id	sid	tid	token	lemma	pos
ejpam-6282	1	1	european	european	PROPN
ejpam-6282	1	2	journal	journal	PROPN
ejpam-6282	1	3	of	of	ADP
ejpam-6282	1	4	pure	pure	ADJ
ejpam-6282	1	5	and	and	CCONJ
ejpam-6282	1	6	applied	applied	ADJ
ejpam-6282	1	7	mathematics	mathematic	NOUN
ejpam-6282	1	8	2025	2025	NUM
ejpam-6282	1	9	,	,	PUNCT
ejpam-6282	1	10	vol	vol	NOUN
ejpam-6282	1	11	.	.	PROPN
ejpam-6282	1	12	18	18	NUM
ejpam-6282	1	13	,	,	PUNCT
ejpam-6282	1	14	issue	issue	NOUN
ejpam-6282	1	15	2	2	NUM
ejpam-6282	1	16	,	,	PUNCT
ejpam-6282	1	17	article	article	NOUN
ejpam-6282	1	18	number	number	NOUN
ejpam-6282	1	19	6282	6282	NUM
ejpam-6282	1	20	issn	issn	VERB
ejpam-6282	1	21	1307	1307	NUM
ejpam-6282	1	22	-	-	SYM
ejpam-6282	1	23	5543	5543	NUM
ejpam-6282	1	24	–	–	PUNCT
ejpam-6282	1	25	ejpam.com	ejpam.com	X
ejpam-6282	1	26	published	publish	VERB
ejpam-6282	1	27	by	by	ADP
ejpam-6282	1	28	new	new	PROPN
ejpam-6282	1	29	york	york	PROPN
ejpam-6282	1	30	business	business	PROPN
ejpam-6282	1	31	global	global	ADJ
ejpam-6282	1	32	fixed	fix	VERB
ejpam-6282	1	33	point	point	NOUN
ejpam-6282	1	34	results	result	NOUN
ejpam-6282	1	35	on	on	ADP
ejpam-6282	1	36	interpolative	interpolative	ADJ
ejpam-6282	1	37	metric	metric	ADJ
ejpam-6282	1	38	spaces	space	NOUN
ejpam-6282	1	39	via	via	ADP
ejpam-6282	1	40	simulation	simulation	NOUN
ejpam-6282	1	41	functions	function	NOUN
ejpam-6282	1	42	ghaziyah	ghaziyah	PROPN
ejpam-6282	1	43	alsahli1	alsahli1	PROPN
ejpam-6282	1	44	,	,	PUNCT
ejpam-6282	1	45	selma	selma	PROPN
ejpam-6282	1	46	gülyaz	gülyaz	PROPN
ejpam-6282	1	47	-	-	PUNCT
ejpam-6282	1	48	özyurt2	özyurt2	PROPN
ejpam-6282	1	49	1	1	NUM
ejpam-6282	1	50	mathematics	mathematic	NOUN
ejpam-6282	1	51	department	department	NOUN
ejpam-6282	1	52	,	,	PUNCT
ejpam-6282	1	53	college	college	NOUN
ejpam-6282	1	54	of	of	ADP
ejpam-6282	1	55	science	science	NOUN
ejpam-6282	1	56	,	,	PUNCT
ejpam-6282	1	57	jouf	jouf	PROPN
ejpam-6282	1	58	university	university	PROPN
ejpam-6282	1	59	,	,	PUNCT
ejpam-6282	1	60	sakaka	sakaka	PROPN
ejpam-6282	1	61	p.o	p.o	PROPN
ejpam-6282	1	62	.	.	PROPN
ejpam-6282	1	63	box	box	PROPN
ejpam-6282	1	64	2014	2014	NUM
ejpam-6282	1	65	,	,	PUNCT
ejpam-6282	1	66	saudi	saudi	PROPN
ejpam-6282	1	67	arabia	arabia	PROPN
ejpam-6282	1	68	2	2	NUM
ejpam-6282	1	69	department	department	NOUN
ejpam-6282	1	70	of	of	ADP
ejpam-6282	1	71	mathematics	mathematics	PROPN
ejpam-6282	1	72	,	,	PUNCT
ejpam-6282	1	73	sivas	sivas	PROPN
ejpam-6282	1	74	cumhuriyet	cumhuriyet	PROPN
ejpam-6282	1	75	university	university	PROPN
ejpam-6282	1	76	,	,	PUNCT
ejpam-6282	1	77	58140	58140	NUM
ejpam-6282	1	78	,	,	PUNCT
ejpam-6282	1	79	sivas	sivas	PROPN
ejpam-6282	1	80	,	,	PUNCT
ejpam-6282	1	81	turkey	turkey	PROPN
ejpam-6282	1	82	abstract	abstract	NOUN
ejpam-6282	1	83	.	.	PUNCT
ejpam-6282	2	1	the	the	DET
ejpam-6282	2	2	aim	aim	NOUN
ejpam-6282	2	3	of	of	ADP
ejpam-6282	2	4	this	this	DET
ejpam-6282	2	5	paper	paper	NOUN
ejpam-6282	2	6	is	be	AUX
ejpam-6282	2	7	to	to	PART
ejpam-6282	2	8	bring	bring	VERB
ejpam-6282	2	9	generalized	generalized	ADJ
ejpam-6282	2	10	fixed	fix	VERB
ejpam-6282	2	11	point	point	NOUN
ejpam-6282	2	12	theorems	theorem	NOUN
ejpam-6282	2	13	via	via	ADP
ejpam-6282	2	14	the	the	DET
ejpam-6282	2	15	interesting	interesting	ADJ
ejpam-6282	2	16	simulation	simulation	NOUN
ejpam-6282	2	17	functions	function	NOUN
ejpam-6282	2	18	in	in	ADP
ejpam-6282	2	19	the	the	DET
ejpam-6282	2	20	context	context	NOUN
ejpam-6282	2	21	of	of	ADP
ejpam-6282	2	22	interpolative	interpolative	ADJ
ejpam-6282	2	23	metric	metric	ADJ
ejpam-6282	2	24	spaces	space	NOUN
ejpam-6282	2	25	.	.	PUNCT
ejpam-6282	3	1	the	the	DET
ejpam-6282	3	2	notion	notion	NOUN
ejpam-6282	3	3	of	of	ADP
ejpam-6282	3	4	interpolative	interpolative	ADJ
ejpam-6282	3	5	metric	metric	ADJ
ejpam-6282	3	6	space	space	NOUN
ejpam-6282	3	7	is	be	AUX
ejpam-6282	3	8	introduced	introduce	VERB
ejpam-6282	3	9	by	by	ADP
ejpam-6282	3	10	karapinar[6	karapinar[6	NOUN
ejpam-6282	3	11	]	]	PUNCT
ejpam-6282	3	12	,	,	PUNCT
ejpam-6282	3	13	very	very	ADV
ejpam-6282	3	14	recently	recently	ADV
ejpam-6282	3	15	.	.	PUNCT
ejpam-6282	4	1	this	this	DET
ejpam-6282	4	2	new	new	ADJ
ejpam-6282	4	3	metric	metric	ADJ
ejpam-6282	4	4	structure	structure	NOUN
ejpam-6282	4	5	is	be	AUX
ejpam-6282	4	6	a	a	DET
ejpam-6282	4	7	concrete	concrete	ADJ
ejpam-6282	4	8	generalization	generalization	NOUN
ejpam-6282	4	9	of	of	ADP
ejpam-6282	4	10	the	the	DET
ejpam-6282	4	11	usual	usual	ADJ
ejpam-6282	4	12	metric	metric	ADJ
ejpam-6282	4	13	space	space	NOUN
ejpam-6282	4	14	which	which	PRON
ejpam-6282	4	15	is	be	AUX
ejpam-6282	4	16	indicated	indicate	VERB
ejpam-6282	4	17	by	by	ADP
ejpam-6282	4	18	examples	example	NOUN
ejpam-6282	4	19	.	.	PUNCT
ejpam-6282	5	1	2020	2020	NUM
ejpam-6282	5	2	mathematics	mathematic	NOUN
ejpam-6282	5	3	subject	subject	NOUN
ejpam-6282	5	4	classifications	classification	NOUN
ejpam-6282	5	5	:	:	PUNCT
ejpam-6282	5	6	47h10	47h10	NUM
ejpam-6282	5	7	,	,	PUNCT
ejpam-6282	5	8	54h25	54h25	NUM
ejpam-6282	5	9	key	key	ADJ
ejpam-6282	5	10	words	word	NOUN
ejpam-6282	5	11	and	and	CCONJ
ejpam-6282	5	12	phrases	phrase	NOUN
ejpam-6282	5	13	:	:	PUNCT
ejpam-6282	5	14	interpolative	interpolative	ADJ
ejpam-6282	5	15	metric	metric	ADJ
ejpam-6282	5	16	space	space	NOUN
ejpam-6282	5	17	,	,	PUNCT
ejpam-6282	5	18	metric	metric	ADJ
ejpam-6282	5	19	space	space	NOUN
ejpam-6282	5	20	,	,	PUNCT
ejpam-6282	5	21	simulation	simulation	NOUN
ejpam-6282	5	22	functions	function	NOUN
ejpam-6282	5	23	abstract	abstract	ADJ
ejpam-6282	5	24	.	.	PUNCT
ejpam-6282	6	1	the	the	DET
ejpam-6282	6	2	aim	aim	NOUN
ejpam-6282	6	3	of	of	ADP
ejpam-6282	6	4	this	this	DET
ejpam-6282	6	5	paper	paper	NOUN
ejpam-6282	6	6	is	be	AUX
ejpam-6282	6	7	to	to	PART
ejpam-6282	6	8	bring	bring	VERB
ejpam-6282	6	9	generalized	generalized	ADJ
ejpam-6282	6	10	fixed	fix	VERB
ejpam-6282	6	11	point	point	NOUN
ejpam-6282	6	12	theorems	theorem	NOUN
ejpam-6282	6	13	via	via	ADP
ejpam-6282	6	14	the	the	DET
ejpam-6282	6	15	interesting	interesting	ADJ
ejpam-6282	6	16	simulation	simulation	NOUN
ejpam-6282	6	17	functions	function	NOUN
ejpam-6282	6	18	in	in	ADP
ejpam-6282	6	19	the	the	DET
ejpam-6282	6	20	context	context	NOUN
ejpam-6282	6	21	of	of	ADP
ejpam-6282	6	22	interpolative	interpolative	ADJ
ejpam-6282	6	23	metric	metric	ADJ
ejpam-6282	6	24	spaces	space	NOUN
ejpam-6282	6	25	.	.	PUNCT
ejpam-6282	7	1	the	the	DET
ejpam-6282	7	2	notion	notion	NOUN
ejpam-6282	7	3	of	of	ADP
ejpam-6282	7	4	interpolative	interpolative	ADJ
ejpam-6282	7	5	metric	metric	ADJ
ejpam-6282	7	6	space	space	NOUN
ejpam-6282	7	7	is	be	AUX
ejpam-6282	7	8	introduced	introduce	VERB
ejpam-6282	7	9	by	by	ADP
ejpam-6282	7	10	karapinar[6	karapinar[6	NOUN
ejpam-6282	7	11	]	]	PUNCT
ejpam-6282	7	12	,	,	PUNCT
ejpam-6282	7	13	very	very	ADV
ejpam-6282	7	14	recently	recently	ADV
ejpam-6282	7	15	.	.	PUNCT
ejpam-6282	8	1	this	this	DET
ejpam-6282	8	2	new	new	ADJ
ejpam-6282	8	3	metric	metric	ADJ
ejpam-6282	8	4	structure	structure	NOUN
ejpam-6282	8	5	is	be	AUX
ejpam-6282	8	6	a	a	DET
ejpam-6282	8	7	concrete	concrete	ADJ
ejpam-6282	8	8	generalization	generalization	NOUN
ejpam-6282	8	9	of	of	ADP
ejpam-6282	8	10	the	the	DET
ejpam-6282	8	11	usual	usual	ADJ
ejpam-6282	8	12	metric	metric	ADJ
ejpam-6282	8	13	space	space	NOUN
ejpam-6282	8	14	which	which	PRON
ejpam-6282	8	15	is	be	AUX
ejpam-6282	8	16	indicated	indicate	VERB
ejpam-6282	8	17	by	by	ADP
ejpam-6282	8	18	examples	example	NOUN
ejpam-6282	8	19	.	.	PUNCT
ejpam-6282	9	1	1	1	X
ejpam-6282	9	2	.	.	X
ejpam-6282	9	3	introduction	introduction	NOUN
ejpam-6282	9	4	and	and	CCONJ
ejpam-6282	9	5	preliminaries	preliminary	NOUN
ejpam-6282	9	6	the	the	DET
ejpam-6282	9	7	last	last	ADJ
ejpam-6282	9	8	century	century	NOUN
ejpam-6282	9	9	has	have	AUX
ejpam-6282	9	10	witnessed	witness	VERB
ejpam-6282	9	11	so	so	ADV
ejpam-6282	9	12	many	many	ADJ
ejpam-6282	9	13	developments	development	NOUN
ejpam-6282	9	14	in	in	ADP
ejpam-6282	9	15	mathematics	mathematic	NOUN
ejpam-6282	9	16	,	,	PUNCT
ejpam-6282	9	17	of	of	ADP
ejpam-6282	9	18	such	such	ADJ
ejpam-6282	9	19	great	great	ADJ
ejpam-6282	9	20	beauty	beauty	NOUN
ejpam-6282	9	21	and	and	CCONJ
ejpam-6282	9	22	quality	quality	NOUN
ejpam-6282	9	23	,	,	PUNCT
ejpam-6282	9	24	that	that	SCONJ
ejpam-6282	9	25	it	it	PRON
ejpam-6282	9	26	seems	seem	VERB
ejpam-6282	9	27	impossible	impossible	ADJ
ejpam-6282	9	28	for	for	SCONJ
ejpam-6282	9	29	one	one	NUM
ejpam-6282	9	30	person	person	NOUN
ejpam-6282	9	31	to	to	PART
ejpam-6282	9	32	grasp	grasp	VERB
ejpam-6282	9	33	,	,	PUNCT
ejpam-6282	9	34	collect	collect	VERB
ejpam-6282	9	35	and	and	CCONJ
ejpam-6282	9	36	explain	explain	VERB
ejpam-6282	9	37	them	they	PRON
ejpam-6282	9	38	.	.	PUNCT
ejpam-6282	10	1	very	very	ADV
ejpam-6282	10	2	serious	serious	ADJ
ejpam-6282	10	3	and	and	CCONJ
ejpam-6282	10	4	important	important	ADJ
ejpam-6282	10	5	contributions	contribution	NOUN
ejpam-6282	10	6	have	have	AUX
ejpam-6282	10	7	been	be	AUX
ejpam-6282	10	8	made	make	VERB
ejpam-6282	10	9	from	from	ADP
ejpam-6282	10	10	every	every	DET
ejpam-6282	10	11	field	field	NOUN
ejpam-6282	10	12	of	of	ADP
ejpam-6282	10	13	mathematics	mathematic	NOUN
ejpam-6282	10	14	,	,	PUNCT
ejpam-6282	10	15	especially	especially	ADV
ejpam-6282	10	16	in	in	ADP
ejpam-6282	10	17	analysis	analysis	NOUN
ejpam-6282	10	18	,	,	PUNCT
ejpam-6282	10	19	number	number	NOUN
ejpam-6282	10	20	theory	theory	NOUN
ejpam-6282	10	21	and	and	CCONJ
ejpam-6282	10	22	applied	apply	VERB
ejpam-6282	10	23	mathematics	mathematic	NOUN
ejpam-6282	10	24	.	.	PUNCT
ejpam-6282	11	1	in	in	ADP
ejpam-6282	11	2	this	this	DET
ejpam-6282	11	3	article	article	NOUN
ejpam-6282	11	4	,	,	PUNCT
ejpam-6282	11	5	we	we	PRON
ejpam-6282	11	6	will	will	AUX
ejpam-6282	11	7	focus	focus	VERB
ejpam-6282	11	8	on	on	ADP
ejpam-6282	11	9	the	the	DET
ejpam-6282	11	10	fixed	fix	VERB
ejpam-6282	11	11	point	point	NOUN
ejpam-6282	11	12	theorem	theorem	VERB
ejpam-6282	11	13	,	,	PUNCT
ejpam-6282	11	14	which	which	PRON
ejpam-6282	11	15	can	can	AUX
ejpam-6282	11	16	be	be	AUX
ejpam-6282	11	17	considered	consider	VERB
ejpam-6282	11	18	a	a	DET
ejpam-6282	11	19	drop	drop	NOUN
ejpam-6282	11	20	in	in	ADP
ejpam-6282	11	21	this	this	DET
ejpam-6282	11	22	mathematical	mathematical	ADJ
ejpam-6282	11	23	ocean	ocean	NOUN
ejpam-6282	11	24	.	.	PUNCT
ejpam-6282	12	1	fixed	fix	VERB
ejpam-6282	12	2	point	point	NOUN
ejpam-6282	12	3	theorem	theorem	NOUN
ejpam-6282	12	4	is	be	AUX
ejpam-6282	12	5	actually	actually	ADV
ejpam-6282	12	6	a	a	DET
ejpam-6282	12	7	very	very	ADV
ejpam-6282	12	8	important	important	ADJ
ejpam-6282	12	9	field	field	NOUN
ejpam-6282	12	10	of	of	ADP
ejpam-6282	12	11	study	study	NOUN
ejpam-6282	12	12	that	that	PRON
ejpam-6282	12	13	is	be	AUX
ejpam-6282	12	14	the	the	DET
ejpam-6282	12	15	common	common	ADJ
ejpam-6282	12	16	denominator	denominator	NOUN
ejpam-6282	12	17	of	of	ADP
ejpam-6282	12	18	both	both	DET
ejpam-6282	12	19	topology	topology	NOUN
ejpam-6282	12	20	,	,	PUNCT
ejpam-6282	12	21	analysis	analysis	NOUN
ejpam-6282	12	22	and	and	CCONJ
ejpam-6282	12	23	applied	apply	VERB
ejpam-6282	12	24	mathematics	mathematic	NOUN
ejpam-6282	12	25	.	.	PUNCT
ejpam-6282	13	1	in	in	ADP
ejpam-6282	13	2	fact	fact	NOUN
ejpam-6282	13	3	,	,	PUNCT
ejpam-6282	13	4	the	the	DET
ejpam-6282	13	5	concept	concept	NOUN
ejpam-6282	13	6	of	of	ADP
ejpam-6282	13	7	fixed	fix	VERB
ejpam-6282	13	8	point	point	NOUN
ejpam-6282	13	9	is	be	AUX
ejpam-6282	13	10	a	a	DET
ejpam-6282	13	11	very	very	ADV
ejpam-6282	13	12	natural	natural	ADJ
ejpam-6282	13	13	concept	concept	NOUN
ejpam-6282	13	14	that	that	SCONJ
ejpam-6282	13	15	we	we	PRON
ejpam-6282	13	16	encounter	encounter	VERB
ejpam-6282	13	17	in	in	ADP
ejpam-6282	13	18	every	every	DET
ejpam-6282	13	19	area	area	NOUN
ejpam-6282	13	20	of	of	ADP
ejpam-6282	13	21	life	life	NOUN
ejpam-6282	13	22	;	;	PUNCT
ejpam-6282	13	23	therefore	therefore	ADV
ejpam-6282	13	24	,	,	PUNCT
ejpam-6282	13	25	it	it	PRON
ejpam-6282	13	26	has	have	VERB
ejpam-6282	13	27	a	a	DET
ejpam-6282	13	28	very	very	ADV
ejpam-6282	13	29	wide	wide	ADJ
ejpam-6282	13	30	potential	potential	NOUN
ejpam-6282	13	31	for	for	ADP
ejpam-6282	13	32	study	study	NOUN
ejpam-6282	13	33	and	and	CCONJ
ejpam-6282	13	34	application	application	NOUN
ejpam-6282	13	35	.	.	PUNCT
ejpam-6282	14	1	in	in	ADP
ejpam-6282	14	2	this	this	DET
ejpam-6282	14	3	study	study	NOUN
ejpam-6282	14	4	,	,	PUNCT
ejpam-6282	14	5	we	we	PRON
ejpam-6282	14	6	will	will	AUX
ejpam-6282	14	7	limit	limit	VERB
ejpam-6282	14	8	ourselves	ourselves	PRON
ejpam-6282	14	9	doi	doi	NOUN
ejpam-6282	14	10	:	:	PUNCT
ejpam-6282	14	11	https://doi.org/10.29020/nybg.ejpam.v18i2.6282	https://doi.org/10.29020/nybg.ejpam.v18i2.6282	PROPN
ejpam-6282	14	12	email	email	NOUN
ejpam-6282	14	13	addresses	address	NOUN
ejpam-6282	14	14	:	:	PUNCT
ejpam-6282	14	15	gmsahli@ju.edu.sa	gmsahli@ju.edu.sa	PROPN
ejpam-6282	14	16	(	(	PUNCT
ejpam-6282	14	17	g.	g.	PROPN
ejpam-6282	14	18	alsahli	alsahli	PROPN
ejpam-6282	14	19	)	)	PUNCT
ejpam-6282	14	20	,	,	PUNCT
ejpam-6282	14	21	sgulyaz@cumhuriyet.edu.tr	sgulyaz@cumhuriyet.edu.tr	INTJ
ejpam-6282	14	22	(	(	PUNCT
ejpam-6282	14	23	s.	s.	PROPN
ejpam-6282	14	24	gülyaz	gülyaz	PROPN
ejpam-6282	14	25	-	-	PUNCT
ejpam-6282	14	26	özyurt	özyurt	PROPN
ejpam-6282	14	27	)	)	PUNCT
ejpam-6282	14	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6282	15	1	1	1	NUM
ejpam-6282	15	2	copyright	copyright	NOUN
ejpam-6282	15	3	:	:	PUNCT
ejpam-6282	15	4	©	©	PROPN
ejpam-6282	15	5	2025	2025	NUM
ejpam-6282	15	6	the	the	DET
ejpam-6282	15	7	author(s	author(s	NOUN
ejpam-6282	15	8	)	)	PUNCT
ejpam-6282	15	9	.	.	PUNCT
ejpam-6282	16	1	(	(	PUNCT
ejpam-6282	16	2	cc	cc	NOUN
ejpam-6282	16	3	by	by	ADP
ejpam-6282	16	4	-	-	PUNCT
ejpam-6282	16	5	nc	nc	PROPN
ejpam-6282	16	6	4.0	4.0	NUM
ejpam-6282	16	7	)	)	PUNCT
ejpam-6282	16	8	g.	g.	PROPN
ejpam-6282	16	9	alsahli	alsahli	PROPN
ejpam-6282	16	10	,	,	PUNCT
ejpam-6282	16	11	s.	s.	PROPN
ejpam-6282	16	12	gülyaz	gülyaz	PROPN
ejpam-6282	16	13	-	-	PUNCT
ejpam-6282	16	14	özyurt	özyurt	PROPN
ejpam-6282	16	15	/	/	SYM
ejpam-6282	16	16	eur	eur	PROPN
ejpam-6282	16	17	.	.	PUNCT
ejpam-6282	17	1	j.	j.	PROPN
ejpam-6282	17	2	pure	pure	PROPN
ejpam-6282	17	3	appl	appl	PROPN
ejpam-6282	17	4	.	.	PROPN
ejpam-6282	17	5	math	math	PROPN
ejpam-6282	17	6	,	,	PUNCT
ejpam-6282	17	7	18	18	NUM
ejpam-6282	17	8	(	(	PUNCT
ejpam-6282	17	9	2	2	NUM
ejpam-6282	17	10	)	)	PUNCT
ejpam-6282	17	11	(	(	PUNCT
ejpam-6282	17	12	2025	2025	NUM
ejpam-6282	17	13	)	)	PUNCT
ejpam-6282	17	14	,	,	PUNCT
ejpam-6282	17	15	6282	6282	NUM
ejpam-6282	17	16	2	2	NUM
ejpam-6282	17	17	of	of	ADP
ejpam-6282	17	18	13	13	NUM
ejpam-6282	17	19	to	to	ADP
ejpam-6282	17	20	metric	metric	ADJ
ejpam-6282	17	21	fixed	fix	VERB
ejpam-6282	17	22	points	point	NOUN
ejpam-6282	17	23	.	.	PUNCT
ejpam-6282	18	1	the	the	DET
ejpam-6282	18	2	first	first	ADJ
ejpam-6282	18	3	theorem	theorem	NOUN
ejpam-6282	18	4	historically	historically	ADV
ejpam-6282	18	5	presented	present	VERB
ejpam-6282	18	6	is	be	AUX
ejpam-6282	18	7	the	the	DET
ejpam-6282	18	8	brouwer	brouwer	NOUN
ejpam-6282	18	9	fixed	fix	VERB
ejpam-6282	18	10	-	-	PUNCT
ejpam-6282	18	11	point	point	NOUN
ejpam-6282	18	12	theorem	theorem	ADJ
ejpam-6282	18	13	brouwer	brouwer	NOUN
ejpam-6282	18	14	.	.	PUNCT
ejpam-6282	19	1	it	it	PRON
ejpam-6282	19	2	guarantees	guarantee	VERB
ejpam-6282	19	3	that	that	SCONJ
ejpam-6282	19	4	every	every	DET
ejpam-6282	19	5	continuous	continuous	ADJ
ejpam-6282	19	6	function	function	NOUN
ejpam-6282	19	7	has	have	VERB
ejpam-6282	19	8	a	a	DET
ejpam-6282	19	9	fixed	fix	VERB
ejpam-6282	19	10	point	point	NOUN
ejpam-6282	19	11	on	on	ADP
ejpam-6282	19	12	a	a	DET
ejpam-6282	19	13	closed	closed	ADJ
ejpam-6282	19	14	interval	interval	NOUN
ejpam-6282	19	15	.	.	PUNCT
ejpam-6282	20	1	on	on	ADP
ejpam-6282	20	2	the	the	DET
ejpam-6282	20	3	other	other	ADJ
ejpam-6282	20	4	hand	hand	NOUN
ejpam-6282	20	5	,	,	PUNCT
ejpam-6282	20	6	it	it	PRON
ejpam-6282	20	7	does	do	AUX
ejpam-6282	20	8	not	not	PART
ejpam-6282	20	9	discuss	discuss	VERB
ejpam-6282	20	10	how	how	SCONJ
ejpam-6282	20	11	this	this	DET
ejpam-6282	20	12	point	point	NOUN
ejpam-6282	20	13	can	can	AUX
ejpam-6282	20	14	be	be	AUX
ejpam-6282	20	15	found	find	VERB
ejpam-6282	20	16	or	or	CCONJ
ejpam-6282	20	17	whether	whether	SCONJ
ejpam-6282	20	18	it	it	PRON
ejpam-6282	20	19	is	be	AUX
ejpam-6282	20	20	unique	unique	ADJ
ejpam-6282	20	21	.	.	PUNCT
ejpam-6282	21	1	this	this	PRON
ejpam-6282	21	2	theorem	theorem	VERB
ejpam-6282	21	3	’s	’s	PART
ejpam-6282	21	4	topology	topology	NOUN
ejpam-6282	21	5	structure	structure	NOUN
ejpam-6282	21	6	is	be	AUX
ejpam-6282	21	7	emphasized	emphasize	VERB
ejpam-6282	21	8	,	,	PUNCT
ejpam-6282	21	9	not	not	PART
ejpam-6282	21	10	its	its	PRON
ejpam-6282	21	11	metric	metric	ADJ
ejpam-6282	21	12	structure	structure	NOUN
ejpam-6282	21	13	;	;	PUNCT
ejpam-6282	21	14	that	that	PRON
ejpam-6282	21	15	is	be	AUX
ejpam-6282	21	16	why	why	SCONJ
ejpam-6282	21	17	it	it	PRON
ejpam-6282	21	18	is	be	AUX
ejpam-6282	21	19	not	not	PART
ejpam-6282	21	20	seen	see	VERB
ejpam-6282	21	21	as	as	ADP
ejpam-6282	21	22	the	the	DET
ejpam-6282	21	23	first	first	ADJ
ejpam-6282	21	24	metric	metric	ADJ
ejpam-6282	21	25	fixed	fix	VERB
ejpam-6282	21	26	point	point	NOUN
ejpam-6282	21	27	.	.	PUNCT
ejpam-6282	22	1	in	in	ADP
ejpam-6282	22	2	the	the	DET
ejpam-6282	22	3	literature	literature	NOUN
ejpam-6282	22	4	,	,	PUNCT
ejpam-6282	22	5	the	the	DET
ejpam-6282	22	6	first	first	ADJ
ejpam-6282	22	7	metric	metric	ADJ
ejpam-6282	22	8	fixed	fix	VERB
ejpam-6282	22	9	point	point	NOUN
ejpam-6282	22	10	theory	theory	NOUN
ejpam-6282	22	11	is	be	AUX
ejpam-6282	22	12	attributed	attribute	VERB
ejpam-6282	22	13	to	to	ADP
ejpam-6282	22	14	the	the	DET
ejpam-6282	22	15	famous	famous	ADJ
ejpam-6282	22	16	and	and	CCONJ
ejpam-6282	22	17	genius	genius	NOUN
ejpam-6282	22	18	polish	polish	PROPN
ejpam-6282	22	19	mathematician	mathematician	PROPN
ejpam-6282	22	20	s.	s.	PROPN
ejpam-6282	22	21	banach	banach	PROPN
ejpam-6282	23	1	[	[	X
ejpam-6282	23	2	1	1	NUM
ejpam-6282	23	3	]	]	PUNCT
ejpam-6282	23	4	.	.	PUNCT
ejpam-6282	24	1	in	in	ADP
ejpam-6282	24	2	addition	addition	NOUN
ejpam-6282	24	3	,	,	PUNCT
ejpam-6282	24	4	some	some	DET
ejpam-6282	24	5	researchers	researcher	NOUN
ejpam-6282	24	6	claim	claim	VERB
ejpam-6282	24	7	that	that	SCONJ
ejpam-6282	24	8	the	the	DET
ejpam-6282	24	9	theorem	theorem	NOUN
ejpam-6282	24	10	put	put	VERB
ejpam-6282	24	11	forward	forward	ADV
ejpam-6282	24	12	by	by	ADP
ejpam-6282	24	13	banach	banach	NOUN
ejpam-6282	24	14	was	be	AUX
ejpam-6282	24	15	actually	actually	ADV
ejpam-6282	24	16	implicitly	implicitly	ADV
ejpam-6282	24	17	expressed	express	VERB
ejpam-6282	24	18	by	by	ADP
ejpam-6282	24	19	picard	picard	PROPN
ejpam-6282	24	20	.	.	PUNCT
ejpam-6282	25	1	indeed	indeed	ADV
ejpam-6282	25	2	,	,	PUNCT
ejpam-6282	25	3	the	the	DET
ejpam-6282	25	4	”	"	PUNCT
ejpam-6282	25	5	successive	successive	ADJ
ejpam-6282	25	6	approximation	approximation	NOUN
ejpam-6282	25	7	”	"	PUNCT
ejpam-6282	25	8	method	method	NOUN
ejpam-6282	25	9	used	use	VERB
ejpam-6282	25	10	by	by	ADP
ejpam-6282	25	11	picard	picard	NOUN
ejpam-6282	26	1	[	[	X
ejpam-6282	26	2	11	11	NUM
ejpam-6282	26	3	]	]	PUNCT
ejpam-6282	26	4	is	be	AUX
ejpam-6282	26	5	the	the	DET
ejpam-6282	26	6	backbone	backbone	NOUN
ejpam-6282	26	7	of	of	ADP
ejpam-6282	26	8	the	the	DET
ejpam-6282	26	9	proof	proof	NOUN
ejpam-6282	26	10	of	of	ADP
ejpam-6282	26	11	the	the	DET
ejpam-6282	26	12	banach	banach	ADV
ejpam-6282	26	13	fixed	fix	VERB
ejpam-6282	26	14	-	-	PUNCT
ejpam-6282	26	15	point	point	NOUN
ejpam-6282	26	16	theorem	theorem	VERB
ejpam-6282	26	17	.	.	PUNCT
ejpam-6282	27	1	that	that	PRON
ejpam-6282	27	2	is	be	AUX
ejpam-6282	27	3	why	why	SCONJ
ejpam-6282	27	4	we	we	PRON
ejpam-6282	27	5	come	come	VERB
ejpam-6282	27	6	across	across	ADP
ejpam-6282	27	7	sources	source	NOUN
ejpam-6282	27	8	where	where	SCONJ
ejpam-6282	27	9	the	the	DET
ejpam-6282	27	10	expression	expression	NOUN
ejpam-6282	27	11	picard	picard	NOUN
ejpam-6282	27	12	-	-	PUNCT
ejpam-6282	27	13	banach	banach	ADV
ejpam-6282	27	14	fixed	fix	VERB
ejpam-6282	27	15	point	point	NOUN
ejpam-6282	27	16	theorem	theorem	NOUN
ejpam-6282	27	17	is	be	AUX
ejpam-6282	27	18	used	use	VERB
ejpam-6282	27	19	.	.	PUNCT
ejpam-6282	28	1	on	on	ADP
ejpam-6282	28	2	the	the	DET
ejpam-6282	28	3	other	other	ADJ
ejpam-6282	28	4	hand	hand	NOUN
ejpam-6282	28	5	,	,	PUNCT
ejpam-6282	28	6	the	the	DET
ejpam-6282	28	7	theorem	theorem	NOUN
ejpam-6282	28	8	put	put	VERB
ejpam-6282	28	9	forward	forward	ADV
ejpam-6282	28	10	by	by	ADP
ejpam-6282	28	11	banach	banach	NOUN
ejpam-6282	28	12	is	be	AUX
ejpam-6282	28	13	constructed	construct	VERB
ejpam-6282	28	14	within	within	ADP
ejpam-6282	28	15	a	a	DET
ejpam-6282	28	16	complete	complete	ADJ
ejpam-6282	28	17	normed	normed	ADJ
ejpam-6282	28	18	space	space	NOUN
ejpam-6282	28	19	.	.	PUNCT
ejpam-6282	29	1	the	the	DET
ejpam-6282	29	2	famous	famous	ADJ
ejpam-6282	29	3	italian	italian	ADJ
ejpam-6282	29	4	mathematician	mathematician	ADJ
ejpam-6282	29	5	caccioppoli	caccioppoli	NOUN
ejpam-6282	29	6	[	[	X
ejpam-6282	29	7	5	5	NUM
ejpam-6282	29	8	]	]	PUNCT
ejpam-6282	29	9	contributed	contribute	VERB
ejpam-6282	29	10	to	to	ADP
ejpam-6282	29	11	its	its	PRON
ejpam-6282	29	12	current	current	ADJ
ejpam-6282	29	13	form	form	NOUN
ejpam-6282	29	14	.	.	PUNCT
ejpam-6282	30	1	that	that	PRON
ejpam-6282	30	2	’s	’	VERB
ejpam-6282	30	3	why	why	SCONJ
ejpam-6282	30	4	it	it	PRON
ejpam-6282	30	5	is	be	AUX
ejpam-6282	30	6	expressed	express	VERB
ejpam-6282	30	7	as	as	ADP
ejpam-6282	30	8	the	the	DET
ejpam-6282	30	9	banach	banach	NOUN
ejpam-6282	30	10	-	-	PUNCT
ejpam-6282	30	11	caccioppoli	caccioppoli	NOUN
ejpam-6282	30	12	fixed	fix	VERB
ejpam-6282	30	13	point	point	NOUN
ejpam-6282	30	14	in	in	ADP
ejpam-6282	30	15	some	some	DET
ejpam-6282	30	16	sources	source	NOUN
ejpam-6282	30	17	.	.	PUNCT
ejpam-6282	31	1	it	it	PRON
ejpam-6282	31	2	is	be	AUX
ejpam-6282	31	3	very	very	ADV
ejpam-6282	31	4	useful	useful	ADJ
ejpam-6282	31	5	to	to	PART
ejpam-6282	31	6	underline	underline	VERB
ejpam-6282	31	7	that	that	SCONJ
ejpam-6282	31	8	the	the	DET
ejpam-6282	31	9	banach	banach	NOUN
ejpam-6282	31	10	-	-	PUNCT
ejpam-6282	31	11	caccioppoli	caccioppoli	NOUN
ejpam-6282	31	12	theorem	theorem	NOUN
ejpam-6282	31	13	is	be	AUX
ejpam-6282	31	14	actually	actually	ADV
ejpam-6282	31	15	a	a	DET
ejpam-6282	31	16	generalization	generalization	NOUN
ejpam-6282	31	17	study	study	NOUN
ejpam-6282	31	18	:	:	PUNCT
ejpam-6282	31	19	the	the	DET
ejpam-6282	31	20	expression	expression	NOUN
ejpam-6282	31	21	”	"	PUNCT
ejpam-6282	31	22	every	every	DET
ejpam-6282	31	23	contraction	contraction	NOUN
ejpam-6282	31	24	has	have	VERB
ejpam-6282	31	25	a	a	DET
ejpam-6282	31	26	single	single	ADJ
ejpam-6282	31	27	fixed	fix	VERB
ejpam-6282	31	28	point	point	NOUN
ejpam-6282	31	29	”	"	PUNCT
ejpam-6282	31	30	was	be	AUX
ejpam-6282	31	31	first	first	ADV
ejpam-6282	31	32	expressed	express	VERB
ejpam-6282	31	33	in	in	ADP
ejpam-6282	31	34	a	a	DET
ejpam-6282	31	35	complete	complete	ADJ
ejpam-6282	31	36	norm	norm	NOUN
ejpam-6282	31	37	space	space	NOUN
ejpam-6282	31	38	,	,	PUNCT
ejpam-6282	31	39	but	but	CCONJ
ejpam-6282	31	40	now	now	ADV
ejpam-6282	31	41	it	it	PRON
ejpam-6282	31	42	has	have	AUX
ejpam-6282	31	43	been	be	AUX
ejpam-6282	31	44	generalized	generalize	VERB
ejpam-6282	31	45	as	as	ADP
ejpam-6282	31	46	a	a	DET
ejpam-6282	31	47	complete	complete	ADJ
ejpam-6282	31	48	metric	metric	ADJ
ejpam-6282	31	49	space	space	NOUN
ejpam-6282	31	50	.	.	PUNCT
ejpam-6282	32	1	due	due	ADP
ejpam-6282	32	2	to	to	ADP
ejpam-6282	32	3	the	the	DET
ejpam-6282	32	4	nature	nature	NOUN
ejpam-6282	32	5	of	of	ADP
ejpam-6282	32	6	mathematics	mathematic	NOUN
ejpam-6282	32	7	and	and	CCONJ
ejpam-6282	32	8	human	human	ADJ
ejpam-6282	32	9	beings	being	NOUN
ejpam-6282	32	10	,	,	PUNCT
ejpam-6282	32	11	every	every	DET
ejpam-6282	32	12	concept	concept	NOUN
ejpam-6282	32	13	,	,	PUNCT
ejpam-6282	32	14	every	every	DET
ejpam-6282	32	15	structure	structure	NOUN
ejpam-6282	32	16	is	be	AUX
ejpam-6282	32	17	tried	try	VERB
ejpam-6282	32	18	to	to	PART
ejpam-6282	32	19	be	be	AUX
ejpam-6282	32	20	expanded	expand	VERB
ejpam-6282	32	21	and	and	CCONJ
ejpam-6282	32	22	developed	develop	VERB
ejpam-6282	32	23	.	.	PUNCT
ejpam-6282	33	1	the	the	DET
ejpam-6282	33	2	subject	subject	NOUN
ejpam-6282	33	3	of	of	ADP
ejpam-6282	33	4	this	this	DET
ejpam-6282	33	5	article	article	NOUN
ejpam-6282	33	6	is	be	AUX
ejpam-6282	33	7	the	the	DET
ejpam-6282	33	8	attempt	attempt	NOUN
ejpam-6282	33	9	to	to	PART
ejpam-6282	33	10	add	add	VERB
ejpam-6282	33	11	a	a	DET
ejpam-6282	33	12	final	final	ADJ
ejpam-6282	33	13	link	link	NOUN
ejpam-6282	33	14	to	to	ADP
ejpam-6282	33	15	such	such	ADJ
ejpam-6282	33	16	generalizations	generalization	NOUN
ejpam-6282	33	17	,	,	PUNCT
ejpam-6282	33	18	see	see	VERB
ejpam-6282	33	19	e.g.	e.g.	ADV
ejpam-6282	33	20	[	[	X
ejpam-6282	33	21	6–9	6–9	NOUN
ejpam-6282	33	22	]	]	PUNCT
ejpam-6282	33	23	.	.	PUNCT
ejpam-6282	34	1	we	we	PRON
ejpam-6282	34	2	underline	underline	VERB
ejpam-6282	34	3	that	that	SCONJ
ejpam-6282	34	4	the	the	DET
ejpam-6282	34	5	picard	picard	NOUN
ejpam-6282	34	6	’s	’s	PART
ejpam-6282	34	7	successive	successive	ADJ
ejpam-6282	34	8	approximation	approximation	NOUN
ejpam-6282	34	9	method	method	NOUN
ejpam-6282	34	10	should	should	AUX
ejpam-6282	34	11	be	be	AUX
ejpam-6282	34	12	accepted	accept	VERB
ejpam-6282	34	13	as	as	ADP
ejpam-6282	34	14	an	an	DET
ejpam-6282	34	15	initial	initial	ADJ
ejpam-6282	34	16	application	application	NOUN
ejpam-6282	34	17	for	for	ADP
ejpam-6282	34	18	the	the	DET
ejpam-6282	34	19	usage	usage	NOUN
ejpam-6282	34	20	of	of	ADP
ejpam-6282	34	21	fixed	fix	VERB
ejpam-6282	34	22	point	point	NOUN
ejpam-6282	34	23	hypothesis	hypothesis	NOUN
ejpam-6282	34	24	.	.	PUNCT
ejpam-6282	35	1	in	in	ADP
ejpam-6282	35	2	other	other	ADJ
ejpam-6282	35	3	words	word	NOUN
ejpam-6282	35	4	,	,	PUNCT
ejpam-6282	35	5	picard	picard	NOUN
ejpam-6282	35	6	result	result	NOUN
ejpam-6282	35	7	is	be	AUX
ejpam-6282	35	8	exceptionally	exceptionally	ADV
ejpam-6282	35	9	critical	critical	ADJ
ejpam-6282	35	10	and	and	CCONJ
ejpam-6282	35	11	basic	basic	ADJ
ejpam-6282	35	12	to	to	PART
ejpam-6282	35	13	indicate	indicate	VERB
ejpam-6282	35	14	the	the	DET
ejpam-6282	35	15	connection	connection	NOUN
ejpam-6282	35	16	of	of	ADP
ejpam-6282	35	17	the	the	DET
ejpam-6282	35	18	theory	theory	NOUN
ejpam-6282	35	19	with	with	ADP
ejpam-6282	35	20	the	the	DET
ejpam-6282	35	21	applications	application	NOUN
ejpam-6282	35	22	in	in	ADP
ejpam-6282	35	23	mathematics	mathematic	NOUN
ejpam-6282	35	24	.	.	PUNCT
ejpam-6282	36	1	indeed	indeed	ADV
ejpam-6282	36	2	,	,	PUNCT
ejpam-6282	36	3	the	the	DET
ejpam-6282	36	4	metric	metric	ADJ
ejpam-6282	36	5	fixed	fix	VERB
ejpam-6282	36	6	point	point	NOUN
ejpam-6282	36	7	has	have	VERB
ejpam-6282	36	8	a	a	DET
ejpam-6282	36	9	key	key	ADJ
ejpam-6282	36	10	role	role	NOUN
ejpam-6282	36	11	not	not	PART
ejpam-6282	36	12	only	only	ADV
ejpam-6282	36	13	in	in	ADP
ejpam-6282	36	14	solving	solve	VERB
ejpam-6282	36	15	mathematics	mathematic	NOUN
ejpam-6282	36	16	problems	problem	NOUN
ejpam-6282	36	17	,	,	PUNCT
ejpam-6282	36	18	but	but	CCONJ
ejpam-6282	36	19	in	in	ADP
ejpam-6282	36	20	nearly	nearly	ADV
ejpam-6282	36	21	all	all	PRON
ejpam-6282	36	22	quantitative	quantitative	ADJ
ejpam-6282	36	23	sciences	science	NOUN
ejpam-6282	36	24	.	.	PUNCT
ejpam-6282	37	1	in	in	ADP
ejpam-6282	37	2	other	other	ADJ
ejpam-6282	37	3	words	word	NOUN
ejpam-6282	37	4	,	,	PUNCT
ejpam-6282	37	5	the	the	DET
ejpam-6282	37	6	metric	metric	ADJ
ejpam-6282	37	7	fixed	fix	VERB
ejpam-6282	37	8	-	-	PUNCT
ejpam-6282	37	9	point	point	NOUN
ejpam-6282	37	10	techniques	technique	NOUN
ejpam-6282	37	11	are	be	AUX
ejpam-6282	37	12	very	very	ADV
