id	sid	tid	token	lemma	pos
ejpam-6659	1	1	european	european	PROPN
ejpam-6659	1	2	journal	journal	PROPN
ejpam-6659	1	3	of	of	ADP
ejpam-6659	1	4	pure	pure	ADJ
ejpam-6659	1	5	and	and	CCONJ
ejpam-6659	1	6	applied	applied	ADJ
ejpam-6659	1	7	mathematics	mathematic	NOUN
ejpam-6659	1	8	2025	2025	NUM
ejpam-6659	1	9	,	,	PUNCT
ejpam-6659	1	10	vol	vol	NOUN
ejpam-6659	1	11	.	.	PROPN
ejpam-6659	1	12	18	18	NUM
ejpam-6659	1	13	,	,	PUNCT
ejpam-6659	1	14	issue	issue	NOUN
ejpam-6659	1	15	3	3	NUM
ejpam-6659	1	16	,	,	PUNCT
ejpam-6659	1	17	article	article	NOUN
ejpam-6659	1	18	number	number	NOUN
ejpam-6659	1	19	6659	6659	NUM
ejpam-6659	1	20	issn	issn	VERB
ejpam-6659	1	21	1307	1307	NUM
ejpam-6659	1	22	-	-	SYM
ejpam-6659	1	23	5543	5543	NUM
ejpam-6659	1	24	–	–	PUNCT
ejpam-6659	2	1	ejpam.com	ejpam.com	X
ejpam-6659	2	2	published	publish	VERB
ejpam-6659	2	3	by	by	ADP
ejpam-6659	2	4	new	new	PROPN
ejpam-6659	2	5	york	york	PROPN
ejpam-6659	2	6	business	business	PROPN
ejpam-6659	2	7	global	global	PROPN
ejpam-6659	2	8	on	on	ADP
ejpam-6659	2	9	fixed	fix	VERB
ejpam-6659	2	10	points	point	NOUN
ejpam-6659	2	11	in	in	ADP
ejpam-6659	2	12	complex	complex	ADJ
ejpam-6659	2	13	valued	value	VERB
ejpam-6659	2	14	controlled	control	VERB
ejpam-6659	2	15	s	s	NOUN
ejpam-6659	2	16	-	-	ADJ
ejpam-6659	2	17	metric	metric	ADJ
ejpam-6659	2	18	spaces	space	NOUN
ejpam-6659	2	19	and	and	CCONJ
ejpam-6659	2	20	an	an	DET
ejpam-6659	2	21	application	application	NOUN
ejpam-6659	2	22	haitham	haitham	PROPN
ejpam-6659	2	23	qawaqneh1	qawaqneh1	PROPN
ejpam-6659	2	24	,	,	PUNCT
ejpam-6659	2	25	divyanshu	divyanshu	PROPN
ejpam-6659	2	26	chamoli2	chamoli2	PROPN
ejpam-6659	2	27	,	,	PUNCT
ejpam-6659	2	28	shivam	shivam	PROPN
ejpam-6659	2	29	rawat3	rawat3	PROPN
ejpam-6659	2	30	,	,	PUNCT
ejpam-6659	2	31	hassen	hassen	PROPN
ejpam-6659	2	32	aydi4,5,∗	aydi4,5,∗	PROPN
ejpam-6659	2	33	,	,	PUNCT
ejpam-6659	2	34	monika	monika	PROPN
ejpam-6659	2	35	bisht6	bisht6	PROPN
ejpam-6659	2	36	1	1	NUM
ejpam-6659	2	37	al	al	PROPN
ejpam-6659	2	38	-	-	PUNCT
ejpam-6659	2	39	zaytoonah	zaytoonah	PROPN
ejpam-6659	2	40	university	university	PROPN
ejpam-6659	2	41	of	of	ADP
ejpam-6659	2	42	jordan	jordan	PROPN
ejpam-6659	2	43	,	,	PUNCT
ejpam-6659	2	44	amman	amman	PROPN
ejpam-6659	2	45	11733	11733	NUM
ejpam-6659	2	46	,	,	PUNCT
ejpam-6659	2	47	jordan	jordan	PROPN
ejpam-6659	2	48	2	2	NUM
ejpam-6659	2	49	department	department	NOUN
ejpam-6659	2	50	of	of	ADP
ejpam-6659	2	51	mathematics	mathematic	NOUN
ejpam-6659	2	52	,	,	PUNCT
ejpam-6659	2	53	h.n.b	h.n.b	NOUN
ejpam-6659	2	54	.	.	PUNCT
ejpam-6659	2	55	garhwal	garhwal	PROPN
ejpam-6659	2	56	university	university	PROPN
ejpam-6659	2	57	,	,	PUNCT
ejpam-6659	2	58	srinagar	srinagar	NOUN
ejpam-6659	2	59	(	(	PUNCT
ejpam-6659	2	60	garhwal	garhwal	NOUN
ejpam-6659	2	61	)	)	PUNCT
ejpam-6659	2	62	,	,	PUNCT
ejpam-6659	2	63	uttarakhand	uttarakhand	PROPN
ejpam-6659	2	64	246174	246174	NUM
ejpam-6659	2	65	,	,	PUNCT
ejpam-6659	2	66	india	india	PROPN
ejpam-6659	2	67	.	.	PROPN
ejpam-6659	2	68	3	3	NUM
ejpam-6659	2	69	department	department	NOUN
ejpam-6659	2	70	of	of	ADP
ejpam-6659	2	71	mathematics	mathematic	NOUN
ejpam-6659	2	72	,	,	PUNCT
ejpam-6659	2	73	graphic	graphic	ADJ
ejpam-6659	2	74	era	era	NOUN
ejpam-6659	2	75	deemed	deem	VERB
ejpam-6659	2	76	to	to	PART
ejpam-6659	2	77	be	be	AUX
ejpam-6659	2	78	university	university	NOUN
ejpam-6659	2	79	,	,	PUNCT
ejpam-6659	2	80	dehradun	dehradun	PROPN
ejpam-6659	2	81	,	,	PUNCT
ejpam-6659	2	82	uttarakhand	uttarakhand	PROPN
ejpam-6659	2	83	,	,	PUNCT
ejpam-6659	2	84	248002	248002	NUM
ejpam-6659	2	85	,	,	PUNCT
ejpam-6659	2	86	india	india	PROPN
ejpam-6659	2	87	.	.	PROPN
ejpam-6659	2	88	4	4	NUM
ejpam-6659	2	89	institut	institut	PROPN
ejpam-6659	2	90	supérieur	supérieur	PROPN
ejpam-6659	2	91	d’informatique	d’informatique	PROPN
ejpam-6659	2	92	et	et	NOUN
ejpam-6659	2	93	des	des	X
ejpam-6659	2	94	techniques	techniques	X
ejpam-6659	2	95	de	de	X
ejpam-6659	2	96	communication	communication	NOUN
ejpam-6659	2	97	,	,	PUNCT
ejpam-6659	2	98	université	université	ADJ
ejpam-6659	2	99	de	de	X
ejpam-6659	2	100	sousse	sousse	PROPN
ejpam-6659	2	101	,	,	PUNCT
ejpam-6659	2	102	h.	h.	PROPN
ejpam-6659	2	103	sousse	sousse	PROPN
ejpam-6659	2	104	4000	4000	NUM
ejpam-6659	2	105	,	,	PUNCT
ejpam-6659	2	106	tunisia	tunisia	PROPN
ejpam-6659	2	107	5	5	NUM
ejpam-6659	2	108	department	department	NOUN
ejpam-6659	2	109	of	of	ADP
ejpam-6659	2	110	mathematics	mathematic	NOUN
ejpam-6659	2	111	and	and	CCONJ
ejpam-6659	2	112	applied	apply	VERB
ejpam-6659	2	113	mathematics	mathematic	NOUN
ejpam-6659	2	114	,	,	PUNCT
ejpam-6659	2	115	sefako	sefako	VERB
ejpam-6659	2	116	makgatho	makgatho	PROPN
ejpam-6659	2	117	health	health	PROPN
ejpam-6659	2	118	sciences	sciences	PROPN
ejpam-6659	2	119	university	university	PROPN
ejpam-6659	2	120	,	,	PUNCT
ejpam-6659	2	121	ga	ga	PROPN
ejpam-6659	2	122	-	-	NOUN
ejpam-6659	2	123	rankuwa	rankuwa	PROPN
ejpam-6659	2	124	,	,	PUNCT
ejpam-6659	2	125	south	south	PROPN
ejpam-6659	2	126	africa	africa	PROPN
ejpam-6659	2	127	6	6	NUM
ejpam-6659	2	128	department	department	NOUN
ejpam-6659	2	129	of	of	ADP
ejpam-6659	2	130	mathematics	mathematic	NOUN
ejpam-6659	2	131	,	,	PUNCT
ejpam-6659	2	132	graphic	graphic	ADJ
ejpam-6659	2	133	era	era	NOUN
ejpam-6659	2	134	hill	hill	PROPN
ejpam-6659	2	135	university	university	PROPN
ejpam-6659	2	136	,	,	PUNCT
ejpam-6659	2	137	dehradun	dehradun	PROPN
ejpam-6659	2	138	campus	campus	PROPN
ejpam-6659	2	139	,	,	PUNCT
ejpam-6659	2	140	uttarakhand	uttarakhand	PROPN
ejpam-6659	2	141	,	,	PUNCT
ejpam-6659	2	142	248001	248001	NUM
ejpam-6659	2	143	,	,	PUNCT
ejpam-6659	2	144	india	india	PROPN
ejpam-6659	2	145	abstract	abstract	NOUN
ejpam-6659	2	146	.	.	PUNCT
ejpam-6659	3	1	in	in	ADP
ejpam-6659	3	2	this	this	DET
ejpam-6659	3	3	paper	paper	NOUN
ejpam-6659	3	4	,	,	PUNCT
ejpam-6659	3	5	we	we	PRON
ejpam-6659	3	6	present	present	VERB
ejpam-6659	3	7	complex	complex	NOUN
ejpam-6659	3	8	valued	value	VERB
ejpam-6659	3	9	controlled	control	VERB
ejpam-6659	3	10	s	s	NOUN
ejpam-6659	3	11	-	-	ADJ
ejpam-6659	3	12	metric	metric	ADJ
ejpam-6659	3	13	spaces	space	NOUN
ejpam-6659	3	14	,	,	PUNCT
ejpam-6659	3	15	a	a	DET
ejpam-6659	3	16	new	new	ADJ
ejpam-6659	3	17	generalisation	generalisation	NOUN
ejpam-6659	3	18	of	of	ADP
ejpam-6659	3	19	controlled	control	VERB
ejpam-6659	3	20	s	s	NOUN
ejpam-6659	3	21	-	-	ADJ
ejpam-6659	3	22	metric	metric	ADJ
ejpam-6659	3	23	spaces	space	NOUN
ejpam-6659	3	24	.	.	PUNCT
ejpam-6659	4	1	this	this	DET
ejpam-6659	4	2	generalization	generalization	NOUN
ejpam-6659	4	3	is	be	AUX
ejpam-6659	4	4	also	also	ADV
ejpam-6659	4	5	a	a	DET
ejpam-6659	4	6	new	new	ADJ
ejpam-6659	4	7	extension	extension	NOUN
ejpam-6659	4	8	of	of	ADP
ejpam-6659	4	9	the	the	DET
ejpam-6659	4	10	notion	notion	NOUN
ejpam-6659	4	11	of	of	ADP
ejpam-6659	4	12	a	a	DET
ejpam-6659	4	13	complex	complex	ADJ
ejpam-6659	4	14	valued	value	VERB
ejpam-6659	4	15	sb	sb	NOUN
ejpam-6659	4	16	-	-	ADJ
ejpam-6659	4	17	metric	metric	ADJ
ejpam-6659	4	18	space	space	NOUN
ejpam-6659	4	19	,	,	PUNCT
ejpam-6659	4	20	which	which	PRON
ejpam-6659	4	21	differs	differ	VERB
ejpam-6659	4	22	from	from	ADP
ejpam-6659	4	23	the	the	DET
ejpam-6659	4	24	complex	complex	NOUN
ejpam-6659	4	25	valued	value	VERB
ejpam-6659	4	26	extended	extend	VERB
ejpam-6659	4	27	sb	sb	NOUN
ejpam-6659	4	28	-	-	ADJ
ejpam-6659	4	29	metric	metric	ADJ
ejpam-6659	4	30	space	space	NOUN
ejpam-6659	4	31	.	.	PUNCT
ejpam-6659	5	1	moreover	moreover	ADV
ejpam-6659	5	2	,	,	PUNCT
ejpam-6659	5	3	in	in	ADP
ejpam-6659	5	4	this	this	DET
ejpam-6659	5	5	newly	newly	ADV
ejpam-6659	5	6	generalized	generalize	VERB
ejpam-6659	5	7	notion	notion	NOUN
ejpam-6659	5	8	,	,	PUNCT
ejpam-6659	5	9	we	we	PRON
ejpam-6659	5	10	derive	derive	VERB
ejpam-6659	5	11	certain	certain	ADJ
ejpam-6659	5	12	fixed	fix	VERB
ejpam-6659	5	13	point	point	NOUN
ejpam-6659	5	14	results	result	NOUN
ejpam-6659	5	15	along	along	ADP
ejpam-6659	5	16	with	with	ADP
ejpam-6659	5	17	an	an	DET
ejpam-6659	5	18	example	example	NOUN
ejpam-6659	5	19	.	.	PUNCT
ejpam-6659	6	1	many	many	ADJ
ejpam-6659	6	2	results	result	NOUN
ejpam-6659	6	3	from	from	ADP
ejpam-6659	6	4	the	the	DET
ejpam-6659	6	5	existing	exist	VERB
ejpam-6659	6	6	literature	literature	NOUN
ejpam-6659	6	7	are	be	AUX
ejpam-6659	6	8	also	also	ADV
ejpam-6659	6	9	derived	derive	VERB
ejpam-6659	6	10	as	as	ADP
ejpam-6659	6	11	corollaries	corollary	NOUN
ejpam-6659	6	12	of	of	ADP
ejpam-6659	6	13	our	our	PRON
ejpam-6659	6	14	main	main	ADJ
ejpam-6659	6	15	results	result	NOUN
ejpam-6659	6	16	.	.	PUNCT
ejpam-6659	7	1	as	as	ADP
ejpam-6659	7	2	an	an	DET
ejpam-6659	7	3	application	application	NOUN
ejpam-6659	7	4	of	of	ADP
ejpam-6659	7	5	our	our	PRON
ejpam-6659	7	6	result	result	NOUN
ejpam-6659	7	7	,	,	PUNCT
ejpam-6659	7	8	we	we	PRON
ejpam-6659	7	9	demonstrate	demonstrate	VERB
ejpam-6659	7	10	the	the	DET
ejpam-6659	7	11	existence	existence	NOUN
ejpam-6659	7	12	of	of	ADP
ejpam-6659	7	13	a	a	DET
ejpam-6659	7	14	solution	solution	NOUN
ejpam-6659	7	15	of	of	ADP
ejpam-6659	7	16	a	a	DET
ejpam-6659	7	17	volterra	volterra	NOUN
ejpam-6659	7	18	integral	integral	ADJ
ejpam-6659	7	19	equation	equation	NOUN
ejpam-6659	7	20	.	.	PUNCT
ejpam-6659	8	1	2020	2020	NUM
ejpam-6659	8	2	mathematics	mathematic	NOUN
ejpam-6659	8	3	subject	subject	NOUN
ejpam-6659	8	4	classifications	classification	NOUN
ejpam-6659	8	5	:	:	PUNCT
ejpam-6659	8	6	47h10	47h10	NUM
ejpam-6659	8	7	,	,	PUNCT
ejpam-6659	8	8	54h25	54h25	NUM
ejpam-6659	8	9	key	key	ADJ
ejpam-6659	8	10	words	word	NOUN
ejpam-6659	8	11	and	and	CCONJ
ejpam-6659	8	12	phrases	phrase	NOUN
ejpam-6659	8	13	:	:	PUNCT
ejpam-6659	8	14	fixed	fixed	ADJ
ejpam-6659	8	15	point	point	NOUN
ejpam-6659	8	16	,	,	PUNCT
ejpam-6659	8	17	complex	complex	PROPN
ejpam-6659	8	18	valued	value	VERB
ejpam-6659	8	19	controlled	control	VERB
ejpam-6659	8	20	s	s	NOUN
ejpam-6659	8	21	-	-	ADJ
ejpam-6659	8	22	metric	metric	ADJ
ejpam-6659	8	23	spaces	space	NOUN
ejpam-6659	8	24	,	,	PUNCT
ejpam-6659	8	25	volterra	volterra	PROPN
ejpam-6659	8	26	integral	integral	ADJ
ejpam-6659	8	27	equation	equation	NOUN
ejpam-6659	8	28	1	1	NUM
ejpam-6659	8	29	.	.	PUNCT
ejpam-6659	8	30	introduction	introduction	NOUN
ejpam-6659	8	31	the	the	DET
ejpam-6659	8	32	framework	framework	NOUN
ejpam-6659	8	33	of	of	ADP
ejpam-6659	8	34	fixed	fix	VERB
ejpam-6659	8	35	point	point	NOUN
ejpam-6659	8	36	theory	theory	NOUN
ejpam-6659	8	37	serves	serve	VERB
ejpam-6659	8	38	as	as	ADP
ejpam-6659	8	39	a	a	DET
ejpam-6659	8	40	fundamental	fundamental	ADJ
ejpam-6659	8	41	tool	tool	NOUN
ejpam-6659	8	42	in	in	ADP
ejpam-6659	8	43	understanding	understand	VERB
ejpam-6659	8	44	the	the	DET
ejpam-6659	8	45	behavior	behavior	NOUN
ejpam-6659	8	46	of	of	ADP
ejpam-6659	8	47	mappings	mapping	NOUN
ejpam-6659	8	48	and	and	CCONJ
ejpam-6659	8	49	has	have	AUX
ejpam-6659	8	50	found	find	VERB
ejpam-6659	8	51	extensive	extensive	ADJ
ejpam-6659	8	52	applications	application	NOUN
ejpam-6659	8	53	in	in	ADP
ejpam-6659	8	54	diverse	diverse	ADJ
ejpam-6659	8	55	branches	branch	NOUN
ejpam-6659	8	56	of	of	ADP
ejpam-6659	8	57	∗corresponding	∗corresponde	VERB
ejpam-6659	8	58	author	author	NOUN
ejpam-6659	8	59	.	.	PUNCT
ejpam-6659	9	1	doi	doi	NOUN
ejpam-6659	9	2	:	:	PUNCT
ejpam-6659	9	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6659	https://doi.org/10.29020/nybg.ejpam.v18i3.6659	ADJ
ejpam-6659	9	4	email	email	NOUN
ejpam-6659	9	5	addresses	address	VERB
ejpam-6659	9	6	:	:	PUNCT
ejpam-6659	9	7	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-6659	9	8	(	(	PUNCT
ejpam-6659	9	9	h.	h.	PROPN
ejpam-6659	9	10	qawaqneh	qawaqneh	PROPN
ejpam-6659	9	11	)	)	PUNCT
ejpam-6659	9	12	,	,	PUNCT
ejpam-6659	9	13	chamoli.divyanshu25@gmail.com	chamoli.divyanshu25@gmail.com	X
ejpam-6659	9	14	(	(	PUNCT
ejpam-6659	9	15	d.	d.	PROPN
ejpam-6659	9	16	chamoli	chamoli	PROPN
ejpam-6659	9	17	)	)	PUNCT
ejpam-6659	9	18	,	,	PUNCT
ejpam-6659	9	19	rawat.shivam09@gmail.com	rawat.shivam09@gmail.com	X
ejpam-6659	9	20	(	(	PUNCT
ejpam-6659	9	21	s.	s.	PROPN
ejpam-6659	9	22	rawat	rawat	PROPN
ejpam-6659	9	23	)	)	PUNCT
ejpam-6659	9	24	,	,	PUNCT
ejpam-6659	9	25	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	PROPN
ejpam-6659	9	26	(	(	PUNCT
ejpam-6659	9	27	h.	h.	PROPN
ejpam-6659	9	28	aydi	aydi	VERB
ejpam-6659	9	29	)	)	PUNCT
ejpam-6659	9	30	,	,	PUNCT
ejpam-6659	9	31	monikabisht391@gmail.com	monikabisht391@gmail.com	PROPN
ejpam-6659	9	32	(	(	PUNCT
ejpam-6659	9	33	m.	m.	NOUN
ejpam-6659	9	34	bisht	bisht	PROPN
ejpam-6659	9	35	)	)	PUNCT
ejpam-6659	9	36	,	,	PUNCT
ejpam-6659	9	37	monikabisht391@gmail.com	monikabisht391@gmail.com	PROPN
ejpam-6659	9	38	(	(	PUNCT
ejpam-6659	9	39	m.	m.	NOUN
ejpam-6659	9	40	bisht	bisht	PROPN
ejpam-6659	9	41	)	)	PUNCT
ejpam-6659	9	42	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6659	10	1	1	1	NUM
ejpam-6659	10	2	copyright	copyright	NOUN
ejpam-6659	10	3	:	:	PUNCT
ejpam-6659	10	4	©	©	PROPN
ejpam-6659	10	5	2025	2025	NUM
ejpam-6659	10	6	the	the	DET
ejpam-6659	10	7	author(s	author(s	NOUN
ejpam-6659	10	8	)	)	PUNCT
ejpam-6659	10	9	.	.	PUNCT
ejpam-6659	11	1	(	(	PUNCT
ejpam-6659	11	2	cc	cc	NOUN
ejpam-6659	11	3	by	by	ADP
ejpam-6659	11	4	-	-	PUNCT
ejpam-6659	11	5	nc	nc	PROPN
ejpam-6659	11	6	4.0	4.0	NUM
ejpam-6659	11	7	)	)	PUNCT
ejpam-6659	11	8	h.	h.	PROPN
ejpam-6659	11	9	qawaqneh	qawaqneh	PROPN
ejpam-6659	11	10	et	et	PROPN
ejpam-6659	11	11	al	al	PROPN
ejpam-6659	11	12	.	.	PUNCT
ejpam-6659	11	13	/	/	SYM
ejpam-6659	11	14	eur	eur	PROPN
ejpam-6659	11	15	.	.	PUNCT
ejpam-6659	12	1	j.	j.	PROPN
ejpam-6659	12	2	pure	pure	PROPN
ejpam-6659	12	3	appl	appl	PROPN
ejpam-6659	12	4	.	.	PROPN
ejpam-6659	12	5	math	math	PROPN
ejpam-6659	12	6	,	,	PUNCT
ejpam-6659	12	7	18	18	NUM
ejpam-6659	12	8	(	(	PUNCT
ejpam-6659	12	9	3	3	NUM
ejpam-6659	12	10	)	)	PUNCT
ejpam-6659	12	11	(	(	PUNCT
ejpam-6659	12	12	2025	2025	NUM
ejpam-6659	12	13	)	)	PUNCT
ejpam-6659	12	14	,	,	PUNCT
ejpam-6659	12	15	6659	6659	NUM
ejpam-6659	12	16	2	2	NUM
ejpam-6659	12	17	of	of	ADP
ejpam-6659	12	18	16	16	NUM
ejpam-6659	12	19	mathematics	mathematic	NOUN
ejpam-6659	12	20	,	,	PUNCT
ejpam-6659	12	21	including	include	VERB
ejpam-6659	12	22	numerical	numerical	ADJ
ejpam-6659	12	23	analysis	analysis	NOUN
ejpam-6659	12	24	,	,	PUNCT
ejpam-6659	12	25	optimization	optimization	NOUN
ejpam-6659	12	26	,	,	PUNCT
ejpam-6659	12	27	and	and	CCONJ
ejpam-6659	12	28	mathematical	mathematical	ADJ
ejpam-6659	12	29	modeling	modeling	NOUN
ejpam-6659	12	30	,	,	PUNCT
ejpam-6659	12	31	see	see	VERB
ejpam-6659	12	32	[	[	X
ejpam-6659	12	33	1–4	1–4	PRON
ejpam-6659	12	34	,	,	PUNCT
ejpam-6659	12	35	4–7	4–7	NOUN
ejpam-6659	12	36	]	]	X
ejpam-6659	12	37	.	.	PUNCT
ejpam-6659	13	1	fréchet	fréchet	PROPN
ejpam-6659	14	1	[	[	X
ejpam-6659	14	2	8	8	NUM
ejpam-6659	14	3	]	]	PUNCT
ejpam-6659	14	4	initially	initially	ADV
ejpam-6659	14	5	put	put	VERB
ejpam-6659	14	6	forth	forth	ADP
ejpam-6659	14	7	the	the	DET
ejpam-6659	14	8	metric	metric	ADJ
ejpam-6659	14	9	space	space	NOUN
ejpam-6659	14	10	idea	idea	NOUN
ejpam-6659	14	11	in	in	ADP
ejpam-6659	14	12	1906	1906	NUM
ejpam-6659	14	13	.	.	PUNCT
ejpam-6659	15	1	subsequently	subsequently	ADV
ejpam-6659	15	2	,	,	PUNCT
ejpam-6659	15	3	numerous	numerous	ADJ
ejpam-6659	15	4	researchers	researcher	NOUN
ejpam-6659	15	5	have	have	AUX
ejpam-6659	15	6	extended	extend	VERB
ejpam-6659	15	7	the	the	DET
ejpam-6659	15	8	concept	concept	NOUN
ejpam-6659	15	9	of	of	ADP
ejpam-6659	15	10	metric	metric	ADJ
ejpam-6659	15	11	space	space	NOUN
ejpam-6659	15	12	by	by	ADP
ejpam-6659	15	13	altering	alter	VERB
ejpam-6659	15	14	the	the	DET
ejpam-6659	15	15	metric	metric	ADJ
ejpam-6659	15	16	function	function	NOUN
ejpam-6659	15	17	and	and	CCONJ
ejpam-6659	15	18	weakening	weaken	VERB
ejpam-6659	15	19	different	different	ADJ
ejpam-6659	15	20	conditions	condition	NOUN
ejpam-6659	15	21	(	(	PUNCT
ejpam-6659	15	22	see	see	VERB
ejpam-6659	15	23	,	,	PUNCT
ejpam-6659	15	24	for	for	ADP
ejpam-6659	15	25	example	example	NOUN
ejpam-6659	15	26	,	,	PUNCT
ejpam-6659	15	27	[	[	X
ejpam-6659	15	28	9–14	9–14	NOUN
ejpam-6659	15	29	]	]	PUNCT
ejpam-6659	15	30	)	)	PUNCT
ejpam-6659	15	31	.	.	PUNCT
ejpam-6659	16	1	in	in	ADP
ejpam-6659	16	2	1993	1993	NUM
ejpam-6659	16	3	,	,	PUNCT
ejpam-6659	16	4	czerwik	czerwik	PROPN
ejpam-6659	16	5	[	[	X
ejpam-6659	16	6	12	12	NUM
ejpam-6659	16	7	]	]	PUNCT
ejpam-6659	16	8	introduced	introduce	VERB
ejpam-6659	16	9	the	the	DET
ejpam-6659	16	10	notion	notion	NOUN
ejpam-6659	16	11	of	of	ADP
ejpam-6659	16	12	a	a	DET
ejpam-6659	16	13	b	b	NOUN
ejpam-6659	16	14	-	-	PUNCT
ejpam-6659	16	15	metric	metric	ADJ
ejpam-6659	16	16	space	space	NOUN
ejpam-6659	16	17	as	as	ADP
ejpam-6659	16	18	an	an	DET
ejpam-6659	16	19	extension	extension	NOUN
ejpam-6659	16	20	of	of	ADP
ejpam-6659	16	21	the	the	DET
ejpam-6659	16	22	concept	concept	NOUN
ejpam-6659	16	23	of	of	ADP
ejpam-6659	16	24	a	a	DET
ejpam-6659	16	25	metric	metric	ADJ
ejpam-6659	16	26	space	space	NOUN
ejpam-6659	16	27	.	.	PUNCT
ejpam-6659	17	1	to	to	PART
ejpam-6659	17	2	broaden	broaden	VERB
ejpam-6659	17	3	the	the	DET
ejpam-6659	17	4	definition	definition	NOUN
ejpam-6659	17	5	of	of	ADP
ejpam-6659	17	6	b	b	NOUN
ejpam-6659	17	7	-	-	PUNCT
ejpam-6659	17	8	metric	metric	ADJ
ejpam-6659	17	9	space	space	NOUN
ejpam-6659	17	10	,	,	PUNCT
ejpam-6659	17	11	kamran	kamran	PROPN
ejpam-6659	17	12	et	et	PROPN
ejpam-6659	17	13	al	al	PROPN
ejpam-6659	17	14	.	.	PUNCT
ejpam-6659	18	1	[	[	X
ejpam-6659	18	2	15	15	NUM
ejpam-6659	18	3	]	]	PUNCT
ejpam-6659	18	4	presented	present	VERB
ejpam-6659	18	5	the	the	DET
ejpam-6659	18	6	notion	notion	NOUN
ejpam-6659	18	7	of	of	ADP
ejpam-6659	18	8	an	an	DET
ejpam-6659	18	9	extended	extended	ADJ
ejpam-6659	18	10	b	b	X
ejpam-6659	18	11	-	-	PUNCT
ejpam-6659	18	12	metric	metric	ADJ
ejpam-6659	18	13	space	space	NOUN
ejpam-6659	18	14	in	in	ADP
ejpam-6659	18	15	the	the	DET
ejpam-6659	18	16	year	year	NOUN
ejpam-6659	18	17	2017	2017	NUM
ejpam-6659	18	18	.	.	PUNCT
ejpam-6659	19	1	mlaiki	mlaiki	PROPN
ejpam-6659	19	2	et	et	PROPN
ejpam-6659	19	3	al	al	PROPN
ejpam-6659	19	4	.	.	PUNCT
ejpam-6659	20	1	[	[	X
ejpam-6659	20	2	16	16	NUM
ejpam-6659	20	3	]	]	PUNCT
ejpam-6659	20	4	further	far	ADV
ejpam-6659	20	5	introduced	introduce	VERB
ejpam-6659	20	6	controlled	control	VERB
ejpam-6659	20	7	metric	metric	ADJ
ejpam-6659	20	8	space	space	NOUN
ejpam-6659	20	9	,	,	PUNCT
ejpam-6659	20	10	which	which	PRON
ejpam-6659	20	11	is	be	AUX
ejpam-6659	20	12	a	a	DET
ejpam-6659	20	13	novel	novel	ADJ
ejpam-6659	20	14	type	type	NOUN
ejpam-6659	20	15	of	of	ADP
ejpam-6659	20	16	extended	extended	ADJ
ejpam-6659	20	17	b	b	X
ejpam-6659	20	18	-	-	PUNCT
ejpam-6659	20	19	metric	metric	ADJ
ejpam-6659	20	20	space	space	NOUN
ejpam-6659	20	21	.	.	PUNCT
ejpam-6659	20	22	sedghi	sedghi	VERB
ejpam-6659	20	23	et	et	PROPN
ejpam-6659	20	24	al	al	PROPN
ejpam-6659	20	25	.	.	PUNCT
ejpam-6659	21	1	[	[	X
ejpam-6659	21	2	17	17	NUM
ejpam-6659	21	3	]	]	PUNCT
ejpam-6659	21	4	presented	present	VERB
ejpam-6659	21	5	s	s	ADJ
ejpam-6659	21	6	-	-	ADJ
ejpam-6659	21	7	metric	metric	ADJ
ejpam-6659	21	8	spaces	space	NOUN
ejpam-6659	21	9	in	in	ADP
ejpam-6659	21	10	2012	2012	NUM
ejpam-6659	21	11	as	as	ADP
ejpam-6659	21	12	a	a	DET
ejpam-6659	21	13	generalization	generalization	NOUN
ejpam-6659	21	14	of	of	ADP
ejpam-6659	21	15	g	g	NOUN
ejpam-6659	21	16	-	-	PUNCT
ejpam-6659	21	17	metric	metric	ADJ
ejpam-6659	21	18	spaces	space	NOUN
ejpam-6659	21	19	[	[	X
ejpam-6659	21	20	18	18	NUM
ejpam-6659	21	21	]	]	PUNCT
ejpam-6659	21	22	and	and	CCONJ
ejpam-6659	21	23	d∗-metric	d∗-metric	ADJ
ejpam-6659	21	24	spaces	space	NOUN
ejpam-6659	21	25	[	[	X
ejpam-6659	21	26	19	19	NUM
ejpam-6659	21	27	]	]	PUNCT
ejpam-6659	21	28	.	.	PUNCT
ejpam-6659	22	1	several	several	ADJ
ejpam-6659	22	2	fixed	fix	VERB
ejpam-6659	22	3	point	point	NOUN
ejpam-6659	22	4	theorems	theorem	NOUN
ejpam-6659	22	5	for	for	ADP
ejpam-6659	22	6	s	s	ADJ
ejpam-6659	22	7	-	-	ADJ
ejpam-6659	22	8	metric	metric	ADJ
ejpam-6659	22	9	spaces	space	NOUN
ejpam-6659	22	10	were	be	AUX
ejpam-6659	22	11	also	also	ADV
ejpam-6659	22	12	found	find	VERB
ejpam-6659	22	13	by	by	ADP
ejpam-6659	22	14	them	they	PRON
ejpam-6659	22	15	.	.	PUNCT
ejpam-6659	23	1	in	in	ADP
ejpam-6659	23	2	2019	2019	NUM
ejpam-6659	23	3	,	,	PUNCT
ejpam-6659	23	4	rezaee	rezaee	VERB
ejpam-6659	23	5	et	et	PROPN
ejpam-6659	23	6	al	al	PROPN
ejpam-6659	23	7	.	.	PUNCT
ejpam-6659	24	1	[	[	X
ejpam-6659	24	2	20	20	NUM
ejpam-6659	24	3	]	]	PUNCT
ejpam-6659	24	4	introduced	introduce	VERB
ejpam-6659	24	5	a	a	DET
ejpam-6659	24	6	new	new	ADJ
ejpam-6659	24	7	class	class	NOUN
ejpam-6659	24	8	of	of	ADP
ejpam-6659	24	9	generalized	generalized	ADJ
ejpam-6659	24	10	metric	metric	ADJ
ejpam-6659	24	11	spaces	space	NOUN
ejpam-6659	24	12	,	,	PUNCT
ejpam-6659	24	13	called	call	VERB
ejpam-6659	24	14	partial	partial	ADJ
ejpam-6659	24	15	s	s	NOUN
ejpam-6659	24	16	-	-	ADJ
ejpam-6659	24	17	metric	metric	ADJ
ejpam-6659	24	18	spaces	space	NOUN
ejpam-6659	24	19	.	.	PUNCT
ejpam-6659	25	1	in	in	ADP
ejpam-6659	25	2	2017	2017	NUM
ejpam-6659	25	3	,	,	PUNCT
ejpam-6659	25	4	rohen	rohen	VERB
ejpam-6659	25	5	et	et	PROPN
ejpam-6659	25	6	al	al	PROPN
ejpam-6659	25	7	.	.	PUNCT
ejpam-6659	26	1	[	[	X
ejpam-6659	26	2	21	21	NUM
ejpam-6659	26	3	]	]	X
ejpam-6659	26	4	modified	modify	VERB
ejpam-6659	26	5	the	the	DET
ejpam-6659	26	6	definition	definition	NOUN
ejpam-6659	26	7	of	of	ADP
ejpam-6659	26	8	sb	sb	NOUN
ejpam-6659	26	9	-	-	ADJ
ejpam-6659	26	10	metric	metric	ADJ
ejpam-6659	26	11	introduced	introduce	VERB
ejpam-6659	26	12	by	by	ADP
ejpam-6659	26	13	souayan	souayan	ADJ
ejpam-6659	26	14	and	and	CCONJ
ejpam-6659	26	15	mlaiki	mlaiki	PROPN
ejpam-6659	27	1	[	[	X
ejpam-6659	27	2	22	22	NUM
ejpam-6659	27	3	]	]	PUNCT
ejpam-6659	27	4	,	,	PUNCT
ejpam-6659	27	5	and	and	CCONJ
ejpam-6659	27	6	proved	prove	VERB
ejpam-6659	27	7	some	some	DET
ejpam-6659	27	8	coupled	couple	VERB
ejpam-6659	27	9	common	common	ADJ
ejpam-6659	27	10	fixed	fix	VERB
ejpam-6659	27	11	point	point	NOUN
ejpam-6659	27	12	theorems	theorem	NOUN
ejpam-6659	27	13	in	in	ADP
ejpam-6659	27	14	sb	sb	NOUN
ejpam-6659	27	15	-	-	ADJ
ejpam-6659	27	16	metric	metric	ADJ
ejpam-6659	27	17	spaces	space	NOUN
ejpam-6659	27	18	.	.	PUNCT
ejpam-6659	28	1	the	the	DET
ejpam-6659	28	2	concept	concept	NOUN
ejpam-6659	28	3	of	of	ADP
ejpam-6659	28	4	controlled	control	VERB
ejpam-6659	28	5	-	-	PUNCT
ejpam-6659	28	6	s	s	PART
ejpam-6659	28	7	metric	metric	ADJ
ejpam-6659	28	8	spaces	space	NOUN
ejpam-6659	28	9	was	be	AUX
ejpam-6659	28	10	first	first	ADV
ejpam-6659	28	11	developed	develop	VERB
ejpam-6659	28	12	by	by	ADP
ejpam-6659	28	13	gangwar	gangwar	NOUN
ejpam-6659	28	14	et	et	PROPN
ejpam-6659	28	15	al	al	PROPN
ejpam-6659	28	16	.	.	PUNCT
ejpam-6659	29	1	[	[	X
ejpam-6659	29	2	23	23	NUM
ejpam-6659	29	3	]	]	PUNCT
ejpam-6659	29	4	in	in	ADP
ejpam-6659	29	5	2023	2023	NUM
ejpam-6659	29	6	.	.	PUNCT
ejpam-6659	30	1	recently	recently	ADV
ejpam-6659	30	2	,	,	PUNCT
ejpam-6659	30	3	azmi	azmi	PROPN
ejpam-6659	30	4	[	[	X
ejpam-6659	30	5	24	24	NUM
ejpam-6659	30	6	]	]	PUNCT
ejpam-6659	30	7	extended	extend	VERB
ejpam-6659	30	8	the	the	DET
ejpam-6659	30	9	idea	idea	NOUN
ejpam-6659	30	10	of	of	ADP
ejpam-6659	30	11	a	a	DET
ejpam-6659	30	12	controlled	control	VERB
ejpam-6659	30	13	s	s	ADJ
ejpam-6659	30	14	-	-	ADJ
ejpam-6659	30	15	metric	metric	ADJ
ejpam-6659	30	16	type	type	NOUN
ejpam-6659	30	17	space	space	NOUN
ejpam-6659	30	18	to	to	PART
ejpam-6659	30	19	present	present	VERB
ejpam-6659	30	20	the	the	DET
ejpam-6659	30	21	concept	concept	NOUN
ejpam-6659	30	22	of	of	ADP
ejpam-6659	30	23	a	a	DET
ejpam-6659	30	24	triple	triple	ADV
ejpam-6659	30	25	controlled	control	VERB
ejpam-6659	30	26	s	s	NOUN
ejpam-6659	30	27	-	-	ADJ
ejpam-6659	30	28	metric	metric	ADJ
ejpam-6659	30	29	type	type	NOUN
ejpam-6659	30	30	space	space	NOUN
ejpam-6659	30	31	,	,	PUNCT
ejpam-6659	30	32	characterized	characterize	VERB
ejpam-6659	30	33	by	by	ADP
ejpam-6659	30	34	three	three	NUM
ejpam-6659	30	35	control	control	NOUN
ejpam-6659	30	36	functions	function	NOUN
ejpam-6659	30	37	:	:	PUNCT
ejpam-6659	30	38	β	β	X
ejpam-6659	30	39	,	,	PUNCT
ejpam-6659	30	40	µ	µ	NOUN
ejpam-6659	30	41	,	,	PUNCT
ejpam-6659	30	42	and	and	CCONJ
ejpam-6659	30	43	γ	γ	X
ejpam-6659	30	44	.	.	PROPN
ejpam-6659	31	1	they	they	PRON
ejpam-6659	31	2	also	also	ADV
ejpam-6659	31	3	proved	prove	VERB
ejpam-6659	31	4	that	that	SCONJ
ejpam-6659	31	5	fixed	fix	VERB
ejpam-6659	31	6	points	point	NOUN
ejpam-6659	31	7	of	of	ADP
ejpam-6659	31	8	multivalued	multivalue	VERB
ejpam-6659	31	9	mappings	mapping	NOUN
ejpam-6659	31	10	exist	exist	VERB
ejpam-6659	31	11	within	within	ADP
ejpam-6659	31	12	the	the	DET
ejpam-6659	31	13	context	context	NOUN
ejpam-6659	31	14	of	of	ADP
ejpam-6659	31	15	controlled	control	VERB
ejpam-6659	31	16	s	s	NOUN
ejpam-6659	31	17	-	-	ADJ
ejpam-6659	31	18	metric	metric	ADJ
ejpam-6659	31	19	spaces	space	NOUN
ejpam-6659	31	20	.	.	PUNCT
ejpam-6659	32	1	the	the	DET
ejpam-6659	32	2	concept	concept	NOUN
ejpam-6659	32	3	of	of	ADP
ejpam-6659	32	4	complex	complex	ADJ
ejpam-6659	32	5	valued	value	VERB
ejpam-6659	32	6	metric	metric	ADJ
ejpam-6659	32	7	spaces	space	NOUN
ejpam-6659	32	8	was	be	AUX
ejpam-6659	32	9	introduced	introduce	VERB
ejpam-6659	32	10	by	by	ADP
ejpam-6659	32	11	azam	azam	PROPN
ejpam-6659	32	12	et	et	PROPN
ejpam-6659	32	13	al	al	PROPN
ejpam-6659	32	14	.	.	PUNCT
ejpam-6659	33	1	[	[	X
ejpam-6659	33	2	25	25	NUM
ejpam-6659	33	3	]	]	PUNCT
ejpam-6659	33	4	in	in	ADP
ejpam-6659	33	5	2011	2011	NUM
ejpam-6659	33	6	.	.	PUNCT
ejpam-6659	34	1	they	they	PRON
ejpam-6659	34	2	established	establish	VERB
ejpam-6659	34	3	certain	certain	ADJ
ejpam-6659	34	4	fixed	fix	VERB
ejpam-6659	34	5	point	point	NOUN
ejpam-6659	34	6	theorems	theorem	NOUN
ejpam-6659	34	7	for	for	ADP
ejpam-6659	34	8	a	a	DET
ejpam-6659	34	9	pair	pair	NOUN
ejpam-6659	34	10	of	of	ADP
ejpam-6659	34	11	mappings	mapping	NOUN
ejpam-6659	34	12	involving	involve	VERB
ejpam-6659	34	13	a	a	DET
ejpam-6659	34	14	contraction	contraction	NOUN
ejpam-6659	34	15	condition	condition	NOUN
ejpam-6659	34	16	expressed	express	VERB
ejpam-6659	34	17	through	through	ADP
ejpam-6659	34	18	a	a	DET
ejpam-6659	34	19	rational	rational	ADJ
ejpam-6659	34	20	function	function	NOUN
ejpam-6659	34	21	.	.	PUNCT
ejpam-6659	35	1	additionally	additionally	ADV
ejpam-6659	35	2	,	,	PUNCT
ejpam-6659	35	3	kang	kang	PROPN
ejpam-6659	35	4	et	et	PROPN
ejpam-6659	35	5	al	al	PROPN
ejpam-6659	35	6	.	.	PUNCT
ejpam-6659	36	1	[	[	X
ejpam-6659	36	2	26	26	NUM
ejpam-6659	36	3	]	]	PUNCT
ejpam-6659	36	4	introduced	introduce	VERB
ejpam-6659	36	5	the	the	DET
ejpam-6659	36	6	idea	idea	NOUN
ejpam-6659	36	7	of	of	ADP
ejpam-6659	36	8	complex	complex	NOUN
ejpam-6659	36	9	valued	value	VERB
ejpam-6659	36	10	g	g	NOUN
ejpam-6659	36	11	-	-	PUNCT
ejpam-6659	36	12	metric	metric	ADJ
ejpam-6659	36	13	spaces	space	NOUN
ejpam-6659	36	14	and	and	CCONJ
ejpam-6659	36	15	defined	define	VERB
ejpam-6659	36	16	contraction	contraction	NOUN
ejpam-6659	36	17	mappings	mapping	NOUN
ejpam-6659	36	18	in	in	ADP
ejpam-6659	36	19	this	this	DET
ejpam-6659	36	20	domain	domain	NOUN
ejpam-6659	36	21	.	.	PUNCT
ejpam-6659	37	1	further	far	ADV
ejpam-6659	37	2	,	,	PUNCT
ejpam-6659	37	3	mlaiki	mlaiki	PROPN
ejpam-6659	37	4	[	[	X
ejpam-6659	37	5	27	27	NUM
ejpam-6659	37	6	]	]	PUNCT
ejpam-6659	37	7	presented	present	VERB
ejpam-6659	37	8	the	the	DET
ejpam-6659	37	9	notion	notion	NOUN
ejpam-6659	37	10	of	of	ADP
ejpam-6659	37	11	a	a	DET
ejpam-6659	37	12	new	new	ADJ
ejpam-6659	37	13	metric	metric	ADJ
ejpam-6659	37	14	space	space	NOUN
ejpam-6659	37	15	,	,	PUNCT
ejpam-6659	37	16	named	name	VERB
ejpam-6659	37	17	,	,	PUNCT
ejpam-6659	37	18	a	a	DET
ejpam-6659	37	19	complex	complex	NOUN
ejpam-6659	37	20	valued	value	VERB
ejpam-6659	37	21	s	s	NOUN
ejpam-6659	37	22	-	-	ADJ
ejpam-6659	37	23	metric	metric	ADJ
ejpam-6659	37	24	space	space	NOUN
ejpam-6659	37	25	and	and	CCONJ
ejpam-6659	37	26	established	establish	VERB
ejpam-6659	37	27	the	the	DET
ejpam-6659	37	28	existence	existence	NOUN
ejpam-6659	37	29	and	and	CCONJ
ejpam-6659	37	30	the	the	DET
ejpam-6659	37	31	uniqueness	uniqueness	NOUN
ejpam-6659	37	32	of	of	ADP
ejpam-6659	37	33	a	a	DET
ejpam-6659	37	34	common	common	ADJ
ejpam-6659	37	35	fixed	fix	VERB
ejpam-6659	37	36	point	point	NOUN
ejpam-6659	37	37	for	for	ADP
ejpam-6659	37	38	two	two	NUM
ejpam-6659	37	39	self	self	NOUN
ejpam-6659	37	40	mappings	mapping	NOUN
ejpam-6659	37	41	.	.	PUNCT
ejpam-6659	38	1	recently	recently	ADV
ejpam-6659	38	2	,	,	PUNCT
ejpam-6659	38	3	ozgur	ozgur	PROPN
ejpam-6659	38	4	[	[	X
ejpam-6659	38	5	28	28	NUM
ejpam-6659	38	6	]	]	PUNCT
ejpam-6659	38	7	presented	present	VERB
ejpam-6659	38	8	the	the	DET
ejpam-6659	38	9	notion	notion	NOUN
ejpam-6659	38	10	of	of	ADP
ejpam-6659	38	11	complex	complex	ADJ
ejpam-6659	38	12	valued	value	VERB
ejpam-6659	38	13	gb	gb	ADV
ejpam-6659	38	14	-	-	PUNCT
ejpam-6659	38	15	metric	metric	ADJ
ejpam-6659	38	16	spaces	space	NOUN
ejpam-6659	38	17	and	and	CCONJ
ejpam-6659	38	18	presented	present	VERB
ejpam-6659	38	19	kannan	kannan	PROPN
ejpam-6659	38	20	fixed	fix	VERB
ejpam-6659	38	21	point	point	NOUN
ejpam-6659	38	22	theorem	theorem	NOUN
ejpam-6659	38	23	and	and	CCONJ
ejpam-6659	38	24	banach	banach	NOUN
ejpam-6659	38	25	contraction	contraction	NOUN
ejpam-6659	38	26	principle	principle	NOUN
ejpam-6659	38	27	in	in	ADP
ejpam-6659	38	28	this	this	DET
ejpam-6659	38	29	setting	setting	NOUN
ejpam-6659	38	30	.	.	PUNCT
ejpam-6659	39	1	in	in	ADP
ejpam-6659	39	2	2017	2017	NUM
ejpam-6659	39	3	,	,	PUNCT
ejpam-6659	39	4	priyobarta	priyobarta	NOUN
ejpam-6659	39	5	et	et	NOUN
ejpam-6659	39	6	al	al	PROPN
ejpam-6659	39	7	.	.	PUNCT
ejpam-6659	40	1	[	[	X
ejpam-6659	40	2	29	29	NUM
ejpam-6659	40	3	]	]	SYM
ejpam-6659	40	4	defined	define	VERB
ejpam-6659	40	5	complex	complex	ADJ
ejpam-6659	40	6	valued	value	VERB
ejpam-6659	40	7	sb	sb	NOUN
ejpam-6659	40	8	-	-	ADJ
ejpam-6659	40	9	metric	metric	ADJ
ejpam-6659	40	10	spaces	space	NOUN
ejpam-6659	40	11	and	and	CCONJ
ejpam-6659	40	12	proved	prove	VERB
ejpam-6659	40	13	very	very	ADV
ejpam-6659	40	14	interesting	interesting	ADJ
ejpam-6659	40	15	fixed	fix	VERB
ejpam-6659	40	16	point	point	NOUN
ejpam-6659	40	17	theorems	theorem	NOUN
ejpam-6659	40	18	.	.	PUNCT
ejpam-6659	40	19	motivated	motivate	VERB
ejpam-6659	40	20	by	by	ADP
ejpam-6659	40	21	the	the	DET
ejpam-6659	40	22	existing	exist	VERB
ejpam-6659	40	23	research	research	NOUN
ejpam-6659	40	24	in	in	ADP
ejpam-6659	40	25	the	the	DET
ejpam-6659	40	26	fields	field	NOUN
ejpam-6659	40	27	of	of	ADP
ejpam-6659	40	28	fixed	fix	VERB
ejpam-6659	40	29	point	point	NOUN
ejpam-6659	40	30	theory	theory	NOUN
ejpam-6659	40	31	,	,	PUNCT
ejpam-6659	40	32	complex	complex	ADV
ejpam-6659	40	33	-	-	PUNCT
ejpam-6659	40	34	valued	value	VERB
ejpam-6659	40	35	metric	metric	ADJ
ejpam-6659	40	36	spaces	space	NOUN
ejpam-6659	40	37	and	and	CCONJ
ejpam-6659	40	38	controlled	control	VERB
ejpam-6659	40	39	s	s	NOUN
ejpam-6659	40	40	-	-	ADJ
ejpam-6659	40	41	metric	metric	ADJ
ejpam-6659	40	42	spaces	space	NOUN
ejpam-6659	40	43	,	,	PUNCT
ejpam-6659	40	44	the	the	DET
ejpam-6659	40	45	notion	notion	NOUN
ejpam-6659	40	46	of	of	ADP
ejpam-6659	40	47	complex	complex	ADJ
ejpam-6659	40	48	valued	value	VERB
ejpam-6659	40	49	controlled	control	VERB
ejpam-6659	40	50	s	s	PROPN
ejpam-6659	40	51	-	-	ADJ
ejpam-6659	40	52	metric	metric	ADJ
ejpam-6659	40	53	spaces	space	NOUN
ejpam-6659	40	54	(	(	PUNCT
ejpam-6659	40	55	cvcs	cvcs	ADJ
ejpam-6659	40	56	-	-	PUNCT
ejpam-6659	40	57	metric	metric	ADJ
ejpam-6659	40	58	spaces	space	NOUN
ejpam-6659	40	59	)	)	PUNCT
ejpam-6659	40	60	is	be	AUX
ejpam-6659	40	61	introduced	introduce	VERB
ejpam-6659	40	62	as	as	ADP
ejpam-6659	40	63	a	a	DET
ejpam-6659	40	64	means	means	NOUN
ejpam-6659	40	65	of	of	ADP
ejpam-6659	40	66	incorporating	incorporate	VERB
ejpam-6659	40	67	complexvalued	complexvalue	VERB
ejpam-6659	40	68	functions	function	NOUN
ejpam-6659	40	69	and	and	CCONJ
ejpam-6659	40	70	providing	provide	VERB
ejpam-6659	40	71	a	a	DET
ejpam-6659	40	72	more	more	ADV
ejpam-6659	40	73	flexible	flexible	ADJ
ejpam-6659	40	74	framework	framework	NOUN
ejpam-6659	40	75	for	for	ADP
ejpam-6659	40	76	addressing	address	VERB
ejpam-6659	40	77	the	the	DET
ejpam-6659	40	78	challenges	challenge	NOUN
ejpam-6659	40	79	posed	pose	VERB
ejpam-6659	40	80	by	by	ADP
ejpam-6659	40	81	complex	complex	ADJ
ejpam-6659	40	82	-	-	PUNCT
ejpam-6659	40	83	valued	value	VERB
ejpam-6659	40	84	systems	system	NOUN
ejpam-6659	40	85	.	.	PUNCT
ejpam-6659	41	1	this	this	DET
ejpam-6659	41	2	research	research	NOUN
ejpam-6659	41	3	article	article	NOUN
ejpam-6659	41	4	aims	aim	VERB
ejpam-6659	41	5	to	to	PART
ejpam-6659	41	6	present	present	VERB
ejpam-6659	41	7	and	and	CCONJ
ejpam-6659	41	8	analyze	analyze	VERB
ejpam-6659	41	9	a	a	DET
ejpam-6659	41	10	series	series	NOUN
ejpam-6659	41	11	of	of	ADP
ejpam-6659	41	12	novel	novel	ADJ
ejpam-6659	41	13	fixed	fix	VERB
ejpam-6659	41	14	point	point	NOUN
ejpam-6659	41	15	results	result	NOUN
ejpam-6659	41	16	within	within	ADP
ejpam-6659	41	17	the	the	DET
ejpam-6659	41	18	context	context	NOUN
ejpam-6659	41	19	of	of	ADP
ejpam-6659	41	20	this	this	DET
ejpam-6659	41	21	specialized	specialized	ADJ
ejpam-6659	41	22	setting	setting	NOUN
ejpam-6659	41	23	.	.	PUNCT
ejpam-6659	42	1	this	this	DET
ejpam-6659	42	2	extension	extension	NOUN
ejpam-6659	42	3	has	have	AUX
ejpam-6659	42	4	proved	prove	VERB
ejpam-6659	42	5	to	to	PART
