id	sid	tid	token	lemma	pos
ejpam-2584	1	1	european	european	PROPN
ejpam-2584	1	2	journal	journal	PROPN
ejpam-2584	1	3	of	of	ADP
ejpam-2584	1	4	pure	pure	ADJ
ejpam-2584	1	5	and	and	CCONJ
ejpam-2584	1	6	applied	apply	VERB
ejpam-2584	1	7	mathematics	mathematic	NOUN
ejpam-2584	1	8	vol	vol	NOUN
ejpam-2584	1	9	.	.	PROPN
ejpam-2584	2	1	9	9	NUM
ejpam-2584	2	2	,	,	PUNCT
ejpam-2584	2	3	no	no	INTJ
ejpam-2584	2	4	.	.	NOUN
ejpam-2584	2	5	4	4	NUM
ejpam-2584	2	6	,	,	PUNCT
ejpam-2584	2	7	2016	2016	NUM
ejpam-2584	2	8	,	,	PUNCT
ejpam-2584	2	9	443	443	NUM
ejpam-2584	2	10	-	-	SYM
ejpam-2584	2	11	451	451	NUM
ejpam-2584	2	12	issn	issn	PROPN
ejpam-2584	2	13	1307	1307	NUM
ejpam-2584	2	14	-	-	SYM
ejpam-2584	2	15	5543	5543	NUM
ejpam-2584	2	16	–	–	PUNCT
ejpam-2584	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2584	2	18	generalized	generalize	VERB
ejpam-2584	2	19	fixed	fix	VERB
ejpam-2584	2	20	point	point	NOUN
ejpam-2584	2	21	theorems	theorem	NOUN
ejpam-2584	2	22	in	in	ADP
ejpam-2584	2	23	partial	partial	ADJ
ejpam-2584	2	24	metric	metric	ADJ
ejpam-2584	2	25	spaces	space	NOUN
ejpam-2584	2	26	mehmet	mehmet	PROPN
ejpam-2584	2	27	kir	kir	PROPN
ejpam-2584	3	1	1,∗and	1,∗and	PROPN
ejpam-2584	3	2	hukmi	hukmi	PROPN
ejpam-2584	3	3	kiziltunc	kiziltunc	VERB
ejpam-2584	3	4	2	2	NUM
ejpam-2584	3	5	1	1	NUM
ejpam-2584	3	6	department	department	NOUN
ejpam-2584	3	7	of	of	ADP
ejpam-2584	3	8	civil	civil	ADJ
ejpam-2584	3	9	engineering	engineering	NOUN
ejpam-2584	3	10	,	,	PUNCT
ejpam-2584	3	11	faculty	faculty	NOUN
ejpam-2584	3	12	of	of	ADP
ejpam-2584	3	13	engineering	engineering	PROPN
ejpam-2584	3	14	şırnak	şırnak	PROPN
ejpam-2584	3	15	university	university	PROPN
ejpam-2584	3	16	,	,	PUNCT
ejpam-2584	3	17	şırnak	şırnak	PROPN
ejpam-2584	3	18	,	,	PUNCT
ejpam-2584	3	19	turkey	turkey	NOUN
ejpam-2584	3	20	2	2	NUM
ejpam-2584	3	21	department	department	NOUN
ejpam-2584	3	22	of	of	ADP
ejpam-2584	3	23	mathematics	mathematic	NOUN
ejpam-2584	3	24	,	,	PUNCT
ejpam-2584	3	25	faculty	faculty	NOUN
ejpam-2584	3	26	of	of	ADP
ejpam-2584	3	27	science	science	NOUN
ejpam-2584	3	28	,	,	PUNCT
ejpam-2584	3	29	ataturk	ataturk	PROPN
ejpam-2584	3	30	university	university	PROPN
ejpam-2584	3	31	,	,	PUNCT
ejpam-2584	3	32	erzurum	erzurum	PROPN
ejpam-2584	3	33	,	,	PUNCT
ejpam-2584	3	34	25240	25240	NUM
ejpam-2584	3	35	,	,	PUNCT
ejpam-2584	3	36	turkey	turkey	NOUN
ejpam-2584	3	37	abstract	abstract	NOUN
ejpam-2584	3	38	.	.	PUNCT
ejpam-2584	4	1	this	this	DET
ejpam-2584	4	2	paper	paper	NOUN
ejpam-2584	4	3	consist	consist	NOUN
ejpam-2584	4	4	of	of	ADP
ejpam-2584	4	5	some	some	DET
ejpam-2584	4	6	generalized	generalized	ADJ
ejpam-2584	4	7	fixed	fix	VERB
ejpam-2584	4	8	point	point	NOUN
ejpam-2584	4	9	theorems	theorem	NOUN
ejpam-2584	4	10	in	in	ADP
ejpam-2584	4	11	partial	partial	ADJ
ejpam-2584	4	12	metric	metric	ADJ
ejpam-2584	4	13	spaces	space	NOUN
ejpam-2584	4	14	.	.	PUNCT
ejpam-2584	5	1	the	the	DET
ejpam-2584	5	2	concept	concept	NOUN
ejpam-2584	5	3	of	of	ADP
ejpam-2584	5	4	tf	tf	NUM
ejpam-2584	5	5	-contractive	-contractive	ADJ
ejpam-2584	5	6	mappings	mapping	NOUN
ejpam-2584	5	7	are	be	AUX
ejpam-2584	5	8	introduced	introduce	VERB
ejpam-2584	5	9	in	in	ADP
ejpam-2584	5	10	partial	partial	ADJ
ejpam-2584	5	11	metric	metric	ADJ
ejpam-2584	5	12	space	space	NOUN
ejpam-2584	5	13	and	and	CCONJ
ejpam-2584	5	14	thus	thus	ADV
ejpam-2584	5	15	,	,	PUNCT
ejpam-2584	5	16	a	a	DET
ejpam-2584	5	17	generalization	generalization	NOUN
ejpam-2584	5	18	of	of	ADP
ejpam-2584	5	19	banach	banach	NOUN
ejpam-2584	5	20	’s	’s	ADV
ejpam-2584	5	21	,	,	PUNCT
ejpam-2584	5	22	kannan	kannan	PROPN
ejpam-2584	5	23	’s	’s	PROPN
ejpam-2584	5	24	,	,	PUNCT
ejpam-2584	5	25	chatterjea	chatterjea	PROPN
ejpam-2584	5	26	’s	’s	NOUN
ejpam-2584	5	27	,	,	PUNCT
ejpam-2584	5	28	bianciari	bianciari	PROPN
ejpam-2584	5	29	’s	’s	PART
ejpam-2584	5	30	fixed	fix	VERB
ejpam-2584	5	31	point	point	NOUN
ejpam-2584	5	32	theorems	theorem	NOUN
ejpam-2584	5	33	are	be	AUX
ejpam-2584	5	34	established	establish	VERB
ejpam-2584	5	35	for	for	ADP
ejpam-2584	5	36	concept	concept	NOUN
ejpam-2584	5	37	of	of	ADP
ejpam-2584	5	38	partial	partial	ADJ
ejpam-2584	5	39	metric	metric	ADJ
ejpam-2584	5	40	space	space	NOUN
ejpam-2584	5	41	.	.	PUNCT
ejpam-2584	6	1	2010	2010	NUM
ejpam-2584	6	2	mathematics	mathematic	NOUN
ejpam-2584	6	3	subject	subject	NOUN
ejpam-2584	6	4	classifications	classification	NOUN
ejpam-2584	6	5	:	:	PUNCT
ejpam-2584	6	6	47h10	47h10	NUM
ejpam-2584	6	7	,	,	PUNCT
ejpam-2584	6	8	54h25	54h25	NUM
ejpam-2584	6	9	key	key	ADJ
ejpam-2584	6	10	words	word	NOUN
ejpam-2584	6	11	and	and	CCONJ
ejpam-2584	6	12	phrases	phrase	NOUN
ejpam-2584	6	13	:	:	PUNCT
ejpam-2584	6	14	fixed	fix	VERB
ejpam-2584	6	15	point	point	NOUN
ejpam-2584	6	16	,	,	PUNCT
ejpam-2584	6	17	kannan	kannan	PROPN
ejpam-2584	6	18	fixed	fix	VERB
ejpam-2584	6	19	point	point	NOUN
ejpam-2584	6	20	theorem	theorem	VERB
ejpam-2584	6	21	,	,	PUNCT
ejpam-2584	6	22	chatterjea	chatterjea	ADJ
ejpam-2584	6	23	fixed	fix	VERB
ejpam-2584	6	24	point	point	NOUN
ejpam-2584	6	25	theorem	theorem	VERB
ejpam-2584	6	26	,	,	PUNCT
ejpam-2584	6	27	contraction	contraction	NOUN
ejpam-2584	6	28	mappings	mapping	NOUN
ejpam-2584	6	29	,	,	PUNCT
ejpam-2584	6	30	tf	tf	PROPN
ejpam-2584	6	31	-contraction	-contraction	NOUN
ejpam-2584	6	32	,	,	PUNCT
ejpam-2584	6	33	partial	partial	ADJ
ejpam-2584	6	34	metric	metric	ADJ
ejpam-2584	6	35	space	space	NOUN
ejpam-2584	6	36	1	1	NUM
ejpam-2584	6	37	.	.	PUNCT
ejpam-2584	7	1	introduction	introduction	NOUN
ejpam-2584	7	2	and	and	CCONJ
ejpam-2584	7	3	preliminaries	preliminary	NOUN
ejpam-2584	7	4	the	the	DET
ejpam-2584	7	5	notion	notion	NOUN
ejpam-2584	7	6	of	of	ADP
ejpam-2584	7	7	partial	partial	ADJ
ejpam-2584	7	8	metric	metric	ADJ
ejpam-2584	7	9	space	space	NOUN
ejpam-2584	7	10	was	be	AUX
ejpam-2584	7	11	introduced	introduce	VERB
ejpam-2584	7	12	by	by	ADP
ejpam-2584	7	13	matthews	matthews	PROPN
ejpam-2584	7	14	in	in	ADP
ejpam-2584	7	15	1992	1992	NUM
ejpam-2584	7	16	[	[	X
ejpam-2584	7	17	2	2	NUM
ejpam-2584	7	18	]	]	PUNCT
ejpam-2584	7	19	.	.	PUNCT
ejpam-2584	8	1	a	a	DET
ejpam-2584	8	2	partial	partial	ADJ
ejpam-2584	8	3	metric	metric	NOUN
ejpam-2584	8	4	is	be	AUX
ejpam-2584	8	5	a	a	DET
ejpam-2584	8	6	extension	extension	NOUN
ejpam-2584	8	7	of	of	ADP
ejpam-2584	8	8	metric	metric	NOUN
ejpam-2584	8	9	by	by	ADP
ejpam-2584	8	10	replacing	replace	VERB
ejpam-2584	8	11	the	the	DET
ejpam-2584	8	12	condition	condition	NOUN
ejpam-2584	8	13	d	d	NOUN
ejpam-2584	8	14	(	(	PUNCT
ejpam-2584	8	15	x	x	INTJ
ejpam-2584	8	16	,	,	PUNCT
ejpam-2584	8	17	x	x	NOUN
ejpam-2584	8	18	)	)	PUNCT
ejpam-2584	8	19	=	=	SYM
ejpam-2584	8	20	0	0	NUM
ejpam-2584	8	21	of	of	ADP
ejpam-2584	8	22	the	the	DET
ejpam-2584	8	23	(	(	PUNCT
ejpam-2584	8	24	usual	usual	ADJ
ejpam-2584	8	25	)	)	PUNCT
ejpam-2584	8	26	metric	metric	NOUN
ejpam-2584	8	27	with	with	ADP
ejpam-2584	8	28	the	the	DET
ejpam-2584	8	29	inequality	inequality	NOUN
ejpam-2584	8	30	d	d	NOUN
ejpam-2584	8	31	(	(	PUNCT
ejpam-2584	8	32	x	x	INTJ
ejpam-2584	8	33	,	,	PUNCT
ejpam-2584	8	34	x	x	NOUN
ejpam-2584	8	35	)	)	PUNCT
ejpam-2584	8	36	≤	≤	NOUN
ejpam-2584	8	37	d	d	SYM
ejpam-2584	8	38	�	�	PROPN
ejpam-2584	8	39	x	x	SYM
ejpam-2584	8	40	,	,	PUNCT
ejpam-2584	8	41	y	y	PROPN
ejpam-2584	8	42	�	�	PROPN
ejpam-2584	8	43	for	for	ADP
ejpam-2584	8	44	all	all	DET
ejpam-2584	8	45	x	x	SYM
ejpam-2584	8	46	,	,	PUNCT
ejpam-2584	8	47	y	y	PROPN
ejpam-2584	8	48	.	.	PUNCT
ejpam-2584	9	1	also	also	ADV
ejpam-2584	9	2	,	,	PUNCT
ejpam-2584	9	3	this	this	DET
ejpam-2584	9	4	concept	concept	NOUN
ejpam-2584	9	5	provide	provide	VERB
ejpam-2584	9	6	to	to	PART
ejpam-2584	9	7	study	study	VERB
ejpam-2584	9	8	denotational	denotational	ADJ
ejpam-2584	9	9	semantics	semantic	NOUN
ejpam-2584	9	10	of	of	ADP
ejpam-2584	9	11	dataflow	dataflow	ADJ
ejpam-2584	9	12	networks	network	NOUN
ejpam-2584	9	13	[	[	X
ejpam-2584	9	14	1–4	1–4	NOUN
ejpam-2584	9	15	]	]	X
ejpam-2584	9	16	.	.	PUNCT
ejpam-2584	10	1	matthews	matthews	PROPN
ejpam-2584	10	2	gave	give	VERB
ejpam-2584	10	3	some	some	DET
ejpam-2584	10	4	basic	basic	ADJ
ejpam-2584	10	5	definitions	definition	NOUN
ejpam-2584	10	6	and	and	CCONJ
ejpam-2584	10	7	properties	property	NOUN
ejpam-2584	10	8	on	on	ADP
ejpam-2584	10	9	partial	partial	ADJ
ejpam-2584	10	10	metric	metric	ADJ
ejpam-2584	10	11	space	space	NOUN
ejpam-2584	10	12	such	such	ADJ
ejpam-2584	10	13	as	as	ADP
ejpam-2584	10	14	cauchy	cauchy	NOUN
ejpam-2584	10	15	sequence	sequence	NOUN
ejpam-2584	10	16	,	,	PUNCT
ejpam-2584	10	17	convergent	convergent	NOUN
ejpam-2584	10	18	sequence	sequence	NOUN
ejpam-2584	10	19	etc	etc	X
ejpam-2584	10	20	.	.	X
ejpam-2584	11	1	one	one	NUM
ejpam-2584	11	2	of	of	ADP
ejpam-2584	11	3	the	the	DET
ejpam-2584	11	4	most	most	ADV
ejpam-2584	11	5	interesting	interesting	ADJ
ejpam-2584	11	6	properties	property	NOUN
ejpam-2584	11	7	of	of	ADP
ejpam-2584	11	8	this	this	DET
ejpam-2584	11	9	space	space	NOUN
ejpam-2584	11	10	is	be	AUX
ejpam-2584	11	11	the	the	DET
ejpam-2584	11	12	self	self	NOUN
ejpam-2584	11	13	-	-	PUNCT
ejpam-2584	11	14	distance	distance	NOUN
ejpam-2584	11	15	(	(	PUNCT
ejpam-2584	11	16	p	p	X
ejpam-2584	11	17	(	(	PUNCT
ejpam-2584	11	18	x	x	INTJ
ejpam-2584	11	19	,	,	PUNCT
ejpam-2584	11	20	x	x	NOUN
ejpam-2584	11	21	)	)	PUNCT
ejpam-2584	11	22	)	)	PUNCT
ejpam-2584	11	23	for	for	ADP
ejpam-2584	11	24	any	any	DET
ejpam-2584	11	25	point	point	NOUN
ejpam-2584	11	26	may	may	AUX
ejpam-2584	11	27	not	not	PART
ejpam-2584	11	28	be	be	AUX
ejpam-2584	11	29	zero	zero	NUM
ejpam-2584	11	30	.	.	PUNCT
ejpam-2584	12	1	he	he	PRON
ejpam-2584	12	2	also	also	ADV
ejpam-2584	12	3	introduced	introduce	VERB
ejpam-2584	12	4	the	the	DET
ejpam-2584	12	5	first	first	ADJ
ejpam-2584	12	6	fixed	fix	VERB
ejpam-2584	12	7	point	point	NOUN
ejpam-2584	12	8	theorem	theorem	VERB
ejpam-2584	12	9	that	that	PRON
ejpam-2584	12	10	re	re	VERB
ejpam-2584	12	11	-	-	VERB
ejpam-2584	12	12	named	name	VERB
ejpam-2584	12	13	partial	partial	ADJ
ejpam-2584	12	14	contraction	contraction	NOUN
ejpam-2584	12	15	mapping	mapping	NOUN
ejpam-2584	12	16	theorem	theorem	VERB
ejpam-2584	12	17	.	.	PUNCT
ejpam-2584	13	1	due	due	ADP
ejpam-2584	13	2	to	to	ADP
ejpam-2584	13	3	importance	importance	NOUN
ejpam-2584	13	4	of	of	ADP
ejpam-2584	13	5	the	the	DET
ejpam-2584	13	6	fixed	fix	VERB
ejpam-2584	13	7	point	point	NOUN
ejpam-2584	13	8	theory	theory	NOUN
ejpam-2584	13	9	it	it	PRON
ejpam-2584	13	10	is	be	AUX
ejpam-2584	13	11	very	very	ADV
ejpam-2584	13	12	interesting	interesting	ADJ
ejpam-2584	13	13	to	to	PART
ejpam-2584	13	14	study	study	VERB
ejpam-2584	13	15	fixed	fix	VERB
ejpam-2584	13	16	point	point	NOUN
ejpam-2584	13	17	theorems	theorem	NOUN
ejpam-2584	13	18	on	on	ADP
ejpam-2584	13	19	different	different	ADJ
ejpam-2584	13	20	concepts	concept	NOUN
ejpam-2584	13	21	.	.	PUNCT
ejpam-2584	14	1	recently	recently	ADV
ejpam-2584	14	2	,	,	PUNCT
ejpam-2584	14	3	many	many	ADJ
ejpam-2584	14	4	mathematicians	mathematician	NOUN
ejpam-2584	14	5	have	have	AUX
ejpam-2584	14	6	studied	study	VERB
ejpam-2584	14	7	generalized	generalized	ADJ
ejpam-2584	14	8	fixed	fix	VERB
ejpam-2584	14	9	point	point	NOUN
ejpam-2584	14	10	theorems	theorem	VERB
ejpam-2584	14	11	that	that	SCONJ
ejpam-2584	14	12	arising	arise	VERB
ejpam-2584	14	13	from	from	ADP
ejpam-2584	14	14	concept	concept	NOUN
ejpam-2584	14	15	of	of	ADP
ejpam-2584	14	16	partial	partial	ADJ
ejpam-2584	14	17	metric	metric	ADJ
ejpam-2584	14	18	space	space	NOUN
ejpam-2584	14	19	and	and	CCONJ
ejpam-2584	14	20	the	the	DET
ejpam-2584	14	21	authors	author	NOUN
ejpam-2584	14	22	obtained	obtain	VERB
ejpam-2584	14	23	some	some	DET
ejpam-2584	14	24	useful	useful	ADJ
ejpam-2584	14	25	results	result	NOUN
ejpam-2584	14	26	[	[	X
ejpam-2584	14	27	8	8	NUM
ejpam-2584	14	28	,	,	PUNCT
ejpam-2584	14	29	9	9	NUM
ejpam-2584	14	30	]	]	PUNCT
ejpam-2584	14	31	.	.	PUNCT
ejpam-2584	15	1	now	now	ADV
ejpam-2584	15	2	,	,	PUNCT
ejpam-2584	15	3	we	we	PRON
ejpam-2584	15	4	give	give	VERB
ejpam-2584	15	5	some	some	DET
ejpam-2584	15	6	basic	basic	ADJ
ejpam-2584	15	7	structures	structure	NOUN
ejpam-2584	15	8	and	and	CCONJ
ejpam-2584	15	9	results	result	NOUN
ejpam-2584	15	10	on	on	ADP
ejpam-2584	15	11	the	the	DET
ejpam-2584	15	12	concept	concept	NOUN
ejpam-2584	15	13	of	of	ADP
ejpam-2584	15	14	partial	partial	ADJ
ejpam-2584	15	15	metric	metric	ADJ
ejpam-2584	15	16	space	space	NOUN
ejpam-2584	15	17	.	.	PUNCT
ejpam-2584	16	1	definition	definition	NOUN
ejpam-2584	16	2	1	1	NUM
ejpam-2584	16	3	(	(	PUNCT
ejpam-2584	16	4	[	[	X
ejpam-2584	16	5	1	1	NUM
ejpam-2584	16	6	]	]	PUNCT
ejpam-2584	16	7	)	)	PUNCT
ejpam-2584	16	8	.	.	PUNCT
ejpam-2584	17	1	let	let	VERB
ejpam-2584	17	2	x	x	PRON
ejpam-2584	17	3	be	be	AUX
ejpam-2584	17	4	a	a	DET
ejpam-2584	17	5	nonempty	nonempty	ADV
ejpam-2584	17	6	set	set	VERB
ejpam-2584	17	7	and	and	CCONJ
ejpam-2584	17	8	p	p	X
ejpam-2584	17	9	:	:	PUNCT
ejpam-2584	17	10	x	x	PUNCT
ejpam-2584	17	11	×	×	NOUN
ejpam-2584	17	12	x	x	INTJ
ejpam-2584	17	13	→	→	X
ejpam-2584	18	1	[	[	X
ejpam-2584	18	2	0,∞	0,∞	NOUN
ejpam-2584	18	3	)	)	PUNCT
ejpam-2584	18	4	be	be	VERB
ejpam-2584	18	5	such	such	ADJ
ejpam-2584	18	6	that	that	SCONJ
ejpam-2584	18	7	for	for	SCONJ
ejpam-2584	18	8	all	all	DET
ejpam-2584	18	9	x	x	SYM
ejpam-2584	18	10	,	,	PUNCT
ejpam-2584	18	11	y	y	PROPN
ejpam-2584	18	12	,	,	PUNCT
ejpam-2584	18	13	z	z	NOUN
ejpam-2584	18	14	∈	∈	PROPN
ejpam-2584	18	15	x	x	PUNCT
ejpam-2584	18	16	the	the	DET
ejpam-2584	18	17	followings	following	NOUN
ejpam-2584	18	18	are	be	AUX
ejpam-2584	18	19	satisfied	satisfied	ADJ
ejpam-2584	18	20	:	:	PUNCT
ejpam-2584	18	21	∗corresponding	∗corresponde	VERB
ejpam-2584	18	22	author	author	NOUN
ejpam-2584	18	23	.	.	PUNCT
ejpam-2584	19	1	email	email	NOUN
ejpam-2584	19	2	addresses	address	NOUN
ejpam-2584	19	3	:	:	PUNCT
ejpam-2584	20	1	mehmetkir04@gmail.com	mehmetkir04@gmail.com	X
ejpam-2584	20	2	(	(	PUNCT
ejpam-2584	20	3	m.	m.	PROPN
ejpam-2584	20	4	kir	kir	PROPN
ejpam-2584	20	5	)	)	PUNCT
ejpam-2584	20	6	,	,	PUNCT
ejpam-2584	20	7	hukmu@atauni.edu.tr	hukmu@atauni.edu.tr	PROPN
ejpam-2584	20	8	(	(	PUNCT
ejpam-2584	20	9	h.	h.	PROPN
ejpam-2584	20	10	kiziltunc	kiziltunc	PROPN
ejpam-2584	20	11	)	)	PUNCT
ejpam-2584	20	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2584	21	1	443	443	NUM
ejpam-2584	22	1	c	c	X
ejpam-2584	22	2	©	©	PROPN
ejpam-2584	22	3	2016	2016	NUM
ejpam-2584	22	4	ejpam	ejpam	VERB
ejpam-2584	22	5	all	all	DET
ejpam-2584	22	6	rights	right	NOUN
ejpam-2584	22	7	reserved	reserve	VERB
ejpam-2584	22	8	.	.	PUNCT
ejpam-2584	23	1	m.	m.	PROPN
ejpam-2584	23	2	kir	kir	PROPN
ejpam-2584	23	3	,	,	PUNCT
ejpam-2584	23	4	h.	h.	PROPN
ejpam-2584	23	5	kiziltunc	kiziltunc	PROPN
ejpam-2584	23	6	/	/	SYM
ejpam-2584	23	7	eur	eur	PROPN
ejpam-2584	23	8	.	.	PUNCT
ejpam-2584	24	1	j.	j.	PROPN
ejpam-2584	24	2	pure	pure	PROPN
ejpam-2584	24	3	appl	appl	PROPN
ejpam-2584	24	4	.	.	PROPN
ejpam-2584	24	5	math	math	PROPN
ejpam-2584	24	6	,	,	PUNCT
ejpam-2584	24	7	9	9	NUM
ejpam-2584	24	8	(	(	PUNCT
ejpam-2584	24	9	2016	2016	NUM
ejpam-2584	24	10	)	)	PUNCT
ejpam-2584	24	11	,	,	PUNCT
ejpam-2584	24	12	443	443	NUM
ejpam-2584	24	13	-	-	SYM
ejpam-2584	24	14	451	451	NUM
ejpam-2584	24	15	444	444	NUM
ejpam-2584	24	16	p1	p1	NOUN
ejpam-2584	24	17	)	)	PUNCT
ejpam-2584	24	18	x	x	X
ejpam-2584	25	1	=	=	PUNCT
ejpam-2584	25	2	y	y	PROPN
ejpam-2584	25	3	if	if	SCONJ
ejpam-2584	25	4	and	and	CCONJ
ejpam-2584	25	5	only	only	ADV
ejpam-2584	25	6	if	if	SCONJ
ejpam-2584	25	7	p	p	X
ejpam-2584	25	8	(	(	PUNCT
ejpam-2584	25	9	x	x	INTJ
ejpam-2584	25	10	,	,	PUNCT
ejpam-2584	25	11	x	x	NOUN
ejpam-2584	25	12	)	)	PUNCT
ejpam-2584	25	13	=	=	SYM
ejpam-2584	26	1	p	p	PROPN
ejpam-2584	26	2	�	�	PROPN
ejpam-2584	26	3	y	y	PROPN
ejpam-2584	26	4	,	,	PUNCT
ejpam-2584	26	5	y	y	PROPN
ejpam-2584	26	6	�	�	PROPN
ejpam-2584	26	7	=	=	PROPN
ejpam-2584	26	8	p	p	X
ejpam-2584	26	9	�	�	PROPN
ejpam-2584	26	10	x	x	SYM
ejpam-2584	26	11	,	,	PUNCT
ejpam-2584	26	12	y	y	PROPN
ejpam-2584	26	13	�	�	PROPN
ejpam-2584	26	14	,	,	PUNCT
ejpam-2584	26	15	p2	p2	PROPN
ejpam-2584	26	16	)	)	PUNCT
ejpam-2584	26	17	p	p	NOUN
ejpam-2584	26	18	(	(	PUNCT
ejpam-2584	26	19	x	x	INTJ
ejpam-2584	26	20	,	,	PUNCT
ejpam-2584	26	21	x)≤	x)≤	PROPN
ejpam-2584	27	1	p	p	PROPN
ejpam-2584	27	2	�	�	PROPN
ejpam-2584	27	3	x	x	SYM
ejpam-2584	27	4	,	,	PUNCT
ejpam-2584	27	5	y	y	PROPN
ejpam-2584	27	6	�	�	PROPN
ejpam-2584	27	7	,	,	PUNCT
ejpam-2584	27	8	p3	p3	PROPN
ejpam-2584	27	9	)	)	PUNCT
ejpam-2584	28	1	p	p	X
ejpam-2584	28	2	�	�	PROPN
ejpam-2584	28	3	x	x	SYM
ejpam-2584	28	4	,	,	PUNCT
ejpam-2584	28	5	y	y	PROPN
ejpam-2584	28	6	�	�	PROPN
ejpam-2584	28	7	=	=	PROPN
ejpam-2584	28	8	p	p	PROPN
ejpam-2584	28	9	�	�	PROPN
ejpam-2584	28	10	y	y	PROPN
ejpam-2584	28	11	,	,	PUNCT
ejpam-2584	28	12	x	x	PROPN
ejpam-2584	28	13	�	�	PROPN
ejpam-2584	28	14	,	,	PUNCT
ejpam-2584	28	15	p4	p4	ADJ
ejpam-2584	28	16	)	)	PUNCT
ejpam-2584	28	17	p	p	NOUN
ejpam-2584	28	18	�	�	PROPN
ejpam-2584	28	19	x	x	SYM
ejpam-2584	28	20	,	,	PUNCT
ejpam-2584	28	21	y	y	PROPN
ejpam-2584	28	22	�	�	PROPN
ejpam-2584	28	23	≤	≤	PROPN
ejpam-2584	29	1	p	p	X
ejpam-2584	29	2	(	(	PUNCT
ejpam-2584	29	3	x	x	INTJ
ejpam-2584	29	4	,	,	PUNCT
ejpam-2584	29	5	z	z	NOUN
ejpam-2584	29	6	)	)	PUNCT
ejpam-2584	30	1	+	+	CCONJ
ejpam-2584	30	2	p	p	X
ejpam-2584	30	3	�	�	PROPN
ejpam-2584	30	4	z	z	PROPN
ejpam-2584	30	5	,	,	PUNCT
ejpam-2584	30	6	y	y	PROPN
ejpam-2584	30	7	�	�	PROPN
ejpam-2584	30	8	−	−	PROPN
ejpam-2584	31	1	p	p	X
ejpam-2584	31	2	(	(	PUNCT
ejpam-2584	31	3	z	z	PROPN
ejpam-2584	31	4	,	,	PUNCT
ejpam-2584	31	5	z	z	NOUN
ejpam-2584	31	6	)	)	PUNCT
ejpam-2584	31	7	.	.	PUNCT
ejpam-2584	32	1	then	then	ADV
ejpam-2584	32	2	,	,	PUNCT
ejpam-2584	32	3	p	p	NOUN
ejpam-2584	32	4	is	be	AUX
ejpam-2584	32	5	called	call	VERB
ejpam-2584	32	6	partial	partial	ADJ
ejpam-2584	32	7	metric	metric	NOUN
ejpam-2584	32	8	on	on	ADP
ejpam-2584	32	9	x	x	PUNCT
ejpam-2584	32	10	and	and	CCONJ
ejpam-2584	32	11	the	the	DET
ejpam-2584	32	12	pair	pair	NOUN
ejpam-2584	32	13	�	�	PROPN
ejpam-2584	32	14	x	x	INTJ
ejpam-2584	32	15	,	,	PUNCT
ejpam-2584	32	16	p	p	PROPN
ejpam-2584	32	17	�	�	PROPN
ejpam-2584	32	18	is	be	AUX
ejpam-2584	32	19	called	call	VERB
ejpam-2584	32	20	partial	partial	ADJ
ejpam-2584	32	21	metric	metric	ADJ
ejpam-2584	32	22	space	space	NOUN
ejpam-2584	32	23	.	.	PUNCT
ejpam-2584	33	1	remark	remark	PROPN
ejpam-2584	33	2	1	1	NUM
ejpam-2584	33	3	.	.	PUNCT
ejpam-2584	34	1	it	it	PRON
ejpam-2584	34	2	is	be	AUX
ejpam-2584	34	3	clear	clear	ADJ
ejpam-2584	34	4	that	that	SCONJ
ejpam-2584	34	5	if	if	SCONJ
ejpam-2584	34	6	p	p	X
ejpam-2584	34	7	(	(	PUNCT
ejpam-2584	34	8	x	x	INTJ
ejpam-2584	34	9	,	,	PUNCT
ejpam-2584	34	10	x	x	NOUN
ejpam-2584	34	11	)	)	PUNCT
ejpam-2584	34	12	=	=	SYM
ejpam-2584	34	13	0	0	NUM
ejpam-2584	34	14	,	,	PUNCT
ejpam-2584	34	15	then	then	ADV
ejpam-2584	34	16	x	x	X
ejpam-2584	34	17	=	=	PUNCT