ejpam-6282	37	13	crucial	crucial	ADJ
ejpam-6282	37	14	in	in	ADP
ejpam-6282	37	15	numerous	numerous	ADJ
ejpam-6282	37	16	research	research	NOUN
ejpam-6282	37	17	areas	area	NOUN
ejpam-6282	37	18	.	.	PUNCT
ejpam-6282	38	1	subsequently	subsequently	ADV
ejpam-6282	38	2	,	,	PUNCT
ejpam-6282	38	3	this	this	DET
ejpam-6282	38	4	theory	theory	NOUN
ejpam-6282	38	5	has	have	AUX
ejpam-6282	38	6	been	be	AUX
ejpam-6282	38	7	alluring	alluring	ADJ
ejpam-6282	38	8	to	to	ADP
ejpam-6282	38	9	several	several	ADJ
ejpam-6282	38	10	mathematicians	mathematician	NOUN
ejpam-6282	38	11	.	.	PUNCT
ejpam-6282	39	1	[	[	X
ejpam-6282	39	2	3	3	NUM
ejpam-6282	39	3	,	,	PUNCT
ejpam-6282	39	4	8	8	NUM
ejpam-6282	39	5	,	,	PUNCT
ejpam-6282	39	6	9	9	NUM
ejpam-6282	39	7	,	,	PUNCT
ejpam-6282	39	8	12	12	NUM
ejpam-6282	39	9	]	]	PUNCT
ejpam-6282	39	10	,	,	PUNCT
ejpam-6282	39	11	see	see	VERB
ejpam-6282	39	12	also	also	ADV
ejpam-6282	39	13	[	[	X
ejpam-6282	39	14	2	2	NUM
ejpam-6282	39	15	,	,	PUNCT
ejpam-6282	39	16	10	10	NUM
ejpam-6282	39	17	,	,	PUNCT
ejpam-6282	39	18	14	14	NUM
ejpam-6282	39	19	,	,	PUNCT
ejpam-6282	39	20	16	16	NUM
ejpam-6282	39	21	,	,	PUNCT
ejpam-6282	39	22	19	19	NUM
ejpam-6282	39	23	]	]	PUNCT
ejpam-6282	39	24	.	.	PUNCT
ejpam-6282	40	1	it	it	PRON
ejpam-6282	40	2	turned	turn	VERB
ejpam-6282	40	3	out	out	ADP
ejpam-6282	40	4	that	that	SCONJ
ejpam-6282	40	5	numerous	numerous	ADJ
ejpam-6282	40	6	publications	publication	NOUN
ejpam-6282	40	7	in	in	ADP
ejpam-6282	40	8	the	the	DET
ejpam-6282	40	9	related	relate	VERB
ejpam-6282	40	10	literature	literature	NOUN
ejpam-6282	40	11	overlap	overlap	NOUN
ejpam-6282	40	12	the	the	DET
ejpam-6282	40	13	published	publish	VERB
ejpam-6282	40	14	results	result	NOUN
ejpam-6282	40	15	,	,	PUNCT
ejpam-6282	40	16	whereas	whereas	SCONJ
ejpam-6282	40	17	others	other	NOUN
ejpam-6282	40	18	were	be	AUX
ejpam-6282	40	19	identical	identical	ADJ
ejpam-6282	40	20	to	to	ADP
ejpam-6282	40	21	the	the	DET
ejpam-6282	40	22	results	result	NOUN
ejpam-6282	40	23	in	in	ADP
ejpam-6282	40	24	the	the	DET
ejpam-6282	40	25	existing	exist	VERB
ejpam-6282	40	26	publications	publication	NOUN
ejpam-6282	40	27	.	.	PUNCT
ejpam-6282	41	1	for	for	ADP
ejpam-6282	41	2	more	more	ADJ
ejpam-6282	41	3	details	detail	NOUN
ejpam-6282	41	4	and	and	CCONJ
ejpam-6282	41	5	concrete	concrete	ADJ
ejpam-6282	41	6	examples	example	NOUN
ejpam-6282	41	7	about	about	ADP
ejpam-6282	41	8	this	this	DET
ejpam-6282	41	9	discussion	discussion	NOUN
ejpam-6282	41	10	,	,	PUNCT
ejpam-6282	41	11	see	see	VERB
ejpam-6282	41	12	e.g.	e.g.	ADV
ejpam-6282	41	13	[	[	X
ejpam-6282	41	14	8	8	NUM
ejpam-6282	41	15	]	]	PUNCT
ejpam-6282	41	16	and	and	CCONJ
ejpam-6282	41	17	related	related	ADJ
ejpam-6282	41	18	references	reference	NOUN
ejpam-6282	41	19	therein	therein	ADV
ejpam-6282	41	20	.	.	PUNCT
ejpam-6282	42	1	on	on	ADP
ejpam-6282	42	2	the	the	DET
ejpam-6282	42	3	other	other	ADJ
ejpam-6282	42	4	hand	hand	NOUN
ejpam-6282	42	5	,	,	PUNCT
ejpam-6282	42	6	as	as	ADP
ejpam-6282	42	7	a	a	DET
ejpam-6282	42	8	nature	nature	NOUN
ejpam-6282	42	9	of	of	ADP
ejpam-6282	42	10	science	science	NOUN
ejpam-6282	42	11	and	and	CCONJ
ejpam-6282	42	12	in	in	ADP
ejpam-6282	42	13	particular	particular	ADJ
ejpam-6282	42	14	mathematics	mathematic	NOUN
ejpam-6282	42	15	,	,	PUNCT
ejpam-6282	42	16	researchers	researcher	NOUN
ejpam-6282	42	17	have	have	AUX
ejpam-6282	42	18	been	be	AUX
ejpam-6282	42	19	continuing	continue	VERB
ejpam-6282	42	20	to	to	PART
ejpam-6282	42	21	improve	improve	VERB
ejpam-6282	42	22	,	,	PUNCT
ejpam-6282	42	23	generalize	generalize	VERB
ejpam-6282	42	24	and	and	CCONJ
ejpam-6282	42	25	extend	extend	VERB
ejpam-6282	42	26	the	the	DET
ejpam-6282	42	27	existing	exist	VERB
ejpam-6282	42	28	results	result	NOUN
ejpam-6282	42	29	.	.	PUNCT
ejpam-6282	43	1	indeed	indeed	ADV
ejpam-6282	43	2	,	,	PUNCT
ejpam-6282	43	3	the	the	DET
ejpam-6282	43	4	advancement	advancement	NOUN
ejpam-6282	43	5	of	of	ADP
ejpam-6282	43	6	the	the	DET
ejpam-6282	43	7	hypothesis	hypothesis	NOUN
ejpam-6282	43	8	has	have	VERB
ejpam-6282	43	9	two	two	NUM
ejpam-6282	43	10	primary	primary	ADJ
ejpam-6282	43	11	cornerstone	cornerstone	NOUN
ejpam-6282	43	12	:	:	PUNCT
ejpam-6282	43	13	the	the	DET
ejpam-6282	43	14	first	first	ADJ
ejpam-6282	43	15	one	one	NOUN
ejpam-6282	43	16	is	be	AUX
ejpam-6282	43	17	to	to	PART
ejpam-6282	43	18	debilitate	debilitate	VERB
ejpam-6282	43	19	,	,	PUNCT
ejpam-6282	43	20	generalize	generalize	VERB
ejpam-6282	43	21	,	,	PUNCT
ejpam-6282	43	22	and	and	CCONJ
ejpam-6282	43	23	progress	progress	VERB
ejpam-6282	43	24	the	the	DET
ejpam-6282	43	25	definition	definition	NOUN
ejpam-6282	43	26	of	of	ADP
ejpam-6282	43	27	the	the	DET
ejpam-6282	43	28	existing	exist	VERB
ejpam-6282	43	29	contraction	contraction	NOUN
ejpam-6282	43	30	.	.	PUNCT
ejpam-6282	44	1	the	the	DET
ejpam-6282	44	2	other	other	ADJ
ejpam-6282	44	3	is	be	AUX
ejpam-6282	44	4	to	to	PART
ejpam-6282	44	5	expand	expand	VERB
ejpam-6282	44	6	the	the	DET
ejpam-6282	44	7	construction	construction	NOUN
ejpam-6282	44	8	of	of	ADP
ejpam-6282	44	9	the	the	DET
ejpam-6282	44	10	abstract	abstract	ADJ
ejpam-6282	44	11	space	space	NOUN
ejpam-6282	44	12	where	where	SCONJ
ejpam-6282	44	13	the	the	DET
ejpam-6282	44	14	presence	presence	NOUN
ejpam-6282	44	15	of	of	ADP
ejpam-6282	44	16	the	the	DET
ejpam-6282	44	17	fixed	fix	VERB
ejpam-6282	44	18	point	point	NOUN
ejpam-6282	44	19	is	be	AUX
ejpam-6282	44	20	examined	examine	VERB
ejpam-6282	44	21	and	and	CCONJ
ejpam-6282	44	22	questioned	question	VERB
ejpam-6282	44	23	.	.	PUNCT
ejpam-6282	45	1	the	the	DET
ejpam-6282	45	2	examples	example	NOUN
ejpam-6282	45	3	of	of	ADP
ejpam-6282	45	4	the	the	DET
ejpam-6282	45	5	second	second	ADJ
ejpam-6282	45	6	trend	trend	NOUN
ejpam-6282	45	7	,	,	PUNCT
ejpam-6282	45	8	one	one	PRON
ejpam-6282	45	9	can	can	AUX
ejpam-6282	45	10	list	list	VERB
ejpam-6282	45	11	quasi	quasi	ADJ
ejpam-6282	45	12	-	-	ADJ
ejpam-6282	45	13	metric	metric	ADJ
ejpam-6282	45	14	spaces	space	NOUN
ejpam-6282	45	15	,	,	PUNCT
ejpam-6282	45	16	modular	modular	ADJ
ejpam-6282	45	17	metric	metric	ADJ
ejpam-6282	45	18	spaces	space	NOUN
ejpam-6282	45	19	,	,	PUNCT
ejpam-6282	45	20	banach	banach	ADV
ejpam-6282	45	21	-	-	PUNCT
ejpam-6282	45	22	valued	value	VERB
ejpam-6282	45	23	metric	metric	ADJ
ejpam-6282	45	24	spaces	space	NOUN
ejpam-6282	45	25	,	,	PUNCT
ejpam-6282	45	26	partial	partial	ADJ
ejpam-6282	45	27	metric	metric	ADJ
ejpam-6282	45	28	spaces	space	NOUN
ejpam-6282	45	29	,	,	PUNCT
ejpam-6282	45	30	metric	metric	ADJ
ejpam-6282	45	31	-	-	PUNCT
ejpam-6282	45	32	like	like	ADJ
ejpam-6282	45	33	(	(	PUNCT
ejpam-6282	45	34	dislocated	dislocated	ADJ
ejpam-6282	45	35	)	)	PUNCT
ejpam-6282	45	36	spaces	space	NOUN
ejpam-6282	45	37	,	,	PUNCT
ejpam-6282	45	38	symmetric	symmetric	ADJ
ejpam-6282	45	39	spaces	space	NOUN
ejpam-6282	45	40	,	,	PUNCT
ejpam-6282	45	41	b	b	X
ejpam-6282	45	42	-	-	PUNCT
ejpam-6282	45	43	metric	metric	ADJ
ejpam-6282	45	44	spaces	space	NOUN
ejpam-6282	45	45	,	,	PUNCT
ejpam-6282	45	46	ultra	ultra	ADJ
ejpam-6282	45	47	-	-	ADJ
ejpam-6282	45	48	metric	metric	ADJ
ejpam-6282	45	49	spaces	space	NOUN
ejpam-6282	45	50	,	,	PUNCT
ejpam-6282	45	51	g	g	NOUN
ejpam-6282	45	52	-	-	PUNCT
ejpam-6282	45	53	metric	metric	ADJ
ejpam-6282	45	54	space	space	NOUN
ejpam-6282	45	55	,	,	PUNCT
ejpam-6282	45	56	a	a	DET
ejpam-6282	45	57	-	-	PUNCT
ejpam-6282	45	58	metric	metric	ADJ
ejpam-6282	45	59	space	space	NOUN
ejpam-6282	45	60	,	,	PUNCT
ejpam-6282	45	61	quaternion	quaternion	NOUN
ejpam-6282	45	62	-	-	PUNCT
ejpam-6282	45	63	valued	value	VERB
ejpam-6282	45	64	metric	metric	ADJ
ejpam-6282	45	65	spaces	space	NOUN
ejpam-6282	45	66	,	,	PUNCT
ejpam-6282	45	67	tvs	tvs	PROPN
ejpam-6282	45	68	-	-	PUNCT
ejpam-6282	45	69	valued	value	VERB
ejpam-6282	45	70	metric	metric	ADJ
ejpam-6282	45	71	spaces	space	NOUN
ejpam-6282	45	72	,	,	PUNCT
ejpam-6282	45	73	s	s	NOUN
ejpam-6282	45	74	-	-	ADJ
ejpam-6282	45	75	metric	metric	ADJ
ejpam-6282	45	76	spaces	space	NOUN
ejpam-6282	45	77	,	,	PUNCT
ejpam-6282	45	78	d	d	ADJ
ejpam-6282	45	79	-	-	ADJ
ejpam-6282	45	80	metric	metric	ADJ
ejpam-6282	45	81	space	space	NOUN
ejpam-6282	45	82	,	,	PUNCT
ejpam-6282	45	83	intuitionistic	intuitionistic	ADJ
ejpam-6282	45	84	fuzzy	fuzzy	ADJ
ejpam-6282	45	85	metric	metric	ADJ
ejpam-6282	45	86	space	space	NOUN
ejpam-6282	45	87	,	,	PUNCT
ejpam-6282	45	88	multiplicative	multiplicative	ADJ
ejpam-6282	45	89	metric	metric	ADJ
ejpam-6282	45	90	spaces	space	NOUN
ejpam-6282	45	91	,	,	PUNCT
ejpam-6282	45	92	interpolative	interpolative	ADJ
ejpam-6282	45	93	metric	metric	ADJ
ejpam-6282	45	94	spaces	space	NOUN
ejpam-6282	45	95	,	,	PUNCT
ejpam-6282	45	96	and	and	CCONJ
ejpam-6282	45	97	so	so	ADV
ejpam-6282	45	98	on	on	ADV
ejpam-6282	45	99	.	.	PUNCT
ejpam-6282	46	1	as	as	SCONJ
ejpam-6282	46	2	it	it	PRON
ejpam-6282	46	3	was	be	AUX
ejpam-6282	46	4	discussed	discuss	VERB
ejpam-6282	46	5	above	above	ADV
ejpam-6282	46	6	,	,	PUNCT
ejpam-6282	46	7	some	some	PRON
ejpam-6282	46	8	of	of	ADP
ejpam-6282	46	9	these	these	DET
ejpam-6282	46	10	abstract	abstract	ADJ
ejpam-6282	46	11	structures	structure	NOUN
ejpam-6282	46	12	are	be	AUX
ejpam-6282	46	13	novel	novel	ADJ
ejpam-6282	46	14	and	and	CCONJ
ejpam-6282	46	15	interesting	interesting	ADJ
ejpam-6282	46	16	generalizations	generalization	NOUN
ejpam-6282	46	17	of	of	ADP
ejpam-6282	46	18	the	the	DET
ejpam-6282	46	19	usual	usual	ADJ
ejpam-6282	46	20	metric	metric	ADJ
ejpam-6282	46	21	space	space	NOUN
ejpam-6282	46	22	,	,	PUNCT
ejpam-6282	46	23	whereas	whereas	SCONJ
ejpam-6282	46	24	g.	g.	PROPN
ejpam-6282	46	25	alsahli	alsahli	PROPN
ejpam-6282	46	26	,	,	PUNCT
ejpam-6282	46	27	s.	s.	PROPN
ejpam-6282	46	28	gülyaz	gülyaz	PROPN
ejpam-6282	46	29	-	-	PUNCT
ejpam-6282	46	30	özyurt	özyurt	PROPN
ejpam-6282	46	31	/	/	SYM
ejpam-6282	46	32	eur	eur	PROPN
ejpam-6282	46	33	.	.	PUNCT
ejpam-6282	47	1	j.	j.	PROPN
ejpam-6282	47	2	pure	pure	PROPN
ejpam-6282	47	3	appl	appl	PROPN
ejpam-6282	47	4	.	.	PROPN
ejpam-6282	47	5	math	math	PROPN
ejpam-6282	47	6	,	,	PUNCT
ejpam-6282	47	7	18	18	NUM
ejpam-6282	47	8	(	(	PUNCT
ejpam-6282	47	9	2	2	NUM
ejpam-6282	47	10	)	)	PUNCT
ejpam-6282	47	11	(	(	PUNCT
ejpam-6282	47	12	2025	2025	NUM
ejpam-6282	47	13	)	)	PUNCT
ejpam-6282	47	14	,	,	PUNCT
ejpam-6282	47	15	6282	6282	NUM
ejpam-6282	47	16	3	3	NUM
ejpam-6282	47	17	of	of	ADP
ejpam-6282	47	18	13	13	NUM
ejpam-6282	47	19	some	some	PRON
ejpam-6282	47	20	of	of	ADP
ejpam-6282	47	21	them	they	PRON
ejpam-6282	47	22	are	be	AUX
ejpam-6282	47	23	original	original	ADJ
ejpam-6282	47	24	,	,	PUNCT
ejpam-6282	47	25	see	see	VERB
ejpam-6282	47	26	e.g.	e.g.	ADV
ejpam-6282	47	27	[	[	X
ejpam-6282	47	28	8	8	NUM
ejpam-6282	47	29	]	]	PUNCT
ejpam-6282	47	30	.	.	PUNCT
ejpam-6282	48	1	this	this	DET
ejpam-6282	48	2	paper	paper	NOUN
ejpam-6282	48	3	focuses	focus	VERB
ejpam-6282	48	4	on	on	ADP
ejpam-6282	48	5	the	the	DET
ejpam-6282	48	6	second	second	ADJ
ejpam-6282	48	7	trend	trend	NOUN
ejpam-6282	48	8	,	,	PUNCT
ejpam-6282	48	9	and	and	CCONJ
ejpam-6282	48	10	we	we	PRON
ejpam-6282	48	11	consider	consider	VERB
ejpam-6282	48	12	one	one	NUM
ejpam-6282	48	13	of	of	ADP
ejpam-6282	48	14	the	the	DET
ejpam-6282	48	15	recently	recently	ADV
ejpam-6282	48	16	presented	present	VERB
ejpam-6282	48	17	improvements	improvement	NOUN
ejpam-6282	48	18	of	of	ADP
ejpam-6282	48	19	the	the	DET
ejpam-6282	48	20	standard	standard	ADJ
ejpam-6282	48	21	metric	metric	ADJ
ejpam-6282	48	22	spaces	space	NOUN
ejpam-6282	48	23	,	,	PUNCT
ejpam-6282	48	24	namely	namely	ADV
ejpam-6282	48	25	,	,	PUNCT
ejpam-6282	48	26	interpolative	interpolative	ADJ
ejpam-6282	48	27	metric	metric	ADJ
ejpam-6282	48	28	spaces	space	NOUN
ejpam-6282	48	29	[	[	X
ejpam-6282	48	30	6	6	NUM
ejpam-6282	48	31	,	,	PUNCT
ejpam-6282	48	32	7	7	NUM
ejpam-6282	48	33	,	,	PUNCT
ejpam-6282	48	34	25	25	NUM
ejpam-6282	48	35	]	]	PUNCT
ejpam-6282	48	36	.	.	PUNCT
ejpam-6282	49	1	shortly	shortly	ADV
ejpam-6282	49	2	and	and	CCONJ
ejpam-6282	49	3	simply	simply	ADV
ejpam-6282	49	4	expressing	express	VERB
ejpam-6282	49	5	,	,	PUNCT
ejpam-6282	49	6	an	an	DET
ejpam-6282	49	7	interpolative	interpolative	ADJ
ejpam-6282	49	8	metric	metric	ADJ
ejpam-6282	49	9	structure	structure	NOUN
ejpam-6282	49	10	is	be	AUX
ejpam-6282	49	11	the	the	DET
ejpam-6282	49	12	natural	natural	ADJ
ejpam-6282	49	13	extension	extension	NOUN
ejpam-6282	49	14	of	of	ADP
ejpam-6282	49	15	the	the	DET
ejpam-6282	49	16	standard	standard	ADJ
ejpam-6282	49	17	metric	metric	ADJ
ejpam-6282	49	18	concept	concept	NOUN
ejpam-6282	49	19	by	by	ADP
ejpam-6282	49	20	changing	change	VERB
ejpam-6282	49	21	the	the	DET
ejpam-6282	49	22	triangle	triangle	NOUN
ejpam-6282	49	23	inequality	inequality	NOUN
ejpam-6282	49	24	condition	condition	NOUN
ejpam-6282	49	25	with	with	ADP
ejpam-6282	49	26	another	another	DET
ejpam-6282	49	27	new	new	ADJ
ejpam-6282	49	28	inequality	inequality	NOUN
ejpam-6282	49	29	,	,	PUNCT
ejpam-6282	49	30	so	so	ADV
ejpam-6282	49	31	-	-	PUNCT
ejpam-6282	49	32	called	call	VERB
ejpam-6282	49	33	,	,	PUNCT
ejpam-6282	49	34	interpolative	interpolative	ADJ
ejpam-6282	49	35	inequality	inequality	NOUN
ejpam-6282	49	36	.	.	PUNCT
ejpam-6282	50	1	this	this	DET
ejpam-6282	50	2	modern	modern	ADJ
ejpam-6282	50	3	condition	condition	NOUN
ejpam-6282	50	4	can	can	AUX
ejpam-6282	50	5	be	be	AUX
ejpam-6282	50	6	exceptionally	exceptionally	ADV
ejpam-6282	50	7	valuable	valuable	ADJ
ejpam-6282	50	8	in	in	ADP
ejpam-6282	50	9	estimations	estimation	NOUN
ejpam-6282	50	10	in	in	ADP
ejpam-6282	50	11	possible	possible	ADJ
ejpam-6282	50	12	applications	application	NOUN
ejpam-6282	50	13	.	.	PUNCT
ejpam-6282	51	1	next	next	ADV
ejpam-6282	51	2	,	,	PUNCT
ejpam-6282	51	3	we	we	PRON
ejpam-6282	51	4	review	review	VERB
ejpam-6282	51	5	the	the	DET
ejpam-6282	51	6	idea	idea	NOUN
ejpam-6282	51	7	of	of	ADP
ejpam-6282	51	8	the	the	DET
ejpam-6282	51	9	interpolative	interpolative	ADJ
ejpam-6282	51	10	metric	metric	NOUN
ejpam-6282	51	11	,	,	PUNCT
ejpam-6282	51	12	that	that	PRON
ejpam-6282	51	13	can	can	AUX
ejpam-6282	51	14	be	be	AUX
ejpam-6282	51	15	expressed	express	VERB
ejpam-6282	51	16	as	as	ADP
ejpam-6282	51	17	an	an	DET
ejpam-6282	51	18	inevitable	inevitable	ADJ
ejpam-6282	51	19	generalization	generalization	NOUN
ejpam-6282	51	20	of	of	ADP
ejpam-6282	51	21	a	a	DET
ejpam-6282	51	22	usual	usual	ADJ
ejpam-6282	51	23	metric	metric	ADJ
ejpam-6282	51	24	structure	structure	NOUN
ejpam-6282	51	25	.	.	PUNCT
ejpam-6282	52	1	definition	definition	NOUN
ejpam-6282	52	2	1	1	NUM
ejpam-6282	52	3	.	.	PUNCT
ejpam-6282	53	1	[	[	X
ejpam-6282	53	2	6	6	NUM
ejpam-6282	53	3	,	,	PUNCT
ejpam-6282	53	4	7	7	NUM
ejpam-6282	53	5	]	]	PUNCT
ejpam-6282	53	6	.	.	PUNCT
ejpam-6282	54	1	for	for	ADP
ejpam-6282	54	2	a	a	DET
ejpam-6282	54	3	nonempty	nonempty	ADJ
ejpam-6282	54	4	set	set	VERB
ejpam-6282	54	5	s	s	PROPN
ejpam-6282	54	6	,	,	PUNCT
ejpam-6282	54	7	a	a	DET
ejpam-6282	54	8	distance	distance	NOUN
ejpam-6282	54	9	function	function	NOUN
ejpam-6282	54	10	d	d	NOUN
ejpam-6282	54	11	:	:	PUNCT
ejpam-6282	54	12	s	s	VERB
ejpam-6282	54	13	×	×	PROPN
ejpam-6282	54	14	s	s	X
ejpam-6282	54	15	→	→	SYM
ejpam-6282	54	16	[	[	X
ejpam-6282	54	17	0,+∞	0,+∞	NUM
ejpam-6282	54	18	)	)	PUNCT
ejpam-6282	54	19	is	be	AUX
ejpam-6282	54	20	called	call	VERB
ejpam-6282	54	21	(	(	PUNCT
ejpam-6282	54	22	ξ	ξ	PROPN
ejpam-6282	54	23	,	,	PUNCT
ejpam-6282	54	24	c)-interpolative	c)-interpolative	ADJ
ejpam-6282	54	25	metric	metric	ADJ
ejpam-6282	54	26	if	if	SCONJ
ejpam-6282	54	27	(	(	PUNCT
ejpam-6282	54	28	im0	im0	ADJ
ejpam-6282	54	29	)	)	PUNCT
ejpam-6282	54	30	d(t	d(t	PROPN
ejpam-6282	54	31	,	,	PUNCT
ejpam-6282	54	32	y	y	PROPN
ejpam-6282	54	33	)	)	PUNCT
ejpam-6282	54	34	>	>	X
ejpam-6282	54	35	0	0	NUM
ejpam-6282	54	36	,	,	PUNCT
ejpam-6282	54	37	for	for	ADP
ejpam-6282	54	38	all	all	DET
ejpam-6282	54	39	distinct	distinct	PROPN
ejpam-6282	54	40	t	t	PROPN
ejpam-6282	54	41	,	,	PUNCT
ejpam-6282	54	42	y	y	PROPN
ejpam-6282	54	43	∈	∈	PROPN
ejpam-6282	54	44	s	s	PART
ejpam-6282	54	45	;	;	PUNCT
ejpam-6282	54	46	(	(	PUNCT
ejpam-6282	54	47	im1a	im1a	NOUN
ejpam-6282	54	48	)	)	PUNCT
ejpam-6282	54	49	d(t	d(t	PROPN
ejpam-6282	54	50	,	,	PUNCT
ejpam-6282	54	51	y	y	NOUN
ejpam-6282	54	52	)	)	PUNCT
ejpam-6282	54	53	=	=	SYM
ejpam-6282	54	54	0	0	NUM
ejpam-6282	54	55	,	,	PUNCT
ejpam-6282	54	56	implies	imply	VERB
ejpam-6282	54	57	that	that	SCONJ
ejpam-6282	54	58	t	t	NOUN
ejpam-6282	54	59	=	=	SYM
ejpam-6282	54	60	y	y	PROPN
ejpam-6282	54	61	(	(	PUNCT
ejpam-6282	54	62	im1b	im1b	PROPN
ejpam-6282	54	63	)	)	PUNCT
ejpam-6282	54	64	t	t	NOUN
ejpam-6282	54	65	=	=	SYM
ejpam-6282	54	66	y	y	PROPN
ejpam-6282	54	67	implies	imply	VERB
ejpam-6282	54	68	that	that	SCONJ
ejpam-6282	54	69	d(t	d(t	PROPN
ejpam-6282	54	70	,	,	PUNCT
ejpam-6282	54	71	y	y	NOUN
ejpam-6282	54	72	)	)	PUNCT
ejpam-6282	54	73	=	=	SYM
ejpam-6282	54	74	0	0	NUM
ejpam-6282	54	75	;	;	PUNCT
ejpam-6282	54	76	(	(	PUNCT
ejpam-6282	54	77	im2	im2	PROPN
ejpam-6282	54	78	)	)	PUNCT
ejpam-6282	54	79	d(y	d(y	PROPN
ejpam-6282	54	80	,	,	PUNCT
ejpam-6282	54	81	t	t	PROPN
ejpam-6282	54	82	)	)	PUNCT
ejpam-6282	54	83	=	=	SYM
ejpam-6282	54	84	d(t	d(t	PROPN
ejpam-6282	54	85	,	,	PUNCT
ejpam-6282	54	86	y	y	PROPN
ejpam-6282	54	87	)	)	PUNCT
ejpam-6282	54	88	,	,	PUNCT
ejpam-6282	54	89	for	for	ADP
ejpam-6282	54	90	all	all	DET
ejpam-6282	54	91	t	t	PROPN
ejpam-6282	54	92	,	,	PUNCT
ejpam-6282	54	93	y	y	PROPN
ejpam-6282	54	94	∈	∈	PROPN
ejpam-6282	54	95	s	s	PART
ejpam-6282	54	96	;	;	PUNCT
ejpam-6282	54	97	(	(	PUNCT
ejpam-6282	54	98	im3	im3	PROPN
ejpam-6282	54	99	)	)	PUNCT
ejpam-6282	54	100	there	there	PRON
ejpam-6282	54	101	exist	exist	VERB
ejpam-6282	54	102	k	k	PROPN
ejpam-6282	54	103	≥	≥	X
ejpam-6282	54	104	0	0	NUM
ejpam-6282	54	105	and	and	CCONJ
ejpam-6282	54	106	ξ	ξ	PROPN
ejpam-6282	54	107	∈	∈	PROPN
ejpam-6282	54	108	(	(	PUNCT
ejpam-6282	54	109	0	0	NUM
ejpam-6282	54	110	,	,	PUNCT
ejpam-6282	54	111	1	1	NUM
ejpam-6282	54	112	)	)	PUNCT
ejpam-6282	54	113	in	in	ADP
ejpam-6282	54	114	a	a	DET
ejpam-6282	54	115	way	way	NOUN
ejpam-6282	54	116	that	that	PRON
ejpam-6282	54	117	the	the	DET
ejpam-6282	54	118	following	follow	VERB
ejpam-6282	54	119	inequality	inequality	NOUN
ejpam-6282	54	120	is	be	AUX
ejpam-6282	54	121	satisfied	satisfied	ADJ
ejpam-6282	54	122	for	for	ADP
ejpam-6282	54	123	any	any	DET
ejpam-6282	54	124	choice	choice	NOUN
ejpam-6282	54	125	of	of	ADP
ejpam-6282	54	126	t	t	PROPN
ejpam-6282	54	127	,	,	PUNCT
ejpam-6282	54	128	y	y	PROPN
ejpam-6282	54	129	,	,	PUNCT
ejpam-6282	54	130	w	w	PROPN
ejpam-6282	54	131	∈	∈	PROPN
ejpam-6282	54	132	s.	s.	PROPN
ejpam-6282	54	133	d(t	d(t	PROPN
ejpam-6282	54	134	,	,	PUNCT
ejpam-6282	54	135	y	y	NOUN
ejpam-6282	54	136	)	)	PUNCT
ejpam-6282	54	137	≤	≤	NOUN
ejpam-6282	54	138	d(t	d(t	PROPN
ejpam-6282	54	139	,	,	PUNCT
ejpam-6282	54	140	w	w	NOUN
ejpam-6282	54	141	)	)	PUNCT
ejpam-6282	54	142	+	+	CCONJ
ejpam-6282	54	143	d(w	d(w	PROPN
ejpam-6282	54	144	,	,	PUNCT
ejpam-6282	54	145	y	y	PROPN
ejpam-6282	54	146	)	)	PUNCT
ejpam-6282	55	1	+	+	CCONJ
ejpam-6282	55	2	k	k	X
ejpam-6282	55	3	[	[	PUNCT
ejpam-6282	55	4	(	(	PUNCT
ejpam-6282	55	5	d(t	d(t	PROPN
ejpam-6282	55	6	,	,	PUNCT
ejpam-6282	55	7	w))ξ	w))ξ	NOUN
ejpam-6282	55	8	(	(	PUNCT
ejpam-6282	55	9	d(w	d(w	PROPN
ejpam-6282	55	10	,	,	PUNCT
ejpam-6282	55	11	y))1−ξ	y))1−ξ	NUM
ejpam-6282	55	12	.	.	PUNCT
ejpam-6282	55	13	]	]	PUNCT
ejpam-6282	56	1	here	here	ADV
ejpam-6282	56	2	,	,	PUNCT
ejpam-6282	56	3	the	the	DET
ejpam-6282	56	4	pair	pair	NOUN
ejpam-6282	56	5	(	(	PUNCT
ejpam-6282	56	6	s	s	X
ejpam-6282	56	7	,	,	PUNCT
ejpam-6282	56	8	d	d	NOUN
ejpam-6282	56	9	)	)	PUNCT
ejpam-6282	56	10	is	be	AUX
ejpam-6282	56	11	said	say	VERB
ejpam-6282	56	12	to	to	PART
ejpam-6282	56	13	be	be	AUX
ejpam-6282	56	14	an	an	DET
ejpam-6282	56	15	(	(	PUNCT
ejpam-6282	56	16	ξ	ξ	PROPN
ejpam-6282	56	17	,	,	PUNCT
ejpam-6282	56	18	c)-interpolative	c)-interpolative	ADJ
ejpam-6282	56	19	metric	metric	ADJ
ejpam-6282	56	20	space	space	NOUN
ejpam-6282	56	21	(	(	PUNCT
ejpam-6282	56	22	in	in	ADP
ejpam-6282	56	23	short	short	ADJ
ejpam-6282	56	24	,	,	PUNCT
ejpam-6282	56	25	ims	im	NOUN
ejpam-6282	56	26	)	)	PUNCT
ejpam-6282	56	27	.	.	PUNCT
ejpam-6282	57	1	remark	remark	PROPN
ejpam-6282	57	2	1	1	NUM
ejpam-6282	57	3	.	.	PUNCT
ejpam-6282	58	1	[	[	X
ejpam-6282	58	2	6	6	NUM
ejpam-6282	58	3	,	,	PUNCT
ejpam-6282	58	4	7	7	NUM
ejpam-6282	58	5	]	]	PUNCT
ejpam-6282	58	6	.	.	PUNCT
ejpam-6282	59	1	as	as	SCONJ
ejpam-6282	59	2	it	it	PRON
ejpam-6282	59	3	is	be	AUX
ejpam-6282	59	4	clear	clear	ADJ
ejpam-6282	59	5	,	,	PUNCT
ejpam-6282	59	6	for	for	ADP
ejpam-6282	59	7	c	c	NOUN
ejpam-6282	59	8	=	=	SYM
ejpam-6282	59	9	0	0	PROPN
ejpam-6282	59	10	,	,	PUNCT
ejpam-6282	59	11	an	an	DET
ejpam-6282	59	12	(	(	PUNCT
ejpam-6282	59	13	ξ	ξ	PROPN
ejpam-6282	59	14	,	,	PUNCT
ejpam-6282	59	15	c)-interpolative	c)-interpolative	ADJ
ejpam-6282	59	16	metric	metric	ADJ
ejpam-6282	59	17	space	space	NOUN
ejpam-6282	59	18	(	(	PUNCT
ejpam-6282	59	19	s	s	X
ejpam-6282	59	20	,	,	PUNCT
ejpam-6282	59	21	d	d	NOUN
ejpam-6282	59	22	)	)	PUNCT
ejpam-6282	59	23	turns	turn	VERB
ejpam-6282	59	24	into	into	ADP
ejpam-6282	59	25	the	the	DET
ejpam-6282	59	26	usual	usual	ADJ
ejpam-6282	59	27	metric	metric	ADJ
ejpam-6282	59	28	space	space	NOUN
ejpam-6282	59	29	.	.	PUNCT
ejpam-6282	60	1	inspired	inspire	VERB
ejpam-6282	60	2	from	from	ADP
ejpam-6282	60	3	the	the	DET
ejpam-6282	60	4	examples	example	NOUN
ejpam-6282	60	5	in	in	ADP
ejpam-6282	60	6	[	[	X
ejpam-6282	60	7	6	6	NUM
ejpam-6282	60	8	,	,	PUNCT
ejpam-6282	60	9	7	7	NUM
ejpam-6282	60	10	]	]	PUNCT
ejpam-6282	60	11	,	,	PUNCT
ejpam-6282	60	12	we	we	PRON
ejpam-6282	60	13	shall	shall	AUX
ejpam-6282	60	14	construct	construct	VERB
ejpam-6282	60	15	the	the	DET
ejpam-6282	60	16	following	following	ADJ
ejpam-6282	60	17	example	example	NOUN
ejpam-6282	60	18	to	to	PART
ejpam-6282	60	19	indicate	indicate	VERB
ejpam-6282	60	20	that	that	SCONJ
ejpam-6282	60	21	the	the	DET
ejpam-6282	60	22	converse	converse	NOUN
ejpam-6282	60	23	is	be	AUX
ejpam-6282	60	24	false	false	ADJ
ejpam-6282	60	25	.	.	PUNCT
ejpam-6282	60	26	example	example	NOUN
ejpam-6282	61	1	1	1	NUM
ejpam-6282	61	2	.	.	X
ejpam-6282	61	3	set	set	VERB
ejpam-6282	61	4	s	s	PART
ejpam-6282	61	5	=	=	PUNCT
ejpam-6282	62	1	[	[	X
ejpam-6282	62	2	0	0	NUM
ejpam-6282	62	3	,	,	PUNCT
ejpam-6282	62	4	1	1	NUM
ejpam-6282	62	5	]	]	PUNCT
ejpam-6282	62	6	and	and	CCONJ
ejpam-6282	62	7	consider	consider	VERB
ejpam-6282	62	8	a	a	DET
ejpam-6282	62	9	mapping	mapping	NOUN
ejpam-6282	63	1	d	d	NOUN
ejpam-6282	63	2	:	:	PUNCT
ejpam-6282	63	3	s	s	VERB
ejpam-6282	63	4	×	×	PROPN
ejpam-6282	63	5	s	s	X
ejpam-6282	63	6	→	→	SYM
ejpam-6282	63	7	[	[	X
ejpam-6282	63	8	0	0	NUM
ejpam-6282	63	9	,	,	PUNCT
ejpam-6282	63	10	∞	∞	PROPN
ejpam-6282	63	11	)	)	PUNCT
ejpam-6282	63	12	which	which	PRON
ejpam-6282	63	13	is	be	AUX
ejpam-6282	63	14	defined	define	VERB
ejpam-6282	63	15	by	by	ADP
ejpam-6282	63	16	d(t	d(t	PROPN
ejpam-6282	63	17	,	,	PUNCT
ejpam-6282	63	18	y	y	PROPN
ejpam-6282	63	19	)	)	PUNCT
ejpam-6282	63	20	:	:	PUNCT
ejpam-6282	64	1	=	=	PUNCT
ejpam-6282	64	2	|t	|t	VERB
ejpam-6282	64	3	−	−	PROPN
ejpam-6282	64	4	y|6	y|6	PROPN
ejpam-6282	64	5	,	,	PUNCT
ejpam-6282	64	6	for	for	ADP
ejpam-6282	64	7	all	all	DET
ejpam-6282	64	8	t	t	PROPN
ejpam-6282	64	9	,	,	PUNCT
ejpam-6282	64	10	y	y	PROPN
ejpam-6282	64	11	∈	∈	PROPN
ejpam-6282	64	12	s.	s.	PROPN
ejpam-6282	64	13	g.	g.	PROPN
ejpam-6282	64	14	alsahli	alsahli	PROPN
ejpam-6282	64	15	,	,	PUNCT
ejpam-6282	64	16	s.	s.	PROPN
ejpam-6282	64	17	gülyaz	gülyaz	PROPN
ejpam-6282	64	18	-	-	PUNCT
ejpam-6282	64	19	özyurt	özyurt	PROPN
ejpam-6282	64	20	/	/	SYM
ejpam-6282	64	21	eur	eur	PROPN
ejpam-6282	64	22	.	.	PUNCT
ejpam-6282	65	1	j.	j.	PROPN
ejpam-6282	65	2	pure	pure	PROPN
ejpam-6282	65	3	appl	appl	PROPN
ejpam-6282	65	4	.	.	PROPN
ejpam-6282	65	5	math	math	PROPN
ejpam-6282	65	6	,	,	PUNCT
ejpam-6282	65	7	18	18	NUM
ejpam-6282	65	8	(	(	PUNCT
ejpam-6282	65	9	2	2	NUM
ejpam-6282	65	10	)	)	PUNCT
ejpam-6282	65	11	(	(	PUNCT
ejpam-6282	65	12	2025	2025	NUM
ejpam-6282	65	13	)	)	PUNCT
ejpam-6282	65	14	,	,	PUNCT
ejpam-6282	65	15	6282	6282	NUM
ejpam-6282	65	16	4	4	NUM
ejpam-6282	65	17	of	of	ADP
ejpam-6282	65	18	13	13	NUM
ejpam-6282	65	19	it	it	PRON
ejpam-6282	65	20	is	be	AUX
ejpam-6282	65	21	obvious	obvious	ADJ
ejpam-6282	65	22	to	to	PART
ejpam-6282	65	23	see	see	VERB
ejpam-6282	65	24	that	that	DET
ejpam-6282	65	25	axioms	axiom	NOUN
ejpam-6282	65	26	(	(	PUNCT
ejpam-6282	65	27	im1	im1	PROPN
ejpam-6282	65	28	)	)	PUNCT
ejpam-6282	65	29	and	and	CCONJ
ejpam-6282	65	30	(	(	PUNCT
ejpam-6282	65	31	im2	im2	PROPN
ejpam-6282	65	32	)	)	PUNCT
ejpam-6282	65	33	are	be	AUX
ejpam-6282	65	34	easily	easily	ADV
ejpam-6282	65	35	derived	derive	VERB
ejpam-6282	65	36	.	.	PUNCT
ejpam-6282	66	1	for	for	ADP
ejpam-6282	66	2	(	(	PUNCT
ejpam-6282	66	3	im3	im3	PROPN
ejpam-6282	66	4	)	)	PUNCT
ejpam-6282	66	5	,	,	PUNCT
ejpam-6282	66	6	we	we	PRON
ejpam-6282	66	7	have	have	VERB
ejpam-6282	66	8	d(t	d(t	PROPN
ejpam-6282	66	9	,	,	PUNCT
ejpam-6282	66	10	y	y	PROPN
ejpam-6282	66	11	)	)	PUNCT
ejpam-6282	66	12	=	=	VERB
ejpam-6282	67	1	|t	|t	VERB
ejpam-6282	68	1	−	−	PROPN
ejpam-6282	68	2	y|6	y|6	PROPN
ejpam-6282	68	3	=	=	PUNCT
ejpam-6282	68	4	|t	|t	PROPN
ejpam-6282	68	5	−	−	PROPN
ejpam-6282	68	6	w	w	PROPN
ejpam-6282	69	1	+	+	CCONJ
ejpam-6282	69	2	w	w	PROPN
ejpam-6282	69	3	−	−	PROPN
ejpam-6282	69	4	y|6	y|6	PROPN
ejpam-6282	69	5	=	=	NOUN
ejpam-6282	69	6	|t	|t	NOUN
ejpam-6282	70	1	−	−	PROPN
ejpam-6282	70	2	w|6	w|6	PROPN
ejpam-6282	70	3	+	+	CCONJ
ejpam-6282	70	4	6|t	6|t	PROPN
ejpam-6282	70	5	−	−	NOUN
ejpam-6282	70	6	w|5|w	w|5|w	PROPN
ejpam-6282	70	7	−	−	PROPN
ejpam-6282	70	8	y|+	y|+	PROPN
ejpam-6282	70	9	15|t	15|t	NUM
ejpam-6282	70	10	−	−	PROPN
ejpam-6282	70	11	w|4|w	w|4|w	NOUN
ejpam-6282	70	12	−	−	PROPN
ejpam-6282	70	13	y|2	y|2	PROPN
ejpam-6282	70	14	+20|t	+20|t	PROPN
ejpam-6282	70	15	−	−	PROPN
ejpam-6282	70	16	w|3|w	w|3|w	PROPN
ejpam-6282	70	17	−	−	PROPN
ejpam-6282	70	18	y|3	y|3	PROPN
ejpam-6282	70	19	+	+	CCONJ
ejpam-6282	70	20	15|t	15|t	NUM
ejpam-6282	70	21	−	−	PROPN
ejpam-6282	70	22	w|2|w	w|2|w	PROPN
ejpam-6282	70	23	−	−	PROPN
ejpam-6282	70	24	y|4	y|4	PROPN
ejpam-6282	70	25	+6|t	+6|t	NOUN
ejpam-6282	71	1	−	−	PROPN
ejpam-6282	71	2	w||w	w||w	PROPN
ejpam-6282	71	3	−	−	PROPN
ejpam-6282	72	1	y|5	y|5	INTJ
ejpam-6282	72	2	+	+	CCONJ
ejpam-6282	72	3	|w	|w	ADJ
ejpam-6282	72	4	−	−	PROPN
ejpam-6282	72	5	y|6	y|6	PROPN
ejpam-6282	72	6	≤	≤	PROPN
ejpam-6282	72	7	|t	|t	VERB
ejpam-6282	73	1	−	−	PROPN
ejpam-6282	73	2	w|6	w|6	PROPN
ejpam-6282	73	3	+	+	PROPN
ejpam-6282	73	4	|w	|w	ADJ
ejpam-6282	73	5	−	−	PROPN
ejpam-6282	73	6	y|6	y|6	PROPN
ejpam-6282	73	7	+	+	PROPN
ejpam-6282	73	8	6|t	6|t	PROPN
ejpam-6282	73	9	−	−	NOUN
ejpam-6282	73	10	w|5|w	w|5|w	PROPN
ejpam-6282	73	11	−	−	PROPN
ejpam-6282	73	12	y|+	y|+	PROPN
ejpam-6282	73	13	6|t	6|t	SYM
ejpam-6282	73	14	−	−	NOUN
ejpam-6282	73	15	w||w	w||w	NOUN
ejpam-6282	74	1	−	−	PROPN
ejpam-6282	75	1	y|5	y|5	PROPN
ejpam-6282	75	2	+15|t	+15|t	PROPN
ejpam-6282	75	3	−	−	PROPN
ejpam-6282	75	4	w|4|w	w|4|w	NOUN
ejpam-6282	75	5	−	−	PROPN
ejpam-6282	75	6	y|2	y|2	PROPN
ejpam-6282	76	1	+	+	CCONJ
ejpam-6282	76	2	15|t	15|t	NUM
ejpam-6282	76	3	−	−	PROPN
ejpam-6282	76	4	w|2|w	w|2|w	PROPN
ejpam-6282	76	5	−	−	PROPN
ejpam-6282	76	6	y|4	y|4	PROPN
ejpam-6282	77	1	+20|t	+20|t	PROPN
ejpam-6282	77	2	−	−	PROPN
ejpam-6282	77	3	w|3|w	w|3|w	PROPN
ejpam-6282	77	4	−	−	PROPN
ejpam-6282	77	5	y|3	y|3	PROPN
ejpam-6282	77	6	≤	≤	PROPN
ejpam-6282	77	7	d(t	d(t	PROPN
ejpam-6282	77	8	,	,	PUNCT
ejpam-6282	77	9	w	w	NOUN
ejpam-6282	77	10	)	)	PUNCT
ejpam-6282	77	11	+	+	CCONJ
ejpam-6282	78	1	d(w	d(w	PROPN
ejpam-6282	78	2	,	,	PUNCT
ejpam-6282	78	3	y	y	PROPN
ejpam-6282	78	4	)	)	PUNCT
ejpam-6282	79	1	+	+	CCONJ
ejpam-6282	79	2	6	6	NUM
ejpam-6282	79	3	[	[	PUNCT
ejpam-6282	79	4	(	(	PUNCT
