id	sid	tid	token	lemma	pos
ejpam-7116	1	1	european	european	PROPN
ejpam-7116	1	2	journal	journal	PROPN
ejpam-7116	1	3	of	of	ADP
ejpam-7116	1	4	pure	pure	ADJ
ejpam-7116	1	5	and	and	CCONJ
ejpam-7116	1	6	applied	applied	ADJ
ejpam-7116	1	7	mathematics	mathematic	NOUN
ejpam-7116	1	8	2025	2025	NUM
ejpam-7116	1	9	,	,	PUNCT
ejpam-7116	1	10	vol	vol	NOUN
ejpam-7116	1	11	.	.	PROPN
ejpam-7116	1	12	18	18	NUM
ejpam-7116	1	13	,	,	PUNCT
ejpam-7116	1	14	issue	issue	NOUN
ejpam-7116	1	15	4	4	NUM
ejpam-7116	1	16	,	,	PUNCT
ejpam-7116	1	17	article	article	NOUN
ejpam-7116	1	18	number	number	NOUN
ejpam-7116	1	19	7116	7116	NUM
ejpam-7116	1	20	issn	issn	PROPN
ejpam-7116	1	21	1307	1307	NUM
ejpam-7116	1	22	-	-	SYM
ejpam-7116	1	23	5543	5543	NUM
ejpam-7116	1	24	–	–	PUNCT
ejpam-7116	1	25	ejpam.com	ejpam.com	X
ejpam-7116	1	26	published	publish	VERB
ejpam-7116	1	27	by	by	ADP
ejpam-7116	1	28	new	new	PROPN
ejpam-7116	1	29	york	york	PROPN
ejpam-7116	1	30	business	business	PROPN
ejpam-7116	1	31	global	global	ADJ
ejpam-7116	1	32	generalized	generalize	VERB
ejpam-7116	1	33	branciari	branciari	NOUN
ejpam-7116	1	34	metrics	metric	NOUN
ejpam-7116	1	35	:	:	PUNCT
ejpam-7116	1	36	fixed	fix	VERB
ejpam-7116	1	37	point	point	NOUN
ejpam-7116	1	38	results	result	NOUN
ejpam-7116	1	39	and	and	CCONJ
ejpam-7116	1	40	open	open	ADJ
ejpam-7116	1	41	problems	problem	NOUN
ejpam-7116	1	42	aleksandar	aleksandar	PROPN
ejpam-7116	1	43	kostić1,∗	kostić1,∗	PROPN
ejpam-7116	1	44	1	1	NUM
ejpam-7116	1	45	department	department	NOUN
ejpam-7116	1	46	of	of	ADP
ejpam-7116	1	47	mathematics	mathematic	NOUN
ejpam-7116	1	48	,	,	PUNCT
ejpam-7116	1	49	faculty	faculty	NOUN
ejpam-7116	1	50	of	of	ADP
ejpam-7116	1	51	sciences	science	NOUN
ejpam-7116	1	52	and	and	CCONJ
ejpam-7116	1	53	mathematics	mathematic	NOUN
ejpam-7116	1	54	,	,	PUNCT
ejpam-7116	1	55	university	university	NOUN
ejpam-7116	1	56	of	of	ADP
ejpam-7116	1	57	niš	niš	PROPN
ejpam-7116	1	58	,	,	PUNCT
ejpam-7116	1	59	serbia	serbia	PROPN
ejpam-7116	1	60	abstract	abstract	ADJ
ejpam-7116	1	61	.	.	PUNCT
ejpam-7116	2	1	the	the	DET
ejpam-7116	2	2	notion	notion	NOUN
ejpam-7116	2	3	of	of	ADP
ejpam-7116	2	4	generalized	generalized	ADJ
ejpam-7116	2	5	metric	metric	ADJ
ejpam-7116	2	6	,	,	PUNCT
ejpam-7116	2	7	more	more	ADV
ejpam-7116	2	8	commonly	commonly	ADV
ejpam-7116	2	9	known	know	VERB
ejpam-7116	2	10	as	as	ADP
ejpam-7116	2	11	the	the	DET
ejpam-7116	2	12	rectangular	rectangular	ADJ
ejpam-7116	2	13	metric	metric	NOUN
ejpam-7116	2	14	,	,	PUNCT
ejpam-7116	2	15	was	be	AUX
ejpam-7116	2	16	introduced	introduce	VERB
ejpam-7116	2	17	by	by	ADP
ejpam-7116	2	18	branciari	branciari	NOUN
ejpam-7116	2	19	in	in	ADP
ejpam-7116	2	20	2000	2000	NUM
ejpam-7116	2	21	,	,	PUNCT
ejpam-7116	2	22	replacing	replace	VERB
ejpam-7116	2	23	the	the	DET
ejpam-7116	2	24	triangle	triangle	NOUN
ejpam-7116	2	25	inequality	inequality	NOUN
ejpam-7116	2	26	of	of	ADP
ejpam-7116	2	27	metric	metric	ADJ
ejpam-7116	2	28	spaces	space	NOUN
ejpam-7116	2	29	by	by	ADP
ejpam-7116	2	30	the	the	DET
ejpam-7116	2	31	socalled	socalled	ADJ
ejpam-7116	2	32	rectangular	rectangular	ADJ
ejpam-7116	2	33	inequality	inequality	NOUN
ejpam-7116	2	34	.	.	PUNCT
ejpam-7116	3	1	in	in	ADP
ejpam-7116	3	2	this	this	DET
ejpam-7116	3	3	paper	paper	NOUN
ejpam-7116	3	4	we	we	PRON
ejpam-7116	3	5	further	far	ADV
ejpam-7116	3	6	generalize	generalize	VERB
ejpam-7116	3	7	this	this	DET
ejpam-7116	3	8	notion	notion	NOUN
ejpam-7116	3	9	by	by	ADP
ejpam-7116	3	10	adding	add	VERB
ejpam-7116	3	11	two	two	NUM
ejpam-7116	3	12	more	more	ADJ
ejpam-7116	3	13	terms	term	NOUN
ejpam-7116	3	14	to	to	ADP
ejpam-7116	3	15	the	the	DET
ejpam-7116	3	16	right	right	ADJ
ejpam-7116	3	17	-	-	PUNCT
ejpam-7116	3	18	hand	hand	NOUN
ejpam-7116	3	19	side	side	NOUN
ejpam-7116	3	20	of	of	ADP
ejpam-7116	3	21	the	the	DET
ejpam-7116	3	22	rectangular	rectangular	ADJ
ejpam-7116	3	23	inequality	inequality	NOUN
ejpam-7116	3	24	.	.	PUNCT
ejpam-7116	4	1	we	we	PRON
ejpam-7116	4	2	study	study	VERB
ejpam-7116	4	3	basic	basic	ADJ
ejpam-7116	4	4	properties	property	NOUN
ejpam-7116	4	5	of	of	ADP
ejpam-7116	4	6	spaces	space	NOUN
ejpam-7116	4	7	endowed	endow	VERB
ejpam-7116	4	8	by	by	ADP
ejpam-7116	4	9	such	such	ADJ
ejpam-7116	4	10	distance	distance	NOUN
ejpam-7116	4	11	functions	function	NOUN
ejpam-7116	4	12	,	,	PUNCT
ejpam-7116	4	13	and	and	CCONJ
ejpam-7116	4	14	prove	prove	VERB
ejpam-7116	4	15	the	the	DET
ejpam-7116	4	16	modified	modify	VERB
ejpam-7116	4	17	versions	version	NOUN
ejpam-7116	4	18	of	of	ADP
ejpam-7116	4	19	banach	banach	NOUN
ejpam-7116	4	20	and	and	CCONJ
ejpam-7116	4	21	kannan	kannan	PROPN
ejpam-7116	4	22	fixed	fix	VERB
ejpam-7116	4	23	point	point	NOUN
ejpam-7116	4	24	theorems	theorem	NOUN
ejpam-7116	4	25	on	on	ADP
ejpam-7116	4	26	these	these	DET
ejpam-7116	4	27	spaces	space	NOUN
ejpam-7116	4	28	.	.	PUNCT
ejpam-7116	5	1	the	the	DET
ejpam-7116	5	2	results	result	NOUN
ejpam-7116	5	3	are	be	AUX
ejpam-7116	5	4	substantiated	substantiate	VERB
ejpam-7116	5	5	by	by	ADP
ejpam-7116	5	6	examples	example	NOUN
ejpam-7116	5	7	.	.	PUNCT
ejpam-7116	6	1	finally	finally	ADV
ejpam-7116	6	2	,	,	PUNCT
ejpam-7116	6	3	we	we	PRON
ejpam-7116	6	4	state	state	VERB
ejpam-7116	6	5	some	some	DET
ejpam-7116	6	6	open	open	ADJ
ejpam-7116	6	7	problems	problem	NOUN
ejpam-7116	6	8	related	relate	VERB
ejpam-7116	6	9	to	to	ADP
ejpam-7116	6	10	topological	topological	ADJ
ejpam-7116	6	11	structure	structure	NOUN
ejpam-7116	6	12	and	and	CCONJ
ejpam-7116	6	13	fixed	fix	VERB
ejpam-7116	6	14	point	point	NOUN
ejpam-7116	6	15	theory	theory	NOUN
ejpam-7116	6	16	on	on	ADP
ejpam-7116	6	17	generalized	generalized	ADJ
ejpam-7116	6	18	branciari	branciari	NOUN
ejpam-7116	6	19	metric	metric	ADJ
ejpam-7116	6	20	spaces	space	NOUN
ejpam-7116	6	21	.	.	PUNCT
ejpam-7116	7	1	2020	2020	NUM
ejpam-7116	7	2	mathematics	mathematic	NOUN
ejpam-7116	7	3	subject	subject	NOUN
ejpam-7116	7	4	classifications	classification	NOUN
ejpam-7116	7	5	:	:	PUNCT
ejpam-7116	7	6	47h10	47h10	NUM
ejpam-7116	7	7	,	,	PUNCT
ejpam-7116	7	8	54h25	54h25	NUM
ejpam-7116	7	9	key	key	ADJ
ejpam-7116	7	10	words	word	NOUN
ejpam-7116	7	11	and	and	CCONJ
ejpam-7116	7	12	phrases	phrase	NOUN
ejpam-7116	7	13	:	:	PUNCT
ejpam-7116	7	14	generalized	generalize	VERB
ejpam-7116	7	15	metric	metric	ADJ
ejpam-7116	7	16	spaces	space	NOUN
ejpam-7116	7	17	,	,	PUNCT
ejpam-7116	7	18	fixed	fix	VERB
ejpam-7116	7	19	point	point	NOUN
ejpam-7116	7	20	theorems	theorem	NOUN
ejpam-7116	7	21	1	1	NUM
ejpam-7116	7	22	.	.	X
ejpam-7116	7	23	introduction	introduction	NOUN
ejpam-7116	7	24	and	and	CCONJ
ejpam-7116	7	25	preliminaries	preliminary	NOUN
ejpam-7116	7	26	metric	metric	ADJ
ejpam-7116	7	27	fixed	fix	VERB
ejpam-7116	7	28	point	point	NOUN
ejpam-7116	7	29	theory	theory	NOUN
ejpam-7116	7	30	continues	continue	VERB
ejpam-7116	7	31	to	to	PART
ejpam-7116	7	32	be	be	AUX
ejpam-7116	7	33	one	one	NUM
ejpam-7116	7	34	of	of	ADP
ejpam-7116	7	35	the	the	DET
ejpam-7116	7	36	most	most	ADV
ejpam-7116	7	37	widely	widely	ADV
ejpam-7116	7	38	studied	study	VERB
ejpam-7116	7	39	areas	area	NOUN
ejpam-7116	7	40	of	of	ADP
ejpam-7116	7	41	modern	modern	ADJ
ejpam-7116	7	42	mathematics	mathematic	NOUN
ejpam-7116	7	43	,	,	PUNCT
ejpam-7116	7	44	mostly	mostly	ADV
ejpam-7116	7	45	motivated	motivate	VERB
ejpam-7116	7	46	by	by	ADP
ejpam-7116	7	47	numerous	numerous	ADJ
ejpam-7116	7	48	applications	application	NOUN
ejpam-7116	7	49	,	,	PUNCT
ejpam-7116	7	50	while	while	SCONJ
ejpam-7116	7	51	pertaining	pertain	VERB
ejpam-7116	7	52	to	to	ADP
ejpam-7116	7	53	relatively	relatively	ADV
ejpam-7116	7	54	elementary	elementary	ADJ
ejpam-7116	7	55	theoretical	theoretical	ADJ
ejpam-7116	7	56	apparatus	apparatus	NOUN
ejpam-7116	7	57	.	.	PUNCT
ejpam-7116	8	1	the	the	DET
ejpam-7116	8	2	study	study	NOUN
ejpam-7116	8	3	was	be	AUX
ejpam-7116	8	4	initiated	initiate	VERB
ejpam-7116	8	5	in	in	ADP
ejpam-7116	8	6	1922	1922	NUM
ejpam-7116	8	7	by	by	ADP
ejpam-7116	8	8	the	the	DET
ejpam-7116	8	9	famous	famous	ADJ
ejpam-7116	8	10	banach	banach	NOUN
ejpam-7116	8	11	fixed	fix	VERB
ejpam-7116	8	12	point	point	NOUN
ejpam-7116	8	13	theorem	theorem	VERB
ejpam-7116	8	14	[	[	X
ejpam-7116	8	15	1	1	NUM
ejpam-7116	8	16	]	]	PUNCT
ejpam-7116	8	17	.	.	PUNCT
ejpam-7116	9	1	this	this	DET
ejpam-7116	9	2	basic	basic	ADJ
ejpam-7116	9	3	result	result	NOUN
ejpam-7116	9	4	was	be	AUX
ejpam-7116	9	5	mainly	mainly	ADV
ejpam-7116	9	6	generalized	generalize	VERB
ejpam-7116	9	7	either	either	CCONJ
ejpam-7116	9	8	by	by	ADP
ejpam-7116	9	9	weakening	weaken	VERB
ejpam-7116	9	10	the	the	DET
ejpam-7116	9	11	contractive	contractive	ADJ
ejpam-7116	9	12	condition	condition	NOUN
ejpam-7116	9	13	,	,	PUNCT
ejpam-7116	9	14	or	or	CCONJ
ejpam-7116	9	15	weakening	weaken	VERB
ejpam-7116	9	16	the	the	DET
ejpam-7116	9	17	metric	metric	ADJ
ejpam-7116	9	18	structure	structure	NOUN
ejpam-7116	9	19	,	,	PUNCT
ejpam-7116	9	20	or	or	CCONJ
ejpam-7116	9	21	combining	combine	VERB
ejpam-7116	9	22	these	these	DET
ejpam-7116	9	23	two	two	NUM
ejpam-7116	9	24	approaches	approach	NOUN
ejpam-7116	9	25	.	.	PUNCT
ejpam-7116	10	1	however	however	ADV
ejpam-7116	10	2	,	,	PUNCT
ejpam-7116	10	3	most	most	ADJ
ejpam-7116	10	4	of	of	ADP
ejpam-7116	10	5	the	the	DET
ejpam-7116	10	6	new	new	ADJ
ejpam-7116	10	7	“	"	PUNCT
ejpam-7116	10	8	generalized	generalized	ADJ
ejpam-7116	10	9	metric	metric	ADJ
ejpam-7116	10	10	”	"	PUNCT
ejpam-7116	10	11	structures	structure	NOUN
ejpam-7116	10	12	obtained	obtain	VERB
ejpam-7116	10	13	in	in	ADP
ejpam-7116	10	14	this	this	DET
ejpam-7116	10	15	way	way	NOUN
ejpam-7116	10	16	were	be	AUX
ejpam-7116	10	17	shown	show	VERB
ejpam-7116	10	18	to	to	PART
ejpam-7116	10	19	be	be	AUX
ejpam-7116	10	20	metrizable	metrizable	ADJ
ejpam-7116	10	21	,	,	PUNCT
ejpam-7116	10	22	or	or	CCONJ
ejpam-7116	10	23	the	the	DET
ejpam-7116	10	24	new	new	ADJ
ejpam-7116	10	25	fixed	fix	VERB
ejpam-7116	10	26	point	point	NOUN
ejpam-7116	10	27	results	result	NOUN
ejpam-7116	10	28	on	on	ADP
ejpam-7116	10	29	these	these	DET
ejpam-7116	10	30	spaces	space	NOUN
ejpam-7116	10	31	can	can	AUX
ejpam-7116	10	32	be	be	AUX
ejpam-7116	10	33	reduced	reduce	VERB
ejpam-7116	10	34	to	to	ADP
ejpam-7116	10	35	their	their	PRON
ejpam-7116	10	36	metric	metric	ADJ
ejpam-7116	10	37	counterparts	counterpart	NOUN
ejpam-7116	10	38	(	(	PUNCT
ejpam-7116	10	39	see	see	VERB
ejpam-7116	11	1	e.g.	e.g.	ADV
ejpam-7116	11	2	[	[	X
ejpam-7116	11	3	2	2	NUM
ejpam-7116	11	4	,	,	PUNCT
ejpam-7116	11	5	3	3	NUM
ejpam-7116	11	6	]	]	PUNCT
ejpam-7116	11	7	and	and	CCONJ
ejpam-7116	11	8	references	reference	NOUN
ejpam-7116	11	9	therein	therein	ADV
ejpam-7116	11	10	)	)	PUNCT
ejpam-7116	11	11	.	.	PUNCT
ejpam-7116	12	1	one	one	NUM
ejpam-7116	12	2	notable	notable	ADJ
ejpam-7116	12	3	exception	exception	NOUN
ejpam-7116	12	4	are	be	AUX
ejpam-7116	12	5	the	the	DET
ejpam-7116	12	6	so	so	ADV
ejpam-7116	12	7	-	-	PUNCT
ejpam-7116	12	8	called	call	VERB
ejpam-7116	12	9	generalized	generalized	ADJ
ejpam-7116	12	10	metric	metric	ADJ
ejpam-7116	12	11	spaces	space	NOUN
ejpam-7116	12	12	of	of	ADP
ejpam-7116	12	13	branciari	branciari	NOUN
ejpam-7116	12	14	[	[	X
ejpam-7116	12	15	4	4	NUM
ejpam-7116	12	16	]	]	PUNCT
ejpam-7116	12	17	,	,	PUNCT
ejpam-7116	12	18	more	more	ADV
ejpam-7116	12	19	commonly	commonly	ADV
ejpam-7116	12	20	referred	refer	VERB
ejpam-7116	12	21	to	to	ADP
ejpam-7116	12	22	in	in	ADP
ejpam-7116	12	23	the	the	DET
ejpam-7116	12	24	literature	literature	NOUN
ejpam-7116	12	25	as	as	ADP
ejpam-7116	12	26	the	the	DET
ejpam-7116	12	27	rectangular	rectangular	ADJ
ejpam-7116	12	28	metric	metric	ADJ
ejpam-7116	12	29	spaces	space	NOUN
ejpam-7116	12	30	(	(	PUNCT
ejpam-7116	12	31	see	see	VERB
ejpam-7116	12	32	[	[	X
ejpam-7116	12	33	5	5	NUM
ejpam-7116	12	34	]	]	NUM
ejpam-7116	12	35	)	)	PUNCT
ejpam-7116	12	36	.	.	PUNCT
ejpam-7116	13	1	we	we	PRON
ejpam-7116	13	2	recall	recall	VERB
ejpam-7116	13	3	the	the	DET
ejpam-7116	13	4	definition	definition	NOUN
ejpam-7116	13	5	of	of	ADP
ejpam-7116	13	6	rectangular	rectangular	ADJ
ejpam-7116	13	7	metric	metric	ADJ
ejpam-7116	13	8	space	space	NOUN
ejpam-7116	13	9	as	as	SCONJ
ejpam-7116	13	10	follows	follow	VERB
ejpam-7116	13	11	:	:	PUNCT
ejpam-7116	13	12	definition	definition	NOUN
ejpam-7116	13	13	1.1	1.1	NUM
ejpam-7116	13	14	(	(	PUNCT
ejpam-7116	13	15	[	[	X
ejpam-7116	13	16	4	4	NUM
ejpam-7116	13	17	]	]	NUM
ejpam-7116	13	18	)	)	PUNCT
ejpam-7116	13	19	.	.	PUNCT
ejpam-7116	14	1	let	let	VERB
ejpam-7116	14	2	x	x	PRON
ejpam-7116	14	3	be	be	AUX
ejpam-7116	14	4	a	a	DET
ejpam-7116	14	5	set	set	NOUN
ejpam-7116	14	6	and	and	CCONJ
ejpam-7116	14	7	d	d	NOUN
ejpam-7116	14	8	:	:	PUNCT
ejpam-7116	14	9	x	x	X
ejpam-7116	14	10	×x	×x	X
ejpam-7116	14	11	→	→	PUNCT
ejpam-7116	14	12	[	[	X
ejpam-7116	14	13	0,+∞	0,+∞	NUM
ejpam-7116	14	14	)	)	PUNCT
ejpam-7116	14	15	a	a	DET
ejpam-7116	14	16	mapping	mapping	NOUN
ejpam-7116	14	17	such	such	ADJ
ejpam-7116	14	18	that	that	PRON
ejpam-7116	14	19	for	for	ADP
ejpam-7116	14	20	all	all	DET
ejpam-7116	14	21	x	x	NOUN
ejpam-7116	14	22	,	,	PUNCT
ejpam-7116	14	23	y	y	PROPN
ejpam-7116	14	24	∈	∈	PROPN
ejpam-7116	14	25	x	x	X
ejpam-7116	14	26	and	and	CCONJ
ejpam-7116	14	27	for	for	ADP
ejpam-7116	14	28	all	all	DET
ejpam-7116	14	29	u	u	NOUN
ejpam-7116	14	30	,	,	PUNCT
ejpam-7116	14	31	v	v	NOUN
ejpam-7116	14	32	∈	∈	PROPN
ejpam-7116	14	33	x	x	X
ejpam-7116	14	34	\	\	X
ejpam-7116	14	35	{	{	PUNCT
ejpam-7116	14	36	x	x	NOUN
ejpam-7116	14	37	,	,	PUNCT
ejpam-7116	14	38	y	y	NOUN
ejpam-7116	14	39	}	}	PUNCT
ejpam-7116	14	40	with	with	ADP
ejpam-7116	14	41	u	u	PROPN
ejpam-7116	14	42	̸=	̸=	PROPN
ejpam-7116	14	43	v	v	NUM
ejpam-7116	14	44	we	we	PRON
ejpam-7116	14	45	have	have	VERB
ejpam-7116	14	46	:	:	PUNCT
ejpam-7116	14	47	∗corresponding	∗corresponde	VERB
ejpam-7116	14	48	author	author	NOUN
ejpam-7116	14	49	.	.	PUNCT
ejpam-7116	15	1	doi	doi	NOUN
ejpam-7116	15	2	:	:	PUNCT
ejpam-7116	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7116	https://doi.org/10.29020/nybg.ejpam.v18i4.7116	ADJ
ejpam-7116	15	4	email	email	NOUN
ejpam-7116	15	5	address	address	NOUN
ejpam-7116	15	6	:	:	PUNCT
ejpam-7116	15	7	akos2804@gmail.com	akos2804@gmail.com	X
ejpam-7116	15	8	(	(	PUNCT
ejpam-7116	15	9	a.	a.	PROPN
ejpam-7116	15	10	kostić	kostić	PROPN
ejpam-7116	15	11	)	)	PUNCT
ejpam-7116	15	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-7116	16	1	1	1	NUM
ejpam-7116	16	2	copyright	copyright	NOUN
ejpam-7116	16	3	:	:	PUNCT
ejpam-7116	16	4	©	©	PROPN
ejpam-7116	16	5	2025	2025	NUM
ejpam-7116	16	6	the	the	DET
ejpam-7116	16	7	author(s	author(s	NOUN
ejpam-7116	16	8	)	)	PUNCT
ejpam-7116	16	9	.	.	PUNCT
ejpam-7116	17	1	(	(	PUNCT
ejpam-7116	17	2	cc	cc	NOUN
ejpam-7116	17	3	by	by	ADP
ejpam-7116	17	4	-	-	PUNCT
ejpam-7116	17	5	nc	nc	PROPN
ejpam-7116	17	6	4.0	4.0	NUM
ejpam-7116	17	7	)	)	PUNCT
ejpam-7116	17	8	a.	a.	NOUN
ejpam-7116	17	9	kostić	kostić	VERB
ejpam-7116	17	10	/	/	SYM
ejpam-7116	17	11	eur	eur	PROPN
ejpam-7116	17	12	.	.	PUNCT
ejpam-7116	18	1	j.	j.	PROPN
ejpam-7116	18	2	pure	pure	PROPN
ejpam-7116	18	3	appl	appl	PROPN
ejpam-7116	18	4	.	.	PROPN
ejpam-7116	18	5	math	math	PROPN
ejpam-7116	18	6	,	,	PUNCT
ejpam-7116	18	7	18	18	NUM
ejpam-7116	18	8	(	(	PUNCT
ejpam-7116	18	9	4	4	NUM
ejpam-7116	18	10	)	)	PUNCT
ejpam-7116	18	11	(	(	PUNCT
ejpam-7116	18	12	2025	2025	NUM
ejpam-7116	18	13	)	)	PUNCT
ejpam-7116	18	14	,	,	PUNCT
ejpam-7116	18	15	7116	7116	NUM
ejpam-7116	18	16	2	2	NUM
ejpam-7116	18	17	of	of	ADP
ejpam-7116	18	18	10	10	NUM
ejpam-7116	18	19	(	(	PUNCT
ejpam-7116	18	20	i	i	NOUN
ejpam-7116	18	21	)	)	PUNCT
ejpam-7116	18	22	d(x	d(x	PROPN
ejpam-7116	18	23	,	,	PUNCT
ejpam-7116	18	24	y	y	NOUN
ejpam-7116	18	25	)	)	PUNCT
ejpam-7116	18	26	=	=	SYM
ejpam-7116	18	27	0	0	NUM
ejpam-7116	18	28	⇔	⇔	X
ejpam-7116	18	29	x	x	X
ejpam-7116	18	30	=	=	SYM
ejpam-7116	18	31	y	y	PROPN
ejpam-7116	18	32	,	,	PUNCT
ejpam-7116	18	33	(	(	PUNCT
ejpam-7116	18	34	ii	ii	NOUN
ejpam-7116	18	35	)	)	PUNCT
ejpam-7116	18	36	d(x	d(x	PROPN
ejpam-7116	18	37	,	,	PUNCT
ejpam-7116	18	38	y	y	NOUN
ejpam-7116	18	39	)	)	PUNCT
ejpam-7116	18	40	=	=	SYM
ejpam-7116	19	1	d(y	d(y	NOUN
ejpam-7116	19	2	,	,	PUNCT
ejpam-7116	19	3	x	x	NOUN
ejpam-7116	19	4	)	)	PUNCT
ejpam-7116	19	5	,	,	PUNCT
ejpam-7116	19	6	and	and	CCONJ
ejpam-7116	19	7	(	(	PUNCT
ejpam-7116	19	8	iii	iii	NOUN
ejpam-7116	19	9	)	)	PUNCT
ejpam-7116	19	10	d(x	d(x	PROPN
ejpam-7116	19	11	,	,	PUNCT
ejpam-7116	19	12	y	y	NOUN
ejpam-7116	19	13	)	)	PUNCT
ejpam-7116	19	14	≤	≤	NOUN
ejpam-7116	19	15	d(x	d(x	NOUN
ejpam-7116	19	16	,	,	PUNCT
ejpam-7116	19	17	u	u	NOUN
ejpam-7116	19	18	)	)	PUNCT
ejpam-7116	19	19	+	+	CCONJ
ejpam-7116	19	20	d(u	d(u	PROPN
ejpam-7116	19	21	,	,	PUNCT
ejpam-7116	19	22	v	v	NOUN
ejpam-7116	19	23	)	)	PUNCT
ejpam-7116	19	24	+	+	X
ejpam-7116	20	1	d(v	d(v	PROPN
ejpam-7116	20	2	,	,	PUNCT
ejpam-7116	20	3	y	y	NOUN
ejpam-7116	20	4	)	)	PUNCT
ejpam-7116	20	5	.	.	PUNCT
ejpam-7116	21	1	then	then	ADV
ejpam-7116	21	2	we	we	PRON
ejpam-7116	21	3	will	will	AUX
ejpam-7116	21	4	say	say	VERB
ejpam-7116	21	5	that	that	SCONJ
ejpam-7116	21	6	(	(	PUNCT
ejpam-7116	21	7	x	x	X
ejpam-7116	21	8	,	,	PUNCT
ejpam-7116	21	9	d	d	NOUN
ejpam-7116	21	10	)	)	PUNCT
ejpam-7116	21	11	is	be	AUX
ejpam-7116	21	12	a	a	DET
ejpam-7116	21	13	generalized	generalize	VERB
ejpam-7116	21	14	,	,	PUNCT
ejpam-7116	21	15	or	or	CCONJ
ejpam-7116	21	16	rectangular	rectangular	ADJ
ejpam-7116	21	17	metric	metric	ADJ
ejpam-7116	21	18	space	space	NOUN
ejpam-7116	21	19	(	(	PUNCT
ejpam-7116	21	20	r.m.s	r.m.s	NOUN
ejpam-7116	21	21	.	.	PUNCT
ejpam-7116	22	1	for	for	ADP
ejpam-7116	22	2	short	short	ADJ
ejpam-7116	22	3	)	)	PUNCT
ejpam-7116	22	4	.	.	PUNCT
ejpam-7116	23	1	the	the	DET
ejpam-7116	23	2	notions	notion	NOUN
ejpam-7116	23	3	of	of	ADP
ejpam-7116	23	4	convergence	convergence	NOUN
ejpam-7116	23	5	,	,	PUNCT
ejpam-7116	23	6	completeness	completeness	NOUN
ejpam-7116	23	7	,	,	PUNCT
ejpam-7116	23	8	continuity	continuity	NOUN
ejpam-7116	23	9	,	,	PUNCT
ejpam-7116	23	10	etc	etc	X
ejpam-7116	23	11	.	.	X
ejpam-7116	23	12	are	be	AUX
ejpam-7116	23	13	defined	define	VERB
ejpam-7116	23	14	the	the	DET
ejpam-7116	23	15	same	same	ADJ
ejpam-7116	23	16	as	as	ADP
ejpam-7116	23	17	in	in	ADP
ejpam-7116	23	18	metric	metric	ADJ
ejpam-7116	23	19	spaces	space	NOUN
ejpam-7116	23	20	.	.	PUNCT
ejpam-7116	24	1	however	however	ADV
ejpam-7116	24	2	,	,	PUNCT
ejpam-7116	24	3	r.m.s	r.m.	NOUN
ejpam-7116	24	4	.	.	PUNCT
ejpam-7116	25	1	possess	possess	VERB
ejpam-7116	25	2	some	some	DET
ejpam-7116	25	3	aberrant	aberrant	ADJ
ejpam-7116	25	4	properties	property	NOUN
ejpam-7116	25	5	different	different	ADJ
ejpam-7116	25	6	from	from	ADP
ejpam-7116	25	7	standard	standard	ADJ
ejpam-7116	25	8	metrics	metric	NOUN
ejpam-7116	25	9	,	,	PUNCT
ejpam-7116	25	10	for	for	ADP
ejpam-7116	25	11	example	example	NOUN
ejpam-7116	25	12	:	:	PUNCT
ejpam-7116	25	13	the	the	DET
ejpam-7116	25	14	limit	limit	NOUN
ejpam-7116	25	15	of	of	ADP
ejpam-7116	25	16	a	a	DET
ejpam-7116	25	17	convergent	convergent	NOUN
ejpam-7116	25	18	sequence	sequence	NOUN
ejpam-7116	25	19	needs	needs	AUX
ejpam-7116	25	20	not	not	PART
ejpam-7116	25	21	be	be	AUX
ejpam-7116	25	22	unique	unique	ADJ
ejpam-7116	25	23	;	;	PUNCT
ejpam-7116	25	24	a	a	DET
ejpam-7116	25	25	convergent	convergent	NOUN
ejpam-7116	25	26	sequence	sequence	NOUN
ejpam-7116	25	27	needs	needs	AUX
ejpam-7116	25	28	not	not	PART
ejpam-7116	25	29	be	be	AUX
ejpam-7116	25	30	cauchy	cauchy	ADJ
ejpam-7116	25	31	;	;	PUNCT
ejpam-7116	25	32	rectangular	rectangular	ADJ
ejpam-7116	25	33	metric	metric	ADJ
ejpam-7116	25	34	needs	need	NOUN
ejpam-7116	25	35	not	not	PART
ejpam-7116	25	36	be	be	AUX
ejpam-7116	25	37	a	a	DET
ejpam-7116	25	38	continuous	continuous	ADJ
ejpam-7116	25	39	function	function	NOUN
ejpam-7116	25	40	in	in	ADP
ejpam-7116	25	41	any	any	PRON
ejpam-7116	25	42	of	of	ADP
ejpam-7116	25	43	the	the	DET
ejpam-7116	25	44	variables	variable	NOUN
ejpam-7116	25	45	;	;	PUNCT
ejpam-7116	25	46	see	see	VERB
ejpam-7116	25	47	[	[	X
ejpam-7116	25	48	6	6	NUM
ejpam-7116	25	49	]	]	PUNCT
