id	sid	tid	token	lemma	pos
ejpam-6433	1	1	european	european	PROPN
ejpam-6433	1	2	journal	journal	PROPN
ejpam-6433	1	3	of	of	ADP
ejpam-6433	1	4	pure	pure	ADJ
ejpam-6433	1	5	and	and	CCONJ
ejpam-6433	1	6	applied	applied	ADJ
ejpam-6433	1	7	mathematics	mathematic	NOUN
ejpam-6433	1	8	2025	2025	NUM
ejpam-6433	1	9	,	,	PUNCT
ejpam-6433	1	10	vol	vol	NOUN
ejpam-6433	1	11	.	.	PROPN
ejpam-6433	1	12	18	18	NUM
ejpam-6433	1	13	,	,	PUNCT
ejpam-6433	1	14	issue	issue	NOUN
ejpam-6433	1	15	3	3	NUM
ejpam-6433	1	16	,	,	PUNCT
ejpam-6433	1	17	article	article	NOUN
ejpam-6433	1	18	number	number	NOUN
ejpam-6433	1	19	6433	6433	NUM
ejpam-6433	1	20	issn	issn	PROPN
ejpam-6433	1	21	1307	1307	NUM
ejpam-6433	1	22	-	-	SYM
ejpam-6433	1	23	5543	5543	NUM
ejpam-6433	1	24	–	–	PUNCT
ejpam-6433	1	25	ejpam.com	ejpam.com	X
ejpam-6433	1	26	published	publish	VERB
ejpam-6433	1	27	by	by	ADP
ejpam-6433	1	28	new	new	PROPN
ejpam-6433	1	29	york	york	PROPN
ejpam-6433	1	30	business	business	PROPN
ejpam-6433	1	31	global	global	ADJ
ejpam-6433	1	32	revisiting	revisit	VERB
ejpam-6433	1	33	best	good	ADJ
ejpam-6433	1	34	proximity	proximity	NOUN
ejpam-6433	1	35	results	result	NOUN
ejpam-6433	1	36	of	of	ADP
ejpam-6433	1	37	relatively	relatively	ADV
ejpam-6433	1	38	meir	meir	ADJ
ejpam-6433	1	39	-	-	ADJ
ejpam-6433	1	40	keeler	keeler	ADJ
ejpam-6433	1	41	condensing	condense	VERB
ejpam-6433	1	42	operators	operator	NOUN
ejpam-6433	1	43	in	in	ADP
ejpam-6433	1	44	hyperconvex	hyperconvex	ADJ
ejpam-6433	1	45	spaces	space	NOUN
ejpam-6433	1	46	moosa	moosa	PROPN
ejpam-6433	1	47	gabeleh1,2	gabeleh1,2	PROPN
ejpam-6433	1	48	,	,	PUNCT
ejpam-6433	1	49	jack	jack	PROPN
ejpam-6433	1	50	markin3	markin3	PROPN
ejpam-6433	1	51	,	,	PUNCT
ejpam-6433	1	52	maggie	maggie	VERB
ejpam-6433	1	53	aphane2	aphane2	PROPN
ejpam-6433	1	54	1	1	NUM
ejpam-6433	1	55	department	department	NOUN
ejpam-6433	1	56	of	of	ADP
ejpam-6433	1	57	mathematics	mathematic	NOUN
ejpam-6433	1	58	,	,	PUNCT
ejpam-6433	1	59	faculty	faculty	NOUN
ejpam-6433	1	60	of	of	ADP
ejpam-6433	1	61	basic	basic	ADJ
ejpam-6433	1	62	sciences	science	NOUN
ejpam-6433	1	63	,	,	PUNCT
ejpam-6433	1	64	ayatollah	ayatollah	PROPN
ejpam-6433	1	65	boroujerdi	boroujerdi	PROPN
ejpam-6433	1	66	university	university	PROPN
ejpam-6433	1	67	,	,	PUNCT
ejpam-6433	1	68	boroujerd	boroujerd	NOUN
ejpam-6433	1	69	,	,	PUNCT
ejpam-6433	1	70	iran	iran	PROPN
ejpam-6433	1	71	2	2	NUM
ejpam-6433	1	72	department	department	NOUN
ejpam-6433	1	73	of	of	ADP
ejpam-6433	1	74	mathematics	mathematic	NOUN
ejpam-6433	1	75	and	and	CCONJ
ejpam-6433	1	76	applied	apply	VERB
ejpam-6433	1	77	mathematics	mathematic	NOUN
ejpam-6433	1	78	,	,	PUNCT
ejpam-6433	1	79	sefako	sefako	VERB
ejpam-6433	1	80	makgatho	makgatho	PROPN
ejpam-6433	1	81	health	health	PROPN
ejpam-6433	1	82	sciences	sciences	PROPN
ejpam-6433	1	83	university	university	PROPN
ejpam-6433	1	84	,	,	PUNCT
ejpam-6433	1	85	ga	ga	PROPN
ejpam-6433	1	86	-	-	NOUN
ejpam-6433	1	87	rankuwa	rankuwa	ADJ
ejpam-6433	1	88	,	,	PUNCT
ejpam-6433	1	89	pretoria	pretoria	NOUN
ejpam-6433	1	90	,	,	PUNCT
ejpam-6433	1	91	medunsa	medunsa	ADJ
ejpam-6433	1	92	0204	0204	NUM
ejpam-6433	1	93	,	,	PUNCT
ejpam-6433	1	94	south	south	PROPN
ejpam-6433	1	95	africa	africa	PROPN
ejpam-6433	1	96	3	3	NUM
ejpam-6433	1	97	1440	1440	NUM
ejpam-6433	1	98	8th	8th	PROPN
ejpam-6433	1	99	st	st	PROPN
ejpam-6433	1	100	.	.	PROPN
ejpam-6433	1	101	,	,	PUNCT
ejpam-6433	1	102	golden	golden	ADJ
ejpam-6433	1	103	,	,	PUNCT
ejpam-6433	1	104	co	co	ADJ
ejpam-6433	1	105	80401	80401	NUM
ejpam-6433	1	106	,	,	PUNCT
ejpam-6433	1	107	usa	usa	PROPN
ejpam-6433	1	108	abstract	abstract	NOUN
ejpam-6433	1	109	.	.	PUNCT
ejpam-6433	2	1	we	we	PRON
ejpam-6433	2	2	first	first	ADV
ejpam-6433	2	3	prove	prove	VERB
ejpam-6433	2	4	that	that	SCONJ
ejpam-6433	2	5	if	if	SCONJ
ejpam-6433	2	6	(	(	PUNCT
ejpam-6433	2	7	g	g	NOUN
ejpam-6433	2	8	,	,	PUNCT
ejpam-6433	2	9	h	h	NOUN
ejpam-6433	2	10	)	)	PUNCT
ejpam-6433	2	11	is	be	AUX
ejpam-6433	2	12	a	a	DET
ejpam-6433	2	13	nonempty	nonempty	ADJ
ejpam-6433	2	14	,	,	PUNCT
ejpam-6433	2	15	compact	compact	ADJ
ejpam-6433	2	16	and	and	CCONJ
ejpam-6433	2	17	hyperconvex	hyperconvex	ADJ
ejpam-6433	2	18	pair	pair	NOUN
ejpam-6433	2	19	of	of	ADP
ejpam-6433	2	20	subsets	subset	NOUN
ejpam-6433	2	21	of	of	ADP
ejpam-6433	2	22	a	a	DET
ejpam-6433	2	23	hyperconvex	hyperconvex	ADJ
ejpam-6433	2	24	metric	metric	ADJ
ejpam-6433	2	25	space	space	NOUN
ejpam-6433	2	26	(	(	PUNCT
ejpam-6433	2	27	m	m	PROPN
ejpam-6433	2	28	,	,	PUNCT
ejpam-6433	2	29	d	d	PROPN
ejpam-6433	2	30	)	)	PUNCT
ejpam-6433	2	31	,	,	PUNCT
ejpam-6433	2	32	then	then	ADV
ejpam-6433	2	33	every	every	DET
ejpam-6433	2	34	cyclic	cyclic	ADJ
ejpam-6433	2	35	relatively	relatively	ADV
ejpam-6433	2	36	u	u	NOUN
ejpam-6433	2	37	-	-	ADJ
ejpam-6433	2	38	continuous	continuous	ADJ
ejpam-6433	2	39	mapping	mapping	NOUN
ejpam-6433	2	40	t	t	NOUN
ejpam-6433	2	41	defined	define	VERB
ejpam-6433	2	42	on	on	ADP
ejpam-6433	2	43	g	g	PROPN
ejpam-6433	2	44	∪h	∪h	NUM
ejpam-6433	2	45	has	have	VERB
ejpam-6433	2	46	a	a	DET
ejpam-6433	2	47	best	good	ADJ
ejpam-6433	2	48	proximity	proximity	NOUN
ejpam-6433	2	49	point	point	NOUN
ejpam-6433	2	50	.	.	PUNCT
ejpam-6433	3	1	the	the	DET
ejpam-6433	3	2	same	same	ADJ
ejpam-6433	3	3	result	result	NOUN
ejpam-6433	3	4	is	be	AUX
ejpam-6433	3	5	valid	valid	ADJ
ejpam-6433	3	6	for	for	ADP
ejpam-6433	3	7	the	the	DET
ejpam-6433	3	8	case	case	NOUN
ejpam-6433	3	9	that	that	SCONJ
ejpam-6433	3	10	t	t	PROPN
ejpam-6433	3	11	is	be	AUX
ejpam-6433	3	12	the	the	DET
ejpam-6433	3	13	noncyclic	noncyclic	NOUN
ejpam-6433	3	14	relatively	relatively	ADV
ejpam-6433	3	15	u	u	ADJ
ejpam-6433	3	16	-	-	ADJ
ejpam-6433	3	17	continuous	continuous	ADJ
ejpam-6433	3	18	map	map	NOUN
ejpam-6433	3	19	and	and	CCONJ
ejpam-6433	3	20	(	(	PUNCT
ejpam-6433	3	21	g	g	NOUN
ejpam-6433	3	22	,	,	PUNCT
ejpam-6433	3	23	h	h	NOUN
ejpam-6433	3	24	)	)	PUNCT
ejpam-6433	3	25	is	be	AUX
ejpam-6433	3	26	a	a	DET
ejpam-6433	3	27	semi	semi	ADJ
ejpam-6433	3	28	-	-	ADJ
ejpam-6433	3	29	sharp	sharp	ADJ
ejpam-6433	3	30	proximinal	proximinal	ADJ
ejpam-6433	3	31	pair	pair	NOUN
ejpam-6433	3	32	to	to	PART
ejpam-6433	3	33	obtain	obtain	VERB
ejpam-6433	3	34	the	the	DET
ejpam-6433	3	35	existence	existence	NOUN
ejpam-6433	3	36	of	of	ADP
ejpam-6433	3	37	best	good	ADJ
ejpam-6433	3	38	proximity	proximity	NOUN
ejpam-6433	3	39	pairs	pair	NOUN
ejpam-6433	3	40	.	.	PUNCT
ejpam-6433	4	1	we	we	PRON
ejpam-6433	4	2	then	then	ADV
ejpam-6433	4	3	consider	consider	VERB
ejpam-6433	4	4	the	the	DET
ejpam-6433	4	5	class	class	NOUN
ejpam-6433	4	6	of	of	ADP
ejpam-6433	4	7	relatively	relatively	ADV
ejpam-6433	4	8	h	h	NOUN
ejpam-6433	4	9	-	-	PUNCT
ejpam-6433	4	10	meir	meir	ADJ
ejpam-6433	4	11	-	-	PUNCT
ejpam-6433	4	12	keeler	keeler	NOUN
ejpam-6433	4	13	condensing	condense	VERB
ejpam-6433	4	14	operators	operator	NOUN
ejpam-6433	4	15	by	by	ADP
ejpam-6433	4	16	applying	apply	VERB
ejpam-6433	4	17	a	a	DET
ejpam-6433	4	18	concept	concept	NOUN
ejpam-6433	4	19	of	of	ADP
ejpam-6433	4	20	measure	measure	NOUN
ejpam-6433	4	21	of	of	ADP
ejpam-6433	4	22	noncompactness	noncompactness	ADJ
ejpam-6433	4	23	in	in	ADP
ejpam-6433	4	24	the	the	DET
ejpam-6433	4	25	framework	framework	NOUN
ejpam-6433	4	26	of	of	ADP
ejpam-6433	4	27	hyperconvex	hyperconvex	ADJ
ejpam-6433	4	28	spaces	space	NOUN
ejpam-6433	4	29	and	and	CCONJ
ejpam-6433	4	30	in	in	ADP
ejpam-6433	4	31	a	a	DET
ejpam-6433	4	32	special	special	ADJ
ejpam-6433	4	33	case	case	NOUN
ejpam-6433	4	34	in	in	ADP
ejpam-6433	4	35	the	the	DET
ejpam-6433	4	36	nonreflexive	nonreflexive	ADJ
ejpam-6433	4	37	banach	banach	NOUN
ejpam-6433	4	38	space	space	NOUN
ejpam-6433	4	39	ℓ∞	ℓ∞	PROPN
ejpam-6433	4	40	and	and	CCONJ
ejpam-6433	4	41	revisit	revisit	VERB
ejpam-6433	4	42	the	the	DET
ejpam-6433	4	43	previous	previous	ADJ
ejpam-6433	4	44	best	good	ADJ
ejpam-6433	4	45	proximity	proximity	NOUN
ejpam-6433	4	46	point	point	NOUN
ejpam-6433	4	47	(	(	PUNCT
ejpam-6433	4	48	pair	pair	NOUN
ejpam-6433	4	49	)	)	PUNCT
ejpam-6433	4	50	results	result	NOUN
ejpam-6433	4	51	of	of	ADP
ejpam-6433	4	52	the	the	DET
ejpam-6433	4	53	paper	paper	NOUN
ejpam-6433	4	54	by	by	ADP
ejpam-6433	4	55	m.	m.	NOUN
ejpam-6433	4	56	gabeleh	gabeleh	PROPN
ejpam-6433	4	57	and	and	CCONJ
ejpam-6433	4	58	c.	c.	PROPN
ejpam-6433	4	59	vetro	vetro	PROPN
ejpam-6433	5	1	[	[	X
ejpam-6433	5	2	m.	m.	NOUN
ejpam-6433	5	3	gabeleh	gabeleh	NOUN
ejpam-6433	5	4	,	,	PUNCT
ejpam-6433	5	5	c.	c.	PROPN
ejpam-6433	5	6	vetro	vetro	PROPN
ejpam-6433	5	7	,	,	PUNCT
ejpam-6433	5	8	a	a	DET
ejpam-6433	5	9	new	new	ADJ
ejpam-6433	5	10	extension	extension	NOUN
ejpam-6433	5	11	of	of	ADP
ejpam-6433	5	12	darbo	darbo	NOUN
ejpam-6433	5	13	’s	’s	PART
ejpam-6433	5	14	fixed	fix	VERB
ejpam-6433	5	15	point	point	NOUN
ejpam-6433	5	16	theorem	theorem	ADJ
ejpam-6433	5	17	using	use	VERB
ejpam-6433	5	18	relatively	relatively	ADV
ejpam-6433	5	19	meir	meir	ADJ
ejpam-6433	5	20	-	-	PUNCT
ejpam-6433	5	21	keeler	keeler	NOUN
ejpam-6433	5	22	condensing	condense	VERB
ejpam-6433	5	23	operators	operator	NOUN
ejpam-6433	5	24	,	,	PUNCT
ejpam-6433	5	25	*	*	PUNCT
ejpam-6433	5	26	bull	bull	NOUN
ejpam-6433	5	27	.	.	PUNCT
ejpam-6433	6	1	aust	aust	PROPN
ejpam-6433	6	2	.	.	PUNCT
ejpam-6433	6	3	math	math	PROPN
ejpam-6433	6	4	.	.	PUNCT
ejpam-6433	7	1	soc	soc	PROPN
