id	sid	tid	token	lemma	pos
ejpam-2592	1	1	compile	compile	NOUN
ejpam-2592	1	2	/	/	SYM
ejpam-2592	1	3	output.dvi	output.dvi	PRON
ejpam-2592	1	4	fixed	fix	VERB
ejpam-2592	1	5	point	point	NOUN
ejpam-2592	1	6	results	result	NOUN
ejpam-2592	1	7	for	for	ADP
ejpam-2592	1	8	α−ψ−ϕ−	α−ψ−ϕ−	NUM
ejpam-2592	1	9	contractive	contractive	ADJ
ejpam-2592	1	10	type	type	NOUN
ejpam-2592	1	11	mappings	mapping	NOUN
ejpam-2592	1	12	in	in	ADP
ejpam-2592	1	13	b	b	NOUN
ejpam-2592	1	14	-	-	PUNCT
ejpam-2592	1	15	metric	metric	ADJ
ejpam-2592	1	16	-	-	PUNCT
ejpam-2592	1	17	like	like	ADJ
ejpam-2592	1	18	spaces	space	NOUN
ejpam-2592	1	19	m.	m.	NOUN
ejpam-2592	1	20	a.	a.	NOUN
ejpam-2592	1	21	akturk1,∗	akturk1,∗	PROPN
ejpam-2592	1	22	,	,	PUNCT
ejpam-2592	1	23	m.	m.	NOUN
ejpam-2592	1	24	kır2	kır2	PROPN
ejpam-2592	1	25	and	and	CCONJ
ejpam-2592	1	26	e.	e.	PROPN
ejpam-2592	1	27	yolacan	yolacan	PROPN
ejpam-2592	1	28	3	3	NUM
ejpam-2592	1	29	1	1	NUM
ejpam-2592	1	30	department	department	NOUN
ejpam-2592	1	31	of	of	ADP
ejpam-2592	1	32	engineering	engineering	PROPN
ejpam-2592	1	33	sciences	sciences	PROPN
ejpam-2592	1	34	,	,	PUNCT
ejpam-2592	1	35	istanbul	istanbul	PROPN
ejpam-2592	1	36	university	university	PROPN
ejpam-2592	1	37	,	,	PUNCT
ejpam-2592	1	38	34320	34320	NUM
ejpam-2592	1	39	istanbul	istanbul	PROPN
ejpam-2592	1	40	,	,	PUNCT
ejpam-2592	1	41	turkey	turkey	PROPN
ejpam-2592	1	42	2	2	NUM
ejpam-2592	1	43	department	department	NOUN
ejpam-2592	1	44	of	of	ADP
ejpam-2592	1	45	civil	civil	ADJ
ejpam-2592	1	46	engineering	engineering	NOUN
ejpam-2592	1	47	,	,	PUNCT
ejpam-2592	1	48	faculty	faculty	NOUN
ejpam-2592	1	49	of	of	ADP
ejpam-2592	1	50	engineering	engineering	PROPN
ejpam-2592	1	51	şırnak	şırnak	PROPN
ejpam-2592	1	52	university	university	PROPN
ejpam-2592	1	53	,	,	PUNCT
ejpam-2592	1	54	şırnak	şırnak	PROPN
ejpam-2592	1	55	,	,	PUNCT
ejpam-2592	1	56	turkey	turkey	PROPN
ejpam-2592	1	57	3	3	NUM
ejpam-2592	1	58	department	department	NOUN
ejpam-2592	1	59	of	of	ADP
ejpam-2592	1	60	mathematics	mathematic	NOUN
ejpam-2592	1	61	,	,	PUNCT
ejpam-2592	1	62	faculty	faculty	NOUN
ejpam-2592	1	63	of	of	ADP
ejpam-2592	1	64	science	science	NOUN
ejpam-2592	1	65	,	,	PUNCT
ejpam-2592	1	66	ataturk	ataturk	PROPN
ejpam-2592	1	67	university	university	PROPN
ejpam-2592	1	68	,	,	PUNCT
ejpam-2592	1	69	erzurum	erzurum	PROPN
ejpam-2592	1	70	,	,	PUNCT
ejpam-2592	1	71	25240	25240	NUM
ejpam-2592	1	72	,	,	PUNCT
ejpam-2592	1	73	turkey	turkey	NOUN
ejpam-2592	1	74	abstract	abstract	NOUN
ejpam-2592	1	75	.	.	PUNCT
ejpam-2592	2	1	in	in	ADP
ejpam-2592	2	2	this	this	DET
ejpam-2592	2	3	paper	paper	NOUN
ejpam-2592	2	4	,	,	PUNCT
ejpam-2592	2	5	we	we	PRON
ejpam-2592	2	6	introduce	introduce	VERB
ejpam-2592	2	7	the	the	DET
ejpam-2592	2	8	concept	concept	NOUN
ejpam-2592	2	9	of	of	ADP
ejpam-2592	2	10	α−ψ−ϕcontractive	α−ψ−ϕcontractive	ADJ
ejpam-2592	2	11	type	type	NOUN
ejpam-2592	2	12	mappings	mapping	NOUN
ejpam-2592	2	13	in	in	ADP
ejpam-2592	2	14	b	b	NOUN
ejpam-2592	2	15	-	-	PUNCT
ejpam-2592	2	16	metriclike	metriclike	ADJ
ejpam-2592	2	17	spaces	space	NOUN
ejpam-2592	2	18	and	and	CCONJ
ejpam-2592	2	19	state	state	VERB
ejpam-2592	2	20	some	some	DET
ejpam-2592	2	21	related	related	ADJ
ejpam-2592	2	22	fixed	fix	VERB
ejpam-2592	2	23	point	point	NOUN
ejpam-2592	2	24	theorems	theorem	NOUN
ejpam-2592	2	25	.	.	PUNCT
ejpam-2592	3	1	our	our	PRON
ejpam-2592	3	2	results	result	NOUN
ejpam-2592	3	3	generalize	generalize	VERB
ejpam-2592	3	4	related	related	ADJ
ejpam-2592	3	5	results	result	NOUN
ejpam-2592	3	6	in	in	ADP
ejpam-2592	3	7	the	the	DET
ejpam-2592	3	8	literature	literature	NOUN
ejpam-2592	3	9	.	.	PUNCT
ejpam-2592	4	1	furthermore	furthermore	ADV
ejpam-2592	4	2	,	,	PUNCT
ejpam-2592	4	3	an	an	DET
ejpam-2592	4	4	example	example	NOUN
ejpam-2592	4	5	and	and	CCONJ
ejpam-2592	4	6	an	an	DET
ejpam-2592	4	7	application	application	NOUN
ejpam-2592	4	8	to	to	ADP
ejpam-2592	4	9	integral	integral	ADJ
ejpam-2592	4	10	equations	equation	NOUN
ejpam-2592	4	11	are	be	AUX
ejpam-2592	4	12	provided	provide	VERB
ejpam-2592	4	13	to	to	PART
ejpam-2592	4	14	illustrate	illustrate	VERB
ejpam-2592	4	15	the	the	DET
ejpam-2592	4	16	usability	usability	NOUN
ejpam-2592	4	17	of	of	ADP
ejpam-2592	4	18	obtained	obtain	VERB
ejpam-2592	4	19	results	result	NOUN
ejpam-2592	4	20	.	.	PUNCT
ejpam-2592	5	1	2010	2010	NUM
ejpam-2592	5	2	mathematics	mathematic	NOUN
ejpam-2592	5	3	subject	subject	NOUN
ejpam-2592	5	4	classifications	classification	NOUN
ejpam-2592	5	5	:	:	PUNCT
ejpam-2592	5	6	47h10	47h10	NUM
ejpam-2592	5	7	,	,	PUNCT
ejpam-2592	5	8	54h25	54h25	NUM
ejpam-2592	5	9	key	key	ADJ
ejpam-2592	5	10	words	word	NOUN
ejpam-2592	5	11	and	and	CCONJ
ejpam-2592	5	12	phrases	phrase	NOUN
ejpam-2592	5	13	:	:	PUNCT
ejpam-2592	5	14	b	b	X
ejpam-2592	5	15	-	-	ADJ
ejpam-2592	5	16	metric	metric	ADJ
ejpam-2592	5	17	-	-	PUNCT
ejpam-2592	5	18	like	like	ADJ
ejpam-2592	5	19	,	,	PUNCT
ejpam-2592	5	20	α	α	X
ejpam-2592	5	21	-	-	PUNCT
ejpam-2592	5	22	admissible	admissible	ADJ
ejpam-2592	5	23	mappings	mapping	NOUN
ejpam-2592	5	24	,	,	PUNCT
ejpam-2592	5	25	fixed	fix	VERB
ejpam-2592	5	26	point	point	NOUN
ejpam-2592	5	27	,	,	PUNCT
ejpam-2592	5	28	integral	integral	ADJ
ejpam-2592	5	29	equations	equation	NOUN
ejpam-2592	5	30	1	1	NUM
ejpam-2592	5	31	.	.	PUNCT
ejpam-2592	6	1	introduction	introduction	NOUN
ejpam-2592	6	2	there	there	PRON
ejpam-2592	6	3	are	be	VERB
ejpam-2592	6	4	a	a	DET
ejpam-2592	6	5	lot	lot	NOUN
ejpam-2592	6	6	of	of	ADP
ejpam-2592	6	7	generalizations	generalization	NOUN
ejpam-2592	6	8	of	of	ADP
ejpam-2592	6	9	the	the	DET
ejpam-2592	6	10	concept	concept	NOUN
ejpam-2592	6	11	of	of	ADP
ejpam-2592	6	12	metric	metric	ADJ
ejpam-2592	6	13	space	space	NOUN
ejpam-2592	6	14	in	in	ADP
ejpam-2592	6	15	the	the	DET
ejpam-2592	6	16	literature	literature	NOUN
ejpam-2592	6	17	.	.	PUNCT
ejpam-2592	7	1	the	the	DET
ejpam-2592	7	2	notion	notion	NOUN
ejpam-2592	7	3	of	of	ADP
ejpam-2592	7	4	b	b	NOUN
ejpam-2592	7	5	-	-	PUNCT
ejpam-2592	7	6	metric	metric	ADJ
ejpam-2592	7	7	-	-	PUNCT
ejpam-2592	7	8	like	like	ADJ
ejpam-2592	7	9	space	space	NOUN
ejpam-2592	7	10	was	be	AUX
ejpam-2592	7	11	initiated	initiate	VERB
ejpam-2592	7	12	by	by	ADP
ejpam-2592	7	13	alghamdi	alghamdi	NOUN
ejpam-2592	7	14	[	[	X
ejpam-2592	7	15	1	1	NUM
ejpam-2592	7	16	]	]	PUNCT
ejpam-2592	7	17	in	in	ADP
ejpam-2592	7	18	2013	2013	NUM
ejpam-2592	7	19	as	as	ADP
ejpam-2592	7	20	a	a	DET
ejpam-2592	7	21	new	new	ADJ
ejpam-2592	7	22	generalization	generalization	NOUN
ejpam-2592	7	23	of	of	ADP
ejpam-2592	7	24	metric	metric	ADJ
ejpam-2592	7	25	-	-	PUNCT
ejpam-2592	7	26	like	like	ADJ
ejpam-2592	7	27	space	space	NOUN
ejpam-2592	7	28	.	.	PUNCT
ejpam-2592	8	1	recently	recently	ADV
ejpam-2592	8	2	,	,	PUNCT
ejpam-2592	8	3	hussain	hussain	PROPN
ejpam-2592	8	4	et	et	PROPN
ejpam-2592	8	5	al	al	PROPN
ejpam-2592	8	6	.	.	PUNCT
ejpam-2592	9	1	[	[	X
ejpam-2592	9	2	4	4	X
ejpam-2592	9	3	]	]	PUNCT
ejpam-2592	9	4	examined	examine	VERB
ejpam-2592	9	5	topological	topological	ADJ
ejpam-2592	9	6	structure	structure	NOUN
ejpam-2592	9	7	of	of	ADP
ejpam-2592	9	8	these	these	DET
ejpam-2592	9	9	spaces	space	NOUN
ejpam-2592	9	10	and	and	CCONJ
ejpam-2592	9	11	presented	present	VERB
ejpam-2592	9	12	some	some	DET
ejpam-2592	9	13	fixed	fix	VERB
ejpam-2592	9	14	point	point	NOUN
ejpam-2592	9	15	results	result	NOUN
ejpam-2592	9	16	in	in	ADP
ejpam-2592	9	17	b	b	NOUN
ejpam-2592	9	18	-	-	PUNCT
ejpam-2592	9	19	metric	metric	ADJ
ejpam-2592	9	20	-	-	PUNCT
ejpam-2592	9	21	like	like	ADJ
ejpam-2592	9	22	space	space	NOUN
ejpam-2592	9	23	.	.	PUNCT
ejpam-2592	10	1	very	very	ADV
ejpam-2592	10	2	recently	recently	ADV
ejpam-2592	10	3	,	,	PUNCT
ejpam-2592	10	4	chen	chen	PROPN
ejpam-2592	10	5	et	et	PROPN
ejpam-2592	10	6	al	al	PROPN
ejpam-2592	10	7	.	.	PUNCT
ejpam-2592	11	1	[	[	X
ejpam-2592	11	2	3	3	X
ejpam-2592	11	3	]	]	PUNCT
ejpam-2592	11	4	established	establish	VERB
ejpam-2592	11	5	some	some	DET
ejpam-2592	11	6	fixed	fix	VERB
ejpam-2592	11	7	point	point	NOUN
ejpam-2592	11	8	theorems	theorem	NOUN
ejpam-2592	11	9	in	in	ADP
ejpam-2592	11	10	b	b	NOUN
ejpam-2592	11	11	-	-	ADJ
ejpam-2592	11	12	metric	metric	ADJ
ejpam-2592	11	13	-	-	PUNCT
ejpam-2592	11	14	like	like	ADJ
ejpam-2592	11	15	space	space	NOUN
ejpam-2592	11	16	and	and	CCONJ
ejpam-2592	11	17	showed	show	VERB
ejpam-2592	11	18	existence	existence	NOUN
ejpam-2592	11	19	of	of	ADP
ejpam-2592	11	20	a	a	DET
ejpam-2592	11	21	solution	solution	NOUN
ejpam-2592	11	22	for	for	ADP
ejpam-2592	11	23	an	an	DET
ejpam-2592	11	24	integral	integral	ADJ
ejpam-2592	11	25	equation	equation	NOUN
ejpam-2592	11	26	.	.	PUNCT
ejpam-2592	12	1	in	in	ADP
ejpam-2592	12	2	this	this	DET
ejpam-2592	12	3	paper	paper	NOUN
ejpam-2592	12	4	we	we	PRON
ejpam-2592	12	5	introduce	introduce	VERB
ejpam-2592	12	6	the	the	DET
ejpam-2592	12	7	concept	concept	NOUN
ejpam-2592	12	8	of	of	ADP
ejpam-2592	12	9	α−ψ−ϕ-contractive	α−ψ−ϕ-contractive	ADJ
ejpam-2592	12	10	type	type	NOUN
ejpam-2592	12	11	mappings	mapping	NOUN
ejpam-2592	12	12	in	in	ADP
ejpam-2592	12	13	b	b	NOUN
ejpam-2592	12	14	-	-	PUNCT
ejpam-2592	12	15	metric	metric	ADJ
ejpam-2592	12	16	-	-	PUNCT
ejpam-2592	12	17	like	like	ADJ
ejpam-2592	12	18	spaces	space	NOUN
ejpam-2592	12	19	and	and	CCONJ
ejpam-2592	12	20	state	state	VERB
ejpam-2592	12	21	some	some	DET
ejpam-2592	12	22	related	related	ADJ
ejpam-2592	12	23	fixed	fix	VERB
ejpam-2592	12	24	point	point	NOUN
ejpam-2592	12	25	theorems	theorem	NOUN
ejpam-2592	12	26	.	.	PUNCT
ejpam-2592	13	1	our	our	PRON
ejpam-2592	13	2	results	result	NOUN
ejpam-2592	13	3	generalize	generalize	VERB
ejpam-2592	13	4	related	related	ADJ
ejpam-2592	13	5	results	result	NOUN
ejpam-2592	13	6	in	in	ADP
ejpam-2592	13	7	the	the	DET
ejpam-2592	13	8	literature	literature	NOUN
ejpam-2592	13	9	.	.	PUNCT
ejpam-2592	14	1	furthermore	furthermore	ADV
ejpam-2592	14	2	,	,	PUNCT
ejpam-2592	14	3	an	an	DET
ejpam-2592	14	4	example	example	NOUN
ejpam-2592	14	5	and	and	CCONJ
ejpam-2592	14	6	an	an	DET
ejpam-2592	14	7	application	application	NOUN
ejpam-2592	14	8	to	to	ADP
ejpam-2592	14	9	integral	integral	ADJ
ejpam-2592	14	10	equations	equation	NOUN
ejpam-2592	14	11	are	be	AUX
ejpam-2592	14	12	provided	provide	VERB
ejpam-2592	14	13	to	to	PART
ejpam-2592	14	14	illustrate	illustrate	VERB
ejpam-2592	14	15	the	the	DET
ejpam-2592	14	16	usability	usability	NOUN
ejpam-2592	14	17	of	of	ADP
ejpam-2592	14	18	obtained	obtain	VERB
ejpam-2592	14	19	results	result	NOUN
ejpam-2592	14	20	.	.	PUNCT
ejpam-2592	15	1	2	2	X
ejpam-2592	15	2	.	.	X
ejpam-2592	15	3	b	b	X
ejpam-2592	15	4	-	-	PUNCT
ejpam-2592	15	5	metric	metric	ADJ
ejpam-2592	15	6	-	-	PUNCT
ejpam-2592	15	7	like	like	ADJ
ejpam-2592	15	8	spaces	space	NOUN
ejpam-2592	15	9	definition	definition	NOUN
ejpam-2592	15	10	1	1	NUM
ejpam-2592	15	11	(	(	PUNCT
ejpam-2592	15	12	[	[	X
ejpam-2592	15	13	1	1	NUM
ejpam-2592	15	14	]	]	PUNCT
ejpam-2592	15	15	)	)	PUNCT
ejpam-2592	15	16	.	.	PUNCT
ejpam-2592	16	1	let	let	VERB
ejpam-2592	16	2	x	x	PRON
ejpam-2592	16	3	be	be	AUX
ejpam-2592	16	4	a	a	DET
ejpam-2592	16	5	nonempty	nonempty	ADV
ejpam-2592	16	6	set	set	VERB
ejpam-2592	16	7	and	and	CCONJ
ejpam-2592	16	8	κ≥	κ≥	PROPN
ejpam-2592	16	9	1	1	NUM
ejpam-2592	16	10	a	a	DET
ejpam-2592	16	11	given	give	VERB
ejpam-2592	16	12	real	real	ADJ
ejpam-2592	16	13	number	number	NOUN
ejpam-2592	16	14	.	.	PUNCT
ejpam-2592	17	1	a	a	DET
ejpam-2592	17	2	function	function	NOUN
ejpam-2592	17	3	ς	ς	X
ejpam-2592	17	4	:	:	PUNCT
ejpam-2592	17	5	x	x	SYM
ejpam-2592	17	6	×	×	NOUN
ejpam-2592	17	7	x	x	PUNCT
ejpam-2592	17	8	→	→	X
ejpam-2592	17	9	r+	r+	PRON
ejpam-2592	17	10	is	be	AUX
ejpam-2592	17	11	b	b	NOUN
ejpam-2592	17	12	-	-	PUNCT
ejpam-2592	17	13	metric	metric	ADJ
ejpam-2592	17	14	-	-	PUNCT
ejpam-2592	17	15	like	like	ADJ
ejpam-2592	17	16	if	if	SCONJ
ejpam-2592	17	17	,	,	PUNCT
ejpam-2592	17	18	for	for	ADP
ejpam-2592	17	19	all	all	DET
ejpam-2592	17	20	x	x	SYM
ejpam-2592	17	21	,	,	PUNCT
ejpam-2592	17	22	y	y	PROPN
ejpam-2592	17	23	,	,	PUNCT
ejpam-2592	17	24	z	z	NOUN
ejpam-2592	17	25	∈	∈	PROPN
ejpam-2592	17	26	x	x	X
ejpam-2592	17	27	,	,	PUNCT
ejpam-2592	17	28	the	the	DET
ejpam-2592	17	29	following	follow	VERB
ejpam-2592	17	30	conditions	condition	NOUN
ejpam-2592	17	31	are	be	AUX
ejpam-2592	17	32	satisfied	satisfied	ADJ
ejpam-2592	17	33	:	:	PUNCT
ejpam-2592	17	34	∗corresponding	∗corresponde	VERB
ejpam-2592	17	35	author	author	NOUN
ejpam-2592	17	36	.	.	PUNCT
ejpam-2592	18	1	email	email	NOUN
ejpam-2592	18	2	addresses	address	NOUN
ejpam-2592	18	3	:	:	PUNCT
ejpam-2592	18	4	mehmetaliakturk@yandex.com	mehmetaliakturk@yandex.com	X
ejpam-2592	18	5	(	(	PUNCT
ejpam-2592	18	6	m.	m.	NOUN
ejpam-2592	18	7	akturk	akturk	PROPN
ejpam-2592	18	8	)	)	PUNCT
ejpam-2592	18	9	,	,	PUNCT
ejpam-2592	19	1	mehmetkir04@gmail.com	mehmetkir04@gmail.com	PROPN
ejpam-2592	19	2	(	(	PUNCT
ejpam-2592	19	3	m.	m.	NOUN
ejpam-2592	19	4	kır),yolacanesra@gmail.com	kır),yolacanesra@gmail.com	PROPN
ejpam-2592	19	5	(	(	PUNCT
ejpam-2592	19	6	e.	e.	PROPN
ejpam-2592	19	7	yolacan	yolacan	PROPN
ejpam-2592	19	8	)	)	PUNCT
ejpam-2592	19	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2592	20	1	175	175	NUM
ejpam-2592	20	2	c	c	X
ejpam-2592	20	3	©	©	PROPN
ejpam-2592	20	4	2016	2016	NUM
ejpam-2592	20	5	ejpam	ejpam	VERB
ejpam-2592	20	6	all	all	DET
ejpam-2592	20	7	rights	right	NOUN
ejpam-2592	20	8	reserved	reserve	VERB
ejpam-2592	20	9	.	.	PUNCT
ejpam-2592	21	1	european	european	ADJ
ejpam-2592	21	2	journal	journal	PROPN
ejpam-2592	21	3	of	of	ADP
ejpam-2592	21	4	pure	pure	ADJ
ejpam-2592	21	5	and	and	CCONJ
ejpam-2592	21	6	applied	apply	VERB
ejpam-2592	21	7	mathematics	mathematic	NOUN
ejpam-2592	21	8	vol	vol	NOUN
ejpam-2592	21	9	.	.	PROPN
ejpam-2592	22	1	9	9	NUM
ejpam-2592	22	2	,	,	PUNCT
ejpam-2592	22	3	no	no	INTJ
ejpam-2592	22	4	.	.	NOUN
ejpam-2592	22	5	2	2	NUM
ejpam-2592	22	6	,	,	PUNCT
ejpam-2592	22	7	2016	2016	NUM
ejpam-2592	22	8	,	,	PUNCT
ejpam-2592	22	9	175	175	NUM
ejpam-2592	22	10	-	-	SYM
ejpam-2592	22	11	185	185	NUM
ejpam-2592	22	12	issn	issn	PROPN
ejpam-2592	22	13	1307	1307	NUM
ejpam-2592	22	14	-	-	SYM
ejpam-2592	22	15	5543	5543	NUM
ejpam-2592	22	16	–	–	PUNCT
ejpam-2592	22	17	www.ejpam.com	www.ejpam.com	X
ejpam-2592	22	18	m.	m.	NOUN
ejpam-2592	22	19	akturk	akturk	PROPN
ejpam-2592	22	20	,	,	PUNCT
ejpam-2592	22	21	m.	m.	NOUN
ejpam-2592	22	22	kır	kır	PROPN
ejpam-2592	22	23	,	,	PUNCT
ejpam-2592	22	24	e.	e.	PROPN
ejpam-2592	22	25	yolacan	yolacan	PROPN
ejpam-2592	22	26	/	/	SYM
ejpam-2592	22	27	eur	eur	PROPN
ejpam-2592	22	28	.	.	PUNCT
ejpam-2592	23	1	j.	j.	PROPN
ejpam-2592	23	2	pure	pure	PROPN
ejpam-2592	23	3	appl	appl	PROPN
ejpam-2592	23	4	.	.	PROPN
ejpam-2592	23	5	math	math	PROPN
ejpam-2592	23	6	,	,	PUNCT
ejpam-2592	23	7	9	9	NUM
ejpam-2592	23	8	(	(	PUNCT
ejpam-2592	23	9	2016	2016	NUM
ejpam-2592	23	10	)	)	PUNCT
ejpam-2592	23	11	,	,	PUNCT
ejpam-2592	23	12	175	175	NUM
ejpam-2592	23	13	-	-	SYM
ejpam-2592	23	14	185	185	NUM
ejpam-2592	23	15	176	176	NUM
ejpam-2592	23	16	(	(	PUNCT
ejpam-2592	23	17	a1	a1	PROPN
ejpam-2592	23	18	)	)	PUNCT
ejpam-2592	23	19	if	if	SCONJ
ejpam-2592	23	20	ς	ς	PROPN
ejpam-2592	23	21	�	�	PROPN
ejpam-2592	23	22	x	x	SYM
ejpam-2592	23	23	,	,	PUNCT
ejpam-2592	23	24	y	y	PROPN
ejpam-2592	23	25	�	�	PROPN
ejpam-2592	23	26	=	=	SYM
ejpam-2592	23	27	0⇒	0⇒	NOUN
ejpam-2592	24	1	x	x	X
ejpam-2592	24	2	=	=	SYM
ejpam-2592	24	3	y	y	PROPN
ejpam-2592	24	4	;	;	PUNCT
ejpam-2592	24	5	(	(	PUNCT
ejpam-2592	24	6	a2	a2	PROPN
ejpam-2592	24	7	)	)	PUNCT
ejpam-2592	24	8	ς	ς	PROPN
ejpam-2592	24	9	�	�	PROPN
ejpam-2592	24	10	x	x	SYM
ejpam-2592	24	11	,	,	PUNCT
ejpam-2592	24	12	y	y	PROPN
ejpam-2592	24	13	�	�	PROPN
ejpam-2592	24	14	=	=	SYM
ejpam-2592	24	15	ς	ς	PROPN
ejpam-2592	24	16	�	�	PROPN
ejpam-2592	24	17	y	y	PROPN
ejpam-2592	24	18	,	,	PUNCT
ejpam-2592	24	19	x	x	PROPN
ejpam-2592	24	20	�	�	PROPN
ejpam-2592	24	21	;	;	PUNCT
ejpam-2592	24	22	(	(	PUNCT
ejpam-2592	24	23	a3	a3	NOUN
ejpam-2592	24	24	)	)	PUNCT
ejpam-2592	24	25	ς	ς	PROPN
ejpam-2592	24	26	�	�	PROPN
ejpam-2592	24	27	x	x	SYM
ejpam-2592	24	28	,	,	PUNCT
ejpam-2592	24	29	y	y	PROPN
ejpam-2592	24	30	�	�	PROPN
ejpam-2592	24	31	≤	≤	PROPN
ejpam-2592	24	32	κ	κ	PRON
ejpam-2592	24	33	�	�	PROPN
ejpam-2592	24	34	ς	ς	PROPN
ejpam-2592	24	35	(	(	PUNCT
ejpam-2592	24	36	x	x	INTJ
ejpam-2592	24	37	,	,	PUNCT
ejpam-2592	24	38	z	z	NOUN
ejpam-2592	24	39	)	)	PUNCT
ejpam-2592	25	1	+	+	CCONJ
ejpam-2592	25	2	ς	ς	PROPN
ejpam-2592	25	3	�	�	PROPN
ejpam-2592	25	4	y	y	PROPN
ejpam-2592	25	5	,	,	PUNCT
ejpam-2592	25	6	z	z	PROPN
ejpam-2592	25	7	�	�	PROPN
ejpam-2592	25	8	�	�	PROPN
ejpam-2592	25	9	.	.	PUNCT
ejpam-2592	26	1	a	a	DET
ejpam-2592	26	2	b	b	X
ejpam-2592	26	3	-	-	PUNCT
ejpam-2592	26	4	metric	metric	ADJ
ejpam-2592	26	5	-	-	PUNCT
ejpam-2592	26	6	like	like	ADJ
ejpam-2592	26	7	space	space	NOUN
ejpam-2592	26	8	is	be	AUX
ejpam-2592	26	9	a	a	DET
ejpam-2592	26	10	pair	pair	NOUN
ejpam-2592	26	11	(	(	PUNCT
ejpam-2592	26	12	x	x	X
ejpam-2592	26	13	,	,	PUNCT
ejpam-2592	26	14	ς	ς	PROPN
ejpam-2592	26	15	)	)	PUNCT
ejpam-2592	26	16	such	such	ADJ
ejpam-2592	26	17	that	that	SCONJ
ejpam-2592	26	18	x	x	PRON
ejpam-2592	26	19	is	be	AUX
ejpam-2592	26	20	nonempty	nonempty	ADV
ejpam-2592	26	21	set	set	VERB
ejpam-2592	26	22	and	and	CCONJ
ejpam-2592	26	23	ς	ς	PROPN
ejpam-2592	26	24	is	be	AUX
ejpam-2592	26	25	b	b	NOUN
ejpam-2592	26	26	-	-	PUNCT
ejpam-2592	26	27	metric	metric	ADJ
ejpam-2592	26	28	-	-	PUNCT
ejpam-2592	26	29	like	like	NOUN
ejpam-2592	26	30	on	on	ADP
ejpam-2592	26	31	x	x	X
ejpam-2592	26	32	.	.	PUNCT
ejpam-2592	27	1	the	the	DET
ejpam-2592	27	2	number	number	NOUN
ejpam-2592	27	3	κ	κ	NOUN
ejpam-2592	27	4	is	be	AUX
ejpam-2592	27	5	called	call	VERB
ejpam-2592	27	6	the	the	DET
ejpam-2592	27	7	coefficient	coefficient	NOUN
ejpam-2592	27	8	of	of	ADP
ejpam-2592	27	9	(	(	PUNCT
ejpam-2592	27	10	x	x	INTJ
ejpam-2592	27	11	,	,	PUNCT
ejpam-2592	27	12	ς	ς	PROPN
ejpam-2592	27	13	)	)	PUNCT
ejpam-2592	27	14	.	.	PUNCT
ejpam-2592	28	1	each	each	DET
ejpam-2592	28	2	b	b	X
ejpam-2592	28	3	-	-	PUNCT
ejpam-2592	28	4	metric	metric	ADJ
ejpam-2592	28	5	-	-	PUNCT
ejpam-2592	28	6	like	like	ADJ
ejpam-2592	28	7	ς	ς	PROPN
ejpam-2592	28	8	on	on	ADP
ejpam-2592	28	9	x	x	PUNCT
ejpam-2592	28	10	generates	generate	VERB
ejpam-2592	28	11	a	a	DET
ejpam-2592	28	12	topology	topology	NOUN
ejpam-2592	28	13	τς	τς	ADP
ejpam-2592	28	14	on	on	ADP
ejpam-2592	28	15	x	x	PUNCT
ejpam-2592	28	16	whose	whose	DET
ejpam-2592	28	17	base	base	NOUN
ejpam-2592	28	18	is	be	AUX
ejpam-2592	28	19	the	the	DET
ejpam-2592	28	20	family	family	NOUN
ejpam-2592	28	21	of	of	ADP
ejpam-2592	28	22	all	all	DET
ejpam-2592	28	23	open	open	ADJ
ejpam-2592	28	24	ς−	ς−	PROPN
ejpam-2592	28	25	balls	ball	NOUN
ejpam-2592	28	26	�	�	PROPN
ejpam-2592	28	27	dς	dς	PROPN
ejpam-2592	28	28	(	(	PUNCT
ejpam-2592	28	29	x	x	X
ejpam-2592	28	30	,	,	PUNCT
ejpam-2592	28	31	ǫ	ǫ	NOUN
ejpam-2592	28	32	)	)	PUNCT
ejpam-2592	28	33	:	:	PUNCT
ejpam-2592	28	34	x	x	PUNCT
ejpam-2592	28	35	∈	∈	NOUN
ejpam-2592	28	36	x	x	X
ejpam-2592	28	37	,	,	PUNCT
ejpam-2592	28	38	ǫ	ǫ	X
ejpam-2592	28	39	>	>	X
ejpam-2592	28	40	0	0	NUM
ejpam-2592	28	41	,	,	PUNCT
ejpam-2592	28	42	where	where	SCONJ
ejpam-2592	28	43	dς	dς	X
ejpam-2592	28	44	(	(	PUNCT
ejpam-2592	28	45	x	x	INTJ
ejpam-2592	28	46	,	,	PUNCT
ejpam-2592	28	47	ǫ	ǫ	X
ejpam-2592	28	48	)	)	PUNCT
ejpam-2592	28	49	=	=	SYM
ejpam-2592	28	50	{	{	PUNCT
ejpam-2592	28	51	a	a	DET
ejpam-2592	28	52	∈	∈	NOUN
ejpam-2592	28	53	x	x	X
ejpam-2592	28	54	:	:	PUNCT
ejpam-2592	28	55	|ς	|ς	PROPN
ejpam-2592	28	56	(	(	PUNCT
ejpam-2592	28	57	x	x	X
ejpam-2592	28	58	,	,	PUNCT
ejpam-2592	28	59	a)−	a)−	PROPN
ejpam-2592	28	60	ς	ς	PROPN
ejpam-2592	28	61	(	(	PUNCT
ejpam-2592	28	62	x	x	INTJ
ejpam-2592	28	63	,	,	PUNCT
ejpam-2592	28	64	x)|	x)|	PROPN
ejpam-2592	28	65	<	<	X
ejpam-2592	28	66	ǫ	ǫ	X
ejpam-2592	28	67	}	}	PUNCT
ejpam-2592	28	68	for	for	ADP
ejpam-2592	28	69	all	all	DET
ejpam-2592	28	70	x	x	SYM
ejpam-2592	28	71	∈	∈	PROPN
ejpam-2592	28	72	x	x	X
ejpam-2592	28	73	and	and	CCONJ
ejpam-2592	28	74	ǫ	ǫ	ADJ
ejpam-2592	28	75	>	>	X
ejpam-2592	28	76	0	0	X
ejpam-2592	28	77	.	.	PUNCT
ejpam-2592	29	1	definition	definition	NOUN
ejpam-2592	29	2	2	2	NUM
ejpam-2592	29	3	(	(	PUNCT
ejpam-2592	29	4	[	[	X
ejpam-2592	29	5	1	1	NUM
ejpam-2592	29	6	]	]	PUNCT
ejpam-2592	29	7	)	)	PUNCT
ejpam-2592	29	8	.	.	PUNCT
ejpam-2592	30	1	let	let	VERB
ejpam-2592	30	2	(	(	PUNCT
ejpam-2592	30	3	x	x	X
ejpam-2592	30	4	,	,	PUNCT
ejpam-2592	30	5	ς	ς	PROPN
ejpam-2592	30	6	)	)	PUNCT
ejpam-2592	30	7	be	be	VERB
ejpam-2592	30	8	a	a	DET
ejpam-2592	30	9	b	b	NOUN
ejpam-2592	30	10	-	-	PUNCT
ejpam-2592	30	11	metric	metric	ADJ
ejpam-2592	30	12	-	-	PUNCT