ejpam-7116	25	50	.	.	PUNCT
ejpam-7116	26	1	moreover	moreover	ADV
ejpam-7116	26	2	,	,	PUNCT
ejpam-7116	26	3	r.m.s	r.m.	NOUN
ejpam-7116	26	4	.	.	PUNCT
ejpam-7116	27	1	are	be	AUX
ejpam-7116	27	2	metrizable	metrizable	ADJ
ejpam-7116	27	3	only	only	ADV
ejpam-7116	27	4	under	under	ADP
ejpam-7116	27	5	certain	certain	ADJ
ejpam-7116	27	6	special	special	ADJ
ejpam-7116	27	7	conditions	condition	NOUN
ejpam-7116	27	8	(	(	PUNCT
ejpam-7116	27	9	[	[	X
ejpam-7116	27	10	7	7	NUM
ejpam-7116	27	11	]	]	NUM
ejpam-7116	27	12	)	)	PUNCT
ejpam-7116	27	13	.	.	PUNCT
ejpam-7116	28	1	therefore	therefore	ADV
ejpam-7116	28	2	the	the	DET
ejpam-7116	28	3	fixed	fix	VERB
ejpam-7116	28	4	point	point	NOUN
ejpam-7116	28	5	results	result	NOUN
ejpam-7116	28	6	on	on	ADP
ejpam-7116	28	7	r.m.s	r.m.s	NOUN
ejpam-7116	28	8	.	.	PUNCT
ejpam-7116	29	1	can	can	AUX
ejpam-7116	29	2	not	not	PART
ejpam-7116	29	3	be	be	AUX
ejpam-7116	29	4	obtained	obtain	VERB
ejpam-7116	29	5	from	from	ADP
ejpam-7116	29	6	the	the	DET
ejpam-7116	29	7	corresponding	corresponding	ADJ
ejpam-7116	29	8	results	result	NOUN
ejpam-7116	29	9	on	on	ADP
ejpam-7116	29	10	metric	metric	ADJ
ejpam-7116	29	11	spaces	space	NOUN
ejpam-7116	29	12	.	.	PUNCT
ejpam-7116	30	1	according	accord	VERB
ejpam-7116	30	2	to	to	ADP
ejpam-7116	30	3	[	[	X
ejpam-7116	30	4	8	8	NUM
ejpam-7116	30	5	]	]	PUNCT
ejpam-7116	30	6	this	this	DET
ejpam-7116	30	7	fact	fact	NOUN
ejpam-7116	30	8	among	among	ADP
ejpam-7116	30	9	other	other	ADJ
ejpam-7116	30	10	things	thing	NOUN
ejpam-7116	30	11	is	be	AUX
ejpam-7116	30	12	somewhat	somewhat	ADV
ejpam-7116	30	13	limiting	limit	VERB
ejpam-7116	30	14	the	the	DET
ejpam-7116	30	15	applicative	applicative	ADJ
ejpam-7116	30	16	potential	potential	NOUN
ejpam-7116	30	17	of	of	ADP
ejpam-7116	30	18	such	such	ADJ
ejpam-7116	30	19	results	result	NOUN
ejpam-7116	30	20	.	.	PUNCT
ejpam-7116	31	1	nevertheless	nevertheless	ADV
ejpam-7116	31	2	,	,	PUNCT
ejpam-7116	31	3	the	the	DET
ejpam-7116	31	4	study	study	NOUN
ejpam-7116	31	5	of	of	ADP
ejpam-7116	31	6	fixed	fix	VERB
ejpam-7116	31	7	point	point	NOUN
ejpam-7116	31	8	theory	theory	NOUN
ejpam-7116	31	9	,	,	PUNCT
ejpam-7116	31	10	as	as	ADV
ejpam-7116	31	11	well	well	ADV
ejpam-7116	31	12	as	as	ADP
ejpam-7116	31	13	toplogical	toplogical	ADJ
ejpam-7116	31	14	properties	property	NOUN
ejpam-7116	31	15	on	on	ADP
ejpam-7116	31	16	r.m.s	r.m.s	NOUN
ejpam-7116	31	17	.	.	PUNCT
ejpam-7116	32	1	remains	remain	VERB
ejpam-7116	32	2	very	very	ADV
ejpam-7116	32	3	active	active	ADJ
ejpam-7116	32	4	and	and	CCONJ
ejpam-7116	32	5	fruitful	fruitful	ADJ
ejpam-7116	32	6	,	,	PUNCT
ejpam-7116	32	7	see	see	VERB
ejpam-7116	32	8	[	[	X
ejpam-7116	32	9	5	5	NUM
ejpam-7116	32	10	]	]	PUNCT
ejpam-7116	32	11	and	and	CCONJ
ejpam-7116	32	12	references	reference	NOUN
ejpam-7116	32	13	therein	therein	ADV
ejpam-7116	32	14	.	.	PUNCT
ejpam-7116	33	1	with	with	ADP
ejpam-7116	33	2	this	this	PRON
ejpam-7116	33	3	in	in	ADP
ejpam-7116	33	4	mind	mind	NOUN
ejpam-7116	33	5	,	,	PUNCT
ejpam-7116	33	6	in	in	ADP
ejpam-7116	33	7	the	the	DET
ejpam-7116	33	8	present	present	ADJ
ejpam-7116	33	9	paper	paper	NOUN
ejpam-7116	33	10	we	we	PRON
ejpam-7116	33	11	further	far	ADV
ejpam-7116	33	12	generalize	generalize	VERB
ejpam-7116	33	13	rectangular	rectangular	ADJ
ejpam-7116	33	14	metrics	metric	NOUN
ejpam-7116	33	15	to	to	PART
ejpam-7116	33	16	obtain	obtain	VERB
ejpam-7116	33	17	so	so	ADV
ejpam-7116	33	18	called	call	VERB
ejpam-7116	33	19	generalized	generalized	ADJ
ejpam-7116	33	20	branciari	branciari	ADJ
ejpam-7116	33	21	metric	metric	ADJ
ejpam-7116	33	22	spaces	space	NOUN
ejpam-7116	33	23	.	.	PUNCT
ejpam-7116	34	1	we	we	PRON
ejpam-7116	34	2	notice	notice	VERB
ejpam-7116	34	3	that	that	SCONJ
ejpam-7116	34	4	the	the	DET
ejpam-7116	34	5	rectangular	rectangular	ADJ
ejpam-7116	34	6	inequality	inequality	NOUN
ejpam-7116	34	7	(	(	PUNCT
ejpam-7116	34	8	iii	iii	NOUN
ejpam-7116	34	9	)	)	PUNCT
ejpam-7116	34	10	of	of	ADP
ejpam-7116	34	11	definition	definition	NOUN
ejpam-7116	34	12	1.1	1.1	NUM
ejpam-7116	34	13	does	do	AUX
ejpam-7116	34	14	not	not	PART
ejpam-7116	34	15	contain	contain	VERB
ejpam-7116	34	16	all	all	DET
ejpam-7116	34	17	possible	possible	ADJ
ejpam-7116	34	18	distances	distance	NOUN
ejpam-7116	34	19	between	between	ADP
ejpam-7116	34	20	four	four	NUM
ejpam-7116	34	21	points	point	NOUN
ejpam-7116	34	22	x	x	NOUN
ejpam-7116	34	23	,	,	PUNCT
ejpam-7116	34	24	y	y	PROPN
ejpam-7116	34	25	,	,	PUNCT
ejpam-7116	34	26	u	u	NOUN
ejpam-7116	34	27	and	and	CCONJ
ejpam-7116	34	28	v.	v.	X
ejpam-7116	34	29	by	by	ADP
ejpam-7116	34	30	taking	take	VERB
ejpam-7116	34	31	into	into	ADP
ejpam-7116	34	32	account	account	NOUN
ejpam-7116	34	33	remaining	remain	VERB
ejpam-7116	34	34	distances	distance	NOUN
ejpam-7116	34	35	,	,	PUNCT
ejpam-7116	34	36	i.e.	i.e.	X
ejpam-7116	34	37	adding	add	VERB
ejpam-7116	34	38	d(x	d(x	PROPN
ejpam-7116	34	39	,	,	PUNCT
ejpam-7116	34	40	v	v	NOUN
ejpam-7116	34	41	)	)	PUNCT
ejpam-7116	34	42	and	and	CCONJ
ejpam-7116	34	43	d(y	d(y	PROPN
ejpam-7116	34	44	,	,	PUNCT
ejpam-7116	34	45	u	u	NOUN
ejpam-7116	34	46	)	)	PUNCT
ejpam-7116	34	47	to	to	ADP
ejpam-7116	34	48	the	the	DET
ejpam-7116	34	49	sum	sum	NOUN
ejpam-7116	34	50	on	on	ADP
ejpam-7116	34	51	the	the	DET
ejpam-7116	34	52	right	right	ADJ
ejpam-7116	34	53	-	-	PUNCT
ejpam-7116	34	54	hand	hand	NOUN
ejpam-7116	34	55	side	side	NOUN
ejpam-7116	34	56	of	of	ADP
ejpam-7116	34	57	the	the	DET
ejpam-7116	34	58	inequality	inequality	NOUN
ejpam-7116	34	59	,	,	PUNCT
ejpam-7116	34	60	we	we	PRON
ejpam-7116	34	61	obtain	obtain	VERB
ejpam-7116	34	62	the	the	DET
ejpam-7116	34	63	desired	desire	VERB
ejpam-7116	34	64	generalization	generalization	NOUN
ejpam-7116	34	65	.	.	PUNCT
ejpam-7116	35	1	the	the	DET
ejpam-7116	35	2	following	follow	VERB
ejpam-7116	35	3	section	section	NOUN
ejpam-7116	35	4	outlines	outline	VERB
ejpam-7116	35	5	the	the	DET
ejpam-7116	35	6	definition	definition	NOUN
ejpam-7116	35	7	,	,	PUNCT
ejpam-7116	35	8	examples	example	NOUN
ejpam-7116	35	9	and	and	CCONJ
ejpam-7116	35	10	basic	basic	ADJ
ejpam-7116	35	11	properties	property	NOUN
ejpam-7116	35	12	of	of	ADP
ejpam-7116	35	13	these	these	DET
ejpam-7116	35	14	spaces	space	NOUN
ejpam-7116	35	15	which	which	PRON
ejpam-7116	35	16	will	will	AUX
ejpam-7116	35	17	be	be	AUX
ejpam-7116	35	18	needed	need	VERB
ejpam-7116	35	19	in	in	ADP
ejpam-7116	35	20	the	the	DET
ejpam-7116	35	21	sequel	sequel	NOUN
ejpam-7116	35	22	.	.	PUNCT
ejpam-7116	36	1	in	in	ADP
ejpam-7116	36	2	the	the	DET
ejpam-7116	36	3	next	next	ADJ
ejpam-7116	36	4	section	section	NOUN
ejpam-7116	36	5	we	we	PRON
ejpam-7116	36	6	state	state	VERB
ejpam-7116	36	7	and	and	CCONJ
ejpam-7116	36	8	prove	prove	VERB
ejpam-7116	36	9	two	two	NUM
ejpam-7116	36	10	classical	classical	ADJ
ejpam-7116	36	11	fixed	fix	VERB
ejpam-7116	36	12	point	point	NOUN
ejpam-7116	36	13	theorems	theorem	NOUN
ejpam-7116	36	14	of	of	ADP
ejpam-7116	36	15	banach	banach	NOUN
ejpam-7116	36	16	[	[	X
ejpam-7116	36	17	1	1	X
ejpam-7116	36	18	]	]	PUNCT
ejpam-7116	36	19	and	and	CCONJ
ejpam-7116	36	20	kannan	kannan	PROPN
ejpam-7116	37	1	[	[	X
ejpam-7116	37	2	9	9	NUM
ejpam-7116	37	3	]	]	PUNCT
ejpam-7116	37	4	in	in	ADP
ejpam-7116	37	5	generalized	generalized	ADJ
ejpam-7116	37	6	branciari	branciari	NOUN
ejpam-7116	37	7	metric	metric	ADJ
ejpam-7116	37	8	spaces	space	NOUN
ejpam-7116	37	9	as	as	ADP
ejpam-7116	37	10	our	our	PRON
ejpam-7116	37	11	main	main	ADJ
ejpam-7116	37	12	results	result	NOUN
ejpam-7116	37	13	.	.	PUNCT
ejpam-7116	38	1	to	to	PART
ejpam-7116	38	2	conclude	conclude	VERB
ejpam-7116	38	3	the	the	DET
ejpam-7116	38	4	paper	paper	NOUN
ejpam-7116	38	5	,	,	PUNCT
ejpam-7116	38	6	we	we	PRON
ejpam-7116	38	7	list	list	VERB
ejpam-7116	38	8	some	some	DET
ejpam-7116	38	9	open	open	ADJ
ejpam-7116	38	10	problems	problem	NOUN
ejpam-7116	38	11	arising	arise	VERB
ejpam-7116	38	12	in	in	ADP
ejpam-7116	38	13	the	the	DET
ejpam-7116	38	14	study	study	NOUN
ejpam-7116	38	15	of	of	ADP
ejpam-7116	38	16	fixed	fix	VERB
ejpam-7116	38	17	point	point	NOUN
ejpam-7116	38	18	theory	theory	NOUN
ejpam-7116	38	19	and	and	CCONJ
ejpam-7116	38	20	topology	topology	NOUN
ejpam-7116	38	21	of	of	ADP
ejpam-7116	38	22	our	our	PRON
ejpam-7116	38	23	novel	novel	ADJ
ejpam-7116	38	24	spaces	space	NOUN
ejpam-7116	38	25	,	,	PUNCT
ejpam-7116	38	26	also	also	ADV
ejpam-7116	38	27	providing	provide	VERB
ejpam-7116	38	28	directions	direction	NOUN
ejpam-7116	38	29	for	for	ADP
ejpam-7116	38	30	further	further	ADJ
ejpam-7116	38	31	research	research	NOUN
ejpam-7116	38	32	.	.	PUNCT
ejpam-7116	39	1	2	2	X
ejpam-7116	39	2	.	.	X
ejpam-7116	39	3	generalized	generalize	VERB
ejpam-7116	39	4	branciari	branciari	NOUN
ejpam-7116	39	5	metric	metric	ADJ
ejpam-7116	39	6	spaces	space	NOUN
ejpam-7116	39	7	we	we	PRON
ejpam-7116	39	8	begin	begin	VERB
ejpam-7116	39	9	by	by	ADP
ejpam-7116	39	10	giving	give	VERB
ejpam-7116	39	11	the	the	DET
ejpam-7116	39	12	formal	formal	ADJ
ejpam-7116	39	13	definition	definition	NOUN
ejpam-7116	39	14	of	of	ADP
ejpam-7116	39	15	generalized	generalized	ADJ
ejpam-7116	39	16	branciari	branciari	ADJ
ejpam-7116	39	17	metrics	metric	NOUN
ejpam-7116	39	18	.	.	PUNCT
ejpam-7116	40	1	definition	definition	NOUN
ejpam-7116	40	2	2.1	2.1	NUM
ejpam-7116	40	3	.	.	PUNCT
ejpam-7116	41	1	let	let	VERB
ejpam-7116	41	2	x	x	PRON
ejpam-7116	41	3	be	be	AUX
ejpam-7116	41	4	a	a	DET
ejpam-7116	41	5	nonempty	nonempty	ADV
ejpam-7116	41	6	set	set	VERB
ejpam-7116	41	7	.	.	PUNCT
ejpam-7116	42	1	a	a	DET
ejpam-7116	42	2	mapping	mapping	NOUN
ejpam-7116	42	3	d	d	NOUN
ejpam-7116	42	4	:	:	PUNCT
ejpam-7116	42	5	x	x	PROPN
ejpam-7116	42	6	×x	×x	X
ejpam-7116	42	7	→	→	PUNCT
ejpam-7116	42	8	[	[	X
ejpam-7116	42	9	0,+∞	0,+∞	NUM
ejpam-7116	42	10	)	)	PUNCT
ejpam-7116	42	11	satisfying	satisfy	VERB
ejpam-7116	42	12	the	the	DET
ejpam-7116	42	13	following	follow	VERB
ejpam-7116	42	14	conditions	condition	NOUN
ejpam-7116	42	15	for	for	ADP
ejpam-7116	42	16	all	all	DET
ejpam-7116	42	17	x	x	NOUN
ejpam-7116	42	18	,	,	PUNCT
ejpam-7116	42	19	y	y	PROPN
ejpam-7116	42	20	∈	∈	PROPN
ejpam-7116	42	21	x	x	X
ejpam-7116	42	22	and	and	CCONJ
ejpam-7116	42	23	u	u	NOUN
ejpam-7116	42	24	,	,	PUNCT
ejpam-7116	42	25	v	v	NOUN
ejpam-7116	42	26	∈	∈	PROPN
ejpam-7116	42	27	x	x	X
ejpam-7116	42	28	\	\	X
ejpam-7116	42	29	{	{	PUNCT
ejpam-7116	42	30	x	x	NOUN
ejpam-7116	42	31	,	,	PUNCT
ejpam-7116	42	32	y	y	NOUN
ejpam-7116	42	33	}	}	PUNCT
ejpam-7116	42	34	with	with	ADP
ejpam-7116	42	35	u	u	PROPN
ejpam-7116	42	36	̸=	̸=	PROPN
ejpam-7116	42	37	v	v	NOUN
ejpam-7116	42	38	:	:	PUNCT
ejpam-7116	42	39	(	(	PUNCT
ejpam-7116	42	40	i	i	NOUN
ejpam-7116	42	41	)	)	PUNCT
ejpam-7116	42	42	d(x	d(x	PROPN
ejpam-7116	42	43	,	,	PUNCT
ejpam-7116	42	44	y	y	NOUN
ejpam-7116	42	45	)	)	PUNCT
ejpam-7116	42	46	=	=	SYM
ejpam-7116	42	47	0	0	NUM
ejpam-7116	42	48	⇔	⇔	X
ejpam-7116	42	49	x	x	X
ejpam-7116	42	50	=	=	SYM
ejpam-7116	42	51	y	y	PROPN
ejpam-7116	42	52	,	,	PUNCT
ejpam-7116	42	53	(	(	PUNCT
ejpam-7116	42	54	ii	ii	NOUN
ejpam-7116	42	55	)	)	PUNCT
ejpam-7116	42	56	d(x	d(x	PROPN
ejpam-7116	42	57	,	,	PUNCT
ejpam-7116	42	58	y	y	NOUN
ejpam-7116	42	59	)	)	PUNCT
ejpam-7116	42	60	=	=	SYM
ejpam-7116	42	61	d(y	d(y	NOUN
ejpam-7116	42	62	,	,	PUNCT
ejpam-7116	42	63	x	x	NOUN
ejpam-7116	42	64	)	)	PUNCT
ejpam-7116	42	65	,	,	PUNCT
ejpam-7116	42	66	and	and	CCONJ
ejpam-7116	42	67	(	(	PUNCT
ejpam-7116	42	68	iii	iii	NOUN
ejpam-7116	42	69	)	)	PUNCT
ejpam-7116	42	70	d(x	d(x	PROPN
ejpam-7116	42	71	,	,	PUNCT
ejpam-7116	42	72	y	y	NOUN
ejpam-7116	42	73	)	)	PUNCT
ejpam-7116	42	74	≤	≤	NOUN
ejpam-7116	42	75	d(x	d(x	NOUN
ejpam-7116	42	76	,	,	PUNCT
ejpam-7116	42	77	u	u	NOUN
ejpam-7116	42	78	)	)	PUNCT
ejpam-7116	42	79	+	+	CCONJ
ejpam-7116	42	80	d(u	d(u	PROPN
ejpam-7116	42	81	,	,	PUNCT
ejpam-7116	42	82	v	v	NOUN
ejpam-7116	42	83	)	)	PUNCT
ejpam-7116	42	84	+	+	X
ejpam-7116	43	1	d(v	d(v	PROPN
ejpam-7116	43	2	,	,	PUNCT
ejpam-7116	43	3	y	y	NOUN
ejpam-7116	43	4	)	)	PUNCT
ejpam-7116	44	1	+	+	CCONJ
ejpam-7116	44	2	d(x	d(x	PROPN
ejpam-7116	44	3	,	,	PUNCT
ejpam-7116	44	4	v	v	NOUN
ejpam-7116	44	5	)	)	PUNCT
ejpam-7116	44	6	+	+	CCONJ
ejpam-7116	44	7	d(y	d(y	PROPN
ejpam-7116	44	8	,	,	PUNCT
ejpam-7116	44	9	u	u	NOUN
ejpam-7116	44	10	)	)	PUNCT
ejpam-7116	44	11	a.	a.	NOUN
ejpam-7116	44	12	kostić	kostić	VERB
ejpam-7116	44	13	/	/	SYM
ejpam-7116	44	14	eur	eur	PROPN
ejpam-7116	44	15	.	.	PUNCT
ejpam-7116	45	1	j.	j.	PROPN
ejpam-7116	45	2	pure	pure	PROPN
ejpam-7116	45	3	appl	appl	PROPN
ejpam-7116	45	4	.	.	PROPN
ejpam-7116	45	5	math	math	PROPN
ejpam-7116	45	6	,	,	PUNCT
ejpam-7116	45	7	18	18	NUM
ejpam-7116	45	8	(	(	PUNCT
ejpam-7116	45	9	4	4	NUM
ejpam-7116	45	10	)	)	PUNCT
ejpam-7116	45	11	(	(	PUNCT
ejpam-7116	45	12	2025	2025	NUM
ejpam-7116	45	13	)	)	PUNCT
ejpam-7116	45	14	,	,	PUNCT
ejpam-7116	45	15	7116	7116	NUM
ejpam-7116	45	16	3	3	NUM
ejpam-7116	45	17	of	of	ADP
ejpam-7116	45	18	10	10	NUM
ejpam-7116	45	19	x	x	SYM
ejpam-7116	45	20	y	y	NOUN
ejpam-7116	45	21	z	z	NOUN
ejpam-7116	45	22	x	x	SYM
ejpam-7116	45	23	y	y	PROPN
ejpam-7116	45	24	u	u	NOUN
ejpam-7116	45	25	v	v	NOUN
ejpam-7116	45	26	x	x	SYM
ejpam-7116	45	27	y	y	NOUN
ejpam-7116	45	28	u	u	NOUN
ejpam-7116	45	29	v	v	NUM
ejpam-7116	45	30	figure	figure	NOUN
ejpam-7116	45	31	1	1	NUM
ejpam-7116	45	32	:	:	PUNCT
ejpam-7116	45	33	graphical	graphical	ADJ
ejpam-7116	45	34	representation	representation	NOUN
ejpam-7116	45	35	of	of	ADP
ejpam-7116	45	36	metric	metric	ADJ
ejpam-7116	45	37	space	space	NOUN
ejpam-7116	45	38	,	,	PUNCT
ejpam-7116	45	39	r.m.s	r.m.s	NOUN
ejpam-7116	45	40	.	.	PUNCT
ejpam-7116	46	1	and	and	CCONJ
ejpam-7116	46	2	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	46	3	.	.	PUNCT
ejpam-7116	47	1	in	in	ADP
ejpam-7116	47	2	each	each	DET
ejpam-7116	47	3	graph	graph	NOUN
ejpam-7116	47	4	,	,	PUNCT
ejpam-7116	47	5	the	the	DET
ejpam-7116	47	6	length	length	NOUN
ejpam-7116	47	7	of	of	ADP
ejpam-7116	47	8	each	each	DET
ejpam-7116	47	9	edge	edge	NOUN
ejpam-7116	47	10	is	be	AUX
ejpam-7116	47	11	less	less	ADJ
ejpam-7116	47	12	than	than	ADP
ejpam-7116	47	13	the	the	DET
ejpam-7116	47	14	sum	sum	NOUN
ejpam-7116	47	15	of	of	ADP
ejpam-7116	47	16	lengths	length	NOUN
ejpam-7116	47	17	of	of	ADP
ejpam-7116	47	18	all	all	DET
ejpam-7116	47	19	remaining	remain	VERB
ejpam-7116	47	20	edges	edge	NOUN
ejpam-7116	47	21	.	.	PUNCT
ejpam-7116	48	1	is	be	AUX
ejpam-7116	48	2	called	call	VERB
ejpam-7116	48	3	a	a	DET
ejpam-7116	48	4	generalized	generalize	VERB
ejpam-7116	48	5	branciari	branciari	NOUN
ejpam-7116	48	6	metric	metric	ADJ
ejpam-7116	48	7	(	(	PUNCT
ejpam-7116	48	8	g.b.m	g.b.m	NOUN
ejpam-7116	48	9	.	.	PUNCT
ejpam-7116	48	10	for	for	ADP
ejpam-7116	48	11	short	short	ADJ
ejpam-7116	48	12	)	)	PUNCT
ejpam-7116	48	13	on	on	ADP
ejpam-7116	48	14	x	x	SYM
ejpam-7116	48	15	,	,	PUNCT
ejpam-7116	48	16	while	while	SCONJ
ejpam-7116	48	17	the	the	DET
ejpam-7116	48	18	pair	pair	NOUN
ejpam-7116	48	19	(	(	PUNCT
ejpam-7116	48	20	x	x	X
ejpam-7116	48	21	,	,	PUNCT
ejpam-7116	48	22	d	d	NOUN
ejpam-7116	48	23	)	)	PUNCT
ejpam-7116	48	24	is	be	AUX
ejpam-7116	48	25	a	a	DET
ejpam-7116	48	26	generalized	generalized	ADJ
ejpam-7116	48	27	branciari	branciari	ADJ
ejpam-7116	48	28	metric	metric	ADJ
ejpam-7116	48	29	space	space	NOUN
ejpam-7116	48	30	(	(	PUNCT
ejpam-7116	48	31	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	48	32	.	.	PUNCT
ejpam-7116	48	33	in	in	ADP
ejpam-7116	48	34	short	short	ADJ
ejpam-7116	48	35	)	)	PUNCT
ejpam-7116	48	36	.	.	PUNCT
ejpam-7116	49	1	consider	consider	VERB
ejpam-7116	49	2	the	the	DET
ejpam-7116	49	3	four	four	NUM
ejpam-7116	49	4	points	point	NOUN
ejpam-7116	49	5	x	x	NOUN
ejpam-7116	49	6	,	,	PUNCT
ejpam-7116	49	7	y	y	PROPN
ejpam-7116	49	8	,	,	PUNCT
ejpam-7116	49	9	u	u	NOUN
ejpam-7116	49	10	and	and	CCONJ
ejpam-7116	49	11	v	v	NOUN
ejpam-7116	49	12	as	as	ADP
ejpam-7116	49	13	vertices	vertex	NOUN
ejpam-7116	49	14	of	of	ADP
ejpam-7116	49	15	a	a	DET
ejpam-7116	49	16	quadrilateral	quadrilateral	NOUN
ejpam-7116	49	17	in	in	ADP
ejpam-7116	49	18	a	a	DET
ejpam-7116	49	19	euclidean	euclidean	ADJ
ejpam-7116	49	20	space	space	NOUN
ejpam-7116	49	21	.	.	PUNCT
ejpam-7116	50	1	then	then	ADV
ejpam-7116	50	2	the	the	DET
ejpam-7116	50	3	distances	distance	NOUN
ejpam-7116	50	4	featuring	feature	VERB
ejpam-7116	50	5	in	in	ADP
ejpam-7116	50	6	the	the	DET
ejpam-7116	50	7	rectangular	rectangular	ADJ
ejpam-7116	50	8	inequality	inequality	NOUN
ejpam-7116	50	9	(	(	PUNCT
ejpam-7116	50	10	iii	iii	NOUN
ejpam-7116	50	11	)	)	PUNCT
ejpam-7116	50	12	in	in	ADP
ejpam-7116	50	13	definition	definition	NOUN
ejpam-7116	50	14	1.1	1.1	NUM
ejpam-7116	50	15	can	can	AUX
ejpam-7116	50	16	be	be	AUX
ejpam-7116	50	17	thought	think	VERB
ejpam-7116	50	18	of	of	ADP
ejpam-7116	50	19	as	as	ADP
ejpam-7116	50	20	the	the	DET
ejpam-7116	50	21	lengths	length	NOUN
ejpam-7116	50	22	of	of	ADP
ejpam-7116	50	23	its	its	PRON
ejpam-7116	50	24	sides	side	NOUN
ejpam-7116	50	25	.	.	PUNCT
ejpam-7116	51	1	hence	hence	ADV
ejpam-7116	51	2	the	the	DET
ejpam-7116	51	3	rectangular	rectangular	ADJ
ejpam-7116	51	4	inequality	inequality	NOUN
ejpam-7116	51	5	states	state	VERB
ejpam-7116	51	6	that	that	SCONJ
ejpam-7116	51	7	the	the	DET
ejpam-7116	51	8	length	length	NOUN
ejpam-7116	51	9	of	of	ADP
ejpam-7116	51	10	each	each	DET
ejpam-7116	51	11	side	side	NOUN
ejpam-7116	51	12	is	be	AUX
ejpam-7116	51	13	not	not	PART
ejpam-7116	51	14	greater	great	ADJ
ejpam-7116	51	15	than	than	ADP
ejpam-7116	51	16	the	the	DET
ejpam-7116	51	17	sum	sum	NOUN
ejpam-7116	51	18	of	of	ADP
ejpam-7116	51	19	lengths	length	NOUN
ejpam-7116	51	20	of	of	ADP
ejpam-7116	51	21	remaining	remain	VERB
ejpam-7116	51	22	sides	side	NOUN
ejpam-7116	51	23	,	,	PUNCT
ejpam-7116	51	24	as	as	SCONJ
ejpam-7116	51	25	is	be	AUX
ejpam-7116	51	26	well	well	ADV
ejpam-7116	51	27	known	know	VERB
ejpam-7116	51	28	from	from	ADP
ejpam-7116	51	29	geometry	geometry	NOUN
ejpam-7116	51	30	.	.	PUNCT
ejpam-7116	52	1	therefore	therefore	ADV
ejpam-7116	52	2	,	,	PUNCT
ejpam-7116	52	3	our	our	PRON
ejpam-7116	52	4	generalization	generalization	NOUN
ejpam-7116	52	5	in	in	ADP
ejpam-7116	52	6	definition	definition	NOUN
ejpam-7116	52	7	2.1	2.1	NUM
ejpam-7116	52	8	(	(	PUNCT
ejpam-7116	52	9	iii	iii	NOUN
ejpam-7116	52	10	)	)	PUNCT
ejpam-7116	52	11	involves	involve	VERB
ejpam-7116	52	12	adding	add	VERB
ejpam-7116	52	13	lengths	length	NOUN
ejpam-7116	52	14	of	of	ADP
ejpam-7116	52	15	diagonals	diagonal	NOUN
ejpam-7116	52	16	to	to	ADP
ejpam-7116	52	17	the	the	DET
ejpam-7116	52	18	right	right	ADJ
ejpam-7116	52	19	-	-	PUNCT
ejpam-7116	52	20	hand	hand	NOUN
ejpam-7116	52	21	side	side	NOUN
ejpam-7116	52	22	of	of	ADP
ejpam-7116	52	23	the	the	DET
ejpam-7116	52	24	rectangular	rectangular	ADJ
ejpam-7116	52	25	inequality	inequality	NOUN
ejpam-7116	52	26	(	(	PUNCT
ejpam-7116	52	27	see	see	VERB
ejpam-7116	52	28	figure	figure	NOUN
ejpam-7116	52	29	1	1	NUM
ejpam-7116	52	30	below	below	ADP
ejpam-7116	52	31	)	)	PUNCT
ejpam-7116	52	32	.	.	PUNCT
ejpam-7116	53	1	from	from	ADP
ejpam-7116	53	2	the	the	DET
ejpam-7116	53	3	definition	definition	NOUN
ejpam-7116	53	4	it	it	PRON
ejpam-7116	53	5	is	be	AUX
ejpam-7116	53	6	obvious	obvious	ADJ
ejpam-7116	53	7	that	that	SCONJ
ejpam-7116	53	8	every	every	DET
ejpam-7116	53	9	r.m.s	r.m.s	NOUN
ejpam-7116	53	10	.	.	PUNCT
ejpam-7116	54	1	is	be	AUX
ejpam-7116	54	2	a	a	DET
ejpam-7116	54	3	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	54	4	.	.	PUNCT
ejpam-7116	55	1	however	however	ADV
ejpam-7116	55	2	,	,	PUNCT
ejpam-7116	55	3	the	the	DET
ejpam-7116	55	4	converse	converse	NOUN
ejpam-7116	55	5	in	in	ADP
ejpam-7116	55	6	general	general	ADJ
ejpam-7116	55	7	does	do	AUX
ejpam-7116	55	8	not	not	PART
ejpam-7116	55	9	hold	hold	VERB
ejpam-7116	55	10	,	,	PUNCT
ejpam-7116	55	11	as	as	SCONJ
ejpam-7116	55	12	the	the	DET
ejpam-7116	55	13	following	follow	VERB
ejpam-7116	55	14	two	two	NUM
ejpam-7116	55	15	examples	example	NOUN
ejpam-7116	55	16	show	show	NOUN
ejpam-7116	55	17	.	.	PUNCT
ejpam-7116	56	1	example	example	NOUN
