id	sid	tid	token	lemma	pos
ejpam-5440	1	1	european	european	PROPN
ejpam-5440	1	2	journal	journal	PROPN
ejpam-5440	1	3	of	of	ADP
ejpam-5440	1	4	pure	pure	ADJ
ejpam-5440	1	5	and	and	CCONJ
ejpam-5440	1	6	applied	apply	VERB
ejpam-5440	1	7	mathematics	mathematic	NOUN
ejpam-5440	1	8	vol	vol	NOUN
ejpam-5440	1	9	.	.	PROPN
ejpam-5440	2	1	17	17	NUM
ejpam-5440	2	2	,	,	PUNCT
ejpam-5440	2	3	no	no	INTJ
ejpam-5440	2	4	.	.	NOUN
ejpam-5440	2	5	4	4	NUM
ejpam-5440	2	6	,	,	PUNCT
ejpam-5440	2	7	2024	2024	NUM
ejpam-5440	2	8	,	,	PUNCT
ejpam-5440	2	9	2370	2370	NUM
ejpam-5440	2	10	-	-	SYM
ejpam-5440	2	11	2383	2383	NUM
ejpam-5440	2	12	issn	issn	PROPN
ejpam-5440	2	13	1307	1307	NUM
ejpam-5440	2	14	-	-	SYM
ejpam-5440	2	15	5543	5543	NUM
ejpam-5440	2	16	–	–	PUNCT
ejpam-5440	2	17	ejpam.com	ejpam.com	X
ejpam-5440	2	18	published	publish	VERB
ejpam-5440	2	19	by	by	ADP
ejpam-5440	2	20	new	new	PROPN
ejpam-5440	2	21	york	york	PROPN
ejpam-5440	2	22	business	business	PROPN
ejpam-5440	2	23	global	global	PROPN
ejpam-5440	2	24	on	on	ADP
ejpam-5440	2	25	the	the	DET
ejpam-5440	2	26	family	family	NOUN
ejpam-5440	2	27	of	of	ADP
ejpam-5440	2	28	theorems	theorem	NOUN
ejpam-5440	2	29	on	on	ADP
ejpam-5440	2	30	metric	metric	ADJ
ejpam-5440	2	31	completeness	completeness	NOUN
ejpam-5440	2	32	sehie	sehie	NOUN
ejpam-5440	2	33	park1,2	park1,2	PROPN
ejpam-5440	2	34	1	1	NUM
ejpam-5440	2	35	the	the	DET
ejpam-5440	2	36	national	national	PROPN
ejpam-5440	2	37	academy	academy	PROPN
ejpam-5440	2	38	of	of	ADP
ejpam-5440	2	39	sciences	sciences	PROPN
ejpam-5440	2	40	,	,	PUNCT
ejpam-5440	2	41	republic	republic	NOUN
ejpam-5440	2	42	of	of	ADP
ejpam-5440	2	43	korea	korea	PROPN
ejpam-5440	2	44	,	,	PUNCT
ejpam-5440	2	45	seoul	seoul	PROPN
ejpam-5440	2	46	06579	06579	NUM
ejpam-5440	2	47	,	,	PUNCT
ejpam-5440	2	48	korea	korea	PROPN
ejpam-5440	2	49	2	2	NUM
ejpam-5440	2	50	department	department	NOUN
ejpam-5440	2	51	of	of	ADP
ejpam-5440	2	52	mathematical	mathematical	ADJ
ejpam-5440	2	53	sciences	sciences	PROPN
ejpam-5440	2	54	,	,	PUNCT
ejpam-5440	2	55	seoul	seoul	PROPN
ejpam-5440	2	56	national	national	PROPN
ejpam-5440	2	57	university	university	PROPN
ejpam-5440	2	58	,	,	PUNCT
ejpam-5440	2	59	seoul	seoul	PROPN
ejpam-5440	2	60	08826	08826	NUM
ejpam-5440	2	61	,	,	PUNCT
ejpam-5440	2	62	korea	korea	PROPN
ejpam-5440	2	63	abstract	abstract	NOUN
ejpam-5440	2	64	.	.	PUNCT
ejpam-5440	3	1	there	there	PRON
ejpam-5440	3	2	have	have	AUX
ejpam-5440	3	3	appeared	appear	VERB
ejpam-5440	3	4	a	a	DET
ejpam-5440	3	5	large	large	ADJ
ejpam-5440	3	6	family	family	NOUN
ejpam-5440	3	7	of	of	ADP
ejpam-5440	3	8	theorems	theorem	NOUN
ejpam-5440	3	9	related	relate	VERB
ejpam-5440	3	10	the	the	DET
ejpam-5440	3	11	metric	metric	ADJ
ejpam-5440	3	12	completeness	completeness	NOUN
ejpam-5440	3	13	.	.	PUNCT
ejpam-5440	4	1	they	they	PRON
ejpam-5440	4	2	are	be	AUX
ejpam-5440	4	3	mainly	mainly	ADV
ejpam-5440	4	4	concerned	concern	VERB
ejpam-5440	4	5	with	with	ADP
ejpam-5440	4	6	generalizations	generalization	NOUN
ejpam-5440	4	7	of	of	ADP
ejpam-5440	4	8	the	the	DET
ejpam-5440	4	9	banach	banach	NOUN
ejpam-5440	4	10	contraction	contraction	NOUN
ejpam-5440	4	11	on	on	ADP
ejpam-5440	4	12	quasi	quasi	ADJ
ejpam-5440	4	13	-	-	ADJ
ejpam-5440	4	14	metric	metric	ADJ
ejpam-5440	4	15	spaces	space	NOUN
ejpam-5440	4	16	and	and	CCONJ
ejpam-5440	4	17	their	their	PRON
ejpam-5440	4	18	extended	extended	ADJ
ejpam-5440	4	19	artificial	artificial	ADJ
ejpam-5440	4	20	spaces	space	NOUN
ejpam-5440	4	21	.	.	PUNCT
ejpam-5440	5	1	in	in	ADP
ejpam-5440	5	2	this	this	DET
ejpam-5440	5	3	survey	survey	NOUN
ejpam-5440	5	4	article	article	NOUN
ejpam-5440	5	5	,	,	PUNCT
ejpam-5440	5	6	we	we	PRON
ejpam-5440	5	7	classify	classify	VERB
ejpam-5440	5	8	the	the	DET
ejpam-5440	5	9	family	family	NOUN
ejpam-5440	5	10	according	accord	VERB
ejpam-5440	5	11	to	to	ADP
ejpam-5440	5	12	our	our	PRON
ejpam-5440	5	13	2023	2023	NUM
ejpam-5440	5	14	metatheorem	metatheorem	VERB
ejpam-5440	5	15	.	.	PUNCT
ejpam-5440	6	1	many	many	ADJ
ejpam-5440	6	2	known	know	VERB
ejpam-5440	6	3	metric	metric	ADJ
ejpam-5440	6	4	fixed	fix	VERB
ejpam-5440	6	5	point	point	NOUN
ejpam-5440	6	6	theorems	theorem	NOUN
ejpam-5440	6	7	belong	belong	VERB
ejpam-5440	6	8	to	to	ADP
ejpam-5440	6	9	the	the	DET
ejpam-5440	6	10	family	family	NOUN
ejpam-5440	6	11	including	include	VERB
ejpam-5440	6	12	the	the	DET
ejpam-5440	6	13	rushicks	rushick	NOUN
ejpam-5440	6	14	-	-	PUNCT
ejpam-5440	6	15	rhoades	rhoade	NOUN
ejpam-5440	6	16	(	(	PUNCT
ejpam-5440	6	17	rhr	rhr	PROPN
ejpam-5440	6	18	)	)	PUNCT
ejpam-5440	6	19	theorem	theorem	VERB
ejpam-5440	6	20	.	.	PUNCT
ejpam-5440	7	1	such	such	ADJ
ejpam-5440	7	2	results	result	NOUN
ejpam-5440	7	3	on	on	ADP
ejpam-5440	7	4	metric	metric	ADJ
ejpam-5440	7	5	spaces	space	NOUN
ejpam-5440	7	6	are	be	AUX
ejpam-5440	7	7	consequences	consequence	NOUN
ejpam-5440	7	8	of	of	ADP
ejpam-5440	7	9	our	our	PRON
ejpam-5440	7	10	generalized	generalized	ADJ
ejpam-5440	7	11	forms	form	NOUN
ejpam-5440	7	12	of	of	ADP
ejpam-5440	7	13	the	the	DET
ejpam-5440	7	14	banach	banach	NOUN
ejpam-5440	7	15	contraction	contraction	NOUN
ejpam-5440	7	16	principle	principle	NOUN
ejpam-5440	7	17	for	for	ADP
ejpam-5440	7	18	weak	weak	ADJ
ejpam-5440	7	19	contractions	contraction	NOUN
ejpam-5440	7	20	or	or	CCONJ
ejpam-5440	7	21	the	the	DET
ejpam-5440	7	22	rhr	rhr	PROPN
ejpam-5440	7	23	maps	map	NOUN
ejpam-5440	7	24	on	on	ADP
ejpam-5440	7	25	quasi	quasi	ADJ
ejpam-5440	7	26	-	-	ADJ
ejpam-5440	7	27	metric	metric	ADJ
ejpam-5440	7	28	spaces	space	NOUN
ejpam-5440	7	29	.	.	PUNCT
ejpam-5440	8	1	we	we	PRON
ejpam-5440	8	2	list	list	VERB
ejpam-5440	8	3	a	a	DET
ejpam-5440	8	4	large	large	ADJ
ejpam-5440	8	5	number	number	NOUN
ejpam-5440	8	6	of	of	ADP
ejpam-5440	8	7	examples	example	NOUN
ejpam-5440	8	8	of	of	ADP
ejpam-5440	8	9	metric	metric	ADJ
ejpam-5440	8	10	fixed	fix	VERB
ejpam-5440	8	11	point	point	NOUN
ejpam-5440	8	12	theorems	theorem	NOUN
ejpam-5440	8	13	which	which	PRON
ejpam-5440	8	14	follow	follow	VERB
ejpam-5440	8	15	from	from	ADP
ejpam-5440	8	16	our	our	PRON
ejpam-5440	8	17	principles	principle	NOUN
ejpam-5440	8	18	.	.	PUNCT
ejpam-5440	9	1	moreover	moreover	ADV
ejpam-5440	9	2	,	,	PUNCT
ejpam-5440	9	3	we	we	PRON
ejpam-5440	9	4	add	add	VERB
ejpam-5440	9	5	some	some	DET
ejpam-5440	9	6	comments	comment	NOUN
ejpam-5440	9	7	on	on	ADP
ejpam-5440	9	8	related	related	ADJ
ejpam-5440	9	9	papers	paper	NOUN
ejpam-5440	9	10	in	in	ADP
ejpam-5440	9	11	order	order	NOUN
ejpam-5440	9	12	to	to	PART
ejpam-5440	9	13	improve	improve	VERB
ejpam-5440	9	14	them	they	PRON
ejpam-5440	9	15	.	.	PUNCT
ejpam-5440	10	1	2020	2020	NUM
ejpam-5440	10	2	mathematics	mathematic	NOUN
ejpam-5440	10	3	subject	subject	NOUN
ejpam-5440	10	4	classifications	classification	NOUN
ejpam-5440	10	5	:	:	PUNCT
ejpam-5440	10	6	06a75	06a75	NUM
ejpam-5440	10	7	,	,	PUNCT
ejpam-5440	10	8	47h10	47h10	NUM
ejpam-5440	10	9	,	,	PUNCT
ejpam-5440	10	10	54e35	54e35	NUM
ejpam-5440	10	11	,	,	PUNCT
ejpam-5440	10	12	54h25	54h25	NUM
ejpam-5440	10	13	,	,	PUNCT
ejpam-5440	10	14	58e30	58e30	NUM
ejpam-5440	10	15	,	,	PUNCT
ejpam-5440	10	16	65k10	65k10	NUM
ejpam-5440	10	17	key	key	ADJ
ejpam-5440	10	18	words	word	NOUN
ejpam-5440	10	19	and	and	CCONJ
ejpam-5440	10	20	phrases	phrase	NOUN
ejpam-5440	10	21	:	:	PUNCT
ejpam-5440	10	22	banach	banach	NOUN
ejpam-5440	10	23	contraction	contraction	NOUN
ejpam-5440	10	24	,	,	PUNCT
ejpam-5440	10	25	rus	rus	NOUN
ejpam-5440	10	26	-	-	PUNCT
ejpam-5440	10	27	hicks	hick	NOUN
ejpam-5440	10	28	-	-	PUNCT
ejpam-5440	10	29	rhoades	rhoade	NOUN
ejpam-5440	10	30	contraction	contraction	NOUN
ejpam-5440	10	31	,	,	PUNCT
ejpam-5440	10	32	suzuki	suzuki	NOUN
ejpam-5440	10	33	type	type	NOUN
ejpam-5440	10	34	maps	map	NOUN
ejpam-5440	10	35	,	,	PUNCT
ejpam-5440	10	36	fixed	fix	VERB
ejpam-5440	10	37	point	point	NOUN
ejpam-5440	10	38	,	,	PUNCT
ejpam-5440	10	39	quasi	quasi	ADJ
ejpam-5440	10	40	-	-	ADJ
ejpam-5440	10	41	metric	metric	ADJ
ejpam-5440	10	42	1	1	NUM
ejpam-5440	10	43	.	.	PUNCT
ejpam-5440	11	1	prologue	prologue	NOUN
ejpam-5440	11	2	it	it	PRON
ejpam-5440	11	3	is	be	AUX
ejpam-5440	11	4	well	well	ADV
ejpam-5440	11	5	-	-	PUNCT
ejpam-5440	11	6	known	know	VERB
ejpam-5440	11	7	that	that	PRON
ejpam-5440	11	8	complete	complete	ADJ
ejpam-5440	11	9	metric	metric	ADJ
ejpam-5440	11	10	spaces	space	NOUN
ejpam-5440	11	11	have	have	VERB
ejpam-5440	11	12	a	a	DET
ejpam-5440	11	13	large	large	ADJ
ejpam-5440	11	14	number	number	NOUN
ejpam-5440	11	15	of	of	ADP
ejpam-5440	11	16	properties	property	NOUN
ejpam-5440	11	17	and	and	CCONJ
ejpam-5440	11	18	,	,	PUNCT
ejpam-5440	11	19	conversely	conversely	ADV
ejpam-5440	11	20	,	,	PUNCT
ejpam-5440	11	21	many	many	ADJ
ejpam-5440	11	22	of	of	ADP
ejpam-5440	11	23	them	they	PRON
ejpam-5440	11	24	characterize	characterize	VERB
ejpam-5440	11	25	the	the	DET
ejpam-5440	11	26	completeness	completeness	NOUN
ejpam-5440	11	27	.	.	PUNCT
ejpam-5440	12	1	in	in	ADP
ejpam-5440	12	2	our	our	PRON
ejpam-5440	12	3	study	study	NOUN
ejpam-5440	12	4	in	in	ADP
ejpam-5440	12	5	the	the	DET
ejpam-5440	12	6	ordered	order	VERB
ejpam-5440	12	7	fixed	fix	VERB
ejpam-5440	12	8	point	point	NOUN
ejpam-5440	12	9	theory	theory	NOUN
ejpam-5440	12	10	,	,	PUNCT
ejpam-5440	12	11	we	we	PRON
ejpam-5440	12	12	derived	derive	VERB
ejpam-5440	12	13	the	the	DET
ejpam-5440	12	14	2023	2023	NUM
ejpam-5440	12	15	metatheorem	metatheorem	VERB
ejpam-5440	12	16	which	which	PRON
ejpam-5440	12	17	is	be	AUX
ejpam-5440	12	18	a	a	DET
ejpam-5440	12	19	set	set	NOUN
ejpam-5440	12	20	of	of	ADP
ejpam-5440	12	21	equivalent	equivalent	ADJ
ejpam-5440	12	22	logical	logical	ADJ
ejpam-5440	12	23	statements	statement	NOUN
ejpam-5440	12	24	.	.	PUNCT
ejpam-5440	13	1	from	from	ADP
ejpam-5440	13	2	2022	2022	NUM
ejpam-5440	13	3	,	,	PUNCT
ejpam-5440	13	4	we	we	PRON
ejpam-5440	13	5	applied	apply	VERB
ejpam-5440	13	6	it	it	PRON
ejpam-5440	13	7	to	to	ADP
ejpam-5440	13	8	almost	almost	ADV
ejpam-5440	13	9	one	one	NUM
ejpam-5440	13	10	hundred	hundred	NUM
ejpam-5440	13	11	theorems	theorem	NOUN
ejpam-5440	13	12	and	and	CCONJ
ejpam-5440	13	13	obtained	obtain	VERB
ejpam-5440	13	14	nearly	nearly	ADV
ejpam-5440	13	15	one	one	NUM
ejpam-5440	13	16	thousand	thousand	NUM
ejpam-5440	13	17	new	new	ADJ
ejpam-5440	13	18	facts	fact	NOUN
ejpam-5440	13	19	in	in	ADP
ejpam-5440	13	20	mathematics	mathematic	NOUN
ejpam-5440	13	21	.	.	PUNCT
ejpam-5440	14	1	let	let	VERB
ejpam-5440	14	2	(	(	PUNCT
ejpam-5440	14	3	x	x	X
ejpam-5440	14	4	,	,	PUNCT
ejpam-5440	14	5	q	q	X
ejpam-5440	14	6	)	)	PUNCT
ejpam-5440	14	7	be	be	AUX
ejpam-5440	14	8	a	a	DET
ejpam-5440	14	9	quasi	quasi	ADJ
ejpam-5440	14	10	-	-	ADJ
ejpam-5440	14	11	metric	metric	ADJ
ejpam-5440	14	12	space	space	NOUN
ejpam-5440	14	13	(	(	PUNCT
ejpam-5440	14	14	without	without	ADP
ejpam-5440	14	15	assuming	assume	VERB
ejpam-5440	14	16	the	the	DET
ejpam-5440	14	17	symmetry	symmetry	NOUN
ejpam-5440	14	18	of	of	ADP
ejpam-5440	14	19	a	a	DET
ejpam-5440	14	20	metric	metric	NOUN
ejpam-5440	14	21	)	)	PUNCT
ejpam-5440	14	22	.	.	PUNCT
ejpam-5440	15	1	a	a	DET
ejpam-5440	15	2	selfmap	selfmap	NOUN
ejpam-5440	15	3	f	f	NOUN
ejpam-5440	15	4	:	:	PUNCT
ejpam-5440	15	5	x	x	X
ejpam-5440	15	6	→	→	PUNCT
ejpam-5440	15	7	x	x	X
ejpam-5440	15	8	is	be	AUX
ejpam-5440	15	9	called	call	VERB
ejpam-5440	15	10	a	a	DET
ejpam-5440	15	11	banach	banach	NOUN
ejpam-5440	15	12	contraction	contraction	NOUN
ejpam-5440	15	13	with	with	ADP
ejpam-5440	15	14	a	a	DET
ejpam-5440	15	15	constant	constant	ADJ
ejpam-5440	15	16	α	α	NOUN
ejpam-5440	15	17	∈	∈	PROPN
ejpam-5440	15	18	(	(	PUNCT
ejpam-5440	15	19	0	0	NUM
ejpam-5440	15	20	,	,	PUNCT
ejpam-5440	15	21	1	1	NUM
ejpam-5440	15	22	)	)	PUNCT
ejpam-5440	15	23	if	if	SCONJ
ejpam-5440	15	24	q(f(x	q(f(x	PROPN
ejpam-5440	15	25	)	)	PUNCT
ejpam-5440	15	26	,	,	PUNCT
ejpam-5440	15	27	f(y	f(y	NOUN
ejpam-5440	15	28	)	)	PUNCT
ejpam-5440	15	29	)	)	PUNCT
ejpam-5440	15	30	≤	≤	NUM
ejpam-5440	15	31	α	α	PROPN
ejpam-5440	15	32	q(x	q(x	PROPN
ejpam-5440	15	33	,	,	PUNCT
ejpam-5440	15	34	y	y	NOUN
ejpam-5440	15	35	)	)	PUNCT
ejpam-5440	15	36	∀x	∀x	NUM
ejpam-5440	15	37	,	,	PUNCT
ejpam-5440	15	38	y	y	PROPN
ejpam-5440	15	39	∈	∈	PROPN
ejpam-5440	15	40	x.	x.	NOUN
ejpam-5440	15	41	a	a	DET
ejpam-5440	15	42	selfmap	selfmap	NOUN
ejpam-5440	15	43	f	f	NOUN
ejpam-5440	15	44	:	:	PUNCT
ejpam-5440	15	45	x	x	X
ejpam-5440	15	46	→	→	PUNCT
ejpam-5440	15	47	x	x	X
ejpam-5440	15	48	is	be	AUX
ejpam-5440	15	49	called	call	VERB
ejpam-5440	15	50	a	a	DET
ejpam-5440	15	51	weak	weak	ADJ
ejpam-5440	15	52	contraction	contraction	NOUN
ejpam-5440	15	53	or	or	CCONJ
ejpam-5440	15	54	a	a	DET
ejpam-5440	15	55	rus	rus	NOUN
ejpam-5440	15	56	-	-	PUNCT
ejpam-5440	15	57	hicks	hick	NOUN
ejpam-5440	15	58	-	-	PUNCT
ejpam-5440	15	59	rhoades	rhoade	NOUN
ejpam-5440	15	60	contraction	contraction	NOUN
ejpam-5440	15	61	(	(	PUNCT
ejpam-5440	15	62	or	or	CCONJ
ejpam-5440	15	63	simply	simply	ADV
ejpam-5440	15	64	an	an	DET
ejpam-5440	15	65	rhr	rhr	NOUN
ejpam-5440	15	66	map	map	NOUN
ejpam-5440	15	67	)	)	PUNCT
ejpam-5440	15	68	with	with	ADP
ejpam-5440	15	69	α	α	PROPN
ejpam-5440	15	70	∈	∈	PROPN
ejpam-5440	15	71	(	(	PUNCT
ejpam-5440	15	72	0	0	NUM
ejpam-5440	15	73	,	,	PUNCT
ejpam-5440	15	74	1	1	X
ejpam-5440	15	75	)	)	PUNCT
ejpam-5440	15	76	whenever	whenever	SCONJ
ejpam-5440	15	77	q(f(x	q(f(x	PROPN
ejpam-5440	15	78	)	)	PUNCT
ejpam-5440	15	79	,	,	PUNCT
ejpam-5440	15	80	f2(x	f2(x	PROPN
ejpam-5440	15	81	)	)	PUNCT
ejpam-5440	15	82	)	)	PUNCT
ejpam-5440	15	83	≤	≤	NUM
ejpam-5440	15	84	α	α	PROPN
ejpam-5440	15	85	q(x	q(x	PROPN
ejpam-5440	15	86	,	,	PUNCT
ejpam-5440	15	87	f(x	f(x	PROPN
ejpam-5440	15	88	)	)	PUNCT
ejpam-5440	15	89	)	)	PUNCT
ejpam-5440	16	1	∀x	∀x	VERB
ejpam-5440	16	2	∈	∈	PROPN
ejpam-5440	16	3	x.	x.	NOUN
ejpam-5440	16	4	doi	doi	PROPN
ejpam-5440	16	5	:	:	PUNCT
ejpam-5440	16	6	https://doi.org/10.29020/nybg.ejpam.v17i4.5440	https://doi.org/10.29020/nybg.ejpam.v17i4.5440	ADP
ejpam-5440	16	7	email	email	NOUN
ejpam-5440	16	8	addresses	address	NOUN
ejpam-5440	16	9	:	:	PUNCT
ejpam-5440	16	10	park35@snu.ac.kr	park35@snu.ac.kr	NUM
ejpam-5440	16	11	;	;	PUNCT
ejpam-5440	16	12	sehiepark@gmail.com	sehiepark@gmail.com	X
ejpam-5440	16	13	(	(	PUNCT
ejpam-5440	16	14	s.	s.	PROPN
ejpam-5440	16	15	park	park	PROPN
ejpam-5440	16	16	)	)	PUNCT
ejpam-5440	16	17	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5440	16	18	2370	2370	NUM
ejpam-5440	16	19	copyright	copyright	NOUN
ejpam-5440	16	20	:	:	PUNCT
ejpam-5440	16	21	©	©	PROPN
ejpam-5440	16	22	2024	2024	NUM
ejpam-5440	16	23	the	the	DET
ejpam-5440	16	24	author(s	author(s	NOUN
ejpam-5440	16	25	)	)	PUNCT
ejpam-5440	16	26	.	.	PUNCT
ejpam-5440	17	1	(	(	PUNCT
ejpam-5440	17	2	cc	cc	NOUN
ejpam-5440	17	3	by	by	ADP
ejpam-5440	17	4	-	-	PUNCT
ejpam-5440	17	5	nc	nc	PROPN
ejpam-5440	17	6	4.0	4.0	NUM
ejpam-5440	17	7	)	)	PUNCT
ejpam-5440	17	8	s.	s.	PROPN
ejpam-5440	17	9	park	park	PROPN
ejpam-5440	17	10	/	/	SYM
ejpam-5440	17	11	eur	eur	PROPN
ejpam-5440	17	12	.	.	PUNCT
ejpam-5440	18	1	j.	j.	PROPN
ejpam-5440	18	2	pure	pure	PROPN
ejpam-5440	18	3	appl	appl	PROPN
ejpam-5440	18	4	.	.	PROPN
ejpam-5440	18	5	math	math	PROPN
ejpam-5440	18	6	,	,	PUNCT
ejpam-5440	18	7	17	17	NUM
ejpam-5440	18	8	(	(	PUNCT
ejpam-5440	18	9	4	4	NUM
ejpam-5440	18	10	)	)	PUNCT
ejpam-5440	18	11	(	(	PUNCT
ejpam-5440	18	12	2024	2024	NUM
ejpam-5440	18	13	)	)	PUNCT
ejpam-5440	18	14	,	,	PUNCT
ejpam-5440	18	15	2370	2370	NUM
ejpam-5440	18	16	-	-	SYM
ejpam-5440	18	17	2383	2383	NUM
ejpam-5440	18	18	2371	2371	NUM
ejpam-5440	18	19	since	since	SCONJ
ejpam-5440	18	20	2023	2023	NUM
ejpam-5440	19	1	,	,	PUNCT
ejpam-5440	19	2	we	we	PRON
ejpam-5440	19	3	studied	study	VERB
ejpam-5440	19	4	rhr	rhr	PROPN
ejpam-5440	19	5	maps	map	NOUN
ejpam-5440	19	6	and	and	CCONJ
ejpam-5440	19	7	related	related	ADJ
ejpam-5440	19	8	topics	topic	NOUN
ejpam-5440	19	9	in	in	ADP
ejpam-5440	19	10	[	[	X
ejpam-5440	19	11	16]–[21	16]–[21	X
ejpam-5440	19	12	]	]	X
ejpam-5440	19	13	.	.	PUNCT
ejpam-5440	20	1	we	we	PRON
ejpam-5440	20	2	obtained	obtain	VERB
ejpam-5440	20	3	the	the	DET
ejpam-5440	20	4	generalized	generalized	ADJ
ejpam-5440	20	5	banach	banach	NOUN
ejpam-5440	20	6	contraction	contraction	NOUN
ejpam-5440	20	7	principle	principle	NOUN
ejpam-5440	20	8	and	and	CCONJ
ejpam-5440	20	9	the	the	DET
ejpam-5440	20	10	rhr	rhr	PROPN
ejpam-5440	20	11	contraction	contraction	PROPN
ejpam-5440	20	12	principle	principle	NOUN
ejpam-5440	20	13	(	(	PUNCT
ejpam-5440	20	14	theorem	theorem	VERB
ejpam-5440	20	15	p	p	X
ejpam-5440	20	16	)	)	PUNCT
ejpam-5440	20	17	with	with	ADP
ejpam-5440	20	18	their	their	PRON
ejpam-5440	20	19	applications	application	NOUN
ejpam-5440	20	20	to	to	ADP
ejpam-5440	20	21	scores	score	NOUN
ejpam-5440	20	22	of	of	ADP
ejpam-5440	20	23	examples	example	NOUN
ejpam-5440	20	24	in	in	ADP
ejpam-5440	20	25	the	the	DET
ejpam-5440	20	26	literature	literature	NOUN
ejpam-5440	20	27	.	.	PUNCT
ejpam-5440	21	1	even	even	ADV
ejpam-5440	21	2	for	for	ADP
ejpam-5440	21	3	metric	metric	ADJ
ejpam-5440	21	4	spaces	space	NOUN
ejpam-5440	21	5	our	our	PRON
ejpam-5440	21	6	previous	previous	ADJ
ejpam-5440	21	7	theorem	theorem	ADJ
ejpam-5440	21	8	h	h	NOUN
ejpam-5440	21	9	in	in	ADP
ejpam-5440	21	10	[	[	X
ejpam-5440	21	11	17	17	NUM
ejpam-5440	21	12	]	]	PUNCT
ejpam-5440	21	13	,	,	PUNCT
ejpam-5440	21	14	[	[	X
ejpam-5440	21	15	19	19	NUM
ejpam-5440	21	16	]	]	PUNCT
ejpam-5440	21	17	gave	give	VERB
ejpam-5440	21	18	equivalent	equivalent	ADJ
ejpam-5440	21	19	formulations	formulation	NOUN
ejpam-5440	21	20	of	of	ADP
ejpam-5440	21	21	extensions	extension	NOUN
ejpam-5440	21	22	of	of	ADP
ejpam-5440	21	23	fixed	fix	VERB
ejpam-5440	21	24	point	point	NOUN
ejpam-5440	21	25	theorems	theorem	NOUN
ejpam-5440	21	26	due	due	ADP
ejpam-5440	21	27	to	to	ADP
ejpam-5440	21	28	banach	banach	NOUN
ejpam-5440	21	29	,	,	PUNCT
ejpam-5440	21	30	rus	rus	NOUN
ejpam-5440	21	31	-	-	PUNCT
ejpam-5440	21	32	hicks	hick	NOUN
ejpam-5440	21	33	-	-	PUNCT
ejpam-5440	21	34	rhoades	rhoade	NOUN
ejpam-5440	21	35	,	,	PUNCT
ejpam-5440	21	36	nadler	nadler	PROPN
ejpam-5440	21	37	,	,	PUNCT
ejpam-5440	21	38	covitz	covitz	PROPN
ejpam-5440	21	39	-	-	PUNCT
ejpam-5440	21	40	nadler	nadler	NOUN
ejpam-5440	21	41	,	,	PUNCT
ejpam-5440	21	42	ekeland	ekeland	NOUN
ejpam-5440	21	43	,	,	PUNCT
ejpam-5440	21	44	takahashi	takahashi	PROPN
ejpam-5440	21	45	,	,	PUNCT
ejpam-5440	21	46	caristi	caristi	PROPN
ejpam-5440	21	47	-	-	PUNCT
ejpam-5440	21	48	kirk	kirk	PROPN
ejpam-5440	21	49	,	,	PUNCT
ejpam-5440	21	50	oettli	oettli	PROPN
ejpam-5440	21	51	-	-	PUNCT
ejpam-5440	21	52	théra	théra	NUM
ejpam-5440	21	53	and	and	CCONJ
ejpam-5440	21	54	others	other	NOUN
ejpam-5440	21	55	.	.	PUNCT
ejpam-5440	22	1	consequently	consequently	ADV
ejpam-5440	22	2	,	,	PUNCT
ejpam-5440	22	3	we	we	PRON
ejpam-5440	22	4	give	give	VERB
ejpam-5440	22	5	the	the	DET
ejpam-5440	22	6	common	common	ADJ
ejpam-5440	22	7	unified	unified	ADJ
ejpam-5440	22	8	new	new	ADJ
ejpam-5440	22	9	proofs	proof	NOUN
ejpam-5440	22	10	of	of	ADP
ejpam-5440	22	11	them	they	PRON
ejpam-5440	22	12	.	.	PUNCT
ejpam-5440	23	1	the	the	DET
ejpam-5440	23	2	present	present	ADJ
ejpam-5440	23	3	survey	survey	NOUN
ejpam-5440	23	4	is	be	AUX
ejpam-5440	23	5	to	to	PART
ejpam-5440	23	6	classify	classify	VERB
ejpam-5440	23	7	many	many	ADJ
ejpam-5440	23	8	known	know	VERB
ejpam-5440	23	9	fixed	fix	VERB
ejpam-5440	23	10	point	point	NOUN
ejpam-5440	23	11	theorems	theorem	NOUN
ejpam-5440	23	12	for	for	ADP
ejpam-5440	23	13	quasi	quasi	ADJ
ejpam-5440	23	14	-	-	ADJ
ejpam-5440	23	15	metric	metric	ADJ
ejpam-5440	23	16	spaces	space	NOUN
ejpam-5440	23	17	which	which	PRON
ejpam-5440	23	18	characterize	characterize	VERB
ejpam-5440	23	19	their	their	PRON
ejpam-5440	23	20	completeness	completeness	NOUN
ejpam-5440	23	21	.	.	PUNCT
ejpam-5440	24	1	in	in	ADP
ejpam-5440	24	2	fact	fact	NOUN
ejpam-5440	24	3	,	,	PUNCT
ejpam-5440	24	4	we	we	PRON
ejpam-5440	24	5	obtain	obtain	VERB
ejpam-5440	24	6	a	a	DET
ejpam-5440	24	7	family	family	NOUN
ejpam-5440	24	8	of	of	ADP
ejpam-5440	24	9	old	old	ADJ
ejpam-5440	24	10	or	or	CCONJ
ejpam-5440	24	11	new	new	ADJ
ejpam-5440	24	12	theorems	theorem	NOUN
ejpam-5440	24	13	and	and	CCONJ
ejpam-5440	24	14	can	can	AUX
ejpam-5440	24	15	give	give	VERB
ejpam-5440	24	16	them	they	PRON
ejpam-5440	24	17	a	a	DET
ejpam-5440	24	18	unified	unified	ADJ
ejpam-5440	24	19	proof	proof	NOUN
ejpam-5440	24	20	.	.	PUNCT
ejpam-5440	25	1	consequently	consequently	ADV
ejpam-5440	25	2	,	,	PUNCT
ejpam-5440	25	3	this	this	PRON
ejpam-5440	25	4	will	will	AUX
ejpam-5440	25	5	enhance	enhance	VERB
ejpam-5440	25	6	the	the	DET
ejpam-5440	25	7	reader	reader	NOUN
ejpam-5440	25	8	’s	’s	PART
ejpam-5440	25	9	understanding	understanding	NOUN
ejpam-5440	25	10	of	of	ADP
ejpam-5440	25	11	metric	metric	ADJ
ejpam-5440	25	12	fixed	fix	VERB
ejpam-5440	25	13	point	point	NOUN
ejpam-5440	25	14	theory	theory	NOUN
ejpam-5440	25	15	.	.	PUNCT
ejpam-5440	26	1	this	this	DET
ejpam-5440	26	2	survey	survey	NOUN
ejpam-5440	26	3	is	be	AUX
ejpam-5440	26	4	organized	organize	VERB
ejpam-5440	26	5	as	as	SCONJ
ejpam-5440	26	6	follows	follow	VERB
ejpam-5440	26	7	:	:	PUNCT
ejpam-5440	26	8	section	section	NOUN
ejpam-5440	26	9	2	2	NUM
ejpam-5440	26	10	is	be	AUX
ejpam-5440	26	11	for	for	ADP
ejpam-5440	26	12	preliminaries	preliminary	NOUN
ejpam-5440	26	13	on	on	ADP
ejpam-5440	26	14	quasi	quasi	ADJ
ejpam-5440	26	15	-	-	ADJ
ejpam-5440	26	16	metric	metric	ADJ
ejpam-5440	26	17	spaces	space	NOUN
ejpam-5440	26	18	.	.	PUNCT
ejpam-5440	27	1	in	in	ADP
ejpam-5440	27	2	section	section	NOUN
ejpam-5440	27	3	3	3	NUM
ejpam-5440	27	4	,	,	PUNCT
ejpam-5440	27	5	we	we	PRON
ejpam-5440	27	6	introduce	introduce	VERB
ejpam-5440	27	7	theorem	theorem	ADJ
ejpam-5440	27	8	h	h	NOUN
ejpam-5440	27	9	in	in	ADP
ejpam-5440	27	10	[	[	X
ejpam-5440	27	11	17	17	NUM
ejpam-5440	27	12	]	]	PUNCT
ejpam-5440	27	13	,	,	PUNCT
ejpam-5440	27	14	[	[	X
ejpam-5440	27	15	19	19	NUM
ejpam-5440	27	16	]	]	PUNCT
ejpam-5440	27	17	,	,	PUNCT
ejpam-5440	27	18	which	which	PRON
ejpam-5440	27	19	is	be	AUX
ejpam-5440	27	20	a	a	DET
ejpam-5440	27	21	consequence	consequence	NOUN
ejpam-5440	27	22	of	of	ADP
ejpam-5440	27	23	the	the	DET
ejpam-5440	27	24	2023	2023	NUM
ejpam-5440	27	25	metatheorem	metatheorem	ADJ
ejpam-5440	27	26	implying	implying	ADJ
ejpam-5440	27	27	equivalent	equivalent	ADJ
ejpam-5440	27	28	formulations	formulation	NOUN
ejpam-5440	27	29	of	of	ADP
ejpam-5440	27	30	quasi	quasi	ADJ
ejpam-5440	27	31	-	-	ADJ
ejpam-5440	27	32	metric	metric	ADJ
ejpam-5440	27	33	completeness	completeness	NOUN
ejpam-5440	27	34	.	.	PUNCT
ejpam-5440	28	1	section	section	NOUN
ejpam-5440	28	2	4	4	NUM
ejpam-5440	28	3	devotes	devote	VERB
ejpam-5440	28	4	some	some	DET
ejpam-5440	28	5	remarks	remark	NOUN
ejpam-5440	28	6	on	on	ADP
ejpam-5440	28	7	the	the	DET
ejpam-5440	28	8	family	family	NOUN
ejpam-5440	28	9	(	(	PUNCT
ejpam-5440	28	10	0	0	NUM
ejpam-5440	28	11	)	)	PUNCT
ejpam-5440	28	12	of	of	ADP
ejpam-5440	28	13	theorems	theorem	NOUN
ejpam-5440	28	14	related	relate	VERB
ejpam-5440	28	15	metric	metric	ADJ
ejpam-5440	28	16	completeness	completeness	NOUN
ejpam-5440	28	17	.	.	PUNCT
ejpam-5440	29	1	in	in	ADP
ejpam-5440	29	2	sections	section	NOUN
ejpam-5440	29	3	5	5	NUM
ejpam-5440	29	4	-	-	SYM
ejpam-5440	29	5	10	10	NUM
ejpam-5440	29	6	,	,	PUNCT
ejpam-5440	29	7	we	we	PRON
ejpam-5440	29	8	introduce	introduce	VERB
ejpam-5440	29	9	major	major	ADJ
ejpam-5440	29	10	results	result	NOUN
ejpam-5440	29	11	in	in	ADP
ejpam-5440	29	12	the	the	DET
ejpam-5440	29	13	subfamilies	subfamily	NOUN
ejpam-5440	29	14	(	(	PUNCT
ejpam-5440	29	15	α)−	α)−	PROPN
ejpam-5440	29	16	(	(	PUNCT
ejpam-5440	29	17	η	η	NOUN
ejpam-5440	29	18	)	)	PUNCT
ejpam-5440	29	19	of	of	ADP
ejpam-5440	29	20	the	the	DET
ejpam-5440	29	21	family	family	NOUN
ejpam-5440	29	22	(	(	PUNCT
ejpam-5440	29	23	0	0	NUM
ejpam-5440	29	24	)	)	PUNCT
ejpam-5440	29	25	corresponding	correspond	VERB
ejpam-5440	29	26	to	to	ADP
ejpam-5440	29	27	each	each	DET
ejpam-5440	29	28	equivalent	equivalent	ADJ
ejpam-5440	29	29	formulations	formulation	NOUN
ejpam-5440	29	30	to	to	ADP
ejpam-5440	29	31	the	the	DET
ejpam-5440	29	32	completeness	completeness	NOUN
ejpam-5440	29	33	in	in	ADP
ejpam-5440	29	34	theorem	theorem	PROPN
ejpam-5440	29	35	h.	h.	PROPN
ejpam-5440	29	36	finally	finally	ADV
ejpam-5440	29	37	,	,	PUNCT
ejpam-5440	29	38	section	section	NOUN
ejpam-5440	29	39	11	11	NUM
ejpam-5440	29	40	is	be	AUX
ejpam-5440	29	41	for	for	ADP
ejpam-5440	29	42	the	the	DET
ejpam-5440	29	43	epilogue	epilogue	NOUN
ejpam-5440	29	44	.	.	PUNCT
ejpam-5440	30	1	there	there	PRON
ejpam-5440	30	2	are	be	VERB
ejpam-5440	30	3	a	a	DET
ejpam-5440	30	4	large	large	ADJ
ejpam-5440	30	5	number	number	NOUN
ejpam-5440	30	6	of	of	ADP
ejpam-5440	30	7	articles	article	NOUN
ejpam-5440	30	8	concerning	concern	VERB
ejpam-5440	30	9	metric	metric	ADJ
ejpam-5440	30	10	completeness	completeness	NOUN
ejpam-5440	30	11	.	.	PUNCT
ejpam-5440	31	1	however	however	ADV
ejpam-5440	31	2	this	this	DET
ejpam-5440	31	3	survey	survey	NOUN
ejpam-5440	31	4	would	would	AUX
ejpam-5440	31	5	be	be	AUX
ejpam-5440	31	6	a	a	DET
ejpam-5440	31	7	precious	precious	ADJ
ejpam-5440	31	8	supplement	supplement	NOUN
ejpam-5440	31	9	of	of	ADP
ejpam-5440	31	10	the	the	DET
ejpam-5440	31	11	history	history	NOUN
ejpam-5440	31	12	of	of	ADP
ejpam-5440	31	13	metric	metric	ADJ
ejpam-5440	31	14	fixed	fix	VERB
ejpam-5440	31	15	pint	pint	NOUN
ejpam-5440	31	16	theory	theory	NOUN
ejpam-5440	31	17	.	.	PUNCT
ejpam-5440	32	1	2	2	X
ejpam-5440	32	2	.	.	X
ejpam-5440	32	3	preliminaries	preliminary	NOUN
ejpam-5440	32	4	we	we	PRON
ejpam-5440	32	5	recall	recall	VERB
ejpam-5440	32	6	the	the	DET
ejpam-5440	32	7	following	following	NOUN
ejpam-5440	32	8	:	:	PUNCT
ejpam-5440	32	9	definition	definition	NOUN
ejpam-5440	32	10	2.1	2.1	NUM
ejpam-5440	32	11	.	.	PUNCT
ejpam-5440	33	1	a	a	DET
ejpam-5440	33	2	quasi	quasi	NOUN
ejpam-5440	33	3	-	-	ADJ
ejpam-5440	33	4	metric	metric	ADJ
ejpam-5440	33	5	on	on	ADP
ejpam-5440	33	6	a	a	DET
ejpam-5440	33	7	non	non	ADJ
ejpam-5440	33	8	-	-	ADJ
ejpam-5440	33	9	empty	empty	ADJ
ejpam-5440	33	10	set	set	NOUN
ejpam-5440	33	11	x	x	PUNCT
ejpam-5440	33	12	is	be	AUX
ejpam-5440	33	13	a	a	DET
ejpam-5440	33	14	function	function	NOUN
ejpam-5440	33	15	q	q	NOUN
ejpam-5440	33	16	:	:	PUNCT
ejpam-5440	33	17	x	x	X
ejpam-5440	33	18	×x	×x	ADP
ejpam-5440	33	19	→	→	SYM
ejpam-5440	33	20	r+	r+	NOUN
ejpam-5440	33	21	=	=	PUNCT
ejpam-5440	34	1	[	[	X
ejpam-5440	34	2	0,∞	0,∞	NOUN
ejpam-5440	34	3	)	)	PUNCT
ejpam-5440	34	4	verifying	verify	VERB
ejpam-5440	34	5	the	the	DET
ejpam-5440	34	6	following	follow	VERB
ejpam-5440	34	7	conditions	condition	NOUN
ejpam-5440	34	8	for	for	ADP
ejpam-5440	34	9	all	all	DET
ejpam-5440	34	10	x	x	NOUN
ejpam-5440	34	11	,	,	PUNCT
ejpam-5440	34	12	y	y	PROPN
ejpam-5440	34	13	,	,	PUNCT
ejpam-5440	34	14	z	z	PROPN
ejpam-5440	34	15	∈	∈	PROPN
ejpam-5440	35	1	x	x	X
ejpam-5440	35	2	:	:	PUNCT
ejpam-5440	35	3	(	(	PUNCT
ejpam-5440	35	4	a	a	X
ejpam-5440	35	5	)	)	PUNCT
ejpam-5440	35	6	(	(	PUNCT
ejpam-5440	35	7	self	self	NOUN
ejpam-5440	35	8	-	-	PUNCT
ejpam-5440	35	9	distance	distance	NOUN
ejpam-5440	35	10	)	)	PUNCT
ejpam-5440	35	11	q(x	q(x	PROPN
ejpam-5440	35	12	,	,	PUNCT
ejpam-5440	35	13	y	y	NOUN
ejpam-5440	35	14	)	)	PUNCT
ejpam-5440	35	15	=	=	PUNCT
ejpam-5440	36	1	q(y	q(y	NOUN
ejpam-5440	36	2	,	,	PUNCT
ejpam-5440	36	3	x	x	X
ejpam-5440	36	4	)	)	PUNCT
ejpam-5440	36	5	=	=	SYM
ejpam-5440	36	6	0	0	NUM
ejpam-5440	36	7	⇐	⇐	ADJ
ejpam-5440	36	8	⇒	⇒	NOUN
ejpam-5440	36	9	x	x	PUNCT
ejpam-5440	36	10	=	=	SYM
ejpam-5440	36	11	y	y	PROPN
ejpam-5440	36	12	;	;	PUNCT
ejpam-5440	36	13	(	(	PUNCT
ejpam-5440	36	14	b	b	X
ejpam-5440	36	15	)	)	PUNCT
ejpam-5440	36	16	(	(	PUNCT
ejpam-5440	36	17	triangle	triangle	NOUN
ejpam-5440	36	18	inequality	inequality	NOUN
ejpam-5440	36	19	)	)	PUNCT
ejpam-5440	36	20	q(x	q(x	PROPN
ejpam-5440	36	21	,	,	PUNCT
ejpam-5440	36	22	z	z	NOUN
ejpam-5440	36	23	)	)	PUNCT
ejpam-5440	36	24	≤	≤	NUM
ejpam-5440	36	25	q(x	q(x	PROPN
ejpam-5440	36	26	,	,	PUNCT
ejpam-5440	36	27	y	y	NOUN
ejpam-5440	36	28	)	)	PUNCT
ejpam-5440	37	1	+	+	CCONJ
ejpam-5440	37	2	d(y	d(y	NOUN
ejpam-5440	37	3	,	,	PUNCT
ejpam-5440	37	4	z	z	NOUN
ejpam-5440	37	5	)	)	PUNCT
ejpam-5440	37	6	.	.	PUNCT
ejpam-5440	38	1	a	a	DET
ejpam-5440	38	2	metric	metric	NOUN
ejpam-5440	38	3	in	in	ADP
ejpam-5440	38	4	a	a	DET
ejpam-5440	38	5	set	set	NOUN
ejpam-5440	38	6	x	x	PUNCT
ejpam-5440	38	7	is	be	AUX
ejpam-5440	38	8	a	a	DET
ejpam-5440	38	9	quasi	quasi	ADJ
ejpam-5440	38	10	-	-	ADJ
ejpam-5440	38	11	metric	metric	ADJ
ejpam-5440	38	12	satisfying	satisfying	NOUN
ejpam-5440	38	13	that	that	SCONJ
ejpam-5440	38	14	for	for	ADP
ejpam-5440	38	15	all	all	DET
ejpam-5440	38	16	x	x	NOUN
ejpam-5440	38	17	,	,	PUNCT
ejpam-5440	38	18	y	y	PROPN
ejpam-5440	38	19	∈	∈	PROPN
ejpam-5440	38	20	x	x	X
ejpam-5440	38	21	,	,	PUNCT
ejpam-5440	38	22	(	(	PUNCT
ejpam-5440	38	23	c	c	X
ejpam-5440	38	24	)	)	PUNCT
ejpam-5440	38	25	(	(	PUNCT
ejpam-5440	38	26	symmetry	symmetry	NOUN
ejpam-5440	38	27	)	)	PUNCT
ejpam-5440	38	28	q(x	q(x	PROPN
ejpam-5440	38	29	,	,	PUNCT
ejpam-5440	38	30	y	y	NOUN
ejpam-5440	38	31	)	)	PUNCT
ejpam-5440	38	32	=	=	PUNCT
ejpam-5440	38	33	q(y	q(y	NOUN
ejpam-5440	38	34	,	,	PUNCT
ejpam-5440	38	35	x	x	NOUN
ejpam-5440	38	36	)	)	PUNCT
ejpam-5440	38	37	.	.	PUNCT
ejpam-5440	39	1	for	for	ADP
ejpam-5440	39	2	quasi	quasi	ADJ
ejpam-5440	39	3	-	-	ADJ
ejpam-5440	39	4	metric	metric	ADJ
ejpam-5440	39	5	spaces	space	NOUN
ejpam-5440	39	6	,	,	PUNCT
ejpam-5440	39	7	the	the	DET
ejpam-5440	39	8	convergence	convergence	NOUN
