feng	PROPN
ejpam-5730	431	2	and	and	CCONJ
ejpam-5730	431	3	liu	liu	PROPN
ejpam-5730	432	1	[	[	X
ejpam-5730	432	2	11	11	NUM
ejpam-5730	432	3	]	]	PUNCT
ejpam-5730	432	4	in	in	ADP
ejpam-5730	432	5	2006	2006	NUM
ejpam-5730	432	6	let	let	VERB
ejpam-5730	432	7	(	(	PUNCT
ejpam-5730	432	8	x	x	NOUN
ejpam-5730	432	9	,	,	PUNCT
ejpam-5730	432	10	d	d	NOUN
ejpam-5730	432	11	)	)	PUNCT
ejpam-5730	432	12	be	be	AUX
ejpam-5730	432	13	a	a	DET
ejpam-5730	432	14	complete	complete	ADJ
ejpam-5730	432	15	metric	metric	ADJ
ejpam-5730	432	16	space	space	NOUN
ejpam-5730	432	17	.	.	PUNCT
ejpam-5730	433	1	cl(x	cl(x	NOUN
ejpam-5730	433	2	)	)	PUNCT
ejpam-5730	434	1	denotes	denote	VERB
ejpam-5730	434	2	the	the	DET
ejpam-5730	434	3	collection	collection	NOUN
ejpam-5730	434	4	of	of	ADP
ejpam-5730	434	5	all	all	DET
ejpam-5730	434	6	nonempty	nonempty	ADV
ejpam-5730	434	7	closed	close	VERB
ejpam-5730	434	8	subsets	subset	NOUN
ejpam-5730	434	9	.	.	PUNCT
ejpam-5730	435	1	let	let	VERB
ejpam-5730	435	2	t	t	NOUN
ejpam-5730	435	3	:	:	PUNCT
ejpam-5730	435	4	x	x	SYM
ejpam-5730	435	5	→	→	SYM
ejpam-5730	435	6	cl(x	cl(x	X
ejpam-5730	435	7	)	)	PUNCT
ejpam-5730	435	8	be	be	VERB
ejpam-5730	435	9	a	a	DET
ejpam-5730	435	10	multi	multi	ADJ
ejpam-5730	435	11	-	-	ADJ
ejpam-5730	435	12	valued	value	VERB
ejpam-5730	435	13	mapping	mapping	NOUN
ejpam-5730	435	14	.	.	PUNCT
ejpam-5730	436	1	define	define	VERB
ejpam-5730	436	2	a	a	DET
ejpam-5730	436	3	function	function	NOUN
ejpam-5730	436	4	f	f	NOUN
ejpam-5730	436	5	:	:	PUNCT
ejpam-5730	436	6	x	x	X
ejpam-5730	436	7	→	→	SYM
ejpam-5730	436	8	r	r	NOUN
ejpam-5730	436	9	as	as	ADP
ejpam-5730	436	10	f(x	f(x	PROPN
ejpam-5730	436	11	)	)	PUNCT
ejpam-5730	437	1	=	=	SYM
ejpam-5730	437	2	d(x	d(x	PROPN
ejpam-5730	437	3	,	,	PUNCT
ejpam-5730	437	4	t	t	PROPN
ejpam-5730	437	5	(	(	PUNCT
ejpam-5730	437	6	x	x	NOUN
ejpam-5730	437	7	)	)	PUNCT
ejpam-5730	437	8	)	)	PUNCT
ejpam-5730	437	9	.	.	PUNCT
ejpam-5730	438	1	for	for	ADP
ejpam-5730	438	2	a	a	DET
ejpam-5730	438	3	positive	positive	ADJ
ejpam-5730	438	4	constant	constant	ADJ
ejpam-5730	438	5	b	b	PROPN
ejpam-5730	438	6	∈	∈	PROPN
ejpam-5730	438	7	(	(	PUNCT
ejpam-5730	438	8	0	0	NUM
ejpam-5730	438	9	,	,	PUNCT
ejpam-5730	438	10	1	1	NUM
ejpam-5730	438	11	)	)	PUNCT
ejpam-5730	438	12	,	,	PUNCT
ejpam-5730	438	13	define	define	VERB
ejpam-5730	438	14	the	the	DET
ejpam-5730	438	15	set	set	NOUN
ejpam-5730	438	16	ixb	ixb	PROPN
ejpam-5730	438	17	⊂	⊂	PROPN
ejpam-5730	438	18	x	x	PUNCT
ejpam-5730	438	19	as	as	ADP
ejpam-5730	438	20	ixb	ixb	PROPN
ejpam-5730	438	21	=	=	SYM
ejpam-5730	438	22	{	{	PUNCT
ejpam-5730	438	23	y	y	PROPN
ejpam-5730	438	24	∈	∈	PROPN
ejpam-5730	438	25	t	t	PROPN
ejpam-5730	438	26	(	(	PUNCT
ejpam-5730	438	27	x	x	X
ejpam-5730	438	28	)	)	PUNCT
ejpam-5730	438	29	:	:	PUNCT
ejpam-5730	438	30	b	b	X
ejpam-5730	438	31	d(x	d(x	PROPN
ejpam-5730	438	32	,	,	PUNCT
ejpam-5730	438	33	y	y	NOUN
ejpam-5730	438	34	)	)	PUNCT
ejpam-5730	438	35	≤	≤	NOUN
ejpam-5730	438	36	d(x	d(x	PROPN
ejpam-5730	438	37	,	,	PUNCT
ejpam-5730	438	38	t	t	PROPN
ejpam-5730	438	39	(	(	PUNCT
ejpam-5730	438	40	x	x	NOUN
ejpam-5730	438	41	)	)	PUNCT
ejpam-5730	438	42	)	)	PUNCT
ejpam-5730	438	43	}	}	PUNCT
ejpam-5730	438	44	.	.	PUNCT
ejpam-5730	439	1	the	the	DET
ejpam-5730	439	2	following	follow	VERB
ejpam-5730	439	3	theorem	theorem	NOUN
ejpam-5730	439	4	is	be	AUX
ejpam-5730	439	5	the	the	DET
ejpam-5730	439	6	main	main	ADJ
ejpam-5730	439	7	result	result	NOUN
ejpam-5730	439	8	:	:	PUNCT
ejpam-5730	439	9	theorem	theorem	VERB
ejpam-5730	439	10	8.5	8.5	NUM
ejpam-5730	439	11	.	.	PUNCT
ejpam-5730	440	1	(	(	PUNCT
ejpam-5730	440	2	feng	feng	PROPN
ejpam-5730	440	3	-	-	PUNCT
ejpam-5730	440	4	liu	liu	PROPN
ejpam-5730	440	5	)	)	PUNCT
ejpam-5730	440	6	let	let	AUX
ejpam-5730	440	7	(	(	PUNCT
ejpam-5730	440	8	x	x	NOUN
ejpam-5730	440	9	,	,	PUNCT
ejpam-5730	440	10	d	d	NOUN
ejpam-5730	440	11	)	)	PUNCT
ejpam-5730	440	12	be	be	AUX
ejpam-5730	440	13	a	a	DET
ejpam-5730	440	14	complete	complete	ADJ
ejpam-5730	440	15	metric	metric	ADJ
ejpam-5730	440	16	space	space	NOUN
ejpam-5730	440	17	,	,	PUNCT
ejpam-5730	440	18	t	t	X
ejpam-5730	440	19	:	:	PUNCT
ejpam-5730	440	20	x	x	SYM
ejpam-5730	440	21	→	→	SYM
ejpam-5730	440	22	cl(x	cl(x	X
ejpam-5730	440	23	)	)	PUNCT
ejpam-5730	440	24	be	be	VERB
ejpam-5730	440	25	a	a	DET
ejpam-5730	440	26	multi	multi	ADJ
ejpam-5730	440	27	-	-	ADJ
ejpam-5730	440	28	valued	value	VERB
ejpam-5730	440	29	mapping	mapping	NOUN
ejpam-5730	440	30	.	.	PUNCT
ejpam-5730	441	1	if	if	SCONJ
ejpam-5730	441	2	there	there	PRON
ejpam-5730	441	3	exists	exist	VERB
ejpam-5730	441	4	a	a	DET
ejpam-5730	441	5	constant	constant	ADJ
ejpam-5730	441	6	c	c	NOUN
ejpam-5730	441	7	∈	∈	PROPN
ejpam-5730	441	8	(	(	PUNCT
ejpam-5730	441	9	0	0	NUM
ejpam-5730	441	10	,	,	PUNCT
ejpam-5730	441	11	1	1	NUM
ejpam-5730	441	12	)	)	PUNCT
ejpam-5730	441	13	such	such	ADJ
ejpam-5730	441	14	that	that	PRON
ejpam-5730	441	15	for	for	ADP
ejpam-5730	441	16	any	any	DET
ejpam-5730	441	17	x	x	SYM
ejpam-5730	441	18	∈	∈	PROPN
ejpam-5730	441	19	x	x	PUNCT
ejpam-5730	441	20	there	there	PRON
ejpam-5730	441	21	is	be	VERB
ejpam-5730	441	22	y	y	PROPN
ejpam-5730	441	23	∈	∈	PROPN
ejpam-5730	441	24	ixb	ixb	NOUN
ejpam-5730	441	25	satisfying	satisfy	VERB
ejpam-5730	441	26	d(y	d(y	PROPN
ejpam-5730	441	27	,	,	PUNCT
ejpam-5730	441	28	t	t	PROPN
ejpam-5730	441	29	(	(	PUNCT
ejpam-5730	441	30	y	y	NOUN
ejpam-5730	441	31	)	)	PUNCT
ejpam-5730	441	32	)	)	PUNCT
ejpam-5730	442	1	≤	≤	NUM
ejpam-5730	443	1	c	c	ADP
ejpam-5730	443	2	d(x	d(x	PROPN
ejpam-5730	443	3	,	,	PUNCT
ejpam-5730	443	4	y	y	PROPN
ejpam-5730	443	5	)	)	PUNCT
ejpam-5730	443	6	,	,	PUNCT
ejpam-5730	443	7	then	then	ADV
ejpam-5730	443	8	t	t	PROPN
ejpam-5730	443	9	has	have	VERB
ejpam-5730	443	10	a	a	DET
ejpam-5730	443	11	fixed	fix	VERB
ejpam-5730	443	12	point	point	NOUN
ejpam-5730	443	13	in	in	ADP
ejpam-5730	443	14	x	x	PUNCT
ejpam-5730	443	15	provided	provide	VERB
ejpam-5730	443	16	c	c	PROPN
ejpam-5730	443	17	<	<	X
ejpam-5730	443	18	b	b	PROPN
ejpam-5730	443	19	and	and	CCONJ
ejpam-5730	443	20	f	f	PROPN
ejpam-5730	443	21	is	be	AUX
ejpam-5730	443	22	lower	low	ADJ
ejpam-5730	443	23	semi	semi	ADJ
ejpam-5730	443	24	-	-	ADJ
ejpam-5730	443	25	continuous	continuous	ADJ
ejpam-5730	443	26	.	.	PUNCT
ejpam-5730	444	1	corollary	corollary	ADJ
ejpam-5730	444	2	8.6	8.6	NUM
ejpam-5730	444	3	.	.	PUNCT
ejpam-5730	445	1	(	(	PUNCT
ejpam-5730	445	2	feng	feng	PROPN
ejpam-5730	445	3	-	-	PUNCT
ejpam-5730	445	4	liu	liu	PROPN
ejpam-5730	445	5	)	)	PUNCT
ejpam-5730	445	6	let	let	AUX
ejpam-5730	445	7	(	(	PUNCT
ejpam-5730	445	8	x	x	NOUN
ejpam-5730	445	9	,	,	PUNCT
ejpam-5730	445	10	d	d	NOUN
ejpam-5730	445	11	)	)	PUNCT
ejpam-5730	445	12	be	be	AUX
ejpam-5730	445	13	a	a	DET
ejpam-5730	445	14	complete	complete	ADJ
ejpam-5730	445	15	metric	metric	ADJ
ejpam-5730	445	16	space	space	NOUN
ejpam-5730	445	17	,	,	PUNCT
ejpam-5730	445	18	t	t	X
ejpam-5730	445	19	:	:	PUNCT
ejpam-5730	445	20	x	x	SYM
ejpam-5730	445	21	→	→	SYM
ejpam-5730	445	22	cl(x	cl(x	X
ejpam-5730	445	23	)	)	PUNCT
ejpam-5730	445	24	be	be	VERB
ejpam-5730	445	25	a	a	DET
ejpam-5730	445	26	multi	multi	ADJ
ejpam-5730	445	27	-	-	ADJ
ejpam-5730	445	28	valued	value	VERB
ejpam-5730	445	29	mapping	mapping	NOUN
ejpam-5730	445	30	.	.	PUNCT
ejpam-5730	446	1	if	if	SCONJ
ejpam-5730	446	2	there	there	PRON
ejpam-5730	446	3	exists	exist	VERB
ejpam-5730	446	4	a	a	DET
ejpam-5730	446	5	constant	constant	ADJ
ejpam-5730	446	6	c	c	NOUN
ejpam-5730	446	7	∈	∈	PROPN
ejpam-5730	446	8	(	(	PUNCT
ejpam-5730	446	9	0	0	NUM
ejpam-5730	446	10	,	,	PUNCT
ejpam-5730	446	11	1	1	NUM
ejpam-5730	446	12	)	)	PUNCT
ejpam-5730	446	13	such	such	ADJ
ejpam-5730	446	14	that	that	PRON
ejpam-5730	446	15	for	for	ADP
ejpam-5730	446	16	any	any	DET
ejpam-5730	446	17	x	x	SYM
ejpam-5730	446	18	∈	∈	PROPN
ejpam-5730	446	19	x	x	NOUN
ejpam-5730	446	20	,	,	PUNCT
ejpam-5730	446	21	y	y	PROPN
ejpam-5730	446	22	∈	∈	PROPN
ejpam-5730	446	23	t	t	PROPN
ejpam-5730	446	24	(	(	PUNCT
ejpam-5730	446	25	x	x	NOUN
ejpam-5730	446	26	)	)	PUNCT
ejpam-5730	446	27	,	,	PUNCT
ejpam-5730	446	28	d(y	d(y	PROPN
ejpam-5730	446	29	,	,	PUNCT
ejpam-5730	446	30	t	t	PROPN
ejpam-5730	446	31	(	(	PUNCT
ejpam-5730	446	32	y	y	NOUN
ejpam-5730	446	33	)	)	PUNCT
ejpam-5730	446	34	)	)	PUNCT
ejpam-5730	447	1	≤	≤	NUM
ejpam-5730	448	1	c	c	ADP
ejpam-5730	448	2	d(x	d(x	PROPN
ejpam-5730	448	3	,	,	PUNCT
ejpam-5730	448	4	y	y	PROPN
ejpam-5730	448	5	)	)	PUNCT
ejpam-5730	448	6	,	,	PUNCT
ejpam-5730	448	7	then	then	ADV
ejpam-5730	448	8	t	t	PROPN
ejpam-5730	448	9	has	have	VERB
ejpam-5730	448	10	a	a	DET
ejpam-5730	448	11	fixed	fix	VERB
ejpam-5730	448	12	point	point	NOUN
ejpam-5730	448	13	in	in	ADP
ejpam-5730	448	14	x	x	PUNCT
ejpam-5730	448	15	provided	provide	VERB
ejpam-5730	448	16	f	f	PROPN
ejpam-5730	448	17	is	be	AUX
ejpam-5730	448	18	lower	low	ADJ
ejpam-5730	448	19	semi	semi	ADJ
ejpam-5730	448	20	-	-	ADJ
ejpam-5730	448	21	continuous	continuous	ADJ
ejpam-5730	448	22	.	.	PUNCT
ejpam-5730	449	1	this	this	PRON
ejpam-5730	449	2	extends	extend	VERB
ejpam-5730	449	3	the	the	DET
ejpam-5730	449	4	covitz	covitz	PROPN
ejpam-5730	449	5	-	-	PUNCT
ejpam-5730	449	6	nadler	nadler	NOUN
ejpam-5730	449	7	fixed	fix	VERB
ejpam-5730	449	8	point	point	NOUN
ejpam-5730	449	9	theorem	theorem	VERB
ejpam-5730	449	10	[	[	X
ejpam-5730	449	11	9	9	NUM
ejpam-5730	449	12	]	]	PUNCT
ejpam-5730	449	13	or	or	CCONJ
ejpam-5730	449	14	theorem	theorem	VERB
ejpam-5730	449	15	h(δ1	h(δ1	NOUN
ejpam-5730	449	16	)	)	PUNCT
ejpam-5730	449	17	for	for	ADP
ejpam-5730	449	18	metric	metric	ADJ
ejpam-5730	449	19	spaces	space	NOUN
ejpam-5730	449	20	.	.	PUNCT
ejpam-5730	450	1	kumam	kumam	NOUN