ejpam-7116	56	2	2.1	2.1	NUM
ejpam-7116	56	3	.	.	PUNCT
ejpam-7116	57	1	let	let	VERB
ejpam-7116	57	2	x	x	PUNCT
ejpam-7116	57	3	=	=	PRON
ejpam-7116	57	4	{	{	PUNCT
ejpam-7116	57	5	ai	ai	INTJ
ejpam-7116	57	6	:	:	PUNCT
ejpam-7116	57	7	i	i	NOUN
ejpam-7116	57	8	=	=	NOUN
ejpam-7116	57	9	1	1	NUM
ejpam-7116	57	10	,	,	PUNCT
ejpam-7116	57	11	4	4	NUM
ejpam-7116	57	12	}	}	PUNCT
ejpam-7116	57	13	and	and	CCONJ
ejpam-7116	57	14	define	define	VERB
ejpam-7116	57	15	the	the	DET
ejpam-7116	57	16	mapping	mapping	NOUN
ejpam-7116	57	17	d	d	NOUN
ejpam-7116	57	18	:	:	PUNCT
ejpam-7116	57	19	x	x	PROPN
ejpam-7116	57	20	×x	×x	X
ejpam-7116	57	21	→	→	PUNCT
ejpam-7116	57	22	[	[	X
ejpam-7116	57	23	0,+∞	0,+∞	NUM
ejpam-7116	57	24	)	)	PUNCT
ejpam-7116	57	25	as	as	ADP
ejpam-7116	57	26	d(ai	d(ai	PROPN
ejpam-7116	57	27	,	,	PUNCT
ejpam-7116	57	28	aj	aj	ADJ
ejpam-7116	57	29	)	)	PUNCT
ejpam-7116	57	30	=	=	SYM
ejpam-7116	58	1			NOUN
ejpam-7116	58	2	0	0	NUM
ejpam-7116	58	3	,	,	PUNCT
ejpam-7116	58	4	i	i	PRON
ejpam-7116	58	5	=	=	SYM
ejpam-7116	58	6	j	j	PROPN
ejpam-7116	58	7	,	,	PUNCT
ejpam-7116	58	8	4	4	NUM
ejpam-7116	58	9	,	,	PUNCT
ejpam-7116	58	10	(	(	PUNCT
ejpam-7116	58	11	i	i	PROPN
ejpam-7116	58	12	,	,	PUNCT
ejpam-7116	58	13	j	j	PROPN
ejpam-7116	58	14	)	)	PUNCT
ejpam-7116	58	15	∈	∈	PROPN
ejpam-7116	58	16	{	{	PUNCT
ejpam-7116	58	17	(	(	PUNCT
ejpam-7116	58	18	1	1	NUM
ejpam-7116	58	19	,	,	PUNCT
ejpam-7116	58	20	2	2	NUM
ejpam-7116	58	21	)	)	PUNCT
ejpam-7116	58	22	,	,	PUNCT
ejpam-7116	58	23	(	(	PUNCT
ejpam-7116	58	24	2	2	NUM
ejpam-7116	58	25	,	,	PUNCT
ejpam-7116	58	26	1	1	NUM
ejpam-7116	58	27	)	)	PUNCT
ejpam-7116	58	28	}	}	PUNCT
ejpam-7116	58	29	,	,	PUNCT
ejpam-7116	58	30	1	1	X
ejpam-7116	58	31	,	,	PUNCT
ejpam-7116	58	32	in	in	ADP
ejpam-7116	58	33	all	all	DET
ejpam-7116	58	34	other	other	ADJ
ejpam-7116	58	35	cases	case	NOUN
ejpam-7116	58	36	.	.	PUNCT
ejpam-7116	59	1	then	then	ADV
ejpam-7116	59	2	it	it	PRON
ejpam-7116	59	3	is	be	AUX
ejpam-7116	59	4	easy	easy	ADJ
ejpam-7116	59	5	to	to	PART
ejpam-7116	59	6	check	check	VERB
ejpam-7116	59	7	that	that	PRON
ejpam-7116	59	8	(	(	PUNCT
ejpam-7116	59	9	x	x	X
ejpam-7116	59	10	,	,	PUNCT
ejpam-7116	59	11	d	d	NOUN
ejpam-7116	59	12	)	)	PUNCT
ejpam-7116	59	13	is	be	AUX
ejpam-7116	59	14	a	a	DET
ejpam-7116	59	15	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	59	16	.	.	PUNCT
ejpam-7116	60	1	however	however	ADV
ejpam-7116	60	2	,	,	PUNCT
ejpam-7116	60	3	it	it	PRON
ejpam-7116	60	4	is	be	AUX
ejpam-7116	60	5	not	not	PART
ejpam-7116	60	6	a	a	DET
ejpam-7116	60	7	r.m.s	r.m.s	NOUN
ejpam-7116	60	8	.	.	PUNCT
ejpam-7116	61	1	because	because	SCONJ
ejpam-7116	61	2	d(a1	d(a1	NOUN
ejpam-7116	61	3	,	,	PUNCT
ejpam-7116	61	4	a2	a2	PROPN
ejpam-7116	61	5	)	)	PUNCT
ejpam-7116	61	6	=	=	SYM
ejpam-7116	61	7	4	4	NUM
ejpam-7116	61	8	>	>	SYM
ejpam-7116	61	9	3	3	NUM
ejpam-7116	61	10	=	=	SYM
ejpam-7116	61	11	d(a1	d(a1	NOUN
ejpam-7116	61	12	,	,	PUNCT
ejpam-7116	61	13	a3	a3	NOUN
ejpam-7116	61	14	)	)	PUNCT
ejpam-7116	61	15	+	+	SYM
ejpam-7116	61	16	d(a3	d(a3	NOUN
ejpam-7116	61	17	,	,	PUNCT
ejpam-7116	61	18	a4	a4	PROPN
ejpam-7116	61	19	)	)	PUNCT
ejpam-7116	61	20	+	+	CCONJ
ejpam-7116	61	21	d(a4	d(a4	PROPN
ejpam-7116	61	22	,	,	PUNCT
ejpam-7116	61	23	a2	a2	PROPN
ejpam-7116	61	24	)	)	PUNCT
ejpam-7116	61	25	.	.	PUNCT
ejpam-7116	62	1	a.	a.	NOUN
ejpam-7116	62	2	kostić	kostić	VERB
ejpam-7116	62	3	/	/	SYM
ejpam-7116	62	4	eur	eur	PROPN
ejpam-7116	62	5	.	.	PUNCT
ejpam-7116	63	1	j.	j.	PROPN
ejpam-7116	63	2	pure	pure	PROPN
ejpam-7116	63	3	appl	appl	PROPN
ejpam-7116	63	4	.	.	PROPN
ejpam-7116	63	5	math	math	PROPN
ejpam-7116	63	6	,	,	PUNCT
ejpam-7116	63	7	18	18	NUM
ejpam-7116	63	8	(	(	PUNCT
ejpam-7116	63	9	4	4	NUM
ejpam-7116	63	10	)	)	PUNCT
ejpam-7116	63	11	(	(	PUNCT
ejpam-7116	63	12	2025	2025	NUM
ejpam-7116	63	13	)	)	PUNCT
ejpam-7116	63	14	,	,	PUNCT
ejpam-7116	63	15	7116	7116	NUM
ejpam-7116	63	16	4	4	NUM
ejpam-7116	63	17	of	of	ADP
ejpam-7116	63	18	10	10	NUM
ejpam-7116	63	19	example	example	NOUN
ejpam-7116	63	20	2.2	2.2	NUM
ejpam-7116	63	21	.	.	PUNCT
ejpam-7116	64	1	let	let	VERB
ejpam-7116	64	2	x	x	SYM
ejpam-7116	64	3	=	=	PUNCT
ejpam-7116	64	4	n	n	PROPN
ejpam-7116	64	5	and	and	CCONJ
ejpam-7116	64	6	d	d	NOUN
ejpam-7116	64	7	:	:	PUNCT
ejpam-7116	64	8	x	x	X
ejpam-7116	64	9	×x	×x	X
ejpam-7116	64	10	→	→	SYM
ejpam-7116	64	11	[	[	X
ejpam-7116	64	12	0,+∞	0,+∞	NUM
ejpam-7116	64	13	)	)	PUNCT
ejpam-7116	64	14	be	be	AUX
ejpam-7116	64	15	defined	define	VERB
ejpam-7116	64	16	by	by	ADP
ejpam-7116	64	17	d(x	d(x	PROPN
ejpam-7116	64	18	,	,	PUNCT
ejpam-7116	64	19	y	y	NOUN
ejpam-7116	64	20	)	)	PUNCT
ejpam-7116	64	21	=	=	PUNCT
ejpam-7116	65	1			NOUN
ejpam-7116	65	2	0	0	NUM
ejpam-7116	65	3	,	,	PUNCT
ejpam-7116	65	4	x	x	X
ejpam-7116	65	5	=	=	SYM
ejpam-7116	65	6	y	y	PROPN
ejpam-7116	65	7	,	,	PUNCT
ejpam-7116	65	8	5	5	NUM
ejpam-7116	65	9	,	,	PUNCT
ejpam-7116	65	10	(	(	PUNCT
ejpam-7116	65	11	x	x	NOUN
ejpam-7116	65	12	,	,	PUNCT
ejpam-7116	65	13	y	y	NOUN
ejpam-7116	65	14	)	)	PUNCT
ejpam-7116	65	15	∈	∈	NOUN
ejpam-7116	65	16	{	{	PUNCT
ejpam-7116	65	17	(	(	PUNCT
ejpam-7116	65	18	1	1	NUM
ejpam-7116	65	19	,	,	PUNCT
ejpam-7116	65	20	2	2	NUM
ejpam-7116	65	21	)	)	PUNCT
ejpam-7116	65	22	,	,	PUNCT
ejpam-7116	65	23	(	(	PUNCT
ejpam-7116	65	24	2	2	NUM
ejpam-7116	65	25	,	,	PUNCT
ejpam-7116	65	26	1	1	NUM
ejpam-7116	65	27	)	)	PUNCT
ejpam-7116	65	28	}	}	PUNCT
ejpam-7116	65	29	,	,	PUNCT
ejpam-7116	65	30	1	1	NUM
ejpam-7116	65	31	n	n	NOUN
ejpam-7116	65	32	,	,	PUNCT
ejpam-7116	65	33	(	(	PUNCT
ejpam-7116	65	34	x	x	NOUN
ejpam-7116	65	35	,	,	PUNCT
ejpam-7116	65	36	y	y	NOUN
ejpam-7116	65	37	)	)	PUNCT
ejpam-7116	65	38	∈	∈	NOUN
ejpam-7116	65	39	{	{	PUNCT
ejpam-7116	65	40	(	(	PUNCT
ejpam-7116	65	41	2	2	NUM
ejpam-7116	65	42	,	,	PUNCT
ejpam-7116	65	43	n	n	CCONJ
ejpam-7116	65	44	)	)	PUNCT
ejpam-7116	65	45	,	,	PUNCT
ejpam-7116	65	46	(	(	PUNCT
ejpam-7116	65	47	n	n	CCONJ
ejpam-7116	65	48	,	,	PUNCT
ejpam-7116	65	49	2)}n≥4	2)}n≥4	NOUN
ejpam-7116	65	50	,	,	PUNCT
ejpam-7116	65	51	1	1	NUM
ejpam-7116	65	52	2n	2n	NUM
ejpam-7116	65	53	,	,	PUNCT
ejpam-7116	65	54	(	(	PUNCT
ejpam-7116	65	55	x	x	NOUN
ejpam-7116	65	56	,	,	PUNCT
ejpam-7116	65	57	y	y	NOUN
ejpam-7116	65	58	)	)	PUNCT
ejpam-7116	65	59	∈	∈	NOUN
ejpam-7116	65	60	{	{	PUNCT
ejpam-7116	65	61	(	(	PUNCT
ejpam-7116	65	62	3	3	NUM
ejpam-7116	65	63	,	,	PUNCT
ejpam-7116	65	64	n	n	CCONJ
ejpam-7116	65	65	)	)	PUNCT
ejpam-7116	65	66	,	,	PUNCT
ejpam-7116	65	67	(	(	PUNCT
ejpam-7116	65	68	n	n	CCONJ
ejpam-7116	65	69	,	,	PUNCT
ejpam-7116	65	70	3)}n≥4	3)}n≥4	NOUN
ejpam-7116	65	71	,	,	PUNCT
ejpam-7116	65	72	2	2	NUM
ejpam-7116	65	73	,	,	PUNCT
ejpam-7116	65	74	otherwise	otherwise	ADV
ejpam-7116	65	75	for	for	ADP
ejpam-7116	65	76	all	all	DET
ejpam-7116	65	77	x	x	NOUN
ejpam-7116	65	78	,	,	PUNCT
ejpam-7116	65	79	y	y	PROPN
ejpam-7116	65	80	∈	∈	PROPN
ejpam-7116	65	81	x.	x.	NOUN
ejpam-7116	65	82	then	then	ADV
ejpam-7116	65	83	(	(	PUNCT
ejpam-7116	65	84	x	x	X
ejpam-7116	65	85	,	,	PUNCT
ejpam-7116	65	86	d	d	NOUN
ejpam-7116	65	87	)	)	PUNCT
ejpam-7116	65	88	is	be	AUX
ejpam-7116	65	89	a	a	DET
ejpam-7116	65	90	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	65	91	.	.	PUNCT
ejpam-7116	66	1	but	but	CCONJ
ejpam-7116	66	2	not	not	PART
ejpam-7116	66	3	a	a	DET
ejpam-7116	66	4	r.m.s	r.m.s	NOUN
ejpam-7116	66	5	.	.	PUNCT
ejpam-7116	67	1	since	since	SCONJ
ejpam-7116	67	2	,	,	PUNCT
ejpam-7116	67	3	for	for	ADP
ejpam-7116	67	4	example	example	NOUN
ejpam-7116	67	5	,	,	PUNCT
ejpam-7116	67	6	d(1	d(1	NOUN
ejpam-7116	67	7	,	,	PUNCT
ejpam-7116	67	8	2	2	NUM
ejpam-7116	67	9	)	)	PUNCT
ejpam-7116	67	10	=	=	SYM
ejpam-7116	67	11	5	5	NUM
ejpam-7116	67	12	>	>	SYM
ejpam-7116	67	13	23	23	NUM
ejpam-7116	67	14	8	8	NUM
ejpam-7116	67	15	=	=	SYM
ejpam-7116	67	16	d(1	d(1	PROPN
ejpam-7116	67	17	,	,	PUNCT
ejpam-7116	67	18	3	3	NUM
ejpam-7116	67	19	)	)	PUNCT
ejpam-7116	67	20	+	+	CCONJ
ejpam-7116	67	21	d(3	d(3	PROPN
ejpam-7116	67	22	,	,	PUNCT
ejpam-7116	67	23	4	4	NUM
ejpam-7116	67	24	)	)	PUNCT
ejpam-7116	67	25	+	+	CCONJ
ejpam-7116	67	26	d(4	d(4	NOUN
ejpam-7116	67	27	,	,	PUNCT
ejpam-7116	67	28	2	2	NUM
ejpam-7116	67	29	)	)	PUNCT
ejpam-7116	67	30	.	.	PUNCT
ejpam-7116	68	1	the	the	DET
ejpam-7116	68	2	basic	basic	ADJ
ejpam-7116	68	3	notions	notion	NOUN
ejpam-7116	68	4	such	such	ADJ
ejpam-7116	68	5	as	as	ADP
ejpam-7116	68	6	convergence	convergence	NOUN
ejpam-7116	68	7	,	,	PUNCT
ejpam-7116	68	8	completeness	completeness	NOUN
ejpam-7116	68	9	and	and	CCONJ
ejpam-7116	68	10	continuity	continuity	NOUN
ejpam-7116	68	11	are	be	AUX
ejpam-7116	68	12	defined	define	VERB
ejpam-7116	68	13	in	in	ADP
ejpam-7116	68	14	the	the	DET
ejpam-7116	68	15	same	same	ADJ
ejpam-7116	68	16	way	way	NOUN
ejpam-7116	68	17	as	as	ADP
ejpam-7116	68	18	in	in	ADP
ejpam-7116	68	19	standard	standard	ADJ
ejpam-7116	68	20	metric	metric	ADJ
ejpam-7116	68	21	spaces	space	NOUN
ejpam-7116	68	22	.	.	PUNCT
ejpam-7116	69	1	since	since	SCONJ
ejpam-7116	69	2	r.m.s	r.m.s	NOUN
ejpam-7116	69	3	.	.	PUNCT
ejpam-7116	69	4	are	be	AUX
ejpam-7116	69	5	a	a	DET
ejpam-7116	69	6	proper	proper	ADJ
ejpam-7116	69	7	subclass	subclass	NOUN
ejpam-7116	69	8	of	of	ADP
ejpam-7116	69	9	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	69	10	.	.	PUNCT
ejpam-7116	70	1	all	all	DET
ejpam-7116	70	2	the	the	DET
ejpam-7116	70	3	peculiar	peculiar	ADJ
ejpam-7116	70	4	properties	property	NOUN
ejpam-7116	70	5	of	of	ADP
ejpam-7116	70	6	r.m.s	r.m.s	NOUN
ejpam-7116	70	7	.	.	PUNCT
ejpam-7116	71	1	mentioned	mention	VERB
ejpam-7116	71	2	in	in	ADP
ejpam-7116	71	3	the	the	DET
ejpam-7116	71	4	previous	previous	ADJ
ejpam-7116	71	5	section	section	NOUN
ejpam-7116	71	6	are	be	AUX
ejpam-7116	71	7	also	also	ADV
ejpam-7116	71	8	possessed	possess	VERB
ejpam-7116	71	9	by	by	ADP
ejpam-7116	71	10	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	71	11	.	.	PUNCT
ejpam-7116	72	1	indeed	indeed	ADV
ejpam-7116	72	2	,	,	PUNCT
ejpam-7116	72	3	in	in	ADP
ejpam-7116	72	4	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	72	5	.	.	PUNCT
ejpam-7116	73	1	(	(	PUNCT
ejpam-7116	73	2	x	x	X
ejpam-7116	73	3	,	,	PUNCT
ejpam-7116	73	4	d	d	NOUN
ejpam-7116	73	5	)	)	PUNCT
ejpam-7116	73	6	from	from	ADP
ejpam-7116	73	7	the	the	DET
ejpam-7116	73	8	example	example	NOUN
ejpam-7116	73	9	2.2	2.2	NUM
ejpam-7116	73	10	:	:	PUNCT
ejpam-7116	73	11	the	the	DET
ejpam-7116	73	12	sequence	sequence	NOUN
ejpam-7116	73	13	an	an	DET
ejpam-7116	73	14	=	=	PUNCT
ejpam-7116	73	15	n	n	NOUN
ejpam-7116	73	16	converges	converge	VERB
ejpam-7116	73	17	to	to	ADP
ejpam-7116	73	18	both	both	DET
ejpam-7116	73	19	2	2	NUM
ejpam-7116	73	20	and	and	CCONJ
ejpam-7116	73	21	3	3	NUM
ejpam-7116	73	22	;	;	PUNCT
ejpam-7116	73	23	the	the	DET
ejpam-7116	73	24	sequence	sequence	NOUN
ejpam-7116	73	25	an	an	PRON
ejpam-7116	73	26	=	=	NOUN
ejpam-7116	73	27	n	n	NOUN
ejpam-7116	73	28	is	be	AUX
ejpam-7116	73	29	not	not	PART
ejpam-7116	73	30	cauchy	cauchy	ADJ
ejpam-7116	73	31	,	,	PUNCT
ejpam-7116	73	32	as	as	SCONJ
ejpam-7116	73	33	limn→+∞	limn→+∞	ADP
ejpam-7116	73	34	d(n	d(n	PROPN
ejpam-7116	73	35	,	,	PUNCT
ejpam-7116	73	36	n+	n+	X
ejpam-7116	73	37	p	p	X
ejpam-7116	73	38	)	)	PUNCT
ejpam-7116	73	39	=	=	SYM
ejpam-7116	73	40	2	2	NUM
ejpam-7116	73	41	for	for	ADP
ejpam-7116	73	42	all	all	DET
ejpam-7116	73	43	p	p	NOUN
ejpam-7116	73	44	∈	∈	PROPN
ejpam-7116	73	45	n	n	CCONJ
ejpam-7116	73	46	;	;	PUNCT
ejpam-7116	73	47	the	the	DET
ejpam-7116	73	48	function	function	NOUN
ejpam-7116	73	49	d	d	NOUN
ejpam-7116	73	50	is	be	AUX
ejpam-7116	73	51	not	not	PART
ejpam-7116	73	52	continuous	continuous	ADJ
ejpam-7116	73	53	,	,	PUNCT
ejpam-7116	73	54	since	since	SCONJ
ejpam-7116	73	55	limn→+∞	limn→+∞	ADP
ejpam-7116	73	56	d(1	d(1	PROPN
ejpam-7116	73	57	,	,	PUNCT
ejpam-7116	73	58	n	n	CCONJ
ejpam-7116	73	59	)	)	PUNCT
ejpam-7116	73	60	=	=	SYM
ejpam-7116	73	61	2	2	NUM
ejpam-7116	73	62	̸=	̸=	PROPN
ejpam-7116	73	63	5	5	NUM
ejpam-7116	73	64	=	=	SYM
ejpam-7116	73	65	d(1	d(1	PROPN
ejpam-7116	73	66	,	,	PUNCT
ejpam-7116	73	67	2	2	NUM
ejpam-7116	73	68	)	)	PUNCT
ejpam-7116	73	69	.	.	PUNCT
ejpam-7116	74	1	the	the	DET
ejpam-7116	74	2	limit	limit	NOUN
ejpam-7116	74	3	of	of	ADP
ejpam-7116	74	4	a	a	DET
ejpam-7116	74	5	convergent	convergent	NOUN
ejpam-7116	74	6	sequence	sequence	NOUN
ejpam-7116	74	7	in	in	ADP
ejpam-7116	74	8	r.m.s	r.m.s	NOUN
ejpam-7116	74	9	.	.	PUNCT
ejpam-7116	75	1	is	be	AUX
ejpam-7116	75	2	unique	unique	ADJ
ejpam-7116	75	3	if	if	SCONJ
ejpam-7116	75	4	the	the	DET
ejpam-7116	75	5	sequence	sequence	NOUN
ejpam-7116	75	6	is	be	AUX
ejpam-7116	75	7	cauchy	cauchy	ADJ
ejpam-7116	75	8	and	and	CCONJ
ejpam-7116	75	9	all	all	DET
ejpam-7116	75	10	its	its	PRON
ejpam-7116	75	11	members	member	NOUN
ejpam-7116	75	12	are	be	AUX
ejpam-7116	75	13	pairwise	pairwise	NOUN
ejpam-7116	75	14	distinct	distinct	ADJ
ejpam-7116	75	15	(	(	PUNCT
ejpam-7116	75	16	see	see	VERB
ejpam-7116	76	1	e.g.	e.g.	ADV
ejpam-7116	76	2	[	[	X
ejpam-7116	76	3	5	5	NUM
ejpam-7116	76	4	,	,	PUNCT
ejpam-7116	76	5	lemma	lemma	PROPN
ejpam-7116	76	6	3.1	3.1	NUM
ejpam-7116	76	7	]	]	PUNCT
ejpam-7116	76	8	)	)	PUNCT
ejpam-7116	76	9	,	,	PUNCT
ejpam-7116	76	10	a	a	DET
ejpam-7116	76	11	property	property	NOUN
ejpam-7116	76	12	which	which	PRON
ejpam-7116	76	13	is	be	AUX
ejpam-7116	76	14	very	very	ADV
ejpam-7116	76	15	useful	useful	ADJ
ejpam-7116	76	16	in	in	ADP
ejpam-7116	76	17	proving	prove	VERB
ejpam-7116	76	18	fixed	fix	VERB
ejpam-7116	76	19	point	point	NOUN
ejpam-7116	76	20	results	result	NOUN
ejpam-7116	76	21	.	.	PUNCT
ejpam-7116	77	1	the	the	DET
ejpam-7116	77	2	next	next	ADJ
ejpam-7116	77	3	lemma	lemma	PROPN
ejpam-7116	77	4	states	state	VERB
ejpam-7116	77	5	that	that	SCONJ
ejpam-7116	77	6	the	the	DET
ejpam-7116	77	7	same	same	ADJ
ejpam-7116	77	8	is	be	AUX
ejpam-7116	77	9	true	true	ADJ
ejpam-7116	77	10	in	in	ADP
ejpam-7116	77	11	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	77	12	.	.	PUNCT
ejpam-7116	77	13	as	as	ADV
ejpam-7116	77	14	well	well	ADV
ejpam-7116	77	15	.	.	PUNCT
ejpam-7116	78	1	lemma	lemma	PROPN
ejpam-7116	78	2	2.1	2.1	NUM
ejpam-7116	78	3	.	.	PUNCT
ejpam-7116	79	1	let	let	VERB
ejpam-7116	79	2	(	(	PUNCT
ejpam-7116	79	3	x	x	NOUN
ejpam-7116	79	4	,	,	PUNCT
ejpam-7116	79	5	d	d	NOUN
ejpam-7116	79	6	)	)	PUNCT
ejpam-7116	79	7	be	be	AUX
ejpam-7116	79	8	a	a	DET
ejpam-7116	79	9	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	79	10	.	.	PUNCT
ejpam-7116	79	11	and	and	CCONJ
ejpam-7116	79	12	let	let	VERB
ejpam-7116	79	13	{	{	PUNCT
ejpam-7116	79	14	xn	xn	VERB
ejpam-7116	79	15	}	}	PUNCT
ejpam-7116	79	16	be	be	AUX
ejpam-7116	79	17	a	a	DET
ejpam-7116	79	18	convergent	convergent	NOUN
ejpam-7116	79	19	sequence	sequence	NOUN
ejpam-7116	79	20	in	in	ADP
ejpam-7116	79	21	x.	x.	NOUN
ejpam-7116	79	22	if	if	SCONJ
ejpam-7116	79	23	the	the	DET
ejpam-7116	79	24	sequence	sequence	NOUN
ejpam-7116	79	25	{	{	PUNCT
ejpam-7116	79	26	xn	xn	NOUN
ejpam-7116	79	27	}	}	PUNCT
ejpam-7116	79	28	is	be	AUX
ejpam-7116	79	29	cauchy	cauchy	NOUN
ejpam-7116	79	30	,	,	PUNCT
ejpam-7116	79	31	and	and	CCONJ
ejpam-7116	79	32	xn	xn	PROPN
ejpam-7116	79	33	̸=	̸=	PROPN
ejpam-7116	79	34	xm	xm	PROPN
ejpam-7116	79	35	for	for	ADP
ejpam-7116	79	36	all	all	DET
ejpam-7116	79	37	n	n	NOUN
ejpam-7116	79	38	,	,	PUNCT
ejpam-7116	79	39	m	m	VERB
ejpam-7116	79	40	∈	∈	PROPN
ejpam-7116	79	41	n	n	NOUN
ejpam-7116	79	42	with	with	ADP
ejpam-7116	79	43	m	m	PROPN
ejpam-7116	79	44	̸=	̸=	PROPN
ejpam-7116	79	45	n	n	CCONJ
ejpam-7116	79	46	,	,	PUNCT
ejpam-7116	79	47	then	then	ADV
ejpam-7116	79	48	the	the	DET
ejpam-7116	79	49	limit	limit	NOUN
ejpam-7116	79	50	of	of	ADP
ejpam-7116	79	51	{	{	PUNCT
ejpam-7116	79	52	xn	xn	PROPN
ejpam-7116	79	53	}	}	PUNCT
ejpam-7116	79	54	is	be	AUX
ejpam-7116	79	55	unique	unique	ADJ
ejpam-7116	79	56	.	.	PUNCT
ejpam-7116	80	1	proof	proof	NOUN
ejpam-7116	80	2	.	.	PUNCT
ejpam-7116	81	1	suppose	suppose	VERB
ejpam-7116	81	2	that	that	SCONJ
ejpam-7116	81	3	{	{	PUNCT
ejpam-7116	81	4	xn	xn	X
ejpam-7116	81	5	}	}	PUNCT
ejpam-7116	81	6	⊆	⊆	NUM
ejpam-7116	81	7	x	x	X
ejpam-7116	81	8	is	be	AUX
ejpam-7116	81	9	a	a	DET
ejpam-7116	81	10	sequence	sequence	NOUN
ejpam-7116	81	11	satisfying	satisfy	VERB
ejpam-7116	81	12	the	the	DET
ejpam-7116	81	13	conditions	condition	NOUN
ejpam-7116	81	14	of	of	ADP
ejpam-7116	81	15	the	the	DET
ejpam-7116	81	16	lemma	lemma	PROPN
ejpam-7116	81	17	,	,	PUNCT
ejpam-7116	81	18	and	and	CCONJ
ejpam-7116	81	19	suppose	suppose	VERB
ejpam-7116	81	20	that	that	PRON
ejpam-7116	81	21	limn→+∞	limn→+∞	VERB
ejpam-7116	81	22	d(xn	d(xn	PROPN
ejpam-7116	81	23	,	,	PUNCT
ejpam-7116	81	24	x	x	X
ejpam-7116	81	25	)	)	PUNCT
ejpam-7116	81	26	=	=	PUNCT
ejpam-7116	81	27	limn→+∞	limn→+∞	VERB
ejpam-7116	81	28	d(xn	d(xn	PROPN
ejpam-7116	81	29	,	,	PUNCT
ejpam-7116	81	30	y	y	NOUN
ejpam-7116	81	31	)	)	PUNCT
ejpam-7116	81	32	=	=	SYM
ejpam-7116	81	33	0	0	NUM
ejpam-7116	81	34	for	for	ADP
ejpam-7116	81	35	some	some	DET
ejpam-7116	81	36	x	x	NOUN
ejpam-7116	81	37	,	,	PUNCT
ejpam-7116	81	38	y	y	PROPN
ejpam-7116	81	39	∈	∈	PROPN
ejpam-7116	81	40	x.	x.	NOUN
ejpam-7116	82	1	because	because	SCONJ
ejpam-7116	82	2	xn	xn	PROPN
ejpam-7116	82	3	̸=	̸=	PROPN
ejpam-7116	82	4	xm	xm	PROPN
ejpam-7116	82	5	for	for	ADP
ejpam-7116	82	6	all	all	DET
ejpam-7116	82	7	n	n	NOUN
ejpam-7116	82	8	,	,	PUNCT
ejpam-7116	82	9	m	m	VERB
ejpam-7116	82	10	∈	∈	PROPN
ejpam-7116	82	11	n	n	NOUN
ejpam-7116	82	12	with	with	ADP
ejpam-7116	82	13	m	m	PROPN
ejpam-7116	82	14	̸=	̸=	PROPN
ejpam-7116	82	15	n	n	CCONJ
ejpam-7116	82	16	,	,	PUNCT
ejpam-7116	82	17	there	there	PRON
ejpam-7116	82	18	exists	exist	VERB
ejpam-7116	82	19	p	p	PROPN
ejpam-7116	82	20	∈	∈	PROPN
ejpam-7116	82	21	n	n	PRON
ejpam-7116	82	22	such	such	ADJ
ejpam-7116	82	23	that	that	SCONJ
ejpam-7116	82	24	xn	xn	PROPN
ejpam-7116	82	25	∈	∈	PROPN
ejpam-7116	82	26	x	x	X
ejpam-7116	82	27	\	\	X
ejpam-7116	82	28	{	{	PUNCT
ejpam-7116	82	29	x	x	NOUN
ejpam-7116	82	30	,	,	PUNCT
ejpam-7116	82	31	y	y	NOUN
ejpam-7116	82	32	}	}	PUNCT
ejpam-7116	82	33	for	for	ADP
ejpam-7116	82	34	all	all	DET
ejpam-7116	82	35	n	n	DET
ejpam-7116	82	36	≥	≥	NOUN
ejpam-7116	83	1	p.	p.	NOUN
ejpam-7116	83	2	then	then	ADV
ejpam-7116	83	3	for	for	ADP
ejpam-7116	83	4	m	m	PROPN
ejpam-7116	83	5	>	>	X
ejpam-7116	83	6	n	n	PRON
ejpam-7116	83	7	≥	≥	NOUN
ejpam-7116	83	8	p	p	NOUN
ejpam-7116	83	9	we	we	PRON
ejpam-7116	83	10	have	have	VERB
ejpam-7116	83	11	:	:	PUNCT
ejpam-7116	83	12	d(x	d(x	PROPN
ejpam-7116	83	13	,	,	PUNCT
ejpam-7116	83	14	y	y	NOUN
ejpam-7116	83	15	)	)	PUNCT
ejpam-7116	83	16	≤	≤	NOUN
ejpam-7116	83	17	d(x	d(x	NOUN
ejpam-7116	83	18	,	,	PUNCT
ejpam-7116	83	19	xn	xn	PUNCT
ejpam-7116	83	20	)	)	PUNCT
ejpam-7116	84	1	+	+	CCONJ
ejpam-7116	84	2	d(xn	d(xn	PROPN
ejpam-7116	84	3	,	,	PUNCT
ejpam-7116	84	4	xm	xm	PROPN
ejpam-7116	84	5	)	)	PUNCT
ejpam-7116	85	1	+	+	CCONJ
ejpam-7116	85	2	d(xm	d(xm	PROPN
ejpam-7116	85	3	,	,	PUNCT
ejpam-7116	85	4	y	y	NOUN
ejpam-7116	85	5	)	)	PUNCT
ejpam-7116	86	1	+	+	CCONJ
ejpam-7116	86	2	d(x	d(x	PROPN
ejpam-7116	86	3	,	,	PUNCT
ejpam-7116	86	4	xm	xm	PROPN
ejpam-7116	86	5	)	)	PUNCT
ejpam-7116	87	1	+	+	CCONJ
ejpam-7116	87	2	d(xn	d(xn	PROPN
ejpam-7116	87	3	,	,	PUNCT
ejpam-7116	87	4	y	y	NOUN
ejpam-7116	87	5	)	)	PUNCT
ejpam-7116	87	6	→	→	SYM
ejpam-7116	87	7	0	0	NUM
ejpam-7116	87	8	as	as	ADP
ejpam-7116	87	9	n	n	CCONJ
ejpam-7116	87	10	,	,	PUNCT
ejpam-7116	87	11	m	m	PROPN
ejpam-7116	87	12	→	→	SYM
ejpam-7116	87	13	+	+	NOUN
ejpam-7116	87	14	∞.	∞.	PROPN
ejpam-7116	87	15	but	but	CCONJ
ejpam-7116	87	16	this	this	PRON
ejpam-7116	87	17	implies	imply	VERB
ejpam-7116	87	18	d(x	d(x	PROPN
ejpam-7116	87	19	,	,	PUNCT
ejpam-7116	87	20	y	y	NOUN
ejpam-7116	87	21	)	)	PUNCT
ejpam-7116	87	22	=	=	SYM
ejpam-7116	87	23	0	0	NUM
ejpam-7116	87	24	,	,	PUNCT
ejpam-7116	87	25	and	and	CCONJ
ejpam-7116	87	26	hence	hence	ADV
ejpam-7116	87	27	x	x	PUNCT
ejpam-7116	88	1	=	=	PUNCT
ejpam-7116	88	2	y.	y.	NOUN
ejpam-7116	88	3	3	3	NUM
ejpam-7116	88	4	.	.	PUNCT
ejpam-7116	88	5	main	main	ADJ
ejpam-7116	88	6	results	result	NOUN
ejpam-7116	88	7	we	we	PRON
ejpam-7116	88	8	are	be	AUX
ejpam-7116	88	9	now	now	ADV