ejpam-6433	7	2	.	.	PUNCT
ejpam-6433	8	1	*	*	PUNCT
ejpam-6433	8	2	,	,	PUNCT
ejpam-6433	8	3	98	98	NUM
ejpam-6433	8	4	(	(	PUNCT
ejpam-6433	8	5	2018	2018	NUM
ejpam-6433	8	6	)	)	PUNCT
ejpam-6433	8	7	286–297	286–297	NUM
ejpam-6433	8	8	]	]	PUNCT
ejpam-6433	8	9	.	.	PUNCT
ejpam-6433	9	1	examples	example	NOUN
ejpam-6433	9	2	are	be	AUX
ejpam-6433	9	3	given	give	VERB
ejpam-6433	9	4	to	to	PART
ejpam-6433	9	5	support	support	VERB
ejpam-6433	9	6	our	our	PRON
ejpam-6433	9	7	main	main	ADJ
ejpam-6433	9	8	discussions	discussion	NOUN
ejpam-6433	9	9	.	.	PUNCT
ejpam-6433	10	1	2020	2020	NUM
ejpam-6433	10	2	mathematics	mathematic	NOUN
ejpam-6433	10	3	subject	subject	NOUN
ejpam-6433	10	4	classifications	classification	NOUN
ejpam-6433	10	5	:	:	PUNCT
ejpam-6433	10	6	47h10	47h10	NUM
ejpam-6433	10	7	,	,	PUNCT
ejpam-6433	10	8	51f99	51f99	NUM
ejpam-6433	10	9	,	,	PUNCT
ejpam-6433	10	10	54h25	54h25	NUM
ejpam-6433	10	11	key	key	ADJ
ejpam-6433	10	12	words	word	NOUN
ejpam-6433	10	13	and	and	CCONJ
ejpam-6433	10	14	phrases	phrase	NOUN
ejpam-6433	10	15	:	:	PUNCT
ejpam-6433	10	16	hyperconvex	hyperconvex	ADJ
ejpam-6433	10	17	metric	metric	ADJ
ejpam-6433	10	18	space	space	NOUN
ejpam-6433	10	19	,	,	PUNCT
ejpam-6433	10	20	best	good	ADJ
ejpam-6433	10	21	proximity	proximity	NOUN
ejpam-6433	10	22	point	point	NOUN
ejpam-6433	10	23	,	,	PUNCT
ejpam-6433	10	24	relatively	relatively	ADV
ejpam-6433	10	25	ucontinuous	ucontinuous	ADJ
ejpam-6433	10	26	map	map	NOUN
ejpam-6433	10	27	,	,	PUNCT
ejpam-6433	10	28	meir	meir	PROPN
ejpam-6433	10	29	-	-	PUNCT
ejpam-6433	10	30	keeler	keeler	NOUN
ejpam-6433	10	31	condensing	condense	VERB
ejpam-6433	10	32	operator	operator	NOUN
ejpam-6433	10	33	1	1	NUM
ejpam-6433	10	34	.	.	PUNCT
ejpam-6433	11	1	introduction	introduction	NOUN
ejpam-6433	11	2	let	let	VERB
ejpam-6433	11	3	(	(	PUNCT
ejpam-6433	11	4	g	g	NOUN
ejpam-6433	11	5	,	,	PUNCT
ejpam-6433	11	6	h	h	NOUN
ejpam-6433	11	7	)	)	PUNCT
ejpam-6433	11	8	be	be	VERB
ejpam-6433	11	9	a	a	DET
ejpam-6433	11	10	nonempty	nonempty	ADJ
ejpam-6433	11	11	pair	pair	NOUN
ejpam-6433	11	12	of	of	ADP
ejpam-6433	11	13	subsets	subset	NOUN
ejpam-6433	11	14	of	of	ADP
ejpam-6433	11	15	a	a	DET
ejpam-6433	11	16	metric	metric	ADJ
ejpam-6433	11	17	space	space	NOUN
ejpam-6433	11	18	(	(	PUNCT
ejpam-6433	11	19	m	m	PROPN
ejpam-6433	11	20	,	,	PUNCT
ejpam-6433	11	21	d	d	NOUN
ejpam-6433	11	22	)	)	PUNCT
ejpam-6433	11	23	.	.	PUNCT
ejpam-6433	12	1	a	a	DET
ejpam-6433	12	2	mapping	mapping	NOUN
ejpam-6433	12	3	t	t	NOUN
ejpam-6433	12	4	:	:	PUNCT
ejpam-6433	12	5	g	g	PROPN
ejpam-6433	12	6	∪	∪	ADP
ejpam-6433	12	7	h	h	NOUN
ejpam-6433	12	8	→	→	SYM
ejpam-6433	12	9	g∪h	g∪h	NOUN
ejpam-6433	12	10	is	be	AUX
ejpam-6433	12	11	said	say	VERB
ejpam-6433	12	12	to	to	PART
ejpam-6433	12	13	be	be	AUX
ejpam-6433	12	14	relatively	relatively	ADV
ejpam-6433	12	15	nonexpansive	nonexpansive	ADJ
ejpam-6433	12	16	if	if	SCONJ
ejpam-6433	12	17	d(tx	d(tx	PROPN
ejpam-6433	12	18	,	,	PUNCT
ejpam-6433	12	19	ty	ty	NOUN
ejpam-6433	12	20	)	)	PUNCT
ejpam-6433	12	21	≤	≤	NOUN
ejpam-6433	12	22	d(x	d(x	PROPN
ejpam-6433	12	23	,	,	PUNCT
ejpam-6433	12	24	y	y	NOUN
ejpam-6433	12	25	)	)	PUNCT
ejpam-6433	12	26	for	for	ADP
ejpam-6433	12	27	all	all	DET
ejpam-6433	12	28	(	(	PUNCT
ejpam-6433	12	29	x	x	NOUN
ejpam-6433	12	30	,	,	PUNCT
ejpam-6433	12	31	y	y	NOUN
ejpam-6433	12	32	)	)	PUNCT
ejpam-6433	12	33	∈	∈	PROPN
ejpam-6433	12	34	g×h	g×h	PROPN
ejpam-6433	12	35	.	.	PUNCT
ejpam-6433	13	1	in	in	ADP
ejpam-6433	13	2	particular	particular	ADJ
ejpam-6433	13	3	case	case	NOUN
ejpam-6433	13	4	,	,	PUNCT
ejpam-6433	13	5	if	if	SCONJ
ejpam-6433	13	6	g	g	PROPN
ejpam-6433	13	7	=	=	SYM
ejpam-6433	13	8	h	h	NOUN
ejpam-6433	13	9	,	,	PUNCT
ejpam-6433	13	10	then	then	ADV
ejpam-6433	13	11	t	t	PROPN
ejpam-6433	13	12	is	be	AUX
ejpam-6433	13	13	well	well	ADV
ejpam-6433	13	14	-	-	PUNCT
ejpam-6433	13	15	known	know	VERB
ejpam-6433	13	16	as	as	ADP
ejpam-6433	13	17	a	a	DET
ejpam-6433	13	18	nonexpansive	nonexpansive	ADJ
ejpam-6433	13	19	self	self	NOUN
ejpam-6433	13	20	-	-	PUNCT
ejpam-6433	13	21	mapping	mapping	NOUN
ejpam-6433	13	22	.	.	PUNCT
ejpam-6433	14	1	the	the	DET
ejpam-6433	14	2	mapping	mapping	NOUN
ejpam-6433	14	3	t	t	PROPN
ejpam-6433	14	4	is	be	AUX
ejpam-6433	14	5	cyclic	cyclic	ADJ
ejpam-6433	14	6	on	on	ADP
ejpam-6433	14	7	g	g	PROPN
ejpam-6433	14	8	∪	∪	ADP
ejpam-6433	14	9	h	h	NOUN
ejpam-6433	14	10	if	if	SCONJ
ejpam-6433	14	11	t	t	PROPN
ejpam-6433	14	12	(	(	PUNCT
ejpam-6433	14	13	g	g	NOUN
ejpam-6433	14	14	)	)	PUNCT
ejpam-6433	14	15	⊆	⊆	NUM
ejpam-6433	14	16	h	h	NOUN
ejpam-6433	14	17	,	,	PUNCT
ejpam-6433	14	18	t	t	PROPN
ejpam-6433	14	19	(	(	PUNCT
ejpam-6433	14	20	h	h	NOUN
ejpam-6433	14	21	)	)	PUNCT
ejpam-6433	14	22	⊆	⊆	NUM
ejpam-6433	14	23	g	g	NOUN
ejpam-6433	14	24	,	,	PUNCT
ejpam-6433	14	25	doi	doi	NOUN
ejpam-6433	14	26	:	:	PUNCT
ejpam-6433	14	27	https://doi.org/10.29020/nybg.ejpam.v18i3.6433	https://doi.org/10.29020/nybg.ejpam.v18i3.6433	NOUN
ejpam-6433	14	28	email	email	NOUN
ejpam-6433	14	29	addresses	address	NOUN
ejpam-6433	14	30	:	:	PUNCT
ejpam-6433	14	31	gabeleh@abru.ac.ir	gabeleh@abru.ac.ir	ADJ
ejpam-6433	14	32	gab.moo@gmail.com	gab.moo@gmail.com	NOUN
ejpam-6433	14	33	(	(	PUNCT
ejpam-6433	14	34	m.	m.	NOUN
ejpam-6433	14	35	gabeleh	gabeleh	PROPN
ejpam-6433	14	36	)	)	PUNCT
ejpam-6433	14	37	,	,	PUNCT
ejpam-6433	14	38	jmarkin@cybermesa.com	jmarkin@cybermesa.com	X
ejpam-6433	14	39	(	(	PUNCT
ejpam-6433	14	40	j.	j.	PROPN
ejpam-6433	14	41	markin	markin	PROPN
ejpam-6433	14	42	)	)	PUNCT
ejpam-6433	14	43	,	,	PUNCT
ejpam-6433	14	44	maggie.aphane@smu.ac.za	maggie.aphane@smu.ac.za	PROPN
ejpam-6433	14	45	(	(	PUNCT
ejpam-6433	14	46	m.	m.	NOUN
ejpam-6433	14	47	aphane	aphane	NOUN
ejpam-6433	14	48	)	)	PUNCT
ejpam-6433	14	49	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6433	15	1	1	1	NUM
ejpam-6433	15	2	copyright	copyright	NOUN
ejpam-6433	15	3	:	:	PUNCT
ejpam-6433	15	4	©	©	PROPN
ejpam-6433	15	5	2025	2025	NUM
ejpam-6433	15	6	the	the	DET
ejpam-6433	15	7	author(s	author(s	NOUN
ejpam-6433	15	8	)	)	PUNCT
ejpam-6433	15	9	.	.	PUNCT
ejpam-6433	16	1	(	(	PUNCT
ejpam-6433	16	2	cc	cc	NOUN
ejpam-6433	16	3	by	by	ADP
ejpam-6433	16	4	-	-	PUNCT
ejpam-6433	16	5	nc	nc	PROPN
ejpam-6433	16	6	4.0	4.0	NUM
ejpam-6433	16	7	)	)	PUNCT
ejpam-6433	16	8	m.	m.	NOUN
ejpam-6433	16	9	gabeleh	gabeleh	NOUN
ejpam-6433	16	10	,	,	PUNCT
ejpam-6433	16	11	j.	j.	PROPN
ejpam-6433	16	12	markin	markin	PROPN
ejpam-6433	16	13	,	,	PUNCT
ejpam-6433	16	14	m.	m.	NOUN
ejpam-6433	16	15	aphane	aphane	PROPN
ejpam-6433	16	16	/	/	SYM
ejpam-6433	16	17	eur	eur	PROPN
ejpam-6433	16	18	.	.	PUNCT
ejpam-6433	17	1	j.	j.	PROPN
ejpam-6433	17	2	pure	pure	PROPN
ejpam-6433	17	3	appl	appl	PROPN
ejpam-6433	17	4	.	.	PROPN
ejpam-6433	17	5	math	math	PROPN
ejpam-6433	17	6	,	,	PUNCT
ejpam-6433	17	7	18	18	NUM
ejpam-6433	17	8	(	(	PUNCT
ejpam-6433	17	9	3	3	NUM
ejpam-6433	17	10	)	)	PUNCT
ejpam-6433	17	11	(	(	PUNCT
ejpam-6433	17	12	2025	2025	NUM
ejpam-6433	17	13	)	)	PUNCT
ejpam-6433	17	14	,	,	PUNCT
ejpam-6433	17	15	6433	6433	NUM
ejpam-6433	17	16	2	2	NUM
ejpam-6433	17	17	of	of	ADP
ejpam-6433	17	18	17	17	NUM
ejpam-6433	17	19	and	and	CCONJ
ejpam-6433	17	20	t	t	PROPN
ejpam-6433	17	21	is	be	AUX
ejpam-6433	17	22	noncyclic	noncyclic	ADJ
ejpam-6433	17	23	provided	provide	VERB
ejpam-6433	17	24	that	that	SCONJ
ejpam-6433	17	25	t	t	NOUN
ejpam-6433	17	26	(	(	PUNCT
ejpam-6433	17	27	g	g	NOUN
ejpam-6433	17	28	)	)	PUNCT
ejpam-6433	17	29	⊆	⊆	NUM
ejpam-6433	17	30	g	g	NOUN
ejpam-6433	17	31	,	,	PUNCT
ejpam-6433	17	32	t	t	PROPN
ejpam-6433	17	33	(	(	PUNCT
ejpam-6433	17	34	h	h	NOUN
ejpam-6433	17	35	)	)	PUNCT
ejpam-6433	18	1	⊆	⊆	NUM
ejpam-6433	18	2	h.	h.	NOUN
ejpam-6433	18	3	it	it	PRON
ejpam-6433	18	4	is	be	AUX
ejpam-6433	18	5	worth	worth	ADJ
ejpam-6433	18	6	mentioning	mention	VERB
ejpam-6433	18	7	that	that	SCONJ
ejpam-6433	18	8	if	if	SCONJ
ejpam-6433	18	9	the	the	DET
ejpam-6433	18	10	map	map	NOUN
ejpam-6433	18	11	t	t	NOUN
ejpam-6433	18	12	is	be	AUX
ejpam-6433	18	13	cyclic	cyclic	ADJ
ejpam-6433	18	14	and	and	CCONJ
ejpam-6433	18	15	g	g	PROPN
ejpam-6433	18	16	∩	∩	ADJ
ejpam-6433	18	17	h	h	NOUN
ejpam-6433	18	18	=	=	NOUN
ejpam-6433	18	19	∅	∅	NOUN
ejpam-6433	18	20	,	,	PUNCT
ejpam-6433	18	21	then	then	ADV
ejpam-6433	18	22	the	the	DET
ejpam-6433	18	23	fixed	fixed	ADJ
ejpam-6433	18	24	point	point	NOUN
ejpam-6433	18	25	equation	equation	NOUN
ejpam-6433	18	26	tx	tx	NOUN
ejpam-6433	18	27	=	=	PUNCT
ejpam-6433	19	1	x	x	PRON
ejpam-6433	19	2	does	do	AUX
ejpam-6433	19	3	not	not	PART
ejpam-6433	19	4	have	have	VERB
ejpam-6433	19	5	any	any	DET
ejpam-6433	19	6	solution	solution	NOUN
ejpam-6433	19	7	.	.	PUNCT
ejpam-6433	20	1	indeed	indeed	ADV
ejpam-6433	20	2	,	,	PUNCT
ejpam-6433	20	3	for	for	ADP
ejpam-6433	20	4	any	any	DET
ejpam-6433	20	5	x	x	SYM
ejpam-6433	20	6	∈	∈	PROPN
ejpam-6433	20	7	g∪h	g∪h	NOUN
ejpam-6433	20	8	we	we	PRON
ejpam-6433	20	9	have	have	VERB
ejpam-6433	20	10	d(x	d(x	NOUN
ejpam-6433	20	11	,	,	PUNCT
ejpam-6433	20	12	tx	tx	PROPN
ejpam-6433	20	13	)	)	PUNCT
ejpam-6433	20	14	≥	≥	NOUN
ejpam-6433	20	15	d(g	d(g	PROPN
ejpam-6433	20	16	,	,	PUNCT
ejpam-6433	20	17	h	h	NOUN
ejpam-6433	20	18	)	)	PUNCT
ejpam-6433	20	19	:	:	PUNCT
ejpam-6433	20	20	=	=	SYM
ejpam-6433	20	21	inf{d(u	inf{d(u	PROPN
ejpam-6433	20	22	,	,	PUNCT
ejpam-6433	20	23	v	v	NOUN