ejpam-2584	34	18	y.	y.	PROPN
ejpam-2584	34	19	but	but	CCONJ
ejpam-2584	34	20	,	,	PUNCT
ejpam-2584	34	21	on	on	ADP
ejpam-2584	34	22	the	the	DET
ejpam-2584	34	23	contrary	contrary	ADJ
ejpam-2584	34	24	p	p	NOUN
ejpam-2584	34	25	(	(	PUNCT
ejpam-2584	34	26	x	x	INTJ
ejpam-2584	34	27	,	,	PUNCT
ejpam-2584	34	28	x	x	NOUN
ejpam-2584	34	29	)	)	PUNCT
ejpam-2584	34	30	need	need	AUX
ejpam-2584	34	31	not	not	PART
ejpam-2584	34	32	be	be	AUX
ejpam-2584	34	33	zero	zero	NUM
ejpam-2584	34	34	.	.	PUNCT
ejpam-2584	34	35	example	example	NOUN
ejpam-2584	35	1	1	1	NUM
ejpam-2584	35	2	.	.	PUNCT
ejpam-2584	36	1	[	[	X
ejpam-2584	36	2	[	[	X
ejpam-2584	36	3	8	8	NUM
ejpam-2584	36	4	]	]	X
ejpam-2584	36	5	]	]	X
ejpam-2584	36	6	a	a	X
ejpam-2584	36	7	)	)	PUNCT
ejpam-2584	36	8	let	let	VERB
ejpam-2584	36	9	x	x	PUNCT
ejpam-2584	36	10	=	=	PRON
ejpam-2584	36	11	{	{	PUNCT
ejpam-2584	36	12	[	[	X
ejpam-2584	36	13	a	a	X
ejpam-2584	36	14	,	,	PUNCT
ejpam-2584	36	15	b	b	NOUN
ejpam-2584	36	16	]	]	X
ejpam-2584	36	17	:	:	PUNCT
ejpam-2584	36	18	a	a	DET
ejpam-2584	36	19	,	,	PUNCT
ejpam-2584	36	20	b	b	X
ejpam-2584	36	21	∈	∈	PROPN
ejpam-2584	36	22	r	r	NOUN
ejpam-2584	36	23	,	,	PUNCT
ejpam-2584	36	24	a	a	DET
ejpam-2584	36	25	≤	≤	PROPN
ejpam-2584	36	26	b	b	NOUN
ejpam-2584	36	27	}	}	PUNCT
ejpam-2584	36	28	and	and	CCONJ
ejpam-2584	36	29	define	define	VERB
ejpam-2584	36	30	p	p	X
ejpam-2584	36	31	(	(	PUNCT
ejpam-2584	36	32	[	[	X
ejpam-2584	36	33	a	a	X
ejpam-2584	36	34	,	,	PUNCT
ejpam-2584	36	35	b	b	NOUN
ejpam-2584	36	36	]	]	PUNCT
ejpam-2584	36	37	,	,	PUNCT
ejpam-2584	37	1	[	[	X
ejpam-2584	37	2	c	c	X
ejpam-2584	37	3	,	,	PUNCT
ejpam-2584	37	4	d	d	NOUN
ejpam-2584	37	5	]	]	X
ejpam-2584	37	6	)	)	PUNCT
ejpam-2584	37	7	=	=	X
ejpam-2584	37	8	max	max	X
ejpam-2584	37	9	{	{	PUNCT
ejpam-2584	37	10	b	b	PROPN
ejpam-2584	37	11	,	,	PUNCT
ejpam-2584	37	12	d}−min	d}−min	PROPN
ejpam-2584	37	13	{	{	PUNCT
ejpam-2584	37	14	a	a	X
ejpam-2584	37	15	,	,	PUNCT
ejpam-2584	37	16	c	c	NOUN
ejpam-2584	37	17	}	}	PUNCT
ejpam-2584	37	18	.	.	PUNCT
ejpam-2584	38	1	then	then	ADV
ejpam-2584	38	2	,	,	PUNCT
ejpam-2584	38	3	�	�	PROPN
ejpam-2584	38	4	x	x	SYM
ejpam-2584	38	5	,	,	PUNCT
ejpam-2584	38	6	p	p	PROPN
ejpam-2584	38	7	�	�	PROPN
ejpam-2584	38	8	is	be	AUX
ejpam-2584	38	9	a	a	DET
ejpam-2584	38	10	partial	partial	ADJ
ejpam-2584	38	11	metric	metric	ADJ
ejpam-2584	38	12	space	space	NOUN
ejpam-2584	38	13	.	.	PUNCT
ejpam-2584	39	1	b	b	X
ejpam-2584	39	2	)	)	PUNCT
ejpam-2584	39	3	let	let	VERB
ejpam-2584	39	4	x	x	PUNCT
ejpam-2584	39	5	=	=	PUNCT
ejpam-2584	40	1	[	[	X
ejpam-2584	40	2	0,∞	0,∞	NUM
ejpam-2584	40	3	)	)	PUNCT
ejpam-2584	40	4	and	and	CCONJ
ejpam-2584	40	5	define	define	VERB
ejpam-2584	40	6	p	p	PROPN
ejpam-2584	40	7	�	�	PROPN
ejpam-2584	40	8	x	x	SYM
ejpam-2584	40	9	,	,	PUNCT
ejpam-2584	40	10	y	y	PROPN
ejpam-2584	40	11	�	�	PROPN
ejpam-2584	40	12	=	=	NUM
ejpam-2584	40	13	max	max	PROPN
ejpam-2584	40	14	�	�	PROPN
ejpam-2584	40	15	x	x	SYM
ejpam-2584	40	16	,	,	PUNCT
ejpam-2584	40	17	y	y	PROPN
ejpam-2584	40	18	.	.	PUNCT
ejpam-2584	41	1	then	then	ADV
ejpam-2584	41	2	,	,	PUNCT
ejpam-2584	41	3	�	�	PROPN
ejpam-2584	41	4	x	x	SYM
ejpam-2584	41	5	,	,	PUNCT
ejpam-2584	41	6	p	p	PROPN
ejpam-2584	41	7	�	�	PROPN
ejpam-2584	41	8	is	be	AUX
ejpam-2584	41	9	a	a	DET
ejpam-2584	41	10	partial	partial	ADJ
ejpam-2584	41	11	metric	metric	ADJ
ejpam-2584	41	12	space	space	NOUN
ejpam-2584	41	13	.	.	PUNCT
ejpam-2584	42	1	note	note	VERB
ejpam-2584	42	2	that	that	SCONJ
ejpam-2584	42	3	each	each	DET
ejpam-2584	42	4	partial	partial	ADJ
ejpam-2584	42	5	metric	metric	NOUN
ejpam-2584	42	6	p	p	NOUN
ejpam-2584	42	7	that	that	PRON
ejpam-2584	42	8	defined	define	VERB
ejpam-2584	42	9	on	on	ADP
ejpam-2584	42	10	x	x	PUNCT
ejpam-2584	42	11	generates	generate	VERB
ejpam-2584	42	12	a	a	DET
ejpam-2584	42	13	t0	t0	PROPN
ejpam-2584	42	14	topology	topology	NOUN
ejpam-2584	42	15	τ	τ	PROPN
ejpam-2584	42	16	that	that	PRON
ejpam-2584	42	17	has	have	VERB
ejpam-2584	42	18	a	a	DET
ejpam-2584	42	19	base	base	NOUN
ejpam-2584	42	20	the	the	DET
ejpam-2584	42	21	family	family	NOUN
ejpam-2584	42	22	of	of	ADP
ejpam-2584	42	23	open	open	ADJ
ejpam-2584	42	24	balls	ball	NOUN
ejpam-2584	42	25	{	{	PUNCT
ejpam-2584	42	26	b	b	X
ejpam-2584	42	27	(	(	PUNCT
ejpam-2584	42	28	x	x	PROPN
ejpam-2584	42	29	,	,	PUNCT
ejpam-2584	42	30	ε	ε	PROPN
ejpam-2584	42	31	)	)	PUNCT
ejpam-2584	42	32	:	:	PUNCT
ejpam-2584	43	1	x	x	PUNCT
ejpam-2584	43	2	∈	∈	NOUN
ejpam-2584	43	3	x	x	X
ejpam-2584	43	4	,	,	PUNCT
ejpam-2584	43	5	ε	ε	PROPN
ejpam-2584	43	6	>	>	X
ejpam-2584	43	7	0	0	NUM
ejpam-2584	43	8	}	}	PUNCT
ejpam-2584	43	9	such	such	ADJ
ejpam-2584	43	10	that	that	DET
ejpam-2584	43	11	b	b	X
ejpam-2584	43	12	(	(	PUNCT
ejpam-2584	43	13	x	x	PROPN
ejpam-2584	43	14	,	,	PUNCT
ejpam-2584	43	15	ε	ε	PROPN
ejpam-2584	43	16	)	)	PUNCT
ejpam-2584	43	17	=	=	SYM
ejpam-2584	43	18	�	�	PROPN
ejpam-2584	43	19	y	y	PROPN
ejpam-2584	43	20	∈	∈	PROPN
ejpam-2584	43	21	x	x	X
ejpam-2584	43	22	:	:	PUNCT
ejpam-2584	43	23	p	p	X
ejpam-2584	43	24	�	�	PROPN
ejpam-2584	43	25	x	x	SYM
ejpam-2584	43	26	,	,	PUNCT
ejpam-2584	43	27	y	y	PROPN
ejpam-2584	43	28	�	�	PROPN
ejpam-2584	43	29	<	<	X
ejpam-2584	43	30	ε+	ε+	X
ejpam-2584	43	31	p	p	X
ejpam-2584	43	32	(	(	PUNCT
ejpam-2584	43	33	x	x	INTJ
ejpam-2584	43	34	,	,	PUNCT
ejpam-2584	43	35	x	x	X
ejpam-2584	43	36	)	)	PUNCT
ejpam-2584	43	37	remark	remark	NOUN
ejpam-2584	43	38	2	2	NUM
ejpam-2584	43	39	.	.	PUNCT
ejpam-2584	44	1	[	[	X
ejpam-2584	44	2	9	9	NUM
ejpam-2584	44	3	]	]	PUNCT
ejpam-2584	44	4	let	let	VERB
ejpam-2584	44	5	�	�	PROPN
ejpam-2584	44	6	x	x	SYM
ejpam-2584	44	7	,	,	PUNCT
ejpam-2584	44	8	p	p	PROPN
ejpam-2584	44	9	�	�	PROPN
ejpam-2584	44	10	be	be	AUX
ejpam-2584	44	11	a	a	DET
ejpam-2584	44	12	partial	partial	ADJ
ejpam-2584	44	13	metric	metric	ADJ
ejpam-2584	44	14	space	space	NOUN
ejpam-2584	44	15	.	.	PUNCT
ejpam-2584	45	1	m1	m1	NOUN
ejpam-2584	45	2	)	)	PUNCT
ejpam-2584	45	3	the	the	DET
ejpam-2584	45	4	function	function	NOUN
ejpam-2584	45	5	ds	ds	NOUN
ejpam-2584	45	6	:	:	PUNCT
ejpam-2584	45	7	x	x	X
ejpam-2584	45	8	→	→	SYM
ejpam-2584	45	9	x	x	PUNCT
ejpam-2584	45	10	defined	define	VERB
ejpam-2584	45	11	by	by	ADP
ejpam-2584	45	12	ds	ds	PRON
ejpam-2584	45	13	�	�	PROPN
ejpam-2584	45	14	x	x	SYM
ejpam-2584	45	15	,	,	PUNCT
ejpam-2584	45	16	y	y	PROPN
ejpam-2584	45	17	�	�	PROPN
ejpam-2584	45	18	=	=	PROPN
ejpam-2584	45	19	2p	2p	NUM
ejpam-2584	45	20	�	�	PROPN
ejpam-2584	45	21	x	x	SYM
ejpam-2584	45	22	,	,	PUNCT
ejpam-2584	45	23	y	y	PROPN
ejpam-2584	45	24	�	�	PROPN
ejpam-2584	46	1	−	−	PROPN
ejpam-2584	47	1	p	p	NOUN
ejpam-2584	47	2	(	(	PUNCT
ejpam-2584	47	3	x	x	INTJ
ejpam-2584	47	4	,	,	PUNCT
ejpam-2584	47	5	x)−	x)−	PROPN
ejpam-2584	47	6	p	p	PROPN
ejpam-2584	47	7	�	�	PROPN
ejpam-2584	47	8	y	y	PROPN
ejpam-2584	47	9	,	,	PUNCT
ejpam-2584	47	10	y	y	PROPN
ejpam-2584	47	11	�	�	PROPN
ejpam-2584	47	12	is	be	AUX
ejpam-2584	47	13	a	a	DET
ejpam-2584	47	14	(	(	PUNCT
ejpam-2584	47	15	usual	usual	ADJ
ejpam-2584	47	16	)	)	PUNCT
ejpam-2584	47	17	metric	metric	NOUN
ejpam-2584	47	18	on	on	ADP
ejpam-2584	47	19	x	x	PUNCT
ejpam-2584	47	20	and	and	CCONJ
ejpam-2584	47	21	(	(	PUNCT
ejpam-2584	47	22	x	x	X
ejpam-2584	47	23	,	,	PUNCT
ejpam-2584	47	24	ds	ds	PROPN
ejpam-2584	47	25	)	)	PUNCT
ejpam-2584	47	26	is	be	AUX
ejpam-2584	47	27	a	a	DET
ejpam-2584	47	28	(	(	PUNCT
ejpam-2584	47	29	usual	usual	ADJ
ejpam-2584	47	30	)	)	PUNCT
ejpam-2584	47	31	metric	metric	ADJ
ejpam-2584	47	32	space	space	NOUN
ejpam-2584	47	33	.	.	PUNCT
ejpam-2584	48	1	m2	m2	PROPN
ejpam-2584	48	2	)	)	PUNCT
ejpam-2584	48	3	the	the	DET
ejpam-2584	48	4	function	function	NOUN
ejpam-2584	48	5	dm	dm	X
ejpam-2584	48	6	:	:	PUNCT
ejpam-2584	48	7	x	x	X
ejpam-2584	48	8	→	→	SYM
ejpam-2584	48	9	x	x	PUNCT
ejpam-2584	48	10	defined	define	VERB
ejpam-2584	48	11	by	by	ADP
ejpam-2584	48	12	dm	dm	PROPN
ejpam-2584	48	13	�	�	PROPN
ejpam-2584	48	14	x	x	SYM
ejpam-2584	48	15	,	,	PUNCT
ejpam-2584	48	16	y	y	PROPN
ejpam-2584	48	17	�	�	PROPN
ejpam-2584	48	18	=	=	NUM
ejpam-2584	48	19	max	max	PROPN
ejpam-2584	48	20	�	�	PROPN
ejpam-2584	48	21	p(x	p(x	PROPN
ejpam-2584	48	22	,	,	PUNCT
ejpam-2584	48	23	y)−	y)−	PROPN
ejpam-2584	48	24	p(x	p(x	PROPN
ejpam-2584	48	25	,	,	PUNCT
ejpam-2584	48	26	x	x	NOUN
ejpam-2584	48	27	)	)	PUNCT
ejpam-2584	48	28	,	,	PUNCT
ejpam-2584	48	29	p(x	p(x	PROPN
ejpam-2584	48	30	,	,	PUNCT
ejpam-2584	48	31	y)−	y)−	PROPN
ejpam-2584	48	32	p(y	p(y	PROPN
ejpam-2584	48	33	,	,	PUNCT
ejpam-2584	48	34	y	y	NOUN
ejpam-2584	48	35	)	)	PUNCT
ejpam-2584	48	36	is	be	AUX
ejpam-2584	48	37	a	a	DET
ejpam-2584	48	38	(	(	PUNCT
ejpam-2584	48	39	usual	usual	ADJ
ejpam-2584	48	40	)	)	PUNCT
ejpam-2584	48	41	metric	metric	NOUN
ejpam-2584	48	42	on	on	ADP
ejpam-2584	48	43	x	x	PUNCT
ejpam-2584	48	44	and	and	CCONJ
ejpam-2584	48	45	�	�	PROPN
ejpam-2584	48	46	x	x	SYM
ejpam-2584	48	47	,	,	PUNCT
ejpam-2584	48	48	dm	dm	PROPN
ejpam-2584	48	49	�	�	PROPN
ejpam-2584	48	50	is	be	AUX
ejpam-2584	48	51	a	a	DET
ejpam-2584	48	52	(	(	PUNCT
ejpam-2584	48	53	usual	usual	ADJ
ejpam-2584	48	54	)	)	PUNCT
ejpam-2584	48	55	metric	metric	ADJ
ejpam-2584	48	56	space	space	NOUN
ejpam-2584	48	57	.	.	PUNCT
ejpam-2584	49	1	corollary	corollary	ADJ
ejpam-2584	49	2	1	1	NUM
ejpam-2584	49	3	(	(	PUNCT
ejpam-2584	49	4	[	[	X
ejpam-2584	49	5	9	9	NUM
ejpam-2584	49	6	]	]	PUNCT
ejpam-2584	49	7	)	)	PUNCT
ejpam-2584	49	8	.	.	PUNCT
ejpam-2584	50	1	let	let	VERB
ejpam-2584	50	2	�	�	PROPN
ejpam-2584	50	3	x	x	SYM
ejpam-2584	50	4	,	,	PUNCT
ejpam-2584	50	5	p	p	PROPN
ejpam-2584	50	6	�	�	PROPN
ejpam-2584	50	7	be	be	AUX
ejpam-2584	50	8	a	a	DET
ejpam-2584	50	9	partial	partial	ADJ
ejpam-2584	50	10	metric	metric	ADJ
ejpam-2584	50	11	space	space	NOUN
ejpam-2584	50	12	.	.	PUNCT
ejpam-2584	51	1	then	then	ADV
ejpam-2584	51	2	,	,	PUNCT
ejpam-2584	51	3	ds	ds	ADJ
ejpam-2584	51	4	and	and	CCONJ
ejpam-2584	51	5	dm	dm	PROPN
ejpam-2584	51	6	are	be	AUX
ejpam-2584	51	7	equivalent	equivalent	ADJ
ejpam-2584	51	8	metric	metric	ADJ
ejpam-2584	51	9	on	on	ADP
ejpam-2584	51	10	x	x	X
ejpam-2584	51	11	.	.	PUNCT
ejpam-2584	52	1	furthermore	furthermore	ADV
ejpam-2584	52	2	,	,	PUNCT
ejpam-2584	52	3	if	if	SCONJ
ejpam-2584	52	4	we	we	PRON
ejpam-2584	52	5	take	take	VERB
ejpam-2584	52	6	�	�	PROPN
ejpam-2584	52	7	x	x	SYM
ejpam-2584	52	8	,	,	PUNCT
ejpam-2584	52	9	p	p	PROPN
ejpam-2584	52	10	�	�	PROPN
ejpam-2584	52	11	as	as	ADP
ejpam-2584	52	12	in	in	ADP
ejpam-2584	52	13	example	example	NOUN
ejpam-2584	52	14	1	1	NUM
ejpam-2584	52	15	,	,	PUNCT
ejpam-2584	52	16	part	part	NOUN
ejpam-2584	52	17	b	b	NOUN
ejpam-2584	52	18	)	)	PUNCT
ejpam-2584	52	19	,	,	PUNCT
ejpam-2584	52	20	we	we	PRON
ejpam-2584	52	21	obtain	obtain	VERB
ejpam-2584	52	22	the	the	DET
ejpam-2584	52	23	following	follow	VERB
ejpam-2584	52	24	equality	equality	NOUN
ejpam-2584	52	25	;	;	PUNCT
ejpam-2584	52	26	dm	dm	PROPN
ejpam-2584	52	27	�	�	PROPN
ejpam-2584	52	28	x	x	SYM
ejpam-2584	52	29	,	,	PUNCT
ejpam-2584	52	30	y	y	PROPN
ejpam-2584	52	31	�	�	PROPN
ejpam-2584	52	32	=	=	PUNCT
ejpam-2584	52	33	ds	ds	PROPN
ejpam-2584	52	34	�	�	PROPN
ejpam-2584	52	35	x	x	SYM
ejpam-2584	52	36	,	,	PUNCT
ejpam-2584	52	37	y	y	PROPN
ejpam-2584	52	38	�	�	PROPN
ejpam-2584	52	39	=	=	SYM
ejpam-2584	52	40	�	�	PROPN
ejpam-2584	52	41	�	�	PROPN
ejpam-2584	52	42	x	x	PROPN
ejpam-2584	52	43	−	−	PROPN
ejpam-2584	52	44	y	y	PROPN
ejpam-2584	52	45	�	�	PROPN
ejpam-2584	52	46	�	�	PROPN
ejpam-2584	52	47	.	.	PUNCT
ejpam-2584	53	1	definition	definition	NOUN
ejpam-2584	53	2	2	2	NUM
ejpam-2584	53	3	(	(	PUNCT
ejpam-2584	53	4	[	[	X
ejpam-2584	53	5	8	8	NUM
ejpam-2584	53	6	]	]	PUNCT
ejpam-2584	53	7	)	)	PUNCT
ejpam-2584	53	8	.	.	PUNCT
ejpam-2584	54	1	let	let	VERB
ejpam-2584	54	2	�	�	PROPN
ejpam-2584	54	3	x	x	SYM
ejpam-2584	54	4	,	,	PUNCT
ejpam-2584	54	5	p	p	PROPN
ejpam-2584	54	6	�	�	PROPN
ejpam-2584	54	7	be	be	AUX
ejpam-2584	54	8	a	a	DET
ejpam-2584	54	9	partial	partial	ADJ
ejpam-2584	54	10	metric	metric	ADJ
ejpam-2584	54	11	space	space	NOUN
ejpam-2584	54	12	.	.	PUNCT
ejpam-2584	55	1	(	(	PUNCT
ejpam-2584	55	2	i	i	NOUN
ejpam-2584	55	3	)	)	PUNCT
ejpam-2584	55	4	a	a	DET
ejpam-2584	55	5	sequence	sequence	NOUN
ejpam-2584	55	6	�	�	PROPN
ejpam-2584	55	7	xn	xn	PROPN
ejpam-2584	55	8	in	in	ADP
ejpam-2584	55	9	�	�	PROPN
ejpam-2584	55	10	x	x	SYM
ejpam-2584	55	11	,	,	PUNCT
ejpam-2584	55	12	p	p	PROPN
ejpam-2584	55	13	�	�	PROPN
ejpam-2584	55	14	converges	converge	VERB
ejpam-2584	55	15	to	to	ADP
ejpam-2584	55	16	x	x	SYM
ejpam-2584	55	17	∈	∈	PROPN
ejpam-2584	55	18	x	x	SYM
ejpam-2584	55	19	if	if	SCONJ
ejpam-2584	56	1	and	and	CCONJ
ejpam-2584	56	2	only	only	ADV
ejpam-2584	56	3	if	if	SCONJ
ejpam-2584	56	4	p	p	X
ejpam-2584	56	5	(	(	PUNCT
ejpam-2584	56	6	x	x	INTJ
ejpam-2584	56	7	,	,	PUNCT
ejpam-2584	56	8	x	x	NOUN
ejpam-2584	56	9	)	)	PUNCT
ejpam-2584	56	10	=	=	SYM
ejpam-2584	56	11	lim	lim	PROPN
ejpam-2584	56	12	n→∞	n→∞	NUM
ejpam-2584	56	13	p	p	PROPN
ejpam-2584	56	14	�	�	PROPN
ejpam-2584	56	15	xn	xn	PROPN
ejpam-2584	56	16	,	,	PUNCT
ejpam-2584	56	17	x	x	PROPN
ejpam-2584	56	18	�	�	PROPN
ejpam-2584	56	19	.	.	PUNCT
ejpam-2584	57	1	m.	m.	PROPN
ejpam-2584	57	2	kir	kir	PROPN
ejpam-2584	57	3	,	,	PUNCT
ejpam-2584	57	4	h.	h.	PROPN
ejpam-2584	57	5	kiziltunc	kiziltunc	PROPN
ejpam-2584	57	6	/	/	SYM
ejpam-2584	57	7	eur	eur	PROPN
ejpam-2584	57	8	.	.	PUNCT
ejpam-2584	58	1	j.	j.	PROPN
ejpam-2584	58	2	pure	pure	PROPN
ejpam-2584	58	3	appl	appl	PROPN
ejpam-2584	58	4	.	.	PROPN
ejpam-2584	58	5	math	math	PROPN
ejpam-2584	58	6	,	,	PUNCT
ejpam-2584	58	7	9	9	NUM
ejpam-2584	58	8	(	(	PUNCT
ejpam-2584	58	9	2016	2016	NUM
ejpam-2584	58	10	)	)	PUNCT
ejpam-2584	58	11	,	,	PUNCT
ejpam-2584	58	12	443	443	NUM
ejpam-2584	58	13	-	-	SYM
ejpam-2584	58	14	451	451	NUM
ejpam-2584	58	15	445	445	NUM
ejpam-2584	58	16	(	(	PUNCT
ejpam-2584	58	17	ii	ii	NOUN
ejpam-2584	58	18	)	)	PUNCT
ejpam-2584	58	19	a	a	DET
ejpam-2584	58	20	sequence	sequence	NOUN
ejpam-2584	58	21	�	�	PROPN
ejpam-2584	58	22	xn	xn	PROPN
ejpam-2584	58	23	in	in	ADP
ejpam-2584	58	24	�	�	PROPN
ejpam-2584	58	25	x	x	SYM
ejpam-2584	58	26	,	,	PUNCT
ejpam-2584	58	27	p	p	PROPN
ejpam-2584	58	28	�	�	PROPN
ejpam-2584	58	29	is	be	AUX
ejpam-2584	58	30	called	call	VERB
ejpam-2584	58	31	a	a	DET
ejpam-2584	58	32	cauchy	cauchy	ADJ
ejpam-2584	58	33	sequence	sequence	NOUN
ejpam-2584	58	34	if	if	SCONJ
ejpam-2584	58	35	and	and	CCONJ
ejpam-2584	58	36	only	only	ADV
ejpam-2584	58	37	if	if	SCONJ
ejpam-2584	58	38	lim	lim	PROPN
ejpam-2584	58	39	n	n	CCONJ
ejpam-2584	58	40	,	,	PUNCT
ejpam-2584	58	41	m→∞	m→∞	NOUN
ejpam-2584	58	42	p	p	PROPN
ejpam-2584	58	43	�	�	PROPN
ejpam-2584	58	44	xn	xn	PROPN
ejpam-2584	58	45	,	,	PUNCT
ejpam-2584	58	46	xm	xm	PROPN
ejpam-2584	58	47	�	�	PROPN
ejpam-2584	58	48	exists	exist	VERB
ejpam-2584	58	49	(	(	PUNCT
ejpam-2584	58	50	and	and	CCONJ
ejpam-2584	58	51	finite	finite	ADJ
ejpam-2584	58	52	)	)	PUNCT
ejpam-2584	58	53	.	.	PUNCT
ejpam-2584	59	1	(	(	PUNCT
ejpam-2584	59	2	iii	iii	X
ejpam-2584	59	3	)	)	PUNCT
ejpam-2584	59	4	a	a	DET
ejpam-2584	59	5	partial	partial	ADJ
ejpam-2584	59	6	metric	metric	ADJ
ejpam-2584	59	7	space	space	NOUN
ejpam-2584	59	8	is	be	AUX
ejpam-2584	59	9	called	call	VERB
ejpam-2584	59	10	complete	complete	ADJ
ejpam-2584	59	11	if	if	SCONJ
ejpam-2584	59	12	every	every	DET
ejpam-2584	59	13	cauchy	cauchy	ADJ
ejpam-2584	59	14	sequence	sequence	NOUN
ejpam-2584	59	15	�	�	PROPN
ejpam-2584	59	16	xn	xn	PROPN
ejpam-2584	59	17	in	in	ADP
ejpam-2584	59	18	x	x	NOUN
ejpam-2584	59	19	converges	converge	NOUN
ejpam-2584	59	20	,	,	PUNCT
ejpam-2584	59	21	with	with	ADP
ejpam-2584	59	22	respect	respect	NOUN
ejpam-2584	59	23	to	to	ADP
ejpam-2584	59	24	τ	τ	PROPN
ejpam-2584	59	25	,	,	PUNCT
ejpam-2584	59	26	to	to	ADP
ejpam-2584	59	27	a	a	DET
ejpam-2584	59	28	point	point	NOUN
ejpam-2584	59	29	x	x	SYM
ejpam-2584	59	30	∈	∈	NOUN
ejpam-2584	59	31	x	x	X
ejpam-2584	59	32	such	such	ADJ
ejpam-2584	59	33	that	that	SCONJ
ejpam-2584	59	34	lim	lim	PROPN
ejpam-2584	59	35	n	n	CCONJ
ejpam-2584	59	36	,	,	PUNCT
ejpam-2584	59	37	m→∞	m→∞	NOUN
ejpam-2584	59	38	p	p	PROPN
ejpam-2584	59	39	�	�	PROPN
ejpam-2584	59	40	xn	xn	PROPN
ejpam-2584	59	41	,	,	PUNCT
ejpam-2584	59	42	xm	xm	PROPN
ejpam-2584	59	43	�	�	PROPN
ejpam-2584	60	1	=	=	PUNCT
ejpam-2584	60	2	p	p	X
ejpam-2584	60	3	(	(	PUNCT
ejpam-2584	60	4	x	x	INTJ
ejpam-2584	60	5	,	,	PUNCT
ejpam-2584	60	6	x	x	NOUN
ejpam-2584	60	7	)	)	PUNCT
ejpam-2584	60	8	.	.	PUNCT
ejpam-2584	61	1	lemma	lemma	PROPN
ejpam-2584	61	2	1	1	NUM
ejpam-2584	61	3	.	.	PUNCT
ejpam-2584	62	1	[	[	X
ejpam-2584	62	2	[	[	X
ejpam-2584	62	3	8	8	NUM
ejpam-2584	62	4	]	]	X
ejpam-2584	62	5	]	]	X
ejpam-2584	62	6	let	let	VERB
ejpam-2584	62	7	�	�	PROPN
ejpam-2584	62	8	x	x	SYM
ejpam-2584	62	9	,	,	PUNCT
ejpam-2584	62	10	p	p	PROPN
ejpam-2584	62	11	�	�	PROPN
ejpam-2584	62	12	be	be	AUX
ejpam-2584	62	13	a	a	DET
ejpam-2584	62	14	partial	partial	ADJ
ejpam-2584	62	15	metric	metric	ADJ
ejpam-2584	62	16	space	space	NOUN
ejpam-2584	62	17	.	.	PUNCT
ejpam-2584	63	1	a	a	DET
ejpam-2584	63	2	)	)	PUNCT
ejpam-2584	63	3	�	�	PROPN
ejpam-2584	63	4	xn	xn	PROPN
ejpam-2584	63	5	is	be	AUX
ejpam-2584	63	6	a	a	DET
ejpam-2584	63	7	cauchy	cauchy	ADJ
ejpam-2584	63	8	sequence	sequence	NOUN
ejpam-2584	63	9	in	in	ADP
ejpam-2584	63	10	�	�	PROPN
ejpam-2584	63	11	x	x	SYM
ejpam-2584	63	12	,	,	PUNCT
ejpam-2584	63	13	p	p	PROPN
ejpam-2584	63	14	�	�	PROPN
ejpam-2584	64	1	if	if	SCONJ
ejpam-2584	64	2	and	and	CCONJ
ejpam-2584	64	3	only	only	ADV
ejpam-2584	64	4	if	if	SCONJ
ejpam-2584	64	5	it	it	PRON
ejpam-2584	64	6	is	be	AUX
ejpam-2584	64	7	cauchy	cauchy	ADJ
ejpam-2584	64	8	sequence	sequence	NOUN
ejpam-2584	64	9	in	in	ADP
ejpam-2584	64	10	(	(	PUNCT
ejpam-2584	64	11	x	x	INTJ
ejpam-2584	64	12	,	,	PUNCT
ejpam-2584	64	13	ds	ds	ADJ
ejpam-2584	64	14	)	)	PUNCT
ejpam-2584	64	15	.	.	PUNCT
ejpam-2584	65	1	b	b	X
ejpam-2584	65	2	)	)	PUNCT
ejpam-2584	65	3	�	�	PROPN
ejpam-2584	65	4	x	x	SYM
ejpam-2584	65	5	,	,	PUNCT
ejpam-2584	65	6	p	p	PROPN
ejpam-2584	65	7	�	�	PROPN
ejpam-2584	65	8	is	be	AUX
ejpam-2584	65	9	complete	complete	ADJ
ejpam-2584	65	10	if	if	SCONJ
ejpam-2584	65	11	and	and	CCONJ
ejpam-2584	65	12	only	only	ADV
ejpam-2584	65	13	if	if	SCONJ
ejpam-2584	65	14	(	(	PUNCT
ejpam-2584	65	15	x	x	X
ejpam-2584	65	16	,	,	PUNCT
ejpam-2584	65	17	ds	ds	PROPN
ejpam-2584	65	18	)	)	PUNCT
ejpam-2584	65	19	is	be	AUX
ejpam-2584	65	20	complete	complete	ADJ
ejpam-2584	65	21	.	.	PUNCT
ejpam-2584	66	1	moreover	moreover	ADV
ejpam-2584	66	2	,	,	PUNCT
ejpam-2584	66	3	lim	lim	PROPN
ejpam-2584	66	4	n→∞	n→∞	PRON
ejpam-2584	66	5	ds	ds	PROPN
ejpam-2584	66	6	�	�	PROPN
ejpam-2584	66	7	xn	xn	PROPN
ejpam-2584	66	8	,	,	PUNCT
ejpam-2584	66	9	x	x	X
ejpam-2584	66	10	�	�	PROPN
ejpam-2584	66	11	=	=	SYM
ejpam-2584	66	12	0	0	PUNCT
ejpam-2584	67	1	if	if	SCONJ
ejpam-2584	67	2	and	and	CCONJ
ejpam-2584	67	3	only	only	ADV
ejpam-2584	67	4	if	if	SCONJ
ejpam-2584	67	5	lim	lim	PROPN
ejpam-2584	67	6	n→∞	n→∞	NUM