ejpam-7116	88	10	ready	ready	ADJ
ejpam-7116	88	11	to	to	PART
ejpam-7116	88	12	state	state	VERB
ejpam-7116	88	13	and	and	CCONJ
ejpam-7116	88	14	prove	prove	VERB
ejpam-7116	88	15	our	our	PRON
ejpam-7116	88	16	main	main	ADJ
ejpam-7116	88	17	results	result	NOUN
ejpam-7116	88	18	in	in	ADP
ejpam-7116	88	19	this	this	DET
ejpam-7116	88	20	section	section	NOUN
ejpam-7116	88	21	.	.	PUNCT
ejpam-7116	89	1	we	we	PRON
ejpam-7116	89	2	begin	begin	VERB
ejpam-7116	89	3	with	with	ADP
ejpam-7116	89	4	banach	banach	NOUN
ejpam-7116	89	5	’s	’s	PART
ejpam-7116	89	6	fixed	fix	VERB
ejpam-7116	89	7	point	point	NOUN
ejpam-7116	89	8	theorem	theorem	VERB
ejpam-7116	89	9	on	on	ADP
ejpam-7116	89	10	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	89	11	.	.	PUNCT
ejpam-7116	89	12	a.	a.	PROPN
ejpam-7116	89	13	kostić	kostić	VERB
ejpam-7116	89	14	/	/	SYM
ejpam-7116	89	15	eur	eur	PROPN
ejpam-7116	89	16	.	.	PUNCT
ejpam-7116	90	1	j.	j.	PROPN
ejpam-7116	90	2	pure	pure	PROPN
ejpam-7116	90	3	appl	appl	PROPN
ejpam-7116	90	4	.	.	PROPN
ejpam-7116	90	5	math	math	PROPN
ejpam-7116	90	6	,	,	PUNCT
ejpam-7116	90	7	18	18	NUM
ejpam-7116	90	8	(	(	PUNCT
ejpam-7116	90	9	4	4	NUM
ejpam-7116	90	10	)	)	PUNCT
ejpam-7116	90	11	(	(	PUNCT
ejpam-7116	90	12	2025	2025	NUM
ejpam-7116	90	13	)	)	PUNCT
ejpam-7116	90	14	,	,	PUNCT
ejpam-7116	90	15	7116	7116	NUM
ejpam-7116	90	16	5	5	NUM
ejpam-7116	90	17	of	of	ADP
ejpam-7116	90	18	10	10	NUM
ejpam-7116	90	19	theorem	theorem	VERB
ejpam-7116	90	20	3.1	3.1	NUM
ejpam-7116	90	21	.	.	PUNCT
ejpam-7116	91	1	let	let	AUX
ejpam-7116	91	2	(	(	PUNCT
ejpam-7116	91	3	x	x	NOUN
ejpam-7116	91	4	,	,	PUNCT
ejpam-7116	91	5	d	d	NOUN
ejpam-7116	91	6	)	)	PUNCT
ejpam-7116	91	7	be	be	AUX
ejpam-7116	91	8	a	a	DET
ejpam-7116	91	9	complete	complete	ADJ
ejpam-7116	91	10	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	91	11	.	.	PUNCT
ejpam-7116	92	1	and	and	CCONJ
ejpam-7116	92	2	let	let	VERB
ejpam-7116	92	3	the	the	DET
ejpam-7116	92	4	mapping	mapping	NOUN
ejpam-7116	92	5	t	t	NOUN
ejpam-7116	92	6	:	:	PUNCT
ejpam-7116	92	7	x	x	X
ejpam-7116	92	8	→	→	PUNCT
ejpam-7116	92	9	x	x	PUNCT
ejpam-7116	92	10	satisfy	satisfy	VERB
ejpam-7116	92	11	the	the	DET
ejpam-7116	92	12	following	follow	VERB
ejpam-7116	92	13	condition	condition	NOUN
ejpam-7116	92	14	:	:	PUNCT
ejpam-7116	92	15	d(tx	d(tx	PROPN
ejpam-7116	92	16	,	,	PUNCT
ejpam-7116	92	17	ty	ty	NOUN
ejpam-7116	92	18	)	)	PUNCT
ejpam-7116	92	19	≤	≤	NOUN
ejpam-7116	92	20	qd(x	qd(x	X
ejpam-7116	92	21	,	,	PUNCT
ejpam-7116	92	22	y	y	NOUN
ejpam-7116	92	23	)	)	PUNCT
ejpam-7116	92	24	,	,	PUNCT
ejpam-7116	92	25	for	for	ADP
ejpam-7116	92	26	all	all	DET
ejpam-7116	92	27	x	x	NOUN
ejpam-7116	92	28	,	,	PUNCT
ejpam-7116	92	29	y	y	PROPN
ejpam-7116	92	30	∈	∈	PROPN
ejpam-7116	92	31	x	x	X
ejpam-7116	92	32	and	and	CCONJ
ejpam-7116	92	33	some	some	DET
ejpam-7116	92	34	q	q	NOUN
ejpam-7116	92	35	∈	∈	PROPN
ejpam-7116	93	1	[	[	X
ejpam-7116	93	2	0	0	NUM
ejpam-7116	93	3	,	,	PUNCT
ejpam-7116	93	4	1	1	NUM
ejpam-7116	93	5	)	)	PUNCT
ejpam-7116	93	6	.	.	PUNCT
ejpam-7116	94	1	(	(	PUNCT
ejpam-7116	94	2	3.1	3.1	NUM
ejpam-7116	94	3	)	)	PUNCT
ejpam-7116	94	4	then	then	ADV
ejpam-7116	94	5	the	the	DET
ejpam-7116	94	6	mapping	mapping	NOUN
ejpam-7116	94	7	t	t	PROPN
ejpam-7116	94	8	has	have	VERB
ejpam-7116	94	9	a	a	DET
ejpam-7116	94	10	unique	unique	ADJ
ejpam-7116	94	11	fixed	fix	VERB
ejpam-7116	94	12	point	point	NOUN
ejpam-7116	94	13	a	a	DET
ejpam-7116	94	14	∈	∈	PROPN
ejpam-7116	94	15	x	x	NOUN
ejpam-7116	94	16	,	,	PUNCT
ejpam-7116	94	17	such	such	ADJ
ejpam-7116	94	18	that	that	SCONJ
ejpam-7116	94	19	limn→∞	limn→∞	PROPN
ejpam-7116	94	20	tnx	tnx	NOUN
ejpam-7116	94	21	=	=	PUNCT
ejpam-7116	94	22	a	a	PRON
ejpam-7116	94	23	for	for	ADP
ejpam-7116	94	24	all	all	DET
ejpam-7116	94	25	x	x	SYM
ejpam-7116	94	26	∈	∈	ADJ
ejpam-7116	94	27	x.	x.	NOUN
ejpam-7116	94	28	proof	proof	NOUN
ejpam-7116	94	29	.	.	PUNCT
ejpam-7116	95	1	let	let	VERB
ejpam-7116	95	2	x	x	SYM
ejpam-7116	95	3	∈	∈	PROPN
ejpam-7116	95	4	x	x	PUNCT
ejpam-7116	95	5	be	be	AUX
ejpam-7116	95	6	an	an	DET
ejpam-7116	95	7	arbitrary	arbitrary	ADJ
ejpam-7116	95	8	point	point	NOUN
ejpam-7116	95	9	,	,	PUNCT
ejpam-7116	95	10	and	and	CCONJ
ejpam-7116	95	11	let	let	VERB
ejpam-7116	95	12	xn	xn	PUNCT
ejpam-7116	95	13	=	=	PUNCT
ejpam-7116	96	1	tnx	tnx	NOUN
ejpam-7116	96	2	for	for	ADP
ejpam-7116	96	3	all	all	PRON
ejpam-7116	96	4	n	n	PRON
ejpam-7116	96	5	∈	∈	PROPN
ejpam-7116	96	6	n0	n0	PROPN
ejpam-7116	96	7	.	.	PUNCT
ejpam-7116	97	1	then	then	ADV
ejpam-7116	97	2	by	by	ADP
ejpam-7116	97	3	the	the	DET
ejpam-7116	97	4	repeated	repeat	VERB
ejpam-7116	97	5	use	use	NOUN
ejpam-7116	97	6	of	of	ADP
ejpam-7116	97	7	the	the	DET
ejpam-7116	97	8	contractive	contractive	ADJ
ejpam-7116	97	9	condition	condition	NOUN
ejpam-7116	97	10	(	(	PUNCT
ejpam-7116	97	11	3.1	3.1	NUM
ejpam-7116	97	12	)	)	PUNCT
ejpam-7116	97	13	we	we	PRON
ejpam-7116	97	14	get	get	VERB
ejpam-7116	97	15	:	:	PUNCT
ejpam-7116	97	16	d(xn	d(xn	PROPN
ejpam-7116	97	17	,	,	PUNCT
ejpam-7116	97	18	xn+1	xn+1	NUM
ejpam-7116	97	19	)	)	PUNCT
ejpam-7116	97	20	≤	≤	NUM
ejpam-7116	98	1	qd(xn−1	qd(xn−1	PROPN
ejpam-7116	98	2	,	,	PUNCT
ejpam-7116	98	3	xn	xn	PROPN
ejpam-7116	98	4	)	)	PUNCT
ejpam-7116	98	5	≤	≤	NOUN
ejpam-7116	98	6	·	·	PUNCT
ejpam-7116	98	7	·	·	PUNCT
ejpam-7116	98	8	·	·	PUNCT
ejpam-7116	99	1	≤	≤	NUM
ejpam-7116	99	2	qnd(x0	qnd(x0	NOUN
ejpam-7116	99	3	,	,	PUNCT
ejpam-7116	99	4	x1	x1	PROPN
ejpam-7116	99	5	)	)	PUNCT
ejpam-7116	99	6	for	for	ADP
ejpam-7116	99	7	all	all	PRON
ejpam-7116	99	8	n	n	PRON
ejpam-7116	99	9	∈	∈	PROPN
ejpam-7116	99	10	n0	n0	PROPN
ejpam-7116	99	11	.	.	PUNCT
ejpam-7116	100	1	hence	hence	ADV
ejpam-7116	100	2	,	,	PUNCT
ejpam-7116	100	3	lim	lim	PROPN
ejpam-7116	100	4	n→+∞	n→+∞	VERB
ejpam-7116	100	5	d(xn	d(xn	PROPN
ejpam-7116	100	6	,	,	PUNCT
ejpam-7116	100	7	xn+1	xn+1	NUM
ejpam-7116	100	8	)	)	PUNCT
ejpam-7116	100	9	=	=	SYM
ejpam-7116	101	1	0	0	X
ejpam-7116	101	2	.	.	PUNCT
ejpam-7116	102	1	if	if	SCONJ
ejpam-7116	102	2	xn	xn	PROPN
ejpam-7116	102	3	=	=	SYM
ejpam-7116	102	4	xn+1	xn+1	PROPN
ejpam-7116	102	5	for	for	ADP
ejpam-7116	102	6	some	some	DET
ejpam-7116	102	7	n	n	PRON
ejpam-7116	102	8	∈	∈	PROPN
ejpam-7116	102	9	n0	n0	NOUN
ejpam-7116	102	10	then	then	ADV
ejpam-7116	102	11	xn	xn	PUNCT
ejpam-7116	103	1	=	=	SYM
ejpam-7116	103	2	txn	txn	NOUN
ejpam-7116	103	3	,	,	PUNCT
ejpam-7116	103	4	i.e.	i.e.	X
ejpam-7116	103	5	xn	xn	PROPN
ejpam-7116	103	6	is	be	AUX
ejpam-7116	103	7	a	a	DET
ejpam-7116	103	8	fixed	fix	VERB
ejpam-7116	103	9	point	point	NOUN
ejpam-7116	103	10	of	of	ADP
ejpam-7116	103	11	mapping	mapping	NOUN
ejpam-7116	103	12	t	t	NOUN
ejpam-7116	103	13	.	.	PUNCT
ejpam-7116	104	1	therefore	therefore	ADV
ejpam-7116	104	2	we	we	PRON
ejpam-7116	104	3	can	can	AUX
ejpam-7116	104	4	assume	assume	VERB
ejpam-7116	104	5	that	that	SCONJ
ejpam-7116	104	6	xn	xn	PROPN
ejpam-7116	104	7	̸=	̸=	PROPN
ejpam-7116	104	8	xn+1	xn+1	PROPN
ejpam-7116	104	9	for	for	ADP
ejpam-7116	104	10	all	all	PRON
ejpam-7116	104	11	n	n	PRON
ejpam-7116	104	12	∈	∈	PROPN
ejpam-7116	104	13	n0	n0	PROPN
ejpam-7116	104	14	.	.	PUNCT
ejpam-7116	105	1	then	then	ADV
ejpam-7116	105	2	,	,	PUNCT
ejpam-7116	105	3	without	without	ADP
ejpam-7116	105	4	loss	loss	NOUN
ejpam-7116	105	5	of	of	ADP
ejpam-7116	105	6	generality	generality	NOUN
ejpam-7116	105	7	,	,	PUNCT
ejpam-7116	105	8	we	we	PRON
ejpam-7116	105	9	can	can	AUX
ejpam-7116	105	10	also	also	ADV
ejpam-7116	105	11	suppose	suppose	VERB
ejpam-7116	105	12	that	that	SCONJ
ejpam-7116	105	13	xn	xn	PROPN
ejpam-7116	105	14	̸=	̸=	PROPN
ejpam-7116	105	15	xm	xm	PROPN
ejpam-7116	105	16	for	for	ADP
ejpam-7116	105	17	all	all	DET
ejpam-7116	105	18	n	n	CCONJ
ejpam-7116	105	19	,	,	PUNCT
ejpam-7116	105	20	m	m	PROPN
ejpam-7116	105	21	∈	∈	PROPN
ejpam-7116	105	22	n0	n0	NOUN
ejpam-7116	105	23	with	with	ADP
ejpam-7116	105	24	m	m	PROPN
ejpam-7116	105	25	̸=	̸=	PROPN
ejpam-7116	105	26	n.	n.	NOUN
ejpam-7116	105	27	indeed	indeed	ADV
ejpam-7116	105	28	,	,	PUNCT
ejpam-7116	105	29	let	let	VERB
ejpam-7116	105	30	xn	xn	PROPN
ejpam-7116	105	31	=	=	PUNCT
ejpam-7116	105	32	xm	xm	PROPN
ejpam-7116	105	33	for	for	ADP
ejpam-7116	105	34	some	some	DET
ejpam-7116	105	35	n	n	CCONJ
ejpam-7116	105	36	,	,	PUNCT
ejpam-7116	105	37	m	m	PROPN
ejpam-7116	105	38	∈	∈	NOUN
ejpam-7116	105	39	n0	n0	NOUN
ejpam-7116	105	40	and	and	CCONJ
ejpam-7116	105	41	let	let	VERB
ejpam-7116	105	42	m	m	PRON
ejpam-7116	105	43	>	>	X
ejpam-7116	105	44	n.	n.	NOUN
ejpam-7116	105	45	then	then	ADV
ejpam-7116	105	46	0	0	PUNCT
ejpam-7116	105	47	<	<	X
ejpam-7116	105	48	d(xn	d(xn	PROPN
ejpam-7116	105	49	,	,	PUNCT
ejpam-7116	105	50	xn+1	xn+1	NUM
ejpam-7116	105	51	)	)	PUNCT
ejpam-7116	106	1	=	=	SYM
ejpam-7116	106	2	d(xm	d(xm	PROPN
ejpam-7116	106	3	,	,	PUNCT
ejpam-7116	106	4	xm+1	xm+1	NUM
ejpam-7116	106	5	)	)	PUNCT
ejpam-7116	106	6	.	.	PUNCT
ejpam-7116	107	1	but	but	CCONJ
ejpam-7116	107	2	on	on	ADP
ejpam-7116	107	3	the	the	DET
ejpam-7116	107	4	other	other	ADJ
ejpam-7116	107	5	hand	hand	NOUN
ejpam-7116	107	6	,	,	PUNCT
ejpam-7116	107	7	by	by	ADP
ejpam-7116	107	8	(	(	PUNCT
ejpam-7116	107	9	3.1	3.1	NUM
ejpam-7116	107	10	)	)	PUNCT
ejpam-7116	107	11	we	we	PRON
ejpam-7116	107	12	have	have	VERB
ejpam-7116	107	13	0	0	NUM
ejpam-7116	107	14	<	<	X
ejpam-7116	107	15	d(xm	d(xm	PROPN
ejpam-7116	107	16	,	,	PUNCT
ejpam-7116	107	17	xm+1	xm+1	NUM
ejpam-7116	107	18	)	)	PUNCT
ejpam-7116	107	19	≤	≤	NOUN
ejpam-7116	107	20	qd(xm−1	qd(xm−1	PROPN
ejpam-7116	107	21	,	,	PUNCT
ejpam-7116	107	22	xm	xm	NOUN
ejpam-7116	107	23	)	)	PUNCT
ejpam-7116	107	24	≤	≤	NOUN
ejpam-7116	107	25	·	·	PUNCT
ejpam-7116	107	26	·	·	PUNCT
ejpam-7116	107	27	·	·	PUNCT
ejpam-7116	107	28	≤	≤	NUM
ejpam-7116	108	1	qm−nd(xn	qm−nd(xn	PUNCT
ejpam-7116	108	2	,	,	PUNCT
ejpam-7116	108	3	xn+1	xn+1	NUM
ejpam-7116	108	4	)	)	PUNCT
ejpam-7116	108	5	<	<	X
ejpam-7116	108	6	d(xn	d(xn	PROPN
ejpam-7116	108	7	,	,	PUNCT
ejpam-7116	108	8	xn+1	xn+1	NUM
ejpam-7116	108	9	)	)	PUNCT
ejpam-7116	108	10	,	,	PUNCT
ejpam-7116	108	11	which	which	PRON
ejpam-7116	108	12	is	be	AUX
ejpam-7116	108	13	a	a	DET
ejpam-7116	108	14	contradiction	contradiction	NOUN
ejpam-7116	108	15	.	.	PUNCT
ejpam-7116	109	1	next	next	ADV
ejpam-7116	109	2	,	,	PUNCT
ejpam-7116	109	3	by	by	ADP
ejpam-7116	109	4	two	two	NUM
ejpam-7116	109	5	-	-	PUNCT
ejpam-7116	109	6	step	step	NOUN
ejpam-7116	109	7	induction	induction	NOUN
ejpam-7116	109	8	we	we	PRON
ejpam-7116	109	9	will	will	AUX
ejpam-7116	109	10	prove	prove	VERB
ejpam-7116	109	11	that	that	DET
ejpam-7116	109	12	d(x0	d(x0	NOUN
ejpam-7116	109	13	,	,	PUNCT
ejpam-7116	109	14	xn	xn	NUM
ejpam-7116	109	15	)	)	PUNCT
ejpam-7116	109	16	≤	≤	NUM
ejpam-7116	109	17	c	c	ADP
ejpam-7116	109	18	n−1∑	n−1∑	NUM
ejpam-7116	109	19	k=0	k=0	PROPN
ejpam-7116	109	20	fk+1q	fk+1q	NOUN
ejpam-7116	109	21	k	k	PROPN
ejpam-7116	109	22	for	for	ADP
ejpam-7116	109	23	all	all	PRON
ejpam-7116	109	24	n	n	PRON
ejpam-7116	109	25	∈	∈	PROPN
ejpam-7116	109	26	n	n	CCONJ
ejpam-7116	109	27	,	,	PUNCT
ejpam-7116	109	28	(	(	PUNCT
ejpam-7116	109	29	3.2	3.2	NUM
ejpam-7116	109	30	)	)	PUNCT
ejpam-7116	109	31	where	where	SCONJ
ejpam-7116	109	32	c	c	NOUN
ejpam-7116	109	33	=	=	SYM
ejpam-7116	109	34	d(x0	d(x0	NOUN
ejpam-7116	109	35	,	,	PUNCT
ejpam-7116	109	36	x1)+d(x1	x1)+d(x1	PROPN
ejpam-7116	109	37	,	,	PUNCT
ejpam-7116	109	38	x2)+d(x0	x2)+d(x0	PROPN
ejpam-7116	109	39	,	,	PUNCT
ejpam-7116	109	40	x2	x2	PROPN
ejpam-7116	109	41	)	)	PUNCT
ejpam-7116	109	42	,	,	PUNCT
ejpam-7116	109	43	and	and	CCONJ
ejpam-7116	109	44	{	{	PUNCT
ejpam-7116	109	45	fk}k∈n	fk}k∈n	NOUN
ejpam-7116	109	46	is	be	AUX
ejpam-7116	109	47	the	the	DET
ejpam-7116	109	48	fibonacci	fibonacci	NOUN
ejpam-7116	109	49	sequence	sequence	NOUN
ejpam-7116	109	50	,	,	PUNCT
ejpam-7116	109	51	defined	define	VERB
ejpam-7116	109	52	recursively	recursively	ADV
ejpam-7116	109	53	by	by	ADP
ejpam-7116	109	54	f1	f1	NOUN
ejpam-7116	109	55	=	=	SYM
ejpam-7116	109	56	f2	f2	PROPN
ejpam-7116	109	57	=	=	SYM
ejpam-7116	109	58	1	1	NUM
ejpam-7116	109	59	and	and	CCONJ
ejpam-7116	109	60	fn	fn	NOUN
ejpam-7116	109	61	=	=	PUNCT
ejpam-7116	109	62	fn−1	fn−1	PROPN
ejpam-7116	109	63	+	+	CCONJ
ejpam-7116	109	64	fn−2	fn−2	ADJ
ejpam-7116	109	65	for	for	ADP
ejpam-7116	109	66	n	n	X
ejpam-7116	109	67	≥	≥	NOUN
ejpam-7116	109	68	3	3	NUM
ejpam-7116	109	69	.	.	PUNCT
ejpam-7116	109	70	for	for	ADP
ejpam-7116	109	71	n	n	NOUN
ejpam-7116	109	72	=	=	SYM
ejpam-7116	109	73	1	1	NUM
ejpam-7116	109	74	and	and	CCONJ
ejpam-7116	109	75	n	n	CCONJ
ejpam-7116	109	76	=	=	SYM
ejpam-7116	109	77	2	2	NUM
ejpam-7116	109	78	,	,	PUNCT
ejpam-7116	109	79	the	the	DET
ejpam-7116	109	80	statement	statement	NOUN
ejpam-7116	109	81	(	(	PUNCT
ejpam-7116	109	82	3.2	3.2	NUM
ejpam-7116	109	83	)	)	PUNCT
ejpam-7116	109	84	holds	hold	VERB
ejpam-7116	109	85	trivially	trivially	ADV
ejpam-7116	109	86	.	.	PUNCT
ejpam-7116	110	1	now	now	ADV
ejpam-7116	110	2	,	,	PUNCT
ejpam-7116	110	3	for	for	ADP
ejpam-7116	110	4	an	an	DET
ejpam-7116	110	5	arbitrary	arbitrary	ADJ
ejpam-7116	110	6	n	n	PRON
ejpam-7116	110	7	≥	≥	NOUN
ejpam-7116	110	8	3	3	NUM
ejpam-7116	110	9	suppose	suppose	VERB
ejpam-7116	110	10	that	that	SCONJ
ejpam-7116	110	11	(	(	PUNCT
ejpam-7116	110	12	3.2	3.2	NUM
ejpam-7116	110	13	)	)	PUNCT
ejpam-7116	110	14	is	be	AUX
ejpam-7116	110	15	true	true	ADJ
ejpam-7116	110	16	for	for	ADP
ejpam-7116	110	17	n−	n−	PROPN
ejpam-7116	110	18	1	1	NUM
ejpam-7116	110	19	and	and	CCONJ
ejpam-7116	110	20	n−	n−	NOUN
ejpam-7116	110	21	2	2	NUM
ejpam-7116	110	22	.	.	PUNCT
ejpam-7116	111	1	then	then	ADV
ejpam-7116	111	2	we	we	PRON
ejpam-7116	111	3	obtain	obtain	VERB
ejpam-7116	111	4	:	:	PUNCT
ejpam-7116	111	5	d(x0	d(x0	NOUN
ejpam-7116	111	6	,	,	PUNCT
ejpam-7116	111	7	xn	xn	NUM
ejpam-7116	111	8	)	)	PUNCT
ejpam-7116	111	9	≤	≤	NUM
ejpam-7116	111	10	d(x0	d(x0	NOUN
ejpam-7116	111	11	,	,	PUNCT
ejpam-7116	111	12	x1	x1	PROPN
ejpam-7116	111	13	)	)	PUNCT
ejpam-7116	111	14	+	+	CCONJ
ejpam-7116	111	15	d(x1	d(x1	NOUN
ejpam-7116	111	16	,	,	PUNCT
ejpam-7116	111	17	x2	x2	PROPN
ejpam-7116	111	18	)	)	PUNCT
ejpam-7116	111	19	+	+	NUM
ejpam-7116	112	1	d(x2	d(x2	NOUN
ejpam-7116	113	1	,	,	PUNCT
ejpam-7116	114	1	xn	xn	PROPN
ejpam-7116	114	2	)	)	PUNCT
ejpam-7116	115	1	+	+	NUM
ejpam-7116	115	2	d(x0	d(x0	NOUN
ejpam-7116	115	3	,	,	PUNCT
ejpam-7116	115	4	x2	x2	PROPN
ejpam-7116	115	5	)	)	PUNCT
ejpam-7116	116	1	+	+	CCONJ
ejpam-7116	116	2	d(x1	d(x1	NOUN
ejpam-7116	116	3	,	,	PUNCT
ejpam-7116	116	4	xn	xn	NUM
ejpam-7116	116	5	)	)	PUNCT
ejpam-7116	116	6	≤	≤	NUM
ejpam-7116	116	7	d(x0	d(x0	NOUN
ejpam-7116	116	8	,	,	PUNCT
ejpam-7116	116	9	x1	x1	PROPN
ejpam-7116	116	10	)	)	PUNCT
ejpam-7116	117	1	+	+	CCONJ
ejpam-7116	117	2	d(x1	d(x1	NOUN
ejpam-7116	117	3	,	,	PUNCT
ejpam-7116	117	4	x2	x2	PROPN
ejpam-7116	117	5	)	)	PUNCT
ejpam-7116	117	6	+	+	NUM
ejpam-7116	117	7	d(x0	d(x0	NOUN
ejpam-7116	117	8	,	,	PUNCT
ejpam-7116	117	9	x2	x2	PROPN
ejpam-7116	117	10	)	)	PUNCT
ejpam-7116	118	1	+	+	CCONJ
ejpam-7116	118	2	q2d(x0	q2d(x0	PROPN
ejpam-7116	118	3	,	,	PUNCT
ejpam-7116	118	4	xn−2	xn−2	PROPN
ejpam-7116	118	5	)	)	PUNCT
ejpam-7116	118	6	+	+	CCONJ
ejpam-7116	118	7	qd(x0	qd(x0	ADJ
ejpam-7116	118	8	,	,	PUNCT
ejpam-7116	118	9	xn−1	xn−1	PROPN
ejpam-7116	118	10	)	)	PUNCT
ejpam-7116	118	11	≤	≤	NUM
ejpam-7116	118	12	c+	c+	VERB
ejpam-7116	118	13	cq2	cq2	NOUN
ejpam-7116	118	14	n−3∑	n−3∑	NUM
ejpam-7116	118	15	k=0	k=0	PROPN
ejpam-7116	118	16	fk+1q	fk+1q	VERB
ejpam-7116	118	17	k	k	PROPN
ejpam-7116	118	18	+	+	CCONJ
ejpam-7116	118	19	cq	cq	PROPN
ejpam-7116	118	20	n−2∑	n−2∑	PUNCT
ejpam-7116	118	21	k=0	k=0	PROPN
ejpam-7116	118	22	fk+1q	fk+1q	NOUN
ejpam-7116	118	23	k	k	X
ejpam-7116	118	24	=	=	PUNCT
ejpam-7116	119	1	c+	c+	VERB
ejpam-7116	119	2	c	c	NOUN
ejpam-7116	119	3	n−3∑	n−3∑	NUM
ejpam-7116	119	4	k=0	k=0	PROPN
ejpam-7116	119	5	fk+1q	fk+1q	NOUN
ejpam-7116	119	6	k+2	k+2	PROPN
ejpam-7116	119	7	+	+	CCONJ
ejpam-7116	119	8	c	c	PROPN
ejpam-7116	119	9	n−2∑	n−2∑	PROPN
ejpam-7116	119	10	k=0	k=0	PROPN
ejpam-7116	119	11	fk+1q	fk+1q	VERB
ejpam-7116	119	12	k+1	k+1	PRON
ejpam-7116	119	13	a.	a.	NOUN
ejpam-7116	119	14	kostić	kostić	NOUN
ejpam-7116	119	15	/	/	SYM
ejpam-7116	119	16	eur	eur	PROPN
ejpam-7116	119	17	.	.	PUNCT
ejpam-7116	120	1	j.	j.	PROPN
ejpam-7116	120	2	pure	pure	PROPN
ejpam-7116	120	3	appl	appl	PROPN
ejpam-7116	120	4	.	.	PROPN
ejpam-7116	120	5	math	math	PROPN
ejpam-7116	120	6	,	,	PUNCT
ejpam-7116	120	7	18	18	NUM
ejpam-7116	120	8	(	(	PUNCT
ejpam-7116	120	9	4	4	NUM
ejpam-7116	120	10	)	)	PUNCT
ejpam-7116	120	11	(	(	PUNCT
ejpam-7116	120	12	2025	2025	NUM
ejpam-7116	120	13	)	)	PUNCT
ejpam-7116	120	14	,	,	PUNCT
ejpam-7116	120	15	7116	7116	NUM
ejpam-7116	120	16	6	6	NUM
ejpam-7116	120	17	of	of	ADP
ejpam-7116	120	18	10	10	NUM
ejpam-7116	120	19	=	=	SYM
ejpam-7116	120	20	c+	c+	X
ejpam-7116	121	1	cq	cq	NOUN
ejpam-7116	122	1	+	+	CCONJ
ejpam-7116	122	2	c	c	PROPN
ejpam-7116	122	3	n−1∑	n−1∑	NUM
ejpam-7116	122	4	k=2	k=2	PROPN
ejpam-7116	122	5	(	(	PUNCT
ejpam-7116	122	6	fk−1	fk−1	NOUN
ejpam-7116	122	7	+	+	NUM
ejpam-7116	122	8	fk)q	fk)q	NOUN
ejpam-7116	122	9	k	k	NOUN
ejpam-7116	123	1	=	=	PUNCT
ejpam-7116	123	2	c	c	PROPN
ejpam-7116	123	3	n−1∑	n−1∑	PROPN
ejpam-7116	123	4	k=0	k=0	PROPN
ejpam-7116	123	5	fk+1q	fk+1q	NOUN
ejpam-7116	124	1	k	k	ADP
ejpam-7116	125	1	it	it	PRON
ejpam-7116	125	2	is	be	AUX
ejpam-7116	125	3	known	know	VERB
ejpam-7116	125	4	that	that	SCONJ
ejpam-7116	125	5	+	+	ADP
ejpam-7116	125	6	∞∑	∞∑	ADJ
ejpam-7116	125	7	k=0	k=0	PROPN
ejpam-7116	125	8	fk+1q	fk+1q	NOUN
ejpam-7116	125	9	k	k	NOUN
ejpam-7116	126	1	=	=	SYM
ejpam-7116	126	2	1	1	NUM
ejpam-7116	126	3	1−	1−	NUM
ejpam-7116	126	4	q	q	NOUN
ejpam-7116	126	5	−	−	PROPN
ejpam-7116	126	6	q2	q2	NOUN
ejpam-7116	126	7	for	for	ADP
ejpam-7116	126	8	|q|	|q|	PRON
ejpam-7116	126	9	<	<	X
ejpam-7116	126	10	φ−1	φ−1	PROPN
ejpam-7116	126	11	,	,	PUNCT
ejpam-7116	126	12	(	(	PUNCT
ejpam-7116	126	13	3.3	3.3	NUM
ejpam-7116	126	14	)	)	PUNCT
ejpam-7116	126	15	where	where	SCONJ
ejpam-7116	126	16	φ	φ	PROPN
ejpam-7116	126	17	=	=	NOUN
ejpam-7116	126	18	√	√	ADP
ejpam-7116	126	19	5	5	NUM
ejpam-7116	126	20	+	+	NOUN
ejpam-7116	126	21	1	1	NUM
ejpam-7116	126	22	2	2	NUM
ejpam-7116	126	23	is	be	AUX
ejpam-7116	126	24	the	the	DET
ejpam-7116	126	25	“	"	PUNCT
ejpam-7116	126	26	golden	golden	ADJ
ejpam-7116	126	27	ratio	ratio	NOUN
ejpam-7116	126	28	”	"	PUNCT
ejpam-7116	126	29	constant	constant	ADJ
ejpam-7116	126	30	(	(	PUNCT
ejpam-7116	126	31	see	see	VERB
ejpam-7116	126	32	e.g.	e.g.	ADV
ejpam-7116	126	33	[	[	X
ejpam-7116	126	34	10	10	NUM
ejpam-7116	126	35	]	]	NUM
ejpam-7116	126	36	)	)	PUNCT
ejpam-7116	126	37	.	.	PUNCT
ejpam-7116	127	1	hence	hence	ADV
ejpam-7116	127	2	,	,	PUNCT
ejpam-7116	127	3	to	to	PART
ejpam-7116	127	4	finally	finally	ADV
ejpam-7116	127	5	prove	prove	VERB
ejpam-7116	127	6	that	that	SCONJ
ejpam-7116	127	7	the	the	DET
ejpam-7116	127	8	sequence	sequence	NOUN
ejpam-7116	127	9	{	{	PUNCT
ejpam-7116	127	10	xn	xn	NOUN
ejpam-7116	127	11	}	}	PUNCT
ejpam-7116	127	12	is	be	AUX
ejpam-7116	127	13	cauchy	cauchy	PROPN
ejpam-7116	127	14	,	,	PUNCT
ejpam-7116	127	15	we	we	PRON
ejpam-7116	127	16	distinguish	distinguish	VERB
ejpam-7116	127	17	two	two	NUM
ejpam-7116	127	18	cases	case	NOUN
ejpam-7116	127	19	.	.	PUNCT
ejpam-7116	128	1	1	1	X
ejpam-7116	128	2	.	.	PUNCT
ejpam-7116	128	3	q	q	PROPN
ejpam-7116	128	4	∈	∈	PROPN
ejpam-7116	129	1	[	[	X
ejpam-7116	129	2	0	0	NUM
ejpam-7116	129	3	,	,	PUNCT
ejpam-7116	129	4	φ−1	φ−1	PROPN
ejpam-7116	129	5	):	):	PUNCT
ejpam-7116	129	6	then	then	ADV
ejpam-7116	129	7	by	by	ADP
ejpam-7116	129	8	(	(	PUNCT
ejpam-7116	129	9	3.1	3.1	NUM
ejpam-7116	129	10	)	)	PUNCT
ejpam-7116	129	11	,	,	PUNCT
ejpam-7116	129	12	(	(	PUNCT
ejpam-7116	129	13	3.2	3.2	NUM
ejpam-7116	129	14	)	)	PUNCT
ejpam-7116	129	15	and	and	CCONJ
ejpam-7116	129	16	(	(	PUNCT
ejpam-7116	129	17	3.3	3.3	NUM
ejpam-7116	129	18	)	)	PUNCT
ejpam-7116	129	19	,	,	PUNCT
ejpam-7116	129	20	for	for	ADP
ejpam-7116	129	21	all	all	DET
ejpam-7116	129	22	m	m	PROPN
ejpam-7116	129	23	,	,	PUNCT
ejpam-7116	129	24	n	n	PRON