ejpam-5730	450	2	,	,	PUNCT
ejpam-5730	450	3	dung	dung	NOUN
ejpam-5730	450	4	,	,	PUNCT
ejpam-5730	450	5	sitytithakerngkiet	sitytithakerngkiet	ADJ
ejpam-5730	450	6	[	[	X
ejpam-5730	450	7	26	26	NUM
ejpam-5730	450	8	]	]	PUNCT
ejpam-5730	450	9	in	in	ADP
ejpam-5730	450	10	2015	2015	NUM
ejpam-5730	450	11	kumam	kumam	NOUN
ejpam-5730	450	12	et	et	PROPN
ejpam-5730	450	13	al	al	PROPN
ejpam-5730	450	14	.	.	PROPN
ejpam-5730	450	15	obtained	obtain	VERB
ejpam-5730	450	16	in	in	ADP
ejpam-5730	450	17	[	[	X
ejpam-5730	450	18	26	26	NUM
ejpam-5730	450	19	]	]	PUNCT
ejpam-5730	450	20	the	the	DET
ejpam-5730	450	21	following	follow	VERB
ejpam-5730	450	22	improvement	improvement	NOUN
ejpam-5730	450	23	of	of	ADP
ejpam-5730	450	24	ćirić	ćirić	PROPN
ejpam-5730	450	25	’s	’s	PART
ejpam-5730	450	26	theorem	theorem	PROPN
ejpam-5730	450	27	.	.	PUNCT
ejpam-5730	450	28	theorem	theorem	PROPN
ejpam-5730	450	29	8.7	8.7	NUM
ejpam-5730	450	30	.	.	PUNCT
ejpam-5730	451	1	(	(	PUNCT
ejpam-5730	451	2	kumam	kumam	NOUN
ejpam-5730	451	3	et	et	PROPN
ejpam-5730	451	4	al	al	PROPN
ejpam-5730	451	5	.	.	PROPN
ejpam-5730	451	6	)	)	PUNCT
ejpam-5730	452	1	let	let	VERB
ejpam-5730	452	2	t	t	NOUN
ejpam-5730	452	3	be	be	AUX
ejpam-5730	452	4	a	a	DET
ejpam-5730	452	5	self	self	NOUN
ejpam-5730	452	6	map	map	NOUN
ejpam-5730	452	7	of	of	ADP
ejpam-5730	452	8	a	a	DET
ejpam-5730	452	9	complete	complete	ADJ
ejpam-5730	452	10	metric	metric	ADJ
ejpam-5730	452	11	space	space	NOUN
ejpam-5730	452	12	(	(	PUNCT
ejpam-5730	452	13	x	x	X
ejpam-5730	452	14	,	,	PUNCT
ejpam-5730	452	15	d	d	NOUN
ejpam-5730	452	16	)	)	PUNCT
ejpam-5730	452	17	.	.	PUNCT
ejpam-5730	453	1	if	if	SCONJ
ejpam-5730	453	2	there	there	PRON
ejpam-5730	453	3	is	be	VERB
ejpam-5730	453	4	a	a	DET
ejpam-5730	453	5	constant	constant	ADJ
ejpam-5730	453	6	α	α	NOUN
ejpam-5730	453	7	∈	∈	PROPN
ejpam-5730	453	8	(	(	PUNCT
ejpam-5730	453	9	0	0	NUM
ejpam-5730	453	10	,	,	PUNCT
ejpam-5730	453	11	1	1	NUM
ejpam-5730	453	12	)	)	PUNCT
ejpam-5730	453	13	such	such	ADJ
ejpam-5730	453	14	that	that	SCONJ
ejpam-5730	453	15	d(tx	d(tx	PROPN
ejpam-5730	453	16	,	,	PUNCT
ejpam-5730	453	17	ty	ty	NOUN
ejpam-5730	453	18	)	)	PUNCT
ejpam-5730	453	19	≤	≤	NOUN
ejpam-5730	453	20	αmax{d(x	αmax{d(x	NOUN
ejpam-5730	453	21	,	,	PUNCT
ejpam-5730	453	22	y	y	NOUN
ejpam-5730	453	23	)	)	PUNCT
ejpam-5730	453	24	,	,	PUNCT
ejpam-5730	453	25	d(x	d(x	PROPN
ejpam-5730	453	26	,	,	PUNCT
ejpam-5730	453	27	tx	tx	PROPN
ejpam-5730	453	28	)	)	PUNCT
ejpam-5730	453	29	,	,	PUNCT
ejpam-5730	453	30	d(y	d(y	PROPN
ejpam-5730	453	31	,	,	PUNCT
ejpam-5730	453	32	ty	ty	NOUN
ejpam-5730	453	33	)	)	PUNCT
ejpam-5730	453	34	,	,	PUNCT
ejpam-5730	453	35	d(x	d(x	PROPN
ejpam-5730	453	36	,	,	PUNCT
ejpam-5730	453	37	ty	ty	NOUN
ejpam-5730	453	38	)	)	PUNCT
ejpam-5730	453	39	,	,	PUNCT
ejpam-5730	453	40	d(y	d(y	PROPN
ejpam-5730	453	41	,	,	PUNCT
ejpam-5730	453	42	tx	tx	PROPN
ejpam-5730	453	43	)	)	PUNCT
ejpam-5730	453	44	,	,	PUNCT
ejpam-5730	453	45	s.	s.	PROPN
ejpam-5730	453	46	park	park	PROPN
ejpam-5730	453	47	/	/	SYM
ejpam-5730	453	48	eur	eur	PROPN
ejpam-5730	453	49	.	.	PUNCT
ejpam-5730	454	1	j.	j.	PROPN
ejpam-5730	454	2	pure	pure	PROPN
ejpam-5730	454	3	appl	appl	PROPN
ejpam-5730	454	4	.	.	PROPN
ejpam-5730	454	5	math	math	PROPN
ejpam-5730	454	6	,	,	PUNCT
ejpam-5730	454	7	18	18	NUM
ejpam-5730	454	8	(	(	PUNCT
ejpam-5730	454	9	1	1	NUM
ejpam-5730	454	10	)	)	PUNCT
ejpam-5730	454	11	(	(	PUNCT
ejpam-5730	454	12	2025	2025	NUM
ejpam-5730	454	13	)	)	PUNCT
ejpam-5730	454	14	,	,	PUNCT
ejpam-5730	454	15	5730	5730	NUM
ejpam-5730	454	16	18	18	NUM
ejpam-5730	454	17	of	of	ADP
ejpam-5730	454	18	21	21	NUM
ejpam-5730	454	19	d(x	d(x	NOUN
ejpam-5730	454	20	,	,	PUNCT
ejpam-5730	454	21	t	t	PROPN
ejpam-5730	454	22	2x	2x	NUM
ejpam-5730	454	23	)	)	PUNCT
ejpam-5730	454	24	,	,	PUNCT
ejpam-5730	454	25	d(tx	d(tx	PROPN
ejpam-5730	454	26	,	,	PUNCT
ejpam-5730	454	27	t	t	NOUN
ejpam-5730	454	28	2x	2x	NUM
ejpam-5730	454	29	)	)	PUNCT
ejpam-5730	454	30	,	,	PUNCT
ejpam-5730	454	31	d(x	d(x	PROPN
ejpam-5730	454	32	,	,	PUNCT
ejpam-5730	454	33	t	t	PROPN
ejpam-5730	454	34	2y	2y	NUM
ejpam-5730	454	35	)	)	PUNCT
ejpam-5730	454	36	,	,	PUNCT
ejpam-5730	454	37	d(t	d(t	NOUN
ejpam-5730	454	38	2x	2x	NUM
ejpam-5730	454	39	,	,	PUNCT
ejpam-5730	454	40	ty	ty	INTJ
ejpam-5730	454	41	)	)	PUNCT
ejpam-5730	454	42	for	for	ADP
ejpam-5730	454	43	all	all	DET
ejpam-5730	454	44	x	x	NOUN
ejpam-5730	454	45	,	,	PUNCT
ejpam-5730	454	46	y	y	PROPN
ejpam-5730	454	47	∈	∈	PROPN
ejpam-5730	455	1	x	x	X
ejpam-5730	455	2	,	,	PUNCT
ejpam-5730	455	3	then	then	ADV
ejpam-5730	455	4	t	t	PROPN
ejpam-5730	455	5	has	have	VERB
ejpam-5730	455	6	a	a	DET
ejpam-5730	455	7	unique	unique	ADJ
ejpam-5730	455	8	fixed	fix	VERB
ejpam-5730	455	9	point	point	NOUN
ejpam-5730	455	10	z	z	NOUN
ejpam-5730	455	11	∈	∈	PROPN
ejpam-5730	455	12	x	x	X
ejpam-5730	455	13	and	and	CCONJ
ejpam-5730	455	14	d(z	d(z	PROPN
ejpam-5730	455	15	,	,	PUNCT
ejpam-5730	455	16	tnx0	tnx0	PROPN
ejpam-5730	455	17	)	)	PUNCT
ejpam-5730	455	18	→	→	SYM
ejpam-5730	455	19	0	0	NUM
ejpam-5730	455	20	as	as	ADP
ejpam-5730	455	21	n	n	NUM
ejpam-5730	455	22	→	→	SYM
ejpam-5730	455	23	∞	∞	PROPN
ejpam-5730	455	24	,	,	PUNCT
ejpam-5730	455	25	for	for	ADP
ejpam-5730	455	26	all	all	DET
ejpam-5730	455	27	x0	x0	PROPN
ejpam-5730	455	28	∈	∈	PROPN
ejpam-5730	455	29	x.	x.	NOUN
ejpam-5730	455	30	some	some	DET
ejpam-5730	455	31	corollaries	corollary	NOUN
ejpam-5730	455	32	and	and	CCONJ
ejpam-5730	455	33	multi	multi	ADJ
ejpam-5730	455	34	-	-	ADJ
ejpam-5730	455	35	valued	value	VERB
ejpam-5730	455	36	versions	version	NOUN
ejpam-5730	455	37	of	of	ADP
ejpam-5730	455	38	them	they	PRON
ejpam-5730	455	39	are	be	AUX
ejpam-5730	455	40	added	add	VERB
ejpam-5730	455	41	.	.	PUNCT
ejpam-5730	456	1	comment	comment	NOUN
ejpam-5730	456	2	:	:	PUNCT
ejpam-5730	456	3	the	the	DET
ejpam-5730	456	4	contractive	contractive	ADJ
ejpam-5730	456	5	condition	condition	NOUN
ejpam-5730	456	6	implies	imply	VERB
ejpam-5730	456	7	the	the	DET
ejpam-5730	456	8	hegedüs	hegedüs	PRON
ejpam-5730	456	9	condition	condition	NOUN
ejpam-5730	456	10	d(tx	d(tx	PROPN
ejpam-5730	456	11	,	,	PUNCT
ejpam-5730	456	12	ty	ty	NOUN
ejpam-5730	456	13	)	)	PUNCT
ejpam-5730	456	14	≤	≤	NOUN
ejpam-5730	456	15	q	q	PUNCT
ejpam-5730	456	16	diam{ot	diam{ot	NOUN
ejpam-5730	456	17	(	(	PUNCT
ejpam-5730	456	18	x	x	NOUN
ejpam-5730	456	19	)	)	PUNCT
ejpam-5730	456	20	∪ot	∪ot	VERB
ejpam-5730	456	21	(	(	PUNCT
ejpam-5730	456	22	y	y	NOUN
ejpam-5730	456	23	)	)	PUNCT
ejpam-5730	456	24	}	}	PUNCT
ejpam-5730	456	25	.	.	PUNCT
ejpam-5730	457	1	hence	hence	ADV
ejpam-5730	457	2	the	the	DET
ejpam-5730	457	3	main	main	ADJ
ejpam-5730	457	4	theorem	theorem	NOUN
ejpam-5730	457	5	was	be	AUX
ejpam-5730	457	6	already	already	ADV
ejpam-5730	457	7	known	know	VERB
ejpam-5730	457	8	;	;	PUNCT
ejpam-5730	457	9	see	see	VERB
ejpam-5730	457	10	park	park	NOUN
ejpam-5730	457	11	[	[	X
ejpam-5730	457	12	29	29	NUM
ejpam-5730	457	13	]	]	PUNCT
ejpam-5730	457	14	.	.	PUNCT
ejpam-5730	458	1	the	the	DET
ejpam-5730	458	2	map	map	NOUN
ejpam-5730	458	3	t	t	NOUN
ejpam-5730	458	4	is	be	AUX
ejpam-5730	458	5	not	not	PART
ejpam-5730	458	6	in	in	ADP
ejpam-5730	458	7	β	β	NOUN
ejpam-5730	458	8	-	-	NOUN
ejpam-5730	458	9	class	class	NOUN
ejpam-5730	458	10	.	.	PUNCT
ejpam-5730	459	1	9	9	X
ejpam-5730	459	2	.	.	X
ejpam-5730	459	3	conclusion	conclusion	NOUN
ejpam-5730	459	4	in	in	ADP
ejpam-5730	459	5	this	this	DET
ejpam-5730	459	6	paper	paper	NOUN
ejpam-5730	459	7	,	,	PUNCT
ejpam-5730	459	8	we	we	PRON
ejpam-5730	459	9	introduced	introduce	VERB
ejpam-5730	459	10	theorem	theorem	ADJ
ejpam-5730	459	11	h	h	NOUN
ejpam-5730	459	12	based	base	VERB
ejpam-5730	459	13	on	on	ADP
ejpam-5730	459	14	our	our	PRON
ejpam-5730	459	15	previous	previous	ADJ
ejpam-5730	459	16	2023	2023	NUM
ejpam-5730	459	17	metatheorem	metatheorem	VERB
ejpam-5730	459	18	.	.	PUNCT
ejpam-5730	460	1	theorem	theorem	PROPN
ejpam-5730	460	2	h	h	NOUN
ejpam-5730	460	3	claims	claim	VERB
ejpam-5730	460	4	that	that	SCONJ
ejpam-5730	460	5	the	the	DET
ejpam-5730	460	6	six	six	NUM
ejpam-5730	460	7	statements	statement	NOUN
ejpam-5730	460	8	(	(	PUNCT
ejpam-5730	460	9	α)-(ϵ	α)-(ϵ	NUM
ejpam-5730	460	10	)	)	PUNCT
ejpam-5730	460	11	and	and	CCONJ
ejpam-5730	460	12	(	(	PUNCT
ejpam-5730	460	13	η	η	NOUN
ejpam-5730	460	14	)	)	PUNCT
ejpam-5730	460	15	are	be	AUX
ejpam-5730	460	16	equivalent	equivalent	ADJ
ejpam-5730	460	17	and	and	CCONJ
ejpam-5730	460	18	that	that	SCONJ
ejpam-5730	460	19	they	they	PRON
ejpam-5730	460	20	characterize	characterize	VERB
ejpam-5730	460	21	the	the	DET
ejpam-5730	460	22	metric	metric	ADJ
ejpam-5730	460	23	completeness	completeness	NOUN
ejpam-5730	460	24	(	(	PUNCT
ejpam-5730	460	25	0	0	NUM
ejpam-5730	460	26	)	)	PUNCT
ejpam-5730	460	27	.	.	PUNCT
ejpam-5730	461	1	we	we	PRON
ejpam-5730	461	2	classified	classify	VERB
ejpam-5730	461	3	multi	multi	ADJ
ejpam-5730	461	4	-	-	ADJ
ejpam-5730	461	5	valued	value	VERB
ejpam-5730	461	6	selfmaps	selfmap	NOUN
ejpam-5730	461	7	on	on	ADP
ejpam-5730	461	8	quasimetric	quasimetric	ADJ
ejpam-5730	461	9	spaces	space	NOUN
ejpam-5730	461	10	satisfying	satisfy	VERB
ejpam-5730	461	11	each	each	PRON
ejpam-5730	461	12	of	of	ADP
ejpam-5730	461	13	the	the	DET
ejpam-5730	461	14	statements	statement	NOUN
ejpam-5730	461	15	(	(	PUNCT
ejpam-5730	461	16	α)-(ϵ	α)-(ϵ	NUM
ejpam-5730	461	17	)	)	PUNCT
ejpam-5730	461	18	.	.	PUNCT
ejpam-5730	462	1	such	such	ADJ
ejpam-5730	462	2	classes	class	NOUN
ejpam-5730	462	3	of	of	ADP
ejpam-5730	462	4	multimaps	multimap	NOUN
ejpam-5730	462	5	have	have	VERB
ejpam-5730	462	6	extremal	extremal	ADJ
ejpam-5730	462	7	elements	element	NOUN