ejpam-6282	79	5	d(t	d(t	PROPN
ejpam-6282	79	6	,	,	PUNCT
ejpam-6282	79	7	w	w	NOUN
ejpam-6282	79	8	)	)	PUNCT
ejpam-6282	79	9	)	)	PUNCT
ejpam-6282	79	10	5	5	NUM
ejpam-6282	79	11	6	6	NUM
ejpam-6282	79	12	(	(	PUNCT
ejpam-6282	79	13	d(w	d(w	PROPN
ejpam-6282	79	14	,	,	PUNCT
ejpam-6282	79	15	y	y	NOUN
ejpam-6282	79	16	)	)	PUNCT
ejpam-6282	79	17	)	)	PUNCT
ejpam-6282	79	18	1	1	NUM
ejpam-6282	79	19	6	6	NUM
ejpam-6282	79	20	]	]	PUNCT
ejpam-6282	79	21	+6	+6	PROPN
ejpam-6282	79	22	[	[	PUNCT
ejpam-6282	79	23	(	(	PUNCT
ejpam-6282	79	24	d(t	d(t	PROPN
ejpam-6282	79	25	,	,	PUNCT
ejpam-6282	79	26	w	w	NOUN
ejpam-6282	79	27	)	)	PUNCT
ejpam-6282	79	28	)	)	PUNCT
ejpam-6282	79	29	1	1	NUM
ejpam-6282	79	30	6	6	NUM
ejpam-6282	79	31	(	(	PUNCT
ejpam-6282	79	32	d(w	d(w	PROPN
ejpam-6282	79	33	,	,	PUNCT
ejpam-6282	79	34	y	y	NOUN
ejpam-6282	79	35	)	)	PUNCT
ejpam-6282	79	36	)	)	PUNCT
ejpam-6282	79	37	5	5	NUM
ejpam-6282	79	38	6	6	NUM
ejpam-6282	79	39	]	]	PUNCT
ejpam-6282	79	40	+	+	CCONJ
ejpam-6282	79	41	15	15	NUM
ejpam-6282	79	42	[	[	PUNCT
ejpam-6282	79	43	(	(	PUNCT
ejpam-6282	79	44	d(t	d(t	PROPN
ejpam-6282	79	45	,	,	PUNCT
ejpam-6282	79	46	w	w	NOUN
ejpam-6282	79	47	)	)	PUNCT
ejpam-6282	79	48	)	)	PUNCT
ejpam-6282	79	49	4	4	NUM
ejpam-6282	79	50	6	6	NUM
ejpam-6282	79	51	(	(	PUNCT
ejpam-6282	79	52	d(w	d(w	PROPN
ejpam-6282	79	53	,	,	PUNCT
ejpam-6282	79	54	y	y	NOUN
ejpam-6282	79	55	)	)	PUNCT
ejpam-6282	79	56	)	)	PUNCT
ejpam-6282	79	57	2	2	NUM
ejpam-6282	79	58	6	6	NUM
ejpam-6282	79	59	]	]	PUNCT
ejpam-6282	79	60	+15	+15	PROPN
ejpam-6282	79	61	[	[	PUNCT
ejpam-6282	79	62	(	(	PUNCT
ejpam-6282	79	63	d(t	d(t	PROPN
ejpam-6282	79	64	,	,	PUNCT
ejpam-6282	79	65	w	w	NOUN
ejpam-6282	79	66	)	)	PUNCT
ejpam-6282	79	67	)	)	PUNCT
ejpam-6282	79	68	2	2	NUM
ejpam-6282	79	69	6	6	NUM
ejpam-6282	79	70	(	(	PUNCT
ejpam-6282	79	71	d(w	d(w	PROPN
ejpam-6282	79	72	,	,	PUNCT
ejpam-6282	79	73	y	y	NOUN
ejpam-6282	79	74	)	)	PUNCT
ejpam-6282	79	75	)	)	PUNCT
ejpam-6282	79	76	4	4	NUM
ejpam-6282	79	77	6	6	NUM
ejpam-6282	79	78	]	]	PUNCT
ejpam-6282	80	1	+	+	CCONJ
ejpam-6282	80	2	20	20	NUM
ejpam-6282	80	3	[	[	PUNCT
ejpam-6282	80	4	(	(	PUNCT
ejpam-6282	80	5	d(t	d(t	PROPN
ejpam-6282	80	6	,	,	PUNCT
ejpam-6282	80	7	w	w	NOUN
ejpam-6282	80	8	)	)	PUNCT
ejpam-6282	80	9	)	)	PUNCT
ejpam-6282	80	10	3	3	NUM
ejpam-6282	80	11	6	6	NUM
ejpam-6282	80	12	(	(	PUNCT
ejpam-6282	80	13	d(w	d(w	PROPN
ejpam-6282	80	14	,	,	PUNCT
ejpam-6282	80	15	y	y	NOUN
ejpam-6282	80	16	)	)	PUNCT
ejpam-6282	80	17	)	)	PUNCT
ejpam-6282	80	18	3	3	NUM
ejpam-6282	80	19	6	6	NUM
ejpam-6282	80	20	]	]	PUNCT
ejpam-6282	80	21	without	without	ADP
ejpam-6282	80	22	loss	loss	NOUN
ejpam-6282	80	23	of	of	ADP
ejpam-6282	80	24	generality	generality	NOUN
ejpam-6282	80	25	,	,	PUNCT
ejpam-6282	80	26	we	we	PRON
ejpam-6282	80	27	assume	assume	VERB
ejpam-6282	80	28	d(t	d(t	PROPN
ejpam-6282	80	29	,	,	PUNCT
ejpam-6282	80	30	w	w	NOUN
ejpam-6282	80	31	)	)	PUNCT
ejpam-6282	80	32	≥	≥	NOUN
ejpam-6282	80	33	d(w	d(w	PROPN
ejpam-6282	80	34	,	,	PUNCT
ejpam-6282	80	35	y	y	PROPN
ejpam-6282	80	36	)	)	PUNCT
ejpam-6282	80	37	≤	≤	NOUN
ejpam-6282	80	38	d(t	d(t	PROPN
ejpam-6282	80	39	,	,	PUNCT
ejpam-6282	80	40	w	w	NOUN
ejpam-6282	80	41	)	)	PUNCT
ejpam-6282	80	42	+	+	CCONJ
ejpam-6282	80	43	d(w	d(w	PROPN
ejpam-6282	80	44	,	,	PUNCT
ejpam-6282	80	45	y	y	PROPN
ejpam-6282	80	46	)	)	PUNCT
ejpam-6282	81	1	+	+	CCONJ
ejpam-6282	81	2	30	30	NUM
ejpam-6282	81	3	[	[	PUNCT
ejpam-6282	81	4	(	(	PUNCT
ejpam-6282	81	5	d(t	d(t	PROPN
ejpam-6282	81	6	,	,	PUNCT
ejpam-6282	81	7	w	w	NOUN
ejpam-6282	81	8	)	)	PUNCT
ejpam-6282	81	9	)	)	PUNCT
ejpam-6282	81	10	1	1	NUM
ejpam-6282	81	11	6	6	NUM
ejpam-6282	81	12	(	(	PUNCT
ejpam-6282	81	13	d(w	d(w	PROPN
ejpam-6282	81	14	,	,	PUNCT
ejpam-6282	81	15	y	y	NOUN
ejpam-6282	81	16	)	)	PUNCT
ejpam-6282	81	17	)	)	PUNCT
ejpam-6282	81	18	5	5	NUM
ejpam-6282	81	19	6	6	NUM
ejpam-6282	81	20	.	.	PUNCT
ejpam-6282	81	21	]	]	PUNCT
ejpam-6282	81	22	(	(	PUNCT
ejpam-6282	81	23	1.1	1.1	NUM
ejpam-6282	81	24	)	)	PUNCT
ejpam-6282	82	1	so	so	ADV
ejpam-6282	82	2	,	,	PUNCT
ejpam-6282	82	3	we	we	PRON
ejpam-6282	82	4	find	find	VERB
ejpam-6282	82	5	that	that	SCONJ
ejpam-6282	82	6	(	(	PUNCT
ejpam-6282	82	7	im3	im3	PROPN
ejpam-6282	82	8	)	)	PUNCT
ejpam-6282	82	9	is	be	AUX
ejpam-6282	82	10	satisfied	satisfied	ADJ
ejpam-6282	82	11	for	for	ADP
ejpam-6282	82	12	c	c	PROPN
ejpam-6282	82	13	≥	≥	NUM
ejpam-6282	82	14	14	14	NUM
ejpam-6282	82	15	for	for	ADP
ejpam-6282	82	16	all	all	DET
ejpam-6282	82	17	ξ	ξ	X
ejpam-6282	82	18	=	=	SYM
ejpam-6282	82	19	1	1	NUM
ejpam-6282	82	20	6	6	NUM
ejpam-6282	82	21	∈	∈	NOUN
ejpam-6282	82	22	(	(	PUNCT
ejpam-6282	82	23	0	0	NUM
ejpam-6282	82	24	,	,	PUNCT
ejpam-6282	82	25	1	1	NUM
ejpam-6282	82	26	)	)	PUNCT
ejpam-6282	82	27	.	.	PUNCT
ejpam-6282	83	1	as	as	ADP
ejpam-6282	83	2	a	a	DET
ejpam-6282	83	3	result	result	NOUN
ejpam-6282	83	4	,	,	PUNCT
ejpam-6282	83	5	(	(	PUNCT
ejpam-6282	83	6	s	s	X
ejpam-6282	83	7	,	,	PUNCT
ejpam-6282	83	8	d	d	NOUN
ejpam-6282	83	9	)	)	PUNCT
ejpam-6282	83	10	forms	form	NOUN
ejpam-6282	83	11	(	(	PUNCT
ejpam-6282	83	12	1	1	NUM
ejpam-6282	83	13	6	6	NUM
ejpam-6282	83	14	,	,	PUNCT
ejpam-6282	83	15	62)-interpolative	62)-interpolative	ADJ
ejpam-6282	83	16	metric	metric	ADJ
ejpam-6282	83	17	space	space	NOUN
ejpam-6282	83	18	.	.	PUNCT
ejpam-6282	84	1	in	in	ADP
ejpam-6282	84	2	conclusion	conclusion	NOUN
ejpam-6282	84	3	,	,	PUNCT
ejpam-6282	84	4	(	(	PUNCT
ejpam-6282	84	5	s	s	X
ejpam-6282	84	6	,	,	PUNCT
ejpam-6282	84	7	d	d	NOUN
ejpam-6282	84	8	)	)	PUNCT
ejpam-6282	84	9	is	be	AUX
ejpam-6282	84	10	(	(	PUNCT
ejpam-6282	84	11	1	1	NUM
ejpam-6282	84	12	6	6	NUM
ejpam-6282	84	13	,	,	PUNCT
ejpam-6282	84	14	62)-interpolative	62)-interpolative	ADJ
ejpam-6282	84	15	metric	metric	ADJ
ejpam-6282	84	16	space	space	NOUN
ejpam-6282	84	17	.	.	PUNCT
ejpam-6282	85	1	inspired	inspire	VERB
ejpam-6282	85	2	by	by	ADP
ejpam-6282	85	3	the	the	DET
ejpam-6282	85	4	example	example	NOUN
ejpam-6282	85	5	in	in	ADP
ejpam-6282	85	6	[	[	X
ejpam-6282	85	7	6	6	NUM
ejpam-6282	85	8	,	,	PUNCT
ejpam-6282	85	9	7	7	NUM
ejpam-6282	85	10	]	]	PUNCT
ejpam-6282	85	11	,	,	PUNCT
ejpam-6282	85	12	we	we	PRON
ejpam-6282	85	13	consider	consider	VERB
ejpam-6282	85	14	the	the	DET
ejpam-6282	85	15	following	follow	VERB
ejpam-6282	85	16	sample	sample	NOUN
ejpam-6282	85	17	:	:	PUNCT
ejpam-6282	85	18	example	example	NOUN
ejpam-6282	86	1	2	2	NUM
ejpam-6282	86	2	.	.	X
ejpam-6282	87	1	the	the	DET
ejpam-6282	87	2	(	(	PUNCT
ejpam-6282	87	3	s	s	PROPN
ejpam-6282	87	4	,	,	PUNCT
ejpam-6282	87	5	ρ	ρ	NOUN
ejpam-6282	87	6	)	)	PUNCT
ejpam-6282	87	7	denotes	denote	VERB
ejpam-6282	87	8	a	a	DET
ejpam-6282	87	9	usual	usual	ADJ
ejpam-6282	87	10	metric	metric	ADJ
ejpam-6282	87	11	space	space	NOUN
ejpam-6282	87	12	.	.	PUNCT
ejpam-6282	88	1	we	we	PRON
ejpam-6282	88	2	consider	consider	VERB
ejpam-6282	88	3	the	the	DET
ejpam-6282	88	4	following	follow	VERB
ejpam-6282	88	5	distance	distance	NOUN
ejpam-6282	88	6	function	function	NOUN
ejpam-6282	88	7	d	d	NOUN
ejpam-6282	88	8	:	:	PUNCT
ejpam-6282	88	9	s	s	VERB
ejpam-6282	88	10	×	×	PROPN
ejpam-6282	88	11	s	s	X
ejpam-6282	88	12	→	→	SYM
ejpam-6282	88	13	[	[	X
ejpam-6282	88	14	0	0	NUM
ejpam-6282	88	15	,	,	PUNCT
ejpam-6282	88	16	∞	∞	PROPN
ejpam-6282	88	17	)	)	PUNCT
ejpam-6282	88	18	defined	define	VERB
ejpam-6282	88	19	by	by	ADP
ejpam-6282	88	20	d(t	d(t	PROPN
ejpam-6282	88	21	,	,	PUNCT
ejpam-6282	88	22	y	y	PROPN
ejpam-6282	88	23	)	)	PUNCT
ejpam-6282	88	24	:	:	PUNCT
ejpam-6282	88	25	=	=	X
ejpam-6282	89	1	[	[	X
ejpam-6282	89	2	ρ(t	ρ(t	PROPN
ejpam-6282	89	3	,	,	PUNCT
ejpam-6282	89	4	y)]2	y)]2	PROPN
ejpam-6282	89	5	+	+	CCONJ
ejpam-6282	89	6	∆ρ(t	∆ρ(t	PROPN
ejpam-6282	89	7	,	,	PUNCT
ejpam-6282	89	8	y	y	NOUN
ejpam-6282	89	9	)	)	PUNCT
ejpam-6282	89	10	,	,	PUNCT
ejpam-6282	89	11	for	for	ADP
ejpam-6282	89	12	all	all	DET
ejpam-6282	89	13	t	t	PROPN
ejpam-6282	89	14	,	,	PUNCT
ejpam-6282	89	15	y	y	PROPN
ejpam-6282	89	16	∈	∈	PROPN
ejpam-6282	89	17	s	s	PROPN
ejpam-6282	89	18	,	,	PUNCT
ejpam-6282	89	19	where	where	SCONJ
ejpam-6282	89	20	∆	∆	PROPN
ejpam-6282	89	21	≥	≥	NOUN
ejpam-6282	89	22	1	1	NUM
ejpam-6282	89	23	.	.	PUNCT
ejpam-6282	90	1	due	due	ADP
ejpam-6282	90	2	to	to	ADP
ejpam-6282	90	3	fact	fact	NOUN
ejpam-6282	90	4	that	that	SCONJ
ejpam-6282	90	5	ρ	ρ	PROPN
ejpam-6282	90	6	is	be	AUX
ejpam-6282	90	7	a	a	DET
ejpam-6282	90	8	standard	standard	ADJ
ejpam-6282	90	9	metric	metric	NOUN
ejpam-6282	90	10	on	on	ADP
ejpam-6282	90	11	s	s	PROPN
ejpam-6282	90	12	,	,	PUNCT
ejpam-6282	90	13	we	we	PRON
ejpam-6282	90	14	have	have	VERB
ejpam-6282	90	15	(	(	PUNCT
ejpam-6282	90	16	im1	im1	PROPN
ejpam-6282	90	17	)	)	PUNCT
ejpam-6282	90	18	and	and	CCONJ
ejpam-6282	90	19	(	(	PUNCT
ejpam-6282	90	20	im2	im2	PROPN
ejpam-6282	90	21	)	)	PUNCT
ejpam-6282	90	22	.	.	PUNCT
ejpam-6282	91	1	furthermore	furthermore	ADV
ejpam-6282	91	2	,	,	PUNCT
ejpam-6282	91	3	to	to	PART
ejpam-6282	91	4	indicate	indicate	VERB
ejpam-6282	91	5	that	that	SCONJ
ejpam-6282	91	6	(	(	PUNCT
ejpam-6282	91	7	im3	im3	PROPN
ejpam-6282	91	8	)	)	PUNCT
ejpam-6282	91	9	is	be	AUX
ejpam-6282	91	10	fulfilled	fulfil	VERB
ejpam-6282	91	11	,	,	PUNCT
ejpam-6282	91	12	it	it	PRON
ejpam-6282	91	13	is	be	AUX
ejpam-6282	91	14	enough	enough	ADJ
ejpam-6282	91	15	to	to	PART
ejpam-6282	91	16	let	let	VERB
ejpam-6282	91	17	c	c	PROPN
ejpam-6282	91	18	≥	≥	VERB
ejpam-6282	91	19	2	2	NUM
ejpam-6282	91	20	for	for	ADP
ejpam-6282	91	21	any	any	DET
ejpam-6282	91	22	ξ	ξ	PROPN
ejpam-6282	91	23	∈	∈	PROPN
ejpam-6282	91	24	(	(	PUNCT
ejpam-6282	91	25	0	0	NUM
ejpam-6282	91	26	,	,	PUNCT
ejpam-6282	91	27	1	1	NUM
ejpam-6282	91	28	)	)	PUNCT
ejpam-6282	91	29	.	.	PUNCT
ejpam-6282	92	1	therefore	therefore	ADV
ejpam-6282	92	2	,	,	PUNCT
ejpam-6282	92	3	(	(	PUNCT
ejpam-6282	92	4	s	s	X
ejpam-6282	92	5	,	,	PUNCT
ejpam-6282	92	6	d	d	NOUN
ejpam-6282	92	7	)	)	PUNCT
ejpam-6282	92	8	forms	form	VERB
ejpam-6282	92	9	a	a	DET
ejpam-6282	92	10	(	(	PUNCT
ejpam-6282	92	11	1	1	NUM
ejpam-6282	92	12	2	2	NUM
ejpam-6282	92	13	,	,	PUNCT
ejpam-6282	92	14	2)-interpolative	2)-interpolative	NUM
ejpam-6282	92	15	metric	metric	ADJ
ejpam-6282	92	16	space	space	NOUN
ejpam-6282	92	17	.	.	PUNCT
ejpam-6282	93	1	in	in	ADP
ejpam-6282	93	2	fact	fact	NOUN
ejpam-6282	93	3	,	,	PUNCT
ejpam-6282	93	4	it	it	PRON
ejpam-6282	93	5	is	be	AUX
ejpam-6282	93	6	easy	easy	ADJ
ejpam-6282	93	7	to	to	PART
ejpam-6282	93	8	find	find	VERB
ejpam-6282	93	9	that	that	SCONJ
ejpam-6282	93	10	d(t	d(t	PROPN
ejpam-6282	93	11	,	,	PUNCT
ejpam-6282	93	12	y	y	NOUN
ejpam-6282	93	13	)	)	PUNCT
ejpam-6282	93	14	=	=	PUNCT
ejpam-6282	94	1	[	[	X
ejpam-6282	94	2	ρ(t	ρ(t	PROPN
ejpam-6282	94	3	,	,	PUNCT
ejpam-6282	94	4	y)]2	y)]2	PROPN
ejpam-6282	94	5	+	+	CCONJ
ejpam-6282	94	6	∆ρ(t	∆ρ(t	PROPN
ejpam-6282	94	7	,	,	PUNCT
ejpam-6282	94	8	y	y	NOUN
ejpam-6282	94	9	)	)	PUNCT
ejpam-6282	94	10	≤	≤	NOUN
ejpam-6282	94	11	(	(	PUNCT
ejpam-6282	94	12	ρ(t	ρ(t	NUM
ejpam-6282	94	13	,	,	PUNCT
ejpam-6282	94	14	w	w	NOUN
ejpam-6282	94	15	)	)	PUNCT
ejpam-6282	94	16	+	+	CCONJ
ejpam-6282	94	17	ρ(w	ρ(w	NOUN
ejpam-6282	94	18	,	,	PUNCT
ejpam-6282	94	19	y))(ρ(t	y))(ρ(t	NOUN
ejpam-6282	94	20	,	,	PUNCT
ejpam-6282	94	21	w	w	NOUN
ejpam-6282	94	22	)	)	PUNCT
ejpam-6282	94	23	+	+	CCONJ
ejpam-6282	94	24	ρ(w	ρ(w	PROPN
ejpam-6282	94	25	,	,	PUNCT
ejpam-6282	94	26	y	y	NOUN
ejpam-6282	94	27	)	)	PUNCT
ejpam-6282	94	28	+	+	CCONJ
ejpam-6282	94	29	∆	∆	X
ejpam-6282	94	30	)	)	PUNCT
ejpam-6282	94	31	≤	≤	NOUN
ejpam-6282	94	32	(	(	PUNCT
ejpam-6282	94	33	ρ(t	ρ(t	NUM
ejpam-6282	94	34	,	,	PUNCT
ejpam-6282	94	35	w	w	NOUN
ejpam-6282	94	36	)	)	PUNCT
ejpam-6282	95	1	+	+	CCONJ
ejpam-6282	95	2	ρ(w	ρ(w	NOUN
ejpam-6282	95	3	,	,	PUNCT
ejpam-6282	95	4	y))(ρ(t	y))(ρ(t	NOUN
ejpam-6282	95	5	,	,	PUNCT
ejpam-6282	95	6	w	w	NOUN
ejpam-6282	95	7	)	)	PUNCT
ejpam-6282	96	1	+	+	CCONJ
ejpam-6282	96	2	ρ(w	ρ(w	PROPN
ejpam-6282	96	3	,	,	PUNCT
ejpam-6282	96	4	y	y	NOUN
ejpam-6282	96	5	)	)	PUNCT
ejpam-6282	96	6	+	+	CCONJ
ejpam-6282	96	7	∆	∆	X
ejpam-6282	96	8	)	)	PUNCT
ejpam-6282	97	1	≤	≤	NOUN
ejpam-6282	98	1	[	[	X
ejpam-6282	98	2	ρ(t	ρ(t	NUM
ejpam-6282	98	3	,	,	PUNCT
ejpam-6282	98	4	w)(ρ(t	w)(ρ(t	X
ejpam-6282	98	5	,	,	PUNCT
ejpam-6282	98	6	w	w	NOUN
ejpam-6282	98	7	)	)	PUNCT
ejpam-6282	98	8	+	+	CCONJ
ejpam-6282	98	9	∆	∆	X
ejpam-6282	98	10	)	)	PUNCT
ejpam-6282	98	11	+	+	CCONJ
ejpam-6282	98	12	ρ(t	ρ(t	NUM
ejpam-6282	98	13	,	,	PUNCT
ejpam-6282	98	14	w)ρ(w	w)ρ(w	PROPN
ejpam-6282	98	15	,	,	PUNCT
ejpam-6282	98	16	y	y	NOUN
ejpam-6282	98	17	)	)	PUNCT
ejpam-6282	98	18	]	]	PUNCT
ejpam-6282	99	1	+	+	PROPN
ejpam-6282	99	2	[	[	X
ejpam-6282	99	3	ρ(w	ρ(w	NOUN
ejpam-6282	99	4	,	,	PUNCT
ejpam-6282	99	5	y)(ρ(w	y)(ρ(w	PROPN
ejpam-6282	99	6	,	,	PUNCT
ejpam-6282	99	7	y	y	NOUN
ejpam-6282	99	8	)	)	PUNCT
ejpam-6282	99	9	+	+	CCONJ
ejpam-6282	99	10	∆	∆	X
ejpam-6282	99	11	)	)	PUNCT
ejpam-6282	100	1	+	+	CCONJ
ejpam-6282	100	2	ρ(w	ρ(w	NOUN
ejpam-6282	100	3	,	,	PUNCT
ejpam-6282	100	4	y)ρ(t	y)ρ(t	PROPN
ejpam-6282	100	5	,	,	PUNCT
ejpam-6282	100	6	w	w	PROPN
ejpam-6282	100	7	)	)	PUNCT
ejpam-6282	100	8	]	]	PUNCT
ejpam-6282	100	9	≤	≤	NOUN
ejpam-6282	101	1	[	[	X
ejpam-6282	101	2	ρ(t	ρ(t	NUM
ejpam-6282	101	3	,	,	PUNCT
ejpam-6282	101	4	w)(ρ(t	w)(ρ(t	X
ejpam-6282	101	5	,	,	PUNCT
ejpam-6282	101	6	w	w	NOUN
ejpam-6282	101	7	)	)	PUNCT
ejpam-6282	101	8	+	+	CCONJ
ejpam-6282	101	9	∆	∆	X
ejpam-6282	101	10	)	)	PUNCT
ejpam-6282	101	11	]	]	PUNCT
ejpam-6282	102	1	+	+	CCONJ
ejpam-6282	102	2	[	[	X
ejpam-6282	102	3	ρ(w	ρ(w	NOUN
ejpam-6282	102	4	,	,	PUNCT
ejpam-6282	102	5	y)(ρ(w	y)(ρ(w	PROPN
ejpam-6282	102	6	,	,	PUNCT
ejpam-6282	102	7	y	y	NOUN
ejpam-6282	102	8	)	)	PUNCT
ejpam-6282	102	9	+	+	CCONJ
ejpam-6282	102	10	∆	∆	X
ejpam-6282	102	11	)	)	PUNCT
ejpam-6282	102	12	]	]	PUNCT
ejpam-6282	103	1	+	+	CCONJ
ejpam-6282	103	2	2ρ(t	2ρ(t	NUM
ejpam-6282	103	3	,	,	PUNCT
ejpam-6282	103	4	w)ρ(w	w)ρ(w	PROPN
ejpam-6282	103	5	,	,	PUNCT
ejpam-6282	103	6	y	y	NOUN
ejpam-6282	103	7	)	)	PUNCT
ejpam-6282	103	8	≤	≤	NOUN
ejpam-6282	103	9	d(t	d(t	PROPN
ejpam-6282	103	10	,	,	PUNCT
ejpam-6282	103	11	w	w	NOUN
ejpam-6282	103	12	)	)	PUNCT
ejpam-6282	103	13	+	+	CCONJ
ejpam-6282	103	14	d(w	d(w	PROPN
ejpam-6282	103	15	,	,	PUNCT
ejpam-6282	103	16	y	y	PROPN
ejpam-6282	103	17	)	)	PUNCT
ejpam-6282	103	18	+	+	CCONJ
ejpam-6282	103	19	2	2	NUM
ejpam-6282	103	20	(	(	PUNCT
ejpam-6282	103	21	ρ(t	ρ(t	NUM
ejpam-6282	103	22	,	,	PUNCT
ejpam-6282	103	23	w	w	NOUN
ejpam-6282	103	24	)	)	PUNCT
ejpam-6282	103	25	)	)	PUNCT
ejpam-6282	103	26	1	1	NUM
ejpam-6282	103	27	2	2	NUM
ejpam-6282	103	28	(	(	PUNCT
ejpam-6282	103	29	ρ(t	ρ(t	PROPN
ejpam-6282	103	30	,	,	PUNCT
ejpam-6282	103	31	w	w	NOUN
ejpam-6282	103	32	)	)	PUNCT
ejpam-6282	103	33	)	)	PUNCT
ejpam-6282	103	34	1	1	NUM
ejpam-6282	103	35	2	2	NUM
ejpam-6282	103	36	(	(	PUNCT
ejpam-6282	103	37	ρ(w	ρ(w	PROPN
ejpam-6282	103	38	,	,	PUNCT
ejpam-6282	103	39	y	y	NOUN
ejpam-6282	103	40	)	)	PUNCT
ejpam-6282	103	41	)	)	PUNCT
ejpam-6282	103	42	1	1	NUM
ejpam-6282	103	43	2	2	NUM
ejpam-6282	103	44	(	(	PUNCT
ejpam-6282	103	45	ρ(w	ρ(w	PROPN
ejpam-6282	103	46	,	,	PUNCT
ejpam-6282	103	47	y	y	NOUN
ejpam-6282	103	48	)	)	PUNCT
ejpam-6282	103	49	)	)	PUNCT
ejpam-6282	103	50	1	1	NUM
ejpam-6282	103	51	2	2	NUM
ejpam-6282	103	52	≤	≤	NOUN
ejpam-6282	103	53	d(t	d(t	PROPN
ejpam-6282	103	54	,	,	PUNCT
ejpam-6282	103	55	w	w	NOUN
ejpam-6282	103	56	)	)	PUNCT
ejpam-6282	103	57	+	+	CCONJ
ejpam-6282	103	58	d(w	d(w	PROPN
ejpam-6282	103	59	,	,	PUNCT
ejpam-6282	103	60	y	y	PROPN
ejpam-6282	103	61	)	)	PUNCT
ejpam-6282	103	62	+	+	CCONJ
ejpam-6282	103	63	2	2	NUM
ejpam-6282	103	64	(	(	PUNCT
ejpam-6282	103	65	ρ(t	ρ(t	NUM
ejpam-6282	103	66	,	,	PUNCT
ejpam-6282	103	67	w	w	NOUN
ejpam-6282	103	68	)	)	PUNCT
ejpam-6282	103	69	)	)	PUNCT
ejpam-6282	103	70	1	1	NUM
ejpam-6282	103	71	2	2	NUM
ejpam-6282	103	72	[	[	X
ejpam-6282	103	73	ρ(t	ρ(t	NUM
ejpam-6282	103	74	,	,	PUNCT
ejpam-6282	103	75	w	w	NOUN
ejpam-6282	103	76	)	)	PUNCT
ejpam-6282	103	77	+	+	CCONJ
ejpam-6282	103	78	∆	∆	X
ejpam-6282	103	79	]	]	X
ejpam-6282	103	80	1	1	NUM
ejpam-6282	103	81	2	2	NUM
ejpam-6282	103	82	(	(	PUNCT
ejpam-6282	103	83	ρ(w	ρ(w	PROPN
ejpam-6282	103	84	,	,	PUNCT
ejpam-6282	103	85	y	y	NOUN
ejpam-6282	103	86	)	)	PUNCT
ejpam-6282	103	87	)	)	PUNCT
ejpam-6282	103	88	1	1	NUM
ejpam-6282	103	89	2	2	NUM
ejpam-6282	104	1	[	[	X
ejpam-6282	104	2	ρ(w	ρ(w	PROPN
ejpam-6282	104	3	,	,	PUNCT
ejpam-6282	104	4	y	y	NOUN
ejpam-6282	104	5	)	)	PUNCT
ejpam-6282	104	6	+	+	CCONJ
ejpam-6282	104	7	∆	∆	X
ejpam-6282	104	8	]	]	X
ejpam-6282	104	9	1	1	NUM
ejpam-6282	104	10	2	2	NUM
ejpam-6282	104	11	≤	≤	NOUN
ejpam-6282	104	12	d(t	d(t	PROPN
ejpam-6282	104	13	,	,	PUNCT
ejpam-6282	104	14	w	w	NOUN
ejpam-6282	104	15	)	)	PUNCT
ejpam-6282	104	16	+	+	CCONJ
ejpam-6282	104	17	d(w	d(w	PROPN
ejpam-6282	104	18	,	,	PUNCT
ejpam-6282	104	19	y	y	PROPN
ejpam-6282	104	20	)	)	PUNCT
ejpam-6282	104	21	+	+	CCONJ
ejpam-6282	104	22	2(d(t	2(d(t	NUM
ejpam-6282	104	23	,	,	PUNCT
ejpam-6282	104	24	w	w	NOUN
ejpam-6282	104	25	)	)	PUNCT
ejpam-6282	104	26	)	)	PUNCT
ejpam-6282	104	27	1	1	NUM
ejpam-6282	104	28	2	2	NUM
ejpam-6282	104	29	(	(	PUNCT
ejpam-6282	104	30	d(w	d(w	PROPN
ejpam-6282	104	31	,	,	PUNCT
ejpam-6282	104	32	y	y	NOUN
ejpam-6282	104	33	)	)	PUNCT
ejpam-6282	104	34	)	)	PUNCT
ejpam-6282	104	35	1	1	NUM
ejpam-6282	104	36	2	2	NUM
ejpam-6282	104	37	.	.	PUNCT
ejpam-6282	105	1	as	as	ADP
ejpam-6282	105	2	a	a	DET
ejpam-6282	105	3	result	result	NOUN
ejpam-6282	105	4	,	,	PUNCT
ejpam-6282	105	5	the	the	DET
ejpam-6282	105	6	distance	distance	NOUN
ejpam-6282	105	7	function	function	NOUN
ejpam-6282	105	8	d(t	d(t	PROPN
ejpam-6282	105	9	,	,	PUNCT
ejpam-6282	105	10	y	y	NOUN
ejpam-6282	105	11	)	)	PUNCT
ejpam-6282	105	12	can	can	AUX
ejpam-6282	105	13	not	not	PART
ejpam-6282	105	14	fulfills	fulfills	VERB
ejpam-6282	105	15	the	the	DET
ejpam-6282	105	16	metric	metric	ADJ
ejpam-6282	105	17	conditions	condition	NOUN
ejpam-6282	105	18	.	.	PUNCT
ejpam-6282	106	1	g.	g.	PROPN
ejpam-6282	106	2	alsahli	alsahli	PROPN
ejpam-6282	106	3	,	,	PUNCT
ejpam-6282	106	4	s.	s.	PROPN
ejpam-6282	106	5	gülyaz	gülyaz	PROPN
ejpam-6282	106	6	-	-	PUNCT
ejpam-6282	106	7	özyurt	özyurt	PROPN
ejpam-6282	106	8	/	/	SYM
ejpam-6282	106	9	eur	eur	PROPN
ejpam-6282	106	10	.	.	PUNCT
ejpam-6282	107	1	j.	j.	PROPN
ejpam-6282	107	2	pure	pure	PROPN
ejpam-6282	107	3	appl	appl	PROPN
ejpam-6282	107	4	.	.	PROPN
ejpam-6282	107	5	math	math	PROPN
ejpam-6282	107	6	,	,	PUNCT
ejpam-6282	107	7	18	18	NUM
ejpam-6282	107	8	(	(	PUNCT
ejpam-6282	107	9	2	2	NUM
ejpam-6282	107	10	)	)	PUNCT
ejpam-6282	107	11	(	(	PUNCT
ejpam-6282	107	12	2025	2025	NUM
ejpam-6282	107	13	)	)	PUNCT
ejpam-6282	107	14	,	,	PUNCT
ejpam-6282	107	15	6282	6282	NUM
ejpam-6282	107	16	5	5	NUM
ejpam-6282	107	17	of	of	ADP
ejpam-6282	107	18	13	13	NUM
ejpam-6282	107	19	for	for	ADP
ejpam-6282	107	20	r	r	NOUN
ejpam-6282	107	21	>	>	PUNCT
ejpam-6282	107	22	0	0	PUNCT
ejpam-6282	108	1	and	and	CCONJ
ejpam-6282	108	2	t	t	PROPN
ejpam-6282	108	3	∈	∈	PROPN
ejpam-6282	108	4	s	s	PART
ejpam-6282	108	5	,	,	PUNCT
ejpam-6282	108	6	in	in	ADP
ejpam-6282	108	7	the	the	DET
ejpam-6282	108	8	setting	setting	NOUN
ejpam-6282	108	9	of	of	ADP
ejpam-6282	108	10	(	(	PUNCT
ejpam-6282	108	11	ξ	ξ	PROPN
ejpam-6282	108	12	,	,	PUNCT
ejpam-6282	108	13	c)-interpolative	c)-interpolative	ADJ
ejpam-6282	108	14	metric	metric	ADJ
ejpam-6282	108	15	space	space	NOUN
ejpam-6282	108	16	(	(	PUNCT
ejpam-6282	108	17	s	s	X
ejpam-6282	108	18	,	,	PUNCT
ejpam-6282	108	19	d	d	X
ejpam-6282	108	20	)	)	PUNCT
ejpam-6282	108	21	we	we	PRON
ejpam-6282	108	22	set	set	VERB
ejpam-6282	108	23	an	an	DET
ejpam-6282	108	24	open	open	ADJ
ejpam-6282	108	25	ball	ball	NOUN
ejpam-6282	108	26	b(t	b(t	NOUN
ejpam-6282	108	27	,	,	PUNCT
ejpam-6282	108	28	r	r	NOUN
ejpam-6282	108	29	)	)	PUNCT
ejpam-6282	108	30	=	=	NOUN
ejpam-6282	108	31	{	{	PUNCT
ejpam-6282	108	32	w	w	PROPN
ejpam-6282	108	33	∈	∈	PROPN
ejpam-6282	108	34	s	s	PART
ejpam-6282	108	35	:	:	PUNCT
ejpam-6282	108	36	d(t	d(t	PROPN
ejpam-6282	108	37	,	,	PUNCT
ejpam-6282	108	38	w	w	NOUN
ejpam-6282	108	39	)	)	PUNCT
ejpam-6282	108	40	<	<	X
ejpam-6282	108	41	r	r	X
ejpam-6282	108	42	}	}	PUNCT
ejpam-6282	108	43	.	.	PUNCT
ejpam-6282	109	1	definition	definition	NOUN
ejpam-6282	109	2	2	2	NUM
ejpam-6282	109	3	.	.	PUNCT
ejpam-6282	110	1	(	(	PUNCT
ejpam-6282	110	2	see	see	VERB
ejpam-6282	110	3	,	,	PUNCT
ejpam-6282	110	4	e.g.	e.g.	ADV
ejpam-6282	110	5	[	[	X
ejpam-6282	110	6	6	6	NUM
ejpam-6282	110	7	]	]	PUNCT
ejpam-6282	110	8	)	)	PUNCT
ejpam-6282	110	9	suppose	suppose	VERB
ejpam-6282	110	10	a	a	DET
ejpam-6282	110	11	self	self	NOUN
ejpam-6282	110	12	-	-	PUNCT
ejpam-6282	110	13	mapping	mapping	NOUN
ejpam-6282	110	14	t	t	NOUN
ejpam-6282	110	15	defined	define	VERB
ejpam-6282	110	16	on	on	ADP
ejpam-6282	110	17	a	a	DET
ejpam-6282	110	18	(	(	PUNCT
ejpam-6282	110	19	ξ	ξ	PROPN
ejpam-6282	110	20	,	,	PUNCT
ejpam-6282	110	21	c)-interpolative	c)-interpolative	ADJ
ejpam-6282	110	22	metric	metric	ADJ
ejpam-6282	110	23	(	(	PUNCT
ejpam-6282	110	24	s	s	PROPN
ejpam-6282	110	25	,	,	PUNCT
ejpam-6282	110	26	d	d	NOUN
ejpam-6282	110	27	)	)	PUNCT
ejpam-6282	110	28	,	,	PUNCT
ejpam-6282	110	29	construct	construct	VERB
ejpam-6282	110	30	an	an	DET
ejpam-6282	110	31	iterative	iterative	NOUN
ejpam-6282	110	32	sequence	sequence	NOUN
ejpam-6282	110	33	{	{	PUNCT
ejpam-6282	110	34	tn−1	tn−1	PROPN
ejpam-6282	110	35	m	m	NOUN
ejpam-6282	110	36	}	}	PUNCT
ejpam-6282	110	37	in	in	ADP
ejpam-6282	110	38	s.	s.	PROPN
ejpam-6282	110	39	the	the	DET
ejpam-6282	110	40	sequence{tn−1	sequence{tn−1	PROPN
ejpam-6282	110	41	m	m	PRON
ejpam-6282	110	42	}	}	PUNCT
ejpam-6282	110	43	is	be	AUX
ejpam-6282	110	44	convergent	convergent	ADJ
ejpam-6282	110	45	to	to	ADP
ejpam-6282	110	46	m∗	m∗	NOUN
ejpam-6282	110	47	in	in	ADP
ejpam-6282	110	48	s	s	PRON
ejpam-6282	110	49	when	when	SCONJ
ejpam-6282	110	50	d(tn−1	d(tn−1	PROPN
ejpam-6282	110	51	m	m	NOUN
ejpam-6282	110	52	,	,	PUNCT
ejpam-6282	110	53	x	x	NOUN
ejpam-6282	110	54	)	)	PUNCT
ejpam-6282	110	55	→	→	SYM
ejpam-6282	110	56	0	0	NUM
ejpam-6282	110	57	,	,	PUNCT
ejpam-6282	110	58	as	as	SCONJ
ejpam-6282	110	59	n	n	PROPN
ejpam-6282	110	60	→	→	SYM
ejpam-6282	110	61	∞.	∞.	PROPN
ejpam-6282	110	62	in	in	ADP
ejpam-6282	110	63	addition	addition	NOUN
ejpam-6282	110	64	,	,	PUNCT
ejpam-6282	110	65	it	it	PRON
ejpam-6282	110	66	is	be	AUX
ejpam-6282	110	67	called	call	VERB
ejpam-6282	110	68	a	a	DET
ejpam-6282	110	69	cauchy	cauchy	ADJ
ejpam-6282	110	70	sequence	sequence	NOUN
ejpam-6282	110	71	in	in	ADP
ejpam-6282	110	72	s	s	PROPN
ejpam-6282	110	73	,	,	PUNCT
ejpam-6282	110	74	when	when	SCONJ
ejpam-6282	110	75	limn→∞	limn→∞	PROPN
ejpam-6282	110	76	sup{d(tn−1	sup{d(tn−1	PROPN
ejpam-6282	110	77	m	m	PROPN
ejpam-6282	110	78	,	,	PUNCT
ejpam-6282	110	79	ts−1	ts−1	NOUN
ejpam-6282	110	80	m	m	NOUN
ejpam-6282	110	81	)	)	PUNCT
ejpam-6282	110	82	:	:	PUNCT
ejpam-6282	111	1	m	m	VERB
ejpam-6282	111	2	>	>	X
ejpam-6282	111	3	n	n	CCONJ
ejpam-6282	111	4	}	}	PUNCT
ejpam-6282	111	5	=	=	SYM
ejpam-6282	111	6	0	0	X
ejpam-6282	111	7	.	.	PUNCT
ejpam-6282	112	1	furthermore	furthermore	ADV
ejpam-6282	112	2	,	,	PUNCT
ejpam-6282	112	3	a	a	DET
ejpam-6282	112	4	(	(	PUNCT
ejpam-6282	112	5	ξ	ξ	PROPN
ejpam-6282	112	6	,	,	PUNCT
ejpam-6282	112	7	c)-interpolative	c)-interpolative	ADJ
ejpam-6282	112	8	metric	metric	ADJ
ejpam-6282	112	9	space	space	NOUN
ejpam-6282	112	10	(	(	PUNCT
ejpam-6282	112	11	s	s	X
ejpam-6282	112	12	,	,	PUNCT
ejpam-6282	112	13	d	d	NOUN
ejpam-6282	112	14	)	)	PUNCT
ejpam-6282	112	15	is	be	AUX
ejpam-6282	112	16	called	call	VERB
ejpam-6282	112	17	complete	complete	ADJ
ejpam-6282	112	18	when	when	SCONJ
ejpam-6282	112	19	every	every	DET
ejpam-6282	112	20	cauchy	cauchy	ADJ
ejpam-6282	112	21	sequence	sequence	NOUN
ejpam-6282	112	22	converges	converge	VERB
ejpam-6282	112	23	in	in	ADP
ejpam-6282	112	24	s.	s.	PROPN
ejpam-6282	112	25	the	the	DET
ejpam-6282	112	26	thought	thought	NOUN
ejpam-6282	112	27	of	of	ADP
ejpam-6282	112	28	the	the	DET
ejpam-6282	112	29	simulation	simulation	NOUN
ejpam-6282	112	30	function	function	NOUN
ejpam-6282	112	31	can	can	AUX
ejpam-6282	112	32	be	be	AUX
ejpam-6282	112	33	displayed	display	VERB
ejpam-6282	112	34	in	in	ADP
ejpam-6282	112	35	[	[	X
ejpam-6282	112	36	14	14	NUM
ejpam-6282	112	37	]	]	SYM
ejpam-6282	112	38	:	:	PUNCT
ejpam-6282	112	39	definition	definition	NOUN
ejpam-6282	112	40	3	3	NUM
ejpam-6282	112	41	.	.	PUNCT
ejpam-6282	113	1	[	[	X
ejpam-6282	113	2	14	14	NUM
ejpam-6282	113	3	]	]	X
ejpam-6282	113	4	if	if	SCONJ
ejpam-6282	113	5	the	the	DET
ejpam-6282	113	6	mapping	mapping	NOUN
ejpam-6282	113	7	α	α	NOUN
ejpam-6282	113	8	:	:	PUNCT
ejpam-6282	114	1	[	[	X
ejpam-6282	114	2	0	0	NUM
ejpam-6282	114	3	,	,	PUNCT
ejpam-6282	114	4	∞)×	∞)×	X
ejpam-6282	114	5	[	[	X
ejpam-6282	114	6	0	0	NUM
ejpam-6282	114	7	,	,	PUNCT
ejpam-6282	114	8	∞	∞	PROPN
ejpam-6282	114	9	)	)	PUNCT
ejpam-6282	114	10	→	→	SYM
ejpam-6282	114	11	r	r	NOUN
ejpam-6282	114	12	is	be	AUX
ejpam-6282	114	13	called	call	VERB
ejpam-6282	114	14	a	a	DET
ejpam-6282	114	15	simulation	simulation	NOUN
ejpam-6282	114	16	function	function	NOUN
ejpam-6282	114	17	when	when	SCONJ
ejpam-6282	114	18	(	(	PUNCT
ejpam-6282	114	19	α1	α1	PROPN
ejpam-6282	114	20	)	)	PUNCT
ejpam-6282	114	21	α(0	α(0	PROPN
ejpam-6282	114	22	,	,	PUNCT
ejpam-6282	114	23	0	0	NUM
ejpam-6282	114	24	)	)	PUNCT
ejpam-6282	114	25	=	=	SYM
ejpam-6282	114	26	0	0	NUM
ejpam-6282	114	27	;	;	PUNCT
ejpam-6282	114	28	(	(	PUNCT
ejpam-6282	114	29	α2	α2	ADV
ejpam-6282	114	30	)	)	PUNCT
ejpam-6282	114	31	α(m	α(m	PROPN
ejpam-6282	114	32	,	,	PUNCT
ejpam-6282	114	33	n	n	CCONJ
ejpam-6282	114	34	)	)	PUNCT
ejpam-6282	114	35	<	<	X
ejpam-6282	115	1	n	n	PRON
ejpam-6282	115	2	−	−	PROPN
ejpam-6282	115	3	m	m	VERB
ejpam-6282	116	1	for	for	ADP
ejpam-6282	116	2	all	all	DET
ejpam-6282	116	3	m	m	NOUN
ejpam-6282	116	4	,	,	PUNCT
ejpam-6282	116	5	n	n	PROPN
ejpam-6282	116	6	>	>	X
ejpam-6282	116	7	0	0	NUM
ejpam-6282	116	8	;	;	PUNCT
ejpam-6282	116	9	(	(	PUNCT
ejpam-6282	116	10	α3	α3	NOUN
ejpam-6282	116	11	)	)	PUNCT
ejpam-6282	116	12	if	if	SCONJ
ejpam-6282	116	13	{	{	PUNCT
ejpam-6282	116	14	mn	mn	NOUN
ejpam-6282	116	15	}	}	PUNCT
ejpam-6282	116	16	,	,	PUNCT
ejpam-6282	116	17	{	{	PUNCT
ejpam-6282	116	18	kn	kn	NOUN
ejpam-6282	116	19	}	}	PUNCT
ejpam-6282	116	20	are	be	AUX
ejpam-6282	116	21	sequences	sequence	NOUN
ejpam-6282	116	22	in	in	ADP
ejpam-6282	116	23	(	(	PUNCT
ejpam-6282	116	24	0	0	NUM
ejpam-6282	116	25	,	,	PUNCT
ejpam-6282	116	26	∞	∞	PROPN
ejpam-6282	116	27	)	)	PUNCT
ejpam-6282	116	28	such	such	DET
ejpam-6282	116	29	a	a	DET
ejpam-6282	116	30	way	way	NOUN
ejpam-6282	116	31	that	that	PRON
ejpam-6282	116	32	lim	lim	PROPN
ejpam-6282	116	33	n→∞	n→∞	NUM
ejpam-6282	117	1	mn	mn	PROPN
ejpam-6282	118	1	=	=	PROPN
ejpam-6282	118	2	lim	lim	PROPN
ejpam-6282	118	3	n→∞	n→∞	PROPN
ejpam-6282	119	1	kn	kn	PROPN
ejpam-6282	119	2	>	>	X
ejpam-6282	119	3	0	0	PUNCT
ejpam-6282	120	1	then	then	ADV
ejpam-6282	120	2	lim	lim	PROPN
ejpam-6282	120	3	sup	sup	VERB
ejpam-6282	120	4	n→∞	n→∞	NUM
ejpam-6282	120	5	α(mn	α(mn	PROPN
ejpam-6282	120	6	,	,	PUNCT
ejpam-6282	120	7	kn	kn	NOUN
ejpam-6282	120	8	)	)	PUNCT
ejpam-6282	120	9	<	<	X
ejpam-6282	120	10	0	0	X
ejpam-6282	120	11	.	.	PUNCT
ejpam-6282	121	1	let	let	VERB
ejpam-6282	121	2	t	t	PROPN
ejpam-6282	121	3	represent	represent	VERB
ejpam-6282	121	4	the	the	DET
ejpam-6282	121	5	collection	collection	NOUN
ejpam-6282	121	6	of	of	ADP
ejpam-6282	121	7	all	all	DET
ejpam-6282	121	8	simulation	simulation	NOUN
ejpam-6282	121	9	functions	function	NOUN
ejpam-6282	121	10	.	.	PUNCT
ejpam-6282	122	1	we	we	PRON
ejpam-6282	122	2	infer	infer	VERB
ejpam-6282	122	3	from	from	ADP
ejpam-6282	122	4	the	the	DET
ejpam-6282	122	5	above	above	ADJ
ejpam-6282	122	6	definition	definition	NOUN
ejpam-6282	122	7	that	that	SCONJ
ejpam-6282	122	8	α(m	α(m	PROPN
ejpam-6282	122	9	,	,	PUNCT
ejpam-6282	122	10	m	m	PROPN
ejpam-6282	122	11	)	)	PUNCT