ejpam-7116	129	25	∈	∈	PROPN
ejpam-7116	129	26	n	n	PRON
ejpam-7116	129	27	such	such	ADJ
ejpam-7116	129	28	that	that	SCONJ
ejpam-7116	129	29	m	m	VERB
ejpam-7116	129	30	>	>	X
ejpam-7116	129	31	n	n	CCONJ
ejpam-7116	129	32	,	,	PUNCT
ejpam-7116	129	33	we	we	PRON
ejpam-7116	129	34	have	have	VERB
ejpam-7116	129	35	d(xn	d(xn	PROPN
ejpam-7116	129	36	,	,	PUNCT
ejpam-7116	129	37	xm	xm	PROPN
ejpam-7116	129	38	)	)	PUNCT
ejpam-7116	129	39	≤	≤	NUM
ejpam-7116	130	1	qnd(x0	qnd(x0	NOUN
ejpam-7116	130	2	,	,	PUNCT
ejpam-7116	130	3	xm−n	xm−n	PROPN
ejpam-7116	130	4	)	)	PUNCT
ejpam-7116	130	5	≤	≤	PUNCT
ejpam-7116	131	1	cqn	cqn	NOUN
ejpam-7116	131	2	m−n−1∑	m−n−1∑	PROPN
ejpam-7116	131	3	k=0	k=0	PROPN
ejpam-7116	131	4	fk+1q	fk+1q	NOUN
ejpam-7116	131	5	k	k	PROPN
ejpam-7116	131	6	≤	≤	PROPN
ejpam-7116	131	7	cqn	cqn	NOUN
ejpam-7116	132	1	+	+	NOUN
ejpam-7116	132	2	∞∑	∞∑	ADJ
ejpam-7116	132	3	k=0	k=0	PROPN
ejpam-7116	132	4	fk+1q	fk+1q	NOUN
ejpam-7116	132	5	k	k	NOUN
ejpam-7116	132	6	=	=	PUNCT
ejpam-7116	132	7	c	c	PROPN
ejpam-7116	132	8	qn	qn	NOUN
ejpam-7116	132	9	1−	1−	NUM
ejpam-7116	132	10	q	q	NOUN
ejpam-7116	132	11	−	−	PROPN
ejpam-7116	132	12	q2	q2	NOUN
ejpam-7116	132	13	→	→	SYM
ejpam-7116	132	14	0	0	PROPN
ejpam-7116	132	15	as	as	ADP
ejpam-7116	132	16	m	m	PROPN
ejpam-7116	132	17	,	,	PUNCT
ejpam-7116	132	18	n	n	PROPN
ejpam-7116	132	19	→	→	SYM
ejpam-7116	132	20	+	+	PROPN
ejpam-7116	132	21	∞	∞	PROPN
ejpam-7116	132	22	,	,	PUNCT
ejpam-7116	132	23	2	2	NUM
ejpam-7116	132	24	.	.	PUNCT
ejpam-7116	133	1	q	q	PROPN
ejpam-7116	133	2	∈	∈	PROPN
ejpam-7116	134	1	[	[	X
ejpam-7116	134	2	φ−1	φ−1	PROPN
ejpam-7116	134	3	,	,	PUNCT
ejpam-7116	134	4	1	1	NUM
ejpam-7116	134	5	):	):	PUNCT
ejpam-7116	134	6	there	there	PRON
ejpam-7116	134	7	exists	exist	VERB
ejpam-7116	134	8	a	a	DET
ejpam-7116	134	9	suitably	suitably	ADV
ejpam-7116	134	10	large	large	ADJ
ejpam-7116	134	11	n0	n0	X
ejpam-7116	134	12	∈	∈	PROPN
ejpam-7116	134	13	n	n	PRON
ejpam-7116	134	14	such	such	ADJ
ejpam-7116	134	15	that	that	SCONJ
ejpam-7116	134	16	qn0	qn0	PROPN
ejpam-7116	134	17	<	<	X
ejpam-7116	134	18	φ−1	φ−1	PROPN
ejpam-7116	134	19	.	.	PUNCT
ejpam-7116	135	1	then	then	ADV
ejpam-7116	135	2	by	by	ADP
ejpam-7116	135	3	(	(	PUNCT
ejpam-7116	135	4	3.1	3.1	NUM
ejpam-7116	135	5	)	)	PUNCT
ejpam-7116	135	6	we	we	PRON
ejpam-7116	135	7	have	have	VERB
ejpam-7116	135	8	that	that	PRON
ejpam-7116	135	9	d(tn0x	d(tn0x	PROPN
ejpam-7116	135	10	,	,	PUNCT
ejpam-7116	135	11	t	t	PROPN
ejpam-7116	135	12	n0y	n0y	AUX
ejpam-7116	135	13	)	)	PUNCT
ejpam-7116	135	14	≤	≤	NUM
ejpam-7116	135	15	qn0d(x	qn0d(x	PROPN
ejpam-7116	135	16	,	,	PUNCT
ejpam-7116	135	17	y	y	NOUN
ejpam-7116	135	18	)	)	PUNCT
ejpam-7116	135	19	for	for	ADP
ejpam-7116	135	20	all	all	DET
ejpam-7116	135	21	x	x	NOUN
ejpam-7116	135	22	,	,	PUNCT
ejpam-7116	135	23	y	y	PROPN
ejpam-7116	135	24	∈	∈	PROPN
ejpam-7116	135	25	x.	x.	NOUN
ejpam-7116	135	26	therefore	therefore	ADV
ejpam-7116	135	27	,	,	PUNCT
ejpam-7116	135	28	this	this	DET
ejpam-7116	135	29	case	case	NOUN
ejpam-7116	135	30	is	be	AUX
ejpam-7116	135	31	reduced	reduce	VERB
ejpam-7116	135	32	to	to	ADP
ejpam-7116	135	33	the	the	DET
ejpam-7116	135	34	previous	previous	ADJ
ejpam-7116	135	35	one	one	NUM
ejpam-7116	135	36	by	by	ADP
ejpam-7116	135	37	applying	apply	VERB
ejpam-7116	135	38	the	the	DET
ejpam-7116	135	39	same	same	ADJ
ejpam-7116	135	40	procedure	procedure	NOUN
ejpam-7116	135	41	to	to	ADP
ejpam-7116	135	42	the	the	DET
ejpam-7116	135	43	mapping	mapping	NOUN
ejpam-7116	135	44	tn0	tn0	NOUN
ejpam-7116	135	45	.	.	PUNCT
ejpam-7116	136	1	since	since	SCONJ
ejpam-7116	136	2	(	(	PUNCT
ejpam-7116	136	3	x	x	X
ejpam-7116	136	4	,	,	PUNCT
ejpam-7116	136	5	d	d	NOUN
ejpam-7116	136	6	)	)	PUNCT
ejpam-7116	136	7	is	be	AUX
ejpam-7116	136	8	a	a	DET
ejpam-7116	136	9	complete	complete	ADJ
ejpam-7116	136	10	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	136	11	.	.	PUNCT
ejpam-7116	137	1	there	there	PRON
ejpam-7116	137	2	exists	exist	VERB
ejpam-7116	137	3	a	a	DET
ejpam-7116	137	4	∈	∈	NOUN
ejpam-7116	137	5	x	x	PUNCT
ejpam-7116	137	6	such	such	ADJ
ejpam-7116	137	7	that	that	SCONJ
ejpam-7116	137	8	lim	lim	PROPN
ejpam-7116	137	9	n→+∞	n→+∞	VERB
ejpam-7116	137	10	d(xn	d(xn	PROPN
ejpam-7116	137	11	,	,	PUNCT
ejpam-7116	137	12	a	a	PRON
ejpam-7116	137	13	)	)	PUNCT
ejpam-7116	137	14	=	=	SYM
ejpam-7116	137	15	0	0	X
ejpam-7116	137	16	.	.	PUNCT
ejpam-7116	138	1	by	by	ADP
ejpam-7116	138	2	lemma	lemma	PROPN
ejpam-7116	138	3	2.1	2.1	NUM
ejpam-7116	138	4	the	the	DET
ejpam-7116	138	5	limit	limit	NOUN
ejpam-7116	138	6	a	a	PRON
ejpam-7116	138	7	is	be	AUX
ejpam-7116	138	8	unique	unique	ADJ
ejpam-7116	138	9	,	,	PUNCT
ejpam-7116	138	10	as	as	SCONJ
ejpam-7116	138	11	{	{	PUNCT
ejpam-7116	138	12	xn	xn	PRON
ejpam-7116	138	13	}	}	PUNCT
ejpam-7116	138	14	is	be	AUX
ejpam-7116	138	15	a	a	DET
ejpam-7116	138	16	cauchy	cauchy	ADJ
ejpam-7116	138	17	sequence	sequence	NOUN
ejpam-7116	138	18	of	of	ADP
ejpam-7116	138	19	pairwise	pairwise	NOUN
ejpam-7116	138	20	distinct	distinct	ADJ
ejpam-7116	138	21	points	point	NOUN
ejpam-7116	138	22	.	.	PUNCT
ejpam-7116	139	1	then	then	ADV
ejpam-7116	139	2	from	from	ADP
ejpam-7116	139	3	d(xn+1	d(xn+1	PROPN
ejpam-7116	139	4	,	,	PUNCT
ejpam-7116	139	5	ta	ta	NOUN
ejpam-7116	139	6	)	)	PUNCT
ejpam-7116	139	7	≤	≤	NOUN
ejpam-7116	140	1	qd(xn	qd(xn	NOUN
ejpam-7116	140	2	,	,	PUNCT
ejpam-7116	140	3	a	a	PRON
ejpam-7116	140	4	)	)	PUNCT
ejpam-7116	140	5	→	→	SYM
ejpam-7116	140	6	0	0	NUM
ejpam-7116	140	7	as	as	ADP
ejpam-7116	140	8	n	n	PROPN
ejpam-7116	140	9	→	→	SYM
ejpam-7116	140	10	∞	∞	NUM
ejpam-7116	140	11	we	we	PRON
ejpam-7116	140	12	conclude	conclude	VERB
ejpam-7116	140	13	that	that	PRON
ejpam-7116	140	14	ta	ta	SCONJ
ejpam-7116	140	15	=	=	SYM
ejpam-7116	140	16	a	a	PROPN
ejpam-7116	140	17	,	,	PUNCT
ejpam-7116	140	18	i.e.	i.e.	X
ejpam-7116	140	19	a	a	PRON
ejpam-7116	140	20	is	be	AUX
ejpam-7116	140	21	a	a	DET
ejpam-7116	140	22	fixed	fix	VERB
ejpam-7116	140	23	point	point	NOUN
ejpam-7116	140	24	of	of	ADP
ejpam-7116	140	25	the	the	DET
ejpam-7116	140	26	mapping	mapping	NOUN
ejpam-7116	140	27	t	t	NOUN
ejpam-7116	140	28	.	.	PUNCT
ejpam-7116	141	1	its	its	PRON
ejpam-7116	141	2	uniqueness	uniqueness	NOUN
ejpam-7116	141	3	is	be	AUX
ejpam-7116	141	4	easily	easily	ADV
ejpam-7116	141	5	shown	show	VERB
ejpam-7116	141	6	by	by	ADP
ejpam-7116	141	7	contradiction	contradiction	NOUN
ejpam-7116	141	8	,	,	PUNCT
ejpam-7116	141	9	using	use	VERB
ejpam-7116	141	10	the	the	DET
ejpam-7116	141	11	contractive	contractive	ADJ
ejpam-7116	141	12	condition	condition	NOUN
ejpam-7116	141	13	(	(	PUNCT
ejpam-7116	141	14	3.1	3.1	NUM
ejpam-7116	141	15	)	)	PUNCT
ejpam-7116	141	16	.	.	PUNCT
ejpam-7116	142	1	our	our	PRON
ejpam-7116	142	2	next	next	ADJ
ejpam-7116	142	3	main	main	ADJ
ejpam-7116	142	4	result	result	NOUN
ejpam-7116	142	5	is	be	AUX
ejpam-7116	142	6	the	the	DET
ejpam-7116	142	7	kannan	kannan	PROPN
ejpam-7116	142	8	fixed	fix	VERB
ejpam-7116	142	9	point	point	NOUN
ejpam-7116	142	10	theorem	theorem	VERB
ejpam-7116	142	11	on	on	ADP
ejpam-7116	142	12	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	142	13	.	.	PUNCT
ejpam-7116	142	14	theorem	theorem	PROPN
ejpam-7116	142	15	3.2	3.2	NUM
ejpam-7116	142	16	.	.	PUNCT
ejpam-7116	143	1	let	let	VERB
ejpam-7116	143	2	(	(	PUNCT
ejpam-7116	143	3	x	x	NOUN
ejpam-7116	143	4	,	,	PUNCT
ejpam-7116	143	5	d	d	NOUN
ejpam-7116	143	6	)	)	PUNCT
ejpam-7116	143	7	be	be	AUX
ejpam-7116	143	8	a	a	DET
ejpam-7116	143	9	complete	complete	ADJ
ejpam-7116	143	10	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	143	11	.	.	PUNCT
ejpam-7116	143	12	and	and	CCONJ
ejpam-7116	143	13	let	let	VERB
ejpam-7116	143	14	t	t	NOUN
ejpam-7116	143	15	:	:	PUNCT
ejpam-7116	143	16	x	x	X
ejpam-7116	143	17	→	→	PUNCT
ejpam-7116	143	18	x	x	PUNCT
ejpam-7116	143	19	be	be	AUX
ejpam-7116	143	20	a	a	DET
ejpam-7116	143	21	mapping	mapping	NOUN
ejpam-7116	143	22	such	such	ADJ
ejpam-7116	143	23	that	that	SCONJ
ejpam-7116	143	24	d(tx	d(tx	PROPN
ejpam-7116	143	25	,	,	PUNCT
ejpam-7116	143	26	ty	ty	NOUN
ejpam-7116	143	27	)	)	PUNCT
ejpam-7116	143	28	≤	≤	NOUN
ejpam-7116	143	29	q(d(x	q(d(x	PROPN
ejpam-7116	143	30	,	,	PUNCT
ejpam-7116	143	31	tx	tx	PROPN
ejpam-7116	143	32	)	)	PUNCT
ejpam-7116	144	1	+	+	CCONJ
ejpam-7116	144	2	d(y	d(y	PROPN
ejpam-7116	144	3	,	,	PUNCT
ejpam-7116	144	4	ty	ty	NOUN
ejpam-7116	144	5	)	)	PUNCT
ejpam-7116	144	6	)	)	PUNCT
ejpam-7116	144	7	for	for	ADP
ejpam-7116	144	8	all	all	DET
ejpam-7116	144	9	x	x	NOUN
ejpam-7116	144	10	,	,	PUNCT
ejpam-7116	144	11	y	y	PROPN
ejpam-7116	144	12	∈	∈	PROPN
ejpam-7116	144	13	x	x	X
ejpam-7116	144	14	and	and	CCONJ
ejpam-7116	144	15	some	some	DET
ejpam-7116	144	16	q	q	NOUN
ejpam-7116	144	17	∈	∈	PROPN
ejpam-7116	144	18	[	[	PUNCT
ejpam-7116	144	19	0	0	NUM
ejpam-7116	144	20	,	,	PUNCT
ejpam-7116	144	21	1	1	NUM
ejpam-7116	144	22	2	2	NUM
ejpam-7116	144	23	)	)	PUNCT
ejpam-7116	144	24	.	.	PUNCT
ejpam-7116	145	1	(	(	PUNCT
ejpam-7116	145	2	3.4	3.4	NUM
ejpam-7116	145	3	)	)	PUNCT
ejpam-7116	145	4	then	then	ADV
ejpam-7116	145	5	t	t	PROPN
ejpam-7116	145	6	possesses	possess	VERB
ejpam-7116	145	7	a	a	DET
ejpam-7116	145	8	unique	unique	ADJ
ejpam-7116	145	9	fixed	fix	VERB
ejpam-7116	145	10	point	point	NOUN
ejpam-7116	145	11	a	a	DET
ejpam-7116	145	12	∈	∈	PROPN
ejpam-7116	145	13	x	x	NOUN
ejpam-7116	145	14	,	,	PUNCT
ejpam-7116	145	15	such	such	ADJ
ejpam-7116	145	16	that	that	SCONJ
ejpam-7116	145	17	limn→+∞	limn→+∞	ADP
ejpam-7116	145	18	d(tnx	d(tnx	PROPN
ejpam-7116	145	19	,	,	PUNCT
ejpam-7116	145	20	a	a	PRON
ejpam-7116	145	21	)	)	PUNCT
ejpam-7116	145	22	=	=	SYM
ejpam-7116	145	23	0	0	NUM
ejpam-7116	145	24	for	for	ADP
ejpam-7116	145	25	any	any	DET
ejpam-7116	145	26	x	x	SYM
ejpam-7116	145	27	∈	∈	PROPN
ejpam-7116	145	28	x.	x.	NOUN
ejpam-7116	145	29	a.	a.	NOUN
ejpam-7116	145	30	kostić	kostić	VERB
ejpam-7116	145	31	/	/	SYM
ejpam-7116	145	32	eur	eur	PROPN
ejpam-7116	145	33	.	.	PUNCT
ejpam-7116	146	1	j.	j.	PROPN
ejpam-7116	146	2	pure	pure	PROPN
ejpam-7116	146	3	appl	appl	PROPN
ejpam-7116	146	4	.	.	PROPN
ejpam-7116	146	5	math	math	PROPN
ejpam-7116	146	6	,	,	PUNCT
ejpam-7116	146	7	18	18	NUM
ejpam-7116	146	8	(	(	PUNCT
ejpam-7116	146	9	4	4	NUM
ejpam-7116	146	10	)	)	PUNCT
ejpam-7116	146	11	(	(	PUNCT
ejpam-7116	146	12	2025	2025	NUM
ejpam-7116	146	13	)	)	PUNCT
ejpam-7116	146	14	,	,	PUNCT
ejpam-7116	146	15	7116	7116	NUM
ejpam-7116	146	16	7	7	NUM
ejpam-7116	146	17	of	of	ADP
ejpam-7116	146	18	10	10	NUM
ejpam-7116	146	19	proof	proof	NOUN
ejpam-7116	146	20	.	.	PUNCT
ejpam-7116	147	1	again	again	ADV
ejpam-7116	147	2	,	,	PUNCT
ejpam-7116	147	3	let	let	VERB
ejpam-7116	147	4	x	x	PUNCT
ejpam-7116	147	5	∈	∈	PROPN
ejpam-7116	147	6	x	x	PUNCT
ejpam-7116	147	7	be	be	AUX
ejpam-7116	147	8	any	any	DET
ejpam-7116	147	9	point	point	NOUN
ejpam-7116	147	10	,	,	PUNCT
ejpam-7116	147	11	and	and	CCONJ
ejpam-7116	147	12	let	let	VERB
ejpam-7116	147	13	xn	xn	PUNCT
ejpam-7116	148	1	=	=	PUNCT
ejpam-7116	148	2	tnx	tnx	NOUN
ejpam-7116	148	3	for	for	ADP
ejpam-7116	148	4	all	all	PRON
ejpam-7116	148	5	n	n	PRON
ejpam-7116	148	6	∈	∈	PROPN
ejpam-7116	148	7	n0	n0	PROPN
ejpam-7116	148	8	.	.	PUNCT
ejpam-7116	149	1	by	by	ADP
ejpam-7116	149	2	(	(	PUNCT
ejpam-7116	149	3	3.4	3.4	NUM
ejpam-7116	149	4	)	)	PUNCT
ejpam-7116	149	5	,	,	PUNCT
ejpam-7116	149	6	for	for	ADP
ejpam-7116	149	7	all	all	DET
ejpam-7116	149	8	n	n	PRON
ejpam-7116	149	9	∈	∈	PROPN
ejpam-7116	149	10	n0	n0	NOUN
ejpam-7116	149	11	we	we	PRON
ejpam-7116	149	12	have	have	VERB
ejpam-7116	149	13	d(xn	d(xn	NOUN
ejpam-7116	149	14	,	,	PUNCT
ejpam-7116	149	15	xn+1	xn+1	NUM
ejpam-7116	149	16	)	)	PUNCT
ejpam-7116	149	17	≤	≤	PUNCT
ejpam-7116	150	1	q(d(xn−1	q(d(xn−1	PROPN
ejpam-7116	150	2	,	,	PUNCT
ejpam-7116	150	3	xn	xn	PUNCT
ejpam-7116	150	4	)	)	PUNCT
ejpam-7116	151	1	+	+	CCONJ
ejpam-7116	151	2	d(xn	d(xn	PROPN
ejpam-7116	151	3	,	,	PUNCT
ejpam-7116	151	4	xn+1	xn+1	NUM
ejpam-7116	151	5	)	)	PUNCT
ejpam-7116	151	6	)	)	PUNCT
ejpam-7116	151	7	,	,	PUNCT
ejpam-7116	151	8	i.e.	i.e.	X
ejpam-7116	151	9	d(xn	d(xn	X
ejpam-7116	151	10	,	,	PUNCT
ejpam-7116	151	11	xn+1	xn+1	NUM
ejpam-7116	151	12	)	)	PUNCT
ejpam-7116	151	13	≤	≤	NUM
ejpam-7116	151	14	q	q	NOUN
ejpam-7116	152	1	1−	1−	NUM
ejpam-7116	152	2	q	q	NOUN
ejpam-7116	152	3	d(xn−1	d(xn−1	PROPN
ejpam-7116	152	4	,	,	PUNCT
ejpam-7116	152	5	xn	xn	PROPN
ejpam-7116	152	6	)	)	PUNCT
ejpam-7116	152	7	.	.	PUNCT
ejpam-7116	153	1	since	since	SCONJ
ejpam-7116	153	2	q	q	PROPN
ejpam-7116	153	3	∈	∈	PROPN
ejpam-7116	154	1	[	[	X
ejpam-7116	154	2	0	0	NUM
ejpam-7116	154	3	,	,	PUNCT
ejpam-7116	154	4	12	12	NUM
ejpam-7116	154	5	)	)	PUNCT
ejpam-7116	154	6	,	,	PUNCT
ejpam-7116	154	7	we	we	PRON
ejpam-7116	154	8	have	have	VERB
ejpam-7116	154	9	q	q	ADJ
ejpam-7116	154	10	1−q	1−q	NUM
ejpam-7116	154	11	∈	∈	PROPN
ejpam-7116	155	1	[	[	X
ejpam-7116	155	2	0	0	NUM
ejpam-7116	155	3	,	,	PUNCT
ejpam-7116	155	4	1	1	NUM
ejpam-7116	155	5	)	)	PUNCT
ejpam-7116	155	6	and	and	CCONJ
ejpam-7116	155	7	thus	thus	ADV
ejpam-7116	155	8	limn→∞	limn→∞	ADJ
ejpam-7116	155	9	d(xn	d(xn	NOUN
ejpam-7116	155	10	,	,	PUNCT
ejpam-7116	155	11	xn+1	xn+1	NUM
ejpam-7116	155	12	)	)	PUNCT
ejpam-7116	156	1	=	=	SYM
ejpam-7116	156	2	0	0	NUM
ejpam-7116	156	3	,	,	PUNCT
ejpam-7116	156	4	so	so	SCONJ
ejpam-7116	156	5	we	we	PRON
ejpam-7116	156	6	can	can	AUX
ejpam-7116	156	7	use	use	VERB
ejpam-7116	156	8	the	the	DET
ejpam-7116	156	9	same	same	ADJ
ejpam-7116	156	10	method	method	NOUN
ejpam-7116	156	11	as	as	ADP
ejpam-7116	156	12	in	in	ADP
ejpam-7116	156	13	the	the	DET
ejpam-7116	156	14	proof	proof	NOUN
ejpam-7116	156	15	of	of	ADP
ejpam-7116	156	16	theorem	theorem	ADJ
ejpam-7116	156	17	3.1	3.1	NUM
ejpam-7116	156	18	to	to	PART
ejpam-7116	156	19	show	show	VERB
ejpam-7116	156	20	that	that	SCONJ
ejpam-7116	156	21	{	{	PUNCT
ejpam-7116	156	22	xn	xn	X
ejpam-7116	156	23	}	}	PUNCT
ejpam-7116	156	24	is	be	AUX
ejpam-7116	156	25	a	a	DET
ejpam-7116	156	26	cauchy	cauchy	ADJ
ejpam-7116	156	27	sequence	sequence	NOUN
ejpam-7116	156	28	in	in	ADP
ejpam-7116	156	29	x.	x.	NOUN
ejpam-7116	156	30	as	as	SCONJ
ejpam-7116	156	31	is	be	AUX
ejpam-7116	156	32	well	well	ADV
ejpam-7116	156	33	known	know	VERB
ejpam-7116	156	34	,	,	PUNCT
ejpam-7116	156	35	if	if	SCONJ
ejpam-7116	156	36	a	a	DET
ejpam-7116	156	37	mapping	mapping	NOUN
ejpam-7116	156	38	t	t	NOUN
ejpam-7116	156	39	satisfies	satisfy	VERB
ejpam-7116	156	40	the	the	DET
ejpam-7116	156	41	kannan	kannan	PROPN
ejpam-7116	156	42	contractive	contractive	ADJ
ejpam-7116	156	43	condition	condition	NOUN
ejpam-7116	156	44	(	(	PUNCT
ejpam-7116	156	45	3.4	3.4	NUM
ejpam-7116	156	46	)	)	PUNCT
ejpam-7116	156	47	,	,	PUNCT
ejpam-7116	156	48	then	then	ADV
ejpam-7116	156	49	the	the	DET
ejpam-7116	156	50	mapping	mapping	NOUN
ejpam-7116	156	51	tn	tn	NOUN
ejpam-7116	156	52	satisfies	satisfy	VERB
ejpam-7116	156	53	the	the	DET
ejpam-7116	156	54	same	same	ADJ
ejpam-7116	156	55	condition	condition	NOUN
ejpam-7116	156	56	with	with	ADP
ejpam-7116	156	57	the	the	DET
ejpam-7116	156	58	contractive	contractive	ADJ
ejpam-7116	156	59	constant	constant	ADJ
ejpam-7116	156	60	qn	qn	NOUN
ejpam-7116	156	61	(	(	PUNCT
ejpam-7116	156	62	1−q)n−1	1−q)n−1	PROPN
ejpam-7116	156	63	for	for	ADP
ejpam-7116	156	64	all	all	PRON
ejpam-7116	156	65	n	n	DET
ejpam-7116	156	66	∈	∈	PROPN
ejpam-7116	156	67	n.	n.	NOUN
ejpam-7116	156	68	hence	hence	ADV
ejpam-7116	156	69	,	,	PUNCT
ejpam-7116	156	70	notice	notice	VERB
ejpam-7116	156	71	we	we	PRON
ejpam-7116	156	72	can	can	AUX
ejpam-7116	156	73	now	now	ADV
ejpam-7116	156	74	distinguish	distinguish	VERB
ejpam-7116	156	75	the	the	DET
ejpam-7116	156	76	cases	case	NOUN
ejpam-7116	156	77	q	q	NOUN
ejpam-7116	156	78	1−q	1−q	NUM
ejpam-7116	156	79	∈	∈	PROPN
ejpam-7116	157	1	[	[	X
ejpam-7116	157	2	0	0	NUM
ejpam-7116	157	3	,	,	PUNCT
ejpam-7116	157	4	φ−1	φ−1	PROPN
ejpam-7116	157	5	)	)	PUNCT
ejpam-7116	157	6	and	and	CCONJ
ejpam-7116	157	7	q	q	NOUN
ejpam-7116	157	8	1−q	1−q	NUM
ejpam-7116	157	9	∈	∈	PROPN
ejpam-7116	158	1	[	[	X
ejpam-7116	158	2	φ−1	φ−1	PROPN
ejpam-7116	158	3	,	,	PUNCT
ejpam-7116	158	4	1	1	NUM
ejpam-7116	158	5	)	)	PUNCT
ejpam-7116	158	6	.	.	PUNCT
ejpam-7116	159	1	since	since	SCONJ
ejpam-7116	159	2	(	(	PUNCT
ejpam-7116	159	3	x	x	X
ejpam-7116	159	4	,	,	PUNCT
ejpam-7116	159	5	d	d	NOUN
ejpam-7116	159	6	)	)	PUNCT
ejpam-7116	159	7	is	be	AUX
ejpam-7116	159	8	complete	complete	ADJ
ejpam-7116	159	9	,	,	PUNCT
ejpam-7116	159	10	the	the	DET
ejpam-7116	159	11	sequence	sequence	NOUN
ejpam-7116	159	12	{	{	PUNCT
ejpam-7116	159	13	xn	xn	NOUN
ejpam-7116	159	14	}	}	PUNCT
ejpam-7116	159	15	converges	converge	NOUN
ejpam-7116	159	16	(	(	PUNCT
ejpam-7116	159	17	uniquely	uniquely	ADV
ejpam-7116	159	18	)	)	PUNCT
ejpam-7116	159	19	to	to	ADP
ejpam-7116	159	20	some	some	PRON
ejpam-7116	159	21	a	a	DET
ejpam-7116	159	22	∈	∈	NOUN
ejpam-7116	159	23	x.	x.	NOUN
ejpam-7116	159	24	from	from	ADP
ejpam-7116	159	25	(	(	PUNCT
ejpam-7116	159	26	3.4	3.4	NUM
ejpam-7116	159	27	)	)	PUNCT
ejpam-7116	159	28	,	,	PUNCT
ejpam-7116	159	29	for	for	ADP
ejpam-7116	159	30	all	all	DET
ejpam-7116	159	31	n	n	PRON
ejpam-7116	159	32	∈	∈	NOUN
ejpam-7116	159	33	n	n	CCONJ
ejpam-7116	159	34	we	we	PRON
ejpam-7116	159	35	get	get	VERB
ejpam-7116	159	36	d(a	d(a	PROPN
ejpam-7116	159	37	,	,	PUNCT
ejpam-7116	159	38	ta	ta	NOUN
ejpam-7116	159	39	)	)	PUNCT
ejpam-7116	159	40	≤	≤	NOUN
ejpam-7116	160	1	d(a	d(a	PROPN
ejpam-7116	160	2	,	,	PUNCT
ejpam-7116	160	3	xn	xn	PROPN
ejpam-7116	160	4	)	)	PUNCT
ejpam-7116	161	1	+	+	CCONJ
ejpam-7116	161	2	d(xn	d(xn	PROPN
ejpam-7116	161	3	,	,	PUNCT
ejpam-7116	161	4	xn+1	xn+1	NUM
ejpam-7116	161	5	)	)	PUNCT
ejpam-7116	162	1	+	+	X
ejpam-7116	162	2	d(xn+1	d(xn+1	PROPN
ejpam-7116	162	3	,	,	PUNCT
ejpam-7116	162	4	ta	ta	NOUN
ejpam-7116	162	5	)	)	PUNCT
ejpam-7116	163	1	+	+	CCONJ
ejpam-7116	163	2	d(a	d(a	PROPN
ejpam-7116	163	3	,	,	PUNCT
ejpam-7116	163	4	xn+1	xn+1	NUM
ejpam-7116	163	5	)	)	PUNCT
ejpam-7116	164	1	+	+	CCONJ
ejpam-7116	164	2	d(xn	d(xn	PROPN
ejpam-7116	164	3	,	,	PUNCT
ejpam-7116	164	4	ta	ta	NOUN
ejpam-7116	164	5	)	)	PUNCT
ejpam-7116	164	6	≤	≤	NOUN
ejpam-7116	165	1	d(a	d(a	PROPN
ejpam-7116	165	2	,	,	PUNCT
ejpam-7116	165	3	xn	xn	PROPN
ejpam-7116	165	4	)	)	PUNCT
ejpam-7116	166	1	+	+	CCONJ
ejpam-7116	166	2	d(xn	d(xn	PROPN
ejpam-7116	166	3	,	,	PUNCT
ejpam-7116	166	4	xn+1	xn+1	NUM
ejpam-7116	166	5	)	)	PUNCT
ejpam-7116	166	6	+	+	CCONJ
ejpam-7116	166	7	q(d(xn	q(d(xn	NOUN
ejpam-7116	166	8	,	,	PUNCT
ejpam-7116	166	9	xn+1	xn+1	NUM
ejpam-7116	166	10	)	)	PUNCT
ejpam-7116	166	11	+	+	CCONJ
ejpam-7116	167	1	d(a	d(a	PROPN
ejpam-7116	167	2	,	,	PUNCT
ejpam-7116	167	3	ta	ta	NOUN
ejpam-7116	167	4	)	)	PUNCT
ejpam-7116	167	5	)	)	PUNCT
ejpam-7116	168	1	+	+	CCONJ
ejpam-7116	168	2	d(a	d(a	PROPN
ejpam-7116	168	3	,	,	PUNCT
ejpam-7116	168	4	xn+1	xn+1	NUM
ejpam-7116	168	5	)	)	PUNCT
ejpam-7116	169	1	+	+	CCONJ
ejpam-7116	169	2	q(d(xn−1	q(d(xn−1	ADJ
ejpam-7116	169	3	,	,	PUNCT
ejpam-7116	169	4	xn	xn	PUNCT
ejpam-7116	169	5	)	)	PUNCT
ejpam-7116	170	1	+	+	CCONJ
ejpam-7116	170	2	d(a	d(a	PROPN
ejpam-7116	170	3	,	,	PUNCT
ejpam-7116	170	4	ta	ta	NOUN
ejpam-7116	170	5	)	)	PUNCT
ejpam-7116	170	6	)	)	PUNCT
ejpam-7116	170	7	.	.	PUNCT
ejpam-7116	171	1	therefore	therefore	ADV
ejpam-7116	171	2	,	,	PUNCT
ejpam-7116	171	3	d(a	d(a	PROPN
ejpam-7116	171	4	,	,	PUNCT
ejpam-7116	171	5	ta	ta	NOUN
ejpam-7116	171	6	)	)	PUNCT
ejpam-7116	171	7	≤	≤	NUM
ejpam-7116	171	8	1	1	NUM
ejpam-7116	171	9	1−	1−	NUM
ejpam-7116	171	10	2q	2q	NUM
ejpam-7116	171	11	(	(	PUNCT
ejpam-7116	171	12	d(a	d(a	PROPN
ejpam-7116	171	13	,	,	PUNCT
ejpam-7116	171	14	xn	xn	PUNCT
ejpam-7116	171	15	)	)	PUNCT
ejpam-7116	172	1	+	+	CCONJ
ejpam-7116	172	2	(	(	PUNCT
ejpam-7116	172	3	1	1	NUM
ejpam-7116	172	4	+	+	NUM
ejpam-7116	172	5	q)d(xn	q)d(xn	NUM
ejpam-7116	172	6	,	,	PUNCT
ejpam-7116	172	7	xn+1	xn+1	NUM
ejpam-7116	172	8	)	)	PUNCT
ejpam-7116	172	9	+	+	CCONJ
ejpam-7116	172	10	d(a	d(a	PROPN
ejpam-7116	172	11	,	,	PUNCT
ejpam-7116	172	12	xn+1	xn+1	NUM
ejpam-7116	172	13	)	)	PUNCT
ejpam-7116	173	1	+	+	CCONJ
ejpam-7116	173	2	qd(xn−1	qd(xn−1	PROPN