ejpam-5730	462	8	,	,	PUNCT
ejpam-5730	462	9	fixed	fix	VERB
ejpam-5730	462	10	points	point	NOUN
ejpam-5730	462	11	,	,	PUNCT
ejpam-5730	462	12	common	common	ADJ
ejpam-5730	462	13	fixed	fix	VERB
ejpam-5730	462	14	points	point	NOUN
ejpam-5730	462	15	,	,	PUNCT
ejpam-5730	462	16	stationary	stationary	ADJ
ejpam-5730	462	17	points	point	NOUN
ejpam-5730	462	18	,	,	PUNCT
ejpam-5730	462	19	common	common	ADJ
ejpam-5730	462	20	stationary	stationary	ADJ
ejpam-5730	462	21	points	point	NOUN
ejpam-5730	462	22	by	by	ADP
ejpam-5730	462	23	the	the	DET
ejpam-5730	462	24	metatheorem	metatheorem	PROPN
ejpam-5730	462	25	.	.	PUNCT
ejpam-5730	463	1	for	for	ADP
ejpam-5730	463	2	example	example	NOUN
ejpam-5730	463	3	,	,	PUNCT
ejpam-5730	463	4	the	the	DET
ejpam-5730	463	5	subfamily	subfamily	ADJ
ejpam-5730	463	6	{	{	PUNCT
ejpam-5730	463	7	γ	γ	X
ejpam-5730	463	8	}	}	PUNCT
ejpam-5730	463	9	consisting	consist	VERB
ejpam-5730	463	10	of	of	ADP
ejpam-5730	463	11	the	the	DET
ejpam-5730	463	12	rus	rus	NOUN
ejpam-5730	463	13	-	-	PUNCT
ejpam-5730	463	14	hicks	hick	NOUN
ejpam-5730	463	15	-rhoades	-rhoade	NOUN
ejpam-5730	463	16	theorem	theorem	ADJ
ejpam-5730	463	17	and	and	CCONJ
ejpam-5730	463	18	other	other	ADJ
ejpam-5730	463	19	theorems	theorem	NOUN
ejpam-5730	463	20	can	can	AUX
ejpam-5730	463	21	be	be	AUX
ejpam-5730	463	22	easily	easily	ADV
ejpam-5730	463	23	obtained	obtain	VERB
ejpam-5730	463	24	by	by	ADP
ejpam-5730	463	25	the	the	DET
ejpam-5730	463	26	statement	statement	NOUN
ejpam-5730	463	27	(	(	PUNCT
ejpam-5730	463	28	γ1	γ1	PROPN
ejpam-5730	463	29	)	)	PUNCT
ejpam-5730	463	30	in	in	ADP
ejpam-5730	463	31	the	the	DET
ejpam-5730	463	32	metatheorem	metatheorem	PROPN
ejpam-5730	463	33	.	.	PUNCT
ejpam-5730	464	1	the	the	DET
ejpam-5730	464	2	numbers	number	NOUN
ejpam-5730	464	3	of	of	ADP
ejpam-5730	464	4	theorems	theorem	NOUN
ejpam-5730	464	5	in	in	ADP
ejpam-5730	464	6	other	other	ADJ
ejpam-5730	464	7	subfamilies	subfamily	NOUN
ejpam-5730	464	8	are	be	AUX
ejpam-5730	464	9	relatively	relatively	ADV
ejpam-5730	464	10	small	small	ADJ
ejpam-5730	464	11	.	.	PUNCT
ejpam-5730	465	1	we	we	PRON
ejpam-5730	465	2	add	add	VERB
ejpam-5730	465	3	some	some	DET
ejpam-5730	465	4	examples	example	NOUN
ejpam-5730	465	5	of	of	ADP
ejpam-5730	465	6	multimaps	multimap	NOUN
ejpam-5730	465	7	not	not	PART
ejpam-5730	465	8	belonging	belong	VERB
ejpam-5730	465	9	to	to	ADP
ejpam-5730	465	10	any	any	PRON
ejpam-5730	465	11	of	of	ADP
ejpam-5730	465	12	{	{	PUNCT
ejpam-5730	465	13	α}-{ϵ	α}-{ϵ	ADJ
ejpam-5730	465	14	}	}	PUNCT
ejpam-5730	465	15	classes	class	NOUN
ejpam-5730	465	16	.	.	PUNCT
ejpam-5730	466	1	usually	usually	ADV
ejpam-5730	466	2	such	such	ADJ
ejpam-5730	466	3	type	type	NOUN
ejpam-5730	466	4	of	of	ADP
ejpam-5730	466	5	theorems	theorem	NOUN
ejpam-5730	466	6	have	have	VERB
ejpam-5730	466	7	relatively	relatively	ADV
ejpam-5730	466	8	long	long	ADJ
ejpam-5730	466	9	and	and	CCONJ
ejpam-5730	466	10	difficult	difficult	ADJ
ejpam-5730	466	11	proofs	proof	NOUN
ejpam-5730	466	12	.	.	PUNCT
ejpam-5730	467	1	consequently	consequently	ADV
ejpam-5730	467	2	,	,	PUNCT
ejpam-5730	467	3	we	we	PRON
ejpam-5730	467	4	can	can	AUX
ejpam-5730	467	5	destroy	destroy	VERB
ejpam-5730	467	6	possible	possible	ADJ
ejpam-5730	467	7	theorems	theorem	NOUN
ejpam-5730	467	8	in	in	ADP
ejpam-5730	467	9	the	the	DET
ejpam-5730	467	10	subfamily	subfamily	ADJ
ejpam-5730	467	11	{	{	PUNCT
ejpam-5730	467	12	γ	γ	NOUN
ejpam-5730	467	13	}	}	PUNCT
ejpam-5730	467	14	on	on	ADP
ejpam-5730	467	15	thousands	thousand	NOUN
ejpam-5730	467	16	of	of	ADP
ejpam-5730	467	17	artificial	artificial	ADJ
ejpam-5730	467	18	metric	metric	ADJ
ejpam-5730	467	19	type	type	NOUN
ejpam-5730	467	20	spaces	space	NOUN
ejpam-5730	467	21	.	.	PUNCT
ejpam-5730	468	1	this	this	PRON
ejpam-5730	468	2	will	will	AUX
ejpam-5730	468	3	save	save	VERB
ejpam-5730	468	4	the	the	DET
ejpam-5730	468	5	energy	energy	NOUN
ejpam-5730	468	6	of	of	ADP
ejpam-5730	468	7	many	many	ADJ
ejpam-5730	468	8	researchers	researcher	NOUN
ejpam-5730	468	9	.	.	PUNCT
ejpam-5730	469	1	references	reference	NOUN
ejpam-5730	469	2	[	[	X
ejpam-5730	469	3	1	1	NUM
ejpam-5730	469	4	]	]	PUNCT
ejpam-5730	469	5	i.	i.	NOUN
ejpam-5730	469	6	altun	altun	PROPN
ejpam-5730	469	7	,	,	PUNCT
ejpam-5730	469	8	a.	a.	PROPN
ejpam-5730	469	9	erduran	erduran	PROPN
ejpam-5730	469	10	,	,	PUNCT
ejpam-5730	469	11	a	a	DET
ejpam-5730	469	12	suzuki	suzuki	NOUN
ejpam-5730	469	13	type	type	NOUN
ejpam-5730	469	14	fixed	fix	VERB
ejpam-5730	469	15	-	-	PUNCT
ejpam-5730	469	16	point	point	NOUN
ejpam-5730	469	17	theorem	theorem	VERB
ejpam-5730	469	18	,	,	PUNCT
ejpam-5730	469	19	inter	inter	PROPN
ejpam-5730	469	20	.	.	PUNCT
ejpam-5730	470	1	j.	j.	PROPN
ejpam-5730	470	2	math	math	PROPN
ejpam-5730	470	3	.	.	PUNCT
ejpam-5730	471	1	math	math	NOUN
ejpam-5730	471	2	.	.	PUNCT
ejpam-5730	472	1	sci	sci	PROPN
ejpam-5730	472	2	.	.	PROPN
ejpam-5730	472	3	2011	2011	NUM
ejpam-5730	472	4	,	,	PUNCT
ejpam-5730	472	5	article	article	NOUN
ejpam-5730	472	6	i	i	PROPN
ejpam-5730	472	7	d	d	PROPN
ejpam-5730	472	8	736063	736063	NUM
ejpam-5730	472	9	,	,	PUNCT
ejpam-5730	472	10	9	9	NUM
ejpam-5730	472	11	pages	page	NOUN
ejpam-5730	472	12	.	.	PUNCT
ejpam-5730	473	1	doi:10.1155/2011/736063	doi:10.1155/2011/736063	VERB
ejpam-5730	473	2	[	[	X
ejpam-5730	473	3	2	2	NUM
ejpam-5730	473	4	]	]	X
ejpam-5730	473	5	a.c	a.c	PROPN
ejpam-5730	473	6	.	.	PROPN
ejpam-5730	473	7	aouiney	aouiney	PROPN
ejpam-5730	473	8	,	,	PUNCT
ejpam-5730	473	9	a	a	DET
ejpam-5730	473	10	fixed	fix	VERB
ejpam-5730	473	11	point	point	NOUN
ejpam-5730	473	12	theorem	theorem	NOUN
ejpam-5730	473	13	for	for	ADP
ejpam-5730	473	14	p	p	NOUN
ejpam-5730	473	15	-	-	PUNCT
ejpam-5730	473	16	contraction	contraction	NOUN
ejpam-5730	473	17	mappings	mapping	NOUN
ejpam-5730	473	18	in	in	ADP
ejpam-5730	473	19	partially	partially	ADV
ejpam-5730	473	20	ordered	order	VERB
ejpam-5730	473	21	metric	metric	ADJ
ejpam-5730	473	22	spaces	space	NOUN
ejpam-5730	473	23	and	and	CCONJ
ejpam-5730	473	24	application	application	NOUN
ejpam-5730	473	25	to	to	ADP
ejpam-5730	473	26	ordinary	ordinary	ADJ
ejpam-5730	473	27	differential	differential	ADJ
ejpam-5730	473	28	equations	equation	NOUN
ejpam-5730	473	29	,	,	PUNCT
ejpam-5730	473	30	bul	bul	PROPN
ejpam-5730	473	31	.	.	PUNCT
ejpam-5730	474	1	acad	acad	PROPN
ejpam-5730	474	2	.	.	PUNCT
ejpam-5730	475	1	stiint	stiint	PROPN
ejpam-5730	475	2	e	e	PROPN
ejpam-5730	475	3	a	a	PROPN
ejpam-5730	475	4	,	,	PUNCT
ejpam-5730	475	5	rep	rep	PROPN
ejpam-5730	475	6	.	.	PROPN
ejpam-5730	475	7	moldova	moldova	PROPN
ejpam-5730	475	8	.	.	PUNCT
ejpam-5730	476	1	math	math	PROPN
ejpam-5730	476	2	.	.	PUNCT
ejpam-5730	477	1	3(100	3(100	NUM
ejpam-5730	477	2	)	)	PUNCT
ejpam-5730	477	3	(	(	PUNCT
ejpam-5730	477	4	2022	2022	NUM
ejpam-5730	477	5	)	)	PUNCT
ejpam-5730	477	6	15–21	15–21	PROPN
ejpam-5730	477	7	.	.	PUNCT
ejpam-5730	478	1	issn	issn	PROPN
ejpam-5730	478	2	1024	1024	NUM
ejpam-5730	478	3	-	-	SYM
ejpam-5730	478	4	7696	7696	NUM
ejpam-5730	478	5	,	,	PUNCT
ejpam-5730	478	6	e	e	X
ejpam-5730	478	7	-	-	PUNCT
ejpam-5730	478	8	issn	issn	VERB
ejpam-5730	478	9	2587	2587	NUM
ejpam-5730	478	10	-	-	SYM
ejpam-5730	478	11	4322	4322	NUM
ejpam-5730	478	12	[	[	X
ejpam-5730	478	13	3	3	NUM
ejpam-5730	478	14	]	]	X
ejpam-5730	478	15	a.c	a.c	PROPN
ejpam-5730	478	16	.	.	PROPN
ejpam-5730	478	17	aouiney	aouiney	PROPN
ejpam-5730	478	18	,	,	PUNCT
ejpam-5730	478	19	a.	a.	PROPN
ejpam-5730	478	20	aliouche	aliouche	PROPN
ejpam-5730	478	21	,	,	PUNCT
ejpam-5730	478	22	fixed	fix	VERB
ejpam-5730	478	23	point	point	NOUN
ejpam-5730	478	24	theorems	theorem	NOUN
ejpam-5730	478	25	of	of	ADP
ejpam-5730	478	26	kannan	kannan	PROPN
ejpam-5730	478	27	type	type	NOUN
ejpam-5730	478	28	with	with	ADP
ejpam-5730	478	29	an	an	DET
ejpam-5730	478	30	application	application	NOUN
ejpam-5730	478	31	to	to	PART
ejpam-5730	478	32	control	control	VERB
ejpam-5730	478	33	theory	theory	NOUN
ejpam-5730	478	34	,	,	PUNCT
ejpam-5730	478	35	appl	appl	PROPN
ejpam-5730	478	36	.	.	PROPN
ejpam-5730	478	37	math	math	NOUN
ejpam-5730	478	38	.	.	PUNCT
ejpam-5730	479	1	e	e	X
ejpam-5730	479	2	-	-	NOUN
ejpam-5730	479	3	notes	note	NOUN
ejpam-5730	479	4	21	21	NUM
ejpam-5730	479	5	(	(	PUNCT
ejpam-5730	479	6	2021	2021	NUM
ejpam-5730	479	7	)	)	PUNCT
ejpam-5730	479	8	238–249	238–249	NUM
ejpam-5730	479	9	.	.	PUNCT
ejpam-5730	480	1	issn	issn	PROPN
ejpam-5730	480	2	1607	1607	PROPN
ejpam-5730	480	3	-	-	PUNCT
ejpam-5730	480	4	2510	2510	NUM
ejpam-5730	480	5	[	[	X
ejpam-5730	480	6	4	4	NUM
ejpam-5730	480	7	]	]	PUNCT
ejpam-5730	480	8	s.	s.	PROPN
ejpam-5730	480	9	banach	banach	PROPN
ejpam-5730	480	10	,	,	PUNCT
ejpam-5730	480	11	sur	sur	PROPN
ejpam-5730	480	12	les	les	X
ejpam-5730	480	13	opérations	opération	NOUN
ejpam-5730	480	14	dans	dan	NOUN
ejpam-5730	480	15	les	les	X
ejpam-5730	480	16	ensembles	ensemble	NOUN
ejpam-5730	480	17	abstraits	abstrait	NOUN
ejpam-5730	480	18	et	et	PROPN
ejpam-5730	480	19	leur	leur	X
ejpam-5730	480	20	application	application	PROPN
ejpam-5730	480	21	aux	aux	PROPN
ejpam-5730	480	22	équations	équations	PROPN
ejpam-5730	480	23	intégrales	intégrale	NOUN
ejpam-5730	480	24	,	,	PUNCT
ejpam-5730	480	25	fund	fund	NOUN
ejpam-5730	480	26	.	.	PUNCT
ejpam-5730	481	1	math	math	NOUN
ejpam-5730	481	2	.	.	PUNCT
ejpam-5730	482	1	,	,	PUNCT
ejpam-5730	482	2	3	3	NUM
ejpam-5730	482	3	(	(	PUNCT
ejpam-5730	482	4	1922	1922	NUM
ejpam-5730	482	5	)	)	PUNCT
ejpam-5730	482	6	133–181	133–181	NUM
ejpam-5730	482	7	.	.	PUNCT
ejpam-5730	483	1	[	[	X
ejpam-5730	483	2	5	5	X
ejpam-5730	483	3	]	]	PUNCT
ejpam-5730	483	4	j.	j.	PROPN
ejpam-5730	483	5	bogin	bogin	PROPN
ejpam-5730	483	6	,	,	PUNCT