ejpam-2592	30	13	like	like	ADJ
ejpam-2592	30	14	space	space	NOUN
ejpam-2592	30	15	with	with	ADP
ejpam-2592	30	16	coefficient	coefficient	NOUN
ejpam-2592	30	17	κ	κ	NOUN
ejpam-2592	30	18	,	,	PUNCT
ejpam-2592	30	19	and	and	CCONJ
ejpam-2592	30	20	let	let	VERB
ejpam-2592	30	21	�	�	PROPN
ejpam-2592	30	22	xn	xn	PROPN
ejpam-2592	30	23	be	be	AUX
ejpam-2592	30	24	any	any	DET
ejpam-2592	30	25	sequence	sequence	NOUN
ejpam-2592	30	26	in	in	ADP
ejpam-2592	30	27	x	x	PUNCT
ejpam-2592	30	28	and	and	CCONJ
ejpam-2592	30	29	x	x	SYM
ejpam-2592	30	30	∈	∈	PROPN
ejpam-2592	30	31	x	x	X
ejpam-2592	30	32	.	.	PUNCT
ejpam-2592	31	1	then	then	ADV
ejpam-2592	31	2	(	(	PUNCT
ejpam-2592	31	3	a	a	X
ejpam-2592	31	4	)	)	PUNCT
ejpam-2592	31	5	a	a	DET
ejpam-2592	31	6	sequence	sequence	NOUN
ejpam-2592	31	7	�	�	PROPN
ejpam-2592	31	8	xn	xn	PROPN
ejpam-2592	31	9	is	be	AUX
ejpam-2592	31	10	convergent	convergent	ADJ
ejpam-2592	31	11	to	to	PART
ejpam-2592	31	12	x	x	PUNCT
ejpam-2592	31	13	with	with	ADP
ejpam-2592	31	14	respect	respect	NOUN
ejpam-2592	31	15	to	to	ADP
ejpam-2592	31	16	τς	τς	ADP
ejpam-2592	31	17	,	,	PUNCT
ejpam-2592	31	18	if	if	SCONJ
ejpam-2592	31	19	limn→∞	limn→∞	PROPN
ejpam-2592	31	20	ς	ς	PROPN
ejpam-2592	31	21	�	�	PROPN
ejpam-2592	31	22	xn	xn	PROPN
ejpam-2592	31	23	,	,	PUNCT
ejpam-2592	31	24	x	x	X
ejpam-2592	31	25	�	�	PROPN
ejpam-2592	31	26	=	=	SYM
ejpam-2592	31	27	ς	ς	PROPN
ejpam-2592	31	28	(	(	PUNCT
ejpam-2592	31	29	x	x	NOUN
ejpam-2592	31	30	,	,	PUNCT
ejpam-2592	31	31	x	x	NOUN
ejpam-2592	31	32	)	)	PUNCT
ejpam-2592	31	33	;	;	PUNCT
ejpam-2592	31	34	(	(	PUNCT
ejpam-2592	31	35	b	b	X
ejpam-2592	31	36	)	)	PUNCT
ejpam-2592	31	37	a	a	DET
ejpam-2592	31	38	sequence	sequence	NOUN
ejpam-2592	31	39	�	�	PROPN
ejpam-2592	31	40	xn	xn	PROPN
ejpam-2592	31	41	is	be	AUX
ejpam-2592	31	42	a	a	DET
ejpam-2592	31	43	cauchy	cauchy	ADJ
ejpam-2592	31	44	sequence	sequence	NOUN
ejpam-2592	31	45	in	in	ADP
ejpam-2592	31	46	(	(	PUNCT
ejpam-2592	31	47	x	x	INTJ
ejpam-2592	31	48	,	,	PUNCT
ejpam-2592	31	49	ς	ς	PROPN
ejpam-2592	31	50	)	)	PUNCT
ejpam-2592	31	51	if	if	SCONJ
ejpam-2592	31	52	limn	limn	NOUN
ejpam-2592	31	53	,	,	PUNCT
ejpam-2592	31	54	m→∞	m→∞	NUM
ejpam-2592	31	55	ς	ς	PROPN
ejpam-2592	31	56	�	�	PROPN
ejpam-2592	31	57	xn	xn	PROPN
ejpam-2592	31	58	,	,	PUNCT
ejpam-2592	31	59	xm	xm	PROPN
ejpam-2592	31	60	�	�	PROPN
ejpam-2592	31	61	exists	exist	VERB
ejpam-2592	31	62	and	and	CCONJ
ejpam-2592	31	63	is	be	AUX
ejpam-2592	31	64	finite	finite	ADJ
ejpam-2592	31	65	;	;	PUNCT
ejpam-2592	31	66	(	(	PUNCT
ejpam-2592	31	67	c	c	X
ejpam-2592	31	68	)	)	PUNCT
ejpam-2592	31	69	(	(	PUNCT
ejpam-2592	31	70	x	x	X
ejpam-2592	31	71	,	,	PUNCT
ejpam-2592	31	72	ς	ς	PROPN
ejpam-2592	31	73	)	)	PUNCT
ejpam-2592	31	74	is	be	AUX
ejpam-2592	31	75	a	a	DET
ejpam-2592	31	76	complete	complete	ADJ
ejpam-2592	31	77	b	b	X
ejpam-2592	31	78	-	-	PUNCT
ejpam-2592	31	79	metric	metric	ADJ
ejpam-2592	31	80	-	-	PUNCT
ejpam-2592	31	81	like	like	ADJ
ejpam-2592	31	82	space	space	NOUN
ejpam-2592	31	83	if	if	SCONJ
ejpam-2592	31	84	for	for	ADP
ejpam-2592	31	85	every	every	DET
ejpam-2592	31	86	cauchy	cauchy	ADJ
ejpam-2592	31	87	sequence	sequence	NOUN
ejpam-2592	31	88	�	�	PROPN
ejpam-2592	31	89	xn	xn	PROPN
ejpam-2592	32	1	in	in	ADP
ejpam-2592	32	2	x	x	SYM
ejpam-2592	32	3	there	there	PRON
ejpam-2592	32	4	exists	exist	VERB
ejpam-2592	32	5	x	x	X
ejpam-2592	32	6	∈	∈	PROPN
ejpam-2592	32	7	x	x	PUNCT
ejpam-2592	32	8	such	such	ADJ
ejpam-2592	32	9	that	that	DET
ejpam-2592	32	10	limn	limn	NOUN
ejpam-2592	32	11	,	,	PUNCT
ejpam-2592	32	12	m→∞	m→∞	NUM
ejpam-2592	32	13	ς	ς	PROPN
ejpam-2592	32	14	�	�	PROPN
ejpam-2592	32	15	xn	xn	PROPN
ejpam-2592	32	16	,	,	PUNCT
ejpam-2592	32	17	xm	xm	PROPN
ejpam-2592	32	18	�	�	PROPN
ejpam-2592	32	19	=	=	SYM
ejpam-2592	32	20	limn→∞	limn→∞	PROPN
ejpam-2592	32	21	ς	ς	PROPN
ejpam-2592	32	22	�	�	PROPN
ejpam-2592	32	23	xn	xn	PROPN
ejpam-2592	32	24	,	,	PUNCT
ejpam-2592	32	25	x	x	X
ejpam-2592	32	26	�	�	PROPN
ejpam-2592	32	27	=	=	SYM
ejpam-2592	32	28	ς	ς	PROPN
ejpam-2592	32	29	(	(	PUNCT
ejpam-2592	32	30	x	x	NOUN
ejpam-2592	32	31	,	,	PUNCT
ejpam-2592	32	32	x	x	NOUN
ejpam-2592	32	33	)	)	PUNCT
ejpam-2592	32	34	.	.	PUNCT
ejpam-2592	33	1	it	it	PRON
ejpam-2592	33	2	is	be	AUX
ejpam-2592	33	3	obvious	obvious	ADJ
ejpam-2592	33	4	that	that	SCONJ
ejpam-2592	33	5	the	the	DET
ejpam-2592	33	6	limit	limit	NOUN
ejpam-2592	33	7	of	of	ADP
ejpam-2592	33	8	a	a	DET
ejpam-2592	33	9	sequence	sequence	NOUN
ejpam-2592	33	10	in	in	ADP
ejpam-2592	33	11	b	b	NOUN
ejpam-2592	33	12	-	-	PUNCT
ejpam-2592	33	13	metric	metric	ADJ
ejpam-2592	33	14	-	-	PUNCT
ejpam-2592	33	15	like	like	ADJ
ejpam-2592	33	16	space	space	NOUN
ejpam-2592	33	17	is	be	AUX
ejpam-2592	33	18	usually	usually	ADV
ejpam-2592	33	19	not	not	PART
ejpam-2592	33	20	unique	unique	ADJ
ejpam-2592	33	21	(	(	PUNCT
ejpam-2592	33	22	see	see	VERB
ejpam-2592	33	23	[	[	X
ejpam-2592	33	24	3	3	NUM
ejpam-2592	33	25	,	,	PUNCT
ejpam-2592	33	26	remark	remark	VERB
ejpam-2592	33	27	1.1	1.1	NUM
ejpam-2592	33	28	]	]	PUNCT
ejpam-2592	33	29	)	)	PUNCT
ejpam-2592	33	30	.	.	PUNCT
ejpam-2592	34	1	lemma	lemma	PROPN
ejpam-2592	34	2	1	1	NUM
ejpam-2592	34	3	(	(	PUNCT
ejpam-2592	34	4	[	[	X
ejpam-2592	34	5	4	4	NUM
ejpam-2592	34	6	]	]	NUM
ejpam-2592	34	7	)	)	PUNCT
ejpam-2592	34	8	.	.	PUNCT
ejpam-2592	35	1	let	let	VERB
ejpam-2592	35	2	(	(	PUNCT
ejpam-2592	35	3	x	x	X
ejpam-2592	35	4	,	,	PUNCT
ejpam-2592	35	5	ς	ς	PROPN
ejpam-2592	35	6	)	)	PUNCT
ejpam-2592	35	7	be	be	VERB
ejpam-2592	35	8	a	a	DET
ejpam-2592	35	9	b	b	NOUN
ejpam-2592	35	10	-	-	PUNCT
ejpam-2592	35	11	metric	metric	ADJ
ejpam-2592	35	12	-	-	PUNCT
ejpam-2592	35	13	like	like	ADJ
ejpam-2592	35	14	space	space	NOUN
ejpam-2592	35	15	with	with	ADP
ejpam-2592	35	16	coefficient	coefficient	NOUN
ejpam-2592	35	17	κ	κ	NOUN
ejpam-2592	35	18	,	,	PUNCT
ejpam-2592	35	19	and	and	CCONJ
ejpam-2592	35	20	suppose	suppose	VERB
ejpam-2592	35	21	that	that	SCONJ
ejpam-2592	35	22	�	�	PROPN
ejpam-2592	35	23	xn	xn	PROPN
ejpam-2592	35	24	and	and	CCONJ
ejpam-2592	35	25	�	�	PROPN
ejpam-2592	35	26	yn	yn	PROPN
ejpam-2592	35	27	are	be	AUX
ejpam-2592	35	28	convergent	convergent	ADJ
ejpam-2592	35	29	to	to	ADP
ejpam-2592	35	30	x	x	PROPN
ejpam-2592	35	31	and	and	CCONJ
ejpam-2592	35	32	y	y	PROPN
ejpam-2592	35	33	,	,	PUNCT
ejpam-2592	35	34	respectively	respectively	ADV
ejpam-2592	35	35	.	.	PUNCT
ejpam-2592	36	1	then	then	ADV
ejpam-2592	36	2	one	one	PRON
ejpam-2592	36	3	has	have	VERB
ejpam-2592	36	4	1	1	NUM
ejpam-2592	36	5	κ2	κ2	NOUN
ejpam-2592	36	6	ς	ς	PROPN
ejpam-2592	36	7	�	�	PROPN
ejpam-2592	36	8	x	x	SYM
ejpam-2592	36	9	,	,	PUNCT
ejpam-2592	36	10	y	y	PROPN
ejpam-2592	36	11	�	�	PROPN
ejpam-2592	37	1	−	−	PROPN
ejpam-2592	37	2	1	1	NUM
ejpam-2592	37	3	κ	κ	PROPN
ejpam-2592	37	4	ς	ς	PROPN
ejpam-2592	37	5	(	(	PUNCT
ejpam-2592	37	6	x	x	INTJ
ejpam-2592	37	7	,	,	PUNCT
ejpam-2592	37	8	x)−	x)−	PROPN
ejpam-2592	37	9	ς	ς	PROPN
ejpam-2592	37	10	�	�	PROPN
ejpam-2592	37	11	y	y	PROPN
ejpam-2592	37	12	,	,	PUNCT
ejpam-2592	37	13	y	y	PROPN
ejpam-2592	37	14	�	�	PROPN
ejpam-2592	37	15	≤	≤	PROPN
ejpam-2592	37	16	lim	lim	PROPN
ejpam-2592	37	17	inf	inf	PROPN
ejpam-2592	37	18	n→∞	n→∞	X
ejpam-2592	37	19	ς	ς	PROPN
ejpam-2592	37	20	�	�	PROPN
ejpam-2592	37	21	xn	xn	PROPN
ejpam-2592	37	22	,	,	PUNCT
ejpam-2592	37	23	yn	yn	PROPN
ejpam-2592	37	24	�	�	PROPN
ejpam-2592	37	25	≤	≤	PROPN
ejpam-2592	37	26	lim	lim	PROPN
ejpam-2592	37	27	sup	sup	VERB
ejpam-2592	37	28	n→∞	n→∞	NUM
ejpam-2592	37	29	ς	ς	PROPN
ejpam-2592	37	30	�	�	PROPN
ejpam-2592	37	31	xn	xn	PROPN
ejpam-2592	37	32	,	,	PUNCT
ejpam-2592	37	33	yn	yn	PROPN
ejpam-2592	37	34	�	�	PROPN
ejpam-2592	37	35	≤κς	≤κς	PROPN
ejpam-2592	37	36	(	(	PUNCT
ejpam-2592	37	37	x	x	INTJ
ejpam-2592	37	38	,	,	PUNCT
ejpam-2592	37	39	x	x	NOUN
ejpam-2592	37	40	)	)	PUNCT
ejpam-2592	37	41	+	+	CCONJ
ejpam-2592	37	42	κ2ς	κ2ς	PROPN
ejpam-2592	37	43	�	�	PROPN
ejpam-2592	37	44	y	y	PROPN
ejpam-2592	37	45	,	,	PUNCT
ejpam-2592	37	46	y	y	PROPN
ejpam-2592	37	47	�	�	PROPN
ejpam-2592	37	48	+	+	CCONJ
ejpam-2592	37	49	κ2ς	κ2ς	PROPN
ejpam-2592	37	50	�	�	PROPN
ejpam-2592	37	51	x	x	SYM
ejpam-2592	37	52	,	,	PUNCT
ejpam-2592	37	53	y	y	PROPN
ejpam-2592	37	54	�	�	PROPN
ejpam-2592	37	55	.	.	PUNCT
ejpam-2592	38	1	in	in	ADP
ejpam-2592	38	2	particular	particular	ADJ
ejpam-2592	38	3	,	,	PUNCT
ejpam-2592	38	4	if	if	SCONJ
ejpam-2592	38	5	ς	ς	PROPN
ejpam-2592	38	6	�	�	PROPN
ejpam-2592	38	7	x	x	SYM
ejpam-2592	38	8	,	,	PUNCT
ejpam-2592	38	9	y	y	PROPN
ejpam-2592	38	10	�	�	PROPN
ejpam-2592	38	11	=	=	SYM
ejpam-2592	38	12	0	0	PROPN
ejpam-2592	38	13	,	,	PUNCT
ejpam-2592	38	14	then	then	ADV
ejpam-2592	38	15	one	one	PRON
ejpam-2592	38	16	has	have	VERB
ejpam-2592	38	17	limn→∞	limn→∞	PROPN
ejpam-2592	38	18	ς	ς	PROPN
ejpam-2592	38	19	�	�	PROPN
ejpam-2592	38	20	xn	xn	PROPN
ejpam-2592	38	21	,	,	PUNCT
ejpam-2592	38	22	yn	yn	PROPN
ejpam-2592	38	23	�	�	PROPN
ejpam-2592	38	24	=	=	SYM
ejpam-2592	38	25	0	0	X
ejpam-2592	38	26	.	.	PUNCT
ejpam-2592	39	1	moreover	moreover	ADV
ejpam-2592	39	2	,	,	PUNCT
ejpam-2592	39	3	for	for	ADP
ejpam-2592	39	4	each	each	DET
ejpam-2592	39	5	z	z	NOUN
ejpam-2592	39	6	∈	∈	PROPN
ejpam-2592	39	7	x	x	X
ejpam-2592	39	8	one	one	NOUN
ejpam-2592	39	9	has	have	VERB
ejpam-2592	39	10	1	1	NUM
ejpam-2592	39	11	κ	κ	NOUN
ejpam-2592	39	12	ς	ς	PROPN
ejpam-2592	39	13	(	(	PUNCT
ejpam-2592	39	14	x	x	PROPN
ejpam-2592	39	15	,	,	PUNCT
ejpam-2592	39	16	z)−	z)−	PROPN
ejpam-2592	39	17	ς	ς	PROPN
ejpam-2592	39	18	(	(	PUNCT
ejpam-2592	39	19	x	x	INTJ
ejpam-2592	39	20	,	,	PUNCT
ejpam-2592	39	21	x	x	NOUN
ejpam-2592	39	22	)	)	PUNCT
ejpam-2592	39	23	≤	≤	NOUN
ejpam-2592	39	24	lim	lim	PROPN
ejpam-2592	39	25	inf	inf	PROPN
ejpam-2592	39	26	n→∞	n→∞	X
ejpam-2592	39	27	ς	ς	PROPN
ejpam-2592	39	28	�	�	PROPN
ejpam-2592	39	29	xn	xn	PROPN
ejpam-2592	39	30	,	,	PUNCT
ejpam-2592	39	31	z	z	PROPN
ejpam-2592	39	32	�	�	PROPN
ejpam-2592	39	33	≤	≤	PROPN
ejpam-2592	39	34	lim	lim	PROPN
ejpam-2592	39	35	sup	sup	VERB
ejpam-2592	39	36	n→∞	n→∞	NUM
ejpam-2592	39	37	ς	ς	PROPN
ejpam-2592	39	38	�	�	PROPN
ejpam-2592	39	39	xn	xn	PROPN
ejpam-2592	39	40	,	,	PUNCT
ejpam-2592	39	41	z	z	PROPN
ejpam-2592	39	42	�	�	PROPN
ejpam-2592	40	1	≤κς	≤κς	PROPN
ejpam-2592	40	2	(	(	PUNCT
ejpam-2592	40	3	x	x	INTJ
ejpam-2592	40	4	,	,	PUNCT
ejpam-2592	40	5	z	z	NOUN
ejpam-2592	40	6	)	)	PUNCT
ejpam-2592	40	7	+	+	CCONJ
ejpam-2592	40	8	κς	κς	ADP
ejpam-2592	40	9	(	(	PUNCT
ejpam-2592	40	10	x	x	INTJ
ejpam-2592	40	11	,	,	PUNCT
ejpam-2592	40	12	x	x	NOUN
ejpam-2592	40	13	)	)	PUNCT
ejpam-2592	40	14	.	.	PUNCT
ejpam-2592	41	1	3	3	X
ejpam-2592	41	2	.	.	X
ejpam-2592	41	3	preliminaries	preliminary	NOUN
ejpam-2592	41	4	let	let	VERB
ejpam-2592	41	5	ψ	ψ	PART
ejpam-2592	41	6	be	be	AUX
ejpam-2592	41	7	the	the	DET
ejpam-2592	41	8	family	family	NOUN
ejpam-2592	41	9	of	of	ADP
ejpam-2592	41	10	function	function	NOUN
ejpam-2592	41	11	ψ	ψ	X
ejpam-2592	41	12	:	:	PUNCT
ejpam-2592	42	1	[	[	X
ejpam-2592	42	2	0,∞)→	0,∞)→	NOUN
ejpam-2592	42	3	[	[	X
ejpam-2592	42	4	0,∞	0,∞	NOUN
ejpam-2592	42	5	)	)	PUNCT
ejpam-2592	42	6	satisfying	satisfy	VERB
ejpam-2592	42	7	the	the	DET
ejpam-2592	42	8	following	follow	VERB
ejpam-2592	42	9	conditions	condition	NOUN
ejpam-2592	42	10	:	:	PUNCT
ejpam-2592	42	11	(	(	PUNCT
ejpam-2592	42	12	i	i	NOUN
ejpam-2592	42	13	)	)	PUNCT
ejpam-2592	42	14	ψ	ψ	NOUN
ejpam-2592	42	15	is	be	AUX
ejpam-2592	42	16	continuous	continuous	ADJ
ejpam-2592	42	17	and	and	CCONJ
ejpam-2592	42	18	nondecreasing	nondecreasing	ADJ
ejpam-2592	42	19	;	;	PUNCT
ejpam-2592	42	20	(	(	PUNCT
ejpam-2592	42	21	ii	ii	NOUN
ejpam-2592	42	22	)	)	PUNCT
ejpam-2592	42	23	ψ	ψ	PROPN
ejpam-2592	42	24	(	(	PUNCT
ejpam-2592	42	25	t	t	PROPN
ejpam-2592	42	26	)	)	PUNCT
ejpam-2592	42	27	=	=	SYM
ejpam-2592	42	28	0	0	PUNCT
ejpam-2592	43	1	if	if	SCONJ
ejpam-2592	43	2	and	and	CCONJ
ejpam-2592	43	3	only	only	ADV
ejpam-2592	43	4	if	if	SCONJ
ejpam-2592	43	5	t	t	NOUN
ejpam-2592	43	6	=	=	SYM
ejpam-2592	43	7	0	0	PROPN
ejpam-2592	43	8	.	.	PUNCT
ejpam-2592	43	9	m.	m.	NOUN
ejpam-2592	43	10	akturk	akturk	PROPN
ejpam-2592	43	11	,	,	PUNCT
ejpam-2592	43	12	m.	m.	NOUN
ejpam-2592	43	13	kır	kır	PROPN
ejpam-2592	43	14	,	,	PUNCT
ejpam-2592	43	15	e.	e.	PROPN
ejpam-2592	43	16	yolacan	yolacan	PROPN
ejpam-2592	43	17	/	/	SYM
ejpam-2592	43	18	eur	eur	PROPN
ejpam-2592	43	19	.	.	PUNCT
ejpam-2592	44	1	j.	j.	PROPN
ejpam-2592	44	2	pure	pure	PROPN
ejpam-2592	44	3	appl	appl	PROPN
ejpam-2592	44	4	.	.	PROPN
ejpam-2592	44	5	math	math	PROPN
ejpam-2592	44	6	,	,	PUNCT
ejpam-2592	44	7	9	9	NUM
ejpam-2592	44	8	(	(	PUNCT
ejpam-2592	44	9	2016	2016	NUM
ejpam-2592	44	10	)	)	PUNCT
ejpam-2592	44	11	,	,	PUNCT
ejpam-2592	44	12	175	175	NUM
ejpam-2592	44	13	-	-	SYM
ejpam-2592	44	14	185	185	NUM
ejpam-2592	44	15	177	177	NUM
ejpam-2592	44	16	samet	samet	NOUN
ejpam-2592	44	17	et	et	PROPN
ejpam-2592	44	18	al	al	PROPN
ejpam-2592	44	19	.	.	PUNCT
ejpam-2592	45	1	[	[	X
ejpam-2592	45	2	5	5	NUM
ejpam-2592	45	3	]	]	PUNCT
ejpam-2592	45	4	introduced	introduce	VERB
ejpam-2592	45	5	the	the	DET
ejpam-2592	45	6	class	class	NOUN
ejpam-2592	45	7	of	of	ADP
ejpam-2592	45	8	α−admissable	α−admissable	NUM
ejpam-2592	45	9	mappings	mapping	NOUN
ejpam-2592	45	10	.	.	PUNCT
ejpam-2592	46	1	definition	definition	NOUN
ejpam-2592	46	2	3	3	NUM
ejpam-2592	46	3	(	(	PUNCT
ejpam-2592	46	4	[	[	X
ejpam-2592	46	5	5	5	NUM
ejpam-2592	46	6	]	]	PUNCT
ejpam-2592	46	7	)	)	PUNCT
ejpam-2592	46	8	.	.	PUNCT
ejpam-2592	47	1	for	for	ADP
ejpam-2592	47	2	a	a	DET
ejpam-2592	47	3	nonempty	nonempty	ADV
ejpam-2592	47	4	set	set	VERB
ejpam-2592	47	5	x	x	SYM
ejpam-2592	47	6	,	,	PUNCT
ejpam-2592	47	7	let	let	VERB
ejpam-2592	47	8	t	t	NOUN
ejpam-2592	47	9	:	:	PUNCT
ejpam-2592	47	10	x	x	X
ejpam-2592	47	11	→	→	SYM
ejpam-2592	47	12	x	x	X
ejpam-2592	47	13	and	and	CCONJ
ejpam-2592	47	14	α	α	NOUN
ejpam-2592	47	15	:	:	PUNCT
ejpam-2592	48	1	x	x	SYM
ejpam-2592	48	2	×	×	NOUN
ejpam-2592	48	3	x	x	INTJ
ejpam-2592	48	4	→	→	X
ejpam-2592	48	5	[	[	X
ejpam-2592	48	6	0,∞	0,∞	NOUN
ejpam-2592	48	7	)	)	PUNCT
ejpam-2592	48	8	be	be	AUX
ejpam-2592	48	9	given	give	VERB
ejpam-2592	48	10	mappings	mapping	NOUN
ejpam-2592	48	11	.	.	PUNCT
ejpam-2592	49	1	we	we	PRON
ejpam-2592	49	2	say	say	VERB
ejpam-2592	49	3	that	that	SCONJ
ejpam-2592	49	4	t	t	PROPN
ejpam-2592	49	5	is	be	AUX
ejpam-2592	49	6	α	α	NOUN
ejpam-2592	49	7	-	-	ADJ
ejpam-2592	49	8	admissible	admissible	ADJ
ejpam-2592	49	9	if	if	SCONJ
ejpam-2592	49	10	for	for	ADP
ejpam-2592	49	11	all	all	DET
ejpam-2592	49	12	x	x	SYM
ejpam-2592	49	13	,	,	PUNCT
ejpam-2592	49	14	y	y	PROPN
ejpam-2592	49	15	∈	∈	PROPN
ejpam-2592	49	16	x	x	INTJ
ejpam-2592	49	17	,	,	PUNCT
ejpam-2592	49	18	we	we	PRON
ejpam-2592	49	19	have	have	VERB
ejpam-2592	49	20	α	α	DET
ejpam-2592	49	21	�	�	PROPN
ejpam-2592	49	22	x	x	SYM
ejpam-2592	49	23	,	,	PUNCT
ejpam-2592	49	24	y	y	PROPN
ejpam-2592	49	25	�	�	PROPN
ejpam-2592	49	26	≥	≥	NUM
ejpam-2592	49	27	1⇒	1⇒	PROPN
ejpam-2592	49	28	α	α	PROPN
ejpam-2592	49	29	�	�	PROPN
ejpam-2592	49	30	�	�	PROPN
ejpam-2592	49	31	t	t	PROPN
ejpam-2592	49	32	x	x	X
ejpam-2592	49	33	,	,	PUNCT
ejpam-2592	49	34	t	t	PROPN
ejpam-2592	49	35	y	y	PROPN
ejpam-2592	49	36	�	�	PROPN
ejpam-2592	49	37	�	�	PROPN
ejpam-2592	49	38	≥	≥	NUM
ejpam-2592	49	39	1	1	NUM
ejpam-2592	49	40	.	.	PUNCT
ejpam-2592	50	1	now	now	ADV
ejpam-2592	50	2	,	,	PUNCT
ejpam-2592	50	3	we	we	PRON
ejpam-2592	50	4	establish	establish	VERB
ejpam-2592	50	5	the	the	DET
ejpam-2592	50	6	α−ψ−ϕ-contractive	α−ψ−ϕ-contractive	ADJ
ejpam-2592	50	7	type	type	NOUN
ejpam-2592	50	8	mapping	mapping	NOUN
ejpam-2592	50	9	on	on	ADP
ejpam-2592	50	10	b	b	X
ejpam-2592	50	11	-	-	PUNCT
ejpam-2592	50	12	metric	metric	ADJ
ejpam-2592	50	13	-	-	PUNCT
ejpam-2592	50	14	like	like	ADJ
ejpam-2592	50	15	space	space	NOUN
ejpam-2592	50	16	.	.	PUNCT
ejpam-2592	51	1	definition	definition	NOUN
ejpam-2592	51	2	4	4	NUM
ejpam-2592	51	3	.	.	PUNCT
ejpam-2592	52	1	let	let	AUX
ejpam-2592	52	2	(	(	PUNCT
ejpam-2592	52	3	x	x	X
ejpam-2592	52	4	,	,	PUNCT
ejpam-2592	52	5	ς	ς	PROPN
ejpam-2592	52	6	)	)	PUNCT
ejpam-2592	52	7	be	be	VERB
ejpam-2592	52	8	a	a	DET
ejpam-2592	52	9	b	b	NOUN
ejpam-2592	52	10	-	-	PUNCT
ejpam-2592	52	11	metric	metric	ADJ
ejpam-2592	52	12	-	-	PUNCT
ejpam-2592	52	13	like	like	ADJ
ejpam-2592	52	14	space	space	NOUN
ejpam-2592	52	15	with	with	ADP
ejpam-2592	52	16	coefficient	coefficient	NOUN
ejpam-2592	52	17	κ	κ	PRON
ejpam-2592	52	18	≥	≥	NOUN
ejpam-2592	52	19	1	1	NUM
ejpam-2592	52	20	.	.	PUNCT
ejpam-2592	53	1	we	we	PRON
ejpam-2592	53	2	say	say	VERB
ejpam-2592	53	3	that	that	PRON
ejpam-2592	53	4	t	t	NOUN
ejpam-2592	53	5	:	:	PUNCT
ejpam-2592	53	6	x	x	X
ejpam-2592	53	7	→	→	PUNCT
ejpam-2592	53	8	x	x	X
ejpam-2592	53	9	is	be	AUX
ejpam-2592	53	10	an	an	DET
ejpam-2592	53	11	α−ψ−ϕcontractive	α−ψ−ϕcontractive	ADJ
ejpam-2592	53	12	type	type	NOUN
ejpam-2592	53	13	mapping	mapping	NOUN
ejpam-2592	53	14	if	if	SCONJ
ejpam-2592	53	15	there	there	PRON
ejpam-2592	53	16	exists	exist	VERB
ejpam-2592	53	17	three	three	NUM
ejpam-2592	53	18	functions	function	NOUN
ejpam-2592	53	19	α	α	NOUN
ejpam-2592	53	20	:	:	PUNCT
ejpam-2592	53	21	x	x	SYM
ejpam-2592	53	22	×	×	NOUN
ejpam-2592	53	23	x	x	INTJ
ejpam-2592	53	24	→	→	X
ejpam-2592	53	25	[	[	X
ejpam-2592	53	26	0,∞	0,∞	NUM
ejpam-2592	53	27	)	)	PUNCT
ejpam-2592	53	28	and	and	CCONJ
ejpam-2592	53	29	ψ,ϕ	ψ,ϕ	NOUN
ejpam-2592	53	30	∈	∈	NOUN
ejpam-2592	53	31	ψ	ψ	ADP
ejpam-2592	53	32	such	such	ADJ
ejpam-2592	53	33	that	that	SCONJ
ejpam-2592	53	34	α	α	PROPN
ejpam-2592	53	35	�	�	PROPN
ejpam-2592	53	36	x	x	SYM
ejpam-2592	53	37	,	,	PUNCT
ejpam-2592	53	38	y	y	PROPN
ejpam-2592	53	39	�	�	PROPN
ejpam-2592	53	40	ψ	ψ	ADP
ejpam-2592	53	41	�	�	PROPN
ejpam-2592	53	42	κς	κς	ADP
ejpam-2592	53	43	�	�	PROPN
ejpam-2592	53	44	t	t	PROPN
ejpam-2592	53	45	x	x	PROPN
ejpam-2592	53	46	,	,	PUNCT
ejpam-2592	53	47	t	t	PROPN
ejpam-2592	53	48	y	y	PROPN
ejpam-2592	53	49	�	�	PROPN
ejpam-2592	53	50	�	�	PROPN
ejpam-2592	53	51	≤ψ	≤ψ	PROPN
ejpam-2592	53	52	�	�	PROPN
ejpam-2592	53	53	m	m	PROPN
ejpam-2592	53	54	�	�	PROPN
ejpam-2592	53	55	x	x	SYM
ejpam-2592	53	56	,	,	PUNCT
ejpam-2592	53	57	y	y	PROPN
ejpam-2592	53	58	�	�	PROPN
ejpam-2592	53	59	�	�	PROPN
ejpam-2592	53	60	−ϕ	−ϕ	ADV
ejpam-2592	53	61	�	�	PROPN
ejpam-2592	53	62	m	m	PROPN
ejpam-2592	53	63	�	�	PROPN
ejpam-2592	53	64	x	x	SYM
ejpam-2592	53	65	,	,	PUNCT
ejpam-2592	53	66	y	y	PROPN
ejpam-2592	53	67	�	�	PROPN
ejpam-2592	53	68	�	�	PROPN
ejpam-2592	53	69	(	(	PUNCT
ejpam-2592	53	70	1	1	NUM
ejpam-2592	53	71	)	)	PUNCT
ejpam-2592	53	72	where	where	SCONJ
ejpam-2592	53	73	m	m	VERB
ejpam-2592	53	74	�	�	PROPN
ejpam-2592	53	75	x	x	SYM
ejpam-2592	53	76	,	,	PUNCT
ejpam-2592	53	77	y	y	PROPN
ejpam-2592	53	78	�	�	PROPN
ejpam-2592	53	79	=	=	NUM
ejpam-2592	53	80	max	max	PROPN
ejpam-2592	53	81	¨	¨	NOUN
ejpam-2592	53	82	ς	ς	PROPN
ejpam-2592	53	83	�	�	PROPN
ejpam-2592	53	84	x	x	SYM
ejpam-2592	53	85	,	,	PUNCT
ejpam-2592	53	86	y	y	PROPN
ejpam-2592	53	87	�	�	PROPN
ejpam-2592	53	88	,	,	PUNCT
ejpam-2592	53	89	ς	ς	PROPN
ejpam-2592	53	90	(	(	PUNCT
ejpam-2592	53	91	x	x	PROPN
ejpam-2592	53	92	,	,	PUNCT
ejpam-2592	53	93	t	t	PROPN
ejpam-2592	53	94	x	x	PROPN
ejpam-2592	53	95	)	)	PUNCT
ejpam-2592	53	96	,	,	PUNCT
ejpam-2592	53	97	ς	ς	PROPN
ejpam-2592	53	98	�	�	PROPN
ejpam-2592	53	99	y	y	PROPN
ejpam-2592	53	100	,	,	PUNCT
ejpam-2592	53	101	t	t	PROPN
ejpam-2592	53	102	y	y	PROPN
ejpam-2592	53	103	�	�	PROPN
ejpam-2592	53	104	,	,	PUNCT
ejpam-2592	53	105	ς	ς	PROPN
ejpam-2592	53	106	�	�	PROPN
ejpam-2592	53	107	x	x	SYM
ejpam-2592	53	108	,	,	PUNCT
ejpam-2592	53	109	t	t	PROPN
ejpam-2592	53	110	y	y	PROPN
ejpam-2592	53	111	�	�	PROPN
ejpam-2592	53	112	+	+	CCONJ
ejpam-2592	53	113	ς	ς	PROPN
ejpam-2592	53	114	�	�	PROPN
ejpam-2592	53	115	y	y	PROPN
ejpam-2592	53	116	,	,	PUNCT
ejpam-2592	53	117	t	t	PROPN
ejpam-2592	53	118	x	x	SYM
ejpam-2592	53	119	�	�	PROPN
ejpam-2592	53	120	2κ	2κ	NOUN
ejpam-2592	53	121	«	«	PUNCT
ejpam-2592	53	122	(	(	PUNCT
ejpam-2592	53	123	2	2	NUM
ejpam-2592	53	124	)	)	PUNCT
ejpam-2592	53	125	for	for	ADP
ejpam-2592	53	126	all	all	DET
ejpam-2592	53	127	x	x	SYM
ejpam-2592	53	128	,	,	PUNCT
ejpam-2592	53	129	y	y	PROPN
ejpam-2592	53	130	∈	∈	PROPN
ejpam-2592	53	131	x	x	X
ejpam-2592	53	132	.	.	PUNCT
ejpam-2592	54	1	4	4	X
ejpam-2592	54	2	.	.	X
ejpam-2592	54	3	main	main	ADJ
ejpam-2592	54	4	results	result	NOUN
ejpam-2592	54	5	theorem	theorem	VERB
ejpam-2592	54	6	1	1	NUM
ejpam-2592	54	7	.	.	PUNCT
ejpam-2592	55	1	let	let	AUX
ejpam-2592	55	2	(	(	PUNCT
ejpam-2592	55	3	x	x	X
ejpam-2592	55	4	,	,	PUNCT
ejpam-2592	55	5	ς	ς	PROPN
ejpam-2592	55	6	)	)	PUNCT
ejpam-2592	55	7	be	be	AUX
ejpam-2592	55	8	a	a	DET
ejpam-2592	55	9	complete	complete	ADJ
ejpam-2592	55	10	b	b	X