ejpam-5440	39	9	of	of	ADP
ejpam-5440	39	10	a	a	DET
ejpam-5440	39	11	sequence	sequence	NOUN
ejpam-5440	39	12	,	,	PUNCT
ejpam-5440	39	13	cauchy	cauchy	NOUN
ejpam-5440	39	14	sequences	sequence	NOUN
ejpam-5440	39	15	,	,	PUNCT
ejpam-5440	39	16	completeness	completeness	NOUN
ejpam-5440	39	17	,	,	PUNCT
ejpam-5440	39	18	orbits	orbit	NOUN
ejpam-5440	39	19	,	,	PUNCT
ejpam-5440	39	20	and	and	CCONJ
ejpam-5440	39	21	orbital	orbital	ADJ
ejpam-5440	39	22	continuity	continuity	NOUN
ejpam-5440	39	23	are	be	AUX
ejpam-5440	39	24	routinely	routinely	ADV
ejpam-5440	39	25	defined	define	VERB
ejpam-5440	39	26	as	as	SCONJ
ejpam-5440	39	27	follows	follow	VERB
ejpam-5440	39	28	:	:	PUNCT
ejpam-5440	39	29	definition	definition	NOUN
ejpam-5440	39	30	2.2	2.2	NUM
ejpam-5440	39	31	.	.	PUNCT
ejpam-5440	40	1	(	(	PUNCT
ejpam-5440	40	2	[	[	X
ejpam-5440	40	3	2	2	NUM
ejpam-5440	40	4	]	]	PUNCT
ejpam-5440	40	5	,	,	PUNCT
ejpam-5440	40	6	[	[	X
ejpam-5440	40	7	9	9	NUM
ejpam-5440	40	8	]	]	SYM
ejpam-5440	40	9	)	)	PUNCT
ejpam-5440	40	10	(	(	PUNCT
ejpam-5440	40	11	1	1	X
ejpam-5440	40	12	)	)	PUNCT
ejpam-5440	40	13	a	a	DET
ejpam-5440	40	14	sequence	sequence	NOUN
ejpam-5440	40	15	(	(	PUNCT
ejpam-5440	40	16	xn	xn	X
ejpam-5440	40	17	)	)	PUNCT
ejpam-5440	40	18	in	in	ADP
ejpam-5440	40	19	x	x	SYM
ejpam-5440	40	20	converges	converge	NOUN
ejpam-5440	40	21	to	to	ADP
ejpam-5440	40	22	x	x	SYM
ejpam-5440	40	23	∈	∈	PROPN
ejpam-5440	40	24	x	x	INTJ
ejpam-5440	40	25	if	if	SCONJ
ejpam-5440	40	26	lim	lim	PROPN
ejpam-5440	40	27	n→∞	n→∞	PRON
ejpam-5440	40	28	q(xn	q(xn	PROPN
ejpam-5440	40	29	,	,	PUNCT
ejpam-5440	40	30	x	x	X
ejpam-5440	40	31	)	)	PUNCT
ejpam-5440	40	32	=	=	SYM
ejpam-5440	40	33	lim	lim	PROPN
ejpam-5440	40	34	n→∞	n→∞	NUM
ejpam-5440	40	35	q(x	q(x	PROPN
ejpam-5440	40	36	,	,	PUNCT
ejpam-5440	40	37	xn	xn	PUNCT
ejpam-5440	40	38	)	)	PUNCT
ejpam-5440	40	39	=	=	SYM
ejpam-5440	40	40	0	0	X
ejpam-5440	40	41	.	.	PUNCT
ejpam-5440	40	42	(	(	PUNCT
ejpam-5440	40	43	2	2	X
ejpam-5440	40	44	)	)	PUNCT
ejpam-5440	40	45	a	a	DET
ejpam-5440	40	46	sequence	sequence	NOUN
ejpam-5440	40	47	(	(	PUNCT
ejpam-5440	40	48	xn	xn	X
ejpam-5440	40	49	)	)	PUNCT
ejpam-5440	40	50	is	be	AUX
ejpam-5440	40	51	left	leave	VERB
ejpam-5440	40	52	-	-	PUNCT
ejpam-5440	40	53	cauchy	cauchy	NOUN
ejpam-5440	40	54	if	if	SCONJ
ejpam-5440	40	55	for	for	ADP
ejpam-5440	40	56	every	every	DET
ejpam-5440	40	57	ε	ε	PROPN
ejpam-5440	40	58	>	>	X
ejpam-5440	40	59	0	0	PROPN
ejpam-5440	40	60	,	,	PUNCT
ejpam-5440	40	61	there	there	PRON
ejpam-5440	40	62	is	be	VERB
ejpam-5440	40	63	a	a	DET
ejpam-5440	40	64	positive	positive	ADJ
ejpam-5440	40	65	integer	integer	NOUN
ejpam-5440	40	66	n	n	NOUN
ejpam-5440	40	67	=	=	SYM
ejpam-5440	40	68	n(ε	n(ε	NOUN
ejpam-5440	40	69	)	)	PUNCT
ejpam-5440	40	70	such	such	ADJ
ejpam-5440	40	71	that	that	SCONJ
ejpam-5440	40	72	q(xn	q(xn	PROPN
ejpam-5440	40	73	,	,	PUNCT
ejpam-5440	40	74	xm	xm	PROPN
ejpam-5440	40	75	)	)	PUNCT
ejpam-5440	40	76	<	<	X
ejpam-5440	40	77	ε	ε	PROPN
ejpam-5440	40	78	for	for	ADP
ejpam-5440	40	79	all	all	DET
ejpam-5440	40	80	n	n	NOUN
ejpam-5440	40	81	>	>	X
ejpam-5440	40	82	m	m	VERB
ejpam-5440	40	83	>	>	X
ejpam-5440	40	84	n	n	PROPN
ejpam-5440	40	85	.	.	PUNCT
ejpam-5440	41	1	(	(	PUNCT
ejpam-5440	41	2	3	3	X
ejpam-5440	41	3	)	)	PUNCT
ejpam-5440	41	4	a	a	DET
ejpam-5440	41	5	sequence	sequence	NOUN
ejpam-5440	41	6	(	(	PUNCT
ejpam-5440	41	7	xn	xn	X
ejpam-5440	41	8	)	)	PUNCT
ejpam-5440	41	9	is	be	AUX
ejpam-5440	41	10	right	right	ADJ
ejpam-5440	41	11	-	-	PUNCT
ejpam-5440	41	12	cauchy	cauchy	NOUN
ejpam-5440	41	13	if	if	SCONJ
ejpam-5440	41	14	for	for	ADP
ejpam-5440	41	15	every	every	DET
ejpam-5440	41	16	ε	ε	PROPN
ejpam-5440	41	17	>	>	X
ejpam-5440	41	18	0	0	PROPN
ejpam-5440	41	19	,	,	PUNCT
ejpam-5440	41	20	there	there	PRON
ejpam-5440	41	21	is	be	VERB
ejpam-5440	41	22	a	a	DET
ejpam-5440	41	23	positive	positive	ADJ
ejpam-5440	41	24	integer	integer	NOUN
ejpam-5440	41	25	n	n	NOUN
ejpam-5440	41	26	=	=	SYM
ejpam-5440	41	27	n(ε	n(ε	NOUN
ejpam-5440	41	28	)	)	PUNCT
ejpam-5440	42	1	such	such	ADJ
ejpam-5440	42	2	that	that	SCONJ
ejpam-5440	42	3	q(xn	q(xn	PROPN
ejpam-5440	42	4	,	,	PUNCT
ejpam-5440	42	5	xm	xm	PROPN
ejpam-5440	42	6	)	)	PUNCT
ejpam-5440	42	7	<	<	X
ejpam-5440	42	8	ε	ε	PROPN
ejpam-5440	42	9	for	for	ADP
ejpam-5440	42	10	all	all	DET
ejpam-5440	42	11	m	m	VERB
ejpam-5440	42	12	>	>	X
ejpam-5440	42	13	n	n	X
ejpam-5440	42	14	>	>	X
ejpam-5440	42	15	n	n	PROPN
ejpam-5440	42	16	.	.	PUNCT
ejpam-5440	43	1	s.	s.	PROPN
ejpam-5440	43	2	park	park	PROPN
ejpam-5440	43	3	/	/	SYM
ejpam-5440	43	4	eur	eur	PROPN
ejpam-5440	43	5	.	.	PUNCT
ejpam-5440	44	1	j.	j.	PROPN
ejpam-5440	44	2	pure	pure	PROPN
ejpam-5440	44	3	appl	appl	PROPN
ejpam-5440	44	4	.	.	PROPN
ejpam-5440	44	5	math	math	PROPN
ejpam-5440	44	6	,	,	PUNCT
ejpam-5440	44	7	17	17	NUM
ejpam-5440	44	8	(	(	PUNCT
ejpam-5440	44	9	4	4	NUM
ejpam-5440	44	10	)	)	PUNCT
ejpam-5440	44	11	(	(	PUNCT
ejpam-5440	44	12	2024	2024	NUM
ejpam-5440	44	13	)	)	PUNCT
ejpam-5440	44	14	,	,	PUNCT
ejpam-5440	44	15	2370	2370	NUM
ejpam-5440	44	16	-	-	SYM
ejpam-5440	44	17	2383	2383	NUM
ejpam-5440	44	18	2372	2372	NUM
ejpam-5440	44	19	(	(	PUNCT
ejpam-5440	44	20	4	4	NUM
ejpam-5440	44	21	)	)	PUNCT
ejpam-5440	44	22	a	a	DET
ejpam-5440	44	23	sequence	sequence	NOUN
ejpam-5440	44	24	(	(	PUNCT
ejpam-5440	44	25	xn	xn	X
ejpam-5440	44	26	)	)	PUNCT
ejpam-5440	44	27	is	be	AUX
ejpam-5440	44	28	cauchy	cauchy	ADJ
ejpam-5440	44	29	if	if	SCONJ
ejpam-5440	44	30	for	for	ADP
ejpam-5440	44	31	every	every	DET
ejpam-5440	44	32	ε	ε	PROPN
ejpam-5440	44	33	>	>	X
ejpam-5440	44	34	0	0	PUNCT
ejpam-5440	45	1	there	there	PRON
ejpam-5440	45	2	is	be	VERB
ejpam-5440	45	3	positive	positive	ADJ
ejpam-5440	45	4	integer	integer	NOUN
ejpam-5440	45	5	n	n	PROPN
ejpam-5440	45	6	=	=	SYM
ejpam-5440	45	7	n(ε	n(ε	NOUN
ejpam-5440	45	8	)	)	PUNCT
ejpam-5440	45	9	such	such	ADJ
ejpam-5440	45	10	that	that	SCONJ
ejpam-5440	45	11	q(xn	q(xn	PROPN
ejpam-5440	45	12	,	,	PUNCT
ejpam-5440	45	13	xm	xm	PROPN
ejpam-5440	45	14	)	)	PUNCT
ejpam-5440	45	15	<	<	X
ejpam-5440	45	16	ε	ε	PROPN
ejpam-5440	45	17	for	for	ADP
ejpam-5440	45	18	all	all	DET
ejpam-5440	45	19	m	m	PROPN
ejpam-5440	45	20	,	,	PUNCT
ejpam-5440	45	21	n	n	PROPN
ejpam-5440	45	22	>	>	X
ejpam-5440	45	23	n	n	PROPN
ejpam-5440	45	24	;	;	PUNCT
ejpam-5440	45	25	that	that	PRON
ejpam-5440	45	26	is	is	ADV
ejpam-5440	45	27	(	(	PUNCT
ejpam-5440	45	28	xn	xn	X
ejpam-5440	45	29	)	)	PUNCT
ejpam-5440	45	30	is	be	AUX
ejpam-5440	45	31	a	a	DET
ejpam-5440	45	32	cauchy	cauchy	ADJ
ejpam-5440	45	33	sequence	sequence	NOUN
ejpam-5440	45	34	if	if	SCONJ
ejpam-5440	45	35	it	it	PRON
ejpam-5440	45	36	is	be	AUX
ejpam-5440	45	37	left	leave	VERB
ejpam-5440	45	38	and	and	CCONJ
ejpam-5440	45	39	right	right	ADJ
ejpam-5440	45	40	cauchy	cauchy	PROPN
ejpam-5440	45	41	.	.	PUNCT
ejpam-5440	46	1	definition	definition	NOUN
ejpam-5440	46	2	2.3	2.3	NUM
ejpam-5440	46	3	.	.	PUNCT
ejpam-5440	47	1	(	(	PUNCT
ejpam-5440	47	2	[	[	X
ejpam-5440	47	3	2	2	NUM
ejpam-5440	47	4	]	]	PUNCT
ejpam-5440	47	5	,	,	PUNCT
ejpam-5440	47	6	[	[	X
ejpam-5440	47	7	9	9	NUM
ejpam-5440	47	8	]	]	SYM
ejpam-5440	47	9	)	)	PUNCT
ejpam-5440	47	10	(	(	PUNCT
ejpam-5440	47	11	1	1	X
ejpam-5440	47	12	)	)	PUNCT
ejpam-5440	47	13	(	(	PUNCT
ejpam-5440	47	14	x	x	X
ejpam-5440	47	15	,	,	PUNCT
ejpam-5440	47	16	q	q	X
ejpam-5440	47	17	)	)	PUNCT
ejpam-5440	47	18	is	be	AUX
ejpam-5440	47	19	left	leave	VERB
ejpam-5440	47	20	-	-	PUNCT
ejpam-5440	47	21	complete	complete	ADJ
ejpam-5440	47	22	if	if	SCONJ
ejpam-5440	47	23	every	every	DET
ejpam-5440	47	24	left	left	ADJ
ejpam-5440	47	25	-	-	PUNCT
ejpam-5440	47	26	cauchy	cauchy	NOUN
ejpam-5440	47	27	sequence	sequence	NOUN
ejpam-5440	47	28	in	in	ADP
ejpam-5440	47	29	x	x	PROPN
ejpam-5440	47	30	is	be	AUX
ejpam-5440	47	31	convergent	convergent	ADJ
ejpam-5440	47	32	;	;	PUNCT
ejpam-5440	47	33	(	(	PUNCT
ejpam-5440	47	34	2	2	X
ejpam-5440	47	35	)	)	PUNCT
ejpam-5440	47	36	(	(	PUNCT
ejpam-5440	47	37	x	x	X
ejpam-5440	47	38	,	,	PUNCT
ejpam-5440	47	39	q	q	X
ejpam-5440	47	40	)	)	PUNCT
ejpam-5440	47	41	is	be	AUX
ejpam-5440	47	42	right	right	ADJ
ejpam-5440	47	43	-	-	PUNCT
ejpam-5440	47	44	complete	complete	ADJ
ejpam-5440	47	45	if	if	SCONJ
ejpam-5440	47	46	every	every	DET
ejpam-5440	47	47	right	right	ADJ
ejpam-5440	47	48	-	-	PUNCT
ejpam-5440	47	49	cauchy	cauchy	NOUN
ejpam-5440	47	50	sequence	sequence	NOUN
ejpam-5440	47	51	in	in	ADP
ejpam-5440	47	52	x	x	PROPN
ejpam-5440	47	53	is	be	AUX
ejpam-5440	47	54	convergent	convergent	ADJ
ejpam-5440	47	55	;	;	PUNCT
ejpam-5440	47	56	(	(	PUNCT
ejpam-5440	47	57	3	3	X
ejpam-5440	47	58	)	)	PUNCT
ejpam-5440	47	59	(	(	PUNCT
ejpam-5440	47	60	x	x	X
ejpam-5440	47	61	,	,	PUNCT
ejpam-5440	47	62	q	q	X
ejpam-5440	47	63	)	)	PUNCT
ejpam-5440	47	64	is	be	AUX
ejpam-5440	47	65	complete	complete	ADJ
ejpam-5440	47	66	if	if	SCONJ
ejpam-5440	47	67	every	every	DET
ejpam-5440	47	68	cauchy	cauchy	ADJ
ejpam-5440	47	69	sequence	sequence	NOUN
ejpam-5440	47	70	in	in	ADP
ejpam-5440	47	71	x	x	PROPN
ejpam-5440	47	72	is	be	AUX
ejpam-5440	47	73	convergent	convergent	ADJ
ejpam-5440	47	74	.	.	PUNCT
ejpam-5440	48	1	definition	definition	NOUN
ejpam-5440	48	2	2.4	2.4	NUM
ejpam-5440	48	3	.	.	PUNCT
ejpam-5440	49	1	let	let	AUX
ejpam-5440	49	2	(	(	PUNCT
ejpam-5440	49	3	x	x	NOUN
ejpam-5440	49	4	,	,	PUNCT
ejpam-5440	49	5	q	q	X
ejpam-5440	49	6	)	)	PUNCT
ejpam-5440	49	7	be	be	AUX
ejpam-5440	49	8	a	a	DET
ejpam-5440	49	9	quasi	quasi	ADJ
ejpam-5440	49	10	-	-	ADJ
ejpam-5440	49	11	metric	metric	ADJ
ejpam-5440	49	12	space	space	NOUN
ejpam-5440	49	13	and	and	CCONJ
ejpam-5440	49	14	t	t	NOUN
ejpam-5440	49	15	:	:	PUNCT
ejpam-5440	49	16	x	x	X
ejpam-5440	49	17	→	→	PUNCT
ejpam-5440	49	18	x	x	X
ejpam-5440	49	19	a	a	DET
ejpam-5440	49	20	selfmap	selfmap	NOUN
ejpam-5440	49	21	.	.	PUNCT
ejpam-5440	50	1	the	the	DET
ejpam-5440	50	2	orbit	orbit	NOUN
ejpam-5440	50	3	of	of	ADP
ejpam-5440	50	4	t	t	PROPN
ejpam-5440	50	5	at	at	ADP
ejpam-5440	50	6	x	x	PUNCT
ejpam-5440	50	7	∈	∈	PROPN
ejpam-5440	50	8	x	x	X
ejpam-5440	50	9	is	be	AUX
ejpam-5440	50	10	the	the	DET
ejpam-5440	50	11	set	set	ADJ
ejpam-5440	50	12	ot	ot	INTJ
ejpam-5440	50	13	(	(	PUNCT
ejpam-5440	50	14	x	x	NOUN
ejpam-5440	50	15	)	)	PUNCT
ejpam-5440	50	16	=	=	SYM
ejpam-5440	50	17	{	{	PUNCT
ejpam-5440	50	18	x	x	PROPN
ejpam-5440	50	19	,	,	PUNCT
ejpam-5440	50	20	t	t	PROPN
ejpam-5440	50	21	(	(	PUNCT
ejpam-5440	50	22	x	x	NOUN
ejpam-5440	50	23	)	)	PUNCT
ejpam-5440	50	24	,	,	PUNCT
ejpam-5440	50	25	·	·	PUNCT
ejpam-5440	50	26	·	·	PUNCT
ejpam-5440	50	27	·	·	PUNCT
ejpam-5440	50	28	,	,	PUNCT
ejpam-5440	50	29	tn(x	tn(x	ADP
ejpam-5440	50	30	)	)	PUNCT
ejpam-5440	50	31	,	,	PUNCT
ejpam-5440	50	32	·	·	PUNCT
ejpam-5440	50	33	·	·	PUNCT
ejpam-5440	50	34	·	·	PUNCT
ejpam-5440	50	35	}	}	PUNCT
ejpam-5440	50	36	.	.	PUNCT
ejpam-5440	51	1	the	the	DET
ejpam-5440	51	2	space	space	NOUN
ejpam-5440	51	3	x	x	PUNCT
ejpam-5440	51	4	is	be	AUX
ejpam-5440	51	5	said	say	VERB
ejpam-5440	51	6	to	to	PART
ejpam-5440	51	7	be	be	AUX
ejpam-5440	51	8	t	t	NOUN
ejpam-5440	51	9	-	-	PUNCT
ejpam-5440	51	10	orbitally	orbitally	ADV
ejpam-5440	51	11	complete	complete	ADJ
ejpam-5440	51	12	if	if	SCONJ
ejpam-5440	51	13	every	every	DET
ejpam-5440	51	14	right	right	ADJ
ejpam-5440	51	15	-	-	PUNCT
ejpam-5440	51	16	cauchy	cauchy	NOUN
ejpam-5440	51	17	sequence	sequence	NOUN
ejpam-5440	51	18	in	in	ADP
ejpam-5440	51	19	ot	ot	INTJ
ejpam-5440	51	20	(	(	PUNCT
ejpam-5440	51	21	x	x	X
ejpam-5440	51	22	)	)	PUNCT
ejpam-5440	51	23	is	be	AUX
ejpam-5440	51	24	convergent	convergent	ADJ
ejpam-5440	51	25	in	in	ADP
ejpam-5440	51	26	x.	x.	PROPN
ejpam-5440	51	27	a	a	DET
ejpam-5440	51	28	selfmap	selfmap	NOUN
ejpam-5440	51	29	t	t	PROPN
ejpam-5440	51	30	of	of	ADP
ejpam-5440	51	31	x	x	PROPN
ejpam-5440	51	32	is	be	AUX
ejpam-5440	51	33	said	say	VERB
ejpam-5440	51	34	to	to	PART
ejpam-5440	51	35	be	be	AUX
ejpam-5440	51	36	orbitally	orbitally	ADV
ejpam-5440	51	37	continuous	continuous	ADJ
ejpam-5440	51	38	at	at	ADP
ejpam-5440	51	39	x0	x0	PROPN
ejpam-5440	51	40	∈	∈	PROPN
ejpam-5440	52	1	x	x	X
ejpam-5440	52	2	if	if	SCONJ
ejpam-5440	52	3	lim	lim	PROPN
ejpam-5440	52	4	n→∞	n→∞	X
ejpam-5440	52	5	tn(x	tn(x	PUNCT
ejpam-5440	52	6	)	)	PUNCT
ejpam-5440	52	7	=	=	SYM
ejpam-5440	53	1	x0	x0	PUNCT
ejpam-5440	54	1	=	=	AUX
ejpam-5440	54	2	⇒	⇒	PROPN
ejpam-5440	54	3	lim	lim	PROPN
ejpam-5440	54	4	n→∞	n→∞	NUM
ejpam-5440	54	5	tn+1(x	tn+1(x	NUM
ejpam-5440	54	6	)	)	PUNCT
ejpam-5440	55	1	=	=	SYM
ejpam-5440	55	2	t	t	PROPN
ejpam-5440	55	3	(	(	PUNCT
ejpam-5440	55	4	x0	x0	PROPN
ejpam-5440	55	5	)	)	PUNCT
ejpam-5440	55	6	for	for	ADP
ejpam-5440	55	7	any	any	DET
ejpam-5440	55	8	x	x	SYM
ejpam-5440	55	9	∈	∈	PROPN
ejpam-5440	55	10	x.	x.	NOUN
ejpam-5440	55	11	note	note	VERB
ejpam-5440	55	12	that	that	SCONJ
ejpam-5440	55	13	every	every	DET
ejpam-5440	55	14	complete	complete	ADJ
ejpam-5440	55	15	metric	metric	ADJ
ejpam-5440	55	16	space	space	NOUN
ejpam-5440	55	17	is	be	AUX
ejpam-5440	55	18	t	t	NOUN
ejpam-5440	55	19	-orbitally	-orbitally	ADV
ejpam-5440	55	20	complete	complete	ADJ
ejpam-5440	55	21	for	for	ADP
ejpam-5440	55	22	all	all	DET
ejpam-5440	55	23	maps	map	NOUN
ejpam-5440	55	24	t	t	NOUN
ejpam-5440	55	25	:	:	PUNCT
ejpam-5440	55	26	x	x	X
ejpam-5440	55	27	→	→	PUNCT
ejpam-5440	55	28	x.	x.	NOUN
ejpam-5440	55	29	there	there	PRON
ejpam-5440	55	30	exists	exist	VERB
ejpam-5440	55	31	a	a	DET
ejpam-5440	55	32	t	t	NOUN
ejpam-5440	55	33	-orbitally	-orbitally	NOUN
ejpam-5440	55	34	complete	complete	ADJ
ejpam-5440	55	35	metric	metric	ADJ
ejpam-5440	55	36	space	space	NOUN
ejpam-5440	55	37	but	but	CCONJ
ejpam-5440	55	38	it	it	PRON
ejpam-5440	55	39	is	be	AUX
ejpam-5440	55	40	not	not	PART
ejpam-5440	55	41	complete	complete	ADJ
ejpam-5440	55	42	.	.	PUNCT
ejpam-5440	56	1	moreover	moreover	ADV
ejpam-5440	56	2	,	,	PUNCT
ejpam-5440	56	3	there	there	PRON
ejpam-5440	56	4	exists	exist	VERB
ejpam-5440	56	5	an	an	DET
ejpam-5440	56	6	orbitally	orbitally	ADV
ejpam-5440	56	7	continuous	continuous	ADJ
ejpam-5440	56	8	map	map	NOUN
ejpam-5440	56	9	but	but	CCONJ
ejpam-5440	56	10	it	it	PRON
ejpam-5440	56	11	is	be	AUX
ejpam-5440	56	12	not	not	PART
ejpam-5440	56	13	continuous	continuous	ADJ
ejpam-5440	56	14	.	.	PUNCT
ejpam-5440	57	1	for	for	ADP
ejpam-5440	57	2	other	other	ADJ
ejpam-5440	57	3	terminology	terminology	NOUN
ejpam-5440	57	4	related	relate	VERB
ejpam-5440	57	5	quasi	quasi	ADJ
ejpam-5440	57	6	-	-	ADJ
ejpam-5440	57	7	metric	metric	ADJ
ejpam-5440	57	8	spaces	space	NOUN
ejpam-5440	57	9	,	,	PUNCT
ejpam-5440	57	10	see	see	VERB
ejpam-5440	57	11	[	[	X
ejpam-5440	57	12	2	2	NUM
ejpam-5440	57	13	]	]	PUNCT
ejpam-5440	57	14	,	,	PUNCT
ejpam-5440	57	15	[	[	X
ejpam-5440	57	16	9	9	NUM
ejpam-5440	57	17	]	]	PUNCT
ejpam-5440	57	18	,	,	PUNCT
ejpam-5440	57	19	3	3	X
ejpam-5440	57	20	.	.	PUNCT
ejpam-5440	58	1	the	the	DET
ejpam-5440	58	2	basic	basic	ADJ
ejpam-5440	58	3	principle	principle	NOUN
ejpam-5440	58	4	and	and	CCONJ
ejpam-5440	58	5	subfamilies	subfamily	NOUN
ejpam-5440	58	6	(	(	PUNCT
ejpam-5440	58	7	α)−	α)−	PROPN
ejpam-5440	58	8	(	(	PUNCT
ejpam-5440	58	9	η	η	NOUN
ejpam-5440	58	10	)	)	PUNCT
ejpam-5440	58	11	let	let	VERB
ejpam-5440	58	12	(	(	PUNCT
ejpam-5440	58	13	x	x	NOUN
ejpam-5440	58	14	,	,	PUNCT
ejpam-5440	58	15	q	q	X
ejpam-5440	58	16	)	)	PUNCT
ejpam-5440	58	17	be	be	AUX
ejpam-5440	58	18	a	a	DET
ejpam-5440	58	19	quasi	quasi	ADJ
ejpam-5440	58	20	-	-	ADJ
ejpam-5440	58	21	metric	metric	ADJ
ejpam-5440	58	22	space	space	NOUN
ejpam-5440	58	23	and	and	CCONJ
ejpam-5440	58	24	cl(x	cl(x	PROPN
ejpam-5440	58	25	)	)	PUNCT
ejpam-5440	58	26	denote	denote	VERB
ejpam-5440	58	27	the	the	DET
ejpam-5440	58	28	family	family	NOUN
ejpam-5440	58	29	of	of	ADP
ejpam-5440	58	30	all	all	DET
ejpam-5440	58	31	nonempty	nonempty	ADV
ejpam-5440	58	32	closed	close	VERB
ejpam-5440	58	33	subsets	subset	NOUN
ejpam-5440	58	34	of	of	ADP
ejpam-5440	58	35	x	x	PUNCT
ejpam-5440	58	36	(	(	PUNCT
ejpam-5440	58	37	not	not	PART
ejpam-5440	58	38	necessarily	necessarily	ADV
ejpam-5440	58	39	bounded	bound	VERB
ejpam-5440	58	40	)	)	PUNCT
ejpam-5440	58	41	.	.	PUNCT
ejpam-5440	59	1	for	for	ADP
ejpam-5440	59	2	a	a	DET
ejpam-5440	59	3	,	,	PUNCT
ejpam-5440	59	4	b	b	PROPN
ejpam-5440	59	5	∈	∈	NOUN
ejpam-5440	59	6	cl(x	cl(x	NOUN
ejpam-5440	59	7	)	)	PUNCT
ejpam-5440	59	8	,	,	PUNCT
ejpam-5440	59	9	set	set	VERB
ejpam-5440	59	10	h(a	h(a	PROPN
ejpam-5440	59	11	,	,	PUNCT
ejpam-5440	59	12	b	b	NOUN
ejpam-5440	59	13	)	)	PUNCT
ejpam-5440	59	14	=	=	SYM
ejpam-5440	59	15	max{sup{q(a	max{sup{q(a	NOUN
ejpam-5440	59	16	,	,	PUNCT
ejpam-5440	59	17	b	b	NOUN
ejpam-5440	59	18	)	)	PUNCT
ejpam-5440	59	19	:	:	PUNCT
ejpam-5440	59	20	a	a	DET
ejpam-5440	59	21	∈	∈	PROPN
ejpam-5440	59	22	a	a	PRON
ejpam-5440	59	23	}	}	PUNCT
ejpam-5440	59	24	,	,	PUNCT
ejpam-5440	59	25	sup{q(b	sup{q(b	NOUN
ejpam-5440	59	26	,	,	PUNCT
ejpam-5440	59	27	a	a	PRON
ejpam-5440	59	28	)	)	PUNCT
ejpam-5440	59	29	:	:	PUNCT
ejpam-5440	59	30	b	b	X
ejpam-5440	59	31	∈	∈	ADJ
ejpam-5440	59	32	b	b	NOUN
ejpam-5440	59	33	}	}	PUNCT
ejpam-5440	59	34	}	}	PUNCT
ejpam-5440	59	35	,	,	PUNCT
ejpam-5440	59	36	where	where	SCONJ
ejpam-5440	59	37	q(a	q(a	NOUN
ejpam-5440	59	38	,	,	PUNCT
ejpam-5440	59	39	b	b	NOUN
ejpam-5440	59	40	)	)	PUNCT
ejpam-5440	60	1	=	=	SYM
ejpam-5440	60	2	inf{q(a	inf{q(a	NOUN
ejpam-5440	60	3	,	,	PUNCT
ejpam-5440	60	4	b	b	NOUN
ejpam-5440	60	5	)	)	PUNCT
ejpam-5440	60	6	:	:	PUNCT
ejpam-5440	61	1	b	b	X
ejpam-5440	61	2	∈	∈	PROPN
ejpam-5440	61	3	b	b	NOUN
ejpam-5440	61	4	}	}	PUNCT
ejpam-5440	61	5	.	.	PUNCT
ejpam-5440	62	1	then	then	ADV
ejpam-5440	62	2	h	h	PROPN
ejpam-5440	62	3	is	be	AUX
ejpam-5440	62	4	called	call	VERB
ejpam-5440	62	5	a	a	DET
ejpam-5440	62	6	generalized	generalized	ADJ
ejpam-5440	62	7	hausdorff	hausdorff	NOUN
ejpam-5440	62	8	distance	distance	NOUN
ejpam-5440	62	9	and	and	CCONJ
ejpam-5440	62	10	it	it	PRON
ejpam-5440	62	11	may	may	AUX
ejpam-5440	62	12	have	have	VERB
ejpam-5440	62	13	infinite	infinite	ADJ
ejpam-5440	62	14	values	value	NOUN
ejpam-5440	62	15	.	.	PUNCT
ejpam-5440	63	1	based	base	VERB
ejpam-5440	63	2	on	on	ADP
ejpam-5440	63	3	our	our	PRON
ejpam-5440	63	4	2023	2023	NUM
ejpam-5440	63	5	metatheorem	metatheorem	ADJ
ejpam-5440	63	6	[	[	X
ejpam-5440	63	7	14	14	NUM
ejpam-5440	63	8	]	]	PUNCT
ejpam-5440	63	9	and	and	CCONJ
ejpam-5440	63	10	the	the	DET
ejpam-5440	63	11	rhr	rhr	PROPN
ejpam-5440	63	12	theorem	theorem	PROPN
ejpam-5440	63	13	,	,	PUNCT
ejpam-5440	63	14	we	we	PRON
ejpam-5440	63	15	obtained	obtain	VERB
ejpam-5440	63	16	the	the	DET
ejpam-5440	63	17	following	following	NOUN
ejpam-5440	63	18	in	in	ADP
ejpam-5440	63	19	[	[	X
ejpam-5440	63	20	17	17	NUM
ejpam-5440	63	21	]	]	PUNCT
ejpam-5440	63	22	,	,	PUNCT
ejpam-5440	64	1	[	[	X
ejpam-5440	64	2	19	19	NUM
ejpam-5440	64	3	]	]	X
ejpam-5440	64	4	:	:	PUNCT
ejpam-5440	64	5	theorem	theorem	PROPN
ejpam-5440	64	6	h.	h.	PROPN
ejpam-5440	64	7	let	let	VERB
ejpam-5440	64	8	(	(	PUNCT
ejpam-5440	64	9	x	x	NOUN
ejpam-5440	64	10	,	,	PUNCT
ejpam-5440	64	11	q	q	X
ejpam-5440	64	12	)	)	PUNCT
ejpam-5440	64	13	be	be	AUX
ejpam-5440	64	14	a	a	DET
ejpam-5440	64	15	quasi	quasi	ADJ
ejpam-5440	64	16	-	-	ADJ
ejpam-5440	64	17	metric	metric	ADJ
ejpam-5440	64	18	space	space	NOUN
ejpam-5440	64	19	and	and	CCONJ
ejpam-5440	64	20	0	0	NUM
ejpam-5440	64	21	<	<	X
ejpam-5440	64	22	α	α	X
ejpam-5440	64	23	<	<	X
ejpam-5440	64	24	1	1	NUM
ejpam-5440	64	25	.	.	PUNCT
ejpam-5440	65	1	then	then	ADV
ejpam-5440	65	2	the	the	DET
ejpam-5440	65	3	following	following	ADJ
ejpam-5440	65	4	statements	statement	NOUN
ejpam-5440	65	5	are	be	AUX
ejpam-5440	65	6	equivalent	equivalent	ADJ
ejpam-5440	65	7	:	:	PUNCT
ejpam-5440	65	8	(	(	PUNCT
ejpam-5440	65	9	0	0	NUM
ejpam-5440	65	10	)	)	PUNCT
ejpam-5440	65	11	(	(	PUNCT
ejpam-5440	65	12	x	x	X
ejpam-5440	65	13	,	,	PUNCT
ejpam-5440	65	14	q	q	X
ejpam-5440	65	15	)	)	PUNCT
ejpam-5440	65	16	is	be	AUX
ejpam-5440	65	17	complete	complete	ADJ
ejpam-5440	65	18	.	.	PUNCT
ejpam-5440	66	1	(	(	PUNCT
ejpam-5440	66	2	α	α	X
ejpam-5440	66	3	)	)	PUNCT
ejpam-5440	66	4	for	for	ADP
ejpam-5440	66	5	a	a	DET
ejpam-5440	66	6	multimap	multimap	NOUN
ejpam-5440	66	7	t	t	NOUN
ejpam-5440	66	8	:	:	PUNCT
ejpam-5440	66	9	x	x	X
ejpam-5440	66	10	→	→	SYM
ejpam-5440	66	11	cl(x	cl(x	NOUN
ejpam-5440	66	12	)	)	PUNCT
ejpam-5440	66	13	,	,	PUNCT
ejpam-5440	66	14	there	there	PRON
ejpam-5440	66	15	exists	exist	VERB
ejpam-5440	66	16	an	an	DET
ejpam-5440	66	17	element	element	NOUN
ejpam-5440	66	18	v	v	ADP
ejpam-5440	66	19	∈	∈	PROPN
ejpam-5440	66	20	x	x	PUNCT
ejpam-5440	66	21	such	such	ADJ
ejpam-5440	66	22	that	that	SCONJ
ejpam-5440	66	23	h(t	h(t	PROPN
ejpam-5440	66	24	(	(	PUNCT
ejpam-5440	66	25	v	v	NOUN
ejpam-5440	66	26	)	)	PUNCT
ejpam-5440	66	27	,	,	PUNCT
ejpam-5440	66	28	t	t	PROPN
ejpam-5440	66	29	(	(	PUNCT
ejpam-5440	66	30	w	w	NOUN
ejpam-5440	66	31	)	)	PUNCT
ejpam-5440	66	32	)	)	PUNCT
ejpam-5440	66	33	>	>	X
ejpam-5440	67	1	αq(v	αq(v	X
ejpam-5440	67	2	,	,	PUNCT
ejpam-5440	67	3	w	w	NOUN
ejpam-5440	67	4	)	)	PUNCT
ejpam-5440	67	5	for	for	ADP
ejpam-5440	67	6	any	any	DET
ejpam-5440	67	7	w	w	PROPN
ejpam-5440	67	8	∈	∈	PROPN
ejpam-5440	67	9	x\{v	x\{v	PROPN
ejpam-5440	67	10	}	}	PUNCT
ejpam-5440	67	11	.	.	PUNCT
ejpam-5440	68	1	(	(	PUNCT
ejpam-5440	68	2	β	β	X
ejpam-5440	68	3	)	)	PUNCT
ejpam-5440	68	4	if	if	SCONJ
ejpam-5440	68	5	f	f	PROPN
ejpam-5440	68	6	is	be	AUX
ejpam-5440	68	7	a	a	DET
ejpam-5440	68	8	family	family	NOUN
ejpam-5440	68	9	of	of	ADP
ejpam-5440	68	10	maps	map	NOUN
ejpam-5440	68	11	f	f	X
ejpam-5440	68	12	:	:	PUNCT
ejpam-5440	68	13	x	x	X
ejpam-5440	69	1	→	→	PUNCT
ejpam-5440	69	2	x	x	X
ejpam-5440	69	3	such	such	ADJ
ejpam-5440	69	4	that	that	SCONJ
ejpam-5440	69	5	,	,	PUNCT
ejpam-5440	69	6	for	for	ADP
ejpam-5440	69	7	any	any	DET
ejpam-5440	69	8	x	x	PROPN
ejpam-5440	69	9	∈	∈	PROPN
ejpam-5440	69	10	x\{f(x	x\{f(x	PROPN
ejpam-5440	69	11	)	)	PUNCT
ejpam-5440	69	12	}	}	PUNCT
ejpam-5440	69	13	,	,	PUNCT
ejpam-5440	69	14	there	there	PRON
ejpam-5440	69	15	exists	exist	VERB
ejpam-5440	69	16	a	a	DET
ejpam-5440	69	17	y	y	PROPN
ejpam-5440	69	18	∈	∈	PROPN
ejpam-5440	69	19	x\{x	x\{x	PROPN
ejpam-5440	69	20	}	}	PUNCT
ejpam-5440	69	21	satisfying	satisfy	VERB
ejpam-5440	69	22	q(f(x	q(f(x	PROPN
ejpam-5440	69	23	)	)	PUNCT
ejpam-5440	69	24	,	,	PUNCT
ejpam-5440	69	25	f(y	f(y	NOUN
ejpam-5440	69	26	)	)	PUNCT
ejpam-5440	69	27	)	)	PUNCT
ejpam-5440	69	28	≤	≤	NUM
ejpam-5440	69	29	α	α	PROPN
ejpam-5440	69	30	q(x	q(x	PROPN
ejpam-5440	69	31	,	,	PUNCT
ejpam-5440	69	32	y	y	PROPN
ejpam-5440	69	33	)	)	PUNCT
ejpam-5440	69	34	,	,	PUNCT
ejpam-5440	69	35	then	then	ADV
ejpam-5440	69	36	f	f	PROPN
ejpam-5440	69	37	has	have	VERB
ejpam-5440	69	38	a	a	DET
ejpam-5440	69	39	common	common	ADJ
ejpam-5440	69	40	fixed	fix	VERB
ejpam-5440	69	41	element	element	NOUN
ejpam-5440	69	42	v	v	ADP
ejpam-5440	69	43	∈	∈	PROPN
ejpam-5440	69	44	x	x	NOUN
ejpam-5440	69	45	,	,	PUNCT
ejpam-5440	69	46	that	that	ADV
ejpam-5440	69	47	is	is	ADV
ejpam-5440	69	48	,	,	PUNCT
ejpam-5440	69	49	v	v	NOUN
ejpam-5440	69	50	=	=	PUNCT
ejpam-5440	69	51	f(v	f(v	NOUN
ejpam-5440	69	52	)	)	PUNCT
ejpam-5440	69	53	for	for	ADP
ejpam-5440	69	54	all	all	DET
ejpam-5440	69	55	f	f	PROPN
ejpam-5440	69	56	∈	∈	PROPN
ejpam-5440	69	57	f.	f.	PROPN
ejpam-5440	69	58	s.	s.	PROPN
ejpam-5440	69	59	park	park	PROPN
ejpam-5440	69	60	/	/	SYM
ejpam-5440	69	61	eur	eur	PROPN
ejpam-5440	69	62	.	.	PUNCT
ejpam-5440	70	1	j.	j.	PROPN
ejpam-5440	70	2	pure	pure	PROPN
ejpam-5440	70	3	appl	appl	PROPN
ejpam-5440	70	4	.	.	PROPN
ejpam-5440	70	5	math	math	PROPN
ejpam-5440	70	6	,	,	PUNCT
ejpam-5440	70	7	17	17	NUM
ejpam-5440	70	8	(	(	PUNCT
ejpam-5440	70	9	4	4	NUM
ejpam-5440	70	10	)	)	PUNCT
ejpam-5440	70	11	(	(	PUNCT
ejpam-5440	70	12	2024	2024	NUM
ejpam-5440	70	13	)	)	PUNCT
ejpam-5440	70	14	,	,	PUNCT
ejpam-5440	70	15	2370	2370	NUM
ejpam-5440	70	16	-	-	SYM
ejpam-5440	70	17	2383	2383	NUM
ejpam-5440	70	18	2373	2373	NUM
ejpam-5440	70	19	(	(	PUNCT
ejpam-5440	70	20	γ	γ	X
ejpam-5440	70	21	)	)	PUNCT
ejpam-5440	70	22	if	if	SCONJ
ejpam-5440	70	23	f	f	PROPN
ejpam-5440	70	24	is	be	AUX
ejpam-5440	70	25	a	a	DET
ejpam-5440	70	26	family	family	NOUN
ejpam-5440	70	27	of	of	ADP
ejpam-5440	70	28	maps	map	NOUN
ejpam-5440	70	29	f	f	X
ejpam-5440	70	30	:	:	PUNCT
ejpam-5440	70	31	x	x	X
ejpam-5440	70	32	→	→	SYM
ejpam-5440	70	33	x	x	SYM
ejpam-5440	70	34	satisfying	satisfy	VERB
ejpam-5440	70	35	q(f(x	q(f(x	PROPN
ejpam-5440	70	36	)	)	PUNCT
ejpam-5440	70	37	,	,	PUNCT
ejpam-5440	70	38	f2(x	f2(x	PROPN
ejpam-5440	70	39	)	)	PUNCT
ejpam-5440	70	40	)	)	PUNCT
ejpam-5440	70	41	≤	≤	NUM
ejpam-5440	70	42	α	α	PROPN
ejpam-5440	70	43	q(x	q(x	PROPN
ejpam-5440	70	44	,	,	PUNCT
ejpam-5440	70	45	f(x	f(x	PROPN
ejpam-5440	70	46	)	)	PUNCT
ejpam-5440	70	47	)	)	PUNCT
ejpam-5440	70	48	for	for	ADP
ejpam-5440	70	49	all	all	DET
ejpam-5440	70	50	x	x	SYM
ejpam-5440	70	51	∈	∈	PROPN
ejpam-5440	70	52	x\{f(x	x\{f(x	PROPN
ejpam-5440	70	53	)	)	PUNCT
ejpam-5440	70	54	}	}	PUNCT
ejpam-5440	70	55	,	,	PUNCT
ejpam-5440	70	56	then	then	ADV
ejpam-5440	70	57	f	f	PROPN
ejpam-5440	70	58	has	have	VERB
ejpam-5440	70	59	a	a	DET
ejpam-5440	70	60	common	common	ADJ
ejpam-5440	70	61	fixed	fix	VERB
ejpam-5440	70	62	element	element	NOUN
ejpam-5440	70	63	v	v	ADP
ejpam-5440	70	64	∈	∈	PROPN
ejpam-5440	70	65	x	x	NOUN
ejpam-5440	70	66	,	,	PUNCT
ejpam-5440	70	67	that	that	ADV
ejpam-5440	70	68	is	is	ADV
ejpam-5440	70	69	,	,	PUNCT
ejpam-5440	70	70	v	v	NOUN
ejpam-5440	70	71	=	=	PUNCT
ejpam-5440	70	72	f(v	f(v	NOUN
ejpam-5440	70	73	)	)	PUNCT
ejpam-5440	70	74	for	for	ADP
ejpam-5440	70	75	all	all	DET
ejpam-5440	70	76	f	f	PROPN
ejpam-5440	70	77	∈	∈	PROPN
ejpam-5440	70	78	f.	f.	PROPN
ejpam-5440	70	79	(	(	PUNCT
ejpam-5440	70	80	δ	δ	PROPN
ejpam-5440	70	81	)	)	PUNCT
ejpam-5440	70	82	let	let	VERB
ejpam-5440	70	83	f	f	PRON
ejpam-5440	70	84	be	be	AUX
ejpam-5440	70	85	a	a	DET
ejpam-5440	70	86	family	family	NOUN
ejpam-5440	70	87	of	of	ADP
ejpam-5440	70	88	multimaps	multimap	NOUN
ejpam-5440	70	89	t	t	PROPN
ejpam-5440	70	90	:	:	PUNCT
ejpam-5440	70	91	x	x	X
ejpam-5440	70	92	→	→	SYM
ejpam-5440	70	93	cl(x	cl(x	NOUN
ejpam-5440	70	94	)	)	PUNCT
ejpam-5440	70	95	such	such	ADJ
ejpam-5440	70	96	that	that	SCONJ
ejpam-5440	70	97	,	,	PUNCT
ejpam-5440	70	98	for	for	ADP
ejpam-5440	70	99	any	any	DET
ejpam-5440	70	100	x	x	SYM
ejpam-5440	70	101	∈	∈	PROPN
ejpam-5440	70	102	x\t	x\t	PUNCT
ejpam-5440	71	1	(	(	PUNCT
ejpam-5440	71	2	x	x	X
ejpam-5440	71	3	)	)	PUNCT
ejpam-5440	71	4	,	,	PUNCT
ejpam-5440	71	5	there	there	PRON
ejpam-5440	71	6	exists	exist	VERB
ejpam-5440	71	7	y	y	PROPN
ejpam-5440	71	8	∈	∈	PROPN
ejpam-5440	71	9	x\{x	x\{x	PROPN
ejpam-5440	71	10	}	}	PUNCT
ejpam-5440	71	11	satisfying	satisfy	VERB
ejpam-5440	71	12	h(t	h(t	PROPN
ejpam-5440	71	13	(	(	PUNCT
ejpam-5440	71	14	x	x	NOUN
ejpam-5440	71	15	)	)	PUNCT
ejpam-5440	71	16	,	,	PUNCT
ejpam-5440	71	17	t	t	PROPN
ejpam-5440	71	18	(	(	PUNCT
ejpam-5440	71	19	y	y	NOUN
ejpam-5440	71	20	)	)	PUNCT
ejpam-5440	71	21	)	)	PUNCT
ejpam-5440	71	22	≤	≤	NUM
ejpam-5440	71	23	α	α	PROPN
ejpam-5440	71	24	q(x	q(x	PROPN
ejpam-5440	71	25	,	,	PUNCT
ejpam-5440	71	26	y	y	NOUN
ejpam-5440	71	27	)	)	PUNCT
ejpam-5440	71	28	.	.	PUNCT
ejpam-5440	72	1	then	then	ADV
ejpam-5440	72	2	f	f	PROPN
ejpam-5440	72	3	has	have	VERB
ejpam-5440	72	4	a	a	DET
ejpam-5440	72	5	common	common	ADJ
ejpam-5440	72	6	fixed	fix	VERB
ejpam-5440	72	7	element	element	NOUN
ejpam-5440	72	8	v	v	ADP
ejpam-5440	72	9	∈	∈	PROPN
ejpam-5440	72	10	x	x	NOUN
ejpam-5440	72	11	,	,	PUNCT
ejpam-5440	72	12	that	that	ADV
ejpam-5440	72	13	is	is	ADV
ejpam-5440	72	14	,	,	PUNCT
ejpam-5440	72	15	v	v	PROPN
ejpam-5440	72	16	∈	∈	PROPN
ejpam-5440	72	17	t	t	NOUN
ejpam-5440	72	18	(	(	PUNCT
ejpam-5440	72	19	v	v	NOUN
ejpam-5440	72	20	)	)	PUNCT
ejpam-5440	72	21	for	for	ADP
ejpam-5440	72	22	all	all	DET
ejpam-5440	72	23	t	t	PROPN
ejpam-5440	72	24	∈	∈	PROPN
ejpam-5440	72	25	f.	f.	PROPN
ejpam-5440	72	26	(	(	PUNCT
ejpam-5440	72	27	ϵ	ϵ	X
ejpam-5440	72	28	)	)	PUNCT
ejpam-5440	72	29	if	if	SCONJ
ejpam-5440	72	30	f	f	PROPN
ejpam-5440	72	31	is	be	AUX
ejpam-5440	72	32	a	a	DET
ejpam-5440	72	33	family	family	NOUN
ejpam-5440	72	34	of	of	ADP
ejpam-5440	72	35	multimaps	multimap	NOUN
ejpam-5440	72	36	t	t	PROPN
ejpam-5440	72	37	:	:	PUNCT
ejpam-5440	72	38	x	x	X
ejpam-5440	72	39	→	→	SYM
ejpam-5440	72	40	cl(x	cl(x	X
ejpam-5440	72	41	)	)	PUNCT
ejpam-5440	72	42	satisfying	satisfy	VERB
ejpam-5440	72	43	h(t	h(t	PROPN
ejpam-5440	72	44	(	(	PUNCT
ejpam-5440	72	45	x	x	NOUN
ejpam-5440	72	46	)	)	PUNCT
ejpam-5440	72	47	,	,	PUNCT
ejpam-5440	72	48	t	t	PROPN
ejpam-5440	72	49	(	(	PUNCT
ejpam-5440	72	50	y	y	NOUN
ejpam-5440	72	51	)	)	PUNCT
ejpam-5440	72	52	)	)	PUNCT
ejpam-5440	72	53	≤	≤	NUM
ejpam-5440	72	54	α	α	PROPN
ejpam-5440	72	55	q(x	q(x	PROPN
ejpam-5440	72	56	,	,	PUNCT
ejpam-5440	72	57	y	y	NOUN
ejpam-5440	72	58	)	)	PUNCT
ejpam-5440	72	59	for	for	ADP
ejpam-5440	72	60	all	all	PRON
ejpam-5440	72	61	x	x	SYM
ejpam-5440	72	62	∈	∈	PROPN
ejpam-5440	72	63	x	x	X
ejpam-5440	72	64	and	and	CCONJ
ejpam-5440	72	65	any	any	DET
ejpam-5440	72	66	y	y	PROPN
ejpam-5440	72	67	∈	∈	PROPN
ejpam-5440	72	68	t	t	PROPN
ejpam-5440	72	69	(	(	PUNCT
ejpam-5440	72	70	x)\{x	x)\{x	PROPN
ejpam-5440	72	71	}	}	PUNCT
ejpam-5440	72	72	,	,	PUNCT
ejpam-5440	72	73	then	then	ADV
ejpam-5440	72	74	f	f	PROPN
ejpam-5440	72	75	has	have	VERB
ejpam-5440	72	76	a	a	DET
ejpam-5440	72	77	common	common	ADJ
ejpam-5440	72	78	stationary	stationary	ADJ
ejpam-5440	72	79	element	element	NOUN
ejpam-5440	72	80	v	v	ADP
ejpam-5440	72	81	∈	∈	PROPN
ejpam-5440	72	82	x	x	NOUN
ejpam-5440	72	83	,	,	PUNCT
ejpam-5440	72	84	that	that	ADV
ejpam-5440	72	85	is	is	ADV
ejpam-5440	72	86	,	,	PUNCT
