id	sid	tid	token	lemma	pos
ejpam-3294	1	1	european	european	PROPN
ejpam-3294	1	2	journal	journal	PROPN
ejpam-3294	1	3	of	of	ADP
ejpam-3294	1	4	pure	pure	ADJ
ejpam-3294	1	5	and	and	CCONJ
ejpam-3294	1	6	applied	apply	VERB
ejpam-3294	1	7	mathematics	mathematic	NOUN
ejpam-3294	1	8	vol	vol	NOUN
ejpam-3294	1	9	.	.	PUNCT
ejpam-3294	2	1	11	11	NUM
ejpam-3294	2	2	,	,	PUNCT
ejpam-3294	2	3	no	no	INTJ
ejpam-3294	2	4	.	.	NOUN
ejpam-3294	2	5	3	3	NUM
ejpam-3294	2	6	,	,	PUNCT
ejpam-3294	2	7	2018	2018	NUM
ejpam-3294	2	8	,	,	PUNCT
ejpam-3294	2	9	702	702	NUM
ejpam-3294	2	10	-	-	SYM
ejpam-3294	2	11	716	716	NUM
ejpam-3294	2	12	issn	issn	PROPN
ejpam-3294	2	13	1307	1307	NUM
ejpam-3294	2	14	-	-	SYM
ejpam-3294	2	15	5543	5543	NUM
ejpam-3294	2	16	–	–	PUNCT
ejpam-3294	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3294	2	18	published	publish	VERB
ejpam-3294	2	19	by	by	ADP
ejpam-3294	2	20	new	new	PROPN
ejpam-3294	2	21	york	york	PROPN
ejpam-3294	2	22	business	business	PROPN
ejpam-3294	2	23	global	global	ADJ
ejpam-3294	2	24	fixed	fix	VERB
ejpam-3294	2	25	point	point	NOUN
ejpam-3294	2	26	results	result	NOUN
ejpam-3294	2	27	for	for	ADP
ejpam-3294	2	28	geraghty	geraghty	PROPN
ejpam-3294	2	29	type	type	NOUN
ejpam-3294	2	30	generalized	generalize	VERB
ejpam-3294	2	31	f	f	NOUN
ejpam-3294	2	32	-	-	PUNCT
ejpam-3294	2	33	contraction	contraction	NOUN
ejpam-3294	2	34	for	for	ADP
ejpam-3294	2	35	weak	weak	ADJ
ejpam-3294	2	36	α−admissible	α−admissible	NUM
ejpam-3294	2	37	mappings	mapping	NOUN
ejpam-3294	2	38	in	in	ADP
ejpam-3294	2	39	metric	metric	ADJ
ejpam-3294	2	40	-	-	PUNCT
ejpam-3294	2	41	like	like	ADJ
ejpam-3294	2	42	spaces	space	NOUN
ejpam-3294	2	43	haitham	haitham	PROPN
ejpam-3294	2	44	qawaqneh1,∗	qawaqneh1,∗	PROPN
ejpam-3294	2	45	,	,	PUNCT
ejpam-3294	2	46	mohd	mohd	PROPN
ejpam-3294	2	47	selmi	selmi	PROPN
ejpam-3294	2	48	noorani1	noorani1	ADV
ejpam-3294	2	49	,	,	PUNCT
ejpam-3294	2	50	wasfi	wasfi	NOUN
ejpam-3294	2	51	shatanawi2,3	shatanawi2,3	PROPN
ejpam-3294	2	52	1	1	NUM
ejpam-3294	2	53	school	school	NOUN
ejpam-3294	2	54	of	of	ADP
ejpam-3294	2	55	mathematical	mathematical	ADJ
ejpam-3294	2	56	sciences	science	NOUN
ejpam-3294	2	57	,	,	PUNCT
ejpam-3294	2	58	faculty	faculty	NOUN
ejpam-3294	2	59	of	of	ADP
ejpam-3294	2	60	science	science	NOUN
ejpam-3294	2	61	and	and	CCONJ
ejpam-3294	2	62	technology	technology	NOUN
ejpam-3294	2	63	,	,	PUNCT
ejpam-3294	2	64	universiti	universiti	PROPN
ejpam-3294	2	65	kebangsaan	kebangsaan	PROPN
ejpam-3294	2	66	malaysia	malaysia	PROPN
ejpam-3294	2	67	,	,	PUNCT
ejpam-3294	2	68	43600	43600	NUM
ejpam-3294	2	69	ukm	ukm	PROPN
ejpam-3294	2	70	,	,	PUNCT
ejpam-3294	2	71	selangor	selangor	PROPN
ejpam-3294	2	72	darul	darul	PROPN
ejpam-3294	2	73	ehsan	ehsan	PROPN
ejpam-3294	2	74	,	,	PUNCT
ejpam-3294	2	75	malaysia	malaysia	PROPN
ejpam-3294	2	76	2	2	NUM
ejpam-3294	2	77	department	department	NOUN
ejpam-3294	2	78	of	of	ADP
ejpam-3294	2	79	mathematics	mathematic	NOUN
ejpam-3294	2	80	,	,	PUNCT
ejpam-3294	2	81	hashemite	hashemite	PROPN
ejpam-3294	2	82	university	university	NOUN
ejpam-3294	2	83	,	,	PUNCT
ejpam-3294	2	84	zarqa	zarqa	PROPN
ejpam-3294	2	85	1315	1315	NUM
ejpam-3294	2	86	,	,	PUNCT
ejpam-3294	2	87	jordan	jordan	PROPN
ejpam-3294	2	88	3	3	NUM
ejpam-3294	2	89	department	department	PROPN
ejpam-3294	2	90	of	of	ADP
ejpam-3294	2	91	mathematics	mathematics	PROPN
ejpam-3294	2	92	and	and	CCONJ
ejpam-3294	2	93	general	general	ADJ
ejpam-3294	2	94	courses	course	NOUN
ejpam-3294	2	95	,	,	PUNCT
ejpam-3294	2	96	prince	prince	PROPN
ejpam-3294	2	97	sultan	sultan	PROPN
ejpam-3294	2	98	university	university	PROPN
ejpam-3294	2	99	,	,	PUNCT
ejpam-3294	2	100	riyadh	riyadh	PROPN
ejpam-3294	2	101	,	,	PUNCT
ejpam-3294	2	102	saudi	saudi	PROPN
ejpam-3294	2	103	arabia	arabia	PROPN
ejpam-3294	2	104	abstract	abstract	NOUN
ejpam-3294	2	105	.	.	PUNCT
ejpam-3294	3	1	in	in	ADP
ejpam-3294	3	2	this	this	DET
ejpam-3294	3	3	paper	paper	NOUN
ejpam-3294	3	4	,	,	PUNCT
ejpam-3294	3	5	we	we	PRON
ejpam-3294	3	6	establish	establish	VERB
ejpam-3294	3	7	the	the	DET
ejpam-3294	3	8	existence	existence	NOUN
ejpam-3294	3	9	of	of	ADP
ejpam-3294	3	10	some	some	DET
ejpam-3294	3	11	fixed	fix	VERB
ejpam-3294	3	12	point	point	NOUN
ejpam-3294	3	13	results	result	NOUN
ejpam-3294	3	14	for	for	ADP
ejpam-3294	3	15	generalized	generalized	ADJ
ejpam-3294	3	16	(	(	PUNCT
ejpam-3294	3	17	α	α	NOUN
ejpam-3294	3	18	,	,	PUNCT
ejpam-3294	3	19	β	β	X
ejpam-3294	3	20	,	,	PUNCT
ejpam-3294	3	21	f	f	NOUN
ejpam-3294	3	22	)	)	PUNCT
ejpam-3294	3	23	-geraghty	-geraghty	PROPN
ejpam-3294	3	24	contraction	contraction	NOUN
ejpam-3294	3	25	in	in	ADP
ejpam-3294	3	26	metric	metric	ADJ
ejpam-3294	3	27	-	-	PUNCT
ejpam-3294	3	28	like	like	ADJ
ejpam-3294	3	29	spaces	space	NOUN
ejpam-3294	3	30	.	.	PUNCT
ejpam-3294	4	1	we	we	PRON
ejpam-3294	4	2	provide	provide	VERB
ejpam-3294	4	3	an	an	DET
ejpam-3294	4	4	example	example	NOUN
ejpam-3294	4	5	in	in	ADP
ejpam-3294	4	6	order	order	NOUN
ejpam-3294	4	7	to	to	PART
ejpam-3294	4	8	support	support	VERB
ejpam-3294	4	9	our	our	PRON
ejpam-3294	4	10	results	result	NOUN
ejpam-3294	4	11	where	where	SCONJ
ejpam-3294	4	12	some	some	DET
ejpam-3294	4	13	consequence	consequence	NOUN
ejpam-3294	4	14	applications	application	NOUN
ejpam-3294	4	15	of	of	ADP
ejpam-3294	4	16	such	such	ADJ
ejpam-3294	4	17	result	result	NOUN
ejpam-3294	4	18	will	will	AUX
ejpam-3294	4	19	be	be	AUX
ejpam-3294	4	20	considered	consider	VERB
ejpam-3294	4	21	in	in	ADP
ejpam-3294	4	22	this	this	DET
ejpam-3294	4	23	article	article	NOUN
ejpam-3294	4	24	.	.	PUNCT
ejpam-3294	5	1	the	the	DET
ejpam-3294	5	2	obtained	obtain	VERB
ejpam-3294	5	3	results	result	NOUN
ejpam-3294	5	4	improve	improve	VERB
ejpam-3294	5	5	and	and	CCONJ
ejpam-3294	5	6	extend	extend	VERB
ejpam-3294	5	7	some	some	DET
ejpam-3294	5	8	well	well	ADV
ejpam-3294	5	9	-	-	PUNCT
ejpam-3294	5	10	known	know	VERB
ejpam-3294	5	11	common	common	ADJ
ejpam-3294	5	12	fixed	fix	VERB
ejpam-3294	5	13	point	point	NOUN
ejpam-3294	5	14	results	result	NOUN
ejpam-3294	5	15	in	in	ADP
ejpam-3294	5	16	the	the	DET
ejpam-3294	5	17	literature	literature	NOUN
ejpam-3294	5	18	.	.	PUNCT
ejpam-3294	6	1	2010	2010	NUM
ejpam-3294	6	2	mathematics	mathematic	NOUN
ejpam-3294	6	3	subject	subject	NOUN
ejpam-3294	6	4	classifications	classification	NOUN
ejpam-3294	6	5	:	:	PUNCT
ejpam-3294	6	6	47h10,54h25	47h10,54h25	NOUN
ejpam-3294	6	7	key	key	ADJ
ejpam-3294	6	8	words	word	NOUN
ejpam-3294	6	9	and	and	CCONJ
ejpam-3294	6	10	phrases	phrase	NOUN
ejpam-3294	6	11	:	:	PUNCT
ejpam-3294	6	12	fixed	fix	VERB
ejpam-3294	6	13	point	point	NOUN
ejpam-3294	6	14	,	,	PUNCT
ejpam-3294	6	15	metric	metric	ADJ
ejpam-3294	6	16	-	-	PUNCT
ejpam-3294	6	17	like	like	ADJ
ejpam-3294	6	18	space	space	NOUN
ejpam-3294	6	19	,	,	PUNCT
ejpam-3294	6	20	α−admissible	α−admissible	X
ejpam-3294	6	21	mapping	mapping	NOUN
ejpam-3294	6	22	,	,	PUNCT
ejpam-3294	6	23	weak	weak	ADJ
ejpam-3294	6	24	α−admissible	α−admissible	ADJ
ejpam-3294	6	25	mapping	mapping	NOUN
ejpam-3294	6	26	,	,	PUNCT
ejpam-3294	6	27	f−	f−	PROPN
ejpam-3294	6	28	contraction	contraction	NOUN
ejpam-3294	6	29	.	.	PUNCT
ejpam-3294	7	1	1	1	X
ejpam-3294	7	2	.	.	X
ejpam-3294	7	3	introduction	introduction	NOUN
ejpam-3294	7	4	and	and	CCONJ
ejpam-3294	7	5	preliminaries	preliminary	NOUN
ejpam-3294	7	6	during	during	ADP
ejpam-3294	7	7	the	the	DET
ejpam-3294	7	8	last	last	ADJ
ejpam-3294	7	9	decades	decade	NOUN
ejpam-3294	7	10	,	,	PUNCT
ejpam-3294	7	11	issues	issue	NOUN
ejpam-3294	7	12	related	relate	VERB
ejpam-3294	7	13	to	to	ADP
ejpam-3294	7	14	”	"	PUNCT
ejpam-3294	7	15	fixed	fix	VERB
ejpam-3294	7	16	point	point	NOUN
ejpam-3294	7	17	theory	theory	NOUN
ejpam-3294	7	18	”	"	PUNCT
ejpam-3294	7	19	in	in	ADP
ejpam-3294	7	20	order	order	NOUN
ejpam-3294	7	21	to	to	PART
ejpam-3294	7	22	semantics	semantic	NOUN
ejpam-3294	7	23	domain	domain	NOUN
ejpam-3294	7	24	with	with	ADP
ejpam-3294	7	25	a	a	DET
ejpam-3294	7	26	notion	notion	NOUN
ejpam-3294	7	27	of	of	ADP
ejpam-3294	7	28	distance	distance	NOUN
ejpam-3294	7	29	that	that	PRON
ejpam-3294	7	30	has	have	AUX
ejpam-3294	7	31	been	be	AUX
ejpam-3294	7	32	extensively	extensively	ADV
ejpam-3294	7	33	researched	research	VERB
ejpam-3294	7	34	in	in	ADP
ejpam-3294	7	35	different	different	ADJ
ejpam-3294	7	36	spaces	space	NOUN
ejpam-3294	7	37	.	.	PUNCT
ejpam-3294	8	1	recently	recently	ADV
ejpam-3294	8	2	,	,	PUNCT
ejpam-3294	8	3	different	different	ADJ
ejpam-3294	8	4	generalizations	generalization	NOUN
ejpam-3294	8	5	of	of	ADP
ejpam-3294	8	6	metric	metric	ADJ
ejpam-3294	8	7	spaces	space	NOUN
ejpam-3294	8	8	have	have	AUX
ejpam-3294	8	9	been	be	AUX
ejpam-3294	8	10	introduced	introduce	VERB
ejpam-3294	8	11	(	(	PUNCT
ejpam-3294	8	12	for	for	ADP
ejpam-3294	8	13	example	example	NOUN
ejpam-3294	8	14	see	see	VERB
ejpam-3294	8	15	[	[	X
ejpam-3294	8	16	12],[10],[22],[2],[28],[8],[10],[7],[6],[23],[27],[29],[32	12],[10],[22],[2],[28],[8],[10],[7],[6],[23],[27],[29],[32	NUM
ejpam-3294	8	17	]	]	X
ejpam-3294	8	18	)	)	PUNCT
ejpam-3294	8	19	.	.	PUNCT
ejpam-3294	9	1	in	in	ADP
ejpam-3294	9	2	1994	1994	NUM
ejpam-3294	9	3	,	,	PUNCT
ejpam-3294	9	4	matthews	matthews	PROPN
ejpam-3294	9	5	[	[	X
ejpam-3294	9	6	19	19	NUM
ejpam-3294	9	7	]	]	PUNCT
ejpam-3294	9	8	introduced	introduce	VERB
ejpam-3294	9	9	the	the	DET
ejpam-3294	9	10	notion	notion	NOUN
ejpam-3294	9	11	of	of	ADP
ejpam-3294	9	12	partial	partial	ADJ
ejpam-3294	9	13	metric	metric	ADJ
ejpam-3294	9	14	space	space	NOUN
ejpam-3294	9	15	as	as	ADP
ejpam-3294	9	16	a	a	DET
ejpam-3294	9	17	part	part	NOUN
ejpam-3294	9	18	of	of	ADP
ejpam-3294	9	19	the	the	DET
ejpam-3294	9	20	study	study	NOUN
ejpam-3294	9	21	of	of	ADP
ejpam-3294	9	22	denotational	denotational	ADJ
ejpam-3294	9	23	semantics	semantic	NOUN
ejpam-3294	9	24	of	of	ADP
ejpam-3294	9	25	dataflow	dataflow	ADJ
ejpam-3294	9	26	networks	network	NOUN
ejpam-3294	9	27	,	,	PUNCT
ejpam-3294	9	28	showing	show	VERB
ejpam-3294	9	29	that	that	SCONJ
ejpam-3294	9	30	the	the	DET
ejpam-3294	9	31	contraction	contraction	NOUN
ejpam-3294	9	32	mapping	map	VERB
ejpam-3294	9	33	principle	principle	NOUN
ejpam-3294	9	34	[	[	X
ejpam-3294	9	35	9	9	NUM
ejpam-3294	9	36	]	]	PUNCT
ejpam-3294	9	37	can	can	AUX
ejpam-3294	9	38	be	be	AUX
ejpam-3294	9	39	generalized	generalize	VERB
ejpam-3294	9	40	to	to	ADP
ejpam-3294	9	41	the	the	DET
ejpam-3294	9	42	partial	partial	ADJ
ejpam-3294	9	43	metric	metric	ADJ
ejpam-3294	9	44	context	context	NOUN
ejpam-3294	9	45	for	for	ADP
ejpam-3294	9	46	applications	application	NOUN
ejpam-3294	9	47	in	in	ADP
ejpam-3294	9	48	program	program	NOUN
ejpam-3294	9	49	verifications	verification	NOUN
ejpam-3294	9	50	.	.	PUNCT
ejpam-3294	10	1	later	later	ADV
ejpam-3294	10	2	on	on	ADV
ejpam-3294	10	3	,	,	PUNCT
ejpam-3294	10	4	there	there	PRON
ejpam-3294	10	5	have	have	AUX
ejpam-3294	10	6	been	be	AUX
ejpam-3294	10	7	several	several	ADJ
ejpam-3294	10	8	recent	recent	ADJ
ejpam-3294	10	9	extensive	extensive	ADJ
ejpam-3294	10	10	researches	research	NOUN
ejpam-3294	10	11	on	on	ADP
ejpam-3294	10	12	(	(	PUNCT
ejpam-3294	10	13	common	common	ADJ
ejpam-3294	10	14	)	)	PUNCT
ejpam-3294	10	15	fixed	fix	VERB
ejpam-3294	10	16	points	point	NOUN
ejpam-3294	10	17	for	for	ADP
ejpam-3294	10	18	different	different	ADJ
ejpam-3294	10	19	contractions	contraction	NOUN
ejpam-3294	10	20	on	on	ADP
ejpam-3294	10	21	partial	partial	ADJ
ejpam-3294	10	22	metric	metric	ADJ
ejpam-3294	10	23	spaces	space	NOUN
ejpam-3294	10	24	,	,	PUNCT
ejpam-3294	10	25	see	see	VERB
ejpam-3294	10	26	[	[	X
ejpam-3294	10	27	[	[	X
ejpam-3294	10	28	10],[1],[17],[1],[30],[24],[16],21,[3],[5	10],[1],[17],[1],[30],[24],[16],21,[3],[5	NUM
ejpam-3294	10	29	]	]	X
ejpam-3294	10	30	,	,	PUNCT
ejpam-3294	10	31	[	[	X
ejpam-3294	10	32	11],[13],[25],[15],[20],[4	11],[13],[25],[15],[20],[4	X
ejpam-3294	10	33	]	]	X
ejpam-3294	10	34	]	]	PUNCT
ejpam-3294	10	35	.	.	PUNCT
ejpam-3294	11	1	in	in	ADP
ejpam-3294	11	2	this	this	DET
ejpam-3294	11	3	section	section	NOUN
ejpam-3294	11	4	,	,	PUNCT
ejpam-3294	11	5	we	we	PRON
ejpam-3294	11	6	recall	recall	VERB
ejpam-3294	11	7	some	some	DET
ejpam-3294	11	8	basic	basic	ADJ
ejpam-3294	11	9	definitions	definition	NOUN
ejpam-3294	11	10	and	and	CCONJ
ejpam-3294	11	11	concepts	concept	NOUN
ejpam-3294	11	12	.	.	PUNCT
ejpam-3294	12	1	∗corresponding	∗corresponde	VERB
ejpam-3294	12	2	author	author	NOUN
ejpam-3294	12	3	.	.	PUNCT
ejpam-3294	13	1	doi	doi	NOUN
ejpam-3294	13	2	:	:	PUNCT
ejpam-3294	13	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3294	https://doi.org/10.29020/nybg.ejpam.v11i3.3294	NOUN
ejpam-3294	13	4	email	email	NOUN
ejpam-3294	13	5	addresses	address	NOUN
ejpam-3294	13	6	:	:	PUNCT
ejpam-3294	13	7	haitham.math77@gmail.com	haitham.math77@gmail.com	X
ejpam-3294	13	8	(	(	PUNCT
ejpam-3294	13	9	h.	h.	PROPN
ejpam-3294	13	10	qawaqneh	qawaqneh	PROPN
ejpam-3294	13	11	)	)	PUNCT
ejpam-3294	13	12	,	,	PUNCT
ejpam-3294	13	13	msn@ukm.my	msn@ukm.my	X
ejpam-3294	13	14	(	(	PUNCT
ejpam-3294	13	15	m.s	m.s	PROPN
ejpam-3294	13	16	.	.	PROPN
ejpam-3294	13	17	noorani	noorani	PROPN
ejpam-3294	13	18	)	)	PUNCT
ejpam-3294	13	19	,	,	PUNCT
ejpam-3294	13	20	swasfi@hu.edu.jo	swasfi@hu.edu.jo	PROPN
ejpam-3294	13	21	(	(	PUNCT
ejpam-3294	13	22	w.	w.	PROPN
ejpam-3294	13	23	shatanawi	shatanawi	PROPN
ejpam-3294	13	24	)	)	PUNCT
ejpam-3294	13	25	,	,	PUNCT
ejpam-3294	13	26	wshatanawi@psu.edu.sa	wshatanawi@psu.edu.sa	PROPN
ejpam-3294	13	27	(	(	PUNCT
ejpam-3294	13	28	w.	w.	PROPN
ejpam-3294	13	29	shatanawi	shatanawi	PROPN
ejpam-3294	13	30	)	)	PUNCT
ejpam-3294	13	31	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3294	14	1	702	702	NUM
ejpam-3294	14	2	c	c	NOUN
ejpam-3294	14	3	©	©	PROPN
ejpam-3294	14	4	2018	2018	NUM
ejpam-3294	14	5	ejpam	ejpam	VERB
ejpam-3294	14	6	all	all	DET
ejpam-3294	14	7	rights	right	NOUN
ejpam-3294	14	8	reserved	reserve	VERB
ejpam-3294	14	9	.	.	PUNCT
ejpam-3294	15	1	h.	h.	PROPN
ejpam-3294	15	2	qawaqneh	qawaqneh	PROPN
ejpam-3294	15	3	,	,	PUNCT
ejpam-3294	15	4	m.s	m.s	PROPN
ejpam-3294	15	5	.	.	PROPN
ejpam-3294	15	6	noorani	noorani	PROPN
ejpam-3294	15	7	,	,	PUNCT
ejpam-3294	15	8	w.	w.	PROPN
ejpam-3294	15	9	shatanawi	shatanawi	PROPN
ejpam-3294	15	10	/	/	SYM
ejpam-3294	15	11	eur	eur	PROPN
ejpam-3294	15	12	.	.	PUNCT
ejpam-3294	16	1	j.	j.	PROPN
ejpam-3294	16	2	pure	pure	PROPN
ejpam-3294	16	3	appl	appl	PROPN
ejpam-3294	16	4	.	.	PROPN
ejpam-3294	16	5	math	math	PROPN
ejpam-3294	16	6	,	,	PUNCT
ejpam-3294	16	7	11	11	NUM
ejpam-3294	16	8	(	(	PUNCT
ejpam-3294	16	9	3	3	NUM
ejpam-3294	16	10	)	)	PUNCT
ejpam-3294	16	11	(	(	PUNCT
ejpam-3294	16	12	2018	2018	NUM
ejpam-3294	16	13	)	)	PUNCT
ejpam-3294	16	14	,	,	PUNCT
ejpam-3294	16	15	702	702	NUM
ejpam-3294	16	16	-	-	SYM
ejpam-3294	16	17	716	716	NUM
ejpam-3294	16	18	703	703	NUM
ejpam-3294	16	19	definition	definition	NOUN
ejpam-3294	16	20	1	1	NUM
ejpam-3294	16	21	.	.	PUNCT
ejpam-3294	17	1	[	[	X
ejpam-3294	17	2	19	19	NUM
ejpam-3294	17	3	]	]	PUNCT
ejpam-3294	17	4	let	let	VERB
ejpam-3294	17	5	x	x	PRON
ejpam-3294	17	6	be	be	AUX
ejpam-3294	17	7	a	a	DET
ejpam-3294	17	8	nonempty	nonempty	ADV
ejpam-3294	17	9	set	set	VERB
ejpam-3294	17	10	.	.	PUNCT
ejpam-3294	18	1	a	a	DET
ejpam-3294	18	2	function	function	NOUN
ejpam-3294	18	3	p	p	X
ejpam-3294	18	4	:	:	PUNCT
ejpam-3294	18	5	x	x	PROPN
ejpam-3294	18	6	×x	×x	X
ejpam-3294	18	7	→	→	X
ejpam-3294	18	8	[	[	X
ejpam-3294	18	9	0,∞	0,∞	NOUN
ejpam-3294	18	10	)	)	PUNCT
ejpam-3294	18	11	is	be	AUX
ejpam-3294	18	12	called	call	VERB
ejpam-3294	18	13	a	a	DET
ejpam-3294	18	14	partial	partial	ADJ
ejpam-3294	18	15	metric	metric	ADJ
ejpam-3294	18	16	space	space	NOUN
ejpam-3294	18	17	if	if	SCONJ
ejpam-3294	18	18	for	for	SCONJ
ejpam-3294	18	19	all	all	DET
ejpam-3294	18	20	x	x	NOUN
ejpam-3294	18	21	,	,	PUNCT
ejpam-3294	18	22	y	y	PROPN
ejpam-3294	18	23	,	,	PUNCT
ejpam-3294	18	24	z	z	PROPN
ejpam-3294	18	25	∈	∈	PROPN
ejpam-3294	18	26	x	x	SYM
ejpam-3294	18	27	,	,	PUNCT
ejpam-3294	18	28	the	the	DET
ejpam-3294	18	29	following	follow	VERB
ejpam-3294	18	30	conditions	condition	NOUN
ejpam-3294	18	31	are	be	AUX
ejpam-3294	18	32	satisfied	satisfied	ADJ
ejpam-3294	18	33	:	:	PUNCT
ejpam-3294	18	34	(	(	PUNCT
ejpam-3294	18	35	p1	p1	NOUN
ejpam-3294	18	36	)	)	PUNCT
ejpam-3294	18	37	x	x	X
ejpam-3294	19	1	=	=	SYM
ejpam-3294	19	2	y	y	PROPN
ejpam-3294	19	3	⇔	⇔	PROPN
ejpam-3294	19	4	p(x	p(x	PROPN
ejpam-3294	19	5	,	,	PUNCT
ejpam-3294	19	6	x	x	NOUN
ejpam-3294	19	7	)	)	PUNCT
ejpam-3294	19	8	=	=	SYM
ejpam-3294	19	9	p(x	p(x	PROPN
ejpam-3294	19	10	,	,	PUNCT
ejpam-3294	19	11	y	y	NOUN
ejpam-3294	19	12	)	)	PUNCT
ejpam-3294	19	13	=	=	SYM
ejpam-3294	19	14	p(y	p(y	PROPN
ejpam-3294	19	15	,	,	PUNCT
ejpam-3294	19	16	y	y	NOUN
ejpam-3294	19	17	)	)	PUNCT
ejpam-3294	19	18	,	,	PUNCT
ejpam-3294	19	19	(	(	PUNCT
ejpam-3294	19	20	p2	p2	X
ejpam-3294	19	21	)	)	PUNCT
ejpam-3294	19	22	p(x	p(x	PROPN
ejpam-3294	19	23	,	,	PUNCT
ejpam-3294	19	24	x	x	NOUN
ejpam-3294	19	25	)	)	PUNCT
ejpam-3294	19	26	≤	≤	NOUN
ejpam-3294	19	27	p(x	p(x	PROPN
ejpam-3294	19	28	,	,	PUNCT
ejpam-3294	19	29	y	y	PROPN
ejpam-3294	19	30	)	)	PUNCT
ejpam-3294	19	31	,	,	PUNCT
ejpam-3294	19	32	(	(	PUNCT
ejpam-3294	19	33	p3	p3	NOUN
ejpam-3294	19	34	)	)	PUNCT
ejpam-3294	19	35	p(x	p(x	PROPN
ejpam-3294	19	36	,	,	PUNCT
ejpam-3294	19	37	y	y	NOUN
ejpam-3294	19	38	)	)	PUNCT
ejpam-3294	19	39	=	=	SYM
ejpam-3294	19	40	p(y	p(y	NOUN
ejpam-3294	19	41	,	,	PUNCT
ejpam-3294	19	42	x	x	NOUN
ejpam-3294	19	43	)	)	PUNCT
ejpam-3294	19	44	,	,	PUNCT
ejpam-3294	19	45	(	(	PUNCT
ejpam-3294	19	46	p4	p4	ADJ
ejpam-3294	19	47	)	)	PUNCT
ejpam-3294	19	48	p(x	p(x	PROPN
ejpam-3294	19	49	,	,	PUNCT
ejpam-3294	19	50	y	y	NOUN
ejpam-3294	19	51	)	)	PUNCT
ejpam-3294	19	52	≤	≤	NOUN
ejpam-3294	19	53	p(x	p(x	PROPN
ejpam-3294	19	54	,	,	PUNCT
ejpam-3294	19	55	z	z	NOUN
ejpam-3294	19	56	)	)	PUNCT
ejpam-3294	20	1	+	+	CCONJ
ejpam-3294	20	2	p(z	p(z	NOUN
ejpam-3294	20	3	,	,	PUNCT
ejpam-3294	20	4	y)−	y)−	PROPN
ejpam-3294	20	5	p(z	p(z	NOUN
ejpam-3294	20	6	,	,	PUNCT
ejpam-3294	20	7	z	z	NOUN
ejpam-3294	20	8	)	)	PUNCT
ejpam-3294	20	9	.	.	PUNCT
ejpam-3294	21	1	the	the	DET
ejpam-3294	21	2	pair	pair	NOUN
ejpam-3294	21	3	(	(	PUNCT
ejpam-3294	21	4	x	x	X
ejpam-3294	21	5	,	,	PUNCT
ejpam-3294	21	6	p	p	NOUN
ejpam-3294	21	7	)	)	PUNCT
ejpam-3294	21	8	is	be	AUX
ejpam-3294	21	9	called	call	VERB
ejpam-3294	21	10	the	the	DET
ejpam-3294	21	11	notion	notion	NOUN
ejpam-3294	21	12	of	of	ADP
ejpam-3294	21	13	a	a	DET
ejpam-3294	21	14	partial	partial	ADJ
ejpam-3294	21	15	metric	metric	ADJ
ejpam-3294	21	16	space(pms	space(pms	PROPN
ejpam-3294	21	17	)	)	PUNCT
ejpam-3294	21	18	.	.	PUNCT
ejpam-3294	22	1	the	the	DET
ejpam-3294	22	2	sequence	sequence	NOUN
ejpam-3294	22	3	{	{	PUNCT
ejpam-3294	22	4	xn	xn	NOUN
ejpam-3294	22	5	}	}	PUNCT
ejpam-3294	22	6	in	in	ADP
ejpam-3294	22	7	x	x	SYM
ejpam-3294	22	8	converges	converge	NOUN
ejpam-3294	22	9	to	to	ADP
ejpam-3294	22	10	a	a	DET
ejpam-3294	22	11	point	point	NOUN
ejpam-3294	22	12	x	x	SYM
ejpam-3294	22	13	∈	∈	NOUN
ejpam-3294	22	14	x	x	SYM
ejpam-3294	22	15	if	if	SCONJ
ejpam-3294	22	16	limn→∞	limn→∞	PROPN
ejpam-3294	22	17	p(xn	p(xn	NOUN
ejpam-3294	22	18	,	,	PUNCT
ejpam-3294	22	19	x	x	NOUN
ejpam-3294	22	20	)	)	PUNCT
ejpam-3294	22	21	=	=	SYM
ejpam-3294	22	22	p(x	p(x	PROPN
ejpam-3294	22	23	,	,	PUNCT
ejpam-3294	22	24	x	x	NOUN
ejpam-3294	22	25	)	)	PUNCT
ejpam-3294	22	26	.	.	PUNCT
ejpam-3294	23	1	also	also	ADV
ejpam-3294	23	2	the	the	DET
ejpam-3294	23	3	sequence	sequence	NOUN
ejpam-3294	23	4	{	{	PUNCT
ejpam-3294	23	5	xn	xn	NOUN
ejpam-3294	23	6	}	}	PUNCT
ejpam-3294	23	7	is	be	AUX
ejpam-3294	23	8	called	call	VERB
ejpam-3294	23	9	p−cauchy	p−cauchy	PROPN
ejpam-3294	23	10	if	if	SCONJ
ejpam-3294	23	11	the	the	DET
ejpam-3294	23	12	limn	limn	NOUN
ejpam-3294	23	13	,	,	PUNCT
ejpam-3294	23	14	m→∞p(xn	m→∞p(xn	PROPN
ejpam-3294	23	15	,	,	PUNCT
ejpam-3294	23	16	ym	ym	PRON
ejpam-3294	23	17	)	)	PUNCT
ejpam-3294	23	18	exists	exist	VERB
ejpam-3294	23	19	.	.	PUNCT
ejpam-3294	24	1	the	the	DET
ejpam-3294	24	2	partial	partial	ADJ
ejpam-3294	24	3	metric	metric	ADJ
ejpam-3294	24	4	space	space	NOUN
ejpam-3294	24	5	(	(	PUNCT
ejpam-3294	24	6	x	x	X
ejpam-3294	24	7	,	,	PUNCT
ejpam-3294	24	8	p	p	NOUN
ejpam-3294	24	9	)	)	PUNCT
ejpam-3294	24	10	is	be	AUX
ejpam-3294	24	11	called	call	VERB
ejpam-3294	24	12	complete	complete	ADJ
ejpam-3294	24	13	if	if	SCONJ
ejpam-3294	24	14	for	for	ADP
ejpam-3294	24	15	every	every	DET
ejpam-3294	24	16	p	p	ADJ
ejpam-3294	24	17	-	-	PUNCT
ejpam-3294	24	18	cauchy	cauchy	ADJ
ejpam-3294	24	19	sequence	sequence	NOUN
ejpam-3294	24	20	{	{	PUNCT
ejpam-3294	24	21	xn}n∞	xn}n∞	PROPN
ejpam-3294	24	22	,	,	PUNCT
ejpam-3294	24	23	there	there	PRON
ejpam-3294	24	24	is	be	VERB
ejpam-3294	24	25	some	some	DET
ejpam-3294	24	26	x	x	SYM
ejpam-3294	24	27	∈	∈	PROPN
ejpam-3294	24	28	x	x	PUNCT
ejpam-3294	24	29	such	such	ADJ
ejpam-3294	24	30	that	that	DET
ejpam-3294	24	31	p(x	p(x	NOUN
ejpam-3294	24	32	,	,	PUNCT
ejpam-3294	24	33	x	x	NOUN
ejpam-3294	24	34	)	)	PUNCT
ejpam-3294	24	35	=	=	SYM
ejpam-3294	24	36	lim	lim	PROPN
ejpam-3294	24	37	n→∞	n→∞	NUM
ejpam-3294	24	38	p(xn	p(xn	NOUN
ejpam-3294	24	39	,	,	PUNCT
ejpam-3294	24	40	x	x	NOUN
ejpam-3294	24	41	)	)	PUNCT
ejpam-3294	24	42	=	=	SYM
ejpam-3294	24	43	lim	lim	PROPN
ejpam-3294	24	44	n	n	CCONJ
ejpam-3294	24	45	,	,	PUNCT
ejpam-3294	24	46	m→∞	m→∞	NOUN
ejpam-3294	24	47	p(xn	p(xn	NOUN
ejpam-3294	24	48	,	,	PUNCT
ejpam-3294	24	49	xm	xm	PROPN
ejpam-3294	24	50	)	)	PUNCT
ejpam-3294	24	51	.	.	PUNCT
ejpam-3294	25	1	a	a	DET
ejpam-3294	25	2	basic	basic	ADJ
ejpam-3294	25	3	example	example	NOUN
ejpam-3294	25	4	of	of	ADP
ejpam-3294	25	5	a	a	DET
ejpam-3294	25	6	partial	partial	ADJ
ejpam-3294	25	7	metric	metric	ADJ
ejpam-3294	25	8	space	space	NOUN
ejpam-3294	25	9	is	be	AUX
ejpam-3294	25	10	the	the	DET
ejpam-3294	25	11	pair	pair	NOUN
ejpam-3294	25	12	(	(	PUNCT
ejpam-3294	25	13	r+	r+	X
ejpam-3294	25	14	,	,	PUNCT
ejpam-3294	25	15	p	p	NOUN
ejpam-3294	25	16	)	)	PUNCT
ejpam-3294	25	17	,	,	PUNCT
ejpam-3294	25	18	where	where	SCONJ
ejpam-3294	25	19	p(x	p(x	PROPN
ejpam-3294	25	20	,	,	PUNCT
ejpam-3294	25	21	y	y	NOUN
ejpam-3294	25	22	)	)	PUNCT
ejpam-3294	25	23	=	=	SYM
ejpam-3294	25	24	max{x	max{x	PROPN
ejpam-3294	25	25	,	,	PUNCT
ejpam-3294	25	26	y	y	NOUN
ejpam-3294	25	27	}	}	PUNCT
ejpam-3294	25	28	for	for	ADP
ejpam-3294	25	29	all	all	DET
ejpam-3294	25	30	x	x	NOUN
ejpam-3294	25	31	,	,	PUNCT
ejpam-3294	25	32	y	y	PROPN
ejpam-3294	25	33	∈	∈	PROPN
ejpam-3294	25	34	r+	r+	X
ejpam-3294	25	35	.	.	PUNCT
ejpam-3294	26	1	harandi	harandi	PROPN
ejpam-3294	27	1	[	[	X
ejpam-3294	27	2	14	14	NUM
ejpam-3294	27	3	]	]	PUNCT
ejpam-3294	27	4	introduced	introduce	VERB
ejpam-3294	27	5	a	a	DET
ejpam-3294	27	6	new	new	ADJ
ejpam-3294	27	7	generalization	generalization	NOUN
ejpam-3294	27	8	of	of	ADP
ejpam-3294	27	9	partial	partial	ADJ
ejpam-3294	27	10	metric	metric	ADJ
ejpam-3294	27	11	space	space	NOUN
ejpam-3294	27	12	,	,	PUNCT
ejpam-3294	27	13	called	call	VERB
ejpam-3294	27	14	a	a	DET
ejpam-3294	27	15	metriclike	metriclike	NOUN
ejpam-3294	27	16	space	space	NOUN
ejpam-3294	27	17	.	.	PUNCT
ejpam-3294	28	1	he	he	PRON
ejpam-3294	28	2	established	establish	VERB
ejpam-3294	28	3	the	the	DET
ejpam-3294	28	4	existence	existence	NOUN
ejpam-3294	28	5	and	and	CCONJ
ejpam-3294	28	6	uniqueness	uniqueness	NOUN
ejpam-3294	28	7	of	of	ADP
ejpam-3294	28	8	fixed	fix	VERB
ejpam-3294	28	9	points	point	NOUN
ejpam-3294	28	10	in	in	ADP
ejpam-3294	28	11	a	a	DET
ejpam-3294	28	12	metric	metric	ADJ
ejpam-3294	28	13	-	-	PUNCT
ejpam-3294	28	14	like	like	ADJ
ejpam-3294	28	15	space	space	NOUN
ejpam-3294	28	16	as	as	ADV
ejpam-3294	28	17	well	well	ADV
ejpam-3294	28	18	as	as	ADP
ejpam-3294	28	19	in	in	ADP
ejpam-3294	28	20	a	a	DET
ejpam-3294	28	21	partially	partially	ADV
ejpam-3294	28	22	ordered	order	VERB
ejpam-3294	28	23	metric	metric	ADJ
ejpam-3294	28	24	-	-	PUNCT
ejpam-3294	28	25	like	like	ADJ
ejpam-3294	28	26	space	space	NOUN
ejpam-3294	28	27	.	.	PUNCT
ejpam-3294	29	1	definition	definition	NOUN
ejpam-3294	29	2	2	2	NUM
ejpam-3294	29	3	.	.	PUNCT
ejpam-3294	30	1	[	[	X
ejpam-3294	30	2	14	14	NUM
ejpam-3294	30	3	]	]	PUNCT
ejpam-3294	30	4	let	let	VERB
ejpam-3294	30	5	x	x	PRON
ejpam-3294	30	6	be	be	AUX
ejpam-3294	30	7	a	a	DET
ejpam-3294	30	8	nonempty	nonempty	ADV
ejpam-3294	30	9	set	set	VERB
ejpam-3294	30	10	.	.	PUNCT
ejpam-3294	31	1	a	a	DET
ejpam-3294	31	2	function	function	NOUN
ejpam-3294	31	3	σ	σ	NOUN
ejpam-3294	31	4	:	:	PUNCT
ejpam-3294	31	5	x	x	X
ejpam-3294	31	6	×x	×x	X
ejpam-3294	31	7	→	→	X
ejpam-3294	31	8	[	[	X
ejpam-3294	31	9	0,∞	0,∞	NOUN
ejpam-3294	31	10	)	)	PUNCT
ejpam-3294	31	11	is	be	AUX
ejpam-3294	31	12	said	say	VERB
ejpam-3294	31	13	to	to	PART
ejpam-3294	31	14	be	be	AUX
ejpam-3294	31	15	a	a	DET
ejpam-3294	31	16	metric	metric	ADJ
ejpam-3294	31	17	like	like	ADP
ejpam-3294	31	18	space	space	NOUN
ejpam-3294	31	19	on	on	ADP
ejpam-3294	31	20	x	x	SYM
ejpam-3294	31	21	if	if	SCONJ
ejpam-3294	31	22	for	for	ADP
ejpam-3294	31	23	any	any	DET
ejpam-3294	31	24	x	x	NOUN
ejpam-3294	31	25	,	,	PUNCT
ejpam-3294	31	26	y	y	PROPN
ejpam-3294	31	27	,	,	PUNCT
ejpam-3294	31	28	z	z	PROPN
ejpam-3294	31	29	∈	∈	PROPN
ejpam-3294	32	1	x	x	SYM
ejpam-3294	32	2	,	,	PUNCT
ejpam-3294	32	3	the	the	DET
ejpam-3294	32	4	following	follow	VERB
ejpam-3294	32	5	conditions	condition	NOUN
ejpam-3294	32	6	hold	hold	VERB
ejpam-3294	32	7	:	:	PUNCT
ejpam-3294	32	8	(	(	PUNCT
ejpam-3294	32	9	σ1	σ1	NOUN
ejpam-3294	32	10	)	)	PUNCT
ejpam-3294	32	11	σ(x	σ(x	PROPN
ejpam-3294	32	12	,	,	PUNCT
ejpam-3294	32	13	y	y	NOUN
ejpam-3294	32	14	)	)	PUNCT
ejpam-3294	32	15	=	=	SYM
ejpam-3294	33	1	0⇒	0⇒	NOUN
ejpam-3294	34	1	x	x	X
ejpam-3294	34	2	=	=	SYM
ejpam-3294	34	3	y	y	PROPN
ejpam-3294	34	4	,	,	PUNCT
ejpam-3294	34	5	(	(	PUNCT
ejpam-3294	34	6	σ2	σ2	NOUN
ejpam-3294	34	7	)	)	PUNCT
ejpam-3294	34	8	σ(x	σ(x	PROPN
ejpam-3294	34	9	,	,	PUNCT
ejpam-3294	34	10	y	y	NOUN
ejpam-3294	34	11	)	)	PUNCT
ejpam-3294	34	12	=	=	SYM
ejpam-3294	34	13	σ(y	σ(y	NOUN
ejpam-3294	34	14	,	,	PUNCT
ejpam-3294	34	15	x	x	NOUN
ejpam-3294	34	16	)	)	PUNCT
ejpam-3294	34	17	,	,	PUNCT
ejpam-3294	34	18	(	(	PUNCT
ejpam-3294	34	19	σ3	σ3	PROPN
ejpam-3294	34	20	)	)	PUNCT
ejpam-3294	34	21	σ(x	σ(x	PROPN
ejpam-3294	34	22	,	,	PUNCT
ejpam-3294	34	23	z	z	NOUN
ejpam-3294	34	24	)	)	PUNCT
ejpam-3294	34	25	≤	≤	NOUN
ejpam-3294	34	26	σ(x	σ(x	PROPN
ejpam-3294	34	27	,	,	PUNCT
ejpam-3294	34	28	y	y	NOUN
ejpam-3294	34	29	)	)	PUNCT
ejpam-3294	34	30	+	+	CCONJ
ejpam-3294	34	31	σ(y	σ(y	NOUN
ejpam-3294	34	32	,	,	PUNCT
ejpam-3294	34	33	z	z	NOUN
ejpam-3294	34	34	)	)	PUNCT
ejpam-3294	34	35	.	.	PUNCT
ejpam-3294	35	1	the	the	DET
ejpam-3294	35	2	pair	pair	NOUN
ejpam-3294	35	3	(	(	PUNCT
ejpam-3294	35	4	x	x	NOUN
ejpam-3294	35	5	,	,	PUNCT
ejpam-3294	35	6	σ	σ	PROPN
ejpam-3294	35	7	)	)	PUNCT
ejpam-3294	35	8	is	be	AUX
ejpam-3294	35	9	called	call	VERB
ejpam-3294	35	10	a	a	DET
ejpam-3294	35	11	metric	metric	ADJ
ejpam-3294	35	12	-	-	PUNCT
ejpam-3294	35	13	like	like	ADJ
ejpam-3294	35	14	space	space	NOUN
ejpam-3294	35	15	.	.	PUNCT
ejpam-3294	36	1	it	it	PRON
ejpam-3294	36	2	is	be	AUX
ejpam-3294	36	3	clear	clear	ADJ
ejpam-3294	36	4	that	that	SCONJ
ejpam-3294	36	5	every	every	DET
ejpam-3294	36	6	partial	partial	ADJ
ejpam-3294	36	7	metric	metric	ADJ
ejpam-3294	36	8	space	space	NOUN
ejpam-3294	36	9	is	be	AUX
ejpam-3294	36	10	a	a	DET
ejpam-3294	36	11	metric	metric	ADJ
ejpam-3294	36	12	-	-	PUNCT
ejpam-3294	36	13	like	like	ADJ
ejpam-3294	36	14	space	space	NOUN
ejpam-3294	36	15	but	but	CCONJ
ejpam-3294	36	16	the	the	DET
ejpam-3294	36	17	converse	converse	NOUN
ejpam-3294	36	18	is	be	AUX
ejpam-3294	36	19	not	not	PART
ejpam-3294	36	20	true	true	ADJ
ejpam-3294	36	21	.	.	PUNCT
ejpam-3294	37	1	example	example	NOUN
ejpam-3294	38	1	1	1	NUM
ejpam-3294	38	2	.	.	PUNCT
ejpam-3294	39	1	[	[	X
ejpam-3294	39	2	14	14	NUM
ejpam-3294	39	3	]	]	PUNCT
ejpam-3294	39	4	let	let	VERB