ejpam-5730	483	7	a	a	DET
ejpam-5730	483	8	generalization	generalization	NOUN
ejpam-5730	483	9	of	of	ADP
ejpam-5730	483	10	a	a	DET
ejpam-5730	483	11	fixed	fix	VERB
ejpam-5730	483	12	point	point	NOUN
ejpam-5730	483	13	theorem	theorem	NOUN
ejpam-5730	483	14	of	of	ADP
ejpam-5730	483	15	goebel	goebel	NOUN
ejpam-5730	483	16	,	,	PUNCT
ejpam-5730	483	17	kirk	kirk	PROPN
ejpam-5730	483	18	,	,	PUNCT
ejpam-5730	483	19	and	and	CCONJ
ejpam-5730	483	20	shimi	shimi	PROPN
ejpam-5730	483	21	,	,	PUNCT
ejpam-5730	483	22	canad	canad	PROPN
ejpam-5730	483	23	.	.	PUNCT
ejpam-5730	484	1	math	math	NOUN
ejpam-5730	484	2	.	.	PUNCT
ejpam-5730	485	1	bull	bull	NOUN
ejpam-5730	485	2	.	.	PUNCT
ejpam-5730	486	1	19(1	19(1	NUM
ejpam-5730	486	2	)	)	PUNCT
ejpam-5730	486	3	(	(	PUNCT
ejpam-5730	486	4	1976	1976	NUM
ejpam-5730	486	5	)	)	PUNCT
ejpam-5730	486	6	7–12	7–12	NOUN
ejpam-5730	486	7	.	.	PUNCT
ejpam-5730	487	1	[	[	X
ejpam-5730	487	2	6	6	NUM
ejpam-5730	487	3	]	]	PUNCT
ejpam-5730	487	4	lj.b	lj.b	NOUN
ejpam-5730	487	5	.	.	PUNCT
ejpam-5730	488	1	ćirić	ćirić	PROPN
ejpam-5730	488	2	,	,	PUNCT
ejpam-5730	488	3	on	on	ADP
ejpam-5730	488	4	some	some	DET
ejpam-5730	488	5	maps	map	NOUN
ejpam-5730	488	6	with	with	ADP
ejpam-5730	488	7	a	a	DET
ejpam-5730	488	8	non	non	ADJ
ejpam-5730	488	9	-	-	ADJ
ejpam-5730	488	10	unique	unique	ADJ
ejpam-5730	488	11	fixed	fix	VERB
ejpam-5730	488	12	point	point	NOUN
ejpam-5730	488	13	,	,	PUNCT
ejpam-5730	488	14	publ	publ	NOUN
ejpam-5730	488	15	.	.	PUNCT
ejpam-5730	489	1	inst	inst	PROPN
ejpam-5730	489	2	.	.	PUNCT
ejpam-5730	490	1	math	math	NOUN
ejpam-5730	490	2	.	.	PUNCT
ejpam-5730	491	1	17	17	NUM
ejpam-5730	491	2	(	(	PUNCT
ejpam-5730	491	3	1974	1974	NUM
ejpam-5730	491	4	)	)	PUNCT
ejpam-5730	492	1	52–58	52–58	NUM
ejpam-5730	492	2	.	.	PUNCT
ejpam-5730	493	1	s.	s.	PROPN
ejpam-5730	493	2	park	park	PROPN
ejpam-5730	493	3	/	/	SYM
ejpam-5730	493	4	eur	eur	PROPN
ejpam-5730	493	5	.	.	PUNCT
ejpam-5730	494	1	j.	j.	PROPN
ejpam-5730	494	2	pure	pure	PROPN
ejpam-5730	494	3	appl	appl	PROPN
ejpam-5730	494	4	.	.	PROPN
ejpam-5730	494	5	math	math	PROPN
ejpam-5730	494	6	,	,	PUNCT
ejpam-5730	494	7	18	18	NUM
ejpam-5730	494	8	(	(	PUNCT
ejpam-5730	494	9	1	1	NUM
ejpam-5730	494	10	)	)	PUNCT
ejpam-5730	494	11	(	(	PUNCT
ejpam-5730	494	12	2025	2025	NUM
ejpam-5730	494	13	)	)	PUNCT
ejpam-5730	494	14	,	,	PUNCT
ejpam-5730	494	15	5730	5730	NUM
ejpam-5730	494	16	19	19	NUM
ejpam-5730	494	17	of	of	ADP
ejpam-5730	494	18	21	21	NUM
ejpam-5730	494	19	[	[	X
ejpam-5730	494	20	7	7	NUM
ejpam-5730	494	21	]	]	SYM
ejpam-5730	494	22	lj.b	lj.b	NOUN
ejpam-5730	494	23	.	.	PUNCT
ejpam-5730	495	1	ćirić	ćirić	PROPN
ejpam-5730	495	2	,	,	PUNCT
ejpam-5730	495	3	a	a	DET
ejpam-5730	495	4	generalization	generalization	NOUN
ejpam-5730	495	5	of	of	ADP
ejpam-5730	495	6	banach	banach	NOUN
ejpam-5730	495	7	’s	’s	PART
ejpam-5730	495	8	contraction	contraction	NOUN
ejpam-5730	495	9	principle	principle	NOUN
ejpam-5730	495	10	,	,	PUNCT
ejpam-5730	495	11	proc	proc	PROPN
ejpam-5730	495	12	.	.	PUNCT
ejpam-5730	496	1	amer	amer	PROPN
ejpam-5730	496	2	.	.	PUNCT
ejpam-5730	496	3	math	math	PROPN
ejpam-5730	496	4	.	.	PUNCT
ejpam-5730	497	1	soc	soc	PROPN
ejpam-5730	497	2	.	.	PUNCT
ejpam-5730	498	1	45	45	NUM
ejpam-5730	498	2	(	(	PUNCT
ejpam-5730	498	3	1974	1974	NUM
ejpam-5730	498	4	)	)	PUNCT
ejpam-5730	498	5	267–273	267–273	NUM
ejpam-5730	498	6	.	.	PUNCT
ejpam-5730	499	1	[	[	X
ejpam-5730	499	2	8	8	NUM
ejpam-5730	499	3	]	]	SYM
ejpam-5730	499	4	lj.b	lj.b	NOUN
ejpam-5730	499	5	.	.	PUNCT
ejpam-5730	500	1	ćirić	ćirić	PROPN
ejpam-5730	500	2	,	,	PUNCT
ejpam-5730	500	3	on	on	ADP
ejpam-5730	500	4	some	some	DET
ejpam-5730	500	5	discontinuous	discontinuous	ADJ
ejpam-5730	500	6	fixed	fix	VERB
ejpam-5730	500	7	point	point	NOUN
ejpam-5730	500	8	mappings	mapping	NOUN
ejpam-5730	500	9	in	in	ADP
ejpam-5730	500	10	convex	convex	ADJ
ejpam-5730	500	11	metric	metric	ADJ
ejpam-5730	500	12	spaces	space	NOUN
ejpam-5730	500	13	,	,	PUNCT
ejpam-5730	500	14	czechoslovak	czechoslovak	PROPN
ejpam-5730	500	15	mathematical	mathematical	ADJ
ejpam-5730	500	16	journal	journal	PROPN
ejpam-5730	500	17	43(2	43(2	PROPN
ejpam-5730	500	18	)	)	PUNCT
ejpam-5730	500	19	(	(	PUNCT
ejpam-5730	500	20	1993	1993	NUM
ejpam-5730	500	21	)	)	PUNCT
ejpam-5730	501	1	319–326	319–326	NUM
ejpam-5730	501	2	.	.	PUNCT
ejpam-5730	502	1	[	[	X
ejpam-5730	502	2	9	9	NUM
ejpam-5730	502	3	]	]	X
ejpam-5730	502	4	h.	h.	PROPN
ejpam-5730	502	5	covitz	covitz	PROPN
ejpam-5730	502	6	,	,	PUNCT
ejpam-5730	502	7	s.b	s.b	PROPN
ejpam-5730	502	8	.	.	PROPN
ejpam-5730	502	9	nadler	nadler	PROPN
ejpam-5730	502	10	,	,	PUNCT
ejpam-5730	502	11	,	,	PUNCT
ejpam-5730	502	12	jr	jr	PROPN
ejpam-5730	502	13	.	.	PUNCT
ejpam-5730	502	14	multi	multi	ADJ
ejpam-5730	502	15	-	-	ADJ
ejpam-5730	502	16	valued	value	VERB
ejpam-5730	502	17	contraction	contraction	NOUN
ejpam-5730	502	18	mappings	mapping	NOUN
ejpam-5730	502	19	in	in	ADP
ejpam-5730	502	20	generalized	generalized	ADJ
ejpam-5730	502	21	metric	metric	ADJ
ejpam-5730	502	22	spaces	space	NOUN
ejpam-5730	502	23	,	,	PUNCT
ejpam-5730	502	24	israel	israel	PROPN
ejpam-5730	502	25	j.	j.	PROPN
ejpam-5730	502	26	math	math	PROPN
ejpam-5730	502	27	.	.	PUNCT
ejpam-5730	502	28	8	8	NUM
ejpam-5730	502	29	(	(	PUNCT
ejpam-5730	502	30	1970	1970	NUM
ejpam-5730	502	31	)	)	PUNCT
ejpam-5730	502	32	5–11	5–11	PROPN
ejpam-5730	502	33	.	.	PUNCT
ejpam-5730	503	1	[	[	X
ejpam-5730	503	2	10	10	NUM
ejpam-5730	503	3	]	]	X
ejpam-5730	503	4	b.k	b.k	PROPN
ejpam-5730	503	5	.	.	PROPN
ejpam-5730	503	6	dass	dass	PROPN
ejpam-5730	503	7	,	,	PUNCT
ejpam-5730	503	8	s.	s.	PROPN
ejpam-5730	503	9	gupta	gupta	PROPN
ejpam-5730	503	10	,	,	PUNCT
ejpam-5730	503	11	an	an	DET
ejpam-5730	503	12	extension	extension	NOUN
ejpam-5730	503	13	of	of	ADP
ejpam-5730	503	14	banach	banach	NOUN
ejpam-5730	503	15	contraction	contraction	NOUN
ejpam-5730	503	16	principle	principle	NOUN
ejpam-5730	503	17	through	through	ADP
ejpam-5730	503	18	rational	rational	ADJ
ejpam-5730	503	19	expressions	expression	NOUN
ejpam-5730	503	20	,	,	PUNCT
ejpam-5730	503	21	indian	indian	ADJ
ejpam-5730	503	22	j.	j.	PROPN
ejpam-5730	503	23	pure	pure	PROPN
ejpam-5730	503	24	appl	appl	PROPN
ejpam-5730	503	25	.	.	PUNCT
ejpam-5730	503	26	math	math	NOUN
ejpam-5730	503	27	.	.	PUNCT
ejpam-5730	504	1	6	6	NUM
ejpam-5730	504	2	(	(	PUNCT
ejpam-5730	504	3	1975	1975	NUM
ejpam-5730	504	4	)	)	PUNCT
ejpam-5730	504	5	1455–1458	1455–1458	NUM
ejpam-5730	504	6	.	.	PUNCT
ejpam-5730	505	1	[	[	X
ejpam-5730	505	2	11	11	NUM
ejpam-5730	505	3	]	]	X
ejpam-5730	505	4	y.	y.	PROPN
ejpam-5730	505	5	feng	feng	PROPN
ejpam-5730	505	6	,	,	PUNCT
ejpam-5730	505	7	s.	s.	PROPN
ejpam-5730	505	8	liu	liu	PROPN
ejpam-5730	505	9	,	,	PUNCT
ejpam-5730	505	10	fixed	fix	VERB
ejpam-5730	505	11	point	point	NOUN
ejpam-5730	505	12	theorems	theorem	NOUN
ejpam-5730	505	13	for	for	ADP
ejpam-5730	505	14	multi	multi	ADJ
ejpam-5730	505	15	-	-	ADJ
ejpam-5730	505	16	valued	value	VERB
ejpam-5730	505	17	contractive	contractive	ADJ
ejpam-5730	505	18	mappings	mapping	NOUN
ejpam-5730	505	19	and	and	CCONJ
ejpam-5730	505	20	multivalued	multivalued	ADJ
ejpam-5730	505	21	caristi	caristi	NOUN
ejpam-5730	505	22	type	type	NOUN
ejpam-5730	505	23	mappings	mapping	NOUN
ejpam-5730	505	24	,	,	PUNCT
ejpam-5730	505	25	j.	j.	PROPN
ejpam-5730	505	26	math	math	PROPN
ejpam-5730	505	27	.	.	PUNCT
ejpam-5730	506	1	anal	anal	PROPN
ejpam-5730	506	2	.	.	PUNCT
ejpam-5730	507	1	appl	appl	PROPN
ejpam-5730	507	2	.	.	PROPN
ejpam-5730	508	1	317	317	NUM
ejpam-5730	508	2	(	(	PUNCT
ejpam-5730	508	3	2006	2006	NUM
ejpam-5730	508	4	)	)	PUNCT
ejpam-5730	509	1	103–112	103–112	NUM
ejpam-5730	509	2	.	.	PUNCT
ejpam-5730	510	1	[	[	X
ejpam-5730	510	2	12	12	NUM
ejpam-5730	510	3	]	]	X
ejpam-5730	510	4	r.	r.	PROPN
ejpam-5730	510	5	fierro	fierro	PROPN
ejpam-5730	510	6	,	,	PUNCT
ejpam-5730	510	7	s.	s.	PROPN
ejpam-5730	510	8	pizarro	pizarro	PROPN
ejpam-5730	510	9	,	,	PUNCT
ejpam-5730	510	10	fixed	fix	VERB
ejpam-5730	510	11	points	point	NOUN
ejpam-5730	510	12	of	of	ADP
ejpam-5730	510	13	set	set	NOUN
ejpam-5730	510	14	-	-	PUNCT
ejpam-5730	510	15	valued	value	VERB
ejpam-5730	510	16	mappings	mapping	NOUN
ejpam-5730	510	17	satisfying	satisfy	VERB
ejpam-5730	510	18	a	a	DET
ejpam-5730	510	19	banach	banach	ADV
ejpam-5730	510	20	orbital	orbital	ADJ
ejpam-5730	510	21	condition	condition	NOUN
ejpam-5730	510	22	,	,	PUNCT
ejpam-5730	510	23	cubo	cubo	NOUN
ejpam-5730	510	24	,	,	PUNCT
ejpam-5730	510	25	a	a	DET
ejpam-5730	510	26	math	math	NOUN
ejpam-5730	510	27	.	.	PUNCT
ejpam-5730	511	1	jour	jour	PROPN
ejpam-5730	511	2	.	.	PUNCT
ejpam-5730	512	1	25(1	25(1	NUM
ejpam-5730	512	2	)	)	PUNCT
ejpam-5730	512	3	(	(	PUNCT
ejpam-5730	512	4	2023	2023	NUM
ejpam-5730	512	5	)	)	PUNCT
ejpam-5730	513	1	151–159	151–159	NUM
ejpam-5730	513	2	.	.	PUNCT
ejpam-5730	514	1	[	[	X
ejpam-5730	514	2	13	13	NUM
ejpam-5730	514	3	]	]	SYM
ejpam-5730	514	4	g.e	g.e	PROPN
ejpam-5730	514	5	.	.	PROPN
ejpam-5730	514	6	hardy	hardy	PROPN
ejpam-5730	514	7	,	,	PUNCT
ejpam-5730	514	8	t.d	t.d	PROPN
ejpam-5730	514	9	.	.	PROPN
ejpam-5730	514	10	rogers	rogers	PROPN
ejpam-5730	514	11	,	,	PUNCT
ejpam-5730	514	12	a	a	DET
ejpam-5730	514	13	generalization	generalization	NOUN
ejpam-5730	514	14	of	of	ADP
ejpam-5730	514	15	a	a	DET
ejpam-5730	514	16	fixed	fix	VERB
ejpam-5730	514	17	point	point	NOUN
ejpam-5730	514	18	theorem	theorem	NOUN
ejpam-5730	514	19	of	of	ADP
ejpam-5730	514	20	reich	reich	PROPN
ejpam-5730	514	21	,	,	PUNCT
ejpam-5730	514	22	canad	canad	PROPN
ejpam-5730	514	23	.	.	PUNCT
ejpam-5730	515	1	math	math	NOUN
ejpam-5730	515	2	.	.	PUNCT
ejpam-5730	516	1	bull	bull	NOUN