ejpam-5440	72	87	{	{	PUNCT
ejpam-5440	72	88	v	v	NOUN
ejpam-5440	72	89	}	}	PUNCT
ejpam-5440	72	90	=	=	SYM
ejpam-5440	72	91	t	t	PROPN
ejpam-5440	72	92	(	(	PUNCT
ejpam-5440	72	93	v	v	NOUN
ejpam-5440	72	94	)	)	PUNCT
ejpam-5440	72	95	for	for	ADP
ejpam-5440	72	96	all	all	DET
ejpam-5440	72	97	t	t	PROPN
ejpam-5440	72	98	∈	∈	PROPN
ejpam-5440	72	99	f.	f.	PROPN
ejpam-5440	72	100	(	(	PUNCT
ejpam-5440	72	101	η	η	PROPN
ejpam-5440	72	102	)	)	PUNCT
ejpam-5440	72	103	if	if	SCONJ
ejpam-5440	72	104	y	y	PROPN
ejpam-5440	72	105	is	be	AUX
ejpam-5440	72	106	a	a	DET
ejpam-5440	72	107	subset	subset	NOUN
ejpam-5440	72	108	of	of	ADP
ejpam-5440	72	109	x	x	SYM
ejpam-5440	72	110	such	such	ADJ
ejpam-5440	72	111	that	that	PRON
ejpam-5440	72	112	for	for	ADP
ejpam-5440	72	113	each	each	DET
ejpam-5440	72	114	x	x	SYM
ejpam-5440	72	115	∈	∈	PROPN
ejpam-5440	72	116	x\y	x\y	X
ejpam-5440	73	1	there	there	PRON
ejpam-5440	73	2	exists	exist	VERB
ejpam-5440	73	3	a	a	DET
ejpam-5440	73	4	z	z	NOUN
ejpam-5440	73	5	∈	∈	PROPN
ejpam-5440	73	6	x\{x	x\{x	AUX
ejpam-5440	73	7	}	}	PUNCT
ejpam-5440	73	8	satisfying	satisfy	VERB
ejpam-5440	73	9	h(t	h(t	PROPN
ejpam-5440	73	10	(	(	PUNCT
ejpam-5440	73	11	x	x	NOUN
ejpam-5440	73	12	)	)	PUNCT
ejpam-5440	73	13	,	,	PUNCT
ejpam-5440	73	14	t	t	PROPN
ejpam-5440	73	15	(	(	PUNCT
ejpam-5440	73	16	z	z	NOUN
ejpam-5440	73	17	)	)	PUNCT
ejpam-5440	73	18	)	)	PUNCT
ejpam-5440	73	19	≤	≤	NUM
ejpam-5440	73	20	α	α	PROPN
ejpam-5440	73	21	q(x	q(x	PROPN
ejpam-5440	73	22	,	,	PUNCT
ejpam-5440	73	23	z	z	NOUN
ejpam-5440	73	24	)	)	PUNCT
ejpam-5440	73	25	for	for	ADP
ejpam-5440	73	26	a	a	DET
ejpam-5440	73	27	t	t	NOUN
ejpam-5440	73	28	:	:	PUNCT
ejpam-5440	73	29	x	x	X
ejpam-5440	73	30	→	→	SYM
ejpam-5440	73	31	cl(x	cl(x	NOUN
ejpam-5440	73	32	)	)	PUNCT
ejpam-5440	73	33	,	,	PUNCT
ejpam-5440	73	34	then	then	ADV
ejpam-5440	73	35	there	there	PRON
ejpam-5440	73	36	exists	exist	VERB
ejpam-5440	73	37	a	a	DET
ejpam-5440	73	38	v	v	NOUN
ejpam-5440	73	39	∈	∈	NOUN
ejpam-5440	73	40	x	x	SYM
ejpam-5440	73	41	∩	∩	ADJ
ejpam-5440	73	42	y	y	PROPN
ejpam-5440	73	43	=	=	SYM
ejpam-5440	73	44	y	y	PROPN
ejpam-5440	73	45	.	.	PUNCT
ejpam-5440	74	1	remark	remark	PROPN
ejpam-5440	74	2	3.1	3.1	NUM
ejpam-5440	74	3	.	.	PUNCT
ejpam-5440	75	1	(	(	PUNCT
ejpam-5440	75	2	1	1	X
ejpam-5440	75	3	)	)	PUNCT
ejpam-5440	75	4	the	the	DET
ejpam-5440	75	5	completeness	completeness	NOUN
ejpam-5440	75	6	in	in	ADP
ejpam-5440	75	7	(	(	PUNCT
ejpam-5440	75	8	0	0	NUM
ejpam-5440	75	9	)	)	PUNCT
ejpam-5440	75	10	can	can	AUX
ejpam-5440	75	11	be	be	AUX
ejpam-5440	75	12	replaced	replace	VERB
ejpam-5440	75	13	by	by	ADP
ejpam-5440	75	14	f	f	PROPN
ejpam-5440	75	15	-orbitally	-orbitally	PROPN
ejpam-5440	75	16	or	or	CCONJ
ejpam-5440	75	17	t	t	PROPN
ejpam-5440	75	18	-orbitally	-orbitally	PROPN
ejpam-5440	75	19	completeness	completeness	NOUN
ejpam-5440	75	20	according	accord	VERB
ejpam-5440	75	21	to	to	ADP
ejpam-5440	75	22	the	the	DET
ejpam-5440	75	23	corresponding	corresponding	ADJ
ejpam-5440	75	24	situation	situation	NOUN
ejpam-5440	75	25	.	.	PUNCT
ejpam-5440	76	1	(	(	PUNCT
ejpam-5440	76	2	2	2	X
ejpam-5440	76	3	)	)	PUNCT
ejpam-5440	76	4	note	note	NOUN
ejpam-5440	76	5	that	that	SCONJ
ejpam-5440	76	6	there	there	PRON
ejpam-5440	76	7	are	be	VERB
ejpam-5440	76	8	many	many	ADJ
ejpam-5440	76	9	characterizations	characterization	NOUN
ejpam-5440	76	10	of	of	ADP
ejpam-5440	76	11	the	the	DET
ejpam-5440	76	12	metric	metric	ADJ
ejpam-5440	76	13	completeness	completeness	NOUN
ejpam-5440	76	14	;	;	PUNCT
ejpam-5440	76	15	see	see	VERB
ejpam-5440	76	16	[	[	X
ejpam-5440	76	17	20	20	NUM
ejpam-5440	76	18	]	]	PUNCT
ejpam-5440	76	19	.	.	PUNCT
ejpam-5440	77	1	theorem	theorem	PROPN
ejpam-5440	77	2	h	h	PROPN
ejpam-5440	77	3	covers	cover	VERB
ejpam-5440	77	4	some	some	PRON
ejpam-5440	77	5	of	of	ADP
ejpam-5440	77	6	them	they	PRON
ejpam-5440	77	7	.	.	PUNCT
ejpam-5440	78	1	it	it	PRON
ejpam-5440	78	2	is	be	AUX
ejpam-5440	78	3	well	well	ADV
ejpam-5440	78	4	-	-	PUNCT
ejpam-5440	78	5	known	know	VERB
ejpam-5440	78	6	that	that	SCONJ
ejpam-5440	78	7	the	the	DET
ejpam-5440	78	8	banach	banach	NOUN
ejpam-5440	78	9	contraction	contraction	NOUN
ejpam-5440	78	10	does	do	AUX
ejpam-5440	78	11	not	not	PART
ejpam-5440	78	12	characterize	characterize	VERB
ejpam-5440	78	13	the	the	DET
ejpam-5440	78	14	metric	metric	ADJ
ejpam-5440	78	15	completeness	completeness	NOUN
ejpam-5440	78	16	.	.	PUNCT
ejpam-5440	79	1	however	however	ADV
ejpam-5440	79	2	the	the	DET
ejpam-5440	79	3	extended	extended	ADJ
ejpam-5440	79	4	rhr	rhr	PROPN
ejpam-5440	79	5	principle	principle	NOUN
ejpam-5440	79	6	does	do	AUX
ejpam-5440	79	7	by	by	ADP
ejpam-5440	79	8	theorem	theorem	VERB
ejpam-5440	79	9	h(γ	h(γ	PROPN
ejpam-5440	79	10	)	)	PUNCT
ejpam-5440	79	11	,	,	PUNCT
ejpam-5440	79	12	(	(	PUNCT
ejpam-5440	79	13	2	2	X
ejpam-5440	79	14	)	)	PUNCT
ejpam-5440	79	15	note	note	NOUN
ejpam-5440	79	16	that	that	SCONJ
ejpam-5440	79	17	theorem	theorem	VERB
ejpam-5440	79	18	h(β	h(β	NOUN
ejpam-5440	79	19	)	)	PUNCT
ejpam-5440	79	20	properly	properly	ADV
ejpam-5440	79	21	extends	extend	VERB
ejpam-5440	79	22	the	the	DET
ejpam-5440	79	23	banach	banach	NOUN
ejpam-5440	79	24	principle	principle	NOUN
ejpam-5440	79	25	,	,	PUNCT
ejpam-5440	79	26	(	(	PUNCT
ejpam-5440	79	27	γ	γ	X
ejpam-5440	79	28	)	)	PUNCT
ejpam-5440	79	29	the	the	DET
ejpam-5440	79	30	rhr	rhr	PROPN
ejpam-5440	79	31	principle	principle	NOUN
ejpam-5440	79	32	,	,	PUNCT
ejpam-5440	79	33	and	and	CCONJ
ejpam-5440	79	34	(	(	PUNCT
ejpam-5440	79	35	δ	δ	NOUN
ejpam-5440	79	36	)	)	PUNCT
ejpam-5440	79	37	,	,	PUNCT
ejpam-5440	79	38	(	(	PUNCT
ejpam-5440	79	39	ϵ	ϵ	X
ejpam-5440	79	40	)	)	PUNCT
ejpam-5440	79	41	the	the	DET
ejpam-5440	79	42	nadler	nadler	NOUN
ejpam-5440	79	43	and	and	CCONJ
ejpam-5440	79	44	covitz	covitz	PROPN
ejpam-5440	79	45	-	-	PUNCT
ejpam-5440	79	46	nadler	nadler	NOUN
ejpam-5440	79	47	theorems	theorem	NOUN
ejpam-5440	79	48	.	.	PUNCT
ejpam-5440	80	1	moreover	moreover	ADV
ejpam-5440	80	2	,	,	PUNCT
ejpam-5440	80	3	theorem	theorem	ADJ
ejpam-5440	80	4	h	h	NOUN
ejpam-5440	80	5	gives	give	VERB
ejpam-5440	80	6	unified	unified	ADJ
ejpam-5440	80	7	short	short	ADJ
ejpam-5440	80	8	-	-	PUNCT
ejpam-5440	80	9	cut	cut	VERB
ejpam-5440	80	10	proofs	proof	NOUN
ejpam-5440	80	11	of	of	ADP
ejpam-5440	80	12	such	such	ADJ
ejpam-5440	80	13	extensions	extension	NOUN
ejpam-5440	80	14	.	.	PUNCT
ejpam-5440	81	1	(	(	PUNCT
ejpam-5440	81	2	3	3	X
ejpam-5440	81	3	)	)	PUNCT
ejpam-5440	81	4	let	let	NOUN
ejpam-5440	81	5	(	(	PUNCT
ejpam-5440	81	6	α1	α1	PROPN
ejpam-5440	81	7	)	)	PUNCT
ejpam-5440	81	8	and	and	CCONJ
ejpam-5440	81	9	(	(	PUNCT
ejpam-5440	81	10	η1	η1	NOUN
ejpam-5440	81	11	)	)	PUNCT
ejpam-5440	81	12	denote	denote	VERB
ejpam-5440	81	13	the	the	DET
ejpam-5440	81	14	case	case	NOUN
ejpam-5440	81	15	(	(	PUNCT
ejpam-5440	81	16	α	α	NOUN
ejpam-5440	81	17	)	)	PUNCT
ejpam-5440	81	18	and	and	CCONJ
ejpam-5440	81	19	(	(	PUNCT
ejpam-5440	81	20	η	η	PROPN
ejpam-5440	81	21	)	)	PUNCT
ejpam-5440	81	22	for	for	ADP
ejpam-5440	81	23	single	single	ADV
ejpam-5440	81	24	-	-	PUNCT
ejpam-5440	81	25	valued	value	VERB
ejpam-5440	81	26	t	t	NOUN
ejpam-5440	81	27	=	=	SYM
ejpam-5440	81	28	f	f	PROPN
ejpam-5440	81	29	,	,	PUNCT
ejpam-5440	81	30	resp	resp	PROPN
ejpam-5440	81	31	.	.	PUNCT
ejpam-5440	82	1	when	when	SCONJ
ejpam-5440	82	2	f	f	PROPN
ejpam-5440	82	3	is	be	AUX
ejpam-5440	82	4	a	a	DET
ejpam-5440	82	5	singleton	singleton	NOUN
ejpam-5440	82	6	,	,	PUNCT
ejpam-5440	82	7	(	(	PUNCT
ejpam-5440	82	8	β	β	NOUN
ejpam-5440	82	9	)	)	PUNCT
ejpam-5440	82	10	−	−	PROPN
ejpam-5440	82	11	(	(	PUNCT
ejpam-5440	82	12	ϵ	ϵ	X
ejpam-5440	82	13	)	)	PUNCT
ejpam-5440	82	14	are	be	AUX
ejpam-5440	82	15	denoted	denote	VERB
ejpam-5440	82	16	by	by	ADP
ejpam-5440	82	17	(	(	PUNCT
ejpam-5440	82	18	β1	β1	PROPN
ejpam-5440	82	19	)	)	PUNCT
ejpam-5440	82	20	−	−	PROPN
ejpam-5440	83	1	(	(	PUNCT
ejpam-5440	83	2	ϵ1	ϵ1	ADJ
ejpam-5440	83	3	)	)	PUNCT
ejpam-5440	83	4	,	,	PUNCT
ejpam-5440	83	5	resp	resp	NOUN
ejpam-5440	83	6	.	.	PUNCT
ejpam-5440	84	1	these	these	PRON
ejpam-5440	84	2	are	be	AUX
ejpam-5440	84	3	also	also	ADV
ejpam-5440	84	4	equivalent	equivalent	ADJ
ejpam-5440	84	5	to	to	ADP
ejpam-5440	84	6	(	(	PUNCT
ejpam-5440	84	7	0)−	0)−	NUM
ejpam-5440	84	8	(	(	PUNCT
ejpam-5440	84	9	η	η	NOUN
ejpam-5440	84	10	)	)	PUNCT
ejpam-5440	84	11	.	.	PUNCT
ejpam-5440	85	1	therefore	therefore	ADV
ejpam-5440	85	2	,	,	PUNCT
ejpam-5440	85	3	actually	actually	ADV
ejpam-5440	85	4	theorem	theorem	VERB
ejpam-5440	85	5	h	h	NOUN
ejpam-5440	85	6	consists	consist	VERB
ejpam-5440	85	7	of	of	ADP
ejpam-5440	85	8	equivalent	equivalent	ADJ
ejpam-5440	85	9	13	13	NUM
ejpam-5440	85	10	statements	statement	NOUN
ejpam-5440	85	11	and	and	CCONJ
ejpam-5440	85	12	gives	give	VERB
ejpam-5440	85	13	a	a	DET
ejpam-5440	85	14	unified	unified	ADJ
ejpam-5440	85	15	proofs	proof	NOUN
ejpam-5440	85	16	for	for	ADP
ejpam-5440	85	17	their	their	PRON
ejpam-5440	85	18	equivalencies	equivalencie	NOUN
ejpam-5440	85	19	.	.	PUNCT
ejpam-5440	86	1	definition	definition	NOUN
ejpam-5440	86	2	3.2	3.2	NUM
ejpam-5440	86	3	.	.	PUNCT
ejpam-5440	87	1	let	let	VERB
ejpam-5440	87	2	us	we	PRON
ejpam-5440	87	3	consider	consider	VERB
ejpam-5440	87	4	the	the	DET
ejpam-5440	87	5	family	family	NOUN
ejpam-5440	87	6	(	(	PUNCT
ejpam-5440	87	7	0	0	NUM
ejpam-5440	87	8	)	)	PUNCT
ejpam-5440	87	9	of	of	ADP
ejpam-5440	87	10	theorems	theorem	NOUN
ejpam-5440	87	11	related	relate	VERB
ejpam-5440	87	12	to	to	ADP
ejpam-5440	87	13	the	the	DET
ejpam-5440	87	14	completeness	completeness	NOUN
ejpam-5440	87	15	of	of	ADP
ejpam-5440	87	16	quasi	quasi	ADJ
ejpam-5440	87	17	-	-	ADJ
ejpam-5440	87	18	metric	metric	ADJ
ejpam-5440	87	19	spaces	space	NOUN
ejpam-5440	87	20	.	.	PUNCT
ejpam-5440	88	1	each	each	PRON
ejpam-5440	88	2	subfamily	subfamily	ADV
ejpam-5440	88	3	(	(	PUNCT
ejpam-5440	88	4	α)−	α)−	PROPN
ejpam-5440	88	5	(	(	PUNCT
ejpam-5440	88	6	η	η	NOUN
ejpam-5440	88	7	)	)	PUNCT
ejpam-5440	88	8	without	without	ADP
ejpam-5440	88	9	(	(	PUNCT
ejpam-5440	88	10	ζ	ζ	NOUN
ejpam-5440	88	11	)	)	PUNCT
ejpam-5440	88	12	of	of	ADP
ejpam-5440	88	13	the	the	DET
ejpam-5440	88	14	family	family	NOUN
ejpam-5440	88	15	(	(	PUNCT
ejpam-5440	88	16	0	0	NUM
ejpam-5440	88	17	)	)	PUNCT
ejpam-5440	88	18	consists	consist	VERB
ejpam-5440	88	19	of	of	ADP
ejpam-5440	88	20	theorems	theorem	NOUN
ejpam-5440	88	21	related	relate	VERB
ejpam-5440	88	22	the	the	DET
ejpam-5440	88	23	statement	statement	NOUN
ejpam-5440	88	24	(	(	PUNCT
ejpam-5440	88	25	α)−	α)−	PROPN
ejpam-5440	88	26	(	(	PUNCT
ejpam-5440	88	27	η	η	NOUN
ejpam-5440	88	28	)	)	PUNCT
ejpam-5440	88	29	,	,	PUNCT
ejpam-5440	88	30	resp	resp	NOUN
ejpam-5440	88	31	.	.	PUNCT
ejpam-5440	89	1	4	4	X
ejpam-5440	89	2	.	.	X
ejpam-5440	89	3	the	the	DET
ejpam-5440	89	4	family	family	NOUN
ejpam-5440	89	5	(	(	PUNCT
ejpam-5440	89	6	0	0	NUM
ejpam-5440	89	7	)	)	PUNCT
ejpam-5440	89	8	in	in	ADP
ejpam-5440	89	9	our	our	PRON
ejpam-5440	89	10	earlier	early	ADJ
ejpam-5440	89	11	paper	paper	NOUN
ejpam-5440	89	12	[	[	X
ejpam-5440	89	13	13	13	NUM
ejpam-5440	89	14	]	]	PUNCT
ejpam-5440	89	15	in	in	ADP
ejpam-5440	89	16	1984	1984	NUM
ejpam-5440	89	17	,	,	PUNCT
ejpam-5440	89	18	we	we	PRON
ejpam-5440	89	19	gave	give	VERB
ejpam-5440	89	20	some	some	DET
ejpam-5440	89	21	necessary	necessary	ADJ
ejpam-5440	89	22	and	and	CCONJ
ejpam-5440	89	23	sufficient	sufficient	ADJ
ejpam-5440	89	24	conditions	condition	NOUN
ejpam-5440	89	25	for	for	ADP
ejpam-5440	89	26	a	a	DET
ejpam-5440	89	27	metric	metric	ADJ
ejpam-5440	89	28	space	space	NOUN
ejpam-5440	89	29	(	(	PUNCT
ejpam-5440	89	30	x	x	X
ejpam-5440	89	31	,	,	PUNCT
ejpam-5440	89	32	d	d	NOUN
ejpam-5440	89	33	)	)	PUNCT
ejpam-5440	89	34	to	to	PART
ejpam-5440	89	35	be	be	AUX
ejpam-5440	89	36	complete	complete	ADJ
ejpam-5440	89	37	.	.	PUNCT
ejpam-5440	90	1	such	such	ADJ
ejpam-5440	90	2	characterizations	characterization	NOUN
ejpam-5440	90	3	of	of	ADP
ejpam-5440	90	4	metric	metric	ADJ
ejpam-5440	90	5	completeness	completeness	NOUN
ejpam-5440	90	6	were	be	AUX
ejpam-5440	90	7	given	give	VERB
ejpam-5440	90	8	mainly	mainly	ADV
ejpam-5440	90	9	by	by	ADP
ejpam-5440	90	10	results	result	NOUN
ejpam-5440	90	11	relevant	relevant	ADJ
ejpam-5440	90	12	to	to	ADP
ejpam-5440	90	13	caristi	caristi	PROPN
ejpam-5440	90	14	’s	’s	PART
ejpam-5440	90	15	fixed	fix	VERB
ejpam-5440	90	16	point	point	NOUN
ejpam-5440	90	17	theorem	theorem	NOUN
ejpam-5440	90	18	(	(	PUNCT
ejpam-5440	90	19	1976	1976	NUM
ejpam-5440	90	20	)	)	PUNCT
ejpam-5440	90	21	.	.	PUNCT
ejpam-5440	91	1	works	work	NOUN
ejpam-5440	91	2	of	of	ADP
ejpam-5440	91	3	cantor	cantor	PROPN
ejpam-5440	91	4	,	,	PUNCT
ejpam-5440	91	5	kuratowski	kuratowski	PROPN
ejpam-5440	91	6	(	(	PUNCT
ejpam-5440	91	7	1930	1930	NUM
ejpam-5440	91	8	)	)	PUNCT
ejpam-5440	91	9	,	,	PUNCT
ejpam-5440	91	10	ekeland	ekeland	NOUN
ejpam-5440	91	11	(	(	PUNCT
ejpam-5440	91	12	1972	1972	NUM
ejpam-5440	91	13	)	)	PUNCT
ejpam-5440	91	14	,	,	PUNCT
ejpam-5440	91	15	caristi	caristi	X
ejpam-5440	91	16	(	(	PUNCT
ejpam-5440	91	17	1976	1976	NUM
ejpam-5440	91	18	)	)	PUNCT
ejpam-5440	91	19	,	,	PUNCT
ejpam-5440	91	20	kirk	kirk	PROPN
ejpam-5440	91	21	(	(	PUNCT
ejpam-5440	91	22	1976	1976	NUM
ejpam-5440	91	23	)	)	PUNCT
ejpam-5440	91	24	,	,	PUNCT
ejpam-5440	91	25	boyd	boyd	PROPN
ejpam-5440	91	26	-	-	PUNCT
ejpam-5440	91	27	wong	wong	PROPN
ejpam-5440	91	28	(	(	PUNCT
ejpam-5440	91	29	1976	1976	NUM
ejpam-5440	91	30	)	)	PUNCT
ejpam-5440	91	31	,	,	PUNCT
ejpam-5440	91	32	kolodner	kolodner	X
ejpam-5440	91	33	(	(	PUNCT
ejpam-5440	91	34	1967	1967	NUM
ejpam-5440	91	35	)	)	PUNCT
ejpam-5440	91	36	,	,	PUNCT
ejpam-5440	91	37	weston	weston	PROPN
ejpam-5440	91	38	(	(	PUNCT
ejpam-5440	91	39	1977	1977	NUM
ejpam-5440	91	40	)	)	PUNCT
ejpam-5440	91	41	,	,	PUNCT
ejpam-5440	91	42	ćirić	ćirić	PROPN
ejpam-5440	91	43	(	(	PUNCT
ejpam-5440	91	44	1971	1971	NUM
ejpam-5440	91	45	)	)	PUNCT
ejpam-5440	91	46	,	,	PUNCT
ejpam-5440	91	47	hu	hu	PROPN
ejpam-5440	91	48	(	(	PUNCT
ejpam-5440	91	49	1967	1967	NUM
ejpam-5440	91	50	)	)	PUNCT
ejpam-5440	91	51	,	,	PUNCT
ejpam-5440	91	52	reich	reich	PROPN
ejpam-5440	91	53	(	(	PUNCT
ejpam-5440	91	54	1971	1971	NUM
ejpam-5440	91	55	)	)	PUNCT
ejpam-5440	91	56	,	,	PUNCT
ejpam-5440	91	57	subrahmanyam	subrahmanyam	NOUN
ejpam-5440	91	58	(	(	PUNCT
ejpam-5440	91	59	1975	1975	NUM
ejpam-5440	91	60	)	)	PUNCT
ejpam-5440	91	61	,	,	PUNCT
ejpam-5440	91	62	and	and	CCONJ
ejpam-5440	91	63	others	other	NOUN
ejpam-5440	91	64	are	be	AUX
ejpam-5440	91	65	combined	combine	VERB
ejpam-5440	91	66	.	.	PUNCT
ejpam-5440	92	1	actually	actually	ADV
ejpam-5440	92	2	we	we	PRON
ejpam-5440	92	3	combined	combine	VERB
ejpam-5440	92	4	those	those	DET
ejpam-5440	92	5	results	result	NOUN
ejpam-5440	92	6	and	and	CCONJ
ejpam-5440	92	7	stated	state	VERB
ejpam-5440	92	8	our	our	PRON
ejpam-5440	92	9	characterizations	characterization	NOUN
ejpam-5440	92	10	of	of	ADP
ejpam-5440	92	11	the	the	DET
ejpam-5440	92	12	metric	metric	ADJ
ejpam-5440	92	13	completeness	completeness	NOUN
ejpam-5440	92	14	as	as	ADP
ejpam-5440	92	15	theorem	theorem	NOUN
ejpam-5440	92	16	of	of	ADP
ejpam-5440	92	17	[	[	X
ejpam-5440	92	18	13	13	NUM
ejpam-5440	92	19	]	]	PUNCT
ejpam-5440	92	20	.	.	PUNCT
ejpam-5440	93	1	the	the	DET
ejpam-5440	93	2	first	first	ADJ
ejpam-5440	93	3	response	response	NOUN
ejpam-5440	93	4	to	to	ADP
ejpam-5440	93	5	the	the	DET
ejpam-5440	93	6	article	article	NOUN
ejpam-5440	93	7	was	be	AUX
ejpam-5440	93	8	that	that	PRON
ejpam-5440	93	9	:	:	PUNCT
ejpam-5440	93	10	“	"	PUNCT
ejpam-5440	93	11	who	who	PRON
ejpam-5440	93	12	dare	dare	VERB
ejpam-5440	93	13	use	use	VERB
ejpam-5440	93	14	this	this	DET
ejpam-5440	93	15	kind	kind	NOUN
ejpam-5440	93	16	of	of	ADP
ejpam-5440	93	17	things	thing	NOUN
ejpam-5440	93	18	to	to	PART
ejpam-5440	93	19	check	check	VERB
ejpam-5440	93	20	the	the	DET
ejpam-5440	93	21	completeness	completeness	NOUN
ejpam-5440	93	22	of	of	ADP
ejpam-5440	93	23	a	a	DET
ejpam-5440	93	24	metric	metric	ADJ
ejpam-5440	93	25	space	space	NOUN
ejpam-5440	93	26	?	?	PUNCT
ejpam-5440	93	27	”	"	PUNCT
ejpam-5440	94	1	a	a	DET
ejpam-5440	94	2	few	few	ADJ
ejpam-5440	94	3	years	year	NOUN
ejpam-5440	94	4	later	later	ADV
ejpam-5440	94	5	in	in	ADP
ejpam-5440	94	6	1986	1986	NUM
ejpam-5440	94	7	,	,	PUNCT
ejpam-5440	94	8	the	the	DET
ejpam-5440	94	9	author	author	NOUN
ejpam-5440	94	10	and	and	CCONJ
ejpam-5440	94	11	billy	billy	PROPN
ejpam-5440	94	12	e.	e.	PROPN
ejpam-5440	94	13	rhoades	rhoades	PROPN
ejpam-5440	94	14	published	publish	VERB
ejpam-5440	94	15	[	[	PUNCT
ejpam-5440	94	16	22	22	NUM
ejpam-5440	94	17	]	]	PUNCT
ejpam-5440	94	18	.	.	PUNCT
ejpam-5440	95	1	its	its	PRON
ejpam-5440	95	2	abstract	abstract	NOUN
ejpam-5440	95	3	says	say	VERB
ejpam-5440	95	4	:	:	PUNCT
ejpam-5440	95	5	several	several	ADJ
ejpam-5440	95	6	authors	author	NOUN
ejpam-5440	95	7	have	have	AUX
ejpam-5440	95	8	characterized	characterize	VERB
ejpam-5440	95	9	completeness	completeness	NOUN
ejpam-5440	95	10	of	of	ADP
ejpam-5440	95	11	a	a	DET
ejpam-5440	95	12	metric	metric	ADJ
ejpam-5440	95	13	space	space	NOUN
ejpam-5440	95	14	by	by	ADP
ejpam-5440	95	15	using	use	VERB
ejpam-5440	95	16	a	a	DET
ejpam-5440	95	17	fixed	fix	VERB
ejpam-5440	95	18	s.	s.	PROPN
ejpam-5440	95	19	park	park	PROPN
ejpam-5440	95	20	/	/	SYM
ejpam-5440	95	21	eur	eur	PROPN
ejpam-5440	95	22	.	.	PUNCT
ejpam-5440	96	1	j.	j.	PROPN
ejpam-5440	96	2	pure	pure	PROPN
ejpam-5440	96	3	appl	appl	PROPN
ejpam-5440	96	4	.	.	PROPN
ejpam-5440	96	5	math	math	PROPN
ejpam-5440	96	6	,	,	PUNCT
ejpam-5440	96	7	17	17	NUM
ejpam-5440	96	8	(	(	PUNCT
ejpam-5440	96	9	4	4	NUM
ejpam-5440	96	10	)	)	PUNCT
ejpam-5440	96	11	(	(	PUNCT
ejpam-5440	96	12	2024	2024	NUM
ejpam-5440	96	13	)	)	PUNCT
ejpam-5440	96	14	,	,	PUNCT
ejpam-5440	96	15	2370	2370	NUM
ejpam-5440	96	16	-	-	SYM
ejpam-5440	96	17	2383	2383	NUM
ejpam-5440	96	18	2374	2374	NUM
ejpam-5440	96	19	point	point	NOUN
ejpam-5440	96	20	theorem	theorem	VERB
ejpam-5440	96	21	.	.	PUNCT
ejpam-5440	97	1	the	the	DET
ejpam-5440	97	2	two	two	NUM
ejpam-5440	97	3	theorems	theorem	NOUN
ejpam-5440	97	4	of	of	ADP
ejpam-5440	97	5	this	this	DET
ejpam-5440	97	6	paper	paper	NOUN
ejpam-5440	97	7	encompass	encompass	VERB
ejpam-5440	97	8	some	some	DET
ejpam-5440	97	9	previous	previous	ADJ
ejpam-5440	97	10	results	result	NOUN
ejpam-5440	97	11	as	as	ADV
ejpam-5440	97	12	well	well	ADV
ejpam-5440	97	13	as	as	ADP
ejpam-5440	97	14	future	future	ADJ
ejpam-5440	97	15	theorems	theorem	NOUN
ejpam-5440	97	16	of	of	ADP
ejpam-5440	97	17	this	this	DET
ejpam-5440	97	18	type	type	NOUN
ejpam-5440	97	19	.	.	PUNCT
ejpam-5440	98	1	we	we	PRON
ejpam-5440	98	2	introduce	introduce	VERB
ejpam-5440	98	3	the	the	DET
ejpam-5440	98	4	two	two	NUM
ejpam-5440	98	5	theorems	theorem	NOUN
ejpam-5440	98	6	in	in	ADP
ejpam-5440	98	7	[	[	X
ejpam-5440	98	8	22	22	NUM
ejpam-5440	98	9	]	]	PUNCT
ejpam-5440	98	10	as	as	SCONJ
ejpam-5440	98	11	follows	follow	VERB
ejpam-5440	98	12	:	:	PUNCT
ejpam-5440	98	13	let	let	VERB
ejpam-5440	98	14	b	b	X
ejpam-5440	98	15	be	be	AUX
ejpam-5440	98	16	a	a	DET
ejpam-5440	98	17	class	class	NOUN
ejpam-5440	98	18	of	of	ADP
ejpam-5440	98	19	selfmaps	selfmap	NOUN
ejpam-5440	98	20	of	of	ADP
ejpam-5440	98	21	closed	closed	ADJ
ejpam-5440	98	22	subsets	subset	NOUN
ejpam-5440	98	23	of	of	ADP
ejpam-5440	98	24	a	a	DET
ejpam-5440	98	25	metric	metric	ADJ
ejpam-5440	98	26	space	space	NOUN
ejpam-5440	98	27	x	x	PUNCT
ejpam-5440	98	28	such	such	ADJ
ejpam-5440	98	29	that	that	SCONJ
ejpam-5440	98	30	if	if	SCONJ
ejpam-5440	98	31	any	any	DET
ejpam-5440	98	32	g	g	PROPN
ejpam-5440	98	33	∈	∈	PROPN
ejpam-5440	98	34	b	b	PROPN
ejpam-5440	98	35	has	have	VERB
ejpam-5440	98	36	a	a	DET
ejpam-5440	98	37	fixed	fix	VERB
ejpam-5440	98	38	point	point	NOUN
ejpam-5440	98	39	then	then	ADV
ejpam-5440	98	40	x	x	PRON
ejpam-5440	98	41	is	be	AUX
ejpam-5440	98	42	complete	complete	ADJ
ejpam-5440	98	43	.	.	PUNCT
ejpam-5440	99	1	examples	example	NOUN
ejpam-5440	99	2	of	of	ADP
ejpam-5440	99	3	b	b	NOUN
ejpam-5440	99	4	are	be	AUX
ejpam-5440	99	5	the	the	DET
ejpam-5440	99	6	classes	class	NOUN
ejpam-5440	99	7	of	of	ADP
ejpam-5440	99	8	the	the	DET
ejpam-5440	99	9	banach	banach	NOUN
ejpam-5440	99	10	contractions	contraction	NOUN
ejpam-5440	99	11	(	(	PUNCT
ejpam-5440	99	12	hu	hu	PROPN
ejpam-5440	99	13	(	(	PUNCT
ejpam-5440	99	14	1967	1967	NUM
ejpam-5440	99	15	)	)	PUNCT
ejpam-5440	99	16	)	)	PUNCT
ejpam-5440	99	17	and	and	CCONJ
ejpam-5440	99	18	the	the	DET
ejpam-5440	99	19	kannan	kannan	PROPN
ejpam-5440	99	20	type	type	NOUN
ejpam-5440	99	21	contractions	contraction	NOUN
ejpam-5440	99	22	.	.	PUNCT
ejpam-5440	100	1	let	let	VERB
ejpam-5440	100	2	a	a	PRON
ejpam-5440	100	3	be	be	AUX
ejpam-5440	100	4	a	a	DET
ejpam-5440	100	5	class	class	NOUN
ejpam-5440	100	6	of	of	ADP
ejpam-5440	100	7	selfmaps	selfmap	NOUN
ejpam-5440	100	8	of	of	ADP
ejpam-5440	100	9	closed	closed	ADJ
ejpam-5440	100	10	subsets	subset	NOUN
ejpam-5440	100	11	of	of	ADP
ejpam-5440	100	12	x	x	PUNCT
ejpam-5440	100	13	containing	contain	VERB
ejpam-5440	100	14	b	b	NOUN
ejpam-5440	100	15	such	such	ADJ
ejpam-5440	100	16	that	that	DET
ejpam-5440	100	17	completeness	completeness	NOUN
ejpam-5440	100	18	of	of	ADP
ejpam-5440	100	19	x	x	PRON
ejpam-5440	100	20	implies	imply	VERB
ejpam-5440	100	21	the	the	DET
ejpam-5440	100	22	existence	existence	NOUN
ejpam-5440	100	23	of	of	ADP
ejpam-5440	100	24	a	a	DET
ejpam-5440	100	25	fixed	fix	VERB
ejpam-5440	100	26	point	point	NOUN
ejpam-5440	100	27	for	for	ADP
ejpam-5440	100	28	any	any	DET
ejpam-5440	100	29	map	map	NOUN
ejpam-5440	100	30	in	in	ADP
ejpam-5440	100	31	a.	a.	NOUN
ejpam-5440	100	32	examples	example	NOUN
ejpam-5440	100	33	of	of	ADP
ejpam-5440	100	34	a	a	DET
ejpam-5440	100	35	containing	contain	VERB
ejpam-5440	100	36	the	the	DET
ejpam-5440	100	37	preceding	precede	VERB
ejpam-5440	100	38	examples	example	NOUN
ejpam-5440	100	39	of	of	ADP
ejpam-5440	100	40	b	b	NOUN
ejpam-5440	100	41	are	be	AUX
ejpam-5440	100	42	classes	class	NOUN
ejpam-5440	100	43	of	of	ADP
ejpam-5440	100	44	maps	map	NOUN
ejpam-5440	100	45	satisfying	satisfy	VERB
ejpam-5440	100	46	the	the	DET
ejpam-5440	100	47	conditions	condition	NOUN
ejpam-5440	100	48	of	of	ADP
ejpam-5440	100	49	meir	meir	PROPN
ejpam-5440	100	50	-	-	PUNCT
ejpam-5440	100	51	keeler	keeler	PROPN
ejpam-5440	100	52	(	(	PUNCT
ejpam-5440	100	53	1969	1969	NUM
ejpam-5440	100	54	)	)	PUNCT
ejpam-5440	100	55	,	,	PUNCT
ejpam-5440	100	56	hegedüs	hegedü	NOUN
ejpam-5440	100	57	-	-	PUNCT
ejpam-5440	100	58	szilágyi	szilágyi	NOUN
ejpam-5440	100	59	(	(	PUNCT
ejpam-5440	100	60	1980	1980	NUM
ejpam-5440	100	61	)	)	PUNCT
ejpam-5440	100	62	,	,	PUNCT
ejpam-5440	100	63	caristi	caristi	X
ejpam-5440	100	64	(	(	PUNCT
ejpam-5440	100	65	1976	1976	NUM
ejpam-5440	100	66	)	)	PUNCT
ejpam-5440	100	67	,	,	PUNCT
ejpam-5440	100	68	tasković	tasković	PUNCT
ejpam-5440	101	1	(	(	PUNCT
ejpam-5440	101	2	1978	1978	NUM
ejpam-5440	101	3	,	,	PUNCT
ejpam-5440	101	4	1984	1984	NUM
ejpam-5440	101	5	)	)	PUNCT
ejpam-5440	101	6	,	,	PUNCT
ejpam-5440	101	7	and	and	CCONJ
ejpam-5440	101	8	hikida	hikida	PROPN
ejpam-5440	101	9	(	(	PUNCT
ejpam-5440	101	10	1984	1984	NUM
ejpam-5440	101	11	)	)	PUNCT
ejpam-5440	101	12	.	.	PUNCT
ejpam-5440	102	1	the	the	DET
ejpam-5440	102	2	following	follow	VERB
ejpam-5440	102	3	is	be	AUX
ejpam-5440	102	4	the	the	DET
ejpam-5440	102	5	main	main	ADJ
ejpam-5440	102	6	result	result	NOUN
ejpam-5440	102	7	of	of	ADP
ejpam-5440	102	8	[	[	X
ejpam-5440	102	9	22	22	NUM
ejpam-5440	102	10	]	]	PUNCT
ejpam-5440	102	11	:	:	PUNCT
ejpam-5440	102	12	theorem	theorem	VERB
ejpam-5440	102	13	4.1	4.1	NUM
ejpam-5440	102	14	.	.	PUNCT
ejpam-5440	103	1	x	x	PUNCT
ejpam-5440	103	2	is	be	AUX
ejpam-5440	103	3	complete	complete	ADJ
ejpam-5440	103	4	if	if	SCONJ
ejpam-5440	103	5	and	and	CCONJ
ejpam-5440	103	6	only	only	ADV
ejpam-5440	103	7	if	if	SCONJ
ejpam-5440	103	8	any	any	DET
ejpam-5440	103	9	map	map	NOUN
ejpam-5440	103	10	in	in	ADP
ejpam-5440	103	11	a	a	PRON
ejpam-5440	103	12	has	have	VERB
ejpam-5440	103	13	a	a	DET
ejpam-5440	103	14	fixed	fix	VERB
ejpam-5440	103	15	point	point	NOUN
ejpam-5440	103	16	.	.	PUNCT
ejpam-5440	104	1	let	let	VERB
ejpam-5440	104	2	b′	b′	NOUN
ejpam-5440	104	3	be	be	AUX
ejpam-5440	104	4	a	a	DET
ejpam-5440	104	5	class	class	NOUN
ejpam-5440	104	6	of	of	ADP
ejpam-5440	104	7	selfmaps	selfmap	NOUN
ejpam-5440	104	8	defined	define	VERB
ejpam-5440	104	9	on	on	ADP
ejpam-5440	104	10	x	x	SYM
ejpam-5440	104	11	such	such	ADJ
ejpam-5440	104	12	that	that	SCONJ
ejpam-5440	104	13	every	every	DET
ejpam-5440	104	14	map	map	NOUN
ejpam-5440	104	15	in	in	ADP
ejpam-5440	104	16	b′	b′	NUM
ejpam-5440	104	17	satisfies	satisfie	NOUN
ejpam-5440	104	18	a	a	DET
ejpam-5440	104	19	certain	certain	ADJ
ejpam-5440	104	20	condition	condition	NOUN
ejpam-5440	104	21	q	q	NOUN
ejpam-5440	104	22	,	,	PUNCT
ejpam-5440	104	23	then	then	ADV
ejpam-5440	104	24	x	x	PUNCT
ejpam-5440	104	25	is	be	AUX
ejpam-5440	104	26	complete	complete	ADJ
ejpam-5440	104	27	.	.	PUNCT
ejpam-5440	105	1	an	an	DET
ejpam-5440	105	2	example	example	NOUN
ejpam-5440	105	3	of	of	ADP
ejpam-5440	105	4	b′	b′	NUM
ejpam-5440	105	5	is	be	AUX
ejpam-5440	105	6	the	the	DET
ejpam-5440	105	7	map	map	NOUN
ejpam-5440	105	8	satisfying	satisfy	VERB
ejpam-5440	105	9	an	an	DET
ejpam-5440	105	10	equivalent	equivalent	ADJ
ejpam-5440	105	11	formulation	formulation	NOUN
ejpam-5440	105	12	of	of	ADP
ejpam-5440	105	13	caristi	caristi	PROPN
ejpam-5440	105	14	’s	’s	PART
ejpam-5440	105	15	theorem	theorem	NOUN
ejpam-5440	105	16	as	as	ADP
ejpam-5440	105	17	in	in	ADP
ejpam-5440	105	18	weston	weston	PROPN
ejpam-5440	105	19	(	(	PUNCT
ejpam-5440	105	20	1977	1977	NUM
ejpam-5440	105	21	)	)	PUNCT
ejpam-5440	105	22	.	.	PUNCT
ejpam-5440	106	1	let	let	VERB
ejpam-5440	106	2	a′	a′	NOUN
ejpam-5440	106	3	be	be	AUX
ejpam-5440	106	4	a	a	DET
ejpam-5440	106	5	class	class	NOUN
ejpam-5440	106	6	of	of	ADP
ejpam-5440	106	7	maps	map	NOUN
ejpam-5440	106	8	defined	define	VERB
ejpam-5440	106	9	on	on	ADP
ejpam-5440	106	10	x	x	PUNCT
ejpam-5440	106	11	containing	contain	VERB
ejpam-5440	106	12	b′	b′	NOUN
ejpam-5440	106	13	such	such	ADJ
ejpam-5440	106	14	that	that	SCONJ
ejpam-5440	106	15	completeness	completeness	NOUN
ejpam-5440	106	16	of	of	ADP
ejpam-5440	106	17	x	x	PRON
ejpam-5440	106	18	implies	imply	VERB
ejpam-5440	106	19	that	that	SCONJ
ejpam-5440	106	20	every	every	DET
ejpam-5440	106	21	map	map	NOUN
ejpam-5440	106	22	in	in	ADP
ejpam-5440	106	23	a′	a′	NOUN
ejpam-5440	106	24	satisfies	satisfie	NOUN
ejpam-5440	106	25	a	a	DET
ejpam-5440	106	26	condition	condition	NOUN
ejpam-5440	106	27	p	p	NOUN
ejpam-5440	106	28	,	,	PUNCT
ejpam-5440	106	29	where	where	SCONJ
ejpam-5440	106	30	p	p	NOUN
ejpam-5440	106	31	implies	imply	VERB
ejpam-5440	106	32	q.	q.	PROPN
ejpam-5440	106	33	an	an	DET
ejpam-5440	106	34	example	example	NOUN
ejpam-5440	106	35	of	of	ADP
ejpam-5440	106	36	a′	a′	PROPN
ejpam-5440	106	37	is	be	AUX
ejpam-5440	106	38	the	the	DET
ejpam-5440	106	39	maps	map	NOUN
ejpam-5440	106	40	satisfying	satisfy	VERB
ejpam-5440	106	41	ekeland	ekeland	NOUN
ejpam-5440	106	42	’s	’s	PART
ejpam-5440	106	43	variational	variational	ADJ
ejpam-5440	106	44	principle	principle	NOUN
ejpam-5440	106	45	as	as	ADP
ejpam-5440	106	46	in	in	ADP
ejpam-5440	106	47	sullivan	sullivan	PROPN
ejpam-5440	106	48	(	(	PUNCT
ejpam-5440	106	49	1981	1981	NUM
ejpam-5440	106	50	)	)	PUNCT
ejpam-5440	106	51	.	.	PUNCT
ejpam-5440	107	1	theorem	theorem	VERB
ejpam-5440	107	2	4.2	4.2	NUM
ejpam-5440	107	3	.	.	PUNCT
ejpam-5440	108	1	x	x	PUNCT
ejpam-5440	108	2	is	be	AUX
ejpam-5440	108	3	complete	complete	ADJ
ejpam-5440	108	4	if	if	SCONJ
ejpam-5440	108	5	and	and	CCONJ
ejpam-5440	108	6	only	only	ADV
ejpam-5440	108	7	if	if	SCONJ
ejpam-5440	108	8	every	every	DET
ejpam-5440	108	9	map	map	NOUN
ejpam-5440	108	10	in	in	ADP
ejpam-5440	108	11	a′	a′	NOUN
ejpam-5440	108	12	satisfies	satisfie	NOUN
ejpam-5440	108	13	the	the	DET
ejpam-5440	108	14	condition	condition	NOUN
ejpam-5440	108	15	p.	p.	NOUN
ejpam-5440	108	16	in	in	ADP
ejpam-5440	108	17	mr835839	mr835839	PROPN
ejpam-5440	108	18	(	(	PUNCT
ejpam-5440	108	19	87m:54125	87m:54125	NUM
ejpam-5440	108	20	)	)	PUNCT
ejpam-5440	108	21	,	,	PUNCT
ejpam-5440	108	22	the	the	DET
ejpam-5440	108	23	reviewer	reviewer	NOUN
ejpam-5440	108	24	j.	j.	PROPN
ejpam-5440	108	25	matkowski	matkowski	PROPN
ejpam-5440	108	26	stated	state	VERB
ejpam-5440	108	27	:	:	PUNCT
ejpam-5440	108	28	there	there	PRON
ejpam-5440	108	29	are	be	VERB
ejpam-5440	108	30	many	many	ADJ
ejpam-5440	108	31	papers	paper	NOUN
ejpam-5440	108	32	in	in	ADP
ejpam-5440	108	33	which	which	PRON
ejpam-5440	108	34	the	the	DET
ejpam-5440	108	35	completeness	completeness	NOUN
ejpam-5440	108	36	of	of	ADP
ejpam-5440	108	37	a	a	DET
ejpam-5440	108	38	metric	metric	ADJ
ejpam-5440	108	39	space	space	NOUN
ejpam-5440	108	40	is	be	AUX
ejpam-5440	108	41	characterized	characterize	VERB
ejpam-5440	108	42	by	by	ADP
ejpam-5440	108	43	using	use	VERB
ejpam-5440	108	44	a	a	DET
ejpam-5440	108	45	fixed	fix	VERB
ejpam-5440	108	46	point	point	NOUN
ejpam-5440	108	47	theorem	theorem	VERB
ejpam-5440	108	48	.	.	PUNCT
ejpam-5440	109	1	in	in	ADP
ejpam-5440	109	2	the	the	DET
ejpam-5440	109	3	present	present	ADJ
ejpam-5440	109	4	paper	paper	NOUN
ejpam-5440	109	5	[	[	X
ejpam-5440	109	6	23	23	NUM
ejpam-5440	109	7	]	]	PUNCT
ejpam-5440	109	8	,	,	PUNCT
ejpam-5440	109	9	the	the	DET
ejpam-5440	109	10	authors	author	NOUN
ejpam-5440	109	11	prove	prove	VERB
ejpam-5440	109	12	two	two	NUM
ejpam-5440	109	13	very	very	ADV
ejpam-5440	109	14	simple	simple	ADJ
ejpam-5440	109	15	and	and	CCONJ