ejpam-6659	42	6	be	be	AUX
ejpam-6659	42	7	instrumental	instrumental	ADJ
ejpam-6659	42	8	in	in	ADP
ejpam-6659	42	9	capturing	capture	VERB
ejpam-6659	42	10	the	the	DET
ejpam-6659	42	11	intricacies	intricacy	NOUN
ejpam-6659	42	12	of	of	ADP
ejpam-6659	42	13	complex	complex	ADV
ejpam-6659	42	14	-	-	PUNCT
ejpam-6659	42	15	valued	value	VERB
ejpam-6659	42	16	dynamics	dynamic	NOUN
ejpam-6659	42	17	and	and	CCONJ
ejpam-6659	42	18	has	have	AUX
ejpam-6659	42	19	facilitated	facilitate	VERB
ejpam-6659	42	20	the	the	DET
ejpam-6659	42	21	study	study	NOUN
ejpam-6659	42	22	of	of	ADP
ejpam-6659	42	23	various	various	ADJ
ejpam-6659	42	24	properties	property	NOUN
ejpam-6659	42	25	,	,	PUNCT
ejpam-6659	42	26	such	such	ADJ
ejpam-6659	42	27	as	as	ADP
ejpam-6659	42	28	convergence	convergence	NOUN
ejpam-6659	42	29	,	,	PUNCT
ejpam-6659	42	30	continuity	continuity	NOUN
ejpam-6659	42	31	,	,	PUNCT
ejpam-6659	42	32	and	and	CCONJ
ejpam-6659	42	33	completeness	completeness	NOUN
ejpam-6659	42	34	,	,	PUNCT
ejpam-6659	42	35	within	within	ADP
ejpam-6659	42	36	this	this	DET
ejpam-6659	42	37	complex	complex	NOUN
ejpam-6659	42	38	-	-	PUNCT
ejpam-6659	42	39	valued	value	VERB
ejpam-6659	42	40	setting	setting	NOUN
ejpam-6659	42	41	.	.	PUNCT
ejpam-6659	43	1	by	by	ADP
ejpam-6659	43	2	establishing	establish	VERB
ejpam-6659	43	3	crucial	crucial	ADJ
ejpam-6659	43	4	fixed	fix	VERB
ejpam-6659	43	5	point	point	NOUN
ejpam-6659	43	6	theorems	theorem	NOUN
ejpam-6659	43	7	and	and	CCONJ
ejpam-6659	43	8	exploring	explore	VERB
ejpam-6659	43	9	their	their	PRON
ejpam-6659	43	10	implications	implication	NOUN
ejpam-6659	43	11	in	in	ADP
ejpam-6659	43	12	the	the	DET
ejpam-6659	43	13	broader	broad	ADJ
ejpam-6659	43	14	context	context	NOUN
ejpam-6659	43	15	of	of	ADP
ejpam-6659	43	16	cvcs	cvcs	ADJ
ejpam-6659	43	17	-	-	PUNCT
ejpam-6659	43	18	metric	metric	ADJ
ejpam-6659	43	19	spaces	space	NOUN
ejpam-6659	43	20	,	,	PUNCT
ejpam-6659	43	21	we	we	PRON
ejpam-6659	43	22	aim	aim	VERB
ejpam-6659	43	23	to	to	PART
ejpam-6659	43	24	provide	provide	VERB
ejpam-6659	43	25	a	a	DET
ejpam-6659	43	26	deeper	deep	ADJ
ejpam-6659	43	27	understanding	understanding	NOUN
ejpam-6659	43	28	of	of	ADP
ejpam-6659	43	29	the	the	DET
ejpam-6659	43	30	underlying	underlie	VERB
ejpam-6659	43	31	dynamics	dynamic	NOUN
ejpam-6659	43	32	and	and	CCONJ
ejpam-6659	43	33	behaviors	behavior	NOUN
ejpam-6659	43	34	of	of	ADP
ejpam-6659	43	35	mappings	mapping	NOUN
ejpam-6659	43	36	within	within	ADP
ejpam-6659	43	37	this	this	DET
ejpam-6659	43	38	complex	complex	ADJ
ejpam-6659	43	39	domain	domain	NOUN
ejpam-6659	43	40	.	.	PUNCT
ejpam-6659	44	1	h.	h.	PROPN
ejpam-6659	44	2	qawaqneh	qawaqneh	PROPN
ejpam-6659	44	3	et	et	PROPN
ejpam-6659	44	4	al	al	PROPN
ejpam-6659	44	5	.	.	PUNCT
ejpam-6659	44	6	/	/	SYM
ejpam-6659	44	7	eur	eur	PROPN
ejpam-6659	44	8	.	.	PUNCT
ejpam-6659	45	1	j.	j.	PROPN
ejpam-6659	45	2	pure	pure	PROPN
ejpam-6659	45	3	appl	appl	PROPN
ejpam-6659	45	4	.	.	PROPN
ejpam-6659	45	5	math	math	PROPN
ejpam-6659	45	6	,	,	PUNCT
ejpam-6659	45	7	18	18	NUM
ejpam-6659	45	8	(	(	PUNCT
ejpam-6659	45	9	3	3	NUM
ejpam-6659	45	10	)	)	PUNCT
ejpam-6659	45	11	(	(	PUNCT
ejpam-6659	45	12	2025	2025	NUM
ejpam-6659	45	13	)	)	PUNCT
ejpam-6659	45	14	,	,	PUNCT
ejpam-6659	45	15	6659	6659	NUM
ejpam-6659	45	16	3	3	NUM
ejpam-6659	45	17	of	of	ADP
ejpam-6659	45	18	16	16	NUM
ejpam-6659	45	19	2	2	NUM
ejpam-6659	45	20	.	.	PUNCT
ejpam-6659	45	21	preliminaries	preliminary	NOUN
ejpam-6659	45	22	if	if	SCONJ
ejpam-6659	45	23	c	c	PROPN
ejpam-6659	45	24	denotes	denote	VERB
ejpam-6659	45	25	the	the	DET
ejpam-6659	45	26	set	set	NOUN
ejpam-6659	45	27	of	of	ADP
ejpam-6659	45	28	complex	complex	ADJ
ejpam-6659	45	29	numbers	number	NOUN
ejpam-6659	45	30	and	and	CCONJ
ejpam-6659	45	31	ϖ1	ϖ1	VERB
ejpam-6659	45	32	,	,	PUNCT
ejpam-6659	45	33	ϖ2	ϖ2	NOUN
ejpam-6659	45	34	∈	∈	PROPN
ejpam-6659	45	35	c	c	NOUN
ejpam-6659	45	36	,	,	PUNCT
ejpam-6659	45	37	then	then	ADV
ejpam-6659	45	38	the	the	DET
ejpam-6659	45	39	partial	partial	ADJ
ejpam-6659	45	40	order	order	NOUN
ejpam-6659	45	41	≾	≾	NOUN
ejpam-6659	45	42	is	be	AUX
ejpam-6659	45	43	defined	define	VERB
ejpam-6659	45	44	on	on	ADP
ejpam-6659	45	45	c	c	PROPN
ejpam-6659	45	46	in	in	ADP
ejpam-6659	45	47	the	the	DET
ejpam-6659	45	48	following	following	ADJ
ejpam-6659	45	49	manner	manner	NOUN
ejpam-6659	45	50	:	:	PUNCT
ejpam-6659	45	51	ϖ1	ϖ1	ADJ
ejpam-6659	45	52	≺	≺	NOUN
ejpam-6659	45	53	ϖ2	ϖ2	NOUN
ejpam-6659	45	54	if	if	SCONJ
ejpam-6659	45	55	and	and	CCONJ
ejpam-6659	45	56	only	only	ADV
ejpam-6659	45	57	if	if	SCONJ
ejpam-6659	45	58	re(ϖ1	re(ϖ1	VERB
ejpam-6659	45	59	)	)	PUNCT
ejpam-6659	45	60	<	<	X
ejpam-6659	45	61	re(ϖ2	re(ϖ2	NOUN
ejpam-6659	45	62	)	)	PUNCT
ejpam-6659	45	63	,	,	PUNCT
ejpam-6659	45	64	im(ϖ1	im(ϖ1	VERB
ejpam-6659	45	65	)	)	PUNCT
ejpam-6659	45	66	<	<	X
ejpam-6659	45	67	im(ϖ2	im(ϖ2	NOUN
ejpam-6659	45	68	)	)	PUNCT
ejpam-6659	45	69	and	and	CCONJ
ejpam-6659	45	70	ϖ1	ϖ1	VERB
ejpam-6659	45	71	≾	≾	PROPN
ejpam-6659	45	72	ϖ2	ϖ2	NOUN
ejpam-6659	45	73	if	if	SCONJ
ejpam-6659	45	74	and	and	CCONJ
ejpam-6659	45	75	only	only	ADV
ejpam-6659	45	76	if	if	SCONJ
ejpam-6659	45	77	re(ϖ1	re(ϖ1	VERB
ejpam-6659	45	78	)	)	PUNCT
ejpam-6659	45	79	≤	≤	NOUN
ejpam-6659	45	80	re(ϖ2	re(ϖ2	NOUN
ejpam-6659	45	81	)	)	PUNCT
ejpam-6659	45	82	,	,	PUNCT
ejpam-6659	45	83	im(ϖ1	im(ϖ1	VERB
ejpam-6659	45	84	)	)	PUNCT
ejpam-6659	45	85	≤	≤	NUM
ejpam-6659	45	86	im(ϖ2	im(ϖ2	NOUN
ejpam-6659	45	87	)	)	PUNCT
ejpam-6659	45	88	.	.	PUNCT
ejpam-6659	46	1	we	we	PRON
ejpam-6659	46	2	also	also	ADV
ejpam-6659	46	3	express	express	VERB
ejpam-6659	46	4	ϖ1	ϖ1	PROPN
ejpam-6659	46	5	≾	≾	PROPN
ejpam-6659	46	6	ϖ2	ϖ2	NOUN
ejpam-6659	46	7	if	if	SCONJ
ejpam-6659	46	8	any	any	DET
ejpam-6659	46	9	one	one	NUM
ejpam-6659	46	10	of	of	ADP
ejpam-6659	46	11	the	the	DET
ejpam-6659	46	12	following	follow	VERB
ejpam-6659	46	13	conditions	condition	NOUN
ejpam-6659	46	14	is	be	AUX
ejpam-6659	46	15	met	meet	VERB
ejpam-6659	46	16	:	:	PUNCT
ejpam-6659	46	17	(	(	PUNCT
ejpam-6659	46	18	i	i	NOUN
ejpam-6659	46	19	)	)	PUNCT
ejpam-6659	46	20	im(ϖ1	im(ϖ1	VERB
ejpam-6659	46	21	)	)	PUNCT
ejpam-6659	46	22	<	<	X
ejpam-6659	46	23	im(ϖ2	im(ϖ2	NOUN
ejpam-6659	46	24	)	)	PUNCT
ejpam-6659	46	25	and	and	CCONJ
ejpam-6659	46	26	re(ϖ1	re(ϖ1	VERB
ejpam-6659	46	27	)	)	PUNCT
ejpam-6659	46	28	=	=	SYM
ejpam-6659	46	29	re(ϖ2	re(ϖ2	NOUN
ejpam-6659	46	30	)	)	PUNCT
ejpam-6659	46	31	,	,	PUNCT
ejpam-6659	46	32	(	(	PUNCT
ejpam-6659	46	33	ii	ii	NOUN
ejpam-6659	46	34	)	)	PUNCT
ejpam-6659	46	35	im(ϖ1	im(ϖ1	NOUN
ejpam-6659	46	36	)	)	PUNCT
ejpam-6659	46	37	=	=	SYM
ejpam-6659	46	38	im(ϖ2	im(ϖ2	NOUN
ejpam-6659	46	39	)	)	PUNCT
ejpam-6659	46	40	and	and	CCONJ
ejpam-6659	46	41	re(ϖ1	re(ϖ1	VERB
ejpam-6659	46	42	)	)	PUNCT
ejpam-6659	46	43	<	<	X
ejpam-6659	46	44	re(ϖ2	re(ϖ2	NOUN
ejpam-6659	46	45	)	)	PUNCT
ejpam-6659	46	46	,	,	PUNCT
ejpam-6659	46	47	(	(	PUNCT
ejpam-6659	46	48	iii	iii	NOUN
ejpam-6659	46	49	)	)	PUNCT
ejpam-6659	46	50	im(ϖ1	im(ϖ1	NOUN
ejpam-6659	46	51	)	)	PUNCT
ejpam-6659	46	52	=	=	SYM
ejpam-6659	46	53	im(ϖ2	im(ϖ2	NOUN
ejpam-6659	46	54	)	)	PUNCT
ejpam-6659	46	55	and	and	CCONJ
ejpam-6659	46	56	re(ϖ1	re(ϖ1	VERB
ejpam-6659	46	57	)	)	PUNCT
ejpam-6659	46	58	=	=	SYM
ejpam-6659	46	59	re(ϖ2	re(ϖ2	NOUN
ejpam-6659	46	60	)	)	PUNCT
ejpam-6659	46	61	.	.	PUNCT
ejpam-6659	47	1	note	note	VERB
ejpam-6659	47	2	that	that	SCONJ
ejpam-6659	47	3	0	0	NUM
ejpam-6659	47	4	≾	≾	PROPN
ejpam-6659	47	5	ϖ1	ϖ1	VERB
ejpam-6659	47	6	⪵	⪵	PROPN
ejpam-6659	47	7	ϖ2	ϖ2	PROPN
ejpam-6659	47	8	implies	imply	VERB
ejpam-6659	47	9	|ϖ1|	|ϖ1|	PROPN
ejpam-6659	47	10	<	<	X
ejpam-6659	47	11	|ϖ2|	|ϖ2|	NOUN
ejpam-6659	47	12	;	;	PUNCT
ejpam-6659	47	13	and	and	CCONJ
ejpam-6659	47	14	ϖ1	ϖ1	VERB
ejpam-6659	47	15	≾	≾	PROPN
ejpam-6659	47	16	ϖ2	ϖ2	NOUN
ejpam-6659	47	17	,	,	PUNCT
ejpam-6659	47	18	ϖ2	ϖ2	NOUN
ejpam-6659	47	19	≺	≺	NOUN
ejpam-6659	47	20	ϖ3	ϖ3	NOUN
ejpam-6659	47	21	implies	imply	VERB
ejpam-6659	47	22	ϖ1	ϖ1	VERB
ejpam-6659	47	23	≺	≺	NOUN
ejpam-6659	47	24	ϖ3	ϖ3	NOUN
ejpam-6659	47	25	.	.	PUNCT
ejpam-6659	48	1	now	now	ADV
ejpam-6659	48	2	,	,	PUNCT
ejpam-6659	48	3	we	we	PRON
ejpam-6659	48	4	recall	recall	VERB
ejpam-6659	48	5	some	some	DET
ejpam-6659	48	6	definitions	definition	NOUN
ejpam-6659	48	7	as	as	ADV
ejpam-6659	48	8	well	well	ADV
ejpam-6659	48	9	as	as	ADP
ejpam-6659	48	10	established	establish	VERB
ejpam-6659	48	11	lemmas	lemma	NOUN
ejpam-6659	48	12	which	which	PRON
ejpam-6659	48	13	are	be	AUX
ejpam-6659	48	14	outlined	outline	VERB
ejpam-6659	48	15	in	in	ADP
ejpam-6659	48	16	the	the	DET
ejpam-6659	48	17	references	reference	NOUN
ejpam-6659	48	18	.	.	PUNCT
ejpam-6659	49	1	definition	definition	NOUN
ejpam-6659	49	2	1	1	NUM
ejpam-6659	49	3	.	.	PUNCT
ejpam-6659	50	1	[	[	X
ejpam-6659	50	2	27	27	NUM
ejpam-6659	50	3	]	]	PUNCT
ejpam-6659	50	4	consider	consider	VERB
ejpam-6659	50	5	a	a	DET
ejpam-6659	50	6	nonempty	nonempty	ADJ
ejpam-6659	50	7	set	set	VERB
ejpam-6659	50	8	γ	γ	NOUN
ejpam-6659	50	9	.	.	PROPN
ejpam-6659	51	1	then	then	ADV
ejpam-6659	51	2	a	a	DET
ejpam-6659	51	3	function	function	NOUN
ejpam-6659	51	4	s	s	PART
ejpam-6659	51	5	:	:	PUNCT
ejpam-6659	51	6	γ×	γ×	NOUN
ejpam-6659	51	7	γ×	γ×	NOUN
ejpam-6659	51	8	γ	γ	X
ejpam-6659	51	9	→	→	SYM
ejpam-6659	51	10	c	c	PROPN
ejpam-6659	51	11	is	be	AUX
ejpam-6659	51	12	a	a	DET
ejpam-6659	51	13	complex	complex	ADJ
ejpam-6659	51	14	valued	value	VERB
ejpam-6659	51	15	s	s	NOUN
ejpam-6659	51	16	-	-	NOUN
ejpam-6659	51	17	metric	metric	ADJ
ejpam-6659	51	18	on	on	ADP
ejpam-6659	51	19	γ	γ	PROPN
ejpam-6659	51	20	if	if	SCONJ
ejpam-6659	51	21	it	it	PRON
ejpam-6659	51	22	satisfies	satisfy	VERB
ejpam-6659	51	23	the	the	DET
ejpam-6659	51	24	following	follow	VERB
ejpam-6659	51	25	conditions	condition	NOUN
ejpam-6659	51	26	for	for	ADP
ejpam-6659	51	27	all	all	DET
ejpam-6659	51	28	ϖ	ϖ	PROPN
ejpam-6659	51	29	,	,	PUNCT
ejpam-6659	51	30	ρ	ρ	PROPN
ejpam-6659	51	31	,	,	PUNCT
ejpam-6659	51	32	q	q	X
ejpam-6659	51	33	,	,	PUNCT
ejpam-6659	51	34	t	t	PROPN
ejpam-6659	51	35	∈	∈	PROPN
ejpam-6659	51	36	γ	γ	X
ejpam-6659	51	37	:	:	PUNCT
ejpam-6659	51	38	(	(	PUNCT
ejpam-6659	51	39	i	i	NOUN
ejpam-6659	51	40	)	)	PUNCT
ejpam-6659	51	41	s(ϖ	s(ϖ	PROPN
ejpam-6659	51	42	,	,	PUNCT
ejpam-6659	51	43	ρ	ρ	NOUN
ejpam-6659	51	44	,	,	PUNCT
ejpam-6659	51	45	q	q	NOUN
ejpam-6659	51	46	)	)	PUNCT
ejpam-6659	51	47	⪰	⪰	NOUN
ejpam-6659	51	48	0	0	NUM
ejpam-6659	51	49	,	,	PUNCT
ejpam-6659	51	50	(	(	PUNCT
ejpam-6659	51	51	ii	ii	NOUN
ejpam-6659	51	52	)	)	PUNCT
ejpam-6659	51	53	s(ϖ	s(ϖ	NOUN
ejpam-6659	51	54	,	,	PUNCT
ejpam-6659	51	55	ρ	ρ	NOUN
ejpam-6659	51	56	,	,	PUNCT
ejpam-6659	51	57	q	q	NOUN
ejpam-6659	51	58	)	)	PUNCT
ejpam-6659	51	59	=	=	SYM
ejpam-6659	51	60	0	0	PUNCT
ejpam-6659	52	1	if	if	SCONJ
ejpam-6659	52	2	and	and	CCONJ
ejpam-6659	52	3	only	only	ADV
ejpam-6659	52	4	if	if	SCONJ
ejpam-6659	52	5	ϖ	ϖ	PROPN
ejpam-6659	52	6	=	=	SYM
ejpam-6659	52	7	ρ	ρ	PROPN
ejpam-6659	52	8	=	=	SYM
ejpam-6659	52	9	q	q	NOUN
ejpam-6659	52	10	,	,	PUNCT
ejpam-6659	52	11	(	(	PUNCT
ejpam-6659	52	12	iii	iii	NOUN
ejpam-6659	52	13	)	)	PUNCT
ejpam-6659	52	14	s(ϖ	s(ϖ	NOUN
ejpam-6659	52	15	,	,	PUNCT
ejpam-6659	52	16	ρ	ρ	NOUN
ejpam-6659	52	17	,	,	PUNCT
ejpam-6659	52	18	q	q	NOUN
ejpam-6659	52	19	)	)	PUNCT
ejpam-6659	52	20	≾	≾	NOUN
ejpam-6659	52	21	s(ϖ,ϖ	s(ϖ,ϖ	NOUN
ejpam-6659	52	22	,	,	PUNCT
ejpam-6659	52	23	t	t	PROPN
ejpam-6659	52	24	)	)	PUNCT
ejpam-6659	52	25	+	+	CCONJ
ejpam-6659	53	1	s(ρ	s(ρ	PROPN
ejpam-6659	53	2	,	,	PUNCT
ejpam-6659	53	3	ρ	ρ	PROPN
ejpam-6659	53	4	,	,	PUNCT
ejpam-6659	53	5	t	t	PROPN
ejpam-6659	53	6	)	)	PUNCT
ejpam-6659	53	7	+	+	CCONJ
ejpam-6659	53	8	s(q	s(q	NOUN
ejpam-6659	53	9	,	,	PUNCT
ejpam-6659	53	10	q	q	X
ejpam-6659	53	11	,	,	PUNCT
ejpam-6659	53	12	t	t	PROPN
ejpam-6659	53	13	)	)	PUNCT
ejpam-6659	53	14	.	.	PUNCT
ejpam-6659	54	1	a	a	DET
ejpam-6659	54	2	complex	complex	ADJ
ejpam-6659	54	3	valued	value	VERB
ejpam-6659	54	4	s	s	NOUN
ejpam-6659	54	5	-	-	ADJ
ejpam-6659	54	6	metric	metric	ADJ
ejpam-6659	54	7	space	space	NOUN
ejpam-6659	54	8	is	be	AUX
ejpam-6659	54	9	denoted	denote	VERB
ejpam-6659	54	10	by	by	ADP
ejpam-6659	54	11	(	(	PUNCT
ejpam-6659	54	12	γ	γ	X
ejpam-6659	54	13	,	,	PUNCT
ejpam-6659	54	14	s	s	PART
ejpam-6659	54	15	)	)	PUNCT
ejpam-6659	54	16	.	.	PUNCT
ejpam-6659	55	1	definition	definition	NOUN
ejpam-6659	55	2	2	2	NUM
ejpam-6659	55	3	.	.	PUNCT
ejpam-6659	56	1	[	[	X
ejpam-6659	56	2	27	27	NUM
ejpam-6659	56	3	]	]	PUNCT
ejpam-6659	56	4	consider	consider	VERB
ejpam-6659	56	5	a	a	DET
ejpam-6659	56	6	complex	complex	ADJ
ejpam-6659	56	7	valued	value	VERB
ejpam-6659	56	8	s	s	NOUN
ejpam-6659	56	9	-	-	ADJ
ejpam-6659	56	10	metric	metric	ADJ
ejpam-6659	56	11	space	space	NOUN
ejpam-6659	56	12	(	(	PUNCT
ejpam-6659	56	13	γ	γ	X
ejpam-6659	56	14	,	,	PUNCT
ejpam-6659	56	15	s	s	PART
ejpam-6659	56	16	)	)	PUNCT
ejpam-6659	56	17	.	.	PUNCT
ejpam-6659	57	1	(	(	PUNCT
ejpam-6659	57	2	i	i	NOUN
ejpam-6659	57	3	)	)	PUNCT
ejpam-6659	57	4	a	a	DET
ejpam-6659	57	5	sequence	sequence	NOUN
ejpam-6659	57	6	{	{	PUNCT
ejpam-6659	57	7	τω	τω	INTJ
ejpam-6659	57	8	}	}	PUNCT
ejpam-6659	57	9	∈	∈	PROPN
ejpam-6659	57	10	γ	γ	NOUN
ejpam-6659	57	11	converges	converge	NOUN
ejpam-6659	57	12	to	to	ADP
ejpam-6659	57	13	τ	τ	PROPN
ejpam-6659	57	14	if	if	SCONJ
ejpam-6659	57	15	and	and	CCONJ
ejpam-6659	57	16	only	only	ADV
ejpam-6659	57	17	if	if	SCONJ
ejpam-6659	57	18	for	for	ADP
ejpam-6659	57	19	all	all	PRON
ejpam-6659	57	20	ϵ	ϵ	ADP
ejpam-6659	57	21	such	such	ADJ
ejpam-6659	57	22	that	that	SCONJ
ejpam-6659	57	23	0	0	NUM
ejpam-6659	57	24	≺	≺	NOUN
ejpam-6659	57	25	ϵ	ϵ	X
ejpam-6659	57	26	∈	∈	PROPN
ejpam-6659	57	27	c	c	NOUN
ejpam-6659	57	28	there	there	PRON
ejpam-6659	57	29	exists	exist	VERB
ejpam-6659	57	30	a	a	DET
ejpam-6659	57	31	natural	natural	ADJ
ejpam-6659	57	32	number	number	NOUN
ejpam-6659	57	33	ω0	ω0	NOUN
ejpam-6659	57	34	such	such	ADJ
ejpam-6659	57	35	that	that	SCONJ
ejpam-6659	57	36	for	for	ADP
ejpam-6659	57	37	all	all	DET
ejpam-6659	57	38	ω	ω	NUM
ejpam-6659	57	39	≥	≥	NOUN
ejpam-6659	57	40	ω0	ω0	NOUN
ejpam-6659	57	41	,	,	PUNCT
ejpam-6659	57	42	we	we	PRON
ejpam-6659	57	43	have	have	AUX
ejpam-6659	57	44	s(τω	s(τω	PROPN
ejpam-6659	57	45	,	,	PUNCT
ejpam-6659	57	46	τω	τω	INTJ
ejpam-6659	57	47	,	,	PUNCT
ejpam-6659	57	48	τ	τ	NOUN
ejpam-6659	57	49	)	)	PUNCT
ejpam-6659	57	50	≾	≾	PROPN
ejpam-6659	57	51	ϵ	ϵ	NOUN
ejpam-6659	57	52	and	and	CCONJ
ejpam-6659	57	53	it	it	PRON
ejpam-6659	57	54	is	be	AUX
ejpam-6659	57	55	denoted	denote	VERB
ejpam-6659	57	56	by	by	ADP
ejpam-6659	57	57	lim	lim	PROPN
ejpam-6659	57	58	lim	lim	PROPN
ejpam-6659	58	1	ω→+∞	ω→+∞	PROPN
ejpam-6659	58	2	τω	τω	ADP
ejpam-6659	58	3	=	=	PROPN
ejpam-6659	58	4	τ	τ	X
ejpam-6659	58	5	.	.	PUNCT
ejpam-6659	59	1	(	(	PUNCT
ejpam-6659	59	2	ii	ii	NOUN
ejpam-6659	59	3	)	)	PUNCT
ejpam-6659	59	4	a	a	DET
ejpam-6659	59	5	sequence	sequence	NOUN
ejpam-6659	59	6	τω	τω	INTJ
ejpam-6659	59	7	∈	∈	PROPN
ejpam-6659	59	8	γ	γ	NOUN
ejpam-6659	59	9	is	be	AUX
ejpam-6659	59	10	called	call	VERB
ejpam-6659	59	11	a	a	DET
ejpam-6659	59	12	cauchy	cauchy	ADJ
ejpam-6659	59	13	sequence	sequence	NOUN
ejpam-6659	59	14	if	if	SCONJ
ejpam-6659	59	15	for	for	ADP
ejpam-6659	59	16	all	all	PRON
ejpam-6659	59	17	ϵ	ϵ	ADP
ejpam-6659	59	18	such	such	ADJ
ejpam-6659	59	19	that	that	SCONJ
ejpam-6659	59	20	0	0	NUM
ejpam-6659	59	21	≺	≺	NOUN
ejpam-6659	59	22	ϵ	ϵ	X
ejpam-6659	59	23	∈	∈	PROPN
ejpam-6659	59	24	c	c	NOUN
ejpam-6659	59	25	there	there	PRON
ejpam-6659	59	26	exists	exist	VERB
ejpam-6659	59	27	a	a	DET
ejpam-6659	59	28	natural	natural	ADJ
ejpam-6659	59	29	number	number	NOUN
ejpam-6659	59	30	ω0	ω0	NOUN
ejpam-6659	59	31	such	such	ADJ
ejpam-6659	59	32	that	that	SCONJ
ejpam-6659	59	33	for	for	ADP
ejpam-6659	59	34	all	all	DET
ejpam-6659	59	35	ω	ω	NOUN
ejpam-6659	59	36	,	,	PUNCT
ejpam-6659	59	37	ϱ	ϱ	PROPN
ejpam-6659	59	38	≥	≥	NOUN
ejpam-6659	59	39	ω0	ω0	NOUN
ejpam-6659	59	40	,	,	PUNCT
ejpam-6659	59	41	we	we	PRON
ejpam-6659	59	42	have	have	VERB
ejpam-6659	59	43	s(τω	s(τω	PROPN
ejpam-6659	59	44	,	,	PUNCT
ejpam-6659	59	45	τω	τω	INTJ
ejpam-6659	59	46	,	,	PUNCT
ejpam-6659	59	47	τϱ	τϱ	NOUN
ejpam-6659	59	48	)	)	PUNCT
ejpam-6659	59	49	≺	≺	NOUN
ejpam-6659	59	50	ϵ.	ϵ.	NOUN
ejpam-6659	59	51	(	(	PUNCT
ejpam-6659	59	52	iii	iii	NOUN
ejpam-6659	59	53	)	)	PUNCT
ejpam-6659	59	54	a	a	DET
ejpam-6659	59	55	complex	complex	NOUN
ejpam-6659	59	56	valued	value	VERB
ejpam-6659	59	57	s	s	NOUN
ejpam-6659	59	58	-	-	ADJ
ejpam-6659	59	59	metric	metric	ADJ
ejpam-6659	59	60	space	space	NOUN
ejpam-6659	59	61	(	(	PUNCT
ejpam-6659	59	62	γ	γ	X
ejpam-6659	59	63	,	,	PUNCT
ejpam-6659	59	64	s	s	PART
ejpam-6659	59	65	)	)	PUNCT
ejpam-6659	59	66	is	be	AUX
ejpam-6659	59	67	called	call	VERB
ejpam-6659	59	68	complete	complete	ADJ
ejpam-6659	59	69	if	if	SCONJ
ejpam-6659	59	70	every	every	DET
ejpam-6659	59	71	cauchy	cauchy	ADJ
ejpam-6659	59	72	sequence	sequence	NOUN
ejpam-6659	59	73	in	in	ADP
ejpam-6659	59	74	γ	γ	PROPN
ejpam-6659	59	75	is	be	AUX
ejpam-6659	59	76	convergent	convergent	ADJ
ejpam-6659	59	77	.	.	PUNCT
ejpam-6659	60	1	lemma	lemma	PROPN
ejpam-6659	60	2	1	1	NUM
ejpam-6659	60	3	.	.	PUNCT
ejpam-6659	61	1	[	[	X
ejpam-6659	61	2	27	27	NUM
ejpam-6659	61	3	]	]	PUNCT
ejpam-6659	61	4	consider	consider	VERB
ejpam-6659	61	5	a	a	DET
ejpam-6659	61	6	complex	complex	ADJ
ejpam-6659	61	7	valued	value	VERB
ejpam-6659	61	8	s	s	NOUN
ejpam-6659	61	9	-	-	ADJ
ejpam-6659	61	10	metric	metric	ADJ
ejpam-6659	61	11	space	space	NOUN
ejpam-6659	61	12	(	(	PUNCT
ejpam-6659	61	13	γ	γ	X
ejpam-6659	61	14	,	,	PUNCT
ejpam-6659	61	15	s	s	PART
ejpam-6659	61	16	)	)	PUNCT
ejpam-6659	61	17	and	and	CCONJ
ejpam-6659	61	18	a	a	DET
ejpam-6659	61	19	sequence	sequence	NOUN
ejpam-6659	61	20	{	{	PUNCT
ejpam-6659	61	21	τω	τω	INTJ
ejpam-6659	61	22	}	}	PUNCT
ejpam-6659	61	23	in	in	ADP
ejpam-6659	61	24	γ	γ	PROPN
ejpam-6659	61	25	.	.	PROPN
ejpam-6659	62	1	then	then	ADV
ejpam-6659	62	2	{	{	PUNCT
ejpam-6659	62	3	τω	τω	INTJ
ejpam-6659	62	4	}	}	PUNCT
ejpam-6659	62	5	is	be	AUX
ejpam-6659	62	6	said	say	VERB
ejpam-6659	62	7	to	to	PART
ejpam-6659	62	8	converge	converge	VERB
ejpam-6659	62	9	to	to	ADP
ejpam-6659	62	10	τ	τ	PROPN
ejpam-6659	62	11	if	if	SCONJ
ejpam-6659	62	12	and	and	CCONJ
ejpam-6659	62	13	only	only	ADV
ejpam-6659	62	14	if	if	SCONJ
ejpam-6659	62	15	|s(τω	|s(τω	PROPN
ejpam-6659	62	16	,	,	PUNCT
ejpam-6659	62	17	τω	τω	INTJ
ejpam-6659	62	18	,	,	PUNCT
ejpam-6659	62	19	τ)|	τ)|	PROPN
ejpam-6659	62	20	→	→	SYM
ejpam-6659	62	21	0	0	PUNCT
ejpam-6659	62	22	as	as	ADP
ejpam-6659	62	23	ω	ω	PROPN
ejpam-6659	62	24	→	→	SYM
ejpam-6659	63	1	+	+	PROPN
ejpam-6659	63	2	∞.	∞.	PROPN
ejpam-6659	63	3	lemma	lemma	PROPN
ejpam-6659	63	4	2	2	NUM
ejpam-6659	63	5	.	.	PUNCT
ejpam-6659	64	1	[	[	X
ejpam-6659	64	2	27	27	NUM
ejpam-6659	64	3	]	]	PUNCT
ejpam-6659	64	4	consider	consider	VERB
ejpam-6659	64	5	a	a	DET
ejpam-6659	64	6	complex	complex	ADJ
ejpam-6659	64	7	valued	value	VERB
ejpam-6659	64	8	s	s	NOUN
ejpam-6659	64	9	-	-	ADJ
ejpam-6659	64	10	metric	metric	ADJ
ejpam-6659	64	11	space	space	NOUN
ejpam-6659	64	12	(	(	PUNCT
ejpam-6659	64	13	γ	γ	X
ejpam-6659	64	14	,	,	PUNCT
ejpam-6659	64	15	s	s	PART
ejpam-6659	64	16	)	)	PUNCT
ejpam-6659	64	17	and	and	CCONJ
ejpam-6659	64	18	a	a	DET
ejpam-6659	64	19	sequence	sequence	NOUN
ejpam-6659	64	20	{	{	PUNCT
ejpam-6659	64	21	τω	τω	INTJ
ejpam-6659	64	22	}	}	PUNCT
ejpam-6659	64	23	in	in	ADP
ejpam-6659	64	24	γ	γ	PROPN
ejpam-6659	64	25	.	.	PROPN
ejpam-6659	65	1	then	then	ADV
ejpam-6659	65	2	{	{	PUNCT
ejpam-6659	65	3	τω	τω	INTJ
ejpam-6659	65	4	}	}	PUNCT
ejpam-6659	65	5	is	be	AUX
ejpam-6659	65	6	a	a	DET
ejpam-6659	65	7	cauchy	cauchy	ADJ
ejpam-6659	65	8	sequence	sequence	NOUN
ejpam-6659	65	9	if	if	SCONJ
ejpam-6659	65	10	and	and	CCONJ
ejpam-6659	65	11	only	only	ADV
ejpam-6659	65	12	if	if	SCONJ
ejpam-6659	65	13	|s(τω	|s(τω	PROPN
ejpam-6659	65	14	,	,	PUNCT
ejpam-6659	65	15	τω	τω	INTJ
ejpam-6659	65	16	,	,	PUNCT
ejpam-6659	65	17	τω+ϱ)|	τω+ϱ)|	PUNCT
ejpam-6659	66	1	→	→	PUNCT
ejpam-6659	66	2	0	0	NUM
ejpam-6659	67	1	as	as	ADP
ejpam-6659	67	2	ω	ω	PROPN
ejpam-6659	67	3	,	,	PUNCT
ejpam-6659	67	4	ϱ	ϱ	PROPN
ejpam-6659	67	5	→	→	SYM
ejpam-6659	67	6	+	+	PROPN
ejpam-6659	67	7	∞.	∞.	PROPN
ejpam-6659	67	8	lemma	lemma	PROPN
ejpam-6659	67	9	3	3	X
ejpam-6659	67	10	.	.	PUNCT
ejpam-6659	68	1	[	[	X
ejpam-6659	68	2	27	27	NUM
ejpam-6659	68	3	]	]	PUNCT
ejpam-6659	68	4	consider	consider	VERB
ejpam-6659	68	5	a	a	DET
ejpam-6659	68	6	complex	complex	ADJ
ejpam-6659	68	7	valued	value	VERB
ejpam-6659	68	8	s	s	NOUN
ejpam-6659	68	9	-	-	ADJ
ejpam-6659	68	10	metric	metric	ADJ
ejpam-6659	68	11	space	space	NOUN
ejpam-6659	68	12	(	(	PUNCT
ejpam-6659	68	13	γ	γ	X
ejpam-6659	68	14	,	,	PUNCT
ejpam-6659	68	15	s	s	PART
ejpam-6659	68	16	)	)	PUNCT
ejpam-6659	68	17	,	,	PUNCT
ejpam-6659	68	18	then	then	ADV
ejpam-6659	68	19	s(ς	s(ς	PROPN
ejpam-6659	68	20	,	,	PUNCT
ejpam-6659	68	21	ς	ς	PROPN
ejpam-6659	68	22	,	,	PUNCT
ejpam-6659	68	23	τ	τ	NOUN
ejpam-6659	68	24	)	)	PUNCT
ejpam-6659	68	25	=	=	SYM
ejpam-6659	69	1	s(τ	s(τ	PROPN
ejpam-6659	69	2	,	,	PUNCT
ejpam-6659	69	3	τ	τ	PROPN
ejpam-6659	69	4	,	,	PUNCT
ejpam-6659	69	5	ς	ς	PROPN
ejpam-6659	69	6	)	)	PUNCT
ejpam-6659	69	7	for	for	ADP
ejpam-6659	69	8	all	all	DET
ejpam-6659	69	9	τ	τ	PROPN
ejpam-6659	69	10	,	,	PUNCT
ejpam-6659	69	11	ς	ς	PROPN
ejpam-6659	69	12	∈	∈	PROPN
ejpam-6659	69	13	γ	γ	X
ejpam-6659	69	14	.	.	PUNCT
ejpam-6659	69	15	h.	h.	PROPN
ejpam-6659	69	16	qawaqneh	qawaqneh	PROPN
ejpam-6659	69	17	et	et	PROPN
ejpam-6659	69	18	al	al	PROPN
ejpam-6659	69	19	.	.	PUNCT
ejpam-6659	69	20	/	/	SYM
ejpam-6659	69	21	eur	eur	PROPN
ejpam-6659	69	22	.	.	PUNCT
ejpam-6659	70	1	j.	j.	PROPN
ejpam-6659	70	2	pure	pure	PROPN
ejpam-6659	70	3	appl	appl	PROPN
ejpam-6659	70	4	.	.	PROPN
ejpam-6659	70	5	math	math	PROPN
ejpam-6659	70	6	,	,	PUNCT
ejpam-6659	70	7	18	18	NUM
ejpam-6659	70	8	(	(	PUNCT
ejpam-6659	70	9	3	3	NUM
ejpam-6659	70	10	)	)	PUNCT
ejpam-6659	70	11	(	(	PUNCT
ejpam-6659	70	12	2025	2025	NUM
ejpam-6659	70	13	)	)	PUNCT
ejpam-6659	70	14	,	,	PUNCT
ejpam-6659	70	15	6659	6659	NUM
ejpam-6659	70	16	4	4	NUM
ejpam-6659	70	17	of	of	ADP
ejpam-6659	70	18	16	16	NUM
ejpam-6659	70	19	3	3	NUM
ejpam-6659	70	20	.	.	PUNCT
ejpam-6659	70	21	fixed	fix	VERB
ejpam-6659	70	22	point	point	NOUN
ejpam-6659	70	23	results	result	VERB
ejpam-6659	70	24	the	the	DET
ejpam-6659	70	25	need	need	NOUN
ejpam-6659	70	26	to	to	PART
ejpam-6659	70	27	generalize	generalize	VERB
ejpam-6659	70	28	s	s	NOUN
ejpam-6659	70	29	-	-	ADJ
ejpam-6659	70	30	metric	metric	ADJ
ejpam-6659	70	31	spaces	space	NOUN
ejpam-6659	70	32	to	to	PART
ejpam-6659	70	33	handle	handle	VERB
ejpam-6659	70	34	complex	complex	ADV
ejpam-6659	70	35	-	-	PUNCT
ejpam-6659	70	36	valued	value	VERB
ejpam-6659	70	37	distances	distance	NOUN
ejpam-6659	70	38	under	under	ADP
ejpam-6659	70	39	additional	additional	ADJ
ejpam-6659	70	40	control	control	NOUN
ejpam-6659	70	41	conditions	condition	NOUN
ejpam-6659	70	42	motivates	motivate	VERB
ejpam-6659	70	43	the	the	DET
ejpam-6659	70	44	introduction	introduction	NOUN
ejpam-6659	70	45	of	of	ADP
ejpam-6659	70	46	the	the	DET
ejpam-6659	70	47	concept	concept	NOUN
ejpam-6659	70	48	of	of	ADP
ejpam-6659	70	49	a	a	DET
ejpam-6659	70	50	cvcs	cvcs	ADJ
ejpam-6659	70	51	-	-	PUNCT
ejpam-6659	70	52	metric	metric	ADJ
ejpam-6659	70	53	space	space	NOUN
ejpam-6659	70	54	as	as	SCONJ
ejpam-6659	70	55	follows	follow	VERB
ejpam-6659	70	56	.	.	PUNCT
ejpam-6659	71	1	definition	definition	NOUN
ejpam-6659	71	2	3	3	NUM
ejpam-6659	71	3	.	.	PUNCT
ejpam-6659	71	4	consider	consider	VERB
ejpam-6659	71	5	a	a	DET
ejpam-6659	71	6	set	set	NOUN
ejpam-6659	71	7	γ	γ	PROPN
ejpam-6659	71	8	̸=	̸=	PROPN
ejpam-6659	71	9	∅	∅	NOUN
ejpam-6659	71	10	and	and	CCONJ
ejpam-6659	71	11	let	let	VERB
ejpam-6659	71	12	s	s	PRON
ejpam-6659	71	13	:	:	PUNCT
ejpam-6659	71	14	γ×γ×γ	γ×γ×γ	PROPN
ejpam-6659	71	15	→	→	SYM
ejpam-6659	71	16	c	c	PROPN
ejpam-6659	71	17	and	and	CCONJ
ejpam-6659	71	18	α	α	NOUN
ejpam-6659	71	19	:	:	PUNCT
ejpam-6659	71	20	γ×γ×γ	γ×γ×γ	PUNCT
ejpam-6659	72	1	→	→	PUNCT
ejpam-6659	72	2	[	[	X
ejpam-6659	72	3	1,+∞	1,+∞	NUM
ejpam-6659	72	4	)	)	PUNCT
ejpam-6659	72	5	be	be	VERB
ejpam-6659	72	6	two	two	NUM
ejpam-6659	72	7	functions	function	NOUN
ejpam-6659	72	8	adhering	adhere	VERB
ejpam-6659	72	9	to	to	ADP
ejpam-6659	72	10	the	the	DET
ejpam-6659	72	11	following	follow	VERB
ejpam-6659	72	12	conditions	condition	NOUN
ejpam-6659	72	13	for	for	ADP
ejpam-6659	72	14	all	all	DET
ejpam-6659	72	15	τ	τ	PROPN
ejpam-6659	72	16	,	,	PUNCT
ejpam-6659	72	17	ς	ς	PROPN
ejpam-6659	72	18	,	,	PUNCT
ejpam-6659	72	19	ρ,ϖ	ρ,ϖ	NOUN
ejpam-6659	72	20	∈	∈	PROPN
ejpam-6659	72	21	γ	γ	X
ejpam-6659	72	22	:	:	PUNCT
ejpam-6659	72	23	(	(	PUNCT
ejpam-6659	72	24	cv	cv	PROPN
ejpam-6659	72	25	cs1	cs1	PROPN
ejpam-6659	72	26	)	)	PUNCT
ejpam-6659	72	27	0	0	PUNCT
ejpam-6659	73	1	≾	≾	PROPN
ejpam-6659	73	2	s(τ	s(τ	PROPN
ejpam-6659	73	3	,	,	PUNCT
ejpam-6659	73	4	ς	ς	PROPN
ejpam-6659	73	5	,	,	PUNCT
ejpam-6659	73	6	ρ	ρ	PROPN
ejpam-6659	73	7	)	)	PUNCT
ejpam-6659	73	8	;	;	PUNCT
ejpam-6659	73	9	(	(	PUNCT
ejpam-6659	73	10	cv	cv	PROPN
ejpam-6659	73	11	cs2	cs2	NOUN
ejpam-6659	73	12	)	)	PUNCT
ejpam-6659	74	1	s(τ	s(τ	PROPN
ejpam-6659	74	2	,	,	PUNCT
ejpam-6659	74	3	ς	ς	PROPN
ejpam-6659	74	4	,	,	PUNCT
ejpam-6659	74	5	ρ	ρ	NOUN
ejpam-6659	74	6	)	)	PUNCT
ejpam-6659	74	7	=	=	SYM
ejpam-6659	74	8	0	0	PUNCT
ejpam-6659	75	1	if	if	SCONJ
ejpam-6659	75	2	and	and	CCONJ
ejpam-6659	75	3	only	only	ADV
ejpam-6659	75	4	if	if	SCONJ
ejpam-6659	75	5	τ	τ	PROPN
ejpam-6659	75	6	=	=	SYM
ejpam-6659	75	7	ς	ς	PROPN
ejpam-6659	75	8	=	=	SYM
ejpam-6659	75	9	ρ	ρ	PROPN
ejpam-6659	75	10	;	;	PUNCT
ejpam-6659	75	11	(	(	PUNCT
ejpam-6659	75	12	cv	cv	PROPN
ejpam-6659	75	13	cs3	cs3	PROPN
ejpam-6659	75	14	)	)	PUNCT
ejpam-6659	75	15	s(τ	s(τ	PROPN
ejpam-6659	75	16	,	,	PUNCT
ejpam-6659	75	17	ς	ς	PROPN
ejpam-6659	75	18	,	,	PUNCT
ejpam-6659	75	19	ρ	ρ	NOUN
ejpam-6659	75	20	)	)	PUNCT
ejpam-6659	75	21	≾	≾	PROPN
ejpam-6659	75	22	α(τ	α(τ	PROPN
ejpam-6659	75	23	,	,	PUNCT
ejpam-6659	75	24	τ,ϖ)s(τ	τ,ϖ)s(τ	NOUN
ejpam-6659	75	25	,	,	PUNCT
ejpam-6659	75	26	τ,ϖ	τ,ϖ	NOUN
ejpam-6659	75	27	)	)	PUNCT
ejpam-6659	75	28	+	+	CCONJ
ejpam-6659	75	29	α(ς	α(ς	PROPN
ejpam-6659	75	30	,	,	PUNCT
ejpam-6659	75	31	ς,ϖ)s(ς	ς,ϖ)s(ς	PROPN
ejpam-6659	75	32	,	,	PUNCT
ejpam-6659	75	33	ς,ϖ	ς,ϖ	NUM
ejpam-6659	75	34	)	)	PUNCT
ejpam-6659	75	35	+	+	CCONJ
ejpam-6659	75	36	α(ρ	α(ρ	NOUN
ejpam-6659	75	37	,	,	PUNCT
ejpam-6659	75	38	ρ,ϖ)s(ρ	ρ,ϖ)s(ρ	NOUN
ejpam-6659	75	39	,	,	PUNCT
ejpam-6659	75	40	ρ,ϖ	ρ,ϖ	NOUN
ejpam-6659	75	41	)	)	PUNCT
ejpam-6659	75	42	.	.	PUNCT
ejpam-6659	76	1	then	then	ADV
ejpam-6659	76	2	,	,	PUNCT
ejpam-6659	76	3	the	the	DET
ejpam-6659	76	4	tuple	tuple	NOUN
ejpam-6659	76	5	(	(	PUNCT
ejpam-6659	76	6	γ	γ	X
ejpam-6659	76	7	,	,	PUNCT
ejpam-6659	76	8	s	s	PROPN
ejpam-6659	76	9	,	,	PUNCT
ejpam-6659	76	10	α	α	NOUN
ejpam-6659	76	11	)	)	PUNCT
ejpam-6659	76	12	is	be	AUX
ejpam-6659	76	13	called	call	VERB
ejpam-6659	76	14	a	a	DET
ejpam-6659	76	15	cvcs	cvcs	ADJ
ejpam-6659	76	16	-	-	PUNCT
ejpam-6659	76	17	metric	metric	ADJ
ejpam-6659	76	18	space	space	NOUN
ejpam-6659	76	19	.	.	PUNCT
ejpam-6659	77	1	definition	definition	NOUN
ejpam-6659	77	2	2.2	2.2	NUM
ejpam-6659	77	3	,	,	PUNCT
ejpam-6659	77	4	lemma	lemma	PROPN
ejpam-6659	77	5	2.3	2.3	NUM
ejpam-6659	77	6	,	,	PUNCT
ejpam-6659	77	7	2.4	2.4	NUM
ejpam-6659	77	8	and	and	CCONJ
ejpam-6659	77	9	2.5	2.5	NUM
ejpam-6659	77	10	can	can	AUX
ejpam-6659	77	11	be	be	AUX
ejpam-6659	77	12	stated	state	VERB
ejpam-6659	77	13	and	and	CCONJ
ejpam-6659	77	14	proved	prove	VERB
ejpam-6659	77	15	in	in	ADP
ejpam-6659	77	16	a	a	DET
ejpam-6659	77	17	similar	similar	ADJ
ejpam-6659	77	18	way	way	NOUN
ejpam-6659	77	19	for	for	ADP
ejpam-6659	77	20	a	a	DET
ejpam-6659	77	21	cvcs	cvcs	ADJ
ejpam-6659	77	22	-	-	PUNCT
ejpam-6659	77	23	metric	metric	ADJ
ejpam-6659	77	24	space	space	NOUN
ejpam-6659	77	25	.	.	PUNCT
ejpam-6659	78	1	definition	definition	NOUN
ejpam-6659	78	2	4	4	NUM
ejpam-6659	78	3	.	.	PUNCT
ejpam-6659	78	4	consider	consider	VERB
ejpam-6659	78	5	a	a	DET
ejpam-6659	78	6	cvcs	cvcs	ADJ
ejpam-6659	78	7	-	-	PUNCT
ejpam-6659	78	8	metric	metric	ADJ
ejpam-6659	78	9	space	space	NOUN
ejpam-6659	78	10	(	(	PUNCT
ejpam-6659	78	11	γ	γ	X
ejpam-6659	78	12	,	,	PUNCT
ejpam-6659	78	13	s	s	PROPN
ejpam-6659	78	14	,	,	PUNCT
ejpam-6659	78	15	α	α	NOUN
ejpam-6659	78	16	)	)	PUNCT
ejpam-6659	78	17	.	.	PUNCT
ejpam-6659	79	1	(	(	PUNCT
ejpam-6659	79	2	i	i	NOUN
ejpam-6659	79	3	)	)	PUNCT
ejpam-6659	79	4	a	a	DET
ejpam-6659	79	5	sequence	sequence	NOUN
ejpam-6659	79	6	{	{	PUNCT
ejpam-6659	79	7	τω	τω	INTJ
ejpam-6659	79	8	}	}	PUNCT
ejpam-6659	79	9	∈	∈	PROPN
ejpam-6659	79	10	γ	γ	NOUN
ejpam-6659	79	11	is	be	AUX
ejpam-6659	79	12	cvcs	cvcs	ADJ
ejpam-6659	79	13	-	-	PUNCT
ejpam-6659	79	14	convergent	convergent	NOUN
ejpam-6659	79	15	to	to	ADP
ejpam-6659	79	16	τ	τ	PROPN
ejpam-6659	79	17	if	if	SCONJ
ejpam-6659	79	18	and	and	CCONJ
ejpam-6659	79	19	only	only	ADV
ejpam-6659	79	20	if	if	SCONJ
ejpam-6659	79	21	for	for	ADP
ejpam-6659	79	22	all	all	PRON
ejpam-6659	79	23	ϵ	ϵ	ADP
ejpam-6659	79	24	such	such	ADJ
ejpam-6659	79	25	that	that	SCONJ
ejpam-6659	79	26	0	0	NUM
ejpam-6659	79	27	≺	≺	NOUN
ejpam-6659	79	28	ϵ	ϵ	X
ejpam-6659	79	29	∈	∈	PROPN
ejpam-6659	79	30	c	c	NOUN
ejpam-6659	79	31	there	there	PRON
ejpam-6659	79	32	exists	exist	VERB
ejpam-6659	79	33	a	a	DET
ejpam-6659	79	34	natural	natural	ADJ
ejpam-6659	79	35	number	number	NOUN
ejpam-6659	79	36	ω0	ω0	NOUN
ejpam-6659	79	37	such	such	ADJ
ejpam-6659	79	38	that	that	SCONJ
ejpam-6659	79	39	for	for	ADP
ejpam-6659	79	40	all	all	DET
ejpam-6659	79	41	ω	ω	NUM
ejpam-6659	79	42	≥	≥	NOUN
ejpam-6659	79	43	ω0	ω0	NOUN
ejpam-6659	79	44	,	,	PUNCT
ejpam-6659	79	45	we	we	PRON
ejpam-6659	79	46	have	have	AUX
ejpam-6659	79	47	s(τω	s(τω	PROPN
ejpam-6659	79	48	,	,	PUNCT
ejpam-6659	79	49	τω	τω	INTJ
ejpam-6659	79	50	,	,	PUNCT
ejpam-6659	79	51	τ	τ	NOUN
ejpam-6659	79	52	)	)	PUNCT
ejpam-6659	79	53	≾	≾	PROPN
ejpam-6659	79	54	ϵ	ϵ	NOUN
ejpam-6659	79	55	and	and	CCONJ
ejpam-6659	79	56	it	it	PRON
ejpam-6659	79	57	is	be	AUX
ejpam-6659	79	58	denoted	denote	VERB
ejpam-6659	79	59	by	by	ADP
ejpam-6659	79	60	lim	lim	PROPN
ejpam-6659	79	61	lim	lim	PROPN
ejpam-6659	80	1	ω→+∞	ω→+∞	PROPN
ejpam-6659	80	2	τω	τω	ADP
ejpam-6659	80	3	=	=	PROPN
ejpam-6659	80	4	τ	τ	X
ejpam-6659	80	5	.	.	PUNCT
ejpam-6659	81	1	(	(	PUNCT
ejpam-6659	81	2	ii	ii	NOUN
ejpam-6659	81	3	)	)	PUNCT
ejpam-6659	81	4	a	a	DET
ejpam-6659	81	5	sequence	sequence	NOUN
ejpam-6659	81	6	τω	τω	INTJ
ejpam-6659	81	7	∈	∈	PROPN
ejpam-6659	81	8	γ	γ	NOUN
ejpam-6659	81	9	is	be	AUX
ejpam-6659	81	10	called	call	VERB
ejpam-6659	81	11	a	a	DET
ejpam-6659	81	12	cvcs	cvcs	ADJ
ejpam-6659	81	13	-	-	PUNCT
ejpam-6659	81	14	cauchy	cauchy	ADJ
ejpam-6659	81	15	sequence	sequence	NOUN
ejpam-6659	81	16	if	if	SCONJ
ejpam-6659	81	17	for	for	ADP
ejpam-6659	81	18	all	all	PRON
ejpam-6659	81	19	ϵ	ϵ	ADP
ejpam-6659	81	20	such	such	ADJ
ejpam-6659	81	21	that	that	SCONJ
ejpam-6659	81	22	0	0	NUM
ejpam-6659	81	23	≺	≺	NOUN
ejpam-6659	81	24	ϵ	ϵ	X
ejpam-6659	81	25	∈	∈	PROPN
ejpam-6659	81	26	c	c	NOUN
ejpam-6659	81	27	there	there	PRON
ejpam-6659	81	28	exists	exist	VERB
ejpam-6659	81	29	a	a	DET
ejpam-6659	81	30	natural	natural	ADJ
ejpam-6659	81	31	number	number	NOUN
ejpam-6659	81	32	ω0	ω0	NOUN
ejpam-6659	81	33	such	such	ADJ
ejpam-6659	81	34	that	that	SCONJ
ejpam-6659	81	35	for	for	ADP
ejpam-6659	81	36	all	all	DET
ejpam-6659	81	37	ω	ω	NOUN
ejpam-6659	81	38	,	,	PUNCT
ejpam-6659	81	39	ϱ	ϱ	PROPN
ejpam-6659	81	40	≥	≥	NOUN
ejpam-6659	81	41	ω0	ω0	NOUN
ejpam-6659	81	42	,	,	PUNCT
ejpam-6659	81	43	we	we	PRON
ejpam-6659	81	44	have	have	VERB
ejpam-6659	81	45	s(τω	s(τω	PROPN
ejpam-6659	81	46	,	,	PUNCT
ejpam-6659	81	47	τω	τω	INTJ
ejpam-6659	81	48	,	,	PUNCT
ejpam-6659	81	49	τϱ	τϱ	NOUN
ejpam-6659	81	50	)	)	PUNCT
ejpam-6659	81	51	≺	≺	NOUN
ejpam-6659	81	52	ϵ.	ϵ.	NOUN
ejpam-6659	81	53	(	(	PUNCT
ejpam-6659	81	54	iii	iii	NOUN
ejpam-6659	81	55	)	)	PUNCT
ejpam-6659	81	56	a	a	DET
ejpam-6659	81	57	cvcs	cvcs	ADJ
ejpam-6659	81	58	-	-	PUNCT
ejpam-6659	81	59	metric	metric	ADJ
ejpam-6659	81	60	space	space	NOUN
ejpam-6659	81	61	(	(	PUNCT
ejpam-6659	81	62	γ	γ	X
ejpam-6659	81	63	,	,	PUNCT
ejpam-6659	81	64	s	s	PROPN
ejpam-6659	81	65	,	,	PUNCT
ejpam-6659	81	66	α	α	NOUN
ejpam-6659	81	67	)	)	PUNCT
ejpam-6659	81	68	is	be	AUX
ejpam-6659	81	69	called	call	VERB
ejpam-6659	81	70	complete	complete	ADJ
ejpam-6659	81	71	if	if	SCONJ
ejpam-6659	81	72	every	every	DET
ejpam-6659	81	73	cvcs	cvcs	ADJ
ejpam-6659	81	74	-	-	PUNCT
ejpam-6659	81	75	cauchy	cauchy	ADJ
ejpam-6659	81	76	sequence	sequence	NOUN
ejpam-6659	81	77	in	in	ADP
ejpam-6659	81	78	γ	γ	PROPN
ejpam-6659	81	79	is	be	AUX
ejpam-6659	81	80	convergent	convergent	ADJ
ejpam-6659	81	81	.	.	PUNCT
ejpam-6659	82	1	lemma	lemma	PROPN
ejpam-6659	82	2	4	4	X
ejpam-6659	82	3	.	.	PUNCT
ejpam-6659	82	4	consider	consider	VERB
ejpam-6659	82	5	a	a	DET
ejpam-6659	82	6	cvcs	cvcs	ADJ
ejpam-6659	82	7	-	-	PUNCT
ejpam-6659	82	8	metric	metric	ADJ
ejpam-6659	82	9	space	space	NOUN
ejpam-6659	82	10	(	(	PUNCT
ejpam-6659	82	11	γ	γ	X
ejpam-6659	82	12	,	,	PUNCT
ejpam-6659	82	13	s	s	PROPN
ejpam-6659	82	14	,	,	PUNCT
ejpam-6659	82	15	α	α	NOUN
ejpam-6659	82	16	)	)	PUNCT
ejpam-6659	82	17	and	and	CCONJ
ejpam-6659	82	18	a	a	DET
ejpam-6659	82	19	sequence	sequence	NOUN
ejpam-6659	82	20	{	{	PUNCT
ejpam-6659	82	21	τω	τω	INTJ
ejpam-6659	82	22	}	}	PUNCT
ejpam-6659	82	23	in	in	ADP
ejpam-6659	82	24	γ	γ	PROPN
ejpam-6659	82	25	.	.	PROPN
ejpam-6659	83	1	then	then	ADV
ejpam-6659	83	2	{	{	PUNCT
