id	sid	tid	token	lemma	pos
ejpam-3747	1	1	european	european	PROPN
ejpam-3747	1	2	journal	journal	PROPN
ejpam-3747	1	3	of	of	ADP
ejpam-3747	1	4	pure	pure	ADJ
ejpam-3747	1	5	and	and	CCONJ
ejpam-3747	1	6	applied	apply	VERB
ejpam-3747	1	7	mathematics	mathematic	NOUN
ejpam-3747	1	8	vol	vol	NOUN
ejpam-3747	1	9	.	.	PROPN
ejpam-3747	2	1	13	13	NUM
ejpam-3747	2	2	,	,	PUNCT
ejpam-3747	2	3	no	no	INTJ
ejpam-3747	2	4	.	.	NOUN
ejpam-3747	2	5	5	5	NUM
ejpam-3747	2	6	,	,	PUNCT
ejpam-3747	2	7	2020	2020	NUM
ejpam-3747	2	8	,	,	PUNCT
ejpam-3747	2	9	1072	1072	NUM
ejpam-3747	2	10	-	-	SYM
ejpam-3747	2	11	1087	1087	NUM
ejpam-3747	2	12	issn	issn	PROPN
ejpam-3747	2	13	1307	1307	NUM
ejpam-3747	2	14	-	-	SYM
ejpam-3747	2	15	5543	5543	NUM
ejpam-3747	2	16	–	–	PUNCT
ejpam-3747	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3747	2	18	published	publish	VERB
ejpam-3747	2	19	by	by	ADP
ejpam-3747	2	20	new	new	PROPN
ejpam-3747	2	21	york	york	PROPN
ejpam-3747	2	22	business	business	PROPN
ejpam-3747	2	23	global	global	ADJ
ejpam-3747	2	24	special	special	ADJ
ejpam-3747	2	25	issue	issue	NOUN
ejpam-3747	2	26	dedicated	dedicate	VERB
ejpam-3747	2	27	to	to	ADP
ejpam-3747	2	28	professor	professor	NOUN
ejpam-3747	2	29	hari	hari	PROPN
ejpam-3747	2	30	m.	m.	PROPN
ejpam-3747	2	31	srivastava	srivastava	PROPN
ejpam-3747	2	32	on	on	ADP
ejpam-3747	2	33	the	the	DET
ejpam-3747	2	34	occasion	occasion	NOUN
ejpam-3747	2	35	of	of	ADP
ejpam-3747	2	36	his	his	PRON
ejpam-3747	2	37	80th	80th	ADJ
ejpam-3747	2	38	birthday	birthday	NOUN
ejpam-3747	2	39	common	common	ADJ
ejpam-3747	2	40	fixed	fix	VERB
ejpam-3747	2	41	point	point	NOUN
ejpam-3747	2	42	results	result	NOUN
ejpam-3747	2	43	for	for	ADP
ejpam-3747	2	44	set	set	NOUN
ejpam-3747	2	45	-	-	PUNCT
ejpam-3747	2	46	valued	value	VERB
ejpam-3747	2	47	integral	integral	ADJ
ejpam-3747	2	48	type	type	NOUN
ejpam-3747	2	49	contractions	contraction	NOUN
ejpam-3747	2	50	on	on	ADP
ejpam-3747	2	51	metric	metric	ADJ
ejpam-3747	2	52	spaces	space	NOUN
ejpam-3747	2	53	with	with	ADP
ejpam-3747	2	54	directed	direct	VERB
ejpam-3747	2	55	graph	graph	NOUN
ejpam-3747	2	56	saadia	saadia	PROPN
ejpam-3747	2	57	benchabane1,∗	benchabane1,∗	PROPN
ejpam-3747	2	58	,	,	PUNCT
ejpam-3747	2	59	smäıl	smäıl	NOUN
ejpam-3747	2	60	djebali1,2	djebali1,2	PROPN
ejpam-3747	2	61	,	,	PUNCT
ejpam-3747	2	62	talat	talat	PROPN
ejpam-3747	2	63	nazir3,4	nazir3,4	PROPN
ejpam-3747	2	64	1	1	NUM
ejpam-3747	2	65	laboratoire	laboratoire	NOUN
ejpam-3747	2	66	“	"	PUNCT
ejpam-3747	2	67	théorie	théorie	PROPN
ejpam-3747	2	68	du	du	PROPN
ejpam-3747	2	69	point	point	NOUN
ejpam-3747	2	70	fixe	fixe	PROPN
ejpam-3747	2	71	et	et	PROPN
ejpam-3747	2	72	applications	application	NOUN
ejpam-3747	2	73	”	"	PUNCT
ejpam-3747	2	74	,	,	PUNCT
ejpam-3747	2	75	école	école	ADJ
ejpam-3747	2	76	normale	normale	PROPN
ejpam-3747	2	77	supérieure	supérieure	PROPN
ejpam-3747	2	78	,	,	PUNCT
ejpam-3747	2	79	bp	bp	PROPN
ejpam-3747	2	80	92	92	NUM
ejpam-3747	2	81	kouba	kouba	PROPN
ejpam-3747	2	82	,	,	PUNCT
ejpam-3747	2	83	algiers	algiers	PROPN
ejpam-3747	2	84	16006	16006	NUM
ejpam-3747	2	85	,	,	PUNCT
ejpam-3747	2	86	algeria	algeria	PROPN
ejpam-3747	2	87	2	2	NUM
ejpam-3747	2	88	department	department	NOUN
ejpam-3747	2	89	of	of	ADP
ejpam-3747	2	90	mathematics	mathematic	NOUN
ejpam-3747	2	91	,	,	PUNCT
ejpam-3747	2	92	faculty	faculty	NOUN
ejpam-3747	2	93	of	of	ADP
ejpam-3747	2	94	sciences	science	NOUN
ejpam-3747	2	95	,	,	PUNCT
ejpam-3747	2	96	imam	imam	PROPN
ejpam-3747	2	97	mohammad	mohammad	PROPN
ejpam-3747	2	98	ibn	ibn	PROPN
ejpam-3747	2	99	saud	saud	PROPN
ejpam-3747	2	100	islamic	islamic	PROPN
ejpam-3747	2	101	university	university	PROPN
ejpam-3747	2	102	(	(	PUNCT
ejpam-3747	2	103	imsiu	imsiu	PROPN
ejpam-3747	2	104	)	)	PUNCT
ejpam-3747	2	105	,	,	PUNCT
ejpam-3747	2	106	pb	pb	ADP
ejpam-3747	2	107	90950	90950	NUM
ejpam-3747	2	108	.	.	PUNCT
ejpam-3747	3	1	riyadh	riyadh	PROPN
ejpam-3747	3	2	11623	11623	NUM
ejpam-3747	3	3	,	,	PUNCT
ejpam-3747	3	4	saudi	saudi	PROPN
ejpam-3747	3	5	arabia	arabia	PROPN
ejpam-3747	3	6	3	3	NUM
ejpam-3747	3	7	department	department	NOUN
ejpam-3747	3	8	of	of	ADP
ejpam-3747	3	9	mathematics	mathematic	NOUN
ejpam-3747	3	10	,	,	PUNCT
ejpam-3747	3	11	comsats	comsats	ADJ
ejpam-3747	3	12	,	,	PUNCT
ejpam-3747	3	13	university	university	NOUN
ejpam-3747	3	14	islamabad	islamabad	NOUN
ejpam-3747	3	15	,	,	PUNCT
ejpam-3747	3	16	abbottabad	abbottabad	PROPN
ejpam-3747	3	17	campus	campus	PROPN
ejpam-3747	3	18	22060	22060	NUM
ejpam-3747	3	19	,	,	PUNCT
ejpam-3747	3	20	pakistan	pakistan	PROPN
ejpam-3747	3	21	3	3	NUM
ejpam-3747	3	22	department	department	PROPN
ejpam-3747	3	23	of	of	ADP
ejpam-3747	3	24	mathematical	mathematical	ADJ
ejpam-3747	3	25	science	science	NOUN
ejpam-3747	3	26	,	,	PUNCT
ejpam-3747	3	27	university	university	NOUN
ejpam-3747	3	28	of	of	ADP
ejpam-3747	3	29	south	south	PROPN
ejpam-3747	3	30	africa	africa	PROPN
ejpam-3747	3	31	,	,	PUNCT
ejpam-3747	3	32	florida	florida	PROPN
ejpam-3747	3	33	campus	campus	PROPN
ejpam-3747	3	34	,	,	PUNCT
ejpam-3747	3	35	johannesburg	johannesburg	PROPN
ejpam-3747	3	36	1709	1709	NUM
ejpam-3747	3	37	,	,	PUNCT
ejpam-3747	3	38	south	south	PROPN
ejpam-3747	3	39	africa	africa	PROPN
ejpam-3747	3	40	abstract	abstract	PROPN
ejpam-3747	3	41	.	.	PUNCT
ejpam-3747	4	1	the	the	DET
ejpam-3747	4	2	aim	aim	NOUN
ejpam-3747	4	3	of	of	ADP
ejpam-3747	4	4	this	this	DET
ejpam-3747	4	5	paper	paper	NOUN
ejpam-3747	4	6	is	be	AUX
ejpam-3747	4	7	to	to	PART
ejpam-3747	4	8	establish	establish	VERB
ejpam-3747	4	9	new	new	ADJ
ejpam-3747	4	10	common	common	ADJ
ejpam-3747	4	11	fixed	fix	VERB
ejpam-3747	4	12	point	point	NOUN
ejpam-3747	4	13	results	result	NOUN
ejpam-3747	4	14	for	for	ADP
ejpam-3747	4	15	multivalued	multivalued	ADJ
ejpam-3747	4	16	integral	integral	ADJ
ejpam-3747	4	17	type	type	NOUN
ejpam-3747	4	18	contraction	contraction	NOUN
ejpam-3747	4	19	mappings	mapping	NOUN
ejpam-3747	4	20	on	on	ADP
ejpam-3747	4	21	a	a	DET
ejpam-3747	4	22	family	family	NOUN
ejpam-3747	4	23	of	of	ADP
ejpam-3747	4	24	sets	set	NOUN
ejpam-3747	4	25	endowed	endow	VERB
ejpam-3747	4	26	with	with	ADP
ejpam-3747	4	27	a	a	DET
ejpam-3747	4	28	graph	graph	NOUN
ejpam-3747	4	29	.	.	PUNCT
ejpam-3747	5	1	the	the	DET
ejpam-3747	5	2	obtained	obtain	VERB
ejpam-3747	5	3	results	result	NOUN
ejpam-3747	5	4	generalize	generalize	VERB
ejpam-3747	5	5	several	several	ADJ
ejpam-3747	5	6	recent	recent	ADJ
ejpam-3747	5	7	ones	one	NOUN
ejpam-3747	5	8	.	.	PUNCT
ejpam-3747	6	1	an	an	DET
ejpam-3747	6	2	example	example	NOUN
ejpam-3747	6	3	of	of	ADP
ejpam-3747	6	4	application	application	NOUN
ejpam-3747	6	5	is	be	AUX
ejpam-3747	6	6	included	include	VERB
ejpam-3747	6	7	to	to	PART
ejpam-3747	6	8	illustrate	illustrate	VERB
ejpam-3747	6	9	the	the	DET
ejpam-3747	6	10	main	main	ADJ
ejpam-3747	6	11	existence	existence	NOUN
ejpam-3747	6	12	theorem	theorem	VERB
ejpam-3747	6	13	.	.	PROPN
ejpam-3747	6	14	2020	2020	NUM
ejpam-3747	6	15	mathematics	mathematics	PROPN
ejpam-3747	6	16	subject	subject	NOUN
ejpam-3747	6	17	classifications	classification	NOUN
ejpam-3747	6	18	:	:	PUNCT
ejpam-3747	6	19	47h10	47h10	NUM
ejpam-3747	6	20	,	,	PUNCT
ejpam-3747	6	21	54e50	54e50	NUM
ejpam-3747	6	22	,	,	PUNCT
ejpam-3747	6	23	54h25	54h25	NUM
ejpam-3747	6	24	key	key	ADJ
ejpam-3747	6	25	words	word	NOUN
ejpam-3747	6	26	and	and	CCONJ
ejpam-3747	6	27	phrases	phrase	NOUN
ejpam-3747	6	28	:	:	PUNCT
ejpam-3747	6	29	common	common	ADJ
ejpam-3747	6	30	fixed	fix	VERB
ejpam-3747	6	31	point	point	NOUN
ejpam-3747	6	32	,	,	PUNCT
ejpam-3747	6	33	multi	multi	ADJ
ejpam-3747	6	34	-	-	ADJ
ejpam-3747	6	35	valued	value	VERB
ejpam-3747	6	36	mapping	mapping	NOUN
ejpam-3747	6	37	,	,	PUNCT
ejpam-3747	6	38	graphic	graphic	ADJ
ejpam-3747	6	39	contraction	contraction	NOUN
ejpam-3747	6	40	,	,	PUNCT
ejpam-3747	6	41	directed	direct	VERB
ejpam-3747	6	42	graph	graph	NOUN
ejpam-3747	6	43	1	1	NUM
ejpam-3747	6	44	.	.	PUNCT
ejpam-3747	7	1	introduction	introduction	NOUN
ejpam-3747	7	2	the	the	DET
ejpam-3747	7	3	banach	banach	NOUN
ejpam-3747	7	4	contraction	contraction	NOUN
ejpam-3747	7	5	principle	principle	NOUN
ejpam-3747	7	6	is	be	AUX
ejpam-3747	7	7	one	one	NUM
ejpam-3747	7	8	of	of	ADP
ejpam-3747	7	9	the	the	DET
ejpam-3747	7	10	most	most	ADV
ejpam-3747	7	11	important	important	ADJ
ejpam-3747	7	12	tools	tool	NOUN
ejpam-3747	7	13	in	in	ADP
ejpam-3747	7	14	nonlinear	nonlinear	ADJ
ejpam-3747	7	15	analysis	analysis	NOUN
ejpam-3747	7	16	and	and	CCONJ
ejpam-3747	7	17	is	be	AUX
ejpam-3747	7	18	considered	consider	VERB
ejpam-3747	7	19	as	as	ADP
ejpam-3747	7	20	the	the	DET
ejpam-3747	7	21	main	main	ADJ
ejpam-3747	7	22	source	source	NOUN
ejpam-3747	7	23	of	of	ADP
ejpam-3747	7	24	inspiration	inspiration	NOUN
ejpam-3747	7	25	in	in	ADP
ejpam-3747	7	26	metric	metric	ADJ
ejpam-3747	7	27	fixed	fix	VERB
ejpam-3747	7	28	point	point	NOUN
ejpam-3747	7	29	theory	theory	NOUN
ejpam-3747	7	30	.	.	PUNCT
ejpam-3747	8	1	since	since	SCONJ
ejpam-3747	8	2	its	its	PRON
ejpam-3747	8	3	proof	proof	NOUN
ejpam-3747	8	4	by	by	ADP
ejpam-3747	8	5	s.	s.	PROPN
ejpam-3747	8	6	banach	banach	NOUN
ejpam-3747	8	7	in	in	ADP
ejpam-3747	8	8	1922	1922	NUM
ejpam-3747	8	9	,	,	PUNCT
ejpam-3747	8	10	this	this	DET
ejpam-3747	8	11	existence	existence	NOUN
ejpam-3747	8	12	principle	principle	NOUN
ejpam-3747	8	13	has	have	AUX
ejpam-3747	8	14	been	be	AUX
ejpam-3747	8	15	generalized	generalize	VERB
ejpam-3747	8	16	in	in	ADP
ejpam-3747	8	17	many	many	ADJ
ejpam-3747	8	18	∗corresponding	∗corresponde	VERB
ejpam-3747	8	19	author	author	NOUN
ejpam-3747	8	20	.	.	PUNCT
ejpam-3747	9	1	doi	doi	NOUN
ejpam-3747	9	2	:	:	PUNCT
ejpam-3747	9	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3747	https://doi.org/10.29020/nybg.ejpam.v13i5.3747	PROPN
ejpam-3747	9	4	email	email	NOUN
ejpam-3747	9	5	addresses	address	NOUN
ejpam-3747	9	6	:	:	PUNCT
ejpam-3747	9	7	benchabane.saadia@ymail.com	benchabane.saadia@ymail.com	X
ejpam-3747	9	8	(	(	PUNCT
ejpam-3747	9	9	s.	s.	PROPN
ejpam-3747	9	10	benchabane	benchabane	PROPN
ejpam-3747	9	11	)	)	PUNCT
ejpam-3747	9	12	,	,	PUNCT
ejpam-3747	9	13	djebali@hotmail.com	djebali@hotmail.com	X
ejpam-3747	9	14	(	(	PUNCT
ejpam-3747	9	15	s.	s.	PROPN
ejpam-3747	9	16	djebali	djebali	PROPN
ejpam-3747	9	17	)	)	PUNCT
ejpam-3747	9	18	,	,	PUNCT
ejpam-3747	9	19	dr.talatnazir@gmail.com	dr.talatnazir@gmail.com	X
ejpam-3747	9	20	(	(	PUNCT
ejpam-3747	9	21	t.	t.	PROPN
ejpam-3747	9	22	nazir	nazir	PROPN
ejpam-3747	9	23	)	)	PUNCT
ejpam-3747	9	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3747	9	25	1072	1072	NUM
ejpam-3747	10	1	c	c	NOUN
ejpam-3747	10	2	©	©	PROPN
ejpam-3747	10	3	2020	2020	NUM
ejpam-3747	10	4	ejpam	ejpam	VERB
ejpam-3747	10	5	all	all	DET
ejpam-3747	10	6	rights	right	NOUN
ejpam-3747	10	7	reserved	reserve	VERB
ejpam-3747	10	8	.	.	PUNCT
ejpam-3747	11	1	s.	s.	PROPN
ejpam-3747	11	2	benchabane	benchabane	PROPN
ejpam-3747	11	3	,	,	PUNCT
ejpam-3747	11	4	s.	s.	PROPN
ejpam-3747	11	5	djebali	djebali	PROPN
ejpam-3747	11	6	,	,	PUNCT
ejpam-3747	11	7	t.	t.	PROPN
ejpam-3747	11	8	nazir	nazir	PROPN
ejpam-3747	11	9	/	/	SYM
ejpam-3747	11	10	eur	eur	PROPN
ejpam-3747	11	11	.	.	PUNCT
ejpam-3747	12	1	j.	j.	PROPN
ejpam-3747	12	2	pure	pure	PROPN
ejpam-3747	12	3	appl	appl	PROPN
ejpam-3747	12	4	.	.	PROPN
ejpam-3747	12	5	math	math	PROPN
ejpam-3747	12	6	,	,	PUNCT
ejpam-3747	12	7	13	13	NUM
ejpam-3747	12	8	(	(	PUNCT
ejpam-3747	12	9	5	5	NUM
ejpam-3747	12	10	)	)	PUNCT
ejpam-3747	12	11	(	(	PUNCT
ejpam-3747	12	12	2020	2020	NUM
ejpam-3747	12	13	)	)	PUNCT
ejpam-3747	12	14	,	,	PUNCT
ejpam-3747	12	15	1072	1072	NUM
ejpam-3747	12	16	-	-	SYM
ejpam-3747	12	17	1087	1087	NUM
ejpam-3747	12	18	1073	1073	NUM
ejpam-3747	12	19	directions	direction	NOUN
ejpam-3747	12	20	over	over	ADP
ejpam-3747	12	21	various	various	ADJ
ejpam-3747	12	22	spaces	space	NOUN
ejpam-3747	12	23	by	by	ADP
ejpam-3747	12	24	several	several	ADJ
ejpam-3747	12	25	authors	author	NOUN
ejpam-3747	12	26	.	.	PUNCT
ejpam-3747	13	1	among	among	ADP
ejpam-3747	13	2	these	these	DET
ejpam-3747	13	3	generalizations	generalization	NOUN
ejpam-3747	13	4	,	,	PUNCT
ejpam-3747	13	5	the	the	DET
ejpam-3747	13	6	multivalued	multivalue	VERB
ejpam-3747	13	7	version	version	NOUN
ejpam-3747	13	8	was	be	AUX
ejpam-3747	13	9	established	establish	VERB
ejpam-3747	13	10	by	by	ADP
ejpam-3747	13	11	covitz	covitz	NOUN
ejpam-3747	13	12	and	and	CCONJ
ejpam-3747	13	13	nadler	nadler	NOUN
ejpam-3747	13	14	[	[	X
ejpam-3747	13	15	14	14	NUM
ejpam-3747	13	16	]	]	PUNCT
ejpam-3747	13	17	in	in	ADP
ejpam-3747	13	18	1969	1969	NUM
ejpam-3747	13	19	using	use	VERB
ejpam-3747	13	20	hausdorff	hausdorff	NOUN
ejpam-3747	13	21	-	-	PUNCT
ejpam-3747	13	22	pompeiu	pompeiu	NOUN
ejpam-3747	13	23	metric	metric	ADJ
ejpam-3747	13	24	h	h	NOUN
ejpam-3747	13	25	in	in	ADP
ejpam-3747	13	26	complete	complete	ADJ
ejpam-3747	13	27	metric	metric	ADJ
ejpam-3747	13	28	spaces	space	NOUN
ejpam-3747	13	29	.	.	PUNCT
ejpam-3747	14	1	recall	recall	PROPN
ejpam-3747	14	2	h(a	h(a	PROPN
ejpam-3747	14	3	,	,	PUNCT
ejpam-3747	14	4	b	b	NOUN
ejpam-3747	14	5	)	)	PUNCT
ejpam-3747	14	6	=	=	NOUN
ejpam-3747	14	7	max(sup	max(sup	NOUN
ejpam-3747	14	8	x∈a	x∈a	ADJ
ejpam-3747	14	9	d(x	d(x	PROPN
ejpam-3747	14	10	,	,	PUNCT
ejpam-3747	14	11	b	b	NOUN
ejpam-3747	14	12	)	)	PUNCT
ejpam-3747	14	13	,	,	PUNCT
ejpam-3747	14	14	sup	sup	NOUN
ejpam-3747	14	15	x∈b	x∈b	ADJ
ejpam-3747	14	16	d(x	d(x	PROPN
ejpam-3747	14	17	,	,	PUNCT
ejpam-3747	14	18	a	a	PRON
ejpam-3747	14	19	)	)	PUNCT
ejpam-3747	14	20	)	)	PUNCT
ejpam-3747	14	21	,	,	PUNCT
ejpam-3747	14	22	for	for	ADP
ejpam-3747	14	23	bounded	bounded	ADJ
ejpam-3747	14	24	subsets	subset	NOUN
ejpam-3747	14	25	a	a	PRON
ejpam-3747	14	26	,	,	PUNCT
ejpam-3747	14	27	b.	b.	PROPN
ejpam-3747	14	28	a	a	DET
ejpam-3747	14	29	large	large	ADJ
ejpam-3747	14	30	amount	amount	NOUN
ejpam-3747	14	31	of	of	ADP
ejpam-3747	14	32	research	research	NOUN
ejpam-3747	14	33	works	work	NOUN
ejpam-3747	14	34	have	have	AUX
ejpam-3747	14	35	followed	follow	VERB
ejpam-3747	14	36	these	these	DET
ejpam-3747	14	37	theorems	theorem	NOUN
ejpam-3747	14	38	.	.	PUNCT
ejpam-3747	15	1	we	we	PRON
ejpam-3747	15	2	briefly	briefly	ADV
ejpam-3747	15	3	describe	describe	VERB
ejpam-3747	15	4	most	most	ADJ
ejpam-3747	15	5	recent	recent	ADJ
ejpam-3747	15	6	papers	paper	NOUN
ejpam-3747	15	7	and	and	CCONJ
ejpam-3747	15	8	results	result	NOUN
ejpam-3747	15	9	.	.	PUNCT
ejpam-3747	16	1	in	in	ADP
ejpam-3747	16	2	2002	2002	NUM
ejpam-3747	16	3	,	,	PUNCT
ejpam-3747	16	4	branciari	branciari	NOUN
ejpam-3747	16	5	[	[	X
ejpam-3747	16	6	8	8	NUM
ejpam-3747	16	7	]	]	PUNCT
ejpam-3747	16	8	obtained	obtain	VERB
ejpam-3747	16	9	a	a	DET
ejpam-3747	16	10	fixed	fix	VERB
ejpam-3747	16	11	point	point	NOUN
ejpam-3747	16	12	theorem	theorem	NOUN
ejpam-3747	16	13	for	for	ADP
ejpam-3747	16	14	single	single	ADJ
ejpam-3747	16	15	valued	value	VERB
ejpam-3747	16	16	maps	map	NOUN
ejpam-3747	16	17	satisfying	satisfy	VERB
ejpam-3747	16	18	an	an	DET
ejpam-3747	16	19	analogue	analogue	NOUN
ejpam-3747	16	20	of	of	ADP
ejpam-3747	16	21	banach	banach	NOUN
ejpam-3747	16	22	contraction	contraction	NOUN
ejpam-3747	16	23	principle	principle	NOUN
ejpam-3747	16	24	for	for	ADP
ejpam-3747	16	25	integral	integral	ADJ
ejpam-3747	16	26	type	type	NOUN
ejpam-3747	16	27	inequality	inequality	NOUN
ejpam-3747	16	28	.	.	PUNCT
ejpam-3747	17	1	this	this	DET
ejpam-3747	17	2	result	result	NOUN
ejpam-3747	17	3	was	be	AUX
ejpam-3747	17	4	further	far	ADV
ejpam-3747	17	5	extended	extend	VERB
ejpam-3747	17	6	by	by	ADP
ejpam-3747	17	7	many	many	ADJ
ejpam-3747	17	8	authors	author	NOUN
ejpam-3747	17	9	(	(	PUNCT
ejpam-3747	17	10	we	we	PRON
ejpam-3747	17	11	refer	refer	VERB
ejpam-3747	17	12	the	the	DET
ejpam-3747	17	13	reader	reader	NOUN
ejpam-3747	17	14	to	to	ADP
ejpam-3747	17	15	[	[	X
ejpam-3747	17	16	4	4	NUM
ejpam-3747	17	17	]	]	PUNCT
ejpam-3747	17	18	,	,	PUNCT
ejpam-3747	17	19	[	[	X
ejpam-3747	17	20	5	5	NUM
ejpam-3747	17	21	]	]	PUNCT
ejpam-3747	17	22	,	,	PUNCT
ejpam-3747	17	23	[	[	X
ejpam-3747	17	24	10	10	NUM
ejpam-3747	17	25	]	]	PUNCT
ejpam-3747	17	26	,	,	PUNCT
ejpam-3747	17	27	[	[	X
ejpam-3747	17	28	15	15	NUM
ejpam-3747	17	29	]	]	PUNCT
ejpam-3747	17	30	,	,	PUNCT
ejpam-3747	17	31	[	[	X
ejpam-3747	17	32	18	18	NUM
ejpam-3747	17	33	]	]	PUNCT
ejpam-3747	17	34	,	,	PUNCT
ejpam-3747	17	35	and	and	CCONJ
ejpam-3747	17	36	references	reference	NOUN
ejpam-3747	17	37	therein	therein	ADV
ejpam-3747	17	38	)	)	PUNCT
ejpam-3747	17	39	.	.	PUNCT
ejpam-3747	18	1	in	in	ADP
ejpam-3747	18	2	2008	2008	NUM
ejpam-3747	18	3	,	,	PUNCT
ejpam-3747	18	4	jachymski	jachymski	PROPN
ejpam-3747	18	5	[	[	X
ejpam-3747	18	6	11	11	NUM
ejpam-3747	18	7	]	]	PUNCT
ejpam-3747	18	8	introduced	introduce	VERB
ejpam-3747	18	9	the	the	DET
ejpam-3747	18	10	concept	concept	NOUN
ejpam-3747	18	11	of	of	ADP
ejpam-3747	18	12	g	g	NOUN
ejpam-3747	18	13	-	-	PUNCT
ejpam-3747	18	14	contraction	contraction	NOUN
ejpam-3747	18	15	,	,	PUNCT
ejpam-3747	18	16	that	that	PRON
ejpam-3747	18	17	is	be	AUX
ejpam-3747	18	18	a	a	DET
ejpam-3747	18	19	single	single	ADV
ejpam-3747	18	20	-	-	PUNCT
ejpam-3747	18	21	valued	value	VERB
ejpam-3747	18	22	contraction	contraction	NOUN
ejpam-3747	18	23	mapping	mapping	NOUN
ejpam-3747	18	24	defined	define	VERB
ejpam-3747	18	25	on	on	ADP
ejpam-3747	18	26	a	a	DET
ejpam-3747	18	27	metric	metric	ADJ
ejpam-3747	18	28	space	space	NOUN
ejpam-3747	18	29	with	with	ADP
ejpam-3747	18	30	a	a	DET
ejpam-3747	18	31	graph	graph	NOUN
ejpam-3747	18	32	structure	structure	NOUN
ejpam-3747	18	33	(	(	PUNCT
ejpam-3747	18	34	it	it	PRON
ejpam-3747	18	35	preserves	preserve	VERB
ejpam-3747	18	36	the	the	DET
ejpam-3747	18	37	edges	edge	NOUN
ejpam-3747	18	38	and	and	CCONJ
ejpam-3747	18	39	decreases	decrease	VERB
ejpam-3747	18	40	weights	weight	NOUN
ejpam-3747	18	41	of	of	ADP
ejpam-3747	18	42	edges	edge	NOUN
ejpam-3747	18	43	of	of	ADP
ejpam-3747	18	44	the	the	DET
ejpam-3747	18	45	graph	graph	NOUN
ejpam-3747	18	46	)	)	PUNCT
ejpam-3747	18	47	.	.	PUNCT
ejpam-3747	19	1	then	then	ADV
ejpam-3747	19	2	banach	banach	VERB
ejpam-3747	19	3	’s	’s	PART
ejpam-3747	19	4	contraction	contraction	NOUN
ejpam-3747	19	5	principle	principle	NOUN
ejpam-3747	19	6	in	in	ADP
ejpam-3747	19	7	ordered	order	VERB
ejpam-3747	19	8	metric	metric	ADJ
ejpam-3747	19	9	spaces	space	NOUN
ejpam-3747	19	10	was	be	AUX
ejpam-3747	19	11	generalized	generalize	VERB
ejpam-3747	19	12	in	in	ADP
ejpam-3747	19	13	this	this	DET
ejpam-3747	19	14	new	new	ADJ
ejpam-3747	19	15	class	class	NOUN
ejpam-3747	19	16	of	of	ADP
ejpam-3747	19	17	metric	metric	ADJ
ejpam-3747	19	18	spaces	space	NOUN
ejpam-3747	19	19	.	.	PUNCT
ejpam-3747	20	1	recently	recently	ADV
ejpam-3747	20	2	,	,	PUNCT
ejpam-3747	20	3	abbas	abbas	PROPN
ejpam-3747	20	4	et	et	PROPN
ejpam-3747	20	5	al	al	PROPN
ejpam-3747	20	6	.	.	PUNCT
ejpam-3747	21	1	[	[	X
ejpam-3747	21	2	1	1	NUM
ejpam-3747	21	3	]	]	PUNCT
ejpam-3747	21	4	obtained	obtain	VERB
ejpam-3747	21	5	the	the	DET
ejpam-3747	21	6	existence	existence	NOUN
ejpam-3747	21	7	of	of	ADP
ejpam-3747	21	8	some	some	DET
ejpam-3747	21	9	fixed	fix	VERB
ejpam-3747	21	10	points	point	NOUN
ejpam-3747	21	11	for	for	ADP
ejpam-3747	21	12	set	set	ADJ
ejpam-3747	21	13	valued	value	VERB
ejpam-3747	21	14	mappings	mapping	NOUN
ejpam-3747	21	15	satisfying	satisfy	VERB
ejpam-3747	21	16	certain	certain	ADJ
ejpam-3747	21	17	graphic	graphic	ADJ
ejpam-3747	21	18	contraction	contraction	NOUN
ejpam-3747	21	19	conditions	condition	NOUN
ejpam-3747	21	20	on	on	ADP
ejpam-3747	21	21	a	a	DET
ejpam-3747	21	22	domain	domain	NOUN
ejpam-3747	21	23	of	of	ADP
ejpam-3747	21	24	sets	set	NOUN
ejpam-3747	21	25	endowed	endow	VERB
ejpam-3747	21	26	with	with	ADP
ejpam-3747	21	27	a	a	DET
ejpam-3747	21	28	directed	direct	VERB
ejpam-3747	21	29	graph	graph	NOUN
ejpam-3747	21	30	.	.	PUNCT
ejpam-3747	22	1	the	the	DET
ejpam-3747	22	2	concept	concept	NOUN
ejpam-3747	22	3	of	of	ADP
ejpam-3747	22	4	a	a	DET
ejpam-3747	22	5	multivalued	multivalue	VERB
ejpam-3747	22	6	mappings	mapping	NOUN
ejpam-3747	22	7	has	have	AUX
ejpam-3747	22	8	been	be	AUX
ejpam-3747	22	9	used	use	VERB
ejpam-3747	22	10	more	more	ADV
ejpam-3747	22	11	recently	recently	ADV
ejpam-3747	22	12	by	by	ADP
ejpam-3747	22	13	nazir	nazir	PROPN
ejpam-3747	22	14	et	et	PROPN
ejpam-3747	22	15	al	al	PROPN
ejpam-3747	22	16	.	.	PUNCT
ejpam-3747	23	1	[	[	X
ejpam-3747	23	2	3	3	X
ejpam-3747	23	3	]	]	PUNCT
ejpam-3747	23	4	and	and	CCONJ
ejpam-3747	23	5	abbas	abbas	PROPN
ejpam-3747	23	6	et	et	PROPN
ejpam-3747	23	7	al	al	PROPN
ejpam-3747	23	8	.	.	PUNCT
ejpam-3747	24	1	[	[	X
ejpam-3747	24	2	2	2	NUM
ejpam-3747	24	3	]	]	PUNCT
ejpam-3747	24	4	in	in	ADP
ejpam-3747	24	5	order	order	NOUN
ejpam-3747	24	6	to	to	PART
ejpam-3747	24	7	prove	prove	VERB
ejpam-3747	24	8	some	some	DET
ejpam-3747	24	9	common	common	ADJ
ejpam-3747	24	10	fixed	fix	VERB
ejpam-3747	24	11	point	point	NOUN
ejpam-3747	24	12	theorems	theorem	NOUN
ejpam-3747	24	13	on	on	ADP
ejpam-3747	24	14	a	a	DET
ejpam-3747	24	15	domain	domain	NOUN
ejpam-3747	24	16	of	of	ADP
ejpam-3747	24	17	sets	set	NOUN
ejpam-3747	24	18	endowed	endow	VERB
ejpam-3747	24	19	with	with	ADP
ejpam-3747	24	20	a	a	DET
ejpam-3747	24	21	directed	direct	VERB
ejpam-3747	24	22	graph	graph	NOUN
ejpam-3747	24	23	.	.	PUNCT
ejpam-3747	24	24	based	base	VERB
ejpam-3747	24	25	essentially	essentially	ADV
ejpam-3747	24	26	on	on	ADP
ejpam-3747	24	27	works	work	NOUN
ejpam-3747	24	28	[	[	X
ejpam-3747	24	29	1	1	NUM
ejpam-3747	24	30	]	]	PUNCT
ejpam-3747	24	31	,	,	PUNCT
ejpam-3747	24	32	[	[	X
ejpam-3747	24	33	2	2	NUM
ejpam-3747	24	34	]	]	PUNCT
ejpam-3747	24	35	,	,	PUNCT
ejpam-3747	24	36	[	[	X
ejpam-3747	24	37	7	7	NUM
ejpam-3747	24	38	]	]	PUNCT
ejpam-3747	24	39	,	,	PUNCT
ejpam-3747	24	40	[	[	X
ejpam-3747	24	41	12	12	NUM
ejpam-3747	24	42	]	]	PUNCT
ejpam-3747	24	43	and	and	CCONJ
ejpam-3747	24	44	[	[	X
ejpam-3747	24	45	15	15	NUM
ejpam-3747	24	46	]	]	PUNCT
ejpam-3747	24	47	,	,	PUNCT
ejpam-3747	24	48	we	we	PRON
ejpam-3747	24	49	will	will	AUX
ejpam-3747	24	50	introduce	introduce	VERB
ejpam-3747	24	51	in	in	ADP
ejpam-3747	24	52	this	this	DET
ejpam-3747	24	53	paper	paper	NOUN
ejpam-3747	24	54	the	the	DET
ejpam-3747	24	55	concept	concept	NOUN
ejpam-3747	24	56	of	of	ADP
ejpam-3747	24	57	graph	graph	NOUN
ejpam-3747	24	58	(	(	PUNCT
ejpam-3747	24	59	ψ	ψ	NOUN
ejpam-3747	24	60	,	,	PUNCT
ejpam-3747	24	61	φ)-weak	φ)-weak	VERB
ejpam-3747	24	62	contraction	contraction	NOUN
ejpam-3747	24	63	which	which	PRON
ejpam-3747	24	64	allows	allow	VERB
ejpam-3747	24	65	us	we	PRON
ejpam-3747	24	66	to	to	PART
ejpam-3747	24	67	derive	derive	VERB
ejpam-3747	24	68	some	some	DET
ejpam-3747	24	69	new	new	ADJ
ejpam-3747	24	70	common	common	ADJ
ejpam-3747	24	71	fixed	fix	VERB
ejpam-3747	24	72	point	point	NOUN
ejpam-3747	24	73	results	result	NOUN
ejpam-3747	24	74	on	on	ADP
ejpam-3747	24	75	the	the	DET
ejpam-3747	24	76	domain	domain	NOUN
ejpam-3747	24	77	of	of	ADP
ejpam-3747	24	78	sets	set	NOUN
ejpam-3747	24	79	endowed	endow	VERB
ejpam-3747	24	80	with	with	ADP
ejpam-3747	24	81	a	a	DET
ejpam-3747	24	82	graph	graph	NOUN
ejpam-3747	24	83	for	for	ADP
ejpam-3747	24	84	this	this	DET
ejpam-3747	24	85	class	class	NOUN
ejpam-3747	24	86	of	of	ADP
ejpam-3747	24	87	mappings	mapping	NOUN
ejpam-3747	24	88	.	.	PUNCT
ejpam-3747	25	1	first	first	ADV
ejpam-3747	25	2	of	of	ADP
ejpam-3747	25	3	all	all	PRON
ejpam-3747	25	4	,	,	PUNCT
ejpam-3747	25	5	we	we	PRON
ejpam-3747	25	6	collect	collect	VERB
ejpam-3747	25	7	some	some	DET
ejpam-3747	25	8	basic	basic	ADJ
ejpam-3747	25	9	notions	notion	NOUN
ejpam-3747	25	10	and	and	CCONJ
ejpam-3747	25	11	primary	primary	ADJ
ejpam-3747	25	12	results	result	NOUN
ejpam-3747	25	13	we	we	PRON
ejpam-3747	25	14	need	need	VERB
ejpam-3747	25	15	to	to	PART
ejpam-3747	25	16	develop	develop	VERB
ejpam-3747	25	17	our	our	PRON
ejpam-3747	25	18	results	result	NOUN
ejpam-3747	25	19	.	.	PUNCT
ejpam-3747	26	1	let	let	VERB
ejpam-3747	26	2	(	(	PUNCT
ejpam-3747	26	3	x	x	NOUN
ejpam-3747	26	4	,	,	PUNCT
ejpam-3747	26	5	d	d	NOUN
ejpam-3747	26	6	)	)	PUNCT
ejpam-3747	26	7	be	be	AUX
ejpam-3747	26	8	a	a	DET
ejpam-3747	26	9	metric	metric	ADJ
ejpam-3747	26	10	space	space	NOUN
ejpam-3747	26	11	and	and	CCONJ
ejpam-3747	26	12	denote	denote	VERB
ejpam-3747	26	13	by	by	ADP
ejpam-3747	26	14	p	p	PROPN
ejpam-3747	26	15	(	(	PUNCT
ejpam-3747	26	16	x	x	X
ejpam-3747	26	17	)	)	PUNCT
ejpam-3747	26	18	the	the	DET
ejpam-3747	26	19	family	family	NOUN
ejpam-3747	26	20	of	of	ADP
ejpam-3747	26	21	all	all	DET
ejpam-3747	26	22	nonempty	nonempty	ADJ
ejpam-3747	26	23	subsets	subset	NOUN
ejpam-3747	26	24	of	of	ADP
ejpam-3747	26	25	x	x	X
ejpam-3747	26	26	and	and	CCONJ
ejpam-3747	26	27	by	by	ADP
ejpam-3747	26	28	cb(x	cb(x	NOUN
ejpam-3747	26	29	)	)	PUNCT
ejpam-3747	26	30	the	the	DET
ejpam-3747	26	31	family	family	NOUN
ejpam-3747	26	32	of	of	ADP
ejpam-3747	26	33	all	all	DET
ejpam-3747	26	34	nonempty	nonempty	ADJ
ejpam-3747	26	35	,	,	PUNCT
ejpam-3747	26	36	closed	closed	ADJ
ejpam-3747	26	37	,	,	PUNCT
ejpam-3747	26	38	and	and	CCONJ
ejpam-3747	26	39	bounded	bound	VERB
ejpam-3747	26	40	subsets	subset	NOUN
ejpam-3747	26	41	of	of	ADP
ejpam-3747	26	42	x.	x.	NOUN
ejpam-3747	26	43	we	we	PRON
ejpam-3747	26	44	need	need	VERB
ejpam-3747	26	45	to	to	PART
ejpam-3747	26	46	consider	consider	VERB
ejpam-3747	26	47	two	two	NUM
ejpam-3747	26	48	classes	class	NOUN
ejpam-3747	26	49	of	of	ADP
ejpam-3747	26	50	functions	function	NOUN
ejpam-3747	26	51	:	:	PUNCT
ejpam-3747	26	52	definition	definition	NOUN
ejpam-3747	26	53	1	1	NUM
ejpam-3747	26	54	.	.	PUNCT
ejpam-3747	27	1	the	the	DET
ejpam-3747	27	2	class	class	NOUN
ejpam-3747	27	3	ψ	ψ	NOUN
ejpam-3747	27	4	consists	consist	VERB
ejpam-3747	27	5	of	of	ADP
ejpam-3747	27	6	nondecreasing	nondecrease	VERB
ejpam-3747	27	7	continuous	continuous	ADJ
ejpam-3747	27	8	functions	function	NOUN
ejpam-3747	27	9	ψ	ψ	NOUN
ejpam-3747	27	10	:	:	PUNCT
ejpam-3747	28	1	[	[	X
ejpam-3747	28	2	0,+∞)→	0,+∞)→	PUNCT
ejpam-3747	29	1	[	[	X
ejpam-3747	29	2	0,+∞	0,+∞	NUM
ejpam-3747	29	3	)	)	PUNCT
ejpam-3747	29	4	such	such	ADJ
ejpam-3747	29	5	that	that	DET
ejpam-3747	29	6	ψ(0	ψ(0	NOUN
ejpam-3747	29	7	)	)	PUNCT
ejpam-3747	29	8	=	=	SYM
ejpam-3747	29	9	0	0	NUM
ejpam-3747	29	10	and	and	CCONJ
ejpam-3747	29	11	ψ	ψ	NOUN
ejpam-3747	29	12	is	be	AUX
ejpam-3747	29	13	sub	sub	ADJ
ejpam-3747	29	14	-	-	ADJ
ejpam-3747	29	15	additive	additive	ADJ
ejpam-3747	29	16	,	,	PUNCT
ejpam-3747	29	17	i.e.	i.e.	X
ejpam-3747	29	18	,	,	PUNCT
ejpam-3747	29	19	for	for	ADP
ejpam-3747	29	20	every	every	DET
ejpam-3747	29	21	t1	t1	NOUN
ejpam-3747	29	22	,	,	PUNCT
ejpam-3747	29	23	t2	t2	PROPN
ejpam-3747	29	24	∈	∈	PROPN
ejpam-3747	29	25	r+	r+	ADV
ejpam-3747	29	26	,	,	PUNCT
ejpam-3747	29	27	ψ(t1	ψ(t1	VERB
ejpam-3747	29	28	+	+	CCONJ
ejpam-3747	29	29	t2	t2	NOUN
ejpam-3747	29	30	)	)	PUNCT
ejpam-3747	29	31	≤	≤	NOUN
ejpam-3747	29	32	ψ(t1	ψ(t1	NOUN
ejpam-3747	29	33	)	)	PUNCT
ejpam-3747	29	34	+	+	CCONJ
ejpam-3747	29	35	ψ(t2	ψ(t2	NOUN
ejpam-3747	29	36	)	)	PUNCT
ejpam-3747	29	37	.	.	PUNCT
ejpam-3747	30	1	definition	definition	NOUN
ejpam-3747	30	2	2	2	NUM
ejpam-3747	30	3	.	.	PUNCT
ejpam-3747	31	1	the	the	DET
ejpam-3747	31	2	class	class	NOUN
ejpam-3747	31	3	φ	φ	PROPN
ejpam-3747	31	4	is	be	AUX
ejpam-3747	31	5	the	the	DET
ejpam-3747	31	6	set	set	NOUN
ejpam-3747	31	7	of	of	ADP
ejpam-3747	31	8	functions	function	NOUN
ejpam-3747	31	9	ϕ	ϕ	NOUN
ejpam-3747	31	10	:	:	PUNCT
ejpam-3747	32	1	[	[	X
ejpam-3747	32	2	0,+∞)→	0,+∞)→	PUNCT
ejpam-3747	33	1	[	[	X
ejpam-3747	33	2	0,+∞	0,+∞	NUM
ejpam-3747	33	3	)	)	PUNCT
ejpam-3747	33	4	which	which	PRON
ejpam-3747	33	5	satisfy	satisfy	VERB
ejpam-3747	33	6	the	the	DET
ejpam-3747	33	7	following	follow	VERB
ejpam-3747	33	8	conditions	condition	NOUN
ejpam-3747	33	9	:	:	PUNCT
ejpam-3747	33	10	(	(	PUNCT
ejpam-3747	33	11	i	i	NOUN
ejpam-3747	33	12	)	)	PUNCT
ejpam-3747	33	13	ϕ	ϕ	PROPN
ejpam-3747	33	14	is	be	AUX
ejpam-3747	33	15	lebesgue	lebesgue	NOUN
ejpam-3747	33	16	integrable	integrable	ADJ
ejpam-3747	33	17	and	and	CCONJ
ejpam-3747	33	18	summable	summable	ADJ
ejpam-3747	33	19	on	on	ADP
ejpam-3747	33	20	each	each	DET
ejpam-3747	33	21	compact	compact	ADJ
ejpam-3747	33	22	subset	subset	NOUN
ejpam-3747	33	23	of	of	ADP
ejpam-3747	33	24	[	[	X
ejpam-3747	33	25	0,+∞	0,+∞	NUM
ejpam-3747	33	26	)	)	PUNCT
ejpam-3747	33	27	,	,	PUNCT
ejpam-3747	33	28	(	(	PUNCT
ejpam-3747	33	29	ii	ii	NOUN
ejpam-3747	33	30	)	)	PUNCT
ejpam-3747	33	31	∫	∫	PROPN
ejpam-3747	33	32	ε	ε	PROPN
ejpam-3747	33	33	0	0	PROPN
ejpam-3747	33	34	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	33	35	>	>	X
ejpam-3747	33	36	0	0	PROPN
ejpam-3747	33	37	,	,	PUNCT
ejpam-3747	33	38	for	for	ADP
ejpam-3747	33	39	each	each	DET
ejpam-3747	33	40	ε	ε	PROPN
ejpam-3747	33	41	>	>	X
ejpam-3747	33	42	0	0	PROPN
ejpam-3747	33	43	.	.	PUNCT
ejpam-3747	34	1	we	we	PRON
ejpam-3747	34	2	now	now	ADV
ejpam-3747	34	3	recall	recall	VERB
ejpam-3747	34	4	some	some	DET
ejpam-3747	34	5	lemmas	lemma	NOUN
ejpam-3747	34	6	that	that	PRON
ejpam-3747	34	7	will	will	AUX
ejpam-3747	34	8	be	be	AUX
ejpam-3747	34	9	used	use	VERB
ejpam-3747	34	10	in	in	ADP
ejpam-3747	34	11	the	the	DET
ejpam-3747	34	12	sequel	sequel	NOUN
ejpam-3747	34	13	.	.	PUNCT
ejpam-3747	35	1	lemma	lemma	PROPN
ejpam-3747	35	2	1	1	NUM
ejpam-3747	35	3	.	.	PUNCT
ejpam-3747	36	1	[	[	X
ejpam-3747	36	2	13	13	NUM
ejpam-3747	36	3	]	]	PUNCT
ejpam-3747	36	4	let	let	NOUN
ejpam-3747	36	5	(	(	PUNCT
ejpam-3747	36	6	rn)n	rn)n	PROPN
ejpam-3747	36	7	be	be	AUX
ejpam-3747	36	8	a	a	DET
ejpam-3747	36	9	nonnegative	nonnegative	ADJ
ejpam-3747	36	10	sequence	sequence	NOUN
ejpam-3747	36	11	and	and	CCONJ
ejpam-3747	36	12	ϕ	ϕ	PROPN
ejpam-3747	36	13	∈	∈	PROPN
ejpam-3747	36	14	φ	φ	X
ejpam-3747	36	15	.	.	PUNCT
ejpam-3747	37	1	then	then	ADV
ejpam-3747	37	2	lim	lim	PROPN
ejpam-3747	37	3	n→+∞	n→+∞	PROPN
ejpam-3747	37	4	∫	∫	PROPN
ejpam-3747	37	5	rn	rn	PROPN
ejpam-3747	37	6	0	0	PROPN
ejpam-3747	37	7	ϕ(t)dt	ϕ(t)dt	NOUN
ejpam-3747	38	1	=	=	NOUN
ejpam-3747	38	2	0	0	PUNCT
ejpam-3747	39	1	if	if	SCONJ
ejpam-3747	39	2	and	and	CCONJ
ejpam-3747	39	3	only	only	ADV
ejpam-3747	39	4	if	if	SCONJ
ejpam-3747	39	5	lim	lim	PROPN
ejpam-3747	39	6	n→+∞	n→+∞	PROPN
ejpam-3747	39	7	rn	rn	PROPN
ejpam-3747	39	8	=	=	PROPN
ejpam-3747	39	9	0	0	PROPN
ejpam-3747	39	10	.	.	PUNCT
ejpam-3747	40	1	s.	s.	PROPN
ejpam-3747	40	2	benchabane	benchabane	PROPN
ejpam-3747	40	3	,	,	PUNCT
ejpam-3747	40	4	s.	s.	PROPN
ejpam-3747	40	5	djebali	djebali	PROPN
ejpam-3747	40	6	,	,	PUNCT
ejpam-3747	40	7	t.	t.	PROPN
ejpam-3747	40	8	nazir	nazir	PROPN
ejpam-3747	40	9	/	/	SYM
ejpam-3747	40	10	eur	eur	PROPN
ejpam-3747	40	11	.	.	PUNCT
ejpam-3747	41	1	j.	j.	PROPN
ejpam-3747	41	2	pure	pure	PROPN
ejpam-3747	41	3	appl	appl	PROPN
ejpam-3747	41	4	.	.	PROPN
ejpam-3747	41	5	math	math	PROPN
ejpam-3747	41	6	,	,	PUNCT
ejpam-3747	41	7	13	13	NUM
ejpam-3747	41	8	(	(	PUNCT
ejpam-3747	41	9	5	5	NUM
ejpam-3747	41	10	)	)	PUNCT
ejpam-3747	41	11	(	(	PUNCT
ejpam-3747	41	12	2020	2020	NUM
ejpam-3747	41	13	)	)	PUNCT
ejpam-3747	41	14	,	,	PUNCT
ejpam-3747	41	15	1072	1072	NUM
ejpam-3747	41	16	-	-	SYM
ejpam-3747	41	17	1087	1087	NUM
ejpam-3747	41	18	1074	1074	NUM
ejpam-3747	41	19	lemma	lemma	PROPN
ejpam-3747	41	20	2	2	NUM
ejpam-3747	41	21	.	.	PUNCT
ejpam-3747	42	1	[	[	X
ejpam-3747	42	2	19	19	NUM
ejpam-3747	42	3	]	]	PUNCT
ejpam-3747	42	4	for	for	ADP
ejpam-3747	42	5	every	every	DET
ejpam-3747	42	6	ϕ	ϕ	PROPN
ejpam-3747	42	7	∈	∈	PROPN
ejpam-3747	42	8	φ	φ	NOUN
ejpam-3747	42	9	,	,	PUNCT
ejpam-3747	42	10	we	we	PRON
ejpam-3747	42	11	have∫	have∫	VERB
ejpam-3747	42	12	a+b	a+b	NUM
ejpam-3747	42	13	0	0	NUM
ejpam-3747	42	14	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	42	15	≤	≤	NUM
ejpam-3747	42	16	∫	∫	PROPN
ejpam-3747	43	1	a	a	PRON
ejpam-3747	43	2	0	0	NUM
ejpam-3747	43	3	ϕ(t)dt+	ϕ(t)dt+	NUM
ejpam-3747	43	4	∫	∫	PROPN
ejpam-3747	44	1	b	b	PROPN
ejpam-3747	44	2	0	0	NUM
ejpam-3747	44	3	ϕ(t)dt	ϕ(t)dt	NOUN
ejpam-3747	44	4	,	,	PUNCT
ejpam-3747	44	5	∀	∀	X
ejpam-3747	44	6	a	a	PRON
ejpam-3747	44	7	,	,	PUNCT
ejpam-3747	44	8	b	b	NOUN
ejpam-3747	44	9	≥	≥	NOUN
ejpam-3747	44	10	0	0	NUM
ejpam-3747	44	11	.	.	PUNCT
ejpam-3747	45	1	lemma	lemma	PROPN
ejpam-3747	45	2	3	3	X
ejpam-3747	45	3	.	.	PUNCT
ejpam-3747	46	1	[	[	X
ejpam-3747	46	2	14	14	NUM
ejpam-3747	46	3	]	]	X
ejpam-3747	46	4	if	if	SCONJ
ejpam-3747	46	5	a	a	DET
ejpam-3747	46	6	,	,	PUNCT
ejpam-3747	46	7	b	b	NOUN
ejpam-3747	46	8	∈	∈	PROPN
ejpam-3747	46	9	cb(x	cb(x	NUM
ejpam-3747	46	10	)	)	PUNCT
ejpam-3747	46	11	with	with	ADP
ejpam-3747	46	12	h(a	h(a	PROPN
ejpam-3747	46	13	,	,	PUNCT
ejpam-3747	46	14	b	b	NOUN
ejpam-3747	46	15	)	)	PUNCT
ejpam-3747	46	16	<	<	X
ejpam-3747	46	17	ε	ε	PROPN
ejpam-3747	46	18	,	,	PUNCT
ejpam-3747	46	19	then	then	ADV
ejpam-3747	46	20	for	for	ADP
ejpam-3747	46	21	each	each	PRON
ejpam-3747	46	22	a	a	DET
ejpam-3747	46	23	∈	∈	PROPN
ejpam-3747	46	24	a	a	PRON
ejpam-3747	46	25	,	,	PUNCT
ejpam-3747	46	26	there	there	PRON
ejpam-3747	46	27	exists	exist	VERB
ejpam-3747	46	28	an	an	DET
ejpam-3747	46	29	element	element	NOUN