ejpam-6282	122	12	<	<	X
ejpam-6282	122	13	0	0	PUNCT
ejpam-6282	122	14	for	for	ADP
ejpam-6282	122	15	all	all	DET
ejpam-6282	122	16	m	m	NOUN
ejpam-6282	122	17	>	>	X
ejpam-6282	122	18	0	0	X
ejpam-6282	122	19	.	.	PUNCT
ejpam-6282	122	20	a.	a.	PROPN
ejpam-6282	122	21	roldan	roldan	PROPN
ejpam-6282	122	22	et	et	PROPN
ejpam-6282	122	23	al	al	PROPN
ejpam-6282	122	24	.	.	PUNCT
ejpam-6282	123	1	[	[	X
ejpam-6282	123	2	23	23	NUM
ejpam-6282	123	3	]	]	PUNCT
ejpam-6282	123	4	reconsider	reconsider	VERB
ejpam-6282	123	5	definition	definition	NOUN
ejpam-6282	123	6	3	3	NUM
ejpam-6282	123	7	in	in	ADP
ejpam-6282	123	8	order	order	NOUN
ejpam-6282	123	9	to	to	PART
ejpam-6282	123	10	widen	widen	VERB
ejpam-6282	123	11	the	the	DET
ejpam-6282	123	12	class	class	NOUN
ejpam-6282	123	13	of	of	ADP
ejpam-6282	123	14	all	all	DET
ejpam-6282	123	15	simulation	simulation	NOUN
ejpam-6282	123	16	functions	function	NOUN
ejpam-6282	123	17	by	by	ADP
ejpam-6282	123	18	replacing	replace	VERB
ejpam-6282	123	19	the	the	DET
ejpam-6282	123	20	assumption	assumption	NOUN
ejpam-6282	123	21	(	(	PUNCT
ejpam-6282	123	22	α3	α3	NOUN
ejpam-6282	123	23	)	)	PUNCT
ejpam-6282	123	24	by	by	ADP
ejpam-6282	123	25	the	the	DET
ejpam-6282	123	26	following	follow	VERB
ejpam-6282	123	27	one	one	NUM
ejpam-6282	123	28	:	:	PUNCT
ejpam-6282	123	29	(	(	PUNCT
ejpam-6282	123	30	α3)′	α3)′	NOUN
ejpam-6282	123	31	if	if	SCONJ
ejpam-6282	123	32	{	{	PUNCT
ejpam-6282	123	33	mn	mn	NOUN
ejpam-6282	123	34	}	}	PUNCT
ejpam-6282	123	35	and	and	CCONJ
ejpam-6282	123	36	{	{	PUNCT
ejpam-6282	123	37	kn	kn	NOUN
ejpam-6282	123	38	}	}	PUNCT
ejpam-6282	123	39	are	be	AUX
ejpam-6282	123	40	two	two	NUM
ejpam-6282	123	41	positive	positive	ADJ
ejpam-6282	123	42	sequences	sequence	NOUN
ejpam-6282	123	43	in	in	ADP
ejpam-6282	123	44	a	a	DET
ejpam-6282	123	45	way	way	NOUN
ejpam-6282	124	1	that	that	PRON
ejpam-6282	124	2	lim	lim	PROPN
ejpam-6282	124	3	n→∞	n→∞	NUM
ejpam-6282	124	4	mn	mn	PROPN
ejpam-6282	125	1	=	=	PROPN
ejpam-6282	125	2	lim	lim	PROPN
ejpam-6282	125	3	n→∞	n→∞	PROPN
ejpam-6282	126	1	kn	kn	PROPN
ejpam-6282	126	2	>	>	X
ejpam-6282	126	3	0	0	PUNCT
ejpam-6282	127	1	and	and	CCONJ
ejpam-6282	127	2	mn	mn	PROPN
ejpam-6282	127	3	<	<	X
ejpam-6282	127	4	kn	kn	PROPN
ejpam-6282	127	5	,	,	PUNCT
ejpam-6282	127	6	then	then	ADV
ejpam-6282	127	7	lim	lim	PROPN
ejpam-6282	127	8	sup	sup	PROPN
ejpam-6282	127	9	n→∞	n→∞	NUM
ejpam-6282	127	10	α(mn	α(mn	PROPN
ejpam-6282	127	11	,	,	PUNCT
ejpam-6282	127	12	kn	kn	NOUN
ejpam-6282	127	13	)	)	PUNCT
ejpam-6282	127	14	<	<	X
ejpam-6282	128	1	0	0	X
ejpam-6282	128	2	.	.	PUNCT
ejpam-6282	129	1	a	a	DET
ejpam-6282	129	2	number	number	NOUN
ejpam-6282	129	3	of	of	ADP
ejpam-6282	129	4	outlines	outline	NOUN
ejpam-6282	129	5	of	of	ADP
ejpam-6282	129	6	the	the	DET
ejpam-6282	129	7	diversion	diversion	NOUN
ejpam-6282	129	8	work	work	NOUN
ejpam-6282	129	9	are	be	AUX
ejpam-6282	129	10	given	give	VERB
ejpam-6282	129	11	in	in	ADP
ejpam-6282	129	12	[	[	X
ejpam-6282	129	13	14	14	NUM
ejpam-6282	129	14	]	]	SYM
ejpam-6282	129	15	:	:	PUNCT
ejpam-6282	129	16	example	example	NOUN
ejpam-6282	129	17	3	3	X
ejpam-6282	129	18	.	.	PUNCT
ejpam-6282	129	19	let	let	VERB
ejpam-6282	129	20	the	the	DET
ejpam-6282	129	21	functions	function	NOUN
ejpam-6282	129	22	h	h	NOUN
ejpam-6282	129	23	,	,	PUNCT
ejpam-6282	129	24	g	g	NOUN
ejpam-6282	129	25	:	:	PUNCT
ejpam-6282	130	1	[	[	X
ejpam-6282	130	2	0	0	NUM
ejpam-6282	130	3	,	,	PUNCT
ejpam-6282	130	4	∞	∞	PROPN
ejpam-6282	130	5	)	)	PUNCT
ejpam-6282	130	6	→	→	PUNCT
ejpam-6282	130	7	[	[	X
ejpam-6282	130	8	0	0	NUM
ejpam-6282	130	9	,	,	PUNCT
ejpam-6282	130	10	∞	∞	PROPN
ejpam-6282	130	11	)	)	PUNCT
ejpam-6282	130	12	be	be	AUX
ejpam-6282	130	13	continuous	continuous	ADJ
ejpam-6282	130	14	in	in	ADP
ejpam-6282	130	15	a	a	DET
ejpam-6282	130	16	way	way	NOUN
ejpam-6282	130	17	that	that	PRON
ejpam-6282	130	18	g(t	g(t	PROPN
ejpam-6282	130	19	)	)	PUNCT
ejpam-6282	130	20	=	=	SYM
ejpam-6282	130	21	h(t	h(t	X
ejpam-6282	130	22	)	)	PUNCT
ejpam-6282	131	1	=	=	SYM
ejpam-6282	131	2	0	0	PUNCT
ejpam-6282	132	1	if	if	SCONJ
ejpam-6282	132	2	and	and	CCONJ
ejpam-6282	132	3	only	only	ADV
ejpam-6282	132	4	if	if	SCONJ
ejpam-6282	132	5	t	t	NOUN
ejpam-6282	132	6	=	=	SYM
ejpam-6282	132	7	0	0	NUM
ejpam-6282	132	8	and	and	CCONJ
ejpam-6282	132	9	g(t	g(t	PROPN
ejpam-6282	132	10	)	)	PUNCT
ejpam-6282	132	11	<	<	X
ejpam-6282	132	12	t	t	X
ejpam-6282	132	13	≤	≤	NUM
ejpam-6282	132	14	h(t	h(t	PROPN
ejpam-6282	132	15	)	)	PUNCT
ejpam-6282	132	16	for	for	ADP
ejpam-6282	132	17	all	all	DET
ejpam-6282	132	18	t	t	PROPN
ejpam-6282	132	19	>	>	X
ejpam-6282	132	20	0	0	X
ejpam-6282	132	21	.	.	PUNCT
ejpam-6282	133	1	for	for	ADP
ejpam-6282	133	2	i	i	PRON
ejpam-6282	133	3	=	=	NOUN
ejpam-6282	133	4	1	1	NUM
ejpam-6282	133	5	,	,	PUNCT
ejpam-6282	133	6	2	2	NUM
ejpam-6282	133	7	,	,	PUNCT
ejpam-6282	133	8	3	3	NUM
ejpam-6282	133	9	,	,	PUNCT
ejpam-6282	133	10	we	we	PRON
ejpam-6282	133	11	define	define	VERB
ejpam-6282	133	12	αi	αi	NOUN
ejpam-6282	133	13	:	:	PUNCT
ejpam-6282	133	14	r+	r+	NOUN
ejpam-6282	133	15	0	0	NUM
ejpam-6282	133	16	×	×	NOUN
ejpam-6282	133	17	r+	r+	NOUN
ejpam-6282	133	18	0	0	NUM
ejpam-6282	133	19	→	→	SYM
ejpam-6282	133	20	r	r	NOUN
ejpam-6282	133	21	,	,	PUNCT
ejpam-6282	133	22	as	as	ADP
ejpam-6282	133	23	(	(	PUNCT
ejpam-6282	133	24	i	i	NOUN
ejpam-6282	133	25	)	)	PUNCT
ejpam-6282	133	26	then	then	ADV
ejpam-6282	133	27	,	,	PUNCT
ejpam-6282	133	28	for	for	ADP
ejpam-6282	133	29	every	every	DET
ejpam-6282	133	30	t	t	NOUN
ejpam-6282	133	31	,	,	PUNCT
ejpam-6282	133	32	s	s	PART
ejpam-6282	133	33	∈	∈	PROPN
ejpam-6282	134	1	[	[	X
ejpam-6282	134	2	0	0	NUM
ejpam-6282	134	3	,	,	PUNCT
ejpam-6282	134	4	∞	∞	PROPN
ejpam-6282	134	5	)	)	PUNCT
ejpam-6282	134	6	,	,	PUNCT
ejpam-6282	134	7	α1(t	α1(t	X
ejpam-6282	134	8	,	,	PUNCT
ejpam-6282	134	9	s	s	NOUN
ejpam-6282	134	10	)	)	PUNCT
ejpam-6282	134	11	=	=	PUNCT
ejpam-6282	134	12	g(s)−	g(s)−	ADP
ejpam-6282	134	13	h(t	h(t	NUM
ejpam-6282	134	14	)	)	PUNCT
ejpam-6282	134	15	∈	∈	PROPN
ejpam-6282	134	16	t	t	PROPN
ejpam-6282	134	17	.	.	PUNCT
ejpam-6282	135	1	(	(	PUNCT
ejpam-6282	135	2	ii	ii	NOUN
ejpam-6282	135	3	)	)	PUNCT
ejpam-6282	135	4	for	for	ADP
ejpam-6282	135	5	every	every	DET
ejpam-6282	135	6	t	t	PROPN
ejpam-6282	135	7	,	,	PUNCT
ejpam-6282	135	8	s	s	PART
ejpam-6282	135	9	∈	∈	PROPN
ejpam-6282	136	1	[	[	X
ejpam-6282	136	2	0	0	NUM
ejpam-6282	136	3	,	,	PUNCT
ejpam-6282	136	4	∞	∞	PROPN
ejpam-6282	136	5	)	)	PUNCT
ejpam-6282	136	6	,	,	PUNCT
ejpam-6282	136	7	α2(t	α2(t	NUM
ejpam-6282	136	8	,	,	PUNCT
ejpam-6282	136	9	s	s	PART
ejpam-6282	136	10	)	)	PUNCT
ejpam-6282	136	11	=	=	SYM
ejpam-6282	136	12	s−	s−	PROPN
ejpam-6282	136	13	h(t	h(t	PROPN
ejpam-6282	136	14	,	,	PUNCT
ejpam-6282	136	15	s	s	PART
ejpam-6282	136	16	)	)	PUNCT
ejpam-6282	136	17	f(t	f(t	NOUN
ejpam-6282	136	18	,	,	PUNCT
ejpam-6282	136	19	s	s	NOUN
ejpam-6282	136	20	)	)	PUNCT
ejpam-6282	136	21	t	t	PROPN
ejpam-6282	136	22	,	,	PUNCT
ejpam-6282	136	23	where	where	SCONJ
ejpam-6282	136	24	the	the	DET
ejpam-6282	136	25	functions	function	NOUN
ejpam-6282	136	26	h	h	NOUN
ejpam-6282	136	27	,	,	PUNCT
ejpam-6282	136	28	t	t	PROPN
ejpam-6282	136	29	:	:	PUNCT
ejpam-6282	136	30	r+	r+	NOUN
ejpam-6282	136	31	0	0	PUNCT
ejpam-6282	136	32	×r+	×r+	ADV
ejpam-6282	136	33	0	0	NUM
ejpam-6282	136	34	→	→	SYM
ejpam-6282	136	35	r+	r+	NOUN
ejpam-6282	136	36	0	0	NUM
ejpam-6282	136	37	are	be	AUX
ejpam-6282	136	38	continuous	continuous	ADJ
ejpam-6282	136	39	in	in	ADP
ejpam-6282	136	40	each	each	DET
ejpam-6282	136	41	variable	variable	NOUN
ejpam-6282	136	42	such	such	ADJ
ejpam-6282	136	43	that	that	SCONJ
ejpam-6282	136	44	h(t	h(t	PROPN
ejpam-6282	136	45	,	,	PUNCT
ejpam-6282	136	46	s	s	NOUN
ejpam-6282	136	47	)	)	PUNCT
ejpam-6282	136	48	>	>	X
ejpam-6282	137	1	f(t	f(t	PROPN
ejpam-6282	137	2	,	,	PUNCT
ejpam-6282	137	3	s	s	NOUN
ejpam-6282	137	4	)	)	PUNCT
ejpam-6282	137	5	for	for	ADP
ejpam-6282	137	6	all	all	DET
ejpam-6282	137	7	t	t	PROPN
ejpam-6282	137	8	,	,	PUNCT
ejpam-6282	137	9	s	s	VERB
ejpam-6282	137	10	>	>	X
ejpam-6282	137	11	0	0	NUM
ejpam-6282	137	12	.	.	PUNCT
ejpam-6282	138	1	g.	g.	PROPN
ejpam-6282	138	2	alsahli	alsahli	PROPN
ejpam-6282	138	3	,	,	PUNCT
ejpam-6282	138	4	s.	s.	PROPN
ejpam-6282	138	5	gülyaz	gülyaz	PROPN
ejpam-6282	138	6	-	-	PUNCT
ejpam-6282	138	7	özyurt	özyurt	PROPN
ejpam-6282	138	8	/	/	SYM
ejpam-6282	138	9	eur	eur	PROPN
ejpam-6282	138	10	.	.	PUNCT
ejpam-6282	139	1	j.	j.	PROPN
ejpam-6282	139	2	pure	pure	PROPN
ejpam-6282	139	3	appl	appl	PROPN
ejpam-6282	139	4	.	.	PROPN
ejpam-6282	139	5	math	math	PROPN
ejpam-6282	139	6	,	,	PUNCT
ejpam-6282	139	7	18	18	NUM
ejpam-6282	139	8	(	(	PUNCT
ejpam-6282	139	9	2	2	NUM
ejpam-6282	139	10	)	)	PUNCT
ejpam-6282	139	11	(	(	PUNCT
ejpam-6282	139	12	2025	2025	NUM
ejpam-6282	139	13	)	)	PUNCT
ejpam-6282	139	14	,	,	PUNCT
ejpam-6282	139	15	6282	6282	NUM
ejpam-6282	139	16	6	6	NUM
ejpam-6282	139	17	of	of	ADP
ejpam-6282	139	18	13	13	NUM
ejpam-6282	139	19	(	(	PUNCT
ejpam-6282	139	20	iii	iii	NOUN
ejpam-6282	139	21	)	)	PUNCT
ejpam-6282	139	22	for	for	ADP
ejpam-6282	139	23	any	any	DET
ejpam-6282	139	24	t	t	NOUN
ejpam-6282	139	25	,	,	PUNCT
ejpam-6282	139	26	s	s	PART
ejpam-6282	139	27	∈	∈	PROPN
ejpam-6282	140	1	[	[	X
ejpam-6282	140	2	0	0	NUM
ejpam-6282	140	3	,	,	PUNCT
ejpam-6282	140	4	∞	∞	PROPN
ejpam-6282	140	5	)	)	PUNCT
ejpam-6282	140	6	,	,	PUNCT
ejpam-6282	140	7	α3(t	α3(t	NUM
ejpam-6282	140	8	,	,	PUNCT
ejpam-6282	140	9	s	s	PART
ejpam-6282	140	10	)	)	PUNCT
ejpam-6282	140	11	=	=	SYM
ejpam-6282	140	12	s	s	PART
ejpam-6282	140	13	−	−	PROPN
ejpam-6282	140	14	p(s	p(s	NOUN
ejpam-6282	140	15	)	)	PUNCT
ejpam-6282	141	1	−	−	PROPN
ejpam-6282	142	1	t	t	PROPN
ejpam-6282	142	2	∈	∈	PROPN
ejpam-6282	142	3	t	t	PROPN
ejpam-6282	142	4	,	,	PUNCT
ejpam-6282	142	5	where	where	SCONJ
ejpam-6282	142	6	p	p	NOUN
ejpam-6282	142	7	:	:	PUNCT
ejpam-6282	143	1	[	[	X
ejpam-6282	143	2	0	0	NUM
ejpam-6282	143	3	,	,	PUNCT
ejpam-6282	143	4	∞	∞	PROPN
ejpam-6282	143	5	)	)	PUNCT
ejpam-6282	143	6	→	→	PUNCT
ejpam-6282	143	7	[	[	X
ejpam-6282	143	8	0	0	NUM
ejpam-6282	143	9	,	,	PUNCT
ejpam-6282	143	10	∞	∞	NUM
ejpam-6282	143	11	)	)	PUNCT
ejpam-6282	143	12	is	be	AUX
ejpam-6282	143	13	a	a	DET
ejpam-6282	143	14	continuous	continuous	ADJ
ejpam-6282	143	15	function	function	NOUN
ejpam-6282	143	16	such	such	ADJ
ejpam-6282	143	17	that	that	DET
ejpam-6282	143	18	p(t	p(t	NOUN
ejpam-6282	143	19	)	)	PUNCT
ejpam-6282	144	1	=	=	SYM
ejpam-6282	144	2	0	0	PUNCT
ejpam-6282	145	1	if	if	SCONJ
ejpam-6282	145	2	and	and	CCONJ
ejpam-6282	145	3	only	only	ADV
ejpam-6282	145	4	if	if	SCONJ
ejpam-6282	145	5	t	t	PROPN
ejpam-6282	145	6	=	=	SYM
ejpam-6282	145	7	0	0	X
ejpam-6282	145	8	.	.	PUNCT
ejpam-6282	146	1	next	next	ADV
ejpam-6282	146	2	,	,	PUNCT
ejpam-6282	146	3	we	we	PRON
ejpam-6282	146	4	recall	recall	VERB
ejpam-6282	146	5	the	the	DET
ejpam-6282	146	6	definition	definition	NOUN
ejpam-6282	146	7	of	of	ADP
ejpam-6282	146	8	zα	zα	PROPN
ejpam-6282	146	9	-	-	PUNCT
ejpam-6282	146	10	contraction	contraction	NOUN
ejpam-6282	146	11	,	,	PUNCT
ejpam-6282	146	12	khojasteh	khojasteh	PROPN
ejpam-6282	146	13	et	et	PROPN
ejpam-6282	146	14	al	al	PROPN
ejpam-6282	146	15	.	.	PUNCT
ejpam-6282	147	1	[	[	X
ejpam-6282	147	2	14	14	NUM
ejpam-6282	147	3	]	]	PUNCT
ejpam-6282	147	4	.	.	PUNCT
ejpam-6282	148	1	for	for	ADP
ejpam-6282	148	2	more	more	ADJ
ejpam-6282	148	3	examples	example	NOUN
ejpam-6282	148	4	and	and	CCONJ
ejpam-6282	148	5	details	detail	NOUN
ejpam-6282	148	6	,	,	PUNCT
ejpam-6282	148	7	see	see	VERB
ejpam-6282	148	8	e.g.	e.g.	ADV
ejpam-6282	148	9	[	[	X
ejpam-6282	148	10	13	13	NUM
ejpam-6282	148	11	,	,	PUNCT
ejpam-6282	148	12	15–22	15–22	NUM
ejpam-6282	148	13	,	,	PUNCT
ejpam-6282	148	14	24	24	NUM
ejpam-6282	148	15	]	]	PUNCT
ejpam-6282	148	16	.	.	PUNCT
ejpam-6282	149	1	definition	definition	NOUN
ejpam-6282	149	2	4	4	NUM
ejpam-6282	149	3	.	.	PUNCT
ejpam-6282	150	1	[	[	X
ejpam-6282	150	2	14	14	NUM
ejpam-6282	150	3	]	]	X
ejpam-6282	150	4	let	let	VERB
ejpam-6282	150	5	(	(	PUNCT
ejpam-6282	150	6	s	s	X
ejpam-6282	150	7	,	,	PUNCT
ejpam-6282	150	8	d	d	NOUN
ejpam-6282	150	9	)	)	PUNCT
ejpam-6282	150	10	form	form	VERB
ejpam-6282	150	11	an	an	DET
ejpam-6282	150	12	usual	usual	ADJ
ejpam-6282	150	13	metric	metric	ADJ
ejpam-6282	150	14	space	space	NOUN
ejpam-6282	150	15	.	.	PUNCT
ejpam-6282	151	1	let	let	VERB
ejpam-6282	151	2	t	t	NOUN
ejpam-6282	151	3	be	be	AUX
ejpam-6282	151	4	a	a	DET
ejpam-6282	151	5	self	self	NOUN
ejpam-6282	151	6	-	-	PUNCT
ejpam-6282	151	7	mapping	mapping	NOUN
ejpam-6282	151	8	on	on	ADP
ejpam-6282	151	9	s	s	NOUN
ejpam-6282	151	10	,	,	PUNCT
ejpam-6282	151	11	and	and	CCONJ
ejpam-6282	151	12	α	α	PRON
ejpam-6282	151	13	∈	∈	PROPN
ejpam-6282	151	14	t	t	PROPN
ejpam-6282	151	15	.	.	PUNCT
ejpam-6282	152	1	for	for	ADP
ejpam-6282	152	2	any	any	DET
ejpam-6282	152	3	m	m	NOUN
ejpam-6282	152	4	,	,	PUNCT
ejpam-6282	152	5	n	n	PROPN
ejpam-6282	152	6	∈	∈	PROPN
ejpam-6282	152	7	s	s	PROPN
ejpam-6282	152	8	,	,	PUNCT
ejpam-6282	152	9	t	t	PROPN
ejpam-6282	152	10	is	be	AUX
ejpam-6282	152	11	referred	refer	VERB
ejpam-6282	152	12	to	to	PART
ejpam-6282	152	13	be	be	AUX
ejpam-6282	152	14	a	a	DET
ejpam-6282	152	15	zα	zα	NUM
ejpam-6282	152	16	-	-	PUNCT
ejpam-6282	152	17	contraction	contraction	NOUN
ejpam-6282	152	18	if	if	SCONJ
ejpam-6282	152	19	α(d(tm	α(d(tm	NOUN
ejpam-6282	152	20	,	,	PUNCT
ejpam-6282	152	21	tn	tn	PROPN
ejpam-6282	152	22	)	)	PUNCT
ejpam-6282	152	23	,	,	PUNCT
ejpam-6282	152	24	d(m	d(m	PROPN
ejpam-6282	152	25	,	,	PUNCT
ejpam-6282	152	26	n	n	CCONJ
ejpam-6282	152	27	)	)	PUNCT
ejpam-6282	152	28	)	)	PUNCT
ejpam-6282	152	29	≥	≥	NOUN
ejpam-6282	152	30	0	0	NUM
ejpam-6282	152	31	.	.	PUNCT
ejpam-6282	153	1	(	(	PUNCT
ejpam-6282	153	2	1.2	1.2	NUM
ejpam-6282	153	3	)	)	PUNCT
ejpam-6282	153	4	remark	remark	NOUN
ejpam-6282	153	5	2	2	NUM
ejpam-6282	153	6	.	.	PUNCT
ejpam-6282	154	1	[	[	X
ejpam-6282	154	2	14	14	NUM
ejpam-6282	154	3	]	]	PUNCT
ejpam-6282	154	4	(	(	PUNCT
ejpam-6282	154	5	i	i	NOUN
ejpam-6282	154	6	)	)	PUNCT
ejpam-6282	154	7	the	the	DET
ejpam-6282	154	8	famous	famous	ADJ
ejpam-6282	154	9	banach	banach	NOUN
ejpam-6282	154	10	fixed	fix	VERB
ejpam-6282	154	11	point	point	NOUN
ejpam-6282	154	12	theorem	theorem	NOUN
ejpam-6282	154	13	is	be	AUX
ejpam-6282	154	14	a	a	DET
ejpam-6282	154	15	straightforward	straightforward	ADJ
ejpam-6282	154	16	consequence	consequence	NOUN
ejpam-6282	154	17	of	of	ADP
ejpam-6282	154	18	sα	sα	NOUN
ejpam-6282	154	19	-	-	NOUN
ejpam-6282	154	20	contraction	contraction	NOUN
ejpam-6282	154	21	,	,	PUNCT
ejpam-6282	154	22	which	which	PRON
ejpam-6282	154	23	can	can	AUX
ejpam-6282	154	24	be	be	AUX
ejpam-6282	154	25	derived	derive	VERB
ejpam-6282	154	26	by	by	ADP
ejpam-6282	154	27	taking	take	VERB
ejpam-6282	154	28	λ	λ	PROPN
ejpam-6282	154	29	∈	∈	PROPN
ejpam-6282	155	1	[	[	X
ejpam-6282	155	2	0	0	NUM
ejpam-6282	155	3	,	,	PUNCT
ejpam-6282	155	4	1	1	NUM
ejpam-6282	155	5	)	)	PUNCT
ejpam-6282	155	6	and	and	CCONJ
ejpam-6282	155	7	α(n	α(n	NOUN
ejpam-6282	155	8	,	,	PUNCT
ejpam-6282	155	9	m	m	NOUN
ejpam-6282	155	10	)	)	PUNCT
ejpam-6282	156	1	=	=	SYM
ejpam-6282	156	2	λm	λm	ADP
ejpam-6282	156	3	−	−	PROPN
ejpam-6282	156	4	n	n	CCONJ
ejpam-6282	156	5	for	for	ADP
ejpam-6282	156	6	all	all	DET
ejpam-6282	156	7	m	m	PROPN
ejpam-6282	156	8	,	,	PUNCT
ejpam-6282	156	9	n	n	PRON
ejpam-6282	156	10	∈	∈	PROPN
ejpam-6282	157	1	[	[	X
ejpam-6282	157	2	0	0	NUM
ejpam-6282	157	3	,	,	PUNCT
ejpam-6282	157	4	∞	∞	NUM
ejpam-6282	157	5	)	)	PUNCT
ejpam-6282	157	6	in	in	ADP
ejpam-6282	157	7	the	the	DET
ejpam-6282	157	8	formulation	formulation	NOUN
ejpam-6282	157	9	above	above	ADV
ejpam-6282	157	10	.	.	PUNCT
ejpam-6282	158	1	(	(	PUNCT
ejpam-6282	158	2	ii	ii	X
ejpam-6282	158	3	)	)	PUNCT
ejpam-6282	158	4	it	it	PRON
ejpam-6282	158	5	is	be	AUX
ejpam-6282	158	6	crystal	crystal	NOUN
ejpam-6282	158	7	clear	clear	ADJ
ejpam-6282	158	8	from	from	ADP
ejpam-6282	158	9	the	the	DET
ejpam-6282	158	10	simulation	simulation	NOUN
ejpam-6282	158	11	function	function	NOUN
ejpam-6282	158	12	formulation	formulation	NOUN
ejpam-6282	158	13	that	that	SCONJ
ejpam-6282	158	14	for	for	ADP
ejpam-6282	158	15	every	every	DET
ejpam-6282	158	16	b	b	NOUN
ejpam-6282	158	17	≥	≥	NOUN
ejpam-6282	158	18	a	a	PRON
ejpam-6282	158	19	>	>	X
ejpam-6282	158	20	0	0	NUM
ejpam-6282	158	21	,	,	PUNCT
ejpam-6282	158	22	α(b	α(b	NOUN
ejpam-6282	158	23	,	,	PUNCT
ejpam-6282	158	24	a	a	PRON
ejpam-6282	158	25	)	)	PUNCT
ejpam-6282	158	26	<	<	X
ejpam-6282	158	27	0	0	NUM
ejpam-6282	158	28	.	.	PUNCT
ejpam-6282	159	1	thus	thus	ADV
ejpam-6282	159	2	,	,	PUNCT
ejpam-6282	159	3	for	for	ADP
ejpam-6282	159	4	every	every	DET
ejpam-6282	159	5	unique	unique	ADJ
ejpam-6282	159	6	m	m	NOUN
ejpam-6282	159	7	,	,	PUNCT
ejpam-6282	159	8	n	n	PROPN
ejpam-6282	159	9	∈	∈	PROPN
ejpam-6282	159	10	s	s	X
ejpam-6282	159	11	,	,	PUNCT
ejpam-6282	159	12	we	we	PRON
ejpam-6282	159	13	get	get	VERB
ejpam-6282	159	14	d(tm	d(tm	NOUN
ejpam-6282	159	15	,	,	PUNCT
ejpam-6282	159	16	tn	tn	PROPN
ejpam-6282	159	17	)	)	PUNCT
ejpam-6282	159	18	<	<	X
ejpam-6282	159	19	d(m	d(m	PROPN
ejpam-6282	159	20	,	,	PUNCT
ejpam-6282	159	21	n	n	CCONJ
ejpam-6282	159	22	)	)	PUNCT
ejpam-6282	159	23	.	.	PUNCT
ejpam-6282	160	1	this	this	PRON
ejpam-6282	160	2	indicates	indicate	VERB
ejpam-6282	160	3	that	that	SCONJ
ejpam-6282	160	4	each	each	DET
ejpam-6282	160	5	zα	zα	PROPN
ejpam-6282	160	6	-	-	PUNCT
ejpam-6282	160	7	contraction	contraction	NOUN
ejpam-6282	160	8	mapping	mapping	NOUN
ejpam-6282	160	9	is	be	AUX
ejpam-6282	160	10	continuous	continuous	ADJ
ejpam-6282	160	11	since	since	SCONJ
ejpam-6282	160	12	it	it	PRON
ejpam-6282	160	13	is	be	AUX
ejpam-6282	160	14	contractive	contractive	ADJ
ejpam-6282	160	15	.	.	PUNCT
ejpam-6282	161	1	we	we	PRON
ejpam-6282	161	2	now	now	ADV
ejpam-6282	161	3	present	present	VERB
ejpam-6282	161	4	the	the	DET
ejpam-6282	161	5	lemmas	lemma	NOUN
ejpam-6282	161	6	and	and	CCONJ
ejpam-6282	161	7	results	result	NOUN
ejpam-6282	161	8	demonstrated	demonstrate	VERB
ejpam-6282	161	9	in	in	ADP
ejpam-6282	161	10	[	[	X
ejpam-6282	161	11	14	14	NUM
ejpam-6282	161	12	]	]	X
ejpam-6282	161	13	:	:	PUNCT
ejpam-6282	161	14	lemma	lemma	PROPN
ejpam-6282	161	15	1	1	X
ejpam-6282	161	16	.	.	PUNCT
ejpam-6282	162	1	[	[	X
ejpam-6282	162	2	14	14	NUM
ejpam-6282	162	3	]	]	PUNCT
ejpam-6282	162	4	let	let	VERB
ejpam-6282	162	5	t	t	NOUN
ejpam-6282	162	6	:	:	PUNCT
ejpam-6282	162	7	s	s	X
ejpam-6282	162	8	→	→	SYM
ejpam-6282	162	9	s	s	PART
ejpam-6282	162	10	be	be	AUX
ejpam-6282	162	11	a	a	DET
ejpam-6282	162	12	zα	zα	NUM
ejpam-6282	162	13	-	-	PUNCT
ejpam-6282	162	14	contraction	contraction	NOUN
ejpam-6282	162	15	where	where	SCONJ
ejpam-6282	162	16	(	(	PUNCT
ejpam-6282	162	17	s	s	X
ejpam-6282	162	18	,	,	PUNCT
ejpam-6282	162	19	d	d	NOUN
ejpam-6282	162	20	)	)	PUNCT
ejpam-6282	162	21	is	be	AUX
ejpam-6282	162	22	a	a	DET
ejpam-6282	162	23	metric	metric	ADJ
ejpam-6282	162	24	space	space	NOUN
ejpam-6282	162	25	.	.	PUNCT
ejpam-6282	163	1	then	then	ADV
ejpam-6282	163	2	,	,	PUNCT
ejpam-6282	163	3	1	1	X
ejpam-6282	163	4	.	.	PUNCT
ejpam-6282	164	1	the	the	DET
ejpam-6282	164	2	mapping	mapping	NOUN
ejpam-6282	164	3	t	t	PROPN
ejpam-6282	164	4	possesses	possess	VERB
ejpam-6282	164	5	a	a	DET
ejpam-6282	164	6	unique	unique	ADJ
ejpam-6282	164	7	fixed	fix	VERB
ejpam-6282	164	8	point	point	NOUN
ejpam-6282	164	9	in	in	ADP
ejpam-6282	164	10	s	s	PROPN
ejpam-6282	164	11	(	(	PUNCT
ejpam-6282	164	12	provided	provide	VERB
ejpam-6282	164	13	it	it	PRON
ejpam-6282	164	14	exists	exist	VERB
ejpam-6282	164	15	)	)	PUNCT
ejpam-6282	164	16	;	;	PUNCT
ejpam-6282	164	17	2	2	X
ejpam-6282	164	18	.	.	X
ejpam-6282	164	19	t	t	PROPN
ejpam-6282	164	20	is	be	AUX
ejpam-6282	164	21	asymptotically	asymptotically	ADV
ejpam-6282	164	22	regular	regular	ADJ
ejpam-6282	164	23	at	at	ADP
ejpam-6282	164	24	every	every	DET
ejpam-6282	164	25	m	m	NOUN
ejpam-6282	164	26	∈	∈	NOUN
ejpam-6282	164	27	s	s	NOUN
ejpam-6282	164	28	;	;	PUNCT
ejpam-6282	164	29	3	3	X
ejpam-6282	164	30	.	.	X
ejpam-6282	164	31	let	let	VERB
ejpam-6282	164	32	mn	mn	PROPN
ejpam-6282	164	33	=	=	PUNCT
ejpam-6282	165	1	tmn−1	tmn−1	PROPN
ejpam-6282	165	2	for	for	ADP
ejpam-6282	165	3	each	each	DET
ejpam-6282	165	4	n	n	PRON
ejpam-6282	165	5	∈	∈	PROPN
ejpam-6282	165	6	n	n	NOUN
ejpam-6282	165	7	with	with	ADP
ejpam-6282	165	8	an	an	DET
ejpam-6282	165	9	initial	initial	ADJ
ejpam-6282	165	10	value	value	NOUN
ejpam-6282	165	11	m0	m0	NOUN
ejpam-6282	165	12	∈	∈	PROPN
ejpam-6282	165	13	m	m	AUX
ejpam-6282	165	14	(	(	PUNCT
ejpam-6282	165	15	arbitrarily	arbitrarily	ADV
ejpam-6282	165	16	chosen	choose	VERB
ejpam-6282	165	17	point	point	NOUN
ejpam-6282	165	18	m	m	AUX
ejpam-6282	165	19	renamed	rename	VERB
ejpam-6282	165	20	as	as	ADP
ejpam-6282	165	21	m0	m0	NOUN
ejpam-6282	165	22	:	:	PUNCT
ejpam-6282	165	23	=	=	NOUN
ejpam-6282	165	24	m	m	NOUN
ejpam-6282	165	25	)	)	PUNCT
ejpam-6282	165	26	.	.	PUNCT
ejpam-6282	166	1	then	then	ADV
ejpam-6282	166	2	,	,	PUNCT
ejpam-6282	166	3	the	the	DET
ejpam-6282	166	4	constructed	construct	VERB
ejpam-6282	166	5	sequence	sequence	NOUN
ejpam-6282	166	6	{	{	PUNCT
ejpam-6282	166	7	mn	mn	NOUN
ejpam-6282	166	8	}	}	PUNCT
ejpam-6282	166	9	,	,	PUNCT
ejpam-6282	166	10	generated	generate	VERB
ejpam-6282	166	11	by	by	ADP
ejpam-6282	166	12	picard	picard	NOUN
ejpam-6282	166	13	operator	operator	NOUN
ejpam-6282	166	14	t	t	PROPN
ejpam-6282	166	15	,	,	PUNCT
ejpam-6282	166	16	is	be	AUX
ejpam-6282	166	17	bounded	bound	VERB
ejpam-6282	166	18	.	.	PUNCT
ejpam-6282	167	1	theorem	theorem	NOUN
ejpam-6282	167	2	1	1	NUM
ejpam-6282	167	3	.	.	PUNCT
ejpam-6282	168	1	if	if	SCONJ
ejpam-6282	168	2	a	a	DET
ejpam-6282	168	3	self	self	NOUN
ejpam-6282	168	4	-	-	PUNCT
ejpam-6282	168	5	mapping	mapping	NOUN
ejpam-6282	168	6	t	t	NOUN
ejpam-6282	168	7	,	,	PUNCT
ejpam-6282	168	8	on	on	ADP
ejpam-6282	168	9	a	a	DET
ejpam-6282	168	10	metric	metric	ADJ
ejpam-6282	168	11	space	space	NOUN
ejpam-6282	168	12	(	(	PUNCT
ejpam-6282	168	13	s	s	X
ejpam-6282	168	14	,	,	PUNCT
ejpam-6282	168	15	d	d	NOUN
ejpam-6282	168	16	)	)	PUNCT
ejpam-6282	168	17	,	,	PUNCT
ejpam-6282	168	18	forms	form	VERB
ejpam-6282	168	19	an	an	DET
ejpam-6282	168	20	zα	zα	NUM
ejpam-6282	168	21	-	-	PUNCT
ejpam-6282	168	22	contraction	contraction	NOUN
ejpam-6282	168	23	,	,	PUNCT
ejpam-6282	168	24	then	then	ADV
ejpam-6282	168	25	t	t	PROPN
ejpam-6282	168	26	has	have	VERB
ejpam-6282	168	27	a	a	DET
ejpam-6282	168	28	unique	unique	ADJ
ejpam-6282	168	29	fixed	fix	VERB
ejpam-6282	168	30	point	point	NOUN
ejpam-6282	168	31	m∗	m∗	NOUN
ejpam-6282	168	32	in	in	ADP
ejpam-6282	168	33	m.	m.	NOUN
ejpam-6282	168	34	furthermore	furthermore	ADV
ejpam-6282	168	35	,	,	PUNCT
ejpam-6282	168	36	for	for	ADP
ejpam-6282	168	37	arbitrary	arbitrary	ADJ
ejpam-6282	168	38	initial	initial	ADJ
ejpam-6282	168	39	point	point	NOUN
ejpam-6282	168	40	m0	m0	PROPN
ejpam-6282	168	41	∈	∈	PROPN
ejpam-6282	168	42	m	m	VERB
ejpam-6282	168	43	the	the	DET
ejpam-6282	168	44	constructed	construct	VERB
ejpam-6282	168	45	sequence	sequence	NOUN
ejpam-6282	168	46	{	{	PUNCT
ejpam-6282	168	47	mn	mn	NOUN
ejpam-6282	168	48	}	}	PUNCT
ejpam-6282	168	49	,	,	PUNCT
ejpam-6282	168	50	converges	converge	VERB
ejpam-6282	168	51	to	to	ADP
ejpam-6282	168	52	the	the	DET
ejpam-6282	168	53	fixed	fix	VERB
ejpam-6282	168	54	point	point	NOUN
ejpam-6282	168	55	of	of	ADP
ejpam-6282	168	56	t	t	PROPN
ejpam-6282	168	57	,	,	PUNCT
ejpam-6282	168	58	where	where	SCONJ
ejpam-6282	168	59	mn	mn	PROPN
ejpam-6282	169	1	=	=	PUNCT
ejpam-6282	169	2	tmn−1	tmn−1	PROPN
ejpam-6282	169	3	for	for	ADP
ejpam-6282	169	4	all	all	DET
ejpam-6282	169	5	n	n	PRON
ejpam-6282	169	6	∈	∈	PROPN
ejpam-6282	169	7	n.	n.	NOUN
ejpam-6282	169	8	2	2	NUM
ejpam-6282	169	9	.	.	PUNCT
ejpam-6282	169	10	main	main	ADJ
ejpam-6282	169	11	results	result	NOUN
ejpam-6282	169	12	we	we	PRON
ejpam-6282	169	13	start	start	VERB
ejpam-6282	169	14	this	this	DET
ejpam-6282	169	15	section	section	NOUN
ejpam-6282	169	16	by	by	ADP
ejpam-6282	169	17	stating	state	VERB
ejpam-6282	169	18	the	the	DET
ejpam-6282	169	19	very	very	ADV
ejpam-6282	169	20	important	important	ADJ
ejpam-6282	169	21	auxiliary	auxiliary	ADJ
ejpam-6282	169	22	function	function	NOUN
ejpam-6282	169	23	in	in	ADP
ejpam-6282	169	24	the	the	DET
ejpam-6282	169	25	metric	metric	ADJ
ejpam-6282	169	26	fixed	fix	VERB
ejpam-6282	169	27	point	point	NOUN
ejpam-6282	169	28	theory	theory	NOUN
ejpam-6282	169	29	.	.	PUNCT
ejpam-6282	170	1	a	a	DET
ejpam-6282	170	2	function	function	NOUN
ejpam-6282	170	3	ψ	ψ	X
ejpam-6282	170	4	:	:	PUNCT
ejpam-6282	171	1	[	[	X
ejpam-6282	171	2	0	0	NUM
ejpam-6282	171	3	,	,	PUNCT
ejpam-6282	171	4	∞	∞	PROPN
ejpam-6282	171	5	)	)	PUNCT
ejpam-6282	171	6	→	→	PUNCT
ejpam-6282	171	7	[	[	X
ejpam-6282	171	8	0	0	NUM
ejpam-6282	171	9	,	,	PUNCT
ejpam-6282	171	10	∞	∞	PROPN
ejpam-6282	171	11	)	)	PUNCT
ejpam-6282	171	12	is	be	AUX
ejpam-6282	171	13	called	call	VERB
ejpam-6282	171	14	c	c	NOUN
ejpam-6282	171	15	-	-	PUNCT
ejpam-6282	171	16	comparison	comparison	NOUN
ejpam-6282	171	17	function	function	NOUN
ejpam-6282	171	18	when	when	SCONJ
ejpam-6282	171	19	(	(	PUNCT
ejpam-6282	171	20	ψ1	ψ1	NOUN
ejpam-6282	171	21	)	)	PUNCT
ejpam-6282	171	22	ψ	ψ	NOUN
ejpam-6282	171	23	is	be	AUX
ejpam-6282	171	24	increasing	increase	VERB
ejpam-6282	171	25	;	;	PUNCT
ejpam-6282	171	26	g.	g.	PROPN
ejpam-6282	171	27	alsahli	alsahli	PROPN
ejpam-6282	171	28	,	,	PUNCT
ejpam-6282	171	29	s.	s.	PROPN
ejpam-6282	171	30	gülyaz	gülyaz	PROPN
ejpam-6282	171	31	-	-	PUNCT
ejpam-6282	171	32	özyurt	özyurt	PROPN
ejpam-6282	171	33	/	/	SYM
ejpam-6282	171	34	eur	eur	PROPN
ejpam-6282	171	35	.	.	PUNCT
ejpam-6282	172	1	j.	j.	PROPN
ejpam-6282	172	2	pure	pure	PROPN
ejpam-6282	172	3	appl	appl	PROPN
ejpam-6282	172	4	.	.	PROPN
ejpam-6282	172	5	math	math	PROPN
ejpam-6282	172	6	,	,	PUNCT
ejpam-6282	172	7	18	18	NUM
ejpam-6282	172	8	(	(	PUNCT
ejpam-6282	172	9	2	2	NUM
ejpam-6282	172	10	)	)	PUNCT
ejpam-6282	172	11	(	(	PUNCT
ejpam-6282	172	12	2025	2025	NUM
ejpam-6282	172	13	)	)	PUNCT
ejpam-6282	172	14	,	,	PUNCT
ejpam-6282	172	15	6282	6282	NUM
ejpam-6282	172	16	7	7	NUM
ejpam-6282	172	17	of	of	ADP
ejpam-6282	172	18	13	13	NUM
ejpam-6282	172	19	(	(	PUNCT
ejpam-6282	172	20	ψ2	ψ2	NOUN
ejpam-6282	172	21	)	)	PUNCT
ejpam-6282	173	1	+	+	NUM
ejpam-6282	173	2	∞	∞	NUM
ejpam-6282	173	3	∑	∑	PUNCT
ejpam-6282	173	4	n=1	n=1	PROPN
ejpam-6282	173	5	ψn(x	ψn(x	ADP
ejpam-6282	173	6	)	)	PUNCT
ejpam-6282	173	7	<	<	X
ejpam-6282	173	8	∞	∞	PROPN
ejpam-6282	173	9	for	for	ADP
ejpam-6282	173	10	any	any	DET
ejpam-6282	173	11	x	x	SYM
ejpam-6282	173	12	>	>	X
ejpam-6282	173	13	0	0	PROPN
ejpam-6282	173	14	,	,	PUNCT
ejpam-6282	173	15	where	where	SCONJ
ejpam-6282	173	16	ψn	ψn	ADV
ejpam-6282	173	17	is	be	AUX
ejpam-6282	173	18	observed	observe	VERB
ejpam-6282	173	19	by	by	ADP
ejpam-6282	173	20	recursively	recursively	ADV
ejpam-6282	173	21	compose	compose	VERB
ejpam-6282	173	22	the	the	DET
ejpam-6282	173	23	function	function	NOUN
ejpam-6282	173	24	ψ	ψ	X
ejpam-6282	173	25	with	with	ADP
ejpam-6282	173	26	itself	itself	PRON
ejpam-6282	173	27	n	n	DET
ejpam-6282	173	28	times	time	NOUN
ejpam-6282	173	29	.	.	PUNCT
ejpam-6282	174	1	the	the	DET
ejpam-6282	174	2	letter	letter	NOUN
ejpam-6282	174	3	ψ	ψ	X
ejpam-6282	174	4	to	to	PART
ejpam-6282	174	5	hold	hold	VERB
ejpam-6282	174	6	forth	forth	ADP
ejpam-6282	174	7	the	the	DET
ejpam-6282	174	8	family	family	NOUN
ejpam-6282	174	9	of	of	ADP
ejpam-6282	174	10	all	all	DET
ejpam-6282	174	11	c	c	NOUN
ejpam-6282	174	12	-	-	PUNCT
ejpam-6282	174	13	comparison	comparison	NOUN
ejpam-6282	174	14	functions	function	NOUN
ejpam-6282	174	15	.	.	PUNCT
ejpam-6282	175	1	lemma	lemma	PROPN
ejpam-6282	175	2	2	2	NUM
ejpam-6282	175	3	.	.	PUNCT
ejpam-6282	176	1	(	(	PUNCT
ejpam-6282	176	2	[	[	X
ejpam-6282	176	3	3	3	NUM
ejpam-6282	176	4	]	]	PUNCT
ejpam-6282	176	5	,	,	PUNCT
ejpam-6282	176	6	[	[	X