ejpam-5730	516	2	.	.	PUNCT
ejpam-5730	517	1	16	16	NUM
ejpam-5730	517	2	(	(	PUNCT
ejpam-5730	517	3	1973	1973	NUM
ejpam-5730	517	4	)	)	PUNCT
ejpam-5730	518	1	201–206	201–206	NUM
ejpam-5730	518	2	.	.	PUNCT
ejpam-5730	519	1	[	[	X
ejpam-5730	519	2	14	14	NUM
ejpam-5730	519	3	]	]	X
ejpam-5730	519	4	t.l	t.l	PROPN
ejpam-5730	519	5	.	.	PROPN
ejpam-5730	519	6	hicks	hicks	PROPN
ejpam-5730	519	7	,	,	PUNCT
ejpam-5730	519	8	b.e	b.e	PROPN
ejpam-5730	519	9	.	.	PROPN
ejpam-5730	519	10	rhoades	rhoades	PROPN
ejpam-5730	519	11	,	,	PUNCT
ejpam-5730	519	12	a	a	DET
ejpam-5730	519	13	banach	banach	NOUN
ejpam-5730	519	14	type	type	NOUN
ejpam-5730	519	15	fixed	fix	VERB
ejpam-5730	519	16	point	point	NOUN
ejpam-5730	519	17	theorem	theorem	ADJ
ejpam-5730	519	18	,	,	PUNCT
ejpam-5730	519	19	math	math	NOUN
ejpam-5730	519	20	.	.	PUNCT
ejpam-5730	520	1	japon	japon	PROPN
ejpam-5730	520	2	.	.	PUNCT
ejpam-5730	521	1	24	24	NUM
ejpam-5730	521	2	(	(	PUNCT
ejpam-5730	521	3	1979	1979	NUM
ejpam-5730	521	4	)	)	PUNCT
ejpam-5730	521	5	327–330	327–330	NUM
ejpam-5730	521	6	.	.	PUNCT
ejpam-5730	522	1	[	[	X
ejpam-5730	522	2	15	15	NUM
ejpam-5730	522	3	]	]	X
ejpam-5730	522	4	d.s	d.s	PROPN
ejpam-5730	522	5	.	.	PROPN
ejpam-5730	522	6	jaggi	jaggi	PROPN
ejpam-5730	522	7	,	,	PUNCT
ejpam-5730	522	8	some	some	DET
ejpam-5730	522	9	unique	unique	ADJ
ejpam-5730	522	10	fixed	fix	VERB
ejpam-5730	522	11	point	point	NOUN
ejpam-5730	522	12	theorems	theorem	NOUN
ejpam-5730	522	13	,	,	PUNCT
ejpam-5730	522	14	indian	indian	ADJ
ejpam-5730	522	15	j.	j.	PROPN
ejpam-5730	522	16	pure	pure	PROPN
ejpam-5730	522	17	appl	appl	PROPN
ejpam-5730	522	18	.	.	PUNCT
ejpam-5730	522	19	math	math	NOUN
ejpam-5730	522	20	.	.	PUNCT
ejpam-5730	523	1	8	8	NUM
ejpam-5730	523	2	(	(	PUNCT
ejpam-5730	523	3	1977	1977	NUM
ejpam-5730	523	4	)	)	PUNCT
ejpam-5730	524	1	223–230	223–230	NUM
ejpam-5730	524	2	.	.	PUNCT
ejpam-5730	525	1	[	[	X
ejpam-5730	525	2	16	16	NUM
ejpam-5730	525	3	]	]	X
ejpam-5730	525	4	m.	m.	NOUN
ejpam-5730	525	5	jleli	jleli	PROPN
ejpam-5730	525	6	,	,	PUNCT
ejpam-5730	525	7	b.	b.	PROPN
ejpam-5730	525	8	samet	samet	PROPN
ejpam-5730	525	9	,	,	PUNCT
ejpam-5730	525	10	remarks	remark	VERB
ejpam-5730	525	11	on	on	ADP
ejpam-5730	525	12	g	g	NOUN
ejpam-5730	525	13	-	-	PUNCT
ejpam-5730	525	14	metric	metric	ADJ
ejpam-5730	525	15	spaces	space	NOUN
ejpam-5730	525	16	and	and	CCONJ
ejpam-5730	525	17	fixed	fix	VERB
ejpam-5730	525	18	point	point	NOUN
ejpam-5730	525	19	theorems	theorem	NOUN
ejpam-5730	525	20	,	,	PUNCT
ejpam-5730	525	21	fixed	fix	VERB
ejpam-5730	525	22	point	point	NOUN
ejpam-5730	525	23	theory	theory	NOUN
ejpam-5730	525	24	appl	appl	PROPN
ejpam-5730	525	25	.	.	PUNCT
ejpam-5730	526	1	2012:210	2012:210	NOUN
ejpam-5730	526	2	,	,	PUNCT
ejpam-5730	526	3	2012	2012	NUM
ejpam-5730	526	4	.	.	PUNCT
ejpam-5730	527	1	[	[	X
ejpam-5730	527	2	17	17	NUM
ejpam-5730	527	3	]	]	X
ejpam-5730	527	4	r.	r.	PROPN
ejpam-5730	527	5	kannan	kannan	PROPN
ejpam-5730	527	6	,	,	PUNCT
ejpam-5730	527	7	some	some	DET
ejpam-5730	527	8	results	result	NOUN
ejpam-5730	527	9	on	on	ADP
ejpam-5730	527	10	fixed	fix	VERB
ejpam-5730	527	11	point	point	PROPN
ejpam-5730	527	12	ii	ii	PROPN
ejpam-5730	527	13	.	.	PUNCT
ejpam-5730	527	14	amer	amer	PROPN
ejpam-5730	527	15	.	.	PUNCT
ejpam-5730	527	16	math	math	PROPN
ejpam-5730	527	17	.	.	PUNCT
ejpam-5730	528	1	monthly	monthly	ADJ
ejpam-5730	528	2	76	76	NUM
ejpam-5730	528	3	(	(	PUNCT
ejpam-5730	528	4	1969	1969	NUM
ejpam-5730	528	5	)	)	PUNCT
ejpam-5730	528	6	405–408	405–408	NUM
ejpam-5730	528	7	.	.	PUNCT
ejpam-5730	529	1	[	[	X
ejpam-5730	529	2	18	18	NUM
ejpam-5730	529	3	]	]	X
ejpam-5730	529	4	e.	e.	PROPN
ejpam-5730	529	5	karapinar	karapinar	PROPN
ejpam-5730	529	6	,	,	PUNCT
ejpam-5730	529	7	revisiting	revisit	VERB
ejpam-5730	529	8	the	the	DET
ejpam-5730	529	9	kannan	kannan	PROPN
ejpam-5730	529	10	type	type	NOUN
ejpam-5730	529	11	contractions	contraction	NOUN
ejpam-5730	529	12	via	via	ADP
ejpam-5730	529	13	interpolation	interpolation	NOUN
ejpam-5730	529	14	,	,	PUNCT
ejpam-5730	529	15	adv	adv	PROPN
ejpam-5730	529	16	.	.	PUNCT
ejpam-5730	530	1	th	th	X
ejpam-5730	530	2	.	.	PUNCT
ejpam-5730	531	1	nonlinear	nonlinear	PROPN
ejpam-5730	531	2	anal	anal	PROPN
ejpam-5730	531	3	.	.	PUNCT
ejpam-5730	532	1	appl	appl	PROPN
ejpam-5730	532	2	.	.	PUNCT
ejpam-5730	533	1	2(2	2(2	NUM
ejpam-5730	533	2	)	)	PUNCT
ejpam-5730	534	1	(	(	PUNCT
ejpam-5730	534	2	2018	2018	NUM
ejpam-5730	534	3	)	)	PUNCT
ejpam-5730	534	4	85–87	85–87	NUM
ejpam-5730	534	5	.	.	PUNCT
ejpam-5730	535	1	https://doi.org/10.31197/atnaa.431135	https://doi.org/10.31197/atnaa.431135	NOUN
ejpam-5730	535	2	[	[	X
ejpam-5730	535	3	19	19	NUM
ejpam-5730	535	4	]	]	PUNCT
ejpam-5730	535	5	e.	e.	PROPN
ejpam-5730	535	6	karapinar	karapinar	PROPN
ejpam-5730	535	7	,	,	PUNCT
ejpam-5730	535	8	ćirić	ćirić	NOUN
ejpam-5730	535	9	type	type	NOUN
ejpam-5730	535	10	nonunique	nonunique	ADJ
ejpam-5730	535	11	fixed	fix	VERB
ejpam-5730	535	12	points	point	NOUN
ejpam-5730	535	13	results	result	NOUN
ejpam-5730	535	14	:	:	PUNCT
ejpam-5730	535	15	a	a	DET
ejpam-5730	535	16	review	review	NOUN
ejpam-5730	535	17	,	,	PUNCT
ejpam-5730	535	18	appl	appl	PROPN
ejpam-5730	535	19	.	.	PUNCT
ejpam-5730	536	1	comput	comput	PROPN
ejpam-5730	536	2	.	.	PUNCT
ejpam-5730	537	1	math	math	NOUN
ejpam-5730	537	2	.	.	PUNCT
ejpam-5730	538	1	18(1	18(1	X
ejpam-5730	538	2	)	)	PUNCT
ejpam-5730	538	3	(	(	PUNCT
ejpam-5730	538	4	2019	2019	NUM
ejpam-5730	538	5	)	)	PUNCT
ejpam-5730	538	6	3–21	3–21	NOUN
ejpam-5730	538	7	.	.	PUNCT
ejpam-5730	539	1	[	[	X
ejpam-5730	539	2	20	20	NUM
ejpam-5730	539	3	]	]	PUNCT
ejpam-5730	539	4	e.	e.	PROPN
ejpam-5730	539	5	karapinar	karapinar	PROPN
ejpam-5730	539	6	,	,	PUNCT
ejpam-5730	539	7	interpolative	interpolative	ADJ
ejpam-5730	539	8	kannan	kannan	PROPN
ejpam-5730	539	9	-	-	PUNCT
ejpam-5730	539	10	meir	meir	PROPN
ejpam-5730	539	11	-	-	PUNCT
ejpam-5730	539	12	keeler	keeler	PROPN
ejpam-5730	539	13	type	type	NOUN
ejpam-5730	539	14	contraction	contraction	NOUN
ejpam-5730	539	15	,	,	PUNCT
ejpam-5730	539	16	adv	adv	PROPN
ejpam-5730	539	17	.	.	PUNCT
ejpam-5730	539	18	theory	theory	PROPN
ejpam-5730	539	19	nonlinear	nonlinear	PROPN
ejpam-5730	539	20	anal	anal	PROPN
ejpam-5730	539	21	.	.	PUNCT
ejpam-5730	540	1	appl	appl	PROPN
ejpam-5730	540	2	.	.	PUNCT
ejpam-5730	541	1	2021(4	2021(4	NUM
ejpam-5730	541	2	)	)	PUNCT
ejpam-5730	541	3	(	(	PUNCT
ejpam-5730	541	4	2021	2021	NUM
ejpam-5730	541	5	)	)	PUNCT
ejpam-5730	542	1	611–614	611–614	NUM
ejpam-5730	542	2	.	.	PUNCT
ejpam-5730	543	1	[	[	X
ejpam-5730	543	2	21	21	NUM
ejpam-5730	543	3	]	]	X
ejpam-5730	543	4	e.	e.	PROPN
ejpam-5730	543	5	karapinar	karapinar	PROPN
ejpam-5730	543	6	,	,	PUNCT
ejpam-5730	543	7	revisiting	revisiting	ADJ
ejpam-5730	543	8	ćirić-type	ćirić-type	ADJ
ejpam-5730	543	9	nonunique	nonunique	ADJ
ejpam-5730	543	10	fixed	fix	VERB
ejpam-5730	543	11	point	point	NOUN
ejpam-5730	543	12	theorem	theorem	VERB
ejpam-5730	543	13	via	via	ADP
ejpam-5730	543	14	interpolation	interpolation	NOUN
ejpam-5730	543	15	,	,	PUNCT
ejpam-5730	543	16	applied	apply	VERB
ejpam-5730	543	17	general	general	ADJ
ejpam-5730	543	18	topology	topology	NOUN
ejpam-5730	543	19	22(2	22(2	NUM
ejpam-5730	543	20	)	)	PUNCT
ejpam-5730	543	21	(	(	PUNCT
ejpam-5730	543	22	2021	2021	NUM
ejpam-5730	543	23	)	)	PUNCT
ejpam-5730	543	24	483–496	483–496	NOUN
ejpam-5730	543	25	.	.	PUNCT
ejpam-5730	544	1	[	[	X
ejpam-5730	544	2	22	22	NUM
ejpam-5730	544	3	]	]	X
ejpam-5730	544	4	e.	e.	PROPN
ejpam-5730	544	5	karapinar	karapinar	PROPN
ejpam-5730	544	6	,	,	PUNCT
ejpam-5730	544	7	r.	r.	PROPN
ejpam-5730	544	8	agarwal	agarwal	PROPN
ejpam-5730	544	9	,	,	PUNCT
ejpam-5730	544	10	interpolative	interpolative	ADJ
ejpam-5730	544	11	rus	rus	PROPN
ejpam-5730	544	12	-	-	PUNCT
ejpam-5730	544	13	reich	reich	NOUN
ejpam-5730	544	14	-	-	PUNCT
ejpam-5730	544	15	ćirić	ćirić	NOUN
ejpam-5730	544	16	type	type	NOUN
ejpam-5730	544	17	¢¥	¢¥	NOUN
ejpam-5730	544	18	contractions	contraction	NOUN
ejpam-5730	544	19	via	via	ADP
ejpam-5730	544	20	simulation	simulation	NOUN
ejpam-5730	544	21	functions	function	NOUN
ejpam-5730	544	22	,	,	PUNCT
ejpam-5730	544	23	an	an	PRON
ejpam-5730	544	24	.	.	PUNCT
ejpam-5730	545	1	şt	şt	PROPN
ejpam-5730	545	2	.	.	PROPN
ejpam-5730	545	3	univ	univ	PROPN
ejpam-5730	545	4	.	.	PUNCT
ejpam-5730	546	1	ovidius	ovidius	PROPN
ejpam-5730	546	2	constanţa	constanţa	NOUN
ejpam-5730	546	3	27(3	27(3	NUM
ejpam-5730	546	4	)	)	PUNCT
ejpam-5730	546	5	(	(	PUNCT
ejpam-5730	546	6	2019	2019	NUM
ejpam-5730	546	7	)	)	PUNCT
ejpam-5730	547	1	137–152	137–152	NUM
ejpam-5730	547	2	.	.	PUNCT
ejpam-5730	548	1	doi	doi	NOUN
ejpam-5730	548	2	:	:	PUNCT
ejpam-5730	548	3	10.2478	10.2478	NUM
ejpam-5730	548	4	/	/	SYM
ejpam-5730	548	5	auom-2019	auom-2019	NOUN
ejpam-5730	548	6	-	-	PUNCT
ejpam-5730	548	7	0038	0038	NUM
ejpam-5730	549	1	[	[	X
ejpam-5730	549	2	23	23	NUM
ejpam-5730	549	3	]	]	X
ejpam-5730	549	4	e.	e.	PROPN
ejpam-5730	549	5	karapinar	karapinar	PROPN
ejpam-5730	549	6	,	,	PUNCT
ejpam-5730	549	7	r.p	r.p	PROPN
ejpam-5730	549	8	.	.	PROPN
ejpam-5730	549	9	agarwal	agarwal	PROPN
ejpam-5730	549	10	,	,	PUNCT
ejpam-5730	549	11	h.	h.	PROPN
ejpam-5730	549	12	aydi	aydi	PROPN
ejpam-5730	549	13	,	,	PUNCT
ejpam-5730	549	14	interpolative	interpolative	ADJ
ejpam-5730	549	15	reich	reich	NOUN
ejpam-5730	549	16	-	-	PUNCT
ejpam-5730	549	17	rus	rus	NOUN
ejpam-5730	549	18	-	-	ADJ
ejpam-5730	549	19	ćirić	ćirić	NOUN
ejpam-5730	549	20	type	type	NOUN
ejpam-5730	549	21	contractions	contraction	NOUN
ejpam-5730	549	22	on	on	ADP
ejpam-5730	549	23	partial	partial	ADJ
ejpam-5730	549	24	metric	metric	ADJ
ejpam-5730	549	25	spaces	space	NOUN