ejpam-3294	39	5	x	x	PUNCT
ejpam-3294	39	6	=	=	PUNCT
ejpam-3294	39	7	{	{	PUNCT
ejpam-3294	39	8	0	0	NUM
ejpam-3294	39	9	,	,	PUNCT
ejpam-3294	39	10	1	1	NUM
ejpam-3294	39	11	}	}	PUNCT
ejpam-3294	39	12	and	and	CCONJ
ejpam-3294	39	13	σ(x	σ(x	PROPN
ejpam-3294	39	14	,	,	PUNCT
ejpam-3294	39	15	y	y	NOUN
ejpam-3294	39	16	)	)	PUNCT
ejpam-3294	39	17	=	=	PUNCT
ejpam-3294	40	1			PROPN
ejpam-3294	40	2	2	2	NUM
ejpam-3294	40	3	,	,	PUNCT
ejpam-3294	40	4	if	if	SCONJ
ejpam-3294	40	5	x	x	ADP
ejpam-3294	40	6	=	=	PUNCT
ejpam-3294	40	7	y	y	PROPN
ejpam-3294	40	8	=	=	SYM
ejpam-3294	40	9	0	0	NUM
ejpam-3294	40	10	;	;	PUNCT
ejpam-3294	40	11	1	1	NUM
ejpam-3294	40	12	,	,	PUNCT
ejpam-3294	40	13	otherwise	otherwise	ADV
ejpam-3294	40	14	.	.	PUNCT
ejpam-3294	41	1	then	then	ADV
ejpam-3294	41	2	(	(	PUNCT
ejpam-3294	41	3	x	x	X
ejpam-3294	41	4	,	,	PUNCT
ejpam-3294	41	5	σ	σ	PROPN
ejpam-3294	41	6	)	)	PUNCT
ejpam-3294	41	7	is	be	AUX
ejpam-3294	41	8	a	a	DET
ejpam-3294	41	9	metric	metric	ADJ
ejpam-3294	41	10	-	-	PUNCT
ejpam-3294	41	11	like	like	ADJ
ejpam-3294	41	12	space	space	NOUN
ejpam-3294	41	13	but	but	CCONJ
ejpam-3294	41	14	it	it	PRON
ejpam-3294	41	15	is	be	AUX
ejpam-3294	41	16	not	not	PART
ejpam-3294	41	17	a	a	DET
ejpam-3294	41	18	partial	partial	ADJ
ejpam-3294	41	19	metric	metric	ADJ
ejpam-3294	41	20	space	space	NOUN
ejpam-3294	41	21	.	.	PUNCT
ejpam-3294	42	1	note	note	VERB
ejpam-3294	42	2	that	that	SCONJ
ejpam-3294	42	3	σ(0	σ(0	PROPN
ejpam-3294	42	4	,	,	PUNCT
ejpam-3294	42	5	0	0	NUM
ejpam-3294	42	6	)	)	PUNCT
ejpam-3294	42	7	6≤	6≤	NUM
ejpam-3294	42	8	σ(0	σ(0	PROPN
ejpam-3294	42	9	,	,	PUNCT
ejpam-3294	42	10	1	1	NUM
ejpam-3294	42	11	)	)	PUNCT
ejpam-3294	42	12	.	.	PUNCT
ejpam-3294	43	1	h.	h.	PROPN
ejpam-3294	43	2	qawaqneh	qawaqneh	PROPN
ejpam-3294	43	3	,	,	PUNCT
ejpam-3294	43	4	m.s	m.s	PROPN
ejpam-3294	43	5	.	.	PROPN
ejpam-3294	43	6	noorani	noorani	PROPN
ejpam-3294	43	7	,	,	PUNCT
ejpam-3294	43	8	w.	w.	PROPN
ejpam-3294	43	9	shatanawi	shatanawi	PROPN
ejpam-3294	43	10	/	/	SYM
ejpam-3294	43	11	eur	eur	PROPN
ejpam-3294	43	12	.	.	PUNCT
ejpam-3294	44	1	j.	j.	PROPN
ejpam-3294	44	2	pure	pure	PROPN
ejpam-3294	44	3	appl	appl	PROPN
ejpam-3294	44	4	.	.	PROPN
ejpam-3294	44	5	math	math	PROPN
ejpam-3294	44	6	,	,	PUNCT
ejpam-3294	44	7	11	11	NUM
ejpam-3294	44	8	(	(	PUNCT
ejpam-3294	44	9	3	3	NUM
ejpam-3294	44	10	)	)	PUNCT
ejpam-3294	44	11	(	(	PUNCT
ejpam-3294	44	12	2018	2018	NUM
ejpam-3294	44	13	)	)	PUNCT
ejpam-3294	44	14	,	,	PUNCT
ejpam-3294	44	15	702	702	NUM
ejpam-3294	44	16	-	-	SYM
ejpam-3294	44	17	716	716	NUM
ejpam-3294	44	18	704	704	NUM
ejpam-3294	44	19	moreover	moreover	ADV
ejpam-3294	44	20	,	,	PUNCT
ejpam-3294	44	21	each	each	DET
ejpam-3294	44	22	metric	metric	ADJ
ejpam-3294	44	23	-	-	PUNCT
ejpam-3294	44	24	like	like	ADJ
ejpam-3294	44	25	space	space	NOUN
ejpam-3294	44	26	σ	σ	NOUN
ejpam-3294	44	27	on	on	ADP
ejpam-3294	44	28	x	x	PUNCT
ejpam-3294	44	29	generates	generate	VERB
ejpam-3294	44	30	a	a	DET
ejpam-3294	44	31	topology	topology	NOUN
ejpam-3294	44	32	τσ	τσ	NOUN
ejpam-3294	44	33	on	on	ADP
ejpam-3294	44	34	x	x	PUNCT
ejpam-3294	44	35	whose	whose	DET
ejpam-3294	44	36	base	base	NOUN
ejpam-3294	44	37	is	be	AUX
ejpam-3294	44	38	the	the	DET
ejpam-3294	44	39	family	family	NOUN
ejpam-3294	44	40	of	of	ADP
ejpam-3294	44	41	open	open	ADJ
ejpam-3294	44	42	σ	σ	NOUN
ejpam-3294	44	43	-	-	PUNCT
ejpam-3294	44	44	balls	ball	NOUN
ejpam-3294	44	45	bσ(x	bσ(x	VERB
ejpam-3294	44	46	,	,	PUNCT
ejpam-3294	44	47	ε	ε	PROPN
ejpam-3294	44	48	)	)	PUNCT
ejpam-3294	44	49	=	=	PRON
ejpam-3294	44	50	{	{	PUNCT
ejpam-3294	44	51	y	y	PROPN
ejpam-3294	44	52	∈	∈	PROPN
ejpam-3294	45	1	x	x	X
ejpam-3294	45	2	:|	:|	PUNCT
ejpam-3294	45	3	σ(x	σ(x	PROPN
ejpam-3294	45	4	,	,	PUNCT
ejpam-3294	45	5	y)−	y)−	PROPN
ejpam-3294	45	6	σ(x	σ(x	PROPN
ejpam-3294	45	7	,	,	PUNCT
ejpam-3294	45	8	x	x	X
ejpam-3294	45	9	)	)	PUNCT
ejpam-3294	45	10	|	|	ADV
ejpam-3294	45	11	<	<	X
ejpam-3294	45	12	ε	ε	PROPN
ejpam-3294	45	13	}	}	PUNCT
ejpam-3294	45	14	,	,	PUNCT
ejpam-3294	45	15	for	for	ADP
ejpam-3294	45	16	all	all	PRON
ejpam-3294	45	17	x	x	SYM
ejpam-3294	45	18	∈	∈	PROPN
ejpam-3294	45	19	x	x	X
ejpam-3294	45	20	and	and	CCONJ
ejpam-3294	45	21	ε	ε	PROPN
ejpam-3294	45	22	>	>	X
ejpam-3294	45	23	0	0	X
ejpam-3294	45	24	.	.	PUNCT
ejpam-3294	46	1	let	let	VERB
ejpam-3294	46	2	(	(	PUNCT
ejpam-3294	46	3	x	x	NOUN
ejpam-3294	46	4	,	,	PUNCT
ejpam-3294	46	5	σ	σ	PROPN
ejpam-3294	46	6	)	)	PUNCT
ejpam-3294	46	7	and	and	CCONJ
ejpam-3294	46	8	(	(	PUNCT
ejpam-3294	46	9	y	y	PROPN
ejpam-3294	46	10	,	,	PUNCT
ejpam-3294	46	11	σ	σ	PROPN
ejpam-3294	46	12	)	)	PUNCT
ejpam-3294	46	13	be	be	AUX
ejpam-3294	46	14	metric	metric	ADJ
ejpam-3294	46	15	-	-	PUNCT
ejpam-3294	46	16	like	like	ADJ
ejpam-3294	46	17	spaces	space	NOUN
ejpam-3294	46	18	,	,	PUNCT
ejpam-3294	46	19	and	and	CCONJ
ejpam-3294	46	20	let	let	VERB
ejpam-3294	46	21	f	f	PRON
ejpam-3294	46	22	:	:	PUNCT
ejpam-3294	46	23	x	x	X
ejpam-3294	46	24	→	→	SYM
ejpam-3294	46	25	y	y	X
ejpam-3294	46	26	be	be	AUX
ejpam-3294	46	27	a	a	DET
ejpam-3294	46	28	continuous	continuous	ADJ
ejpam-3294	46	29	mapping	mapping	NOUN
ejpam-3294	46	30	.	.	PUNCT
ejpam-3294	47	1	then	then	ADV
ejpam-3294	47	2	lim	lim	PROPN
ejpam-3294	47	3	n→∞	n→∞	X
ejpam-3294	47	4	xn	xn	PUNCT
ejpam-3294	48	1	=	=	PUNCT
ejpam-3294	48	2	x	x	PROPN
ejpam-3294	48	3	⇒	⇒	PROPN
ejpam-3294	48	4	lim	lim	PROPN
ejpam-3294	48	5	n→∞	n→∞	NUM
ejpam-3294	48	6	fxn	fxn	NOUN
ejpam-3294	48	7	=	=	SYM
ejpam-3294	48	8	fx	fx	PROPN
ejpam-3294	48	9	.	.	PUNCT
ejpam-3294	49	1	a	a	DET
ejpam-3294	49	2	sequence	sequence	NOUN
ejpam-3294	49	3	{	{	PUNCT
ejpam-3294	49	4	xn}n=0	xn}n=0	NOUN
ejpam-3294	49	5	∞	∞	PROPN
ejpam-3294	49	6	of	of	ADP
ejpam-3294	49	7	elements	element	NOUN
ejpam-3294	49	8	of	of	ADP
ejpam-3294	49	9	x	x	SYM
ejpam-3294	49	10	is	be	AUX
ejpam-3294	49	11	called	call	VERB
ejpam-3294	49	12	σ	σ	PROPN
ejpam-3294	49	13	-	-	PUNCT
ejpam-3294	49	14	cauchy	cauchy	NOUN
ejpam-3294	49	15	if	if	SCONJ
ejpam-3294	49	16	the	the	DET
ejpam-3294	49	17	limit	limit	NOUN
ejpam-3294	49	18	limn	limn	NOUN
ejpam-3294	49	19	,	,	PUNCT
ejpam-3294	49	20	m→∞	m→∞	NOUN
ejpam-3294	49	21	σ(xn	σ(xn	NOUN
ejpam-3294	49	22	,	,	PUNCT
ejpam-3294	49	23	xm	xm	NUM
ejpam-3294	49	24	)	)	PUNCT
ejpam-3294	49	25	exists	exist	VERB
ejpam-3294	49	26	.	.	PUNCT
ejpam-3294	50	1	the	the	DET
ejpam-3294	50	2	metric	metric	ADJ
ejpam-3294	50	3	-	-	PUNCT
ejpam-3294	50	4	like	like	ADJ
ejpam-3294	50	5	space	space	NOUN
ejpam-3294	50	6	(	(	PUNCT
ejpam-3294	50	7	x	x	X
ejpam-3294	50	8	,	,	PUNCT
ejpam-3294	50	9	σ	σ	PROPN
ejpam-3294	50	10	)	)	PUNCT
ejpam-3294	50	11	is	be	AUX
ejpam-3294	50	12	called	call	VERB
ejpam-3294	50	13	complete	complete	ADJ
ejpam-3294	50	14	if	if	SCONJ
ejpam-3294	50	15	for	for	ADP
ejpam-3294	50	16	each	each	DET
ejpam-3294	50	17	σ	σ	PROPN
ejpam-3294	50	18	-	-	PUNCT
ejpam-3294	50	19	cauchy	cauchy	ADJ
ejpam-3294	50	20	sequence	sequence	NOUN
ejpam-3294	50	21	{	{	PUNCT
ejpam-3294	50	22	xn}∞n	xn}∞n	PROPN
ejpam-3294	50	23	,	,	PUNCT
ejpam-3294	50	24	there	there	PRON
ejpam-3294	50	25	exists	exist	VERB
ejpam-3294	50	26	x	x	X
ejpam-3294	50	27	∈	∈	PROPN
ejpam-3294	50	28	x	x	X
ejpam-3294	50	29	such	such	ADJ
ejpam-3294	50	30	that	that	SCONJ
ejpam-3294	50	31	lim	lim	PROPN
ejpam-3294	50	32	n→∞	n→∞	NUM
ejpam-3294	50	33	σ(xn	σ(xn	NOUN
ejpam-3294	50	34	,	,	PUNCT
ejpam-3294	50	35	x	x	NOUN
ejpam-3294	50	36	)	)	PUNCT
ejpam-3294	51	1	=	=	SYM
ejpam-3294	51	2	σ(x	σ(x	PROPN
ejpam-3294	51	3	,	,	PUNCT
ejpam-3294	51	4	x	x	X
ejpam-3294	51	5	)	)	PUNCT
ejpam-3294	51	6	=	=	SYM
ejpam-3294	51	7	lim	lim	PROPN
ejpam-3294	51	8	n	n	CCONJ
ejpam-3294	51	9	,	,	PUNCT
ejpam-3294	51	10	m→∞	m→∞	NOUN
ejpam-3294	51	11	σ(xn	σ(xn	NOUN
ejpam-3294	51	12	,	,	PUNCT
ejpam-3294	51	13	xm	xm	PROPN
ejpam-3294	51	14	)	)	PUNCT
ejpam-3294	51	15	.	.	PUNCT
ejpam-3294	52	1	remark	remark	PROPN
ejpam-3294	52	2	1	1	NUM
ejpam-3294	52	3	.	.	PUNCT
ejpam-3294	53	1	[	[	X
ejpam-3294	53	2	16	16	NUM
ejpam-3294	53	3	]	]	X
ejpam-3294	53	4	let	let	VERB
ejpam-3294	53	5	x	x	PUNCT
ejpam-3294	53	6	=	=	PUNCT
ejpam-3294	53	7	{	{	PUNCT
ejpam-3294	53	8	0	0	NUM
ejpam-3294	53	9	,	,	PUNCT
ejpam-3294	53	10	1	1	NUM
ejpam-3294	53	11	}	}	PUNCT
ejpam-3294	53	12	,	,	PUNCT
ejpam-3294	53	13	and	and	CCONJ
ejpam-3294	53	14	σ(x	σ(x	PROPN
ejpam-3294	53	15	,	,	PUNCT
ejpam-3294	53	16	y	y	NOUN
ejpam-3294	53	17	)	)	PUNCT
ejpam-3294	53	18	=	=	SYM
ejpam-3294	53	19	1	1	NUM
ejpam-3294	53	20	for	for	ADP
ejpam-3294	53	21	each	each	DET
ejpam-3294	53	22	x	x	NOUN
ejpam-3294	53	23	,	,	PUNCT
ejpam-3294	53	24	y	y	PROPN
ejpam-3294	53	25	∈	∈	PROPN
ejpam-3294	53	26	x.	x.	NOUN
ejpam-3294	53	27	consider	consider	VERB
ejpam-3294	53	28	the	the	DET
ejpam-3294	53	29	sequence	sequence	NOUN
ejpam-3294	53	30	{	{	PUNCT
ejpam-3294	53	31	xn	xn	X
ejpam-3294	53	32	}	}	PUNCT
ejpam-3294	53	33	such	such	ADJ
ejpam-3294	53	34	that	that	SCONJ
ejpam-3294	53	35	xn	xn	PUNCT
ejpam-3294	54	1	=	=	SYM
ejpam-3294	54	2	1	1	NUM
ejpam-3294	54	3	for	for	ADP
ejpam-3294	54	4	each	each	DET
ejpam-3294	54	5	n	n	PRON
ejpam-3294	54	6	∈	∈	PROPN
ejpam-3294	54	7	n.	n.	NOUN
ejpam-3294	54	8	then	then	ADV
ejpam-3294	54	9	it	it	PRON
ejpam-3294	54	10	is	be	AUX
ejpam-3294	54	11	easy	easy	ADJ
ejpam-3294	54	12	to	to	PART
ejpam-3294	54	13	see	see	VERB
ejpam-3294	54	14	that	that	PRON
ejpam-3294	54	15	xn	xn	PUNCT
ejpam-3294	55	1	→	→	SYM
ejpam-3294	55	2	0	0	NUM
ejpam-3294	55	3	and	and	CCONJ
ejpam-3294	55	4	xn	xn	PROPN
ejpam-3294	56	1	→	→	SYM
ejpam-3294	56	2	1	1	NUM
ejpam-3294	56	3	,	,	PUNCT
ejpam-3294	56	4	therefore	therefore	ADV
ejpam-3294	56	5	the	the	DET
ejpam-3294	56	6	limit	limit	NOUN
ejpam-3294	56	7	of	of	ADP
ejpam-3294	56	8	a	a	DET
ejpam-3294	56	9	convergent	convergent	NOUN
ejpam-3294	56	10	sequence	sequence	NOUN
ejpam-3294	56	11	is	be	AUX
ejpam-3294	56	12	not	not	PART
ejpam-3294	56	13	necessarily	necessarily	ADV
ejpam-3294	56	14	unique	unique	ADJ
ejpam-3294	56	15	.	.	PUNCT
ejpam-3294	57	1	lemma	lemma	PROPN
ejpam-3294	57	2	1	1	NUM
ejpam-3294	57	3	.	.	PUNCT
ejpam-3294	58	1	[	[	X
ejpam-3294	58	2	16	16	NUM
ejpam-3294	58	3	]	]	X
ejpam-3294	58	4	let	let	AUX
ejpam-3294	58	5	(	(	PUNCT
ejpam-3294	58	6	x	x	NOUN
ejpam-3294	58	7	,	,	PUNCT
ejpam-3294	58	8	σ	σ	PROPN
ejpam-3294	58	9	)	)	PUNCT
ejpam-3294	58	10	be	be	AUX
ejpam-3294	58	11	a	a	DET
ejpam-3294	58	12	metric	metric	ADJ
ejpam-3294	58	13	-	-	PUNCT
ejpam-3294	58	14	like	like	ADJ
ejpam-3294	58	15	space	space	NOUN
ejpam-3294	58	16	.	.	PUNCT
ejpam-3294	59	1	let	let	VERB
ejpam-3294	59	2	{	{	PUNCT
ejpam-3294	59	3	xn	xn	VERB
ejpam-3294	59	4	}	}	PUNCT
ejpam-3294	59	5	be	be	AUX
ejpam-3294	59	6	a	a	DET
ejpam-3294	59	7	sequence	sequence	NOUN
ejpam-3294	59	8	in	in	ADP
ejpam-3294	59	9	x	x	PUNCT
ejpam-3294	59	10	that	that	PRON
ejpam-3294	59	11	converges	converge	VERB
ejpam-3294	59	12	to	to	ADP
ejpam-3294	59	13	x	x	SYM
ejpam-3294	59	14	∈	∈	PROPN
ejpam-3294	59	15	x	x	PUNCT
ejpam-3294	59	16	such	such	ADJ
ejpam-3294	59	17	that	that	SCONJ
ejpam-3294	59	18	,	,	PUNCT
ejpam-3294	59	19	σ(x	σ(x	PROPN
ejpam-3294	59	20	,	,	PUNCT
ejpam-3294	59	21	x	x	NOUN
ejpam-3294	59	22	)	)	PUNCT
ejpam-3294	59	23	=	=	SYM
ejpam-3294	60	1	0	0	X
ejpam-3294	60	2	.	.	PUNCT
ejpam-3294	61	1	then	then	ADV
ejpam-3294	61	2	,	,	PUNCT
ejpam-3294	61	3	for	for	ADP
ejpam-3294	61	4	all	all	DET
ejpam-3294	61	5	y	y	PROPN
ejpam-3294	61	6	∈	∈	PROPN
ejpam-3294	61	7	x	x	PRON
ejpam-3294	61	8	,	,	PUNCT
ejpam-3294	61	9	we	we	PRON
ejpam-3294	61	10	have	have	VERB
ejpam-3294	61	11	limn→∞	limn→∞	ADP
ejpam-3294	61	12	σ(xn	σ(xn	NOUN
ejpam-3294	61	13	,	,	PUNCT
ejpam-3294	61	14	y	y	NOUN
ejpam-3294	61	15	)	)	PUNCT
ejpam-3294	61	16	=	=	SYM
ejpam-3294	62	1	σ(x	σ(x	PROPN
ejpam-3294	62	2	,	,	PUNCT
ejpam-3294	62	3	y	y	PROPN
ejpam-3294	62	4	)	)	PUNCT
ejpam-3294	62	5	.	.	PUNCT
ejpam-3294	63	1	example	example	NOUN
ejpam-3294	64	1	2	2	NUM
ejpam-3294	64	2	.	.	PUNCT
ejpam-3294	64	3	let	let	VERB
ejpam-3294	64	4	x	x	PUNCT
ejpam-3294	64	5	=	=	SYM
ejpam-3294	64	6	r	r	NOUN
ejpam-3294	64	7	and	and	CCONJ
ejpam-3294	64	8	σ	σ	NOUN
ejpam-3294	64	9	:	:	PUNCT
ejpam-3294	64	10	x	x	X
ejpam-3294	64	11	×x	×x	ADP
ejpam-3294	64	12	→	→	SYM
ejpam-3294	64	13	[	[	X
ejpam-3294	64	14	0,+∞	0,+∞	NUM
ejpam-3294	64	15	)	)	PUNCT
ejpam-3294	64	16	be	be	AUX
ejpam-3294	64	17	defined	define	VERB
ejpam-3294	64	18	by	by	ADP
ejpam-3294	64	19	σ(x	σ(x	PROPN
ejpam-3294	64	20	,	,	PUNCT
ejpam-3294	64	21	y	y	NOUN
ejpam-3294	64	22	)	)	PUNCT
ejpam-3294	64	23	=	=	PUNCT
ejpam-3294	64	24			PUNCT
ejpam-3294	64	25	2k	2k	NUM
ejpam-3294	64	26	,	,	PUNCT
ejpam-3294	64	27	if	if	SCONJ
ejpam-3294	64	28	x	x	ADP
ejpam-3294	64	29	=	=	PUNCT
ejpam-3294	64	30	y	y	PROPN
ejpam-3294	64	31	=	=	SYM
ejpam-3294	64	32	0	0	NUM
ejpam-3294	64	33	;	;	PUNCT
ejpam-3294	64	34	k	k	X
ejpam-3294	64	35	,	,	PUNCT
ejpam-3294	64	36	otherwise	otherwise	ADV
ejpam-3294	64	37	.	.	PUNCT
ejpam-3294	65	1	then	then	ADV
ejpam-3294	65	2	(	(	PUNCT
ejpam-3294	65	3	x	x	X
ejpam-3294	65	4	,	,	PUNCT
ejpam-3294	65	5	σ	σ	PROPN
ejpam-3294	65	6	)	)	PUNCT
ejpam-3294	65	7	is	be	AUX
ejpam-3294	65	8	a	a	DET
ejpam-3294	65	9	metric	metric	ADJ
ejpam-3294	65	10	-	-	PUNCT
ejpam-3294	65	11	like	like	ADJ
ejpam-3294	65	12	space	space	NOUN
ejpam-3294	65	13	,	,	PUNCT
ejpam-3294	65	14	but	but	CCONJ
ejpam-3294	65	15	for	for	ADP
ejpam-3294	65	16	k	k	PROPN
ejpam-3294	65	17	>	>	X
ejpam-3294	65	18	0	0	PROPN
ejpam-3294	65	19	,	,	PUNCT
ejpam-3294	65	20	it	it	PRON
ejpam-3294	65	21	is	be	AUX
ejpam-3294	65	22	not	not	PART
ejpam-3294	65	23	a	a	DET
ejpam-3294	65	24	partial	partial	ADJ
ejpam-3294	65	25	metric	metric	ADJ
ejpam-3294	65	26	space	space	NOUN
ejpam-3294	65	27	,	,	PUNCT
ejpam-3294	65	28	as	as	ADP
ejpam-3294	65	29	σ(0	σ(0	PROPN
ejpam-3294	65	30	,	,	PUNCT
ejpam-3294	65	31	0	0	NUM
ejpam-3294	65	32	)	)	PUNCT
ejpam-3294	65	33	6≤	6≤	NUM
ejpam-3294	66	1	σ(0	σ(0	PROPN
ejpam-3294	66	2	,	,	PUNCT
ejpam-3294	66	3	1	1	NUM
ejpam-3294	66	4	)	)	PUNCT
ejpam-3294	66	5	.	.	PUNCT
ejpam-3294	67	1	now	now	ADV
ejpam-3294	67	2	let	let	VERB
ejpam-3294	67	3	f	f	PRON
ejpam-3294	67	4	be	be	AUX
ejpam-3294	67	5	the	the	DET
ejpam-3294	67	6	family	family	NOUN
ejpam-3294	67	7	of	of	ADP
ejpam-3294	67	8	all	all	DET
ejpam-3294	67	9	functions	function	NOUN
ejpam-3294	67	10	β	β	NOUN
ejpam-3294	67	11	:	:	PUNCT
ejpam-3294	68	1	[	[	X
ejpam-3294	68	2	0,∞)→	0,∞)→	NOUN
ejpam-3294	68	3	[	[	X
ejpam-3294	68	4	0	0	NUM
ejpam-3294	68	5	,	,	PUNCT
ejpam-3294	68	6	1	1	NUM
ejpam-3294	68	7	)	)	PUNCT
ejpam-3294	68	8	which	which	PRON
ejpam-3294	68	9	satisfy	satisfy	VERB
ejpam-3294	68	10	the	the	DET
ejpam-3294	68	11	condition	condition	NOUN
ejpam-3294	68	12	limn→∞	limn→∞	ADJ
ejpam-3294	68	13	β(tn	β(tn	NOUN
ejpam-3294	68	14	)	)	PUNCT
ejpam-3294	68	15	=	=	SYM
ejpam-3294	68	16	1	1	NUM
ejpam-3294	68	17	implies	imply	VERB
ejpam-3294	68	18	limn→∞	limn→∞	PROPN
ejpam-3294	68	19	tn	tn	NOUN
ejpam-3294	68	20	=	=	SYM
ejpam-3294	68	21	0	0	NUM
ejpam-3294	68	22	.	.	PUNCT
ejpam-3294	69	1	in	in	ADP
ejpam-3294	69	2	2015	2015	NUM
ejpam-3294	69	3	,	,	PUNCT
ejpam-3294	69	4	karapinar	karapinar	VERB
ejpam-3294	69	5	et	et	NOUN
ejpam-3294	69	6	al.[18	al.[18	PROPN
ejpam-3294	69	7	]	]	PUNCT
ejpam-3294	69	8	proved	prove	VERB
ejpam-3294	69	9	the	the	DET
ejpam-3294	69	10	following	follow	VERB
ejpam-3294	69	11	particular	particular	ADJ
ejpam-3294	69	12	result(it	result(it	PROPN
ejpam-3294	69	13	corresponds	correspond	VERB
ejpam-3294	69	14	to	to	ADP
ejpam-3294	69	15	s	s	NOUN
ejpam-3294	69	16	=	=	SYM
ejpam-3294	69	17	1	1	NUM
ejpam-3294	69	18	and	and	CCONJ
ejpam-3294	69	19	ψ(t	ψ(t	PROPN
ejpam-3294	69	20	)	)	PUNCT
ejpam-3294	69	21	=	=	SYM
ejpam-3294	69	22	t	t	PROPN
ejpam-3294	69	23	)	)	PUNCT
ejpam-3294	69	24	.	.	PUNCT
ejpam-3294	70	1	theorem	theorem	NOUN
ejpam-3294	70	2	1	1	NUM
ejpam-3294	70	3	.	.	PUNCT
ejpam-3294	71	1	[	[	X
ejpam-3294	71	2	18	18	NUM
ejpam-3294	71	3	]	]	X
ejpam-3294	71	4	let	let	AUX
ejpam-3294	71	5	(	(	PUNCT
ejpam-3294	71	6	x	x	NOUN
ejpam-3294	71	7	,	,	PUNCT
ejpam-3294	71	8	σ	σ	PROPN
ejpam-3294	71	9	)	)	PUNCT
ejpam-3294	71	10	be	be	AUX
ejpam-3294	71	11	a	a	DET
ejpam-3294	71	12	complete	complete	ADJ
ejpam-3294	71	13	metric	metric	ADJ
ejpam-3294	71	14	-	-	PUNCT
ejpam-3294	71	15	like	like	ADJ
ejpam-3294	71	16	space	space	NOUN
ejpam-3294	71	17	and	and	CCONJ
ejpam-3294	71	18	f	f	NOUN
ejpam-3294	71	19	:	:	PUNCT
ejpam-3294	71	20	x	x	X
ejpam-3294	71	21	→	→	PUNCT
ejpam-3294	71	22	x	x	PUNCT
ejpam-3294	71	23	be	be	AUX
ejpam-3294	71	24	a	a	DET
ejpam-3294	71	25	mapping	mapping	NOUN
ejpam-3294	71	26	.	.	PUNCT
ejpam-3294	72	1	suppose	suppose	VERB
ejpam-3294	72	2	that	that	SCONJ
ejpam-3294	72	3	there	there	PRON
ejpam-3294	72	4	exists	exist	VERB
ejpam-3294	72	5	β	β	X
ejpam-3294	72	6	∈	∈	PROPN
ejpam-3294	72	7	f	f	PROPN
ejpam-3294	73	1	such	such	ADJ
ejpam-3294	73	2	that	that	SCONJ
ejpam-3294	73	3	σ(fx	σ(fx	PROPN
ejpam-3294	73	4	,	,	PUNCT
ejpam-3294	73	5	fy	fy	PROPN
ejpam-3294	73	6	)	)	PUNCT
ejpam-3294	73	7	≤	≤	NOUN
ejpam-3294	73	8	β(σ(x	β(σ(x	PROPN
ejpam-3294	73	9	,	,	PUNCT
ejpam-3294	73	10	y))σ(x	y))σ(x	PROPN
ejpam-3294	73	11	,	,	PUNCT
ejpam-3294	73	12	y	y	PROPN
ejpam-3294	73	13	)	)	PUNCT
ejpam-3294	73	14	,	,	PUNCT
ejpam-3294	73	15	(	(	PUNCT
ejpam-3294	73	16	1	1	X
ejpam-3294	73	17	)	)	PUNCT
ejpam-3294	73	18	for	for	ADP
ejpam-3294	73	19	all	all	DET
ejpam-3294	73	20	x	x	NOUN
ejpam-3294	73	21	,	,	PUNCT
ejpam-3294	73	22	y	y	PROPN
ejpam-3294	73	23	∈	∈	PROPN
ejpam-3294	73	24	x.	x.	NOUN
ejpam-3294	73	25	then	then	ADV
ejpam-3294	73	26	f	f	PROPN
ejpam-3294	73	27	has	have	VERB
ejpam-3294	73	28	a	a	DET
ejpam-3294	73	29	unique	unique	ADJ
ejpam-3294	73	30	fixed	fix	VERB
ejpam-3294	73	31	point	point	NOUN
ejpam-3294	73	32	.	.	PUNCT
ejpam-3294	74	1	h.	h.	PROPN
ejpam-3294	74	2	qawaqneh	qawaqneh	PROPN
ejpam-3294	74	3	,	,	PUNCT
ejpam-3294	74	4	m.s	m.s	PROPN
ejpam-3294	74	5	.	.	PROPN
ejpam-3294	74	6	noorani	noorani	PROPN
ejpam-3294	74	7	,	,	PUNCT
ejpam-3294	74	8	w.	w.	PROPN
ejpam-3294	74	9	shatanawi	shatanawi	PROPN
ejpam-3294	74	10	/	/	SYM
ejpam-3294	74	11	eur	eur	PROPN
ejpam-3294	74	12	.	.	PUNCT
ejpam-3294	75	1	j.	j.	PROPN
ejpam-3294	75	2	pure	pure	PROPN
ejpam-3294	75	3	appl	appl	PROPN
ejpam-3294	75	4	.	.	PROPN
ejpam-3294	75	5	math	math	PROPN
ejpam-3294	75	6	,	,	PUNCT
ejpam-3294	75	7	11	11	NUM
ejpam-3294	75	8	(	(	PUNCT
ejpam-3294	75	9	3	3	NUM
ejpam-3294	75	10	)	)	PUNCT
ejpam-3294	75	11	(	(	PUNCT
ejpam-3294	75	12	2018	2018	NUM
ejpam-3294	75	13	)	)	PUNCT
ejpam-3294	75	14	,	,	PUNCT
ejpam-3294	75	15	702	702	NUM
ejpam-3294	75	16	-	-	SYM
ejpam-3294	75	17	716	716	NUM
ejpam-3294	75	18	705	705	NUM
ejpam-3294	75	19	in	in	ADP
ejpam-3294	75	20	2012	2012	NUM
ejpam-3294	75	21	,	,	PUNCT
ejpam-3294	75	22	samet	samet	PROPN
ejpam-3294	75	23	et	et	PROPN
ejpam-3294	75	24	al	al	PROPN
ejpam-3294	75	25	.	.	PUNCT
ejpam-3294	76	1	[	[	X
ejpam-3294	76	2	26	26	NUM
ejpam-3294	76	3	]	]	PUNCT
ejpam-3294	76	4	introduced	introduce	VERB
ejpam-3294	76	5	the	the	DET
ejpam-3294	76	6	concept	concept	NOUN
ejpam-3294	76	7	of	of	ADP
ejpam-3294	76	8	α	α	NOUN
ejpam-3294	76	9	-	-	PUNCT
ejpam-3294	76	10	admissible	admissible	ADJ
ejpam-3294	76	11	mappings	mapping	NOUN
ejpam-3294	76	12	as	as	ADP
ejpam-3294	76	13	the	the	DET
ejpam-3294	76	14	following	following	NOUN
ejpam-3294	76	15	.	.	PUNCT
ejpam-3294	77	1	definition	definition	NOUN
ejpam-3294	77	2	3	3	NUM
ejpam-3294	77	3	.	.	PUNCT
ejpam-3294	78	1	[	[	X
ejpam-3294	78	2	26	26	NUM
ejpam-3294	78	3	]	]	PUNCT
ejpam-3294	78	4	let	let	VERB
ejpam-3294	78	5	f	f	PRON
ejpam-3294	78	6	:	:	PUNCT
ejpam-3294	78	7	x	x	X
ejpam-3294	78	8	→	→	SYM
ejpam-3294	78	9	x	x	X
ejpam-3294	78	10	and	and	CCONJ
ejpam-3294	78	11	α	α	NOUN
ejpam-3294	78	12	:	:	PUNCT
ejpam-3294	79	1	x×x	x×x	PROPN
ejpam-3294	79	2	→	→	PUNCT
ejpam-3294	79	3	[	[	X
ejpam-3294	79	4	0,∞	0,∞	NOUN
ejpam-3294	79	5	)	)	PUNCT
ejpam-3294	79	6	.	.	PUNCT
ejpam-3294	80	1	then	then	ADV
ejpam-3294	80	2	f	f	PROPN
ejpam-3294	80	3	is	be	AUX
ejpam-3294	80	4	called	call	VERB
ejpam-3294	80	5	α	α	PRON
ejpam-3294	80	6	-	-	ADJ
ejpam-3294	80	7	admissible	admissible	ADJ
ejpam-3294	80	8	if	if	SCONJ
ejpam-3294	80	9	for	for	ADP
ejpam-3294	80	10	all	all	DET
ejpam-3294	80	11	x	x	NOUN
ejpam-3294	80	12	,	,	PUNCT
ejpam-3294	80	13	y	y	PROPN
ejpam-3294	80	14	∈	∈	PROPN
ejpam-3294	80	15	x	x	PUNCT
ejpam-3294	80	16	with	with	ADP
ejpam-3294	80	17	α(x	α(x	PROPN
ejpam-3294	80	18	,	,	PUNCT
ejpam-3294	80	19	y	y	PROPN
ejpam-3294	80	20	)	)	PUNCT
ejpam-3294	80	21	≥	≥	NOUN
ejpam-3294	80	22	1	1	NUM
ejpam-3294	80	23	implies	imply	VERB
ejpam-3294	80	24	α(fx	α(fx	PROPN
ejpam-3294	80	25	,	,	PUNCT
ejpam-3294	80	26	fy	fy	PROPN
ejpam-3294	80	27	)	)	PUNCT
ejpam-3294	80	28	≥	≥	NOUN
ejpam-3294	81	1	1	1	NUM
ejpam-3294	81	2	.	.	PUNCT
ejpam-3294	81	3	sintunavarat	sintunavarat	NOUN
ejpam-3294	82	1	[	[	X
ejpam-3294	82	2	30	30	NUM
ejpam-3294	82	3	]	]	PUNCT
ejpam-3294	82	4	presented	present	VERB
ejpam-3294	82	5	the	the	DET
ejpam-3294	82	6	notion	notion	NOUN
ejpam-3294	82	7	of	of	ADP
ejpam-3294	82	8	weak	weak	ADJ
ejpam-3294	82	9	α	α	ADJ
ejpam-3294	82	10	-	-	ADJ
ejpam-3294	82	11	admissible	admissible	ADJ
ejpam-3294	82	12	mappings	mapping	NOUN
ejpam-3294	82	13	as	as	SCONJ
ejpam-3294	82	14	follows	follow	VERB
ejpam-3294	82	15	:	:	PUNCT
ejpam-3294	82	16	definition	definition	NOUN
ejpam-3294	82	17	4	4	NUM
ejpam-3294	82	18	.	.	PUNCT
ejpam-3294	83	1	[	[	X
ejpam-3294	83	2	30	30	NUM
ejpam-3294	83	3	]	]	PUNCT
ejpam-3294	83	4	let	let	VERB
ejpam-3294	83	5	x	x	PRON
ejpam-3294	83	6	be	be	AUX
ejpam-3294	83	7	a	a	DET
ejpam-3294	83	8	nonempty	nonempty	ADV
ejpam-3294	83	9	set	set	VERB
ejpam-3294	83	10	and	and	CCONJ
ejpam-3294	83	11	let	let	VERB
ejpam-3294	83	12	α	α	PRON
ejpam-3294	83	13	:	:	PUNCT
ejpam-3294	83	14	x	x	SYM
ejpam-3294	83	15	×	×	NOUN
ejpam-3294	83	16	x	x	INTJ
ejpam-3294	83	17	→	→	X
ejpam-3294	83	18	[	[	X
ejpam-3294	83	19	0,∞	0,∞	NOUN
ejpam-3294	83	20	)	)	PUNCT
ejpam-3294	83	21	be	be	VERB
ejpam-3294	83	22	a	a	DET
ejpam-3294	83	23	given	give	VERB
ejpam-3294	83	24	mapping	mapping	NOUN
ejpam-3294	83	25	.	.	PUNCT
ejpam-3294	84	1	a	a	DET
ejpam-3294	84	2	mapping	mapping	NOUN
ejpam-3294	84	3	f	f	NOUN
ejpam-3294	84	4	:	:	PUNCT
ejpam-3294	84	5	x	x	X
ejpam-3294	84	6	→	→	PUNCT
ejpam-3294	84	7	x	x	X
ejpam-3294	84	8	is	be	AUX
ejpam-3294	84	9	said	say	VERB
ejpam-3294	84	10	to	to	PART
ejpam-3294	84	11	be	be	AUX
ejpam-3294	84	12	a	a	DET
ejpam-3294	84	13	weak	weak	ADJ
ejpam-3294	84	14	α	α	PRON
ejpam-3294	84	15	-	-	ADJ
ejpam-3294	84	16	admissible	admissible	ADJ
ejpam-3294	84	17	mappings	mapping	NOUN
ejpam-3294	84	18	if	if	SCONJ
ejpam-3294	84	19	the	the	DET
ejpam-3294	84	20	following	follow	VERB
ejpam-3294	84	21	condition	condition	NOUN
ejpam-3294	84	22	holds	hold	VERB
ejpam-3294	84	23	:	:	PUNCT
ejpam-3294	84	24	x	x	SYM
ejpam-3294	84	25	∈	∈	PROPN
ejpam-3294	84	26	x	x	PUNCT
ejpam-3294	84	27	with	with	ADP
ejpam-3294	84	28	α(x	α(x	PROPN
ejpam-3294	84	29	,	,	PUNCT
ejpam-3294	84	30	fx	fx	PROPN
ejpam-3294	84	31	)	)	PUNCT
ejpam-3294	84	32	≥	≥	NOUN
ejpam-3294	84	33	1⇒	1⇒	PROPN
ejpam-3294	84	34	α(fx	α(fx	PROPN
ejpam-3294	84	35	,	,	PUNCT
ejpam-3294	84	36	f2x	f2x	X
ejpam-3294	84	37	)	)	PUNCT
ejpam-3294	84	38	≥	≥	NOUN
ejpam-3294	84	39	1	1	NUM
ejpam-3294	84	40	.	.	PUNCT
ejpam-3294	84	41	remark	remark	NOUN
ejpam-3294	84	42	2	2	NUM
ejpam-3294	84	43	.	.	PUNCT
ejpam-3294	85	1	[	[	X
ejpam-3294	85	2	30	30	NUM
ejpam-3294	85	3	]	]	X
ejpam-3294	85	4	it	it	PRON
ejpam-3294	85	5	is	be	AUX
ejpam-3294	85	6	customary	customary	ADJ
ejpam-3294	85	7	to	to	PART
ejpam-3294	85	8	write	write	VERB
ejpam-3294	85	9	a(x	a(x	NOUN
ejpam-3294	85	10	,	,	PUNCT
ejpam-3294	85	11	α	α	NOUN
ejpam-3294	85	12	)	)	PUNCT
ejpam-3294	85	13	and	and	CCONJ
ejpam-3294	85	14	wa(x	wa(x	NOUN
ejpam-3294	85	15	,	,	PUNCT
ejpam-3294	85	16	α	α	NOUN
ejpam-3294	85	17	)	)	PUNCT
ejpam-3294	85	18	to	to	PART
ejpam-3294	85	19	denote	denote	VERB
ejpam-3294	85	20	the	the	DET
ejpam-3294	85	21	collection	collection	NOUN
ejpam-3294	85	22	of	of	ADP
ejpam-3294	85	23	all	all	DET
ejpam-3294	85	24	α	α	PRON
ejpam-3294	85	25	-	-	ADJ
ejpam-3294	85	26	admissible	admissible	ADJ
ejpam-3294	85	27	mappings	mapping	NOUN
ejpam-3294	85	28	on	on	ADP
ejpam-3294	85	29	x	x	PUNCT
ejpam-3294	85	30	and	and	CCONJ
ejpam-3294	85	31	the	the	DET
ejpam-3294	85	32	collection	collection	NOUN
ejpam-3294	85	33	of	of	ADP
ejpam-3294	85	34	all	all	DET
ejpam-3294	85	35	weak	weak	ADJ
ejpam-3294	85	36	α	α	PRON
ejpam-3294	85	37	-	-	ADJ
ejpam-3294	85	38	admissible	admissible	ADJ
ejpam-3294	85	39	mappings	mapping	NOUN
ejpam-3294	85	40	on	on	ADP
ejpam-3294	85	41	x.	x.	NOUN
ejpam-3294	85	42	one	one	PRON
ejpam-3294	85	43	can	can	AUX
ejpam-3294	85	44	verify	verify	VERB
ejpam-3294	85	45	that	that	SCONJ
ejpam-3294	85	46	a(x	a(x	NOUN
ejpam-3294	85	47	,	,	PUNCT
ejpam-3294	85	48	α	α	NOUN
ejpam-3294	85	49	)	)	PUNCT
ejpam-3294	85	50	⊆	⊆	NUM
ejpam-3294	85	51	wa(x	wa(x	NOUN
ejpam-3294	85	52	,	,	PUNCT
ejpam-3294	85	53	α	α	NOUN
ejpam-3294	85	54	)	)	PUNCT
ejpam-3294	85	55	.	.	PUNCT
ejpam-3294	86	1	on	on	ADP
ejpam-3294	86	2	the	the	DET
ejpam-3294	86	3	other	other	ADJ
ejpam-3294	86	4	hand	hand	NOUN
ejpam-3294	86	5	,	,	PUNCT
ejpam-3294	86	6	the	the	DET
ejpam-3294	86	7	concept	concept	NOUN
ejpam-3294	86	8	of	of	ADP
ejpam-3294	86	9	f	f	PROPN
ejpam-3294	86	10	-contraction	-contraction	PROPN
ejpam-3294	86	11	was	be	AUX
ejpam-3294	86	12	introduced	introduce	VERB
ejpam-3294	86	13	by	by	ADP
ejpam-3294	86	14	wardowski	wardowski	NOUN
ejpam-3294	86	15	in	in	ADP
ejpam-3294	86	16	[	[	X
ejpam-3294	86	17	31	31	NUM
ejpam-3294	86	18	]	]	PUNCT
ejpam-3294	86	19	.	.	PUNCT
ejpam-3294	87	1	definition	definition	NOUN
ejpam-3294	87	2	5	5	NUM
ejpam-3294	87	3	.	.	PUNCT
ejpam-3294	88	1	[	[	X
ejpam-3294	88	2	31	31	NUM
ejpam-3294	88	3	]	]	PUNCT
ejpam-3294	88	4	let	let	VERB
ejpam-3294	88	5	f	f	PRON
ejpam-3294	88	6	:	:	PUNCT
ejpam-3294	88	7	r+	r+	X
ejpam-3294	88	8	→	→	PUNCT
ejpam-3294	88	9	r	r	NOUN
ejpam-3294	88	10	be	be	AUX
ejpam-3294	88	11	a	a	DET
ejpam-3294	88	12	mapping	mapping	NOUN
ejpam-3294	88	13	satisfying	satisfy	VERB
ejpam-3294	88	14	the	the	DET
ejpam-3294	88	15	following	following	NOUN
ejpam-3294	88	16	:	:	PUNCT
ejpam-3294	88	17	(	(	PUNCT
ejpam-3294	88	18	f1	f1	NOUN
ejpam-3294	88	19	)	)	PUNCT
ejpam-3294	88	20	f	f	PROPN
ejpam-3294	88	21	be	be	AUX
ejpam-3294	88	22	a	a	DET
ejpam-3294	88	23	strictly	strictly	ADV
ejpam-3294	88	24	increasing	increase	VERB
ejpam-3294	88	25	,	,	PUNCT
ejpam-3294	88	26	that	that	ADV
ejpam-3294	88	27	is	is	ADV
ejpam-3294	88	28	,	,	PUNCT
ejpam-3294	88	29	for	for	ADP
ejpam-3294	88	30	α	α	NOUN
ejpam-3294	88	31	,	,	PUNCT
ejpam-3294	88	32	β	β	X
ejpam-3294	88	33	∈	∈	PROPN
ejpam-3294	88	34	r+	r+	NOUN
ejpam-3294	88	35	such	such	ADJ
ejpam-3294	88	36	that	that	SCONJ
ejpam-3294	88	37	α	α	PRON
ejpam-3294	88	38	<	<	X
ejpam-3294	88	39	β	β	PROPN
ejpam-3294	88	40	implies	imply	VERB
ejpam-3294	88	41	f	f	PROPN
ejpam-3294	88	42	(	(	PUNCT
ejpam-3294	88	43	α	α	NOUN
ejpam-3294	88	44	)	)	PUNCT
ejpam-3294	88	45	<	<	X
ejpam-3294	88	46	f	f	X
ejpam-3294	88	47	(	(	PUNCT
ejpam-3294	88	48	β	β	NOUN
ejpam-3294	88	49	)	)	PUNCT
ejpam-3294	88	50	,	,	PUNCT
ejpam-3294	88	51	(	(	PUNCT
ejpam-3294	88	52	f2	f2	PROPN
ejpam-3294	88	53	)	)	PUNCT
ejpam-3294	88	54	for	for	ADP
ejpam-3294	88	55	each	each	DET
ejpam-3294	88	56	sequence	sequence	NOUN
ejpam-3294	88	57	{	{	PUNCT
ejpam-3294	88	58	αn	αn	NOUN
ejpam-3294	88	59	}	}	PUNCT
ejpam-3294	88	60	of	of	ADP
ejpam-3294	88	61	positive	positive	ADJ
ejpam-3294	88	62	numbers	number	NOUN
ejpam-3294	88	63	,	,	PUNCT
ejpam-3294	88	64	limn→∞	limn→∞	X
ejpam-3294	88	65	αn	αn	NOUN
ejpam-3294	89	1	=	=	SYM
ejpam-3294	89	2	0	0	PUNCT
ejpam-3294	90	1	if	if	SCONJ
ejpam-3294	90	2	and	and	CCONJ
ejpam-3294	90	3	only	only	ADV
ejpam-3294	90	4	if	if	SCONJ
ejpam-3294	90	5	limn→∞	limn→∞	PROPN
ejpam-3294	90	6	f	f	X
ejpam-3294	90	7	(	(	PUNCT
ejpam-3294	90	8	αn	αn	NOUN
ejpam-3294	90	9	)	)	PUNCT
ejpam-3294	90	10	=	=	SYM