ejpam-6659	83	3	τω	τω	INTJ
ejpam-6659	83	4	}	}	PUNCT
ejpam-6659	83	5	is	be	AUX
ejpam-6659	83	6	said	say	VERB
ejpam-6659	83	7	to	to	PART
ejpam-6659	83	8	be	be	AUX
ejpam-6659	83	9	cvcs	cvcs	NOUN
ejpam-6659	83	10	-	-	PUNCT
ejpam-6659	83	11	convergent	convergent	NOUN
ejpam-6659	83	12	to	to	ADP
ejpam-6659	83	13	τ	τ	PROPN
ejpam-6659	83	14	if	if	SCONJ
ejpam-6659	83	15	and	and	CCONJ
ejpam-6659	83	16	only	only	ADV
ejpam-6659	83	17	if	if	SCONJ
ejpam-6659	83	18	|s(τω	|s(τω	PROPN
ejpam-6659	83	19	,	,	PUNCT
ejpam-6659	83	20	τω	τω	INTJ
ejpam-6659	83	21	,	,	PUNCT
ejpam-6659	83	22	τ)|	τ)|	PROPN
ejpam-6659	83	23	→	→	SYM
ejpam-6659	83	24	0	0	PUNCT
ejpam-6659	83	25	as	as	ADP
ejpam-6659	83	26	ω	ω	PROPN
ejpam-6659	83	27	→	→	SYM
ejpam-6659	84	1	+	+	PROPN
ejpam-6659	84	2	∞.	∞.	PROPN
ejpam-6659	84	3	lemma	lemma	PROPN
ejpam-6659	84	4	5	5	NUM
ejpam-6659	84	5	.	.	PUNCT
ejpam-6659	85	1	consider	consider	VERB
ejpam-6659	85	2	a	a	DET
ejpam-6659	85	3	cvcs	cvcs	ADJ
ejpam-6659	85	4	-	-	PUNCT
ejpam-6659	85	5	metric	metric	ADJ
ejpam-6659	85	6	space	space	NOUN
ejpam-6659	85	7	(	(	PUNCT
ejpam-6659	85	8	γ	γ	X
ejpam-6659	85	9	,	,	PUNCT
ejpam-6659	85	10	s	s	PROPN
ejpam-6659	85	11	,	,	PUNCT
ejpam-6659	85	12	α	α	NOUN
ejpam-6659	85	13	)	)	PUNCT
ejpam-6659	85	14	and	and	CCONJ
ejpam-6659	85	15	a	a	DET
ejpam-6659	85	16	sequence	sequence	NOUN
ejpam-6659	85	17	{	{	PUNCT
ejpam-6659	85	18	τω	τω	INTJ
ejpam-6659	85	19	}	}	PUNCT
ejpam-6659	85	20	in	in	ADP
ejpam-6659	85	21	γ	γ	PROPN
ejpam-6659	85	22	.	.	PROPN
ejpam-6659	86	1	then	then	ADV
ejpam-6659	86	2	{	{	PUNCT
ejpam-6659	86	3	τω	τω	INTJ
ejpam-6659	86	4	}	}	PUNCT
ejpam-6659	86	5	is	be	AUX
ejpam-6659	86	6	a	a	DET
ejpam-6659	86	7	cvcs	cvcs	ADJ
ejpam-6659	86	8	-	-	PUNCT
ejpam-6659	86	9	cauchy	cauchy	ADJ
ejpam-6659	86	10	sequence	sequence	NOUN
ejpam-6659	86	11	if	if	SCONJ
ejpam-6659	86	12	and	and	CCONJ
ejpam-6659	86	13	only	only	ADV
ejpam-6659	86	14	if	if	SCONJ
ejpam-6659	86	15	|s(τω	|s(τω	PROPN
ejpam-6659	86	16	,	,	PUNCT
ejpam-6659	86	17	τω	τω	INTJ
ejpam-6659	86	18	,	,	PUNCT
ejpam-6659	86	19	τω+ϱ)|	τω+ϱ)|	PUNCT
ejpam-6659	87	1	→	→	PUNCT
ejpam-6659	87	2	0	0	NUM
ejpam-6659	88	1	as	as	SCONJ
ejpam-6659	88	2	ω	ω	PROPN
ejpam-6659	88	3	,	,	PUNCT
ejpam-6659	88	4	ϱ	ϱ	PROPN
ejpam-6659	88	5	→	→	SYM
ejpam-6659	88	6	+	+	PROPN
ejpam-6659	88	7	∞.	∞.	PROPN
ejpam-6659	88	8	lemma	lemma	PROPN
ejpam-6659	88	9	6	6	NUM
ejpam-6659	88	10	.	.	PUNCT
ejpam-6659	88	11	consider	consider	VERB
ejpam-6659	88	12	a	a	DET
ejpam-6659	88	13	cvcs	cvcs	ADJ
ejpam-6659	88	14	-	-	PUNCT
ejpam-6659	88	15	metric	metric	ADJ
ejpam-6659	88	16	space	space	NOUN
ejpam-6659	88	17	(	(	PUNCT
ejpam-6659	88	18	γ	γ	X
ejpam-6659	88	19	,	,	PUNCT
ejpam-6659	88	20	s	s	PROPN
ejpam-6659	88	21	,	,	PUNCT
ejpam-6659	88	22	α	α	NOUN
ejpam-6659	88	23	)	)	PUNCT
ejpam-6659	88	24	,	,	PUNCT
ejpam-6659	88	25	then	then	ADV
ejpam-6659	88	26	s(ς	s(ς	PROPN
ejpam-6659	88	27	,	,	PUNCT
ejpam-6659	88	28	ς	ς	PROPN
ejpam-6659	88	29	,	,	PUNCT
ejpam-6659	88	30	τ	τ	NOUN
ejpam-6659	88	31	)	)	PUNCT
ejpam-6659	89	1	=	=	SYM
ejpam-6659	90	1	s(τ	s(τ	PROPN
ejpam-6659	90	2	,	,	PUNCT
ejpam-6659	90	3	τ	τ	PROPN
ejpam-6659	90	4	,	,	PUNCT
ejpam-6659	90	5	ς	ς	PROPN
ejpam-6659	90	6	)	)	PUNCT
ejpam-6659	90	7	for	for	ADP
ejpam-6659	90	8	all	all	DET
ejpam-6659	90	9	τ	τ	PROPN
ejpam-6659	90	10	,	,	PUNCT
ejpam-6659	90	11	ς	ς	PROPN
ejpam-6659	90	12	∈	∈	PROPN
ejpam-6659	90	13	γ	γ	X
ejpam-6659	90	14	.	.	PROPN
ejpam-6659	90	15	theorem	theorem	NOUN
ejpam-6659	90	16	1	1	X
ejpam-6659	90	17	.	.	PUNCT
ejpam-6659	90	18	consider	consider	VERB
ejpam-6659	90	19	a	a	DET
ejpam-6659	90	20	cvcs	cvcs	ADJ
ejpam-6659	90	21	-	-	PUNCT
ejpam-6659	90	22	metric	metric	ADJ
ejpam-6659	90	23	space	space	NOUN
ejpam-6659	90	24	(	(	PUNCT
ejpam-6659	90	25	γ	γ	X
ejpam-6659	90	26	,	,	PUNCT
ejpam-6659	90	27	s	s	PROPN
ejpam-6659	90	28	,	,	PUNCT
ejpam-6659	90	29	α	α	NOUN
ejpam-6659	90	30	)	)	PUNCT
ejpam-6659	90	31	and	and	CCONJ
ejpam-6659	90	32	a	a	DET
ejpam-6659	90	33	sequence	sequence	NOUN
ejpam-6659	90	34	{	{	PUNCT
ejpam-6659	90	35	τω	τω	INTJ
ejpam-6659	90	36	}	}	PUNCT
ejpam-6659	90	37	in	in	ADP
ejpam-6659	90	38	γ	γ	PROPN
ejpam-6659	90	39	.	.	PUNCT
ejpam-6659	91	1	then	then	ADV
ejpam-6659	91	2	,	,	PUNCT
ejpam-6659	91	3	{	{	PUNCT
ejpam-6659	91	4	τω	τω	INTJ
ejpam-6659	91	5	}	}	PUNCT
ejpam-6659	91	6	is	be	AUX
ejpam-6659	91	7	a	a	DET
ejpam-6659	91	8	cvcs	cvcs	ADJ
ejpam-6659	91	9	-	-	PUNCT
ejpam-6659	91	10	cauchy	cauchy	ADJ
ejpam-6659	91	11	sequence	sequence	NOUN
ejpam-6659	91	12	if	if	SCONJ
ejpam-6659	91	13	and	and	CCONJ
ejpam-6659	91	14	only	only	ADV
ejpam-6659	91	15	if	if	SCONJ
ejpam-6659	91	16	|s(τω	|s(τω	NOUN
ejpam-6659	91	17	,	,	PUNCT
ejpam-6659	91	18	τϱ	τϱ	ADP
ejpam-6659	91	19	,	,	PUNCT
ejpam-6659	91	20	τl)|	τl)|	PUNCT
ejpam-6659	91	21	→	→	SYM
ejpam-6659	91	22	0	0	NUM
ejpam-6659	91	23	as	as	ADP
ejpam-6659	91	24	ω	ω	PROPN
ejpam-6659	91	25	,	,	PUNCT
ejpam-6659	91	26	ϱ	ϱ	NOUN
ejpam-6659	91	27	,	,	PUNCT
ejpam-6659	91	28	l	l	NOUN
ejpam-6659	91	29	→	→	PUNCT
ejpam-6659	91	30	+	+	ADJ
ejpam-6659	91	31	∞.	∞.	PROPN
ejpam-6659	91	32	proof	proof	NOUN
ejpam-6659	91	33	.	.	PUNCT
ejpam-6659	92	1	the	the	DET
ejpam-6659	92	2	proof	proof	NOUN
ejpam-6659	92	3	is	be	AUX
ejpam-6659	92	4	on	on	ADP
ejpam-6659	92	5	the	the	DET
ejpam-6659	92	6	similar	similar	ADJ
ejpam-6659	92	7	lines	line	NOUN
ejpam-6659	92	8	as	as	ADP
ejpam-6659	92	9	in	in	ADP
ejpam-6659	92	10	theorem	theorem	ADJ
ejpam-6659	92	11	3.3	3.3	NUM
ejpam-6659	92	12	of	of	ADP
ejpam-6659	92	13	[	[	X
ejpam-6659	92	14	29	29	NUM
ejpam-6659	92	15	]	]	PUNCT
ejpam-6659	92	16	.	.	PUNCT
ejpam-6659	93	1	theorem	theorem	NOUN
ejpam-6659	93	2	2	2	NUM
ejpam-6659	93	3	.	.	X
ejpam-6659	93	4	consider	consider	VERB
ejpam-6659	93	5	a	a	DET
ejpam-6659	93	6	complete	complete	ADJ
ejpam-6659	93	7	cvcs	cvcs	ADJ
ejpam-6659	93	8	-	-	PUNCT
ejpam-6659	93	9	metric	metric	ADJ
ejpam-6659	93	10	space	space	NOUN
ejpam-6659	93	11	(	(	PUNCT
ejpam-6659	93	12	γ	γ	X
ejpam-6659	93	13	,	,	PUNCT
ejpam-6659	93	14	s	s	PROPN
ejpam-6659	93	15	,	,	PUNCT
ejpam-6659	93	16	α	α	NOUN
ejpam-6659	93	17	)	)	PUNCT
ejpam-6659	93	18	.	.	PUNCT
ejpam-6659	94	1	define	define	VERB
ejpam-6659	94	2	a	a	DET
ejpam-6659	94	3	function	function	NOUN
ejpam-6659	94	4	f	f	NOUN
ejpam-6659	94	5	:	:	PUNCT
ejpam-6659	94	6	γ	γ	X
ejpam-6659	94	7	→	→	SYM
ejpam-6659	94	8	γ	γ	X
ejpam-6659	94	9	such	such	ADJ
ejpam-6659	94	10	that	that	SCONJ
ejpam-6659	94	11	s(fτ	s(fτ	PROPN
ejpam-6659	94	12	,	,	PUNCT
ejpam-6659	94	13	fτ	fτ	NOUN
ejpam-6659	94	14	,	,	PUNCT
ejpam-6659	94	15	fς	fς	X
ejpam-6659	94	16	)	)	PUNCT
ejpam-6659	94	17	≾	≾	NOUN
ejpam-6659	94	18	θs(τ	θs(τ	NUM
ejpam-6659	94	19	,	,	PUNCT
ejpam-6659	94	20	τ	τ	PROPN
ejpam-6659	94	21	,	,	PUNCT
ejpam-6659	94	22	ς	ς	PROPN
ejpam-6659	94	23	)	)	PUNCT
ejpam-6659	94	24	,	,	PUNCT
ejpam-6659	94	25	(	(	PUNCT
ejpam-6659	94	26	1	1	X
ejpam-6659	94	27	)	)	PUNCT
ejpam-6659	94	28	h.	h.	NOUN
ejpam-6659	94	29	qawaqneh	qawaqneh	PROPN
ejpam-6659	94	30	et	et	PROPN
ejpam-6659	94	31	al	al	PROPN
ejpam-6659	94	32	.	.	PUNCT
ejpam-6659	94	33	/	/	SYM
ejpam-6659	94	34	eur	eur	PROPN
ejpam-6659	94	35	.	.	PUNCT
ejpam-6659	95	1	j.	j.	PROPN
ejpam-6659	95	2	pure	pure	PROPN
ejpam-6659	95	3	appl	appl	PROPN
ejpam-6659	95	4	.	.	PROPN
ejpam-6659	95	5	math	math	PROPN
ejpam-6659	95	6	,	,	PUNCT
ejpam-6659	95	7	18	18	NUM
ejpam-6659	95	8	(	(	PUNCT
ejpam-6659	95	9	3	3	NUM
ejpam-6659	95	10	)	)	PUNCT
ejpam-6659	95	11	(	(	PUNCT
ejpam-6659	95	12	2025	2025	NUM
ejpam-6659	95	13	)	)	PUNCT
ejpam-6659	95	14	,	,	PUNCT
ejpam-6659	95	15	6659	6659	NUM
ejpam-6659	95	16	5	5	NUM
ejpam-6659	95	17	of	of	ADP
ejpam-6659	95	18	16	16	NUM
ejpam-6659	95	19	where	where	SCONJ
ejpam-6659	95	20	θ	θ	PROPN
ejpam-6659	95	21	∈	∈	PROPN
ejpam-6659	95	22	(	(	PUNCT
ejpam-6659	95	23	0	0	NUM
ejpam-6659	95	24	,	,	PUNCT
ejpam-6659	95	25	1	1	NUM
ejpam-6659	95	26	)	)	PUNCT
ejpam-6659	95	27	.	.	PUNCT
ejpam-6659	96	1	for	for	ADP
ejpam-6659	96	2	τ0	τ0	NOUN
ejpam-6659	96	3	∈	∈	PROPN
ejpam-6659	96	4	γ	γ	X
ejpam-6659	96	5	,	,	PUNCT
ejpam-6659	96	6	choose	choose	VERB
ejpam-6659	96	7	a	a	DET
ejpam-6659	96	8	sequence	sequence	NOUN
ejpam-6659	96	9	τω	τω	PRON
ejpam-6659	96	10	=	=	NOUN
ejpam-6659	96	11	f(τω−1	f(τω−1	NUM
ejpam-6659	96	12	)	)	PUNCT
ejpam-6659	96	13	,	,	PUNCT
ejpam-6659	96	14	ω	ω	PROPN
ejpam-6659	96	15	∈	∈	PROPN
ejpam-6659	96	16	n.	n.	NOUN
ejpam-6659	96	17	suppose	suppose	VERB
ejpam-6659	96	18	that	that	SCONJ
ejpam-6659	96	19	sup	sup	PROPN
ejpam-6659	96	20	ϱ≥1	ϱ≥1	PROPN
ejpam-6659	96	21	lim	lim	PROPN
ejpam-6659	96	22	i→+∞	i→+∞	PROPN
ejpam-6659	96	23	α(τi+1	α(τi+1	PROPN
ejpam-6659	96	24	,	,	PUNCT
ejpam-6659	96	25	τi+1	τi+1	X
ejpam-6659	96	26	,	,	PUNCT
ejpam-6659	96	27	τi+2).α(τϱ	τi+2).α(τϱ	NUM
ejpam-6659	96	28	,	,	PUNCT
ejpam-6659	96	29	τϱ	τϱ	X
ejpam-6659	96	30	,	,	PUNCT
ejpam-6659	96	31	τi+1	τi+1	NOUN
ejpam-6659	96	32	)	)	PUNCT
ejpam-6659	96	33	α(τi	α(τi	NOUN
ejpam-6659	96	34	,	,	PUNCT
ejpam-6659	96	35	τi	τi	ADP
ejpam-6659	96	36	,	,	PUNCT
ejpam-6659	96	37	τi+1	τi+1	X
ejpam-6659	96	38	)	)	PUNCT
ejpam-6659	96	39	<	<	X
ejpam-6659	96	40	1	1	NUM
ejpam-6659	96	41	2θ	2θ	NUM
ejpam-6659	96	42	,	,	PUNCT
ejpam-6659	96	43	(	(	PUNCT
ejpam-6659	96	44	2	2	NUM
ejpam-6659	96	45	)	)	PUNCT
ejpam-6659	96	46	and	and	CCONJ
ejpam-6659	96	47	lim	lim	PROPN
ejpam-6659	97	1	ω→+∞	ω→+∞	PROPN
ejpam-6659	97	2	α(τω	α(τω	NUM
ejpam-6659	97	3	,	,	PUNCT
ejpam-6659	97	4	τω	τω	INTJ
ejpam-6659	97	5	,	,	PUNCT
ejpam-6659	97	6	τω+1	τω+1	NUM
ejpam-6659	97	7	)	)	PUNCT
ejpam-6659	97	8	exists	exist	VERB
ejpam-6659	97	9	.	.	PUNCT
ejpam-6659	98	1	then	then	ADV
ejpam-6659	98	2	there	there	PRON
ejpam-6659	98	3	is	be	VERB
ejpam-6659	98	4	a	a	DET
ejpam-6659	98	5	unique	unique	ADJ
ejpam-6659	98	6	fixed	fix	VERB
ejpam-6659	98	7	point	point	NOUN
ejpam-6659	98	8	of	of	ADP
ejpam-6659	98	9	f	f	PROPN
ejpam-6659	98	10	.	.	PUNCT
ejpam-6659	99	1	proof	proof	NOUN
ejpam-6659	99	2	.	.	PUNCT
ejpam-6659	100	1	consider	consider	VERB
ejpam-6659	100	2	an	an	DET
ejpam-6659	100	3	arbitrary	arbitrary	ADJ
ejpam-6659	100	4	element	element	NOUN
ejpam-6659	100	5	τ0	τ0	NOUN
ejpam-6659	100	6	of	of	ADP
ejpam-6659	100	7	γ	γ	PROPN
ejpam-6659	100	8	.	.	PROPN
ejpam-6659	100	9	define	define	VERB
ejpam-6659	100	10	a	a	DET
ejpam-6659	100	11	sequence	sequence	NOUN
ejpam-6659	100	12	{	{	PUNCT
ejpam-6659	100	13	τω	τω	INTJ
ejpam-6659	100	14	}	}	PUNCT
ejpam-6659	100	15	in	in	ADP
ejpam-6659	100	16	γ	γ	NOUN
ejpam-6659	100	17	by	by	ADP
ejpam-6659	100	18	τω	τω	X
ejpam-6659	100	19	=	=	NOUN
ejpam-6659	100	20	f(τω−1	f(τω−1	NUM
ejpam-6659	100	21	)	)	PUNCT
ejpam-6659	100	22	=	=	SYM
ejpam-6659	100	23	fω(τ0	fω(τ0	NOUN
ejpam-6659	100	24	)	)	PUNCT
ejpam-6659	100	25	.	.	PUNCT
ejpam-6659	101	1	let	let	VERB
ejpam-6659	101	2	τω	τω	DET
ejpam-6659	101	3	̸=	̸=	PROPN
ejpam-6659	101	4	τω+1	τω+1	PUNCT
ejpam-6659	101	5	for	for	ADP
ejpam-6659	101	6	all	all	DET
ejpam-6659	101	7	ω	ω	NOUN
ejpam-6659	101	8	.	.	PUNCT
ejpam-6659	102	1	from	from	ADP
ejpam-6659	102	2	(	(	PUNCT
ejpam-6659	102	3	1	1	NUM
ejpam-6659	102	4	)	)	PUNCT
ejpam-6659	102	5	,	,	PUNCT
ejpam-6659	102	6	we	we	PRON
ejpam-6659	102	7	obtain	obtain	VERB
ejpam-6659	102	8	s(τω	s(τω	PROPN
ejpam-6659	102	9	,	,	PUNCT
ejpam-6659	102	10	τω	τω	INTJ
ejpam-6659	102	11	,	,	PUNCT
ejpam-6659	102	12	τω+1	τω+1	NUM
ejpam-6659	102	13	)	)	PUNCT
ejpam-6659	102	14	≾	≾	NOUN
ejpam-6659	102	15	θs(τω−1	θs(τω−1	NOUN
ejpam-6659	102	16	,	,	PUNCT
ejpam-6659	102	17	τω−1	τω−1	PROPN
ejpam-6659	102	18	,	,	PUNCT
ejpam-6659	102	19	τω	τω	INTJ
ejpam-6659	102	20	)	)	PUNCT
ejpam-6659	102	21	≾	≾	NOUN
ejpam-6659	102	22	θ2s(τω−2	θ2s(τω−2	NOUN
ejpam-6659	102	23	,	,	PUNCT
ejpam-6659	102	24	τω−2	τω−2	ADJ
ejpam-6659	102	25	,	,	PUNCT
ejpam-6659	102	26	τω−1	τω−1	PROPN
ejpam-6659	102	27	)	)	PUNCT
ejpam-6659	102	28	...	...	PUNCT
ejpam-6659	103	1	≾	≾	PROPN
ejpam-6659	103	2	θωs(τ0	θωs(τ0	PROPN
ejpam-6659	103	3	,	,	PUNCT
ejpam-6659	103	4	τ0	τ0	NOUN
ejpam-6659	103	5	,	,	PUNCT
ejpam-6659	103	6	τ1	τ1	NOUN
ejpam-6659	103	7	)	)	PUNCT
ejpam-6659	103	8	.	.	PUNCT
ejpam-6659	104	1	considering	consider	VERB
ejpam-6659	104	2	ϱ	ϱ	ADP
ejpam-6659	104	3	>	>	X
ejpam-6659	104	4	ω	ω	PROPN
ejpam-6659	104	5	and	and	CCONJ
ejpam-6659	104	6	using	use	VERB
ejpam-6659	104	7	triangle	triangle	NOUN
ejpam-6659	104	8	inequality	inequality	NOUN
ejpam-6659	104	9	,	,	PUNCT
ejpam-6659	104	10	we	we	PRON
ejpam-6659	104	11	obtain	obtain	VERB
ejpam-6659	104	12	s(τϱ	s(τϱ	ADV
ejpam-6659	104	13	,	,	PUNCT
ejpam-6659	104	14	τϱ	τϱ	PROPN
ejpam-6659	104	15	,	,	PUNCT
ejpam-6659	104	16	τω	τω	INTJ
ejpam-6659	104	17	)	)	PUNCT
ejpam-6659	104	18	≾	≾	PROPN
ejpam-6659	104	19	α(τϱ	α(τϱ	PROPN
ejpam-6659	104	20	,	,	PUNCT
ejpam-6659	104	21	τϱ	τϱ	PROPN
ejpam-6659	104	22	,	,	PUNCT
ejpam-6659	104	23	τω+1)s(τϱ	τω+1)s(τϱ	PROPN
ejpam-6659	104	24	,	,	PUNCT
ejpam-6659	104	25	τϱ	τϱ	X
ejpam-6659	104	26	,	,	PUNCT
ejpam-6659	104	27	τω+1	τω+1	PUNCT
ejpam-6659	104	28	)	)	PUNCT
ejpam-6659	104	29	+	+	CCONJ
ejpam-6659	104	30	α(τϱ	α(τϱ	NUM
ejpam-6659	104	31	,	,	PUNCT
ejpam-6659	104	32	τϱ	τϱ	PROPN
ejpam-6659	104	33	,	,	PUNCT
ejpam-6659	104	34	τω+1)s(τϱ	τω+1)s(τϱ	PROPN
ejpam-6659	104	35	,	,	PUNCT
ejpam-6659	104	36	τϱ	τϱ	X
ejpam-6659	104	37	,	,	PUNCT
ejpam-6659	104	38	τω+1	τω+1	PUNCT
ejpam-6659	104	39	)	)	PUNCT
ejpam-6659	104	40	+	+	CCONJ
ejpam-6659	104	41	α(τω	α(τω	NUM
ejpam-6659	104	42	,	,	PUNCT
ejpam-6659	104	43	τω	τω	INTJ
ejpam-6659	104	44	,	,	PUNCT
ejpam-6659	104	45	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	104	46	,	,	PUNCT
ejpam-6659	104	47	τω	τω	INTJ
ejpam-6659	104	48	,	,	PUNCT
ejpam-6659	104	49	τω+1	τω+1	NUM
ejpam-6659	104	50	)	)	PUNCT
ejpam-6659	104	51	≾	≾	NOUN
ejpam-6659	104	52	2α(τϱ	2α(τϱ	NUM
ejpam-6659	104	53	,	,	PUNCT
ejpam-6659	104	54	τϱ	τϱ	X
ejpam-6659	104	55	,	,	PUNCT
ejpam-6659	104	56	τω+1)s(τϱ	τω+1)s(τϱ	PROPN
ejpam-6659	104	57	,	,	PUNCT
ejpam-6659	104	58	τϱ	τϱ	X
ejpam-6659	104	59	,	,	PUNCT
ejpam-6659	104	60	τω+1	τω+1	PUNCT
ejpam-6659	104	61	)	)	PUNCT
ejpam-6659	104	62	+	+	CCONJ
ejpam-6659	104	63	α(τω	α(τω	NUM
ejpam-6659	104	64	,	,	PUNCT
ejpam-6659	104	65	τω	τω	INTJ
ejpam-6659	104	66	,	,	PUNCT
ejpam-6659	104	67	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	104	68	,	,	PUNCT
ejpam-6659	104	69	τω	τω	INTJ
ejpam-6659	104	70	,	,	PUNCT
ejpam-6659	104	71	τω+1	τω+1	NUM
ejpam-6659	104	72	)	)	PUNCT
ejpam-6659	104	73	.	.	PUNCT
ejpam-6659	105	1	once	once	ADV
ejpam-6659	105	2	more	more	ADV
ejpam-6659	105	3	,	,	PUNCT
ejpam-6659	105	4	applying	apply	VERB
ejpam-6659	105	5	the	the	DET
ejpam-6659	105	6	triangle	triangle	NOUN
ejpam-6659	105	7	inequality	inequality	NOUN
ejpam-6659	105	8	to	to	ADP
ejpam-6659	105	9	s(uϱ	s(uϱ	PROPN
ejpam-6659	105	10	,	,	PUNCT
ejpam-6659	105	11	uϱ	uϱ	NOUN
ejpam-6659	105	12	,	,	PUNCT
ejpam-6659	105	13	uω+1	uω+1	NOUN
ejpam-6659	105	14	)	)	PUNCT
ejpam-6659	105	15	,	,	PUNCT
ejpam-6659	105	16	we	we	PRON
ejpam-6659	105	17	obtain	obtain	VERB
ejpam-6659	105	18	s(τϱ	s(τϱ	ADV
ejpam-6659	105	19	,	,	PUNCT
ejpam-6659	105	20	τϱ	τϱ	PROPN
ejpam-6659	105	21	,	,	PUNCT
ejpam-6659	105	22	τω	τω	INTJ
ejpam-6659	105	23	)	)	PUNCT
ejpam-6659	105	24	≾	≾	PROPN
ejpam-6659	105	25	2α(τϱ	2α(τϱ	NUM
ejpam-6659	105	26	,	,	PUNCT
ejpam-6659	105	27	τϱ	τϱ	PROPN
ejpam-6659	105	28	,	,	PUNCT
ejpam-6659	105	29	τω+1)(2α(τϱ	τω+1)(2α(τϱ	PRON
ejpam-6659	105	30	,	,	PUNCT
ejpam-6659	105	31	τϱ	τϱ	PROPN
ejpam-6659	105	32	,	,	PUNCT
ejpam-6659	105	33	τω+2)s(τϱ	τω+2)s(τϱ	PROPN
ejpam-6659	105	34	,	,	PUNCT
ejpam-6659	105	35	τϱ	τϱ	PROPN
ejpam-6659	105	36	,	,	PUNCT
ejpam-6659	105	37	τω+2	τω+2	NUM
ejpam-6659	105	38	)	)	PUNCT
ejpam-6659	105	39	+	+	NUM
ejpam-6659	105	40	α(τω+1	α(τω+1	NOUN
ejpam-6659	105	41	,	,	PUNCT
ejpam-6659	105	42	τω+1	τω+1	X
ejpam-6659	105	43	,	,	PUNCT
ejpam-6659	105	44	τω+2)s(τω+1	τω+2)s(τω+1	NOUN
ejpam-6659	105	45	,	,	PUNCT
ejpam-6659	105	46	τω+1	τω+1	SYM
ejpam-6659	105	47	,	,	PUNCT
ejpam-6659	105	48	τω+2	τω+2	NUM
ejpam-6659	105	49	)	)	PUNCT
ejpam-6659	105	50	)	)	PUNCT
ejpam-6659	106	1	+	+	CCONJ
ejpam-6659	106	2	α(τω	α(τω	NUM
ejpam-6659	106	3	,	,	PUNCT
ejpam-6659	106	4	τω	τω	INTJ
ejpam-6659	106	5	,	,	PUNCT
ejpam-6659	106	6	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	106	7	,	,	PUNCT
ejpam-6659	106	8	τω	τω	INTJ
ejpam-6659	106	9	,	,	PUNCT
ejpam-6659	106	10	τω+1	τω+1	NUM
ejpam-6659	106	11	)	)	PUNCT
ejpam-6659	106	12	≾	≾	NOUN
ejpam-6659	106	13	α(τω	α(τω	NUM
ejpam-6659	106	14	,	,	PUNCT
ejpam-6659	106	15	τω	τω	INTJ
ejpam-6659	106	16	,	,	PUNCT
ejpam-6659	106	17	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	106	18	,	,	PUNCT
ejpam-6659	106	19	τω	τω	INTJ
ejpam-6659	106	20	,	,	PUNCT
ejpam-6659	106	21	τω+1	τω+1	PUNCT
ejpam-6659	106	22	)	)	PUNCT
ejpam-6659	106	23	+	+	CCONJ
ejpam-6659	106	24	2α(τϱ	2α(τϱ	NUM
ejpam-6659	106	25	,	,	PUNCT
ejpam-6659	106	26	τϱ	τϱ	NOUN
ejpam-6659	106	27	,	,	PUNCT
ejpam-6659	106	28	τω+1)α(τω+1	τω+1)α(τω+1	NOUN
ejpam-6659	106	29	,	,	PUNCT
ejpam-6659	106	30	τω+1	τω+1	CCONJ
ejpam-6659	106	31	,	,	PUNCT
ejpam-6659	106	32	τω+2)s(τω+1	τω+2)s(τω+1	NOUN
ejpam-6659	106	33	,	,	PUNCT
ejpam-6659	106	34	τω+1	τω+1	X
ejpam-6659	106	35	,	,	PUNCT
ejpam-6659	106	36	τω+2	τω+2	NUM
ejpam-6659	106	37	)	)	PUNCT
ejpam-6659	106	38	+	+	CCONJ
ejpam-6659	106	39	22α(τϱ	22α(τϱ	NUM
ejpam-6659	106	40	,	,	PUNCT
ejpam-6659	106	41	τϱ	τϱ	X
ejpam-6659	106	42	,	,	PUNCT
ejpam-6659	106	43	τω+1	τω+1	X
ejpam-6659	106	44	)	)	PUNCT
ejpam-6659	106	45	α(τϱ	α(τϱ	NUM
ejpam-6659	106	46	,	,	PUNCT
ejpam-6659	106	47	τϱ	τϱ	PROPN
ejpam-6659	106	48	,	,	PUNCT
ejpam-6659	106	49	τω+2)s(τϱ	τω+2)s(τϱ	PROPN
ejpam-6659	106	50	,	,	PUNCT
ejpam-6659	106	51	τϱ	τϱ	PROPN
ejpam-6659	106	52	,	,	PUNCT
ejpam-6659	106	53	τω+2	τω+2	NUM
ejpam-6659	106	54	)	)	PUNCT
ejpam-6659	106	55	.	.	PUNCT
ejpam-6659	107	1	proceeding	proceed	VERB
ejpam-6659	107	2	with	with	ADP
ejpam-6659	107	3	the	the	DET
ejpam-6659	107	4	continuous	continuous	ADJ
ejpam-6659	107	5	application	application	NOUN
ejpam-6659	107	6	of	of	ADP
ejpam-6659	107	7	triangle	triangle	NOUN
ejpam-6659	107	8	inequality	inequality	NOUN
ejpam-6659	107	9	in	in	ADP
ejpam-6659	107	10	the	the	DET
ejpam-6659	107	11	same	same	ADJ
ejpam-6659	107	12	manner	manner	NOUN
ejpam-6659	107	13	,	,	PUNCT
ejpam-6659	107	14	we	we	PRON
ejpam-6659	107	15	obtain	obtain	VERB
ejpam-6659	107	16	s(τϱ	s(τϱ	ADV
ejpam-6659	107	17	,	,	PUNCT
ejpam-6659	107	18	τϱ	τϱ	PROPN
ejpam-6659	107	19	,	,	PUNCT
ejpam-6659	107	20	τω	τω	INTJ
ejpam-6659	107	21	)	)	PUNCT
ejpam-6659	107	22	≾	≾	PROPN
ejpam-6659	107	23	α(τω	α(τω	NUM
ejpam-6659	107	24	,	,	PUNCT
ejpam-6659	107	25	τω	τω	INTJ
ejpam-6659	107	26	,	,	PUNCT
ejpam-6659	107	27	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	107	28	,	,	PUNCT
ejpam-6659	107	29	τω	τω	INTJ
ejpam-6659	107	30	,	,	PUNCT
ejpam-6659	107	31	τω+1	τω+1	PUNCT
ejpam-6659	107	32	)	)	PUNCT
ejpam-6659	107	33	+	+	CCONJ
ejpam-6659	107	34	ϱ−2∑	ϱ−2∑	PROPN
ejpam-6659	107	35	i	i	NOUN
ejpam-6659	107	36	=	=	NOUN
ejpam-6659	107	37	ω+1	ω+1	NUM
ejpam-6659	107	38	2i−ω	2i−ω	NOUN
ejpam-6659	107	39	i∏	i∏	VERB
ejpam-6659	107	40	j	j	NOUN
ejpam-6659	107	41	=	=	PROPN
ejpam-6659	107	42	ω+1	ω+1	SYM
ejpam-6659	107	43	α(τϱ	α(τϱ	NUM
ejpam-6659	107	44	,	,	PUNCT
ejpam-6659	107	45	τϱ	τϱ	NOUN
ejpam-6659	107	46	,	,	PUNCT
ejpam-6659	107	47	τj)α(τi	τj)α(τi	PRON
ejpam-6659	107	48	,	,	PUNCT
ejpam-6659	107	49	τi	τi	NOUN
ejpam-6659	107	50	,	,	PUNCT
ejpam-6659	107	51	τi+1)s(τi	τi+1)s(τi	NOUN
ejpam-6659	107	52	,	,	PUNCT
ejpam-6659	107	53	τi	τi	NOUN
ejpam-6659	107	54	,	,	PUNCT
ejpam-6659	107	55	τi+1	τi+1	PROPN
ejpam-6659	107	56	)	)	PUNCT
ejpam-6659	107	57	+	+	NUM
ejpam-6659	108	1	2ϱ−ω−1	2ϱ−ω−1	NUM
ejpam-6659	108	2	ϱ−1∏	ϱ−1∏	VERB
ejpam-6659	108	3	k	k	NOUN
ejpam-6659	108	4	=	=	PROPN
ejpam-6659	108	5	ω+1	ω+1	SYM
ejpam-6659	108	6	α(τϱ	α(τϱ	NUM
ejpam-6659	108	7	,	,	PUNCT
ejpam-6659	108	8	τϱ	τϱ	PROPN
ejpam-6659	108	9	,	,	PUNCT
ejpam-6659	108	10	τk)s(τϱ	τk)s(τϱ	NUM
ejpam-6659	108	11	,	,	PUNCT
ejpam-6659	108	12	τϱ	τϱ	PROPN
ejpam-6659	108	13	,	,	PUNCT
ejpam-6659	108	14	τϱ−1	τϱ−1	NOUN
ejpam-6659	108	15	)	)	PUNCT
ejpam-6659	108	16	≾	≾	PROPN
ejpam-6659	108	17	α(τω	α(τω	NUM
ejpam-6659	108	18	,	,	PUNCT
ejpam-6659	108	19	τω	τω	INTJ
ejpam-6659	108	20	,	,	PUNCT
ejpam-6659	108	21	τω+1)(θ	τω+1)(θ	PROPN
ejpam-6659	108	22	ωs(τ0	ωs(τ0	PROPN
ejpam-6659	108	23	,	,	PUNCT
ejpam-6659	108	24	τ0	τ0	NOUN
ejpam-6659	108	25	,	,	PUNCT
ejpam-6659	108	26	τ1	τ1	NOUN
ejpam-6659	108	27	)	)	PUNCT
ejpam-6659	108	28	)	)	PUNCT
ejpam-6659	109	1	+	+	CCONJ
ejpam-6659	109	2	ϱ−1∑	ϱ−1∑	NUM
ejpam-6659	109	3	i	i	NOUN
ejpam-6659	109	4	=	=	NOUN
ejpam-6659	109	5	ω+1	ω+1	NUM
ejpam-6659	109	6	2i−ω	2i−ω	NOUN
ejpam-6659	109	7	i∏	i∏	VERB
ejpam-6659	109	8	j	j	NOUN
ejpam-6659	109	9	=	=	PROPN
ejpam-6659	109	10	ω+1	ω+1	SYM
ejpam-6659	109	11	α(τϱ	α(τϱ	NUM
ejpam-6659	109	12	,	,	PUNCT
ejpam-6659	109	13	τϱ	τϱ	NOUN
ejpam-6659	109	14	,	,	PUNCT
ejpam-6659	109	15	τj)α(τi	τj)α(τi	PRON
ejpam-6659	109	16	,	,	PUNCT
ejpam-6659	109	17	τi	τi	ADP
ejpam-6659	109	18	,	,	PUNCT
ejpam-6659	109	19	τi+1)(θ	τi+1)(θ	PROPN
ejpam-6659	109	20	is(τ0	is(τ0	PROPN
ejpam-6659	109	21	,	,	PUNCT
ejpam-6659	109	22	τ0	τ0	NOUN
ejpam-6659	109	23	,	,	PUNCT
ejpam-6659	109	24	τ1	τ1	NOUN
ejpam-6659	109	25	)	)	PUNCT
ejpam-6659	109	26	)	)	PUNCT
ejpam-6659	109	27	.	.	PUNCT
ejpam-6659	110	1	h.	h.	PROPN
ejpam-6659	110	2	qawaqneh	qawaqneh	PROPN
ejpam-6659	110	3	et	et	PROPN
ejpam-6659	110	4	al	al	PROPN
ejpam-6659	110	5	.	.	PUNCT
ejpam-6659	110	6	/	/	SYM
ejpam-6659	110	7	eur	eur	PROPN
ejpam-6659	110	8	.	.	PUNCT
ejpam-6659	111	1	j.	j.	PROPN
ejpam-6659	111	2	pure	pure	PROPN
ejpam-6659	111	3	appl	appl	PROPN
ejpam-6659	111	4	.	.	PROPN
ejpam-6659	111	5	math	math	PROPN
ejpam-6659	111	6	,	,	PUNCT
ejpam-6659	111	7	18	18	NUM
ejpam-6659	111	8	(	(	PUNCT
ejpam-6659	111	9	3	3	NUM
ejpam-6659	111	10	)	)	PUNCT
ejpam-6659	111	11	(	(	PUNCT
ejpam-6659	111	12	2025	2025	NUM
ejpam-6659	111	13	)	)	PUNCT
ejpam-6659	111	14	,	,	PUNCT
ejpam-6659	111	15	6659	6659	NUM
ejpam-6659	111	16	6	6	NUM
ejpam-6659	111	17	of	of	ADP
ejpam-6659	111	18	16	16	NUM
ejpam-6659	111	19	now	now	ADV
ejpam-6659	111	20	,	,	PUNCT
ejpam-6659	111	21	consider	consider	VERB
ejpam-6659	111	22	the	the	DET
ejpam-6659	111	23	series	series	NOUN
ejpam-6659	111	24	sϱ	sϱ	PROPN
ejpam-6659	111	25	=	=	PUNCT
ejpam-6659	111	26	∑ϱ−1	∑ϱ−1	NOUN
ejpam-6659	112	1	i	i	PROPN
ejpam-6659	112	2	=	=	NOUN
ejpam-6659	112	3	ω	ω	NUM
ejpam-6659	112	4	2i−ω	2i−ω	NOUN
ejpam-6659	112	5	∏i	∏i	PROPN
ejpam-6659	112	6	j	j	X
ejpam-6659	112	7	=	=	PROPN
ejpam-6659	112	8	ω	ω	PROPN
ejpam-6659	112	9	α(τϱ	α(τϱ	PROPN
ejpam-6659	112	10	,	,	PUNCT
ejpam-6659	112	11	τϱ	τϱ	NOUN
ejpam-6659	112	12	,	,	PUNCT
ejpam-6659	112	13	τj)α(τi	τj)α(τi	PRON
ejpam-6659	112	14	,	,	PUNCT
ejpam-6659	112	15	τi	τi	ADP
ejpam-6659	112	16	,	,	PUNCT
ejpam-6659	112	17	τi+1)(θ	τi+1)(θ	PROPN
ejpam-6659	112	18	i	i	NOUN
ejpam-6659	112	19	)	)	PUNCT
ejpam-6659	112	20	.	.	PUNCT
ejpam-6659	113	1	this	this	DET
ejpam-6659	113	2	series	series	NOUN
ejpam-6659	113	3	converges	converge	VERB
ejpam-6659	113	4	by	by	ADP
ejpam-6659	113	5	ratio	ratio	NOUN
ejpam-6659	113	6	test	test	NOUN
ejpam-6659	113	7	under	under	ADP
ejpam-6659	113	8	the	the	DET
ejpam-6659	113	9	condition	condition	NOUN
ejpam-6659	113	10	:	:	PUNCT
ejpam-6659	113	11	supϱ≥i	supϱ≥i	PROPN
ejpam-6659	113	12	lim	lim	PROPN
ejpam-6659	113	13	i→+∞	i→+∞	PROPN
ejpam-6659	113	14	α(τi+1,τi+1,τi+2).α(τϱ,τϱ,τi+1	α(τi+1,τi+1,τi+2).α(τϱ,τϱ,τi+1	PROPN
ejpam-6659	113	15	)	)	PUNCT
ejpam-6659	113	16	α(τi	α(τi	NOUN
ejpam-6659	113	17	,	,	PUNCT
ejpam-6659	113	18	τi	τi	ADP
ejpam-6659	113	19	,	,	PUNCT
ejpam-6659	113	20	τi+1	τi+1	X
ejpam-6659	113	21	)	)	PUNCT
ejpam-6659	113	22	<	<	X
ejpam-6659	113	23	1	1	NUM
ejpam-6659	113	24	2θ	2θ	NUM
ejpam-6659	113	25	.	.	PUNCT
ejpam-6659	114	1	letting	let	VERB
ejpam-6659	114	2	ϱ	ϱ	ADP
ejpam-6659	114	3	,	,	PUNCT
ejpam-6659	114	4	ω	ω	PROPN
ejpam-6659	114	5	→	→	SYM
ejpam-6659	114	6	+	+	PROPN
ejpam-6659	114	7	∞	∞	PROPN
ejpam-6659	114	8	,	,	PUNCT
ejpam-6659	114	9	we	we	PRON
ejpam-6659	114	10	obtain	obtain	VERB
ejpam-6659	114	11	lim	lim	PROPN
ejpam-6659	114	12	ϱ,ω→+∞	ϱ,ω→+∞	VERB
ejpam-6659	114	13	s(τϱ	s(τϱ	ADV
ejpam-6659	114	14	,	,	PUNCT
ejpam-6659	114	15	τϱ	τϱ	PROPN
ejpam-6659	114	16	,	,	PUNCT
ejpam-6659	114	17	τω	τω	INTJ
ejpam-6659	114	18	)	)	PUNCT
ejpam-6659	114	19	=	=	SYM
ejpam-6659	114	20	0	0	X
ejpam-6659	114	21	.	.	PUNCT
ejpam-6659	115	1	by	by	ADP
ejpam-6659	115	2	cv	cv	PROPN
ejpam-6659	115	3	cs3	cs3	PROPN
ejpam-6659	115	4	,	,	PUNCT
ejpam-6659	115	5	we	we	PRON
ejpam-6659	115	6	have	have	VERB
ejpam-6659	115	7	s(τω	s(τω	PROPN
ejpam-6659	115	8	,	,	PUNCT
ejpam-6659	115	9	τϱ	τϱ	PROPN
ejpam-6659	115	10	,	,	PUNCT
ejpam-6659	115	11	τl	τl	ADJ
ejpam-6659	115	12	)	)	PUNCT
ejpam-6659	115	13	≾	≾	PROPN
ejpam-6659	115	14	α(τϱ	α(τϱ	PROPN
ejpam-6659	115	15	,	,	PUNCT
ejpam-6659	115	16	τϱ	τϱ	PROPN
ejpam-6659	115	17	,	,	PUNCT
ejpam-6659	115	18	τω)s(τϱ	τω)s(τϱ	PRON
ejpam-6659	115	19	,	,	PUNCT
ejpam-6659	115	20	τϱ	τϱ	PROPN
ejpam-6659	115	21	,	,	PUNCT
ejpam-6659	115	22	τω	τω	INTJ
ejpam-6659	115	23	)	)	PUNCT
ejpam-6659	115	24	+	+	NUM
ejpam-6659	115	25	α(τl	α(τl	NOUN
ejpam-6659	115	26	,	,	PUNCT
ejpam-6659	115	27	τl	τl	NOUN
ejpam-6659	115	28	,	,	PUNCT
ejpam-6659	115	29	τω)s(τl	τω)s(τl	NOUN
ejpam-6659	115	30	,	,	PUNCT
ejpam-6659	115	31	τl	τl	ADV
ejpam-6659	115	32	,	,	PUNCT
ejpam-6659	115	33	τω	τω	INTJ
ejpam-6659	115	34	)	)	PUNCT
ejpam-6659	115	35	for	for	ADP
ejpam-6659	115	36	all	all	DET
ejpam-6659	115	37	ω	ω	PROPN
ejpam-6659	115	38	,	,	PUNCT
ejpam-6659	115	39	ϱ	ϱ	NOUN
ejpam-6659	115	40	,	,	PUNCT
ejpam-6659	115	41	l	l	PROPN
ejpam-6659	115	42	∈	∈	PROPN
ejpam-6659	115	43	n.	n.	PROPN
ejpam-6659	115	44	thus	thus	ADV
ejpam-6659	115	45	,	,	PUNCT
ejpam-6659	115	46	|s(τω	|s(τω	PROPN
ejpam-6659	115	47	,	,	PUNCT
ejpam-6659	115	48	τϱ	τϱ	X
ejpam-6659	115	49	,	,	PUNCT
ejpam-6659	115	50	τl)|	τl)|	PUNCT
ejpam-6659	115	51	≤	≤	NUM
ejpam-6659	115	52	α(τϱ	α(τϱ	NUM
ejpam-6659	115	53	,	,	PUNCT
ejpam-6659	115	54	τϱ	τϱ	PROPN
ejpam-6659	115	55	,	,	PUNCT
ejpam-6659	115	56	τω)|s(τϱ	τω)|s(τϱ	PROPN
ejpam-6659	115	57	,	,	PUNCT
ejpam-6659	115	58	τϱ	τϱ	PROPN
ejpam-6659	115	59	,	,	PUNCT
ejpam-6659	115	60	τω)|+	τω)|+	VERB
ejpam-6659	115	61	α(τl	α(τl	NUM
ejpam-6659	115	62	,	,	PUNCT
ejpam-6659	115	63	τl	τl	NOUN
ejpam-6659	115	64	,	,	PUNCT
ejpam-6659	115	65	τω)|s(τl	τω)|s(τl	NOUN
ejpam-6659	115	66	,	,	PUNCT
ejpam-6659	115	67	τl	τl	ADJ
ejpam-6659	115	68	,	,	PUNCT
ejpam-6659	115	69	τω)|	τω)|	PRON
ejpam-6659	115	70	.	.	PUNCT
ejpam-6659	116	1	taking	take	VERB
ejpam-6659	116	2	limit	limit	NOUN
ejpam-6659	116	3	ω	ω	PROPN
ejpam-6659	116	4	,	,	PUNCT
ejpam-6659	116	5	ϱ	ϱ	ADP
ejpam-6659	116	6	,	,	PUNCT
ejpam-6659	116	7	l	l	NOUN
ejpam-6659	116	8	→	→	SYM
ejpam-6659	116	9	+	+	NOUN
ejpam-6659	116	10	∞	∞	PROPN
ejpam-6659	116	11	,	,	PUNCT
ejpam-6659	116	12	we	we	PRON
ejpam-6659	116	13	obtain	obtain	VERB
ejpam-6659	116	14	|s(τω	|s(τω	PROPN
ejpam-6659	116	15	,	,	PUNCT
ejpam-6659	116	16	τϱ	τϱ	X
ejpam-6659	116	17	,	,	PUNCT
ejpam-6659	116	18	τl)|	τl)|	PUNCT
ejpam-6659	116	19	→	→	SYM
ejpam-6659	116	20	0	0	X
ejpam-6659	116	21	.	.	PUNCT
ejpam-6659	117	1	so	so	ADV
ejpam-6659	117	2	{	{	PUNCT
ejpam-6659	117	3	τω	τω	INTJ
ejpam-6659	117	4	}	}	PUNCT
ejpam-6659	117	5	is	be	AUX
ejpam-6659	117	6	a	a	DET
ejpam-6659	117	7	cvcs	cvcs	ADJ
ejpam-6659	117	8	-	-	PUNCT
ejpam-6659	117	9	cauchy	cauchy	ADJ
ejpam-6659	117	10	sequence	sequence	NOUN
ejpam-6659	117	11	.	.	PUNCT
ejpam-6659	118	1	completeness	completeness	NOUN
ejpam-6659	118	2	of	of	ADP
ejpam-6659	118	3	(	(	PUNCT
ejpam-6659	118	4	γ	γ	PROPN
ejpam-6659	118	5	,	,	PUNCT
ejpam-6659	118	6	s	s	PROPN
ejpam-6659	118	7	,	,	PUNCT
ejpam-6659	118	8	α	α	NOUN
ejpam-6659	118	9	)	)	PUNCT
ejpam-6659	118	10	gives	give	VERB
ejpam-6659	118	11	us	we	PRON
ejpam-6659	118	12	that	that	SCONJ
ejpam-6659	118	13	there	there	PRON
ejpam-6659	118	14	is	be	VERB
ejpam-6659	118	15	an	an	DET
ejpam-6659	118	16	element	element	ADJ
ejpam-6659	118	17	ς∗	ς∗	NOUN
ejpam-6659	118	18	∈	∈	PROPN
ejpam-6659	118	19	γ	γ	NOUN
ejpam-6659	118	20	such	such	ADJ
ejpam-6659	118	21	that	that	SCONJ
ejpam-6659	118	22	{	{	PUNCT
ejpam-6659	118	23	τω	τω	INTJ
ejpam-6659	118	24	}	}	PUNCT
ejpam-6659	118	25	is	be	AUX
ejpam-6659	118	26	cvcs	cvcs	ADJ
ejpam-6659	118	27	-	-	PUNCT
ejpam-6659	118	28	convergent	convergent	NOUN
ejpam-6659	118	29	to	to	ADP
ejpam-6659	118	30	ς∗.	ς∗.	PROPN
ejpam-6659	118	31	now	now	ADV
ejpam-6659	118	32	,	,	PUNCT
ejpam-6659	118	33	we	we	PRON
ejpam-6659	118	34	’ll	’ll	AUX
ejpam-6659	118	35	prove	prove	VERB
ejpam-6659	118	36	that	that	SCONJ
ejpam-6659	118	37	f(ς∗	f(ς∗	VERB
ejpam-6659	118	38	)	)	PUNCT
ejpam-6659	118	39	=	=	SYM
ejpam-6659	118	40	ς∗.	ς∗.	NOUN
ejpam-6659	118	41	consider	consider	VERB
ejpam-6659	118	42	,	,	PUNCT
ejpam-6659	118	43	s(τω+1	s(τω+1	ADV
ejpam-6659	118	44	,	,	PUNCT
ejpam-6659	118	45	τω+1	τω+1	ADP
ejpam-6659	118	46	,	,	PUNCT
ejpam-6659	118	47	f(ς	f(ς	PROPN
ejpam-6659	118	48	∗	∗	NOUN
ejpam-6659	118	49	)	)	PUNCT
ejpam-6659	118	50	)	)	PUNCT
ejpam-6659	119	1	≾	≾	PROPN
ejpam-6659	119	2	θs(τω	θs(τω	PROPN
ejpam-6659	119	3	,	,	PUNCT
ejpam-6659	119	4	τω	τω	INTJ
ejpam-6659	119	5	,	,	PUNCT
ejpam-6659	119	6	ς	ς	PROPN
ejpam-6659	119	7	∗	∗	NOUN
ejpam-6659	119	8	)	)	PUNCT
ejpam-6659	119	9	,	,	PUNCT
ejpam-6659	119	10	that	that	ADV
ejpam-6659	119	11	is	is	ADV
ejpam-6659	119	12	,	,	PUNCT
ejpam-6659	119	13	|s(τω+1	|s(τω+1	NOUN
ejpam-6659	119	14	,	,	PUNCT
ejpam-6659	119	15	τω+1	τω+1	PROPN
ejpam-6659	119	16	,	,	PUNCT
ejpam-6659	120	1	f(ς	f(ς	PROPN
ejpam-6659	120	2	∗))|	∗))|	PROPN
ejpam-6659	120	3	≤	≤	PROPN
ejpam-6659	120	4	θ|s(τω	θ|s(τω	PROPN
ejpam-6659	120	5	,	,	PUNCT
ejpam-6659	120	6	τω	τω	INTJ
ejpam-6659	120	7	,	,	PUNCT
ejpam-6659	120	8	ς∗)|	ς∗)|	PROPN
ejpam-6659	120	9	.	.	PUNCT
ejpam-6659	121	1	letting	let	VERB
ejpam-6659	121	2	ω	ω	X
ejpam-6659	121	3	→	→	SYM
ejpam-6659	121	4	+	+	PROPN
ejpam-6659	121	5	∞	∞	PROPN
ejpam-6659	121	6	,	,	PUNCT
ejpam-6659	121	7	we	we	PRON
ejpam-6659	121	8	obtain	obtain	VERB
ejpam-6659	121	9	f(ς∗	f(ς∗	PRON
ejpam-6659	121	10	)	)	PUNCT
ejpam-6659	121	11	=	=	SYM
ejpam-6659	121	12	ς∗.	ς∗.	NOUN
ejpam-6659	121	13	now	now	ADV
ejpam-6659	121	14	towards	towards	ADP
ejpam-6659	121	15	the	the	DET
ejpam-6659	121	16	end	end	NOUN
ejpam-6659	121	17	,	,	PUNCT
ejpam-6659	121	18	the	the	DET
ejpam-6659	121	19	uniqueness	uniqueness	NOUN
ejpam-6659	121	20	will	will	AUX
ejpam-6659	121	21	be	be	AUX
ejpam-6659	121	22	proved	prove	VERB
ejpam-6659	121	23	.	.	PUNCT
ejpam-6659	122	1	let	let	VERB
ejpam-6659	122	2	τ∗	τ∗	NOUN
ejpam-6659	122	3	be	be	AUX
ejpam-6659	122	4	some	some	DET
ejpam-6659	122	5	other	other	ADJ
ejpam-6659	122	6	fixed	fix	VERB
ejpam-6659	122	7	point	point	NOUN
ejpam-6659	122	8	of	of	ADP
ejpam-6659	122	9	f	f	PROPN
ejpam-6659	122	10	.	.	PUNCT
ejpam-6659	123	1	consider	consider	VERB
ejpam-6659	123	2	s(ς∗	s(ς∗	ADJ
ejpam-6659	123	3	,	,	PUNCT
ejpam-6659	123	4	ς∗	ς∗	ADJ
ejpam-6659	123	5	,	,	PUNCT
ejpam-6659	123	6	τ∗	τ∗	ADJ
ejpam-6659	123	7	)	)	PUNCT
ejpam-6659	123	8	=	=	SYM
ejpam-6659	123	9	s(f(ς∗	s(f(ς∗	PROPN
ejpam-6659	123	10	)	)	PUNCT
ejpam-6659	123	11	,	,	PUNCT
ejpam-6659	123	12	f(ς∗	f(ς∗	NOUN
ejpam-6659	123	13	)	)	PUNCT
ejpam-6659	123	14	,	,	PUNCT
ejpam-6659	123	15	f(τ∗	f(τ∗	NOUN
ejpam-6659	123	16	)	)	PUNCT
ejpam-6659	123	17	)	)	PUNCT
ejpam-6659	124	1	≾	≾	PROPN
ejpam-6659	124	2	θs(ς∗	θs(ς∗	NOUN
ejpam-6659	124	3	,	,	PUNCT
ejpam-6659	124	4	ς∗	ς∗	ADJ
ejpam-6659	124	5	,	,	PUNCT
ejpam-6659	124	6	τ∗	τ∗	NOUN
ejpam-6659	124	7	)	)	PUNCT
ejpam-6659	124	8	,	,	PUNCT
ejpam-6659	124	9	that	that	ADV
ejpam-6659	124	10	is	is	ADV
ejpam-6659	124	11	,	,	PUNCT
ejpam-6659	124	12	|s(f(ς∗	|s(f(ς∗	X
ejpam-6659	124	13	)	)	PUNCT
ejpam-6659	124	14	,	,	PUNCT
ejpam-6659	124	15	f(ς∗	f(ς∗	NOUN
ejpam-6659	124	16	)	)	PUNCT
ejpam-6659	124	17	,	,	PUNCT
ejpam-6659	124	18	f(τ∗))|	f(τ∗))|	VERB
ejpam-6659	124	19	≤	≤	PUNCT
ejpam-6659	124	20	θ|s(ς∗	θ|s(ς∗	NOUN
ejpam-6659	124	21	,	,	PUNCT
ejpam-6659	124	22	ς∗	ς∗	NOUN
ejpam-6659	124	23	,	,	PUNCT
ejpam-6659	124	24	τ∗)|	τ∗)|	PROPN
ejpam-6659	124	25	.	.	PUNCT
ejpam-6659	125	1	this	this	PRON
ejpam-6659	125	2	implies	imply	VERB
ejpam-6659	125	3	that	that	SCONJ
ejpam-6659	125	4	|s(ς∗	|s(ς∗	ADJ
ejpam-6659	125	5	,	,	PUNCT
ejpam-6659	125	6	ς∗	ς∗	NOUN
ejpam-6659	125	7	,	,	PUNCT
ejpam-6659	125	8	τ∗)|	τ∗)|	ADJ
ejpam-6659	125	9	≤	≤	NUM
ejpam-6659	125	10	0	0	NUM
ejpam-6659	125	11	.	.	PUNCT
ejpam-6659	126	1	thus	thus	ADV
ejpam-6659	126	2	,	,	PUNCT
ejpam-6659	126	3	ς∗	ς∗	PROPN
ejpam-6659	126	4	=	=	SYM
ejpam-6659	126	5	τ∗	τ∗	NOUN
ejpam-6659	126	6	,	,	PUNCT
ejpam-6659	126	7	that	that	ADV
ejpam-6659	126	8	is	is	ADV
ejpam-6659	126	9	,	,	PUNCT
ejpam-6659	126	10	τ∗	τ∗	PROPN
ejpam-6659	126	11	is	be	AUX
ejpam-6659	126	12	the	the	DET
ejpam-6659	126	13	unique	unique	ADJ
ejpam-6659	126	14	fixed	fix	VERB
ejpam-6659	126	15	point	point	NOUN
ejpam-6659	126	16	of	of	ADP
ejpam-6659	126	17	f	f	PROPN
ejpam-6659	126	18	.	.	PUNCT
ejpam-6659	127	1	example	example	NOUN
ejpam-6659	128	1	1	1	NUM
ejpam-6659	128	2	.	.	X
ejpam-6659	128	3	consider	consider	VERB
ejpam-6659	128	4	the	the	DET
ejpam-6659	128	5	complex	complex	ADJ
ejpam-6659	128	6	plane	plane	NOUN
ejpam-6659	128	7	γ	γ	NOUN
ejpam-6659	128	8	=	=	SYM
ejpam-6659	128	9	c	c	PROPN
ejpam-6659	128	10	equipped	equip	VERB
ejpam-6659	128	11	with	with	ADP
ejpam-6659	128	12	a	a	DET
ejpam-6659	128	13	controlled	control	VERB
ejpam-6659	128	14	function	function	NOUN
ejpam-6659	128	15	α	α	NOUN
ejpam-6659	128	16	:	:	PUNCT
ejpam-6659	128	17	γ3	γ3	NOUN
ejpam-6659	128	18	→	→	PUNCT
ejpam-6659	129	1	[	[	X
ejpam-6659	129	2	1,+∞	1,+∞	NUM