ejpam-5730	549	26	,	,	PUNCT
ejpam-5730	549	27	mathematics	mathematics	PROPN
ejpam-5730	549	28	2018	2018	NUM
ejpam-5730	549	29	,	,	PUNCT
ejpam-5730	549	30	6(11	6(11	NUM
ejpam-5730	549	31	)	)	PUNCT
ejpam-5730	549	32	,	,	PUNCT
ejpam-5730	549	33	256	256	NUM
ejpam-5730	549	34	.	.	PUNCT
ejpam-5730	550	1	[	[	X
ejpam-5730	550	2	24	24	NUM
ejpam-5730	550	3	]	]	X
ejpam-5730	550	4	e.	e.	PROPN
ejpam-5730	550	5	karapinar	karapinar	PROPN
ejpam-5730	550	6	,	,	PUNCT
ejpam-5730	550	7	o.	o.	PROPN
ejpam-5730	550	8	alqahtani	alqahtani	PROPN
ejpam-5730	550	9	,	,	PUNCT
ejpam-5730	550	10	h.	h.	PROPN
ejpam-5730	550	11	aydi	aydi	PROPN
ejpam-5730	550	12	,	,	PUNCT
ejpam-5730	550	13	on	on	ADP
ejpam-5730	550	14	interpolative	interpolative	ADJ
ejpam-5730	550	15	hardy	hardy	ADJ
ejpam-5730	550	16	-	-	PUNCT
ejpam-5730	550	17	rogers	rogers	NOUN
ejpam-5730	550	18	type	type	NOUN
ejpam-5730	550	19	contractions	contraction	NOUN
ejpam-5730	550	20	,	,	PUNCT
ejpam-5730	550	21	symmetry	symmetry	NOUN
ejpam-5730	550	22	2018	2018	NUM
ejpam-5730	550	23	,	,	PUNCT
ejpam-5730	550	24	11	11	NUM
ejpam-5730	550	25	,	,	PUNCT
ejpam-5730	550	26	8	8	NUM
ejpam-5730	550	27	;	;	PUNCT
ejpam-5730	550	28	doi:10.3390	doi:10.3390	NOUN
ejpam-5730	550	29	/	/	SYM
ejpam-5730	550	30	sym11010008	sym11010008	NOUN
ejpam-5730	550	31	[	[	X
ejpam-5730	550	32	25	25	NUM
ejpam-5730	550	33	]	]	PUNCT
ejpam-5730	550	34	f.	f.	PROPN
ejpam-5730	550	35	khojasteh	khojasteh	PROPN
ejpam-5730	550	36	,	,	PUNCT
ejpam-5730	550	37	m.	m.	NOUN
ejpam-5730	550	38	abbas	abbas	PROPN
ejpam-5730	550	39	,	,	PUNCT
ejpam-5730	550	40	s.	s.	PROPN
ejpam-5730	550	41	costache	costache	PROPN
ejpam-5730	550	42	,	,	PUNCT
ejpam-5730	550	43	two	two	NUM
ejpam-5730	550	44	new	new	ADJ
ejpam-5730	550	45	types	type	NOUN
ejpam-5730	550	46	of	of	ADP
ejpam-5730	550	47	fixed	fix	VERB
ejpam-5730	550	48	point	point	NOUN
ejpam-5730	550	49	theorems	theorem	NOUN
ejpam-5730	550	50	in	in	ADP
ejpam-5730	550	51	complete	complete	ADJ
ejpam-5730	550	52	metric	metric	ADJ
ejpam-5730	550	53	spaces	space	NOUN
ejpam-5730	550	54	,	,	PUNCT
ejpam-5730	550	55	abstr	abstr	PROPN
ejpam-5730	550	56	.	.	PUNCT
ejpam-5730	551	1	appl	appl	PROPN
ejpam-5730	551	2	.	.	PUNCT
ejpam-5730	552	1	anal	anal	PROPN
ejpam-5730	552	2	.	.	PROPN
ejpam-5730	552	3	,	,	PUNCT
ejpam-5730	552	4	2014	2014	NUM
ejpam-5730	552	5	,	,	PUNCT
ejpam-5730	552	6	art	art	NOUN
ejpam-5730	552	7	.	.	PUNCT
ejpam-5730	553	1	i	i	PRON
ejpam-5730	553	2	d	d	PROPN
ejpam-5730	553	3	325840	325840	NUM
ejpam-5730	553	4	,	,	PUNCT
ejpam-5730	553	5	5pp	5pp	NOUN
ejpam-5730	553	6	.	.	PUNCT
ejpam-5730	554	1	[	[	X
ejpam-5730	554	2	26	26	NUM
ejpam-5730	554	3	]	]	PUNCT
ejpam-5730	554	4	p.	p.	NOUN
ejpam-5730	554	5	kumam	kumam	PROPN
ejpam-5730	554	6	,	,	PUNCT
ejpam-5730	554	7	n.v	n.v	PROPN
ejpam-5730	554	8	.	.	PROPN
ejpam-5730	554	9	dung	dung	PROPN
ejpam-5730	554	10	,	,	PUNCT
ejpam-5730	554	11	k.	k.	PROPN
ejpam-5730	554	12	sitytithakerngkiet	sitytithakerngkiet	PROPN
ejpam-5730	554	13	,	,	PUNCT
ejpam-5730	554	14	a	a	DET
ejpam-5730	554	15	generalization	generalization	NOUN
ejpam-5730	554	16	of	of	ADP
ejpam-5730	554	17	ćirić	ćirić	PROPN
ejpam-5730	554	18	fixed	fix	VERB
ejpam-5730	554	19	point	point	NOUN
ejpam-5730	554	20	theorems	theorem	NOUN
ejpam-5730	554	21	,	,	PUNCT
ejpam-5730	554	22	filomat	filomat	NOUN
ejpam-5730	554	23	29	29	NUM
ejpam-5730	554	24	(	(	PUNCT
ejpam-5730	554	25	2015	2015	NUM
ejpam-5730	554	26	)	)	PUNCT
ejpam-5730	554	27	1549–1556	1549–1556	NUM
ejpam-5730	554	28	.	.	PUNCT
ejpam-5730	555	1	[	[	X
ejpam-5730	555	2	27	27	NUM
ejpam-5730	555	3	]	]	X
ejpam-5730	555	4	j.-j	j.-j	PROPN
ejpam-5730	555	5	.	.	PUNCT
ejpam-5730	555	6	miñana	miñana	PROPN
ejpam-5730	555	7	.	.	PUNCT
ejpam-5730	556	1	o.	o.	PROPN
ejpam-5730	556	2	valero	valero	PROPN
ejpam-5730	556	3	,	,	PUNCT
ejpam-5730	556	4	are	be	AUX
ejpam-5730	556	5	fixed	fix	VERB
ejpam-5730	556	6	point	point	NOUN
ejpam-5730	556	7	theorems	theorem	NOUN
ejpam-5730	556	8	in	in	ADP
ejpam-5730	556	9	g	g	NOUN
ejpam-5730	556	10	-	-	PUNCT
ejpam-5730	556	11	metric	metric	ADJ
ejpam-5730	556	12	spaces	space	NOUN
ejpam-5730	556	13	an	an	DET
ejpam-5730	556	14	authentic	authentic	ADJ
ejpam-5730	556	15	generalization	generalization	NOUN
ejpam-5730	556	16	of	of	ADP
ejpam-5730	556	17	their	their	PRON
ejpam-5730	556	18	classical	classical	ADJ
ejpam-5730	556	19	counterparts	counterpart	NOUN
ejpam-5730	556	20	?	?	PUNCT
ejpam-5730	557	1	j.	j.	PROPN
ejpam-5730	557	2	fixed	fix	VERB
ejpam-5730	557	3	point	point	PROPN
ejpam-5730	557	4	theory	theory	NOUN
ejpam-5730	557	5	appl	appl	PROPN
ejpam-5730	557	6	.	.	PUNCT
ejpam-5730	558	1	(	(	PUNCT
ejpam-5730	558	2	2019	2019	NUM
ejpam-5730	558	3	)	)	PUNCT
ejpam-5730	558	4	21:70	21:70	NUM
ejpam-5730	558	5	https://doi.org/10.1007/s11784-019-0705-z	https://doi.org/10.1007/s11784-019-0705-z	PROPN
ejpam-5730	558	6	s.	s.	PROPN
ejpam-5730	558	7	park	park	PROPN
ejpam-5730	558	8	/	/	SYM
ejpam-5730	558	9	eur	eur	PROPN
ejpam-5730	558	10	.	.	PUNCT
ejpam-5730	559	1	j.	j.	PROPN
ejpam-5730	559	2	pure	pure	PROPN
ejpam-5730	559	3	appl	appl	PROPN
ejpam-5730	559	4	.	.	PROPN
ejpam-5730	559	5	math	math	PROPN
ejpam-5730	559	6	,	,	PUNCT
ejpam-5730	559	7	18	18	NUM
ejpam-5730	559	8	(	(	PUNCT
ejpam-5730	559	9	1	1	NUM
ejpam-5730	559	10	)	)	PUNCT
ejpam-5730	559	11	(	(	PUNCT
ejpam-5730	559	12	2025	2025	NUM
ejpam-5730	559	13	)	)	PUNCT
ejpam-5730	559	14	,	,	PUNCT
ejpam-5730	559	15	5730	5730	NUM
ejpam-5730	559	16	20	20	NUM
ejpam-5730	559	17	of	of	ADP
ejpam-5730	559	18	21	21	NUM
ejpam-5730	559	19	[	[	SYM
ejpam-5730	559	20	28	28	NUM
ejpam-5730	559	21	]	]	X
ejpam-5730	559	22	s.b	s.b	PROPN
ejpam-5730	559	23	.	.	PROPN
ejpam-5730	559	24	nadler	nadler	PROPN
ejpam-5730	559	25	,	,	PUNCT
ejpam-5730	559	26	jr	jr	PROPN
ejpam-5730	559	27	.	.	PUNCT
ejpam-5730	559	28	multi	multi	ADJ
ejpam-5730	559	29	-	-	ADJ
ejpam-5730	559	30	valued	value	VERB
ejpam-5730	559	31	contraction	contraction	NOUN
ejpam-5730	559	32	mappings	mapping	NOUN
ejpam-5730	559	33	,	,	PUNCT
ejpam-5730	559	34	pacific	pacific	PROPN
ejpam-5730	559	35	j.	j.	PROPN
ejpam-5730	559	36	math	math	PROPN
ejpam-5730	559	37	.	.	PUNCT
ejpam-5730	560	1	30	30	NUM
ejpam-5730	560	2	(	(	PUNCT
ejpam-5730	560	3	1969	1969	NUM
ejpam-5730	560	4	)	)	PUNCT
ejpam-5730	560	5	475488	475488	NUM
ejpam-5730	560	6	.	.	PUNCT
ejpam-5730	561	1	[	[	X
ejpam-5730	561	2	29	29	NUM
ejpam-5730	561	3	]	]	PUNCT
ejpam-5730	561	4	s.	s.	PROPN
ejpam-5730	561	5	park	park	PROPN
ejpam-5730	561	6	,	,	PUNCT
ejpam-5730	561	7	a	a	DET
ejpam-5730	561	8	unified	unified	ADJ
ejpam-5730	561	9	approach	approach	NOUN
ejpam-5730	561	10	to	to	ADP
ejpam-5730	561	11	fixed	fix	VERB
ejpam-5730	561	12	points	point	NOUN
ejpam-5730	561	13	of	of	ADP
ejpam-5730	561	14	contractive	contractive	ADJ
ejpam-5730	561	15	maps	map	NOUN
ejpam-5730	561	16	.	.	PUNCT
ejpam-5730	562	1	j.	j.	PROPN
ejpam-5730	562	2	korean	korean	PROPN
ejpam-5730	562	3	math	math	PROPN
ejpam-5730	562	4	.	.	PUNCT
ejpam-5730	563	1	soc	soc	PROPN
ejpam-5730	563	2	.	.	PUNCT
ejpam-5730	564	1	16	16	NUM
ejpam-5730	564	2	(	(	PUNCT
ejpam-5730	564	3	1980	1980	NUM
ejpam-5730	564	4	)	)	PUNCT
ejpam-5730	565	1	95–105	95–105	NUM
ejpam-5730	565	2	.	.	PUNCT
ejpam-5730	566	1	[	[	X
ejpam-5730	566	2	30	30	NUM
ejpam-5730	566	3	]	]	X
ejpam-5730	566	4	s.	s.	PROPN
ejpam-5730	566	5	park	park	PROPN
ejpam-5730	566	6	,	,	PUNCT
ejpam-5730	566	7	foundations	foundation	NOUN
ejpam-5730	566	8	of	of	ADP
ejpam-5730	566	9	ordered	order	VERB
ejpam-5730	566	10	fixed	fix	VERB
ejpam-5730	566	11	point	point	NOUN
ejpam-5730	566	12	theory	theory	NOUN
ejpam-5730	566	13	,	,	PUNCT
ejpam-5730	566	14	j.	j.	PROPN
ejpam-5730	566	15	nat	nat	PROPN
ejpam-5730	566	16	.	.	PUNCT
ejpam-5730	567	1	acad	acad	PROPN
ejpam-5730	567	2	.	.	PUNCT
ejpam-5730	568	1	sci	sci	PROPN
ejpam-5730	568	2	.	.	PROPN
ejpam-5730	568	3	,	,	PUNCT
ejpam-5730	568	4	rok	rok	PROPN
ejpam-5730	568	5	,	,	PUNCT
ejpam-5730	568	6	nat	nat	PROPN
ejpam-5730	568	7	.	.	PUNCT
ejpam-5730	569	1	sci	sci	PROPN
ejpam-5730	569	2	.	.	PUNCT
ejpam-5730	569	3	ser	ser	PROPN
ejpam-5730	569	4	.	.	PROPN
ejpam-5730	569	5	61(2	61(2	NUM
ejpam-5730	569	6	)	)	PUNCT
ejpam-5730	569	7	(	(	PUNCT
ejpam-5730	569	8	2022	2022	NUM
ejpam-5730	569	9	)	)	PUNCT
ejpam-5730	569	10	247–287	247–287	NUM
ejpam-5730	569	11	.	.	PUNCT
ejpam-5730	570	1	[	[	X
ejpam-5730	570	2	31	31	NUM
ejpam-5730	570	3	]	]	PUNCT
ejpam-5730	570	4	s.	s.	PROPN
ejpam-5730	570	5	park	park	PROPN
ejpam-5730	570	6	,	,	PUNCT
ejpam-5730	570	7	remarks	remark	VERB
ejpam-5730	570	8	on	on	ADP
ejpam-5730	570	9	the	the	DET
ejpam-5730	570	10	metatheorem	metatheorem	ADJ
ejpam-5730	570	11	in	in	ADP
ejpam-5730	570	12	ordered	order	VERB
ejpam-5730	570	13	fixed	fix	VERB
ejpam-5730	570	14	point	point	NOUN
ejpam-5730	570	15	theory	theory	NOUN
ejpam-5730	570	16	,	,	PUNCT
ejpam-5730	570	17	advanced	advanced	ADJ
ejpam-5730	570	18	mathematical	mathematical	ADJ
ejpam-5730	570	19	analysis	analysis	NOUN
ejpam-5730	570	20	and	and	CCONJ
ejpam-5730	570	21	its	its	PRON
ejpam-5730	570	22	applications	application	NOUN
ejpam-5730	570	23	(	(	PUNCT
ejpam-5730	570	24	edited	edit	VERB
ejpam-5730	570	25	by	by	ADP
ejpam-5730	570	26	p.	p.	PROPN
ejpam-5730	570	27	debnath	debnath	PROPN
ejpam-5730	570	28	,	,	PUNCT
ejpam-5730	570	29	d.	d.	PROPN
ejpam-5730	570	30	f.	f.	PROPN
ejpam-5730	570	31	m.	m.	PROPN
ejpam-5730	570	32	torres	torres	PROPN
ejpam-5730	570	33	,	,	PUNCT
ejpam-5730	571	1	y.	y.	PROPN
ejpam-5730	571	2	j.	j.	PROPN
ejpam-5730	571	3	cho	cho	PROPN
ejpam-5730	571	4	)	)	PUNCT
ejpam-5730	571	5	crc	crc	PROPN
ejpam-5730	571	6	press	press	NOUN
ejpam-5730	571	7	(	(	PUNCT
ejpam-5730	571	8	2023	2023	NUM