ejpam-6433	20	24	)	)	PUNCT
ejpam-6433	20	25	:	:	PUNCT
ejpam-6433	20	26	(	(	PUNCT
ejpam-6433	20	27	u	u	NOUN
ejpam-6433	20	28	,	,	PUNCT
ejpam-6433	20	29	v	v	NOUN
ejpam-6433	20	30	)	)	PUNCT
ejpam-6433	20	31	∈	∈	PROPN
ejpam-6433	20	32	g	g	ADP
ejpam-6433	20	33	×	×	PROPN
ejpam-6433	20	34	h	h	NOUN
ejpam-6433	20	35	}	}	PUNCT
ejpam-6433	20	36	.	.	PUNCT
ejpam-6433	21	1	so	so	ADV
ejpam-6433	21	2	,	,	PUNCT
ejpam-6433	21	3	in	in	ADP
ejpam-6433	21	4	this	this	DET
ejpam-6433	21	5	case	case	NOUN
ejpam-6433	21	6	,	,	PUNCT
ejpam-6433	21	7	instead	instead	ADV
ejpam-6433	21	8	of	of	ADP
ejpam-6433	21	9	finding	find	VERB
ejpam-6433	21	10	a	a	DET
ejpam-6433	21	11	fixed	fix	VERB
ejpam-6433	21	12	point	point	NOUN
ejpam-6433	21	13	for	for	ADP
ejpam-6433	21	14	the	the	DET
ejpam-6433	21	15	cyclic	cyclic	ADJ
ejpam-6433	21	16	mapping	mapping	NOUN
ejpam-6433	21	17	t	t	NOUN
ejpam-6433	21	18	we	we	PRON
ejpam-6433	21	19	can	can	AUX
ejpam-6433	21	20	think	think	VERB
ejpam-6433	21	21	about	about	ADP
ejpam-6433	21	22	the	the	DET
ejpam-6433	21	23	existence	existence	NOUN
ejpam-6433	21	24	of	of	ADP
ejpam-6433	21	25	a	a	DET
ejpam-6433	21	26	point	point	NOUN
ejpam-6433	21	27	x∗	x∗	PROPN
ejpam-6433	21	28	∈	∈	PROPN
ejpam-6433	21	29	g	g	PROPN
ejpam-6433	21	30	∪h	∪h	NUM
ejpam-6433	21	31	for	for	ADP
ejpam-6433	21	32	which	which	PRON
ejpam-6433	21	33	d(x∗	d(x∗	NOUN
ejpam-6433	21	34	,	,	PUNCT
ejpam-6433	21	35	tx∗	tx∗	NOUN
ejpam-6433	21	36	)	)	PUNCT
ejpam-6433	22	1	=	=	SYM
ejpam-6433	22	2	d(g	d(g	PROPN
ejpam-6433	22	3	,	,	PUNCT
ejpam-6433	22	4	h	h	NOUN
ejpam-6433	22	5	)	)	PUNCT
ejpam-6433	22	6	.	.	PUNCT
ejpam-6433	23	1	such	such	ADJ
ejpam-6433	23	2	points	point	NOUN
ejpam-6433	23	3	are	be	AUX
ejpam-6433	23	4	called	call	VERB
ejpam-6433	23	5	best	good	ADJ
ejpam-6433	23	6	proximity	proximity	NOUN
ejpam-6433	23	7	points	point	NOUN
ejpam-6433	23	8	of	of	ADP
ejpam-6433	23	9	the	the	DET
ejpam-6433	23	10	cyclic	cyclic	ADJ
ejpam-6433	23	11	mapping	mapping	NOUN
ejpam-6433	23	12	t	t	NOUN
ejpam-6433	23	13	.	.	PUNCT
ejpam-6433	24	1	on	on	ADP
ejpam-6433	24	2	the	the	DET
ejpam-6433	24	3	other	other	ADJ
ejpam-6433	24	4	hand	hand	NOUN
ejpam-6433	24	5	,	,	PUNCT
ejpam-6433	24	6	if	if	SCONJ
ejpam-6433	24	7	t	t	PROPN
ejpam-6433	24	8	is	be	AUX
ejpam-6433	24	9	noncyclic	noncyclic	ADJ
ejpam-6433	24	10	,	,	PUNCT
ejpam-6433	24	11	then	then	ADV
ejpam-6433	24	12	the	the	DET
ejpam-6433	24	13	fixed	fix	VERB
ejpam-6433	24	14	point	point	NOUN
ejpam-6433	24	15	equation	equation	NOUN
ejpam-6433	24	16	may	may	AUX
ejpam-6433	24	17	have	have	VERB
ejpam-6433	24	18	a	a	DET
ejpam-6433	24	19	fixed	fix	VERB
ejpam-6433	24	20	point	point	NOUN
ejpam-6433	24	21	,	,	PUNCT
ejpam-6433	24	22	but	but	CCONJ
ejpam-6433	24	23	it	it	PRON
ejpam-6433	24	24	is	be	AUX
ejpam-6433	24	25	interesting	interesting	ADJ
ejpam-6433	24	26	to	to	PART
ejpam-6433	24	27	find	find	VERB
ejpam-6433	24	28	a	a	DET
ejpam-6433	24	29	pair	pair	NOUN
ejpam-6433	24	30	of	of	ADP
ejpam-6433	24	31	fixed	fix	VERB
ejpam-6433	24	32	points	point	NOUN
ejpam-6433	24	33	(	(	PUNCT
ejpam-6433	24	34	x∗	x∗	PROPN
ejpam-6433	24	35	,	,	PUNCT
ejpam-6433	24	36	y∗	y∗	PROPN
ejpam-6433	25	1	)	)	PUNCT
ejpam-6433	25	2	∈	∈	PROPN
ejpam-6433	25	3	g	g	PROPN
ejpam-6433	25	4	×	×	PROPN
ejpam-6433	25	5	h	h	NOUN
ejpam-6433	25	6	(	(	PUNCT
ejpam-6433	25	7	i.e.	i.e.	X
ejpam-6433	25	8	tx∗	tx∗	X
ejpam-6433	25	9	=	=	PUNCT
ejpam-6433	25	10	x∗	x∗	PROPN
ejpam-6433	25	11	,	,	PUNCT
ejpam-6433	25	12	t	t	PROPN
ejpam-6433	25	13	y∗	y∗	PROPN
ejpam-6433	25	14	=	=	SYM
ejpam-6433	25	15	y∗	y∗	PROPN
ejpam-6433	25	16	)	)	PUNCT
ejpam-6433	25	17	such	such	ADJ
ejpam-6433	25	18	that	that	DET
ejpam-6433	25	19	d(x∗	d(x∗	NOUN
ejpam-6433	25	20	,	,	PUNCT
ejpam-6433	25	21	y∗	y∗	PROPN
ejpam-6433	25	22	)	)	PUNCT
ejpam-6433	26	1	=	=	SYM
ejpam-6433	26	2	d(g	d(g	PROPN
ejpam-6433	26	3	,	,	PUNCT
ejpam-6433	26	4	h	h	NOUN
ejpam-6433	26	5	)	)	PUNCT
ejpam-6433	26	6	.	.	PUNCT
ejpam-6433	27	1	these	these	DET
ejpam-6433	27	2	kinds	kind	NOUN
ejpam-6433	27	3	of	of	ADP
ejpam-6433	27	4	points	point	NOUN
ejpam-6433	27	5	are	be	AUX
ejpam-6433	27	6	called	call	VERB
ejpam-6433	27	7	best	good	ADJ
ejpam-6433	27	8	proximity	proximity	NOUN
ejpam-6433	27	9	pairs	pair	NOUN
ejpam-6433	27	10	for	for	ADP
ejpam-6433	27	11	the	the	DET
ejpam-6433	27	12	noncyclic	noncyclic	PROPN
ejpam-6433	27	13	mapping	mapping	PROPN
ejpam-6433	27	14	t	t	PROPN
ejpam-6433	27	15	.	.	PUNCT
ejpam-6433	28	1	existence	existence	NOUN
ejpam-6433	28	2	of	of	ADP
ejpam-6433	28	3	best	good	ADJ
ejpam-6433	28	4	proximity	proximity	NOUN
ejpam-6433	28	5	points	point	NOUN
ejpam-6433	28	6	(	(	PUNCT
ejpam-6433	28	7	pairs	pair	NOUN
ejpam-6433	28	8	)	)	PUNCT
ejpam-6433	28	9	for	for	ADP
ejpam-6433	28	10	cyclic	cyclic	ADJ
ejpam-6433	28	11	(	(	PUNCT
ejpam-6433	28	12	noncyclic	noncyclic	NOUN
ejpam-6433	28	13	)	)	PUNCT
ejpam-6433	28	14	relatively	relatively	ADV
ejpam-6433	28	15	nonexpansive	nonexpansive	ADJ
ejpam-6433	28	16	mappings	mapping	NOUN
ejpam-6433	28	17	was	be	AUX
ejpam-6433	28	18	first	first	ADV
ejpam-6433	28	19	established	establish	VERB
ejpam-6433	28	20	by	by	ADP
ejpam-6433	28	21	eldred	eldred	PROPN
ejpam-6433	28	22	et	et	PROPN
ejpam-6433	28	23	al	al	PROPN
ejpam-6433	28	24	.	.	PUNCT
ejpam-6433	29	1	in	in	ADP
ejpam-6433	29	2	[	[	X
ejpam-6433	29	3	1	1	NUM
ejpam-6433	29	4	]	]	PUNCT
ejpam-6433	29	5	and	and	CCONJ
ejpam-6433	29	6	after	after	ADP
ejpam-6433	29	7	that	that	DET
ejpam-6433	29	8	r.	r.	PROPN
ejpam-6433	29	9	espinola	espinola	PROPN
ejpam-6433	29	10	(	(	PUNCT
ejpam-6433	29	11	[	[	X
ejpam-6433	29	12	2	2	NUM
ejpam-6433	29	13	]	]	PUNCT
ejpam-6433	29	14	)	)	PUNCT
ejpam-6433	29	15	used	use	VERB
ejpam-6433	29	16	a	a	DET
ejpam-6433	29	17	different	different	ADJ
ejpam-6433	29	18	approach	approach	NOUN
ejpam-6433	29	19	to	to	PART
ejpam-6433	29	20	obtain	obtain	VERB
ejpam-6433	29	21	the	the	DET
ejpam-6433	29	22	existence	existence	NOUN
ejpam-6433	29	23	results	result	NOUN
ejpam-6433	29	24	of	of	ADP
ejpam-6433	29	25	[	[	X
ejpam-6433	29	26	1	1	NUM
ejpam-6433	29	27	]	]	PUNCT
ejpam-6433	29	28	(	(	PUNCT
ejpam-6433	29	29	see	see	VERB
ejpam-6433	29	30	also	also	ADV
ejpam-6433	29	31	[	[	X
ejpam-6433	29	32	3	3	NUM
ejpam-6433	29	33	,	,	PUNCT
ejpam-6433	29	34	4	4	NUM
ejpam-6433	29	35	]	]	PUNCT
ejpam-6433	29	36	for	for	ADP
ejpam-6433	29	37	more	more	ADJ
ejpam-6433	29	38	information	information	NOUN
ejpam-6433	29	39	about	about	ADP
ejpam-6433	29	40	cyclic	cyclic	ADJ
ejpam-6433	29	41	maps	map	NOUN
ejpam-6433	29	42	which	which	PRON
ejpam-6433	29	43	satisfy	satisfy	VERB
ejpam-6433	29	44	contractive	contractive	ADJ
ejpam-6433	29	45	conditions	condition	NOUN
ejpam-6433	29	46	)	)	PUNCT
ejpam-6433	29	47	.	.	PUNCT
ejpam-6433	30	1	here	here	ADV
ejpam-6433	30	2	is	be	AUX
ejpam-6433	30	3	a	a	DET
ejpam-6433	30	4	main	main	ADJ
ejpam-6433	30	5	result	result	NOUN
ejpam-6433	30	6	of	of	ADP
ejpam-6433	30	7	[	[	X
ejpam-6433	30	8	1	1	NUM
ejpam-6433	30	9	]	]	PUNCT
ejpam-6433	30	10	.	.	PUNCT
ejpam-6433	31	1	theorem	theorem	NOUN
ejpam-6433	31	2	1	1	X
ejpam-6433	31	3	.	.	PUNCT
ejpam-6433	32	1	let	let	VERB
ejpam-6433	32	2	(	(	PUNCT
ejpam-6433	32	3	g	g	NOUN
ejpam-6433	32	4	,	,	PUNCT
ejpam-6433	32	5	h	h	NOUN
ejpam-6433	32	6	)	)	PUNCT
ejpam-6433	32	7	be	be	AUX
ejpam-6433	32	8	a	a	DET
ejpam-6433	32	9	nonempty	nonempty	ADJ
ejpam-6433	32	10	,	,	PUNCT
ejpam-6433	32	11	compact	compact	ADJ
ejpam-6433	32	12	and	and	CCONJ
ejpam-6433	32	13	convex	convex	ADJ
ejpam-6433	32	14	pair	pair	NOUN
ejpam-6433	32	15	of	of	ADP
ejpam-6433	32	16	subsets	subset	NOUN
ejpam-6433	32	17	of	of	ADP
ejpam-6433	32	18	a	a	DET
ejpam-6433	32	19	banach	banach	NOUN
ejpam-6433	32	20	space	space	NOUN
ejpam-6433	32	21	x.	x.	NOUN
ejpam-6433	33	1	if	if	SCONJ
ejpam-6433	33	2	t	t	PROPN
ejpam-6433	33	3	:	:	PUNCT
ejpam-6433	33	4	g	g	PROPN
ejpam-6433	33	5	∪h	∪h	NUM
ejpam-6433	33	6	→	→	SYM
ejpam-6433	33	7	g	g	PROPN
ejpam-6433	33	8	∪h	∪h	NUM
ejpam-6433	33	9	is	be	AUX
ejpam-6433	33	10	a	a	DET
ejpam-6433	33	11	cyclic	cyclic	ADJ
ejpam-6433	33	12	relatively	relatively	ADV
ejpam-6433	33	13	nonexpansive	nonexpansive	ADJ
ejpam-6433	33	14	mapping	mapping	NOUN
ejpam-6433	33	15	,	,	PUNCT
ejpam-6433	33	16	then	then	ADV
ejpam-6433	33	17	t	t	PROPN
ejpam-6433	33	18	has	have	VERB
ejpam-6433	33	19	a	a	DET
ejpam-6433	33	20	best	good	ADJ
ejpam-6433	33	21	proximity	proximity	NOUN
ejpam-6433	33	22	point	point	NOUN
ejpam-6433	33	23	.	.	PUNCT
ejpam-6433	34	1	we	we	PRON
ejpam-6433	34	2	mention	mention	VERB
ejpam-6433	34	3	that	that	SCONJ
ejpam-6433	34	4	the	the	DET
ejpam-6433	34	5	proof	proof	NOUN
ejpam-6433	34	6	of	of	ADP
ejpam-6433	34	7	the	the	DET
ejpam-6433	34	8	above	above	ADJ
ejpam-6433	34	9	theorem	theorem	NOUN
ejpam-6433	34	10	is	be	AUX
ejpam-6433	34	11	based	base	VERB
ejpam-6433	34	12	on	on	ADP
ejpam-6433	34	13	the	the	DET
ejpam-6433	34	14	fact	fact	NOUN
ejpam-6433	34	15	that	that	SCONJ
ejpam-6433	34	16	every	every	DET
ejpam-6433	34	17	nonempty	nonempty	ADJ
ejpam-6433	34	18	,	,	PUNCT
ejpam-6433	34	19	compact	compact	ADJ
ejpam-6433	34	20	and	and	CCONJ
ejpam-6433	34	21	convex	convex	ADJ
ejpam-6433	34	22	pair	pair	NOUN
ejpam-6433	34	23	of	of	ADP
ejpam-6433	34	24	subsets	subset	NOUN
ejpam-6433	34	25	of	of	ADP
ejpam-6433	34	26	a	a	DET
ejpam-6433	34	27	banach	banach	NOUN