ejpam-6659	129	3	)	)	PUNCT
ejpam-6659	129	4	defined	define	VERB
ejpam-6659	129	5	by	by	ADP
ejpam-6659	129	6	α(τ	α(τ	NUM
ejpam-6659	129	7	,	,	PUNCT
ejpam-6659	129	8	ς,ϖ	ς,ϖ	NUM
ejpam-6659	129	9	)	)	PUNCT
ejpam-6659	129	10	=	=	SYM
ejpam-6659	129	11	1	1	NUM
ejpam-6659	129	12	+	+	CCONJ
ejpam-6659	129	13	|τ	|τ	ADJ
ejpam-6659	129	14	|+	|+	NOUN
ejpam-6659	129	15	|ς|+	|ς|+	NOUN
ejpam-6659	129	16	|ϖ|	|ϖ|	VERB
ejpam-6659	129	17	1	1	NUM
ejpam-6659	129	18	+	+	CCONJ
ejpam-6659	129	19	|τ	|τ	ADJ
ejpam-6659	129	20	|+	|+	NOUN
ejpam-6659	130	1	|ς|+	|ς|+	NOUN
ejpam-6659	130	2	|ϖ|	|ϖ|	NUM
ejpam-6659	130	3	,	,	PUNCT
ejpam-6659	130	4	and	and	CCONJ
ejpam-6659	130	5	a	a	DET
ejpam-6659	130	6	complex	complex	ADV
ejpam-6659	130	7	-	-	PUNCT
ejpam-6659	130	8	valued	value	VERB
ejpam-6659	130	9	s	s	NOUN
ejpam-6659	130	10	-	-	ADJ
ejpam-6659	130	11	metric	metric	ADJ
ejpam-6659	130	12	s	s	NOUN
ejpam-6659	130	13	:	:	PUNCT
ejpam-6659	130	14	γ3	γ3	NOUN
ejpam-6659	130	15	→	→	SYM
ejpam-6659	130	16	c	c	NOUN
ejpam-6659	130	17	given	give	VERB
ejpam-6659	130	18	by	by	ADP
ejpam-6659	130	19	s(τ	s(τ	PROPN
ejpam-6659	130	20	,	,	PUNCT
ejpam-6659	130	21	ς,ϖ	ς,ϖ	NUM
ejpam-6659	130	22	)	)	PUNCT
ejpam-6659	130	23	=	=	SYM
ejpam-6659	130	24	max	max	PROPN
ejpam-6659	130	25	{	{	PUNCT
ejpam-6659	130	26	|τ	|τ	ADJ
ejpam-6659	130	27	−ϖ|	−ϖ|	NOUN
ejpam-6659	130	28	,	,	PUNCT
ejpam-6659	130	29	|ς	|ς	VERB
ejpam-6659	130	30	−ϖ|	−ϖ|	NOUN
ejpam-6659	130	31	,	,	PUNCT
ejpam-6659	130	32	|τ	|τ	ADJ
ejpam-6659	130	33	−	−	PROPN
ejpam-6659	130	34	ς|	ς|	NOUN
ejpam-6659	130	35	2	2	NUM
ejpam-6659	130	36	}	}	PUNCT
ejpam-6659	130	37	.	.	PUNCT
ejpam-6659	131	1	h.	h.	PROPN
ejpam-6659	131	2	qawaqneh	qawaqneh	PROPN
ejpam-6659	131	3	et	et	PROPN
ejpam-6659	131	4	al	al	PROPN
ejpam-6659	131	5	.	.	PUNCT
ejpam-6659	131	6	/	/	SYM
ejpam-6659	131	7	eur	eur	PROPN
ejpam-6659	131	8	.	.	PUNCT
ejpam-6659	132	1	j.	j.	PROPN
ejpam-6659	132	2	pure	pure	PROPN
ejpam-6659	132	3	appl	appl	PROPN
ejpam-6659	132	4	.	.	PROPN
ejpam-6659	132	5	math	math	PROPN
ejpam-6659	132	6	,	,	PUNCT
ejpam-6659	132	7	18	18	NUM
ejpam-6659	132	8	(	(	PUNCT
ejpam-6659	132	9	3	3	NUM
ejpam-6659	132	10	)	)	PUNCT
ejpam-6659	132	11	(	(	PUNCT
ejpam-6659	132	12	2025	2025	NUM
ejpam-6659	132	13	)	)	PUNCT
ejpam-6659	132	14	,	,	PUNCT
ejpam-6659	132	15	6659	6659	NUM
ejpam-6659	132	16	7	7	NUM
ejpam-6659	132	17	of	of	ADP
ejpam-6659	132	18	16	16	NUM
ejpam-6659	132	19	then	then	ADV
ejpam-6659	132	20	(	(	PUNCT
ejpam-6659	132	21	γ	γ	X
ejpam-6659	132	22	,	,	PUNCT
ejpam-6659	132	23	s	s	PROPN
ejpam-6659	132	24	,	,	PUNCT
ejpam-6659	132	25	α	α	NOUN
ejpam-6659	132	26	)	)	PUNCT
ejpam-6659	132	27	is	be	AUX
ejpam-6659	132	28	a	a	DET
ejpam-6659	132	29	complete	complete	ADJ
ejpam-6659	132	30	cvcs	cvcs	ADJ
ejpam-6659	132	31	-	-	PUNCT
ejpam-6659	132	32	metric	metric	ADJ
ejpam-6659	132	33	space	space	NOUN
ejpam-6659	132	34	.	.	PUNCT
ejpam-6659	133	1	define	define	VERB
ejpam-6659	133	2	the	the	DET
ejpam-6659	133	3	mapping	mapping	NOUN
ejpam-6659	133	4	f	f	NOUN
ejpam-6659	133	5	:	:	PUNCT
ejpam-6659	133	6	γ	γ	X
ejpam-6659	133	7	→	→	SYM
ejpam-6659	133	8	γ	γ	X
ejpam-6659	133	9	as	as	ADP
ejpam-6659	133	10	f(τ	f(τ	NOUN
ejpam-6659	133	11	)	)	PUNCT
ejpam-6659	133	12	=	=	PUNCT
ejpam-6659	134	1	τ	τ	X
ejpam-6659	134	2	5	5	NUM
ejpam-6659	134	3	.	.	PUNCT
ejpam-6659	135	1	now	now	ADV
ejpam-6659	135	2	,	,	PUNCT
ejpam-6659	135	3	for	for	ADP
ejpam-6659	135	4	any	any	DET
ejpam-6659	135	5	τ	τ	PROPN
ejpam-6659	135	6	,	,	PUNCT
ejpam-6659	135	7	ς	ς	PROPN
ejpam-6659	135	8	∈	∈	PROPN
ejpam-6659	135	9	γ	γ	X
ejpam-6659	135	10	,	,	PUNCT
ejpam-6659	135	11	s(fτ	s(fτ	PROPN
ejpam-6659	135	12	,	,	PUNCT
ejpam-6659	135	13	fτ	fτ	NOUN
ejpam-6659	135	14	,	,	PUNCT
ejpam-6659	135	15	fς	fς	NOUN
ejpam-6659	135	16	)	)	PUNCT
ejpam-6659	135	17	=	=	SYM
ejpam-6659	135	18	max	max	PROPN
ejpam-6659	135	19	{	{	PUNCT
ejpam-6659	135	20	∣∣∣τ	∣∣∣τ	NOUN
ejpam-6659	135	21	3	3	NUM
ejpam-6659	135	22	−	−	NOUN
ejpam-6659	135	23	ς	ς	PROPN
ejpam-6659	135	24	3	3	NUM
ejpam-6659	135	25	∣∣∣	∣∣∣	NOUN
ejpam-6659	135	26	,	,	PUNCT
ejpam-6659	135	27	|τ	|τ	ADJ
ejpam-6659	135	28	−	−	PROPN
ejpam-6659	135	29	ς|	ς|	NOUN
ejpam-6659	135	30	2	2	NUM
ejpam-6659	135	31	}	}	PUNCT
ejpam-6659	135	32	=	=	SYM
ejpam-6659	135	33	|τ	|τ	ADJ
ejpam-6659	135	34	−	−	PROPN
ejpam-6659	135	35	ς|	ς|	PROPN
ejpam-6659	135	36	3	3	NUM
ejpam-6659	135	37	≾	≾	PROPN
ejpam-6659	135	38	θs(τ	θs(τ	NUM
ejpam-6659	135	39	,	,	PUNCT
ejpam-6659	135	40	τ	τ	PROPN
ejpam-6659	135	41	,	,	PUNCT
ejpam-6659	135	42	ς	ς	PROPN
ejpam-6659	135	43	)	)	PUNCT
ejpam-6659	135	44	,	,	PUNCT
ejpam-6659	135	45	for	for	ADP
ejpam-6659	135	46	any	any	DET
ejpam-6659	135	47	θ	θ	PROPN
ejpam-6659	135	48	∈	∈	PROPN
ejpam-6659	135	49	(	(	PUNCT
ejpam-6659	135	50	15	15	NUM
ejpam-6659	135	51	,	,	PUNCT
ejpam-6659	135	52	1	1	NUM
ejpam-6659	135	53	)	)	PUNCT
ejpam-6659	135	54	.	.	PUNCT
ejpam-6659	136	1	also	also	ADV
ejpam-6659	136	2	,	,	PUNCT
ejpam-6659	136	3	let	let	VERB
ejpam-6659	136	4	τ0	τ0	NOUN
ejpam-6659	136	5	=	=	SYM
ejpam-6659	136	6	1	1	NUM
ejpam-6659	136	7	and	and	CCONJ
ejpam-6659	136	8	τω	τω	ADJ
ejpam-6659	136	9	=	=	NOUN
ejpam-6659	137	1	fω(τ0	fω(τ0	NOUN
ejpam-6659	137	2	)	)	PUNCT
ejpam-6659	138	1	=	=	SYM
ejpam-6659	138	2	1	1	NUM
ejpam-6659	138	3	5ω	5ω	NOUN
ejpam-6659	138	4	.	.	PUNCT
ejpam-6659	139	1	then	then	ADV
ejpam-6659	139	2	,	,	PUNCT
ejpam-6659	139	3	α(τω	α(τω	NUM
ejpam-6659	139	4	,	,	PUNCT
ejpam-6659	139	5	τω	τω	INTJ
ejpam-6659	139	6	,	,	PUNCT
ejpam-6659	139	7	τω+1	τω+1	NUM
ejpam-6659	139	8	)	)	PUNCT
ejpam-6659	139	9	=	=	SYM
ejpam-6659	140	1	1	1	NUM
ejpam-6659	140	2	+	+	NUM
ejpam-6659	140	3	2	2	NUM
ejpam-6659	140	4	5ω	5ω	NOUN
ejpam-6659	140	5	+	+	CCONJ
ejpam-6659	140	6	1	1	NUM
ejpam-6659	140	7	5ω+1	5ω+1	PROPN
ejpam-6659	140	8	1	1	NUM
ejpam-6659	140	9	+	+	SYM
ejpam-6659	140	10	2	2	NUM
ejpam-6659	140	11	5ω	5ω	NOUN
ejpam-6659	140	12	+	+	CCONJ
ejpam-6659	140	13	1	1	NUM
ejpam-6659	140	14	5ω+1	5ω+1	PROPN
ejpam-6659	140	15	→	→	SYM
ejpam-6659	140	16	1	1	NUM
ejpam-6659	140	17	as	as	ADP
ejpam-6659	140	18	ω	ω	NUM
ejpam-6659	140	19	→	→	SYM
ejpam-6659	140	20	+	+	PROPN
ejpam-6659	140	21	∞	∞	PROPN
ejpam-6659	140	22	,	,	PUNCT
ejpam-6659	140	23	and	and	CCONJ
ejpam-6659	140	24	sup	sup	NOUN
ejpam-6659	140	25	ϱ≥1	ϱ≥1	PROPN
ejpam-6659	140	26	lim	lim	PROPN
ejpam-6659	140	27	ω→+∞	ω→+∞	PROPN
ejpam-6659	140	28	α(τω+1	α(τω+1	PROPN
ejpam-6659	140	29	,	,	PUNCT
ejpam-6659	140	30	τω+1	τω+1	SYM
ejpam-6659	140	31	,	,	PUNCT
ejpam-6659	140	32	τω+2)α(τϱ	τω+2)α(τϱ	PROPN
ejpam-6659	140	33	,	,	PUNCT
ejpam-6659	140	34	τϱ	τϱ	X
ejpam-6659	140	35	,	,	PUNCT
ejpam-6659	140	36	τω+1	τω+1	NUM
ejpam-6659	140	37	)	)	PUNCT
ejpam-6659	140	38	α(τω	α(τω	NUM
ejpam-6659	140	39	,	,	PUNCT
ejpam-6659	140	40	τω	τω	INTJ
ejpam-6659	140	41	,	,	PUNCT
ejpam-6659	140	42	τω+1	τω+1	NUM
ejpam-6659	140	43	)	)	PUNCT
ejpam-6659	140	44	=	=	SYM
ejpam-6659	140	45	1	1	NUM
ejpam-6659	140	46	<	<	SYM
ejpam-6659	140	47	1	1	NUM
ejpam-6659	140	48	2	2	NUM
ejpam-6659	140	49	·	·	SYM
ejpam-6659	140	50	1	1	NUM
ejpam-6659	140	51	3	3	NUM
ejpam-6659	140	52	=	=	SYM
ejpam-6659	140	53	3	3	NUM
ejpam-6659	140	54	2	2	NUM
ejpam-6659	140	55	.	.	PUNCT
ejpam-6659	141	1	thus	thus	ADV
ejpam-6659	141	2	,	,	PUNCT
ejpam-6659	141	3	(	(	PUNCT
ejpam-6659	141	4	2	2	X
ejpam-6659	141	5	)	)	PUNCT
ejpam-6659	141	6	holds	hold	NOUN
ejpam-6659	141	7	and	and	CCONJ
ejpam-6659	141	8	the	the	DET
ejpam-6659	141	9	sequence	sequence	NOUN
ejpam-6659	141	10	{	{	PUNCT
ejpam-6659	141	11	τω	τω	INTJ
ejpam-6659	141	12	}	}	PUNCT
ejpam-6659	141	13	converges	converge	NOUN
ejpam-6659	141	14	to	to	ADP
ejpam-6659	141	15	0	0	NUM
ejpam-6659	141	16	,	,	PUNCT
ejpam-6659	141	17	and	and	CCONJ
ejpam-6659	141	18	f(0	f(0	NOUN
ejpam-6659	141	19	)	)	PUNCT
ejpam-6659	142	1	=	=	SYM
ejpam-6659	142	2	0	0	NUM
ejpam-6659	142	3	is	be	AUX
ejpam-6659	142	4	the	the	DET
ejpam-6659	142	5	unique	unique	ADJ
ejpam-6659	142	6	fixed	fix	VERB
ejpam-6659	142	7	point	point	NOUN
ejpam-6659	142	8	.	.	PUNCT
ejpam-6659	143	1	corollary	corollary	ADJ
ejpam-6659	143	2	1	1	NUM
ejpam-6659	143	3	.	.	PUNCT
ejpam-6659	144	1	let	let	AUX
ejpam-6659	144	2	(	(	PUNCT
ejpam-6659	144	3	γ	γ	X
ejpam-6659	144	4	,	,	PUNCT
ejpam-6659	144	5	s	s	PART
ejpam-6659	144	6	)	)	PUNCT
ejpam-6659	144	7	be	be	AUX
ejpam-6659	144	8	a	a	DET
ejpam-6659	144	9	complete	complete	ADJ
ejpam-6659	144	10	complex	complex	NOUN
ejpam-6659	144	11	valued	value	VERB
ejpam-6659	144	12	s	s	NOUN
ejpam-6659	144	13	-	-	ADJ
ejpam-6659	144	14	metric	metric	ADJ
ejpam-6659	144	15	space	space	NOUN
ejpam-6659	144	16	and	and	CCONJ
ejpam-6659	144	17	f	f	NOUN
ejpam-6659	144	18	:	:	PUNCT
ejpam-6659	144	19	γ	γ	X
ejpam-6659	144	20	→	→	SYM
ejpam-6659	144	21	γ	γ	X
ejpam-6659	144	22	be	be	AUX
ejpam-6659	144	23	a	a	DET
ejpam-6659	144	24	mapping	mapping	NOUN
ejpam-6659	144	25	,	,	PUNCT
ejpam-6659	144	26	such	such	ADJ
ejpam-6659	144	27	that	that	PRON
ejpam-6659	144	28	for	for	ADP
ejpam-6659	144	29	τ	τ	PROPN
ejpam-6659	144	30	,	,	PUNCT
ejpam-6659	144	31	ς	ς	PROPN
ejpam-6659	144	32	∈	∈	PROPN
ejpam-6659	144	33	γ	γ	X
ejpam-6659	144	34	sh(f(τ	sh(f(τ	ADJ
ejpam-6659	144	35	)	)	PUNCT
ejpam-6659	144	36	,	,	PUNCT
ejpam-6659	144	37	f(τ	f(τ	PROPN
ejpam-6659	144	38	)	)	PUNCT
ejpam-6659	144	39	,	,	PUNCT
ejpam-6659	144	40	f(ς	f(ς	PROPN
ejpam-6659	144	41	)	)	PUNCT
ejpam-6659	144	42	)	)	PUNCT
ejpam-6659	145	1	≾	≾	PROPN
ejpam-6659	145	2	θs(τ	θs(τ	NUM
ejpam-6659	145	3	,	,	PUNCT
ejpam-6659	145	4	τ	τ	PROPN
ejpam-6659	145	5	,	,	PUNCT
ejpam-6659	145	6	ς	ς	PROPN
ejpam-6659	145	7	)	)	PUNCT
ejpam-6659	145	8	,	,	PUNCT
ejpam-6659	145	9	where	where	SCONJ
ejpam-6659	145	10	θ	θ	PROPN
ejpam-6659	145	11	∈	∈	PROPN
ejpam-6659	145	12	(	(	PUNCT
ejpam-6659	145	13	0	0	NUM
ejpam-6659	145	14	,	,	PUNCT
ejpam-6659	145	15	1	1	NUM
ejpam-6659	145	16	)	)	PUNCT
ejpam-6659	145	17	.	.	PUNCT
ejpam-6659	146	1	then	then	ADV
ejpam-6659	146	2	,	,	PUNCT
ejpam-6659	146	3	f	f	PROPN
ejpam-6659	146	4	has	have	VERB
ejpam-6659	146	5	a	a	DET
ejpam-6659	146	6	unique	unique	ADJ
ejpam-6659	146	7	fixed	fix	VERB
ejpam-6659	146	8	point	point	NOUN
ejpam-6659	146	9	.	.	PUNCT
ejpam-6659	147	1	proof	proof	NOUN
ejpam-6659	147	2	.	.	PUNCT
ejpam-6659	148	1	the	the	DET
ejpam-6659	148	2	required	require	VERB
ejpam-6659	148	3	result	result	NOUN
ejpam-6659	148	4	is	be	AUX
ejpam-6659	148	5	obtained	obtain	VERB
ejpam-6659	148	6	by	by	ADP
ejpam-6659	148	7	taking	take	VERB
ejpam-6659	148	8	α(τ	α(τ	NUM
ejpam-6659	148	9	,	,	PUNCT
ejpam-6659	148	10	ς,ϖ	ς,ϖ	NUM
ejpam-6659	148	11	)	)	PUNCT
ejpam-6659	148	12	=	=	SYM
ejpam-6659	148	13	1	1	NUM
ejpam-6659	148	14	and	and	CCONJ
ejpam-6659	148	15	following	follow	VERB
ejpam-6659	148	16	the	the	DET
ejpam-6659	148	17	same	same	ADJ
ejpam-6659	148	18	procedures	procedure	NOUN
ejpam-6659	148	19	as	as	ADP
ejpam-6659	148	20	in	in	ADP
ejpam-6659	148	21	the	the	DET
ejpam-6659	148	22	preceding	precede	VERB
ejpam-6659	148	23	theorem	theorem	NOUN
ejpam-6659	148	24	.	.	PUNCT
ejpam-6659	149	1	theorem	theorem	NOUN
ejpam-6659	149	2	3	3	X
ejpam-6659	149	3	.	.	PUNCT
ejpam-6659	150	1	let	let	AUX
ejpam-6659	150	2	(	(	PUNCT
ejpam-6659	150	3	γ	γ	X
ejpam-6659	150	4	,	,	PUNCT
ejpam-6659	150	5	s	s	PROPN
ejpam-6659	150	6	,	,	PUNCT
ejpam-6659	150	7	α	α	NOUN
ejpam-6659	150	8	)	)	PUNCT
ejpam-6659	150	9	be	be	VERB
ejpam-6659	150	10	a	a	DET
ejpam-6659	150	11	complete	complete	ADJ
ejpam-6659	150	12	cvcs	cvcs	ADJ
ejpam-6659	150	13	-	-	PUNCT
ejpam-6659	150	14	metric	metric	ADJ
ejpam-6659	150	15	space	space	NOUN
ejpam-6659	150	16	and	and	CCONJ
ejpam-6659	150	17	f	f	NOUN
ejpam-6659	150	18	:	:	PUNCT
ejpam-6659	150	19	γ	γ	X
ejpam-6659	150	20	→	→	SYM
ejpam-6659	150	21	γ	γ	X
ejpam-6659	150	22	satisfy	satisfy	VERB
ejpam-6659	150	23	the	the	DET
ejpam-6659	150	24	following	following	NOUN
ejpam-6659	150	25	for	for	ADP
ejpam-6659	150	26	every	every	DET
ejpam-6659	150	27	τ	τ	PROPN
ejpam-6659	150	28	,	,	PUNCT
ejpam-6659	150	29	ς	ς	PROPN
ejpam-6659	150	30	∈	∈	PROPN
ejpam-6659	150	31	γ	γ	NOUN
ejpam-6659	150	32	:	:	PUNCT
ejpam-6659	150	33	s(f(τ	s(f(τ	NOUN
ejpam-6659	150	34	)	)	PUNCT
ejpam-6659	150	35	,	,	PUNCT
ejpam-6659	150	36	f(τ	f(τ	PROPN
ejpam-6659	150	37	)	)	PUNCT
ejpam-6659	150	38	,	,	PUNCT
ejpam-6659	150	39	f(ς	f(ς	PROPN
ejpam-6659	150	40	)	)	PUNCT
ejpam-6659	150	41	)	)	PUNCT
ejpam-6659	151	1	≾	≾	PROPN
ejpam-6659	151	2	as(τ	as(τ	PROPN
ejpam-6659	151	3	,	,	PUNCT
ejpam-6659	151	4	τ	τ	PROPN
ejpam-6659	151	5	,	,	PUNCT
ejpam-6659	151	6	f(τ	f(τ	PROPN
ejpam-6659	151	7	)	)	PUNCT
ejpam-6659	151	8	)	)	PUNCT
ejpam-6659	152	1	+	+	CCONJ
ejpam-6659	152	2	bs(ς	bs(ς	NOUN
ejpam-6659	152	3	,	,	PUNCT
ejpam-6659	152	4	ς	ς	PROPN
ejpam-6659	152	5	,	,	PUNCT
ejpam-6659	152	6	f(ς	f(ς	PROPN
ejpam-6659	152	7	)	)	PUNCT
ejpam-6659	152	8	)	)	PUNCT
ejpam-6659	152	9	,	,	PUNCT
ejpam-6659	152	10	(	(	PUNCT
ejpam-6659	152	11	3	3	X
ejpam-6659	152	12	)	)	PUNCT
ejpam-6659	152	13	where	where	SCONJ
ejpam-6659	152	14	a	a	DET
ejpam-6659	152	15	,	,	PUNCT
ejpam-6659	152	16	b	b	NOUN
ejpam-6659	152	17	∈	∈	PROPN
ejpam-6659	152	18	(	(	PUNCT
ejpam-6659	152	19	0	0	NUM
ejpam-6659	152	20	,	,	PUNCT
ejpam-6659	152	21	1	1	NUM
ejpam-6659	152	22	)	)	PUNCT
ejpam-6659	152	23	with	with	ADP
ejpam-6659	152	24	a	a	DET
ejpam-6659	152	25	+	+	NOUN
ejpam-6659	152	26	b	b	NOUN
ejpam-6659	152	27	<	<	X
ejpam-6659	152	28	1	1	NUM
ejpam-6659	152	29	.	.	PUNCT
ejpam-6659	152	30	for	for	ADP
ejpam-6659	152	31	τ0	τ0	NOUN
ejpam-6659	152	32	∈	∈	PROPN
ejpam-6659	152	33	γ	γ	X
ejpam-6659	152	34	,	,	PUNCT
ejpam-6659	152	35	choose	choose	VERB
ejpam-6659	152	36	a	a	DET
ejpam-6659	152	37	sequence	sequence	NOUN
ejpam-6659	152	38	τω	τω	PRON
ejpam-6659	152	39	=	=	NOUN
ejpam-6659	152	40	f(τω−1	f(τω−1	NUM
ejpam-6659	152	41	)	)	PUNCT
ejpam-6659	152	42	,	,	PUNCT
ejpam-6659	152	43	ω	ω	PROPN
ejpam-6659	152	44	∈	∈	PROPN
ejpam-6659	152	45	n.	n.	NOUN
ejpam-6659	152	46	suppose	suppose	VERB
ejpam-6659	152	47	that	that	SCONJ
ejpam-6659	152	48	sup	sup	PROPN
ejpam-6659	152	49	ϱ≥1	ϱ≥1	PROPN
ejpam-6659	152	50	lim	lim	PROPN
ejpam-6659	152	51	i→+∞	i→+∞	PROPN
ejpam-6659	152	52	α(τi+1	α(τi+1	PROPN
ejpam-6659	152	53	,	,	PUNCT
ejpam-6659	152	54	τi+1	τi+1	X
ejpam-6659	152	55	,	,	PUNCT
ejpam-6659	152	56	τi+2).α(τϱ	τi+2).α(τϱ	NUM
ejpam-6659	152	57	,	,	PUNCT
ejpam-6659	152	58	τϱ	τϱ	X
ejpam-6659	152	59	,	,	PUNCT
ejpam-6659	152	60	τi+1	τi+1	NOUN
ejpam-6659	152	61	)	)	PUNCT
ejpam-6659	152	62	α(τi	α(τi	NOUN
ejpam-6659	152	63	,	,	PUNCT
ejpam-6659	152	64	τi	τi	ADP
ejpam-6659	152	65	,	,	PUNCT
ejpam-6659	152	66	τi+1	τi+1	X
ejpam-6659	152	67	)	)	PUNCT
ejpam-6659	152	68	<	<	X
ejpam-6659	152	69	1−	1−	NUM
ejpam-6659	152	70	b	b	PROPN
ejpam-6659	152	71	2a	2a	NUM
ejpam-6659	152	72	,	,	PUNCT
ejpam-6659	152	73	(	(	PUNCT
ejpam-6659	152	74	4	4	NUM
ejpam-6659	152	75	)	)	PUNCT
ejpam-6659	152	76	and	and	CCONJ
ejpam-6659	152	77	lim	lim	PROPN
ejpam-6659	153	1	ω→+∞	ω→+∞	PROPN
ejpam-6659	153	2	α(τω	α(τω	NUM
ejpam-6659	153	3	,	,	PUNCT
ejpam-6659	153	4	τω	τω	INTJ
ejpam-6659	153	5	,	,	PUNCT
ejpam-6659	153	6	τω+1	τω+1	NUM
ejpam-6659	153	7	)	)	PUNCT
ejpam-6659	153	8	exists	exist	VERB
ejpam-6659	153	9	.	.	PUNCT
ejpam-6659	154	1	then	then	ADV
ejpam-6659	154	2	,	,	PUNCT
ejpam-6659	154	3	f	f	PROPN
ejpam-6659	154	4	admits	admit	VERB
ejpam-6659	154	5	a	a	DET
ejpam-6659	154	6	unique	unique	ADJ
ejpam-6659	154	7	fixed	fix	VERB
ejpam-6659	154	8	point	point	NOUN
ejpam-6659	154	9	.	.	PUNCT
ejpam-6659	155	1	proof	proof	NOUN
ejpam-6659	155	2	.	.	PUNCT
ejpam-6659	156	1	consider	consider	VERB
ejpam-6659	156	2	an	an	DET
ejpam-6659	156	3	arbitrary	arbitrary	ADJ
ejpam-6659	156	4	τ0	τ0	NOUN
ejpam-6659	156	5	∈	∈	PROPN
ejpam-6659	156	6	γ	γ	X
ejpam-6659	156	7	.	.	PROPN
ejpam-6659	156	8	define	define	VERB
ejpam-6659	156	9	a	a	DET
ejpam-6659	156	10	sequence	sequence	NOUN
ejpam-6659	156	11	{	{	PUNCT
ejpam-6659	156	12	τω	τω	INTJ
ejpam-6659	156	13	}	}	PUNCT
ejpam-6659	156	14	in	in	ADP
ejpam-6659	156	15	γ	γ	NOUN
ejpam-6659	156	16	by	by	ADP
ejpam-6659	156	17	τω	τω	X
ejpam-6659	156	18	=	=	NOUN
ejpam-6659	156	19	f(τω−1	f(τω−1	NUM
ejpam-6659	156	20	)	)	PUNCT
ejpam-6659	156	21	=	=	SYM
ejpam-6659	156	22	fω(τ0	fω(τ0	NOUN
ejpam-6659	156	23	)	)	PUNCT
ejpam-6659	156	24	.	.	PUNCT
ejpam-6659	157	1	suppose	suppose	VERB
ejpam-6659	157	2	that	that	SCONJ
ejpam-6659	157	3	τω	τω	DET
ejpam-6659	157	4	̸=	̸=	PROPN
ejpam-6659	157	5	τω+1	τω+1	PUNCT
ejpam-6659	157	6	for	for	ADP
ejpam-6659	157	7	all	all	DET
ejpam-6659	157	8	ω	ω	NOUN
ejpam-6659	157	9	.	.	PUNCT
ejpam-6659	158	1	from	from	ADP
ejpam-6659	158	2	(	(	PUNCT
ejpam-6659	158	3	3	3	NUM
ejpam-6659	158	4	)	)	PUNCT
ejpam-6659	158	5	,	,	PUNCT
ejpam-6659	158	6	we	we	PRON
ejpam-6659	158	7	obtain	obtain	VERB
ejpam-6659	158	8	s(τω	s(τω	PROPN
ejpam-6659	158	9	,	,	PUNCT
ejpam-6659	158	10	τω	τω	INTJ
ejpam-6659	158	11	,	,	PUNCT
ejpam-6659	158	12	τω+1	τω+1	NUM
ejpam-6659	158	13	)	)	PUNCT
ejpam-6659	158	14	≾	≾	NOUN
ejpam-6659	158	15	as(τω−1	as(τω−1	ADJ
ejpam-6659	158	16	,	,	PUNCT
ejpam-6659	158	17	τω−1	τω−1	PROPN
ejpam-6659	158	18	,	,	PUNCT
ejpam-6659	158	19	τω	τω	INTJ
ejpam-6659	158	20	)	)	PUNCT
ejpam-6659	158	21	+	+	CCONJ
ejpam-6659	158	22	bs(τω	bs(τω	PROPN
ejpam-6659	158	23	,	,	PUNCT
ejpam-6659	158	24	τω	τω	INTJ
ejpam-6659	158	25	,	,	PUNCT
ejpam-6659	158	26	τω+1	τω+1	SYM
ejpam-6659	158	27	)	)	PUNCT
ejpam-6659	158	28	that	that	PRON
ejpam-6659	158	29	is	be	AUX
ejpam-6659	158	30	s(τω	s(τω	PROPN
ejpam-6659	158	31	,	,	PUNCT
ejpam-6659	158	32	τω	τω	INTJ
ejpam-6659	158	33	,	,	PUNCT
ejpam-6659	158	34	τω+1	τω+1	NUM
ejpam-6659	158	35	)	)	PUNCT
ejpam-6659	158	36	≾	≾	NOUN
ejpam-6659	158	37	a	a	DET
ejpam-6659	158	38	1−	1−	NUM
ejpam-6659	158	39	b	b	NOUN
ejpam-6659	158	40	s(τω−1	s(τω−1	NOUN
ejpam-6659	158	41	,	,	PUNCT
ejpam-6659	158	42	τω−1	τω−1	PROPN
ejpam-6659	158	43	,	,	PUNCT
ejpam-6659	158	44	τω	τω	PROPN
ejpam-6659	158	45	)	)	PUNCT
ejpam-6659	158	46	h.	h.	PROPN
ejpam-6659	158	47	qawaqneh	qawaqneh	PROPN
ejpam-6659	158	48	et	et	PROPN
ejpam-6659	158	49	al	al	PROPN
ejpam-6659	158	50	.	.	PUNCT
ejpam-6659	158	51	/	/	SYM
ejpam-6659	158	52	eur	eur	PROPN
ejpam-6659	158	53	.	.	PUNCT
ejpam-6659	159	1	j.	j.	PROPN
ejpam-6659	159	2	pure	pure	PROPN
ejpam-6659	159	3	appl	appl	PROPN
ejpam-6659	159	4	.	.	PROPN
ejpam-6659	159	5	math	math	PROPN
ejpam-6659	159	6	,	,	PUNCT
ejpam-6659	159	7	18	18	NUM
ejpam-6659	159	8	(	(	PUNCT
ejpam-6659	159	9	3	3	NUM
ejpam-6659	159	10	)	)	PUNCT
ejpam-6659	159	11	(	(	PUNCT
ejpam-6659	159	12	2025	2025	NUM
ejpam-6659	159	13	)	)	PUNCT
ejpam-6659	159	14	,	,	PUNCT
ejpam-6659	159	15	6659	6659	NUM
ejpam-6659	159	16	8	8	NUM
ejpam-6659	159	17	of	of	ADP
ejpam-6659	159	18	16	16	NUM
ejpam-6659	159	19	≾	≾	PROPN
ejpam-6659	159	20	a2	a2	PROPN
ejpam-6659	159	21	(	(	PUNCT
ejpam-6659	159	22	1−	1−	NUM
ejpam-6659	159	23	b)2	b)2	PROPN
ejpam-6659	159	24	s(τω−2	s(τω−2	NUM
ejpam-6659	159	25	,	,	PUNCT
ejpam-6659	159	26	τω−2	τω−2	ADJ
ejpam-6659	159	27	,	,	PUNCT
ejpam-6659	159	28	fτω−1	fτω−1	NOUN
ejpam-6659	159	29	)	)	PUNCT
ejpam-6659	159	30	...	...	PUNCT
ejpam-6659	160	1	≾	≾	PROPN
ejpam-6659	160	2	aω	aω	PROPN
ejpam-6659	160	3	(	(	PUNCT
ejpam-6659	160	4	1−	1−	NUM
ejpam-6659	160	5	b)ω	b)ω	PROPN
ejpam-6659	160	6	s(τ0	s(τ0	NOUN
ejpam-6659	160	7	,	,	PUNCT
ejpam-6659	160	8	τ0	τ0	NOUN
ejpam-6659	160	9	,	,	PUNCT
ejpam-6659	160	10	τ1	τ1	NOUN
ejpam-6659	160	11	)	)	PUNCT
ejpam-6659	160	12	.	.	PUNCT
ejpam-6659	161	1	let	let	VERB
ejpam-6659	161	2	ϱ	ϱ	ADP
ejpam-6659	161	3	>	>	X
ejpam-6659	161	4	ω	ω	PROPN
ejpam-6659	161	5	,	,	PUNCT
ejpam-6659	161	6	where	where	SCONJ
ejpam-6659	161	7	ϱ	ϱ	PROPN
ejpam-6659	161	8	,	,	PUNCT
ejpam-6659	161	9	ω	ω	PROPN
ejpam-6659	161	10	∈	∈	PROPN
ejpam-6659	161	11	n.	n.	NOUN
ejpam-6659	161	12	using	use	VERB
ejpam-6659	161	13	the	the	DET
ejpam-6659	161	14	triangle	triangle	NOUN
ejpam-6659	161	15	inequality	inequality	NOUN
ejpam-6659	161	16	,	,	PUNCT
ejpam-6659	161	17	we	we	PRON
ejpam-6659	161	18	obtain	obtain	VERB
ejpam-6659	161	19	s(τϱ	s(τϱ	ADV
ejpam-6659	161	20	,	,	PUNCT
ejpam-6659	161	21	τϱ	τϱ	PROPN
ejpam-6659	161	22	,	,	PUNCT
ejpam-6659	161	23	τω	τω	INTJ
ejpam-6659	161	24	)	)	PUNCT
ejpam-6659	161	25	≾	≾	PROPN
ejpam-6659	161	26	α(τϱ	α(τϱ	PROPN
ejpam-6659	161	27	,	,	PUNCT
ejpam-6659	161	28	τϱ	τϱ	PROPN
ejpam-6659	161	29	,	,	PUNCT
ejpam-6659	161	30	τω+1)s(τϱ	τω+1)s(τϱ	PROPN
ejpam-6659	161	31	,	,	PUNCT
ejpam-6659	161	32	τϱ	τϱ	X
ejpam-6659	161	33	,	,	PUNCT
ejpam-6659	161	34	τω+1	τω+1	PUNCT
ejpam-6659	161	35	)	)	PUNCT
ejpam-6659	162	1	+	+	CCONJ
ejpam-6659	162	2	α(τϱ	α(τϱ	NUM
ejpam-6659	162	3	,	,	PUNCT
ejpam-6659	162	4	τϱ	τϱ	PROPN
ejpam-6659	162	5	,	,	PUNCT
ejpam-6659	162	6	τω+1)s(τϱ	τω+1)s(τϱ	PROPN
ejpam-6659	162	7	,	,	PUNCT
ejpam-6659	162	8	τϱ	τϱ	X
ejpam-6659	162	9	,	,	PUNCT
ejpam-6659	162	10	τω+1	τω+1	PUNCT
ejpam-6659	162	11	)	)	PUNCT
ejpam-6659	162	12	+	+	CCONJ
ejpam-6659	162	13	α(τω	α(τω	NUM
ejpam-6659	162	14	,	,	PUNCT
ejpam-6659	162	15	τω	τω	INTJ
ejpam-6659	162	16	,	,	PUNCT
ejpam-6659	162	17	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	162	18	,	,	PUNCT
ejpam-6659	162	19	τω	τω	INTJ
ejpam-6659	162	20	,	,	PUNCT
ejpam-6659	162	21	τω+1	τω+1	NUM
ejpam-6659	162	22	)	)	PUNCT
ejpam-6659	162	23	=	=	SYM
ejpam-6659	162	24	2α(τϱ	2α(τϱ	NUM
ejpam-6659	162	25	,	,	PUNCT
ejpam-6659	162	26	τϱ	τϱ	X
ejpam-6659	162	27	,	,	PUNCT
ejpam-6659	162	28	τω+1)s(τϱ	τω+1)s(τϱ	PROPN
ejpam-6659	162	29	,	,	PUNCT
ejpam-6659	162	30	τϱ	τϱ	X
ejpam-6659	162	31	,	,	PUNCT
ejpam-6659	162	32	τω+1	τω+1	PUNCT
ejpam-6659	162	33	)	)	PUNCT
ejpam-6659	162	34	+	+	CCONJ
ejpam-6659	162	35	α(τω	α(τω	NUM
ejpam-6659	162	36	,	,	PUNCT
ejpam-6659	162	37	τω	τω	INTJ
ejpam-6659	162	38	,	,	PUNCT
ejpam-6659	162	39	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	162	40	,	,	PUNCT
ejpam-6659	162	41	τω	τω	INTJ
ejpam-6659	162	42	,	,	PUNCT
ejpam-6659	162	43	τω+1	τω+1	NUM
ejpam-6659	162	44	)	)	PUNCT
ejpam-6659	162	45	.	.	PUNCT
ejpam-6659	163	1	again	again	ADV
ejpam-6659	163	2	,	,	PUNCT
ejpam-6659	163	3	using	use	VERB
ejpam-6659	163	4	the	the	DET
ejpam-6659	163	5	triangle	triangle	NOUN
ejpam-6659	163	6	inequality	inequality	NOUN
ejpam-6659	163	7	on	on	ADP
ejpam-6659	163	8	s(τϱ	s(τϱ	PROPN
ejpam-6659	163	9	,	,	PUNCT
ejpam-6659	163	10	τϱ	τϱ	X
ejpam-6659	163	11	,	,	PUNCT
ejpam-6659	163	12	τω+1	τω+1	NUM
ejpam-6659	163	13	)	)	PUNCT
ejpam-6659	163	14	,	,	PUNCT
ejpam-6659	163	15	one	one	NUM
ejpam-6659	163	16	writes	write	VERB
ejpam-6659	163	17	s(τϱ	s(τϱ	ADV
ejpam-6659	163	18	,	,	PUNCT
ejpam-6659	163	19	τϱ	τϱ	PROPN
ejpam-6659	163	20	,	,	PUNCT
ejpam-6659	163	21	τω	τω	INTJ
ejpam-6659	163	22	)	)	PUNCT
ejpam-6659	163	23	≾	≾	PROPN
ejpam-6659	163	24	2α(τϱ	2α(τϱ	NUM
ejpam-6659	163	25	,	,	PUNCT
ejpam-6659	163	26	τϱ	τϱ	PROPN
ejpam-6659	163	27	,	,	PUNCT
ejpam-6659	163	28	τω+1)(2α(τϱ	τω+1)(2α(τϱ	PRON
ejpam-6659	163	29	,	,	PUNCT
ejpam-6659	163	30	τϱ	τϱ	PROPN
ejpam-6659	163	31	,	,	PUNCT
ejpam-6659	163	32	τω+2)s(τϱ	τω+2)s(τϱ	PROPN
ejpam-6659	163	33	,	,	PUNCT
ejpam-6659	163	34	τϱ	τϱ	PROPN
ejpam-6659	163	35	,	,	PUNCT
ejpam-6659	163	36	τω+2	τω+2	NUM
ejpam-6659	163	37	)	)	PUNCT
ejpam-6659	163	38	+	+	NUM
ejpam-6659	163	39	α(τω+1	α(τω+1	NOUN
ejpam-6659	163	40	,	,	PUNCT
ejpam-6659	163	41	τω+1	τω+1	X
ejpam-6659	163	42	,	,	PUNCT
ejpam-6659	163	43	τω+2)s(τω+1	τω+2)s(τω+1	NOUN
ejpam-6659	163	44	,	,	PUNCT
ejpam-6659	163	45	τω+1	τω+1	SYM
ejpam-6659	163	46	,	,	PUNCT
ejpam-6659	163	47	τω+2	τω+2	NUM
ejpam-6659	163	48	)	)	PUNCT
ejpam-6659	163	49	)	)	PUNCT
ejpam-6659	164	1	+	+	CCONJ
ejpam-6659	164	2	α(τω	α(τω	NUM
ejpam-6659	164	3	,	,	PUNCT
ejpam-6659	164	4	τω	τω	INTJ
ejpam-6659	164	5	,	,	PUNCT
ejpam-6659	164	6	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	164	7	,	,	PUNCT
ejpam-6659	164	8	τω	τω	INTJ
ejpam-6659	164	9	,	,	PUNCT
ejpam-6659	164	10	τω+1	τω+1	NUM
ejpam-6659	164	11	)	)	PUNCT
ejpam-6659	164	12	=	=	SYM
ejpam-6659	164	13	α(τω	α(τω	NOUN
ejpam-6659	164	14	,	,	PUNCT
ejpam-6659	164	15	τω	τω	INTJ
ejpam-6659	164	16	,	,	PUNCT
ejpam-6659	164	17	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	164	18	,	,	PUNCT
ejpam-6659	164	19	τω	τω	INTJ
ejpam-6659	164	20	,	,	PUNCT
ejpam-6659	164	21	τω+1	τω+1	PUNCT
ejpam-6659	164	22	)	)	PUNCT
ejpam-6659	164	23	+	+	CCONJ
ejpam-6659	164	24	2α(τϱ	2α(τϱ	NUM
ejpam-6659	164	25	,	,	PUNCT
ejpam-6659	164	26	τϱ	τϱ	NOUN
ejpam-6659	164	27	,	,	PUNCT
ejpam-6659	164	28	τω+1)α(τω+1	τω+1)α(τω+1	NOUN
ejpam-6659	164	29	,	,	PUNCT
ejpam-6659	164	30	τω+1	τω+1	CCONJ
ejpam-6659	164	31	,	,	PUNCT
ejpam-6659	164	32	τω+2)s(τω+1	τω+2)s(τω+1	NOUN
ejpam-6659	164	33	,	,	PUNCT
ejpam-6659	164	34	τω+1	τω+1	X
ejpam-6659	164	35	,	,	PUNCT
ejpam-6659	164	36	τω+2	τω+2	NUM
ejpam-6659	164	37	)	)	PUNCT
ejpam-6659	164	38	+	+	CCONJ
ejpam-6659	164	39	22α(τϱ	22α(τϱ	NUM
ejpam-6659	164	40	,	,	PUNCT
ejpam-6659	164	41	τϱ	τϱ	X
ejpam-6659	164	42	,	,	PUNCT
ejpam-6659	164	43	τω+1	τω+1	X
ejpam-6659	164	44	)	)	PUNCT
ejpam-6659	164	45	α(τϱ	α(τϱ	NUM
ejpam-6659	164	46	,	,	PUNCT
ejpam-6659	164	47	τϱ	τϱ	PROPN
ejpam-6659	164	48	,	,	PUNCT
ejpam-6659	164	49	τω+2)s(τϱ	τω+2)s(τϱ	PROPN
ejpam-6659	164	50	,	,	PUNCT
ejpam-6659	164	51	τϱ	τϱ	PROPN
ejpam-6659	164	52	,	,	PUNCT
ejpam-6659	164	53	τω+2	τω+2	NUM
ejpam-6659	164	54	)	)	PUNCT
ejpam-6659	164	55	.	.	PUNCT
ejpam-6659	165	1	using	use	VERB
ejpam-6659	165	2	triangle	triangle	NOUN
ejpam-6659	165	3	inequality	inequality	NOUN
ejpam-6659	165	4	again	again	ADV
ejpam-6659	165	5	in	in	ADP
ejpam-6659	165	6	a	a	DET
ejpam-6659	165	7	same	same	ADJ
ejpam-6659	165	8	way	way	NOUN
ejpam-6659	165	9	,	,	PUNCT
ejpam-6659	165	10	we	we	PRON
ejpam-6659	165	11	obtain	obtain	VERB
ejpam-6659	165	12	s(τϱ	s(τϱ	ADV
ejpam-6659	165	13	,	,	PUNCT
ejpam-6659	165	14	τϱ	τϱ	PROPN
ejpam-6659	165	15	,	,	PUNCT
ejpam-6659	165	16	τω	τω	INTJ
ejpam-6659	165	17	)	)	PUNCT
ejpam-6659	165	18	≾	≾	PROPN
ejpam-6659	165	19	α(τω	α(τω	NUM
ejpam-6659	165	20	,	,	PUNCT
ejpam-6659	165	21	τω	τω	INTJ
ejpam-6659	165	22	,	,	PUNCT
ejpam-6659	165	23	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	165	24	,	,	PUNCT
ejpam-6659	165	25	τω	τω	INTJ
ejpam-6659	165	26	,	,	PUNCT
ejpam-6659	165	27	τω+1	τω+1	PUNCT
ejpam-6659	165	28	)	)	PUNCT
ejpam-6659	165	29	+	+	CCONJ
ejpam-6659	165	30	ϱ−2∑	ϱ−2∑	PROPN
ejpam-6659	165	31	i	i	NOUN
ejpam-6659	165	32	=	=	NOUN
ejpam-6659	165	33	ω+1	ω+1	NUM
ejpam-6659	165	34	2i−ω	2i−ω	NOUN
ejpam-6659	165	35	i∏	i∏	VERB
ejpam-6659	165	36	j	j	NOUN
ejpam-6659	165	37	=	=	PROPN
ejpam-6659	165	38	ω+1	ω+1	SYM
ejpam-6659	165	39	α(τϱ	α(τϱ	NUM
ejpam-6659	165	40	,	,	PUNCT
ejpam-6659	165	41	τϱ	τϱ	NOUN
ejpam-6659	165	42	,	,	PUNCT
ejpam-6659	165	43	τj)α(τi	τj)α(τi	PRON
ejpam-6659	165	44	,	,	PUNCT
ejpam-6659	165	45	τi	τi	NOUN
ejpam-6659	165	46	,	,	PUNCT
ejpam-6659	165	47	τi+1)s(τi	τi+1)s(τi	NOUN
ejpam-6659	165	48	,	,	PUNCT
ejpam-6659	165	49	τi	τi	NOUN
ejpam-6659	165	50	,	,	PUNCT
ejpam-6659	165	51	τi+1	τi+1	PROPN
ejpam-6659	165	52	)	)	PUNCT
ejpam-6659	165	53	+	+	NUM
ejpam-6659	166	1	2ϱ−ω−1	2ϱ−ω−1	NUM
ejpam-6659	166	2	ϱ−1∏	ϱ−1∏	VERB
ejpam-6659	166	3	k	k	NOUN
ejpam-6659	166	4	=	=	PROPN
ejpam-6659	166	5	ω+1	ω+1	SYM
ejpam-6659	166	6	α(τϱ	α(τϱ	NUM
ejpam-6659	166	7	,	,	PUNCT
ejpam-6659	166	8	τϱ	τϱ	PROPN
ejpam-6659	166	9	,	,	PUNCT
ejpam-6659	166	10	τk)s(τϱ−1	τk)s(τϱ−1	PROPN
ejpam-6659	166	11	,	,	PUNCT
ejpam-6659	166	12	τϱ−1	τϱ−1	NOUN
ejpam-6659	166	13	,	,	PUNCT
ejpam-6659	166	14	τϱ	τϱ	X
ejpam-6659	166	15	)	)	PUNCT
ejpam-6659	166	16	≾	≾	NOUN
ejpam-6659	166	17	α(τω	α(τω	NUM
ejpam-6659	166	18	,	,	PUNCT
ejpam-6659	166	19	τω	τω	INTJ
ejpam-6659	166	20	,	,	PUNCT
ejpam-6659	166	21	τω+1	τω+1	NUM
ejpam-6659	166	22	)	)	PUNCT
ejpam-6659	166	23	(	(	PUNCT
ejpam-6659	166	24	a	a	DET
ejpam-6659	166	25	1−	1−	NUM
ejpam-6659	166	26	b	b	PROPN
ejpam-6659	166	27	)	)	PUNCT
ejpam-6659	166	28	ω	ω	PROPN
ejpam-6659	166	29	s(τ0	s(τ0	NOUN
ejpam-6659	166	30	,	,	PUNCT
ejpam-6659	166	31	τ0	τ0	NOUN
ejpam-6659	166	32	,	,	PUNCT
ejpam-6659	166	33	τ1	τ1	NOUN
ejpam-6659	166	34	)	)	PUNCT
ejpam-6659	167	1	+	+	CCONJ
ejpam-6659	167	2	ϱ−1∑	ϱ−1∑	NUM
ejpam-6659	167	3	i	i	NOUN
ejpam-6659	167	4	=	=	NOUN
ejpam-6659	167	5	ω+1	ω+1	NUM
ejpam-6659	167	6	2i−ω	2i−ω	NOUN
ejpam-6659	167	7	i∏	i∏	VERB
ejpam-6659	167	8	j	j	NOUN
ejpam-6659	167	9	=	=	PROPN
ejpam-6659	167	10	ω+1	ω+1	SYM
ejpam-6659	167	11	α(τϱ	α(τϱ	NUM
ejpam-6659	167	12	,	,	PUNCT
ejpam-6659	167	13	τϱ	τϱ	NOUN
ejpam-6659	167	14	,	,	PUNCT
ejpam-6659	167	15	τj)α(τi	τj)α(τi	PRON
ejpam-6659	167	16	,	,	PUNCT
ejpam-6659	167	17	τi	τi	NOUN
ejpam-6659	167	18	,	,	PUNCT
ejpam-6659	167	19	τi+1	τi+1	PROPN
ejpam-6659	167	20	)	)	PUNCT
ejpam-6659	167	21	(	(	PUNCT
ejpam-6659	167	22	a	a	DET
ejpam-6659	167	23	1−	1−	NUM
ejpam-6659	167	24	b	b	NOUN
ejpam-6659	167	25	)	)	PUNCT
ejpam-6659	167	26	i	i	PRON
ejpam-6659	167	27	s(τ0	s(τ0	NOUN
ejpam-6659	167	28	,	,	PUNCT
ejpam-6659	167	29	τ0	τ0	NOUN
ejpam-6659	167	30	,	,	PUNCT
ejpam-6659	167	31	τ1	τ1	NOUN
ejpam-6659	167	32	)	)	PUNCT
ejpam-6659	167	33	.	.	PUNCT
ejpam-6659	168	1	as	as	ADP
ejpam-6659	168	2	ω	ω	PROPN
ejpam-6659	168	3	,	,	PUNCT
ejpam-6659	168	4	ϱ	ϱ	PROPN
ejpam-6659	168	5	→	→	SYM
ejpam-6659	168	6	+	+	PROPN
ejpam-6659	168	7	∞	∞	PROPN
ejpam-6659	168	8	,	,	PUNCT
ejpam-6659	168	9	one	one	NUM
ejpam-6659	168	10	has	have	VERB
ejpam-6659	168	11	ϱ−1∑	ϱ−1∑	PROPN
ejpam-6659	168	12	i	i	PROPN
ejpam-6659	168	13	=	=	NOUN
ejpam-6659	168	14	ω+1	ω+1	NUM
ejpam-6659	168	15	2i−ω	2i−ω	NOUN
ejpam-6659	168	16	i∏	i∏	VERB
ejpam-6659	168	17	j	j	NOUN
ejpam-6659	168	18	=	=	PROPN
ejpam-6659	168	19	ω+1	ω+1	SYM
ejpam-6659	168	20	α(τϱ	α(τϱ	NUM
ejpam-6659	168	21	,	,	PUNCT
ejpam-6659	168	22	τϱ	τϱ	NOUN
ejpam-6659	168	23	,	,	PUNCT
ejpam-6659	168	24	τj)α(τi	τj)α(τi	PRON
ejpam-6659	168	25	,	,	PUNCT
ejpam-6659	168	26	τi	τi	NOUN
ejpam-6659	168	27	,	,	PUNCT
ejpam-6659	168	28	τi+1	τi+1	PROPN
ejpam-6659	168	29	)	)	PUNCT
ejpam-6659	168	30	(	(	PUNCT
ejpam-6659	168	31	a	a	DET
ejpam-6659	168	32	1−	1−	NUM
ejpam-6659	168	33	b	b	NOUN
ejpam-6659	168	34	)	)	PUNCT
ejpam-6659	168	35	i	i	PROPN
ejpam-6659	168	36	→	→	PROPN
ejpam-6659	168	37	0	0	PROPN
ejpam-6659	168	38	,	,	PUNCT
ejpam-6659	168	39	h.	h.	PROPN
ejpam-6659	168	40	qawaqneh	qawaqneh	PROPN
ejpam-6659	168	41	et	et	PROPN
ejpam-6659	168	42	al	al	PROPN
ejpam-6659	168	43	.	.	PUNCT
ejpam-6659	168	44	/	/	SYM
ejpam-6659	168	45	eur	eur	PROPN
ejpam-6659	168	46	.	.	PUNCT
ejpam-6659	169	1	j.	j.	PROPN
ejpam-6659	169	2	pure	pure	PROPN
ejpam-6659	169	3	appl	appl	PROPN
ejpam-6659	169	4	.	.	PROPN
ejpam-6659	169	5	math	math	PROPN
ejpam-6659	169	6	,	,	PUNCT
ejpam-6659	169	7	18	18	NUM
ejpam-6659	169	8	(	(	PUNCT
ejpam-6659	169	9	3	3	NUM
ejpam-6659	169	10	)	)	PUNCT
ejpam-6659	169	11	(	(	PUNCT
ejpam-6659	169	12	2025	2025	NUM
ejpam-6659	169	13	)	)	PUNCT
ejpam-6659	169	14	,	,	PUNCT
ejpam-6659	169	15	6659	6659	NUM
ejpam-6659	169	16	9	9	NUM
ejpam-6659	169	17	of	of	ADP
ejpam-6659	169	18	16	16	NUM
ejpam-6659	169	19	if	if	SCONJ
ejpam-6659	169	20	supϱ≥1	supϱ≥1	PROPN
ejpam-6659	169	21	lim	lim	PROPN
ejpam-6659	169	22	i→+∞	i→+∞	PROPN
ejpam-6659	169	23	α(τi+1,τi+1,τi+2).α(τϱ,τϱ,τi+1	α(τi+1,τi+1,τi+2).α(τϱ,τϱ,τi+1	PROPN
ejpam-6659	169	24	)	)	PUNCT
ejpam-6659	169	25	α(τi	α(τi	NOUN
ejpam-6659	169	26	,	,	PUNCT
ejpam-6659	169	27	τi	τi	ADP
ejpam-6659	169	28	,	,	PUNCT
ejpam-6659	169	29	τi+1	τi+1	PUNCT
ejpam-6659	169	30	)	)	PUNCT
ejpam-6659	169	31	<	<	X
ejpam-6659	169	32	1−b	1−b	NUM
ejpam-6659	169	33	2a	2a	NUM
ejpam-6659	169	34	.	.	PUNCT
ejpam-6659	170	1	for	for	ADP
ejpam-6659	170	2	ϱ	ϱ	PROPN
ejpam-6659	170	3	>	>	X
ejpam-6659	170	4	n	n	CCONJ
ejpam-6659	170	5	,	,	PUNCT
ejpam-6659	170	6	we	we	PRON
ejpam-6659	170	7	obtain	obtain	VERB
ejpam-6659	170	8	lim	lim	PROPN
ejpam-6659	170	9	ϱ,ω→+∞	ϱ,ω→+∞	VERB
ejpam-6659	170	10	s(τϱ	s(τϱ	ADV
ejpam-6659	170	11	,	,	PUNCT
ejpam-6659	170	12	τϱ	τϱ	PROPN
ejpam-6659	170	13	,	,	PUNCT
ejpam-6659	170	14	τω	τω	INTJ
ejpam-6659	170	15	)	)	PUNCT
ejpam-6659	170	16	=	=	SYM
ejpam-6659	170	17	0	0	X
ejpam-6659	170	18	.	.	PUNCT
ejpam-6659	171	1	by	by	ADP
ejpam-6659	171	2	cv	cv	PROPN
ejpam-6659	171	3	cs3	cs3	PROPN
ejpam-6659	171	4	,	,	PUNCT
ejpam-6659	171	5	we	we	PRON
ejpam-6659	171	6	have	have	VERB
ejpam-6659	171	7	s(τω	s(τω	PROPN
ejpam-6659	171	8	,	,	PUNCT
ejpam-6659	171	9	τϱ	τϱ	PROPN
ejpam-6659	171	10	,	,	PUNCT
ejpam-6659	171	11	τl	τl	ADJ
ejpam-6659	171	12	)	)	PUNCT
ejpam-6659	171	13	≾	≾	PROPN
ejpam-6659	171	14	α(τϱ	α(τϱ	PROPN
ejpam-6659	171	15	,	,	PUNCT
ejpam-6659	171	16	τϱ	τϱ	PROPN
ejpam-6659	171	17	,	,	PUNCT
ejpam-6659	171	18	τω)s(τϱ	τω)s(τϱ	PRON
ejpam-6659	171	19	,	,	PUNCT
ejpam-6659	171	20	τϱ	τϱ	PROPN
ejpam-6659	171	21	,	,	PUNCT
ejpam-6659	171	22	τω	τω	INTJ
ejpam-6659	171	23	)	)	PUNCT
ejpam-6659	171	24	+	+	NUM
ejpam-6659	171	25	α(τl	α(τl	NOUN
ejpam-6659	171	26	,	,	PUNCT
ejpam-6659	171	27	τl	τl	NOUN
ejpam-6659	171	28	,	,	PUNCT
ejpam-6659	171	29	τω)s(τl	τω)s(τl	NOUN
ejpam-6659	171	30	,	,	PUNCT
ejpam-6659	171	31	τl	τl	ADV
ejpam-6659	171	32	,	,	PUNCT
ejpam-6659	171	33	τω	τω	INTJ
ejpam-6659	171	34	)	)	PUNCT
ejpam-6659	171	35	for	for	ADP
ejpam-6659	171	36	all	all	DET
ejpam-6659	171	37	ω	ω	PROPN
ejpam-6659	171	38	,	,	PUNCT
ejpam-6659	171	39	ϱ	ϱ	NOUN
ejpam-6659	171	40	,	,	PUNCT
ejpam-6659	171	41	l	l	PROPN
ejpam-6659	171	42	∈	∈	PROPN
ejpam-6659	171	43	n.	n.	PROPN
ejpam-6659	171	44	thus	thus	ADV
ejpam-6659	171	45	,	,	PUNCT
ejpam-6659	171	46	|s(τω	|s(τω	PROPN
ejpam-6659	171	47	,	,	PUNCT
ejpam-6659	171	48	τϱ	τϱ	X
ejpam-6659	171	49	,	,	PUNCT
ejpam-6659	171	50	τl)|	τl)|	PUNCT
ejpam-6659	171	51	≤	≤	NUM
ejpam-6659	171	52	α(τϱ	α(τϱ	NUM
ejpam-6659	171	53	,	,	PUNCT
ejpam-6659	171	54	τϱ	τϱ	PROPN
ejpam-6659	171	55	,	,	PUNCT
ejpam-6659	171	56	τω)|s(τϱ	τω)|s(τϱ	PROPN
ejpam-6659	171	57	,	,	PUNCT
ejpam-6659	171	58	τϱ	τϱ	PROPN
ejpam-6659	171	59	,	,	PUNCT
ejpam-6659	171	60	τω)|+	τω)|+	VERB