ejpam-6282	176	7	12],[24	12],[24	NUM
ejpam-6282	176	8	]	]	X
ejpam-6282	176	9	)	)	PUNCT
ejpam-6282	176	10	if	if	SCONJ
ejpam-6282	176	11	ψ	ψ	X
ejpam-6282	176	12	:	:	PUNCT
ejpam-6282	177	1	[	[	X
ejpam-6282	177	2	0	0	NUM
ejpam-6282	177	3	,	,	PUNCT
ejpam-6282	177	4	∞	∞	PROPN
ejpam-6282	177	5	)	)	PUNCT
ejpam-6282	177	6	→	→	PUNCT
ejpam-6282	177	7	[	[	X
ejpam-6282	177	8	0	0	NUM
ejpam-6282	177	9	,	,	PUNCT
ejpam-6282	177	10	∞	∞	NUM
ejpam-6282	177	11	)	)	PUNCT
ejpam-6282	177	12	is	be	AUX
ejpam-6282	177	13	a	a	DET
ejpam-6282	177	14	comparison	comparison	NOUN
ejpam-6282	177	15	function	function	NOUN
ejpam-6282	177	16	,	,	PUNCT
ejpam-6282	177	17	then	then	ADV
ejpam-6282	177	18	:	:	PUNCT
ejpam-6282	177	19	(	(	PUNCT
ejpam-6282	177	20	1	1	X
ejpam-6282	177	21	)	)	PUNCT
ejpam-6282	177	22	each	each	DET
ejpam-6282	177	23	iterate	iterate	NOUN
ejpam-6282	177	24	ψk	ψk	NOUN
ejpam-6282	177	25	of	of	ADP
ejpam-6282	177	26	ψ	ψ	PROPN
ejpam-6282	177	27	,	,	PUNCT
ejpam-6282	177	28	k	k	PROPN
ejpam-6282	177	29	≥	≥	NUM
ejpam-6282	177	30	1	1	NUM
ejpam-6282	177	31	,	,	PUNCT
ejpam-6282	177	32	is	be	AUX
ejpam-6282	177	33	also	also	ADV
ejpam-6282	177	34	a	a	DET
ejpam-6282	177	35	comparison	comparison	NOUN
ejpam-6282	177	36	function	function	NOUN
ejpam-6282	177	37	;	;	PUNCT
ejpam-6282	177	38	(	(	PUNCT
ejpam-6282	177	39	2	2	X
ejpam-6282	177	40	)	)	PUNCT
ejpam-6282	177	41	ψ	ψ	NOUN
ejpam-6282	177	42	is	be	AUX
ejpam-6282	177	43	continuous	continuous	ADJ
ejpam-6282	177	44	at	at	ADP
ejpam-6282	177	45	0	0	NUM
ejpam-6282	177	46	;	;	PUNCT
ejpam-6282	177	47	(	(	PUNCT
ejpam-6282	177	48	3	3	X
ejpam-6282	177	49	)	)	PUNCT
ejpam-6282	177	50	ψ(t	ψ(t	PROPN
ejpam-6282	177	51	)	)	PUNCT
ejpam-6282	177	52	<	<	X
ejpam-6282	177	53	t	t	PROPN
ejpam-6282	177	54	,	,	PUNCT
ejpam-6282	177	55	for	for	ADP
ejpam-6282	177	56	any	any	DET
ejpam-6282	177	57	t	t	NOUN
ejpam-6282	177	58	>	>	X
ejpam-6282	177	59	0	0	X
ejpam-6282	177	60	.	.	PUNCT
ejpam-6282	178	1	here	here	ADV
ejpam-6282	178	2	,	,	PUNCT
ejpam-6282	178	3	we	we	PRON
ejpam-6282	178	4	shall	shall	AUX
ejpam-6282	178	5	introduce	introduce	VERB
ejpam-6282	178	6	the	the	DET
ejpam-6282	178	7	notion	notion	NOUN
ejpam-6282	178	8	of	of	ADP
ejpam-6282	178	9	zα	zα	PROPN
ejpam-6282	178	10	-	-	PUNCT
ejpam-6282	178	11	contraction	contraction	PROPN
ejpam-6282	178	12	,	,	PUNCT
ejpam-6282	178	13	a	a	DET
ejpam-6282	178	14	new	new	ADJ
ejpam-6282	178	15	contraction	contraction	NOUN
ejpam-6282	178	16	condition	condition	NOUN
ejpam-6282	178	17	defined	define	VERB
ejpam-6282	178	18	within	within	ADP
ejpam-6282	178	19	interpolative	interpolative	ADJ
ejpam-6282	178	20	metric	metric	ADJ
ejpam-6282	178	21	spaces	space	NOUN
ejpam-6282	178	22	:	:	PUNCT
ejpam-6282	178	23	definition	definition	NOUN
ejpam-6282	178	24	5	5	NUM
ejpam-6282	178	25	.	.	PUNCT
ejpam-6282	179	1	let	let	VERB
ejpam-6282	179	2	t	t	NOUN
ejpam-6282	179	3	:	:	PUNCT
ejpam-6282	179	4	s	s	AUX
ejpam-6282	179	5	→	→	SYM
ejpam-6282	179	6	s	s	PART
ejpam-6282	179	7	be	be	AUX
ejpam-6282	179	8	a	a	DET
ejpam-6282	179	9	mapping	mapping	NOUN
ejpam-6282	179	10	,	,	PUNCT
ejpam-6282	179	11	where	where	SCONJ
ejpam-6282	179	12	(	(	PUNCT
ejpam-6282	179	13	s	s	X
ejpam-6282	179	14	,	,	PUNCT
ejpam-6282	179	15	d	d	NOUN
ejpam-6282	179	16	)	)	PUNCT
ejpam-6282	179	17	is	be	AUX
ejpam-6282	179	18	a	a	DET
ejpam-6282	179	19	(	(	PUNCT
ejpam-6282	179	20	ξ	ξ	PROPN
ejpam-6282	179	21	,	,	PUNCT
ejpam-6282	179	22	c)-interpolative	c)-interpolative	ADJ
ejpam-6282	179	23	metric	metric	ADJ
ejpam-6282	179	24	space	space	NOUN
ejpam-6282	179	25	,	,	PUNCT
ejpam-6282	179	26	and	and	CCONJ
ejpam-6282	179	27	ψ	ψ	X
ejpam-6282	179	28	∈	∈	PROPN
ejpam-6282	179	29	σ	σ	PROPN
ejpam-6282	179	30	.	.	PUNCT
ejpam-6282	180	1	the	the	DET
ejpam-6282	180	2	mapping	mapping	NOUN
ejpam-6282	180	3	t	t	PROPN
ejpam-6282	180	4	is	be	AUX
ejpam-6282	180	5	called	call	VERB
ejpam-6282	180	6	an	an	DET
ejpam-6282	180	7	interpolative	interpolative	ADJ
ejpam-6282	180	8	zα	zα	PROPN
ejpam-6282	180	9	-	-	NOUN
ejpam-6282	180	10	contraction	contraction	NOUN
ejpam-6282	180	11	in	in	ADP
ejpam-6282	180	12	case	case	NOUN
ejpam-6282	180	13	:	:	PUNCT
ejpam-6282	180	14	α(d(tm	α(d(tm	NOUN
ejpam-6282	180	15	,	,	PUNCT
ejpam-6282	180	16	tl	tl	PROPN
ejpam-6282	180	17	)	)	PUNCT
ejpam-6282	180	18	,	,	PUNCT
ejpam-6282	180	19	ψ(d(m	ψ(d(m	PROPN
ejpam-6282	180	20	,	,	PUNCT
ejpam-6282	180	21	l	l	NOUN
ejpam-6282	180	22	)	)	PUNCT
ejpam-6282	180	23	)	)	PUNCT
ejpam-6282	180	24	)	)	PUNCT
ejpam-6282	180	25	≥	≥	NOUN
ejpam-6282	180	26	0	0	NUM
ejpam-6282	180	27	,	,	PUNCT
ejpam-6282	180	28	(	(	PUNCT
ejpam-6282	180	29	2.1	2.1	NUM
ejpam-6282	180	30	)	)	PUNCT
ejpam-6282	180	31	for	for	ADP
ejpam-6282	180	32	each	each	DET
ejpam-6282	180	33	m	m	NOUN
ejpam-6282	180	34	,	,	PUNCT
ejpam-6282	180	35	l	l	PROPN
ejpam-6282	180	36	∈	∈	PROPN
ejpam-6282	180	37	m.	m.	NOUN
ejpam-6282	180	38	proposition	proposition	NOUN
ejpam-6282	180	39	1	1	NUM
ejpam-6282	180	40	.	.	PUNCT
ejpam-6282	181	1	let	let	VERB
ejpam-6282	181	2	t	t	NOUN
ejpam-6282	181	3	:	:	PUNCT
ejpam-6282	181	4	s	s	X
ejpam-6282	181	5	→	→	SYM
ejpam-6282	181	6	s	s	AUX
ejpam-6282	181	7	be	be	AUX
ejpam-6282	181	8	an	an	DET
ejpam-6282	181	9	interpolative	interpolative	ADJ
ejpam-6282	181	10	zα	zα	NUM
ejpam-6282	181	11	-	-	PUNCT
ejpam-6282	181	12	contraction	contraction	NOUN
ejpam-6282	181	13	,	,	PUNCT
ejpam-6282	181	14	where	where	SCONJ
ejpam-6282	181	15	(	(	PUNCT
ejpam-6282	181	16	s	s	X
ejpam-6282	181	17	,	,	PUNCT
ejpam-6282	181	18	d	d	NOUN
ejpam-6282	181	19	)	)	PUNCT
ejpam-6282	181	20	is	be	AUX
ejpam-6282	181	21	an	an	DET
ejpam-6282	181	22	interpolative	interpolative	ADJ
ejpam-6282	181	23	metric	metric	ADJ
ejpam-6282	181	24	space	space	NOUN
ejpam-6282	181	25	.	.	PUNCT
ejpam-6282	182	1	then	then	ADV
ejpam-6282	182	2	the	the	DET
ejpam-6282	182	3	fixed	fixed	ADJ
ejpam-6282	182	4	point	point	NOUN
ejpam-6282	182	5	of	of	ADP
ejpam-6282	182	6	t	t	PROPN
ejpam-6282	182	7	in	in	ADP
ejpam-6282	182	8	s	s	PROPN
ejpam-6282	182	9	is	be	AUX
ejpam-6282	182	10	unique	unique	ADJ
ejpam-6282	182	11	,	,	PUNCT
ejpam-6282	182	12	provided	provide	VERB
ejpam-6282	182	13	that	that	SCONJ
ejpam-6282	182	14	there	there	PRON
ejpam-6282	182	15	exists	exist	VERB
ejpam-6282	182	16	a	a	DET
ejpam-6282	182	17	fixed	fix	VERB
ejpam-6282	182	18	point	point	NOUN
ejpam-6282	182	19	.	.	PUNCT
ejpam-6282	183	1	proof	proof	NOUN
ejpam-6282	183	2	.	.	PUNCT
ejpam-6282	184	1	suppose	suppose	VERB
ejpam-6282	184	2	that	that	SCONJ
ejpam-6282	184	3	our	our	PRON
ejpam-6282	184	4	assertion	assertion	NOUN
ejpam-6282	184	5	fails	fail	VERB
ejpam-6282	184	6	.	.	PUNCT
ejpam-6282	185	1	it	it	PRON
ejpam-6282	185	2	means	mean	VERB
ejpam-6282	185	3	that	that	SCONJ
ejpam-6282	185	4	there	there	PRON
ejpam-6282	185	5	are	be	VERB
ejpam-6282	185	6	two	two	NUM
ejpam-6282	185	7	fixed	fix	VERB
ejpam-6282	185	8	points	point	NOUN
ejpam-6282	185	9	m	m	PROPN
ejpam-6282	185	10	,	,	PUNCT
ejpam-6282	185	11	l	l	PROPN
ejpam-6282	185	12	∈	∈	PROPN
ejpam-6282	185	13	s	s	VERB
ejpam-6282	185	14	that	that	PRON
ejpam-6282	185	15	are	be	AUX
ejpam-6282	185	16	distinct	distinct	ADJ
ejpam-6282	185	17	t(m	t(m	PROPN
ejpam-6282	185	18	)	)	PUNCT
ejpam-6282	186	1	=	=	PUNCT
ejpam-6282	187	1	m	m	PROPN
ejpam-6282	187	2	̸=	̸=	PROPN
ejpam-6282	187	3	l	l	NOUN
ejpam-6282	187	4	=	=	SYM
ejpam-6282	187	5	t(l	t(l	PROPN
ejpam-6282	187	6	)	)	PUNCT
ejpam-6282	187	7	.	.	PUNCT
ejpam-6282	188	1	naturally	naturally	ADV
ejpam-6282	188	2	,	,	PUNCT
ejpam-6282	188	3	d(m	d(m	PROPN
ejpam-6282	188	4	,	,	PUNCT
ejpam-6282	188	5	l	l	NOUN
ejpam-6282	188	6	)	)	PUNCT
ejpam-6282	188	7	>	>	X
ejpam-6282	189	1	0	0	X
ejpam-6282	189	2	.	.	PUNCT
ejpam-6282	190	1	on	on	ADP
ejpam-6282	190	2	account	account	NOUN
ejpam-6282	190	3	of	of	ADP
ejpam-6282	190	4	the	the	DET
ejpam-6282	190	5	inequality	inequality	NOUN
ejpam-6282	190	6	,	,	PUNCT
ejpam-6282	190	7	(	(	PUNCT
ejpam-6282	190	8	2.1	2.1	NUM
ejpam-6282	190	9	)	)	PUNCT
ejpam-6282	190	10	one	one	PRON
ejpam-6282	190	11	can	can	AUX
ejpam-6282	190	12	derive	derive	VERB
ejpam-6282	190	13	0	0	NUM
ejpam-6282	190	14	≤	≤	NUM
ejpam-6282	190	15	α(d(tm	α(d(tm	NOUN
ejpam-6282	190	16	,	,	PUNCT
ejpam-6282	190	17	tl	tl	PROPN
ejpam-6282	190	18	)	)	PUNCT
ejpam-6282	190	19	,	,	PUNCT
ejpam-6282	190	20	ψ(d(m	ψ(d(m	PROPN
ejpam-6282	190	21	,	,	PUNCT
ejpam-6282	190	22	l	l	NOUN
ejpam-6282	190	23	)	)	PUNCT
ejpam-6282	190	24	)	)	PUNCT
ejpam-6282	191	1	<	<	X
ejpam-6282	191	2	ψ(d(m	ψ(d(m	PROPN
ejpam-6282	191	3	,	,	PUNCT
ejpam-6282	191	4	l))−	l))−	PROPN
ejpam-6282	191	5	d(m	d(m	PROPN
ejpam-6282	191	6	,	,	PUNCT
ejpam-6282	191	7	l	l	NOUN
ejpam-6282	191	8	)	)	PUNCT
ejpam-6282	191	9	,	,	PUNCT
ejpam-6282	191	10	yields	yield	NOUN
ejpam-6282	191	11	from	from	ADP
ejpam-6282	191	12	the	the	DET
ejpam-6282	191	13	fact	fact	NOUN
ejpam-6282	191	14	,	,	PUNCT
ejpam-6282	191	15	ψ(t	ψ(t	PROPN
ejpam-6282	191	16	)	)	PUNCT
ejpam-6282	191	17	<	<	X
ejpam-6282	191	18	t	t	PROPN
ejpam-6282	191	19	for	for	ADP
ejpam-6282	191	20	any	any	DET
ejpam-6282	191	21	t	t	PROPN
ejpam-6282	191	22	>	>	X
ejpam-6282	191	23	0	0	PROPN
ejpam-6282	191	24	,	,	PUNCT
ejpam-6282	191	25	that	that	DET
ejpam-6282	191	26	d(m	d(m	NOUN
ejpam-6282	191	27	,	,	PUNCT
ejpam-6282	191	28	l	l	NOUN
ejpam-6282	191	29	)	)	PUNCT
ejpam-6282	191	30	≤	≤	NOUN
ejpam-6282	191	31	ψ(d(m	ψ(d(m	PROPN
ejpam-6282	191	32	,	,	PUNCT
ejpam-6282	191	33	l	l	NOUN
ejpam-6282	191	34	)	)	PUNCT
ejpam-6282	191	35	)	)	PUNCT
ejpam-6282	192	1	<	<	X
ejpam-6282	192	2	d(m	d(m	PROPN
ejpam-6282	192	3	,	,	PUNCT
ejpam-6282	192	4	l	l	PROPN
ejpam-6282	192	5	)	)	PUNCT
ejpam-6282	192	6	,	,	PUNCT
ejpam-6282	192	7	a	a	DET
ejpam-6282	192	8	contradiction	contradiction	NOUN
ejpam-6282	192	9	.	.	PUNCT
ejpam-6282	193	1	theorem	theorem	NOUN
ejpam-6282	193	2	2	2	NUM
ejpam-6282	193	3	.	.	PUNCT
ejpam-6282	194	1	let	let	VERB
ejpam-6282	194	2	t	t	NOUN
ejpam-6282	194	3	:	:	PUNCT
ejpam-6282	194	4	s	s	X
ejpam-6282	194	5	→	→	SYM
ejpam-6282	194	6	s	s	AUX
ejpam-6282	194	7	be	be	AUX
ejpam-6282	194	8	an	an	DET
ejpam-6282	194	9	interpolative	interpolative	ADJ
ejpam-6282	194	10	zα	zα	NUM
ejpam-6282	194	11	-	-	PUNCT
ejpam-6282	194	12	contraction	contraction	NOUN
ejpam-6282	194	13	,	,	PUNCT
ejpam-6282	194	14	where	where	SCONJ
ejpam-6282	194	15	(	(	PUNCT
ejpam-6282	194	16	s	s	X
ejpam-6282	194	17	,	,	PUNCT
ejpam-6282	194	18	d	d	NOUN
ejpam-6282	194	19	)	)	PUNCT
ejpam-6282	194	20	is	be	AUX
ejpam-6282	194	21	a	a	DET
ejpam-6282	194	22	complete	complete	ADJ
ejpam-6282	194	23	(	(	PUNCT
ejpam-6282	194	24	ξ	ξ	PROPN
ejpam-6282	194	25	,	,	PUNCT
ejpam-6282	194	26	c)-interpolative	c)-interpolative	ADJ
ejpam-6282	194	27	metric	metric	ADJ
ejpam-6282	194	28	space	space	NOUN
ejpam-6282	194	29	.	.	PUNCT
ejpam-6282	195	1	then	then	ADV
ejpam-6282	195	2	t	t	PROPN
ejpam-6282	195	3	possesses	possess	VERB
ejpam-6282	195	4	a	a	DET
ejpam-6282	195	5	unique	unique	ADJ
ejpam-6282	195	6	fixed	fix	VERB
ejpam-6282	195	7	point	point	NOUN
ejpam-6282	195	8	m∗	m∗	NOUN
ejpam-6282	195	9	in	in	ADP
ejpam-6282	195	10	m	m	PROPN
ejpam-6282	195	11	and	and	CCONJ
ejpam-6282	195	12	for	for	ADP
ejpam-6282	195	13	every	every	DET
ejpam-6282	195	14	m0	m0	NOUN
ejpam-6282	195	15	∈	∈	PROPN
ejpam-6282	195	16	s	s	VERB
ejpam-6282	195	17	the	the	DET
ejpam-6282	195	18	picard	picard	NOUN
ejpam-6282	195	19	sequence	sequence	NOUN
ejpam-6282	195	20	{	{	PUNCT
ejpam-6282	195	21	mn	mn	PROPN
ejpam-6282	195	22	}	}	PUNCT
ejpam-6282	195	23	,	,	PUNCT
ejpam-6282	195	24	where	where	SCONJ
ejpam-6282	195	25	mn	mn	PROPN
ejpam-6282	195	26	=	=	PUNCT
ejpam-6282	195	27	tmn−1	tmn−1	PROPN
ejpam-6282	195	28	for	for	ADP
ejpam-6282	195	29	all	all	DET
ejpam-6282	195	30	n	n	PRON
ejpam-6282	195	31	∈	∈	NOUN
ejpam-6282	195	32	n	n	PRON
ejpam-6282	195	33	converges	converge	VERB
ejpam-6282	195	34	to	to	ADP
ejpam-6282	195	35	the	the	DET
ejpam-6282	195	36	fixed	fix	VERB
ejpam-6282	195	37	point	point	NOUN
ejpam-6282	195	38	of	of	ADP
ejpam-6282	195	39	t.	t.	PROPN
ejpam-6282	195	40	g.	g.	PROPN
ejpam-6282	195	41	alsahli	alsahli	PROPN
ejpam-6282	195	42	,	,	PUNCT
ejpam-6282	195	43	s.	s.	PROPN
ejpam-6282	195	44	gülyaz	gülyaz	PROPN
ejpam-6282	195	45	-	-	PUNCT
ejpam-6282	195	46	özyurt	özyurt	PROPN
ejpam-6282	195	47	/	/	SYM
ejpam-6282	195	48	eur	eur	PROPN
ejpam-6282	195	49	.	.	PUNCT
ejpam-6282	196	1	j.	j.	PROPN
ejpam-6282	196	2	pure	pure	PROPN
ejpam-6282	196	3	appl	appl	PROPN
ejpam-6282	196	4	.	.	PROPN
ejpam-6282	196	5	math	math	PROPN
ejpam-6282	196	6	,	,	PUNCT
ejpam-6282	196	7	18	18	NUM
ejpam-6282	196	8	(	(	PUNCT
ejpam-6282	196	9	2	2	NUM
ejpam-6282	196	10	)	)	PUNCT
ejpam-6282	196	11	(	(	PUNCT
ejpam-6282	196	12	2025	2025	NUM
ejpam-6282	196	13	)	)	PUNCT
ejpam-6282	196	14	,	,	PUNCT
ejpam-6282	196	15	6282	6282	NUM
ejpam-6282	196	16	8	8	NUM
ejpam-6282	196	17	of	of	ADP
ejpam-6282	196	18	13	13	NUM
ejpam-6282	196	19	proof	proof	NOUN
ejpam-6282	196	20	.	.	PUNCT
ejpam-6282	197	1	due	due	ADP
ejpam-6282	197	2	to	to	ADP
ejpam-6282	197	3	proposition	proposition	NOUN
ejpam-6282	197	4	1	1	NUM
ejpam-6282	197	5	,	,	PUNCT
ejpam-6282	197	6	it	it	PRON
ejpam-6282	197	7	guarantees	guarantee	VERB
ejpam-6282	197	8	that	that	SCONJ
ejpam-6282	197	9	if	if	SCONJ
ejpam-6282	197	10	there	there	PRON
ejpam-6282	197	11	is	be	VERB
ejpam-6282	197	12	a	a	DET
ejpam-6282	197	13	fixed	fix	VERB
ejpam-6282	197	14	point	point	NOUN
ejpam-6282	197	15	,	,	PUNCT
ejpam-6282	197	16	the	the	DET
ejpam-6282	197	17	mapping	mapping	NOUN
ejpam-6282	197	18	t	t	PROPN
ejpam-6282	197	19	,	,	PUNCT
ejpam-6282	197	20	it	it	PRON
ejpam-6282	197	21	is	be	AUX
ejpam-6282	197	22	unique	unique	ADJ
ejpam-6282	197	23	.	.	PUNCT
ejpam-6282	198	1	to	to	PART
ejpam-6282	198	2	finalize	finalize	VERB
ejpam-6282	198	3	the	the	DET
ejpam-6282	198	4	proof	proof	NOUN
ejpam-6282	198	5	,	,	PUNCT
ejpam-6282	198	6	it	it	PRON
ejpam-6282	198	7	is	be	AUX
ejpam-6282	198	8	enough	enough	ADJ
ejpam-6282	198	9	to	to	PART
ejpam-6282	198	10	guarantee	guarantee	VERB
ejpam-6282	198	11	the	the	DET
ejpam-6282	198	12	existence	existence	NOUN
ejpam-6282	198	13	of	of	ADP
ejpam-6282	198	14	a	a	DET
ejpam-6282	198	15	fixed	fix	VERB
ejpam-6282	198	16	point	point	NOUN
ejpam-6282	198	17	of	of	ADP
ejpam-6282	198	18	the	the	DET
ejpam-6282	198	19	mapping	mapping	NOUN
ejpam-6282	198	20	t.	t.	NOUN
ejpam-6282	198	21	for	for	ADP
ejpam-6282	198	22	this	this	DET
ejpam-6282	198	23	goal	goal	NOUN
ejpam-6282	198	24	,	,	PUNCT
ejpam-6282	198	25	it	it	PRON
ejpam-6282	198	26	is	be	AUX
ejpam-6282	198	27	sufficient	sufficient	ADJ
ejpam-6282	198	28	to	to	PART
ejpam-6282	198	29	construct	construct	VERB
ejpam-6282	198	30	a	a	DET
ejpam-6282	198	31	recursive	recursive	ADJ
ejpam-6282	198	32	sequence	sequence	NOUN
ejpam-6282	198	33	starting	start	VERB
ejpam-6282	198	34	with	with	ADP
ejpam-6282	198	35	an	an	DET
ejpam-6282	198	36	arbitrary	arbitrary	ADJ
ejpam-6282	198	37	choice	choice	NOUN
ejpam-6282	198	38	m	m	NOUN
ejpam-6282	198	39	∈	∈	NOUN
ejpam-6282	198	40	s	s	PART
ejpam-6282	198	41	that	that	DET
ejpam-6282	198	42	sequence	sequence	NOUN
ejpam-6282	198	43	has	have	VERB
ejpam-6282	198	44	a	a	DET
ejpam-6282	198	45	limit	limit	NOUN
ejpam-6282	198	46	.	.	PUNCT
ejpam-6282	199	1	we	we	PRON
ejpam-6282	199	2	start	start	VERB
ejpam-6282	199	3	with	with	ADP
ejpam-6282	199	4	renaming	rename	VERB
ejpam-6282	199	5	this	this	DET
ejpam-6282	199	6	arbitrarily	arbitrarily	ADV
ejpam-6282	199	7	chosen	choose	VERB
ejpam-6282	199	8	initial	initial	ADJ
ejpam-6282	199	9	point	point	NOUN
ejpam-6282	199	10	as	as	ADP
ejpam-6282	199	11	m0	m0	NOUN
ejpam-6282	199	12	:	:	PUNCT
ejpam-6282	199	13	=	=	PUNCT
ejpam-6282	200	1	m	m	VERB
ejpam-6282	200	2	that	that	PRON
ejpam-6282	200	3	produces	produce	VERB
ejpam-6282	200	4	the	the	DET
ejpam-6282	200	5	sequence	sequence	NOUN
ejpam-6282	200	6	with	with	ADP
ejpam-6282	200	7	the	the	DET
ejpam-6282	200	8	general	general	ADJ
ejpam-6282	200	9	term	term	NOUN
ejpam-6282	200	10	mn	mn	PROPN
ejpam-6282	201	1	=	=	PUNCT
ejpam-6282	201	2	tmn−1	tmn−1	PROPN
ejpam-6282	201	3	for	for	ADP
ejpam-6282	201	4	all	all	PRON
ejpam-6282	201	5	n	n	DET
ejpam-6282	201	6	∈	∈	PROPN
ejpam-6282	201	7	n.	n.	NOUN
ejpam-6282	201	8	without	without	ADP
ejpam-6282	201	9	loss	loss	NOUN
ejpam-6282	201	10	of	of	ADP
ejpam-6282	201	11	generality	generality	NOUN
ejpam-6282	201	12	,	,	PUNCT
ejpam-6282	201	13	one	one	PRON
ejpam-6282	201	14	can	can	AUX
ejpam-6282	201	15	suppose	suppose	VERB
ejpam-6282	201	16	that	that	SCONJ
ejpam-6282	201	17	the	the	DET
ejpam-6282	201	18	successive	successive	ADJ
ejpam-6282	201	19	terms	term	NOUN
ejpam-6282	201	20	in	in	ADP
ejpam-6282	201	21	this	this	DET
ejpam-6282	201	22	hand	hand	NOUN
ejpam-6282	201	23	made	make	VERB
ejpam-6282	201	24	sequence	sequence	NOUN
ejpam-6282	201	25	are	be	AUX
ejpam-6282	201	26	pairwise	pairwise	NOUN
ejpam-6282	201	27	distinct	distinct	ADJ
ejpam-6282	201	28	.	.	PUNCT
ejpam-6282	202	1	suppose	suppose	VERB
ejpam-6282	202	2	,	,	PUNCT
ejpam-6282	202	3	on	on	ADP
ejpam-6282	202	4	the	the	DET
ejpam-6282	202	5	contrary	contrary	NOUN
ejpam-6282	202	6	,	,	PUNCT
ejpam-6282	202	7	that	that	SCONJ
ejpam-6282	202	8	there	there	PRON
ejpam-6282	202	9	exists	exist	VERB
ejpam-6282	202	10	a	a	DET
ejpam-6282	202	11	k	k	PROPN
ejpam-6282	202	12	∈	∈	PROPN
ejpam-6282	202	13	n	n	PRON
ejpam-6282	202	14	such	such	ADJ
ejpam-6282	202	15	that	that	DET
ejpam-6282	202	16	consecutive	consecutive	ADJ
ejpam-6282	202	17	kth	kth	NOUN
ejpam-6282	202	18	and	and	CCONJ
ejpam-6282	202	19	k	k	PROPN
ejpam-6282	203	1	+	+	CCONJ
ejpam-6282	203	2	1th	1th	ADJ
ejpam-6282	203	3	terms	term	NOUN
ejpam-6282	203	4	equal	equal	ADJ
ejpam-6282	203	5	,	,	PUNCT
ejpam-6282	203	6	then	then	ADV
ejpam-6282	203	7	the	the	DET
ejpam-6282	203	8	proof	proof	NOUN
ejpam-6282	203	9	is	be	AUX
ejpam-6282	203	10	fulfilled	fulfil	VERB
ejpam-6282	203	11	.	.	PUNCT
ejpam-6282	204	1	in	in	ADP
ejpam-6282	204	2	fact	fact	NOUN
ejpam-6282	204	3	,	,	PUNCT
ejpam-6282	204	4	we	we	PRON
ejpam-6282	204	5	have	have	VERB
ejpam-6282	204	6	tkm	tkm	PROPN
ejpam-6282	204	7	=	=	PROPN
ejpam-6282	204	8	tk−1	tk−1	PROPN
ejpam-6282	204	9	m	m	PROPN
ejpam-6282	204	10	,	,	PUNCT
ejpam-6282	204	11	that	that	ADV
ejpam-6282	204	12	is	is	ADV
ejpam-6282	204	13	,	,	PUNCT
ejpam-6282	204	14	tl	tl	PROPN
ejpam-6282	204	15	=	=	PUNCT
ejpam-6282	204	16	l	l	NOUN
ejpam-6282	204	17	is	be	AUX
ejpam-6282	204	18	claimed	claim	VERB
ejpam-6282	204	19	fixed	fix	VERB
ejpam-6282	204	20	point	point	NOUN
ejpam-6282	204	21	inequality	inequality	NOUN
ejpam-6282	204	22	,	,	PUNCT
ejpam-6282	204	23	with	with	ADP
ejpam-6282	204	24	l	l	NOUN
ejpam-6282	204	25	=	=	PUNCT
ejpam-6282	204	26	tk−1	tk−1	PROPN
ejpam-6282	204	27	m.	m.	NOUN
ejpam-6282	204	28	throughout	throughout	ADP
ejpam-6282	204	29	the	the	DET
ejpam-6282	204	30	proof	proof	NOUN
ejpam-6282	204	31	,	,	PUNCT
ejpam-6282	204	32	without	without	ADP
ejpam-6282	204	33	loss	loss	NOUN
ejpam-6282	204	34	of	of	ADP
ejpam-6282	204	35	generality	generality	NOUN
ejpam-6282	204	36	,	,	PUNCT
ejpam-6282	204	37	we	we	PRON
ejpam-6282	204	38	suppose	suppose	VERB
ejpam-6282	204	39	that	that	SCONJ
ejpam-6282	204	40	for	for	ADP
ejpam-6282	204	41	all	all	DET
ejpam-6282	204	42	n	n	PRON
ejpam-6282	204	43	∈	∈	PROPN
ejpam-6282	204	44	n	n	CCONJ
ejpam-6282	204	45	,	,	PUNCT
ejpam-6282	204	46	that	that	SCONJ
ejpam-6282	204	47	tnm	tnm	PROPN
ejpam-6282	204	48	̸=	̸=	PROPN
ejpam-6282	204	49	tn−1	tn−1	ADJ
ejpam-6282	204	50	m.	m.	NOUN
ejpam-6282	204	51	on	on	ADP
ejpam-6282	204	52	account	account	NOUN
ejpam-6282	204	53	of	of	ADP
ejpam-6282	204	54	the	the	DET
ejpam-6282	204	55	inequality	inequality	NOUN
ejpam-6282	204	56	(	(	PUNCT
ejpam-6282	204	57	2.1	2.1	NUM
ejpam-6282	204	58	)	)	PUNCT
ejpam-6282	204	59	,	,	PUNCT
ejpam-6282	204	60	we	we	PRON
ejpam-6282	204	61	find	find	VERB
ejpam-6282	204	62	that	that	SCONJ
ejpam-6282	204	63	0	0	NUM
ejpam-6282	204	64	≤	≤	NUM
ejpam-6282	204	65	α(d(tn+1	α(d(tn+1	NUM
ejpam-6282	204	66	m	m	PROPN
ejpam-6282	204	67	,	,	PUNCT
ejpam-6282	204	68	tnm	tnm	PROPN
ejpam-6282	204	69	)	)	PUNCT
ejpam-6282	204	70	,	,	PUNCT
ejpam-6282	204	71	ψ(d(tnm	ψ(d(tnm	PROPN
ejpam-6282	204	72	,	,	PUNCT
ejpam-6282	204	73	tn−1	tn−1	PROPN
ejpam-6282	204	74	m	m	NOUN
ejpam-6282	204	75	)	)	PUNCT
ejpam-6282	204	76	)	)	PUNCT
ejpam-6282	204	77	)	)	PUNCT
ejpam-6282	205	1	=	=	SYM
ejpam-6282	205	2	α(d(ttnm	α(d(ttnm	NOUN
ejpam-6282	205	3	,	,	PUNCT
ejpam-6282	205	4	ttn−1	ttn−1	PROPN
ejpam-6282	205	5	m	m	NOUN
ejpam-6282	205	6	)	)	PUNCT
ejpam-6282	205	7	,	,	PUNCT
ejpam-6282	205	8	ψ(d(tnm	ψ(d(tnm	PROPN
ejpam-6282	205	9	,	,	PUNCT
ejpam-6282	205	10	tn−1	tn−1	PROPN
ejpam-6282	205	11	m	m	NOUN
ejpam-6282	205	12	)	)	PUNCT
ejpam-6282	205	13	)	)	PUNCT
ejpam-6282	205	14	)	)	PUNCT
ejpam-6282	206	1	<	<	X
ejpam-6282	206	2	ψ(d(tnm	ψ(d(tnm	NOUN
ejpam-6282	206	3	,	,	PUNCT
ejpam-6282	206	4	tn−1m))−	tn−1m))−	ADP
ejpam-6282	206	5	d(tn+1	d(tn+1	PROPN
ejpam-6282	206	6	m	m	PROPN
ejpam-6282	206	7	,	,	PUNCT
ejpam-6282	206	8	tnm	tnm	PROPN
ejpam-6282	206	9	)	)	PUNCT
ejpam-6282	206	10	.	.	PUNCT
ejpam-6282	207	1	regarding	regard	VERB
ejpam-6282	207	2	the	the	DET
ejpam-6282	207	3	successive	successive	ADJ
ejpam-6282	207	4	terms	term	NOUN
ejpam-6282	207	5	being	be	AUX
ejpam-6282	207	6	distinct	distinct	ADJ
ejpam-6282	207	7	,	,	PUNCT
ejpam-6282	207	8	the	the	DET
ejpam-6282	207	9	inequality	inequality	NOUN
ejpam-6282	207	10	above	above	ADP
ejpam-6282	207	11	yields	yield	NOUN
ejpam-6282	207	12	d(tn+1	d(tn+1	PROPN
ejpam-6282	207	13	m	m	PROPN
ejpam-6282	207	14	,	,	PUNCT
ejpam-6282	207	15	tnm	tnm	PROPN
ejpam-6282	207	16	)	)	PUNCT
ejpam-6282	207	17	≤	≤	NOUN
ejpam-6282	207	18	ψ(d(tnm	ψ(d(tnm	PROPN
ejpam-6282	207	19	,	,	PUNCT
ejpam-6282	207	20	tn−1	tn−1	PROPN
ejpam-6282	207	21	m	m	NOUN
ejpam-6282	207	22	)	)	PUNCT
ejpam-6282	207	23	)	)	PUNCT
ejpam-6282	207	24	<	<	X
ejpam-6282	208	1	d(tnm	d(tnm	NOUN
ejpam-6282	208	2	,	,	PUNCT
ejpam-6282	208	3	tn−1	tn−1	PROPN
ejpam-6282	208	4	m	m	NOUN
ejpam-6282	208	5	)	)	PUNCT
ejpam-6282	208	6	)	)	PUNCT
ejpam-6282	208	7	.	.	PUNCT
ejpam-6282	209	1	(	(	PUNCT
ejpam-6282	209	2	2.2	2.2	NUM
ejpam-6282	209	3	)	)	PUNCT
ejpam-6282	209	4	recursively	recursively	NOUN
ejpam-6282	209	5	,	,	PUNCT
ejpam-6282	209	6	one	one	PRON
ejpam-6282	209	7	can	can	AUX
ejpam-6282	209	8	derive	derive	VERB
ejpam-6282	209	9	from	from	ADP
ejpam-6282	209	10	(	(	PUNCT
ejpam-6282	209	11	2.2	2.2	NUM
ejpam-6282	209	12	)	)	PUNCT
ejpam-6282	209	13	d(tn+1	d(tn+1	PROPN
ejpam-6282	209	14	m	m	PROPN
ejpam-6282	209	15	,	,	PUNCT
ejpam-6282	209	16	tnm	tnm	PROPN
ejpam-6282	209	17	)	)	PUNCT
ejpam-6282	209	18	≤	≤	NUM
ejpam-6282	209	19	ψn−1(d(t2	ψn−1(d(t2	NOUN
ejpam-6282	209	20	m	m	NOUN
ejpam-6282	209	21	,	,	PUNCT
ejpam-6282	209	22	tm	tm	NOUN
ejpam-6282	209	23	)	)	PUNCT
ejpam-6282	209	24	)	)	PUNCT
ejpam-6282	209	25	.	.	PUNCT
ejpam-6282	210	1	(	(	PUNCT
ejpam-6282	210	2	2.3	2.3	NUM
ejpam-6282	210	3	)	)	PUNCT
ejpam-6282	210	4	thus	thus	ADV
ejpam-6282	210	5	,	,	PUNCT
ejpam-6282	210	6	we	we	PRON
ejpam-6282	210	7	conclude	conclude	VERB
ejpam-6282	210	8	,	,	PUNCT
ejpam-6282	210	9	from	from	ADP
ejpam-6282	210	10	the	the	DET
ejpam-6282	210	11	inequality	inequality	NOUN
ejpam-6282	210	12	(	(	PUNCT
ejpam-6282	210	13	2.2	2.2	NUM
ejpam-6282	210	14	)	)	PUNCT
ejpam-6282	210	15	,	,	PUNCT
ejpam-6282	210	16	that	that	SCONJ
ejpam-6282	210	17	the	the	DET
ejpam-6282	210	18	sequence	sequence	NOUN
ejpam-6282	210	19	of	of	ADP
ejpam-6282	210	20	nonnegative	nonnegative	ADJ
ejpam-6282	210	21	reals	real	NOUN
ejpam-6282	210	22	{	{	PUNCT
ejpam-6282	210	23	d(tnm	d(tnm	NOUN
ejpam-6282	210	24	,	,	PUNCT
ejpam-6282	210	25	tn−1	tn−1	PROPN
ejpam-6282	210	26	m	m	NOUN
ejpam-6282	210	27	)	)	PUNCT
ejpam-6282	210	28	}	}	PUNCT
ejpam-6282	210	29	is	be	AUX
ejpam-6282	210	30	monotonically	monotonically	ADV
ejpam-6282	210	31	decreasing	decrease	VERB
ejpam-6282	210	32	.	.	PUNCT
ejpam-6282	211	1	further	far	ADV
ejpam-6282	211	2	,	,	PUNCT
ejpam-6282	211	3	it	it	PRON
ejpam-6282	211	4	is	be	AUX
ejpam-6282	211	5	necessarily	necessarily	ADV
ejpam-6282	211	6	a	a	DET
ejpam-6282	211	7	convergent	convergent	NOUN
ejpam-6282	211	8	sequence	sequence	NOUN
ejpam-6282	211	9	.	.	PUNCT
ejpam-6282	212	1	let	let	VERB
ejpam-6282	212	2	us	we	PRON
ejpam-6282	212	3	denote	denote	VERB
ejpam-6282	212	4	lim	lim	PROPN
ejpam-6282	212	5	n→∞	n→∞	NUM
ejpam-6282	213	1	d(tnm	d(tnm	PROPN
ejpam-6282	213	2	,	,	PUNCT
ejpam-6282	213	3	tn+1	tn+1	NOUN
ejpam-6282	213	4	m	m	NOUN
ejpam-6282	213	5	)	)	PUNCT
ejpam-6282	214	1	=	=	SYM
ejpam-6282	214	2	κ	κ	X
ejpam-6282	214	3	≥	≥	NOUN
ejpam-6282	214	4	0	0	NUM
ejpam-6282	214	5	.	.	PUNCT
ejpam-6282	215	1	we	we	PRON
ejpam-6282	215	2	claim	claim	VERB
ejpam-6282	215	3	that	that	SCONJ
ejpam-6282	215	4	κ	κ	NOUN
ejpam-6282	215	5	=	=	NOUN
ejpam-6282	215	6	0	0	PROPN
ejpam-6282	215	7	.	.	PUNCT
ejpam-6282	216	1	in	in	ADP
ejpam-6282	216	2	this	this	DET
ejpam-6282	216	3	step	step	NOUN
ejpam-6282	216	4	,	,	PUNCT
ejpam-6282	216	5	we	we	PRON
ejpam-6282	216	6	use	use	VERB
ejpam-6282	216	7	the	the	DET
ejpam-6282	216	8	method	method	NOUN
ejpam-6282	216	9	of	of	ADP
ejpam-6282	216	10	reductio	reductio	NOUN
ejpam-6282	216	11	ad	ad	NOUN
ejpam-6282	216	12	absurdum	absurdum	NOUN
ejpam-6282	216	13	.	.	PUNCT
ejpam-6282	217	1	for	for	ADP
ejpam-6282	217	2	this	this	DET
ejpam-6282	217	3	purpose	purpose	NOUN
ejpam-6282	217	4	,	,	PUNCT
ejpam-6282	217	5	we	we	PRON
ejpam-6282	217	6	suppose	suppose	VERB
ejpam-6282	217	7	,	,	PUNCT
ejpam-6282	217	8	on	on	ADP
ejpam-6282	217	9	the	the	DET
ejpam-6282	217	10	contrary	contrary	NOUN
ejpam-6282	217	11	,	,	PUNCT
ejpam-6282	217	12	that	that	PRON
ejpam-6282	217	13	κ	κ	AUX
ejpam-6282	217	14	>	>	X
ejpam-6282	217	15	0	0	NUM
ejpam-6282	217	16	.	.	PUNCT
ejpam-6282	218	1	by	by	ADP
ejpam-6282	218	2	keeping	keep	VERB
ejpam-6282	218	3	the	the	DET
ejpam-6282	218	4	fact	fact	NOUN
ejpam-6282	218	5	that	that	SCONJ
ejpam-6282	218	6	t	t	PROPN
ejpam-6282	218	7	is	be	AUX
ejpam-6282	218	8	(	(	PUNCT
ejpam-6282	218	9	ξ	ξ	PROPN
ejpam-6282	218	10	,	,	PUNCT
ejpam-6282	218	11	c)-interpolative	c)-interpolative	PUNCT
ejpam-6282	218	12	zα	zα	PROPN
ejpam-6282	218	13	-	-	PUNCT
ejpam-6282	218	14	contraction	contraction	NOUN
ejpam-6282	218	15	in	in	ADP
ejpam-6282	218	16	mind	mind	NOUN
ejpam-6282	218	17	,	,	PUNCT
ejpam-6282	218	18	and	and	CCONJ
ejpam-6282	218	19	considering	consider	VERB
ejpam-6282	218	20	the	the	DET
ejpam-6282	218	21	assumption	assumption	NOUN
ejpam-6282	218	22	(	(	PUNCT
ejpam-6282	218	23	α3	α3	NOUN
ejpam-6282	218	24	)	)	PUNCT
ejpam-6282	218	25	,	,	PUNCT
ejpam-6282	218	26	we	we	PRON
ejpam-6282	218	27	find	find	VERB
ejpam-6282	218	28	0	0	NUM
ejpam-6282	218	29	≤	≤	PROPN
ejpam-6282	218	30	lim	lim	PROPN
ejpam-6282	218	31	n→∞	n→∞	NUM
ejpam-6282	218	32	sup	sup	PROPN
ejpam-6282	218	33	α(d(tn+1	α(d(tn+1	PROPN
ejpam-6282	218	34	m	m	PROPN
ejpam-6282	218	35	,	,	PUNCT
ejpam-6282	218	36	tnm	tnm	PROPN
ejpam-6282	218	37	)	)	PUNCT
ejpam-6282	218	38	,	,	PUNCT
ejpam-6282	218	39	d(tnm	d(tnm	NOUN
ejpam-6282	218	40	,	,	PUNCT
ejpam-6282	218	41	tn−1	tn−1	PROPN
ejpam-6282	218	42	m	m	NOUN
ejpam-6282	218	43	)	)	PUNCT
ejpam-6282	218	44	)	)	PUNCT
ejpam-6282	219	1	<	<	X
ejpam-6282	219	2	0	0	NUM
ejpam-6282	219	3	,	,	PUNCT
ejpam-6282	219	4	a	a	DET
ejpam-6282	219	5	contradiction	contradiction	NOUN
ejpam-6282	219	6	.	.	PUNCT
ejpam-6282	220	1	consequently	consequently	ADV
ejpam-6282	220	2	,	,	PUNCT
ejpam-6282	220	3	the	the	DET
ejpam-6282	220	4	limit	limit	NOUN
ejpam-6282	220	5	κ	κ	X
ejpam-6282	220	6	=	=	SYM
ejpam-6282	220	7	0	0	PROPN
ejpam-6282	220	8	,	,	PUNCT
ejpam-6282	220	9	that	that	ADV
ejpam-6282	220	10	is	is	ADV
ejpam-6282	220	11	,	,	PUNCT
ejpam-6282	221	1	lim	lim	PROPN
ejpam-6282	221	2	n→∞	n→∞	NUM
ejpam-6282	221	3	d(tnm	d(tnm	PROPN
ejpam-6282	221	4	,	,	PUNCT
ejpam-6282	221	5	tn+1	tn+1	NOUN
ejpam-6282	221	6	m	m	NOUN
ejpam-6282	221	7	)	)	PUNCT
ejpam-6282	222	1	=	=	SYM
ejpam-6282	222	2	0	0	X