ejpam-3747	46	30	b	b	PROPN
ejpam-3747	46	31	∈	∈	PROPN
ejpam-3747	46	32	b	b	NOUN
ejpam-3747	46	33	such	such	ADJ
ejpam-3747	46	34	that	that	SCONJ
ejpam-3747	46	35	d(a	d(a	PROPN
ejpam-3747	46	36	,	,	PUNCT
ejpam-3747	46	37	b	b	NOUN
ejpam-3747	46	38	)	)	PUNCT
ejpam-3747	46	39	<	<	X
ejpam-3747	46	40	ε	ε	PROPN
ejpam-3747	46	41	.	.	PROPN
ejpam-3747	47	1	in	in	ADP
ejpam-3747	47	2	2010	2010	NUM
ejpam-3747	47	3	,	,	PUNCT
ejpam-3747	47	4	ojha	ojha	VERB
ejpam-3747	47	5	et	et	PROPN
ejpam-3747	47	6	al	al	PROPN
ejpam-3747	47	7	.	.	PROPN
ejpam-3747	47	8	obtained	obtain	VERB
ejpam-3747	47	9	the	the	DET
ejpam-3747	47	10	following	following	ADJ
ejpam-3747	47	11	fixed	fix	VERB
ejpam-3747	47	12	point	point	NOUN
ejpam-3747	47	13	result	result	NOUN
ejpam-3747	47	14	for	for	ADP
ejpam-3747	47	15	a	a	DET
ejpam-3747	47	16	multivalued	multivalue	VERB
ejpam-3747	47	17	mapping	mapping	NOUN
ejpam-3747	47	18	satisfying	satisfy	VERB
ejpam-3747	47	19	an	an	DET
ejpam-3747	47	20	analogue	analogue	NOUN
ejpam-3747	47	21	of	of	ADP
ejpam-3747	47	22	banach	banach	NOUN
ejpam-3747	47	23	’s	’s	PART
ejpam-3747	47	24	contraction	contraction	NOUN
ejpam-3747	47	25	principle	principle	NOUN
ejpam-3747	47	26	for	for	ADP
ejpam-3747	47	27	an	an	DET
ejpam-3747	47	28	integral	integral	ADJ
ejpam-3747	47	29	type	type	NOUN
ejpam-3747	47	30	inequality	inequality	NOUN
ejpam-3747	47	31	.	.	PUNCT
ejpam-3747	48	1	theorem	theorem	NOUN
ejpam-3747	48	2	1	1	NUM
ejpam-3747	48	3	.	.	PUNCT
ejpam-3747	49	1	[	[	X
ejpam-3747	49	2	15	15	NUM
ejpam-3747	49	3	]	]	X
ejpam-3747	49	4	let	let	VERB
ejpam-3747	49	5	(	(	PUNCT
ejpam-3747	49	6	x	x	NOUN
ejpam-3747	49	7	,	,	PUNCT
ejpam-3747	49	8	d	d	NOUN
ejpam-3747	49	9	)	)	PUNCT
ejpam-3747	49	10	be	be	AUX
ejpam-3747	49	11	a	a	DET
ejpam-3747	49	12	complete	complete	ADJ
ejpam-3747	49	13	metric	metric	ADJ
ejpam-3747	49	14	space	space	NOUN
ejpam-3747	49	15	.	.	PUNCT
ejpam-3747	50	1	suppose	suppose	VERB
ejpam-3747	51	1	t	t	NOUN
ejpam-3747	51	2	:	:	PUNCT
ejpam-3747	51	3	x	x	SYM
ejpam-3747	51	4	→	→	X
ejpam-3747	51	5	cb(x	cb(x	NUM
ejpam-3747	51	6	)	)	PUNCT
ejpam-3747	51	7	is	be	AUX
ejpam-3747	51	8	a	a	DET
ejpam-3747	51	9	multivalued	multivalue	VERB
ejpam-3747	51	10	contraction	contraction	NOUN
ejpam-3747	51	11	mapping	mapping	NOUN
ejpam-3747	51	12	such	such	ADJ
ejpam-3747	51	13	that	that	PRON
ejpam-3747	51	14	for	for	ADP
ejpam-3747	51	15	some	some	DET
ejpam-3747	51	16	0	0	NUM
ejpam-3747	51	17	≤	≤	NUM
ejpam-3747	51	18	α	α	PRON
ejpam-3747	51	19	<	<	X
ejpam-3747	51	20	1,∫	1,∫	NUM
ejpam-3747	51	21	h(t	h(t	PROPN
ejpam-3747	51	22	(	(	PUNCT
ejpam-3747	51	23	x),t	x),t	PROPN
ejpam-3747	51	24	(	(	PUNCT
ejpam-3747	51	25	y	y	NOUN
ejpam-3747	51	26	)	)	PUNCT
ejpam-3747	51	27	)	)	PUNCT
ejpam-3747	51	28	0	0	NUM
ejpam-3747	52	1	ϕ(t)dt	ϕ(t)dt	DET
ejpam-3747	52	2	≤	≤	NOUN
ejpam-3747	53	1	α	α	DET
ejpam-3747	53	2	∫	∫	PROPN
ejpam-3747	53	3	m(x	m(x	PROPN
ejpam-3747	53	4	,	,	PUNCT
ejpam-3747	53	5	y	y	NOUN
ejpam-3747	53	6	)	)	PUNCT
ejpam-3747	53	7	0	0	NUM
ejpam-3747	54	1	ϕ(t)dt	ϕ(t)dt	NOUN
ejpam-3747	54	2	,	,	PUNCT
ejpam-3747	54	3	where	where	SCONJ
ejpam-3747	54	4	ϕ	ϕ	NOUN
ejpam-3747	54	5	is	be	AUX
ejpam-3747	54	6	lower	low	ADJ
ejpam-3747	54	7	semi	semi	ADJ
ejpam-3747	54	8	-	-	ADJ
ejpam-3747	54	9	continuous	continuous	ADJ
ejpam-3747	54	10	,	,	PUNCT
ejpam-3747	54	11	ϕ(0	ϕ(0	PROPN
ejpam-3747	54	12	)	)	PUNCT
ejpam-3747	54	13	=	=	PUNCT
ejpam-3747	54	14	0	0	NUM
ejpam-3747	54	15	,	,	PUNCT
ejpam-3747	54	16	and	and	CCONJ
ejpam-3747	54	17	ϕ(t	ϕ(t	NUM
ejpam-3747	54	18	)	)	PUNCT
ejpam-3747	54	19	>	>	X
ejpam-3747	54	20	0	0	NUM
ejpam-3747	54	21	,	,	PUNCT
ejpam-3747	54	22	∀	∀	X
ejpam-3747	54	23	t	t	NOUN
ejpam-3747	54	24	>	>	X
ejpam-3747	54	25	0	0	PUNCT
ejpam-3747	54	26	and	and	CCONJ
ejpam-3747	54	27	for	for	ADP
ejpam-3747	54	28	all	all	DET
ejpam-3747	54	29	x	x	NOUN
ejpam-3747	54	30	,	,	PUNCT
ejpam-3747	54	31	y	y	PROPN
ejpam-3747	54	32	∈	∈	PROPN
ejpam-3747	54	33	x	x	SYM
ejpam-3747	54	34	m(x	m(x	PROPN
ejpam-3747	54	35	,	,	PUNCT
ejpam-3747	54	36	y	y	NOUN
ejpam-3747	54	37	)	)	PUNCT
ejpam-3747	54	38	=	=	SYM
ejpam-3747	54	39	max	max	PROPN
ejpam-3747	54	40	{	{	PUNCT
ejpam-3747	54	41	d(x	d(x	PROPN
ejpam-3747	54	42	,	,	PUNCT
ejpam-3747	54	43	y	y	NOUN
ejpam-3747	54	44	)	)	PUNCT
ejpam-3747	54	45	,	,	PUNCT
ejpam-3747	54	46	d(x	d(x	PROPN
ejpam-3747	54	47	,	,	PUNCT
ejpam-3747	54	48	t	t	PROPN
ejpam-3747	54	49	(	(	PUNCT
ejpam-3747	54	50	x	x	NOUN
ejpam-3747	54	51	)	)	PUNCT
ejpam-3747	54	52	)	)	PUNCT
ejpam-3747	54	53	,	,	PUNCT
ejpam-3747	54	54	d(y	d(y	PROPN
ejpam-3747	54	55	,	,	PUNCT
ejpam-3747	54	56	t	t	PROPN
ejpam-3747	54	57	(	(	PUNCT
ejpam-3747	54	58	y	y	NOUN
ejpam-3747	54	59	)	)	PUNCT
ejpam-3747	54	60	)	)	PUNCT
ejpam-3747	54	61	,	,	PUNCT
ejpam-3747	54	62	1	1	NUM
ejpam-3747	54	63	2	2	NUM
ejpam-3747	55	1	[	[	X
ejpam-3747	55	2	d(x	d(x	PROPN
ejpam-3747	55	3	,	,	PUNCT
ejpam-3747	55	4	t	t	PROPN
ejpam-3747	55	5	(	(	PUNCT
ejpam-3747	55	6	y	y	NOUN
ejpam-3747	55	7	)	)	PUNCT
ejpam-3747	55	8	)	)	PUNCT
ejpam-3747	56	1	+	+	ADP
ejpam-3747	56	2	d(y	d(y	NOUN
ejpam-3747	56	3	,	,	PUNCT
ejpam-3747	56	4	t	t	PROPN
ejpam-3747	56	5	(	(	PUNCT
ejpam-3747	56	6	x	x	NOUN
ejpam-3747	56	7	)	)	PUNCT
ejpam-3747	56	8	)	)	PUNCT
ejpam-3747	56	9	]	]	PUNCT
ejpam-3747	56	10	}	}	PUNCT
ejpam-3747	56	11	.	.	PUNCT
ejpam-3747	57	1	then	then	ADV
ejpam-3747	57	2	t	t	PROPN
ejpam-3747	57	3	has	have	VERB
ejpam-3747	57	4	a	a	DET
ejpam-3747	57	5	fixed	fix	VERB
ejpam-3747	57	6	point	point	NOUN
ejpam-3747	57	7	in	in	ADP
ejpam-3747	57	8	x.	x.	NOUN
ejpam-3747	57	9	the	the	DET
ejpam-3747	57	10	second	second	ADJ
ejpam-3747	57	11	part	part	NOUN
ejpam-3747	57	12	of	of	ADP
ejpam-3747	57	13	this	this	DET
ejpam-3747	57	14	introduction	introduction	NOUN
ejpam-3747	57	15	is	be	AUX
ejpam-3747	57	16	devoted	devote	VERB
ejpam-3747	57	17	to	to	PART
ejpam-3747	57	18	graph	graph	VERB
ejpam-3747	57	19	and	and	CCONJ
ejpam-3747	57	20	fixed	fix	VERB
ejpam-3747	57	21	point	point	NOUN
ejpam-3747	57	22	theories	theory	NOUN
ejpam-3747	57	23	.	.	PUNCT
ejpam-3747	58	1	first	first	ADV
ejpam-3747	58	2	,	,	PUNCT
ejpam-3747	58	3	by	by	ADP
ejpam-3747	58	4	∆	∆	PROPN
ejpam-3747	58	5	=	=	SYM
ejpam-3747	58	6	∆(x	∆(x	PROPN
ejpam-3747	58	7	)	)	PUNCT
ejpam-3747	58	8	it	it	PRON
ejpam-3747	58	9	meant	mean	VERB
ejpam-3747	58	10	throughout	throughout	ADP
ejpam-3747	58	11	the	the	DET
ejpam-3747	58	12	diagonal	diagonal	NOUN
ejpam-3747	58	13	of	of	ADP
ejpam-3747	58	14	the	the	DET
ejpam-3747	58	15	metric	metric	ADJ
ejpam-3747	58	16	space	space	NOUN
ejpam-3747	58	17	x.	x.	NOUN
ejpam-3747	59	1	a	a	DET
ejpam-3747	59	2	graph	graph	NOUN
ejpam-3747	59	3	g	g	NOUN
ejpam-3747	59	4	is	be	AUX
ejpam-3747	59	5	an	an	DET
ejpam-3747	59	6	ordered	order	VERB
ejpam-3747	59	7	pair	pair	NOUN
ejpam-3747	59	8	(	(	PUNCT
ejpam-3747	59	9	v	v	NOUN
ejpam-3747	59	10	,	,	PUNCT
ejpam-3747	59	11	e	e	NOUN
ejpam-3747	59	12	)	)	PUNCT
ejpam-3747	59	13	,	,	PUNCT
ejpam-3747	59	14	where	where	SCONJ
ejpam-3747	59	15	v	v	NOUN
ejpam-3747	59	16	is	be	AUX
ejpam-3747	59	17	a	a	DET
ejpam-3747	59	18	set	set	NOUN
ejpam-3747	59	19	and	and	CCONJ
ejpam-3747	59	20	e	e	NOUN
ejpam-3747	59	21	⊂	⊂	PROPN
ejpam-3747	59	22	v	v	ADP
ejpam-3747	59	23	×	×	PROPN
ejpam-3747	59	24	v	v	NOUN
ejpam-3747	59	25	is	be	AUX
ejpam-3747	59	26	a	a	DET
ejpam-3747	59	27	binary	binary	ADJ
ejpam-3747	59	28	relation	relation	NOUN
ejpam-3747	59	29	on	on	ADP
ejpam-3747	59	30	v	v	NUM
ejpam-3747	59	31	.	.	PUNCT
ejpam-3747	60	1	elements	element	NOUN
ejpam-3747	60	2	of	of	ADP
ejpam-3747	60	3	e	e	NOUN
ejpam-3747	60	4	are	be	AUX
ejpam-3747	60	5	called	call	VERB
ejpam-3747	60	6	edges	edge	NOUN
ejpam-3747	60	7	and	and	CCONJ
ejpam-3747	60	8	are	be	AUX
ejpam-3747	60	9	denoted	denote	VERB
ejpam-3747	60	10	by	by	ADP
ejpam-3747	60	11	e(g	e(g	PROPN
ejpam-3747	60	12	)	)	PUNCT
ejpam-3747	60	13	while	while	SCONJ
ejpam-3747	60	14	elements	element	NOUN
ejpam-3747	60	15	of	of	ADP
ejpam-3747	60	16	v	v	NOUN
ejpam-3747	60	17	,	,	PUNCT
ejpam-3747	60	18	denoted	denote	VERB
ejpam-3747	60	19	v	v	ADP
ejpam-3747	60	20	(	(	PUNCT
ejpam-3747	60	21	g	g	NOUN
ejpam-3747	60	22	)	)	PUNCT
ejpam-3747	60	23	,	,	PUNCT
ejpam-3747	60	24	are	be	AUX
ejpam-3747	60	25	called	call	VERB
ejpam-3747	60	26	vertices	vertex	NOUN
ejpam-3747	60	27	.	.	PUNCT
ejpam-3747	61	1	if	if	SCONJ
ejpam-3747	61	2	the	the	DET
ejpam-3747	61	3	direction	direction	NOUN
ejpam-3747	61	4	is	be	AUX
ejpam-3747	61	5	imposed	impose	VERB
ejpam-3747	61	6	in	in	ADP
ejpam-3747	61	7	e	e	NOUN
ejpam-3747	61	8	,	,	PUNCT
ejpam-3747	61	9	that	that	PRON
ejpam-3747	61	10	is	be	AUX
ejpam-3747	61	11	the	the	DET
ejpam-3747	61	12	edges	edge	NOUN
ejpam-3747	61	13	are	be	AUX
ejpam-3747	61	14	directed	direct	VERB
ejpam-3747	61	15	,	,	PUNCT
ejpam-3747	61	16	then	then	ADV
ejpam-3747	61	17	we	we	PRON
ejpam-3747	61	18	get	get	VERB
ejpam-3747	61	19	a	a	DET
ejpam-3747	61	20	digraph	digraph	NOUN
ejpam-3747	61	21	(	(	PUNCT
ejpam-3747	61	22	directed	direct	VERB
ejpam-3747	61	23	graph	graph	NOUN
ejpam-3747	61	24	)	)	PUNCT
ejpam-3747	61	25	.	.	PUNCT
ejpam-3747	62	1	we	we	PRON
ejpam-3747	62	2	assume	assume	VERB
ejpam-3747	62	3	that	that	SCONJ
ejpam-3747	62	4	g	g	PROPN
ejpam-3747	62	5	has	have	VERB
ejpam-3747	62	6	no	no	DET
ejpam-3747	62	7	parallel	parallel	ADJ
ejpam-3747	62	8	edges	edge	NOUN
ejpam-3747	62	9	,	,	PUNCT
ejpam-3747	62	10	i.e.	i.e.	X
ejpam-3747	62	11	two	two	NUM
ejpam-3747	62	12	vertices	vertex	NOUN
ejpam-3747	62	13	can	can	AUX
ejpam-3747	62	14	not	not	PART
ejpam-3747	62	15	be	be	AUX
ejpam-3747	62	16	connected	connect	VERB
ejpam-3747	62	17	by	by	ADP
ejpam-3747	62	18	more	more	ADJ
ejpam-3747	62	19	than	than	ADP
ejpam-3747	62	20	one	one	NUM
ejpam-3747	62	21	edge	edge	NOUN
ejpam-3747	62	22	.	.	PUNCT
ejpam-3747	63	1	then	then	ADV
ejpam-3747	63	2	g	g	PROPN
ejpam-3747	63	3	can	can	AUX
ejpam-3747	63	4	be	be	AUX
ejpam-3747	63	5	identified	identify	VERB
ejpam-3747	63	6	with	with	ADP
ejpam-3747	63	7	the	the	DET
ejpam-3747	63	8	pair	pair	NOUN
ejpam-3747	63	9	(	(	PUNCT
ejpam-3747	63	10	v	v	NOUN
ejpam-3747	63	11	(	(	PUNCT
ejpam-3747	63	12	g	g	NOUN
ejpam-3747	63	13	)	)	PUNCT
ejpam-3747	63	14	,	,	PUNCT
ejpam-3747	63	15	e(g	e(g	PROPN
ejpam-3747	63	16	)	)	PUNCT
ejpam-3747	63	17	)	)	PUNCT
ejpam-3747	63	18	.	.	PUNCT
ejpam-3747	64	1	if	if	SCONJ
ejpam-3747	64	2	x	x	PRON
ejpam-3747	64	3	and	and	CCONJ
ejpam-3747	64	4	y	y	PROPN
ejpam-3747	64	5	are	be	AUX
ejpam-3747	64	6	vertices	vertex	NOUN
ejpam-3747	64	7	of	of	ADP
ejpam-3747	64	8	g	g	NOUN
ejpam-3747	64	9	,	,	PUNCT
ejpam-3747	64	10	then	then	ADV
ejpam-3747	64	11	a	a	DET
ejpam-3747	64	12	path	path	NOUN
ejpam-3747	64	13	in	in	ADP
ejpam-3747	64	14	g	g	NOUN
ejpam-3747	64	15	from	from	ADP
ejpam-3747	64	16	x	x	PUNCT
ejpam-3747	64	17	to	to	ADP
ejpam-3747	64	18	y	y	PROPN
ejpam-3747	64	19	of	of	ADP
ejpam-3747	64	20	length	length	NOUN
ejpam-3747	64	21	k	k	PROPN
ejpam-3747	64	22	∈	∈	PROPN
ejpam-3747	64	23	n	n	PRON
ejpam-3747	64	24	is	be	AUX
ejpam-3747	64	25	a	a	DET
ejpam-3747	64	26	finite	finite	ADJ
ejpam-3747	64	27	sequence	sequence	NOUN
ejpam-3747	64	28	(	(	PUNCT
ejpam-3747	64	29	xn)n	xn)n	PROPN
ejpam-3747	64	30	,	,	PUNCT
ejpam-3747	64	31	n	n	PRON
ejpam-3747	64	32	∈	∈	PROPN
ejpam-3747	64	33	{	{	PUNCT
ejpam-3747	64	34	0	0	NUM
ejpam-3747	64	35	,	,	PUNCT
ejpam-3747	64	36	1	1	NUM
ejpam-3747	64	37	,	,	PUNCT
ejpam-3747	64	38	2	2	NUM
ejpam-3747	64	39	,	,	PUNCT
ejpam-3747	64	40	.	.	PUNCT
ejpam-3747	64	41	.	.	PUNCT
ejpam-3747	64	42	.	.	PUNCT
ejpam-3747	65	1	k	k	X
ejpam-3747	65	2	}	}	PUNCT
ejpam-3747	65	3	of	of	ADP
ejpam-3747	65	4	vertices	vertex	NOUN
ejpam-3747	65	5	such	such	ADJ
ejpam-3747	65	6	that	that	SCONJ
ejpam-3747	65	7	x	x	X
ejpam-3747	65	8	=	=	SYM
ejpam-3747	65	9	x0	x0	PROPN
ejpam-3747	65	10	,	,	PUNCT
ejpam-3747	65	11	.	.	PUNCT
ejpam-3747	65	12	.	.	PUNCT
ejpam-3747	65	13	.	.	PUNCT
ejpam-3747	66	1	,	,	PUNCT
ejpam-3747	66	2	xk	xk	PROPN
ejpam-3747	66	3	=	=	PUNCT
ejpam-3747	66	4	y	y	PROPN
ejpam-3747	66	5	and	and	CCONJ
ejpam-3747	66	6	(	(	PUNCT
ejpam-3747	66	7	xn−1	xn−1	PROPN
ejpam-3747	66	8	,	,	PUNCT
ejpam-3747	66	9	xn	xn	PROPN
ejpam-3747	66	10	)	)	PUNCT
ejpam-3747	66	11	∈	∈	PROPN
ejpam-3747	66	12	e(g	e(g	PROPN
ejpam-3747	66	13	)	)	PUNCT
ejpam-3747	66	14	for	for	ADP
ejpam-3747	66	15	n	n	PRON
ejpam-3747	66	16	∈	∈	PROPN
ejpam-3747	66	17	{	{	PUNCT
ejpam-3747	66	18	1	1	NUM
ejpam-3747	66	19	,	,	PUNCT
ejpam-3747	66	20	2	2	NUM
ejpam-3747	66	21	,	,	PUNCT
ejpam-3747	66	22	.	.	PUNCT
ejpam-3747	66	23	.	.	PUNCT
ejpam-3747	66	24	.	.	PUNCT
ejpam-3747	67	1	,	,	PUNCT
ejpam-3747	67	2	k	k	X
ejpam-3747	67	3	}	}	PUNCT
ejpam-3747	67	4	.	.	PUNCT
ejpam-3747	68	1	a	a	DET
ejpam-3747	68	2	graph	graph	NOUN
ejpam-3747	68	3	g	g	NOUN
ejpam-3747	68	4	is	be	AUX
ejpam-3747	68	5	connected	connect	VERB
ejpam-3747	68	6	if	if	SCONJ
ejpam-3747	68	7	there	there	PRON
ejpam-3747	68	8	is	be	VERB
ejpam-3747	68	9	a	a	DET
ejpam-3747	68	10	path	path	NOUN
ejpam-3747	68	11	between	between	ADP
ejpam-3747	68	12	any	any	DET
ejpam-3747	68	13	two	two	NUM
ejpam-3747	68	14	vertices	vertex	NOUN
ejpam-3747	68	15	and	and	CCONJ
ejpam-3747	68	16	it	it	PRON
ejpam-3747	68	17	is	be	AUX
ejpam-3747	68	18	weakly	weakly	ADV
ejpam-3747	68	19	connected	connected	ADJ
ejpam-3747	68	20	if	if	SCONJ
ejpam-3747	68	21	g̃	g̃	PROPN
ejpam-3747	68	22	is	be	AUX
ejpam-3747	68	23	connected	connect	VERB
ejpam-3747	68	24	,	,	PUNCT
ejpam-3747	68	25	where	where	SCONJ
ejpam-3747	68	26	g̃	g̃	PROPN
ejpam-3747	68	27	denotes	denote	VERB
ejpam-3747	68	28	the	the	DET
ejpam-3747	68	29	undirected	undirected	ADJ
ejpam-3747	68	30	graph	graph	NOUN
ejpam-3747	68	31	obtained	obtain	VERB
ejpam-3747	68	32	from	from	ADP
ejpam-3747	68	33	g	g	NOUN
ejpam-3747	68	34	by	by	ADP
ejpam-3747	68	35	ignoring	ignore	VERB
ejpam-3747	68	36	the	the	DET
ejpam-3747	68	37	direction	direction	NOUN
ejpam-3747	68	38	of	of	ADP
ejpam-3747	68	39	edges	edge	NOUN
ejpam-3747	68	40	.	.	PUNCT
ejpam-3747	69	1	let	let	VERB
ejpam-3747	69	2	g−1	g−1	PROPN
ejpam-3747	69	3	be	be	AUX
ejpam-3747	69	4	the	the	DET
ejpam-3747	69	5	graph	graph	NOUN
ejpam-3747	69	6	obtained	obtain	VERB
ejpam-3747	69	7	from	from	ADP
ejpam-3747	69	8	g	g	NOUN
ejpam-3747	69	9	by	by	ADP
ejpam-3747	69	10	reversing	reverse	VERB
ejpam-3747	69	11	the	the	DET
ejpam-3747	69	12	direction	direction	NOUN
ejpam-3747	69	13	of	of	ADP
ejpam-3747	69	14	edges	edge	NOUN
ejpam-3747	69	15	(	(	PUNCT
ejpam-3747	69	16	the	the	DET
ejpam-3747	69	17	conversion	conversion	NOUN
ejpam-3747	69	18	of	of	ADP
ejpam-3747	69	19	the	the	DET
ejpam-3747	69	20	graph	graph	NOUN
ejpam-3747	69	21	g	g	NOUN
ejpam-3747	69	22	)	)	PUNCT
ejpam-3747	69	23	.	.	PUNCT
ejpam-3747	70	1	we	we	PRON
ejpam-3747	70	2	have	have	AUX
ejpam-3747	70	3	e(g−1	e(g−1	VERB
ejpam-3747	70	4	)	)	PUNCT
ejpam-3747	71	1	=	=	PRON
ejpam-3747	71	2	{	{	PUNCT
ejpam-3747	71	3	(	(	PUNCT
ejpam-3747	71	4	x	x	NOUN
ejpam-3747	71	5	,	,	PUNCT
ejpam-3747	71	6	y	y	NOUN
ejpam-3747	71	7	)	)	PUNCT
ejpam-3747	71	8	∈	∈	PROPN
ejpam-3747	71	9	x	x	X
ejpam-3747	71	10	×x	×x	X
ejpam-3747	71	11	:	:	PUNCT
ejpam-3747	71	12	(	(	PUNCT
ejpam-3747	71	13	y	y	NOUN
ejpam-3747	71	14	,	,	PUNCT
ejpam-3747	71	15	x	x	NOUN
ejpam-3747	71	16	)	)	PUNCT
ejpam-3747	71	17	∈	∈	PROPN
ejpam-3747	71	18	e(g	e(g	PROPN
ejpam-3747	71	19	)	)	PUNCT
ejpam-3747	71	20	}	}	PUNCT
ejpam-3747	71	21	.	.	PUNCT
ejpam-3747	72	1	it	it	PRON
ejpam-3747	72	2	is	be	AUX
ejpam-3747	72	3	more	more	ADV
ejpam-3747	72	4	convenient	convenient	ADJ
ejpam-3747	72	5	to	to	PART
ejpam-3747	72	6	treat	treat	VERB
ejpam-3747	72	7	g̃	g̃	PROPN
ejpam-3747	72	8	as	as	ADP
ejpam-3747	72	9	a	a	DET
ejpam-3747	72	10	directed	direct	VERB
ejpam-3747	72	11	graph	graph	NOUN
ejpam-3747	72	12	for	for	ADP
ejpam-3747	72	13	which	which	PRON
ejpam-3747	72	14	the	the	DET
ejpam-3747	72	15	set	set	NOUN
ejpam-3747	72	16	of	of	ADP
ejpam-3747	72	17	edges	edge	NOUN
ejpam-3747	72	18	is	be	AUX
ejpam-3747	72	19	symmetric	symmetric	ADJ
ejpam-3747	72	20	,	,	PUNCT
ejpam-3747	72	21	then	then	ADV
ejpam-3747	72	22	e(g̃	e(g̃	PROPN
ejpam-3747	72	23	)	)	PUNCT
ejpam-3747	72	24	=	=	SYM
ejpam-3747	72	25	e(g	e(g	PROPN
ejpam-3747	72	26	)	)	PUNCT
ejpam-3747	72	27	∪	∪	ADP
ejpam-3747	72	28	e(g−1	e(g−1	PROPN
ejpam-3747	72	29	)	)	PUNCT
ejpam-3747	72	30	.	.	PUNCT
ejpam-3747	73	1	definition	definition	NOUN
ejpam-3747	73	2	3	3	NUM
ejpam-3747	73	3	.	.	PUNCT
ejpam-3747	74	1	[	[	X
ejpam-3747	74	2	1	1	X
ejpam-3747	74	3	]	]	PUNCT
ejpam-3747	74	4	let	let	VERB
ejpam-3747	74	5	a	a	PRON
ejpam-3747	74	6	and	and	CCONJ
ejpam-3747	74	7	b	b	NOUN
ejpam-3747	74	8	be	be	AUX
ejpam-3747	74	9	two	two	NUM
ejpam-3747	74	10	nonempty	nonempty	ADJ
ejpam-3747	74	11	subsets	subset	NOUN
ejpam-3747	74	12	of	of	ADP
ejpam-3747	74	13	x.	x.	NOUN
ejpam-3747	74	14	then	then	ADV
ejpam-3747	74	15	(	(	PUNCT
ejpam-3747	74	16	a	a	X
ejpam-3747	74	17	)	)	PUNCT
ejpam-3747	74	18	”	"	PUNCT
ejpam-3747	74	19	there	there	PRON
ejpam-3747	74	20	is	be	VERB
ejpam-3747	74	21	an	an	DET
ejpam-3747	74	22	edge	edge	NOUN
ejpam-3747	74	23	between	between	ADP
ejpam-3747	74	24	a	a	PRON
ejpam-3747	74	25	and	and	CCONJ
ejpam-3747	74	26	b	b	NOUN
ejpam-3747	74	27	”	"	PUNCT
ejpam-3747	74	28	,	,	PUNCT
ejpam-3747	74	29	means	mean	VERB
ejpam-3747	74	30	there	there	PRON
ejpam-3747	74	31	is	be	VERB
ejpam-3747	74	32	an	an	DET
ejpam-3747	74	33	edge	edge	NOUN
ejpam-3747	74	34	between	between	ADP
ejpam-3747	74	35	some	some	DET
ejpam-3747	74	36	a	a	DET
ejpam-3747	74	37	∈	∈	PROPN
ejpam-3747	74	38	a	a	PRON
ejpam-3747	74	39	and	and	CCONJ
ejpam-3747	74	40	b	b	NOUN
ejpam-3747	74	41	∈	∈	PROPN
ejpam-3747	74	42	b	b	PROPN
ejpam-3747	74	43	which	which	PRON
ejpam-3747	74	44	we	we	PRON
ejpam-3747	74	45	denote	denote	VERB
ejpam-3747	74	46	by	by	ADP
ejpam-3747	74	47	(	(	PUNCT
ejpam-3747	74	48	a	a	DET
ejpam-3747	74	49	,	,	PUNCT
ejpam-3747	74	50	b	b	NOUN
ejpam-3747	74	51	)	)	PUNCT
ejpam-3747	74	52	⊂	⊂	PROPN
ejpam-3747	74	53	e(g	e(g	PROPN
ejpam-3747	74	54	)	)	PUNCT
ejpam-3747	74	55	.	.	PUNCT
ejpam-3747	75	1	s.	s.	PROPN
ejpam-3747	75	2	benchabane	benchabane	PROPN
ejpam-3747	75	3	,	,	PUNCT
ejpam-3747	75	4	s.	s.	PROPN
ejpam-3747	75	5	djebali	djebali	PROPN
ejpam-3747	75	6	,	,	PUNCT
ejpam-3747	75	7	t.	t.	PROPN
ejpam-3747	75	8	nazir	nazir	PROPN
ejpam-3747	75	9	/	/	SYM
ejpam-3747	75	10	eur	eur	PROPN
ejpam-3747	75	11	.	.	PUNCT
ejpam-3747	76	1	j.	j.	PROPN
ejpam-3747	76	2	pure	pure	PROPN
ejpam-3747	76	3	appl	appl	PROPN
ejpam-3747	76	4	.	.	PROPN
ejpam-3747	76	5	math	math	PROPN
ejpam-3747	76	6	,	,	PUNCT
ejpam-3747	76	7	13	13	NUM
ejpam-3747	76	8	(	(	PUNCT
ejpam-3747	76	9	5	5	NUM
ejpam-3747	76	10	)	)	PUNCT
ejpam-3747	76	11	(	(	PUNCT
ejpam-3747	76	12	2020	2020	NUM
ejpam-3747	76	13	)	)	PUNCT
ejpam-3747	76	14	,	,	PUNCT
ejpam-3747	76	15	1072	1072	NUM
ejpam-3747	76	16	-	-	SYM
ejpam-3747	76	17	1087	1087	NUM
ejpam-3747	76	18	1075	1075	NUM
ejpam-3747	76	19	(	(	PUNCT
ejpam-3747	76	20	b	b	NOUN
ejpam-3747	76	21	)	)	PUNCT
ejpam-3747	76	22	”	"	PUNCT
ejpam-3747	76	23	there	there	PRON
ejpam-3747	76	24	is	be	VERB
ejpam-3747	76	25	a	a	DET
ejpam-3747	76	26	path	path	NOUN
ejpam-3747	76	27	between	between	ADP
ejpam-3747	76	28	a	a	PRON
ejpam-3747	76	29	and	and	CCONJ
ejpam-3747	76	30	b	b	NOUN
ejpam-3747	76	31	”	"	PUNCT
ejpam-3747	76	32	,	,	PUNCT
ejpam-3747	76	33	means	mean	VERB
ejpam-3747	76	34	that	that	SCONJ
ejpam-3747	76	35	there	there	PRON
ejpam-3747	76	36	is	be	VERB
ejpam-3747	76	37	a	a	DET
ejpam-3747	76	38	path	path	NOUN
ejpam-3747	76	39	between	between	ADP
ejpam-3747	76	40	some	some	DET
ejpam-3747	76	41	a	a	DET
ejpam-3747	76	42	∈	∈	PROPN
ejpam-3747	76	43	a	a	PRON
ejpam-3747	76	44	and	and	CCONJ
ejpam-3747	76	45	b	b	PROPN
ejpam-3747	76	46	∈	∈	PROPN
ejpam-3747	76	47	b.	b.	PROPN
ejpam-3747	76	48	in	in	ADP
ejpam-3747	76	49	cb(x	cb(x	NUM
ejpam-3747	76	50	)	)	PUNCT
ejpam-3747	76	51	,	,	PUNCT
ejpam-3747	76	52	we	we	PRON
ejpam-3747	76	53	define	define	VERB
ejpam-3747	76	54	a	a	DET
ejpam-3747	76	55	relation	relation	NOUN
ejpam-3747	76	56	r	r	NOUN
ejpam-3747	76	57	in	in	ADP
ejpam-3747	76	58	the	the	DET
ejpam-3747	76	59	following	following	ADJ
ejpam-3747	76	60	way	way	NOUN
ejpam-3747	76	61	:	:	PUNCT
ejpam-3747	76	62	for	for	ADP
ejpam-3747	76	63	a	a	DET
ejpam-3747	76	64	,	,	PUNCT
ejpam-3747	76	65	b	b	X
ejpam-3747	76	66	∈	∈	PROPN
ejpam-3747	76	67	cb(x	cb(x	NUM
ejpam-3747	76	68	)	)	PUNCT
ejpam-3747	76	69	,	,	PUNCT
ejpam-3747	76	70	arb	arb	VERB
ejpam-3747	76	71	if	if	SCONJ
ejpam-3747	76	72	and	and	CCONJ
ejpam-3747	76	73	only	only	ADV
ejpam-3747	76	74	if	if	SCONJ
ejpam-3747	76	75	there	there	PRON
ejpam-3747	76	76	is	be	VERB
ejpam-3747	76	77	a	a	DET
ejpam-3747	76	78	path	path	NOUN
ejpam-3747	76	79	between	between	ADP
ejpam-3747	76	80	a	a	PRON
ejpam-3747	76	81	and	and	CCONJ
ejpam-3747	76	82	b.	b.	NOUN
ejpam-3747	77	1	we	we	PRON
ejpam-3747	77	2	say	say	VERB
ejpam-3747	77	3	that	that	SCONJ
ejpam-3747	77	4	the	the	DET
ejpam-3747	77	5	relation	relation	NOUN
ejpam-3747	77	6	r	r	NOUN
ejpam-3747	77	7	on	on	ADP
ejpam-3747	77	8	cb(x	cb(x	NUM
ejpam-3747	77	9	)	)	PUNCT
ejpam-3747	77	10	is	be	AUX
ejpam-3747	77	11	transitive	transitive	ADJ
ejpam-3747	77	12	if	if	SCONJ
ejpam-3747	77	13	there	there	PRON
ejpam-3747	77	14	is	be	VERB
ejpam-3747	77	15	a	a	DET
ejpam-3747	77	16	path	path	NOUN
ejpam-3747	77	17	between	between	ADP
ejpam-3747	77	18	a	a	PRON
ejpam-3747	77	19	and	and	CCONJ
ejpam-3747	77	20	b	b	NOUN
ejpam-3747	77	21	and	and	CCONJ
ejpam-3747	77	22	there	there	PRON
ejpam-3747	77	23	is	be	VERB
ejpam-3747	77	24	a	a	DET
ejpam-3747	77	25	path	path	NOUN
ejpam-3747	77	26	between	between	ADP
ejpam-3747	77	27	b	b	PROPN
ejpam-3747	77	28	and	and	CCONJ
ejpam-3747	77	29	c	c	NOUN
ejpam-3747	77	30	,	,	PUNCT
ejpam-3747	77	31	then	then	ADV
ejpam-3747	77	32	there	there	PRON
ejpam-3747	77	33	is	be	VERB
ejpam-3747	77	34	a	a	DET
ejpam-3747	77	35	path	path	NOUN
ejpam-3747	77	36	between	between	ADP
ejpam-3747	77	37	a	a	DET
ejpam-3747	77	38	and	and	CCONJ
ejpam-3747	77	39	c.	c.	NOUN
ejpam-3747	77	40	definition	definition	NOUN
ejpam-3747	77	41	4	4	X
ejpam-3747	77	42	.	.	PUNCT
ejpam-3747	78	1	let	let	VERB
ejpam-3747	78	2	s	s	PRON
ejpam-3747	78	3	:	:	PUNCT
ejpam-3747	78	4	cb(x)→	cb(x)→	VERB
ejpam-3747	78	5	cb(x	cb(x	NUM
ejpam-3747	78	6	)	)	PUNCT
ejpam-3747	78	7	be	be	AUX
ejpam-3747	78	8	a	a	DET
ejpam-3747	78	9	multivalued	multivalue	VERB
ejpam-3747	78	10	mapping	mapping	NOUN
ejpam-3747	78	11	.	.	PUNCT
ejpam-3747	79	1	the	the	DET
ejpam-3747	79	2	set	set	NOUN
ejpam-3747	79	3	a	a	DET
ejpam-3747	79	4	∈	∈	NOUN
ejpam-3747	79	5	cb(x	cb(x	NUM
ejpam-3747	79	6	)	)	PUNCT
ejpam-3747	79	7	is	be	AUX
ejpam-3747	79	8	said	say	VERB
ejpam-3747	79	9	to	to	PART
ejpam-3747	79	10	be	be	AUX
ejpam-3747	79	11	a	a	DET
ejpam-3747	79	12	fixed	fix	VERB
ejpam-3747	79	13	point	point	NOUN
ejpam-3747	79	14	of	of	ADP
ejpam-3747	79	15	s	s	PRON
ejpam-3747	79	16	if	if	SCONJ
ejpam-3747	79	17	s(a	s(a	NOUN
ejpam-3747	79	18	)	)	PUNCT
ejpam-3747	79	19	=	=	PUNCT
ejpam-3747	79	20	a.	a.	NOUN
ejpam-3747	79	21	the	the	DET
ejpam-3747	79	22	set	set	NOUN
ejpam-3747	79	23	of	of	ADP
ejpam-3747	79	24	all	all	DET
ejpam-3747	79	25	fixed	fix	VERB
ejpam-3747	79	26	points	point	NOUN
ejpam-3747	79	27	of	of	ADP
ejpam-3747	79	28	s	s	NOUN
ejpam-3747	79	29	is	be	AUX
ejpam-3747	79	30	denoted	denote	VERB
ejpam-3747	79	31	by	by	ADP
ejpam-3747	79	32	f	f	PROPN
ejpam-3747	79	33	(	(	PUNCT
ejpam-3747	79	34	s	s	NOUN
ejpam-3747	79	35	)	)	PUNCT
ejpam-3747	79	36	.	.	PUNCT
ejpam-3747	80	1	consider	consider	VERB
ejpam-3747	80	2	the	the	DET
ejpam-3747	80	3	set	set	NOUN
ejpam-3747	80	4	:	:	PUNCT
ejpam-3747	80	5	xs	xs	PROPN
ejpam-3747	81	1	:	:	PUNCT
ejpam-3747	81	2	=	=	SYM
ejpam-3747	81	3	{	{	PUNCT
ejpam-3747	81	4	u	u	NOUN
ejpam-3747	81	5	∈	∈	PROPN
ejpam-3747	81	6	cb(x	cb(x	NUM
ejpam-3747	81	7	)	)	PUNCT
ejpam-3747	81	8	:	:	PUNCT
ejpam-3747	81	9	(	(	PUNCT
ejpam-3747	81	10	u	u	NOUN
ejpam-3747	81	11	,	,	PUNCT
ejpam-3747	81	12	s(u	s(u	PROPN
ejpam-3747	81	13	)	)	PUNCT
ejpam-3747	81	14	)	)	PUNCT
ejpam-3747	82	1	⊂	⊂	PROPN
ejpam-3747	82	2	e(g	e(g	PROPN
ejpam-3747	82	3	)	)	PUNCT
ejpam-3747	82	4	}	}	PUNCT
ejpam-3747	82	5	.	.	PUNCT
ejpam-3747	83	1	a	a	DET
ejpam-3747	83	2	subset	subset	NOUN
ejpam-3747	83	3	a	a	PRON
ejpam-3747	83	4	of	of	ADP
ejpam-3747	83	5	cb(x	cb(x	NUM
ejpam-3747	83	6	)	)	PUNCT
ejpam-3747	83	7	is	be	AUX
ejpam-3747	83	8	said	say	VERB
ejpam-3747	83	9	to	to	PART
ejpam-3747	83	10	be	be	AUX
ejpam-3747	83	11	complete	complete	ADJ
ejpam-3747	83	12	if	if	SCONJ
ejpam-3747	83	13	for	for	ADP
ejpam-3747	83	14	any	any	DET
ejpam-3747	83	15	set	set	NOUN
ejpam-3747	83	16	x	x	NOUN
ejpam-3747	83	17	,	,	PUNCT
ejpam-3747	83	18	y	y	PROPN
ejpam-3747	83	19	∈	∈	PROPN
ejpam-3747	83	20	a	a	PRON
ejpam-3747	83	21	,	,	PUNCT
ejpam-3747	83	22	there	there	PRON
ejpam-3747	83	23	is	be	VERB
ejpam-3747	83	24	an	an	DET
ejpam-3747	83	25	edge	edge	NOUN
ejpam-3747	83	26	between	between	ADP
ejpam-3747	83	27	x	x	PROPN
ejpam-3747	83	28	and	and	CCONJ
ejpam-3747	83	29	y	y	PROPN
ejpam-3747	83	30	.	.	PUNCT
ejpam-3747	84	1	abbas	abbas	PROPN
ejpam-3747	84	2	et	et	PROPN
ejpam-3747	84	3	al	al	PROPN
ejpam-3747	84	4	.	.	PUNCT
ejpam-3747	85	1	[	[	X
ejpam-3747	85	2	1	1	X
ejpam-3747	85	3	]	]	PUNCT
ejpam-3747	85	4	have	have	AUX
ejpam-3747	85	5	used	use	VERB
ejpam-3747	85	6	the	the	DET
ejpam-3747	85	7	following	follow	VERB
ejpam-3747	85	8	property	property	NOUN
ejpam-3747	85	9	:	:	PUNCT
ejpam-3747	85	10	definition	definition	NOUN
ejpam-3747	85	11	5	5	NUM
ejpam-3747	85	12	.	.	PUNCT
ejpam-3747	86	1	a	a	DET
ejpam-3747	86	2	graph	graph	NOUN
ejpam-3747	86	3	g	g	NOUN
ejpam-3747	86	4	is	be	AUX
ejpam-3747	86	5	said	say	VERB
ejpam-3747	86	6	to	to	PART
ejpam-3747	86	7	have	have	VERB
ejpam-3747	86	8	property	property	NOUN
ejpam-3747	86	9	(	(	PUNCT
ejpam-3747	86	10	p	p	NOUN
ejpam-3747	86	11	?	?	PUNCT
ejpam-3747	86	12	)	)	PUNCT
ejpam-3747	86	13	if	if	SCONJ
ejpam-3747	86	14	for	for	ADP
ejpam-3747	86	15	any	any	DET
ejpam-3747	86	16	sequence	sequence	NOUN
ejpam-3747	86	17	(	(	PUNCT
ejpam-3747	86	18	xn)n	xn)n	PROPN
ejpam-3747	86	19	in	in	ADP
ejpam-3747	86	20	cb(x	cb(x	NUM
ejpam-3747	86	21	)	)	PUNCT
ejpam-3747	86	22	with	with	ADP
ejpam-3747	86	23	xn	xn	PROPN
ejpam-3747	86	24	→	→	SYM
ejpam-3747	86	25	x	x	SYM
ejpam-3747	86	26	,	,	PUNCT
ejpam-3747	86	27	as	as	SCONJ
ejpam-3747	86	28	n	n	X
ejpam-3747	86	29	→	→	SYM
ejpam-3747	86	30	∞	∞	PROPN
ejpam-3747	86	31	,	,	PUNCT
ejpam-3747	86	32	the	the	DET
ejpam-3747	86	33	existence	existence	NOUN
ejpam-3747	86	34	of	of	ADP
ejpam-3747	86	35	an	an	DET
ejpam-3747	86	36	edge	edge	NOUN
ejpam-3747	86	37	between	between	ADP
ejpam-3747	86	38	xn	xn	PROPN
ejpam-3747	86	39	and	and	CCONJ
ejpam-3747	86	40	xn+1	xn+1	PROPN
ejpam-3747	86	41	for	for	ADP
ejpam-3747	86	42	n	n	PRON
ejpam-3747	86	43	∈	∈	NOUN
ejpam-3747	86	44	n	n	NOUN
ejpam-3747	86	45	implies	imply	VERB
ejpam-3747	86	46	the	the	DET
ejpam-3747	86	47	existence	existence	NOUN
ejpam-3747	86	48	of	of	ADP
ejpam-3747	86	49	a	a	DET
ejpam-3747	86	50	subsequence	subsequence	NOUN
ejpam-3747	86	51	(	(	PUNCT
ejpam-3747	86	52	xnk	xnk	PROPN
ejpam-3747	86	53	)	)	PUNCT
ejpam-3747	87	1	k	k	PROPN
ejpam-3747	87	2	of	of	ADP
ejpam-3747	87	3	(	(	PUNCT
ejpam-3747	87	4	xn	xn	PROPN
ejpam-3747	87	5	)	)	PUNCT
ejpam-3747	87	6	with	with	ADP
ejpam-3747	87	7	an	an	DET
ejpam-3747	87	8	edge	edge	NOUN
ejpam-3747	87	9	between	between	ADP
ejpam-3747	87	10	xnk	xnk	PROPN
ejpam-3747	87	11	and	and	CCONJ
ejpam-3747	87	12	x	x	NOUN
ejpam-3747	87	13	,	,	PUNCT
ejpam-3747	87	14	for	for	ADP
ejpam-3747	87	15	k	k	PROPN
ejpam-3747	87	16	∈	∈	PROPN
ejpam-3747	87	17	n.	n.	NOUN
ejpam-3747	87	18	then	then	ADV
ejpam-3747	87	19	the	the	DET
ejpam-3747	87	20	authors	author	NOUN
ejpam-3747	87	21	of	of	ADP
ejpam-3747	87	22	[	[	X
ejpam-3747	87	23	1	1	NUM
ejpam-3747	87	24	]	]	PUNCT
ejpam-3747	87	25	obtained	obtain	VERB
ejpam-3747	87	26	some	some	DET
ejpam-3747	87	27	fixed	fix	VERB
ejpam-3747	87	28	point	point	NOUN
ejpam-3747	87	29	results	result	NOUN
ejpam-3747	87	30	for	for	ADP
ejpam-3747	87	31	multivalued	multivalue	VERB
ejpam-3747	87	32	self	self	NOUN
ejpam-3747	87	33	mappings	mapping	NOUN
ejpam-3747	87	34	on	on	ADP
ejpam-3747	87	35	cb(x	cb(x	ADJ
ejpam-3747	87	36	)	)	PUNCT
ejpam-3747	87	37	satisfying	satisfy	VERB
ejpam-3747	87	38	certain	certain	ADJ
ejpam-3747	87	39	graph	graph	NOUN
ejpam-3747	87	40	contraction	contraction	NOUN
ejpam-3747	87	41	conditions	condition	NOUN
ejpam-3747	87	42	according	accord	VERB
ejpam-3747	87	43	to	to	ADP
ejpam-3747	87	44	the	the	DET
ejpam-3747	87	45	following	follow	VERB
ejpam-3747	87	46	definition	definition	NOUN
ejpam-3747	87	47	.	.	PUNCT
ejpam-3747	88	1	definition	definition	NOUN
ejpam-3747	88	2	6	6	NUM
ejpam-3747	88	3	.	.	PUNCT
ejpam-3747	89	1	let	let	AUX
ejpam-3747	89	2	t	t	NOUN
ejpam-3747	89	3	:	:	PUNCT
ejpam-3747	89	4	cb(x	cb(x	NUM
ejpam-3747	89	5	)	)	PUNCT
ejpam-3747	89	6	→	→	PUNCT
ejpam-3747	89	7	cb(x	cb(x	NUM
ejpam-3747	89	8	)	)	PUNCT
ejpam-3747	89	9	be	be	AUX
ejpam-3747	89	10	a	a	DET
ejpam-3747	89	11	set	set	NOUN
ejpam-3747	89	12	-	-	PUNCT
ejpam-3747	89	13	valued	value	VERB
ejpam-3747	89	14	mapping	mapping	NOUN
ejpam-3747	89	15	.	.	PUNCT
ejpam-3747	90	1	the	the	DET
ejpam-3747	90	2	mapping	mapping	NOUN
ejpam-3747	90	3	t	t	PROPN
ejpam-3747	90	4	is	be	AUX
ejpam-3747	90	5	said	say	VERB
ejpam-3747	90	6	to	to	PART
ejpam-3747	90	7	be	be	AUX
ejpam-3747	90	8	a	a	DET
ejpam-3747	90	9	graph	graph	NOUN
ejpam-3747	90	10	φ	φ	NOUN
ejpam-3747	90	11	-	-	NOUN
ejpam-3747	90	12	contraction	contraction	NOUN
ejpam-3747	90	13	if	if	SCONJ
ejpam-3747	90	14	the	the	DET
ejpam-3747	90	15	following	follow	VERB
ejpam-3747	90	16	conditions	condition	NOUN
ejpam-3747	90	17	hold	hold	VERB
ejpam-3747	90	18	:	:	PUNCT
ejpam-3747	90	19	(	(	PUNCT
ejpam-3747	90	20	i	i	NOUN
ejpam-3747	90	21	)	)	PUNCT
ejpam-3747	90	22	there	there	PRON
ejpam-3747	90	23	is	be	VERB
ejpam-3747	90	24	an	an	DET
ejpam-3747	90	25	edge	edge	NOUN
ejpam-3747	90	26	between	between	ADP
ejpam-3747	90	27	a	a	PRON
ejpam-3747	90	28	and	and	CCONJ
ejpam-3747	90	29	b	b	NOUN
ejpam-3747	90	30	implies	imply	VERB
ejpam-3747	90	31	there	there	PRON
ejpam-3747	90	32	is	be	VERB
ejpam-3747	90	33	an	an	DET
ejpam-3747	90	34	edge	edge	NOUN
ejpam-3747	90	35	between	between	ADP
ejpam-3747	90	36	t	t	PROPN
ejpam-3747	90	37	(	(	PUNCT
ejpam-3747	90	38	a	a	NOUN
ejpam-3747	90	39	)	)	PUNCT
ejpam-3747	90	40	and	and	CCONJ
ejpam-3747	90	41	t	t	PROPN
ejpam-3747	90	42	(	(	PUNCT
ejpam-3747	90	43	b	b	NOUN
ejpam-3747	90	44	)	)	PUNCT
ejpam-3747	90	45	for	for	ADP
ejpam-3747	90	46	all	all	DET
ejpam-3747	90	47	a	a	DET
ejpam-3747	90	48	,	,	PUNCT
ejpam-3747	90	49	b	b	X
ejpam-3747	90	50	∈	∈	PROPN
ejpam-3747	90	51	cb(x	cb(x	NUM
ejpam-3747	90	52	)	)	PUNCT
ejpam-3747	90	53	.	.	PUNCT
ejpam-3747	91	1	(	(	PUNCT
ejpam-3747	91	2	ii	ii	NOUN
ejpam-3747	91	3	)	)	PUNCT
ejpam-3747	91	4	there	there	PRON
ejpam-3747	91	5	is	be	VERB
ejpam-3747	91	6	a	a	DET
ejpam-3747	91	7	path	path	NOUN
ejpam-3747	91	8	between	between	ADP
ejpam-3747	91	9	a	a	DET
ejpam-3747	91	10	and	and	CCONJ
ejpam-3747	91	11	b	b	NOUN
ejpam-3747	91	12	implies	imply	VERB
ejpam-3747	91	13	there	there	PRON
ejpam-3747	91	14	is	be	VERB
ejpam-3747	91	15	a	a	DET
ejpam-3747	91	16	path	path	NOUN
ejpam-3747	91	17	between	between	ADP
ejpam-3747	91	18	t	t	PROPN
ejpam-3747	91	19	(	(	PUNCT
ejpam-3747	91	20	a	a	NOUN
ejpam-3747	91	21	)	)	PUNCT
ejpam-3747	91	22	and	and	CCONJ
ejpam-3747	91	23	t	t	PROPN
ejpam-3747	91	24	(	(	PUNCT
ejpam-3747	91	25	b	b	NOUN
ejpam-3747	91	26	)	)	PUNCT
ejpam-3747	91	27	for	for	ADP
ejpam-3747	91	28	all	all	DET
ejpam-3747	91	29	a	a	DET
ejpam-3747	91	30	,	,	PUNCT
ejpam-3747	91	31	b	b	X
ejpam-3747	91	32	∈	∈	X
ejpam-3747	91	33	cb(x	cb(x	NUM
ejpam-3747	91	34	)	)	PUNCT
ejpam-3747	91	35	(	(	PUNCT
ejpam-3747	91	36	iii	iii	X
ejpam-3747	91	37	)	)	PUNCT
ejpam-3747	91	38	there	there	PRON
ejpam-3747	91	39	exists	exist	VERB
ejpam-3747	91	40	an	an	DET
ejpam-3747	91	41	upper	upper	ADJ
ejpam-3747	91	42	semi	semi	ADJ
ejpam-3747	91	43	-	-	ADJ
ejpam-3747	91	44	continuous	continuous	ADJ
ejpam-3747	91	45	and	and	CCONJ
ejpam-3747	91	46	nondecreasing	nondecreasing	ADJ
ejpam-3747	91	47	function	function	NOUN
ejpam-3747	91	48	φ	φ	NOUN
ejpam-3747	91	49	:	:	PUNCT
ejpam-3747	91	50	r+	r+	NOUN
ejpam-3747	91	51	→	→	SYM
ejpam-3747	91	52	r+	r+	NOUN
ejpam-3747	91	53	with	with	ADP
ejpam-3747	91	54	φ(t	φ(t	NOUN
ejpam-3747	91	55	)	)	PUNCT
ejpam-3747	91	56	<	<	X
ejpam-3747	91	57	t	t	PROPN
ejpam-3747	91	58	for	for	ADP
ejpam-3747	91	59	each	each	DET
ejpam-3747	91	60	t	t	PROPN
ejpam-3747	91	61	>	>	X
ejpam-3747	91	62	0	0	NUM
ejpam-3747	91	63	such	such	ADJ
ejpam-3747	91	64	that	that	SCONJ
ejpam-3747	91	65	there	there	PRON
ejpam-3747	91	66	is	be	VERB
ejpam-3747	91	67	an	an	DET
ejpam-3747	91	68	edge	edge	NOUN
ejpam-3747	91	69	between	between	ADP
ejpam-3747	91	70	a	a	PRON
ejpam-3747	91	71	and	and	CCONJ
ejpam-3747	91	72	b	b	NOUN
ejpam-3747	91	73	implies	imply	VERB
ejpam-3747	91	74	h(t	h(t	PROPN
ejpam-3747	91	75	(	(	PUNCT
ejpam-3747	91	76	a	a	NOUN
ejpam-3747	91	77	)	)	PUNCT
ejpam-3747	91	78	,	,	PUNCT
ejpam-3747	91	79	t	t	PROPN