ejpam-6659	171	61	α(τl	α(τl	NUM
ejpam-6659	171	62	,	,	PUNCT
ejpam-6659	171	63	τl	τl	NOUN
ejpam-6659	171	64	,	,	PUNCT
ejpam-6659	171	65	τω)|s(τl	τω)|s(τl	NOUN
ejpam-6659	171	66	,	,	PUNCT
ejpam-6659	171	67	τl	τl	ADJ
ejpam-6659	171	68	,	,	PUNCT
ejpam-6659	171	69	τω)|	τω)|	PRON
ejpam-6659	171	70	.	.	PUNCT
ejpam-6659	172	1	considering	consider	VERB
ejpam-6659	172	2	the	the	DET
ejpam-6659	172	3	limit	limit	NOUN
ejpam-6659	172	4	as	as	ADP
ejpam-6659	172	5	ω	ω	PROPN
ejpam-6659	172	6	,	,	PUNCT
ejpam-6659	172	7	ϱ	ϱ	NOUN
ejpam-6659	172	8	,	,	PUNCT
ejpam-6659	172	9	l	l	NOUN
ejpam-6659	172	10	→	→	SYM
ejpam-6659	172	11	+	+	NOUN
ejpam-6659	172	12	∞	∞	PROPN
ejpam-6659	172	13	,	,	PUNCT
ejpam-6659	172	14	we	we	PRON
ejpam-6659	172	15	have	have	VERB
ejpam-6659	172	16	|s(τω	|s(τω	PROPN
ejpam-6659	172	17	,	,	PUNCT
ejpam-6659	172	18	τϱ	τϱ	ADP
ejpam-6659	172	19	,	,	PUNCT
ejpam-6659	172	20	τl)|	τl)|	PUNCT
ejpam-6659	172	21	→	→	SYM
ejpam-6659	172	22	0	0	X
ejpam-6659	172	23	.	.	PUNCT
ejpam-6659	173	1	so	so	ADV
ejpam-6659	173	2	{	{	PUNCT
ejpam-6659	173	3	τω	τω	INTJ
ejpam-6659	173	4	}	}	PUNCT
ejpam-6659	173	5	is	be	AUX
ejpam-6659	173	6	a	a	DET
ejpam-6659	173	7	cvcscauchy	cvcscauchy	ADJ
ejpam-6659	173	8	sequence	sequence	NOUN
ejpam-6659	173	9	.	.	PUNCT
ejpam-6659	174	1	completeness	completeness	NOUN
ejpam-6659	174	2	of	of	ADP
ejpam-6659	174	3	(	(	PUNCT
ejpam-6659	174	4	γ	γ	PROPN
ejpam-6659	174	5	,	,	PUNCT
ejpam-6659	174	6	s	s	PROPN
ejpam-6659	174	7	,	,	PUNCT
ejpam-6659	174	8	α	α	NOUN
ejpam-6659	174	9	)	)	PUNCT
ejpam-6659	174	10	gives	give	VERB
ejpam-6659	174	11	us	we	PRON
ejpam-6659	174	12	that	that	SCONJ
ejpam-6659	174	13	there	there	PRON
ejpam-6659	174	14	is	be	VERB
ejpam-6659	174	15	an	an	DET
ejpam-6659	174	16	element	element	ADJ
ejpam-6659	174	17	ς∗	ς∗	NOUN
ejpam-6659	174	18	∈	∈	PROPN
ejpam-6659	174	19	γ	γ	NOUN
ejpam-6659	174	20	such	such	ADJ
ejpam-6659	174	21	that	that	SCONJ
ejpam-6659	174	22	{	{	PUNCT
ejpam-6659	174	23	τω	τω	INTJ
ejpam-6659	174	24	}	}	PUNCT
ejpam-6659	174	25	is	be	AUX
ejpam-6659	174	26	cvcs	cvcs	ADJ
ejpam-6659	174	27	-	-	PUNCT
ejpam-6659	174	28	convergent	convergent	NOUN
ejpam-6659	174	29	to	to	ADP
ejpam-6659	174	30	ς∗.	ς∗.	PROPN
ejpam-6659	174	31	now	now	ADV
ejpam-6659	174	32	,	,	PUNCT
ejpam-6659	174	33	we	we	PRON
ejpam-6659	174	34	’ll	’ll	AUX
ejpam-6659	174	35	prove	prove	VERB
ejpam-6659	174	36	that	that	SCONJ
ejpam-6659	174	37	f(ς∗	f(ς∗	VERB
ejpam-6659	174	38	)	)	PUNCT
ejpam-6659	174	39	=	=	SYM
ejpam-6659	174	40	ς∗.	ς∗.	NOUN
ejpam-6659	174	41	consider	consider	VERB
ejpam-6659	174	42	,	,	PUNCT
ejpam-6659	174	43	s(τω+1	s(τω+1	ADV
ejpam-6659	174	44	,	,	PUNCT
ejpam-6659	174	45	τω+1	τω+1	ADP
ejpam-6659	174	46	,	,	PUNCT
ejpam-6659	174	47	f(ς	f(ς	PROPN
ejpam-6659	174	48	∗	∗	NOUN
ejpam-6659	174	49	)	)	PUNCT
ejpam-6659	174	50	)	)	PUNCT
ejpam-6659	175	1	≾	≾	PROPN
ejpam-6659	175	2	as(τω	as(τω	PROPN
ejpam-6659	175	3	,	,	PUNCT
ejpam-6659	175	4	τω	τω	INTJ
ejpam-6659	175	5	,	,	PUNCT
ejpam-6659	175	6	τω+1	τω+1	NUM
ejpam-6659	175	7	)	)	PUNCT
ejpam-6659	175	8	+	+	SYM
ejpam-6659	175	9	bs(ς∗	bs(ς∗	NUM
ejpam-6659	175	10	,	,	PUNCT
ejpam-6659	175	11	ς∗	ς∗	NOUN
ejpam-6659	175	12	,	,	PUNCT
ejpam-6659	175	13	f(ς∗	f(ς∗	NOUN
ejpam-6659	175	14	)	)	PUNCT
ejpam-6659	175	15	)	)	PUNCT
ejpam-6659	175	16	that	that	ADV
ejpam-6659	175	17	is	be	AUX
ejpam-6659	175	18	,	,	PUNCT
ejpam-6659	175	19	|s(τω+1	|s(τω+1	NOUN
ejpam-6659	175	20	,	,	PUNCT
ejpam-6659	175	21	τω+1	τω+1	PROPN
ejpam-6659	175	22	,	,	PUNCT
ejpam-6659	175	23	f(ς	f(ς	PROPN
ejpam-6659	175	24	∗))|	∗))|	PROPN
ejpam-6659	175	25	≤	≤	PROPN
ejpam-6659	175	26	a|s(τω	a|s(τω	ADV
ejpam-6659	175	27	,	,	PUNCT
ejpam-6659	175	28	τω	τω	INTJ
ejpam-6659	175	29	,	,	PUNCT
ejpam-6659	175	30	τω+1)|+	τω+1)|+	X
ejpam-6659	175	31	b|s(ς∗	b|s(ς∗	NOUN
ejpam-6659	175	32	,	,	PUNCT
ejpam-6659	175	33	ς∗	ς∗	NOUN
ejpam-6659	175	34	,	,	PUNCT
ejpam-6659	175	35	f(ς∗))|	f(ς∗))|	PROPN
ejpam-6659	175	36	.	.	PUNCT
ejpam-6659	176	1	letting	let	VERB
ejpam-6659	176	2	ω	ω	X
ejpam-6659	176	3	→	→	SYM
ejpam-6659	176	4	+	+	PROPN
ejpam-6659	176	5	∞	∞	PROPN
ejpam-6659	176	6	,	,	PUNCT
ejpam-6659	176	7	we	we	PRON
ejpam-6659	176	8	obtain	obtain	VERB
ejpam-6659	176	9	|s(ς∗	|s(ς∗	ADJ
ejpam-6659	176	10	,	,	PUNCT
ejpam-6659	176	11	ς∗	ς∗	NOUN
ejpam-6659	176	12	,	,	PUNCT
ejpam-6659	176	13	f(ς∗))|	f(ς∗))|	NOUN
ejpam-6659	176	14	≤	≤	NOUN
ejpam-6659	176	15	b|s(ς∗	b|s(ς∗	PROPN
ejpam-6659	176	16	,	,	PUNCT
ejpam-6659	176	17	ς∗	ς∗	NOUN
ejpam-6659	176	18	,	,	PUNCT
ejpam-6659	176	19	f(ς∗))|	f(ς∗))|	PROPN
ejpam-6659	176	20	,	,	PUNCT
ejpam-6659	176	21	which	which	PRON
ejpam-6659	176	22	implies	imply	VERB
ejpam-6659	176	23	f(ς∗	f(ς∗	NOUN
ejpam-6659	176	24	)	)	PUNCT
ejpam-6659	176	25	=	=	SYM
ejpam-6659	176	26	ς∗.	ς∗.	NOUN
ejpam-6659	176	27	now	now	ADV
ejpam-6659	176	28	towards	towards	ADP
ejpam-6659	176	29	the	the	DET
ejpam-6659	176	30	end	end	NOUN
ejpam-6659	176	31	,	,	PUNCT
ejpam-6659	176	32	the	the	DET
ejpam-6659	176	33	uniqueness	uniqueness	NOUN
ejpam-6659	176	34	will	will	AUX
ejpam-6659	176	35	be	be	AUX
ejpam-6659	176	36	proved	prove	VERB
ejpam-6659	176	37	.	.	PUNCT
ejpam-6659	177	1	let	let	VERB
ejpam-6659	177	2	τ∗	τ∗	NOUN
ejpam-6659	177	3	be	be	AUX
ejpam-6659	177	4	some	some	DET
ejpam-6659	177	5	other	other	ADJ
ejpam-6659	177	6	fixed	fix	VERB
ejpam-6659	177	7	point	point	NOUN
ejpam-6659	177	8	of	of	ADP
ejpam-6659	177	9	f	f	PROPN
ejpam-6659	177	10	.	.	PUNCT
ejpam-6659	178	1	consider	consider	VERB
ejpam-6659	178	2	s(ς∗	s(ς∗	ADJ
ejpam-6659	178	3	,	,	PUNCT
ejpam-6659	178	4	ς∗	ς∗	ADJ
ejpam-6659	178	5	,	,	PUNCT
ejpam-6659	178	6	τ∗	τ∗	ADJ
ejpam-6659	178	7	)	)	PUNCT
ejpam-6659	178	8	=	=	SYM
ejpam-6659	178	9	s(f(ς∗	s(f(ς∗	PROPN
ejpam-6659	178	10	)	)	PUNCT
ejpam-6659	178	11	,	,	PUNCT
ejpam-6659	178	12	f(ς∗	f(ς∗	NOUN
ejpam-6659	178	13	)	)	PUNCT
ejpam-6659	178	14	,	,	PUNCT
ejpam-6659	178	15	f(τ∗	f(τ∗	NOUN
ejpam-6659	178	16	)	)	PUNCT
ejpam-6659	178	17	)	)	PUNCT
ejpam-6659	179	1	≾	≾	PROPN
ejpam-6659	179	2	as(ς∗	as(ς∗	PROPN
ejpam-6659	179	3	,	,	PUNCT
ejpam-6659	179	4	ς∗	ς∗	NOUN
ejpam-6659	179	5	,	,	PUNCT
ejpam-6659	179	6	f(ς∗	f(ς∗	NOUN
ejpam-6659	179	7	)	)	PUNCT
ejpam-6659	179	8	)	)	PUNCT
ejpam-6659	180	1	+	+	CCONJ
ejpam-6659	180	2	bs(τ∗	bs(τ∗	NUM
ejpam-6659	180	3	,	,	PUNCT
ejpam-6659	180	4	τ∗	τ∗	NOUN
ejpam-6659	180	5	,	,	PUNCT
ejpam-6659	180	6	f(τ∗	f(τ∗	NOUN
ejpam-6659	180	7	)	)	PUNCT
ejpam-6659	180	8	)	)	PUNCT
ejpam-6659	180	9	,	,	PUNCT
ejpam-6659	180	10	that	that	ADV
ejpam-6659	180	11	is	is	ADV
ejpam-6659	180	12	,	,	PUNCT
ejpam-6659	180	13	|s(f(ς∗	|s(f(ς∗	X
ejpam-6659	180	14	)	)	PUNCT
ejpam-6659	180	15	,	,	PUNCT
ejpam-6659	180	16	f(ς∗	f(ς∗	NOUN
ejpam-6659	180	17	)	)	PUNCT
ejpam-6659	180	18	,	,	PUNCT
ejpam-6659	180	19	f(τ∗))|	f(τ∗))|	VERB
ejpam-6659	180	20	≤	≤	ADV
ejpam-6659	180	21	0	0	NUM
ejpam-6659	180	22	.	.	PUNCT
ejpam-6659	181	1	this	this	PRON
ejpam-6659	181	2	implies	imply	VERB
ejpam-6659	181	3	that	that	SCONJ
ejpam-6659	181	4	|s(ς∗	|s(ς∗	ADJ
ejpam-6659	181	5	,	,	PUNCT
ejpam-6659	181	6	ς∗	ς∗	NOUN
ejpam-6659	181	7	,	,	PUNCT
ejpam-6659	181	8	τ∗)|	τ∗)|	ADJ
ejpam-6659	181	9	≤	≤	NUM
ejpam-6659	181	10	0	0	NUM
ejpam-6659	181	11	.	.	PUNCT
ejpam-6659	182	1	thus	thus	ADV
ejpam-6659	182	2	,	,	PUNCT
ejpam-6659	182	3	ς∗	ς∗	PROPN
ejpam-6659	182	4	=	=	SYM
ejpam-6659	182	5	τ∗	τ∗	NOUN
ejpam-6659	182	6	,	,	PUNCT
ejpam-6659	182	7	i.e.	i.e.	X
ejpam-6659	182	8	,	,	PUNCT
ejpam-6659	182	9	τ∗	τ∗	NOUN
ejpam-6659	182	10	is	be	AUX
ejpam-6659	182	11	the	the	DET
ejpam-6659	182	12	unique	unique	ADJ
ejpam-6659	182	13	fixed	fix	VERB
ejpam-6659	182	14	point	point	NOUN
ejpam-6659	182	15	of	of	ADP
ejpam-6659	182	16	f	f	PROPN
ejpam-6659	182	17	.	.	PUNCT
ejpam-6659	183	1	corollary	corollary	ADJ
ejpam-6659	183	2	2	2	NUM
ejpam-6659	183	3	.	.	PUNCT
ejpam-6659	184	1	let	let	AUX
ejpam-6659	184	2	(	(	PUNCT
ejpam-6659	184	3	γ	γ	X
ejpam-6659	184	4	,	,	PUNCT
ejpam-6659	184	5	s	s	PROPN
ejpam-6659	184	6	,	,	PUNCT
ejpam-6659	184	7	α	α	NOUN
ejpam-6659	184	8	)	)	PUNCT
ejpam-6659	184	9	be	be	VERB
ejpam-6659	184	10	a	a	DET
ejpam-6659	184	11	complete	complete	ADJ
ejpam-6659	184	12	complex	complex	NOUN
ejpam-6659	184	13	valued	value	VERB
ejpam-6659	184	14	s	s	NOUN
ejpam-6659	184	15	-	-	ADJ
ejpam-6659	184	16	metric	metric	ADJ
ejpam-6659	184	17	space	space	NOUN
ejpam-6659	184	18	.	.	PUNCT
ejpam-6659	185	1	let	let	VERB
ejpam-6659	185	2	f	f	NOUN
ejpam-6659	185	3	:	:	PUNCT
ejpam-6659	185	4	γ	γ	X
ejpam-6659	185	5	→	→	SYM
ejpam-6659	185	6	γ	γ	X
ejpam-6659	185	7	be	be	AUX
ejpam-6659	185	8	a	a	DET
ejpam-6659	185	9	mapping	mapping	NOUN
ejpam-6659	185	10	such	such	ADJ
ejpam-6659	185	11	that	that	SCONJ
ejpam-6659	185	12	,	,	PUNCT
ejpam-6659	185	13	for	for	ADP
ejpam-6659	185	14	τ	τ	PROPN
ejpam-6659	185	15	,	,	PUNCT
ejpam-6659	185	16	ς	ς	PROPN
ejpam-6659	185	17	∈	∈	PROPN
ejpam-6659	185	18	γ	γ	NOUN
ejpam-6659	185	19	,	,	PUNCT
ejpam-6659	185	20	s(f(τ	s(f(τ	NOUN
ejpam-6659	185	21	)	)	PUNCT
ejpam-6659	185	22	,	,	PUNCT
ejpam-6659	185	23	f(τ	f(τ	PROPN
ejpam-6659	185	24	)	)	PUNCT
ejpam-6659	185	25	,	,	PUNCT
ejpam-6659	185	26	f(ς	f(ς	PROPN
ejpam-6659	185	27	)	)	PUNCT
ejpam-6659	185	28	)	)	PUNCT
ejpam-6659	186	1	≾	≾	PROPN
ejpam-6659	186	2	as(τ	as(τ	PROPN
ejpam-6659	186	3	,	,	PUNCT
ejpam-6659	186	4	τ	τ	PROPN
ejpam-6659	186	5	,	,	PUNCT
ejpam-6659	186	6	f(τ	f(τ	PROPN
ejpam-6659	186	7	)	)	PUNCT
ejpam-6659	186	8	)	)	PUNCT
ejpam-6659	187	1	+	+	CCONJ
ejpam-6659	187	2	bs(ς	bs(ς	NOUN
ejpam-6659	187	3	,	,	PUNCT
ejpam-6659	187	4	ς	ς	PROPN
ejpam-6659	187	5	,	,	PUNCT
ejpam-6659	187	6	f(ς	f(ς	PROPN
ejpam-6659	187	7	)	)	PUNCT
ejpam-6659	187	8	)	)	PUNCT
ejpam-6659	187	9	,	,	PUNCT
ejpam-6659	187	10	(	(	PUNCT
ejpam-6659	187	11	5	5	X
ejpam-6659	187	12	)	)	PUNCT
ejpam-6659	187	13	where	where	SCONJ
ejpam-6659	187	14	a	a	DET
ejpam-6659	187	15	∈	∈	NOUN
ejpam-6659	187	16	[	[	X
ejpam-6659	187	17	0	0	NUM
ejpam-6659	187	18	,	,	PUNCT
ejpam-6659	187	19	12	12	NUM
ejpam-6659	187	20	)	)	PUNCT
ejpam-6659	187	21	,	,	PUNCT
ejpam-6659	187	22	with	with	ADP
ejpam-6659	187	23	2a+	2a+	NUM
ejpam-6659	187	24	b	b	NOUN
ejpam-6659	187	25	<	<	X
ejpam-6659	187	26	1	1	NUM
ejpam-6659	187	27	.	.	PUNCT
ejpam-6659	187	28	then	then	ADV
ejpam-6659	187	29	,	,	PUNCT
ejpam-6659	187	30	there	there	PRON
ejpam-6659	187	31	exists	exist	VERB
ejpam-6659	187	32	a	a	DET
ejpam-6659	187	33	fixed	fix	VERB
ejpam-6659	187	34	point	point	NOUN
ejpam-6659	187	35	for	for	ADP
ejpam-6659	187	36	f	f	PROPN
ejpam-6659	187	37	in	in	ADP
ejpam-6659	187	38	γ	γ	PROPN
ejpam-6659	187	39	.	.	PUNCT
ejpam-6659	187	40	proof	proof	NOUN
ejpam-6659	187	41	.	.	PUNCT
ejpam-6659	188	1	if	if	SCONJ
ejpam-6659	188	2	we	we	PRON
ejpam-6659	188	3	take	take	VERB
ejpam-6659	188	4	α(τ	α(τ	NUM
ejpam-6659	188	5	,	,	PUNCT
ejpam-6659	188	6	ς,ϖ	ς,ϖ	NUM
ejpam-6659	188	7	)	)	PUNCT
ejpam-6659	188	8	=	=	SYM
ejpam-6659	188	9	1	1	NUM
ejpam-6659	188	10	and	and	CCONJ
ejpam-6659	188	11	proceed	proceed	VERB
ejpam-6659	188	12	with	with	ADP
ejpam-6659	188	13	the	the	DET
ejpam-6659	188	14	same	same	ADJ
ejpam-6659	188	15	steps	step	NOUN
ejpam-6659	188	16	as	as	SCONJ
ejpam-6659	188	17	outlined	outline	VERB
ejpam-6659	188	18	in	in	ADP
ejpam-6659	188	19	the	the	DET
ejpam-6659	188	20	proof	proof	NOUN
ejpam-6659	188	21	of	of	ADP
ejpam-6659	188	22	theorem	theorem	NOUN
ejpam-6659	188	23	3	3	NUM
ejpam-6659	188	24	,	,	PUNCT
ejpam-6659	188	25	the	the	DET
ejpam-6659	188	26	corollary	corollary	NOUN
ejpam-6659	188	27	is	be	AUX
ejpam-6659	188	28	proved	prove	VERB
ejpam-6659	188	29	.	.	PUNCT
ejpam-6659	189	1	theorem	theorem	ADJ
ejpam-6659	189	2	4	4	NUM
ejpam-6659	189	3	.	.	PUNCT
ejpam-6659	190	1	let	let	AUX
ejpam-6659	190	2	(	(	PUNCT
ejpam-6659	190	3	γ	γ	X
ejpam-6659	190	4	,	,	PUNCT
ejpam-6659	190	5	s	s	PROPN
ejpam-6659	190	6	,	,	PUNCT
ejpam-6659	190	7	α	α	NOUN
ejpam-6659	190	8	)	)	PUNCT
ejpam-6659	190	9	be	be	VERB
ejpam-6659	190	10	a	a	DET
ejpam-6659	190	11	complete	complete	ADJ
ejpam-6659	190	12	complex	complex	NOUN
ejpam-6659	190	13	valued	value	VERB
ejpam-6659	190	14	s	s	NOUN
ejpam-6659	190	15	-	-	ADJ
ejpam-6659	190	16	metric	metric	ADJ
ejpam-6659	190	17	space	space	NOUN
ejpam-6659	190	18	.	.	PUNCT
ejpam-6659	191	1	let	let	VERB
ejpam-6659	191	2	f	f	PROPN
ejpam-6659	191	3	and	and	CCONJ
ejpam-6659	191	4	g	g	PROPN
ejpam-6659	191	5	be	be	VERB
ejpam-6659	191	6	two	two	NUM
ejpam-6659	191	7	self	self	NOUN
ejpam-6659	191	8	mappings	mapping	NOUN
ejpam-6659	191	9	on	on	ADP
ejpam-6659	191	10	γ	γ	NOUN
ejpam-6659	191	11	that	that	PRON
ejpam-6659	191	12	meet	meet	VERB
ejpam-6659	191	13	the	the	DET
ejpam-6659	191	14	contraction	contraction	NOUN
ejpam-6659	191	15	condition	condition	NOUN
ejpam-6659	191	16	given	give	VERB
ejpam-6659	191	17	below	below	ADV
ejpam-6659	191	18	:	:	PUNCT
ejpam-6659	192	1	s(fτ	s(fτ	PROPN
ejpam-6659	192	2	,	,	PUNCT
ejpam-6659	192	3	fτ	fτ	NOUN
ejpam-6659	192	4	,	,	PUNCT
ejpam-6659	192	5	gς	gς	NOUN
ejpam-6659	192	6	)	)	PUNCT
ejpam-6659	192	7	≾	≾	PROPN
ejpam-6659	192	8	γs(τ	γs(τ	X
ejpam-6659	192	9	,	,	PUNCT
ejpam-6659	192	10	τ	τ	X
ejpam-6659	192	11	,	,	PUNCT
ejpam-6659	192	12	ς)+β	ς)+β	PROPN
ejpam-6659	192	13	s(τ	s(τ	PROPN
ejpam-6659	192	14	,	,	PUNCT
ejpam-6659	192	15	τ	τ	PROPN
ejpam-6659	192	16	,	,	PUNCT
ejpam-6659	192	17	fτ)s(ς	fτ)s(ς	NOUN
ejpam-6659	192	18	,	,	PUNCT
ejpam-6659	192	19	ς	ς	NOUN
ejpam-6659	192	20	,	,	PUNCT
ejpam-6659	192	21	gς	gς	PROPN
ejpam-6659	192	22	)	)	PUNCT
ejpam-6659	192	23	2α(gς	2α(gς	NUM
ejpam-6659	192	24	,	,	PUNCT
ejpam-6659	192	25	gς	gς	NOUN
ejpam-6659	192	26	,	,	PUNCT
ejpam-6659	192	27	τ)s(τ	τ)s(τ	NOUN
ejpam-6659	192	28	,	,	PUNCT
ejpam-6659	192	29	τ	τ	PROPN
ejpam-6659	192	30	,	,	PUNCT
ejpam-6659	192	31	gς	gς	PROPN
ejpam-6659	192	32	)	)	PUNCT
ejpam-6659	192	33	+	+	CCONJ
ejpam-6659	192	34	α(fτ	α(fτ	PROPN
ejpam-6659	192	35	,	,	PUNCT
ejpam-6659	192	36	fτ	fτ	X
ejpam-6659	192	37	,	,	PUNCT
ejpam-6659	192	38	ς)s(ς	ς)s(ς	NOUN
ejpam-6659	192	39	,	,	PUNCT
ejpam-6659	192	40	ς	ς	NOUN
ejpam-6659	192	41	,	,	PUNCT
ejpam-6659	192	42	fτ	fτ	ADJ
ejpam-6659	192	43	)	)	PUNCT
ejpam-6659	192	44	+	+	CCONJ
ejpam-6659	192	45	α(ς	α(ς	PROPN
ejpam-6659	192	46	,	,	PUNCT
ejpam-6659	192	47	ς	ς	NOUN
ejpam-6659	192	48	,	,	PUNCT
ejpam-6659	192	49	τ)s(τ	τ)s(τ	NOUN
ejpam-6659	192	50	,	,	PUNCT
ejpam-6659	192	51	τ	τ	PROPN
ejpam-6659	192	52	,	,	PUNCT
ejpam-6659	192	53	ς	ς	PROPN
ejpam-6659	192	54	)	)	PUNCT
ejpam-6659	192	55	h.	h.	PROPN
ejpam-6659	192	56	qawaqneh	qawaqneh	PROPN
ejpam-6659	192	57	et	et	PROPN
ejpam-6659	192	58	al	al	PROPN
ejpam-6659	192	59	.	.	PUNCT
ejpam-6659	192	60	/	/	SYM
ejpam-6659	192	61	eur	eur	PROPN
ejpam-6659	192	62	.	.	PUNCT
ejpam-6659	193	1	j.	j.	PROPN
ejpam-6659	193	2	pure	pure	PROPN
ejpam-6659	193	3	appl	appl	PROPN
ejpam-6659	193	4	.	.	PROPN
ejpam-6659	193	5	math	math	PROPN
ejpam-6659	193	6	,	,	PUNCT
ejpam-6659	193	7	18	18	NUM
ejpam-6659	193	8	(	(	PUNCT
ejpam-6659	193	9	3	3	NUM
ejpam-6659	193	10	)	)	PUNCT
ejpam-6659	193	11	(	(	PUNCT
ejpam-6659	193	12	2025	2025	NUM
ejpam-6659	193	13	)	)	PUNCT
ejpam-6659	193	14	,	,	PUNCT
ejpam-6659	193	15	6659	6659	NUM
ejpam-6659	193	16	10	10	NUM
ejpam-6659	193	17	of	of	ADP
ejpam-6659	193	18	16	16	NUM
ejpam-6659	193	19	for	for	ADP
ejpam-6659	193	20	all	all	DET
ejpam-6659	193	21	τ	τ	PROPN
ejpam-6659	193	22	,	,	PUNCT
ejpam-6659	193	23	ς	ς	PROPN
ejpam-6659	193	24	∈	∈	PROPN
ejpam-6659	193	25	γ	γ	NOUN
ejpam-6659	193	26	such	such	ADJ
ejpam-6659	193	27	that	that	SCONJ
ejpam-6659	193	28	τ	τ	PROPN
ejpam-6659	193	29	̸=	̸=	PROPN
ejpam-6659	193	30	ς	ς	PROPN
ejpam-6659	193	31	,	,	PUNCT
ejpam-6659	193	32	s(τ	s(τ	PROPN
ejpam-6659	193	33	,	,	PUNCT
ejpam-6659	193	34	τ	τ	PROPN
ejpam-6659	193	35	,	,	PUNCT
ejpam-6659	193	36	gς	gς	PROPN
ejpam-6659	193	37	)	)	PUNCT
ejpam-6659	193	38	+	+	CCONJ
ejpam-6659	193	39	s(ς	s(ς	PROPN
ejpam-6659	193	40	,	,	PUNCT
ejpam-6659	193	41	ς	ς	NOUN
ejpam-6659	193	42	,	,	PUNCT
ejpam-6659	193	43	fτ	fτ	ADJ
ejpam-6659	193	44	)	)	PUNCT
ejpam-6659	193	45	+	+	CCONJ
ejpam-6659	194	1	s(τ	s(τ	PROPN
ejpam-6659	194	2	,	,	PUNCT
ejpam-6659	194	3	τ	τ	PROPN
ejpam-6659	194	4	,	,	PUNCT
ejpam-6659	194	5	ς	ς	NOUN
ejpam-6659	194	6	)	)	PUNCT
ejpam-6659	194	7	̸=	̸=	PROPN
ejpam-6659	194	8	0	0	NUM
ejpam-6659	194	9	for	for	ADP
ejpam-6659	194	10	any	any	DET
ejpam-6659	194	11	two	two	NUM
ejpam-6659	194	12	nonnegative	nonnegative	ADJ
ejpam-6659	194	13	real	real	ADJ
ejpam-6659	194	14	numbers	number	NOUN
ejpam-6659	194	15	γ	γ	X
ejpam-6659	194	16	,	,	PUNCT
ejpam-6659	194	17	β	β	X
ejpam-6659	194	18	satisfying	satisfy	VERB
ejpam-6659	194	19	the	the	DET
ejpam-6659	194	20	condition	condition	NOUN
ejpam-6659	194	21	γ	γ	X
ejpam-6659	194	22	+	+	X
ejpam-6659	194	23	β	β	X
ejpam-6659	194	24	<	<	X
ejpam-6659	194	25	1	1	NUM
ejpam-6659	194	26	or	or	CCONJ
ejpam-6659	194	27	s(fτ	s(fτ	PROPN
ejpam-6659	194	28	,	,	PUNCT
ejpam-6659	194	29	fτ	fτ	NOUN
ejpam-6659	194	30	,	,	PUNCT
ejpam-6659	194	31	gς	gς	PROPN
ejpam-6659	194	32	)	)	PUNCT
ejpam-6659	194	33	=	=	SYM
ejpam-6659	194	34	0	0	PUNCT
ejpam-6659	194	35	if	if	SCONJ
ejpam-6659	194	36	s(τ	s(τ	PROPN
ejpam-6659	194	37	,	,	PUNCT
ejpam-6659	194	38	τ	τ	PROPN
ejpam-6659	194	39	,	,	PUNCT
ejpam-6659	194	40	gς	gς	PROPN
ejpam-6659	194	41	)	)	PUNCT
ejpam-6659	194	42	+	+	CCONJ
ejpam-6659	194	43	s(ς	s(ς	PROPN
ejpam-6659	194	44	,	,	PUNCT
ejpam-6659	194	45	ς	ς	NOUN
ejpam-6659	194	46	,	,	PUNCT
ejpam-6659	194	47	fτ	fτ	ADJ
ejpam-6659	194	48	)	)	PUNCT
ejpam-6659	194	49	+	+	CCONJ
ejpam-6659	194	50	s(τ	s(τ	PROPN
ejpam-6659	194	51	,	,	PUNCT
ejpam-6659	194	52	τ	τ	PROPN
ejpam-6659	194	53	,	,	PUNCT
ejpam-6659	194	54	ς	ς	PROPN
ejpam-6659	194	55	)	)	PUNCT
ejpam-6659	194	56	=	=	SYM
ejpam-6659	194	57	0	0	X
ejpam-6659	194	58	.	.	PUNCT
ejpam-6659	194	59	suppose	suppose	VERB
ejpam-6659	194	60	that	that	SCONJ
ejpam-6659	194	61	sup	sup	PROPN
ejpam-6659	194	62	ϱ≥1	ϱ≥1	PROPN
ejpam-6659	194	63	lim	lim	PROPN
ejpam-6659	194	64	i→+∞	i→+∞	PROPN
ejpam-6659	194	65	α(τi+1	α(τi+1	PROPN
ejpam-6659	194	66	,	,	PUNCT
ejpam-6659	194	67	τi+1	τi+1	X
ejpam-6659	194	68	,	,	PUNCT
ejpam-6659	194	69	τi+2).α(τϱ	τi+2).α(τϱ	NUM
ejpam-6659	194	70	,	,	PUNCT
ejpam-6659	194	71	τϱ	τϱ	X
ejpam-6659	194	72	,	,	PUNCT
ejpam-6659	194	73	τi+1	τi+1	NOUN
ejpam-6659	194	74	)	)	PUNCT
ejpam-6659	194	75	α(τi	α(τi	NOUN
ejpam-6659	194	76	,	,	PUNCT
ejpam-6659	194	77	τi	τi	ADP
ejpam-6659	194	78	,	,	PUNCT
ejpam-6659	194	79	τi+1	τi+1	X
ejpam-6659	194	80	)	)	PUNCT
ejpam-6659	194	81	<	<	X
ejpam-6659	194	82	1	1	NUM
ejpam-6659	194	83	2(γ	2(γ	NUM
ejpam-6659	194	84	+	+	CCONJ
ejpam-6659	194	85	β	β	NOUN
ejpam-6659	194	86	)	)	PUNCT
ejpam-6659	194	87	,	,	PUNCT
ejpam-6659	194	88	(	(	PUNCT
ejpam-6659	194	89	6	6	NUM
ejpam-6659	194	90	)	)	PUNCT
ejpam-6659	194	91	and	and	CCONJ
ejpam-6659	194	92	lim	lim	PROPN
ejpam-6659	195	1	ω→+∞	ω→+∞	PROPN
ejpam-6659	195	2	α(τω	α(τω	NUM
ejpam-6659	195	3	,	,	PUNCT
ejpam-6659	195	4	τω	τω	INTJ
ejpam-6659	195	5	,	,	PUNCT
ejpam-6659	195	6	τω+1	τω+1	NUM
ejpam-6659	195	7	)	)	PUNCT
ejpam-6659	195	8	exists	exist	VERB
ejpam-6659	195	9	.	.	PUNCT
ejpam-6659	196	1	then	then	ADV
ejpam-6659	196	2	there	there	PRON
ejpam-6659	196	3	exists	exist	VERB
ejpam-6659	196	4	a	a	DET
ejpam-6659	196	5	unique	unique	ADJ
ejpam-6659	196	6	common	common	ADJ
ejpam-6659	196	7	fixed	fix	VERB
ejpam-6659	196	8	point	point	NOUN
ejpam-6659	196	9	for	for	ADP
ejpam-6659	196	10	f	f	PROPN
ejpam-6659	196	11	and	and	CCONJ
ejpam-6659	196	12	g.	g.	PROPN
ejpam-6659	196	13	proof	proof	NOUN
ejpam-6659	196	14	.	.	PUNCT
ejpam-6659	197	1	let	let	VERB
ejpam-6659	197	2	τ0	τ0	NOUN
ejpam-6659	197	3	∈	∈	PROPN
ejpam-6659	197	4	γ	γ	X
ejpam-6659	197	5	and	and	CCONJ
ejpam-6659	197	6	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	197	7	=	=	SYM
ejpam-6659	197	8	fτ2κ	fτ2κ	NOUN
ejpam-6659	197	9	,	,	PUNCT
ejpam-6659	197	10	τ2κ+2	τ2κ+2	SYM
ejpam-6659	197	11	=	=	SYM
ejpam-6659	197	12	gτ2κ+1	gτ2κ+1	PROPN
ejpam-6659	197	13	,	,	PUNCT
ejpam-6659	197	14	κ	κ	PROPN
ejpam-6659	197	15	∈	∈	PROPN
ejpam-6659	197	16	{	{	PUNCT
ejpam-6659	197	17	0	0	NUM
ejpam-6659	197	18	,	,	PUNCT
ejpam-6659	197	19	1	1	NUM
ejpam-6659	197	20	,	,	PUNCT
ejpam-6659	197	21	2	2	NUM
ejpam-6659	197	22	,	,	PUNCT
ejpam-6659	197	23	}	}	PUNCT
ejpam-6659	197	24	.	.	PUNCT
ejpam-6659	198	1	thus	thus	ADV
ejpam-6659	198	2	,	,	PUNCT
ejpam-6659	198	3	s(τ2κ+1	s(τ2κ+1	ADJ
ejpam-6659	198	4	,	,	PUNCT
ejpam-6659	198	5	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	198	6	,	,	PUNCT
ejpam-6659	198	7	τ2κ+2	τ2κ+2	NUM
ejpam-6659	198	8	)	)	PUNCT
ejpam-6659	198	9	=	=	SYM
ejpam-6659	198	10	s(fτ2κ	s(fτ2κ	NOUN
ejpam-6659	198	11	,	,	PUNCT
ejpam-6659	198	12	fτ2κ	fτ2κ	NOUN
ejpam-6659	198	13	,	,	PUNCT
ejpam-6659	198	14	gτ2κ+1	gτ2κ+1	NOUN
ejpam-6659	198	15	)	)	PUNCT
ejpam-6659	198	16	≾	≾	PROPN
ejpam-6659	198	17	γs(τ2κ	γs(τ2κ	PROPN
ejpam-6659	198	18	,	,	PUNCT
ejpam-6659	198	19	τ2κ	τ2κ	ADJ
ejpam-6659	198	20	,	,	PUNCT
ejpam-6659	198	21	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	198	22	)	)	PUNCT
ejpam-6659	198	23	+	+	CCONJ
ejpam-6659	198	24	βs(τ2κ	βs(τ2κ	NOUN
ejpam-6659	198	25	,	,	PUNCT
ejpam-6659	198	26	τ2κ	τ2κ	ADJ
ejpam-6659	198	27	,	,	PUNCT
ejpam-6659	198	28	fτ2κ)s(τ2κ+1	fτ2κ)s(τ2κ+1	ADJ
ejpam-6659	198	29	,	,	PUNCT
ejpam-6659	198	30	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	198	31	,	,	PUNCT
ejpam-6659	198	32	gτ2κ+1	gτ2κ+1	PROPN
ejpam-6659	198	33	)	)	PUNCT
ejpam-6659	198	34	(	(	PUNCT
ejpam-6659	198	35	2α(gτ2κ+1	2α(gτ2κ+1	NUM
ejpam-6659	198	36	,	,	PUNCT
ejpam-6659	198	37	gτ2κ+1	gτ2κ+1	PROPN
ejpam-6659	198	38	,	,	PUNCT
ejpam-6659	198	39	τ2κ)s(τ2κ	τ2κ)s(τ2κ	ADJ
ejpam-6659	198	40	,	,	PUNCT
ejpam-6659	198	41	τ2κ	τ2κ	ADV
ejpam-6659	198	42	,	,	PUNCT
ejpam-6659	198	43	gτ2κ+1	gτ2κ+1	PROPN
ejpam-6659	198	44	)	)	PUNCT
ejpam-6659	198	45	+	+	NUM
ejpam-6659	198	46	α(fτ2κ	α(fτ2κ	NOUN
ejpam-6659	198	47	,	,	PUNCT
ejpam-6659	198	48	fτ2κ	fτ2κ	NOUN
ejpam-6659	198	49	,	,	PUNCT
ejpam-6659	198	50	τ2κ+1)s(τ2κ+1	τ2κ+1)s(τ2κ+1	NUM
ejpam-6659	198	51	,	,	PUNCT
ejpam-6659	198	52	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	198	53	,	,	PUNCT
ejpam-6659	198	54	fτ2κ	fτ2κ	NOUN
ejpam-6659	198	55	)	)	PUNCT
ejpam-6659	199	1	+	+	CCONJ
ejpam-6659	199	2	α(τ2κ+1	α(τ2κ+1	ADJ
ejpam-6659	199	3	,	,	PUNCT
ejpam-6659	199	4	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	199	5	,	,	PUNCT
ejpam-6659	199	6	τ2κ)s(τ2κ	τ2κ)s(τ2κ	ADJ
ejpam-6659	199	7	,	,	PUNCT
ejpam-6659	199	8	τ2κ	τ2κ	ADV
ejpam-6659	199	9	,	,	PUNCT
ejpam-6659	199	10	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	199	11	)	)	PUNCT
ejpam-6659	199	12	)	)	PUNCT
ejpam-6659	200	1	=	=	SYM
ejpam-6659	200	2	γs(τ2κ	γs(τ2κ	PROPN
ejpam-6659	200	3	,	,	PUNCT
ejpam-6659	200	4	τ2κ	τ2κ	ADJ
ejpam-6659	200	5	,	,	PUNCT
ejpam-6659	200	6	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	200	7	)	)	PUNCT
ejpam-6659	200	8	+	+	CCONJ
ejpam-6659	200	9	βs(τ2κ	βs(τ2κ	NOUN
ejpam-6659	200	10	,	,	PUNCT
ejpam-6659	200	11	τ2κ	τ2κ	X
ejpam-6659	200	12	,	,	PUNCT
ejpam-6659	200	13	τ2κ+1)s(τ2κ+1	τ2κ+1)s(τ2κ+1	PRON
ejpam-6659	200	14	,	,	PUNCT
ejpam-6659	200	15	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	200	16	,	,	PUNCT
ejpam-6659	200	17	τ2κ+2	τ2κ+2	NUM
ejpam-6659	200	18	)	)	PUNCT
ejpam-6659	200	19	(	(	PUNCT
ejpam-6659	200	20	2α(τ2κ+2	2α(τ2κ+2	NUM
ejpam-6659	200	21	,	,	PUNCT
ejpam-6659	200	22	τ2κ+2	τ2κ+2	NUM
ejpam-6659	200	23	,	,	PUNCT
ejpam-6659	200	24	τ2κ)s(τ2κ	τ2κ)s(τ2κ	ADJ
ejpam-6659	200	25	,	,	PUNCT
ejpam-6659	200	26	τ2κ	τ2κ	ADV
ejpam-6659	200	27	,	,	PUNCT
ejpam-6659	200	28	τ2κ+2	τ2κ+2	NUM
ejpam-6659	200	29	)	)	PUNCT
ejpam-6659	200	30	+	+	CCONJ
ejpam-6659	200	31	α(τ2κ+1	α(τ2κ+1	ADJ
ejpam-6659	200	32	,	,	PUNCT
ejpam-6659	200	33	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	200	34	,	,	PUNCT
ejpam-6659	200	35	τ2κ+1)s(τ2κ+1	τ2κ+1)s(τ2κ+1	NUM
ejpam-6659	200	36	,	,	PUNCT
ejpam-6659	200	37	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	200	38	,	,	PUNCT
ejpam-6659	200	39	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	200	40	)	)	PUNCT
ejpam-6659	200	41	+	+	CCONJ
ejpam-6659	200	42	α(τ2κ+1	α(τ2κ+1	ADJ
ejpam-6659	200	43	,	,	PUNCT
ejpam-6659	200	44	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	200	45	,	,	PUNCT
ejpam-6659	200	46	τ2κ)s(τ2κ	τ2κ)s(τ2κ	ADJ
ejpam-6659	200	47	,	,	PUNCT
ejpam-6659	200	48	τ2κ	τ2κ	ADV
ejpam-6659	200	49	,	,	PUNCT
ejpam-6659	200	50	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	200	51	)	)	PUNCT
ejpam-6659	200	52	)	)	PUNCT
ejpam-6659	200	53	.	.	PUNCT
ejpam-6659	201	1	hence	hence	ADV
ejpam-6659	201	2	,	,	PUNCT
ejpam-6659	201	3	|s(τ2κ+1	|s(τ2κ+1	ADJ
ejpam-6659	201	4	,	,	PUNCT
ejpam-6659	201	5	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	201	6	,	,	PUNCT
ejpam-6659	201	7	τ2κ+2)|	τ2κ+2)|	PROPN
ejpam-6659	201	8	≤	≤	ADV
ejpam-6659	201	9	γ|s(τ2κ	γ|s(τ2κ	NOUN
ejpam-6659	201	10	,	,	PUNCT
ejpam-6659	201	11	τ2κ	τ2κ	PROPN
ejpam-6659	201	12	,	,	PUNCT
ejpam-6659	201	13	τ2κ+1)|	τ2κ+1)|	PRON
ejpam-6659	201	14	+	+	NUM
ejpam-6659	201	15	β|s(τ2κ	β|s(τ2κ	PROPN
ejpam-6659	201	16	,	,	PUNCT
ejpam-6659	201	17	τ2κ	τ2κ	ADJ
ejpam-6659	201	18	,	,	PUNCT
ejpam-6659	201	19	τ2κ+1)||s(τ2κ+1	τ2κ+1)||s(τ2κ+1	ADP
ejpam-6659	201	20	,	,	PUNCT
ejpam-6659	201	21	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	201	22	,	,	PUNCT
ejpam-6659	201	23	τ2κ+2)|	τ2κ+2)|	PROPN
ejpam-6659	201	24	(	(	PUNCT
ejpam-6659	201	25	|2α(τ2κ+2	|2α(τ2κ+2	PROPN
ejpam-6659	201	26	,	,	PUNCT
ejpam-6659	201	27	τ2κ+2	τ2κ+2	ADJ
ejpam-6659	201	28	,	,	PUNCT
ejpam-6659	201	29	τ2κ)s(τ2κ	τ2κ)s(τ2κ	ADJ
ejpam-6659	201	30	,	,	PUNCT
ejpam-6659	201	31	τ2κ	τ2κ	ADV
ejpam-6659	201	32	,	,	PUNCT
ejpam-6659	201	33	τ2κ+2	τ2κ+2	NUM
ejpam-6659	201	34	)	)	PUNCT
ejpam-6659	201	35	+	+	CCONJ
ejpam-6659	201	36	α(τ2κ+1	α(τ2κ+1	ADJ
ejpam-6659	201	37	,	,	PUNCT
ejpam-6659	201	38	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	201	39	,	,	PUNCT
ejpam-6659	201	40	τ2κ)s(τ2κ	τ2κ)s(τ2κ	ADJ
ejpam-6659	201	41	,	,	PUNCT
ejpam-6659	201	42	τ2κ	τ2κ	PROPN
ejpam-6659	201	43	,	,	PUNCT
ejpam-6659	201	44	τ2κ+1)|	τ2κ+1)|	PROPN
ejpam-6659	201	45	)	)	PUNCT
ejpam-6659	201	46	.	.	PUNCT
ejpam-6659	202	1	by	by	ADP
ejpam-6659	202	2	cv	cv	PROPN
ejpam-6659	202	3	cs3	cs3	PROPN
ejpam-6659	202	4	and	and	CCONJ
ejpam-6659	202	5	lemma	lemma	PROPN
ejpam-6659	202	6	3	3	NUM
ejpam-6659	202	7	,	,	PUNCT
ejpam-6659	202	8	we	we	PRON
ejpam-6659	202	9	see	see	VERB
ejpam-6659	202	10	that	that	DET
ejpam-6659	202	11	|s(τ2κ+1	|s(τ2κ+1	ADJ
ejpam-6659	202	12	,	,	PUNCT
ejpam-6659	202	13	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	202	14	,	,	PUNCT
ejpam-6659	202	15	τ2κ+2)|	τ2κ+2)|	PROPN
ejpam-6659	202	16	=	=	SYM
ejpam-6659	202	17	|s(τ2κ+2	|s(τ2κ+2	PROPN
ejpam-6659	202	18	,	,	PUNCT
ejpam-6659	202	19	τ2κ+2	τ2κ+2	PROPN
ejpam-6659	202	20	,	,	PUNCT
ejpam-6659	202	21	τ2κ+1)|	τ2κ+1)|	DET
ejpam-6659	202	22	≤	≤	PROPN
ejpam-6659	202	23	|2α(τ2κ+2	|2α(τ2κ+2	ADJ
ejpam-6659	202	24	,	,	PUNCT
ejpam-6659	202	25	τ2κ+2	τ2κ+2	PROPN
ejpam-6659	202	26	,	,	PUNCT
ejpam-6659	202	27	τ2κ)s(τ2κ+2	τ2κ)s(τ2κ+2	ADJ
ejpam-6659	202	28	,	,	PUNCT
ejpam-6659	202	29	τ2κ+2	τ2κ+2	NUM
ejpam-6659	202	30	,	,	PUNCT
ejpam-6659	202	31	τ2κ	τ2κ	PUNCT
ejpam-6659	202	32	)	)	PUNCT
ejpam-6659	202	33	+	+	CCONJ
ejpam-6659	202	34	α(τ2κ+1	α(τ2κ+1	ADJ
ejpam-6659	202	35	,	,	PUNCT
ejpam-6659	202	36	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	202	37	,	,	PUNCT
ejpam-6659	202	38	τ2κ)s(τ2κ+1	τ2κ)s(τ2κ+1	PRON
ejpam-6659	202	39	,	,	PUNCT
ejpam-6659	202	40	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	202	41	,	,	PUNCT
ejpam-6659	202	42	τ2κ)|	τ2κ)|	PUNCT
ejpam-6659	202	43	=	=	SYM
ejpam-6659	202	44	|2α(τ2κ+2	|2α(τ2κ+2	PROPN
ejpam-6659	202	45	,	,	PUNCT
ejpam-6659	202	46	τ2κ+2	τ2κ+2	ADJ
ejpam-6659	202	47	,	,	PUNCT
ejpam-6659	202	48	τ2κ)s(τ2κ	τ2κ)s(τ2κ	ADJ
ejpam-6659	202	49	,	,	PUNCT
ejpam-6659	202	50	τ2κ	τ2κ	ADV
ejpam-6659	202	51	,	,	PUNCT
ejpam-6659	202	52	τ2κ+2	τ2κ+2	NUM
ejpam-6659	202	53	)	)	PUNCT
ejpam-6659	202	54	+	+	CCONJ
ejpam-6659	202	55	α(τ2κ+1	α(τ2κ+1	ADJ
ejpam-6659	202	56	,	,	PUNCT
ejpam-6659	202	57	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	202	58	,	,	PUNCT
ejpam-6659	202	59	τ2κ)s(τ2κ	τ2κ)s(τ2κ	ADJ
ejpam-6659	202	60	,	,	PUNCT
ejpam-6659	202	61	τ2κ	τ2κ	PROPN
ejpam-6659	202	62	,	,	PUNCT
ejpam-6659	202	63	τ2κ+1)|	τ2κ+1)|	PROPN
ejpam-6659	202	64	.	.	PUNCT
ejpam-6659	203	1	thus	thus	ADV
ejpam-6659	203	2	,	,	PUNCT
ejpam-6659	203	3	|s(τ2κ+1	|s(τ2κ+1	ADJ
ejpam-6659	203	4	,	,	PUNCT
ejpam-6659	203	5	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	203	6	,	,	PUNCT
ejpam-6659	203	7	τ2κ+2)|	τ2κ+2)|	PROPN
ejpam-6659	203	8	≤	≤	ADV
ejpam-6659	203	9	γ|s(τ2κ	γ|s(τ2κ	NOUN
ejpam-6659	203	10	,	,	PUNCT
ejpam-6659	203	11	τ2κ	τ2κ	PROPN
ejpam-6659	203	12	,	,	PUNCT
ejpam-6659	203	13	τ2κ+1)|+	τ2κ+1)|+	PUNCT
ejpam-6659	203	14	β|s(τ2κ	β|s(τ2κ	NOUN
ejpam-6659	203	15	,	,	PUNCT
ejpam-6659	203	16	τ2κ	τ2κ	PROPN
ejpam-6659	203	17	,	,	PUNCT
ejpam-6659	203	18	τ2κ+1)|	τ2κ+1)|	PROPN
ejpam-6659	203	19	=	=	SYM
ejpam-6659	203	20	(	(	PUNCT
ejpam-6659	203	21	γ	γ	X
ejpam-6659	203	22	+	+	X
ejpam-6659	203	23	β)|s(τ2κ	β)|s(τ2κ	NOUN
ejpam-6659	203	24	,	,	PUNCT
ejpam-6659	203	25	τ2κ	τ2κ	PROPN
ejpam-6659	203	26	,	,	PUNCT
ejpam-6659	203	27	τ2κ+1)|	τ2κ+1)|	PROPN
ejpam-6659	203	28	.	.	PUNCT
ejpam-6659	204	1	likewise	likewise	ADV
ejpam-6659	204	2	,	,	PUNCT
ejpam-6659	204	3	we	we	PRON
ejpam-6659	204	4	obtain	obtain	VERB
ejpam-6659	204	5	|s(τ2κ+2	|s(τ2κ+2	NOUN
ejpam-6659	204	6	,	,	PUNCT
ejpam-6659	204	7	τ2κ+2	τ2κ+2	PROPN
ejpam-6659	204	8	,	,	PUNCT
ejpam-6659	204	9	τ2κ+3)|	τ2κ+3)|	PROPN
ejpam-6659	204	10	=	=	SYM
ejpam-6659	204	11	(	(	PUNCT
ejpam-6659	204	12	γ	γ	X
ejpam-6659	204	13	+	+	CCONJ
ejpam-6659	204	14	β)|s(τ2κ+1	β)|s(τ2κ+1	PROPN
ejpam-6659	204	15	,	,	PUNCT
ejpam-6659	204	16	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	204	17	,	,	PUNCT
ejpam-6659	204	18	τ2κ+2)|	τ2κ+2)|	PROPN
ejpam-6659	204	19	.	.	PUNCT
ejpam-6659	205	1	therefore	therefore	ADV
ejpam-6659	205	2	,	,	PUNCT
ejpam-6659	205	3	|s(τω	|s(τω	PROPN
ejpam-6659	205	4	,	,	PUNCT
ejpam-6659	205	5	τω	τω	INTJ
ejpam-6659	205	6	,	,	PUNCT
ejpam-6659	205	7	τω+1)|	τω+1)|	NUM
ejpam-6659	205	8	≤	≤	NOUN
ejpam-6659	205	9	(	(	PUNCT
ejpam-6659	205	10	γ	γ	X
ejpam-6659	205	11	+	+	PROPN
ejpam-6659	205	12	β)|s(τω−1	β)|s(τω−1	PROPN
ejpam-6659	205	13	,	,	PUNCT
ejpam-6659	205	14	τω−1	τω−1	PROPN
ejpam-6659	205	15	,	,	PUNCT
ejpam-6659	205	16	τω|	τω|	X
ejpam-6659	205	17	≤	≤	NUM
ejpam-6659	205	18	...	...	PUNCT
ejpam-6659	206	1	≤	≤	NUM
ejpam-6659	206	2	(	(	PUNCT
ejpam-6659	206	3	γ	γ	X
ejpam-6659	206	4	+	+	SYM
ejpam-6659	206	5	β)ω|s(τ0	β)ω|s(τ0	PROPN
ejpam-6659	206	6	,	,	PUNCT
ejpam-6659	206	7	τ0	τ0	NOUN
ejpam-6659	206	8	,	,	PUNCT
ejpam-6659	206	9	τ1	τ1	NOUN
ejpam-6659	206	10	)	)	PUNCT
ejpam-6659	206	11	.	.	PUNCT
ejpam-6659	207	1	h.	h.	PROPN
ejpam-6659	207	2	qawaqneh	qawaqneh	PROPN
ejpam-6659	207	3	et	et	PROPN
ejpam-6659	207	4	al	al	PROPN
ejpam-6659	207	5	.	.	PUNCT
ejpam-6659	207	6	/	/	SYM
ejpam-6659	207	7	eur	eur	PROPN
ejpam-6659	207	8	.	.	PUNCT
ejpam-6659	208	1	j.	j.	PROPN
ejpam-6659	208	2	pure	pure	PROPN
ejpam-6659	208	3	appl	appl	PROPN
ejpam-6659	208	4	.	.	PROPN
ejpam-6659	208	5	math	math	PROPN
ejpam-6659	208	6	,	,	PUNCT
ejpam-6659	208	7	18	18	NUM
ejpam-6659	208	8	(	(	PUNCT
ejpam-6659	208	9	3	3	NUM
ejpam-6659	208	10	)	)	PUNCT
ejpam-6659	208	11	(	(	PUNCT
ejpam-6659	208	12	2025	2025	NUM
ejpam-6659	208	13	)	)	PUNCT
ejpam-6659	208	14	,	,	PUNCT
ejpam-6659	208	15	6659	6659	NUM
ejpam-6659	208	16	11	11	NUM
ejpam-6659	208	17	of	of	ADP
ejpam-6659	208	18	16	16	NUM
ejpam-6659	208	19	hence	hence	ADV
ejpam-6659	208	20	,	,	PUNCT
ejpam-6659	208	21	for	for	ADP
ejpam-6659	208	22	any	any	DET
ejpam-6659	208	23	ϱ	ϱ	PROPN
ejpam-6659	208	24	>	>	X
ejpam-6659	208	25	ω	ω	PROPN
ejpam-6659	208	26	,	,	PUNCT
ejpam-6659	208	27	we	we	PRON
ejpam-6659	208	28	have	have	VERB
ejpam-6659	208	29	s(τϱ	s(τϱ	ADV
ejpam-6659	208	30	,	,	PUNCT
ejpam-6659	208	31	τϱ	τϱ	PROPN
ejpam-6659	208	32	,	,	PUNCT
ejpam-6659	208	33	τω	τω	INTJ
ejpam-6659	208	34	)	)	PUNCT
ejpam-6659	208	35	≾	≾	PROPN
ejpam-6659	208	36	2α(τϱ	2α(τϱ	NUM
ejpam-6659	208	37	,	,	PUNCT
ejpam-6659	208	38	τϱ	τϱ	PROPN
ejpam-6659	208	39	,	,	PUNCT
ejpam-6659	208	40	τω+1)(2α(τϱ	τω+1)(2α(τϱ	PRON
ejpam-6659	208	41	,	,	PUNCT
ejpam-6659	208	42	τϱ	τϱ	PROPN
ejpam-6659	208	43	,	,	PUNCT
ejpam-6659	208	44	τω+2)s(τϱ	τω+2)s(τϱ	PROPN
ejpam-6659	208	45	,	,	PUNCT
ejpam-6659	208	46	τϱ	τϱ	PROPN
ejpam-6659	208	47	,	,	PUNCT
ejpam-6659	208	48	τω+2	τω+2	NUM
ejpam-6659	208	49	)	)	PUNCT
ejpam-6659	209	1	+	+	NUM
ejpam-6659	209	2	α(τω+1	α(τω+1	NOUN
ejpam-6659	209	3	,	,	PUNCT
ejpam-6659	209	4	τω+1	τω+1	X
ejpam-6659	209	5	,	,	PUNCT
ejpam-6659	209	6	τω+2)s(τω+1	τω+2)s(τω+1	NOUN
ejpam-6659	209	7	,	,	PUNCT
ejpam-6659	209	8	τω+1	τω+1	SYM
ejpam-6659	209	9	,	,	PUNCT
ejpam-6659	209	10	τω+2	τω+2	NUM
ejpam-6659	209	11	)	)	PUNCT
ejpam-6659	209	12	)	)	PUNCT
ejpam-6659	210	1	+	+	CCONJ
ejpam-6659	210	2	α(τω	α(τω	NUM
ejpam-6659	210	3	,	,	PUNCT
ejpam-6659	210	4	τω	τω	INTJ
ejpam-6659	210	5	,	,	PUNCT
ejpam-6659	210	6	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	210	7	,	,	PUNCT
ejpam-6659	210	8	τω	τω	INTJ
ejpam-6659	210	9	,	,	PUNCT
ejpam-6659	210	10	τω+1	τω+1	NUM
ejpam-6659	210	11	)	)	PUNCT
ejpam-6659	210	12	=	=	SYM
ejpam-6659	210	13	α(τω	α(τω	NOUN
ejpam-6659	210	14	,	,	PUNCT
ejpam-6659	210	15	τω	τω	INTJ
ejpam-6659	210	16	,	,	PUNCT
ejpam-6659	210	17	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	210	18	,	,	PUNCT
ejpam-6659	210	19	τω	τω	INTJ
ejpam-6659	210	20	,	,	PUNCT
ejpam-6659	210	21	τω+1	τω+1	PUNCT
ejpam-6659	210	22	)	)	PUNCT
ejpam-6659	210	23	+	+	CCONJ
ejpam-6659	210	24	2α(τϱ	2α(τϱ	NUM
ejpam-6659	210	25	,	,	PUNCT