ejpam-2584	67	7	p	p	PROPN
ejpam-2584	67	8	�	�	PROPN
ejpam-2584	67	9	xn	xn	PROPN
ejpam-2584	67	10	,	,	PUNCT
ejpam-2584	67	11	x	x	X
ejpam-2584	67	12	�	�	PROPN
ejpam-2584	67	13	=	=	SYM
ejpam-2584	67	14	lim	lim	PROPN
ejpam-2584	67	15	n→∞	n→∞	NUM
ejpam-2584	67	16	p	p	PROPN
ejpam-2584	67	17	�	�	PROPN
ejpam-2584	67	18	xn	xn	PROPN
ejpam-2584	67	19	,	,	PUNCT
ejpam-2584	67	20	xm	xm	PROPN
ejpam-2584	67	21	�	�	PROPN
ejpam-2584	68	1	=	=	PUNCT
ejpam-2584	68	2	p	p	X
ejpam-2584	68	3	(	(	PUNCT
ejpam-2584	68	4	x	x	INTJ
ejpam-2584	68	5	,	,	PUNCT
ejpam-2584	68	6	x	x	NOUN
ejpam-2584	68	7	)	)	PUNCT
ejpam-2584	68	8	.	.	PUNCT
ejpam-2584	69	1	moradi	moradi	NOUN
ejpam-2584	69	2	and	and	CCONJ
ejpam-2584	69	3	beiranvand	beiranvand	NOUN
ejpam-2584	70	1	[	[	X
ejpam-2584	70	2	12	12	NUM
ejpam-2584	70	3	]	]	PUNCT
ejpam-2584	70	4	introduced	introduce	VERB
ejpam-2584	70	5	tf	tf	PROPN
ejpam-2584	70	6	type	type	NOUN
ejpam-2584	70	7	contraction	contraction	NOUN
ejpam-2584	70	8	mappings	mapping	NOUN
ejpam-2584	70	9	as	as	SCONJ
ejpam-2584	70	10	follows	follow	VERB
ejpam-2584	70	11	:	:	PUNCT
ejpam-2584	70	12	definition	definition	NOUN
ejpam-2584	70	13	3	3	NUM
ejpam-2584	70	14	(	(	PUNCT
ejpam-2584	70	15	[	[	X
ejpam-2584	70	16	12	12	NUM
ejpam-2584	70	17	]	]	PUNCT
ejpam-2584	70	18	)	)	PUNCT
ejpam-2584	70	19	.	.	PUNCT
ejpam-2584	71	1	let	let	VERB
ejpam-2584	71	2	(	(	PUNCT
ejpam-2584	71	3	x	x	X
ejpam-2584	71	4	,	,	PUNCT
ejpam-2584	71	5	d	d	X
ejpam-2584	71	6	)	)	PUNCT
ejpam-2584	71	7	be	be	AUX
ejpam-2584	71	8	a	a	DET
ejpam-2584	71	9	metric	metric	ADJ
ejpam-2584	71	10	space	space	NOUN
ejpam-2584	71	11	.	.	PUNCT
ejpam-2584	72	1	a	a	DET
ejpam-2584	72	2	mapping	mapping	NOUN
ejpam-2584	72	3	t	t	NOUN
ejpam-2584	72	4	:	:	PUNCT
ejpam-2584	72	5	x	x	X
ejpam-2584	72	6	→	→	PUNCT
ejpam-2584	72	7	x	x	X
ejpam-2584	72	8	is	be	AUX
ejpam-2584	72	9	said	say	VERB
ejpam-2584	72	10	to	to	PART
ejpam-2584	72	11	be	be	AUX
ejpam-2584	72	12	graph	graph	NOUN
ejpam-2584	72	13	closed	close	VERB
ejpam-2584	72	14	if	if	SCONJ
ejpam-2584	72	15	for	for	ADP
ejpam-2584	72	16	every	every	DET
ejpam-2584	72	17	sequence	sequence	NOUN
ejpam-2584	72	18	�	�	PROPN
ejpam-2584	72	19	xn	xn	PROPN
ejpam-2584	72	20	such	such	ADJ
ejpam-2584	72	21	that	that	SCONJ
ejpam-2584	72	22	lim	lim	PROPN
ejpam-2584	72	23	n→∞	n→∞	X
ejpam-2584	72	24	t	t	NOUN
ejpam-2584	72	25	xn	xn	PROPN
ejpam-2584	73	1	=	=	PUNCT
ejpam-2584	73	2	a	a	DET
ejpam-2584	73	3	then	then	ADV
ejpam-2584	73	4	for	for	ADP
ejpam-2584	73	5	some	some	DET
ejpam-2584	73	6	b	b	NOUN
ejpam-2584	73	7	∈	∈	PROPN
ejpam-2584	73	8	x	x	X
ejpam-2584	73	9	,	,	PUNCT
ejpam-2584	73	10	t	t	PROPN
ejpam-2584	73	11	b	b	X
ejpam-2584	73	12	=	=	NOUN
ejpam-2584	73	13	a.	a.	NOUN
ejpam-2584	73	14	definition	definition	NOUN
ejpam-2584	73	15	4	4	NUM
ejpam-2584	73	16	(	(	PUNCT
ejpam-2584	73	17	[	[	X
ejpam-2584	73	18	12	12	NUM
ejpam-2584	73	19	]	]	PUNCT
ejpam-2584	73	20	)	)	PUNCT
ejpam-2584	73	21	.	.	PUNCT
ejpam-2584	74	1	let	let	VERB
ejpam-2584	74	2	(	(	PUNCT
ejpam-2584	74	3	x	x	X
ejpam-2584	74	4	,	,	PUNCT
ejpam-2584	74	5	d	d	X
ejpam-2584	74	6	)	)	PUNCT
ejpam-2584	74	7	be	be	AUX
ejpam-2584	74	8	a	a	DET
ejpam-2584	74	9	metric	metric	ADJ
ejpam-2584	74	10	space	space	NOUN
ejpam-2584	74	11	and	and	CCONJ
ejpam-2584	74	12	f	f	PROPN
ejpam-2584	74	13	,	,	PUNCT
ejpam-2584	74	14	t	t	X
ejpam-2584	74	15	:	:	PUNCT
ejpam-2584	74	16	x	x	X
ejpam-2584	74	17	→	→	PUNCT
ejpam-2584	74	18	x	x	PUNCT
ejpam-2584	74	19	be	be	AUX
ejpam-2584	74	20	two	two	NUM
ejpam-2584	74	21	functions	function	NOUN
ejpam-2584	74	22	.	.	PUNCT
ejpam-2584	75	1	the	the	DET
ejpam-2584	75	2	mapping	mapping	NOUN
ejpam-2584	75	3	f	f	PROPN
ejpam-2584	75	4	is	be	AUX
ejpam-2584	75	5	said	say	VERB
ejpam-2584	75	6	to	to	PART
ejpam-2584	75	7	be	be	AUX
ejpam-2584	75	8	a	a	DET
ejpam-2584	75	9	tf	tf	NOUN
ejpam-2584	75	10	-contraction	-contraction	NOUN
ejpam-2584	75	11	if	if	SCONJ
ejpam-2584	75	12	there	there	PRON
ejpam-2584	75	13	exists	exist	VERB
ejpam-2584	75	14	α	α	PRON
ejpam-2584	75	15	∈	∈	PROPN
ejpam-2584	76	1	[	[	X
ejpam-2584	76	2	0	0	NUM
ejpam-2584	76	3	,	,	PUNCT
ejpam-2584	76	4	1	1	NUM
ejpam-2584	76	5	)	)	PUNCT
ejpam-2584	76	6	such	such	ADJ
ejpam-2584	76	7	that	that	DET
ejpam-2584	76	8	for	for	ADP
ejpam-2584	76	9	all	all	DET
ejpam-2584	76	10	x	x	SYM
ejpam-2584	76	11	,	,	PUNCT
ejpam-2584	76	12	y	y	PROPN
ejpam-2584	76	13	∈	∈	PROPN
ejpam-2584	76	14	x	x	X
ejpam-2584	76	15	f	f	X
ejpam-2584	76	16	�	�	PROPN
ejpam-2584	76	17	d	d	PROPN
ejpam-2584	76	18	�	�	PROPN
ejpam-2584	76	19	t	t	PROPN
ejpam-2584	76	20	f	f	PROPN
ejpam-2584	76	21	x	x	X
ejpam-2584	76	22	,	,	PUNCT
ejpam-2584	76	23	t	t	PROPN
ejpam-2584	76	24	f	f	PROPN
ejpam-2584	76	25	y	y	PROPN
ejpam-2584	76	26	�	�	PROPN
ejpam-2584	76	27	�	�	PROPN
ejpam-2584	76	28	≤	≤	NOUN
ejpam-2584	76	29	αf	αf	ADP
ejpam-2584	76	30	�	�	PROPN
ejpam-2584	76	31	d	d	PROPN
ejpam-2584	76	32	�	�	PROPN
ejpam-2584	76	33	t	t	PROPN
ejpam-2584	76	34	x	x	X
ejpam-2584	76	35	,	,	PUNCT
ejpam-2584	76	36	t	t	PROPN
ejpam-2584	76	37	y	y	PROPN
ejpam-2584	76	38	�	�	PROPN
ejpam-2584	76	39	�	�	PROPN
ejpam-2584	76	40	(	(	PUNCT
ejpam-2584	76	41	1	1	NUM
ejpam-2584	76	42	)	)	PUNCT
ejpam-2584	76	43	where	where	SCONJ
ejpam-2584	76	44	1	1	X
ejpam-2584	76	45	)	)	PUNCT
ejpam-2584	76	46	f	f	NOUN
ejpam-2584	76	47	:	:	PUNCT
ejpam-2584	77	1	[	[	X
ejpam-2584	77	2	0,∞)→	0,∞)→	NOUN
ejpam-2584	77	3	[	[	X
ejpam-2584	77	4	0,∞	0,∞	NOUN
ejpam-2584	77	5	)	)	PUNCT
ejpam-2584	77	6	,	,	PUNCT
ejpam-2584	77	7	f	f	PROPN
ejpam-2584	77	8	is	be	AUX
ejpam-2584	77	9	nondecreasing	nondecrease	VERB
ejpam-2584	77	10	continuous	continuous	ADJ
ejpam-2584	77	11	from	from	ADP
ejpam-2584	77	12	the	the	DET
ejpam-2584	77	13	right	right	NOUN
ejpam-2584	77	14	and	and	CCONJ
ejpam-2584	77	15	f−1	f−1	PROPN
ejpam-2584	77	16	(	(	PUNCT
ejpam-2584	77	17	0	0	NUM
ejpam-2584	77	18	)	)	PUNCT
ejpam-2584	77	19	=	=	PRON
ejpam-2584	77	20	{	{	PUNCT
ejpam-2584	77	21	0	0	NUM
ejpam-2584	77	22	}	}	PUNCT
ejpam-2584	77	23	.	.	PUNCT
ejpam-2584	78	1	2	2	X
ejpam-2584	78	2	)	)	PUNCT
ejpam-2584	78	3	t	t	NOUN
ejpam-2584	78	4	is	be	AUX
ejpam-2584	78	5	one	one	NUM
ejpam-2584	78	6	to	to	ADP
ejpam-2584	78	7	one	one	NUM
ejpam-2584	78	8	and	and	CCONJ
ejpam-2584	78	9	graph	graph	NOUN
ejpam-2584	78	10	closed	close	VERB
ejpam-2584	78	11	.	.	PUNCT
ejpam-2584	79	1	theorem	theorem	NOUN
ejpam-2584	79	2	1	1	NUM
ejpam-2584	79	3	(	(	PUNCT
ejpam-2584	79	4	[	[	X
ejpam-2584	79	5	12	12	NUM
ejpam-2584	79	6	]	]	PUNCT
ejpam-2584	79	7	)	)	PUNCT
ejpam-2584	79	8	.	.	PUNCT
ejpam-2584	80	1	let	let	VERB
ejpam-2584	80	2	(	(	PUNCT
ejpam-2584	80	3	x	x	X
ejpam-2584	80	4	,	,	PUNCT
ejpam-2584	80	5	d	d	X
ejpam-2584	80	6	)	)	PUNCT
ejpam-2584	80	7	be	be	AUX
ejpam-2584	80	8	a	a	DET
ejpam-2584	80	9	complete	complete	ADJ
ejpam-2584	80	10	metric	metric	ADJ
ejpam-2584	80	11	space	space	NOUN
ejpam-2584	80	12	.	.	PUNCT
ejpam-2584	81	1	if	if	SCONJ
ejpam-2584	81	2	f	f	PROPN
ejpam-2584	81	3	:	:	PUNCT
ejpam-2584	81	4	x	x	X
ejpam-2584	81	5	→	→	PUNCT
ejpam-2584	81	6	x	x	X
ejpam-2584	81	7	is	be	AUX
ejpam-2584	81	8	a	a	DET
ejpam-2584	81	9	tf	tf	PROPN
ejpam-2584	81	10	-contraction	-contraction	PROPN
ejpam-2584	81	11	mapping	mapping	NOUN
ejpam-2584	81	12	then	then	ADV
ejpam-2584	81	13	f	f	PROPN
ejpam-2584	81	14	has	have	VERB
ejpam-2584	81	15	a	a	DET
ejpam-2584	81	16	unique	unique	ADJ
ejpam-2584	81	17	fixed	fix	VERB
ejpam-2584	81	18	point	point	NOUN
ejpam-2584	81	19	in	in	ADP
ejpam-2584	81	20	complete	complete	ADJ
ejpam-2584	81	21	metric	metric	ADJ
ejpam-2584	81	22	space	space	NOUN
ejpam-2584	81	23	(	(	PUNCT
ejpam-2584	81	24	x	x	NOUN
ejpam-2584	81	25	,	,	PUNCT
ejpam-2584	81	26	d	d	NOUN
ejpam-2584	81	27	)	)	PUNCT
ejpam-2584	81	28	.	.	PUNCT
ejpam-2584	82	1	kir	kir	PROPN
ejpam-2584	82	2	and	and	CCONJ
ejpam-2584	82	3	kiziltunc	kiziltunc	VERB
ejpam-2584	82	4	[	[	PUNCT
ejpam-2584	82	5	13	13	NUM
ejpam-2584	82	6	]	]	PUNCT
ejpam-2584	82	7	introduced	introduce	VERB
ejpam-2584	82	8	tf	tf	NUM
ejpam-2584	82	9	-contractive	-contractive	ADJ
ejpam-2584	82	10	conditions	condition	NOUN
ejpam-2584	82	11	for	for	SCONJ
ejpam-2584	82	12	kannan	kannan	PROPN
ejpam-2584	82	13	fixed	fix	VERB
ejpam-2584	82	14	point	point	NOUN
ejpam-2584	82	15	theorem	theorem	NOUN
ejpam-2584	82	16	and	and	CCONJ
ejpam-2584	82	17	chatterjea	chatterjea	ADJ
ejpam-2584	82	18	fixed	fix	VERB
ejpam-2584	82	19	point	point	NOUN
ejpam-2584	82	20	theorem	theorem	VERB
ejpam-2584	82	21	.	.	PUNCT
ejpam-2584	83	1	definition	definition	NOUN
ejpam-2584	83	2	5	5	NUM
ejpam-2584	83	3	(	(	PUNCT
ejpam-2584	83	4	[	[	X
ejpam-2584	83	5	10	10	NUM
ejpam-2584	83	6	,	,	PUNCT
ejpam-2584	83	7	11	11	NUM
ejpam-2584	83	8	]	]	NUM
ejpam-2584	83	9	)	)	PUNCT
ejpam-2584	83	10	.	.	PUNCT
ejpam-2584	84	1	let	let	VERB
ejpam-2584	84	2	(	(	PUNCT
ejpam-2584	84	3	x	x	X
ejpam-2584	84	4	,	,	PUNCT
ejpam-2584	84	5	d	d	X
ejpam-2584	84	6	)	)	PUNCT
ejpam-2584	84	7	be	be	AUX
ejpam-2584	84	8	a	a	DET
ejpam-2584	84	9	metric	metric	ADJ
ejpam-2584	84	10	space	space	NOUN
ejpam-2584	84	11	.	.	PUNCT
ejpam-2584	85	1	(	(	PUNCT
ejpam-2584	85	2	i	i	NOUN
ejpam-2584	85	3	)	)	PUNCT
ejpam-2584	85	4	a	a	DET
ejpam-2584	85	5	mapping	mapping	NOUN
ejpam-2584	85	6	t	t	NOUN
ejpam-2584	85	7	:	:	PUNCT
ejpam-2584	85	8	x	x	X
ejpam-2584	85	9	→	→	PUNCT
ejpam-2584	85	10	x	x	X
ejpam-2584	85	11	is	be	AUX
ejpam-2584	85	12	said	say	VERB
ejpam-2584	85	13	to	to	PART
ejpam-2584	85	14	be	be	AUX
ejpam-2584	85	15	sequentially	sequentially	ADV
ejpam-2584	85	16	convergent	convergent	ADJ
ejpam-2584	85	17	if	if	SCONJ
ejpam-2584	85	18	we	we	PRON
ejpam-2584	85	19	have	have	VERB
ejpam-2584	85	20	,	,	PUNCT
ejpam-2584	85	21	for	for	ADP
ejpam-2584	85	22	every	every	DET
ejpam-2584	85	23	sequence	sequence	NOUN
ejpam-2584	85	24	�	�	PROPN
ejpam-2584	85	25	yn	yn	PROPN
ejpam-2584	85	26	,	,	PUNCT
ejpam-2584	85	27	if	if	SCONJ
ejpam-2584	85	28	�	�	PROPN
ejpam-2584	85	29	t	t	PROPN
ejpam-2584	85	30	yn	yn	PROPN
ejpam-2584	85	31	is	be	AUX
ejpam-2584	85	32	convergent	convergent	NOUN
ejpam-2584	85	33	then	then	ADV
ejpam-2584	85	34	�	�	PROPN
ejpam-2584	85	35	yn	yn	PROPN
ejpam-2584	85	36	is	be	AUX
ejpam-2584	85	37	also	also	ADV
ejpam-2584	85	38	convergent	convergent	ADJ
ejpam-2584	85	39	.	.	PUNCT
ejpam-2584	86	1	(	(	PUNCT
ejpam-2584	86	2	ii	ii	NOUN
ejpam-2584	86	3	)	)	PUNCT
ejpam-2584	86	4	t	t	PROPN
ejpam-2584	86	5	is	be	AUX
ejpam-2584	86	6	said	say	VERB
ejpam-2584	86	7	to	to	PART
ejpam-2584	86	8	be	be	AUX
ejpam-2584	86	9	subsequentially	subsequentially	ADV
ejpam-2584	86	10	convergent	convergent	ADJ
ejpam-2584	86	11	if	if	SCONJ
ejpam-2584	86	12	we	we	PRON
ejpam-2584	86	13	have	have	VERB
ejpam-2584	86	14	,	,	PUNCT
ejpam-2584	86	15	for	for	ADP
ejpam-2584	86	16	every	every	DET
ejpam-2584	86	17	sequence	sequence	NOUN
ejpam-2584	86	18	�	�	PROPN
ejpam-2584	86	19	yn	yn	PROPN
ejpam-2584	86	20	,	,	PUNCT
ejpam-2584	86	21	if	if	SCONJ
ejpam-2584	86	22	�	�	PROPN
ejpam-2584	86	23	t	t	PROPN
ejpam-2584	86	24	yn	yn	PROPN
ejpam-2584	86	25	is	be	AUX
ejpam-2584	86	26	convergence	convergence	NOUN
ejpam-2584	86	27	then	then	ADV
ejpam-2584	86	28	�	�	PROPN
ejpam-2584	86	29	yn	yn	PROPN
ejpam-2584	86	30	has	have	VERB
ejpam-2584	86	31	a	a	DET
ejpam-2584	86	32	convergent	convergent	NOUN
ejpam-2584	86	33	subsequence	subsequence	NOUN
ejpam-2584	86	34	.	.	PUNCT
ejpam-2584	87	1	for	for	ADP
ejpam-2584	87	2	instance	instance	NOUN
ejpam-2584	87	3	,	,	PUNCT
ejpam-2584	87	4	the	the	DET
ejpam-2584	87	5	mappings	mapping	NOUN
ejpam-2584	87	6	t	t	NOUN
ejpam-2584	87	7	x	x	SYM
ejpam-2584	87	8	=	=	SYM
ejpam-2584	87	9	x	x	X
ejpam-2584	87	10	,	,	PUNCT
ejpam-2584	87	11	t	t	NOUN
ejpam-2584	87	12	x	x	X
ejpam-2584	87	13	=	=	PUNCT
ejpam-2584	87	14	ln	ln	PROPN
ejpam-2584	87	15	x(x	x(x	PROPN
ejpam-2584	87	16	>	>	X
ejpam-2584	87	17	0	0	NUM
ejpam-2584	87	18	)	)	PUNCT
ejpam-2584	87	19	are	be	AUX
ejpam-2584	87	20	sequentially	sequentially	ADV
ejpam-2584	87	21	convergent	convergent	ADJ
ejpam-2584	87	22	on	on	ADP
ejpam-2584	87	23	the	the	DET
ejpam-2584	87	24	metric	metric	ADJ
ejpam-2584	87	25	space	space	NOUN
ejpam-2584	87	26	(	(	PUNCT
ejpam-2584	87	27	r	r	NOUN
ejpam-2584	87	28	,	,	PUNCT
ejpam-2584	87	29	|·|	|·|	NOUN
ejpam-2584	87	30	)	)	PUNCT
ejpam-2584	87	31	.	.	PUNCT
ejpam-2584	88	1	the	the	DET
ejpam-2584	88	2	mapping	mapping	NOUN
ejpam-2584	88	3	t	t	NOUN
ejpam-2584	88	4	x	x	PUNCT
ejpam-2584	89	1	=	=	SYM
ejpam-2584	89	2	x2	x2	PROPN
ejpam-2584	89	3	is	be	AUX
ejpam-2584	89	4	not	not	PART
ejpam-2584	89	5	sequentially	sequentially	ADV
ejpam-2584	89	6	convergent	convergent	NOUN
ejpam-2584	89	7	on	on	ADP
ejpam-2584	89	8	the	the	DET
ejpam-2584	89	9	metric	metric	ADJ
ejpam-2584	89	10	space	space	NOUN
ejpam-2584	89	11	(	(	PUNCT
ejpam-2584	89	12	r	r	NOUN
ejpam-2584	89	13	,	,	PUNCT
ejpam-2584	89	14	|·|	|·|	NOUN
ejpam-2584	89	15	)	)	PUNCT
ejpam-2584	89	16	but	but	CCONJ
ejpam-2584	89	17	it	it	PRON
ejpam-2584	89	18	is	be	AUX
ejpam-2584	89	19	subsequentially	subsequentially	ADV
ejpam-2584	89	20	convergent	convergent	ADJ
ejpam-2584	89	21	.	.	PUNCT
ejpam-2584	90	1	in	in	ADP
ejpam-2584	90	2	this	this	DET
ejpam-2584	90	3	study	study	NOUN
ejpam-2584	90	4	,	,	PUNCT
ejpam-2584	90	5	we	we	PRON
ejpam-2584	90	6	aim	aim	VERB
ejpam-2584	90	7	to	to	PART
ejpam-2584	90	8	introduce	introduce	VERB
ejpam-2584	90	9	tf	tf	PROPN
ejpam-2584	90	10	type	type	NOUN
ejpam-2584	90	11	fixed	fix	VERB
ejpam-2584	90	12	point	point	NOUN
ejpam-2584	90	13	theorems	theorem	NOUN
ejpam-2584	90	14	in	in	ADP
ejpam-2584	90	15	partial	partial	ADJ
ejpam-2584	90	16	metric	metric	ADJ
ejpam-2584	90	17	space	space	NOUN
ejpam-2584	90	18	.	.	PUNCT
ejpam-2584	91	1	m.	m.	PROPN
ejpam-2584	91	2	kir	kir	PROPN
ejpam-2584	91	3	,	,	PUNCT
ejpam-2584	91	4	h.	h.	PROPN
ejpam-2584	91	5	kiziltunc	kiziltunc	PROPN
ejpam-2584	91	6	/	/	SYM
ejpam-2584	91	7	eur	eur	PROPN
ejpam-2584	91	8	.	.	PUNCT
ejpam-2584	92	1	j.	j.	PROPN
ejpam-2584	92	2	pure	pure	PROPN
ejpam-2584	92	3	appl	appl	PROPN
ejpam-2584	92	4	.	.	PROPN
ejpam-2584	92	5	math	math	PROPN
ejpam-2584	92	6	,	,	PUNCT
ejpam-2584	92	7	9	9	NUM
ejpam-2584	92	8	(	(	PUNCT
ejpam-2584	92	9	2016	2016	NUM
ejpam-2584	92	10	)	)	PUNCT
ejpam-2584	92	11	,	,	PUNCT
ejpam-2584	92	12	443	443	NUM
ejpam-2584	92	13	-	-	SYM
ejpam-2584	92	14	451	451	NUM
ejpam-2584	92	15	446	446	NUM
ejpam-2584	92	16	2	2	NUM
ejpam-2584	92	17	.	.	PUNCT
ejpam-2584	93	1	tf−	tf−	NUM
ejpam-2584	93	2	type	type	VERB
ejpam-2584	93	3	contractive	contractive	ADJ
ejpam-2584	93	4	conditions	condition	NOUN
ejpam-2584	93	5	for	for	ADP
ejpam-2584	93	6	banach	banach	NOUN
ejpam-2584	93	7	’s	’s	ADV
ejpam-2584	93	8	,	,	PUNCT
ejpam-2584	93	9	kannan	kannan	PROPN
ejpam-2584	93	10	’s	’s	PART
ejpam-2584	93	11	and	and	CCONJ
ejpam-2584	93	12	chatterjea	chatterjea	PROPN
ejpam-2584	93	13	’s	’s	PART
ejpam-2584	93	14	fixed	fix	VERB
ejpam-2584	93	15	point	point	NOUN
ejpam-2584	93	16	theorems	theorem	NOUN
ejpam-2584	93	17	theorem	theorem	VERB
ejpam-2584	93	18	2	2	NUM
ejpam-2584	93	19	.	.	PUNCT
ejpam-2584	94	1	let	let	VERB
ejpam-2584	94	2	�	�	PROPN
ejpam-2584	94	3	x	x	SYM
ejpam-2584	94	4	,	,	PUNCT
ejpam-2584	94	5	p	p	PROPN
ejpam-2584	94	6	�	�	PROPN
ejpam-2584	94	7	be	be	AUX
ejpam-2584	94	8	a	a	DET
ejpam-2584	94	9	complete	complete	ADJ
ejpam-2584	94	10	partial	partial	ADJ
ejpam-2584	94	11	metric	metric	ADJ
ejpam-2584	94	12	space	space	NOUN
ejpam-2584	94	13	and	and	CCONJ
ejpam-2584	94	14	t	t	PROPN
ejpam-2584	94	15	,	,	PUNCT
ejpam-2584	94	16	f	f	X
ejpam-2584	94	17	:	:	PUNCT
ejpam-2584	94	18	x	x	X
ejpam-2584	94	19	→	→	PUNCT
ejpam-2584	94	20	x	x	PUNCT
ejpam-2584	94	21	be	be	AUX
ejpam-2584	94	22	mappings	mapping	NOUN
ejpam-2584	94	23	such	such	ADJ
ejpam-2584	94	24	that	that	SCONJ
ejpam-2584	94	25	t	t	PROPN
ejpam-2584	94	26	is	be	AUX
ejpam-2584	94	27	one	one	NUM
ejpam-2584	94	28	to	to	ADP
ejpam-2584	94	29	one	one	NUM
ejpam-2584	94	30	and	and	CCONJ
ejpam-2584	94	31	subsequentially	subsequentially	ADV
ejpam-2584	94	32	convergent	convergent	NOUN
ejpam-2584	94	33	.	.	PUNCT
ejpam-2584	95	1	if	if	SCONJ
ejpam-2584	95	2	for	for	ADP
ejpam-2584	95	3	all	all	DET
ejpam-2584	95	4	k	k	PROPN
ejpam-2584	95	5	∈	∈	PROPN
ejpam-2584	96	1	[	[	X
ejpam-2584	96	2	0	0	NUM
ejpam-2584	96	3	,	,	PUNCT
ejpam-2584	96	4	1	1	NUM
ejpam-2584	96	5	)	)	PUNCT
ejpam-2584	97	1	and	and	CCONJ
ejpam-2584	97	2	x	x	X
ejpam-2584	97	3	,	,	PUNCT
ejpam-2584	97	4	y	y	PROPN
ejpam-2584	97	5	∈	∈	PROPN
ejpam-2584	97	6	x	x	X
ejpam-2584	97	7	f	f	X
ejpam-2584	97	8	�	�	PROPN
ejpam-2584	97	9	p	p	PROPN
ejpam-2584	97	10	�	�	PROPN
ejpam-2584	98	1	t	t	PROPN
ejpam-2584	98	2	f	f	PROPN
ejpam-2584	98	3	x	x	X
ejpam-2584	98	4	,	,	PUNCT
ejpam-2584	98	5	t	t	PROPN
ejpam-2584	98	6	f	f	PROPN
ejpam-2584	98	7	y	y	PROPN
ejpam-2584	98	8	�	�	PROPN
ejpam-2584	98	9	�	�	PROPN
ejpam-2584	98	10	≤	≤	PROPN
ejpam-2584	98	11	kf	kf	PROPN
ejpam-2584	98	12	�	�	PROPN
ejpam-2584	98	13	p	p	PROPN
ejpam-2584	98	14	�	�	PROPN
ejpam-2584	98	15	t	t	PROPN
ejpam-2584	98	16	x	x	X
ejpam-2584	98	17	,	,	PUNCT
ejpam-2584	98	18	t	t	PROPN
ejpam-2584	98	19	y	y	PROPN
ejpam-2584	98	20	�	�	PROPN
ejpam-2584	98	21	�	�	PROPN
ejpam-2584	98	22	(	(	PUNCT
ejpam-2584	98	23	2	2	NUM
ejpam-2584	98	24	)	)	PUNCT
ejpam-2584	98	25	where	where	SCONJ
ejpam-2584	98	26	f	f	NOUN
ejpam-2584	99	1	:	:	PUNCT
ejpam-2584	99	2	[	[	X
ejpam-2584	99	3	0,∞)→	0,∞)→	NOUN
ejpam-2584	99	4	[	[	X
ejpam-2584	99	5	0,∞	0,∞	NOUN
ejpam-2584	99	6	)	)	PUNCT
ejpam-2584	99	7	is	be	AUX
ejpam-2584	99	8	nondecreasing	nondecrease	VERB
ejpam-2584	99	9	continuous	continuous	ADJ
ejpam-2584	99	10	and	and	CCONJ
ejpam-2584	99	11	f	f	PROPN
ejpam-2584	99	12	(	(	PUNCT
ejpam-2584	99	13	t	t	PROPN
ejpam-2584	99	14	)	)	PUNCT
ejpam-2584	99	15	=	=	SYM
ejpam-2584	99	16	0	0	PUNCT
ejpam-2584	100	1	if	if	SCONJ
ejpam-2584	100	2	and	and	CCONJ
ejpam-2584	100	3	only	only	ADV
ejpam-2584	100	4	if	if	SCONJ
ejpam-2584	100	5	t	t	PROPN
ejpam-2584	100	6	=	=	SYM
ejpam-2584	100	7	0	0	X
ejpam-2584	100	8	.	.	PUNCT
ejpam-2584	101	1	then	then	ADV
ejpam-2584	101	2	f	f	PROPN
ejpam-2584	101	3	has	have	VERB
ejpam-2584	101	4	a	a	DET
ejpam-2584	101	5	unique	unique	ADJ
ejpam-2584	101	6	fixed	fix	VERB
ejpam-2584	101	7	point	point	NOUN
ejpam-2584	101	8	in	in	ADP
ejpam-2584	101	9	x	x	X
ejpam-2584	101	10	.	.	PUNCT
ejpam-2584	102	1	proof	proof	NOUN
ejpam-2584	102	2	.	.	PUNCT
ejpam-2584	103	1	let	let	VERB
ejpam-2584	103	2	x0	x0	PROPN
ejpam-2584	103	3	∈	∈	PROPN
ejpam-2584	103	4	x	x	PRON
ejpam-2584	103	5	be	be	AUX
ejpam-2584	103	6	an	an	DET
ejpam-2584	103	7	arbitrary	arbitrary	ADJ
ejpam-2584	103	8	point	point	NOUN
ejpam-2584	103	9	and	and	CCONJ
ejpam-2584	103	10	xn	xn	NUM
ejpam-2584	104	1	=	=	SYM
ejpam-2584	104	2	f	f	X
ejpam-2584	104	3	xn−1	xn−1	PROPN
ejpam-2584	104	4	=	=	PUNCT
ejpam-2584	104	5	f	f	PROPN
ejpam-2584	104	6	n	n	CCONJ
ejpam-2584	104	7	x0	x0	PROPN
ejpam-2584	104	8	,	,	PUNCT
ejpam-2584	104	9	n=	n=	ADJ
ejpam-2584	104	10	1	1	NUM
ejpam-2584	104	11	,	,	PUNCT
ejpam-2584	104	12	2,3	2,3	NUM