ejpam-3747	91	80	(	(	PUNCT
ejpam-3747	91	81	b	b	NOUN
ejpam-3747	91	82	)	)	PUNCT
ejpam-3747	91	83	)	)	PUNCT
ejpam-3747	92	1	≤	≤	PROPN
ejpam-3747	92	2	φ(h(a	φ(h(a	PROPN
ejpam-3747	92	3	,	,	PUNCT
ejpam-3747	92	4	b	b	NOUN
ejpam-3747	92	5	)	)	PUNCT
ejpam-3747	92	6	)	)	PUNCT
ejpam-3747	92	7	,	,	PUNCT
ejpam-3747	92	8	for	for	ADP
ejpam-3747	92	9	all	all	DET
ejpam-3747	92	10	a	a	DET
ejpam-3747	92	11	,	,	PUNCT
ejpam-3747	92	12	b	b	X
ejpam-3747	92	13	∈	∈	PROPN
ejpam-3747	92	14	cb(x	cb(x	NUM
ejpam-3747	92	15	)	)	PUNCT
ejpam-3747	92	16	.	.	PUNCT
ejpam-3747	93	1	then	then	ADV
ejpam-3747	93	2	they	they	PRON
ejpam-3747	93	3	have	have	AUX
ejpam-3747	93	4	established	establish	VERB
ejpam-3747	93	5	theorem	theorem	NOUN
ejpam-3747	93	6	2	2	NUM
ejpam-3747	93	7	.	.	PUNCT
ejpam-3747	94	1	let	let	AUX
ejpam-3747	94	2	(	(	PUNCT
ejpam-3747	94	3	x	x	NOUN
ejpam-3747	94	4	,	,	PUNCT
ejpam-3747	94	5	d	d	NOUN
ejpam-3747	94	6	)	)	PUNCT
ejpam-3747	94	7	be	be	AUX
ejpam-3747	94	8	a	a	DET
ejpam-3747	94	9	complete	complete	ADJ
ejpam-3747	94	10	metric	metric	ADJ
ejpam-3747	94	11	space	space	NOUN
ejpam-3747	94	12	endowed	endow	VERB
ejpam-3747	94	13	with	with	ADP
ejpam-3747	94	14	a	a	DET
ejpam-3747	94	15	directed	direct	VERB
ejpam-3747	94	16	graph	graph	NOUN
ejpam-3747	94	17	g	g	ADP
ejpam-3747	94	18	such	such	DET
ejpam-3747	94	19	that	that	DET
ejpam-3747	94	20	v	v	NOUN
ejpam-3747	94	21	(	(	PUNCT
ejpam-3747	94	22	g	g	NOUN
ejpam-3747	94	23	)	)	PUNCT
ejpam-3747	94	24	=	=	SYM
ejpam-3747	95	1	x	x	PROPN
ejpam-3747	95	2	and	and	CCONJ
ejpam-3747	95	3	∆	∆	PROPN
ejpam-3747	96	1	⊂	⊂	PROPN
ejpam-3747	96	2	e(g	e(g	PROPN
ejpam-3747	96	3	)	)	PUNCT
ejpam-3747	96	4	.	.	PUNCT
ejpam-3747	97	1	if	if	SCONJ
ejpam-3747	97	2	t	t	NOUN
ejpam-3747	97	3	:	:	PUNCT
ejpam-3747	97	4	cb(x)→	cb(x)→	VERB
ejpam-3747	97	5	cb(x	cb(x	NUM
ejpam-3747	97	6	)	)	PUNCT
ejpam-3747	97	7	is	be	AUX
ejpam-3747	97	8	a	a	DET
ejpam-3747	97	9	graph	graph	NOUN
ejpam-3747	97	10	φ	φ	NUM
ejpam-3747	97	11	-	-	NOUN
ejpam-3747	97	12	contraction	contraction	NOUN
ejpam-3747	97	13	mapping	mapping	NOUN
ejpam-3747	97	14	such	such	ADJ
ejpam-3747	97	15	that	that	SCONJ
ejpam-3747	97	16	the	the	DET
ejpam-3747	97	17	relation	relation	NOUN
ejpam-3747	97	18	r	r	NOUN
ejpam-3747	97	19	on	on	ADP
ejpam-3747	97	20	cb(x	cb(x	NUM
ejpam-3747	97	21	)	)	PUNCT
ejpam-3747	97	22	is	be	AUX
ejpam-3747	97	23	transitive	transitive	ADJ
ejpam-3747	97	24	,	,	PUNCT
ejpam-3747	97	25	then	then	ADV
ejpam-3747	97	26	the	the	DET
ejpam-3747	97	27	following	following	ADJ
ejpam-3747	97	28	statements	statement	NOUN
ejpam-3747	97	29	hold	hold	VERB
ejpam-3747	97	30	:	:	PUNCT
ejpam-3747	97	31	(	(	PUNCT
ejpam-3747	97	32	i	i	NOUN
ejpam-3747	97	33	)	)	PUNCT
ejpam-3747	97	34	if	if	SCONJ
ejpam-3747	97	35	f	f	PROPN
ejpam-3747	97	36	(	(	PUNCT
ejpam-3747	97	37	t	t	PROPN
ejpam-3747	97	38	)	)	PUNCT
ejpam-3747	97	39	is	be	AUX
ejpam-3747	97	40	complete	complete	ADJ
ejpam-3747	97	41	,	,	PUNCT
ejpam-3747	97	42	then	then	ADV
ejpam-3747	97	43	the	the	DET
ejpam-3747	97	44	pompeiu	pompeiu	NOUN
ejpam-3747	97	45	-	-	PUNCT
ejpam-3747	97	46	hausdorff	hausdorff	NOUN
ejpam-3747	97	47	weight	weight	NOUN
ejpam-3747	97	48	assigned	assign	VERB
ejpam-3747	97	49	to	to	ADP
ejpam-3747	97	50	the	the	DET
ejpam-3747	97	51	u	u	NOUN
ejpam-3747	97	52	,	,	PUNCT
ejpam-3747	97	53	v	v	PROPN
ejpam-3747	97	54	∈	∈	PROPN
ejpam-3747	97	55	f	f	X
ejpam-3747	97	56	(	(	PUNCT
ejpam-3747	97	57	t	t	PROPN
ejpam-3747	97	58	)	)	PUNCT
ejpam-3747	97	59	is	be	AUX
ejpam-3747	97	60	0	0	NUM
ejpam-3747	97	61	.	.	PUNCT
ejpam-3747	98	1	(	(	PUNCT
ejpam-3747	98	2	ii	ii	PROPN
ejpam-3747	98	3	)	)	PUNCT
ejpam-3747	98	4	xt	xt	PROPN
ejpam-3747	99	1	6=	6=	ADP
ejpam-3747	99	2	∅	∅	NOUN
ejpam-3747	99	3	provided	provide	VERB
ejpam-3747	99	4	f	f	PROPN
ejpam-3747	99	5	(	(	PUNCT
ejpam-3747	99	6	t	t	PROPN
ejpam-3747	99	7	)	)	PUNCT
ejpam-3747	99	8	6=	6=	ADP
ejpam-3747	99	9	∅.	∅.	PROPN
ejpam-3747	99	10	(	(	PUNCT
ejpam-3747	99	11	iii	iii	NOUN
ejpam-3747	99	12	)	)	PUNCT
ejpam-3747	99	13	if	if	SCONJ
ejpam-3747	99	14	xt	xt	PROPN
ejpam-3747	99	15	6=	6=	ADP
ejpam-3747	99	16	∅	∅	NOUN
ejpam-3747	99	17	and	and	CCONJ
ejpam-3747	99	18	the	the	DET
ejpam-3747	99	19	weakly	weakly	ADJ
ejpam-3747	99	20	connected	connected	ADJ
ejpam-3747	99	21	graph	graph	NOUN
ejpam-3747	99	22	g	g	NOUN
ejpam-3747	99	23	satisfies	satisfy	VERB
ejpam-3747	99	24	the	the	DET
ejpam-3747	99	25	property	property	NOUN
ejpam-3747	99	26	(	(	PUNCT
ejpam-3747	99	27	p	p	NOUN
ejpam-3747	99	28	?	?	PUNCT
ejpam-3747	99	29	)	)	PUNCT
ejpam-3747	99	30	,	,	PUNCT
ejpam-3747	99	31	then	then	ADV
ejpam-3747	99	32	t	t	PROPN
ejpam-3747	99	33	has	have	VERB
ejpam-3747	99	34	a	a	DET
ejpam-3747	99	35	fixed	fix	VERB
ejpam-3747	99	36	point	point	NOUN
ejpam-3747	99	37	.	.	PUNCT
ejpam-3747	100	1	(	(	PUNCT
ejpam-3747	100	2	iv	iv	X
ejpam-3747	100	3	)	)	PUNCT
ejpam-3747	100	4	f	f	PROPN
ejpam-3747	100	5	(	(	PUNCT
ejpam-3747	100	6	t	t	PROPN
ejpam-3747	100	7	)	)	PUNCT
ejpam-3747	100	8	is	be	AUX
ejpam-3747	100	9	complete	complete	ADJ
ejpam-3747	100	10	if	if	SCONJ
ejpam-3747	101	1	and	and	CCONJ
ejpam-3747	101	2	only	only	ADV
ejpam-3747	101	3	if	if	SCONJ
ejpam-3747	101	4	f	f	PROPN
ejpam-3747	101	5	(	(	PUNCT
ejpam-3747	101	6	t	t	PROPN
ejpam-3747	101	7	)	)	PUNCT
ejpam-3747	101	8	is	be	AUX
ejpam-3747	101	9	a	a	DET
ejpam-3747	101	10	singleton	singleton	NOUN
ejpam-3747	101	11	.	.	PUNCT
ejpam-3747	102	1	s.	s.	PROPN
ejpam-3747	102	2	benchabane	benchabane	PROPN
ejpam-3747	102	3	,	,	PUNCT
ejpam-3747	102	4	s.	s.	PROPN
ejpam-3747	102	5	djebali	djebali	PROPN
ejpam-3747	102	6	,	,	PUNCT
ejpam-3747	102	7	t.	t.	PROPN
ejpam-3747	102	8	nazir	nazir	PROPN
ejpam-3747	102	9	/	/	SYM
ejpam-3747	102	10	eur	eur	PROPN
ejpam-3747	102	11	.	.	PUNCT
ejpam-3747	103	1	j.	j.	PROPN
ejpam-3747	103	2	pure	pure	PROPN
ejpam-3747	103	3	appl	appl	PROPN
ejpam-3747	103	4	.	.	PROPN
ejpam-3747	103	5	math	math	PROPN
ejpam-3747	103	6	,	,	PUNCT
ejpam-3747	103	7	13	13	NUM
ejpam-3747	103	8	(	(	PUNCT
ejpam-3747	103	9	5	5	NUM
ejpam-3747	103	10	)	)	PUNCT
ejpam-3747	103	11	(	(	PUNCT
ejpam-3747	103	12	2020	2020	NUM
ejpam-3747	103	13	)	)	PUNCT
ejpam-3747	103	14	,	,	PUNCT
ejpam-3747	103	15	1072	1072	NUM
ejpam-3747	103	16	-	-	SYM
ejpam-3747	103	17	1087	1087	NUM
ejpam-3747	103	18	1076	1076	NUM
ejpam-3747	103	19	2	2	NUM
ejpam-3747	103	20	.	.	PUNCT
ejpam-3747	103	21	main	main	ADJ
ejpam-3747	103	22	existence	existence	NOUN
ejpam-3747	103	23	result	result	VERB
ejpam-3747	103	24	we	we	PRON
ejpam-3747	103	25	first	first	ADV
ejpam-3747	103	26	introduce	introduce	VERB
ejpam-3747	103	27	definition	definition	NOUN
ejpam-3747	103	28	7	7	NUM
ejpam-3747	103	29	.	.	PUNCT
ejpam-3747	104	1	let	let	VERB
ejpam-3747	104	2	(	(	PUNCT
ejpam-3747	104	3	x	x	NOUN
ejpam-3747	104	4	,	,	PUNCT
ejpam-3747	104	5	d	d	NOUN
ejpam-3747	104	6	)	)	PUNCT
ejpam-3747	104	7	be	be	AUX
ejpam-3747	104	8	a	a	DET
ejpam-3747	104	9	metric	metric	ADJ
ejpam-3747	104	10	space	space	NOUN
ejpam-3747	104	11	endowed	endow	VERB
ejpam-3747	104	12	with	with	ADP
ejpam-3747	104	13	a	a	DET
ejpam-3747	104	14	directed	direct	VERB
ejpam-3747	104	15	graph	graph	NOUN
ejpam-3747	104	16	g	g	ADP
ejpam-3747	104	17	such	such	DET
ejpam-3747	104	18	that	that	DET
ejpam-3747	104	19	v	v	NOUN
ejpam-3747	104	20	(	(	PUNCT
ejpam-3747	104	21	g	g	NOUN
ejpam-3747	104	22	)	)	PUNCT
ejpam-3747	104	23	=	=	SYM
ejpam-3747	105	1	x	x	PROPN
ejpam-3747	105	2	and	and	CCONJ
ejpam-3747	105	3	∆	∆	PROPN
ejpam-3747	106	1	⊂	⊂	PROPN
ejpam-3747	106	2	e(g	e(g	PROPN
ejpam-3747	106	3	)	)	PUNCT
ejpam-3747	106	4	.	.	PUNCT
ejpam-3747	107	1	let	let	VERB
ejpam-3747	107	2	s	s	NOUN
ejpam-3747	107	3	,	,	PUNCT
ejpam-3747	107	4	t	t	PROPN
ejpam-3747	107	5	:	:	PUNCT
ejpam-3747	107	6	cb(x	cb(x	NUM
ejpam-3747	107	7	)	)	PUNCT
ejpam-3747	107	8	→	→	PUNCT
ejpam-3747	107	9	cb(x	cb(x	NUM
ejpam-3747	107	10	)	)	PUNCT
ejpam-3747	107	11	be	be	VERB
ejpam-3747	107	12	two	two	NUM
ejpam-3747	107	13	multivalued	multivalued	ADJ
ejpam-3747	107	14	mappings	mapping	NOUN
ejpam-3747	107	15	.	.	PUNCT
ejpam-3747	108	1	the	the	DET
ejpam-3747	108	2	pair	pair	NOUN
ejpam-3747	108	3	(	(	PUNCT
ejpam-3747	108	4	s	s	PROPN
ejpam-3747	108	5	,	,	PUNCT
ejpam-3747	108	6	t	t	PROPN
ejpam-3747	108	7	)	)	PUNCT
ejpam-3747	108	8	of	of	ADP
ejpam-3747	108	9	maps	map	NOUN
ejpam-3747	108	10	is	be	AUX
ejpam-3747	108	11	said	say	VERB
ejpam-3747	108	12	to	to	PART
ejpam-3747	108	13	be	be	AUX
ejpam-3747	108	14	graph	graph	NOUN
ejpam-3747	108	15	(	(	PUNCT
ejpam-3747	108	16	ψ	ψ	NOUN
ejpam-3747	108	17	,	,	PUNCT
ejpam-3747	108	18	φ)-weak	φ)-weak	VERB
ejpam-3747	108	19	contraction	contraction	NOUN
ejpam-3747	108	20	pair	pair	NOUN
ejpam-3747	108	21	if	if	SCONJ
ejpam-3747	108	22	(	(	PUNCT
ejpam-3747	108	23	i	i	NOUN
ejpam-3747	108	24	)	)	PUNCT
ejpam-3747	108	25	for	for	ADP
ejpam-3747	108	26	every	every	DET
ejpam-3747	108	27	u	u	NOUN
ejpam-3747	108	28	in	in	ADP
ejpam-3747	108	29	cb(x	cb(x	NUM
ejpam-3747	108	30	)	)	PUNCT
ejpam-3747	108	31	,	,	PUNCT
ejpam-3747	108	32	(	(	PUNCT
ejpam-3747	108	33	u	u	NOUN
ejpam-3747	108	34	,	,	PUNCT
ejpam-3747	108	35	s(u	s(u	PROPN
ejpam-3747	108	36	)	)	PUNCT
ejpam-3747	108	37	)	)	PUNCT
ejpam-3747	109	1	⊂	⊂	PROPN
ejpam-3747	109	2	e(g	e(g	PROPN
ejpam-3747	109	3	)	)	PUNCT
ejpam-3747	109	4	and	and	CCONJ
ejpam-3747	109	5	(	(	PUNCT
ejpam-3747	109	6	u	u	PROPN
ejpam-3747	109	7	,	,	PUNCT
ejpam-3747	109	8	t	t	PROPN
ejpam-3747	109	9	(	(	PUNCT
ejpam-3747	109	10	u	u	NOUN
ejpam-3747	109	11	)	)	PUNCT
ejpam-3747	109	12	)	)	PUNCT
ejpam-3747	110	1	⊂	⊂	PROPN
ejpam-3747	110	2	e(g	e(g	PROPN
ejpam-3747	110	3	)	)	PUNCT
ejpam-3747	110	4	,	,	PUNCT
ejpam-3747	110	5	(	(	PUNCT
ejpam-3747	110	6	ii	ii	NOUN
ejpam-3747	110	7	)	)	PUNCT
ejpam-3747	110	8	there	there	PRON
ejpam-3747	110	9	exists	exist	VERB
ejpam-3747	110	10	an	an	DET
ejpam-3747	110	11	nondecreasing	nondecreasing	ADJ
ejpam-3747	110	12	function	function	NOUN
ejpam-3747	110	13	φ	φ	NOUN
ejpam-3747	110	14	:	:	PUNCT
ejpam-3747	110	15	r+	r+	NOUN
ejpam-3747	110	16	→	→	SYM
ejpam-3747	110	17	r+	r+	NOUN
ejpam-3747	110	18	with	with	ADP
ejpam-3747	110	19	∑∞	∑∞	NOUN
ejpam-3747	110	20	i=0	i=0	PROPN
ejpam-3747	110	21	φ	φ	PROPN
ejpam-3747	110	22	i(t	i(t	PROPN
ejpam-3747	110	23	)	)	PUNCT
ejpam-3747	110	24	is	be	AUX
ejpam-3747	110	25	convergent	convergent	ADJ
ejpam-3747	110	26	for	for	ADP
ejpam-3747	110	27	all	all	DET
ejpam-3747	110	28	t	t	PROPN
ejpam-3747	110	29	>	>	X
ejpam-3747	110	30	0	0	PROPN
ejpam-3747	110	31	,	,	PUNCT
ejpam-3747	110	32	ϕ	ϕ	PROPN
ejpam-3747	110	33	∈	∈	PROPN
ejpam-3747	110	34	φ	φ	PROPN
ejpam-3747	110	35	,	,	PUNCT
ejpam-3747	110	36	ψ	ψ	PROPN
ejpam-3747	110	37	∈	∈	PROPN
ejpam-3747	110	38	ψ	ψ	NOUN
ejpam-3747	110	39	,	,	PUNCT
ejpam-3747	110	40	and	and	CCONJ
ejpam-3747	110	41	l	l	NOUN
ejpam-3747	110	42	≥	≥	NUM
ejpam-3747	110	43	0	0	NUM
ejpam-3747	110	44	such	such	ADJ
ejpam-3747	110	45	that	that	SCONJ
ejpam-3747	110	46	if	if	SCONJ
ejpam-3747	110	47	there	there	PRON
ejpam-3747	110	48	is	be	VERB
ejpam-3747	110	49	an	an	DET
ejpam-3747	110	50	edge	edge	NOUN
ejpam-3747	110	51	between	between	ADP
ejpam-3747	110	52	a	a	PRON
ejpam-3747	110	53	and	and	CCONJ
ejpam-3747	110	54	b	b	NOUN
ejpam-3747	110	55	with	with	ADP
ejpam-3747	110	56	s(a	s(a	PROPN
ejpam-3747	110	57	)	)	PUNCT
ejpam-3747	110	58	6=	6=	ADP
ejpam-3747	110	59	t	t	PROPN
ejpam-3747	110	60	(	(	PUNCT
ejpam-3747	110	61	b	b	NOUN
ejpam-3747	110	62	)	)	PUNCT
ejpam-3747	110	63	,	,	PUNCT
ejpam-3747	110	64	then	then	ADV
ejpam-3747	110	65	ψ	ψ	X
ejpam-3747	110	66	(	(	PUNCT
ejpam-3747	110	67	∫	∫	PROPN
ejpam-3747	110	68	h(s(a),t	h(s(a),t	PROPN
ejpam-3747	110	69	(	(	PUNCT
ejpam-3747	110	70	b	b	NOUN
ejpam-3747	110	71	)	)	PUNCT
ejpam-3747	110	72	)	)	PUNCT
ejpam-3747	110	73	0	0	NUM
ejpam-3747	111	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	111	2	)	)	PUNCT
ejpam-3747	112	1	≤	≤	PROPN
ejpam-3747	112	2	φ	φ	PROPN
ejpam-3747	112	3	(	(	PUNCT
ejpam-3747	112	4	ψ	ψ	X
ejpam-3747	112	5	(	(	PUNCT
ejpam-3747	112	6	∫	∫	PROPN
ejpam-3747	112	7	ms	ms	PROPN
ejpam-3747	112	8	,	,	PUNCT
ejpam-3747	112	9	t	t	PROPN
ejpam-3747	112	10	(	(	PUNCT
ejpam-3747	112	11	a	a	DET
ejpam-3747	112	12	,	,	PUNCT
ejpam-3747	112	13	b	b	NOUN
ejpam-3747	112	14	)	)	PUNCT
ejpam-3747	112	15	0	0	NUM
ejpam-3747	112	16	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	112	17	)	)	PUNCT
ejpam-3747	112	18	)	)	PUNCT
ejpam-3747	113	1	+	+	CCONJ
ejpam-3747	113	2	l	l	NOUN
ejpam-3747	113	3	∫	∫	PROPN
ejpam-3747	113	4	ns	ns	PROPN
ejpam-3747	113	5	,	,	PUNCT
ejpam-3747	113	6	t	t	PROPN
ejpam-3747	113	7	(	(	PUNCT
ejpam-3747	113	8	a	a	DET
ejpam-3747	113	9	,	,	PUNCT
ejpam-3747	113	10	b	b	NOUN
ejpam-3747	113	11	)	)	PUNCT
ejpam-3747	113	12	0	0	NUM
ejpam-3747	114	1	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-3747	114	2	,	,	PUNCT
ejpam-3747	114	3	where	where	SCONJ
ejpam-3747	114	4	ms	ms	PROPN
ejpam-3747	114	5	,	,	PUNCT
ejpam-3747	114	6	t	t	PROPN
ejpam-3747	114	7	(	(	PUNCT
ejpam-3747	114	8	a	a	DET
ejpam-3747	114	9	,	,	PUNCT
ejpam-3747	114	10	b	b	NOUN
ejpam-3747	114	11	)	)	PUNCT
ejpam-3747	114	12	=	=	SYM
ejpam-3747	114	13	max	max	PROPN
ejpam-3747	114	14	{	{	PUNCT
ejpam-3747	114	15	h(a	h(a	PROPN
ejpam-3747	114	16	,	,	PUNCT
ejpam-3747	114	17	b	b	NOUN
ejpam-3747	114	18	)	)	PUNCT
ejpam-3747	114	19	,	,	PUNCT
ejpam-3747	114	20	h(a	h(a	PROPN
ejpam-3747	114	21	,	,	PUNCT
ejpam-3747	114	22	s(a	s(a	PROPN
ejpam-3747	114	23	)	)	PUNCT
ejpam-3747	114	24	)	)	PUNCT
ejpam-3747	114	25	,	,	PUNCT
ejpam-3747	114	26	h(b	h(b	PROPN
ejpam-3747	114	27	,	,	PUNCT
ejpam-3747	114	28	t	t	PROPN
ejpam-3747	114	29	(	(	PUNCT
ejpam-3747	114	30	b	b	NOUN
ejpam-3747	114	31	)	)	PUNCT
ejpam-3747	114	32	)	)	PUNCT
ejpam-3747	114	33	,	,	PUNCT
ejpam-3747	114	34	h(a	h(a	PROPN
ejpam-3747	114	35	,	,	PUNCT
ejpam-3747	114	36	t	t	PROPN
ejpam-3747	114	37	(	(	PUNCT
ejpam-3747	114	38	b	b	NOUN
ejpam-3747	114	39	)	)	PUNCT
ejpam-3747	114	40	)	)	PUNCT
ejpam-3747	115	1	+	+	X
ejpam-3747	115	2	h(b	h(b	ADJ
ejpam-3747	115	3	,	,	PUNCT
ejpam-3747	115	4	s(a	s(a	PROPN
ejpam-3747	115	5	)	)	PUNCT
ejpam-3747	115	6	)	)	PUNCT
ejpam-3747	115	7	2	2	X
ejpam-3747	115	8	}	}	PUNCT
ejpam-3747	115	9	and	and	CCONJ
ejpam-3747	115	10	ns	ns	NUM
ejpam-3747	115	11	,	,	PUNCT
ejpam-3747	115	12	t	t	PROPN
ejpam-3747	115	13	(	(	PUNCT
ejpam-3747	115	14	a	a	DET
ejpam-3747	115	15	,	,	PUNCT
ejpam-3747	115	16	b	b	NOUN
ejpam-3747	115	17	)	)	PUNCT
ejpam-3747	115	18	=	=	SYM
ejpam-3747	115	19	min{h(a	min{h(a	PROPN
ejpam-3747	115	20	,	,	PUNCT
ejpam-3747	115	21	s(a	s(a	PROPN
ejpam-3747	115	22	)	)	PUNCT
ejpam-3747	115	23	)	)	PUNCT
ejpam-3747	115	24	,	,	PUNCT
ejpam-3747	115	25	h(b	h(b	PROPN
ejpam-3747	115	26	,	,	PUNCT
ejpam-3747	115	27	t	t	PROPN
ejpam-3747	115	28	(	(	PUNCT
ejpam-3747	115	29	b	b	NOUN
ejpam-3747	115	30	)	)	PUNCT
ejpam-3747	115	31	)	)	PUNCT
ejpam-3747	115	32	,	,	PUNCT
ejpam-3747	115	33	h(a	h(a	PROPN
ejpam-3747	115	34	,	,	PUNCT
ejpam-3747	115	35	t	t	PROPN
ejpam-3747	115	36	(	(	PUNCT
ejpam-3747	115	37	b	b	NOUN
ejpam-3747	115	38	)	)	PUNCT
ejpam-3747	115	39	)	)	PUNCT
ejpam-3747	115	40	,	,	PUNCT
ejpam-3747	115	41	h(b	h(b	PROPN
ejpam-3747	115	42	,	,	PUNCT
ejpam-3747	115	43	s(a	s(a	PROPN
ejpam-3747	115	44	)	)	PUNCT
ejpam-3747	115	45	)	)	PUNCT
ejpam-3747	115	46	}	}	PUNCT
ejpam-3747	115	47	.	.	PUNCT
ejpam-3747	116	1	remark	remark	NOUN
ejpam-3747	116	2	1	1	NUM
ejpam-3747	116	3	.	.	PUNCT
ejpam-3747	117	1	(	(	PUNCT
ejpam-3747	117	2	[	[	X
ejpam-3747	117	3	16	16	NUM
ejpam-3747	117	4	]	]	PUNCT
ejpam-3747	117	5	,	,	PUNCT
ejpam-3747	117	6	[	[	X
ejpam-3747	117	7	17	17	NUM
ejpam-3747	117	8	]	]	PUNCT
ejpam-3747	117	9	)	)	PUNCT
ejpam-3747	117	10	it	it	PRON
ejpam-3747	117	11	is	be	AUX
ejpam-3747	117	12	obvious	obvious	ADJ
ejpam-3747	117	13	that	that	SCONJ
ejpam-3747	117	14	for	for	ADP
ejpam-3747	117	15	each	each	DET
ejpam-3747	117	16	nondecreasing	nondecreasing	ADJ
ejpam-3747	117	17	function	function	NOUN
ejpam-3747	117	18	φ	φ	NOUN
ejpam-3747	117	19	:	:	PUNCT
ejpam-3747	117	20	r+	r+	NOUN
ejpam-3747	117	21	→	→	SYM
ejpam-3747	117	22	r+	r+	NOUN
ejpam-3747	117	23	with	with	ADP
ejpam-3747	117	24	∑∞	∑∞	NOUN
ejpam-3747	117	25	i=0	i=0	PROPN
ejpam-3747	117	26	φ	φ	PROPN
ejpam-3747	117	27	i(t	i(t	PROPN
ejpam-3747	117	28	)	)	PUNCT
ejpam-3747	117	29	is	be	AUX
ejpam-3747	117	30	convergent	convergent	ADJ
ejpam-3747	117	31	for	for	ADP
ejpam-3747	117	32	all	all	DET
ejpam-3747	117	33	t	t	PROPN
ejpam-3747	117	34	>	>	X
ejpam-3747	117	35	0	0	PROPN
ejpam-3747	117	36	,	,	PUNCT
ejpam-3747	117	37	the	the	DET
ejpam-3747	117	38	following	follow	VERB
ejpam-3747	117	39	statements	statement	NOUN
ejpam-3747	117	40	are	be	AUX
ejpam-3747	117	41	satisfied	satisfied	ADJ
ejpam-3747	117	42	:	:	PUNCT
ejpam-3747	117	43	(	(	PUNCT
ejpam-3747	117	44	i	i	NOUN
ejpam-3747	117	45	)	)	PUNCT
ejpam-3747	117	46	lim	lim	PROPN
ejpam-3747	117	47	i→∞	i→∞	VERB
ejpam-3747	117	48	φi(t	φi(t	NOUN
ejpam-3747	117	49	)	)	PUNCT
ejpam-3747	117	50	=	=	SYM
ejpam-3747	117	51	0	0	NUM
ejpam-3747	117	52	for	for	ADP
ejpam-3747	117	53	all	all	DET
ejpam-3747	117	54	t	t	PROPN
ejpam-3747	117	55	>	>	X
ejpam-3747	117	56	0	0	NUM
ejpam-3747	117	57	,	,	PUNCT
ejpam-3747	117	58	(	(	PUNCT
ejpam-3747	117	59	ii	ii	NOUN
ejpam-3747	117	60	)	)	PUNCT
ejpam-3747	117	61	φ(t	φ(t	PROPN
ejpam-3747	117	62	)	)	PUNCT
ejpam-3747	117	63	<	<	X
ejpam-3747	117	64	t	t	PROPN
ejpam-3747	117	65	for	for	ADP
ejpam-3747	117	66	all	all	DET
ejpam-3747	117	67	t	t	PROPN
ejpam-3747	117	68	>	>	X
ejpam-3747	117	69	0	0	NUM
ejpam-3747	117	70	,	,	PUNCT
ejpam-3747	117	71	(	(	PUNCT
ejpam-3747	117	72	iii	iii	NOUN
ejpam-3747	117	73	)	)	PUNCT
ejpam-3747	117	74	φ(0	φ(0	ADJ
ejpam-3747	117	75	)	)	PUNCT
ejpam-3747	117	76	=	=	SYM
ejpam-3747	117	77	0	0	X
ejpam-3747	117	78	.	.	PUNCT
ejpam-3747	117	79	remark	remark	NOUN
ejpam-3747	117	80	2	2	NUM
ejpam-3747	117	81	.	.	PUNCT
ejpam-3747	118	1	it	it	PRON
ejpam-3747	118	2	is	be	AUX
ejpam-3747	118	3	obvious	obvious	ADJ
ejpam-3747	118	4	that	that	SCONJ
ejpam-3747	118	5	if	if	SCONJ
ejpam-3747	118	6	a	a	DET
ejpam-3747	118	7	pair	pair	NOUN
ejpam-3747	118	8	(	(	PUNCT
ejpam-3747	118	9	s	s	PROPN
ejpam-3747	118	10	,	,	PUNCT
ejpam-3747	118	11	t	t	PROPN
ejpam-3747	118	12	)	)	PUNCT
ejpam-3747	118	13	of	of	ADP
ejpam-3747	118	14	multivalued	multivalue	VERB
ejpam-3747	118	15	mappings	mapping	NOUN
ejpam-3747	118	16	on	on	ADP
ejpam-3747	118	17	cb(x	cb(x	NOUN
ejpam-3747	118	18	)	)	PUNCT
ejpam-3747	118	19	is	be	AUX
ejpam-3747	118	20	a	a	DET
ejpam-3747	118	21	graph	graph	NOUN
ejpam-3747	118	22	(	(	PUNCT
ejpam-3747	118	23	ψ	ψ	NOUN
ejpam-3747	118	24	,	,	PUNCT
ejpam-3747	118	25	φ)-weak	φ)-weak	VERB
ejpam-3747	118	26	contraction	contraction	NOUN
ejpam-3747	118	27	for	for	ADP
ejpam-3747	118	28	a	a	DET
ejpam-3747	118	29	graph	graph	NOUN
ejpam-3747	118	30	g	g	NOUN
ejpam-3747	118	31	,	,	PUNCT
ejpam-3747	118	32	then	then	ADV
ejpam-3747	118	33	the	the	DET
ejpam-3747	118	34	pair	pair	NOUN
ejpam-3747	118	35	(	(	PUNCT
ejpam-3747	118	36	s	s	PROPN
ejpam-3747	118	37	,	,	PUNCT
ejpam-3747	118	38	t	t	PROPN
ejpam-3747	118	39	)	)	PUNCT
ejpam-3747	118	40	is	be	AUX
ejpam-3747	118	41	also	also	ADV
ejpam-3747	118	42	a	a	DET
ejpam-3747	118	43	graph	graph	NOUN
ejpam-3747	118	44	(	(	PUNCT
ejpam-3747	118	45	ψ	ψ	NOUN
ejpam-3747	118	46	,	,	PUNCT
ejpam-3747	118	47	φ)weak	φ)weak	NUM
ejpam-3747	118	48	contraction	contraction	NOUN
ejpam-3747	118	49	for	for	ADP
ejpam-3747	118	50	the	the	DET
ejpam-3747	118	51	graphs	graph	NOUN
ejpam-3747	118	52	g−1	g−1	PROPN
ejpam-3747	118	53	,	,	PUNCT
ejpam-3747	118	54	g̃	g̃	PROPN
ejpam-3747	118	55	,	,	PUNCT
ejpam-3747	118	56	and	and	CCONJ
ejpam-3747	118	57	g0	g0	NOUN
ejpam-3747	118	58	.	.	PUNCT
ejpam-3747	119	1	here	here	ADV
ejpam-3747	119	2	the	the	DET
ejpam-3747	119	3	graph	graph	NOUN
ejpam-3747	119	4	g0	g0	NOUN
ejpam-3747	119	5	is	be	AUX
ejpam-3747	119	6	defined	define	VERB
ejpam-3747	119	7	by	by	ADP
ejpam-3747	119	8	e(g0	e(g0	NOUN
ejpam-3747	119	9	)	)	PUNCT
ejpam-3747	120	1	=	=	SYM
ejpam-3747	120	2	x	x	SYM
ejpam-3747	120	3	×x	×x	X
ejpam-3747	120	4	.	.	PUNCT
ejpam-3747	121	1	we	we	PRON
ejpam-3747	121	2	are	be	AUX
ejpam-3747	121	3	in	in	ADP
ejpam-3747	121	4	position	position	NOUN
ejpam-3747	121	5	to	to	ADP
ejpam-3747	121	6	state	state	NOUN
ejpam-3747	121	7	and	and	CCONJ
ejpam-3747	121	8	prove	prove	VERB
ejpam-3747	121	9	an	an	DET
ejpam-3747	121	10	existence	existence	NOUN
ejpam-3747	121	11	result	result	NOUN
ejpam-3747	121	12	of	of	ADP
ejpam-3747	121	13	common	common	ADJ
ejpam-3747	121	14	fixed	fix	VERB
ejpam-3747	121	15	point	point	NOUN
ejpam-3747	121	16	results	result	NOUN
ejpam-3747	121	17	for	for	ADP
ejpam-3747	121	18	multivalued	multivalue	VERB
ejpam-3747	121	19	self	self	NOUN
ejpam-3747	121	20	maps	map	NOUN
ejpam-3747	121	21	on	on	ADP
ejpam-3747	121	22	cb(x	cb(x	ADJ
ejpam-3747	121	23	)	)	PUNCT
ejpam-3747	121	24	satisfying	satisfy	VERB
ejpam-3747	121	25	graph	graph	NOUN
ejpam-3747	121	26	(	(	PUNCT
ejpam-3747	121	27	ψ	ψ	NOUN
ejpam-3747	121	28	,	,	PUNCT
ejpam-3747	121	29	φ)-weak	φ)-weak	VERB
ejpam-3747	121	30	contraction	contraction	NOUN
ejpam-3747	121	31	conditions	condition	NOUN
ejpam-3747	121	32	on	on	ADP
ejpam-3747	121	33	a	a	DET
ejpam-3747	121	34	metric	metric	ADJ
ejpam-3747	121	35	space	space	NOUN
ejpam-3747	121	36	endowed	endow	VERB
ejpam-3747	121	37	with	with	ADP
ejpam-3747	121	38	a	a	DET
ejpam-3747	121	39	graph	graph	NOUN
ejpam-3747	121	40	.	.	PUNCT
ejpam-3747	122	1	theorem	theorem	NOUN
ejpam-3747	122	2	3	3	X
ejpam-3747	122	3	.	.	PUNCT
ejpam-3747	123	1	let	let	AUX
ejpam-3747	123	2	(	(	PUNCT
ejpam-3747	123	3	x	x	NOUN
ejpam-3747	123	4	,	,	PUNCT
ejpam-3747	123	5	d	d	NOUN
ejpam-3747	123	6	)	)	PUNCT
ejpam-3747	123	7	be	be	AUX
ejpam-3747	123	8	a	a	DET
ejpam-3747	123	9	metric	metric	ADJ
ejpam-3747	123	10	space	space	NOUN
ejpam-3747	123	11	endowed	endow	VERB
ejpam-3747	123	12	with	with	ADP
ejpam-3747	123	13	a	a	DET
ejpam-3747	123	14	directed	direct	VERB
ejpam-3747	123	15	graph	graph	NOUN
ejpam-3747	123	16	g	g	ADP
ejpam-3747	124	1	such	such	DET
ejpam-3747	124	2	that	that	PRON
ejpam-3747	124	3	v	v	NOUN
ejpam-3747	124	4	(	(	PUNCT
ejpam-3747	124	5	g	g	NOUN
ejpam-3747	124	6	)	)	PUNCT
ejpam-3747	124	7	=	=	SYM
ejpam-3747	124	8	x	x	NOUN
ejpam-3747	124	9	,	,	PUNCT
ejpam-3747	124	10	∆	∆	PROPN
ejpam-3747	124	11	⊂	⊂	PROPN
ejpam-3747	124	12	e(g	e(g	PROPN
ejpam-3747	124	13	)	)	PUNCT
ejpam-3747	124	14	,	,	PUNCT
ejpam-3747	124	15	the	the	DET
ejpam-3747	124	16	relation	relation	NOUN
ejpam-3747	124	17	r	r	NOUN
ejpam-3747	124	18	on	on	ADP
ejpam-3747	124	19	cb(x	cb(x	NUM
ejpam-3747	124	20	)	)	PUNCT
ejpam-3747	124	21	is	be	AUX
ejpam-3747	124	22	transitive	transitive	ADJ
ejpam-3747	124	23	,	,	PUNCT
ejpam-3747	124	24	and	and	CCONJ
ejpam-3747	124	25	s	s	PROPN
ejpam-3747	124	26	,	,	PUNCT
ejpam-3747	124	27	t	t	PROPN
ejpam-3747	124	28	:	:	PUNCT
ejpam-3747	124	29	cb(x	cb(x	NUM
ejpam-3747	124	30	)	)	PUNCT
ejpam-3747	124	31	→	→	PUNCT
ejpam-3747	124	32	cb(x	cb(x	NUM
ejpam-3747	124	33	)	)	PUNCT
ejpam-3747	125	1	is	be	AUX
ejpam-3747	125	2	a	a	DET
ejpam-3747	125	3	graph	graph	NOUN
ejpam-3747	125	4	(	(	PUNCT
ejpam-3747	125	5	ψ	ψ	NOUN
ejpam-3747	125	6	,	,	PUNCT
ejpam-3747	125	7	φ)-weak	φ)-weak	VERB
ejpam-3747	125	8	contraction	contraction	NOUN
ejpam-3747	125	9	pair	pair	NOUN
ejpam-3747	125	10	.	.	PUNCT
ejpam-3747	126	1	then	then	ADV
ejpam-3747	126	2	the	the	DET
ejpam-3747	126	3	following	following	ADJ
ejpam-3747	126	4	statements	statement	NOUN
ejpam-3747	126	5	hold	hold	VERB
ejpam-3747	126	6	:	:	PUNCT
ejpam-3747	126	7	(	(	PUNCT
ejpam-3747	126	8	i	i	NOUN
ejpam-3747	126	9	)	)	PUNCT
ejpam-3747	126	10	f	f	PROPN
ejpam-3747	126	11	(	(	PUNCT
ejpam-3747	126	12	s	s	NOUN
ejpam-3747	126	13	)	)	PUNCT
ejpam-3747	126	14	or	or	CCONJ
ejpam-3747	126	15	f	f	PROPN
ejpam-3747	126	16	(	(	PUNCT
ejpam-3747	126	17	t	t	PROPN
ejpam-3747	126	18	)	)	PUNCT
ejpam-3747	126	19	6=	6=	ADP
ejpam-3747	126	20	∅	∅	NOUN
ejpam-3747	126	21	if	if	SCONJ
ejpam-3747	127	1	and	and	CCONJ
ejpam-3747	127	2	only	only	ADV
ejpam-3747	127	3	if	if	SCONJ
ejpam-3747	127	4	f	f	PROPN
ejpam-3747	127	5	(	(	PUNCT
ejpam-3747	127	6	s	s	NOUN
ejpam-3747	127	7	)	)	PUNCT
ejpam-3747	127	8	∩	∩	ADJ
ejpam-3747	127	9	f	f	X
ejpam-3747	127	10	(	(	PUNCT
ejpam-3747	127	11	t	t	PROPN
ejpam-3747	127	12	)	)	PUNCT
ejpam-3747	127	13	6=	6=	ADP
ejpam-3747	127	14	∅.	∅.	PROPN
ejpam-3747	127	15	(	(	PUNCT
ejpam-3747	127	16	ii	ii	NOUN
ejpam-3747	127	17	)	)	PUNCT
ejpam-3747	127	18	f	f	PROPN
ejpam-3747	127	19	(	(	PUNCT
ejpam-3747	127	20	s	s	NOUN
ejpam-3747	127	21	)	)	PUNCT
ejpam-3747	127	22	∩	∩	ADJ
ejpam-3747	127	23	f	f	X
ejpam-3747	127	24	(	(	PUNCT
ejpam-3747	127	25	t	t	PROPN
ejpam-3747	127	26	)	)	PUNCT
ejpam-3747	127	27	6=	6=	ADP
ejpam-3747	127	28	∅	∅	NOUN
ejpam-3747	127	29	provided	provide	VERB
ejpam-3747	127	30	that	that	SCONJ
ejpam-3747	127	31	g	g	PROPN
ejpam-3747	127	32	is	be	AUX
ejpam-3747	127	33	weakly	weakly	ADV
ejpam-3747	127	34	connected	connected	ADJ
ejpam-3747	127	35	and	and	CCONJ
ejpam-3747	127	36	satisfies	satisfy	VERB
ejpam-3747	127	37	the	the	DET
ejpam-3747	127	38	property	property	NOUN
ejpam-3747	127	39	(	(	PUNCT
ejpam-3747	127	40	p	p	NOUN
ejpam-3747	127	41	?	?	PUNCT
ejpam-3747	127	42	)	)	PUNCT
ejpam-3747	127	43	.	.	PUNCT
ejpam-3747	128	1	(	(	PUNCT
ejpam-3747	128	2	iii	iii	X
ejpam-3747	128	3	)	)	PUNCT
ejpam-3747	128	4	if	if	SCONJ
ejpam-3747	128	5	f	f	PROPN
ejpam-3747	128	6	(	(	PUNCT
ejpam-3747	128	7	s	s	NOUN
ejpam-3747	128	8	)	)	PUNCT
ejpam-3747	128	9	∩	∩	ADJ
ejpam-3747	128	10	f	f	X
ejpam-3747	128	11	(	(	PUNCT
ejpam-3747	128	12	t	t	PROPN
ejpam-3747	128	13	)	)	PUNCT
ejpam-3747	128	14	is	be	AUX
ejpam-3747	128	15	complete	complete	ADJ
ejpam-3747	128	16	,	,	PUNCT
ejpam-3747	128	17	then	then	ADV
ejpam-3747	128	18	the	the	DET
ejpam-3747	128	19	pompeiu	pompeiu	NOUN
ejpam-3747	128	20	-	-	PUNCT
ejpam-3747	128	21	hausdorff	hausdorff	NOUN
ejpam-3747	128	22	weight	weight	NOUN
ejpam-3747	128	23	assigned	assign	VERB
ejpam-3747	128	24	to	to	ADP
ejpam-3747	128	25	u	u	NOUN
ejpam-3747	128	26	,	,	PUNCT
ejpam-3747	128	27	v	v	PROPN
ejpam-3747	128	28	∈	∈	X
ejpam-3747	128	29	f	f	X
ejpam-3747	128	30	(	(	PUNCT
ejpam-3747	128	31	s	s	NOUN
ejpam-3747	128	32	)	)	PUNCT
ejpam-3747	128	33	∩	∩	ADJ
ejpam-3747	128	34	f	f	X
ejpam-3747	128	35	(	(	PUNCT
ejpam-3747	128	36	t	t	PROPN
ejpam-3747	128	37	)	)	PUNCT
ejpam-3747	128	38	is	be	AUX
ejpam-3747	128	39	0	0	NUM
ejpam-3747	128	40	.	.	PUNCT
ejpam-3747	129	1	(	(	PUNCT
ejpam-3747	129	2	iv	iv	X
ejpam-3747	129	3	)	)	PUNCT
ejpam-3747	129	4	f	f	NOUN
ejpam-3747	129	5	(	(	PUNCT
ejpam-3747	129	6	s	s	NOUN
ejpam-3747	129	7	)	)	PUNCT
ejpam-3747	129	8	∩	∩	ADJ
ejpam-3747	129	9	f	f	X
ejpam-3747	129	10	(	(	PUNCT
ejpam-3747	129	11	t	t	PROPN
ejpam-3747	129	12	)	)	PUNCT
ejpam-3747	129	13	is	be	AUX
ejpam-3747	129	14	complete	complete	ADJ
ejpam-3747	129	15	if	if	SCONJ
ejpam-3747	130	1	and	and	CCONJ
ejpam-3747	130	2	only	only	ADV
ejpam-3747	130	3	if	if	SCONJ
ejpam-3747	130	4	f	f	PROPN
ejpam-3747	130	5	(	(	PUNCT
ejpam-3747	130	6	s	s	NOUN
ejpam-3747	130	7	)	)	PUNCT
ejpam-3747	130	8	∩	∩	ADJ
ejpam-3747	130	9	f	f	X
ejpam-3747	130	10	(	(	PUNCT
ejpam-3747	130	11	t	t	PROPN
ejpam-3747	130	12	)	)	PUNCT
ejpam-3747	130	13	is	be	AUX
ejpam-3747	130	14	a	a	DET
ejpam-3747	130	15	singleton	singleton	NOUN
ejpam-3747	130	16	.	.	PUNCT
ejpam-3747	131	1	s.	s.	PROPN
ejpam-3747	131	2	benchabane	benchabane	PROPN
ejpam-3747	131	3	,	,	PUNCT
ejpam-3747	131	4	s.	s.	PROPN
ejpam-3747	131	5	djebali	djebali	PROPN
ejpam-3747	131	6	,	,	PUNCT
ejpam-3747	131	7	t.	t.	PROPN
ejpam-3747	131	8	nazir	nazir	PROPN
ejpam-3747	131	9	/	/	SYM
ejpam-3747	131	10	eur	eur	PROPN
ejpam-3747	131	11	.	.	PUNCT
ejpam-3747	132	1	j.	j.	PROPN
ejpam-3747	132	2	pure	pure	PROPN
ejpam-3747	132	3	appl	appl	PROPN
ejpam-3747	132	4	.	.	PROPN
ejpam-3747	132	5	math	math	PROPN
ejpam-3747	132	6	,	,	PUNCT
ejpam-3747	132	7	13	13	NUM
ejpam-3747	132	8	(	(	PUNCT
ejpam-3747	132	9	5	5	NUM
ejpam-3747	132	10	)	)	PUNCT
ejpam-3747	132	11	(	(	PUNCT
ejpam-3747	132	12	2020	2020	NUM
ejpam-3747	132	13	)	)	PUNCT
ejpam-3747	132	14	,	,	PUNCT
ejpam-3747	132	15	1072	1072	NUM
ejpam-3747	132	16	-	-	SYM
ejpam-3747	132	17	1087	1087	NUM
ejpam-3747	132	18	1077	1077	NUM
ejpam-3747	132	19	proof	proof	NOUN
ejpam-3747	132	20	.	.	PUNCT
ejpam-3747	133	1	(	(	PUNCT
ejpam-3747	133	2	1	1	X
ejpam-3747	133	3	)	)	PUNCT
ejpam-3747	133	4	suppose	suppose	VERB
ejpam-3747	133	5	that	that	SCONJ
ejpam-3747	133	6	f	f	PROPN
ejpam-3747	133	7	(	(	PUNCT
ejpam-3747	133	8	s	s	PROPN
ejpam-3747	133	9	)	)	PUNCT
ejpam-3747	133	10	6=	6=	ADP
ejpam-3747	133	11	∅.	∅.	ADP
ejpam-3747	133	12	by	by	ADP
ejpam-3747	133	13	assumption	assumption	NOUN
ejpam-3747	133	14	,	,	PUNCT
ejpam-3747	133	15	(	(	PUNCT
ejpam-3747	133	16	u	u	NOUN
ejpam-3747	133	17	,	,	PUNCT
ejpam-3747	133	18	s(u	s(u	PROPN
ejpam-3747	133	19	)	)	PUNCT
ejpam-3747	133	20	)	)	PUNCT
ejpam-3747	134	1	⊂	⊂	PROPN
ejpam-3747	134	2	e(g	e(g	PROPN
ejpam-3747	134	3	)	)	PUNCT
ejpam-3747	134	4	.	.	PUNCT
ejpam-3747	135	1	to	to	PART
ejpam-3747	135	2	prove	prove	VERB
ejpam-3747	135	3	that	that	SCONJ
ejpam-3747	135	4	u	u	PROPN
ejpam-3747	135	5	∈	∈	PROPN
ejpam-3747	135	6	f	f	X
ejpam-3747	135	7	(	(	PUNCT
ejpam-3747	135	8	t	t	PROPN
ejpam-3747	135	9	)	)	PUNCT
ejpam-3747	135	10	,	,	PUNCT
ejpam-3747	135	11	assume	assume	VERB
ejpam-3747	135	12	on	on	ADP
ejpam-3747	135	13	contrary	contrary	ADJ
ejpam-3747	135	14	that	that	SCONJ
ejpam-3747	135	15	u	u	NOUN
ejpam-3747	135	16	/∈	/∈	PROPN
ejpam-3747	136	1	f	f	PROPN
ejpam-3747	136	2	(	(	PUNCT
ejpam-3747	136	3	t	t	PROPN
ejpam-3747	136	4	)	)	PUNCT
ejpam-3747	136	5	.	.	PUNCT
ejpam-3747	137	1	since	since	SCONJ
ejpam-3747	137	2	the	the	DET
ejpam-3747	137	3	pair	pair	NOUN
ejpam-3747	137	4	(	(	PUNCT
ejpam-3747	137	5	s	s	PROPN
ejpam-3747	137	6	,	,	PUNCT
ejpam-3747	137	7	t	t	PROPN
ejpam-3747	137	8	)	)	PUNCT
ejpam-3747	137	9	is	be	AUX
ejpam-3747	137	10	a	a	DET
ejpam-3747	137	11	graph	graph	NOUN
ejpam-3747	137	12	(	(	PUNCT
ejpam-3747	137	13	ψ	ψ	NOUN
ejpam-3747	137	14	,	,	PUNCT
ejpam-3747	137	15	φ)-weak	φ)-weak	VERB
ejpam-3747	137	16	contraction	contraction	NOUN
ejpam-3747	137	17	and	and	CCONJ
ejpam-3747	137	18	(	(	PUNCT
ejpam-3747	137	19	u	u	NOUN
ejpam-3747	137	20	,	,	PUNCT
ejpam-3747	137	21	u	u	NOUN
ejpam-3747	137	22	)	)	PUNCT
ejpam-3747	137	23	⊂	⊂	PROPN
ejpam-3747	137	24	e(g	e(g	PROPN
ejpam-3747	137	25	)	)	PUNCT
ejpam-3747	137	26	,	,	PUNCT
ejpam-3747	137	27	then	then	ADV
ejpam-3747	137	28	ψ	ψ	X
ejpam-3747	137	29	(	(	PUNCT
ejpam-3747	137	30	∫	∫	PROPN
ejpam-3747	137	31	h(u	h(u	PROPN
ejpam-3747	137	32	,	,	PUNCT
ejpam-3747	137	33	t	t	PROPN
ejpam-3747	137	34	(	(	PUNCT
ejpam-3747	137	35	u	u	NOUN
ejpam-3747	137	36	)	)	PUNCT
ejpam-3747	137	37	)	)	PUNCT
ejpam-3747	137	38	0	0	NUM
ejpam-3747	138	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	138	2	)	)	PUNCT
ejpam-3747	139	1	=	=	SYM
ejpam-3747	139	2	ψ	ψ	X
ejpam-3747	139	3	(	(	PUNCT
ejpam-3747	139	4	∫	∫	PROPN
ejpam-3747	139	5	h(s(u),t	h(s(u),t	PROPN
ejpam-3747	139	6	(	(	PUNCT
ejpam-3747	139	7	u	u	NOUN
ejpam-3747	139	8	)	)	PUNCT
ejpam-3747	139	9	)	)	PUNCT
ejpam-3747	139	10	0	0	NUM
ejpam-3747	140	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	140	2	)	)	PUNCT
ejpam-3747	141	1	≤	≤	PROPN
ejpam-3747	141	2	φ	φ	PROPN
ejpam-3747	141	3	(	(	PUNCT
ejpam-3747	141	4	ψ	ψ	X
ejpam-3747	141	5	(	(	PUNCT
ejpam-3747	141	6	∫ms	∫ms	PROPN
ejpam-3747	141	7	,	,	PUNCT
ejpam-3747	141	8	t	t	PROPN
ejpam-3747	141	9	(	(	PUNCT
ejpam-3747	141	10	u	u	NOUN
ejpam-3747	141	11	,	,	PUNCT
ejpam-3747	141	12	u	u	NOUN
ejpam-3747	141	13	)	)	PUNCT
ejpam-3747	141	14	0	0	NUM
ejpam-3747	141	15	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	141	16	)	)	PUNCT
ejpam-3747	141	17	)	)	PUNCT
ejpam-3747	142	1	+	+	CCONJ
ejpam-3747	142	2	l	l	NOUN
ejpam-3747	142	3	∫	∫	PROPN
ejpam-3747	142	4	ns	ns	PROPN
ejpam-3747	142	5	,	,	PUNCT
ejpam-3747	142	6	t	t	PROPN
ejpam-3747	142	7	(	(	PUNCT
ejpam-3747	142	8	u	u	NOUN
ejpam-3747	142	9	,	,	PUNCT
ejpam-3747	142	10	u	u	NOUN
ejpam-3747	142	11	)	)	PUNCT
ejpam-3747	142	12	0	0	NUM
ejpam-3747	143	1	ϕ(t)dt	ϕ(t)dt	DET
ejpam-3747	143	2	≤	≤	PROPN
ejpam-3747	143	3	φ	φ	PROPN
ejpam-3747	143	4	(	(	PUNCT
ejpam-3747	143	5	ψ	ψ	X
ejpam-3747	143	6	(	(	PUNCT
ejpam-3747	143	7	∫ms	∫ms	PROPN
ejpam-3747	143	8	,	,	PUNCT
ejpam-3747	143	9	t	t	PROPN
ejpam-3747	143	10	(	(	PUNCT
ejpam-3747	143	11	u	u	NOUN
ejpam-3747	143	12	,	,	PUNCT
ejpam-3747	143	13	u	u	NOUN
ejpam-3747	143	14	)	)	PUNCT
ejpam-3747	143	15	0	0	NUM
ejpam-3747	143	16	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	143	17	)	)	PUNCT
ejpam-3747	143	18	)	)	PUNCT
ejpam-3747	144	1	+	+	CCONJ
ejpam-3747	144	2	l	l	NOUN
ejpam-3747	144	3	∫	∫	PROPN
ejpam-3747	144	4	h(u	h(u	PROPN
ejpam-3747	144	5	,	,	PUNCT
ejpam-3747	144	6	s(u	s(u	PROPN
ejpam-3747	144	7	)	)	PUNCT
ejpam-3747	144	8	)	)	PUNCT
ejpam-3747	144	9	0	0	NUM
ejpam-3747	145	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	145	2	=	=	SYM
ejpam-3747	145	3	φ	φ	PROPN
ejpam-3747	145	4	(	(	PUNCT
ejpam-3747	145	5	ψ	ψ	X
ejpam-3747	145	6	(	(	PUNCT
ejpam-3747	145	7	∫ms	∫ms	PROPN
ejpam-3747	145	8	,	,	PUNCT