ejpam-3294	90	11	−∞	−∞	PROPN
ejpam-3294	90	12	,	,	PUNCT
ejpam-3294	90	13	(	(	PUNCT
ejpam-3294	90	14	f3	f3	ADJ
ejpam-3294	90	15	)	)	PUNCT
ejpam-3294	90	16	there	there	PRON
ejpam-3294	90	17	exists	exist	VERB
ejpam-3294	90	18	k	k	PROPN
ejpam-3294	90	19	∈	∈	PROPN
ejpam-3294	90	20	(	(	PUNCT
ejpam-3294	90	21	0	0	NUM
ejpam-3294	90	22	,	,	PUNCT
ejpam-3294	90	23	1	1	NUM
ejpam-3294	90	24	)	)	PUNCT
ejpam-3294	90	25	such	such	ADJ
ejpam-3294	90	26	that	that	DET
ejpam-3294	90	27	limα→0	limα→0	NOUN
ejpam-3294	90	28	+	+	CCONJ
ejpam-3294	90	29	α	α	PROPN
ejpam-3294	90	30	kf	kf	PROPN
ejpam-3294	90	31	(	(	PUNCT
ejpam-3294	90	32	α	α	NOUN
ejpam-3294	90	33	)	)	PUNCT
ejpam-3294	90	34	=	=	SYM
ejpam-3294	91	1	0	0	X
ejpam-3294	91	2	.	.	PUNCT
ejpam-3294	92	1	recently	recently	ADV
ejpam-3294	92	2	,	,	PUNCT
ejpam-3294	92	3	piri	piri	NOUN
ejpam-3294	92	4	and	and	CCONJ
ejpam-3294	92	5	kumam	kumam	NOUN
ejpam-3294	93	1	[	[	X
ejpam-3294	93	2	21	21	NUM
ejpam-3294	93	3	]	]	PUNCT
ejpam-3294	93	4	investigated	investigate	VERB
ejpam-3294	93	5	some	some	DET
ejpam-3294	93	6	fixed	fix	VERB
ejpam-3294	93	7	point	point	NOUN
ejpam-3294	93	8	theorems	theorem	NOUN
ejpam-3294	93	9	concerning	concern	VERB
ejpam-3294	93	10	f	f	PROPN
ejpam-3294	93	11	contraction	contraction	NOUN
ejpam-3294	93	12	in	in	ADP
ejpam-3294	93	13	complete	complete	ADJ
ejpam-3294	93	14	metric	metric	ADJ
ejpam-3294	93	15	spaces	space	NOUN
ejpam-3294	93	16	by	by	ADP
ejpam-3294	93	17	replacing	replace	VERB
ejpam-3294	93	18	the	the	DET
ejpam-3294	93	19	condition	condition	NOUN
ejpam-3294	93	20	(	(	PUNCT
ejpam-3294	93	21	f3	f3	ADJ
ejpam-3294	93	22	)	)	PUNCT
ejpam-3294	93	23	with	with	ADP
ejpam-3294	93	24	the	the	DET
ejpam-3294	93	25	condition	condition	NOUN
ejpam-3294	93	26	:	:	PUNCT
ejpam-3294	93	27	(	(	PUNCT
ejpam-3294	93	28	f3̀	f3̀	NOUN
ejpam-3294	93	29	)	)	PUNCT
ejpam-3294	93	30	f	f	PROPN
ejpam-3294	93	31	is	be	AUX
ejpam-3294	93	32	continuous	continuous	ADJ
ejpam-3294	93	33	on	on	ADP
ejpam-3294	93	34	(	(	PUNCT
ejpam-3294	93	35	0,∞	0,∞	NUM
ejpam-3294	93	36	)	)	PUNCT
ejpam-3294	93	37	.	.	PUNCT
ejpam-3294	94	1	definition	definition	NOUN
ejpam-3294	94	2	6	6	NUM
ejpam-3294	94	3	.	.	PUNCT
ejpam-3294	95	1	[	[	X
ejpam-3294	95	2	31	31	NUM
ejpam-3294	95	3	]	]	X
ejpam-3294	95	4	let	let	AUX
ejpam-3294	95	5	(	(	PUNCT
ejpam-3294	95	6	x	x	NOUN
ejpam-3294	95	7	,	,	PUNCT
ejpam-3294	95	8	d	d	NOUN
ejpam-3294	95	9	)	)	PUNCT
ejpam-3294	95	10	be	be	AUX
ejpam-3294	95	11	a	a	DET
ejpam-3294	95	12	metric	metric	ADJ
ejpam-3294	95	13	space	space	NOUN
ejpam-3294	95	14	.	.	PUNCT
ejpam-3294	96	1	a	a	DET
ejpam-3294	96	2	mapping	mapping	NOUN
ejpam-3294	96	3	t	t	NOUN
ejpam-3294	96	4	:	:	PUNCT
ejpam-3294	96	5	x	x	X
ejpam-3294	96	6	→	→	PUNCT
ejpam-3294	96	7	x	x	X
ejpam-3294	96	8	is	be	AUX
ejpam-3294	96	9	said	say	VERB
ejpam-3294	96	10	to	to	PART
ejpam-3294	96	11	be	be	AUX
ejpam-3294	96	12	an	an	DET
ejpam-3294	96	13	f	f	PROPN
ejpam-3294	96	14	-contraction	-contraction	NOUN
ejpam-3294	96	15	if	if	SCONJ
ejpam-3294	96	16	there	there	PRON
ejpam-3294	96	17	exist	exist	VERB
ejpam-3294	96	18	f	f	PROPN
ejpam-3294	96	19	∈	∈	PROPN
ejpam-3294	96	20	f	f	PROPN
ejpam-3294	96	21	and	and	CCONJ
ejpam-3294	96	22	τ	τ	PROPN
ejpam-3294	96	23	>	>	X
ejpam-3294	96	24	0	0	NUM
ejpam-3294	97	1	such	such	ADJ
ejpam-3294	97	2	that	that	SCONJ
ejpam-3294	97	3	d(tx	d(tx	PROPN
ejpam-3294	97	4	,	,	PUNCT
ejpam-3294	97	5	ty	ty	NOUN
ejpam-3294	97	6	)	)	PUNCT
ejpam-3294	97	7	>	>	X
ejpam-3294	97	8	0⇒	0⇒	PROPN
ejpam-3294	97	9	(	(	PUNCT
ejpam-3294	97	10	τ	τ	X
ejpam-3294	97	11	+	+	NUM
ejpam-3294	97	12	f	f	X
ejpam-3294	97	13	(	(	PUNCT
ejpam-3294	97	14	d(tx	d(tx	PROPN
ejpam-3294	97	15	,	,	PUNCT
ejpam-3294	97	16	ty	ty	NOUN
ejpam-3294	97	17	)	)	PUNCT
ejpam-3294	97	18	)	)	PUNCT
ejpam-3294	98	1	≤	≤	NUM
ejpam-3294	98	2	f	f	X
ejpam-3294	98	3	(	(	PUNCT
ejpam-3294	98	4	d(x	d(x	PROPN
ejpam-3294	98	5	,	,	PUNCT
ejpam-3294	98	6	y	y	NOUN
ejpam-3294	98	7	)	)	PUNCT
ejpam-3294	98	8	)	)	PUNCT
ejpam-3294	98	9	,	,	PUNCT
ejpam-3294	98	10	for	for	ADP
ejpam-3294	98	11	all	all	DET
ejpam-3294	98	12	x	x	NOUN
ejpam-3294	98	13	,	,	PUNCT
ejpam-3294	98	14	y	y	PROPN
ejpam-3294	98	15	∈	∈	PROPN
ejpam-3294	98	16	x.	x.	NOUN
ejpam-3294	98	17	2	2	X
ejpam-3294	98	18	.	.	X
ejpam-3294	98	19	main	main	ADJ
ejpam-3294	98	20	result	result	NOUN
ejpam-3294	98	21	in	in	ADP
ejpam-3294	98	22	this	this	DET
ejpam-3294	98	23	section	section	NOUN
ejpam-3294	98	24	,	,	PUNCT
ejpam-3294	98	25	we	we	PRON
ejpam-3294	98	26	shall	shall	AUX
ejpam-3294	98	27	state	state	NOUN
ejpam-3294	98	28	and	and	CCONJ
ejpam-3294	98	29	prove	prove	VERB
ejpam-3294	98	30	our	our	PRON
ejpam-3294	98	31	main	main	ADJ
ejpam-3294	98	32	results	result	NOUN
ejpam-3294	98	33	.	.	PUNCT
ejpam-3294	99	1	we	we	PRON
ejpam-3294	99	2	firstly	firstly	ADV
ejpam-3294	99	3	recall	recall	VERB
ejpam-3294	99	4	the	the	DET
ejpam-3294	99	5	following	follow	VERB
ejpam-3294	99	6	classes	class	NOUN
ejpam-3294	99	7	of	of	ADP
ejpam-3294	99	8	functions	function	NOUN
ejpam-3294	99	9	.	.	PUNCT
ejpam-3294	100	1	let	let	VERB
ejpam-3294	100	2	f	f	NOUN
ejpam-3294	100	3	:	:	PUNCT
ejpam-3294	100	4	r+	r+	X
ejpam-3294	100	5	→	→	PUNCT
ejpam-3294	100	6	r	r	NOUN
ejpam-3294	100	7	is	be	AUX
ejpam-3294	100	8	strictly	strictly	ADV
ejpam-3294	100	9	increasing	increase	VERB
ejpam-3294	100	10	contraction	contraction	NOUN
ejpam-3294	100	11	function	function	NOUN
ejpam-3294	100	12	.	.	PUNCT
ejpam-3294	101	1	let	let	VERB
ejpam-3294	101	2	f	f	PRON
ejpam-3294	101	3	be	be	AUX
ejpam-3294	101	4	the	the	DET
ejpam-3294	101	5	family	family	NOUN
ejpam-3294	101	6	of	of	ADP
ejpam-3294	101	7	all	all	DET
ejpam-3294	101	8	functions	function	NOUN
ejpam-3294	101	9	β	β	NOUN
ejpam-3294	101	10	:	:	PUNCT
ejpam-3294	102	1	[	[	X
ejpam-3294	102	2	0,∞)→	0,∞)→	NOUN
ejpam-3294	102	3	[	[	X
ejpam-3294	102	4	0	0	NUM
ejpam-3294	102	5	,	,	PUNCT
ejpam-3294	102	6	1	1	NUM
ejpam-3294	102	7	)	)	PUNCT
ejpam-3294	102	8	which	which	PRON
ejpam-3294	102	9	satisfy	satisfy	VERB
ejpam-3294	102	10	the	the	DET
ejpam-3294	102	11	condition	condition	NOUN
ejpam-3294	102	12	limn→∞	limn→∞	ADJ
ejpam-3294	102	13	β(tn	β(tn	NOUN
ejpam-3294	102	14	)	)	PUNCT
ejpam-3294	102	15	=	=	SYM
ejpam-3294	102	16	1	1	NUM
ejpam-3294	102	17	implies	imply	VERB
ejpam-3294	102	18	limn→∞	limn→∞	PROPN
ejpam-3294	102	19	tn	tn	NOUN
ejpam-3294	102	20	=	=	SYM
ejpam-3294	102	21	0	0	PROPN
ejpam-3294	102	22	.	.	PUNCT
ejpam-3294	103	1	h.	h.	PROPN
ejpam-3294	103	2	qawaqneh	qawaqneh	PROPN
ejpam-3294	103	3	,	,	PUNCT
ejpam-3294	103	4	m.s	m.s	PROPN
ejpam-3294	103	5	.	.	PROPN
ejpam-3294	103	6	noorani	noorani	PROPN
ejpam-3294	103	7	,	,	PUNCT
ejpam-3294	103	8	w.	w.	PROPN
ejpam-3294	103	9	shatanawi	shatanawi	PROPN
ejpam-3294	103	10	/	/	SYM
ejpam-3294	103	11	eur	eur	PROPN
ejpam-3294	103	12	.	.	PUNCT
ejpam-3294	104	1	j.	j.	PROPN
ejpam-3294	104	2	pure	pure	PROPN
ejpam-3294	104	3	appl	appl	PROPN
ejpam-3294	104	4	.	.	PROPN
ejpam-3294	104	5	math	math	PROPN
ejpam-3294	104	6	,	,	PUNCT
ejpam-3294	104	7	11	11	NUM
ejpam-3294	104	8	(	(	PUNCT
ejpam-3294	104	9	3	3	NUM
ejpam-3294	104	10	)	)	PUNCT
ejpam-3294	104	11	(	(	PUNCT
ejpam-3294	104	12	2018	2018	NUM
ejpam-3294	104	13	)	)	PUNCT
ejpam-3294	104	14	,	,	PUNCT
ejpam-3294	104	15	702	702	NUM
ejpam-3294	104	16	-	-	SYM
ejpam-3294	104	17	716	716	NUM
ejpam-3294	104	18	706	706	NUM
ejpam-3294	104	19	definition	definition	NOUN
ejpam-3294	104	20	7	7	NUM
ejpam-3294	104	21	.	.	PUNCT
ejpam-3294	105	1	let	let	VERB
ejpam-3294	105	2	(	(	PUNCT
ejpam-3294	105	3	x	x	NOUN
ejpam-3294	105	4	,	,	PUNCT
ejpam-3294	105	5	σ	σ	PROPN
ejpam-3294	105	6	)	)	PUNCT
ejpam-3294	105	7	be	be	AUX
ejpam-3294	105	8	a	a	DET
ejpam-3294	105	9	metric	metric	ADJ
ejpam-3294	105	10	-	-	PUNCT
ejpam-3294	105	11	like	like	ADJ
ejpam-3294	105	12	space	space	NOUN
ejpam-3294	105	13	and	and	CCONJ
ejpam-3294	105	14	α	α	NOUN
ejpam-3294	105	15	:	:	PUNCT
ejpam-3294	105	16	x	x	SYM
ejpam-3294	105	17	×	×	NOUN
ejpam-3294	105	18	x	x	INTJ
ejpam-3294	105	19	→	→	X
ejpam-3294	105	20	[	[	X
ejpam-3294	105	21	0,∞	0,∞	NOUN
ejpam-3294	105	22	)	)	PUNCT
ejpam-3294	105	23	.	.	PUNCT
ejpam-3294	106	1	a	a	DET
ejpam-3294	106	2	mapping	mapping	NOUN
ejpam-3294	106	3	f	f	NOUN
ejpam-3294	106	4	:	:	PUNCT
ejpam-3294	106	5	x	x	X
ejpam-3294	106	6	→	→	PUNCT
ejpam-3294	106	7	x	x	X
ejpam-3294	106	8	is	be	AUX
ejpam-3294	106	9	said	say	VERB
ejpam-3294	106	10	to	to	PART
ejpam-3294	106	11	be	be	AUX
ejpam-3294	106	12	an	an	DET
ejpam-3294	106	13	(	(	PUNCT
ejpam-3294	106	14	α	α	NOUN
ejpam-3294	106	15	,	,	PUNCT
ejpam-3294	106	16	β	β	X
ejpam-3294	106	17	,	,	PUNCT
ejpam-3294	106	18	f	f	NOUN
ejpam-3294	106	19	)	)	PUNCT
ejpam-3294	106	20	-geraghty	-geraghty	PROPN
ejpam-3294	106	21	contraction	contraction	NOUN
ejpam-3294	106	22	mapping	mapping	NOUN
ejpam-3294	106	23	if	if	SCONJ
ejpam-3294	106	24	there	there	PRON
ejpam-3294	106	25	exist	exist	VERB
ejpam-3294	106	26	β	β	X
ejpam-3294	106	27	∈	∈	PROPN
ejpam-3294	106	28	f	f	PROPN
ejpam-3294	106	29	and	and	CCONJ
ejpam-3294	106	30	τ	τ	PROPN
ejpam-3294	106	31	>	>	X
ejpam-3294	106	32	0	0	NUM
ejpam-3294	106	33	such	such	ADJ
ejpam-3294	106	34	that	that	SCONJ
ejpam-3294	106	35	,	,	PUNCT
ejpam-3294	106	36	for	for	ADP
ejpam-3294	106	37	all	all	DET
ejpam-3294	106	38	x	x	NOUN
ejpam-3294	106	39	,	,	PUNCT
ejpam-3294	106	40	y	y	PROPN
ejpam-3294	106	41	∈	∈	PROPN
ejpam-3294	106	42	x	x	PUNCT
ejpam-3294	106	43	with	with	ADP
ejpam-3294	106	44	σ(fx	σ(fx	PROPN
ejpam-3294	106	45	,	,	PUNCT
ejpam-3294	106	46	fy	fy	PROPN
ejpam-3294	106	47	)	)	PUNCT
ejpam-3294	106	48	>	>	X
ejpam-3294	106	49	0	0	PUNCT
ejpam-3294	106	50	and	and	CCONJ
ejpam-3294	106	51	α(x	α(x	PROPN
ejpam-3294	106	52	,	,	PUNCT
ejpam-3294	106	53	y	y	PROPN
ejpam-3294	106	54	)	)	PUNCT
ejpam-3294	106	55	≥	≥	NOUN
ejpam-3294	106	56	1	1	NUM
ejpam-3294	106	57	,	,	PUNCT
ejpam-3294	106	58	α(x	α(x	NOUN
ejpam-3294	106	59	,	,	PUNCT
ejpam-3294	106	60	y)(τ	y)(τ	PROPN
ejpam-3294	107	1	+	+	CCONJ
ejpam-3294	107	2	f	f	X
ejpam-3294	107	3	(	(	PUNCT
ejpam-3294	107	4	σ(fx	σ(fx	PROPN
ejpam-3294	107	5	,	,	PUNCT
ejpam-3294	107	6	fy	fy	PROPN
ejpam-3294	107	7	)	)	PUNCT
ejpam-3294	107	8	)	)	PUNCT
ejpam-3294	107	9	≤	≤	NUM
ejpam-3294	107	10	β(mx	β(mx	NOUN
ejpam-3294	107	11	,	,	PUNCT
ejpam-3294	107	12	y)f	y)f	NOUN
ejpam-3294	107	13	(	(	PUNCT
ejpam-3294	107	14	mx	mx	PROPN
ejpam-3294	107	15	,	,	PUNCT
ejpam-3294	107	16	y	y	PROPN
ejpam-3294	107	17	)	)	PUNCT
ejpam-3294	107	18	,	,	PUNCT
ejpam-3294	107	19	(	(	PUNCT
ejpam-3294	107	20	2	2	X
ejpam-3294	107	21	)	)	PUNCT
ejpam-3294	107	22	where	where	SCONJ
ejpam-3294	107	23	mx	mx	PROPN
ejpam-3294	107	24	,	,	PUNCT
ejpam-3294	107	25	y	y	PROPN
ejpam-3294	107	26	=	=	SYM
ejpam-3294	107	27	max{σ(x	max{σ(x	PROPN
ejpam-3294	107	28	,	,	PUNCT
ejpam-3294	107	29	y	y	PROPN
ejpam-3294	107	30	)	)	PUNCT
ejpam-3294	107	31	,	,	PUNCT
ejpam-3294	107	32	σ(x	σ(x	PROPN
ejpam-3294	107	33	,	,	PUNCT
ejpam-3294	107	34	fx	fx	PROPN
ejpam-3294	107	35	)	)	PUNCT
ejpam-3294	107	36	,	,	PUNCT
ejpam-3294	107	37	σ(y	σ(y	PROPN
ejpam-3294	107	38	,	,	PUNCT
ejpam-3294	107	39	fy	fy	PROPN
ejpam-3294	107	40	)	)	PUNCT
ejpam-3294	107	41	,	,	PUNCT
ejpam-3294	107	42	σ(fx	σ(fx	PROPN
ejpam-3294	107	43	,	,	PUNCT
ejpam-3294	107	44	y	y	PROPN
ejpam-3294	107	45	)	)	PUNCT
ejpam-3294	108	1	+	+	CCONJ
ejpam-3294	108	2	σ(x	σ(x	PROPN
ejpam-3294	108	3	,	,	PUNCT
ejpam-3294	108	4	fy	fy	PROPN
ejpam-3294	108	5	)	)	PUNCT
ejpam-3294	108	6	4	4	NUM
ejpam-3294	108	7	,	,	PUNCT
ejpam-3294	109	1	[	[	X
ejpam-3294	109	2	1	1	NUM
ejpam-3294	109	3	+	+	NUM
ejpam-3294	109	4	σ(x	σ(x	PROPN
ejpam-3294	109	5	,	,	PUNCT
ejpam-3294	109	6	fx)]σ(y	fx)]σ(y	PROPN
ejpam-3294	109	7	,	,	PUNCT
ejpam-3294	109	8	fy	fy	PROPN
ejpam-3294	109	9	)	)	PUNCT
ejpam-3294	109	10	σ(x	σ(x	PROPN
ejpam-3294	109	11	,	,	PUNCT
ejpam-3294	109	12	y	y	NOUN
ejpam-3294	109	13	)	)	PUNCT
ejpam-3294	109	14	+	+	CCONJ
ejpam-3294	109	15	1	1	NUM
ejpam-3294	109	16	}	}	PUNCT
ejpam-3294	109	17	.	.	PUNCT
ejpam-3294	110	1	remark	remark	NOUN
ejpam-3294	110	2	3	3	NUM
ejpam-3294	110	3	.	.	PUNCT
ejpam-3294	111	1	since	since	SCONJ
ejpam-3294	111	2	the	the	DET
ejpam-3294	111	3	functions	function	NOUN
ejpam-3294	111	4	belonging	belong	VERB
ejpam-3294	111	5	to	to	ADP
ejpam-3294	111	6	f	f	PROPN
ejpam-3294	111	7	are	be	AUX
ejpam-3294	111	8	strictly	strictly	ADV
ejpam-3294	111	9	smaller	small	ADJ
ejpam-3294	111	10	than	than	ADP
ejpam-3294	111	11	1	1	NUM
ejpam-3294	111	12	,	,	PUNCT
ejpam-3294	111	13	the	the	DET
ejpam-3294	111	14	expression	expression	NOUN
ejpam-3294	111	15	β(mx	β(mx	NOUN
ejpam-3294	111	16	,	,	PUNCT
ejpam-3294	111	17	y	y	NOUN
ejpam-3294	111	18	)	)	PUNCT
ejpam-3294	111	19	in	in	ADP
ejpam-3294	111	20	20	20	NUM
ejpam-3294	111	21	can	can	AUX
ejpam-3294	111	22	be	be	AUX
ejpam-3294	111	23	estimated	estimate	VERB
ejpam-3294	111	24	from	from	ADP
ejpam-3294	111	25	above	above	ADV
ejpam-3294	111	26	as	as	SCONJ
ejpam-3294	111	27	follows	follow	VERB
ejpam-3294	111	28	:	:	PUNCT
ejpam-3294	111	29	β(mx	β(mx	NUM
ejpam-3294	111	30	,	,	PUNCT
ejpam-3294	111	31	y	y	NOUN
ejpam-3294	111	32	)	)	PUNCT
ejpam-3294	111	33	<	<	X
ejpam-3294	111	34	1	1	NUM
ejpam-3294	111	35	,	,	PUNCT
ejpam-3294	111	36	for	for	ADP
ejpam-3294	111	37	all	all	DET
ejpam-3294	111	38	x	x	NOUN
ejpam-3294	111	39	,	,	PUNCT
ejpam-3294	111	40	y	y	PROPN
ejpam-3294	111	41	∈	∈	PROPN
ejpam-3294	111	42	x	x	PUNCT
ejpam-3294	111	43	with	with	ADP
ejpam-3294	111	44	σ(fx	σ(fx	PROPN
ejpam-3294	111	45	,	,	PUNCT
ejpam-3294	111	46	fy	fy	PROPN
ejpam-3294	111	47	)	)	PUNCT
ejpam-3294	111	48	>	>	X
ejpam-3294	112	1	0	0	X
ejpam-3294	112	2	.	.	PUNCT
ejpam-3294	113	1	lemma	lemma	PROPN
ejpam-3294	113	2	2	2	X
ejpam-3294	113	3	.	.	PUNCT
ejpam-3294	114	1	let	let	AUX
ejpam-3294	114	2	(	(	PUNCT
ejpam-3294	114	3	x	x	NOUN
ejpam-3294	114	4	,	,	PUNCT
ejpam-3294	114	5	σ	σ	PROPN
ejpam-3294	114	6	)	)	PUNCT
ejpam-3294	114	7	be	be	AUX
ejpam-3294	114	8	a	a	DET
ejpam-3294	114	9	metric	metric	ADJ
ejpam-3294	114	10	-	-	PUNCT
ejpam-3294	114	11	like	like	ADJ
ejpam-3294	114	12	space	space	NOUN
ejpam-3294	114	13	,	,	PUNCT
ejpam-3294	114	14	and	and	CCONJ
ejpam-3294	114	15	let	let	VERB
ejpam-3294	114	16	f	f	PRON
ejpam-3294	114	17	:	:	PUNCT
ejpam-3294	114	18	x	x	X
ejpam-3294	114	19	→	→	PUNCT
ejpam-3294	114	20	x	x	X
ejpam-3294	114	21	is	be	AUX
ejpam-3294	114	22	said	say	VERB
ejpam-3294	114	23	to	to	PART
ejpam-3294	114	24	be	be	AUX
ejpam-3294	114	25	an	an	DET
ejpam-3294	114	26	(	(	PUNCT
ejpam-3294	114	27	α	α	NOUN
ejpam-3294	114	28	,	,	PUNCT
ejpam-3294	114	29	β	β	X
ejpam-3294	114	30	,	,	PUNCT
ejpam-3294	114	31	f	f	PROPN
ejpam-3294	114	32	)	)	PUNCT
ejpam-3294	114	33	−geraghty	−geraghty	PROPN
ejpam-3294	114	34	contraction	contraction	PROPN
ejpam-3294	114	35	mapping	mapping	NOUN
ejpam-3294	114	36	.	.	PUNCT
ejpam-3294	115	1	define	define	VERB
ejpam-3294	115	2	a	a	DET
ejpam-3294	115	3	sequence	sequence	NOUN
ejpam-3294	115	4	{	{	PUNCT
ejpam-3294	115	5	xn	xn	VERB
ejpam-3294	115	6	}	}	PUNCT
ejpam-3294	115	7	by	by	ADP
ejpam-3294	115	8	xn+1	xn+1	PROPN
ejpam-3294	115	9	=	=	SYM
ejpam-3294	115	10	fxn	fxn	NOUN
ejpam-3294	115	11	for	for	ADP
ejpam-3294	115	12	all	all	PRON
ejpam-3294	115	13	n	n	DET
ejpam-3294	115	14	∈	∈	PROPN
ejpam-3294	115	15	n.	n.	NOUN
ejpam-3294	115	16	if	if	SCONJ
ejpam-3294	115	17	the	the	DET
ejpam-3294	115	18	sequence	sequence	NOUN
ejpam-3294	115	19	{	{	PUNCT
ejpam-3294	115	20	xn	xn	NOUN
ejpam-3294	115	21	}	}	PUNCT
ejpam-3294	115	22	is	be	AUX
ejpam-3294	115	23	non	non	ADJ
ejpam-3294	115	24	-	-	ADJ
ejpam-3294	115	25	decreasing	decrease	VERB
ejpam-3294	115	26	and	and	CCONJ
ejpam-3294	115	27	limn→∞	limn→∞	ADJ
ejpam-3294	115	28	σ(xn	σ(xn	NOUN
ejpam-3294	115	29	,	,	PUNCT
ejpam-3294	115	30	xn+1	xn+1	NUM
ejpam-3294	115	31	)	)	PUNCT
ejpam-3294	115	32	=	=	SYM
ejpam-3294	116	1	0	0	NUM
ejpam-3294	116	2	,	,	PUNCT
ejpam-3294	116	3	then	then	ADV
ejpam-3294	116	4	{	{	PUNCT
ejpam-3294	116	5	xn	xn	X
ejpam-3294	116	6	}	}	PUNCT
ejpam-3294	116	7	is	be	AUX
ejpam-3294	116	8	a	a	DET
ejpam-3294	116	9	cauchy	cauchy	ADJ
ejpam-3294	116	10	sequence	sequence	NOUN
ejpam-3294	116	11	.	.	PUNCT
ejpam-3294	117	1	proof	proof	NOUN
ejpam-3294	117	2	.	.	PUNCT
ejpam-3294	118	1	suppose	suppose	VERB
ejpam-3294	118	2	that	that	SCONJ
ejpam-3294	118	3	the	the	DET
ejpam-3294	118	4	sequence	sequence	NOUN
ejpam-3294	118	5	{	{	PUNCT
ejpam-3294	118	6	xn	xn	NOUN
ejpam-3294	118	7	}	}	PUNCT
ejpam-3294	118	8	is	be	AUX
ejpam-3294	118	9	not	not	PART
ejpam-3294	118	10	a	a	DET
ejpam-3294	118	11	cauchy	cauchy	NOUN
ejpam-3294	118	12	,	,	PUNCT
ejpam-3294	118	13	then	then	ADV
ejpam-3294	118	14	there	there	PRON
ejpam-3294	118	15	exists	exist	VERB
ejpam-3294	118	16	ε	ε	PROPN
ejpam-3294	118	17	>	>	PUNCT
ejpam-3294	118	18	0	0	NUM
ejpam-3294	119	1	and	and	CCONJ
ejpam-3294	119	2	two	two	NUM
ejpam-3294	119	3	subsequences	subsequence	NOUN
ejpam-3294	119	4	{	{	PUNCT
ejpam-3294	119	5	xpn	xpn	PROPN
ejpam-3294	119	6	}	}	PUNCT
ejpam-3294	119	7	and	and	CCONJ
ejpam-3294	119	8	{	{	PUNCT
ejpam-3294	119	9	xqn	xqn	NOUN
ejpam-3294	119	10	}	}	PUNCT
ejpam-3294	119	11	of	of	ADP
ejpam-3294	119	12	the	the	DET
ejpam-3294	119	13	sequence	sequence	NOUN
ejpam-3294	119	14	{	{	PUNCT
ejpam-3294	119	15	xn	xn	X
ejpam-3294	119	16	}	}	PUNCT
ejpam-3294	119	17	such	such	ADJ
ejpam-3294	119	18	that	that	DET
ejpam-3294	119	19	pn	pn	PROPN
ejpam-3294	119	20	>	>	X
ejpam-3294	119	21	qn	qn	PROPN
ejpam-3294	119	22	>	>	X
ejpam-3294	119	23	n	n	CCONJ
ejpam-3294	119	24	,	,	PUNCT
ejpam-3294	119	25	σ(xpn−1	σ(xpn−1	PROPN
ejpam-3294	119	26	,	,	PUNCT
ejpam-3294	119	27	xqn	xqn	PROPN
ejpam-3294	119	28	)	)	PUNCT
ejpam-3294	119	29	<	<	X
ejpam-3294	119	30	ε	ε	PROPN
ejpam-3294	119	31	and	and	CCONJ
ejpam-3294	119	32	σ(xpn	σ(xpn	PROPN
ejpam-3294	119	33	,	,	PUNCT
ejpam-3294	119	34	xqn	xqn	PROPN
ejpam-3294	119	35	)	)	PUNCT
ejpam-3294	119	36	≤	≤	PUNCT
ejpam-3294	119	37	ε	ε	PROPN
ejpam-3294	119	38	.	.	PUNCT
ejpam-3294	120	1	this	this	PRON
ejpam-3294	120	2	implies	imply	VERB
ejpam-3294	120	3	that	that	SCONJ
ejpam-3294	120	4	ε	ε	PROPN
ejpam-3294	120	5	≤	≤	ADJ
ejpam-3294	120	6	σ(xpn	σ(xpn	PROPN
ejpam-3294	120	7	,	,	PUNCT
ejpam-3294	120	8	xqn	xqn	PROPN
ejpam-3294	120	9	)	)	PUNCT
ejpam-3294	120	10	≤	≤	NOUN
ejpam-3294	120	11	σ(xpn	σ(xpn	PROPN
ejpam-3294	120	12	,	,	PUNCT
ejpam-3294	120	13	xqn−1	xqn−1	PROPN
ejpam-3294	120	14	)	)	PUNCT
ejpam-3294	121	1	+	+	CCONJ
ejpam-3294	121	2	σ(xqn−1	σ(xqn−1	PROPN
ejpam-3294	121	3	,	,	PUNCT
ejpam-3294	121	4	xqn	xqn	NOUN
ejpam-3294	121	5	)	)	PUNCT
ejpam-3294	121	6	≤	≤	PUNCT
ejpam-3294	122	1	σ(xpn	σ(xpn	PROPN
ejpam-3294	122	2	,	,	PUNCT
ejpam-3294	122	3	xpn−1	xpn−1	PROPN
ejpam-3294	122	4	)	)	PUNCT
ejpam-3294	122	5	+	+	CCONJ
ejpam-3294	122	6	σ(xpn−1	σ(xpn−1	ADJ
ejpam-3294	122	7	,	,	PUNCT
ejpam-3294	122	8	xqn−1	xqn−1	PROPN
ejpam-3294	122	9	)	)	PUNCT
ejpam-3294	123	1	+	+	CCONJ
ejpam-3294	123	2	σ(xqn−1	σ(xqn−1	PROPN
ejpam-3294	123	3	,	,	PUNCT
ejpam-3294	123	4	xqn	xqn	NOUN
ejpam-3294	123	5	)	)	PUNCT
ejpam-3294	123	6	≤	≤	PUNCT
ejpam-3294	124	1	σ(xpn	σ(xpn	PROPN
ejpam-3294	124	2	,	,	PUNCT
ejpam-3294	124	3	xpn−1	xpn−1	PROPN
ejpam-3294	124	4	)	)	PUNCT
ejpam-3294	124	5	+	+	CCONJ
ejpam-3294	124	6	σ(xpn−1	σ(xpn−1	ADJ
ejpam-3294	124	7	,	,	PUNCT
ejpam-3294	124	8	xqn	xqn	NOUN
ejpam-3294	124	9	)	)	PUNCT
ejpam-3294	124	10	+	+	CCONJ
ejpam-3294	124	11	2σ(xqn−1	2σ(xqn−1	NUM
ejpam-3294	124	12	,	,	PUNCT
ejpam-3294	124	13	xqn	xqn	PROPN
ejpam-3294	124	14	)	)	PUNCT
ejpam-3294	124	15	<	<	X
ejpam-3294	125	1	σ(xpn	σ(xpn	X
ejpam-3294	125	2	,	,	PUNCT
ejpam-3294	125	3	xpn−1	xpn−1	PROPN
ejpam-3294	125	4	)	)	PUNCT
ejpam-3294	125	5	+	+	NUM
ejpam-3294	125	6	ε+	ε+	X
ejpam-3294	125	7	2σ(xqn−1	2σ(xqn−1	NUM
ejpam-3294	125	8	,	,	PUNCT
ejpam-3294	125	9	xqn	xqn	PROPN
ejpam-3294	125	10	)	)	PUNCT
ejpam-3294	125	11	.	.	PUNCT
ejpam-3294	126	1	since	since	SCONJ
ejpam-3294	126	2	σ(xn	σ(xn	NUM
ejpam-3294	126	3	,	,	PUNCT
ejpam-3294	126	4	xn+1	xn+1	NUM
ejpam-3294	126	5	)	)	PUNCT
ejpam-3294	126	6	6=	6=	ADP
ejpam-3294	126	7	0	0	NUM
ejpam-3294	126	8	,	,	PUNCT
ejpam-3294	126	9	we	we	PRON
ejpam-3294	126	10	have	have	VERB
ejpam-3294	126	11	lim	lim	PROPN
ejpam-3294	126	12	n→∞	n→∞	PRON
ejpam-3294	126	13	σ(xpn	σ(xpn	PROPN
ejpam-3294	126	14	,	,	PUNCT
ejpam-3294	126	15	xqn	xqn	PROPN
ejpam-3294	126	16	)	)	PUNCT
ejpam-3294	127	1	=	=	VERB
ejpam-3294	127	2	lim	lim	PROPN
ejpam-3294	127	3	n→∞	n→∞	X
ejpam-3294	128	1	σ(xpn	σ(xpn	PROPN
ejpam-3294	128	2	,	,	PUNCT
ejpam-3294	128	3	xqn−1	xqn−1	PROPN
ejpam-3294	128	4	)	)	PUNCT
ejpam-3294	128	5	(	(	PUNCT
ejpam-3294	128	6	3	3	X
ejpam-3294	128	7	)	)	PUNCT
ejpam-3294	128	8	=	=	VERB
ejpam-3294	128	9	lim	lim	PROPN
ejpam-3294	128	10	n→∞	n→∞	X
ejpam-3294	128	11	σ(xpn−1	σ(xpn−1	PROPN
ejpam-3294	128	12	,	,	PUNCT
ejpam-3294	128	13	xqn−1	xqn−1	PROPN
ejpam-3294	128	14	)	)	PUNCT
ejpam-3294	128	15	(	(	PUNCT
ejpam-3294	128	16	4	4	X
ejpam-3294	128	17	)	)	PUNCT
ejpam-3294	128	18	=	=	VERB
ejpam-3294	129	1	lim	lim	PROPN
ejpam-3294	129	2	n→∞	n→∞	X
ejpam-3294	129	3	σ(xpn−1	σ(xpn−1	PROPN
ejpam-3294	129	4	,	,	PUNCT
ejpam-3294	129	5	xqn	xqn	PROPN
ejpam-3294	129	6	)	)	PUNCT
ejpam-3294	129	7	(	(	PUNCT
ejpam-3294	129	8	5	5	X
ejpam-3294	129	9	)	)	PUNCT
ejpam-3294	129	10	=	=	SYM
ejpam-3294	129	11	ε	ε	PROPN
ejpam-3294	129	12	.	.	PUNCT
ejpam-3294	130	1	since	since	SCONJ
ejpam-3294	130	2	f	f	PROPN
ejpam-3294	130	3	is	be	AUX
ejpam-3294	130	4	an	an	DET
ejpam-3294	130	5	(	(	PUNCT
ejpam-3294	130	6	α	α	NOUN
ejpam-3294	130	7	,	,	PUNCT
ejpam-3294	130	8	β	β	X
ejpam-3294	130	9	,	,	PUNCT
ejpam-3294	130	10	f	f	NOUN
ejpam-3294	130	11	)	)	PUNCT
ejpam-3294	130	12	-geraghty	-geraghty	PROPN
ejpam-3294	130	13	contraction	contraction	NOUN
ejpam-3294	130	14	mapping	mapping	NOUN
ejpam-3294	130	15	and	and	CCONJ
ejpam-3294	130	16	α(x	α(x	PROPN
ejpam-3294	130	17	,	,	PUNCT
ejpam-3294	130	18	y	y	PROPN
ejpam-3294	130	19	)	)	PUNCT
ejpam-3294	130	20	≥	≥	NOUN
ejpam-3294	130	21	1	1	NUM
ejpam-3294	130	22	,	,	PUNCT
ejpam-3294	130	23	we	we	PRON
ejpam-3294	130	24	have	have	VERB
ejpam-3294	130	25	(	(	PUNCT
ejpam-3294	130	26	τ	τ	X
ejpam-3294	130	27	+	+	NUM
ejpam-3294	130	28	f	f	X
ejpam-3294	130	29	(	(	PUNCT
ejpam-3294	130	30	σ(xpn−1	σ(xpn−1	PROPN
ejpam-3294	130	31	,	,	PUNCT
ejpam-3294	130	32	xqn−1	xqn−1	PROPN
ejpam-3294	130	33	)	)	PUNCT
ejpam-3294	130	34	)	)	PUNCT
ejpam-3294	130	35	)	)	PUNCT
ejpam-3294	130	36	≤	≤	NUM
ejpam-3294	130	37	α(xpn−1	α(xpn−1	PROPN
ejpam-3294	130	38	,	,	PUNCT
ejpam-3294	130	39	xqn−1)(τ	xqn−1)(τ	PUNCT
ejpam-3294	131	1	+	+	CCONJ
ejpam-3294	131	2	f	f	X
ejpam-3294	131	3	(	(	PUNCT
ejpam-3294	131	4	σ(xpn−1	σ(xpn−1	PROPN
ejpam-3294	131	5	,	,	PUNCT
ejpam-3294	131	6	xqn−1	xqn−1	PROPN
ejpam-3294	131	7	)	)	PUNCT
ejpam-3294	131	8	)	)	PUNCT
ejpam-3294	131	9	)	)	PUNCT
ejpam-3294	132	1	≤	≤	NUM
ejpam-3294	132	2	β(mxpn−1,xqn−1)f	β(mxpn−1,xqn−1)f	ADJ
ejpam-3294	132	3	(	(	PUNCT
ejpam-3294	132	4	mxpn−1,xqn−1	mxpn−1,xqn−1	NUM
ejpam-3294	132	5	)	)	PUNCT
ejpam-3294	132	6	,	,	PUNCT
ejpam-3294	132	7	where	where	SCONJ
ejpam-3294	132	8	mxpn−1,xqn−1	mxpn−1,xqn−1	ADJ
ejpam-3294	132	9	=	=	SYM
ejpam-3294	132	10	max{σ(xpn−1	max{σ(xpn−1	PROPN
ejpam-3294	132	11	,	,	PUNCT
ejpam-3294	132	12	xqn−1	xqn−1	PROPN
ejpam-3294	132	13	)	)	PUNCT
ejpam-3294	132	14	,	,	PUNCT
ejpam-3294	132	15	σ(xpn−1	σ(xpn−1	PROPN
ejpam-3294	132	16	,	,	PUNCT
ejpam-3294	132	17	fxpn−1	fxpn−1	NOUN
ejpam-3294	132	18	)	)	PUNCT
ejpam-3294	132	19	,	,	PUNCT
ejpam-3294	132	20	σ(xqn−1	σ(xqn−1	PROPN
ejpam-3294	132	21	,	,	PUNCT
ejpam-3294	132	22	fxqn−1	fxqn−1	PROPN
ejpam-3294	132	23	)	)	PUNCT
ejpam-3294	132	24	,	,	PUNCT
ejpam-3294	132	25	h.	h.	PROPN
ejpam-3294	132	26	qawaqneh	qawaqneh	PROPN
ejpam-3294	132	27	,	,	PUNCT
ejpam-3294	132	28	m.s	m.s	PROPN
ejpam-3294	132	29	.	.	PROPN
ejpam-3294	132	30	noorani	noorani	PROPN
ejpam-3294	132	31	,	,	PUNCT
ejpam-3294	132	32	w.	w.	PROPN
ejpam-3294	132	33	shatanawi	shatanawi	PROPN
ejpam-3294	132	34	/	/	SYM
ejpam-3294	132	35	eur	eur	PROPN
ejpam-3294	132	36	.	.	PUNCT
ejpam-3294	133	1	j.	j.	PROPN
ejpam-3294	133	2	pure	pure	PROPN
ejpam-3294	133	3	appl	appl	PROPN
ejpam-3294	133	4	.	.	PROPN
ejpam-3294	133	5	math	math	PROPN
ejpam-3294	133	6	,	,	PUNCT
ejpam-3294	133	7	11	11	NUM
ejpam-3294	133	8	(	(	PUNCT
ejpam-3294	133	9	3	3	NUM
ejpam-3294	133	10	)	)	PUNCT
ejpam-3294	133	11	(	(	PUNCT
ejpam-3294	133	12	2018	2018	NUM
ejpam-3294	133	13	)	)	PUNCT
ejpam-3294	133	14	,	,	PUNCT
ejpam-3294	133	15	702	702	NUM
ejpam-3294	133	16	-	-	SYM
ejpam-3294	133	17	716	716	NUM
ejpam-3294	133	18	707	707	NUM
ejpam-3294	133	19	σ(fxpn−1	σ(fxpn−1	PROPN
ejpam-3294	133	20	,	,	PUNCT
ejpam-3294	133	21	xqn−1	xqn−1	PROPN
ejpam-3294	133	22	)	)	PUNCT
ejpam-3294	134	1	+	+	CCONJ
ejpam-3294	134	2	σ(xpn−1	σ(xpn−1	ADJ
ejpam-3294	134	3	,	,	PUNCT
ejpam-3294	134	4	fxqn−1	fxqn−1	ADJ
ejpam-3294	134	5	)	)	PUNCT
ejpam-3294	134	6	4	4	NUM
ejpam-3294	134	7	,	,	PUNCT
ejpam-3294	134	8	[	[	X
ejpam-3294	134	9	1	1	NUM
ejpam-3294	134	10	+	+	CCONJ
ejpam-3294	134	11	σ(xpn−1	σ(xpn−1	ADJ
ejpam-3294	134	12	,	,	PUNCT
ejpam-3294	134	13	fxpn−1)]σ(xqn−1	fxpn−1)]σ(xqn−1	ADJ
ejpam-3294	134	14	,	,	PUNCT
ejpam-3294	134	15	fxqn−1	fxqn−1	ADJ
ejpam-3294	134	16	)	)	PUNCT
ejpam-3294	134	17	σ(xpn−1	σ(xpn−1	PROPN
ejpam-3294	134	18	,	,	PUNCT
ejpam-3294	134	19	xqn−1	xqn−1	PROPN
ejpam-3294	134	20	)	)	PUNCT
ejpam-3294	135	1	+	+	CCONJ
ejpam-3294	135	2	1	1	X
ejpam-3294	135	3	}	}	PUNCT
ejpam-3294	135	4	=	=	PUNCT
ejpam-3294	135	5	max{σ(xpn−1	max{σ(xpn−1	PROPN
ejpam-3294	135	6	,	,	PUNCT
ejpam-3294	135	7	xqn−1	xqn−1	PROPN
ejpam-3294	135	8	)	)	PUNCT
ejpam-3294	135	9	,	,	PUNCT
ejpam-3294	135	10	σ(xpn−1	σ(xpn−1	PROPN
ejpam-3294	135	11	,	,	PUNCT
ejpam-3294	135	12	xpn	xpn	PROPN
ejpam-3294	135	13	)	)	PUNCT
ejpam-3294	135	14	,	,	PUNCT
ejpam-3294	135	15	σ(xqn−1	σ(xqn−1	PROPN
ejpam-3294	135	16	,	,	PUNCT
ejpam-3294	135	17	xqn	xqn	PROPN
ejpam-3294	135	18	)	)	PUNCT
ejpam-3294	135	19	,	,	PUNCT
ejpam-3294	135	20	σ(xpn	σ(xpn	PROPN
ejpam-3294	135	21	,	,	PUNCT
ejpam-3294	135	22	xqn−1	xqn−1	PROPN
ejpam-3294	135	23	)	)	PUNCT
ejpam-3294	135	24	+	+	CCONJ
ejpam-3294	135	25	σ(xpn−1	σ(xpn−1	ADJ
ejpam-3294	135	26	,	,	PUNCT
ejpam-3294	135	27	xqn	xqn	NOUN
ejpam-3294	135	28	)	)	PUNCT
ejpam-3294	135	29	4	4	NUM
ejpam-3294	135	30	,	,	PUNCT
ejpam-3294	135	31	[	[	X
ejpam-3294	135	32	1	1	NUM
ejpam-3294	135	33	+	+	CCONJ
ejpam-3294	135	34	σ(xpn−1	σ(xpn−1	ADJ
ejpam-3294	135	35	,	,	PUNCT
ejpam-3294	135	36	xpn)]σ(xqn−1	xpn)]σ(xqn−1	PROPN
ejpam-3294	135	37	,	,	PUNCT
ejpam-3294	135	38	xqn	xqn	PROPN
ejpam-3294	135	39	)	)	PUNCT
ejpam-3294	135	40	σ(xpn−1	σ(xpn−1	PROPN
ejpam-3294	135	41	,	,	PUNCT
ejpam-3294	135	42	xqn−1	xqn−1	PROPN
ejpam-3294	135	43	)	)	PUNCT
ejpam-3294	135	44	+	+	CCONJ
ejpam-3294	135	45	1	1	NUM
ejpam-3294	135	46	}	}	PUNCT
ejpam-3294	135	47	.	.	PUNCT
ejpam-3294	136	1	letting	let	VERB
ejpam-3294	136	2	n→∞	n→∞	PRON
ejpam-3294	136	3	in	in	ADP
ejpam-3294	136	4	the	the	DET
ejpam-3294	136	5	above	above	ADJ
ejpam-3294	136	6	inequalities	inequality	NOUN
ejpam-3294	136	7	and	and	CCONJ
ejpam-3294	136	8	using	use	VERB
ejpam-3294	136	9	(	(	PUNCT
ejpam-3294	136	10	2.2	2.2	NUM
ejpam-3294	136	11	)	)	PUNCT
ejpam-3294	136	12	,	,	PUNCT
ejpam-3294	136	13	(	(	PUNCT
ejpam-3294	136	14	2.3	2.3	NUM
ejpam-3294	136	15	)	)	PUNCT
ejpam-3294	136	16	and	and	CCONJ
ejpam-3294	136	17	(	(	PUNCT
ejpam-3294	136	18	2.4	2.4	NUM
ejpam-3294	136	19	)	)	PUNCT
ejpam-3294	136	20	,	,	PUNCT
ejpam-3294	136	21	we	we	PRON
ejpam-3294	136	22	obtain	obtain	VERB
ejpam-3294	136	23	lim	lim	PROPN
ejpam-3294	136	24	n→∞	n→∞	X
ejpam-3294	136	25	m(xpn−1	m(xpn−1	PROPN
ejpam-3294	136	26	,	,	PUNCT
ejpam-3294	136	27	xqn−1	xqn−1	PROPN
ejpam-3294	136	28	)	)	PUNCT
ejpam-3294	137	1	=	=	SYM
ejpam-3294	137	2	ε	ε	PROPN
ejpam-3294	137	3	.	.	PUNCT
ejpam-3294	137	4	(	(	PUNCT
ejpam-3294	137	5	6	6	NUM
ejpam-3294	137	6	)	)	PUNCT
ejpam-3294	137	7	since	since	SCONJ
ejpam-3294	137	8	limn→∞	limn→∞	PROPN
ejpam-3294	137	9	β(m(xpn−1	β(m(xpn−1	NOUN
ejpam-3294	137	10	,	,	PUNCT