ejpam-5440	109	16	general	general	ADJ
ejpam-5440	109	17	theorems	theorem	NOUN
ejpam-5440	109	18	that	that	SCONJ
ejpam-5440	109	19	“	"	PUNCT
ejpam-5440	109	20	encompass	encompass	VERB
ejpam-5440	109	21	some	some	DET
ejpam-5440	109	22	previous	previous	ADJ
ejpam-5440	109	23	as	as	ADV
ejpam-5440	109	24	well	well	ADV
ejpam-5440	109	25	as	as	ADP
ejpam-5440	109	26	future	future	ADJ
ejpam-5440	109	27	theorems	theorem	NOUN
ejpam-5440	109	28	of	of	ADP
ejpam-5440	109	29	this	this	DET
ejpam-5440	109	30	type	type	NOUN
ejpam-5440	109	31	.	.	PUNCT
ejpam-5440	109	32	”	"	PUNCT
ejpam-5440	110	1	in	in	ADP
ejpam-5440	110	2	2020	2020	NUM
ejpam-5440	110	3	,	,	PUNCT
ejpam-5440	110	4	s.	s.	PROPN
ejpam-5440	110	5	cobzaş	cobzaş	PROPN
ejpam-5440	111	1	[	[	X
ejpam-5440	111	2	6	6	NUM
ejpam-5440	111	3	]	]	PUNCT
ejpam-5440	111	4	published	publish	VERB
ejpam-5440	111	5	an	an	DET
ejpam-5440	111	6	article	article	NOUN
ejpam-5440	111	7	entitled	entitle	VERB
ejpam-5440	111	8	“	"	PUNCT
ejpam-5440	111	9	fixed	fix	VERB
ejpam-5440	111	10	points	point	NOUN
ejpam-5440	111	11	and	and	CCONJ
ejpam-5440	111	12	completeness	completeness	NOUN
ejpam-5440	111	13	in	in	ADP
ejpam-5440	111	14	metric	metric	ADJ
ejpam-5440	111	15	and	and	CCONJ
ejpam-5440	111	16	generalized	generalized	ADJ
ejpam-5440	111	17	metric	metric	ADJ
ejpam-5440	111	18	spaces	space	NOUN
ejpam-5440	111	19	”	"	PUNCT
ejpam-5440	111	20	with	with	ADP
ejpam-5440	111	21	the	the	DET
ejpam-5440	111	22	following	following	NOUN
ejpam-5440	111	23	in	in	ADP
ejpam-5440	111	24	abstract	abstract	ADJ
ejpam-5440	111	25	:	:	PUNCT
ejpam-5440	111	26	“	"	PUNCT
ejpam-5440	111	27	the	the	DET
ejpam-5440	111	28	famous	famous	ADJ
ejpam-5440	111	29	banach	banach	NOUN
ejpam-5440	111	30	contraction	contraction	NOUN
ejpam-5440	111	31	principle	principle	NOUN
ejpam-5440	111	32	holds	hold	VERB
ejpam-5440	111	33	in	in	ADP
ejpam-5440	111	34	complete	complete	ADJ
ejpam-5440	111	35	metric	metric	ADJ
ejpam-5440	111	36	spaces	space	NOUN
ejpam-5440	111	37	,	,	PUNCT
ejpam-5440	111	38	but	but	CCONJ
ejpam-5440	111	39	completeness	completeness	NOUN
ejpam-5440	111	40	is	be	AUX
ejpam-5440	111	41	not	not	PART
ejpam-5440	111	42	a	a	DET
ejpam-5440	111	43	necessary	necessary	ADJ
ejpam-5440	111	44	condition	condition	NOUN
ejpam-5440	111	45	:	:	PUNCT
ejpam-5440	111	46	there	there	PRON
ejpam-5440	111	47	are	be	VERB
ejpam-5440	111	48	incomplete	incomplete	ADJ
ejpam-5440	111	49	metric	metric	ADJ
ejpam-5440	111	50	spaces	space	NOUN
ejpam-5440	111	51	on	on	ADP
ejpam-5440	111	52	which	which	PRON
ejpam-5440	111	53	every	every	DET
ejpam-5440	111	54	contraction	contraction	NOUN
ejpam-5440	111	55	has	have	VERB
ejpam-5440	111	56	a	a	DET
ejpam-5440	111	57	fixed	fix	VERB
ejpam-5440	111	58	point	point	NOUN
ejpam-5440	111	59	.	.	PUNCT
ejpam-5440	112	1	the	the	DET
ejpam-5440	112	2	aim	aim	NOUN
ejpam-5440	112	3	of	of	ADP
ejpam-5440	112	4	his	his	PRON
ejpam-5440	112	5	paper	paper	NOUN
ejpam-5440	112	6	[	[	X
ejpam-5440	112	7	6	6	NUM
ejpam-5440	112	8	]	]	PUNCT
ejpam-5440	112	9	is	be	AUX
ejpam-5440	112	10	to	to	PART
ejpam-5440	112	11	present	present	VERB
ejpam-5440	112	12	various	various	ADJ
ejpam-5440	112	13	circumstances	circumstance	NOUN
ejpam-5440	112	14	in	in	ADP
ejpam-5440	112	15	which	which	PRON
ejpam-5440	112	16	fixed	fix	VERB
ejpam-5440	112	17	point	point	NOUN
ejpam-5440	112	18	results	result	NOUN
ejpam-5440	112	19	imply	imply	VERB
ejpam-5440	112	20	completeness	completeness	NOUN
ejpam-5440	112	21	.	.	PUNCT
ejpam-5440	113	1	for	for	ADP
ejpam-5440	113	2	metric	metric	ADJ
ejpam-5440	113	3	spaces	space	NOUN
ejpam-5440	113	4	,	,	PUNCT
ejpam-5440	113	5	this	this	PRON
ejpam-5440	113	6	is	be	AUX
ejpam-5440	113	7	the	the	DET
ejpam-5440	113	8	case	case	NOUN
ejpam-5440	113	9	of	of	ADP
ejpam-5440	113	10	ekeland	ekeland	NOUN
ejpam-5440	113	11	’s	’s	PART
ejpam-5440	113	12	variational	variational	ADJ
ejpam-5440	113	13	principle	principle	NOUN
ejpam-5440	113	14	and	and	CCONJ
ejpam-5440	113	15	of	of	ADP
ejpam-5440	113	16	its	its	PRON
ejpam-5440	113	17	equivalent	equivalent	NOUN
ejpam-5440	113	18	,	,	PUNCT
ejpam-5440	113	19	caristi	caristi	PROPN
ejpam-5440	113	20	’s	’s	PART
ejpam-5440	113	21	fixed	fix	VERB
ejpam-5440	113	22	point	point	NOUN
ejpam-5440	113	23	theorem	theorem	VERB
ejpam-5440	113	24	.	.	PUNCT
ejpam-5440	114	1	other	other	ADJ
ejpam-5440	114	2	fixed	fix	VERB
ejpam-5440	114	3	point	point	NOUN
ejpam-5440	114	4	results	result	NOUN
ejpam-5440	114	5	having	have	VERB
ejpam-5440	114	6	this	this	DET
ejpam-5440	114	7	property	property	NOUN
ejpam-5440	114	8	will	will	AUX
ejpam-5440	114	9	also	also	ADV
ejpam-5440	114	10	be	be	AUX
ejpam-5440	114	11	presented	present	VERB
ejpam-5440	114	12	in	in	ADP
ejpam-5440	114	13	metric	metric	ADJ
ejpam-5440	114	14	spaces	space	NOUN
ejpam-5440	114	15	,	,	PUNCT
ejpam-5440	114	16	in	in	ADP
ejpam-5440	114	17	quasi	quasi	ADJ
ejpam-5440	114	18	-	-	ADJ
ejpam-5440	114	19	metric	metric	ADJ
ejpam-5440	114	20	spaces	space	NOUN
ejpam-5440	114	21	,	,	PUNCT
ejpam-5440	114	22	and	and	CCONJ
ejpam-5440	114	23	in	in	ADP
ejpam-5440	114	24	partial	partial	ADJ
ejpam-5440	114	25	metric	metric	ADJ
ejpam-5440	114	26	spaces	space	NOUN
ejpam-5440	114	27	.	.	PUNCT
ejpam-5440	114	28	”	"	PUNCT
ejpam-5440	115	1	forty	forty	NUM
ejpam-5440	115	2	years	year	NOUN
ejpam-5440	115	3	later	later	ADV
ejpam-5440	115	4	from	from	ADP
ejpam-5440	115	5	[	[	X
ejpam-5440	115	6	13	13	NUM
ejpam-5440	115	7	]	]	PUNCT
ejpam-5440	115	8	,	,	PUNCT
ejpam-5440	115	9	now	now	ADV
ejpam-5440	115	10	we	we	PRON
ejpam-5440	115	11	have	have	VERB
ejpam-5440	115	12	another	another	DET
ejpam-5440	115	13	scores	score	NOUN
ejpam-5440	115	14	of	of	ADP
ejpam-5440	115	15	papers	paper	NOUN
ejpam-5440	115	16	on	on	ADP
ejpam-5440	115	17	the	the	DET
ejpam-5440	115	18	metric	metric	ADJ
ejpam-5440	115	19	completeness	completeness	NOUN
ejpam-5440	115	20	.	.	PUNCT
ejpam-5440	116	1	a	a	DET
ejpam-5440	116	2	relatively	relatively	ADV
ejpam-5440	116	3	new	new	ADJ
ejpam-5440	116	4	ones	one	NOUN
ejpam-5440	116	5	can	can	AUX
ejpam-5440	116	6	be	be	AUX
ejpam-5440	116	7	seen	see	VERB
ejpam-5440	116	8	in	in	ADP
ejpam-5440	116	9	park	park	NOUN
ejpam-5440	116	10	[	[	X
ejpam-5440	116	11	17],[18],[20	17],[18],[20	X
ejpam-5440	116	12	]	]	PUNCT
ejpam-5440	116	13	and	and	CCONJ
ejpam-5440	116	14	others	other	NOUN
ejpam-5440	116	15	,	,	PUNCT
ejpam-5440	116	16	where	where	SCONJ
ejpam-5440	116	17	many	many	ADJ
ejpam-5440	116	18	known	know	VERB
ejpam-5440	116	19	theorems	theorem	NOUN
ejpam-5440	116	20	on	on	ADP
ejpam-5440	116	21	metric	metric	ADJ
ejpam-5440	116	22	spaces	space	NOUN
ejpam-5440	116	23	also	also	ADV
ejpam-5440	116	24	work	work	VERB
ejpam-5440	116	25	on	on	ADP
ejpam-5440	116	26	quasi	quasi	ADJ
ejpam-5440	116	27	-	-	ADJ
ejpam-5440	116	28	metric	metric	ADJ
ejpam-5440	116	29	spaces	space	NOUN
ejpam-5440	116	30	.	.	PUNCT
ejpam-5440	117	1	it	it	PRON
ejpam-5440	117	2	would	would	AUX
ejpam-5440	117	3	be	be	AUX
ejpam-5440	117	4	interesting	interesting	ADJ
ejpam-5440	117	5	whether	whether	SCONJ
ejpam-5440	117	6	any	any	PRON
ejpam-5440	117	7	of	of	ADP
ejpam-5440	117	8	the	the	DET
ejpam-5440	117	9	works	work	NOUN
ejpam-5440	117	10	mentioned	mention	VERB
ejpam-5440	117	11	above	above	ADP
ejpam-5440	117	12	[	[	X
ejpam-5440	117	13	13	13	NUM
ejpam-5440	117	14	]	]	PUNCT
ejpam-5440	117	15	also	also	ADV
ejpam-5440	117	16	hold	hold	VERB
ejpam-5440	117	17	for	for	ADP
ejpam-5440	117	18	quasi	quasi	ADJ
ejpam-5440	117	19	-	-	ADJ
ejpam-5440	117	20	metric	metric	ADJ
ejpam-5440	117	21	spaces	space	NOUN
ejpam-5440	117	22	.	.	PUNCT
ejpam-5440	118	1	the	the	DET
ejpam-5440	118	2	family	family	NOUN
ejpam-5440	118	3	(	(	PUNCT
ejpam-5440	118	4	0	0	NUM
ejpam-5440	118	5	)	)	PUNCT
ejpam-5440	118	6	consists	consist	VERB
ejpam-5440	118	7	of	of	ADP
ejpam-5440	118	8	theorems	theorem	NOUN
ejpam-5440	118	9	on	on	ADP
ejpam-5440	118	10	completeness	completeness	NOUN
ejpam-5440	118	11	of	of	ADP
ejpam-5440	118	12	quasi	quasi	ADJ
ejpam-5440	118	13	-	-	ADJ
ejpam-5440	118	14	metric	metric	ADJ
ejpam-5440	118	15	spaces	space	NOUN
ejpam-5440	118	16	.	.	PUNCT
ejpam-5440	119	1	of	of	ADP
ejpam-5440	119	2	course	course	ADV
ejpam-5440	119	3	,	,	PUNCT
ejpam-5440	119	4	it	it	PRON
ejpam-5440	119	5	has	have	VERB
ejpam-5440	119	6	a	a	DET
ejpam-5440	119	7	large	large	ADJ
ejpam-5440	119	8	number	number	NOUN
ejpam-5440	119	9	of	of	ADP
ejpam-5440	119	10	theorems	theorem	NOUN
ejpam-5440	119	11	containing	contain	VERB
ejpam-5440	119	12	(	(	PUNCT
ejpam-5440	119	13	α)−	α)−	PROPN
ejpam-5440	119	14	(	(	PUNCT
ejpam-5440	119	15	η	η	NOUN
ejpam-5440	119	16	)	)	PUNCT
ejpam-5440	119	17	and	and	CCONJ
ejpam-5440	119	18	others	other	NOUN
ejpam-5440	119	19	.	.	PUNCT
ejpam-5440	120	1	in	in	ADP
ejpam-5440	120	2	the	the	DET
ejpam-5440	120	3	present	present	ADJ
ejpam-5440	120	4	article	article	NOUN
ejpam-5440	120	5	,	,	PUNCT
ejpam-5440	120	6	we	we	PRON
ejpam-5440	120	7	do	do	AUX
ejpam-5440	120	8	not	not	PART
ejpam-5440	120	9	try	try	VERB
ejpam-5440	120	10	to	to	PART
ejpam-5440	120	11	collect	collect	VERB
ejpam-5440	120	12	all	all	DET
ejpam-5440	120	13	theorems	theorem	NOUN
ejpam-5440	120	14	in	in	ADP
ejpam-5440	120	15	the	the	DET
ejpam-5440	120	16	family	family	NOUN
ejpam-5440	120	17	(	(	PUNCT
ejpam-5440	120	18	0	0	NUM
ejpam-5440	120	19	)	)	PUNCT
ejpam-5440	120	20	.	.	PUNCT
ejpam-5440	121	1	even	even	ADV
ejpam-5440	121	2	for	for	ADP
ejpam-5440	121	3	the	the	DET
ejpam-5440	121	4	subfamilies	subfamily	NOUN
ejpam-5440	121	5	(	(	PUNCT
ejpam-5440	121	6	α	α	NOUN
ejpam-5440	121	7	)	)	PUNCT
ejpam-5440	121	8	−	−	PROPN
ejpam-5440	121	9	(	(	PUNCT
ejpam-5440	121	10	η	η	PROPN
ejpam-5440	121	11	)	)	PUNCT
ejpam-5440	121	12	,	,	PUNCT
ejpam-5440	121	13	we	we	PRON
ejpam-5440	121	14	consider	consider	VERB
ejpam-5440	121	15	only	only	ADV
ejpam-5440	121	16	theorems	theorem	NOUN
ejpam-5440	121	17	closely	closely	ADV
ejpam-5440	121	18	related	relate	VERB
ejpam-5440	121	19	our	our	PRON
ejpam-5440	121	20	metatheorem	metatheorem	ADJ
ejpam-5440	121	21	or	or	CCONJ
ejpam-5440	121	22	theorem	theorem	VERB
ejpam-5440	121	23	h.	h.	PROPN
ejpam-5440	121	24	s.	s.	PROPN
ejpam-5440	121	25	park	park	PROPN
ejpam-5440	121	26	/	/	SYM
ejpam-5440	121	27	eur	eur	PROPN
ejpam-5440	121	28	.	.	PUNCT
ejpam-5440	122	1	j.	j.	PROPN
ejpam-5440	122	2	pure	pure	PROPN
ejpam-5440	122	3	appl	appl	PROPN
ejpam-5440	122	4	.	.	PROPN
ejpam-5440	122	5	math	math	PROPN
ejpam-5440	122	6	,	,	PUNCT
ejpam-5440	122	7	17	17	NUM
ejpam-5440	122	8	(	(	PUNCT
ejpam-5440	122	9	4	4	NUM
ejpam-5440	122	10	)	)	PUNCT
ejpam-5440	122	11	(	(	PUNCT
ejpam-5440	122	12	2024	2024	NUM
ejpam-5440	122	13	)	)	PUNCT
ejpam-5440	122	14	,	,	PUNCT
ejpam-5440	122	15	2370	2370	NUM
ejpam-5440	122	16	-	-	SYM
ejpam-5440	122	17	2383	2383	NUM
ejpam-5440	122	18	2375	2375	NUM
ejpam-5440	122	19	5	5	NUM
ejpam-5440	122	20	.	.	PUNCT
ejpam-5440	123	1	the	the	DET
ejpam-5440	123	2	subfamily	subfamily	ADV
ejpam-5440	123	3	(	(	PUNCT
ejpam-5440	123	4	α	α	X
ejpam-5440	123	5	)	)	PUNCT
ejpam-5440	123	6	the	the	DET
ejpam-5440	123	7	case	case	NOUN
ejpam-5440	123	8	(	(	PUNCT
ejpam-5440	123	9	α	α	NOUN
ejpam-5440	123	10	)	)	PUNCT
ejpam-5440	123	11	implies	imply	VERB
ejpam-5440	123	12	the	the	DET
ejpam-5440	123	13	following	following	NOUN
ejpam-5440	123	14	:	:	PUNCT
ejpam-5440	123	15	theorem	theorem	VERB
ejpam-5440	123	16	5.1	5.1	NUM
ejpam-5440	123	17	.	.	PUNCT
ejpam-5440	124	1	for	for	ADP
ejpam-5440	124	2	a	a	DET
ejpam-5440	124	3	quasi	quasi	ADJ
ejpam-5440	124	4	-	-	ADJ
ejpam-5440	124	5	metric	metric	ADJ
ejpam-5440	124	6	space	space	NOUN
ejpam-5440	124	7	(	(	PUNCT
ejpam-5440	124	8	x	x	X
ejpam-5440	124	9	,	,	PUNCT
ejpam-5440	124	10	q	q	NOUN
ejpam-5440	124	11	)	)	PUNCT
ejpam-5440	124	12	,	,	PUNCT
ejpam-5440	124	13	the	the	DET
ejpam-5440	124	14	following	follow	VERB
ejpam-5440	124	15	are	be	AUX
ejpam-5440	124	16	equivalent	equivalent	ADJ
ejpam-5440	124	17	:	:	PUNCT
ejpam-5440	124	18	(	(	PUNCT
ejpam-5440	124	19	0	0	NUM
ejpam-5440	124	20	)	)	PUNCT
ejpam-5440	124	21	(	(	PUNCT
ejpam-5440	124	22	x	x	X
ejpam-5440	124	23	,	,	PUNCT
ejpam-5440	124	24	q	q	X
ejpam-5440	124	25	)	)	PUNCT
ejpam-5440	124	26	is	be	AUX
ejpam-5440	124	27	complete	complete	ADJ
ejpam-5440	124	28	.	.	PUNCT
ejpam-5440	125	1	(	(	PUNCT
ejpam-5440	125	2	α1	α1	PROPN
ejpam-5440	125	3	)	)	PUNCT
ejpam-5440	125	4	for	for	ADP
ejpam-5440	125	5	a	a	DET
ejpam-5440	125	6	map	map	NOUN
ejpam-5440	126	1	f	f	NOUN
ejpam-5440	126	2	:	:	PUNCT
ejpam-5440	126	3	x	x	X
ejpam-5440	126	4	→	→	SYM
ejpam-5440	126	5	x	x	X
ejpam-5440	126	6	,	,	PUNCT
ejpam-5440	126	7	there	there	PRON
ejpam-5440	126	8	exists	exist	VERB
ejpam-5440	126	9	an	an	DET
ejpam-5440	126	10	element	element	NOUN
ejpam-5440	126	11	v	v	ADP
ejpam-5440	126	12	∈	∈	PROPN
ejpam-5440	126	13	x	x	PUNCT
ejpam-5440	126	14	such	such	ADJ
ejpam-5440	126	15	that	that	DET
ejpam-5440	126	16	q(f(v	q(f(v	NOUN
ejpam-5440	126	17	)	)	PUNCT
ejpam-5440	126	18	,	,	PUNCT
ejpam-5440	126	19	f(w	f(w	PROPN
ejpam-5440	126	20	)	)	PUNCT
ejpam-5440	126	21	)	)	PUNCT
ejpam-5440	126	22	>	>	X
ejpam-5440	127	1	αq(v	αq(v	X
ejpam-5440	127	2	,	,	PUNCT
ejpam-5440	127	3	w	w	NOUN
ejpam-5440	127	4	)	)	PUNCT
ejpam-5440	127	5	for	for	ADP
ejpam-5440	127	6	any	any	DET
ejpam-5440	127	7	w	w	PROPN
ejpam-5440	127	8	∈	∈	PROPN
ejpam-5440	127	9	x\{v	x\{v	PROPN
ejpam-5440	127	10	}	}	PUNCT
ejpam-5440	127	11	.	.	PUNCT
ejpam-5440	128	1	(	(	PUNCT
ejpam-5440	128	2	α	α	X
ejpam-5440	128	3	)	)	PUNCT
ejpam-5440	128	4	for	for	ADP
ejpam-5440	128	5	a	a	DET
ejpam-5440	128	6	multimap	multimap	NOUN
ejpam-5440	128	7	t	t	NOUN
ejpam-5440	128	8	:	:	PUNCT
ejpam-5440	128	9	x	x	X
ejpam-5440	128	10	→	→	SYM
ejpam-5440	128	11	cl(x	cl(x	NOUN
ejpam-5440	128	12	)	)	PUNCT
ejpam-5440	128	13	,	,	PUNCT
ejpam-5440	128	14	there	there	PRON
ejpam-5440	128	15	exists	exist	VERB
ejpam-5440	128	16	an	an	DET
ejpam-5440	128	17	element	element	NOUN
ejpam-5440	128	18	v	v	ADP
ejpam-5440	128	19	∈	∈	PROPN
ejpam-5440	128	20	x	x	PUNCT
ejpam-5440	128	21	such	such	ADJ
ejpam-5440	128	22	that	that	SCONJ
ejpam-5440	128	23	h(t	h(t	PROPN
ejpam-5440	128	24	(	(	PUNCT
ejpam-5440	128	25	v	v	NOUN
ejpam-5440	128	26	)	)	PUNCT
ejpam-5440	128	27	,	,	PUNCT
ejpam-5440	128	28	t	t	PROPN
ejpam-5440	128	29	(	(	PUNCT
ejpam-5440	128	30	w	w	NOUN
ejpam-5440	128	31	)	)	PUNCT
ejpam-5440	128	32	)	)	PUNCT
ejpam-5440	128	33	>	>	X
ejpam-5440	129	1	αq(v	αq(v	X
ejpam-5440	129	2	,	,	PUNCT
ejpam-5440	129	3	w	w	NOUN
ejpam-5440	129	4	)	)	PUNCT
ejpam-5440	129	5	for	for	ADP
ejpam-5440	129	6	any	any	DET
ejpam-5440	129	7	w	w	PROPN
ejpam-5440	129	8	∈	∈	PROPN
ejpam-5440	129	9	x\{v	x\{v	PROPN
ejpam-5440	129	10	}	}	PUNCT
ejpam-5440	129	11	.	.	PUNCT
ejpam-5440	130	1	as	as	SCONJ
ejpam-5440	130	2	we	we	PRON
ejpam-5440	130	3	have	have	AUX
ejpam-5440	130	4	shown	show	VERB
ejpam-5440	130	5	in	in	ADP
ejpam-5440	130	6	our	our	PRON
ejpam-5440	130	7	earlier	early	ADJ
ejpam-5440	130	8	paper	paper	NOUN
ejpam-5440	130	9	[	[	X
ejpam-5440	130	10	13	13	NUM
ejpam-5440	130	11	]	]	PUNCT
ejpam-5440	130	12	in	in	ADP
ejpam-5440	130	13	1984	1984	NUM
ejpam-5440	130	14	,	,	PUNCT
ejpam-5440	130	15	many	many	ADJ
ejpam-5440	130	16	known	know	VERB
ejpam-5440	130	17	theorems	theorem	NOUN
ejpam-5440	130	18	belong	belong	VERB
ejpam-5440	130	19	to	to	ADP
ejpam-5440	130	20	the	the	DET
ejpam-5440	130	21	subfamily	subfamily	NOUN
ejpam-5440	130	22	(	(	PUNCT
ejpam-5440	130	23	α	α	NOUN
ejpam-5440	130	24	)	)	PUNCT
ejpam-5440	130	25	.	.	PUNCT
ejpam-5440	131	1	6	6	X
ejpam-5440	131	2	.	.	X
ejpam-5440	131	3	the	the	DET
ejpam-5440	131	4	subfamily	subfamily	ADV
ejpam-5440	131	5	(	(	PUNCT
ejpam-5440	131	6	β	β	NOUN
ejpam-5440	131	7	)	)	PUNCT
ejpam-5440	131	8	in	in	ADP
ejpam-5440	131	9	theorem	theorem	ADJ
ejpam-5440	131	10	h	h	NOUN
ejpam-5440	131	11	,	,	PUNCT
ejpam-5440	131	12	consider	consider	VERB
ejpam-5440	131	13	the	the	DET
ejpam-5440	131	14	following	following	NOUN
ejpam-5440	131	15	:	:	PUNCT
ejpam-5440	131	16	(	(	PUNCT
ejpam-5440	131	17	β	β	X
ejpam-5440	131	18	)	)	PUNCT
ejpam-5440	131	19	if	if	SCONJ
ejpam-5440	131	20	f	f	PROPN
ejpam-5440	131	21	is	be	AUX
ejpam-5440	131	22	a	a	DET
ejpam-5440	131	23	family	family	NOUN
ejpam-5440	131	24	of	of	ADP
ejpam-5440	131	25	maps	map	NOUN
ejpam-5440	131	26	f	f	X
ejpam-5440	131	27	:	:	PUNCT
ejpam-5440	131	28	x	x	X
ejpam-5440	131	29	→	→	PUNCT
ejpam-5440	131	30	x	x	X
ejpam-5440	131	31	such	such	ADJ
ejpam-5440	131	32	that	that	SCONJ
ejpam-5440	131	33	,	,	PUNCT
ejpam-5440	131	34	for	for	ADP
ejpam-5440	131	35	any	any	DET
ejpam-5440	131	36	x	x	PROPN
ejpam-5440	131	37	∈	∈	PROPN
ejpam-5440	131	38	x\{f(x	x\{f(x	PROPN
ejpam-5440	131	39	)	)	PUNCT
ejpam-5440	131	40	}	}	PUNCT
ejpam-5440	131	41	,	,	PUNCT
ejpam-5440	131	42	there	there	PRON
ejpam-5440	131	43	exists	exist	VERB
ejpam-5440	131	44	a	a	DET
ejpam-5440	131	45	y	y	PROPN
ejpam-5440	131	46	∈	∈	PROPN
ejpam-5440	131	47	x\{x	x\{x	AUX
ejpam-5440	131	48	}	}	PUNCT
ejpam-5440	131	49	satisfying	satisfy	VERB
ejpam-5440	131	50	q(f(x	q(f(x	PROPN
ejpam-5440	131	51	)	)	PUNCT
ejpam-5440	131	52	,	,	PUNCT
ejpam-5440	131	53	f(y	f(y	NOUN
ejpam-5440	131	54	)	)	PUNCT
ejpam-5440	131	55	)	)	PUNCT
ejpam-5440	131	56	≤	≤	NUM
ejpam-5440	131	57	α	α	PROPN
ejpam-5440	131	58	q(x	q(x	PROPN
ejpam-5440	131	59	,	,	PUNCT
ejpam-5440	131	60	y	y	PROPN
ejpam-5440	131	61	)	)	PUNCT
ejpam-5440	131	62	,	,	PUNCT
ejpam-5440	131	63	then	then	ADV
ejpam-5440	131	64	f	f	PROPN
ejpam-5440	131	65	has	have	VERB
ejpam-5440	131	66	a	a	DET
ejpam-5440	131	67	common	common	ADJ
ejpam-5440	131	68	fixed	fix	VERB
ejpam-5440	131	69	element	element	NOUN
ejpam-5440	131	70	v	v	ADP
ejpam-5440	131	71	∈	∈	PROPN
ejpam-5440	131	72	x	x	NOUN
ejpam-5440	131	73	,	,	PUNCT
ejpam-5440	131	74	that	that	ADV
ejpam-5440	131	75	is	is	ADV
ejpam-5440	131	76	,	,	PUNCT
ejpam-5440	131	77	v	v	NOUN
ejpam-5440	131	78	=	=	PUNCT
ejpam-5440	131	79	f(v	f(v	NOUN
ejpam-5440	131	80	)	)	PUNCT
ejpam-5440	131	81	for	for	ADP
ejpam-5440	131	82	all	all	DET
ejpam-5440	131	83	f	f	PROPN
ejpam-5440	131	84	∈	∈	PROPN
ejpam-5440	131	85	f.	f.	PROPN
ejpam-5440	131	86	note	note	VERB
ejpam-5440	131	87	that	that	SCONJ
ejpam-5440	131	88	the	the	DET
ejpam-5440	131	89	f	f	PROPN
ejpam-5440	131	90	-orbital	-orbital	PROPN
ejpam-5440	131	91	completeness	completeness	NOUN
ejpam-5440	131	92	of	of	ADP
ejpam-5440	131	93	(	(	PUNCT
ejpam-5440	131	94	x	x	NOUN
ejpam-5440	131	95	,	,	PUNCT
ejpam-5440	131	96	q	q	NOUN
ejpam-5440	131	97	)	)	PUNCT
ejpam-5440	131	98	for	for	ADP
ejpam-5440	131	99	any	any	DET
ejpam-5440	131	100	map	map	NOUN
ejpam-5440	132	1	f	f	NOUN
ejpam-5440	132	2	:	:	PUNCT
ejpam-5440	132	3	x	x	SYM
ejpam-5440	132	4	→	→	SYM
ejpam-5440	132	5	x	x	X
ejpam-5440	132	6	in	in	ADP
ejpam-5440	132	7	f	f	PROPN
ejpam-5440	132	8	implies	imply	VERB
ejpam-5440	132	9	(	(	PUNCT
ejpam-5440	132	10	β	β	NOUN
ejpam-5440	132	11	)	)	PUNCT
ejpam-5440	132	12	.	.	PUNCT
ejpam-5440	133	1	from	from	ADP
ejpam-5440	133	2	(	(	PUNCT
ejpam-5440	133	3	β	β	NOUN
ejpam-5440	133	4	)	)	PUNCT
ejpam-5440	133	5	,	,	PUNCT
ejpam-5440	133	6	we	we	PRON
ejpam-5440	133	7	obtain	obtain	VERB
ejpam-5440	133	8	the	the	DET
ejpam-5440	133	9	following	follow	VERB
ejpam-5440	133	10	consequence	consequence	NOUN
ejpam-5440	133	11	of	of	ADP
ejpam-5440	133	12	theorem	theorem	NOUN
ejpam-5440	133	13	p	p	PROPN
ejpam-5440	133	14	in	in	ADP
ejpam-5440	133	15	park	park	NOUN
ejpam-5440	133	16	[	[	X
ejpam-5440	133	17	16]-[19	16]-[19	X
ejpam-5440	133	18	]	]	X
ejpam-5440	133	19	,	,	PUNCT
ejpam-5440	133	20	[	[	X
ejpam-5440	133	21	21	21	NUM
ejpam-5440	133	22	]	]	X
ejpam-5440	133	23	(	(	PUNCT
ejpam-5440	133	24	or	or	CCONJ
ejpam-5440	133	25	in	in	ADP
ejpam-5440	133	26	the	the	DET
ejpam-5440	133	27	next	next	ADJ
ejpam-5440	133	28	section	section	NOUN
ejpam-5440	133	29	)	)	PUNCT
ejpam-5440	133	30	,	,	PUNCT
ejpam-5440	133	31	the	the	DET
ejpam-5440	133	32	generalized	generalized	ADJ
ejpam-5440	133	33	banach	banach	NOUN
ejpam-5440	133	34	contraction	contraction	NOUN
ejpam-5440	133	35	principle	principle	NOUN
ejpam-5440	133	36	:	:	PUNCT
ejpam-5440	133	37	theorem	theorem	ADJ
ejpam-5440	133	38	q.	q.	PROPN
ejpam-5440	133	39	let	let	VERB
ejpam-5440	133	40	(	(	PUNCT
ejpam-5440	133	41	x	x	NOUN
ejpam-5440	133	42	,	,	PUNCT
ejpam-5440	133	43	q	q	X
ejpam-5440	133	44	)	)	PUNCT
ejpam-5440	133	45	be	be	AUX
ejpam-5440	133	46	a	a	DET
ejpam-5440	133	47	quasi	quasi	ADJ
ejpam-5440	133	48	-	-	ADJ
ejpam-5440	133	49	metric	metric	ADJ
ejpam-5440	133	50	space	space	NOUN
ejpam-5440	133	51	and	and	CCONJ
ejpam-5440	133	52	let	let	VERB
ejpam-5440	133	53	t	t	NOUN
ejpam-5440	133	54	:	:	PUNCT
ejpam-5440	133	55	x	x	X
ejpam-5440	133	56	→	→	PUNCT
ejpam-5440	133	57	x	x	PUNCT
ejpam-5440	133	58	be	be	AUX
ejpam-5440	133	59	a	a	DET
ejpam-5440	133	60	generalized	generalized	ADJ
ejpam-5440	133	61	banach	banach	NOUN
ejpam-5440	133	62	contraction	contraction	NOUN
ejpam-5440	133	63	,	,	PUNCT
ejpam-5440	133	64	that	that	ADV
ejpam-5440	133	65	is	is	ADV
ejpam-5440	133	66	,	,	PUNCT
ejpam-5440	133	67	for	for	ADP
ejpam-5440	133	68	each	each	DET
ejpam-5440	133	69	x	x	SYM
ejpam-5440	133	70	∈	∈	PROPN
ejpam-5440	133	71	x	x	X
ejpam-5440	133	72	,	,	PUNCT
ejpam-5440	133	73	there	there	PRON
ejpam-5440	133	74	exists	exist	VERB
ejpam-5440	133	75	a	a	DET
ejpam-5440	133	76	y	y	PROPN
ejpam-5440	133	77	∈	∈	PROPN
ejpam-5440	133	78	x\{x	x\{x	PROPN
ejpam-5440	133	79	}	}	PUNCT
ejpam-5440	133	80	such	such	ADJ
ejpam-5440	133	81	that	that	SCONJ
ejpam-5440	133	82	q(t	q(t	PROPN
ejpam-5440	133	83	(	(	PUNCT
ejpam-5440	133	84	x	x	NOUN
ejpam-5440	133	85	)	)	PUNCT
ejpam-5440	133	86	,	,	PUNCT
ejpam-5440	133	87	t	t	PROPN
ejpam-5440	133	88	(	(	PUNCT
ejpam-5440	133	89	y	y	NOUN
ejpam-5440	133	90	)	)	PUNCT
ejpam-5440	133	91	)	)	PUNCT
ejpam-5440	133	92	≤	≤	NUM
ejpam-5440	133	93	α	α	PROPN
ejpam-5440	133	94	q(x	q(x	PROPN
ejpam-5440	133	95	,	,	PUNCT
ejpam-5440	133	96	y	y	NOUN
ejpam-5440	133	97	)	)	PUNCT
ejpam-5440	133	98	where	where	SCONJ
ejpam-5440	133	99	0	0	NUM
ejpam-5440	133	100	<	<	X
ejpam-5440	133	101	α	α	X
ejpam-5440	133	102	<	<	X
ejpam-5440	133	103	1	1	NUM
ejpam-5440	133	104	.	.	PUNCT
ejpam-5440	134	1	(	(	PUNCT
ejpam-5440	134	2	q	q	X
ejpam-5440	134	3	)	)	PUNCT
ejpam-5440	134	4	(	(	PUNCT
ejpam-5440	134	5	i	i	NOUN
ejpam-5440	134	6	)	)	PUNCT
ejpam-5440	134	7	if	if	SCONJ
ejpam-5440	134	8	x	x	PRON
ejpam-5440	134	9	is	be	AUX
ejpam-5440	134	10	t	t	NOUN
ejpam-5440	134	11	-orbitally	-orbitally	ADV
ejpam-5440	134	12	complete	complete	ADJ
ejpam-5440	134	13	,	,	PUNCT
ejpam-5440	134	14	then	then	ADV
ejpam-5440	134	15	,	,	PUNCT
ejpam-5440	134	16	for	for	ADP
ejpam-5440	134	17	each	each	DET
ejpam-5440	134	18	x	x	SYM
ejpam-5440	134	19	∈	∈	PROPN
ejpam-5440	134	20	x	x	X
ejpam-5440	134	21	,	,	PUNCT
ejpam-5440	134	22	there	there	PRON
ejpam-5440	134	23	exists	exist	VERB
ejpam-5440	134	24	a	a	DET
ejpam-5440	134	25	point	point	NOUN
ejpam-5440	134	26	x0	x0	PROPN
ejpam-5440	134	27	∈	∈	PROPN
ejpam-5440	134	28	x	x	PUNCT
ejpam-5440	134	29	such	such	ADJ
ejpam-5440	134	30	that	that	SCONJ
ejpam-5440	134	31	lim	lim	PROPN
ejpam-5440	134	32	n→∞	n→∞	X
ejpam-5440	134	33	tn(x	tn(x	PUNCT
ejpam-5440	134	34	)	)	PUNCT
ejpam-5440	135	1	=	=	SYM
ejpam-5440	135	2	x0	x0	PROPN
ejpam-5440	135	3	and	and	CCONJ
ejpam-5440	135	4	q(tn(x	q(tn(x	PROPN
ejpam-5440	135	5	)	)	PUNCT
ejpam-5440	135	6	,	,	PUNCT
ejpam-5440	135	7	x0	x0	PROPN
ejpam-5440	135	8	)	)	PUNCT
ejpam-5440	135	9	≤	≤	NUM
ejpam-5440	135	10	αn	αn	NOUN
ejpam-5440	135	11	1−	1−	NUM
ejpam-5440	135	12	α	α	PROPN
ejpam-5440	135	13	q(x	q(x	PROPN
ejpam-5440	135	14	,	,	PUNCT
ejpam-5440	135	15	t	t	PROPN
ejpam-5440	135	16	(	(	PUNCT
ejpam-5440	135	17	x	x	NOUN
ejpam-5440	135	18	)	)	PUNCT
ejpam-5440	135	19	)	)	PUNCT
ejpam-5440	135	20	,	,	PUNCT
ejpam-5440	135	21	n	n	NOUN
ejpam-5440	135	22	=	=	SYM
ejpam-5440	135	23	1	1	NUM
ejpam-5440	135	24	,	,	PUNCT
ejpam-5440	135	25	2	2	NUM
ejpam-5440	135	26	,	,	PUNCT
ejpam-5440	135	27	·	·	PUNCT
ejpam-5440	135	28	·	·	PUNCT
ejpam-5440	135	29	·	·	PUNCT
ejpam-5440	135	30	,	,	PUNCT
ejpam-5440	135	31	q(tn(x	q(tn(x	PROPN
ejpam-5440	135	32	)	)	PUNCT
ejpam-5440	135	33	,	,	PUNCT
ejpam-5440	135	34	x0	x0	PROPN
ejpam-5440	135	35	)	)	PUNCT
ejpam-5440	135	36	≤	≤	PUNCT
ejpam-5440	136	1	α	α	PRON
ejpam-5440	136	2	1−	1−	NUM
ejpam-5440	136	3	α	α	DET
ejpam-5440	136	4	q(tn−1(x	q(tn−1(x	NOUN
ejpam-5440	136	5	)	)	PUNCT
ejpam-5440	136	6	,	,	PUNCT
ejpam-5440	136	7	tn(x	tn(x	NOUN
ejpam-5440	136	8	)	)	PUNCT
ejpam-5440	136	9	)	)	PUNCT
ejpam-5440	136	10	,	,	PUNCT
ejpam-5440	136	11	n	n	NOUN
ejpam-5440	136	12	=	=	SYM
ejpam-5440	136	13	1	1	NUM
ejpam-5440	136	14	,	,	PUNCT
ejpam-5440	136	15	2	2	NUM
ejpam-5440	136	16	,	,	PUNCT
ejpam-5440	136	17	·	·	PUNCT
ejpam-5440	136	18	·	·	PUNCT
ejpam-5440	136	19	·	·	PUNCT
ejpam-5440	136	20	.	.	PUNCT
ejpam-5440	137	1	(	(	PUNCT
ejpam-5440	137	2	ii	ii	NOUN
ejpam-5440	137	3	)	)	PUNCT
ejpam-5440	137	4	x0	x0	PROPN
ejpam-5440	137	5	is	be	AUX
ejpam-5440	137	6	the	the	DET
ejpam-5440	137	7	unique	unique	ADJ
ejpam-5440	137	8	fixed	fix	VERB
ejpam-5440	137	9	point	point	NOUN
ejpam-5440	137	10	of	of	ADP
ejpam-5440	137	11	t	t	PROPN
ejpam-5440	137	12	(	(	PUNCT
ejpam-5440	137	13	equivalently	equivalently	ADV
ejpam-5440	137	14	,	,	PUNCT
ejpam-5440	137	15	t	t	X
ejpam-5440	137	16	:	:	PUNCT
ejpam-5440	137	17	x	x	X
ejpam-5440	137	18	→	→	PUNCT
ejpam-5440	137	19	x	x	X
ejpam-5440	137	20	is	be	AUX
ejpam-5440	137	21	orbitally	orbitally	ADV
ejpam-5440	137	22	continuous	continuous	ADJ
ejpam-5440	137	23	at	at	ADP
ejpam-5440	137	24	x0	x0	PROPN
ejpam-5440	137	25	∈	∈	PROPN
ejpam-5440	137	26	x	x	NOUN
ejpam-5440	137	27	)	)	PUNCT
ejpam-5440	137	28	.	.	PUNCT
ejpam-5440	138	1	theorem	theorem	NOUN
ejpam-5440	138	2	q	q	PUNCT
ejpam-5440	138	3	extends	extend	VERB
ejpam-5440	138	4	a	a	DET
ejpam-5440	138	5	part	part	NOUN
ejpam-5440	138	6	of	of	ADP
ejpam-5440	138	7	the	the	DET
ejpam-5440	138	8	following	follow	VERB
ejpam-5440	138	9	theorem	theorem	ADJ
ejpam-5440	138	10	h(0	h(0	PROPN
ejpam-5440	138	11	)	)	PUNCT
ejpam-5440	138	12	⇐	⇐	ADJ
ejpam-5440	138	13	⇒	⇒	NOUN
ejpam-5440	138	14	(	(	PUNCT
ejpam-5440	138	15	β1	β1	PROPN
ejpam-5440	138	16	):	):	PUNCT
ejpam-5440	138	17	s.	s.	PROPN
ejpam-5440	138	18	park	park	PROPN
ejpam-5440	138	19	/	/	SYM
ejpam-5440	138	20	eur	eur	PROPN
ejpam-5440	138	21	.	.	PUNCT
ejpam-5440	139	1	j.	j.	PROPN
ejpam-5440	139	2	pure	pure	PROPN
ejpam-5440	139	3	appl	appl	PROPN
ejpam-5440	139	4	.	.	PROPN
ejpam-5440	139	5	math	math	PROPN
ejpam-5440	139	6	,	,	PUNCT
ejpam-5440	139	7	17	17	NUM
ejpam-5440	139	8	(	(	PUNCT
ejpam-5440	139	9	4	4	NUM
ejpam-5440	139	10	)	)	PUNCT
ejpam-5440	139	11	(	(	PUNCT
ejpam-5440	139	12	2024	2024	NUM
ejpam-5440	139	13	)	)	PUNCT
ejpam-5440	139	14	,	,	PUNCT
ejpam-5440	139	15	2370	2370	NUM
ejpam-5440	139	16	-	-	SYM
ejpam-5440	139	17	2383	2383	NUM
ejpam-5440	139	18	2376	2376	NUM
ejpam-5440	139	19	theorem	theorem	VERB
ejpam-5440	139	20	6.1	6.1	NUM
ejpam-5440	139	21	.	.	PUNCT
ejpam-5440	140	1	let	let	AUX
ejpam-5440	140	2	(	(	PUNCT
ejpam-5440	140	3	x	x	NOUN
ejpam-5440	140	4	,	,	PUNCT
ejpam-5440	140	5	q	q	X
ejpam-5440	140	6	)	)	PUNCT
ejpam-5440	140	7	be	be	AUX
ejpam-5440	140	8	a	a	DET
ejpam-5440	140	9	quasi	quasi	ADJ
ejpam-5440	140	10	-	-	ADJ
ejpam-5440	140	11	metric	metric	ADJ
ejpam-5440	140	12	space	space	NOUN
ejpam-5440	140	13	.	.	PUNCT
ejpam-5440	141	1	then	then	ADV
ejpam-5440	141	2	it	it	PRON
ejpam-5440	141	3	is	be	AUX
ejpam-5440	141	4	complete	complete	ADJ
ejpam-5440	141	5	if	if	SCONJ
ejpam-5440	142	1	and	and	CCONJ
ejpam-5440	142	2	only	only	ADV
ejpam-5440	142	3	if	if	SCONJ
ejpam-5440	142	4	(	(	PUNCT
ejpam-5440	142	5	β1	β1	PROPN
ejpam-5440	142	6	)	)	PUNCT
ejpam-5440	142	7	let	let	VERB
ejpam-5440	142	8	f	f	NOUN
ejpam-5440	142	9	:	:	PUNCT
ejpam-5440	142	10	x	x	X
ejpam-5440	142	11	→	→	PUNCT
ejpam-5440	142	12	x	x	PUNCT
ejpam-5440	142	13	be	be	AUX
ejpam-5440	142	14	a	a	DET
ejpam-5440	142	15	map	map	NOUN
ejpam-5440	142	16	such	such	ADJ
ejpam-5440	142	17	that	that	SCONJ
ejpam-5440	142	18	,	,	PUNCT
ejpam-5440	142	19	for	for	ADP
ejpam-5440	142	20	any	any	DET
ejpam-5440	142	21	x	x	PROPN
ejpam-5440	142	22	∈	∈	PROPN
ejpam-5440	142	23	x\{f(x	x\{f(x	PROPN
ejpam-5440	142	24	)	)	PUNCT
ejpam-5440	142	25	}	}	PUNCT
ejpam-5440	142	26	,	,	PUNCT
ejpam-5440	142	27	there	there	PRON
ejpam-5440	142	28	exists	exist	VERB
ejpam-5440	142	29	y	y	PROPN
ejpam-5440	142	30	∈	∈	PROPN
ejpam-5440	142	31	x\{x	x\{x	PROPN
ejpam-5440	142	32	}	}	PUNCT
ejpam-5440	142	33	satisfying	satisfy	VERB
ejpam-5440	142	34	q(f(x	q(f(x	PROPN
ejpam-5440	142	35	)	)	PUNCT
ejpam-5440	142	36	,	,	PUNCT
ejpam-5440	142	37	f(y	f(y	NOUN
ejpam-5440	142	38	)	)	PUNCT
ejpam-5440	142	39	)	)	PUNCT
ejpam-5440	142	40	≤	≤	NUM
ejpam-5440	142	41	α	α	PROPN
ejpam-5440	142	42	q(x	q(x	PROPN
ejpam-5440	142	43	,	,	PUNCT
ejpam-5440	142	44	y	y	NOUN
ejpam-5440	142	45	)	)	PUNCT
ejpam-5440	142	46	.	.	PUNCT
ejpam-5440	143	1	then	then	ADV
ejpam-5440	143	2	f	f	PROPN
ejpam-5440	143	3	has	have	VERB
ejpam-5440	143	4	a	a	DET
ejpam-5440	143	5	fixed	fix	VERB
ejpam-5440	143	6	element	element	NOUN
ejpam-5440	143	7	v	v	ADP
ejpam-5440	143	8	∈	∈	PROPN
ejpam-5440	143	9	x	x	NOUN
ejpam-5440	143	10	,	,	PUNCT
ejpam-5440	143	11	that	that	ADV
ejpam-5440	143	12	is	is	ADV
ejpam-5440	143	13	,	,	PUNCT
ejpam-5440	143	14	v	v	NOUN
ejpam-5440	143	15	=	=	SYM
ejpam-5440	143	16	f(v	f(v	NOUN
ejpam-5440	143	17	)	)	PUNCT
ejpam-5440	143	18	.	.	PUNCT
ejpam-5440	144	1	the	the	DET
ejpam-5440	144	2	only	only	ADJ
ejpam-5440	144	3	if	if	SCONJ
ejpam-5440	144	4	part	part	NOUN
ejpam-5440	144	5	extends	extend	VERB
ejpam-5440	144	6	the	the	DET
ejpam-5440	144	7	so	so	ADV