ejpam-3747	145	9	t	t	PROPN
ejpam-3747	145	10	(	(	PUNCT
ejpam-3747	145	11	u	u	NOUN
ejpam-3747	145	12	,	,	PUNCT
ejpam-3747	145	13	u	u	NOUN
ejpam-3747	145	14	)	)	PUNCT
ejpam-3747	145	15	0	0	NUM
ejpam-3747	145	16	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	145	17	)	)	PUNCT
ejpam-3747	145	18	)	)	PUNCT
ejpam-3747	145	19	,	,	PUNCT
ejpam-3747	145	20	where	where	SCONJ
ejpam-3747	145	21	ms	ms	PROPN
ejpam-3747	145	22	,	,	PUNCT
ejpam-3747	145	23	t	t	PROPN
ejpam-3747	145	24	(	(	PUNCT
ejpam-3747	145	25	u	u	NOUN
ejpam-3747	145	26	,	,	PUNCT
ejpam-3747	145	27	u	u	NOUN
ejpam-3747	145	28	)	)	PUNCT
ejpam-3747	145	29	=	=	SYM
ejpam-3747	145	30	max	max	PROPN
ejpam-3747	145	31	=	=	SYM
ejpam-3747	145	32	{	{	PUNCT
ejpam-3747	145	33	h(u	h(u	PROPN
ejpam-3747	145	34	,	,	PUNCT
ejpam-3747	145	35	u	u	NOUN
ejpam-3747	145	36	)	)	PUNCT
ejpam-3747	145	37	,	,	PUNCT
ejpam-3747	145	38	h(u	h(u	PROPN
ejpam-3747	145	39	,	,	PUNCT
ejpam-3747	145	40	s(u	s(u	PROPN
ejpam-3747	145	41	)	)	PUNCT
ejpam-3747	145	42	)	)	PUNCT
ejpam-3747	145	43	,	,	PUNCT
ejpam-3747	145	44	h(u	h(u	PROPN
ejpam-3747	145	45	,	,	PUNCT
ejpam-3747	145	46	t	t	PROPN
ejpam-3747	145	47	(	(	PUNCT
ejpam-3747	145	48	u	u	NOUN
ejpam-3747	145	49	)	)	PUNCT
ejpam-3747	145	50	)	)	PUNCT
ejpam-3747	145	51	,	,	PUNCT
ejpam-3747	145	52	h(u	h(u	PROPN
ejpam-3747	145	53	,	,	PUNCT
ejpam-3747	145	54	t	t	PROPN
ejpam-3747	145	55	(	(	PUNCT
ejpam-3747	145	56	u	u	NOUN
ejpam-3747	145	57	)	)	PUNCT
ejpam-3747	145	58	)	)	PUNCT
ejpam-3747	146	1	+	+	PROPN
ejpam-3747	146	2	h(u	h(u	PROPN
ejpam-3747	146	3	,	,	PUNCT
ejpam-3747	146	4	s(u	s(u	PROPN
ejpam-3747	146	5	)	)	PUNCT
ejpam-3747	146	6	)	)	PUNCT
ejpam-3747	146	7	2	2	X
ejpam-3747	146	8	}	}	PUNCT
ejpam-3747	146	9	=	=	SYM
ejpam-3747	146	10	h(u	h(u	PROPN
ejpam-3747	146	11	,	,	PUNCT
ejpam-3747	146	12	t	t	PROPN
ejpam-3747	146	13	(	(	PUNCT
ejpam-3747	146	14	u	u	NOUN
ejpam-3747	146	15	)	)	PUNCT
ejpam-3747	146	16	)	)	PUNCT
ejpam-3747	146	17	.	.	PUNCT
ejpam-3747	147	1	by	by	ADP
ejpam-3747	147	2	property	property	NOUN
ejpam-3747	147	3	of	of	ADP
ejpam-3747	147	4	φ	φ	PROPN
ejpam-3747	147	5	,	,	PUNCT
ejpam-3747	147	6	we	we	PRON
ejpam-3747	147	7	have	have	VERB
ejpam-3747	147	8	ψ	ψ	X
ejpam-3747	147	9	(	(	PUNCT
ejpam-3747	147	10	∫	∫	PROPN
ejpam-3747	147	11	h(u	h(u	PROPN
ejpam-3747	147	12	,	,	PUNCT
ejpam-3747	147	13	t	t	PROPN
ejpam-3747	147	14	(	(	PUNCT
ejpam-3747	147	15	u	u	NOUN
ejpam-3747	147	16	)	)	PUNCT
ejpam-3747	147	17	)	)	PUNCT
ejpam-3747	147	18	0	0	NUM
ejpam-3747	148	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	148	2	)	)	PUNCT
ejpam-3747	149	1	≤	≤	PROPN
ejpam-3747	149	2	φ	φ	PROPN
ejpam-3747	149	3	(	(	PUNCT
ejpam-3747	149	4	ψ	ψ	X
ejpam-3747	149	5	(	(	PUNCT
ejpam-3747	149	6	∫	∫	PROPN
ejpam-3747	149	7	h(u	h(u	PROPN
ejpam-3747	149	8	,	,	PUNCT
ejpam-3747	149	9	t	t	PROPN
ejpam-3747	149	10	(	(	PUNCT
ejpam-3747	149	11	u	u	NOUN
ejpam-3747	149	12	)	)	PUNCT
ejpam-3747	149	13	)	)	PUNCT
ejpam-3747	149	14	0	0	NUM
ejpam-3747	149	15	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	149	16	)	)	PUNCT
ejpam-3747	149	17	)	)	PUNCT
ejpam-3747	150	1	<	<	X
ejpam-3747	150	2	ψ	ψ	X
ejpam-3747	150	3	(	(	PUNCT
ejpam-3747	150	4	∫	∫	PROPN
ejpam-3747	150	5	h(u	h(u	PROPN
ejpam-3747	150	6	,	,	PUNCT
ejpam-3747	150	7	t	t	PROPN
ejpam-3747	150	8	(	(	PUNCT
ejpam-3747	150	9	u	u	NOUN
ejpam-3747	150	10	)	)	PUNCT
ejpam-3747	150	11	)	)	PUNCT
ejpam-3747	150	12	0	0	NUM
ejpam-3747	150	13	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	150	14	)	)	PUNCT
ejpam-3747	150	15	,	,	PUNCT
ejpam-3747	150	16	leading	lead	VERB
ejpam-3747	150	17	to	to	ADP
ejpam-3747	150	18	a	a	DET
ejpam-3747	150	19	contradiction	contradiction	NOUN
ejpam-3747	150	20	.	.	PUNCT
ejpam-3747	151	1	(	(	PUNCT
ejpam-3747	151	2	2	2	X
ejpam-3747	151	3	)	)	PUNCT
ejpam-3747	151	4	let	let	VERB
ejpam-3747	151	5	a0	a0	PROPN
ejpam-3747	151	6	∈	∈	PROPN
ejpam-3747	151	7	cb(x	cb(x	PUNCT
ejpam-3747	151	8	)	)	PUNCT
ejpam-3747	151	9	be	be	AUX
ejpam-3747	151	10	arbitrary	arbitrary	ADJ
ejpam-3747	151	11	.	.	PUNCT
ejpam-3747	152	1	if	if	SCONJ
ejpam-3747	152	2	a0	a0	PROPN
ejpam-3747	152	3	∈	∈	PROPN
ejpam-3747	152	4	f	f	X
ejpam-3747	152	5	(	(	PUNCT
ejpam-3747	152	6	s	s	NOUN
ejpam-3747	152	7	)	)	PUNCT
ejpam-3747	152	8	or	or	CCONJ
ejpam-3747	152	9	a0	a0	PROPN
ejpam-3747	152	10	∈	∈	PROPN
ejpam-3747	152	11	f	f	X
ejpam-3747	152	12	(	(	PUNCT
ejpam-3747	152	13	t	t	PROPN
ejpam-3747	152	14	)	)	PUNCT
ejpam-3747	152	15	,	,	PUNCT
ejpam-3747	152	16	then	then	ADV
ejpam-3747	152	17	from	from	ADP
ejpam-3747	152	18	(	(	PUNCT
ejpam-3747	152	19	i	i	NOUN
ejpam-3747	152	20	)	)	PUNCT
ejpam-3747	152	21	,	,	PUNCT
ejpam-3747	152	22	f	f	PROPN
ejpam-3747	152	23	(	(	PUNCT
ejpam-3747	152	24	s	s	NOUN
ejpam-3747	152	25	)	)	PUNCT
ejpam-3747	152	26	∩	∩	ADJ
ejpam-3747	152	27	f	f	X
ejpam-3747	152	28	(	(	PUNCT
ejpam-3747	152	29	t	t	PROPN
ejpam-3747	152	30	)	)	PUNCT
ejpam-3747	152	31	6=	6=	ADP
ejpam-3747	152	32	∅.	∅.	PROPN
ejpam-3747	152	33	now	now	ADV
ejpam-3747	152	34	suppose	suppose	VERB
ejpam-3747	152	35	that	that	SCONJ
ejpam-3747	152	36	a0	a0	PROPN
ejpam-3747	152	37	/∈	/∈	PUNCT
ejpam-3747	153	1	f	f	X
ejpam-3747	153	2	(	(	PUNCT
ejpam-3747	153	3	s	s	X
ejpam-3747	153	4	)	)	PUNCT
ejpam-3747	153	5	and	and	CCONJ
ejpam-3747	153	6	a0	a0	PROPN
ejpam-3747	153	7	/∈	/∈	PUNCT
ejpam-3747	154	1	f	f	PROPN
ejpam-3747	154	2	(	(	PUNCT
ejpam-3747	154	3	t	t	PROPN
ejpam-3747	154	4	)	)	PUNCT
ejpam-3747	154	5	.	.	PUNCT
ejpam-3747	155	1	by	by	ADP
ejpam-3747	155	2	the	the	DET
ejpam-3747	155	3	definition	definition	NOUN
ejpam-3747	155	4	of	of	ADP
ejpam-3747	155	5	a	a	DET
ejpam-3747	155	6	(	(	PUNCT
ejpam-3747	155	7	ψ	ψ	NOUN
ejpam-3747	155	8	,	,	PUNCT
ejpam-3747	155	9	φ)-weak	φ)-weak	VERB
ejpam-3747	155	10	contraction	contraction	NOUN
ejpam-3747	155	11	contraction	contraction	NOUN
ejpam-3747	155	12	,	,	PUNCT
ejpam-3747	155	13	we	we	PRON
ejpam-3747	155	14	have	have	VERB
ejpam-3747	155	15	(	(	PUNCT
ejpam-3747	155	16	a0	a0	NOUN
ejpam-3747	155	17	,	,	PUNCT
ejpam-3747	155	18	s(a0	s(a0	NOUN
ejpam-3747	155	19	)	)	PUNCT
ejpam-3747	155	20	)	)	PUNCT
ejpam-3747	156	1	⊂	⊂	PROPN
ejpam-3747	156	2	e(g	e(g	PROPN
ejpam-3747	156	3	)	)	PUNCT
ejpam-3747	156	4	which	which	PRON
ejpam-3747	156	5	implies	imply	VERB
ejpam-3747	156	6	that	that	SCONJ
ejpam-3747	156	7	there	there	PRON
ejpam-3747	156	8	exists	exist	VERB
ejpam-3747	156	9	some	some	DET
ejpam-3747	156	10	x0	x0	PROPN
ejpam-3747	156	11	in	in	ADP
ejpam-3747	156	12	a0	a0	NOUN
ejpam-3747	156	13	such	such	ADJ
ejpam-3747	156	14	that	that	SCONJ
ejpam-3747	156	15	there	there	PRON
ejpam-3747	156	16	is	be	VERB
ejpam-3747	156	17	an	an	DET
ejpam-3747	156	18	edge	edge	NOUN
ejpam-3747	156	19	between	between	ADP
ejpam-3747	156	20	x0	x0	PROPN
ejpam-3747	156	21	and	and	CCONJ
ejpam-3747	156	22	some	some	DET
ejpam-3747	156	23	x1	x1	PROPN
ejpam-3747	156	24	∈	∈	PROPN
ejpam-3747	156	25	s(a0	s(a0	NOUN
ejpam-3747	156	26	)	)	PUNCT
ejpam-3747	156	27	.	.	PUNCT
ejpam-3747	157	1	let	let	VERB
ejpam-3747	157	2	a1	a1	NOUN
ejpam-3747	157	3	=	=	NOUN
ejpam-3747	157	4	s(a0	s(a0	NOUN
ejpam-3747	157	5	)	)	PUNCT
ejpam-3747	157	6	;	;	PUNCT
ejpam-3747	157	7	then	then	ADV
ejpam-3747	157	8	by	by	ADP
ejpam-3747	157	9	definition	definition	NOUN
ejpam-3747	157	10	,	,	PUNCT
ejpam-3747	157	11	(	(	PUNCT
ejpam-3747	157	12	a1	a1	PROPN
ejpam-3747	157	13	,	,	PUNCT
ejpam-3747	157	14	t	t	PROPN
ejpam-3747	157	15	(	(	PUNCT
ejpam-3747	157	16	a1	a1	PROPN
ejpam-3747	157	17	)	)	PUNCT
ejpam-3747	157	18	)	)	PUNCT
ejpam-3747	158	1	⊂	⊂	PROPN
ejpam-3747	158	2	e(g	e(g	PROPN
ejpam-3747	158	3	)	)	PUNCT
ejpam-3747	158	4	which	which	PRON
ejpam-3747	158	5	implies	imply	VERB
ejpam-3747	158	6	that	that	SCONJ
ejpam-3747	158	7	there	there	PRON
ejpam-3747	158	8	is	be	VERB
ejpam-3747	158	9	an	an	DET
ejpam-3747	158	10	edge	edge	NOUN
ejpam-3747	158	11	between	between	ADP
ejpam-3747	158	12	x1	x1	PROPN
ejpam-3747	158	13	and	and	CCONJ
ejpam-3747	158	14	some	some	DET
ejpam-3747	158	15	x2	x2	PROPN
ejpam-3747	158	16	∈	∈	PROPN
ejpam-3747	158	17	t	t	PROPN
ejpam-3747	158	18	(	(	PUNCT
ejpam-3747	158	19	a1	a1	PROPN
ejpam-3747	158	20	)	)	PUNCT
ejpam-3747	158	21	.	.	PUNCT
ejpam-3747	159	1	then	then	ADV
ejpam-3747	159	2	a2	a2	PROPN
ejpam-3747	159	3	=	=	PROPN
ejpam-3747	159	4	t	t	PROPN
ejpam-3747	159	5	(	(	PUNCT
ejpam-3747	159	6	a1	a1	PROPN
ejpam-3747	159	7	)	)	PUNCT
ejpam-3747	159	8	.	.	PUNCT
ejpam-3747	160	1	by	by	ADP
ejpam-3747	160	2	induction	induction	NOUN
ejpam-3747	160	3	,	,	PUNCT
ejpam-3747	160	4	we	we	PRON
ejpam-3747	160	5	thus	thus	ADV
ejpam-3747	160	6	construct	construct	VERB
ejpam-3747	160	7	a	a	DET
ejpam-3747	160	8	sequence	sequence	NOUN
ejpam-3747	160	9	(	(	PUNCT
ejpam-3747	160	10	an)n	an)n	PROPN
ejpam-3747	160	11	such	such	ADJ
ejpam-3747	160	12	that	that	DET
ejpam-3747	160	13	a2n+1	a2n+1	PROPN
ejpam-3747	160	14	=	=	SYM
ejpam-3747	160	15	s(a2n	s(a2n	PROPN
ejpam-3747	160	16	)	)	PUNCT
ejpam-3747	160	17	,	,	PUNCT
ejpam-3747	160	18	a2n+2	a2n+2	ADP
ejpam-3747	160	19	=	=	SYM
ejpam-3747	160	20	t	t	PROPN
ejpam-3747	160	21	(	(	PUNCT
ejpam-3747	160	22	a2n+1	a2n+1	PROPN
ejpam-3747	160	23	)	)	PUNCT
ejpam-3747	160	24	,	,	PUNCT
ejpam-3747	160	25	and	and	CCONJ
ejpam-3747	160	26	(	(	PUNCT
ejpam-3747	160	27	an	an	DET
ejpam-3747	160	28	,	,	PUNCT
ejpam-3747	160	29	an+1	an+1	NOUN
ejpam-3747	160	30	)	)	PUNCT
ejpam-3747	161	1	⊂	⊂	PROPN
ejpam-3747	161	2	e(g	e(g	PROPN
ejpam-3747	161	3	)	)	PUNCT
ejpam-3747	161	4	for	for	ADP
ejpam-3747	161	5	n	n	PRON
ejpam-3747	161	6	∈	∈	PROPN
ejpam-3747	161	7	n.	n.	NOUN
ejpam-3747	161	8	observe	observe	VERB
ejpam-3747	161	9	that	that	SCONJ
ejpam-3747	161	10	we	we	PRON
ejpam-3747	161	11	have	have	AUX
ejpam-3747	161	12	assumed	assume	VERB
ejpam-3747	161	13	a2n	a2n	PROPN
ejpam-3747	161	14	6=	6=	SYM
ejpam-3747	161	15	a2n+1	a2n+1	VERB
ejpam-3747	161	16	,	,	PUNCT
ejpam-3747	161	17	otherwise	otherwise	ADV
ejpam-3747	161	18	a2n	a2n	ADJ
ejpam-3747	161	19	=	=	SYM
ejpam-3747	161	20	a2n+1	a2n+1	PROPN
ejpam-3747	161	21	,	,	PUNCT
ejpam-3747	161	22	for	for	ADP
ejpam-3747	161	23	some	some	DET
ejpam-3747	161	24	n	n	CCONJ
ejpam-3747	161	25	,	,	PUNCT
ejpam-3747	161	26	s(a2n	s(a2n	PROPN
ejpam-3747	161	27	)	)	PUNCT
ejpam-3747	161	28	=	=	PUNCT
ejpam-3747	161	29	a2n+1	a2n+1	PROPN
ejpam-3747	161	30	=	=	SYM
ejpam-3747	161	31	a2n	a2n	ADJ
ejpam-3747	161	32	,	,	PUNCT
ejpam-3747	161	33	and	and	CCONJ
ejpam-3747	161	34	thus	thus	ADV
ejpam-3747	161	35	a2n	a2n	PROPN
ejpam-3747	161	36	∈	∈	PROPN
ejpam-3747	161	37	f	f	X
ejpam-3747	161	38	(	(	PUNCT
ejpam-3747	161	39	s	s	NOUN
ejpam-3747	161	40	)	)	PUNCT
ejpam-3747	161	41	.	.	PUNCT
ejpam-3747	162	1	by	by	ADP
ejpam-3747	162	2	(	(	PUNCT
ejpam-3747	162	3	i	i	NOUN
ejpam-3747	162	4	)	)	PUNCT
ejpam-3747	162	5	,	,	PUNCT
ejpam-3747	162	6	a2n	a2n	PROPN
ejpam-3747	162	7	∈	∈	PROPN
ejpam-3747	162	8	f	f	X
ejpam-3747	162	9	(	(	PUNCT
ejpam-3747	162	10	s	s	NOUN
ejpam-3747	162	11	)	)	PUNCT
ejpam-3747	162	12	∩	∩	ADJ
ejpam-3747	162	13	f	f	X
ejpam-3747	162	14	(	(	PUNCT
ejpam-3747	162	15	t	t	PROPN
ejpam-3747	162	16	)	)	PUNCT
ejpam-3747	162	17	.	.	PUNCT
ejpam-3747	163	1	since	since	SCONJ
ejpam-3747	163	2	the	the	DET
ejpam-3747	163	3	pair	pair	NOUN
ejpam-3747	163	4	(	(	PUNCT
ejpam-3747	163	5	s	s	PROPN
ejpam-3747	163	6	,	,	PUNCT
ejpam-3747	163	7	t	t	PROPN
ejpam-3747	163	8	)	)	PUNCT
ejpam-3747	163	9	is	be	AUX
ejpam-3747	163	10	a	a	DET
ejpam-3747	163	11	graph	graph	NOUN
ejpam-3747	163	12	(	(	PUNCT
ejpam-3747	163	13	ψ	ψ	NOUN
ejpam-3747	163	14	,	,	PUNCT
ejpam-3747	163	15	φ)-weak	φ)-weak	VERB
ejpam-3747	163	16	contraction	contraction	NOUN
ejpam-3747	163	17	and	and	CCONJ
ejpam-3747	163	18	(	(	PUNCT
ejpam-3747	163	19	a2n	a2n	ADJ
ejpam-3747	163	20	,	,	PUNCT
ejpam-3747	163	21	a2n+1	a2n+1	ADJ
ejpam-3747	163	22	)	)	PUNCT
ejpam-3747	163	23	⊂	⊂	PROPN
ejpam-3747	163	24	e(g	e(g	PROPN
ejpam-3747	163	25	)	)	PUNCT
ejpam-3747	163	26	,	,	PUNCT
ejpam-3747	163	27	we	we	PRON
ejpam-3747	163	28	derive	derive	VERB
ejpam-3747	163	29	the	the	DET
ejpam-3747	163	30	estimates	estimate	NOUN
ejpam-3747	163	31	ψ	ψ	X
ejpam-3747	163	32	(	(	PUNCT
ejpam-3747	163	33	∫	∫	PROPN
ejpam-3747	163	34	h(a2n+1a2n+2	h(a2n+1a2n+2	PROPN
ejpam-3747	163	35	)	)	PUNCT
ejpam-3747	163	36	0	0	NUM
ejpam-3747	164	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	164	2	)	)	PUNCT
ejpam-3747	165	1	=	=	SYM
ejpam-3747	165	2	ψ	ψ	X
ejpam-3747	165	3	(	(	PUNCT
ejpam-3747	165	4	∫	∫	PROPN
ejpam-3747	165	5	h(s(a2n),t	h(s(a2n),t	PROPN
ejpam-3747	165	6	(	(	PUNCT
ejpam-3747	165	7	a2n+1	a2n+1	NOUN
ejpam-3747	165	8	)	)	PUNCT
ejpam-3747	165	9	)	)	PUNCT
ejpam-3747	165	10	0	0	NUM
ejpam-3747	166	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	166	2	)	)	PUNCT
ejpam-3747	167	1	≤	≤	PROPN
ejpam-3747	167	2	φ	φ	PROPN
ejpam-3747	167	3	(	(	PUNCT
ejpam-3747	167	4	ψ	ψ	X
ejpam-3747	167	5	(	(	PUNCT
ejpam-3747	167	6	∫ms	∫ms	PROPN
ejpam-3747	167	7	,	,	PUNCT
ejpam-3747	167	8	t	t	PROPN
ejpam-3747	167	9	(	(	PUNCT
ejpam-3747	167	10	a2n	a2n	ADV
ejpam-3747	167	11	,	,	PUNCT
ejpam-3747	167	12	a2n+1	a2n+1	NOUN
ejpam-3747	167	13	)	)	PUNCT
ejpam-3747	167	14	0	0	NUM
ejpam-3747	167	15	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	167	16	)	)	PUNCT
ejpam-3747	167	17	)	)	PUNCT
ejpam-3747	168	1	+	+	PUNCT
ejpam-3747	168	2	l	l	NOUN
ejpam-3747	168	3	∫	∫	PROPN
ejpam-3747	168	4	ns	ns	PROPN
ejpam-3747	168	5	,	,	PUNCT
ejpam-3747	168	6	t	t	PROPN
ejpam-3747	168	7	(	(	PUNCT
ejpam-3747	168	8	a2n	a2n	ADV
ejpam-3747	168	9	,	,	PUNCT
ejpam-3747	168	10	a2n+1	a2n+1	NOUN
ejpam-3747	168	11	)	)	PUNCT
ejpam-3747	168	12	0	0	NUM
ejpam-3747	168	13	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	169	1	≤	≤	PROPN
ejpam-3747	169	2	φ	φ	PROPN
ejpam-3747	169	3	(	(	PUNCT
ejpam-3747	169	4	ψ	ψ	X
ejpam-3747	169	5	(	(	PUNCT
ejpam-3747	169	6	∫ms	∫ms	PROPN
ejpam-3747	169	7	,	,	PUNCT
ejpam-3747	169	8	t	t	PROPN
ejpam-3747	169	9	(	(	PUNCT
ejpam-3747	169	10	a2n	a2n	ADV
ejpam-3747	169	11	,	,	PUNCT
ejpam-3747	169	12	a2n+1	a2n+1	NOUN
ejpam-3747	169	13	)	)	PUNCT
ejpam-3747	169	14	0	0	NUM
ejpam-3747	170	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	170	2	)	)	PUNCT
ejpam-3747	170	3	)	)	PUNCT
ejpam-3747	171	1	+	+	PUNCT
ejpam-3747	171	2	l	l	NOUN
ejpam-3747	171	3	∫	∫	PROPN
ejpam-3747	171	4	h(a2n+1,s(a2n	h(a2n+1,s(a2n	PROPN
ejpam-3747	171	5	)	)	PUNCT
ejpam-3747	171	6	)	)	PUNCT
ejpam-3747	171	7	0	0	NUM
ejpam-3747	172	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	172	2	=	=	SYM
ejpam-3747	172	3	φ	φ	PROPN
ejpam-3747	172	4	(	(	PUNCT
ejpam-3747	172	5	ψ	ψ	X
ejpam-3747	172	6	(	(	PUNCT
ejpam-3747	172	7	∫ms	∫ms	PROPN
ejpam-3747	172	8	,	,	PUNCT
ejpam-3747	172	9	t	t	PROPN
ejpam-3747	172	10	(	(	PUNCT
ejpam-3747	172	11	a2n	a2n	ADV
ejpam-3747	172	12	,	,	PUNCT
ejpam-3747	172	13	a2n+1	a2n+1	NOUN
ejpam-3747	172	14	)	)	PUNCT
ejpam-3747	172	15	0	0	NUM
ejpam-3747	173	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	173	2	)	)	PUNCT
ejpam-3747	173	3	)	)	PUNCT
ejpam-3747	174	1	,	,	PUNCT
ejpam-3747	174	2	s.	s.	PROPN
ejpam-3747	174	3	benchabane	benchabane	PROPN
ejpam-3747	174	4	,	,	PUNCT
ejpam-3747	174	5	s.	s.	PROPN
ejpam-3747	174	6	djebali	djebali	PROPN
ejpam-3747	174	7	,	,	PUNCT
ejpam-3747	174	8	t.	t.	PROPN
ejpam-3747	174	9	nazir	nazir	PROPN
ejpam-3747	174	10	/	/	SYM
ejpam-3747	174	11	eur	eur	PROPN
ejpam-3747	174	12	.	.	PUNCT
ejpam-3747	175	1	j.	j.	PROPN
ejpam-3747	175	2	pure	pure	PROPN
ejpam-3747	175	3	appl	appl	PROPN
ejpam-3747	175	4	.	.	PROPN
ejpam-3747	175	5	math	math	PROPN
ejpam-3747	175	6	,	,	PUNCT
ejpam-3747	175	7	13	13	NUM
ejpam-3747	175	8	(	(	PUNCT
ejpam-3747	175	9	5	5	NUM
ejpam-3747	175	10	)	)	PUNCT
ejpam-3747	175	11	(	(	PUNCT
ejpam-3747	175	12	2020	2020	NUM
ejpam-3747	175	13	)	)	PUNCT
ejpam-3747	175	14	,	,	PUNCT
ejpam-3747	175	15	1072	1072	NUM
ejpam-3747	175	16	-	-	SYM
ejpam-3747	175	17	1087	1087	NUM
ejpam-3747	175	18	1078	1078	NUM
ejpam-3747	175	19	where	where	SCONJ
ejpam-3747	175	20	ms	ms	PROPN
ejpam-3747	175	21	,	,	PUNCT
ejpam-3747	175	22	t	t	PROPN
ejpam-3747	175	23	(	(	PUNCT
ejpam-3747	175	24	a2n	a2n	PROPN
ejpam-3747	175	25	,	,	PUNCT
ejpam-3747	175	26	a2n+1	a2n+1	ADJ
ejpam-3747	175	27	)	)	PUNCT
ejpam-3747	175	28	=	=	SYM
ejpam-3747	175	29	max	max	PROPN
ejpam-3747	175	30	{	{	PUNCT
ejpam-3747	175	31	h(a2n	h(a2n	PROPN
ejpam-3747	175	32	,	,	PUNCT
ejpam-3747	175	33	a2n+1	a2n+1	NOUN
ejpam-3747	175	34	)	)	PUNCT
ejpam-3747	175	35	,	,	PUNCT
ejpam-3747	175	36	h(a2n	h(a2n	PROPN
ejpam-3747	175	37	,	,	PUNCT
ejpam-3747	175	38	s(a2n	s(a2n	NOUN
ejpam-3747	175	39	)	)	PUNCT
ejpam-3747	175	40	)	)	PUNCT
ejpam-3747	175	41	,	,	PUNCT
ejpam-3747	175	42	h(a2n+1	h(a2n+1	PROPN
ejpam-3747	175	43	,	,	PUNCT
ejpam-3747	175	44	t	t	PROPN
ejpam-3747	175	45	(	(	PUNCT
ejpam-3747	175	46	a2n+1	a2n+1	PROPN
ejpam-3747	175	47	)	)	PUNCT
ejpam-3747	175	48	)	)	PUNCT
ejpam-3747	175	49	,	,	PUNCT
ejpam-3747	175	50	h(a2n	h(a2n	PROPN
ejpam-3747	175	51	,	,	PUNCT
ejpam-3747	175	52	t	t	PROPN
ejpam-3747	175	53	(	(	PUNCT
ejpam-3747	175	54	a2n+1	a2n+1	PROPN
ejpam-3747	175	55	)	)	PUNCT
ejpam-3747	175	56	)	)	PUNCT
ejpam-3747	176	1	+	+	PUNCT
ejpam-3747	176	2	h(a2n+1	h(a2n+1	NOUN
ejpam-3747	176	3	,	,	PUNCT
ejpam-3747	176	4	s(a2n	s(a2n	NOUN
ejpam-3747	176	5	)	)	PUNCT
ejpam-3747	176	6	)	)	PUNCT
ejpam-3747	176	7	2	2	X
ejpam-3747	176	8	}	}	PUNCT
ejpam-3747	176	9	=	=	SYM
ejpam-3747	176	10	max	max	PROPN
ejpam-3747	176	11	{	{	PUNCT
ejpam-3747	176	12	h(a2n	h(a2n	PROPN
ejpam-3747	176	13	,	,	PUNCT
ejpam-3747	176	14	a2n+1	a2n+1	NOUN
ejpam-3747	176	15	)	)	PUNCT
ejpam-3747	176	16	,	,	PUNCT
ejpam-3747	176	17	h(a2n	h(a2n	NOUN
ejpam-3747	176	18	,	,	PUNCT
ejpam-3747	176	19	a2n+1	a2n+1	NOUN
ejpam-3747	176	20	)	)	PUNCT
ejpam-3747	176	21	,	,	PUNCT
ejpam-3747	176	22	h(a2n+1	h(a2n+1	PROPN
ejpam-3747	176	23	,	,	PUNCT
ejpam-3747	176	24	a2n+2	a2n+2	PRON
ejpam-3747	176	25	)	)	PUNCT
ejpam-3747	176	26	,	,	PUNCT
ejpam-3747	176	27	h(a2n	h(a2n	PROPN
ejpam-3747	176	28	,	,	PUNCT
ejpam-3747	176	29	a2n+2	a2n+2	PRON
ejpam-3747	176	30	)	)	PUNCT
ejpam-3747	177	1	+	+	ADJ
ejpam-3747	177	2	h(a2n+1	h(a2n+1	NOUN
ejpam-3747	177	3	,	,	PUNCT
ejpam-3747	177	4	a2n+1	a2n+1	NOUN
ejpam-3747	177	5	)	)	PUNCT
ejpam-3747	177	6	2	2	NUM
ejpam-3747	177	7	}	}	PUNCT
ejpam-3747	177	8	≤	≤	NUM
ejpam-3747	177	9	max	max	PROPN
ejpam-3747	177	10	{	{	PUNCT
ejpam-3747	177	11	h(a2n	h(a2n	PROPN
ejpam-3747	177	12	,	,	PUNCT
ejpam-3747	177	13	a2n+1	a2n+1	NOUN
ejpam-3747	177	14	)	)	PUNCT
ejpam-3747	177	15	,	,	PUNCT
ejpam-3747	177	16	h(a2n+1	h(a2n+1	PROPN
ejpam-3747	177	17	,	,	PUNCT
ejpam-3747	177	18	a2n+2	a2n+2	PRON
ejpam-3747	177	19	)	)	PUNCT
ejpam-3747	177	20	,	,	PUNCT
ejpam-3747	177	21	h(a2n	h(a2n	PROPN
ejpam-3747	177	22	,	,	PUNCT
ejpam-3747	177	23	a2n+1	a2n+1	NOUN
ejpam-3747	177	24	)	)	PUNCT
ejpam-3747	177	25	+	+	NOUN
ejpam-3747	177	26	h(a2n+1	h(a2n+1	NOUN
ejpam-3747	177	27	,	,	PUNCT
ejpam-3747	177	28	a2n+2	a2n+2	PRON
ejpam-3747	177	29	)	)	PUNCT
ejpam-3747	177	30	2	2	X
ejpam-3747	177	31	}	}	PUNCT
ejpam-3747	177	32	=	=	SYM
ejpam-3747	177	33	max	max	PROPN
ejpam-3747	177	34	{	{	PUNCT
ejpam-3747	177	35	h(a2n	h(a2n	PROPN
ejpam-3747	177	36	,	,	PUNCT
ejpam-3747	177	37	a2n+1	a2n+1	NOUN
ejpam-3747	177	38	)	)	PUNCT
ejpam-3747	177	39	,	,	PUNCT
ejpam-3747	177	40	h(a2n+1	h(a2n+1	PROPN
ejpam-3747	177	41	,	,	PUNCT
ejpam-3747	177	42	a2n+2	a2n+2	PRON
ejpam-3747	177	43	)	)	PUNCT
ejpam-3747	177	44	}	}	PUNCT
ejpam-3747	177	45	.	.	PUNCT
ejpam-3747	178	1	hence	hence	ADV
ejpam-3747	178	2	ψ	ψ	X
ejpam-3747	178	3	(	(	PUNCT
ejpam-3747	178	4	∫	∫	PROPN
ejpam-3747	178	5	h(a2n+1,a2n+2	h(a2n+1,a2n+2	PROPN
ejpam-3747	178	6	)	)	PUNCT
ejpam-3747	178	7	0	0	NUM
ejpam-3747	179	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	179	2	)	)	PUNCT
ejpam-3747	180	1	≤	≤	PROPN
ejpam-3747	180	2	φ	φ	PROPN
ejpam-3747	180	3	(	(	PUNCT
ejpam-3747	180	4	ψ	ψ	X
ejpam-3747	180	5	(	(	PUNCT
ejpam-3747	180	6	∫	∫	PROPN
ejpam-3747	180	7	max{h(a2n	max{h(a2n	PROPN
ejpam-3747	180	8	,	,	PUNCT
ejpam-3747	180	9	a2n+1),h(a2n+1,a2n+2	a2n+1),h(a2n+1,a2n+2	PROPN
ejpam-3747	180	10	)	)	PUNCT
ejpam-3747	180	11	}	}	PUNCT
ejpam-3747	180	12	0	0	NUM
ejpam-3747	180	13	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	180	14	)	)	PUNCT
ejpam-3747	180	15	)	)	PUNCT
ejpam-3747	180	16	.	.	PUNCT
ejpam-3747	181	1	by	by	ADP
ejpam-3747	181	2	the	the	DET
ejpam-3747	181	3	property	property	NOUN
ejpam-3747	181	4	of	of	ADP
ejpam-3747	181	5	φ	φ	PROPN
ejpam-3747	181	6	,	,	PUNCT
ejpam-3747	181	7	we	we	PRON
ejpam-3747	181	8	have	have	VERB
ejpam-3747	181	9	for	for	ADP
ejpam-3747	181	10	all	all	PRON
ejpam-3747	181	11	n	n	PRON
ejpam-3747	181	12	∈	∈	PROPN
ejpam-3747	181	13	n	n	ADP
ejpam-3747	181	14	ψ	ψ	X
ejpam-3747	181	15	(	(	PUNCT
ejpam-3747	181	16	∫	∫	PROPN
ejpam-3747	181	17	h(a2n+1,a2n+2	h(a2n+1,a2n+2	PROPN
ejpam-3747	181	18	)	)	PUNCT
ejpam-3747	181	19	0	0	NUM
ejpam-3747	182	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	182	2	)	)	PUNCT
ejpam-3747	183	1	≤	≤	PROPN
ejpam-3747	183	2	φ	φ	PROPN
ejpam-3747	183	3	(	(	PUNCT
ejpam-3747	183	4	ψ	ψ	X
ejpam-3747	183	5	(	(	PUNCT
ejpam-3747	183	6	∫	∫	PROPN
ejpam-3747	183	7	h(a2n	h(a2n	PROPN
ejpam-3747	183	8	,	,	PUNCT
ejpam-3747	183	9	a2n+1	a2n+1	PROPN
ejpam-3747	183	10	)	)	PUNCT
ejpam-3747	183	11	0	0	NUM
ejpam-3747	184	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	184	2	)	)	PUNCT
ejpam-3747	184	3	)	)	PUNCT
ejpam-3747	184	4	.	.	PUNCT
ejpam-3747	185	1	since	since	SCONJ
ejpam-3747	185	2	the	the	DET
ejpam-3747	185	3	pair	pair	NOUN
ejpam-3747	185	4	(	(	PUNCT
ejpam-3747	185	5	s	s	PROPN
ejpam-3747	185	6	,	,	PUNCT
ejpam-3747	185	7	t	t	PROPN
ejpam-3747	185	8	)	)	PUNCT
ejpam-3747	185	9	is	be	AUX
ejpam-3747	185	10	a	a	DET
ejpam-3747	185	11	graph	graph	NOUN
ejpam-3747	185	12	(	(	PUNCT
ejpam-3747	185	13	ψ	ψ	NOUN
ejpam-3747	185	14	,	,	PUNCT
ejpam-3747	185	15	φ)-weak	φ)-weak	VERB
ejpam-3747	185	16	contraction	contraction	NOUN
ejpam-3747	185	17	and	and	CCONJ
ejpam-3747	185	18	(	(	PUNCT
ejpam-3747	185	19	a2n+2	a2n+2	ADV
ejpam-3747	185	20	,	,	PUNCT
ejpam-3747	185	21	a2n+1	a2n+1	PROPN
ejpam-3747	185	22	)	)	PUNCT
ejpam-3747	185	23	⊂	⊂	PROPN
ejpam-3747	185	24	e(g	e(g	PROPN
ejpam-3747	185	25	)	)	PUNCT
ejpam-3747	185	26	,	,	PUNCT
ejpam-3747	185	27	we	we	PRON
ejpam-3747	185	28	have	have	VERB
ejpam-3747	185	29	that	that	DET
ejpam-3747	185	30	ψ	ψ	X
ejpam-3747	185	31	(	(	PUNCT
ejpam-3747	185	32	∫	∫	PROPN
ejpam-3747	185	33	h(a2n+2a2n+3	h(a2n+2a2n+3	PROPN
ejpam-3747	185	34	)	)	PUNCT
ejpam-3747	185	35	0	0	NUM
ejpam-3747	186	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	186	2	)	)	PUNCT
ejpam-3747	187	1	=	=	SYM
ejpam-3747	187	2	ψ	ψ	X
ejpam-3747	187	3	(	(	PUNCT
ejpam-3747	187	4	∫	∫	PROPN
ejpam-3747	187	5	h(t	h(t	PROPN
ejpam-3747	187	6	(	(	PUNCT
ejpam-3747	187	7	a2n+1),s(a2n+2	a2n+1),s(a2n+2	PROPN
ejpam-3747	187	8	)	)	PUNCT
ejpam-3747	187	9	)	)	PUNCT
ejpam-3747	187	10	0	0	NUM
ejpam-3747	188	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	188	2	)	)	PUNCT
ejpam-3747	189	1	=	=	SYM
ejpam-3747	189	2	ψ	ψ	X
ejpam-3747	189	3	(	(	PUNCT
ejpam-3747	189	4	∫	∫	PROPN
ejpam-3747	189	5	h(s(a2n+2),t	h(s(a2n+2),t	PROPN
ejpam-3747	189	6	(	(	PUNCT
ejpam-3747	189	7	a2n+1	a2n+1	NOUN
ejpam-3747	189	8	)	)	PUNCT
ejpam-3747	189	9	)	)	PUNCT
ejpam-3747	189	10	0	0	NUM
ejpam-3747	190	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	190	2	)	)	PUNCT
ejpam-3747	191	1	≤	≤	PROPN
ejpam-3747	191	2	φ	φ	PROPN
ejpam-3747	191	3	(	(	PUNCT
ejpam-3747	191	4	ψ	ψ	X
ejpam-3747	191	5	(	(	PUNCT
ejpam-3747	191	6	∫ms	∫ms	PROPN
ejpam-3747	191	7	,	,	PUNCT
ejpam-3747	191	8	t	t	PROPN
ejpam-3747	191	9	(	(	PUNCT
ejpam-3747	191	10	a2n+2,a2n+1	a2n+2,a2n+1	PROPN
ejpam-3747	191	11	)	)	PUNCT
ejpam-3747	191	12	0	0	NUM
ejpam-3747	192	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	192	2	)	)	PUNCT
ejpam-3747	192	3	)	)	PUNCT
ejpam-3747	193	1	+	+	PUNCT
ejpam-3747	193	2	l	l	NOUN
ejpam-3747	193	3	∫	∫	PROPN
ejpam-3747	193	4	ns	ns	PROPN
ejpam-3747	193	5	,	,	PUNCT
ejpam-3747	193	6	t	t	PROPN
ejpam-3747	193	7	(	(	PUNCT
ejpam-3747	193	8	a2n+2,a2n+1	a2n+2,a2n+1	PROPN
ejpam-3747	193	9	)	)	PUNCT
ejpam-3747	193	10	0	0	NUM
ejpam-3747	194	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	194	2	≤	≤	PROPN
ejpam-3747	194	3	φ	φ	PROPN
ejpam-3747	194	4	(	(	PUNCT
ejpam-3747	194	5	ψ	ψ	X
ejpam-3747	194	6	(	(	PUNCT
ejpam-3747	194	7	∫ms	∫ms	PROPN
ejpam-3747	194	8	,	,	PUNCT
ejpam-3747	194	9	t	t	PROPN
ejpam-3747	194	10	(	(	PUNCT
ejpam-3747	194	11	a2n+2,a2n+1	a2n+2,a2n+1	PROPN
ejpam-3747	194	12	)	)	PUNCT
ejpam-3747	194	13	0	0	NUM
ejpam-3747	195	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	195	2	)	)	PUNCT
ejpam-3747	195	3	)	)	PUNCT
ejpam-3747	196	1	+	+	PUNCT
ejpam-3747	196	2	l	l	NOUN
ejpam-3747	196	3	∫	∫	PROPN
ejpam-3747	196	4	h(a2n+2,t	h(a2n+2,t	X
ejpam-3747	196	5	(	(	PUNCT
ejpam-3747	196	6	a2n+1	a2n+1	NOUN
ejpam-3747	196	7	)	)	PUNCT
ejpam-3747	196	8	)	)	PUNCT
ejpam-3747	196	9	0	0	NUM
ejpam-3747	197	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	197	2	=	=	SYM
ejpam-3747	197	3	φ	φ	PROPN
ejpam-3747	197	4	(	(	PUNCT
ejpam-3747	197	5	ψ	ψ	X
ejpam-3747	197	6	(	(	PUNCT
ejpam-3747	197	7	∫ms	∫ms	PROPN
ejpam-3747	197	8	,	,	PUNCT
ejpam-3747	197	9	t	t	PROPN
ejpam-3747	197	10	(	(	PUNCT
ejpam-3747	197	11	a2n+2,a2n+1	a2n+2,a2n+1	PROPN
ejpam-3747	197	12	)	)	PUNCT
ejpam-3747	197	13	0	0	NUM
ejpam-3747	198	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	198	2	)	)	PUNCT
ejpam-3747	198	3	)	)	PUNCT
ejpam-3747	199	1	,	,	PUNCT
ejpam-3747	199	2	s.	s.	PROPN
ejpam-3747	199	3	benchabane	benchabane	PROPN
ejpam-3747	199	4	,	,	PUNCT
ejpam-3747	199	5	s.	s.	PROPN
ejpam-3747	199	6	djebali	djebali	PROPN
ejpam-3747	199	7	,	,	PUNCT
ejpam-3747	199	8	t.	t.	PROPN
ejpam-3747	199	9	nazir	nazir	PROPN
ejpam-3747	199	10	/	/	SYM
ejpam-3747	199	11	eur	eur	PROPN
ejpam-3747	199	12	.	.	PUNCT
ejpam-3747	200	1	j.	j.	PROPN
ejpam-3747	200	2	pure	pure	PROPN
ejpam-3747	200	3	appl	appl	PROPN
ejpam-3747	200	4	.	.	PROPN
ejpam-3747	200	5	math	math	PROPN
ejpam-3747	200	6	,	,	PUNCT
ejpam-3747	200	7	13	13	NUM
ejpam-3747	200	8	(	(	PUNCT
ejpam-3747	200	9	5	5	NUM
ejpam-3747	200	10	)	)	PUNCT
ejpam-3747	200	11	(	(	PUNCT
ejpam-3747	200	12	2020	2020	NUM
ejpam-3747	200	13	)	)	PUNCT
ejpam-3747	200	14	,	,	PUNCT
ejpam-3747	200	15	1072	1072	NUM
ejpam-3747	200	16	-	-	SYM
ejpam-3747	200	17	1087	1087	NUM
ejpam-3747	200	18	1079	1079	NUM
ejpam-3747	200	19	where	where	SCONJ
ejpam-3747	200	20	ms	ms	PROPN
ejpam-3747	200	21	,	,	PUNCT
ejpam-3747	200	22	t	t	PROPN
ejpam-3747	200	23	(	(	PUNCT
ejpam-3747	200	24	a2n+2	a2n+2	ADV
ejpam-3747	200	25	,	,	PUNCT
ejpam-3747	200	26	a2n+1	a2n+1	PROPN
ejpam-3747	200	27	)	)	PUNCT
ejpam-3747	200	28	=	=	SYM
ejpam-3747	200	29	max	max	PROPN
ejpam-3747	200	30	{	{	PUNCT
ejpam-3747	200	31	h(a2n+2	h(a2n+2	PROPN
ejpam-3747	200	32	,	,	PUNCT
ejpam-3747	200	33	a2n+1	a2n+1	NOUN
ejpam-3747	200	34	)	)	PUNCT
ejpam-3747	200	35	,	,	PUNCT
ejpam-3747	200	36	h(a2n+2	h(a2n+2	NUM
ejpam-3747	200	37	,	,	PUNCT
ejpam-3747	200	38	s(a2n+2	s(a2n+2	NOUN
ejpam-3747	200	39	)	)	PUNCT
ejpam-3747	200	40	)	)	PUNCT
ejpam-3747	200	41	,	,	PUNCT
ejpam-3747	200	42	h(a2n+1	h(a2n+1	PROPN
ejpam-3747	200	43	,	,	PUNCT
ejpam-3747	200	44	t	t	PROPN
ejpam-3747	200	45	(	(	PUNCT
ejpam-3747	200	46	a2n+1	a2n+1	PROPN
ejpam-3747	200	47	)	)	PUNCT
ejpam-3747	200	48	)	)	PUNCT
ejpam-3747	200	49	,	,	PUNCT
ejpam-3747	200	50	h(a2n+2	h(a2n+2	PROPN
ejpam-3747	200	51	,	,	PUNCT
ejpam-3747	200	52	t	t	PROPN
ejpam-3747	200	53	(	(	PUNCT
ejpam-3747	200	54	a2n+1	a2n+1	PROPN
ejpam-3747	200	55	)	)	PUNCT
ejpam-3747	200	56	)	)	PUNCT
ejpam-3747	201	1	+	+	PUNCT
ejpam-3747	201	2	h(a2n+1	h(a2n+1	NOUN
ejpam-3747	201	3	,	,	PUNCT
ejpam-3747	201	4	s(a2n+2	s(a2n+2	NOUN
ejpam-3747	201	5	)	)	PUNCT
ejpam-3747	201	6	)	)	PUNCT
ejpam-3747	201	7	2	2	X
ejpam-3747	201	8	}	}	PUNCT
ejpam-3747	201	9	=	=	SYM
ejpam-3747	201	10	max	max	X
ejpam-3747	201	11	{	{	PUNCT
ejpam-3747	201	12	h(a2n+2	h(a2n+2	PROPN
ejpam-3747	201	13	,	,	PUNCT
ejpam-3747	201	14	a2n+1	a2n+1	NOUN
ejpam-3747	201	15	)	)	PUNCT
ejpam-3747	201	16	,	,	PUNCT
ejpam-3747	201	17	h(a2n+2	h(a2n+2	NUM
ejpam-3747	201	18	,	,	PUNCT
ejpam-3747	201	19	a2n+3	a2n+3	PROPN
ejpam-3747	201	20	)	)	PUNCT
ejpam-3747	201	21	,	,	PUNCT
ejpam-3747	201	22	h(a2n+1	h(a2n+1	NOUN
ejpam-3747	201	23	,	,	PUNCT
ejpam-3747	201	24	a2n+2	a2n+2	PRON
ejpam-3747	201	25	)	)	PUNCT
ejpam-3747	201	26	,	,	PUNCT
ejpam-3747	201	27	h(a2n+2	h(a2n+2	NUM
ejpam-3747	201	28	,	,	PUNCT
ejpam-3747	201	29	a2n+2	a2n+2	PRON
ejpam-3747	201	30	)	)	PUNCT
ejpam-3747	202	1	+	+	NOUN
ejpam-3747	202	2	h(a2n+1	h(a2n+1	NOUN
ejpam-3747	202	3	,	,	PUNCT
ejpam-3747	202	4	a2n+3	a2n+3	PROPN
ejpam-3747	202	5	)	)	PUNCT
ejpam-3747	202	6	2	2	NUM
ejpam-3747	202	7	}	}	PUNCT
ejpam-3747	202	8	≤	≤	NUM
ejpam-3747	202	9	max	max	PROPN
ejpam-3747	202	10	{	{	PUNCT
ejpam-3747	202	11	h(a2n+2	h(a2n+2	PROPN
ejpam-3747	202	12	,	,	PUNCT
ejpam-3747	202	13	a2n+1	a2n+1	NOUN
ejpam-3747	202	14	)	)	PUNCT
ejpam-3747	202	15	,	,	PUNCT
ejpam-3747	202	16	h(a2n+2	h(a2n+2	NUM
ejpam-3747	202	17	,	,	PUNCT
ejpam-3747	202	18	a2n+3	a2n+3	PROPN
ejpam-3747	202	19	)	)	PUNCT
ejpam-3747	202	20	,	,	PUNCT
ejpam-3747	202	21	h(a2n+1	h(a2n+1	NOUN
ejpam-3747	202	22	,	,	PUNCT
ejpam-3747	202	23	a2n+2	a2n+2	PUNCT
ejpam-3747	202	24	)	)	PUNCT
ejpam-3747	203	1	+	+	ADJ
ejpam-3747	203	2	h(a2n+2	h(a2n+2	NUM
ejpam-3747	203	3	,	,	PUNCT
ejpam-3747	203	4	a2n+3	a2n+3	PROPN
ejpam-3747	203	5	)	)	PUNCT
ejpam-3747	203	6	2	2	NUM
ejpam-3747	203	7	}	}	PUNCT
ejpam-3747	203	8	=	=	SYM
ejpam-3747	203	9	max	max	X
ejpam-3747	203	10	{	{	PUNCT
ejpam-3747	203	11	h(a2n+2	h(a2n+2	PROPN
ejpam-3747	203	12	,	,	PUNCT
ejpam-3747	203	13	a2n+1	a2n+1	NOUN
ejpam-3747	203	14	)	)	PUNCT
ejpam-3747	203	15	,	,	PUNCT
ejpam-3747	203	16	h(a2n+2	h(a2n+2	NUM
ejpam-3747	203	17	,	,	PUNCT
ejpam-3747	203	18	a2n+3	a2n+3	PROPN
ejpam-3747	203	19	)	)	PUNCT
ejpam-3747	203	20	}	}	PUNCT
ejpam-3747	203	21	.	.	PUNCT
ejpam-3747	204	1	then	then	ADV
ejpam-3747	204	2	ψ	ψ	X
ejpam-3747	204	3	(	(	PUNCT
ejpam-3747	204	4	∫	∫	PROPN
ejpam-3747	204	5	h(a2n+2,a2n+3	h(a2n+2,a2n+3	PROPN
ejpam-3747	204	6	)	)	PUNCT
ejpam-3747	204	7	0	0	NUM
ejpam-3747	205	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	205	2	)	)	PUNCT
ejpam-3747	206	1	≤	≤	PROPN
ejpam-3747	206	2	φ	φ	PROPN
ejpam-3747	206	3	(	(	PUNCT
ejpam-3747	206	4	ψ	ψ	X
ejpam-3747	206	5	(	(	PUNCT
ejpam-3747	206	6	∫	∫	PROPN
ejpam-3747	206	7	max{h(a2n+2,a2n+1),h(a2n+2,a2n+3	max{h(a2n+2,a2n+1),h(a2n+2,a2n+3	PROPN
ejpam-3747	206	8	)	)	PUNCT
ejpam-3747	206	9	}	}	PUNCT
ejpam-3747	206	10	0	0	NUM
ejpam-3747	206	11	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	206	12	)	)	PUNCT
ejpam-3747	206	13	)	)	PUNCT
ejpam-3747	206	14	.	.	PUNCT
ejpam-3747	207	1	by	by	ADP
ejpam-3747	207	2	the	the	DET
ejpam-3747	207	3	property	property	NOUN
ejpam-3747	207	4	of	of	ADP
ejpam-3747	207	5	φ	φ	PROPN
ejpam-3747	207	6	,	,	PUNCT
ejpam-3747	207	7	we	we	PRON
ejpam-3747	207	8	obtain	obtain	VERB
ejpam-3747	207	9	for	for	ADP
ejpam-3747	207	10	all	all	PRON
ejpam-3747	207	11	n	n	PRON
ejpam-3747	207	12	∈	∈	PROPN
ejpam-3747	207	13	n	n	ADP
ejpam-3747	207	14	ψ	ψ	X
ejpam-3747	207	15	(	(	PUNCT
ejpam-3747	207	16	∫	∫	PROPN
ejpam-3747	207	17	h(a2n+2,a2n+3	h(a2n+2,a2n+3	PROPN
ejpam-3747	207	18	)	)	PUNCT
ejpam-3747	207	19	0	0	NUM
ejpam-3747	208	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	208	2	)	)	PUNCT
ejpam-3747	209	1	≤	≤	PROPN
ejpam-3747	209	2	φ	φ	PROPN
ejpam-3747	209	3	(	(	PUNCT
ejpam-3747	209	4	ψ	ψ	X
ejpam-3747	209	5	(	(	PUNCT
ejpam-3747	209	6	∫	∫	PROPN
ejpam-3747	209	7	h(a2n+1,a2n+2	h(a2n+1,a2n+2	PROPN
ejpam-3747	209	8	)	)	PUNCT
ejpam-3747	209	9	0	0	NUM
ejpam-3747	209	10	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	209	11	)	)	PUNCT
ejpam-3747	209	12	)	)	PUNCT
ejpam-3747	209	13	.	.	PUNCT
ejpam-3747	210	1	hence	hence	ADV
ejpam-3747	210	2	ψ	ψ	X
ejpam-3747	210	3	(	(	PUNCT
ejpam-3747	210	4	∫	∫	PROPN
ejpam-3747	210	5	h(an	h(an	PROPN
ejpam-3747	210	6	,	,	PUNCT
ejpam-3747	210	7	an+1	an+1	NOUN
ejpam-3747	210	8	)	)	PUNCT
ejpam-3747	210	9	0	0	NUM
ejpam-3747	211	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	211	2	)	)	PUNCT
ejpam-3747	212	1	≤	≤	PROPN
ejpam-3747	212	2	φ	φ	PROPN
ejpam-3747	212	3	(	(	PUNCT
ejpam-3747	212	4	ψ	ψ	X
ejpam-3747	212	5	(	(	PUNCT
ejpam-3747	212	6	∫	∫	PROPN
ejpam-3747	212	7	h(an−1,an	h(an−1,an	PROPN
ejpam-3747	212	8	)	)	PUNCT
ejpam-3747	212	9	0	0	NUM
ejpam-3747	213	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	213	2	)	)	PUNCT
ejpam-3747	213	3	)	)	PUNCT
ejpam-3747	213	4	.	.	PUNCT
ejpam-3747	214	1	(	(	PUNCT
ejpam-3747	214	2	1	1	X
ejpam-3747	214	3	)	)	PUNCT
ejpam-3747	214	4	(	(	PUNCT
ejpam-3747	214	5	1	1	X
ejpam-3747	214	6	)	)	PUNCT
ejpam-3747	214	7	guarantees	guarantee	VERB
ejpam-3747	214	8	that	that	SCONJ
ejpam-3747	214	9	ψ	ψ	X
ejpam-3747	214	10	(	(	PUNCT
ejpam-3747	214	11	∫	∫	PROPN
ejpam-3747	214	12	h(an	h(an	PROPN
ejpam-3747	214	13	,	,	PUNCT
ejpam-3747	214	14	an+1	an+1	NOUN
ejpam-3747	214	15	)	)	PUNCT
ejpam-3747	214	16	0	0	NUM
ejpam-3747	214	17	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	214	18	)	)	PUNCT
ejpam-3747	214	19	≤	≤	PROPN
ejpam-3747	215	1	φ	φ	PROPN
ejpam-3747	215	2	(	(	PUNCT