ejpam-6282	222	3	.	.	PUNCT
ejpam-6282	223	1	(	(	PUNCT
ejpam-6282	223	2	2.4	2.4	NUM
ejpam-6282	223	3	)	)	PUNCT
ejpam-6282	223	4	hence	hence	ADV
ejpam-6282	223	5	,	,	PUNCT
ejpam-6282	223	6	we	we	PRON
ejpam-6282	223	7	conclude	conclude	VERB
ejpam-6282	223	8	that	that	SCONJ
ejpam-6282	223	9	the	the	DET
ejpam-6282	223	10	self	self	NOUN
ejpam-6282	223	11	-	-	PUNCT
ejpam-6282	223	12	mapping	mapping	NOUN
ejpam-6282	223	13	t	t	NOUN
ejpam-6282	223	14	is	be	AUX
ejpam-6282	223	15	an	an	DET
ejpam-6282	223	16	asymptotically	asymptotically	ADV
ejpam-6282	223	17	regular	regular	ADJ
ejpam-6282	223	18	mapping	mapping	NOUN
ejpam-6282	223	19	in	in	ADP
ejpam-6282	223	20	s.	s.	PROPN
ejpam-6282	223	21	for	for	ADP
ejpam-6282	223	22	this	this	DET
ejpam-6282	223	23	purpose	purpose	NOUN
ejpam-6282	223	24	,	,	PUNCT
ejpam-6282	223	25	we	we	PRON
ejpam-6282	223	26	claim	claim	VERB
ejpam-6282	223	27	that	that	SCONJ
ejpam-6282	223	28	lim	lim	PROPN
ejpam-6282	223	29	n→∞	n→∞	PRON
ejpam-6282	223	30	d(tn−1	d(tn−1	PROPN
ejpam-6282	223	31	m	m	NOUN
ejpam-6282	223	32	,	,	PUNCT
ejpam-6282	223	33	tn+rm	tn+rm	NOUN
ejpam-6282	223	34	)	)	PUNCT
ejpam-6282	223	35	=	=	SYM
ejpam-6282	224	1	0	0	X
ejpam-6282	224	2	.	.	PUNCT
ejpam-6282	225	1	(	(	PUNCT
ejpam-6282	225	2	2.5	2.5	NUM
ejpam-6282	225	3	)	)	PUNCT
ejpam-6282	225	4	g.	g.	PROPN
ejpam-6282	225	5	alsahli	alsahli	PROPN
ejpam-6282	225	6	,	,	PUNCT
ejpam-6282	225	7	s.	s.	PROPN
ejpam-6282	225	8	gülyaz	gülyaz	PROPN
ejpam-6282	225	9	-	-	PUNCT
ejpam-6282	225	10	özyurt	özyurt	PROPN
ejpam-6282	225	11	/	/	SYM
ejpam-6282	225	12	eur	eur	PROPN
ejpam-6282	225	13	.	.	PUNCT
ejpam-6282	226	1	j.	j.	PROPN
ejpam-6282	226	2	pure	pure	PROPN
ejpam-6282	226	3	appl	appl	PROPN
ejpam-6282	226	4	.	.	PROPN
ejpam-6282	226	5	math	math	PROPN
ejpam-6282	226	6	,	,	PUNCT
ejpam-6282	226	7	18	18	NUM
ejpam-6282	226	8	(	(	PUNCT
ejpam-6282	226	9	2	2	NUM
ejpam-6282	226	10	)	)	PUNCT
ejpam-6282	226	11	(	(	PUNCT
ejpam-6282	226	12	2025	2025	NUM
ejpam-6282	226	13	)	)	PUNCT
ejpam-6282	226	14	,	,	PUNCT
ejpam-6282	226	15	6282	6282	NUM
ejpam-6282	226	16	9	9	NUM
ejpam-6282	226	17	of	of	ADP
ejpam-6282	226	18	13	13	NUM
ejpam-6282	226	19	the	the	DET
ejpam-6282	226	20	method	method	NOUN
ejpam-6282	226	21	of	of	ADP
ejpam-6282	226	22	induction	induction	NOUN
ejpam-6282	226	23	shall	shall	AUX
ejpam-6282	226	24	be	be	AUX
ejpam-6282	226	25	used	use	VERB
ejpam-6282	226	26	to	to	PART
ejpam-6282	226	27	prove	prove	VERB
ejpam-6282	226	28	the	the	DET
ejpam-6282	226	29	claim	claim	NOUN
ejpam-6282	226	30	above	above	ADV
ejpam-6282	226	31	.	.	PUNCT
ejpam-6282	227	1	first	first	ADV
ejpam-6282	227	2	,	,	PUNCT
ejpam-6282	227	3	we	we	PRON
ejpam-6282	227	4	consider	consider	VERB
ejpam-6282	227	5	the	the	DET
ejpam-6282	227	6	inequality	inequality	NOUN
ejpam-6282	227	7	below	below	ADP
ejpam-6282	227	8	,	,	PUNCT
ejpam-6282	227	9	d(tn−1	d(tn−1	PROPN
ejpam-6282	227	10	m	m	NOUN
ejpam-6282	227	11	,	,	PUNCT
ejpam-6282	227	12	tn+1	tn+1	NOUN
ejpam-6282	227	13	m	m	NOUN
ejpam-6282	227	14	)	)	PUNCT
ejpam-6282	227	15	≤	≤	PUNCT
ejpam-6282	228	1	d(xn	d(xn	PROPN
ejpam-6282	228	2	,	,	PUNCT
ejpam-6282	228	3	tnm	tnm	PROPN
ejpam-6282	228	4	)	)	PUNCT
ejpam-6282	229	1	+	+	CCONJ
ejpam-6282	229	2	d(tnm	d(tnm	ADJ
ejpam-6282	229	3	,	,	PUNCT
ejpam-6282	229	4	tn+1	tn+1	NOUN
ejpam-6282	229	5	m	m	NOUN
ejpam-6282	229	6	)	)	PUNCT
ejpam-6282	230	1	+	+	NOUN
ejpam-6282	230	2	c	c	X
ejpam-6282	230	3	[	[	PUNCT
ejpam-6282	230	4	(	(	PUNCT
ejpam-6282	230	5	d(xn	d(xn	ADJ
ejpam-6282	230	6	,	,	PUNCT
ejpam-6282	230	7	tnm))ξ	tnm))ξ	NOUN
ejpam-6282	230	8	(	(	PUNCT
ejpam-6282	230	9	d(tnm	d(tnm	PROPN
ejpam-6282	230	10	,	,	PUNCT
ejpam-6282	230	11	tn+1	tn+1	NOUN
ejpam-6282	230	12	m	m	NOUN
ejpam-6282	230	13	)	)	PUNCT
ejpam-6282	230	14	)	)	PUNCT
ejpam-6282	230	15	1−ξ	1−ξ	NUM
ejpam-6282	230	16	]	]	PUNCT
ejpam-6282	230	17	(	(	PUNCT
ejpam-6282	230	18	2.6	2.6	NUM
ejpam-6282	230	19	)	)	PUNCT
ejpam-6282	230	20	by	by	ADP
ejpam-6282	230	21	letting	let	VERB
ejpam-6282	230	22	n	n	PRON
ejpam-6282	230	23	→	→	SYM
ejpam-6282	230	24	∞	∞	NUM
ejpam-6282	230	25	in	in	ADP
ejpam-6282	230	26	the	the	DET
ejpam-6282	230	27	inequality	inequality	NOUN
ejpam-6282	230	28	above	above	ADV
ejpam-6282	230	29	,	,	PUNCT
ejpam-6282	230	30	together	together	ADV
ejpam-6282	230	31	with	with	ADP
ejpam-6282	230	32	expression	expression	NOUN
ejpam-6282	230	33	(	(	PUNCT
ejpam-6282	230	34	2.4	2.4	NUM
ejpam-6282	230	35	)	)	PUNCT
ejpam-6282	230	36	,	,	PUNCT
ejpam-6282	230	37	we	we	PRON
ejpam-6282	230	38	find	find	VERB
ejpam-6282	230	39	that	that	SCONJ
ejpam-6282	230	40	lim	lim	PROPN
ejpam-6282	230	41	n→∞	n→∞	PRON
ejpam-6282	230	42	d(tn−1	d(tn−1	PROPN
ejpam-6282	230	43	m	m	PROPN
ejpam-6282	230	44	,	,	PUNCT
ejpam-6282	230	45	tn+1	tn+1	NOUN
ejpam-6282	230	46	m	m	NOUN
ejpam-6282	230	47	)	)	PUNCT
ejpam-6282	230	48	=	=	SYM
ejpam-6282	231	1	0	0	X
ejpam-6282	231	2	.	.	PUNCT
ejpam-6282	232	1	(	(	PUNCT
ejpam-6282	232	2	2.7	2.7	NUM
ejpam-6282	232	3	)	)	PUNCT
ejpam-6282	232	4	in	in	ADP
ejpam-6282	232	5	addition	addition	NOUN
ejpam-6282	232	6	,	,	PUNCT
ejpam-6282	232	7	we	we	PRON
ejpam-6282	232	8	have	have	VERB
ejpam-6282	232	9	d(tn−1	d(tn−1	NOUN
ejpam-6282	232	10	m	m	NOUN
ejpam-6282	232	11	,	,	PUNCT
ejpam-6282	232	12	tn+2	tn+2	X
ejpam-6282	232	13	m	m	NOUN
ejpam-6282	232	14	)	)	PUNCT
ejpam-6282	232	15	≤	≤	PUNCT
ejpam-6282	233	1	d(xn	d(xn	PROPN
ejpam-6282	233	2	,	,	PUNCT
ejpam-6282	233	3	tn+1	tn+1	NOUN
ejpam-6282	233	4	m	m	NOUN
ejpam-6282	233	5	)	)	PUNCT
ejpam-6282	234	1	+	+	CCONJ
ejpam-6282	234	2	d(tn+1	d(tn+1	PROPN
ejpam-6282	234	3	m	m	NOUN
ejpam-6282	234	4	,	,	PUNCT
ejpam-6282	234	5	tn+2	tn+2	ADV
ejpam-6282	234	6	m	m	NOUN
ejpam-6282	234	7	)	)	PUNCT
ejpam-6282	235	1	+	+	VERB
ejpam-6282	235	2	c	c	X
ejpam-6282	235	3	[	[	X
ejpam-6282	235	4	(	(	PUNCT
ejpam-6282	235	5	d(xn	d(xn	PROPN
ejpam-6282	235	6	,	,	PUNCT
ejpam-6282	235	7	tn+1	tn+1	NOUN
ejpam-6282	235	8	m	m	NOUN
ejpam-6282	235	9	)	)	PUNCT
ejpam-6282	235	10	)	)	PUNCT
ejpam-6282	236	1	ξ	ξ	PROPN
ejpam-6282	236	2	(	(	PUNCT
ejpam-6282	236	3	d(tnm	d(tnm	NOUN
ejpam-6282	236	4	,	,	PUNCT
ejpam-6282	236	5	tn+2	tn+2	NOUN
ejpam-6282	236	6	m	m	NOUN
ejpam-6282	236	7	)	)	PUNCT
ejpam-6282	236	8	)	)	PUNCT
ejpam-6282	236	9	1−ξ	1−ξ	NUM
ejpam-6282	236	10	]	]	PUNCT
ejpam-6282	236	11	(	(	PUNCT
ejpam-6282	236	12	2.8	2.8	NUM
ejpam-6282	236	13	)	)	PUNCT
ejpam-6282	236	14	taking	take	VERB
ejpam-6282	236	15	(	(	PUNCT
ejpam-6282	236	16	2.4	2.4	NUM
ejpam-6282	236	17	)	)	PUNCT
ejpam-6282	236	18	and	and	CCONJ
ejpam-6282	236	19	(	(	PUNCT
ejpam-6282	236	20	2.8	2.8	NUM
ejpam-6282	236	21	)	)	PUNCT
ejpam-6282	236	22	into	into	ADP
ejpam-6282	236	23	account	account	NOUN
ejpam-6282	236	24	together	together	ADV
ejpam-6282	236	25	by	by	ADP
ejpam-6282	236	26	taking	take	VERB
ejpam-6282	236	27	n	n	PRON
ejpam-6282	236	28	→	→	SYM
ejpam-6282	236	29	∞	∞	NUM
ejpam-6282	236	30	in	in	ADP
ejpam-6282	236	31	the	the	DET
ejpam-6282	236	32	above	above	ADJ
ejpam-6282	236	33	inequality	inequality	NOUN
ejpam-6282	236	34	we	we	PRON
ejpam-6282	236	35	find	find	VERB
ejpam-6282	236	36	that	that	SCONJ
ejpam-6282	236	37	lim	lim	PROPN
ejpam-6282	236	38	n→∞	n→∞	PRON
ejpam-6282	236	39	d(tn−1	d(tn−1	PROPN
ejpam-6282	236	40	m	m	NOUN
ejpam-6282	236	41	,	,	PUNCT
ejpam-6282	236	42	tn+2	tn+2	PRON
ejpam-6282	236	43	m	m	NOUN
ejpam-6282	236	44	)	)	PUNCT
ejpam-6282	236	45	=	=	SYM
ejpam-6282	237	1	0	0	X
ejpam-6282	237	2	.	.	PUNCT
ejpam-6282	238	1	(	(	PUNCT
ejpam-6282	238	2	2.9	2.9	NUM
ejpam-6282	238	3	)	)	PUNCT
ejpam-6282	238	4	in	in	ADP
ejpam-6282	238	5	this	this	DET
ejpam-6282	238	6	step	step	NOUN
ejpam-6282	238	7	,	,	PUNCT
ejpam-6282	238	8	we	we	PRON
ejpam-6282	238	9	presume	presume	VERB
ejpam-6282	238	10	our	our	PRON
ejpam-6282	238	11	claims	claim	NOUN
ejpam-6282	238	12	hold	hold	VERB
ejpam-6282	238	13	for	for	ADP
ejpam-6282	238	14	some	some	DET
ejpam-6282	238	15	natural	natural	ADJ
ejpam-6282	238	16	number	number	NOUN
ejpam-6282	238	17	r	r	NOUN
ejpam-6282	238	18	>	>	X
ejpam-6282	238	19	1	1	NUM
ejpam-6282	238	20	;	;	PUNCT
ejpam-6282	238	21	that	that	PRON
ejpam-6282	238	22	is	is	ADV
ejpam-6282	238	23	,	,	PUNCT
ejpam-6282	238	24	lim	lim	PROPN
ejpam-6282	238	25	n→∞	n→∞	NUM
ejpam-6282	238	26	d(tn−1	d(tn−1	PROPN
ejpam-6282	238	27	m	m	NOUN
ejpam-6282	238	28	,	,	PUNCT
ejpam-6282	238	29	tn+r−1	tn+r−1	PROPN
ejpam-6282	238	30	m	m	NOUN
ejpam-6282	238	31	)	)	PUNCT
ejpam-6282	238	32	=	=	SYM
ejpam-6282	239	1	0	0	NUM
ejpam-6282	239	2	,	,	PUNCT
ejpam-6282	239	3	for	for	ADP
ejpam-6282	239	4	some	some	DET
ejpam-6282	239	5	r	r	NOUN
ejpam-6282	239	6	∈	∈	PROPN
ejpam-6282	239	7	n.	n.	NOUN
ejpam-6282	239	8	(	(	PUNCT
ejpam-6282	239	9	2.10	2.10	NUM
ejpam-6282	239	10	)	)	PUNCT
ejpam-6282	239	11	accordingly	accordingly	ADV
ejpam-6282	239	12	,	,	PUNCT
ejpam-6282	239	13	employing	employ	VERB
ejpam-6282	239	14	of	of	ADP
ejpam-6282	239	15	the	the	DET
ejpam-6282	239	16	theorem	theorem	NOUN
ejpam-6282	239	17	,	,	PUNCT
ejpam-6282	239	18	we	we	PRON
ejpam-6282	239	19	find	find	VERB
ejpam-6282	239	20	d(tn−1	d(tn−1	NOUN
ejpam-6282	239	21	m	m	NOUN
ejpam-6282	239	22	,	,	PUNCT
ejpam-6282	239	23	tn+rm	tn+rm	NOUN
ejpam-6282	239	24	)	)	PUNCT
ejpam-6282	239	25	≤	≤	NOUN
ejpam-6282	239	26	d(tn−1	d(tn−1	PROPN
ejpam-6282	239	27	m	m	NOUN
ejpam-6282	239	28	,	,	PUNCT
ejpam-6282	239	29	tn+r−1	tn+r−1	PROPN
ejpam-6282	239	30	m	m	NOUN
ejpam-6282	239	31	)	)	PUNCT
ejpam-6282	240	1	+	+	CCONJ
ejpam-6282	240	2	d(tn+r−1	d(tn+r−1	PROPN
ejpam-6282	240	3	m	m	NOUN
ejpam-6282	240	4	,	,	PUNCT
ejpam-6282	240	5	tn+rm	tn+rm	NOUN
ejpam-6282	240	6	)	)	PUNCT
ejpam-6282	241	1	+	+	NOUN
ejpam-6282	241	2	c	c	X
ejpam-6282	241	3	[	[	X
ejpam-6282	241	4	(	(	PUNCT
ejpam-6282	241	5	d(tn−1	d(tn−1	PROPN
ejpam-6282	241	6	m	m	NOUN
ejpam-6282	241	7	,	,	PUNCT
ejpam-6282	241	8	tn+r−1	tn+r−1	PROPN
ejpam-6282	241	9	m	m	NOUN
ejpam-6282	241	10	)	)	PUNCT
ejpam-6282	241	11	)	)	PUNCT
ejpam-6282	242	1	ξ	ξ	X
ejpam-6282	242	2	(	(	PUNCT
ejpam-6282	242	3	d(tn+r−1	d(tn+r−1	PROPN
ejpam-6282	242	4	m	m	NOUN
ejpam-6282	242	5	,	,	PUNCT
ejpam-6282	242	6	tn+rm	tn+rm	NOUN
ejpam-6282	242	7	)	)	PUNCT
ejpam-6282	242	8	)	)	PUNCT
ejpam-6282	242	9	1−ξ	1−ξ	NUM
ejpam-6282	242	10	]	]	PUNCT
ejpam-6282	242	11	(	(	PUNCT
ejpam-6282	242	12	2.11	2.11	NUM
ejpam-6282	242	13	)	)	PUNCT
ejpam-6282	242	14	employing	employ	VERB
ejpam-6282	242	15	the	the	DET
ejpam-6282	242	16	limits	limit	NOUN
ejpam-6282	242	17	(	(	PUNCT
ejpam-6282	242	18	2.4	2.4	NUM
ejpam-6282	242	19	)	)	PUNCT
ejpam-6282	242	20	and	and	CCONJ
ejpam-6282	242	21	(	(	PUNCT
ejpam-6282	242	22	2.10	2.10	NUM
ejpam-6282	242	23	)	)	PUNCT
ejpam-6282	242	24	,	,	PUNCT
ejpam-6282	242	25	together	together	ADV
ejpam-6282	242	26	with	with	ADP
ejpam-6282	242	27	letting	let	VERB
ejpam-6282	242	28	n	n	X
ejpam-6282	242	29	→	→	SYM
ejpam-6282	242	30	∞	∞	NUM
ejpam-6282	242	31	in	in	ADP
ejpam-6282	242	32	the	the	DET
ejpam-6282	242	33	inequality	inequality	NOUN
ejpam-6282	242	34	above	above	ADV
ejpam-6282	242	35	,	,	PUNCT
ejpam-6282	242	36	we	we	PRON
ejpam-6282	242	37	obtain	obtain	VERB
ejpam-6282	242	38	lim	lim	PROPN
ejpam-6282	242	39	n→∞	n→∞	X
ejpam-6282	242	40	d(tn−1	d(tn−1	PROPN
ejpam-6282	242	41	m	m	NOUN
ejpam-6282	242	42	,	,	PUNCT
ejpam-6282	242	43	tn+rm	tn+rm	NOUN
ejpam-6282	242	44	)	)	PUNCT
ejpam-6282	242	45	=	=	SYM
ejpam-6282	243	1	0	0	X
ejpam-6282	243	2	.	.	PUNCT
ejpam-6282	243	3	(	(	PUNCT
ejpam-6282	243	4	2.12	2.12	NUM
ejpam-6282	243	5	)	)	PUNCT
ejpam-6282	243	6	as	as	ADP
ejpam-6282	243	7	a	a	DET
ejpam-6282	243	8	result	result	NOUN
ejpam-6282	243	9	,	,	PUNCT
ejpam-6282	243	10	our	our	PRON
ejpam-6282	243	11	claim	claim	NOUN
ejpam-6282	243	12	(	(	PUNCT
ejpam-6282	243	13	2.5	2.5	NUM
ejpam-6282	243	14	)	)	PUNCT
ejpam-6282	243	15	holds	hold	VERB
ejpam-6282	243	16	.	.	PUNCT
ejpam-6282	244	1	keeping	keep	VERB
ejpam-6282	244	2	this	this	DET
ejpam-6282	244	3	observation	observation	NOUN
ejpam-6282	244	4	in	in	ADP
ejpam-6282	244	5	mind	mind	NOUN
ejpam-6282	244	6	,	,	PUNCT
ejpam-6282	244	7	it	it	PRON
ejpam-6282	244	8	is	be	AUX
ejpam-6282	244	9	concluded	conclude	VERB
ejpam-6282	244	10	that	that	SCONJ
ejpam-6282	244	11	d(tnm	d(tnm	NOUN
ejpam-6282	244	12	,	,	PUNCT
ejpam-6282	244	13	ts−1	ts−1	NOUN
ejpam-6282	244	14	m	m	NOUN
ejpam-6282	244	15	)	)	PUNCT
ejpam-6282	244	16	<	<	X
ejpam-6282	244	17	1	1	NUM
ejpam-6282	244	18	,	,	PUNCT
ejpam-6282	244	19	(	(	PUNCT
ejpam-6282	244	20	2.13	2.13	NUM
ejpam-6282	244	21	)	)	PUNCT
ejpam-6282	244	22	for	for	ADP
ejpam-6282	244	23	m	m	PROPN
ejpam-6282	244	24	>	>	X
ejpam-6282	244	25	n	n	PROPN
ejpam-6282	244	26	>	>	X
ejpam-6282	244	27	m1	m1	NOUN
ejpam-6282	244	28	for	for	ADP
ejpam-6282	244	29	some	some	DET
ejpam-6282	244	30	m1	m1	PROPN
ejpam-6282	244	31	∈	∈	PROPN
ejpam-6282	244	32	n.	n.	NOUN
ejpam-6282	244	33	as	as	ADP
ejpam-6282	244	34	a	a	DET
ejpam-6282	244	35	next	next	ADJ
ejpam-6282	244	36	step	step	NOUN
ejpam-6282	244	37	,	,	PUNCT
ejpam-6282	244	38	we	we	PRON
ejpam-6282	244	39	shall	shall	AUX
ejpam-6282	244	40	discuss	discuss	VERB
ejpam-6282	244	41	whether	whether	SCONJ
ejpam-6282	244	42	the	the	DET
ejpam-6282	244	43	sequence	sequence	NOUN
ejpam-6282	244	44	{	{	PUNCT
ejpam-6282	244	45	tn−1	tn−1	PROPN
ejpam-6282	244	46	m	m	PRON
ejpam-6282	244	47	}	}	PUNCT
ejpam-6282	244	48	is	be	AUX
ejpam-6282	244	49	cauchy	cauchy	PROPN
ejpam-6282	244	50	.	.	PUNCT
ejpam-6282	245	1	for	for	ADP
ejpam-6282	245	2	for	for	ADP
ejpam-6282	245	3	m	m	PROPN
ejpam-6282	245	4	>	>	X
ejpam-6282	245	5	n	n	PROPN
ejpam-6282	245	6	>	>	X
ejpam-6282	245	7	k	k	PROPN
ejpam-6282	245	8	=	=	PUNCT
ejpam-6282	245	9	{	{	PUNCT
ejpam-6282	245	10	m	m	PROPN
ejpam-6282	245	11	,	,	PUNCT
ejpam-6282	245	12	m1	m1	PROPN
ejpam-6282	245	13	}	}	PUNCT
ejpam-6282	245	14	,	,	PUNCT
ejpam-6282	245	15	we	we	PRON
ejpam-6282	245	16	have	have	VERB
ejpam-6282	245	17	d(tn−1	d(tn−1	NOUN
ejpam-6282	245	18	m	m	NOUN
ejpam-6282	245	19	,	,	PUNCT
ejpam-6282	245	20	ts−1	ts−1	NOUN
ejpam-6282	245	21	m	m	NOUN
ejpam-6282	245	22	)	)	PUNCT
ejpam-6282	245	23	≤	≤	NOUN
ejpam-6282	245	24	d(tn−1	d(tn−1	PROPN
ejpam-6282	245	25	m	m	PROPN
ejpam-6282	245	26	,	,	PUNCT
ejpam-6282	245	27	tnm	tnm	PROPN
ejpam-6282	245	28	)	)	PUNCT
ejpam-6282	246	1	+	+	CCONJ
ejpam-6282	246	2	d(tnm	d(tnm	ADJ
ejpam-6282	246	3	,	,	PUNCT
ejpam-6282	246	4	ts−1	ts−1	NOUN
ejpam-6282	246	5	m	m	NOUN
ejpam-6282	246	6	)	)	PUNCT
ejpam-6282	247	1	+	+	NOUN
ejpam-6282	247	2	c[(d(tn−1	c[(d(tn−1	PROPN
ejpam-6282	247	3	m	m	PROPN
ejpam-6282	247	4	,	,	PUNCT
ejpam-6282	247	5	tnm))ξ(d(tnm	tnm))ξ(d(tnm	PROPN
ejpam-6282	247	6	,	,	PUNCT
ejpam-6282	247	7	ts−1m))1−ξ	ts−1m))1−ξ	PRON
ejpam-6282	247	8	]	]	PUNCT
ejpam-6282	247	9	≤	≤	X
ejpam-6282	247	10	ψn−k(d(tk−1	ψn−k(d(tk−1	PROPN
ejpam-6282	247	11	m	m	PROPN
ejpam-6282	247	12	,	,	PUNCT
ejpam-6282	247	13	tkm	tkm	PROPN
ejpam-6282	247	14	)	)	PUNCT
ejpam-6282	247	15	)	)	PUNCT
ejpam-6282	248	1	+	+	CCONJ
ejpam-6282	248	2	d(tnm	d(tnm	ADJ
ejpam-6282	248	3	,	,	PUNCT
ejpam-6282	248	4	ts−1	ts−1	NOUN
ejpam-6282	248	5	m	m	NOUN
ejpam-6282	248	6	)	)	PUNCT
ejpam-6282	248	7	+	+	NOUN
ejpam-6282	248	8	c[(ψn−k(d(tk−1	c[(ψn−k(d(tk−1	PROPN
ejpam-6282	248	9	m	m	PROPN
ejpam-6282	248	10	,	,	PUNCT
ejpam-6282	248	11	tkm)))ξ(d(tnm	tkm)))ξ(d(tnm	PROPN
ejpam-6282	248	12	,	,	PUNCT
ejpam-6282	248	13	ts−1m))1−ξ	ts−1m))1−ξ	X
ejpam-6282	248	14	]	]	PUNCT
ejpam-6282	248	15	.	.	PUNCT
ejpam-6282	249	1	(	(	PUNCT
ejpam-6282	249	2	2.14	2.14	NUM
ejpam-6282	249	3	)	)	PUNCT
ejpam-6282	249	4	g.	g.	PROPN
ejpam-6282	249	5	alsahli	alsahli	PROPN
ejpam-6282	249	6	,	,	PUNCT
ejpam-6282	249	7	s.	s.	PROPN
ejpam-6282	249	8	gülyaz	gülyaz	PROPN
ejpam-6282	249	9	-	-	PUNCT
ejpam-6282	249	10	özyurt	özyurt	PROPN
ejpam-6282	249	11	/	/	SYM
ejpam-6282	249	12	eur	eur	PROPN
ejpam-6282	249	13	.	.	PUNCT
ejpam-6282	250	1	j.	j.	PROPN
ejpam-6282	250	2	pure	pure	PROPN
ejpam-6282	250	3	appl	appl	PROPN
ejpam-6282	250	4	.	.	PROPN
ejpam-6282	250	5	math	math	PROPN
ejpam-6282	250	6	,	,	PUNCT
ejpam-6282	250	7	18	18	NUM
ejpam-6282	250	8	(	(	PUNCT
ejpam-6282	250	9	2	2	NUM
ejpam-6282	250	10	)	)	PUNCT
ejpam-6282	250	11	(	(	PUNCT
ejpam-6282	250	12	2025	2025	NUM
ejpam-6282	250	13	)	)	PUNCT
ejpam-6282	250	14	,	,	PUNCT
ejpam-6282	250	15	6282	6282	NUM
ejpam-6282	250	16	10	10	NUM
ejpam-6282	250	17	of	of	ADP
ejpam-6282	250	18	13	13	NUM
ejpam-6282	250	19	due	due	ADP
ejpam-6282	250	20	to	to	ADP
ejpam-6282	250	21	(	(	PUNCT
ejpam-6282	250	22	2.13	2.13	NUM
ejpam-6282	250	23	)	)	PUNCT
ejpam-6282	250	24	,	,	PUNCT
ejpam-6282	250	25	we	we	PRON
ejpam-6282	250	26	get	get	VERB
ejpam-6282	250	27	d(tnm	d(tnm	ADJ
ejpam-6282	250	28	,	,	PUNCT
ejpam-6282	250	29	ts−1	ts−1	NOUN
ejpam-6282	250	30	m	m	NOUN
ejpam-6282	250	31	)	)	PUNCT
ejpam-6282	250	32	<	<	X
ejpam-6282	251	1	1	1	X
ejpam-6282	251	2	.	.	PUNCT
ejpam-6282	251	3	consequently	consequently	ADV
ejpam-6282	251	4	,	,	PUNCT
ejpam-6282	251	5	we	we	PRON
ejpam-6282	251	6	find	find	VERB
ejpam-6282	251	7	(	(	PUNCT
ejpam-6282	251	8	d(tnm	d(tnm	NOUN
ejpam-6282	251	9	,	,	PUNCT
ejpam-6282	251	10	ts−1m))1−ξ	ts−1m))1−ξ	PRON
ejpam-6282	251	11	<	<	X
ejpam-6282	251	12	1	1	NUM
ejpam-6282	251	13	.	.	PUNCT
ejpam-6282	251	14	(	(	PUNCT
ejpam-6282	251	15	2.15	2.15	NUM
ejpam-6282	251	16	)	)	PUNCT
ejpam-6282	251	17	keeping	keep	VERB
ejpam-6282	251	18	this	this	DET
ejpam-6282	251	19	observation	observation	NOUN
ejpam-6282	251	20	in	in	ADP
ejpam-6282	251	21	mind	mind	NOUN
ejpam-6282	251	22	,	,	PUNCT
ejpam-6282	251	23	we	we	PRON
ejpam-6282	251	24	shall	shall	AUX
ejpam-6282	251	25	estimate	estimate	VERB
ejpam-6282	251	26	the	the	DET
ejpam-6282	251	27	right	right	ADJ
ejpam-6282	251	28	-	-	PUNCT
ejpam-6282	251	29	hand	hand	NOUN
ejpam-6282	251	30	side	side	NOUN
ejpam-6282	251	31	of	of	ADP
ejpam-6282	251	32	(	(	PUNCT
ejpam-6282	251	33	2.14	2.14	NUM
ejpam-6282	251	34	):	):	PUNCT
ejpam-6282	251	35	≤	≤	PUNCT
ejpam-6282	251	36	ψn−k(d(tk−1	ψn−k(d(tk−1	PROPN
ejpam-6282	251	37	m	m	PROPN
ejpam-6282	251	38	,	,	PUNCT
ejpam-6282	251	39	tkm	tkm	PROPN
ejpam-6282	251	40	)	)	PUNCT
ejpam-6282	251	41	)	)	PUNCT
ejpam-6282	252	1	+	+	CCONJ
ejpam-6282	252	2	d(tnm	d(tnm	ADJ
ejpam-6282	252	3	,	,	PUNCT
ejpam-6282	252	4	ts−1	ts−1	NOUN
ejpam-6282	252	5	m	m	NOUN
ejpam-6282	252	6	)	)	PUNCT
ejpam-6282	253	1	+	+	PROPN
ejpam-6282	253	2	[	[	X
ejpam-6282	253	3	c(ψn−k(d(tk−1	c(ψn−k(d(tk−1	NOUN
ejpam-6282	253	4	m	m	PROPN
ejpam-6282	253	5	,	,	PUNCT
ejpam-6282	253	6	tkm)))ξ(d(tnm	tkm)))ξ(d(tnm	PROPN
ejpam-6282	253	7	,	,	PUNCT
ejpam-6282	253	8	ts−1m))ξ	ts−1m))ξ	ADJ
ejpam-6282	253	9	]	]	X
ejpam-6282	253	10	d(tnm	d(tnm	NOUN
ejpam-6282	253	11	,	,	PUNCT
ejpam-6282	253	12	ts−1	ts−1	NOUN
ejpam-6282	253	13	m	m	NOUN
ejpam-6282	253	14	)	)	PUNCT
ejpam-6282	253	15	≤	≤	NOUN
ejpam-6282	253	16	ψn−k(d(tk−1	ψn−k(d(tk−1	PROPN
ejpam-6282	253	17	m	m	PROPN
ejpam-6282	253	18	,	,	PUNCT
ejpam-6282	253	19	tkm	tkm	PROPN
ejpam-6282	253	20	)	)	PUNCT
ejpam-6282	253	21	)	)	PUNCT
ejpam-6282	254	1	+	+	PUNCT
ejpam-6282	254	2	[	[	X
ejpam-6282	254	3	1	1	NUM
ejpam-6282	254	4	+	+	NUM
ejpam-6282	254	5	c(ψn−k(d(tk−1	c(ψn−k(d(tk−1	PROPN
ejpam-6282	254	6	m	m	PROPN
ejpam-6282	254	7	,	,	PUNCT
ejpam-6282	254	8	tkm)))ξ(d(tnm	tkm)))ξ(d(tnm	PROPN
ejpam-6282	254	9	,	,	PUNCT
ejpam-6282	254	10	ts−1m))ξ	ts−1m))ξ	ADJ
ejpam-6282	254	11	]	]	X
ejpam-6282	254	12	d(tnm	d(tnm	NOUN
ejpam-6282	254	13	,	,	PUNCT
ejpam-6282	254	14	ts−1	ts−1	NOUN
ejpam-6282	254	15	m	m	NOUN
ejpam-6282	254	16	)	)	PUNCT
ejpam-6282	254	17	(	(	PUNCT
ejpam-6282	254	18	due	due	ADP
ejpam-6282	254	19	to	to	ADP
ejpam-6282	254	20	(	(	PUNCT
ejpam-6282	254	21	2.15	2.15	NUM
ejpam-6282	254	22	)	)	PUNCT
ejpam-6282	254	23	)	)	PUNCT
ejpam-6282	254	24	≤	≤	PUNCT
ejpam-6282	254	25	ψn−k(d(tk−1	ψn−k(d(tk−1	PROPN
ejpam-6282	254	26	m	m	PROPN
ejpam-6282	254	27	,	,	PUNCT
ejpam-6282	254	28	tkm	tkm	PROPN
ejpam-6282	254	29	)	)	PUNCT
ejpam-6282	254	30	)	)	PUNCT
ejpam-6282	255	1	+	+	PUNCT
ejpam-6282	255	2	[	[	X
ejpam-6282	255	3	1	1	NUM
ejpam-6282	255	4	+	+	NUM
ejpam-6282	255	5	c(ψn−k(d(tk−1	c(ψn−k(d(tk−1	PROPN
ejpam-6282	255	6	m	m	NOUN
ejpam-6282	255	7	,	,	PUNCT
ejpam-6282	255	8	tkm)))ξ	tkm)))ξ	NUM
ejpam-6282	255	9	]	]	X
ejpam-6282	255	10	d(tnm	d(tnm	ADJ
ejpam-6282	255	11	,	,	PUNCT
ejpam-6282	255	12	ts−1	ts−1	NOUN
ejpam-6282	255	13	m	m	NOUN
ejpam-6282	255	14	)	)	PUNCT
ejpam-6282	255	15	.	.	PUNCT
ejpam-6282	256	1	(	(	PUNCT
ejpam-6282	256	2	2.16	2.16	NUM
ejpam-6282	256	3	)	)	PUNCT
ejpam-6282	256	4	in	in	ADP
ejpam-6282	256	5	conclusion	conclusion	NOUN
ejpam-6282	256	6	,	,	PUNCT
ejpam-6282	256	7	we	we	PRON
ejpam-6282	256	8	have	have	VERB
ejpam-6282	256	9	d(tn−1	d(tn−1	NOUN
ejpam-6282	256	10	m	m	NOUN
ejpam-6282	256	11	,	,	PUNCT
ejpam-6282	256	12	ts−1	ts−1	NOUN
ejpam-6282	256	13	m	m	NOUN
ejpam-6282	256	14	)	)	PUNCT
ejpam-6282	256	15	≤	≤	NOUN
ejpam-6282	256	16	ψn−k(d(tk−1	ψn−k(d(tk−1	PROPN
ejpam-6282	256	17	m	m	NOUN
ejpam-6282	256	18	,	,	PUNCT
ejpam-6282	256	19	tkm))+	tkm))+	X
ejpam-6282	257	1	[	[	X
ejpam-6282	257	2	1	1	NUM
ejpam-6282	257	3	+	+	NUM
ejpam-6282	257	4	c(ψn−k(d(tk−1	c(ψn−k(d(tk−1	PROPN
ejpam-6282	257	5	m	m	NOUN
ejpam-6282	257	6	,	,	PUNCT
ejpam-6282	257	7	tkm)))ξ	tkm)))ξ	NUM
ejpam-6282	257	8	]	]	X
ejpam-6282	257	9	d(tnm	d(tnm	ADJ
ejpam-6282	257	10	,	,	PUNCT
ejpam-6282	257	11	ts−1	ts−1	NOUN
ejpam-6282	257	12	m	m	NOUN
ejpam-6282	257	13	)	)	PUNCT
ejpam-6282	257	14	.	.	PUNCT
ejpam-6282	258	1	(	(	PUNCT
ejpam-6282	258	2	2.17	2.17	NUM
ejpam-6282	258	3	)	)	PUNCT
ejpam-6282	258	4	notice	notice	NOUN
ejpam-6282	258	5	also	also	ADV
ejpam-6282	258	6	that	that	SCONJ
ejpam-6282	258	7	d(tnm	d(tnm	NOUN
ejpam-6282	258	8	,	,	PUNCT
ejpam-6282	258	9	ts−1	ts−1	NOUN
ejpam-6282	258	10	m	m	NOUN
ejpam-6282	258	11	)	)	PUNCT
ejpam-6282	258	12	≤	≤	PUNCT
ejpam-6282	258	13	d(tnm	d(tnm	NOUN
ejpam-6282	258	14	,	,	PUNCT
ejpam-6282	258	15	tn+1	tn+1	NOUN
ejpam-6282	258	16	m	m	NOUN
ejpam-6282	258	17	)	)	PUNCT
ejpam-6282	259	1	+	+	CCONJ
ejpam-6282	260	1	d(tn+1	d(tn+1	PROPN
ejpam-6282	260	2	m	m	NOUN
ejpam-6282	260	3	,	,	PUNCT
ejpam-6282	260	4	ts−1	ts−1	NOUN
ejpam-6282	260	5	m	m	NOUN
ejpam-6282	260	6	)	)	PUNCT
ejpam-6282	261	1	+	+	ADJ
ejpam-6282	261	2	c[(d(tk−1	c[(d(tk−1	NOUN
ejpam-6282	261	3	m	m	ADP
ejpam-6282	261	4	,	,	PUNCT
ejpam-6282	261	5	tkm))ξ(d(tn+1	tkm))ξ(d(tn+1	ADJ
ejpam-6282	261	6	m	m	NOUN
ejpam-6282	261	7	,	,	PUNCT
ejpam-6282	261	8	ts−1m))1−ξ	ts−1m))1−ξ	X
ejpam-6282	261	9	]	]	PUNCT
ejpam-6282	261	10	≤	≤	NUM
ejpam-6282	261	11	ψn−k+1(d(tk−1	ψn−k+1(d(tk−1	PROPN
ejpam-6282	261	12	m	m	PROPN
ejpam-6282	261	13	,	,	PUNCT
ejpam-6282	261	14	tkm	tkm	PROPN
ejpam-6282	261	15	)	)	PUNCT
ejpam-6282	261	16	)	)	PUNCT
ejpam-6282	262	1	+	+	PUNCT
ejpam-6282	262	2	d(tn+1	d(tn+1	NOUN
ejpam-6282	262	3	m	m	NOUN
ejpam-6282	262	4	,	,	PUNCT
ejpam-6282	262	5	ts−1	ts−1	NOUN
ejpam-6282	262	6	m	m	NOUN
ejpam-6282	262	7	)	)	PUNCT
ejpam-6282	263	1	+	+	PROPN
ejpam-6282	263	2	[	[	X
ejpam-6282	263	3	c(ψn−k+1(d(tk−1	c(ψn−k+1(d(tk−1	NOUN
ejpam-6282	263	4	m	m	NOUN
ejpam-6282	263	5	,	,	PUNCT
ejpam-6282	263	6	tkm)))ξ(d(tn+1	tkm)))ξ(d(tn+1	NOUN
ejpam-6282	263	7	m	m	NOUN
ejpam-6282	263	8	,	,	PUNCT
ejpam-6282	263	9	ts−1m))ξ	ts−1m))ξ	ADJ
ejpam-6282	263	10	]	]	X
ejpam-6282	263	11	d(tn+1	d(tn+1	NOUN
ejpam-6282	263	12	m	m	NOUN
ejpam-6282	263	13	,	,	PUNCT
ejpam-6282	263	14	ts−1	ts−1	PROPN
ejpam-6282	263	15	m	m	NOUN
ejpam-6282	263	16	)	)	PUNCT
ejpam-6282	263	17	≤	≤	NOUN
ejpam-6282	263	18	ψn−k+1(d(tk−1	ψn−k+1(d(tk−1	PROPN
ejpam-6282	263	19	m	m	PROPN
ejpam-6282	263	20	,	,	PUNCT
ejpam-6282	263	21	tkm	tkm	PROPN
ejpam-6282	263	22	)	)	PUNCT
ejpam-6282	263	23	)	)	PUNCT
ejpam-6282	264	1	+	+	PUNCT
ejpam-6282	265	1	[	[	X
ejpam-6282	265	2	1	1	NUM
ejpam-6282	265	3	+	+	NUM
ejpam-6282	265	4	c(ψn−k+1(d(tk−1	c(ψn−k+1(d(tk−1	PROPN
ejpam-6282	265	5	m	m	NOUN
ejpam-6282	265	6	,	,	PUNCT
ejpam-6282	265	7	tkm)))ξ	tkm)))ξ	PUNCT
ejpam-6282	265	8	]	]	SYM
ejpam-6282	265	9	d(tn+1	d(tn+1	NOUN
ejpam-6282	265	10	m	m	NOUN
ejpam-6282	265	11	,	,	PUNCT
ejpam-6282	265	12	ts−1	ts−1	NOUN
ejpam-6282	265	13	m	m	NOUN
ejpam-6282	265	14	)	)	PUNCT
ejpam-6282	265	15	.	.	PUNCT
ejpam-6282	266	1	(	(	PUNCT
ejpam-6282	266	2	2.18	2.18	NUM
ejpam-6282	266	3	)	)	PUNCT
ejpam-6282	266	4	gathering	gathering	NOUN
ejpam-6282	266	5	(	(	PUNCT
ejpam-6282	266	6	2.17	2.17	NUM
ejpam-6282	266	7	)	)	PUNCT
ejpam-6282	266	8	and	and	CCONJ
ejpam-6282	266	9	(	(	PUNCT
ejpam-6282	266	10	2.18	2.18	NUM
ejpam-6282	266	11	)	)	PUNCT
ejpam-6282	266	12	yields	yield	NOUN
ejpam-6282	266	13	that	that	PRON
ejpam-6282	266	14	d(tn−1	d(tn−1	PROPN
ejpam-6282	266	15	m	m	NOUN
ejpam-6282	266	16	,	,	PUNCT
ejpam-6282	266	17	ts−1	ts−1	NOUN
ejpam-6282	266	18	m	m	NOUN
ejpam-6282	266	19	)	)	PUNCT
ejpam-6282	266	20	≤	≤	NOUN
ejpam-6282	266	21	ψn−k(d(tk−1	ψn−k(d(tk−1	PROPN
ejpam-6282	266	22	m	m	PROPN
ejpam-6282	266	23	,	,	PUNCT
ejpam-6282	266	24	tkm	tkm	PROPN
ejpam-6282	266	25	)	)	PUNCT
ejpam-6282	266	26	)	)	PUNCT
ejpam-6282	267	1	+	+	CCONJ
ejpam-6282	267	2	ψn−k+1(d(tk−1	ψn−k+1(d(tk−1	PROPN
ejpam-6282	267	3	m	m	PRON
ejpam-6282	267	4	,	,	PUNCT
ejpam-6282	267	5	tkm))[1	tkm))[1	PROPN
ejpam-6282	267	6	+	+	CCONJ
ejpam-6282	267	7	c(ψn−k)ξ	c(ψn−k)ξ	NOUN
ejpam-6282	267	8	]	]	PUNCT
ejpam-6282	267	9	+	+	PUNCT
ejpam-6282	267	10	[	[	X
ejpam-6282	267	11	1	1	NUM
ejpam-6282	267	12	+	+	NUM
ejpam-6282	267	13	c(ψn−k(d(tk−1	c(ψn−k(d(tk−1	PROPN
ejpam-6282	267	14	m	m	NOUN
ejpam-6282	267	15	,	,	PUNCT
ejpam-6282	267	16	tkm)))ξ	tkm)))ξ	PUNCT
ejpam-6282	267	17	]	]	PUNCT
ejpam-6282	267	18	[	[	X
ejpam-6282	267	19	1	1	NUM
ejpam-6282	267	20	+	+	NUM
ejpam-6282	267	21	c(ψn−k+1(d(tk−1	c(ψn−k+1(d(tk−1	PROPN
ejpam-6282	267	22	m	m	NOUN
ejpam-6282	267	23	,	,	PUNCT
ejpam-6282	267	24	tkm)))ξ	tkm)))ξ	PUNCT
ejpam-6282	267	25	]	]	SYM
ejpam-6282	267	26	d(tn+1	d(tn+1	NOUN
ejpam-6282	267	27	m	m	NOUN
ejpam-6282	267	28	,	,	PUNCT
ejpam-6282	267	29	ts−1	ts−1	NOUN
ejpam-6282	267	30	m	m	NOUN
ejpam-6282	267	31	)	)	PUNCT
ejpam-6282	267	32	(	(	PUNCT
ejpam-6282	267	33	2.19	2.19	NUM
ejpam-6282	267	34	)	)	PUNCT
ejpam-6282	267	35	by	by	ADP
ejpam-6282	267	36	collecting	collect	VERB
ejpam-6282	267	37	all	all	DET
ejpam-6282	267	38	observations	observation	NOUN
ejpam-6282	267	39	above	above	ADV
ejpam-6282	267	40	,	,	PUNCT
ejpam-6282	267	41	we	we	PRON
ejpam-6282	267	42	find	find	VERB
ejpam-6282	267	43	d(tn−1	d(tn−1	NOUN
ejpam-6282	267	44	m	m	NOUN
ejpam-6282	267	45	,	,	PUNCT
ejpam-6282	267	46	ts−1	ts−1	NOUN
ejpam-6282	267	47	m	m	NOUN
ejpam-6282	267	48	)	)	PUNCT
ejpam-6282	267	49	≤	≤	NOUN
ejpam-6282	267	50	ψn−k(d(tk−1	ψn−k(d(tk−1	PROPN
ejpam-6282	267	51	m	m	NOUN
ejpam-6282	267	52	,	,	PUNCT
ejpam-6282	267	53	tkm))∑m−n−1	tkm))∑m−n−1	PROPN
ejpam-6282	267	54	i=0	i=0	PROPN
ejpam-6282	267	55	ψi	ψi	ADP
ejpam-6282	267	56	∏i−1	∏i−1	PROPN
ejpam-6282	267	57	j=0(1	j=0(1	PROPN
ejpam-6282	267	58	+	+	CCONJ
ejpam-6282	267	59	cψn−k+j(d(tk−1	cψn−k+j(d(tk−1	PROPN
ejpam-6282	267	60	m	m	NOUN
ejpam-6282	267	61	,	,	PUNCT
ejpam-6282	267	62	tkm)))ξ	tkm)))ξ	VERB
ejpam-6282	267	63	≤	≤	ADV
ejpam-6282	267	64	ψn−k(d(tk−1	ψn−k(d(tk−1	PROPN
ejpam-6282	267	65	m	m	NOUN
ejpam-6282	267	66	,	,	PUNCT
ejpam-6282	267	67	tkm))∑m−n−1	tkm))∑m−n−1	PROPN
ejpam-6282	267	68	i=0	i=0	PROPN
ejpam-6282	267	69	ψi(d(tk−1	ψi(d(tk−1	PROPN
ejpam-6282	267	70	m	m	NOUN
ejpam-6282	267	71	,	,	PUNCT
ejpam-6282	267	72	tkm))∏i−1	tkm))∏i−1	PROPN
ejpam-6282	267	73	j=0(1	j=0(1	PROPN
ejpam-6282	267	74	+	+	CCONJ
ejpam-6282	267	75	cψj(d(tk−1	cψj(d(tk−1	NOUN
ejpam-6282	267	76	m	m	NOUN
ejpam-6282	267	77	,	,	PUNCT
ejpam-6282	267	78	tkm)))ξ	tkm)))ξ	PUNCT
ejpam-6282	267	79	.	.	PUNCT
ejpam-6282	268	1	(	(	PUNCT
ejpam-6282	268	2	2.20	2.20	NUM
ejpam-6282	268	3	)	)	PUNCT
ejpam-6282	268	4	notice	notice	VERB
ejpam-6282	268	5	that	that	SCONJ
ejpam-6282	268	6	the	the	DET
ejpam-6282	268	7	sequence	sequence	NOUN
ejpam-6282	268	8	∑∞	∑∞	NOUN
ejpam-6282	268	9	i=0	i=0	PROPN
ejpam-6282	268	10	si	si	X
ejpam-6282	268	11	dominates	dominate	VERB
ejpam-6282	268	12	the	the	DET
ejpam-6282	268	13	right	right	ADJ
ejpam-6282	268	14	-	-	PUNCT