ejpam-2592	55	11	-	-	PUNCT
ejpam-2592	55	12	metric	metric	ADJ
ejpam-2592	55	13	-	-	PUNCT
ejpam-2592	55	14	like	like	ADJ
ejpam-2592	55	15	space	space	NOUN
ejpam-2592	55	16	with	with	ADP
ejpam-2592	55	17	the	the	DET
ejpam-2592	55	18	constant	constant	ADJ
ejpam-2592	55	19	κ	κ	X
ejpam-2592	55	20	≥	≥	NOUN
ejpam-2592	55	21	1	1	NUM
ejpam-2592	55	22	and	and	CCONJ
ejpam-2592	55	23	t	t	NOUN
ejpam-2592	55	24	:	:	PUNCT
ejpam-2592	55	25	x	x	X
ejpam-2592	55	26	→	→	PUNCT
ejpam-2592	55	27	x	x	PUNCT
ejpam-2592	55	28	be	be	AUX
ejpam-2592	55	29	an	an	DET
ejpam-2592	55	30	α−ψ−ϕ-contractive	α−ψ−ϕ-contractive	ADJ
ejpam-2592	55	31	mapping	mapping	NOUN
ejpam-2592	55	32	.	.	PUNCT
ejpam-2592	56	1	suppose	suppose	VERB
ejpam-2592	56	2	that	that	SCONJ
ejpam-2592	56	3	(	(	PUNCT
ejpam-2592	56	4	i	i	NOUN
ejpam-2592	56	5	)	)	PUNCT
ejpam-2592	56	6	t	t	PROPN
ejpam-2592	56	7	is	be	AUX
ejpam-2592	56	8	α	α	PRON
ejpam-2592	56	9	-	-	ADJ
ejpam-2592	56	10	admissible	admissible	ADJ
ejpam-2592	56	11	;	;	PUNCT
ejpam-2592	56	12	(	(	PUNCT
ejpam-2592	56	13	ii	ii	NOUN
ejpam-2592	56	14	)	)	PUNCT
ejpam-2592	56	15	there	there	PRON
ejpam-2592	56	16	exists	exist	VERB
ejpam-2592	56	17	x0	x0	PROPN
ejpam-2592	56	18	∈	∈	PROPN
ejpam-2592	56	19	x	x	PUNCT
ejpam-2592	56	20	such	such	ADJ
ejpam-2592	56	21	that	that	SCONJ
ejpam-2592	56	22	α	α	PRON
ejpam-2592	56	23	�	�	PROPN
ejpam-2592	56	24	x0	x0	PROPN
ejpam-2592	56	25	,	,	PUNCT
ejpam-2592	56	26	t	t	PROPN
ejpam-2592	56	27	x0	x0	PROPN
ejpam-2592	56	28	�	�	PROPN
ejpam-2592	56	29	≥	≥	NUM
ejpam-2592	56	30	1	1	NUM
ejpam-2592	56	31	;	;	PUNCT
ejpam-2592	56	32	(	(	PUNCT
ejpam-2592	56	33	iii	iii	X
ejpam-2592	56	34	)	)	PUNCT
ejpam-2592	56	35	t	t	PROPN
ejpam-2592	56	36	is	be	AUX
ejpam-2592	56	37	continuous	continuous	ADJ
ejpam-2592	56	38	and	and	CCONJ
ejpam-2592	56	39	if	if	SCONJ
ejpam-2592	56	40	ς	ς	PROPN
ejpam-2592	56	41	(	(	PUNCT
ejpam-2592	56	42	x	x	NOUN
ejpam-2592	56	43	,	,	PUNCT
ejpam-2592	56	44	x	x	NOUN
ejpam-2592	56	45	)	)	PUNCT
ejpam-2592	56	46	=	=	SYM
ejpam-2592	56	47	0	0	NUM
ejpam-2592	56	48	for	for	ADP
ejpam-2592	56	49	some	some	DET
ejpam-2592	56	50	x	x	SYM
ejpam-2592	56	51	∈	∈	PROPN
ejpam-2592	56	52	x	x	X
ejpam-2592	56	53	,	,	PUNCT
ejpam-2592	56	54	then	then	ADV
ejpam-2592	56	55	α	α	X
ejpam-2592	56	56	(	(	PUNCT
ejpam-2592	56	57	ω	ω	PROPN
ejpam-2592	56	58	,	,	PUNCT
ejpam-2592	56	59	ω	ω	NOUN
ejpam-2592	56	60	)	)	PUNCT
ejpam-2592	56	61	≥	≥	NOUN
ejpam-2592	56	62	1	1	NUM
ejpam-2592	56	63	.	.	PUNCT
ejpam-2592	57	1	then	then	ADV
ejpam-2592	57	2	,	,	PUNCT
ejpam-2592	57	3	such	such	ADJ
ejpam-2592	57	4	ω	ω	PROPN
ejpam-2592	57	5	is	be	AUX
ejpam-2592	57	6	a	a	DET
ejpam-2592	57	7	fixed	fix	VERB
ejpam-2592	57	8	point	point	NOUN
ejpam-2592	57	9	of	of	ADP
ejpam-2592	57	10	t	t	PROPN
ejpam-2592	57	11	,	,	PUNCT
ejpam-2592	57	12	that	that	PRON
ejpam-2592	57	13	is	be	AUX
ejpam-2592	57	14	tω	tω	PROPN
ejpam-2592	57	15	=	=	PROPN
ejpam-2592	57	16	ω	ω	PROPN
ejpam-2592	57	17	.	.	PUNCT
ejpam-2592	58	1	proof	proof	NOUN
ejpam-2592	58	2	.	.	PUNCT
ejpam-2592	59	1	from	from	ADP
ejpam-2592	59	2	condition	condition	NOUN
ejpam-2592	59	3	(	(	PUNCT
ejpam-2592	59	4	ii	ii	NOUN
ejpam-2592	59	5	)	)	PUNCT
ejpam-2592	59	6	,	,	PUNCT
ejpam-2592	59	7	there	there	PRON
ejpam-2592	59	8	exists	exist	VERB
ejpam-2592	59	9	x0	x0	PROPN
ejpam-2592	59	10	∈	∈	PROPN
ejpam-2592	59	11	x	x	PUNCT
ejpam-2592	60	1	such	such	ADJ
ejpam-2592	60	2	that	that	SCONJ
ejpam-2592	60	3	α	α	PRON
ejpam-2592	60	4	�	�	PROPN
ejpam-2592	60	5	x0	x0	PROPN
ejpam-2592	60	6	,	,	PUNCT
ejpam-2592	60	7	t	t	PROPN
ejpam-2592	60	8	x0	x0	PROPN
ejpam-2592	60	9	�	�	PROPN
ejpam-2592	60	10	≥	≥	PROPN
ejpam-2592	60	11	1	1	NUM
ejpam-2592	60	12	.	.	PUNCT
ejpam-2592	60	13	define	define	VERB
ejpam-2592	60	14	xn+1	xn+1	PROPN
ejpam-2592	60	15	=	=	SYM
ejpam-2592	60	16	t	t	PROPN
ejpam-2592	60	17	xn	xn	PROPN
ejpam-2592	61	1	=	=	SYM
ejpam-2592	61	2	t	t	PROPN
ejpam-2592	61	3	n+1	n+1	NUM
ejpam-2592	61	4	x0	x0	PROPN
ejpam-2592	61	5	for	for	ADP
ejpam-2592	61	6	all	all	DET
ejpam-2592	61	7	n	n	PRON
ejpam-2592	61	8	≥	≥	NOUN
ejpam-2592	61	9	0	0	NUM
ejpam-2592	61	10	.	.	PUNCT
ejpam-2592	62	1	if	if	SCONJ
ejpam-2592	62	2	xn0	xn0	PROPN
ejpam-2592	62	3	=	=	SYM
ejpam-2592	63	1	xn0	xn0	PROPN
ejpam-2592	64	1	+	+	ADJ
ejpam-2592	64	2	1	1	NUM
ejpam-2592	64	3	for	for	ADP
ejpam-2592	64	4	some	some	DET
ejpam-2592	64	5	n0	n0	NUM
ejpam-2592	64	6	,	,	PUNCT
ejpam-2592	64	7	then	then	ADV
ejpam-2592	64	8	it	it	PRON
ejpam-2592	64	9	is	be	AUX
ejpam-2592	64	10	clear	clear	ADJ
ejpam-2592	64	11	that	that	SCONJ
ejpam-2592	64	12	xn0	xn0	PROPN
ejpam-2592	64	13	is	be	AUX
ejpam-2592	64	14	a	a	DET
ejpam-2592	64	15	fixed	fix	VERB
ejpam-2592	64	16	point	point	NOUN
ejpam-2592	64	17	of	of	ADP
ejpam-2592	64	18	t	t	PROPN
ejpam-2592	64	19	.	.	PUNCT
ejpam-2592	65	1	suppose	suppose	VERB
ejpam-2592	65	2	that	that	SCONJ
ejpam-2592	65	3	xn	xn	PROPN
ejpam-2592	65	4	6=	6=	NUM
ejpam-2592	65	5	xn+1	xn+1	NUM
ejpam-2592	65	6	for	for	ADP
ejpam-2592	65	7	all	all	DET
ejpam-2592	65	8	n.	n.	NOUN
ejpam-2592	65	9	observe	observe	VERB
ejpam-2592	65	10	that	that	SCONJ
ejpam-2592	65	11	α	α	PRON
ejpam-2592	65	12	�	�	PROPN
ejpam-2592	65	13	x0	x0	PROPN
ejpam-2592	65	14	,	,	PUNCT
ejpam-2592	65	15	t	t	PROPN
ejpam-2592	65	16	x0	x0	PROPN
ejpam-2592	65	17	�	�	PROPN
ejpam-2592	66	1	=	=	PUNCT
ejpam-2592	66	2	α	α	PROPN
ejpam-2592	66	3	�	�	PROPN
ejpam-2592	66	4	x0	x0	PROPN
ejpam-2592	66	5	,	,	PUNCT
ejpam-2592	66	6	x1	x1	PROPN
ejpam-2592	66	7	�	�	PROPN
ejpam-2592	66	8	≥	≥	NUM
ejpam-2592	66	9	1=⇒	1=⇒	NUM
ejpam-2592	66	10	α	α	PROPN
ejpam-2592	66	11	�	�	PROPN
ejpam-2592	66	12	t	t	PROPN
ejpam-2592	66	13	x0	x0	PROPN
ejpam-2592	66	14	,	,	PUNCT
ejpam-2592	66	15	t	t	PROPN
ejpam-2592	66	16	x1	x1	PROPN
ejpam-2592	66	17	�	�	PROPN
ejpam-2592	66	18	=	=	SYM
ejpam-2592	66	19	α	α	PROPN
ejpam-2592	66	20	�	�	PROPN
ejpam-2592	66	21	x1	x1	PROPN
ejpam-2592	66	22	,	,	PUNCT
ejpam-2592	66	23	x2	x2	PROPN
ejpam-2592	66	24	�	�	PROPN
ejpam-2592	66	25	≥	≥	NUM
ejpam-2592	66	26	1	1	NUM
ejpam-2592	66	27	,	,	PUNCT
ejpam-2592	66	28	since	since	SCONJ
ejpam-2592	66	29	t	t	PROPN
ejpam-2592	66	30	is	be	AUX
ejpam-2592	66	31	α	α	PRON
ejpam-2592	66	32	-	-	ADJ
ejpam-2592	66	33	admissible	admissible	ADJ
ejpam-2592	66	34	.	.	PUNCT
ejpam-2592	67	1	by	by	ADP
ejpam-2592	67	2	repeating	repeat	VERB
ejpam-2592	67	3	the	the	DET
ejpam-2592	67	4	process	process	NOUN
ejpam-2592	67	5	above	above	ADV
ejpam-2592	67	6	,	,	PUNCT
ejpam-2592	67	7	we	we	PRON
ejpam-2592	67	8	derive	derive	VERB
ejpam-2592	67	9	α	α	DET
ejpam-2592	67	10	�	�	PROPN
ejpam-2592	67	11	xn	xn	PROPN
ejpam-2592	67	12	,	,	PUNCT
ejpam-2592	67	13	xn+1	xn+1	PROPN
ejpam-2592	67	14	�	�	PROPN
ejpam-2592	67	15	≥	≥	NUM
ejpam-2592	67	16	1	1	NUM
ejpam-2592	67	17	,	,	PUNCT
ejpam-2592	67	18	for	for	ADP
ejpam-2592	67	19	all	all	DET
ejpam-2592	67	20	n	n	PRON
ejpam-2592	67	21	∈	∈	PROPN
ejpam-2592	67	22	n.	n.	NOUN
ejpam-2592	67	23	(	(	PUNCT
ejpam-2592	67	24	3	3	X
ejpam-2592	67	25	)	)	PUNCT
ejpam-2592	67	26	using	use	VERB
ejpam-2592	67	27	(	(	PUNCT
ejpam-2592	67	28	1	1	NUM
ejpam-2592	67	29	)	)	PUNCT
ejpam-2592	67	30	and	and	CCONJ
ejpam-2592	67	31	(	(	PUNCT
ejpam-2592	67	32	3	3	X
ejpam-2592	67	33	)	)	PUNCT
ejpam-2592	67	34	for	for	ADP
ejpam-2592	67	35	all	all	DET
ejpam-2592	67	36	n	n	PRON
ejpam-2592	67	37	∈	∈	PROPN
ejpam-2592	67	38	n	n	CCONJ
ejpam-2592	67	39	,	,	PUNCT
ejpam-2592	67	40	we	we	PRON
ejpam-2592	67	41	have	have	VERB
ejpam-2592	67	42	ψ	ψ	ADP
ejpam-2592	67	43	�	�	PROPN
ejpam-2592	67	44	κς	κς	ADP
ejpam-2592	67	45	�	�	PROPN
ejpam-2592	67	46	xn+1	xn+1	PROPN
ejpam-2592	67	47	,	,	PUNCT
ejpam-2592	67	48	xn+2	xn+2	PROPN
ejpam-2592	67	49	�	�	PROPN
ejpam-2592	67	50	�	�	PROPN
ejpam-2592	67	51	=	=	SYM
ejpam-2592	67	52	ψ	ψ	NOUN
ejpam-2592	67	53	�	�	PROPN
ejpam-2592	67	54	κς	κς	ADP
ejpam-2592	67	55	�	�	PROPN
ejpam-2592	67	56	t	t	PROPN
ejpam-2592	67	57	xn	xn	PROPN
ejpam-2592	67	58	,	,	PUNCT
ejpam-2592	67	59	t	t	PROPN
ejpam-2592	67	60	xn+1	xn+1	PROPN
ejpam-2592	67	61	�	�	PROPN
ejpam-2592	67	62	�	�	PROPN
ejpam-2592	67	63	≤α	≤α	PROPN
ejpam-2592	67	64	�	�	PROPN
ejpam-2592	67	65	xn	xn	PROPN
ejpam-2592	67	66	,	,	PUNCT
ejpam-2592	67	67	xn+1	xn+1	PROPN
ejpam-2592	67	68	�	�	PROPN
ejpam-2592	67	69	ψ	ψ	ADP
ejpam-2592	67	70	�	�	PROPN
ejpam-2592	67	71	κς	κς	ADP
ejpam-2592	67	72	�	�	PROPN
ejpam-2592	67	73	t	t	PROPN
ejpam-2592	67	74	xn	xn	PROPN
ejpam-2592	67	75	,	,	PUNCT
ejpam-2592	67	76	t	t	PROPN
ejpam-2592	67	77	xn+1	xn+1	PROPN
ejpam-2592	67	78	�	�	PROPN
ejpam-2592	67	79	�	�	PROPN
ejpam-2592	67	80	m.	m.	NOUN
ejpam-2592	67	81	akturk	akturk	PROPN
ejpam-2592	67	82	,	,	PUNCT
ejpam-2592	67	83	m.	m.	NOUN
ejpam-2592	67	84	kır	kır	PROPN
ejpam-2592	67	85	,	,	PUNCT
ejpam-2592	67	86	e.	e.	PROPN
ejpam-2592	67	87	yolacan	yolacan	PROPN
ejpam-2592	67	88	/	/	SYM
ejpam-2592	67	89	eur	eur	PROPN
ejpam-2592	67	90	.	.	PUNCT
ejpam-2592	68	1	j.	j.	PROPN
ejpam-2592	68	2	pure	pure	PROPN
ejpam-2592	68	3	appl	appl	PROPN
ejpam-2592	68	4	.	.	PROPN
ejpam-2592	68	5	math	math	PROPN
ejpam-2592	68	6	,	,	PUNCT
ejpam-2592	68	7	9	9	NUM
ejpam-2592	68	8	(	(	PUNCT
ejpam-2592	68	9	2016	2016	NUM
ejpam-2592	68	10	)	)	PUNCT
ejpam-2592	68	11	,	,	PUNCT
ejpam-2592	68	12	175	175	NUM
ejpam-2592	68	13	-	-	SYM
ejpam-2592	68	14	185	185	NUM
ejpam-2592	68	15	178	178	NUM
ejpam-2592	68	16	≤ψ	≤ψ	ADJ
ejpam-2592	68	17	�	�	PROPN
ejpam-2592	68	18	m	m	PROPN
ejpam-2592	68	19	�	�	PROPN
ejpam-2592	68	20	xn	xn	PROPN
ejpam-2592	68	21	,	,	PUNCT
ejpam-2592	68	22	xn+1	xn+1	PROPN
ejpam-2592	68	23	�	�	PROPN
ejpam-2592	68	24	�	�	PROPN
ejpam-2592	68	25	−ϕ	−ϕ	ADV
ejpam-2592	68	26	�	�	PROPN
ejpam-2592	68	27	m	m	PROPN
ejpam-2592	68	28	�	�	PROPN
ejpam-2592	68	29	xn	xn	PROPN
ejpam-2592	68	30	,	,	PUNCT
ejpam-2592	68	31	xn+1	xn+1	PROPN
ejpam-2592	68	32	�	�	PROPN
ejpam-2592	68	33	�	�	PROPN
ejpam-2592	68	34	(	(	PUNCT
ejpam-2592	68	35	4	4	NUM
ejpam-2592	68	36	)	)	PUNCT
ejpam-2592	68	37	where	where	SCONJ
ejpam-2592	68	38	m	m	VERB
ejpam-2592	68	39	�	�	PROPN
ejpam-2592	68	40	xn	xn	PROPN
ejpam-2592	68	41	,	,	PUNCT
ejpam-2592	68	42	xn+1	xn+1	PROPN
ejpam-2592	68	43	�	�	PROPN
ejpam-2592	69	1	=	=	NUM
ejpam-2592	69	2	max	max	PROPN
ejpam-2592	69	3	¨	¨	NOUN
ejpam-2592	69	4	ς	ς	PROPN
ejpam-2592	69	5	�	�	PROPN
ejpam-2592	69	6	xn	xn	PROPN
ejpam-2592	69	7	,	,	PUNCT
ejpam-2592	69	8	xn+1	xn+1	PROPN
ejpam-2592	69	9	�	�	PROPN
ejpam-2592	69	10	,	,	PUNCT
ejpam-2592	69	11	ς	ς	PROPN
ejpam-2592	69	12	�	�	PROPN
ejpam-2592	69	13	xn	xn	PROPN
ejpam-2592	69	14	,	,	PUNCT
ejpam-2592	69	15	t	t	PROPN
ejpam-2592	69	16	xn	xn	PROPN
ejpam-2592	69	17	�	�	PROPN
ejpam-2592	69	18	,	,	PUNCT
ejpam-2592	69	19	ς	ς	PROPN
ejpam-2592	69	20	�	�	PROPN
ejpam-2592	69	21	xn+1	xn+1	PROPN
ejpam-2592	69	22	,	,	PUNCT
ejpam-2592	69	23	t	t	PROPN
ejpam-2592	69	24	xn+1	xn+1	PROPN
ejpam-2592	69	25	�	�	PROPN
ejpam-2592	69	26	,	,	PUNCT
ejpam-2592	69	27	ς	ς	PROPN
ejpam-2592	69	28	�	�	PROPN
ejpam-2592	69	29	xn	xn	PROPN
ejpam-2592	69	30	,	,	PUNCT
ejpam-2592	69	31	t	t	PROPN
ejpam-2592	69	32	xn+1	xn+1	PROPN
ejpam-2592	69	33	�	�	PROPN
ejpam-2592	69	34	+	+	CCONJ
ejpam-2592	69	35	ς	ς	PROPN
ejpam-2592	69	36	�	�	PROPN
ejpam-2592	69	37	xn+1	xn+1	PROPN
ejpam-2592	69	38	,	,	PUNCT
ejpam-2592	69	39	t	t	PROPN
ejpam-2592	69	40	xn	xn	PROPN
ejpam-2592	69	41	�	�	PROPN
ejpam-2592	69	42	2κ	2κ	NOUN
ejpam-2592	69	43	«	«	PUNCT
ejpam-2592	69	44	=	=	NUM
ejpam-2592	69	45	max	max	NOUN
ejpam-2592	69	46	¨	¨	NOUN
ejpam-2592	69	47	ς	ς	PROPN
ejpam-2592	69	48	�	�	PROPN
ejpam-2592	69	49	xn	xn	PROPN
ejpam-2592	69	50	,	,	PUNCT
ejpam-2592	69	51	xn+1	xn+1	PROPN
ejpam-2592	69	52	�	�	PROPN
ejpam-2592	69	53	,	,	PUNCT
ejpam-2592	69	54	ς	ς	PROPN
ejpam-2592	69	55	�	�	PROPN
ejpam-2592	69	56	xn+1	xn+1	PROPN
ejpam-2592	69	57	,	,	PUNCT
ejpam-2592	69	58	xn+2	xn+2	PROPN
ejpam-2592	69	59	�	�	PROPN
ejpam-2592	69	60	,	,	PUNCT
ejpam-2592	69	61	ς	ς	PROPN
ejpam-2592	69	62	�	�	PROPN
ejpam-2592	69	63	xn	xn	PROPN
ejpam-2592	69	64	,	,	PUNCT
ejpam-2592	69	65	xn+2	xn+2	PROPN
ejpam-2592	69	66	�	�	PROPN
ejpam-2592	69	67	+	+	CCONJ
ejpam-2592	69	68	ς	ς	PROPN
ejpam-2592	69	69	�	�	PROPN
ejpam-2592	69	70	xn+1	xn+1	PROPN
ejpam-2592	69	71	,	,	PUNCT
ejpam-2592	69	72	xn+1	xn+1	PROPN
ejpam-2592	69	73	�	�	PROPN
ejpam-2592	69	74	2κ	2κ	NOUN
ejpam-2592	69	75	«	«	PUNCT
ejpam-2592	69	76	≤max	≤max	NUM
ejpam-2592	69	77	¨	¨	NOUN
ejpam-2592	69	78	ς	ς	PROPN
ejpam-2592	69	79	�	�	PROPN
ejpam-2592	69	80	xn	xn	PROPN
ejpam-2592	69	81	,	,	PUNCT
ejpam-2592	69	82	xn+1	xn+1	PROPN
ejpam-2592	69	83	�	�	PROPN
ejpam-2592	69	84	,	,	PUNCT
ejpam-2592	69	85	ς	ς	PROPN
ejpam-2592	69	86	�	�	PROPN
ejpam-2592	69	87	xn+1	xn+1	PROPN
ejpam-2592	69	88	,	,	PUNCT
ejpam-2592	69	89	xn+2	xn+2	PROPN
ejpam-2592	69	90	�	�	PROPN
ejpam-2592	69	91	,	,	PUNCT
ejpam-2592	69	92	κς	κς	ADP
ejpam-2592	69	93	�	�	PROPN
ejpam-2592	69	94	xn	xn	PROPN
ejpam-2592	69	95	,	,	PUNCT
ejpam-2592	69	96	xn+1	xn+1	PROPN
ejpam-2592	69	97	�	�	PROPN
ejpam-2592	69	98	+	+	CCONJ
ejpam-2592	69	99	κς	κς	ADP
ejpam-2592	69	100	�	�	PROPN
ejpam-2592	69	101	xn+1	xn+1	PROPN
ejpam-2592	69	102	,	,	PUNCT
ejpam-2592	69	103	xn+2	xn+2	PROPN
ejpam-2592	69	104	�	�	PROPN
ejpam-2592	69	105	+	+	CCONJ
ejpam-2592	69	106	ς	ς	PROPN
ejpam-2592	69	107	�	�	PROPN
ejpam-2592	69	108	xn+1	xn+1	PROPN
ejpam-2592	69	109	,	,	PUNCT
ejpam-2592	69	110	xn+1	xn+1	PROPN
ejpam-2592	69	111	�	�	PROPN
ejpam-2592	69	112	2κ	2κ	NOUN
ejpam-2592	69	113	«	«	PUNCT
ejpam-2592	69	114	.	.	PUNCT
ejpam-2592	70	1	since	since	SCONJ
ejpam-2592	70	2	ς	ς	PROPN
ejpam-2592	70	3	(	(	PUNCT
ejpam-2592	70	4	x	x	NOUN
ejpam-2592	70	5	,	,	PUNCT
ejpam-2592	70	6	x	x	NOUN
ejpam-2592	70	7	)	)	PUNCT
ejpam-2592	70	8	≤	≤	NUM
ejpam-2592	70	9	ς	ς	PROPN
ejpam-2592	70	10	�	�	PROPN
ejpam-2592	70	11	x	x	SYM
ejpam-2592	70	12	,	,	PUNCT
ejpam-2592	70	13	y	y	PROPN
ejpam-2592	70	14	�	�	PROPN
ejpam-2592	70	15	≤	≤	PROPN
ejpam-2592	70	16	kς	kς	PROPN
ejpam-2592	70	17	�	�	PROPN
ejpam-2592	70	18	x	x	SYM
ejpam-2592	70	19	,	,	PUNCT
ejpam-2592	70	20	y	y	PROPN
ejpam-2592	70	21	�	�	PROPN
ejpam-2592	70	22	for	for	ADP
ejpam-2592	70	23	each	each	PRON
ejpam-2592	70	24	x	x	NOUN
ejpam-2592	70	25	,	,	PUNCT
ejpam-2592	70	26	y	y	PROPN
ejpam-2592	70	27	∈	∈	PROPN
ejpam-2592	70	28	x	x	INTJ
ejpam-2592	70	29	,	,	PUNCT
ejpam-2592	70	30	we	we	PRON
ejpam-2592	70	31	arrive	arrive	VERB
ejpam-2592	70	32	at	at	ADP
ejpam-2592	70	33	m	m	PROPN
ejpam-2592	70	34	�	�	PROPN
ejpam-2592	70	35	xn	xn	PROPN
ejpam-2592	70	36	,	,	PUNCT
ejpam-2592	70	37	xn+1	xn+1	PROPN
ejpam-2592	70	38	�	�	PROPN
ejpam-2592	71	1	=	=	NUM
ejpam-2592	71	2	max	max	PROPN
ejpam-2592	71	3	¨	¨	NOUN
ejpam-2592	71	4	ς	ς	PROPN
ejpam-2592	71	5	�	�	PROPN
ejpam-2592	71	6	xn	xn	PROPN
ejpam-2592	71	7	,	,	PUNCT
ejpam-2592	71	8	xn+1	xn+1	PROPN
ejpam-2592	71	9	�	�	PROPN
ejpam-2592	71	10	,	,	PUNCT
ejpam-2592	71	11	ς	ς	PROPN
ejpam-2592	71	12	�	�	PROPN
ejpam-2592	71	13	xn+1	xn+1	PROPN
ejpam-2592	71	14	,	,	PUNCT
ejpam-2592	71	15	xn+2	xn+2	PROPN
ejpam-2592	71	16	�	�	PROPN
ejpam-2592	71	17	,	,	PUNCT
ejpam-2592	71	18	2ς	2ς	NUM
ejpam-2592	71	19	�	�	PROPN
ejpam-2592	71	20	xn	xn	PROPN
ejpam-2592	71	21	,	,	PUNCT
ejpam-2592	71	22	xn+1	xn+1	PROPN
ejpam-2592	71	23	�	�	PROPN
ejpam-2592	71	24	+	+	CCONJ
ejpam-2592	71	25	ς	ς	PROPN
ejpam-2592	71	26	�	�	PROPN
ejpam-2592	71	27	xn+1	xn+1	PROPN
ejpam-2592	71	28	,	,	PUNCT
ejpam-2592	71	29	xn+2	xn+2	PROPN
ejpam-2592	71	30	�	�	PROPN
ejpam-2592	71	31	2	2	NUM
ejpam-2592	71	32	«	«	PUNCT
ejpam-2592	71	33	=	=	NUM
ejpam-2592	71	34	max	max	NOUN
ejpam-2592	71	35	¨	¨	NOUN
ejpam-2592	71	36	ς	ς	PROPN
ejpam-2592	71	37	�	�	PROPN
ejpam-2592	71	38	xn+1	xn+1	PROPN
ejpam-2592	71	39	,	,	PUNCT
ejpam-2592	71	40	xn+2	xn+2	PROPN
ejpam-2592	71	41	�	�	PROPN
ejpam-2592	71	42	,	,	PUNCT
ejpam-2592	71	43	2ς	2ς	NUM
ejpam-2592	71	44	�	�	PROPN
ejpam-2592	71	45	xn	xn	PROPN
ejpam-2592	71	46	,	,	PUNCT
ejpam-2592	71	47	xn+1	xn+1	PROPN
ejpam-2592	71	48	�	�	PROPN
ejpam-2592	71	49	+	+	CCONJ
ejpam-2592	71	50	ς	ς	PROPN
ejpam-2592	71	51	�	�	PROPN
ejpam-2592	71	52	xn+1	xn+1	PROPN
ejpam-2592	71	53	,	,	PUNCT
ejpam-2592	71	54	xn+2	xn+2	PROPN
ejpam-2592	71	55	�	�	PROPN
ejpam-2592	71	56	2	2	NUM
ejpam-2592	71	57	«	«	PUNCT
ejpam-2592	71	58	.	.	PUNCT
ejpam-2592	72	1	(	(	PUNCT
ejpam-2592	72	2	5	5	X
ejpam-2592	72	3	)	)	PUNCT
ejpam-2592	72	4	if	if	SCONJ
ejpam-2592	72	5	for	for	ADP
ejpam-2592	72	6	some	some	DET
ejpam-2592	72	7	n	n	CCONJ
ejpam-2592	72	8	,	,	PUNCT
ejpam-2592	72	9	m	m	VERB
ejpam-2592	72	10	�	�	PROPN
ejpam-2592	72	11	xn	xn	PROPN
ejpam-2592	72	12	,	,	PUNCT
ejpam-2592	72	13	xn+1	xn+1	PROPN
ejpam-2592	72	14	�	�	PROPN
ejpam-2592	72	15	=	=	SYM
ejpam-2592	72	16	ς	ς	PROPN
ejpam-2592	72	17	�	�	PROPN
ejpam-2592	72	18	xn+1	xn+1	PROPN
ejpam-2592	72	19	,	,	PUNCT
ejpam-2592	72	20	xn+2	xn+2	PROPN
ejpam-2592	72	21	�	�	PROPN
ejpam-2592	72	22	(	(	PUNCT
ejpam-2592	72	23	6=	6=	NOUN
ejpam-2592	72	24	0	0	NUM
ejpam-2592	72	25	)	)	PUNCT
ejpam-2592	72	26	then	then	ADV
ejpam-2592	72	27	(	(	PUNCT
ejpam-2592	72	28	4	4	NUM
ejpam-2592	72	29	)	)	PUNCT
ejpam-2592	72	30	and	and	CCONJ
ejpam-2592	72	31	(	(	PUNCT
ejpam-2592	72	32	5	5	X
ejpam-2592	72	33	)	)	PUNCT
ejpam-2592	72	34	turn	turn	VERB
ejpam-2592	72	35	into	into	ADP
ejpam-2592	72	36	ψ	ψ	ADP
ejpam-2592	72	37	�	�	PROPN
ejpam-2592	72	38	κς	κς	ADP
ejpam-2592	72	39	�	�	PROPN
ejpam-2592	72	40	xn+1	xn+1	PROPN
ejpam-2592	72	41	,	,	PUNCT
ejpam-2592	72	42	xn+2	xn+2	NUM
ejpam-2592	72	43	�	�	PROPN
ejpam-2592	72	44	�	�	PROPN
ejpam-2592	72	45	≤ψ	≤ψ	PROPN
ejpam-2592	72	46	�	�	PROPN
ejpam-2592	72	47	ς	ς	PROPN
ejpam-2592	72	48	�	�	PROPN
ejpam-2592	72	49	xn+1	xn+1	PROPN
ejpam-2592	72	50	,	,	PUNCT
ejpam-2592	72	51	xn+2	xn+2	PROPN
ejpam-2592	72	52	�	�	PROPN
ejpam-2592	72	53	�	�	PROPN
ejpam-2592	72	54	−ϕ	−ϕ	PROPN
ejpam-2592	72	55	�	�	PROPN
ejpam-2592	72	56	ς	ς	PROPN
ejpam-2592	72	57	�	�	PROPN
ejpam-2592	72	58	xn+1	xn+1	PROPN
ejpam-2592	72	59	,	,	PUNCT
ejpam-2592	72	60	xn+2	xn+2	PROPN
ejpam-2592	72	61	�	�	PROPN
ejpam-2592	72	62	�	�	PROPN
ejpam-2592	72	63	<	<	X
ejpam-2592	72	64	ψ	ψ	X
ejpam-2592	72	65	�	�	PROPN
ejpam-2592	72	66	ς	ς	PROPN
ejpam-2592	72	67	�	�	PROPN
ejpam-2592	72	68	xn+1	xn+1	PROPN
ejpam-2592	72	69	,	,	PUNCT
ejpam-2592	72	70	xn+2	xn+2	PROPN
ejpam-2592	72	71	�	�	PROPN
ejpam-2592	72	72	�	�	PROPN
ejpam-2592	72	73	,	,	PUNCT
ejpam-2592	72	74	which	which	PRON
ejpam-2592	72	75	is	be	AUX
ejpam-2592	72	76	a	a	DET
ejpam-2592	72	77	contraction	contraction	NOUN
ejpam-2592	72	78	.	.	PUNCT
ejpam-2592	73	1	hence	hence	ADV
ejpam-2592	73	2	,	,	PUNCT
ejpam-2592	73	3	m	m	VERB
ejpam-2592	73	4	�	�	PROPN
ejpam-2592	73	5	xn	xn	PROPN
ejpam-2592	73	6	,	,	PUNCT
ejpam-2592	73	7	xn+1	xn+1	PROPN
ejpam-2592	73	8	�	�	PROPN
ejpam-2592	73	9	=	=	SYM
ejpam-2592	73	10	ς	ς	PROPN
ejpam-2592	73	11	�	�	PROPN
ejpam-2592	73	12	xn	xn	PROPN
ejpam-2592	73	13	,	,	PUNCT
ejpam-2592	73	14	xn+1	xn+1	PROPN
ejpam-2592	73	15	�	�	PROPN
ejpam-2592	73	16	for	for	ADP
ejpam-2592	73	17	all	all	PRON
ejpam-2592	73	18	n	n	PRON
ejpam-2592	73	19	∈	∈	NOUN
ejpam-2592	73	20	n	n	NOUN
ejpam-2592	73	21	and	and	CCONJ
ejpam-2592	73	22	(	(	PUNCT
ejpam-2592	73	23	4	4	NUM
ejpam-2592	73	24	)	)	PUNCT
ejpam-2592	73	25	with	with	ADP
ejpam-2592	73	26	(	(	PUNCT
ejpam-2592	73	27	5	5	X
ejpam-2592	73	28	)	)	PUNCT
ejpam-2592	73	29	we	we	PRON
ejpam-2592	73	30	obtain	obtain	VERB
ejpam-2592	73	31	ψ	ψ	ADP
ejpam-2592	73	32	�	�	PROPN
ejpam-2592	73	33	κς	κς	ADP
ejpam-2592	73	34	�	�	PROPN
ejpam-2592	73	35	xn+1	xn+1	PROPN
ejpam-2592	73	36	,	,	PUNCT
ejpam-2592	73	37	xn+2	xn+2	NUM
ejpam-2592	73	38	�	�	PROPN
ejpam-2592	73	39	�	�	PROPN
ejpam-2592	73	40	≤ψ	≤ψ	PROPN
ejpam-2592	73	41	�	�	PROPN
ejpam-2592	73	42	ς	ς	PROPN
ejpam-2592	73	43	�	�	PROPN
ejpam-2592	73	44	xn	xn	PROPN
ejpam-2592	73	45	,	,	PUNCT
ejpam-2592	73	46	xn+1	xn+1	PROPN
ejpam-2592	73	47	�	�	PROPN
ejpam-2592	73	48	�	�	PROPN
ejpam-2592	73	49	−ϕ	−ϕ	PROPN
ejpam-2592	73	50	�	�	PROPN
ejpam-2592	73	51	ς	ς	PROPN
ejpam-2592	73	52	�	�	PROPN
ejpam-2592	73	53	xn	xn	PROPN
ejpam-2592	73	54	,	,	PUNCT
ejpam-2592	73	55	xn+1	xn+1	PROPN
ejpam-2592	73	56	�	�	PROPN
ejpam-2592	73	57	�	�	PROPN
ejpam-2592	73	58	.	.	PUNCT
ejpam-2592	74	1	(	(	PUNCT
ejpam-2592	74	2	6	6	NUM
ejpam-2592	74	3	)	)	PUNCT
ejpam-2592	74	4	consequently	consequently	ADV
ejpam-2592	74	5	,	,	PUNCT
ejpam-2592	74	6	the	the	DET
ejpam-2592	74	7	sequence	sequence	NOUN
ejpam-2592	74	8	�	�	PROPN
ejpam-2592	74	9	ς	ς	PROPN
ejpam-2592	74	10	�	�	PROPN
ejpam-2592	74	11	xn+1	xn+1	PROPN
ejpam-2592	74	12	,	,	PUNCT
ejpam-2592	74	13	xn+2	xn+2	PROPN
ejpam-2592	74	14	�	�	PROPN
ejpam-2592	74	15	is	be	AUX
ejpam-2592	74	16	non	non	ADJ
ejpam-2592	74	17	-	-	ADJ
ejpam-2592	74	18	increasing	increase	VERB
ejpam-2592	74	19	for	for	ADP
ejpam-2592	74	20	all	all	PRON
ejpam-2592	74	21	n	n	DET