ejpam-6433	34	28	space	space	NOUN
ejpam-6433	34	29	x	x	PRON
ejpam-6433	34	30	has	have	AUX
ejpam-6433	34	31	the	the	DET
ejpam-6433	34	32	proximal	proximal	ADJ
ejpam-6433	34	33	normal	normal	ADJ
ejpam-6433	34	34	structure	structure	NOUN
ejpam-6433	34	35	(	(	PUNCT
ejpam-6433	34	36	see	see	VERB
ejpam-6433	34	37	proposition	proposition	NOUN
ejpam-6433	34	38	2.2	2.2	NUM
ejpam-6433	34	39	and	and	CCONJ
ejpam-6433	34	40	theorem	theorem	VERB
ejpam-6433	34	41	2.1	2.1	NUM
ejpam-6433	34	42	of	of	ADP
ejpam-6433	34	43	[	[	X
ejpam-6433	34	44	1	1	NUM
ejpam-6433	34	45	]	]	NUM
ejpam-6433	34	46	)	)	PUNCT
ejpam-6433	34	47	.	.	PUNCT
ejpam-6433	35	1	another	another	DET
ejpam-6433	35	2	way	way	NOUN
ejpam-6433	35	3	to	to	PART
ejpam-6433	35	4	prove	prove	VERB
ejpam-6433	35	5	theorem	theorem	VERB
ejpam-6433	35	6	1	1	NUM
ejpam-6433	35	7	was	be	AUX
ejpam-6433	35	8	presented	present	VERB
ejpam-6433	35	9	in	in	ADP
ejpam-6433	35	10	[	[	X
ejpam-6433	35	11	5	5	NUM
ejpam-6433	35	12	]	]	PUNCT
ejpam-6433	35	13	by	by	ADP
ejpam-6433	35	14	applying	apply	VERB
ejpam-6433	35	15	a	a	DET
ejpam-6433	35	16	concept	concept	NOUN
ejpam-6433	35	17	of	of	ADP
ejpam-6433	35	18	proximal	proximal	ADJ
ejpam-6433	35	19	diametral	diametral	ADJ
ejpam-6433	35	20	sequences	sequence	NOUN
ejpam-6433	35	21	.	.	PUNCT
ejpam-6433	36	1	in	in	ADP
ejpam-6433	36	2	order	order	NOUN
ejpam-6433	36	3	to	to	PART
ejpam-6433	36	4	state	state	VERB
ejpam-6433	36	5	the	the	DET
ejpam-6433	36	6	noncyclic	noncyclic	ADJ
ejpam-6433	36	7	version	version	NOUN
ejpam-6433	36	8	of	of	ADP
ejpam-6433	36	9	theorem	theorem	NOUN
ejpam-6433	36	10	1	1	NUM
ejpam-6433	36	11	we	we	PRON
ejpam-6433	36	12	need	need	VERB
ejpam-6433	36	13	to	to	PART
ejpam-6433	36	14	recall	recall	VERB
ejpam-6433	36	15	that	that	SCONJ
ejpam-6433	36	16	a	a	DET
ejpam-6433	36	17	banach	banach	NOUN
ejpam-6433	36	18	space	space	NOUN
ejpam-6433	36	19	x	x	PUNCT
ejpam-6433	36	20	is	be	AUX
ejpam-6433	36	21	strictly	strictly	ADV
ejpam-6433	36	22	convex	convex	ADJ
ejpam-6433	36	23	if	if	SCONJ
ejpam-6433	36	24	for	for	ADP
ejpam-6433	36	25	any	any	DET
ejpam-6433	36	26	two	two	NUM
ejpam-6433	36	27	distinct	distinct	ADJ
ejpam-6433	36	28	elements	element	NOUN
ejpam-6433	36	29	u	u	NOUN
ejpam-6433	36	30	,	,	PUNCT
ejpam-6433	36	31	v	v	PROPN
ejpam-6433	36	32	∈	∈	PROPN
ejpam-6433	36	33	sx	sx	NOUN
ejpam-6433	36	34	:	:	PUNCT
ejpam-6433	36	35	=	=	SYM
ejpam-6433	36	36	{	{	PUNCT
ejpam-6433	36	37	x	x	PUNCT
ejpam-6433	36	38	∈	∈	NOUN
ejpam-6433	36	39	x	x	X
ejpam-6433	36	40	:	:	PUNCT
ejpam-6433	36	41	∥x∥	∥x∥	NOUN
ejpam-6433	36	42	=	=	NOUN
ejpam-6433	36	43	1	1	X
ejpam-6433	36	44	}	}	PUNCT
ejpam-6433	36	45	we	we	PRON
ejpam-6433	36	46	have	have	VERB
ejpam-6433	36	47	∥u+v	∥u+v	NOUN
ejpam-6433	36	48	2	2	NUM
ejpam-6433	36	49	∥	∥	NOUN
ejpam-6433	36	50	<	<	X
ejpam-6433	37	1	1	1	X
ejpam-6433	37	2	.	.	PUNCT
ejpam-6433	37	3	hilbert	hilbert	PROPN
ejpam-6433	37	4	and	and	CCONJ
ejpam-6433	37	5	lp(1	lp(1	X
ejpam-6433	37	6	<	<	X
ejpam-6433	37	7	p	p	X
ejpam-6433	37	8	<	<	X
ejpam-6433	37	9	+	+	PROPN
ejpam-6433	37	10	∞	∞	NOUN
ejpam-6433	37	11	)	)	PUNCT
ejpam-6433	37	12	spaces	space	NOUN
ejpam-6433	37	13	are	be	AUX
ejpam-6433	37	14	instances	instance	NOUN
ejpam-6433	37	15	of	of	ADP
ejpam-6433	37	16	strictly	strictly	ADV
ejpam-6433	37	17	convex	convex	ADJ
ejpam-6433	37	18	banach	banach	NOUN
ejpam-6433	37	19	spaces	space	NOUN
ejpam-6433	37	20	.	.	PUNCT
ejpam-6433	38	1	theorem	theorem	NOUN
ejpam-6433	38	2	2	2	NUM
ejpam-6433	38	3	.	.	PUNCT
ejpam-6433	39	1	(	(	PUNCT
ejpam-6433	39	2	see	see	VERB
ejpam-6433	39	3	theorem	theorem	VERB
ejpam-6433	39	4	2.2	2.2	NUM
ejpam-6433	39	5	of	of	ADP
ejpam-6433	39	6	[	[	X
ejpam-6433	39	7	1	1	NUM
ejpam-6433	39	8	]	]	PUNCT
ejpam-6433	39	9	)	)	PUNCT
ejpam-6433	39	10	let	let	VERB
ejpam-6433	39	11	(	(	PUNCT
ejpam-6433	39	12	g	g	NOUN
ejpam-6433	39	13	,	,	PUNCT
ejpam-6433	39	14	h	h	NOUN
ejpam-6433	39	15	)	)	PUNCT
ejpam-6433	39	16	be	be	AUX
ejpam-6433	39	17	a	a	DET
ejpam-6433	39	18	nonempty	nonempty	ADJ
ejpam-6433	39	19	,	,	PUNCT
ejpam-6433	39	20	compact	compact	ADJ
ejpam-6433	39	21	and	and	CCONJ
ejpam-6433	39	22	convex	convex	ADJ
ejpam-6433	39	23	pair	pair	NOUN
ejpam-6433	39	24	of	of	ADP
ejpam-6433	39	25	subsets	subset	NOUN
ejpam-6433	39	26	of	of	ADP
ejpam-6433	39	27	a	a	DET
ejpam-6433	39	28	strictly	strictly	ADV
ejpam-6433	39	29	convex	convex	ADJ
ejpam-6433	39	30	banach	banach	NOUN
ejpam-6433	39	31	space	space	NOUN
ejpam-6433	39	32	x.	x.	NOUN
ejpam-6433	40	1	if	if	SCONJ
ejpam-6433	40	2	t	t	PROPN
ejpam-6433	40	3	:	:	PUNCT
ejpam-6433	40	4	g	g	PROPN
ejpam-6433	40	5	∪	∪	ADJ
ejpam-6433	40	6	h	h	NOUN
ejpam-6433	40	7	→	→	SYM
ejpam-6433	40	8	g	g	PROPN
ejpam-6433	40	9	∪	∪	NOUN
ejpam-6433	40	10	h	h	NOUN
ejpam-6433	40	11	is	be	AUX
ejpam-6433	40	12	a	a	DET
ejpam-6433	40	13	noncyclic	noncyclic	ADJ
ejpam-6433	40	14	relatively	relatively	ADV
ejpam-6433	40	15	nonexpansive	nonexpansive	ADJ
ejpam-6433	40	16	mapping	mapping	NOUN
ejpam-6433	40	17	,	,	PUNCT
ejpam-6433	40	18	then	then	ADV
ejpam-6433	40	19	t	t	PROPN
ejpam-6433	40	20	has	have	VERB
ejpam-6433	40	21	a	a	DET
ejpam-6433	40	22	best	good	ADJ
ejpam-6433	40	23	proximity	proximity	NOUN
ejpam-6433	40	24	pair	pair	NOUN
ejpam-6433	40	25	.	.	PUNCT
ejpam-6433	41	1	it	it	PRON
ejpam-6433	41	2	was	be	AUX
ejpam-6433	41	3	announced	announce	VERB
ejpam-6433	41	4	in	in	ADP
ejpam-6433	41	5	[	[	X
ejpam-6433	41	6	6	6	NUM
ejpam-6433	41	7	]	]	PUNCT
ejpam-6433	41	8	that	that	SCONJ
ejpam-6433	41	9	if	if	SCONJ
ejpam-6433	41	10	the	the	DET
ejpam-6433	41	11	banach	banach	NOUN
ejpam-6433	41	12	space	space	NOUN
ejpam-6433	41	13	x	x	PUNCT
ejpam-6433	41	14	in	in	ADP
ejpam-6433	41	15	theorem	theorem	NOUN
ejpam-6433	41	16	1	1	NUM
ejpam-6433	41	17	is	be	AUX
ejpam-6433	41	18	strictly	strictly	ADV
ejpam-6433	41	19	convex	convex	ADJ
ejpam-6433	41	20	,	,	PUNCT
ejpam-6433	41	21	then	then	ADV
ejpam-6433	41	22	theorem	theorem	VERB
ejpam-6433	41	23	1	1	NUM
ejpam-6433	41	24	is	be	AUX
ejpam-6433	41	25	a	a	DET
ejpam-6433	41	26	special	special	ADJ
ejpam-6433	41	27	case	case	NOUN
ejpam-6433	41	28	of	of	ADP
ejpam-6433	41	29	theorem	theorem	NOUN
ejpam-6433	41	30	2	2	NUM
ejpam-6433	41	31	.	.	PUNCT
ejpam-6433	42	1	in	in	ADP
ejpam-6433	42	2	what	what	PRON
ejpam-6433	42	3	follows	follow	VERB
ejpam-6433	42	4	we	we	PRON
ejpam-6433	42	5	recall	recall	VERB
ejpam-6433	42	6	the	the	DET
ejpam-6433	42	7	extensions	extension	NOUN
ejpam-6433	42	8	of	of	ADP
ejpam-6433	42	9	theorem	theorem	ADJ
ejpam-6433	42	10	1	1	NUM
ejpam-6433	42	11	and	and	CCONJ
ejpam-6433	42	12	theorem	theorem	VERB
ejpam-6433	42	13	2	2	NUM
ejpam-6433	42	14	to	to	ADP
ejpam-6433	42	15	a	a	DET
ejpam-6433	42	16	more	more	ADV
ejpam-6433	42	17	extensive	extensive	ADJ
ejpam-6433	42	18	family	family	NOUN
ejpam-6433	42	19	of	of	ADP
ejpam-6433	42	20	cyclic	cyclic	PROPN
ejpam-6433	42	21	(	(	PUNCT
ejpam-6433	42	22	noncyclic	noncyclic	NOUN
ejpam-6433	42	23	)	)	PUNCT
ejpam-6433	42	24	relatively	relatively	ADV
ejpam-6433	42	25	nonexpansive	nonexpansive	ADJ
ejpam-6433	42	26	mappings	mapping	NOUN
ejpam-6433	42	27	.	.	PUNCT
ejpam-6433	43	1	definition	definition	NOUN
ejpam-6433	43	2	1	1	NUM
ejpam-6433	43	3	.	.	PUNCT
ejpam-6433	44	1	(	(	PUNCT
ejpam-6433	44	2	[	[	X
ejpam-6433	44	3	7	7	NUM
ejpam-6433	44	4	]	]	PUNCT
ejpam-6433	44	5	)	)	PUNCT
ejpam-6433	44	6	let	let	VERB
ejpam-6433	44	7	(	(	PUNCT
ejpam-6433	44	8	g	g	NOUN
ejpam-6433	44	9	,	,	PUNCT
ejpam-6433	44	10	h	h	NOUN
ejpam-6433	44	11	)	)	PUNCT
ejpam-6433	44	12	be	be	VERB
ejpam-6433	44	13	a	a	DET
ejpam-6433	44	14	nonempty	nonempty	ADJ
ejpam-6433	44	15	pair	pair	NOUN
ejpam-6433	44	16	in	in	ADP
ejpam-6433	44	17	a	a	DET
ejpam-6433	44	18	metric	metric	ADJ
ejpam-6433	44	19	space	space	NOUN
ejpam-6433	44	20	(	(	PUNCT
ejpam-6433	44	21	m	m	PROPN
ejpam-6433	44	22	,	,	PUNCT
ejpam-6433	44	23	d	d	NOUN
ejpam-6433	44	24	)	)	PUNCT
ejpam-6433	44	25	.	.	PUNCT
ejpam-6433	45	1	a	a	DET
ejpam-6433	45	2	mapping	mapping	NOUN
ejpam-6433	45	3	t	t	NOUN
ejpam-6433	45	4	:	:	PUNCT
ejpam-6433	45	5	g	g	PROPN
ejpam-6433	45	6	∪	∪	ADJ
ejpam-6433	45	7	h	h	NOUN
ejpam-6433	45	8	→	→	SYM
ejpam-6433	45	9	g	g	NOUN
ejpam-6433	45	10	∪	∪	ADJ
ejpam-6433	45	11	h	h	NOUN
ejpam-6433	45	12	is	be	AUX
ejpam-6433	45	13	called	call	VERB
ejpam-6433	45	14	relatively	relatively	ADV
ejpam-6433	45	15	u	u	NOUN
ejpam-6433	45	16	-	-	NOUN
ejpam-6433	45	17	continuous	continuous	ADJ
ejpam-6433	45	18	if	if	SCONJ
ejpam-6433	45	19	for	for	ADP
ejpam-6433	45	20	each	each	DET
ejpam-6433	45	21	ε	ε	PROPN
ejpam-6433	45	22	>	>	X
ejpam-6433	45	23	0	0	PUNCT
ejpam-6433	46	1	there	there	PRON
ejpam-6433	46	2	exists	exist	VERB
ejpam-6433	46	3	δ	δ	PROPN
ejpam-6433	46	4	>	>	X
ejpam-6433	46	5	0	0	NUM
ejpam-6433	47	1	such	such	ADJ
ejpam-6433	47	2	that	that	SCONJ
ejpam-6433	47	3	d(tx	d(tx	PROPN
ejpam-6433	47	4	,	,	PUNCT
ejpam-6433	47	5	ty	ty	NOUN
ejpam-6433	47	6	)	)	PUNCT
ejpam-6433	47	7	<	<	X
ejpam-6433	47	8	ε+d(g	ε+d(g	SYM
ejpam-6433	47	9	,	,	PUNCT
ejpam-6433	47	10	h	h	NOUN
ejpam-6433	47	11	)	)	PUNCT
ejpam-6433	47	12	,	,	PUNCT
ejpam-6433	47	13	whenever	whenever	SCONJ
ejpam-6433	47	14	d(x	d(x	PROPN
ejpam-6433	47	15	,	,	PUNCT
ejpam-6433	47	16	y	y	NOUN
ejpam-6433	47	17	)	)	PUNCT
ejpam-6433	47	18	<	<	X
ejpam-6433	47	19	δ+d(g	δ+d(g	PROPN
ejpam-6433	47	20	,	,	PUNCT
ejpam-6433	47	21	h	h	NOUN