ejpam-6282	268	15	hand	hand	NOUN
ejpam-6282	268	16	side	side	NOUN
ejpam-6282	268	17	of	of	ADP
ejpam-6282	268	18	(	(	PUNCT
ejpam-6282	268	19	2.20	2.20	NUM
ejpam-6282	268	20	)	)	PUNCT
ejpam-6282	268	21	.	.	PUNCT
ejpam-6282	269	1	hence	hence	ADV
ejpam-6282	269	2	,	,	PUNCT
ejpam-6282	269	3	by	by	ADP
ejpam-6282	269	4	letting	let	VERB
ejpam-6282	269	5	n	n	CCONJ
ejpam-6282	269	6	,	,	PUNCT
ejpam-6282	269	7	m	m	PROPN
ejpam-6282	269	8	→	→	SYM
ejpam-6282	269	9	∞	∞	PROPN
ejpam-6282	269	10	,	,	PUNCT
ejpam-6282	269	11	we	we	PRON
ejpam-6282	269	12	conclude	conclude	VERB
ejpam-6282	269	13	that	that	SCONJ
ejpam-6282	269	14	it	it	PRON
ejpam-6282	269	15	converges	converge	VERB
ejpam-6282	269	16	,	,	PUNCT
ejpam-6282	269	17	where	where	SCONJ
ejpam-6282	269	18	,	,	PUNCT
ejpam-6282	269	19	si	si	PROPN
ejpam-6282	269	20	=	=	PUNCT
ejpam-6282	269	21	ψi(d(tk−1	ψi(d(tk−1	PROPN
ejpam-6282	269	22	m	m	NOUN
ejpam-6282	269	23	,	,	PUNCT
ejpam-6282	269	24	tkm	tkm	PROPN
ejpam-6282	269	25	)	)	PUNCT
ejpam-6282	269	26	)	)	PUNCT
ejpam-6282	270	1	i−1	i−1	PROPN
ejpam-6282	270	2	∏	∏	PROPN
ejpam-6282	270	3	j=0	j=0	PROPN
ejpam-6282	270	4	(	(	PUNCT
ejpam-6282	270	5	1	1	NUM
ejpam-6282	270	6	+	+	NUM
ejpam-6282	270	7	cψj(d(tk−1	cψj(d(tk−1	NOUN
ejpam-6282	270	8	m	m	NOUN
ejpam-6282	270	9	,	,	PUNCT
ejpam-6282	270	10	tkm)))ξ	tkm)))ξ	VERB
ejpam-6282	270	11	<	<	X
ejpam-6282	270	12	ψi(d(tk−1	ψi(d(tk−1	PROPN
ejpam-6282	270	13	m	m	PRON
ejpam-6282	270	14	,	,	PUNCT
ejpam-6282	270	15	tkm	tkm	PROPN
ejpam-6282	270	16	)	)	PUNCT
ejpam-6282	270	17	)	)	PUNCT
ejpam-6282	270	18	i−1	i−1	PROPN
ejpam-6282	270	19	∏	∏	PROPN
ejpam-6282	270	20	j=0	j=0	PROPN
ejpam-6282	270	21	(	(	PUNCT
ejpam-6282	270	22	1	1	NUM
ejpam-6282	270	23	+	+	NUM
ejpam-6282	270	24	cd(tk−1	cd(tk−1	PROPN
ejpam-6282	270	25	m	m	PROPN
ejpam-6282	270	26	,	,	PUNCT
ejpam-6282	270	27	tkm))ξ	tkm))ξ	NOUN
ejpam-6282	270	28	.	.	PUNCT
ejpam-6282	271	1	g.	g.	PROPN
ejpam-6282	271	2	alsahli	alsahli	PROPN
ejpam-6282	271	3	,	,	PUNCT
ejpam-6282	271	4	s.	s.	PROPN
ejpam-6282	271	5	gülyaz	gülyaz	PROPN
ejpam-6282	271	6	-	-	PUNCT
ejpam-6282	271	7	özyurt	özyurt	PROPN
ejpam-6282	271	8	/	/	SYM
ejpam-6282	271	9	eur	eur	PROPN
ejpam-6282	271	10	.	.	PUNCT
ejpam-6282	272	1	j.	j.	PROPN
ejpam-6282	272	2	pure	pure	PROPN
ejpam-6282	272	3	appl	appl	PROPN
ejpam-6282	272	4	.	.	PROPN
ejpam-6282	272	5	math	math	PROPN
ejpam-6282	272	6	,	,	PUNCT
ejpam-6282	272	7	18	18	NUM
ejpam-6282	272	8	(	(	PUNCT
ejpam-6282	272	9	2	2	NUM
ejpam-6282	272	10	)	)	PUNCT
ejpam-6282	272	11	(	(	PUNCT
ejpam-6282	272	12	2025	2025	NUM
ejpam-6282	272	13	)	)	PUNCT
ejpam-6282	272	14	,	,	PUNCT
ejpam-6282	272	15	6282	6282	NUM
ejpam-6282	272	16	11	11	NUM
ejpam-6282	272	17	of	of	ADP
ejpam-6282	272	18	13	13	NUM
ejpam-6282	272	19	in	in	ADP
ejpam-6282	272	20	conclusion	conclusion	NOUN
ejpam-6282	272	21	,	,	PUNCT
ejpam-6282	272	22	{	{	PUNCT
ejpam-6282	272	23	tn−1	tn−1	PROPN
ejpam-6282	272	24	m	m	PRON
ejpam-6282	272	25	}	}	PUNCT
ejpam-6282	272	26	is	be	AUX
ejpam-6282	272	27	cauchy	cauchy	NOUN
ejpam-6282	272	28	.	.	PUNCT
ejpam-6282	273	1	we	we	PRON
ejpam-6282	273	2	recall	recall	VERB
ejpam-6282	273	3	that	that	PRON
ejpam-6282	273	4	(	(	PUNCT
ejpam-6282	273	5	s	s	X
ejpam-6282	273	6	,	,	PUNCT
ejpam-6282	273	7	d	d	NOUN
ejpam-6282	273	8	)	)	PUNCT
ejpam-6282	273	9	is	be	AUX
ejpam-6282	273	10	a	a	DET
ejpam-6282	273	11	complete	complete	ADJ
ejpam-6282	273	12	(	(	PUNCT
ejpam-6282	273	13	ξ	ξ	PROPN
ejpam-6282	273	14	,	,	PUNCT
ejpam-6282	273	15	c)-interpolative	c)-interpolative	ADJ
ejpam-6282	273	16	metric	metric	ADJ
ejpam-6282	273	17	space	space	NOUN
ejpam-6282	273	18	.	.	PUNCT
ejpam-6282	274	1	it	it	PRON
ejpam-6282	274	2	implies	imply	VERB
ejpam-6282	274	3	that	that	SCONJ
ejpam-6282	274	4	the	the	DET
ejpam-6282	274	5	sequence	sequence	NOUN
ejpam-6282	274	6	{	{	PUNCT
ejpam-6282	274	7	tn−1	tn−1	PROPN
ejpam-6282	274	8	m	m	NOUN
ejpam-6282	274	9	}	}	PUNCT
ejpam-6282	274	10	converges	converge	NOUN
ejpam-6282	274	11	to	to	ADP
ejpam-6282	274	12	m∗	m∗	PROPN
ejpam-6282	274	13	∈	∈	PROPN
ejpam-6282	274	14	s.	s.	PROPN
ejpam-6282	274	15	in	in	ADP
ejpam-6282	274	16	this	this	DET
ejpam-6282	274	17	step	step	NOUN
ejpam-6282	274	18	,	,	PUNCT
ejpam-6282	274	19	we	we	PRON
ejpam-6282	274	20	need	need	VERB
ejpam-6282	274	21	to	to	PART
ejpam-6282	274	22	show	show	VERB
ejpam-6282	274	23	that	that	SCONJ
ejpam-6282	274	24	m∗	m∗	NOUN
ejpam-6282	274	25	is	be	AUX
ejpam-6282	274	26	the	the	DET
ejpam-6282	274	27	fixed	fix	VERB
ejpam-6282	274	28	point	point	NOUN
ejpam-6282	274	29	of	of	ADP
ejpam-6282	274	30	t.	t.	PROPN
ejpam-6282	274	31	to	to	PART
ejpam-6282	274	32	prove	prove	VERB
ejpam-6282	274	33	it	it	PRON
ejpam-6282	274	34	,	,	PUNCT
ejpam-6282	274	35	assume	assume	VERB
ejpam-6282	274	36	not	not	PART
ejpam-6282	274	37	,	,	PUNCT
ejpam-6282	274	38	that	that	ADV
ejpam-6282	274	39	is	is	ADV
ejpam-6282	274	40	,	,	PUNCT
ejpam-6282	274	41	d(m∗	d(m∗	NOUN
ejpam-6282	274	42	,	,	PUNCT
ejpam-6282	274	43	tm∗	tm∗	NOUN
ejpam-6282	274	44	)	)	PUNCT
ejpam-6282	274	45	>	>	X
ejpam-6282	275	1	0	0	X
ejpam-6282	275	2	.	.	PUNCT
ejpam-6282	275	3	note	note	VERB
ejpam-6282	275	4	that	that	SCONJ
ejpam-6282	275	5	d(tnm	d(tnm	NOUN
ejpam-6282	275	6	,	,	PUNCT
ejpam-6282	275	7	tm∗	tm∗	NOUN
ejpam-6282	275	8	)	)	PUNCT
ejpam-6282	275	9	=	=	SYM
ejpam-6282	275	10	d(ttn−1	d(ttn−1	PROPN
ejpam-6282	275	11	m	m	NOUN
ejpam-6282	275	12	,	,	PUNCT
ejpam-6282	275	13	tm∗	tm∗	NOUN
ejpam-6282	275	14	)	)	PUNCT
ejpam-6282	275	15	≤	≤	NOUN
ejpam-6282	276	1	ψ	ψ	X
ejpam-6282	276	2	(	(	PUNCT
ejpam-6282	276	3	max{d(tn−1	max{d(tn−1	PROPN
ejpam-6282	276	4	m	m	PROPN
ejpam-6282	276	5	,	,	PUNCT
ejpam-6282	276	6	m∗	m∗	PROPN
ejpam-6282	276	7	)	)	PUNCT
ejpam-6282	276	8	,	,	PUNCT
ejpam-6282	276	9	d(tn−1	d(tn−1	PROPN
ejpam-6282	276	10	m	m	PROPN
ejpam-6282	276	11	,	,	PUNCT
ejpam-6282	276	12	tnm	tnm	PROPN
ejpam-6282	276	13	)	)	PUNCT
ejpam-6282	276	14	,	,	PUNCT
ejpam-6282	276	15	d(tm∗	d(tm∗	PROPN
ejpam-6282	276	16	,	,	PUNCT
ejpam-6282	276	17	m∗	m∗	NOUN
ejpam-6282	276	18	)	)	PUNCT
ejpam-6282	276	19	}	}	PUNCT
ejpam-6282	276	20	)	)	PUNCT
ejpam-6282	276	21	(	(	PUNCT
ejpam-6282	276	22	2.21	2.21	NUM
ejpam-6282	276	23	)	)	PUNCT
ejpam-6282	276	24	applying	apply	VERB
ejpam-6282	276	25	lim	lim	PROPN
ejpam-6282	276	26	sup	sup	PROPN
ejpam-6282	276	27	to	to	ADP
ejpam-6282	276	28	(	(	PUNCT
ejpam-6282	276	29	2.21	2.21	NUM
ejpam-6282	276	30	)	)	PUNCT
ejpam-6282	276	31	,	,	PUNCT
ejpam-6282	276	32	we	we	PRON
ejpam-6282	276	33	find	find	VERB
ejpam-6282	276	34	d(tm∗	d(tm∗	NOUN
ejpam-6282	276	35	,	,	PUNCT
ejpam-6282	276	36	m∗	m∗	NOUN
ejpam-6282	276	37	)	)	PUNCT
ejpam-6282	276	38	≤	≤	NOUN
ejpam-6282	276	39	ψ(d(tm∗	ψ(d(tm∗	PROPN
ejpam-6282	276	40	,	,	PUNCT
ejpam-6282	276	41	m∗	m∗	NOUN
ejpam-6282	276	42	)	)	PUNCT
ejpam-6282	276	43	)	)	PUNCT
ejpam-6282	277	1	<	<	X
ejpam-6282	277	2	d(tm∗	d(tm∗	PROPN
ejpam-6282	277	3	,	,	PUNCT
ejpam-6282	277	4	m∗	m∗	NOUN
ejpam-6282	277	5	)	)	PUNCT
ejpam-6282	277	6	due	due	ADP
ejpam-6282	277	7	to	to	ADP
ejpam-6282	277	8	assumptiond(m∗	assumptiond(m∗	NOUN
ejpam-6282	277	9	,	,	PUNCT
ejpam-6282	277	10	tm∗	tm∗	NOUN
ejpam-6282	277	11	)	)	PUNCT
ejpam-6282	277	12	>	>	X
ejpam-6282	277	13	0	0	PUNCT
ejpam-6282	277	14	(	(	PUNCT
ejpam-6282	277	15	2.22	2.22	NUM
ejpam-6282	277	16	)	)	PUNCT
ejpam-6282	277	17	a	a	DET
ejpam-6282	277	18	contradiction	contradiction	NOUN
ejpam-6282	277	19	.	.	PUNCT
ejpam-6282	278	1	therefore	therefore	ADV
ejpam-6282	278	2	,	,	PUNCT
ejpam-6282	278	3	tm∗	tm∗	NOUN
ejpam-6282	278	4	=	=	SYM
ejpam-6282	278	5	m∗	m∗	NOUN
ejpam-6282	278	6	forms	form	VERB
ejpam-6282	278	7	a	a	DET
ejpam-6282	278	8	fixed	fixed	ADJ
ejpam-6282	278	9	point	point	NOUN
ejpam-6282	278	10	of	of	ADP
ejpam-6282	278	11	t	t	PROPN
ejpam-6282	278	12	in	in	ADP
ejpam-6282	278	13	s.	s.	PROPN
ejpam-6282	278	14	3	3	NUM
ejpam-6282	278	15	.	.	PUNCT
ejpam-6282	278	16	consequences	consequence	NOUN
ejpam-6282	278	17	in	in	ADP
ejpam-6282	278	18	this	this	DET
ejpam-6282	278	19	part	part	NOUN
ejpam-6282	278	20	,	,	PUNCT
ejpam-6282	278	21	we	we	PRON
ejpam-6282	278	22	shall	shall	AUX
ejpam-6282	278	23	consider	consider	VERB
ejpam-6282	278	24	the	the	DET
ejpam-6282	278	25	immediate	immediate	ADJ
ejpam-6282	278	26	consequences	consequence	NOUN
ejpam-6282	278	27	of	of	ADP
ejpam-6282	278	28	this	this	DET
ejpam-6282	278	29	paper	paper	NOUN
ejpam-6282	278	30	’s	’s	PART
ejpam-6282	278	31	main	main	ADJ
ejpam-6282	278	32	result	result	NOUN
ejpam-6282	278	33	.	.	PUNCT
ejpam-6282	279	1	corollary	corollary	ADJ
ejpam-6282	279	2	1	1	NUM
ejpam-6282	279	3	.	.	PUNCT
ejpam-6282	280	1	let	let	VERB
ejpam-6282	280	2	(	(	PUNCT
ejpam-6282	280	3	s	s	X
ejpam-6282	280	4	,	,	PUNCT
ejpam-6282	280	5	d	d	NOUN
ejpam-6282	280	6	)	)	PUNCT
ejpam-6282	280	7	be	be	AUX
ejpam-6282	280	8	a	a	DET
ejpam-6282	280	9	complete	complete	ADJ
ejpam-6282	280	10	(	(	PUNCT
ejpam-6282	280	11	ξ	ξ	PROPN
ejpam-6282	280	12	,	,	PUNCT
ejpam-6282	280	13	c)-ims	c)-im	NOUN
ejpam-6282	280	14	,	,	PUNCT
ejpam-6282	280	15	and	and	CCONJ
ejpam-6282	280	16	let	let	VERB
ejpam-6282	280	17	t	t	NOUN
ejpam-6282	280	18	:	:	PUNCT
ejpam-6282	280	19	s	s	AUX
ejpam-6282	280	20	→	→	SYM
ejpam-6282	280	21	s	s	PART
ejpam-6282	280	22	be	be	AUX
ejpam-6282	280	23	a	a	DET
ejpam-6282	280	24	mapping	mapping	NOUN
ejpam-6282	280	25	.	.	PUNCT
ejpam-6282	281	1	if	if	SCONJ
ejpam-6282	281	2	there	there	PRON
ejpam-6282	281	3	is	be	VERB
ejpam-6282	281	4	an	an	DET
ejpam-6282	281	5	auxiliary	auxiliary	ADJ
ejpam-6282	281	6	mapping	mapping	NOUN
ejpam-6282	281	7	ψ	ψ	ADP
ejpam-6282	281	8	∈	∈	PROPN
ejpam-6282	281	9	ψ	ψ	ADP
ejpam-6282	281	10	such	such	ADJ
ejpam-6282	281	11	that	that	SCONJ
ejpam-6282	281	12	d(tx	d(tx	PROPN
ejpam-6282	281	13	,	,	PUNCT
ejpam-6282	281	14	ty	ty	NOUN
ejpam-6282	281	15	)	)	PUNCT
ejpam-6282	281	16	≤	≤	NOUN
ejpam-6282	281	17	ψ(d(x	ψ(d(x	NOUN
ejpam-6282	281	18	,	,	PUNCT
ejpam-6282	281	19	y	y	NOUN
ejpam-6282	281	20	)	)	PUNCT
ejpam-6282	281	21	)	)	PUNCT
ejpam-6282	281	22	,	,	PUNCT
ejpam-6282	281	23	(	(	PUNCT
ejpam-6282	281	24	3.1	3.1	NUM
ejpam-6282	281	25	)	)	PUNCT
ejpam-6282	281	26	for	for	ADP
ejpam-6282	281	27	all	all	DET
ejpam-6282	281	28	x	x	NOUN
ejpam-6282	281	29	,	,	PUNCT
ejpam-6282	281	30	y	y	PROPN
ejpam-6282	281	31	∈	∈	PROPN
ejpam-6282	281	32	s	s	PROPN
ejpam-6282	281	33	,	,	PUNCT
ejpam-6282	281	34	then	then	ADV
ejpam-6282	281	35	,	,	PUNCT
ejpam-6282	281	36	t	t	PROPN
ejpam-6282	281	37	guarantees	guarantee	VERB
ejpam-6282	281	38	to	to	PART
ejpam-6282	281	39	possess	possess	VERB
ejpam-6282	281	40	a	a	DET
ejpam-6282	281	41	unique	unique	ADJ
ejpam-6282	281	42	fixed	fix	VERB
ejpam-6282	281	43	point	point	NOUN
ejpam-6282	281	44	in	in	ADP
ejpam-6282	281	45	s.	s.	PROPN
ejpam-6282	281	46	sketch	sketch	PROPN
ejpam-6282	281	47	of	of	ADP
ejpam-6282	281	48	the	the	DET
ejpam-6282	281	49	proof	proof	NOUN
ejpam-6282	281	50	1	1	NUM
ejpam-6282	281	51	.	.	PUNCT
ejpam-6282	281	52	note	note	VERB
ejpam-6282	281	53	that	that	SCONJ
ejpam-6282	281	54	the	the	DET
ejpam-6282	281	55	full	full	ADJ
ejpam-6282	281	56	proof	proof	NOUN
ejpam-6282	281	57	mimics	mimic	VERB
ejpam-6282	281	58	the	the	DET
ejpam-6282	281	59	proof	proof	NOUN
ejpam-6282	281	60	of	of	ADP
ejpam-6282	281	61	the	the	DET
ejpam-6282	281	62	main	main	ADJ
ejpam-6282	281	63	theorem	theorem	NOUN
ejpam-6282	281	64	,	,	PUNCT
ejpam-6282	281	65	thus	thus	ADV
ejpam-6282	281	66	we	we	PRON
ejpam-6282	281	67	prefer	prefer	VERB
ejpam-6282	281	68	the	the	DET
ejpam-6282	281	69	avoid	avoid	VERB
ejpam-6282	281	70	the	the	DET
ejpam-6282	281	71	repetition	repetition	NOUN
ejpam-6282	281	72	.	.	PUNCT
ejpam-6282	282	1	instead	instead	ADV
ejpam-6282	282	2	,	,	PUNCT
ejpam-6282	282	3	we	we	PRON
ejpam-6282	282	4	give	give	VERB
ejpam-6282	282	5	the	the	DET
ejpam-6282	282	6	sketch	sketch	NOUN
ejpam-6282	282	7	of	of	ADP
ejpam-6282	282	8	the	the	DET
ejpam-6282	282	9	proof	proof	NOUN
ejpam-6282	282	10	:	:	PUNCT
ejpam-6282	282	11	it	it	PRON
ejpam-6282	282	12	is	be	AUX
ejpam-6282	282	13	sufficient	sufficient	ADJ
ejpam-6282	282	14	to	to	PART
ejpam-6282	282	15	consider	consider	VERB
ejpam-6282	282	16	the	the	DET
ejpam-6282	282	17	proper	proper	ADJ
ejpam-6282	282	18	function	function	NOUN
ejpam-6282	282	19	α(t	α(t	PROPN
ejpam-6282	282	20	,	,	PUNCT
ejpam-6282	282	21	s	s	PART
ejpam-6282	282	22	)	)	PUNCT
ejpam-6282	282	23	=	=	PUNCT
ejpam-6282	282	24	ψ(s)−	ψ(s)−	PROPN
ejpam-6282	282	25	t	t	NOUN
ejpam-6282	282	26	in	in	ADP
ejpam-6282	282	27	the	the	DET
ejpam-6282	282	28	main	main	ADJ
ejpam-6282	282	29	theorem	theorem	NOUN
ejpam-6282	282	30	.	.	PUNCT
ejpam-6282	283	1	note	note	VERB
ejpam-6282	283	2	that	that	SCONJ
ejpam-6282	283	3	the	the	DET
ejpam-6282	283	4	famous	famous	ADJ
ejpam-6282	283	5	banach	banach	NOUN
ejpam-6282	283	6	’s	’s	PART
ejpam-6282	283	7	contraction	contraction	NOUN
ejpam-6282	283	8	principle	principle	NOUN
ejpam-6282	283	9	can	can	AUX
ejpam-6282	283	10	be	be	AUX
ejpam-6282	283	11	transformed	transform	VERB
ejpam-6282	283	12	into	into	ADP
ejpam-6282	283	13	an	an	DET
ejpam-6282	283	14	interpolative	interpolative	ADJ
ejpam-6282	283	15	metric	metric	ADJ
ejpam-6282	283	16	space	space	NOUN
ejpam-6282	283	17	as	as	SCONJ
ejpam-6282	283	18	follows	follow	VERB
ejpam-6282	283	19	.	.	PUNCT
ejpam-6282	284	1	corollary	corollary	ADJ
ejpam-6282	284	2	2	2	NUM
ejpam-6282	284	3	.	.	PUNCT
ejpam-6282	285	1	let	let	VERB
ejpam-6282	285	2	(	(	PUNCT
ejpam-6282	285	3	s	s	X
ejpam-6282	285	4	,	,	PUNCT
ejpam-6282	285	5	d	d	NOUN
ejpam-6282	285	6	)	)	PUNCT
ejpam-6282	285	7	be	be	AUX
ejpam-6282	285	8	a	a	DET
ejpam-6282	285	9	complete	complete	ADJ
ejpam-6282	285	10	(	(	PUNCT
ejpam-6282	285	11	ξ	ξ	PROPN
ejpam-6282	285	12	,	,	PUNCT
ejpam-6282	285	13	c	c	NOUN
ejpam-6282	285	14	)	)	PUNCT
ejpam-6282	285	15	ims	im	NOUN
ejpam-6282	285	16	,	,	PUNCT
ejpam-6282	285	17	and	and	CCONJ
ejpam-6282	285	18	let	let	VERB
ejpam-6282	285	19	t	t	NOUN
ejpam-6282	285	20	:	:	PUNCT
ejpam-6282	285	21	s	s	AUX
ejpam-6282	285	22	→	→	SYM
ejpam-6282	285	23	s	s	PART
ejpam-6282	285	24	be	be	AUX
ejpam-6282	285	25	a	a	DET
ejpam-6282	285	26	mapping	mapping	NOUN
ejpam-6282	285	27	.	.	PUNCT
ejpam-6282	286	1	if	if	SCONJ
ejpam-6282	286	2	there	there	PRON
ejpam-6282	286	3	is	be	VERB
ejpam-6282	286	4	an	an	DET
ejpam-6282	286	5	real	real	ADJ
ejpam-6282	286	6	number	number	NOUN
ejpam-6282	286	7	q	q	NOUN
ejpam-6282	286	8	∈	∈	PROPN
ejpam-6282	286	9	(	(	PUNCT
ejpam-6282	286	10	0	0	NUM
ejpam-6282	286	11	,	,	PUNCT
ejpam-6282	286	12	1	1	NUM
ejpam-6282	286	13	)	)	PUNCT
ejpam-6282	286	14	such	such	ADJ
ejpam-6282	286	15	that	that	SCONJ
ejpam-6282	286	16	d(tx	d(tx	PROPN
ejpam-6282	286	17	,	,	PUNCT
ejpam-6282	286	18	ty	ty	NOUN
ejpam-6282	286	19	)	)	PUNCT
ejpam-6282	286	20	≤	≤	NOUN
ejpam-6282	286	21	qd(x	qd(x	X
ejpam-6282	286	22	,	,	PUNCT
ejpam-6282	286	23	y	y	PROPN
ejpam-6282	286	24	)	)	PUNCT
ejpam-6282	286	25	,	,	PUNCT
ejpam-6282	286	26	(	(	PUNCT
ejpam-6282	286	27	3.2	3.2	NUM
ejpam-6282	286	28	)	)	PUNCT
ejpam-6282	286	29	for	for	ADP
ejpam-6282	286	30	all	all	DET
ejpam-6282	286	31	x	x	NOUN
ejpam-6282	286	32	,	,	PUNCT
ejpam-6282	286	33	y	y	PROPN
ejpam-6282	286	34	∈	∈	PROPN
ejpam-6282	286	35	s	s	PROPN
ejpam-6282	286	36	,	,	PUNCT
ejpam-6282	286	37	then	then	ADV
ejpam-6282	286	38	,	,	PUNCT
ejpam-6282	286	39	t	t	PROPN
ejpam-6282	286	40	guarantees	guarantee	VERB
ejpam-6282	286	41	to	to	PART
ejpam-6282	286	42	possess	possess	VERB
ejpam-6282	286	43	a	a	DET
ejpam-6282	286	44	unique	unique	ADJ
ejpam-6282	286	45	fixed	fix	VERB
ejpam-6282	286	46	point	point	NOUN
ejpam-6282	286	47	in	in	ADP
ejpam-6282	286	48	s.	s.	PROPN
ejpam-6282	286	49	sketch	sketch	PROPN
ejpam-6282	286	50	of	of	ADP
ejpam-6282	286	51	the	the	DET
ejpam-6282	286	52	proof	proof	NOUN
ejpam-6282	286	53	2	2	NUM
ejpam-6282	286	54	.	.	PUNCT
ejpam-6282	287	1	for	for	ADP
ejpam-6282	287	2	this	this	DET
ejpam-6282	287	3	corollary	corollary	NOUN
ejpam-6282	287	4	,	,	PUNCT
ejpam-6282	287	5	the	the	DET
ejpam-6282	287	6	full	full	ADJ
ejpam-6282	287	7	proof	proof	NOUN
ejpam-6282	287	8	is	be	AUX
ejpam-6282	287	9	the	the	DET
ejpam-6282	287	10	mimics	mimic	NOUN
ejpam-6282	287	11	of	of	ADP
ejpam-6282	287	12	the	the	DET
ejpam-6282	287	13	proof	proof	NOUN
ejpam-6282	287	14	of	of	ADP
ejpam-6282	287	15	the	the	DET
ejpam-6282	287	16	main	main	ADJ
ejpam-6282	287	17	theorem	theorem	NOUN
ejpam-6282	287	18	,	,	PUNCT
ejpam-6282	287	19	thus	thus	ADV
ejpam-6282	287	20	we	we	PRON
ejpam-6282	287	21	skip	skip	VERB
ejpam-6282	287	22	it	it	PRON
ejpam-6282	287	23	.	.	PUNCT
ejpam-6282	288	1	indeed	indeed	ADV
ejpam-6282	288	2	,	,	PUNCT
ejpam-6282	288	3	it	it	PRON
ejpam-6282	288	4	is	be	AUX
ejpam-6282	288	5	sufficient	sufficient	ADJ
ejpam-6282	288	6	to	to	PART
ejpam-6282	288	7	consider	consider	VERB
ejpam-6282	288	8	ψ(t	ψ(t	VERB
ejpam-6282	288	9	)	)	PUNCT
ejpam-6282	288	10	=	=	PUNCT
ejpam-6282	289	1	qt	qt	NOUN
ejpam-6282	289	2	where	where	SCONJ
ejpam-6282	289	3	q	q	NOUN
ejpam-6282	289	4	∈	∈	PROPN
ejpam-6282	289	5	(	(	PUNCT
ejpam-6282	289	6	0	0	NUM
ejpam-6282	289	7	,	,	PUNCT
ejpam-6282	289	8	1	1	NUM
ejpam-6282	289	9	)	)	PUNCT
ejpam-6282	289	10	.	.	PUNCT
ejpam-6282	290	1	note	note	VERB
ejpam-6282	290	2	that	that	SCONJ
ejpam-6282	290	3	regarding	regard	VERB
ejpam-6282	290	4	example	example	NOUN
ejpam-6282	290	5	3	3	NUM
ejpam-6282	290	6	,	,	PUNCT
ejpam-6282	290	7	we	we	PRON
ejpam-6282	290	8	may	may	AUX
ejpam-6282	290	9	list	list	VERB
ejpam-6282	290	10	several	several	ADJ
ejpam-6282	290	11	new	new	ADJ
ejpam-6282	290	12	fixed	fix	VERB
ejpam-6282	290	13	-	-	PUNCT
ejpam-6282	290	14	point	point	NOUN
ejpam-6282	290	15	theorems	theorem	NOUN
ejpam-6282	290	16	as	as	ADP
ejpam-6282	290	17	consequences	consequence	NOUN
ejpam-6282	290	18	of	of	ADP
ejpam-6282	290	19	theorem	theorem	NOUN
ejpam-6282	290	20	2	2	NUM
ejpam-6282	290	21	.	.	PUNCT
ejpam-6282	290	22	in	in	ADP
ejpam-6282	290	23	other	other	ADJ
ejpam-6282	290	24	words	word	NOUN
ejpam-6282	290	25	,	,	PUNCT
ejpam-6282	290	26	by	by	ADP
ejpam-6282	290	27	considering	consider	VERB
ejpam-6282	290	28	different	different	ADJ
ejpam-6282	290	29	simulation	simulation	NOUN
ejpam-6282	290	30	functions	function	NOUN
ejpam-6282	290	31	,	,	PUNCT
ejpam-6282	290	32	we	we	PRON
ejpam-6282	290	33	get	get	VERB
ejpam-6282	290	34	different	different	ADJ
ejpam-6282	290	35	fixed	fix	VERB
ejpam-6282	290	36	-	-	PUNCT
ejpam-6282	290	37	point	point	NOUN
ejpam-6282	290	38	theorems	theorem	NOUN
ejpam-6282	290	39	that	that	PRON
ejpam-6282	290	40	are	be	AUX
ejpam-6282	290	41	generalizations	generalization	NOUN
ejpam-6282	290	42	of	of	ADP
ejpam-6282	290	43	the	the	DET
ejpam-6282	290	44	existing	exist	VERB
ejpam-6282	290	45	results	result	NOUN
ejpam-6282	290	46	in	in	ADP
ejpam-6282	290	47	the	the	DET
ejpam-6282	290	48	setting	setting	NOUN
ejpam-6282	290	49	of	of	ADP
ejpam-6282	290	50	interpolative	interpolative	ADJ
ejpam-6282	290	51	metric	metric	ADJ
ejpam-6282	290	52	structure	structure	NOUN
ejpam-6282	290	53	.	.	PUNCT
ejpam-6282	291	1	further	far	ADV
ejpam-6282	291	2	,	,	PUNCT
ejpam-6282	291	3	employing	employ	VERB
ejpam-6282	291	4	different	different	ADJ
ejpam-6282	291	5	types	type	NOUN
ejpam-6282	291	6	of	of	ADP
ejpam-6282	291	7	ccomparison	ccomparison	NOUN
ejpam-6282	291	8	functions	function	NOUN
ejpam-6282	291	9	,	,	PUNCT
ejpam-6282	291	10	we	we	PRON
ejpam-6282	291	11	shall	shall	AUX
ejpam-6282	291	12	get	get	VERB
ejpam-6282	291	13	more	more	ADJ
ejpam-6282	291	14	results	result	NOUN
ejpam-6282	291	15	.	.	PUNCT
ejpam-6282	292	1	note	note	VERB
ejpam-6282	292	2	that	that	SCONJ
ejpam-6282	292	3	all	all	DET
ejpam-6282	292	4	these	these	DET
ejpam-6282	292	5	results	result	NOUN
ejpam-6282	292	6	improve	improve	VERB
ejpam-6282	292	7	and	and	CCONJ
ejpam-6282	292	8	generalize	generalize	VERB
ejpam-6282	292	9	the	the	DET
ejpam-6282	292	10	published	publish	VERB
ejpam-6282	292	11	results	result	NOUN
ejpam-6282	292	12	.	.	PUNCT
ejpam-6282	293	1	additionally	additionally	ADV
ejpam-6282	293	2	,	,	PUNCT
ejpam-6282	293	3	it	it	PRON
ejpam-6282	293	4	is	be	AUX
ejpam-6282	293	5	important	important	ADJ
ejpam-6282	293	6	to	to	PART
ejpam-6282	293	7	note	note	VERB
ejpam-6282	293	8	that	that	SCONJ
ejpam-6282	293	9	the	the	DET
ejpam-6282	293	10	findings	finding	NOUN
ejpam-6282	293	11	achieved	achieve	VERB
ejpam-6282	293	12	here	here	ADV
ejpam-6282	293	13	are	be	AUX
ejpam-6282	293	14	also	also	ADV
ejpam-6282	293	15	applicable	applicable	ADJ
ejpam-6282	293	16	in	in	ADP
ejpam-6282	293	17	the	the	DET
ejpam-6282	293	18	normal	normal	ADJ
ejpam-6282	293	19	metric	metric	ADJ
ejpam-6282	293	20	spaces	space	NOUN
ejpam-6282	293	21	.	.	PUNCT
ejpam-6282	294	1	g.	g.	PROPN
ejpam-6282	294	2	alsahli	alsahli	PROPN
ejpam-6282	294	3	,	,	PUNCT
ejpam-6282	294	4	s.	s.	PROPN
ejpam-6282	294	5	gülyaz	gülyaz	PROPN
ejpam-6282	294	6	-	-	PUNCT
ejpam-6282	294	7	özyurt	özyurt	PROPN
ejpam-6282	294	8	/	/	SYM
ejpam-6282	294	9	eur	eur	PROPN
ejpam-6282	294	10	.	.	PUNCT
ejpam-6282	295	1	j.	j.	PROPN
ejpam-6282	295	2	pure	pure	PROPN
ejpam-6282	295	3	appl	appl	PROPN
ejpam-6282	295	4	.	.	PROPN
ejpam-6282	295	5	math	math	PROPN
ejpam-6282	295	6	,	,	PUNCT
ejpam-6282	295	7	18	18	NUM
ejpam-6282	295	8	(	(	PUNCT
ejpam-6282	295	9	2	2	NUM
ejpam-6282	295	10	)	)	PUNCT
ejpam-6282	295	11	(	(	PUNCT
ejpam-6282	295	12	2025	2025	NUM
ejpam-6282	295	13	)	)	PUNCT
ejpam-6282	295	14	,	,	PUNCT
ejpam-6282	295	15	6282	6282	NUM
ejpam-6282	295	16	12	12	NUM
ejpam-6282	295	17	of	of	ADP
ejpam-6282	295	18	13	13	NUM
ejpam-6282	295	19	4	4	NUM
ejpam-6282	295	20	.	.	PUNCT
ejpam-6282	295	21	conclusion	conclusion	NOUN
ejpam-6282	295	22	this	this	DET
ejpam-6282	295	23	study	study	NOUN
ejpam-6282	295	24	aims	aim	VERB
ejpam-6282	295	25	to	to	PART
ejpam-6282	295	26	explore	explore	VERB
ejpam-6282	295	27	the	the	DET
ejpam-6282	295	28	existence	existence	NOUN
ejpam-6282	295	29	of	of	ADP
ejpam-6282	295	30	fixed	fix	VERB
ejpam-6282	295	31	points	point	NOUN
ejpam-6282	295	32	for	for	ADP
ejpam-6282	295	33	certain	certain	ADJ
ejpam-6282	295	34	contractions	contraction	NOUN
ejpam-6282	295	35	defined	define	VERB
ejpam-6282	295	36	with	with	ADP
ejpam-6282	295	37	the	the	DET
ejpam-6282	295	38	help	help	NOUN
ejpam-6282	295	39	of	of	ADP
ejpam-6282	295	40	simulation	simulation	NOUN
ejpam-6282	295	41	functions	function	NOUN
ejpam-6282	295	42	in	in	ADP
ejpam-6282	295	43	interpolative	interpolative	ADJ
ejpam-6282	295	44	metric	metric	ADJ
ejpam-6282	295	45	spaces	space	NOUN
ejpam-6282	295	46	,	,	PUNCT
ejpam-6282	295	47	which	which	PRON
ejpam-6282	295	48	is	be	AUX
ejpam-6282	295	49	a	a	DET
ejpam-6282	295	50	newly	newly	ADV
ejpam-6282	295	51	defined	define	VERB
ejpam-6282	295	52	abstract	abstract	ADJ
ejpam-6282	295	53	structure	structure	NOUN
ejpam-6282	295	54	.	.	PUNCT
ejpam-6282	296	1	these	these	DET
ejpam-6282	296	2	simulation	simulation	NOUN
ejpam-6282	296	3	functions	function	NOUN
ejpam-6282	296	4	are	be	AUX
ejpam-6282	296	5	quite	quite	ADV
ejpam-6282	296	6	special	special	ADJ
ejpam-6282	296	7	and	and	CCONJ
ejpam-6282	296	8	interesting	interesting	ADJ
ejpam-6282	296	9	,	,	PUNCT
ejpam-6282	296	10	and	and	CCONJ
ejpam-6282	296	11	they	they	PRON
ejpam-6282	296	12	enable	enable	VERB
ejpam-6282	296	13	us	we	PRON
ejpam-6282	296	14	to	to	PART
ejpam-6282	296	15	make	make	VERB
ejpam-6282	296	16	the	the	DET
ejpam-6282	296	17	numerous	numerous	ADJ
ejpam-6282	296	18	contractions	contraction	NOUN
ejpam-6282	296	19	in	in	ADP
ejpam-6282	296	20	the	the	DET
ejpam-6282	296	21	literature	literature	NOUN
ejpam-6282	296	22	the	the	DET
ejpam-6282	296	23	consequences	consequence	NOUN
ejpam-6282	296	24	of	of	ADP
ejpam-6282	296	25	our	our	PRON
ejpam-6282	296	26	presented	present	VERB
ejpam-6282	296	27	result	result	NOUN
ejpam-6282	296	28	.	.	PUNCT
ejpam-6282	297	1	this	this	PRON
ejpam-6282	297	2	is	be	AUX
ejpam-6282	297	3	our	our	PRON
ejpam-6282	297	4	first	first	ADJ
ejpam-6282	297	5	result	result	NOUN
ejpam-6282	297	6	in	in	ADP
ejpam-6282	297	7	this	this	DET
ejpam-6282	297	8	newly	newly	ADV
ejpam-6282	297	9	defined	define	VERB
ejpam-6282	297	10	structure	structure	NOUN
ejpam-6282	297	11	,	,	PUNCT
ejpam-6282	297	12	and	and	CCONJ
ejpam-6282	297	13	it	it	PRON
ejpam-6282	297	14	is	be	AUX
ejpam-6282	297	15	a	a	DET
ejpam-6282	297	16	very	very	ADV
ejpam-6282	297	17	basic	basic	ADJ
ejpam-6282	297	18	result	result	NOUN
ejpam-6282	297	19	.	.	PUNCT
ejpam-6282	298	1	consequently	consequently	ADV
ejpam-6282	298	2	,	,	PUNCT
ejpam-6282	298	3	this	this	DET
ejpam-6282	298	4	result	result	NOUN
ejpam-6282	298	5	can	can	AUX
ejpam-6282	298	6	be	be	AUX
ejpam-6282	298	7	enriched	enrich	VERB
ejpam-6282	298	8	in	in	ADP
ejpam-6282	298	9	several	several	ADJ
ejpam-6282	298	10	ways	way	NOUN
ejpam-6282	298	11	that	that	PRON
ejpam-6282	298	12	can	can	AUX
ejpam-6282	298	13	be	be	AUX
ejpam-6282	298	14	potential	potential	ADJ
ejpam-6282	298	15	future	future	ADJ
ejpam-6282	298	16	works	work	NOUN
ejpam-6282	298	17	.	.	PUNCT
ejpam-6282	299	1	as	as	ADP
ejpam-6282	299	2	a	a	DET
ejpam-6282	299	3	next	next	ADJ
ejpam-6282	299	4	step	step	NOUN
ejpam-6282	299	5	,	,	PUNCT
ejpam-6282	299	6	it	it	PRON
ejpam-6282	299	7	is	be	AUX
ejpam-6282	299	8	also	also	ADV
ejpam-6282	299	9	quite	quite	ADV
ejpam-6282	299	10	reasonable	reasonable	ADJ
ejpam-6282	299	11	to	to	PART
ejpam-6282	299	12	investigate	investigate	VERB
ejpam-6282	299	13	the	the	DET
ejpam-6282	299	14	possible	possible	ADJ
ejpam-6282	299	15	applications	application	NOUN
ejpam-6282	299	16	,	,	PUNCT
ejpam-6282	299	17	especially	especially	ADV
ejpam-6282	299	18	in	in	ADP
ejpam-6282	299	19	the	the	DET
ejpam-6282	299	20	economy	economy	NOUN
ejpam-6282	299	21	and	and	CCONJ
ejpam-6282	299	22	industrial	industrial	ADJ
ejpam-6282	299	23	engineering	engineering	NOUN
ejpam-6282	299	24	.	.	PUNCT
ejpam-6282	300	1	in	in	ADP
ejpam-6282	300	2	such	such	ADJ
ejpam-6282	300	3	generalizations	generalization	NOUN
ejpam-6282	300	4	,	,	PUNCT
ejpam-6282	300	5	one	one	NUM
ejpam-6282	300	6	of	of	ADP
ejpam-6282	300	7	the	the	DET
ejpam-6282	300	8	remarkable	remarkable	ADJ
ejpam-6282	300	9	studies	study	NOUN
ejpam-6282	300	10	is	be	AUX
ejpam-6282	300	11	finding	find	VERB
ejpam-6282	300	12	an	an	DET
ejpam-6282	300	13	answer	answer	NOUN
ejpam-6282	300	14	to	to	ADP
ejpam-6282	300	15	the	the	DET
ejpam-6282	300	16	following	following	ADJ
ejpam-6282	300	17	question	question	NOUN
ejpam-6282	300	18	:	:	PUNCT
ejpam-6282	300	19	in	in	ADP
ejpam-6282	300	20	which	which	PRON
ejpam-6282	300	21	abstract	abstract	ADJ
ejpam-6282	300	22	structure	structure	NOUN
ejpam-6282	300	23	does	do	VERB
ejpam-6282	300	24	,	,	PUNCT
ejpam-6282	300	25	picard	picard	NOUN
ejpam-6282	300	26	sequence	sequence	NOUN
ejpam-6282	300	27	converge	converge	VERB
ejpam-6282	300	28	fastest	fast	ADV
ejpam-6282	300	29	?	?	PUNCT
ejpam-6282	301	1	in	in	ADP
ejpam-6282	301	2	other	other	ADJ
ejpam-6282	301	3	words	word	NOUN
ejpam-6282	301	4	,	,	PUNCT
ejpam-6282	301	5	how	how	SCONJ
ejpam-6282	301	6	can	can	AUX
ejpam-6282	301	7	one	one	PRON
ejpam-6282	301	8	compare	compare	VERB
ejpam-6282	301	9	the	the	DET
ejpam-6282	301	10	rates	rate	NOUN
ejpam-6282	301	11	of	of	ADP
ejpam-6282	301	12	convergence	convergence	NOUN
ejpam-6282	301	13	in	in	ADP
ejpam-6282	301	14	these	these	DET
ejpam-6282	301	15	distinct	distinct	ADJ
ejpam-6282	301	16	structures	structure	NOUN
ejpam-6282	301	17	?	?	PUNCT
ejpam-6282	302	1	references	reference	NOUN
ejpam-6282	302	2	[	[	X
ejpam-6282	302	3	1	1	NUM
ejpam-6282	302	4	]	]	PUNCT
ejpam-6282	302	5	banach	banach	NOUN
ejpam-6282	302	6	,	,	PUNCT
ejpam-6282	302	7	s.	s.	PROPN
ejpam-6282	302	8	sur	sur	PROPN
ejpam-6282	302	9	les	les	PROPN
ejpam-6282	302	10	opérations	opération	NOUN
ejpam-6282	302	11	dans	dan	NOUN
ejpam-6282	302	12	les	les	X
ejpam-6282	302	13	ensembles	ensemble	NOUN
ejpam-6282	302	14	abstraits	abstrait	NOUN
ejpam-6282	302	15	et	et	PROPN
ejpam-6282	302	16	leur	leur	X