ejpam-3294	137	11	xqn−1	xqn−1	PROPN
ejpam-3294	137	12	)	)	PUNCT
ejpam-3294	137	13	≤	≤	NUM
ejpam-3294	137	14	1	1	NUM
ejpam-3294	137	15	,	,	PUNCT
ejpam-3294	137	16	we	we	PRON
ejpam-3294	137	17	conclude	conclude	VERB
ejpam-3294	137	18	that	that	SCONJ
ejpam-3294	137	19	τ	τ	PROPN
ejpam-3294	137	20	+	+	NUM
ejpam-3294	137	21	f	f	PROPN
ejpam-3294	137	22	(	(	PUNCT
ejpam-3294	137	23	ε	ε	PROPN
ejpam-3294	137	24	)	)	PUNCT
ejpam-3294	137	25	≤	≤	NOUN
ejpam-3294	137	26	β(ε)f	β(ε)f	PROPN
ejpam-3294	137	27	(	(	PUNCT
ejpam-3294	137	28	ε	ε	PROPN
ejpam-3294	137	29	)	)	PUNCT
ejpam-3294	137	30	≤	≤	NOUN
ejpam-3294	137	31	f	f	X
ejpam-3294	137	32	(	(	PUNCT
ejpam-3294	137	33	ε	ε	PROPN
ejpam-3294	137	34	)	)	PUNCT
ejpam-3294	137	35	,	,	PUNCT
ejpam-3294	137	36	(	(	PUNCT
ejpam-3294	137	37	7	7	X
ejpam-3294	137	38	)	)	PUNCT
ejpam-3294	137	39	a	a	DET
ejpam-3294	137	40	contradiction	contradiction	NOUN
ejpam-3294	137	41	since	since	SCONJ
ejpam-3294	137	42	τ	τ	PROPN
ejpam-3294	137	43	>	>	X
ejpam-3294	137	44	0	0	PROPN
ejpam-3294	137	45	.	.	PUNCT
ejpam-3294	138	1	hence	hence	ADV
ejpam-3294	138	2	lim	lim	PROPN
ejpam-3294	138	3	n→∞	n→∞	NUM
ejpam-3294	138	4	σ(xn	σ(xn	NOUN
ejpam-3294	138	5	,	,	PUNCT
ejpam-3294	138	6	xm	xm	PROPN
ejpam-3294	138	7	)	)	PUNCT
ejpam-3294	139	1	=	=	SYM
ejpam-3294	139	2	0	0	X
ejpam-3294	139	3	.	.	PUNCT
ejpam-3294	140	1	we	we	PRON
ejpam-3294	140	2	denote	denote	VERB
ejpam-3294	140	3	with	with	ADP
ejpam-3294	140	4	ξ(x	ξ(x	NOUN
ejpam-3294	140	5	,	,	PUNCT
ejpam-3294	140	6	α	α	NOUN
ejpam-3294	140	7	,	,	PUNCT
ejpam-3294	140	8	β	β	X
ejpam-3294	140	9	,	,	PUNCT
ejpam-3294	140	10	f	f	PROPN
ejpam-3294	140	11	)	)	PUNCT
ejpam-3294	140	12	the	the	DET
ejpam-3294	140	13	collection	collection	NOUN
ejpam-3294	140	14	of	of	ADP
ejpam-3294	140	15	all	all	PRON
ejpam-3294	140	16	almost	almost	ADV
ejpam-3294	140	17	generalized	generalize	VERB
ejpam-3294	140	18	(	(	PUNCT
ejpam-3294	140	19	α	α	X
ejpam-3294	140	20	,	,	PUNCT
ejpam-3294	140	21	β	β	X
ejpam-3294	140	22	,	,	PUNCT
ejpam-3294	140	23	f	f	NOUN
ejpam-3294	140	24	)	)	PUNCT
ejpam-3294	140	25	−contractive	−contractive	ADJ
ejpam-3294	140	26	mappings	mapping	NOUN
ejpam-3294	140	27	.	.	PUNCT
ejpam-3294	141	1	theorem	theorem	NOUN
ejpam-3294	141	2	2	2	NUM
ejpam-3294	141	3	.	.	X
ejpam-3294	142	1	let	let	AUX
ejpam-3294	142	2	(	(	PUNCT
ejpam-3294	142	3	x	x	NOUN
ejpam-3294	142	4	,	,	PUNCT
ejpam-3294	142	5	σ	σ	PROPN
ejpam-3294	142	6	)	)	PUNCT
ejpam-3294	142	7	be	be	AUX
ejpam-3294	142	8	a	a	DET
ejpam-3294	142	9	metric	metric	ADJ
ejpam-3294	142	10	-	-	PUNCT
ejpam-3294	142	11	like	like	ADJ
ejpam-3294	142	12	space	space	NOUN
ejpam-3294	142	13	and	and	CCONJ
ejpam-3294	142	14	α	α	NOUN
ejpam-3294	142	15	:	:	PUNCT
ejpam-3294	143	1	x	x	SYM
ejpam-3294	143	2	×	×	NOUN
ejpam-3294	143	3	x	x	INTJ
ejpam-3294	143	4	→	→	X
ejpam-3294	143	5	[	[	X
ejpam-3294	143	6	0,∞	0,∞	NOUN
ejpam-3294	143	7	)	)	PUNCT
ejpam-3294	143	8	.	.	PUNCT
ejpam-3294	144	1	a	a	DET
ejpam-3294	144	2	mapping	mapping	NOUN
ejpam-3294	144	3	f	f	NOUN
ejpam-3294	144	4	:	:	PUNCT
ejpam-3294	144	5	x	x	X
ejpam-3294	144	6	→	→	PUNCT
ejpam-3294	144	7	x	x	PUNCT
ejpam-3294	144	8	be	be	AUX
ejpam-3294	144	9	an	an	DET
ejpam-3294	144	10	(	(	PUNCT
ejpam-3294	144	11	α	α	NOUN
ejpam-3294	144	12	,	,	PUNCT
ejpam-3294	144	13	β	β	X
ejpam-3294	144	14	,	,	PUNCT
ejpam-3294	144	15	f	f	PROPN
ejpam-3294	144	16	)	)	PUNCT
ejpam-3294	144	17	−geraghty	−geraghty	PROPN
ejpam-3294	144	18	contraction	contraction	PROPN
ejpam-3294	144	19	mapping	mapping	NOUN
ejpam-3294	144	20	.	.	PUNCT
ejpam-3294	145	1	assume	assume	VERB
ejpam-3294	145	2	that	that	SCONJ
ejpam-3294	145	3	the	the	DET
ejpam-3294	145	4	following	follow	VERB
ejpam-3294	145	5	conditions	condition	NOUN
ejpam-3294	145	6	are	be	AUX
ejpam-3294	145	7	satisfied	satisfied	ADJ
ejpam-3294	145	8	:	:	PUNCT
ejpam-3294	145	9	(	(	PUNCT
ejpam-3294	145	10	i	i	NOUN
ejpam-3294	145	11	)	)	PUNCT
ejpam-3294	145	12	f	f	PROPN
ejpam-3294	145	13	∈	∈	PROPN
ejpam-3294	145	14	ξ(x	ξ(x	PROPN
ejpam-3294	145	15	,	,	PUNCT
ejpam-3294	145	16	α	α	X
ejpam-3294	145	17	,	,	PUNCT
ejpam-3294	145	18	β	β	X
ejpam-3294	145	19	,	,	PUNCT
ejpam-3294	145	20	f	f	PROPN
ejpam-3294	145	21	)	)	PUNCT
ejpam-3294	145	22	∩wa(x	∩wa(x	PROPN
ejpam-3294	145	23	,	,	PUNCT
ejpam-3294	145	24	α	α	NOUN
ejpam-3294	145	25	)	)	PUNCT
ejpam-3294	145	26	.	.	PUNCT
ejpam-3294	146	1	(	(	PUNCT
ejpam-3294	146	2	ii	ii	X
ejpam-3294	146	3	)	)	PUNCT
ejpam-3294	146	4	there	there	PRON
ejpam-3294	146	5	exists	exist	VERB
ejpam-3294	146	6	x0	x0	PROPN
ejpam-3294	146	7	∈	∈	PROPN
ejpam-3294	146	8	x	x	PUNCT
ejpam-3294	146	9	such	such	ADJ
ejpam-3294	146	10	that	that	DET
ejpam-3294	146	11	σ(x0	σ(x0	NOUN
ejpam-3294	146	12	,	,	PUNCT
ejpam-3294	146	13	fx0	fx0	PROPN
ejpam-3294	146	14	)	)	PUNCT
ejpam-3294	146	15	≥	≥	NOUN
ejpam-3294	147	1	1	1	NUM
ejpam-3294	147	2	.	.	PUNCT
ejpam-3294	147	3	(	(	PUNCT
ejpam-3294	147	4	iii	iii	X
ejpam-3294	147	5	)	)	PUNCT
ejpam-3294	147	6	f	f	PROPN
ejpam-3294	147	7	is	be	AUX
ejpam-3294	147	8	σ−continuous	σ−continuous	PROPN
ejpam-3294	147	9	.	.	PUNCT
ejpam-3294	148	1	then	then	ADV
ejpam-3294	148	2	f	f	PROPN
ejpam-3294	148	3	has	have	VERB
ejpam-3294	148	4	a	a	DET
ejpam-3294	148	5	unique	unique	ADJ
ejpam-3294	148	6	fixed	fix	VERB
ejpam-3294	148	7	point	point	NOUN
ejpam-3294	148	8	z	z	NOUN
ejpam-3294	148	9	∈	∈	PROPN
ejpam-3294	148	10	x	x	PUNCT
ejpam-3294	148	11	with	with	ADP
ejpam-3294	148	12	σ(z	σ(z	NOUN
ejpam-3294	148	13	,	,	PUNCT
ejpam-3294	148	14	z	z	NOUN
ejpam-3294	148	15	)	)	PUNCT
ejpam-3294	148	16	=	=	SYM
ejpam-3294	149	1	0	0	X
ejpam-3294	149	2	.	.	PUNCT
ejpam-3294	149	3	proof	proof	NOUN
ejpam-3294	149	4	.	.	PUNCT
ejpam-3294	150	1	let	let	VERB
ejpam-3294	150	2	x0	x0	PROPN
ejpam-3294	150	3	∈	∈	PROPN
ejpam-3294	150	4	x	x	PUNCT
ejpam-3294	150	5	such	such	ADJ
ejpam-3294	150	6	that	that	DET
ejpam-3294	150	7	α(x0	α(x0	ADJ
ejpam-3294	150	8	,	,	PUNCT
ejpam-3294	150	9	fx0	fx0	PROPN
ejpam-3294	150	10	)	)	PUNCT
ejpam-3294	150	11	≥	≥	NOUN
ejpam-3294	151	1	1	1	NUM
ejpam-3294	151	2	.	.	PUNCT
ejpam-3294	152	1	we	we	PRON
ejpam-3294	152	2	define	define	VERB
ejpam-3294	152	3	a	a	DET
ejpam-3294	152	4	sequence	sequence	NOUN
ejpam-3294	152	5	{	{	PUNCT
ejpam-3294	152	6	xn	xn	NOUN
ejpam-3294	152	7	}	}	PUNCT
ejpam-3294	152	8	in	in	ADP
ejpam-3294	152	9	x	x	SYM
ejpam-3294	152	10	such	such	ADJ
ejpam-3294	152	11	that	that	PRON
ejpam-3294	152	12	xn	xn	PROPN
ejpam-3294	153	1	=	=	PUNCT
ejpam-3294	153	2	fxn−1	fxn−1	PROPN
ejpam-3294	153	3	for	for	ADP
ejpam-3294	153	4	all	all	DET
ejpam-3294	153	5	n	n	PRON
ejpam-3294	153	6	∈	∈	PROPN
ejpam-3294	153	7	n.	n.	NOUN
ejpam-3294	153	8	if	if	SCONJ
ejpam-3294	153	9	σ(xn	σ(xn	NOUN
ejpam-3294	153	10	,	,	PUNCT
ejpam-3294	153	11	xn+1	xn+1	NUM
ejpam-3294	153	12	)	)	PUNCT
ejpam-3294	153	13	=	=	SYM
ejpam-3294	153	14	0	0	NUM
ejpam-3294	154	1	for	for	ADP
ejpam-3294	154	2	some	some	DET
ejpam-3294	154	3	n0	n0	PROPN
ejpam-3294	154	4	∈	∈	PROPN
ejpam-3294	154	5	n	n	CCONJ
ejpam-3294	154	6	,	,	PUNCT
ejpam-3294	154	7	then	then	ADV
ejpam-3294	154	8	xn0	xn0	PROPN
ejpam-3294	154	9	is	be	AUX
ejpam-3294	154	10	a	a	DET
ejpam-3294	154	11	fixed	fix	VERB
ejpam-3294	154	12	point	point	NOUN
ejpam-3294	154	13	of	of	ADP
ejpam-3294	154	14	f	f	PROPN
ejpam-3294	154	15	and	and	CCONJ
ejpam-3294	154	16	it	it	PRON
ejpam-3294	154	17	is	be	AUX
ejpam-3294	154	18	done	do	VERB
ejpam-3294	154	19	.	.	PUNCT
ejpam-3294	155	1	now	now	ADV
ejpam-3294	155	2	,	,	PUNCT
ejpam-3294	155	3	suppose	suppose	VERB
ejpam-3294	155	4	that	that	SCONJ
ejpam-3294	155	5	xn	xn	PROPN
ejpam-3294	155	6	6=	6=	NUM
ejpam-3294	155	7	xn+1	xn+1	NUM
ejpam-3294	155	8	for	for	ADP
ejpam-3294	155	9	all	all	PRON
ejpam-3294	155	10	n	n	DET
ejpam-3294	155	11	∈	∈	PROPN
ejpam-3294	155	12	n.	n.	NOUN
ejpam-3294	155	13	since	since	SCONJ
ejpam-3294	155	14	f	f	PROPN
ejpam-3294	155	15	∈	∈	PROPN
ejpam-3294	155	16	wa(x	wa(x	NOUN
ejpam-3294	155	17	,	,	PUNCT
ejpam-3294	155	18	α	α	X
ejpam-3294	155	19	,	,	PUNCT
ejpam-3294	155	20	β	β	NOUN
ejpam-3294	155	21	)	)	PUNCT
ejpam-3294	155	22	and	and	CCONJ
ejpam-3294	155	23	α(x0	α(x0	ADJ
ejpam-3294	155	24	,	,	PUNCT
ejpam-3294	155	25	fx0	fx0	PROPN
ejpam-3294	155	26	)	)	PUNCT
ejpam-3294	155	27	≥	≥	NOUN
ejpam-3294	155	28	1	1	NUM
ejpam-3294	155	29	,	,	PUNCT
ejpam-3294	155	30	we	we	PRON
ejpam-3294	155	31	have	have	VERB
ejpam-3294	155	32	α(x1	α(x1	ADJ
ejpam-3294	155	33	,	,	PUNCT
ejpam-3294	155	34	x2	x2	PROPN
ejpam-3294	155	35	)	)	PUNCT
ejpam-3294	155	36	=	=	PUNCT
ejpam-3294	155	37	α(fx0	α(fx0	ADJ
ejpam-3294	155	38	,	,	PUNCT
ejpam-3294	155	39	ffx0	ffx0	PROPN
ejpam-3294	155	40	)	)	PUNCT
ejpam-3294	155	41	≥	≥	NOUN
ejpam-3294	155	42	1	1	NUM
ejpam-3294	155	43	,	,	PUNCT
ejpam-3294	155	44	α(x2	α(x2	NOUN
ejpam-3294	155	45	,	,	PUNCT
ejpam-3294	155	46	x3	x3	ADJ
ejpam-3294	155	47	)	)	PUNCT
ejpam-3294	155	48	=	=	SYM
ejpam-3294	155	49	α(fx1	α(fx1	NOUN
ejpam-3294	155	50	,	,	PUNCT
ejpam-3294	155	51	ffx1	ffx1	PROPN
ejpam-3294	155	52	)	)	PUNCT
ejpam-3294	155	53	≥	≥	NOUN
ejpam-3294	155	54	1	1	NUM
ejpam-3294	155	55	.	.	PUNCT
ejpam-3294	156	1	h.	h.	PROPN
ejpam-3294	156	2	qawaqneh	qawaqneh	PROPN
ejpam-3294	156	3	,	,	PUNCT
ejpam-3294	156	4	m.s	m.s	PROPN
ejpam-3294	156	5	.	.	PROPN
ejpam-3294	156	6	noorani	noorani	PROPN
ejpam-3294	156	7	,	,	PUNCT
ejpam-3294	156	8	w.	w.	PROPN
ejpam-3294	156	9	shatanawi	shatanawi	PROPN
ejpam-3294	156	10	/	/	SYM
ejpam-3294	156	11	eur	eur	PROPN
ejpam-3294	156	12	.	.	PUNCT
ejpam-3294	157	1	j.	j.	PROPN
ejpam-3294	157	2	pure	pure	PROPN
ejpam-3294	157	3	appl	appl	PROPN
ejpam-3294	157	4	.	.	PROPN
ejpam-3294	157	5	math	math	PROPN
ejpam-3294	157	6	,	,	PUNCT
ejpam-3294	157	7	11	11	NUM
ejpam-3294	157	8	(	(	PUNCT
ejpam-3294	157	9	3	3	NUM
ejpam-3294	157	10	)	)	PUNCT
ejpam-3294	157	11	(	(	PUNCT
ejpam-3294	157	12	2018	2018	NUM
ejpam-3294	157	13	)	)	PUNCT
ejpam-3294	157	14	,	,	PUNCT
ejpam-3294	157	15	702	702	NUM
ejpam-3294	157	16	-	-	SYM
ejpam-3294	157	17	716	716	NUM
ejpam-3294	157	18	708	708	NUM
ejpam-3294	157	19	using	use	VERB
ejpam-3294	157	20	this	this	DET
ejpam-3294	157	21	process	process	NOUN
ejpam-3294	157	22	again	again	ADV
ejpam-3294	157	23	,	,	PUNCT
ejpam-3294	157	24	we	we	PRON
ejpam-3294	157	25	get	get	VERB
ejpam-3294	157	26	α(xn	α(xn	NOUN
ejpam-3294	157	27	,	,	PUNCT
ejpam-3294	157	28	xn+1	xn+1	NUM
ejpam-3294	157	29	)	)	PUNCT
ejpam-3294	157	30	≥	≥	NOUN
ejpam-3294	158	1	1	1	NUM
ejpam-3294	158	2	.	.	PUNCT
ejpam-3294	159	1	since	since	SCONJ
ejpam-3294	159	2	f	f	PROPN
ejpam-3294	159	3	:	:	PUNCT
ejpam-3294	159	4	x	x	X
ejpam-3294	159	5	→	→	PUNCT
ejpam-3294	159	6	x	x	X
ejpam-3294	159	7	is	be	AUX
ejpam-3294	159	8	(	(	PUNCT
ejpam-3294	159	9	α	α	NOUN
ejpam-3294	159	10	,	,	PUNCT
ejpam-3294	159	11	β	β	X
ejpam-3294	159	12	,	,	PUNCT
ejpam-3294	159	13	f	f	NOUN
ejpam-3294	159	14	)	)	PUNCT
ejpam-3294	159	15	-geraghty	-geraghty	PROPN
ejpam-3294	159	16	contraction	contraction	NOUN
ejpam-3294	159	17	mapping	mapping	NOUN
ejpam-3294	159	18	with	with	ADP
ejpam-3294	159	19	α(fxn−1	α(fxn−1	PROPN
ejpam-3294	159	20	,	,	PUNCT
ejpam-3294	159	21	ffxn−1	ffxn−1	PROPN
ejpam-3294	159	22	)	)	PUNCT
ejpam-3294	159	23	=	=	SYM
ejpam-3294	159	24	α(xn	α(xn	PROPN
ejpam-3294	159	25	,	,	PUNCT
ejpam-3294	159	26	xn+1	xn+1	NUM
ejpam-3294	159	27	)	)	PUNCT
ejpam-3294	159	28	≥	≥	NOUN
ejpam-3294	159	29	1	1	NUM
ejpam-3294	159	30	,	,	PUNCT
ejpam-3294	159	31	we	we	PRON
ejpam-3294	159	32	have	have	VERB
ejpam-3294	159	33	0	0	NUM
ejpam-3294	159	34	<	<	X
ejpam-3294	159	35	τ	τ	PROPN
ejpam-3294	160	1	+	+	NUM
ejpam-3294	160	2	f	f	X
ejpam-3294	160	3	(	(	PUNCT
ejpam-3294	160	4	σ(xn	σ(xn	X
ejpam-3294	160	5	,	,	PUNCT
ejpam-3294	160	6	xn+1	xn+1	NUM
ejpam-3294	160	7	)	)	PUNCT
ejpam-3294	160	8	)	)	PUNCT
ejpam-3294	160	9	≤	≤	PROPN
ejpam-3294	160	10	α(xn	α(xn	NUM
ejpam-3294	160	11	,	,	PUNCT
ejpam-3294	160	12	xn+1)(τ	xn+1)(τ	PROPN
ejpam-3294	161	1	+	+	CCONJ
ejpam-3294	161	2	f	f	X
ejpam-3294	161	3	(	(	PUNCT
ejpam-3294	161	4	σ(fxn−1	σ(fxn−1	PROPN
ejpam-3294	161	5	,	,	PUNCT
ejpam-3294	161	6	fxn	fxn	NOUN
ejpam-3294	161	7	)	)	PUNCT
ejpam-3294	161	8	)	)	PUNCT
ejpam-3294	161	9	≤	≤	NUM
ejpam-3294	161	10	β(mxn−1,xn)f	β(mxn−1,xn)f	PUNCT
ejpam-3294	162	1	(	(	PUNCT
ejpam-3294	162	2	mxn−1,xn	mxn−1,xn	PROPN
ejpam-3294	162	3	)	)	PUNCT
ejpam-3294	162	4	,	,	PUNCT
ejpam-3294	162	5	(	(	PUNCT
ejpam-3294	162	6	8)	8)	NUM
ejpam-3294	162	7	where	where	SCONJ
ejpam-3294	162	8	mxn−1,xn	mxn−1,xn	PROPN
ejpam-3294	162	9	=	=	SYM
ejpam-3294	162	10	max{σ(xn−1	max{σ(xn−1	PROPN
ejpam-3294	162	11	,	,	PUNCT
ejpam-3294	162	12	xn	xn	PROPN
ejpam-3294	162	13	)	)	PUNCT
ejpam-3294	162	14	,	,	PUNCT
ejpam-3294	162	15	σ(xn−1	σ(xn−1	X
ejpam-3294	162	16	,	,	PUNCT
ejpam-3294	162	17	fxn−1	fxn−1	PROPN
ejpam-3294	162	18	)	)	PUNCT
ejpam-3294	162	19	,	,	PUNCT
ejpam-3294	162	20	σ(xn	σ(xn	NUM
ejpam-3294	162	21	,	,	PUNCT
ejpam-3294	162	22	fxn	fxn	NOUN
ejpam-3294	162	23	)	)	PUNCT
ejpam-3294	162	24	,	,	PUNCT
ejpam-3294	162	25	σ(xn−1	σ(xn−1	PROPN
ejpam-3294	162	26	,	,	PUNCT
ejpam-3294	162	27	fxn	fxn	NOUN
ejpam-3294	162	28	)	)	PUNCT
ejpam-3294	163	1	+	+	CCONJ
ejpam-3294	163	2	σ(fxn−1	σ(fxn−1	PROPN
ejpam-3294	163	3	,	,	PUNCT
ejpam-3294	163	4	xn	xn	PROPN
ejpam-3294	163	5	4	4	NUM
ejpam-3294	163	6	,	,	PUNCT
ejpam-3294	163	7	[	[	X
ejpam-3294	163	8	1	1	NUM
ejpam-3294	163	9	+	+	SYM
ejpam-3294	163	10	σ(xn−1	σ(xn−1	NOUN
ejpam-3294	163	11	,	,	PUNCT
ejpam-3294	163	12	fxn−1)]σ(xn	fxn−1)]σ(xn	PROPN
ejpam-3294	163	13	,	,	PUNCT
ejpam-3294	163	14	fxn	fxn	NOUN
ejpam-3294	163	15	)	)	PUNCT
ejpam-3294	163	16	σ(xn−1	σ(xn−1	PROPN
ejpam-3294	163	17	,	,	PUNCT
ejpam-3294	163	18	xn	xn	PUNCT
ejpam-3294	163	19	)	)	PUNCT
ejpam-3294	164	1	+	+	CCONJ
ejpam-3294	164	2	1	1	X
ejpam-3294	164	3	}	}	PUNCT
ejpam-3294	164	4	=	=	SYM
ejpam-3294	164	5	max{σ(xn−1	max{σ(xn−1	PROPN
ejpam-3294	164	6	,	,	PUNCT
ejpam-3294	164	7	xn	xn	PROPN
ejpam-3294	164	8	)	)	PUNCT
ejpam-3294	164	9	,	,	PUNCT
ejpam-3294	164	10	σ(xn−1	σ(xn−1	PROPN
ejpam-3294	164	11	,	,	PUNCT
ejpam-3294	164	12	xn	xn	NUM
ejpam-3294	164	13	)	)	PUNCT
ejpam-3294	164	14	,	,	PUNCT
ejpam-3294	164	15	σ(xn	σ(xn	X
ejpam-3294	164	16	,	,	PUNCT
ejpam-3294	164	17	xn+1	xn+1	NUM
ejpam-3294	164	18	)	)	PUNCT
ejpam-3294	164	19	,	,	PUNCT
ejpam-3294	164	20	σ(xn−1	σ(xn−1	PROPN
ejpam-3294	164	21	,	,	PUNCT
ejpam-3294	164	22	xn+1	xn+1	NUM
ejpam-3294	164	23	)	)	PUNCT
ejpam-3294	165	1	+	+	CCONJ
ejpam-3294	165	2	σ(xn	σ(xn	NOUN
ejpam-3294	165	3	,	,	PUNCT
ejpam-3294	165	4	xn	xn	PROPN
ejpam-3294	165	5	4	4	NUM
ejpam-3294	165	6	,	,	PUNCT
ejpam-3294	165	7	[	[	X
ejpam-3294	165	8	1	1	NUM
ejpam-3294	165	9	+	+	NUM
ejpam-3294	165	10	σ(xn−1	σ(xn−1	NUM
ejpam-3294	165	11	,	,	PUNCT
ejpam-3294	165	12	xn)]σ(xn	xn)]σ(xn	PROPN
ejpam-3294	165	13	,	,	PUNCT
ejpam-3294	165	14	xn+1	xn+1	NUM
ejpam-3294	165	15	)	)	PUNCT
ejpam-3294	165	16	σ(xn−1	σ(xn−1	NOUN
ejpam-3294	165	17	,	,	PUNCT
ejpam-3294	165	18	xn	xn	PUNCT
ejpam-3294	165	19	)	)	PUNCT
ejpam-3294	166	1	+	+	CCONJ
ejpam-3294	166	2	1	1	X
ejpam-3294	166	3	}	}	PUNCT
ejpam-3294	166	4	=	=	SYM
ejpam-3294	166	5	max{σ(xn−1	max{σ(xn−1	PROPN
ejpam-3294	166	6	,	,	PUNCT
ejpam-3294	166	7	xn	xn	PROPN
ejpam-3294	166	8	)	)	PUNCT
ejpam-3294	166	9	,	,	PUNCT
ejpam-3294	166	10	σ(xn	σ(xn	X
ejpam-3294	166	11	,	,	PUNCT
ejpam-3294	166	12	xn+1	xn+1	NUM
ejpam-3294	166	13	)	)	PUNCT
ejpam-3294	166	14	,	,	PUNCT
ejpam-3294	166	15	σ(xn−1	σ(xn−1	X
ejpam-3294	166	16	,	,	PUNCT
ejpam-3294	166	17	xn+1	xn+1	NUM
ejpam-3294	166	18	)	)	PUNCT
ejpam-3294	166	19	4	4	NUM
ejpam-3294	166	20	,	,	PUNCT
ejpam-3294	166	21	σ(xn	σ(xn	NUM
ejpam-3294	166	22	,	,	PUNCT
ejpam-3294	166	23	xn+1	xn+1	NUM
ejpam-3294	166	24	)	)	PUNCT
ejpam-3294	166	25	}	}	PUNCT
ejpam-3294	166	26	<	<	X
ejpam-3294	166	27	max{σ(xn−1	max{σ(xn−1	PROPN
ejpam-3294	166	28	,	,	PUNCT
ejpam-3294	166	29	xn	xn	PROPN
ejpam-3294	166	30	)	)	PUNCT
ejpam-3294	166	31	,	,	PUNCT
ejpam-3294	166	32	σ(xn	σ(xn	X
ejpam-3294	166	33	,	,	PUNCT
ejpam-3294	166	34	xn+1	xn+1	NUM
ejpam-3294	166	35	)	)	PUNCT
ejpam-3294	166	36	,	,	PUNCT
ejpam-3294	166	37	σ(xn−1	σ(xn−1	PROPN
ejpam-3294	166	38	,	,	PUNCT
ejpam-3294	166	39	xn	xn	PUNCT
ejpam-3294	166	40	)	)	PUNCT
ejpam-3294	167	1	+	+	CCONJ
ejpam-3294	167	2	σ(xn	σ(xn	NOUN
ejpam-3294	167	3	,	,	PUNCT
ejpam-3294	167	4	xn+1	xn+1	NUM
ejpam-3294	167	5	)	)	PUNCT
ejpam-3294	167	6	4	4	NUM
ejpam-3294	167	7	}	}	PUNCT
ejpam-3294	167	8	=	=	SYM
ejpam-3294	167	9	max{σ(xn−1	max{σ(xn−1	PROPN
ejpam-3294	167	10	,	,	PUNCT
ejpam-3294	167	11	xn	xn	PROPN
ejpam-3294	167	12	)	)	PUNCT
ejpam-3294	167	13	,	,	PUNCT
ejpam-3294	167	14	σ(xn	σ(xn	X
ejpam-3294	167	15	,	,	PUNCT
ejpam-3294	167	16	xn+1	xn+1	NUM
ejpam-3294	167	17	)	)	PUNCT
ejpam-3294	167	18	,	,	PUNCT
ejpam-3294	167	19	σ(xn−1	σ(xn−1	PROPN
ejpam-3294	167	20	,	,	PUNCT
ejpam-3294	167	21	xn	xn	PUNCT
ejpam-3294	167	22	)	)	PUNCT
ejpam-3294	168	1	+	+	CCONJ
ejpam-3294	168	2	σ(xn	σ(xn	NOUN
ejpam-3294	168	3	,	,	PUNCT
ejpam-3294	168	4	xn+1	xn+1	NUM
ejpam-3294	168	5	)	)	PUNCT
ejpam-3294	168	6	4	4	NUM
ejpam-3294	168	7	}	}	PUNCT
ejpam-3294	168	8	=	=	SYM
ejpam-3294	168	9	max{σ(xn−1	max{σ(xn−1	PROPN
ejpam-3294	168	10	,	,	PUNCT
ejpam-3294	168	11	xn	xn	PROPN
ejpam-3294	168	12	)	)	PUNCT
ejpam-3294	168	13	,	,	PUNCT
ejpam-3294	168	14	σ(xn	σ(xn	X
ejpam-3294	168	15	,	,	PUNCT
ejpam-3294	168	16	xn+1	xn+1	NUM
ejpam-3294	168	17	)	)	PUNCT
ejpam-3294	168	18	}	}	PUNCT
ejpam-3294	168	19	.	.	PUNCT
ejpam-3294	169	1	(	(	PUNCT
ejpam-3294	169	2	9	9	X
ejpam-3294	169	3	)	)	PUNCT
ejpam-3294	169	4	if	if	SCONJ
ejpam-3294	169	5	max{σ(xn−1	max{σ(xn−1	PROPN
ejpam-3294	169	6	,	,	PUNCT
ejpam-3294	169	7	xn	xn	PROPN
ejpam-3294	169	8	)	)	PUNCT
ejpam-3294	169	9	,	,	PUNCT
ejpam-3294	169	10	σ(xn	σ(xn	X
ejpam-3294	169	11	,	,	PUNCT
ejpam-3294	169	12	xn+1	xn+1	NUM
ejpam-3294	169	13	)	)	PUNCT
ejpam-3294	169	14	}	}	PUNCT
ejpam-3294	170	1	=	=	PUNCT
ejpam-3294	170	2	σ(xn−1	σ(xn−1	PROPN
ejpam-3294	170	3	,	,	PUNCT
ejpam-3294	170	4	xn	xn	PROPN
ejpam-3294	170	5	)	)	PUNCT
ejpam-3294	170	6	,	,	PUNCT
ejpam-3294	170	7	then	then	ADV
ejpam-3294	170	8	f	f	X
ejpam-3294	170	9	(	(	PUNCT
ejpam-3294	170	10	σ(xn−1	σ(xn−1	PROPN
ejpam-3294	170	11	,	,	PUNCT
ejpam-3294	170	12	xn	xn	NUM
ejpam-3294	170	13	)	)	PUNCT
ejpam-3294	170	14	)	)	PUNCT
ejpam-3294	170	15	≤	≤	NUM
ejpam-3294	171	1	β(σ(xn−1	β(σ(xn−1	PROPN
ejpam-3294	171	2	,	,	PUNCT
ejpam-3294	171	3	xn))f	xn))f	PROPN
ejpam-3294	171	4	(	(	PUNCT
ejpam-3294	171	5	σ(xn−1	σ(xn−1	PROPN
ejpam-3294	171	6	,	,	PUNCT
ejpam-3294	171	7	xn)−	xn)−	X
ejpam-3294	171	8	τ	τ	PROPN
ejpam-3294	171	9	≤	≤	PROPN
ejpam-3294	171	10	f	f	X
ejpam-3294	171	11	(	(	PUNCT
ejpam-3294	171	12	σ(xn−1	σ(xn−1	PROPN
ejpam-3294	171	13	,	,	PUNCT
ejpam-3294	171	14	xn	xn	PROPN
ejpam-3294	171	15	)	)	PUNCT
ejpam-3294	171	16	)	)	PUNCT
ejpam-3294	171	17	,	,	PUNCT
ejpam-3294	171	18	which	which	PRON
ejpam-3294	171	19	is	be	AUX
ejpam-3294	171	20	a	a	DET
ejpam-3294	171	21	contradiction	contradiction	NOUN
ejpam-3294	171	22	.	.	PUNCT
ejpam-3294	172	1	thus	thus	ADV
ejpam-3294	172	2	,	,	PUNCT
ejpam-3294	172	3	we	we	PRON
ejpam-3294	172	4	conclude	conclude	VERB
ejpam-3294	172	5	that	that	SCONJ
ejpam-3294	172	6	max{σ(xn−1	max{σ(xn−1	PROPN
ejpam-3294	172	7	,	,	PUNCT
ejpam-3294	172	8	xn	xn	PROPN
ejpam-3294	172	9	)	)	PUNCT
ejpam-3294	172	10	,	,	PUNCT
ejpam-3294	172	11	σ(xn	σ(xn	X
ejpam-3294	172	12	,	,	PUNCT
ejpam-3294	172	13	xn+1	xn+1	NUM
ejpam-3294	172	14	)	)	PUNCT
ejpam-3294	172	15	}	}	PUNCT
ejpam-3294	172	16	=	=	SYM
ejpam-3294	172	17	σ(xn	σ(xn	NOUN
ejpam-3294	172	18	,	,	PUNCT
ejpam-3294	172	19	xn+1	xn+1	NUM
ejpam-3294	172	20	)	)	PUNCT
ejpam-3294	172	21	,	,	PUNCT
ejpam-3294	172	22	for	for	ADP
ejpam-3294	172	23	all	all	DET
ejpam-3294	172	24	n	n	PRON
ejpam-3294	172	25	∈	∈	PROPN
ejpam-3294	172	26	n.	n.	NOUN
ejpam-3294	173	1	then	then	ADV
ejpam-3294	173	2	f	f	X
ejpam-3294	173	3	(	(	PUNCT
ejpam-3294	173	4	σ(xn	σ(xn	X
ejpam-3294	173	5	,	,	PUNCT
ejpam-3294	173	6	xn+1	xn+1	NUM
ejpam-3294	173	7	)	)	PUNCT
ejpam-3294	173	8	)	)	PUNCT
ejpam-3294	173	9	≤	≤	NUM
ejpam-3294	173	10	f	f	X
ejpam-3294	173	11	(	(	PUNCT
ejpam-3294	173	12	σ(xn	σ(xn	NUM
ejpam-3294	173	13	,	,	PUNCT
ejpam-3294	173	14	xn+1))−	xn+1))−	PROPN
ejpam-3294	173	15	τ	τ	PROPN
ejpam-3294	173	16	,	,	PUNCT
ejpam-3294	173	17	for	for	ADP
ejpam-3294	173	18	all	all	DET
ejpam-3294	173	19	n	n	PRON
ejpam-3294	173	20	∈	∈	PROPN
ejpam-3294	173	21	n.	n.	NOUN
ejpam-3294	173	22	repeating	repeat	VERB
ejpam-3294	173	23	this	this	DET
ejpam-3294	173	24	process	process	NOUN
ejpam-3294	173	25	,	,	PUNCT
ejpam-3294	173	26	we	we	PRON
ejpam-3294	173	27	obtain	obtain	VERB
ejpam-3294	173	28	f	f	X
ejpam-3294	173	29	(	(	PUNCT
ejpam-3294	173	30	σ(xn	σ(xn	X
ejpam-3294	173	31	,	,	PUNCT
ejpam-3294	173	32	xn+1	xn+1	NUM
ejpam-3294	173	33	)	)	PUNCT
ejpam-3294	173	34	)	)	PUNCT
ejpam-3294	174	1	≤	≤	NUM
ejpam-3294	174	2	f	f	X
ejpam-3294	174	3	(	(	PUNCT
ejpam-3294	174	4	σ(x0	σ(x0	PROPN
ejpam-3294	174	5	,	,	PUNCT
ejpam-3294	174	6	x1))−	x1))−	ADJ
ejpam-3294	174	7	nτ	nτ	ADJ
ejpam-3294	174	8	(	(	PUNCT
ejpam-3294	174	9	10	10	NUM
ejpam-3294	174	10	)	)	PUNCT
ejpam-3294	174	11	by	by	ADP
ejpam-3294	174	12	taking	take	VERB
ejpam-3294	174	13	n→∞	n→∞	PRON
ejpam-3294	174	14	in	in	ADP
ejpam-3294	174	15	(	(	PUNCT
ejpam-3294	174	16	2.11	2.11	NUM
ejpam-3294	174	17	)	)	PUNCT
ejpam-3294	174	18	that	that	PRON
ejpam-3294	174	19	shows	show	VERB
ejpam-3294	174	20	limn→∞	limn→∞	PROPN
ejpam-3294	174	21	f	f	X
ejpam-3294	174	22	(	(	PUNCT
ejpam-3294	174	23	σ(xn	σ(xn	X
ejpam-3294	174	24	,	,	PUNCT
ejpam-3294	174	25	xn+1	xn+1	NUM
ejpam-3294	174	26	)	)	PUNCT
ejpam-3294	174	27	)	)	PUNCT
ejpam-3294	175	1	=	=	PUNCT
ejpam-3294	175	2	−∞	−∞	NOUN
ejpam-3294	175	3	,	,	PUNCT
ejpam-3294	175	4	hence	hence	ADV
ejpam-3294	175	5	lim	lim	PROPN
ejpam-3294	175	6	n→∞	n→∞	NUM
ejpam-3294	175	7	σ(xn	σ(xn	NOUN
ejpam-3294	175	8	,	,	PUNCT
ejpam-3294	175	9	xn+1	xn+1	NUM
ejpam-3294	175	10	)	)	PUNCT
ejpam-3294	175	11	=	=	SYM
ejpam-3294	175	12	0	0	X
ejpam-3294	175	13	.	.	PUNCT
ejpam-3294	176	1	(	(	PUNCT
ejpam-3294	176	2	11	11	NUM
ejpam-3294	176	3	)	)	PUNCT
ejpam-3294	176	4	now	now	ADV
ejpam-3294	176	5	,	,	PUNCT
ejpam-3294	176	6	by	by	ADP
ejpam-3294	176	7	lemma	lemma	PROPN
ejpam-3294	176	8	2	2	NUM
ejpam-3294	176	9	,	,	PUNCT
ejpam-3294	176	10	{	{	PUNCT
ejpam-3294	176	11	xn	xn	X
ejpam-3294	176	12	}	}	PUNCT
ejpam-3294	176	13	is	be	AUX
ejpam-3294	176	14	a	a	DET
ejpam-3294	176	15	cauchy	cauchy	ADJ
ejpam-3294	176	16	sequence	sequence	NOUN
ejpam-3294	176	17	.	.	PUNCT
ejpam-3294	177	1	since	since	SCONJ
ejpam-3294	177	2	x	x	PRON
ejpam-3294	177	3	is	be	AUX
ejpam-3294	177	4	complete	complete	ADJ
ejpam-3294	177	5	,	,	PUNCT
ejpam-3294	177	6	there	there	PRON
ejpam-3294	177	7	exists	exist	VERB
ejpam-3294	177	8	z	z	NOUN
ejpam-3294	177	9	∈	∈	PROPN
ejpam-3294	177	10	x	x	PUNCT
ejpam-3294	177	11	such	such	ADJ
ejpam-3294	177	12	that	that	SCONJ
ejpam-3294	177	13	lim	lim	PROPN
ejpam-3294	177	14	n→∞	n→∞	NUM
ejpam-3294	177	15	σ(xn	σ(xn	NOUN
ejpam-3294	177	16	,	,	PUNCT
ejpam-3294	177	17	z	z	NOUN
ejpam-3294	177	18	)	)	PUNCT
ejpam-3294	177	19	=	=	SYM
ejpam-3294	177	20	σ(z	σ(z	PROPN
ejpam-3294	177	21	,	,	PUNCT
ejpam-3294	177	22	z	z	NOUN
ejpam-3294	177	23	)	)	PUNCT
ejpam-3294	177	24	=	=	SYM
ejpam-3294	177	25	lim	lim	PROPN
ejpam-3294	177	26	n	n	CCONJ
ejpam-3294	177	27	,	,	PUNCT
ejpam-3294	177	28	m→∞	m→∞	NOUN
ejpam-3294	177	29	σ(xn	σ(xn	NOUN
ejpam-3294	177	30	,	,	PUNCT
ejpam-3294	177	31	xm	xm	PROPN
ejpam-3294	177	32	)	)	PUNCT
ejpam-3294	178	1	=	=	SYM
ejpam-3294	178	2	0	0	X
ejpam-3294	178	3	.	.	PUNCT
ejpam-3294	179	1	(	(	PUNCT
ejpam-3294	179	2	12	12	NUM
ejpam-3294	179	3	)	)	PUNCT
ejpam-3294	179	4	h.	h.	PROPN
ejpam-3294	179	5	qawaqneh	qawaqneh	PROPN
ejpam-3294	179	6	,	,	PUNCT
ejpam-3294	179	7	m.s	m.s	PROPN
ejpam-3294	179	8	.	.	PROPN
ejpam-3294	179	9	noorani	noorani	PROPN
ejpam-3294	179	10	,	,	PUNCT
ejpam-3294	179	11	w.	w.	PROPN
ejpam-3294	179	12	shatanawi	shatanawi	PROPN
ejpam-3294	179	13	/	/	SYM
ejpam-3294	179	14	eur	eur	PROPN
ejpam-3294	179	15	.	.	PUNCT
ejpam-3294	180	1	j.	j.	PROPN
ejpam-3294	180	2	pure	pure	PROPN
ejpam-3294	180	3	appl	appl	PROPN
ejpam-3294	180	4	.	.	PROPN
ejpam-3294	180	5	math	math	PROPN
ejpam-3294	180	6	,	,	PUNCT
ejpam-3294	180	7	11	11	NUM
ejpam-3294	180	8	(	(	PUNCT
ejpam-3294	180	9	3	3	NUM
ejpam-3294	180	10	)	)	PUNCT
ejpam-3294	180	11	(	(	PUNCT
ejpam-3294	180	12	2018	2018	NUM
ejpam-3294	180	13	)	)	PUNCT
ejpam-3294	180	14	,	,	PUNCT
ejpam-3294	180	15	702	702	NUM
ejpam-3294	180	16	-	-	SYM
ejpam-3294	180	17	716	716	NUM
ejpam-3294	180	18	709	709	NUM
ejpam-3294	180	19	since	since	SCONJ
ejpam-3294	180	20	f	f	PROPN
ejpam-3294	180	21	is	be	AUX
ejpam-3294	180	22	continuous	continuous	ADJ
ejpam-3294	180	23	,	,	PUNCT
ejpam-3294	180	24	we	we	PRON
ejpam-3294	180	25	claim	claim	VERB
ejpam-3294	180	26	z	z	NOUN
ejpam-3294	180	27	=	=	SYM
ejpam-3294	180	28	fz	fz	PROPN
ejpam-3294	180	29	.	.	PROPN
ejpam-3294	181	1	assume	assume	VERB
ejpam-3294	181	2	the	the	DET
ejpam-3294	181	3	contrary	contrary	NOUN
ejpam-3294	181	4	,	,	PUNCT
ejpam-3294	181	5	that	that	ADV
ejpam-3294	181	6	is	be	AUX
ejpam-3294	181	7	z	z	PROPN
ejpam-3294	181	8	6=	6=	NUM
ejpam-3294	181	9	fz	fz	PROPN
ejpam-3294	181	10	.	.	PUNCT
ejpam-3294	182	1	in	in	ADP
ejpam-3294	182	2	this	this	DET
ejpam-3294	182	3	case	case	NOUN
ejpam-3294	182	4	,	,	PUNCT
ejpam-3294	182	5	there	there	PRON
ejpam-3294	182	6	exists	exist	VERB
ejpam-3294	182	7	a	a	DET
ejpam-3294	182	8	sequence	sequence	NOUN
ejpam-3294	182	9	{	{	PUNCT
ejpam-3294	182	10	xn	xn	NOUN
ejpam-3294	182	11	}	}	PUNCT
ejpam-3294	182	12	for	for	ADP
ejpam-3294	182	13	n0	n0	PROPN
ejpam-3294	182	14	∈	∈	PROPN
ejpam-3294	182	15	n	n	PRON
ejpam-3294	182	16	such	such	ADJ
ejpam-3294	182	17	that	that	DET
ejpam-3294	182	18	σ(fxn	σ(fxn	PROPN
ejpam-3294	182	19	,	,	PUNCT
ejpam-3294	182	20	fz	fz	PROPN
ejpam-3294	182	21	)	)	PUNCT
ejpam-3294	182	22	>	>	X
ejpam-3294	182	23	0	0	PUNCT
ejpam-3294	183	1	for	for	ADP
ejpam-3294	183	2	all	all	DET
ejpam-3294	183	3	n	n	PRON
ejpam-3294	183	4	≥	≥	NOUN
ejpam-3294	183	5	n0	n0	NUM
ejpam-3294	183	6	.	.	PUNCT
ejpam-3294	184	1	then	then	ADV
ejpam-3294	184	2	from	from	ADP
ejpam-3294	184	3	our	our	PRON
ejpam-3294	184	4	assumption	assumption	NOUN
ejpam-3294	184	5	(	(	PUNCT
ejpam-3294	184	6	with	with	ADP
ejpam-3294	184	7	n	n	PRON
ejpam-3294	184	8	≥	≥	NOUN
ejpam-3294	184	9	n0	n0	NUM
ejpam-3294	184	10	)	)	PUNCT
ejpam-3294	184	11	,	,	PUNCT
ejpam-3294	184	12	we	we	PRON
ejpam-3294	184	13	have	have	VERB
ejpam-3294	184	14	τ	τ	PROPN
ejpam-3294	185	1	+	+	NUM
ejpam-3294	185	2	f	f	X
ejpam-3294	185	3	(	(	PUNCT
ejpam-3294	185	4	σ(xn+1	σ(xn+1	PROPN
ejpam-3294	185	5	,	,	PUNCT
ejpam-3294	185	6	fz	fz	NOUN
ejpam-3294	185	7	)	)	PUNCT
ejpam-3294	185	8	)	)	PUNCT
ejpam-3294	185	9	=	=	PUNCT
ejpam-3294	186	1	τ	τ	X
ejpam-3294	187	1	+	+	NUM
ejpam-3294	187	2	f	f	X
ejpam-3294	187	3	(	(	PUNCT
ejpam-3294	187	4	σ(fxn	σ(fxn	PROPN
ejpam-3294	187	5	,	,	PUNCT
ejpam-3294	187	6	fz	fz	NOUN
ejpam-3294	187	7	)	)	PUNCT
ejpam-3294	187	8	)	)	PUNCT
ejpam-3294	187	9	≤	≤	PROPN
ejpam-3294	188	1	α(xn	α(xn	NUM
ejpam-3294	188	2	,	,	PUNCT
ejpam-3294	188	3	z)(τ	z)(τ	PUNCT
ejpam-3294	189	1	+	+	CCONJ
ejpam-3294	189	2	f	f	X
ejpam-3294	189	3	(	(	PUNCT
ejpam-3294	189	4	σ(xn	σ(xn	X
ejpam-3294	189	5	,	,	PUNCT
ejpam-3294	189	6	fz	fz	NOUN
ejpam-3294	189	7	)	)	PUNCT
ejpam-3294	189	8	)	)	PUNCT
ejpam-3294	189	9	)	)	PUNCT
ejpam-3294	189	10	≤	≤	NUM
ejpam-3294	189	11	β(mxn	β(mxn	NOUN
ejpam-3294	189	12	,	,	PUNCT
ejpam-3294	189	13	z)f	z)f	X
ejpam-3294	189	14	(	(	PUNCT
ejpam-3294	189	15	mxn	mxn	PROPN
ejpam-3294	189	16	,	,	PUNCT
ejpam-3294	189	17	z	z	NOUN
ejpam-3294	189	18	)	)	PUNCT
ejpam-3294	189	19	,	,	PUNCT
ejpam-3294	189	20	(	(	PUNCT
ejpam-3294	189	21	13	13	NUM
ejpam-3294	189	22	)	)	PUNCT
ejpam-3294	189	23	where	where	SCONJ
ejpam-3294	189	24	mxn	mxn	PROPN
ejpam-3294	189	25	,	,	PUNCT
ejpam-3294	189	26	z	z	PROPN
ejpam-3294	189	27	=	=	SYM
ejpam-3294	189	28	max{σ(xn	max{σ(xn	PROPN
ejpam-3294	189	29	,	,	PUNCT