ejpam-6433	47	22	)	)	PUNCT
ejpam-6433	47	23	,	,	PUNCT
ejpam-6433	47	24	for	for	ADP
ejpam-6433	47	25	all	all	DET
ejpam-6433	47	26	(	(	PUNCT
ejpam-6433	47	27	x	x	NOUN
ejpam-6433	47	28	,	,	PUNCT
ejpam-6433	47	29	y	y	NOUN
ejpam-6433	47	30	)	)	PUNCT
ejpam-6433	47	31	∈	∈	PROPN
ejpam-6433	47	32	g×h	g×h	PROPN
ejpam-6433	47	33	.	.	PUNCT
ejpam-6433	48	1	if	if	SCONJ
ejpam-6433	48	2	moreover	moreover	ADV
ejpam-6433	48	3	,	,	PUNCT
ejpam-6433	48	4	t	t	PROPN
ejpam-6433	48	5	is	be	AUX
ejpam-6433	48	6	also	also	ADV
ejpam-6433	48	7	cyclic	cyclic	ADJ
ejpam-6433	48	8	(	(	PUNCT
ejpam-6433	48	9	noncyclic	noncyclic	NOUN
ejpam-6433	48	10	)	)	PUNCT
ejpam-6433	48	11	,	,	PUNCT
ejpam-6433	48	12	then	then	ADV
ejpam-6433	48	13	t	t	PROPN
ejpam-6433	48	14	is	be	AUX
ejpam-6433	48	15	said	say	VERB
ejpam-6433	48	16	to	to	PART
ejpam-6433	48	17	be	be	AUX
ejpam-6433	48	18	cyclic	cyclic	ADJ
ejpam-6433	48	19	(	(	PUNCT
ejpam-6433	48	20	noncyclic	noncyclic	NOUN
ejpam-6433	48	21	)	)	PUNCT
ejpam-6433	48	22	relatively	relatively	ADV
ejpam-6433	48	23	u	u	NOUN
ejpam-6433	48	24	-	-	ADJ
ejpam-6433	48	25	continuous	continuous	ADJ
ejpam-6433	48	26	.	.	PUNCT
ejpam-6433	48	27	m.	m.	NOUN
ejpam-6433	48	28	gabeleh	gabeleh	PROPN
ejpam-6433	48	29	,	,	PUNCT
ejpam-6433	48	30	j.	j.	PROPN
ejpam-6433	48	31	markin	markin	PROPN
ejpam-6433	48	32	,	,	PUNCT
ejpam-6433	48	33	m.	m.	NOUN
ejpam-6433	48	34	aphane	aphane	PROPN
ejpam-6433	48	35	/	/	SYM
ejpam-6433	48	36	eur	eur	PROPN
ejpam-6433	48	37	.	.	PUNCT
ejpam-6433	49	1	j.	j.	PROPN
ejpam-6433	49	2	pure	pure	PROPN
ejpam-6433	49	3	appl	appl	PROPN
ejpam-6433	49	4	.	.	PROPN
ejpam-6433	49	5	math	math	PROPN
ejpam-6433	49	6	,	,	PUNCT
ejpam-6433	49	7	18	18	NUM
ejpam-6433	49	8	(	(	PUNCT
ejpam-6433	49	9	3	3	NUM
ejpam-6433	49	10	)	)	PUNCT
ejpam-6433	49	11	(	(	PUNCT
ejpam-6433	49	12	2025	2025	NUM
ejpam-6433	49	13	)	)	PUNCT
ejpam-6433	49	14	,	,	PUNCT
ejpam-6433	49	15	6433	6433	NUM
ejpam-6433	49	16	3	3	NUM
ejpam-6433	49	17	of	of	ADP
ejpam-6433	49	18	17	17	NUM
ejpam-6433	49	19	clearly	clearly	ADV
ejpam-6433	49	20	,	,	PUNCT
ejpam-6433	49	21	every	every	DET
ejpam-6433	49	22	relatively	relatively	ADV
ejpam-6433	49	23	nonexpansive	nonexpansive	ADJ
ejpam-6433	49	24	map	map	NOUN
ejpam-6433	49	25	is	be	AUX
ejpam-6433	49	26	relatively	relatively	ADV
ejpam-6433	49	27	u	u	NOUN
ejpam-6433	49	28	-	-	ADJ
ejpam-6433	49	29	continuous	continuous	ADJ
ejpam-6433	49	30	,	,	PUNCT
ejpam-6433	49	31	but	but	CCONJ
ejpam-6433	49	32	the	the	DET
ejpam-6433	49	33	inverse	inverse	NOUN
ejpam-6433	49	34	implication	implication	NOUN
ejpam-6433	49	35	may	may	AUX
ejpam-6433	49	36	not	not	PART
ejpam-6433	49	37	be	be	AUX
ejpam-6433	49	38	hold	hold	NOUN
ejpam-6433	49	39	(	(	PUNCT
ejpam-6433	49	40	see	see	VERB
ejpam-6433	49	41	example	example	NOUN
ejpam-6433	49	42	2.1	2.1	NUM
ejpam-6433	49	43	of	of	ADP
ejpam-6433	49	44	[	[	X
ejpam-6433	49	45	7	7	NUM
ejpam-6433	49	46	]	]	NUM
ejpam-6433	49	47	)	)	PUNCT
ejpam-6433	49	48	.	.	PUNCT
ejpam-6433	50	1	theorem	theorem	NOUN
ejpam-6433	50	2	3	3	NUM
ejpam-6433	50	3	.	.	PUNCT
ejpam-6433	51	1	(	(	PUNCT
ejpam-6433	51	2	theorem	theorem	VERB
ejpam-6433	51	3	3.1	3.1	NUM
ejpam-6433	51	4	of	of	ADP
ejpam-6433	51	5	[	[	X
ejpam-6433	51	6	7	7	NUM
ejpam-6433	51	7	]	]	PUNCT
ejpam-6433	51	8	)	)	PUNCT
ejpam-6433	51	9	let	let	VERB
ejpam-6433	51	10	(	(	PUNCT
ejpam-6433	51	11	g	g	NOUN
ejpam-6433	51	12	,	,	PUNCT
ejpam-6433	51	13	h	h	NOUN
ejpam-6433	51	14	)	)	PUNCT
ejpam-6433	51	15	be	be	AUX
ejpam-6433	51	16	a	a	DET
ejpam-6433	51	17	nonempty	nonempty	ADJ
ejpam-6433	51	18	,	,	PUNCT
ejpam-6433	51	19	compact	compact	ADJ
ejpam-6433	51	20	and	and	CCONJ
ejpam-6433	51	21	convex	convex	ADJ
ejpam-6433	51	22	pair	pair	NOUN
ejpam-6433	51	23	of	of	ADP
ejpam-6433	51	24	subsets	subset	NOUN
ejpam-6433	51	25	of	of	ADP
ejpam-6433	51	26	a	a	DET
ejpam-6433	51	27	strictly	strictly	ADV
ejpam-6433	51	28	convex	convex	ADJ
ejpam-6433	51	29	banach	banach	NOUN
ejpam-6433	51	30	space	space	NOUN
ejpam-6433	51	31	x.	x.	NOUN
ejpam-6433	52	1	if	if	SCONJ
ejpam-6433	52	2	t	t	PROPN
ejpam-6433	52	3	:	:	PUNCT
ejpam-6433	52	4	g	g	PROPN
ejpam-6433	52	5	∪	∪	ADJ
ejpam-6433	52	6	h	h	NOUN
ejpam-6433	52	7	→	→	SYM
ejpam-6433	52	8	g	g	PROPN
ejpam-6433	52	9	∪	∪	NOUN
ejpam-6433	52	10	h	h	NOUN
ejpam-6433	52	11	is	be	AUX
ejpam-6433	52	12	a	a	DET
ejpam-6433	52	13	cyclic	cyclic	ADJ
ejpam-6433	52	14	relatively	relatively	ADV
ejpam-6433	52	15	u	u	ADJ
ejpam-6433	52	16	-	-	ADJ
ejpam-6433	52	17	continuous	continuous	ADJ
ejpam-6433	52	18	mapping	mapping	NOUN
ejpam-6433	52	19	,	,	PUNCT
ejpam-6433	52	20	then	then	ADV
ejpam-6433	52	21	t	t	PROPN
ejpam-6433	52	22	has	have	VERB
ejpam-6433	52	23	a	a	DET
ejpam-6433	52	24	best	good	ADJ
ejpam-6433	52	25	proximity	proximity	NOUN
ejpam-6433	52	26	point	point	NOUN
ejpam-6433	52	27	.	.	PUNCT
ejpam-6433	53	1	the	the	DET
ejpam-6433	53	2	noncyclic	noncyclic	PROPN
ejpam-6433	53	3	version	version	NOUN
ejpam-6433	53	4	of	of	ADP
ejpam-6433	53	5	theorem	theorem	NOUN
ejpam-6433	53	6	3	3	NUM
ejpam-6433	53	7	is	be	AUX
ejpam-6433	53	8	as	as	SCONJ
ejpam-6433	53	9	follows	follow	VERB
ejpam-6433	53	10	.	.	PUNCT
ejpam-6433	54	1	theorem	theorem	ADJ
ejpam-6433	54	2	4	4	NUM
ejpam-6433	54	3	.	.	PUNCT
ejpam-6433	55	1	(	(	PUNCT
ejpam-6433	55	2	theorem	theorem	VERB
ejpam-6433	55	3	4.2	4.2	NUM
ejpam-6433	55	4	of	of	ADP
ejpam-6433	55	5	[	[	X
ejpam-6433	55	6	8	8	NUM
ejpam-6433	55	7	]	]	PUNCT
ejpam-6433	55	8	)	)	PUNCT
ejpam-6433	55	9	let	let	VERB
ejpam-6433	55	10	(	(	PUNCT
ejpam-6433	55	11	g	g	NOUN
ejpam-6433	55	12	,	,	PUNCT
ejpam-6433	55	13	h	h	NOUN
ejpam-6433	55	14	)	)	PUNCT
ejpam-6433	55	15	be	be	AUX
ejpam-6433	55	16	a	a	DET
ejpam-6433	55	17	nonempty	nonempty	ADJ
ejpam-6433	55	18	,	,	PUNCT
ejpam-6433	55	19	compact	compact	ADJ
ejpam-6433	55	20	and	and	CCONJ
ejpam-6433	55	21	convex	convex	ADJ
ejpam-6433	55	22	pair	pair	NOUN
ejpam-6433	55	23	of	of	ADP
ejpam-6433	55	24	subsets	subset	NOUN
ejpam-6433	55	25	of	of	ADP
ejpam-6433	55	26	a	a	DET
ejpam-6433	55	27	strictly	strictly	ADV
ejpam-6433	55	28	convex	convex	ADJ
ejpam-6433	55	29	banach	banach	NOUN
ejpam-6433	55	30	space	space	NOUN
ejpam-6433	55	31	x.	x.	NOUN
ejpam-6433	56	1	if	if	SCONJ
ejpam-6433	56	2	t	t	PROPN
ejpam-6433	56	3	:	:	PUNCT
ejpam-6433	56	4	g∪h	g∪h	NOUN
ejpam-6433	56	5	→	→	SYM
ejpam-6433	56	6	g∪h	g∪h	NOUN
ejpam-6433	56	7	is	be	AUX
ejpam-6433	56	8	a	a	DET
ejpam-6433	56	9	noncyclic	noncyclic	ADJ
ejpam-6433	56	10	relatively	relatively	ADV
ejpam-6433	56	11	u	u	ADJ
ejpam-6433	56	12	-	-	ADJ
ejpam-6433	56	13	continuous	continuous	ADJ
ejpam-6433	56	14	mapping	mapping	NOUN
ejpam-6433	56	15	,	,	PUNCT
ejpam-6433	56	16	then	then	ADV
ejpam-6433	56	17	t	t	PROPN
ejpam-6433	56	18	has	have	VERB
ejpam-6433	56	19	a	a	DET
ejpam-6433	56	20	best	good	ADJ
ejpam-6433	56	21	proximity	proximity	NOUN
ejpam-6433	56	22	pair	pair	NOUN
ejpam-6433	56	23	.	.	PUNCT
ejpam-6433	57	1	motivated	motivate	VERB
ejpam-6433	57	2	by	by	ADP
ejpam-6433	57	3	schauder	schauder	PROPN
ejpam-6433	57	4	’s	’s	PART
ejpam-6433	57	5	fixed	fix	VERB
ejpam-6433	57	6	point	point	NOUN
ejpam-6433	57	7	problem	problem	NOUN
ejpam-6433	57	8	for	for	ADP
ejpam-6433	57	9	compact	compact	ADJ
ejpam-6433	57	10	and	and	CCONJ
ejpam-6433	57	11	continuous	continuous	ADJ
ejpam-6433	57	12	self	self	NOUN
ejpam-6433	57	13	-	-	PUNCT
ejpam-6433	57	14	mappings	mapping	NOUN
ejpam-6433	57	15	defined	define	VERB
ejpam-6433	57	16	on	on	ADP
ejpam-6433	57	17	a	a	DET
ejpam-6433	57	18	bounded	bound	VERB
ejpam-6433	57	19	,	,	PUNCT
ejpam-6433	57	20	closed	closed	ADJ
ejpam-6433	57	21	and	and	CCONJ
ejpam-6433	57	22	convex	convex	PROPN
ejpam-6433	57	23	subset	subset	NOUN
ejpam-6433	57	24	of	of	ADP
ejpam-6433	57	25	a	a	DET
ejpam-6433	57	26	banach	banach	NOUN
ejpam-6433	57	27	space	space	NOUN
ejpam-6433	57	28	,	,	PUNCT
ejpam-6433	57	29	the	the	DET
ejpam-6433	57	30	current	current	ADJ
ejpam-6433	57	31	authors	author	NOUN
ejpam-6433	57	32	presented	present	VERB
ejpam-6433	57	33	the	the	DET
ejpam-6433	57	34	extensions	extension	NOUN
ejpam-6433	57	35	of	of	ADP
ejpam-6433	57	36	theorem	theorem	ADJ
ejpam-6433	57	37	1	1	NUM
ejpam-6433	57	38	and	and	CCONJ
ejpam-6433	57	39	theorem	theorem	VERB
ejpam-6433	57	40	2	2	NUM
ejpam-6433	57	41	by	by	ADP
ejpam-6433	57	42	shifting	shift	VERB
ejpam-6433	57	43	the	the	DET
ejpam-6433	57	44	compactness	compactness	NOUN
ejpam-6433	57	45	assumption	assumption	NOUN
ejpam-6433	57	46	on	on	ADP
ejpam-6433	57	47	the	the	DET
ejpam-6433	57	48	pair	pair	NOUN
ejpam-6433	57	49	(	(	PUNCT
ejpam-6433	57	50	g	g	NOUN
ejpam-6433	57	51	,	,	PUNCT
ejpam-6433	57	52	h	h	NOUN
ejpam-6433	57	53	)	)	PUNCT
ejpam-6433	57	54	to	to	ADP
ejpam-6433	57	55	the	the	DET
ejpam-6433	57	56	cyclic	cyclic	ADJ
ejpam-6433	57	57	(	(	PUNCT
ejpam-6433	57	58	noncyclic	noncyclic	NOUN
ejpam-6433	57	59	)	)	PUNCT
ejpam-6433	57	60	mapping	mapping	NOUN
ejpam-6433	57	61	t	t	NOUN
ejpam-6433	57	62	which	which	PRON
ejpam-6433	57	63	may	may	AUX
ejpam-6433	57	64	not	not	PART
ejpam-6433	57	65	be	be	AUX
ejpam-6433	57	66	continuous	continuous	ADJ
ejpam-6433	57	67	(	(	PUNCT
ejpam-6433	57	68	see	see	NOUN
ejpam-6433	57	69	theorem	theorem	ADJ
ejpam-6433	57	70	3.2	3.2	NUM
ejpam-6433	57	71	and	and	CCONJ
ejpam-6433	57	72	theorem	theorem	VERB
ejpam-6433	57	73	4.1	4.1	NUM
ejpam-6433	57	74	of	of	ADP