ejpam-7116	173	3	,	,	PUNCT
ejpam-7116	173	4	xn	xn	PROPN
ejpam-7116	173	5	)	)	PUNCT
ejpam-7116	173	6	)	)	PUNCT
ejpam-7116	174	1	→	→	SYM
ejpam-7116	174	2	0	0	PUNCT
ejpam-7116	174	3	as	as	ADP
ejpam-7116	174	4	n	n	PRON
ejpam-7116	174	5	→	→	SYM
ejpam-7116	174	6	+	+	NOUN
ejpam-7116	174	7	∞	∞	PROPN
ejpam-7116	174	8	,	,	PUNCT
ejpam-7116	174	9	i.e.	i.e.	X
ejpam-7116	174	10	d(a	d(a	PROPN
ejpam-7116	174	11	,	,	PUNCT
ejpam-7116	174	12	ta	ta	NOUN
ejpam-7116	174	13	)	)	PUNCT
ejpam-7116	174	14	=	=	SYM
ejpam-7116	174	15	0	0	PUNCT
ejpam-7116	175	1	and	and	CCONJ
ejpam-7116	175	2	so	so	ADV
ejpam-7116	175	3	a	a	DET
ejpam-7116	175	4	=	=	SYM
ejpam-7116	175	5	ta	ta	PROPN
ejpam-7116	175	6	.	.	PUNCT
ejpam-7116	175	7	uniqueness	uniqueness	NOUN
ejpam-7116	175	8	of	of	ADP
ejpam-7116	175	9	the	the	DET
ejpam-7116	175	10	fixed	fix	VERB
ejpam-7116	175	11	point	point	NOUN
ejpam-7116	175	12	is	be	AUX
ejpam-7116	175	13	again	again	ADV
ejpam-7116	175	14	easy	easy	ADJ
ejpam-7116	175	15	to	to	PART
ejpam-7116	175	16	check	check	VERB
ejpam-7116	175	17	.	.	PUNCT
ejpam-7116	176	1	the	the	DET
ejpam-7116	176	2	following	follow	VERB
ejpam-7116	176	3	example	example	NOUN
ejpam-7116	176	4	illustrates	illustrate	VERB
ejpam-7116	176	5	theorems	theorem	NOUN
ejpam-7116	176	6	3.1	3.1	NUM
ejpam-7116	176	7	and	and	CCONJ
ejpam-7116	176	8	3.2	3.2	NUM
ejpam-7116	176	9	.	.	PUNCT
ejpam-7116	176	10	example	example	NOUN
ejpam-7116	176	11	3.1	3.1	NUM
ejpam-7116	176	12	.	.	PUNCT
ejpam-7116	177	1	let	let	VERB
ejpam-7116	177	2	x	x	PUNCT
ejpam-7116	177	3	=	=	PRON
ejpam-7116	177	4	{	{	PUNCT
ejpam-7116	177	5	1	1	NUM
ejpam-7116	177	6	,	,	PUNCT
ejpam-7116	177	7	2	2	NUM
ejpam-7116	177	8	,	,	PUNCT
ejpam-7116	177	9	3	3	NUM
ejpam-7116	177	10	,	,	PUNCT
ejpam-7116	177	11	4	4	NUM
ejpam-7116	177	12	,	,	PUNCT
ejpam-7116	177	13	5	5	NUM
ejpam-7116	177	14	,	,	PUNCT
ejpam-7116	177	15	6	6	NUM
ejpam-7116	177	16	}	}	PUNCT
ejpam-7116	177	17	,	,	PUNCT
ejpam-7116	177	18	and	and	CCONJ
ejpam-7116	177	19	let	let	VERB
ejpam-7116	177	20	d	d	NOUN
ejpam-7116	177	21	:	:	PUNCT
ejpam-7116	177	22	x	x	PROPN
ejpam-7116	177	23	×x	×x	X
ejpam-7116	177	24	→	→	SYM
ejpam-7116	177	25	[	[	X
ejpam-7116	177	26	0,+∞	0,+∞	NUM
ejpam-7116	177	27	)	)	PUNCT
ejpam-7116	177	28	be	be	AUX
ejpam-7116	177	29	defined	define	VERB
ejpam-7116	177	30	as	as	ADP
ejpam-7116	177	31	d(i	d(i	PROPN
ejpam-7116	177	32	,	,	PUNCT
ejpam-7116	177	33	j	j	NOUN
ejpam-7116	177	34	)	)	PUNCT
ejpam-7116	177	35	=	=	PUNCT
ejpam-7116	177	36			NOUN
ejpam-7116	177	37	0	0	NUM
ejpam-7116	177	38	,	,	PUNCT
ejpam-7116	177	39	i	i	PRON
ejpam-7116	177	40	=	=	SYM
ejpam-7116	177	41	j	j	PROPN
ejpam-7116	177	42	,	,	PUNCT
ejpam-7116	177	43	3	3	NUM
ejpam-7116	177	44	,	,	PUNCT
ejpam-7116	177	45	i	i	PRON
ejpam-7116	177	46	=	=	NOUN
ejpam-7116	177	47	1	1	NUM
ejpam-7116	177	48	and	and	CCONJ
ejpam-7116	177	49	j	j	NOUN
ejpam-7116	177	50	=	=	SYM
ejpam-7116	177	51	2	2	NUM
ejpam-7116	177	52	,	,	PUNCT
ejpam-7116	177	53	3	3	NUM
ejpam-7116	177	54	,	,	PUNCT
ejpam-7116	177	55	or	or	CCONJ
ejpam-7116	177	56	i	i	NOUN
ejpam-7116	177	57	=	=	NOUN
ejpam-7116	177	58	2	2	NUM
ejpam-7116	177	59	,	,	PUNCT
ejpam-7116	177	60	3	3	NUM
ejpam-7116	177	61	and	and	CCONJ
ejpam-7116	177	62	j	j	PROPN
ejpam-7116	177	63	=	=	SYM
ejpam-7116	177	64	1	1	NUM
ejpam-7116	177	65	,	,	PUNCT
ejpam-7116	177	66	6	6	NUM
ejpam-7116	177	67	,	,	PUNCT
ejpam-7116	177	68	i	i	PRON
ejpam-7116	177	69	=	=	NOUN
ejpam-7116	177	70	1	1	NUM
ejpam-7116	177	71	and	and	CCONJ
ejpam-7116	177	72	j	j	NOUN
ejpam-7116	177	73	=	=	SYM
ejpam-7116	177	74	4	4	NUM
ejpam-7116	177	75	,	,	PUNCT
ejpam-7116	177	76	6	6	NUM
ejpam-7116	177	77	,	,	PUNCT
ejpam-7116	177	78	or	or	CCONJ
ejpam-7116	177	79	i	i	NOUN
ejpam-7116	177	80	=	=	NOUN
ejpam-7116	177	81	4	4	NUM
ejpam-7116	177	82	,	,	PUNCT
ejpam-7116	177	83	6	6	NUM
ejpam-7116	177	84	and	and	CCONJ
ejpam-7116	177	85	j	j	NOUN
ejpam-7116	177	86	=	=	SYM
ejpam-7116	177	87	1	1	NUM
ejpam-7116	177	88	,	,	PUNCT
ejpam-7116	177	89	1	1	NUM
ejpam-7116	177	90	,	,	PUNCT
ejpam-7116	177	91	otherwise	otherwise	ADV
ejpam-7116	177	92	.	.	PUNCT
ejpam-7116	178	1	then	then	ADV
ejpam-7116	178	2	it	it	PRON
ejpam-7116	178	3	is	be	AUX
ejpam-7116	178	4	easily	easily	ADV
ejpam-7116	178	5	checked	check	VERB
ejpam-7116	178	6	that	that	SCONJ
ejpam-7116	178	7	(	(	PUNCT
ejpam-7116	178	8	x	x	X
ejpam-7116	178	9	,	,	PUNCT
ejpam-7116	178	10	d	d	NOUN
ejpam-7116	178	11	)	)	PUNCT
ejpam-7116	178	12	is	be	AUX
ejpam-7116	178	13	a	a	DET
ejpam-7116	178	14	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	178	15	.	.	PUNCT
ejpam-7116	179	1	that	that	PRON
ejpam-7116	179	2	is	be	AUX
ejpam-7116	179	3	not	not	PART
ejpam-7116	179	4	a	a	DET
ejpam-7116	179	5	r.m.s	r.m.s	NOUN
ejpam-7116	179	6	.	.	PUNCT
ejpam-7116	180	1	the	the	DET
ejpam-7116	180	2	only	only	ADJ
ejpam-7116	180	3	convergent	convergent	NOUN
ejpam-7116	180	4	(	(	PUNCT
ejpam-7116	180	5	respectively	respectively	ADV
ejpam-7116	180	6	,	,	PUNCT
ejpam-7116	180	7	cauchy	cauchy	PROPN
ejpam-7116	180	8	)	)	PUNCT
ejpam-7116	180	9	sequences	sequence	NOUN
ejpam-7116	180	10	in	in	ADP
ejpam-7116	180	11	x	x	SYM
ejpam-7116	180	12	are	be	AUX
ejpam-7116	180	13	eventually	eventually	ADV
ejpam-7116	180	14	constant	constant	ADJ
ejpam-7116	180	15	,	,	PUNCT
ejpam-7116	180	16	so	so	CCONJ
ejpam-7116	180	17	(	(	PUNCT
ejpam-7116	180	18	x	x	NOUN
ejpam-7116	180	19	,	,	PUNCT
ejpam-7116	180	20	d	d	NOUN
ejpam-7116	180	21	)	)	PUNCT
ejpam-7116	180	22	is	be	AUX
ejpam-7116	180	23	complete	complete	ADJ
ejpam-7116	180	24	.	.	PUNCT
ejpam-7116	181	1	also	also	ADV
ejpam-7116	181	2	,	,	PUNCT
ejpam-7116	181	3	let	let	VERB
ejpam-7116	181	4	the	the	DET
ejpam-7116	181	5	mapping	mapping	NOUN
ejpam-7116	181	6	t	t	NOUN
ejpam-7116	181	7	:	:	PUNCT
ejpam-7116	181	8	x	x	X
ejpam-7116	181	9	→	→	PUNCT
ejpam-7116	181	10	x	x	AUX
ejpam-7116	181	11	be	be	AUX
ejpam-7116	181	12	defined	define	VERB
ejpam-7116	181	13	as	as	ADP
ejpam-7116	181	14	t	t	PROPN
ejpam-7116	181	15	(	(	PUNCT
ejpam-7116	181	16	i	i	NOUN
ejpam-7116	181	17	)	)	PUNCT
ejpam-7116	182	1	=	=	PRON
ejpam-7116	182	2	{	{	PUNCT
ejpam-7116	182	3	3	3	NUM
ejpam-7116	182	4	,	,	PUNCT
ejpam-7116	182	5	i	i	PRON
ejpam-7116	182	6	=	=	NOUN
ejpam-7116	182	7	1	1	NUM
ejpam-7116	182	8	,	,	PUNCT
ejpam-7116	182	9	6	6	NUM
ejpam-7116	182	10	,	,	PUNCT
ejpam-7116	182	11	i	i	PRON
ejpam-7116	182	12	=	=	NOUN
ejpam-7116	182	13	2	2	NUM
ejpam-7116	182	14	,	,	PUNCT
ejpam-7116	182	15	6	6	NUM
ejpam-7116	182	16	.	.	PUNCT
ejpam-7116	183	1	then	then	ADV
ejpam-7116	183	2	the	the	DET
ejpam-7116	183	3	mapping	mapping	NOUN
ejpam-7116	183	4	t	t	PROPN
ejpam-7116	183	5	is	be	AUX
ejpam-7116	183	6	a	a	DET
ejpam-7116	183	7	banach	banach	NOUN
ejpam-7116	183	8	contraction	contraction	NOUN
ejpam-7116	183	9	on	on	ADP
ejpam-7116	183	10	(	(	PUNCT
ejpam-7116	183	11	x	x	NOUN
ejpam-7116	183	12	,	,	PUNCT
ejpam-7116	183	13	d	d	NOUN
ejpam-7116	183	14	)	)	PUNCT
ejpam-7116	183	15	,	,	PUNCT
ejpam-7116	183	16	i.e.	i.e.	X
ejpam-7116	183	17	it	it	PRON
ejpam-7116	183	18	satisfies	satisfy	VERB
ejpam-7116	183	19	the	the	DET
ejpam-7116	183	20	condition	condition	NOUN
ejpam-7116	183	21	(	(	PUNCT
ejpam-7116	183	22	3.1	3.1	NUM
ejpam-7116	183	23	)	)	PUNCT
ejpam-7116	183	24	with	with	ADP
ejpam-7116	183	25	q	q	NOUN
ejpam-7116	183	26	=	=	SYM
ejpam-7116	183	27	1	1	NUM
ejpam-7116	183	28	3	3	NUM
ejpam-7116	183	29	.	.	PUNCT
ejpam-7116	184	1	a.	a.	NOUN
ejpam-7116	184	2	kostić	kostić	VERB
ejpam-7116	184	3	/	/	SYM
ejpam-7116	184	4	eur	eur	PROPN
ejpam-7116	184	5	.	.	PUNCT
ejpam-7116	185	1	j.	j.	PROPN
ejpam-7116	185	2	pure	pure	PROPN
ejpam-7116	185	3	appl	appl	PROPN
ejpam-7116	185	4	.	.	PROPN
ejpam-7116	185	5	math	math	PROPN
ejpam-7116	185	6	,	,	PUNCT
ejpam-7116	185	7	18	18	NUM
ejpam-7116	185	8	(	(	PUNCT
ejpam-7116	185	9	4	4	NUM
ejpam-7116	185	10	)	)	PUNCT
ejpam-7116	185	11	(	(	PUNCT
ejpam-7116	185	12	2025	2025	NUM
ejpam-7116	185	13	)	)	PUNCT
ejpam-7116	185	14	,	,	PUNCT
ejpam-7116	185	15	7116	7116	NUM
ejpam-7116	185	16	8	8	NUM
ejpam-7116	185	17	of	of	ADP
ejpam-7116	185	18	10	10	NUM
ejpam-7116	185	19	indeed	indeed	ADV
ejpam-7116	185	20	,	,	PUNCT
ejpam-7116	185	21	we	we	PRON
ejpam-7116	185	22	have	have	AUX
ejpam-7116	185	23	d(t	d(t	PROPN
ejpam-7116	185	24	(	(	PUNCT
ejpam-7116	185	25	1	1	NUM
ejpam-7116	185	26	)	)	PUNCT
ejpam-7116	185	27	,	,	PUNCT
ejpam-7116	185	28	t	t	PROPN
ejpam-7116	185	29	(	(	PUNCT
ejpam-7116	185	30	i	i	NOUN
ejpam-7116	185	31	)	)	PUNCT
ejpam-7116	185	32	)	)	PUNCT
ejpam-7116	186	1	=	=	PUNCT
ejpam-7116	186	2	1	1	NUM
ejpam-7116	186	3	≤	≤	NUM
ejpam-7116	186	4	1	1	NUM
ejpam-7116	186	5	=	=	SYM
ejpam-7116	186	6	1	1	NUM
ejpam-7116	186	7	3	3	NUM
ejpam-7116	186	8	d(1	d(1	PROPN
ejpam-7116	186	9	,	,	PUNCT
ejpam-7116	186	10	i	i	PROPN
ejpam-7116	186	11	)	)	PUNCT
ejpam-7116	186	12	,	,	PUNCT
ejpam-7116	186	13	for	for	ADP
ejpam-7116	186	14	i	i	PROPN
ejpam-7116	186	15	=	=	SYM
ejpam-7116	186	16	2	2	NUM
ejpam-7116	186	17	,	,	PUNCT
ejpam-7116	186	18	3	3	NUM
ejpam-7116	186	19	,	,	PUNCT
ejpam-7116	186	20	d(t	d(t	NOUN
ejpam-7116	186	21	(	(	PUNCT
ejpam-7116	186	22	1	1	NUM
ejpam-7116	186	23	)	)	PUNCT
ejpam-7116	186	24	,	,	PUNCT
ejpam-7116	186	25	t	t	PROPN
ejpam-7116	186	26	(	(	PUNCT
ejpam-7116	186	27	i	i	NOUN
ejpam-7116	186	28	)	)	PUNCT
ejpam-7116	186	29	)	)	PUNCT
ejpam-7116	187	1	=	=	PUNCT
ejpam-7116	187	2	1	1	NUM
ejpam-7116	187	3	≤	≤	NUM
ejpam-7116	187	4	2	2	NUM
ejpam-7116	187	5	=	=	SYM
ejpam-7116	187	6	1	1	NUM
ejpam-7116	187	7	3	3	NUM
ejpam-7116	187	8	d(1	d(1	PROPN
ejpam-7116	187	9	,	,	PUNCT
ejpam-7116	187	10	i	i	PROPN
ejpam-7116	187	11	)	)	PUNCT
ejpam-7116	187	12	,	,	PUNCT
ejpam-7116	187	13	for	for	ADP
ejpam-7116	187	14	i	i	PROPN
ejpam-7116	187	15	=	=	SYM
ejpam-7116	187	16	4	4	NUM
ejpam-7116	187	17	,	,	PUNCT
ejpam-7116	187	18	6	6	NUM
ejpam-7116	187	19	and	and	CCONJ
ejpam-7116	187	20	d(t	d(t	PROPN
ejpam-7116	187	21	(	(	PUNCT
ejpam-7116	187	22	i	i	PROPN
ejpam-7116	187	23	)	)	PUNCT
ejpam-7116	187	24	,	,	PUNCT
ejpam-7116	187	25	t	t	PROPN
ejpam-7116	187	26	(	(	PUNCT
ejpam-7116	187	27	j	j	NOUN
ejpam-7116	187	28	)	)	PUNCT
ejpam-7116	187	29	)	)	PUNCT
ejpam-7116	188	1	=	=	SYM
ejpam-7116	188	2	0	0	X
ejpam-7116	188	3	≤	≤	NUM
ejpam-7116	188	4	1	1	NUM
ejpam-7116	188	5	3	3	NUM
ejpam-7116	188	6	d(i	d(i	PROPN
ejpam-7116	188	7	,	,	PUNCT
ejpam-7116	188	8	j	j	PROPN
ejpam-7116	188	9	)	)	PUNCT
ejpam-7116	188	10	,	,	PUNCT
ejpam-7116	188	11	for	for	ADP
ejpam-7116	188	12	i	i	PRON
ejpam-7116	188	13	,	,	PUNCT
ejpam-7116	188	14	j	j	PROPN
ejpam-7116	188	15	=	=	SYM
ejpam-7116	188	16	2	2	NUM
ejpam-7116	188	17	,	,	PUNCT
ejpam-7116	188	18	6	6	NUM
ejpam-7116	188	19	.	.	PUNCT
ejpam-7116	188	20	hence	hence	ADV
ejpam-7116	188	21	,	,	PUNCT
ejpam-7116	188	22	theorem	theorem	VERB
ejpam-7116	188	23	3.1	3.1	NUM
ejpam-7116	188	24	can	can	AUX
ejpam-7116	188	25	be	be	AUX
ejpam-7116	188	26	applied	apply	VERB
ejpam-7116	188	27	to	to	PART
ejpam-7116	188	28	conclude	conclude	VERB
ejpam-7116	188	29	that	that	SCONJ
ejpam-7116	188	30	t	t	PROPN
ejpam-7116	188	31	has	have	VERB
ejpam-7116	188	32	a	a	DET
ejpam-7116	188	33	unique	unique	ADJ
ejpam-7116	188	34	fixed	fix	VERB
ejpam-7116	188	35	point	point	NOUN
ejpam-7116	188	36	a	a	DET
ejpam-7116	188	37	=	=	NOUN
ejpam-7116	188	38	6	6	NUM
ejpam-7116	188	39	in	in	ADP
ejpam-7116	188	40	x.	x.	NOUN
ejpam-7116	188	41	notice	notice	VERB
ejpam-7116	188	42	that	that	SCONJ
ejpam-7116	188	43	the	the	DET
ejpam-7116	188	44	mapping	mapping	NOUN
ejpam-7116	188	45	t	t	PROPN
ejpam-7116	188	46	is	be	AUX
ejpam-7116	188	47	not	not	PART
ejpam-7116	188	48	a	a	DET
ejpam-7116	188	49	banach	banach	NOUN
ejpam-7116	188	50	contraction	contraction	NOUN
ejpam-7116	188	51	with	with	ADP
ejpam-7116	188	52	respect	respect	NOUN
ejpam-7116	188	53	to	to	ADP
ejpam-7116	188	54	the	the	DET
ejpam-7116	188	55	standard	standard	NOUN
ejpam-7116	188	56	metric	metric	ADJ
ejpam-7116	188	57	ϱ	ϱ	NOUN
ejpam-7116	188	58	on	on	ADP
ejpam-7116	188	59	x	x	SYM
ejpam-7116	188	60	,	,	PUNCT
ejpam-7116	188	61	because	because	SCONJ
ejpam-7116	188	62	,	,	PUNCT
ejpam-7116	188	63	for	for	ADP
ejpam-7116	188	64	example	example	NOUN
ejpam-7116	188	65	ϱ(t	ϱ(t	PROPN
ejpam-7116	188	66	(	(	PUNCT
ejpam-7116	188	67	1	1	NUM
ejpam-7116	188	68	)	)	PUNCT
ejpam-7116	188	69	,	,	PUNCT
ejpam-7116	188	70	t	t	PROPN
ejpam-7116	188	71	(	(	PUNCT
ejpam-7116	188	72	2	2	NUM
ejpam-7116	188	73	)	)	PUNCT
ejpam-7116	188	74	)	)	PUNCT
ejpam-7116	189	1	=	=	PUNCT
ejpam-7116	190	1	|3−	|3−	ADV
ejpam-7116	190	2	6|	6|	NUM
ejpam-7116	190	3	>	>	X
ejpam-7116	190	4	|1−	|1−	INTJ
ejpam-7116	190	5	2|	2|	NUM
ejpam-7116	191	1	=	=	SYM
ejpam-7116	192	1	ϱ(1	ϱ(1	NOUN
ejpam-7116	192	2	,	,	PUNCT
ejpam-7116	192	3	2	2	NUM
ejpam-7116	192	4	)	)	PUNCT
ejpam-7116	192	5	.	.	PUNCT
ejpam-7116	193	1	we	we	PRON
ejpam-7116	193	2	also	also	ADV
ejpam-7116	193	3	have	have	VERB
ejpam-7116	193	4	that	that	DET
ejpam-7116	193	5	d(t	d(t	PROPN
ejpam-7116	193	6	(	(	PUNCT
ejpam-7116	193	7	1	1	NUM
ejpam-7116	193	8	)	)	PUNCT
ejpam-7116	193	9	,	,	PUNCT
ejpam-7116	193	10	t	t	PROPN
ejpam-7116	193	11	(	(	PUNCT
ejpam-7116	193	12	i	i	NOUN
ejpam-7116	193	13	)	)	PUNCT
ejpam-7116	193	14	)	)	PUNCT
ejpam-7116	194	1	=	=	PUNCT
ejpam-7116	194	2	1	1	NUM
ejpam-7116	194	3	≤	≤	NUM
ejpam-7116	194	4	4	4	NUM
ejpam-7116	194	5	3	3	NUM
ejpam-7116	194	6	=	=	SYM
ejpam-7116	194	7	1	1	NUM
ejpam-7116	194	8	3	3	NUM
ejpam-7116	194	9	(	(	PUNCT
ejpam-7116	194	10	d(1	d(1	PROPN
ejpam-7116	194	11	,	,	PUNCT
ejpam-7116	194	12	t	t	PROPN
ejpam-7116	194	13	(	(	PUNCT
ejpam-7116	194	14	1	1	NUM
ejpam-7116	194	15	)	)	PUNCT
ejpam-7116	194	16	)	)	PUNCT
ejpam-7116	195	1	+	+	CCONJ
ejpam-7116	195	2	d(i	d(i	PROPN
ejpam-7116	195	3	,	,	PUNCT
ejpam-7116	195	4	t	t	PROPN
ejpam-7116	195	5	(	(	PUNCT
ejpam-7116	195	6	i	i	NOUN
ejpam-7116	195	7	)	)	PUNCT
ejpam-7116	195	8	)	)	PUNCT
ejpam-7116	195	9	,	,	PUNCT
ejpam-7116	195	10	for	for	ADP
ejpam-7116	195	11	i	i	PROPN
ejpam-7116	195	12	=	=	SYM
ejpam-7116	195	13	2	2	NUM
ejpam-7116	195	14	,	,	PUNCT
ejpam-7116	195	15	5	5	NUM
ejpam-7116	195	16	,	,	PUNCT
ejpam-7116	195	17	d(t	d(t	NOUN
ejpam-7116	195	18	(	(	PUNCT
ejpam-7116	195	19	1	1	NUM
ejpam-7116	195	20	)	)	PUNCT
ejpam-7116	195	21	,	,	PUNCT
ejpam-7116	195	22	t	t	PROPN
ejpam-7116	195	23	(	(	PUNCT
ejpam-7116	195	24	6	6	NUM
ejpam-7116	195	25	)	)	PUNCT
ejpam-7116	195	26	)	)	PUNCT
ejpam-7116	196	1	=	=	SYM
ejpam-7116	197	1	1	1	NUM
ejpam-7116	197	2	≤	≤	NUM
ejpam-7116	197	3	1	1	NUM
ejpam-7116	197	4	=	=	SYM
ejpam-7116	197	5	1	1	NUM
ejpam-7116	197	6	3	3	NUM
ejpam-7116	197	7	(	(	PUNCT
ejpam-7116	197	8	d(1	d(1	PROPN
ejpam-7116	197	9	,	,	PUNCT
ejpam-7116	197	10	t	t	PROPN
ejpam-7116	197	11	(	(	PUNCT
ejpam-7116	197	12	1	1	NUM
ejpam-7116	197	13	)	)	PUNCT
ejpam-7116	197	14	)	)	PUNCT
ejpam-7116	198	1	+	+	CCONJ
ejpam-7116	199	1	d(6	d(6	PROPN
ejpam-7116	199	2	,	,	PUNCT
ejpam-7116	199	3	t	t	PROPN
ejpam-7116	199	4	(	(	PUNCT
ejpam-7116	199	5	6	6	NUM
ejpam-7116	199	6	)	)	PUNCT
ejpam-7116	199	7	)	)	PUNCT
ejpam-7116	199	8	and	and	CCONJ
ejpam-7116	199	9	d(t	d(t	PROPN
ejpam-7116	199	10	(	(	PUNCT
ejpam-7116	199	11	i	i	PROPN
ejpam-7116	199	12	)	)	PUNCT
ejpam-7116	199	13	,	,	PUNCT
ejpam-7116	199	14	t	t	PROPN
ejpam-7116	199	15	(	(	PUNCT
ejpam-7116	199	16	j	j	NOUN
ejpam-7116	199	17	)	)	PUNCT
ejpam-7116	199	18	)	)	PUNCT
ejpam-7116	200	1	=	=	SYM
ejpam-7116	200	2	0	0	X
ejpam-7116	201	1	≤	≤	NUM
ejpam-7116	201	2	1	1	NUM
ejpam-7116	201	3	3	3	NUM
ejpam-7116	201	4	(	(	PUNCT
ejpam-7116	201	5	d(i	d(i	PROPN
ejpam-7116	201	6	,	,	PUNCT
ejpam-7116	201	7	t	t	PROPN
ejpam-7116	201	8	(	(	PUNCT
ejpam-7116	201	9	i	i	NOUN
ejpam-7116	201	10	)	)	PUNCT
ejpam-7116	201	11	)	)	PUNCT
ejpam-7116	202	1	+	+	CCONJ
ejpam-7116	202	2	d(j	d(j	PROPN
ejpam-7116	202	3	,	,	PUNCT
ejpam-7116	202	4	t	t	PROPN
ejpam-7116	202	5	(	(	PUNCT
ejpam-7116	202	6	j	j	PROPN
ejpam-7116	202	7	)	)	PUNCT
ejpam-7116	202	8	)	)	PUNCT
ejpam-7116	202	9	,	,	PUNCT
ejpam-7116	202	10	for	for	ADP
ejpam-7116	202	11	i	i	PRON
ejpam-7116	202	12	,	,	PUNCT
ejpam-7116	202	13	j	j	PROPN
ejpam-7116	202	14	=	=	SYM
ejpam-7116	202	15	2	2	NUM
ejpam-7116	202	16	,	,	PUNCT
ejpam-7116	202	17	6	6	NUM
ejpam-7116	202	18	.	.	PUNCT
ejpam-7116	203	1	hence	hence	ADV
ejpam-7116	203	2	,	,	PUNCT
ejpam-7116	203	3	t	t	PROPN
ejpam-7116	203	4	is	be	AUX
ejpam-7116	203	5	also	also	ADV
ejpam-7116	203	6	a	a	DET
ejpam-7116	203	7	kannan	kannan	PROPN
ejpam-7116	203	8	contraction	contraction	NOUN
ejpam-7116	203	9	on	on	ADP
ejpam-7116	203	10	(	(	PUNCT
ejpam-7116	203	11	x	x	NOUN
ejpam-7116	203	12	,	,	PUNCT
ejpam-7116	203	13	d	d	NOUN
ejpam-7116	203	14	)	)	PUNCT
ejpam-7116	203	15	with	with	ADP
ejpam-7116	203	16	the	the	DET
ejpam-7116	203	17	constant	constant	ADJ
ejpam-7116	203	18	q	q	NOUN
ejpam-7116	203	19	=	=	SYM
ejpam-7116	203	20	1	1	NUM
ejpam-7116	203	21	3	3	NUM
ejpam-7116	203	22	,	,	PUNCT
ejpam-7116	203	23	so	so	ADV
ejpam-7116	203	24	by	by	ADP
ejpam-7116	203	25	theorem	theorem	NOUN
ejpam-7116	203	26	3.2	3.2	NUM
ejpam-7116	203	27	it	it	PRON
ejpam-7116	203	28	has	have	VERB
ejpam-7116	203	29	a	a	DET
ejpam-7116	203	30	unique	unique	ADJ
ejpam-7116	203	31	fixed	fix	VERB
ejpam-7116	203	32	point	point	NOUN
ejpam-7116	203	33	a	a	DET
ejpam-7116	203	34	=	=	ADJ
ejpam-7116	203	35	6	6	NUM
ejpam-7116	203	36	.	.	PUNCT
ejpam-7116	203	37	again	again	ADV
ejpam-7116	203	38	,	,	PUNCT
ejpam-7116	203	39	t	t	PROPN
ejpam-7116	203	40	is	be	AUX
ejpam-7116	203	41	not	not	PART
ejpam-7116	203	42	a	a	DET
ejpam-7116	203	43	kannan	kannan	PROPN
ejpam-7116	203	44	contraction	contraction	NOUN
ejpam-7116	203	45	on	on	ADP
ejpam-7116	203	46	(	(	PUNCT
ejpam-7116	203	47	x	x	NOUN
ejpam-7116	203	48	,	,	PUNCT
ejpam-7116	203	49	ϱ	ϱ	NOUN
ejpam-7116	203	50	)	)	PUNCT
ejpam-7116	203	51	,	,	PUNCT
ejpam-7116	203	52	as	as	ADP
ejpam-7116	203	53	ϱ(t	ϱ(t	PROPN
ejpam-7116	203	54	(	(	PUNCT
ejpam-7116	203	55	1	1	NUM
ejpam-7116	203	56	)	)	PUNCT
ejpam-7116	203	57	,	,	PUNCT
ejpam-7116	203	58	t	t	PROPN
ejpam-7116	203	59	(	(	PUNCT
ejpam-7116	203	60	2	2	NUM
ejpam-7116	203	61	)	)	PUNCT
ejpam-7116	203	62	)	)	PUNCT
ejpam-7116	204	1	=	=	PUNCT
ejpam-7116	205	1	|3−	|3−	ADV
ejpam-7116	205	2	6|	6|	NUM
ejpam-7116	205	3	=	=	SYM
ejpam-7116	205	4	3	3	NUM
ejpam-7116	205	5	=	=	SYM
ejpam-7116	205	6	1	1	NUM
ejpam-7116	205	7	2	2	NUM
ejpam-7116	205	8	(	(	PUNCT
ejpam-7116	205	9	ϱ(1	ϱ(1	NOUN
ejpam-7116	205	10	,	,	PUNCT
ejpam-7116	205	11	t	t	PROPN
ejpam-7116	205	12	(	(	PUNCT
ejpam-7116	205	13	1	1	NUM
ejpam-7116	205	14	)	)	PUNCT
ejpam-7116	205	15	)	)	PUNCT
ejpam-7116	206	1	+	+	CCONJ
ejpam-7116	206	2	ϱ(2	ϱ(2	PROPN
ejpam-7116	206	3	,	,	PUNCT
ejpam-7116	206	4	t	t	PROPN
ejpam-7116	206	5	(	(	PUNCT
ejpam-7116	206	6	2	2	NUM
ejpam-7116	206	7	)	)	PUNCT
ejpam-7116	206	8	)	)	PUNCT
ejpam-7116	206	9	.	.	PUNCT
ejpam-7116	207	1	4	4	X
ejpam-7116	207	2	.	.	X
ejpam-7116	207	3	conclusion	conclusion	NOUN
ejpam-7116	207	4	and	and	CCONJ
ejpam-7116	207	5	open	open	ADJ
ejpam-7116	207	6	problems	problem	NOUN
ejpam-7116	207	7	in	in	ADP
ejpam-7116	207	8	this	this	DET
ejpam-7116	207	9	paper	paper	NOUN
ejpam-7116	207	10	we	we	PRON
ejpam-7116	207	11	have	have	AUX
ejpam-7116	207	12	introduced	introduce	VERB
ejpam-7116	207	13	the	the	DET
ejpam-7116	207	14	concept	concept	NOUN
ejpam-7116	207	15	of	of	ADP
ejpam-7116	207	16	generalized	generalized	ADJ
ejpam-7116	207	17	branciari	branciari	NOUN
ejpam-7116	207	18	metric	metric	ADJ
ejpam-7116	207	19	space	space	NOUN
ejpam-7116	207	20	(	(	PUNCT
ejpam-7116	207	21	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	207	22	.	.	PUNCT
ejpam-7116	207	23	)	)	PUNCT
ejpam-7116	207	24	and	and	CCONJ
ejpam-7116	207	25	studied	study	VERB
ejpam-7116	207	26	its	its	PRON
ejpam-7116	207	27	basic	basic	ADJ
ejpam-7116	207	28	properties	property	NOUN
ejpam-7116	207	29	and	and	CCONJ
ejpam-7116	207	30	fixed	fix	VERB
ejpam-7116	207	31	point	point	NOUN
ejpam-7116	207	32	theorems	theorem	NOUN
ejpam-7116	207	33	on	on	ADP
ejpam-7116	207	34	such	such	ADJ
ejpam-7116	207	35	spaces	space	NOUN
ejpam-7116	207	36	.	.	PUNCT
ejpam-7116	208	1	these	these	DET
ejpam-7116	208	2	spaces	space	NOUN
ejpam-7116	208	3	are	be	AUX