ejpam-2592	74	22	∈	∈	PROPN
ejpam-2592	74	23	n.	n.	NOUN
ejpam-2592	74	24	hence	hence	ADV
ejpam-2592	74	25	,	,	PUNCT
ejpam-2592	74	26	there	there	PRON
ejpam-2592	74	27	exists	exist	VERB
ejpam-2592	74	28	a	a	DET
ejpam-2592	74	29	≥	≥	NOUN
ejpam-2592	74	30	0	0	NUM
ejpam-2592	74	31	such	such	ADJ
ejpam-2592	74	32	that	that	SCONJ
ejpam-2592	74	33	limn→∞	limn→∞	PROPN
ejpam-2592	74	34	ς	ς	PROPN
ejpam-2592	74	35	�	�	PROPN
ejpam-2592	74	36	xn+1	xn+1	PROPN
ejpam-2592	74	37	,	,	PUNCT
ejpam-2592	74	38	xn+2	xn+2	PROPN
ejpam-2592	74	39	�	�	PROPN
ejpam-2592	74	40	=	=	PRON
ejpam-2592	74	41	a.	a.	NOUN
ejpam-2592	74	42	taking	take	VERB
ejpam-2592	74	43	n→∞	n→∞	PRON
ejpam-2592	74	44	in	in	ADP
ejpam-2592	74	45	(	(	PUNCT
ejpam-2592	74	46	6	6	NUM
ejpam-2592	74	47	)	)	PUNCT
ejpam-2592	74	48	,	,	PUNCT
ejpam-2592	74	49	the	the	DET
ejpam-2592	74	50	continuity	continuity	NOUN
ejpam-2592	74	51	ofψ	ofψ	NOUN
ejpam-2592	74	52	and	and	CCONJ
ejpam-2592	74	53	ϕ	ϕ	PROPN
ejpam-2592	74	54	and	and	CCONJ
ejpam-2592	74	55	limn→∞	limn→∞	PROPN
ejpam-2592	74	56	ς	ς	PROPN
ejpam-2592	74	57	�	�	PROPN
ejpam-2592	74	58	xn+1	xn+1	PROPN
ejpam-2592	74	59	,	,	PUNCT
ejpam-2592	74	60	xn+2	xn+2	PROPN
ejpam-2592	74	61	�	�	PROPN
ejpam-2592	74	62	=	=	PUNCT
ejpam-2592	74	63	a	a	DET
ejpam-2592	74	64	show	show	NOUN
ejpam-2592	74	65	that	that	SCONJ
ejpam-2592	74	66	ψ	ψ	X
ejpam-2592	74	67	(	(	PUNCT
ejpam-2592	74	68	κa)≤ψ	κa)≤ψ	X
ejpam-2592	74	69	(	(	PUNCT
ejpam-2592	74	70	a)−ϕ	a)−ϕ	PROPN
ejpam-2592	74	71	(	(	PUNCT
ejpam-2592	74	72	a	a	NOUN
ejpam-2592	74	73	)	)	PUNCT
ejpam-2592	74	74	,	,	PUNCT
ejpam-2592	74	75	yielding	yield	VERB
ejpam-2592	74	76	a	a	DET
ejpam-2592	74	77	=	=	NOUN
ejpam-2592	74	78	0	0	NUM
ejpam-2592	74	79	.	.	PUNCT
ejpam-2592	75	1	so	so	ADV
ejpam-2592	75	2	,	,	PUNCT
ejpam-2592	75	3	we	we	PRON
ejpam-2592	75	4	have	have	VERB
ejpam-2592	75	5	lim	lim	PROPN
ejpam-2592	75	6	n→∞	n→∞	NUM
ejpam-2592	75	7	ς	ς	PROPN
ejpam-2592	75	8	�	�	PROPN
ejpam-2592	75	9	xn+1	xn+1	PROPN
ejpam-2592	75	10	,	,	PUNCT
ejpam-2592	75	11	xn+2	xn+2	PROPN
ejpam-2592	75	12	�	�	PROPN
ejpam-2592	76	1	=	=	SYM
ejpam-2592	76	2	0	0	PROPN
ejpam-2592	76	3	.	.	PUNCT
ejpam-2592	77	1	(	(	PUNCT
ejpam-2592	77	2	7	7	X
ejpam-2592	77	3	)	)	PUNCT
ejpam-2592	77	4	next	next	ADV
ejpam-2592	77	5	,	,	PUNCT
ejpam-2592	77	6	we	we	PRON
ejpam-2592	77	7	show	show	VERB
ejpam-2592	77	8	that	that	SCONJ
ejpam-2592	77	9	�	�	PROPN
ejpam-2592	77	10	xn	xn	PROPN
ejpam-2592	77	11	is	be	AUX
ejpam-2592	77	12	a	a	DET
ejpam-2592	77	13	cauchy	cauchy	ADJ
ejpam-2592	77	14	sequence	sequence	NOUN
ejpam-2592	77	15	.	.	PUNCT
ejpam-2592	78	1	if	if	SCONJ
ejpam-2592	78	2	it	it	PRON
ejpam-2592	78	3	is	be	AUX
ejpam-2592	78	4	not	not	PART
ejpam-2592	78	5	,	,	PUNCT
ejpam-2592	78	6	then	then	ADV
ejpam-2592	78	7	there	there	PRON
ejpam-2592	78	8	exists	exist	VERB
ejpam-2592	78	9	ǫ	ǫ	PRON
ejpam-2592	78	10	>	>	X
ejpam-2592	78	11	0	0	PUNCT
ejpam-2592	79	1	for	for	ADP
ejpam-2592	79	2	which	which	PRON
ejpam-2592	79	3	we	we	PRON
ejpam-2592	79	4	can	can	AUX
ejpam-2592	79	5	find	find	VERB
ejpam-2592	79	6	subsequences	subsequence	NOUN
ejpam-2592	79	7	�	�	PROPN
ejpam-2592	79	8	xmk	xmk	PROPN
ejpam-2592	79	9	and	and	CCONJ
ejpam-2592	79	10	�	�	PROPN
ejpam-2592	79	11	xnk	xnk	PROPN
ejpam-2592	79	12	of	of	ADP
ejpam-2592	79	13	sequence	sequence	NOUN
ejpam-2592	79	14	�	�	PROPN
ejpam-2592	79	15	xn	xn	PROPN
ejpam-2592	79	16	where	where	SCONJ
ejpam-2592	79	17	nk	nk	PROPN
ejpam-2592	79	18	is	be	AUX
ejpam-2592	79	19	the	the	DET
ejpam-2592	79	20	smallest	small	ADJ
ejpam-2592	79	21	index	index	NOUN
ejpam-2592	79	22	for	for	ADP
ejpam-2592	79	23	which	which	PRON
ejpam-2592	79	24	nk	nk	PROPN
ejpam-2592	79	25	>	>	X
ejpam-2592	79	26	mk	mk	PROPN
ejpam-2592	79	27	>	>	X
ejpam-2592	79	28	k	k	PROPN
ejpam-2592	79	29	with	with	ADP
ejpam-2592	79	30	ς	ς	PROPN
ejpam-2592	79	31	�	�	PROPN
ejpam-2592	79	32	xmk	xmk	PROPN
ejpam-2592	79	33	,	,	PUNCT
ejpam-2592	79	34	xnk	xnk	PROPN
ejpam-2592	79	35	�	�	PROPN
ejpam-2592	79	36	≥	≥	NUM
ejpam-2592	79	37	ǫ	ǫ	NOUN
ejpam-2592	79	38	.	.	PUNCT
ejpam-2592	80	1	(	(	PUNCT
ejpam-2592	80	2	8)	8)	NUM
ejpam-2592	80	3	then	then	ADV
ejpam-2592	80	4	ς	ς	PROPN
ejpam-2592	80	5	�	�	PROPN
ejpam-2592	80	6	xmk	xmk	PROPN
ejpam-2592	80	7	,	,	PUNCT
ejpam-2592	80	8	xnk−1	xnk−1	PROPN
ejpam-2592	80	9	�	�	PROPN
ejpam-2592	80	10	<	<	X
ejpam-2592	80	11	ǫ	ǫ	X
ejpam-2592	80	12	.	.	PUNCT
ejpam-2592	81	1	(	(	PUNCT
ejpam-2592	81	2	9	9	X
ejpam-2592	81	3	)	)	PUNCT
ejpam-2592	81	4	using	use	VERB
ejpam-2592	81	5	(	(	PUNCT
ejpam-2592	81	6	8)	8)	NUM
ejpam-2592	81	7	and	and	CCONJ
ejpam-2592	81	8	(	(	PUNCT
ejpam-2592	81	9	9	9	NUM
ejpam-2592	81	10	)	)	PUNCT
ejpam-2592	81	11	,	,	PUNCT
ejpam-2592	81	12	we	we	PRON
ejpam-2592	81	13	obtain	obtain	VERB
ejpam-2592	81	14	ǫ	ǫ	NOUN
ejpam-2592	81	15	≤	≤	NUM
ejpam-2592	81	16	ς	ς	PROPN
ejpam-2592	81	17	�	�	PROPN
ejpam-2592	81	18	xmk	xmk	PROPN
ejpam-2592	81	19	,	,	PUNCT
ejpam-2592	81	20	xnk	xnk	PROPN
ejpam-2592	81	21	�	�	PROPN
ejpam-2592	81	22	≤	≤	PROPN
ejpam-2592	81	23	κ	κ	PRON
ejpam-2592	81	24	�	�	PROPN
ejpam-2592	81	25	ς	ς	PROPN
ejpam-2592	81	26	�	�	PROPN
ejpam-2592	81	27	xmk	xmk	PROPN
ejpam-2592	81	28	,	,	PUNCT
ejpam-2592	81	29	xnk−1	xnk−1	PROPN
ejpam-2592	81	30	�	�	PROPN
ejpam-2592	81	31	+	+	CCONJ
ejpam-2592	81	32	ς	ς	PROPN
ejpam-2592	81	33	�	�	PROPN
ejpam-2592	81	34	xnk−1	xnk−1	PROPN
ejpam-2592	81	35	,	,	PUNCT
ejpam-2592	81	36	xnk	xnk	PROPN
ejpam-2592	81	37	�	�	PROPN
ejpam-2592	81	38	�	�	PROPN
ejpam-2592	81	39	<	<	X
ejpam-2592	81	40	κǫ	κǫ	PROPN
ejpam-2592	81	41	+	+	X
ejpam-2592	81	42	κς	κς	ADP
ejpam-2592	81	43	�	�	PROPN
ejpam-2592	81	44	xnk−1	xnk−1	PROPN
ejpam-2592	81	45	,	,	PUNCT
ejpam-2592	81	46	xnk	xnk	PROPN
ejpam-2592	81	47	�	�	PROPN
ejpam-2592	81	48	.	.	PUNCT
ejpam-2592	82	1	(	(	PUNCT
ejpam-2592	82	2	10	10	NUM
ejpam-2592	82	3	)	)	PUNCT
ejpam-2592	82	4	m.	m.	NOUN
ejpam-2592	82	5	akturk	akturk	NOUN
ejpam-2592	82	6	,	,	PUNCT
ejpam-2592	82	7	m.	m.	NOUN
ejpam-2592	82	8	kır	kır	PROPN
ejpam-2592	82	9	,	,	PUNCT
ejpam-2592	82	10	e.	e.	PROPN
ejpam-2592	82	11	yolacan	yolacan	PROPN
ejpam-2592	82	12	/	/	SYM
ejpam-2592	82	13	eur	eur	PROPN
ejpam-2592	82	14	.	.	PUNCT
ejpam-2592	83	1	j.	j.	PROPN
ejpam-2592	83	2	pure	pure	PROPN
ejpam-2592	83	3	appl	appl	PROPN
ejpam-2592	83	4	.	.	PROPN
ejpam-2592	83	5	math	math	PROPN
ejpam-2592	83	6	,	,	PUNCT
ejpam-2592	83	7	9	9	NUM
ejpam-2592	83	8	(	(	PUNCT
ejpam-2592	83	9	2016	2016	NUM
ejpam-2592	83	10	)	)	PUNCT
ejpam-2592	83	11	,	,	PUNCT
ejpam-2592	83	12	175	175	NUM
ejpam-2592	83	13	-	-	SYM
ejpam-2592	83	14	185	185	NUM
ejpam-2592	83	15	179	179	NUM
ejpam-2592	83	16	taking	take	VERB
ejpam-2592	83	17	the	the	DET
ejpam-2592	83	18	upper	upper	ADJ
ejpam-2592	83	19	and	and	CCONJ
ejpam-2592	83	20	lower	low	ADJ
ejpam-2592	83	21	limits	limit	NOUN
ejpam-2592	83	22	as	as	ADP
ejpam-2592	83	23	k→∞	k→∞	NOUN
ejpam-2592	83	24	,	,	PUNCT
ejpam-2592	83	25	we	we	PRON
ejpam-2592	83	26	conclude	conclude	VERB
ejpam-2592	83	27	ǫ	ǫ	NOUN
ejpam-2592	83	28	≤	≤	NUM
ejpam-2592	83	29	lim	lim	PROPN
ejpam-2592	83	30	inf	inf	PROPN
ejpam-2592	83	31	k→∞	k→∞	NOUN
ejpam-2592	83	32	ς	ς	PROPN
ejpam-2592	83	33	�	�	PROPN
ejpam-2592	83	34	xmk	xmk	PROPN
ejpam-2592	83	35	,	,	PUNCT
ejpam-2592	83	36	xnk	xnk	PROPN
ejpam-2592	83	37	�	�	PROPN
ejpam-2592	83	38	≤	≤	PROPN
ejpam-2592	83	39	lim	lim	PROPN
ejpam-2592	83	40	sup	sup	PROPN
ejpam-2592	83	41	k→∞	k→∞	NOUN
ejpam-2592	83	42	ς	ς	PROPN
ejpam-2592	83	43	�	�	PROPN
ejpam-2592	83	44	xmk	xmk	PROPN
ejpam-2592	83	45	,	,	PUNCT
ejpam-2592	83	46	xnk	xnk	PROPN
ejpam-2592	83	47	�	�	PROPN
ejpam-2592	83	48	≤	≤	PROPN
ejpam-2592	83	49	κǫ	κǫ	PROPN
ejpam-2592	83	50	.	.	PUNCT
ejpam-2592	84	1	(	(	PUNCT
ejpam-2592	84	2	11	11	NUM
ejpam-2592	84	3	)	)	PUNCT
ejpam-2592	84	4	by	by	ADP
ejpam-2592	84	5	using	use	VERB
ejpam-2592	84	6	(	(	PUNCT
ejpam-2592	84	7	a3	a3	NOUN
ejpam-2592	84	8	)	)	PUNCT
ejpam-2592	84	9	and	and	CCONJ
ejpam-2592	84	10	we	we	PRON
ejpam-2592	84	11	deduce	deduce	VERB
ejpam-2592	84	12	ς	ς	PROPN
ejpam-2592	84	13	�	�	PROPN
ejpam-2592	84	14	xmk+1	xmk+1	PROPN
ejpam-2592	84	15	,	,	PUNCT
ejpam-2592	84	16	xnk	xnk	PROPN
ejpam-2592	84	17	�	�	PROPN
ejpam-2592	84	18	≤	≤	PROPN
ejpam-2592	84	19	κς	κς	ADP
ejpam-2592	84	20	�	�	PROPN
ejpam-2592	84	21	xmk+1	xmk+1	PROPN
ejpam-2592	84	22	,	,	PUNCT
ejpam-2592	84	23	xmk	xmk	PROPN
ejpam-2592	84	24	�	�	PROPN
ejpam-2592	84	25	+	+	CCONJ
ejpam-2592	84	26	κ2ς	κ2ς	PROPN
ejpam-2592	84	27	�	�	PROPN
ejpam-2592	84	28	xmk	xmk	PROPN
ejpam-2592	84	29	,	,	PUNCT
ejpam-2592	84	30	xnk−1	xnk−1	PROPN
ejpam-2592	84	31	�	�	PROPN
ejpam-2592	84	32	+	+	CCONJ
ejpam-2592	84	33	κ2ς	κ2ς	PROPN
ejpam-2592	84	34	�	�	PROPN
ejpam-2592	84	35	xnk−1	xnk−1	PROPN
ejpam-2592	84	36	,	,	PUNCT
ejpam-2592	84	37	xnk	xnk	PROPN
ejpam-2592	84	38	�	�	PROPN
ejpam-2592	84	39	,	,	PUNCT
ejpam-2592	84	40	(	(	PUNCT
ejpam-2592	84	41	12	12	NUM
ejpam-2592	84	42	)	)	PUNCT
ejpam-2592	84	43	with	with	ADP
ejpam-2592	84	44	taking	take	VERB
ejpam-2592	84	45	the	the	DET
ejpam-2592	84	46	upper	upper	ADJ
ejpam-2592	84	47	limit	limit	NOUN
ejpam-2592	84	48	as	as	ADP
ejpam-2592	84	49	k→∞	k→∞	ADV
ejpam-2592	84	50	in	in	ADP
ejpam-2592	84	51	(	(	PUNCT
ejpam-2592	84	52	12	12	NUM
ejpam-2592	84	53	)	)	PUNCT
ejpam-2592	84	54	,	,	PUNCT
ejpam-2592	84	55	we	we	PRON
ejpam-2592	84	56	obtain	obtain	VERB
ejpam-2592	84	57	lim	lim	PROPN
ejpam-2592	84	58	sup	sup	PROPN
ejpam-2592	84	59	k→∞	k→∞	NOUN
ejpam-2592	84	60	ς	ς	PROPN
ejpam-2592	84	61	�	�	PROPN
ejpam-2592	84	62	xmk+1	xmk+1	PROPN
ejpam-2592	84	63	,	,	PUNCT
ejpam-2592	84	64	xnk	xnk	PROPN
ejpam-2592	84	65	�	�	PROPN
ejpam-2592	84	66	≤	≤	PROPN
ejpam-2592	84	67	κ2ǫ	κ2ǫ	PROPN
ejpam-2592	84	68	.	.	PUNCT
ejpam-2592	85	1	(	(	PUNCT
ejpam-2592	85	2	13	13	NUM
ejpam-2592	85	3	)	)	PUNCT
ejpam-2592	85	4	use	use	NOUN
ejpam-2592	85	5	(	(	PUNCT
ejpam-2592	85	6	a3	a3	NOUN
ejpam-2592	85	7	)	)	PUNCT
ejpam-2592	85	8	and	and	CCONJ
ejpam-2592	85	9	we	we	PRON
ejpam-2592	85	10	find	find	VERB
ejpam-2592	85	11	ς	ς	PROPN
ejpam-2592	85	12	�	�	PROPN
ejpam-2592	85	13	xmk+1	xmk+1	PROPN
ejpam-2592	85	14	,	,	PUNCT
ejpam-2592	85	15	xnk−1	xnk−1	PROPN
ejpam-2592	85	16	�	�	PROPN
ejpam-2592	85	17	≤	≤	PROPN
ejpam-2592	85	18	κς	κς	ADP
ejpam-2592	85	19	�	�	PROPN
ejpam-2592	85	20	xmk+1	xmk+1	PROPN
ejpam-2592	85	21	,	,	PUNCT
ejpam-2592	85	22	xmk	xmk	PROPN
ejpam-2592	85	23	�	�	PROPN
ejpam-2592	85	24	+	+	CCONJ
ejpam-2592	85	25	κς	κς	ADP
ejpam-2592	85	26	�	�	PROPN
ejpam-2592	85	27	xmk	xmk	PROPN
ejpam-2592	85	28	,	,	PUNCT
ejpam-2592	85	29	xnk−1	xnk−1	PROPN
ejpam-2592	85	30	�	�	PROPN
ejpam-2592	85	31	(	(	PUNCT
ejpam-2592	85	32	14	14	NUM
ejpam-2592	85	33	)	)	PUNCT
ejpam-2592	85	34	by	by	ADP
ejpam-2592	85	35	taking	take	VERB
ejpam-2592	85	36	the	the	DET
ejpam-2592	85	37	upper	upper	ADJ
ejpam-2592	85	38	limit	limit	NOUN
ejpam-2592	85	39	as	as	ADP
ejpam-2592	85	40	k→∞	k→∞	ADV
ejpam-2592	85	41	in	in	ADP
ejpam-2592	85	42	(	(	PUNCT
ejpam-2592	85	43	14	14	NUM
ejpam-2592	85	44	)	)	PUNCT
ejpam-2592	85	45	,	,	PUNCT
ejpam-2592	85	46	we	we	PRON
ejpam-2592	85	47	get	get	VERB
ejpam-2592	85	48	lim	lim	PROPN
ejpam-2592	85	49	sup	sup	PROPN
ejpam-2592	85	50	k→∞	k→∞	NOUN
ejpam-2592	85	51	ς	ς	PROPN
ejpam-2592	85	52	�	�	PROPN
ejpam-2592	85	53	xmk+1	xmk+1	PROPN
ejpam-2592	85	54	,	,	PUNCT
ejpam-2592	85	55	xnk−1	xnk−1	PROPN
ejpam-2592	85	56	�	�	PROPN
ejpam-2592	85	57	≤	≤	PROPN
ejpam-2592	85	58	κǫ	κǫ	PROPN
ejpam-2592	85	59	.	.	PUNCT
ejpam-2592	86	1	(	(	PUNCT
ejpam-2592	86	2	15	15	NUM
ejpam-2592	86	3	)	)	PUNCT
ejpam-2592	86	4	on	on	ADP
ejpam-2592	86	5	the	the	DET
ejpam-2592	86	6	other	other	ADJ
ejpam-2592	86	7	hand	hand	NOUN
ejpam-2592	86	8	,	,	PUNCT
ejpam-2592	86	9	ς	ς	PROPN
ejpam-2592	86	10	�	�	PROPN
ejpam-2592	86	11	xmk	xmk	PROPN
ejpam-2592	86	12	,	,	PUNCT
ejpam-2592	86	13	xnk	xnk	PROPN
ejpam-2592	86	14	�	�	PROPN
ejpam-2592	86	15	≤	≤	PROPN
ejpam-2592	86	16	κς	κς	ADP
ejpam-2592	86	17	�	�	PROPN
ejpam-2592	86	18	xmk	xmk	PROPN
ejpam-2592	86	19	,	,	PUNCT
ejpam-2592	86	20	xmk+1	xmk+1	PROPN
ejpam-2592	86	21	�	�	PROPN
ejpam-2592	86	22	+	+	CCONJ
ejpam-2592	86	23	κ2ς	κ2ς	PROPN
ejpam-2592	86	24	�	�	PROPN
ejpam-2592	86	25	xmk+1	xmk+1	PROPN
ejpam-2592	86	26	,	,	PUNCT
ejpam-2592	86	27	xnk−1	xnk−1	PROPN
ejpam-2592	86	28	�	�	PROPN
ejpam-2592	86	29	+	+	CCONJ
ejpam-2592	86	30	κ2ς	κ2ς	PROPN
ejpam-2592	86	31	�	�	PROPN
ejpam-2592	86	32	xnk−1	xnk−1	PROPN
ejpam-2592	86	33	,	,	PUNCT
ejpam-2592	86	34	xnk	xnk	PROPN
ejpam-2592	86	35	�	�	PROPN
ejpam-2592	86	36	.	.	PUNCT
ejpam-2592	87	1	(	(	PUNCT
ejpam-2592	87	2	16	16	NUM
ejpam-2592	87	3	)	)	PUNCT
ejpam-2592	87	4	using	use	VERB
ejpam-2592	87	5	(	(	PUNCT
ejpam-2592	87	6	11	11	NUM
ejpam-2592	87	7	)	)	PUNCT
ejpam-2592	87	8	and	and	CCONJ
ejpam-2592	87	9	(	(	PUNCT
ejpam-2592	87	10	7	7	NUM
ejpam-2592	87	11	)	)	PUNCT
ejpam-2592	87	12	,	,	PUNCT
ejpam-2592	87	13	we	we	PRON
ejpam-2592	87	14	obtain	obtain	VERB
ejpam-2592	87	15	ǫ	ǫ	NUM
ejpam-2592	87	16	κ2	κ2	PROPN
ejpam-2592	87	17	≤	≤	NUM
ejpam-2592	87	18	lim	lim	PROPN
ejpam-2592	87	19	inf	inf	PROPN
ejpam-2592	87	20	k→∞	k→∞	NOUN
ejpam-2592	87	21	ς	ς	PROPN
ejpam-2592	87	22	�	�	PROPN
ejpam-2592	87	23	xmk+1	xmk+1	PROPN
ejpam-2592	87	24	,	,	PUNCT
ejpam-2592	87	25	xnk−1	xnk−1	PROPN
ejpam-2592	87	26	�	�	PROPN
ejpam-2592	87	27	.	.	PUNCT
ejpam-2592	88	1	(	(	PUNCT
ejpam-2592	88	2	17	17	NUM
ejpam-2592	88	3	)	)	PUNCT
ejpam-2592	88	4	moreover	moreover	ADV
ejpam-2592	88	5	,	,	PUNCT
ejpam-2592	88	6	ǫ	ǫ	NOUN
ejpam-2592	88	7	≤	≤	NOUN
ejpam-2592	88	8	ς	ς	PROPN
ejpam-2592	88	9	�	�	PROPN
ejpam-2592	88	10	xmk	xmk	PROPN
ejpam-2592	88	11	,	,	PUNCT
ejpam-2592	88	12	xnk	xnk	PROPN
ejpam-2592	88	13	�	�	PROPN
ejpam-2592	88	14	≤	≤	PROPN
ejpam-2592	88	15	κς	κς	ADP
ejpam-2592	88	16	�	�	PROPN
ejpam-2592	88	17	xmk	xmk	PROPN
ejpam-2592	88	18	,	,	PUNCT
ejpam-2592	88	19	xmk+1	xmk+1	X
ejpam-2592	88	20	�	�	PROPN
ejpam-2592	88	21	+	+	CCONJ
ejpam-2592	88	22	κς	κς	ADP
ejpam-2592	88	23	�	�	PROPN
ejpam-2592	88	24	xmk+1	xmk+1	PROPN
ejpam-2592	88	25	,	,	PUNCT
ejpam-2592	88	26	xnk	xnk	PROPN
ejpam-2592	88	27	�	�	PROPN
ejpam-2592	88	28	,	,	PUNCT
ejpam-2592	88	29	(	(	PUNCT
ejpam-2592	88	30	18	18	NUM
ejpam-2592	88	31	)	)	PUNCT
ejpam-2592	88	32	with	with	ADP
ejpam-2592	88	33	taking	take	VERB
ejpam-2592	88	34	the	the	DET
ejpam-2592	88	35	upper	upper	ADJ
ejpam-2592	88	36	limit	limit	NOUN
ejpam-2592	88	37	as	as	ADP
ejpam-2592	88	38	k→∞	k→∞	ADV
ejpam-2592	88	39	in	in	ADP
ejpam-2592	88	40	(	(	PUNCT
ejpam-2592	88	41	18	18	NUM
ejpam-2592	88	42	)	)	PUNCT
ejpam-2592	88	43	,	,	PUNCT
ejpam-2592	88	44	we	we	PRON
ejpam-2592	88	45	have	have	VERB
ejpam-2592	88	46	ǫ	ǫ	NOUN
ejpam-2592	88	47	κ	κ	X
ejpam-2592	88	48	≤	≤	NOUN
ejpam-2592	88	49	lim	lim	PROPN
ejpam-2592	88	50	sup	sup	PROPN
ejpam-2592	88	51	k→∞	k→∞	NOUN
ejpam-2592	88	52	ς	ς	PROPN
ejpam-2592	88	53	�	�	PROPN
ejpam-2592	88	54	xmk+1	xmk+1	PROPN
ejpam-2592	88	55	,	,	PUNCT
ejpam-2592	88	56	xnk	xnk	PROPN
ejpam-2592	88	57	�	�	PROPN
ejpam-2592	88	58	.	.	PUNCT
ejpam-2592	89	1	(	(	PUNCT
ejpam-2592	89	2	19	19	NUM
ejpam-2592	89	3	)	)	PUNCT
ejpam-2592	89	4	by	by	ADP
ejpam-2592	89	5	using	use	VERB
ejpam-2592	89	6	(	(	PUNCT
ejpam-2592	89	7	1	1	NUM
ejpam-2592	89	8	)	)	PUNCT
ejpam-2592	89	9	,	,	PUNCT
ejpam-2592	89	10	we	we	PRON
ejpam-2592	89	11	have	have	VERB
ejpam-2592	89	12	ψ	ψ	ADP
ejpam-2592	89	13	�	�	PROPN
ejpam-2592	89	14	κς	κς	ADP
ejpam-2592	89	15	�	�	PROPN
ejpam-2592	89	16	xmk+1	xmk+1	PROPN
ejpam-2592	89	17	,	,	PUNCT
ejpam-2592	89	18	xnk	xnk	PROPN
ejpam-2592	89	19	�	�	PROPN
ejpam-2592	89	20	�	�	PROPN
ejpam-2592	89	21	≤α	≤α	PROPN
ejpam-2592	89	22	�	�	PROPN
ejpam-2592	89	23	xmk	xmk	PROPN
ejpam-2592	89	24	,	,	PUNCT
ejpam-2592	89	25	xnk−1	xnk−1	PROPN
ejpam-2592	89	26	�	�	PROPN
ejpam-2592	89	27	ψ	ψ	ADP
ejpam-2592	89	28	�	�	PROPN
ejpam-2592	89	29	κς	κς	ADP
ejpam-2592	89	30	�	�	PROPN
ejpam-2592	89	31	t	t	PROPN
ejpam-2592	89	32	xmk	xmk	PROPN
ejpam-2592	89	33	,	,	PUNCT
ejpam-2592	89	34	t	t	PROPN
ejpam-2592	89	35	xnk−1	xnk−1	PROPN
ejpam-2592	89	36	�	�	PROPN
ejpam-2592	89	37	�	�	PROPN
ejpam-2592	89	38	≤ψ	≤ψ	PROPN
ejpam-2592	89	39	�	�	PROPN
ejpam-2592	89	40	m	m	PROPN
ejpam-2592	89	41	�	�	PROPN
ejpam-2592	89	42	xmk	xmk	PROPN
ejpam-2592	89	43	,	,	PUNCT
ejpam-2592	89	44	xnk−1	xnk−1	PROPN
ejpam-2592	89	45	�	�	PROPN
ejpam-2592	89	46	�	�	PROPN
ejpam-2592	89	47	−ϕ	−ϕ	PROPN
ejpam-2592	89	48	�	�	PROPN
ejpam-2592	89	49	m	m	PROPN
ejpam-2592	89	50	�	�	PROPN
ejpam-2592	89	51	xmk	xmk	PROPN
ejpam-2592	89	52	,	,	PUNCT
ejpam-2592	89	53	xnk−1	xnk−1	PROPN
ejpam-2592	89	54	�	�	PROPN
ejpam-2592	89	55	�	�	PROPN
ejpam-2592	89	56	(	(	PUNCT
ejpam-2592	89	57	20	20	NUM
ejpam-2592	89	58	)	)	PUNCT
ejpam-2592	89	59	where	where	SCONJ
ejpam-2592	89	60	m	m	VERB
ejpam-2592	89	61	�	�	PROPN
ejpam-2592	89	62	xmk	xmk	PROPN
ejpam-2592	89	63	,	,	PUNCT
ejpam-2592	89	64	xnk−1	xnk−1	PROPN
ejpam-2592	89	65	�	�	PROPN
ejpam-2592	90	1	=	=	NUM
ejpam-2592	90	2	max	max	PROPN
ejpam-2592	90	3	§	§	PROPN
ejpam-2592	90	4	ς	ς	PROPN
ejpam-2592	90	5	�	�	PROPN
ejpam-2592	90	6	xmk	xmk	PROPN
ejpam-2592	90	7	,	,	PUNCT
ejpam-2592	90	8	xnk−1	xnk−1	PROPN
ejpam-2592	90	9	�	�	PROPN
ejpam-2592	90	10	,	,	PUNCT
ejpam-2592	90	11	ς	ς	PROPN
ejpam-2592	90	12	�	�	PROPN
ejpam-2592	90	13	xmk	xmk	PROPN
ejpam-2592	90	14	,	,	PUNCT
ejpam-2592	90	15	xmk+1	xmk+1	PROPN
ejpam-2592	90	16	�	�	PROPN
ejpam-2592	90	17	,	,	PUNCT
ejpam-2592	90	18	ς	ς	PROPN
ejpam-2592	90	19	�	�	PROPN
ejpam-2592	90	20	xnk−1	xnk−1	PROPN
ejpam-2592	90	21	,	,	PUNCT
ejpam-2592	90	22	xnk	xnk	PROPN
ejpam-2592	90	23	�	�	PROPN
ejpam-2592	90	24	(	(	PUNCT
ejpam-2592	90	25	21	21	NUM
ejpam-2592	90	26	)	)	PUNCT
ejpam-2592	90	27	,	,	PUNCT
ejpam-2592	90	28	ς	ς	PROPN
ejpam-2592	90	29	�	�	PROPN
ejpam-2592	90	30	xmk	xmk	PROPN
ejpam-2592	90	31	,	,	PUNCT
ejpam-2592	90	32	xnk	xnk	PROPN
ejpam-2592	90	33	�	�	PROPN
ejpam-2592	90	34	+	+	CCONJ
ejpam-2592	90	35	ς	ς	PROPN
ejpam-2592	90	36	�	�	PROPN
ejpam-2592	90	37	xnk−1	xnk−1	PROPN
ejpam-2592	90	38	,	,	PUNCT
ejpam-2592	90	39	xmk+1	xmk+1	PRON
ejpam-2592	90	40	�	�	X
ejpam-2592	90	41	2κ	2κ	NOUN
ejpam-2592	90	42	ª	ª	ADP
ejpam-2592	90	43	m.	m.	NOUN
ejpam-2592	90	44	akturk	akturk	NOUN
ejpam-2592	90	45	,	,	PUNCT
ejpam-2592	90	46	m.	m.	NOUN
ejpam-2592	90	47	kır	kır	PROPN
ejpam-2592	90	48	,	,	PUNCT
ejpam-2592	90	49	e.	e.	PROPN
ejpam-2592	90	50	yolacan	yolacan	PROPN
ejpam-2592	90	51	/	/	SYM
ejpam-2592	90	52	eur	eur	PROPN
ejpam-2592	90	53	.	.	PUNCT
ejpam-2592	91	1	j.	j.	PROPN
ejpam-2592	91	2	pure	pure	PROPN
ejpam-2592	91	3	appl	appl	PROPN
ejpam-2592	91	4	.	.	PROPN
ejpam-2592	91	5	math	math	PROPN
ejpam-2592	91	6	,	,	PUNCT
ejpam-2592	91	7	9	9	NUM
ejpam-2592	91	8	(	(	PUNCT
ejpam-2592	91	9	2016	2016	NUM
ejpam-2592	91	10	)	)	PUNCT
ejpam-2592	91	11	,	,	PUNCT
ejpam-2592	91	12	175	175	NUM
ejpam-2592	91	13	-	-	SYM
ejpam-2592	91	14	185	185	NUM
ejpam-2592	91	15	180	180	NUM
ejpam-2592	91	16	from	from	ADP
ejpam-2592	91	17	on	on	ADP
ejpam-2592	91	18	taking	take	VERB
ejpam-2592	91	19	the	the	DET
ejpam-2592	91	20	upper	upper	ADJ
ejpam-2592	91	21	limit	limit	NOUN
ejpam-2592	91	22	as	as	ADP
ejpam-2592	91	23	k→∞	k→∞	ADV
ejpam-2592	91	24	,	,	PUNCT
ejpam-2592	91	25	from	from	ADP
ejpam-2592	91	26	(	(	PUNCT
ejpam-2592	91	27	7	7	NUM
ejpam-2592	91	28	)	)	PUNCT
ejpam-2592	91	29	,	,	PUNCT
ejpam-2592	91	30	(	(	PUNCT
ejpam-2592	91	31	9	9	NUM
ejpam-2592	91	32	)	)	PUNCT
ejpam-2592	91	33	,	,	PUNCT
ejpam-2592	91	34	(	(	PUNCT
ejpam-2592	91	35	11	11	NUM
ejpam-2592	91	36	)	)	PUNCT
ejpam-2592	91	37	and	and	CCONJ
ejpam-2592	91	38	(	(	PUNCT
ejpam-2592	91	39	15	15	X
ejpam-2592	91	40	)	)	PUNCT
ejpam-2592	91	41	we	we	PRON
ejpam-2592	91	42	obtain	obtain	VERB
ejpam-2592	91	43	lim	lim	PROPN
ejpam-2592	91	44	k→∞	k→∞	PROPN
ejpam-2592	91	45	sup	sup	PROPN
ejpam-2592	91	46	m	m	PROPN
ejpam-2592	91	47	�	�	PROPN
ejpam-2592	91	48	xmk	xmk	PROPN
ejpam-2592	91	49	,	,	PUNCT
ejpam-2592	91	50	xnk−1	xnk−1	PROPN
ejpam-2592	91	51	�	�	PROPN
ejpam-2592	92	1	=	=	NUM
ejpam-2592	92	2	max	max	PROPN
ejpam-2592	92	3	§	§	PROPN
ejpam-2592	92	4	ǫ	ǫ	PROPN
ejpam-2592	92	5	,	,	PUNCT
ejpam-2592	92	6	0	0	NUM
ejpam-2592	92	7	,	,	PUNCT
ejpam-2592	92	8	0	0	NUM
ejpam-2592	92	9	,	,	PUNCT
ejpam-2592	92	10	κǫ	κǫ	NOUN
ejpam-2592	93	1	+	+	NOUN
ejpam-2592	93	2	κǫ	κǫ	PRON
ejpam-2592	93	3	2κ	2κ	NOUN
ejpam-2592	93	4	ª	ª	SYM
ejpam-2592	93	5	=	=	SYM
ejpam-2592	93	6	ǫ	ǫ	NOUN
ejpam-2592	93	7	.	.	PUNCT
ejpam-2592	94	1	(	(	PUNCT
ejpam-2592	94	2	22	22	NUM
ejpam-2592	94	3	)	)	PUNCT
ejpam-2592	94	4	thus	thus	ADV
ejpam-2592	94	5	,	,	PUNCT
ejpam-2592	94	6	from	from	ADP
ejpam-2592	94	7	(	(	PUNCT
ejpam-2592	94	8	19	19	NUM
ejpam-2592	94	9	)	)	PUNCT
ejpam-2592	94	10	and	and	CCONJ
ejpam-2592	94	11	(	(	PUNCT
ejpam-2592	94	12	20	20	NUM
ejpam-2592	94	13	)	)	PUNCT