ejpam-2584	104	13	,	,	PUNCT
ejpam-2584	104	14	·	·	PUNCT
ejpam-2584	104	15	·	·	PUNCT
ejpam-2584	104	16	·	·	PUNCT
ejpam-2584	105	1	f	f	X
ejpam-2584	105	2	�	�	PROPN
ejpam-2584	105	3	p	p	PROPN
ejpam-2584	105	4	�	�	PROPN
ejpam-2584	105	5	t	t	PROPN
ejpam-2584	105	6	xn	xn	PROPN
ejpam-2584	105	7	,	,	PUNCT
ejpam-2584	105	8	t	t	PROPN
ejpam-2584	105	9	xn+1	xn+1	PROPN
ejpam-2584	105	10	�	�	PROPN
ejpam-2584	105	11	�	�	PROPN
ejpam-2584	105	12	=	=	SYM
ejpam-2584	105	13	f	f	PROPN
ejpam-2584	105	14	�	�	PROPN
ejpam-2584	105	15	p	p	PROPN
ejpam-2584	105	16	�	�	PROPN
ejpam-2584	105	17	t	t	PROPN
ejpam-2584	105	18	f	f	PROPN
ejpam-2584	105	19	xn−1	xn−1	PROPN
ejpam-2584	105	20	,	,	PUNCT
ejpam-2584	105	21	t	t	PROPN
ejpam-2584	105	22	f	f	PROPN
ejpam-2584	105	23	xn	xn	PROPN
ejpam-2584	105	24	�	�	PROPN
ejpam-2584	105	25	�	�	PROPN
ejpam-2584	105	26	≤kf	≤kf	PROPN
ejpam-2584	105	27	�	�	PROPN
ejpam-2584	105	28	p	p	PROPN
ejpam-2584	105	29	�	�	PROPN
ejpam-2584	105	30	t	t	PROPN
ejpam-2584	105	31	xn−1	xn−1	PROPN
ejpam-2584	105	32	,	,	PUNCT
ejpam-2584	105	33	t	t	PROPN
ejpam-2584	105	34	xn	xn	PROPN
ejpam-2584	105	35	�	�	PROPN
ejpam-2584	105	36	�	�	PROPN
ejpam-2584	105	37	...	...	PUNCT
ejpam-2584	105	38	≤kn−1f	≤kn−1f	PROPN
ejpam-2584	105	39	�	�	PROPN
ejpam-2584	105	40	p	p	PROPN
ejpam-2584	105	41	�	�	PROPN
ejpam-2584	105	42	t	t	PROPN
ejpam-2584	105	43	x0	x0	PROPN
ejpam-2584	105	44	,	,	PUNCT
ejpam-2584	105	45	t	t	PROPN
ejpam-2584	105	46	x1	x1	PROPN
ejpam-2584	105	47	�	�	PROPN
ejpam-2584	105	48	�	�	PROPN
ejpam-2584	105	49	.	.	PUNCT
ejpam-2584	106	1	(	(	PUNCT
ejpam-2584	106	2	3	3	X
ejpam-2584	106	3	)	)	PUNCT
ejpam-2584	106	4	also	also	ADV
ejpam-2584	106	5	,	,	PUNCT
ejpam-2584	106	6	for	for	ADP
ejpam-2584	106	7	all	all	DET
ejpam-2584	106	8	m	m	PROPN
ejpam-2584	106	9	,	,	PUNCT
ejpam-2584	106	10	n	n	PROPN
ejpam-2584	106	11	∈	∈	PROPN
ejpam-2584	106	12	n	n	CCONJ
ejpam-2584	106	13	,	,	PUNCT
ejpam-2584	106	14	for	for	ADP
ejpam-2584	106	15	m	m	PROPN
ejpam-2584	106	16	>	>	X
ejpam-2584	106	17	n	n	CCONJ
ejpam-2584	106	18	,	,	PUNCT
ejpam-2584	106	19	we	we	PRON
ejpam-2584	106	20	have	have	VERB
ejpam-2584	106	21	f	f	PROPN
ejpam-2584	106	22	�	�	PROPN
ejpam-2584	106	23	p	p	PROPN
ejpam-2584	106	24	�	�	PROPN
ejpam-2584	106	25	t	t	PROPN
ejpam-2584	106	26	xn	xn	PROPN
ejpam-2584	106	27	,	,	PUNCT
ejpam-2584	106	28	t	t	PROPN
ejpam-2584	106	29	xm	xm	PROPN
ejpam-2584	106	30	�	�	PROPN
ejpam-2584	106	31	�	�	PROPN
ejpam-2584	106	32	=	=	SYM
ejpam-2584	106	33	f	f	PROPN
ejpam-2584	106	34	�	�	PROPN
ejpam-2584	106	35	p	p	PROPN
ejpam-2584	106	36	�	�	PROPN
ejpam-2584	106	37	t	t	PROPN
ejpam-2584	106	38	f	f	PROPN
ejpam-2584	106	39	n	n	CCONJ
ejpam-2584	106	40	x0	x0	PROPN
ejpam-2584	106	41	,	,	PUNCT
ejpam-2584	106	42	t	t	PROPN
ejpam-2584	106	43	f	f	PROPN
ejpam-2584	106	44	m	m	VERB
ejpam-2584	106	45	x0	x0	PROPN
ejpam-2584	106	46	�	�	PROPN
ejpam-2584	106	47	�	�	PROPN
ejpam-2584	106	48	≤knf	≤knf	NUM
ejpam-2584	106	49	�	�	PROPN
ejpam-2584	106	50	p	p	PROPN
ejpam-2584	106	51	�	�	PROPN
ejpam-2584	106	52	t	t	PROPN
ejpam-2584	106	53	x0	x0	PROPN
ejpam-2584	106	54	,	,	PUNCT
ejpam-2584	106	55	t	t	PROPN
ejpam-2584	106	56	f	f	PROPN
ejpam-2584	106	57	m−n	m−n	PROPN
ejpam-2584	106	58	x0	x0	PROPN
ejpam-2584	106	59	�	�	PROPN
ejpam-2584	106	60	�	�	PROPN
ejpam-2584	106	61	.	.	PUNCT
ejpam-2584	107	1	(	(	PUNCT
ejpam-2584	107	2	4	4	X
ejpam-2584	107	3	)	)	PUNCT
ejpam-2584	107	4	let	let	VERB
ejpam-2584	107	5	m	m	PRON
ejpam-2584	107	6	,	,	PUNCT
ejpam-2584	107	7	n→∞	n→∞	X
ejpam-2584	107	8	in	in	ADP
ejpam-2584	107	9	(	(	PUNCT
ejpam-2584	107	10	4	4	NUM
ejpam-2584	107	11	)	)	PUNCT
ejpam-2584	107	12	,	,	PUNCT
ejpam-2584	107	13	we	we	PRON
ejpam-2584	107	14	obtain	obtain	VERB
ejpam-2584	107	15	f	f	PROPN
ejpam-2584	107	16	�	�	PROPN
ejpam-2584	107	17	p	p	PROPN
ejpam-2584	107	18	�	�	PROPN
ejpam-2584	107	19	t	t	PROPN
ejpam-2584	107	20	xn	xn	PROPN
ejpam-2584	107	21	,	,	PUNCT
ejpam-2584	107	22	t	t	PROPN
ejpam-2584	107	23	xm	xm	PROPN
ejpam-2584	107	24	�	�	PROPN
ejpam-2584	107	25	�	�	PROPN
ejpam-2584	107	26	→	→	SYM
ejpam-2584	107	27	0	0	NUM
ejpam-2584	107	28	+	+	CCONJ
ejpam-2584	107	29	as	as	ADP
ejpam-2584	107	30	m	m	PROPN
ejpam-2584	107	31	,	,	PUNCT
ejpam-2584	107	32	n→∞.	n→∞.	VERB
ejpam-2584	107	33	as	as	SCONJ
ejpam-2584	107	34	f	f	PROPN
ejpam-2584	107	35	is	be	AUX
ejpam-2584	107	36	continuous	continuous	ADJ
ejpam-2584	107	37	,	,	PUNCT
ejpam-2584	107	38	we	we	PRON
ejpam-2584	107	39	obtain	obtain	VERB
ejpam-2584	107	40	lim	lim	PROPN
ejpam-2584	107	41	m	m	PROPN
ejpam-2584	107	42	,	,	PUNCT
ejpam-2584	107	43	n→∞	n→∞	X
ejpam-2584	108	1	p	p	PROPN
ejpam-2584	108	2	�	�	PROPN
ejpam-2584	108	3	t	t	PROPN
ejpam-2584	108	4	xn	xn	PROPN
ejpam-2584	108	5	,	,	PUNCT
ejpam-2584	108	6	t	t	PROPN
ejpam-2584	108	7	xm	xm	PROPN
ejpam-2584	108	8	�	�	PROPN
ejpam-2584	108	9	=	=	PUNCT
ejpam-2584	108	10	0	0	PROPN
ejpam-2584	108	11	.	.	PUNCT
ejpam-2584	109	1	(	(	PUNCT
ejpam-2584	109	2	5	5	NUM
ejpam-2584	109	3	)	)	PUNCT
ejpam-2584	109	4	thus	thus	ADV
ejpam-2584	109	5	,	,	PUNCT
ejpam-2584	109	6	we	we	PRON
ejpam-2584	109	7	see	see	VERB
ejpam-2584	109	8	that	that	SCONJ
ejpam-2584	109	9	�	�	PROPN
ejpam-2584	109	10	t	t	PROPN
ejpam-2584	109	11	xn	xn	PROPN
ejpam-2584	109	12	is	be	AUX
ejpam-2584	109	13	a	a	DET
ejpam-2584	109	14	cauchy	cauchy	ADJ
ejpam-2584	109	15	sequence	sequence	NOUN
ejpam-2584	109	16	in	in	ADP
ejpam-2584	109	17	�	�	PROPN
ejpam-2584	109	18	x	x	SYM
ejpam-2584	109	19	,	,	PUNCT
ejpam-2584	109	20	p	p	PROPN
ejpam-2584	109	21	�	�	PROPN
ejpam-2584	109	22	.	.	PUNCT
ejpam-2584	110	1	from	from	ADP
ejpam-2584	110	2	lemma	lemma	PROPN
ejpam-2584	110	3	1	1	NUM
ejpam-2584	110	4	,	,	PUNCT
ejpam-2584	110	5	we	we	PRON
ejpam-2584	110	6	get	get	VERB
ejpam-2584	110	7	that	that	PRON
ejpam-2584	110	8	�	�	PROPN
ejpam-2584	110	9	t	t	PROPN
ejpam-2584	110	10	xn	xn	PROPN
ejpam-2584	110	11	is	be	AUX
ejpam-2584	110	12	cauchy	cauchy	ADJ
ejpam-2584	110	13	sequence	sequence	NOUN
ejpam-2584	110	14	in	in	ADP
ejpam-2584	110	15	(	(	PUNCT
ejpam-2584	110	16	x	x	INTJ
ejpam-2584	110	17	,	,	PUNCT
ejpam-2584	110	18	ds	ds	ADJ
ejpam-2584	110	19	)	)	PUNCT
ejpam-2584	110	20	.	.	PUNCT
ejpam-2584	111	1	since	since	SCONJ
ejpam-2584	111	2	�	�	PROPN
ejpam-2584	111	3	x	x	SYM
ejpam-2584	111	4	,	,	PUNCT
ejpam-2584	111	5	p	p	PROPN
ejpam-2584	111	6	�	�	PROPN
ejpam-2584	111	7	is	be	AUX
ejpam-2584	111	8	a	a	DET
ejpam-2584	111	9	complete	complete	ADJ
ejpam-2584	111	10	partial	partial	ADJ
ejpam-2584	111	11	metric	metric	ADJ
ejpam-2584	111	12	space	space	NOUN
ejpam-2584	111	13	then	then	ADV
ejpam-2584	111	14	(	(	PUNCT
ejpam-2584	111	15	x	x	X
ejpam-2584	111	16	,	,	PUNCT
ejpam-2584	111	17	ds	ds	PROPN
ejpam-2584	111	18	)	)	PUNCT
ejpam-2584	111	19	is	be	AUX
ejpam-2584	111	20	also	also	ADV
ejpam-2584	111	21	complete	complete	ADJ
ejpam-2584	111	22	metric	metric	ADJ
ejpam-2584	111	23	space	space	NOUN
ejpam-2584	111	24	and	and	CCONJ
ejpam-2584	111	25	there	there	PRON
ejpam-2584	111	26	exists	exist	VERB
ejpam-2584	111	27	v	v	ADP
ejpam-2584	111	28	∈	∈	PROPN
ejpam-2584	111	29	x	x	PUNCT
ejpam-2584	111	30	such	such	ADJ
ejpam-2584	111	31	that	that	DET
ejpam-2584	111	32	�	�	PROPN
ejpam-2584	111	33	t	t	PROPN
ejpam-2584	111	34	xn	xn	PROPN
ejpam-2584	111	35	converges	converge	NOUN
ejpam-2584	111	36	to	to	ADP
ejpam-2584	111	37	v	v	NOUN
ejpam-2584	111	38	∈	∈	PROPN
ejpam-2584	111	39	x	x	X
ejpam-2584	111	40	.	.	PUNCT
ejpam-2584	112	1	note	note	VERB
ejpam-2584	112	2	that	that	SCONJ
ejpam-2584	112	3	t	t	PROPN
ejpam-2584	112	4	is	be	AUX
ejpam-2584	112	5	subsequentially	subsequentially	ADV
ejpam-2584	112	6	convergent	convergent	ADJ
ejpam-2584	112	7	,	,	PUNCT
ejpam-2584	112	8	then	then	ADV
ejpam-2584	112	9	there	there	PRON
ejpam-2584	112	10	exists	exist	VERB
ejpam-2584	112	11	an	an	DET
ejpam-2584	112	12	u	u	NOUN
ejpam-2584	112	13	∈	∈	PROPN
ejpam-2584	112	14	x	x	PUNCT
ejpam-2584	112	15	such	such	ADJ
ejpam-2584	112	16	that	that	SCONJ
ejpam-2584	112	17	lim	lim	PROPN
ejpam-2584	112	18	k→∞	k→∞	NOUN
ejpam-2584	112	19	p	p	PROPN
ejpam-2584	112	20	�	�	PROPN
ejpam-2584	112	21	xn(k	xn(k	NUM
ejpam-2584	112	22	)	)	PUNCT
ejpam-2584	112	23	,	,	PUNCT
ejpam-2584	112	24	u	u	PROPN
ejpam-2584	112	25	�	�	PROPN
ejpam-2584	112	26	=	=	SYM
ejpam-2584	112	27	lim	lim	PROPN
ejpam-2584	112	28	k→∞	k→∞	PROPN
ejpam-2584	113	1	p	p	PROPN
ejpam-2584	113	2	(	(	PUNCT
ejpam-2584	113	3	u	u	NOUN
ejpam-2584	113	4	,	,	PUNCT
ejpam-2584	113	5	u	u	NOUN
ejpam-2584	113	6	)	)	PUNCT
ejpam-2584	113	7	.	.	PUNCT
ejpam-2584	114	1	also	also	ADV
ejpam-2584	114	2	,	,	PUNCT
ejpam-2584	114	3	t	t	PROPN
ejpam-2584	114	4	is	be	AUX
ejpam-2584	114	5	continuous	continuous	ADJ
ejpam-2584	114	6	and	and	CCONJ
ejpam-2584	114	7	xn(k)→	xn(k)→	PROPN
ejpam-2584	114	8	u	u	PROPN
ejpam-2584	114	9	,	,	PUNCT
ejpam-2584	114	10	therefore	therefore	ADV
ejpam-2584	114	11	lim	lim	PROPN
ejpam-2584	114	12	k→∞	k→∞	PROPN
ejpam-2584	114	13	t	t	PROPN
ejpam-2584	114	14	xn(k	xn(k	NUM
ejpam-2584	114	15	)	)	PUNCT
ejpam-2584	115	1	=	=	SYM
ejpam-2584	115	2	tu	tu	PROPN
ejpam-2584	115	3	and	and	CCONJ
ejpam-2584	115	4	lim	lim	PROPN
ejpam-2584	115	5	k→∞	k→∞	PROPN
ejpam-2584	116	1	p	p	PROPN
ejpam-2584	116	2	�	�	PROPN
ejpam-2584	116	3	t	t	PROPN
ejpam-2584	116	4	xn(k	xn(k	NUM
ejpam-2584	116	5	)	)	PUNCT
ejpam-2584	116	6	,	,	PUNCT
ejpam-2584	116	7	tu	tu	PROPN
ejpam-2584	116	8	�	�	PROPN
ejpam-2584	116	9	=	=	SYM
ejpam-2584	116	10	p	p	PROPN
ejpam-2584	116	11	(	(	PUNCT
ejpam-2584	116	12	tu	tu	PROPN
ejpam-2584	116	13	,	,	PUNCT
ejpam-2584	116	14	tu	tu	PROPN
ejpam-2584	116	15	)	)	PUNCT
ejpam-2584	116	16	.	.	PUNCT
ejpam-2584	117	1	since	since	SCONJ
ejpam-2584	117	2	,	,	PUNCT
ejpam-2584	117	3	�	�	PROPN
ejpam-2584	117	4	t	t	PROPN
ejpam-2584	117	5	xn(k	xn(k	NUM
ejpam-2584	117	6	)	)	PUNCT
ejpam-2584	117	7	is	be	AUX
ejpam-2584	117	8	a	a	DET
ejpam-2584	117	9	subsequence	subsequence	NOUN
ejpam-2584	117	10	of	of	ADP
ejpam-2584	117	11	�	�	PROPN
ejpam-2584	117	12	t	t	PROPN
ejpam-2584	117	13	xn	xn	PROPN
ejpam-2584	117	14	,	,	PUNCT
ejpam-2584	117	15	so	so	ADV
ejpam-2584	117	16	we	we	PRON
ejpam-2584	117	17	obtain	obtain	VERB
ejpam-2584	117	18	tu=	tu=	NOUN
ejpam-2584	117	19	v.	v.	ADP
ejpam-2584	117	20	m.	m.	PROPN
ejpam-2584	117	21	kir	kir	PROPN
ejpam-2584	117	22	,	,	PUNCT
ejpam-2584	117	23	h.	h.	PROPN
ejpam-2584	117	24	kiziltunc	kiziltunc	PROPN
ejpam-2584	117	25	/	/	SYM
ejpam-2584	117	26	eur	eur	PROPN
ejpam-2584	117	27	.	.	PUNCT
ejpam-2584	118	1	j.	j.	PROPN
ejpam-2584	118	2	pure	pure	PROPN
ejpam-2584	118	3	appl	appl	PROPN
ejpam-2584	118	4	.	.	PROPN
ejpam-2584	118	5	math	math	PROPN
ejpam-2584	118	6	,	,	PUNCT
ejpam-2584	118	7	9	9	NUM
ejpam-2584	118	8	(	(	PUNCT
ejpam-2584	118	9	2016	2016	NUM
ejpam-2584	118	10	)	)	PUNCT
ejpam-2584	118	11	,	,	PUNCT
ejpam-2584	118	12	443	443	NUM
ejpam-2584	118	13	-	-	SYM
ejpam-2584	118	14	451	451	NUM
ejpam-2584	118	15	447	447	NUM
ejpam-2584	118	16	also	also	ADV
ejpam-2584	118	17	,	,	PUNCT
ejpam-2584	118	18	ds	ds	PROPN
ejpam-2584	118	19	�	�	PROPN
ejpam-2584	118	20	t	t	PROPN
ejpam-2584	118	21	xn	xn	PROPN
ejpam-2584	118	22	,	,	PUNCT
ejpam-2584	118	23	tu	tu	PROPN
ejpam-2584	118	24	�	�	PROPN
ejpam-2584	118	25	=	=	PROPN
ejpam-2584	118	26	2p	2p	NUM
ejpam-2584	118	27	�	�	PROPN
ejpam-2584	118	28	t	t	PROPN
ejpam-2584	118	29	xn	xn	PROPN
ejpam-2584	118	30	,	,	PUNCT
ejpam-2584	118	31	tu	tu	PROPN
ejpam-2584	118	32	�	�	PROPN
ejpam-2584	119	1	−	−	PROPN
ejpam-2584	119	2	p	p	PROPN
ejpam-2584	119	3	�	�	PROPN
ejpam-2584	119	4	t	t	PROPN
ejpam-2584	119	5	xn	xn	PROPN
ejpam-2584	119	6	,	,	PUNCT
ejpam-2584	119	7	t	t	PROPN
ejpam-2584	119	8	xn	xn	PROPN
ejpam-2584	119	9	�	�	PROPN
ejpam-2584	120	1	−	−	PROPN
ejpam-2584	120	2	p	p	PROPN
ejpam-2584	120	3	(	(	PUNCT
ejpam-2584	120	4	tu	tu	PROPN
ejpam-2584	120	5	,	,	PUNCT
ejpam-2584	120	6	tu	tu	PROPN
ejpam-2584	120	7	)	)	PUNCT
ejpam-2584	120	8	.	.	PUNCT
ejpam-2584	121	1	(	(	PUNCT
ejpam-2584	121	2	6	6	X
ejpam-2584	121	3	)	)	PUNCT
ejpam-2584	121	4	let	let	VERB
ejpam-2584	121	5	n→∞	n→∞	PRON
ejpam-2584	121	6	in	in	ADP
ejpam-2584	121	7	(	(	PUNCT
ejpam-2584	121	8	6	6	NUM
ejpam-2584	121	9	)	)	PUNCT
ejpam-2584	121	10	,	,	PUNCT
ejpam-2584	121	11	we	we	PRON
ejpam-2584	121	12	have	have	VERB
ejpam-2584	121	13	lim	lim	PROPN
ejpam-2584	121	14	n→∞	n→∞	PRON
ejpam-2584	121	15	ds	ds	PROPN
ejpam-2584	121	16	�	�	PROPN
ejpam-2584	121	17	t	t	PROPN
ejpam-2584	121	18	xn	xn	PROPN
ejpam-2584	121	19	,	,	PUNCT
ejpam-2584	121	20	tu	tu	PROPN
ejpam-2584	121	21	�	�	PROPN
ejpam-2584	121	22	=	=	SYM
ejpam-2584	121	23	0	0	X
ejpam-2584	121	24	.	.	PUNCT
ejpam-2584	122	1	consider	consider	VERB
ejpam-2584	122	2	lemma	lemma	PROPN
ejpam-2584	122	3	1	1	NUM
ejpam-2584	122	4	/	/	SYM
ejpam-2584	122	5	part	part	NOUN
ejpam-2584	122	6	b	b	NOUN
ejpam-2584	122	7	)	)	PUNCT
ejpam-2584	122	8	and	and	CCONJ
ejpam-2584	122	9	(	(	PUNCT
ejpam-2584	122	10	5	5	X
ejpam-2584	122	11	)	)	PUNCT
ejpam-2584	122	12	we	we	PRON
ejpam-2584	122	13	hold	hold	VERB
ejpam-2584	122	14	lim	lim	PROPN
ejpam-2584	122	15	n→∞	n→∞	NUM
ejpam-2584	123	1	p	p	PROPN
ejpam-2584	123	2	�	�	PROPN
ejpam-2584	123	3	t	t	PROPN
ejpam-2584	123	4	xn	xn	PROPN
ejpam-2584	123	5	,	,	PUNCT
ejpam-2584	123	6	tu	tu	PROPN
ejpam-2584	123	7	�	�	PROPN
ejpam-2584	123	8	=	=	PROPN
ejpam-2584	123	9	lim	lim	PROPN
ejpam-2584	123	10	m	m	PROPN
ejpam-2584	123	11	,	,	PUNCT
ejpam-2584	123	12	n→∞	n→∞	X
ejpam-2584	123	13	p	p	PROPN
ejpam-2584	123	14	�	�	PROPN
ejpam-2584	123	15	t	t	PROPN
ejpam-2584	123	16	xn	xn	PROPN
ejpam-2584	123	17	,	,	PUNCT
ejpam-2584	123	18	t	t	PROPN
ejpam-2584	123	19	xm	xm	PROPN
ejpam-2584	123	20	�	�	PROPN
ejpam-2584	124	1	=	=	PRON
ejpam-2584	124	2	p	p	PROPN
ejpam-2584	124	3	(	(	PUNCT
ejpam-2584	124	4	tu	tu	PROPN
ejpam-2584	124	5	,	,	PUNCT
ejpam-2584	124	6	tu	tu	PROPN
ejpam-2584	124	7	)	)	PUNCT
ejpam-2584	124	8	=	=	PUNCT
ejpam-2584	124	9	0	0	X
ejpam-2584	124	10	.	.	PUNCT
ejpam-2584	125	1	now	now	ADV
ejpam-2584	125	2	,	,	PUNCT
ejpam-2584	125	3	we	we	PRON
ejpam-2584	125	4	will	will	AUX
ejpam-2584	125	5	show	show	VERB
ejpam-2584	125	6	that	that	SCONJ
ejpam-2584	125	7	u	u	PRON
ejpam-2584	125	8	∈	∈	PROPN
ejpam-2584	125	9	x	x	X
ejpam-2584	125	10	is	be	AUX
ejpam-2584	125	11	a	a	DET
ejpam-2584	125	12	fixed	fix	VERB
ejpam-2584	125	13	point	point	NOUN
ejpam-2584	125	14	of	of	ADP
ejpam-2584	125	15	f	f	PROPN
ejpam-2584	125	16	.	.	PUNCT
ejpam-2584	126	1	indeed	indeed	ADV
ejpam-2584	126	2	,	,	PUNCT
ejpam-2584	126	3	as	as	SCONJ
ejpam-2584	126	4	f	f	PROPN
ejpam-2584	126	5	is	be	AUX
ejpam-2584	126	6	continuous	continuous	ADJ
ejpam-2584	126	7	f	f	PROPN
ejpam-2584	126	8	�	�	PROPN
ejpam-2584	126	9	p	p	PROPN
ejpam-2584	126	10	�	�	PROPN
ejpam-2584	126	11	t	t	PROPN
ejpam-2584	126	12	f	f	PROPN
ejpam-2584	126	13	u	u	PROPN
ejpam-2584	126	14	,	,	PUNCT
ejpam-2584	126	15	t	t	PROPN
ejpam-2584	126	16	xn+1	xn+1	PROPN
ejpam-2584	126	17	�	�	PROPN
ejpam-2584	126	18	�	�	PROPN
ejpam-2584	126	19	=	=	SYM
ejpam-2584	126	20	f	f	PROPN
ejpam-2584	126	21	�	�	PROPN
ejpam-2584	126	22	p	p	PROPN
ejpam-2584	126	23	�	�	PROPN
ejpam-2584	126	24	t	t	PROPN
ejpam-2584	126	25	f	f	PROPN
ejpam-2584	126	26	u	u	PROPN
ejpam-2584	126	27	,	,	PUNCT
ejpam-2584	126	28	t	t	PROPN
ejpam-2584	126	29	f	f	PROPN
ejpam-2584	126	30	xn	xn	PROPN
ejpam-2584	126	31	�	�	PROPN
ejpam-2584	126	32	�	�	PROPN
ejpam-2584	126	33	≤kf	≤kf	PROPN
ejpam-2584	126	34	�	�	PROPN
ejpam-2584	126	35	p	p	PROPN
ejpam-2584	126	36	�	�	PROPN
ejpam-2584	126	37	tu	tu	PROPN
ejpam-2584	126	38	,	,	PUNCT
ejpam-2584	126	39	t	t	PROPN
ejpam-2584	126	40	xn	xn	PROPN
ejpam-2584	126	41	�	�	PROPN
ejpam-2584	126	42	�	�	PROPN
ejpam-2584	126	43	.	.	PUNCT
ejpam-2584	127	1	(	(	PUNCT
ejpam-2584	127	2	7	7	X
ejpam-2584	127	3	)	)	PUNCT
ejpam-2584	127	4	let	let	VERB
ejpam-2584	127	5	n→∞	n→∞	PRON
ejpam-2584	127	6	in	in	ADP
ejpam-2584	127	7	(	(	PUNCT
ejpam-2584	127	8	7	7	NUM
ejpam-2584	127	9	)	)	PUNCT
ejpam-2584	127	10	,	,	PUNCT
ejpam-2584	127	11	we	we	PRON
ejpam-2584	127	12	obtain	obtain	VERB
ejpam-2584	127	13	f(p	f(p	PROPN
ejpam-2584	127	14	�	�	PROPN
ejpam-2584	127	15	t	t	PROPN
ejpam-2584	127	16	f	f	PROPN
ejpam-2584	127	17	u	u	PROPN
ejpam-2584	127	18	,	,	PUNCT
ejpam-2584	127	19	tu	tu	PROPN
ejpam-2584	127	20	�	�	PROPN
ejpam-2584	127	21	)	)	PUNCT
ejpam-2584	127	22	≤	≤	NOUN
ejpam-2584	127	23	0	0	NUM
ejpam-2584	128	1	this	this	PRON
ejpam-2584	128	2	implies	imply	VERB
ejpam-2584	128	3	that	that	SCONJ
ejpam-2584	128	4	p	p	PROPN
ejpam-2584	128	5	�	�	PROPN
ejpam-2584	128	6	tu	tu	PROPN
ejpam-2584	128	7	,	,	PUNCT
ejpam-2584	128	8	t	t	PROPN
ejpam-2584	128	9	f	f	PROPN
ejpam-2584	128	10	u	u	X
ejpam-2584	128	11	�	�	PROPN
ejpam-2584	128	12	=	=	SYM
ejpam-2584	128	13	0	0	NUM
ejpam-2584	128	14	and	and	CCONJ
ejpam-2584	128	15	hence	hence	ADV
ejpam-2584	128	16	tu	tu	PROPN
ejpam-2584	128	17	=	=	SYM
ejpam-2584	128	18	t	t	PROPN
ejpam-2584	128	19	f	f	PROPN
ejpam-2584	128	20	u.	u.	PROPN
ejpam-2584	128	21	also	also	ADV
ejpam-2584	128	22	,	,	PUNCT
ejpam-2584	128	23	t	t	PROPN
ejpam-2584	128	24	is	be	AUX
ejpam-2584	128	25	one	one	NUM
ejpam-2584	128	26	to	to	ADP
ejpam-2584	128	27	one	one	NUM
ejpam-2584	128	28	,	,	PUNCT
ejpam-2584	128	29	we	we	PRON
ejpam-2584	128	30	obtain	obtain	VERB
ejpam-2584	128	31	f	f	PROPN
ejpam-2584	128	32	u=	u=	ADV
ejpam-2584	128	33	u.	u.	ADV
ejpam-2584	128	34	now	now	ADV
ejpam-2584	128	35	,	,	PUNCT
ejpam-2584	128	36	we	we	PRON
ejpam-2584	128	37	show	show	VERB
ejpam-2584	128	38	that	that	SCONJ
ejpam-2584	128	39	the	the	DET
ejpam-2584	128	40	fixed	fix	VERB
ejpam-2584	128	41	point	point	NOUN
ejpam-2584	128	42	is	be	AUX
ejpam-2584	128	43	unique	unique	ADJ
ejpam-2584	128	44	.	.	PUNCT
ejpam-2584	129	1	assume	assume	VERB
ejpam-2584	129	2	u′	u′	PROPN
ejpam-2584	129	3	is	be	AUX
ejpam-2584	129	4	an	an	DET
ejpam-2584	129	5	other	other	ADJ
ejpam-2584	129	6	fixed	fix	VERB
ejpam-2584	129	7	point	point	NOUN
ejpam-2584	129	8	of	of	ADP
ejpam-2584	129	9	f	f	PROPN
ejpam-2584	129	10	then	then	ADV
ejpam-2584	129	11	,	,	PUNCT
ejpam-2584	129	12	we	we	PRON
ejpam-2584	129	13	have	have	VERB
ejpam-2584	129	14	f	f	PROPN
ejpam-2584	129	15	u′	u′	PROPN
ejpam-2584	129	16	=	=	SYM
ejpam-2584	129	17	u′	u′	PROPN
ejpam-2584	129	18	and	and	CCONJ
ejpam-2584	129	19	f(p	f(p	PROPN
ejpam-2584	129	20	�	�	PROPN
ejpam-2584	129	21	tu	tu	PROPN
ejpam-2584	129	22	,	,	PUNCT
ejpam-2584	129	23	tu′	tu′	PROPN
ejpam-2584	129	24	�	�	PROPN
ejpam-2584	129	25	)	)	PUNCT
ejpam-2584	130	1	=	=	PROPN
ejpam-2584	130	2	f(p	f(p	PROPN
ejpam-2584	130	3	�	�	PROPN
ejpam-2584	130	4	t	t	PROPN
ejpam-2584	130	5	f	f	PROPN
ejpam-2584	130	6	u	u	PROPN
ejpam-2584	130	7	,	,	PUNCT
ejpam-2584	130	8	t	t	PROPN
ejpam-2584	130	9	f	f	PROPN
ejpam-2584	130	10	u′	u′	PROPN
ejpam-2584	130	11	�	�	PROPN
ejpam-2584	130	12	)	)	PUNCT
ejpam-2584	130	13	≤kf	≤kf	PROPN
ejpam-2584	130	14	�	�	PROPN
ejpam-2584	130	15	p	p	PROPN
ejpam-2584	130	16	�	�	PROPN
ejpam-2584	130	17	tu	tu	PROPN
ejpam-2584	130	18	,	,	PUNCT