ejpam-3747	215	3	ψ	ψ	X
ejpam-3747	215	4	(	(	PUNCT
ejpam-3747	215	5	∫	∫	PROPN
ejpam-3747	215	6	h(an−1,an	h(an−1,an	PROPN
ejpam-3747	215	7	)	)	PUNCT
ejpam-3747	215	8	0	0	NUM
ejpam-3747	215	9	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	215	10	)	)	PUNCT
ejpam-3747	215	11	)	)	PUNCT
ejpam-3747	216	1	≤	≤	NUM
ejpam-3747	216	2	φ2	φ2	PROPN
ejpam-3747	216	3	(	(	PUNCT
ejpam-3747	216	4	ψ	ψ	X
ejpam-3747	216	5	(	(	PUNCT
ejpam-3747	216	6	∫	∫	PROPN
ejpam-3747	216	7	h(an−2,an−1	h(an−2,an−1	NUM
ejpam-3747	216	8	)	)	PUNCT
ejpam-3747	216	9	0	0	NUM
ejpam-3747	216	10	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	216	11	)	)	PUNCT
ejpam-3747	216	12	)	)	PUNCT
ejpam-3747	216	13	...	...	PUNCT
ejpam-3747	217	1	≤	≤	X
ejpam-3747	217	2	φn	φn	ADP
ejpam-3747	217	3	(	(	PUNCT
ejpam-3747	217	4	ψ	ψ	X
ejpam-3747	217	5	(	(	PUNCT
ejpam-3747	217	6	∫	∫	PROPN
ejpam-3747	217	7	h(a0,a1	h(a0,a1	NOUN
ejpam-3747	217	8	)	)	PUNCT
ejpam-3747	217	9	0	0	NUM
ejpam-3747	217	10	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	217	11	)	)	PUNCT
ejpam-3747	217	12	)	)	PUNCT
ejpam-3747	217	13	.	.	PUNCT
ejpam-3747	218	1	we	we	PRON
ejpam-3747	218	2	prove	prove	VERB
ejpam-3747	218	3	now	now	ADV
ejpam-3747	218	4	that	that	SCONJ
ejpam-3747	218	5	(	(	PUNCT
ejpam-3747	218	6	an)n	an)n	PROPN
ejpam-3747	218	7	is	be	AUX
ejpam-3747	218	8	a	a	DET
ejpam-3747	218	9	cauchy	cauchy	ADJ
ejpam-3747	218	10	sequence	sequence	NOUN
ejpam-3747	218	11	in	in	ADP
ejpam-3747	218	12	cb(x	cb(x	NUM
ejpam-3747	218	13	)	)	PUNCT
ejpam-3747	218	14	.	.	PUNCT
ejpam-3747	219	1	by	by	ADP
ejpam-3747	219	2	lemma	lemma	PROPN
ejpam-3747	219	3	2	2	PROPN
ejpam-3747	219	4	and	and	CCONJ
ejpam-3747	219	5	the	the	DET
ejpam-3747	219	6	property	property	NOUN
ejpam-3747	219	7	of	of	ADP
ejpam-3747	219	8	ψ	ψ	NOUN
ejpam-3747	219	9	,	,	PUNCT
ejpam-3747	219	10	we	we	PRON
ejpam-3747	219	11	have	have	VERB
ejpam-3747	219	12	the	the	DET
ejpam-3747	219	13	estimates	estimate	NOUN
ejpam-3747	219	14	ψ	ψ	X
ejpam-3747	219	15	(	(	PUNCT
ejpam-3747	219	16	∫	∫	PROPN
ejpam-3747	219	17	h(anam	h(anam	PROPN
ejpam-3747	219	18	)	)	PUNCT
ejpam-3747	219	19	0	0	NUM
ejpam-3747	220	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	220	2	)	)	PUNCT
ejpam-3747	221	1	≤	≤	NUM
ejpam-3747	221	2	ψ	ψ	X
ejpam-3747	221	3	(	(	PUNCT
ejpam-3747	221	4	∫∑m−1	∫∑m−1	PROPN
ejpam-3747	221	5	i	i	PROPN
ejpam-3747	221	6	=	=	PROPN
ejpam-3747	221	7	n	n	PRON
ejpam-3747	221	8	h(ai	h(ai	PROPN
ejpam-3747	221	9	,	,	PUNCT
ejpam-3747	221	10	ai+1	ai+1	NOUN
ejpam-3747	221	11	)	)	PUNCT
ejpam-3747	221	12	0	0	NUM
ejpam-3747	221	13	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	221	14	)	)	PUNCT
ejpam-3747	221	15	≤	≤	NUM
ejpam-3747	221	16	ψ	ψ	X
ejpam-3747	221	17	(	(	PUNCT
ejpam-3747	221	18	∑m−1	∑m−1	X
ejpam-3747	221	19	i	i	PRON
ejpam-3747	221	20	=	=	NOUN
ejpam-3747	221	21	n	n	PART
ejpam-3747	221	22	∫	∫	NOUN
ejpam-3747	221	23	h(ai	h(ai	PROPN
ejpam-3747	221	24	,	,	PUNCT
ejpam-3747	221	25	ai+1	ai+1	NOUN
ejpam-3747	221	26	)	)	PUNCT
ejpam-3747	221	27	0	0	NUM
ejpam-3747	221	28	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	221	29	)	)	PUNCT
ejpam-3747	221	30	≤	≤	NOUN
ejpam-3747	221	31	∑m−1	∑m−1	VERB
ejpam-3747	221	32	i	i	PRON
ejpam-3747	221	33	=	=	NOUN
ejpam-3747	221	34	n	n	PART
ejpam-3747	221	35	ψ	ψ	X
ejpam-3747	221	36	(	(	PUNCT
ejpam-3747	221	37	∫	∫	PROPN
ejpam-3747	221	38	h(ai	h(ai	PROPN
ejpam-3747	221	39	,	,	PUNCT
ejpam-3747	221	40	ai+1	ai+1	NOUN
ejpam-3747	221	41	)	)	PUNCT
ejpam-3747	221	42	0	0	NUM
ejpam-3747	221	43	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	221	44	)	)	PUNCT
ejpam-3747	221	45	≤	≤	NOUN
ejpam-3747	221	46	∑m−1	∑m−1	VERB
ejpam-3747	221	47	i	i	PRON
ejpam-3747	221	48	=	=	PROPN
ejpam-3747	221	49	n	n	PROPN
ejpam-3747	221	50	φi	φi	ADV
ejpam-3747	221	51	(	(	PUNCT
ejpam-3747	221	52	ψ	ψ	X
ejpam-3747	221	53	(	(	PUNCT
ejpam-3747	221	54	∫	∫	PROPN
ejpam-3747	221	55	h(a0,a1	h(a0,a1	NOUN
ejpam-3747	221	56	)	)	PUNCT
ejpam-3747	221	57	0	0	NUM
ejpam-3747	221	58	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	221	59	)	)	PUNCT
ejpam-3747	221	60	)	)	PUNCT
ejpam-3747	221	61	,	,	PUNCT
ejpam-3747	221	62	s.	s.	PROPN
ejpam-3747	221	63	benchabane	benchabane	PROPN
ejpam-3747	221	64	,	,	PUNCT
ejpam-3747	221	65	s.	s.	PROPN
ejpam-3747	221	66	djebali	djebali	PROPN
ejpam-3747	221	67	,	,	PUNCT
ejpam-3747	221	68	t.	t.	PROPN
ejpam-3747	221	69	nazir	nazir	PROPN
ejpam-3747	221	70	/	/	SYM
ejpam-3747	221	71	eur	eur	PROPN
ejpam-3747	221	72	.	.	PUNCT
ejpam-3747	222	1	j.	j.	PROPN
ejpam-3747	222	2	pure	pure	PROPN
ejpam-3747	222	3	appl	appl	PROPN
ejpam-3747	222	4	.	.	PROPN
ejpam-3747	222	5	math	math	PROPN
ejpam-3747	222	6	,	,	PUNCT
ejpam-3747	222	7	13	13	NUM
ejpam-3747	222	8	(	(	PUNCT
ejpam-3747	222	9	5	5	NUM
ejpam-3747	222	10	)	)	PUNCT
ejpam-3747	222	11	(	(	PUNCT
ejpam-3747	222	12	2020	2020	NUM
ejpam-3747	222	13	)	)	PUNCT
ejpam-3747	222	14	,	,	PUNCT
ejpam-3747	222	15	1072	1072	NUM
ejpam-3747	222	16	-	-	SYM
ejpam-3747	222	17	1087	1087	NUM
ejpam-3747	222	18	1080	1080	NUM
ejpam-3747	222	19	for	for	ADP
ejpam-3747	222	20	each	each	DET
ejpam-3747	222	21	m	m	NOUN
ejpam-3747	222	22	,	,	PUNCT
ejpam-3747	222	23	n	n	PROPN
ejpam-3747	222	24	∈	∈	PROPN
ejpam-3747	222	25	n	n	X
ejpam-3747	222	26	with	with	ADP
ejpam-3747	222	27	m	m	PROPN
ejpam-3747	222	28	>	>	X
ejpam-3747	222	29	n.	n.	NOUN
ejpam-3747	222	30	by	by	ADP
ejpam-3747	222	31	taking	take	VERB
ejpam-3747	222	32	the	the	DET
ejpam-3747	222	33	limit	limit	NOUN
ejpam-3747	222	34	,	,	PUNCT
ejpam-3747	222	35	as	as	ADP
ejpam-3747	222	36	n	n	CCONJ
ejpam-3747	222	37	,	,	PUNCT
ejpam-3747	222	38	m	m	PROPN
ejpam-3747	222	39	→	→	SYM
ejpam-3747	222	40	∞	∞	PROPN
ejpam-3747	222	41	,	,	PUNCT
ejpam-3747	222	42	we	we	PRON
ejpam-3747	222	43	find	find	VERB
ejpam-3747	222	44	that	that	SCONJ
ejpam-3747	222	45	ψ	ψ	X
ejpam-3747	222	46	(	(	PUNCT
ejpam-3747	222	47	∫	∫	PROPN
ejpam-3747	222	48	h(an	h(an	PROPN
ejpam-3747	222	49	,	,	PUNCT
ejpam-3747	222	50	am	be	AUX
ejpam-3747	222	51	)	)	PUNCT
ejpam-3747	222	52	0	0	NUM
ejpam-3747	223	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	223	2	)	)	PUNCT
ejpam-3747	224	1	→	→	ADP
ejpam-3747	224	2	0	0	NUM
ejpam-3747	224	3	;	;	PUNCT
ejpam-3747	224	4	then	then	ADV
ejpam-3747	224	5	∫	∫	PROPN
ejpam-3747	224	6	h(an	h(an	PROPN
ejpam-3747	224	7	,	,	PUNCT
ejpam-3747	224	8	am	be	AUX
ejpam-3747	224	9	)	)	PUNCT
ejpam-3747	224	10	0	0	NUM
ejpam-3747	225	1	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-3747	225	2	→	→	SYM
ejpam-3747	225	3	0	0	NUM
ejpam-3747	225	4	,	,	PUNCT
ejpam-3747	225	5	as	as	ADP
ejpam-3747	225	6	n	n	CCONJ
ejpam-3747	225	7	,	,	PUNCT
ejpam-3747	225	8	m	m	PROPN
ejpam-3747	225	9	→	→	SYM
ejpam-3747	225	10	∞.	∞.	PROPN
ejpam-3747	225	11	by	by	ADP
ejpam-3747	225	12	lemma	lemma	PROPN
ejpam-3747	225	13	1	1	NUM
ejpam-3747	225	14	,	,	PUNCT
ejpam-3747	225	15	h(an	h(an	PROPN
ejpam-3747	225	16	,	,	PUNCT
ejpam-3747	225	17	am)→	am)→	ADJ
ejpam-3747	225	18	0	0	NUM
ejpam-3747	225	19	,	,	PUNCT
ejpam-3747	225	20	as	as	ADP
ejpam-3747	225	21	n	n	NUM
ejpam-3747	225	22	,	,	PUNCT
ejpam-3747	225	23	m→∞.	m→∞.	PROPN
ejpam-3747	225	24	thus	thus	ADV
ejpam-3747	225	25	(	(	PUNCT
ejpam-3747	225	26	an)n	an)n	PROPN
ejpam-3747	225	27	is	be	AUX
ejpam-3747	225	28	a	a	DET
ejpam-3747	225	29	cauchy	cauchy	ADJ
ejpam-3747	225	30	sequence	sequence	NOUN
ejpam-3747	225	31	in	in	ADP
ejpam-3747	225	32	cb(x	cb(x	NUM
ejpam-3747	225	33	)	)	PUNCT
ejpam-3747	225	34	.	.	PUNCT
ejpam-3747	226	1	since	since	SCONJ
ejpam-3747	226	2	(	(	PUNCT
ejpam-3747	226	3	x	x	X
ejpam-3747	226	4	,	,	PUNCT
ejpam-3747	226	5	d	d	NOUN
ejpam-3747	226	6	)	)	PUNCT
ejpam-3747	226	7	is	be	AUX
ejpam-3747	226	8	complete	complete	ADJ
ejpam-3747	226	9	,	,	PUNCT
ejpam-3747	226	10	(	(	PUNCT
ejpam-3747	226	11	cb(x	cb(x	NUM
ejpam-3747	226	12	)	)	PUNCT
ejpam-3747	226	13	,	,	PUNCT
ejpam-3747	226	14	h	h	NOUN
ejpam-3747	226	15	)	)	PUNCT
ejpam-3747	226	16	is	be	AUX
ejpam-3747	226	17	complete	complete	ADJ
ejpam-3747	226	18	too	too	ADV
ejpam-3747	226	19	and	and	CCONJ
ejpam-3747	226	20	we	we	PRON
ejpam-3747	226	21	deduce	deduce	VERB
ejpam-3747	226	22	that	that	SCONJ
ejpam-3747	226	23	an	an	DET
ejpam-3747	226	24	→	→	SYM
ejpam-3747	226	25	v	v	NOUN
ejpam-3747	226	26	,	,	PUNCT
ejpam-3747	226	27	as	as	ADP
ejpam-3747	226	28	n	n	PROPN
ejpam-3747	226	29	→	→	SYM
ejpam-3747	226	30	∞	∞	NUM
ejpam-3747	226	31	for	for	ADP
ejpam-3747	226	32	some	some	PRON
ejpam-3747	226	33	v	v	ADP
ejpam-3747	226	34	∈	∈	NOUN
ejpam-3747	226	35	cb(x	cb(x	NUM
ejpam-3747	226	36	)	)	PUNCT
ejpam-3747	226	37	.	.	PUNCT
ejpam-3747	227	1	to	to	PART
ejpam-3747	227	2	prove	prove	VERB
ejpam-3747	227	3	that	that	PRON
ejpam-3747	227	4	v	v	NOUN
ejpam-3747	227	5	=	=	SYM
ejpam-3747	227	6	s(v	s(v	PROPN
ejpam-3747	227	7	)	)	PUNCT
ejpam-3747	228	1	=	=	SYM
ejpam-3747	228	2	t	t	PROPN
ejpam-3747	228	3	(	(	PUNCT
ejpam-3747	228	4	v	v	NOUN
ejpam-3747	228	5	)	)	PUNCT
ejpam-3747	228	6	,	,	PUNCT
ejpam-3747	228	7	it	it	PRON
ejpam-3747	228	8	is	be	AUX
ejpam-3747	228	9	sufficient	sufficient	ADJ
ejpam-3747	228	10	to	to	PART
ejpam-3747	228	11	show	show	VERB
ejpam-3747	228	12	that	that	SCONJ
ejpam-3747	228	13	v	v	X
ejpam-3747	228	14	=	=	SYM
ejpam-3747	228	15	s(v	s(v	PROPN
ejpam-3747	228	16	)	)	PUNCT
ejpam-3747	228	17	,	,	PUNCT
ejpam-3747	228	18	the	the	DET
ejpam-3747	228	19	result	result	NOUN
ejpam-3747	228	20	then	then	ADV
ejpam-3747	228	21	follows	follow	VERB
ejpam-3747	228	22	from	from	ADP
ejpam-3747	228	23	(	(	PUNCT
ejpam-3747	228	24	i	i	NOUN
ejpam-3747	228	25	)	)	PUNCT
ejpam-3747	228	26	.	.	PUNCT
ejpam-3747	229	1	suppose	suppose	VERB
ejpam-3747	229	2	that	that	SCONJ
ejpam-3747	229	3	v	v	X
ejpam-3747	229	4	6=	6=	NUM
ejpam-3747	229	5	s(v	s(v	PROPN
ejpam-3747	229	6	)	)	PUNCT
ejpam-3747	229	7	.	.	PUNCT
ejpam-3747	230	1	since	since	SCONJ
ejpam-3747	230	2	(	(	PUNCT
ejpam-3747	230	3	a2n+1	a2n+1	VERB
ejpam-3747	230	4	,	,	PUNCT
ejpam-3747	230	5	a2n+2	a2n+2	PUNCT
ejpam-3747	230	6	)	)	PUNCT
ejpam-3747	230	7	=	=	SYM
ejpam-3747	230	8	(	(	PUNCT
ejpam-3747	230	9	a2n+1	a2n+1	PROPN
ejpam-3747	230	10	,	,	PUNCT
ejpam-3747	230	11	t	t	PROPN
ejpam-3747	230	12	(	(	PUNCT
ejpam-3747	230	13	a2n+1	a2n+1	PROPN
ejpam-3747	230	14	)	)	PUNCT
ejpam-3747	230	15	)	)	PUNCT
ejpam-3747	231	1	⊂	⊂	PROPN
ejpam-3747	231	2	e(g	e(g	PROPN
ejpam-3747	231	3	)	)	PUNCT
ejpam-3747	231	4	for	for	ADP
ejpam-3747	231	5	all	all	DET
ejpam-3747	231	6	n	n	PRON
ejpam-3747	231	7	∈	∈	PROPN
ejpam-3747	231	8	n	n	CCONJ
ejpam-3747	231	9	,	,	PUNCT
ejpam-3747	231	10	by	by	ADP
ejpam-3747	231	11	property	property	NOUN
ejpam-3747	231	12	(	(	PUNCT
ejpam-3747	231	13	p	p	NOUN
ejpam-3747	231	14	?	?	PUNCT
ejpam-3747	231	15	)	)	PUNCT
ejpam-3747	231	16	,	,	PUNCT
ejpam-3747	231	17	there	there	PRON
ejpam-3747	231	18	exists	exist	VERB
ejpam-3747	231	19	a	a	DET
ejpam-3747	231	20	subsequence	subsequence	NOUN
ejpam-3747	231	21	(	(	PUNCT
ejpam-3747	231	22	a2nk+1)k	a2nk+1)k	PROPN
ejpam-3747	231	23	of	of	ADP
ejpam-3747	231	24	(	(	PUNCT
ejpam-3747	231	25	a2n+1)n	a2n+1)n	X
ejpam-3747	231	26	such	such	ADJ
ejpam-3747	231	27	that	that	SCONJ
ejpam-3747	231	28	there	there	PRON
ejpam-3747	231	29	is	be	VERB
ejpam-3747	231	30	an	an	DET
ejpam-3747	231	31	edge	edge	NOUN
ejpam-3747	231	32	between	between	ADP
ejpam-3747	231	33	a2nk+1	a2nk+1	NOUN
ejpam-3747	231	34	and	and	CCONJ
ejpam-3747	231	35	v	v	NOUN
ejpam-3747	231	36	for	for	ADP
ejpam-3747	231	37	every	every	DET
ejpam-3747	231	38	k	k	PROPN
ejpam-3747	231	39	∈	∈	PROPN
ejpam-3747	231	40	n.	n.	NOUN
ejpam-3747	231	41	since	since	SCONJ
ejpam-3747	231	42	the	the	DET
ejpam-3747	231	43	pair	pair	NOUN
ejpam-3747	231	44	(	(	PUNCT
ejpam-3747	231	45	s	s	PROPN
ejpam-3747	231	46	,	,	PUNCT
ejpam-3747	231	47	t	t	PROPN
ejpam-3747	231	48	)	)	PUNCT
ejpam-3747	231	49	is	be	AUX
ejpam-3747	231	50	a	a	DET
ejpam-3747	231	51	graph	graph	NOUN
ejpam-3747	231	52	(	(	PUNCT
ejpam-3747	231	53	ψ	ψ	NOUN
ejpam-3747	231	54	,	,	PUNCT
ejpam-3747	231	55	φ)-weak	φ)-weak	VERB
ejpam-3747	231	56	contraction	contraction	NOUN
ejpam-3747	231	57	and	and	CCONJ
ejpam-3747	231	58	(	(	PUNCT
ejpam-3747	231	59	v	v	NOUN
ejpam-3747	231	60	,	,	PUNCT
ejpam-3747	231	61	a2nk+1	a2nk+1	ADV
ejpam-3747	231	62	)	)	PUNCT
ejpam-3747	232	1	⊂	⊂	PROPN
ejpam-3747	232	2	e(g	e(g	PROPN
ejpam-3747	232	3	)	)	PUNCT
ejpam-3747	232	4	,	,	PUNCT
ejpam-3747	232	5	we	we	PRON
ejpam-3747	232	6	have	have	VERB
ejpam-3747	232	7	that	that	PRON
ejpam-3747	232	8	ψ	ψ	X
ejpam-3747	232	9	(	(	PUNCT
ejpam-3747	232	10	∫	∫	PROPN
ejpam-3747	232	11	h(s(v	h(s(v	PROPN
ejpam-3747	232	12	)	)	PUNCT
ejpam-3747	232	13	,	,	PUNCT
ejpam-3747	232	14	a2nk+2	a2nk+2	NOUN
ejpam-3747	232	15	)	)	PUNCT
ejpam-3747	232	16	0	0	NUM
ejpam-3747	233	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	233	2	)	)	PUNCT
ejpam-3747	234	1	=	=	SYM
ejpam-3747	234	2	ψ	ψ	X
ejpam-3747	234	3	(	(	PUNCT
ejpam-3747	234	4	∫	∫	PROPN
ejpam-3747	234	5	h(s(v	h(s(v	PROPN
ejpam-3747	234	6	)	)	PUNCT
ejpam-3747	234	7	,	,	PUNCT
ejpam-3747	234	8	t	t	PROPN
ejpam-3747	234	9	(	(	PUNCT
ejpam-3747	234	10	a2nk+1	a2nk+1	PROPN
ejpam-3747	234	11	)	)	PUNCT
ejpam-3747	234	12	)	)	PUNCT
ejpam-3747	234	13	ϕ(t)dt	ϕ(t)dt	X
ejpam-3747	234	14	)	)	PUNCT
ejpam-3747	234	15	≤	≤	PROPN
ejpam-3747	235	1	φ	φ	PROPN
ejpam-3747	235	2	(	(	PUNCT
ejpam-3747	235	3	ψ	ψ	X
ejpam-3747	235	4	(	(	PUNCT
ejpam-3747	235	5	∫ms	∫ms	PROPN
ejpam-3747	235	6	,	,	PUNCT
ejpam-3747	235	7	t	t	PROPN
ejpam-3747	235	8	(	(	PUNCT
ejpam-3747	235	9	v	v	NOUN
ejpam-3747	235	10	,	,	PUNCT
ejpam-3747	235	11	a2nk+1	a2nk+1	ADJ
ejpam-3747	235	12	)	)	PUNCT
ejpam-3747	235	13	0	0	NUM
ejpam-3747	235	14	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	235	15	)	)	PUNCT
ejpam-3747	235	16	)	)	PUNCT
ejpam-3747	236	1	+	+	PUNCT
ejpam-3747	236	2	l	l	NOUN
ejpam-3747	236	3	∫	∫	PROPN
ejpam-3747	236	4	ns	ns	PROPN
ejpam-3747	236	5	,	,	PUNCT
ejpam-3747	236	6	t	t	PROPN
ejpam-3747	236	7	(	(	PUNCT
ejpam-3747	236	8	v	v	NOUN
ejpam-3747	236	9	,	,	PUNCT
ejpam-3747	236	10	a2nk+1	a2nk+1	ADJ
ejpam-3747	236	11	)	)	PUNCT
ejpam-3747	236	12	0	0	NUM
ejpam-3747	237	1	ϕ(t)dt	ϕ(t)dt	DET
ejpam-3747	237	2	≤	≤	PROPN
ejpam-3747	237	3	φ	φ	PROPN
ejpam-3747	237	4	(	(	PUNCT
ejpam-3747	237	5	ψ	ψ	X
ejpam-3747	237	6	(	(	PUNCT
ejpam-3747	237	7	∫ms	∫ms	PROPN
ejpam-3747	237	8	,	,	PUNCT
ejpam-3747	237	9	t	t	PROPN
ejpam-3747	237	10	(	(	PUNCT
ejpam-3747	237	11	v	v	NOUN
ejpam-3747	237	12	,	,	PUNCT
ejpam-3747	237	13	a2nk+1	a2nk+1	ADJ
ejpam-3747	237	14	)	)	PUNCT
ejpam-3747	237	15	0	0	NUM
ejpam-3747	237	16	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	237	17	)	)	PUNCT
ejpam-3747	237	18	)	)	PUNCT
ejpam-3747	238	1	+	+	PUNCT
ejpam-3747	238	2	l	l	NOUN
ejpam-3747	238	3	∫	∫	PROPN
ejpam-3747	238	4	h(v	h(v	PROPN
ejpam-3747	238	5	,	,	PUNCT
ejpam-3747	238	6	t	t	PROPN
ejpam-3747	238	7	(	(	PUNCT
ejpam-3747	238	8	a2nk+1	a2nk+1	PROPN
ejpam-3747	238	9	)	)	PUNCT
ejpam-3747	238	10	)	)	PUNCT
ejpam-3747	238	11	0	0	NUM
ejpam-3747	239	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	239	2	=	=	SYM
ejpam-3747	239	3	φ	φ	PROPN
ejpam-3747	239	4	(	(	PUNCT
ejpam-3747	239	5	ψ	ψ	X
ejpam-3747	239	6	(	(	PUNCT
ejpam-3747	239	7	∫ms	∫ms	PROPN
ejpam-3747	239	8	,	,	PUNCT
ejpam-3747	239	9	t	t	PROPN
ejpam-3747	239	10	(	(	PUNCT
ejpam-3747	239	11	v	v	NOUN
ejpam-3747	239	12	,	,	PUNCT
ejpam-3747	239	13	a2nk+1	a2nk+1	ADJ
ejpam-3747	239	14	)	)	PUNCT
ejpam-3747	239	15	0	0	NUM
ejpam-3747	240	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	240	2	)	)	PUNCT
ejpam-3747	240	3	)	)	PUNCT
ejpam-3747	241	1	+	+	PUNCT
ejpam-3747	241	2	l	l	NOUN
ejpam-3747	241	3	∫	∫	PROPN
ejpam-3747	241	4	h(v	h(v	NOUN
ejpam-3747	241	5	,	,	PUNCT
ejpam-3747	241	6	a2nk+2	a2nk+2	NOUN
ejpam-3747	241	7	)	)	PUNCT
ejpam-3747	241	8	0	0	NUM
ejpam-3747	242	1	ϕ(t)dt	ϕ(t)dt	NOUN
ejpam-3747	242	2	,	,	PUNCT
ejpam-3747	242	3	where	where	SCONJ
ejpam-3747	242	4	ms	ms	PROPN
ejpam-3747	242	5	,	,	PUNCT
ejpam-3747	242	6	t	t	PROPN
ejpam-3747	242	7	(	(	PUNCT
ejpam-3747	242	8	v	v	NOUN
ejpam-3747	242	9	,	,	PUNCT
ejpam-3747	242	10	a2nk+1	a2nk+1	ADV
ejpam-3747	242	11	)	)	PUNCT
ejpam-3747	243	1	=	=	SYM
ejpam-3747	243	2	max	max	PROPN
ejpam-3747	243	3	{	{	PUNCT
ejpam-3747	243	4	h(v	h(v	PROPN
ejpam-3747	243	5	,	,	PUNCT
ejpam-3747	243	6	a2nk+1	a2nk+1	ADV
ejpam-3747	243	7	)	)	PUNCT
ejpam-3747	243	8	,	,	PUNCT
ejpam-3747	243	9	h(v	h(v	PROPN
ejpam-3747	243	10	,	,	PUNCT
ejpam-3747	243	11	s(v	s(v	PROPN
ejpam-3747	243	12	)	)	PUNCT
ejpam-3747	243	13	)	)	PUNCT
ejpam-3747	243	14	,	,	PUNCT
ejpam-3747	243	15	h(a2nk+1	h(a2nk+1	NOUN
ejpam-3747	243	16	,	,	PUNCT
ejpam-3747	243	17	t	t	PROPN
ejpam-3747	243	18	(	(	PUNCT
ejpam-3747	243	19	a2nk+1	a2nk+1	PROPN
ejpam-3747	243	20	)	)	PUNCT
ejpam-3747	243	21	)	)	PUNCT
ejpam-3747	243	22	,	,	PUNCT
ejpam-3747	243	23	h(v	h(v	PROPN
ejpam-3747	243	24	,	,	PUNCT
ejpam-3747	243	25	t	t	PROPN
ejpam-3747	243	26	(	(	PUNCT
ejpam-3747	243	27	a2nk+1	a2nk+1	PROPN
ejpam-3747	243	28	)	)	PUNCT
ejpam-3747	243	29	)	)	PUNCT
ejpam-3747	244	1	+	+	ADV
ejpam-3747	244	2	h(a2nk+1	h(a2nk+1	NOUN
ejpam-3747	244	3	,	,	PUNCT
ejpam-3747	244	4	s(v	s(v	PROPN
ejpam-3747	244	5	)	)	PUNCT
ejpam-3747	244	6	)	)	PUNCT
ejpam-3747	244	7	2	2	X
ejpam-3747	244	8	}	}	PUNCT
ejpam-3747	244	9	=	=	SYM
ejpam-3747	244	10	max	max	X
ejpam-3747	244	11	{	{	PUNCT
ejpam-3747	244	12	h(v	h(v	PROPN
ejpam-3747	244	13	,	,	PUNCT
ejpam-3747	244	14	a2nk+1	a2nk+1	ADV
ejpam-3747	244	15	)	)	PUNCT
ejpam-3747	244	16	,	,	PUNCT
ejpam-3747	244	17	h(v	h(v	PROPN
ejpam-3747	244	18	,	,	PUNCT
ejpam-3747	244	19	s(v	s(v	PROPN
ejpam-3747	244	20	)	)	PUNCT
ejpam-3747	244	21	)	)	PUNCT
ejpam-3747	244	22	,	,	PUNCT
ejpam-3747	244	23	h(a2nk+1	h(a2nk+1	NOUN
ejpam-3747	244	24	,	,	PUNCT
ejpam-3747	244	25	a2nk+2	a2nk+2	NOUN
ejpam-3747	244	26	)	)	PUNCT
ejpam-3747	244	27	,	,	PUNCT
ejpam-3747	244	28	h(v	h(v	PROPN
ejpam-3747	244	29	,	,	PUNCT
ejpam-3747	244	30	a2nk+2	a2nk+2	NOUN
ejpam-3747	244	31	)	)	PUNCT
ejpam-3747	245	1	+	+	PUNCT
ejpam-3747	245	2	h(a2nk+1	h(a2nk+1	NOUN
ejpam-3747	245	3	,	,	PUNCT
ejpam-3747	245	4	s(v	s(v	PROPN
ejpam-3747	245	5	)	)	PUNCT
ejpam-3747	245	6	)	)	PUNCT
ejpam-3747	245	7	2	2	NUM
ejpam-3747	245	8	}	}	PUNCT
ejpam-3747	245	9	.	.	PUNCT
ejpam-3747	246	1	since	since	SCONJ
ejpam-3747	246	2	lim	lim	PROPN
ejpam-3747	246	3	k→+∞	k→+∞	PROPN
ejpam-3747	246	4	h(v	h(v	PROPN
ejpam-3747	246	5	,	,	PUNCT
ejpam-3747	246	6	a2nk+1	a2nk+1	ADV
ejpam-3747	246	7	)	)	PUNCT
ejpam-3747	247	1	=	=	PUNCT
ejpam-3747	248	1	h(v	h(v	NOUN
ejpam-3747	248	2	,	,	PUNCT
ejpam-3747	248	3	v	v	NOUN
ejpam-3747	248	4	)	)	PUNCT
ejpam-3747	248	5	=	=	SYM
ejpam-3747	248	6	0	0	NUM
ejpam-3747	248	7	,	,	PUNCT
ejpam-3747	248	8	then	then	ADV
ejpam-3747	248	9	there	there	PRON
ejpam-3747	248	10	exists	exist	VERB
ejpam-3747	248	11	k1	k1	PROPN
ejpam-3747	248	12	∈	∈	PROPN
ejpam-3747	248	13	n	n	PRON
ejpam-3747	248	14	such	such	ADJ
ejpam-3747	248	15	that	that	SCONJ
ejpam-3747	248	16	h(v	h(v	PROPN
ejpam-3747	248	17	,	,	PUNCT
ejpam-3747	248	18	a2nk+1	a2nk+1	ADV
ejpam-3747	248	19	)	)	PUNCT
ejpam-3747	248	20	≤	≤	NOUN
ejpam-3747	249	1	h(v	h(v	PROPN
ejpam-3747	249	2	,	,	PUNCT
ejpam-3747	249	3	s(v	s(v	PROPN
ejpam-3747	249	4	)	)	PUNCT
ejpam-3747	249	5	)	)	PUNCT
ejpam-3747	249	6	2	2	NUM
ejpam-3747	249	7	,	,	PUNCT
ejpam-3747	249	8	∀	∀	X
ejpam-3747	249	9	k	k	X
ejpam-3747	249	10	≥	≥	PROPN
ejpam-3747	249	11	k1	k1	PROPN
ejpam-3747	249	12	.	.	PUNCT
ejpam-3747	250	1	since	since	SCONJ
ejpam-3747	250	2	lim	lim	PROPN
ejpam-3747	250	3	k→+∞	k→+∞	PROPN
ejpam-3747	250	4	h(a2nk+1	h(a2nk+1	PROPN
ejpam-3747	250	5	,	,	PUNCT
ejpam-3747	250	6	a2nk+2	a2nk+2	NOUN
ejpam-3747	250	7	)	)	PUNCT
ejpam-3747	250	8	=	=	SYM
ejpam-3747	250	9	0	0	NUM
ejpam-3747	250	10	,	,	PUNCT
ejpam-3747	250	11	then	then	ADV
ejpam-3747	250	12	there	there	PRON
ejpam-3747	250	13	exists	exist	VERB
ejpam-3747	250	14	k2	k2	PROPN
ejpam-3747	250	15	∈	∈	PROPN
ejpam-3747	250	16	n	n	PRON
ejpam-3747	250	17	such	such	ADJ
ejpam-3747	250	18	that	that	SCONJ
ejpam-3747	250	19	h(a2nk+1	h(a2nk+1	NOUN
ejpam-3747	250	20	,	,	PUNCT
ejpam-3747	250	21	a2nk+2	a2nk+2	NOUN
ejpam-3747	250	22	)	)	PUNCT
ejpam-3747	250	23	≤	≤	NOUN
ejpam-3747	251	1	h(v	h(v	PROPN
ejpam-3747	251	2	,	,	PUNCT
ejpam-3747	251	3	s(v	s(v	PROPN
ejpam-3747	251	4	)	)	PUNCT
ejpam-3747	251	5	)	)	PUNCT
ejpam-3747	251	6	2	2	NUM
ejpam-3747	251	7	,	,	PUNCT
ejpam-3747	251	8	∀	∀	X
ejpam-3747	251	9	k	k	PROPN
ejpam-3747	251	10	≥	≥	X
ejpam-3747	251	11	k2	k2	PROPN
ejpam-3747	251	12	.	.	PUNCT
ejpam-3747	252	1	in	in	ADP
ejpam-3747	252	2	addition	addition	NOUN
ejpam-3747	252	3	lim	lim	PROPN
ejpam-3747	252	4	k→+∞	k→+∞	PROPN
ejpam-3747	252	5	h(v	h(v	PROPN
ejpam-3747	252	6	,	,	PUNCT
ejpam-3747	252	7	a2nk+2	a2nk+2	NOUN
ejpam-3747	252	8	)	)	PUNCT
ejpam-3747	253	1	+	+	PUNCT
ejpam-3747	253	2	h(a2nk+1	h(a2nk+1	NOUN
ejpam-3747	253	3	,	,	PUNCT
ejpam-3747	253	4	s(v	s(v	PROPN
ejpam-3747	253	5	)	)	PUNCT
ejpam-3747	253	6	)	)	PUNCT
ejpam-3747	253	7	2	2	NUM
ejpam-3747	253	8	=	=	SYM
ejpam-3747	253	9	h(v	h(v	PROPN
ejpam-3747	253	10	,	,	PUNCT
ejpam-3747	253	11	s(v	s(v	PROPN
ejpam-3747	253	12	)	)	PUNCT
ejpam-3747	253	13	)	)	PUNCT
ejpam-3747	253	14	2	2	NUM
ejpam-3747	253	15	s.	s.	PROPN
ejpam-3747	253	16	benchabane	benchabane	PROPN
ejpam-3747	253	17	,	,	PUNCT
ejpam-3747	253	18	s.	s.	PROPN
ejpam-3747	253	19	djebali	djebali	PROPN
ejpam-3747	253	20	,	,	PUNCT
ejpam-3747	253	21	t.	t.	PROPN
ejpam-3747	253	22	nazir	nazir	PROPN
ejpam-3747	253	23	/	/	SYM
ejpam-3747	253	24	eur	eur	PROPN
ejpam-3747	253	25	.	.	PUNCT
ejpam-3747	254	1	j.	j.	PROPN
ejpam-3747	254	2	pure	pure	PROPN
ejpam-3747	254	3	appl	appl	PROPN
ejpam-3747	254	4	.	.	PROPN
ejpam-3747	254	5	math	math	PROPN
ejpam-3747	254	6	,	,	PUNCT
ejpam-3747	254	7	13	13	NUM
ejpam-3747	254	8	(	(	PUNCT
ejpam-3747	254	9	5	5	NUM
ejpam-3747	254	10	)	)	PUNCT
ejpam-3747	254	11	(	(	PUNCT
ejpam-3747	254	12	2020	2020	NUM
ejpam-3747	254	13	)	)	PUNCT
ejpam-3747	254	14	,	,	PUNCT
ejpam-3747	254	15	1072	1072	NUM
ejpam-3747	254	16	-	-	SYM
ejpam-3747	254	17	1087	1087	NUM
ejpam-3747	254	18	1081	1081	NUM
ejpam-3747	254	19	provides	provide	VERB
ejpam-3747	254	20	the	the	DET
ejpam-3747	254	21	existence	existence	NOUN
ejpam-3747	254	22	of	of	ADP
ejpam-3747	254	23	some	some	DET
ejpam-3747	254	24	k3	k3	ADJ
ejpam-3747	254	25	∈	∈	PROPN
ejpam-3747	254	26	n	n	PRON
ejpam-3747	254	27	such	such	ADJ
ejpam-3747	254	28	that	that	SCONJ
ejpam-3747	254	29	h(v	h(v	PROPN
ejpam-3747	254	30	,	,	PUNCT
ejpam-3747	254	31	a2nk+2	a2nk+2	NOUN
ejpam-3747	254	32	)	)	PUNCT
ejpam-3747	255	1	+	+	PUNCT
ejpam-3747	255	2	h(a2nk+1	h(a2nk+1	NOUN
ejpam-3747	255	3	,	,	PUNCT
ejpam-3747	255	4	s(v	s(v	PROPN
ejpam-3747	255	5	)	)	PUNCT
ejpam-3747	255	6	)	)	PUNCT
ejpam-3747	255	7	2	2	NUM
ejpam-3747	255	8	≤	≤	NOUN
ejpam-3747	255	9	h(v	h(v	PROPN
ejpam-3747	255	10	,	,	PUNCT
ejpam-3747	255	11	s(v	s(v	PROPN
ejpam-3747	255	12	)	)	PUNCT
ejpam-3747	255	13	)	)	PUNCT
ejpam-3747	255	14	,	,	PUNCT
ejpam-3747	255	15	∀	∀	PUNCT
ejpam-3747	255	16	k	k	X
ejpam-3747	255	17	≥	≥	PRON
ejpam-3747	255	18	k3	k3	VERB
ejpam-3747	255	19	.	.	PUNCT
ejpam-3747	256	1	as	as	ADP
ejpam-3747	256	2	a	a	DET
ejpam-3747	256	3	consequence	consequence	NOUN
ejpam-3747	256	4	for	for	ADP
ejpam-3747	256	5	k	k	PROPN
ejpam-3747	256	6	≥	≥	PROPN
ejpam-3747	256	7	k0	k0	PROPN
ejpam-3747	256	8	=	=	PROPN
ejpam-3747	256	9	max{k1	max{k1	PROPN
ejpam-3747	256	10	,	,	PUNCT
ejpam-3747	256	11	k2	k2	NOUN
ejpam-3747	256	12	,	,	PUNCT
ejpam-3747	256	13	k3	k3	VERB
ejpam-3747	256	14	}	}	PUNCT
ejpam-3747	256	15	,	,	PUNCT
ejpam-3747	256	16	we	we	PRON
ejpam-3747	256	17	have	have	VERB
ejpam-3747	256	18	ms	ms	PROPN
ejpam-3747	256	19	,	,	PUNCT
ejpam-3747	256	20	t	t	PROPN
ejpam-3747	256	21	(	(	PUNCT
ejpam-3747	256	22	v	v	NOUN
ejpam-3747	256	23	,	,	PUNCT
ejpam-3747	256	24	a2nk+1	a2nk+1	ADV
ejpam-3747	256	25	)	)	PUNCT
ejpam-3747	257	1	=	=	PUNCT
ejpam-3747	257	2	h(v	h(v	PROPN
ejpam-3747	257	3	,	,	PUNCT
ejpam-3747	257	4	s(v	s(v	PROPN
ejpam-3747	257	5	)	)	PUNCT
ejpam-3747	257	6	)	)	PUNCT
ejpam-3747	257	7	,	,	PUNCT
ejpam-3747	257	8	∀	∀	PUNCT
ejpam-3747	258	1	k	k	PROPN
ejpam-3747	258	2	≥	≥	PROPN
ejpam-3747	258	3	k0	k0	PROPN
ejpam-3747	258	4	.	.	PUNCT
ejpam-3747	259	1	hence	hence	ADV
ejpam-3747	259	2	for	for	SCONJ
ejpam-3747	259	3	all	all	DET
ejpam-3747	259	4	k	k	PROPN
ejpam-3747	259	5	≥	≥	PROPN
ejpam-3747	259	6	k0	k0	PROPN
ejpam-3747	259	7	,	,	PUNCT
ejpam-3747	259	8	ψ	ψ	X
ejpam-3747	259	9	(	(	PUNCT
ejpam-3747	259	10	∫	∫	PROPN
ejpam-3747	259	11	h(s(v	h(s(v	PROPN
ejpam-3747	259	12	)	)	PUNCT
ejpam-3747	259	13	,	,	PUNCT
ejpam-3747	259	14	a2nk+1	a2nk+1	ADV
ejpam-3747	259	15	)	)	PUNCT
ejpam-3747	259	16	0	0	NUM
ejpam-3747	260	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	260	2	)	)	PUNCT
ejpam-3747	261	1	≤	≤	PROPN
ejpam-3747	261	2	φ	φ	PROPN
ejpam-3747	261	3	(	(	PUNCT
ejpam-3747	261	4	ψ	ψ	X
ejpam-3747	261	5	(	(	PUNCT
ejpam-3747	261	6	∫	∫	PROPN
ejpam-3747	261	7	h(v	h(v	PROPN
ejpam-3747	261	8	,	,	PUNCT
ejpam-3747	261	9	s(v	s(v	PROPN
ejpam-3747	261	10	)	)	PUNCT
ejpam-3747	261	11	)	)	PUNCT
ejpam-3747	261	12	0	0	NUM
ejpam-3747	261	13	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	261	14	)	)	PUNCT
ejpam-3747	261	15	)	)	PUNCT
ejpam-3747	262	1	+	+	CCONJ
ejpam-3747	262	2	l	l	NOUN
ejpam-3747	262	3	∫	∫	PROPN
ejpam-3747	262	4	h(v	h(v	NOUN
ejpam-3747	262	5	,	,	PUNCT
ejpam-3747	262	6	a2nk+2	a2nk+2	NOUN
ejpam-3747	262	7	)	)	PUNCT
ejpam-3747	262	8	0	0	NUM
ejpam-3747	263	1	ϕ(t)dt	ϕ(t)dt	NOUN
ejpam-3747	263	2	.	.	PUNCT
ejpam-3747	264	1	taking	take	VERB
ejpam-3747	264	2	the	the	DET
ejpam-3747	264	3	limit	limit	NOUN
ejpam-3747	264	4	as	as	ADP
ejpam-3747	264	5	k	k	PROPN
ejpam-3747	264	6	→	→	PROPN
ejpam-3747	264	7	+	+	PROPN
ejpam-3747	264	8	∞	∞	NUM
ejpam-3747	264	9	and	and	CCONJ
ejpam-3747	264	10	using	use	VERB
ejpam-3747	264	11	properties	property	NOUN
ejpam-3747	264	12	of	of	ADP
ejpam-3747	264	13	φ	φ	PROPN
ejpam-3747	264	14	and	and	CCONJ
ejpam-3747	264	15	ψ	ψ	PROPN
ejpam-3747	264	16	,	,	PUNCT
ejpam-3747	264	17	we	we	PRON
ejpam-3747	264	18	find	find	VERB
ejpam-3747	264	19	ψ	ψ	X
ejpam-3747	264	20	(	(	PUNCT
ejpam-3747	264	21	∫	∫	PROPN
ejpam-3747	264	22	h(s(v	h(s(v	PROPN
ejpam-3747	264	23	)	)	PUNCT
ejpam-3747	264	24	,	,	PUNCT
ejpam-3747	264	25	v	v	NOUN
ejpam-3747	264	26	)	)	PUNCT
ejpam-3747	264	27	0	0	NUM
ejpam-3747	264	28	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	264	29	)	)	PUNCT
ejpam-3747	265	1	≤	≤	PROPN
ejpam-3747	265	2	φ	φ	PROPN
ejpam-3747	265	3	(	(	PUNCT
ejpam-3747	265	4	ψ	ψ	X
ejpam-3747	265	5	(	(	PUNCT
ejpam-3747	265	6	∫	∫	PROPN
ejpam-3747	265	7	h(s(v	h(s(v	PROPN
ejpam-3747	265	8	)	)	PUNCT
ejpam-3747	265	9	,	,	PUNCT
ejpam-3747	265	10	v	v	NOUN
ejpam-3747	265	11	)	)	PUNCT
ejpam-3747	265	12	0	0	NUM
ejpam-3747	265	13	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	265	14	)	)	PUNCT
ejpam-3747	265	15	)	)	PUNCT
ejpam-3747	266	1	<	<	X
ejpam-3747	266	2	ψ	ψ	X
ejpam-3747	266	3	(	(	PUNCT
ejpam-3747	266	4	∫	∫	PROPN
ejpam-3747	266	5	h(s(v	h(s(v	PROPN
ejpam-3747	266	6	)	)	PUNCT
ejpam-3747	266	7	,	,	PUNCT
ejpam-3747	266	8	v	v	NOUN
ejpam-3747	266	9	)	)	PUNCT
ejpam-3747	266	10	0	0	NUM
ejpam-3747	267	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	267	2	)	)	PUNCT
ejpam-3747	267	3	,	,	PUNCT
ejpam-3747	267	4	which	which	PRON
ejpam-3747	267	5	is	be	AUX
ejpam-3747	267	6	a	a	DET
ejpam-3747	267	7	contradiction	contradiction	NOUN
ejpam-3747	267	8	.	.	PUNCT
ejpam-3747	268	1	then	then	ADV
ejpam-3747	268	2	s(v	s(v	PROPN
ejpam-3747	268	3	)	)	PUNCT
ejpam-3747	269	1	=	=	SYM
ejpam-3747	269	2	v	v	NOUN
ejpam-3747	269	3	,	,	PUNCT
ejpam-3747	269	4	that	that	PRON
ejpam-3747	269	5	is	be	AUX
ejpam-3747	269	6	v	v	ADP
ejpam-3747	269	7	∈	∈	PROPN
ejpam-3747	269	8	f	f	X
ejpam-3747	269	9	(	(	PUNCT
ejpam-3747	269	10	s	s	NOUN
ejpam-3747	269	11	)	)	PUNCT
ejpam-3747	269	12	.	.	PUNCT
ejpam-3747	270	1	by	by	ADP
ejpam-3747	270	2	(	(	PUNCT
ejpam-3747	270	3	i	i	NOUN
ejpam-3747	270	4	)	)	PUNCT
ejpam-3747	270	5	,	,	PUNCT
ejpam-3747	270	6	f	f	PROPN
ejpam-3747	270	7	(	(	PUNCT
ejpam-3747	270	8	s	s	NOUN
ejpam-3747	270	9	)	)	PUNCT
ejpam-3747	270	10	∩	∩	ADJ
ejpam-3747	270	11	f	f	X
ejpam-3747	270	12	(	(	PUNCT
ejpam-3747	270	13	t	t	PROPN
ejpam-3747	270	14	)	)	PUNCT
ejpam-3747	270	15	6=	6=	ADP
ejpam-3747	270	16	∅.	∅.	PROPN
ejpam-3747	270	17	(	(	PUNCT
ejpam-3747	270	18	3	3	X
ejpam-3747	270	19	)	)	PUNCT
ejpam-3747	270	20	suppose	suppose	VERB
ejpam-3747	270	21	that	that	SCONJ
ejpam-3747	270	22	f	f	PROPN
ejpam-3747	270	23	(	(	PUNCT
ejpam-3747	270	24	s)∩f	s)∩f	NOUN
ejpam-3747	270	25	(	(	PUNCT
ejpam-3747	270	26	t	t	PROPN
ejpam-3747	270	27	)	)	PUNCT
ejpam-3747	270	28	is	be	AUX
ejpam-3747	270	29	complete	complete	ADJ
ejpam-3747	270	30	.	.	PUNCT
ejpam-3747	271	1	let	let	VERB
ejpam-3747	271	2	u	u	NOUN
ejpam-3747	271	3	,	,	PUNCT
ejpam-3747	271	4	v	v	PROPN
ejpam-3747	271	5	∈	∈	ADJ
ejpam-3747	271	6	f	f	X
ejpam-3747	271	7	(	(	PUNCT
ejpam-3747	271	8	s)∩f	s)∩f	NOUN
ejpam-3747	271	9	(	(	PUNCT
ejpam-3747	271	10	t	t	PROPN
ejpam-3747	271	11	)	)	PUNCT
ejpam-3747	271	12	and	and	CCONJ
ejpam-3747	271	13	suppose	suppose	VERB
ejpam-3747	271	14	that	that	SCONJ
ejpam-3747	271	15	h(u	h(u	PROPN
ejpam-3747	271	16	,	,	PUNCT
ejpam-3747	271	17	v	v	NOUN
ejpam-3747	271	18	)	)	PUNCT
ejpam-3747	271	19	6=	6=	ADP
ejpam-3747	271	20	0	0	X
ejpam-3747	271	21	.	.	PUNCT
ejpam-3747	272	1	since	since	SCONJ
ejpam-3747	272	2	the	the	DET
ejpam-3747	272	3	pair	pair	NOUN
ejpam-3747	272	4	(	(	PUNCT
ejpam-3747	272	5	s	s	PROPN
ejpam-3747	272	6	,	,	PUNCT
ejpam-3747	272	7	t	t	PROPN
ejpam-3747	272	8	)	)	PUNCT
ejpam-3747	272	9	is	be	AUX
ejpam-3747	272	10	a	a	DET
ejpam-3747	272	11	graph	graph	NOUN
ejpam-3747	272	12	(	(	PUNCT
ejpam-3747	272	13	ψ	ψ	NOUN
ejpam-3747	272	14	,	,	PUNCT
ejpam-3747	272	15	φ)-weak	φ)-weak	VERB
ejpam-3747	272	16	contraction	contraction	NOUN
ejpam-3747	272	17	,	,	PUNCT
ejpam-3747	272	18	we	we	PRON
ejpam-3747	272	19	have	have	VERB
ejpam-3747	272	20	ψ	ψ	X
ejpam-3747	272	21	(	(	PUNCT
ejpam-3747	272	22	∫	∫	PROPN
ejpam-3747	272	23	h(u	h(u	PROPN
ejpam-3747	272	24	,	,	PUNCT
ejpam-3747	272	25	v	v	NOUN
ejpam-3747	272	26	)	)	PUNCT
ejpam-3747	272	27	0	0	NUM
ejpam-3747	273	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	273	2	)	)	PUNCT
ejpam-3747	274	1	=	=	SYM
ejpam-3747	274	2	ψ	ψ	X
ejpam-3747	274	3	(	(	PUNCT
ejpam-3747	274	4	∫	∫	PROPN
ejpam-3747	274	5	h(s(u),t	h(s(u),t	PROPN
ejpam-3747	274	6	(	(	PUNCT
ejpam-3747	274	7	v	v	NOUN
ejpam-3747	274	8	)	)	PUNCT
ejpam-3747	274	9	)	)	PUNCT
ejpam-3747	274	10	0	0	NUM
ejpam-3747	275	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	275	2	)	)	PUNCT
ejpam-3747	276	1	≤	≤	PROPN
ejpam-3747	276	2	φ	φ	PROPN
ejpam-3747	276	3	(	(	PUNCT
ejpam-3747	276	4	ψ	ψ	X
ejpam-3747	276	5	(	(	PUNCT
ejpam-3747	276	6	∫ms	∫ms	PROPN
ejpam-3747	276	7	,	,	PUNCT
ejpam-3747	276	8	t	t	PROPN
ejpam-3747	276	9	(	(	PUNCT
ejpam-3747	276	10	u	u	NOUN
ejpam-3747	276	11	,	,	PUNCT
ejpam-3747	276	12	v	v	NOUN
ejpam-3747	276	13	)	)	PUNCT
ejpam-3747	276	14	0	0	NUM
ejpam-3747	277	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	277	2	)	)	PUNCT
ejpam-3747	277	3	)	)	PUNCT
ejpam-3747	278	1	+	+	CCONJ
ejpam-3747	278	2	l	l	NOUN
ejpam-3747	278	3	∫	∫	PROPN
ejpam-3747	278	4	ns	ns	PROPN
ejpam-3747	278	5	,	,	PUNCT
ejpam-3747	278	6	t	t	PROPN
ejpam-3747	278	7	(	(	PUNCT
ejpam-3747	278	8	u	u	NOUN
ejpam-3747	278	9	,	,	PUNCT
ejpam-3747	278	10	v	v	NOUN
ejpam-3747	278	11	)	)	PUNCT
ejpam-3747	278	12	0	0	NUM
ejpam-3747	279	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	279	2	=	=	SYM
ejpam-3747	279	3	φ	φ	PROPN
ejpam-3747	279	4	(	(	PUNCT
ejpam-3747	279	5	ψ	ψ	X
ejpam-3747	279	6	(	(	PUNCT
ejpam-3747	279	7	∫ms	∫ms	PROPN
ejpam-3747	279	8	,	,	PUNCT
ejpam-3747	279	9	t	t	PROPN
ejpam-3747	279	10	(	(	PUNCT
ejpam-3747	279	11	u	u	NOUN
ejpam-3747	279	12	,	,	PUNCT
ejpam-3747	279	13	v	v	NOUN
ejpam-3747	279	14	)	)	PUNCT
ejpam-3747	279	15	0	0	NUM
ejpam-3747	279	16	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	279	17	)	)	PUNCT
ejpam-3747	279	18	)	)	PUNCT
ejpam-3747	279	19	,	,	PUNCT
ejpam-3747	279	20	where	where	SCONJ
ejpam-3747	279	21	ms	ms	PROPN
ejpam-3747	279	22	,	,	PUNCT
ejpam-3747	279	23	t	t	PROPN
ejpam-3747	279	24	(	(	PUNCT
ejpam-3747	279	25	u	u	NOUN
ejpam-3747	279	26	,	,	PUNCT
ejpam-3747	279	27	v	v	NOUN
ejpam-3747	279	28	)	)	PUNCT
ejpam-3747	279	29	=	=	SYM
ejpam-3747	279	30	max	max	PROPN
ejpam-3747	280	1	=	=	SYM
ejpam-3747	280	2	{	{	PUNCT
ejpam-3747	280	3	h(u	h(u	PROPN
ejpam-3747	280	4	,	,	PUNCT
ejpam-3747	280	5	v	v	NOUN
ejpam-3747	280	6	)	)	PUNCT
ejpam-3747	280	7	,	,	PUNCT
ejpam-3747	280	8	h(u	h(u	PROPN
ejpam-3747	280	9	,	,	PUNCT
ejpam-3747	280	10	s(u	s(u	PROPN
ejpam-3747	280	11	)	)	PUNCT
ejpam-3747	280	12	)	)	PUNCT
ejpam-3747	280	13	,	,	PUNCT
ejpam-3747	280	14	h(v	h(v	PROPN
ejpam-3747	280	15	,	,	PUNCT
ejpam-3747	280	16	t	t	PROPN
ejpam-3747	280	17	(	(	PUNCT
ejpam-3747	280	18	v	v	NOUN
ejpam-3747	280	19	)	)	PUNCT
ejpam-3747	280	20	)	)	PUNCT
ejpam-3747	280	21	,	,	PUNCT
ejpam-3747	280	22	h(u	h(u	PROPN
ejpam-3747	280	23	,	,	PUNCT
ejpam-3747	280	24	t	t	PROPN
ejpam-3747	280	25	(	(	PUNCT
ejpam-3747	280	26	v	v	NOUN
ejpam-3747	280	27	)	)	PUNCT
ejpam-3747	280	28	)	)	PUNCT