ejpam-5440	144	8	-	-	PUNCT
ejpam-5440	144	9	called	call	VERB
ejpam-5440	144	10	banach	banach	NOUN
ejpam-5440	144	11	contraction	contraction	NOUN
ejpam-5440	144	12	principle	principle	NOUN
ejpam-5440	144	13	.	.	PUNCT
ejpam-5440	145	1	the	the	DET
ejpam-5440	145	2	traditional	traditional	ADJ
ejpam-5440	145	3	banach	banach	NOUN
ejpam-5440	145	4	contraction	contraction	NOUN
ejpam-5440	145	5	principle	principle	NOUN
ejpam-5440	145	6	is	be	AUX
ejpam-5440	145	7	a	a	DET
ejpam-5440	145	8	particular	particular	ADJ
ejpam-5440	145	9	form	form	NOUN
ejpam-5440	145	10	of	of	ADP
ejpam-5440	145	11	theorem	theorem	NOUN
ejpam-5440	145	12	q	q	PROPN
ejpam-5440	145	13	when	when	SCONJ
ejpam-5440	145	14	x	x	PRON
ejpam-5440	145	15	is	be	AUX
ejpam-5440	145	16	a	a	DET
ejpam-5440	145	17	metric	metric	ADJ
ejpam-5440	145	18	space	space	NOUN
ejpam-5440	145	19	and	and	CCONJ
ejpam-5440	145	20	(	(	PUNCT
ejpam-5440	145	21	q	q	X
ejpam-5440	145	22	)	)	PUNCT
ejpam-5440	145	23	holds	hold	VERB
ejpam-5440	145	24	for	for	ADP
ejpam-5440	145	25	all	all	DET
ejpam-5440	145	26	x	x	NOUN
ejpam-5440	145	27	,	,	PUNCT
ejpam-5440	145	28	y	y	PROPN
ejpam-5440	145	29	∈	∈	PROPN
ejpam-5440	145	30	x.	x.	NOUN
ejpam-5440	146	1	it	it	PRON
ejpam-5440	146	2	appears	appear	VERB
ejpam-5440	146	3	in	in	ADP
ejpam-5440	146	4	thousands	thousand	NOUN
ejpam-5440	146	5	of	of	ADP
ejpam-5440	146	6	publications	publication	NOUN
ejpam-5440	146	7	and	and	CCONJ
ejpam-5440	146	8	should	should	AUX
ejpam-5440	146	9	be	be	AUX
ejpam-5440	146	10	corrected	correct	VERB
ejpam-5440	146	11	or	or	CCONJ
ejpam-5440	146	12	replaced	replace	VERB
ejpam-5440	146	13	by	by	ADP
ejpam-5440	146	14	theorem	theorem	NOUN
ejpam-5440	146	15	q.	q.	PROPN
ejpam-5440	146	16	the	the	DET
ejpam-5440	146	17	origin	origin	NOUN
ejpam-5440	146	18	of	of	ADP
ejpam-5440	146	19	the	the	DET
ejpam-5440	146	20	subfamily	subfamily	ADJ
ejpam-5440	146	21	(	(	PUNCT
ejpam-5440	146	22	β	β	NOUN
ejpam-5440	146	23	)	)	PUNCT
ejpam-5440	146	24	is	be	AUX
ejpam-5440	146	25	the	the	DET
ejpam-5440	146	26	following	following	NOUN
ejpam-5440	146	27	due	due	ADJ
ejpam-5440	146	28	to	to	PART
ejpam-5440	146	29	banach	banach	ADV
ejpam-5440	146	30	in	in	ADP
ejpam-5440	146	31	1922	1922	NUM
ejpam-5440	146	32	:	:	PUNCT
ejpam-5440	146	33	theorem	theorem	VERB
ejpam-5440	146	34	6.2	6.2	NUM
ejpam-5440	146	35	.	.	PUNCT
ejpam-5440	147	1	(	(	PUNCT
ejpam-5440	147	2	banach	banach	NOUN
ejpam-5440	147	3	)	)	PUNCT
ejpam-5440	147	4	if	if	SCONJ
ejpam-5440	147	5	10	10	NUM
ejpam-5440	147	6	u(x	u(x	NOUN
ejpam-5440	147	7	)	)	PUNCT
ejpam-5440	147	8	be	be	VERB
ejpam-5440	147	9	a	a	DET
ejpam-5440	147	10	continuous	continuous	ADJ
ejpam-5440	147	11	operator	operator	NOUN
ejpam-5440	147	12	in	in	ADP
ejpam-5440	147	13	e	e	NOUN
ejpam-5440	147	14	,	,	PUNCT
ejpam-5440	147	15	the	the	DET
ejpam-5440	147	16	counter	counter	NOUN
ejpam-5440	147	17	-	-	NOUN
ejpam-5440	147	18	domain	domain	NOUN
ejpam-5440	147	19	of	of	ADP
ejpam-5440	147	20	u(x	u(x	NOUN
ejpam-5440	147	21	)	)	PUNCT
ejpam-5440	147	22	is	be	AUX
ejpam-5440	147	23	contained	contain	VERB
ejpam-5440	147	24	in	in	ADP
ejpam-5440	147	25	e1	e1	PROPN
ejpam-5440	147	26	.	.	PUNCT
ejpam-5440	148	1	20	20	NUM
ejpam-5440	148	2	there	there	PRON
ejpam-5440	148	3	exists	exist	VERB
ejpam-5440	148	4	a	a	DET
ejpam-5440	148	5	number	number	NOUN
ejpam-5440	148	6	0	0	NUM
ejpam-5440	148	7	<	<	X
ejpam-5440	148	8	m	m	X
ejpam-5440	148	9	<	<	X
ejpam-5440	148	10	1	1	NUM
ejpam-5440	148	11	which	which	PRON
ejpam-5440	148	12	implies	imply	VERB
ejpam-5440	148	13	,	,	PUNCT
ejpam-5440	148	14	for	for	ADP
ejpam-5440	148	15	every	every	DET
ejpam-5440	148	16	x	x	NOUN
ejpam-5440	148	17	′	′	NUM
ejpam-5440	148	18	and	and	CCONJ
ejpam-5440	148	19	x	x	PART
ejpam-5440	148	20	′′	′′	PROPN
ejpam-5440	148	21	,	,	PUNCT
ejpam-5440	148	22	the	the	DET
ejpam-5440	148	23	inequality	inequality	NOUN
ejpam-5440	148	24	||u(x	||u(x	VERB
ejpam-5440	148	25	′)−	′)−	PROPN
ejpam-5440	148	26	u(x	u(x	VERB
ejpam-5440	148	27	′′)||	′′)||	NUM
ejpam-5440	148	28	≤	≤	NUM
ejpam-5440	148	29	m.||x	m.||x	NOUN
ejpam-5440	148	30	′	′	NUM
ejpam-5440	148	31	−x	−x	NUM
ejpam-5440	148	32	′′||	′′||	NOUN
ejpam-5440	148	33	.	.	PUNCT
ejpam-5440	149	1	—	—	PUNCT
ejpam-5440	149	2	there	there	PRON
ejpam-5440	149	3	exists	exist	VERB
ejpam-5440	149	4	an	an	DET
ejpam-5440	149	5	element	element	NOUN
ejpam-5440	149	6	x	x	PUNCT
ejpam-5440	149	7	such	such	ADJ
ejpam-5440	149	8	that	that	SCONJ
ejpam-5440	149	9	x	x	NOUN
ejpam-5440	149	10	=	=	SYM
ejpam-5440	149	11	u(x	u(x	PROPN
ejpam-5440	149	12	)	)	PUNCT
ejpam-5440	149	13	.	.	PUNCT
ejpam-5440	150	1	here	here	ADV
ejpam-5440	150	2	e	e	X
ejpam-5440	150	3	and	and	CCONJ
ejpam-5440	150	4	e1	e1	PROPN
ejpam-5440	150	5	is	be	AUX
ejpam-5440	150	6	a	a	DET
ejpam-5440	150	7	normed	normed	ADJ
ejpam-5440	150	8	space	space	NOUN
ejpam-5440	150	9	and	and	CCONJ
ejpam-5440	150	10	its	its	PRON
ejpam-5440	150	11	complete	complete	ADJ
ejpam-5440	150	12	subset	subset	NOUN
ejpam-5440	150	13	,	,	PUNCT
ejpam-5440	150	14	resp	resp	NOUN
ejpam-5440	150	15	.	.	PUNCT
ejpam-5440	151	1	7	7	X
ejpam-5440	151	2	.	.	X
ejpam-5440	151	3	the	the	DET
ejpam-5440	151	4	subfamily	subfamily	ADV
ejpam-5440	151	5	(	(	PUNCT
ejpam-5440	151	6	γ	γ	NOUN
ejpam-5440	151	7	)	)	PUNCT
ejpam-5440	151	8	in	in	ADP
ejpam-5440	151	9	theorem	theorem	ADJ
ejpam-5440	151	10	h	h	NOUN
ejpam-5440	151	11	,	,	PUNCT
ejpam-5440	151	12	consider	consider	VERB
ejpam-5440	151	13	the	the	DET
ejpam-5440	151	14	following	follow	VERB
ejpam-5440	151	15	:	:	PUNCT
ejpam-5440	151	16	(	(	PUNCT
ejpam-5440	151	17	γ	γ	X
ejpam-5440	151	18	)	)	PUNCT
ejpam-5440	151	19	if	if	SCONJ
ejpam-5440	151	20	f	f	PROPN
ejpam-5440	151	21	is	be	AUX
ejpam-5440	151	22	a	a	DET
ejpam-5440	151	23	family	family	NOUN
ejpam-5440	151	24	of	of	ADP
ejpam-5440	151	25	maps	map	NOUN
ejpam-5440	151	26	f	f	X
ejpam-5440	151	27	:	:	PUNCT
ejpam-5440	151	28	x	x	X
ejpam-5440	151	29	→	→	SYM
ejpam-5440	151	30	x	x	SYM
ejpam-5440	151	31	satisfying	satisfy	VERB
ejpam-5440	151	32	q(f(x	q(f(x	PROPN
ejpam-5440	151	33	)	)	PUNCT
ejpam-5440	151	34	,	,	PUNCT
ejpam-5440	151	35	f2(x	f2(x	PROPN
ejpam-5440	151	36	)	)	PUNCT
ejpam-5440	151	37	)	)	PUNCT
ejpam-5440	151	38	≤	≤	NUM
ejpam-5440	151	39	α	α	PROPN
ejpam-5440	151	40	q(x	q(x	PROPN
ejpam-5440	151	41	,	,	PUNCT
ejpam-5440	151	42	f(x	f(x	PROPN
ejpam-5440	151	43	)	)	PUNCT
ejpam-5440	151	44	)	)	PUNCT
ejpam-5440	151	45	for	for	ADP
ejpam-5440	151	46	all	all	DET
ejpam-5440	151	47	x	x	SYM
ejpam-5440	151	48	∈	∈	PROPN
ejpam-5440	151	49	x\{f(x	x\{f(x	PROPN
ejpam-5440	151	50	)	)	PUNCT
ejpam-5440	151	51	}	}	PUNCT
ejpam-5440	151	52	,	,	PUNCT
ejpam-5440	151	53	then	then	ADV
ejpam-5440	151	54	f	f	PROPN
ejpam-5440	151	55	has	have	VERB
ejpam-5440	151	56	a	a	DET
ejpam-5440	151	57	common	common	ADJ
ejpam-5440	151	58	fixed	fix	VERB
ejpam-5440	151	59	element	element	NOUN
ejpam-5440	151	60	v	v	ADP
ejpam-5440	151	61	∈	∈	PROPN
ejpam-5440	151	62	x	x	NOUN
ejpam-5440	151	63	,	,	PUNCT
ejpam-5440	151	64	that	that	ADV
ejpam-5440	151	65	is	is	ADV
ejpam-5440	151	66	,	,	PUNCT
ejpam-5440	151	67	v	v	NOUN
ejpam-5440	151	68	=	=	PUNCT
ejpam-5440	151	69	f(v	f(v	NOUN
ejpam-5440	151	70	)	)	PUNCT
ejpam-5440	151	71	for	for	ADP
ejpam-5440	151	72	all	all	DET
ejpam-5440	151	73	f	f	PROPN
ejpam-5440	151	74	∈	∈	PROPN
ejpam-5440	151	75	f.	f.	PROPN
ejpam-5440	151	76	note	note	VERB
ejpam-5440	151	77	that	that	SCONJ
ejpam-5440	151	78	the	the	DET
ejpam-5440	151	79	f	f	PROPN
ejpam-5440	151	80	-orbital	-orbital	PROPN
ejpam-5440	151	81	completeness	completeness	NOUN
ejpam-5440	151	82	of	of	ADP
ejpam-5440	151	83	(	(	PUNCT
ejpam-5440	151	84	x	x	NOUN
ejpam-5440	151	85	,	,	PUNCT
ejpam-5440	151	86	q	q	NOUN
ejpam-5440	151	87	)	)	PUNCT
ejpam-5440	151	88	for	for	ADP
ejpam-5440	151	89	any	any	DET
ejpam-5440	151	90	rhr	rhr	PROPN
ejpam-5440	151	91	map	map	NOUN
ejpam-5440	152	1	f	f	X
ejpam-5440	152	2	:	:	PUNCT
ejpam-5440	152	3	x	x	SYM
ejpam-5440	152	4	→	→	SYM
ejpam-5440	152	5	x	x	X
ejpam-5440	152	6	in	in	ADP
ejpam-5440	152	7	f	f	PROPN
ejpam-5440	152	8	implies	imply	VERB
ejpam-5440	152	9	(	(	PUNCT
ejpam-5440	152	10	γ	γ	X
ejpam-5440	152	11	)	)	PUNCT
ejpam-5440	152	12	.	.	PUNCT
ejpam-5440	153	1	such	such	ADJ
ejpam-5440	153	2	map	map	NOUN
ejpam-5440	153	3	is	be	AUX
ejpam-5440	153	4	traditionally	traditionally	ADV
ejpam-5440	153	5	called	call	VERB
ejpam-5440	153	6	as	as	ADP
ejpam-5440	153	7	graphic	graphic	ADJ
ejpam-5440	153	8	contraction	contraction	NOUN
ejpam-5440	153	9	,	,	PUNCT
ejpam-5440	153	10	iterative	iterative	NOUN
ejpam-5440	153	11	contraction	contraction	NOUN
ejpam-5440	153	12	,	,	PUNCT
ejpam-5440	153	13	weakly	weakly	ADJ
ejpam-5440	153	14	contraction	contraction	NOUN
ejpam-5440	153	15	,	,	PUNCT
ejpam-5440	153	16	banach	banach	NOUN
ejpam-5440	153	17	mapping	mapping	NOUN
ejpam-5440	153	18	,	,	PUNCT
ejpam-5440	153	19	.	.	PUNCT
ejpam-5440	153	20	.	.	PUNCT
ejpam-5440	154	1	.	.	PUNCT
ejpam-5440	155	1	.	.	PUNCT
ejpam-5440	156	1	we	we	PRON
ejpam-5440	156	2	prefer	prefer	VERB
ejpam-5440	156	3	to	to	PART
ejpam-5440	156	4	call	call	VERB
ejpam-5440	156	5	it	it	PRON
ejpam-5440	156	6	a	a	DET
ejpam-5440	156	7	weak	weak	ADJ
ejpam-5440	156	8	contraction	contraction	NOUN
ejpam-5440	156	9	.	.	PUNCT
ejpam-5440	157	1	the	the	DET
ejpam-5440	157	2	following	follow	VERB
ejpam-5440	157	3	consequence	consequence	NOUN
ejpam-5440	157	4	of	of	ADP
ejpam-5440	157	5	(	(	PUNCT
ejpam-5440	157	6	γ	γ	X
ejpam-5440	157	7	)	)	PUNCT
ejpam-5440	157	8	was	be	AUX
ejpam-5440	157	9	independently	independently	ADV
ejpam-5440	157	10	obtained	obtain	VERB
ejpam-5440	157	11	in	in	ADP
ejpam-5440	157	12	park	park	NOUN
ejpam-5440	157	13	[	[	X
ejpam-5440	157	14	16]-[19	16]-[19	X
ejpam-5440	157	15	]	]	X
ejpam-5440	157	16	,	,	PUNCT
ejpam-5440	157	17	[	[	X
ejpam-5440	157	18	21	21	NUM
ejpam-5440	157	19	]	]	PUNCT
ejpam-5440	157	20	.	.	PUNCT
ejpam-5440	158	1	it	it	PRON
ejpam-5440	158	2	is	be	AUX
ejpam-5440	158	3	called	call	VERB
ejpam-5440	158	4	the	the	DET
ejpam-5440	158	5	rus	rus	NOUN
ejpam-5440	158	6	-	-	PUNCT
ejpam-5440	158	7	hicks	hick	NOUN
ejpam-5440	158	8	-	-	PUNCT
ejpam-5440	158	9	rhoades	rhoade	NOUN
ejpam-5440	158	10	(	(	PUNCT
ejpam-5440	158	11	rhr	rhr	PROPN
ejpam-5440	158	12	)	)	PUNCT
ejpam-5440	158	13	contraction	contraction	NOUN
ejpam-5440	158	14	principle	principle	NOUN
ejpam-5440	158	15	:	:	PUNCT
ejpam-5440	158	16	theorem	theorem	ADJ
ejpam-5440	158	17	p.	p.	NOUN
ejpam-5440	158	18	let	let	AUX
ejpam-5440	158	19	(	(	PUNCT
ejpam-5440	158	20	x	x	X
ejpam-5440	158	21	,	,	PUNCT
ejpam-5440	158	22	q	q	X
ejpam-5440	158	23	)	)	PUNCT
ejpam-5440	158	24	be	be	AUX
ejpam-5440	158	25	a	a	DET
ejpam-5440	158	26	quasi	quasi	ADJ
ejpam-5440	158	27	-	-	ADJ
ejpam-5440	158	28	metric	metric	ADJ
ejpam-5440	158	29	space	space	NOUN
ejpam-5440	158	30	and	and	CCONJ
ejpam-5440	158	31	let	let	VERB
ejpam-5440	158	32	t	t	NOUN
ejpam-5440	158	33	:	:	PUNCT
ejpam-5440	158	34	x	x	X
ejpam-5440	158	35	→	→	PUNCT
ejpam-5440	158	36	x	x	AUX
ejpam-5440	158	37	be	be	AUX
ejpam-5440	158	38	an	an	DET
ejpam-5440	158	39	rhr	rhr	NOUN
ejpam-5440	158	40	map	map	NOUN
ejpam-5440	158	41	;	;	PUNCT
ejpam-5440	158	42	that	that	PRON
ejpam-5440	158	43	is	is	ADV
ejpam-5440	158	44	,	,	PUNCT
ejpam-5440	158	45	q(t	q(t	PROPN
ejpam-5440	158	46	(	(	PUNCT
ejpam-5440	158	47	x	x	NOUN
ejpam-5440	158	48	)	)	PUNCT
ejpam-5440	158	49	,	,	PUNCT
ejpam-5440	158	50	t	t	PROPN
ejpam-5440	158	51	2(x	2(x	NUM
ejpam-5440	158	52	)	)	PUNCT
ejpam-5440	158	53	)	)	PUNCT
ejpam-5440	158	54	≤	≤	NUM
ejpam-5440	158	55	α	α	PROPN
ejpam-5440	158	56	q(x	q(x	PROPN
ejpam-5440	158	57	,	,	PUNCT
ejpam-5440	158	58	t	t	PROPN
ejpam-5440	158	59	(	(	PUNCT
ejpam-5440	158	60	x	x	NOUN
ejpam-5440	158	61	)	)	PUNCT
ejpam-5440	158	62	)	)	PUNCT
ejpam-5440	158	63	for	for	ADP
ejpam-5440	158	64	every	every	DET
ejpam-5440	158	65	x	x	SYM
ejpam-5440	158	66	∈	∈	PROPN
ejpam-5440	158	67	x	x	X
ejpam-5440	158	68	,	,	PUNCT
ejpam-5440	158	69	(	(	PUNCT
ejpam-5440	158	70	p	p	NOUN
ejpam-5440	158	71	)	)	PUNCT
ejpam-5440	158	72	where	where	SCONJ
ejpam-5440	158	73	0	0	NUM
ejpam-5440	158	74	<	<	X
ejpam-5440	158	75	α	α	X
ejpam-5440	158	76	<	<	X
ejpam-5440	158	77	1	1	NUM
ejpam-5440	158	78	.	.	PUNCT
ejpam-5440	158	79	(	(	PUNCT
ejpam-5440	158	80	i	i	NOUN
ejpam-5440	158	81	)	)	PUNCT
ejpam-5440	158	82	if	if	SCONJ
ejpam-5440	158	83	x	x	PRON
ejpam-5440	158	84	is	be	AUX
ejpam-5440	158	85	t	t	NOUN
ejpam-5440	158	86	-orbitally	-orbitally	ADV
ejpam-5440	158	87	complete	complete	ADJ
ejpam-5440	158	88	,	,	PUNCT
ejpam-5440	158	89	then	then	ADV
ejpam-5440	158	90	,	,	PUNCT
ejpam-5440	158	91	for	for	ADP
ejpam-5440	158	92	each	each	DET
ejpam-5440	158	93	x	x	SYM
ejpam-5440	158	94	∈	∈	PROPN
ejpam-5440	158	95	x	x	X
ejpam-5440	158	96	,	,	PUNCT
ejpam-5440	158	97	there	there	PRON
ejpam-5440	158	98	exists	exist	VERB
ejpam-5440	158	99	a	a	DET
ejpam-5440	158	100	point	point	NOUN
ejpam-5440	158	101	x0	x0	PROPN
ejpam-5440	158	102	∈	∈	PROPN
ejpam-5440	158	103	x	x	PUNCT
ejpam-5440	158	104	such	such	ADJ
ejpam-5440	158	105	that	that	SCONJ
ejpam-5440	158	106	lim	lim	PROPN
ejpam-5440	158	107	n→∞	n→∞	X
ejpam-5440	158	108	tn(x	tn(x	PUNCT
ejpam-5440	158	109	)	)	PUNCT
ejpam-5440	159	1	=	=	SYM
ejpam-5440	159	2	x0	x0	PROPN
ejpam-5440	159	3	and	and	CCONJ
ejpam-5440	159	4	q(tn(x	q(tn(x	PROPN
ejpam-5440	159	5	)	)	PUNCT
ejpam-5440	159	6	,	,	PUNCT
ejpam-5440	159	7	x0	x0	PROPN
ejpam-5440	159	8	)	)	PUNCT
ejpam-5440	159	9	≤	≤	NUM
ejpam-5440	159	10	αn	αn	NOUN
ejpam-5440	159	11	1−	1−	NUM
ejpam-5440	159	12	α	α	PROPN
ejpam-5440	159	13	q(x	q(x	PROPN
ejpam-5440	159	14	,	,	PUNCT
ejpam-5440	159	15	t	t	PROPN
ejpam-5440	159	16	(	(	PUNCT
ejpam-5440	159	17	x	x	NOUN
ejpam-5440	159	18	)	)	PUNCT
ejpam-5440	159	19	)	)	PUNCT
ejpam-5440	159	20	,	,	PUNCT
ejpam-5440	159	21	n	n	NOUN
ejpam-5440	159	22	=	=	SYM
ejpam-5440	159	23	1	1	NUM
ejpam-5440	159	24	,	,	PUNCT
ejpam-5440	159	25	2	2	NUM
ejpam-5440	159	26	,	,	PUNCT
ejpam-5440	159	27	·	·	PUNCT
ejpam-5440	159	28	·	·	PUNCT
ejpam-5440	159	29	·	·	PUNCT
ejpam-5440	159	30	,	,	PUNCT
ejpam-5440	159	31	q(tn(x	q(tn(x	PROPN
ejpam-5440	159	32	)	)	PUNCT
ejpam-5440	159	33	,	,	PUNCT
ejpam-5440	159	34	x0	x0	PROPN
ejpam-5440	159	35	)	)	PUNCT
ejpam-5440	159	36	≤	≤	PUNCT
ejpam-5440	160	1	α	α	PRON
ejpam-5440	160	2	1−	1−	NUM
ejpam-5440	160	3	α	α	DET
ejpam-5440	160	4	q(tn−1(x	q(tn−1(x	NOUN
ejpam-5440	160	5	)	)	PUNCT
ejpam-5440	160	6	,	,	PUNCT
ejpam-5440	160	7	tn(x	tn(x	NOUN
ejpam-5440	160	8	)	)	PUNCT
ejpam-5440	160	9	)	)	PUNCT
ejpam-5440	160	10	,	,	PUNCT
ejpam-5440	160	11	n	n	NOUN
ejpam-5440	160	12	=	=	SYM
ejpam-5440	160	13	1	1	NUM
ejpam-5440	160	14	,	,	PUNCT
ejpam-5440	160	15	2	2	NUM
ejpam-5440	160	16	,	,	PUNCT
ejpam-5440	160	17	·	·	PUNCT
ejpam-5440	160	18	·	·	PUNCT
ejpam-5440	160	19	·	·	PUNCT
ejpam-5440	160	20	.	.	PUNCT
ejpam-5440	161	1	s.	s.	PROPN
ejpam-5440	161	2	park	park	PROPN
ejpam-5440	161	3	/	/	SYM
ejpam-5440	161	4	eur	eur	PROPN
ejpam-5440	161	5	.	.	PUNCT
ejpam-5440	162	1	j.	j.	PROPN
ejpam-5440	162	2	pure	pure	PROPN
ejpam-5440	162	3	appl	appl	PROPN
ejpam-5440	162	4	.	.	PROPN
ejpam-5440	162	5	math	math	PROPN
ejpam-5440	162	6	,	,	PUNCT
ejpam-5440	162	7	17	17	NUM
ejpam-5440	162	8	(	(	PUNCT
ejpam-5440	162	9	4	4	NUM
ejpam-5440	162	10	)	)	PUNCT
ejpam-5440	162	11	(	(	PUNCT
ejpam-5440	162	12	2024	2024	NUM
ejpam-5440	162	13	)	)	PUNCT
ejpam-5440	162	14	,	,	PUNCT
ejpam-5440	162	15	2370	2370	NUM
ejpam-5440	162	16	-	-	SYM
ejpam-5440	162	17	2383	2383	NUM
ejpam-5440	162	18	2377	2377	NUM
ejpam-5440	162	19	(	(	PUNCT
ejpam-5440	162	20	ii	ii	NOUN
ejpam-5440	162	21	)	)	PUNCT
ejpam-5440	163	1	x0	x0	PROPN
ejpam-5440	163	2	is	be	AUX
ejpam-5440	163	3	a	a	DET
ejpam-5440	163	4	fixed	fix	VERB
ejpam-5440	163	5	point	point	NOUN
ejpam-5440	163	6	of	of	ADP
ejpam-5440	163	7	t	t	PROPN
ejpam-5440	163	8	,	,	PUNCT
ejpam-5440	163	9	and	and	CCONJ
ejpam-5440	163	10	,	,	PUNCT
ejpam-5440	163	11	equivalently	equivalently	ADV
ejpam-5440	163	12	,	,	PUNCT
ejpam-5440	163	13	(	(	PUNCT
ejpam-5440	163	14	iii	iii	X
ejpam-5440	163	15	)	)	PUNCT
ejpam-5440	163	16	t	t	NOUN
ejpam-5440	163	17	:	:	PUNCT
ejpam-5440	163	18	x	x	X
ejpam-5440	163	19	→	→	PUNCT
ejpam-5440	163	20	x	x	X
ejpam-5440	163	21	is	be	AUX
ejpam-5440	163	22	orbitally	orbitally	ADV
ejpam-5440	163	23	continuous	continuous	ADJ
ejpam-5440	163	24	at	at	ADP
ejpam-5440	163	25	x0	x0	PROPN
ejpam-5440	163	26	∈	∈	PROPN
ejpam-5440	163	27	x.	x.	NOUN
ejpam-5440	163	28	example	example	NOUN
ejpam-5440	163	29	7.1	7.1	NUM
ejpam-5440	163	30	.	.	PUNCT
ejpam-5440	164	1	for	for	ADP
ejpam-5440	164	2	any	any	DET
ejpam-5440	164	3	quasi	quasi	ADJ
ejpam-5440	164	4	-	-	ADJ
ejpam-5440	164	5	metric	metric	ADJ
ejpam-5440	164	6	space	space	NOUN
ejpam-5440	164	7	(	(	PUNCT
ejpam-5440	164	8	x	x	X
ejpam-5440	164	9	,	,	PUNCT
ejpam-5440	164	10	q	q	NOUN
ejpam-5440	164	11	)	)	PUNCT
ejpam-5440	164	12	,	,	PUNCT
ejpam-5440	164	13	let	let	VERB
ejpam-5440	164	14	t	t	NOUN
ejpam-5440	164	15	=	=	SYM
ejpam-5440	164	16	1x	1x	NUM
ejpam-5440	164	17	be	be	AUX
ejpam-5440	164	18	the	the	DET
ejpam-5440	164	19	identity	identity	NOUN
ejpam-5440	164	20	map	map	NOUN
ejpam-5440	164	21	.	.	PUNCT
ejpam-5440	165	1	then	then	ADV
ejpam-5440	165	2	theorem	theorem	VERB
ejpam-5440	165	3	p	p	PROPN
ejpam-5440	165	4	holds	hold	VERB
ejpam-5440	165	5	for	for	ADP
ejpam-5440	165	6	1x	1x	NUM
ejpam-5440	165	7	.	.	PUNCT
ejpam-5440	166	1	example	example	NOUN
ejpam-5440	166	2	7.2	7.2	NUM
ejpam-5440	166	3	.	.	PUNCT
ejpam-5440	167	1	let	let	VERB
ejpam-5440	167	2	x	x	PUNCT
ejpam-5440	167	3	=	=	PUNCT
ejpam-5440	167	4	{	{	PUNCT
ejpam-5440	167	5	0	0	NUM
ejpam-5440	167	6	,	,	PUNCT
ejpam-5440	167	7	1	1	NUM
ejpam-5440	167	8	}	}	PUNCT
ejpam-5440	167	9	with	with	ADP
ejpam-5440	167	10	the	the	DET
ejpam-5440	167	11	usual	usual	ADJ
ejpam-5440	167	12	metric	metric	NOUN
ejpam-5440	167	13	and	and	CCONJ
ejpam-5440	167	14	t	t	NOUN
ejpam-5440	167	15	=	=	SYM
ejpam-5440	167	16	1x	1x	PROPN
ejpam-5440	167	17	.	.	PUNCT
ejpam-5440	168	1	then	then	ADV
ejpam-5440	168	2	condition	condition	NOUN
ejpam-5440	168	3	(	(	PUNCT
ejpam-5440	168	4	p	p	NOUN
ejpam-5440	168	5	)	)	PUNCT
ejpam-5440	168	6	holds	hold	NOUN
ejpam-5440	168	7	,	,	PUNCT
ejpam-5440	168	8	but	but	CCONJ
ejpam-5440	168	9	not	not	PART
ejpam-5440	168	10	(	(	PUNCT
ejpam-5440	168	11	q	q	NOUN
ejpam-5440	168	12	)	)	PUNCT
ejpam-5440	168	13	.	.	PUNCT
ejpam-5440	169	1	hence	hence	ADV
ejpam-5440	169	2	theorem	theorem	VERB
ejpam-5440	169	3	p	p	NOUN
ejpam-5440	169	4	is	be	AUX
ejpam-5440	169	5	a	a	DET
ejpam-5440	169	6	proper	proper	ADJ
ejpam-5440	169	7	generalization	generalization	NOUN
ejpam-5440	169	8	of	of	ADP
ejpam-5440	169	9	theorem	theorem	PROPN
ejpam-5440	169	10	q.	q.	PROPN
ejpam-5440	169	11	example	example	PROPN
ejpam-5440	169	12	7.3	7.3	NUM
ejpam-5440	169	13	.	.	PUNCT
ejpam-5440	170	1	let	let	VERB
ejpam-5440	170	2	x	x	PRON
ejpam-5440	170	3	:	:	PUNCT
ejpam-5440	170	4	=	=	PRON
ejpam-5440	170	5	{	{	PUNCT
ejpam-5440	170	6	−1	−1	NOUN
ejpam-5440	170	7	}	}	PUNCT
ejpam-5440	170	8	∪	∪	X
ejpam-5440	170	9	{	{	PUNCT
ejpam-5440	170	10	0	0	NUM
ejpam-5440	170	11	}	}	PUNCT
ejpam-5440	170	12	∪	∪	NOUN
ejpam-5440	170	13	{	{	PUNCT
ejpam-5440	170	14	1	1	NUM
ejpam-5440	170	15	n	n	NOUN
ejpam-5440	170	16	:	:	PUNCT
ejpam-5440	170	17	n	n	NOUN
ejpam-5440	170	18	=	=	SYM
ejpam-5440	170	19	1	1	NUM
ejpam-5440	170	20	,	,	PUNCT
ejpam-5440	170	21	2	2	NUM
ejpam-5440	170	22	,	,	PUNCT
ejpam-5440	170	23	·	·	PUNCT
ejpam-5440	170	24	·	·	PUNCT
ejpam-5440	170	25	·	·	PUNCT
ejpam-5440	170	26	,	,	PUNCT
ejpam-5440	170	27	100	100	NUM
ejpam-5440	170	28	}	}	PUNCT
ejpam-5440	170	29	.	.	PUNCT
ejpam-5440	171	1	let	let	VERB
ejpam-5440	171	2	q	q	NOUN
ejpam-5440	171	3	:	:	PUNCT
ejpam-5440	171	4	x	x	X
ejpam-5440	171	5	×x	×x	NUM
ejpam-5440	171	6	→	→	SYM
ejpam-5440	171	7	r	r	NOUN
ejpam-5440	171	8	be	be	AUX
ejpam-5440	171	9	the	the	DET
ejpam-5440	171	10	ordinary	ordinary	ADJ
ejpam-5440	171	11	metric	metric	NOUN
ejpam-5440	171	12	except	except	SCONJ
ejpam-5440	171	13	q(−1	q(−1	PROPN
ejpam-5440	171	14	,	,	PUNCT
ejpam-5440	171	15	0	0	NUM
ejpam-5440	171	16	)	)	PUNCT
ejpam-5440	171	17	=	=	SYM
ejpam-5440	171	18	1	1	NUM
ejpam-5440	171	19	and	and	CCONJ
ejpam-5440	171	20	q(0,−1	q(0,−1	PROPN
ejpam-5440	171	21	)	)	PUNCT
ejpam-5440	172	1	=	=	SYM
ejpam-5440	172	2	0	0	X
ejpam-5440	172	3	.	.	PUNCT
ejpam-5440	173	1	then	then	ADV
ejpam-5440	173	2	(	(	PUNCT
ejpam-5440	173	3	x	x	X
ejpam-5440	173	4	,	,	PUNCT
ejpam-5440	173	5	q	q	X
ejpam-5440	173	6	)	)	PUNCT
ejpam-5440	173	7	is	be	AUX
ejpam-5440	173	8	a	a	DET
ejpam-5440	173	9	quasi	quasi	ADJ
ejpam-5440	173	10	-	-	ADJ
ejpam-5440	173	11	metric	metric	ADJ
ejpam-5440	173	12	space	space	NOUN
ejpam-5440	173	13	.	.	PUNCT
ejpam-5440	174	1	let	let	VERB
ejpam-5440	174	2	t	t	NOUN
ejpam-5440	174	3	:	:	PUNCT
ejpam-5440	174	4	x	x	X
ejpam-5440	174	5	→	→	PUNCT
ejpam-5440	174	6	x	x	PUNCT
ejpam-5440	174	7	be	be	AUX
ejpam-5440	174	8	a	a	DET
ejpam-5440	174	9	map	map	NOUN
ejpam-5440	174	10	such	such	ADJ
ejpam-5440	174	11	that	that	DET
ejpam-5440	174	12	t	t	PROPN
ejpam-5440	174	13	(	(	PUNCT
ejpam-5440	174	14	−1	−1	NOUN
ejpam-5440	174	15	)	)	PUNCT
ejpam-5440	174	16	=	=	SYM
ejpam-5440	175	1	0	0	NUM
ejpam-5440	175	2	,	,	PUNCT
ejpam-5440	175	3	t	t	PROPN
ejpam-5440	175	4	(	(	PUNCT
ejpam-5440	175	5	0	0	NUM
ejpam-5440	175	6	)	)	PUNCT
ejpam-5440	175	7	=	=	SYM
ejpam-5440	175	8	0	0	NUM
ejpam-5440	175	9	,	,	PUNCT
ejpam-5440	175	10	and	and	CCONJ
ejpam-5440	175	11	t	t	PROPN
ejpam-5440	175	12	(	(	PUNCT
ejpam-5440	175	13	1	1	NUM
ejpam-5440	175	14	n	n	NOUN
ejpam-5440	175	15	)	)	PUNCT
ejpam-5440	175	16	=	=	SYM
ejpam-5440	175	17	1	1	NUM
ejpam-5440	175	18	n+	n+	SYM
ejpam-5440	175	19	1	1	NUM
ejpam-5440	175	20	.	.	PUNCT
ejpam-5440	176	1	then	then	ADV
ejpam-5440	176	2	we	we	PRON
ejpam-5440	176	3	can	can	AUX
ejpam-5440	176	4	check	check	VERB
ejpam-5440	176	5	q(t	q(t	PROPN
ejpam-5440	176	6	(	(	PUNCT
ejpam-5440	176	7	x	x	NOUN
ejpam-5440	176	8	)	)	PUNCT
ejpam-5440	176	9	,	,	PUNCT
ejpam-5440	176	10	t	t	PROPN
ejpam-5440	176	11	2(x	2(x	NUM
ejpam-5440	176	12	)	)	PUNCT
ejpam-5440	176	13	)	)	PUNCT
ejpam-5440	176	14	≤	≤	NUM
ejpam-5440	177	1	α	α	PROPN
ejpam-5440	177	2	q(x	q(x	PROPN
ejpam-5440	177	3	,	,	PUNCT
ejpam-5440	177	4	t	t	PROPN
ejpam-5440	177	5	(	(	PUNCT
ejpam-5440	177	6	x	x	NOUN
ejpam-5440	177	7	)	)	PUNCT
ejpam-5440	177	8	)	)	PUNCT
ejpam-5440	177	9	with	with	ADP
ejpam-5440	177	10	α	α	PROPN
ejpam-5440	177	11	=	=	NOUN
ejpam-5440	177	12	100	100	NUM
ejpam-5440	177	13	102	102	NUM
ejpam-5440	177	14	.	.	PUNCT
ejpam-5440	178	1	therefore	therefore	ADV
ejpam-5440	178	2	theorem	theorem	VERB
ejpam-5440	178	3	p	p	NOUN
ejpam-5440	178	4	works	work	NOUN
ejpam-5440	178	5	.	.	PUNCT
ejpam-5440	179	1	the	the	DET
ejpam-5440	179	2	following	follow	VERB
ejpam-5440	179	3	form	form	NOUN
ejpam-5440	179	4	of	of	ADP
ejpam-5440	179	5	the	the	DET
ejpam-5440	179	6	rhr	rhr	PROPN
ejpam-5440	179	7	theorem	theorem	NOUN
ejpam-5440	179	8	is	be	AUX
ejpam-5440	179	9	a	a	DET
ejpam-5440	179	10	consequence	consequence	NOUN
ejpam-5440	179	11	of	of	ADP
ejpam-5440	179	12	theorems	theorem	NOUN
ejpam-5440	179	13	p	p	NOUN
ejpam-5440	179	14	and	and	CCONJ
ejpam-5440	179	15	h	h	NOUN
ejpam-5440	179	16	,	,	PUNCT
ejpam-5440	179	17	and	and	CCONJ
ejpam-5440	179	18	useful	useful	ADJ
ejpam-5440	179	19	in	in	ADP
ejpam-5440	179	20	practice	practice	NOUN
ejpam-5440	179	21	.	.	PUNCT
ejpam-5440	180	1	theorem	theorem	ADJ
ejpam-5440	180	2	h(γ1	h(γ1	NOUN
ejpam-5440	180	3	)	)	PUNCT
ejpam-5440	180	4	.	.	PUNCT
ejpam-5440	181	1	let	let	VERB
ejpam-5440	181	2	(	(	PUNCT
ejpam-5440	181	3	x	x	X
ejpam-5440	181	4	,	,	PUNCT
ejpam-5440	181	5	q	q	X
ejpam-5440	181	6	)	)	PUNCT
ejpam-5440	181	7	be	be	AUX
ejpam-5440	181	8	a	a	DET
ejpam-5440	181	9	quasi	quasi	ADJ
ejpam-5440	181	10	-	-	ADJ
ejpam-5440	181	11	metric	metric	ADJ
ejpam-5440	181	12	space	space	NOUN
ejpam-5440	181	13	,	,	PUNCT
ejpam-5440	181	14	0	0	PUNCT
ejpam-5440	181	15	<	<	X
ejpam-5440	181	16	α	α	X
ejpam-5440	181	17	<	<	X
ejpam-5440	181	18	1	1	NUM
ejpam-5440	181	19	,	,	PUNCT
ejpam-5440	181	20	and	and	CCONJ
ejpam-5440	181	21	f	f	X
ejpam-5440	181	22	:	:	PUNCT
ejpam-5440	181	23	x	x	X
ejpam-5440	181	24	→	→	PUNCT
ejpam-5440	181	25	x	x	PUNCT
ejpam-5440	181	26	be	be	AUX
ejpam-5440	181	27	a	a	DET
ejpam-5440	181	28	map	map	NOUN
ejpam-5440	181	29	satisfying	satisfy	VERB
ejpam-5440	181	30	q(f(x	q(f(x	PROPN
ejpam-5440	181	31	)	)	PUNCT
ejpam-5440	181	32	,	,	PUNCT
ejpam-5440	181	33	f2(x	f2(x	PROPN
ejpam-5440	181	34	)	)	PUNCT
ejpam-5440	181	35	)	)	PUNCT
ejpam-5440	181	36	≤	≤	NUM
ejpam-5440	182	1	α	α	PROPN
ejpam-5440	182	2	q(x	q(x	PROPN
ejpam-5440	182	3	,	,	PUNCT
ejpam-5440	182	4	f(x	f(x	PROPN
ejpam-5440	182	5	)	)	PUNCT
ejpam-5440	182	6	)	)	PUNCT
ejpam-5440	183	1	for	for	ADP
ejpam-5440	183	2	all	all	DET
ejpam-5440	183	3	x	x	SYM
ejpam-5440	183	4	∈	∈	PROPN
ejpam-5440	183	5	x\{f(x	x\{f(x	PROPN
ejpam-5440	183	6	)	)	PUNCT
ejpam-5440	183	7	}	}	PUNCT
ejpam-5440	183	8	.	.	PUNCT
ejpam-5440	184	1	then	then	ADV
ejpam-5440	184	2	f	f	PROPN
ejpam-5440	184	3	has	have	VERB
ejpam-5440	184	4	a	a	DET
ejpam-5440	184	5	fixed	fix	VERB
ejpam-5440	184	6	element	element	NOUN
ejpam-5440	184	7	v	v	ADP
ejpam-5440	184	8	∈	∈	PROPN
ejpam-5440	184	9	x	x	PUNCT
ejpam-5440	184	10	if	if	SCONJ
ejpam-5440	184	11	x	x	PRON
ejpam-5440	184	12	is	be	AUX
ejpam-5440	184	13	f	f	NOUN
ejpam-5440	184	14	-	-	PUNCT
ejpam-5440	184	15	orbitally	orbitally	ADV
ejpam-5440	184	16	complete	complete	ADJ
ejpam-5440	184	17	.	.	PUNCT
ejpam-5440	185	1	in	in	ADP
ejpam-5440	185	2	our	our	PRON
ejpam-5440	185	3	previous	previous	ADJ
ejpam-5440	185	4	works	work	NOUN
ejpam-5440	185	5	[	[	X
ejpam-5440	185	6	16]–[19	16]–[19	NUM
ejpam-5440	185	7	]	]	X
ejpam-5440	185	8	,	,	PUNCT
ejpam-5440	185	9	[	[	X
ejpam-5440	185	10	21	21	NUM
ejpam-5440	185	11	]	]	PUNCT
ejpam-5440	185	12	,	,	PUNCT
ejpam-5440	185	13	we	we	PRON
ejpam-5440	185	14	applied	apply	VERB
ejpam-5440	185	15	theorems	theorem	NOUN
ejpam-5440	185	16	p	p	NOUN
ejpam-5440	185	17	and	and	CCONJ
ejpam-5440	185	18	h(γ1	h(γ1	NOUN
ejpam-5440	185	19	)	)	PUNCT
ejpam-5440	185	20	to	to	ADP
ejpam-5440	185	21	a	a	DET
ejpam-5440	185	22	large	large	ADJ
ejpam-5440	185	23	number	number	NOUN
ejpam-5440	185	24	of	of	ADP
ejpam-5440	185	25	early	early	ADJ
ejpam-5440	185	26	extensions	extension	NOUN
ejpam-5440	185	27	or	or	CCONJ
ejpam-5440	185	28	relatives	relative	NOUN
ejpam-5440	185	29	of	of	ADP
ejpam-5440	185	30	theorems	theorem	NOUN
ejpam-5440	185	31	of	of	ADP
ejpam-5440	185	32	rus	rus	NOUN
ejpam-5440	185	33	[	[	X
ejpam-5440	185	34	24	24	NUM
ejpam-5440	185	35	]	]	PUNCT
ejpam-5440	185	36	in	in	ADP
ejpam-5440	185	37	1973	1973	NUM
ejpam-5440	185	38	and	and	CCONJ
ejpam-5440	185	39	hicks	hick	NOUN
ejpam-5440	185	40	-	-	PUNCT
ejpam-5440	185	41	rhoades	rhoade	NOUN
ejpam-5440	185	42	[	[	X
ejpam-5440	185	43	8	8	NUM
ejpam-5440	185	44	]	]	PUNCT
ejpam-5440	185	45	in	in	ADP
ejpam-5440	185	46	1979	1979	NUM
ejpam-5440	185	47	.	.	PUNCT
ejpam-5440	186	1	theorem	theorem	VERB
ejpam-5440	186	2	7.4	7.4	NUM
ejpam-5440	186	3	.	.	PUNCT
ejpam-5440	187	1	(	(	PUNCT
ejpam-5440	187	2	hicks	hick	NOUN
ejpam-5440	187	3	-	-	PUNCT
ejpam-5440	187	4	rhoades	rhoade	NOUN
ejpam-5440	187	5	)	)	PUNCT
ejpam-5440	187	6	let	let	AUX
ejpam-5440	187	7	(	(	PUNCT
ejpam-5440	187	8	x	x	NOUN
ejpam-5440	187	9	,	,	PUNCT
ejpam-5440	187	10	d	d	NOUN
ejpam-5440	187	11	)	)	PUNCT
ejpam-5440	187	12	be	be	AUX
ejpam-5440	187	13	a	a	DET
ejpam-5440	187	14	complete	complete	ADJ
ejpam-5440	187	15	metric	metric	ADJ
ejpam-5440	187	16	space	space	NOUN
ejpam-5440	187	17	,	,	PUNCT
ejpam-5440	187	18	g	g	NOUN
ejpam-5440	187	19	:	:	PUNCT
ejpam-5440	187	20	x	x	SYM
ejpam-5440	187	21	→	→	SYM
ejpam-5440	187	22	x	x	X
ejpam-5440	187	23	and	and	CCONJ
ejpam-5440	187	24	0	0	NUM
ejpam-5440	187	25	≤	≤	NUM
ejpam-5440	187	26	h	h	NOUN
ejpam-5440	187	27	<	<	X
ejpam-5440	187	28	1	1	X
ejpam-5440	187	29	.	.	PUNCT
ejpam-5440	187	30	suppose	suppose	VERB
ejpam-5440	187	31	there	there	PRON
ejpam-5440	187	32	exists	exist	VERB
ejpam-5440	187	33	an	an	DET
ejpam-5440	187	34	x	x	NOUN
ejpam-5440	187	35	such	such	ADJ
ejpam-5440	187	36	that	that	SCONJ
ejpam-5440	187	37	d(gy	d(gy	NOUN
ejpam-5440	187	38	,	,	PUNCT
ejpam-5440	187	39	g2y	g2y	NOUN
ejpam-5440	187	40	)	)	PUNCT
ejpam-5440	187	41	≤	≤	NUM
ejpam-5440	187	42	h	h	NOUN
ejpam-5440	187	43	d(y	d(y	NOUN
ejpam-5440	187	44	,	,	PUNCT
ejpam-5440	187	45	gy	gy	NOUN
ejpam-5440	187	46	)	)	PUNCT
ejpam-5440	187	47	for	for	ADP
ejpam-5440	187	48	every	every	DET
ejpam-5440	187	49	y	y	PROPN
ejpam-5440	187	50	∈	∈	PROPN
ejpam-5440	187	51	{	{	PUNCT
ejpam-5440	187	52	x	x	PROPN
ejpam-5440	187	53	,	,	PUNCT
ejpam-5440	187	54	gx	gx	PROPN
ejpam-5440	187	55	,	,	PUNCT
ejpam-5440	187	56	g2x	g2x	PROPN
ejpam-5440	187	57	,	,	PUNCT
ejpam-5440	187	58	.	.	PUNCT
ejpam-5440	187	59	.	.	PUNCT
ejpam-5440	187	60	.	.	PUNCT
ejpam-5440	188	1	}	}	PUNCT
ejpam-5440	188	2	.	.	PUNCT
ejpam-5440	189	1	then	then	ADV
ejpam-5440	189	2	,	,	PUNCT
ejpam-5440	189	3	(	(	PUNCT
ejpam-5440	189	4	i	i	NOUN
ejpam-5440	189	5	)	)	PUNCT
ejpam-5440	189	6	limn	limn	PROPN
ejpam-5440	189	7	g	g	PROPN
ejpam-5440	189	8	nx	nx	PROPN
ejpam-5440	189	9	=	=	X
ejpam-5440	189	10	q	q	NOUN
ejpam-5440	189	11	exists	exist	VERB
ejpam-5440	189	12	;	;	PUNCT
ejpam-5440	189	13	(	(	PUNCT
ejpam-5440	189	14	ii	ii	NOUN
ejpam-5440	189	15	)	)	PUNCT
ejpam-5440	189	16	d(gnx	d(gnx	NOUN
ejpam-5440	189	17	,	,	PUNCT
ejpam-5440	189	18	q	q	NOUN
ejpam-5440	189	19	)	)	PUNCT
ejpam-5440	189	20	≤	≤	NOUN
ejpam-5440	190	1	hn	hn	DET
ejpam-5440	190	2	1−hd(x	1−hd(x	PROPN
ejpam-5440	190	3	,	,	PUNCT
ejpam-5440	190	4	gx	gx	PROPN
ejpam-5440	190	5	)	)	PUNCT