ejpam-7116	208	4	a	a	DET
ejpam-7116	208	5	generalization	generalization	NOUN
ejpam-7116	208	6	of	of	ADP
ejpam-7116	208	7	rectangular	rectangular	ADJ
ejpam-7116	208	8	metric	metric	ADJ
ejpam-7116	208	9	spaces	space	NOUN
ejpam-7116	208	10	,	,	PUNCT
ejpam-7116	208	11	which	which	PRON
ejpam-7116	208	12	are	be	AUX
ejpam-7116	208	13	generally	generally	ADV
ejpam-7116	208	14	not	not	PART
ejpam-7116	208	15	metrizable	metrizable	ADJ
ejpam-7116	208	16	,	,	PUNCT
ejpam-7116	208	17	and	and	CCONJ
ejpam-7116	208	18	fixed	fix	VERB
ejpam-7116	208	19	point	point	NOUN
ejpam-7116	208	20	results	result	NOUN
ejpam-7116	208	21	on	on	ADP
ejpam-7116	208	22	them	they	PRON
ejpam-7116	208	23	can	can	AUX
ejpam-7116	208	24	not	not	PART
ejpam-7116	208	25	be	be	AUX
ejpam-7116	208	26	obtained	obtain	VERB
ejpam-7116	208	27	from	from	ADP
ejpam-7116	208	28	corresponding	correspond	VERB
ejpam-7116	208	29	results	result	NOUN
ejpam-7116	208	30	on	on	ADP
ejpam-7116	208	31	metric	metric	ADJ
ejpam-7116	208	32	spaces	space	NOUN
ejpam-7116	208	33	.	.	PUNCT
ejpam-7116	209	1	hence	hence	ADV
ejpam-7116	209	2	we	we	PRON
ejpam-7116	209	3	believe	believe	VERB
ejpam-7116	209	4	that	that	SCONJ
ejpam-7116	209	5	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	209	6	.	.	PROPN
ejpam-7116	209	7	are	be	AUX
ejpam-7116	209	8	a	a	DET
ejpam-7116	209	9	powerful	powerful	ADJ
ejpam-7116	209	10	and	and	CCONJ
ejpam-7116	209	11	interesting	interesting	ADJ
ejpam-7116	209	12	addition	addition	NOUN
ejpam-7116	209	13	to	to	ADP
ejpam-7116	209	14	the	the	DET
ejpam-7116	209	15	study	study	NOUN
ejpam-7116	209	16	of	of	ADP
ejpam-7116	209	17	fixed	fix	VERB
ejpam-7116	209	18	point	point	NOUN
ejpam-7116	209	19	theory	theory	NOUN
ejpam-7116	209	20	and	and	CCONJ
ejpam-7116	209	21	topology	topology	NOUN
ejpam-7116	209	22	of	of	ADP
ejpam-7116	209	23	distance	distance	NOUN
ejpam-7116	209	24	spaces	space	NOUN
ejpam-7116	209	25	,	,	PUNCT
ejpam-7116	209	26	as	as	SCONJ
ejpam-7116	209	27	we	we	PRON
ejpam-7116	209	28	will	will	AUX
ejpam-7116	209	29	illustrate	illustrate	VERB
ejpam-7116	209	30	by	by	ADP
ejpam-7116	209	31	various	various	ADJ
ejpam-7116	209	32	open	open	ADJ
ejpam-7116	209	33	problems	problem	NOUN
ejpam-7116	209	34	listed	list	VERB
ejpam-7116	209	35	in	in	ADP
ejpam-7116	209	36	this	this	DET
ejpam-7116	209	37	section	section	NOUN
ejpam-7116	209	38	.	.	PUNCT
ejpam-7116	210	1	as	as	ADV
ejpam-7116	210	2	generally	generally	ADV
ejpam-7116	210	3	in	in	ADP
ejpam-7116	210	4	metric	metric	ADJ
ejpam-7116	210	5	fixed	fix	VERB
ejpam-7116	210	6	point	point	NOUN
ejpam-7116	210	7	theory	theory	NOUN
ejpam-7116	210	8	,	,	PUNCT
ejpam-7116	210	9	further	further	ADJ
ejpam-7116	210	10	research	research	NOUN
ejpam-7116	210	11	scope	scope	NOUN
ejpam-7116	210	12	could	could	AUX
ejpam-7116	210	13	be	be	AUX
ejpam-7116	210	14	focused	focus	VERB
ejpam-7116	210	15	on	on	ADP
ejpam-7116	210	16	proving	prove	VERB
ejpam-7116	210	17	analogues	analogue	NOUN
ejpam-7116	210	18	of	of	ADP
ejpam-7116	210	19	standard	standard	ADJ
ejpam-7116	210	20	metric	metric	ADJ
ejpam-7116	210	21	fixed	fix	VERB
ejpam-7116	210	22	point	point	NOUN
ejpam-7116	210	23	theorems	theorem	NOUN
ejpam-7116	210	24	,	,	PUNCT
ejpam-7116	210	25	or	or	CCONJ
ejpam-7116	210	26	further	further	ADJ
ejpam-7116	210	27	generalization	generalization	NOUN
ejpam-7116	210	28	of	of	ADP
ejpam-7116	210	29	the	the	DET
ejpam-7116	210	30	underlying	underlying	ADJ
ejpam-7116	210	31	structure	structure	NOUN
ejpam-7116	210	32	of	of	ADP
ejpam-7116	210	33	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	210	34	.	.	PUNCT
ejpam-7116	211	1	(	(	PUNCT
ejpam-7116	211	2	or	or	CCONJ
ejpam-7116	211	3	both	both	PRON
ejpam-7116	211	4	)	)	PUNCT
ejpam-7116	211	5	.	.	PUNCT
ejpam-7116	212	1	a.	a.	NOUN
ejpam-7116	212	2	kostić	kostić	VERB
ejpam-7116	212	3	/	/	SYM
ejpam-7116	212	4	eur	eur	PROPN
ejpam-7116	212	5	.	.	PUNCT
ejpam-7116	213	1	j.	j.	PROPN
ejpam-7116	213	2	pure	pure	PROPN
ejpam-7116	213	3	appl	appl	PROPN
ejpam-7116	213	4	.	.	PROPN
ejpam-7116	213	5	math	math	PROPN
ejpam-7116	213	6	,	,	PUNCT
ejpam-7116	213	7	18	18	NUM
ejpam-7116	213	8	(	(	PUNCT
ejpam-7116	213	9	4	4	NUM
ejpam-7116	213	10	)	)	PUNCT
ejpam-7116	213	11	(	(	PUNCT
ejpam-7116	213	12	2025	2025	NUM
ejpam-7116	213	13	)	)	PUNCT
ejpam-7116	213	14	,	,	PUNCT
ejpam-7116	213	15	7116	7116	NUM
ejpam-7116	213	16	9	9	NUM
ejpam-7116	213	17	of	of	ADP
ejpam-7116	213	18	10	10	NUM
ejpam-7116	213	19	x0	x0	PROPN
ejpam-7116	213	20	x1	x1	PROPN
ejpam-7116	214	1	x2	x2	NOUN
ejpam-7116	214	2	x3	x3	PROPN
ejpam-7116	214	3	x4	x4	PROPN
ejpam-7116	214	4	figure	figure	NOUN
ejpam-7116	214	5	2	2	NUM
ejpam-7116	214	6	:	:	PUNCT
ejpam-7116	214	7	graphical	graphical	ADJ
ejpam-7116	214	8	representation	representation	NOUN
ejpam-7116	214	9	of	of	ADP
ejpam-7116	214	10	3	3	NUM
ejpam-7116	214	11	-	-	PUNCT
ejpam-7116	214	12	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	214	13	.	.	PUNCT
ejpam-7116	215	1	the	the	DET
ejpam-7116	215	2	length	length	NOUN
ejpam-7116	215	3	of	of	ADP
ejpam-7116	215	4	each	each	DET
ejpam-7116	215	5	edge	edge	NOUN
ejpam-7116	215	6	of	of	ADP
ejpam-7116	215	7	the	the	DET
ejpam-7116	215	8	graph	graph	NOUN
ejpam-7116	215	9	is	be	AUX
ejpam-7116	215	10	less	less	ADJ
ejpam-7116	215	11	than	than	ADP
ejpam-7116	215	12	the	the	DET
ejpam-7116	215	13	sum	sum	NOUN
ejpam-7116	215	14	of	of	ADP
ejpam-7116	215	15	lengths	length	NOUN
ejpam-7116	215	16	of	of	ADP
ejpam-7116	215	17	all	all	DET
ejpam-7116	215	18	other	other	ADJ
ejpam-7116	215	19	edges	edge	NOUN
ejpam-7116	215	20	.	.	PUNCT
ejpam-7116	216	1	now	now	ADV
ejpam-7116	216	2	we	we	PRON
ejpam-7116	216	3	state	state	VERB
ejpam-7116	216	4	a	a	DET
ejpam-7116	216	5	number	number	NOUN
ejpam-7116	216	6	of	of	ADP
ejpam-7116	216	7	specific	specific	ADJ
ejpam-7116	216	8	open	open	ADJ
ejpam-7116	216	9	problems	problem	NOUN
ejpam-7116	216	10	and	and	CCONJ
ejpam-7116	216	11	questions	question	NOUN
ejpam-7116	216	12	which	which	PRON
ejpam-7116	216	13	arise	arise	VERB
ejpam-7116	216	14	already	already	ADV
ejpam-7116	216	15	in	in	ADP
ejpam-7116	216	16	the	the	DET
ejpam-7116	216	17	initial	initial	ADJ
ejpam-7116	216	18	study	study	NOUN
ejpam-7116	216	19	of	of	ADP
ejpam-7116	216	20	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	216	21	.	.	PROPN
ejpam-7116	216	22	1	1	NUM
ejpam-7116	216	23	.	.	X
ejpam-7116	216	24	prove	prove	VERB
ejpam-7116	216	25	an	an	DET
ejpam-7116	216	26	analogue	analogue	NOUN
ejpam-7116	216	27	of	of	ADP
ejpam-7116	216	28	the	the	DET
ejpam-7116	216	29	fixed	fix	VERB
ejpam-7116	216	30	point	point	NOUN
ejpam-7116	216	31	theorem	theorem	NOUN
ejpam-7116	216	32	of	of	ADP
ejpam-7116	216	33	chatterjea	chatterjea	PROPN
ejpam-7116	217	1	[	[	X
ejpam-7116	217	2	11	11	NUM
ejpam-7116	217	3	]	]	PUNCT
ejpam-7116	217	4	on	on	ADP
ejpam-7116	217	5	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	217	6	.	.	PUNCT
ejpam-7116	218	1	in	in	ADP
ejpam-7116	218	2	particular	particular	ADJ
ejpam-7116	218	3	,	,	PUNCT
ejpam-7116	218	4	can	can	AUX
ejpam-7116	218	5	the	the	DET
ejpam-7116	218	6	theorem	theorem	NOUN
ejpam-7116	218	7	be	be	AUX
ejpam-7116	218	8	proved	prove	VERB
ejpam-7116	218	9	without	without	ADP
ejpam-7116	218	10	restricting	restrict	VERB
ejpam-7116	218	11	the	the	DET
ejpam-7116	218	12	domain	domain	NOUN
ejpam-7116	218	13	of	of	ADP
ejpam-7116	218	14	the	the	DET
ejpam-7116	218	15	contractive	contractive	ADJ
ejpam-7116	218	16	constant	constant	ADJ
ejpam-7116	218	17	(	(	PUNCT
ejpam-7116	218	18	[	[	X
ejpam-7116	218	19	0	0	NUM
ejpam-7116	218	20	,	,	PUNCT
ejpam-7116	218	21	12	12	NUM
ejpam-7116	218	22	)	)	PUNCT
ejpam-7116	218	23	)	)	PUNCT
ejpam-7116	218	24	in	in	ADP
ejpam-7116	218	25	the	the	DET
ejpam-7116	218	26	original	original	ADJ
ejpam-7116	218	27	version	version	NOUN
ejpam-7116	218	28	?	?	PUNCT
ejpam-7116	219	1	if	if	SCONJ
ejpam-7116	219	2	not	not	PART
ejpam-7116	219	3	,	,	PUNCT
ejpam-7116	219	4	what	what	PRON
ejpam-7116	219	5	is	be	AUX
ejpam-7116	219	6	the	the	DET
ejpam-7116	219	7	minimal	minimal	ADJ
ejpam-7116	219	8	upper	upper	ADJ
ejpam-7116	219	9	bound	bind	VERB
ejpam-7116	219	10	for	for	ADP
ejpam-7116	219	11	the	the	DET
ejpam-7116	219	12	contractive	contractive	ADJ
ejpam-7116	219	13	constant	constant	NOUN
ejpam-7116	219	14	?	?	PUNCT
ejpam-7116	220	1	does	do	AUX
ejpam-7116	220	2	there	there	PRON
ejpam-7116	220	3	exist	exist	VERB
ejpam-7116	220	4	a	a	DET
ejpam-7116	220	5	sharp	sharp	ADJ
ejpam-7116	220	6	upper	upper	ADJ
ejpam-7116	220	7	bound	bind	VERB
ejpam-7116	220	8	,	,	PUNCT
ejpam-7116	220	9	in	in	ADP
ejpam-7116	220	10	the	the	DET
ejpam-7116	220	11	sense	sense	NOUN
ejpam-7116	220	12	that	that	SCONJ
ejpam-7116	220	13	the	the	DET
ejpam-7116	220	14	theorem	theorem	NOUN
ejpam-7116	220	15	remains	remain	VERB
ejpam-7116	220	16	true	true	ADJ
ejpam-7116	220	17	when	when	SCONJ
ejpam-7116	220	18	the	the	DET
ejpam-7116	220	19	contractive	contractive	ADJ
ejpam-7116	220	20	constant	constant	ADJ
ejpam-7116	220	21	attains	attain	NOUN
ejpam-7116	220	22	that	that	PRON
ejpam-7116	220	23	upper	upper	ADJ
ejpam-7116	220	24	bound	bind	VERB
ejpam-7116	220	25	?	?	PUNCT
ejpam-7116	220	26	2	2	X
ejpam-7116	220	27	.	.	X
ejpam-7116	220	28	prove	prove	VERB
ejpam-7116	220	29	analogues	analogue	NOUN
ejpam-7116	220	30	of	of	ADP
ejpam-7116	220	31	hardy	hardy	ADJ
ejpam-7116	220	32	-	-	PUNCT
ejpam-7116	220	33	rogers	roger	NOUN
ejpam-7116	220	34	[	[	X
ejpam-7116	220	35	12	12	NUM
ejpam-7116	220	36	]	]	PUNCT
ejpam-7116	220	37	and	and	CCONJ
ejpam-7116	220	38	ćirić	ćirić	NOUN
ejpam-7116	220	39	[	[	X
ejpam-7116	220	40	13	13	NUM
ejpam-7116	220	41	]	]	PUNCT
ejpam-7116	220	42	fixed	fix	VERB
ejpam-7116	220	43	point	point	NOUN
ejpam-7116	220	44	theorems	theorem	NOUN
ejpam-7116	220	45	on	on	ADP
ejpam-7116	220	46	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	220	47	.	.	PUNCT
ejpam-7116	220	48	with	with	ADP
ejpam-7116	220	49	same	same	ADJ
ejpam-7116	220	50	discussion	discussion	NOUN
ejpam-7116	220	51	as	as	ADP
ejpam-7116	220	52	in	in	ADP
ejpam-7116	220	53	the	the	DET
ejpam-7116	220	54	first	first	ADJ
ejpam-7116	220	55	problem	problem	NOUN
ejpam-7116	220	56	.	.	PUNCT
ejpam-7116	221	1	3	3	X
ejpam-7116	221	2	.	.	X
ejpam-7116	221	3	prove	prove	VERB
ejpam-7116	221	4	a	a	DET
ejpam-7116	221	5	version	version	NOUN
ejpam-7116	221	6	of	of	ADP
ejpam-7116	221	7	fixed	fix	VERB
ejpam-7116	221	8	point	point	NOUN
ejpam-7116	221	9	theorem	theorem	VERB
ejpam-7116	221	10	with	with	ADP
ejpam-7116	221	11	“	"	PUNCT
ejpam-7116	221	12	simulation	simulation	NOUN
ejpam-7116	221	13	functions	function	NOUN
ejpam-7116	221	14	”	"	PUNCT
ejpam-7116	221	15	of	of	ADP
ejpam-7116	221	16	khojasteh	khojasteh	PROPN
ejpam-7116	221	17	et	et	PROPN
ejpam-7116	221	18	al	al	PROPN
ejpam-7116	221	19	.	.	PUNCT
ejpam-7116	222	1	[	[	X
ejpam-7116	222	2	14	14	NUM
ejpam-7116	222	3	]	]	PUNCT
ejpam-7116	222	4	in	in	ADP
ejpam-7116	222	5	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	222	6	.	.	PROPN
ejpam-7116	222	7	4	4	NUM
ejpam-7116	222	8	.	.	X
ejpam-7116	222	9	an	an	DET
ejpam-7116	222	10	et	et	NOUN
ejpam-7116	222	11	al	al	PROPN
ejpam-7116	222	12	.	.	PUNCT
ejpam-7116	223	1	[	[	X
ejpam-7116	223	2	7	7	X
ejpam-7116	223	3	]	]	PUNCT
ejpam-7116	223	4	proved	prove	VERB
ejpam-7116	223	5	that	that	SCONJ
ejpam-7116	223	6	a	a	DET
ejpam-7116	223	7	rectangular	rectangular	ADJ
ejpam-7116	223	8	metric	metric	ADJ
ejpam-7116	223	9	space	space	NOUN
ejpam-7116	223	10	is	be	AUX
ejpam-7116	223	11	metrizable	metrizable	ADJ
ejpam-7116	223	12	if	if	SCONJ
ejpam-7116	223	13	and	and	CCONJ
ejpam-7116	223	14	only	only	ADV
ejpam-7116	223	15	if	if	SCONJ
ejpam-7116	223	16	the	the	DET
ejpam-7116	223	17	limit	limit	NOUN
ejpam-7116	223	18	of	of	ADP
ejpam-7116	223	19	every	every	DET
ejpam-7116	223	20	convergent	convergent	NOUN
ejpam-7116	223	21	sequence	sequence	NOUN
ejpam-7116	223	22	in	in	ADP
ejpam-7116	223	23	it	it	PRON
ejpam-7116	223	24	is	be	AUX
ejpam-7116	223	25	unique	unique	ADJ
ejpam-7116	223	26	.	.	PUNCT
ejpam-7116	224	1	does	do	AUX
ejpam-7116	224	2	the	the	DET
ejpam-7116	224	3	same	same	ADJ
ejpam-7116	224	4	result	result	NOUN
ejpam-7116	224	5	hold	hold	NOUN
ejpam-7116	224	6	in	in	ADP
ejpam-7116	224	7	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	224	8	?	?	PROPN
ejpam-7116	224	9	5	5	NUM
ejpam-7116	224	10	.	.	PUNCT
ejpam-7116	225	1	as	as	ADP
ejpam-7116	225	2	in	in	ADP
ejpam-7116	225	3	[	[	X
ejpam-7116	225	4	4	4	X
ejpam-7116	225	5	]	]	PUNCT
ejpam-7116	225	6	we	we	PRON
ejpam-7116	225	7	can	can	AUX
ejpam-7116	225	8	further	far	ADV
ejpam-7116	225	9	generalize	generalize	VERB
ejpam-7116	225	10	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	225	11	.	.	PUNCT
ejpam-7116	226	1	by	by	ADP
ejpam-7116	226	2	considering	consider	VERB
ejpam-7116	226	3	an	an	DET
ejpam-7116	226	4	extended	extended	ADJ
ejpam-7116	226	5	“	"	PUNCT
ejpam-7116	226	6	polygonal	polygonal	ADJ
ejpam-7116	226	7	inequality	inequality	NOUN
ejpam-7116	226	8	”	"	PUNCT
ejpam-7116	226	9	(	(	PUNCT
ejpam-7116	226	10	for	for	ADP
ejpam-7116	226	11	some	some	DET
ejpam-7116	226	12	ν	ν	NOUN
ejpam-7116	226	13	≥	≥	NOUN
ejpam-7116	226	14	3	3	NUM
ejpam-7116	226	15	)	)	PUNCT
ejpam-7116	226	16	instead	instead	ADV
ejpam-7116	226	17	of	of	ADP
ejpam-7116	226	18	(	(	PUNCT
ejpam-7116	226	19	iii	iii	NOUN
ejpam-7116	226	20	)	)	PUNCT
ejpam-7116	226	21	in	in	ADP
ejpam-7116	226	22	definition	definition	NOUN
ejpam-7116	226	23	2.1	2.1	NUM
ejpam-7116	226	24	as	as	SCONJ
ejpam-7116	226	25	follows	follow	VERB
ejpam-7116	226	26	:	:	PUNCT
ejpam-7116	226	27	(	(	PUNCT
ejpam-7116	226	28	ν	ν	NOUN
ejpam-7116	226	29	-	-	PUNCT
ejpam-7116	226	30	iii	iii	NOUN
ejpam-7116	226	31	)	)	PUNCT
ejpam-7116	226	32	2d(x0	2d(x0	NUM
ejpam-7116	226	33	,	,	PUNCT
ejpam-7116	226	34	xν+1	xν+1	NOUN
ejpam-7116	226	35	)	)	PUNCT
ejpam-7116	226	36	≤	≤	NOUN
ejpam-7116	226	37	ν∑	ν∑	PUNCT
ejpam-7116	227	1	i=0	i=0	PROPN
ejpam-7116	227	2	ν+1∑	ν+1∑	PROPN
ejpam-7116	227	3	j	j	X
ejpam-7116	227	4	=	=	NOUN
ejpam-7116	227	5	i+1	i+1	NOUN
ejpam-7116	227	6	d(xi	d(xi	PROPN
ejpam-7116	227	7	,	,	PUNCT
ejpam-7116	227	8	xj	xj	PROPN
ejpam-7116	227	9	)	)	PUNCT
ejpam-7116	227	10	for	for	ADP
ejpam-7116	227	11	all	all	DET
ejpam-7116	227	12	x0	x0	PROPN
ejpam-7116	227	13	,	,	PUNCT
ejpam-7116	227	14	x1	x1	PROPN
ejpam-7116	227	15	,	,	PUNCT
ejpam-7116	227	16	.	.	PUNCT
ejpam-7116	227	17	.	.	PUNCT
ejpam-7116	227	18	.	.	PUNCT
ejpam-7116	228	1	,	,	PUNCT
ejpam-7116	228	2	xν	xν	INTJ
ejpam-7116	228	3	,	,	PUNCT
ejpam-7116	228	4	xν+1	xν+1	PROPN
ejpam-7116	228	5	∈	∈	PROPN
ejpam-7116	228	6	x	x	PUNCT
ejpam-7116	229	1	such	such	ADJ
ejpam-7116	229	2	that	that	PRON
ejpam-7116	229	3	xi	xi	PROPN
ejpam-7116	229	4	̸=	̸=	PROPN
ejpam-7116	229	5	xj	xj	PROPN
ejpam-7116	229	6	for	for	ADP
ejpam-7116	229	7	all	all	DET
ejpam-7116	229	8	1	1	NUM
ejpam-7116	229	9	≤	≤	NUM
ejpam-7116	229	10	i	i	PRON
ejpam-7116	229	11	<	<	X
ejpam-7116	229	12	j	j	PROPN
ejpam-7116	229	13	≤	≤	X
ejpam-7116	229	14	ν	ν	NOUN
ejpam-7116	229	15	and	and	CCONJ
ejpam-7116	229	16	x1	x1	NUM
ejpam-7116	229	17	,	,	PUNCT
ejpam-7116	229	18	.	.	PUNCT
ejpam-7116	229	19	.	.	PUNCT
ejpam-7116	230	1	.	.	PUNCT
ejpam-7116	231	1	,	,	PUNCT
ejpam-7116	231	2	xν	xν	NOUN
ejpam-7116	231	3	∈	∈	PROPN
ejpam-7116	231	4	x	x	SYM
ejpam-7116	231	5	\	\	PROPN
ejpam-7116	231	6	{	{	PUNCT
ejpam-7116	231	7	x0	x0	PROPN
ejpam-7116	231	8	,	,	PUNCT
ejpam-7116	231	9	xν+1	xν+1	PROPN
ejpam-7116	231	10	}	}	PUNCT
ejpam-7116	231	11	(	(	PUNCT
ejpam-7116	231	12	coefficient	coefficient	NOUN
ejpam-7116	231	13	2	2	NUM
ejpam-7116	231	14	is	be	AUX
ejpam-7116	231	15	used	use	VERB
ejpam-7116	231	16	for	for	ADP
ejpam-7116	231	17	convenience	convenience	NOUN
ejpam-7116	231	18	,	,	PUNCT
ejpam-7116	231	19	since	since	SCONJ
ejpam-7116	231	20	the	the	DET
ejpam-7116	231	21	same	same	ADJ
ejpam-7116	231	22	term	term	NOUN
ejpam-7116	231	23	appears	appear	VERB
ejpam-7116	231	24	in	in	ADP
ejpam-7116	231	25	the	the	DET
ejpam-7116	231	26	sum	sum	NOUN
ejpam-7116	231	27	on	on	ADP
ejpam-7116	231	28	the	the	DET
ejpam-7116	231	29	righthand	righthand	NOUN
ejpam-7116	231	30	side	side	NOUN
ejpam-7116	231	31	)	)	PUNCT
ejpam-7116	231	32	.	.	PUNCT
ejpam-7116	232	1	by	by	ADP
ejpam-7116	232	2	analogy	analogy	NOUN
ejpam-7116	232	3	with	with	ADP
ejpam-7116	232	4	[	[	X
ejpam-7116	232	5	4	4	NUM
ejpam-7116	232	6	]	]	PUNCT
ejpam-7116	232	7	,	,	PUNCT
ejpam-7116	232	8	we	we	PRON
ejpam-7116	232	9	will	will	AUX
ejpam-7116	232	10	say	say	VERB
ejpam-7116	232	11	that	that	SCONJ
ejpam-7116	232	12	(	(	PUNCT
ejpam-7116	232	13	x	x	X
ejpam-7116	232	14	,	,	PUNCT
ejpam-7116	232	15	d	d	NOUN
ejpam-7116	232	16	)	)	PUNCT
ejpam-7116	232	17	is	be	AUX
ejpam-7116	232	18	a	a	DET
ejpam-7116	232	19	ν	ν	NOUN
ejpam-7116	232	20	-	-	PUNCT
ejpam-7116	232	21	generalized	generalized	ADJ
ejpam-7116	232	22	branciari	branciari	NOUN
ejpam-7116	232	23	metric	metric	ADJ
ejpam-7116	232	24	space	space	NOUN
ejpam-7116	232	25	(	(	PUNCT
ejpam-7116	232	26	ν	ν	NOUN
ejpam-7116	232	27	-	-	PUNCT
ejpam-7116	232	28	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	232	29	.	.	PUNCT
ejpam-7116	232	30	in	in	ADP
ejpam-7116	232	31	short	short	ADJ
ejpam-7116	232	32	)	)	PUNCT
ejpam-7116	232	33	if	if	SCONJ
ejpam-7116	232	34	it	it	PRON
ejpam-7116	232	35	satisfies	satisfy	VERB
ejpam-7116	232	36	(	(	PUNCT
ejpam-7116	232	37	ν	ν	NOUN
ejpam-7116	232	38	-	-	PUNCT
ejpam-7116	232	39	iii	iii	NOUN
ejpam-7116	232	40	)	)	PUNCT
ejpam-7116	232	41	alongside	alongside	NOUN
ejpam-7116	232	42	(	(	PUNCT
ejpam-7116	232	43	i	i	NOUN
ejpam-7116	232	44	)	)	PUNCT
ejpam-7116	232	45	and	and	CCONJ
ejpam-7116	232	46	(	(	PUNCT
ejpam-7116	232	47	ii	ii	NOUN
ejpam-7116	232	48	)	)	PUNCT
ejpam-7116	232	49	of	of	ADP
ejpam-7116	232	50	definition	definition	NOUN
ejpam-7116	232	51	2.1	2.1	NUM
ejpam-7116	232	52	.	.	PUNCT
ejpam-7116	233	1	inequality	inequality	NOUN
ejpam-7116	233	2	(	(	PUNCT
ejpam-7116	233	3	ν	ν	NOUN
ejpam-7116	233	4	-	-	PUNCT
ejpam-7116	233	5	iii	iii	NOUN
ejpam-7116	233	6	)	)	PUNCT
ejpam-7116	233	7	can	can	AUX
ejpam-7116	233	8	be	be	AUX
ejpam-7116	233	9	geometrically	geometrically	ADV
ejpam-7116	233	10	interpreted	interpret	VERB
ejpam-7116	233	11	as	as	ADP
ejpam-7116	233	12	stating	state	VERB
ejpam-7116	233	13	that	that	DET
ejpam-7116	233	14	length	length	NOUN
ejpam-7116	233	15	of	of	ADP
ejpam-7116	233	16	each	each	DET
ejpam-7116	233	17	side	side	NOUN
ejpam-7116	233	18	of	of	ADP
ejpam-7116	233	19	a	a	DET
ejpam-7116	233	20	(	(	PUNCT
ejpam-7116	233	21	ν	ν	X
ejpam-7116	233	22	+	+	CCONJ
ejpam-7116	233	23	2)-gon	2)-gon	NUM
ejpam-7116	233	24	is	be	AUX
ejpam-7116	233	25	less	less	ADJ
ejpam-7116	233	26	than	than	ADP
ejpam-7116	233	27	the	the	DET
ejpam-7116	233	28	sum	sum	NOUN
ejpam-7116	233	29	of	of	ADP
ejpam-7116	233	30	lengths	length	NOUN
ejpam-7116	233	31	of	of	ADP
ejpam-7116	233	32	all	all	DET
ejpam-7116	233	33	its	its	PRON
ejpam-7116	233	34	remaining	remain	VERB
ejpam-7116	233	35	sides	side	NOUN
ejpam-7116	233	36	and	and	CCONJ
ejpam-7116	233	37	all	all	DET
ejpam-7116	233	38	its	its	PRON
ejpam-7116	233	39	diagonals	diagonal	NOUN
ejpam-7116	233	40	(	(	PUNCT
ejpam-7116	233	41	see	see	VERB
ejpam-7116	233	42	figure	figure	NOUN
ejpam-7116	233	43	2	2	NUM
ejpam-7116	233	44	below	below	ADV
ejpam-7116	233	45	)	)	PUNCT
ejpam-7116	233	46	.	.	PUNCT
ejpam-7116	234	1	our	our	PRON
ejpam-7116	234	2	next	next	ADJ
ejpam-7116	234	3	open	open	ADJ
ejpam-7116	234	4	problem	problem	NOUN
ejpam-7116	234	5	concerns	concern	NOUN
ejpam-7116	234	6	proving	prove	VERB
ejpam-7116	234	7	banach	banach	NOUN
ejpam-7116	234	8	and	and	CCONJ
ejpam-7116	234	9	kannan	kannan	PROPN
ejpam-7116	234	10	fixed	fix	VERB
ejpam-7116	234	11	point	point	NOUN
ejpam-7116	234	12	theorems	theorem	NOUN
ejpam-7116	234	13	on	on	ADP
ejpam-7116	234	14	ν	ν	PROPN
ejpam-7116	234	15	-	-	PUNCT
ejpam-7116	234	16	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	234	17	.	.	PROPN
ejpam-7116	234	18	6	6	NUM
ejpam-7116	234	19	.	.	PUNCT
ejpam-7116	234	20	suzuki	suzuki	PROPN
ejpam-7116	234	21	et	et	PROPN