ejpam-6659	210	26	τϱ	τϱ	NOUN
ejpam-6659	210	27	,	,	PUNCT
ejpam-6659	210	28	τω+1)α(τω+1	τω+1)α(τω+1	NOUN
ejpam-6659	210	29	,	,	PUNCT
ejpam-6659	210	30	τω+1	τω+1	CCONJ
ejpam-6659	210	31	,	,	PUNCT
ejpam-6659	210	32	τω+2)s(τω+1	τω+2)s(τω+1	NOUN
ejpam-6659	210	33	,	,	PUNCT
ejpam-6659	210	34	τω+1	τω+1	X
ejpam-6659	210	35	,	,	PUNCT
ejpam-6659	210	36	τω+2	τω+2	NUM
ejpam-6659	210	37	)	)	PUNCT
ejpam-6659	210	38	+	+	CCONJ
ejpam-6659	210	39	22α(τϱ	22α(τϱ	NUM
ejpam-6659	210	40	,	,	PUNCT
ejpam-6659	210	41	τϱ	τϱ	X
ejpam-6659	210	42	,	,	PUNCT
ejpam-6659	210	43	τω+1	τω+1	X
ejpam-6659	210	44	)	)	PUNCT
ejpam-6659	210	45	α(τϱ	α(τϱ	NUM
ejpam-6659	210	46	,	,	PUNCT
ejpam-6659	210	47	τϱ	τϱ	PROPN
ejpam-6659	210	48	,	,	PUNCT
ejpam-6659	210	49	τω+2)s(τϱ	τω+2)s(τϱ	PROPN
ejpam-6659	210	50	,	,	PUNCT
ejpam-6659	210	51	τϱ	τϱ	PROPN
ejpam-6659	210	52	,	,	PUNCT
ejpam-6659	210	53	τω+2	τω+2	NUM
ejpam-6659	210	54	)	)	PUNCT
ejpam-6659	210	55	.	.	PUNCT
ejpam-6659	211	1	using	use	VERB
ejpam-6659	211	2	triangle	triangle	NOUN
ejpam-6659	211	3	inequality	inequality	NOUN
ejpam-6659	211	4	again	again	ADV
ejpam-6659	211	5	in	in	ADP
ejpam-6659	211	6	a	a	DET
ejpam-6659	211	7	same	same	ADJ
ejpam-6659	211	8	way	way	NOUN
ejpam-6659	211	9	,	,	PUNCT
ejpam-6659	211	10	we	we	PRON
ejpam-6659	211	11	obtain	obtain	VERB
ejpam-6659	211	12	s(τϱ	s(τϱ	ADV
ejpam-6659	211	13	,	,	PUNCT
ejpam-6659	211	14	τϱ	τϱ	PROPN
ejpam-6659	211	15	,	,	PUNCT
ejpam-6659	211	16	τω	τω	INTJ
ejpam-6659	211	17	)	)	PUNCT
ejpam-6659	211	18	≾	≾	PROPN
ejpam-6659	211	19	α(τω	α(τω	NUM
ejpam-6659	211	20	,	,	PUNCT
ejpam-6659	211	21	τω	τω	INTJ
ejpam-6659	211	22	,	,	PUNCT
ejpam-6659	211	23	τω+1)s(τω	τω+1)s(τω	PROPN
ejpam-6659	211	24	,	,	PUNCT
ejpam-6659	211	25	τω	τω	INTJ
ejpam-6659	211	26	,	,	PUNCT
ejpam-6659	211	27	τω+1	τω+1	PUNCT
ejpam-6659	211	28	)	)	PUNCT
ejpam-6659	211	29	+	+	CCONJ
ejpam-6659	211	30	ϱ−2∑	ϱ−2∑	PROPN
ejpam-6659	211	31	i	i	NOUN
ejpam-6659	211	32	=	=	NOUN
ejpam-6659	211	33	ω+1	ω+1	NUM
ejpam-6659	211	34	2i−ω	2i−ω	NOUN
ejpam-6659	211	35	i∏	i∏	VERB
ejpam-6659	211	36	j	j	NOUN
ejpam-6659	211	37	=	=	PROPN
ejpam-6659	211	38	ω+1	ω+1	SYM
ejpam-6659	211	39	α(τϱ	α(τϱ	NUM
ejpam-6659	211	40	,	,	PUNCT
ejpam-6659	211	41	τϱ	τϱ	NOUN
ejpam-6659	211	42	,	,	PUNCT
ejpam-6659	211	43	τj)α(τi	τj)α(τi	PRON
ejpam-6659	211	44	,	,	PUNCT
ejpam-6659	211	45	τi	τi	NOUN
ejpam-6659	211	46	,	,	PUNCT
ejpam-6659	211	47	τi+1)s(τi	τi+1)s(τi	NOUN
ejpam-6659	211	48	,	,	PUNCT
ejpam-6659	211	49	τi	τi	NOUN
ejpam-6659	211	50	,	,	PUNCT
ejpam-6659	211	51	τi+1	τi+1	PROPN
ejpam-6659	211	52	)	)	PUNCT
ejpam-6659	211	53	+	+	NUM
ejpam-6659	212	1	2ϱ−ω−1	2ϱ−ω−1	NUM
ejpam-6659	212	2	ϱ−1∏	ϱ−1∏	VERB
ejpam-6659	212	3	k	k	NOUN
ejpam-6659	212	4	=	=	PROPN
ejpam-6659	212	5	ω+1	ω+1	SYM
ejpam-6659	212	6	α(τϱ	α(τϱ	NUM
ejpam-6659	212	7	,	,	PUNCT
ejpam-6659	212	8	τϱ	τϱ	PROPN
ejpam-6659	212	9	,	,	PUNCT
ejpam-6659	212	10	τk)s(τϱ−1	τk)s(τϱ−1	PROPN
ejpam-6659	212	11	,	,	PUNCT
ejpam-6659	212	12	τϱ−1	τϱ−1	NOUN
ejpam-6659	212	13	,	,	PUNCT
ejpam-6659	212	14	τϱ	τϱ	X
ejpam-6659	212	15	)	)	PUNCT
ejpam-6659	212	16	≾	≾	NOUN
ejpam-6659	212	17	α(τω	α(τω	NUM
ejpam-6659	212	18	,	,	PUNCT
ejpam-6659	212	19	τω	τω	INTJ
ejpam-6659	212	20	,	,	PUNCT
ejpam-6659	212	21	τω+1)(γ	τω+1)(γ	PUNCT
ejpam-6659	212	22	+	+	NUM
ejpam-6659	212	23	β)ωs(τ0	β)ωs(τ0	PROPN
ejpam-6659	212	24	,	,	PUNCT
ejpam-6659	212	25	τ0	τ0	NOUN
ejpam-6659	212	26	,	,	PUNCT
ejpam-6659	212	27	τ1	τ1	NOUN
ejpam-6659	212	28	)	)	PUNCT
ejpam-6659	213	1	+	+	CCONJ
ejpam-6659	213	2	ϱ−1∑	ϱ−1∑	NUM
ejpam-6659	213	3	i	i	NOUN
ejpam-6659	213	4	=	=	NOUN
ejpam-6659	213	5	ω+1	ω+1	NUM
ejpam-6659	213	6	2i−ω	2i−ω	NOUN
ejpam-6659	213	7	i∏	i∏	VERB
ejpam-6659	213	8	j	j	NOUN
ejpam-6659	213	9	=	=	PROPN
ejpam-6659	213	10	ω+1	ω+1	SYM
ejpam-6659	213	11	α(τϱ	α(τϱ	NUM
ejpam-6659	213	12	,	,	PUNCT
ejpam-6659	213	13	τϱ	τϱ	NOUN
ejpam-6659	213	14	,	,	PUNCT
ejpam-6659	213	15	τj)α(τi	τj)α(τi	PRON
ejpam-6659	213	16	,	,	PUNCT
ejpam-6659	213	17	τi	τi	ADP
ejpam-6659	213	18	,	,	PUNCT
ejpam-6659	213	19	τi+1)(γ	τi+1)(γ	NOUN
ejpam-6659	213	20	+	+	CCONJ
ejpam-6659	213	21	β)is(τ0	β)is(τ0	PROPN
ejpam-6659	213	22	,	,	PUNCT
ejpam-6659	213	23	τ0	τ0	NOUN
ejpam-6659	213	24	,	,	PUNCT
ejpam-6659	213	25	τ1	τ1	NOUN
ejpam-6659	213	26	)	)	PUNCT
ejpam-6659	213	27	.	.	PUNCT
ejpam-6659	214	1	as	as	ADP
ejpam-6659	214	2	ω	ω	PROPN
ejpam-6659	214	3	,	,	PUNCT
ejpam-6659	214	4	ϱ	ϱ	PROPN
ejpam-6659	214	5	→	→	SYM
ejpam-6659	214	6	+	+	PROPN
ejpam-6659	214	7	∞	∞	PROPN
ejpam-6659	214	8	,	,	PUNCT
ejpam-6659	214	9	one	one	NUM
ejpam-6659	214	10	has	have	VERB
ejpam-6659	214	11	ϱ−1∑	ϱ−1∑	PROPN
ejpam-6659	214	12	i	i	PROPN
ejpam-6659	214	13	=	=	NOUN
ejpam-6659	214	14	ω+1	ω+1	NUM
ejpam-6659	214	15	2i−ω	2i−ω	NOUN
ejpam-6659	214	16	i∏	i∏	VERB
ejpam-6659	214	17	j	j	NOUN
ejpam-6659	214	18	=	=	PROPN
ejpam-6659	214	19	ω+1	ω+1	SYM
ejpam-6659	214	20	α(τϱ	α(τϱ	NUM
ejpam-6659	214	21	,	,	PUNCT
ejpam-6659	214	22	τϱ	τϱ	NOUN
ejpam-6659	214	23	,	,	PUNCT
ejpam-6659	214	24	τj)α(τi	τj)α(τi	PRON
ejpam-6659	214	25	,	,	PUNCT
ejpam-6659	214	26	τi	τi	ADP
ejpam-6659	214	27	,	,	PUNCT
ejpam-6659	214	28	τi+1)(γ	τi+1)(γ	X
ejpam-6659	214	29	+	+	CCONJ
ejpam-6659	214	30	β)i	β)i	ADJ
ejpam-6659	214	31	→	→	X
ejpam-6659	214	32	0	0	NUM
ejpam-6659	214	33	,	,	PUNCT
ejpam-6659	214	34	if	if	SCONJ
ejpam-6659	214	35	supϱ≥1	supϱ≥1	PROPN
ejpam-6659	214	36	lim	lim	PROPN
ejpam-6659	214	37	i→+∞	i→+∞	PROPN
ejpam-6659	214	38	α(τi+1,τi+1,τi+2).α(τϱ,τϱ,τi+1	α(τi+1,τi+1,τi+2).α(τϱ,τϱ,τi+1	PROPN
ejpam-6659	214	39	)	)	PUNCT
ejpam-6659	214	40	α(τi	α(τi	NOUN
ejpam-6659	214	41	,	,	PUNCT
ejpam-6659	214	42	τi	τi	ADP
ejpam-6659	214	43	,	,	PUNCT
ejpam-6659	214	44	τi+1	τi+1	X
ejpam-6659	214	45	)	)	PUNCT
ejpam-6659	214	46	<	<	X
ejpam-6659	214	47	1	1	NUM
ejpam-6659	214	48	2(γ+β	2(γ+β	NUM
ejpam-6659	214	49	)	)	PUNCT
ejpam-6659	214	50	.	.	PUNCT
ejpam-6659	215	1	for	for	ADP
ejpam-6659	215	2	ϱ	ϱ	PROPN
ejpam-6659	215	3	>	>	X
ejpam-6659	215	4	ω	ω	PROPN
ejpam-6659	215	5	,	,	PUNCT
ejpam-6659	215	6	we	we	PRON
ejpam-6659	215	7	obtain	obtain	VERB
ejpam-6659	215	8	lim	lim	PROPN
ejpam-6659	215	9	ϱ,ω→+∞	ϱ,ω→+∞	PROPN
ejpam-6659	215	10	s(τω	s(τω	PROPN
ejpam-6659	215	11	,	,	PUNCT
ejpam-6659	215	12	τω	τω	INTJ
ejpam-6659	215	13	,	,	PUNCT
ejpam-6659	215	14	τϱ	τϱ	NOUN
ejpam-6659	215	15	)	)	PUNCT
ejpam-6659	215	16	=	=	SYM
ejpam-6659	215	17	0	0	X
ejpam-6659	215	18	.	.	PUNCT
ejpam-6659	216	1	by	by	ADP
ejpam-6659	216	2	cv	cv	PROPN
ejpam-6659	216	3	cs3	cs3	PROPN
ejpam-6659	216	4	,	,	PUNCT
ejpam-6659	216	5	we	we	PRON
ejpam-6659	216	6	have	have	VERB
ejpam-6659	216	7	s(τω	s(τω	PROPN
ejpam-6659	216	8	,	,	PUNCT
ejpam-6659	216	9	τϱ	τϱ	PROPN
ejpam-6659	216	10	,	,	PUNCT
ejpam-6659	216	11	τl	τl	ADJ
ejpam-6659	216	12	)	)	PUNCT
ejpam-6659	216	13	≾	≾	PROPN
ejpam-6659	216	14	α(τϱ	α(τϱ	PROPN
ejpam-6659	216	15	,	,	PUNCT
ejpam-6659	216	16	τϱ	τϱ	PROPN
ejpam-6659	216	17	,	,	PUNCT
ejpam-6659	216	18	τω)s(τϱ	τω)s(τϱ	PRON
ejpam-6659	216	19	,	,	PUNCT
ejpam-6659	216	20	τϱ	τϱ	PROPN
ejpam-6659	216	21	,	,	PUNCT
ejpam-6659	216	22	τω	τω	INTJ
ejpam-6659	216	23	)	)	PUNCT
ejpam-6659	216	24	+	+	NUM
ejpam-6659	216	25	α(τl	α(τl	NOUN
ejpam-6659	216	26	,	,	PUNCT
ejpam-6659	216	27	τl	τl	NOUN
ejpam-6659	216	28	,	,	PUNCT
ejpam-6659	216	29	τω)s(τl	τω)s(τl	NOUN
ejpam-6659	216	30	,	,	PUNCT
ejpam-6659	216	31	τl	τl	ADV
ejpam-6659	216	32	,	,	PUNCT
ejpam-6659	216	33	τω	τω	INTJ
ejpam-6659	216	34	)	)	PUNCT
ejpam-6659	216	35	for	for	ADP
ejpam-6659	216	36	all	all	DET
ejpam-6659	216	37	ω	ω	PROPN
ejpam-6659	216	38	,	,	PUNCT
ejpam-6659	216	39	ϱ	ϱ	NOUN
ejpam-6659	216	40	,	,	PUNCT
ejpam-6659	216	41	l	l	PROPN
ejpam-6659	216	42	∈	∈	PROPN
ejpam-6659	216	43	n.	n.	PROPN
ejpam-6659	216	44	thus	thus	ADV
ejpam-6659	216	45	,	,	PUNCT
ejpam-6659	216	46	|s(τω	|s(τω	PROPN
ejpam-6659	216	47	,	,	PUNCT
ejpam-6659	216	48	τϱ	τϱ	X
ejpam-6659	216	49	,	,	PUNCT
ejpam-6659	216	50	τl)|	τl)|	PUNCT
ejpam-6659	216	51	≤	≤	NUM
ejpam-6659	216	52	α(τϱ	α(τϱ	NUM
ejpam-6659	216	53	,	,	PUNCT
ejpam-6659	216	54	τϱ	τϱ	PROPN
ejpam-6659	216	55	,	,	PUNCT
ejpam-6659	216	56	τω)|s(τϱ	τω)|s(τϱ	PROPN
ejpam-6659	216	57	,	,	PUNCT
ejpam-6659	216	58	τϱ	τϱ	PROPN
ejpam-6659	216	59	,	,	PUNCT
ejpam-6659	216	60	τω)|+	τω)|+	VERB
ejpam-6659	216	61	α(τl	α(τl	NUM
ejpam-6659	216	62	,	,	PUNCT
ejpam-6659	216	63	τl	τl	NOUN
ejpam-6659	216	64	,	,	PUNCT
ejpam-6659	216	65	τω)|s(τl	τω)|s(τl	NOUN
ejpam-6659	216	66	,	,	PUNCT
ejpam-6659	216	67	τl	τl	ADJ
ejpam-6659	216	68	,	,	PUNCT
ejpam-6659	216	69	τω)|	τω)|	PRON
ejpam-6659	216	70	.	.	PUNCT
ejpam-6659	217	1	considering	consider	VERB
ejpam-6659	217	2	the	the	DET
ejpam-6659	217	3	limit	limit	NOUN
ejpam-6659	217	4	as	as	ADP
ejpam-6659	217	5	ω	ω	PROPN
ejpam-6659	217	6	,	,	PUNCT
ejpam-6659	217	7	ϱ	ϱ	NOUN
ejpam-6659	217	8	,	,	PUNCT
ejpam-6659	217	9	l	l	NOUN
ejpam-6659	217	10	→	→	SYM
ejpam-6659	217	11	+	+	NOUN
ejpam-6659	217	12	∞	∞	PROPN
ejpam-6659	217	13	,	,	PUNCT
ejpam-6659	217	14	we	we	PRON
ejpam-6659	217	15	have	have	VERB
ejpam-6659	217	16	|s(τω	|s(τω	PROPN
ejpam-6659	217	17	,	,	PUNCT
ejpam-6659	217	18	τϱ	τϱ	ADP
ejpam-6659	217	19	,	,	PUNCT
ejpam-6659	217	20	τl)|	τl)|	PUNCT
ejpam-6659	217	21	→	→	SYM
ejpam-6659	217	22	0	0	X
ejpam-6659	217	23	.	.	PUNCT
ejpam-6659	218	1	so	so	ADV
ejpam-6659	218	2	{	{	PUNCT
ejpam-6659	218	3	τω	τω	INTJ
ejpam-6659	218	4	}	}	PUNCT
ejpam-6659	218	5	is	be	AUX
ejpam-6659	218	6	a	a	DET
ejpam-6659	218	7	cvcscauchy	cvcscauchy	ADJ
ejpam-6659	218	8	sequence	sequence	NOUN
ejpam-6659	218	9	.	.	PUNCT
ejpam-6659	219	1	completeness	completeness	NOUN
ejpam-6659	219	2	of	of	ADP
ejpam-6659	219	3	(	(	PUNCT
ejpam-6659	219	4	γ	γ	PROPN
ejpam-6659	219	5	,	,	PUNCT
ejpam-6659	219	6	s	s	PROPN
ejpam-6659	219	7	,	,	PUNCT
ejpam-6659	219	8	α	α	NOUN
ejpam-6659	219	9	)	)	PUNCT
ejpam-6659	219	10	gives	give	VERB
ejpam-6659	219	11	us	we	PRON
ejpam-6659	219	12	that	that	SCONJ
ejpam-6659	219	13	there	there	PRON
ejpam-6659	219	14	is	be	VERB
ejpam-6659	219	15	an	an	DET
ejpam-6659	219	16	element	element	ADJ
ejpam-6659	219	17	ς∗	ς∗	NOUN
ejpam-6659	219	18	∈	∈	PROPN
ejpam-6659	219	19	γ	γ	PROPN
ejpam-6659	219	20	such	such	ADJ
ejpam-6659	219	21	h.	h.	PROPN
ejpam-6659	219	22	qawaqneh	qawaqneh	PROPN
ejpam-6659	219	23	et	et	PROPN
ejpam-6659	219	24	al	al	PROPN
ejpam-6659	219	25	.	.	PUNCT
ejpam-6659	219	26	/	/	SYM
ejpam-6659	219	27	eur	eur	PROPN
ejpam-6659	219	28	.	.	PUNCT
ejpam-6659	220	1	j.	j.	PROPN
ejpam-6659	220	2	pure	pure	PROPN
ejpam-6659	220	3	appl	appl	PROPN
ejpam-6659	220	4	.	.	PROPN
ejpam-6659	220	5	math	math	PROPN
ejpam-6659	220	6	,	,	PUNCT
ejpam-6659	220	7	18	18	NUM
ejpam-6659	220	8	(	(	PUNCT
ejpam-6659	220	9	3	3	NUM
ejpam-6659	220	10	)	)	PUNCT
ejpam-6659	220	11	(	(	PUNCT
ejpam-6659	220	12	2025	2025	NUM
ejpam-6659	220	13	)	)	PUNCT
ejpam-6659	220	14	,	,	PUNCT
ejpam-6659	220	15	6659	6659	NUM
ejpam-6659	220	16	12	12	NUM
ejpam-6659	220	17	of	of	ADP
ejpam-6659	220	18	16	16	NUM
ejpam-6659	220	19	that	that	SCONJ
ejpam-6659	220	20	{	{	PUNCT
ejpam-6659	220	21	τω	τω	INTJ
ejpam-6659	220	22	}	}	PUNCT
ejpam-6659	220	23	is	be	AUX
ejpam-6659	220	24	cvcs	cvcs	ADJ
ejpam-6659	220	25	-	-	PUNCT
ejpam-6659	220	26	convergent	convergent	NOUN
ejpam-6659	220	27	to	to	ADP
ejpam-6659	220	28	ς∗.	ς∗.	PROPN
ejpam-6659	220	29	now	now	ADV
ejpam-6659	221	1	,	,	PUNCT
ejpam-6659	221	2	we	we	PRON
ejpam-6659	221	3	’ll	’ll	AUX
ejpam-6659	221	4	prove	prove	VERB
ejpam-6659	221	5	that	that	SCONJ
ejpam-6659	221	6	f(ς∗	f(ς∗	VERB
ejpam-6659	221	7	)	)	PUNCT
ejpam-6659	221	8	=	=	SYM
ejpam-6659	221	9	g(ς∗	g(ς∗	X
ejpam-6659	221	10	)	)	PUNCT
ejpam-6659	221	11	=	=	SYM
ejpam-6659	221	12	ς∗.	ς∗.	NOUN
ejpam-6659	221	13	assume	assume	VERB
ejpam-6659	221	14	that	that	SCONJ
ejpam-6659	221	15	fς∗	fς∗	ADV
ejpam-6659	221	16	̸=	̸=	PROPN
ejpam-6659	221	17	ς∗.	ς∗.	NOUN
ejpam-6659	221	18	thus	thus	ADV
ejpam-6659	221	19	,	,	PUNCT
ejpam-6659	221	20	0	0	NUM
ejpam-6659	221	21	≺	≺	NOUN
ejpam-6659	221	22	ϖ	ϖ	X
ejpam-6659	221	23	=	=	SYM
ejpam-6659	221	24	s(ς∗	s(ς∗	ADJ
ejpam-6659	221	25	,	,	PUNCT
ejpam-6659	221	26	ς∗	ς∗	ADJ
ejpam-6659	221	27	,	,	PUNCT
ejpam-6659	221	28	fς∗	fς∗	ADJ
ejpam-6659	221	29	)	)	PUNCT
ejpam-6659	221	30	.	.	PUNCT
ejpam-6659	222	1	therefore	therefore	ADV
ejpam-6659	222	2	,	,	PUNCT
ejpam-6659	222	3	ϖ	ϖ	PROPN
ejpam-6659	222	4	≾	≾	NOUN
ejpam-6659	222	5	2α(ς∗	2α(ς∗	NOUN
ejpam-6659	222	6	,	,	PUNCT
ejpam-6659	222	7	ς∗	ς∗	PROPN
ejpam-6659	222	8	,	,	PUNCT
ejpam-6659	222	9	τ2κ+2)s(ς	τ2κ+2)s(ς	NOUN
ejpam-6659	222	10	∗	∗	NOUN
ejpam-6659	222	11	,	,	PUNCT
ejpam-6659	222	12	ς∗	ς∗	NOUN
ejpam-6659	222	13	,	,	PUNCT
ejpam-6659	222	14	τ2κ+2	τ2κ+2	PROPN
ejpam-6659	222	15	)	)	PUNCT
ejpam-6659	222	16	+	+	CCONJ
ejpam-6659	222	17	α(τ2κ+2	α(τ2κ+2	NUM
ejpam-6659	222	18	,	,	PUNCT
ejpam-6659	222	19	τ2κ+2	τ2κ+2	NUM
ejpam-6659	222	20	,	,	PUNCT
ejpam-6659	222	21	fς	fς	PRON
ejpam-6659	222	22	∗)s(τ2κ+2	∗)s(τ2κ+2	NOUN
ejpam-6659	222	23	,	,	PUNCT
ejpam-6659	222	24	τ2κ+2	τ2κ+2	NUM
ejpam-6659	222	25	,	,	PUNCT
ejpam-6659	222	26	fς	fς	DET
ejpam-6659	222	27	∗	∗	NOUN
ejpam-6659	222	28	)	)	PUNCT
ejpam-6659	222	29	≾	≾	NOUN
ejpam-6659	222	30	2α(ς∗	2α(ς∗	NOUN
ejpam-6659	222	31	,	,	PUNCT
ejpam-6659	222	32	ς∗	ς∗	PROPN
ejpam-6659	222	33	,	,	PUNCT
ejpam-6659	222	34	τ2κ+2)s(ς	τ2κ+2)s(ς	NOUN
ejpam-6659	222	35	∗	∗	NOUN
ejpam-6659	222	36	,	,	PUNCT
ejpam-6659	222	37	ς∗	ς∗	NOUN
ejpam-6659	222	38	,	,	PUNCT
ejpam-6659	222	39	τ2κ+2	τ2κ+2	PROPN
ejpam-6659	222	40	)	)	PUNCT
ejpam-6659	222	41	+	+	CCONJ
ejpam-6659	222	42	α(τ2κ+2	α(τ2κ+2	NUM
ejpam-6659	222	43	,	,	PUNCT
ejpam-6659	222	44	τ2κ+2	τ2κ+2	NUM
ejpam-6659	222	45	,	,	PUNCT
ejpam-6659	222	46	fς	fς	PRON
ejpam-6659	222	47	∗)s(gτ2κ+1	∗)s(gτ2κ+1	PROPN
ejpam-6659	222	48	,	,	PUNCT
ejpam-6659	222	49	gτ2κ+1	gτ2κ+1	PROPN
ejpam-6659	222	50	,	,	PUNCT
ejpam-6659	222	51	fς	fς	DET
ejpam-6659	222	52	∗	∗	NOUN
ejpam-6659	222	53	)	)	PUNCT
ejpam-6659	222	54	≾	≾	NOUN
ejpam-6659	222	55	2α(ς∗	2α(ς∗	NOUN
ejpam-6659	222	56	,	,	PUNCT
ejpam-6659	222	57	ς∗	ς∗	PROPN
ejpam-6659	222	58	,	,	PUNCT
ejpam-6659	222	59	τ2κ+2)s(ς	τ2κ+2)s(ς	NOUN
ejpam-6659	222	60	∗	∗	NOUN
ejpam-6659	222	61	,	,	PUNCT
ejpam-6659	222	62	ς∗	ς∗	NOUN
ejpam-6659	222	63	,	,	PUNCT
ejpam-6659	222	64	τ2κ+2	τ2κ+2	NUM
ejpam-6659	222	65	)	)	PUNCT
ejpam-6659	222	66	+	+	CCONJ
ejpam-6659	222	67	γα(τ2κ+2	γα(τ2κ+2	PROPN
ejpam-6659	222	68	,	,	PUNCT
ejpam-6659	222	69	τ2κ+2	τ2κ+2	NUM
ejpam-6659	222	70	,	,	PUNCT
ejpam-6659	222	71	fς	fς	DET
ejpam-6659	222	72	∗)s(τ2κ+1	∗)s(τ2κ+1	NOUN
ejpam-6659	222	73	,	,	PUNCT
ejpam-6659	222	74	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	222	75	,	,	PUNCT
ejpam-6659	222	76	ς	ς	PROPN
ejpam-6659	222	77	∗	∗	NOUN
ejpam-6659	222	78	)	)	PUNCT
ejpam-6659	223	1	+	+	CCONJ
ejpam-6659	223	2	βα(τ2κ+2	βα(τ2κ+2	PROPN
ejpam-6659	223	3	,	,	PUNCT
ejpam-6659	223	4	τ2κ+2	τ2κ+2	NUM
ejpam-6659	223	5	,	,	PUNCT
ejpam-6659	223	6	fς	fς	DET
ejpam-6659	223	7	∗)s(τ2κ+1	∗)s(τ2κ+1	NOUN
ejpam-6659	223	8	,	,	PUNCT
ejpam-6659	223	9	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	223	10	,	,	PUNCT
ejpam-6659	223	11	τ2κ+2)s(ς	τ2κ+2)s(ς	PROPN
ejpam-6659	223	12	∗	∗	NOUN
ejpam-6659	223	13	,	,	PUNCT
ejpam-6659	223	14	ς∗	ς∗	NOUN
ejpam-6659	223	15	,	,	PUNCT
ejpam-6659	223	16	fς∗	fς∗	ADJ
ejpam-6659	223	17	)	)	PUNCT
ejpam-6659	223	18	2α(fς∗	2α(fς∗	NOUN
ejpam-6659	223	19	,	,	PUNCT
ejpam-6659	223	20	fς∗	fς∗	ADV
ejpam-6659	223	21	,	,	PUNCT
ejpam-6659	223	22	τ2κ+1)s(τ2κ+1	τ2κ+1)s(τ2κ+1	NUM
ejpam-6659	223	23	,	,	PUNCT
ejpam-6659	223	24	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	223	25	,	,	PUNCT
ejpam-6659	223	26	fς	fς	NOUN
ejpam-6659	223	27	∗	∗	NOUN
ejpam-6659	223	28	)	)	PUNCT
ejpam-6659	224	1	+	+	CCONJ
ejpam-6659	224	2	α(τ2κ+2	α(τ2κ+2	ADJ
ejpam-6659	224	3	,	,	PUNCT
ejpam-6659	224	4	τ2κ+2	τ2κ+2	PROPN
ejpam-6659	224	5	,	,	PUNCT
ejpam-6659	224	6	ς	ς	PROPN
ejpam-6659	224	7	∗)s(ς∗	∗)s(ς∗	NOUN
ejpam-6659	224	8	,	,	PUNCT
ejpam-6659	224	9	ς∗	ς∗	NOUN
ejpam-6659	224	10	,	,	PUNCT
ejpam-6659	224	11	τ2κ+2	τ2κ+2	PROPN
ejpam-6659	224	12	)	)	PUNCT
ejpam-6659	224	13	+	+	X
ejpam-6659	224	14	α(ς∗	α(ς∗	NUM
ejpam-6659	224	15	,	,	PUNCT
ejpam-6659	224	16	ς∗	ς∗	ADJ
ejpam-6659	224	17	,	,	PUNCT
ejpam-6659	224	18	τ2κ+1)s(τ2κ+1	τ2κ+1)s(τ2κ+1	NUM
ejpam-6659	224	19	,	,	PUNCT
ejpam-6659	224	20	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	224	21	,	,	PUNCT
ejpam-6659	224	22	ς	ς	PROPN
ejpam-6659	224	23	∗	∗	NOUN
ejpam-6659	224	24	)	)	PUNCT
ejpam-6659	224	25	.	.	PUNCT
ejpam-6659	225	1	hence	hence	ADV
ejpam-6659	225	2	,	,	PUNCT
ejpam-6659	225	3	|ϖ|	|ϖ|	ADJ
ejpam-6659	225	4	≤	≤	NOUN
ejpam-6659	225	5	2α(ς∗	2α(ς∗	NOUN
ejpam-6659	225	6	,	,	PUNCT
ejpam-6659	225	7	ς∗	ς∗	NOUN
ejpam-6659	225	8	,	,	PUNCT
ejpam-6659	225	9	τ2κ+2)|s(ς∗	τ2κ+2)|s(ς∗	ADJ
ejpam-6659	225	10	,	,	PUNCT
ejpam-6659	225	11	ς∗	ς∗	PROPN
ejpam-6659	225	12	,	,	PUNCT
ejpam-6659	225	13	τ2κ+2)|+	τ2κ+2)|+	X
ejpam-6659	225	14	γα(τ2κ+2	γα(τ2κ+2	PROPN
ejpam-6659	225	15	,	,	PUNCT
ejpam-6659	225	16	τ2κ+2	τ2κ+2	NUM
ejpam-6659	225	17	,	,	PUNCT
ejpam-6659	225	18	fς	fς	DET
ejpam-6659	225	19	∗)|s(τ2κ+1	∗)|s(τ2κ+1	PROPN
ejpam-6659	225	20	,	,	PUNCT
ejpam-6659	225	21	τ2κ+1	τ2κ+1	PROPN
ejpam-6659	225	22	,	,	PUNCT
ejpam-6659	225	23	ς	ς	PROPN
ejpam-6659	225	24	∗)|	∗)|	PROPN
ejpam-6659	225	25	+	+	CCONJ
ejpam-6659	225	26	βα(τ2κ+2	βα(τ2κ+2	PROPN
ejpam-6659	225	27	,	,	PUNCT
ejpam-6659	225	28	τ2κ+2	τ2κ+2	PROPN
ejpam-6659	225	29	,	,	PUNCT
ejpam-6659	225	30	fς	fς	DET
ejpam-6659	225	31	∗)|s(τ2κ+1	∗)|s(τ2κ+1	PROPN
ejpam-6659	225	32	,	,	PUNCT
ejpam-6659	225	33	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	225	34	,	,	PUNCT
ejpam-6659	225	35	τ2κ+2)||z|	τ2κ+2)||z|	VERB
ejpam-6659	225	36	2α(fς∗	2α(fς∗	NUM
ejpam-6659	225	37	,	,	PUNCT
ejpam-6659	225	38	fς∗	fς∗	ADV
ejpam-6659	225	39	,	,	PUNCT
ejpam-6659	225	40	τ2κ+1)|s(τ2κ+1	τ2κ+1)|s(τ2κ+1	ADJ
ejpam-6659	225	41	,	,	PUNCT
ejpam-6659	225	42	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	225	43	,	,	PUNCT
ejpam-6659	225	44	fς	fς	PRON
ejpam-6659	225	45	∗)|+	∗)|+	PROPN
ejpam-6659	225	46	α(τ2κ+2	α(τ2κ+2	NUM
ejpam-6659	225	47	,	,	PUNCT
ejpam-6659	225	48	τ2κ+2	τ2κ+2	PROPN
ejpam-6659	225	49	,	,	PUNCT
ejpam-6659	225	50	ς	ς	PROPN
ejpam-6659	225	51	∗)|s(ς∗	∗)|s(ς∗	PROPN
ejpam-6659	225	52	,	,	PUNCT
ejpam-6659	225	53	ς∗	ς∗	PROPN
ejpam-6659	225	54	,	,	PUNCT
ejpam-6659	225	55	τ2κ+2)|+	τ2κ+2)|+	X
ejpam-6659	225	56	α(ς∗	α(ς∗	NUM
ejpam-6659	225	57	,	,	PUNCT
ejpam-6659	225	58	ς∗	ς∗	PROPN
ejpam-6659	225	59	,	,	PUNCT
ejpam-6659	225	60	τ2κ+1)|s(τ2κ+1	τ2κ+1)|s(τ2κ+1	ADJ
ejpam-6659	225	61	,	,	PUNCT
ejpam-6659	225	62	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	225	63	,	,	PUNCT
ejpam-6659	225	64	ς	ς	PROPN
ejpam-6659	225	65	∗)|	∗)|	PROPN
ejpam-6659	225	66	.	.	PUNCT
ejpam-6659	226	1	our	our	PRON
ejpam-6659	226	2	assumption	assumption	NOUN
ejpam-6659	226	3	on	on	ADP
ejpam-6659	226	4	ϖ	ϖ	PROPN
ejpam-6659	226	5	is	be	AUX
ejpam-6659	226	6	contradicted	contradict	VERB
ejpam-6659	226	7	by	by	ADP
ejpam-6659	226	8	the	the	DET
ejpam-6659	226	9	fact	fact	NOUN
ejpam-6659	226	10	that	that	SCONJ
ejpam-6659	226	11	the	the	DET
ejpam-6659	226	12	right	right	ADJ
ejpam-6659	226	13	-	-	PUNCT
ejpam-6659	226	14	hand	hand	NOUN
ejpam-6659	226	15	side	side	NOUN
ejpam-6659	226	16	of	of	ADP
ejpam-6659	226	17	the	the	DET
ejpam-6659	226	18	preceding	precede	VERB
ejpam-6659	226	19	inequality	inequality	NOUN
ejpam-6659	226	20	tends	tend	VERB
ejpam-6659	226	21	to	to	ADP
ejpam-6659	226	22	0	0	NUM
ejpam-6659	226	23	as	as	ADP
ejpam-6659	226	24	κ	κ	PROPN
ejpam-6659	226	25	→	→	SYM
ejpam-6659	226	26	+	+	PROPN
ejpam-6659	226	27	∞.	∞.	PROPN
ejpam-6659	226	28	consequently	consequently	ADV
ejpam-6659	226	29	,	,	PUNCT
ejpam-6659	226	30	it	it	PRON
ejpam-6659	226	31	is	be	AUX
ejpam-6659	226	32	possible	possible	ADJ
ejpam-6659	226	33	to	to	PART
ejpam-6659	226	34	demonstrate	demonstrate	VERB
ejpam-6659	226	35	that	that	SCONJ
ejpam-6659	226	36	fς∗	fς∗	ADV
ejpam-6659	226	37	=	=	X
ejpam-6659	226	38	ς∗	ς∗	NOUN
ejpam-6659	226	39	and	and	CCONJ
ejpam-6659	226	40	that	that	SCONJ
ejpam-6659	226	41	gς∗	gς∗	NOUN
ejpam-6659	226	42	=	=	SYM
ejpam-6659	226	43	ς∗.	ς∗.	NOUN
ejpam-6659	226	44	as	as	ADP
ejpam-6659	226	45	a	a	DET
ejpam-6659	226	46	result	result	NOUN
ejpam-6659	226	47	,	,	PUNCT
ejpam-6659	226	48	f	f	PROPN
ejpam-6659	226	49	and	and	CCONJ
ejpam-6659	226	50	g	g	PROPN
ejpam-6659	226	51	have	have	VERB
ejpam-6659	226	52	a	a	DET
ejpam-6659	226	53	common	common	ADJ
ejpam-6659	226	54	fixed	fix	VERB
ejpam-6659	226	55	point	point	NOUN
ejpam-6659	226	56	.	.	PUNCT
ejpam-6659	227	1	in	in	ADP
ejpam-6659	227	2	order	order	NOUN
ejpam-6659	227	3	to	to	PART
ejpam-6659	227	4	demonstrate	demonstrate	VERB
ejpam-6659	227	5	uniqueness	uniqueness	NOUN
ejpam-6659	227	6	assume	assume	VERB
ejpam-6659	227	7	that	that	SCONJ
ejpam-6659	227	8	there	there	PRON
ejpam-6659	227	9	is	be	VERB
ejpam-6659	227	10	another	another	DET
ejpam-6659	227	11	common	common	ADJ
ejpam-6659	227	12	fixed	fix	VERB
ejpam-6659	227	13	point	point	NOUN
ejpam-6659	227	14	of	of	ADP
ejpam-6659	227	15	f	f	PROPN
ejpam-6659	227	16	and	and	CCONJ
ejpam-6659	227	17	g	g	PROPN
ejpam-6659	227	18	,	,	PUNCT
ejpam-6659	227	19	say	say	VERB
ejpam-6659	227	20	ρ∗.	ρ∗.	VERB
ejpam-6659	227	21	therefore	therefore	ADV
ejpam-6659	227	22	,	,	PUNCT
ejpam-6659	227	23	s(ς∗	s(ς∗	ADJ
ejpam-6659	227	24	,	,	PUNCT
ejpam-6659	227	25	ς∗	ς∗	PROPN
ejpam-6659	227	26	,	,	PUNCT
ejpam-6659	227	27	ρ∗	ρ∗	NOUN
ejpam-6659	227	28	)	)	PUNCT
ejpam-6659	227	29	=	=	SYM
ejpam-6659	228	1	s(fς∗	s(fς∗	ADV
ejpam-6659	228	2	,	,	PUNCT
ejpam-6659	228	3	fς∗	fς∗	ADV
ejpam-6659	228	4	,	,	PUNCT
ejpam-6659	228	5	gρ∗	gρ∗	NOUN
ejpam-6659	228	6	)	)	PUNCT
ejpam-6659	228	7	≾	≾	PROPN
ejpam-6659	228	8	γs(ς∗	γs(ς∗	NOUN
ejpam-6659	228	9	,	,	PUNCT
ejpam-6659	228	10	ς∗	ς∗	NOUN
ejpam-6659	228	11	,	,	PUNCT
ejpam-6659	228	12	ρ∗	ρ∗	PROPN
ejpam-6659	228	13	)	)	PUNCT
ejpam-6659	229	1	+	+	CCONJ
ejpam-6659	229	2	β	β	X
ejpam-6659	229	3	s(ς∗	s(ς∗	ADJ
ejpam-6659	229	4	,	,	PUNCT
ejpam-6659	229	5	ς∗	ς∗	PROPN
ejpam-6659	229	6	,	,	PUNCT
ejpam-6659	229	7	fς∗)s(ρ∗	fς∗)s(ρ∗	PROPN
ejpam-6659	229	8	,	,	PUNCT
ejpam-6659	229	9	ρ∗	ρ∗	PROPN
ejpam-6659	229	10	,	,	PUNCT
ejpam-6659	229	11	gρ∗	gρ∗	NOUN
ejpam-6659	229	12	)	)	PUNCT
ejpam-6659	229	13	2α(gρ∗	2α(gρ∗	NOUN
ejpam-6659	229	14	,	,	PUNCT
ejpam-6659	229	15	gρ∗	gρ∗	NOUN
ejpam-6659	229	16	,	,	PUNCT
ejpam-6659	229	17	ς∗)s(ς∗	ς∗)s(ς∗	PROPN
ejpam-6659	229	18	,	,	PUNCT
ejpam-6659	229	19	ς∗	ς∗	NOUN
ejpam-6659	229	20	,	,	PUNCT
ejpam-6659	229	21	gρ∗	gρ∗	PROPN
ejpam-6659	229	22	)	)	PUNCT
ejpam-6659	230	1	+	+	CCONJ
ejpam-6659	230	2	α(fς∗	α(fς∗	ADV
ejpam-6659	230	3	,	,	PUNCT
ejpam-6659	230	4	fς∗	fς∗	ADV
ejpam-6659	230	5	,	,	PUNCT
ejpam-6659	230	6	ρ∗)s(ρ∗	ρ∗)s(ρ∗	PROPN
ejpam-6659	230	7	,	,	PUNCT
ejpam-6659	230	8	ρ∗	ρ∗	PROPN
ejpam-6659	230	9	,	,	PUNCT
ejpam-6659	230	10	fς∗	fς∗	ADV
ejpam-6659	230	11	)	)	PUNCT
ejpam-6659	231	1	+	+	CCONJ
ejpam-6659	231	2	α(ρ∗	α(ρ∗	ADV
ejpam-6659	231	3	,	,	PUNCT
ejpam-6659	231	4	ρ∗	ρ∗	PROPN
ejpam-6659	231	5	,	,	PUNCT
ejpam-6659	231	6	ς∗)s(ς∗	ς∗)s(ς∗	PROPN
ejpam-6659	231	7	,	,	PUNCT
ejpam-6659	231	8	ς∗	ς∗	NOUN
ejpam-6659	231	9	,	,	PUNCT
ejpam-6659	231	10	ρ∗	ρ∗	PROPN
ejpam-6659	231	11	)	)	PUNCT
ejpam-6659	231	12	=	=	SYM
ejpam-6659	231	13	γs(ς∗	γs(ς∗	X
ejpam-6659	231	14	,	,	PUNCT
ejpam-6659	231	15	ς∗	ς∗	NOUN
ejpam-6659	231	16	,	,	PUNCT
ejpam-6659	231	17	ρ∗	ρ∗	PROPN
ejpam-6659	231	18	)	)	PUNCT
ejpam-6659	231	19	.	.	PUNCT
ejpam-6659	232	1	this	this	PRON
ejpam-6659	232	2	implies	imply	VERB
ejpam-6659	232	3	that	that	SCONJ
ejpam-6659	232	4	|s(ς∗	|s(ς∗	ADJ
ejpam-6659	232	5	,	,	PUNCT
ejpam-6659	232	6	ς∗	ς∗	PROPN
ejpam-6659	232	7	,	,	PUNCT
ejpam-6659	232	8	ρ∗)|	ρ∗)|	NUM
ejpam-6659	232	9	≤	≤	NOUN
ejpam-6659	232	10	γ|s(ς∗	γ|s(ς∗	PROPN
ejpam-6659	232	11	,	,	PUNCT
ejpam-6659	232	12	ς∗	ς∗	PROPN
ejpam-6659	232	13	,	,	PUNCT
ejpam-6659	232	14	ρ∗)|	ρ∗)|	PROPN
ejpam-6659	232	15	.	.	PUNCT
ejpam-6659	233	1	however	however	ADV
ejpam-6659	233	2	,	,	PUNCT
ejpam-6659	233	3	since	since	SCONJ
ejpam-6659	233	4	γ	γ	X
ejpam-6659	233	5	<	<	X
ejpam-6659	233	6	1	1	NUM
ejpam-6659	233	7	,	,	PUNCT
ejpam-6659	233	8	we	we	PRON
ejpam-6659	233	9	can	can	AUX
ejpam-6659	233	10	thus	thus	ADV
ejpam-6659	233	11	conclude	conclude	VERB
ejpam-6659	233	12	that	that	SCONJ
ejpam-6659	233	13	s(ς∗	s(ς∗	PROPN
ejpam-6659	233	14	,	,	PUNCT
ejpam-6659	233	15	ς∗	ς∗	PROPN
ejpam-6659	233	16	,	,	PUNCT
ejpam-6659	233	17	ρ∗	ρ∗	NOUN
ejpam-6659	233	18	)	)	PUNCT
ejpam-6659	233	19	=	=	PUNCT
ejpam-6659	233	20	0	0	NUM
ejpam-6659	233	21	,	,	PUNCT
ejpam-6659	233	22	and	and	CCONJ
ejpam-6659	233	23	as	as	ADP
ejpam-6659	233	24	a	a	DET
ejpam-6659	233	25	result	result	NOUN
ejpam-6659	233	26	,	,	PUNCT
ejpam-6659	233	27	ς∗	ς∗	PROPN
ejpam-6659	233	28	=	=	PROPN
ejpam-6659	233	29	ρ∗	ρ∗	PROPN
ejpam-6659	233	30	as	as	SCONJ
ejpam-6659	233	31	intended	intend	VERB
ejpam-6659	233	32	.	.	PUNCT
ejpam-6659	234	1	to	to	PART
ejpam-6659	234	2	complete	complete	VERB
ejpam-6659	234	3	our	our	PRON
ejpam-6659	234	4	proof	proof	NOUN
ejpam-6659	234	5	,	,	PUNCT
ejpam-6659	234	6	suppose	suppose	VERB
ejpam-6659	234	7	that	that	SCONJ
ejpam-6659	234	8	for	for	ADP
ejpam-6659	234	9	every	every	DET
ejpam-6659	234	10	natural	natural	ADJ
ejpam-6659	234	11	number	number	NOUN
ejpam-6659	234	12	κ	κ	NOUN
ejpam-6659	234	13	,	,	PUNCT
ejpam-6659	234	14	if	if	SCONJ
ejpam-6659	234	15	we	we	PRON
ejpam-6659	234	16	obtain	obtain	VERB
ejpam-6659	234	17	s(τ2κ	s(τ2κ	NOUN
ejpam-6659	234	18	,	,	PUNCT
ejpam-6659	234	19	τ2κ	τ2κ	ADJ
ejpam-6659	234	20	,	,	PUNCT
ejpam-6659	234	21	gτ2κ+1	gτ2κ+1	PROPN
ejpam-6659	234	22	)	)	PUNCT
ejpam-6659	235	1	+	+	CCONJ
ejpam-6659	235	2	s(τ2κ+1	s(τ2κ+1	ADJ
ejpam-6659	235	3	,	,	PUNCT
ejpam-6659	235	4	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	235	5	,	,	PUNCT
ejpam-6659	235	6	fτ2κ	fτ2κ	NOUN
ejpam-6659	235	7	)	)	PUNCT
ejpam-6659	236	1	+	+	SYM
ejpam-6659	236	2	s(τ2κ	s(τ2κ	NOUN
ejpam-6659	236	3	,	,	PUNCT
ejpam-6659	236	4	τ2κ	τ2κ	ADJ
ejpam-6659	236	5	,	,	PUNCT
ejpam-6659	236	6	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	236	7	)	)	PUNCT
ejpam-6659	236	8	=	=	SYM
ejpam-6659	236	9	0	0	NUM
ejpam-6659	236	10	,	,	PUNCT
ejpam-6659	236	11	then	then	ADV
ejpam-6659	236	12	s(fτ2κ	s(fτ2κ	NOUN
ejpam-6659	236	13	,	,	PUNCT
ejpam-6659	236	14	fτ2κ	fτ2κ	NOUN
ejpam-6659	236	15	,	,	PUNCT
ejpam-6659	236	16	gτ2κ+1	gτ2κ+1	NOUN
ejpam-6659	236	17	)	)	PUNCT
ejpam-6659	236	18	=	=	SYM
ejpam-6659	236	19	0	0	NUM
ejpam-6659	236	20	,	,	PUNCT
ejpam-6659	236	21	which	which	PRON
ejpam-6659	236	22	implies	imply	VERB
ejpam-6659	236	23	τ2κ	τ2κ	PUNCT
ejpam-6659	236	24	=	=	SYM
ejpam-6659	236	25	fτ2κ	fτ2κ	NOUN
ejpam-6659	236	26	=	=	SYM
ejpam-6659	236	27	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	236	28	=	=	NOUN
ejpam-6659	236	29	gτ2κ+1	gτ2κ+1	PROPN
ejpam-6659	236	30	=	=	SYM
ejpam-6659	236	31	τ2κ+2	τ2κ+2	PROPN
ejpam-6659	236	32	.	.	PUNCT
ejpam-6659	236	33	therefore	therefore	ADV
ejpam-6659	236	34	,	,	PUNCT
ejpam-6659	236	35	τ2κ+1	τ2κ+1	NOUN
ejpam-6659	236	36	=	=	PUNCT
ejpam-6659	236	37	fτ2κ	fτ2κ	NOUN
ejpam-6659	236	38	=	=	SYM
ejpam-6659	236	39	τ2κ	τ2κ	X
ejpam-6659	236	40	,	,	PUNCT
ejpam-6659	236	41	hence	hence	ADV
ejpam-6659	236	42	there	there	PRON
ejpam-6659	236	43	exist	exist	VERB
ejpam-6659	236	44	ω1	ω1	NOUN
ejpam-6659	236	45	,	,	PUNCT
ejpam-6659	236	46	ϱ1	ϱ1	NOUN
ejpam-6659	236	47	such	such	ADJ
ejpam-6659	236	48	that	that	DET
ejpam-6659	236	49	ω1	ω1	PROPN
ejpam-6659	236	50	=	=	SYM
ejpam-6659	236	51	fϱ1	fϱ1	NOUN
ejpam-6659	236	52	=	=	SYM
ejpam-6659	236	53	ϱ1	ϱ1	NOUN
ejpam-6659	236	54	.	.	PUNCT
ejpam-6659	237	1	similarly	similarly	ADV
ejpam-6659	237	2	,	,	PUNCT
ejpam-6659	237	3	there	there	PRON
ejpam-6659	237	4	exist	exist	VERB
ejpam-6659	237	5	ω2	ω2	ADJ
ejpam-6659	237	6	,	,	PUNCT
ejpam-6659	237	7	ϱ2	ϱ2	NOUN
ejpam-6659	237	8	such	such	ADJ
ejpam-6659	237	9	that	that	DET
ejpam-6659	237	10	ω2	ω2	NOUN
ejpam-6659	237	11	=	=	PROPN
ejpam-6659	237	12	gϱ2	gϱ2	PROPN
ejpam-6659	237	13	=	=	SYM
ejpam-6659	237	14	ϱ2	ϱ2	PROPN
ejpam-6659	237	15	.	.	PUNCT
ejpam-6659	238	1	we	we	PRON
ejpam-6659	238	2	know	know	VERB
ejpam-6659	238	3	that	that	SCONJ
ejpam-6659	238	4	s(ϱ1	s(ϱ1	NOUN
ejpam-6659	238	5	,	,	PUNCT
ejpam-6659	238	6	ϱ1	ϱ1	PROPN
ejpam-6659	238	7	,	,	PUNCT
ejpam-6659	238	8	gϱ2	gϱ2	PROPN
ejpam-6659	238	9	)	)	PUNCT
ejpam-6659	238	10	+	+	CCONJ
ejpam-6659	238	11	s(ϱ2	s(ϱ2	ADJ
ejpam-6659	238	12	,	,	PUNCT
ejpam-6659	238	13	ϱ2	ϱ2	NOUN
ejpam-6659	238	14	,	,	PUNCT
ejpam-6659	238	15	fϱ1	fϱ1	NOUN
ejpam-6659	238	16	)	)	PUNCT
ejpam-6659	238	17	+	+	CCONJ
ejpam-6659	238	18	s(ϱ1	s(ϱ1	ADJ
ejpam-6659	238	19	,	,	PUNCT
ejpam-6659	238	20	ϱ1	ϱ1	NOUN
ejpam-6659	238	21	,	,	PUNCT
ejpam-6659	238	22	ϱ2	ϱ2	NOUN
ejpam-6659	238	23	)	)	PUNCT
ejpam-6659	238	24	=	=	SYM
ejpam-6659	239	1	0	0	X
ejpam-6659	239	2	.	.	PUNCT
ejpam-6659	240	1	we	we	PRON
ejpam-6659	240	2	deduce	deduce	VERB
ejpam-6659	240	3	that	that	SCONJ
ejpam-6659	240	4	s(fϱ1	s(fϱ1	PROPN
ejpam-6659	240	5	,	,	PUNCT
ejpam-6659	240	6	fϱ1	fϱ1	NOUN
ejpam-6659	240	7	,	,	PUNCT
ejpam-6659	240	8	gϱ2	gϱ2	PROPN
ejpam-6659	240	9	)	)	PUNCT
ejpam-6659	240	10	=	=	SYM
ejpam-6659	240	11	0	0	NUM
ejpam-6659	240	12	,	,	PUNCT
ejpam-6659	240	13	which	which	PRON
ejpam-6659	240	14	implies	imply	VERB
ejpam-6659	240	15	that	that	DET
ejpam-6659	240	16	ω1	ω1	PROPN
ejpam-6659	240	17	=	=	SYM
ejpam-6659	240	18	fϱ1	fϱ1	NOUN
ejpam-6659	240	19	=	=	NOUN
ejpam-6659	240	20	gϱ2	gϱ2	PROPN
ejpam-6659	240	21	=	=	SYM
ejpam-6659	240	22	ω2	ω2	PROPN
ejpam-6659	240	23	.	.	PUNCT
ejpam-6659	241	1	therefore	therefore	ADV
ejpam-6659	241	2	,	,	PUNCT
ejpam-6659	241	3	ω1	ω1	PROPN
ejpam-6659	241	4	=	=	SYM
ejpam-6659	241	5	fϱ1	fϱ1	PROPN
ejpam-6659	241	6	=	=	SYM
ejpam-6659	241	7	fω1	fω1	PROPN
ejpam-6659	241	8	.	.	PUNCT
ejpam-6659	242	1	similarly	similarly	ADV
ejpam-6659	242	2	,	,	PUNCT
ejpam-6659	242	3	we	we	PRON
ejpam-6659	242	4	get	get	VERB
ejpam-6659	242	5	ω2	ω2	ADV
ejpam-6659	242	6	=	=	PROPN
ejpam-6659	242	7	gϱ2	gϱ2	PROPN
ejpam-6659	242	8	=	=	PUNCT
ejpam-6659	242	9	gω2	gω2	PROPN
ejpam-6659	242	10	.	.	PUNCT
ejpam-6659	243	1	since	since	SCONJ
ejpam-6659	243	2	ω1	ω1	PROPN
ejpam-6659	243	3	=	=	SYM
ejpam-6659	243	4	ω2	ω2	PROPN
ejpam-6659	243	5	,	,	PUNCT
ejpam-6659	243	6	we	we	PRON
ejpam-6659	243	7	deduce	deduce	VERB
ejpam-6659	243	8	that	that	DET
ejpam-6659	243	9	fω1	fω1	NOUN
ejpam-6659	243	10	=	=	X
ejpam-6659	243	11	gω1	gω1	NOUN
ejpam-6659	243	12	=	=	SYM
ejpam-6659	243	13	ω1	ω1	PROPN
ejpam-6659	243	14	.	.	PROPN
ejpam-6659	244	1	as	as	ADP
ejpam-6659	244	2	a	a	DET
ejpam-6659	244	3	result	result	NOUN
ejpam-6659	244	4	,	,	PUNCT
ejpam-6659	244	5	f	f	PROPN
ejpam-6659	244	6	and	and	CCONJ
ejpam-6659	244	7	g	g	PROPN
ejpam-6659	244	8	have	have	VERB
ejpam-6659	244	9	a	a	DET
ejpam-6659	244	10	common	common	ADJ
ejpam-6659	244	11	fixed	fix	VERB
ejpam-6659	244	12	point	point	NOUN
ejpam-6659	244	13	,	,	PUNCT
ejpam-6659	244	14	namely	namely	ADV
ejpam-6659	244	15	ω1	ω1	PROPN
ejpam-6659	244	16	.	.	PROPN
ejpam-6659	244	17	to	to	PART
ejpam-6659	244	18	prove	prove	VERB
ejpam-6659	244	19	uniqueness	uniqueness	NOUN
ejpam-6659	244	20	,	,	PUNCT
ejpam-6659	244	21	assume	assume	VERB
ejpam-6659	244	22	that	that	SCONJ
ejpam-6659	244	23	f	f	PROPN
ejpam-6659	244	24	and	and	CCONJ
ejpam-6659	244	25	g	g	PROPN
ejpam-6659	244	26	have	have	VERB
ejpam-6659	244	27	τ	τ	PROPN
ejpam-6659	244	28	and	and	CCONJ
ejpam-6659	244	29	ς	ς	PROPN
ejpam-6659	244	30	as	as	ADP
ejpam-6659	244	31	common	common	ADJ
ejpam-6659	244	32	fixed	fix	VERB
ejpam-6659	244	33	points	point	NOUN
ejpam-6659	244	34	.	.	PUNCT
ejpam-6659	245	1	we	we	PRON
ejpam-6659	245	2	know	know	VERB
ejpam-6659	245	3	that	that	SCONJ
ejpam-6659	245	4	s(τ	s(τ	PROPN
ejpam-6659	245	5	,	,	PUNCT
ejpam-6659	245	6	τ	τ	PROPN
ejpam-6659	245	7	,	,	PUNCT
ejpam-6659	245	8	gς	gς	PROPN
ejpam-6659	245	9	)	)	PUNCT
ejpam-6659	245	10	+	+	CCONJ
ejpam-6659	246	1	s(ς	s(ς	PROPN
ejpam-6659	246	2	,	,	PUNCT
ejpam-6659	246	3	ς	ς	NOUN
ejpam-6659	246	4	,	,	PUNCT
ejpam-6659	246	5	fu	fu	ADJ
ejpam-6659	246	6	)	)	PUNCT
ejpam-6659	247	1	+	+	CCONJ
ejpam-6659	248	1	s(τ	s(τ	PROPN
ejpam-6659	248	2	,	,	PUNCT
ejpam-6659	248	3	τ	τ	PROPN
ejpam-6659	248	4	,	,	PUNCT
ejpam-6659	248	5	ς	ς	PROPN
ejpam-6659	248	6	)	)	PUNCT
ejpam-6659	248	7	=	=	SYM
ejpam-6659	248	8	0	0	X
ejpam-6659	248	9	.	.	PUNCT
ejpam-6659	249	1	thus	thus	ADV
ejpam-6659	249	2	,	,	PUNCT
ejpam-6659	249	3	s(τ	s(τ	PROPN
ejpam-6659	249	4	,	,	PUNCT
ejpam-6659	249	5	τ	τ	PROPN
ejpam-6659	249	6	,	,	PUNCT
ejpam-6659	249	7	ς	ς	NOUN
ejpam-6659	249	8	)	)	PUNCT
ejpam-6659	249	9	=	=	SYM
ejpam-6659	249	10	s(fτ	s(fτ	PROPN
ejpam-6659	249	11	,	,	PUNCT
ejpam-6659	249	12	fτ	fτ	NOUN
ejpam-6659	249	13	,	,	PUNCT
ejpam-6659	249	14	gς	gς	PROPN
ejpam-6659	249	15	)	)	PUNCT
ejpam-6659	249	16	=	=	SYM
ejpam-6659	249	17	0	0	NUM
ejpam-6659	249	18	which	which	PRON
ejpam-6659	249	19	implies	imply	VERB
ejpam-6659	249	20	that	that	SCONJ
ejpam-6659	249	21	τ	τ	PROPN
ejpam-6659	249	22	=	=	SYM
ejpam-6659	249	23	ς	ς	PROPN
ejpam-6659	249	24	as	as	SCONJ
ejpam-6659	249	25	required	require	VERB
ejpam-6659	249	26	.	.	PUNCT
ejpam-6659	250	1	h.	h.	PROPN
ejpam-6659	250	2	qawaqneh	qawaqneh	PROPN
ejpam-6659	250	3	et	et	PROPN
ejpam-6659	250	4	al	al	PROPN
ejpam-6659	250	5	.	.	PUNCT
ejpam-6659	250	6	/	/	SYM
ejpam-6659	250	7	eur	eur	PROPN
ejpam-6659	250	8	.	.	PUNCT
ejpam-6659	251	1	j.	j.	PROPN
ejpam-6659	251	2	pure	pure	PROPN
ejpam-6659	251	3	appl	appl	PROPN
ejpam-6659	251	4	.	.	PROPN
ejpam-6659	251	5	math	math	PROPN
ejpam-6659	251	6	,	,	PUNCT
ejpam-6659	251	7	18	18	NUM
ejpam-6659	251	8	(	(	PUNCT
ejpam-6659	251	9	3	3	NUM
ejpam-6659	251	10	)	)	PUNCT
ejpam-6659	251	11	(	(	PUNCT