ejpam-3747	281	1	+	+	ADP
ejpam-3747	281	2	h(v	h(v	PROPN
ejpam-3747	281	3	,	,	PUNCT
ejpam-3747	281	4	s(u	s(u	PROPN
ejpam-3747	281	5	)	)	PUNCT
ejpam-3747	281	6	)	)	PUNCT
ejpam-3747	281	7	2	2	X
ejpam-3747	281	8	}	}	PUNCT
ejpam-3747	281	9	=	=	SYM
ejpam-3747	281	10	max	max	PROPN
ejpam-3747	281	11	{	{	PUNCT
ejpam-3747	281	12	h(u	h(u	PROPN
ejpam-3747	281	13	,	,	PUNCT
ejpam-3747	281	14	v	v	NOUN
ejpam-3747	281	15	)	)	PUNCT
ejpam-3747	281	16	,	,	PUNCT
ejpam-3747	281	17	h(u	h(u	PROPN
ejpam-3747	281	18	,	,	PUNCT
ejpam-3747	281	19	u	u	NOUN
ejpam-3747	281	20	)	)	PUNCT
ejpam-3747	281	21	,	,	PUNCT
ejpam-3747	281	22	h(v	h(v	PROPN
ejpam-3747	281	23	,	,	PUNCT
ejpam-3747	281	24	v	v	NOUN
ejpam-3747	281	25	)	)	PUNCT
ejpam-3747	281	26	,	,	PUNCT
ejpam-3747	281	27	h(u	h(u	PROPN
ejpam-3747	281	28	,	,	PUNCT
ejpam-3747	281	29	v	v	NOUN
ejpam-3747	281	30	)	)	PUNCT
ejpam-3747	281	31	+	+	ADP
ejpam-3747	281	32	h(v	h(v	PROPN
ejpam-3747	281	33	,	,	PUNCT
ejpam-3747	281	34	u	u	NOUN
ejpam-3747	281	35	)	)	PUNCT
ejpam-3747	281	36	2	2	NUM
ejpam-3747	281	37	}	}	PUNCT
ejpam-3747	281	38	=	=	SYM
ejpam-3747	281	39	h(u	h(u	PROPN
ejpam-3747	281	40	,	,	PUNCT
ejpam-3747	281	41	v	v	NOUN
ejpam-3747	281	42	)	)	PUNCT
ejpam-3747	281	43	.	.	PUNCT
ejpam-3747	282	1	again	again	ADV
ejpam-3747	282	2	the	the	DET
ejpam-3747	282	3	property	property	NOUN
ejpam-3747	282	4	of	of	ADP
ejpam-3747	282	5	φ	φ	PROPN
ejpam-3747	282	6	yields	yields	PROPN
ejpam-3747	282	7	ψ	ψ	X
ejpam-3747	282	8	(	(	PUNCT
ejpam-3747	282	9	∫	∫	PROPN
ejpam-3747	282	10	h(u	h(u	PROPN
ejpam-3747	282	11	,	,	PUNCT
ejpam-3747	282	12	v	v	NOUN
ejpam-3747	282	13	)	)	PUNCT
ejpam-3747	282	14	0	0	NUM
ejpam-3747	283	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	283	2	)	)	PUNCT
ejpam-3747	284	1	≤	≤	PROPN
ejpam-3747	284	2	φ	φ	PROPN
ejpam-3747	284	3	(	(	PUNCT
ejpam-3747	284	4	ψ	ψ	X
ejpam-3747	284	5	(	(	PUNCT
ejpam-3747	284	6	∫	∫	PROPN
ejpam-3747	284	7	h(u	h(u	PROPN
ejpam-3747	284	8	,	,	PUNCT
ejpam-3747	284	9	v	v	NOUN
ejpam-3747	284	10	)	)	PUNCT
ejpam-3747	284	11	0	0	NUM
ejpam-3747	284	12	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	284	13	)	)	PUNCT
ejpam-3747	284	14	)	)	PUNCT
ejpam-3747	285	1	<	<	X
ejpam-3747	285	2	ψ	ψ	X
ejpam-3747	285	3	(	(	PUNCT
ejpam-3747	285	4	∫	∫	PROPN
ejpam-3747	285	5	h(u	h(u	PROPN
ejpam-3747	285	6	,	,	PUNCT
ejpam-3747	285	7	v	v	NOUN
ejpam-3747	285	8	)	)	PUNCT
ejpam-3747	285	9	0	0	NUM
ejpam-3747	285	10	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	285	11	)	)	PUNCT
ejpam-3747	285	12	,	,	PUNCT
ejpam-3747	285	13	leading	lead	VERB
ejpam-3747	285	14	to	to	ADP
ejpam-3747	285	15	a	a	DET
ejpam-3747	285	16	contradiction	contradiction	NOUN
ejpam-3747	285	17	.	.	PUNCT
ejpam-3747	286	1	(	(	PUNCT
ejpam-3747	286	2	4	4	X
ejpam-3747	286	3	)	)	PUNCT
ejpam-3747	286	4	suppose	suppose	VERB
ejpam-3747	286	5	that	that	SCONJ
ejpam-3747	286	6	f	f	PROPN
ejpam-3747	286	7	(	(	PUNCT
ejpam-3747	286	8	s	s	NOUN
ejpam-3747	286	9	)	)	PUNCT
ejpam-3747	286	10	∩	∩	ADJ
ejpam-3747	286	11	f	f	X
ejpam-3747	286	12	(	(	PUNCT
ejpam-3747	286	13	t	t	PROPN
ejpam-3747	286	14	)	)	PUNCT
ejpam-3747	286	15	is	be	AUX
ejpam-3747	286	16	complete	complete	ADJ
ejpam-3747	286	17	.	.	PUNCT
ejpam-3747	287	1	let	let	VERB
ejpam-3747	287	2	u	u	NOUN
ejpam-3747	287	3	,	,	PUNCT
ejpam-3747	287	4	v	v	NOUN
ejpam-3747	287	5	∈	∈	NOUN
ejpam-3747	287	6	cb(x	cb(x	NUM
ejpam-3747	287	7	)	)	PUNCT
ejpam-3747	287	8	be	be	AUX
ejpam-3747	287	9	such	such	ADJ
ejpam-3747	287	10	that	that	SCONJ
ejpam-3747	287	11	u	u	NOUN
ejpam-3747	287	12	,	,	PUNCT
ejpam-3747	287	13	v	v	PROPN
ejpam-3747	287	14	∈	∈	X
ejpam-3747	287	15	f	f	X
ejpam-3747	287	16	(	(	PUNCT
ejpam-3747	287	17	s	s	NOUN
ejpam-3747	287	18	)	)	PUNCT
ejpam-3747	287	19	∩	∩	ADJ
ejpam-3747	287	20	f	f	X
ejpam-3747	287	21	(	(	PUNCT
ejpam-3747	287	22	t	t	PROPN
ejpam-3747	287	23	)	)	PUNCT
ejpam-3747	287	24	.	.	PUNCT
ejpam-3747	288	1	by	by	ADP
ejpam-3747	288	2	(	(	PUNCT
ejpam-3747	288	3	iii	iii	NOUN
ejpam-3747	288	4	)	)	PUNCT
ejpam-3747	288	5	,	,	PUNCT
ejpam-3747	288	6	we	we	PRON
ejpam-3747	288	7	have	have	VERB
ejpam-3747	288	8	h(u	h(u	PROPN
ejpam-3747	288	9	,	,	PUNCT
ejpam-3747	288	10	v	v	NOUN
ejpam-3747	288	11	)	)	PUNCT
ejpam-3747	288	12	=	=	SYM
ejpam-3747	288	13	0	0	NUM
ejpam-3747	288	14	,	,	PUNCT
ejpam-3747	288	15	i.e.	i.e.	X
ejpam-3747	288	16	,	,	PUNCT
ejpam-3747	288	17	f	f	PROPN
ejpam-3747	288	18	(	(	PUNCT
ejpam-3747	288	19	s	s	NOUN
ejpam-3747	288	20	)	)	PUNCT
ejpam-3747	288	21	∩	∩	ADJ
ejpam-3747	288	22	f	f	X
ejpam-3747	288	23	(	(	PUNCT
ejpam-3747	288	24	t	t	PROPN
ejpam-3747	288	25	)	)	PUNCT
ejpam-3747	288	26	is	be	AUX
ejpam-3747	288	27	singleton	singleton	NOUN
ejpam-3747	288	28	.	.	PUNCT
ejpam-3747	289	1	conversely	conversely	ADV
ejpam-3747	289	2	,	,	PUNCT
ejpam-3747	289	3	suppose	suppose	VERB
ejpam-3747	289	4	that	that	SCONJ
ejpam-3747	289	5	f	f	PROPN
ejpam-3747	289	6	(	(	PUNCT
ejpam-3747	289	7	s	s	NOUN
ejpam-3747	289	8	)	)	PUNCT
ejpam-3747	289	9	∩	∩	ADJ
ejpam-3747	289	10	f	f	X
ejpam-3747	289	11	(	(	PUNCT
ejpam-3747	289	12	t	t	PROPN
ejpam-3747	289	13	)	)	PUNCT
ejpam-3747	289	14	is	be	AUX
ejpam-3747	289	15	singleton	singleton	NOUN
ejpam-3747	289	16	.	.	PUNCT
ejpam-3747	290	1	since	since	SCONJ
ejpam-3747	290	2	∆	∆	PROPN
ejpam-3747	290	3	⊂	⊂	PROPN
ejpam-3747	290	4	e(g	e(g	PROPN
ejpam-3747	290	5	)	)	PUNCT
ejpam-3747	290	6	,	,	PUNCT
ejpam-3747	290	7	then	then	ADV
ejpam-3747	290	8	f	f	PROPN
ejpam-3747	290	9	(	(	PUNCT
ejpam-3747	290	10	s	s	NOUN
ejpam-3747	290	11	)	)	PUNCT
ejpam-3747	290	12	∩	∩	ADJ
ejpam-3747	290	13	f	f	X
ejpam-3747	290	14	(	(	PUNCT
ejpam-3747	290	15	t	t	PROPN
ejpam-3747	290	16	)	)	PUNCT
ejpam-3747	290	17	is	be	AUX
ejpam-3747	290	18	complete	complete	ADJ
ejpam-3747	290	19	.	.	PUNCT
ejpam-3747	291	1	s.	s.	PROPN
ejpam-3747	291	2	benchabane	benchabane	PROPN
ejpam-3747	291	3	,	,	PUNCT
ejpam-3747	291	4	s.	s.	PROPN
ejpam-3747	291	5	djebali	djebali	PROPN
ejpam-3747	291	6	,	,	PUNCT
ejpam-3747	291	7	t.	t.	PROPN
ejpam-3747	291	8	nazir	nazir	PROPN
ejpam-3747	291	9	/	/	SYM
ejpam-3747	291	10	eur	eur	PROPN
ejpam-3747	291	11	.	.	PUNCT
ejpam-3747	292	1	j.	j.	PROPN
ejpam-3747	292	2	pure	pure	PROPN
ejpam-3747	292	3	appl	appl	PROPN
ejpam-3747	292	4	.	.	PROPN
ejpam-3747	292	5	math	math	PROPN
ejpam-3747	292	6	,	,	PUNCT
ejpam-3747	292	7	13	13	NUM
ejpam-3747	292	8	(	(	PUNCT
ejpam-3747	292	9	5	5	NUM
ejpam-3747	292	10	)	)	PUNCT
ejpam-3747	292	11	(	(	PUNCT
ejpam-3747	292	12	2020	2020	NUM
ejpam-3747	292	13	)	)	PUNCT
ejpam-3747	292	14	,	,	PUNCT
ejpam-3747	292	15	1072	1072	NUM
ejpam-3747	292	16	-	-	SYM
ejpam-3747	292	17	1087	1087	NUM
ejpam-3747	292	18	1082	1082	NUM
ejpam-3747	292	19	example	example	NOUN
ejpam-3747	292	20	1	1	NUM
ejpam-3747	292	21	.	.	PUNCT
ejpam-3747	293	1	let	let	VERB
ejpam-3747	293	2	x	x	PUNCT
ejpam-3747	293	3	=	=	PRON
ejpam-3747	293	4	{	{	PUNCT
ejpam-3747	293	5	1	1	NUM
ejpam-3747	293	6	,	,	PUNCT
ejpam-3747	293	7	2	2	NUM
ejpam-3747	293	8	,	,	PUNCT
ejpam-3747	293	9	3	3	NUM
ejpam-3747	293	10	,	,	PUNCT
ejpam-3747	293	11	·	·	PUNCT
ejpam-3747	293	12	·	·	PUNCT
ejpam-3747	293	13	·	·	PUNCT
ejpam-3747	293	14	,	,	PUNCT
ejpam-3747	293	15	n	n	CCONJ
ejpam-3747	293	16	}	}	PUNCT
ejpam-3747	293	17	(	(	PUNCT
ejpam-3747	293	18	with	with	ADP
ejpam-3747	293	19	n	n	NOUN
ejpam-3747	293	20	>	>	SYM
ejpam-3747	293	21	3	3	X
ejpam-3747	293	22	)	)	PUNCT
ejpam-3747	293	23	be	be	AUX
ejpam-3747	293	24	the	the	DET
ejpam-3747	293	25	set	set	NOUN
ejpam-3747	293	26	of	of	ADP
ejpam-3747	293	27	integers	integer	NOUN
ejpam-3747	293	28	endowed	endow	VERB
ejpam-3747	293	29	with	with	ADP
ejpam-3747	293	30	the	the	DET
ejpam-3747	293	31	metric	metric	ADJ
ejpam-3747	293	32	d	d	NOUN
ejpam-3747	293	33	:	:	PUNCT
ejpam-3747	293	34	x	x	PROPN
ejpam-3747	294	1	×x	×x	X
ejpam-3747	294	2	→	→	SYM
ejpam-3747	294	3	[	[	X
ejpam-3747	294	4	0,+∞	0,+∞	NUM
ejpam-3747	294	5	)	)	PUNCT
ejpam-3747	294	6	defined	define	VERB
ejpam-3747	294	7	by	by	ADP
ejpam-3747	294	8	d(x	d(x	PROPN
ejpam-3747	294	9	,	,	PUNCT
ejpam-3747	294	10	y	y	NOUN
ejpam-3747	294	11	)	)	PUNCT
ejpam-3747	294	12	=	=	PUNCT
ejpam-3747	295	1			PROPN
ejpam-3747	295	2	0	0	NUM
ejpam-3747	295	3	,	,	PUNCT
ejpam-3747	295	4	if	if	SCONJ
ejpam-3747	295	5	x	x	ADP
ejpam-3747	295	6	=	=	SYM
ejpam-3747	295	7	y	y	PROPN
ejpam-3747	295	8	,	,	PUNCT
ejpam-3747	295	9	1	1	NUM
ejpam-3747	295	10	n	n	NOUN
ejpam-3747	295	11	,	,	PUNCT
ejpam-3747	295	12	if	if	SCONJ
ejpam-3747	295	13	x	x	X
ejpam-3747	295	14	,	,	PUNCT
ejpam-3747	295	15	y	y	PROPN
ejpam-3747	295	16	∈	∈	PROPN
ejpam-3747	295	17	{	{	PUNCT
ejpam-3747	295	18	1	1	NUM
ejpam-3747	295	19	,	,	PUNCT
ejpam-3747	295	20	2	2	NUM
ejpam-3747	295	21	,	,	PUNCT
ejpam-3747	295	22	3	3	NUM
ejpam-3747	295	23	,	,	PUNCT
ejpam-3747	295	24	4	4	NUM
ejpam-3747	295	25	}	}	PUNCT
ejpam-3747	295	26	,	,	PUNCT
ejpam-3747	295	27	x	x	SYM
ejpam-3747	295	28	6=	6=	ADP
ejpam-3747	295	29	y	y	PROPN
ejpam-3747	295	30	,	,	PUNCT
ejpam-3747	295	31	n+2	n+2	PRON
ejpam-3747	295	32	n+3	n+3	PROPN
ejpam-3747	295	33	,	,	PUNCT
ejpam-3747	295	34	if	if	SCONJ
ejpam-3747	295	35	otherwise	otherwise	ADV
ejpam-3747	295	36	.	.	PUNCT
ejpam-3747	296	1	the	the	DET
ejpam-3747	296	2	pompeiu	pompeiu	NOUN
ejpam-3747	296	3	-	-	PUNCT
ejpam-3747	296	4	hausdorff	hausdorff	NOUN
ejpam-3747	296	5	metric	metric	NOUN
ejpam-3747	296	6	is	be	AUX
ejpam-3747	296	7	given	give	VERB
ejpam-3747	296	8	by	by	ADP
ejpam-3747	296	9	h(a	h(a	PROPN
ejpam-3747	296	10	,	,	PUNCT
ejpam-3747	296	11	b	b	NOUN
ejpam-3747	296	12	)	)	PUNCT
ejpam-3747	296	13	=	=	PUNCT
ejpam-3747	297	1			PROPN
ejpam-3747	297	2	0	0	NUM
ejpam-3747	297	3	,	,	PUNCT
ejpam-3747	297	4	if	if	SCONJ
ejpam-3747	297	5	a	a	DET
ejpam-3747	297	6	=	=	SYM
ejpam-3747	297	7	b	b	NOUN
ejpam-3747	297	8	,	,	PUNCT
ejpam-3747	297	9	1	1	NUM
ejpam-3747	297	10	n	n	NOUN
ejpam-3747	297	11	,	,	PUNCT
ejpam-3747	297	12	if	if	SCONJ
ejpam-3747	297	13	a	a	DET
ejpam-3747	297	14	,	,	PUNCT
ejpam-3747	297	15	b	b	NOUN
ejpam-3747	297	16	⊆	⊆	NUM
ejpam-3747	297	17	{	{	SYM
ejpam-3747	297	18	1	1	NUM
ejpam-3747	297	19	,	,	PUNCT
ejpam-3747	297	20	2	2	NUM
ejpam-3747	297	21	,	,	PUNCT
ejpam-3747	297	22	3	3	NUM
ejpam-3747	297	23	,	,	PUNCT
ejpam-3747	297	24	4	4	NUM
ejpam-3747	297	25	}	}	PUNCT
ejpam-3747	297	26	,	,	PUNCT
ejpam-3747	297	27	a	a	DET
ejpam-3747	297	28	6=	6=	PROPN
ejpam-3747	297	29	b	b	NOUN
ejpam-3747	297	30	,	,	PUNCT
ejpam-3747	297	31	n+2	n+2	PRON
ejpam-3747	297	32	n+3	n+3	PROPN
ejpam-3747	297	33	,	,	PUNCT
ejpam-3747	297	34	if	if	SCONJ
ejpam-3747	297	35	otherwise	otherwise	ADV
ejpam-3747	297	36	.	.	PUNCT
ejpam-3747	298	1	define	define	VERB
ejpam-3747	298	2	the	the	DET
ejpam-3747	298	3	graph	graph	NOUN
ejpam-3747	298	4	g	g	PROPN
ejpam-3747	298	5	=	=	PUNCT
ejpam-3747	298	6	(	(	PUNCT
ejpam-3747	298	7	v	v	NOUN
ejpam-3747	298	8	(	(	PUNCT
ejpam-3747	298	9	g	g	NOUN
ejpam-3747	298	10	)	)	PUNCT
ejpam-3747	298	11	,	,	PUNCT
ejpam-3747	298	12	e(g	e(g	PROPN
ejpam-3747	298	13	)	)	PUNCT
ejpam-3747	298	14	)	)	PUNCT
ejpam-3747	298	15	with	with	ADP
ejpam-3747	298	16	v	v	NOUN
ejpam-3747	298	17	(	(	PUNCT
ejpam-3747	298	18	g	g	NOUN
ejpam-3747	298	19	)	)	PUNCT
ejpam-3747	298	20	=	=	SYM
ejpam-3747	298	21	x	x	PROPN
ejpam-3747	298	22	and	and	CCONJ
ejpam-3747	298	23	e(g	e(g	PROPN
ejpam-3747	298	24	)	)	PUNCT
ejpam-3747	299	1	=	=	PRON
ejpam-3747	299	2	{	{	PUNCT
ejpam-3747	299	3	(	(	PUNCT
ejpam-3747	299	4	i	i	PROPN
ejpam-3747	299	5	,	,	PUNCT
ejpam-3747	299	6	j	j	PROPN
ejpam-3747	299	7	)	)	PUNCT
ejpam-3747	299	8	∈	∈	PROPN
ejpam-3747	299	9	x×x	x×x	PROPN
ejpam-3747	299	10	:	:	PUNCT
ejpam-3747	300	1	i	i	PROPN
ejpam-3747	300	2	≤	≤	PUNCT
ejpam-3747	300	3	j	j	X
ejpam-3747	300	4	}	}	PUNCT
ejpam-3747	300	5	.	.	PUNCT
ejpam-3747	301	1	the	the	DET
ejpam-3747	301	2	graph	graph	NOUN
ejpam-3747	301	3	g	g	NOUN
ejpam-3747	301	4	for	for	ADP
ejpam-3747	301	5	n	n	NOUN
ejpam-3747	301	6	=	=	SYM
ejpam-3747	301	7	4	4	NUM
ejpam-3747	301	8	and	and	CCONJ
ejpam-3747	301	9	n	n	NOUN
ejpam-3747	301	10	=	=	NUM
ejpam-3747	301	11	5	5	NUM
ejpam-3747	301	12	along	along	ADP
ejpam-3747	301	13	with	with	ADP
ejpam-3747	301	14	pompeiu	pompeiu	NOUN
ejpam-3747	301	15	-	-	PUNCT
ejpam-3747	301	16	hausdorff	hausdorff	NOUN
ejpam-3747	301	17	distance	distance	NOUN
ejpam-3747	301	18	assigned	assign	VERB
ejpam-3747	301	19	are	be	AUX
ejpam-3747	301	20	shown	show	VERB
ejpam-3747	301	21	in	in	ADP
ejpam-3747	301	22	figure	figure	NOUN
ejpam-3747	301	23	1	1	NUM
ejpam-3747	301	24	and	and	CCONJ
ejpam-3747	301	25	2	2	NUM
ejpam-3747	301	26	,	,	PUNCT
ejpam-3747	301	27	respectively	respectively	ADV
ejpam-3747	301	28	.	.	PUNCT
ejpam-3747	302	1	figure	figure	NOUN
ejpam-3747	302	2	1	1	NUM
ejpam-3747	302	3	:	:	PUNCT
ejpam-3747	302	4	the	the	DET
ejpam-3747	302	5	graph	graph	NOUN
ejpam-3747	302	6	g	g	NOUN
ejpam-3747	302	7	for	for	ADP
ejpam-3747	302	8	n	n	NOUN
ejpam-3747	302	9	=	=	SYM
ejpam-3747	302	10	4	4	X
ejpam-3747	302	11	.	.	X
ejpam-3747	302	12	figure	figure	NOUN
ejpam-3747	302	13	2	2	NUM
ejpam-3747	302	14	:	:	PUNCT
ejpam-3747	302	15	the	the	DET
ejpam-3747	302	16	graph	graph	NOUN
ejpam-3747	302	17	g	g	NOUN
ejpam-3747	302	18	for	for	ADP
ejpam-3747	302	19	n	n	NOUN
ejpam-3747	302	20	=	=	SYM
ejpam-3747	302	21	5	5	X
ejpam-3747	302	22	.	.	PUNCT
ejpam-3747	303	1	let	let	VERB
ejpam-3747	303	2	s	s	PRON
ejpam-3747	303	3	and	and	CCONJ
ejpam-3747	303	4	t	t	PROPN
ejpam-3747	303	5	:	:	PUNCT
ejpam-3747	303	6	cb(x)→	cb(x)→	VERB
ejpam-3747	303	7	cb(x	cb(x	NUM
ejpam-3747	303	8	)	)	PUNCT
ejpam-3747	303	9	be	be	AUX
ejpam-3747	303	10	defined	define	VERB
ejpam-3747	303	11	by	by	ADP
ejpam-3747	303	12	s(u	s(u	PROPN
ejpam-3747	303	13	)	)	PUNCT
ejpam-3747	303	14	=	=	PUNCT
ejpam-3747	303	15			PUNCT
ejpam-3747	303	16	{	{	PUNCT
ejpam-3747	303	17	1	1	NUM
ejpam-3747	303	18	,	,	PUNCT
ejpam-3747	303	19	2	2	NUM
ejpam-3747	303	20	}	}	PUNCT
ejpam-3747	303	21	,	,	PUNCT
ejpam-3747	303	22	if	if	SCONJ
ejpam-3747	303	23	u	u	PROPN
ejpam-3747	303	24	⊆	⊆	NUM
ejpam-3747	303	25	{	{	PUNCT
ejpam-3747	303	26	1	1	NUM
ejpam-3747	303	27	,	,	PUNCT
ejpam-3747	303	28	2	2	NUM
ejpam-3747	303	29	,	,	PUNCT
ejpam-3747	303	30	3	3	NUM
ejpam-3747	303	31	,	,	PUNCT
ejpam-3747	303	32	4	4	NUM
ejpam-3747	303	33	}	}	PUNCT
ejpam-3747	303	34	,	,	PUNCT
ejpam-3747	303	35	{	{	PUNCT
ejpam-3747	303	36	3	3	NUM
ejpam-3747	303	37	,	,	PUNCT
ejpam-3747	303	38	4	4	NUM
ejpam-3747	303	39	}	}	PUNCT
ejpam-3747	303	40	,	,	PUNCT
ejpam-3747	303	41	if	if	SCONJ
ejpam-3747	303	42	u	u	PROPN
ejpam-3747	303	43	⊆	⊆	NUM
ejpam-3747	303	44	{	{	PUNCT
ejpam-3747	303	45	5	5	NUM
ejpam-3747	303	46	,	,	PUNCT
ejpam-3747	303	47	6	6	NUM
ejpam-3747	303	48	}	}	PUNCT
ejpam-3747	303	49	,	,	PUNCT
ejpam-3747	303	50	{	{	PUNCT
ejpam-3747	303	51	1	1	NUM
ejpam-3747	303	52	,	,	PUNCT
ejpam-3747	303	53	2	2	NUM
ejpam-3747	303	54	,	,	PUNCT
ejpam-3747	303	55	3	3	NUM
ejpam-3747	303	56	,	,	PUNCT
ejpam-3747	303	57	4	4	NUM
ejpam-3747	303	58	}	}	PUNCT
ejpam-3747	303	59	,	,	PUNCT
ejpam-3747	303	60	if	if	SCONJ
ejpam-3747	303	61	otherwise	otherwise	ADV
ejpam-3747	303	62	.	.	PUNCT
ejpam-3747	304	1	s.	s.	PROPN
ejpam-3747	304	2	benchabane	benchabane	PROPN
ejpam-3747	304	3	,	,	PUNCT
ejpam-3747	304	4	s.	s.	PROPN
ejpam-3747	304	5	djebali	djebali	PROPN
ejpam-3747	304	6	,	,	PUNCT
ejpam-3747	304	7	t.	t.	PROPN
ejpam-3747	304	8	nazir	nazir	PROPN
ejpam-3747	304	9	/	/	SYM
ejpam-3747	304	10	eur	eur	PROPN
ejpam-3747	304	11	.	.	PUNCT
ejpam-3747	305	1	j.	j.	PROPN
ejpam-3747	305	2	pure	pure	PROPN
ejpam-3747	305	3	appl	appl	PROPN
ejpam-3747	305	4	.	.	PROPN
ejpam-3747	305	5	math	math	PROPN
ejpam-3747	305	6	,	,	PUNCT
ejpam-3747	305	7	13	13	NUM
ejpam-3747	305	8	(	(	PUNCT
ejpam-3747	305	9	5	5	NUM
ejpam-3747	305	10	)	)	PUNCT
ejpam-3747	305	11	(	(	PUNCT
ejpam-3747	305	12	2020	2020	NUM
ejpam-3747	305	13	)	)	PUNCT
ejpam-3747	305	14	,	,	PUNCT
ejpam-3747	305	15	1072	1072	NUM
ejpam-3747	305	16	-	-	SYM
ejpam-3747	305	17	1087	1087	NUM
ejpam-3747	305	18	1083	1083	NUM
ejpam-3747	305	19	t	t	PROPN
ejpam-3747	305	20	(	(	PUNCT
ejpam-3747	305	21	u	u	NOUN
ejpam-3747	305	22	)	)	PUNCT
ejpam-3747	305	23	=	=	SYM
ejpam-3747	305	24	{	{	PUNCT
ejpam-3747	305	25	{	{	PUNCT
ejpam-3747	305	26	1	1	NUM
ejpam-3747	305	27	,	,	PUNCT
ejpam-3747	305	28	2	2	NUM
ejpam-3747	305	29	}	}	PUNCT
ejpam-3747	305	30	,	,	PUNCT
ejpam-3747	305	31	if	if	SCONJ
ejpam-3747	305	32	u	u	PROPN
ejpam-3747	305	33	⊆	⊆	NUM
ejpam-3747	305	34	{	{	PUNCT
ejpam-3747	305	35	1	1	NUM
ejpam-3747	305	36	,	,	PUNCT
ejpam-3747	305	37	2	2	NUM
ejpam-3747	305	38	,	,	PUNCT
ejpam-3747	305	39	3	3	NUM
ejpam-3747	305	40	,	,	PUNCT
ejpam-3747	305	41	4	4	NUM
ejpam-3747	305	42	}	}	PUNCT
ejpam-3747	305	43	,	,	PUNCT
ejpam-3747	305	44	{	{	PUNCT
ejpam-3747	305	45	3	3	NUM
ejpam-3747	305	46	}	}	PUNCT
ejpam-3747	305	47	,	,	PUNCT
ejpam-3747	305	48	if	if	SCONJ
ejpam-3747	305	49	u	u	NOUN
ejpam-3747	305	50	{	{	PUNCT
ejpam-3747	305	51	1	1	NUM
ejpam-3747	305	52	,	,	PUNCT
ejpam-3747	305	53	2	2	NUM
ejpam-3747	305	54	,	,	PUNCT
ejpam-3747	305	55	3	3	NUM
ejpam-3747	305	56	,	,	PUNCT
ejpam-3747	305	57	4	4	NUM
ejpam-3747	305	58	}	}	PUNCT
ejpam-3747	305	59	.	.	PUNCT
ejpam-3747	306	1	define	define	VERB
ejpam-3747	306	2	the	the	DET
ejpam-3747	306	3	mappings	mapping	NOUN
ejpam-3747	306	4	ψ	ψ	X
ejpam-3747	306	5	,	,	PUNCT
ejpam-3747	306	6	ϕ	ϕ	PROPN
ejpam-3747	306	7	,	,	PUNCT
ejpam-3747	306	8	φ	φ	NOUN
ejpam-3747	306	9	:	:	PUNCT
ejpam-3747	307	1	[	[	X
ejpam-3747	307	2	0,+∞)→	0,+∞)→	X
ejpam-3747	308	1	[	[	X
ejpam-3747	308	2	0,+∞	0,+∞	NUM
ejpam-3747	308	3	)	)	PUNCT
ejpam-3747	308	4	by	by	ADP
ejpam-3747	308	5	ψ(t	ψ(t	NOUN
ejpam-3747	308	6	)	)	PUNCT
ejpam-3747	308	7	=	=	PUNCT
ejpam-3747	309	1	5	5	NUM
ejpam-3747	309	2	t	t	NOUN
ejpam-3747	309	3	3t+3	3t+3	NUM
ejpam-3747	309	4	,	,	PUNCT
ejpam-3747	309	5	ϕ(t	ϕ(t	NUM
ejpam-3747	309	6	)	)	PUNCT
ejpam-3747	309	7	=	=	SYM
ejpam-3747	309	8	t	t	PROPN
ejpam-3747	309	9	,	,	PUNCT
ejpam-3747	309	10	and	and	CCONJ
ejpam-3747	309	11	φ(t	φ(t	PROPN
ejpam-3747	309	12	)	)	PUNCT
ejpam-3747	309	13	=	=	PRON
ejpam-3747	309	14	{	{	PUNCT
ejpam-3747	309	15	t2	t2	NOUN
ejpam-3747	309	16	,	,	PUNCT
ejpam-3747	309	17	if	if	SCONJ
ejpam-3747	309	18	t	t	PROPN
ejpam-3747	309	19	∈	∈	PROPN
ejpam-3747	310	1	[	[	X
ejpam-3747	310	2	0	0	NUM
ejpam-3747	310	3	,	,	PUNCT
ejpam-3747	310	4	13	13	NUM
ejpam-3747	310	5	]	]	PUNCT
ejpam-3747	310	6	,	,	PUNCT
ejpam-3747	310	7	t	t	PROPN
ejpam-3747	310	8	3	3	NUM
ejpam-3747	310	9	,	,	PUNCT
ejpam-3747	310	10	if	if	SCONJ
ejpam-3747	310	11	t	t	PROPN
ejpam-3747	310	12	∈	∈	PROPN
ejpam-3747	310	13	(	(	PUNCT
ejpam-3747	310	14	13	13	NUM
ejpam-3747	310	15	,	,	PUNCT
ejpam-3747	310	16	+	+	NOUN
ejpam-3747	310	17	∞	∞	NOUN
ejpam-3747	310	18	)	)	PUNCT
ejpam-3747	310	19	.	.	PUNCT
ejpam-3747	311	1	given	give	VERB
ejpam-3747	311	2	l	l	PROPN
ejpam-3747	311	3	>	>	X
ejpam-3747	311	4	0	0	NUM
ejpam-3747	311	5	,	,	PUNCT
ejpam-3747	311	6	then	then	ADV
ejpam-3747	311	7	s	s	PRON
ejpam-3747	311	8	and	and	CCONJ
ejpam-3747	311	9	t	t	PROPN
ejpam-3747	311	10	form	form	VERB
ejpam-3747	311	11	a	a	DET
ejpam-3747	311	12	graph	graph	NOUN
ejpam-3747	311	13	(	(	PUNCT
ejpam-3747	311	14	ψ	ψ	NOUN
ejpam-3747	311	15	,	,	PUNCT
ejpam-3747	311	16	φ)-weak	φ)-weak	VERB
ejpam-3747	311	17	contraction	contraction	NOUN
ejpam-3747	311	18	and	and	CCONJ
ejpam-3747	311	19	{	{	PUNCT
ejpam-3747	311	20	1	1	NUM
ejpam-3747	311	21	,	,	PUNCT
ejpam-3747	311	22	2	2	NUM
ejpam-3747	311	23	}	}	PUNCT
ejpam-3747	311	24	is	be	AUX
ejpam-3747	311	25	the	the	DET
ejpam-3747	311	26	common	common	ADJ
ejpam-3747	311	27	fixed	fix	VERB
ejpam-3747	311	28	point	point	NOUN
ejpam-3747	311	29	of	of	ADP
ejpam-3747	311	30	s	s	PRON
ejpam-3747	311	31	and	and	CCONJ
ejpam-3747	311	32	t	t	PROPN
ejpam-3747	311	33	.	.	PUNCT
ejpam-3747	312	1	we	we	PRON
ejpam-3747	312	2	check	check	VERB
ejpam-3747	312	3	this	this	PRON
ejpam-3747	312	4	(	(	PUNCT
ejpam-3747	312	5	i	i	NOUN
ejpam-3747	312	6	)	)	PUNCT
ejpam-3747	312	7	it	it	PRON
ejpam-3747	312	8	clear	clear	VERB
ejpam-3747	312	9	that	that	SCONJ
ejpam-3747	312	10	for	for	ADP
ejpam-3747	312	11	all	all	PRON
ejpam-3747	312	12	u	u	NOUN
ejpam-3747	312	13	∈	∈	NOUN
ejpam-3747	312	14	cb(x	cb(x	NUM
ejpam-3747	312	15	)	)	PUNCT
ejpam-3747	312	16	,	,	PUNCT
ejpam-3747	312	17	(	(	PUNCT
ejpam-3747	312	18	u	u	NOUN
ejpam-3747	312	19	,	,	PUNCT
ejpam-3747	312	20	s(u	s(u	PROPN
ejpam-3747	312	21	)	)	PUNCT
ejpam-3747	312	22	)	)	PUNCT
ejpam-3747	312	23	⊂	⊂	PROPN
ejpam-3747	312	24	e(g	e(g	PROPN
ejpam-3747	312	25	)	)	PUNCT
ejpam-3747	312	26	and	and	CCONJ
ejpam-3747	312	27	(	(	PUNCT
ejpam-3747	312	28	u	u	PROPN
ejpam-3747	312	29	,	,	PUNCT
ejpam-3747	312	30	t	t	PROPN
ejpam-3747	312	31	(	(	PUNCT
ejpam-3747	312	32	u	u	NOUN
ejpam-3747	312	33	)	)	PUNCT
ejpam-3747	312	34	)	)	PUNCT
ejpam-3747	313	1	⊂	⊂	PROPN
ejpam-3747	313	2	e(g	e(g	PROPN
ejpam-3747	313	3	)	)	PUNCT
ejpam-3747	313	4	,	,	PUNCT
ejpam-3747	313	5	(	(	PUNCT
ejpam-3747	313	6	ii	ii	NOUN
ejpam-3747	313	7	)	)	PUNCT
ejpam-3747	313	8	for	for	ADP
ejpam-3747	313	9	all	all	PRON
ejpam-3747	313	10	(	(	PUNCT
ejpam-3747	313	11	a	a	DET
ejpam-3747	313	12	,	,	PUNCT
ejpam-3747	313	13	b	b	NOUN
ejpam-3747	313	14	)	)	PUNCT
ejpam-3747	313	15	⊂	⊂	PROPN
ejpam-3747	313	16	e(g	e(g	PROPN
ejpam-3747	313	17	)	)	PUNCT
ejpam-3747	313	18	and	and	CCONJ
ejpam-3747	313	19	s(a	s(a	PROPN
ejpam-3747	313	20	)	)	PUNCT
ejpam-3747	313	21	6=	6=	ADP
ejpam-3747	313	22	t	t	PROPN
ejpam-3747	313	23	(	(	PUNCT
ejpam-3747	313	24	b	b	NOUN
ejpam-3747	313	25	)	)	PUNCT
ejpam-3747	313	26	,	,	PUNCT
ejpam-3747	313	27	consider	consider	VERB
ejpam-3747	313	28	five	five	NUM
ejpam-3747	313	29	cases	case	NOUN
ejpam-3747	313	30	:	:	PUNCT
ejpam-3747	313	31	case	case	NOUN
ejpam-3747	313	32	1	1	NUM
ejpam-3747	313	33	.	.	PUNCT
ejpam-3747	314	1	if	if	SCONJ
ejpam-3747	314	2	a	a	DET
ejpam-3747	314	3	⊆	⊆	NUM
ejpam-3747	314	4	{	{	SYM
ejpam-3747	314	5	1	1	NUM
ejpam-3747	314	6	,	,	PUNCT
ejpam-3747	314	7	2	2	NUM
ejpam-3747	314	8	,	,	PUNCT
ejpam-3747	314	9	3	3	NUM
ejpam-3747	314	10	,	,	PUNCT
ejpam-3747	314	11	4	4	NUM
ejpam-3747	314	12	}	}	PUNCT
ejpam-3747	314	13	,	,	PUNCT
ejpam-3747	314	14	b	b	X
ejpam-3747	314	15	{	{	PUNCT
ejpam-3747	314	16	1	1	NUM
ejpam-3747	314	17	,	,	PUNCT
ejpam-3747	314	18	2	2	NUM
ejpam-3747	314	19	,	,	PUNCT
ejpam-3747	314	20	3	3	NUM
ejpam-3747	314	21	,	,	PUNCT
ejpam-3747	314	22	4	4	NUM
ejpam-3747	314	23	}	}	PUNCT
ejpam-3747	314	24	,	,	PUNCT
ejpam-3747	314	25	then	then	ADV
ejpam-3747	314	26	ψ	ψ	X
ejpam-3747	314	27	(	(	PUNCT
ejpam-3747	314	28	∫	∫	PROPN
ejpam-3747	314	29	h({1,2},{1,3,4	h({1,2},{1,3,4	PROPN
ejpam-3747	314	30	}	}	PUNCT
ejpam-3747	314	31	)	)	PUNCT
ejpam-3747	314	32	0	0	NUM
ejpam-3747	314	33	ϕ(t)dt	ϕ(t)dt	NUM
ejpam-3747	314	34	)	)	PUNCT
ejpam-3747	314	35	=	=	SYM
ejpam-3747	314	36	5	5	NUM
ejpam-3747	314	37	3	3	NUM
ejpam-3747	314	38	+	+	NOUN
ejpam-3747	314	39	6n2	6n2	NUM
ejpam-3747	314	40	≤	≤	NOUN
ejpam-3747	314	41	5(n+2)2	5(n+2)2	NUM
ejpam-3747	314	42	9(n+2)2	9(n+2)2	NUM
ejpam-3747	314	43	+	+	NOUN
ejpam-3747	314	44	18(n+3)2	18(n+3)2	NUM
ejpam-3747	314	45	≤	≤	ADJ
ejpam-3747	314	46	φ(ψ	φ(ψ	PROPN
ejpam-3747	314	47	(	(	PUNCT
ejpam-3747	314	48	∫ms	∫ms	PROPN
ejpam-3747	314	49	,	,	PUNCT
ejpam-3747	314	50	t	t	PROPN
ejpam-3747	314	51	(	(	PUNCT
ejpam-3747	314	52	a	a	DET
ejpam-3747	314	53	,	,	PUNCT
ejpam-3747	314	54	b	b	NOUN
ejpam-3747	314	55	)	)	PUNCT
ejpam-3747	314	56	0	0	NUM
ejpam-3747	314	57	ϕ(t)dt	ϕ(t)dt	NUM
ejpam-3747	314	58	)	)	PUNCT
ejpam-3747	314	59	)	)	PUNCT
ejpam-3747	315	1	+	+	CCONJ
ejpam-3747	315	2	l	l	NOUN
ejpam-3747	315	3	∫	∫	PROPN
ejpam-3747	315	4	ns	ns	PROPN
ejpam-3747	315	5	,	,	PUNCT
ejpam-3747	315	6	t	t	PROPN
ejpam-3747	315	7	(	(	PUNCT
ejpam-3747	315	8	a	a	DET
ejpam-3747	315	9	,	,	PUNCT
ejpam-3747	315	10	b	b	NOUN
ejpam-3747	315	11	)	)	PUNCT
ejpam-3747	315	12	0	0	NUM
ejpam-3747	316	1	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-3747	316	2	.	.	PUNCT
ejpam-3747	317	1	case	case	NOUN
ejpam-3747	317	2	2	2	NUM
ejpam-3747	317	3	.	.	PUNCT
ejpam-3747	318	1	if	if	SCONJ
ejpam-3747	318	2	a	a	DET
ejpam-3747	318	3	⊆	⊆	NUM
ejpam-3747	318	4	{	{	SYM
ejpam-3747	318	5	5	5	NUM
ejpam-3747	318	6	,	,	PUNCT
ejpam-3747	318	7	6	6	NUM
ejpam-3747	318	8	}	}	PUNCT
ejpam-3747	318	9	,	,	PUNCT
ejpam-3747	318	10	b	b	X
ejpam-3747	318	11	⊆	⊆	NUM
ejpam-3747	318	12	{	{	PUNCT
ejpam-3747	318	13	1	1	NUM
ejpam-3747	318	14	,	,	PUNCT
ejpam-3747	318	15	2	2	NUM
ejpam-3747	318	16	,	,	PUNCT
ejpam-3747	318	17	3	3	NUM
ejpam-3747	318	18	,	,	PUNCT
ejpam-3747	318	19	4	4	NUM
ejpam-3747	318	20	}	}	PUNCT
ejpam-3747	318	21	,	,	PUNCT
ejpam-3747	318	22	then	then	ADV
ejpam-3747	318	23	ψ	ψ	PROPN
ejpam-3747	318	24	(	(	PUNCT
ejpam-3747	318	25	∫	∫	PROPN
ejpam-3747	318	26	h({3,4},{1,2	h({3,4},{1,2	ADJ
ejpam-3747	318	27	}	}	PUNCT
ejpam-3747	318	28	)	)	PUNCT
ejpam-3747	318	29	0	0	NUM
ejpam-3747	319	1	ϕ(t)dt	ϕ(t)dt	NUM
ejpam-3747	319	2	)	)	PUNCT
ejpam-3747	320	1	=	=	SYM
ejpam-3747	320	2	5	5	NUM
ejpam-3747	320	3	3	3	NUM
ejpam-3747	320	4	+	+	NOUN
ejpam-3747	320	5	6n2	6n2	NUM
ejpam-3747	320	6	≤	≤	NOUN
ejpam-3747	320	7	5(n+2)2	5(n+2)2	NUM
ejpam-3747	320	8	9(n+2)2	9(n+2)2	NUM
ejpam-3747	320	9	+	+	NOUN
ejpam-3747	320	10	18(n+3)2	18(n+3)2	NUM
ejpam-3747	320	11	≤	≤	ADJ
ejpam-3747	320	12	φ(ψ	φ(ψ	PROPN
ejpam-3747	320	13	(	(	PUNCT
ejpam-3747	320	14	∫ms	∫ms	PROPN
ejpam-3747	320	15	,	,	PUNCT
ejpam-3747	320	16	t	t	PROPN
ejpam-3747	320	17	(	(	PUNCT
ejpam-3747	320	18	a	a	DET
ejpam-3747	320	19	,	,	PUNCT
ejpam-3747	320	20	b	b	NOUN
ejpam-3747	320	21	)	)	PUNCT
ejpam-3747	320	22	0	0	NUM
ejpam-3747	320	23	ϕ(t)dt	ϕ(t)dt	NUM
ejpam-3747	320	24	)	)	PUNCT
ejpam-3747	320	25	)	)	PUNCT
ejpam-3747	321	1	+	+	CCONJ
ejpam-3747	321	2	l	l	NOUN
ejpam-3747	321	3	∫	∫	PROPN
ejpam-3747	321	4	ns	ns	PROPN
ejpam-3747	321	5	,	,	PUNCT
ejpam-3747	321	6	t	t	PROPN
ejpam-3747	321	7	(	(	PUNCT
ejpam-3747	321	8	a	a	DET
ejpam-3747	321	9	,	,	PUNCT
ejpam-3747	321	10	b	b	NOUN
ejpam-3747	321	11	)	)	PUNCT
ejpam-3747	321	12	0	0	NUM
ejpam-3747	322	1	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-3747	322	2	.	.	PUNCT
ejpam-3747	323	1	case	case	NOUN
ejpam-3747	323	2	3	3	X
ejpam-3747	323	3	.	.	PUNCT
ejpam-3747	324	1	if	if	SCONJ
ejpam-3747	324	2	a	a	DET
ejpam-3747	324	3	⊆	⊆	NUM
ejpam-3747	324	4	{	{	SYM
ejpam-3747	324	5	5	5	NUM
ejpam-3747	324	6	,	,	PUNCT
ejpam-3747	324	7	6	6	NUM
ejpam-3747	324	8	}	}	PUNCT
ejpam-3747	324	9	,	,	PUNCT
ejpam-3747	324	10	b	b	X
ejpam-3747	324	11	{	{	PUNCT
ejpam-3747	324	12	1	1	NUM
ejpam-3747	324	13	,	,	PUNCT
ejpam-3747	324	14	2	2	NUM
ejpam-3747	324	15	,	,	PUNCT
ejpam-3747	324	16	3	3	NUM
ejpam-3747	324	17	,	,	PUNCT
ejpam-3747	324	18	4	4	NUM
ejpam-3747	324	19	}	}	PUNCT
ejpam-3747	324	20	,	,	PUNCT
ejpam-3747	324	21	then	then	ADV
ejpam-3747	324	22	ψ	ψ	X
ejpam-3747	324	23	(	(	PUNCT
ejpam-3747	324	24	∫	∫	PROPN
ejpam-3747	324	25	h({3,4},{1,3,4	h({3,4},{1,3,4	ADJ
ejpam-3747	324	26	}	}	PUNCT
ejpam-3747	324	27	)	)	PUNCT
ejpam-3747	324	28	0	0	NUM
ejpam-3747	325	1	ϕ(t)dt	ϕ(t)dt	NUM
ejpam-3747	325	2	)	)	PUNCT
ejpam-3747	326	1	=	=	SYM
ejpam-3747	326	2	5	5	NUM
ejpam-3747	326	3	3	3	NUM
ejpam-3747	326	4	+	+	NOUN
ejpam-3747	326	5	6n2	6n2	NUM
ejpam-3747	326	6	≤	≤	NOUN
ejpam-3747	326	7	5(n+2)2	5(n+2)2	NUM
ejpam-3747	326	8	9(n+2)2	9(n+2)2	NUM
ejpam-3747	326	9	+	+	NOUN
ejpam-3747	326	10	18(n+3)2	18(n+3)2	NUM
ejpam-3747	326	11	≤	≤	ADJ
ejpam-3747	326	12	φ(ψ	φ(ψ	PROPN
ejpam-3747	326	13	(	(	PUNCT
ejpam-3747	326	14	∫ms	∫ms	PROPN
ejpam-3747	326	15	,	,	PUNCT
ejpam-3747	326	16	t	t	PROPN
ejpam-3747	326	17	(	(	PUNCT
ejpam-3747	326	18	a	a	DET
ejpam-3747	326	19	,	,	PUNCT
ejpam-3747	326	20	b	b	NOUN
ejpam-3747	326	21	)	)	PUNCT
ejpam-3747	326	22	0	0	NUM
ejpam-3747	326	23	ϕ(t)dt	ϕ(t)dt	NUM
ejpam-3747	326	24	)	)	PUNCT
ejpam-3747	326	25	)	)	PUNCT
ejpam-3747	327	1	+	+	CCONJ
ejpam-3747	327	2	l	l	NOUN
ejpam-3747	327	3	∫	∫	PROPN
ejpam-3747	327	4	ns	ns	PROPN
ejpam-3747	327	5	,	,	PUNCT
ejpam-3747	327	6	t	t	PROPN
ejpam-3747	327	7	(	(	PUNCT
ejpam-3747	327	8	a	a	DET
ejpam-3747	327	9	,	,	PUNCT
ejpam-3747	327	10	b	b	NOUN
ejpam-3747	327	11	)	)	PUNCT
ejpam-3747	327	12	0	0	NUM
ejpam-3747	328	1	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-3747	328	2	.	.	PUNCT
ejpam-3747	329	1	case	case	NOUN
ejpam-3747	329	2	4	4	NUM
ejpam-3747	329	3	.	.	PUNCT
ejpam-3747	330	1	if	if	SCONJ
ejpam-3747	330	2	a	a	DET
ejpam-3747	330	3	{	{	PUNCT
ejpam-3747	330	4	1	1	NUM
ejpam-3747	330	5	,	,	PUNCT
ejpam-3747	330	6	2	2	NUM
ejpam-3747	330	7	,	,	PUNCT
ejpam-3747	330	8	3	3	NUM
ejpam-3747	330	9	,	,	PUNCT
ejpam-3747	330	10	4	4	NUM
ejpam-3747	330	11	,	,	PUNCT
ejpam-3747	330	12	5	5	NUM
ejpam-3747	330	13	,	,	PUNCT
ejpam-3747	330	14	6	6	NUM
ejpam-3747	330	15	}	}	PUNCT
ejpam-3747	330	16	,	,	PUNCT
ejpam-3747	330	17	b	b	X
ejpam-3747	330	18	⊆	⊆	NUM
ejpam-3747	330	19	{	{	PUNCT
ejpam-3747	330	20	1	1	NUM
ejpam-3747	330	21	,	,	PUNCT
ejpam-3747	330	22	2	2	NUM
ejpam-3747	330	23	,	,	PUNCT
ejpam-3747	330	24	3	3	NUM
ejpam-3747	330	25	,	,	PUNCT
ejpam-3747	330	26	4	4	NUM
ejpam-3747	330	27	}	}	PUNCT
ejpam-3747	330	28	,	,	PUNCT
ejpam-3747	330	29	then	then	ADV
ejpam-3747	330	30	ψ	ψ	PROPN
ejpam-3747	330	31	(	(	PUNCT
ejpam-3747	330	32	∫	∫	PROPN
ejpam-3747	330	33	h({1,2,3,4},{1,2	h({1,2,3,4},{1,2	PROPN
ejpam-3747	330	34	}	}	PUNCT
ejpam-3747	330	35	)	)	PUNCT
ejpam-3747	330	36	0	0	NUM
ejpam-3747	330	37	ϕ(t)dt	ϕ(t)dt	NUM
ejpam-3747	330	38	)	)	PUNCT
ejpam-3747	330	39	=	=	SYM
ejpam-3747	330	40	5	5	NUM
ejpam-3747	330	41	3	3	NUM
ejpam-3747	330	42	+	+	NOUN
ejpam-3747	330	43	6n2	6n2	NUM
ejpam-3747	330	44	≤	≤	NOUN
ejpam-3747	330	45	5(n+2)2	5(n+2)2	NUM
ejpam-3747	330	46	9(n+2)2	9(n+2)2	NUM
ejpam-3747	330	47	+	+	NOUN
ejpam-3747	330	48	18(n+3)2	18(n+3)2	NUM
ejpam-3747	330	49	≤	≤	ADJ
ejpam-3747	330	50	φ(ψ	φ(ψ	PROPN
ejpam-3747	330	51	(	(	PUNCT
ejpam-3747	330	52	∫ms	∫ms	PROPN
ejpam-3747	330	53	,	,	PUNCT
ejpam-3747	330	54	t	t	PROPN
ejpam-3747	330	55	(	(	PUNCT
ejpam-3747	330	56	a	a	DET
ejpam-3747	330	57	,	,	PUNCT
ejpam-3747	330	58	b	b	NOUN
ejpam-3747	330	59	)	)	PUNCT
ejpam-3747	330	60	0	0	NUM
ejpam-3747	330	61	ϕ(t)dt	ϕ(t)dt	NUM
ejpam-3747	330	62	)	)	PUNCT
ejpam-3747	330	63	)	)	PUNCT
ejpam-3747	331	1	+	+	CCONJ
ejpam-3747	331	2	l	l	NOUN
ejpam-3747	331	3	∫	∫	PROPN
ejpam-3747	331	4	ns	ns	PROPN
ejpam-3747	331	5	,	,	PUNCT
ejpam-3747	331	6	t	t	PROPN
ejpam-3747	331	7	(	(	PUNCT
ejpam-3747	331	8	a	a	DET
ejpam-3747	331	9	,	,	PUNCT
ejpam-3747	331	10	b	b	NOUN
ejpam-3747	331	11	)	)	PUNCT
ejpam-3747	331	12	0	0	NUM
ejpam-3747	332	1	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-3747	332	2	.	.	PUNCT
ejpam-3747	333	1	case	case	NOUN
ejpam-3747	333	2	5	5	NUM
ejpam-3747	333	3	.	.	PUNCT
ejpam-3747	334	1	if	if	SCONJ
ejpam-3747	334	2	a	a	DET
ejpam-3747	334	3	{	{	PUNCT
ejpam-3747	334	4	1	1	NUM
ejpam-3747	334	5	,	,	PUNCT
ejpam-3747	334	6	2	2	NUM
ejpam-3747	334	7	,	,	PUNCT
ejpam-3747	334	8	3	3	NUM
ejpam-3747	334	9	,	,	PUNCT
ejpam-3747	334	10	4	4	NUM
ejpam-3747	334	11	,	,	PUNCT
ejpam-3747	334	12	5	5	NUM
ejpam-3747	334	13	,	,	PUNCT
ejpam-3747	334	14	6	6	NUM
ejpam-3747	334	15	}	}	PUNCT
ejpam-3747	334	16	,	,	PUNCT
ejpam-3747	334	17	b	b	X
ejpam-3747	334	18	{	{	PUNCT
ejpam-3747	334	19	1	1	NUM
ejpam-3747	334	20	,	,	PUNCT
ejpam-3747	334	21	2	2	NUM
ejpam-3747	334	22	,	,	PUNCT
ejpam-3747	334	23	3	3	NUM
ejpam-3747	334	24	,	,	PUNCT
ejpam-3747	334	25	4	4	NUM
ejpam-3747	334	26	}	}	PUNCT
ejpam-3747	334	27	,	,	PUNCT
ejpam-3747	334	28	then	then	ADV
ejpam-3747	334	29	ψ	ψ	X
ejpam-3747	334	30	(	(	PUNCT
ejpam-3747	334	31	∫	∫	PROPN
ejpam-3747	334	32	h({1,2,3,4},{1,3,4	h({1,2,3,4},{1,3,4	PROPN
ejpam-3747	334	33	}	}	PUNCT
ejpam-3747	334	34	)	)	PUNCT
ejpam-3747	334	35	0	0	NUM
ejpam-3747	335	1	ϕ(t)dt	ϕ(t)dt	NUM
ejpam-3747	335	2	)	)	PUNCT
ejpam-3747	336	1	=	=	SYM
ejpam-3747	336	2	5	5	NUM
ejpam-3747	336	3	3	3	NUM
ejpam-3747	336	4	+	+	NOUN
ejpam-3747	336	5	6n2	6n2	NUM
ejpam-3747	336	6	≤	≤	NOUN
ejpam-3747	336	7	5(n+2)2	5(n+2)2	NUM
ejpam-3747	336	8	9(n+2)2	9(n+2)2	NUM
ejpam-3747	336	9	+	+	NOUN
ejpam-3747	336	10	18(n+3)2	18(n+3)2	NUM
ejpam-3747	336	11	≤	≤	ADJ
ejpam-3747	336	12	φ(ψ	φ(ψ	PROPN
ejpam-3747	336	13	(	(	PUNCT
ejpam-3747	336	14	∫ms	∫ms	PROPN
ejpam-3747	336	15	,	,	PUNCT
ejpam-3747	336	16	t	t	PROPN
ejpam-3747	336	17	(	(	PUNCT
ejpam-3747	336	18	a	a	DET
ejpam-3747	336	19	,	,	PUNCT
ejpam-3747	336	20	b	b	NOUN
ejpam-3747	336	21	)	)	PUNCT
ejpam-3747	336	22	0	0	NUM
ejpam-3747	336	23	ϕ(t)dt	ϕ(t)dt	NUM
ejpam-3747	336	24	)	)	PUNCT
ejpam-3747	336	25	)	)	PUNCT
ejpam-3747	337	1	+	+	CCONJ
ejpam-3747	337	2	l	l	NOUN
ejpam-3747	337	3	∫	∫	PROPN
ejpam-3747	337	4	ns	ns	PROPN
ejpam-3747	337	5	,	,	PUNCT
ejpam-3747	337	6	t	t	PROPN
ejpam-3747	337	7	(	(	PUNCT
ejpam-3747	337	8	a	a	DET
ejpam-3747	337	9	,	,	PUNCT
ejpam-3747	337	10	b	b	NOUN
ejpam-3747	337	11	)	)	PUNCT
ejpam-3747	337	12	0	0	NUM
ejpam-3747	338	1	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-3747	338	2	.	.	PUNCT
ejpam-3747	339	1	s.	s.	PROPN
ejpam-3747	339	2	benchabane	benchabane	PROPN
ejpam-3747	339	3	,	,	PUNCT
ejpam-3747	339	4	s.	s.	PROPN
ejpam-3747	339	5	djebali	djebali	PROPN
ejpam-3747	339	6	,	,	PUNCT
ejpam-3747	339	7	t.	t.	PROPN
ejpam-3747	339	8	nazir	nazir	PROPN
ejpam-3747	339	9	/	/	SYM
ejpam-3747	339	10	eur	eur	PROPN