ejpam-7116	234	22	al	al	PROPN
ejpam-7116	234	23	.	.	PUNCT
ejpam-7116	235	1	[	[	X
ejpam-7116	235	2	15	15	NUM
ejpam-7116	235	3	]	]	PUNCT
ejpam-7116	235	4	proved	prove	VERB
ejpam-7116	235	5	that	that	SCONJ
ejpam-7116	235	6	every	every	DET
ejpam-7116	235	7	3	3	NUM
ejpam-7116	235	8	-	-	PUNCT
ejpam-7116	235	9	generalized	generalize	VERB
ejpam-7116	235	10	metric	metric	ADJ
ejpam-7116	235	11	space	space	NOUN
ejpam-7116	235	12	is	be	AUX
ejpam-7116	235	13	metrizable	metrizable	ADJ
ejpam-7116	235	14	.	.	PUNCT
ejpam-7116	236	1	does	do	AUX
ejpam-7116	236	2	the	the	DET
ejpam-7116	236	3	same	same	ADJ
ejpam-7116	236	4	hold	hold	NOUN
ejpam-7116	236	5	for	for	ADP
ejpam-7116	236	6	3	3	NUM
ejpam-7116	236	7	-	-	PUNCT
ejpam-7116	236	8	g.b.m.s	g.b.m.s	NOUN
ejpam-7116	236	9	?	?	PUNCT
ejpam-7116	236	10	more	more	ADV
ejpam-7116	236	11	generally	generally	ADV
ejpam-7116	236	12	,	,	PUNCT
ejpam-7116	236	13	prove	prove	VERB
ejpam-7116	236	14	suzuki	suzuki	NOUN
ejpam-7116	236	15	-	-	NOUN
ejpam-7116	236	16	type	type	NOUN
ejpam-7116	236	17	[	[	X
ejpam-7116	236	18	16	16	NUM
ejpam-7116	236	19	]	]	X
ejpam-7116	236	20	metrization	metrization	NOUN
ejpam-7116	236	21	results	result	NOUN
ejpam-7116	236	22	for	for	ADP
ejpam-7116	236	23	ν	ν	NOUN
ejpam-7116	236	24	-	-	PUNCT
ejpam-7116	236	25	g.b.m.s	g.b.m.s	PROPN
ejpam-7116	236	26	.	.	PUNCT
ejpam-7116	237	1	a.	a.	PROPN
ejpam-7116	237	2	kostić	kostić	VERB
ejpam-7116	237	3	/	/	SYM
ejpam-7116	237	4	eur	eur	PROPN
ejpam-7116	237	5	.	.	PUNCT
ejpam-7116	238	1	j.	j.	PROPN
ejpam-7116	238	2	pure	pure	PROPN
ejpam-7116	238	3	appl	appl	PROPN
ejpam-7116	238	4	.	.	PROPN
ejpam-7116	238	5	math	math	PROPN
ejpam-7116	238	6	,	,	PUNCT
ejpam-7116	238	7	18	18	NUM
ejpam-7116	238	8	(	(	PUNCT
ejpam-7116	238	9	4	4	NUM
ejpam-7116	238	10	)	)	PUNCT
ejpam-7116	238	11	(	(	PUNCT
ejpam-7116	238	12	2025	2025	NUM
ejpam-7116	238	13	)	)	PUNCT
ejpam-7116	238	14	,	,	PUNCT
ejpam-7116	238	15	7116	7116	NUM
ejpam-7116	238	16	10	10	NUM
ejpam-7116	238	17	of	of	ADP
ejpam-7116	238	18	10	10	NUM
ejpam-7116	238	19	acknowledgements	acknowledgement	NOUN
ejpam-7116	238	20	this	this	DET
ejpam-7116	238	21	research	research	NOUN
ejpam-7116	238	22	has	have	AUX
ejpam-7116	238	23	been	be	AUX
ejpam-7116	238	24	supported	support	VERB
ejpam-7116	238	25	by	by	ADP
ejpam-7116	238	26	the	the	DET
ejpam-7116	238	27	ministry	ministry	PROPN
ejpam-7116	238	28	of	of	ADP
ejpam-7116	238	29	science	science	PROPN
ejpam-7116	238	30	,	,	PUNCT
ejpam-7116	238	31	technological	technological	ADJ
ejpam-7116	238	32	development	development	NOUN
ejpam-7116	238	33	and	and	CCONJ
ejpam-7116	238	34	innovation	innovation	NOUN
ejpam-7116	238	35	of	of	ADP
ejpam-7116	238	36	the	the	DET
ejpam-7116	238	37	republic	republic	NOUN
ejpam-7116	238	38	of	of	ADP
ejpam-7116	238	39	serbia	serbia	PROPN
ejpam-7116	238	40	,	,	PUNCT
ejpam-7116	238	41	contract	contract	NOUN
ejpam-7116	238	42	no	no	INTJ
ejpam-7116	238	43	.	.	PUNCT
ejpam-7116	239	1	451	451	NUM
ejpam-7116	239	2	-	-	SYM
ejpam-7116	239	3	03	03	NUM
ejpam-7116	239	4	-	-	PUNCT
ejpam-7116	239	5	136/2025	136/2025	NUM
ejpam-7116	239	6	-	-	PUNCT
ejpam-7116	239	7	03/200124	03/200124	NOUN
ejpam-7116	239	8	.	.	PUNCT
ejpam-7116	240	1	references	reference	NOUN
ejpam-7116	240	2	[	[	X
ejpam-7116	240	3	1	1	X
ejpam-7116	240	4	]	]	PUNCT
ejpam-7116	240	5	s.	s.	PROPN
ejpam-7116	240	6	banach	banach	PROPN
ejpam-7116	240	7	.	.	PUNCT
ejpam-7116	241	1	sur	sur	PROPN
ejpam-7116	241	2	les	les	PROPN
ejpam-7116	241	3	opérations	opération	NOUN
ejpam-7116	241	4	dans	dan	NOUN
ejpam-7116	241	5	les	les	X
ejpam-7116	241	6	ensembles	ensemble	NOUN
ejpam-7116	241	7	abstraits	abstrait	NOUN
ejpam-7116	241	8	et	et	PROPN
ejpam-7116	241	9	leur	leur	X
ejpam-7116	241	10	application	application	PROPN
ejpam-7116	241	11	aux	aux	PROPN
ejpam-7116	241	12	équations	équations	PROPN
ejpam-7116	241	13	intégrales	intégrale	NOUN
ejpam-7116	241	14	.	.	PUNCT
ejpam-7116	242	1	fundamenta	fundamenta	PROPN
ejpam-7116	242	2	mathematicae	mathematicae	PROPN
ejpam-7116	242	3	,	,	PUNCT
ejpam-7116	242	4	3:133–181	3:133–181	NUM
ejpam-7116	242	5	,	,	PUNCT
ejpam-7116	242	6	1922	1922	NUM
ejpam-7116	242	7	.	.	PUNCT
ejpam-7116	243	1	[	[	X
ejpam-7116	243	2	2	2	X
ejpam-7116	243	3	]	]	PUNCT
ejpam-7116	243	4	t.	t.	PROPN
ejpam-7116	243	5	v.	v.	PROPN
ejpam-7116	243	6	an	an	PRON
ejpam-7116	243	7	,	,	PUNCT
ejpam-7116	243	8	n.	n.	NOUN
ejpam-7116	243	9	v.	v.	ADP
ejpam-7116	243	10	dung	dung	PROPN
ejpam-7116	243	11	,	,	PUNCT
ejpam-7116	243	12	z.	z.	PROPN
ejpam-7116	243	13	kadelburg	kadelburg	PROPN
ejpam-7116	243	14	,	,	PUNCT
ejpam-7116	243	15	and	and	CCONJ
ejpam-7116	243	16	s.	s.	PROPN
ejpam-7116	243	17	radenović	radenović	PROPN
ejpam-7116	243	18	.	.	PUNCT
ejpam-7116	244	1	various	various	ADJ
ejpam-7116	244	2	generalizations	generalization	NOUN
ejpam-7116	244	3	of	of	ADP
ejpam-7116	244	4	metric	metric	ADJ
ejpam-7116	244	5	spaces	space	NOUN
ejpam-7116	244	6	and	and	CCONJ
ejpam-7116	244	7	fixed	fix	VERB
ejpam-7116	244	8	point	point	NOUN
ejpam-7116	244	9	theorems	theorem	NOUN
ejpam-7116	244	10	.	.	PUNCT
ejpam-7116	245	1	revista	revista	PROPN
ejpam-7116	245	2	de	de	X
ejpam-7116	245	3	la	la	PROPN
ejpam-7116	245	4	real	real	PROPN
ejpam-7116	245	5	academia	academia	PROPN
ejpam-7116	245	6	de	de	PROPN
ejpam-7116	245	7	ciencias	ciencias	PROPN
ejpam-7116	245	8	exactas	exacta	NOUN
ejpam-7116	245	9	,	,	PUNCT
ejpam-7116	245	10	físicas	físicas	PROPN
ejpam-7116	245	11	y	y	PROPN
ejpam-7116	245	12	naturales	naturales	PROPN
ejpam-7116	245	13	.	.	PUNCT
ejpam-7116	246	1	serie	serie	PROPN
ejpam-7116	246	2	a.	a.	PROPN
ejpam-7116	246	3	matemáticas	matemáticas	PROPN
ejpam-7116	246	4	(	(	PUNCT
ejpam-7116	246	5	racsam	racsam	PROPN
ejpam-7116	246	6	)	)	PUNCT
ejpam-7116	246	7	,	,	PUNCT
ejpam-7116	246	8	109:175–198	109:175–198	NUM
ejpam-7116	246	9	,	,	PUNCT
ejpam-7116	246	10	2015	2015	NUM
ejpam-7116	246	11	.	.	PUNCT
ejpam-7116	247	1	[	[	X
ejpam-7116	247	2	3	3	X
ejpam-7116	247	3	]	]	PUNCT
ejpam-7116	247	4	v.	v.	ADP
ejpam-7116	247	5	berinde	berinde	NOUN
ejpam-7116	247	6	and	and	CCONJ
ejpam-7116	247	7	m.	m.	NOUN
ejpam-7116	247	8	choban	choban	PROPN
ejpam-7116	247	9	.	.	PUNCT
ejpam-7116	248	1	generalized	generalized	ADJ
ejpam-7116	248	2	distances	distance	NOUN
ejpam-7116	248	3	and	and	CCONJ
ejpam-7116	248	4	their	their	PRON
ejpam-7116	248	5	associate	associate	ADJ
ejpam-7116	248	6	metrics	metric	NOUN
ejpam-7116	248	7	.	.	PUNCT
ejpam-7116	249	1	impact	impact	NOUN
ejpam-7116	249	2	on	on	ADP
ejpam-7116	249	3	fixed	fix	VERB
ejpam-7116	249	4	point	point	NOUN
ejpam-7116	249	5	theory	theory	NOUN
ejpam-7116	249	6	.	.	PUNCT
ejpam-7116	250	1	creative	creative	ADJ
ejpam-7116	250	2	mathematics	mathematic	NOUN
ejpam-7116	250	3	and	and	CCONJ
ejpam-7116	250	4	informatics	informatic	NOUN
ejpam-7116	250	5	,	,	PUNCT
ejpam-7116	250	6	22:23–32	22:23–32	NUM
ejpam-7116	250	7	,	,	PUNCT
ejpam-7116	250	8	2013	2013	NUM
ejpam-7116	250	9	.	.	PUNCT
ejpam-7116	251	1	[	[	X
ejpam-7116	251	2	4	4	NUM
ejpam-7116	251	3	]	]	PUNCT
ejpam-7116	251	4	a.	a.	NOUN
ejpam-7116	251	5	branciari	branciari	PROPN
ejpam-7116	251	6	.	.	PUNCT
ejpam-7116	252	1	a	a	DET
ejpam-7116	252	2	fixed	fix	VERB
ejpam-7116	252	3	point	point	NOUN
ejpam-7116	252	4	theorem	theorem	NOUN
ejpam-7116	252	5	of	of	ADP
ejpam-7116	252	6	banach	banach	NOUN
ejpam-7116	252	7	-	-	PUNCT
ejpam-7116	252	8	caccioppoli	caccioppoli	NOUN
ejpam-7116	252	9	type	type	NOUN
ejpam-7116	252	10	on	on	ADP
ejpam-7116	252	11	a	a	DET
ejpam-7116	252	12	class	class	NOUN
ejpam-7116	252	13	of	of	ADP
ejpam-7116	252	14	generalized	generalized	ADJ
ejpam-7116	252	15	metric	metric	ADJ
ejpam-7116	252	16	spaces	space	NOUN
ejpam-7116	252	17	.	.	PUNCT
ejpam-7116	253	1	publications	publication	NOUN
ejpam-7116	253	2	mathematicae	mathematicae	PROPN
ejpam-7116	253	3	debrecen	debrecen	PROPN
ejpam-7116	253	4	,	,	PUNCT
ejpam-7116	253	5	57(1	57(1	PROPN
ejpam-7116	253	6	-	-	PUNCT
ejpam-7116	253	7	2):31–37	2):31–37	NUM
ejpam-7116	253	8	,	,	PUNCT
ejpam-7116	253	9	2000	2000	NUM
ejpam-7116	253	10	.	.	PUNCT
ejpam-7116	254	1	[	[	X
ejpam-7116	254	2	5	5	X
ejpam-7116	254	3	]	]	PUNCT
ejpam-7116	254	4	z.	z.	PROPN
ejpam-7116	254	5	kadelburg	kadelburg	PROPN
ejpam-7116	254	6	and	and	CCONJ
ejpam-7116	254	7	s.	s.	PROPN
ejpam-7116	254	8	radenović	radenović	PROPN
ejpam-7116	254	9	.	.	PUNCT
ejpam-7116	255	1	on	on	ADP
ejpam-7116	255	2	generalized	generalized	ADJ
ejpam-7116	255	3	metric	metric	ADJ
ejpam-7116	255	4	spaces	space	NOUN
ejpam-7116	255	5	:	:	PUNCT
ejpam-7116	255	6	a	a	DET
ejpam-7116	255	7	survey	survey	NOUN
ejpam-7116	255	8	.	.	PUNCT
ejpam-7116	256	1	twms	twms	PROPN
ejpam-7116	256	2	journal	journal	PROPN
ejpam-7116	256	3	of	of	ADP
ejpam-7116	256	4	pure	pure	ADJ
ejpam-7116	256	5	and	and	CCONJ
ejpam-7116	256	6	applied	applied	ADJ
ejpam-7116	256	7	mathematics	mathematic	NOUN
ejpam-7116	256	8	,	,	PUNCT
ejpam-7116	256	9	5(1):3–13	5(1):3–13	NUM
ejpam-7116	256	10	,	,	PUNCT
ejpam-7116	256	11	2014	2014	NUM
ejpam-7116	256	12	.	.	PUNCT
ejpam-7116	257	1	[	[	X
ejpam-7116	257	2	6	6	NUM
ejpam-7116	257	3	]	]	PUNCT
ejpam-7116	257	4	i.	i.	PROPN
ejpam-7116	257	5	r.	r.	PROPN
ejpam-7116	257	6	sarma	sarma	PROPN
ejpam-7116	257	7	,	,	PUNCT
ejpam-7116	257	8	j.	j.	PROPN
ejpam-7116	257	9	m.	m.	PROPN
ejpam-7116	257	10	rao	rao	PROPN
ejpam-7116	257	11	,	,	PUNCT
ejpam-7116	257	12	and	and	CCONJ
ejpam-7116	257	13	s.	s.	PROPN
ejpam-7116	257	14	s.	s.	PROPN
ejpam-7116	257	15	rao	rao	PROPN
ejpam-7116	257	16	.	.	PUNCT
ejpam-7116	258	1	contractions	contraction	NOUN
ejpam-7116	258	2	over	over	ADP
ejpam-7116	258	3	generalized	generalized	ADJ
ejpam-7116	258	4	metric	metric	ADJ
ejpam-7116	258	5	spaces	space	NOUN
ejpam-7116	258	6	.	.	PUNCT
ejpam-7116	259	1	journal	journal	PROPN
ejpam-7116	259	2	of	of	ADP
ejpam-7116	259	3	nonlinear	nonlinear	ADJ
ejpam-7116	259	4	science	science	NOUN
ejpam-7116	259	5	and	and	CCONJ
ejpam-7116	259	6	applications	application	NOUN
ejpam-7116	259	7	,	,	PUNCT
ejpam-7116	259	8	2(3):180–182	2(3):180–182	NUM
ejpam-7116	259	9	,	,	PUNCT
ejpam-7116	259	10	2009	2009	NUM
ejpam-7116	259	11	.	.	PUNCT
ejpam-7116	260	1	[	[	X
ejpam-7116	260	2	7	7	X
ejpam-7116	260	3	]	]	PUNCT
ejpam-7116	260	4	t.	t.	PROPN
ejpam-7116	260	5	v.	v.	PROPN
ejpam-7116	260	6	an	an	PRON
ejpam-7116	260	7	,	,	PUNCT
ejpam-7116	260	8	n.	n.	NOUN
ejpam-7116	260	9	v.	v.	ADP
ejpam-7116	260	10	dung	dung	NOUN
ejpam-7116	260	11	,	,	PUNCT
ejpam-7116	260	12	and	and	CCONJ
ejpam-7116	260	13	v.	v.	ADP
ejpam-7116	260	14	t.	t.	PROPN
ejpam-7116	260	15	l.	l.	PROPN
ejpam-7116	260	16	hang	hang	PROPN
ejpam-7116	260	17	.	.	PUNCT
ejpam-7116	261	1	remarks	remark	NOUN
ejpam-7116	261	2	on	on	ADP
ejpam-7116	261	3	frink	frink	PROPN
ejpam-7116	261	4	’s	’s	PART
ejpam-7116	261	5	metrization	metrization	NOUN
ejpam-7116	261	6	technique	technique	NOUN
ejpam-7116	261	7	and	and	CCONJ
ejpam-7116	261	8	applications	application	NOUN
ejpam-7116	261	9	.	.	PUNCT
ejpam-7116	262	1	fixed	fix	VERB
ejpam-7116	262	2	point	point	NOUN
ejpam-7116	262	3	theory	theory	NOUN
ejpam-7116	262	4	,	,	PUNCT
ejpam-7116	262	5	20:157–176	20:157–176	PROPN
ejpam-7116	262	6	,	,	PUNCT
ejpam-7116	262	7	2019	2019	NUM
ejpam-7116	262	8	.	.	PUNCT
ejpam-7116	263	1	[	[	X
ejpam-7116	263	2	8	8	X
ejpam-7116	263	3	]	]	X
ejpam-7116	263	4	w.	w.	PROPN
ejpam-7116	263	5	a.	a.	PROPN
ejpam-7116	263	6	kirk	kirk	PROPN
ejpam-7116	263	7	and	and	CCONJ
ejpam-7116	263	8	n.	n.	PROPN
ejpam-7116	263	9	shahzad	shahzad	PROPN
ejpam-7116	263	10	.	.	PUNCT
ejpam-7116	264	1	fixed	fix	VERB
ejpam-7116	264	2	point	point	NOUN
ejpam-7116	264	3	theory	theory	NOUN
ejpam-7116	264	4	in	in	ADP
ejpam-7116	264	5	distance	distance	NOUN
ejpam-7116	264	6	spaces	space	NOUN
ejpam-7116	264	7	.	.	PUNCT
ejpam-7116	265	1	springer	springer	NOUN
ejpam-7116	265	2	,	,	PUNCT
ejpam-7116	265	3	cham	cham	PROPN
ejpam-7116	265	4	,	,	PUNCT
ejpam-7116	265	5	2014	2014	NUM
ejpam-7116	265	6	.	.	PUNCT
ejpam-7116	266	1	[	[	X
ejpam-7116	266	2	9	9	NUM
ejpam-7116	266	3	]	]	PUNCT
ejpam-7116	266	4	r.	r.	PROPN
ejpam-7116	266	5	kannan	kannan	PROPN
ejpam-7116	266	6	.	.	PUNCT
ejpam-7116	267	1	some	some	DET
ejpam-7116	267	2	results	result	NOUN
ejpam-7116	267	3	on	on	ADP
ejpam-7116	267	4	fixed	fix	VERB
ejpam-7116	267	5	points	point	NOUN
ejpam-7116	267	6	.	.	PUNCT
ejpam-7116	268	1	bulletin	bulletin	NOUN
ejpam-7116	268	2	of	of	ADP
ejpam-7116	268	3	the	the	DET
ejpam-7116	268	4	calcutta	calcutta	NOUN
ejpam-7116	268	5	mathematical	mathematical	ADJ
ejpam-7116	268	6	society	society	NOUN
ejpam-7116	268	7	,	,	PUNCT
ejpam-7116	268	8	60:71–76	60:71–76	NUM
ejpam-7116	268	9	,	,	PUNCT
ejpam-7116	268	10	1968	1968	NUM
ejpam-7116	268	11	.	.	PUNCT
ejpam-7116	269	1	[	[	X
ejpam-7116	269	2	10	10	NUM
ejpam-7116	269	3	]	]	X
ejpam-7116	269	4	p.	p.	NOUN
ejpam-7116	269	5	mladenović	mladenović	PROPN
ejpam-7116	269	6	.	.	PUNCT
ejpam-7116	270	1	combinatorics	combinatoric	NOUN
ejpam-7116	270	2	:	:	PUNCT
ejpam-7116	270	3	a	a	DET
ejpam-7116	270	4	problem	problem	NOUN
ejpam-7116	270	5	-	-	PUNCT
ejpam-7116	270	6	based	base	VERB
ejpam-7116	270	7	approach	approach	NOUN
ejpam-7116	270	8	.	.	PUNCT
ejpam-7116	271	1	springer	springer	NOUN
ejpam-7116	271	2	,	,	PUNCT
ejpam-7116	271	3	cham	cham	PROPN
ejpam-7116	271	4	,	,	PUNCT
ejpam-7116	271	5	2019	2019	NUM
ejpam-7116	271	6	.	.	PUNCT
ejpam-7116	272	1	[	[	X
ejpam-7116	272	2	11	11	NUM
ejpam-7116	272	3	]	]	PUNCT
ejpam-7116	272	4	s.	s.	PROPN
ejpam-7116	272	5	k.	k.	PROPN
ejpam-7116	272	6	chatterjea	chatterjea	PROPN
ejpam-7116	272	7	.	.	PUNCT
ejpam-7116	273	1	fixed	fix	VERB
ejpam-7116	273	2	point	point	NOUN
ejpam-7116	273	3	theorems	theorem	NOUN
ejpam-7116	273	4	.	.	PUNCT
ejpam-7116	273	5	comptes	compte	NOUN
ejpam-7116	273	6	rendus	rendus	PROPN
ejpam-7116	273	7	de	de	PROPN
ejpam-7116	273	8	l’académie	l’académie	PROPN
ejpam-7116	273	9	bulgare	bulgare	PROPN
ejpam-7116	273	10	des	des	PROPN
ejpam-7116	273	11	sciences	sciences	PROPN
ejpam-7116	273	12	,	,	PUNCT
ejpam-7116	273	13	25:727–730	25:727–730	NUM
ejpam-7116	273	14	,	,	PUNCT
ejpam-7116	273	15	1972	1972	NUM
ejpam-7116	273	16	.	.	PUNCT
ejpam-7116	274	1	[	[	X
ejpam-7116	274	2	12	12	NUM
ejpam-7116	274	3	]	]	X
ejpam-7116	274	4	g.	g.	PROPN
ejpam-7116	274	5	e.	e.	PROPN
ejpam-7116	274	6	hardy	hardy	PROPN
ejpam-7116	274	7	and	and	CCONJ
ejpam-7116	274	8	t.	t.	PROPN
ejpam-7116	274	9	d.	d.	PROPN
ejpam-7116	274	10	rogers	rogers	PROPN
ejpam-7116	274	11	.	.	PUNCT
ejpam-7116	275	1	a	a	DET
ejpam-7116	275	2	generalization	generalization	NOUN
ejpam-7116	275	3	of	of	ADP
ejpam-7116	275	4	a	a	DET
ejpam-7116	275	5	fixed	fix	VERB
ejpam-7116	275	6	point	point	NOUN
ejpam-7116	275	7	theorem	theorem	NOUN
ejpam-7116	275	8	of	of	ADP
ejpam-7116	275	9	reich	reich	PROPN
ejpam-7116	275	10	.	.	PUNCT
ejpam-7116	276	1	canadian	canadian	PROPN
ejpam-7116	276	2	mathematical	mathematical	ADJ
ejpam-7116	276	3	bulletin	bulletin	NOUN
ejpam-7116	276	4	,	,	PUNCT
ejpam-7116	276	5	16(2):201–206	16(2):201–206	PROPN
ejpam-7116	276	6	,	,	PUNCT
ejpam-7116	276	7	1973	1973	NUM
ejpam-7116	276	8	.	.	PUNCT
ejpam-7116	277	1	[	[	X
ejpam-7116	277	2	13	13	NUM
ejpam-7116	277	3	]	]	X
ejpam-7116	277	4	lj	lj	PROPN
ejpam-7116	277	5	.	.	PUNCT
ejpam-7116	277	6	b.	b.	PROPN
ejpam-7116	277	7	ćirić	ćirić	PROPN
ejpam-7116	277	8	.	.	PUNCT
ejpam-7116	278	1	a	a	DET
ejpam-7116	278	2	generalization	generalization	NOUN
ejpam-7116	278	3	of	of	ADP
ejpam-7116	278	4	banach	banach	NOUN
ejpam-7116	278	5	’s	’s	PART
ejpam-7116	278	6	contraction	contraction	NOUN
ejpam-7116	278	7	principle	principle	NOUN
ejpam-7116	278	8	.	.	PUNCT
ejpam-7116	279	1	proceedings	proceeding	NOUN
ejpam-7116	279	2	of	of	ADP
ejpam-7116	279	3	the	the	DET
ejpam-7116	279	4	american	american	PROPN
ejpam-7116	279	5	mathematical	mathematical	PROPN
ejpam-7116	279	6	society	society	NOUN
ejpam-7116	279	7	,	,	PUNCT
ejpam-7116	279	8	45:267–273	45:267–273	NUM
ejpam-7116	279	9	,	,	PUNCT
ejpam-7116	279	10	1974	1974	NUM
ejpam-7116	279	11	.	.	PUNCT
ejpam-7116	280	1	[	[	X
ejpam-7116	280	2	14	14	NUM
ejpam-7116	280	3	]	]	X
ejpam-7116	280	4	f.	f.	PROPN
ejpam-7116	280	5	khojasteh	khojasteh	PROPN
ejpam-7116	280	6	,	,	PUNCT
ejpam-7116	280	7	s.	s.	PROPN
ejpam-7116	280	8	shukla	shukla	PROPN
ejpam-7116	280	9	,	,	PUNCT
ejpam-7116	280	10	and	and	CCONJ
ejpam-7116	280	11	s.	s.	PROPN
ejpam-7116	280	12	radenović	radenović	PROPN
ejpam-7116	280	13	.	.	PUNCT
ejpam-7116	281	1	a	a	DET
ejpam-7116	281	2	new	new	ADJ
ejpam-7116	281	3	approach	approach	NOUN
ejpam-7116	281	4	to	to	ADP
ejpam-7116	281	5	the	the	DET
ejpam-7116	281	6	study	study	NOUN
ejpam-7116	281	7	of	of	ADP
ejpam-7116	281	8	fixed	fix	VERB
ejpam-7116	281	9	point	point	NOUN
ejpam-7116	281	10	theory	theory	NOUN
ejpam-7116	281	11	for	for	ADP
ejpam-7116	281	12	simulation	simulation	NOUN
ejpam-7116	281	13	functions	function	NOUN
ejpam-7116	281	14	.	.	PUNCT
ejpam-7116	282	1	filomat	filomat	NOUN
ejpam-7116	282	2	,	,	PUNCT
ejpam-7116	282	3	29(6):1189–1194	29(6):1189–1194	PROPN
ejpam-7116	282	4	,	,	PUNCT
ejpam-7116	282	5	2015	2015	NUM
ejpam-7116	282	6	.	.	PUNCT
ejpam-7116	283	1	[	[	X
ejpam-7116	283	2	15	15	NUM
ejpam-7116	283	3	]	]	PUNCT
ejpam-7116	283	4	t.	t.	PROPN
ejpam-7116	283	5	suzuki	suzuki	PROPN
ejpam-7116	283	6	,	,	PUNCT
ejpam-7116	283	7	b.	b.	PROPN
ejpam-7116	283	8	alamri	alamri	PROPN
ejpam-7116	283	9	,	,	PUNCT
ejpam-7116	283	10	and	and	CCONJ
ejpam-7116	283	11	m.	m.	PROPN
ejpam-7116	283	12	kikkawa	kikkawa	PROPN
ejpam-7116	283	13	.	.	PUNCT
ejpam-7116	284	1	only	only	ADV
ejpam-7116	284	2	3	3	NUM
ejpam-7116	284	3	-	-	PUNCT
ejpam-7116	284	4	generalized	generalize	VERB
ejpam-7116	284	5	metric	metric	ADJ
ejpam-7116	284	6	spaces	space	NOUN
ejpam-7116	284	7	have	have	VERB
ejpam-7116	284	8	a	a	DET
ejpam-7116	284	9	compatible	compatible	ADJ
ejpam-7116	284	10	symmetric	symmetric	ADJ
ejpam-7116	284	11	topology	topology	NOUN
ejpam-7116	284	12	.	.	PUNCT
ejpam-7116	285	1	revista	revista	PROPN
ejpam-7116	285	2	de	de	X
ejpam-7116	285	3	la	la	PROPN
ejpam-7116	285	4	real	real	PROPN
ejpam-7116	285	5	academia	academia	PROPN
ejpam-7116	285	6	de	de	PROPN
ejpam-7116	285	7	ciencias	ciencias	PROPN
ejpam-7116	285	8	exactas	exacta	NOUN
ejpam-7116	285	9	,	,	PUNCT
ejpam-7116	285	10	físicas	físicas	PROPN
ejpam-7116	285	11	y	y	PROPN
ejpam-7116	285	12	naturales	naturales	PROPN
ejpam-7116	285	13	.	.	PUNCT
ejpam-7116	286	1	serie	serie	PROPN
ejpam-7116	286	2	a.	a.	PROPN
ejpam-7116	286	3	matemáticas	matemáticas	PROPN
ejpam-7116	286	4	(	(	PUNCT
ejpam-7116	286	5	racsam	racsam	PROPN
ejpam-7116	286	6	)	)	PUNCT
ejpam-7116	286	7	,	,	PUNCT
ejpam-7116	286	8	13:510–517	13:510–517	PROPN
ejpam-7116	286	9	,	,	PUNCT
ejpam-7116	286	10	2015	2015	NUM
ejpam-7116	286	11	.	.	PUNCT
ejpam-7116	287	1	[	[	X
ejpam-7116	287	2	16	16	NUM
ejpam-7116	287	3	]	]	PUNCT
ejpam-7116	287	4	t.	t.	PROPN
ejpam-7116	287	5	suzuki	suzuki	PROPN
ejpam-7116	287	6	.	.	PUNCT
ejpam-7116	288	1	some	some	DET
ejpam-7116	288	2	metrization	metrization	NOUN
ejpam-7116	288	3	problem	problem	NOUN
ejpam-7116	288	4	on	on	ADP
ejpam-7116	288	5	ν	ν	ADJ
ejpam-7116	288	6	-	-	ADJ
ejpam-7116	288	7	generalized	generalize	VERB
ejpam-7116	288	8	metric	metric	ADJ
ejpam-7116	288	9	spaces	space	NOUN
ejpam-7116	288	10	.	.	PUNCT
ejpam-7116	289	1	revista	revista	PROPN
ejpam-7116	289	2	de	de	X
ejpam-7116	289	3	la	la	PROPN
ejpam-7116	289	4	real	real	PROPN
ejpam-7116	289	5	academia	academia	PROPN
ejpam-7116	289	6	de	de	PROPN
ejpam-7116	289	7	ciencias	ciencias	PROPN
ejpam-7116	289	8	exactas	exacta	NOUN
ejpam-7116	289	9	,	,	PUNCT
ejpam-7116	289	10	físicas	físicas	PROPN
ejpam-7116	289	11	y	y	PROPN
ejpam-7116	289	12	naturales	naturales	PROPN
ejpam-7116	289	13	.	.	PUNCT
ejpam-7116	290	1	serie	serie	PROPN
ejpam-7116	290	2	a.	a.	PROPN
ejpam-7116	290	3	matemáticas	matemáticas	PROPN
ejpam-7116	290	4	(	(	PUNCT
ejpam-7116	290	5	racsam	racsam	PROPN
ejpam-7116	290	6	)	)	PUNCT
ejpam-7116	290	7	,	,	PUNCT
ejpam-7116	290	8	113:1267–1278	113:1267–1278	NOUN
ejpam-7116	290	9	,	,	PUNCT
ejpam-7116	290	10	2019	2019	NUM
ejpam-7116	290	11	.	.	PUNCT