ejpam-2584	130	19	tu′	tu′	PROPN
ejpam-2584	130	20	�	�	PROPN
ejpam-2584	130	21	�	�	PROPN
ejpam-2584	130	22	(	(	PUNCT
ejpam-2584	130	23	8)	8)	NUM
ejpam-2584	130	24	the	the	DET
ejpam-2584	130	25	inequality	inequality	NOUN
ejpam-2584	130	26	(	(	PUNCT
ejpam-2584	130	27	8)	8)	NUM
ejpam-2584	130	28	is	be	AUX
ejpam-2584	130	29	contradiction	contradiction	NOUN
ejpam-2584	130	30	unless	unless	SCONJ
ejpam-2584	130	31	p	p	PROPN
ejpam-2584	130	32	�	�	PROPN
ejpam-2584	130	33	tu	tu	PROPN
ejpam-2584	130	34	,	,	PUNCT
ejpam-2584	130	35	tu′	tu′	PROPN
ejpam-2584	130	36	�	�	PROPN
ejpam-2584	130	37	=	=	SYM
ejpam-2584	130	38	0	0	NUM
ejpam-2584	130	39	.	.	PUNCT
ejpam-2584	131	1	thus	thus	ADV
ejpam-2584	131	2	,	,	PUNCT
ejpam-2584	131	3	tu	tu	PROPN
ejpam-2584	131	4	=	=	PUNCT
ejpam-2584	131	5	tu′	tu′	NOUN
ejpam-2584	131	6	with	with	ADP
ejpam-2584	131	7	consideration	consideration	NOUN
ejpam-2584	131	8	t	t	NOUN
ejpam-2584	131	9	is	be	AUX
ejpam-2584	131	10	one	one	NUM
ejpam-2584	131	11	to	to	ADP
ejpam-2584	131	12	one	one	NUM
ejpam-2584	131	13	,	,	PUNCT
ejpam-2584	131	14	we	we	PRON
ejpam-2584	131	15	obtain	obtain	VERB
ejpam-2584	131	16	the	the	DET
ejpam-2584	131	17	fixed	fix	VERB
ejpam-2584	131	18	point	point	NOUN
ejpam-2584	131	19	is	be	AUX
ejpam-2584	131	20	unique	unique	ADJ
ejpam-2584	131	21	.	.	PUNCT
ejpam-2584	132	1	also	also	ADV
ejpam-2584	132	2	,	,	PUNCT
ejpam-2584	132	3	if	if	SCONJ
ejpam-2584	132	4	we	we	PRON
ejpam-2584	132	5	take	take	VERB
ejpam-2584	132	6	t	t	PROPN
ejpam-2584	132	7	is	be	AUX
ejpam-2584	132	8	sequentially	sequentially	ADV
ejpam-2584	132	9	convergent	convergent	NOUN
ejpam-2584	132	10	,	,	PUNCT
ejpam-2584	132	11	by	by	ADP
ejpam-2584	132	12	replacing	replace	VERB
ejpam-2584	132	13	{	{	PUNCT
ejpam-2584	132	14	n	n	CCONJ
ejpam-2584	132	15	}	}	PUNCT
ejpam-2584	132	16	with	with	ADP
ejpam-2584	132	17	{	{	PUNCT
ejpam-2584	132	18	n	n	CCONJ
ejpam-2584	132	19	(	(	PUNCT
ejpam-2584	132	20	k	k	NOUN
ejpam-2584	132	21	)	)	PUNCT
ejpam-2584	132	22	}	}	PUNCT
ejpam-2584	132	23	we	we	PRON
ejpam-2584	132	24	conclude	conclude	VERB
ejpam-2584	132	25	that	that	SCONJ
ejpam-2584	132	26	lim	lim	PROPN
ejpam-2584	132	27	n→∞	n→∞	X
ejpam-2584	132	28	xn	xn	PUNCT
ejpam-2584	133	1	=	=	SYM
ejpam-2584	133	2	u	u	NOUN
ejpam-2584	133	3	this	this	PRON
ejpam-2584	133	4	shows	show	VERB
ejpam-2584	133	5	that	that	SCONJ
ejpam-2584	133	6	�	�	PROPN
ejpam-2584	133	7	xn	xn	PROPN
ejpam-2584	133	8	converges	converge	NOUN
ejpam-2584	133	9	to	to	ADP
ejpam-2584	133	10	the	the	DET
ejpam-2584	133	11	fixed	fix	VERB
ejpam-2584	133	12	point	point	NOUN
ejpam-2584	133	13	of	of	ADP
ejpam-2584	133	14	f	f	PROPN
ejpam-2584	133	15	.	.	PUNCT
ejpam-2584	134	1	in	in	ADP
ejpam-2584	134	2	theorem	theorem	NOUN
ejpam-2584	134	3	2	2	NUM
ejpam-2584	134	4	,	,	PUNCT
ejpam-2584	134	5	if	if	SCONJ
ejpam-2584	134	6	we	we	PRON
ejpam-2584	134	7	consider	consider	VERB
ejpam-2584	134	8	f	f	PROPN
ejpam-2584	134	9	and	and	CCONJ
ejpam-2584	134	10	t	t	PROPN
ejpam-2584	134	11	as	as	ADP
ejpam-2584	134	12	identity	identity	NOUN
ejpam-2584	134	13	,	,	PUNCT
ejpam-2584	134	14	we	we	PRON
ejpam-2584	134	15	get	get	VERB
ejpam-2584	134	16	the	the	DET
ejpam-2584	134	17	following	follow	VERB
ejpam-2584	134	18	result	result	NOUN
ejpam-2584	134	19	given	give	VERB
ejpam-2584	134	20	by	by	ADP
ejpam-2584	134	21	matthews	matthews	PROPN
ejpam-2584	135	1	[	[	X
ejpam-2584	135	2	2	2	NUM
ejpam-2584	135	3	]	]	PUNCT
ejpam-2584	135	4	.	.	PUNCT
ejpam-2584	136	1	corollary	corollary	ADJ
ejpam-2584	136	2	2	2	NUM
ejpam-2584	136	3	.	.	PUNCT
ejpam-2584	137	1	let	let	VERB
ejpam-2584	137	2	�	�	PROPN
ejpam-2584	137	3	x	x	SYM
ejpam-2584	137	4	,	,	PUNCT
ejpam-2584	137	5	p	p	PROPN
ejpam-2584	137	6	�	�	PROPN
ejpam-2584	137	7	be	be	AUX
ejpam-2584	137	8	a	a	DET
ejpam-2584	137	9	complete	complete	ADJ
ejpam-2584	137	10	partial	partial	ADJ
ejpam-2584	137	11	metric	metric	ADJ
ejpam-2584	137	12	space	space	NOUN
ejpam-2584	137	13	and	and	CCONJ
ejpam-2584	137	14	f	f	NOUN
ejpam-2584	137	15	:	:	PUNCT
ejpam-2584	137	16	x	x	X
ejpam-2584	137	17	→	→	PUNCT
ejpam-2584	137	18	x	x	PART
ejpam-2584	137	19	be	be	AUX
ejpam-2584	137	20	mapping	map	VERB
ejpam-2584	137	21	.	.	PUNCT
ejpam-2584	138	1	if	if	SCONJ
ejpam-2584	138	2	α	α	PRON
ejpam-2584	138	3	∈	∈	PROPN
ejpam-2584	139	1	[	[	X
ejpam-2584	139	2	0,1	0,1	NUM
ejpam-2584	139	3	)	)	PUNCT
ejpam-2584	139	4	and	and	CCONJ
ejpam-2584	139	5	x	x	X
ejpam-2584	139	6	,	,	PUNCT
ejpam-2584	139	7	y	y	PROPN
ejpam-2584	139	8	∈	∈	PROPN
ejpam-2584	140	1	x	x	X
ejpam-2584	140	2	,	,	PUNCT
ejpam-2584	140	3	p	p	PROPN
ejpam-2584	140	4	�	�	PROPN
ejpam-2584	140	5	f	f	PROPN
ejpam-2584	140	6	x	x	PROPN
ejpam-2584	140	7	,	,	PUNCT
ejpam-2584	140	8	f	f	PROPN
ejpam-2584	140	9	y	y	PROPN
ejpam-2584	140	10	�	�	PROPN
ejpam-2584	140	11	≤	≤	PROPN
ejpam-2584	140	12	αp	αp	NOUN
ejpam-2584	140	13	�	�	PROPN
ejpam-2584	140	14	x	x	SYM
ejpam-2584	140	15	,	,	PUNCT
ejpam-2584	140	16	y	y	PROPN
ejpam-2584	140	17	�	�	PROPN
ejpam-2584	140	18	(	(	PUNCT
ejpam-2584	140	19	9	9	NUM
ejpam-2584	140	20	)	)	PUNCT
ejpam-2584	140	21	then	then	ADV
ejpam-2584	140	22	,	,	PUNCT
ejpam-2584	140	23	f	f	PROPN
ejpam-2584	140	24	has	have	VERB
ejpam-2584	140	25	a	a	DET
ejpam-2584	140	26	unique	unique	ADJ
ejpam-2584	140	27	fixed	fix	VERB
ejpam-2584	140	28	point	point	NOUN
ejpam-2584	140	29	.	.	PUNCT
ejpam-2584	141	1	m.	m.	PROPN
ejpam-2584	141	2	kir	kir	PROPN
ejpam-2584	141	3	,	,	PUNCT
ejpam-2584	141	4	h.	h.	PROPN
ejpam-2584	141	5	kiziltunc	kiziltunc	PROPN
ejpam-2584	141	6	/	/	SYM
ejpam-2584	141	7	eur	eur	PROPN
ejpam-2584	141	8	.	.	PUNCT
ejpam-2584	142	1	j.	j.	PROPN
ejpam-2584	142	2	pure	pure	PROPN
ejpam-2584	142	3	appl	appl	PROPN
ejpam-2584	142	4	.	.	PROPN
ejpam-2584	142	5	math	math	PROPN
ejpam-2584	142	6	,	,	PUNCT
ejpam-2584	142	7	9	9	NUM
ejpam-2584	142	8	(	(	PUNCT
ejpam-2584	142	9	2016	2016	NUM
ejpam-2584	142	10	)	)	PUNCT
ejpam-2584	142	11	,	,	PUNCT
ejpam-2584	142	12	443	443	NUM
ejpam-2584	142	13	-	-	SYM
ejpam-2584	142	14	451	451	NUM
ejpam-2584	142	15	448	448	NUM
ejpam-2584	142	16	theorem	theorem	NOUN
ejpam-2584	142	17	3	3	X
ejpam-2584	142	18	.	.	PUNCT
ejpam-2584	143	1	let	let	VERB
ejpam-2584	143	2	�	�	PROPN
ejpam-2584	143	3	x	x	SYM
ejpam-2584	143	4	,	,	PUNCT
ejpam-2584	143	5	p	p	PROPN
ejpam-2584	143	6	�	�	PROPN
ejpam-2584	143	7	be	be	AUX
ejpam-2584	143	8	a	a	DET
ejpam-2584	143	9	complete	complete	ADJ
ejpam-2584	143	10	partial	partial	ADJ
ejpam-2584	143	11	metric	metric	ADJ
ejpam-2584	143	12	space	space	NOUN
ejpam-2584	143	13	and	and	CCONJ
ejpam-2584	143	14	t	t	PROPN
ejpam-2584	143	15	,	,	PUNCT
ejpam-2584	143	16	f	f	X
ejpam-2584	143	17	:	:	PUNCT
ejpam-2584	143	18	x	x	X
ejpam-2584	143	19	→	→	PUNCT
ejpam-2584	143	20	x	x	PUNCT
ejpam-2584	143	21	be	be	AUX
ejpam-2584	143	22	mappings	mapping	NOUN
ejpam-2584	143	23	such	such	ADJ
ejpam-2584	143	24	that	that	SCONJ
ejpam-2584	143	25	t	t	PROPN
ejpam-2584	143	26	is	be	AUX
ejpam-2584	143	27	one	one	NUM
ejpam-2584	143	28	to	to	ADP
ejpam-2584	143	29	one	one	NUM
ejpam-2584	143	30	,	,	PUNCT
ejpam-2584	143	31	continuous	continuous	ADJ
ejpam-2584	143	32	and	and	CCONJ
ejpam-2584	143	33	subsequentially	subsequentially	ADV
ejpam-2584	143	34	convergent	convergent	NOUN
ejpam-2584	143	35	(	(	PUNCT
ejpam-2584	143	36	or	or	CCONJ
ejpam-2584	143	37	graph	graph	NOUN
ejpam-2584	143	38	closed	closed	ADJ
ejpam-2584	143	39	)	)	PUNCT
ejpam-2584	143	40	.	.	PUNCT
ejpam-2584	144	1	if	if	SCONJ
ejpam-2584	144	2	for	for	ADP
ejpam-2584	144	3	each	each	DET
ejpam-2584	144	4	β	β	X
ejpam-2584	144	5	∈	∈	PROPN
ejpam-2584	144	6	�	�	PROPN
ejpam-2584	144	7	0	0	NUM
ejpam-2584	144	8	,	,	PUNCT
ejpam-2584	144	9	1	1	NUM
ejpam-2584	144	10	2	2	NUM
ejpam-2584	144	11	�	�	PROPN
ejpam-2584	144	12	and	and	CCONJ
ejpam-2584	144	13	x	x	NOUN
ejpam-2584	144	14	,	,	PUNCT
ejpam-2584	144	15	y	y	PROPN
ejpam-2584	144	16	∈	∈	PROPN
ejpam-2584	144	17	x	x	INTJ
ejpam-2584	144	18	,	,	PUNCT
ejpam-2584	144	19	we	we	PRON
ejpam-2584	144	20	have	have	VERB
ejpam-2584	144	21	f	f	PROPN
ejpam-2584	144	22	�	�	PROPN
ejpam-2584	144	23	p	p	PROPN
ejpam-2584	144	24	�	�	PROPN
ejpam-2584	144	25	t	t	PROPN
ejpam-2584	144	26	f	f	PROPN
ejpam-2584	144	27	x	x	X
ejpam-2584	144	28	,	,	PUNCT
ejpam-2584	144	29	t	t	PROPN
ejpam-2584	144	30	f	f	PROPN
ejpam-2584	144	31	y	y	PROPN
ejpam-2584	144	32	�	�	PROPN
ejpam-2584	144	33	�	�	PROPN
ejpam-2584	144	34	≤	≤	PROPN
ejpam-2584	144	35	β	β	X
ejpam-2584	144	36	�	�	PROPN
ejpam-2584	144	37	f	f	PROPN
ejpam-2584	144	38	�	�	PROPN
ejpam-2584	144	39	p	p	PROPN
ejpam-2584	144	40	�	�	PROPN
ejpam-2584	144	41	t	t	PROPN
ejpam-2584	144	42	x	x	X
ejpam-2584	144	43	,	,	PUNCT
ejpam-2584	144	44	t	t	PROPN
ejpam-2584	144	45	f	f	PROPN
ejpam-2584	144	46	x	x	SYM
ejpam-2584	144	47	�	�	PROPN
ejpam-2584	144	48	�	�	PROPN
ejpam-2584	144	49	+	+	CCONJ
ejpam-2584	144	50	f	f	PROPN
ejpam-2584	144	51	�	�	PROPN
ejpam-2584	144	52	p	p	PROPN
ejpam-2584	144	53	�	�	PROPN
ejpam-2584	144	54	t	t	PROPN
ejpam-2584	144	55	y	y	PROPN
ejpam-2584	144	56	,	,	PUNCT
ejpam-2584	144	57	t	t	PROPN
ejpam-2584	144	58	f	f	PROPN
ejpam-2584	144	59	y	y	PROPN
ejpam-2584	144	60	�	�	PROPN
ejpam-2584	144	61	�	�	PROPN
ejpam-2584	144	62	�	�	PROPN
ejpam-2584	144	63	(	(	PUNCT
ejpam-2584	144	64	10	10	NUM
ejpam-2584	144	65	)	)	PUNCT
ejpam-2584	144	66	where	where	SCONJ
ejpam-2584	144	67	f	f	NOUN
ejpam-2584	144	68	:	:	PUNCT
ejpam-2584	145	1	[	[	X
ejpam-2584	145	2	0,∞)→	0,∞)→	NOUN
ejpam-2584	145	3	[	[	X
ejpam-2584	145	4	0,∞	0,∞	NOUN
ejpam-2584	145	5	)	)	PUNCT
ejpam-2584	145	6	is	be	AUX
ejpam-2584	145	7	nondecreasing	nondecrease	VERB
ejpam-2584	145	8	continuous	continuous	ADJ
ejpam-2584	145	9	and	and	CCONJ
ejpam-2584	145	10	f	f	PROPN
ejpam-2584	145	11	(	(	PUNCT
ejpam-2584	145	12	t	t	PROPN
ejpam-2584	145	13	)	)	PUNCT
ejpam-2584	145	14	=	=	SYM
ejpam-2584	145	15	0	0	PUNCT
ejpam-2584	146	1	if	if	SCONJ
ejpam-2584	146	2	and	and	CCONJ
ejpam-2584	146	3	only	only	ADV
ejpam-2584	146	4	if	if	SCONJ
ejpam-2584	146	5	t	t	PROPN
ejpam-2584	146	6	=	=	SYM
ejpam-2584	146	7	0	0	X
ejpam-2584	146	8	.	.	PUNCT
ejpam-2584	147	1	then	then	ADV
ejpam-2584	147	2	f	f	PROPN
ejpam-2584	147	3	has	have	VERB
ejpam-2584	147	4	a	a	DET
ejpam-2584	147	5	unique	unique	ADJ
ejpam-2584	147	6	fixed	fix	VERB
ejpam-2584	147	7	point	point	NOUN
ejpam-2584	147	8	in	in	ADP
ejpam-2584	147	9	x	x	X
ejpam-2584	147	10	.	.	PUNCT
ejpam-2584	148	1	proof	proof	NOUN
ejpam-2584	148	2	.	.	PUNCT
ejpam-2584	149	1	let	let	VERB
ejpam-2584	149	2	x0	x0	PROPN
ejpam-2584	149	3	∈	∈	PROPN
ejpam-2584	149	4	x	x	PRON
ejpam-2584	149	5	be	be	AUX
ejpam-2584	149	6	an	an	DET
ejpam-2584	149	7	arbitrary	arbitrary	ADJ
ejpam-2584	149	8	point	point	NOUN
ejpam-2584	149	9	and	and	CCONJ
ejpam-2584	149	10	xn	xn	NUM
ejpam-2584	150	1	=	=	SYM
ejpam-2584	150	2	f	f	X
ejpam-2584	150	3	xn−1	xn−1	PROPN
ejpam-2584	150	4	=	=	PUNCT
ejpam-2584	150	5	f	f	PROPN
ejpam-2584	150	6	n	n	CCONJ
ejpam-2584	150	7	x0	x0	PROPN
ejpam-2584	150	8	,	,	PUNCT
ejpam-2584	150	9	n=	n=	ADJ
ejpam-2584	150	10	1	1	NUM
ejpam-2584	150	11	,	,	PUNCT
ejpam-2584	150	12	2,3	2,3	NUM
ejpam-2584	150	13	,	,	PUNCT
ejpam-2584	150	14	.	.	PUNCT
ejpam-2584	150	15	.	.	PUNCT
ejpam-2584	150	16	.	.	PUNCT
ejpam-2584	151	1	f	f	PROPN
ejpam-2584	151	2	�	�	PROPN
ejpam-2584	151	3	p	p	PROPN
ejpam-2584	151	4	�	�	PROPN
ejpam-2584	151	5	t	t	PROPN
ejpam-2584	151	6	xn	xn	PROPN
ejpam-2584	151	7	,	,	PUNCT
ejpam-2584	151	8	t	t	PROPN
ejpam-2584	151	9	xn+1	xn+1	PROPN
ejpam-2584	151	10	�	�	PROPN
ejpam-2584	151	11	�	�	PROPN
ejpam-2584	151	12	=	=	SYM
ejpam-2584	151	13	f	f	PROPN
ejpam-2584	151	14	�	�	PROPN
ejpam-2584	151	15	p	p	PROPN
ejpam-2584	151	16	�	�	PROPN
ejpam-2584	151	17	t	t	PROPN
ejpam-2584	151	18	f	f	PROPN
ejpam-2584	151	19	xn−1	xn−1	PROPN
ejpam-2584	151	20	,	,	PUNCT
ejpam-2584	151	21	t	t	PROPN
ejpam-2584	151	22	f	f	PROPN
ejpam-2584	151	23	xn	xn	PROPN
ejpam-2584	151	24	�	�	PROPN
ejpam-2584	151	25	�	�	PROPN
ejpam-2584	151	26	≤β	≤β	PROPN
ejpam-2584	151	27	�	�	PROPN
ejpam-2584	151	28	f	f	PROPN
ejpam-2584	151	29	�	�	PROPN
ejpam-2584	151	30	p	p	PROPN
ejpam-2584	151	31	�	�	PROPN
ejpam-2584	151	32	t	t	PROPN
ejpam-2584	151	33	xn−1	xn−1	PROPN
ejpam-2584	151	34	,	,	PUNCT
ejpam-2584	151	35	t	t	PROPN
ejpam-2584	151	36	xn	xn	PROPN
ejpam-2584	151	37	�	�	PROPN
ejpam-2584	151	38	�	�	PROPN
ejpam-2584	151	39	+	+	CCONJ
ejpam-2584	151	40	f	f	PROPN
ejpam-2584	151	41	�	�	PROPN
ejpam-2584	151	42	p	p	PROPN
ejpam-2584	151	43	�	�	PROPN
ejpam-2584	151	44	t	t	PROPN
ejpam-2584	151	45	xn	xn	PROPN
ejpam-2584	151	46	,	,	PUNCT
ejpam-2584	151	47	t	t	PROPN
ejpam-2584	151	48	xn+1	xn+1	PROPN
ejpam-2584	151	49	�	�	PROPN
ejpam-2584	151	50	�	�	PROPN
ejpam-2584	151	51	�	�	PROPN
ejpam-2584	151	52	therefore	therefore	ADV
ejpam-2584	151	53	,	,	PUNCT
ejpam-2584	151	54	we	we	PRON
ejpam-2584	151	55	have	have	VERB
ejpam-2584	151	56	f	f	PROPN
ejpam-2584	151	57	�	�	PROPN
ejpam-2584	151	58	p	p	PROPN
ejpam-2584	151	59	�	�	PROPN
ejpam-2584	151	60	t	t	PROPN
ejpam-2584	151	61	xn	xn	PROPN
ejpam-2584	151	62	,	,	PUNCT
ejpam-2584	151	63	t	t	PROPN
ejpam-2584	151	64	xn+1	xn+1	PROPN
ejpam-2584	151	65	�	�	PROPN
ejpam-2584	151	66	�	�	PROPN
ejpam-2584	151	67	≤	≤	NOUN
ejpam-2584	151	68	β	β	X
ejpam-2584	151	69	1−	1−	NUM
ejpam-2584	151	70	β	β	X
ejpam-2584	151	71	f	f	PROPN
ejpam-2584	151	72	�	�	PROPN
ejpam-2584	151	73	p	p	PROPN
ejpam-2584	151	74	�	�	PROPN
ejpam-2584	151	75	t	t	PROPN
ejpam-2584	151	76	xn−1	xn−1	PROPN
ejpam-2584	151	77	,	,	PUNCT
ejpam-2584	151	78	t	t	PROPN
ejpam-2584	151	79	xn	xn	PROPN
ejpam-2584	151	80	�	�	PROPN
ejpam-2584	151	81	�	�	PROPN
ejpam-2584	151	82	.	.	PUNCT
ejpam-2584	152	1	also	also	ADV
ejpam-2584	152	2	,	,	PUNCT
ejpam-2584	152	3	we	we	PRON
ejpam-2584	152	4	obtain	obtain	VERB
ejpam-2584	152	5	that	that	SCONJ
ejpam-2584	152	6	f	f	PROPN
ejpam-2584	152	7	�	�	PROPN
ejpam-2584	152	8	p	p	PROPN
ejpam-2584	152	9	�	�	PROPN
ejpam-2584	152	10	t	t	PROPN
ejpam-2584	152	11	xn	xn	PROPN
ejpam-2584	152	12	,	,	PUNCT
ejpam-2584	152	13	t	t	PROPN
ejpam-2584	152	14	xn+1	xn+1	PROPN
ejpam-2584	152	15	�	�	PROPN
ejpam-2584	152	16	�	�	PROPN
ejpam-2584	152	17	≤	≤	PROPN
ejpam-2584	152	18	�	�	PROPN
ejpam-2584	152	19	β	β	PROPN
ejpam-2584	152	20	1−	1−	NUM
ejpam-2584	152	21	β	β	X
ejpam-2584	152	22	�	�	PROPN
ejpam-2584	152	23	n	n	PROPN
ejpam-2584	152	24	f	f	PROPN
ejpam-2584	152	25	�	�	PROPN
ejpam-2584	152	26	p	p	PROPN
ejpam-2584	152	27	�	�	PROPN
ejpam-2584	152	28	t	t	PROPN
ejpam-2584	152	29	x0	x0	PROPN
ejpam-2584	152	30	,	,	PUNCT
ejpam-2584	152	31	t	t	PROPN
ejpam-2584	152	32	x1	x1	PROPN
ejpam-2584	152	33	�	�	PROPN
ejpam-2584	152	34	�	�	PROPN
ejpam-2584	152	35	.	.	PUNCT
ejpam-2584	153	1	(	(	PUNCT
ejpam-2584	153	2	11	11	X
ejpam-2584	153	3	)	)	PUNCT
ejpam-2584	153	4	let	let	VERB
ejpam-2584	153	5	n→∞	n→∞	PRON
ejpam-2584	153	6	in	in	ADP
ejpam-2584	153	7	(	(	PUNCT
ejpam-2584	153	8	11	11	NUM
ejpam-2584	153	9	)	)	PUNCT
ejpam-2584	153	10	,	,	PUNCT
ejpam-2584	153	11	we	we	PRON
ejpam-2584	153	12	obtain	obtain	VERB
ejpam-2584	153	13	that	that	SCONJ
ejpam-2584	153	14	f	f	PROPN
ejpam-2584	153	15	�	�	PROPN
ejpam-2584	153	16	p	p	PROPN
ejpam-2584	153	17	�	�	PROPN
ejpam-2584	153	18	t	t	PROPN
ejpam-2584	153	19	xn	xn	PROPN
ejpam-2584	153	20	,	,	PUNCT
ejpam-2584	153	21	t	t	PROPN
ejpam-2584	153	22	xn+1	xn+1	PROPN
ejpam-2584	153	23	�	�	PROPN
ejpam-2584	153	24	�	�	PROPN
ejpam-2584	153	25	→	→	SYM
ejpam-2584	153	26	0	0	NUM
ejpam-2584	154	1	+	+	CCONJ
ejpam-2584	154	2	as	as	ADP
ejpam-2584	154	3	n→∞.	n→∞.	ADJ
ejpam-2584	154	4	again	again	ADV
ejpam-2584	154	5	using	use	VERB
ejpam-2584	154	6	(	(	PUNCT
ejpam-2584	154	7	11	11	NUM
ejpam-2584	154	8	)	)	PUNCT
ejpam-2584	154	9	,	,	PUNCT
ejpam-2584	154	10	for	for	ADP
ejpam-2584	154	11	all	all	DET
ejpam-2584	154	12	m	m	PROPN
ejpam-2584	154	13	,	,	PUNCT
ejpam-2584	154	14	n	n	PROPN
ejpam-2584	154	15	∈	∈	PROPN
ejpam-2584	154	16	n	n	CCONJ
ejpam-2584	154	17	,	,	PUNCT
ejpam-2584	154	18	taking	take	VERB
ejpam-2584	154	19	m	m	PRON
ejpam-2584	154	20	>	>	X
ejpam-2584	154	21	n	n	CCONJ
ejpam-2584	154	22	,	,	PUNCT
ejpam-2584	154	23	we	we	PRON
ejpam-2584	154	24	have	have	VERB
ejpam-2584	154	25	f	f	PROPN
ejpam-2584	154	26	�	�	PROPN
ejpam-2584	154	27	p	p	PROPN
ejpam-2584	154	28	�	�	PROPN
ejpam-2584	154	29	t	t	PROPN
ejpam-2584	154	30	xn	xn	PROPN
ejpam-2584	154	31	,	,	PUNCT
ejpam-2584	154	32	t	t	PROPN
ejpam-2584	154	33	xm	xm	PROPN
ejpam-2584	154	34	�	�	PROPN
ejpam-2584	154	35	�	�	PROPN
ejpam-2584	154	36	≤	≤	PROPN
ejpam-2584	154	37	�	�	PROPN
ejpam-2584	154	38	β	β	PROPN
ejpam-2584	154	39	1−	1−	NUM
ejpam-2584	154	40	β	β	X
ejpam-2584	154	41	�	�	PROPN
ejpam-2584	154	42	n	n	PROPN
ejpam-2584	154	43	f	f	PROPN
ejpam-2584	154	44	�	�	PROPN
ejpam-2584	154	45	p	p	PROPN
ejpam-2584	154	46	�	�	PROPN
ejpam-2584	154	47	t	t	PROPN
ejpam-2584	154	48	x0	x0	PROPN
ejpam-2584	154	49	,	,	PUNCT
ejpam-2584	154	50	t	t	PROPN
ejpam-2584	154	51	f	f	PROPN
ejpam-2584	154	52	m−n	m−n	PROPN
ejpam-2584	154	53	x0	x0	PROPN
ejpam-2584	154	54	�	�	PROPN
ejpam-2584	154	55	�	�	PROPN
ejpam-2584	154	56	(	(	PUNCT
ejpam-2584	154	57	12	12	NUM
ejpam-2584	154	58	)	)	PUNCT
ejpam-2584	154	59	letting	let	VERB
ejpam-2584	154	60	m	m	PRON
ejpam-2584	154	61	,	,	PUNCT
ejpam-2584	154	62	n→∞	n→∞	X
ejpam-2584	154	63	in	in	ADP
ejpam-2584	154	64	(	(	PUNCT
ejpam-2584	154	65	12	12	NUM
ejpam-2584	154	66	)	)	PUNCT
ejpam-2584	154	67	,	,	PUNCT
ejpam-2584	154	68	we	we	PRON
ejpam-2584	154	69	have	have	VERB
ejpam-2584	154	70	f	f	PROPN
ejpam-2584	154	71	�	�	PROPN
ejpam-2584	154	72	p	p	PROPN
ejpam-2584	154	73	�	�	PROPN
ejpam-2584	154	74	t	t	PROPN
ejpam-2584	154	75	xn	xn	PROPN
ejpam-2584	154	76	,	,	PUNCT
ejpam-2584	154	77	t	t	PROPN
ejpam-2584	154	78	xm	xm	PROPN
ejpam-2584	154	79	�	�	PROPN
ejpam-2584	154	80	�	�	PROPN
ejpam-2584	154	81	→	→	SYM
ejpam-2584	154	82	0	0	NUM
ejpam-2584	154	83	+	+	CCONJ
ejpam-2584	154	84	as	as	ADP
ejpam-2584	154	85	m	m	PROPN
ejpam-2584	154	86	,	,	PUNCT
ejpam-2584	154	87	n→∞.	n→∞.	VERB
ejpam-2584	155	1	so	so	ADV
ejpam-2584	155	2	,	,	PUNCT
ejpam-2584	155	3	we	we	PRON
ejpam-2584	155	4	have	have	VERB
ejpam-2584	155	5	p	p	PROPN
ejpam-2584	155	6	�	�	PROPN
ejpam-2584	155	7	t	t	PROPN
ejpam-2584	155	8	xn	xn	PROPN
ejpam-2584	155	9	,	,	PUNCT
ejpam-2584	155	10	t	t	PROPN
ejpam-2584	155	11	xm	xm	PROPN
ejpam-2584	155	12	�	�	PROPN
ejpam-2584	155	13	→	→	SYM
ejpam-2584	155	14	0	0	PROPN
ejpam-2584	155	15	as	as	ADP
ejpam-2584	155	16	m	m	PROPN
ejpam-2584	155	17	,	,	PUNCT
ejpam-2584	155	18	n→∞.	n→∞.	VERB
ejpam-2584	155	19	in	in	ADP
ejpam-2584	155	20	the	the	DET
ejpam-2584	155	21	next	next	ADJ
ejpam-2584	155	22	stage	stage	NOUN
ejpam-2584	155	23	,	,	PUNCT
ejpam-2584	155	24	by	by	ADP
ejpam-2584	155	25	using	use	VERB
ejpam-2584	155	26	similar	similar	ADJ
ejpam-2584	155	27	methods	method	NOUN
ejpam-2584	155	28	in	in	ADP
ejpam-2584	155	29	theorem	theorem	NOUN
ejpam-2584	155	30	2	2	NUM
ejpam-2584	155	31	,	,	PUNCT
ejpam-2584	155	32	we	we	PRON
ejpam-2584	155	33	obtain	obtain	VERB