ejpam-5440	190	6	;	;	PUNCT
ejpam-5440	190	7	s.	s.	PROPN
ejpam-5440	190	8	park	park	PROPN
ejpam-5440	190	9	/	/	SYM
ejpam-5440	190	10	eur	eur	PROPN
ejpam-5440	190	11	.	.	PUNCT
ejpam-5440	191	1	j.	j.	PROPN
ejpam-5440	191	2	pure	pure	PROPN
ejpam-5440	191	3	appl	appl	PROPN
ejpam-5440	191	4	.	.	PROPN
ejpam-5440	191	5	math	math	PROPN
ejpam-5440	191	6	,	,	PUNCT
ejpam-5440	191	7	17	17	NUM
ejpam-5440	191	8	(	(	PUNCT
ejpam-5440	191	9	4	4	NUM
ejpam-5440	191	10	)	)	PUNCT
ejpam-5440	191	11	(	(	PUNCT
ejpam-5440	191	12	2024	2024	NUM
ejpam-5440	191	13	)	)	PUNCT
ejpam-5440	191	14	,	,	PUNCT
ejpam-5440	191	15	2370	2370	NUM
ejpam-5440	191	16	-	-	SYM
ejpam-5440	191	17	2383	2383	NUM
ejpam-5440	191	18	2378	2378	NUM
ejpam-5440	191	19	(	(	PUNCT
ejpam-5440	191	20	iii	iii	NOUN
ejpam-5440	191	21	)	)	PUNCT
ejpam-5440	191	22	q	q	PUNCT
ejpam-5440	191	23	is	be	AUX
ejpam-5440	191	24	a	a	DET
ejpam-5440	191	25	fixed	fix	VERB
ejpam-5440	191	26	point	point	NOUN
ejpam-5440	191	27	of	of	ADP
ejpam-5440	191	28	g	g	PROPN
ejpam-5440	191	29	if	if	SCONJ
ejpam-5440	192	1	and	and	CCONJ
ejpam-5440	192	2	only	only	ADV
ejpam-5440	192	3	if	if	SCONJ
ejpam-5440	192	4	g(x	g(x	NOUN
ejpam-5440	192	5	)	)	PUNCT
ejpam-5440	193	1	=	=	SYM
ejpam-5440	193	2	d(x	d(x	PROPN
ejpam-5440	193	3	,	,	PUNCT
ejpam-5440	193	4	gx	gx	PROPN
ejpam-5440	193	5	)	)	PUNCT
ejpam-5440	193	6	is	be	AUX
ejpam-5440	193	7	g	g	NOUN
ejpam-5440	193	8	-	-	PUNCT
ejpam-5440	193	9	orbitally	orbitally	ADV
ejpam-5440	193	10	lower	low	ADJ
ejpam-5440	193	11	semicontinuous	semicontinuous	ADJ
ejpam-5440	193	12	at	at	ADP
ejpam-5440	193	13	q.	q.	NOUN
ejpam-5440	193	14	the	the	DET
ejpam-5440	193	15	following	following	NOUN
ejpam-5440	193	16	appears	appear	VERB
ejpam-5440	193	17	in	in	ADP
ejpam-5440	193	18	a	a	DET
ejpam-5440	193	19	text	text	NOUN
ejpam-5440	193	20	-	-	PUNCT
ejpam-5440	193	21	book	book	NOUN
ejpam-5440	193	22	of	of	ADP
ejpam-5440	193	23	aubin	aubin	PROPN
ejpam-5440	194	1	[	[	X
ejpam-5440	194	2	1	1	X
ejpam-5440	194	3	]	]	PUNCT
ejpam-5440	194	4	in	in	ADP
ejpam-5440	194	5	1979	1979	NUM
ejpam-5440	194	6	:	:	PUNCT
ejpam-5440	194	7	theorem	theorem	VERB
ejpam-5440	194	8	7.5	7.5	NUM
ejpam-5440	194	9	.	.	PUNCT
ejpam-5440	195	1	(	(	PUNCT
ejpam-5440	195	2	aubin	aubin	PROPN
ejpam-5440	195	3	)	)	PUNCT
ejpam-5440	195	4	let	let	VERB
ejpam-5440	195	5	v	v	PART
ejpam-5440	195	6	be	be	AUX
ejpam-5440	195	7	a	a	DET
ejpam-5440	195	8	complete	complete	ADJ
ejpam-5440	195	9	metric	metric	ADJ
ejpam-5440	195	10	space	space	NOUN
ejpam-5440	195	11	and	and	CCONJ
ejpam-5440	195	12	f	f	NOUN
ejpam-5440	195	13	:	:	PUNCT
ejpam-5440	195	14	v	v	X
ejpam-5440	195	15	→	→	SYM
ejpam-5440	195	16	v	v	X
ejpam-5440	195	17	be	be	AUX
ejpam-5440	195	18	a	a	DET
ejpam-5440	195	19	map	map	NOUN
ejpam-5440	195	20	such	such	ADJ
ejpam-5440	195	21	that	that	SCONJ
ejpam-5440	195	22	there	there	PRON
ejpam-5440	195	23	exists	exist	VERB
ejpam-5440	195	24	an	an	DET
ejpam-5440	195	25	l	l	NOUN
ejpam-5440	195	26	∈	∈	PROPN
ejpam-5440	196	1	[	[	X
ejpam-5440	196	2	0	0	NUM
ejpam-5440	196	3	,	,	PUNCT
ejpam-5440	196	4	1	1	NUM
ejpam-5440	196	5	)	)	PUNCT
ejpam-5440	196	6	satisfying	satisfy	VERB
ejpam-5440	196	7	d(fx	d(fx	NOUN
ejpam-5440	196	8	,	,	PUNCT
ejpam-5440	196	9	f2x	f2x	NOUN
ejpam-5440	196	10	)	)	PUNCT
ejpam-5440	196	11	≤	≤	NOUN
ejpam-5440	196	12	ld(x	ld(x	PUNCT
ejpam-5440	196	13	,	,	PUNCT
ejpam-5440	196	14	fx	fx	NOUN
ejpam-5440	196	15	)	)	PUNCT
ejpam-5440	196	16	∀	∀	X
ejpam-5440	196	17	x	x	X
ejpam-5440	196	18	∈	∈	NOUN
ejpam-5440	197	1	v.	v.	CCONJ
ejpam-5440	197	2	if	if	SCONJ
ejpam-5440	197	3	f	f	PROPN
ejpam-5440	197	4	(	(	PUNCT
ejpam-5440	197	5	x	x	X
ejpam-5440	197	6	)	)	PUNCT
ejpam-5440	197	7	=	=	SYM
ejpam-5440	197	8	d(x	d(x	PROPN
ejpam-5440	197	9	,	,	PUNCT
ejpam-5440	197	10	fx	fx	PROPN
ejpam-5440	197	11	)	)	PUNCT
ejpam-5440	197	12	on	on	ADP
ejpam-5440	197	13	v	v	NUM
ejpam-5440	197	14	is	be	AUX
ejpam-5440	197	15	l.s.c	l.s.c	ADJ
ejpam-5440	197	16	.	.	PUNCT
ejpam-5440	197	17	,	,	PUNCT
ejpam-5440	197	18	then	then	ADV
ejpam-5440	197	19	(	(	PUNCT
ejpam-5440	197	20	1	1	X
ejpam-5440	197	21	)	)	PUNCT
ejpam-5440	197	22	lim	lim	PROPN
ejpam-5440	197	23	fnx	fnx	PROPN
ejpam-5440	198	1	=	=	PRON
ejpam-5440	198	2	p	p	PROPN
ejpam-5440	198	3	exists	exist	VERB
ejpam-5440	198	4	for	for	ADP
ejpam-5440	198	5	all	all	DET
ejpam-5440	198	6	x	x	SYM
ejpam-5440	198	7	∈	∈	PROPN
ejpam-5440	198	8	v	v	NOUN
ejpam-5440	198	9	,	,	PUNCT
ejpam-5440	198	10	d(fnx	d(fnx	PROPN
ejpam-5440	198	11	,	,	PUNCT
ejpam-5440	198	12	p	p	X
ejpam-5440	198	13	)	)	PUNCT
ejpam-5440	198	14	≤	≤	NOUN
ejpam-5440	198	15	ln	ln	ADP
ejpam-5440	198	16	1−	1−	NUM
ejpam-5440	198	17	l	l	NOUN
ejpam-5440	198	18	d(x	d(x	PROPN
ejpam-5440	198	19	,	,	PUNCT
ejpam-5440	198	20	fx	fx	NOUN
ejpam-5440	198	21	)	)	PUNCT
ejpam-5440	198	22	,	,	PUNCT
ejpam-5440	198	23	and	and	CCONJ
ejpam-5440	198	24	p	p	NOUN
ejpam-5440	198	25	is	be	AUX
ejpam-5440	198	26	a	a	DET
ejpam-5440	198	27	fixed	fix	VERB
ejpam-5440	198	28	point	point	NOUN
ejpam-5440	198	29	of	of	ADP
ejpam-5440	198	30	f	f	PROPN
ejpam-5440	198	31	,	,	PUNCT
ejpam-5440	198	32	and	and	CCONJ
ejpam-5440	198	33	(	(	PUNCT
ejpam-5440	198	34	2	2	X
ejpam-5440	198	35	)	)	PUNCT
ejpam-5440	198	36	for	for	ADP
ejpam-5440	198	37	any	any	DET
ejpam-5440	198	38	u	u	PROPN
ejpam-5440	198	39	∈	∈	PROPN
ejpam-5440	198	40	v	v	NOUN
ejpam-5440	198	41	and	and	CCONJ
ejpam-5440	198	42	ε	ε	PROPN
ejpam-5440	198	43	>	>	X
ejpam-5440	198	44	0	0	PUNCT
ejpam-5440	199	1	satisfying	satisfy	VERB
ejpam-5440	199	2	f	f	X
ejpam-5440	199	3	(	(	PUNCT
ejpam-5440	199	4	u	u	NOUN
ejpam-5440	199	5	)	)	PUNCT
ejpam-5440	199	6	≤	≤	NOUN
ejpam-5440	199	7	(	(	PUNCT
ejpam-5440	199	8	1−	1−	NUM
ejpam-5440	199	9	l)ε	l)ε	NOUN
ejpam-5440	199	10	,	,	PUNCT
ejpam-5440	199	11	f	f	PROPN
ejpam-5440	199	12	has	have	VERB
ejpam-5440	199	13	a	a	DET
ejpam-5440	199	14	fixed	fix	VERB
ejpam-5440	199	15	point	point	NOUN
ejpam-5440	199	16	in	in	ADP
ejpam-5440	199	17	b(u	b(u	PROPN
ejpam-5440	199	18	,	,	PUNCT
ejpam-5440	199	19	ε	ε	PROPN
ejpam-5440	199	20	)	)	PUNCT
ejpam-5440	199	21	.	.	PUNCT
ejpam-5440	200	1	further	far	ADV
ejpam-5440	200	2	,	,	PUNCT
ejpam-5440	200	3	if	if	SCONJ
ejpam-5440	200	4	f	f	PROPN
ejpam-5440	200	5	is	be	AUX
ejpam-5440	200	6	a	a	DET
ejpam-5440	200	7	quasi	quasi	NOUN
ejpam-5440	200	8	-	-	ADJ
ejpam-5440	200	9	lipshitzian	lipshitzian	ADJ
ejpam-5440	200	10	with	with	ADP
ejpam-5440	200	11	constant	constant	ADJ
ejpam-5440	200	12	k	k	NOUN
ejpam-5440	200	13	,	,	PUNCT
ejpam-5440	200	14	then	then	ADV
ejpam-5440	200	15	either	either	CCONJ
ejpam-5440	200	16	u	u	NOUN
ejpam-5440	200	17	is	be	AUX
ejpam-5440	200	18	a	a	DET
ejpam-5440	200	19	fixed	fix	VERB
ejpam-5440	200	20	point	point	NOUN
ejpam-5440	200	21	of	of	ADP
ejpam-5440	200	22	f	f	PROPN
ejpam-5440	200	23	or	or	CCONJ
ejpam-5440	200	24	f	f	PROPN
ejpam-5440	200	25	has	have	VERB
ejpam-5440	200	26	a	a	DET
ejpam-5440	200	27	fixed	fix	VERB
ejpam-5440	200	28	point	point	NOUN
ejpam-5440	200	29	in	in	ADP
ejpam-5440	200	30	b(u	b(u	PROPN
ejpam-5440	200	31	,	,	PUNCT
ejpam-5440	200	32	ε)\b(u	ε)\b(u	PROPN
ejpam-5440	200	33	,	,	PUNCT
ejpam-5440	200	34	s	s	NOUN
ejpam-5440	200	35	)	)	PUNCT
ejpam-5440	200	36	where	where	SCONJ
ejpam-5440	200	37	s	s	VERB
ejpam-5440	200	38	=	=	SYM
ejpam-5440	200	39	f	f	X
ejpam-5440	200	40	(	(	PUNCT
ejpam-5440	200	41	u)(1	u)(1	NUM
ejpam-5440	200	42	+	+	CCONJ
ejpam-5440	200	43	k)−1	k)−1	NOUN
ejpam-5440	200	44	.	.	PUNCT
ejpam-5440	200	45	theorem	theorem	NOUN
ejpam-5440	200	46	7.6	7.6	NUM
ejpam-5440	200	47	.	.	PUNCT
ejpam-5440	201	1	(	(	PUNCT
ejpam-5440	201	2	rus	rus	NOUN
ejpam-5440	201	3	)	)	PUNCT
ejpam-5440	201	4	let	let	VERB
ejpam-5440	201	5	f	f	PRON
ejpam-5440	201	6	be	be	AUX
ejpam-5440	201	7	a	a	DET
ejpam-5440	201	8	continuous	continuous	ADJ
ejpam-5440	201	9	selfmap	selfmap	NOUN
ejpam-5440	201	10	of	of	ADP
ejpam-5440	201	11	a	a	DET
ejpam-5440	201	12	complete	complete	ADJ
ejpam-5440	201	13	metric	metric	ADJ
ejpam-5440	201	14	space	space	NOUN
ejpam-5440	201	15	(	(	PUNCT
ejpam-5440	201	16	x	x	X
ejpam-5440	201	17	,	,	PUNCT
ejpam-5440	201	18	d	d	NOUN
ejpam-5440	201	19	)	)	PUNCT
ejpam-5440	201	20	satisfying	satisfy	VERB
ejpam-5440	201	21	d(fx	d(fx	NOUN
ejpam-5440	201	22	,	,	PUNCT
ejpam-5440	201	23	f2x	f2x	NOUN
ejpam-5440	201	24	)	)	PUNCT
ejpam-5440	201	25	≤	≤	NOUN
ejpam-5440	201	26	αd(x	αd(x	PUNCT
ejpam-5440	201	27	,	,	PUNCT
ejpam-5440	201	28	fx	fx	PROPN
ejpam-5440	201	29	)	)	PUNCT
ejpam-5440	201	30	for	for	ADP
ejpam-5440	201	31	every	every	DET
ejpam-5440	201	32	x	x	SYM
ejpam-5440	201	33	∈	∈	PROPN
ejpam-5440	201	34	x	x	NOUN
ejpam-5440	201	35	,	,	PUNCT
ejpam-5440	201	36	where	where	SCONJ
ejpam-5440	201	37	0	0	X
ejpam-5440	201	38	<	<	X
ejpam-5440	201	39	α	α	X
ejpam-5440	201	40	<	<	X
ejpam-5440	201	41	1	1	NUM
ejpam-5440	201	42	.	.	PUNCT
ejpam-5440	202	1	then	then	ADV
ejpam-5440	202	2	f	f	PROPN
ejpam-5440	202	3	has	have	VERB
ejpam-5440	202	4	a	a	DET
ejpam-5440	202	5	fixed	fix	VERB
ejpam-5440	202	6	point	point	NOUN
ejpam-5440	202	7	.	.	PUNCT
ejpam-5440	203	1	theorems	theorem	NOUN
ejpam-5440	203	2	7.4–7.6	7.4–7.6	INTJ
ejpam-5440	203	3	are	be	AUX
ejpam-5440	203	4	the	the	DET
ejpam-5440	203	5	origins	origin	NOUN
ejpam-5440	203	6	of	of	ADP
ejpam-5440	203	7	our	our	PRON
ejpam-5440	203	8	theorems	theorem	NOUN
ejpam-5440	203	9	p	p	NOUN
ejpam-5440	203	10	and	and	CCONJ
ejpam-5440	203	11	q	q	NOUN
ejpam-5440	203	12	,	,	PUNCT
ejpam-5440	203	13	and	and	CCONJ
ejpam-5440	203	14	seem	seem	VERB
ejpam-5440	203	15	to	to	PART
ejpam-5440	203	16	be	be	AUX
ejpam-5440	203	17	independently	independently	ADV
ejpam-5440	203	18	obtained	obtain	VERB
ejpam-5440	203	19	.	.	PUNCT
ejpam-5440	204	1	berinde	berinde	NOUN
ejpam-5440	205	1	[	[	X
ejpam-5440	205	2	3	3	X
ejpam-5440	205	3	]	]	PUNCT
ejpam-5440	205	4	in	in	ADP
ejpam-5440	205	5	2003	2003	NUM
ejpam-5440	205	6	mentioned	mention	VERB
ejpam-5440	205	7	the	the	DET
ejpam-5440	205	8	so	so	ADV
ejpam-5440	205	9	called	call	VERB
ejpam-5440	205	10	banach	banach	ADV
ejpam-5440	205	11	orbital	orbital	ADJ
ejpam-5440	205	12	condition	condition	NOUN
ejpam-5440	205	13	d(tx	d(tx	PROPN
ejpam-5440	205	14	,	,	PUNCT
ejpam-5440	205	15	t	t	PROPN
ejpam-5440	205	16	2x	2x	NUM
ejpam-5440	205	17	)	)	PUNCT
ejpam-5440	205	18	≤	≤	NOUN
ejpam-5440	205	19	αd(x	αd(x	PUNCT
ejpam-5440	205	20	,	,	PUNCT
ejpam-5440	205	21	tx	tx	PROPN
ejpam-5440	205	22	)	)	PUNCT
ejpam-5440	205	23	,	,	PUNCT
ejpam-5440	205	24	for	for	SCONJ
ejpam-5440	205	25	all	all	DET
ejpam-5440	205	26	x	x	SYM
ejpam-5440	205	27	∈	∈	PROPN
ejpam-5440	205	28	x	x	NOUN
ejpam-5440	205	29	,	,	PUNCT
ejpam-5440	205	30	studied	study	VERB
ejpam-5440	205	31	by	by	ADP
ejpam-5440	205	32	various	various	ADJ
ejpam-5440	205	33	authors	author	NOUN
ejpam-5440	205	34	in	in	ADP
ejpam-5440	205	35	the	the	DET
ejpam-5440	205	36	context	context	NOUN
ejpam-5440	205	37	of	of	ADP
ejpam-5440	205	38	fixed	fix	VERB
ejpam-5440	205	39	point	point	NOUN
ejpam-5440	205	40	theorems	theorem	NOUN
ejpam-5440	205	41	,	,	PUNCT
ejpam-5440	205	42	see	see	VERB
ejpam-5440	205	43	for	for	ADP
ejpam-5440	205	44	example	example	NOUN
ejpam-5440	205	45	kasahara	kasahara	PROPN
ejpam-5440	205	46	,	,	PUNCT
ejpam-5440	205	47	hicks	hick	NOUN
ejpam-5440	205	48	and	and	CCONJ
ejpam-5440	205	49	rhoades	rhoade	NOUN
ejpam-5440	205	50	,	,	PUNCT
ejpam-5440	205	51	ivanov	ivanov	PROPN
ejpam-5440	205	52	,	,	PUNCT
ejpam-5440	205	53	rus	rus	NOUN
ejpam-5440	205	54	and	and	CCONJ
ejpam-5440	205	55	taskovic	taskovic	NOUN
ejpam-5440	205	56	given	give	VERB
ejpam-5440	205	57	in	in	ADP
ejpam-5440	205	58	[	[	X
ejpam-5440	205	59	3	3	NUM
ejpam-5440	205	60	]	]	PUNCT
ejpam-5440	205	61	.	.	PUNCT
ejpam-5440	206	1	berinde	berinde	NOUN
ejpam-5440	206	2	-	-	PUNCT
ejpam-5440	206	3	pacurar	pacurar	NOUN
ejpam-5440	206	4	[	[	X
ejpam-5440	206	5	4	4	NUM
ejpam-5440	206	6	]	]	PUNCT
ejpam-5440	206	7	in	in	ADP
ejpam-5440	206	8	2022	2022	NUM
ejpam-5440	206	9	defined	define	VERB
ejpam-5440	206	10	a	a	DET
ejpam-5440	206	11	graphic	graphic	ADJ
ejpam-5440	206	12	contraction	contraction	NOUN
ejpam-5440	206	13	(	(	PUNCT
ejpam-5440	206	14	orbital	orbital	ADJ
ejpam-5440	206	15	contraction	contraction	NOUN
ejpam-5440	206	16	)	)	PUNCT
ejpam-5440	206	17	and	and	CCONJ
ejpam-5440	206	18	give	give	VERB
ejpam-5440	206	19	examples	example	NOUN
ejpam-5440	206	20	as	as	SCONJ
ejpam-5440	206	21	follows	follow	VERB
ejpam-5440	206	22	:	:	PUNCT
ejpam-5440	206	23	banach	banach	NOUN
ejpam-5440	206	24	contraction	contraction	NOUN
ejpam-5440	206	25	,	,	PUNCT
ejpam-5440	206	26	kannan	kannan	PROPN
ejpam-5440	206	27	mapping	mapping	PROPN
ejpam-5440	206	28	,	,	PUNCT
ejpam-5440	206	29	ćirić-reich	ćirić-reich	NOUN
ejpam-5440	206	30	-	-	PUNCT
ejpam-5440	206	31	rus	rus	NOUN
ejpam-5440	206	32	contraction	contraction	NOUN
ejpam-5440	206	33	,	,	PUNCT
ejpam-5440	206	34	bianchini	bianchini	PROPN
ejpam-5440	206	35	mapping	mapping	NOUN
ejpam-5440	206	36	,	,	PUNCT
ejpam-5440	206	37	chatterjea	chatterjea	PROPN
ejpam-5440	206	38	mapping	mapping	NOUN
ejpam-5440	206	39	,	,	PUNCT
ejpam-5440	206	40	zamfirescu	zamfirescu	PROPN
ejpam-5440	206	41	mapping	mapping	PROPN
ejpam-5440	206	42	,	,	PUNCT
ejpam-5440	206	43	ćirić	ćirić	PROPN
ejpam-5440	206	44	quasi	quasi	NOUN
ejpam-5440	206	45	-	-	NOUN
ejpam-5440	206	46	contraction	contraction	NOUN
ejpam-5440	206	47	,	,	PUNCT
ejpam-5440	206	48	hardy	hardy	ADJ
ejpam-5440	206	49	and	and	CCONJ
ejpam-5440	206	50	rogers	rogers	PROPN
ejpam-5440	206	51	contraction	contraction	PROPN
ejpam-5440	206	52	,	,	PUNCT
ejpam-5440	206	53	berinde	berinde	PROPN
ejpam-5440	206	54	’s	’s	PART
ejpam-5440	206	55	almost	almost	ADV
ejpam-5440	206	56	contraction	contraction	NOUN
ejpam-5440	206	57	,	,	PUNCT
ejpam-5440	206	58	in	in	ADP
ejpam-5440	206	59	2023	2023	NUM
ejpam-5440	206	60	,	,	PUNCT
ejpam-5440	206	61	berinde	berinde	NOUN
ejpam-5440	206	62	,	,	PUNCT
ejpam-5440	206	63	petrusȩl	petrusȩl	PROPN
ejpam-5440	206	64	and	and	CCONJ
ejpam-5440	206	65	i.a	i.a	PROPN
ejpam-5440	206	66	.	.	PROPN
ejpam-5440	206	67	rus	rus	NOUN
ejpam-5440	207	1	[	[	X
ejpam-5440	207	2	5	5	NUM
ejpam-5440	207	3	]	]	PUNCT
ejpam-5440	207	4	listed	list	VERB
ejpam-5440	207	5	previous	previous	ADJ
ejpam-5440	207	6	names	name	NOUN
ejpam-5440	207	7	of	of	ADP
ejpam-5440	207	8	the	the	DET
ejpam-5440	207	9	rhr	rhr	PROPN
ejpam-5440	207	10	maps	maps	PROPN
ejpam-5440	207	11	as	as	ADP
ejpam-5440	207	12	graphic	graphic	ADJ
ejpam-5440	207	13	contraction	contraction	NOUN
ejpam-5440	207	14	,	,	PUNCT
ejpam-5440	207	15	iterative	iterative	NOUN
ejpam-5440	207	16	contraction	contraction	NOUN
ejpam-5440	207	17	,	,	PUNCT
ejpam-5440	207	18	weakly	weakly	ADJ
ejpam-5440	207	19	contraction	contraction	NOUN
ejpam-5440	207	20	,	,	PUNCT
ejpam-5440	207	21	banach	banach	NOUN
ejpam-5440	207	22	mapping	mapping	NOUN
ejpam-5440	207	23	,	,	PUNCT
ejpam-5440	207	24	.	.	PUNCT
ejpam-5440	207	25	.	.	PUNCT
ejpam-5440	207	26	.	.	PUNCT
ejpam-5440	208	1	.	.	PUNCT
ejpam-5440	209	1	in	in	ADP
ejpam-5440	209	2	our	our	PRON
ejpam-5440	209	3	previous	previous	ADJ
ejpam-5440	209	4	work	work	NOUN
ejpam-5440	209	5	[	[	X
ejpam-5440	209	6	17	17	NUM
ejpam-5440	209	7	]	]	PUNCT
ejpam-5440	209	8	,	,	PUNCT
ejpam-5440	209	9	we	we	PRON
ejpam-5440	209	10	give	give	VERB
ejpam-5440	209	11	the	the	DET
ejpam-5440	209	12	numbers	number	NOUN
ejpam-5440	209	13	of	of	ADP
ejpam-5440	209	14	articles	article	NOUN
ejpam-5440	209	15	having	have	VERB
ejpam-5440	209	16	examples	example	NOUN
ejpam-5440	209	17	of	of	ADP
ejpam-5440	209	18	the	the	DET
ejpam-5440	209	19	rhr	rhr	PROPN
ejpam-5440	209	20	maps	map	NOUN
ejpam-5440	209	21	as	as	SCONJ
ejpam-5440	209	22	follows	follow	VERB
ejpam-5440	209	23	:	:	PUNCT
ejpam-5440	209	24	s.	s.	PROPN
ejpam-5440	209	25	park	park	PROPN
ejpam-5440	209	26	/	/	SYM
ejpam-5440	209	27	eur	eur	PROPN
ejpam-5440	209	28	.	.	PUNCT
ejpam-5440	210	1	j.	j.	PROPN
ejpam-5440	210	2	pure	pure	PROPN
ejpam-5440	210	3	appl	appl	PROPN
ejpam-5440	210	4	.	.	PROPN
ejpam-5440	210	5	math	math	PROPN
ejpam-5440	210	6	,	,	PUNCT
ejpam-5440	210	7	17	17	NUM
ejpam-5440	210	8	(	(	PUNCT
ejpam-5440	210	9	4	4	NUM
ejpam-5440	210	10	)	)	PUNCT
ejpam-5440	210	11	(	(	PUNCT
ejpam-5440	210	12	2024	2024	NUM
ejpam-5440	210	13	)	)	PUNCT
ejpam-5440	210	14	,	,	PUNCT
ejpam-5440	210	15	2370	2370	NUM
ejpam-5440	210	16	-	-	SYM
ejpam-5440	210	17	2383	2383	NUM
ejpam-5440	210	18	2379	2379	NUM
ejpam-5440	210	19	early	early	ADJ
ejpam-5440	210	20	examples	example	NOUN
ejpam-5440	210	21	of	of	ADP
ejpam-5440	210	22	the	the	DET
ejpam-5440	210	23	rhr	rhr	PROPN
ejpam-5440	210	24	maps	maps	PROPN
ejpam-5440	210	25	(	(	PUNCT
ejpam-5440	210	26	1973–2009	1973–2009	NUM
ejpam-5440	210	27	)	)	PUNCT
ejpam-5440	210	28	:	:	PUNCT
ejpam-5440	210	29	26	26	NUM
ejpam-5440	210	30	suzuki	suzuki	NOUN
ejpam-5440	210	31	types	type	NOUN
ejpam-5440	210	32	of	of	ADP
ejpam-5440	210	33	the	the	DET
ejpam-5440	210	34	rhr	rhr	PROPN
ejpam-5440	210	35	maps	maps	PROPN
ejpam-5440	210	36	(	(	PUNCT
ejpam-5440	210	37	2001–2010	2001–2010	NUM
ejpam-5440	210	38	)	)	PUNCT
ejpam-5440	210	39	:	:	PUNCT
ejpam-5440	210	40	10	10	NUM
ejpam-5440	210	41	recent	recent	ADJ
ejpam-5440	210	42	rhr	rhr	PROPN
ejpam-5440	210	43	type	type	NOUN
ejpam-5440	210	44	maps	map	NOUN
ejpam-5440	210	45	(	(	PUNCT
ejpam-5440	210	46	2011–2023	2011–2023	NUM
ejpam-5440	210	47	)	)	PUNCT
ejpam-5440	210	48	:	:	PUNCT
ejpam-5440	210	49	37	37	NUM
ejpam-5440	210	50	almost	almost	ADV
ejpam-5440	210	51	all	all	PRON
ejpam-5440	210	52	of	of	ADP
ejpam-5440	210	53	main	main	ADJ
ejpam-5440	210	54	theorems	theorem	NOUN
ejpam-5440	210	55	of	of	ADP
ejpam-5440	210	56	these	these	DET
ejpam-5440	210	57	papers	paper	NOUN
ejpam-5440	210	58	are	be	AUX
ejpam-5440	210	59	consequences	consequence	NOUN
ejpam-5440	210	60	of	of	ADP
ejpam-5440	210	61	theorem	theorem	NOUN
ejpam-5440	210	62	p	p	NOUN
ejpam-5440	210	63	for	for	ADP
ejpam-5440	210	64	metric	metric	ADJ
ejpam-5440	210	65	spaces	space	NOUN
ejpam-5440	210	66	.	.	PUNCT
ejpam-5440	211	1	these	these	PRON
ejpam-5440	211	2	can	can	AUX
ejpam-5440	211	3	be	be	AUX
ejpam-5440	211	4	applied	apply	VERB
ejpam-5440	211	5	to	to	ADP
ejpam-5440	211	6	nearly	nearly	ADV
ejpam-5440	211	7	one	one	NUM
ejpam-5440	211	8	thousand	thousand	NUM
ejpam-5440	211	9	artificial	artificial	ADJ
ejpam-5440	211	10	metric	metric	ADJ
ejpam-5440	211	11	type	type	NOUN
ejpam-5440	211	12	spaces	space	NOUN
ejpam-5440	211	13	.	.	PUNCT
ejpam-5440	212	1	8	8	X
ejpam-5440	212	2	.	.	X
ejpam-5440	213	1	the	the	DET
ejpam-5440	213	2	subfamily	subfamily	ADV
ejpam-5440	213	3	(	(	PUNCT
ejpam-5440	213	4	δ	δ	NOUN
ejpam-5440	213	5	)	)	PUNCT
ejpam-5440	213	6	in	in	ADP
ejpam-5440	213	7	theorem	theorem	ADJ
ejpam-5440	213	8	h	h	NOUN
ejpam-5440	213	9	,	,	PUNCT
ejpam-5440	213	10	consider	consider	VERB
ejpam-5440	213	11	the	the	DET
ejpam-5440	213	12	following	following	NOUN
ejpam-5440	213	13	:	:	PUNCT
ejpam-5440	213	14	(	(	PUNCT
ejpam-5440	213	15	δ	δ	NOUN
ejpam-5440	213	16	)	)	PUNCT
ejpam-5440	213	17	let	let	VERB
ejpam-5440	213	18	f	f	PRON
ejpam-5440	213	19	be	be	AUX
ejpam-5440	213	20	a	a	DET
ejpam-5440	213	21	family	family	NOUN
ejpam-5440	213	22	of	of	ADP
ejpam-5440	213	23	multimaps	multimap	NOUN
ejpam-5440	213	24	t	t	PROPN
ejpam-5440	213	25	:	:	PUNCT
ejpam-5440	213	26	x	x	X
ejpam-5440	213	27	→	→	SYM
ejpam-5440	213	28	cl(x	cl(x	NOUN
ejpam-5440	213	29	)	)	PUNCT
ejpam-5440	213	30	such	such	ADJ
ejpam-5440	213	31	that	that	SCONJ
ejpam-5440	213	32	,	,	PUNCT
ejpam-5440	213	33	for	for	ADP
ejpam-5440	213	34	any	any	DET
ejpam-5440	213	35	x	x	SYM
ejpam-5440	213	36	∈	∈	PROPN
ejpam-5440	213	37	x\t	x\t	PUNCT
ejpam-5440	214	1	(	(	PUNCT
ejpam-5440	214	2	x	x	X
ejpam-5440	214	3	)	)	PUNCT
ejpam-5440	214	4	,	,	PUNCT
ejpam-5440	214	5	there	there	PRON
ejpam-5440	214	6	exists	exist	VERB
ejpam-5440	214	7	y	y	PROPN
ejpam-5440	214	8	∈	∈	PROPN
ejpam-5440	214	9	x\{x	x\{x	PROPN
ejpam-5440	214	10	}	}	PUNCT
ejpam-5440	214	11	satisfying	satisfy	VERB
ejpam-5440	214	12	h(t	h(t	PROPN
ejpam-5440	214	13	(	(	PUNCT
ejpam-5440	214	14	x	x	NOUN
ejpam-5440	214	15	)	)	PUNCT
ejpam-5440	214	16	,	,	PUNCT
ejpam-5440	214	17	t	t	PROPN
ejpam-5440	214	18	(	(	PUNCT
ejpam-5440	214	19	y	y	NOUN
ejpam-5440	214	20	)	)	PUNCT
ejpam-5440	214	21	)	)	PUNCT
ejpam-5440	214	22	≤	≤	NUM
ejpam-5440	214	23	α	α	PROPN
ejpam-5440	214	24	q(x	q(x	PROPN
ejpam-5440	214	25	,	,	PUNCT
ejpam-5440	214	26	y	y	NOUN
ejpam-5440	214	27	)	)	PUNCT
ejpam-5440	214	28	.	.	PUNCT
ejpam-5440	215	1	then	then	ADV
ejpam-5440	215	2	f	f	PROPN
ejpam-5440	215	3	has	have	VERB
ejpam-5440	215	4	a	a	DET
ejpam-5440	215	5	common	common	ADJ
ejpam-5440	215	6	fixed	fix	VERB
ejpam-5440	215	7	element	element	NOUN
ejpam-5440	215	8	v	v	ADP
ejpam-5440	215	9	∈	∈	PROPN
ejpam-5440	215	10	x	x	NOUN
ejpam-5440	215	11	,	,	PUNCT
ejpam-5440	215	12	that	that	ADV
ejpam-5440	215	13	is	is	ADV
ejpam-5440	215	14	,	,	PUNCT
ejpam-5440	215	15	v	v	PROPN
ejpam-5440	215	16	∈	∈	PROPN
ejpam-5440	215	17	t	t	NOUN
ejpam-5440	215	18	(	(	PUNCT
ejpam-5440	215	19	v	v	NOUN
ejpam-5440	215	20	)	)	PUNCT
ejpam-5440	215	21	for	for	ADP
ejpam-5440	215	22	all	all	PRON
ejpam-5440	215	23	t	t	PROPN
ejpam-5440	215	24	∈	∈	PROPN
ejpam-5440	215	25	f.	f.	PROPN
ejpam-5440	215	26	note	note	VERB
ejpam-5440	215	27	that	that	SCONJ
ejpam-5440	215	28	the	the	DET
ejpam-5440	215	29	t	t	NOUN
ejpam-5440	215	30	-orbital	-orbital	PROPN
ejpam-5440	215	31	completeness	completeness	NOUN
ejpam-5440	215	32	of	of	ADP
ejpam-5440	215	33	(	(	PUNCT
ejpam-5440	215	34	x	x	NOUN
ejpam-5440	215	35	,	,	PUNCT
ejpam-5440	215	36	q	q	NOUN
ejpam-5440	215	37	)	)	PUNCT
ejpam-5440	215	38	for	for	ADP
ejpam-5440	215	39	any	any	DET
ejpam-5440	215	40	multimap	multimap	NOUN
ejpam-5440	215	41	t	t	NOUN
ejpam-5440	215	42	:	:	PUNCT
ejpam-5440	215	43	x	x	X
ejpam-5440	215	44	→	→	SYM
ejpam-5440	215	45	cl(x	cl(x	NOUN
ejpam-5440	215	46	)	)	PUNCT
ejpam-5440	215	47	in	in	ADP
ejpam-5440	215	48	f	f	PROPN
ejpam-5440	215	49	implies	imply	VERB
ejpam-5440	215	50	(	(	PUNCT
ejpam-5440	215	51	δ	δ	NOUN
ejpam-5440	215	52	)	)	PUNCT
ejpam-5440	215	53	.	.	PUNCT
ejpam-5440	216	1	when	when	SCONJ
ejpam-5440	216	2	f	f	PROPN
ejpam-5440	216	3	is	be	AUX
ejpam-5440	216	4	a	a	DET
ejpam-5440	216	5	singleton	singleton	NOUN
ejpam-5440	216	6	,	,	PUNCT
ejpam-5440	216	7	we	we	PRON
ejpam-5440	216	8	have	have	VERB
ejpam-5440	216	9	extensions	extension	NOUN
ejpam-5440	216	10	of	of	ADP
ejpam-5440	216	11	the	the	DET
ejpam-5440	216	12	nadler	nadler	NOUN
ejpam-5440	216	13	and	and	CCONJ
ejpam-5440	216	14	covitz	covitz	PROPN
ejpam-5440	216	15	-	-	PUNCT
ejpam-5440	216	16	nadler	nadler	NOUN
ejpam-5440	216	17	fixed	fix	VERB
ejpam-5440	216	18	point	point	NOUN
ejpam-5440	216	19	theorems	theorem	NOUN
ejpam-5440	216	20	[	[	X
ejpam-5440	216	21	7	7	NUM
ejpam-5440	216	22	]	]	PUNCT
ejpam-5440	216	23	,	,	PUNCT
ejpam-5440	216	24	[	[	X
ejpam-5440	216	25	10	10	NUM
ejpam-5440	216	26	]	]	PUNCT
ejpam-5440	216	27	and	and	CCONJ
ejpam-5440	216	28	their	their	PRON
ejpam-5440	216	29	converses	converse	NOUN
ejpam-5440	216	30	,	,	PUNCT
ejpam-5440	216	31	that	that	ADV
ejpam-5440	216	32	is	is	ADV
ejpam-5440	216	33	,	,	PUNCT
ejpam-5440	216	34	theorem	theorem	ADJ
ejpam-5440	216	35	h(0	h(0	PROPN
ejpam-5440	216	36	)	)	PUNCT
ejpam-5440	216	37	is	be	AUX
ejpam-5440	216	38	equivalent	equivalent	ADJ
ejpam-5440	216	39	to	to	ADP
ejpam-5440	216	40	(	(	PUNCT
ejpam-5440	216	41	δ1	δ1	NOUN
ejpam-5440	216	42	)	)	PUNCT
ejpam-5440	216	43	as	as	SCONJ
ejpam-5440	216	44	follows	follow	VERB
ejpam-5440	216	45	:	:	PUNCT
ejpam-5440	216	46	theorem	theorem	NOUN
ejpam-5440	216	47	8.1	8.1	NUM
ejpam-5440	216	48	.	.	PUNCT
ejpam-5440	217	1	let	let	VERB
ejpam-5440	217	2	(	(	PUNCT
ejpam-5440	217	3	x	x	X
ejpam-5440	217	4	,	,	PUNCT
ejpam-5440	217	5	q	q	X
ejpam-5440	217	6	)	)	PUNCT
ejpam-5440	217	7	be	be	AUX
ejpam-5440	217	8	a	a	DET
ejpam-5440	217	9	quasi	quasi	ADJ
ejpam-5440	217	10	-	-	ADJ
ejpam-5440	217	11	metric	metric	ADJ
ejpam-5440	217	12	space	space	NOUN
ejpam-5440	217	13	.	.	PUNCT
ejpam-5440	218	1	then	then	ADV
ejpam-5440	218	2	it	it	PRON
ejpam-5440	218	3	is	be	AUX
ejpam-5440	218	4	complete	complete	ADJ
ejpam-5440	218	5	if	if	SCONJ
ejpam-5440	218	6	and	and	CCONJ
ejpam-5440	218	7	only	only	ADV
ejpam-5440	218	8	if	if	SCONJ
ejpam-5440	218	9	(	(	PUNCT
ejpam-5440	218	10	δ1	δ1	NOUN
ejpam-5440	218	11	)	)	PUNCT
ejpam-5440	218	12	let	let	VERB
ejpam-5440	218	13	t	t	NOUN
ejpam-5440	218	14	:	:	PUNCT
ejpam-5440	218	15	x	x	SYM
ejpam-5440	218	16	→	→	SYM
ejpam-5440	218	17	cl(x	cl(x	X
ejpam-5440	218	18	)	)	PUNCT
ejpam-5440	218	19	be	be	AUX
ejpam-5440	218	20	a	a	DET
ejpam-5440	218	21	multimap	multimap	NOUN
ejpam-5440	218	22	such	such	ADJ
ejpam-5440	218	23	that	that	PRON
ejpam-5440	218	24	,	,	PUNCT
ejpam-5440	218	25	for	for	ADP
ejpam-5440	218	26	any	any	DET
ejpam-5440	218	27	x	x	SYM
ejpam-5440	218	28	∈	∈	PROPN
ejpam-5440	218	29	x\{tx	x\{tx	PROPN
ejpam-5440	218	30	}	}	PUNCT
ejpam-5440	218	31	,	,	PUNCT
ejpam-5440	218	32	there	there	PRON
ejpam-5440	218	33	exists	exist	VERB
ejpam-5440	218	34	y	y	PROPN
ejpam-5440	218	35	∈	∈	PROPN
ejpam-5440	218	36	x\{x	x\{x	PROPN
ejpam-5440	218	37	}	}	PUNCT
ejpam-5440	218	38	satisfying	satisfy	VERB
ejpam-5440	218	39	h(t	h(t	PROPN
ejpam-5440	218	40	(	(	PUNCT
ejpam-5440	218	41	x	x	NOUN
ejpam-5440	218	42	)	)	PUNCT
ejpam-5440	218	43	,	,	PUNCT
ejpam-5440	218	44	t	t	PROPN
ejpam-5440	218	45	(	(	PUNCT
ejpam-5440	218	46	y	y	NOUN
ejpam-5440	218	47	)	)	PUNCT
ejpam-5440	218	48	)	)	PUNCT
ejpam-5440	218	49	≤	≤	NUM
ejpam-5440	218	50	α	α	PROPN
ejpam-5440	218	51	q(x	q(x	PROPN
ejpam-5440	218	52	,	,	PUNCT
ejpam-5440	218	53	y	y	NOUN
ejpam-5440	218	54	)	)	PUNCT
ejpam-5440	218	55	.	.	PUNCT
ejpam-5440	219	1	then	then	ADV
ejpam-5440	219	2	t	t	PROPN
ejpam-5440	219	3	has	have	VERB
ejpam-5440	219	4	a	a	DET
ejpam-5440	219	5	fixed	fix	VERB
ejpam-5440	219	6	element	element	NOUN
ejpam-5440	219	7	v	v	ADP
ejpam-5440	219	8	∈	∈	PROPN
ejpam-5440	219	9	x	x	NOUN
ejpam-5440	219	10	,	,	PUNCT
ejpam-5440	219	11	that	that	ADV
ejpam-5440	219	12	is	is	ADV
ejpam-5440	219	13	,	,	PUNCT
ejpam-5440	219	14	v	v	PROPN
ejpam-5440	219	15	∈	∈	PROPN
ejpam-5440	219	16	t	t	NOUN
ejpam-5440	219	17	(	(	PUNCT
ejpam-5440	219	18	v	v	NOUN
ejpam-5440	219	19	)	)	PUNCT
ejpam-5440	219	20	.	.	PUNCT
ejpam-5440	220	1	the	the	PRON
ejpam-5440	220	2	only	only	ADJ
ejpam-5440	220	3	if	if	SCONJ
ejpam-5440	220	4	part	part	NOUN
ejpam-5440	220	5	extends	extend	VERB
ejpam-5440	220	6	also	also	ADV
ejpam-5440	220	7	the	the	DET
ejpam-5440	220	8	so	so	ADV
ejpam-5440	220	9	-	-	PUNCT
ejpam-5440	220	10	called	call	VERB
ejpam-5440	220	11	banach	banach	NOUN
ejpam-5440	220	12	contraction	contraction	NOUN
ejpam-5440	220	13	principle	principle	NOUN
ejpam-5440	220	14	.	.	PUNCT
ejpam-5440	221	1	9	9	X
ejpam-5440	221	2	.	.	X
ejpam-5440	221	3	the	the	DET
ejpam-5440	221	4	subfamily	subfamily	ADV
ejpam-5440	221	5	(	(	PUNCT
ejpam-5440	221	6	ϵ	ϵ	NOUN
ejpam-5440	221	7	)	)	PUNCT
ejpam-5440	221	8	.	.	PUNCT
ejpam-5440	222	1	in	in	ADP
ejpam-5440	222	2	theorem	theorem	ADJ
ejpam-5440	222	3	h	h	NOUN
ejpam-5440	222	4	,	,	PUNCT
ejpam-5440	222	5	consider	consider	VERB
ejpam-5440	222	6	the	the	DET
ejpam-5440	222	7	following	following	NOUN
ejpam-5440	222	8	:	:	PUNCT
ejpam-5440	222	9	(	(	PUNCT
ejpam-5440	222	10	ϵ	ϵ	X
ejpam-5440	222	11	)	)	PUNCT
ejpam-5440	222	12	if	if	SCONJ
ejpam-5440	222	13	f	f	PROPN
ejpam-5440	222	14	is	be	AUX
ejpam-5440	222	15	a	a	DET
ejpam-5440	222	16	family	family	NOUN
ejpam-5440	222	17	of	of	ADP
ejpam-5440	222	18	multimaps	multimap	NOUN
ejpam-5440	222	19	t	t	PROPN
ejpam-5440	222	20	:	:	PUNCT
ejpam-5440	223	1	x	x	X
ejpam-5440	223	2	→	→	SYM
ejpam-5440	223	3	cl(x	cl(x	X
ejpam-5440	223	4	)	)	PUNCT
ejpam-5440	223	5	satisfying	satisfy	VERB
ejpam-5440	223	6	h(t	h(t	PROPN
ejpam-5440	223	7	(	(	PUNCT
ejpam-5440	223	8	x	x	NOUN
ejpam-5440	223	9	)	)	PUNCT
ejpam-5440	223	10	,	,	PUNCT
ejpam-5440	223	11	t	t	PROPN
ejpam-5440	223	12	(	(	PUNCT
ejpam-5440	223	13	y	y	NOUN
ejpam-5440	223	14	)	)	PUNCT
ejpam-5440	223	15	)	)	PUNCT
ejpam-5440	223	16	≤	≤	NUM
ejpam-5440	223	17	α	α	PROPN
ejpam-5440	223	18	q(x	q(x	PROPN
ejpam-5440	223	19	,	,	PUNCT
ejpam-5440	223	20	y	y	NOUN
ejpam-5440	223	21	)	)	PUNCT
ejpam-5440	223	22	for	for	ADP
ejpam-5440	223	23	all	all	PRON
ejpam-5440	223	24	x	x	SYM
ejpam-5440	223	25	∈	∈	PROPN
ejpam-5440	223	26	x	x	X
ejpam-5440	223	27	and	and	CCONJ
ejpam-5440	223	28	any	any	DET
ejpam-5440	223	29	y	y	PROPN
ejpam-5440	223	30	∈	∈	PROPN
ejpam-5440	223	31	t	t	PROPN
ejpam-5440	223	32	(	(	PUNCT
ejpam-5440	223	33	x)\{x	x)\{x	PROPN
ejpam-5440	223	34	}	}	PUNCT
ejpam-5440	223	35	,	,	PUNCT
ejpam-5440	223	36	then	then	ADV
ejpam-5440	223	37	f	f	PROPN
ejpam-5440	223	38	has	have	VERB
ejpam-5440	223	39	a	a	DET
ejpam-5440	223	40	common	common	ADJ
ejpam-5440	223	41	stationary	stationary	ADJ
ejpam-5440	223	42	element	element	NOUN
ejpam-5440	223	43	v	v	ADP
ejpam-5440	223	44	∈	∈	PROPN
ejpam-5440	223	45	x	x	NOUN
ejpam-5440	223	46	,	,	PUNCT
ejpam-5440	223	47	that	that	ADV
ejpam-5440	223	48	is	is	ADV
ejpam-5440	223	49	,	,	PUNCT
ejpam-5440	223	50	{	{	PUNCT
ejpam-5440	223	51	v	v	NOUN
ejpam-5440	223	52	}	}	PUNCT
ejpam-5440	223	53	=	=	SYM
ejpam-5440	223	54	t	t	PROPN
ejpam-5440	223	55	(	(	PUNCT
ejpam-5440	223	56	v	v	NOUN
ejpam-5440	223	57	)	)	PUNCT
ejpam-5440	223	58	for	for	ADP
ejpam-5440	223	59	all	all	PRON
ejpam-5440	223	60	t	t	PROPN
ejpam-5440	223	61	∈	∈	PROPN
ejpam-5440	223	62	f.	f.	PROPN
ejpam-5440	223	63	note	note	VERB
ejpam-5440	223	64	that	that	SCONJ
ejpam-5440	223	65	the	the	DET
ejpam-5440	223	66	t	t	NOUN
ejpam-5440	223	67	-orbital	-orbital	PROPN
ejpam-5440	223	68	completeness	completeness	NOUN