ejpam-2592	94	14	,	,	PUNCT
ejpam-2592	94	15	we	we	PRON
ejpam-2592	94	16	have	have	VERB
ejpam-2592	94	17	ψ	ψ	X
ejpam-2592	94	18	�	�	PROPN
ejpam-2592	94	19	κ	κ	ADP
ejpam-2592	94	20	ǫ	ǫ	ADP
ejpam-2592	94	21	κ	κ	PRON
ejpam-2592	94	22	�	�	PROPN
ejpam-2592	94	23	≤ψ	≤ψ	PROPN
ejpam-2592	94	24	(	(	PUNCT
ejpam-2592	94	25	ǫ)−ϕ	ǫ)−ϕ	NUM
ejpam-2592	94	26	(	(	PUNCT
ejpam-2592	94	27	ǫ	ǫ	NOUN
ejpam-2592	94	28	)	)	PUNCT
ejpam-2592	94	29	(	(	PUNCT
ejpam-2592	94	30	23	23	NUM
ejpam-2592	94	31	)	)	PUNCT
ejpam-2592	94	32	which	which	PRON
ejpam-2592	94	33	is	be	AUX
ejpam-2592	94	34	a	a	DET
ejpam-2592	94	35	contradiction	contradiction	NOUN
ejpam-2592	94	36	.	.	PUNCT
ejpam-2592	95	1	hence	hence	ADV
ejpam-2592	95	2	�	�	PROPN
ejpam-2592	95	3	xn	xn	PROPN
ejpam-2592	95	4	is	be	AUX
ejpam-2592	95	5	a	a	DET
ejpam-2592	95	6	cauchy	cauchy	ADJ
ejpam-2592	95	7	sequence	sequence	NOUN
ejpam-2592	95	8	in	in	ADP
ejpam-2592	95	9	x	x	X
ejpam-2592	95	10	.	.	PUNCT
ejpam-2592	96	1	since	since	SCONJ
ejpam-2592	96	2	x	x	PRON
ejpam-2592	96	3	is	be	AUX
ejpam-2592	96	4	complete	complete	ADJ
ejpam-2592	96	5	,	,	PUNCT
ejpam-2592	96	6	there	there	PRON
ejpam-2592	96	7	exists	exist	VERB
ejpam-2592	96	8	ω	ω	PROPN
ejpam-2592	96	9	∈	∈	PROPN
ejpam-2592	96	10	x	x	PUNCT
ejpam-2592	96	11	such	such	ADJ
ejpam-2592	96	12	that	that	PRON
ejpam-2592	96	13	0=	0=	NUM
ejpam-2592	96	14	lim	lim	PROPN
ejpam-2592	96	15	n	n	CCONJ
ejpam-2592	96	16	,	,	PUNCT
ejpam-2592	96	17	m→∞	m→∞	NUM
ejpam-2592	96	18	ς	ς	PROPN
ejpam-2592	96	19	�	�	PROPN
ejpam-2592	96	20	xn	xn	PROPN
ejpam-2592	96	21	,	,	PUNCT
ejpam-2592	96	22	xm	xm	PROPN
ejpam-2592	96	23	�	�	PROPN
ejpam-2592	97	1	=	=	PROPN
ejpam-2592	97	2	lim	lim	PROPN
ejpam-2592	97	3	n→∞	n→∞	NUM
ejpam-2592	97	4	ς	ς	PROPN
ejpam-2592	97	5	�	�	PROPN
ejpam-2592	97	6	xn	xn	PROPN
ejpam-2592	97	7	,	,	PUNCT
ejpam-2592	97	8	ω	ω	PROPN
ejpam-2592	97	9	�	�	PROPN
ejpam-2592	97	10	=	=	SYM
ejpam-2592	97	11	ς	ς	PROPN
ejpam-2592	97	12	(	(	PUNCT
ejpam-2592	97	13	ω	ω	PROPN
ejpam-2592	97	14	,	,	PUNCT
ejpam-2592	97	15	ω	ω	NOUN
ejpam-2592	97	16	)	)	PUNCT
ejpam-2592	97	17	.	.	PUNCT
ejpam-2592	98	1	(	(	PUNCT
ejpam-2592	98	2	24	24	NUM
ejpam-2592	98	3	)	)	PUNCT
ejpam-2592	98	4	by	by	ADP
ejpam-2592	98	5	using	use	VERB
ejpam-2592	98	6	(	(	PUNCT
ejpam-2592	98	7	a3	a3	NOUN
ejpam-2592	98	8	)	)	PUNCT
ejpam-2592	98	9	,	,	PUNCT
ejpam-2592	98	10	we	we	PRON
ejpam-2592	98	11	deduce	deduce	VERB
ejpam-2592	98	12	ς	ς	PROPN
ejpam-2592	98	13	(	(	PUNCT
ejpam-2592	98	14	ω	ω	PROPN
ejpam-2592	98	15	,	,	PUNCT
ejpam-2592	98	16	tω	tω	PROPN
ejpam-2592	98	17	)	)	PUNCT
ejpam-2592	98	18	≤	≤	NOUN
ejpam-2592	98	19	κς	κς	ADP
ejpam-2592	98	20	�	�	PROPN
ejpam-2592	98	21	ω	ω	PROPN
ejpam-2592	98	22	,	,	PUNCT
ejpam-2592	98	23	t	t	PROPN
ejpam-2592	98	24	xn	xn	PROPN
ejpam-2592	98	25	�	�	PROPN
ejpam-2592	98	26	+	+	CCONJ
ejpam-2592	98	27	κς	κς	ADP
ejpam-2592	98	28	�	�	PROPN
ejpam-2592	98	29	t	t	PROPN
ejpam-2592	98	30	xn	xn	PROPN
ejpam-2592	98	31	,	,	PUNCT
ejpam-2592	98	32	tω	tω	PROPN
ejpam-2592	98	33	�	�	PROPN
ejpam-2592	98	34	.	.	PUNCT
ejpam-2592	99	1	(	(	PUNCT
ejpam-2592	99	2	25	25	NUM
ejpam-2592	99	3	)	)	PUNCT
ejpam-2592	99	4	taking	take	VERB
ejpam-2592	99	5	the	the	DET
ejpam-2592	99	6	upper	upper	ADJ
ejpam-2592	99	7	limit	limit	NOUN
ejpam-2592	99	8	as	as	ADP
ejpam-2592	99	9	n→∞	n→∞	NUM
ejpam-2592	99	10	in	in	ADP
ejpam-2592	99	11	(	(	PUNCT
ejpam-2592	99	12	25	25	NUM
ejpam-2592	99	13	)	)	PUNCT
ejpam-2592	99	14	and	and	CCONJ
ejpam-2592	99	15	using	use	VERB
ejpam-2592	99	16	the	the	DET
ejpam-2592	99	17	continuity	continuity	NOUN
ejpam-2592	99	18	of	of	ADP
ejpam-2592	99	19	t	t	NOUN
ejpam-2592	99	20	we	we	PRON
ejpam-2592	99	21	have	have	VERB
ejpam-2592	99	22	ς	ς	PROPN
ejpam-2592	99	23	(	(	PUNCT
ejpam-2592	99	24	ω	ω	PROPN
ejpam-2592	99	25	,	,	PUNCT
ejpam-2592	99	26	tω)≤	tω)≤	NOUN
ejpam-2592	99	27	κς	κς	X
ejpam-2592	99	28	(	(	PUNCT
ejpam-2592	99	29	tω	tω	PROPN
ejpam-2592	99	30	,	,	PUNCT
ejpam-2592	99	31	tω	tω	PROPN
ejpam-2592	99	32	)	)	PUNCT
ejpam-2592	99	33	.	.	PUNCT
ejpam-2592	100	1	(	(	PUNCT
ejpam-2592	100	2	26	26	NUM
ejpam-2592	100	3	)	)	PUNCT
ejpam-2592	100	4	since	since	SCONJ
ejpam-2592	100	5	α	α	PROPN
ejpam-2592	100	6	(	(	PUNCT
ejpam-2592	100	7	ω	ω	NOUN
ejpam-2592	100	8	,	,	PUNCT
ejpam-2592	100	9	ω)≥	ω)≥	DET
ejpam-2592	100	10	1	1	NUM
ejpam-2592	100	11	and	and	CCONJ
ejpam-2592	100	12	using	use	VERB
ejpam-2592	100	13	(	(	PUNCT
ejpam-2592	100	14	1	1	X
ejpam-2592	100	15	)	)	PUNCT
ejpam-2592	100	16	we	we	PRON
ejpam-2592	100	17	have	have	VERB
ejpam-2592	100	18	ψ	ψ	X
ejpam-2592	100	19	(	(	PUNCT
ejpam-2592	100	20	κς	κς	X
ejpam-2592	100	21	(	(	PUNCT
ejpam-2592	100	22	tω	tω	PROPN
ejpam-2592	100	23	,	,	PUNCT
ejpam-2592	100	24	tω))≤	tω))≤	SYM
ejpam-2592	100	25	α	α	PROPN
ejpam-2592	100	26	(	(	PUNCT
ejpam-2592	100	27	ω	ω	NOUN
ejpam-2592	100	28	,	,	PUNCT
ejpam-2592	100	29	ω)ψ	ω)ψ	X
ejpam-2592	100	30	(	(	PUNCT
ejpam-2592	100	31	κς	κς	X
ejpam-2592	100	32	(	(	PUNCT
ejpam-2592	100	33	tω	tω	INTJ
ejpam-2592	100	34	,	,	PUNCT
ejpam-2592	100	35	tω))≤ψ	tω))≤ψ	X
ejpam-2592	100	36	(	(	PUNCT
ejpam-2592	100	37	m	m	PROPN
ejpam-2592	100	38	(	(	PUNCT
ejpam-2592	100	39	ω	ω	PROPN
ejpam-2592	100	40	,	,	PUNCT
ejpam-2592	100	41	ω))−ϕ	ω))−ϕ	ADJ
ejpam-2592	100	42	(	(	PUNCT
ejpam-2592	100	43	m	m	PROPN
ejpam-2592	100	44	(	(	PUNCT
ejpam-2592	100	45	ω	ω	PROPN
ejpam-2592	100	46	,	,	PUNCT
ejpam-2592	100	47	ω	ω	NOUN
ejpam-2592	100	48	)	)	PUNCT
ejpam-2592	100	49	)	)	PUNCT
ejpam-2592	100	50	(	(	PUNCT
ejpam-2592	100	51	27	27	NUM
ejpam-2592	100	52	)	)	PUNCT
ejpam-2592	101	1	where	where	SCONJ
ejpam-2592	101	2	m	m	PROPN
ejpam-2592	101	3	(	(	PUNCT
ejpam-2592	101	4	ω	ω	PROPN
ejpam-2592	101	5	,	,	PUNCT
ejpam-2592	101	6	ω	ω	NOUN
ejpam-2592	101	7	)	)	PUNCT
ejpam-2592	102	1	=	=	NOUN
ejpam-2592	102	2	max	max	PROPN
ejpam-2592	102	3	§	§	PROPN
ejpam-2592	102	4	ς	ς	PROPN
ejpam-2592	102	5	(	(	PUNCT
ejpam-2592	102	6	ω	ω	PROPN
ejpam-2592	102	7	,	,	PUNCT
ejpam-2592	102	8	ω	ω	NOUN
ejpam-2592	102	9	)	)	PUNCT
ejpam-2592	102	10	,	,	PUNCT
ejpam-2592	102	11	ς	ς	PROPN
ejpam-2592	102	12	(	(	PUNCT
ejpam-2592	102	13	ω	ω	PROPN
ejpam-2592	102	14	,	,	PUNCT
ejpam-2592	102	15	tω	tω	PROPN
ejpam-2592	102	16	)	)	PUNCT
ejpam-2592	102	17	,	,	PUNCT
ejpam-2592	102	18	ς	ς	PROPN
ejpam-2592	102	19	(	(	PUNCT
ejpam-2592	102	20	ω	ω	PROPN
ejpam-2592	102	21	,	,	PUNCT
ejpam-2592	102	22	tω	tω	PROPN
ejpam-2592	102	23	)	)	PUNCT
ejpam-2592	102	24	,	,	PUNCT
ejpam-2592	102	25	ς	ς	PROPN
ejpam-2592	102	26	(	(	PUNCT
ejpam-2592	102	27	ω	ω	PROPN
ejpam-2592	102	28	,	,	PUNCT
ejpam-2592	102	29	tω	tω	PROPN
ejpam-2592	102	30	)	)	PUNCT
ejpam-2592	103	1	+	+	CCONJ
ejpam-2592	103	2	ς	ς	PROPN
ejpam-2592	103	3	(	(	PUNCT
ejpam-2592	103	4	ω	ω	PROPN
ejpam-2592	103	5	,	,	PUNCT
ejpam-2592	103	6	tω	tω	PROPN
ejpam-2592	103	7	)	)	PUNCT
ejpam-2592	103	8	2κ	2κ	NOUN
ejpam-2592	103	9	ª	ª	NOUN
ejpam-2592	103	10	=	=	SYM
ejpam-2592	103	11	ς	ς	PROPN
ejpam-2592	103	12	(	(	PUNCT
ejpam-2592	103	13	ω	ω	PROPN
ejpam-2592	103	14	,	,	PUNCT
ejpam-2592	103	15	tω	tω	PROPN
ejpam-2592	103	16	)	)	PUNCT
ejpam-2592	103	17	.	.	PUNCT
ejpam-2592	104	1	(	(	PUNCT
ejpam-2592	104	2	28	28	NUM
ejpam-2592	104	3	)	)	PUNCT
ejpam-2592	104	4	hence	hence	ADV
ejpam-2592	104	5	,	,	PUNCT
ejpam-2592	104	6	ψ	ψ	X
ejpam-2592	104	7	(	(	PUNCT
ejpam-2592	104	8	κς	κς	X
ejpam-2592	104	9	(	(	PUNCT
ejpam-2592	104	10	tω	tω	PROPN
ejpam-2592	104	11	,	,	PUNCT
ejpam-2592	104	12	tω))≤	tω))≤	SYM
ejpam-2592	104	13	α	α	PROPN
ejpam-2592	104	14	(	(	PUNCT
ejpam-2592	104	15	ω	ω	NOUN
ejpam-2592	104	16	,	,	PUNCT
ejpam-2592	104	17	ω)ψ	ω)ψ	X
ejpam-2592	104	18	(	(	PUNCT
ejpam-2592	104	19	κς	κς	X
ejpam-2592	104	20	(	(	PUNCT
ejpam-2592	104	21	tω	tω	INTJ
ejpam-2592	104	22	,	,	PUNCT
ejpam-2592	104	23	tω))≤ψ	tω))≤ψ	X
ejpam-2592	104	24	(	(	PUNCT
ejpam-2592	104	25	ς	ς	PROPN
ejpam-2592	104	26	(	(	PUNCT
ejpam-2592	104	27	ω	ω	PROPN
ejpam-2592	104	28	,	,	PUNCT
ejpam-2592	104	29	tω))−ϕ	tω))−ϕ	PROPN
ejpam-2592	104	30	(	(	PUNCT
ejpam-2592	104	31	ς	ς	PROPN
ejpam-2592	104	32	(	(	PUNCT
ejpam-2592	104	33	ω	ω	PROPN
ejpam-2592	104	34	,	,	PUNCT
ejpam-2592	104	35	tω	tω	PROPN
ejpam-2592	104	36	)	)	PUNCT
ejpam-2592	104	37	)	)	PUNCT
ejpam-2592	104	38	.	.	PUNCT
ejpam-2592	105	1	(	(	PUNCT
ejpam-2592	105	2	29	29	NUM
ejpam-2592	105	3	)	)	PUNCT
ejpam-2592	105	4	the	the	DET
ejpam-2592	105	5	property	property	NOUN
ejpam-2592	105	6	of	of	ADP
ejpam-2592	105	7	ψ	ψ	NOUN
ejpam-2592	105	8	,	,	PUNCT
ejpam-2592	105	9	we	we	PRON
ejpam-2592	105	10	obtain	obtain	VERB
ejpam-2592	105	11	κς	κς	ADP
ejpam-2592	105	12	(	(	PUNCT
ejpam-2592	105	13	tω	tω	PROPN
ejpam-2592	105	14	,	,	PUNCT
ejpam-2592	105	15	tω	tω	PROPN
ejpam-2592	105	16	)	)	PUNCT
ejpam-2592	105	17	≤	≤	NUM
ejpam-2592	105	18	ς	ς	PROPN
ejpam-2592	105	19	(	(	PUNCT
ejpam-2592	105	20	ω	ω	PROPN
ejpam-2592	105	21	,	,	PUNCT
ejpam-2592	105	22	tω	tω	PROPN
ejpam-2592	105	23	)	)	PUNCT
ejpam-2592	105	24	.	.	PUNCT
ejpam-2592	106	1	(	(	PUNCT
ejpam-2592	106	2	30	30	NUM
ejpam-2592	106	3	)	)	PUNCT
ejpam-2592	106	4	here	here	ADV
ejpam-2592	106	5	we	we	PRON
ejpam-2592	106	6	deduce	deduce	VERB
ejpam-2592	106	7	ϕ	ϕ	PROPN
ejpam-2592	106	8	(	(	PUNCT
ejpam-2592	106	9	ς	ς	PROPN
ejpam-2592	106	10	(	(	PUNCT
ejpam-2592	106	11	ω	ω	PROPN
ejpam-2592	106	12	,	,	PUNCT
ejpam-2592	106	13	tω	tω	PROPN
ejpam-2592	106	14	)	)	PUNCT
ejpam-2592	106	15	)	)	PUNCT
ejpam-2592	107	1	=	=	SYM
ejpam-2592	107	2	0	0	X
ejpam-2592	107	3	.	.	X
ejpam-2592	107	4	hold	hold	VERB
ejpam-2592	107	5	ς	ς	PROPN
ejpam-2592	107	6	(	(	PUNCT
ejpam-2592	107	7	tω	tω	PROPN
ejpam-2592	107	8	,	,	PUNCT
ejpam-2592	107	9	ω	ω	NOUN
ejpam-2592	107	10	)	)	PUNCT
ejpam-2592	108	1	=	=	SYM
ejpam-2592	108	2	ς	ς	PROPN
ejpam-2592	108	3	(	(	PUNCT
ejpam-2592	108	4	tω	tω	PROPN
ejpam-2592	108	5	,	,	PUNCT
ejpam-2592	108	6	tω	tω	PROPN
ejpam-2592	108	7	)	)	PUNCT
ejpam-2592	108	8	=	=	SYM
ejpam-2592	108	9	ς	ς	PROPN
ejpam-2592	108	10	(	(	PUNCT
ejpam-2592	108	11	tω	tω	PROPN
ejpam-2592	108	12	,	,	PUNCT
ejpam-2592	108	13	ω	ω	NOUN
ejpam-2592	108	14	)	)	PUNCT
ejpam-2592	108	15	=	=	SYM
ejpam-2592	108	16	0	0	NUM
ejpam-2592	108	17	and	and	CCONJ
ejpam-2592	108	18	tω	tω	PROPN
ejpam-2592	108	19	=	=	NOUN
ejpam-2592	108	20	ω	ω	PROPN
ejpam-2592	108	21	.	.	PUNCT
ejpam-2592	109	1	hence	hence	ADV
ejpam-2592	109	2	,	,	PUNCT
ejpam-2592	109	3	ω	ω	PROPN
ejpam-2592	109	4	is	be	AUX
ejpam-2592	109	5	a	a	DET
ejpam-2592	109	6	fixed	fix	VERB
ejpam-2592	109	7	point	point	NOUN
ejpam-2592	109	8	of	of	ADP
ejpam-2592	109	9	t	t	PROPN
ejpam-2592	109	10	.	.	PUNCT
ejpam-2592	110	1	if	if	SCONJ
ejpam-2592	110	2	we	we	PRON
ejpam-2592	110	3	replace	replace	VERB
ejpam-2592	110	4	the	the	DET
ejpam-2592	110	5	continuity	continuity	NOUN
ejpam-2592	110	6	condition	condition	NOUN
ejpam-2592	110	7	(	(	PUNCT
ejpam-2592	110	8	iii	iii	NOUN
ejpam-2592	110	9	)	)	PUNCT
ejpam-2592	110	10	,	,	PUNCT
ejpam-2592	110	11	theorem	theorem	VERB
ejpam-2592	110	12	1	1	NUM
ejpam-2592	110	13	remains	remain	VERB
ejpam-2592	110	14	true	true	ADJ
ejpam-2592	110	15	.	.	PUNCT
ejpam-2592	111	1	this	this	DET
ejpam-2592	111	2	statement	statement	NOUN
ejpam-2592	111	3	is	be	AUX
ejpam-2592	111	4	given	give	VERB
ejpam-2592	111	5	as	as	SCONJ
ejpam-2592	111	6	follows	follow	VERB
ejpam-2592	111	7	.	.	PUNCT
ejpam-2592	112	1	m.	m.	NOUN
ejpam-2592	112	2	akturk	akturk	PROPN
ejpam-2592	112	3	,	,	PUNCT
ejpam-2592	112	4	m.	m.	NOUN
ejpam-2592	112	5	kır	kır	PROPN
ejpam-2592	112	6	,	,	PUNCT
ejpam-2592	112	7	e.	e.	PROPN
ejpam-2592	112	8	yolacan	yolacan	PROPN
ejpam-2592	112	9	/	/	SYM
ejpam-2592	112	10	eur	eur	PROPN
ejpam-2592	112	11	.	.	PUNCT
ejpam-2592	113	1	j.	j.	PROPN
ejpam-2592	113	2	pure	pure	PROPN
ejpam-2592	113	3	appl	appl	PROPN
ejpam-2592	113	4	.	.	PROPN
ejpam-2592	113	5	math	math	PROPN
ejpam-2592	113	6	,	,	PUNCT
ejpam-2592	113	7	9	9	NUM
ejpam-2592	113	8	(	(	PUNCT
ejpam-2592	113	9	2016	2016	NUM
ejpam-2592	113	10	)	)	PUNCT
ejpam-2592	113	11	,	,	PUNCT
ejpam-2592	113	12	175	175	NUM
ejpam-2592	113	13	-	-	SYM
ejpam-2592	113	14	185	185	NUM
ejpam-2592	113	15	181	181	NUM
ejpam-2592	113	16	theorem	theorem	NOUN
ejpam-2592	113	17	2	2	NUM
ejpam-2592	113	18	.	.	X
ejpam-2592	114	1	let	let	AUX
ejpam-2592	114	2	(	(	PUNCT
ejpam-2592	114	3	x	x	X
ejpam-2592	114	4	,	,	PUNCT
ejpam-2592	114	5	ς	ς	PROPN
ejpam-2592	114	6	)	)	PUNCT
ejpam-2592	114	7	be	be	AUX
ejpam-2592	114	8	a	a	DET
ejpam-2592	114	9	complete	complete	ADJ
ejpam-2592	114	10	b	b	X
ejpam-2592	114	11	-	-	PUNCT
ejpam-2592	114	12	metric	metric	ADJ
ejpam-2592	114	13	-	-	PUNCT
ejpam-2592	114	14	like	like	ADJ
ejpam-2592	114	15	space	space	NOUN
ejpam-2592	114	16	with	with	ADP
ejpam-2592	114	17	the	the	DET
ejpam-2592	114	18	constant	constant	ADJ
ejpam-2592	114	19	κ≥	κ≥	PROPN
ejpam-2592	114	20	1	1	NUM
ejpam-2592	114	21	and	and	CCONJ
ejpam-2592	114	22	let	let	VERB
ejpam-2592	114	23	t	t	NOUN
ejpam-2592	114	24	:	:	PUNCT
ejpam-2592	114	25	x	x	X
ejpam-2592	114	26	→	→	PUNCT
ejpam-2592	114	27	x	x	PUNCT
ejpam-2592	114	28	be	be	AUX
ejpam-2592	114	29	an	an	DET
ejpam-2592	114	30	α−ψ−ϕ-contractive	α−ψ−ϕ-contractive	ADJ
ejpam-2592	114	31	type	type	NOUN
ejpam-2592	114	32	mapping	mapping	NOUN
ejpam-2592	114	33	.	.	PUNCT
ejpam-2592	115	1	suppose	suppose	VERB
ejpam-2592	115	2	that	that	SCONJ
ejpam-2592	115	3	(	(	PUNCT
ejpam-2592	115	4	i	i	NOUN
ejpam-2592	115	5	)	)	PUNCT
ejpam-2592	115	6	t	t	PROPN
ejpam-2592	115	7	is	be	AUX
ejpam-2592	115	8	α	α	PRON
ejpam-2592	115	9	-	-	ADJ
ejpam-2592	115	10	admissible	admissible	ADJ
ejpam-2592	115	11	;	;	PUNCT
ejpam-2592	115	12	(	(	PUNCT
ejpam-2592	115	13	ii	ii	NOUN
ejpam-2592	115	14	)	)	PUNCT
ejpam-2592	115	15	there	there	PRON
ejpam-2592	115	16	exists	exist	VERB
ejpam-2592	115	17	x0	x0	PROPN
ejpam-2592	115	18	∈	∈	PROPN
ejpam-2592	115	19	x	x	PUNCT
ejpam-2592	115	20	such	such	ADJ
ejpam-2592	115	21	that	that	SCONJ
ejpam-2592	115	22	α	α	PRON
ejpam-2592	115	23	�	�	PROPN
ejpam-2592	115	24	x0	x0	PROPN
ejpam-2592	115	25	,	,	PUNCT
ejpam-2592	115	26	t	t	PROPN
ejpam-2592	115	27	x0	x0	PROPN
ejpam-2592	115	28	�	�	PROPN
ejpam-2592	115	29	≥	≥	NUM
ejpam-2592	115	30	1	1	NUM
ejpam-2592	115	31	;	;	PUNCT
ejpam-2592	115	32	(	(	PUNCT
ejpam-2592	115	33	iii	iii	X
ejpam-2592	115	34	)	)	PUNCT
ejpam-2592	115	35	if	if	SCONJ
ejpam-2592	115	36	�	�	PROPN
ejpam-2592	115	37	xn	xn	PROPN
ejpam-2592	115	38	is	be	AUX
ejpam-2592	115	39	a	a	DET
ejpam-2592	115	40	sequence	sequence	NOUN
ejpam-2592	115	41	in	in	ADP
ejpam-2592	115	42	x	x	INTJ
ejpam-2592	115	43	such	such	ADJ
ejpam-2592	115	44	that	that	SCONJ
ejpam-2592	115	45	α	α	PROPN
ejpam-2592	115	46	�	�	PROPN
ejpam-2592	115	47	xn	xn	PROPN
ejpam-2592	115	48	,	,	PUNCT
ejpam-2592	115	49	xn+1	xn+1	PROPN
ejpam-2592	115	50	�	�	PROPN
ejpam-2592	115	51	≥	≥	NUM
ejpam-2592	115	52	1	1	NUM
ejpam-2592	115	53	for	for	ADP
ejpam-2592	115	54	all	all	DET
ejpam-2592	115	55	n	n	NOUN
ejpam-2592	115	56	and	and	CCONJ
ejpam-2592	115	57	xn→	xn→	PUNCT
ejpam-2592	116	1	x	x	PUNCT
ejpam-2592	116	2	∈	∈	PROPN
ejpam-2592	116	3	x	x	PUNCT
ejpam-2592	116	4	as	as	ADP
ejpam-2592	116	5	n→∞	n→∞	NUM
ejpam-2592	116	6	,	,	PUNCT
ejpam-2592	116	7	then	then	ADV
ejpam-2592	116	8	there	there	PRON
ejpam-2592	116	9	exists	exist	VERB
ejpam-2592	116	10	a	a	DET
ejpam-2592	116	11	subsequence	subsequence	NOUN
ejpam-2592	116	12	�	�	PROPN
ejpam-2592	116	13	xnk	xnk	PROPN
ejpam-2592	116	14	of	of	ADP
ejpam-2592	116	15	�	�	PROPN
ejpam-2592	116	16	xn	xn	PROPN
ejpam-2592	116	17	such	such	ADJ
ejpam-2592	116	18	that	that	SCONJ
ejpam-2592	116	19	α	α	PROPN
ejpam-2592	116	20	�	�	PROPN
ejpam-2592	116	21	xnk	xnk	PROPN
ejpam-2592	116	22	,	,	PUNCT
ejpam-2592	116	23	x	x	PROPN
ejpam-2592	116	24	�	�	PROPN
ejpam-2592	116	25	≥	≥	NUM
ejpam-2592	116	26	1	1	NUM
ejpam-2592	116	27	for	for	ADP
ejpam-2592	116	28	all	all	DET
ejpam-2592	116	29	k.	k.	PROPN
ejpam-2592	116	30	then	then	ADV
ejpam-2592	116	31	,	,	PUNCT
ejpam-2592	116	32	such	such	ADJ
ejpam-2592	116	33	ω	ω	PROPN
ejpam-2592	116	34	is	be	AUX
ejpam-2592	116	35	a	a	DET
ejpam-2592	116	36	fixed	fix	VERB
ejpam-2592	116	37	point	point	NOUN
ejpam-2592	116	38	of	of	ADP
ejpam-2592	116	39	t	t	PROPN
ejpam-2592	116	40	,	,	PUNCT
ejpam-2592	116	41	that	that	PRON
ejpam-2592	116	42	is	be	AUX
ejpam-2592	116	43	tω	tω	PROPN
ejpam-2592	116	44	=	=	PROPN
ejpam-2592	116	45	ω	ω	PROPN
ejpam-2592	116	46	.	.	PUNCT
ejpam-2592	117	1	proof	proof	NOUN
ejpam-2592	117	2	.	.	PUNCT
ejpam-2592	118	1	from	from	ADP
ejpam-2592	118	2	proof	proof	NOUN
ejpam-2592	118	3	of	of	ADP
ejpam-2592	118	4	theorem	theorem	NOUN
ejpam-2592	118	5	1	1	NUM
ejpam-2592	118	6	,	,	PUNCT
ejpam-2592	118	7	we	we	PRON
ejpam-2592	118	8	know	know	VERB
ejpam-2592	118	9	that	that	SCONJ
ejpam-2592	118	10	the	the	DET
ejpam-2592	118	11	sequence	sequence	NOUN
ejpam-2592	118	12	�	�	PROPN
ejpam-2592	118	13	xn	xn	PROPN
ejpam-2592	118	14	defined	define	VERB
ejpam-2592	118	15	by	by	ADP
ejpam-2592	118	16	xn+1	xn+1	PROPN
ejpam-2592	118	17	=	=	SYM
ejpam-2592	118	18	t	t	PROPN
ejpam-2592	118	19	xn	xn	PROPN
ejpam-2592	118	20	for	for	ADP
ejpam-2592	118	21	all	all	DET
ejpam-2592	118	22	n	n	PRON
ejpam-2592	118	23	∈	∈	NOUN
ejpam-2592	118	24	n	n	VERB
ejpam-2592	118	25	is	be	AUX
ejpam-2592	118	26	cauchy	cauchy	ADJ
ejpam-2592	118	27	in	in	ADP
ejpam-2592	118	28	(	(	PUNCT
ejpam-2592	118	29	x	x	INTJ
ejpam-2592	118	30	,	,	PUNCT
ejpam-2592	118	31	ς	ς	PROPN
ejpam-2592	118	32	)	)	PUNCT
ejpam-2592	118	33	and	and	CCONJ
ejpam-2592	118	34	converges	converge	VERB
ejpam-2592	118	35	to	to	ADP
ejpam-2592	118	36	some	some	DET
ejpam-2592	118	37	ω	ω	NUM
ejpam-2592	118	38	∈	∈	PROPN
ejpam-2592	118	39	x	x	X
ejpam-2592	118	40	.	.	PUNCT
ejpam-2592	119	1	consider	consider	VERB
ejpam-2592	119	2	(	(	PUNCT
ejpam-2592	119	3	24	24	NUM
ejpam-2592	119	4	)	)	PUNCT
ejpam-2592	119	5	,	,	PUNCT
ejpam-2592	119	6	lim	lim	PROPN
ejpam-2592	119	7	k→∞	k→∞	NOUN
ejpam-2592	119	8	ς	ς	PROPN
ejpam-2592	119	9	�	�	PROPN
ejpam-2592	119	10	xnk+1	xnk+1	PROPN
ejpam-2592	119	11	,	,	PUNCT
ejpam-2592	119	12	tω	tω	X
ejpam-2592	119	13	�	�	PROPN
ejpam-2592	119	14	=	=	SYM
ejpam-2592	119	15	ς	ς	PROPN
ejpam-2592	119	16	(	(	PUNCT
ejpam-2592	119	17	ω	ω	PROPN
ejpam-2592	119	18	,	,	PUNCT
ejpam-2592	119	19	tω	tω	PROPN
ejpam-2592	119	20	)	)	PUNCT
ejpam-2592	119	21	(	(	PUNCT
ejpam-2592	119	22	31	31	NUM
ejpam-2592	119	23	)	)	PUNCT
ejpam-2592	119	24	holds	hold	VERB
ejpam-2592	119	25	.	.	PUNCT
ejpam-2592	120	1	by	by	ADP
ejpam-2592	120	2	the	the	DET
ejpam-2592	120	3	assumption	assumption	NOUN
ejpam-2592	120	4	on	on	ADP
ejpam-2592	120	5	x	x	SYM
ejpam-2592	120	6	,	,	PUNCT
ejpam-2592	120	7	we	we	PRON
ejpam-2592	120	8	have	have	VERB
ejpam-2592	120	9	ψ	ψ	ADP
ejpam-2592	120	10	�	�	PROPN
ejpam-2592	120	11	κς	κς	ADP
ejpam-2592	120	12	�	�	PROPN
ejpam-2592	120	13	xnk+1	xnk+1	PROPN
ejpam-2592	120	14	,	,	PUNCT
ejpam-2592	120	15	tω	tω	PROPN
ejpam-2592	120	16	�	�	PROPN
ejpam-2592	120	17	�	�	PROPN
ejpam-2592	120	18	≤α	≤α	NOUN
ejpam-2592	120	19	�	�	PROPN
ejpam-2592	120	20	xnk	xnk	PROPN
ejpam-2592	120	21	,	,	PUNCT
ejpam-2592	120	22	ω	ω	PROPN
ejpam-2592	120	23	�	�	PROPN
ejpam-2592	120	24	ψ	ψ	ADP
ejpam-2592	120	25	�	�	PROPN
ejpam-2592	120	26	κς	κς	ADP
ejpam-2592	120	27	�	�	PROPN
ejpam-2592	120	28	t	t	PROPN
ejpam-2592	120	29	xnk	xnk	PROPN
ejpam-2592	120	30	,	,	PUNCT
ejpam-2592	120	31	tω	tω	PROPN
ejpam-2592	120	32	�	�	PROPN
ejpam-2592	120	33	�	�	PROPN
ejpam-2592	120	34	≤ψ	≤ψ	PROPN
ejpam-2592	120	35	�	�	PROPN
ejpam-2592	120	36	m	m	PROPN
ejpam-2592	120	37	�	�	PROPN
ejpam-2592	120	38	xnk	xnk	PROPN
ejpam-2592	120	39	,	,	PUNCT
ejpam-2592	120	40	ω	ω	PROPN
ejpam-2592	120	41	�	�	PROPN
ejpam-2592	120	42	�	�	PROPN
ejpam-2592	120	43	−ϕ	−ϕ	ADV
ejpam-2592	120	44	�	�	PROPN
ejpam-2592	120	45	m	m	PROPN
ejpam-2592	120	46	�	�	PROPN
ejpam-2592	120	47	xnk	xnk	PROPN
ejpam-2592	120	48	,	,	PUNCT
ejpam-2592	120	49	ω	ω	PROPN
ejpam-2592	120	50	�	�	PROPN
ejpam-2592	120	51	�	�	PROPN
ejpam-2592	120	52	(	(	PUNCT
ejpam-2592	120	53	32	32	NUM
ejpam-2592	120	54	)	)	PUNCT
ejpam-2592	120	55	where	where	SCONJ
ejpam-2592	120	56	m	m	VERB
ejpam-2592	120	57	�	�	PROPN
ejpam-2592	120	58	xnk	xnk	PROPN
ejpam-2592	120	59	,	,	PUNCT
ejpam-2592	120	60	ω	ω	PROPN
ejpam-2592	120	61	�	�	PROPN
ejpam-2592	120	62	=	=	NUM
ejpam-2592	120	63	max	max	PROPN
ejpam-2592	120	64	¨	¨	NOUN
ejpam-2592	120	65	ς	ς	PROPN
ejpam-2592	120	66	�	�	PROPN
ejpam-2592	120	67	xnk	xnk	PROPN
ejpam-2592	120	68	,	,	PUNCT
ejpam-2592	120	69	ω	ω	PROPN
ejpam-2592	120	70	�	�	PROPN
ejpam-2592	120	71	,	,	PUNCT
ejpam-2592	120	72	ς	ς	PROPN
ejpam-2592	120	73	�	�	PROPN
ejpam-2592	120	74	xnk	xnk	PROPN
ejpam-2592	120	75	,	,	PUNCT
ejpam-2592	120	76	t	t	PROPN
ejpam-2592	120	77	xnk	xnk	PROPN
ejpam-2592	120	78	�	�	PROPN
ejpam-2592	120	79	,	,	PUNCT
ejpam-2592	120	80	ς	ς	PROPN
ejpam-2592	120	81	(	(	PUNCT