ejpam-6659	251	12	2025	2025	NUM
ejpam-6659	251	13	)	)	PUNCT
ejpam-6659	251	14	,	,	PUNCT
ejpam-6659	251	15	6659	6659	NUM
ejpam-6659	251	16	13	13	NUM
ejpam-6659	251	17	of	of	ADP
ejpam-6659	251	18	16	16	NUM
ejpam-6659	251	19	corollary	corollary	ADJ
ejpam-6659	251	20	3	3	NUM
ejpam-6659	251	21	.	.	PUNCT
ejpam-6659	252	1	let	let	AUX
ejpam-6659	252	2	(	(	PUNCT
ejpam-6659	252	3	γ	γ	X
ejpam-6659	252	4	,	,	PUNCT
ejpam-6659	252	5	s	s	PROPN
ejpam-6659	252	6	,	,	PUNCT
ejpam-6659	252	7	α	α	NOUN
ejpam-6659	252	8	)	)	PUNCT
ejpam-6659	252	9	be	be	VERB
ejpam-6659	252	10	a	a	DET
ejpam-6659	252	11	complete	complete	ADJ
ejpam-6659	252	12	complex	complex	NOUN
ejpam-6659	252	13	valued	value	VERB
ejpam-6659	252	14	s	s	NOUN
ejpam-6659	252	15	-	-	ADJ
ejpam-6659	252	16	metric	metric	ADJ
ejpam-6659	252	17	space	space	NOUN
ejpam-6659	252	18	.	.	PUNCT
ejpam-6659	253	1	let	let	VERB
ejpam-6659	253	2	f	f	PROPN
ejpam-6659	253	3	and	and	CCONJ
ejpam-6659	253	4	g	g	PROPN
ejpam-6659	253	5	be	be	VERB
ejpam-6659	253	6	two	two	NUM
ejpam-6659	253	7	self	self	NOUN
ejpam-6659	253	8	mappings	mapping	NOUN
ejpam-6659	253	9	on	on	ADP
ejpam-6659	253	10	γ	γ	NOUN
ejpam-6659	253	11	that	that	PRON
ejpam-6659	253	12	meet	meet	VERB
ejpam-6659	253	13	the	the	DET
ejpam-6659	253	14	contraction	contraction	NOUN
ejpam-6659	253	15	condition	condition	NOUN
ejpam-6659	253	16	given	give	VERB
ejpam-6659	253	17	below	below	ADV
ejpam-6659	253	18	:	:	PUNCT
ejpam-6659	254	1	s(fτ	s(fτ	PROPN
ejpam-6659	254	2	,	,	PUNCT
ejpam-6659	254	3	fτ	fτ	NOUN
ejpam-6659	254	4	,	,	PUNCT
ejpam-6659	254	5	gς	gς	NOUN
ejpam-6659	254	6	)	)	PUNCT
ejpam-6659	254	7	≾	≾	PROPN
ejpam-6659	254	8	γs(τ	γs(τ	X
ejpam-6659	254	9	,	,	PUNCT
ejpam-6659	254	10	τ	τ	PROPN
ejpam-6659	254	11	,	,	PUNCT
ejpam-6659	254	12	ς	ς	PROPN
ejpam-6659	254	13	)	)	PUNCT
ejpam-6659	254	14	+	+	CCONJ
ejpam-6659	254	15	βs(τ	βs(τ	NUM
ejpam-6659	254	16	,	,	PUNCT
ejpam-6659	254	17	τ	τ	PROPN
ejpam-6659	254	18	,	,	PUNCT
ejpam-6659	254	19	fτ)s(ς	fτ)s(ς	NOUN
ejpam-6659	254	20	,	,	PUNCT
ejpam-6659	254	21	ς	ς	NOUN
ejpam-6659	254	22	,	,	PUNCT
ejpam-6659	254	23	gς	gς	PROPN
ejpam-6659	254	24	)	)	PUNCT
ejpam-6659	254	25	b(2s(τ	b(2s(τ	PROPN
ejpam-6659	254	26	,	,	PUNCT
ejpam-6659	254	27	τ	τ	PROPN
ejpam-6659	254	28	,	,	PUNCT
ejpam-6659	254	29	gς	gς	PROPN
ejpam-6659	254	30	)	)	PUNCT
ejpam-6659	254	31	+	+	CCONJ
ejpam-6659	254	32	s(ς	s(ς	PROPN
ejpam-6659	254	33	,	,	PUNCT
ejpam-6659	254	34	ς	ς	NOUN
ejpam-6659	254	35	,	,	PUNCT
ejpam-6659	254	36	fτ	fτ	ADJ
ejpam-6659	254	37	)	)	PUNCT
ejpam-6659	254	38	+	+	CCONJ
ejpam-6659	254	39	s(τ	s(τ	PROPN
ejpam-6659	254	40	,	,	PUNCT
ejpam-6659	254	41	τ	τ	PROPN
ejpam-6659	254	42	,	,	PUNCT
ejpam-6659	254	43	ς	ς	NOUN
ejpam-6659	254	44	)	)	PUNCT
ejpam-6659	254	45	)	)	PUNCT
ejpam-6659	254	46	for	for	ADP
ejpam-6659	254	47	all	all	DET
ejpam-6659	254	48	τ	τ	PROPN
ejpam-6659	254	49	,	,	PUNCT
ejpam-6659	254	50	ς	ς	PROPN
ejpam-6659	254	51	∈	∈	PROPN
ejpam-6659	254	52	γ	γ	NOUN
ejpam-6659	254	53	such	such	ADJ
ejpam-6659	254	54	that	that	SCONJ
ejpam-6659	254	55	τ	τ	PROPN
ejpam-6659	254	56	̸=	̸=	PROPN
ejpam-6659	254	57	ς	ς	PROPN
ejpam-6659	254	58	,	,	PUNCT
ejpam-6659	254	59	s(τ	s(τ	PROPN
ejpam-6659	254	60	,	,	PUNCT
ejpam-6659	254	61	τ	τ	PROPN
ejpam-6659	254	62	,	,	PUNCT
ejpam-6659	254	63	gς	gς	PROPN
ejpam-6659	254	64	)	)	PUNCT
ejpam-6659	254	65	+	+	CCONJ
ejpam-6659	254	66	s(ς	s(ς	PROPN
ejpam-6659	254	67	,	,	PUNCT
ejpam-6659	254	68	ς	ς	NOUN
ejpam-6659	254	69	,	,	PUNCT
ejpam-6659	254	70	fτ	fτ	ADJ
ejpam-6659	254	71	)	)	PUNCT
ejpam-6659	254	72	+	+	CCONJ
ejpam-6659	254	73	s(τ	s(τ	PROPN
ejpam-6659	254	74	,	,	PUNCT
ejpam-6659	254	75	τ	τ	PROPN
ejpam-6659	254	76	,	,	PUNCT
ejpam-6659	254	77	ς	ς	NOUN
ejpam-6659	254	78	)	)	PUNCT
ejpam-6659	254	79	̸=	̸=	PROPN
ejpam-6659	254	80	0	0	NUM
ejpam-6659	254	81	,	,	PUNCT
ejpam-6659	254	82	where	where	SCONJ
ejpam-6659	254	83	γ	γ	X
ejpam-6659	254	84	,	,	PUNCT
ejpam-6659	254	85	β	β	X
ejpam-6659	254	86	are	be	AUX
ejpam-6659	254	87	two	two	NUM
ejpam-6659	254	88	real	real	ADJ
ejpam-6659	254	89	numbers	number	NOUN
ejpam-6659	254	90	which	which	PRON
ejpam-6659	254	91	are	be	AUX
ejpam-6659	254	92	nonnegative	nonnegative	ADJ
ejpam-6659	254	93	and	and	CCONJ
ejpam-6659	254	94	satisfy	satisfy	VERB
ejpam-6659	254	95	the	the	DET
ejpam-6659	254	96	condition	condition	NOUN
ejpam-6659	254	97	γ+β	γ+β	PUNCT
ejpam-6659	254	98	<	<	X
ejpam-6659	254	99	1	1	NUM
ejpam-6659	254	100	b	b	NOUN
ejpam-6659	254	101	or	or	CCONJ
ejpam-6659	254	102	s(fτ	s(fτ	PROPN
ejpam-6659	254	103	,	,	PUNCT
ejpam-6659	254	104	fτ	fτ	NOUN
ejpam-6659	254	105	,	,	PUNCT
ejpam-6659	254	106	gς	gς	PROPN
ejpam-6659	254	107	)	)	PUNCT
ejpam-6659	254	108	=	=	SYM
ejpam-6659	254	109	0	0	PUNCT
ejpam-6659	255	1	if	if	SCONJ
ejpam-6659	255	2	s(τ	s(τ	PROPN
ejpam-6659	255	3	,	,	PUNCT
ejpam-6659	255	4	τ	τ	PROPN
ejpam-6659	255	5	,	,	PUNCT
ejpam-6659	255	6	gς)+s(ς	gς)+s(ς	NOUN
ejpam-6659	255	7	,	,	PUNCT
ejpam-6659	255	8	ς	ς	PROPN
ejpam-6659	255	9	,	,	PUNCT
ejpam-6659	255	10	fτ)+s(τ	fτ)+s(τ	PROPN
ejpam-6659	255	11	,	,	PUNCT
ejpam-6659	255	12	τ	τ	PROPN
ejpam-6659	255	13	,	,	PUNCT
ejpam-6659	255	14	ς	ς	PROPN
ejpam-6659	255	15	)	)	PUNCT
ejpam-6659	255	16	=	=	SYM
ejpam-6659	255	17	0	0	X
ejpam-6659	255	18	.	.	PUNCT
ejpam-6659	256	1	then	then	ADV
ejpam-6659	256	2	there	there	PRON
ejpam-6659	256	3	exists	exist	VERB
ejpam-6659	256	4	a	a	DET
ejpam-6659	256	5	unique	unique	ADJ
ejpam-6659	256	6	common	common	ADJ
ejpam-6659	256	7	fixed	fix	VERB
ejpam-6659	256	8	point	point	NOUN
ejpam-6659	256	9	for	for	ADP
ejpam-6659	256	10	f	f	PROPN
ejpam-6659	256	11	and	and	CCONJ
ejpam-6659	256	12	g.	g.	PROPN
ejpam-6659	256	13	proof	proof	NOUN
ejpam-6659	256	14	.	.	PUNCT
ejpam-6659	257	1	if	if	SCONJ
ejpam-6659	257	2	we	we	PRON
ejpam-6659	257	3	take	take	VERB
ejpam-6659	257	4	α(τ	α(τ	NUM
ejpam-6659	257	5	,	,	PUNCT
ejpam-6659	257	6	ς,ϖ	ς,ϖ	NUM
ejpam-6659	257	7	)	)	PUNCT
ejpam-6659	257	8	=	=	SYM
ejpam-6659	257	9	b	b	X
ejpam-6659	257	10	(	(	PUNCT
ejpam-6659	257	11	b	b	NOUN
ejpam-6659	257	12	is	be	AUX
ejpam-6659	257	13	some	some	DET
ejpam-6659	257	14	constant	constant	ADJ
ejpam-6659	257	15	)	)	PUNCT
ejpam-6659	257	16	and	and	CCONJ
ejpam-6659	257	17	proceed	proceed	VERB
ejpam-6659	257	18	with	with	ADP
ejpam-6659	257	19	the	the	DET
ejpam-6659	257	20	same	same	ADJ
ejpam-6659	257	21	steps	step	NOUN
ejpam-6659	257	22	as	as	SCONJ
ejpam-6659	257	23	outlined	outline	VERB
ejpam-6659	257	24	in	in	ADP
ejpam-6659	257	25	the	the	DET
ejpam-6659	257	26	proof	proof	NOUN
ejpam-6659	257	27	of	of	ADP
ejpam-6659	257	28	theorem	theorem	ADJ
ejpam-6659	257	29	4	4	NUM
ejpam-6659	257	30	,	,	PUNCT
ejpam-6659	257	31	the	the	DET
ejpam-6659	257	32	corollary	corollary	NOUN
ejpam-6659	257	33	can	can	AUX
ejpam-6659	257	34	be	be	AUX
ejpam-6659	257	35	proved	prove	VERB
ejpam-6659	257	36	.	.	PUNCT
ejpam-6659	258	1	corollary	corollary	ADJ
ejpam-6659	258	2	4	4	NUM
ejpam-6659	258	3	.	.	PUNCT
ejpam-6659	259	1	let	let	AUX
ejpam-6659	259	2	(	(	PUNCT
ejpam-6659	259	3	γ	γ	X
ejpam-6659	259	4	,	,	PUNCT
ejpam-6659	259	5	s	s	PROPN
ejpam-6659	259	6	,	,	PUNCT
ejpam-6659	259	7	α	α	NOUN
ejpam-6659	259	8	)	)	PUNCT
ejpam-6659	259	9	be	be	VERB
ejpam-6659	259	10	a	a	DET
ejpam-6659	259	11	complete	complete	ADJ
ejpam-6659	259	12	complex	complex	NOUN
ejpam-6659	259	13	valued	value	VERB
ejpam-6659	259	14	s	s	NOUN
ejpam-6659	259	15	-	-	ADJ
ejpam-6659	259	16	metric	metric	ADJ
ejpam-6659	259	17	space	space	NOUN
ejpam-6659	259	18	.	.	PUNCT
ejpam-6659	260	1	let	let	VERB
ejpam-6659	260	2	f	f	PROPN
ejpam-6659	260	3	and	and	CCONJ
ejpam-6659	260	4	g	g	PROPN
ejpam-6659	260	5	be	be	VERB
ejpam-6659	260	6	two	two	NUM
ejpam-6659	260	7	self	self	NOUN
ejpam-6659	260	8	mappings	mapping	NOUN
ejpam-6659	260	9	on	on	ADP
ejpam-6659	260	10	γ	γ	NOUN
ejpam-6659	260	11	that	that	PRON
ejpam-6659	260	12	meet	meet	VERB
ejpam-6659	260	13	the	the	DET
ejpam-6659	260	14	contraction	contraction	NOUN
ejpam-6659	260	15	condition	condition	NOUN
ejpam-6659	260	16	given	give	VERB
ejpam-6659	260	17	below	below	ADV
ejpam-6659	260	18	:	:	PUNCT
ejpam-6659	261	1	s(fτ	s(fτ	PROPN
ejpam-6659	261	2	,	,	PUNCT
ejpam-6659	261	3	fτ	fτ	NOUN
ejpam-6659	261	4	,	,	PUNCT
ejpam-6659	261	5	gς	gς	NOUN
ejpam-6659	261	6	)	)	PUNCT
ejpam-6659	261	7	≾	≾	PROPN
ejpam-6659	261	8	γs(τ	γs(τ	X
ejpam-6659	261	9	,	,	PUNCT
ejpam-6659	261	10	τ	τ	PROPN
ejpam-6659	261	11	,	,	PUNCT
ejpam-6659	261	12	ς	ς	PROPN
ejpam-6659	261	13	)	)	PUNCT
ejpam-6659	261	14	+	+	CCONJ
ejpam-6659	261	15	βs(τ	βs(τ	NUM
ejpam-6659	261	16	,	,	PUNCT
ejpam-6659	261	17	τ	τ	PROPN
ejpam-6659	261	18	,	,	PUNCT
ejpam-6659	261	19	fτ)s(ς	fτ)s(ς	NOUN
ejpam-6659	261	20	,	,	PUNCT
ejpam-6659	261	21	ς	ς	NOUN
ejpam-6659	261	22	,	,	PUNCT
ejpam-6659	261	23	gς	gς	PROPN
ejpam-6659	261	24	)	)	PUNCT
ejpam-6659	261	25	2s(τ	2s(τ	NUM
ejpam-6659	261	26	,	,	PUNCT
ejpam-6659	261	27	τ	τ	PROPN
ejpam-6659	261	28	,	,	PUNCT
ejpam-6659	261	29	gς	gς	PROPN
ejpam-6659	261	30	)	)	PUNCT
ejpam-6659	261	31	+	+	CCONJ
ejpam-6659	261	32	s(ς	s(ς	PROPN
ejpam-6659	261	33	,	,	PUNCT
ejpam-6659	261	34	ς	ς	NOUN
ejpam-6659	261	35	,	,	PUNCT
ejpam-6659	261	36	fτ	fτ	ADJ
ejpam-6659	261	37	)	)	PUNCT
ejpam-6659	261	38	+	+	CCONJ
ejpam-6659	261	39	s(τ	s(τ	PROPN
ejpam-6659	261	40	,	,	PUNCT
ejpam-6659	261	41	τ	τ	PROPN
ejpam-6659	261	42	,	,	PUNCT
ejpam-6659	261	43	ς	ς	PROPN
ejpam-6659	261	44	)	)	PUNCT
ejpam-6659	261	45	for	for	ADP
ejpam-6659	261	46	all	all	DET
ejpam-6659	261	47	τ	τ	PROPN
ejpam-6659	261	48	,	,	PUNCT
ejpam-6659	261	49	ς	ς	PROPN
ejpam-6659	261	50	∈	∈	PROPN
ejpam-6659	261	51	γ	γ	NOUN
ejpam-6659	261	52	such	such	ADJ
ejpam-6659	261	53	that	that	SCONJ
ejpam-6659	261	54	τ	τ	PROPN
ejpam-6659	261	55	̸=	̸=	PROPN
ejpam-6659	261	56	ς	ς	PROPN
ejpam-6659	261	57	,	,	PUNCT
ejpam-6659	261	58	s(τ	s(τ	PROPN
ejpam-6659	261	59	,	,	PUNCT
ejpam-6659	261	60	τ	τ	PROPN
ejpam-6659	261	61	,	,	PUNCT
ejpam-6659	261	62	gς	gς	PROPN
ejpam-6659	261	63	)	)	PUNCT
ejpam-6659	261	64	+	+	CCONJ
ejpam-6659	261	65	s(ς	s(ς	PROPN
ejpam-6659	261	66	,	,	PUNCT
ejpam-6659	261	67	ς	ς	NOUN
ejpam-6659	261	68	,	,	PUNCT
ejpam-6659	261	69	fτ	fτ	ADJ
ejpam-6659	261	70	)	)	PUNCT
ejpam-6659	261	71	+	+	CCONJ
ejpam-6659	261	72	s(τ	s(τ	PROPN
ejpam-6659	261	73	,	,	PUNCT
ejpam-6659	261	74	τ	τ	PROPN
ejpam-6659	261	75	,	,	PUNCT
ejpam-6659	261	76	ς	ς	NOUN
ejpam-6659	261	77	)	)	PUNCT
ejpam-6659	261	78	̸=	̸=	PROPN
ejpam-6659	261	79	0	0	NUM
ejpam-6659	261	80	,	,	PUNCT
ejpam-6659	261	81	where	where	SCONJ
ejpam-6659	261	82	γ	γ	X
ejpam-6659	261	83	,	,	PUNCT
ejpam-6659	261	84	β	β	X
ejpam-6659	261	85	are	be	AUX
ejpam-6659	261	86	two	two	NUM
ejpam-6659	261	87	real	real	ADJ
ejpam-6659	261	88	numbers	number	NOUN
ejpam-6659	261	89	which	which	PRON
ejpam-6659	261	90	are	be	AUX
ejpam-6659	261	91	nonnegative	nonnegative	ADJ
ejpam-6659	261	92	and	and	CCONJ
ejpam-6659	261	93	satisfy	satisfy	VERB
ejpam-6659	261	94	the	the	DET
ejpam-6659	261	95	condition	condition	NOUN
ejpam-6659	261	96	γ+β	γ+β	PUNCT
ejpam-6659	261	97	<	<	X
ejpam-6659	261	98	1	1	NUM
ejpam-6659	261	99	or	or	CCONJ
ejpam-6659	261	100	s(fτ	s(fτ	PROPN
ejpam-6659	261	101	,	,	PUNCT
ejpam-6659	261	102	fτ	fτ	NOUN
ejpam-6659	261	103	,	,	PUNCT
ejpam-6659	261	104	gς	gς	PROPN
ejpam-6659	261	105	)	)	PUNCT
ejpam-6659	261	106	=	=	SYM
ejpam-6659	261	107	0	0	PUNCT
ejpam-6659	262	1	if	if	SCONJ
ejpam-6659	262	2	s(τ	s(τ	PROPN
ejpam-6659	262	3	,	,	PUNCT
ejpam-6659	262	4	τ	τ	PROPN
ejpam-6659	262	5	,	,	PUNCT
ejpam-6659	262	6	gς)+s(ς	gς)+s(ς	NOUN
ejpam-6659	262	7	,	,	PUNCT
ejpam-6659	262	8	ς	ς	PROPN
ejpam-6659	262	9	,	,	PUNCT
ejpam-6659	262	10	fτ)+s(τ	fτ)+s(τ	PROPN
ejpam-6659	262	11	,	,	PUNCT
ejpam-6659	262	12	τ	τ	PROPN
ejpam-6659	262	13	,	,	PUNCT
ejpam-6659	262	14	ς	ς	PROPN
ejpam-6659	262	15	)	)	PUNCT
ejpam-6659	262	16	=	=	SYM
ejpam-6659	262	17	0	0	X
ejpam-6659	262	18	.	.	PUNCT
ejpam-6659	263	1	then	then	ADV
ejpam-6659	263	2	there	there	PRON
ejpam-6659	263	3	exists	exist	VERB
ejpam-6659	263	4	a	a	DET
ejpam-6659	263	5	unique	unique	ADJ
ejpam-6659	263	6	common	common	ADJ
ejpam-6659	263	7	fixed	fix	VERB
ejpam-6659	263	8	point	point	NOUN
ejpam-6659	263	9	for	for	ADP
ejpam-6659	263	10	f	f	PROPN
ejpam-6659	263	11	,	,	PUNCT
ejpam-6659	263	12	g.	g.	PROPN
ejpam-6659	263	13	proof	proof	NOUN
ejpam-6659	263	14	.	.	PUNCT
ejpam-6659	264	1	if	if	SCONJ
ejpam-6659	264	2	we	we	PRON
ejpam-6659	264	3	take	take	VERB
ejpam-6659	264	4	α(τ	α(τ	NUM
ejpam-6659	264	5	,	,	PUNCT
ejpam-6659	264	6	ς,ϖ	ς,ϖ	NUM
ejpam-6659	264	7	)	)	PUNCT
ejpam-6659	264	8	=	=	SYM
ejpam-6659	264	9	1	1	NUM
ejpam-6659	264	10	and	and	CCONJ
ejpam-6659	264	11	proceed	proceed	VERB
ejpam-6659	264	12	with	with	ADP
ejpam-6659	264	13	the	the	DET
ejpam-6659	264	14	same	same	ADJ
ejpam-6659	264	15	steps	step	NOUN
ejpam-6659	264	16	as	as	SCONJ
ejpam-6659	264	17	outlined	outline	VERB
ejpam-6659	264	18	in	in	ADP
ejpam-6659	264	19	the	the	DET
ejpam-6659	264	20	proof	proof	NOUN
ejpam-6659	264	21	of	of	ADP
ejpam-6659	264	22	theorem	theorem	ADJ
ejpam-6659	264	23	4	4	NUM
ejpam-6659	264	24	,	,	PUNCT
ejpam-6659	264	25	the	the	DET
ejpam-6659	264	26	corollary	corollary	NOUN
ejpam-6659	264	27	can	can	AUX
ejpam-6659	264	28	be	be	AUX
ejpam-6659	264	29	proved	prove	VERB
ejpam-6659	264	30	.	.	PUNCT
ejpam-6659	265	1	4	4	X
ejpam-6659	265	2	.	.	X
ejpam-6659	265	3	an	an	DET
ejpam-6659	265	4	application	application	NOUN
ejpam-6659	265	5	we	we	PRON
ejpam-6659	265	6	examine	examine	VERB
ejpam-6659	265	7	a	a	DET
ejpam-6659	265	8	nonlinear	nonlinear	ADJ
ejpam-6659	265	9	volterra	volterra	NOUN
ejpam-6659	265	10	-	-	PUNCT
ejpam-6659	265	11	type	type	NOUN
ejpam-6659	265	12	integral	integral	ADJ
ejpam-6659	265	13	equation	equation	NOUN
ejpam-6659	265	14	defined	define	VERB
ejpam-6659	265	15	for	for	ADP
ejpam-6659	265	16	complex	complex	ADV
ejpam-6659	265	17	-	-	PUNCT
ejpam-6659	265	18	valued	value	VERB
ejpam-6659	265	19	functions	function	NOUN
ejpam-6659	265	20	u(τ	u(τ	NUM
ejpam-6659	265	21	)	)	PUNCT
ejpam-6659	266	1	=	=	PUNCT
ejpam-6659	266	2	τ2	τ2	NOUN
ejpam-6659	266	3	+	+	CCONJ
ejpam-6659	266	4	i	i	PROPN
ejpam-6659	266	5	4	4	NUM
ejpam-6659	266	6	∫	∫	NOUN
ejpam-6659	266	7	τ	τ	X
ejpam-6659	266	8	0	0	NUM
ejpam-6659	267	1	u(ς)3	u(ς)3	PROPN
ejpam-6659	267	2	1	1	NUM
ejpam-6659	267	3	+	+	CCONJ
ejpam-6659	267	4	|u(ς)|	|u(ς)|	PROPN
ejpam-6659	267	5	dς	dς	PROPN
ejpam-6659	267	6	,	,	PUNCT
ejpam-6659	267	7	τ	τ	PROPN
ejpam-6659	267	8	∈	∈	PROPN
ejpam-6659	268	1	[	[	X
ejpam-6659	268	2	0	0	NUM
ejpam-6659	268	3	,	,	PUNCT
ejpam-6659	268	4	1	1	NUM
ejpam-6659	268	5	]	]	PUNCT
ejpam-6659	268	6	,	,	PUNCT
ejpam-6659	268	7	(	(	PUNCT
ejpam-6659	268	8	7	7	X
ejpam-6659	268	9	)	)	PUNCT
ejpam-6659	268	10	where	where	SCONJ
ejpam-6659	268	11	u(τ	u(τ	ADJ
ejpam-6659	268	12	)	)	PUNCT
ejpam-6659	268	13	∈	∈	PROPN
ejpam-6659	268	14	c	c	NOUN
ejpam-6659	268	15	is	be	AUX
ejpam-6659	268	16	the	the	DET
ejpam-6659	268	17	unknown	unknown	ADJ
ejpam-6659	268	18	function	function	NOUN
ejpam-6659	268	19	and	and	CCONJ
ejpam-6659	268	20	the	the	DET
ejpam-6659	268	21	kernel	kernel	PROPN
ejpam-6659	268	22	k(τ	k(τ	PROPN
ejpam-6659	268	23	,	,	PUNCT
ejpam-6659	268	24	ς	ς	PROPN
ejpam-6659	268	25	,	,	PUNCT
ejpam-6659	268	26	u	u	NOUN
ejpam-6659	268	27	)	)	PUNCT
ejpam-6659	268	28	=	=	VERB
ejpam-6659	268	29	iu3	iu3	VERB
ejpam-6659	268	30	4(1+|u|	4(1+|u|	NOUN
ejpam-6659	268	31	)	)	PUNCT
ejpam-6659	268	32	is	be	AUX
ejpam-6659	268	33	lipschitz	lipschitz	NOUN
ejpam-6659	268	34	continuous	continuous	ADJ
ejpam-6659	268	35	in	in	ADP
ejpam-6659	268	36	u.	u.	NOUN
ejpam-6659	268	37	let	let	VERB
ejpam-6659	268	38	γ	γ	NOUN
ejpam-6659	268	39	be	be	AUX
ejpam-6659	268	40	the	the	DET
ejpam-6659	268	41	space	space	NOUN
ejpam-6659	268	42	of	of	ADP
ejpam-6659	268	43	continuous	continuous	ADJ
ejpam-6659	268	44	functions	function	NOUN
ejpam-6659	268	45	that	that	PRON
ejpam-6659	268	46	map	map	VERB
ejpam-6659	268	47	from	from	ADP
ejpam-6659	268	48	[	[	X
ejpam-6659	268	49	0	0	NUM
ejpam-6659	268	50	,	,	PUNCT
ejpam-6659	268	51	1	1	NUM
ejpam-6659	268	52	]	]	PUNCT
ejpam-6659	268	53	to	to	ADP
ejpam-6659	268	54	the	the	DET
ejpam-6659	268	55	complex	complex	ADJ
ejpam-6659	268	56	numbers	number	NOUN
ejpam-6659	268	57	.	.	PUNCT
ejpam-6659	269	1	we	we	PRON
ejpam-6659	269	2	define	define	VERB
ejpam-6659	269	3	the	the	DET
ejpam-6659	269	4	operator	operator	NOUN
ejpam-6659	269	5	t	t	NOUN
ejpam-6659	269	6	:	:	PUNCT
ejpam-6659	269	7	γ	γ	X
ejpam-6659	269	8	→	→	SYM
ejpam-6659	269	9	γ	γ	X
ejpam-6659	269	10	by	by	ADP
ejpam-6659	269	11	t	t	PROPN
ejpam-6659	269	12	(	(	PUNCT
ejpam-6659	269	13	u(τ	u(τ	PROPN
ejpam-6659	269	14	)	)	PUNCT
ejpam-6659	269	15	)	)	PUNCT
ejpam-6659	269	16	:	:	PUNCT
ejpam-6659	270	1	=	=	SYM
ejpam-6659	270	2	τ2	τ2	NOUN
ejpam-6659	271	1	+	+	CCONJ
ejpam-6659	271	2	i	i	PROPN
ejpam-6659	271	3	4	4	NUM
ejpam-6659	271	4	∫	∫	NOUN
ejpam-6659	271	5	τ	τ	X
ejpam-6659	271	6	0	0	NUM
ejpam-6659	272	1	u(ς)3	u(ς)3	PROPN
ejpam-6659	272	2	1	1	NUM
ejpam-6659	272	3	+	+	CCONJ
ejpam-6659	272	4	|u(ς)|	|u(ς)|	PROPN
ejpam-6659	272	5	dς	dς	NOUN
ejpam-6659	272	6	.	.	PUNCT
ejpam-6659	272	7	consider	consider	VERB
ejpam-6659	272	8	a	a	DET
ejpam-6659	272	9	closed	closed	ADJ
ejpam-6659	272	10	ball	ball	NOUN
ejpam-6659	272	11	br(0	br(0	NOUN
ejpam-6659	272	12	)	)	PUNCT
ejpam-6659	272	13	=	=	PUNCT
ejpam-6659	272	14	{	{	PUNCT
ejpam-6659	272	15	u	u	NOUN
ejpam-6659	272	16	∈	∈	PROPN
ejpam-6659	272	17	γ	γ	X
ejpam-6659	272	18	:	:	PUNCT
ejpam-6659	272	19	∥u∥∞	∥u∥∞	X
ejpam-6659	272	20	≤	≤	X
ejpam-6659	272	21	r	r	X
ejpam-6659	272	22	}	}	PUNCT
ejpam-6659	272	23	for	for	ADP
ejpam-6659	272	24	some	some	DET
ejpam-6659	272	25	r	r	NOUN
ejpam-6659	272	26	>	>	X
ejpam-6659	272	27	0	0	NUM
ejpam-6659	272	28	.	.	PUNCT
ejpam-6659	273	1	also	also	ADV
ejpam-6659	273	2	,	,	PUNCT
ejpam-6659	273	3	define	define	VERB
ejpam-6659	273	4	the	the	DET
ejpam-6659	273	5	metric	metric	NOUN
ejpam-6659	273	6	as	as	ADP
ejpam-6659	273	7	s(u	s(u	PROPN
ejpam-6659	273	8	,	,	PUNCT
ejpam-6659	273	9	v	v	NOUN
ejpam-6659	273	10	,	,	PUNCT
ejpam-6659	273	11	w	w	NOUN
ejpam-6659	273	12	)	)	PUNCT
ejpam-6659	273	13	=	=	SYM
ejpam-6659	273	14	max	max	PROPN
ejpam-6659	273	15	τ∈[0,1	τ∈[0,1	PROPN
ejpam-6659	273	16	]	]	X
ejpam-6659	273	17	{	{	PUNCT
ejpam-6659	273	18	|u(τ)−	|u(τ)−	NOUN
ejpam-6659	273	19	w(τ)|	w(τ)|	NOUN
ejpam-6659	273	20	,	,	PUNCT
ejpam-6659	273	21	|v(τ)−	|v(τ)−	ADJ
ejpam-6659	273	22	w(τ)|	w(τ)|	NOUN
ejpam-6659	273	23	,	,	PUNCT
ejpam-6659	273	24	|u(τ)−	|u(τ)−	NOUN
ejpam-6659	273	25	v(τ)|	v(τ)|	NOUN
ejpam-6659	273	26	2	2	NUM
ejpam-6659	273	27	}	}	PUNCT
ejpam-6659	274	1	h.	h.	PROPN
ejpam-6659	274	2	qawaqneh	qawaqneh	PROPN
ejpam-6659	274	3	et	et	PROPN
ejpam-6659	274	4	al	al	PROPN
ejpam-6659	274	5	.	.	PUNCT
ejpam-6659	274	6	/	/	SYM
ejpam-6659	274	7	eur	eur	PROPN
ejpam-6659	274	8	.	.	PUNCT
ejpam-6659	275	1	j.	j.	PROPN
ejpam-6659	275	2	pure	pure	PROPN
ejpam-6659	275	3	appl	appl	PROPN
ejpam-6659	275	4	.	.	PROPN
ejpam-6659	275	5	math	math	PROPN
ejpam-6659	275	6	,	,	PUNCT
ejpam-6659	275	7	18	18	NUM
ejpam-6659	275	8	(	(	PUNCT
ejpam-6659	275	9	3	3	NUM
ejpam-6659	275	10	)	)	PUNCT
ejpam-6659	275	11	(	(	PUNCT
ejpam-6659	275	12	2025	2025	NUM
ejpam-6659	275	13	)	)	PUNCT
ejpam-6659	275	14	,	,	PUNCT
ejpam-6659	275	15	6659	6659	NUM
ejpam-6659	275	16	14	14	NUM
ejpam-6659	275	17	of	of	ADP
ejpam-6659	275	18	16	16	NUM
ejpam-6659	275	19	and	and	CCONJ
ejpam-6659	275	20	the	the	DET
ejpam-6659	275	21	control	control	NOUN
ejpam-6659	275	22	function	function	NOUN
ejpam-6659	275	23	as	as	ADP
ejpam-6659	275	24	α(u	α(u	NOUN
ejpam-6659	275	25	,	,	PUNCT
ejpam-6659	275	26	v	v	NOUN
ejpam-6659	275	27	,	,	PUNCT
ejpam-6659	275	28	w	w	NOUN
ejpam-6659	275	29	)	)	PUNCT
ejpam-6659	275	30	=	=	SYM
ejpam-6659	275	31	1	1	NUM
ejpam-6659	275	32	+	+	NUM
ejpam-6659	275	33	∥u∥2∞	∥u∥2∞	ADJ
ejpam-6659	276	1	+	+	NOUN
ejpam-6659	276	2	∥v∥∞	∥v∥∞	NOUN
ejpam-6659	276	3	+	+	NUM
ejpam-6659	276	4	∥w∥3∞.	∥w∥3∞.	NOUN
ejpam-6659	276	5	theorem	theorem	NOUN
ejpam-6659	276	6	5	5	NUM
ejpam-6659	276	7	.	.	PUNCT
ejpam-6659	277	1	the	the	DET
ejpam-6659	277	2	integral	integral	ADJ
ejpam-6659	277	3	equation	equation	NOUN
ejpam-6659	277	4	(	(	PUNCT
ejpam-6659	277	5	7	7	X
ejpam-6659	277	6	)	)	PUNCT
ejpam-6659	277	7	admits	admit	VERB
ejpam-6659	277	8	a	a	DET
ejpam-6659	277	9	unique	unique	ADJ
ejpam-6659	277	10	solution	solution	NOUN
ejpam-6659	277	11	u∗	u∗	X
ejpam-6659	277	12	∈	∈	PROPN
ejpam-6659	277	13	γ	γ	NOUN
ejpam-6659	277	14	under	under	ADP
ejpam-6659	277	15	the	the	DET
ejpam-6659	277	16	stated	state	VERB
ejpam-6659	277	17	assumptions	assumption	NOUN
ejpam-6659	277	18	.	.	PUNCT
ejpam-6659	278	1	proof	proof	NOUN
ejpam-6659	278	2	.	.	PUNCT
ejpam-6659	279	1	for	for	ADP
ejpam-6659	279	2	u	u	NOUN
ejpam-6659	279	3	,	,	PUNCT
ejpam-6659	279	4	v	v	NOUN
ejpam-6659	279	5	∈	∈	NOUN
ejpam-6659	279	6	br(0	br(0	NOUN
ejpam-6659	279	7	)	)	PUNCT
ejpam-6659	279	8	with	with	ADP
ejpam-6659	279	9	r	r	NOUN
ejpam-6659	279	10	=	=	SYM
ejpam-6659	279	11	0.35	0.35	NUM
ejpam-6659	279	12	,	,	PUNCT
ejpam-6659	279	13	we	we	PRON
ejpam-6659	279	14	have	have	AUX
ejpam-6659	279	15	|t	|t	VERB
ejpam-6659	279	16	(	(	PUNCT
ejpam-6659	279	17	u(τ))−	u(τ))−	PROPN
ejpam-6659	279	18	t	t	PROPN
ejpam-6659	279	19	(	(	PUNCT
ejpam-6659	279	20	v(τ))|	v(τ))|	PROPN
ejpam-6659	279	21	≤	≤	NUM
ejpam-6659	279	22	1	1	NUM
ejpam-6659	279	23	4	4	NUM
ejpam-6659	279	24	∫	∫	NOUN
ejpam-6659	279	25	τ	τ	PROPN
ejpam-6659	279	26	0	0	NUM
ejpam-6659	279	27	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6659	279	28	u3	u3	NOUN
ejpam-6659	279	29	1	1	NUM
ejpam-6659	279	30	+	+	NUM
ejpam-6659	279	31	|u|	|u|	PROPN
ejpam-6659	279	32	−	−	NOUN
ejpam-6659	279	33	v3	v3	PROPN
ejpam-6659	279	34	1	1	NUM
ejpam-6659	279	35	+	+	NUM
ejpam-6659	280	1	|v|	|v|	PROPN
ejpam-6659	280	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6659	280	3	dς	dς	NOUN
ejpam-6659	280	4	≤	≤	NUM
ejpam-6659	280	5	1	1	NUM
ejpam-6659	280	6	4	4	NUM
ejpam-6659	280	7	∫	∫	PROPN
ejpam-6659	280	8	τ	τ	X
ejpam-6659	280	9	0	0	NUM
ejpam-6659	280	10	(	(	PUNCT
ejpam-6659	280	11	3r2	3r2	NUM
ejpam-6659	280	12	+	+	NUM
ejpam-6659	280	13	r3	r3	NOUN
ejpam-6659	280	14	)	)	PUNCT
ejpam-6659	280	15	|u−	|u−	PROPN
ejpam-6659	280	16	v|	v|	NOUN
ejpam-6659	280	17	dς	dς	PROPN
ejpam-6659	280	18	(	(	PUNCT
ejpam-6659	280	19	using	use	VERB
ejpam-6659	280	20	|k(τ	|k(τ	NOUN
ejpam-6659	280	21	,	,	PUNCT
ejpam-6659	280	22	ς	ς	NOUN
ejpam-6659	280	23	,	,	PUNCT
ejpam-6659	280	24	u)−k(τ	u)−k(τ	NOUN
ejpam-6659	280	25	,	,	PUNCT
ejpam-6659	280	26	ς	ς	PROPN
ejpam-6659	280	27	,	,	PUNCT
ejpam-6659	280	28	v)|	v)|	ADJ
ejpam-6659	280	29	≤	≤	NOUN
ejpam-6659	280	30	(	(	PUNCT
ejpam-6659	280	31	3r2	3r2	NUM
ejpam-6659	280	32	+	+	NUM
ejpam-6659	280	33	r3	r3	NOUN
ejpam-6659	280	34	)	)	PUNCT
ejpam-6659	280	35	|u−	|u−	NOUN
ejpam-6659	280	36	v|	v|	NOUN
ejpam-6659	280	37	)	)	PUNCT
ejpam-6659	280	38	≤	≤	NOUN
ejpam-6659	281	1	3(0.35)2	3(0.35)2	NUM
ejpam-6659	281	2	+	+	CCONJ
ejpam-6659	281	3	(	(	PUNCT
ejpam-6659	281	4	0.35)3	0.35)3	PROPN
ejpam-6659	281	5	4	4	NUM
ejpam-6659	281	6	max	max	PROPN
ejpam-6659	281	7	τ∈[0,1	τ∈[0,1	NUM
ejpam-6659	281	8	]	]	PUNCT
ejpam-6659	281	9	|u(τ)−	|u(τ)−	NOUN
ejpam-6659	281	10	v(τ)|	v(τ)|	NOUN
ejpam-6659	281	11	<	<	X
ejpam-6659	281	12	θs(u	θs(u	PROPN
ejpam-6659	281	13	,	,	PUNCT
ejpam-6659	281	14	u	u	NOUN
ejpam-6659	281	15	,	,	PUNCT
ejpam-6659	281	16	v	v	NOUN
ejpam-6659	281	17	)	)	PUNCT
ejpam-6659	281	18	,	,	PUNCT
ejpam-6659	281	19	where	where	SCONJ
ejpam-6659	281	20	θ	θ	PROPN
ejpam-6659	281	21	=	=	SYM
ejpam-6659	281	22	0.11	0.11	NUM
ejpam-6659	281	23	and	and	CCONJ
ejpam-6659	281	24	hence	hence	ADV
ejpam-6659	281	25	,	,	PUNCT
ejpam-6659	281	26	the	the	DET
ejpam-6659	281	27	contraction	contraction	NOUN
ejpam-6659	281	28	condition	condition	NOUN
ejpam-6659	281	29	is	be	AUX
ejpam-6659	281	30	satisfied	satisfied	ADJ
ejpam-6659	281	31	.	.	PUNCT
ejpam-6659	282	1	for	for	SCONJ
ejpam-6659	282	2	the	the	DET
ejpam-6659	282	3	picard	picard	NOUN
ejpam-6659	282	4	iterates	iterate	VERB
ejpam-6659	282	5	τω	τω	DET
ejpam-6659	282	6	=	=	NOUN
ejpam-6659	282	7	t	t	PROPN
ejpam-6659	282	8	ωτ0	ωτ0	NOUN
ejpam-6659	282	9	,	,	PUNCT
ejpam-6659	282	10	we	we	PRON
ejpam-6659	282	11	obtain	obtain	VERB
ejpam-6659	282	12	∥τω∥∞	∥τω∥∞	NOUN
ejpam-6659	282	13	≤	≤	NOUN
ejpam-6659	282	14	1	1	NUM
ejpam-6659	282	15	+	+	CCONJ
ejpam-6659	282	16	(	(	PUNCT
ejpam-6659	282	17	0.35)3	0.35)3	PROPN
ejpam-6659	282	18	4(1	4(1	NUM
ejpam-6659	282	19	+	+	CCONJ
ejpam-6659	282	20	0.35	0.35	NUM
ejpam-6659	282	21	)	)	PUNCT
ejpam-6659	283	1	≈	≈	PROPN
ejpam-6659	283	2	0.0079	0.0079	NUM
ejpam-6659	283	3	.	.	PUNCT
ejpam-6659	284	1	that	that	PRON
ejpam-6659	284	2	is	be	AUX
ejpam-6659	284	3	,	,	PUNCT
ejpam-6659	284	4	α(τω	α(τω	NUM
ejpam-6659	284	5	,	,	PUNCT
ejpam-6659	284	6	τω	τω	INTJ
ejpam-6659	284	7	,	,	PUNCT
ejpam-6659	284	8	τω+1	τω+1	SYM
ejpam-6659	284	9	)	)	PUNCT
ejpam-6659	284	10	≤	≤	NUM
ejpam-6659	284	11	1	1	NUM
ejpam-6659	285	1	+	+	CCONJ
ejpam-6659	285	2	(	(	PUNCT
ejpam-6659	285	3	0.0079)2	0.0079)2	NUM
ejpam-6659	285	4	+	+	NUM
ejpam-6659	285	5	0.0079	0.0079	NUM
ejpam-6659	285	6	+	+	CCONJ
ejpam-6659	285	7	(	(	PUNCT
ejpam-6659	285	8	0.0079)3	0.0079)3	NOUN
ejpam-6659	285	9	≈	≈	PROPN
ejpam-6659	285	10	1.008	1.008	NUM
ejpam-6659	285	11	.	.	PUNCT
ejpam-6659	286	1	thus	thus	ADV
ejpam-6659	286	2	,	,	PUNCT
ejpam-6659	286	3	sup	sup	INTJ
ejpam-6659	286	4	ϱ≥1	ϱ≥1	PROPN
ejpam-6659	286	5	lim	lim	PROPN
ejpam-6659	286	6	ω→+∞	ω→+∞	PROPN
ejpam-6659	286	7	α(τω+1	α(τω+1	PROPN
ejpam-6659	286	8	,	,	PUNCT
ejpam-6659	286	9	τω+1	τω+1	SYM
ejpam-6659	286	10	,	,	PUNCT
ejpam-6659	286	11	τω+2)α(τϱ	τω+2)α(τϱ	PROPN
ejpam-6659	286	12	,	,	PUNCT
ejpam-6659	286	13	τϱ	τϱ	X
ejpam-6659	286	14	,	,	PUNCT
ejpam-6659	286	15	τω+1	τω+1	NUM
ejpam-6659	286	16	)	)	PUNCT
ejpam-6659	286	17	α(τω	α(τω	NUM
ejpam-6659	286	18	,	,	PUNCT
ejpam-6659	286	19	τω	τω	INTJ
ejpam-6659	286	20	,	,	PUNCT
ejpam-6659	286	21	τω+1	τω+1	SYM
ejpam-6659	286	22	)	)	PUNCT
ejpam-6659	286	23	≤	≤	NOUN
ejpam-6659	286	24	1.008	1.008	NUM
ejpam-6659	286	25	<	<	X
ejpam-6659	286	26	1	1	NUM
ejpam-6659	286	27	2×	2×	NUM
ejpam-6659	286	28	0.11	0.11	NUM
ejpam-6659	286	29	≈	≈	PROPN
ejpam-6659	286	30	4.54	4.54	NUM
ejpam-6659	286	31	by	by	ADP
ejpam-6659	286	32	theorem	theorem	NOUN
ejpam-6659	286	33	2	2	NUM
ejpam-6659	286	34	,	,	PUNCT
ejpam-6659	286	35	t	t	PROPN
ejpam-6659	286	36	admits	admit	VERB
ejpam-6659	286	37	a	a	DET
ejpam-6659	286	38	unique	unique	ADJ
ejpam-6659	286	39	fixed	fix	VERB
ejpam-6659	286	40	point	point	NOUN
ejpam-6659	286	41	in	in	ADP
ejpam-6659	286	42	γ	γ	PROPN
ejpam-6659	286	43	,	,	PUNCT
ejpam-6659	286	44	i.e.	i.e.	X
ejpam-6659	286	45	,	,	PUNCT
ejpam-6659	286	46	the	the	DET
ejpam-6659	286	47	integral	integral	ADJ
ejpam-6659	286	48	equation	equation	NOUN
ejpam-6659	286	49	has	have	VERB
ejpam-6659	286	50	a	a	DET
ejpam-6659	286	51	unique	unique	ADJ
ejpam-6659	286	52	solution	solution	NOUN
ejpam-6659	286	53	.	.	PUNCT
ejpam-6659	287	1	5	5	X
ejpam-6659	287	2	.	.	X
ejpam-6659	287	3	conclusion	conclusion	NOUN
ejpam-6659	287	4	in	in	ADP
ejpam-6659	287	5	this	this	DET
ejpam-6659	287	6	paper	paper	NOUN
ejpam-6659	287	7	,	,	PUNCT
ejpam-6659	287	8	we	we	PRON
ejpam-6659	287	9	introduced	introduce	VERB
ejpam-6659	287	10	the	the	DET
ejpam-6659	287	11	concept	concept	NOUN
ejpam-6659	287	12	of	of	ADP
ejpam-6659	287	13	cvcs	cvcs	ADJ
ejpam-6659	287	14	-	-	PUNCT
ejpam-6659	287	15	metric	metric	ADJ
ejpam-6659	287	16	spaces	space	NOUN
ejpam-6659	287	17	,	,	PUNCT
ejpam-6659	287	18	which	which	PRON
ejpam-6659	287	19	generalizes	generalize	VERB
ejpam-6659	287	20	both	both	DET
ejpam-6659	287	21	complex	complex	ADJ
ejpam-6659	287	22	valued	value	VERB
ejpam-6659	287	23	s	s	NOUN
ejpam-6659	287	24	-	-	PUNCT
ejpam-6659	287	25	metrics	metric	NOUN
ejpam-6659	287	26	and	and	CCONJ
ejpam-6659	287	27	controlled	control	VERB
ejpam-6659	287	28	s	s	NOUN
ejpam-6659	287	29	-	-	ADJ
ejpam-6659	287	30	metric	metric	ADJ
ejpam-6659	287	31	spaces	space	NOUN
ejpam-6659	287	32	.	.	PUNCT
ejpam-6659	288	1	within	within	ADP
ejpam-6659	288	2	this	this	DET
ejpam-6659	288	3	new	new	ADJ
ejpam-6659	288	4	framework	framework	NOUN
ejpam-6659	288	5	,	,	PUNCT
ejpam-6659	288	6	we	we	PRON
ejpam-6659	288	7	established	establish	VERB
ejpam-6659	288	8	several	several	ADJ
ejpam-6659	288	9	fixed	fix	VERB
ejpam-6659	288	10	point	point	NOUN
ejpam-6659	288	11	theorems	theorem	NOUN
ejpam-6659	288	12	under	under	ADP
ejpam-6659	288	13	various	various	ADJ
ejpam-6659	288	14	contractive	contractive	ADJ
ejpam-6659	288	15	conditions	condition	NOUN
ejpam-6659	288	16	.	.	PUNCT
ejpam-6659	289	1	our	our	PRON
ejpam-6659	289	2	results	result	NOUN
ejpam-6659	289	3	not	not	PART
ejpam-6659	289	4	only	only	ADV
ejpam-6659	289	5	extend	extend	VERB
ejpam-6659	289	6	existing	exist	VERB
ejpam-6659	289	7	theorems	theorem	NOUN
ejpam-6659	289	8	from	from	ADP
ejpam-6659	289	9	the	the	DET
ejpam-6659	289	10	literature	literature	NOUN
ejpam-6659	289	11	but	but	CCONJ
ejpam-6659	289	12	also	also	ADV
ejpam-6659	289	13	unify	unify	VERB
ejpam-6659	289	14	them	they	PRON
ejpam-6659	289	15	under	under	ADP
ejpam-6659	289	16	a	a	DET
ejpam-6659	289	17	broader	broad	ADJ
ejpam-6659	289	18	and	and	CCONJ
ejpam-6659	289	19	more	more	ADV
ejpam-6659	289	20	flexible	flexible	ADJ
ejpam-6659	289	21	setting	setting	NOUN
ejpam-6659	289	22	.	.	PUNCT
ejpam-6659	290	1	furthermore	furthermore	ADV
ejpam-6659	290	2	,	,	PUNCT
ejpam-6659	290	3	we	we	PRON
ejpam-6659	290	4	demonstrated	demonstrate	VERB
ejpam-6659	290	5	the	the	DET
ejpam-6659	290	6	applicability	applicability	NOUN
ejpam-6659	290	7	of	of	ADP
ejpam-6659	290	8	our	our	PRON
ejpam-6659	290	9	theoretical	theoretical	ADJ
ejpam-6659	290	10	results	result	NOUN
ejpam-6659	290	11	by	by	ADP
ejpam-6659	290	12	proving	prove	VERB
ejpam-6659	290	13	the	the	DET
ejpam-6659	290	14	existence	existence	NOUN
ejpam-6659	290	15	and	and	CCONJ
ejpam-6659	290	16	uniqueness	uniqueness	NOUN
ejpam-6659	290	17	of	of	ADP
ejpam-6659	290	18	a	a	DET
ejpam-6659	290	19	solution	solution	NOUN
ejpam-6659	290	20	to	to	ADP
ejpam-6659	290	21	a	a	DET
ejpam-6659	290	22	nonlinear	nonlinear	ADJ
ejpam-6659	290	23	volterra	volterra	NOUN
ejpam-6659	290	24	integral	integral	ADJ
ejpam-6659	290	25	equation	equation	NOUN
ejpam-6659	290	26	involving	involve	VERB
ejpam-6659	290	27	complex	complex	ADV
ejpam-6659	290	28	-	-	PUNCT
ejpam-6659	290	29	valued	value	VERB
ejpam-6659	290	30	functions	function	NOUN
ejpam-6659	290	31	.	.	PUNCT
ejpam-6659	291	1	these	these	DET
ejpam-6659	291	2	findings	finding	NOUN
ejpam-6659	291	3	open	open	VERB
ejpam-6659	291	4	new	new	ADJ
ejpam-6659	291	5	avenues	avenue	NOUN
ejpam-6659	291	6	for	for	ADP
ejpam-6659	291	7	future	future	ADJ
ejpam-6659	291	8	research	research	NOUN
ejpam-6659	291	9	,	,	PUNCT
ejpam-6659	291	10	particularly	particularly	ADV
ejpam-6659	291	11	in	in	ADP
ejpam-6659	291	12	analyzing	analyze	VERB
ejpam-6659	291	13	nonlinear	nonlinear	ADJ
ejpam-6659	291	14	problems	problem	NOUN
ejpam-6659	291	15	and	and	CCONJ
ejpam-6659	291	16	integral	integral	ADJ
ejpam-6659	291	17	equations	equation	NOUN
ejpam-6659	291	18	within	within	ADP
ejpam-6659	291	19	complex	complex	ADJ
ejpam-6659	291	20	metric	metric	ADJ
ejpam-6659	291	21	frameworks	framework	NOUN
ejpam-6659	291	22	.	.	PUNCT
ejpam-6659	292	1	potential	potential	ADJ
ejpam-6659	292	2	directions	direction	NOUN
ejpam-6659	292	3	include	include	VERB
ejpam-6659	292	4	extending	extend	VERB
ejpam-6659	292	5	these	these	DET
ejpam-6659	292	6	results	result	NOUN
ejpam-6659	292	7	to	to	ADP
ejpam-6659	292	8	multivalued	multivalued	ADJ
ejpam-6659	292	9	mappings	mapping	NOUN
ejpam-6659	292	10	and	and	CCONJ
ejpam-6659	292	11	exploring	explore	VERB
ejpam-6659	292	12	their	their	PRON
ejpam-6659	292	13	implications	implication	NOUN
ejpam-6659	292	14	in	in	ADP
ejpam-6659	292	15	applied	applied	ADJ
ejpam-6659	292	16	mathematics	mathematic	NOUN
ejpam-6659	292	17	and	and	CCONJ
ejpam-6659	292	18	computational	computational	ADJ
ejpam-6659	292	19	analysis	analysis	NOUN
ejpam-6659	292	20	.	.	PUNCT
ejpam-6659	293	1	h.	h.	PROPN
ejpam-6659	293	2	qawaqneh	qawaqneh	PROPN
ejpam-6659	293	3	et	et	PROPN
ejpam-6659	293	4	al	al	PROPN
ejpam-6659	293	5	.	.	PUNCT
ejpam-6659	293	6	/	/	SYM
ejpam-6659	293	7	eur	eur	PROPN
ejpam-6659	293	8	.	.	PUNCT
ejpam-6659	294	1	j.	j.	PROPN
ejpam-6659	294	2	pure	pure	PROPN
ejpam-6659	294	3	appl	appl	PROPN
ejpam-6659	294	4	.	.	PROPN
ejpam-6659	294	5	math	math	PROPN
ejpam-6659	294	6	,	,	PUNCT
ejpam-6659	294	7	18	18	NUM
ejpam-6659	294	8	(	(	PUNCT
ejpam-6659	294	9	3	3	NUM
ejpam-6659	294	10	)	)	PUNCT
ejpam-6659	294	11	(	(	PUNCT
ejpam-6659	294	12	2025	2025	NUM
ejpam-6659	294	13	)	)	PUNCT
ejpam-6659	294	14	,	,	PUNCT
ejpam-6659	294	15	6659	6659	NUM
ejpam-6659	294	16	15	15	NUM
ejpam-6659	294	17	of	of	ADP
ejpam-6659	294	18	16	16	NUM
ejpam-6659	294	19	authors	author	NOUN
ejpam-6659	294	20	’	'	PUNCT
ejpam-6659	294	21	contributions	contribution	NOUN
ejpam-6659	294	22	all	all	DET
ejpam-6659	294	23	authors	author	NOUN
ejpam-6659	294	24	contribute	contribute	VERB
ejpam-6659	294	25	equally	equally	ADV
ejpam-6659	294	26	in	in	ADP
ejpam-6659	294	27	this	this	DET
ejpam-6659	294	28	paper	paper	NOUN
ejpam-6659	294	29	.	.	PUNCT
ejpam-6659	295	1	conflict	conflict	NOUN
ejpam-6659	295	2	of	of	ADP
ejpam-6659	295	3	interest	interest	NOUN
ejpam-6659	295	4	the	the	DET
ejpam-6659	295	5	authors	author	NOUN
ejpam-6659	295	6	declare	declare	VERB
ejpam-6659	295	7	that	that	SCONJ
ejpam-6659	295	8	they	they	PRON
ejpam-6659	295	9	have	have	VERB
ejpam-6659	295	10	no	no	DET