ejpam-5440	223	69	of	of	ADP
ejpam-5440	223	70	(	(	PUNCT
ejpam-5440	223	71	x	x	NOUN
ejpam-5440	223	72	,	,	PUNCT
ejpam-5440	223	73	q	q	NOUN
ejpam-5440	223	74	)	)	PUNCT
ejpam-5440	223	75	for	for	ADP
ejpam-5440	223	76	any	any	DET
ejpam-5440	223	77	multimap	multimap	NOUN
ejpam-5440	223	78	t	t	NOUN
ejpam-5440	223	79	:	:	PUNCT
ejpam-5440	223	80	x	x	X
ejpam-5440	223	81	→	→	SYM
ejpam-5440	223	82	cl(x	cl(x	NOUN
ejpam-5440	223	83	)	)	PUNCT
ejpam-5440	223	84	in	in	ADP
ejpam-5440	223	85	f	f	PROPN
ejpam-5440	223	86	implies	imply	VERB
ejpam-5440	223	87	(	(	PUNCT
ejpam-5440	223	88	ϵ	ϵ	X
ejpam-5440	223	89	)	)	PUNCT
ejpam-5440	223	90	.	.	PUNCT
ejpam-5440	224	1	from	from	ADP
ejpam-5440	224	2	(	(	PUNCT
ejpam-5440	224	3	ϵ	ϵ	NOUN
ejpam-5440	224	4	)	)	PUNCT
ejpam-5440	224	5	,	,	PUNCT
ejpam-5440	224	6	we	we	PRON
ejpam-5440	224	7	can	can	AUX
ejpam-5440	224	8	deduce	deduce	VERB
ejpam-5440	224	9	at	at	ADV
ejpam-5440	224	10	least	least	ADV
ejpam-5440	224	11	four	four	NUM
ejpam-5440	224	12	particular	particular	ADJ
ejpam-5440	224	13	cases	case	NOUN
ejpam-5440	224	14	.	.	PUNCT
ejpam-5440	225	1	the	the	DET
ejpam-5440	225	2	following	follow	VERB
ejpam-5440	225	3	is	be	AUX
ejpam-5440	225	4	only	only	ADV
ejpam-5440	225	5	one	one	NUM
ejpam-5440	225	6	of	of	ADP
ejpam-5440	225	7	the	the	DET
ejpam-5440	225	8	oldest	old	ADJ
ejpam-5440	225	9	one	one	NUM
ejpam-5440	225	10	for	for	ADP
ejpam-5440	225	11	the	the	DET
ejpam-5440	225	12	singleton	singleton	NOUN
ejpam-5440	225	13	[	[	X
ejpam-5440	225	14	10	10	NUM
ejpam-5440	225	15	]	]	NUM
ejpam-5440	225	16	:	:	PUNCT
ejpam-5440	225	17	theorem	theorem	NOUN
ejpam-5440	225	18	9.1	9.1	NUM
ejpam-5440	225	19	.	.	PUNCT
ejpam-5440	226	1	(	(	PUNCT
ejpam-5440	226	2	nadler	nadler	PROPN
ejpam-5440	226	3	)	)	PUNCT
ejpam-5440	226	4	let	let	VERB
ejpam-5440	226	5	(	(	PUNCT
ejpam-5440	226	6	x	x	NOUN
ejpam-5440	226	7	,	,	PUNCT
ejpam-5440	226	8	d	d	NOUN
ejpam-5440	226	9	)	)	PUNCT
ejpam-5440	226	10	be	be	AUX
ejpam-5440	226	11	a	a	DET
ejpam-5440	226	12	complete	complete	ADJ
ejpam-5440	226	13	metric	metric	ADJ
ejpam-5440	226	14	space	space	NOUN
ejpam-5440	226	15	.	.	PUNCT
ejpam-5440	227	1	if	if	SCONJ
ejpam-5440	227	2	f	f	PROPN
ejpam-5440	227	3	:	:	PUNCT
ejpam-5440	227	4	x	x	X
ejpam-5440	227	5	→	→	SYM
ejpam-5440	227	6	bc(x	bc(x	NOUN
ejpam-5440	227	7	)	)	PUNCT
ejpam-5440	227	8	is	be	AUX
ejpam-5440	227	9	a	a	DET
ejpam-5440	227	10	multi	multi	ADJ
ejpam-5440	227	11	-	-	ADJ
ejpam-5440	227	12	valued	value	VERB
ejpam-5440	227	13	contraction	contraction	NOUN
ejpam-5440	227	14	map	map	NOUN
ejpam-5440	227	15	,	,	PUNCT
ejpam-5440	227	16	then	then	ADV
ejpam-5440	227	17	f	f	PROPN
ejpam-5440	227	18	has	have	VERB
ejpam-5440	227	19	a	a	DET
ejpam-5440	227	20	fixed	fix	VERB
ejpam-5440	227	21	point	point	NOUN
ejpam-5440	227	22	.	.	PUNCT
ejpam-5440	228	1	according	accord	VERB
ejpam-5440	228	2	to	to	ADP
ejpam-5440	228	3	our	our	PRON
ejpam-5440	228	4	(	(	PUNCT
ejpam-5440	228	5	ϵ	ϵ	NOUN
ejpam-5440	228	6	)	)	PUNCT
ejpam-5440	228	7	,	,	PUNCT
ejpam-5440	228	8	the	the	DET
ejpam-5440	228	9	fixed	fix	VERB
ejpam-5440	228	10	point	point	NOUN
ejpam-5440	228	11	should	should	AUX
ejpam-5440	228	12	be	be	AUX
ejpam-5440	228	13	strengthened	strengthen	VERB
ejpam-5440	228	14	to	to	ADP
ejpam-5440	228	15	a	a	DET
ejpam-5440	228	16	stationary	stationary	ADJ
ejpam-5440	228	17	point	point	NOUN
ejpam-5440	228	18	.	.	PUNCT
ejpam-5440	229	1	moreover	moreover	ADV
ejpam-5440	229	2	,	,	PUNCT
ejpam-5440	229	3	covitz	covitz	NOUN
ejpam-5440	229	4	and	and	CCONJ
ejpam-5440	229	5	nadler	nadler	NOUN
ejpam-5440	230	1	[	[	X
ejpam-5440	230	2	7	7	NUM
ejpam-5440	230	3	]	]	X
ejpam-5440	230	4	extended	extended	ADJ
ejpam-5440	230	5	theorems	theorem	NOUN
ejpam-5440	230	6	9.1	9.1	NUM
ejpam-5440	230	7	and	and	CCONJ
ejpam-5440	230	8	others	other	NOUN
ejpam-5440	230	9	to	to	PART
ejpam-5440	230	10	mappings	mapping	NOUN
ejpam-5440	230	11	into	into	ADP
ejpam-5440	230	12	cl(x	cl(x	NOUN
ejpam-5440	230	13	)	)	PUNCT
ejpam-5440	230	14	with	with	ADP
ejpam-5440	230	15	the	the	DET
ejpam-5440	230	16	generalized	generalize	VERB
ejpam-5440	230	17	hausdorff	hausdorff	NOUN
ejpam-5440	230	18	distance	distance	NOUN
ejpam-5440	230	19	.	.	PUNCT
ejpam-5440	231	1	s.	s.	PROPN
ejpam-5440	231	2	park	park	PROPN
ejpam-5440	231	3	/	/	SYM
ejpam-5440	231	4	eur	eur	PROPN
ejpam-5440	231	5	.	.	PUNCT
ejpam-5440	232	1	j.	j.	PROPN
ejpam-5440	232	2	pure	pure	PROPN
ejpam-5440	232	3	appl	appl	PROPN
ejpam-5440	232	4	.	.	PROPN
ejpam-5440	232	5	math	math	PROPN
ejpam-5440	232	6	,	,	PUNCT
ejpam-5440	232	7	17	17	NUM
ejpam-5440	232	8	(	(	PUNCT
ejpam-5440	232	9	4	4	NUM
ejpam-5440	232	10	)	)	PUNCT
ejpam-5440	232	11	(	(	PUNCT
ejpam-5440	232	12	2024	2024	NUM
ejpam-5440	232	13	)	)	PUNCT
ejpam-5440	232	14	,	,	PUNCT
ejpam-5440	232	15	2370	2370	NUM
ejpam-5440	232	16	-	-	SYM
ejpam-5440	232	17	2383	2383	NUM
ejpam-5440	232	18	2380	2380	NUM
ejpam-5440	232	19	10	10	NUM
ejpam-5440	232	20	.	.	PUNCT
ejpam-5440	233	1	the	the	DET
ejpam-5440	233	2	subfamily	subfamily	ADJ
ejpam-5440	233	3	(	(	PUNCT
ejpam-5440	233	4	η	η	NOUN
ejpam-5440	233	5	)	)	PUNCT
ejpam-5440	233	6	in	in	ADP
ejpam-5440	233	7	this	this	DET
ejpam-5440	233	8	section	section	NOUN
ejpam-5440	233	9	,	,	PUNCT
ejpam-5440	233	10	we	we	PRON
ejpam-5440	233	11	follow	follow	VERB
ejpam-5440	233	12	oettli	oettli	NOUN
ejpam-5440	233	13	and	and	CCONJ
ejpam-5440	233	14	théra	théra	NUM
ejpam-5440	233	15	[	[	X
ejpam-5440	233	16	11	11	NUM
ejpam-5440	233	17	]	]	PUNCT
ejpam-5440	233	18	in	in	ADP
ejpam-5440	233	19	1993	1993	NUM
ejpam-5440	233	20	.	.	PUNCT
ejpam-5440	234	1	let	let	AUX
ejpam-5440	234	2	(	(	PUNCT
ejpam-5440	234	3	v	v	NOUN
ejpam-5440	234	4	,	,	PUNCT
ejpam-5440	234	5	d	d	NOUN
ejpam-5440	234	6	)	)	PUNCT
ejpam-5440	234	7	be	be	AUX
ejpam-5440	234	8	a	a	DET
ejpam-5440	234	9	complete	complete	ADJ
ejpam-5440	234	10	metric	metric	ADJ
ejpam-5440	234	11	space	space	NOUN
ejpam-5440	234	12	.	.	PUNCT
ejpam-5440	235	1	let	let	VERB
ejpam-5440	235	2	f	f	NOUN
ejpam-5440	235	3	:	:	PUNCT
ejpam-5440	235	4	v	v	NUM
ejpam-5440	235	5	×v	×v	NOUN
ejpam-5440	235	6	→	→	SYM
ejpam-5440	235	7	(	(	PUNCT
ejpam-5440	235	8	−∞,+∞	−∞,+∞	ADV
ejpam-5440	235	9	]	]	PUNCT
ejpam-5440	235	10	be	be	VERB
ejpam-5440	235	11	a	a	DET
ejpam-5440	235	12	function	function	NOUN
ejpam-5440	235	13	which	which	PRON
ejpam-5440	235	14	is	be	AUX
ejpam-5440	235	15	lower	low	ADJ
ejpam-5440	235	16	semicontinuous	semicontinuous	ADJ
ejpam-5440	235	17	in	in	ADP
ejpam-5440	235	18	the	the	DET
ejpam-5440	235	19	second	second	ADJ
ejpam-5440	235	20	argument	argument	NOUN
ejpam-5440	235	21	and	and	CCONJ
ejpam-5440	235	22	satisfies	satisfie	NOUN
ejpam-5440	235	23	f(v	f(v	NOUN
ejpam-5440	235	24	,	,	PUNCT
ejpam-5440	235	25	v	v	NOUN
ejpam-5440	235	26	)	)	PUNCT
ejpam-5440	235	27	=	=	SYM
ejpam-5440	235	28	0	0	NUM
ejpam-5440	236	1	for	for	ADP
ejpam-5440	236	2	all	all	DET
ejpam-5440	236	3	v	v	ADP
ejpam-5440	236	4	∈	∈	PROPN
ejpam-5440	236	5	v	v	NOUN
ejpam-5440	236	6	,	,	PUNCT
ejpam-5440	236	7	(	(	PUNCT
ejpam-5440	236	8	1	1	X
ejpam-5440	236	9	)	)	PUNCT
ejpam-5440	236	10	f(u	f(u	PROPN
ejpam-5440	236	11	,	,	PUNCT
ejpam-5440	236	12	v	v	NOUN
ejpam-5440	236	13	)	)	PUNCT
ejpam-5440	236	14	<	<	X
ejpam-5440	236	15	f(u	f(u	PROPN
ejpam-5440	236	16	,	,	PUNCT
ejpam-5440	236	17	w	w	NOUN
ejpam-5440	236	18	)	)	PUNCT
ejpam-5440	236	19	+	+	CCONJ
ejpam-5440	236	20	f(w	f(w	PROPN
ejpam-5440	236	21	,	,	PUNCT
ejpam-5440	236	22	v	v	NOUN
ejpam-5440	236	23	)	)	PUNCT
ejpam-5440	236	24	for	for	ADP
ejpam-5440	236	25	all	all	DET
ejpam-5440	236	26	u	u	NOUN
ejpam-5440	236	27	,	,	PUNCT
ejpam-5440	236	28	v	v	NOUN
ejpam-5440	236	29	,	,	PUNCT
ejpam-5440	236	30	w	w	PROPN
ejpam-5440	236	31	∈	∈	PROPN
ejpam-5440	237	1	v.	v.	CCONJ
ejpam-5440	237	2	assume	assume	VERB
ejpam-5440	237	3	that	that	SCONJ
ejpam-5440	237	4	there	there	PRON
ejpam-5440	237	5	exists	exist	VERB
ejpam-5440	237	6	v0	v0	PROPN
ejpam-5440	237	7	∈	∈	PROPN
ejpam-5440	237	8	v	v	ADP
ejpam-5440	237	9	such	such	DET
ejpam-5440	237	10	that	that	DET
ejpam-5440	237	11	inf	inf	PROPN
ejpam-5440	237	12	v→∞	v→∞	NUM
ejpam-5440	237	13	f(v0	f(v0	NOUN
ejpam-5440	237	14	,	,	PUNCT
ejpam-5440	237	15	v	v	NOUN
ejpam-5440	237	16	)	)	PUNCT
ejpam-5440	238	1	>	>	X
ejpam-5440	238	2	−∞.	−∞.	PROPN
ejpam-5440	238	3	let	let	VERB
ejpam-5440	238	4	s0	s0	NOUN
ejpam-5440	238	5	:	:	PUNCT
ejpam-5440	238	6	=	=	SYM
ejpam-5440	238	7	{	{	PUNCT
ejpam-5440	238	8	v	v	NUM
ejpam-5440	238	9	∈	∈	NOUN
ejpam-5440	238	10	v	v	NOUN
ejpam-5440	238	11	:	:	PUNCT
ejpam-5440	238	12	f(v0	f(v0	ADJ
ejpam-5440	238	13	,	,	PUNCT
ejpam-5440	238	14	v	v	NOUN
ejpam-5440	238	15	)	)	PUNCT
ejpam-5440	238	16	+	+	CCONJ
ejpam-5440	238	17	d(v0	d(v0	ADJ
ejpam-5440	238	18	,	,	PUNCT
ejpam-5440	238	19	v	v	NOUN
ejpam-5440	238	20	)	)	PUNCT
ejpam-5440	238	21	≤	≤	NOUN
ejpam-5440	238	22	0	0	NUM
ejpam-5440	238	23	}	}	PUNCT
ejpam-5440	238	24	.	.	PUNCT
ejpam-5440	239	1	from	from	ADP
ejpam-5440	239	2	(	(	PUNCT
ejpam-5440	239	3	1	1	X
ejpam-5440	239	4	)	)	PUNCT
ejpam-5440	239	5	it	it	PRON
ejpam-5440	239	6	follows	follow	VERB
ejpam-5440	239	7	that	that	SCONJ
ejpam-5440	239	8	v0	v0	NOUN
ejpam-5440	239	9	∈	∈	NOUN
ejpam-5440	239	10	s0	s0	PROPN
ejpam-5440	239	11	̸=	̸=	PROPN
ejpam-5440	239	12	∅.	∅.	ADV
ejpam-5440	239	13	under	under	ADP
ejpam-5440	239	14	these	these	DET
ejpam-5440	239	15	specifications	specification	NOUN
ejpam-5440	239	16	the	the	DET
ejpam-5440	239	17	following	follow	VERB
ejpam-5440	239	18	results	result	NOUN
ejpam-5440	239	19	are	be	AUX
ejpam-5440	239	20	true	true	ADJ
ejpam-5440	239	21	:	:	PUNCT
ejpam-5440	239	22	theorem	theorem	ADJ
ejpam-5440	239	23	10.1	10.1	NUM
ejpam-5440	239	24	.	.	PUNCT
ejpam-5440	240	1	(	(	PUNCT
ejpam-5440	240	2	ekeland	ekeland	NOUN
ejpam-5440	240	3	)	)	PUNCT
ejpam-5440	240	4	there	there	PRON
ejpam-5440	240	5	exists	exist	VERB
ejpam-5440	240	6	v∗	v∗	PROPN
ejpam-5440	240	7	∈	∈	PROPN
ejpam-5440	240	8	s0	s0	NOUN
ejpam-5440	240	9	such	such	ADJ
ejpam-5440	240	10	that	that	PRON
ejpam-5440	240	11	f(v∗	f(v∗	PROPN
ejpam-5440	240	12	,	,	PUNCT
ejpam-5440	240	13	v	v	NOUN
ejpam-5440	240	14	)	)	PUNCT
ejpam-5440	240	15	+	+	CCONJ
ejpam-5440	240	16	d(v∗	d(v∗	PROPN
ejpam-5440	240	17	,	,	PUNCT
ejpam-5440	240	18	v	v	NOUN
ejpam-5440	240	19	)	)	PUNCT
ejpam-5440	240	20	>	>	X
ejpam-5440	240	21	0	0	PUNCT
ejpam-5440	240	22	for	for	ADP
ejpam-5440	240	23	all	all	DET
ejpam-5440	240	24	v	v	ADP
ejpam-5440	240	25	∈	∈	PROPN
ejpam-5440	240	26	v	v	NOUN
ejpam-5440	240	27	,	,	PUNCT
ejpam-5440	240	28	v	v	ADP
ejpam-5440	240	29	̸=	̸=	PROPN
ejpam-5440	240	30	v∗.	v∗.	NOUN
ejpam-5440	240	31	theorem	theorem	VERB
ejpam-5440	240	32	10.2	10.2	NUM
ejpam-5440	240	33	.	.	PUNCT
ejpam-5440	241	1	(	(	PUNCT
ejpam-5440	241	2	takahashi	takahashi	PROPN
ejpam-5440	241	3	)	)	PUNCT
ejpam-5440	241	4	assume	assume	VERB
ejpam-5440	241	5	that	that	SCONJ
ejpam-5440	241	6	for	for	ADP
ejpam-5440	241	7	every	every	DET
ejpam-5440	241	8	v	v	NOUN
ejpam-5440	241	9	∈	∈	NOUN
ejpam-5440	241	10	s0	s0	NOUN
ejpam-5440	241	11	with	with	ADP
ejpam-5440	241	12	infv∈v	infv∈v	PROPN
ejpam-5440	241	13	f(v	f(v	NOUN
ejpam-5440	241	14	,	,	PUNCT
ejpam-5440	241	15	v	v	NOUN
ejpam-5440	241	16	)	)	PUNCT
ejpam-5440	241	17	<	<	X
ejpam-5440	241	18	0	0	X
ejpam-5440	242	1	there	there	PRON
ejpam-5440	242	2	exists	exist	VERB
ejpam-5440	242	3	v	v	ADP
ejpam-5440	242	4	∈	∈	PROPN
ejpam-5440	242	5	v	v	ADP
ejpam-5440	242	6	such	such	ADJ
ejpam-5440	242	7	that	that	PRON
ejpam-5440	242	8	v	v	ADP
ejpam-5440	242	9	̸=	̸=	PROPN
ejpam-5440	242	10	v	v	NUM
ejpam-5440	242	11	and	and	CCONJ
ejpam-5440	242	12	f(v	f(v	NOUN
ejpam-5440	242	13	,	,	PUNCT
ejpam-5440	242	14	v	v	NOUN
ejpam-5440	242	15	)	)	PUNCT
ejpam-5440	243	1	+	+	X
ejpam-5440	243	2	d(v	d(v	ADJ
ejpam-5440	243	3	,	,	PUNCT
ejpam-5440	243	4	v	v	NOUN
ejpam-5440	243	5	)	)	PUNCT
ejpam-5440	243	6	≤	≤	NOUN
ejpam-5440	243	7	0	0	NUM
ejpam-5440	243	8	.	.	PUNCT
ejpam-5440	244	1	then	then	ADV
ejpam-5440	244	2	there	there	PRON
ejpam-5440	244	3	exists	exist	VERB
ejpam-5440	244	4	v∗	v∗	PROPN
ejpam-5440	244	5	∈	∈	PROPN
ejpam-5440	244	6	s0	s0	NOUN
ejpam-5440	244	7	such	such	ADJ
ejpam-5440	244	8	that	that	PRON
ejpam-5440	244	9	f(v∗	f(v∗	PROPN
ejpam-5440	244	10	,	,	PUNCT
ejpam-5440	244	11	v	v	NOUN
ejpam-5440	244	12	)	)	PUNCT
ejpam-5440	244	13	≥	≥	NOUN
ejpam-5440	244	14	0	0	NUM
ejpam-5440	244	15	for	for	ADP
ejpam-5440	244	16	all	all	PRON
ejpam-5440	244	17	v	v	ADP
ejpam-5440	244	18	∈	∈	PROPN
ejpam-5440	244	19	v	v	NOUN
ejpam-5440	244	20	.	.	PUNCT
ejpam-5440	245	1	theorem	theorem	VERB
ejpam-5440	245	2	10.3	10.3	NUM
ejpam-5440	245	3	.	.	PUNCT
ejpam-5440	246	1	(	(	PUNCT
ejpam-5440	246	2	caristi	caristi	PROPN
ejpam-5440	246	3	-	-	PUNCT
ejpam-5440	246	4	kirk	kirk	NOUN
ejpam-5440	246	5	)	)	PUNCT
ejpam-5440	246	6	let	let	VERB
ejpam-5440	246	7	t	t	NOUN
ejpam-5440	246	8	:	:	PUNCT
ejpam-5440	246	9	v	v	NUM
ejpam-5440	246	10	⊸	⊸	NOUN
ejpam-5440	246	11	v	v	AUX
ejpam-5440	246	12	be	be	AUX
ejpam-5440	246	13	a	a	DET
ejpam-5440	246	14	multimap	multimap	NOUN
ejpam-5440	246	15	such	such	ADJ
ejpam-5440	246	16	that	that	PRON
ejpam-5440	246	17	for	for	ADP
ejpam-5440	246	18	every	every	DET
ejpam-5440	246	19	v	v	NOUN
ejpam-5440	246	20	∈	∈	NOUN
ejpam-5440	246	21	s0	s0	NOUN
ejpam-5440	246	22	there	there	ADV
ejpam-5440	246	23	exists	exist	VERB
ejpam-5440	246	24	v	v	ADP
ejpam-5440	246	25	∈	∈	PROPN
ejpam-5440	246	26	t	t	PROPN
ejpam-5440	246	27	(	(	PUNCT
ejpam-5440	246	28	v	v	NOUN
ejpam-5440	246	29	)	)	PUNCT
ejpam-5440	246	30	satisfying	satisfy	VERB
ejpam-5440	246	31	v	v	ADP
ejpam-5440	246	32	̸=	̸=	PROPN
ejpam-5440	246	33	v	v	NOUN
ejpam-5440	246	34	and	and	CCONJ
ejpam-5440	246	35	f(v	f(v	NOUN
ejpam-5440	246	36	,	,	PUNCT
ejpam-5440	246	37	v	v	NOUN
ejpam-5440	246	38	)	)	PUNCT
ejpam-5440	247	1	+	+	X
ejpam-5440	247	2	d(v	d(v	ADJ
ejpam-5440	247	3	,	,	PUNCT
ejpam-5440	247	4	v	v	NOUN
ejpam-5440	247	5	)	)	PUNCT
ejpam-5440	247	6	≤	≤	NOUN
ejpam-5440	247	7	0	0	NUM
ejpam-5440	247	8	.	.	PUNCT
ejpam-5440	248	1	then	then	ADV
ejpam-5440	248	2	there	there	PRON
ejpam-5440	248	3	exists	exist	VERB
ejpam-5440	248	4	v∗	v∗	PROPN
ejpam-5440	248	5	∈	∈	PROPN
ejpam-5440	248	6	s0	s0	NOUN
ejpam-5440	248	7	such	such	ADJ
ejpam-5440	248	8	that	that	DET
ejpam-5440	248	9	v∗	v∗	PROPN
ejpam-5440	248	10	∈	∈	PROPN
ejpam-5440	248	11	t	t	PROPN
ejpam-5440	248	12	(	(	PUNCT
ejpam-5440	248	13	v∗	v∗	PROPN
ejpam-5440	248	14	)	)	PUNCT
ejpam-5440	248	15	.	.	PUNCT
ejpam-5440	249	1	the	the	DET
ejpam-5440	249	2	following	follow	VERB
ejpam-5440	249	3	is	be	AUX
ejpam-5440	249	4	the	the	DET
ejpam-5440	249	5	origin	origin	NOUN
ejpam-5440	249	6	of	of	ADP
ejpam-5440	249	7	(	(	PUNCT
ejpam-5440	249	8	η	η	PROPN
ejpam-5440	249	9	)	)	PUNCT
ejpam-5440	249	10	due	due	ADP
ejpam-5440	249	11	to	to	ADP
ejpam-5440	249	12	oettli	oettli	NOUN
ejpam-5440	249	13	and	and	CCONJ
ejpam-5440	249	14	théra	théra	NUM
ejpam-5440	249	15	[	[	X
ejpam-5440	249	16	11	11	NUM
ejpam-5440	249	17	]	]	PUNCT
ejpam-5440	249	18	in	in	ADP
ejpam-5440	249	19	1993	1993	NUM
ejpam-5440	249	20	:	:	PUNCT
ejpam-5440	249	21	theorem	theorem	VERB
ejpam-5440	249	22	10.4	10.4	NUM
ejpam-5440	249	23	.	.	PUNCT
ejpam-5440	250	1	(	(	PUNCT
ejpam-5440	250	2	oettli	oettli	NOUN
ejpam-5440	250	3	-	-	PUNCT
ejpam-5440	250	4	théra	théra	NUM
ejpam-5440	250	5	)	)	PUNCT
ejpam-5440	250	6	let	let	VERB
ejpam-5440	250	7	ψ	ψ	X
ejpam-5440	250	8	⊂	⊂	PROPN
ejpam-5440	250	9	v	v	PART
ejpam-5440	250	10	have	have	VERB
ejpam-5440	250	11	the	the	DET
ejpam-5440	250	12	property	property	NOUN
ejpam-5440	250	13	that	that	PRON
ejpam-5440	250	14	for	for	ADP
ejpam-5440	250	15	every	every	DET
ejpam-5440	250	16	v	v	NOUN
ejpam-5440	250	17	∈	∈	NOUN
ejpam-5440	250	18	s0\ψ	s0\ψ	NOUN
ejpam-5440	250	19	there	there	PRON
ejpam-5440	250	20	exists	exist	VERB
ejpam-5440	250	21	v	v	ADP
ejpam-5440	250	22	∈	∈	PROPN
ejpam-5440	250	23	v	v	ADP
ejpam-5440	250	24	such	such	ADJ
ejpam-5440	250	25	that	that	PRON
ejpam-5440	250	26	v	v	ADP
ejpam-5440	250	27	̸=	̸=	PROPN
ejpam-5440	250	28	v	v	NUM
ejpam-5440	250	29	and	and	CCONJ
ejpam-5440	250	30	f(v	f(v	NOUN
ejpam-5440	250	31	,	,	PUNCT
ejpam-5440	250	32	v	v	NOUN
ejpam-5440	250	33	)	)	PUNCT
ejpam-5440	251	1	+	+	X
ejpam-5440	251	2	d(v	d(v	ADJ
ejpam-5440	251	3	,	,	PUNCT
ejpam-5440	251	4	v	v	NOUN
ejpam-5440	251	5	)	)	PUNCT
ejpam-5440	251	6	≤	≤	NOUN
ejpam-5440	251	7	0	0	NUM
ejpam-5440	251	8	.	.	PUNCT
ejpam-5440	252	1	then	then	ADV
ejpam-5440	252	2	there	there	PRON
ejpam-5440	252	3	exists	exist	VERB
ejpam-5440	252	4	v∗	v∗	PROPN
ejpam-5440	252	5	∈	∈	PROPN
ejpam-5440	252	6	s0	s0	PROPN
ejpam-5440	252	7	∩ψ	∩ψ	PROPN
ejpam-5440	252	8	.	.	PUNCT
ejpam-5440	253	1	oettli	oettli	PROPN
ejpam-5440	253	2	-	-	PUNCT
ejpam-5440	253	3	théra	théra	NUM
ejpam-5440	254	1	[	[	X
ejpam-5440	254	2	11	11	NUM
ejpam-5440	254	3	]	]	PUNCT
ejpam-5440	254	4	finally	finally	ADV
ejpam-5440	254	5	stated	state	VERB
ejpam-5440	254	6	:	:	PUNCT
ejpam-5440	254	7	theorem	theorem	VERB
ejpam-5440	254	8	10.5	10.5	NUM
ejpam-5440	254	9	.	.	PUNCT
ejpam-5440	255	1	(	(	PUNCT
ejpam-5440	255	2	oettli	oettli	NOUN
ejpam-5440	255	3	-	-	PUNCT
ejpam-5440	255	4	théra	théra	NUM
ejpam-5440	255	5	)	)	PUNCT
ejpam-5440	255	6	theorems	theorem	NOUN
ejpam-5440	255	7	10.1	10.1	NUM
ejpam-5440	255	8	through	through	ADP
ejpam-5440	255	9	10.4	10.4	NUM
ejpam-5440	255	10	are	be	AUX
ejpam-5440	255	11	equivalent	equivalent	ADJ
ejpam-5440	255	12	.	.	PUNCT
ejpam-5440	256	1	consider	consider	VERB
ejpam-5440	256	2	our	our	PRON
ejpam-5440	256	3	following	follow	VERB
ejpam-5440	256	4	condition	condition	NOUN
ejpam-5440	256	5	:	:	PUNCT
ejpam-5440	256	6	(	(	PUNCT
ejpam-5440	256	7	η	η	X
ejpam-5440	256	8	)	)	PUNCT
ejpam-5440	256	9	if	if	SCONJ
ejpam-5440	256	10	y	y	PROPN
ejpam-5440	256	11	is	be	AUX
ejpam-5440	256	12	a	a	DET
ejpam-5440	256	13	subset	subset	NOUN
ejpam-5440	256	14	of	of	ADP
ejpam-5440	256	15	x	x	SYM
ejpam-5440	256	16	such	such	ADJ
ejpam-5440	256	17	that	that	PRON
ejpam-5440	256	18	for	for	ADP
ejpam-5440	256	19	each	each	DET
ejpam-5440	256	20	x	x	SYM
ejpam-5440	256	21	∈	∈	PROPN
ejpam-5440	256	22	x\y	x\y	X
ejpam-5440	257	1	there	there	PRON
ejpam-5440	257	2	exists	exist	VERB
ejpam-5440	257	3	a	a	DET
ejpam-5440	257	4	z	z	NOUN
ejpam-5440	257	5	∈	∈	PROPN
ejpam-5440	257	6	x\{x	x\{x	AUX
ejpam-5440	257	7	}	}	PUNCT
ejpam-5440	257	8	satisfying	satisfy	VERB
ejpam-5440	257	9	h(t	h(t	PROPN
ejpam-5440	257	10	(	(	PUNCT
ejpam-5440	257	11	x	x	NOUN
ejpam-5440	257	12	)	)	PUNCT
ejpam-5440	257	13	,	,	PUNCT
ejpam-5440	257	14	t	t	PROPN
ejpam-5440	257	15	(	(	PUNCT
ejpam-5440	257	16	z	z	NOUN
ejpam-5440	257	17	)	)	PUNCT
ejpam-5440	257	18	)	)	PUNCT
ejpam-5440	257	19	≤	≤	NUM
ejpam-5440	257	20	α	α	PROPN
ejpam-5440	257	21	q(x	q(x	PROPN
ejpam-5440	257	22	,	,	PUNCT
ejpam-5440	257	23	z	z	NOUN
ejpam-5440	257	24	)	)	PUNCT
ejpam-5440	257	25	for	for	ADP
ejpam-5440	257	26	a	a	DET
ejpam-5440	257	27	t	t	NOUN
ejpam-5440	257	28	:	:	PUNCT
ejpam-5440	257	29	x	x	X
ejpam-5440	257	30	→	→	SYM
ejpam-5440	257	31	cl(x	cl(x	NOUN
ejpam-5440	257	32	)	)	PUNCT
ejpam-5440	257	33	,	,	PUNCT
ejpam-5440	257	34	then	then	ADV
ejpam-5440	257	35	there	there	PRON
ejpam-5440	257	36	exists	exist	VERB
ejpam-5440	257	37	a	a	DET
ejpam-5440	257	38	v	v	NOUN
ejpam-5440	257	39	∈	∈	NOUN
ejpam-5440	257	40	x	x	SYM
ejpam-5440	257	41	∩	∩	ADJ
ejpam-5440	257	42	y	y	PROPN
ejpam-5440	257	43	=	=	SYM
ejpam-5440	257	44	y	y	PROPN
ejpam-5440	257	45	.	.	PUNCT
ejpam-5440	258	1	actually	actually	ADV
ejpam-5440	258	2	,	,	PUNCT
ejpam-5440	258	3	(	(	PUNCT
ejpam-5440	258	4	η	η	X
ejpam-5440	258	5	)	)	PUNCT
ejpam-5440	258	6	is	be	AUX
ejpam-5440	258	7	motivated	motivate	VERB
ejpam-5440	258	8	from	from	ADP
ejpam-5440	258	9	theorem	theorem	ADJ
ejpam-5440	258	10	10.4	10.4	NUM
ejpam-5440	258	11	of	of	ADP
ejpam-5440	258	12	oettli	oettli	NOUN
ejpam-5440	258	13	-	-	PUNCT
ejpam-5440	258	14	théra	théra	NUM
ejpam-5440	258	15	.	.	PUNCT
ejpam-5440	259	1	we	we	PRON
ejpam-5440	259	2	can	can	AUX
ejpam-5440	259	3	deduce	deduce	VERB
ejpam-5440	259	4	several	several	ADJ
ejpam-5440	259	5	particular	particular	ADJ
ejpam-5440	259	6	existence	existence	NOUN
ejpam-5440	259	7	theorems	theorem	NOUN
ejpam-5440	259	8	which	which	PRON
ejpam-5440	259	9	can	can	AUX
ejpam-5440	259	10	be	be	AUX
ejpam-5440	259	11	called	call	VERB
ejpam-5440	259	12	the	the	DET
ejpam-5440	259	13	subfamily	subfamily	ADJ
ejpam-5440	259	14	(	(	PUNCT
ejpam-5440	259	15	η	η	NOUN
ejpam-5440	259	16	)	)	PUNCT
ejpam-5440	259	17	.	.	PUNCT
ejpam-5440	260	1	references	reference	NOUN
ejpam-5440	260	2	2381	2381	NUM
ejpam-5440	260	3	11	11	NUM
ejpam-5440	260	4	.	.	PUNCT
ejpam-5440	261	1	epilogue	epilogue	NOUN
ejpam-5440	261	2	since	since	SCONJ
ejpam-5440	261	3	there	there	PRON
ejpam-5440	261	4	had	have	AUX
ejpam-5440	261	5	been	be	AUX
ejpam-5440	261	6	a	a	DET
ejpam-5440	261	7	large	large	ADJ
ejpam-5440	261	8	number	number	NOUN
ejpam-5440	261	9	of	of	ADP
ejpam-5440	261	10	metric	metric	ADJ
ejpam-5440	261	11	fixed	fix	VERB
ejpam-5440	261	12	point	point	NOUN
ejpam-5440	261	13	theorem	theorem	VERB
ejpam-5440	261	14	,	,	PUNCT
ejpam-5440	261	15	researchers	researcher	NOUN
ejpam-5440	261	16	tried	try	VERB
ejpam-5440	261	17	to	to	PART
ejpam-5440	261	18	classify	classify	VERB
ejpam-5440	261	19	them	they	PRON
ejpam-5440	261	20	.	.	PUNCT
ejpam-5440	262	1	the	the	DET
ejpam-5440	262	2	first	first	ADJ
ejpam-5440	262	3	attempt	attempt	NOUN
ejpam-5440	262	4	to	to	PART
ejpam-5440	262	5	classify	classify	VERB
ejpam-5440	262	6	the	the	DET
ejpam-5440	262	7	contractive	contractive	ADJ
ejpam-5440	262	8	conditions	condition	NOUN
ejpam-5440	262	9	was	be	AUX
ejpam-5440	262	10	done	do	VERB
ejpam-5440	262	11	by	by	ADP
ejpam-5440	262	12	billy	billy	PROPN
ejpam-5440	262	13	e.	e.	PROPN
ejpam-5440	262	14	rhoades	rhoade	VERB
ejpam-5440	262	15	[	[	X
ejpam-5440	262	16	23	23	NUM
ejpam-5440	262	17	]	]	PUNCT
ejpam-5440	262	18	in	in	ADP
ejpam-5440	262	19	1977	1977	NUM
ejpam-5440	262	20	.	.	PUNCT
ejpam-5440	263	1	our	our	PRON
ejpam-5440	263	2	previous	previous	ADJ
ejpam-5440	263	3	work	work	NOUN
ejpam-5440	263	4	[	[	X
ejpam-5440	263	5	12	12	NUM
ejpam-5440	263	6	]	]	PUNCT
ejpam-5440	263	7	in	in	ADP
ejpam-5440	263	8	1980	1980	NUM
ejpam-5440	263	9	can	can	AUX
ejpam-5440	263	10	be	be	AUX
ejpam-5440	263	11	regarded	regard	VERB
ejpam-5440	263	12	its	its	PRON
ejpam-5440	263	13	continuation	continuation	NOUN
ejpam-5440	263	14	.	.	PUNCT
ejpam-5440	264	1	recently	recently	ADV
ejpam-5440	264	2	,	,	PUNCT
ejpam-5440	264	3	cobzaş	cobzaş	PROPN
ejpam-5440	264	4	[	[	X
ejpam-5440	264	5	6	6	NUM
ejpam-5440	264	6	]	]	PUNCT
ejpam-5440	264	7	in	in	ADP
ejpam-5440	264	8	2020	2020	NUM
ejpam-5440	264	9	is	be	AUX
ejpam-5440	264	10	to	to	PART
ejpam-5440	264	11	indicate	indicate	VERB
ejpam-5440	264	12	the	the	DET
ejpam-5440	264	13	existence	existence	NOUN
ejpam-5440	264	14	of	of	ADP
ejpam-5440	264	15	families	family	NOUN
ejpam-5440	264	16	of	of	ADP
ejpam-5440	264	17	theorems	theorem	NOUN
ejpam-5440	264	18	related	relate	VERB
ejpam-5440	264	19	to	to	ADP
ejpam-5440	264	20	metric	metric	ADJ
ejpam-5440	264	21	completeness	completeness	NOUN
ejpam-5440	264	22	.	.	PUNCT
ejpam-5440	265	1	recall	recall	VERB
ejpam-5440	265	2	that	that	DET
ejpam-5440	265	3	banach	banach	NOUN
ejpam-5440	265	4	’s	’s	PART
ejpam-5440	265	5	original	original	ADJ
ejpam-5440	265	6	fixed	fix	VERB
ejpam-5440	265	7	point	point	NOUN
ejpam-5440	265	8	theorem	theorem	VERB
ejpam-5440	265	9	in	in	ADP
ejpam-5440	265	10	1922	1922	NUM
ejpam-5440	265	11	was	be	AUX
ejpam-5440	265	12	stated	state	VERB
ejpam-5440	265	13	for	for	ADP
ejpam-5440	265	14	normed	normed	ADJ
ejpam-5440	265	15	vector	vector	NOUN
ejpam-5440	265	16	spaces	space	NOUN
ejpam-5440	265	17	.	.	PUNCT
ejpam-5440	266	1	later	later	ADV
ejpam-5440	266	2	several	several	ADJ
ejpam-5440	266	3	researchers	researcher	NOUN
ejpam-5440	266	4	formulated	formulate	VERB
ejpam-5440	266	5	it	it	PRON
ejpam-5440	266	6	to	to	ADP
ejpam-5440	266	7	the	the	DET
ejpam-5440	266	8	form	form	NOUN
ejpam-5440	266	9	of	of	ADP
ejpam-5440	266	10	the	the	DET
ejpam-5440	266	11	banach	banach	NOUN
ejpam-5440	266	12	contraction	contraction	NOUN
ejpam-5440	266	13	principle	principle	NOUN
ejpam-5440	266	14	for	for	ADP
ejpam-5440	266	15	complete	complete	ADJ
ejpam-5440	266	16	metric	metric	ADJ
ejpam-5440	266	17	spaces	space	NOUN
ejpam-5440	266	18	.	.	PUNCT
ejpam-5440	267	1	in	in	ADP
ejpam-5440	267	2	the	the	DET
ejpam-5440	267	3	last	last	ADJ
ejpam-5440	267	4	one	one	NUM
ejpam-5440	267	5	hundred	hundred	NUM
ejpam-5440	267	6	years	year	NOUN
ejpam-5440	267	7	,	,	PUNCT
ejpam-5440	267	8	there	there	PRON
ejpam-5440	267	9	have	have	AUX
ejpam-5440	267	10	been	be	AUX
ejpam-5440	267	11	appeared	appear	VERB
ejpam-5440	267	12	hundreds	hundred	NOUN
ejpam-5440	267	13	of	of	ADP
ejpam-5440	267	14	contraction	contraction	NOUN
ejpam-5440	267	15	type	type	NOUN
ejpam-5440	267	16	conditions	condition	NOUN
ejpam-5440	267	17	and	and	CCONJ
ejpam-5440	267	18	almost	almost	ADV
ejpam-5440	267	19	one	one	NUM
ejpam-5440	267	20	thousand	thousand	NUM
ejpam-5440	267	21	spaces	space	NOUN
ejpam-5440	267	22	which	which	PRON
ejpam-5440	267	23	generalize	generalize	VERB
ejpam-5440	267	24	,	,	PUNCT
ejpam-5440	267	25	extend	extend	VERB
ejpam-5440	267	26	,	,	PUNCT
ejpam-5440	267	27	or	or	CCONJ
ejpam-5440	267	28	modify	modify	VERB
ejpam-5440	267	29	the	the	DET
ejpam-5440	267	30	complete	complete	ADJ
ejpam-5440	267	31	metric	metric	ADJ
ejpam-5440	267	32	spaces	space	NOUN
ejpam-5440	267	33	.	.	PUNCT
ejpam-5440	268	1	recall	recall	VERB
ejpam-5440	268	2	that	that	SCONJ
ejpam-5440	268	3	the	the	DET
ejpam-5440	268	4	banach	banach	NOUN
ejpam-5440	268	5	contraction	contraction	NOUN
ejpam-5440	268	6	does	do	AUX
ejpam-5440	268	7	not	not	PART
ejpam-5440	268	8	characterize	characterize	VERB
ejpam-5440	268	9	the	the	DET
ejpam-5440	268	10	metric	metric	ADJ
ejpam-5440	268	11	completeness	completeness	NOUN
ejpam-5440	268	12	.	.	PUNCT
ejpam-5440	269	1	the	the	DET
ejpam-5440	269	2	advantage	advantage	NOUN
ejpam-5440	269	3	of	of	ADP
ejpam-5440	269	4	our	our	PRON
ejpam-5440	269	5	metatheorem	metatheorem	NOUN
ejpam-5440	269	6	is	be	AUX
ejpam-5440	269	7	as	as	SCONJ
ejpam-5440	269	8	follows	follow	VERB
ejpam-5440	269	9	:	:	PUNCT
ejpam-5440	269	10	the	the	DET
ejpam-5440	269	11	proofs	proof	NOUN
ejpam-5440	269	12	of	of	ADP
ejpam-5440	269	13	each	each	DET
ejpam-5440	269	14	item	item	NOUN
ejpam-5440	269	15	follows	follow	VERB
ejpam-5440	269	16	from	from	ADP
ejpam-5440	269	17	the	the	DET
ejpam-5440	269	18	only	only	ADJ
ejpam-5440	269	19	one	one	NUM
ejpam-5440	269	20	of	of	ADP
ejpam-5440	269	21	them	they	PRON
ejpam-5440	269	22	.	.	PUNCT
ejpam-5440	270	1	this	this	PRON
ejpam-5440	270	2	can	can	AUX
ejpam-5440	270	3	be	be	AUX
ejpam-5440	270	4	seen	see	VERB
ejpam-5440	270	5	from	from	ADP
ejpam-5440	270	6	theorem	theorem	ADJ
ejpam-5440	270	7	h	h	NOUN
ejpam-5440	270	8	or	or	CCONJ
ejpam-5440	270	9	almost	almost	ADV
ejpam-5440	270	10	one	one	NUM
ejpam-5440	270	11	hundred	hundred	NUM
ejpam-5440	270	12	examples	example	NOUN
ejpam-5440	270	13	given	give	VERB
ejpam-5440	270	14	in	in	ADP
ejpam-5440	270	15	our	our	PRON
ejpam-5440	270	16	previous	previous	ADJ
ejpam-5440	270	17	works	work	NOUN
ejpam-5440	270	18	related	relate	VERB
ejpam-5440	270	19	metatheorem	metatheorem	VERB
ejpam-5440	270	20	.	.	PUNCT
ejpam-5440	271	1	consequently	consequently	ADV
ejpam-5440	271	2	,	,	PUNCT
ejpam-5440	271	3	we	we	PRON
ejpam-5440	271	4	found	find	VERB
ejpam-5440	271	5	that	that	SCONJ
ejpam-5440	271	6	the	the	DET
ejpam-5440	271	7	traditional	traditional	ADJ
ejpam-5440	271	8	metric	metric	ADJ
ejpam-5440	271	9	fixed	fix	VERB
ejpam-5440	271	10	point	point	NOUN
ejpam-5440	271	11	theory	theory	NOUN
ejpam-5440	271	12	and	and	CCONJ
ejpam-5440	271	13	many	many	ADJ
ejpam-5440	271	14	of	of	ADP
ejpam-5440	271	15	its	its	PRON
ejpam-5440	271	16	recent	recent	ADJ
ejpam-5440	271	17	works	work	NOUN
ejpam-5440	271	18	should	should	AUX
ejpam-5440	271	19	be	be	AUX
ejpam-5440	271	20	corrected	correct	VERB
ejpam-5440	271	21	or	or	CCONJ
ejpam-5440	271	22	improved	improve	VERB
ejpam-5440	271	23	in	in	ADP
ejpam-5440	271	24	various	various	ADJ
ejpam-5440	271	25	aspects	aspect	NOUN
ejpam-5440	271	26	.	.	PUNCT
ejpam-5440	272	1	recall	recall	VERB
ejpam-5440	272	2	that	that	SCONJ
ejpam-5440	272	3	a	a	DET
ejpam-5440	272	4	few	few	ADJ
ejpam-5440	272	5	researchers	researcher	NOUN
ejpam-5440	272	6	studied	study	VERB
ejpam-5440	272	7	the	the	DET
ejpam-5440	272	8	rus	rus	NOUN
ejpam-5440	272	9	-	-	PUNCT
ejpam-5440	272	10	hicks	hick	NOUN
ejpam-5440	272	11	-	-	PUNCT
ejpam-5440	272	12	rhoades	rhoade	NOUN
ejpam-5440	272	13	(	(	PUNCT
ejpam-5440	272	14	rhr	rhr	PROPN
ejpam-5440	272	15	)	)	PUNCT
ejpam-5440	272	16	maps	map	NOUN
ejpam-5440	272	17	by	by	ADP
ejpam-5440	272	18	using	use	VERB
ejpam-5440	272	19	several	several	ADJ
ejpam-5440	272	20	different	different	ADJ
ejpam-5440	272	21	names	name	NOUN
ejpam-5440	272	22	.	.	PUNCT
ejpam-5440	273	1	from	from	ADP
ejpam-5440	273	2	2023	2023	NUM
ejpam-5440	273	3	,	,	PUNCT
ejpam-5440	273	4	one	one	NUM
ejpam-5440	273	5	hundred	hundred	NUM
ejpam-5440	273	6	years	year	NOUN
ejpam-5440	273	7	later	later	ADV
ejpam-5440	273	8	to	to	ADP
ejpam-5440	273	9	the	the	DET
ejpam-5440	273	10	banach	banach	NOUN
ejpam-5440	273	11	contraction	contraction	NOUN
ejpam-5440	273	12	,	,	PUNCT
ejpam-5440	273	13	the	the	DET
ejpam-5440	273	14	present	present	ADJ
ejpam-5440	273	15	author	author	NOUN
ejpam-5440	273	16	began	begin	VERB
ejpam-5440	273	17	to	to	PART
ejpam-5440	273	18	study	study	VERB
ejpam-5440	273	19	on	on	ADP
ejpam-5440	273	20	rhr	rhr	PROPN