ejpam-3747	339	11	.	.	PUNCT
ejpam-3747	340	1	j.	j.	PROPN
ejpam-3747	340	2	pure	pure	PROPN
ejpam-3747	340	3	appl	appl	PROPN
ejpam-3747	340	4	.	.	PROPN
ejpam-3747	340	5	math	math	PROPN
ejpam-3747	340	6	,	,	PUNCT
ejpam-3747	340	7	13	13	NUM
ejpam-3747	340	8	(	(	PUNCT
ejpam-3747	340	9	5	5	NUM
ejpam-3747	340	10	)	)	PUNCT
ejpam-3747	340	11	(	(	PUNCT
ejpam-3747	340	12	2020	2020	NUM
ejpam-3747	340	13	)	)	PUNCT
ejpam-3747	340	14	,	,	PUNCT
ejpam-3747	340	15	1072	1072	NUM
ejpam-3747	340	16	-	-	SYM
ejpam-3747	340	17	1087	1087	NUM
ejpam-3747	340	18	1084	1084	NUM
ejpam-3747	340	19	3	3	NUM
ejpam-3747	340	20	.	.	PUNCT
ejpam-3747	340	21	consequences	consequence	VERB
ejpam-3747	340	22	the	the	DET
ejpam-3747	340	23	following	follow	VERB
ejpam-3747	340	24	results	result	NOUN
ejpam-3747	340	25	follow	follow	VERB
ejpam-3747	340	26	from	from	ADP
ejpam-3747	340	27	theorem	theorem	ADJ
ejpam-3747	340	28	3	3	NUM
ejpam-3747	340	29	.	.	PUNCT
ejpam-3747	340	30	corollary	corollary	ADJ
ejpam-3747	340	31	1	1	NUM
ejpam-3747	340	32	.	.	PUNCT
ejpam-3747	341	1	let	let	VERB
ejpam-3747	341	2	(	(	PUNCT
ejpam-3747	341	3	x	x	NOUN
ejpam-3747	341	4	,	,	PUNCT
ejpam-3747	341	5	d	d	NOUN
ejpam-3747	341	6	)	)	PUNCT
ejpam-3747	341	7	be	be	AUX
ejpam-3747	341	8	a	a	DET
ejpam-3747	341	9	metric	metric	ADJ
ejpam-3747	341	10	space	space	NOUN
ejpam-3747	341	11	endowed	endow	VERB
ejpam-3747	341	12	with	with	ADP
ejpam-3747	341	13	a	a	DET
ejpam-3747	341	14	directed	direct	VERB
ejpam-3747	341	15	graph	graph	NOUN
ejpam-3747	341	16	g	g	ADP
ejpam-3747	342	1	such	such	DET
ejpam-3747	342	2	that	that	DET
ejpam-3747	342	3	v	v	NOUN
ejpam-3747	342	4	(	(	PUNCT
ejpam-3747	342	5	g	g	NOUN
ejpam-3747	342	6	)	)	PUNCT
ejpam-3747	342	7	=	=	SYM
ejpam-3747	342	8	x	x	PROPN
ejpam-3747	342	9	and	and	CCONJ
ejpam-3747	342	10	∆	∆	PROPN
ejpam-3747	342	11	⊂	⊂	PROPN
ejpam-3747	342	12	e(g	e(g	PROPN
ejpam-3747	342	13	)	)	PUNCT
ejpam-3747	342	14	.	.	PUNCT
ejpam-3747	343	1	suppose	suppose	VERB
ejpam-3747	343	2	that	that	SCONJ
ejpam-3747	343	3	the	the	DET
ejpam-3747	343	4	mappings	mapping	NOUN
ejpam-3747	343	5	s	s	PART
ejpam-3747	343	6	,	,	PUNCT
ejpam-3747	343	7	t	t	PROPN
ejpam-3747	343	8	:	:	PUNCT
ejpam-3747	343	9	cb(x	cb(x	NUM
ejpam-3747	343	10	)	)	PUNCT
ejpam-3747	343	11	→	→	SYM
ejpam-3747	343	12	cb(x	cb(x	NUM
ejpam-3747	343	13	)	)	PUNCT
ejpam-3747	343	14	satisfy	satisfy	VERB
ejpam-3747	343	15	the	the	DET
ejpam-3747	343	16	following	follow	VERB
ejpam-3747	343	17	conditions	condition	NOUN
ejpam-3747	343	18	:	:	PUNCT
ejpam-3747	343	19	(	(	PUNCT
ejpam-3747	343	20	a	a	X
ejpam-3747	343	21	)	)	PUNCT
ejpam-3747	343	22	for	for	ADP
ejpam-3747	343	23	every	every	DET
ejpam-3747	343	24	u	u	NOUN
ejpam-3747	343	25	in	in	ADP
ejpam-3747	343	26	cb(x	cb(x	NUM
ejpam-3747	343	27	)	)	PUNCT
ejpam-3747	343	28	,	,	PUNCT
ejpam-3747	343	29	(	(	PUNCT
ejpam-3747	343	30	u	u	NOUN
ejpam-3747	343	31	,	,	PUNCT
ejpam-3747	343	32	s(u	s(u	PROPN
ejpam-3747	343	33	)	)	PUNCT
ejpam-3747	343	34	)	)	PUNCT
ejpam-3747	344	1	⊂	⊂	PROPN
ejpam-3747	344	2	e(g	e(g	PROPN
ejpam-3747	344	3	)	)	PUNCT
ejpam-3747	344	4	and	and	CCONJ
ejpam-3747	344	5	(	(	PUNCT
ejpam-3747	344	6	u	u	PROPN
ejpam-3747	344	7	,	,	PUNCT
ejpam-3747	344	8	t	t	PROPN
ejpam-3747	344	9	(	(	PUNCT
ejpam-3747	344	10	u	u	NOUN
ejpam-3747	344	11	)	)	PUNCT
ejpam-3747	344	12	)	)	PUNCT
ejpam-3747	345	1	⊂	⊂	PROPN
ejpam-3747	345	2	e(g	e(g	PROPN
ejpam-3747	345	3	)	)	PUNCT
ejpam-3747	345	4	,	,	PUNCT
ejpam-3747	345	5	(	(	PUNCT
ejpam-3747	345	6	b	b	X
ejpam-3747	345	7	)	)	PUNCT
ejpam-3747	345	8	there	there	PRON
ejpam-3747	345	9	exists	exist	VERB
ejpam-3747	345	10	an	an	DET
ejpam-3747	345	11	nondecreasing	nondecreasing	ADJ
ejpam-3747	345	12	function	function	NOUN
ejpam-3747	345	13	φ	φ	NOUN
ejpam-3747	345	14	:	:	PUNCT
ejpam-3747	345	15	r+	r+	NOUN
ejpam-3747	345	16	→	→	SYM
ejpam-3747	345	17	r+	r+	NOUN
ejpam-3747	345	18	with	with	ADP
ejpam-3747	345	19	∑∞	∑∞	NOUN
ejpam-3747	345	20	i=0	i=0	PROPN
ejpam-3747	345	21	φ	φ	PROPN
ejpam-3747	345	22	i(t	i(t	PROPN
ejpam-3747	345	23	)	)	PUNCT
ejpam-3747	345	24	is	be	AUX
ejpam-3747	345	25	convergent	convergent	ADJ
ejpam-3747	345	26	for	for	ADP
ejpam-3747	345	27	all	all	DET
ejpam-3747	345	28	t	t	PROPN
ejpam-3747	345	29	>	>	X
ejpam-3747	345	30	0	0	PROPN
ejpam-3747	345	31	,	,	PUNCT
ejpam-3747	345	32	ψ	ψ	ADP
ejpam-3747	345	33	∈	∈	PROPN
ejpam-3747	345	34	ψ	ψ	NOUN
ejpam-3747	345	35	,	,	PUNCT
ejpam-3747	345	36	and	and	CCONJ
ejpam-3747	345	37	l	l	NOUN
ejpam-3747	345	38	≥	≥	NUM
ejpam-3747	345	39	0	0	NUM
ejpam-3747	345	40	such	such	ADJ
ejpam-3747	345	41	that	that	SCONJ
ejpam-3747	345	42	if	if	SCONJ
ejpam-3747	345	43	there	there	PRON
ejpam-3747	345	44	is	be	VERB
ejpam-3747	345	45	an	an	DET
ejpam-3747	345	46	edge	edge	NOUN
ejpam-3747	345	47	between	between	ADP
ejpam-3747	345	48	a	a	PRON
ejpam-3747	345	49	and	and	CCONJ
ejpam-3747	345	50	b	b	NOUN
ejpam-3747	345	51	with	with	ADP
ejpam-3747	345	52	s(a	s(a	PROPN
ejpam-3747	345	53	)	)	PUNCT
ejpam-3747	345	54	6=	6=	ADP
ejpam-3747	345	55	t	t	PROPN
ejpam-3747	345	56	(	(	PUNCT
ejpam-3747	345	57	b	b	NOUN
ejpam-3747	345	58	)	)	PUNCT
ejpam-3747	345	59	,	,	PUNCT
ejpam-3747	345	60	then	then	ADV
ejpam-3747	345	61	ψ(h(s(a	ψ(h(s(a	PROPN
ejpam-3747	345	62	)	)	PUNCT
ejpam-3747	345	63	,	,	PUNCT
ejpam-3747	345	64	t	t	PROPN
ejpam-3747	345	65	(	(	PUNCT
ejpam-3747	345	66	b	b	NOUN
ejpam-3747	345	67	)	)	PUNCT
ejpam-3747	345	68	)	)	PUNCT
ejpam-3747	345	69	)	)	PUNCT
ejpam-3747	345	70	≤	≤	NOUN
ejpam-3747	346	1	φ(ψ(ms	φ(ψ(ms	ADV
ejpam-3747	346	2	,	,	PUNCT
ejpam-3747	346	3	t	t	PROPN
ejpam-3747	346	4	(	(	PUNCT
ejpam-3747	346	5	a	a	DET
ejpam-3747	346	6	,	,	PUNCT
ejpam-3747	346	7	b	b	NOUN
ejpam-3747	346	8	)	)	PUNCT
ejpam-3747	346	9	)	)	PUNCT
ejpam-3747	346	10	)	)	PUNCT
ejpam-3747	347	1	+	+	CCONJ
ejpam-3747	347	2	lns	lns	PROPN
ejpam-3747	347	3	,	,	PUNCT
ejpam-3747	347	4	t	t	PROPN
ejpam-3747	347	5	(	(	PUNCT
ejpam-3747	347	6	a	a	DET
ejpam-3747	347	7	,	,	PUNCT
ejpam-3747	347	8	b	b	NOUN
ejpam-3747	347	9	)	)	PUNCT
ejpam-3747	347	10	.	.	PUNCT
ejpam-3747	348	1	if	if	SCONJ
ejpam-3747	348	2	the	the	DET
ejpam-3747	348	3	relation	relation	NOUN
ejpam-3747	348	4	r	r	NOUN
ejpam-3747	348	5	on	on	ADP
ejpam-3747	348	6	cb(x	cb(x	NUM
ejpam-3747	348	7	)	)	PUNCT
ejpam-3747	348	8	is	be	AUX
ejpam-3747	348	9	transitive	transitive	ADJ
ejpam-3747	348	10	,	,	PUNCT
ejpam-3747	348	11	then	then	ADV
ejpam-3747	348	12	the	the	DET
ejpam-3747	348	13	following	following	ADJ
ejpam-3747	348	14	statements	statement	NOUN
ejpam-3747	348	15	hold	hold	VERB
ejpam-3747	348	16	:	:	PUNCT
ejpam-3747	348	17	(	(	PUNCT
ejpam-3747	348	18	i	i	NOUN
ejpam-3747	348	19	)	)	PUNCT
ejpam-3747	348	20	f	f	PROPN
ejpam-3747	348	21	(	(	PUNCT
ejpam-3747	348	22	s	s	NOUN
ejpam-3747	348	23	)	)	PUNCT
ejpam-3747	348	24	or	or	CCONJ
ejpam-3747	348	25	f	f	PROPN
ejpam-3747	348	26	(	(	PUNCT
ejpam-3747	348	27	t	t	PROPN
ejpam-3747	348	28	)	)	PUNCT
ejpam-3747	348	29	6=	6=	ADP
ejpam-3747	348	30	∅	∅	NOUN
ejpam-3747	348	31	if	if	SCONJ
ejpam-3747	349	1	and	and	CCONJ
ejpam-3747	349	2	only	only	ADV
ejpam-3747	349	3	if	if	SCONJ
ejpam-3747	349	4	f	f	PROPN
ejpam-3747	349	5	(	(	PUNCT
ejpam-3747	349	6	s	s	NOUN
ejpam-3747	349	7	)	)	PUNCT
ejpam-3747	349	8	∩	∩	ADJ
ejpam-3747	349	9	f	f	X
ejpam-3747	349	10	(	(	PUNCT
ejpam-3747	349	11	t	t	PROPN
ejpam-3747	349	12	)	)	PUNCT
ejpam-3747	349	13	6=	6=	ADP
ejpam-3747	349	14	∅.	∅.	PROPN
ejpam-3747	349	15	(	(	PUNCT
ejpam-3747	349	16	ii	ii	NOUN
ejpam-3747	349	17	)	)	PUNCT
ejpam-3747	349	18	f	f	PROPN
ejpam-3747	349	19	(	(	PUNCT
ejpam-3747	349	20	s	s	NOUN
ejpam-3747	349	21	)	)	PUNCT
ejpam-3747	349	22	∩	∩	ADJ
ejpam-3747	349	23	f	f	X
ejpam-3747	349	24	(	(	PUNCT
ejpam-3747	349	25	t	t	PROPN
ejpam-3747	349	26	)	)	PUNCT
ejpam-3747	349	27	6=	6=	ADP
ejpam-3747	349	28	∅	∅	NOUN
ejpam-3747	349	29	provided	provide	VERB
ejpam-3747	349	30	that	that	SCONJ
ejpam-3747	349	31	g	g	PROPN
ejpam-3747	349	32	is	be	AUX
ejpam-3747	349	33	weakly	weakly	ADV
ejpam-3747	349	34	connected	connected	ADJ
ejpam-3747	349	35	and	and	CCONJ
ejpam-3747	349	36	satisfies	satisfy	VERB
ejpam-3747	349	37	the	the	DET
ejpam-3747	349	38	property	property	NOUN
ejpam-3747	349	39	(	(	PUNCT
ejpam-3747	349	40	p	p	NOUN
ejpam-3747	349	41	?	?	PUNCT
ejpam-3747	349	42	)	)	PUNCT
ejpam-3747	349	43	.	.	PUNCT
ejpam-3747	350	1	(	(	PUNCT
ejpam-3747	350	2	iii	iii	X
ejpam-3747	350	3	)	)	PUNCT
ejpam-3747	350	4	if	if	SCONJ
ejpam-3747	350	5	f	f	PROPN
ejpam-3747	350	6	(	(	PUNCT
ejpam-3747	350	7	s)∩f	s)∩f	PROPN
ejpam-3747	350	8	(	(	PUNCT
ejpam-3747	350	9	t	t	PROPN
ejpam-3747	350	10	)	)	PUNCT
ejpam-3747	350	11	is	be	AUX
ejpam-3747	350	12	complete	complete	ADJ
ejpam-3747	350	13	,	,	PUNCT
ejpam-3747	350	14	then	then	ADV
ejpam-3747	350	15	the	the	DET
ejpam-3747	350	16	pompeiu	pompeiu	NOUN
ejpam-3747	350	17	-	-	PUNCT
ejpam-3747	350	18	hausdorff	hausdorff	NOUN
ejpam-3747	350	19	weight	weight	NOUN
ejpam-3747	350	20	assigned	assign	VERB
ejpam-3747	350	21	to	to	ADP
ejpam-3747	350	22	the	the	DET
ejpam-3747	350	23	u	u	NOUN
ejpam-3747	350	24	,	,	PUNCT
ejpam-3747	350	25	v	v	PROPN
ejpam-3747	350	26	∈	∈	X
ejpam-3747	350	27	f	f	X
ejpam-3747	350	28	(	(	PUNCT
ejpam-3747	350	29	s	s	NOUN
ejpam-3747	350	30	)	)	PUNCT
ejpam-3747	350	31	∩	∩	ADJ
ejpam-3747	350	32	f	f	X
ejpam-3747	350	33	(	(	PUNCT
ejpam-3747	350	34	t	t	PROPN
ejpam-3747	350	35	)	)	PUNCT
ejpam-3747	350	36	is	be	AUX
ejpam-3747	350	37	0	0	NUM
ejpam-3747	350	38	.	.	PUNCT
ejpam-3747	351	1	(	(	PUNCT
ejpam-3747	351	2	iv	iv	X
ejpam-3747	351	3	)	)	PUNCT
ejpam-3747	351	4	f	f	NOUN
ejpam-3747	351	5	(	(	PUNCT
ejpam-3747	351	6	s	s	NOUN
ejpam-3747	351	7	)	)	PUNCT
ejpam-3747	351	8	∩	∩	ADJ
ejpam-3747	351	9	f	f	X
ejpam-3747	351	10	(	(	PUNCT
ejpam-3747	351	11	t	t	PROPN
ejpam-3747	351	12	)	)	PUNCT
ejpam-3747	351	13	is	be	AUX
ejpam-3747	351	14	complete	complete	ADJ
ejpam-3747	351	15	if	if	SCONJ
ejpam-3747	352	1	and	and	CCONJ
ejpam-3747	352	2	only	only	ADV
ejpam-3747	352	3	if	if	SCONJ
ejpam-3747	352	4	f	f	PROPN
ejpam-3747	352	5	(	(	PUNCT
ejpam-3747	352	6	s	s	NOUN
ejpam-3747	352	7	)	)	PUNCT
ejpam-3747	352	8	∩	∩	ADJ
ejpam-3747	352	9	f	f	X
ejpam-3747	352	10	(	(	PUNCT
ejpam-3747	352	11	t	t	PROPN
ejpam-3747	352	12	)	)	PUNCT
ejpam-3747	352	13	is	be	AUX
ejpam-3747	352	14	a	a	DET
ejpam-3747	352	15	singleton	singleton	NOUN
ejpam-3747	352	16	.	.	PUNCT
ejpam-3747	353	1	corollary	corollary	ADJ
ejpam-3747	353	2	2	2	NUM
ejpam-3747	353	3	.	.	PUNCT
ejpam-3747	354	1	let	let	VERB
ejpam-3747	354	2	(	(	PUNCT
ejpam-3747	354	3	x	x	NOUN
ejpam-3747	354	4	,	,	PUNCT
ejpam-3747	354	5	d	d	NOUN
ejpam-3747	354	6	)	)	PUNCT
ejpam-3747	354	7	be	be	AUX
ejpam-3747	354	8	a	a	DET
ejpam-3747	354	9	metric	metric	ADJ
ejpam-3747	354	10	space	space	NOUN
ejpam-3747	354	11	endowed	endow	VERB
ejpam-3747	354	12	with	with	ADP
ejpam-3747	354	13	a	a	DET
ejpam-3747	354	14	directed	direct	VERB
ejpam-3747	354	15	graph	graph	NOUN
ejpam-3747	354	16	g	g	ADP
ejpam-3747	355	1	such	such	DET
ejpam-3747	355	2	that	that	DET
ejpam-3747	355	3	v	v	NOUN
ejpam-3747	355	4	(	(	PUNCT
ejpam-3747	355	5	g	g	NOUN
ejpam-3747	355	6	)	)	PUNCT
ejpam-3747	355	7	=	=	SYM
ejpam-3747	355	8	x	x	NOUN
ejpam-3747	355	9	,	,	PUNCT
ejpam-3747	355	10	∆	∆	PROPN
ejpam-3747	355	11	⊂	⊂	PROPN
ejpam-3747	355	12	e(g	e(g	PROPN
ejpam-3747	355	13	)	)	PUNCT
ejpam-3747	355	14	.	.	PUNCT
ejpam-3747	356	1	suppose	suppose	VERB
ejpam-3747	356	2	that	that	SCONJ
ejpam-3747	356	3	the	the	DET
ejpam-3747	356	4	mapping	mapping	NOUN
ejpam-3747	356	5	s	s	X
ejpam-3747	356	6	:	:	PUNCT
ejpam-3747	356	7	cb(x	cb(x	NUM
ejpam-3747	356	8	)	)	PUNCT
ejpam-3747	356	9	→	→	SYM
ejpam-3747	356	10	cb(x	cb(x	NUM
ejpam-3747	356	11	)	)	PUNCT
ejpam-3747	356	12	satisfy	satisfy	VERB
ejpam-3747	356	13	the	the	DET
ejpam-3747	356	14	following	follow	VERB
ejpam-3747	356	15	conditions	condition	NOUN
ejpam-3747	356	16	:	:	PUNCT
ejpam-3747	356	17	(	(	PUNCT
ejpam-3747	356	18	a	a	X
ejpam-3747	356	19	)	)	PUNCT
ejpam-3747	356	20	for	for	ADP
ejpam-3747	356	21	every	every	DET
ejpam-3747	356	22	u	u	NOUN
ejpam-3747	356	23	in	in	ADP
ejpam-3747	356	24	cb(x	cb(x	NUM
ejpam-3747	356	25	)	)	PUNCT
ejpam-3747	356	26	,	,	PUNCT
ejpam-3747	356	27	(	(	PUNCT
ejpam-3747	356	28	u	u	NOUN
ejpam-3747	356	29	,	,	PUNCT
ejpam-3747	356	30	s(u	s(u	PROPN
ejpam-3747	356	31	)	)	PUNCT
ejpam-3747	356	32	)	)	PUNCT
ejpam-3747	357	1	⊂	⊂	PROPN
ejpam-3747	357	2	e(g	e(g	PROPN
ejpam-3747	357	3	)	)	PUNCT
ejpam-3747	357	4	,	,	PUNCT
ejpam-3747	357	5	(	(	PUNCT
ejpam-3747	357	6	b	b	X
ejpam-3747	357	7	)	)	PUNCT
ejpam-3747	357	8	there	there	PRON
ejpam-3747	357	9	exists	exist	VERB
ejpam-3747	357	10	an	an	DET
ejpam-3747	357	11	nondecreasing	nondecreasing	ADJ
ejpam-3747	357	12	function	function	NOUN
ejpam-3747	357	13	φ	φ	NOUN
ejpam-3747	357	14	:	:	PUNCT
ejpam-3747	357	15	r+	r+	NOUN
ejpam-3747	357	16	→	→	SYM
ejpam-3747	357	17	r+	r+	NOUN
ejpam-3747	357	18	with	with	ADP
ejpam-3747	357	19	∑∞	∑∞	NOUN
ejpam-3747	357	20	i=0	i=0	PROPN
ejpam-3747	357	21	φ	φ	PROPN
ejpam-3747	357	22	i(t	i(t	PROPN
ejpam-3747	357	23	)	)	PUNCT
ejpam-3747	357	24	is	be	AUX
ejpam-3747	357	25	convergent	convergent	ADJ
ejpam-3747	357	26	for	for	ADP
ejpam-3747	357	27	all	all	DET
ejpam-3747	357	28	t	t	PROPN
ejpam-3747	357	29	>	>	X
ejpam-3747	357	30	0	0	PROPN
ejpam-3747	357	31	,	,	PUNCT
ejpam-3747	357	32	ψ	ψ	ADP
ejpam-3747	357	33	∈	∈	PROPN
ejpam-3747	357	34	ψ	ψ	X
ejpam-3747	357	35	,	,	PUNCT
ejpam-3747	357	36	ϕ	ϕ	PROPN
ejpam-3747	357	37	∈	∈	PROPN
ejpam-3747	357	38	φ	φ	NUM
ejpam-3747	357	39	,	,	PUNCT
ejpam-3747	357	40	and	and	CCONJ
ejpam-3747	357	41	l	l	NOUN
ejpam-3747	357	42	≥	≥	NUM
ejpam-3747	357	43	0	0	NUM
ejpam-3747	357	44	such	such	ADJ
ejpam-3747	357	45	that	that	SCONJ
ejpam-3747	357	46	if	if	SCONJ
ejpam-3747	357	47	there	there	PRON
ejpam-3747	357	48	is	be	VERB
ejpam-3747	357	49	an	an	DET
ejpam-3747	357	50	edge	edge	NOUN
ejpam-3747	357	51	between	between	ADP
ejpam-3747	357	52	a	a	PRON
ejpam-3747	357	53	and	and	CCONJ
ejpam-3747	357	54	b	b	NOUN
ejpam-3747	357	55	with	with	ADP
ejpam-3747	357	56	s(a	s(a	PROPN
ejpam-3747	357	57	)	)	PUNCT
ejpam-3747	357	58	6=	6=	ADP
ejpam-3747	357	59	s(b	s(b	NOUN
ejpam-3747	357	60	)	)	PUNCT
ejpam-3747	357	61	,	,	PUNCT
ejpam-3747	357	62	then	then	ADV
ejpam-3747	357	63	ψ	ψ	X
ejpam-3747	357	64	(	(	PUNCT
ejpam-3747	357	65	∫	∫	PROPN
ejpam-3747	357	66	h(s(a),s(b	h(s(a),s(b	NOUN
ejpam-3747	357	67	)	)	PUNCT
ejpam-3747	357	68	)	)	PUNCT
ejpam-3747	357	69	0	0	NUM
ejpam-3747	358	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	358	2	)	)	PUNCT
ejpam-3747	359	1	≤	≤	PROPN
ejpam-3747	359	2	φ	φ	PROPN
ejpam-3747	359	3	(	(	PUNCT
ejpam-3747	359	4	ψ	ψ	X
ejpam-3747	359	5	(	(	PUNCT
ejpam-3747	359	6	∫	∫	PROPN
ejpam-3747	359	7	m(a	m(a	PROPN
ejpam-3747	359	8	,	,	PUNCT
ejpam-3747	359	9	b	b	NOUN
ejpam-3747	359	10	)	)	PUNCT
ejpam-3747	359	11	0	0	NUM
ejpam-3747	359	12	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	359	13	)	)	PUNCT
ejpam-3747	359	14	)	)	PUNCT
ejpam-3747	360	1	+	+	CCONJ
ejpam-3747	360	2	l	l	NOUN
ejpam-3747	360	3	∫	∫	PROPN
ejpam-3747	361	1	n(a	n(a	PROPN
ejpam-3747	361	2	,	,	PUNCT
ejpam-3747	361	3	b	b	NOUN
ejpam-3747	361	4	)	)	PUNCT
ejpam-3747	361	5	0	0	NUM
ejpam-3747	361	6	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-3747	361	7	,	,	PUNCT
ejpam-3747	361	8	where	where	SCONJ
ejpam-3747	361	9	m(a	m(a	NOUN
ejpam-3747	361	10	,	,	PUNCT
ejpam-3747	361	11	b	b	NOUN
ejpam-3747	361	12	)	)	PUNCT
ejpam-3747	361	13	=	=	SYM
ejpam-3747	361	14	max	max	PROPN
ejpam-3747	361	15	{	{	PUNCT
ejpam-3747	361	16	h(a	h(a	PROPN
ejpam-3747	361	17	,	,	PUNCT
ejpam-3747	361	18	b	b	NOUN
ejpam-3747	361	19	)	)	PUNCT
ejpam-3747	361	20	,	,	PUNCT
ejpam-3747	361	21	h(a	h(a	PROPN
ejpam-3747	361	22	,	,	PUNCT
ejpam-3747	361	23	s(a	s(a	PROPN
ejpam-3747	361	24	)	)	PUNCT
ejpam-3747	361	25	)	)	PUNCT
ejpam-3747	361	26	,	,	PUNCT
ejpam-3747	361	27	h(b	h(b	PROPN
ejpam-3747	361	28	,	,	PUNCT
ejpam-3747	361	29	s(b	s(b	NOUN
ejpam-3747	361	30	)	)	PUNCT
ejpam-3747	361	31	)	)	PUNCT
ejpam-3747	361	32	,	,	PUNCT
ejpam-3747	361	33	h(a	h(a	PROPN
ejpam-3747	361	34	,	,	PUNCT
ejpam-3747	361	35	s(b	s(b	NOUN
ejpam-3747	361	36	)	)	PUNCT
ejpam-3747	361	37	)	)	PUNCT
ejpam-3747	362	1	+	+	X
ejpam-3747	362	2	h(b	h(b	ADJ
ejpam-3747	362	3	,	,	PUNCT
ejpam-3747	362	4	s(a	s(a	PROPN
ejpam-3747	362	5	)	)	PUNCT
ejpam-3747	362	6	)	)	PUNCT
ejpam-3747	362	7	2	2	X
ejpam-3747	362	8	}	}	PUNCT
ejpam-3747	362	9	and	and	CCONJ
ejpam-3747	362	10	n(a	n(a	NOUN
ejpam-3747	362	11	,	,	PUNCT
ejpam-3747	362	12	b	b	NOUN
ejpam-3747	362	13	)	)	PUNCT
ejpam-3747	362	14	=	=	SYM
ejpam-3747	362	15	min{h(a	min{h(a	PROPN
ejpam-3747	362	16	,	,	PUNCT
ejpam-3747	362	17	s(a	s(a	PROPN
ejpam-3747	362	18	)	)	PUNCT
ejpam-3747	362	19	)	)	PUNCT
ejpam-3747	362	20	,	,	PUNCT
ejpam-3747	362	21	h(b	h(b	PROPN
ejpam-3747	362	22	,	,	PUNCT
ejpam-3747	362	23	s(b	s(b	NOUN
ejpam-3747	362	24	)	)	PUNCT
ejpam-3747	362	25	)	)	PUNCT
ejpam-3747	362	26	,	,	PUNCT
ejpam-3747	362	27	h(a	h(a	PROPN
ejpam-3747	362	28	,	,	PUNCT
ejpam-3747	362	29	s(b	s(b	PROPN
ejpam-3747	362	30	)	)	PUNCT
ejpam-3747	362	31	)	)	PUNCT
ejpam-3747	362	32	,	,	PUNCT
ejpam-3747	362	33	h(b	h(b	PROPN
ejpam-3747	362	34	,	,	PUNCT
ejpam-3747	362	35	s(a	s(a	PROPN
ejpam-3747	362	36	)	)	PUNCT
ejpam-3747	362	37	)	)	PUNCT
ejpam-3747	362	38	}	}	PUNCT
ejpam-3747	362	39	.	.	PUNCT
ejpam-3747	363	1	if	if	SCONJ
ejpam-3747	363	2	the	the	DET
ejpam-3747	363	3	relation	relation	NOUN
ejpam-3747	363	4	r	r	NOUN
ejpam-3747	363	5	on	on	ADP
ejpam-3747	363	6	cb(x	cb(x	NUM
ejpam-3747	363	7	)	)	PUNCT
ejpam-3747	363	8	is	be	AUX
ejpam-3747	363	9	transitive	transitive	ADJ
ejpam-3747	363	10	,	,	PUNCT
ejpam-3747	363	11	then	then	ADV
ejpam-3747	363	12	the	the	DET
ejpam-3747	363	13	following	follow	VERB
ejpam-3747	363	14	statements	statement	NOUN
ejpam-3747	363	15	hold	hold	VERB
ejpam-3747	363	16	(	(	PUNCT
ejpam-3747	363	17	i	i	NOUN
ejpam-3747	363	18	)	)	PUNCT
ejpam-3747	363	19	f	f	PROPN
ejpam-3747	363	20	(	(	PUNCT
ejpam-3747	363	21	s	s	NOUN
ejpam-3747	363	22	)	)	PUNCT
ejpam-3747	363	23	6=	6=	NOUN
ejpam-3747	363	24	∅	∅	NOUN
ejpam-3747	363	25	provided	provide	VERB
ejpam-3747	363	26	that	that	SCONJ
ejpam-3747	363	27	g	g	PROPN
ejpam-3747	363	28	is	be	AUX
ejpam-3747	363	29	weakly	weakly	ADV
ejpam-3747	363	30	connected	connected	ADJ
ejpam-3747	363	31	and	and	CCONJ
ejpam-3747	363	32	satisfies	satisfy	VERB
ejpam-3747	363	33	the	the	DET
ejpam-3747	363	34	property	property	NOUN
ejpam-3747	363	35	(	(	PUNCT
ejpam-3747	363	36	p	p	NOUN
ejpam-3747	363	37	?	?	PUNCT
ejpam-3747	363	38	)	)	PUNCT
ejpam-3747	363	39	.	.	PUNCT
ejpam-3747	364	1	(	(	PUNCT
ejpam-3747	364	2	ii	ii	X
ejpam-3747	364	3	)	)	PUNCT
ejpam-3747	364	4	if	if	SCONJ
ejpam-3747	364	5	f	f	PROPN
ejpam-3747	364	6	(	(	PUNCT
ejpam-3747	364	7	s	s	X
ejpam-3747	364	8	)	)	PUNCT
ejpam-3747	364	9	is	be	AUX
ejpam-3747	364	10	complete	complete	ADJ
ejpam-3747	364	11	,	,	PUNCT
ejpam-3747	364	12	then	then	ADV
ejpam-3747	364	13	the	the	DET
ejpam-3747	364	14	pompeiu	pompeiu	NOUN
ejpam-3747	364	15	-	-	PUNCT
ejpam-3747	364	16	hausdorff	hausdorff	NOUN
ejpam-3747	364	17	weight	weight	NOUN
ejpam-3747	364	18	assigned	assign	VERB
ejpam-3747	364	19	to	to	ADP
ejpam-3747	364	20	the	the	DET
ejpam-3747	364	21	u	u	NOUN
ejpam-3747	364	22	,	,	PUNCT
ejpam-3747	364	23	v	v	PROPN
ejpam-3747	364	24	∈	∈	X
ejpam-3747	364	25	f	f	X
ejpam-3747	364	26	(	(	PUNCT
ejpam-3747	364	27	s	s	X
ejpam-3747	364	28	)	)	PUNCT
ejpam-3747	364	29	is	be	AUX
ejpam-3747	364	30	0	0	NUM
ejpam-3747	364	31	.	.	PUNCT
ejpam-3747	365	1	(	(	PUNCT
ejpam-3747	365	2	iv	iv	X
ejpam-3747	365	3	)	)	PUNCT
ejpam-3747	365	4	f	f	NOUN
ejpam-3747	365	5	(	(	PUNCT
ejpam-3747	365	6	s	s	X
ejpam-3747	365	7	)	)	PUNCT
ejpam-3747	365	8	is	be	AUX
ejpam-3747	365	9	complete	complete	ADJ
ejpam-3747	365	10	if	if	SCONJ
ejpam-3747	366	1	and	and	CCONJ
ejpam-3747	366	2	only	only	ADV
ejpam-3747	366	3	if	if	SCONJ
ejpam-3747	366	4	f	f	PROPN
ejpam-3747	366	5	(	(	PUNCT
ejpam-3747	366	6	s	s	X
ejpam-3747	366	7	)	)	PUNCT
ejpam-3747	366	8	is	be	AUX
ejpam-3747	366	9	a	a	DET
ejpam-3747	366	10	singleton	singleton	NOUN
ejpam-3747	366	11	.	.	PUNCT
ejpam-3747	367	1	s.	s.	PROPN
ejpam-3747	367	2	benchabane	benchabane	PROPN
ejpam-3747	367	3	,	,	PUNCT
ejpam-3747	367	4	s.	s.	PROPN
ejpam-3747	367	5	djebali	djebali	PROPN
ejpam-3747	367	6	,	,	PUNCT
ejpam-3747	367	7	t.	t.	PROPN
ejpam-3747	367	8	nazir	nazir	PROPN
ejpam-3747	367	9	/	/	SYM
ejpam-3747	367	10	eur	eur	PROPN
ejpam-3747	367	11	.	.	PUNCT
ejpam-3747	368	1	j.	j.	PROPN
ejpam-3747	368	2	pure	pure	PROPN
ejpam-3747	368	3	appl	appl	PROPN
ejpam-3747	368	4	.	.	PROPN
ejpam-3747	368	5	math	math	PROPN
ejpam-3747	368	6	,	,	PUNCT
ejpam-3747	368	7	13	13	NUM
ejpam-3747	368	8	(	(	PUNCT
ejpam-3747	368	9	5	5	NUM
ejpam-3747	368	10	)	)	PUNCT
ejpam-3747	368	11	(	(	PUNCT
ejpam-3747	368	12	2020	2020	NUM
ejpam-3747	368	13	)	)	PUNCT
ejpam-3747	368	14	,	,	PUNCT
ejpam-3747	368	15	1072	1072	NUM
ejpam-3747	368	16	-	-	SYM
ejpam-3747	368	17	1087	1087	NUM
ejpam-3747	368	18	1085	1085	NUM
ejpam-3747	368	19	corollary	corollary	NOUN
ejpam-3747	368	20	3	3	NUM
ejpam-3747	368	21	.	.	PUNCT
ejpam-3747	369	1	let	let	VERB
ejpam-3747	369	2	(	(	PUNCT
ejpam-3747	369	3	x	x	NOUN
ejpam-3747	369	4	,	,	PUNCT
ejpam-3747	369	5	d	d	NOUN
ejpam-3747	369	6	)	)	PUNCT
ejpam-3747	369	7	be	be	AUX
ejpam-3747	369	8	a	a	DET
ejpam-3747	369	9	metric	metric	ADJ
ejpam-3747	369	10	space	space	NOUN
ejpam-3747	369	11	endowed	endow	VERB
ejpam-3747	369	12	with	with	ADP
ejpam-3747	369	13	a	a	DET
ejpam-3747	369	14	directed	direct	VERB
ejpam-3747	369	15	graph	graph	NOUN
ejpam-3747	369	16	g	g	ADP
ejpam-3747	370	1	such	such	DET
ejpam-3747	370	2	that	that	DET
ejpam-3747	370	3	v	v	NOUN
ejpam-3747	370	4	(	(	PUNCT
ejpam-3747	370	5	g	g	NOUN
ejpam-3747	370	6	)	)	PUNCT
ejpam-3747	370	7	=	=	SYM
ejpam-3747	370	8	x	x	PROPN
ejpam-3747	370	9	and	and	CCONJ
ejpam-3747	370	10	∆	∆	PROPN
ejpam-3747	370	11	⊂	⊂	PROPN
ejpam-3747	370	12	e(g	e(g	PROPN
ejpam-3747	370	13	)	)	PUNCT
ejpam-3747	370	14	.	.	PUNCT
ejpam-3747	371	1	suppose	suppose	VERB
ejpam-3747	371	2	that	that	SCONJ
ejpam-3747	371	3	the	the	DET
ejpam-3747	371	4	mapping	mapping	NOUN
ejpam-3747	371	5	s	s	VERB
ejpam-3747	371	6	:	:	PUNCT
ejpam-3747	371	7	cb(x)→	cb(x)→	VERB
ejpam-3747	371	8	cb(x	cb(x	NUM
ejpam-3747	371	9	)	)	PUNCT
ejpam-3747	371	10	satisfies	satisfy	VERB
ejpam-3747	371	11	the	the	DET
ejpam-3747	371	12	following	follow	VERB
ejpam-3747	371	13	conditions	condition	NOUN
ejpam-3747	371	14	:	:	PUNCT
ejpam-3747	371	15	(	(	PUNCT
ejpam-3747	371	16	a	a	X
ejpam-3747	371	17	)	)	PUNCT
ejpam-3747	371	18	for	for	ADP
ejpam-3747	371	19	every	every	DET
ejpam-3747	371	20	u	u	NOUN
ejpam-3747	371	21	in	in	ADP
ejpam-3747	371	22	cb(x	cb(x	NUM
ejpam-3747	371	23	)	)	PUNCT
ejpam-3747	371	24	,	,	PUNCT
ejpam-3747	371	25	(	(	PUNCT
ejpam-3747	371	26	u	u	NOUN
ejpam-3747	371	27	,	,	PUNCT
ejpam-3747	371	28	s(u	s(u	PROPN
ejpam-3747	371	29	)	)	PUNCT
ejpam-3747	371	30	)	)	PUNCT
ejpam-3747	372	1	⊂	⊂	PROPN
ejpam-3747	372	2	e(g	e(g	PROPN
ejpam-3747	372	3	)	)	PUNCT
ejpam-3747	372	4	,	,	PUNCT
ejpam-3747	372	5	(	(	PUNCT
ejpam-3747	372	6	b	b	X
ejpam-3747	372	7	)	)	PUNCT
ejpam-3747	372	8	there	there	PRON
ejpam-3747	372	9	exists	exist	VERB
ejpam-3747	372	10	an	an	DET
ejpam-3747	372	11	nondecreasing	nondecreasing	ADJ
ejpam-3747	372	12	function	function	NOUN
ejpam-3747	372	13	φ	φ	NOUN
ejpam-3747	372	14	:	:	PUNCT
ejpam-3747	372	15	r+	r+	NOUN
ejpam-3747	372	16	→	→	SYM
ejpam-3747	372	17	r+	r+	NOUN
ejpam-3747	372	18	with	with	ADP
ejpam-3747	372	19	∑∞	∑∞	NOUN
ejpam-3747	372	20	i=0	i=0	PROPN
ejpam-3747	372	21	φ	φ	PROPN
ejpam-3747	372	22	i(t	i(t	PROPN
ejpam-3747	372	23	)	)	PUNCT
ejpam-3747	372	24	is	be	AUX
ejpam-3747	372	25	convergent	convergent	ADJ
ejpam-3747	372	26	for	for	ADP
ejpam-3747	372	27	all	all	DET
ejpam-3747	372	28	t	t	PROPN
ejpam-3747	372	29	>	>	X
ejpam-3747	372	30	0	0	PROPN
ejpam-3747	372	31	,	,	PUNCT
ejpam-3747	372	32	ψ	ψ	ADP
ejpam-3747	372	33	∈	∈	PROPN
ejpam-3747	372	34	ψ	ψ	NOUN
ejpam-3747	372	35	,	,	PUNCT
ejpam-3747	372	36	and	and	CCONJ
ejpam-3747	372	37	l	l	NOUN
ejpam-3747	372	38	≥	≥	NUM
ejpam-3747	372	39	0	0	NUM
ejpam-3747	372	40	such	such	ADJ
ejpam-3747	372	41	that	that	SCONJ
ejpam-3747	372	42	if	if	SCONJ
ejpam-3747	372	43	there	there	PRON
ejpam-3747	372	44	is	be	VERB
ejpam-3747	372	45	an	an	DET
ejpam-3747	372	46	edge	edge	NOUN
ejpam-3747	372	47	between	between	ADP
ejpam-3747	372	48	a	a	PRON
ejpam-3747	372	49	and	and	CCONJ
ejpam-3747	372	50	b	b	NOUN
ejpam-3747	372	51	with	with	ADP
ejpam-3747	372	52	s(a	s(a	PROPN
ejpam-3747	372	53	)	)	PUNCT
ejpam-3747	372	54	6=	6=	ADP
ejpam-3747	373	1	s(b	s(b	NOUN
ejpam-3747	373	2	)	)	PUNCT
ejpam-3747	373	3	,	,	PUNCT
ejpam-3747	373	4	then	then	ADV
ejpam-3747	373	5	ψ(h(s(a	ψ(h(s(a	PROPN
ejpam-3747	373	6	)	)	PUNCT
ejpam-3747	373	7	,	,	PUNCT
ejpam-3747	373	8	s(b	s(b	NOUN
ejpam-3747	373	9	)	)	PUNCT
ejpam-3747	373	10	)	)	PUNCT
ejpam-3747	373	11	)	)	PUNCT
ejpam-3747	374	1	≤	≤	NUM
ejpam-3747	374	2	φ(ψ(m(a	φ(ψ(m(a	PROPN
ejpam-3747	374	3	,	,	PUNCT
ejpam-3747	374	4	b	b	NOUN
ejpam-3747	374	5	)	)	PUNCT
ejpam-3747	374	6	)	)	PUNCT
ejpam-3747	374	7	)	)	PUNCT
ejpam-3747	375	1	+	+	CCONJ
ejpam-3747	375	2	ln(a	ln(a	ADP
ejpam-3747	375	3	,	,	PUNCT
ejpam-3747	375	4	b	b	NOUN
ejpam-3747	375	5	)	)	PUNCT
ejpam-3747	375	6	.	.	PUNCT
ejpam-3747	376	1	if	if	SCONJ
ejpam-3747	376	2	the	the	DET
ejpam-3747	376	3	relation	relation	NOUN
ejpam-3747	376	4	r	r	NOUN
ejpam-3747	376	5	on	on	ADP
ejpam-3747	376	6	cb(x	cb(x	NUM
ejpam-3747	376	7	)	)	PUNCT
ejpam-3747	376	8	is	be	AUX
ejpam-3747	376	9	transitive	transitive	ADJ
ejpam-3747	376	10	,	,	PUNCT
ejpam-3747	376	11	then	then	ADV
ejpam-3747	376	12	the	the	DET
ejpam-3747	376	13	following	following	ADJ
ejpam-3747	376	14	statements	statement	NOUN
ejpam-3747	376	15	hold	hold	VERB
ejpam-3747	376	16	:	:	PUNCT
ejpam-3747	376	17	(	(	PUNCT
ejpam-3747	376	18	i	i	NOUN
ejpam-3747	376	19	)	)	PUNCT
ejpam-3747	376	20	f	f	PROPN
ejpam-3747	376	21	(	(	PUNCT
ejpam-3747	376	22	s	s	NOUN
ejpam-3747	376	23	)	)	PUNCT
ejpam-3747	376	24	6=	6=	NOUN
ejpam-3747	376	25	∅	∅	NOUN
ejpam-3747	376	26	provided	provide	VERB
ejpam-3747	376	27	that	that	SCONJ
ejpam-3747	376	28	g	g	PROPN
ejpam-3747	376	29	is	be	AUX
ejpam-3747	376	30	weakly	weakly	ADV
ejpam-3747	376	31	connected	connected	ADJ
ejpam-3747	376	32	and	and	CCONJ
ejpam-3747	376	33	satisfies	satisfy	VERB
ejpam-3747	376	34	the	the	DET
ejpam-3747	376	35	property	property	NOUN
ejpam-3747	376	36	(	(	PUNCT
ejpam-3747	376	37	p	p	NOUN
ejpam-3747	376	38	?	?	PUNCT
ejpam-3747	376	39	)	)	PUNCT
ejpam-3747	376	40	.	.	PUNCT
ejpam-3747	377	1	(	(	PUNCT
ejpam-3747	377	2	ii	ii	X
ejpam-3747	377	3	)	)	PUNCT
ejpam-3747	377	4	if	if	SCONJ
ejpam-3747	377	5	f	f	PROPN
ejpam-3747	377	6	(	(	PUNCT
ejpam-3747	377	7	s	s	X
ejpam-3747	377	8	)	)	PUNCT
ejpam-3747	377	9	is	be	AUX
ejpam-3747	377	10	complete	complete	ADJ
ejpam-3747	377	11	,	,	PUNCT
ejpam-3747	377	12	then	then	ADV
ejpam-3747	377	13	the	the	DET
ejpam-3747	377	14	pompeiu	pompeiu	NOUN
ejpam-3747	377	15	-	-	PUNCT
ejpam-3747	377	16	hausdorff	hausdorff	NOUN
ejpam-3747	377	17	weight	weight	NOUN
ejpam-3747	377	18	assigned	assign	VERB
ejpam-3747	377	19	to	to	ADP
ejpam-3747	377	20	the	the	DET
ejpam-3747	377	21	u	u	NOUN
ejpam-3747	377	22	,	,	PUNCT
ejpam-3747	377	23	v	v	PROPN
ejpam-3747	377	24	∈	∈	X
ejpam-3747	377	25	f	f	X
ejpam-3747	377	26	(	(	PUNCT
ejpam-3747	377	27	s	s	X
ejpam-3747	377	28	)	)	PUNCT
ejpam-3747	377	29	is	be	AUX
ejpam-3747	377	30	0	0	NUM
ejpam-3747	377	31	.	.	PUNCT
ejpam-3747	378	1	(	(	PUNCT
ejpam-3747	378	2	iv	iv	X
ejpam-3747	378	3	)	)	PUNCT
ejpam-3747	378	4	f	f	NOUN
ejpam-3747	378	5	(	(	PUNCT
ejpam-3747	378	6	s	s	X
ejpam-3747	378	7	)	)	PUNCT
ejpam-3747	378	8	is	be	AUX
ejpam-3747	378	9	complete	complete	ADJ
ejpam-3747	378	10	if	if	SCONJ
ejpam-3747	379	1	and	and	CCONJ
ejpam-3747	379	2	only	only	ADV
ejpam-3747	379	3	if	if	SCONJ
ejpam-3747	379	4	f	f	PROPN
ejpam-3747	379	5	(	(	PUNCT
ejpam-3747	379	6	s	s	X
ejpam-3747	379	7	)	)	PUNCT
ejpam-3747	379	8	is	be	AUX
ejpam-3747	379	9	a	a	DET
ejpam-3747	379	10	singleton	singleton	NOUN
ejpam-3747	379	11	.	.	PUNCT
ejpam-3747	380	1	in	in	ADP
ejpam-3747	380	2	case	case	NOUN
ejpam-3747	380	3	of	of	ADP
ejpam-3747	380	4	ε	ε	PROPN
ejpam-3747	380	5	-	-	PUNCT
ejpam-3747	380	6	chainable	chainable	ADJ
ejpam-3747	380	7	complete	complete	ADJ
ejpam-3747	380	8	metric	metric	ADJ
ejpam-3747	380	9	spaces	space	NOUN
ejpam-3747	380	10	,	,	PUNCT
ejpam-3747	380	11	we	we	PRON
ejpam-3747	380	12	have	have	AUX
ejpam-3747	380	13	theorem	theorem	VERB
ejpam-3747	380	14	4	4	NUM
ejpam-3747	380	15	.	.	PUNCT
ejpam-3747	381	1	let	let	AUX
ejpam-3747	381	2	(	(	PUNCT
ejpam-3747	381	3	x	x	NOUN
ejpam-3747	381	4	,	,	PUNCT
ejpam-3747	381	5	d	d	NOUN
ejpam-3747	381	6	)	)	PUNCT
ejpam-3747	381	7	be	be	AUX
ejpam-3747	381	8	a	a	DET
ejpam-3747	381	9	ε	ε	PROPN
ejpam-3747	381	10	-	-	PUNCT
ejpam-3747	381	11	chainable	chainable	ADJ
ejpam-3747	381	12	complete	complete	ADJ
ejpam-3747	381	13	metric	metric	ADJ
ejpam-3747	381	14	space	space	NOUN
ejpam-3747	381	15	for	for	ADP
ejpam-3747	381	16	some	some	DET
ejpam-3747	381	17	ε	ε	PROPN
ejpam-3747	381	18	>	>	X
ejpam-3747	381	19	0	0	PROPN
ejpam-3747	381	20	.	.	PUNCT
ejpam-3747	381	21	suppose	suppose	VERB
ejpam-3747	381	22	that	that	SCONJ
ejpam-3747	381	23	the	the	DET
ejpam-3747	381	24	mappings	mapping	NOUN
ejpam-3747	381	25	s	s	PART
ejpam-3747	381	26	,	,	PUNCT
ejpam-3747	381	27	t	t	PROPN
ejpam-3747	381	28	:	:	PUNCT
ejpam-3747	381	29	cb(x	cb(x	NUM
ejpam-3747	381	30	)	)	PUNCT
ejpam-3747	381	31	→	→	SYM
ejpam-3747	381	32	cb(x	cb(x	NUM
ejpam-3747	381	33	)	)	PUNCT
ejpam-3747	381	34	satisfy	satisfy	VERB
ejpam-3747	381	35	that	that	SCONJ
ejpam-3747	381	36	for	for	ADP
ejpam-3747	381	37	every	every	DET
ejpam-3747	381	38	a	a	PROPN
ejpam-3747	381	39	,	,	PUNCT
ejpam-3747	381	40	b	b	X
ejpam-3747	381	41	∈	∈	PROPN
ejpam-3747	381	42	cb(x	cb(x	NUM
ejpam-3747	381	43	)	)	PUNCT
ejpam-3747	381	44	with	with	ADP
ejpam-3747	381	45	s(a	s(a	PROPN
ejpam-3747	381	46	)	)	PUNCT
ejpam-3747	381	47	6=	6=	ADP
ejpam-3747	381	48	t	t	PROPN
ejpam-3747	381	49	(	(	PUNCT
ejpam-3747	381	50	b	b	NOUN
ejpam-3747	381	51	)	)	PUNCT
ejpam-3747	381	52	and	and	CCONJ
ejpam-3747	381	53	0	0	NUM
ejpam-3747	381	54	<	<	X
ejpam-3747	381	55	h(a	h(a	PROPN
ejpam-3747	381	56	,	,	PUNCT
ejpam-3747	381	57	b	b	NOUN
ejpam-3747	381	58	)	)	PUNCT
ejpam-3747	381	59	<	<	X
ejpam-3747	381	60	ε	ε	PROPN
ejpam-3747	381	61	,	,	PUNCT
ejpam-3747	381	62	there	there	PRON
ejpam-3747	381	63	exists	exist	VERB
ejpam-3747	381	64	an	an	DET
ejpam-3747	381	65	nondecreasing	nondecreasing	ADJ
ejpam-3747	381	66	function	function	NOUN
ejpam-3747	381	67	φ	φ	NOUN
ejpam-3747	381	68	:	:	PUNCT
ejpam-3747	381	69	r+	r+	NOUN
ejpam-3747	381	70	→	→	SYM
ejpam-3747	381	71	r+	r+	NOUN
ejpam-3747	381	72	with	with	ADP
ejpam-3747	381	73	∑∞	∑∞	NOUN
ejpam-3747	381	74	i=0	i=0	PROPN
ejpam-3747	381	75	φ	φ	PROPN
ejpam-3747	381	76	i(t	i(t	PROPN
ejpam-3747	381	77	)	)	PUNCT
ejpam-3747	381	78	is	be	AUX
ejpam-3747	381	79	convergent	convergent	ADJ
ejpam-3747	381	80	for	for	ADP
ejpam-3747	381	81	all	all	DET
ejpam-3747	381	82	t	t	PROPN
ejpam-3747	381	83	>	>	X
ejpam-3747	381	84	0	0	PROPN
ejpam-3747	381	85	,	,	PUNCT
ejpam-3747	381	86	ψ	ψ	ADP
ejpam-3747	381	87	∈	∈	PROPN
ejpam-3747	381	88	ψ	ψ	X
ejpam-3747	381	89	,	,	PUNCT
ejpam-3747	381	90	ϕ	ϕ	PROPN
ejpam-3747	381	91	∈	∈	PROPN
ejpam-3747	381	92	φ	φ	NUM
ejpam-3747	381	93	,	,	PUNCT
ejpam-3747	381	94	and	and	CCONJ
ejpam-3747	381	95	l	l	NOUN
ejpam-3747	381	96	≥	≥	NOUN
ejpam-3747	381	97	0	0	NUM
ejpam-3747	381	98	with	with	ADP
ejpam-3747	381	99	ψ	ψ	X
ejpam-3747	381	100	(	(	PUNCT
ejpam-3747	381	101	∫	∫	PROPN
ejpam-3747	381	102	h(s(a),t	h(s(a),t	PROPN
ejpam-3747	381	103	(	(	PUNCT
ejpam-3747	381	104	b	b	NOUN
ejpam-3747	381	105	)	)	PUNCT
ejpam-3747	381	106	)	)	PUNCT
ejpam-3747	381	107	0	0	NUM
ejpam-3747	382	1	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	382	2	)	)	PUNCT
ejpam-3747	383	1	≤	≤	PROPN
ejpam-3747	383	2	φ	φ	PROPN
ejpam-3747	383	3	(	(	PUNCT
ejpam-3747	383	4	ψ	ψ	X
ejpam-3747	383	5	(	(	PUNCT
ejpam-3747	383	6	∫	∫	PROPN
ejpam-3747	383	7	ms	ms	PROPN
ejpam-3747	383	8	,	,	PUNCT
ejpam-3747	383	9	t	t	PROPN
ejpam-3747	383	10	(	(	PUNCT
ejpam-3747	383	11	a	a	DET
ejpam-3747	383	12	,	,	PUNCT
ejpam-3747	383	13	b	b	NOUN
ejpam-3747	383	14	)	)	PUNCT
ejpam-3747	383	15	0	0	NUM
ejpam-3747	383	16	ϕ(t)dt	ϕ(t)dt	PRON
ejpam-3747	383	17	)	)	PUNCT
ejpam-3747	383	18	)	)	PUNCT
ejpam-3747	384	1	+	+	CCONJ
ejpam-3747	384	2	l	l	NOUN
ejpam-3747	384	3	∫	∫	PROPN
ejpam-3747	384	4	ns	ns	PROPN
ejpam-3747	384	5	,	,	PUNCT
ejpam-3747	384	6	t	t	PROPN
ejpam-3747	384	7	(	(	PUNCT
ejpam-3747	384	8	a	a	DET
ejpam-3747	384	9	,	,	PUNCT
ejpam-3747	384	10	b	b	NOUN
ejpam-3747	384	11	)	)	PUNCT
ejpam-3747	384	12	0	0	NUM
ejpam-3747	385	1	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-3747	385	2	.	.	PUNCT
ejpam-3747	386	1	then	then	ADV
ejpam-3747	386	2	s	s	VERB
ejpam-3747	386	3	and	and	CCONJ
ejpam-3747	386	4	t	t	PROPN
ejpam-3747	386	5	have	have	VERB
ejpam-3747	386	6	a	a	DET
ejpam-3747	386	7	common	common	ADJ