ejpam-5730	571	9	)	)	PUNCT
ejpam-5730	571	10	11–27	11–27	NUM
ejpam-5730	571	11	.	.	PUNCT
ejpam-5730	572	1	doi	doi	NOUN
ejpam-5730	572	2	:	:	PUNCT
ejpam-5730	572	3	10.1201/9781003388678	10.1201/9781003388678	NUM
ejpam-5730	572	4	-	-	SYM
ejpam-5730	572	5	2	2	NUM
ejpam-5730	572	6	[	[	X
ejpam-5730	572	7	32	32	NUM
ejpam-5730	572	8	]	]	PUNCT
ejpam-5730	572	9	s.	s.	PROPN
ejpam-5730	572	10	park	park	PROPN
ejpam-5730	572	11	,	,	PUNCT
ejpam-5730	572	12	history	history	NOUN
ejpam-5730	572	13	of	of	ADP
ejpam-5730	572	14	the	the	DET
ejpam-5730	572	15	metatheorem	metatheorem	PROPN
ejpam-5730	572	16	in	in	ADP
ejpam-5730	572	17	ordered	order	VERB
ejpam-5730	572	18	fixed	fix	VERB
ejpam-5730	572	19	point	point	NOUN
ejpam-5730	572	20	theory	theory	NOUN
ejpam-5730	572	21	,	,	PUNCT
ejpam-5730	572	22	j.	j.	PROPN
ejpam-5730	572	23	nat	nat	PROPN
ejpam-5730	572	24	.	.	PUNCT
ejpam-5730	573	1	acad	acad	PROPN
ejpam-5730	573	2	.	.	PUNCT
ejpam-5730	574	1	sci	sci	PROPN
ejpam-5730	574	2	.	.	PROPN
ejpam-5730	574	3	,	,	PUNCT
ejpam-5730	574	4	rok	rok	PROPN
ejpam-5730	574	5	,	,	PUNCT
ejpam-5730	574	6	nat	nat	PROPN
ejpam-5730	574	7	.	.	PUNCT
ejpam-5730	575	1	sci	sci	PROPN
ejpam-5730	575	2	.	.	PUNCT
ejpam-5730	575	3	ser	ser	PROPN
ejpam-5730	575	4	.	.	PROPN
ejpam-5730	576	1	62(2	62(2	NUM
ejpam-5730	576	2	)	)	PUNCT
ejpam-5730	577	1	(	(	PUNCT
ejpam-5730	577	2	2023	2023	NUM
ejpam-5730	577	3	)	)	PUNCT
ejpam-5730	578	1	373–410	373–410	NUM
ejpam-5730	578	2	.	.	PUNCT
ejpam-5730	579	1	[	[	X
ejpam-5730	579	2	33	33	NUM
ejpam-5730	579	3	]	]	PUNCT
ejpam-5730	579	4	s.	s.	PROPN
ejpam-5730	579	5	park	park	PROPN
ejpam-5730	579	6	,	,	PUNCT
ejpam-5730	579	7	relatives	relative	NOUN
ejpam-5730	579	8	of	of	ADP
ejpam-5730	579	9	a	a	DET
ejpam-5730	579	10	theorem	theorem	NOUN
ejpam-5730	579	11	of	of	ADP
ejpam-5730	579	12	rus	rus	PROPN
ejpam-5730	579	13	-	-	PUNCT
ejpam-5730	579	14	hicks	hick	NOUN
ejpam-5730	579	15	-	-	PUNCT
ejpam-5730	579	16	rhoades	rhoade	NOUN
ejpam-5730	579	17	,	,	PUNCT
ejpam-5730	579	18	letters	letter	VERB
ejpam-5730	579	19	nonlinear	nonlinear	ADJ
ejpam-5730	579	20	anal	anal	PROPN
ejpam-5730	579	21	.	.	PUNCT
ejpam-5730	580	1	appl	appl	PROPN
ejpam-5730	580	2	.	.	PROPN
ejpam-5730	581	1	1	1	NUM
ejpam-5730	581	2	(	(	PUNCT
ejpam-5730	581	3	2023	2023	NUM
ejpam-5730	581	4	)	)	PUNCT
ejpam-5730	581	5	57–63	57–63	NUM
ejpam-5730	581	6	.	.	PUNCT
ejpam-5730	582	1	issn	issn	PROPN
ejpam-5730	582	2	2985	2985	NUM
ejpam-5730	582	3	-	-	PUNCT
ejpam-5730	582	4	874x	874x	NOUN
ejpam-5730	582	5	[	[	X
ejpam-5730	582	6	34	34	NUM
ejpam-5730	582	7	]	]	X
ejpam-5730	582	8	s.	s.	PROPN
ejpam-5730	582	9	park	park	PROPN
ejpam-5730	582	10	,	,	PUNCT
ejpam-5730	582	11	some	some	DET
ejpam-5730	582	12	metric	metric	ADJ
ejpam-5730	582	13	fixed	fix	VERB
ejpam-5730	582	14	point	point	NOUN
ejpam-5730	582	15	theorems	theorem	NOUN
ejpam-5730	582	16	hold	hold	VERB
ejpam-5730	582	17	for	for	ADP
ejpam-5730	582	18	quasimetric	quasimetric	ADJ
ejpam-5730	582	19	spaces	space	NOUN
ejpam-5730	582	20	,	,	PUNCT
ejpam-5730	582	21	results	result	NOUN
ejpam-5730	582	22	in	in	ADP
ejpam-5730	582	23	nonlinear	nonlinear	ADJ
ejpam-5730	582	24	analysis	analysis	NOUN
ejpam-5730	582	25	6(4	6(4	NUM
ejpam-5730	582	26	)	)	PUNCT
ejpam-5730	582	27	(	(	PUNCT
ejpam-5730	582	28	2023	2023	NUM
ejpam-5730	582	29	)	)	PUNCT
ejpam-5730	583	1	116–127	116–127	NUM
ejpam-5730	583	2	.	.	PUNCT
ejpam-5730	584	1	https://doi.org/10.31838/rna/2023.06.04.012	https://doi.org/10.31838/rna/2023.06.04.012	PROPN
ejpam-5730	584	2	.	.	PUNCT
ejpam-5730	585	1	a	a	DET
ejpam-5730	585	2	revised	revise	VERB
ejpam-5730	585	3	and	and	CCONJ
ejpam-5730	585	4	corrected	correct	VERB
ejpam-5730	585	5	version	version	NOUN
ejpam-5730	585	6	appears	appear	VERB
ejpam-5730	585	7	in	in	ADP
ejpam-5730	585	8	research	research	NOUN
ejpam-5730	585	9	gate	gate	NOUN
ejpam-5730	585	10	.	.	PUNCT
ejpam-5730	586	1	[	[	X
ejpam-5730	586	2	35	35	NUM
ejpam-5730	586	3	]	]	X
ejpam-5730	586	4	s.	s.	PROPN
ejpam-5730	586	5	park	park	PROPN
ejpam-5730	586	6	,	,	PUNCT
ejpam-5730	586	7	almost	almost	ADV
ejpam-5730	586	8	all	all	PRON
ejpam-5730	586	9	about	about	ADP
ejpam-5730	586	10	rus	rus	NOUN
ejpam-5730	586	11	-	-	PUNCT
ejpam-5730	586	12	hicks	hick	NOUN
ejpam-5730	586	13	-	-	PUNCT
ejpam-5730	586	14	rhoades	rhoade	NOUN
ejpam-5730	586	15	maps	map	NOUN
ejpam-5730	586	16	in	in	ADP
ejpam-5730	586	17	quasi	quasi	ADJ
ejpam-5730	586	18	-	-	ADJ
ejpam-5730	586	19	metric	metric	ADJ
ejpam-5730	586	20	spaces	space	NOUN
ejpam-5730	586	21	,	,	PUNCT
ejpam-5730	586	22	adv	adv	PROPN
ejpam-5730	586	23	.	.	PUNCT
ejpam-5730	587	1	th	th	X
ejpam-5730	587	2	.	.	PUNCT
ejpam-5730	588	1	nonlinear	nonlinear	PROPN
ejpam-5730	588	2	anal	anal	PROPN
ejpam-5730	588	3	.	.	PUNCT
ejpam-5730	589	1	appl	appl	PROPN
ejpam-5730	589	2	.	.	PUNCT
ejpam-5730	590	1	7(2	7(2	NUM
ejpam-5730	590	2	)	)	PUNCT
ejpam-5730	591	1	(	(	PUNCT
ejpam-5730	591	2	2023	2023	NUM
ejpam-5730	591	3	)	)	PUNCT
ejpam-5730	592	1	455–471	455–471	NUM
ejpam-5730	592	2	.	.	PUNCT
ejpam-5730	593	1	doi	doi	PROPN
ejpam-5730	593	2	0.31197	0.31197	NUM
ejpam-5730	593	3	/	/	SYM
ejpam-5730	593	4	atnaa.1185449	atnaa.1185449	PROPN
ejpam-5730	594	1	[	[	X
ejpam-5730	594	2	36	36	NUM
ejpam-5730	594	3	]	]	PUNCT
ejpam-5730	594	4	s.	s.	PROPN
ejpam-5730	594	5	park	park	PROPN
ejpam-5730	594	6	,	,	PUNCT
ejpam-5730	594	7	comments	comment	NOUN
ejpam-5730	594	8	on	on	ADP
ejpam-5730	594	9	the	the	DET
ejpam-5730	594	10	suzuki	suzuki	NOUN
ejpam-5730	594	11	type	type	NOUN
ejpam-5730	594	12	fixed	fix	VERB
ejpam-5730	594	13	point	point	NOUN
ejpam-5730	594	14	theorems	theorem	NOUN
ejpam-5730	594	15	,	,	PUNCT
ejpam-5730	594	16	adv	adv	PROPN
ejpam-5730	594	17	.	.	PUNCT
ejpam-5730	594	18	theory	theory	PROPN
ejpam-5730	594	19	nonlinear	nonlinear	PROPN
ejpam-5730	594	20	anal	anal	PROPN
ejpam-5730	594	21	.	.	PUNCT
ejpam-5730	595	1	appl	appl	PROPN
ejpam-5730	595	2	.	.	PUNCT
ejpam-5730	596	1	7(3	7(3	NUM
ejpam-5730	596	2	)	)	PUNCT
ejpam-5730	596	3	(	(	PUNCT
ejpam-5730	596	4	2023	2023	NUM
ejpam-5730	596	5	)	)	PUNCT
ejpam-5730	596	6	67–78	67–78	NOUN
ejpam-5730	596	7	.	.	PUNCT
ejpam-5730	597	1	[	[	X
ejpam-5730	597	2	37	37	NUM
ejpam-5730	597	3	]	]	PUNCT
ejpam-5730	597	4	s.	s.	PROPN
ejpam-5730	597	5	park	park	PROPN
ejpam-5730	597	6	,	,	PUNCT
ejpam-5730	597	7	the	the	DET
ejpam-5730	597	8	use	use	NOUN
ejpam-5730	597	9	of	of	ADP
ejpam-5730	597	10	quasi	quasi	NOUN
ejpam-5730	597	11	-	-	ADJ
ejpam-5730	597	12	metric	metric	ADJ
ejpam-5730	597	13	in	in	ADP
ejpam-5730	597	14	the	the	DET
ejpam-5730	597	15	metric	metric	ADJ
ejpam-5730	597	16	fixed	fix	VERB
ejpam-5730	597	17	point	point	NOUN
ejpam-5730	597	18	theory	theory	NOUN
ejpam-5730	597	19	,	,	PUNCT
ejpam-5730	597	20	j.	j.	PROPN
ejpam-5730	597	21	nonlinear	nonlinear	PROPN
ejpam-5730	597	22	convex	convex	PROPN
ejpam-5730	597	23	anal	anal	NOUN
ejpam-5730	597	24	.	.	PUNCT
ejpam-5730	598	1	25(7	25(7	NUM
ejpam-5730	598	2	)	)	PUNCT
ejpam-5730	598	3	(	(	PUNCT
ejpam-5730	598	4	2024	2024	NUM
ejpam-5730	598	5	)	)	PUNCT
ejpam-5730	599	1	1553–1564	1553–1564	NUM
ejpam-5730	599	2	.	.	PUNCT
ejpam-5730	600	1	[	[	X
ejpam-5730	600	2	38	38	NUM
ejpam-5730	600	3	]	]	PUNCT
ejpam-5730	600	4	s.	s.	PROPN
ejpam-5730	600	5	park	park	PROPN
ejpam-5730	600	6	,	,	PUNCT
ejpam-5730	600	7	new	new	ADJ
ejpam-5730	600	8	applications	application	NOUN
ejpam-5730	600	9	of	of	ADP
ejpam-5730	600	10	the	the	DET
ejpam-5730	600	11	metatheorem	metatheorem	ADJ
ejpam-5730	600	12	in	in	ADP
ejpam-5730	600	13	ordered	order	VERB
ejpam-5730	600	14	fixed	fix	VERB
ejpam-5730	600	15	point	point	NOUN
ejpam-5730	600	16	theory	theory	NOUN
ejpam-5730	600	17	,	,	PUNCT
ejpam-5730	600	18	j.	j.	PROPN
ejpam-5730	600	19	nonlinear	nonlinear	PROPN
ejpam-5730	600	20	analysis	analysis	NOUN
ejpam-5730	600	21	optimization	optimization	NOUN
ejpam-5730	600	22	15(2	15(2	NOUN
ejpam-5730	600	23	)	)	PUNCT
ejpam-5730	600	24	(	(	PUNCT
ejpam-5730	600	25	2024	2024	NUM
ejpam-5730	600	26	)	)	PUNCT
ejpam-5730	601	1	[	[	X
ejpam-5730	601	2	39	39	NUM
ejpam-5730	601	3	]	]	PUNCT
ejpam-5730	601	4	s.	s.	PROPN
ejpam-5730	601	5	park	park	PROPN
ejpam-5730	601	6	,	,	PUNCT
ejpam-5730	601	7	the	the	DET
ejpam-5730	601	8	realm	realm	NOUN
ejpam-5730	601	9	of	of	ADP
ejpam-5730	601	10	the	the	DET
ejpam-5730	601	11	rus	rus	NOUN
ejpam-5730	601	12	-	-	PUNCT
ejpam-5730	601	13	hicks	hick	NOUN
ejpam-5730	601	14	-	-	PUNCT
ejpam-5730	601	15	rhoades	rhoade	NOUN
ejpam-5730	601	16	maps	map	NOUN
ejpam-5730	601	17	in	in	ADP
ejpam-5730	601	18	the	the	DET
ejpam-5730	601	19	metric	metric	ADJ
ejpam-5730	601	20	fixed	fix	VERB
ejpam-5730	601	21	point	point	NOUN
ejpam-5730	601	22	theory	theory	NOUN
ejpam-5730	601	23	,	,	PUNCT
ejpam-5730	601	24	j.	j.	PROPN
ejpam-5730	601	25	nat	nat	PROPN
ejpam-5730	601	26	.	.	PUNCT
ejpam-5730	602	1	acad	acad	PROPN
ejpam-5730	602	2	.	.	PUNCT
ejpam-5730	603	1	sci	sci	PROPN
ejpam-5730	603	2	.	.	PROPN
ejpam-5730	603	3	,	,	PUNCT
ejpam-5730	603	4	rok	rok	PROPN
ejpam-5730	603	5	,	,	PUNCT
ejpam-5730	603	6	nat	nat	PROPN
ejpam-5730	603	7	.	.	PUNCT
ejpam-5730	604	1	sci	sci	PROPN
ejpam-5730	604	2	.	.	PUNCT
ejpam-5730	604	3	ser	ser	PROPN
ejpam-5730	604	4	.	.	PUNCT
ejpam-5730	605	1	63(1	63(1	NUM
ejpam-5730	605	2	)	)	PUNCT
ejpam-5730	605	3	(	(	PUNCT
ejpam-5730	605	4	2024	2024	NUM
ejpam-5730	605	5	)	)	PUNCT
ejpam-5730	605	6	1–50	1–50	NOUN
ejpam-5730	605	7	.	.	PUNCT
ejpam-5730	606	1	[	[	X
ejpam-5730	606	2	40	40	NUM
ejpam-5730	606	3	]	]	PUNCT
ejpam-5730	606	4	s.	s.	PROPN
ejpam-5730	606	5	park	park	PROPN
ejpam-5730	606	6	,	,	PUNCT
ejpam-5730	606	7	on	on	ADP
ejpam-5730	606	8	the	the	DET
ejpam-5730	606	9	family	family	NOUN