ejpam-6282	302	17	application	application	PROPN
ejpam-6282	302	18	aux	aux	PROPN
ejpam-6282	302	19	équations	équations	PROPN
ejpam-6282	302	20	intégrales	intégrale	NOUN
ejpam-6282	302	21	,	,	PUNCT
ejpam-6282	302	22	fund	fund	NOUN
ejpam-6282	302	23	.	.	PUNCT
ejpam-6282	303	1	math	math	NOUN
ejpam-6282	303	2	.	.	PUNCT
ejpam-6282	304	1	,3	,3	PUNCT
ejpam-6282	304	2	,	,	PUNCT
ejpam-6282	304	3	133	133	NUM
ejpam-6282	304	4	-	-	SYM
ejpam-6282	304	5	181	181	NUM
ejpam-6282	304	6	,	,	PUNCT
ejpam-6282	304	7	1922	1922	NUM
ejpam-6282	304	8	.	.	PUNCT
ejpam-6282	305	1	[	[	X
ejpam-6282	305	2	2	2	NUM
ejpam-6282	305	3	]	]	SYM
ejpam-6282	305	4	r.m.t	r.m.t	NOUN
ejpam-6282	305	5	.	.	PUNCT
ejpam-6282	305	6	bianchini	bianchini	PROPN
ejpam-6282	305	7	,	,	PUNCT
ejpam-6282	305	8	su	su	PROPN
ejpam-6282	305	9	un	un	PROPN
ejpam-6282	305	10	problema	problema	PROPN
ejpam-6282	305	11	di	di	PROPN
ejpam-6282	305	12	s.	s.	PROPN
ejpam-6282	305	13	reich	reich	PROPN
ejpam-6282	305	14	riguardante	riguardante	PROPN
ejpam-6282	305	15	la	la	PROPN
ejpam-6282	305	16	teoria	teoria	PROPN
ejpam-6282	305	17	del	del	PROPN
ejpam-6282	305	18	punti	punti	PROPN
ejpam-6282	305	19	fissi	fissi	PROPN
ejpam-6282	305	20	,	,	PUNCT
ejpam-6282	305	21	boll	boll	NOUN
ejpam-6282	305	22	.	.	PUNCT
ejpam-6282	306	1	un	un	PROPN
ejpam-6282	306	2	.	.	PROPN
ejpam-6282	306	3	mat	mat	PROPN
ejpam-6282	306	4	.	.	PUNCT
ejpam-6282	306	5	ital	ital	PROPN
ejpam-6282	306	6	.	.	PROPN
ejpam-6282	306	7	,	,	PUNCT
ejpam-6282	306	8	5	5	NUM
ejpam-6282	306	9	,	,	PUNCT
ejpam-6282	306	10	103	103	NUM
ejpam-6282	306	11	-	-	SYM
ejpam-6282	306	12	108	108	NUM
ejpam-6282	306	13	,	,	PUNCT
ejpam-6282	306	14	1972	1972	NUM
ejpam-6282	306	15	.	.	PUNCT
ejpam-6282	307	1	[	[	X
ejpam-6282	307	2	3	3	X
ejpam-6282	307	3	]	]	PUNCT
ejpam-6282	307	4	v.	v.	CCONJ
ejpam-6282	307	5	berinde	berinde	NOUN
ejpam-6282	307	6	,	,	PUNCT
ejpam-6282	307	7	contracţii	contracţii	NOUN
ejpam-6282	307	8	generalizate	generalizate	VERB
ejpam-6282	307	9	şi	şi	NOUN
ejpam-6282	307	10	aplicaţii	aplicaţii	NOUN
ejpam-6282	307	11	,	,	PUNCT
ejpam-6282	307	12	editura	editura	NOUN
ejpam-6282	307	13	club	club	NOUN
ejpam-6282	307	14	press	press	NOUN
ejpam-6282	307	15	22	22	NUM
ejpam-6282	307	16	,	,	PUNCT
ejpam-6282	307	17	baia	baia	PROPN
ejpam-6282	307	18	mare	mare	PROPN
ejpam-6282	307	19	,	,	PUNCT
ejpam-6282	307	20	1997	1997	NUM
ejpam-6282	307	21	.	.	PUNCT
ejpam-6282	308	1	[	[	X
ejpam-6282	308	2	4	4	NUM
ejpam-6282	308	3	]	]	X
ejpam-6282	308	4	brouwer	brouwer	X
ejpam-6282	308	5	,	,	PUNCT
ejpam-6282	308	6	ueber	ueber	PROPN
ejpam-6282	308	7	abbildungen	abbildungen	PROPN
ejpam-6282	308	8	von	von	PROPN
ejpam-6282	308	9	mannigfaltigkeiten	mannigfaltigkeiten	PROPN
ejpam-6282	308	10	.	.	PUNCT
ejpam-6282	309	1	math	math	PROPN
ejpam-6282	309	2	.	.	PUNCT
ejpam-6282	310	1	ann	ann	PROPN
ejpam-6282	310	2	.	.	PROPN
ejpam-6282	310	3	1912	1912	NUM
ejpam-6282	310	4	,	,	PUNCT
ejpam-6282	310	5	71	71	NUM
ejpam-6282	310	6	,	,	PUNCT
ejpam-6282	310	7	97–115	97–115	NUM
ejpam-6282	310	8	.	.	PUNCT
ejpam-6282	311	1	[	[	X
ejpam-6282	311	2	5	5	NUM
ejpam-6282	311	3	]	]	PUNCT
ejpam-6282	311	4	r.	r.	NOUN
ejpam-6282	311	5	caccioppoli	caccioppoli	PROPN
ejpam-6282	311	6	,	,	PUNCT
ejpam-6282	311	7	una	una	PROPN
ejpam-6282	311	8	teorema	teorema	PROPN
ejpam-6282	311	9	generale	generale	PROPN
ejpam-6282	311	10	sull’esistenza	sull’esistenza	PROPN
ejpam-6282	311	11	di	di	X
ejpam-6282	311	12	elementi	elementi	PROPN
ejpam-6282	311	13	uniti	uniti	PROPN
ejpam-6282	311	14	in	in	ADP
ejpam-6282	311	15	una	una	PROPN
ejpam-6282	311	16	transformazione	transformazione	PROPN
ejpam-6282	311	17	funzionale	funzionale	PROPN
ejpam-6282	311	18	,	,	PUNCT
ejpam-6282	311	19	ren	ren	PROPN
ejpam-6282	311	20	.	.	PUNCT
ejpam-6282	311	21	accad	accad	PROPN
ejpam-6282	311	22	.	.	PUNCT
ejpam-6282	312	1	naz	naz	PROPN
ejpam-6282	312	2	lincei	lincei	NOUN
ejpam-6282	312	3	11	11	NUM
ejpam-6282	312	4	794	794	NUM
ejpam-6282	312	5	-	-	SYM
ejpam-6282	312	6	799	799	NUM
ejpam-6282	312	7	,	,	PUNCT
ejpam-6282	312	8	1930	1930	NUM
ejpam-6282	312	9	.	.	PUNCT
ejpam-6282	313	1	[	[	X
ejpam-6282	313	2	6	6	NUM
ejpam-6282	313	3	]	]	PUNCT
ejpam-6282	313	4	e.	e.	PROPN
ejpam-6282	313	5	karapınar	karapınar	PROPN
ejpam-6282	313	6	,	,	PUNCT
ejpam-6282	313	7	an	an	DET
ejpam-6282	313	8	open	open	ADJ
ejpam-6282	313	9	discussion	discussion	NOUN
ejpam-6282	313	10	:	:	PUNCT
ejpam-6282	313	11	interpolative	interpolative	ADJ
ejpam-6282	313	12	metric	metric	ADJ
ejpam-6282	313	13	spaces	space	NOUN
ejpam-6282	313	14	,	,	PUNCT
ejpam-6282	313	15	advances	advance	NOUN
ejpam-6282	313	16	in	in	ADP
ejpam-6282	313	17	the	the	DET
ejpam-6282	313	18	theory	theory	NOUN
ejpam-6282	313	19	of	of	ADP
ejpam-6282	313	20	nonlinear	nonlinear	ADJ
ejpam-6282	313	21	analysis	analysis	NOUN
ejpam-6282	313	22	and	and	CCONJ
ejpam-6282	313	23	its	its	PRON
ejpam-6282	313	24	application	application	NOUN
ejpam-6282	313	25	,	,	PUNCT
ejpam-6282	313	26	7(5	7(5	NUM
ejpam-6282	313	27	)	)	PUNCT
ejpam-6282	313	28	,	,	PUNCT
ejpam-6282	313	29	24	24	NUM
ejpam-6282	313	30	-	-	SYM
ejpam-6282	313	31	27	27	NUM
ejpam-6282	313	32	(	(	PUNCT
ejpam-6282	313	33	2023	2023	NUM
ejpam-6282	313	34	)	)	PUNCT
ejpam-6282	313	35	.	.	PUNCT
ejpam-6282	314	1	https://doi.org/10.17762/atnaa.v7.i5.323	https://doi.org/10.17762/atnaa.v7.i5.323	PROPN
ejpam-6282	315	1	[	[	X
ejpam-6282	315	2	7	7	X
ejpam-6282	315	3	]	]	X
ejpam-6282	315	4	e.	e.	PROPN
ejpam-6282	315	5	karapınar	karapınar	PROPN
ejpam-6282	315	6	,	,	PUNCT
ejpam-6282	315	7	a	a	DET
ejpam-6282	315	8	new	new	ADJ
ejpam-6282	315	9	proposal	proposal	NOUN
ejpam-6282	315	10	:	:	PUNCT
ejpam-6282	315	11	interpolative	interpolative	ADJ
ejpam-6282	315	12	metric	metric	ADJ
ejpam-6282	315	13	spaces	space	NOUN
ejpam-6282	315	14	,	,	PUNCT
ejpam-6282	315	15	filomat	filomat	PROPN
ejpam-6282	315	16	38(22	38(22	NOUN
ejpam-6282	315	17	)	)	PUNCT
ejpam-6282	315	18	,	,	PUNCT
ejpam-6282	315	19	7729–7734	7729–7734	NUM
ejpam-6282	315	20	,	,	PUNCT
ejpam-6282	315	21	2024	2024	NUM
ejpam-6282	315	22	.	.	PUNCT
ejpam-6282	315	23	https://doi.org/10.2298/fil2422729k	https://doi.org/10.2298/fil2422729k	X
ejpam-6282	316	1	[	[	X
ejpam-6282	316	2	8	8	NUM
ejpam-6282	316	3	]	]	PUNCT
ejpam-6282	316	4	e.	e.	PROPN
ejpam-6282	316	5	karapınar	karapınar	PROPN
ejpam-6282	316	6	,	,	PUNCT
ejpam-6282	316	7	recent	recent	ADJ
ejpam-6282	316	8	advances	advance	NOUN
ejpam-6282	316	9	on	on	ADP
ejpam-6282	316	10	metric	metric	ADJ
ejpam-6282	316	11	fixed	fix	VERB
ejpam-6282	316	12	point	point	NOUN
ejpam-6282	316	13	theory	theory	NOUN
ejpam-6282	316	14	:	:	PUNCT
ejpam-6282	316	15	a	a	DET
ejpam-6282	316	16	review	review	NOUN
ejpam-6282	316	17	,	,	PUNCT
ejpam-6282	316	18	applied	apply	VERB
ejpam-6282	316	19	and	and	CCONJ
ejpam-6282	316	20	computational	computational	ADJ
ejpam-6282	316	21	mathematics	mathematic	NOUN
ejpam-6282	316	22	an	an	DET
ejpam-6282	316	23	international	international	ADJ
ejpam-6282	316	24	journal	journal	NOUN
ejpam-6282	316	25	,	,	PUNCT
ejpam-6282	316	26	22(1	22(1	NUM
ejpam-6282	316	27	)	)	PUNCT
ejpam-6282	316	28	,	,	PUNCT
ejpam-6282	316	29	3	3	NUM
ejpam-6282	316	30	-	-	SYM
ejpam-6282	316	31	30	30	NUM
ejpam-6282	316	32	(	(	PUNCT
ejpam-6282	316	33	2023	2023	NUM
ejpam-6282	316	34	)	)	PUNCT
ejpam-6282	316	35	.	.	PUNCT
ejpam-6282	317	1	[	[	X
ejpam-6282	317	2	9	9	X
ejpam-6282	317	3	]	]	PUNCT
ejpam-6282	317	4	e.	e.	PROPN
ejpam-6282	317	5	karapınar	karapınar	PROPN
ejpam-6282	317	6	,	,	PUNCT
ejpam-6282	317	7	r.	r.	PROPN
ejpam-6282	317	8	p.	p.	PROPN
ejpam-6282	317	9	agarwal	agarwal	PROPN
ejpam-6282	317	10	fixed	fix	VERB
ejpam-6282	317	11	point	point	NOUN
ejpam-6282	317	12	theory	theory	NOUN
ejpam-6282	317	13	in	in	ADP
ejpam-6282	317	14	generalized	generalized	ADJ
ejpam-6282	317	15	metric	metric	ADJ
ejpam-6282	317	16	spaces	space	NOUN
ejpam-6282	317	17	,	,	PUNCT
ejpam-6282	317	18	2023	2023	NUM
ejpam-6282	317	19	,	,	PUNCT
ejpam-6282	317	20	synthesis	synthesis	NOUN
ejpam-6282	317	21	lectures	lecture	NOUN
ejpam-6282	317	22	on	on	ADP
ejpam-6282	317	23	mathematics	mathematics	PROPN
ejpam-6282	317	24	&	&	CCONJ
ejpam-6282	317	25	statistics	statistic	NOUN
ejpam-6282	317	26	,	,	PUNCT
ejpam-6282	317	27	springer	springer	NOUN
ejpam-6282	317	28	cham	cham	VERB
ejpam-6282	317	29	https://doi.org/10.1007/978-3-031-14969-6	https://doi.org/10.1007/978-3-031-14969-6	PROPN
ejpam-6282	317	30	[	[	X
ejpam-6282	317	31	10	10	NUM
ejpam-6282	317	32	]	]	X
ejpam-6282	317	33	e.	e.	PROPN
ejpam-6282	317	34	karapınar	karapınar	PROPN
ejpam-6282	317	35	,	,	PUNCT
ejpam-6282	317	36	b.samet	b.samet	NOUN
ejpam-6282	317	37	,	,	PUNCT
ejpam-6282	317	38	generalized	generalize	VERB
ejpam-6282	317	39	ξ	ξ	DET
ejpam-6282	317	40	−	−	NOUN
ejpam-6282	317	41	ψ	ψ	NOUN
ejpam-6282	317	42	-	-	ADJ
ejpam-6282	317	43	contractive	contractive	ADJ
ejpam-6282	317	44	type	type	NOUN
ejpam-6282	317	45	mappings	mapping	NOUN
ejpam-6282	317	46	and	and	CCONJ
ejpam-6282	317	47	related	relate	VERB
ejpam-6282	317	48	fixed	fix	VERB
ejpam-6282	317	49	point	point	NOUN
ejpam-6282	317	50	theorems	theorem	NOUN
ejpam-6282	317	51	with	with	ADP
ejpam-6282	317	52	applications	application	NOUN
ejpam-6282	317	53	abstract	abstract	ADJ
ejpam-6282	317	54	and	and	CCONJ
ejpam-6282	317	55	applied	apply	VERB
ejpam-6282	317	56	analysis	analysis	NOUN
ejpam-6282	317	57	volume	volume	NOUN
ejpam-6282	317	58	2012	2012	NUM
ejpam-6282	317	59	,	,	PUNCT
ejpam-6282	317	60	article	article	NOUN
ejpam-6282	317	61	i	i	PROPN
ejpam-6282	317	62	d	d	PROPN
ejpam-6282	317	63	793486	793486	NUM
ejpam-6282	317	64	,	,	PUNCT
ejpam-6282	317	65	17	17	NUM
ejpam-6282	317	66	pages	page	NOUN
ejpam-6282	317	67	[	[	X
ejpam-6282	317	68	11	11	NUM
ejpam-6282	317	69	]	]	PUNCT
ejpam-6282	317	70	e.	e.	PROPN
ejpam-6282	317	71	picard	picard	PROPN
ejpam-6282	317	72	,	,	PUNCT
ejpam-6282	317	73	memoire	memoire	PROPN
ejpam-6282	317	74	sur	sur	PROPN
ejpam-6282	317	75	la	la	PROPN
ejpam-6282	317	76	theorie	theorie	PROPN
ejpam-6282	317	77	des	des	PROPN
ejpam-6282	317	78	equations	equations	PROPN
ejpam-6282	317	79	aux	aux	PROPN
ejpam-6282	317	80	derivees	derive	VERB
ejpam-6282	317	81	partielles	partielle	NOUN
ejpam-6282	317	82	et	et	PROPN
ejpam-6282	317	83	la	la	PROPN
ejpam-6282	317	84	methode	methode	PROPN
ejpam-6282	317	85	des	des	PROPN
ejpam-6282	317	86	approximations	approximations	PROPN
ejpam-6282	317	87	successives	successive	NOUN
ejpam-6282	317	88	,	,	PUNCT
ejpam-6282	317	89	j.	j.	PROPN
ejpam-6282	317	90	math	math	PROPN
ejpam-6282	317	91	.	.	PUNCT
ejpam-6282	318	1	pures	pure	NOUN
ejpam-6282	318	2	et	et	PROPN
ejpam-6282	318	3	appl	appl	PROPN
ejpam-6282	318	4	.	.	PROPN
ejpam-6282	318	5	,	,	PUNCT
ejpam-6282	318	6	6	6	NUM
ejpam-6282	318	7	,	,	PUNCT
ejpam-6282	318	8	145–210	145–210	NUM
ejpam-6282	318	9	,	,	PUNCT
ejpam-6282	318	10	1890	1890	NUM
ejpam-6282	318	11	.	.	PUNCT
ejpam-6282	319	1	[	[	X
ejpam-6282	319	2	12	12	NUM
ejpam-6282	319	3	]	]	X
ejpam-6282	319	4	i.	i.	PROPN
ejpam-6282	319	5	a.	a.	PROPN
ejpam-6282	319	6	rus	rus	PROPN
ejpam-6282	319	7	,	,	PUNCT
ejpam-6282	319	8	generalized	generalized	ADJ
ejpam-6282	319	9	contractions	contraction	NOUN
ejpam-6282	319	10	and	and	CCONJ
ejpam-6282	319	11	applications	application	NOUN
ejpam-6282	319	12	,	,	PUNCT
ejpam-6282	319	13	cluj	cluj	PROPN
ejpam-6282	319	14	university	university	NOUN
ejpam-6282	319	15	press	press	NOUN
ejpam-6282	319	16	,	,	PUNCT
ejpam-6282	319	17	cluj	cluj	PROPN
ejpam-6282	319	18	-	-	PUNCT
ejpam-6282	319	19	napoca	napoca	NOUN
ejpam-6282	319	20	,	,	PUNCT
ejpam-6282	319	21	2001	2001	NUM
ejpam-6282	319	22	.	.	PUNCT
ejpam-6282	320	1	g.	g.	PROPN
ejpam-6282	320	2	alsahli	alsahli	PROPN
ejpam-6282	320	3	,	,	PUNCT
ejpam-6282	320	4	s.	s.	PROPN
ejpam-6282	320	5	gülyaz	gülyaz	PROPN
ejpam-6282	320	6	-	-	PUNCT
ejpam-6282	320	7	özyurt	özyurt	PROPN
ejpam-6282	320	8	/	/	SYM
ejpam-6282	320	9	eur	eur	PROPN
ejpam-6282	320	10	.	.	PUNCT
ejpam-6282	321	1	j.	j.	PROPN
ejpam-6282	321	2	pure	pure	PROPN
ejpam-6282	321	3	appl	appl	PROPN
ejpam-6282	321	4	.	.	PROPN
ejpam-6282	321	5	math	math	PROPN
ejpam-6282	321	6	,	,	PUNCT
ejpam-6282	321	7	18	18	NUM
ejpam-6282	321	8	(	(	PUNCT
ejpam-6282	321	9	2	2	NUM
ejpam-6282	321	10	)	)	PUNCT
ejpam-6282	321	11	(	(	PUNCT
ejpam-6282	321	12	2025	2025	NUM
ejpam-6282	321	13	)	)	PUNCT
ejpam-6282	321	14	,	,	PUNCT
ejpam-6282	321	15	6282	6282	NUM
ejpam-6282	321	16	13	13	NUM
ejpam-6282	321	17	of	of	ADP
ejpam-6282	321	18	13	13	NUM
ejpam-6282	321	19	[	[	SYM
ejpam-6282	321	20	13	13	NUM
ejpam-6282	321	21	]	]	PUNCT
ejpam-6282	321	22	alsubaie	alsubaie	NOUN
ejpam-6282	321	23	,	,	PUNCT
ejpam-6282	321	24	r.	r.	PROPN
ejpam-6282	321	25	;	;	PUNCT
ejpam-6282	321	26	alqahtani	alqahtani	PROPN
ejpam-6282	321	27	,	,	PUNCT
ejpam-6282	321	28	b.	b.	PROPN
ejpam-6282	321	29	;	;	PUNCT
ejpam-6282	321	30	karapinar	karapinar	PROPN
ejpam-6282	321	31	,	,	PUNCT
ejpam-6282	321	32	e.	e.	PROPN
ejpam-6282	321	33	;	;	PUNCT
ejpam-6282	321	34	hierro	hierro	PROPN
ejpam-6282	321	35	,	,	PUNCT
ejpam-6282	321	36	a.f.r.l	a.f.r.l	PROPN
ejpam-6282	321	37	.	.	PROPN
ejpam-6282	321	38	extended	extend	VERB
ejpam-6282	321	39	simulation	simulation	NOUN
ejpam-6282	321	40	function	function	NOUN
ejpam-6282	321	41	via	via	ADP
ejpam-6282	321	42	rational	rational	ADJ
ejpam-6282	321	43	expressions	expression	NOUN
ejpam-6282	321	44	mathematics	mathematic	NOUN
ejpam-6282	321	45	8	8	NUM
ejpam-6282	321	46	,	,	PUNCT
ejpam-6282	321	47	710	710	NUM
ejpam-6282	321	48	2020	2020	NUM
ejpam-6282	321	49	.	.	PUNCT
ejpam-6282	322	1	[	[	X
ejpam-6282	322	2	14	14	NUM
ejpam-6282	322	3	]	]	X
ejpam-6282	322	4	khojasteh	khojasteh	PROPN
ejpam-6282	322	5	,	,	PUNCT
ejpam-6282	322	6	f.	f.	PROPN
ejpam-6282	322	7	;	;	PUNCT
ejpam-6282	322	8	shukla	shukla	PROPN
ejpam-6282	322	9	,	,	PUNCT
ejpam-6282	322	10	s.	s.	PROPN
ejpam-6282	322	11	;	;	PUNCT
ejpam-6282	322	12	radenović	radenović	VERB
ejpam-6282	322	13	,	,	PUNCT
ejpam-6282	322	14	s.	s.	PROPN
ejpam-6282	322	15	a	a	DET
ejpam-6282	322	16	new	new	ADJ
ejpam-6282	322	17	approach	approach	NOUN
ejpam-6282	322	18	to	to	ADP
ejpam-6282	322	19	the	the	DET
ejpam-6282	322	20	study	study	NOUN
ejpam-6282	322	21	of	of	ADP
ejpam-6282	322	22	fixed	fix	VERB
ejpam-6282	322	23	point	point	NOUN
ejpam-6282	322	24	theorems	theorem	NOUN
ejpam-6282	322	25	via	via	ADP
ejpam-6282	322	26	simulation	simulation	NOUN
ejpam-6282	322	27	functions	function	NOUN
ejpam-6282	322	28	.	.	PUNCT
ejpam-6282	323	1	filomat	filomat	PROPN
ejpam-6282	323	2	2015	2015	NUM
ejpam-6282	323	3	,	,	PUNCT
ejpam-6282	323	4	29	29	NUM
ejpam-6282	323	5	,	,	PUNCT
ejpam-6282	323	6	1189–1194	1189–1194	NUM
ejpam-6282	323	7	.	.	PUNCT
ejpam-6282	324	1	[	[	X
ejpam-6282	324	2	15	15	NUM
ejpam-6282	324	3	]	]	X
ejpam-6282	324	4	alqahtani	alqahtani	ADJ
ejpam-6282	324	5	,	,	PUNCT
ejpam-6282	324	6	o.	o.	PROPN
ejpam-6282	324	7	;	;	PUNCT
ejpam-6282	324	8	karapinar	karapinar	PROPN
ejpam-6282	324	9	,	,	PUNCT
ejpam-6282	324	10	e.	e.	PROPN
ejpam-6282	325	1	a	a	DET
ejpam-6282	325	2	bilateral	bilateral	ADJ
ejpam-6282	325	3	contraction	contraction	NOUN
ejpam-6282	325	4	via	via	ADP
ejpam-6282	325	5	simulation	simulation	NOUN
ejpam-6282	325	6	function	function	PROPN
ejpam-6282	325	7	filomat	filomat	NOUN
ejpam-6282	325	8	,	,	PUNCT
ejpam-6282	325	9	33:15	33:15	NUM
ejpam-6282	325	10	,	,	PUNCT
ejpam-6282	325	11	4837–4843	4837–4843	NUM
ejpam-6282	325	12	2019	2019	NUM
ejpam-6282	325	13	.	.	PUNCT
ejpam-6282	326	1	[	[	X
ejpam-6282	326	2	16	16	NUM
ejpam-6282	326	3	]	]	X
ejpam-6282	326	4	alghamdi	alghamdi	NOUN
ejpam-6282	326	5	,	,	PUNCT
ejpam-6282	326	6	m.a	m.a	PROPN
ejpam-6282	326	7	.	.	PROPN
ejpam-6282	326	8	;	;	PUNCT
ejpam-6282	326	9	gulyaz	gulyaz	NOUN
ejpam-6282	326	10	-	-	PUNCT
ejpam-6282	326	11	ozyurt	ozyurt	NOUN
ejpam-6282	326	12	,	,	PUNCT
ejpam-6282	326	13	s.	s.	PROPN
ejpam-6282	326	14	;	;	PUNCT
ejpam-6282	326	15	karapinar	karapinar	PROPN
ejpam-6282	326	16	,	,	PUNCT
ejpam-6282	326	17	e.	e.	PROPN
ejpam-6282	326	18	a	a	DET
ejpam-6282	326	19	note	note	NOUN
ejpam-6282	326	20	on	on	ADP
ejpam-6282	326	21	extended	extended	ADJ
ejpam-6282	326	22	zcontraction	zcontraction	NOUN
ejpam-6282	326	23	mathematics	mathematic	NOUN
ejpam-6282	326	24	2020	2020	NUM
ejpam-6282	326	25	,	,	PUNCT
ejpam-6282	326	26	8	8	NUM
ejpam-6282	326	27	,	,	PUNCT
ejpam-6282	326	28	195	195	NUM
ejpam-6282	326	29	.	.	PUNCT
ejpam-6282	327	1	[	[	X
ejpam-6282	327	2	17	17	NUM
ejpam-6282	327	3	]	]	X
ejpam-6282	327	4	agarwal	agarwal	PROPN
ejpam-6282	327	5	,	,	PUNCT
ejpam-6282	327	6	r.	r.	PROPN
ejpam-6282	327	7	p.	p.	PROPN
ejpam-6282	327	8	;	;	PUNCT
ejpam-6282	327	9	karapinar	karapinar	PROPN
ejpam-6282	327	10	,	,	PUNCT
ejpam-6282	327	11	e.	e.	PROPN
ejpam-6282	327	12	interpolative	interpolative	PROPN
ejpam-6282	327	13	rus	rus	PROPN
ejpam-6282	327	14	-	-	PUNCT
ejpam-6282	327	15	reich	reich	NOUN
ejpam-6282	327	16	-	-	PUNCT
ejpam-6282	327	17	ciric	ciric	ADJ
ejpam-6282	327	18	type	type	NOUN
ejpam-6282	327	19	contractions	contraction	NOUN
ejpam-6282	327	20	via	via	ADP
ejpam-6282	327	21	simulation	simulation	NOUN
ejpam-6282	327	22	functions	function	NOUN
ejpam-6282	327	23	an	an	PROPN
ejpam-6282	327	24	.	.	PUNCT
ejpam-6282	327	25	st	st	PROPN
ejpam-6282	327	26	.	.	PROPN
ejpam-6282	327	27	univ	univ	PROPN
ejpam-6282	327	28	.	.	PUNCT
ejpam-6282	328	1	ovidius	ovidius	PROPN
ejpam-6282	328	2	constanta	constanta	PROPN
ejpam-6282	328	3	,	,	PUNCT
ejpam-6282	328	4	ser	ser	NOUN
ejpam-6282	328	5	.	.	PROPN
ejpam-6282	328	6	mat	mat	PROPN
ejpam-6282	328	7	.	.	PROPN
ejpam-6282	328	8	27	27	NUM
ejpam-6282	328	9	(	(	PUNCT
ejpam-6282	328	10	3	3	NUM
ejpam-6282	328	11	)	)	PUNCT
ejpam-6282	328	12	,	,	PUNCT
ejpam-6282	328	13	2019	2019	NUM
ejpam-6282	328	14	,	,	PUNCT
ejpam-6282	328	15	137–152	137–152	NUM
ejpam-6282	328	16	.	.	PUNCT
ejpam-6282	329	1	[	[	X
ejpam-6282	329	2	18	18	NUM
ejpam-6282	329	3	]	]	PUNCT
ejpam-6282	329	4	aydi	aydi	ADJ
ejpam-6282	329	5	,	,	PUNCT
ejpam-6282	329	6	h.	h.	PROPN
ejpam-6282	329	7	;	;	PUNCT
ejpam-6282	329	8	karapinar	karapinar	PROPN
ejpam-6282	329	9	,	,	PUNCT
ejpam-6282	329	10	e.	e.	PROPN
ejpam-6282	329	11	;	;	PUNCT
ejpam-6282	329	12	rakocevic	rakocevic	PROPN
ejpam-6282	329	13	,	,	PUNCT
ejpam-6282	329	14	v.	v.	ADV
ejpam-6282	329	15	,	,	PUNCT
ejpam-6282	329	16	nonunique	nonunique	ADJ
ejpam-6282	329	17	fixed	fix	VERB
ejpam-6282	329	18	point	point	NOUN
ejpam-6282	329	19	theorems	theorem	NOUN
ejpam-6282	329	20	on	on	ADP
ejpam-6282	329	21	b	b	X
ejpam-6282	329	22	-	-	ADJ
ejpam-6282	329	23	metric	metric	ADJ
ejpam-6282	329	24	spaces	space	NOUN
ejpam-6282	329	25	via	via	ADP
ejpam-6282	329	26	simulation	simulation	NOUN
ejpam-6282	329	27	functions	function	NOUN
ejpam-6282	329	28	jordan	jordan	PROPN
ejpam-6282	329	29	journal	journal	PROPN
ejpam-6282	329	30	of	of	ADP
ejpam-6282	329	31	mathematics	mathematics	PROPN
ejpam-6282	329	32	and	and	CCONJ
ejpam-6282	329	33	statistics	statistic	NOUN
ejpam-6282	329	34	,	,	PUNCT
ejpam-6282	329	35	12	12	NUM
ejpam-6282	329	36	(	(	PUNCT
ejpam-6282	329	37	3	3	NUM
ejpam-6282	329	38	)	)	PUNCT
ejpam-6282	329	39	,	,	PUNCT
ejpam-6282	329	40	265–288	265–288	NUM
ejpam-6282	329	41	2019	2019	NUM
ejpam-6282	329	42	.	.	PUNCT
ejpam-6282	330	1	[	[	X
ejpam-6282	330	2	19	19	NUM
ejpam-6282	330	3	]	]	X
ejpam-6282	330	4	karapinar	karapinar	PROPN
ejpam-6282	330	5	,	,	PUNCT
ejpam-6282	330	6	e.	e.	PROPN
ejpam-6282	330	7	;	;	PUNCT
ejpam-6282	330	8	khojasteh	khojasteh	PROPN
ejpam-6282	330	9	,	,	PUNCT
ejpam-6282	330	10	f.	f.	PROPN
ejpam-6282	330	11	an	an	DET
ejpam-6282	330	12	approach	approach	NOUN
ejpam-6282	330	13	to	to	ADP
ejpam-6282	330	14	best	good	ADJ
ejpam-6282	330	15	proximity	proximity	NOUN
ejpam-6282	330	16	points	point	NOUN
ejpam-6282	330	17	results	result	NOUN
ejpam-6282	330	18	via	via	ADP
ejpam-6282	330	19	simulation	simulation	NOUN
ejpam-6282	330	20	functions	function	NOUN
ejpam-6282	330	21	journal	journal	PROPN
ejpam-6282	330	22	of	of	ADP
ejpam-6282	330	23	fixed	fix	VERB
ejpam-6282	330	24	point	point	NOUN
ejpam-6282	330	25	theory	theory	NOUN
ejpam-6282	330	26	and	and	CCONJ
ejpam-6282	330	27	applications	application	NOUN
ejpam-6282	330	28	,	,	PUNCT
ejpam-6282	330	29	19	19	NUM
ejpam-6282	330	30	(	(	PUNCT
ejpam-6282	330	31	3	3	NUM
ejpam-6282	330	32	)	)	PUNCT
ejpam-6282	330	33	,	,	PUNCT
ejpam-6282	330	34	1983–1995	1983–1995	NUM
ejpam-6282	330	35	,	,	PUNCT
ejpam-6282	330	36	2017	2017	NUM
ejpam-6282	330	37	.	.	PUNCT
ejpam-6282	331	1	doi:10.1007	doi:10.1007	VERB
ejpam-6282	331	2	/	/	SYM
ejpam-6282	331	3	s11784	s11784	NOUN
ejpam-6282	331	4	-	-	PUNCT
ejpam-6282	331	5	016	016	NUM
ejpam-6282	331	6	-	-	PUNCT
ejpam-6282	331	7	0380	0380	NUM
ejpam-6282	331	8	-	-	SYM
ejpam-6282	331	9	2	2	NUM
ejpam-6282	331	10	[	[	SYM
ejpam-6282	331	11	20	20	NUM
ejpam-6282	331	12	]	]	PUNCT
ejpam-6282	331	13	karapinar	karapinar	PROPN
ejpam-6282	331	14	,	,	PUNCT
ejpam-6282	331	15	e.	e.	PROPN
ejpam-6282	331	16	fixed	fix	VERB
ejpam-6282	331	17	points	point	NOUN
ejpam-6282	331	18	results	result	NOUN
ejpam-6282	331	19	via	via	ADP
ejpam-6282	331	20	simulation	simulation	NOUN
ejpam-6282	331	21	functions	function	NOUN
ejpam-6282	331	22	filomat	filomat	PROPN
ejpam-6282	331	23	2016	2016	NUM
ejpam-6282	331	24	,	,	PUNCT
ejpam-6282	331	25	30	30	NUM
ejpam-6282	331	26	(	(	PUNCT
ejpam-6282	331	27	8)	8)	NUM
ejpam-6282	331	28	,	,	PUNCT
ejpam-6282	331	29	2343	2343	NUM
ejpam-6282	331	30	–	–	PUNCT
ejpam-6282	331	31	2350	2350	NUM
ejpam-6282	331	32	.	.	PUNCT
ejpam-6282	332	1	[	[	X
ejpam-6282	332	2	21	21	NUM
ejpam-6282	332	3	]	]	X
ejpam-6282	332	4	aslantas	aslanta	NOUN
ejpam-6282	332	5	,	,	PUNCT
ejpam-6282	332	6	m.	m.	NOUN
ejpam-6282	332	7	;	;	PUNCT
ejpam-6282	332	8	sahin	sahin	PROPN
ejpam-6282	332	9	,	,	PUNCT
ejpam-6282	332	10	h.	h.	PROPN
ejpam-6282	332	11	;	;	PUNCT
ejpam-6282	332	12	turkoglu	turkoglu	PROPN
ejpam-6282	332	13	,	,	PUNCT
ejpam-6282	332	14	d.	d.	PROPN
ejpam-6282	332	15	some	some	DET
ejpam-6282	332	16	caristi	caristi	PROPN
ejpam-6282	332	17	type	type	NOUN
ejpam-6282	332	18	fixed	fix	VERB
ejpam-6282	332	19	point	point	NOUN
ejpam-6282	332	20	theorems	theorem	NOUN
ejpam-6282	332	21	.	.	PUNCT
ejpam-6282	333	1	j	j	PROPN
ejpam-6282	333	2	anal	anal	PROPN
ejpam-6282	333	3	,	,	PUNCT
ejpam-6282	333	4	29	29	NUM
ejpam-6282	333	5	,	,	PUNCT
ejpam-6282	333	6	89–1032021	89–1032021	NUM
ejpam-6282	333	7	.	.	PUNCT
ejpam-6282	334	1	https://doi.org/10.1007/s41478-020-00248-8	https://doi.org/10.1007/s41478-020-00248-8	NUM
ejpam-6282	335	1	[	[	X
ejpam-6282	335	2	22	22	NUM
ejpam-6282	335	3	]	]	PUNCT
ejpam-6282	335	4	aslantas	aslanta	NOUN
ejpam-6282	335	5	,	,	PUNCT
ejpam-6282	335	6	m.	m.	NOUN
ejpam-6282	335	7	;	;	PUNCT
ejpam-6282	335	8	sahin	sahin	PROPN
ejpam-6282	335	9	,	,	PUNCT
ejpam-6282	335	10	h.	h.	PROPN
ejpam-6282	335	11	;	;	PUNCT
ejpam-6282	335	12	altun	altun	NOUN
ejpam-6282	335	13	,	,	PUNCT
ejpam-6282	335	14	i.	i.	NOUN
ejpam-6282	335	15	;	;	PUNCT
ejpam-6282	335	16	saadoon	saadoon	NOUN
ejpam-6282	335	17	,	,	PUNCT
ejpam-6282	335	18	t.h.s	t.h.s	NOUN
ejpam-6282	335	19	.	.	PUNCT
ejpam-6282	336	1	a	a	DET
ejpam-6282	336	2	new	new	ADJ
ejpam-6282	336	3	type	type	NOUN
ejpam-6282	336	4	of	of	ADP
ejpam-6282	336	5	r	r	NOUN
ejpam-6282	336	6	-	-	PUNCT
ejpam-6282	336	7	contraction	contraction	NOUN
ejpam-6282	336	8	and	and	CCONJ
ejpam-6282	336	9	its	its	PRON
ejpam-6282	336	10	best	good	ADJ
ejpam-6282	336	11	proximity	proximity	NOUN
ejpam-6282	336	12	points	point	NOUN
ejpam-6282	336	13	.	.	PUNCT
ejpam-6282	337	1	aims	aim	VERB
ejpam-6282	337	2	math	math	NOUN
ejpam-6282	337	3	.	.	PUNCT
ejpam-6282	338	1	,	,	PUNCT
ejpam-6282	338	2	9	9	NUM
ejpam-6282	338	3	,	,	PUNCT
ejpam-6282	338	4	9692–9704	9692–9704	NUM
ejpam-6282	338	5	,	,	PUNCT
ejpam-6282	338	6	2024	2024	NUM
ejpam-6282	338	7	.	.	PUNCT
ejpam-6282	339	1	[	[	X
ejpam-6282	339	2	23	23	NUM
ejpam-6282	339	3	]	]	X
ejpam-6282	339	4	roldan	roldan	PROPN
ejpam-6282	339	5	-	-	PUNCT
ejpam-6282	339	6	lopez	lopez	PROPN
ejpam-6282	339	7	-	-	PUNCT
ejpam-6282	339	8	de	de	X
ejpam-6282	339	9	hierro	hierro	PROPN
ejpam-6282	339	10	,	,	PUNCT
ejpam-6282	339	11	a.-f	a.-f	PROPN
ejpam-6282	339	12	.	.	PUNCT
ejpam-6282	339	13	;	;	PUNCT
ejpam-6282	339	14	karapınar	karapınar	PROPN
ejpam-6282	339	15	,	,	PUNCT
ejpam-6282	339	16	e.	e.	PROPN
ejpam-6282	339	17	;	;	PUNCT
ejpam-6282	339	18	roldan	roldan	PROPN
ejpam-6282	339	19	-	-	PUNCT
ejpam-6282	339	20	lopez	lopez	PROPN
ejpam-6282	339	21	-	-	PUNCT
ejpam-6282	339	22	de	de	X
ejpam-6282	339	23	hierro	hierro	PROPN
ejpam-6282	339	24	,	,	PUNCT
ejpam-6282	339	25	c.	c.	PROPN
ejpam-6282	339	26	;	;	PUNCT
ejpam-6282	339	27	martinez	martinez	PROPN
ejpam-6282	339	28	-	-	PUNCT
ejpam-6282	339	29	moreno	moreno	PROPN
ejpam-6282	339	30	,	,	PUNCT
ejpam-6282	339	31	j.	j.	PROPN
ejpam-6282	339	32	coincidence	coincidence	PROPN
ejpam-6282	339	33	point	point	NOUN
ejpam-6282	339	34	theorems	theorem	NOUN
ejpam-6282	339	35	on	on	ADP
ejpam-6282	339	36	metric	metric	ADJ
ejpam-6282	339	37	spaces	space	NOUN
ejpam-6282	339	38	via	via	ADP
ejpam-6282	339	39	simulation	simulation	NOUN
ejpam-6282	339	40	functions	function	NOUN
ejpam-6282	339	41	journal	journal	PROPN
ejpam-6282	339	42	of	of	ADP
ejpam-6282	339	43	computational	computational	ADJ
ejpam-6282	339	44	and	and	CCONJ
ejpam-6282	339	45	applied	applied	ADJ
ejpam-6282	339	46	mathematics	mathematic	NOUN
ejpam-6282	339	47	,	,	PUNCT
ejpam-6282	339	48	275	275	NUM
ejpam-6282	339	49	,	,	PUNCT
ejpam-6282	339	50	345–355,2015	345–355,2015	NUM
ejpam-6282	339	51	.	.	PUNCT
ejpam-6282	340	1	[	[	X
ejpam-6282	340	2	24	24	NUM
ejpam-6282	340	3	]	]	PUNCT
ejpam-6282	340	4	aslantas	aslanta	NOUN
ejpam-6282	340	5	,	,	PUNCT
ejpam-6282	340	6	m.	m.	NOUN
ejpam-6282	340	7	nonunique	nonunique	ADJ
ejpam-6282	340	8	best	good	ADJ
ejpam-6282	340	9	proximity	proximity	NOUN
ejpam-6282	340	10	point	point	NOUN
ejpam-6282	340	11	results	result	NOUN
ejpam-6282	340	12	with	with	ADP
ejpam-6282	340	13	an	an	DET
ejpam-6282	340	14	application	application	NOUN
ejpam-6282	340	15	to	to	ADP
ejpam-6282	340	16	nonlinear	nonlinear	ADJ
ejpam-6282	340	17	fractional	fractional	ADJ
ejpam-6282	340	18	differential	differential	ADJ
ejpam-6282	340	19	equations	equation	NOUN
ejpam-6282	340	20	turkish	turkish	ADJ
ejpam-6282	340	21	journal	journal	NOUN
ejpam-6282	340	22	of	of	ADP
ejpam-6282	340	23	mathematics	mathematics	PROPN
ejpam-6282	340	24	,	,	PUNCT
ejpam-6282	340	25	46	46	NUM
ejpam-6282	340	26	(	(	PUNCT
ejpam-6282	340	27	7	7	NUM
ejpam-6282	340	28	)	)	PUNCT
ejpam-6282	340	29	,	,	PUNCT
ejpam-6282	340	30	article	article	NOUN
ejpam-6282	340	31	25	25	NUM
ejpam-6282	340	32	,	,	PUNCT
ejpam-6282	340	33	2022	2022	NUM
ejpam-6282	340	34	.	.	PUNCT
ejpam-6282	341	1	https://doi.org/10.55730/1300-0098.3311	https://doi.org/10.55730/1300-0098.3311	NOUN
ejpam-6282	342	1	[	[	X
ejpam-6282	342	2	25	25	NUM
ejpam-6282	342	3	]	]	PUNCT
ejpam-6282	342	4	e.	e.	PROPN
ejpam-6282	342	5	karapınar	karapınar	PROPN
ejpam-6282	342	6	,	,	PUNCT
ejpam-6282	342	7	r.p	r.p	PROPN
ejpam-6282	342	8	.	.	PROPN
ejpam-6282	342	9	agarwal	agarwal	PROPN
ejpam-6282	342	10	,	,	PUNCT
ejpam-6282	342	11	some	some	DET
ejpam-6282	342	12	fixed	fix	VERB
ejpam-6282	342	13	point	point	NOUN
ejpam-6282	342	14	results	result	NOUN
ejpam-6282	342	15	on	on	ADP
ejpam-6282	342	16	interpolative	interpolative	ADJ
ejpam-6282	342	17	metric	metric	ADJ
ejpam-6282	342	18	spaces	space	NOUN
ejpam-6282	342	19	,	,	PUNCT
ejpam-6282	342	20	nonlinear	nonlinear	ADJ
ejpam-6282	342	21	anal	anal	NOUN
ejpam-6282	342	22	.	.	PUNCT
ejpam-6282	343	1	real	real	ADJ
ejpam-6282	343	2	world	world	NOUN
ejpam-6282	343	3	appl	appl	PROPN
ejpam-6282	343	4	.	.	PROPN
ejpam-6282	344	1	82	82	NUM
ejpam-6282	344	2	,	,	PUNCT
ejpam-6282	344	3	104244	104244	NUM
ejpam-6282	344	4	,	,	PUNCT
ejpam-6282	344	5	2025	2025	NUM
ejpam-6282	344	6	.	.	PUNCT
ejpam-6282	345	1	https://doi.org/10.1016/j.nonrwa.2024.104244	https://doi.org/10.1016/j.nonrwa.2024.104244	PROPN