ejpam-2592	120	82	ω	ω	PROPN
ejpam-2592	120	83	,	,	PUNCT
ejpam-2592	120	84	tω	tω	PROPN
ejpam-2592	120	85	)	)	PUNCT
ejpam-2592	120	86	,	,	PUNCT
ejpam-2592	120	87	ς	ς	PROPN
ejpam-2592	120	88	�	�	PROPN
ejpam-2592	120	89	xnk	xnk	PROPN
ejpam-2592	120	90	,	,	PUNCT
ejpam-2592	120	91	tω	tω	PROPN
ejpam-2592	120	92	�	�	PROPN
ejpam-2592	120	93	+	+	CCONJ
ejpam-2592	120	94	ς	ς	PROPN
ejpam-2592	120	95	�	�	PROPN
ejpam-2592	120	96	ω	ω	PROPN
ejpam-2592	120	97	,	,	PUNCT
ejpam-2592	121	1	t	t	PROPN
ejpam-2592	121	2	xnk	xnk	PROPN
ejpam-2592	121	3	�	�	PROPN
ejpam-2592	121	4	2κ	2κ	NOUN
ejpam-2592	121	5	«	«	PUNCT
ejpam-2592	121	6	=	=	NUM
ejpam-2592	121	7	max	max	NOUN
ejpam-2592	121	8	¨	¨	NOUN
ejpam-2592	121	9	ς	ς	PROPN
ejpam-2592	121	10	�	�	PROPN
ejpam-2592	121	11	xnk	xnk	PROPN
ejpam-2592	121	12	,	,	PUNCT
ejpam-2592	121	13	ω	ω	PROPN
ejpam-2592	121	14	�	�	PROPN
ejpam-2592	121	15	,	,	PUNCT
ejpam-2592	121	16	ς	ς	PROPN
ejpam-2592	121	17	�	�	PROPN
ejpam-2592	121	18	xnk	xnk	PROPN
ejpam-2592	121	19	,	,	PUNCT
ejpam-2592	121	20	xnk+1	xnk+1	X
ejpam-2592	121	21	�	�	PROPN
ejpam-2592	121	22	,	,	PUNCT
ejpam-2592	121	23	ς	ς	PROPN
ejpam-2592	121	24	(	(	PUNCT
ejpam-2592	121	25	ω	ω	PROPN
ejpam-2592	121	26	,	,	PUNCT
ejpam-2592	121	27	tω	tω	PROPN
ejpam-2592	121	28	)	)	PUNCT
ejpam-2592	121	29	,	,	PUNCT
ejpam-2592	121	30	ς	ς	PROPN
ejpam-2592	121	31	�	�	PROPN
ejpam-2592	121	32	xnk	xnk	PROPN
ejpam-2592	121	33	,	,	PUNCT
ejpam-2592	121	34	tω	tω	PROPN
ejpam-2592	121	35	�	�	PROPN
ejpam-2592	121	36	+	+	CCONJ
ejpam-2592	121	37	ς	ς	PROPN
ejpam-2592	121	38	�	�	PROPN
ejpam-2592	121	39	ω	ω	PROPN
ejpam-2592	121	40	,	,	PUNCT
ejpam-2592	121	41	xnk+1	xnk+1	X
ejpam-2592	121	42	�	�	PROPN
ejpam-2592	121	43	2κ	2κ	NOUN
ejpam-2592	121	44	«	«	PUNCT
ejpam-2592	121	45	.	.	PUNCT
ejpam-2592	122	1	with	with	ADP
ejpam-2592	122	2	(	(	PUNCT
ejpam-2592	122	3	7	7	NUM
ejpam-2592	122	4	)	)	PUNCT
ejpam-2592	122	5	and	and	CCONJ
ejpam-2592	122	6	(	(	PUNCT
ejpam-2592	122	7	31	31	NUM
ejpam-2592	122	8	)	)	PUNCT
ejpam-2592	122	9	,	,	PUNCT
ejpam-2592	122	10	we	we	PRON
ejpam-2592	122	11	have	have	VERB
ejpam-2592	122	12	lim	lim	PROPN
ejpam-2592	122	13	k→∞	k→∞	PROPN
ejpam-2592	122	14	m	m	PROPN
ejpam-2592	122	15	�	�	PROPN
ejpam-2592	122	16	xnk	xnk	PROPN
ejpam-2592	122	17	,	,	PUNCT
ejpam-2592	122	18	ω	ω	PROPN
ejpam-2592	122	19	�	�	PROPN
ejpam-2592	122	20	=	=	SYM
ejpam-2592	122	21	ς	ς	PROPN
ejpam-2592	122	22	(	(	PUNCT
ejpam-2592	122	23	ω	ω	PROPN
ejpam-2592	122	24	,	,	PUNCT
ejpam-2592	122	25	tω	tω	PROPN
ejpam-2592	122	26	)	)	PUNCT
ejpam-2592	122	27	.	.	PUNCT
ejpam-2592	123	1	(	(	PUNCT
ejpam-2592	123	2	33	33	NUM
ejpam-2592	123	3	)	)	PUNCT
ejpam-2592	123	4	since	since	SCONJ
ejpam-2592	123	5	α	α	PROPN
ejpam-2592	123	6	�	�	PROPN
ejpam-2592	123	7	xn	xn	PROPN
ejpam-2592	123	8	,	,	PUNCT
ejpam-2592	123	9	ω	ω	PROPN
ejpam-2592	123	10	�	�	PROPN
ejpam-2592	123	11	≥	≥	NUM
ejpam-2592	123	12	1	1	NUM
ejpam-2592	123	13	we	we	PRON
ejpam-2592	123	14	have	have	VERB
ejpam-2592	123	15	ψ	ψ	X
ejpam-2592	123	16	(	(	PUNCT
ejpam-2592	123	17	ς	ς	PROPN
ejpam-2592	123	18	(	(	PUNCT
ejpam-2592	123	19	tω	tω	PROPN
ejpam-2592	123	20	,	,	PUNCT
ejpam-2592	123	21	ω))≤ψ	ω))≤ψ	ADJ
ejpam-2592	123	22	�	�	PROPN
ejpam-2592	123	23	κ	κ	PROPN
ejpam-2592	123	24	�	�	PROPN
ejpam-2592	123	25	ς	ς	PROPN
ejpam-2592	123	26	�	�	PROPN
ejpam-2592	123	27	tω	tω	PROPN
ejpam-2592	123	28	,	,	PUNCT
ejpam-2592	123	29	t	t	PROPN
ejpam-2592	123	30	xn	xn	PROPN
ejpam-2592	123	31	�	�	PROPN
ejpam-2592	124	1	+	+	CCONJ
ejpam-2592	124	2	ς	ς	PROPN
ejpam-2592	124	3	�	�	PROPN
ejpam-2592	124	4	t	t	PROPN
ejpam-2592	124	5	xn	xn	PROPN
ejpam-2592	124	6	,	,	PUNCT
ejpam-2592	124	7	ω	ω	PROPN
ejpam-2592	124	8	�	�	PROPN
ejpam-2592	124	9	�	�	PROPN
ejpam-2592	124	10	�	�	PROPN
ejpam-2592	124	11	≤ψ	≤ψ	PROPN
ejpam-2592	124	12	�	�	PROPN
ejpam-2592	124	13	κς	κς	ADP
ejpam-2592	124	14	�	�	PROPN
ejpam-2592	124	15	tω	tω	PROPN
ejpam-2592	124	16	,	,	PUNCT
ejpam-2592	124	17	t	t	PROPN
ejpam-2592	124	18	xn	xn	PROPN
ejpam-2592	124	19	�	�	PROPN
ejpam-2592	124	20	�	�	PROPN
ejpam-2592	124	21	+	+	PROPN
ejpam-2592	124	22	ψ	ψ	X
ejpam-2592	124	23	�	�	PROPN
ejpam-2592	124	24	κς	κς	ADP
ejpam-2592	124	25	�	�	PROPN
ejpam-2592	124	26	t	t	PROPN
ejpam-2592	124	27	xn	xn	PROPN
ejpam-2592	124	28	,	,	PUNCT
ejpam-2592	124	29	ω	ω	PROPN
ejpam-2592	124	30	�	�	PROPN
ejpam-2592	124	31	�	�	PROPN
ejpam-2592	124	32	≤α	≤α	PROPN
ejpam-2592	124	33	�	�	PROPN
ejpam-2592	124	34	ω	ω	PROPN
ejpam-2592	124	35	,	,	PUNCT
ejpam-2592	124	36	xn	xn	PROPN
ejpam-2592	124	37	�	�	PROPN
ejpam-2592	124	38	ψ	ψ	ADP
ejpam-2592	124	39	�	�	PROPN
ejpam-2592	124	40	κς	κς	ADP
ejpam-2592	124	41	�	�	PROPN
ejpam-2592	124	42	tω	tω	PROPN
ejpam-2592	124	43	,	,	PUNCT
ejpam-2592	124	44	t	t	PROPN
ejpam-2592	124	45	xn	xn	PROPN
ejpam-2592	124	46	�	�	PROPN
ejpam-2592	124	47	�	�	PROPN
ejpam-2592	124	48	+	+	PROPN
ejpam-2592	124	49	ψ	ψ	X
ejpam-2592	124	50	�	�	PROPN
ejpam-2592	124	51	κς	κς	ADP
ejpam-2592	124	52	�	�	PROPN
ejpam-2592	124	53	t	t	PROPN
ejpam-2592	124	54	xn	xn	PROPN
ejpam-2592	124	55	,	,	PUNCT
ejpam-2592	124	56	ω	ω	PROPN
ejpam-2592	124	57	�	�	PROPN
ejpam-2592	124	58	�	�	PROPN
ejpam-2592	124	59	≤ψ	≤ψ	PROPN
ejpam-2592	124	60	�	�	PROPN
ejpam-2592	124	61	m	m	PROPN
ejpam-2592	124	62	�	�	PROPN
ejpam-2592	124	63	ω	ω	PROPN
ejpam-2592	124	64	,	,	PUNCT
ejpam-2592	124	65	xn	xn	PROPN
ejpam-2592	124	66	�	�	PROPN
ejpam-2592	124	67	�	�	PROPN
ejpam-2592	124	68	−ϕ	−ϕ	PROPN
ejpam-2592	124	69	�	�	PROPN
ejpam-2592	124	70	m	m	PROPN
ejpam-2592	124	71	�	�	PROPN
ejpam-2592	124	72	ω	ω	PROPN
ejpam-2592	124	73	,	,	PUNCT
ejpam-2592	124	74	xn	xn	PROPN
ejpam-2592	124	75	�	�	PROPN
ejpam-2592	124	76	�	�	PROPN
ejpam-2592	124	77	(	(	PUNCT
ejpam-2592	124	78	34	34	NUM
ejpam-2592	124	79	)	)	PUNCT
ejpam-2592	124	80	let	let	VERB
ejpam-2592	124	81	n→∞	n→∞	PRON
ejpam-2592	124	82	in	in	ADP
ejpam-2592	124	83	(	(	PUNCT
ejpam-2592	124	84	34	34	NUM
ejpam-2592	124	85	)	)	PUNCT
ejpam-2592	124	86	,	,	PUNCT
ejpam-2592	124	87	we	we	PRON
ejpam-2592	124	88	haveψ	haveψ	VERB
ejpam-2592	124	89	(	(	PUNCT
ejpam-2592	124	90	ς	ς	PROPN
ejpam-2592	124	91	(	(	PUNCT
ejpam-2592	124	92	tω	tω	PROPN
ejpam-2592	124	93	,	,	PUNCT
ejpam-2592	124	94	ω))≤	ω))≤	PROPN
ejpam-2592	124	95	0	0	NUM
ejpam-2592	124	96	.	.	PUNCT
ejpam-2592	125	1	henceω	henceω	PROPN
ejpam-2592	125	2	is	be	AUX
ejpam-2592	125	3	a	a	DET
ejpam-2592	125	4	fixed	fix	VERB
ejpam-2592	125	5	point	point	NOUN
ejpam-2592	125	6	of	of	ADP
ejpam-2592	125	7	t	t	PROPN
ejpam-2592	125	8	,	,	PUNCT
ejpam-2592	125	9	or	or	CCONJ
ejpam-2592	125	10	equivalently	equivalently	ADV
ejpam-2592	125	11	,	,	PUNCT
ejpam-2592	125	12	ω	ω	PROPN
ejpam-2592	125	13	=	=	SYM
ejpam-2592	125	14	tω	tω	PROPN
ejpam-2592	125	15	.	.	PUNCT
ejpam-2592	125	16	m.	m.	NOUN
ejpam-2592	125	17	akturk	akturk	PROPN
ejpam-2592	125	18	,	,	PUNCT
ejpam-2592	125	19	m.	m.	NOUN
ejpam-2592	125	20	kır	kır	PROPN
ejpam-2592	125	21	,	,	PUNCT
ejpam-2592	125	22	e.	e.	PROPN
ejpam-2592	125	23	yolacan	yolacan	PROPN
ejpam-2592	125	24	/	/	SYM
ejpam-2592	125	25	eur	eur	PROPN
ejpam-2592	125	26	.	.	PUNCT
ejpam-2592	126	1	j.	j.	PROPN
ejpam-2592	126	2	pure	pure	PROPN
ejpam-2592	126	3	appl	appl	PROPN
ejpam-2592	126	4	.	.	PROPN
ejpam-2592	126	5	math	math	PROPN
ejpam-2592	126	6	,	,	PUNCT
ejpam-2592	126	7	9	9	NUM
ejpam-2592	126	8	(	(	PUNCT
ejpam-2592	126	9	2016	2016	NUM
ejpam-2592	126	10	)	)	PUNCT
ejpam-2592	126	11	,	,	PUNCT
ejpam-2592	126	12	175	175	NUM
ejpam-2592	126	13	-	-	SYM
ejpam-2592	126	14	185	185	NUM
ejpam-2592	126	15	182	182	NUM
ejpam-2592	126	16	corollary	corollary	NOUN
ejpam-2592	126	17	1	1	NUM
ejpam-2592	126	18	.	.	PUNCT
ejpam-2592	127	1	let	let	AUX
ejpam-2592	127	2	(	(	PUNCT
ejpam-2592	127	3	x	x	X
ejpam-2592	127	4	,	,	PUNCT
ejpam-2592	127	5	ς	ς	PROPN
ejpam-2592	127	6	)	)	PUNCT
ejpam-2592	127	7	be	be	VERB
ejpam-2592	127	8	a	a	DET
ejpam-2592	127	9	b	b	NOUN
ejpam-2592	127	10	-	-	PUNCT
ejpam-2592	127	11	metric	metric	ADJ
ejpam-2592	127	12	-	-	PUNCT
ejpam-2592	127	13	like	like	ADJ
ejpam-2592	127	14	space	space	NOUN
ejpam-2592	127	15	with	with	ADP
ejpam-2592	127	16	coefficient	coefficient	NOUN
ejpam-2592	127	17	κ	κ	PRON
ejpam-2592	127	18	≥	≥	NOUN
ejpam-2592	127	19	1	1	NUM
ejpam-2592	127	20	and	and	CCONJ
ejpam-2592	127	21	t	t	NOUN
ejpam-2592	127	22	:	:	PUNCT
ejpam-2592	127	23	x	x	X
ejpam-2592	127	24	→	→	PUNCT
ejpam-2592	127	25	x	x	AUX
ejpam-2592	127	26	be	be	AUX
ejpam-2592	127	27	such	such	ADJ
ejpam-2592	127	28	that	that	SCONJ
ejpam-2592	127	29	κς	κς	ADP
ejpam-2592	127	30	�	�	PROPN
ejpam-2592	127	31	t	t	PROPN
ejpam-2592	127	32	x	x	PROPN
ejpam-2592	127	33	,	,	PUNCT
ejpam-2592	127	34	t	t	PROPN
ejpam-2592	127	35	y	y	PROPN
ejpam-2592	127	36	�	�	PROPN
ejpam-2592	127	37	≤	≤	NUM
ejpam-2592	127	38	m	m	VERB
ejpam-2592	127	39	�	�	PROPN
ejpam-2592	127	40	x	x	SYM
ejpam-2592	127	41	,	,	PUNCT
ejpam-2592	127	42	y	y	PROPN
ejpam-2592	127	43	�	�	PROPN
ejpam-2592	127	44	−ϕ	−ϕ	PROPN
ejpam-2592	127	45	�	�	PROPN
ejpam-2592	127	46	m	m	PROPN
ejpam-2592	127	47	�	�	PROPN
ejpam-2592	127	48	x	x	SYM
ejpam-2592	127	49	,	,	PUNCT
ejpam-2592	127	50	y	y	PROPN
ejpam-2592	127	51	�	�	PROPN
ejpam-2592	127	52	�	�	PROPN
ejpam-2592	127	53	for	for	ADP
ejpam-2592	127	54	all	all	DET
ejpam-2592	127	55	x	x	SYM
ejpam-2592	127	56	,	,	PUNCT
ejpam-2592	127	57	y	y	PROPN
ejpam-2592	127	58	∈	∈	PROPN
ejpam-2592	127	59	x	x	PUNCT
ejpam-2592	127	60	where	where	SCONJ
ejpam-2592	127	61	m	m	VERB
ejpam-2592	127	62	�	�	PROPN
ejpam-2592	127	63	x	x	SYM
ejpam-2592	127	64	,	,	PUNCT
ejpam-2592	127	65	y	y	PROPN
ejpam-2592	127	66	�	�	PROPN
ejpam-2592	127	67	defined	define	VERB
ejpam-2592	127	68	by	by	ADP
ejpam-2592	127	69	(	(	PUNCT
ejpam-2592	127	70	2	2	NUM
ejpam-2592	127	71	)	)	PUNCT
ejpam-2592	127	72	.	.	PUNCT
ejpam-2592	128	1	then	then	ADV
ejpam-2592	128	2	,	,	PUNCT
ejpam-2592	128	3	t	t	PROPN
ejpam-2592	128	4	has	have	VERB
ejpam-2592	128	5	a	a	DET
ejpam-2592	128	6	fixed	fix	VERB
ejpam-2592	128	7	point	point	NOUN
ejpam-2592	128	8	.	.	PUNCT
ejpam-2592	129	1	to	to	PART
ejpam-2592	129	2	prove	prove	VERB
ejpam-2592	129	3	corollary	corollary	ADJ
ejpam-2592	129	4	1	1	NUM
ejpam-2592	129	5	it	it	PRON
ejpam-2592	129	6	suffices	suffice	VERB
ejpam-2592	129	7	to	to	PART
ejpam-2592	129	8	take	take	VERB
ejpam-2592	129	9	α	α	DET
ejpam-2592	129	10	�	�	PROPN
ejpam-2592	129	11	x	x	SYM
ejpam-2592	129	12	,	,	PUNCT
ejpam-2592	129	13	y	y	PROPN
ejpam-2592	129	14	�	�	PROPN
ejpam-2592	129	15	=	=	SYM
ejpam-2592	129	16	1	1	NUM
ejpam-2592	129	17	and	and	CCONJ
ejpam-2592	129	18	ψ	ψ	X
ejpam-2592	129	19	(	(	PUNCT
ejpam-2592	129	20	t	t	PROPN
ejpam-2592	129	21	)	)	PUNCT
ejpam-2592	130	1	=	=	SYM
ejpam-2592	130	2	t	t	PROPN
ejpam-2592	130	3	in	in	ADP
ejpam-2592	130	4	theorem	theorem	NOUN
ejpam-2592	130	5	2	2	NUM
ejpam-2592	130	6	.	.	PUNCT
ejpam-2592	130	7	corollary	corollary	ADJ
ejpam-2592	130	8	2	2	NUM
ejpam-2592	130	9	.	.	PUNCT
ejpam-2592	131	1	let	let	AUX
ejpam-2592	131	2	(	(	PUNCT
ejpam-2592	131	3	x	x	X
ejpam-2592	131	4	,	,	PUNCT
ejpam-2592	131	5	ς	ς	PROPN
ejpam-2592	131	6	)	)	PUNCT
ejpam-2592	131	7	be	be	VERB
ejpam-2592	131	8	a	a	DET
ejpam-2592	131	9	b	b	NOUN
ejpam-2592	131	10	-	-	PUNCT
ejpam-2592	131	11	metric	metric	ADJ
ejpam-2592	131	12	-	-	PUNCT
ejpam-2592	131	13	like	like	ADJ
ejpam-2592	131	14	space	space	NOUN
ejpam-2592	131	15	with	with	ADP
ejpam-2592	131	16	coefficient	coefficient	NOUN
ejpam-2592	131	17	κ	κ	PRON
ejpam-2592	131	18	≥	≥	NOUN
ejpam-2592	131	19	1	1	NUM
ejpam-2592	131	20	and	and	CCONJ
ejpam-2592	131	21	t	t	NOUN
ejpam-2592	131	22	:	:	PUNCT
ejpam-2592	131	23	x	x	X
ejpam-2592	131	24	→	→	PUNCT
ejpam-2592	131	25	x	x	AUX
ejpam-2592	131	26	be	be	AUX
ejpam-2592	131	27	such	such	ADJ
ejpam-2592	131	28	that	that	SCONJ
ejpam-2592	131	29	κς	κς	ADP
ejpam-2592	131	30	�	�	PROPN
ejpam-2592	131	31	t	t	PROPN
ejpam-2592	131	32	x	x	PROPN
ejpam-2592	131	33	,	,	PUNCT
ejpam-2592	131	34	t	t	PROPN
ejpam-2592	131	35	y	y	PROPN
ejpam-2592	131	36	�	�	PROPN
ejpam-2592	131	37	≤	≤	PROPN
ejpam-2592	131	38	sm	sm	PROPN
ejpam-2592	131	39	�	�	PROPN
ejpam-2592	131	40	x	x	SYM
ejpam-2592	131	41	,	,	PUNCT
ejpam-2592	131	42	y	y	PROPN
ejpam-2592	131	43	�	�	PROPN
ejpam-2592	131	44	for	for	ADP
ejpam-2592	131	45	all	all	DET
ejpam-2592	131	46	x	x	SYM
ejpam-2592	131	47	,	,	PUNCT
ejpam-2592	131	48	y	y	PROPN
ejpam-2592	131	49	∈	∈	PROPN
ejpam-2592	131	50	x	x	PUNCT
ejpam-2592	131	51	where	where	SCONJ
ejpam-2592	131	52	s	s	AUX
ejpam-2592	131	53	∈	∈	PROPN
ejpam-2592	131	54	(	(	PUNCT
ejpam-2592	131	55	0,1	0,1	NUM
ejpam-2592	131	56	)	)	PUNCT
ejpam-2592	131	57	and	and	CCONJ
ejpam-2592	131	58	m	m	AUX
ejpam-2592	131	59	�	�	PROPN
ejpam-2592	131	60	x	x	SYM
ejpam-2592	131	61	,	,	PUNCT
ejpam-2592	131	62	y	y	PROPN
ejpam-2592	131	63	�	�	PROPN
ejpam-2592	131	64	defined	define	VERB
ejpam-2592	131	65	by	by	ADP
ejpam-2592	131	66	(	(	PUNCT
ejpam-2592	131	67	2	2	NUM
ejpam-2592	131	68	)	)	PUNCT
ejpam-2592	131	69	.	.	PUNCT
ejpam-2592	132	1	then	then	ADV
ejpam-2592	132	2	,	,	PUNCT
ejpam-2592	132	3	t	t	PROPN
ejpam-2592	132	4	has	have	VERB
ejpam-2592	132	5	a	a	DET
ejpam-2592	132	6	fixed	fix	VERB
ejpam-2592	132	7	point	point	NOUN
ejpam-2592	132	8	.	.	PUNCT
ejpam-2592	133	1	to	to	PART
ejpam-2592	133	2	prove	prove	VERB
ejpam-2592	133	3	corollary	corollary	ADJ
ejpam-2592	133	4	2	2	NUM
ejpam-2592	133	5	it	it	PRON
ejpam-2592	133	6	suffices	suffice	VERB
ejpam-2592	133	7	to	to	PART
ejpam-2592	133	8	take	take	VERB
ejpam-2592	133	9	ϕ	ϕ	NOUN
ejpam-2592	133	10	(	(	PUNCT
ejpam-2592	133	11	t	t	NOUN
ejpam-2592	133	12	)	)	PUNCT
ejpam-2592	133	13	=	=	PUNCT
ejpam-2592	134	1	(	(	PUNCT
ejpam-2592	134	2	1−	1−	NUM
ejpam-2592	134	3	s	s	NOUN
ejpam-2592	134	4	)	)	PUNCT
ejpam-2592	134	5	t	t	NOUN
ejpam-2592	134	6	in	in	ADP
ejpam-2592	134	7	corollary	corollary	ADJ
ejpam-2592	134	8	1	1	NUM
ejpam-2592	134	9	.	.	PUNCT
ejpam-2592	134	10	remark	remark	NOUN
ejpam-2592	134	11	1	1	NUM
ejpam-2592	134	12	.	.	NOUN
ejpam-2592	134	13	1	1	NUM
ejpam-2592	134	14	.	.	X
ejpam-2592	134	15	note	note	VERB
ejpam-2592	134	16	that	that	PRON
ejpam-2592	134	17	b	b	X
ejpam-2592	134	18	-	-	ADJ
ejpam-2592	134	19	metric	metric	ADJ
ejpam-2592	134	20	-	-	PUNCT
ejpam-2592	134	21	like	like	ADJ
ejpam-2592	134	22	spaces	space	NOUN
ejpam-2592	134	23	are	be	AUX
ejpam-2592	134	24	a	a	DET
ejpam-2592	134	25	proper	proper	ADJ
ejpam-2592	134	26	extension	extension	NOUN
ejpam-2592	134	27	of	of	ADP
ejpam-2592	134	28	metric	metric	ADJ
ejpam-2592	134	29	-	-	PUNCT
ejpam-2592	134	30	like	like	ADJ
ejpam-2592	134	31	and	and	CCONJ
ejpam-2592	134	32	b	b	NOUN
ejpam-2592	134	33	-	-	PUNCT
ejpam-2592	134	34	metric	metric	ADJ
ejpam-2592	134	35	spaces	space	NOUN
ejpam-2592	134	36	.	.	PUNCT
ejpam-2592	135	1	therefore	therefore	ADV
ejpam-2592	135	2	,	,	PUNCT
ejpam-2592	135	3	it	it	PRON
ejpam-2592	135	4	is	be	AUX
ejpam-2592	135	5	clear	clear	ADJ
ejpam-2592	135	6	that	that	SCONJ
ejpam-2592	135	7	one	one	PRON
ejpam-2592	135	8	can	can	AUX
ejpam-2592	135	9	easily	easily	ADV
ejpam-2592	135	10	state	state	VERB
ejpam-2592	135	11	the	the	DET
ejpam-2592	135	12	analog	analog	NOUN
ejpam-2592	135	13	of	of	ADP
ejpam-2592	135	14	theorem	theorem	ADJ
ejpam-2592	135	15	1	1	NUM
ejpam-2592	135	16	,	,	PUNCT
ejpam-2592	135	17	theorem	theorem	ADJ
ejpam-2592	135	18	2	2	NUM
ejpam-2592	135	19	,	,	PUNCT
ejpam-2592	135	20	corollary	corollary	ADJ
ejpam-2592	135	21	1	1	NUM
ejpam-2592	135	22	,	,	PUNCT
ejpam-2592	135	23	and	and	CCONJ
ejpam-2592	135	24	corollary	corollary	ADJ
ejpam-2592	135	25	2	2	NUM
ejpam-2592	135	26	in	in	ADP
ejpam-2592	135	27	the	the	DET
ejpam-2592	135	28	setting	setting	NOUN
ejpam-2592	135	29	of	of	ADP
ejpam-2592	135	30	metric	metric	ADJ
ejpam-2592	135	31	-	-	PUNCT
ejpam-2592	135	32	like	like	ADJ
ejpam-2592	135	33	and	and	CCONJ
ejpam-2592	135	34	b	b	NOUN
ejpam-2592	135	35	-	-	PUNCT
ejpam-2592	135	36	metric	metric	ADJ
ejpam-2592	135	37	spaces	space	NOUN
ejpam-2592	135	38	.	.	PUNCT
ejpam-2592	136	1	2	2	X
ejpam-2592	136	2	.	.	X
ejpam-2592	136	3	theorem	theorem	ADJ
ejpam-2592	136	4	1	1	NUM
ejpam-2592	136	5	,	,	PUNCT
ejpam-2592	136	6	theorem	theorem	ADJ
ejpam-2592	136	7	2	2	NUM
ejpam-2592	136	8	,	,	PUNCT
ejpam-2592	136	9	and	and	CCONJ
ejpam-2592	136	10	corollary	corollary	ADJ
ejpam-2592	136	11	2	2	NUM
ejpam-2592	136	12	improve	improve	VERB
ejpam-2592	136	13	and	and	CCONJ
ejpam-2592	136	14	generalized	generalize	VERB
ejpam-2592	136	15	theorem	theorem	VERB
ejpam-2592	136	16	2.1	2.1	NUM
ejpam-2592	136	17	in	in	ADP
ejpam-2592	136	18	[	[	X
ejpam-2592	136	19	2	2	NUM
ejpam-2592	136	20	]	]	PUNCT
ejpam-2592	136	21	,	,	PUNCT
ejpam-2592	136	22	theorem	theorem	VERB
ejpam-2592	136	23	2.2	2.2	NUM
ejpam-2592	136	24	in	in	ADP
ejpam-2592	136	25	[	[	X
ejpam-2592	136	26	2	2	NUM
ejpam-2592	136	27	]	]	PUNCT
ejpam-2592	136	28	and	and	CCONJ
ejpam-2592	136	29	corollary	corollary	ADJ
ejpam-2592	136	30	3.2	3.2	NUM
ejpam-2592	136	31	in	in	ADP
ejpam-2592	136	32	[	[	X
ejpam-2592	136	33	2	2	NUM
ejpam-2592	136	34	]	]	PUNCT
ejpam-2592	136	35	,	,	PUNCT
ejpam-2592	136	36	respectively	respectively	ADV
ejpam-2592	136	37	.	.	PUNCT
ejpam-2592	136	38	example	example	NOUN
ejpam-2592	137	1	1	1	NUM
ejpam-2592	137	2	.	.	PUNCT
ejpam-2592	137	3	let	let	VERB
ejpam-2592	137	4	x	x	PUNCT
ejpam-2592	137	5	=	=	PUNCT
ejpam-2592	138	1	[	[	X
ejpam-2592	138	2	0,∞	0,∞	NUM
ejpam-2592	138	3	)	)	PUNCT
ejpam-2592	138	4	and	and	CCONJ
ejpam-2592	138	5	ς	ς	X
ejpam-2592	138	6	on	on	ADP
ejpam-2592	138	7	x	x	PART
ejpam-2592	138	8	be	be	AUX
ejpam-2592	138	9	given	give	VERB
ejpam-2592	138	10	by	by	ADP
ejpam-2592	138	11	ς	ς	PROPN
ejpam-2592	138	12	�	�	PROPN
ejpam-2592	138	13	x	x	SYM
ejpam-2592	138	14	,	,	PUNCT
ejpam-2592	138	15	y	y	PROPN
ejpam-2592	138	16	�	�	PROPN
ejpam-2592	138	17	=	=	SYM
ejpam-2592	138	18	x2	x2	PROPN
ejpam-2592	138	19	+	+	CCONJ
ejpam-2592	138	20	y2	y2	ADJ
ejpam-2592	138	21	+	+	CCONJ
ejpam-2592	138	22	�	�	PROPN
ejpam-2592	138	23	�	�	PROPN
ejpam-2592	138	24	x	x	PROPN
ejpam-2592	138	25	−	−	PROPN
ejpam-2592	138	26	y	y	PROPN
ejpam-2592	138	27	�	�	PROPN
ejpam-2592	138	28	�	�	PROPN
ejpam-2592	138	29	2	2	NUM
ejpam-2592	138	30	for	for	ADP
ejpam-2592	138	31	all	all	DET
ejpam-2592	138	32	x	x	SYM
ejpam-2592	138	33	,	,	PUNCT
ejpam-2592	138	34	y	y	PROPN
ejpam-2592	138	35	∈	∈	PROPN
ejpam-2592	138	36	x	x	X
ejpam-2592	138	37	.	.	PUNCT
ejpam-2592	139	1	(	(	PUNCT
ejpam-2592	139	2	x	x	X
ejpam-2592	139	3	,	,	PUNCT
ejpam-2592	139	4	ς	ς	PROPN
ejpam-2592	139	5	)	)	PUNCT
ejpam-2592	139	6	is	be	AUX
ejpam-2592	139	7	a	a	DET
ejpam-2592	139	8	complete	complete	ADJ
ejpam-2592	139	9	b	b	X
ejpam-2592	139	10	-	-	PUNCT
ejpam-2592	139	11	metric	metric	ADJ
ejpam-2592	139	12	-	-	PUNCT
ejpam-2592	139	13	like	like	ADJ
ejpam-2592	139	14	space	space	NOUN
ejpam-2592	139	15	with	with	ADP
ejpam-2592	139	16	coefficient	coefficient	NOUN
ejpam-2592	139	17	κ	κ	NOUN
ejpam-2592	139	18	=	=	SYM
ejpam-2592	139	19	2	2	NUM
ejpam-2592	139	20	(	(	PUNCT
ejpam-2592	139	21	see	see	VERB
ejpam-2592	139	22	[	[	X
ejpam-2592	139	23	4	4	NUM
ejpam-2592	139	24	,	,	PUNCT
ejpam-2592	139	25	example	example	NOUN
ejpam-2592	139	26	14	14	NUM
ejpam-2592	139	27	]	]	PUNCT
ejpam-2592	139	28	)	)	PUNCT
ejpam-2592	139	29	.	.	PUNCT
ejpam-2592	140	1	define	define	VERB
ejpam-2592	140	2	the	the	DET
ejpam-2592	140	3	mappings	mapping	NOUN
ejpam-2592	140	4	ψ,ϕ	ψ,ϕ	NOUN
ejpam-2592	140	5	:	:	PUNCT
ejpam-2592	141	1	[	[	X
ejpam-2592	141	2	0,∞)→	0,∞)→	NOUN
ejpam-2592	141	3	[	[	X
ejpam-2592	141	4	0,∞	0,∞	NOUN
ejpam-2592	141	5	)	)	PUNCT
ejpam-2592	141	6	by	by	ADP
ejpam-2592	141	7	ψ	ψ	X
ejpam-2592	141	8	(	(	PUNCT
ejpam-2592	141	9	t	t	PROPN
ejpam-2592	141	10	)	)	PUNCT
ejpam-2592	141	11	=	=	SYM
ejpam-2592	141	12	t	t	PROPN
ejpam-2592	141	13	,	,	PUNCT
ejpam-2592	141	14	ϕ	ϕ	X
ejpam-2592	141	15	(	(	PUNCT
ejpam-2592	141	16	t	t	PROPN
ejpam-2592	141	17	)	)	PUNCT
ejpam-2592	141	18	=	=	SYM
ejpam-2592	141	19	t	t	PROPN
ejpam-2592	141	20	2	2	NUM
ejpam-2592	141	21	and	and	CCONJ
ejpam-2592	141	22	α	α	NOUN
ejpam-2592	141	23	:	:	PUNCT
ejpam-2592	141	24	x	x	SYM
ejpam-2592	141	25	×	×	NOUN
ejpam-2592	141	26	x	x	INTJ
ejpam-2592	141	27	→	→	X
ejpam-2592	141	28	[	[	X
ejpam-2592	141	29	0,∞	0,∞	NOUN
ejpam-2592	141	30	)	)	PUNCT
ejpam-2592	141	31	by	by	ADP
ejpam-2592	141	32	α	α	DET
ejpam-2592	141	33	�	�	PROPN
ejpam-2592	141	34	x	x	SYM
ejpam-2592	141	35	,	,	PUNCT
ejpam-2592	141	36	y	y	PROPN
ejpam-2592	141	37	�	�	PROPN
ejpam-2592	141	38	=	=	SYM
ejpam-2592	141	39	¨	¨	NOUN
ejpam-2592	141	40	1	1	NUM
ejpam-2592	141	41	if	if	SCONJ
ejpam-2592	141	42	x	x	PRON
ejpam-2592	141	43	,	,	PUNCT
ejpam-2592	141	44	y	y	PROPN
ejpam-2592	141	45	∈	∈	PROPN
ejpam-2592	142	1	[	[	X
ejpam-2592	142	2	0,1	0,1	NUM
ejpam-2592	142	3	]	]	PUNCT
ejpam-2592	142	4	,	,	PUNCT
ejpam-2592	142	5	0	0	NUM