ejpam-5730	606	10	of	of	ADP
ejpam-5730	606	11	theorems	theorem	NOUN
ejpam-5730	606	12	on	on	ADP
ejpam-5730	606	13	metric	metric	ADJ
ejpam-5730	606	14	completeness	completeness	NOUN
ejpam-5730	606	15	,	,	PUNCT
ejpam-5730	606	16	european	european	PROPN
ejpam-5730	606	17	journal	journal	NOUN
ejpam-5730	606	18	of	of	ADP
ejpam-5730	606	19	pure	pure	ADJ
ejpam-5730	606	20	and	and	CCONJ
ejpam-5730	606	21	applied	applied	ADJ
ejpam-5730	606	22	mathematics	mathematic	NOUN
ejpam-5730	606	23	,	,	PUNCT
ejpam-5730	606	24	17(4	17(4	NUM
ejpam-5730	606	25	)	)	PUNCT
ejpam-5730	606	26	(	(	PUNCT
ejpam-5730	606	27	2024	2024	NUM
ejpam-5730	606	28	)	)	PUNCT
ejpam-5730	606	29	2370–2383	2370–2383	NUM
ejpam-5730	606	30	.	.	PUNCT
ejpam-5730	607	1	[	[	X
ejpam-5730	607	2	41	41	NUM
ejpam-5730	607	3	]	]	X
ejpam-5730	607	4	s.	s.	PROPN
ejpam-5730	607	5	park	park	PROPN
ejpam-5730	607	6	,	,	PUNCT
ejpam-5730	607	7	b.e	b.e	PROPN
ejpam-5730	607	8	.	.	PROPN
ejpam-5730	607	9	rhoades	rhoade	NOUN
ejpam-5730	607	10	,	,	PUNCT
ejpam-5730	607	11	some	some	DET
ejpam-5730	607	12	fixed	fix	VERB
ejpam-5730	607	13	point	point	NOUN
ejpam-5730	607	14	theorems	theorem	NOUN
ejpam-5730	607	15	,	,	PUNCT
ejpam-5730	607	16	sem	sem	NOUN
ejpam-5730	607	17	.	.	PUNCT
ejpam-5730	608	1	in	in	ADP
ejpam-5730	608	2	math	math	NOUN
ejpam-5730	608	3	.	.	PUNCT
ejpam-5730	609	1	lecture	lecture	NOUN
ejpam-5730	609	2	note	note	NOUN
ejpam-5730	609	3	series	series	PROPN
ejpam-5730	609	4	,	,	PUNCT
ejpam-5730	609	5	yonsei	yonsei	PROPN
ejpam-5730	609	6	univ	univ	PROPN
ejpam-5730	609	7	.	.	PROPN
ejpam-5730	609	8	2	2	NUM
ejpam-5730	609	9	(	(	PUNCT
ejpam-5730	609	10	1981	1981	NUM
ejpam-5730	609	11	)	)	PUNCT
ejpam-5730	609	12	113–125	113–125	NUM
ejpam-5730	609	13	.	.	PUNCT
ejpam-5730	610	1	[	[	X
ejpam-5730	610	2	42	42	NUM
ejpam-5730	610	3	]	]	X
ejpam-5730	610	4	e.	e.	PROPN
ejpam-5730	610	5	petrov	petrov	PROPN
ejpam-5730	610	6	,	,	PUNCT
ejpam-5730	610	7	fixed	fix	VERB
ejpam-5730	610	8	point	point	NOUN
ejpam-5730	610	9	theorem	theorem	NOUN
ejpam-5730	610	10	for	for	ADP
ejpam-5730	610	11	generalized	generalized	ADJ
ejpam-5730	610	12	kannan	kannan	PROPN
ejpam-5730	610	13	type	type	NOUN
ejpam-5730	610	14	mappings	mapping	NOUN
ejpam-5730	610	15	,	,	PUNCT
ejpam-5730	610	16	arxiv:2308.05419v1	arxiv:2308.05419v1	NOUN
ejpam-5730	610	17	[	[	X
ejpam-5730	610	18	math.gn	math.gn	X
ejpam-5730	610	19	]	]	X
ejpam-5730	610	20	10aug2023	10aug2023	NUM
ejpam-5730	610	21	.	.	PUNCT
ejpam-5730	611	1	[	[	X
ejpam-5730	611	2	43	43	NUM
ejpam-5730	611	3	]	]	X
ejpam-5730	611	4	a.c.m	a.c.m	X
ejpam-5730	611	5	.	.	PUNCT
ejpam-5730	611	6	ran	ran	NOUN
ejpam-5730	611	7	,	,	PUNCT
ejpam-5730	611	8	m.c.b	m.c.b	NOUN
ejpam-5730	611	9	.	.	PUNCT
ejpam-5730	612	1	reurings	reuring	NOUN
ejpam-5730	612	2	,	,	PUNCT
ejpam-5730	612	3	a	a	DET
ejpam-5730	612	4	fixed	fix	VERB
ejpam-5730	612	5	point	point	NOUN
ejpam-5730	612	6	theorem	theorem	VERB
ejpam-5730	612	7	in	in	ADP
ejpam-5730	612	8	partially	partially	ADV
ejpam-5730	612	9	ordered	order	VERB
ejpam-5730	612	10	sets	set	NOUN
ejpam-5730	612	11	and	and	CCONJ
ejpam-5730	612	12	some	some	DET
ejpam-5730	612	13	application	application	NOUN
ejpam-5730	612	14	to	to	PART
ejpam-5730	612	15	matrix	matrix	NOUN
ejpam-5730	612	16	equations	equation	NOUN
ejpam-5730	612	17	.	.	PUNCT
ejpam-5730	613	1	proc	proc	PROPN
ejpam-5730	613	2	.	.	PUNCT
ejpam-5730	614	1	am	be	AUX
ejpam-5730	614	2	.	.	PUNCT
ejpam-5730	615	1	math	math	PROPN
ejpam-5730	615	2	soc	soc	PROPN
ejpam-5730	615	3	.	.	PUNCT
ejpam-5730	616	1	132	132	NUM
ejpam-5730	616	2	(	(	PUNCT
ejpam-5730	616	3	2004	2004	NUM
ejpam-5730	616	4	)	)	PUNCT
ejpam-5730	616	5	1435–1443	1435–1443	NUM
ejpam-5730	616	6	.	.	PUNCT
ejpam-5730	617	1	[	[	X
ejpam-5730	617	2	44	44	NUM
ejpam-5730	617	3	]	]	PUNCT
ejpam-5730	617	4	s.	s.	PROPN
ejpam-5730	617	5	reich	reich	PROPN
ejpam-5730	617	6	,	,	PUNCT
ejpam-5730	617	7	some	some	DET
ejpam-5730	617	8	remarks	remark	NOUN
ejpam-5730	617	9	concerning	concern	VERB
ejpam-5730	617	10	contraction	contraction	NOUN
ejpam-5730	617	11	mappings	mapping	NOUN
ejpam-5730	617	12	,	,	PUNCT
ejpam-5730	617	13	canad	canad	PROPN
ejpam-5730	617	14	.	.	PUNCT
ejpam-5730	618	1	math	math	NOUN
ejpam-5730	618	2	.	.	PUNCT
ejpam-5730	619	1	bull	bull	NOUN
ejpam-5730	619	2	.	.	PUNCT
ejpam-5730	620	1	14	14	NUM
ejpam-5730	620	2	(	(	PUNCT
ejpam-5730	620	3	1971	1971	NUM
ejpam-5730	620	4	)	)	PUNCT
ejpam-5730	621	1	121–124	121–124	NUM
ejpam-5730	621	2	.	.	PUNCT
ejpam-5730	622	1	[	[	X
ejpam-5730	622	2	45	45	NUM
ejpam-5730	622	3	]	]	X
ejpam-5730	622	4	b.e	b.e	PROPN
ejpam-5730	622	5	.	.	PROPN
ejpam-5730	622	6	rhoades	rhoades	PROPN
ejpam-5730	622	7	,	,	PUNCT
ejpam-5730	622	8	a	a	DET
ejpam-5730	622	9	comparison	comparison	NOUN
ejpam-5730	622	10	of	of	ADP
ejpam-5730	622	11	various	various	ADJ
ejpam-5730	622	12	definitions	definition	NOUN
ejpam-5730	622	13	of	of	ADP
ejpam-5730	622	14	contrctive	contrctive	ADJ
ejpam-5730	622	15	definitions	definition	NOUN
ejpam-5730	622	16	,	,	PUNCT
ejpam-5730	622	17	trans	trans	PROPN
ejpam-5730	622	18	.	.	PROPN
ejpam-5730	622	19	amer	amer	PROPN
ejpam-5730	622	20	.	.	PUNCT
ejpam-5730	622	21	math	math	PROPN
ejpam-5730	622	22	.	.	PUNCT
ejpam-5730	623	1	soc	soc	PROPN
ejpam-5730	623	2	.	.	PUNCT
ejpam-5730	624	1	226	226	NUM
ejpam-5730	624	2	(	(	PUNCT
ejpam-5730	624	3	1977	1977	NUM
ejpam-5730	624	4	)	)	PUNCT
ejpam-5730	624	5	257–290	257–290	NUM
ejpam-5730	624	6	.	.	PUNCT
ejpam-5730	625	1	[	[	X
ejpam-5730	625	2	46	46	NUM
ejpam-5730	625	3	]	]	X
ejpam-5730	625	4	b.e	b.e	PROPN
ejpam-5730	625	5	.	.	PROPN
ejpam-5730	625	6	rhoades	rhoades	PROPN
ejpam-5730	625	7	,	,	PUNCT
ejpam-5730	625	8	a	a	DET
ejpam-5730	625	9	collection	collection	NOUN
ejpam-5730	625	10	of	of	ADP
ejpam-5730	625	11	contractive	contractive	ADJ
ejpam-5730	625	12	definitions	definition	NOUN
ejpam-5730	625	13	,	,	PUNCT
ejpam-5730	625	14	math	math	NOUN
ejpam-5730	625	15	.	.	PUNCT
ejpam-5730	626	1	sem	sem	PROPN
ejpam-5730	626	2	.	.	PUNCT
ejpam-5730	627	1	notes	note	VERB
ejpam-5730	627	2	6	6	NUM
ejpam-5730	627	3	(	(	PUNCT
ejpam-5730	627	4	1978	1978	NUM
ejpam-5730	627	5	)	)	PUNCT
ejpam-5730	627	6	229–235	229–235	NUM
ejpam-5730	627	7	.	.	PUNCT
ejpam-5730	628	1	[	[	X
ejpam-5730	628	2	47	47	NUM
ejpam-5730	628	3	]	]	X
ejpam-5730	628	4	s.	s.	PROPN
ejpam-5730	628	5	romaguera	romaguera	PROPN
ejpam-5730	628	6	,	,	PUNCT
ejpam-5730	628	7	basic	basic	ADJ
ejpam-5730	628	8	contractions	contraction	NOUN
ejpam-5730	628	9	of	of	ADP
ejpam-5730	628	10	suzuki	suzuki	NOUN
ejpam-5730	628	11	-	-	NOUN
ejpam-5730	628	12	type	type	NOUN
ejpam-5730	628	13	on	on	ADP
ejpam-5730	628	14	quasi	quasi	ADJ
ejpam-5730	628	15	-	-	ADJ
ejpam-5730	628	16	metric	metric	ADJ
ejpam-5730	628	17	spaces	space	NOUN
ejpam-5730	628	18	and	and	CCONJ
ejpam-5730	628	19	fixed	fix	VERB
ejpam-5730	628	20	point	point	NOUN
ejpam-5730	628	21	results	result	NOUN
ejpam-5730	628	22	,	,	PUNCT
ejpam-5730	628	23	mathematics	mathematics	NOUN
ejpam-5730	628	24	2022	2022	NUM
ejpam-5730	628	25	,	,	PUNCT
ejpam-5730	628	26	10	10	NUM
ejpam-5730	628	27	,	,	PUNCT
ejpam-5730	628	28	3931	3931	NUM
ejpam-5730	628	29	.	.	PUNCT
ejpam-5730	629	1	https://doi.org/10.3390/math10213931	https://doi.org/10.3390/math10213931	PROPN
ejpam-5730	629	2	s.	s.	PROPN
ejpam-5730	629	3	park	park	PROPN
ejpam-5730	629	4	/	/	SYM
ejpam-5730	629	5	eur	eur	PROPN
ejpam-5730	629	6	.	.	PUNCT
ejpam-5730	630	1	j.	j.	PROPN
ejpam-5730	630	2	pure	pure	PROPN
ejpam-5730	630	3	appl	appl	PROPN
ejpam-5730	630	4	.	.	PROPN
ejpam-5730	630	5	math	math	PROPN
ejpam-5730	630	6	,	,	PUNCT
ejpam-5730	630	7	18	18	NUM
ejpam-5730	630	8	(	(	PUNCT
ejpam-5730	630	9	1	1	NUM
ejpam-5730	630	10	)	)	PUNCT
ejpam-5730	630	11	(	(	PUNCT
ejpam-5730	630	12	2025	2025	NUM
ejpam-5730	630	13	)	)	PUNCT
ejpam-5730	630	14	,	,	PUNCT
ejpam-5730	630	15	5730	5730	NUM
ejpam-5730	630	16	21	21	NUM
ejpam-5730	630	17	of	of	ADP
ejpam-5730	630	18	21	21	NUM
ejpam-5730	630	19	[	[	SYM
ejpam-5730	630	20	48	48	NUM
ejpam-5730	630	21	]	]	X
ejpam-5730	630	22	i.a	i.a	PROPN
ejpam-5730	630	23	.	.	PROPN
ejpam-5730	630	24	rus	rus	PROPN
ejpam-5730	630	25	,	,	PUNCT
ejpam-5730	630	26	teoria	teoria	PROPN
ejpam-5730	630	27	punctului	punctului	PROPN
ejpam-5730	630	28	fix	fix	NOUN
ejpam-5730	630	29	,	,	PUNCT
ejpam-5730	630	30	ii	ii	PROPN
ejpam-5730	630	31	,	,	PUNCT
ejpam-5730	630	32	univ	univ	PROPN
ejpam-5730	630	33	.	.	PUNCT
ejpam-5730	631	1	babes	babes	PROPN
ejpam-5730	631	2	-	-	PUNCT
ejpam-5730	631	3	bolyai	bolyai	NOUN
ejpam-5730	631	4	,	,	PUNCT
ejpam-5730	631	5	cluj	cluj	NOUN
ejpam-5730	631	6	,	,	PUNCT
ejpam-5730	631	7	1973	1973	NUM
ejpam-5730	631	8	.	.	PUNCT
ejpam-5730	632	1	[	[	X
ejpam-5730	632	2	49	49	NUM
ejpam-5730	632	3	]	]	PUNCT
ejpam-5730	632	4	t.	t.	PROPN
ejpam-5730	632	5	suzuki	suzuki	PROPN
ejpam-5730	632	6	,	,	PUNCT
ejpam-5730	632	7	a	a	DET
ejpam-5730	632	8	generalized	generalized	ADJ
ejpam-5730	632	9	banach	banach	NOUN
ejpam-5730	632	10	contraction	contraction	NOUN
ejpam-5730	632	11	principle	principle	NOUN
ejpam-5730	632	12	that	that	PRON
ejpam-5730	632	13	characterizes	characterize	VERB
ejpam-5730	632	14	metric	metric	ADJ
ejpam-5730	632	15	completeness	completeness	NOUN
ejpam-5730	632	16	.	.	PUNCT
ejpam-5730	633	1	proc	proc	PROPN
ejpam-5730	633	2	.	.	PUNCT
ejpam-5730	634	1	amer	amer	PROPN
ejpam-5730	634	2	.	.	PUNCT
ejpam-5730	634	3	math	math	PROPN
ejpam-5730	634	4	.	.	PUNCT
ejpam-5730	635	1	soc	soc	PROPN
ejpam-5730	635	2	.	.	PUNCT
ejpam-5730	636	1	136	136	NUM
ejpam-5730	636	2	(	(	PUNCT
ejpam-5730	636	3	2008	2008	NUM
ejpam-5730	636	4	)	)	PUNCT
ejpam-5730	636	5	1861–1869	1861–1869	NUM
ejpam-5730	636	6	.	.	PUNCT