ejpam-3294	189	30	z	z	NOUN
ejpam-3294	189	31	)	)	PUNCT
ejpam-3294	189	32	,	,	PUNCT
ejpam-3294	189	33	σ(xn	σ(xn	NUM
ejpam-3294	189	34	,	,	PUNCT
ejpam-3294	189	35	fxn	fxn	NOUN
ejpam-3294	189	36	)	)	PUNCT
ejpam-3294	189	37	,	,	PUNCT
ejpam-3294	189	38	σ(z	σ(z	PROPN
ejpam-3294	189	39	,	,	PUNCT
ejpam-3294	189	40	fz	fz	NOUN
ejpam-3294	189	41	)	)	PUNCT
ejpam-3294	189	42	,	,	PUNCT
ejpam-3294	189	43	σ(fxn	σ(fxn	PROPN
ejpam-3294	189	44	,	,	PUNCT
ejpam-3294	189	45	z	z	NOUN
ejpam-3294	189	46	)	)	PUNCT
ejpam-3294	189	47	+	+	CCONJ
ejpam-3294	189	48	σ(xn	σ(xn	NUM
ejpam-3294	189	49	,	,	PUNCT
ejpam-3294	189	50	fz	fz	NOUN
ejpam-3294	189	51	)	)	PUNCT
ejpam-3294	189	52	4	4	NUM
ejpam-3294	189	53	,	,	PUNCT
ejpam-3294	189	54	[	[	X
ejpam-3294	189	55	1	1	NUM
ejpam-3294	189	56	+	+	NUM
ejpam-3294	189	57	σ(xn	σ(xn	NOUN
ejpam-3294	189	58	,	,	PUNCT
ejpam-3294	189	59	fxn)]σ(z	fxn)]σ(z	PROPN
ejpam-3294	189	60	,	,	PUNCT
ejpam-3294	189	61	fz	fz	NOUN
ejpam-3294	189	62	)	)	PUNCT
ejpam-3294	189	63	σ(xn	σ(xn	PROPN
ejpam-3294	189	64	,	,	PUNCT
ejpam-3294	189	65	z	z	NOUN
ejpam-3294	189	66	)	)	PUNCT
ejpam-3294	190	1	+	+	CCONJ
ejpam-3294	190	2	1	1	X
ejpam-3294	190	3	}	}	PUNCT
ejpam-3294	190	4	=	=	SYM
ejpam-3294	190	5	max{σ(xn	max{σ(xn	PROPN
ejpam-3294	190	6	,	,	PUNCT
ejpam-3294	190	7	z	z	NOUN
ejpam-3294	190	8	)	)	PUNCT
ejpam-3294	190	9	,	,	PUNCT
ejpam-3294	190	10	σ(xn	σ(xn	X
ejpam-3294	190	11	,	,	PUNCT
ejpam-3294	190	12	xn+1	xn+1	NUM
ejpam-3294	190	13	)	)	PUNCT
ejpam-3294	190	14	,	,	PUNCT
ejpam-3294	190	15	σ(z	σ(z	PROPN
ejpam-3294	190	16	,	,	PUNCT
ejpam-3294	190	17	fz	fz	NOUN
ejpam-3294	190	18	)	)	PUNCT
ejpam-3294	190	19	,	,	PUNCT
ejpam-3294	190	20	σ(xn+1	σ(xn+1	PROPN
ejpam-3294	190	21	,	,	PUNCT
ejpam-3294	190	22	z	z	NOUN
ejpam-3294	190	23	)	)	PUNCT
ejpam-3294	191	1	+	+	CCONJ
ejpam-3294	191	2	σ(xn	σ(xn	NUM
ejpam-3294	191	3	,	,	PUNCT
ejpam-3294	191	4	fz	fz	NOUN
ejpam-3294	191	5	)	)	PUNCT
ejpam-3294	191	6	4	4	NUM
ejpam-3294	191	7	,	,	PUNCT
ejpam-3294	191	8	[	[	X
ejpam-3294	191	9	1	1	NUM
ejpam-3294	191	10	+	+	NUM
ejpam-3294	191	11	σ(xn	σ(xn	NOUN
ejpam-3294	191	12	,	,	PUNCT
ejpam-3294	191	13	xn+1)]σ(z	xn+1)]σ(z	PROPN
ejpam-3294	191	14	,	,	PUNCT
ejpam-3294	191	15	fz	fz	PROPN
ejpam-3294	191	16	)	)	PUNCT
ejpam-3294	191	17	σ(xn	σ(xn	PROPN
ejpam-3294	191	18	,	,	PUNCT
ejpam-3294	191	19	z	z	NOUN
ejpam-3294	191	20	)	)	PUNCT
ejpam-3294	192	1	+	+	CCONJ
ejpam-3294	192	2	1	1	NUM
ejpam-3294	192	3	}	}	PUNCT
ejpam-3294	192	4	.	.	PUNCT
ejpam-3294	193	1	(	(	PUNCT
ejpam-3294	193	2	14	14	NUM
ejpam-3294	193	3	)	)	PUNCT
ejpam-3294	193	4	by	by	ADP
ejpam-3294	193	5	taking	take	VERB
ejpam-3294	193	6	n→∞	n→∞	NUM
ejpam-3294	193	7	,	,	PUNCT
ejpam-3294	193	8	we	we	PRON
ejpam-3294	193	9	get	get	VERB
ejpam-3294	193	10	lim	lim	PROPN
ejpam-3294	193	11	n→∞	n→∞	X
ejpam-3294	193	12	mxn	mxn	PROPN
ejpam-3294	193	13	,	,	PUNCT
ejpam-3294	193	14	z	z	PROPN
ejpam-3294	193	15	=	=	SYM
ejpam-3294	193	16	max{σ(z	max{σ(z	PROPN
ejpam-3294	193	17	,	,	PUNCT
ejpam-3294	193	18	z	z	NOUN
ejpam-3294	193	19	)	)	PUNCT
ejpam-3294	193	20	,	,	PUNCT
ejpam-3294	193	21	σ(z	σ(z	PROPN
ejpam-3294	193	22	,	,	PUNCT
ejpam-3294	193	23	fz	fz	NOUN
ejpam-3294	193	24	)	)	PUNCT
ejpam-3294	193	25	,	,	PUNCT
ejpam-3294	193	26	σ(z	σ(z	PROPN
ejpam-3294	193	27	,	,	PUNCT
ejpam-3294	193	28	fz	fz	NOUN
ejpam-3294	193	29	)	)	PUNCT
ejpam-3294	193	30	,	,	PUNCT
ejpam-3294	193	31	σ(fz	σ(fz	PROPN
ejpam-3294	193	32	,	,	PUNCT
ejpam-3294	193	33	z	z	NOUN
ejpam-3294	193	34	)	)	PUNCT
ejpam-3294	194	1	+	+	CCONJ
ejpam-3294	194	2	σ(z	σ(z	NOUN
ejpam-3294	194	3	,	,	PUNCT
ejpam-3294	194	4	fz	fz	NOUN
ejpam-3294	194	5	)	)	PUNCT
ejpam-3294	194	6	4	4	NUM
ejpam-3294	194	7	,	,	PUNCT
ejpam-3294	194	8	[	[	X
ejpam-3294	194	9	1	1	NUM
ejpam-3294	194	10	+	+	NUM
ejpam-3294	194	11	σ(z	σ(z	NOUN
ejpam-3294	194	12	,	,	PUNCT
ejpam-3294	194	13	fz)]σ(z	fz)]σ(z	NOUN
ejpam-3294	194	14	,	,	PUNCT
ejpam-3294	194	15	fz	fz	NOUN
ejpam-3294	194	16	)	)	PUNCT
ejpam-3294	194	17	σ(z	σ(z	PROPN
ejpam-3294	194	18	,	,	PUNCT
ejpam-3294	194	19	z	z	NOUN
ejpam-3294	194	20	)	)	PUNCT
ejpam-3294	195	1	+	+	CCONJ
ejpam-3294	195	2	1	1	X
ejpam-3294	195	3	}	}	PUNCT
ejpam-3294	195	4	=	=	SYM
ejpam-3294	195	5	max{σ(z	max{σ(z	PROPN
ejpam-3294	195	6	,	,	PUNCT
ejpam-3294	195	7	fz	fz	NOUN
ejpam-3294	195	8	)	)	PUNCT
ejpam-3294	195	9	,	,	PUNCT
ejpam-3294	195	10	σ(z	σ(z	PROPN
ejpam-3294	195	11	,	,	PUNCT
ejpam-3294	195	12	fz	fz	NOUN
ejpam-3294	195	13	)	)	PUNCT
ejpam-3294	195	14	4	4	NUM
ejpam-3294	195	15	}	}	PUNCT
ejpam-3294	195	16	=	=	SYM
ejpam-3294	195	17	σ(z	σ(z	PROPN
ejpam-3294	195	18	,	,	PUNCT
ejpam-3294	195	19	fz	fz	NOUN
ejpam-3294	195	20	)	)	PUNCT
ejpam-3294	195	21	.	.	PUNCT
ejpam-3294	196	1	(	(	PUNCT
ejpam-3294	196	2	15	15	NUM
ejpam-3294	196	3	)	)	PUNCT
ejpam-3294	196	4	therefore	therefore	ADV
ejpam-3294	196	5	,	,	PUNCT
ejpam-3294	196	6	by	by	ADP
ejpam-3294	196	7	taking	take	VERB
ejpam-3294	196	8	the	the	DET
ejpam-3294	196	9	limits	limit	NOUN
ejpam-3294	196	10	as	as	ADP
ejpam-3294	196	11	n→∞	n→∞	NUM
ejpam-3294	196	12	in	in	ADP
ejpam-3294	196	13	(	(	PUNCT
ejpam-3294	196	14	2.12	2.12	NUM
ejpam-3294	196	15	)	)	PUNCT
ejpam-3294	196	16	,	,	PUNCT
ejpam-3294	196	17	we	we	PRON
ejpam-3294	196	18	get	get	VERB
ejpam-3294	196	19	f	f	PROPN
ejpam-3294	196	20	(	(	PUNCT
ejpam-3294	196	21	σ(z	σ(z	PROPN
ejpam-3294	196	22	,	,	PUNCT
ejpam-3294	196	23	fz	fz	NOUN
ejpam-3294	196	24	)	)	PUNCT
ejpam-3294	196	25	)	)	PUNCT
ejpam-3294	196	26	≤	≤	NOUN
ejpam-3294	196	27	β(σ(z	β(σ(z	PROPN
ejpam-3294	196	28	,	,	PUNCT
ejpam-3294	196	29	fz)))f	fz)))f	NUM
ejpam-3294	196	30	(	(	PUNCT
ejpam-3294	196	31	σ(z	σ(z	PROPN
ejpam-3294	196	32	,	,	PUNCT
ejpam-3294	196	33	fz))−	fz))−	NOUN
ejpam-3294	196	34	τ	τ	X
ejpam-3294	196	35	≤	≤	PROPN
ejpam-3294	196	36	f	f	X
ejpam-3294	196	37	(	(	PUNCT
ejpam-3294	196	38	σ(z	σ(z	PROPN
ejpam-3294	196	39	,	,	PUNCT
ejpam-3294	196	40	fz))−	fz))−	NOUN
ejpam-3294	196	41	τ	τ	NOUN
ejpam-3294	196	42	,	,	PUNCT
ejpam-3294	196	43	(	(	PUNCT
ejpam-3294	196	44	16	16	NUM
ejpam-3294	196	45	)	)	PUNCT
ejpam-3294	196	46	which	which	PRON
ejpam-3294	196	47	gives	give	VERB
ejpam-3294	196	48	a	a	DET
ejpam-3294	196	49	contradiction	contradiction	NOUN
ejpam-3294	196	50	.	.	PUNCT
ejpam-3294	197	1	hence	hence	ADV
ejpam-3294	197	2	,	,	PUNCT
ejpam-3294	197	3	we	we	PRON
ejpam-3294	197	4	conclude	conclude	VERB
ejpam-3294	197	5	z	z	NOUN
ejpam-3294	197	6	is	be	AUX
ejpam-3294	197	7	a	a	DET
ejpam-3294	197	8	fixed	fix	VERB
ejpam-3294	197	9	point	point	NOUN
ejpam-3294	197	10	of	of	ADP
ejpam-3294	197	11	f	f	PROPN
ejpam-3294	197	12	.	.	PUNCT
ejpam-3294	198	1	further	far	ADV
ejpam-3294	198	2	,	,	PUNCT
ejpam-3294	198	3	suppose	suppose	VERB
ejpam-3294	198	4	that	that	SCONJ
ejpam-3294	198	5	z	z	X
ejpam-3294	198	6	,	,	PUNCT
ejpam-3294	198	7	ź	ź	PROPN
ejpam-3294	198	8	are	be	AUX
ejpam-3294	198	9	two	two	NUM
ejpam-3294	198	10	fixed	fix	VERB
ejpam-3294	198	11	points	point	NOUN
ejpam-3294	198	12	of	of	ADP
ejpam-3294	198	13	f	f	PROPN
ejpam-3294	198	14	such	such	ADJ
ejpam-3294	198	15	that	that	DET
ejpam-3294	198	16	z	z	NOUN
ejpam-3294	198	17	6=	6=	ADP
ejpam-3294	198	18	ź	ź	PROPN
ejpam-3294	198	19	and	and	CCONJ
ejpam-3294	198	20	α(fz	α(fz	NOUN
ejpam-3294	198	21	,	,	PUNCT
ejpam-3294	198	22	ff	ff	NOUN
ejpam-3294	198	23	ź	ź	NOUN
ejpam-3294	198	24	)	)	PUNCT
ejpam-3294	199	1	=	=	SYM
ejpam-3294	199	2	α(z	α(z	PROPN
ejpam-3294	199	3	,	,	PUNCT
ejpam-3294	199	4	ź	ź	PROPN
ejpam-3294	199	5	)	)	PUNCT
ejpam-3294	199	6	≥	≥	NOUN
ejpam-3294	199	7	1	1	NUM
ejpam-3294	199	8	and	and	CCONJ
ejpam-3294	199	9	σ(fz	σ(fz	PROPN
ejpam-3294	199	10	,	,	PUNCT
ejpam-3294	199	11	f	f	PROPN
ejpam-3294	199	12	ź	ź	PROPN
ejpam-3294	199	13	)	)	PUNCT
ejpam-3294	199	14	=	=	SYM
ejpam-3294	199	15	σ(z	σ(z	PROPN
ejpam-3294	199	16	,	,	PUNCT
ejpam-3294	199	17	ź	ź	NOUN
ejpam-3294	199	18	)	)	PUNCT
ejpam-3294	199	19	≥	≥	NOUN
ejpam-3294	199	20	0	0	NUM
ejpam-3294	199	21	.	.	PUNCT
ejpam-3294	200	1	from	from	ADP
ejpam-3294	200	2	(	(	PUNCT
ejpam-3294	200	3	2.1	2.1	NUM
ejpam-3294	200	4	)	)	PUNCT
ejpam-3294	200	5	,	,	PUNCT
ejpam-3294	200	6	we	we	PRON
ejpam-3294	200	7	have	have	VERB
ejpam-3294	200	8	τ	τ	PROPN
ejpam-3294	201	1	+	+	NUM
ejpam-3294	201	2	f	f	X
ejpam-3294	201	3	(	(	PUNCT
ejpam-3294	201	4	σ(z	σ(z	PROPN
ejpam-3294	201	5	,	,	PUNCT
ejpam-3294	201	6	ź	ź	NOUN
ejpam-3294	201	7	)	)	PUNCT
ejpam-3294	201	8	)	)	PUNCT
ejpam-3294	202	1	=	=	PUNCT
ejpam-3294	203	1	τ	τ	X
ejpam-3294	203	2	+	+	NUM
ejpam-3294	203	3	f	f	X
ejpam-3294	203	4	(	(	PUNCT
ejpam-3294	203	5	σ(fz	σ(fz	PROPN
ejpam-3294	203	6	,	,	PUNCT
ejpam-3294	203	7	f	f	PROPN
ejpam-3294	203	8	ź	ź	PROPN
ejpam-3294	203	9	)	)	PUNCT
ejpam-3294	203	10	)	)	PUNCT
ejpam-3294	204	1	≤	≤	NUM
ejpam-3294	204	2	α(z	α(z	NOUN
ejpam-3294	204	3	,	,	PUNCT
ejpam-3294	204	4	ź)(τ	ź)(τ	PROPN
ejpam-3294	205	1	+	+	NUM
ejpam-3294	205	2	f	f	X
ejpam-3294	205	3	(	(	PUNCT
ejpam-3294	205	4	σ(fz	σ(fz	PROPN
ejpam-3294	205	5	,	,	PUNCT
ejpam-3294	205	6	f	f	PROPN
ejpam-3294	205	7	ź	ź	PROPN
ejpam-3294	205	8	)	)	PUNCT
ejpam-3294	205	9	)	)	PUNCT
ejpam-3294	205	10	)	)	PUNCT
ejpam-3294	206	1	≤	≤	NOUN
ejpam-3294	206	2	β(mz	β(mz	NOUN
ejpam-3294	206	3	,	,	PUNCT
ejpam-3294	206	4	ź)f	ź)f	NUM
ejpam-3294	206	5	(	(	PUNCT
ejpam-3294	206	6	mz	mz	PROPN
ejpam-3294	206	7	,	,	PUNCT
ejpam-3294	206	8	ź	ź	PROPN
ejpam-3294	206	9	)	)	PUNCT
ejpam-3294	206	10	,	,	PUNCT
ejpam-3294	206	11	where	where	SCONJ
ejpam-3294	206	12	mz	mz	PROPN
ejpam-3294	206	13	,	,	PUNCT
ejpam-3294	206	14	ź	ź	PROPN
ejpam-3294	206	15	=	=	SYM
ejpam-3294	206	16	max{σ(z	max{σ(z	PROPN
ejpam-3294	206	17	,	,	PUNCT
ejpam-3294	206	18	ź	ź	PROPN
ejpam-3294	206	19	)	)	PUNCT
ejpam-3294	206	20	,	,	PUNCT
ejpam-3294	206	21	σ(z	σ(z	PROPN
ejpam-3294	206	22	,	,	PUNCT
ejpam-3294	206	23	f	f	PROPN
ejpam-3294	206	24	ź	ź	PROPN
ejpam-3294	206	25	)	)	PUNCT
ejpam-3294	206	26	,	,	PUNCT
ejpam-3294	206	27	σ(ź	σ(ź	PROPN
ejpam-3294	206	28	,	,	PUNCT
ejpam-3294	206	29	f	f	PROPN
ejpam-3294	206	30	ź	ź	PROPN
ejpam-3294	206	31	)	)	PUNCT
ejpam-3294	206	32	,	,	PUNCT
ejpam-3294	206	33	σ(fz	σ(fz	PROPN
ejpam-3294	206	34	,	,	PUNCT
ejpam-3294	206	35	ź	ź	NOUN
ejpam-3294	206	36	)	)	PUNCT
ejpam-3294	206	37	+	+	NUM
ejpam-3294	206	38	σ(z	σ(z	NOUN
ejpam-3294	206	39	,	,	PUNCT
ejpam-3294	206	40	f	f	PROPN
ejpam-3294	206	41	ź	ź	PROPN
ejpam-3294	206	42	)	)	PUNCT
ejpam-3294	206	43	4	4	NUM
ejpam-3294	206	44	,	,	PUNCT
ejpam-3294	206	45	h.	h.	PROPN
ejpam-3294	206	46	qawaqneh	qawaqneh	PROPN
ejpam-3294	206	47	,	,	PUNCT
ejpam-3294	206	48	m.s	m.s	PROPN
ejpam-3294	206	49	.	.	PROPN
ejpam-3294	206	50	noorani	noorani	PROPN
ejpam-3294	206	51	,	,	PUNCT
ejpam-3294	206	52	w.	w.	PROPN
ejpam-3294	206	53	shatanawi	shatanawi	PROPN
ejpam-3294	206	54	/	/	SYM
ejpam-3294	206	55	eur	eur	PROPN
ejpam-3294	206	56	.	.	PUNCT
ejpam-3294	207	1	j.	j.	PROPN
ejpam-3294	207	2	pure	pure	PROPN
ejpam-3294	207	3	appl	appl	PROPN
ejpam-3294	207	4	.	.	PROPN
ejpam-3294	207	5	math	math	PROPN
ejpam-3294	207	6	,	,	PUNCT
ejpam-3294	207	7	11	11	NUM
ejpam-3294	207	8	(	(	PUNCT
ejpam-3294	207	9	3	3	NUM
ejpam-3294	207	10	)	)	PUNCT
ejpam-3294	207	11	(	(	PUNCT
ejpam-3294	207	12	2018	2018	NUM
ejpam-3294	207	13	)	)	PUNCT
ejpam-3294	207	14	,	,	PUNCT
ejpam-3294	207	15	702	702	NUM
ejpam-3294	207	16	-	-	SYM
ejpam-3294	207	17	716	716	NUM
ejpam-3294	207	18	710	710	NUM
ejpam-3294	207	19	[	[	SYM
ejpam-3294	207	20	1	1	NUM
ejpam-3294	207	21	+	+	NUM
ejpam-3294	207	22	σ(z	σ(z	NOUN
ejpam-3294	207	23	,	,	PUNCT
ejpam-3294	207	24	fz)]σ(ź	fz)]σ(ź	NOUN
ejpam-3294	207	25	,	,	PUNCT
ejpam-3294	207	26	f	f	PROPN
ejpam-3294	207	27	ź	ź	PROPN
ejpam-3294	207	28	)	)	PUNCT
ejpam-3294	207	29	σ(z	σ(z	PROPN
ejpam-3294	207	30	,	,	PUNCT
ejpam-3294	207	31	ź	ź	NOUN
ejpam-3294	207	32	)	)	PUNCT
ejpam-3294	207	33	+	+	CCONJ
ejpam-3294	207	34	1	1	X
ejpam-3294	207	35	}	}	PUNCT
ejpam-3294	207	36	=	=	SYM
ejpam-3294	207	37	max{σ(z	max{σ(z	PROPN
ejpam-3294	207	38	,	,	PUNCT
ejpam-3294	207	39	ź	ź	PROPN
ejpam-3294	207	40	)	)	PUNCT
ejpam-3294	207	41	,	,	PUNCT
ejpam-3294	207	42	σ(z	σ(z	PROPN
ejpam-3294	207	43	,	,	PUNCT
ejpam-3294	207	44	ź	ź	PROPN
ejpam-3294	207	45	)	)	PUNCT
ejpam-3294	207	46	,	,	PUNCT
ejpam-3294	207	47	σ(ź	σ(ź	PROPN
ejpam-3294	207	48	,	,	PUNCT
ejpam-3294	207	49	ź	ź	PROPN
ejpam-3294	207	50	)	)	PUNCT
ejpam-3294	207	51	,	,	PUNCT
ejpam-3294	207	52	σ(z	σ(z	PROPN
ejpam-3294	207	53	,	,	PUNCT
ejpam-3294	207	54	ź	ź	NOUN
ejpam-3294	207	55	)	)	PUNCT
ejpam-3294	207	56	2	2	NUM
ejpam-3294	207	57	,	,	PUNCT
ejpam-3294	207	58	σ(ź	σ(ź	PROPN
ejpam-3294	207	59	,	,	PUNCT
ejpam-3294	207	60	f	f	PROPN
ejpam-3294	207	61	ź	ź	PROPN
ejpam-3294	207	62	)	)	PUNCT
ejpam-3294	207	63	=	=	SYM
ejpam-3294	207	64	max{σ(z	max{σ(z	PROPN
ejpam-3294	207	65	,	,	PUNCT
ejpam-3294	207	66	ź	ź	PROPN
ejpam-3294	207	67	)	)	PUNCT
ejpam-3294	207	68	,	,	PUNCT
ejpam-3294	207	69	σ(z	σ(z	PROPN
ejpam-3294	207	70	,	,	PUNCT
ejpam-3294	207	71	ź	ź	NOUN
ejpam-3294	207	72	)	)	PUNCT
ejpam-3294	207	73	2	2	NUM
ejpam-3294	207	74	=	=	SYM
ejpam-3294	207	75	σ(z	σ(z	PROPN
ejpam-3294	207	76	,	,	PUNCT
ejpam-3294	207	77	ź	ź	NOUN
ejpam-3294	207	78	)	)	PUNCT
ejpam-3294	207	79	.	.	PUNCT
ejpam-3294	208	1	hence	hence	ADV
ejpam-3294	208	2	τ	τ	PROPN
ejpam-3294	208	3	+	+	NUM
ejpam-3294	208	4	f	f	X
ejpam-3294	208	5	(	(	PUNCT
ejpam-3294	208	6	σ(z	σ(z	PROPN
ejpam-3294	208	7	,	,	PUNCT
ejpam-3294	208	8	ź	ź	NOUN
ejpam-3294	208	9	)	)	PUNCT
ejpam-3294	208	10	)	)	PUNCT
ejpam-3294	208	11	≤	≤	NOUN
ejpam-3294	208	12	β(σ(z	β(σ(z	PROPN
ejpam-3294	208	13	,	,	PUNCT
ejpam-3294	208	14	ź))f	ź))f	PROPN
ejpam-3294	208	15	(	(	PUNCT
ejpam-3294	208	16	σ(z	σ(z	PROPN
ejpam-3294	208	17	,	,	PUNCT
ejpam-3294	208	18	ź	ź	NOUN
ejpam-3294	208	19	)	)	PUNCT
ejpam-3294	208	20	)	)	PUNCT
ejpam-3294	209	1	≤	≤	NUM
ejpam-3294	209	2	f	f	X
ejpam-3294	209	3	(	(	PUNCT
ejpam-3294	209	4	σ(z	σ(z	PROPN
ejpam-3294	209	5	,	,	PUNCT
ejpam-3294	209	6	ź	ź	NOUN
ejpam-3294	209	7	)	)	PUNCT
ejpam-3294	209	8	)	)	PUNCT
ejpam-3294	209	9	,	,	PUNCT
ejpam-3294	209	10	which	which	PRON
ejpam-3294	209	11	is	be	AUX
ejpam-3294	209	12	a	a	DET
ejpam-3294	209	13	contradiction	contradiction	NOUN
ejpam-3294	209	14	.	.	PUNCT
ejpam-3294	210	1	hence	hence	ADV
ejpam-3294	210	2	σ(z	σ(z	PROPN
ejpam-3294	210	3	,	,	PUNCT
ejpam-3294	210	4	ź	ź	NOUN
ejpam-3294	210	5	)	)	PUNCT
ejpam-3294	210	6	=	=	SYM
ejpam-3294	211	1	0	0	NUM
ejpam-3294	211	2	,	,	PUNCT
ejpam-3294	211	3	that	that	PRON
ejpam-3294	211	4	is	be	AUX
ejpam-3294	211	5	z	z	NOUN
ejpam-3294	211	6	=	=	PUNCT
ejpam-3294	211	7	ź.	ź.	X
ejpam-3294	211	8	thus	thus	ADV
ejpam-3294	211	9	,	,	PUNCT
ejpam-3294	211	10	we	we	PRON
ejpam-3294	211	11	conclude	conclude	VERB
ejpam-3294	211	12	that	that	SCONJ
ejpam-3294	211	13	the	the	DET
ejpam-3294	211	14	fixed	fix	VERB
ejpam-3294	211	15	point	point	NOUN
ejpam-3294	211	16	of	of	ADP
ejpam-3294	211	17	f	f	PROPN
ejpam-3294	211	18	is	be	AUX
ejpam-3294	211	19	unique	unique	ADJ
ejpam-3294	211	20	.	.	PUNCT
ejpam-3294	212	1	next	next	ADV
ejpam-3294	212	2	,	,	PUNCT
ejpam-3294	212	3	we	we	PRON
ejpam-3294	212	4	will	will	AUX
ejpam-3294	212	5	prove	prove	VERB
ejpam-3294	212	6	that	that	SCONJ
ejpam-3294	212	7	σ(z	σ(z	NOUN
ejpam-3294	212	8	,	,	PUNCT
ejpam-3294	212	9	z	z	NOUN
ejpam-3294	212	10	)	)	PUNCT
ejpam-3294	212	11	=	=	SYM
ejpam-3294	213	1	0	0	X
ejpam-3294	213	2	.	.	PUNCT
ejpam-3294	214	1	if	if	SCONJ
ejpam-3294	214	2	σ(fz	σ(fz	PROPN
ejpam-3294	214	3	,	,	PUNCT
ejpam-3294	214	4	fz	fz	NOUN
ejpam-3294	214	5	)	)	PUNCT
ejpam-3294	214	6	=	=	SYM
ejpam-3294	214	7	σ(z	σ(z	PROPN
ejpam-3294	214	8	,	,	PUNCT
ejpam-3294	214	9	z	z	NOUN
ejpam-3294	214	10	)	)	PUNCT
ejpam-3294	214	11	>	>	X
ejpam-3294	214	12	0	0	NUM
ejpam-3294	214	13	and	and	CCONJ
ejpam-3294	214	14	α(fz	α(fz	NOUN
ejpam-3294	214	15	,	,	PUNCT
ejpam-3294	214	16	ffz	ffz	X
ejpam-3294	214	17	)	)	PUNCT
ejpam-3294	214	18	=	=	SYM
ejpam-3294	214	19	α(z	α(z	NOUN
ejpam-3294	214	20	,	,	PUNCT
ejpam-3294	214	21	z	z	NOUN
ejpam-3294	214	22	)	)	PUNCT
ejpam-3294	214	23	≥	≥	NOUN
ejpam-3294	214	24	1	1	NUM
ejpam-3294	214	25	,	,	PUNCT
ejpam-3294	214	26	then	then	ADV
ejpam-3294	214	27	from	from	ADP
ejpam-3294	214	28	(	(	PUNCT
ejpam-3294	214	29	2.1)and	2.1)and	NUM
ejpam-3294	214	30	applying	apply	VERB
ejpam-3294	214	31	the	the	DET
ejpam-3294	214	32	routine	routine	ADJ
ejpam-3294	214	33	calculation	calculation	NOUN
ejpam-3294	214	34	as	as	SCONJ
ejpam-3294	214	35	mentioned	mention	VERB
ejpam-3294	214	36	above	above	ADV
ejpam-3294	214	37	,	,	PUNCT
ejpam-3294	214	38	we	we	PRON
ejpam-3294	214	39	get	get	VERB
ejpam-3294	214	40	τ	τ	PROPN
ejpam-3294	214	41	+	+	NUM
ejpam-3294	214	42	f	f	X
ejpam-3294	214	43	(	(	PUNCT
ejpam-3294	214	44	σ(z	σ(z	PROPN
ejpam-3294	214	45	,	,	PUNCT
ejpam-3294	214	46	z	z	NOUN
ejpam-3294	214	47	)	)	PUNCT
ejpam-3294	214	48	)	)	PUNCT
ejpam-3294	215	1	=	=	PUNCT
ejpam-3294	216	1	τ	τ	X
ejpam-3294	216	2	+	+	NUM
ejpam-3294	216	3	f	f	X
ejpam-3294	216	4	(	(	PUNCT
ejpam-3294	216	5	σ(fz	σ(fz	PROPN
ejpam-3294	216	6	,	,	PUNCT
ejpam-3294	216	7	fz	fz	NOUN
ejpam-3294	216	8	)	)	PUNCT
ejpam-3294	216	9	)	)	PUNCT
ejpam-3294	217	1	≤	≤	NUM
ejpam-3294	217	2	α(z	α(z	NOUN
ejpam-3294	217	3	,	,	PUNCT
ejpam-3294	217	4	z)(τ	z)(τ	PROPN
ejpam-3294	218	1	+	+	CCONJ
ejpam-3294	218	2	f	f	X
ejpam-3294	218	3	(	(	PUNCT
ejpam-3294	218	4	σ(fz	σ(fz	PROPN
ejpam-3294	218	5	,	,	PUNCT
ejpam-3294	218	6	fz	fz	NOUN
ejpam-3294	218	7	)	)	PUNCT
ejpam-3294	218	8	)	)	PUNCT
ejpam-3294	218	9	)	)	PUNCT
ejpam-3294	218	10	≤	≤	NOUN
ejpam-3294	218	11	β(mz	β(mz	NOUN
ejpam-3294	218	12	,	,	PUNCT
ejpam-3294	218	13	z)f	z)f	X
ejpam-3294	218	14	(	(	PUNCT
ejpam-3294	218	15	mz	mz	PROPN
ejpam-3294	218	16	,	,	PUNCT
ejpam-3294	218	17	z	z	PROPN
ejpam-3294	218	18	)	)	PUNCT
ejpam-3294	218	19	,	,	PUNCT
ejpam-3294	218	20	where	where	SCONJ
ejpam-3294	218	21	mz	mz	PROPN
ejpam-3294	218	22	,	,	PUNCT
ejpam-3294	218	23	z	z	PROPN
ejpam-3294	218	24	=	=	SYM
ejpam-3294	218	25	max{σ(z	max{σ(z	PROPN
ejpam-3294	218	26	,	,	PUNCT
ejpam-3294	218	27	z	z	NOUN
ejpam-3294	218	28	)	)	PUNCT
ejpam-3294	218	29	,	,	PUNCT
ejpam-3294	218	30	σ(z	σ(z	PROPN
ejpam-3294	218	31	,	,	PUNCT
ejpam-3294	218	32	fz	fz	NOUN
ejpam-3294	218	33	)	)	PUNCT
ejpam-3294	218	34	,	,	PUNCT
ejpam-3294	218	35	σ(z	σ(z	PROPN
ejpam-3294	218	36	,	,	PUNCT
ejpam-3294	218	37	fz	fz	NOUN
ejpam-3294	218	38	)	)	PUNCT
ejpam-3294	218	39	,	,	PUNCT
ejpam-3294	218	40	σ(fz	σ(fz	PROPN
ejpam-3294	218	41	,	,	PUNCT
ejpam-3294	218	42	z	z	NOUN
ejpam-3294	218	43	)	)	PUNCT
ejpam-3294	218	44	+	+	CCONJ
ejpam-3294	218	45	σ(z	σ(z	NOUN
ejpam-3294	218	46	,	,	PUNCT
ejpam-3294	218	47	fz	fz	NOUN
ejpam-3294	218	48	)	)	PUNCT
ejpam-3294	218	49	4	4	NUM
ejpam-3294	218	50	,	,	PUNCT
ejpam-3294	218	51	[	[	X
ejpam-3294	218	52	1	1	NUM
ejpam-3294	218	53	+	+	NUM
ejpam-3294	218	54	σ(z	σ(z	NOUN
ejpam-3294	218	55	,	,	PUNCT
ejpam-3294	218	56	fz)]σ(z	fz)]σ(z	NOUN
ejpam-3294	218	57	,	,	PUNCT
ejpam-3294	218	58	fz	fz	NOUN
ejpam-3294	218	59	)	)	PUNCT
ejpam-3294	218	60	σ(z	σ(z	PROPN
ejpam-3294	218	61	,	,	PUNCT
ejpam-3294	218	62	z	z	NOUN
ejpam-3294	218	63	)	)	PUNCT
ejpam-3294	218	64	+	+	CCONJ
ejpam-3294	218	65	1	1	X
ejpam-3294	218	66	}	}	PUNCT
ejpam-3294	218	67	=	=	SYM
ejpam-3294	218	68	σ(z	σ(z	PROPN
ejpam-3294	218	69	,	,	PUNCT
ejpam-3294	218	70	z	z	NOUN
ejpam-3294	218	71	)	)	PUNCT
ejpam-3294	218	72	.	.	PUNCT
ejpam-3294	219	1	hence	hence	ADV
ejpam-3294	219	2	τ	τ	PROPN
ejpam-3294	219	3	+	+	NUM
ejpam-3294	219	4	f	f	X
ejpam-3294	219	5	(	(	PUNCT
ejpam-3294	219	6	σ(z	σ(z	PROPN
ejpam-3294	219	7	,	,	PUNCT
ejpam-3294	219	8	z	z	NOUN
ejpam-3294	219	9	)	)	PUNCT
ejpam-3294	219	10	)	)	PUNCT
ejpam-3294	220	1	<	<	X
ejpam-3294	220	2	β(σ(z	β(σ(z	PROPN
ejpam-3294	220	3	,	,	PUNCT
ejpam-3294	220	4	z))f	z))f	PROPN
ejpam-3294	220	5	(	(	PUNCT
ejpam-3294	220	6	σ(z	σ(z	PROPN
ejpam-3294	220	7	,	,	PUNCT
ejpam-3294	220	8	z	z	NOUN
ejpam-3294	220	9	)	)	PUNCT
ejpam-3294	220	10	)	)	PUNCT
ejpam-3294	220	11	≤	≤	NUM
ejpam-3294	220	12	f	f	X
ejpam-3294	220	13	(	(	PUNCT
ejpam-3294	220	14	σ(z	σ(z	PROPN
ejpam-3294	220	15	,	,	PUNCT
ejpam-3294	220	16	z	z	NOUN
ejpam-3294	220	17	)	)	PUNCT
ejpam-3294	220	18	)	)	PUNCT
ejpam-3294	220	19	,	,	PUNCT
ejpam-3294	220	20	is	be	AUX
ejpam-3294	220	21	a	a	DET
ejpam-3294	220	22	contradiction	contradiction	NOUN
ejpam-3294	220	23	,	,	PUNCT
ejpam-3294	220	24	thus	thus	ADV
ejpam-3294	220	25	,	,	PUNCT
ejpam-3294	220	26	σ(z	σ(z	PROPN
ejpam-3294	220	27	,	,	PUNCT
ejpam-3294	220	28	z	z	NOUN
ejpam-3294	220	29	)	)	PUNCT
ejpam-3294	220	30	=	=	SYM
ejpam-3294	221	1	0	0	X
ejpam-3294	221	2	.	.	PUNCT
ejpam-3294	222	1	the	the	DET
ejpam-3294	222	2	following	follow	VERB
ejpam-3294	222	3	two	two	NUM
ejpam-3294	222	4	corollaries	corollary	NOUN
ejpam-3294	222	5	are	be	AUX
ejpam-3294	222	6	direct	direct	ADJ
ejpam-3294	222	7	results	result	NOUN
ejpam-3294	222	8	of	of	ADP
ejpam-3294	222	9	theorem	theorem	ADJ
ejpam-3294	222	10	2	2	NUM
ejpam-3294	222	11	.	.	PUNCT
ejpam-3294	222	12	corollary	corollary	ADJ
ejpam-3294	222	13	1	1	NUM
ejpam-3294	222	14	.	.	PUNCT
ejpam-3294	223	1	let	let	AUX
ejpam-3294	223	2	(	(	PUNCT
ejpam-3294	223	3	x	x	NOUN
ejpam-3294	223	4	,	,	PUNCT
ejpam-3294	223	5	σ	σ	PROPN
ejpam-3294	223	6	)	)	PUNCT
ejpam-3294	223	7	be	be	AUX
ejpam-3294	223	8	a	a	DET
ejpam-3294	223	9	complete	complete	ADJ
ejpam-3294	223	10	metric	metric	ADJ
ejpam-3294	223	11	-	-	PUNCT
ejpam-3294	223	12	like	like	ADJ
ejpam-3294	223	13	space	space	NOUN
ejpam-3294	223	14	,	,	PUNCT
ejpam-3294	223	15	α	α	NOUN
ejpam-3294	223	16	:	:	PUNCT
ejpam-3294	224	1	x	x	SYM
ejpam-3294	224	2	×	×	NOUN
ejpam-3294	224	3	x	x	INTJ
ejpam-3294	224	4	→	→	X
ejpam-3294	224	5	[	[	X
ejpam-3294	224	6	0,∞	0,∞	NUM
ejpam-3294	224	7	)	)	PUNCT
ejpam-3294	224	8	and	and	CCONJ
ejpam-3294	224	9	f	f	X
ejpam-3294	224	10	:	:	PUNCT
ejpam-3294	224	11	x	x	X
ejpam-3294	224	12	→	→	PUNCT
ejpam-3294	224	13	x	x	PUNCT
ejpam-3294	224	14	be	be	AUX
ejpam-3294	224	15	two	two	NUM
ejpam-3294	224	16	given	give	VERB
ejpam-3294	224	17	mapping	mapping	NOUN
ejpam-3294	224	18	satisfying	satisfy	VERB
ejpam-3294	224	19	the	the	DET
ejpam-3294	224	20	following	follow	VERB
ejpam-3294	224	21	conditions	condition	NOUN
ejpam-3294	224	22	:	:	PUNCT
ejpam-3294	224	23	(	(	PUNCT
ejpam-3294	224	24	i	i	NOUN
ejpam-3294	224	25	)	)	PUNCT
ejpam-3294	224	26	f	f	PROPN
ejpam-3294	224	27	∈	∈	PROPN
ejpam-3294	224	28	ξ(x	ξ(x	PROPN
ejpam-3294	224	29	,	,	PUNCT
ejpam-3294	224	30	α	α	X
ejpam-3294	224	31	,	,	PUNCT
ejpam-3294	224	32	β	β	X
ejpam-3294	224	33	,	,	PUNCT
ejpam-3294	224	34	f	f	PROPN
ejpam-3294	224	35	)	)	PUNCT
ejpam-3294	224	36	∩wa(x	∩wa(x	PROPN
ejpam-3294	224	37	,	,	PUNCT
ejpam-3294	224	38	α	α	NOUN
ejpam-3294	224	39	)	)	PUNCT
ejpam-3294	224	40	.	.	PUNCT
ejpam-3294	225	1	(	(	PUNCT
ejpam-3294	225	2	ii	ii	X
ejpam-3294	225	3	)	)	PUNCT
ejpam-3294	225	4	there	there	PRON
ejpam-3294	225	5	exists	exist	VERB
ejpam-3294	225	6	x0	x0	PROPN
ejpam-3294	225	7	∈	∈	PROPN
ejpam-3294	225	8	x	x	PUNCT
ejpam-3294	225	9	such	such	ADJ
ejpam-3294	225	10	that	that	DET
ejpam-3294	225	11	σ(x0	σ(x0	NOUN
ejpam-3294	225	12	,	,	PUNCT
ejpam-3294	225	13	fx0	fx0	PROPN
ejpam-3294	225	14	)	)	PUNCT
ejpam-3294	225	15	≥	≥	NOUN
ejpam-3294	226	1	1	1	NUM
ejpam-3294	226	2	.	.	PUNCT
ejpam-3294	226	3	(	(	PUNCT
ejpam-3294	226	4	iii	iii	X
ejpam-3294	226	5	)	)	PUNCT
ejpam-3294	226	6	f	f	PROPN
ejpam-3294	226	7	is	be	AUX
ejpam-3294	226	8	σ−continuous	σ−continuous	PROPN
ejpam-3294	226	9	.	.	PUNCT
ejpam-3294	227	1	h.	h.	PROPN
ejpam-3294	227	2	qawaqneh	qawaqneh	PROPN
ejpam-3294	227	3	,	,	PUNCT
ejpam-3294	227	4	m.s	m.s	PROPN
ejpam-3294	227	5	.	.	PROPN
ejpam-3294	227	6	noorani	noorani	PROPN
ejpam-3294	227	7	,	,	PUNCT
ejpam-3294	227	8	w.	w.	PROPN
ejpam-3294	227	9	shatanawi	shatanawi	PROPN
ejpam-3294	227	10	/	/	SYM
ejpam-3294	227	11	eur	eur	PROPN
ejpam-3294	227	12	.	.	PUNCT
ejpam-3294	228	1	j.	j.	PROPN
ejpam-3294	228	2	pure	pure	PROPN
ejpam-3294	228	3	appl	appl	PROPN
ejpam-3294	228	4	.	.	PROPN
ejpam-3294	228	5	math	math	PROPN
ejpam-3294	228	6	,	,	PUNCT
ejpam-3294	228	7	11	11	NUM
ejpam-3294	228	8	(	(	PUNCT
ejpam-3294	228	9	3	3	NUM
ejpam-3294	228	10	)	)	PUNCT
ejpam-3294	228	11	(	(	PUNCT
ejpam-3294	228	12	2018	2018	NUM
ejpam-3294	228	13	)	)	PUNCT
ejpam-3294	228	14	,	,	PUNCT
ejpam-3294	228	15	702	702	NUM
ejpam-3294	228	16	-	-	SYM
ejpam-3294	228	17	716	716	NUM
ejpam-3294	228	18	711	711	NUM
ejpam-3294	228	19	then	then	ADV
ejpam-3294	228	20	f	f	PROPN
ejpam-3294	228	21	has	have	VERB
ejpam-3294	228	22	a	a	DET
ejpam-3294	228	23	unique	unique	ADJ
ejpam-3294	228	24	fixed	fix	VERB
ejpam-3294	228	25	point	point	NOUN
ejpam-3294	228	26	z	z	NOUN
ejpam-3294	228	27	∈	∈	PROPN
ejpam-3294	228	28	x	x	PUNCT
ejpam-3294	228	29	such	such	ADJ
ejpam-3294	228	30	that	that	SCONJ
ejpam-3294	228	31	σ(z	σ(z	NOUN
ejpam-3294	228	32	,	,	PUNCT
ejpam-3294	228	33	z	z	NOUN
ejpam-3294	228	34	)	)	PUNCT
ejpam-3294	228	35	=	=	SYM
ejpam-3294	229	1	0	0	X
ejpam-3294	229	2	.	.	PUNCT
ejpam-3294	229	3	proof	proof	NOUN
ejpam-3294	229	4	.	.	PUNCT
ejpam-3294	230	1	it	it	PRON
ejpam-3294	230	2	follows	follow	VERB
ejpam-3294	230	3	from	from	ADP
ejpam-3294	230	4	theorem	theorem	NOUN
ejpam-3294	230	5	2	2	NUM
ejpam-3294	230	6	by	by	ADP
ejpam-3294	230	7	putting	put	VERB
ejpam-3294	230	8	mx	mx	PROPN
ejpam-3294	230	9	,	,	PUNCT
ejpam-3294	230	10	y	y	PROPN
ejpam-3294	230	11	=	=	SYM
ejpam-3294	230	12	max{σ(x	max{σ(x	PROPN
ejpam-3294	230	13	,	,	PUNCT
ejpam-3294	230	14	y	y	PROPN
ejpam-3294	230	15	)	)	PUNCT
ejpam-3294	230	16	,	,	PUNCT
ejpam-3294	230	17	σ(x	σ(x	PROPN
ejpam-3294	230	18	,	,	PUNCT
ejpam-3294	230	19	fx	fx	PROPN
ejpam-3294	230	20	)	)	PUNCT
ejpam-3294	230	21	,	,	PUNCT
ejpam-3294	230	22	σ(y	σ(y	PROPN
ejpam-3294	230	23	,	,	PUNCT
ejpam-3294	230	24	fy	fy	PROPN
ejpam-3294	230	25	)	)	PUNCT
ejpam-3294	230	26	}	}	PUNCT
ejpam-3294	230	27	.	.	PUNCT
ejpam-3294	231	1	corollary	corollary	ADJ
ejpam-3294	231	2	2	2	NUM
ejpam-3294	231	3	.	.	PUNCT
ejpam-3294	232	1	let	let	AUX
ejpam-3294	232	2	(	(	PUNCT
ejpam-3294	232	3	x	x	NOUN
ejpam-3294	232	4	,	,	PUNCT
ejpam-3294	232	5	σ	σ	PROPN
ejpam-3294	232	6	)	)	PUNCT
ejpam-3294	232	7	be	be	AUX
ejpam-3294	232	8	a	a	DET
ejpam-3294	232	9	complete	complete	ADJ
ejpam-3294	232	10	metric	metric	ADJ
ejpam-3294	232	11	-	-	PUNCT
ejpam-3294	232	12	like	like	ADJ
ejpam-3294	232	13	space	space	NOUN
ejpam-3294	232	14	,	,	PUNCT
ejpam-3294	232	15	α	α	NOUN
ejpam-3294	232	16	:	:	PUNCT
ejpam-3294	233	1	x	x	SYM
ejpam-3294	233	2	×	×	NOUN
ejpam-3294	233	3	x	x	INTJ
ejpam-3294	233	4	→	→	X
ejpam-3294	233	5	[	[	X
ejpam-3294	233	6	0,∞	0,∞	NUM
ejpam-3294	233	7	)	)	PUNCT
ejpam-3294	233	8	and	and	CCONJ
ejpam-3294	233	9	f	f	X
ejpam-3294	233	10	:	:	PUNCT
ejpam-3294	233	11	x	x	X
ejpam-3294	233	12	→	→	PUNCT
ejpam-3294	233	13	x	x	PUNCT
ejpam-3294	233	14	be	be	AUX
ejpam-3294	233	15	two	two	NUM
ejpam-3294	233	16	given	give	VERB
ejpam-3294	233	17	mapping	mapping	NOUN
ejpam-3294	233	18	satisfying	satisfy	VERB
ejpam-3294	233	19	the	the	DET
ejpam-3294	233	20	following	follow	VERB
ejpam-3294	233	21	conditions	condition	NOUN
ejpam-3294	233	22	:	:	PUNCT
ejpam-3294	233	23	(	(	PUNCT
ejpam-3294	233	24	i	i	NOUN
ejpam-3294	233	25	)	)	PUNCT
ejpam-3294	233	26	f	f	PROPN
ejpam-3294	233	27	∈	∈	PROPN
ejpam-3294	233	28	ξ(x	ξ(x	PROPN
ejpam-3294	233	29	,	,	PUNCT
ejpam-3294	233	30	α	α	X
ejpam-3294	233	31	,	,	PUNCT
ejpam-3294	233	32	β	β	X
ejpam-3294	233	33	,	,	PUNCT
ejpam-3294	233	34	f	f	PROPN
ejpam-3294	233	35	)	)	PUNCT
ejpam-3294	233	36	∩wa(x	∩wa(x	PROPN
ejpam-3294	233	37	,	,	PUNCT
ejpam-3294	233	38	α	α	NOUN
ejpam-3294	233	39	)	)	PUNCT
ejpam-3294	233	40	.	.	PUNCT
ejpam-3294	234	1	(	(	PUNCT
ejpam-3294	234	2	ii	ii	X
ejpam-3294	234	3	)	)	PUNCT
ejpam-3294	234	4	there	there	PRON
ejpam-3294	234	5	exists	exist	VERB
ejpam-3294	234	6	x0	x0	PROPN
ejpam-3294	234	7	∈	∈	PROPN
ejpam-3294	234	8	x	x	PUNCT
ejpam-3294	234	9	such	such	ADJ
ejpam-3294	234	10	that	that	DET
ejpam-3294	234	11	σ(x0	σ(x0	NOUN
ejpam-3294	234	12	,	,	PUNCT
ejpam-3294	234	13	fx0	fx0	PROPN
ejpam-3294	234	14	)	)	PUNCT
ejpam-3294	234	15	≥	≥	NOUN