ejpam-2584	155	34	that	that	PRON
ejpam-2584	155	35	�	�	PROPN
ejpam-2584	155	36	t	t	PROPN
ejpam-2584	155	37	xn	xn	PROPN
ejpam-2584	155	38	is	be	AUX
ejpam-2584	155	39	cauchy	cauchy	ADJ
ejpam-2584	155	40	sequence	sequence	NOUN
ejpam-2584	155	41	in	in	ADP
ejpam-2584	155	42	complete	complete	ADJ
ejpam-2584	155	43	partial	partial	ADJ
ejpam-2584	155	44	metric	metric	ADJ
ejpam-2584	155	45	space	space	NOUN
ejpam-2584	155	46	�	�	PROPN
ejpam-2584	156	1	x	x	SYM
ejpam-2584	156	2	,	,	PUNCT
ejpam-2584	156	3	p	p	PROPN
ejpam-2584	156	4	�	�	PROPN
ejpam-2584	156	5	and	and	CCONJ
ejpam-2584	156	6	there	there	PRON
ejpam-2584	156	7	exist	exist	VERB
ejpam-2584	156	8	u	u	NOUN
ejpam-2584	156	9	∈	∈	PROPN
ejpam-2584	156	10	x	x	PUNCT
ejpam-2584	156	11	such	such	ADJ
ejpam-2584	156	12	that	that	DET
ejpam-2584	156	13	�	�	PROPN
ejpam-2584	156	14	t	t	PROPN
ejpam-2584	156	15	xn	xn	PROPN
ejpam-2584	156	16	converges	converge	NOUN
ejpam-2584	156	17	to	to	ADP
ejpam-2584	156	18	tu	tu	PROPN
ejpam-2584	156	19	∈	∈	PROPN
ejpam-2584	156	20	x	x	X
ejpam-2584	156	21	and	and	CCONJ
ejpam-2584	156	22	xn(k)→	xn(k)→	PROPN
ejpam-2584	156	23	u	u	PROPN
ejpam-2584	156	24	,	,	PUNCT
ejpam-2584	156	25	such	such	ADJ
ejpam-2584	156	26	that	that	SCONJ
ejpam-2584	156	27	lim	lim	PROPN
ejpam-2584	156	28	k→∞	k→∞	PROPN
ejpam-2584	156	29	t	t	PROPN
ejpam-2584	156	30	xn(k	xn(k	NUM
ejpam-2584	156	31	)	)	PUNCT
ejpam-2584	157	1	=	=	SYM
ejpam-2584	157	2	tu	tu	PROPN
ejpam-2584	157	3	and	and	CCONJ
ejpam-2584	157	4	lim	lim	PROPN
ejpam-2584	157	5	k→∞	k→∞	PROPN
ejpam-2584	158	1	p	p	PROPN
ejpam-2584	158	2	�	�	PROPN
ejpam-2584	158	3	t	t	PROPN
ejpam-2584	158	4	xn(k	xn(k	NUM
ejpam-2584	158	5	)	)	PUNCT
ejpam-2584	158	6	,	,	PUNCT
ejpam-2584	158	7	tu	tu	PROPN
ejpam-2584	158	8	�	�	PROPN
ejpam-2584	158	9	=	=	SYM
ejpam-2584	158	10	p	p	PROPN
ejpam-2584	158	11	(	(	PUNCT
ejpam-2584	158	12	tu	tu	PROPN
ejpam-2584	158	13	,	,	PUNCT
ejpam-2584	158	14	tu	tu	PROPN
ejpam-2584	158	15	)	)	PUNCT
ejpam-2584	158	16	=	=	PUNCT
ejpam-2584	159	1	0	0	X
ejpam-2584	159	2	.	.	PUNCT
ejpam-2584	160	1	now	now	ADV
ejpam-2584	160	2	,	,	PUNCT
ejpam-2584	160	3	we	we	PRON
ejpam-2584	160	4	will	will	AUX
ejpam-2584	160	5	show	show	VERB
ejpam-2584	160	6	that	that	SCONJ
ejpam-2584	160	7	u	u	PRON
ejpam-2584	160	8	∈	∈	PROPN
ejpam-2584	160	9	x	x	X
ejpam-2584	160	10	is	be	AUX
ejpam-2584	160	11	a	a	DET
ejpam-2584	160	12	fixed	fix	VERB
ejpam-2584	160	13	point	point	NOUN
ejpam-2584	160	14	of	of	ADP
ejpam-2584	160	15	f	f	PROPN
ejpam-2584	160	16	.	.	PUNCT
ejpam-2584	161	1	indeed	indeed	ADV
ejpam-2584	161	2	,	,	PUNCT
ejpam-2584	161	3	we	we	PRON
ejpam-2584	161	4	have	have	VERB
ejpam-2584	161	5	f	f	PROPN
ejpam-2584	161	6	�	�	PROPN
ejpam-2584	161	7	p	p	PROPN
ejpam-2584	161	8	�	�	PROPN
ejpam-2584	161	9	t	t	PROPN
ejpam-2584	161	10	f	f	PROPN
ejpam-2584	161	11	u	u	PROPN
ejpam-2584	161	12	,	,	PUNCT
ejpam-2584	161	13	t	t	PROPN
ejpam-2584	161	14	xn+1	xn+1	PROPN
ejpam-2584	161	15	�	�	PROPN
ejpam-2584	161	16	�	�	PROPN
ejpam-2584	161	17	=	=	SYM
ejpam-2584	161	18	f	f	PROPN
ejpam-2584	161	19	�	�	PROPN
ejpam-2584	161	20	p	p	PROPN
ejpam-2584	161	21	�	�	PROPN
ejpam-2584	161	22	t	t	PROPN
ejpam-2584	161	23	f	f	PROPN
ejpam-2584	161	24	u	u	PROPN
ejpam-2584	161	25	,	,	PUNCT
ejpam-2584	161	26	t	t	PROPN
ejpam-2584	161	27	f	f	PROPN
ejpam-2584	161	28	xn	xn	PROPN
ejpam-2584	161	29	�	�	PROPN
ejpam-2584	161	30	�	�	PROPN
ejpam-2584	161	31	m.	m.	PROPN
ejpam-2584	161	32	kir	kir	PROPN
ejpam-2584	161	33	,	,	PUNCT
ejpam-2584	161	34	h.	h.	PROPN
ejpam-2584	161	35	kiziltunc	kiziltunc	PROPN
ejpam-2584	161	36	/	/	SYM
ejpam-2584	161	37	eur	eur	PROPN
ejpam-2584	161	38	.	.	PUNCT
ejpam-2584	162	1	j.	j.	PROPN
ejpam-2584	162	2	pure	pure	PROPN
ejpam-2584	162	3	appl	appl	PROPN
ejpam-2584	162	4	.	.	PROPN
ejpam-2584	162	5	math	math	PROPN
ejpam-2584	162	6	,	,	PUNCT
ejpam-2584	162	7	9	9	NUM
ejpam-2584	162	8	(	(	PUNCT
ejpam-2584	162	9	2016	2016	NUM
ejpam-2584	162	10	)	)	PUNCT
ejpam-2584	162	11	,	,	PUNCT
ejpam-2584	162	12	443	443	NUM
ejpam-2584	162	13	-	-	SYM
ejpam-2584	162	14	451	451	NUM
ejpam-2584	162	15	449	449	NUM
ejpam-2584	162	16	≤β	≤β	PROPN
ejpam-2584	162	17	�	�	PROPN
ejpam-2584	162	18	f	f	PROPN
ejpam-2584	162	19	�	�	PROPN
ejpam-2584	162	20	p	p	PROPN
ejpam-2584	162	21	�	�	PROPN
ejpam-2584	162	22	tu	tu	PROPN
ejpam-2584	162	23	,	,	PUNCT
ejpam-2584	162	24	t	t	PROPN
ejpam-2584	162	25	f	f	PROPN
ejpam-2584	162	26	u	u	PROPN
ejpam-2584	162	27	�	�	PROPN
ejpam-2584	162	28	�	�	PROPN
ejpam-2584	162	29	+	+	CCONJ
ejpam-2584	162	30	f	f	PROPN
ejpam-2584	162	31	�	�	PROPN
ejpam-2584	162	32	p	p	PROPN
ejpam-2584	162	33	�	�	PROPN
ejpam-2584	162	34	t	t	PROPN
ejpam-2584	162	35	xn	xn	PROPN
ejpam-2584	162	36	,	,	PUNCT
ejpam-2584	162	37	t	t	PROPN
ejpam-2584	162	38	xn+1	xn+1	PROPN
ejpam-2584	162	39	�	�	PROPN
ejpam-2584	162	40	�	�	PROPN
ejpam-2584	162	41	�	�	PROPN
ejpam-2584	162	42	.	.	PUNCT
ejpam-2584	163	1	(	(	PUNCT
ejpam-2584	163	2	13	13	NUM
ejpam-2584	163	3	)	)	PUNCT
ejpam-2584	163	4	let	let	VERB
ejpam-2584	163	5	n→∞	n→∞	PRON
ejpam-2584	163	6	in	in	ADP
ejpam-2584	163	7	(	(	PUNCT
ejpam-2584	163	8	13	13	NUM
ejpam-2584	163	9	)	)	PUNCT
ejpam-2584	163	10	,	,	PUNCT
ejpam-2584	163	11	we	we	PRON
ejpam-2584	163	12	have	have	VERB
ejpam-2584	163	13	f(p	f(p	PROPN
ejpam-2584	163	14	�	�	PROPN
ejpam-2584	163	15	t	t	PROPN
ejpam-2584	163	16	f	f	PROPN
ejpam-2584	163	17	u	u	PROPN
ejpam-2584	163	18	,	,	PUNCT
ejpam-2584	163	19	tu	tu	PROPN
ejpam-2584	163	20	�	�	PROPN
ejpam-2584	163	21	)	)	PUNCT
ejpam-2584	163	22	≤	≤	PROPN
ejpam-2584	163	23	βf	βf	PRON
ejpam-2584	163	24	�	�	PROPN
ejpam-2584	163	25	p	p	PROPN
ejpam-2584	163	26	�	�	PROPN
ejpam-2584	163	27	tu	tu	PROPN
ejpam-2584	163	28	,	,	PUNCT
ejpam-2584	163	29	t	t	PROPN
ejpam-2584	163	30	f	f	PROPN
ejpam-2584	163	31	u	u	PROPN
ejpam-2584	163	32	�	�	PROPN
ejpam-2584	163	33	�	�	PROPN
ejpam-2584	163	34	.	.	PUNCT
ejpam-2584	164	1	(	(	PUNCT
ejpam-2584	164	2	14	14	NUM
ejpam-2584	164	3	)	)	PUNCT
ejpam-2584	164	4	the	the	DET
ejpam-2584	164	5	inequality	inequality	NOUN
ejpam-2584	164	6	(	(	PUNCT
ejpam-2584	164	7	14	14	NUM
ejpam-2584	164	8	)	)	PUNCT
ejpam-2584	164	9	is	be	AUX
ejpam-2584	164	10	contradiction	contradiction	NOUN
ejpam-2584	164	11	unless	unless	SCONJ
ejpam-2584	164	12	p	p	PROPN
ejpam-2584	164	13	�	�	PROPN
ejpam-2584	164	14	tu	tu	PROPN
ejpam-2584	164	15	,	,	PUNCT
ejpam-2584	164	16	t	t	PROPN
ejpam-2584	164	17	f	f	PROPN
ejpam-2584	164	18	u	u	X
ejpam-2584	164	19	�	�	PROPN
ejpam-2584	164	20	=	=	SYM
ejpam-2584	164	21	0	0	NUM
ejpam-2584	164	22	.	.	PUNCT
ejpam-2584	165	1	thus	thus	ADV
ejpam-2584	165	2	,	,	PUNCT
ejpam-2584	165	3	tu	tu	PROPN
ejpam-2584	165	4	=	=	SYM
ejpam-2584	165	5	t	t	PROPN
ejpam-2584	165	6	f	f	PROPN
ejpam-2584	165	7	u.	u.	PROPN
ejpam-2584	165	8	also	also	ADV
ejpam-2584	165	9	,	,	PUNCT
ejpam-2584	165	10	t	t	PROPN
ejpam-2584	165	11	is	be	AUX
ejpam-2584	165	12	one	one	NUM
ejpam-2584	165	13	to	to	ADP
ejpam-2584	165	14	one	one	NUM
ejpam-2584	165	15	,	,	PUNCT
ejpam-2584	165	16	we	we	PRON
ejpam-2584	165	17	obtain	obtain	VERB
ejpam-2584	165	18	f	f	PROPN
ejpam-2584	165	19	u=	u=	ADV
ejpam-2584	165	20	u.	u.	ADV
ejpam-2584	166	1	thus	thus	ADV
ejpam-2584	166	2	we	we	PRON
ejpam-2584	166	3	provide	provide	VERB
ejpam-2584	166	4	u	u	PRON
ejpam-2584	166	5	∈	∈	PROPN
ejpam-2584	166	6	x	x	X
ejpam-2584	166	7	is	be	AUX
ejpam-2584	166	8	a	a	DET
ejpam-2584	166	9	fixed	fix	VERB
ejpam-2584	166	10	point	point	NOUN
ejpam-2584	166	11	of	of	ADP
ejpam-2584	166	12	f	f	PROPN
ejpam-2584	166	13	.	.	PUNCT
ejpam-2584	167	1	the	the	DET
ejpam-2584	167	2	uniqueness	uniqueness	NOUN
ejpam-2584	167	3	of	of	ADP
ejpam-2584	167	4	the	the	DET
ejpam-2584	167	5	fixed	fix	VERB
ejpam-2584	167	6	point	point	NOUN
ejpam-2584	167	7	can	can	AUX
ejpam-2584	167	8	be	be	AUX
ejpam-2584	167	9	shown	show	VERB
ejpam-2584	167	10	easily	easily	ADV
ejpam-2584	167	11	.	.	PUNCT
ejpam-2584	168	1	some	some	DET
ejpam-2584	168	2	results	result	NOUN
ejpam-2584	168	3	of	of	ADP
ejpam-2584	168	4	the	the	DET
ejpam-2584	168	5	theorem	theorem	ADJ
ejpam-2584	168	6	3	3	NUM
ejpam-2584	168	7	are	be	AUX
ejpam-2584	168	8	following	follow	VERB
ejpam-2584	168	9	.	.	PUNCT
ejpam-2584	169	1	corollary	corollary	ADJ
ejpam-2584	169	2	3	3	X
ejpam-2584	169	3	.	.	PUNCT
ejpam-2584	170	1	let	let	VERB
ejpam-2584	170	2	�	�	PROPN
ejpam-2584	170	3	x	x	SYM
ejpam-2584	170	4	,	,	PUNCT
ejpam-2584	170	5	p	p	PROPN
ejpam-2584	170	6	�	�	PROPN
ejpam-2584	170	7	be	be	AUX
ejpam-2584	170	8	a	a	DET
ejpam-2584	170	9	complete	complete	ADJ
ejpam-2584	170	10	partial	partial	ADJ
ejpam-2584	170	11	metric	metric	ADJ
ejpam-2584	170	12	space	space	NOUN
ejpam-2584	170	13	and	and	CCONJ
ejpam-2584	170	14	t	t	PROPN
ejpam-2584	170	15	,	,	PUNCT
ejpam-2584	170	16	f	f	X
ejpam-2584	170	17	:	:	PUNCT
ejpam-2584	170	18	x	x	X
ejpam-2584	170	19	→	→	PUNCT
ejpam-2584	170	20	x	x	PUNCT
ejpam-2584	170	21	be	be	AUX
ejpam-2584	170	22	mappings	mapping	NOUN
ejpam-2584	170	23	such	such	ADJ
ejpam-2584	170	24	that	that	SCONJ
ejpam-2584	170	25	t	t	PROPN
ejpam-2584	170	26	is	be	AUX
ejpam-2584	170	27	one	one	NUM
ejpam-2584	170	28	to	to	ADP
ejpam-2584	170	29	one	one	NUM
ejpam-2584	170	30	,	,	PUNCT
ejpam-2584	170	31	continuous	continuous	ADJ
ejpam-2584	170	32	and	and	CCONJ
ejpam-2584	170	33	subsequentially	subsequentially	ADV
ejpam-2584	170	34	convergent	convergent	NOUN
ejpam-2584	170	35	(	(	PUNCT
ejpam-2584	170	36	or	or	CCONJ
ejpam-2584	170	37	graph	graph	NOUN
ejpam-2584	170	38	closed	closed	ADJ
ejpam-2584	170	39	)	)	PUNCT
ejpam-2584	170	40	.	.	PUNCT
ejpam-2584	171	1	if	if	SCONJ
ejpam-2584	171	2	for	for	ADP
ejpam-2584	171	3	β	β	PROPN
ejpam-2584	171	4	∈	∈	PROPN
ejpam-2584	171	5	�	�	PROPN
ejpam-2584	171	6	0	0	NUM
ejpam-2584	171	7	,	,	PUNCT
ejpam-2584	171	8	1	1	NUM
ejpam-2584	171	9	2	2	NUM
ejpam-2584	171	10	�	�	NOUN
ejpam-2584	171	11	and	and	CCONJ
ejpam-2584	171	12	for	for	ADP
ejpam-2584	171	13	x	x	X
ejpam-2584	171	14	,	,	PUNCT
ejpam-2584	171	15	y	y	PROPN
ejpam-2584	171	16	∈	∈	PROPN
ejpam-2584	171	17	x	x	X
ejpam-2584	171	18	,	,	PUNCT
ejpam-2584	171	19	p	p	PROPN
ejpam-2584	171	20	�	�	PROPN
ejpam-2584	171	21	t	t	PROPN
ejpam-2584	171	22	f	f	PROPN
ejpam-2584	171	23	x	x	X
ejpam-2584	171	24	,	,	PUNCT
ejpam-2584	171	25	t	t	PROPN
ejpam-2584	171	26	f	f	PROPN
ejpam-2584	171	27	y	y	PROPN
ejpam-2584	171	28	�	�	PROPN
ejpam-2584	171	29	≤	≤	PROPN
ejpam-2584	171	30	β	β	X
ejpam-2584	171	31	�	�	PROPN
ejpam-2584	171	32	p	p	PROPN
ejpam-2584	171	33	�	�	PROPN
ejpam-2584	171	34	t	t	PROPN
ejpam-2584	171	35	x	x	X
ejpam-2584	171	36	,	,	PUNCT
ejpam-2584	171	37	t	t	PROPN
ejpam-2584	171	38	f	f	PROPN
ejpam-2584	171	39	x	x	X
ejpam-2584	171	40	�	�	PROPN
ejpam-2584	171	41	+	+	CCONJ
ejpam-2584	171	42	p	p	PROPN
ejpam-2584	171	43	�	�	PROPN
ejpam-2584	171	44	t	t	PROPN
ejpam-2584	171	45	y	y	PROPN
ejpam-2584	171	46	,	,	PUNCT
ejpam-2584	171	47	t	t	PROPN
ejpam-2584	171	48	f	f	PROPN
ejpam-2584	171	49	y	y	PROPN
ejpam-2584	171	50	�	�	PROPN
ejpam-2584	171	51	�	�	PROPN
ejpam-2584	171	52	.	.	PUNCT
ejpam-2584	172	1	then	then	ADV
ejpam-2584	172	2	,	,	PUNCT
ejpam-2584	172	3	f	f	PROPN
ejpam-2584	172	4	has	have	VERB
ejpam-2584	172	5	a	a	DET
ejpam-2584	172	6	unique	unique	ADJ
ejpam-2584	172	7	fixed	fix	VERB
ejpam-2584	172	8	point	point	NOUN
ejpam-2584	172	9	in	in	ADP
ejpam-2584	172	10	�	�	PROPN
ejpam-2584	172	11	x	x	SYM
ejpam-2584	172	12	,	,	PUNCT
ejpam-2584	172	13	p	p	PROPN
ejpam-2584	172	14	�	�	PROPN
ejpam-2584	172	15	.	.	PUNCT
ejpam-2584	173	1	corollary	corollary	ADJ
ejpam-2584	173	2	4	4	NUM
ejpam-2584	173	3	.	.	PUNCT
ejpam-2584	174	1	let	let	VERB
ejpam-2584	174	2	�	�	PROPN
ejpam-2584	174	3	x	x	SYM
ejpam-2584	174	4	,	,	PUNCT
ejpam-2584	174	5	p	p	PROPN
ejpam-2584	174	6	�	�	PROPN
ejpam-2584	174	7	be	be	AUX
ejpam-2584	174	8	a	a	DET
ejpam-2584	174	9	complete	complete	ADJ
ejpam-2584	174	10	partial	partial	ADJ
ejpam-2584	174	11	metric	metric	ADJ
ejpam-2584	174	12	space	space	NOUN
ejpam-2584	174	13	and	and	CCONJ
ejpam-2584	174	14	f	f	NOUN
ejpam-2584	174	15	:	:	PUNCT
ejpam-2584	174	16	x	x	X
ejpam-2584	174	17	→	→	PUNCT
ejpam-2584	174	18	x	x	PUNCT
ejpam-2584	174	19	be	be	AUX
ejpam-2584	174	20	a	a	DET
ejpam-2584	174	21	mapping	mapping	NOUN
ejpam-2584	174	22	.	.	PUNCT
ejpam-2584	175	1	if	if	SCONJ
ejpam-2584	175	2	for	for	ADP
ejpam-2584	175	3	β	β	PROPN
ejpam-2584	175	4	∈	∈	PROPN
ejpam-2584	175	5	�	�	PROPN
ejpam-2584	175	6	0	0	NUM
ejpam-2584	175	7	,	,	PUNCT
ejpam-2584	175	8	1	1	NUM
ejpam-2584	175	9	2	2	NUM
ejpam-2584	175	10	�	�	NOUN
ejpam-2584	175	11	and	and	CCONJ
ejpam-2584	175	12	for	for	ADP
ejpam-2584	175	13	x	x	X
ejpam-2584	175	14	,	,	PUNCT
ejpam-2584	175	15	y	y	PROPN
ejpam-2584	175	16	∈	∈	PROPN
ejpam-2584	175	17	x	x	X
ejpam-2584	175	18	,	,	PUNCT
ejpam-2584	175	19	f	f	PROPN
ejpam-2584	175	20	�	�	PROPN
ejpam-2584	175	21	p	p	PROPN
ejpam-2584	175	22	�	�	PROPN
ejpam-2584	175	23	f	f	PROPN
ejpam-2584	175	24	x	x	PROPN
ejpam-2584	175	25	,	,	PUNCT
ejpam-2584	175	26	f	f	PROPN
ejpam-2584	175	27	y	y	PROPN
ejpam-2584	175	28	�	�	PROPN
ejpam-2584	175	29	�	�	PROPN
ejpam-2584	175	30	≤	≤	PROPN
ejpam-2584	175	31	β	β	X
ejpam-2584	175	32	�	�	PROPN
ejpam-2584	175	33	f	f	PROPN
ejpam-2584	175	34	�	�	PROPN
ejpam-2584	175	35	p	p	PROPN
ejpam-2584	175	36	�	�	PROPN
ejpam-2584	175	37	x	x	SYM
ejpam-2584	175	38	,	,	PUNCT
ejpam-2584	175	39	f	f	PROPN
ejpam-2584	175	40	x	x	SYM
ejpam-2584	175	41	�	�	PROPN
ejpam-2584	175	42	�	�	PROPN
ejpam-2584	175	43	+	+	CCONJ
ejpam-2584	175	44	f	f	PROPN
ejpam-2584	175	45	�	�	PROPN
ejpam-2584	175	46	p	p	PROPN
ejpam-2584	175	47	�	�	PROPN
ejpam-2584	175	48	y	y	PROPN
ejpam-2584	175	49	,	,	PUNCT
ejpam-2584	175	50	f	f	PROPN
ejpam-2584	175	51	y	y	PROPN
ejpam-2584	175	52	�	�	PROPN
ejpam-2584	175	53	�	�	PROPN
ejpam-2584	175	54	�	�	PROPN
ejpam-2584	175	55	where	where	SCONJ
ejpam-2584	175	56	f	f	NOUN
ejpam-2584	175	57	:	:	PUNCT
ejpam-2584	176	1	[	[	X
ejpam-2584	176	2	0,∞	0,∞	NOUN
ejpam-2584	176	3	)	)	PUNCT
ejpam-2584	176	4	→	→	PUNCT
ejpam-2584	177	1	[	[	X
ejpam-2584	177	2	0,∞	0,∞	NOUN
ejpam-2584	177	3	)	)	PUNCT
ejpam-2584	177	4	,	,	PUNCT
ejpam-2584	177	5	f	f	PROPN
ejpam-2584	177	6	is	be	AUX
ejpam-2584	177	7	nondecreasing	nondecrease	VERB
ejpam-2584	177	8	continuous	continuous	ADJ
ejpam-2584	177	9	from	from	ADP
ejpam-2584	177	10	the	the	DET
ejpam-2584	177	11	right	right	NOUN
ejpam-2584	177	12	and	and	CCONJ
ejpam-2584	177	13	f−1	f−1	PROPN
ejpam-2584	177	14	(	(	PUNCT
ejpam-2584	177	15	0	0	NUM
ejpam-2584	177	16	)	)	PUNCT
ejpam-2584	177	17	=	=	PRON
ejpam-2584	177	18	{	{	PUNCT
ejpam-2584	177	19	0	0	NUM
ejpam-2584	177	20	}	}	PUNCT
ejpam-2584	177	21	.	.	PUNCT
ejpam-2584	178	1	then	then	ADV
ejpam-2584	178	2	f	f	PROPN
ejpam-2584	178	3	has	have	VERB
ejpam-2584	178	4	a	a	DET
ejpam-2584	178	5	unique	unique	ADJ
ejpam-2584	178	6	fixed	fix	VERB
ejpam-2584	178	7	point	point	NOUN
ejpam-2584	178	8	.	.	PUNCT
ejpam-2584	179	1	corollary	corollary	ADJ
ejpam-2584	179	2	5	5	NUM
ejpam-2584	179	3	.	.	PUNCT
ejpam-2584	180	1	let	let	VERB
ejpam-2584	180	2	�	�	PROPN
ejpam-2584	180	3	x	x	SYM
ejpam-2584	180	4	,	,	PUNCT
ejpam-2584	180	5	p	p	PROPN
ejpam-2584	180	6	�	�	PROPN
ejpam-2584	180	7	be	be	AUX
ejpam-2584	180	8	a	a	DET
ejpam-2584	180	9	complete	complete	ADJ
ejpam-2584	180	10	partial	partial	ADJ
ejpam-2584	180	11	metric	metric	ADJ
ejpam-2584	180	12	space	space	NOUN
ejpam-2584	180	13	and	and	CCONJ
ejpam-2584	180	14	f	f	NOUN
ejpam-2584	180	15	:	:	PUNCT
ejpam-2584	180	16	x	x	X
ejpam-2584	180	17	→	→	PUNCT
ejpam-2584	180	18	x	x	PART
ejpam-2584	180	19	be	be	AUX
ejpam-2584	180	20	mapping	map	VERB
ejpam-2584	180	21	.	.	PUNCT
ejpam-2584	181	1	if	if	SCONJ
ejpam-2584	181	2	β	β	PROPN
ejpam-2584	181	3	∈	∈	PROPN
ejpam-2584	181	4	�	�	PROPN
ejpam-2584	181	5	0	0	NUM
ejpam-2584	181	6	,	,	PUNCT
ejpam-2584	181	7	1	1	NUM
ejpam-2584	181	8	2	2	NUM
ejpam-2584	181	9	�	�	PROPN
ejpam-2584	181	10	and	and	CCONJ
ejpam-2584	181	11	x	x	NOUN
ejpam-2584	181	12	,	,	PUNCT
ejpam-2584	181	13	y	y	PROPN
ejpam-2584	181	14	∈	∈	PROPN
ejpam-2584	181	15	x	x	X
ejpam-2584	181	16	.	.	PUNCT
ejpam-2584	182	1	p	p	PROPN
ejpam-2584	182	2	�	�	PROPN
ejpam-2584	182	3	f	f	X
ejpam-2584	182	4	x	x	PROPN
ejpam-2584	182	5	,	,	PUNCT
ejpam-2584	182	6	f	f	PROPN
ejpam-2584	182	7	y	y	PROPN
ejpam-2584	182	8	�	�	PROPN
ejpam-2584	182	9	≤	≤	PROPN
ejpam-2584	182	10	β	β	X
ejpam-2584	182	11	�	�	PROPN
ejpam-2584	182	12	p	p	PROPN
ejpam-2584	182	13	�	�	PROPN
ejpam-2584	182	14	x	x	SYM
ejpam-2584	182	15	,	,	PUNCT
ejpam-2584	182	16	f	f	PROPN
ejpam-2584	182	17	x	x	SYM
ejpam-2584	182	18	�	�	PROPN
ejpam-2584	182	19	+	+	CCONJ
ejpam-2584	182	20	p	p	PROPN
ejpam-2584	182	21	�	�	PROPN
ejpam-2584	182	22	y	y	PROPN
ejpam-2584	182	23	,	,	PUNCT
ejpam-2584	182	24	f	f	PROPN
ejpam-2584	182	25	y	y	PROPN
ejpam-2584	182	26	�	�	PROPN
ejpam-2584	182	27	�	�	PROPN
ejpam-2584	182	28	then	then	ADV
ejpam-2584	182	29	,	,	PUNCT
ejpam-2584	182	30	f	f	PROPN
ejpam-2584	182	31	has	have	VERB
ejpam-2584	182	32	a	a	DET
ejpam-2584	182	33	unique	unique	ADJ
ejpam-2584	182	34	fixed	fix	VERB
ejpam-2584	182	35	point	point	NOUN
ejpam-2584	182	36	in	in	ADP
ejpam-2584	182	37	�	�	PROPN
ejpam-2584	182	38	x	x	SYM
ejpam-2584	182	39	,	,	PUNCT
ejpam-2584	182	40	p	p	PROPN
ejpam-2584	182	41	�	�	PROPN
ejpam-2584	182	42	.	.	PUNCT
ejpam-2584	183	1	theorem	theorem	VERB
ejpam-2584	183	2	4	4	NUM
ejpam-2584	183	3	.	.	PUNCT
ejpam-2584	184	1	let	let	VERB
ejpam-2584	184	2	�	�	PROPN
ejpam-2584	184	3	x	x	SYM
ejpam-2584	184	4	,	,	PUNCT
ejpam-2584	184	5	p	p	PROPN
ejpam-2584	184	6	�	�	PROPN
ejpam-2584	184	7	be	be	AUX
ejpam-2584	184	8	a	a	DET
ejpam-2584	184	9	complete	complete	ADJ
ejpam-2584	184	10	partial	partial	ADJ
ejpam-2584	184	11	metric	metric	ADJ
ejpam-2584	184	12	space	space	NOUN
ejpam-2584	184	13	and	and	CCONJ
ejpam-2584	184	14	t	t	PROPN
ejpam-2584	184	15	,	,	PUNCT
ejpam-2584	184	16	f	f	X
ejpam-2584	184	17	:	:	PUNCT
ejpam-2584	184	18	x	x	X
ejpam-2584	184	19	→	→	PUNCT
ejpam-2584	184	20	x	x	PUNCT
ejpam-2584	184	21	be	be	AUX
ejpam-2584	184	22	mappings	mapping	NOUN
ejpam-2584	184	23	such	such	ADJ
ejpam-2584	184	24	that	that	SCONJ
ejpam-2584	184	25	t	t	PROPN
ejpam-2584	184	26	is	be	AUX
ejpam-2584	184	27	one	one	NUM
ejpam-2584	184	28	to	to	ADP
ejpam-2584	184	29	one	one	NUM
ejpam-2584	184	30	,	,	PUNCT
ejpam-2584	184	31	continuous	continuous	ADJ
ejpam-2584	184	32	and	and	CCONJ
ejpam-2584	184	33	subsequentially	subsequentially	ADV
ejpam-2584	184	34	convergent	convergent	NOUN
ejpam-2584	184	35	(	(	PUNCT
ejpam-2584	184	36	or	or	CCONJ
ejpam-2584	184	37	graph	graph	NOUN
ejpam-2584	184	38	closed	closed	ADJ
ejpam-2584	184	39	)	)	PUNCT
ejpam-2584	184	40	.	.	PUNCT
ejpam-2584	185	1	if	if	SCONJ
ejpam-2584	185	2	λ	λ	PROPN
ejpam-2584	185	3	∈	∈	PROPN
ejpam-2584	185	4	�	�	PROPN
ejpam-2584	185	5	0	0	NUM
ejpam-2584	185	6	,	,	PUNCT
ejpam-2584	185	7	1	1	NUM
ejpam-2584	185	8	2	2	NUM
ejpam-2584	185	9	�	�	NOUN
ejpam-2584	185	10	and	and	CCONJ
ejpam-2584	185	11	for	for	ADP