ejpam-2592	142	6	otherwise	otherwise	ADV
ejpam-2592	142	7	.	.	PUNCT
ejpam-2592	143	1	let	let	VERB
ejpam-2592	143	2	t	t	NOUN
ejpam-2592	143	3	:	:	PUNCT
ejpam-2592	143	4	x	x	X
ejpam-2592	143	5	→	→	PUNCT
ejpam-2592	143	6	x	x	AUX
ejpam-2592	143	7	be	be	AUX
ejpam-2592	143	8	defined	define	VERB
ejpam-2592	143	9	by	by	ADP
ejpam-2592	143	10	t	t	NOUN
ejpam-2592	143	11	x	x	SYM
ejpam-2592	143	12	=	=	SYM
ejpam-2592	143	13	ln(x+1	ln(x+1	X
ejpam-2592	143	14	)	)	PUNCT
ejpam-2592	143	15	2	2	NUM
ejpam-2592	143	16	.	.	PUNCT
ejpam-2592	144	1	it	it	PRON
ejpam-2592	144	2	is	be	AUX
ejpam-2592	144	3	easy	easy	ADJ
ejpam-2592	144	4	to	to	PART
ejpam-2592	144	5	see	see	VERB
ejpam-2592	144	6	that	that	PRON
ejpam-2592	144	7	t	t	PROPN
ejpam-2592	144	8	is	be	AUX
ejpam-2592	144	9	a	a	DET
ejpam-2592	144	10	continuous	continuous	ADJ
ejpam-2592	144	11	on	on	ADP
ejpam-2592	144	12	x	x	X
ejpam-2592	144	13	.	.	PUNCT
ejpam-2592	145	1	understandably	understandably	ADV
ejpam-2592	145	2	t	t	PROPN
ejpam-2592	145	3	is	be	AUX
ejpam-2592	145	4	an	an	DET
ejpam-2592	145	5	α−ψ−ϕ-contractive	α−ψ−ϕ-contractive	ADJ
ejpam-2592	145	6	type	type	NOUN
ejpam-2592	145	7	mapping	mapping	NOUN
ejpam-2592	145	8	with	with	ADP
ejpam-2592	145	9	ψ	ψ	X
ejpam-2592	145	10	(	(	PUNCT
ejpam-2592	145	11	t	t	PROPN
ejpam-2592	145	12	)	)	PUNCT
ejpam-2592	145	13	=	=	SYM
ejpam-2592	145	14	t	t	PROPN
ejpam-2592	145	15	and	and	CCONJ
ejpam-2592	145	16	ϕ	ϕ	PROPN
ejpam-2592	145	17	(	(	PUNCT
ejpam-2592	145	18	t	t	PROPN
ejpam-2592	145	19	)	)	PUNCT
ejpam-2592	145	20	=	=	SYM
ejpam-2592	146	1	t	t	PROPN
ejpam-2592	146	2	2	2	NUM
ejpam-2592	146	3	for	for	ADP
ejpam-2592	146	4	all	all	DET
ejpam-2592	146	5	t	t	PROPN
ejpam-2592	146	6	≥	≥	NOUN
ejpam-2592	146	7	0	0	NUM
ejpam-2592	146	8	,	,	PUNCT
ejpam-2592	146	9	for	for	ADP
ejpam-2592	146	10	x	x	SYM
ejpam-2592	146	11	,	,	PUNCT
ejpam-2592	146	12	y	y	PROPN
ejpam-2592	146	13	∈	∈	PROPN
ejpam-2592	147	1	x	x	X
ejpam-2592	147	2	,	,	PUNCT
ejpam-2592	147	3	α	α	PROPN
ejpam-2592	147	4	�	�	PROPN
ejpam-2592	147	5	x	x	SYM
ejpam-2592	147	6	,	,	PUNCT
ejpam-2592	147	7	y	y	PROPN
ejpam-2592	147	8	�	�	PROPN
ejpam-2592	147	9	ψ	ψ	ADP
ejpam-2592	147	10	�	�	PROPN
ejpam-2592	147	11	κς	κς	ADP
ejpam-2592	147	12	�	�	PROPN
ejpam-2592	147	13	t	t	PROPN
ejpam-2592	147	14	x	x	PROPN
ejpam-2592	147	15	,	,	PUNCT
ejpam-2592	147	16	t	t	PROPN
ejpam-2592	147	17	y	y	PROPN
ejpam-2592	147	18	�	�	PROPN
ejpam-2592	147	19	�	�	PROPN
ejpam-2592	147	20	=	=	SYM
ejpam-2592	147	21	ψ	ψ	NOUN
ejpam-2592	147	22	�	�	PROPN
ejpam-2592	147	23	2ς	2ς	NUM
ejpam-2592	147	24	�	�	PROPN
ejpam-2592	147	25	t	t	PROPN
ejpam-2592	147	26	x	x	X
ejpam-2592	147	27	,	,	PUNCT
ejpam-2592	147	28	t	t	PROPN
ejpam-2592	147	29	y	y	PROPN
ejpam-2592	147	30	�	�	PROPN
ejpam-2592	147	31	�	�	PROPN
ejpam-2592	147	32	=	=	NOUN
ejpam-2592	147	33	2ς	2ς	NUM
ejpam-2592	147	34	�	�	PROPN
ejpam-2592	147	35	t	t	PROPN
ejpam-2592	147	36	x	x	X
ejpam-2592	147	37	,	,	PUNCT
ejpam-2592	147	38	t	t	PROPN
ejpam-2592	147	39	y	y	PROPN
ejpam-2592	147	40	�	�	PROPN
ejpam-2592	147	41	=	=	SYM
ejpam-2592	147	42	2	2	NUM
ejpam-2592	147	43	�	�	PROPN
ejpam-2592	147	44	t2	t2	NOUN
ejpam-2592	147	45	x	x	PUNCT
ejpam-2592	148	1	+	+	CCONJ
ejpam-2592	148	2	t2	t2	PROPN
ejpam-2592	148	3	y	y	PROPN
ejpam-2592	148	4	+	+	CCONJ
ejpam-2592	148	5	�	�	PROPN
ejpam-2592	148	6	�	�	PROPN
ejpam-2592	148	7	t	t	NOUN
ejpam-2592	148	8	x	x	PUNCT
ejpam-2592	148	9	−	−	PROPN
ejpam-2592	148	10	t	t	PROPN
ejpam-2592	148	11	y	y	PROPN
ejpam-2592	148	12	�	�	PROPN
ejpam-2592	148	13	�	�	PROPN
ejpam-2592	148	14	2	2	NUM
ejpam-2592	148	15	�	�	PROPN
ejpam-2592	148	16	=	=	SYM
ejpam-2592	148	17	2	2	NUM
ejpam-2592	148	18	�	�	NOUN
ejpam-2592	148	19	ln	ln	NOUN
ejpam-2592	148	20	(	(	PUNCT
ejpam-2592	148	21	x	x	SYM
ejpam-2592	149	1	+	+	NOUN
ejpam-2592	149	2	1	1	NUM
ejpam-2592	149	3	)	)	SYM
ejpam-2592	149	4	2	2	NUM
ejpam-2592	149	5	�	�	SYM
ejpam-2592	149	6	2	2	NUM
ejpam-2592	149	7	+	+	CCONJ
ejpam-2592	149	8	�	�	PROPN
ejpam-2592	149	9	ln	ln	ADJ
ejpam-2592	149	10	�	�	PROPN
ejpam-2592	150	1	y	y	PROPN
ejpam-2592	150	2	+	+	CCONJ
ejpam-2592	150	3	1	1	NUM
ejpam-2592	150	4	�	�	PROPN
ejpam-2592	150	5	2	2	NUM
ejpam-2592	150	6	�	�	PROPN
ejpam-2592	150	7	2	2	NUM
ejpam-2592	150	8	!	!	PUNCT
ejpam-2592	151	1	+	+	CCONJ
ejpam-2592	151	2	2	2	NUM
ejpam-2592	151	3			VERB
ejpam-2592	151	4			NOUN
ejpam-2592	151	5	�	�	PROPN
ejpam-2592	151	6	�	�	PROPN
ejpam-2592	151	7	�	�	PROPN
ejpam-2592	151	8	�	�	PROPN
ejpam-2592	151	9	�	�	PROPN
ejpam-2592	151	10	ln	ln	PROPN
ejpam-2592	151	11	(	(	PUNCT
ejpam-2592	151	12	x	x	SYM
ejpam-2592	151	13	+	+	NOUN
ejpam-2592	151	14	1	1	NUM
ejpam-2592	151	15	)	)	SYM
ejpam-2592	151	16	2	2	NUM
ejpam-2592	151	17	−	−	PROPN
ejpam-2592	151	18	ln	ln	PROPN
ejpam-2592	151	19	�	�	PROPN
ejpam-2592	152	1	y	y	PROPN
ejpam-2592	152	2	+	+	CCONJ
ejpam-2592	152	3	1	1	NUM
ejpam-2592	152	4	�	�	PROPN
ejpam-2592	152	5	2	2	NUM
ejpam-2592	152	6	�	�	PROPN
ejpam-2592	152	7	�	�	PROPN
ejpam-2592	152	8	�	�	PROPN
ejpam-2592	152	9	�	�	PROPN
ejpam-2592	152	10	�	�	PROPN
ejpam-2592	152	11	2	2	PROPN
ejpam-2592	152	12			X
ejpam-2592	152	13			PUNCT
ejpam-2592	152	14	m.	m.	NOUN
ejpam-2592	152	15	akturk	akturk	PROPN
ejpam-2592	152	16	,	,	PUNCT
ejpam-2592	152	17	m.	m.	NOUN
ejpam-2592	152	18	kır	kır	PROPN
ejpam-2592	152	19	,	,	PUNCT
ejpam-2592	152	20	e.	e.	PROPN
ejpam-2592	152	21	yolacan	yolacan	PROPN
ejpam-2592	152	22	/	/	SYM
ejpam-2592	152	23	eur	eur	PROPN
ejpam-2592	152	24	.	.	PUNCT
ejpam-2592	153	1	j.	j.	PROPN
ejpam-2592	153	2	pure	pure	PROPN
ejpam-2592	153	3	appl	appl	PROPN
ejpam-2592	153	4	.	.	PROPN
ejpam-2592	153	5	math	math	PROPN
ejpam-2592	153	6	,	,	PUNCT
ejpam-2592	153	7	9	9	NUM
ejpam-2592	153	8	(	(	PUNCT
ejpam-2592	153	9	2016	2016	NUM
ejpam-2592	153	10	)	)	PUNCT
ejpam-2592	153	11	,	,	PUNCT
ejpam-2592	153	12	175	175	NUM
ejpam-2592	153	13	-	-	SYM
ejpam-2592	153	14	185	185	NUM
ejpam-2592	153	15	183	183	NUM
ejpam-2592	153	16	≤2	≤2	NOUN
ejpam-2592	153	17	�	�	PROPN
ejpam-2592	153	18	x2	x2	ADP
ejpam-2592	153	19	4	4	NUM
ejpam-2592	154	1	+	+	NUM
ejpam-2592	154	2	y2	y2	NOUN
ejpam-2592	154	3	4	4	NUM
ejpam-2592	154	4	+	+	NUM
ejpam-2592	154	5	�	�	PROPN
ejpam-2592	154	6	�	�	PROPN
ejpam-2592	154	7	�	�	PROPN
ejpam-2592	154	8	x	x	PROPN
ejpam-2592	154	9	2	2	NUM
ejpam-2592	154	10	−	−	PROPN
ejpam-2592	154	11	y	y	PROPN
ejpam-2592	154	12	2	2	NUM
ejpam-2592	154	13	�	�	PROPN
ejpam-2592	154	14	�	�	PROPN
ejpam-2592	154	15	�	�	PROPN
ejpam-2592	154	16	2	2	NUM
ejpam-2592	154	17	�	�	PROPN
ejpam-2592	154	18	=	=	SYM
ejpam-2592	154	19	1	1	NUM
ejpam-2592	154	20	2	2	NUM
ejpam-2592	154	21	ς	ς	PROPN
ejpam-2592	154	22	�	�	PROPN
ejpam-2592	154	23	x	x	SYM
ejpam-2592	154	24	,	,	PUNCT
ejpam-2592	154	25	y	y	PROPN
ejpam-2592	154	26	�	�	PROPN
ejpam-2592	154	27	=	=	PROPN
ejpam-2592	154	28	ς	ς	PROPN
ejpam-2592	154	29	�	�	PROPN
ejpam-2592	154	30	x	x	SYM
ejpam-2592	154	31	,	,	PUNCT
ejpam-2592	154	32	y	y	PROPN
ejpam-2592	154	33	�	�	PROPN
ejpam-2592	154	34	−	−	NOUN
ejpam-2592	154	35	1	1	NUM
ejpam-2592	154	36	2	2	NUM
ejpam-2592	154	37	ς	ς	PROPN
ejpam-2592	154	38	�	�	PROPN
ejpam-2592	154	39	x	x	SYM
ejpam-2592	154	40	,	,	PUNCT
ejpam-2592	154	41	y	y	PROPN
ejpam-2592	154	42	�	�	PROPN
ejpam-2592	154	43	=	=	PROPN
ejpam-2592	154	44	ψ	ψ	X
ejpam-2592	154	45	�	�	PROPN
ejpam-2592	154	46	ς	ς	PROPN
ejpam-2592	154	47	�	�	PROPN
ejpam-2592	154	48	x	x	SYM
ejpam-2592	154	49	,	,	PUNCT
ejpam-2592	154	50	y	y	PROPN
ejpam-2592	154	51	�	�	PROPN
ejpam-2592	154	52	�	�	PROPN
ejpam-2592	154	53	−ϕ	−ϕ	ADV
ejpam-2592	154	54	�	�	PROPN
ejpam-2592	154	55	ς	ς	PROPN
ejpam-2592	154	56	�	�	PROPN
ejpam-2592	154	57	x	x	SYM
ejpam-2592	154	58	,	,	PUNCT
ejpam-2592	154	59	y	y	PROPN
ejpam-2592	154	60	�	�	PROPN
ejpam-2592	154	61	�	�	PROPN
ejpam-2592	154	62	≤ψ	≤ψ	PROPN
ejpam-2592	154	63	�	�	PROPN
ejpam-2592	154	64	m	m	PROPN
ejpam-2592	154	65	�	�	PROPN
ejpam-2592	154	66	x	x	SYM
ejpam-2592	154	67	,	,	PUNCT
ejpam-2592	154	68	y	y	PROPN
ejpam-2592	154	69	�	�	PROPN
ejpam-2592	154	70	�	�	PROPN
ejpam-2592	154	71	−ϕ	−ϕ	ADV
ejpam-2592	154	72	�	�	PROPN
ejpam-2592	154	73	m	m	PROPN
ejpam-2592	154	74	�	�	PROPN
ejpam-2592	154	75	x	x	SYM
ejpam-2592	154	76	,	,	PUNCT
ejpam-2592	154	77	y	y	PROPN
ejpam-2592	154	78	�	�	PROPN
ejpam-2592	154	79	�	�	PROPN
ejpam-2592	154	80	.	.	PUNCT
ejpam-2592	155	1	(	(	PUNCT
ejpam-2592	155	2	i	i	NOUN
ejpam-2592	155	3	)	)	PUNCT
ejpam-2592	155	4	now	now	ADV
ejpam-2592	155	5	,	,	PUNCT
ejpam-2592	155	6	we	we	PRON
ejpam-2592	155	7	claim	claim	VERB
ejpam-2592	155	8	that	that	SCONJ
ejpam-2592	155	9	t	t	PROPN
ejpam-2592	155	10	is	be	AUX
ejpam-2592	155	11	α	α	PRON
ejpam-2592	155	12	-	-	ADJ
ejpam-2592	155	13	admissible	admissible	ADJ
ejpam-2592	155	14	.	.	PUNCT
ejpam-2592	156	1	let	let	VERB
ejpam-2592	156	2	�	�	PROPN
ejpam-2592	156	3	x	x	SYM
ejpam-2592	156	4	,	,	PUNCT
ejpam-2592	156	5	y	y	PROPN
ejpam-2592	156	6	�	�	PROPN
ejpam-2592	156	7	∈	∈	PROPN
ejpam-2592	156	8	x	x	PUNCT
ejpam-2592	156	9	×	×	NOUN
ejpam-2592	156	10	x	x	INTJ
ejpam-2592	156	11	such	such	ADJ
ejpam-2592	156	12	that	that	SCONJ
ejpam-2592	156	13	α	α	PROPN
ejpam-2592	156	14	�	�	PROPN
ejpam-2592	156	15	x	x	SYM
ejpam-2592	156	16	,	,	PUNCT
ejpam-2592	156	17	y	y	PROPN
ejpam-2592	156	18	�	�	PROPN
ejpam-2592	156	19	≥	≥	PROPN
ejpam-2592	156	20	1	1	NUM
ejpam-2592	156	21	.	.	PUNCT
ejpam-2592	157	1	from	from	ADP
ejpam-2592	157	2	the	the	DET
ejpam-2592	157	3	definition	definition	NOUN
ejpam-2592	157	4	of	of	ADP
ejpam-2592	157	5	t	t	PROPN
ejpam-2592	157	6	and	and	CCONJ
ejpam-2592	157	7	α	α	PRON
ejpam-2592	157	8	we	we	PRON
ejpam-2592	157	9	have	have	VERB
ejpam-2592	157	10	both	both	DET
ejpam-2592	157	11	t	t	NOUN
ejpam-2592	157	12	x	x	X
ejpam-2592	157	13	=	=	SYM
ejpam-2592	157	14	ln(x+1	ln(x+1	X
ejpam-2592	157	15	)	)	PUNCT
ejpam-2592	157	16	2	2	NUM
ejpam-2592	158	1	and	and	CCONJ
ejpam-2592	158	2	t	t	NOUN
ejpam-2592	158	3	y	y	PROPN
ejpam-2592	158	4	=	=	PUNCT
ejpam-2592	158	5	ln(y+1	ln(y+1	X
ejpam-2592	158	6	)	)	PUNCT
ejpam-2592	158	7	2	2	NUM
ejpam-2592	158	8	are	be	AUX
ejpam-2592	158	9	in	in	ADP
ejpam-2592	158	10	[	[	X
ejpam-2592	158	11	0,1	0,1	NUM
ejpam-2592	158	12	]	]	PUNCT
ejpam-2592	158	13	.	.	PUNCT
ejpam-2592	159	1	therefore	therefore	ADV
ejpam-2592	159	2	,	,	PUNCT
ejpam-2592	159	3	α	α	PROPN
ejpam-2592	159	4	�	�	PROPN
ejpam-2592	159	5	t	t	PROPN
ejpam-2592	159	6	x	x	X
ejpam-2592	159	7	,	,	PUNCT
ejpam-2592	159	8	t	t	PROPN
ejpam-2592	159	9	y	y	PROPN
ejpam-2592	159	10	�	�	PROPN
ejpam-2592	159	11	=	=	SYM
ejpam-2592	159	12	1	1	NUM
ejpam-2592	159	13	≥	≥	NOUN
ejpam-2592	159	14	1	1	NUM
ejpam-2592	159	15	.	.	PUNCT
ejpam-2592	160	1	then	then	ADV
ejpam-2592	160	2	t	t	PROPN
ejpam-2592	160	3	is	be	AUX
ejpam-2592	160	4	α	α	PRON
ejpam-2592	160	5	-	-	ADJ
ejpam-2592	160	6	admissible	admissible	ADJ
ejpam-2592	160	7	.	.	PUNCT
ejpam-2592	161	1	(	(	PUNCT
ejpam-2592	161	2	ii	ii	NOUN
ejpam-2592	161	3	)	)	PUNCT
ejpam-2592	161	4	taking	take	VERB
ejpam-2592	161	5	x0	x0	PROPN
ejpam-2592	161	6	=	=	PUNCT
ejpam-2592	161	7	0	0	NUM
ejpam-2592	161	8	and	and	CCONJ
ejpam-2592	161	9	t	t	X
ejpam-2592	161	10	x0	x0	PROPN
ejpam-2592	162	1	=	=	PUNCT
ejpam-2592	162	2	t0=	t0=	X
ejpam-2592	162	3	ln(0	ln(0	VERB
ejpam-2592	162	4	+	+	NOUN
ejpam-2592	162	5	1	1	NUM
ejpam-2592	162	6	)	)	SYM
ejpam-2592	162	7	2	2	NUM
ejpam-2592	162	8	=	=	SYM
ejpam-2592	162	9	0	0	NUM
ejpam-2592	162	10	,	,	PUNCT
ejpam-2592	162	11	we	we	PRON
ejpam-2592	162	12	have	have	AUX
ejpam-2592	162	13	α	α	DET
ejpam-2592	162	14	�	�	PROPN
ejpam-2592	162	15	x0	x0	PROPN
ejpam-2592	162	16	,	,	PUNCT
ejpam-2592	162	17	t	t	PROPN
ejpam-2592	162	18	x0	x0	PROPN
ejpam-2592	162	19	�	�	PROPN
ejpam-2592	163	1	=	=	PUNCT
ejpam-2592	163	2	α	α	PROPN
ejpam-2592	163	3	(	(	PUNCT
ejpam-2592	163	4	0	0	NUM
ejpam-2592	163	5	,	,	PUNCT
ejpam-2592	163	6	t0	t0	NOUN
ejpam-2592	163	7	)	)	PUNCT
ejpam-2592	163	8	=	=	PUNCT
ejpam-2592	164	1	1≥	1≥	NUM
ejpam-2592	164	2	1	1	X
ejpam-2592	164	3	.	.	PUNCT
ejpam-2592	165	1	it	it	PRON
ejpam-2592	165	2	is	be	AUX
ejpam-2592	165	3	also	also	ADV
ejpam-2592	165	4	obvious	obvious	ADJ
ejpam-2592	165	5	that	that	SCONJ
ejpam-2592	165	6	hypothesis	hypothesis	NOUN
ejpam-2592	165	7	(	(	PUNCT
ejpam-2592	165	8	iii	iii	NOUN
ejpam-2592	165	9	)	)	PUNCT
ejpam-2592	165	10	of	of	ADP
ejpam-2592	165	11	theorem	theorem	NOUN
ejpam-2592	165	12	1	1	NUM
ejpam-2592	165	13	is	be	AUX
ejpam-2592	165	14	satisfied	satisfied	ADJ
ejpam-2592	165	15	.	.	PUNCT
ejpam-2592	166	1	thus	thus	ADV
ejpam-2592	166	2	,	,	PUNCT
ejpam-2592	166	3	we	we	PRON
ejpam-2592	166	4	apply	apply	VERB
ejpam-2592	166	5	theorem	theorem	NOUN
ejpam-2592	166	6	1	1	NUM
ejpam-2592	167	1	and	and	CCONJ
ejpam-2592	167	2	so	so	ADV
ejpam-2592	167	3	t	t	PROPN
ejpam-2592	167	4	has	have	VERB
ejpam-2592	167	5	a	a	DET
ejpam-2592	167	6	fixed	fix	VERB
ejpam-2592	167	7	point	point	NOUN
ejpam-2592	167	8	,	,	PUNCT
ejpam-2592	167	9	which	which	PRON
ejpam-2592	167	10	is	be	AUX
ejpam-2592	167	11	ω	ω	NUM
ejpam-2592	167	12	=	=	SYM
ejpam-2592	167	13	0	0	NUM
ejpam-2592	167	14	.	.	NOUN
ejpam-2592	168	1	5	5	NUM
ejpam-2592	168	2	.	.	X
ejpam-2592	168	3	existence	existence	NOUN
ejpam-2592	168	4	of	of	ADP
ejpam-2592	168	5	the	the	DET
ejpam-2592	168	6	solution	solution	NOUN
ejpam-2592	168	7	for	for	ADP
ejpam-2592	168	8	nonlinear	nonlinear	ADJ
ejpam-2592	168	9	fredholm	fredholm	ADJ
ejpam-2592	168	10	integral	integral	ADJ
ejpam-2592	168	11	equations	equation	NOUN
ejpam-2592	168	12	in	in	ADP
ejpam-2592	168	13	this	this	DET
ejpam-2592	168	14	section	section	NOUN
ejpam-2592	168	15	we	we	PRON
ejpam-2592	168	16	will	will	AUX
ejpam-2592	168	17	present	present	VERB
ejpam-2592	168	18	an	an	DET
ejpam-2592	168	19	existence	existence	NOUN
ejpam-2592	168	20	theorem	theorem	VERB
ejpam-2592	168	21	for	for	ADP
ejpam-2592	168	22	solution	solution	NOUN
ejpam-2592	168	23	of	of	ADP
ejpam-2592	168	24	nonlinear	nonlinear	ADJ
ejpam-2592	168	25	fredholm	fredholm	ADJ
ejpam-2592	168	26	integral	integral	ADJ
ejpam-2592	168	27	equations	equation	NOUN
ejpam-2592	168	28	.	.	PUNCT
ejpam-2592	169	1	define	define	VERB
ejpam-2592	169	2	the	the	DET
ejpam-2592	169	3	nonlinear	nonlinear	ADJ
ejpam-2592	169	4	fredholm	fredholm	ADJ
ejpam-2592	169	5	integral	integral	ADJ
ejpam-2592	169	6	equations	equation	NOUN
ejpam-2592	169	7	by	by	ADP
ejpam-2592	169	8	x	x	X
ejpam-2592	169	9	(	(	PUNCT
ejpam-2592	169	10	s	s	NOUN
ejpam-2592	169	11	)	)	PUNCT
ejpam-2592	169	12	=	=	SYM
ejpam-2592	170	1	t	t	PROPN
ejpam-2592	170	2	∫	∫	PROPN
ejpam-2592	170	3	0	0	NUM
ejpam-2592	171	1	g	g	PROPN
ejpam-2592	171	2	(	(	PUNCT
ejpam-2592	171	3	s	s	X
ejpam-2592	171	4	,	,	PUNCT
ejpam-2592	171	5	r	r	NOUN
ejpam-2592	171	6	,	,	PUNCT
ejpam-2592	171	7	x	x	X
ejpam-2592	171	8	(	(	PUNCT
ejpam-2592	171	9	r	r	NOUN
ejpam-2592	171	10	)	)	PUNCT
ejpam-2592	171	11	)	)	PUNCT
ejpam-2592	171	12	dr	dr	PROPN
ejpam-2592	171	13	where	where	SCONJ
ejpam-2592	171	14	t	t	PROPN
ejpam-2592	171	15	>	>	X
ejpam-2592	171	16	0	0	PROPN
ejpam-2592	171	17	.	.	PUNCT
ejpam-2592	172	1	(	(	PUNCT
ejpam-2592	172	2	35	35	NUM
ejpam-2592	172	3	)	)	PUNCT
ejpam-2592	172	4	we	we	PRON
ejpam-2592	172	5	will	will	AUX
ejpam-2592	172	6	examine	examine	VERB
ejpam-2592	172	7	(	(	PUNCT
ejpam-2592	172	8	35	35	NUM
ejpam-2592	172	9	)	)	PUNCT
ejpam-2592	172	10	under	under	ADP
ejpam-2592	172	11	the	the	DET
ejpam-2592	172	12	following	following	ADJ
ejpam-2592	172	13	conditions	condition	NOUN
ejpam-2592	172	14	:	:	PUNCT
ejpam-2592	172	15	(	(	PUNCT
ejpam-2592	172	16	a	a	X
ejpam-2592	172	17	)	)	PUNCT
ejpam-2592	172	18	g	g	NOUN
ejpam-2592	172	19	:	:	PUNCT
ejpam-2592	173	1	[	[	X
ejpam-2592	173	2	0	0	NUM
ejpam-2592	173	3	,	,	PUNCT
ejpam-2592	173	4	t]×	t]×	X
ejpam-2592	173	5	[	[	X
ejpam-2592	173	6	0	0	NUM
ejpam-2592	173	7	,	,	PUNCT
ejpam-2592	173	8	t]×	t]×	PROPN
ejpam-2592	173	9	r→	r→	PROPN
ejpam-2592	173	10	r	r	NOUN
ejpam-2592	173	11	is	be	AUX
ejpam-2592	173	12	continuous	continuous	ADJ
ejpam-2592	173	13	;	;	PUNCT
ejpam-2592	173	14	(	(	PUNCT
ejpam-2592	173	15	b	b	X
ejpam-2592	173	16	)	)	PUNCT
ejpam-2592	173	17	for	for	ADP
ejpam-2592	173	18	all	all	DET
ejpam-2592	173	19	(	(	PUNCT
ejpam-2592	173	20	s	s	X
ejpam-2592	173	21	,	,	PUNCT
ejpam-2592	173	22	r	r	NOUN
ejpam-2592	173	23	)	)	PUNCT
ejpam-2592	173	24	∈	∈	NOUN
ejpam-2592	174	1	[	[	X
ejpam-2592	174	2	0	0	NUM
ejpam-2592	174	3	,	,	PUNCT
ejpam-2592	174	4	t]2	t]2	PROPN
ejpam-2592	174	5	and	and	CCONJ
ejpam-2592	174	6	x	x	INTJ
ejpam-2592	174	7	,	,	PUNCT
ejpam-2592	174	8	y	y	PROPN
ejpam-2592	174	9	∈	∈	PROPN
ejpam-2592	174	10	r	r	NOUN
ejpam-2592	174	11	,	,	PUNCT
ejpam-2592	174	12	there	there	PRON
ejpam-2592	174	13	exists	exist	VERB
ejpam-2592	174	14	a	a	DET
ejpam-2592	174	15	continuous	continuous	ADJ
ejpam-2592	174	16	a	a	DET
ejpam-2592	174	17	:	:	PUNCT
ejpam-2592	174	18	[	[	X
ejpam-2592	174	19	0	0	NUM
ejpam-2592	174	20	,	,	PUNCT
ejpam-2592	174	21	t]×	t]×	X
ejpam-2592	175	1	[	[	X
ejpam-2592	175	2	0	0	NUM
ejpam-2592	175	3	,	,	PUNCT
ejpam-2592	175	4	t]→	t]→	PRON
ejpam-2592	175	5	r	r	NOUN
ejpam-2592	175	6	such	such	ADJ
ejpam-2592	175	7	that	that	SCONJ
ejpam-2592	175	8	|g	|g	PROPN
ejpam-2592	175	9	(	(	PUNCT
ejpam-2592	175	10	s	s	X
ejpam-2592	175	11	,	,	PUNCT
ejpam-2592	175	12	r	r	NOUN
ejpam-2592	175	13	,	,	PUNCT
ejpam-2592	175	14	x)|+	x)|+	PROPN
ejpam-2592	175	15	�	�	PROPN
ejpam-2592	175	16	�	�	PROPN
ejpam-2592	175	17	g	g	PROPN
ejpam-2592	175	18	�	�	PROPN
ejpam-2592	175	19	s	s	PART
ejpam-2592	175	20	,	,	PUNCT
ejpam-2592	175	21	r	r	PROPN
ejpam-2592	175	22	,	,	PUNCT
ejpam-2592	175	23	y	y	PROPN
ejpam-2592	175	24	�	�	PROPN
ejpam-2592	175	25	�	�	PROPN
ejpam-2592	175	26	�	�	PROPN
ejpam-2592	175	27	≤	≤	PROPN
ejpam-2592	175	28	�	�	PROPN
ejpam-2592	175	29	1	1	NUM
ejpam-2592	175	30	κ3	κ3	PROPN
ejpam-2592	175	31	�	�	PROPN
ejpam-2592	175	32	1	1	NUM
ejpam-2592	175	33	p	p	NOUN
ejpam-2592	175	34	a	a	DET
ejpam-2592	175	35	(	(	PUNCT
ejpam-2592	175	36	s	s	X
ejpam-2592	175	37	,	,	PUNCT
ejpam-2592	175	38	r	r	NOUN
ejpam-2592	175	39	)	)	PUNCT
ejpam-2592	175	40	�	�	PROPN
ejpam-2592	175	41	|x	|x	PROPN
ejpam-2592	175	42	|+	|+	PROPN
ejpam-2592	175	43	�	�	PROPN
ejpam-2592	175	44	�	�	PROPN
ejpam-2592	175	45	y	y	PROPN
ejpam-2592	175	46	�	�	PROPN
ejpam-2592	175	47	�	�	PROPN
ejpam-2592	175	48	�	�	PROPN
ejpam-2592	175	49	(	(	PUNCT
ejpam-2592	175	50	36	36	NUM
ejpam-2592	175	51	)	)	PUNCT
ejpam-2592	175	52	and	and	CCONJ
ejpam-2592	175	53	sup	sup	NOUN
ejpam-2592	175	54	s∈[0,t	s∈[0,t	PROPN
ejpam-2592	175	55	]	]	PUNCT
ejpam-2592	175	56	t	t	PROPN
ejpam-2592	175	57	∫	∫	PROPN
ejpam-2592	175	58	0	0	PROPN
ejpam-2592	176	1	a	a	DET
ejpam-2592	176	2	(	(	PUNCT
ejpam-2592	176	3	s	s	X
ejpam-2592	176	4	,	,	PUNCT
ejpam-2592	176	5	r)≤	r)≤	VERB
ejpam-2592	176	6	1	1	X
ejpam-2592	176	7	.	.	PUNCT
ejpam-2592	176	8	(	(	PUNCT
ejpam-2592	176	9	37	37	NUM
ejpam-2592	176	10	)	)	PUNCT
ejpam-2592	176	11	m.	m.	NOUN
ejpam-2592	176	12	akturk	akturk	PROPN
ejpam-2592	176	13	,	,	PUNCT
ejpam-2592	176	14	m.	m.	NOUN
ejpam-2592	176	15	kır	kır	PROPN
ejpam-2592	176	16	,	,	PUNCT
ejpam-2592	176	17	e.	e.	PROPN
ejpam-2592	176	18	yolacan	yolacan	PROPN
ejpam-2592	176	19	/	/	SYM
ejpam-2592	176	20	eur	eur	PROPN
ejpam-2592	176	21	.	.	PUNCT
ejpam-2592	177	1	j.	j.	PROPN
ejpam-2592	177	2	pure	pure	PROPN
ejpam-2592	177	3	appl	appl	PROPN
ejpam-2592	177	4	.	.	PROPN
ejpam-2592	177	5	math	math	PROPN
ejpam-2592	177	6	,	,	PUNCT
ejpam-2592	177	7	9	9	NUM
ejpam-2592	177	8	(	(	PUNCT
ejpam-2592	177	9	2016	2016	NUM
ejpam-2592	177	10	)	)	PUNCT
ejpam-2592	177	11	,	,	PUNCT
ejpam-2592	177	12	175	175	NUM
ejpam-2592	177	13	-	-	SYM
ejpam-2592	177	14	185	185	NUM
ejpam-2592	177	15	184	184	NUM
ejpam-2592	177	16	let	let	VERB
ejpam-2592	177	17	x	x	PUNCT
ejpam-2592	177	18	=	=	PUNCT
ejpam-2592	177	19	c	c	PROPN
ejpam-2592	178	1	[	[	X
ejpam-2592	178	2	0	0	NUM
ejpam-2592	178	3	,	,	PUNCT
ejpam-2592	178	4	t	t	PROPN
ejpam-2592	178	5	]	]	PUNCT
ejpam-2592	178	6	be	be	AUX
ejpam-2592	178	7	the	the	DET
ejpam-2592	178	8	set	set	NOUN
ejpam-2592	178	9	of	of	ADP
ejpam-2592	178	10	continuous	continuous	ADJ
ejpam-2592	178	11	real	real	ADJ
ejpam-2592	178	12	functions	function	NOUN
ejpam-2592	178	13	defined	define	VERB
ejpam-2592	178	14	on	on	ADP
ejpam-2592	178	15	[	[	X
ejpam-2592	178	16	0,1	0,1	NUM
ejpam-2592	178	17	]	]	PUNCT
ejpam-2592	178	18	.	.	PUNCT
ejpam-2592	179	1	we	we	PRON
ejpam-2592	179	2	endow	endow	VERB
ejpam-2592	179	3	x	x	PUNCT
ejpam-2592	179	4	with	with	ADP
ejpam-2592	179	5	the	the	DET
ejpam-2592	179	6	b	b	NOUN
ejpam-2592	179	7	-	-	PUNCT
ejpam-2592	179	8	metric	metric	ADJ
ejpam-2592	179	9	-	-	PUNCT
ejpam-2592	179	10	like	like	ADJ
ejpam-2592	179	11	ς	ς	PROPN
ejpam-2592	179	12	(	(	PUNCT
ejpam-2592	179	13	u	u	NOUN
ejpam-2592	179	14	,	,	PUNCT
ejpam-2592	179	15	v	v	NOUN