ejpam-6659	295	11	conflict	conflict	NOUN
ejpam-6659	295	12	of	of	ADP
ejpam-6659	295	13	interest	interest	NOUN
ejpam-6659	295	14	.	.	PUNCT
ejpam-6659	296	1	acknowledgements	acknowledgement	NOUN
ejpam-6659	296	2	the	the	DET
ejpam-6659	296	3	authors	author	NOUN
ejpam-6659	296	4	acknowledge	acknowledge	VERB
ejpam-6659	296	5	the	the	DET
ejpam-6659	296	6	financial	financial	ADJ
ejpam-6659	296	7	support	support	NOUN
ejpam-6659	296	8	from	from	ADP
ejpam-6659	296	9	al	al	PROPN
ejpam-6659	296	10	-	-	PROPN
ejpam-6659	296	11	zaytoonah	zaytoonah	PROPN
ejpam-6659	296	12	university	university	PROPN
ejpam-6659	296	13	of	of	ADP
ejpam-6659	296	14	jordan	jordan	PROPN
ejpam-6659	296	15	,	,	PUNCT
ejpam-6659	296	16	amman	amman	PROPN
ejpam-6659	296	17	11733	11733	NUM
ejpam-6659	296	18	,	,	PUNCT
ejpam-6659	296	19	jordan	jordan	PROPN
ejpam-6659	296	20	.	.	PUNCT
ejpam-6659	297	1	references	reference	NOUN
ejpam-6659	297	2	[	[	X
ejpam-6659	297	3	1	1	X
ejpam-6659	297	4	]	]	PUNCT
ejpam-6659	297	5	d.	d.	PROPN
ejpam-6659	297	6	judeh	judeh	PROPN
ejpam-6659	297	7	and	and	CCONJ
ejpam-6659	297	8	m.	m.	PROPN
ejpam-6659	297	9	abu	abu	PROPN
ejpam-6659	297	10	hammad	hammad	PROPN
ejpam-6659	297	11	.	.	PUNCT
ejpam-6659	298	1	applications	application	NOUN
ejpam-6659	298	2	of	of	ADP
ejpam-6659	298	3	conformable	conformable	ADJ
ejpam-6659	298	4	fractional	fractional	ADJ
ejpam-6659	298	5	pareto	pareto	ADJ
ejpam-6659	298	6	probability	probability	NOUN
ejpam-6659	298	7	distribution	distribution	NOUN
ejpam-6659	298	8	.	.	PUNCT
ejpam-6659	299	1	international	international	ADJ
ejpam-6659	299	2	journal	journal	NOUN
ejpam-6659	299	3	of	of	ADP
ejpam-6659	299	4	advances	advance	NOUN
ejpam-6659	299	5	in	in	ADP
ejpam-6659	299	6	soft	soft	ADJ
ejpam-6659	299	7	computing	computing	NOUN
ejpam-6659	299	8	and	and	CCONJ
ejpam-6659	299	9	its	its	PRON
ejpam-6659	299	10	applications	application	NOUN
ejpam-6659	299	11	,	,	PUNCT
ejpam-6659	299	12	14:116–124	14:116–124	NUM
ejpam-6659	299	13	,	,	PUNCT
ejpam-6659	299	14	2022	2022	NUM
ejpam-6659	299	15	.	.	PUNCT
ejpam-6659	300	1	[	[	X
ejpam-6659	300	2	2	2	X
ejpam-6659	300	3	]	]	PUNCT
ejpam-6659	300	4	t.	t.	PROPN
ejpam-6659	300	5	kanan	kanan	PROPN
ejpam-6659	300	6	,	,	PUNCT
ejpam-6659	300	7	m.	m.	NOUN
ejpam-6659	300	8	elbes	elbes	PROPN
ejpam-6659	300	9	,	,	PUNCT
ejpam-6659	300	10	k.	k.	PROPN
ejpam-6659	300	11	abu	abu	PROPN
ejpam-6659	300	12	maria	maria	PROPN
ejpam-6659	300	13	,	,	PUNCT
ejpam-6659	300	14	and	and	CCONJ
ejpam-6659	300	15	m.	m.	NOUN
ejpam-6659	300	16	alia	alia	PROPN
ejpam-6659	300	17	.	.	PUNCT
ejpam-6659	301	1	exploring	explore	VERB
ejpam-6659	301	2	the	the	DET
ejpam-6659	301	3	potential	potential	NOUN
ejpam-6659	301	4	of	of	ADP
ejpam-6659	301	5	iot	iot	NOUN
ejpam-6659	301	6	-	-	PUNCT
ejpam-6659	301	7	based	base	VERB
ejpam-6659	301	8	learning	learning	NOUN
ejpam-6659	301	9	environments	environment	NOUN
ejpam-6659	301	10	in	in	ADP
ejpam-6659	301	11	education	education	NOUN
ejpam-6659	301	12	.	.	PUNCT
ejpam-6659	302	1	[	[	X
ejpam-6659	302	2	3	3	X
ejpam-6659	302	3	]	]	X
ejpam-6659	302	4	h.	h.	PROPN
ejpam-6659	302	5	qawaqneh	qawaqneh	PROPN
ejpam-6659	302	6	,	,	PUNCT
ejpam-6659	302	7	m.	m.	PROPN
ejpam-6659	302	8	s.	s.	PROPN
ejpam-6659	302	9	noorani	noorani	PROPN
ejpam-6659	302	10	,	,	PUNCT
ejpam-6659	302	11	h.	h.	PROPN
ejpam-6659	302	12	aydi	aydi	PROPN
ejpam-6659	302	13	,	,	PUNCT
ejpam-6659	302	14	a.	a.	NOUN
ejpam-6659	302	15	zraiqat	zraiqat	PROPN
ejpam-6659	302	16	,	,	PUNCT
ejpam-6659	302	17	and	and	CCONJ
ejpam-6659	302	18	a.	a.	NOUN
ejpam-6659	302	19	h.	h.	PROPN
ejpam-6659	302	20	ansari	ansari	PROPN
ejpam-6659	302	21	.	.	PUNCT
ejpam-6659	303	1	on	on	ADP
ejpam-6659	303	2	fixed	fix	VERB
ejpam-6659	303	3	pointresults	pointresult	NOUN
ejpam-6659	303	4	in	in	ADP
ejpam-6659	303	5	partial	partial	ADJ
ejpam-6659	303	6	b	b	NOUN
ejpam-6659	303	7	-	-	PUNCT
ejpam-6659	303	8	metric	metric	ADJ
ejpam-6659	303	9	spaces	space	NOUN
ejpam-6659	303	10	.	.	PUNCT
ejpam-6659	304	1	journal	journal	NOUN
ejpam-6659	304	2	of	of	ADP
ejpam-6659	304	3	function	function	NOUN
ejpam-6659	304	4	spaces	space	NOUN
ejpam-6659	304	5	,	,	PUNCT
ejpam-6659	304	6	8769190:9	8769190:9	NUM
ejpam-6659	304	7	pages	page	NOUN
ejpam-6659	304	8	,	,	PUNCT
ejpam-6659	304	9	2021	2021	NUM
ejpam-6659	304	10	.	.	PUNCT
ejpam-6659	305	1	[	[	X
ejpam-6659	305	2	4	4	X
ejpam-6659	305	3	]	]	X
ejpam-6659	305	4	h.	h.	PROPN
ejpam-6659	305	5	qawaqneh	qawaqneh	PROPN
ejpam-6659	305	6	,	,	PUNCT
ejpam-6659	305	7	m.	m.	PROPN
ejpam-6659	305	8	s.	s.	PROPN
ejpam-6659	305	9	noorani	noorani	PROPN
ejpam-6659	305	10	,	,	PUNCT
ejpam-6659	305	11	and	and	CCONJ
ejpam-6659	305	12	h.	h.	PROPN
ejpam-6659	305	13	aydi	aydi	VERB
ejpam-6659	305	14	.	.	PUNCT
ejpam-6659	306	1	some	some	DET
ejpam-6659	306	2	new	new	ADJ
ejpam-6659	306	3	characterizations	characterization	NOUN
ejpam-6659	306	4	and	and	CCONJ
ejpam-6659	306	5	results	result	NOUN
ejpam-6659	306	6	for	for	ADP
ejpam-6659	306	7	fuzzy	fuzzy	ADJ
ejpam-6659	306	8	contractions	contraction	NOUN
ejpam-6659	306	9	in	in	ADP
ejpam-6659	306	10	fuzzy	fuzzy	ADJ
ejpam-6659	306	11	b	b	X
ejpam-6659	306	12	-	-	PUNCT
ejpam-6659	306	13	metric	metric	ADJ
ejpam-6659	306	14	spaces	space	NOUN
ejpam-6659	306	15	and	and	CCONJ
ejpam-6659	306	16	applications	application	NOUN
ejpam-6659	306	17	.	.	PUNCT
ejpam-6659	307	1	aims	aim	VERB
ejpam-6659	307	2	mathematics	mathematic	NOUN
ejpam-6659	307	3	,	,	PUNCT
ejpam-6659	307	4	8:6682–6696	8:6682–6696	NUM
ejpam-6659	307	5	,	,	PUNCT
ejpam-6659	307	6	2023	2023	NUM
ejpam-6659	307	7	.	.	PUNCT
ejpam-6659	308	1	[	[	X
ejpam-6659	308	2	5	5	X
ejpam-6659	308	3	]	]	PUNCT
ejpam-6659	308	4	h.	h.	PROPN
ejpam-6659	308	5	qawaqneh	qawaqneh	PROPN
ejpam-6659	308	6	,	,	PUNCT
ejpam-6659	308	7	h.	h.	PROPN
ejpam-6659	308	8	a.	a.	PROPN
ejpam-6659	308	9	hammad	hammad	PROPN
ejpam-6659	308	10	,	,	PUNCT
ejpam-6659	308	11	and	and	CCONJ
ejpam-6659	308	12	h.	h.	PROPN
ejpam-6659	308	13	aydi	aydi	VERB
ejpam-6659	308	14	.	.	PUNCT
ejpam-6659	309	1	exploring	explore	VERB
ejpam-6659	309	2	new	new	ADJ
ejpam-6659	309	3	geometric	geometric	ADJ
ejpam-6659	309	4	contraction	contraction	NOUN
ejpam-6659	309	5	mappings	mapping	NOUN
ejpam-6659	309	6	and	and	CCONJ
ejpam-6659	309	7	their	their	PRON
ejpam-6659	309	8	applications	application	NOUN
ejpam-6659	309	9	in	in	ADP
ejpam-6659	309	10	fractional	fractional	ADJ
ejpam-6659	309	11	metric	metric	ADJ
ejpam-6659	309	12	spaces	space	NOUN
ejpam-6659	309	13	.	.	PUNCT
ejpam-6659	310	1	advances	advance	NOUN
ejpam-6659	310	2	in	in	ADP
ejpam-6659	310	3	fixed	fix	VERB
ejpam-6659	310	4	point	point	NOUN
ejpam-6659	310	5	theory	theory	NOUN
ejpam-6659	310	6	,	,	PUNCT
ejpam-6659	310	7	9:521–541	9:521–541	NUM
ejpam-6659	310	8	,	,	PUNCT
ejpam-6659	310	9	2024	2024	NUM
ejpam-6659	310	10	.	.	PUNCT
ejpam-6659	311	1	[	[	X
ejpam-6659	311	2	6	6	NUM
ejpam-6659	311	3	]	]	PUNCT
ejpam-6659	311	4	m.	m.	NOUN
ejpam-6659	311	5	nazam	nazam	PROPN
ejpam-6659	311	6	,	,	PUNCT
ejpam-6659	311	7	h.	h.	PROPN
ejpam-6659	311	8	aydi	aydi	PROPN
ejpam-6659	311	9	,	,	PUNCT
ejpam-6659	311	10	m.s	m.s	PROPN
ejpam-6659	311	11	.	.	PROPN
ejpam-6659	311	12	noorani	noorani	PROPN
ejpam-6659	311	13	,	,	PUNCT
ejpam-6659	311	14	and	and	CCONJ
ejpam-6659	311	15	h.	h.	PROPN
ejpam-6659	311	16	qawaqneh	qawaqneh	PROPN
ejpam-6659	311	17	.	.	PUNCT
ejpam-6659	312	1	existence	existence	NOUN
ejpam-6659	312	2	of	of	ADP
ejpam-6659	312	3	fixed	fix	VERB
ejpam-6659	312	4	points	point	NOUN
ejpam-6659	312	5	of	of	ADP
ejpam-6659	312	6	four	four	NUM
ejpam-6659	312	7	maps	map	NOUN
ejpam-6659	312	8	for	for	ADP
ejpam-6659	312	9	a	a	DET
ejpam-6659	312	10	new	new	ADJ
ejpam-6659	312	11	generalized	generalized	ADJ
ejpam-6659	312	12	f−contraction	f−contraction	NOUN
ejpam-6659	312	13	and	and	CCONJ
ejpam-6659	312	14	an	an	DET
ejpam-6659	312	15	application	application	NOUN
ejpam-6659	312	16	.	.	PUNCT
ejpam-6659	313	1	journal	journal	NOUN
ejpam-6659	313	2	of	of	ADP
ejpam-6659	313	3	function	function	NOUN
ejpam-6659	313	4	spaces	space	NOUN
ejpam-6659	313	5	,	,	PUNCT
ejpam-6659	313	6	5980312:8	5980312:8	NUM
ejpam-6659	313	7	pages	page	NOUN
ejpam-6659	313	8	,	,	PUNCT
ejpam-6659	313	9	2019	2019	NUM
ejpam-6659	313	10	.	.	PUNCT
ejpam-6659	314	1	[	[	X
ejpam-6659	314	2	7	7	X
ejpam-6659	314	3	]	]	X
ejpam-6659	314	4	h.	h.	PROPN
ejpam-6659	314	5	qawaqneh	qawaqneh	PROPN
ejpam-6659	314	6	,	,	PUNCT
ejpam-6659	314	7	m.	m.	PROPN
ejpam-6659	314	8	s.	s.	PROPN
ejpam-6659	314	9	noorani	noorani	PROPN
ejpam-6659	314	10	,	,	PUNCT
ejpam-6659	314	11	h.	h.	PROPN
ejpam-6659	314	12	aydi	aydi	PROPN
ejpam-6659	314	13	,	,	PUNCT
ejpam-6659	314	14	and	and	CCONJ
ejpam-6659	314	15	w.	w.	PROPN
ejpam-6659	314	16	shatanawi	shatanawi	PROPN
ejpam-6659	314	17	.	.	PUNCT
ejpam-6659	315	1	,	,	PUNCT
ejpam-6659	315	2	on	on	ADP
ejpam-6659	315	3	common	common	ADJ
ejpam-6659	315	4	fixed	fix	VERB
ejpam-6659	315	5	point	point	NOUN
ejpam-6659	315	6	results	result	NOUN
ejpam-6659	315	7	for	for	ADP
ejpam-6659	315	8	new	new	ADJ
ejpam-6659	315	9	contractions	contraction	NOUN
ejpam-6659	315	10	with	with	ADP
ejpam-6659	315	11	applications	application	NOUN
ejpam-6659	315	12	to	to	PART
ejpam-6659	315	13	graph	graph	VERB
ejpam-6659	315	14	and	and	CCONJ
ejpam-6659	315	15	integral	integral	ADJ
ejpam-6659	315	16	equations	equation	NOUN
ejpam-6659	315	17	.	.	PUNCT
ejpam-6659	316	1	mathematics	mathematic	NOUN
ejpam-6659	316	2	,	,	PUNCT
ejpam-6659	316	3	7:1082	7:1082	NUM
ejpam-6659	316	4	,	,	PUNCT
ejpam-6659	316	5	2019	2019	NUM
ejpam-6659	316	6	.	.	PUNCT
ejpam-6659	317	1	[	[	X
ejpam-6659	317	2	8	8	NUM
ejpam-6659	317	3	]	]	PUNCT
ejpam-6659	317	4	m.	m.	NOUN
ejpam-6659	317	5	fréchet	fréchet	PROPN
ejpam-6659	317	6	.	.	PUNCT
ejpam-6659	318	1	sur	sur	PROPN
ejpam-6659	318	2	quelques	quelques	PROPN
ejpam-6659	318	3	points	point	NOUN
ejpam-6659	318	4	du	du	PROPN
ejpam-6659	318	5	calcul	calcul	PROPN
ejpam-6659	318	6	fonctionnel	fonctionnel	PROPN
ejpam-6659	318	7	.	.	PUNCT
ejpam-6659	319	1	rendiconti	rendiconti	PROPN
ejpam-6659	319	2	del	del	PROPN
ejpam-6659	319	3	circolo	circolo	PROPN
ejpam-6659	319	4	matematico	matematico	NOUN
ejpam-6659	319	5	di	di	NOUN
ejpam-6659	319	6	palermo	palermo	NOUN
ejpam-6659	319	7	,	,	PUNCT
ejpam-6659	319	8	22(1):1–72	22(1):1–72	NUM
ejpam-6659	319	9	,	,	PUNCT
ejpam-6659	319	10	1906	1906	NUM
ejpam-6659	319	11	.	.	PUNCT
ejpam-6659	320	1	[	[	X
ejpam-6659	320	2	9	9	NUM
ejpam-6659	320	3	]	]	PUNCT
ejpam-6659	320	4	t.	t.	PROPN
ejpam-6659	320	5	van	van	PROPN
ejpam-6659	320	6	an	an	PROPN
ejpam-6659	320	7	,	,	PUNCT
ejpam-6659	320	8	n.	n.	PROPN
ejpam-6659	320	9	van	van	PROPN
ejpam-6659	320	10	dung	dung	PROPN
ejpam-6659	320	11	,	,	PUNCT
ejpam-6659	320	12	z.	z.	PROPN
ejpam-6659	320	13	kadelburg	kadelburg	PROPN
ejpam-6659	320	14	,	,	PUNCT
ejpam-6659	320	15	and	and	CCONJ
ejpam-6659	320	16	s.	s.	PROPN
ejpam-6659	320	17	radenović.	radenović.	PROPN
ejpam-6659	320	18	various	various	ADJ
ejpam-6659	320	19	generalizations	generalization	NOUN
ejpam-6659	320	20	of	of	ADP
ejpam-6659	320	21	metric	metric	ADJ
ejpam-6659	320	22	spaces	space	NOUN
ejpam-6659	320	23	and	and	CCONJ
ejpam-6659	320	24	fixed	fix	VERB
ejpam-6659	320	25	point	point	NOUN
ejpam-6659	320	26	theorems	theorem	NOUN
ejpam-6659	320	27	.	.	PUNCT
ejpam-6659	320	28	revista	revista	PROPN
ejpam-6659	320	29	de	de	X
ejpam-6659	320	30	la	la	PROPN
ejpam-6659	320	31	real	real	PROPN
ejpam-6659	320	32	academia	academia	PROPN
ejpam-6659	320	33	de	de	PROPN
ejpam-6659	320	34	ciencias	ciencias	PROPN
ejpam-6659	320	35	exactas	exacta	NOUN
ejpam-6659	320	36	,	,	PUNCT
ejpam-6659	320	37	f́ısicas	f́ısicas	PROPN
ejpam-6659	320	38	y	y	PROPN
ejpam-6659	320	39	naturales	naturale	NOUN
ejpam-6659	320	40	.	.	PUNCT
ejpam-6659	321	1	serie	serie	PROPN
ejpam-6659	321	2	a.	a.	PROPN
ejpam-6659	321	3	matemáticas	matemáticas	PROPN
ejpam-6659	321	4	,	,	PUNCT
ejpam-6659	321	5	109:175–198	109:175–198	NUM
ejpam-6659	321	6	,	,	PUNCT
ejpam-6659	321	7	2015	2015	NUM
ejpam-6659	321	8	.	.	PUNCT
ejpam-6659	322	1	[	[	X
ejpam-6659	322	2	10	10	NUM
ejpam-6659	322	3	]	]	X
ejpam-6659	322	4	i.	i.	PROPN
ejpam-6659	322	5	a.	a.	PROPN
ejpam-6659	322	6	bakhtin	bakhtin	PROPN
ejpam-6659	322	7	.	.	PUNCT
ejpam-6659	323	1	the	the	DET
ejpam-6659	323	2	contraction	contraction	NOUN
ejpam-6659	323	3	mapping	map	VERB
ejpam-6659	323	4	principle	principle	NOUN
ejpam-6659	323	5	in	in	ADP
ejpam-6659	323	6	almost	almost	ADV
ejpam-6659	323	7	metric	metric	ADJ
ejpam-6659	323	8	spaces	space	NOUN
ejpam-6659	323	9	.	.	PUNCT
ejpam-6659	324	1	functional	functional	ADJ
ejpam-6659	324	2	analysis	analysis	NOUN
ejpam-6659	324	3	and	and	CCONJ
ejpam-6659	324	4	its	its	PRON
ejpam-6659	324	5	applications	application	NOUN
ejpam-6659	324	6	,	,	PUNCT
ejpam-6659	324	7	30:26–37	30:26–37	PROPN
ejpam-6659	324	8	,	,	PUNCT
ejpam-6659	324	9	1989	1989	NUM
ejpam-6659	324	10	.	.	PUNCT
ejpam-6659	325	1	h.	h.	PROPN
ejpam-6659	325	2	qawaqneh	qawaqneh	PROPN
ejpam-6659	325	3	et	et	PROPN
ejpam-6659	325	4	al	al	PROPN
ejpam-6659	325	5	.	.	PUNCT
ejpam-6659	325	6	/	/	SYM
ejpam-6659	325	7	eur	eur	PROPN
ejpam-6659	325	8	.	.	PUNCT
ejpam-6659	326	1	j.	j.	PROPN
ejpam-6659	326	2	pure	pure	PROPN
ejpam-6659	326	3	appl	appl	PROPN
ejpam-6659	326	4	.	.	PROPN
ejpam-6659	326	5	math	math	PROPN
ejpam-6659	326	6	,	,	PUNCT
ejpam-6659	326	7	18	18	NUM
ejpam-6659	326	8	(	(	PUNCT
ejpam-6659	326	9	3	3	NUM
ejpam-6659	326	10	)	)	PUNCT
ejpam-6659	326	11	(	(	PUNCT
ejpam-6659	326	12	2025	2025	NUM
ejpam-6659	326	13	)	)	PUNCT
ejpam-6659	326	14	,	,	PUNCT
ejpam-6659	326	15	6659	6659	NUM
ejpam-6659	326	16	16	16	NUM
ejpam-6659	326	17	of	of	ADP
ejpam-6659	326	18	16	16	NUM
ejpam-6659	327	1	[	[	X
ejpam-6659	327	2	11	11	NUM
ejpam-6659	327	3	]	]	PUNCT
ejpam-6659	327	4	a.	a.	NOUN
ejpam-6659	327	5	branciari	branciari	PROPN
ejpam-6659	327	6	.	.	PUNCT
ejpam-6659	328	1	a	a	DET
ejpam-6659	328	2	fixed	fix	VERB
ejpam-6659	328	3	point	point	NOUN
ejpam-6659	328	4	theorem	theorem	NOUN
ejpam-6659	328	5	of	of	ADP
ejpam-6659	328	6	banach	banach	NOUN
ejpam-6659	328	7	–	–	PUNCT
ejpam-6659	328	8	caccioppoli	caccioppoli	NOUN
ejpam-6659	328	9	type	type	NOUN
ejpam-6659	328	10	on	on	ADP
ejpam-6659	328	11	a	a	DET
ejpam-6659	328	12	class	class	NOUN
ejpam-6659	328	13	of	of	ADP
ejpam-6659	328	14	generalized	generalized	ADJ
ejpam-6659	328	15	metric	metric	ADJ
ejpam-6659	328	16	spaces	space	NOUN
ejpam-6659	328	17	.	.	PUNCT
ejpam-6659	329	1	publications	publication	NOUN
ejpam-6659	329	2	mathématiques	mathématiques	PROPN
ejpam-6659	329	3	,	,	PUNCT
ejpam-6659	329	4	57(1–2):31–37	57(1–2):31–37	NOUN
ejpam-6659	329	5	,	,	PUNCT
ejpam-6659	329	6	2000	2000	NUM
ejpam-6659	329	7	.	.	PUNCT
ejpam-6659	330	1	[	[	X
ejpam-6659	330	2	12	12	NUM
ejpam-6659	330	3	]	]	X
ejpam-6659	330	4	s.	s.	PROPN
ejpam-6659	330	5	czerwik	czerwik	PROPN
ejpam-6659	330	6	.	.	PUNCT
ejpam-6659	331	1	contraction	contraction	NOUN
ejpam-6659	331	2	mappings	mapping	NOUN
ejpam-6659	331	3	in	in	ADP
ejpam-6659	331	4	b	b	NOUN
ejpam-6659	331	5	-	-	ADJ
ejpam-6659	331	6	metric	metric	ADJ
ejpam-6659	331	7	spaces	space	NOUN
ejpam-6659	331	8	.	.	PUNCT
ejpam-6659	332	1	acta	acta	PROPN
ejpam-6659	332	2	mathematica	mathematica	PROPN
ejpam-6659	332	3	universitatis	universitatis	PROPN
ejpam-6659	332	4	ostraviensis	ostraviensis	PROPN
ejpam-6659	332	5	,	,	PUNCT
ejpam-6659	332	6	1(1):5–11	1(1):5–11	NUM
ejpam-6659	332	7	,	,	PUNCT
ejpam-6659	332	8	1993	1993	NUM
ejpam-6659	332	9	.	.	PUNCT
ejpam-6659	333	1	[	[	X
ejpam-6659	333	2	13	13	NUM
ejpam-6659	333	3	]	]	PUNCT
ejpam-6659	333	4	s.	s.	PROPN
ejpam-6659	333	5	g.	g.	PROPN
ejpam-6659	333	6	matthews	matthews	PROPN
ejpam-6659	333	7	.	.	PUNCT
ejpam-6659	334	1	partial	partial	ADJ
ejpam-6659	334	2	metric	metric	ADJ
ejpam-6659	334	3	topology	topology	NOUN
ejpam-6659	334	4	.	.	PUNCT
ejpam-6659	335	1	annals	annal	NOUN
ejpam-6659	335	2	of	of	ADP
ejpam-6659	335	3	the	the	DET
ejpam-6659	335	4	new	new	PROPN
ejpam-6659	335	5	york	york	PROPN
ejpam-6659	335	6	academy	academy	PROPN
ejpam-6659	335	7	of	of	ADP
ejpam-6659	335	8	sciences	sciences	PROPN
ejpam-6659	335	9	,	,	PUNCT
ejpam-6659	335	10	728:183–197	728:183–197	NUM
ejpam-6659	335	11	,	,	PUNCT
ejpam-6659	335	12	1994	1994	NUM
ejpam-6659	335	13	.	.	PUNCT
ejpam-6659	336	1	[	[	X
ejpam-6659	336	2	14	14	NUM
ejpam-6659	336	3	]	]	X
ejpam-6659	336	4	s.	s.	PROPN
ejpam-6659	336	5	shukla	shukla	PROPN
ejpam-6659	336	6	.	.	PUNCT
ejpam-6659	337	1	partial	partial	ADJ
ejpam-6659	337	2	rectangular	rectangular	ADJ
ejpam-6659	337	3	metric	metric	ADJ
ejpam-6659	337	4	spaces	space	NOUN
ejpam-6659	337	5	and	and	CCONJ
ejpam-6659	337	6	fixed	fix	VERB
ejpam-6659	337	7	point	point	NOUN
ejpam-6659	337	8	theorems	theorem	NOUN
ejpam-6659	337	9	.	.	PUNCT
ejpam-6659	338	1	the	the	DET
ejpam-6659	338	2	scientific	scientific	ADJ
ejpam-6659	338	3	world	world	NOUN
ejpam-6659	338	4	journal	journal	NOUN
ejpam-6659	338	5	,	,	PUNCT
ejpam-6659	338	6	2014	2014	NUM
ejpam-6659	338	7	.	.	PUNCT
ejpam-6659	339	1	article	article	NOUN
ejpam-6659	339	2	i	i	PROPN
ejpam-6659	339	3	d	d	PROPN
ejpam-6659	339	4	756298	756298	NUM
ejpam-6659	339	5	.	.	PUNCT
ejpam-6659	340	1	[	[	X
ejpam-6659	340	2	15	15	X
ejpam-6659	340	3	]	]	PUNCT
ejpam-6659	340	4	t.	t.	PROPN
ejpam-6659	340	5	kamran	kamran	PROPN
ejpam-6659	340	6	,	,	PUNCT
ejpam-6659	340	7	m.	m.	NOUN
ejpam-6659	340	8	samreen	samreen	PROPN
ejpam-6659	340	9	,	,	PUNCT
ejpam-6659	340	10	and	and	CCONJ
ejpam-6659	340	11	q.	q.	PROPN
ejpam-6659	340	12	u.	u.	PROPN
ejpam-6659	340	13	ain	ain	PROPN
ejpam-6659	340	14	.	.	PUNCT
ejpam-6659	341	1	a	a	DET
ejpam-6659	341	2	generalization	generalization	NOUN
ejpam-6659	341	3	of	of	ADP
ejpam-6659	341	4	b	b	NOUN
ejpam-6659	341	5	-	-	PUNCT
ejpam-6659	341	6	metric	metric	ADJ
ejpam-6659	341	7	space	space	NOUN
ejpam-6659	341	8	and	and	CCONJ
ejpam-6659	341	9	some	some	DET
ejpam-6659	341	10	fixed	fix	VERB
ejpam-6659	341	11	point	point	NOUN
ejpam-6659	341	12	theorems	theorem	NOUN
ejpam-6659	341	13	.	.	PUNCT
ejpam-6659	342	1	mathematics	mathematic	NOUN
ejpam-6659	342	2	,	,	PUNCT
ejpam-6659	342	3	5:19	5:19	NUM
ejpam-6659	342	4	,	,	PUNCT
ejpam-6659	342	5	2017	2017	NUM
ejpam-6659	342	6	.	.	PUNCT
ejpam-6659	343	1	[	[	X
ejpam-6659	343	2	16	16	NUM
ejpam-6659	343	3	]	]	X
ejpam-6659	343	4	n.	n.	PROPN
ejpam-6659	343	5	mlaiki	mlaiki	PROPN
ejpam-6659	343	6	,	,	PUNCT
ejpam-6659	343	7	h.	h.	PROPN
ejpam-6659	343	8	aydi	aydi	PROPN
ejpam-6659	343	9	,	,	PUNCT
ejpam-6659	343	10	n.	n.	NOUN
ejpam-6659	343	11	souayah	souayah	NOUN
ejpam-6659	343	12	,	,	PUNCT
ejpam-6659	343	13	and	and	CCONJ
ejpam-6659	343	14	t.	t.	PROPN
ejpam-6659	343	15	abdeljawad	abdeljawad	NOUN
ejpam-6659	343	16	.	.	PUNCT
ejpam-6659	344	1	controlled	control	VERB
ejpam-6659	344	2	metric	metric	ADJ
ejpam-6659	344	3	type	type	NOUN
ejpam-6659	344	4	spaces	space	NOUN
ejpam-6659	344	5	and	and	CCONJ
ejpam-6659	344	6	the	the	DET
ejpam-6659	344	7	related	related	ADJ
ejpam-6659	344	8	contraction	contraction	NOUN
ejpam-6659	344	9	principle	principle	NOUN
ejpam-6659	344	10	.	.	PUNCT
ejpam-6659	345	1	mathematics	mathematic	NOUN
ejpam-6659	345	2	,	,	PUNCT
ejpam-6659	345	3	6:194	6:194	NOUN
ejpam-6659	345	4	,	,	PUNCT
ejpam-6659	345	5	2018	2018	NUM
ejpam-6659	345	6	.	.	PUNCT
ejpam-6659	346	1	[	[	X
ejpam-6659	346	2	17	17	NUM
ejpam-6659	346	3	]	]	X
ejpam-6659	346	4	s.	s.	PROPN
ejpam-6659	346	5	sedghi	sedghi	PROPN
ejpam-6659	346	6	,	,	PUNCT
ejpam-6659	346	7	n.	n.	PROPN
ejpam-6659	346	8	shobe	shobe	PROPN
ejpam-6659	346	9	,	,	PUNCT
ejpam-6659	346	10	and	and	CCONJ
ejpam-6659	346	11	a.	a.	NOUN
ejpam-6659	346	12	aliouche	aliouche	PROPN
ejpam-6659	346	13	.	.	PUNCT
ejpam-6659	347	1	a	a	DET
ejpam-6659	347	2	generalization	generalization	NOUN
ejpam-6659	347	3	of	of	ADP
ejpam-6659	347	4	fixed	fix	VERB
ejpam-6659	347	5	point	point	NOUN
ejpam-6659	347	6	theorem	theorem	VERB
ejpam-6659	347	7	in	in	ADP
ejpam-6659	347	8	s	s	NOUN
ejpam-6659	347	9	-	-	ADJ
ejpam-6659	347	10	metric	metric	ADJ
ejpam-6659	347	11	spaces	space	NOUN
ejpam-6659	347	12	.	.	PUNCT
ejpam-6659	348	1	matematicki	matematicki	NOUN
ejpam-6659	348	2	vesnik	vesnik	NOUN
ejpam-6659	348	3	,	,	PUNCT
ejpam-6659	348	4	64:258–266	64:258–266	NOUN
ejpam-6659	348	5	,	,	PUNCT
ejpam-6659	348	6	2012	2012	NUM
ejpam-6659	348	7	.	.	PUNCT
ejpam-6659	349	1	[	[	X
ejpam-6659	349	2	18	18	NUM
ejpam-6659	349	3	]	]	X
ejpam-6659	349	4	b.	b.	PROPN
ejpam-6659	349	5	c.	c.	PROPN
ejpam-6659	349	6	dhage	dhage	PROPN
ejpam-6659	349	7	.	.	PUNCT
ejpam-6659	350	1	generalized	generalize	VERB
ejpam-6659	350	2	metric	metric	ADJ
ejpam-6659	350	3	spaces	space	NOUN
ejpam-6659	350	4	mappings	mapping	NOUN
ejpam-6659	350	5	with	with	ADP
ejpam-6659	350	6	fixed	fix	VERB
ejpam-6659	350	7	point	point	NOUN
ejpam-6659	350	8	.	.	PUNCT
ejpam-6659	351	1	bulletin	bulletin	NOUN
ejpam-6659	351	2	of	of	ADP
ejpam-6659	351	3	the	the	DET
ejpam-6659	351	4	calcutta	calcutta	PROPN
ejpam-6659	351	5	mathematical	mathematical	ADJ
ejpam-6659	351	6	society	society	NOUN
ejpam-6659	351	7	,	,	PUNCT
ejpam-6659	351	8	84:329–336	84:329–336	NUM
ejpam-6659	351	9	,	,	PUNCT
ejpam-6659	351	10	1992	1992	NUM
ejpam-6659	351	11	.	.	PUNCT
ejpam-6659	352	1	[	[	X
ejpam-6659	352	2	19	19	NUM
ejpam-6659	352	3	]	]	X
ejpam-6659	352	4	s.	s.	PROPN
ejpam-6659	352	5	sedghi	sedghi	PROPN
ejpam-6659	352	6	,	,	PUNCT
ejpam-6659	352	7	n.	n.	PROPN
ejpam-6659	352	8	shobe	shobe	PROPN
ejpam-6659	352	9	,	,	PUNCT
ejpam-6659	352	10	and	and	CCONJ
ejpam-6659	352	11	h.	h.	PROPN
ejpam-6659	352	12	zhou	zhou	PROPN
ejpam-6659	352	13	.	.	PUNCT
ejpam-6659	353	1	a	a	DET
ejpam-6659	353	2	common	common	ADJ
ejpam-6659	353	3	fixed	fix	VERB
ejpam-6659	353	4	point	point	NOUN
ejpam-6659	353	5	theorem	theorem	VERB
ejpam-6659	353	6	in	in	ADP
ejpam-6659	353	7	d∗-metric	d∗-metric	ADJ
ejpam-6659	353	8	space	space	NOUN
ejpam-6659	353	9	.	.	PUNCT
ejpam-6659	354	1	fixed	fix	VERB
ejpam-6659	354	2	point	point	NOUN
ejpam-6659	354	3	theory	theory	NOUN
ejpam-6659	354	4	and	and	CCONJ
ejpam-6659	354	5	applications	application	NOUN
ejpam-6659	354	6	,	,	PUNCT
ejpam-6659	354	7	2007	2007	NUM
ejpam-6659	354	8	.	.	PUNCT
ejpam-6659	355	1	article	article	NOUN
ejpam-6659	355	2	i	i	PROPN
ejpam-6659	355	3	d	d	PROPN
ejpam-6659	355	4	1–13	1–13	PROPN
ejpam-6659	355	5	.	.	PUNCT
ejpam-6659	356	1	[	[	X
ejpam-6659	356	2	20	20	NUM
ejpam-6659	356	3	]	]	PUNCT
ejpam-6659	356	4	m.	m.	NOUN
ejpam-6659	356	5	m.	m.	PROPN
ejpam-6659	356	6	rezaee	rezaee	PROPN
ejpam-6659	356	7	,	,	PUNCT
ejpam-6659	356	8	s.	s.	PROPN
ejpam-6659	356	9	sedghi	sedghi	PROPN
ejpam-6659	356	10	,	,	PUNCT
ejpam-6659	356	11	a.	a.	NOUN
ejpam-6659	356	12	muckheimer	muckheimer	PROPN
ejpam-6659	356	13	,	,	PUNCT
ejpam-6659	356	14	k.	k.	PROPN
ejpam-6659	356	15	abodayeh	abodayeh	PROPN
ejpam-6659	356	16	,	,	PUNCT
ejpam-6659	356	17	and	and	CCONJ
ejpam-6659	357	1	z.	z.	PROPN
ejpam-6659	357	2	d.	d.	PROPN
ejpam-6659	357	3	mitrović.	mitrović.	PROPN
ejpam-6659	357	4	some	some	DET
ejpam-6659	357	5	fixed	fix	VERB
ejpam-6659	357	6	point	point	NOUN
ejpam-6659	357	7	results	result	NOUN
ejpam-6659	357	8	in	in	ADP
ejpam-6659	357	9	partial	partial	ADJ
ejpam-6659	357	10	s	s	NOUN
ejpam-6659	357	11	-	-	ADJ
ejpam-6659	357	12	metric	metric	ADJ
ejpam-6659	357	13	spaces	space	NOUN
ejpam-6659	357	14	.	.	PUNCT
ejpam-6659	358	1	australian	australian	ADJ
ejpam-6659	358	2	journal	journal	NOUN
ejpam-6659	358	3	of	of	ADP
ejpam-6659	358	4	mathematical	mathematical	ADJ
ejpam-6659	358	5	analysis	analysis	NOUN
ejpam-6659	358	6	and	and	CCONJ
ejpam-6659	358	7	applications	application	NOUN
ejpam-6659	358	8	,	,	PUNCT
ejpam-6659	358	9	16(2	16(2	NUM
ejpam-6659	358	10	)	)	PUNCT
ejpam-6659	358	11	,	,	PUNCT
ejpam-6659	358	12	2019	2019	NUM
ejpam-6659	358	13	.	.	PUNCT
ejpam-6659	359	1	article	article	NOUN
ejpam-6659	359	2	no	no	INTJ
ejpam-6659	359	3	.	.	PROPN
ejpam-6659	359	4	16	16	NUM
ejpam-6659	359	5	,	,	PUNCT
ejpam-6659	359	6	19	19	NUM
ejpam-6659	359	7	pages	page	NOUN
ejpam-6659	359	8	.	.	PUNCT
ejpam-6659	360	1	[	[	X
ejpam-6659	360	2	21	21	NUM
ejpam-6659	360	3	]	]	X
ejpam-6659	360	4	y.	y.	NOUN
ejpam-6659	360	5	rohen	rohen	PROPN
ejpam-6659	360	6	,	,	PUNCT
ejpam-6659	360	7	t.	t.	PROPN
ejpam-6659	360	8	došenović	došenović	PROPN
ejpam-6659	360	9	,	,	PUNCT
ejpam-6659	360	10	and	and	CCONJ
ejpam-6659	360	11	s.	s.	PROPN
ejpam-6659	360	12	radenović.	radenović.	PROPN
ejpam-6659	360	13	a	a	DET
ejpam-6659	360	14	note	note	NOUN
ejpam-6659	360	15	on	on	ADP
ejpam-6659	360	16	the	the	DET
ejpam-6659	360	17	paper	paper	NOUN
ejpam-6659	360	18	“	"	PUNCT
ejpam-6659	360	19	a	a	DET
ejpam-6659	360	20	fixed	fix	VERB
ejpam-6659	360	21	point	point	NOUN
ejpam-6659	360	22	theorems	theorem	NOUN
ejpam-6659	360	23	in	in	ADP
ejpam-6659	360	24	sb	sb	NOUN
ejpam-6659	360	25	-	-	ADJ
ejpam-6659	360	26	metric	metric	ADJ
ejpam-6659	360	27	spaces	space	NOUN
ejpam-6659	360	28	”	"	PUNCT
ejpam-6659	360	29	.	.	PUNCT
ejpam-6659	361	1	filomat	filomat	NOUN
ejpam-6659	361	2	,	,	PUNCT
ejpam-6659	361	3	31(11):3335–3346	31(11):3335–3346	NUM
ejpam-6659	361	4	,	,	PUNCT
ejpam-6659	361	5	2017	2017	NUM
ejpam-6659	361	6	.	.	PUNCT
ejpam-6659	362	1	[	[	X
ejpam-6659	362	2	22	22	NUM
ejpam-6659	362	3	]	]	X
ejpam-6659	362	4	n.	n.	NOUN
ejpam-6659	362	5	souayah	souayah	NOUN
ejpam-6659	362	6	and	and	CCONJ
ejpam-6659	362	7	n.	n.	PROPN
ejpam-6659	362	8	mlaiki	mlaiki	PROPN
ejpam-6659	362	9	.	.	PUNCT
ejpam-6659	363	1	a	a	DET
ejpam-6659	363	2	fixed	fix	VERB
ejpam-6659	363	3	point	point	NOUN
ejpam-6659	363	4	theorem	theorem	VERB
ejpam-6659	363	5	in	in	ADP
ejpam-6659	363	6	sb	sb	NOUN
ejpam-6659	363	7	-	-	ADJ
ejpam-6659	363	8	metric	metric	ADJ
ejpam-6659	363	9	spaces	space	NOUN
ejpam-6659	363	10	.	.	PUNCT
ejpam-6659	364	1	journal	journal	NOUN
ejpam-6659	364	2	of	of	ADP
ejpam-6659	364	3	mathematical	mathematical	ADJ
ejpam-6659	364	4	and	and	CCONJ
ejpam-6659	364	5	computer	computer	NOUN
ejpam-6659	364	6	sciences	science	NOUN
ejpam-6659	364	7	,	,	PUNCT
ejpam-6659	364	8	16:131–139	16:131–139	NUM
ejpam-6659	364	9	,	,	PUNCT
ejpam-6659	364	10	2016	2016	NUM
ejpam-6659	364	11	.	.	PUNCT
ejpam-6659	365	1	[	[	X
ejpam-6659	365	2	23	23	NUM
ejpam-6659	365	3	]	]	PUNCT
ejpam-6659	365	4	a.	a.	NOUN
ejpam-6659	365	5	gangwar	gangwar	PROPN
ejpam-6659	365	6	,	,	PUNCT
ejpam-6659	365	7	s.	s.	PROPN
ejpam-6659	365	8	rawat	rawat	PROPN
ejpam-6659	365	9	,	,	PUNCT
ejpam-6659	365	10	and	and	CCONJ
ejpam-6659	365	11	r.	r.	PROPN
ejpam-6659	365	12	c.	c.	PROPN
ejpam-6659	365	13	dimri	dimri	PROPN
ejpam-6659	365	14	.	.	PUNCT
ejpam-6659	366	1	solution	solution	NOUN
ejpam-6659	366	2	of	of	ADP
ejpam-6659	366	3	differential	differential	ADJ
ejpam-6659	366	4	inclusion	inclusion	NOUN
ejpam-6659	366	5	problem	problem	NOUN
ejpam-6659	366	6	in	in	ADP
ejpam-6659	366	7	controlled	control	VERB
ejpam-6659	366	8	s	s	ADJ
ejpam-6659	366	9	-	-	ADJ
ejpam-6659	366	10	metric	metric	ADJ
ejpam-6659	366	11	spaces	space	NOUN
ejpam-6659	366	12	via	via	ADP
ejpam-6659	366	13	new	new	ADJ
ejpam-6659	366	14	multivalued	multivalue	VERB
ejpam-6659	366	15	fixed	fix	VERB
ejpam-6659	366	16	point	point	NOUN
ejpam-6659	366	17	theorem	theorem	VERB
ejpam-6659	366	18	.	.	PROPN
ejpam-6659	366	19	journal	journal	PROPN
ejpam-6659	366	20	of	of	ADP
ejpam-6659	366	21	analysis	analysis	NOUN
ejpam-6659	366	22	,	,	PUNCT
ejpam-6659	366	23	31:2459–2472	31:2459–2472	NUM
ejpam-6659	366	24	,	,	PUNCT
ejpam-6659	366	25	2023	2023	NUM
ejpam-6659	366	26	.	.	PUNCT
ejpam-6659	367	1	[	[	X
ejpam-6659	367	2	24	24	NUM
ejpam-6659	367	3	]	]	PUNCT
ejpam-6659	367	4	f.	f.	PROPN
ejpam-6659	367	5	m.	m.	PROPN
ejpam-6659	367	6	azmi	azmi	PROPN
ejpam-6659	367	7	.	.	PUNCT
ejpam-6659	368	1	wardowski	wardowski	PROPN
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ejpam-6659	368	3	on	on	ADP
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ejpam-6659	368	5	s	s	ADJ
ejpam-6659	368	6	-	-	ADJ
ejpam-6659	368	7	metric	metric	ADJ
ejpam-6659	368	8	type	type	NOUN
ejpam-6659	368	9	spaces	space	NOUN
ejpam-6659	368	10	with	with	ADP
ejpam-6659	368	11	fixed	fix	VERB
ejpam-6659	368	12	point	point	NOUN
ejpam-6659	368	13	results	result	NOUN
ejpam-6659	368	14	.	.	PUNCT
ejpam-6659	369	1	international	international	ADJ
ejpam-6659	369	2	journal	journal	NOUN
ejpam-6659	369	3	of	of	ADP
ejpam-6659	369	4	analysis	analysis	NOUN
ejpam-6659	369	5	and	and	CCONJ
ejpam-6659	369	6	applications	application	NOUN
ejpam-6659	369	7	,	,	PUNCT
ejpam-6659	369	8	22:151–151	22:151–151	NUM
ejpam-6659	369	9	,	,	PUNCT
ejpam-6659	369	10	2024	2024	NUM
ejpam-6659	369	11	.	.	PUNCT
ejpam-6659	370	1	[	[	X
ejpam-6659	370	2	25	25	NUM
ejpam-6659	370	3	]	]	X
ejpam-6659	370	4	a.	a.	PROPN
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ejpam-6659	370	6	,	,	PUNCT
ejpam-6659	370	7	b.	b.	PROPN
ejpam-6659	370	8	fisher	fisher	PROPN
ejpam-6659	370	9	,	,	PUNCT
ejpam-6659	370	10	and	and	CCONJ
ejpam-6659	370	11	m.	m.	PROPN
ejpam-6659	370	12	khan	khan	PROPN
ejpam-6659	370	13	.	.	PUNCT
ejpam-6659	371	1	common	common	ADJ
ejpam-6659	371	2	fixed	fix	VERB
ejpam-6659	371	3	point	point	NOUN
ejpam-6659	371	4	theorems	theorem	NOUN
ejpam-6659	371	5	in	in	ADP
ejpam-6659	371	6	complex	complex	ADJ
ejpam-6659	371	7	valued	value	VERB
ejpam-6659	371	8	metric	metric	ADJ
ejpam-6659	371	9	spaces	space	NOUN
ejpam-6659	371	10	.	.	PUNCT
ejpam-6659	372	1	numerical	numerical	ADJ
ejpam-6659	372	2	functional	functional	ADJ
ejpam-6659	372	3	analysis	analysis	NOUN
ejpam-6659	372	4	and	and	CCONJ
ejpam-6659	372	5	optimization	optimization	NOUN
ejpam-6659	372	6	,	,	PUNCT
ejpam-6659	372	7	32(3):243–253	32(3):243–253	NUM
ejpam-6659	372	8	,	,	PUNCT
ejpam-6659	372	9	2011	2011	NUM
ejpam-6659	372	10	.	.	PUNCT
ejpam-6659	373	1	[	[	X
ejpam-6659	373	2	26	26	NUM
ejpam-6659	373	3	]	]	PUNCT
ejpam-6659	373	4	s.	s.	PROPN
ejpam-6659	373	5	m.	m.	PROPN
ejpam-6659	373	6	kang	kang	PROPN
ejpam-6659	373	7	,	,	PUNCT
ejpam-6659	373	8	b.	b.	PROPN
ejpam-6659	373	9	singh	singh	PROPN
ejpam-6659	373	10	,	,	PUNCT
ejpam-6659	373	11	v.	v.	PROPN
ejpam-6659	373	12	gupta	gupta	PROPN
ejpam-6659	373	13	,	,	PUNCT
ejpam-6659	373	14	and	and	CCONJ
ejpam-6659	373	15	s.	s.	PROPN
ejpam-6659	373	16	kumar	kumar	PROPN
ejpam-6659	373	17	.	.	PROPN
ejpam-6659	374	1	contraction	contraction	PROPN
ejpam-6659	374	2	principle	principle	NOUN
ejpam-6659	374	3	in	in	ADP
ejpam-6659	374	4	complex	complex	NOUN
ejpam-6659	374	5	valued	value	VERB
ejpam-6659	374	6	g	g	NOUN
ejpam-6659	374	7	-	-	PUNCT
ejpam-6659	374	8	metric	metric	ADJ
ejpam-6659	374	9	spaces	space	NOUN
ejpam-6659	374	10	.	.	PUNCT
ejpam-6659	375	1	international	international	ADJ
ejpam-6659	375	2	journal	journal	PROPN
ejpam-6659	375	3	of	of	ADP
ejpam-6659	375	4	mathematical	mathematical	ADJ
ejpam-6659	375	5	analysis	analysis	NOUN
ejpam-6659	375	6	,	,	PUNCT
ejpam-6659	375	7	7(52):2549	7(52):2549	NUM
ejpam-6659	375	8	–	–	PUNCT
ejpam-6659	375	9	2556	2556	NUM
ejpam-6659	375	10	,	,	PUNCT
ejpam-6659	375	11	2013	2013	NUM
ejpam-6659	375	12	.	.	PUNCT
ejpam-6659	376	1	[	[	X
ejpam-6659	376	2	27	27	NUM
ejpam-6659	376	3	]	]	X
ejpam-6659	376	4	n.	n.	PROPN
ejpam-6659	376	5	mlaiki	mlaiki	PROPN
ejpam-6659	376	6	.	.	PUNCT
ejpam-6659	377	1	common	common	ADJ
ejpam-6659	377	2	fixed	fix	VERB
ejpam-6659	377	3	points	point	NOUN
ejpam-6659	377	4	in	in	ADP
ejpam-6659	377	5	complex	complex	ADJ
ejpam-6659	377	6	s	s	NOUN
ejpam-6659	377	7	-	-	ADJ
ejpam-6659	377	8	metric	metric	ADJ
ejpam-6659	377	9	space	space	NOUN
ejpam-6659	377	10	.	.	PUNCT
ejpam-6659	378	1	advances	advance	NOUN
ejpam-6659	378	2	in	in	ADP
ejpam-6659	378	3	fixed	fix	VERB
ejpam-6659	378	4	point	point	NOUN
ejpam-6659	378	5	theory	theory	NOUN
ejpam-6659	378	6	,	,	PUNCT
ejpam-6659	378	7	4:509–524	4:509–524	PROPN
ejpam-6659	378	8	,	,	PUNCT
ejpam-6659	378	9	2014	2014	NUM
ejpam-6659	378	10	.	.	PUNCT
ejpam-6659	379	1	[	[	X
ejpam-6659	379	2	28	28	NUM
ejpam-6659	379	3	]	]	X
ejpam-6659	379	4	e.	e.	PROPN
ejpam-6659	379	5	ozgur	ozgur	PROPN
ejpam-6659	379	6	.	.	PROPN
ejpam-6659	380	1	complex	complex	PROPN
ejpam-6659	380	2	valued	value	VERB
ejpam-6659	380	3	gb	gb	ADV
ejpam-6659	380	4	-	-	PUNCT
ejpam-6659	380	5	metric	metric	ADJ
ejpam-6659	380	6	space	space	NOUN
ejpam-6659	380	7	.	.	PUNCT
ejpam-6659	381	1	journal	journal	NOUN
ejpam-6659	381	2	of	of	ADP
ejpam-6659	381	3	computational	computational	ADJ
ejpam-6659	381	4	analysis	analysis	NOUN
ejpam-6659	381	5	and	and	CCONJ
ejpam-6659	381	6	applications	application	NOUN
ejpam-6659	381	7	,	,	PUNCT
ejpam-6659	381	8	21(2):363–368	21(2):363–368	PROPN
ejpam-6659	381	9	,	,	PUNCT
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ejpam-6659	381	11	.	.	PUNCT
ejpam-6659	382	1	[	[	X
ejpam-6659	382	2	29	29	NUM
ejpam-6659	382	3	]	]	X
ejpam-6659	382	4	n.	n.	NOUN
ejpam-6659	382	5	priyobarta	priyobarta	PROPN
ejpam-6659	382	6	,	,	PUNCT
ejpam-6659	382	7	y.	y.	PROPN
ejpam-6659	382	8	rohen	rohen	PROPN
ejpam-6659	382	9	,	,	PUNCT
ejpam-6659	382	10	and	and	CCONJ
ejpam-6659	382	11	n.	n.	PROPN
ejpam-6659	382	12	mlaiki	mlaiki	PROPN
ejpam-6659	382	13	.	.	PUNCT
ejpam-6659	383	1	complex	complex	PROPN
ejpam-6659	383	2	valued	value	VERB
ejpam-6659	383	3	sb	sb	NOUN
ejpam-6659	383	4	-	-	ADJ
ejpam-6659	383	5	metric	metric	ADJ
ejpam-6659	383	6	spaces	space	NOUN
ejpam-6659	383	7	.	.	PUNCT
ejpam-6659	384	1	journal	journal	PROPN
ejpam-6659	384	2	of	of	ADP
ejpam-6659	384	3	mathematical	mathematical	ADJ
ejpam-6659	384	4	analysis	analysis	NOUN
ejpam-6659	384	5	,	,	PUNCT
ejpam-6659	384	6	8(3):13–24	8(3):13–24	NUM
ejpam-6659	384	7	,	,	PUNCT
ejpam-6659	384	8	2017	2017	NUM
ejpam-6659	384	9	.	.	PUNCT