ejpam-3294	235	1	1	1	NUM
ejpam-3294	235	2	.	.	PUNCT
ejpam-3294	235	3	(	(	PUNCT
ejpam-3294	235	4	iii	iii	X
ejpam-3294	235	5	)	)	PUNCT
ejpam-3294	235	6	f	f	PROPN
ejpam-3294	235	7	is	be	AUX
ejpam-3294	235	8	σ−continuous	σ−continuous	PROPN
ejpam-3294	235	9	.	.	PUNCT
ejpam-3294	236	1	then	then	ADV
ejpam-3294	236	2	f	f	PROPN
ejpam-3294	236	3	has	have	VERB
ejpam-3294	236	4	a	a	DET
ejpam-3294	236	5	unique	unique	ADJ
ejpam-3294	236	6	fixed	fix	VERB
ejpam-3294	236	7	point	point	NOUN
ejpam-3294	236	8	z	z	NOUN
ejpam-3294	236	9	∈	∈	PROPN
ejpam-3294	236	10	x	x	PUNCT
ejpam-3294	236	11	such	such	ADJ
ejpam-3294	236	12	that	that	SCONJ
ejpam-3294	236	13	σ(z	σ(z	NOUN
ejpam-3294	236	14	,	,	PUNCT
ejpam-3294	236	15	z	z	NOUN
ejpam-3294	236	16	)	)	PUNCT
ejpam-3294	236	17	=	=	SYM
ejpam-3294	237	1	0	0	X
ejpam-3294	237	2	.	.	PUNCT
ejpam-3294	237	3	proof	proof	NOUN
ejpam-3294	237	4	.	.	PUNCT
ejpam-3294	238	1	it	it	PRON
ejpam-3294	238	2	follows	follow	VERB
ejpam-3294	238	3	from	from	ADP
ejpam-3294	238	4	theorem	theorem	NOUN
ejpam-3294	238	5	2	2	NUM
ejpam-3294	238	6	by	by	ADP
ejpam-3294	238	7	putting	put	VERB
ejpam-3294	238	8	mx	mx	PROPN
ejpam-3294	238	9	,	,	PUNCT
ejpam-3294	238	10	y	y	PROPN
ejpam-3294	238	11	=	=	PUNCT
ejpam-3294	238	12	aσ(x	aσ(x	X
ejpam-3294	238	13	,	,	PUNCT
ejpam-3294	238	14	y	y	NOUN
ejpam-3294	238	15	)	)	PUNCT
ejpam-3294	239	1	+	+	CCONJ
ejpam-3294	239	2	bσ(x	bσ(x	NOUN
ejpam-3294	239	3	,	,	PUNCT
ejpam-3294	239	4	fx	fx	NOUN
ejpam-3294	239	5	)	)	PUNCT
ejpam-3294	239	6	+	+	NUM
ejpam-3294	239	7	cσ(y	cσ(y	NOUN
ejpam-3294	239	8	,	,	PUNCT
ejpam-3294	239	9	fy	fy	PROPN
ejpam-3294	239	10	)	)	PUNCT
ejpam-3294	239	11	+	+	NUM
ejpam-3294	239	12	e[σ(fx	e[σ(fx	PROPN
ejpam-3294	239	13	,	,	PUNCT
ejpam-3294	239	14	y)+σ(x	y)+σ(x	PROPN
ejpam-3294	239	15	,	,	PUNCT
ejpam-3294	239	16	fy	fy	PROPN
ejpam-3294	239	17	)	)	PUNCT
ejpam-3294	239	18	4	4	NUM
ejpam-3294	239	19	]	]	PUNCT
ejpam-3294	240	1	+	+	PUNCT
ejpam-3294	240	2	e	e	X
ejpam-3294	240	3	[	[	PUNCT
ejpam-3294	240	4	[	[	X
ejpam-3294	240	5	1+σ(x	1+σ(x	ADJ
ejpam-3294	240	6	,	,	PUNCT
ejpam-3294	240	7	fx)]σ(y	fx)]σ(y	NOUN
ejpam-3294	240	8	,	,	PUNCT
ejpam-3294	240	9	fy	fy	PROPN
ejpam-3294	240	10	)	)	PUNCT
ejpam-3294	240	11	σ(x	σ(x	PROPN
ejpam-3294	240	12	,	,	PUNCT
ejpam-3294	240	13	y)+1	y)+1	NOUN
ejpam-3294	240	14	]	]	PUNCT
ejpam-3294	240	15	.	.	PUNCT
ejpam-3294	241	1	for	for	ADP
ejpam-3294	241	2	all	all	DET
ejpam-3294	241	3	x	x	NOUN
ejpam-3294	241	4	,	,	PUNCT
ejpam-3294	241	5	y	y	PROPN
ejpam-3294	241	6	∈	∈	PROPN
ejpam-3294	241	7	x	x	X
ejpam-3294	241	8	,	,	PUNCT
ejpam-3294	241	9	we	we	PRON
ejpam-3294	241	10	have	have	VERB
ejpam-3294	241	11	mx	mx	PROPN
ejpam-3294	241	12	,	,	PUNCT
ejpam-3294	241	13	y	y	PROPN
ejpam-3294	241	14	=	=	PUNCT
ejpam-3294	241	15	aσ(x	aσ(x	X
ejpam-3294	241	16	,	,	PUNCT
ejpam-3294	241	17	y	y	NOUN
ejpam-3294	241	18	)	)	PUNCT
ejpam-3294	242	1	+	+	CCONJ
ejpam-3294	242	2	bσ(x	bσ(x	NOUN
ejpam-3294	242	3	,	,	PUNCT
ejpam-3294	242	4	fx	fx	NOUN
ejpam-3294	242	5	)	)	PUNCT
ejpam-3294	242	6	+	+	NUM
ejpam-3294	242	7	cσ(y	cσ(y	NOUN
ejpam-3294	242	8	,	,	PUNCT
ejpam-3294	242	9	fy	fy	PROPN
ejpam-3294	242	10	)	)	PUNCT
ejpam-3294	243	1	+	+	CCONJ
ejpam-3294	243	2	e	e	NOUN
ejpam-3294	243	3	[	[	PUNCT
ejpam-3294	243	4	σ(fx	σ(fx	NOUN
ejpam-3294	243	5	,	,	PUNCT
ejpam-3294	243	6	y	y	PROPN
ejpam-3294	243	7	)	)	PUNCT
ejpam-3294	244	1	+	+	CCONJ
ejpam-3294	244	2	σ(x	σ(x	PROPN
ejpam-3294	244	3	,	,	PUNCT
ejpam-3294	244	4	fy	fy	PROPN
ejpam-3294	244	5	)	)	PUNCT
ejpam-3294	244	6	4	4	NUM
ejpam-3294	244	7	]	]	PUNCT
ejpam-3294	244	8	≤	≤	NUM
ejpam-3294	244	9	(	(	PUNCT
ejpam-3294	244	10	a+	a+	X
ejpam-3294	244	11	b+	b+	X
ejpam-3294	244	12	c+	c+	VERB
ejpam-3294	244	13	2e	2e	NUM
ejpam-3294	244	14	)	)	PUNCT
ejpam-3294	245	1	max{σ(x	max{σ(x	PROPN
ejpam-3294	245	2	,	,	PUNCT
ejpam-3294	245	3	y	y	PROPN
ejpam-3294	245	4	)	)	PUNCT
ejpam-3294	245	5	,	,	PUNCT
ejpam-3294	245	6	σ(x	σ(x	PROPN
ejpam-3294	245	7	,	,	PUNCT
ejpam-3294	245	8	fx	fx	PROPN
ejpam-3294	245	9	)	)	PUNCT
ejpam-3294	245	10	,	,	PUNCT
ejpam-3294	245	11	σ(y	σ(y	PROPN
ejpam-3294	245	12	,	,	PUNCT
ejpam-3294	245	13	fy	fy	PROPN
ejpam-3294	245	14	)	)	PUNCT
ejpam-3294	245	15	,	,	PUNCT
ejpam-3294	245	16	σ(fx	σ(fx	PROPN
ejpam-3294	245	17	,	,	PUNCT
ejpam-3294	245	18	y	y	PROPN
ejpam-3294	245	19	)	)	PUNCT
ejpam-3294	245	20	+	+	CCONJ
ejpam-3294	245	21	σ(x	σ(x	PROPN
ejpam-3294	245	22	,	,	PUNCT
ejpam-3294	245	23	fy	fy	PROPN
ejpam-3294	245	24	)	)	PUNCT
ejpam-3294	245	25	4	4	NUM
ejpam-3294	245	26	,	,	PUNCT
ejpam-3294	245	27	[	[	X
ejpam-3294	245	28	1	1	NUM
ejpam-3294	245	29	+	+	NUM
ejpam-3294	245	30	σ(x	σ(x	PROPN
ejpam-3294	245	31	,	,	PUNCT
ejpam-3294	245	32	fx)]σ(y	fx)]σ(y	PROPN
ejpam-3294	245	33	,	,	PUNCT
ejpam-3294	245	34	fy	fy	PROPN
ejpam-3294	245	35	)	)	PUNCT
ejpam-3294	245	36	σ(x	σ(x	PROPN
ejpam-3294	245	37	,	,	PUNCT
ejpam-3294	245	38	y	y	NOUN
ejpam-3294	245	39	)	)	PUNCT
ejpam-3294	246	1	+	+	CCONJ
ejpam-3294	246	2	1	1	NUM
ejpam-3294	247	1	[	[	SYM
ejpam-3294	247	2	1	1	NUM
ejpam-3294	247	3	+	+	NUM
ejpam-3294	247	4	σ(x	σ(x	PROPN
ejpam-3294	247	5	,	,	PUNCT
ejpam-3294	247	6	fx)]σ(y	fx)]σ(y	PROPN
ejpam-3294	247	7	,	,	PUNCT
ejpam-3294	247	8	fy	fy	PROPN
ejpam-3294	247	9	)	)	PUNCT
ejpam-3294	247	10	σ(x	σ(x	PROPN
ejpam-3294	247	11	,	,	PUNCT
ejpam-3294	247	12	y	y	NOUN
ejpam-3294	247	13	)	)	PUNCT
ejpam-3294	247	14	+	+	CCONJ
ejpam-3294	247	15	1	1	X
ejpam-3294	247	16	}	}	PUNCT
ejpam-3294	247	17	≤	≤	NOUN
ejpam-3294	247	18	max{σ(x	max{σ(x	PROPN
ejpam-3294	247	19	,	,	PUNCT
ejpam-3294	247	20	y	y	PROPN
ejpam-3294	247	21	)	)	PUNCT
ejpam-3294	247	22	,	,	PUNCT
ejpam-3294	247	23	σ(x	σ(x	PROPN
ejpam-3294	247	24	,	,	PUNCT
ejpam-3294	247	25	fx	fx	PROPN
ejpam-3294	247	26	)	)	PUNCT
ejpam-3294	247	27	,	,	PUNCT
ejpam-3294	247	28	σ(y	σ(y	PROPN
ejpam-3294	247	29	,	,	PUNCT
ejpam-3294	247	30	fy	fy	PROPN
ejpam-3294	247	31	)	)	PUNCT
ejpam-3294	247	32	,	,	PUNCT
ejpam-3294	247	33	σ(fx	σ(fx	PROPN
ejpam-3294	247	34	,	,	PUNCT
ejpam-3294	247	35	y	y	PROPN
ejpam-3294	247	36	)	)	PUNCT
ejpam-3294	248	1	+	+	CCONJ
ejpam-3294	248	2	σ(x	σ(x	PROPN
ejpam-3294	248	3	,	,	PUNCT
ejpam-3294	248	4	fy	fy	PROPN
ejpam-3294	248	5	)	)	PUNCT
ejpam-3294	248	6	4	4	NUM
ejpam-3294	248	7	,	,	PUNCT
ejpam-3294	249	1	[	[	X
ejpam-3294	249	2	1	1	NUM
ejpam-3294	249	3	+	+	NUM
ejpam-3294	249	4	σ(x	σ(x	PROPN
ejpam-3294	249	5	,	,	PUNCT
ejpam-3294	249	6	fx)]σ(y	fx)]σ(y	PROPN
ejpam-3294	249	7	,	,	PUNCT
ejpam-3294	249	8	fy	fy	PROPN
ejpam-3294	249	9	)	)	PUNCT
ejpam-3294	249	10	σ(x	σ(x	PROPN
ejpam-3294	249	11	,	,	PUNCT
ejpam-3294	249	12	y	y	NOUN
ejpam-3294	249	13	)	)	PUNCT
ejpam-3294	249	14	+	+	CCONJ
ejpam-3294	249	15	1	1	NUM
ejpam-3294	249	16	}	}	PUNCT
ejpam-3294	249	17	.	.	PUNCT
ejpam-3294	250	1	then	then	ADV
ejpam-3294	250	2	,	,	PUNCT
ejpam-3294	250	3	we	we	PRON
ejpam-3294	250	4	see	see	VERB
ejpam-3294	250	5	that	that	SCONJ
ejpam-3294	250	6	(	(	PUNCT
ejpam-3294	250	7	2.1	2.1	NUM
ejpam-3294	250	8	)	)	PUNCT
ejpam-3294	250	9	is	be	AUX
ejpam-3294	250	10	a	a	DET
ejpam-3294	250	11	consequence	consequence	NOUN
ejpam-3294	250	12	of	of	ADP
ejpam-3294	250	13	(	(	PUNCT
ejpam-3294	250	14	2.14	2.14	NUM
ejpam-3294	250	15	)	)	PUNCT
ejpam-3294	250	16	,	,	PUNCT
ejpam-3294	250	17	then	then	ADV
ejpam-3294	250	18	the	the	DET
ejpam-3294	250	19	corollary	corollary	NOUN
ejpam-3294	250	20	is	be	AUX
ejpam-3294	250	21	proved	prove	VERB
ejpam-3294	250	22	.	.	PUNCT
ejpam-3294	251	1	example	example	NOUN
ejpam-3294	252	1	3	3	X
ejpam-3294	252	2	.	.	PUNCT
ejpam-3294	252	3	let	let	VERB
ejpam-3294	252	4	x	x	PUNCT
ejpam-3294	252	5	=	=	PUNCT
ejpam-3294	252	6	{	{	PUNCT
ejpam-3294	252	7	0	0	NUM
ejpam-3294	252	8	,	,	PUNCT
ejpam-3294	252	9	1	1	NUM
ejpam-3294	252	10	,	,	PUNCT
ejpam-3294	252	11	2	2	NUM
ejpam-3294	252	12	}	}	PUNCT
ejpam-3294	252	13	.	.	PUNCT
ejpam-3294	253	1	let	let	VERB
ejpam-3294	253	2	σ	σ	NOUN
ejpam-3294	253	3	:	:	PUNCT
ejpam-3294	253	4	x	x	PROPN
ejpam-3294	253	5	×x	×x	ADP
ejpam-3294	253	6	→	→	SYM
ejpam-3294	253	7	r	r	NOUN
ejpam-3294	253	8	be	be	AUX
ejpam-3294	253	9	a	a	DET
ejpam-3294	253	10	metric	metric	ADJ
ejpam-3294	253	11	like	like	ADP
ejpam-3294	253	12	function	function	NOUN
ejpam-3294	253	13	define	define	VERB
ejpam-3294	253	14	by	by	ADP
ejpam-3294	253	15	σ(0	σ(0	PROPN
ejpam-3294	253	16	,	,	PUNCT
ejpam-3294	253	17	0	0	NUM
ejpam-3294	253	18	)	)	PUNCT
ejpam-3294	253	19	=	=	PUNCT
ejpam-3294	254	1	σ(1	σ(1	PROPN
ejpam-3294	254	2	,	,	PUNCT
ejpam-3294	254	3	1	1	NUM
ejpam-3294	254	4	)	)	PUNCT
ejpam-3294	254	5	=	=	PUNCT
ejpam-3294	255	1	σ(2	σ(2	NOUN
ejpam-3294	255	2	,	,	PUNCT
ejpam-3294	255	3	2	2	NUM
ejpam-3294	255	4	)	)	PUNCT
ejpam-3294	255	5	=	=	SYM
ejpam-3294	255	6	0	0	NUM
ejpam-3294	255	7	,	,	PUNCT
ejpam-3294	255	8	σ(1	σ(1	PROPN
ejpam-3294	255	9	,	,	PUNCT
ejpam-3294	255	10	2	2	NUM
ejpam-3294	255	11	)	)	PUNCT
ejpam-3294	255	12	=	=	PUNCT
ejpam-3294	256	1	σ(2	σ(2	NOUN
ejpam-3294	256	2	,	,	PUNCT
ejpam-3294	256	3	1	1	NUM
ejpam-3294	256	4	)	)	PUNCT
ejpam-3294	256	5	=	=	SYM
ejpam-3294	256	6	3	3	NUM
ejpam-3294	256	7	,	,	PUNCT
ejpam-3294	256	8	σ(2	σ(2	NOUN
ejpam-3294	256	9	,	,	PUNCT
ejpam-3294	256	10	0	0	NUM
ejpam-3294	256	11	)	)	PUNCT
ejpam-3294	256	12	=	=	SYM
ejpam-3294	257	1	σ(0	σ(0	PROPN
ejpam-3294	257	2	,	,	PUNCT
ejpam-3294	257	3	2	2	NUM
ejpam-3294	257	4	)	)	PUNCT
ejpam-3294	257	5	=	=	SYM
ejpam-3294	257	6	2	2	NUM
ejpam-3294	257	7	,	,	PUNCT
ejpam-3294	257	8	σ(0	σ(0	PROPN
ejpam-3294	257	9	,	,	PUNCT
ejpam-3294	257	10	1	1	NUM
ejpam-3294	257	11	)	)	PUNCT
ejpam-3294	257	12	=	=	PUNCT
ejpam-3294	257	13	σ(1	σ(1	PROPN
ejpam-3294	257	14	,	,	PUNCT
ejpam-3294	257	15	0	0	NUM
ejpam-3294	257	16	)	)	PUNCT
ejpam-3294	257	17	=	=	SYM
ejpam-3294	257	18	3	3	NUM
ejpam-3294	257	19	2	2	NUM
ejpam-3294	257	20	.	.	PUNCT
ejpam-3294	258	1	it	it	PRON
ejpam-3294	258	2	is	be	AUX
ejpam-3294	258	3	easy	easy	ADJ
ejpam-3294	258	4	to	to	PART
ejpam-3294	258	5	see	see	VERB
ejpam-3294	258	6	that	that	PRON
ejpam-3294	258	7	(	(	PUNCT
ejpam-3294	258	8	x	x	X
ejpam-3294	258	9	,	,	PUNCT
ejpam-3294	258	10	σ	σ	PROPN
ejpam-3294	258	11	)	)	PUNCT
ejpam-3294	258	12	is	be	AUX
ejpam-3294	258	13	a	a	DET
ejpam-3294	258	14	complete	complete	ADJ
ejpam-3294	258	15	metric	metric	ADJ
ejpam-3294	258	16	-	-	PUNCT
ejpam-3294	258	17	like	like	ADJ
ejpam-3294	258	18	space	space	NOUN
ejpam-3294	258	19	.	.	PUNCT
ejpam-3294	259	1	also	also	ADV
ejpam-3294	259	2	,	,	PUNCT
ejpam-3294	259	3	define	define	VERB
ejpam-3294	259	4	f	f	X
ejpam-3294	259	5	:	:	PUNCT
ejpam-3294	259	6	x	x	X
ejpam-3294	259	7	→	→	PUNCT
ejpam-3294	259	8	x	x	PART
ejpam-3294	259	9	be	be	AUX
ejpam-3294	259	10	given	give	VERB
ejpam-3294	259	11	by	by	ADP
ejpam-3294	259	12	f0	f0	PROPN
ejpam-3294	259	13	=	=	SYM
ejpam-3294	259	14	0	0	PUNCT
ejpam-3294	259	15	=	=	NOUN
ejpam-3294	259	16	f1	f1	NOUN
ejpam-3294	259	17	and	and	CCONJ
ejpam-3294	259	18	f2	f2	NOUN
ejpam-3294	259	19	=	=	NOUN
ejpam-3294	259	20	1	1	X
ejpam-3294	259	21	.	.	PUNCT
ejpam-3294	259	22	define	define	VERB
ejpam-3294	259	23	α	α	NOUN
ejpam-3294	259	24	:	:	PUNCT
ejpam-3294	260	1	[	[	X
ejpam-3294	260	2	0,+∞)→	0,+∞)→	PUNCT
ejpam-3294	260	3	[	[	X
ejpam-3294	260	4	0	0	NUM
ejpam-3294	260	5	,	,	PUNCT
ejpam-3294	260	6	1	1	NUM
ejpam-3294	260	7	)	)	PUNCT
ejpam-3294	260	8	by	by	ADP
ejpam-3294	260	9	α(x	α(x	PROPN
ejpam-3294	260	10	,	,	PUNCT
ejpam-3294	260	11	y	y	PROPN
ejpam-3294	260	12	)	)	PUNCT
ejpam-3294	260	13	=	=	PRON
ejpam-3294	260	14	{	{	PUNCT
ejpam-3294	260	15	1	1	NUM
ejpam-3294	260	16	if	if	SCONJ
ejpam-3294	260	17	x	x	X
ejpam-3294	260	18	∈	∈	NOUN
ejpam-3294	260	19	{	{	PUNCT
ejpam-3294	260	20	0	0	NUM
ejpam-3294	260	21	,	,	PUNCT
ejpam-3294	260	22	1	1	NUM
ejpam-3294	260	23	,	,	PUNCT
ejpam-3294	260	24	2	2	NUM
ejpam-3294	260	25	}	}	PUNCT
ejpam-3294	260	26	0	0	NUM
ejpam-3294	260	27	if	if	SCONJ
ejpam-3294	260	28	otherwise	otherwise	ADV
ejpam-3294	260	29	.	.	PUNCT
ejpam-3294	261	1	define	define	VERB
ejpam-3294	261	2	β	β	NOUN
ejpam-3294	261	3	:	:	PUNCT
ejpam-3294	262	1	[	[	X
ejpam-3294	262	2	0,∞)→	0,∞)→	NOUN
ejpam-3294	262	3	[	[	X
ejpam-3294	262	4	0	0	NUM
ejpam-3294	262	5	,	,	PUNCT
ejpam-3294	262	6	1	1	NUM
ejpam-3294	262	7	)	)	PUNCT
ejpam-3294	262	8	by	by	ADP
ejpam-3294	262	9	β(t	β(t	PROPN
ejpam-3294	262	10	)	)	PUNCT
ejpam-3294	262	11	=	=	PUNCT
ejpam-3294	262	12			NUM
ejpam-3294	262	13	1	1	NUM
ejpam-3294	262	14	1	1	NUM
ejpam-3294	262	15	+	+	CCONJ
ejpam-3294	262	16	1	1	NUM
ejpam-3294	262	17	7	7	NUM
ejpam-3294	262	18	t	t	NOUN
ejpam-3294	262	19	if	if	SCONJ
ejpam-3294	262	20	t	t	PROPN
ejpam-3294	262	21	>	>	X
ejpam-3294	262	22	0	0	NUM
ejpam-3294	262	23	1	1	NUM
ejpam-3294	262	24	2	2	NUM
ejpam-3294	262	25	if	if	SCONJ
ejpam-3294	262	26	t	t	NOUN
ejpam-3294	262	27	=	=	SYM
ejpam-3294	262	28	0	0	PROPN
ejpam-3294	262	29	.	.	PUNCT
ejpam-3294	262	30	h.	h.	PROPN
ejpam-3294	262	31	qawaqneh	qawaqneh	PROPN
ejpam-3294	262	32	,	,	PUNCT
ejpam-3294	262	33	m.s	m.s	PROPN
ejpam-3294	262	34	.	.	PROPN
ejpam-3294	262	35	noorani	noorani	PROPN
ejpam-3294	262	36	,	,	PUNCT
ejpam-3294	262	37	w.	w.	PROPN
ejpam-3294	262	38	shatanawi	shatanawi	PROPN
ejpam-3294	262	39	/	/	SYM
ejpam-3294	262	40	eur	eur	PROPN
ejpam-3294	262	41	.	.	PUNCT
ejpam-3294	263	1	j.	j.	PROPN
ejpam-3294	263	2	pure	pure	PROPN
ejpam-3294	263	3	appl	appl	PROPN
ejpam-3294	263	4	.	.	PROPN
ejpam-3294	263	5	math	math	PROPN
ejpam-3294	263	6	,	,	PUNCT
ejpam-3294	263	7	11	11	NUM
ejpam-3294	263	8	(	(	PUNCT
ejpam-3294	263	9	3	3	NUM
ejpam-3294	263	10	)	)	PUNCT
ejpam-3294	263	11	(	(	PUNCT
ejpam-3294	263	12	2018	2018	NUM
ejpam-3294	263	13	)	)	PUNCT
ejpam-3294	263	14	,	,	PUNCT
ejpam-3294	263	15	702	702	NUM
ejpam-3294	263	16	-	-	SYM
ejpam-3294	263	17	716	716	NUM
ejpam-3294	263	18	712	712	NUM
ejpam-3294	263	19	suppose	suppose	VERB
ejpam-3294	263	20	that	that	SCONJ
ejpam-3294	263	21	f	f	PROPN
ejpam-3294	263	22	(	(	PUNCT
ejpam-3294	263	23	t	t	PROPN
ejpam-3294	263	24	)	)	PUNCT
ejpam-3294	263	25	=	=	SYM
ejpam-3294	263	26	et	et	PROPN
ejpam-3294	263	27	and	and	CCONJ
ejpam-3294	263	28	τ	τ	PROPN
ejpam-3294	263	29	=	=	NOUN
ejpam-3294	263	30	1	1	NUM
ejpam-3294	263	31	4	4	NUM
ejpam-3294	263	32	.	.	PUNCT
ejpam-3294	264	1	the	the	DET
ejpam-3294	264	2	function	function	NOUN
ejpam-3294	264	3	(	(	PUNCT
ejpam-3294	264	4	f	f	X
ejpam-3294	264	5	)	)	PUNCT
ejpam-3294	264	6	satisfies	satisfy	VERB
ejpam-3294	264	7	the	the	DET
ejpam-3294	264	8	inequality	inequality	NOUN
ejpam-3294	264	9	(	(	PUNCT
ejpam-3294	264	10	20	20	NUM
ejpam-3294	264	11	)	)	PUNCT
ejpam-3294	264	12	.	.	PUNCT
ejpam-3294	265	1	for	for	ADP
ejpam-3294	265	2	that	that	PRON
ejpam-3294	265	3	,	,	PUNCT
ejpam-3294	265	4	given	give	VERB
ejpam-3294	265	5	x	x	PRON
ejpam-3294	265	6	,	,	PUNCT
ejpam-3294	265	7	y	y	PROPN
ejpam-3294	265	8	∈	∈	PROPN
ejpam-3294	265	9	x.	x.	NOUN
ejpam-3294	265	10	then	then	ADV
ejpam-3294	265	11	we	we	PRON
ejpam-3294	265	12	have	have	VERB
ejpam-3294	265	13	the	the	DET
ejpam-3294	265	14	following	follow	VERB
ejpam-3294	265	15	cases	case	NOUN
ejpam-3294	265	16	:	:	PUNCT
ejpam-3294	265	17	case	case	NOUN
ejpam-3294	265	18	1	1	NUM
ejpam-3294	265	19	:	:	PUNCT
ejpam-3294	265	20	x	x	SYM
ejpam-3294	265	21	=	=	SYM
ejpam-3294	265	22	0	0	NUM
ejpam-3294	265	23	and	and	CCONJ
ejpam-3294	265	24	x	x	SYM
ejpam-3294	265	25	=	=	SYM
ejpam-3294	265	26	1	1	X
ejpam-3294	265	27	.	.	PUNCT
ejpam-3294	266	1	then	then	ADV
ejpam-3294	266	2	α(0	α(0	PROPN
ejpam-3294	266	3	,	,	PUNCT
ejpam-3294	266	4	1	1	NUM
ejpam-3294	266	5	)	)	PUNCT
ejpam-3294	266	6	=	=	SYM
ejpam-3294	266	7	1	1	NUM
ejpam-3294	266	8	and	and	CCONJ
ejpam-3294	266	9	m0,1	m0,1	PROPN
ejpam-3294	266	10	=	=	SYM
ejpam-3294	266	11	max{0	max{0	PROPN
ejpam-3294	266	12	,	,	PUNCT
ejpam-3294	266	13	0	0	NUM
ejpam-3294	266	14	,	,	PUNCT
ejpam-3294	266	15	0	0	NUM
ejpam-3294	266	16	,	,	PUNCT
ejpam-3294	266	17	0	0	NUM
ejpam-3294	266	18	,	,	PUNCT
ejpam-3294	266	19	1	1	NUM
ejpam-3294	266	20	}	}	PUNCT
ejpam-3294	266	21	=	=	SYM
ejpam-3294	266	22	1	1	NUM
ejpam-3294	266	23	.	.	X
ejpam-3294	266	24	σ(f0	σ(f0	PROPN
ejpam-3294	266	25	,	,	PUNCT
ejpam-3294	266	26	f1	f1	NOUN
ejpam-3294	266	27	)	)	PUNCT
ejpam-3294	266	28	=	=	SYM
ejpam-3294	266	29	σ(0	σ(0	PROPN
ejpam-3294	266	30	,	,	PUNCT
ejpam-3294	266	31	0	0	NUM
ejpam-3294	266	32	)	)	PUNCT
ejpam-3294	266	33	=	=	SYM
ejpam-3294	267	1	0	0	X
ejpam-3294	267	2	.	.	PUNCT
ejpam-3294	268	1	now	now	ADV
ejpam-3294	268	2	0	0	X
ejpam-3294	268	3	<	<	X
ejpam-3294	268	4	α(0	α(0	PROPN
ejpam-3294	268	5	,	,	PUNCT
ejpam-3294	268	6	1)(τ	1)(τ	NUM
ejpam-3294	268	7	+	+	NUM
ejpam-3294	268	8	f	f	PROPN
ejpam-3294	268	9	(	(	PUNCT
ejpam-3294	268	10	σ(f0	σ(f0	NOUN
ejpam-3294	268	11	,	,	PUNCT
ejpam-3294	268	12	f1	f1	NOUN
ejpam-3294	268	13	)	)	PUNCT
ejpam-3294	268	14	)	)	PUNCT
ejpam-3294	268	15	)	)	PUNCT
ejpam-3294	269	1	=	=	PUNCT
ejpam-3294	270	1	τ	τ	X
ejpam-3294	270	2	+	+	NUM
ejpam-3294	270	3	f	f	X
ejpam-3294	270	4	(	(	PUNCT
ejpam-3294	270	5	σ(0	σ(0	PROPN
ejpam-3294	270	6	,	,	PUNCT
ejpam-3294	270	7	0	0	NUM
ejpam-3294	270	8	)	)	PUNCT
ejpam-3294	270	9	)	)	PUNCT
ejpam-3294	271	1	=	=	SYM
ejpam-3294	271	2	(	(	PUNCT
ejpam-3294	271	3	τ	τ	X
ejpam-3294	272	1	+	+	NUM
ejpam-3294	272	2	f	f	X
ejpam-3294	272	3	(	(	PUNCT
ejpam-3294	272	4	0	0	NUM
ejpam-3294	272	5	)	)	PUNCT
ejpam-3294	272	6	=	=	PUNCT
ejpam-3294	272	7	τ	τ	X
ejpam-3294	272	8	≤	≤	NUM
ejpam-3294	272	9	β(m0,1)f	β(m0,1)f	VERB
ejpam-3294	272	10	(	(	PUNCT
ejpam-3294	272	11	m0,1	m0,1	NOUN
ejpam-3294	272	12	)	)	PUNCT
ejpam-3294	272	13	=	=	SYM
ejpam-3294	273	1	β(1)f	β(1)f	X
ejpam-3294	273	2	(	(	PUNCT
ejpam-3294	273	3	1	1	NUM
ejpam-3294	273	4	)	)	PUNCT
ejpam-3294	273	5	=	=	SYM
ejpam-3294	273	6	e	e	X
ejpam-3294	273	7	(	(	PUNCT
ejpam-3294	273	8	17	17	NUM
ejpam-3294	273	9	)	)	PUNCT
ejpam-3294	273	10	case	case	NOUN
ejpam-3294	273	11	2	2	NUM
ejpam-3294	273	12	:	:	PUNCT
ejpam-3294	273	13	x	x	SYM
ejpam-3294	273	14	=	=	SYM
ejpam-3294	273	15	0	0	NUM
ejpam-3294	273	16	and	and	CCONJ
ejpam-3294	273	17	y	y	PROPN
ejpam-3294	273	18	=	=	SYM
ejpam-3294	273	19	2	2	X
ejpam-3294	273	20	.	.	PUNCT
ejpam-3294	273	21	then	then	ADV
ejpam-3294	273	22	α(0	α(0	PROPN
ejpam-3294	273	23	,	,	PUNCT
ejpam-3294	273	24	2	2	NUM
ejpam-3294	273	25	)	)	PUNCT
ejpam-3294	273	26	=	=	SYM
ejpam-3294	273	27	1	1	NUM
ejpam-3294	273	28	and	and	CCONJ
ejpam-3294	273	29	m0,2	m0,2	NOUN
ejpam-3294	273	30	=	=	SYM
ejpam-3294	273	31	max{2	max{2	PROPN
ejpam-3294	273	32	,	,	PUNCT
ejpam-3294	273	33	0	0	NUM
ejpam-3294	273	34	,	,	PUNCT
ejpam-3294	273	35	3	3	NUM
ejpam-3294	273	36	,	,	PUNCT
ejpam-3294	273	37	13	13	NUM
ejpam-3294	273	38	16	16	NUM
ejpam-3294	273	39	,	,	PUNCT
ejpam-3294	273	40	1	1	NUM
ejpam-3294	273	41	}	}	PUNCT
ejpam-3294	273	42	=	=	SYM
ejpam-3294	273	43	3	3	X
ejpam-3294	273	44	.	.	X
ejpam-3294	273	45	σ(f0	σ(f0	PROPN
ejpam-3294	273	46	,	,	PUNCT
ejpam-3294	273	47	f2	f2	PROPN
ejpam-3294	273	48	)	)	PUNCT
ejpam-3294	273	49	=	=	SYM
ejpam-3294	273	50	σ(0	σ(0	PROPN
ejpam-3294	273	51	,	,	PUNCT
ejpam-3294	273	52	1	1	NUM
ejpam-3294	273	53	)	)	PUNCT
ejpam-3294	273	54	=	=	SYM
ejpam-3294	273	55	3	3	NUM
ejpam-3294	273	56	2	2	NUM
ejpam-3294	273	57	.	.	PUNCT
ejpam-3294	274	1	now	now	ADV
ejpam-3294	274	2	0	0	X
ejpam-3294	274	3	<	<	X
ejpam-3294	274	4	α(0	α(0	PROPN
ejpam-3294	274	5	,	,	PUNCT
ejpam-3294	274	6	2)(τ	2)(τ	NUM
ejpam-3294	275	1	+	+	NUM
ejpam-3294	275	2	f	f	PROPN
ejpam-3294	275	3	(	(	PUNCT
ejpam-3294	275	4	σ(f0	σ(f0	NOUN
ejpam-3294	275	5	,	,	PUNCT
ejpam-3294	275	6	f2	f2	PROPN
ejpam-3294	275	7	)	)	PUNCT
ejpam-3294	275	8	)	)	PUNCT
ejpam-3294	275	9	)	)	PUNCT
ejpam-3294	276	1	=	=	PUNCT
ejpam-3294	277	1	τ	τ	X
ejpam-3294	278	1	+	+	NUM
ejpam-3294	278	2	f	f	X
ejpam-3294	278	3	(	(	PUNCT
ejpam-3294	278	4	3	3	NUM
ejpam-3294	278	5	2	2	NUM
ejpam-3294	278	6	)	)	PUNCT
ejpam-3294	278	7	=	=	PUNCT
ejpam-3294	278	8	τ	τ	PROPN
ejpam-3294	278	9	+	+	CCONJ
ejpam-3294	278	10	3	3	NUM
ejpam-3294	278	11	2	2	NUM
ejpam-3294	278	12	≤	≤	NOUN
ejpam-3294	278	13	β(m0,2)f	β(m0,2)f	NOUN
ejpam-3294	278	14	(	(	PUNCT
ejpam-3294	278	15	m0,2	m0,2	NOUN
ejpam-3294	278	16	)	)	PUNCT
ejpam-3294	278	17	=	=	SYM
ejpam-3294	279	1	β(3)f	β(3)f	PROPN
ejpam-3294	279	2	(	(	PUNCT
ejpam-3294	279	3	3	3	NUM
ejpam-3294	279	4	)	)	PUNCT
ejpam-3294	279	5	=	=	SYM
ejpam-3294	279	6	3e3	3e3	NUM
ejpam-3294	279	7	,	,	PUNCT
ejpam-3294	279	8	case	case	NOUN
ejpam-3294	279	9	3	3	NUM
ejpam-3294	279	10	:	:	PUNCT
ejpam-3294	279	11	x	x	SYM
ejpam-3294	279	12	=	=	SYM
ejpam-3294	279	13	1	1	NUM
ejpam-3294	279	14	and	and	CCONJ
ejpam-3294	279	15	y	y	NOUN
ejpam-3294	279	16	=	=	SYM
ejpam-3294	279	17	2	2	X
ejpam-3294	279	18	.	.	PUNCT
ejpam-3294	279	19	then	then	ADV
ejpam-3294	279	20	α(1	α(1	PROPN
ejpam-3294	279	21	,	,	PUNCT
ejpam-3294	279	22	2	2	X
ejpam-3294	279	23	)	)	PUNCT
ejpam-3294	279	24	=	=	SYM
ejpam-3294	279	25	1	1	NUM
ejpam-3294	279	26	and	and	CCONJ
ejpam-3294	279	27	m1,2	m1,2	ADJ
ejpam-3294	279	28	=	=	SYM
ejpam-3294	279	29	max{3	max{3	NOUN
ejpam-3294	279	30	,	,	PUNCT
ejpam-3294	279	31	3	3	NUM
ejpam-3294	279	32	2	2	NUM
ejpam-3294	279	33	,	,	PUNCT
ejpam-3294	279	34	3	3	NUM
ejpam-3294	279	35	,	,	PUNCT
ejpam-3294	279	36	1	1	NUM
ejpam-3294	279	37	2	2	NUM
ejpam-3294	279	38	,	,	PUNCT
ejpam-3294	279	39	15	15	NUM
ejpam-3294	279	40	8	8	NUM
ejpam-3294	279	41	}	}	PUNCT
ejpam-3294	279	42	=	=	SYM
ejpam-3294	279	43	3	3	X
ejpam-3294	279	44	.	.	X
ejpam-3294	279	45	σ(f1	σ(f1	PROPN
ejpam-3294	279	46	,	,	PUNCT
ejpam-3294	279	47	f2	f2	PROPN
ejpam-3294	279	48	)	)	PUNCT
ejpam-3294	279	49	=	=	SYM
ejpam-3294	279	50	σ(0	σ(0	PROPN
ejpam-3294	279	51	,	,	PUNCT
ejpam-3294	279	52	1	1	NUM
ejpam-3294	279	53	)	)	PUNCT
ejpam-3294	279	54	=	=	SYM
ejpam-3294	279	55	3	3	NUM
ejpam-3294	279	56	2	2	NUM
ejpam-3294	279	57	.	.	PUNCT
ejpam-3294	280	1	now	now	ADV
ejpam-3294	280	2	0	0	X
ejpam-3294	280	3	<	<	X
ejpam-3294	280	4	α(0	α(0	PROPN
ejpam-3294	280	5	,	,	PUNCT
ejpam-3294	280	6	2)(τ	2)(τ	NUM
ejpam-3294	281	1	+	+	NUM
ejpam-3294	281	2	f	f	PROPN
ejpam-3294	281	3	(	(	PUNCT
ejpam-3294	281	4	σ(f0	σ(f0	NOUN
ejpam-3294	281	5	,	,	PUNCT
ejpam-3294	281	6	f2	f2	PROPN
ejpam-3294	281	7	)	)	PUNCT
ejpam-3294	281	8	)	)	PUNCT
ejpam-3294	281	9	)	)	PUNCT
ejpam-3294	282	1	=	=	PUNCT
ejpam-3294	283	1	τ	τ	X
ejpam-3294	284	1	+	+	NUM
ejpam-3294	284	2	f	f	X
ejpam-3294	284	3	(	(	PUNCT
ejpam-3294	284	4	3	3	NUM
ejpam-3294	284	5	2	2	NUM
ejpam-3294	284	6	)	)	PUNCT
ejpam-3294	284	7	=	=	PUNCT
ejpam-3294	284	8	τ	τ	PROPN
ejpam-3294	284	9	+	+	CCONJ
ejpam-3294	284	10	3	3	NUM
ejpam-3294	284	11	2	2	NUM
ejpam-3294	284	12	≤	≤	NOUN
ejpam-3294	284	13	β(m0,2)f	β(m0,2)f	NOUN
ejpam-3294	284	14	(	(	PUNCT
ejpam-3294	284	15	m0,2	m0,2	NOUN
ejpam-3294	284	16	)	)	PUNCT
ejpam-3294	284	17	=	=	SYM
ejpam-3294	285	1	β(3)f	β(3)f	PROPN
ejpam-3294	285	2	(	(	PUNCT
ejpam-3294	285	3	3	3	NUM
ejpam-3294	285	4	)	)	PUNCT
ejpam-3294	285	5	=	=	SYM
ejpam-3294	285	6	3e3	3e3	NUM
ejpam-3294	285	7	,	,	PUNCT
ejpam-3294	285	8	thus	thus	ADV
ejpam-3294	285	9	,	,	PUNCT
ejpam-3294	285	10	all	all	DET
ejpam-3294	285	11	the	the	DET
ejpam-3294	285	12	conditions	condition	NOUN
ejpam-3294	285	13	of	of	ADP
ejpam-3294	285	14	theorem	theorem	ADJ
ejpam-3294	285	15	2	2	NUM
ejpam-3294	285	16	are	be	AUX
ejpam-3294	285	17	satisfied	satisfied	ADJ
ejpam-3294	285	18	and	and	CCONJ
ejpam-3294	285	19	hence	hence	ADV
ejpam-3294	285	20	f	f	PROPN
ejpam-3294	285	21	has	have	VERB
ejpam-3294	285	22	a	a	DET
ejpam-3294	285	23	unique	unique	ADJ
ejpam-3294	285	24	fixed	fix	VERB
ejpam-3294	285	25	point	point	NOUN
ejpam-3294	285	26	.	.	PUNCT
ejpam-3294	286	1	3	3	X
ejpam-3294	286	2	.	.	X
ejpam-3294	286	3	consequences	consequence	NOUN
ejpam-3294	286	4	in	in	ADP
ejpam-3294	286	5	this	this	DET
ejpam-3294	286	6	section	section	NOUN
ejpam-3294	286	7	,	,	PUNCT
ejpam-3294	286	8	we	we	PRON
ejpam-3294	286	9	derive	derive	VERB
ejpam-3294	286	10	the	the	DET
ejpam-3294	286	11	analog	analog	NOUN
ejpam-3294	286	12	of	of	ADP
ejpam-3294	286	13	theorem	theorem	NOUN
ejpam-3294	286	14	2	2	NUM
ejpam-3294	286	15	in	in	ADP
ejpam-3294	286	16	the	the	DET
ejpam-3294	286	17	context	context	NOUN
ejpam-3294	286	18	of	of	ADP
ejpam-3294	286	19	partial	partial	ADJ
ejpam-3294	286	20	metric	metric	ADJ
ejpam-3294	286	21	spaces	space	NOUN
ejpam-3294	286	22	(	(	PUNCT
ejpam-3294	286	23	pms	pm	NOUN
ejpam-3294	286	24	)	)	PUNCT
ejpam-3294	286	25	.	.	PUNCT
ejpam-3294	287	1	in	in	ADP
ejpam-3294	287	2	the	the	DET
ejpam-3294	287	3	following	follow	VERB
ejpam-3294	287	4	theorem	theorem	NOUN
ejpam-3294	287	5	we	we	PRON
ejpam-3294	287	6	conclude	conclude	VERB
ejpam-3294	287	7	the	the	DET
ejpam-3294	287	8	existence	existence	NOUN
ejpam-3294	287	9	and	and	CCONJ
ejpam-3294	287	10	the	the	DET
ejpam-3294	287	11	uniqueness	uniqueness	NOUN
ejpam-3294	287	12	of	of	ADP
ejpam-3294	287	13	h.	h.	PROPN
ejpam-3294	287	14	qawaqneh	qawaqneh	PROPN
ejpam-3294	287	15	,	,	PUNCT
ejpam-3294	287	16	m.s	m.s	PROPN
ejpam-3294	287	17	.	.	PROPN
ejpam-3294	287	18	noorani	noorani	PROPN
ejpam-3294	287	19	,	,	PUNCT
ejpam-3294	287	20	w.	w.	PROPN
ejpam-3294	287	21	shatanawi	shatanawi	PROPN
ejpam-3294	287	22	/	/	SYM
ejpam-3294	287	23	eur	eur	PROPN
ejpam-3294	287	24	.	.	PUNCT
ejpam-3294	288	1	j.	j.	PROPN
ejpam-3294	288	2	pure	pure	PROPN
ejpam-3294	288	3	appl	appl	PROPN
ejpam-3294	288	4	.	.	PROPN
ejpam-3294	288	5	math	math	PROPN
ejpam-3294	288	6	,	,	PUNCT
ejpam-3294	288	7	11	11	NUM
ejpam-3294	288	8	(	(	PUNCT
ejpam-3294	288	9	3	3	NUM
ejpam-3294	288	10	)	)	PUNCT
ejpam-3294	288	11	(	(	PUNCT
ejpam-3294	288	12	2018	2018	NUM
ejpam-3294	288	13	)	)	PUNCT
ejpam-3294	288	14	,	,	PUNCT
ejpam-3294	288	15	702	702	NUM
ejpam-3294	288	16	-	-	SYM
ejpam-3294	288	17	716	716	NUM
ejpam-3294	288	18	713	713	NUM
ejpam-3294	288	19	a	a	DET
ejpam-3294	288	20	fixed	fix	VERB
ejpam-3294	288	21	point	point	NOUN
ejpam-3294	288	22	of	of	ADP
ejpam-3294	288	23	the	the	DET
ejpam-3294	288	24	given	give	VERB
ejpam-3294	288	25	mapping	mapping	NOUN
ejpam-3294	288	26	.	.	PUNCT
ejpam-3294	289	1	theorem	theorem	NOUN
ejpam-3294	289	2	3	3	X
ejpam-3294	289	3	.	.	PUNCT
ejpam-3294	290	1	let	let	VERB
ejpam-3294	290	2	(	(	PUNCT
ejpam-3294	290	3	x	x	X
ejpam-3294	290	4	,	,	PUNCT
ejpam-3294	290	5	p	p	X
ejpam-3294	290	6	)	)	PUNCT
ejpam-3294	290	7	be	be	AUX
ejpam-3294	290	8	a	a	DET
ejpam-3294	290	9	a	a	DET
ejpam-3294	290	10	complete	complete	ADJ
ejpam-3294	290	11	partial	partial	ADJ
ejpam-3294	290	12	metric	metric	ADJ
ejpam-3294	290	13	space	space	NOUN
ejpam-3294	290	14	and	and	CCONJ
ejpam-3294	290	15	α	α	NOUN
ejpam-3294	290	16	:	:	PUNCT
ejpam-3294	290	17	x	x	PROPN
ejpam-3294	290	18	×x	×x	X
ejpam-3294	290	19	→	→	X
ejpam-3294	290	20	[	[	X
ejpam-3294	290	21	0,∞	0,∞	NOUN
ejpam-3294	290	22	)	)	PUNCT
ejpam-3294	290	23	.	.	PUNCT
ejpam-3294	291	1	a	a	DET
ejpam-3294	291	2	mapping	mapping	NOUN
ejpam-3294	291	3	f	f	NOUN
ejpam-3294	291	4	:	:	PUNCT
ejpam-3294	291	5	x	x	X
ejpam-3294	291	6	→	→	PUNCT
ejpam-3294	291	7	x	x	PUNCT
ejpam-3294	291	8	be	be	AUX
ejpam-3294	291	9	an	an	DET
ejpam-3294	291	10	(	(	PUNCT
ejpam-3294	291	11	α	α	NOUN
ejpam-3294	291	12	,	,	PUNCT
ejpam-3294	291	13	β	β	X
ejpam-3294	291	14	,	,	PUNCT
ejpam-3294	291	15	f	f	PROPN
ejpam-3294	291	16	)	)	PUNCT
ejpam-3294	291	17	−geraghty	−geraghty	PROPN
ejpam-3294	291	18	contraction	contraction	PROPN
ejpam-3294	291	19	mapping	mapping	NOUN
ejpam-3294	291	20	.	.	PUNCT
ejpam-3294	292	1	suppose	suppose	VERB
ejpam-3294	292	2	there	there	PRON
ejpam-3294	292	3	exist	exist	VERB
ejpam-3294	292	4	f	f	PROPN
ejpam-3294	292	5	∈	∈	PROPN
ejpam-3294	292	6	f	f	PROPN
ejpam-3294	292	7	and	and	CCONJ
ejpam-3294	292	8	τ	τ	PROPN
ejpam-3294	292	9	>	>	X
ejpam-3294	292	10	0	0	NUM
ejpam-3294	292	11	such	such	ADJ
ejpam-3294	292	12	that	that	SCONJ
ejpam-3294	292	13	,	,	PUNCT
ejpam-3294	292	14	for	for	ADP
ejpam-3294	292	15	all	all	DET
ejpam-3294	292	16	x	x	NOUN
ejpam-3294	292	17	,	,	PUNCT
ejpam-3294	292	18	y	y	PROPN
ejpam-3294	292	19	∈	∈	PROPN
ejpam-3294	292	20	x	x	PUNCT
ejpam-3294	292	21	with	with	ADP
ejpam-3294	292	22	σ(fx	σ(fx	PROPN
ejpam-3294	292	23	,	,	PUNCT
ejpam-3294	292	24	fy	fy	PROPN