ejpam-6433	57	75	[	[	X
ejpam-6433	57	76	9	9	NUM
ejpam-6433	57	77	]	]	NUM
ejpam-6433	57	78	)	)	PUNCT
ejpam-6433	57	79	.	.	PUNCT
ejpam-6433	58	1	indeed	indeed	ADV
ejpam-6433	58	2	,	,	PUNCT
ejpam-6433	58	3	the	the	DET
ejpam-6433	58	4	cyclic	cyclic	ADJ
ejpam-6433	58	5	(	(	PUNCT
ejpam-6433	58	6	noncyclic	noncyclic	NOUN
ejpam-6433	58	7	)	)	PUNCT
ejpam-6433	58	8	mapping	mapping	NOUN
ejpam-6433	58	9	t	t	NOUN
ejpam-6433	58	10	:	:	PUNCT
ejpam-6433	58	11	g	g	PROPN
ejpam-6433	58	12	∪h	∪h	NUM
ejpam-6433	58	13	→	→	SYM
ejpam-6433	58	14	g	g	NOUN
ejpam-6433	58	15	∪h	∪h	NUM
ejpam-6433	58	16	is	be	AUX
ejpam-6433	58	17	said	say	VERB
ejpam-6433	58	18	to	to	PART
ejpam-6433	58	19	be	be	AUX
ejpam-6433	58	20	compact	compact	ADJ
ejpam-6433	58	21	whenever	whenever	SCONJ
ejpam-6433	58	22	(	(	PUNCT
ejpam-6433	58	23	t	t	PROPN
ejpam-6433	58	24	(	(	PUNCT
ejpam-6433	58	25	k	k	NOUN
ejpam-6433	58	26	)	)	PUNCT
ejpam-6433	58	27	,	,	PUNCT
ejpam-6433	58	28	t	t	PROPN
ejpam-6433	58	29	(	(	PUNCT
ejpam-6433	58	30	l	l	NOUN
ejpam-6433	58	31	)	)	PUNCT
ejpam-6433	58	32	)	)	PUNCT
ejpam-6433	58	33	is	be	AUX
ejpam-6433	58	34	relatively	relatively	ADV
ejpam-6433	58	35	compact	compact	ADJ
ejpam-6433	58	36	for	for	ADP
ejpam-6433	58	37	any	any	DET
ejpam-6433	58	38	bounded	bounded	ADJ
ejpam-6433	58	39	pair	pair	NOUN
ejpam-6433	58	40	(	(	PUNCT
ejpam-6433	58	41	k	k	NOUN
ejpam-6433	58	42	,	,	PUNCT
ejpam-6433	58	43	l	l	NOUN
ejpam-6433	58	44	)	)	PUNCT
ejpam-6433	58	45	⊆	⊆	NUM
ejpam-6433	58	46	(	(	PUNCT
ejpam-6433	58	47	g	g	NOUN
ejpam-6433	58	48	,	,	PUNCT
ejpam-6433	58	49	h	h	NOUN
ejpam-6433	58	50	)	)	PUNCT
ejpam-6433	58	51	.	.	PUNCT
ejpam-6433	59	1	gabeleh	gabeleh	NOUN
ejpam-6433	59	2	and	and	CCONJ
ejpam-6433	59	3	vetro	vetro	VERB
ejpam-6433	59	4	(	(	PUNCT
ejpam-6433	59	5	[	[	X
ejpam-6433	59	6	10	10	NUM
ejpam-6433	59	7	]	]	PUNCT
ejpam-6433	59	8	)	)	PUNCT
ejpam-6433	59	9	generalized	generalize	VERB
ejpam-6433	59	10	the	the	DET
ejpam-6433	59	11	aforesaid	aforesaid	NOUN
ejpam-6433	59	12	results	result	NOUN
ejpam-6433	59	13	by	by	ADP
ejpam-6433	59	14	relaxing	relax	VERB
ejpam-6433	59	15	the	the	DET
ejpam-6433	59	16	compactness	compactness	NOUN
ejpam-6433	59	17	assumption	assumption	NOUN
ejpam-6433	59	18	of	of	ADP
ejpam-6433	59	19	the	the	DET
ejpam-6433	59	20	cyclic	cyclic	ADJ
ejpam-6433	59	21	(	(	PUNCT
ejpam-6433	59	22	noncyclic	noncyclic	ADJ
ejpam-6433	59	23	)	)	PUNCT
ejpam-6433	59	24	mappings	mapping	NOUN
ejpam-6433	59	25	.	.	PUNCT
ejpam-6433	60	1	to	to	PART
ejpam-6433	60	2	state	state	VERB
ejpam-6433	60	3	their	their	PRON
ejpam-6433	60	4	main	main	ADJ
ejpam-6433	60	5	corollaries	corollary	NOUN
ejpam-6433	60	6	,	,	PUNCT
ejpam-6433	60	7	we	we	PRON
ejpam-6433	60	8	remind	remind	VERB
ejpam-6433	60	9	the	the	DET
ejpam-6433	60	10	reader	reader	NOUN
ejpam-6433	60	11	of	of	ADP
ejpam-6433	60	12	some	some	DET
ejpam-6433	60	13	requirements	requirement	NOUN
ejpam-6433	60	14	.	.	PUNCT
ejpam-6433	61	1	from	from	ADP
ejpam-6433	61	2	now	now	ADV
ejpam-6433	61	3	on	on	ADV
ejpam-6433	61	4	,	,	PUNCT
ejpam-6433	61	5	b(m	b(m	PROPN
ejpam-6433	61	6	)	)	PUNCT
ejpam-6433	61	7	denotes	denote	VERB
ejpam-6433	61	8	the	the	DET
ejpam-6433	61	9	family	family	NOUN
ejpam-6433	61	10	of	of	ADP
ejpam-6433	61	11	all	all	DET
ejpam-6433	61	12	nonempty	nonempty	ADJ
ejpam-6433	61	13	and	and	CCONJ
ejpam-6433	61	14	bounded	bounded	ADJ
ejpam-6433	61	15	subsets	subset	NOUN
ejpam-6433	61	16	of	of	ADP
ejpam-6433	61	17	m.	m.	NOUN
ejpam-6433	61	18	also	also	ADV
ejpam-6433	61	19	k(m	k(m	PROPN
ejpam-6433	61	20	)	)	PUNCT
ejpam-6433	61	21	displays	display	VERB
ejpam-6433	61	22	the	the	DET
ejpam-6433	61	23	family	family	NOUN
ejpam-6433	61	24	of	of	ADP
ejpam-6433	61	25	all	all	DET
ejpam-6433	61	26	nonempty	nonempty	ADJ
ejpam-6433	61	27	and	and	CCONJ
ejpam-6433	61	28	compact	compact	ADJ
ejpam-6433	61	29	subsets	subset	NOUN
ejpam-6433	61	30	of	of	ADP
ejpam-6433	61	31	m.	m.	NOUN
ejpam-6433	61	32	in	in	ADP
ejpam-6433	61	33	the	the	DET
ejpam-6433	61	34	case	case	NOUN
ejpam-6433	61	35	that	that	SCONJ
ejpam-6433	61	36	x	x	PRON
ejpam-6433	61	37	is	be	AUX
ejpam-6433	61	38	a	a	DET
ejpam-6433	61	39	banach	banach	NOUN
ejpam-6433	61	40	space	space	NOUN
ejpam-6433	61	41	,	,	PUNCT
ejpam-6433	61	42	we	we	PRON
ejpam-6433	61	43	use	use	VERB
ejpam-6433	61	44	bcc(x	bcc(x	NOUN
ejpam-6433	61	45	)	)	PUNCT
ejpam-6433	61	46	to	to	PART
ejpam-6433	61	47	denote	denote	VERB
ejpam-6433	61	48	the	the	DET
ejpam-6433	61	49	class	class	NOUN
ejpam-6433	61	50	of	of	ADP
ejpam-6433	61	51	all	all	DET
ejpam-6433	61	52	nonempty	nonempty	NOUN
ejpam-6433	61	53	,	,	PUNCT
ejpam-6433	61	54	bounded	bound	VERB
ejpam-6433	61	55	,	,	PUNCT
ejpam-6433	61	56	closed	closed	ADJ
ejpam-6433	61	57	and	and	CCONJ
ejpam-6433	61	58	convex	convex	ADJ
ejpam-6433	61	59	subsets	subset	NOUN
ejpam-6433	61	60	of	of	ADP
ejpam-6433	61	61	x.	x.	NOUN
ejpam-6433	61	62	definition	definition	NOUN
ejpam-6433	61	63	2	2	NUM
ejpam-6433	61	64	.	.	PUNCT
ejpam-6433	62	1	a	a	DET
ejpam-6433	62	2	measure	measure	NOUN
ejpam-6433	62	3	of	of	ADP
ejpam-6433	62	4	noncompactness	noncompactness	ADJ
ejpam-6433	62	5	(	(	PUNCT
ejpam-6433	62	6	mnc	mnc	PROPN
ejpam-6433	62	7	for	for	ADP
ejpam-6433	62	8	brief	brief	NOUN
ejpam-6433	62	9	)	)	PUNCT
ejpam-6433	62	10	is	be	AUX
ejpam-6433	62	11	a	a	DET
ejpam-6433	62	12	function	function	NOUN
ejpam-6433	62	13	ℵ	ℵ	NOUN
ejpam-6433	62	14	:	:	PUNCT
ejpam-6433	62	15	b(m	b(m	NOUN
ejpam-6433	62	16	)	)	PUNCT
ejpam-6433	62	17	→	→	PUNCT
ejpam-6433	63	1	[	[	X
ejpam-6433	63	2	0,+∞	0,+∞	NUM
ejpam-6433	63	3	)	)	PUNCT
ejpam-6433	63	4	satisfying	satisfy	VERB
ejpam-6433	63	5	the	the	DET
ejpam-6433	63	6	following	follow	VERB
ejpam-6433	63	7	axioms	axiom	NOUN
ejpam-6433	63	8	:	:	PUNCT
ejpam-6433	63	9	1	1	X
ejpam-6433	63	10	.	.	X
ejpam-6433	63	11	ℵ(g	ℵ(g	PROPN
ejpam-6433	63	12	)	)	PUNCT
ejpam-6433	64	1	=	=	PUNCT
ejpam-6433	64	2	0	0	PUNCT
ejpam-6433	65	1	if	if	SCONJ
ejpam-6433	65	2	and	and	CCONJ
ejpam-6433	65	3	only	only	ADV
ejpam-6433	65	4	if	if	SCONJ
ejpam-6433	65	5	g	g	PROPN
ejpam-6433	65	6	is	be	AUX
ejpam-6433	65	7	relatively	relatively	ADV
ejpam-6433	65	8	compact	compact	ADJ
ejpam-6433	65	9	,	,	PUNCT
ejpam-6433	65	10	2	2	NUM
ejpam-6433	65	11	.	.	PUNCT
ejpam-6433	65	12	ℵ(g	ℵ(g	PROPN
ejpam-6433	65	13	)	)	PUNCT
ejpam-6433	66	1	=	=	SYM
ejpam-6433	66	2	ℵ(g	ℵ(g	PROPN
ejpam-6433	66	3	)	)	PUNCT
ejpam-6433	66	4	,	,	PUNCT
ejpam-6433	66	5	g	g	PROPN
ejpam-6433	66	6	∈	∈	PROPN
ejpam-6433	66	7	b(x	b(x	NOUN
ejpam-6433	66	8	)	)	PUNCT
ejpam-6433	66	9	,	,	PUNCT
ejpam-6433	66	10	3	3	X
ejpam-6433	66	11	.	.	X
ejpam-6433	67	1	ℵ(g	ℵ(g	PROPN
ejpam-6433	67	2	∪	∪	PROPN
ejpam-6433	67	3	h	h	PROPN
ejpam-6433	67	4	)	)	PUNCT
ejpam-6433	67	5	=	=	SYM
ejpam-6433	67	6	max{ℵ(g),ℵ(h	max{ℵ(g),ℵ(h	PROPN
ejpam-6433	67	7	)	)	PUNCT
ejpam-6433	67	8	}	}	PUNCT
ejpam-6433	67	9	,	,	PUNCT
ejpam-6433	67	10	where	where	SCONJ
ejpam-6433	67	11	g	g	NOUN
ejpam-6433	67	12	,	,	PUNCT
ejpam-6433	67	13	h	h	PROPN
ejpam-6433	67	14	∈	∈	PROPN
ejpam-6433	67	15	b(m	b(m	PROPN
ejpam-6433	67	16	)	)	PUNCT
ejpam-6433	67	17	.	.	PUNCT
ejpam-6433	68	1	some	some	DET
ejpam-6433	68	2	useful	useful	ADJ
ejpam-6433	68	3	properties	property	NOUN
ejpam-6433	68	4	of	of	ADP
ejpam-6433	68	5	the	the	DET
ejpam-6433	68	6	mnc	mnc	PROPN
ejpam-6433	68	7	ℵ	ℵ	NOUN
ejpam-6433	68	8	on	on	ADP
ejpam-6433	68	9	b(m	b(m	NOUN
ejpam-6433	68	10	)	)	PUNCT
ejpam-6433	68	11	can	can	AUX
ejpam-6433	68	12	be	be	AUX
ejpam-6433	68	13	listed	list	VERB
ejpam-6433	68	14	as	as	ADP
ejpam-6433	68	15	below	below	ADV
ejpam-6433	68	16	(	(	PUNCT
ejpam-6433	68	17	see	see	VERB
ejpam-6433	68	18	[	[	X
ejpam-6433	68	19	11	11	NUM
ejpam-6433	68	20	]	]	PUNCT
ejpam-6433	68	21	for	for	ADP
ejpam-6433	68	22	more	more	ADJ
ejpam-6433	68	23	details	detail	NOUN
ejpam-6433	68	24	)	)	PUNCT
ejpam-6433	68	25	.	.	PUNCT
ejpam-6433	69	1	(	(	PUNCT
ejpam-6433	69	2	a	a	X
ejpam-6433	69	3	)	)	PUNCT
ejpam-6433	69	4	g	g	NOUN
ejpam-6433	69	5	⊆	⊆	NUM
ejpam-6433	69	6	h	h	NOUN
ejpam-6433	69	7	implies	imply	VERB
ejpam-6433	69	8	ℵ(g	ℵ(g	PROPN
ejpam-6433	69	9	)	)	PUNCT
ejpam-6433	69	10	≤	≤	NUM
ejpam-6433	69	11	ℵ(h	ℵ(h	PROPN
ejpam-6433	69	12	)	)	PUNCT
ejpam-6433	69	13	;	;	PUNCT
ejpam-6433	69	14	(	(	PUNCT
ejpam-6433	69	15	b	b	X
ejpam-6433	69	16	)	)	PUNCT
ejpam-6433	69	17	ℵ(g	ℵ(g	PROPN
ejpam-6433	69	18	∩	∩	ADJ
ejpam-6433	69	19	h	h	NOUN
ejpam-6433	69	20	)	)	PUNCT
ejpam-6433	69	21	≤	≤	NOUN
ejpam-6433	69	22	min{ℵ(g),ℵ(h	min{ℵ(g),ℵ(h	PROPN
ejpam-6433	69	23	)	)	PUNCT
ejpam-6433	69	24	}	}	PUNCT
ejpam-6433	69	25	,	,	PUNCT
ejpam-6433	69	26	for	for	ADP
ejpam-6433	69	27	all	all	DET
ejpam-6433	69	28	g	g	NOUN
ejpam-6433	69	29	,	,	PUNCT
ejpam-6433	69	30	h	h	PROPN
ejpam-6433	69	31	∈	∈	PROPN
ejpam-6433	69	32	b(m	b(m	PROPN
ejpam-6433	69	33	)	)	PUNCT
ejpam-6433	69	34	.	.	PUNCT
ejpam-6433	70	1	(	(	PUNCT
ejpam-6433	70	2	c	c	X
ejpam-6433	70	3	)	)	PUNCT
ejpam-6433	70	4	if	if	SCONJ
ejpam-6433	70	5	lim	lim	PROPN
ejpam-6433	70	6	n→+∞	n→+∞	VERB
ejpam-6433	70	7	ℵ(gn	ℵ(gn	NOUN
ejpam-6433	70	8	)	)	PUNCT
ejpam-6433	70	9	=	=	SYM
ejpam-6433	70	10	0	0	NUM
ejpam-6433	70	11	for	for	ADP
ejpam-6433	70	12	a	a	DET
ejpam-6433	70	13	nonincreasing	nonincrease	VERB
ejpam-6433	70	14	sequence	sequence	NOUN
ejpam-6433	70	15	{	{	PUNCT
ejpam-6433	70	16	gn	gn	NOUN
ejpam-6433	70	17	}	}	PUNCT