ejpam-5440	273	21	maps	map	NOUN
ejpam-5440	273	22	.	.	PUNCT
ejpam-5440	274	1	we	we	PRON
ejpam-5440	274	2	found	find	VERB
ejpam-5440	274	3	a	a	DET
ejpam-5440	274	4	large	large	ADJ
ejpam-5440	274	5	number	number	NOUN
ejpam-5440	274	6	of	of	ADP
ejpam-5440	274	7	examples	example	NOUN
ejpam-5440	274	8	of	of	ADP
ejpam-5440	274	9	rhr	rhr	PROPN
ejpam-5440	274	10	maps	map	NOUN
ejpam-5440	274	11	and	and	CCONJ
ejpam-5440	274	12	the	the	DET
ejpam-5440	274	13	so	so	ADV
ejpam-5440	274	14	-	-	PUNCT
ejpam-5440	274	15	called	call	VERB
ejpam-5440	274	16	rhr	rhr	PROPN
ejpam-5440	274	17	contraction	contraction	PROPN
ejpam-5440	274	18	principle	principle	NOUN
ejpam-5440	274	19	extending	extend	VERB
ejpam-5440	274	20	the	the	DET
ejpam-5440	274	21	classical	classical	ADJ
ejpam-5440	274	22	banach	banach	NOUN
ejpam-5440	274	23	one	one	NUM
ejpam-5440	274	24	.	.	PUNCT
ejpam-5440	275	1	moreover	moreover	ADV
ejpam-5440	275	2	,	,	PUNCT
ejpam-5440	275	3	we	we	PRON
ejpam-5440	275	4	found	find	VERB
ejpam-5440	275	5	that	that	SCONJ
ejpam-5440	275	6	the	the	DET
ejpam-5440	275	7	rhr	rhr	PROPN
ejpam-5440	275	8	theorem	theorem	NOUN
ejpam-5440	275	9	is	be	AUX
ejpam-5440	275	10	equivalent	equivalent	ADJ
ejpam-5440	275	11	to	to	ADP
ejpam-5440	275	12	variants	variant	NOUN
ejpam-5440	275	13	of	of	ADP
ejpam-5440	275	14	the	the	DET
ejpam-5440	275	15	nadler	nadler	NOUN
ejpam-5440	275	16	or	or	CCONJ
ejpam-5440	275	17	covitz	covitz	PROPN
ejpam-5440	275	18	-	-	PUNCT
ejpam-5440	275	19	nadler	nadler	NOUN
ejpam-5440	275	20	theorem	theorem	NOUN
ejpam-5440	275	21	for	for	ADP
ejpam-5440	275	22	multivalued	multivalued	ADJ
ejpam-5440	275	23	contractions	contraction	NOUN
ejpam-5440	275	24	.	.	PUNCT
ejpam-5440	276	1	furthermore	furthermore	ADV
ejpam-5440	276	2	,	,	PUNCT
ejpam-5440	276	3	we	we	PRON
ejpam-5440	276	4	found	find	VERB
ejpam-5440	276	5	that	that	SCONJ
ejpam-5440	276	6	the	the	DET
ejpam-5440	276	7	rhr	rhr	PROPN
ejpam-5440	276	8	theorem	theorem	PROPN
ejpam-5440	276	9	characterizes	characterize	VERB
ejpam-5440	276	10	the	the	DET
ejpam-5440	276	11	metric	metric	ADJ
ejpam-5440	276	12	completeness	completeness	NOUN
ejpam-5440	276	13	.	.	PUNCT
ejpam-5440	277	1	such	such	ADJ
ejpam-5440	277	2	studies	study	NOUN
ejpam-5440	277	3	were	be	AUX
ejpam-5440	277	4	done	do	VERB
ejpam-5440	277	5	in	in	ADP
ejpam-5440	277	6	2022–24	2022–24	NUM
ejpam-5440	277	7	.	.	PUNCT
ejpam-5440	278	1	one	one	NUM
ejpam-5440	278	2	of	of	ADP
ejpam-5440	278	3	the	the	DET
ejpam-5440	278	4	significance	significance	NOUN
ejpam-5440	278	5	of	of	ADP
ejpam-5440	278	6	our	our	PRON
ejpam-5440	278	7	recent	recent	ADJ
ejpam-5440	278	8	works	work	NOUN
ejpam-5440	278	9	on	on	ADP
ejpam-5440	278	10	metric	metric	ADJ
ejpam-5440	278	11	fixed	fix	VERB
ejpam-5440	278	12	point	point	NOUN
ejpam-5440	278	13	theory	theory	NOUN
ejpam-5440	278	14	is	be	AUX
ejpam-5440	278	15	to	to	PART
ejpam-5440	278	16	clarify	clarify	VERB
ejpam-5440	278	17	some	some	PRON
ejpam-5440	278	18	incorrectly	incorrectly	ADV
ejpam-5440	278	19	stated	state	VERB
ejpam-5440	278	20	results	result	NOUN
ejpam-5440	278	21	with	with	ADP
ejpam-5440	278	22	unnecessarily	unnecessarily	ADV
ejpam-5440	278	23	long	long	ADJ
ejpam-5440	278	24	proofs	proof	NOUN
ejpam-5440	278	25	given	give	VERB
ejpam-5440	278	26	by	by	ADP
ejpam-5440	278	27	several	several	ADJ
ejpam-5440	278	28	authors	author	NOUN
ejpam-5440	278	29	.	.	PUNCT
ejpam-5440	279	1	in	in	ADP
ejpam-5440	279	2	fact	fact	NOUN
ejpam-5440	279	3	,	,	PUNCT
ejpam-5440	279	4	our	our	PRON
ejpam-5440	279	5	aim	aim	NOUN
ejpam-5440	279	6	of	of	ADP
ejpam-5440	279	7	study	study	NOUN
ejpam-5440	279	8	in	in	ADP
ejpam-5440	279	9	metric	metric	ADJ
ejpam-5440	279	10	fixed	fix	VERB
ejpam-5440	279	11	point	point	NOUN
ejpam-5440	279	12	theory	theory	NOUN
ejpam-5440	279	13	since	since	SCONJ
ejpam-5440	279	14	2022	2022	NUM
ejpam-5440	279	15	is	be	AUX
ejpam-5440	279	16	to	to	PART
ejpam-5440	279	17	improve	improve	VERB
ejpam-5440	279	18	every	every	DET
ejpam-5440	279	19	thing	thing	NOUN
ejpam-5440	279	20	there	there	ADV
ejpam-5440	279	21	without	without	ADP
ejpam-5440	279	22	making	make	VERB
ejpam-5440	279	23	new	new	ADJ
ejpam-5440	279	24	spaces	space	NOUN
ejpam-5440	279	25	or	or	CCONJ
ejpam-5440	279	26	new	new	ADJ
ejpam-5440	279	27	contractive	contractive	ADJ
ejpam-5440	279	28	conditions	condition	NOUN
ejpam-5440	279	29	.	.	PUNCT
ejpam-5440	280	1	references	reference	NOUN
ejpam-5440	280	2	[	[	X
ejpam-5440	280	3	1	1	NUM
ejpam-5440	280	4	]	]	X
ejpam-5440	280	5	j.p	j.p	PROPN
ejpam-5440	280	6	.	.	PROPN
ejpam-5440	280	7	aubin	aubin	PROPN
ejpam-5440	280	8	,	,	PUNCT
ejpam-5440	280	9	applied	apply	VERB
ejpam-5440	280	10	functional	functional	ADJ
ejpam-5440	280	11	analysis	analysis	NOUN
ejpam-5440	280	12	,	,	PUNCT
ejpam-5440	280	13	john	john	PROPN
ejpam-5440	280	14	wiley	wiley	PROPN
ejpam-5440	280	15	&	&	CCONJ
ejpam-5440	280	16	sons	son	NOUN
ejpam-5440	280	17	,	,	PUNCT
ejpam-5440	280	18	new	new	PROPN
ejpam-5440	280	19	york	york	PROPN
ejpam-5440	280	20	,	,	PUNCT
ejpam-5440	280	21	1979	1979	NUM
ejpam-5440	280	22	.	.	PUNCT
ejpam-5440	281	1	[	[	X
ejpam-5440	281	2	2	2	X
ejpam-5440	281	3	]	]	X
ejpam-5440	281	4	h.	h.	PROPN
ejpam-5440	281	5	aydi	aydi	PROPN
ejpam-5440	281	6	,	,	PUNCT
ejpam-5440	281	7	m.	m.	NOUN
ejpam-5440	281	8	jellali	jellali	PROPN
ejpam-5440	281	9	,	,	PUNCT
ejpam-5440	281	10	e.	e.	PROPN
ejpam-5440	281	11	karapinar	karapinar	PROPN
ejpam-5440	281	12	,	,	PUNCT
ejpam-5440	281	13	on	on	ADP
ejpam-5440	281	14	fixed	fix	VERB
ejpam-5440	281	15	point	point	NOUN
ejpam-5440	281	16	results	result	NOUN
ejpam-5440	281	17	for	for	ADP
ejpam-5440	281	18	α	α	NOUN
ejpam-5440	281	19	-	-	ADJ
ejpam-5440	281	20	implicit	implicit	ADJ
ejpam-5440	281	21	contractions	contraction	NOUN
ejpam-5440	281	22	in	in	ADP
ejpam-5440	281	23	quasi	quasi	ADJ
ejpam-5440	281	24	-	-	ADJ
ejpam-5440	281	25	metric	metric	ADJ
ejpam-5440	281	26	spaces	space	NOUN
ejpam-5440	281	27	and	and	CCONJ
ejpam-5440	281	28	consequences	consequence	NOUN
ejpam-5440	281	29	,	,	PUNCT
ejpam-5440	281	30	nonlinear	nonlinear	ADJ
ejpam-5440	281	31	anal	anal	PROPN
ejpam-5440	281	32	.	.	PUNCT
ejpam-5440	282	1	model	model	PROPN
ejpam-5440	282	2	.	.	PUNCT
ejpam-5440	283	1	control	control	NOUN
ejpam-5440	283	2	,	,	PUNCT
ejpam-5440	283	3	21(1	21(1	NUM
ejpam-5440	283	4	)	)	PUNCT
ejpam-5440	283	5	(	(	PUNCT
ejpam-5440	283	6	2016	2016	NUM
ejpam-5440	283	7	)	)	PUNCT
ejpam-5440	283	8	40–56	40–56	NUM
ejpam-5440	283	9	.	.	PUNCT
ejpam-5440	284	1	[	[	X
ejpam-5440	284	2	3	3	X
ejpam-5440	284	3	]	]	PUNCT
ejpam-5440	284	4	v.	v.	CCONJ
ejpam-5440	284	5	berinde	berinde	NOUN
ejpam-5440	284	6	,	,	PUNCT
ejpam-5440	284	7	on	on	ADP
ejpam-5440	284	8	the	the	DET
ejpam-5440	284	9	approximation	approximation	NOUN
ejpam-5440	284	10	of	of	ADP
ejpam-5440	284	11	fixed	fix	VERB
ejpam-5440	284	12	points	point	NOUN
ejpam-5440	284	13	of	of	ADP
ejpam-5440	284	14	weak	weak	ADJ
ejpam-5440	284	15	contractive	contractive	ADJ
ejpam-5440	284	16	mappings	mapping	NOUN
ejpam-5440	284	17	,	,	PUNCT
ejpam-5440	284	18	carpathian	carpathian	ADJ
ejpam-5440	284	19	j.	j.	PROPN
ejpam-5440	284	20	math	math	PROPN
ejpam-5440	284	21	.	.	PUNCT
ejpam-5440	285	1	19(1	19(1	NUM
ejpam-5440	285	2	)	)	PUNCT
ejpam-5440	285	3	(	(	PUNCT
ejpam-5440	285	4	2003	2003	NUM
ejpam-5440	285	5	)	)	PUNCT
ejpam-5440	285	6	7–22	7–22	NOUN
ejpam-5440	285	7	.	.	PUNCT
ejpam-5440	286	1	[	[	X
ejpam-5440	286	2	4	4	X
ejpam-5440	286	3	]	]	X
ejpam-5440	286	4	v.	v.	CCONJ
ejpam-5440	286	5	berinde	berinde	NOUN
ejpam-5440	286	6	,	,	PUNCT
ejpam-5440	286	7	m.	m.	NOUN
ejpam-5440	286	8	pacurar	pacurar	NOUN
ejpam-5440	286	9	,	,	PUNCT
ejpam-5440	286	10	alternative	alternative	ADJ
ejpam-5440	286	11	proofs	proof	NOUN
ejpam-5440	286	12	of	of	ADP
ejpam-5440	286	13	some	some	DET
ejpam-5440	286	14	classical	classical	ADJ
ejpam-5440	286	15	metric	metric	ADJ
ejpam-5440	286	16	fixed	fix	VERB
ejpam-5440	286	17	point	point	NOUN
ejpam-5440	286	18	references	reference	VERB
ejpam-5440	286	19	2382	2382	NUM
ejpam-5440	286	20	theorems	theorem	NOUN
ejpam-5440	286	21	by	by	ADP
ejpam-5440	286	22	using	use	VERB
ejpam-5440	286	23	approximate	approximate	ADJ
ejpam-5440	286	24	fixed	fix	VERB
ejpam-5440	286	25	point	point	NOUN
ejpam-5440	286	26	sequences	sequence	NOUN
ejpam-5440	286	27	,	,	PUNCT
ejpam-5440	286	28	arab	arab	PROPN
ejpam-5440	286	29	.	.	PUNCT
ejpam-5440	287	1	j.	j.	PROPN
ejpam-5440	287	2	math	math	PROPN
ejpam-5440	287	3	.	.	PUNCT
ejpam-5440	288	1	(	(	PUNCT
ejpam-5440	288	2	2022	2022	NUM
ejpam-5440	288	3	)	)	PUNCT
ejpam-5440	288	4	.	.	PUNCT
ejpam-5440	289	1	https://doi.org/10.1007/s40065-022-00398-6	https://doi.org/10.1007/s40065-022-00398-6	NUM
ejpam-5440	290	1	[	[	X
ejpam-5440	290	2	5	5	NUM
ejpam-5440	290	3	]	]	PUNCT
ejpam-5440	290	4	v.	v.	CCONJ
ejpam-5440	290	5	berinde	berinde	NOUN
ejpam-5440	290	6	,	,	PUNCT
ejpam-5440	290	7	a.	a.	NOUN
ejpam-5440	290	8	petrusȩl	petrusȩl	PROPN
ejpam-5440	290	9	,	,	PUNCT
ejpam-5440	290	10	i.a	i.a	PROPN
ejpam-5440	290	11	.	.	PROPN
ejpam-5440	290	12	rus	rus	PROPN
ejpam-5440	290	13	,	,	PUNCT
ejpam-5440	290	14	remarks	remark	NOUN
ejpam-5440	290	15	on	on	ADP
ejpam-5440	290	16	the	the	DET
ejpam-5440	290	17	mappings	mapping	NOUN
ejpam-5440	290	18	in	in	ADP
ejpam-5440	290	19	fixed	fix	VERB
ejpam-5440	290	20	point	point	NOUN
ejpam-5440	290	21	iterative	iterative	NOUN
ejpam-5440	290	22	methods	method	NOUN
ejpam-5440	290	23	in	in	ADP
ejpam-5440	290	24	metric	metric	ADJ
ejpam-5440	290	25	spaces	space	NOUN
ejpam-5440	290	26	,	,	PUNCT
ejpam-5440	290	27	fixed	fix	VERB
ejpam-5440	290	28	point	point	NOUN
ejpam-5440	290	29	theory	theory	NOUN
ejpam-5440	290	30	24(2	24(2	NUM
ejpam-5440	290	31	)	)	PUNCT
ejpam-5440	290	32	(	(	PUNCT
ejpam-5440	290	33	2023	2023	NUM
ejpam-5440	290	34	)	)	PUNCT
ejpam-5440	290	35	525–540	525–540	NUM
ejpam-5440	290	36	.	.	PUNCT
ejpam-5440	291	1	doi	doi	NOUN
ejpam-5440	291	2	:	:	PUNCT
ejpam-5440	291	3	10.24193	10.24193	NUM
ejpam-5440	291	4	/	/	SYM
ejpam-5440	291	5	fpt	fpt	PROPN
ejpam-5440	291	6	-	-	PUNCT
ejpam-5440	291	7	ro.2023.2.05	ro.2023.2.05	NOUN
ejpam-5440	291	8	[	[	X
ejpam-5440	291	9	6	6	NUM
ejpam-5440	291	10	]	]	PUNCT
ejpam-5440	291	11	s.	s.	PROPN
ejpam-5440	291	12	cobzaş	cobzaş	PROPN
ejpam-5440	291	13	,	,	PUNCT
ejpam-5440	291	14	fixed	fix	VERB
ejpam-5440	291	15	points	point	NOUN
ejpam-5440	291	16	and	and	CCONJ
ejpam-5440	291	17	completeness	completeness	NOUN
ejpam-5440	291	18	in	in	ADP
ejpam-5440	291	19	metric	metric	ADJ
ejpam-5440	291	20	and	and	CCONJ
ejpam-5440	291	21	generalized	generalized	ADJ
ejpam-5440	291	22	metric	metric	ADJ
ejpam-5440	291	23	spaces	space	NOUN
ejpam-5440	291	24	,	,	PUNCT
ejpam-5440	291	25	jour	jour	PROPN
ejpam-5440	291	26	.	.	PUNCT
ejpam-5440	291	27	math	math	PROPN
ejpam-5440	291	28	.	.	PUNCT
ejpam-5440	292	1	sci	sci	PROPN
ejpam-5440	292	2	.	.	PUNCT
ejpam-5440	293	1	250(3	250(3	NUM
ejpam-5440	293	2	)	)	PUNCT
ejpam-5440	293	3	(	(	PUNCT
ejpam-5440	293	4	2020	2020	NUM
ejpam-5440	293	5	)	)	PUNCT
ejpam-5440	294	1	475–535	475–535	NUM
ejpam-5440	294	2	.	.	PUNCT
ejpam-5440	295	1	doi	doi	NOUN
ejpam-5440	295	2	:	:	PUNCT
ejpam-5440	295	3	10.1007	10.1007	NUM
ejpam-5440	295	4	/	/	SYM
ejpam-5440	295	5	s10958	s10958	PROPN
ejpam-5440	295	6	-	-	PUNCT
ejpam-5440	295	7	020	020	NUM
ejpam-5440	295	8	-	-	PUNCT
ejpam-5440	295	9	05027	05027	NUM
ejpam-5440	295	10	-	-	SYM
ejpam-5440	295	11	1	1	NUM
ejpam-5440	295	12	[	[	X
ejpam-5440	295	13	7	7	X
ejpam-5440	295	14	]	]	X
ejpam-5440	295	15	h.	h.	PROPN
ejpam-5440	295	16	covitz	covitz	PROPN
ejpam-5440	295	17	,	,	PUNCT
ejpam-5440	295	18	s.b	s.b	PROPN
ejpam-5440	295	19	.	.	PROPN
ejpam-5440	295	20	nadler	nadler	PROPN
ejpam-5440	295	21	,	,	PUNCT
ejpam-5440	295	22	jr	jr	PROPN
ejpam-5440	295	23	.	.	PROPN
ejpam-5440	295	24	,	,	PUNCT
ejpam-5440	295	25	multi	multi	ADJ
ejpam-5440	295	26	-	-	ADJ
ejpam-5440	295	27	valued	value	VERB
ejpam-5440	295	28	contraction	contraction	NOUN
ejpam-5440	295	29	mappings	mapping	NOUN
ejpam-5440	295	30	in	in	ADP
ejpam-5440	295	31	generalized	generalized	ADJ
ejpam-5440	295	32	metric	metric	ADJ
ejpam-5440	295	33	spaces	space	NOUN
ejpam-5440	295	34	,	,	PUNCT
ejpam-5440	295	35	israel	israel	PROPN
ejpam-5440	295	36	j.	j.	PROPN
ejpam-5440	295	37	math	math	PROPN
ejpam-5440	295	38	.	.	PUNCT
ejpam-5440	296	1	8	8	NUM
ejpam-5440	296	2	(	(	PUNCT
ejpam-5440	296	3	1970	1970	NUM
ejpam-5440	296	4	)	)	PUNCT
ejpam-5440	297	1	5–11	5–11	PROPN
ejpam-5440	297	2	.	.	PUNCT
ejpam-5440	298	1	[	[	X
ejpam-5440	298	2	8	8	NUM
ejpam-5440	298	3	]	]	X
ejpam-5440	298	4	t.l	t.l	PROPN
ejpam-5440	298	5	.	.	PROPN
ejpam-5440	298	6	hicks	hicks	PROPN
ejpam-5440	298	7	,	,	PUNCT
ejpam-5440	298	8	b.e	b.e	PROPN
ejpam-5440	298	9	.	.	PROPN
ejpam-5440	298	10	rhoades	rhoades	PROPN
ejpam-5440	298	11	,	,	PUNCT
ejpam-5440	298	12	a	a	DET
ejpam-5440	298	13	banach	banach	NOUN
ejpam-5440	298	14	type	type	NOUN
ejpam-5440	298	15	fixed	fix	VERB
ejpam-5440	298	16	point	point	NOUN
ejpam-5440	298	17	theorem	theorem	ADJ
ejpam-5440	298	18	,	,	PUNCT
ejpam-5440	298	19	math	math	NOUN
ejpam-5440	298	20	.	.	PUNCT
ejpam-5440	299	1	japon	japon	PROPN
ejpam-5440	299	2	.	.	PUNCT
ejpam-5440	300	1	24	24	NUM
ejpam-5440	300	2	(	(	PUNCT
ejpam-5440	300	3	1979	1979	NUM
ejpam-5440	300	4	)	)	PUNCT
ejpam-5440	300	5	327–330	327–330	NUM
ejpam-5440	300	6	.	.	PUNCT
ejpam-5440	301	1	[	[	X
ejpam-5440	301	2	9	9	NUM
ejpam-5440	301	3	]	]	PUNCT
ejpam-5440	301	4	m.	m.	NOUN
ejpam-5440	301	5	jleli	jleli	PROPN
ejpam-5440	301	6	,	,	PUNCT
ejpam-5440	301	7	b.	b.	PROPN
ejpam-5440	301	8	samet	samet	PROPN
ejpam-5440	301	9	,	,	PUNCT
ejpam-5440	301	10	remarks	remark	VERB
ejpam-5440	301	11	on	on	ADP
ejpam-5440	301	12	g	g	NOUN
ejpam-5440	301	13	-	-	PUNCT
ejpam-5440	301	14	metric	metric	ADJ
ejpam-5440	301	15	spaces	space	NOUN
ejpam-5440	301	16	and	and	CCONJ
ejpam-5440	301	17	fixed	fix	VERB
ejpam-5440	301	18	point	point	NOUN
ejpam-5440	301	19	theorems	theorem	NOUN
ejpam-5440	301	20	,	,	PUNCT
ejpam-5440	301	21	fixed	fix	VERB
ejpam-5440	301	22	point	point	NOUN
ejpam-5440	301	23	theory	theory	NOUN
ejpam-5440	301	24	appl	appl	PROPN
ejpam-5440	301	25	.	.	PUNCT
ejpam-5440	302	1	2012:210	2012:210	NOUN
ejpam-5440	302	2	,	,	PUNCT
ejpam-5440	302	3	2012	2012	NUM
ejpam-5440	302	4	.	.	PUNCT
ejpam-5440	303	1	[	[	X
ejpam-5440	303	2	10	10	NUM
ejpam-5440	303	3	]	]	X
ejpam-5440	303	4	s.b	s.b	PROPN
ejpam-5440	303	5	.	.	PROPN
ejpam-5440	303	6	nadler	nadler	PROPN
ejpam-5440	303	7	,	,	PUNCT
ejpam-5440	303	8	jr	jr	PROPN
ejpam-5440	303	9	.	.	PROPN
ejpam-5440	303	10	,	,	PUNCT
ejpam-5440	303	11	multi	multi	ADJ
ejpam-5440	303	12	-	-	ADJ
ejpam-5440	303	13	valued	value	VERB
ejpam-5440	303	14	contraction	contraction	NOUN
ejpam-5440	303	15	mappings	mapping	NOUN
ejpam-5440	303	16	,	,	PUNCT
ejpam-5440	303	17	pacific	pacific	PROPN
ejpam-5440	303	18	j.	j.	PROPN
ejpam-5440	303	19	math	math	PROPN
ejpam-5440	303	20	.	.	PUNCT
ejpam-5440	304	1	30	30	NUM
ejpam-5440	304	2	(	(	PUNCT
ejpam-5440	304	3	1969	1969	NUM
ejpam-5440	304	4	)	)	PUNCT
ejpam-5440	304	5	475	475	NUM
ejpam-5440	304	6	–	–	PUNCT
ejpam-5440	304	7	488	488	NUM
ejpam-5440	304	8	.	.	PUNCT
ejpam-5440	305	1	[	[	X
ejpam-5440	305	2	11	11	NUM
ejpam-5440	305	3	]	]	X
ejpam-5440	305	4	w.	w.	PROPN
ejpam-5440	305	5	oettli	oettli	PROPN
ejpam-5440	305	6	,	,	PUNCT
ejpam-5440	305	7	m.	m.	NOUN
ejpam-5440	305	8	théra	théra	NUM
ejpam-5440	305	9	,	,	PUNCT
ejpam-5440	305	10	equivalents	equivalent	NOUN
ejpam-5440	305	11	of	of	ADP
ejpam-5440	305	12	ekeland	ekeland	NOUN
ejpam-5440	305	13	’s	’s	PART
ejpam-5440	305	14	principle	principle	NOUN
ejpam-5440	305	15	,	,	PUNCT
ejpam-5440	305	16	bull	bull	NOUN
ejpam-5440	305	17	.	.	PUNCT
ejpam-5440	306	1	austral	austral	PROPN
ejpam-5440	306	2	.	.	PUNCT
ejpam-5440	307	1	math	math	NOUN
ejpam-5440	307	2	.	.	PUNCT
ejpam-5440	308	1	soc	soc	PROPN
ejpam-5440	308	2	.	.	PUNCT
ejpam-5440	309	1	48	48	NUM
ejpam-5440	309	2	(	(	PUNCT
ejpam-5440	309	3	1933	1933	NUM
ejpam-5440	309	4	)	)	PUNCT
ejpam-5440	309	5	385–392	385–392	NUM
ejpam-5440	309	6	.	.	PUNCT
ejpam-5440	310	1	[	[	X
ejpam-5440	310	2	12	12	NUM
ejpam-5440	310	3	]	]	X
ejpam-5440	310	4	s.	s.	PROPN
ejpam-5440	310	5	park	park	PROPN
ejpam-5440	310	6	,	,	PUNCT
ejpam-5440	310	7	on	on	ADP
ejpam-5440	310	8	general	general	ADJ
ejpam-5440	310	9	contractive	contractive	ADJ
ejpam-5440	310	10	-	-	PUNCT
ejpam-5440	310	11	type	type	NOUN
ejpam-5440	310	12	conditions	condition	NOUN
ejpam-5440	310	13	,	,	PUNCT
ejpam-5440	310	14	j.	j.	PROPN
ejpam-5440	310	15	korean	korean	PROPN
ejpam-5440	310	16	math	math	PROPN
ejpam-5440	310	17	.	.	PUNCT
ejpam-5440	311	1	soc	soc	PROPN
ejpam-5440	311	2	.	.	PUNCT
ejpam-5440	312	1	17	17	NUM
ejpam-5440	312	2	(	(	PUNCT
ejpam-5440	312	3	1980	1980	NUM
ejpam-5440	312	4	)	)	PUNCT
ejpam-5440	312	5	131	131	NUM
ejpam-5440	312	6	–	–	PUNCT
ejpam-5440	312	7	140	140	NUM
ejpam-5440	312	8	.	.	PUNCT
ejpam-5440	313	1	[	[	X
ejpam-5440	313	2	13	13	NUM
ejpam-5440	313	3	]	]	PUNCT
ejpam-5440	313	4	s.	s.	PROPN
ejpam-5440	313	5	park	park	PROPN
ejpam-5440	313	6	,	,	PUNCT
ejpam-5440	313	7	characterizations	characterization	NOUN
ejpam-5440	313	8	of	of	ADP
ejpam-5440	313	9	metric	metric	ADJ
ejpam-5440	313	10	completeness	completeness	NOUN
ejpam-5440	313	11	,	,	PUNCT
ejpam-5440	313	12	colloq	colloq	PROPN
ejpam-5440	313	13	.	.	PUNCT
ejpam-5440	313	14	math	math	PROPN
ejpam-5440	313	15	.	.	PUNCT
ejpam-5440	314	1	49	49	NUM
ejpam-5440	314	2	(	(	PUNCT
ejpam-5440	314	3	1984	1984	NUM
ejpam-5440	314	4	)	)	PUNCT
ejpam-5440	314	5	21–26	21–26	NUM
ejpam-5440	314	6	.	.	PUNCT
ejpam-5440	315	1	[	[	X
ejpam-5440	315	2	14	14	NUM
ejpam-5440	315	3	]	]	X
ejpam-5440	315	4	s.	s.	PROPN
ejpam-5440	315	5	park	park	PROPN
ejpam-5440	315	6	,	,	PUNCT
ejpam-5440	315	7	foundations	foundation	NOUN
ejpam-5440	315	8	of	of	ADP
ejpam-5440	315	9	ordered	order	VERB
ejpam-5440	315	10	fixed	fix	VERB
ejpam-5440	315	11	point	point	NOUN
ejpam-5440	315	12	theory	theory	NOUN
ejpam-5440	315	13	,	,	PUNCT
ejpam-5440	315	14	j.	j.	PROPN
ejpam-5440	315	15	nat	nat	PROPN
ejpam-5440	315	16	.	.	PUNCT
ejpam-5440	316	1	acad	acad	PROPN
ejpam-5440	316	2	.	.	PUNCT
ejpam-5440	317	1	sci	sci	PROPN
ejpam-5440	317	2	.	.	PROPN
ejpam-5440	317	3	,	,	PUNCT
ejpam-5440	317	4	rok	rok	PROPN
ejpam-5440	317	5	,	,	PUNCT
ejpam-5440	317	6	nat	nat	PROPN
ejpam-5440	317	7	.	.	PUNCT
ejpam-5440	318	1	sci	sci	PROPN
ejpam-5440	318	2	.	.	PUNCT
ejpam-5440	318	3	ser	ser	PROPN
ejpam-5440	318	4	.	.	PROPN
ejpam-5440	318	5	61(2	61(2	NUM
ejpam-5440	318	6	)	)	PUNCT
ejpam-5440	318	7	(	(	PUNCT
ejpam-5440	318	8	2022	2022	NUM
ejpam-5440	318	9	)	)	PUNCT
ejpam-5440	318	10	1–51	1–51	NOUN
ejpam-5440	318	11	.	.	PUNCT
ejpam-5440	319	1	[	[	X
ejpam-5440	319	2	15	15	NUM
ejpam-5440	319	3	]	]	X
ejpam-5440	319	4	s.	s.	PROPN
ejpam-5440	319	5	park	park	PROPN
ejpam-5440	319	6	,	,	PUNCT
ejpam-5440	319	7	remarks	remark	VERB
ejpam-5440	319	8	on	on	ADP
ejpam-5440	319	9	the	the	DET
ejpam-5440	319	10	metatheorem	metatheorem	ADJ
ejpam-5440	319	11	in	in	ADP
ejpam-5440	319	12	ordered	order	VERB
ejpam-5440	319	13	fixed	fix	VERB
ejpam-5440	319	14	point	point	NOUN
ejpam-5440	319	15	theory	theory	NOUN
ejpam-5440	319	16	,	,	PUNCT
ejpam-5440	319	17	advanced	advanced	ADJ
ejpam-5440	319	18	mathematical	mathematical	ADJ
ejpam-5440	319	19	analysis	analysis	NOUN
ejpam-5440	319	20	and	and	CCONJ
ejpam-5440	319	21	its	its	PRON
ejpam-5440	319	22	applications	application	NOUN
ejpam-5440	319	23	,	,	PUNCT
ejpam-5440	319	24	chapter	chapter	NOUN
ejpam-5440	319	25	2	2	NUM
ejpam-5440	319	26	(	(	PUNCT
ejpam-5440	319	27	edited	edit	VERB
ejpam-5440	319	28	by	by	ADP
ejpam-5440	319	29	p.	p.	PROPN
ejpam-5440	319	30	debnath	debnath	PROPN
ejpam-5440	319	31	,	,	PUNCT
ejpam-5440	319	32	d.f.m	d.f.m	PROPN
ejpam-5440	319	33	.	.	PROPN
ejpam-5440	319	34	torres	torres	PROPN
ejpam-5440	319	35	,	,	PUNCT
ejpam-5440	319	36	y.j	y.j	PROPN
ejpam-5440	319	37	.	.	PUNCT
ejpam-5440	319	38	cho	cho	PROPN
ejpam-5440	319	39	)	)	PUNCT
ejpam-5440	319	40	,	,	PUNCT
ejpam-5440	319	41	crc	crc	NOUN
ejpam-5440	319	42	press	press	NOUN
ejpam-5440	319	43	(	(	PUNCT
ejpam-5440	319	44	2023	2023	NUM
ejpam-5440	319	45	)	)	PUNCT
ejpam-5440	319	46	11–27	11–27	NUM
ejpam-5440	319	47	.	.	PUNCT
ejpam-5440	320	1	doi	doi	NOUN
ejpam-5440	320	2	:	:	PUNCT
ejpam-5440	320	3	10.1201/9781003388678	10.1201/9781003388678	NUM
ejpam-5440	320	4	-	-	SYM
ejpam-5440	320	5	2	2	NUM
ejpam-5440	320	6	[	[	X
ejpam-5440	320	7	16	16	NUM
ejpam-5440	320	8	]	]	PUNCT
ejpam-5440	320	9	s.	s.	PROPN
ejpam-5440	320	10	park	park	PROPN
ejpam-5440	320	11	,	,	PUNCT
ejpam-5440	320	12	relatives	relative	NOUN
ejpam-5440	320	13	of	of	ADP
ejpam-5440	320	14	a	a	DET
ejpam-5440	320	15	theorem	theorem	NOUN
ejpam-5440	320	16	of	of	ADP
ejpam-5440	320	17	rus	rus	PROPN
ejpam-5440	320	18	-	-	PUNCT
ejpam-5440	320	19	hicks	hick	NOUN
ejpam-5440	320	20	-	-	PUNCT
ejpam-5440	320	21	rhoades	rhoade	NOUN
ejpam-5440	320	22	,	,	PUNCT
ejpam-5440	320	23	lett	lett	PROPN
ejpam-5440	320	24	.	.	PUNCT
ejpam-5440	321	1	nonlinear	nonlinear	PROPN
ejpam-5440	321	2	anal	anal	PROPN
ejpam-5440	321	3	.	.	PUNCT
ejpam-5440	322	1	appl	appl	PROPN
ejpam-5440	322	2	.	.	PUNCT
ejpam-5440	323	1	1(2	1(2	NUM
ejpam-5440	323	2	)	)	PUNCT
ejpam-5440	323	3	(	(	PUNCT
ejpam-5440	323	4	2023	2023	NUM
ejpam-5440	323	5	)	)	PUNCT
ejpam-5440	323	6	57–63	57–63	NUM
ejpam-5440	323	7	.	.	PUNCT
ejpam-5440	324	1	[	[	X
ejpam-5440	324	2	17	17	NUM
ejpam-5440	324	3	]	]	X
ejpam-5440	324	4	s.	s.	PROPN
ejpam-5440	324	5	park	park	PROPN
ejpam-5440	324	6	,	,	PUNCT
ejpam-5440	324	7	almost	almost	ADV
ejpam-5440	324	8	all	all	PRON
ejpam-5440	324	9	about	about	ADP
ejpam-5440	324	10	rus	rus	NOUN
ejpam-5440	324	11	-	-	PUNCT
ejpam-5440	324	12	hicks	hick	NOUN
ejpam-5440	324	13	-	-	PUNCT
ejpam-5440	324	14	rhoades	rhoade	NOUN
ejpam-5440	324	15	maps	map	NOUN
ejpam-5440	324	16	in	in	ADP
ejpam-5440	324	17	quasi	quasi	ADJ
ejpam-5440	324	18	-	-	ADJ
ejpam-5440	324	19	metric	metric	ADJ
ejpam-5440	324	20	spaces	space	NOUN
ejpam-5440	324	21	,	,	PUNCT
ejpam-5440	324	22	adv	adv	PROPN
ejpam-5440	324	23	.	.	PUNCT
ejpam-5440	325	1	th	th	X
ejpam-5440	325	2	.	.	PUNCT
ejpam-5440	326	1	nonlinear	nonlinear	PROPN
ejpam-5440	326	2	anal	anal	PROPN
ejpam-5440	326	3	.	.	PUNCT
ejpam-5440	327	1	appl	appl	PROPN
ejpam-5440	327	2	.	.	PUNCT
ejpam-5440	328	1	7(2	7(2	NUM
ejpam-5440	328	2	)	)	PUNCT
ejpam-5440	329	1	(	(	PUNCT
ejpam-5440	329	2	2023	2023	NUM
ejpam-5440	329	3	)	)	PUNCT
ejpam-5440	329	4	455–471	455–471	NUM
ejpam-5440	329	5	.	.	PUNCT
ejpam-5440	330	1	doi	doi	NOUN
ejpam-5440	330	2	:	:	PUNCT
ejpam-5440	330	3	0.31197	0.31197	NUM
ejpam-5440	330	4	/	/	SYM
ejpam-5440	330	5	atnaa.1185449	atnaa.1185449	PROPN
ejpam-5440	331	1	[	[	X
ejpam-5440	331	2	18	18	NUM
ejpam-5440	331	3	]	]	X
ejpam-5440	331	4	s.	s.	PROPN
ejpam-5440	331	5	park	park	PROPN
ejpam-5440	331	6	,	,	PUNCT
ejpam-5440	331	7	the	the	DET
ejpam-5440	331	8	use	use	NOUN
ejpam-5440	331	9	of	of	ADP
ejpam-5440	331	10	quasi	quasi	NOUN
ejpam-5440	331	11	-	-	ADJ
ejpam-5440	331	12	metric	metric	ADJ
ejpam-5440	331	13	in	in	ADP
ejpam-5440	331	14	the	the	DET
ejpam-5440	331	15	metric	metric	ADJ
ejpam-5440	331	16	fixed	fix	VERB
ejpam-5440	331	17	point	point	NOUN
ejpam-5440	331	18	theory	theory	NOUN
ejpam-5440	331	19	,	,	PUNCT
ejpam-5440	331	20	j.	j.	PROPN
ejpam-5440	331	21	nonlinear	nonlinear	PROPN
ejpam-5440	331	22	convex	convex	PROPN
ejpam-5440	331	23	anal	anal	NOUN
ejpam-5440	331	24	.	.	PUNCT
ejpam-5440	332	1	25(7	25(7	NUM
ejpam-5440	332	2	)	)	PUNCT
ejpam-5440	332	3	(	(	PUNCT
ejpam-5440	332	4	2024	2024	NUM
ejpam-5440	332	5	)	)	PUNCT
ejpam-5440	333	1	1553–1564	1553–1564	NUM
ejpam-5440	333	2	.	.	PUNCT
ejpam-5440	334	1	[	[	X
ejpam-5440	334	2	19	19	NUM
ejpam-5440	334	3	]	]	PUNCT
ejpam-5440	334	4	s.	s.	PROPN
ejpam-5440	334	5	park	park	PROPN
ejpam-5440	334	6	,	,	PUNCT
ejpam-5440	334	7	the	the	DET
ejpam-5440	334	8	realm	realm	NOUN
ejpam-5440	334	9	of	of	ADP
ejpam-5440	334	10	the	the	DET
ejpam-5440	334	11	rus	rus	NOUN
ejpam-5440	334	12	-	-	PUNCT
ejpam-5440	334	13	hicks	hick	NOUN
ejpam-5440	334	14	-	-	PUNCT
ejpam-5440	334	15	rhoades	rhoade	NOUN
ejpam-5440	334	16	maps	map	NOUN
ejpam-5440	334	17	in	in	ADP
ejpam-5440	334	18	the	the	DET
ejpam-5440	334	19	metric	metric	ADJ
ejpam-5440	334	20	fixed	fix	VERB
ejpam-5440	334	21	point	point	NOUN
ejpam-5440	334	22	theory	theory	NOUN
ejpam-5440	334	23	,	,	PUNCT
ejpam-5440	334	24	j.	j.	PROPN
ejpam-5440	334	25	nat	nat	PROPN
ejpam-5440	334	26	.	.	PUNCT
ejpam-5440	335	1	acad	acad	PROPN
ejpam-5440	335	2	.	.	PUNCT
ejpam-5440	336	1	sci	sci	PROPN
ejpam-5440	336	2	.	.	PROPN
ejpam-5440	336	3	,	,	PUNCT
ejpam-5440	336	4	rok	rok	PROPN
ejpam-5440	336	5	,	,	PUNCT
ejpam-5440	336	6	nat	nat	PROPN
ejpam-5440	336	7	.	.	PUNCT
ejpam-5440	337	1	sci	sci	PROPN
ejpam-5440	337	2	.	.	PUNCT
ejpam-5440	337	3	ser	ser	PROPN
ejpam-5440	337	4	.	.	PUNCT
ejpam-5440	338	1	63(1	63(1	NUM
ejpam-5440	338	2	)	)	PUNCT
ejpam-5440	338	3	(	(	PUNCT
ejpam-5440	338	4	2024	2024	NUM
ejpam-5440	338	5	)	)	PUNCT
ejpam-5440	338	6	1–45	1–45	PROPN
ejpam-5440	338	7	.	.	PUNCT
ejpam-5440	339	1	references	reference	NOUN
ejpam-5440	339	2	2383	2383	NUM
ejpam-5440	339	3	[	[	X
ejpam-5440	339	4	20	20	NUM
ejpam-5440	339	5	]	]	PUNCT
ejpam-5440	339	6	s.	s.	PROPN
ejpam-5440	339	7	park	park	PROPN
ejpam-5440	339	8	,	,	PUNCT
ejpam-5440	339	9	several	several	ADJ
ejpam-5440	339	10	recent	recent	ADJ
ejpam-5440	339	11	episodes	episode	NOUN
ejpam-5440	339	12	on	on	ADP
ejpam-5440	339	13	the	the	DET
ejpam-5440	339	14	metric	metric	ADJ
ejpam-5440	339	15	completeness	completeness	NOUN
ejpam-5440	339	16	,	,	PUNCT
ejpam-5440	339	17	edited	edit	VERB
ejpam-5440	339	18	by	by	ADP
ejpam-5440	339	19	debnath	debnath	PROPN
ejpam-5440	339	20	et	et	PROPN
ejpam-5440	339	21	al	al	PROPN
ejpam-5440	339	22	.	.	PROPN
ejpam-5440	339	23	,	,	PUNCT
ejpam-5440	339	24	to	to	PART
ejpam-5440	339	25	appear	appear	VERB
ejpam-5440	339	26	.	.	PUNCT
ejpam-5440	340	1	rg	rg	VERB
ejpam-5440	340	2	on	on	ADP
ejpam-5440	340	3	jan	jan	PROPN
ejpam-5440	340	4	.	.	PROPN
ejpam-5440	340	5	11	11	NUM
ejpam-5440	340	6	,	,	PUNCT
ejpam-5440	340	7	2024	2024	NUM
ejpam-5440	340	8	.	.	PUNCT
ejpam-5440	341	1	[	[	X
ejpam-5440	341	2	21	21	NUM
ejpam-5440	341	3	]	]	X
ejpam-5440	341	4	s.	s.	PROPN
ejpam-5440	341	5	park	park	PROPN
ejpam-5440	341	6	,	,	PUNCT
ejpam-5440	341	7	improving	improve	VERB
ejpam-5440	341	8	many	many	ADJ
ejpam-5440	341	9	metric	metric	ADJ
ejpam-5440	341	10	fixed	fix	VERB
ejpam-5440	341	11	point	point	NOUN
ejpam-5440	341	12	theorems	theorem	NOUN
ejpam-5440	341	13	,	,	PUNCT
ejpam-5440	341	14	letters	letter	VERB
ejpam-5440	341	15	nonlinear	nonlinear	ADJ
ejpam-5440	341	16	anal	anal	PROPN
ejpam-5440	341	17	.	.	PUNCT
ejpam-5440	342	1	appl	appl	PROPN
ejpam-5440	342	2	.	.	PUNCT
ejpam-5440	343	1	2(2	2(2	NUM
ejpam-5440	343	2	)	)	PUNCT
ejpam-5440	344	1	(	(	PUNCT
ejpam-5440	344	2	2024	2024	NUM
ejpam-5440	344	3	)	)	PUNCT
ejpam-5440	344	4	35–61	35–61	NUM
ejpam-5440	344	5	.	.	PUNCT
ejpam-5440	345	1	[	[	X
ejpam-5440	345	2	22	22	NUM
ejpam-5440	345	3	]	]	PUNCT
ejpam-5440	345	4	s.	s.	PROPN
ejpam-5440	345	5	park	park	PROPN
ejpam-5440	345	6	,	,	PUNCT
ejpam-5440	345	7	b.e	b.e	PROPN
ejpam-5440	345	8	.	.	PROPN
ejpam-5440	345	9	rhoades	rhoade	NOUN
ejpam-5440	345	10	,	,	PUNCT
ejpam-5440	345	11	comments	comment	NOUN
ejpam-5440	345	12	on	on	ADP
ejpam-5440	345	13	characterizations	characterization	NOUN
ejpam-5440	345	14	for	for	ADP
ejpam-5440	345	15	metric	metric	ADJ
ejpam-5440	345	16	completeness	completeness	NOUN
ejpam-5440	345	17	,	,	PUNCT
ejpam-5440	345	18	math	math	NOUN
ejpam-5440	345	19	.	.	PUNCT
ejpam-5440	346	1	japon	japon	PROPN
ejpam-5440	346	2	.	.	PUNCT
ejpam-5440	347	1	31(1	31(1	NUM
ejpam-5440	347	2	)	)	PUNCT
ejpam-5440	347	3	(	(	PUNCT
ejpam-5440	347	4	1986	1986	NUM
ejpam-5440	347	5	)	)	PUNCT
ejpam-5440	348	1	95–97	95–97	NUM
ejpam-5440	348	2	.	.	PUNCT
ejpam-5440	349	1	[	[	X
ejpam-5440	349	2	23	23	NUM
ejpam-5440	349	3	]	]	X
ejpam-5440	349	4	b.e	b.e	PROPN
ejpam-5440	349	5	.	.	PROPN
ejpam-5440	349	6	rhoades	rhoades	PROPN
ejpam-5440	349	7	,	,	PUNCT
ejpam-5440	349	8	a	a	DET
ejpam-5440	349	9	comparison	comparison	NOUN
ejpam-5440	349	10	of	of	ADP
ejpam-5440	349	11	various	various	ADJ
ejpam-5440	349	12	definitions	definition	NOUN
ejpam-5440	349	13	of	of	ADP
ejpam-5440	349	14	contractive	contractive	ADJ
ejpam-5440	349	15	definitions	definition	NOUN
ejpam-5440	349	16	,	,	PUNCT
ejpam-5440	349	17	trans	trans	PROPN
ejpam-5440	349	18	.	.	PROPN
ejpam-5440	349	19	amer	amer	PROPN
ejpam-5440	349	20	.	.	PUNCT
ejpam-5440	349	21	math	math	PROPN
ejpam-5440	349	22	.	.	PUNCT
ejpam-5440	350	1	soc	soc	PROPN
ejpam-5440	350	2	.	.	PUNCT
ejpam-5440	351	1	226	226	NUM
ejpam-5440	351	2	(	(	PUNCT
ejpam-5440	351	3	1977	1977	NUM
ejpam-5440	351	4	)	)	PUNCT
ejpam-5440	351	5	257–290	257–290	NUM
ejpam-5440	351	6	.	.	PUNCT
ejpam-5440	352	1	[	[	X
ejpam-5440	352	2	24	24	NUM
ejpam-5440	352	3	]	]	SYM
ejpam-5440	352	4	i.a	i.a	PROPN
ejpam-5440	352	5	.	.	PROPN
ejpam-5440	352	6	rus	rus	PROPN
ejpam-5440	352	7	,	,	PUNCT
ejpam-5440	352	8	teoria	teoria	PROPN
ejpam-5440	352	9	punctului	punctului	PROPN
ejpam-5440	352	10	fix	fix	NOUN
ejpam-5440	352	11	,	,	PUNCT
ejpam-5440	352	12	ii	ii	PROPN
ejpam-5440	352	13	,	,	PUNCT
ejpam-5440	352	14	univ	univ	PROPN
ejpam-5440	352	15	.	.	PUNCT
ejpam-5440	352	16	babes	babes	PROPN
ejpam-5440	352	17	-	-	PUNCT
ejpam-5440	352	18	bolyai	bolyai	NOUN
ejpam-5440	352	19	,	,	PUNCT
ejpam-5440	352	20	cluj	cluj	NOUN
ejpam-5440	352	21	,	,	PUNCT
ejpam-5440	352	22	1973	1973	NUM
ejpam-5440	352	23	.	.	PUNCT