ejpam-2584	185	12	each	each	DET
ejpam-2584	185	13	x	x	X
ejpam-2584	185	14	,	,	PUNCT
ejpam-2584	185	15	y	y	PROPN
ejpam-2584	185	16	∈	∈	PROPN
ejpam-2584	185	17	x	x	X
ejpam-2584	185	18	f	f	X
ejpam-2584	185	19	�	�	PROPN
ejpam-2584	185	20	p	p	PROPN
ejpam-2584	185	21	�	�	PROPN
ejpam-2584	185	22	t	t	PROPN
ejpam-2584	185	23	f	f	PROPN
ejpam-2584	185	24	x	x	X
ejpam-2584	185	25	,	,	PUNCT
ejpam-2584	185	26	t	t	PROPN
ejpam-2584	185	27	f	f	PROPN
ejpam-2584	185	28	y	y	PROPN
ejpam-2584	185	29	�	�	PROPN
ejpam-2584	185	30	�	�	PROPN
ejpam-2584	185	31	≤	≤	PROPN
ejpam-2584	185	32	λ	λ	PROPN
ejpam-2584	185	33	�	�	PROPN
ejpam-2584	185	34	f	f	PROPN
ejpam-2584	185	35	�	�	PROPN
ejpam-2584	185	36	p	p	PROPN
ejpam-2584	185	37	�	�	PROPN
ejpam-2584	185	38	t	t	PROPN
ejpam-2584	185	39	x	x	X
ejpam-2584	185	40	,	,	PUNCT
ejpam-2584	185	41	t	t	PROPN
ejpam-2584	185	42	f	f	PROPN
ejpam-2584	185	43	y	y	PROPN
ejpam-2584	185	44	�	�	PROPN
ejpam-2584	185	45	�	�	PROPN
ejpam-2584	185	46	+	+	CCONJ
ejpam-2584	185	47	f	f	PROPN
ejpam-2584	185	48	�	�	PROPN
ejpam-2584	185	49	p	p	PROPN
ejpam-2584	185	50	�	�	PROPN
ejpam-2584	185	51	t	t	PROPN
ejpam-2584	185	52	y	y	PROPN
ejpam-2584	185	53	,	,	PUNCT
ejpam-2584	185	54	t	t	PROPN
ejpam-2584	185	55	f	f	PROPN
ejpam-2584	185	56	x	x	SYM
ejpam-2584	185	57	�	�	PROPN
ejpam-2584	185	58	�	�	PROPN
ejpam-2584	185	59	�	�	PROPN
ejpam-2584	185	60	(	(	PUNCT
ejpam-2584	185	61	15	15	NUM
ejpam-2584	185	62	)	)	PUNCT
ejpam-2584	186	1	where	where	SCONJ
ejpam-2584	186	2	f	f	NOUN
ejpam-2584	186	3	:	:	PUNCT
ejpam-2584	187	1	[	[	X
ejpam-2584	187	2	0,∞)→	0,∞)→	NOUN
ejpam-2584	187	3	[	[	X
ejpam-2584	187	4	0,∞	0,∞	NOUN
ejpam-2584	187	5	)	)	PUNCT
ejpam-2584	187	6	is	be	AUX
ejpam-2584	187	7	nondecreasing	nondecrease	VERB
ejpam-2584	187	8	continuous	continuous	ADJ
ejpam-2584	187	9	from	from	ADP
ejpam-2584	187	10	the	the	DET
ejpam-2584	187	11	right	right	NOUN
ejpam-2584	187	12	and	and	CCONJ
ejpam-2584	187	13	f−1	f−1	PROPN
ejpam-2584	187	14	(	(	PUNCT
ejpam-2584	187	15	0	0	NUM
ejpam-2584	187	16	)	)	PUNCT
ejpam-2584	187	17	=	=	PRON
ejpam-2584	187	18	{	{	PUNCT
ejpam-2584	187	19	0	0	NUM
ejpam-2584	187	20	}	}	PUNCT
ejpam-2584	187	21	.	.	PUNCT
ejpam-2584	188	1	then	then	ADV
ejpam-2584	188	2	,	,	PUNCT
ejpam-2584	188	3	f	f	PROPN
ejpam-2584	188	4	has	have	VERB
ejpam-2584	188	5	a	a	DET
ejpam-2584	188	6	unique	unique	ADJ
ejpam-2584	188	7	fixed	fix	VERB
ejpam-2584	188	8	point	point	NOUN
ejpam-2584	188	9	in	in	ADP
ejpam-2584	188	10	x	x	X
ejpam-2584	188	11	.	.	PUNCT
ejpam-2584	189	1	proof	proof	NOUN
ejpam-2584	189	2	.	.	PUNCT
ejpam-2584	190	1	let	let	VERB
ejpam-2584	190	2	x0	x0	PROPN
ejpam-2584	190	3	∈	∈	PROPN
ejpam-2584	190	4	x	x	PRON
ejpam-2584	190	5	be	be	AUX
ejpam-2584	190	6	an	an	DET
ejpam-2584	190	7	arbitrary	arbitrary	ADJ
ejpam-2584	190	8	point	point	NOUN
ejpam-2584	190	9	and	and	CCONJ
ejpam-2584	190	10	xn	xn	NUM
ejpam-2584	191	1	=	=	SYM
ejpam-2584	191	2	f	f	X
ejpam-2584	191	3	xn−1	xn−1	PROPN
ejpam-2584	191	4	=	=	PUNCT
ejpam-2584	191	5	f	f	PROPN
ejpam-2584	191	6	n	n	ADJ
ejpam-2584	191	7	x0	x0	PROPN
ejpam-2584	191	8	.	.	PUNCT
ejpam-2584	192	1	also	also	ADV
ejpam-2584	192	2	consider	consider	VERB
ejpam-2584	192	3	p	p	PROPN
ejpam-2584	192	4	�	�	PROPN
ejpam-2584	192	5	t	t	PROPN
ejpam-2584	192	6	xn	xn	PROPN
ejpam-2584	192	7	,	,	PUNCT
ejpam-2584	192	8	t	t	PROPN
ejpam-2584	192	9	xn	xn	PROPN
ejpam-2584	192	10	�	�	PROPN
ejpam-2584	192	11	≤	≤	PROPN
ejpam-2584	192	12	p	p	PROPN
ejpam-2584	192	13	�	�	PROPN
ejpam-2584	192	14	t	t	PROPN
ejpam-2584	192	15	xn	xn	PROPN
ejpam-2584	192	16	,	,	PUNCT
ejpam-2584	192	17	t	t	PROPN
ejpam-2584	192	18	xn+1	xn+1	PROPN
ejpam-2584	192	19	�	�	PROPN
ejpam-2584	192	20	f(p	f(p	PROPN
ejpam-2584	192	21	�	�	PROPN
ejpam-2584	192	22	t	t	PROPN
ejpam-2584	192	23	xn	xn	PROPN
ejpam-2584	192	24	,	,	PUNCT
ejpam-2584	192	25	t	t	PROPN
ejpam-2584	192	26	xn+1	xn+1	PROPN
ejpam-2584	192	27	�	�	PROPN
ejpam-2584	192	28	)	)	PUNCT
ejpam-2584	193	1	=	=	PROPN
ejpam-2584	193	2	f(p	f(p	PROPN
ejpam-2584	193	3	�	�	PROPN
ejpam-2584	193	4	t	t	PROPN
ejpam-2584	193	5	f	f	PROPN
ejpam-2584	193	6	xn−1	xn−1	PROPN
ejpam-2584	193	7	,	,	PUNCT
ejpam-2584	193	8	t	t	PROPN
ejpam-2584	193	9	f	f	PROPN
ejpam-2584	193	10	xn	xn	PROPN
ejpam-2584	193	11	�	�	PROPN
ejpam-2584	193	12	)	)	PUNCT
ejpam-2584	193	13	m.	m.	NOUN
ejpam-2584	193	14	kir	kir	PROPN
ejpam-2584	193	15	,	,	PUNCT
ejpam-2584	193	16	h.	h.	PROPN
ejpam-2584	193	17	kiziltunc	kiziltunc	PROPN
ejpam-2584	193	18	/	/	SYM
ejpam-2584	193	19	eur	eur	PROPN
ejpam-2584	193	20	.	.	PUNCT
ejpam-2584	194	1	j.	j.	PROPN
ejpam-2584	194	2	pure	pure	PROPN
ejpam-2584	194	3	appl	appl	PROPN
ejpam-2584	194	4	.	.	PROPN
ejpam-2584	194	5	math	math	PROPN
ejpam-2584	194	6	,	,	PUNCT
ejpam-2584	194	7	9	9	NUM
ejpam-2584	194	8	(	(	PUNCT
ejpam-2584	194	9	2016	2016	NUM
ejpam-2584	194	10	)	)	PUNCT
ejpam-2584	194	11	,	,	PUNCT
ejpam-2584	194	12	443	443	NUM
ejpam-2584	194	13	-	-	SYM
ejpam-2584	194	14	451	451	NUM
ejpam-2584	194	15	450	450	NUM
ejpam-2584	194	16	≤λf(p	≤λf(p	PROPN
ejpam-2584	194	17	�	�	PROPN
ejpam-2584	194	18	t	t	PROPN
ejpam-2584	194	19	xn−1	xn−1	PROPN
ejpam-2584	194	20	,	,	PUNCT
ejpam-2584	194	21	t	t	PROPN
ejpam-2584	194	22	xn+1	xn+1	PROPN
ejpam-2584	194	23	�	�	PROPN
ejpam-2584	194	24	)	)	PUNCT
ejpam-2584	195	1	+	+	PROPN
ejpam-2584	195	2	λf(p	λf(p	X
ejpam-2584	195	3	�	�	PROPN
ejpam-2584	195	4	t	t	PROPN
ejpam-2584	195	5	xn	xn	PROPN
ejpam-2584	195	6	,	,	PUNCT
ejpam-2584	195	7	t	t	PROPN
ejpam-2584	195	8	xn	xn	PROPN
ejpam-2584	195	9	�	�	PROPN
ejpam-2584	195	10	)	)	PUNCT
ejpam-2584	195	11	≤λf(p	≤λf(p	PROPN
ejpam-2584	195	12	�	�	PROPN
ejpam-2584	195	13	t	t	PROPN
ejpam-2584	195	14	xn−1	xn−1	PROPN
ejpam-2584	195	15	,	,	PUNCT
ejpam-2584	195	16	t	t	PROPN
ejpam-2584	195	17	xn+1	xn+1	PROPN
ejpam-2584	195	18	�	�	PROPN
ejpam-2584	195	19	)	)	PUNCT
ejpam-2584	196	1	+	+	PROPN
ejpam-2584	196	2	λf(p	λf(p	X
ejpam-2584	196	3	�	�	PROPN
ejpam-2584	196	4	t	t	PROPN
ejpam-2584	196	5	xn+1	xn+1	PROPN
ejpam-2584	196	6	,	,	PUNCT
ejpam-2584	196	7	t	t	PROPN
ejpam-2584	196	8	xn	xn	PROPN
ejpam-2584	196	9	�	�	PROPN
ejpam-2584	196	10	)	)	PUNCT
ejpam-2584	196	11	therefore	therefore	ADV
ejpam-2584	196	12	,	,	PUNCT
ejpam-2584	196	13	we	we	PRON
ejpam-2584	196	14	have	have	VERB
ejpam-2584	196	15	f(p	f(p	PROPN
ejpam-2584	196	16	�	�	PROPN
ejpam-2584	196	17	t	t	PROPN
ejpam-2584	196	18	xn	xn	PROPN
ejpam-2584	196	19	,	,	PUNCT
ejpam-2584	196	20	t	t	PROPN
ejpam-2584	196	21	xn+1	xn+1	PROPN
ejpam-2584	196	22	�	�	PROPN
ejpam-2584	196	23	)	)	PUNCT
ejpam-2584	196	24	≤	≤	NUM
ejpam-2584	197	1	λ	λ	PROPN
ejpam-2584	197	2	1−λ	1−λ	NUM
ejpam-2584	197	3	f(p	f(p	PROPN
ejpam-2584	197	4	�	�	PROPN
ejpam-2584	197	5	t	t	PROPN
ejpam-2584	197	6	xn−1	xn−1	PROPN
ejpam-2584	197	7	,	,	PUNCT
ejpam-2584	197	8	t	t	PROPN
ejpam-2584	197	9	xn+1	xn+1	PROPN
ejpam-2584	197	10	�	�	PROPN
ejpam-2584	197	11	)	)	PUNCT
ejpam-2584	197	12	.	.	PUNCT
ejpam-2584	198	1	also	also	ADV
ejpam-2584	198	2	,	,	PUNCT
ejpam-2584	198	3	for	for	ADP
ejpam-2584	198	4	all	all	DET
ejpam-2584	198	5	m	m	PROPN
ejpam-2584	198	6	(	(	PUNCT
ejpam-2584	198	7	k	k	NOUN
ejpam-2584	198	8	)	)	PUNCT
ejpam-2584	198	9	,	,	PUNCT
ejpam-2584	198	10	n	n	CCONJ
ejpam-2584	198	11	(	(	PUNCT
ejpam-2584	198	12	k	k	X
ejpam-2584	198	13	)	)	PUNCT
ejpam-2584	198	14	∈	∈	PROPN
ejpam-2584	198	15	n	n	CCONJ
ejpam-2584	198	16	,	,	PUNCT
ejpam-2584	198	17	taking	take	VERB
ejpam-2584	198	18	m	m	PRON
ejpam-2584	198	19	(	(	PUNCT
ejpam-2584	198	20	k	k	NOUN
ejpam-2584	198	21	)	)	PUNCT
ejpam-2584	198	22	>	>	X
ejpam-2584	199	1	n	n	PROPN
ejpam-2584	199	2	(	(	PUNCT
ejpam-2584	199	3	k	k	NOUN
ejpam-2584	199	4	)	)	PUNCT
ejpam-2584	199	5	,	,	PUNCT
ejpam-2584	199	6	we	we	PRON
ejpam-2584	199	7	have	have	VERB
ejpam-2584	199	8	f(p	f(p	PROPN
ejpam-2584	199	9	�	�	PROPN
ejpam-2584	199	10	t	t	PROPN
ejpam-2584	199	11	xm(k	xm(k	PUNCT
ejpam-2584	199	12	)	)	PUNCT
ejpam-2584	199	13	,	,	PUNCT
ejpam-2584	199	14	t	t	PROPN
ejpam-2584	199	15	xn(k	xn(k	NUM
ejpam-2584	199	16	)	)	PUNCT
ejpam-2584	199	17	�	�	PROPN
ejpam-2584	199	18	≤	≤	NUM
ejpam-2584	199	19	�	�	PROPN
ejpam-2584	199	20	λ	λ	PROPN
ejpam-2584	199	21	1−λ	1−λ	NUM
ejpam-2584	199	22	�	�	PROPN
ejpam-2584	199	23	n(k	n(k	PROPN
ejpam-2584	199	24	)	)	PUNCT
ejpam-2584	199	25	f(p	f(p	PROPN
ejpam-2584	199	26	�	�	PROPN
ejpam-2584	199	27	t	t	PROPN
ejpam-2584	199	28	xm(k)−n(k	xm(k)−n(k	PROPN
ejpam-2584	199	29	)	)	PUNCT
ejpam-2584	199	30	,	,	PUNCT
ejpam-2584	199	31	t	t	PROPN
ejpam-2584	199	32	xn(k	xn(k	NUM
ejpam-2584	199	33	)	)	PUNCT
ejpam-2584	199	34	�	�	PROPN
ejpam-2584	199	35	)	)	PUNCT
ejpam-2584	199	36	.	.	PUNCT
ejpam-2584	200	1	(	(	PUNCT
ejpam-2584	200	2	16	16	X
ejpam-2584	200	3	)	)	PUNCT
ejpam-2584	200	4	note	note	NOUN
ejpam-2584	200	5	that	that	SCONJ
ejpam-2584	200	6	t	t	PROPN
ejpam-2584	200	7	is	be	AUX
ejpam-2584	200	8	subsequentially	subsequentially	ADV
ejpam-2584	200	9	convergent	convergent	ADJ
ejpam-2584	200	10	,	,	PUNCT
ejpam-2584	200	11	then	then	ADV
ejpam-2584	200	12	there	there	PRON
ejpam-2584	200	13	exists	exist	VERB
ejpam-2584	200	14	u	u	NOUN
ejpam-2584	200	15	∈	∈	PROPN
ejpam-2584	200	16	x	x	PUNCT
ejpam-2584	200	17	such	such	ADJ
ejpam-2584	200	18	that	that	SCONJ
ejpam-2584	200	19	lim	lim	PROPN
ejpam-2584	200	20	k→∞	k→∞	NOUN
ejpam-2584	200	21	p	p	PROPN
ejpam-2584	200	22	�	�	PROPN
ejpam-2584	200	23	xn(k	xn(k	NUM
ejpam-2584	200	24	)	)	PUNCT
ejpam-2584	200	25	,	,	PUNCT
ejpam-2584	200	26	u	u	PROPN
ejpam-2584	200	27	�	�	PROPN
ejpam-2584	200	28	=	=	SYM
ejpam-2584	200	29	lim	lim	PROPN
ejpam-2584	200	30	k→∞	k→∞	PROPN
ejpam-2584	201	1	p	p	PROPN
ejpam-2584	201	2	(	(	PUNCT
ejpam-2584	201	3	u	u	NOUN
ejpam-2584	201	4	,	,	PUNCT
ejpam-2584	201	5	u	u	NOUN
ejpam-2584	201	6	)	)	PUNCT
ejpam-2584	201	7	.	.	PUNCT
ejpam-2584	202	1	let	let	VERB
ejpam-2584	202	2	k→∞	k→∞	NOUN
ejpam-2584	202	3	in	in	ADP
ejpam-2584	202	4	(	(	PUNCT
ejpam-2584	202	5	16	16	NUM
ejpam-2584	202	6	)	)	PUNCT
ejpam-2584	202	7	,	,	PUNCT
ejpam-2584	202	8	we	we	PRON
ejpam-2584	202	9	obtain	obtain	VERB
ejpam-2584	202	10	that	that	SCONJ
ejpam-2584	202	11	f(p	f(p	PROPN
ejpam-2584	202	12	�	�	PROPN
ejpam-2584	202	13	t	t	PROPN
ejpam-2584	202	14	xm(k	xm(k	PUNCT
ejpam-2584	202	15	)	)	PUNCT
ejpam-2584	202	16	,	,	PUNCT
ejpam-2584	202	17	t	t	PROPN
ejpam-2584	202	18	xn(k	xn(k	NUM
ejpam-2584	202	19	)	)	PUNCT
ejpam-2584	202	20	�	�	PROPN
ejpam-2584	202	21	→	→	SYM
ejpam-2584	202	22	0	0	NUM
ejpam-2584	203	1	+	+	PUNCT
ejpam-2584	203	2	as	as	ADP
ejpam-2584	203	3	k→∞.	k→∞.	NOUN
ejpam-2584	203	4	(	(	PUNCT
ejpam-2584	203	5	17	17	NUM
ejpam-2584	203	6	)	)	PUNCT
ejpam-2584	203	7	the	the	DET
ejpam-2584	203	8	inequality	inequality	NOUN
ejpam-2584	203	9	(	(	PUNCT
ejpam-2584	203	10	17	17	NUM
ejpam-2584	203	11	)	)	PUNCT
ejpam-2584	203	12	implies	imply	VERB
ejpam-2584	203	13	that	that	SCONJ
ejpam-2584	203	14	p	p	PROPN
ejpam-2584	203	15	�	�	PROPN
ejpam-2584	203	16	t	t	PROPN
ejpam-2584	203	17	xm(k	xm(k	PUNCT
ejpam-2584	203	18	)	)	PUNCT
ejpam-2584	203	19	,	,	PUNCT
ejpam-2584	203	20	t	t	PROPN
ejpam-2584	203	21	xn(k	xn(k	NUM
ejpam-2584	203	22	)	)	PUNCT
ejpam-2584	203	23	�	�	PROPN
ejpam-2584	203	24	=	=	SYM
ejpam-2584	203	25	0	0	PUNCT
ejpam-2584	204	1	hence	hence	ADV
ejpam-2584	204	2	,	,	PUNCT
ejpam-2584	204	3	we	we	PRON
ejpam-2584	204	4	obtain	obtain	VERB
ejpam-2584	204	5	that	that	PRON
ejpam-2584	204	6	�	�	PROPN
ejpam-2584	204	7	t	t	PROPN
ejpam-2584	204	8	xn	xn	PROPN
ejpam-2584	204	9	is	be	AUX
ejpam-2584	204	10	cauchy	cauchy	ADJ
ejpam-2584	204	11	sequence	sequence	NOUN
ejpam-2584	204	12	in	in	ADP
ejpam-2584	204	13	complete	complete	ADJ
ejpam-2584	204	14	partial	partial	ADJ
ejpam-2584	204	15	metric	metric	ADJ
ejpam-2584	204	16	space	space	NOUN
ejpam-2584	204	17	�	�	PROPN
ejpam-2584	204	18	x	x	SYM
ejpam-2584	204	19	,	,	PUNCT
ejpam-2584	204	20	p	p	PROPN
ejpam-2584	204	21	�	�	PROPN
ejpam-2584	204	22	and	and	CCONJ
ejpam-2584	204	23	there	there	PRON
ejpam-2584	204	24	exist	exist	VERB
ejpam-2584	204	25	a	a	DET
ejpam-2584	204	26	point	point	NOUN
ejpam-2584	204	27	u	u	NOUN
ejpam-2584	204	28	∈	∈	PROPN
ejpam-2584	204	29	x	x	PUNCT
ejpam-2584	204	30	such	such	ADJ
ejpam-2584	204	31	that	that	SCONJ
ejpam-2584	204	32	this	this	DET
ejpam-2584	204	33	point	point	NOUN
ejpam-2584	204	34	the	the	DET
ejpam-2584	204	35	unique	unique	ADJ
ejpam-2584	204	36	fixed	fix	VERB
ejpam-2584	204	37	point	point	NOUN
ejpam-2584	204	38	of	of	ADP
ejpam-2584	204	39	f	f	PROPN
ejpam-2584	204	40	.	.	PUNCT
ejpam-2584	205	1	corollary	corollary	ADJ
ejpam-2584	205	2	6	6	NUM
ejpam-2584	205	3	.	.	PUNCT
ejpam-2584	206	1	let	let	VERB
ejpam-2584	206	2	�	�	PROPN
ejpam-2584	206	3	x	x	SYM
ejpam-2584	206	4	,	,	PUNCT
ejpam-2584	206	5	p	p	PROPN
ejpam-2584	206	6	�	�	PROPN
ejpam-2584	206	7	be	be	AUX
ejpam-2584	206	8	a	a	DET
ejpam-2584	206	9	complete	complete	ADJ
ejpam-2584	206	10	partial	partial	ADJ
ejpam-2584	206	11	metric	metric	ADJ
ejpam-2584	206	12	space	space	NOUN
ejpam-2584	206	13	and	and	CCONJ
ejpam-2584	206	14	t	t	PROPN
ejpam-2584	206	15	,	,	PUNCT
ejpam-2584	206	16	f	f	X
ejpam-2584	206	17	:	:	PUNCT
ejpam-2584	206	18	x	x	X
ejpam-2584	206	19	→	→	PUNCT
ejpam-2584	206	20	x	x	PUNCT
ejpam-2584	206	21	be	be	AUX
ejpam-2584	206	22	mappings	mapping	NOUN
ejpam-2584	206	23	such	such	ADJ
ejpam-2584	206	24	that	that	SCONJ
ejpam-2584	206	25	t	t	PROPN
ejpam-2584	206	26	is	be	AUX
ejpam-2584	206	27	one	one	NUM
ejpam-2584	206	28	to	to	ADP
ejpam-2584	206	29	one	one	NUM
ejpam-2584	206	30	,	,	PUNCT
ejpam-2584	206	31	continuous	continuous	ADJ
ejpam-2584	206	32	and	and	CCONJ
ejpam-2584	206	33	subsequentially	subsequentially	ADV
ejpam-2584	206	34	convergent	convergent	NOUN
ejpam-2584	206	35	(	(	PUNCT
ejpam-2584	206	36	or	or	CCONJ
ejpam-2584	206	37	graph	graph	NOUN
ejpam-2584	206	38	closed	closed	ADJ
ejpam-2584	206	39	)	)	PUNCT
ejpam-2584	206	40	.	.	PUNCT
ejpam-2584	207	1	if	if	SCONJ
ejpam-2584	207	2	λ	λ	PROPN
ejpam-2584	207	3	∈	∈	PROPN
ejpam-2584	207	4	�	�	PROPN
ejpam-2584	207	5	0	0	NUM
ejpam-2584	207	6	,	,	PUNCT
ejpam-2584	207	7	1	1	NUM
ejpam-2584	207	8	2	2	NUM
ejpam-2584	207	9	�	�	NOUN
ejpam-2584	207	10	and	and	CCONJ
ejpam-2584	207	11	for	for	ADP
ejpam-2584	207	12	each	each	DET
ejpam-2584	207	13	x	x	X
ejpam-2584	207	14	,	,	PUNCT
ejpam-2584	207	15	y	y	PROPN
ejpam-2584	207	16	∈	∈	PROPN
ejpam-2584	207	17	x	x	X
ejpam-2584	207	18	,	,	PUNCT
ejpam-2584	207	19	p	p	PROPN
ejpam-2584	207	20	�	�	PROPN
ejpam-2584	207	21	t	t	PROPN
ejpam-2584	207	22	f	f	PROPN
ejpam-2584	207	23	x	x	X
ejpam-2584	207	24	,	,	PUNCT
ejpam-2584	207	25	t	t	PROPN
ejpam-2584	207	26	f	f	PROPN
ejpam-2584	207	27	y	y	PROPN
ejpam-2584	207	28	�	�	PROPN
ejpam-2584	207	29	≤	≤	PROPN
ejpam-2584	207	30	λ	λ	PROPN
ejpam-2584	207	31	�	�	PROPN
ejpam-2584	207	32	p	p	PROPN
ejpam-2584	207	33	�	�	PROPN
ejpam-2584	207	34	t	t	PROPN
ejpam-2584	207	35	x	x	X
ejpam-2584	207	36	,	,	PUNCT
ejpam-2584	207	37	t	t	PROPN
ejpam-2584	207	38	f	f	PROPN
ejpam-2584	207	39	y	y	PROPN
ejpam-2584	207	40	�	�	PROPN
ejpam-2584	207	41	+	+	CCONJ
ejpam-2584	207	42	p	p	PROPN
ejpam-2584	207	43	�	�	PROPN
ejpam-2584	207	44	t	t	PROPN
ejpam-2584	207	45	y	y	PROPN
ejpam-2584	207	46	,	,	PUNCT
ejpam-2584	207	47	t	t	PROPN
ejpam-2584	207	48	f	f	PROPN
ejpam-2584	207	49	x	x	SYM
ejpam-2584	207	50	�	�	PROPN
ejpam-2584	207	51	�	�	PROPN
ejpam-2584	207	52	then	then	ADV
ejpam-2584	207	53	f	f	PROPN
ejpam-2584	207	54	has	have	VERB
ejpam-2584	207	55	a	a	DET
ejpam-2584	207	56	unique	unique	ADJ
ejpam-2584	207	57	fixed	fix	VERB
ejpam-2584	207	58	point	point	NOUN
ejpam-2584	207	59	.	.	PUNCT
ejpam-2584	208	1	also	also	ADV
ejpam-2584	208	2	,	,	PUNCT
ejpam-2584	208	3	if	if	SCONJ
ejpam-2584	208	4	t	t	PROPN
ejpam-2584	208	5	is	be	AUX
ejpam-2584	208	6	sequentially	sequentially	ADV
ejpam-2584	208	7	convergent	convergent	NOUN
ejpam-2584	208	8	then	then	ADV
ejpam-2584	208	9	for	for	ADP
ejpam-2584	208	10	every	every	DET
ejpam-2584	208	11	x0	x0	PROPN
ejpam-2584	208	12	∈	∈	PROPN
ejpam-2584	208	13	x	x	X
ejpam-2584	208	14	the	the	DET
ejpam-2584	208	15	sequence	sequence	NOUN
ejpam-2584	208	16	of	of	ADP
ejpam-2584	208	17	iterates	iterate	VERB
ejpam-2584	208	18	�	�	PROPN
ejpam-2584	208	19	f	f	PROPN
ejpam-2584	208	20	n	n	CCONJ
ejpam-2584	208	21	x0	x0	PROPN
ejpam-2584	208	22	converges	converge	VERB
ejpam-2584	208	23	to	to	ADP
ejpam-2584	208	24	the	the	DET
ejpam-2584	208	25	fixed	fix	VERB
ejpam-2584	208	26	point	point	NOUN
ejpam-2584	208	27	.	.	PUNCT
ejpam-2584	209	1	corollary	corollary	ADJ
ejpam-2584	209	2	7	7	NUM
ejpam-2584	209	3	.	.	PUNCT
ejpam-2584	210	1	let	let	VERB
ejpam-2584	210	2	�	�	PROPN
ejpam-2584	210	3	x	x	SYM
ejpam-2584	210	4	,	,	PUNCT
ejpam-2584	210	5	p	p	PROPN
ejpam-2584	210	6	�	�	PROPN
ejpam-2584	210	7	be	be	AUX
ejpam-2584	210	8	a	a	DET
ejpam-2584	210	9	complete	complete	ADJ
ejpam-2584	210	10	partial	partial	ADJ
ejpam-2584	210	11	metric	metric	ADJ
ejpam-2584	210	12	space	space	NOUN
ejpam-2584	210	13	and	and	CCONJ
ejpam-2584	210	14	f	f	NOUN
ejpam-2584	210	15	:	:	PUNCT
ejpam-2584	210	16	x	x	X
ejpam-2584	210	17	→	→	PUNCT
ejpam-2584	210	18	x	x	PUNCT
ejpam-2584	210	19	be	be	AUX
ejpam-2584	210	20	a	a	DET
ejpam-2584	210	21	mapping	mapping	NOUN
ejpam-2584	210	22	.	.	PUNCT
ejpam-2584	211	1	if	if	SCONJ
ejpam-2584	211	2	λ	λ	PROPN
ejpam-2584	211	3	∈	∈	PROPN
ejpam-2584	211	4	�	�	PROPN
ejpam-2584	211	5	0	0	NUM
ejpam-2584	211	6	,	,	PUNCT
ejpam-2584	211	7	1	1	NUM
ejpam-2584	211	8	2	2	NUM
ejpam-2584	211	9	�	�	NOUN
ejpam-2584	211	10	and	and	CCONJ
ejpam-2584	211	11	for	for	ADP
ejpam-2584	211	12	each	each	DET
ejpam-2584	211	13	x	x	X
ejpam-2584	211	14	,	,	PUNCT
ejpam-2584	211	15	y	y	PROPN
ejpam-2584	211	16	∈	∈	PROPN
ejpam-2584	211	17	x	x	X
ejpam-2584	211	18	,	,	PUNCT
ejpam-2584	211	19	f	f	PROPN
ejpam-2584	211	20	�	�	PROPN
ejpam-2584	211	21	p	p	PROPN
ejpam-2584	211	22	�	�	PROPN
ejpam-2584	211	23	f	f	PROPN
ejpam-2584	211	24	x	x	PROPN
ejpam-2584	211	25	,	,	PUNCT
ejpam-2584	211	26	f	f	PROPN
ejpam-2584	211	27	y	y	PROPN
ejpam-2584	211	28	�	�	PROPN
ejpam-2584	211	29	�	�	PROPN
ejpam-2584	211	30	≤	≤	PROPN
ejpam-2584	211	31	λ	λ	PROPN
ejpam-2584	211	32	�	�	PROPN
ejpam-2584	211	33	f	f	PROPN
ejpam-2584	211	34	�	�	PROPN
ejpam-2584	211	35	p	p	PROPN
ejpam-2584	211	36	�	�	PROPN
ejpam-2584	211	37	x	x	SYM
ejpam-2584	211	38	,	,	PUNCT
ejpam-2584	211	39	f	f	PROPN
ejpam-2584	211	40	y	y	PROPN
ejpam-2584	211	41	�	�	PROPN
ejpam-2584	211	42	�	�	PROPN
ejpam-2584	211	43	+	+	CCONJ
ejpam-2584	211	44	f	f	PROPN
ejpam-2584	211	45	�	�	PROPN
ejpam-2584	211	46	p	p	PROPN
ejpam-2584	211	47	�	�	PROPN
ejpam-2584	211	48	y	y	PROPN
ejpam-2584	211	49	,	,	PUNCT
ejpam-2584	211	50	f	f	PROPN
ejpam-2584	211	51	x	x	SYM
ejpam-2584	211	52	�	�	PROPN
ejpam-2584	211	53	�	�	PROPN
ejpam-2584	211	54	�	�	PROPN
ejpam-2584	211	55	where	where	SCONJ
ejpam-2584	211	56	f	f	NOUN
ejpam-2584	211	57	:	:	PUNCT
ejpam-2584	212	1	[	[	X
ejpam-2584	212	2	0,∞	0,∞	NOUN
ejpam-2584	212	3	)	)	PUNCT
ejpam-2584	212	4	→	→	PUNCT