ejpam-6433	70	18	of	of	ADP
ejpam-6433	70	19	nonempty	nonempty	ADJ
ejpam-6433	70	20	,	,	PUNCT
ejpam-6433	70	21	bounded	bound	VERB
ejpam-6433	70	22	and	and	CCONJ
ejpam-6433	70	23	closed	closed	ADJ
ejpam-6433	70	24	subsets	subset	NOUN
ejpam-6433	70	25	of	of	ADP
ejpam-6433	70	26	m	m	PRON
ejpam-6433	70	27	,	,	PUNCT
ejpam-6433	70	28	then	then	ADV
ejpam-6433	70	29	g∞	g∞	VERB
ejpam-6433	70	30	:	:	PUNCT
ejpam-6433	70	31	=	=	SYM
ejpam-6433	70	32	⋂	⋂	PROPN
ejpam-6433	70	33	n≥1	n≥1	NOUN
ejpam-6433	70	34	gn	gn	PROPN
ejpam-6433	70	35	∈	∈	PROPN
ejpam-6433	70	36	k(m	k(m	PROPN
ejpam-6433	70	37	)	)	PUNCT
ejpam-6433	70	38	.	.	PUNCT
ejpam-6433	71	1	m.	m.	NOUN
ejpam-6433	71	2	gabeleh	gabeleh	PROPN
ejpam-6433	71	3	,	,	PUNCT
ejpam-6433	71	4	j.	j.	PROPN
ejpam-6433	71	5	markin	markin	PROPN
ejpam-6433	71	6	,	,	PUNCT
ejpam-6433	71	7	m.	m.	NOUN
ejpam-6433	71	8	aphane	aphane	PROPN
ejpam-6433	71	9	/	/	SYM
ejpam-6433	71	10	eur	eur	PROPN
ejpam-6433	71	11	.	.	PUNCT
ejpam-6433	72	1	j.	j.	PROPN
ejpam-6433	72	2	pure	pure	PROPN
ejpam-6433	72	3	appl	appl	PROPN
ejpam-6433	72	4	.	.	PROPN
ejpam-6433	72	5	math	math	PROPN
ejpam-6433	72	6	,	,	PUNCT
ejpam-6433	72	7	18	18	NUM
ejpam-6433	72	8	(	(	PUNCT
ejpam-6433	72	9	3	3	NUM
ejpam-6433	72	10	)	)	PUNCT
ejpam-6433	72	11	(	(	PUNCT
ejpam-6433	72	12	2025	2025	NUM
ejpam-6433	72	13	)	)	PUNCT
ejpam-6433	72	14	,	,	PUNCT
ejpam-6433	72	15	6433	6433	NUM
ejpam-6433	72	16	4	4	NUM
ejpam-6433	72	17	of	of	ADP
ejpam-6433	72	18	17	17	NUM
ejpam-6433	72	19	here	here	ADV
ejpam-6433	72	20	are	be	AUX
ejpam-6433	72	21	two	two	NUM
ejpam-6433	72	22	well	well	ADV
ejpam-6433	72	23	-	-	PUNCT
ejpam-6433	72	24	known	know	VERB
ejpam-6433	72	25	examples	example	NOUN
ejpam-6433	72	26	of	of	ADP
ejpam-6433	72	27	mncs	mncs	PROPN
ejpam-6433	72	28	.	.	PUNCT
ejpam-6433	72	29	example	example	NOUN
ejpam-6433	73	1	1	1	NUM
ejpam-6433	73	2	.	.	X
ejpam-6433	73	3	define	define	VERB
ejpam-6433	73	4	α	α	NOUN
ejpam-6433	73	5	:	:	PUNCT
ejpam-6433	73	6	b(m	b(m	PROPN
ejpam-6433	73	7	)	)	PUNCT
ejpam-6433	73	8	→	→	PUNCT
ejpam-6433	74	1	[	[	X
ejpam-6433	74	2	0,+∞	0,+∞	NUM
ejpam-6433	74	3	)	)	PUNCT
ejpam-6433	74	4	as	as	ADP
ejpam-6433	74	5	α(g	α(g	NUM
ejpam-6433	74	6	)	)	PUNCT
ejpam-6433	74	7	=	=	PROPN
ejpam-6433	74	8	inf	inf	NOUN
ejpam-6433	74	9	{	{	PUNCT
ejpam-6433	74	10	ε	ε	PROPN
ejpam-6433	74	11	>	>	X
ejpam-6433	74	12	0	0	NUM
ejpam-6433	74	13	:	:	PUNCT
ejpam-6433	74	14	g	g	PROPN
ejpam-6433	74	15	can	can	AUX
ejpam-6433	74	16	be	be	AUX
ejpam-6433	74	17	covered	cover	VERB
ejpam-6433	74	18	by	by	ADP
ejpam-6433	74	19	finitely	finitely	ADV
ejpam-6433	74	20	many	many	ADJ
ejpam-6433	74	21	sets	set	NOUN
ejpam-6433	74	22	with	with	ADP
ejpam-6433	74	23	diameter	diameter	NOUN
ejpam-6433	74	24	≤	≤	NUM
ejpam-6433	74	25	ε	ε	PROPN
ejpam-6433	74	26	}	}	PUNCT
ejpam-6433	74	27	,	,	PUNCT
ejpam-6433	74	28	for	for	ADP
ejpam-6433	74	29	all	all	DET
ejpam-6433	74	30	g	g	PROPN
ejpam-6433	74	31	∈	∈	PROPN
ejpam-6433	74	32	b(m	b(m	PROPN
ejpam-6433	74	33	)	)	PUNCT
ejpam-6433	74	34	.	.	PUNCT
ejpam-6433	75	1	then	then	ADV
ejpam-6433	75	2	α	α	PROPN
ejpam-6433	75	3	is	be	AUX
ejpam-6433	75	4	an	an	DET
ejpam-6433	75	5	mnc	mnc	NOUN
ejpam-6433	75	6	which	which	PRON
ejpam-6433	75	7	was	be	AUX
ejpam-6433	75	8	first	first	ADV
ejpam-6433	75	9	introduced	introduce	VERB
ejpam-6433	75	10	by	by	ADP
ejpam-6433	75	11	kuratowski	kuratowski	PROPN
ejpam-6433	75	12	(	(	PUNCT
ejpam-6433	75	13	[	[	X
ejpam-6433	75	14	12	12	NUM
ejpam-6433	75	15	]	]	NUM
ejpam-6433	75	16	)	)	PUNCT
ejpam-6433	75	17	.	.	PUNCT
ejpam-6433	76	1	also	also	ADV
ejpam-6433	76	2	a	a	DET
ejpam-6433	76	3	function	function	NOUN
ejpam-6433	76	4	χ	χ	X
ejpam-6433	76	5	:	:	PUNCT
ejpam-6433	76	6	b(m	b(m	PROPN
ejpam-6433	76	7	)	)	PUNCT
ejpam-6433	76	8	→	→	PUNCT
ejpam-6433	77	1	[	[	X
ejpam-6433	77	2	0,+∞	0,+∞	NUM
ejpam-6433	77	3	)	)	PUNCT
ejpam-6433	77	4	which	which	PRON
ejpam-6433	77	5	is	be	AUX
ejpam-6433	77	6	defined	define	VERB
ejpam-6433	77	7	as	as	ADP
ejpam-6433	77	8	χ(g	χ(g	PROPN
ejpam-6433	77	9	)	)	PUNCT
ejpam-6433	77	10	=	=	PROPN
ejpam-6433	77	11	inf	inf	NOUN
ejpam-6433	77	12	{	{	PUNCT
ejpam-6433	77	13	ε	ε	PROPN
ejpam-6433	77	14	>	>	X
ejpam-6433	77	15	0	0	NUM
ejpam-6433	77	16	:	:	PUNCT
ejpam-6433	77	17	g	g	PROPN
ejpam-6433	77	18	can	can	AUX
ejpam-6433	77	19	be	be	AUX
ejpam-6433	77	20	covered	cover	VERB
ejpam-6433	77	21	by	by	ADP
ejpam-6433	77	22	finitely	finitely	ADV
ejpam-6433	77	23	many	many	ADJ
ejpam-6433	77	24	balls	ball	NOUN
ejpam-6433	77	25	with	with	ADP
ejpam-6433	77	26	radii	radius	NOUN
ejpam-6433	77	27	≤	≤	NUM
ejpam-6433	77	28	ε	ε	PROPN
ejpam-6433	77	29	}	}	PUNCT
ejpam-6433	77	30	,	,	PUNCT
ejpam-6433	77	31	for	for	ADP
ejpam-6433	77	32	all	all	DET
ejpam-6433	77	33	g	g	PROPN
ejpam-6433	77	34	∈	∈	PROPN
ejpam-6433	77	35	b(m	b(m	PROPN
ejpam-6433	77	36	)	)	PUNCT
ejpam-6433	77	37	,	,	PUNCT
ejpam-6433	77	38	is	be	AUX
ejpam-6433	77	39	a	a	DET
ejpam-6433	77	40	generalized	generalized	ADJ
ejpam-6433	77	41	version	version	NOUN
ejpam-6433	77	42	of	of	ADP
ejpam-6433	77	43	kuratowski	kuratowski	PROPN
ejpam-6433	77	44	mnc	mnc	PROPN
ejpam-6433	77	45	which	which	PRON
ejpam-6433	77	46	was	be	AUX
ejpam-6433	77	47	presented	present	VERB
ejpam-6433	77	48	later	later	ADV
ejpam-6433	77	49	by	by	ADP
ejpam-6433	77	50	hausdorff	hausdorff	PROPN
ejpam-6433	77	51	.	.	PUNCT
ejpam-6433	78	1	for	for	ADP
ejpam-6433	78	2	a	a	DET
ejpam-6433	78	3	nonempty	nonempty	ADJ
ejpam-6433	78	4	pair	pair	NOUN
ejpam-6433	78	5	(	(	PUNCT
ejpam-6433	78	6	g	g	NOUN
ejpam-6433	78	7	,	,	PUNCT
ejpam-6433	78	8	h	h	NOUN
ejpam-6433	78	9	)	)	PUNCT
ejpam-6433	78	10	in	in	ADP
ejpam-6433	78	11	a	a	DET
ejpam-6433	78	12	metric	metric	ADJ
ejpam-6433	78	13	space	space	NOUN
ejpam-6433	78	14	(	(	PUNCT
ejpam-6433	78	15	m	m	PROPN
ejpam-6433	78	16	,	,	PUNCT
ejpam-6433	78	17	d	d	X
ejpam-6433	78	18	)	)	PUNCT
ejpam-6433	78	19	we	we	PRON
ejpam-6433	78	20	set	set	VERB
ejpam-6433	78	21	g0	g0	NOUN
ejpam-6433	78	22	=	=	PUNCT
ejpam-6433	78	23	{	{	PUNCT
ejpam-6433	78	24	u	u	NOUN
ejpam-6433	78	25	∈	∈	PROPN
ejpam-6433	78	26	g	g	NOUN
ejpam-6433	78	27	:	:	PUNCT
ejpam-6433	78	28	there	there	PRON
ejpam-6433	78	29	exists	exist	VERB
ejpam-6433	78	30	v′	v′	PROPN
ejpam-6433	78	31	∈	∈	PROPN
ejpam-6433	78	32	h	h	NOUN
ejpam-6433	78	33	such	such	ADJ
ejpam-6433	78	34	that	that	SCONJ
ejpam-6433	78	35	d(u	d(u	PROPN
ejpam-6433	78	36	,	,	PUNCT
ejpam-6433	78	37	v′	v′	NOUN
ejpam-6433	78	38	)	)	PUNCT
ejpam-6433	79	1	=	=	SYM
ejpam-6433	79	2	d(g	d(g	PROPN
ejpam-6433	79	3	,	,	PUNCT
ejpam-6433	79	4	h	h	NOUN
ejpam-6433	79	5	)	)	PUNCT
ejpam-6433	79	6	}	}	PUNCT
ejpam-6433	79	7	,	,	PUNCT
ejpam-6433	79	8	h0	h0	NOUN
ejpam-6433	79	9	=	=	SYM
ejpam-6433	79	10	{	{	PUNCT
ejpam-6433	79	11	v	v	NUM
ejpam-6433	79	12	∈	∈	NOUN
ejpam-6433	79	13	h	h	NOUN
ejpam-6433	79	14	:	:	PUNCT
ejpam-6433	79	15	there	there	PRON
ejpam-6433	79	16	exists	exist	VERB
ejpam-6433	79	17	u′	u′	PROPN
ejpam-6433	79	18	∈	∈	PROPN
ejpam-6433	79	19	g	g	PROPN
ejpam-6433	79	20	such	such	ADJ
ejpam-6433	79	21	that	that	DET
ejpam-6433	79	22	d(u′	d(u′	PROPN
ejpam-6433	79	23	,	,	PUNCT
ejpam-6433	79	24	v	v	NOUN
ejpam-6433	79	25	)	)	PUNCT
ejpam-6433	79	26	=	=	SYM
ejpam-6433	79	27	d(g	d(g	PROPN
ejpam-6433	79	28	,	,	PUNCT
ejpam-6433	79	29	h	h	NOUN
ejpam-6433	79	30	)	)	PUNCT
ejpam-6433	79	31	}	}	PUNCT
ejpam-6433	79	32	.	.	PUNCT
ejpam-6433	80	1	the	the	DET
ejpam-6433	80	2	pair	pair	NOUN
ejpam-6433	80	3	(	(	PUNCT
ejpam-6433	80	4	g0,h0	g0,h0	PROPN
ejpam-6433	80	5	)	)	PUNCT
ejpam-6433	80	6	is	be	AUX
ejpam-6433	80	7	said	say	VERB
ejpam-6433	80	8	to	to	PART
ejpam-6433	80	9	be	be	AUX
ejpam-6433	80	10	a	a	DET
ejpam-6433	80	11	proximal	proximal	ADJ
ejpam-6433	80	12	pair	pair	NOUN
ejpam-6433	80	13	of	of	ADP
ejpam-6433	80	14	(	(	PUNCT
ejpam-6433	80	15	g	g	PROPN
ejpam-6433	80	16	,	,	PUNCT
ejpam-6433	80	17	h	h	NOUN
ejpam-6433	80	18	)	)	PUNCT
ejpam-6433	80	19	.	.	PUNCT
ejpam-6433	81	1	there	there	PRON
ejpam-6433	81	2	are	be	VERB
ejpam-6433	81	3	different	different	ADJ
ejpam-6433	81	4	conditions	condition	NOUN
ejpam-6433	81	5	to	to	PART
ejpam-6433	81	6	ensure	ensure	VERB
ejpam-6433	81	7	nonemptyness	nonemptyness	ADV
ejpam-6433	81	8	of	of	ADP
ejpam-6433	81	9	proximal	proximal	ADJ
ejpam-6433	81	10	pairs	pair	NOUN
ejpam-6433	81	11	.	.	PUNCT
ejpam-6433	82	1	for	for	ADP
ejpam-6433	82	2	example	example	NOUN
ejpam-6433	82	3	(	(	PUNCT
ejpam-6433	82	4	g0,h0	g0,h0	PROPN
ejpam-6433	82	5	)	)	PUNCT
ejpam-6433	82	6	is	be	AUX
ejpam-6433	82	7	nonempty	nonempty	ADJ
ejpam-6433	82	8	if	if	SCONJ
ejpam-6433	82	9	one	one	NUM
ejpam-6433	82	10	of	of	ADP
ejpam-6433	82	11	the	the	DET
ejpam-6433	82	12	following	follow	VERB
ejpam-6433	82	13	conditions	condition	NOUN
ejpam-6433	82	14	hold	hold	VERB
ejpam-6433	82	15	:	:	PUNCT
ejpam-6433	82	16	(	(	PUNCT
ejpam-6433	82	17	i	i	NOUN
ejpam-6433	82	18	)	)	PUNCT
ejpam-6433	82	19	(	(	PUNCT
ejpam-6433	82	20	g	g	NOUN
ejpam-6433	82	21	,	,	PUNCT
ejpam-6433	82	22	h	h	NOUN
ejpam-6433	82	23	)	)	PUNCT
ejpam-6433	82	24	is	be	AUX
ejpam-6433	82	25	a	a	DET
ejpam-6433	82	26	nonempty	nonempty	ADJ
ejpam-6433	82	27	and	and	CCONJ
ejpam-6433	82	28	compact	compact	ADJ
ejpam-6433	82	29	pair	pair	NOUN
ejpam-6433	82	30	in	in	ADP
ejpam-6433	82	31	a	a	DET
ejpam-6433	82	32	metric	metric	ADJ
ejpam-6433	82	33	space	space	NOUN