ejpam-2592	179	16	)	)	PUNCT
ejpam-2592	179	17	=	=	SYM
ejpam-2592	179	18	max	max	PROPN
ejpam-2592	179	19	s∈[0,1	s∈[0,1	PROPN
ejpam-2592	179	20	]	]	PUNCT
ejpam-2592	179	21	(	(	PUNCT
ejpam-2592	179	22	|u	|u	ADJ
ejpam-2592	179	23	(	(	PUNCT
ejpam-2592	179	24	s)|+	s)|+	ADJ
ejpam-2592	179	25	|v	|v	X
ejpam-2592	179	26	(	(	PUNCT
ejpam-2592	179	27	s)|)p	s)|)p	NOUN
ejpam-2592	179	28	for	for	ADP
ejpam-2592	179	29	all	all	DET
ejpam-2592	179	30	u	u	NOUN
ejpam-2592	179	31	,	,	PUNCT
ejpam-2592	179	32	v	v	NOUN
ejpam-2592	179	33	∈	∈	PROPN
ejpam-2592	179	34	x	x	PUNCT
ejpam-2592	180	1	where	where	SCONJ
ejpam-2592	180	2	p	p	X
ejpam-2592	180	3	>	>	X
ejpam-2592	180	4	1	1	NUM
ejpam-2592	180	5	.	.	PUNCT
ejpam-2592	180	6	also	also	ADV
ejpam-2592	180	7	,	,	PUNCT
ejpam-2592	180	8	(	(	PUNCT
ejpam-2592	180	9	x	x	X
ejpam-2592	180	10	,	,	PUNCT
ejpam-2592	180	11	ς	ς	PROPN
ejpam-2592	180	12	)	)	PUNCT
ejpam-2592	180	13	is	be	AUX
ejpam-2592	180	14	complete	complete	ADJ
ejpam-2592	180	15	b	b	X
ejpam-2592	180	16	-	-	ADJ
ejpam-2592	180	17	metric	metric	ADJ
ejpam-2592	180	18	-	-	PUNCT
ejpam-2592	180	19	like	like	ADJ
ejpam-2592	180	20	space	space	NOUN
ejpam-2592	180	21	with	with	ADP
ejpam-2592	180	22	the	the	DET
ejpam-2592	180	23	constant	constant	ADJ
ejpam-2592	180	24	κ=	κ=	ADJ
ejpam-2592	180	25	2p−1	2p−1	NUM
ejpam-2592	180	26	(	(	PUNCT
ejpam-2592	180	27	see	see	VERB
ejpam-2592	180	28	more	more	ADJ
ejpam-2592	180	29	details	detail	NOUN
ejpam-2592	180	30	[	[	X
ejpam-2592	180	31	3	3	NUM
ejpam-2592	180	32	]	]	NUM
ejpam-2592	180	33	)	)	PUNCT
ejpam-2592	180	34	.	.	PUNCT
ejpam-2592	181	1	theorem	theorem	NOUN
ejpam-2592	181	2	3	3	NUM
ejpam-2592	181	3	.	.	PUNCT
ejpam-2592	182	1	under	under	ADP
ejpam-2592	182	2	conditions	condition	NOUN
ejpam-2592	182	3	(	(	PUNCT
ejpam-2592	182	4	a	a	X
ejpam-2592	182	5	)	)	PUNCT
ejpam-2592	182	6	and	and	CCONJ
ejpam-2592	182	7	(	(	PUNCT
ejpam-2592	182	8	b	b	NOUN
ejpam-2592	182	9	)	)	PUNCT
ejpam-2592	182	10	,	,	PUNCT
ejpam-2592	182	11	(	(	PUNCT
ejpam-2592	182	12	35	35	NUM
ejpam-2592	182	13	)	)	PUNCT
ejpam-2592	182	14	has	have	VERB
ejpam-2592	182	15	a	a	DET
ejpam-2592	182	16	unique	unique	ADJ
ejpam-2592	182	17	solution	solution	NOUN
ejpam-2592	182	18	in	in	ADP
ejpam-2592	182	19	c	c	PROPN
ejpam-2592	182	20	[	[	X
ejpam-2592	182	21	0	0	NUM
ejpam-2592	182	22	,	,	PUNCT
ejpam-2592	182	23	t	t	PROPN
ejpam-2592	182	24	]	]	PUNCT
ejpam-2592	182	25	.	.	PUNCT
ejpam-2592	183	1	proof	proof	NOUN
ejpam-2592	183	2	.	.	PUNCT
ejpam-2592	184	1	by	by	ADP
ejpam-2592	184	2	(	(	PUNCT
ejpam-2592	184	3	36	36	NUM
ejpam-2592	184	4	)	)	PUNCT
ejpam-2592	184	5	and	and	CCONJ
ejpam-2592	184	6	(	(	PUNCT
ejpam-2592	184	7	37	37	NUM
ejpam-2592	184	8	)	)	PUNCT
ejpam-2592	184	9	,	,	PUNCT
ejpam-2592	184	10	we	we	PRON
ejpam-2592	184	11	have	have	VERB
ejpam-2592	184	12	κς	κς	ADP
ejpam-2592	184	13	�	�	PROPN
ejpam-2592	184	14	t	t	PROPN
ejpam-2592	184	15	x	x	SYM
ejpam-2592	184	16	(	(	PUNCT
ejpam-2592	184	17	s	s	NOUN
ejpam-2592	184	18	)	)	PUNCT
ejpam-2592	184	19	,	,	PUNCT
ejpam-2592	184	20	t	t	PROPN
ejpam-2592	184	21	y	y	PROPN
ejpam-2592	184	22	(	(	PUNCT
ejpam-2592	184	23	s	s	NOUN
ejpam-2592	184	24	)	)	PUNCT
ejpam-2592	184	25	�	�	PROPN
ejpam-2592	185	1	=	=	PROPN
ejpam-2592	185	2	κ	κ	PRON
ejpam-2592	185	3	�	�	PROPN
ejpam-2592	185	4	|t	|t	PROPN
ejpam-2592	185	5	x	x	PROPN
ejpam-2592	185	6	(	(	PUNCT
ejpam-2592	185	7	s)|+	s)|+	ADJ
ejpam-2592	185	8	�	�	PROPN
ejpam-2592	185	9	�	�	PROPN
ejpam-2592	185	10	t	t	PROPN
ejpam-2592	185	11	y	y	PROPN
ejpam-2592	185	12	(	(	PUNCT
ejpam-2592	185	13	s	s	NOUN
ejpam-2592	185	14	)	)	PUNCT
ejpam-2592	185	15	�	�	PROPN
ejpam-2592	185	16	�	�	PROPN
ejpam-2592	185	17	�	�	PROPN
ejpam-2592	185	18	p	p	NOUN
ejpam-2592	185	19	=	=	NOUN
ejpam-2592	185	20	κ	κ	PRON
ejpam-2592	185	21			NOUN
ejpam-2592	185	22			NOUN
ejpam-2592	185	23			PROPN
ejpam-2592	185	24	�	�	PROPN
ejpam-2592	185	25	�	�	PROPN
ejpam-2592	185	26	�	�	PROPN
ejpam-2592	185	27	�	�	PROPN
ejpam-2592	185	28	�	�	PROPN
ejpam-2592	185	29	�	�	PROPN
ejpam-2592	185	30	�	�	PROPN
ejpam-2592	185	31	t	t	PROPN
ejpam-2592	185	32	∫	∫	PROPN
ejpam-2592	185	33	0	0	NUM
ejpam-2592	185	34	g	g	PROPN
ejpam-2592	185	35	(	(	PUNCT
ejpam-2592	185	36	s	s	X
ejpam-2592	185	37	,	,	PUNCT
ejpam-2592	185	38	r	r	NOUN
ejpam-2592	185	39	,	,	PUNCT
ejpam-2592	185	40	x	x	X
ejpam-2592	185	41	(	(	PUNCT
ejpam-2592	185	42	r	r	NOUN
ejpam-2592	185	43	)	)	PUNCT
ejpam-2592	185	44	)	)	PUNCT
ejpam-2592	185	45	dr	dr	PROPN
ejpam-2592	185	46	�	�	PROPN
ejpam-2592	185	47	�	�	PROPN
ejpam-2592	185	48	�	�	PROPN
ejpam-2592	185	49	�	�	PROPN
ejpam-2592	185	50	�	�	PROPN
ejpam-2592	185	51	�	�	PROPN
ejpam-2592	185	52	�	�	PROPN
ejpam-2592	185	53	+	+	CCONJ
ejpam-2592	185	54	�	�	PROPN
ejpam-2592	185	55	�	�	PROPN
ejpam-2592	185	56	�	�	PROPN
ejpam-2592	185	57	�	�	PROPN
ejpam-2592	185	58	�	�	PROPN
ejpam-2592	185	59	�	�	PROPN
ejpam-2592	185	60	�	�	PROPN
ejpam-2592	185	61	t	t	PROPN
ejpam-2592	185	62	∫	∫	PROPN
ejpam-2592	185	63	0	0	PROPN
ejpam-2592	186	1	g	g	PROPN
ejpam-2592	186	2	�	�	PROPN
ejpam-2592	186	3	s	s	PART
ejpam-2592	186	4	,	,	PUNCT
ejpam-2592	186	5	r	r	NOUN
ejpam-2592	186	6	,	,	PUNCT
ejpam-2592	186	7	y	y	PROPN
ejpam-2592	186	8	(	(	PUNCT
ejpam-2592	186	9	r	r	NOUN
ejpam-2592	186	10	)	)	PUNCT
ejpam-2592	186	11	�	�	PROPN
ejpam-2592	186	12	dr	dr	PROPN
ejpam-2592	186	13	�	�	PROPN
ejpam-2592	186	14	�	�	PROPN
ejpam-2592	186	15	�	�	PROPN
ejpam-2592	186	16	�	�	PROPN
ejpam-2592	186	17	�	�	PROPN
ejpam-2592	186	18	�	�	PROPN
ejpam-2592	186	19	�	�	PROPN
ejpam-2592	186	20			PROPN
ejpam-2592	186	21			VERB
ejpam-2592	186	22			PUNCT
ejpam-2592	187	1	p	p	PRON
ejpam-2592	187	2	≤κ	≤κ	PROPN
ejpam-2592	187	3			NOUN
ejpam-2592	187	4			NOUN
ejpam-2592	187	5	t	t	PROPN
ejpam-2592	187	6	∫	∫	PROPN
ejpam-2592	187	7	0	0	NUM
ejpam-2592	187	8	|g	|g	PROPN
ejpam-2592	187	9	(	(	PUNCT
ejpam-2592	187	10	s	s	X
ejpam-2592	187	11	,	,	PUNCT
ejpam-2592	187	12	r	r	NOUN
ejpam-2592	187	13	,	,	PUNCT
ejpam-2592	187	14	x	x	X
ejpam-2592	187	15	(	(	PUNCT
ejpam-2592	187	16	r))|	r))|	PROPN
ejpam-2592	187	17	dr	dr	PROPN
ejpam-2592	187	18	+	+	PROPN
ejpam-2592	187	19	t	t	PROPN
ejpam-2592	187	20	∫	∫	PROPN
ejpam-2592	187	21	0	0	PROPN
ejpam-2592	187	22	�	�	PROPN
ejpam-2592	187	23	�	�	PROPN
ejpam-2592	187	24	g	g	PROPN
ejpam-2592	187	25	�	�	PROPN
ejpam-2592	187	26	s	s	PART
ejpam-2592	187	27	,	,	PUNCT
ejpam-2592	187	28	r	r	NOUN
ejpam-2592	187	29	,	,	PUNCT
ejpam-2592	187	30	y	y	PROPN
ejpam-2592	187	31	(	(	PUNCT
ejpam-2592	187	32	r	r	NOUN
ejpam-2592	187	33	)	)	PUNCT
ejpam-2592	187	34	�	�	PROPN
ejpam-2592	187	35	�	�	PROPN
ejpam-2592	187	36	�	�	PROPN
ejpam-2592	187	37	dr	dr	PROPN
ejpam-2592	187	38			PROPN
ejpam-2592	187	39			PUNCT
ejpam-2592	188	1	p	p	PRON
ejpam-2592	188	2	≤κ	≤κ	PROPN
ejpam-2592	188	3			NOUN
ejpam-2592	188	4			NOUN
ejpam-2592	188	5	t	t	PROPN
ejpam-2592	188	6	∫	∫	PROPN
ejpam-2592	188	7	0	0	PROPN
ejpam-2592	188	8	�	�	PROPN
ejpam-2592	188	9	1	1	NUM
ejpam-2592	188	10	κ3	κ3	PROPN
ejpam-2592	188	11	�	�	PROPN
ejpam-2592	188	12	1	1	NUM
ejpam-2592	188	13	p	p	NOUN
ejpam-2592	188	14	a	a	DET
ejpam-2592	188	15	(	(	PUNCT
ejpam-2592	188	16	s	s	X
ejpam-2592	188	17	,	,	PUNCT
ejpam-2592	188	18	r	r	NOUN
ejpam-2592	188	19	)	)	PUNCT
ejpam-2592	188	20	�	�	PROPN
ejpam-2592	188	21	�	�	PROPN
ejpam-2592	188	22	�	�	PROPN
ejpam-2592	188	23	�	�	PROPN
ejpam-2592	188	24	�	�	PROPN
ejpam-2592	188	25	x	x	SYM
ejpam-2592	188	26	(	(	PUNCT
ejpam-2592	188	27	r	r	NOUN
ejpam-2592	188	28	)	)	PUNCT
ejpam-2592	189	1	+	+	NOUN
ejpam-2592	189	2	y	y	PROPN
ejpam-2592	189	3	(	(	PUNCT
ejpam-2592	189	4	r	r	NOUN
ejpam-2592	189	5	)	)	PUNCT
ejpam-2592	189	6	�	�	PROPN
ejpam-2592	189	7	�	�	PROPN
ejpam-2592	189	8	�	�	PROPN
ejpam-2592	189	9	p	p	PROPN
ejpam-2592	189	10	�	�	PROPN
ejpam-2592	189	11	1	1	NUM
ejpam-2592	189	12	p	p	PROPN
ejpam-2592	189	13	�	�	PROPN
ejpam-2592	189	14	dr	dr	PROPN
ejpam-2592	189	15			PROPN
ejpam-2592	189	16			PUNCT
ejpam-2592	190	1	p	p	PRON
ejpam-2592	190	2	≤κ	≤κ	PROPN
ejpam-2592	190	3			NOUN
ejpam-2592	190	4			NOUN
ejpam-2592	190	5	t	t	PROPN
ejpam-2592	190	6	∫	∫	PROPN
ejpam-2592	190	7	0	0	PROPN
ejpam-2592	190	8	�	�	PROPN
ejpam-2592	190	9	1	1	NUM
ejpam-2592	190	10	κ3	κ3	PROPN
ejpam-2592	190	11	�	�	PROPN
ejpam-2592	190	12	1	1	NUM
ejpam-2592	190	13	p	p	NOUN
ejpam-2592	190	14	a	a	DET
ejpam-2592	190	15	(	(	PUNCT
ejpam-2592	190	16	s	s	PROPN
ejpam-2592	190	17	,	,	PUNCT
ejpam-2592	190	18	r)ς	r)ς	ADJ
ejpam-2592	190	19	1	1	NUM
ejpam-2592	190	20	p	p	NOUN
ejpam-2592	190	21	�	�	PROPN
ejpam-2592	190	22	x	x	SYM
ejpam-2592	190	23	(	(	PUNCT
ejpam-2592	190	24	r	r	NOUN
ejpam-2592	190	25	)	)	PUNCT
ejpam-2592	190	26	,	,	PUNCT
ejpam-2592	190	27	y	y	PROPN
ejpam-2592	190	28	(	(	PUNCT
ejpam-2592	190	29	r	r	NOUN
ejpam-2592	190	30	)	)	PUNCT
ejpam-2592	190	31	�	�	PROPN
ejpam-2592	190	32	dr	dr	PROPN
ejpam-2592	190	33			PROPN
ejpam-2592	190	34			PUNCT
ejpam-2592	191	1	p	p	NOUN
ejpam-2592	191	2	≤	≤	NUM
ejpam-2592	191	3	1	1	NUM
ejpam-2592	191	4	κ2	κ2	NOUN
ejpam-2592	191	5	ς	ς	PROPN
ejpam-2592	191	6	�	�	PROPN
ejpam-2592	191	7	x	x	SYM
ejpam-2592	191	8	(	(	PUNCT
ejpam-2592	191	9	r	r	NOUN
ejpam-2592	191	10	)	)	PUNCT
ejpam-2592	191	11	,	,	PUNCT
ejpam-2592	191	12	y	y	PROPN
ejpam-2592	191	13	(	(	PUNCT
ejpam-2592	191	14	r	r	NOUN
ejpam-2592	191	15	)	)	PUNCT
ejpam-2592	191	16	�	�	PROPN
ejpam-2592	191	17			NOUN
ejpam-2592	191	18			NOUN
ejpam-2592	191	19	t	t	X
ejpam-2592	191	20	∫	∫	PROPN
ejpam-2592	191	21	0	0	PROPN
ejpam-2592	192	1	a	a	DET
ejpam-2592	192	2	(	(	PUNCT
ejpam-2592	192	3	s	s	X
ejpam-2592	192	4	,	,	PUNCT
ejpam-2592	192	5	r	r	NOUN
ejpam-2592	192	6	)	)	PUNCT
ejpam-2592	192	7	dr	dr	PROPN
ejpam-2592	192	8			INTJ
ejpam-2592	192	9			PUNCT
ejpam-2592	193	1	p	p	NOUN
ejpam-2592	193	2	≤	≤	NUM
ejpam-2592	193	3	1	1	NUM
ejpam-2592	193	4	κ2	κ2	NOUN
ejpam-2592	193	5	ς	ς	PROPN
ejpam-2592	193	6	�	�	PROPN
ejpam-2592	193	7	x	x	SYM
ejpam-2592	193	8	(	(	PUNCT
ejpam-2592	193	9	r	r	NOUN
ejpam-2592	193	10	)	)	PUNCT
ejpam-2592	193	11	,	,	PUNCT
ejpam-2592	193	12	y	y	PROPN
ejpam-2592	193	13	(	(	PUNCT
ejpam-2592	193	14	r	r	NOUN
ejpam-2592	193	15	)	)	PUNCT
ejpam-2592	193	16	�	�	PROPN
ejpam-2592	193	17	≤	≤	ADJ
ejpam-2592	193	18	1	1	NUM
ejpam-2592	193	19	κ2	κ2	PROPN
ejpam-2592	193	20	max	max	PROPN
ejpam-2592	193	21	�	�	PROPN
ejpam-2592	193	22	ς	ς	PROPN
ejpam-2592	193	23	�	�	PROPN
ejpam-2592	193	24	x	x	SYM
ejpam-2592	193	25	(	(	PUNCT
ejpam-2592	193	26	r	r	NOUN
ejpam-2592	193	27	)	)	PUNCT
ejpam-2592	193	28	,	,	PUNCT
ejpam-2592	193	29	y	y	PROPN
ejpam-2592	193	30	(	(	PUNCT
ejpam-2592	193	31	r	r	NOUN
ejpam-2592	193	32	)	)	PUNCT
ejpam-2592	193	33	�	�	PROPN
ejpam-2592	193	34	,	,	PUNCT
ejpam-2592	193	35	ς	ς	PROPN
ejpam-2592	193	36	(	(	PUNCT
ejpam-2592	193	37	x	x	X
ejpam-2592	193	38	(	(	PUNCT
ejpam-2592	193	39	r	r	NOUN
ejpam-2592	193	40	)	)	PUNCT
ejpam-2592	193	41	,	,	PUNCT
ejpam-2592	193	42	t	t	NOUN
ejpam-2592	193	43	x	x	PUNCT
ejpam-2592	193	44	(	(	PUNCT
ejpam-2592	193	45	r	r	NOUN
ejpam-2592	193	46	)	)	PUNCT
ejpam-2592	193	47	)	)	PUNCT
ejpam-2592	193	48	,	,	PUNCT
ejpam-2592	193	49	ς	ς	PROPN
ejpam-2592	193	50	�	�	PROPN
ejpam-2592	193	51	y	y	PROPN
ejpam-2592	193	52	(	(	PUNCT
ejpam-2592	193	53	r	r	NOUN
ejpam-2592	193	54	)	)	PUNCT
ejpam-2592	193	55	,	,	PUNCT
ejpam-2592	193	56	t	t	PROPN
ejpam-2592	193	57	y	y	PROPN
ejpam-2592	193	58	(	(	PUNCT
ejpam-2592	193	59	r	r	NOUN
ejpam-2592	193	60	)	)	PUNCT
ejpam-2592	193	61	�	�	PROPN
ejpam-2592	193	62	,	,	PUNCT
ejpam-2592	193	63	ς	ς	PROPN
ejpam-2592	193	64	�	�	PROPN
ejpam-2592	193	65	x	x	SYM
ejpam-2592	193	66	(	(	PUNCT
ejpam-2592	193	67	r	r	NOUN
ejpam-2592	193	68	)	)	PUNCT
ejpam-2592	193	69	,	,	PUNCT
ejpam-2592	193	70	t	t	PROPN
ejpam-2592	193	71	y	y	PROPN
ejpam-2592	193	72	(	(	PUNCT
ejpam-2592	193	73	r	r	NOUN
ejpam-2592	193	74	)	)	PUNCT
ejpam-2592	193	75	�	�	NOUN
ejpam-2592	193	76	+	+	CCONJ
ejpam-2592	193	77	ς	ς	PROPN
ejpam-2592	193	78	�	�	PROPN
ejpam-2592	193	79	y	y	PROPN
ejpam-2592	193	80	(	(	PUNCT
ejpam-2592	193	81	r	r	NOUN
ejpam-2592	193	82	)	)	PUNCT
ejpam-2592	193	83	,	,	PUNCT
ejpam-2592	193	84	t	t	NOUN
ejpam-2592	193	85	x	x	PUNCT
ejpam-2592	193	86	(	(	PUNCT
ejpam-2592	193	87	r	r	NOUN
ejpam-2592	193	88	)	)	PUNCT
ejpam-2592	193	89	�	�	NOUN
ejpam-2592	193	90	2κ	2κ	NOUN
ejpam-2592	193	91	«	«	PUNCT
ejpam-2592	193	92	=	=	ADJ
ejpam-2592	193	93	sm	sm	PROPN
ejpam-2592	193	94	�	�	PROPN
ejpam-2592	193	95	x	x	SYM
ejpam-2592	193	96	(	(	PUNCT
ejpam-2592	193	97	r	r	NOUN
ejpam-2592	193	98	)	)	PUNCT
ejpam-2592	193	99	,	,	PUNCT
ejpam-2592	193	100	y	y	PROPN
ejpam-2592	193	101	(	(	PUNCT
ejpam-2592	193	102	r	r	NOUN
ejpam-2592	193	103	)	)	PUNCT
ejpam-2592	193	104	�	�	NOUN
ejpam-2592	193	105	where	where	SCONJ
ejpam-2592	193	106	s	s	VERB
ejpam-2592	193	107	=	=	SYM
ejpam-2592	193	108	1	1	NUM
ejpam-2592	193	109	κ2	κ2	PROPN
ejpam-2592	193	110	∈	∈	NOUN
ejpam-2592	193	111	(	(	PUNCT
ejpam-2592	193	112	0,1	0,1	NUM
ejpam-2592	193	113	)	)	PUNCT
ejpam-2592	193	114	.	.	PUNCT
ejpam-2592	194	1	now	now	ADV
ejpam-2592	194	2	,	,	PUNCT
ejpam-2592	194	3	all	all	DET
ejpam-2592	194	4	the	the	DET
ejpam-2592	194	5	conditions	condition	NOUN
ejpam-2592	194	6	of	of	ADP
ejpam-2592	194	7	corollary	corollary	ADJ
ejpam-2592	194	8	2	2	NUM
ejpam-2592	194	9	hold	hold	NOUN
ejpam-2592	194	10	and	and	CCONJ
ejpam-2592	194	11	t	t	NOUN
ejpam-2592	194	12	has	have	VERB
ejpam-2592	194	13	a	a	DET
ejpam-2592	194	14	unique	unique	ADJ
ejpam-2592	194	15	fixed	fix	VERB
ejpam-2592	194	16	point	point	NOUN
ejpam-2592	194	17	x	x	SYM
ejpam-2592	194	18	∈	∈	PROPN
ejpam-2592	194	19	x	x	X
ejpam-2592	194	20	,	,	PUNCT
ejpam-2592	194	21	that	that	PRON
ejpam-2592	194	22	is	is	ADV
ejpam-2592	194	23	x	x	PUNCT
ejpam-2592	194	24	is	be	AUX
ejpam-2592	194	25	the	the	DET
ejpam-2592	194	26	unique	unique	ADJ
ejpam-2592	194	27	solution	solution	NOUN
ejpam-2592	194	28	for	for	ADP
ejpam-2592	194	29	the	the	DET
ejpam-2592	194	30	integral	integral	ADJ
ejpam-2592	194	31	equation	equation	NOUN
ejpam-2592	194	32	(	(	PUNCT
ejpam-2592	194	33	35	35	NUM
ejpam-2592	194	34	)	)	PUNCT
ejpam-2592	194	35	.	.	PUNCT
ejpam-2592	195	1	references	reference	NOUN
ejpam-2592	195	2	185	185	NUM
ejpam-2592	195	3	references	reference	NOUN
ejpam-2592	195	4	[	[	X
ejpam-2592	195	5	1	1	NUM
ejpam-2592	195	6	]	]	X
ejpam-2592	195	7	m.a	m.a	PROPN
ejpam-2592	195	8	.	.	PROPN
ejpam-2592	195	9	alghamdi	alghamdi	PROPN
ejpam-2592	195	10	,	,	PUNCT
ejpam-2592	195	11	n.	n.	NOUN
ejpam-2592	195	12	hussain	hussain	PROPN
ejpam-2592	195	13	,	,	PUNCT
ejpam-2592	195	14	and	and	CCONJ
ejpam-2592	195	15	p.	p.	PROPN
ejpam-2592	195	16	salimi	salimi	PROPN
ejpam-2592	195	17	.	.	PUNCT
ejpam-2592	196	1	fixed	fix	VERB
ejpam-2592	196	2	point	point	NOUN
ejpam-2592	196	3	and	and	CCONJ
ejpam-2592	196	4	coupled	couple	VERB
ejpam-2592	196	5	fixed	fix	VERB
ejpam-2592	196	6	point	point	NOUN
ejpam-2592	196	7	theorems	theorem	NOUN
ejpam-2592	196	8	on	on	ADP
ejpam-2592	196	9	b	b	X
ejpam-2592	196	10	-	-	PUNCT
ejpam-2592	196	11	metric	metric	ADJ
ejpam-2592	196	12	-	-	PUNCT
ejpam-2592	196	13	like	like	ADJ
ejpam-2592	196	14	spaces	space	NOUN
ejpam-2592	196	15	,	,	PUNCT
ejpam-2592	196	16	journal	journal	NOUN
ejpam-2592	196	17	of	of	ADP
ejpam-2592	196	18	inequalities	inequality	NOUN
ejpam-2592	196	19	and	and	CCONJ
ejpam-2592	196	20	applications	application	NOUN
ejpam-2592	196	21	2013	2013	NUM
ejpam-2592	196	22	,	,	PUNCT
ejpam-2592	196	23	article	article	NOUN
ejpam-2592	196	24	i	i	PROPN
ejpam-2592	196	25	d	d	PROPN
ejpam-2592	196	26	402	402	NUM
ejpam-2592	196	27	,	,	PUNCT
ejpam-2592	196	28	2013	2013	NUM
ejpam-2592	196	29	.	.	PUNCT
ejpam-2592	197	1	[	[	X
ejpam-2592	197	2	2	2	X
ejpam-2592	197	3	]	]	X
ejpam-2592	197	4	h.	h.	PROPN
ejpam-2592	197	5	aydi	aydi	PROPN
ejpam-2592	197	6	and	and	CCONJ
ejpam-2592	197	7	e.	e.	PROPN
ejpam-2592	197	8	karapinar	karapinar	PROPN
ejpam-2592	197	9	.	.	PUNCT
ejpam-2592	198	1	fixed	fix	VERB
ejpam-2592	198	2	point	point	NOUN
ejpam-2592	198	3	results	result	NOUN
ejpam-2592	198	4	for	for	ADP
ejpam-2592	198	5	generalized	generalized	ADJ
ejpam-2592	198	6	α−ψ−contractions	α−ψ−contraction	NOUN
ejpam-2592	198	7	in	in	ADP
ejpam-2592	198	8	metriclike	metriclike	NOUN
ejpam-2592	198	9	spaces	space	NOUN
ejpam-2592	198	10	and	and	CCONJ
ejpam-2592	198	11	applications	application	NOUN
ejpam-2592	198	12	,	,	PUNCT
ejpam-2592	198	13	electronic	electronic	ADJ
ejpam-2592	198	14	journal	journal	NOUN
ejpam-2592	198	15	of	of	ADP
ejpam-2592	198	16	differential	differential	ADJ
ejpam-2592	198	17	equations	equation	NOUN
ejpam-2592	198	18	,	,	PUNCT
ejpam-2592	198	19	2015(133	2015(133	NUM
ejpam-2592	198	20	)	)	PUNCT
ejpam-2592	198	21	,	,	PUNCT
ejpam-2592	198	22	1	1	NUM
ejpam-2592	198	23	-	-	SYM
ejpam-2592	198	24	15	15	NUM
ejpam-2592	198	25	,	,	PUNCT
ejpam-2592	198	26	2015	2015	NUM
ejpam-2592	198	27	.	.	PUNCT
ejpam-2592	199	1	[	[	X
ejpam-2592	199	2	3	3	X
ejpam-2592	199	3	]	]	X
ejpam-2592	199	4	c.	c.	PROPN
ejpam-2592	199	5	chen	chen	PROPN
ejpam-2592	199	6	,	,	PUNCT
ejpam-2592	199	7	j.	j.	PROPN
ejpam-2592	199	8	dong	dong	PROPN
ejpam-2592	199	9	,	,	PUNCT
ejpam-2592	199	10	and	and	CCONJ
ejpam-2592	199	11	c.	c.	PROPN
ejpam-2592	199	12	zhu	zhu	PROPN
ejpam-2592	199	13	.	.	PUNCT
ejpam-2592	200	1	some	some	DET
ejpam-2592	200	2	fixed	fix	VERB
ejpam-2592	200	3	point	point	NOUN
ejpam-2592	200	4	theorems	theorem	NOUN
ejpam-2592	200	5	in	in	ADP
ejpam-2592	200	6	b	b	NOUN
ejpam-2592	200	7	-	-	ADJ
ejpam-2592	200	8	metric	metric	ADJ
ejpam-2592	200	9	-	-	PUNCT
ejpam-2592	200	10	like	like	ADJ
ejpam-2592	200	11	spaces	space	NOUN
ejpam-2592	200	12	,	,	PUNCT
ejpam-2592	200	13	fixed	fix	VERB
ejpam-2592	200	14	point	point	NOUN
ejpam-2592	200	15	theory	theory	NOUN
ejpam-2592	200	16	and	and	CCONJ
ejpam-2592	200	17	applications	application	NOUN
ejpam-2592	200	18	,	,	PUNCT
ejpam-2592	200	19	2015(122	2015(122	NUM
ejpam-2592	200	20	)	)	PUNCT
ejpam-2592	200	21	,	,	PUNCT
ejpam-2592	200	22	2015	2015	NUM
ejpam-2592	200	23	.	.	PUNCT
ejpam-2592	201	1	[	[	X
ejpam-2592	201	2	4	4	X
ejpam-2592	201	3	]	]	X
ejpam-2592	201	4	n.	n.	PROPN
ejpam-2592	201	5	hussain	hussain	PROPN
ejpam-2592	201	6	,	,	PUNCT
ejpam-2592	201	7	j.r	j.r	PROPN
ejpam-2592	201	8	.	.	PROPN
ejpam-2592	201	9	roshan	roshan	PROPN
ejpam-2592	201	10	,	,	PUNCT
ejpam-2592	201	11	v.	v.	CCONJ
ejpam-2592	201	12	parvaneh	parvaneh	NOUN
ejpam-2592	201	13	,	,	PUNCT
ejpam-2592	201	14	and	and	CCONJ
ejpam-2592	201	15	z.	z.	PROPN
ejpam-2592	201	16	kadelburg	kadelburg	PROPN
ejpam-2592	201	17	.	.	PUNCT
ejpam-2592	202	1	fixed	fix	VERB
ejpam-2592	202	2	points	point	NOUN
ejpam-2592	202	3	of	of	ADP
ejpam-2592	202	4	contractive	contractive	ADJ
ejpam-2592	202	5	mappings	mapping	NOUN
ejpam-2592	202	6	in	in	ADP
ejpam-2592	202	7	b	b	NOUN
ejpam-2592	202	8	-	-	PUNCT
ejpam-2592	202	9	metric	metric	ADJ
ejpam-2592	202	10	-	-	PUNCT
ejpam-2592	202	11	like	like	ADJ
ejpam-2592	202	12	spaces	space	NOUN
ejpam-2592	202	13	,	,	PUNCT
ejpam-2592	202	14	the	the	DET
ejpam-2592	202	15	scientific	scientific	ADJ
ejpam-2592	202	16	world	world	NOUN
ejpam-2592	202	17	journal	journal	PROPN
ejpam-2592	202	18	2014	2014	NUM
ejpam-2592	202	19	,	,	PUNCT
ejpam-2592	202	20	article	article	NOUN
ejpam-2592	202	21	i	i	PROPN
ejpam-2592	202	22	d	d	PROPN
ejpam-2592	202	23	471827	471827	NUM
ejpam-2592	202	24	,	,	PUNCT
ejpam-2592	202	25	2014	2014	NUM
ejpam-2592	202	26	.	.	PUNCT
ejpam-2592	203	1	[	[	X
ejpam-2592	203	2	5	5	X
ejpam-2592	203	3	]	]	PUNCT
ejpam-2592	203	4	b.	b.	PROPN
ejpam-2592	203	5	samet	samet	PROPN
ejpam-2592	203	6	,	,	PUNCT
ejpam-2592	203	7	c.	c.	PROPN
ejpam-2592	203	8	vetro	vetro	PROPN
ejpam-2592	203	9	,	,	PUNCT
ejpam-2592	203	10	and	and	CCONJ
ejpam-2592	203	11	p.	p.	PROPN
ejpam-2592	203	12	vetro	vetro	PROPN
ejpam-2592	203	13	.	.	PUNCT
ejpam-2592	204	1	fixed	fix	VERB
ejpam-2592	204	2	point	point	NOUN
ejpam-2592	204	3	theorems	theorem	NOUN
ejpam-2592	204	4	for	for	ADP
ejpam-2592	204	5	α−ψ−contractive	α−ψ−contractive	ADJ
ejpam-2592	204	6	type	type	NOUN
ejpam-2592	204	7	mappings	mapping	NOUN
ejpam-2592	204	8	,	,	PUNCT
ejpam-2592	204	9	nonlinear	nonlinear	ADJ
ejpam-2592	204	10	analysis	analysis	NOUN
ejpam-2592	204	11	:	:	PUNCT
ejpam-2592	204	12	theory	theory	NOUN
ejpam-2592	204	13	,	,	PUNCT
ejpam-2592	204	14	methods	method	NOUN
ejpam-2592	204	15	and	and	CCONJ
ejpam-2592	204	16	applications	application	NOUN
ejpam-2592	204	17	,	,	PUNCT
ejpam-2592	204	18	75	75	NUM
ejpam-2592	204	19	(	(	PUNCT
ejpam-2592	204	20	4	4	NUM
ejpam-2592	204	21	)	)	PUNCT
ejpam-2592	204	22	,	,	PUNCT
ejpam-2592	204	23	2154	2154	NUM
ejpam-2592	204	24	-	-	SYM
ejpam-2592	204	25	2165	2165	NUM
ejpam-2592	204	26	,	,	PUNCT
ejpam-2592	204	27	2012	2012	NUM
ejpam-2592	204	28	.	.	PUNCT