ejpam-2584	213	1	[	[	X
ejpam-2584	213	2	0,∞	0,∞	NOUN
ejpam-2584	213	3	)	)	PUNCT
ejpam-2584	213	4	,	,	PUNCT
ejpam-2584	213	5	f	f	PROPN
ejpam-2584	213	6	is	be	AUX
ejpam-2584	213	7	nondecreasing	nondecrease	VERB
ejpam-2584	213	8	continuous	continuous	ADJ
ejpam-2584	213	9	from	from	ADP
ejpam-2584	213	10	the	the	DET
ejpam-2584	213	11	right	right	NOUN
ejpam-2584	213	12	and	and	CCONJ
ejpam-2584	213	13	f−1	f−1	PROPN
ejpam-2584	213	14	(	(	PUNCT
ejpam-2584	213	15	0	0	NUM
ejpam-2584	213	16	)	)	PUNCT
ejpam-2584	213	17	=	=	PRON
ejpam-2584	213	18	{	{	PUNCT
ejpam-2584	213	19	0	0	NUM
ejpam-2584	213	20	}	}	PUNCT
ejpam-2584	213	21	.	.	PUNCT
ejpam-2584	214	1	then	then	ADV
ejpam-2584	214	2	f	f	PROPN
ejpam-2584	214	3	has	have	VERB
ejpam-2584	214	4	a	a	DET
ejpam-2584	214	5	unique	unique	ADJ
ejpam-2584	214	6	fixed	fix	VERB
ejpam-2584	214	7	point	point	NOUN
ejpam-2584	214	8	.	.	PUNCT
ejpam-2584	215	1	corollary	corollary	ADJ
ejpam-2584	215	2	8	8	NUM
ejpam-2584	215	3	.	.	PUNCT
ejpam-2584	216	1	let	let	VERB
ejpam-2584	216	2	�	�	PROPN
ejpam-2584	216	3	x	x	SYM
ejpam-2584	216	4	,	,	PUNCT
ejpam-2584	216	5	p	p	PROPN
ejpam-2584	216	6	�	�	PROPN
ejpam-2584	216	7	be	be	AUX
ejpam-2584	216	8	a	a	DET
ejpam-2584	216	9	complete	complete	ADJ
ejpam-2584	216	10	partial	partial	ADJ
ejpam-2584	216	11	metric	metric	ADJ
ejpam-2584	216	12	space	space	NOUN
ejpam-2584	216	13	and	and	CCONJ
ejpam-2584	216	14	f	f	NOUN
ejpam-2584	216	15	:	:	PUNCT
ejpam-2584	216	16	x	x	X
ejpam-2584	216	17	→	→	PUNCT
ejpam-2584	216	18	x	x	PART
ejpam-2584	216	19	be	be	AUX
ejpam-2584	216	20	mapping	map	VERB
ejpam-2584	216	21	.	.	PUNCT
ejpam-2584	217	1	if	if	SCONJ
ejpam-2584	217	2	λ	λ	PROPN
ejpam-2584	217	3	∈	∈	PROPN
ejpam-2584	217	4	�	�	PROPN
ejpam-2584	217	5	0	0	NUM
ejpam-2584	217	6	,	,	PUNCT
ejpam-2584	217	7	1	1	NUM
ejpam-2584	217	8	2	2	NUM
ejpam-2584	217	9	�	�	PROPN
ejpam-2584	217	10	and	and	CCONJ
ejpam-2584	217	11	x	x	NOUN
ejpam-2584	217	12	,	,	PUNCT
ejpam-2584	217	13	y	y	PROPN
ejpam-2584	217	14	∈	∈	PROPN
ejpam-2584	217	15	x	x	X
ejpam-2584	217	16	,	,	PUNCT
ejpam-2584	217	17	p	p	PROPN
ejpam-2584	217	18	�	�	PROPN
ejpam-2584	217	19	f	f	PROPN
ejpam-2584	217	20	x	x	PROPN
ejpam-2584	217	21	,	,	PUNCT
ejpam-2584	217	22	f	f	PROPN
ejpam-2584	217	23	y	y	PROPN
ejpam-2584	217	24	�	�	PROPN
ejpam-2584	217	25	≤	≤	PROPN
ejpam-2584	217	26	λ	λ	PROPN
ejpam-2584	217	27	�	�	PROPN
ejpam-2584	217	28	p	p	PROPN
ejpam-2584	217	29	�	�	PROPN
ejpam-2584	217	30	x	x	SYM
ejpam-2584	217	31	,	,	PUNCT
ejpam-2584	217	32	f	f	PROPN
ejpam-2584	217	33	y	y	PROPN
ejpam-2584	217	34	�	�	PROPN
ejpam-2584	217	35	+	+	CCONJ
ejpam-2584	217	36	p	p	PROPN
ejpam-2584	217	37	�	�	PROPN
ejpam-2584	217	38	y	y	PROPN
ejpam-2584	217	39	,	,	PUNCT
ejpam-2584	217	40	f	f	PROPN
ejpam-2584	217	41	x	x	SYM
ejpam-2584	217	42	�	�	PROPN
ejpam-2584	217	43	�	�	PROPN
ejpam-2584	217	44	then	then	ADV
ejpam-2584	217	45	,	,	PUNCT
ejpam-2584	217	46	f	f	PROPN
ejpam-2584	217	47	has	have	VERB
ejpam-2584	217	48	a	a	DET
ejpam-2584	217	49	unique	unique	ADJ
ejpam-2584	217	50	fixed	fix	VERB
ejpam-2584	217	51	point	point	NOUN
ejpam-2584	217	52	.	.	PUNCT
ejpam-2584	218	1	references	reference	NOUN
ejpam-2584	218	2	451	451	NUM
ejpam-2584	218	3	references	reference	NOUN
ejpam-2584	218	4	[	[	X
ejpam-2584	218	5	1	1	NUM
ejpam-2584	218	6	]	]	X
ejpam-2584	218	7	s.g	s.g	PROPN
ejpam-2584	218	8	.	.	PROPN
ejpam-2584	218	9	matthews	matthews	PROPN
ejpam-2584	218	10	.partially	.partially	ADP
ejpam-2584	218	11	metric	metric	ADJ
ejpam-2584	218	12	topology	topology	NOUN
ejpam-2584	218	13	,	,	PUNCT
ejpam-2584	218	14	research	research	NOUN
ejpam-2584	218	15	report	report	NOUN
ejpam-2584	218	16	212	212	NUM
ejpam-2584	218	17	,	,	PUNCT
ejpam-2584	218	18	department	department	NOUN
ejpam-2584	218	19	of	of	ADP
ejpam-2584	218	20	computer	computer	NOUN
ejpam-2584	218	21	science	science	NOUN
ejpam-2584	218	22	,	,	PUNCT
ejpam-2584	218	23	university	university	PROPN
ejpam-2584	218	24	of	of	ADP
ejpam-2584	218	25	warwick	warwick	PROPN
ejpam-2584	218	26	,	,	PUNCT
ejpam-2584	218	27	1992	1992	NUM
ejpam-2584	218	28	.	.	PUNCT
ejpam-2584	219	1	[	[	X
ejpam-2584	219	2	2	2	NUM
ejpam-2584	219	3	]	]	X
ejpam-2584	219	4	s.g	s.g	PROPN
ejpam-2584	219	5	.	.	PROPN
ejpam-2584	219	6	matthews	matthews	PROPN
ejpam-2584	219	7	.	.	PUNCT
ejpam-2584	220	1	partially	partially	ADV
ejpam-2584	220	2	metric	metric	ADJ
ejpam-2584	220	3	topology	topology	NOUN
ejpam-2584	220	4	,	,	PUNCT
ejpam-2584	220	5	in	in	ADP
ejpam-2584	220	6	proceedings	proceeding	NOUN
ejpam-2584	220	7	of	of	ADP
ejpam-2584	220	8	the	the	DET
ejpam-2584	220	9	8th	8th	ADJ
ejpam-2584	220	10	summer	summer	NOUN
ejpam-2584	220	11	conference	conference	NOUN
ejpam-2584	220	12	,	,	PUNCT
ejpam-2584	220	13	queen	queen	PROPN
ejpam-2584	220	14	’s	’s	PART
ejpam-2584	220	15	college	college	PROPN
ejpam-2584	220	16	,	,	PUNCT
ejpam-2584	220	17	general	general	ADJ
ejpam-2584	220	18	topology	topology	NOUN
ejpam-2584	220	19	and	and	CCONJ
ejpam-2584	220	20	its	its	PRON
ejpam-2584	220	21	applications	application	NOUN
ejpam-2584	220	22	,	,	PUNCT
ejpam-2584	220	23	vol	vol	NOUN
ejpam-2584	220	24	.	.	PROPN
ejpam-2584	220	25	728	728	NUM
ejpam-2584	220	26	of	of	ADP
ejpam-2584	220	27	annals	annal	NOUN
ejpam-2584	220	28	of	of	ADP
ejpam-2584	220	29	the	the	DET
ejpam-2584	220	30	new	new	PROPN
ejpam-2584	220	31	york	york	PROPN
ejpam-2584	220	32	academy	academy	PROPN
ejpam-2584	220	33	of	of	ADP
ejpam-2584	220	34	science	science	PROPN
ejpam-2584	220	35	,	,	PUNCT
ejpam-2584	220	36	183	183	NUM
ejpam-2584	220	37	-	-	SYM
ejpam-2584	220	38	197	197	NUM
ejpam-2584	220	39	.	.	NUM
ejpam-2584	220	40	1992	1992	NUM
ejpam-2584	220	41	.	.	PUNCT
ejpam-2584	221	1	[	[	X
ejpam-2584	221	2	3	3	NUM
ejpam-2584	221	3	]	]	PUNCT
ejpam-2584	221	4	m.	m.	NOUN
ejpam-2584	221	5	schellekens	schellekens	PROPN
ejpam-2584	221	6	.	.	PUNCT
ejpam-2584	222	1	a	a	DET
ejpam-2584	222	2	characterization	characterization	NOUN
ejpam-2584	222	3	of	of	ADP
ejpam-2584	222	4	partial	partial	ADJ
ejpam-2584	222	5	metrizebility	metrizebility	NOUN
ejpam-2584	222	6	:	:	PUNCT
ejpam-2584	222	7	domains	domain	NOUN
ejpam-2584	222	8	are	be	AUX
ejpam-2584	222	9	quantifiable	quantifiable	ADJ
ejpam-2584	222	10	,	,	PUNCT
ejpam-2584	222	11	theoretical	theoretical	ADJ
ejpam-2584	222	12	computer	computer	NOUN
ejpam-2584	222	13	sciences	science	NOUN
ejpam-2584	222	14	,	,	PUNCT
ejpam-2584	222	15	305(1	305(1	NUM
ejpam-2584	222	16	-	-	SYM
ejpam-2584	222	17	3	3	NUM
ejpam-2584	222	18	)	)	PUNCT
ejpam-2584	222	19	,	,	PUNCT
ejpam-2584	222	20	409	409	NUM
ejpam-2584	222	21	-	-	SYM
ejpam-2584	222	22	432	432	NUM
ejpam-2584	222	23	.	.	PUNCT
ejpam-2584	223	1	2003	2003	NUM
ejpam-2584	223	2	.	.	PUNCT
ejpam-2584	224	1	[	[	X
ejpam-2584	224	2	4	4	NUM
ejpam-2584	224	3	]	]	X
ejpam-2584	224	4	p.	p.	NOUN
ejpam-2584	224	5	waszkiewicz	waszkiewicz	NOUN
ejpam-2584	224	6	.	.	PUNCT
ejpam-2584	225	1	partial	partial	ADJ
ejpam-2584	225	2	metrizebility	metrizebility	NOUN
ejpam-2584	225	3	of	of	ADP
ejpam-2584	225	4	continuous	continuous	ADJ
ejpam-2584	225	5	posets	poset	NOUN
ejpam-2584	225	6	,	,	PUNCT
ejpam-2584	225	7	mathematical	mathematical	ADJ
ejpam-2584	225	8	structures	structure	NOUN
ejpam-2584	225	9	in	in	ADP
ejpam-2584	225	10	computer	computer	NOUN
ejpam-2584	225	11	science	science	NOUN
ejpam-2584	225	12	,	,	PUNCT
ejpam-2584	225	13	16(2	16(2	NUM
ejpam-2584	225	14	)	)	PUNCT
ejpam-2584	225	15	,	,	PUNCT
ejpam-2584	225	16	359	359	NUM
ejpam-2584	225	17	-	-	SYM
ejpam-2584	225	18	372	372	NUM
ejpam-2584	225	19	.	.	NOUN
ejpam-2584	225	20	2006	2006	NUM
ejpam-2584	225	21	.	.	PUNCT
ejpam-2584	226	1	[	[	X
ejpam-2584	226	2	5	5	X
ejpam-2584	226	3	]	]	PUNCT
ejpam-2584	226	4	s.	s.	PROPN
ejpam-2584	226	5	banach	banach	PROPN
ejpam-2584	226	6	.	.	PUNCT
ejpam-2584	227	1	sur	sur	PROPN
ejpam-2584	227	2	les	les	PROPN
ejpam-2584	227	3	operations	operation	NOUN
ejpam-2584	227	4	dans	dan	NOUN
ejpam-2584	227	5	les	le	NOUN
ejpam-2584	227	6	ensembles	ensemble	NOUN
ejpam-2584	227	7	abstraits	abstrait	NOUN
ejpam-2584	227	8	et	et	PROPN
ejpam-2584	227	9	leur	leur	X
ejpam-2584	227	10	application	application	PROPN
ejpam-2584	227	11	aux	aux	PROPN
ejpam-2584	227	12	equations	equation	NOUN
ejpam-2584	227	13	integerales	integerale	NOUN
ejpam-2584	227	14	,	,	PUNCT
ejpam-2584	227	15	fundamenta	fundamenta	PROPN
ejpam-2584	227	16	mathematicae	mathematicae	PROPN
ejpam-2584	227	17	,	,	PUNCT
ejpam-2584	227	18	3	3	NUM
ejpam-2584	227	19	,	,	PUNCT
ejpam-2584	227	20	133	133	NUM
ejpam-2584	227	21	-	-	SYM
ejpam-2584	227	22	181	181	NUM
ejpam-2584	227	23	.	.	PUNCT
ejpam-2584	227	24	1922	1922	NUM
ejpam-2584	227	25	.	.	PUNCT
ejpam-2584	228	1	[	[	X
ejpam-2584	228	2	6	6	NUM
ejpam-2584	228	3	]	]	PUNCT
ejpam-2584	228	4	r.	r.	PROPN
ejpam-2584	228	5	kannan	kannan	PROPN
ejpam-2584	228	6	.	.	PUNCT
ejpam-2584	229	1	some	some	DET
ejpam-2584	229	2	results	result	NOUN
ejpam-2584	229	3	on	on	ADP
ejpam-2584	229	4	fixed	fix	VERB
ejpam-2584	229	5	points	point	NOUN
ejpam-2584	229	6	,	,	PUNCT
ejpam-2584	229	7	bulletin	bulletin	NOUN
ejpam-2584	229	8	of	of	ADP
ejpam-2584	229	9	calcutta	calcutta	PROPN
ejpam-2584	229	10	mathematical	mathematical	ADJ
ejpam-2584	229	11	society	society	NOUN
ejpam-2584	229	12	,	,	PUNCT
ejpam-2584	229	13	60	60	NUM
ejpam-2584	229	14	,	,	PUNCT
ejpam-2584	229	15	71	71	NUM
ejpam-2584	229	16	-	-	SYM
ejpam-2584	229	17	76	76	NUM
ejpam-2584	229	18	.	.	PUNCT
ejpam-2584	229	19	1968	1968	NUM
ejpam-2584	229	20	.	.	PUNCT
ejpam-2584	230	1	[	[	X
ejpam-2584	230	2	7	7	X
ejpam-2584	230	3	]	]	PUNCT
ejpam-2584	230	4	s.	s.	PROPN
ejpam-2584	230	5	k.	k.	PROPN
ejpam-2584	230	6	chatterjea	chatterjea	PROPN
ejpam-2584	230	7	.	.	PUNCT
ejpam-2584	231	1	fixed	fix	VERB
ejpam-2584	231	2	point	point	NOUN
ejpam-2584	231	3	theorems	theorem	NOUN
ejpam-2584	231	4	,	,	PUNCT
ejpam-2584	231	5	comptes	compte	VERB
ejpam-2584	231	6	rendus	rendus	PROPN
ejpam-2584	231	7	de	de	PROPN
ejpam-2584	231	8	l’académie	l’académie	PROPN
ejpam-2584	231	9	bulgare	bulgare	PROPN
ejpam-2584	231	10	des	des	PROPN
ejpam-2584	231	11	sciences	sciences	PROPN
ejpam-2584	231	12	,	,	PUNCT
ejpam-2584	231	13	25	25	NUM
ejpam-2584	231	14	,	,	PUNCT
ejpam-2584	231	15	727	727	NUM
ejpam-2584	231	16	-	-	SYM
ejpam-2584	231	17	730	730	NUM
ejpam-2584	231	18	.	.	NOUN
ejpam-2584	231	19	1972	1972	NUM
ejpam-2584	231	20	.	.	PUNCT
ejpam-2584	232	1	[	[	X
ejpam-2584	232	2	8	8	NUM
ejpam-2584	232	3	]	]	X
ejpam-2584	232	4	ö.	ö.	NOUN
ejpam-2584	232	5	acar	acar	NOUN
ejpam-2584	232	6	and	and	CCONJ
ejpam-2584	232	7	i.	i.	NOUN
ejpam-2584	232	8	altun	altun	PROPN
ejpam-2584	232	9	.	.	PUNCT
ejpam-2584	233	1	some	some	DET
ejpam-2584	233	2	generalizations	generalization	NOUN
ejpam-2584	233	3	of	of	ADP
ejpam-2584	233	4	caristi	caristi	PROPN
ejpam-2584	233	5	type	type	NOUN
ejpam-2584	233	6	fixed	fix	VERB
ejpam-2584	233	7	point	point	NOUN
ejpam-2584	233	8	theorem	theorem	VERB
ejpam-2584	233	9	on	on	ADP
ejpam-2584	233	10	partial	partial	ADJ
ejpam-2584	233	11	metric	metric	ADJ
ejpam-2584	233	12	space	space	NOUN
ejpam-2584	233	13	,	,	PUNCT
ejpam-2584	233	14	filomat	filomat	NOUN
ejpam-2584	233	15	,	,	PUNCT
ejpam-2584	233	16	26(4	26(4	NUM
ejpam-2584	233	17	)	)	PUNCT
ejpam-2584	233	18	,	,	PUNCT
ejpam-2584	233	19	833–837	833–837	NUM
ejpam-2584	233	20	.	.	PUNCT
ejpam-2584	233	21	2012	2012	NUM
ejpam-2584	233	22	.	.	PUNCT
ejpam-2584	234	1	[	[	X
ejpam-2584	234	2	9	9	NUM
ejpam-2584	234	3	]	]	PUNCT
ejpam-2584	234	4	e.	e.	PROPN
ejpam-2584	234	5	karapınar	karapınar	PROPN
ejpam-2584	234	6	and	and	CCONJ
ejpam-2584	234	7	u.	u.	PROPN
ejpam-2584	234	8	yüksel	yüksel	PROPN
ejpam-2584	234	9	.	.	PUNCT
ejpam-2584	235	1	some	some	DET
ejpam-2584	235	2	common	common	ADJ
ejpam-2584	235	3	fixed	fix	VERB
ejpam-2584	235	4	point	point	NOUN
ejpam-2584	235	5	theorems	theorem	NOUN
ejpam-2584	235	6	in	in	ADP
ejpam-2584	235	7	partial	partial	ADJ
ejpam-2584	235	8	metric	metric	ADJ
ejpam-2584	235	9	space	space	NOUN
ejpam-2584	235	10	,	,	PUNCT
ejpam-2584	235	11	journal	journal	NOUN
ejpam-2584	235	12	of	of	ADP
ejpam-2584	235	13	applied	apply	VERB
ejpam-2584	235	14	mathematics	mathematic	NOUN
ejpam-2584	235	15	,	,	PUNCT
ejpam-2584	235	16	2011	2011	NUM
ejpam-2584	235	17	,	,	PUNCT
ejpam-2584	235	18	article	article	NOUN
ejpam-2584	235	19	id:263621	id:263621	PROPN
ejpam-2584	235	20	,	,	PUNCT
ejpam-2584	235	21	2011	2011	NUM
ejpam-2584	235	22	.	.	PUNCT
ejpam-2584	236	1	[	[	X
ejpam-2584	236	2	10	10	NUM
ejpam-2584	236	3	]	]	X
ejpam-2584	236	4	s.	s.	PROPN
ejpam-2584	236	5	moradi	moradi	PROPN
ejpam-2584	236	6	and	and	CCONJ
ejpam-2584	236	7	a.	a.	NOUN
ejpam-2584	236	8	davood	davood	PROPN
ejpam-2584	236	9	.	.	PUNCT
ejpam-2584	237	1	new	new	ADJ
ejpam-2584	237	2	extension	extension	NOUN
ejpam-2584	237	3	of	of	ADP
ejpam-2584	237	4	kannan	kannan	PROPN
ejpam-2584	237	5	fixed	fix	VERB
ejpam-2584	237	6	point	point	NOUN
ejpam-2584	237	7	theorem	theorem	VERB
ejpam-2584	237	8	on	on	ADP
ejpam-2584	237	9	complete	complete	ADJ
ejpam-2584	237	10	metric	metric	ADJ
ejpam-2584	237	11	and	and	CCONJ
ejpam-2584	237	12	generalized	generalized	ADJ
ejpam-2584	237	13	metric	metric	ADJ
ejpam-2584	237	14	spaces	space	NOUN
ejpam-2584	237	15	,	,	PUNCT
ejpam-2584	237	16	international	international	ADJ
ejpam-2584	237	17	journal	journal	NOUN
ejpam-2584	237	18	of	of	ADP
ejpam-2584	237	19	mathematical	mathematical	ADJ
ejpam-2584	237	20	analysis	analysis	NOUN
ejpam-2584	237	21	,	,	PUNCT
ejpam-2584	237	22	5(47	5(47	NUM
ejpam-2584	237	23	)	)	PUNCT
ejpam-2584	237	24	,	,	PUNCT
ejpam-2584	237	25	2313	2313	NUM
ejpam-2584	237	26	-	-	SYM
ejpam-2584	237	27	1320	1320	NUM
ejpam-2584	237	28	.	.	PUNCT
ejpam-2584	238	1	2011	2011	NUM
ejpam-2584	238	2	.	.	PUNCT
ejpam-2584	239	1	[	[	X
ejpam-2584	239	2	11	11	NUM
ejpam-2584	239	3	]	]	PUNCT
ejpam-2584	239	4	z.	z.	PROPN
ejpam-2584	239	5	mustafa	mustafa	PROPN
ejpam-2584	239	6	,	,	PUNCT
ejpam-2584	239	7	j.r	j.r	PROPN
ejpam-2584	239	8	.	.	PROPN
ejpam-2584	239	9	roshan	roshan	PROPN
ejpam-2584	239	10	,	,	PUNCT
ejpam-2584	239	11	v.	v.	CCONJ
ejpam-2584	239	12	parvaneh	parvaneh	NOUN
ejpam-2584	239	13	,	,	PUNCT
ejpam-2584	239	14	and	and	CCONJ
ejpam-2584	239	15	z.	z.	PROPN
ejpam-2584	239	16	kadelburg	kadelburg	PROPN
ejpam-2584	239	17	fixed	fix	VERB
ejpam-2584	239	18	point	point	NOUN
ejpam-2584	239	19	theorems	theorem	NOUN
ejpam-2584	239	20	for	for	ADP
ejpam-2584	239	21	weakly	weakly	ADJ
ejpam-2584	239	22	t	t	PROPN
ejpam-2584	239	23	-	-	PUNCT
ejpam-2584	239	24	chatterjea	chatterjea	PROPN
ejpam-2584	239	25	and	and	CCONJ
ejpam-2584	239	26	weakly	weakly	ADJ
ejpam-2584	239	27	t	t	PROPN
ejpam-2584	239	28	-	-	PUNCT
ejpam-2584	239	29	kannan	kannan	PROPN
ejpam-2584	239	30	contractions	contraction	NOUN
ejpam-2584	239	31	in	in	ADP
ejpam-2584	239	32	b	b	NOUN
ejpam-2584	239	33	-	-	ADJ
ejpam-2584	239	34	metric	metric	ADJ
ejpam-2584	239	35	spaces	space	NOUN
ejpam-2584	239	36	,	,	PUNCT
ejpam-2584	239	37	journal	journal	NOUN
ejpam-2584	239	38	of	of	ADP
ejpam-2584	239	39	inequality	inequality	NOUN
ejpam-2584	239	40	and	and	CCONJ
ejpam-2584	239	41	applications	application	NOUN
ejpam-2584	239	42	2014	2014	NUM
ejpam-2584	239	43	,	,	PUNCT
ejpam-2584	239	44	46	46	NUM
ejpam-2584	239	45	,	,	PUNCT
ejpam-2584	239	46	2014	2014	NUM
ejpam-2584	239	47	.	.	PUNCT
ejpam-2584	240	1	[	[	X
ejpam-2584	240	2	12	12	NUM
ejpam-2584	240	3	]	]	X
ejpam-2584	240	4	s.	s.	PROPN
ejpam-2584	240	5	moradi	moradi	PROPN
ejpam-2584	240	6	and	and	CCONJ
ejpam-2584	240	7	a.	a.	NOUN
ejpam-2584	240	8	beiranvand	beiranvand	PROPN
ejpam-2584	240	9	.	.	PUNCT
ejpam-2584	241	1	fixed	fix	VERB
ejpam-2584	241	2	point	point	NOUN
ejpam-2584	241	3	of	of	ADP
ejpam-2584	241	4	tf	tf	NUM
ejpam-2584	241	5	-contractive	-contractive	ADJ
ejpam-2584	241	6	single	single	ADJ
ejpam-2584	241	7	-	-	PUNCT
ejpam-2584	241	8	valued	value	VERB
ejpam-2584	241	9	mappings	mapping	NOUN
ejpam-2584	241	10	,	,	PUNCT
ejpam-2584	241	11	iranian	iranian	ADJ
ejpam-2584	241	12	journal	journal	PROPN
ejpam-2584	241	13	of	of	ADP
ejpam-2584	241	14	mathematical	mathematical	ADJ
ejpam-2584	241	15	sciences	sciences	PROPN
ejpam-2584	241	16	and	and	CCONJ
ejpam-2584	241	17	informatics	informatic	NOUN
ejpam-2584	241	18	,	,	PUNCT
ejpam-2584	241	19	5	5	NUM
ejpam-2584	241	20	,	,	PUNCT
ejpam-2584	241	21	25	25	NUM
ejpam-2584	241	22	-	-	SYM
ejpam-2584	241	23	32	32	NUM
ejpam-2584	241	24	.	.	PUNCT
ejpam-2584	242	1	2010	2010	NUM
ejpam-2584	242	2	.	.	PUNCT
ejpam-2584	243	1	[	[	X
ejpam-2584	243	2	13	13	NUM
ejpam-2584	243	3	]	]	PUNCT
ejpam-2584	243	4	m.	m.	NOUN
ejpam-2584	243	5	kir	kir	PROPN
ejpam-2584	243	6	and	and	CCONJ
ejpam-2584	243	7	h.	h.	PROPN
ejpam-2584	243	8	kızıltuc	kızıltuc	PROPN
ejpam-2584	243	9	.	.	PUNCT
ejpam-2584	244	1	tf	tf	X
ejpam-2584	244	2	-contractive	-contractive	ADJ
ejpam-2584	244	3	conditions	condition	NOUN
ejpam-2584	244	4	for	for	ADP
ejpam-2584	244	5	kannan	kannan	PROPN
ejpam-2584	244	6	and	and	CCONJ
ejpam-2584	244	7	chatterjea	chatterjea	ADJ
ejpam-2584	244	8	fixed	fix	VERB
ejpam-2584	244	9	point	point	NOUN
ejpam-2584	244	10	theorems	theorem	NOUN
ejpam-2584	244	11	,	,	PUNCT
ejpam-2584	244	12	advances	advance	NOUN
ejpam-2584	244	13	in	in	ADP
ejpam-2584	244	14	fixed	fix	VERB
ejpam-2584	244	15	point	point	NOUN
ejpam-2584	244	16	theory	theory	NOUN
ejpam-2584	244	17	,	,	PUNCT
ejpam-2584	244	18	4(1	4(1	NOUN
ejpam-2584	244	19	)	)	PUNCT
ejpam-2584	244	20	,	,	PUNCT
ejpam-2584	244	21	140	140	NUM
ejpam-2584	244	22	-	-	SYM
ejpam-2584	244	23	148	148	NUM
ejpam-2584	244	24	.	.	PUNCT
ejpam-2584	244	25	2014	2014	NUM
ejpam-2584	244	26	.	.	PUNCT
ejpam-2584	245	1	[	[	X
ejpam-2584	245	2	14	14	NUM
ejpam-2584	245	3	]	]	PUNCT
ejpam-2584	245	4	a.	a.	NOUN
ejpam-2584	245	5	branciari	branciari	PROPN
ejpam-2584	245	6	.	.	PUNCT
ejpam-2584	246	1	a	a	DET
ejpam-2584	246	2	fixed	fix	VERB
ejpam-2584	246	3	point	point	NOUN
ejpam-2584	246	4	theorem	theorem	NOUN
ejpam-2584	246	5	for	for	ADP
ejpam-2584	246	6	mapping	mapping	NOUN
ejpam-2584	246	7	satisfying	satisfy	VERB
ejpam-2584	246	8	a	a	DET
ejpam-2584	246	9	general	general	ADJ
ejpam-2584	246	10	contractive	contractive	ADJ
ejpam-2584	246	11	condition	condition	NOUN
ejpam-2584	246	12	of	of	ADP
ejpam-2584	246	13	integral	integral	ADJ
ejpam-2584	246	14	type	type	NOUN
ejpam-2584	246	15	,	,	PUNCT
ejpam-2584	246	16	international	international	ADJ
ejpam-2584	246	17	journal	journal	NOUN
ejpam-2584	246	18	of	of	ADP
ejpam-2584	246	19	mathematics	mathematics	PROPN
ejpam-2584	246	20	and	and	CCONJ
ejpam-2584	246	21	mathematical	mathematical	ADJ
ejpam-2584	246	22	sciences	science	NOUN
ejpam-2584	246	23	,	,	PUNCT
ejpam-2584	246	24	29(9	29(9	NOUN
ejpam-2584	246	25	)	)	PUNCT
ejpam-2584	246	26	,	,	PUNCT
ejpam-2584	246	27	531	531	NUM
ejpam-2584	246	28	-	-	SYM
ejpam-2584	246	29	536	536	NUM
ejpam-2584	246	30	.	.	PUNCT
ejpam-2584	246	31	2002	2002	NUM
ejpam-2584	246	32	.	.	PUNCT