ejpam-3747	386	8	fixed	fix	VERB
ejpam-3747	386	9	point	point	NOUN
ejpam-3747	386	10	.	.	PUNCT
ejpam-3747	387	1	proof	proof	NOUN
ejpam-3747	387	2	.	.	PUNCT
ejpam-3747	388	1	define	define	VERB
ejpam-3747	388	2	the	the	DET
ejpam-3747	388	3	graph	graph	NOUN
ejpam-3747	388	4	g	g	PROPN
ejpam-3747	388	5	=	=	PUNCT
ejpam-3747	388	6	(	(	PUNCT
ejpam-3747	388	7	v	v	NOUN
ejpam-3747	388	8	(	(	PUNCT
ejpam-3747	388	9	g	g	NOUN
ejpam-3747	388	10	)	)	PUNCT
ejpam-3747	388	11	,	,	PUNCT
ejpam-3747	388	12	e(g	e(g	PROPN
ejpam-3747	388	13	)	)	PUNCT
ejpam-3747	388	14	)	)	PUNCT
ejpam-3747	388	15	by	by	ADP
ejpam-3747	388	16	v	v	NUM
ejpam-3747	388	17	(	(	PUNCT
ejpam-3747	388	18	g	g	NOUN
ejpam-3747	388	19	)	)	PUNCT
ejpam-3747	388	20	=	=	SYM
ejpam-3747	388	21	x	x	PROPN
ejpam-3747	388	22	and	and	CCONJ
ejpam-3747	388	23	e(g	e(g	PROPN
ejpam-3747	388	24	)	)	PUNCT
ejpam-3747	389	1	=	=	PRON
ejpam-3747	389	2	{	{	PUNCT
ejpam-3747	389	3	(	(	PUNCT
ejpam-3747	389	4	x	x	NOUN
ejpam-3747	389	5	,	,	PUNCT
ejpam-3747	389	6	y	y	NOUN
ejpam-3747	389	7	)	)	PUNCT
ejpam-3747	389	8	∈	∈	PROPN
ejpam-3747	389	9	x×x	x×x	PROPN
ejpam-3747	389	10	:	:	PUNCT
ejpam-3747	389	11	d(x	d(x	PROPN
ejpam-3747	389	12	,	,	PUNCT
ejpam-3747	389	13	y	y	NOUN
ejpam-3747	389	14	)	)	PUNCT
ejpam-3747	389	15	<	<	X
ejpam-3747	389	16	ε	ε	PROPN
ejpam-3747	389	17	}	}	PUNCT
ejpam-3747	389	18	.	.	PUNCT
ejpam-3747	390	1	it	it	PRON
ejpam-3747	390	2	clear	clear	ADJ
ejpam-3747	390	3	that	that	SCONJ
ejpam-3747	390	4	the	the	DET
ejpam-3747	390	5	ε	ε	PROPN
ejpam-3747	390	6	-	-	PUNCT
ejpam-3747	390	7	chainability	chainability	NOUN
ejpam-3747	390	8	of	of	ADP
ejpam-3747	390	9	(	(	PUNCT
ejpam-3747	390	10	x	x	NOUN
ejpam-3747	390	11	,	,	PUNCT
ejpam-3747	390	12	d	d	NOUN
ejpam-3747	390	13	)	)	PUNCT
ejpam-3747	390	14	implies	imply	VERB
ejpam-3747	390	15	that	that	SCONJ
ejpam-3747	390	16	g	g	PROPN
ejpam-3747	390	17	is	be	AUX
ejpam-3747	390	18	connected	connect	VERB
ejpam-3747	390	19	.	.	PUNCT
ejpam-3747	391	1	let	let	VERB
ejpam-3747	391	2	a	a	DET
ejpam-3747	391	3	,	,	PUNCT
ejpam-3747	391	4	b	b	X
ejpam-3747	391	5	∈	∈	PROPN
ejpam-3747	391	6	cb(x	cb(x	ADJ
ejpam-3747	391	7	)	)	PUNCT
ejpam-3747	391	8	be	be	AUX
ejpam-3747	392	1	such	such	ADJ
ejpam-3747	392	2	that	that	SCONJ
ejpam-3747	392	3	0	0	NUM
ejpam-3747	392	4	<	<	X
ejpam-3747	392	5	h(a	h(a	PROPN
ejpam-3747	392	6	,	,	PUNCT
ejpam-3747	392	7	b	b	NOUN
ejpam-3747	392	8	)	)	PUNCT
ejpam-3747	392	9	<	<	X
ejpam-3747	392	10	ε	ε	PROPN
ejpam-3747	392	11	;	;	PUNCT
ejpam-3747	392	12	by	by	ADP
ejpam-3747	392	13	lemma	lemma	PROPN
ejpam-3747	392	14	3	3	NUM
ejpam-3747	392	15	,	,	PUNCT
ejpam-3747	392	16	(	(	PUNCT
ejpam-3747	392	17	a	a	DET
ejpam-3747	392	18	,	,	PUNCT
ejpam-3747	392	19	b	b	NOUN
ejpam-3747	392	20	)	)	PUNCT
ejpam-3747	392	21	⊂	⊂	PROPN
ejpam-3747	392	22	e(g	e(g	PROPN
ejpam-3747	392	23	)	)	PUNCT
ejpam-3747	392	24	.	.	PUNCT
ejpam-3747	393	1	it	it	PRON
ejpam-3747	393	2	is	be	AUX
ejpam-3747	393	3	easily	easily	ADV
ejpam-3747	393	4	seen	see	VERB
ejpam-3747	393	5	that	that	SCONJ
ejpam-3747	393	6	the	the	DET
ejpam-3747	393	7	pair	pair	NOUN
ejpam-3747	393	8	(	(	PUNCT
ejpam-3747	393	9	s	s	PROPN
ejpam-3747	393	10	,	,	PUNCT
ejpam-3747	393	11	t	t	PROPN
ejpam-3747	393	12	)	)	PUNCT
ejpam-3747	393	13	is	be	AUX
ejpam-3747	393	14	a	a	DET
ejpam-3747	393	15	graph	graph	NOUN
ejpam-3747	393	16	(	(	PUNCT
ejpam-3747	393	17	ψ	ψ	NOUN
ejpam-3747	393	18	,	,	PUNCT
ejpam-3747	393	19	φ)-weak	φ)-weak	VERB
ejpam-3747	393	20	contraction	contraction	NOUN
ejpam-3747	393	21	and	and	CCONJ
ejpam-3747	393	22	that	that	SCONJ
ejpam-3747	393	23	property	property	NOUN
ejpam-3747	393	24	(	(	PUNCT
ejpam-3747	393	25	p	p	NOUN
ejpam-3747	393	26	?	?	PUNCT
ejpam-3747	393	27	)	)	PUNCT
ejpam-3747	393	28	also	also	ADV
ejpam-3747	393	29	holds	hold	VERB
ejpam-3747	393	30	true	true	ADJ
ejpam-3747	393	31	.	.	PUNCT
ejpam-3747	394	1	therefore	therefore	ADV
ejpam-3747	394	2	theorem	theorem	VERB
ejpam-3747	394	3	4	4	NUM
ejpam-3747	394	4	follows	follow	VERB
ejpam-3747	394	5	directly	directly	ADV
ejpam-3747	394	6	from	from	ADP
ejpam-3747	394	7	theorem	theorem	ADJ
ejpam-3747	394	8	3	3	NUM
ejpam-3747	394	9	.	.	NOUN
ejpam-3747	394	10	remark	remark	NOUN
ejpam-3747	394	11	3	3	NUM
ejpam-3747	394	12	(	(	PUNCT
ejpam-3747	394	13	concluding	conclude	VERB
ejpam-3747	394	14	remarks	remark	NOUN
ejpam-3747	394	15	)	)	PUNCT
ejpam-3747	394	16	.	.	PUNCT
ejpam-3747	395	1	(	(	PUNCT
ejpam-3747	395	2	1	1	X
ejpam-3747	395	3	)	)	PUNCT
ejpam-3747	395	4	if	if	SCONJ
ejpam-3747	395	5	in	in	ADP
ejpam-3747	395	6	corollary	corollary	ADJ
ejpam-3747	395	7	2	2	NUM
ejpam-3747	395	8	,	,	PUNCT
ejpam-3747	395	9	we	we	PRON
ejpam-3747	395	10	take	take	VERB
ejpam-3747	395	11	ψ(t	ψ(t	PROPN
ejpam-3747	395	12	)	)	PUNCT
ejpam-3747	395	13	=	=	SYM
ejpam-3747	395	14	t	t	PROPN
ejpam-3747	395	15	,	,	PUNCT
ejpam-3747	395	16	ϕ(t	ϕ(t	NUM
ejpam-3747	395	17	)	)	PUNCT
ejpam-3747	396	1	=	=	SYM
ejpam-3747	396	2	1	1	NUM
ejpam-3747	396	3	,	,	PUNCT
ejpam-3747	396	4	l	l	NOUN
ejpam-3747	396	5	=	=	SYM
ejpam-3747	396	6	0	0	NUM
ejpam-3747	396	7	and	and	CCONJ
ejpam-3747	396	8	e(g	e(g	PROPN
ejpam-3747	396	9	)	)	PUNCT
ejpam-3747	397	1	=	=	PUNCT
ejpam-3747	398	1	x	x	X
ejpam-3747	398	2	×x	×x	VERB
ejpam-3747	398	3	then	then	ADV
ejpam-3747	398	4	g	g	PROPN
ejpam-3747	398	5	is	be	AUX
ejpam-3747	398	6	connected	connect	VERB
ejpam-3747	398	7	and	and	CCONJ
ejpam-3747	398	8	corollary	corollary	ADJ
ejpam-3747	398	9	2	2	NUM
ejpam-3747	398	10	improves	improve	VERB
ejpam-3747	398	11	and	and	CCONJ
ejpam-3747	398	12	generalizes	generalize	VERB
ejpam-3747	398	13	theorem	theorem	VERB
ejpam-3747	398	14	2.1	2.1	NUM
ejpam-3747	398	15	by	by	ADP
ejpam-3747	398	16	abbas	abbas	PROPN
ejpam-3747	398	17	et	et	PROPN
ejpam-3747	398	18	al	al	PROPN
ejpam-3747	398	19	.	.	PUNCT
ejpam-3747	399	1	[	[	X
ejpam-3747	399	2	1	1	NUM
ejpam-3747	399	3	]	]	PUNCT
ejpam-3747	399	4	,	,	PUNCT
ejpam-3747	399	5	theorem	theorem	VERB
ejpam-3747	399	6	3.1	3.1	NUM
ejpam-3747	399	7	by	by	ADP
ejpam-3747	399	8	beg	beg	NOUN
ejpam-3747	399	9	and	and	CCONJ
ejpam-3747	399	10	butt	butt	NOUN
ejpam-3747	399	11	[	[	X
ejpam-3747	399	12	6	6	NUM
ejpam-3747	399	13	]	]	PUNCT
ejpam-3747	399	14	,	,	PUNCT
ejpam-3747	399	15	and	and	CCONJ
ejpam-3747	399	16	theorem	theorem	VERB
ejpam-3747	399	17	3.1	3.1	NUM
ejpam-3747	399	18	by	by	ADP
ejpam-3747	399	19	jachymski	jachymski	NOUN
ejpam-3747	400	1	[	[	X
ejpam-3747	400	2	11	11	NUM
ejpam-3747	400	3	]	]	PUNCT
ejpam-3747	400	4	.	.	PUNCT
ejpam-3747	401	1	(	(	PUNCT
ejpam-3747	401	2	2	2	X
ejpam-3747	401	3	)	)	PUNCT
ejpam-3747	401	4	taking	take	VERB
ejpam-3747	401	5	g	g	NOUN
ejpam-3747	401	6	with	with	ADP
ejpam-3747	401	7	e(g	e(g	NOUN
ejpam-3747	401	8	)	)	PUNCT
ejpam-3747	402	1	=	=	PUNCT
ejpam-3747	402	2	x	x	SYM
ejpam-3747	402	3	×x	×x	X
ejpam-3747	402	4	,	,	PUNCT
ejpam-3747	402	5	ψ(t	ψ(t	PROPN
ejpam-3747	402	6	)	)	PUNCT
ejpam-3747	402	7	=	=	SYM
ejpam-3747	402	8	t	t	PROPN
ejpam-3747	402	9	,	,	PUNCT
ejpam-3747	402	10	φ(t	φ(t	PROPN
ejpam-3747	402	11	)	)	PUNCT
ejpam-3747	402	12	=	=	SYM
ejpam-3747	402	13	αt	αt	NOUN
ejpam-3747	402	14	,	,	PUNCT
ejpam-3747	402	15	and	and	CCONJ
ejpam-3747	402	16	l	l	NOUN
ejpam-3747	403	1	=	=	SYM
ejpam-3747	403	2	0	0	NUM
ejpam-3747	403	3	in	in	ADP
ejpam-3747	403	4	theorem	theorem	NOUN
ejpam-3747	403	5	3	3	NUM
ejpam-3747	403	6	,	,	PUNCT
ejpam-3747	403	7	we	we	PRON
ejpam-3747	403	8	recover	recover	VERB
ejpam-3747	403	9	the	the	DET
ejpam-3747	403	10	main	main	ADJ
ejpam-3747	403	11	common	common	ADJ
ejpam-3747	403	12	fixed	fix	VERB
ejpam-3747	403	13	point	point	NOUN
ejpam-3747	403	14	theorem	theorem	NOUN
ejpam-3747	403	15	proved	prove	VERB
ejpam-3747	403	16	in	in	ADP
ejpam-3747	403	17	[	[	X
ejpam-3747	403	18	15	15	NUM
ejpam-3747	403	19	]	]	PUNCT
ejpam-3747	403	20	.	.	PUNCT
ejpam-3747	404	1	(	(	PUNCT
ejpam-3747	404	2	3	3	X
ejpam-3747	404	3	)	)	PUNCT
ejpam-3747	404	4	if	if	SCONJ
ejpam-3747	404	5	in	in	ADP
ejpam-3747	404	6	theorem	theorem	NOUN
ejpam-3747	404	7	4	4	NUM
ejpam-3747	404	8	s	s	NOUN
ejpam-3747	404	9	=	=	X
ejpam-3747	404	10	t	t	PROPN
ejpam-3747	404	11	,	,	PUNCT
ejpam-3747	404	12	then	then	ADV
ejpam-3747	404	13	we	we	PRON
ejpam-3747	404	14	obtain	obtain	VERB
ejpam-3747	404	15	an	an	DET
ejpam-3747	404	16	extension	extension	NOUN
ejpam-3747	404	17	and	and	CCONJ
ejpam-3747	404	18	generalization	generalization	NOUN
ejpam-3747	404	19	of	of	ADP
ejpam-3747	404	20	[	[	X
ejpam-3747	404	21	9][theorem	9][theorem	NUM
ejpam-3747	404	22	5.1	5.1	NUM
ejpam-3747	404	23	]	]	PUNCT
ejpam-3747	404	24	.	.	PUNCT
ejpam-3747	405	1	(	(	PUNCT
ejpam-3747	405	2	4	4	X
ejpam-3747	405	3	)	)	PUNCT
ejpam-3747	405	4	if	if	SCONJ
ejpam-3747	405	5	in	in	ADP
ejpam-3747	405	6	corollary	corollary	ADJ
ejpam-3747	405	7	2	2	NUM
ejpam-3747	405	8	,	,	PUNCT
ejpam-3747	405	9	we	we	PRON
ejpam-3747	405	10	take	take	VERB
ejpam-3747	405	11	e(g	e(g	NOUN
ejpam-3747	405	12	)	)	PUNCT
ejpam-3747	406	1	=	=	PUNCT
ejpam-3747	407	1	x	x	SYM
ejpam-3747	407	2	×	×	NOUN
ejpam-3747	407	3	x	x	NOUN
ejpam-3747	407	4	,	,	PUNCT
ejpam-3747	407	5	then	then	ADV
ejpam-3747	407	6	we	we	PRON
ejpam-3747	407	7	obtain	obtain	VERB
ejpam-3747	407	8	a	a	DET
ejpam-3747	407	9	generalization	generalization	NOUN
ejpam-3747	407	10	of	of	ADP
ejpam-3747	407	11	[	[	X
ejpam-3747	407	12	8][theorem	8][theorem	NUM
ejpam-3747	407	13	2.1	2.1	NUM
ejpam-3747	407	14	]	]	PUNCT
ejpam-3747	407	15	and	and	CCONJ
ejpam-3747	407	16	[	[	X
ejpam-3747	407	17	18][theorem	18][theorem	NUM
ejpam-3747	407	18	2	2	NUM
ejpam-3747	407	19	]	]	PUNCT
ejpam-3747	407	20	.	.	PUNCT
ejpam-3747	408	1	references	reference	NOUN
ejpam-3747	408	2	1086	1086	NUM
ejpam-3747	408	3	acknowledgements	acknowledgement	NOUN
ejpam-3747	408	4	the	the	DET
ejpam-3747	408	5	authors	author	NOUN
ejpam-3747	408	6	are	be	AUX
ejpam-3747	408	7	grateful	grateful	ADJ
ejpam-3747	408	8	to	to	ADP
ejpam-3747	408	9	the	the	DET
ejpam-3747	408	10	direction	direction	NOUN
ejpam-3747	408	11	générale	générale	PROPN
ejpam-3747	408	12	de	de	X
ejpam-3747	408	13	la	la	X
ejpam-3747	408	14	recherche	recherche	X
ejpam-3747	408	15	scientifique	scientifique	X
ejpam-3747	408	16	et	et	PROPN
ejpam-3747	408	17	de	de	PROPN
ejpam-3747	408	18	développement	développement	PROPN
ejpam-3747	408	19	technologique	technologique	PROPN
ejpam-3747	408	20	in	in	ADP
ejpam-3747	408	21	algeria	algeria	PROPN
ejpam-3747	408	22	for	for	ADP
ejpam-3747	408	23	supporting	support	VERB
ejpam-3747	408	24	this	this	DET
ejpam-3747	408	25	work	work	NOUN
ejpam-3747	408	26	.	.	PUNCT
ejpam-3747	409	1	references	reference	NOUN
ejpam-3747	409	2	[	[	X
ejpam-3747	409	3	1	1	NUM
ejpam-3747	409	4	]	]	PUNCT
ejpam-3747	409	5	m.	m.	NOUN
ejpam-3747	409	6	abbas	abbas	PROPN
ejpam-3747	409	7	,	,	PUNCT
ejpam-3747	409	8	m.r	m.r	PROPN
ejpam-3747	409	9	.	.	PROPN
ejpam-3747	409	10	alfuraidan	alfuraidan	PROPN
ejpam-3747	409	11	,	,	PUNCT
ejpam-3747	409	12	a.r	a.r	PROPN
ejpam-3747	409	13	.	.	PROPN
ejpam-3747	409	14	khan	khan	PROPN
ejpam-3747	409	15	,	,	PUNCT
ejpam-3747	409	16	and	and	CCONJ
ejpam-3747	409	17	t.	t.	PROPN
ejpam-3747	409	18	nazir	nazir	PROPN
ejpam-3747	409	19	.	.	PUNCT
ejpam-3747	410	1	fixed	fix	VERB
ejpam-3747	410	2	point	point	NOUN
ejpam-3747	410	3	results	result	NOUN
ejpam-3747	410	4	for	for	ADP
ejpam-3747	410	5	set	set	VERB
ejpam-3747	410	6	contractions	contraction	NOUN
ejpam-3747	410	7	on	on	ADP
ejpam-3747	410	8	metric	metric	ADJ
ejpam-3747	410	9	spaces	space	NOUN
ejpam-3747	410	10	with	with	ADP
ejpam-3747	410	11	a	a	DET
ejpam-3747	410	12	directed	direct	VERB
ejpam-3747	410	13	graph	graph	NOUN
ejpam-3747	410	14	.	.	PUNCT
ejpam-3747	411	1	fixed	fix	VERB
ejpam-3747	411	2	point	point	NOUN
ejpam-3747	411	3	theory	theory	NOUN
ejpam-3747	411	4	appl	appl	PROPN
ejpam-3747	411	5	.	.	PROPN
ejpam-3747	411	6	,	,	PUNCT
ejpam-3747	411	7	14:1	14:1	NUM
ejpam-3747	411	8	–	–	PUNCT
ejpam-3747	411	9	9	9	NUM
ejpam-3747	411	10	,	,	PUNCT
ejpam-3747	411	11	2015	2015	NUM
ejpam-3747	411	12	.	.	PUNCT
ejpam-3747	412	1	[	[	X
ejpam-3747	412	2	2	2	NUM
ejpam-3747	412	3	]	]	PUNCT
ejpam-3747	412	4	m.	m.	NOUN
ejpam-3747	412	5	abbas	abbas	PROPN
ejpam-3747	412	6	,	,	PUNCT
ejpam-3747	412	7	t.	t.	PROPN
ejpam-3747	412	8	nazir	nazir	PROPN
ejpam-3747	412	9	,	,	PUNCT
ejpam-3747	412	10	t.a	t.a	PROPN
ejpam-3747	412	11	.	.	PROPN
ejpam-3747	412	12	lampert	lampert	PROPN
ejpam-3747	412	13	,	,	PUNCT
ejpam-3747	412	14	and	and	CCONJ
ejpam-3747	412	15	s.	s.	PROPN
ejpam-3747	413	1	radenović.	radenović.	PROPN
ejpam-3747	413	2	common	common	ADJ
ejpam-3747	413	3	fixed	fix	VERB
ejpam-3747	413	4	points	point	NOUN
ejpam-3747	413	5	of	of	ADP
ejpam-3747	413	6	setvalued	setvalue	VERB
ejpam-3747	413	7	f	f	X
ejpam-3747	413	8	-	-	PUNCT
ejpam-3747	413	9	contraction	contraction	NOUN
ejpam-3747	413	10	mappings	mapping	NOUN
ejpam-3747	413	11	on	on	ADP
ejpam-3747	413	12	domain	domain	NOUN
ejpam-3747	413	13	of	of	ADP
ejpam-3747	413	14	sets	set	NOUN
ejpam-3747	413	15	endowed	endow	VERB
ejpam-3747	413	16	with	with	ADP
ejpam-3747	413	17	directed	direct	VERB
ejpam-3747	413	18	graph	graph	NOUN
ejpam-3747	413	19	.	.	PUNCT
ejpam-3747	414	1	comp	comp	PROPN
ejpam-3747	414	2	.	.	PUNCT
ejpam-3747	415	1	appl	appl	PROPN
ejpam-3747	415	2	.	.	PROPN
ejpam-3747	415	3	math	math	PROPN
ejpam-3747	415	4	.	.	PUNCT
ejpam-3747	415	5	,	,	PUNCT
ejpam-3747	415	6	36:1607–1322	36:1607–1322	NUM
ejpam-3747	415	7	,	,	PUNCT
ejpam-3747	415	8	2017	2017	NUM
ejpam-3747	415	9	.	.	PUNCT
ejpam-3747	416	1	[	[	X
ejpam-3747	416	2	3	3	X
ejpam-3747	416	3	]	]	PUNCT
ejpam-3747	416	4	m.	m.	NOUN
ejpam-3747	416	5	abbas	abbas	PROPN
ejpam-3747	416	6	,	,	PUNCT
ejpam-3747	416	7	t.	t.	PROPN
ejpam-3747	416	8	nazir	nazir	PROPN
ejpam-3747	416	9	,	,	PUNCT
ejpam-3747	416	10	b.	b.	PROPN
ejpam-3747	416	11	popović	popović	NOUN
ejpam-3747	416	12	,	,	PUNCT
ejpam-3747	416	13	and	and	CCONJ
ejpam-3747	416	14	s.	s.	PROPN
ejpam-3747	416	15	radenović.	radenović.	PROPN
ejpam-3747	416	16	on	on	ADP
ejpam-3747	416	17	weakly	weakly	ADJ
ejpam-3747	416	18	commuting	commute	VERB
ejpam-3747	416	19	set	set	NOUN
ejpam-3747	416	20	-	-	PUNCT
ejpam-3747	416	21	valued	value	VERB
ejpam-3747	416	22	mappings	mapping	NOUN
ejpam-3747	416	23	on	on	ADP
ejpam-3747	416	24	a	a	DET
ejpam-3747	416	25	domain	domain	NOUN
ejpam-3747	416	26	of	of	ADP
ejpam-3747	416	27	sets	set	NOUN
ejpam-3747	416	28	endowed	endow	VERB
ejpam-3747	416	29	with	with	ADP
ejpam-3747	416	30	directed	direct	VERB
ejpam-3747	416	31	graph	graph	NOUN
ejpam-3747	416	32	.	.	PUNCT
ejpam-3747	417	1	results	result	NOUN
ejpam-3747	417	2	in	in	ADP
ejpam-3747	417	3	mathematics	mathematic	NOUN
ejpam-3747	417	4	,	,	PUNCT
ejpam-3747	417	5	71:1277–1295	71:1277–1295	NUM
ejpam-3747	417	6	,	,	PUNCT
ejpam-3747	417	7	2017	2017	NUM
ejpam-3747	417	8	.	.	PUNCT
ejpam-3747	418	1	[	[	X
ejpam-3747	418	2	4	4	X
ejpam-3747	418	3	]	]	PUNCT
ejpam-3747	418	4	m.	m.	NOUN
ejpam-3747	418	5	abbas	abbas	PROPN
ejpam-3747	418	6	and	and	CCONJ
ejpam-3747	418	7	b.e	b.e	PROPN
ejpam-3747	418	8	.	.	PROPN
ejpam-3747	418	9	rhoades	rhoades	PROPN
ejpam-3747	418	10	.	.	PUNCT
ejpam-3747	419	1	common	common	ADJ
ejpam-3747	419	2	fixed	fix	VERB
ejpam-3747	419	3	point	point	NOUN
ejpam-3747	419	4	theorems	theorem	NOUN
ejpam-3747	419	5	for	for	ADP
ejpam-3747	419	6	hybrid	hybrid	ADJ
ejpam-3747	419	7	pairs	pair	NOUN
ejpam-3747	419	8	of	of	ADP
ejpam-3747	419	9	occasionally	occasionally	ADV
ejpam-3747	419	10	weakly	weakly	ADJ
ejpam-3747	419	11	compatible	compatible	ADJ
ejpam-3747	419	12	mappings	mapping	NOUN
ejpam-3747	419	13	satisfying	satisfy	VERB
ejpam-3747	419	14	generalized	generalize	VERB
ejpam-3747	419	15	contractive	contractive	ADJ
ejpam-3747	419	16	condition	condition	NOUN
ejpam-3747	419	17	of	of	ADP
ejpam-3747	419	18	integral	integral	ADJ
ejpam-3747	419	19	type	type	NOUN
ejpam-3747	419	20	.	.	PUNCT
ejpam-3747	420	1	fixed	fix	VERB
ejpam-3747	420	2	point	point	NOUN
ejpam-3747	420	3	theory	theory	NOUN
ejpam-3747	420	4	appl	appl	PROPN
ejpam-3747	420	5	.	.	PROPN
ejpam-3747	420	6	,	,	PUNCT
ejpam-3747	420	7	054101:1–9	054101:1–9	PROPN
ejpam-3747	420	8	,	,	PUNCT
ejpam-3747	420	9	2007	2007	NUM
ejpam-3747	420	10	.	.	PUNCT
ejpam-3747	421	1	[	[	X
ejpam-3747	421	2	5	5	NUM
ejpam-3747	421	3	]	]	PUNCT
ejpam-3747	421	4	a.	a.	NOUN
ejpam-3747	421	5	aliouche	aliouche	PROPN
ejpam-3747	421	6	.	.	PUNCT
ejpam-3747	422	1	a	a	DET
ejpam-3747	422	2	common	common	ADJ
ejpam-3747	422	3	fixed	fix	VERB
ejpam-3747	422	4	point	point	NOUN
ejpam-3747	422	5	theorems	theorem	NOUN
ejpam-3747	422	6	for	for	ADP
ejpam-3747	422	7	weakly	weakly	ADJ
ejpam-3747	422	8	compatible	compatible	ADJ
ejpam-3747	422	9	mappings	mapping	NOUN
ejpam-3747	422	10	in	in	ADP
ejpam-3747	422	11	symmetric	symmetric	ADJ
ejpam-3747	422	12	spaces	space	NOUN
ejpam-3747	422	13	satisfying	satisfy	VERB
ejpam-3747	422	14	contractive	contractive	ADJ
ejpam-3747	422	15	condition	condition	NOUN
ejpam-3747	422	16	of	of	ADP
ejpam-3747	422	17	integral	integral	ADJ
ejpam-3747	422	18	type	type	NOUN
ejpam-3747	422	19	.	.	PUNCT
ejpam-3747	423	1	j.	j.	PROPN
ejpam-3747	423	2	math	math	PROPN
ejpam-3747	423	3	.	.	PUNCT
ejpam-3747	424	1	anal	anal	PROPN
ejpam-3747	424	2	.	.	PUNCT
ejpam-3747	425	1	appl	appl	PROPN
ejpam-3747	425	2	.	.	PROPN
ejpam-3747	425	3	,	,	PUNCT
ejpam-3747	425	4	7(2):66–68	7(2):66–68	NUM
ejpam-3747	425	5	,	,	PUNCT
ejpam-3747	425	6	2006	2006	NUM
ejpam-3747	425	7	.	.	PUNCT
ejpam-3747	426	1	[	[	X
ejpam-3747	426	2	6	6	NUM
ejpam-3747	426	3	]	]	PUNCT
ejpam-3747	426	4	i.	i.	NOUN
ejpam-3747	426	5	beg	beg	PROPN
ejpam-3747	426	6	and	and	CCONJ
ejpam-3747	426	7	a.r	a.r	PROPN
ejpam-3747	426	8	.	.	PROPN
ejpam-3747	426	9	butt	butt	PROPN
ejpam-3747	426	10	.	.	PUNCT
ejpam-3747	427	1	fixed	fix	VERB
ejpam-3747	427	2	point	point	NOUN
ejpam-3747	427	3	theorems	theorem	NOUN
ejpam-3747	427	4	for	for	ADP
ejpam-3747	427	5	set	set	ADJ
ejpam-3747	427	6	valued	value	VERB
ejpam-3747	427	7	mappings	mapping	NOUN
ejpam-3747	427	8	in	in	ADP
ejpam-3747	427	9	partially	partially	ADV
ejpam-3747	427	10	ordered	order	VERB
ejpam-3747	427	11	metric	metric	ADJ
ejpam-3747	427	12	spaces	space	NOUN
ejpam-3747	427	13	.	.	PUNCT
ejpam-3747	428	1	int	int	NOUN
ejpam-3747	428	2	.	.	PUNCT
ejpam-3747	429	1	j.	j.	PROPN
ejpam-3747	429	2	math	math	PROPN
ejpam-3747	429	3	.	.	PUNCT
ejpam-3747	430	1	sci	sci	PROPN
ejpam-3747	430	2	.	.	PROPN
ejpam-3747	430	3	,	,	PUNCT
ejpam-3747	430	4	55:251–276	55:251–276	PROPN
ejpam-3747	430	5	,	,	PUNCT
ejpam-3747	430	6	2013	2013	NUM
ejpam-3747	430	7	.	.	PUNCT
ejpam-3747	431	1	[	[	X
ejpam-3747	431	2	7	7	X
ejpam-3747	431	3	]	]	PUNCT
ejpam-3747	431	4	s.	s.	PROPN
ejpam-3747	431	5	benchabane	benchabane	PROPN
ejpam-3747	431	6	,	,	PUNCT
ejpam-3747	431	7	s.	s.	PROPN
ejpam-3747	431	8	djebali	djebali	PROPN
ejpam-3747	431	9	,	,	PUNCT
ejpam-3747	431	10	and	and	CCONJ
ejpam-3747	431	11	t.	t.	PROPN
ejpam-3747	431	12	nazir	nazir	PROPN
ejpam-3747	431	13	.	.	PUNCT
ejpam-3747	432	1	common	common	ADJ
ejpam-3747	432	2	fixed	fix	VERB
ejpam-3747	432	3	point	point	NOUN
ejpam-3747	432	4	results	result	NOUN
ejpam-3747	432	5	for	for	ADP
ejpam-3747	432	6	set	set	NOUN
ejpam-3747	432	7	-	-	PUNCT
ejpam-3747	432	8	valued	value	VERB
ejpam-3747	432	9	integral	integral	ADJ
ejpam-3747	432	10	type	type	NOUN
ejpam-3747	432	11	rational	rational	ADJ
ejpam-3747	432	12	contractions	contraction	NOUN
ejpam-3747	432	13	on	on	ADP
ejpam-3747	432	14	semi	semi	ADJ
ejpam-3747	432	15	-	-	ADJ
ejpam-3747	432	16	metric	metric	ADJ
ejpam-3747	432	17	spaces	space	NOUN
ejpam-3747	432	18	with	with	ADP
ejpam-3747	432	19	directed	direct	VERB
ejpam-3747	432	20	graph	graph	NOUN
ejpam-3747	432	21	.	.	PUNCT
ejpam-3747	433	1	canadian	canadian	ADJ
ejpam-3747	433	2	journal	journal	NOUN
ejpam-3747	433	3	of	of	ADP
ejpam-3747	433	4	applied	apply	VERB
ejpam-3747	433	5	mathematics	mathematic	NOUN
ejpam-3747	433	6	,	,	PUNCT
ejpam-3747	433	7	1(1):15–31	1(1):15–31	NUM
ejpam-3747	433	8	,	,	PUNCT
ejpam-3747	433	9	2019	2019	NUM
ejpam-3747	433	10	.	.	PUNCT
ejpam-3747	434	1	[	[	X
ejpam-3747	434	2	8	8	NUM
ejpam-3747	434	3	]	]	PUNCT
ejpam-3747	434	4	a.	a.	NOUN
ejpam-3747	434	5	branciari	branciari	PROPN
ejpam-3747	434	6	.	.	PUNCT
ejpam-3747	435	1	a	a	DET
ejpam-3747	435	2	fixed	fix	VERB
ejpam-3747	435	3	point	point	NOUN
ejpam-3747	435	4	theorem	theorem	NOUN
ejpam-3747	435	5	for	for	ADP
ejpam-3747	435	6	mappings	mapping	NOUN
ejpam-3747	435	7	satisfying	satisfy	VERB
ejpam-3747	435	8	a	a	DET
ejpam-3747	435	9	general	general	ADJ
ejpam-3747	435	10	contractive	contractive	ADJ
ejpam-3747	435	11	condition	condition	NOUN
ejpam-3747	435	12	of	of	ADP
ejpam-3747	435	13	integral	integral	ADJ
ejpam-3747	435	14	type	type	NOUN
ejpam-3747	435	15	.	.	PUNCT
ejpam-3747	436	1	int	int	NOUN
ejpam-3747	436	2	.	.	PUNCT
ejpam-3747	437	1	j.	j.	PROPN
ejpam-3747	437	2	math	math	PROPN
ejpam-3747	437	3	.	.	PUNCT
ejpam-3747	438	1	sci	sci	PROPN
ejpam-3747	438	2	.	.	PROPN
ejpam-3747	438	3	,	,	PUNCT
ejpam-3747	438	4	29(9):531–536	29(9):531–536	NUM
ejpam-3747	438	5	,	,	PUNCT
ejpam-3747	438	6	2002	2002	NUM
ejpam-3747	438	7	.	.	PUNCT
ejpam-3747	439	1	[	[	X
ejpam-3747	439	2	9	9	NUM
ejpam-3747	439	3	]	]	PUNCT
ejpam-3747	439	4	m.	m.	NOUN
ejpam-3747	439	5	edelstein	edelstein	PROPN
ejpam-3747	439	6	.	.	PUNCT
ejpam-3747	440	1	an	an	DET
ejpam-3747	440	2	extension	extension	NOUN
ejpam-3747	440	3	of	of	ADP
ejpam-3747	440	4	banach	banach	NOUN
ejpam-3747	440	5	’s	’s	PART
ejpam-3747	440	6	contraction	contraction	NOUN
ejpam-3747	440	7	principle	principle	NOUN
ejpam-3747	440	8	.	.	PUNCT
ejpam-3747	441	1	proc	proc	PROPN
ejpam-3747	441	2	.	.	PUNCT
ejpam-3747	442	1	amer	amer	PROPN
ejpam-3747	442	2	.	.	PUNCT
ejpam-3747	442	3	math	math	PROPN
ejpam-3747	442	4	.	.	PUNCT
ejpam-3747	443	1	soc	soc	PROPN
ejpam-3747	443	2	.	.	PUNCT
ejpam-3747	443	3	,	,	PUNCT
ejpam-3747	443	4	12:7–10	12:7–10	NUM
ejpam-3747	443	5	,	,	PUNCT
ejpam-3747	443	6	1961	1961	NUM
ejpam-3747	443	7	.	.	PUNCT
ejpam-3747	444	1	[	[	X
ejpam-3747	444	2	10	10	NUM
ejpam-3747	444	3	]	]	X
ejpam-3747	444	4	u.c	u.c	PROPN
ejpam-3747	444	5	.	.	PROPN
ejpam-3747	444	6	gairola	gairola	PROPN
ejpam-3747	444	7	and	and	CCONJ
ejpam-3747	444	8	a.s	a.s	PROPN
ejpam-3747	444	9	.	.	PROPN
ejpam-3747	444	10	rawat	rawat	PROPN
ejpam-3747	444	11	.	.	PUNCT
ejpam-3747	445	1	a	a	DET
ejpam-3747	445	2	fixed	fix	VERB
ejpam-3747	445	3	point	point	NOUN
ejpam-3747	445	4	theorem	theorem	NOUN
ejpam-3747	445	5	for	for	ADP
ejpam-3747	445	6	integral	integral	ADJ
ejpam-3747	445	7	type	type	NOUN
ejpam-3747	445	8	inequality	inequality	NOUN
ejpam-3747	445	9	.	.	PUNCT
ejpam-3747	446	1	int	int	NOUN
ejpam-3747	446	2	.	.	PUNCT
ejpam-3747	447	1	j.	j.	PROPN
ejpam-3747	447	2	math	math	PROPN
ejpam-3747	447	3	.	.	PUNCT
ejpam-3747	448	1	anal	anal	PROPN
ejpam-3747	448	2	.	.	PROPN
ejpam-3747	448	3	,	,	PUNCT
ejpam-3747	448	4	2(15):709–712	2(15):709–712	NOUN
ejpam-3747	448	5	,	,	PUNCT
ejpam-3747	448	6	2008	2008	NUM
ejpam-3747	448	7	.	.	PUNCT
ejpam-3747	449	1	[	[	X
ejpam-3747	449	2	11	11	NUM
ejpam-3747	449	3	]	]	PUNCT
ejpam-3747	449	4	j.	j.	PROPN
ejpam-3747	449	5	jachymski	jachymski	PROPN
ejpam-3747	449	6	.	.	PUNCT
ejpam-3747	450	1	the	the	DET
ejpam-3747	450	2	contraction	contraction	NOUN
ejpam-3747	450	3	principle	principle	NOUN
ejpam-3747	450	4	for	for	ADP
ejpam-3747	450	5	mappings	mapping	NOUN
ejpam-3747	450	6	on	on	ADP
ejpam-3747	450	7	a	a	DET
ejpam-3747	450	8	metric	metric	NOUN
ejpam-3747	450	9	with	with	ADP
ejpam-3747	450	10	a	a	DET
ejpam-3747	450	11	graph	graph	NOUN
ejpam-3747	450	12	.	.	PUNCT
ejpam-3747	451	1	proc	proc	NOUN
ejpam-3747	451	2	.	.	PUNCT
ejpam-3747	452	1	am	be	AUX
ejpam-3747	452	2	.	.	PUNCT
ejpam-3747	453	1	math	math	NOUN
ejpam-3747	453	2	.	.	PUNCT
ejpam-3747	454	1	soc	soc	PROPN
ejpam-3747	454	2	.	.	PUNCT
ejpam-3747	454	3	,	,	PUNCT
ejpam-3747	454	4	136(4):1359–1373	136(4):1359–1373	NUM
ejpam-3747	454	5	,	,	PUNCT
ejpam-3747	454	6	2008	2008	NUM
ejpam-3747	454	7	.	.	PUNCT
ejpam-3747	455	1	references	reference	NOUN
ejpam-3747	455	2	1087	1087	NUM
ejpam-3747	456	1	[	[	X
ejpam-3747	456	2	12	12	NUM
ejpam-3747	456	3	]	]	PUNCT
ejpam-3747	456	4	a.	a.	PROPN
ejpam-3747	456	5	latif	latif	PROPN
ejpam-3747	456	6	,	,	PUNCT
ejpam-3747	456	7	t.	t.	PROPN
ejpam-3747	456	8	nazir	nazir	PROPN
ejpam-3747	456	9	,	,	PUNCT
ejpam-3747	456	10	and	and	CCONJ
ejpam-3747	456	11	m.a	m.a	PROPN
ejpam-3747	456	12	.	.	PROPN
ejpam-3747	456	13	kutbi	kutbi	PROPN
ejpam-3747	456	14	.	.	PUNCT
ejpam-3747	457	1	common	common	ADJ
ejpam-3747	457	2	fixed	fix	VERB
ejpam-3747	457	3	points	point	NOUN
ejpam-3747	457	4	for	for	ADP
ejpam-3747	457	5	class	class	NOUN
ejpam-3747	457	6	of	of	ADP
ejpam-3747	457	7	set	set	NOUN
ejpam-3747	457	8	-	-	PUNCT
ejpam-3747	457	9	contraction	contraction	NOUN
ejpam-3747	457	10	mappings	mapping	NOUN
ejpam-3747	457	11	endowed	endow	VERB
ejpam-3747	457	12	with	with	ADP
ejpam-3747	457	13	a	a	DET
ejpam-3747	457	14	directed	direct	VERB
ejpam-3747	457	15	graph	graph	NOUN
ejpam-3747	457	16	.	.	PUNCT
ejpam-3747	458	1	racsam	racsam	PROPN
ejpam-3747	458	2	serie	serie	PROPN
ejpam-3747	458	3	a.	a.	NOUN
ejpam-3747	458	4	matemáticas	matemáticas	PROPN
ejpam-3747	458	5	,	,	PUNCT
ejpam-3747	458	6	113(4):3207–3222	113(4):3207–3222	NUM
ejpam-3747	458	7	,	,	PUNCT
ejpam-3747	458	8	2019	2019	NUM
ejpam-3747	458	9	.	.	PUNCT
ejpam-3747	459	1	[	[	X
ejpam-3747	459	2	13	13	NUM
ejpam-3747	459	3	]	]	PUNCT
ejpam-3747	459	4	z.	z.	PROPN
ejpam-3747	459	5	liu	liu	PROPN
ejpam-3747	459	6	,	,	PUNCT
ejpam-3747	459	7	j.	j.	PROPN
ejpam-3747	459	8	li	li	PROPN
ejpam-3747	459	9	,	,	PUNCT
ejpam-3747	459	10	and	and	CCONJ
ejpam-3747	459	11	s.m	s.m	PROPN
ejpam-3747	459	12	.	.	PROPN
ejpam-3747	459	13	kang	kang	PROPN
ejpam-3747	459	14	.	.	PUNCT
ejpam-3747	460	1	fixed	fix	VERB
ejpam-3747	460	2	point	point	NOUN
ejpam-3747	460	3	theorems	theorem	NOUN
ejpam-3747	460	4	of	of	ADP
ejpam-3747	460	5	contractive	contractive	ADJ
ejpam-3747	460	6	mappings	mapping	NOUN
ejpam-3747	460	7	of	of	ADP
ejpam-3747	460	8	integral	integral	ADJ
ejpam-3747	460	9	type	type	NOUN
ejpam-3747	460	10	.	.	PUNCT
ejpam-3747	461	1	fixed	fix	VERB
ejpam-3747	461	2	point	point	NOUN
ejpam-3747	461	3	theory	theory	NOUN
ejpam-3747	461	4	appl	appl	PROPN
ejpam-3747	461	5	.	.	PUNCT
ejpam-3747	461	6	,	,	PUNCT
ejpam-3747	461	7	300:1–17	300:1–17	NUM
ejpam-3747	461	8	,	,	PUNCT
ejpam-3747	461	9	2013	2013	NUM
ejpam-3747	461	10	.	.	PUNCT
ejpam-3747	462	1	[	[	X
ejpam-3747	462	2	14	14	NUM
ejpam-3747	462	3	]	]	X
ejpam-3747	462	4	s.	s.	PROPN
ejpam-3747	462	5	b.	b.	PROPN
ejpam-3747	462	6	nadler	nadler	PROPN
ejpam-3747	462	7	.	.	PUNCT
ejpam-3747	463	1	multi	multi	ADJ
ejpam-3747	463	2	-	-	ADJ
ejpam-3747	463	3	valued	value	VERB
ejpam-3747	463	4	contraction	contraction	NOUN
ejpam-3747	463	5	mappings	mapping	NOUN
ejpam-3747	463	6	.	.	PUNCT
ejpam-3747	464	1	pacific	pacific	PROPN
ejpam-3747	464	2	j.	j.	PROPN
ejpam-3747	464	3	math	math	PROPN
ejpam-3747	464	4	.	.	PUNCT
ejpam-3747	464	5	,	,	PUNCT
ejpam-3747	465	1	30:475–488	30:475–488	NUM
ejpam-3747	465	2	,	,	PUNCT
ejpam-3747	465	3	1969	1969	NUM
ejpam-3747	465	4	.	.	PUNCT
ejpam-3747	466	1	[	[	X
ejpam-3747	466	2	15	15	NUM
ejpam-3747	466	3	]	]	X
ejpam-3747	466	4	d.	d.	PROPN
ejpam-3747	466	5	b.	b.	PROPN
ejpam-3747	466	6	ojha	ojha	PROPN
ejpam-3747	466	7	and	and	CCONJ
ejpam-3747	466	8	m.k	m.k	PROPN
ejpam-3747	466	9	.	.	PUNCT
ejpam-3747	466	10	mishra	mishra	PROPN
ejpam-3747	466	11	.	.	PUNCT
ejpam-3747	467	1	some	some	DET
ejpam-3747	467	2	results	result	NOUN
ejpam-3747	467	3	on	on	ADP
ejpam-3747	467	4	common	common	ADJ
ejpam-3747	467	5	fixed	fix	VERB
ejpam-3747	467	6	point	point	NOUN
ejpam-3747	467	7	of	of	ADP
ejpam-3747	467	8	multivalued	multivalued	ADJ
ejpam-3747	467	9	generalized	generalize	VERB
ejpam-3747	467	10	ϕ-weak	ϕ-weak	NOUN
ejpam-3747	467	11	contractive	contractive	ADJ
ejpam-3747	467	12	mappings	mapping	NOUN
ejpam-3747	467	13	in	in	ADP
ejpam-3747	467	14	integral	integral	ADJ
ejpam-3747	467	15	type	type	NOUN
ejpam-3747	467	16	inequality	inequality	NOUN
ejpam-3747	467	17	.	.	PUNCT
ejpam-3747	468	1	research	research	NOUN
ejpam-3747	468	2	journal	journal	PROPN
ejpam-3747	468	3	of	of	ADP
ejpam-3747	468	4	applied	apply	VERB
ejpam-3747	468	5	sciences	science	NOUN
ejpam-3747	468	6	,	,	PUNCT
ejpam-3747	468	7	engineering	engineering	NOUN
ejpam-3747	468	8	and	and	CCONJ
ejpam-3747	468	9	technology	technology	NOUN
ejpam-3747	468	10	,	,	PUNCT
ejpam-3747	468	11	2(4):387–395	2(4):387–395	NUM
ejpam-3747	468	12	,	,	PUNCT
ejpam-3747	468	13	2010	2010	NUM
ejpam-3747	468	14	.	.	PUNCT
ejpam-3747	469	1	[	[	X
ejpam-3747	469	2	16	16	NUM
ejpam-3747	469	3	]	]	PUNCT
ejpam-3747	469	4	p.	p.	PROPN
ejpam-3747	469	5	d.	d.	PROPN
ejpam-3747	469	6	proinov	proinov	PROPN
ejpam-3747	469	7	.	.	PUNCT
ejpam-3747	470	1	a	a	DET
ejpam-3747	470	2	generalization	generalization	NOUN
ejpam-3747	470	3	of	of	ADP
ejpam-3747	470	4	the	the	DET
ejpam-3747	470	5	banach	banach	NOUN
ejpam-3747	470	6	contraction	contraction	NOUN
ejpam-3747	470	7	principle	principle	NOUN
ejpam-3747	470	8	with	with	ADP
ejpam-3747	470	9	high	high	ADJ
ejpam-3747	470	10	order	order	NOUN
ejpam-3747	470	11	of	of	ADP
ejpam-3747	470	12	convergence	convergence	NOUN
ejpam-3747	470	13	of	of	ADP
ejpam-3747	470	14	successive	successive	ADJ
ejpam-3747	470	15	approximations	approximation	NOUN
ejpam-3747	470	16	.	.	PUNCT
ejpam-3747	471	1	nonlinear	nonlinear	ADJ
ejpam-3747	471	2	anal	anal	PROPN
ejpam-3747	471	3	.	.	PUNCT
ejpam-3747	472	1	tma	tma	PROPN
ejpam-3747	472	2	,	,	PUNCT
ejpam-3747	472	3	67:2361–2369	67:2361–2369	PROPN
ejpam-3747	472	4	,	,	PUNCT
ejpam-3747	472	5	2007	2007	NUM
ejpam-3747	472	6	.	.	PUNCT
ejpam-3747	473	1	[	[	X
ejpam-3747	473	2	17	17	NUM
ejpam-3747	473	3	]	]	X
ejpam-3747	473	4	p.	p.	PROPN
ejpam-3747	473	5	d.	d.	PROPN
ejpam-3747	473	6	proinov	proinov	PROPN
ejpam-3747	473	7	.	.	PUNCT
ejpam-3747	474	1	new	new	ADJ
ejpam-3747	474	2	general	general	ADJ
ejpam-3747	474	3	convergence	convergence	NOUN
ejpam-3747	474	4	theory	theory	NOUN
ejpam-3747	474	5	for	for	ADP
ejpam-3747	474	6	iterative	iterative	NOUN
ejpam-3747	474	7	processes	process	NOUN
ejpam-3747	474	8	and	and	CCONJ
ejpam-3747	474	9	its	its	PRON
ejpam-3747	474	10	applications	application	NOUN
ejpam-3747	474	11	to	to	ADP
ejpam-3747	474	12	newton	newton	PROPN
ejpam-3747	474	13	-	-	PUNCT
ejpam-3747	474	14	kantorovich	kantorovich	PROPN
ejpam-3747	474	15	type	type	NOUN
ejpam-3747	474	16	theorems	theorem	NOUN
ejpam-3747	474	17	.	.	PUNCT
ejpam-3747	475	1	j.	j.	PROPN
ejpam-3747	475	2	complex	complex	PROPN
ejpam-3747	475	3	.	.	PROPN
ejpam-3747	475	4	,	,	PUNCT
ejpam-3747	475	5	26:3–42	26:3–42	NUM
ejpam-3747	475	6	,	,	PUNCT
ejpam-3747	475	7	2010	2010	NUM
ejpam-3747	475	8	.	.	PUNCT
ejpam-3747	476	1	[	[	X
ejpam-3747	476	2	18	18	NUM
ejpam-3747	476	3	]	]	X
ejpam-3747	476	4	b.	b.	PROPN
ejpam-3747	476	5	e.	e.	PROPN
ejpam-3747	476	6	rhoades	rhoades	PROPN
ejpam-3747	476	7	.	.	PUNCT
ejpam-3747	477	1	two	two	NUM
ejpam-3747	477	2	fixed	fix	VERB
ejpam-3747	477	3	point	point	NOUN
ejpam-3747	477	4	theorems	theorem	NOUN
ejpam-3747	477	5	for	for	ADP
ejpam-3747	477	6	mapping	map	VERB
ejpam-3747	477	7	satisfying	satisfy	VERB
ejpam-3747	477	8	general	general	ADJ
ejpam-3747	477	9	contractive	contractive	ADJ
ejpam-3747	477	10	condition	condition	NOUN
ejpam-3747	477	11	of	of	ADP
ejpam-3747	477	12	integral	integral	ADJ
ejpam-3747	477	13	type	type	NOUN
ejpam-3747	477	14	.	.	PUNCT
ejpam-3747	478	1	int	int	NOUN
ejpam-3747	478	2	.	.	PUNCT
ejpam-3747	479	1	j.	j.	PROPN
ejpam-3747	479	2	math	math	PROPN
ejpam-3747	479	3	.	.	PUNCT
ejpam-3747	480	1	sci	sci	PROPN
ejpam-3747	480	2	.	.	PROPN
ejpam-3747	480	3	,	,	PUNCT
ejpam-3747	480	4	63:4007–4013	63:4007–4013	NUM
ejpam-3747	480	5	,	,	PUNCT
ejpam-3747	480	6	2003	2003	NUM
ejpam-3747	480	7	.	.	PUNCT
ejpam-3747	481	1	[	[	X
ejpam-3747	481	2	19	19	NUM
ejpam-3747	481	3	]	]	PUNCT
ejpam-3747	481	4	m.	m.	NOUN
ejpam-3747	481	5	stojaković	stojaković	PROPN
ejpam-3747	481	6	,	,	PUNCT
ejpam-3747	481	7	l.	l.	PROPN
ejpam-3747	481	8	gajić	gajić	PROPN
ejpam-3747	481	9	,	,	PUNCT
ejpam-3747	481	10	t.	t.	PROPN
ejpam-3747	481	11	dosenović	dosenović	PROPN
ejpam-3747	481	12	,	,	PUNCT
ejpam-3747	481	13	and	and	CCONJ
ejpam-3747	481	14	b.	b.	PROPN
ejpam-3747	481	15	carić.	carić.	PROPN
ejpam-3747	481	16	fixed	fix	VERB
ejpam-3747	481	17	point	point	NOUN
ejpam-3747	481	18	of	of	ADP
ejpam-3747	481	19	multivalued	multivalued	ADJ
ejpam-3747	481	20	integral	integral	ADJ
ejpam-3747	481	21	type	type	NOUN
ejpam-3747	481	22	of	of	ADP
ejpam-3747	481	23	contraction	contraction	NOUN
ejpam-3747	481	24	mappings	mapping	NOUN
ejpam-3747	481	25	.	.	PUNCT
ejpam-3747	481	26	fixed	fix	VERB
ejpam-3747	481	27	point	point	NOUN
ejpam-3747	481	28	theory	theory	NOUN
ejpam-3747	481	29	and	and	CCONJ
ejpam-3747	481	30	applications	application	NOUN
ejpam-3747	481	31	,	,	PUNCT
ejpam-3747	481	32	146:1	146:1	NUM
ejpam-3747	481	33	–	–	PUNCT
ejpam-3747	481	34	10	10	NUM
ejpam-3747	481	35	,	,	PUNCT
ejpam-3747	481	36	2015	2015	NUM
ejpam-3747	481	37	.	.	PUNCT