ejpam-3294	292	25	)	)	PUNCT
ejpam-3294	292	26	>	>	X
ejpam-3294	292	27	0	0	PUNCT
ejpam-3294	292	28	and	and	CCONJ
ejpam-3294	292	29	α(x	α(x	PROPN
ejpam-3294	292	30	,	,	PUNCT
ejpam-3294	292	31	y	y	PROPN
ejpam-3294	292	32	)	)	PUNCT
ejpam-3294	292	33	≥	≥	NOUN
ejpam-3294	292	34	1	1	NUM
ejpam-3294	292	35	,	,	PUNCT
ejpam-3294	292	36	0	0	NUM
ejpam-3294	292	37	<	<	X
ejpam-3294	292	38	α(x	α(x	PROPN
ejpam-3294	292	39	,	,	PUNCT
ejpam-3294	292	40	y)(τ	y)(τ	PROPN
ejpam-3294	293	1	+	+	CCONJ
ejpam-3294	293	2	f	f	X
ejpam-3294	293	3	(	(	PUNCT
ejpam-3294	293	4	σ(fx	σ(fx	PROPN
ejpam-3294	293	5	,	,	PUNCT
ejpam-3294	293	6	fy	fy	PROPN
ejpam-3294	293	7	)	)	PUNCT
ejpam-3294	293	8	)	)	PUNCT
ejpam-3294	293	9	≤	≤	NUM
ejpam-3294	293	10	β(mx	β(mx	NOUN
ejpam-3294	293	11	,	,	PUNCT
ejpam-3294	293	12	y)f	y)f	NOUN
ejpam-3294	293	13	(	(	PUNCT
ejpam-3294	293	14	mx	mx	PROPN
ejpam-3294	293	15	,	,	PUNCT
ejpam-3294	293	16	y	y	PROPN
ejpam-3294	293	17	)	)	PUNCT
ejpam-3294	293	18	,	,	PUNCT
ejpam-3294	293	19	(	(	PUNCT
ejpam-3294	293	20	18	18	NUM
ejpam-3294	293	21	)	)	PUNCT
ejpam-3294	293	22	where	where	SCONJ
ejpam-3294	293	23	mx	mx	PROPN
ejpam-3294	293	24	,	,	PUNCT
ejpam-3294	293	25	y	y	PROPN
ejpam-3294	293	26	=	=	PUNCT
ejpam-3294	293	27	max{max{p(x	max{max{p(x	PROPN
ejpam-3294	293	28	,	,	PUNCT
ejpam-3294	293	29	y	y	NOUN
ejpam-3294	293	30	)	)	PUNCT
ejpam-3294	293	31	,	,	PUNCT
ejpam-3294	293	32	p(x	p(x	PROPN
ejpam-3294	293	33	,	,	PUNCT
ejpam-3294	293	34	fx	fx	NOUN
ejpam-3294	293	35	)	)	PUNCT
ejpam-3294	293	36	,	,	PUNCT
ejpam-3294	293	37	p(y	p(y	PROPN
ejpam-3294	293	38	,	,	PUNCT
ejpam-3294	293	39	fy	fy	PROPN
ejpam-3294	293	40	)	)	PUNCT
ejpam-3294	293	41	,	,	PUNCT
ejpam-3294	293	42	p(fx	p(fx	PROPN
ejpam-3294	293	43	,	,	PUNCT
ejpam-3294	293	44	y	y	NOUN
ejpam-3294	293	45	)	)	PUNCT
ejpam-3294	293	46	+	+	CCONJ
ejpam-3294	293	47	p(x	p(x	PROPN
ejpam-3294	293	48	,	,	PUNCT
ejpam-3294	293	49	fy	fy	PROPN
ejpam-3294	293	50	)	)	PUNCT
ejpam-3294	293	51	4	4	NUM
ejpam-3294	293	52	,	,	PUNCT
ejpam-3294	293	53	[	[	X
ejpam-3294	293	54	1	1	NUM
ejpam-3294	293	55	+	+	NUM
ejpam-3294	293	56	p(x	p(x	PROPN
ejpam-3294	293	57	,	,	PUNCT
ejpam-3294	293	58	fx)]p(y	fx)]p(y	ADJ
ejpam-3294	293	59	,	,	PUNCT
ejpam-3294	293	60	fy	fy	NOUN
ejpam-3294	293	61	)	)	PUNCT
ejpam-3294	293	62	p(x	p(x	PROPN
ejpam-3294	293	63	,	,	PUNCT
ejpam-3294	293	64	y	y	PROPN
ejpam-3294	293	65	)	)	PUNCT
ejpam-3294	293	66	+	+	CCONJ
ejpam-3294	293	67	1	1	NUM
ejpam-3294	293	68	}	}	PUNCT
ejpam-3294	293	69	.	.	PUNCT
ejpam-3294	294	1	then	then	ADV
ejpam-3294	294	2	f	f	PROPN
ejpam-3294	294	3	has	have	VERB
ejpam-3294	294	4	a	a	DET
ejpam-3294	294	5	unique	unique	ADJ
ejpam-3294	294	6	fixed	fix	VERB
ejpam-3294	294	7	point	point	NOUN
ejpam-3294	294	8	z	z	NOUN
ejpam-3294	294	9	∈	∈	PROPN
ejpam-3294	294	10	x	x	PUNCT
ejpam-3294	294	11	with	with	ADP
ejpam-3294	294	12	p(z	p(z	NOUN
ejpam-3294	294	13	,	,	PUNCT
ejpam-3294	294	14	z	z	NOUN
ejpam-3294	294	15	)	)	PUNCT
ejpam-3294	294	16	=	=	SYM
ejpam-3294	294	17	0	0	X
ejpam-3294	294	18	.	.	PUNCT
ejpam-3294	295	1	proof	proof	NOUN
ejpam-3294	295	2	.	.	PUNCT
ejpam-3294	296	1	since	since	SCONJ
ejpam-3294	296	2	every	every	DET
ejpam-3294	296	3	partial	partial	ADJ
ejpam-3294	296	4	metric	metric	ADJ
ejpam-3294	296	5	space	space	NOUN
ejpam-3294	296	6	is	be	AUX
ejpam-3294	296	7	a	a	DET
ejpam-3294	296	8	metric	metric	ADJ
ejpam-3294	296	9	-	-	PUNCT
ejpam-3294	296	10	like	like	ADJ
ejpam-3294	296	11	space	space	NOUN
ejpam-3294	296	12	,	,	PUNCT
ejpam-3294	296	13	we	we	PRON
ejpam-3294	296	14	obtain	obtain	VERB
ejpam-3294	296	15	the	the	DET
ejpam-3294	296	16	proof	proof	NOUN
ejpam-3294	296	17	by	by	ADP
ejpam-3294	296	18	following	follow	VERB
ejpam-3294	296	19	the	the	DET
ejpam-3294	296	20	proof	proof	NOUN
ejpam-3294	296	21	in	in	ADP
ejpam-3294	296	22	theorem	theorem	NOUN
ejpam-3294	296	23	2	2	X
ejpam-3294	296	24	.	.	PUNCT
ejpam-3294	297	1	we	we	PRON
ejpam-3294	297	2	now	now	ADV
ejpam-3294	297	3	show	show	VERB
ejpam-3294	297	4	the	the	DET
ejpam-3294	297	5	uniqueness	uniqueness	NOUN
ejpam-3294	297	6	of	of	ADP
ejpam-3294	297	7	the	the	DET
ejpam-3294	297	8	fixed	fix	VERB
ejpam-3294	297	9	point	point	NOUN
ejpam-3294	297	10	of	of	ADP
ejpam-3294	297	11	f.	f.	PROPN
ejpam-3294	297	12	suppose	suppose	VERB
ejpam-3294	297	13	there	there	PRON
ejpam-3294	297	14	is	be	VERB
ejpam-3294	297	15	another	another	DET
ejpam-3294	297	16	fixed	fix	VERB
ejpam-3294	297	17	point	point	NOUN
ejpam-3294	297	18	y∗	y∗	PROPN
ejpam-3294	297	19	∈	∈	PROPN
ejpam-3294	297	20	x	x	PUNCT
ejpam-3294	297	21	of	of	ADP
ejpam-3294	297	22	f	f	PROPN
ejpam-3294	297	23	,	,	PUNCT
ejpam-3294	297	24	such	such	ADJ
ejpam-3294	297	25	that	that	DET
ejpam-3294	297	26	x∗	x∗	PROPN
ejpam-3294	297	27	6=	6=	PRON
ejpam-3294	297	28	y∗.	y∗.	PRON
ejpam-3294	297	29	thus	thus	ADV
ejpam-3294	297	30	from	from	ADP
ejpam-3294	297	31	lemma	lemma	PROPN
ejpam-3294	297	32	?	?	PUNCT
ejpam-3294	297	33	?	?	PUNCT
ejpam-3294	298	1	,	,	PUNCT
ejpam-3294	298	2	we	we	PRON
ejpam-3294	298	3	have	have	VERB
ejpam-3294	298	4	p(x∗	p(x∗	NOUN
ejpam-3294	298	5	,	,	PUNCT
ejpam-3294	298	6	y∗	y∗	PROPN
ejpam-3294	298	7	)	)	PUNCT
ejpam-3294	298	8	>	>	X
ejpam-3294	299	1	0	0	X
ejpam-3294	299	2	.	.	PUNCT
ejpam-3294	300	1	from	from	ADP
ejpam-3294	300	2	(	(	PUNCT
ejpam-3294	300	3	p2	p2	NOUN
ejpam-3294	300	4	)	)	PUNCT
ejpam-3294	300	5	,	,	PUNCT
ejpam-3294	300	6	we	we	PRON
ejpam-3294	300	7	have	have	VERB
ejpam-3294	300	8	p(fx∗	p(fx∗	PRON
ejpam-3294	300	9	,	,	PUNCT
ejpam-3294	300	10	fy∗	fy∗	NOUN
ejpam-3294	300	11	)	)	PUNCT
ejpam-3294	300	12	=	=	SYM
ejpam-3294	301	1	p(x∗	p(x∗	NOUN
ejpam-3294	301	2	,	,	PUNCT
ejpam-3294	301	3	y∗	y∗	PROPN
ejpam-3294	301	4	)	)	PUNCT
ejpam-3294	301	5	>	>	X
ejpam-3294	301	6	0	0	X
ejpam-3294	301	7	.	.	PUNCT
ejpam-3294	302	1	thus	thus	ADV
ejpam-3294	302	2	0	0	NUM
ejpam-3294	302	3	<	<	X
ejpam-3294	302	4	τ	τ	PROPN
ejpam-3294	303	1	+	+	NUM
ejpam-3294	303	2	f	f	X
ejpam-3294	303	3	(	(	PUNCT
ejpam-3294	303	4	p(x∗	p(x∗	NOUN
ejpam-3294	303	5	,	,	PUNCT
ejpam-3294	303	6	y∗	y∗	PROPN
ejpam-3294	303	7	)	)	PUNCT
ejpam-3294	303	8	)	)	PUNCT
ejpam-3294	303	9	≤	≤	NUM
ejpam-3294	303	10	α(x∗	α(x∗	NOUN
ejpam-3294	303	11	,	,	PUNCT
ejpam-3294	303	12	y∗)(τ	y∗)(τ	VERB
ejpam-3294	303	13	+	+	CCONJ
ejpam-3294	303	14	f	f	X
ejpam-3294	303	15	(	(	PUNCT
ejpam-3294	303	16	p(fx∗	p(fx∗	NOUN
ejpam-3294	303	17	,	,	PUNCT
ejpam-3294	303	18	fy∗	fy∗	NOUN
ejpam-3294	303	19	)	)	PUNCT
ejpam-3294	303	20	)	)	PUNCT
ejpam-3294	304	1	≤	≤	NUM
ejpam-3294	304	2	β(mx∗,y∗)f	β(mx∗,y∗)f	NOUN
ejpam-3294	304	3	(	(	PUNCT
ejpam-3294	304	4	mx∗,y∗	mx∗,y∗	NOUN
ejpam-3294	304	5	)	)	PUNCT
ejpam-3294	304	6	=	=	SYM
ejpam-3294	304	7	β(p(x∗	β(p(x∗	PROPN
ejpam-3294	304	8	,	,	PUNCT
ejpam-3294	304	9	y∗))f	y∗))f	PROPN
ejpam-3294	304	10	(	(	PUNCT
ejpam-3294	304	11	p(x∗	p(x∗	NOUN
ejpam-3294	304	12	,	,	PUNCT
ejpam-3294	304	13	y∗	y∗	PROPN
ejpam-3294	304	14	)	)	PUNCT
ejpam-3294	304	15	)	)	PUNCT
ejpam-3294	304	16	≤	≤	NUM
ejpam-3294	305	1	f	f	X
ejpam-3294	305	2	(	(	PUNCT
ejpam-3294	305	3	p(x∗	p(x∗	NOUN
ejpam-3294	305	4	,	,	PUNCT
ejpam-3294	305	5	y∗	y∗	PROPN
ejpam-3294	305	6	)	)	PUNCT
ejpam-3294	305	7	)	)	PUNCT
ejpam-3294	305	8	,	,	PUNCT
ejpam-3294	305	9	where	where	SCONJ
ejpam-3294	305	10	mx∗,y∗	mx∗,y∗	NOUN
ejpam-3294	305	11	=	=	SYM
ejpam-3294	305	12	max{p(x∗	max{p(x∗	PROPN
ejpam-3294	305	13	,	,	PUNCT
ejpam-3294	305	14	y∗	y∗	PROPN
ejpam-3294	305	15	)	)	PUNCT
ejpam-3294	305	16	,	,	PUNCT
ejpam-3294	305	17	p(x∗	p(x∗	NOUN
ejpam-3294	305	18	,	,	PUNCT
ejpam-3294	305	19	fx∗	fx∗	ADJ
ejpam-3294	305	20	)	)	PUNCT
ejpam-3294	305	21	,	,	PUNCT
ejpam-3294	305	22	p(y∗	p(y∗	NOUN
ejpam-3294	305	23	,	,	PUNCT
ejpam-3294	305	24	fy∗	fy∗	NOUN
ejpam-3294	305	25	)	)	PUNCT
ejpam-3294	305	26	,	,	PUNCT
ejpam-3294	305	27	p(fx	p(fx	NOUN
ejpam-3294	305	28	∗	∗	NOUN
ejpam-3294	305	29	,	,	PUNCT
ejpam-3294	305	30	y∗	y∗	PROPN
ejpam-3294	305	31	)	)	PUNCT
ejpam-3294	306	1	+	+	CCONJ
ejpam-3294	306	2	p(x∗	p(x∗	NOUN
ejpam-3294	306	3	,	,	PUNCT
ejpam-3294	306	4	fy∗	fy∗	NOUN
ejpam-3294	306	5	4	4	NUM
ejpam-3294	306	6	,	,	PUNCT
ejpam-3294	306	7	[	[	X
ejpam-3294	306	8	1	1	NUM
ejpam-3294	306	9	+	+	NUM
ejpam-3294	306	10	p(x∗	p(x∗	NOUN
ejpam-3294	306	11	,	,	PUNCT
ejpam-3294	306	12	fx∗)]p(y∗	fx∗)]p(y∗	ADJ
ejpam-3294	306	13	,	,	PUNCT
ejpam-3294	306	14	fy∗	fy∗	NOUN
ejpam-3294	306	15	)	)	PUNCT
ejpam-3294	306	16	p(x∗	p(x∗	NOUN
ejpam-3294	306	17	,	,	PUNCT
ejpam-3294	306	18	y∗	y∗	PROPN
ejpam-3294	306	19	)	)	PUNCT
ejpam-3294	307	1	+	+	CCONJ
ejpam-3294	307	2	1	1	X
ejpam-3294	307	3	}	}	PUNCT
ejpam-3294	307	4	=	=	PUNCT
ejpam-3294	307	5	max{p(x∗	max{p(x∗	PROPN
ejpam-3294	307	6	,	,	PUNCT
ejpam-3294	307	7	y∗	y∗	PROPN
ejpam-3294	307	8	)	)	PUNCT
ejpam-3294	307	9	,	,	PUNCT
ejpam-3294	307	10	p(x∗	p(x∗	NOUN
ejpam-3294	307	11	,	,	PUNCT
ejpam-3294	307	12	x∗	x∗	PROPN
ejpam-3294	307	13	)	)	PUNCT
ejpam-3294	307	14	,	,	PUNCT
ejpam-3294	307	15	p(y∗	p(y∗	NOUN
ejpam-3294	307	16	,	,	PUNCT
ejpam-3294	307	17	y∗	y∗	PROPN
ejpam-3294	307	18	)	)	PUNCT
ejpam-3294	307	19	,	,	PUNCT
ejpam-3294	307	20	p(x	p(x	VERB
ejpam-3294	307	21	∗	∗	NOUN
ejpam-3294	307	22	,	,	PUNCT
ejpam-3294	307	23	y∗	y∗	PROPN
ejpam-3294	307	24	)	)	PUNCT
ejpam-3294	308	1	+	+	CCONJ
ejpam-3294	308	2	p(x∗	p(x∗	NOUN
ejpam-3294	308	3	,	,	PUNCT
ejpam-3294	308	4	y∗	y∗	PROPN
ejpam-3294	308	5	)	)	PUNCT
ejpam-3294	308	6	4	4	NUM
ejpam-3294	308	7	,	,	PUNCT
ejpam-3294	309	1	[	[	X
ejpam-3294	309	2	1	1	NUM
ejpam-3294	309	3	+	+	NUM
ejpam-3294	309	4	p(x∗	p(x∗	NOUN
ejpam-3294	309	5	,	,	PUNCT
ejpam-3294	309	6	y∗)]p(y∗	y∗)]p(y∗	PROPN
ejpam-3294	309	7	,	,	PUNCT
ejpam-3294	309	8	y∗	y∗	PROPN
ejpam-3294	309	9	)	)	PUNCT
ejpam-3294	309	10	p(x∗	p(x∗	NOUN
ejpam-3294	309	11	,	,	PUNCT
ejpam-3294	309	12	y∗	y∗	PROPN
ejpam-3294	309	13	)	)	PUNCT
ejpam-3294	310	1	+	+	CCONJ
ejpam-3294	310	2	1	1	X
ejpam-3294	310	3	}	}	PUNCT
ejpam-3294	310	4	=	=	PUNCT
ejpam-3294	310	5	max{p(x∗	max{p(x∗	PROPN
ejpam-3294	310	6	,	,	PUNCT
ejpam-3294	310	7	y∗	y∗	PROPN
ejpam-3294	310	8	)	)	PUNCT
ejpam-3294	310	9	,	,	PUNCT
ejpam-3294	310	10	p(x∗	p(x∗	NOUN
ejpam-3294	310	11	,	,	PUNCT
ejpam-3294	310	12	x∗	x∗	PROPN
ejpam-3294	310	13	)	)	PUNCT
ejpam-3294	310	14	,	,	PUNCT
ejpam-3294	310	15	p(y∗	p(y∗	NOUN
ejpam-3294	310	16	,	,	PUNCT
ejpam-3294	310	17	y∗	y∗	PROPN
ejpam-3294	310	18	)	)	PUNCT
ejpam-3294	310	19	,	,	PUNCT
ejpam-3294	310	20	p(x	p(x	VERB
ejpam-3294	310	21	∗	∗	NOUN
ejpam-3294	310	22	,	,	PUNCT
ejpam-3294	310	23	y∗	y∗	PROPN
ejpam-3294	310	24	)	)	PUNCT
ejpam-3294	310	25	2	2	NUM
ejpam-3294	310	26	,	,	PUNCT
ejpam-3294	310	27	p(y∗	p(y∗	ADJ
ejpam-3294	310	28	,	,	PUNCT
ejpam-3294	310	29	y∗	y∗	PROPN
ejpam-3294	310	30	)	)	PUNCT
ejpam-3294	310	31	}	}	PUNCT
ejpam-3294	311	1	=	=	SYM
ejpam-3294	311	2	p(x∗	p(x∗	NOUN
ejpam-3294	311	3	,	,	PUNCT
ejpam-3294	311	4	y∗	y∗	PROPN
ejpam-3294	311	5	)	)	PUNCT
ejpam-3294	311	6	.	.	PUNCT
ejpam-3294	312	1	this	this	PRON
ejpam-3294	312	2	is	be	AUX
ejpam-3294	312	3	a	a	DET
ejpam-3294	312	4	contradiction	contradiction	NOUN
ejpam-3294	312	5	,	,	PUNCT
ejpam-3294	312	6	and	and	CCONJ
ejpam-3294	312	7	hence	hence	ADV
ejpam-3294	312	8	x∗	x∗	PROPN
ejpam-3294	313	1	=	=	SYM
ejpam-3294	313	2	y∗.	y∗.	NUM
ejpam-3294	313	3	theorem	theorem	VERB
ejpam-3294	313	4	4	4	NUM
ejpam-3294	313	5	.	.	PUNCT
ejpam-3294	314	1	let	let	VERB
ejpam-3294	314	2	(	(	PUNCT
ejpam-3294	314	3	x	x	X
ejpam-3294	314	4	,	,	PUNCT
ejpam-3294	314	5	p	p	X
ejpam-3294	314	6	)	)	PUNCT
ejpam-3294	314	7	be	be	AUX
ejpam-3294	314	8	a	a	DET
ejpam-3294	314	9	a	a	DET
ejpam-3294	314	10	complete	complete	ADJ
ejpam-3294	314	11	partial	partial	ADJ
ejpam-3294	314	12	metric	metric	ADJ
ejpam-3294	314	13	space	space	NOUN
ejpam-3294	314	14	and	and	CCONJ
ejpam-3294	314	15	α	α	NOUN
ejpam-3294	314	16	:	:	PUNCT
ejpam-3294	314	17	x	x	PROPN
ejpam-3294	314	18	×x	×x	X
ejpam-3294	314	19	→	→	X
ejpam-3294	314	20	[	[	X
ejpam-3294	314	21	0,∞	0,∞	NOUN
ejpam-3294	314	22	)	)	PUNCT
ejpam-3294	314	23	.	.	PUNCT
ejpam-3294	315	1	a	a	DET
ejpam-3294	315	2	mapping	mapping	NOUN
ejpam-3294	315	3	f	f	NOUN
ejpam-3294	315	4	:	:	PUNCT
ejpam-3294	315	5	x	x	X
ejpam-3294	315	6	→	→	PUNCT
ejpam-3294	315	7	x	x	PUNCT
ejpam-3294	315	8	be	be	AUX
ejpam-3294	315	9	an	an	DET
ejpam-3294	315	10	(	(	PUNCT
ejpam-3294	315	11	α	α	NOUN
ejpam-3294	315	12	,	,	PUNCT
ejpam-3294	315	13	β	β	X
ejpam-3294	315	14	,	,	PUNCT
ejpam-3294	315	15	f	f	PROPN
ejpam-3294	315	16	)	)	PUNCT
ejpam-3294	315	17	−geraghty	−geraghty	PROPN
ejpam-3294	315	18	contraction	contraction	PROPN
ejpam-3294	315	19	mapping	mapping	NOUN
ejpam-3294	315	20	.	.	PUNCT
ejpam-3294	316	1	suppose	suppose	VERB
ejpam-3294	316	2	there	there	PRON
ejpam-3294	316	3	exist	exist	VERB
ejpam-3294	316	4	f	f	PROPN
ejpam-3294	316	5	∈	∈	PROPN
ejpam-3294	316	6	f	f	PROPN
ejpam-3294	316	7	and	and	CCONJ
ejpam-3294	316	8	τ	τ	PROPN
ejpam-3294	316	9	>	>	X
ejpam-3294	316	10	0	0	NUM
ejpam-3294	316	11	such	such	ADJ
ejpam-3294	316	12	that	that	SCONJ
ejpam-3294	316	13	,	,	PUNCT
ejpam-3294	316	14	for	for	ADP
ejpam-3294	316	15	all	all	DET
ejpam-3294	316	16	x	x	NOUN
ejpam-3294	316	17	,	,	PUNCT
ejpam-3294	316	18	y	y	PROPN
ejpam-3294	316	19	∈	∈	PROPN
ejpam-3294	316	20	x	x	PUNCT
ejpam-3294	316	21	with	with	ADP
ejpam-3294	316	22	σ(fx	σ(fx	PROPN
ejpam-3294	316	23	,	,	PUNCT
ejpam-3294	316	24	fy	fy	PROPN
ejpam-3294	316	25	)	)	PUNCT
ejpam-3294	316	26	>	>	X
ejpam-3294	316	27	0	0	PUNCT
ejpam-3294	316	28	and	and	CCONJ
ejpam-3294	316	29	α(x	α(x	PROPN
ejpam-3294	316	30	,	,	PUNCT
ejpam-3294	316	31	y	y	PROPN
ejpam-3294	316	32	)	)	PUNCT
ejpam-3294	316	33	≥	≥	NOUN
ejpam-3294	316	34	1	1	NUM
ejpam-3294	316	35	,	,	PUNCT
ejpam-3294	316	36	0	0	NUM
ejpam-3294	316	37	<	<	X
ejpam-3294	316	38	α(x	α(x	PROPN
ejpam-3294	316	39	,	,	PUNCT
ejpam-3294	316	40	y)(τ	y)(τ	PROPN
ejpam-3294	317	1	+	+	CCONJ
ejpam-3294	317	2	f	f	X
ejpam-3294	317	3	(	(	PUNCT
ejpam-3294	317	4	σ(fx	σ(fx	PROPN
ejpam-3294	317	5	,	,	PUNCT
ejpam-3294	317	6	fy	fy	PROPN
ejpam-3294	317	7	)	)	PUNCT
ejpam-3294	317	8	)	)	PUNCT
ejpam-3294	317	9	≤	≤	NUM
ejpam-3294	317	10	β(mx	β(mx	NOUN
ejpam-3294	317	11	,	,	PUNCT
ejpam-3294	317	12	y)f	y)f	NOUN
ejpam-3294	317	13	(	(	PUNCT
ejpam-3294	317	14	mx	mx	PROPN
ejpam-3294	317	15	,	,	PUNCT
ejpam-3294	317	16	y	y	PROPN
ejpam-3294	317	17	)	)	PUNCT
ejpam-3294	317	18	,	,	PUNCT
ejpam-3294	317	19	(	(	PUNCT
ejpam-3294	317	20	19	19	NUM
ejpam-3294	317	21	)	)	PUNCT
ejpam-3294	317	22	where	where	SCONJ
ejpam-3294	317	23	mx	mx	PROPN
ejpam-3294	317	24	,	,	PUNCT
ejpam-3294	317	25	y	y	PROPN
ejpam-3294	317	26	=	=	PUNCT
ejpam-3294	317	27	max{max{p(x	max{max{p(x	PROPN
ejpam-3294	317	28	,	,	PUNCT
ejpam-3294	317	29	y	y	NOUN
ejpam-3294	317	30	)	)	PUNCT
ejpam-3294	317	31	,	,	PUNCT
ejpam-3294	317	32	p(x	p(x	PROPN
ejpam-3294	317	33	,	,	PUNCT
ejpam-3294	317	34	fx	fx	NOUN
ejpam-3294	317	35	)	)	PUNCT
ejpam-3294	317	36	,	,	PUNCT
ejpam-3294	317	37	p(y	p(y	PROPN
ejpam-3294	317	38	,	,	PUNCT
ejpam-3294	317	39	fy	fy	PROPN
ejpam-3294	317	40	)	)	PUNCT
ejpam-3294	317	41	}	}	PUNCT
ejpam-3294	317	42	.	.	PUNCT
ejpam-3294	318	1	then	then	ADV
ejpam-3294	318	2	f	f	PROPN
ejpam-3294	318	3	has	have	VERB
ejpam-3294	318	4	a	a	DET
ejpam-3294	318	5	unique	unique	ADJ
ejpam-3294	318	6	fixed	fix	VERB
ejpam-3294	318	7	point	point	NOUN
ejpam-3294	318	8	z	z	NOUN
ejpam-3294	318	9	∈	∈	PROPN
ejpam-3294	318	10	x	x	PUNCT
ejpam-3294	318	11	with	with	ADP
ejpam-3294	318	12	p(z	p(z	NOUN
ejpam-3294	318	13	,	,	PUNCT
ejpam-3294	318	14	z	z	NOUN
ejpam-3294	318	15	)	)	PUNCT
ejpam-3294	318	16	=	=	SYM
ejpam-3294	319	1	0	0	X
ejpam-3294	319	2	.	.	PUNCT
ejpam-3294	319	3	references	reference	NOUN
ejpam-3294	319	4	714	714	NUM
ejpam-3294	319	5	theorem	theorem	NOUN
ejpam-3294	319	6	5	5	NUM
ejpam-3294	319	7	.	.	PUNCT
ejpam-3294	320	1	let	let	VERB
ejpam-3294	320	2	(	(	PUNCT
ejpam-3294	320	3	x	x	X
ejpam-3294	320	4	,	,	PUNCT
ejpam-3294	320	5	p	p	X
ejpam-3294	320	6	)	)	PUNCT
ejpam-3294	320	7	be	be	AUX
ejpam-3294	320	8	a	a	DET
ejpam-3294	320	9	a	a	DET
ejpam-3294	320	10	complete	complete	ADJ
ejpam-3294	320	11	partial	partial	ADJ
ejpam-3294	320	12	metric	metric	ADJ
ejpam-3294	320	13	space	space	NOUN
ejpam-3294	320	14	and	and	CCONJ
ejpam-3294	320	15	α	α	NOUN
ejpam-3294	320	16	:	:	PUNCT
ejpam-3294	320	17	x	x	SYM
ejpam-3294	320	18	×	×	NOUN
ejpam-3294	320	19	x	x	INTJ
ejpam-3294	320	20	→	→	X
ejpam-3294	320	21	[	[	X
ejpam-3294	320	22	0,∞	0,∞	NOUN
ejpam-3294	320	23	)	)	PUNCT
ejpam-3294	320	24	.	.	PUNCT
ejpam-3294	321	1	a	a	DET
ejpam-3294	321	2	mapping	mapping	NOUN
ejpam-3294	321	3	f	f	NOUN
ejpam-3294	321	4	:	:	PUNCT
ejpam-3294	321	5	x	x	X
ejpam-3294	321	6	→	→	PUNCT
ejpam-3294	321	7	x	x	PUNCT
ejpam-3294	321	8	be	be	AUX
ejpam-3294	321	9	an	an	DET
ejpam-3294	321	10	(	(	PUNCT
ejpam-3294	321	11	α	α	NOUN
ejpam-3294	321	12	,	,	PUNCT
ejpam-3294	321	13	β	β	X
ejpam-3294	321	14	,	,	PUNCT
ejpam-3294	321	15	f	f	PROPN
ejpam-3294	321	16	)	)	PUNCT
ejpam-3294	321	17	geraghty	geraghty	PROPN
ejpam-3294	321	18	contraction	contraction	PROPN
ejpam-3294	321	19	mapping	mapping	NOUN
ejpam-3294	321	20	.	.	PUNCT
ejpam-3294	322	1	suppose	suppose	VERB
ejpam-3294	322	2	there	there	PRON
ejpam-3294	322	3	exist	exist	VERB
ejpam-3294	322	4	f	f	PROPN
ejpam-3294	322	5	∈	∈	PROPN
ejpam-3294	322	6	f	f	PROPN
ejpam-3294	322	7	and	and	CCONJ
ejpam-3294	322	8	τ	τ	PROPN
ejpam-3294	322	9	>	>	X
ejpam-3294	322	10	0	0	NUM
ejpam-3294	322	11	such	such	ADJ
ejpam-3294	322	12	that	that	SCONJ
ejpam-3294	322	13	,	,	PUNCT
ejpam-3294	322	14	for	for	ADP
ejpam-3294	322	15	all	all	DET
ejpam-3294	322	16	x	x	NOUN
ejpam-3294	322	17	,	,	PUNCT
ejpam-3294	322	18	y	y	PROPN
ejpam-3294	322	19	∈	∈	PROPN
ejpam-3294	322	20	x	x	PUNCT
ejpam-3294	322	21	with	with	ADP
ejpam-3294	322	22	σ(fx	σ(fx	PROPN
ejpam-3294	322	23	,	,	PUNCT
ejpam-3294	322	24	fy	fy	PROPN
ejpam-3294	322	25	)	)	PUNCT
ejpam-3294	322	26	>	>	X
ejpam-3294	322	27	0	0	PUNCT
ejpam-3294	322	28	and	and	CCONJ
ejpam-3294	322	29	α(x	α(x	PROPN
ejpam-3294	322	30	,	,	PUNCT
ejpam-3294	322	31	y	y	PROPN
ejpam-3294	322	32	)	)	PUNCT
ejpam-3294	322	33	≥	≥	NOUN
ejpam-3294	322	34	1	1	NUM
ejpam-3294	322	35	,	,	PUNCT
ejpam-3294	322	36	0	0	NUM
ejpam-3294	322	37	<	<	X
ejpam-3294	322	38	α(x	α(x	PROPN
ejpam-3294	322	39	,	,	PUNCT
ejpam-3294	322	40	y)(τ	y)(τ	PROPN
ejpam-3294	323	1	+	+	CCONJ
ejpam-3294	323	2	f	f	X
ejpam-3294	323	3	(	(	PUNCT
ejpam-3294	323	4	σ(fx	σ(fx	PROPN
ejpam-3294	323	5	,	,	PUNCT
ejpam-3294	323	6	fy	fy	PROPN
ejpam-3294	323	7	)	)	PUNCT
ejpam-3294	323	8	)	)	PUNCT
ejpam-3294	323	9	≤	≤	NUM
ejpam-3294	323	10	β(mx	β(mx	NOUN
ejpam-3294	323	11	,	,	PUNCT
ejpam-3294	323	12	y)f	y)f	NOUN
ejpam-3294	323	13	(	(	PUNCT
ejpam-3294	323	14	mx	mx	PROPN
ejpam-3294	323	15	,	,	PUNCT
ejpam-3294	323	16	y	y	PROPN
ejpam-3294	323	17	)	)	PUNCT
ejpam-3294	323	18	,	,	PUNCT
ejpam-3294	323	19	(	(	PUNCT
ejpam-3294	323	20	20	20	NUM
ejpam-3294	323	21	)	)	PUNCT
ejpam-3294	323	22	where	where	SCONJ
ejpam-3294	323	23	mx	mx	PROPN
ejpam-3294	323	24	,	,	PUNCT
ejpam-3294	323	25	y	y	NOUN
ejpam-3294	323	26	=	=	PUNCT
ejpam-3294	323	27	p(x	p(x	PROPN
ejpam-3294	323	28	,	,	PUNCT
ejpam-3294	323	29	y	y	NOUN
ejpam-3294	323	30	)	)	PUNCT
ejpam-3294	323	31	.	.	PUNCT
ejpam-3294	324	1	then	then	ADV
ejpam-3294	324	2	f	f	PROPN
ejpam-3294	324	3	has	have	VERB
ejpam-3294	324	4	a	a	DET
ejpam-3294	324	5	unique	unique	ADJ
ejpam-3294	324	6	fixed	fix	VERB
ejpam-3294	324	7	point	point	NOUN
ejpam-3294	324	8	z	z	NOUN
ejpam-3294	324	9	∈	∈	PROPN
ejpam-3294	324	10	x	x	PUNCT
ejpam-3294	324	11	with	with	ADP
ejpam-3294	324	12	p(z	p(z	NOUN
ejpam-3294	324	13	,	,	PUNCT
ejpam-3294	324	14	z	z	NOUN
ejpam-3294	324	15	)	)	PUNCT
ejpam-3294	324	16	=	=	SYM
ejpam-3294	324	17	0	0	X
ejpam-3294	324	18	.	.	PUNCT
ejpam-3294	325	1	acknowledgements	acknowledgement	VERB
ejpam-3294	325	2	the	the	DET
ejpam-3294	325	3	authors	author	NOUN
ejpam-3294	325	4	would	would	AUX
ejpam-3294	325	5	like	like	VERB
ejpam-3294	325	6	to	to	PART
ejpam-3294	325	7	acknowledge	acknowledge	VERB
ejpam-3294	325	8	the	the	DET
ejpam-3294	325	9	grant	grant	NOUN
ejpam-3294	325	10	:	:	PUNCT
ejpam-3294	325	11	ukm	ukm	PROPN
ejpam-3294	325	12	grant	grant	PROPN
ejpam-3294	325	13	dip-2017	dip-2017	PROPN
ejpam-3294	325	14	-	-	PUNCT
ejpam-3294	325	15	011	011	NUM
ejpam-3294	325	16	and	and	CCONJ
ejpam-3294	325	17	ministry	ministry	PROPN
ejpam-3294	325	18	of	of	ADP
ejpam-3294	325	19	education	education	PROPN
ejpam-3294	325	20	,	,	PUNCT
ejpam-3294	325	21	malaysia	malaysia	PROPN
ejpam-3294	325	22	grant	grant	NOUN
ejpam-3294	325	23	frgs/1/2017	frgs/1/2017	NOUN
ejpam-3294	325	24	/	/	SYM
ejpam-3294	325	25	stg06	stg06	NOUN
ejpam-3294	325	26	/	/	SYM
ejpam-3294	325	27	ukm/01/1	ukm/01/1	NOUN
ejpam-3294	325	28	for	for	ADP
ejpam-3294	325	29	financial	financial	ADJ
ejpam-3294	325	30	support	support	NOUN
ejpam-3294	325	31	.	.	PUNCT
ejpam-3294	326	1	references	reference	NOUN
ejpam-3294	326	2	[	[	X
ejpam-3294	326	3	1	1	NUM
ejpam-3294	326	4	]	]	PUNCT
ejpam-3294	326	5	t.	t.	NOUN
ejpam-3294	326	6	abdeljawad	abdeljawad	PROPN
ejpam-3294	326	7	,	,	PUNCT
ejpam-3294	326	8	e.	e.	PROPN
ejpam-3294	326	9	karapnar	karapnar	PROPN
ejpam-3294	326	10	,	,	PUNCT
ejpam-3294	326	11	and	and	CCONJ
ejpam-3294	326	12	k.	k.	PROPN
ejpam-3294	326	13	tas	tas	PROPN
ejpam-3294	326	14	.	.	PROPN
ejpam-3294	327	1	existence	existence	NOUN
ejpam-3294	327	2	and	and	CCONJ
ejpam-3294	327	3	uniqueness	uniqueness	NOUN
ejpam-3294	327	4	of	of	ADP
ejpam-3294	327	5	a	a	DET
ejpam-3294	327	6	common	common	ADJ
ejpam-3294	327	7	fixed	fix	VERB
ejpam-3294	327	8	point	point	NOUN
ejpam-3294	327	9	on	on	ADP
ejpam-3294	327	10	partial	partial	ADJ
ejpam-3294	327	11	metric	metric	ADJ
ejpam-3294	327	12	spaces	space	NOUN
ejpam-3294	327	13	.	.	PUNCT
ejpam-3294	328	1	appl.math	appl.math	NOUN
ejpam-3294	328	2	.	.	PUNCT
ejpam-3294	328	3	lett	lett	PROPN
ejpam-3294	328	4	.	.	PROPN
ejpam-3294	328	5	,	,	PUNCT
ejpam-3294	328	6	24	24	NUM
ejpam-3294	328	7	,	,	PUNCT
ejpam-3294	328	8	2011	2011	NUM
ejpam-3294	328	9	.	.	PUNCT
ejpam-3294	329	1	[	[	X
ejpam-3294	329	2	2	2	X
ejpam-3294	329	3	]	]	PUNCT
ejpam-3294	329	4	h.	h.	PROPN
ejpam-3294	329	5	alsamir	alsamir	PROPN
ejpam-3294	329	6	,	,	PUNCT
ejpam-3294	329	7	m.	m.	NOUN
ejpam-3294	329	8	s.	s.	PROPN
ejpam-3294	329	9	m.	m.	PROPN
ejpam-3294	329	10	noorani	noorani	PROPN
ejpam-3294	329	11	,	,	PUNCT
ejpam-3294	329	12	and	and	CCONJ
ejpam-3294	329	13	w.	w.	PROPN
ejpam-3294	329	14	shatanawi	shatanawi	PROPN
ejpam-3294	329	15	.	.	PUNCT
ejpam-3294	330	1	on	on	ADP
ejpam-3294	330	2	fixed	fix	VERB
ejpam-3294	330	3	points	point	NOUN
ejpam-3294	330	4	of	of	ADP
ejpam-3294	330	5	(	(	PUNCT
ejpam-3294	330	6	η	η	PROPN
ejpam-3294	330	7	,	,	PUNCT
ejpam-3294	330	8	θ)quasicontraction	θ)quasicontraction	NOUN
ejpam-3294	330	9	mappings	mapping	NOUN
ejpam-3294	330	10	in	in	ADP
ejpam-3294	330	11	generalized	generalized	ADJ
ejpam-3294	330	12	metric	metric	ADJ
ejpam-3294	330	13	spaces	space	NOUN
ejpam-3294	330	14	.	.	PUNCT
ejpam-3294	331	1	j.	j.	PROPN
ejpam-3294	331	2	nonlinear	nonlinear	PROPN
ejpam-3294	331	3	sci	sci	PROPN
ejpam-3294	331	4	.	.	PUNCT
ejpam-3294	331	5	appl	appl	PROPN
ejpam-3294	331	6	.	.	PROPN
ejpam-3294	331	7	,	,	PUNCT
ejpam-3294	331	8	9:4651–4658	9:4651–4658	NUM
ejpam-3294	331	9	,	,	PUNCT
ejpam-3294	331	10	2016	2016	NUM
ejpam-3294	331	11	.	.	PUNCT
ejpam-3294	332	1	[	[	X
ejpam-3294	332	2	3	3	X
ejpam-3294	332	3	]	]	X
ejpam-3294	332	4	h.	h.	PROPN
ejpam-3294	332	5	aydi	aydi	PROPN
ejpam-3294	332	6	and	and	CCONJ
ejpam-3294	332	7	a.	a.	NOUN
ejpam-3294	332	8	felhi	felhi	PROPN
ejpam-3294	332	9	.	.	PUNCT
ejpam-3294	333	1	best	good	ADJ
ejpam-3294	333	2	proximity	proximity	NOUN
ejpam-3294	333	3	points	point	NOUN
ejpam-3294	333	4	for	for	ADP
ejpam-3294	333	5	cyclic	cyclic	PROPN
ejpam-3294	333	6	kannan	kannan	PROPN
ejpam-3294	333	7	-	-	PUNCT
ejpam-3294	333	8	chatterjeaciric	chatterjeaciric	PROPN
ejpam-3294	333	9	type	type	NOUN
ejpam-3294	333	10	contractions	contraction	NOUN
ejpam-3294	333	11	on	on	ADP
ejpam-3294	333	12	metric	metric	ADJ
ejpam-3294	333	13	-	-	PUNCT
ejpam-3294	333	14	like	like	ADJ
ejpam-3294	333	15	spaces	space	NOUN
ejpam-3294	333	16	.	.	PUNCT
ejpam-3294	334	1	journal	journal	PROPN
ejpam-3294	334	2	of	of	ADP
ejpam-3294	334	3	nonlinear	nonlinear	PROPN
ejpam-3294	334	4	sciences	sciences	PROPN
ejpam-3294	334	5	and	and	CCONJ
ejpam-3294	334	6	application	application	NOUN
ejpam-3294	334	7	,	,	PUNCT
ejpam-3294	334	8	9:2458–2466	9:2458–2466	NUM
ejpam-3294	334	9	,	,	PUNCT
ejpam-3294	334	10	2016	2016	NUM
ejpam-3294	334	11	.	.	PUNCT
ejpam-3294	335	1	[	[	X
ejpam-3294	335	2	4	4	X
ejpam-3294	335	3	]	]	X
ejpam-3294	335	4	h.	h.	PROPN
ejpam-3294	335	5	aydi	aydi	PROPN
ejpam-3294	335	6	,	,	PUNCT
ejpam-3294	335	7	a.	a.	NOUN
ejpam-3294	335	8	felhi	felhi	PROPN
ejpam-3294	335	9	,	,	PUNCT
ejpam-3294	335	10	and	and	CCONJ
ejpam-3294	335	11	h.	h.	PROPN
ejpam-3294	335	12	afshari	afshari	PROPN
ejpam-3294	335	13	.	.	PUNCT
ejpam-3294	336	1	new	new	ADJ
ejpam-3294	336	2	geraghty	geraghty	PROPN
ejpam-3294	336	3	type	type	NOUN
ejpam-3294	336	4	contractions	contraction	NOUN
ejpam-3294	336	5	on	on	ADP
ejpam-3294	336	6	metric	metric	ADJ
ejpam-3294	336	7	-	-	PUNCT
ejpam-3294	336	8	like	like	ADJ
ejpam-3294	336	9	spaces	space	NOUN
ejpam-3294	336	10	.	.	PUNCT
ejpam-3294	337	1	journal	journal	PROPN
ejpam-3294	337	2	of	of	ADP
ejpam-3294	337	3	nonlinear	nonlinear	PROPN
ejpam-3294	337	4	sciences	sciences	PROPN
ejpam-3294	337	5	and	and	CCONJ
ejpam-3294	337	6	application	application	NOUN
ejpam-3294	337	7	,	,	PUNCT
ejpam-3294	337	8	10	10	NUM
ejpam-3294	337	9	,	,	PUNCT
ejpam-3294	337	10	2017	2017	NUM
ejpam-3294	337	11	.	.	PUNCT
ejpam-3294	338	1	[	[	X
ejpam-3294	338	2	5	5	X
ejpam-3294	338	3	]	]	X
ejpam-3294	338	4	h.	h.	PROPN
ejpam-3294	338	5	aydi	aydi	PROPN
ejpam-3294	338	6	,	,	PUNCT
ejpam-3294	338	7	a.	a.	NOUN
ejpam-3294	338	8	felhi	felhi	PROPN
ejpam-3294	338	9	,	,	PUNCT
ejpam-3294	338	10	and	and	CCONJ
ejpam-3294	338	11	s.	s.	PROPN
ejpam-3294	338	12	sahmim	sahmim	PROPN
ejpam-3294	338	13	.	.	PUNCT
ejpam-3294	339	1	on	on	ADP
ejpam-3294	339	2	common	common	ADJ
ejpam-3294	339	3	fixed	fix	VERB
ejpam-3294	339	4	points	point	NOUN
ejpam-3294	339	5	for	for	ADP
ejpam-3294	339	6	(	(	PUNCT
ejpam-3294	339	7	α	α	NOUN
ejpam-3294	339	8	,	,	PUNCT
ejpam-3294	339	9	ψ)-contractions	ψ)-contraction	NOUN
ejpam-3294	339	10	and	and	CCONJ
ejpam-3294	339	11	generalized	generalize	VERB
ejpam-3294	339	12	cyclic	cyclic	ADJ
ejpam-3294	339	13	contractions	contraction	NOUN
ejpam-3294	339	14	in	in	ADP
ejpam-3294	339	15	b	b	NOUN
ejpam-3294	339	16	-	-	PUNCT
ejpam-3294	339	17	metric	metric	ADJ
ejpam-3294	339	18	-	-	PUNCT
ejpam-3294	339	19	like	like	ADJ
ejpam-3294	339	20	spaces	space	NOUN
ejpam-3294	339	21	and	and	CCONJ
ejpam-3294	339	22	consequences	consequence	NOUN
ejpam-3294	339	23	.	.	PUNCT
ejpam-3294	340	1	journal	journal	NOUN
ejpam-3294	340	2	of	of	ADP
ejpam-3294	340	3	nonlinear	nonlinear	PROPN
ejpam-3294	340	4	sciences	sciences	PROPN
ejpam-3294	340	5	and	and	CCONJ
ejpam-3294	340	6	application	application	NOUN
ejpam-3294	340	7	,	,	PUNCT
ejpam-3294	340	8	9:2492–2510	9:2492–2510	NUM
ejpam-3294	340	9	,	,	PUNCT
ejpam-3294	340	10	2016	2016	NUM
ejpam-3294	340	11	.	.	PUNCT
ejpam-3294	341	1	[	[	X
ejpam-3294	341	2	6	6	NUM
ejpam-3294	341	3	]	]	X
ejpam-3294	341	4	h.	h.	PROPN
ejpam-3294	341	5	aydi	aydi	PROPN
ejpam-3294	341	6	,	,	PUNCT
ejpam-3294	341	7	karapinar	karapinar	PROPN
ejpam-3294	341	8	e.	e.	PROPN
ejpam-3294	341	9	felhi	felhi	PROPN
ejpam-3294	341	10	,	,	PUNCT
ejpam-3294	341	11	a.	a.	NOUN
ejpam-3294	341	12	and	and	CCONJ
ejpam-3294	341	13	,	,	PUNCT
ejpam-3294	341	14	and	and	CCONJ
ejpam-3294	341	15	h.	h.	PROPN
ejpam-3294	341	16	alshaikh	alshaikh	PROPN
ejpam-3294	341	17	.	.	PUNCT
ejpam-3294	342	1	an	an	DET
ejpam-3294	342	2	implicit	implicit	ADJ
ejpam-3294	342	3	relation	relation	NOUN
ejpam-3294	342	4	for	for	ADP
ejpam-3294	342	5	meirkeeler	meirkeeler	NOUN
ejpam-3294	342	6	type	type	NOUN
ejpam-3294	342	7	mappings	mapping	NOUN
ejpam-3294	342	8	on	on	ADP
ejpam-3294	342	9	metric	metric	ADJ
ejpam-3294	342	10	-	-	PUNCT
ejpam-3294	342	11	like	like	ADJ
ejpam-3294	342	12	spaces	space	NOUN
ejpam-3294	342	13	.	.	PUNCT
ejpam-3294	343	1	journal	journal	PROPN
ejpam-3294	343	2	of	of	ADP
ejpam-3294	343	3	mathematical	mathematical	ADJ
ejpam-3294	343	4	analysis	analysis	NOUN
ejpam-3294	343	5	,	,	PUNCT
ejpam-3294	343	6	8	8	NUM
ejpam-3294	343	7	,	,	PUNCT
ejpam-3294	343	8	2017	2017	NUM
ejpam-3294	343	9	.	.	PUNCT
ejpam-3294	344	1	[	[	X
ejpam-3294	344	2	7	7	X
ejpam-3294	344	3	]	]	X
ejpam-3294	344	4	h.	h.	PROPN
ejpam-3294	344	5	aydi	aydi	PROPN
ejpam-3294	344	6	,	,	PUNCT
ejpam-3294	344	7	karapinar	karapinar	PROPN
ejpam-3294	344	8	e.	e.	PROPN
ejpam-3294	344	9	felhi	felhi	PROPN
ejpam-3294	344	10	,	,	PUNCT
ejpam-3294	344	11	a.	a.	NOUN
ejpam-3294	344	12	and	and	CCONJ
ejpam-3294	344	13	,	,	PUNCT
ejpam-3294	344	14	and	and	CCONJ
ejpam-3294	344	15	s.	s.	PROPN
ejpam-3294	344	16	sahmimc	sahmimc	PROPN
ejpam-3294	344	17	.	.	PUNCT
ejpam-3294	345	1	common	common	ADJ
ejpam-3294	345	2	fixed	fix	VERB
ejpam-3294	345	3	points	point	NOUN
ejpam-3294	345	4	via	via	ADP
ejpam-3294	345	5	implicit	implicit	ADJ
ejpam-3294	345	6	contractions	contraction	NOUN
ejpam-3294	345	7	on	on	ADP
ejpam-3294	345	8	b−metric	b−metric	ADJ
ejpam-3294	345	9	-	-	PUNCT
ejpam-3294	345	10	like	like	ADJ
ejpam-3294	345	11	spaces	space	NOUN
ejpam-3294	345	12	.	.	PUNCT
ejpam-3294	346	1	j.nonlinear	j.nonlinear	NOUN
ejpam-3294	346	2	sci	sci	PROPN
ejpam-3294	346	3	.	.	PUNCT
ejpam-3294	346	4	appl	appl	PROPN
ejpam-3294	346	5	.	.	PROPN
ejpam-3294	346	6	,	,	PUNCT
ejpam-3294	346	7	10	10	NUM
ejpam-3294	346	8	,	,	PUNCT
ejpam-3294	346	9	2017	2017	NUM
ejpam-3294	346	10	.	.	PUNCT
ejpam-3294	347	1	[	[	X
ejpam-3294	347	2	8	8	NUM
ejpam-3294	347	3	]	]	X
ejpam-3294	347	4	h.	h.	PROPN
ejpam-3294	347	5	aydi	aydi	PROPN
ejpam-3294	347	6	,	,	PUNCT
ejpam-3294	347	7	w.	w.	PROPN
ejpam-3294	347	8	shatanawi	shatanawi	PROPN
ejpam-3294	347	9	,	,	PUNCT
ejpam-3294	347	10	and	and	CCONJ
ejpam-3294	347	11	c.	c.	PROPN
ejpam-3294	347	12	vetro	vetro	PROPN
ejpam-3294	347	13	.	.	PUNCT
ejpam-3294	348	1	on	on	ADP
ejpam-3294	348	2	generalized	generalized	ADJ
ejpam-3294	348	3	weak	weak	ADJ
ejpam-3294	348	4	g	g	NOUN
ejpam-3294	348	5	-	-	PUNCT
ejpam-3294	348	6	contraction	contraction	NOUN
ejpam-3294	348	7	mapping	mapping	NOUN
ejpam-3294	348	8	in	in	ADP
ejpam-3294	348	9	g	g	NOUN
ejpam-3294	348	10	-	-	PUNCT
ejpam-3294	348	11	metric	metric	ADJ
ejpam-3294	348	12	spaces	space	NOUN
ejpam-3294	348	13	.	.	PUNCT
ejpam-3294	349	1	comput	comput	NOUN
ejpam-3294	349	2	.	.	PUNCT
ejpam-3294	350	1	math	math	NOUN
ejpam-3294	350	2	.	.	PUNCT
ejpam-3294	351	1	appl	appl	PROPN
ejpam-3294	351	2	.	.	PROPN
ejpam-3294	351	3	,	,	PUNCT
ejpam-3294	351	4	62:4223–4229	62:4223–4229	PROPN
ejpam-3294	351	5	,	,	PUNCT
ejpam-3294	351	6	2011	2011	NUM
ejpam-3294	351	7	.	.	PUNCT
ejpam-3294	352	1	references	reference	NOUN
ejpam-3294	352	2	715	715	NUM
ejpam-3294	353	1	[	[	X
ejpam-3294	353	2	9	9	NUM
ejpam-3294	353	3	]	]	PUNCT
ejpam-3294	353	4	s.	s.	PROPN
ejpam-3294	353	5	banach	banach	PROPN
ejpam-3294	353	6	.	.	PUNCT
ejpam-3294	354	1	sur	sur	PROPN
ejpam-3294	354	2	les	les	PROPN
ejpam-3294	354	3	oprations	opration	NOUN
ejpam-3294	354	4	dans	dans	PROPN
ejpam-3294	354	5	les	les	X
ejpam-3294	354	6	ensembles	ensemble	NOUN
ejpam-3294	354	7	abstraits	abstrait	NOUN
ejpam-3294	354	8	et	et	PROPN
ejpam-3294	354	9	leur	leur	X
ejpam-3294	354	10	application	application	PROPN
ejpam-3294	354	11	aux	aux	PROPN
ejpam-3294	354	12	quations	quation	NOUN
ejpam-3294	354	13	intgrales	intgrale	NOUN
ejpam-3294	354	14	.	.	PUNCT
ejpam-3294	355	1	[	[	X
ejpam-3294	355	2	10	10	NUM
ejpam-3294	355	3	]	]	X
ejpam-3294	355	4	s.	s.	PROPN
ejpam-3294	355	5	chandok	chandok	PROPN
ejpam-3294	355	6	.	.	PUNCT
ejpam-3294	356	1	some	some	DET
ejpam-3294	356	2	fixed	fix	VERB
ejpam-3294	356	3	point	point	NOUN
ejpam-3294	356	4	theorems	theorem	NOUN
ejpam-3294	356	5	for	for	ADP
ejpam-3294	356	6	(	(	PUNCT
ejpam-3294	356	7	ψ,ϕ)-admissible	ψ,ϕ)-admissible	ADJ
ejpam-3294	356	8	geraghty	geraghty	ADJ
ejpam-3294	356	9	type	type	NOUN
ejpam-3294	356	10	contractive	contractive	ADJ
ejpam-3294	356	11	mappings	mapping	NOUN
ejpam-3294	356	12	and	and	CCONJ
ejpam-3294	356	13	related	related	ADJ
ejpam-3294	356	14	results	result	NOUN
ejpam-3294	356	15	.	.	PUNCT
ejpam-3294	357	1	mathematical	mathematical	ADJ
ejpam-3294	357	2	sciences	science	NOUN
ejpam-3294	357	3	,	,	PUNCT
ejpam-3294	357	4	9	9	NUM
ejpam-3294	357	5	,	,	PUNCT
ejpam-3294	357	6	2015	2015	NUM
ejpam-3294	357	7	.	.	PUNCT
ejpam-3294	358	1	[	[	X
ejpam-3294	358	2	11	11	NUM
ejpam-3294	358	3	]	]	X
ejpam-3294	358	4	l.	l.	PROPN
ejpam-3294	358	5	ciric	ciric	PROPN
ejpam-3294	358	6	,	,	PUNCT
ejpam-3294	358	7	n.	n.	NOUN
ejpam-3294	358	8	cakid	cakid	PROPN
ejpam-3294	358	9	,	,	PUNCT
ejpam-3294	358	10	m.	m.	NOUN
ejpam-3294	358	11	rajovic	rajovic	NOUN
ejpam-3294	358	12	,	,	PUNCT
ejpam-3294	358	13	and	and	CCONJ
ejpam-3294	358	14	js	js	PROPN
ejpam-3294	358	15	.	.	PUNCT
ejpam-3294	359	1	uma	uma	PROPN
ejpam-3294	359	2	.	.	PUNCT
ejpam-3294	360	1	monotone	monotone	ADJ
ejpam-3294	360	2	generalized	generalized	ADJ
ejpam-3294	360	3	nonlinear	nonlinear	ADJ
ejpam-3294	360	4	contractions	contraction	NOUN
ejpam-3294	360	5	in	in	ADP
ejpam-3294	360	6	partially	partially	ADV
ejpam-3294	360	7	ordered	order	VERB
ejpam-3294	360	8	metric	metric	ADJ
ejpam-3294	360	9	spaces	space	NOUN
ejpam-3294	360	10	.	.	PUNCT
ejpam-3294	361	1	fixed	fix	VERB
ejpam-3294	361	2	point	point	NOUN
ejpam-3294	361	3	theory	theory	NOUN
ejpam-3294	361	4	appl	appl	PROPN
ejpam-3294	361	5	.	.	PROPN
ejpam-3294	361	6	,	,	PUNCT
ejpam-3294	361	7	i	i	PROPN
ejpam-3294	361	8	d	d	PROPN
ejpam-3294	361	9	131294	131294	NUM
ejpam-3294	361	10	,	,	PUNCT
ejpam-3294	361	11	2008	2008	NUM
ejpam-3294	361	12	.	.	PUNCT
ejpam-3294	362	1	[	[	X
ejpam-3294	362	2	12	12	NUM
ejpam-3294	362	3	]	]	PUNCT
ejpam-3294	362	4	m.	m.	NOUN
ejpam-3294	362	5	geraghty	geraghty	PROPN
ejpam-3294	362	6	.	.	PUNCT
ejpam-3294	363	1	on	on	ADP
ejpam-3294	363	2	contractive	contractive	ADJ
ejpam-3294	363	3	mappings	mapping	NOUN
ejpam-3294	363	4	.	.	PUNCT
ejpam-3294	363	5	,	,	PUNCT
ejpam-3294	363	6	volume	volume	NOUN
ejpam-3294	363	7	40	40	NUM
ejpam-3294	363	8	.	.	PUNCT
ejpam-3294	363	9	1973	1973	NUM
ejpam-3294	363	10	.	.	PUNCT
ejpam-3294	364	1	[	[	X
ejpam-3294	364	2	13	13	NUM
ejpam-3294	364	3	]	]	PUNCT
ejpam-3294	364	4	t.	t.	PROPN
ejpam-3294	364	5	gnana	gnana	PROPN
ejpam-3294	364	6	bhaskar	bhaskar	NOUN
ejpam-3294	364	7	and	and	CCONJ
ejpam-3294	364	8	v.	v.	ADP
ejpam-3294	364	9	lakshmikantham	lakshmikantham	NOUN
ejpam-3294	364	10	.	.	PUNCT
ejpam-3294	365	1	fixed	fix	VERB
ejpam-3294	365	2	point	point	NOUN
ejpam-3294	365	3	theorems	theorem	NOUN
ejpam-3294	365	4	in	in	ADP
ejpam-3294	365	5	partially	partially	ADV
ejpam-3294	365	6	ordered	order	VERB
ejpam-3294	365	7	metric	metric	ADJ
ejpam-3294	365	8	spaces	space	NOUN
ejpam-3294	365	9	and	and	CCONJ
ejpam-3294	365	10	applications	application	NOUN
ejpam-3294	365	11	.	.	PUNCT
ejpam-3294	366	1	nonlinear	nonlinear	ADJ
ejpam-3294	366	2	anal	anal	PROPN
ejpam-3294	366	3	.	.	PUNCT
ejpam-3294	366	4	,	,	PUNCT
ejpam-3294	366	5	65	65	NUM
ejpam-3294	366	6	,	,	PUNCT
ejpam-3294	366	7	2006	2006	NUM
ejpam-3294	366	8	.	.	PUNCT
ejpam-3294	367	1	[	[	X
ejpam-3294	367	2	14	14	NUM
ejpam-3294	367	3	]	]	PUNCT
ejpam-3294	367	4	a.	a.	NOUN
ejpam-3294	367	5	a.	a.	PROPN
ejpam-3294	367	6	harandi	harandi	PROPN
ejpam-3294	367	7	.	.	PUNCT
ejpam-3294	368	1	metric	metric	ADJ
ejpam-3294	368	2	-	-	PUNCT
ejpam-3294	368	3	like	like	ADJ
ejpam-3294	368	4	spaces	space	NOUN
ejpam-3294	368	5	,	,	PUNCT
ejpam-3294	368	6	partial	partial	ADJ
ejpam-3294	368	7	metric	metric	ADJ
ejpam-3294	368	8	spaces	space	NOUN
ejpam-3294	368	9	and	and	CCONJ
ejpam-3294	368	10	fixed	fix	VERB
ejpam-3294	368	11	points	point	NOUN
ejpam-3294	368	12	.	.	PUNCT
ejpam-3294	369	1	fixed	fix	VERB
ejpam-3294	369	2	point	point	NOUN
ejpam-3294	369	3	theory	theory	NOUN
ejpam-3294	369	4	appl	appl	PROPN
ejpam-3294	369	5	.	.	PROPN
ejpam-3294	369	6	,	,	PUNCT
ejpam-3294	369	7	2012	2012	NUM
ejpam-3294	369	8	,	,	PUNCT
ejpam-3294	369	9	2012	2012	NUM
ejpam-3294	369	10	.	.	PUNCT
ejpam-3294	370	1	[	[	X
ejpam-3294	370	2	15	15	NUM
ejpam-3294	370	3	]	]	X
ejpam-3294	370	4	j.	j.	PROPN
ejpam-3294	370	5	harjani	harjani	PROPN
ejpam-3294	370	6	and	and	CCONJ
ejpam-3294	370	7	k.	k.	PROPN
ejpam-3294	370	8	sadarangani	sadarangani	PROPN
ejpam-3294	370	9	.	.	PUNCT
ejpam-3294	371	1	generalized	generalized	ADJ
ejpam-3294	371	2	contractions	contraction	NOUN
ejpam-3294	371	3	in	in	ADP
ejpam-3294	371	4	partially	partially	ADV
ejpam-3294	371	5	ordered	order	VERB
ejpam-3294	371	6	metric	metric	ADJ
ejpam-3294	371	7	spaces	space	NOUN
ejpam-3294	371	8	and	and	CCONJ
ejpam-3294	371	9	applications	application	NOUN
ejpam-3294	371	10	to	to	ADP
ejpam-3294	371	11	ordinary	ordinary	ADJ
ejpam-3294	371	12	differential	differential	ADJ
ejpam-3294	371	13	equations	equation	NOUN
ejpam-3294	371	14	.	.	PUNCT
ejpam-3294	372	1	nonlinear	nonlinear	ADJ
ejpam-3294	372	2	anal	anal	PROPN
ejpam-3294	372	3	.	.	PUNCT
ejpam-3294	372	4	,	,	PUNCT
ejpam-3294	372	5	72	72	NUM
ejpam-3294	372	6	,	,	PUNCT
ejpam-3294	372	7	2010	2010	NUM
ejpam-3294	372	8	.	.	PUNCT
ejpam-3294	373	1	[	[	X
ejpam-3294	373	2	16	16	NUM
ejpam-3294	373	3	]	]	X
ejpam-3294	373	4	h.	h.	PROPN
ejpam-3294	373	5	isik	isik	PROPN
ejpam-3294	373	6	and	and	CCONJ
ejpam-3294	373	7	d.	d.	PROPN
ejpam-3294	373	8	turkoglu	turkoglu	PROPN
ejpam-3294	373	9	.	.	PUNCT
ejpam-3294	374	1	fixed	fix	VERB
ejpam-3294	374	2	point	point	NOUN
ejpam-3294	374	3	theorems	theorem	NOUN
ejpam-3294	374	4	for	for	ADP
ejpam-3294	374	5	weakly	weakly	ADJ
ejpam-3294	374	6	contractive	contractive	ADJ
ejpam-3294	374	7	mappings	mapping	NOUN
ejpam-3294	374	8	in	in	ADP
ejpam-3294	374	9	partially	partially	ADV
ejpam-3294	374	10	ordered	order	VERB
ejpam-3294	374	11	metric	metric	ADJ
ejpam-3294	374	12	-	-	PUNCT
ejpam-3294	374	13	like	like	ADJ
ejpam-3294	374	14	spaces	space	NOUN
ejpam-3294	374	15	.	.	PUNCT
ejpam-3294	375	1	fixed	fix	VERB
ejpam-3294	375	2	point	point	NOUN
ejpam-3294	375	3	theory	theory	NOUN
ejpam-3294	375	4	and	and	CCONJ
ejpam-3294	375	5	application	application	NOUN
ejpam-3294	375	6	appl	appl	NOUN
ejpam-3294	375	7	.	.	PROPN
ejpam-3294	375	8	,	,	PUNCT
ejpam-3294	375	9	80	80	NUM
ejpam-3294	375	10	,	,	PUNCT
ejpam-3294	375	11	2012	2012	NUM
ejpam-3294	375	12	.	.	PUNCT
ejpam-3294	376	1	[	[	X
ejpam-3294	376	2	17	17	NUM
ejpam-3294	376	3	]	]	X
ejpam-3294	376	4	e.	e.	PROPN
ejpam-3294	376	5	karapnar	karapnar	PROPN
ejpam-3294	376	6	and	and	CCONJ
ejpam-3294	376	7	erhan	erhan	SCONJ
ejpam-3294	376	8	i	i	PRON
ejpam-3294	376	9	m.	m.	NOUN
ejpam-3294	376	10	fixed	fix	VERB
ejpam-3294	376	11	point	point	NOUN
ejpam-3294	376	12	theorems	theorem	NOUN
ejpam-3294	376	13	for	for	ADP
ejpam-3294	376	14	operators	operator	NOUN
ejpam-3294	376	15	on	on	ADP
ejpam-3294	376	16	partial	partial	ADJ
ejpam-3294	376	17	metric	metric	ADJ
ejpam-3294	376	18	spaces	space	NOUN
ejpam-3294	376	19	.	.	PUNCT
ejpam-3294	377	1	appl.math	appl.math	NOUN
ejpam-3294	377	2	.	.	PUNCT
ejpam-3294	377	3	lett	lett	PROPN
ejpam-3294	377	4	.	.	PROPN
ejpam-3294	377	5	,	,	PUNCT
ejpam-3294	377	6	24	24	NUM
ejpam-3294	377	7	,	,	PUNCT
ejpam-3294	377	8	2011	2011	NUM
ejpam-3294	377	9	.	.	PUNCT
ejpam-3294	378	1	[	[	X
ejpam-3294	378	2	18	18	NUM
ejpam-3294	378	3	]	]	X
ejpam-3294	378	4	e.	e.	PROPN
ejpam-3294	378	5	karapnar	karapnar	PROPN
ejpam-3294	378	6	,	,	PUNCT
ejpam-3294	378	7	h.	h.	PROPN
ejpam-3294	378	8	alsulami	alsulami	PROPN
ejpam-3294	378	9	,	,	PUNCT
ejpam-3294	378	10	and	and	CCONJ
ejpam-3294	378	11	m.	m.	PROPN
ejpam-3294	378	12	noorwali	noorwali	PROPN
ejpam-3294	378	13	.	.	PUNCT
ejpam-3294	379	1	some	some	DET
ejpam-3294	379	2	extensions	extension	NOUN
ejpam-3294	379	3	for	for	ADP
ejpam-3294	379	4	geragthy	geragthy	ADJ
ejpam-3294	379	5	type	type	NOUN
ejpam-3294	379	6	contractive	contractive	ADJ
ejpam-3294	379	7	mappings	mapping	NOUN
ejpam-3294	379	8	.	.	PUNCT
ejpam-3294	380	1	fixed	fix	VERB
ejpam-3294	380	2	point	point	NOUN
ejpam-3294	380	3	theory	theory	NOUN
ejpam-3294	380	4	appl	appl	PROPN
ejpam-3294	380	5	.	.	PROPN
ejpam-3294	380	6	,	,	PUNCT
ejpam-3294	380	7	1	1	NUM
ejpam-3294	380	8	,	,	PUNCT
ejpam-3294	380	9	2015	2015	NUM
ejpam-3294	380	10	.	.	PUNCT
ejpam-3294	381	1	[	[	X
ejpam-3294	381	2	19	19	NUM
ejpam-3294	381	3	]	]	PUNCT
ejpam-3294	381	4	s.	s.	PROPN
ejpam-3294	381	5	g.	g.	PROPN
ejpam-3294	381	6	matthews	matthews	PROPN
ejpam-3294	381	7	.	.	PUNCT
ejpam-3294	382	1	partial	partial	ADJ
ejpam-3294	382	2	metric	metric	ADJ
ejpam-3294	382	3	topology	topology	NOUN
ejpam-3294	382	4	.	.	PUNCT
ejpam-3294	383	1	ann	ann	PROPN
ejpam-3294	383	2	.	.	PUNCT
ejpam-3294	384	1	new	new	PROPN
ejpam-3294	384	2	york	york	PROPN
ejpam-3294	384	3	acad	acad	PROPN
ejpam-3294	384	4	,	,	PUNCT
ejpam-3294	384	5	728	728	NUM
ejpam-3294	384	6	,	,	PUNCT
ejpam-3294	384	7	1994	1994	NUM
ejpam-3294	384	8	.	.	PUNCT
ejpam-3294	385	1	[	[	X
ejpam-3294	385	2	20	20	NUM
ejpam-3294	385	3	]	]	SYM
ejpam-3294	385	4	jj	jj	PROPN
ejpam-3294	385	5	.	.	PROPN
ejpam-3294	385	6	nieto	nieto	PROPN
ejpam-3294	385	7	and	and	CCONJ
ejpam-3294	385	8	r.	r.	PROPN
ejpam-3294	385	9	odŕıguez	odŕıguez	PROPN
ejpam-3294	385	10	lópez	lópez	ADV
ejpam-3294	385	11	.	.	PUNCT
ejpam-3294	386	1	existence	existence	NOUN
ejpam-3294	386	2	of	of	ADP
ejpam-3294	386	3	extremal	extremal	ADJ
ejpam-3294	386	4	solutions	solution	NOUN
ejpam-3294	386	5	for	for	ADP
ejpam-3294	386	6	quadratic	quadratic	ADJ
ejpam-3294	386	7	fuzzy	fuzzy	ADJ
ejpam-3294	386	8	equations	equation	NOUN
ejpam-3294	386	9	.	.	PUNCT
ejpam-3294	387	1	fixed	fix	VERB
ejpam-3294	387	2	point	point	NOUN
ejpam-3294	387	3	theory	theory	NOUN
ejpam-3294	387	4	,	,	PUNCT
ejpam-3294	387	5	pages	page	NOUN
ejpam-3294	387	6	321–342	321–342	NUM
ejpam-3294	387	7	,	,	PUNCT
ejpam-3294	387	8	2005	2005	NUM
ejpam-3294	387	9	.	.	PUNCT
ejpam-3294	388	1	[	[	X
ejpam-3294	388	2	21	21	NUM
ejpam-3294	388	3	]	]	X
ejpam-3294	388	4	h.	h.	NOUN
ejpam-3294	388	5	piri	piri	NOUN
ejpam-3294	388	6	and	and	CCONJ
ejpam-3294	388	7	p.	p.	PROPN
ejpam-3294	388	8	kumam	kumam	PROPN
ejpam-3294	388	9	.	.	PUNCT
ejpam-3294	389	1	some	some	DET
ejpam-3294	389	2	fixed	fix	VERB
ejpam-3294	389	3	point	point	NOUN
ejpam-3294	389	4	theorems	theorem	NOUN
ejpam-3294	389	5	concerning	concern	VERB
ejpam-3294	389	6	f	f	PROPN
ejpam-3294	389	7	-contraction	-contraction	PROPN
ejpam-3294	389	8	in	in	ADP
ejpam-3294	389	9	complete	complete	ADJ
ejpam-3294	389	10	metric	metric	ADJ
ejpam-3294	389	11	spaces	space	NOUN
ejpam-3294	389	12	.	.	PUNCT
ejpam-3294	390	1	fixed	fix	VERB
ejpam-3294	390	2	point	point	NOUN
ejpam-3294	390	3	theory	theory	NOUN
ejpam-3294	390	4	,	,	PUNCT
ejpam-3294	390	5	appl	appl	PROPN
ejpam-3294	390	6	.	.	PROPN
ejpam-3294	390	7	,	,	PUNCT
ejpam-3294	390	8	11	11	NUM
ejpam-3294	390	9	,	,	PUNCT
ejpam-3294	390	10	2014	2014	NUM
ejpam-3294	390	11	.	.	PUNCT
ejpam-3294	391	1	[	[	X
ejpam-3294	391	2	22	22	NUM
ejpam-3294	391	3	]	]	X
ejpam-3294	391	4	h.	h.	PROPN
ejpam-3294	391	5	qawaqneh	qawaqneh	PROPN
ejpam-3294	391	6	,	,	PUNCT
ejpam-3294	391	7	m.	m.	PROPN
ejpam-3294	391	8	s.	s.	PROPN
ejpam-3294	391	9	m.	m.	PROPN
ejpam-3294	391	10	noorani	noorani	PROPN
ejpam-3294	391	11	,	,	PUNCT
ejpam-3294	391	12	w.	w.	PROPN
ejpam-3294	391	13	shatanawi	shatanawi	PROPN
ejpam-3294	391	14	,	,	PUNCT
ejpam-3294	391	15	k.	k.	PROPN
ejpam-3294	391	16	abodayeh	abodayeh	PROPN
ejpam-3294	391	17	,	,	PUNCT
ejpam-3294	391	18	and	and	CCONJ
ejpam-3294	391	19	h.	h.	PROPN
ejpam-3294	391	20	alsamir	alsamir	PROPN
ejpam-3294	391	21	.	.	PUNCT
ejpam-3294	392	1	fixed	fix	VERB
ejpam-3294	392	2	point	point	NOUN
ejpam-3294	392	3	for	for	ADP
ejpam-3294	392	4	mappings	mapping	NOUN
ejpam-3294	392	5	under	under	ADP
ejpam-3294	392	6	contractive	contractive	ADJ
ejpam-3294	392	7	condition	condition	NOUN
ejpam-3294	392	8	based	base	VERB
ejpam-3294	392	9	on	on	ADP
ejpam-3294	392	10	simulation	simulation	NOUN
ejpam-3294	392	11	functions	function	NOUN
ejpam-3294	392	12	and	and	CCONJ
ejpam-3294	392	13	cyclic	cyclic	NOUN
ejpam-3294	392	14	(	(	PUNCT
ejpam-3294	392	15	α	α	NOUN
ejpam-3294	392	16	,	,	PUNCT
ejpam-3294	392	17	β)−admissibility	β)−admissibility	PROPN
ejpam-3294	392	18	.	.	PUNCT
ejpam-3294	393	1	journal	journal	PROPN
ejpam-3294	393	2	of	of	ADP
ejpam-3294	393	3	mathematical	mathematical	ADJ
ejpam-3294	393	4	analysis	analysis	NOUN
ejpam-3294	393	5	,	,	PUNCT
ejpam-3294	393	6	9:38–59	9:38–59	NOUN
ejpam-3294	393	7	,	,	PUNCT
ejpam-3294	393	8	2018	2018	NUM
ejpam-3294	393	9	.	.	PUNCT
ejpam-3294	394	1	[	[	X
ejpam-3294	394	2	23	23	NUM
ejpam-3294	394	3	]	]	X
ejpam-3294	394	4	h.	h.	PROPN
ejpam-3294	394	5	qawaqneh	qawaqneh	PROPN
ejpam-3294	394	6	,	,	PUNCT
ejpam-3294	394	7	m.	m.	PROPN
ejpam-3294	394	8	s.	s.	PROPN
ejpam-3294	394	9	m.	m.	PROPN
ejpam-3294	394	10	noorani	noorani	PROPN
ejpam-3294	394	11	,	,	PUNCT
ejpam-3294	394	12	w.	w.	PROPN
ejpam-3294	394	13	shatanawi	shatanawi	PROPN
ejpam-3294	394	14	,	,	PUNCT
ejpam-3294	394	15	and	and	CCONJ
ejpam-3294	394	16	h.	h.	PROPN
ejpam-3294	394	17	alsamir	alsamir	PROPN
ejpam-3294	394	18	.	.	PUNCT
ejpam-3294	395	1	common	common	ADJ
ejpam-3294	395	2	fixed	fix	VERB
ejpam-3294	395	3	points	point	NOUN
ejpam-3294	395	4	for	for	ADP
ejpam-3294	395	5	pairs	pair	NOUN
ejpam-3294	395	6	of	of	ADP
ejpam-3294	395	7	triangular	triangular	NOUN
ejpam-3294	395	8	(	(	PUNCT
ejpam-3294	395	9	α)−admissible	α)−admissible	ADJ
ejpam-3294	395	10	mappings	mapping	NOUN
ejpam-3294	395	11	.	.	PUNCT
ejpam-3294	396	1	journal	journal	PROPN
ejpam-3294	396	2	of	of	ADP
ejpam-3294	396	3	nonlinear	nonlinear	PROPN
ejpam-3294	396	4	sciences	sciences	PROPN
ejpam-3294	396	5	and	and	CCONJ
ejpam-3294	396	6	application	application	NOUN
ejpam-3294	396	7	,	,	PUNCT
ejpam-3294	396	8	10:61926204	10:61926204	NUM
ejpam-3294	396	9	,	,	PUNCT
ejpam-3294	396	10	2017	2017	NUM
ejpam-3294	396	11	.	.	PUNCT
ejpam-3294	397	1	[	[	X
ejpam-3294	397	2	24	24	NUM
ejpam-3294	397	3	]	]	SYM
ejpam-3294	397	4	acm	acm	PROPN
ejpam-3294	397	5	.	.	PROPN
ejpam-3294	397	6	ran	run	VERB
ejpam-3294	397	7	and	and	CCONJ
ejpam-3294	397	8	mcb	mcb	PROPN
ejpam-3294	397	9	.	.	PUNCT
ejpam-3294	398	1	reurings	reuring	NOUN
ejpam-3294	398	2	.	.	PUNCT
ejpam-3294	399	1	a	a	DET
ejpam-3294	399	2	fixed	fix	VERB
ejpam-3294	399	3	point	point	NOUN
ejpam-3294	399	4	theorem	theorem	VERB
ejpam-3294	399	5	in	in	ADP
ejpam-3294	399	6	partially	partially	ADV
ejpam-3294	399	7	ordered	order	VERB
ejpam-3294	399	8	sets	set	NOUN
ejpam-3294	399	9	and	and	CCONJ
ejpam-3294	399	10	some	some	DET
ejpam-3294	399	11	applications	application	NOUN
ejpam-3294	399	12	to	to	PART
ejpam-3294	399	13	matrix	matrix	VERB
ejpam-3294	399	14	equations	equation	NOUN
ejpam-3294	399	15	.	.	PUNCT
ejpam-3294	400	1	proc	proc	PROPN
ejpam-3294	400	2	.	.	PUNCT
ejpam-3294	401	1	am.math	am.math	NOUN
ejpam-3294	401	2	.	.	PUNCT
ejpam-3294	402	1	soc	soc	PROPN
ejpam-3294	402	2	.	.	PUNCT
ejpam-3294	402	3	,	,	PUNCT
ejpam-3294	402	4	32	32	NUM
ejpam-3294	402	5	,	,	PUNCT
ejpam-3294	402	6	2004	2004	NUM
ejpam-3294	402	7	.	.	PUNCT
ejpam-3294	403	1	references	reference	NOUN
ejpam-3294	403	2	716	716	NUM
ejpam-3294	403	3	[	[	X
ejpam-3294	403	4	25	25	NUM
ejpam-3294	403	5	]	]	PUNCT
ejpam-3294	403	6	s.	s.	PROPN
ejpam-3294	403	7	romaguera	romaguera	PROPN
ejpam-3294	403	8	and	and	CCONJ
ejpam-3294	403	9	o.	o.	PROPN
ejpam-3294	403	10	valero	valero	PROPN
ejpam-3294	403	11	.	.	PUNCT
ejpam-3294	404	1	a	a	DET
ejpam-3294	404	2	quantitative	quantitative	ADJ
ejpam-3294	404	3	computational	computational	ADJ
ejpam-3294	404	4	model	model	NOUN
ejpam-3294	404	5	for	for	ADP
ejpam-3294	404	6	complete	complete	ADJ
ejpam-3294	404	7	partial	partial	ADJ
ejpam-3294	404	8	metric	metric	ADJ
ejpam-3294	404	9	spaces	space	NOUN
ejpam-3294	404	10	via	via	ADP
ejpam-3294	404	11	formal	formal	ADJ
ejpam-3294	404	12	balls	ball	NOUN
ejpam-3294	404	13	.	.	PUNCT
ejpam-3294	405	1	math	math	NOUN
ejpam-3294	405	2	.	.	PUNCT
ejpam-3294	405	3	struct	struct	NOUN
ejpam-3294	405	4	.	.	PUNCT
ejpam-3294	406	1	comput	comput	NOUN
ejpam-3294	406	2	.	.	PUNCT
ejpam-3294	407	1	sci	sci	PROPN
ejpam-3294	407	2	,	,	PUNCT
ejpam-3294	407	3	4	4	NUM
ejpam-3294	407	4	,	,	PUNCT
ejpam-3294	407	5	2011	2011	NUM
ejpam-3294	407	6	.	.	PUNCT
ejpam-3294	408	1	[	[	X
ejpam-3294	408	2	26	26	NUM
ejpam-3294	408	3	]	]	PUNCT
ejpam-3294	408	4	b.	b.	PROPN
ejpam-3294	408	5	samet	samet	PROPN
ejpam-3294	408	6	,	,	PUNCT
ejpam-3294	408	7	c.	c.	PROPN
ejpam-3294	408	8	vetro	vetro	PROPN
ejpam-3294	408	9	,	,	PUNCT
ejpam-3294	408	10	and	and	CCONJ
ejpam-3294	408	11	p.	p.	PROPN
ejpam-3294	408	12	vetro	vetro	PROPN
ejpam-3294	408	13	.	.	PUNCT
ejpam-3294	409	1	fixed	fix	VERB
ejpam-3294	409	2	point	point	NOUN
ejpam-3294	409	3	theorems	theorem	NOUN
ejpam-3294	409	4	for	for	ADP
ejpam-3294	409	5	a	a	DET
ejpam-3294	409	6	α−ψ−contractive	α−ψ−contractive	ADJ
ejpam-3294	409	7	type	type	NOUN
ejpam-3294	409	8	mappings	mapping	NOUN
ejpam-3294	409	9	.	.	PUNCT
ejpam-3294	410	1	nonlinear	nonlinear	ADJ
ejpam-3294	410	2	anal	anal	PROPN
ejpam-3294	410	3	.	.	PUNCT
ejpam-3294	410	4	,	,	PUNCT
ejpam-3294	410	5	75:21542165	75:21542165	NUM
ejpam-3294	410	6	,	,	PUNCT
ejpam-3294	410	7	2012	2012	NUM
ejpam-3294	410	8	.	.	PUNCT
ejpam-3294	411	1	[	[	X
ejpam-3294	411	2	27	27	NUM
ejpam-3294	411	3	]	]	X
ejpam-3294	411	4	w.	w.	PROPN
ejpam-3294	411	5	shatanawi	shatanawi	PROPN
ejpam-3294	411	6	and	and	CCONJ
ejpam-3294	411	7	a.	a.	NOUN
ejpam-3294	411	8	alrawashdeh	alrawashdeh	NOUN
ejpam-3294	411	9	.	.	PUNCT
ejpam-3294	412	1	common	common	ADJ
ejpam-3294	412	2	fixed	fix	VERB
ejpam-3294	412	3	points	point	NOUN
ejpam-3294	412	4	of	of	ADP
ejpam-3294	412	5	almost	almost	ADV
ejpam-3294	412	6	generalized	generalize	VERB
ejpam-3294	412	7	(	(	PUNCT
ejpam-3294	412	8	ψ,ϕ)-contractive	ψ,ϕ)-contractive	ADJ
ejpam-3294	412	9	mappings	mapping	NOUN
ejpam-3294	412	10	in	in	ADP
ejpam-3294	412	11	ordered	order	VERB
ejpam-3294	412	12	metric	metric	ADJ
ejpam-3294	412	13	spaces	space	NOUN
ejpam-3294	412	14	.	.	PUNCT
ejpam-3294	413	1	fixed	fix	VERB
ejpam-3294	413	2	point	point	NOUN
ejpam-3294	413	3	theory	theory	NOUN
ejpam-3294	413	4	appl	appl	PROPN
ejpam-3294	413	5	.	.	PROPN
ejpam-3294	413	6	,	,	PUNCT
ejpam-3294	413	7	15	15	NUM
ejpam-3294	413	8	,	,	PUNCT
ejpam-3294	413	9	2013	2013	NUM
ejpam-3294	413	10	.	.	PUNCT
ejpam-3294	414	1	[	[	X
ejpam-3294	414	2	28	28	NUM
ejpam-3294	414	3	]	]	X
ejpam-3294	414	4	w.	w.	PROPN
ejpam-3294	414	5	shatanawi	shatanawi	PROPN
ejpam-3294	414	6	and	and	CCONJ
ejpam-3294	414	7	h.	h.	PROPN
ejpam-3294	414	8	k.	k.	PROPN
ejpam-3294	414	9	nashine	nashine	PROPN
ejpam-3294	414	10	.	.	PUNCT
ejpam-3294	415	1	a	a	DET
ejpam-3294	415	2	generalization	generalization	NOUN
ejpam-3294	415	3	of	of	ADP
ejpam-3294	415	4	banachs	banachs	PROPN
ejpam-3294	415	5	contraction	contraction	PROPN
ejpam-3294	415	6	principle	principle	NOUN
ejpam-3294	415	7	for	for	ADP
ejpam-3294	415	8	nonlinear	nonlinear	ADJ
ejpam-3294	415	9	contraction	contraction	NOUN
ejpam-3294	415	10	in	in	ADP
ejpam-3294	415	11	a	a	DET
ejpam-3294	415	12	partial	partial	ADJ
ejpam-3294	415	13	metric	metric	ADJ
ejpam-3294	415	14	space	space	NOUN
ejpam-3294	415	15	.	.	PUNCT
ejpam-3294	416	1	j.	j.	PROPN
ejpam-3294	416	2	nonlinear	nonlinear	PROPN
ejpam-3294	416	3	sci	sci	PROPN
ejpam-3294	416	4	.	.	PUNCT
ejpam-3294	416	5	appl	appl	PROPN
ejpam-3294	416	6	.	.	PROPN
ejpam-3294	416	7	,	,	PUNCT
ejpam-3294	416	8	5:3743	5:3743	NUM
ejpam-3294	416	9	,	,	PUNCT
ejpam-3294	416	10	2012	2012	NUM
ejpam-3294	416	11	.	.	PUNCT
ejpam-3294	417	1	[	[	X
ejpam-3294	417	2	29	29	NUM
ejpam-3294	417	3	]	]	X
ejpam-3294	417	4	w.	w.	PROPN
ejpam-3294	417	5	sintunavarat	sintunavarat	PROPN
ejpam-3294	417	6	.	.	PUNCT
ejpam-3294	418	1	fixed	fix	VERB
ejpam-3294	418	2	point	point	NOUN
ejpam-3294	418	3	results	result	NOUN
ejpam-3294	418	4	in	in	ADP
ejpam-3294	418	5	b−metric	b−metric	ADJ
ejpam-3294	418	6	spaces	space	NOUN
ejpam-3294	418	7	approach	approach	VERB
ejpam-3294	418	8	to	to	ADP
ejpam-3294	418	9	the	the	DET
ejpam-3294	418	10	existence	existence	NOUN
ejpam-3294	418	11	of	of	ADP
ejpam-3294	418	12	a	a	DET
ejpam-3294	418	13	solution	solution	NOUN
ejpam-3294	418	14	for	for	ADP
ejpam-3294	418	15	nonlinear	nonlinear	ADJ
ejpam-3294	418	16	integral	integral	ADJ
ejpam-3294	418	17	equations	equation	NOUN
ejpam-3294	418	18	.	.	PUNCT
ejpam-3294	419	1	revista	revista	PROPN
ejpam-3294	419	2	de	de	X
ejpam-3294	419	3	la	la	PROPN
ejpam-3294	419	4	real	real	PROPN
ejpam-3294	419	5	academia	academia	PROPN
ejpam-3294	419	6	de	de	PROPN
ejpam-3294	419	7	ciencias	ciencias	PROPN
ejpam-3294	419	8	exactas	exacta	NOUN
ejpam-3294	419	9	,	,	PUNCT
ejpam-3294	419	10	fisicas	fisicas	PROPN
ejpam-3294	419	11	y	y	PROPN
ejpam-3294	419	12	naturales	naturale	NOUN
ejpam-3294	419	13	,	,	PUNCT
ejpam-3294	419	14	16	16	NUM
ejpam-3294	419	15	,	,	PUNCT
ejpam-3294	419	16	2016	2016	NUM
ejpam-3294	419	17	.	.	PUNCT
ejpam-3294	420	1	[	[	X
ejpam-3294	420	2	30	30	NUM
ejpam-3294	420	3	]	]	X
ejpam-3294	420	4	w.	w.	PROPN
ejpam-3294	420	5	sintunavarat	sintunavarat	PROPN
ejpam-3294	420	6	.	.	PUNCT
ejpam-3294	421	1	nonlinear	nonlinear	ADJ
ejpam-3294	421	2	integral	integral	ADJ
ejpam-3294	421	3	equations	equation	NOUN
ejpam-3294	421	4	with	with	ADP
ejpam-3294	421	5	new	new	ADJ
ejpam-3294	421	6	admissibility	admissibility	NOUN
ejpam-3294	421	7	types	type	NOUN
ejpam-3294	421	8	in	in	ADP
ejpam-3294	421	9	b−metric	b−metric	ADJ
ejpam-3294	421	10	spaces	space	NOUN
ejpam-3294	421	11	.	.	PUNCT
ejpam-3294	422	1	fixed	fix	VERB
ejpam-3294	422	2	point	point	NOUN
ejpam-3294	422	3	theory	theory	NOUN
ejpam-3294	422	4	appl	appl	NOUN
ejpam-3294	422	5	,	,	PUNCT
ejpam-3294	422	6	18	18	NUM
ejpam-3294	422	7	,	,	PUNCT
ejpam-3294	422	8	2016	2016	NUM
ejpam-3294	422	9	.	.	PUNCT
ejpam-3294	423	1	[	[	X
ejpam-3294	423	2	31	31	NUM
ejpam-3294	423	3	]	]	X
ejpam-3294	423	4	d.	d.	PROPN
ejpam-3294	423	5	wardowski	wardowski	PROPN
ejpam-3294	423	6	.	.	PUNCT
ejpam-3294	424	1	fixed	fix	VERB
ejpam-3294	424	2	points	point	NOUN
ejpam-3294	424	3	of	of	ADP
ejpam-3294	424	4	a	a	DET
ejpam-3294	424	5	new	new	ADJ
ejpam-3294	424	6	type	type	NOUN
ejpam-3294	424	7	of	of	ADP
ejpam-3294	424	8	contractive	contractive	ADJ
ejpam-3294	424	9	mappings	mapping	NOUN
ejpam-3294	424	10	in	in	ADP
ejpam-3294	424	11	complete	complete	ADJ
ejpam-3294	424	12	metric	metric	ADJ
ejpam-3294	424	13	spaces	space	NOUN
ejpam-3294	424	14	.	.	PUNCT
ejpam-3294	425	1	fixed	fix	VERB
ejpam-3294	425	2	point	point	NOUN
ejpam-3294	425	3	theory	theory	NOUN
ejpam-3294	425	4	and	and	CCONJ
ejpam-3294	425	5	applications	application	NOUN
ejpam-3294	425	6	,	,	PUNCT
ejpam-3294	425	7	75:21542165	75:21542165	NUM
ejpam-3294	425	8	,	,	PUNCT
ejpam-3294	425	9	2012	2012	NUM
ejpam-3294	425	10	.	.	PUNCT
ejpam-3294	426	1	[	[	X
ejpam-3294	426	2	32	32	NUM
ejpam-3294	426	3	]	]	X
ejpam-3294	426	4	y.	y.	PROPN
ejpam-3294	426	5	wu	wu	PROPN
ejpam-3294	426	6	.	.	PUNCT
ejpam-3294	427	1	new	new	ADJ
ejpam-3294	427	2	fixed	fix	VERB
ejpam-3294	427	3	point	point	NOUN
ejpam-3294	427	4	theorems	theorem	NOUN
ejpam-3294	427	5	and	and	CCONJ
ejpam-3294	427	6	applications	application	NOUN
ejpam-3294	427	7	of	of	ADP
ejpam-3294	427	8	mixed	mixed	ADJ
ejpam-3294	427	9	monotone	monotone	ADJ
ejpam-3294	427	10	operator	operator	NOUN
ejpam-3294	427	11	.	.	PUNCT
ejpam-3294	428	1	j.	j.	PROPN
ejpam-3294	428	2	math	math	PROPN
ejpam-3294	428	3	.	.	PUNCT
ejpam-3294	429	1	anal	anal	PROPN
ejpam-3294	429	2	.	.	PUNCT
ejpam-3294	429	3	appl	appl	PROPN
ejpam-3294	429	4	,	,	PUNCT
ejpam-3294	429	5	341	341	NUM
ejpam-3294	429	6	,	,	PUNCT
ejpam-3294	429	7	2008	2008	NUM
ejpam-3294	429	8	.	.	PUNCT