ejpam-6433	82	34	(	(	PUNCT
ejpam-6433	82	35	m	m	PROPN
ejpam-6433	82	36	,	,	PUNCT
ejpam-6433	82	37	d	d	NOUN
ejpam-6433	82	38	)	)	PUNCT
ejpam-6433	82	39	;	;	PUNCT
ejpam-6433	82	40	(	(	PUNCT
ejpam-6433	82	41	ii	ii	NOUN
ejpam-6433	82	42	)	)	PUNCT
ejpam-6433	82	43	(	(	PUNCT
ejpam-6433	82	44	g	g	NOUN
ejpam-6433	82	45	,	,	PUNCT
ejpam-6433	82	46	h	h	NOUN
ejpam-6433	82	47	)	)	PUNCT
ejpam-6433	82	48	is	be	AUX
ejpam-6433	82	49	a	a	DET
ejpam-6433	82	50	nonempty	nonempty	ADJ
ejpam-6433	82	51	pair	pair	NOUN
ejpam-6433	82	52	in	in	ADP
ejpam-6433	82	53	a	a	DET
ejpam-6433	82	54	metric	metric	ADJ
ejpam-6433	82	55	space	space	NOUN
ejpam-6433	82	56	(	(	PUNCT
ejpam-6433	82	57	m	m	PROPN
ejpam-6433	82	58	,	,	PUNCT
ejpam-6433	82	59	d	d	NOUN
ejpam-6433	82	60	)	)	PUNCT
ejpam-6433	82	61	such	such	ADJ
ejpam-6433	82	62	that	that	SCONJ
ejpam-6433	82	63	g	g	PROPN
ejpam-6433	82	64	is	be	AUX
ejpam-6433	82	65	compact	compact	ADJ
ejpam-6433	82	66	and	and	CCONJ
ejpam-6433	82	67	h	h	NOUN
ejpam-6433	82	68	is	be	AUX
ejpam-6433	82	69	approximatively	approximatively	ADV
ejpam-6433	82	70	compact	compact	ADJ
ejpam-6433	82	71	w.r.t	w.r.t	NOUN
ejpam-6433	82	72	.	.	PUNCT
ejpam-6433	83	1	g.	g.	NOUN
ejpam-6433	83	2	we	we	PRON
ejpam-6433	83	3	recall	recall	VERB
ejpam-6433	83	4	that	that	SCONJ
ejpam-6433	83	5	the	the	DET
ejpam-6433	83	6	set	set	NOUN
ejpam-6433	83	7	h	h	NOUN
ejpam-6433	83	8	is	be	AUX
ejpam-6433	83	9	approximatively	approximatively	ADV
ejpam-6433	83	10	compact	compact	ADJ
ejpam-6433	83	11	w.r.t	w.r.t	NOUN
ejpam-6433	83	12	.	.	PUNCT
ejpam-6433	84	1	the	the	DET
ejpam-6433	84	2	set	set	NOUN
ejpam-6433	84	3	g	g	NOUN
ejpam-6433	84	4	whenever	whenever	SCONJ
ejpam-6433	84	5	for	for	ADP
ejpam-6433	84	6	any	any	DET
ejpam-6433	84	7	point	point	NOUN
ejpam-6433	84	8	x	x	X
ejpam-6433	84	9	∈	∈	PROPN
ejpam-6433	84	10	g	g	NOUN
ejpam-6433	84	11	and	and	CCONJ
ejpam-6433	84	12	any	any	DET
ejpam-6433	84	13	sequence	sequence	NOUN
ejpam-6433	84	14	{	{	PUNCT
ejpam-6433	84	15	yn	yn	NOUN
ejpam-6433	84	16	}	}	PUNCT
ejpam-6433	84	17	in	in	ADP
ejpam-6433	84	18	the	the	DET
ejpam-6433	84	19	set	set	ADJ
ejpam-6433	84	20	h	h	NOUN
ejpam-6433	84	21	for	for	ADP
ejpam-6433	84	22	which	which	PRON
ejpam-6433	84	23	d(x	d(x	PROPN
ejpam-6433	84	24	,	,	PUNCT
ejpam-6433	84	25	yn	yn	PROPN
ejpam-6433	84	26	)	)	PUNCT
ejpam-6433	84	27	→	→	SYM
ejpam-6433	84	28	d({x},h	d({x},h	NOUN
ejpam-6433	84	29	)	)	PUNCT
ejpam-6433	84	30	,	,	PUNCT
ejpam-6433	84	31	then	then	ADV
ejpam-6433	84	32	{	{	PUNCT
ejpam-6433	84	33	yn	yn	NOUN
ejpam-6433	84	34	}	}	PUNCT
ejpam-6433	84	35	has	have	VERB
ejpam-6433	84	36	a	a	DET
ejpam-6433	84	37	convergent	convergent	NOUN
ejpam-6433	84	38	subsequence	subsequence	NOUN
ejpam-6433	84	39	in	in	ADP
ejpam-6433	84	40	h	h	NOUN
ejpam-6433	84	41	;	;	PUNCT
ejpam-6433	84	42	(	(	PUNCT
ejpam-6433	84	43	iii	iii	X
ejpam-6433	84	44	)	)	PUNCT
ejpam-6433	84	45	(	(	PUNCT
ejpam-6433	84	46	g	g	NOUN
ejpam-6433	84	47	,	,	PUNCT
ejpam-6433	84	48	h	h	NOUN
ejpam-6433	84	49	)	)	PUNCT
ejpam-6433	84	50	is	be	AUX
ejpam-6433	84	51	a	a	DET
ejpam-6433	84	52	nonempty	nonempty	ADJ
ejpam-6433	84	53	and	and	CCONJ
ejpam-6433	84	54	weakly	weakly	ADJ
ejpam-6433	84	55	compact	compact	ADJ
ejpam-6433	84	56	pair	pair	NOUN
ejpam-6433	84	57	in	in	ADP
ejpam-6433	84	58	a	a	DET
ejpam-6433	84	59	banach	banach	NOUN
ejpam-6433	84	60	space	space	NOUN
ejpam-6433	84	61	x	x	NOUN
ejpam-6433	84	62	;	;	PUNCT
ejpam-6433	84	63	(	(	PUNCT
ejpam-6433	84	64	iv	iv	X
ejpam-6433	84	65	)	)	PUNCT
ejpam-6433	84	66	(	(	PUNCT
ejpam-6433	84	67	g	g	NOUN
ejpam-6433	84	68	,	,	PUNCT
ejpam-6433	84	69	h	h	NOUN
ejpam-6433	84	70	)	)	PUNCT
ejpam-6433	84	71	is	be	AUX
ejpam-6433	84	72	a	a	DET
ejpam-6433	84	73	nonempty	nonempty	ADJ
ejpam-6433	84	74	,	,	PUNCT
ejpam-6433	84	75	closed	closed	ADJ
ejpam-6433	84	76	and	and	CCONJ
ejpam-6433	84	77	convex	convex	VERB
ejpam-6433	84	78	pair	pair	NOUN
ejpam-6433	84	79	in	in	ADP
ejpam-6433	84	80	a	a	DET
ejpam-6433	84	81	reflexive	reflexive	ADJ
ejpam-6433	84	82	busemann	busemann	NOUN
ejpam-6433	84	83	convex	convex	VERB
ejpam-6433	84	84	metric	metric	ADJ
ejpam-6433	84	85	space	space	NOUN
ejpam-6433	84	86	(	(	PUNCT
ejpam-6433	84	87	m	m	PROPN
ejpam-6433	84	88	,	,	PUNCT
ejpam-6433	84	89	d	d	NOUN
ejpam-6433	84	90	)	)	PUNCT
ejpam-6433	84	91	such	such	ADJ
ejpam-6433	84	92	that	that	SCONJ
ejpam-6433	84	93	h	h	NOUN
ejpam-6433	84	94	is	be	AUX
ejpam-6433	84	95	bounded	bound	VERB
ejpam-6433	84	96	(	(	PUNCT
ejpam-6433	84	97	see	see	VERB
ejpam-6433	84	98	[	[	X
ejpam-6433	84	99	13	13	NUM
ejpam-6433	84	100	]	]	NUM
ejpam-6433	84	101	)	)	PUNCT
ejpam-6433	84	102	;	;	PUNCT
ejpam-6433	84	103	(	(	PUNCT
ejpam-6433	84	104	iv	iv	X
ejpam-6433	84	105	)	)	PUNCT
ejpam-6433	84	106	(	(	PUNCT
ejpam-6433	84	107	g	g	NOUN
ejpam-6433	84	108	,	,	PUNCT
ejpam-6433	84	109	h	h	NOUN
ejpam-6433	84	110	)	)	PUNCT
ejpam-6433	84	111	is	be	AUX
ejpam-6433	84	112	a	a	DET
ejpam-6433	84	113	nonempty	nonempty	ADJ
ejpam-6433	84	114	and	and	CCONJ
ejpam-6433	84	115	admissible	admissible	ADJ
ejpam-6433	84	116	pair	pair	NOUN
ejpam-6433	84	117	in	in	ADP
ejpam-6433	84	118	a	a	DET
ejpam-6433	84	119	hyperconvex	hyperconvex	ADJ
ejpam-6433	84	120	metric	metric	ADJ
ejpam-6433	84	121	space	space	NOUN
ejpam-6433	84	122	(	(	PUNCT
ejpam-6433	84	123	m	m	PROPN
ejpam-6433	84	124	,	,	PUNCT
ejpam-6433	84	125	d	d	NOUN
ejpam-6433	84	126	)	)	PUNCT
ejpam-6433	84	127	(	(	PUNCT
ejpam-6433	84	128	see	see	VERB
ejpam-6433	84	129	[	[	X
ejpam-6433	84	130	14	14	NUM
ejpam-6433	84	131	]	]	NUM
ejpam-6433	84	132	)	)	PUNCT
ejpam-6433	84	133	.	.	PUNCT
ejpam-6433	85	1	we	we	PRON
ejpam-6433	85	2	will	will	AUX
ejpam-6433	85	3	say	say	VERB
ejpam-6433	85	4	that	that	SCONJ
ejpam-6433	85	5	the	the	DET
ejpam-6433	85	6	nonempty	nonempty	ADJ
ejpam-6433	85	7	pair	pair	NOUN
ejpam-6433	85	8	(	(	PUNCT
ejpam-6433	85	9	g	g	NOUN
ejpam-6433	85	10	,	,	PUNCT
ejpam-6433	85	11	h	h	NOUN
ejpam-6433	85	12	)	)	PUNCT
ejpam-6433	85	13	is	be	AUX
ejpam-6433	85	14	proximinal	proximinal	ADJ
ejpam-6433	85	15	whenever	whenever	SCONJ
ejpam-6433	85	16	g0	g0	PROPN
ejpam-6433	85	17	=	=	SYM
ejpam-6433	85	18	g	g	PROPN
ejpam-6433	85	19	,	,	PUNCT
ejpam-6433	85	20	h0	h0	PROPN
ejpam-6433	85	21	=	=	PROPN
ejpam-6433	85	22	h.	h.	PROPN
ejpam-6433	85	23	let	let	VERB
ejpam-6433	85	24	(	(	PUNCT
ejpam-6433	85	25	g	g	NOUN
ejpam-6433	85	26	,	,	PUNCT
ejpam-6433	85	27	h	h	NOUN
ejpam-6433	85	28	)	)	PUNCT
ejpam-6433	85	29	be	be	VERB
ejpam-6433	85	30	a	a	DET
ejpam-6433	85	31	nonempty	nonempty	ADJ
ejpam-6433	85	32	pair	pair	NOUN
ejpam-6433	85	33	in	in	ADP
ejpam-6433	85	34	a	a	DET
ejpam-6433	85	35	banach	banach	NOUN
ejpam-6433	85	36	space	space	NOUN
ejpam-6433	85	37	x	x	PUNCT
ejpam-6433	85	38	and	and	CCONJ
ejpam-6433	85	39	let	let	VERB
ejpam-6433	85	40	t	t	NOUN
ejpam-6433	85	41	:	:	PUNCT
ejpam-6433	85	42	g	g	PROPN
ejpam-6433	85	43	∪h	∪h	NUM
ejpam-6433	85	44	→	→	SYM
ejpam-6433	85	45	g∪h	g∪h	NOUN
ejpam-6433	85	46	be	be	AUX
ejpam-6433	85	47	a	a	DET
ejpam-6433	85	48	cyclic	cyclic	ADJ
ejpam-6433	85	49	(	(	PUNCT
ejpam-6433	85	50	noncyclic	noncyclic	NOUN
ejpam-6433	85	51	)	)	PUNCT
ejpam-6433	85	52	relatively	relatively	ADV
ejpam-6433	85	53	nonexpansive	nonexpansive	ADJ
ejpam-6433	85	54	mapping	mapping	NOUN
ejpam-6433	85	55	.	.	PUNCT
ejpam-6433	86	1	we	we	PRON
ejpam-6433	86	2	set	set	VERB
ejpam-6433	86	3	mg×h(t	mg×h(t	NOUN
ejpam-6433	86	4	)	)	PUNCT
ejpam-6433	87	1	=	=	SYM
ejpam-6433	87	2	{	{	PUNCT
ejpam-6433	87	3	(	(	PUNCT
ejpam-6433	87	4	l1,l2	l1,l2	PROPN
ejpam-6433	87	5	)	)	PUNCT
ejpam-6433	87	6	⊆	⊆	NUM
ejpam-6433	87	7	(	(	PUNCT
ejpam-6433	87	8	g	g	NOUN
ejpam-6433	87	9	,	,	PUNCT
ejpam-6433	87	10	h	h	NOUN
ejpam-6433	87	11	)	)	PUNCT
ejpam-6433	87	12	s.t	s.t	PROPN
ejpam-6433	87	13	.	.	PUNCT
ejpam-6433	88	1	(	(	PUNCT
ejpam-6433	88	2	l1,l2	l1,l2	PROPN
ejpam-6433	88	3	)	)	PUNCT
ejpam-6433	88	4	is	be	AUX
ejpam-6433	88	5	nonempty	nonempty	X
ejpam-6433	88	6	,	,	PUNCT
ejpam-6433	88	7	bounded	bound	VERB
ejpam-6433	88	8	,	,	PUNCT
ejpam-6433	88	9	closed	closed	ADJ
ejpam-6433	88	10	,	,	PUNCT
ejpam-6433	88	11	convex	convex	PROPN
ejpam-6433	88	12	,	,	PUNCT
ejpam-6433	88	13	m.	m.	NOUN
ejpam-6433	88	14	gabeleh	gabeleh	PROPN
ejpam-6433	88	15	,	,	PUNCT
ejpam-6433	88	16	j.	j.	PROPN
ejpam-6433	88	17	markin	markin	PROPN
ejpam-6433	88	18	,	,	PUNCT
ejpam-6433	88	19	m.	m.	NOUN
ejpam-6433	88	20	aphane	aphane	PROPN
ejpam-6433	88	21	/	/	SYM
ejpam-6433	88	22	eur	eur	PROPN
ejpam-6433	88	23	.	.	PUNCT
ejpam-6433	89	1	j.	j.	PROPN
ejpam-6433	89	2	pure	pure	PROPN
ejpam-6433	89	3	appl	appl	PROPN
ejpam-6433	89	4	.	.	PROPN
ejpam-6433	89	5	math	math	PROPN
ejpam-6433	89	6	,	,	PUNCT
ejpam-6433	89	7	18	18	NUM
ejpam-6433	89	8	(	(	PUNCT
ejpam-6433	89	9	3	3	NUM
ejpam-6433	89	10	)	)	PUNCT
ejpam-6433	89	11	(	(	PUNCT
ejpam-6433	89	12	2025	2025	NUM
ejpam-6433	89	13	)	)	PUNCT
ejpam-6433	89	14	,	,	PUNCT
ejpam-6433	89	15	6433	6433	NUM
ejpam-6433	89	16	5	5	NUM
ejpam-6433	89	17	of	of	ADP
ejpam-6433	89	18	17	17	NUM
ejpam-6433	89	19	proximinal	proximinal	ADJ
ejpam-6433	89	20	and	and	CCONJ
ejpam-6433	89	21	t	t	NOUN
ejpam-6433	89	22	−	−	PROPN
ejpam-6433	89	23	invariant	invariant	ADJ
ejpam-6433	89	24	with	with	ADP
ejpam-6433	89	25	d(l1,l2	d(l1,l2	NOUN
ejpam-6433	89	26	)	)	PUNCT
ejpam-6433	89	27	=	=	SYM
ejpam-6433	90	1	d(g	d(g	PROPN
ejpam-6433	90	2	,	,	PUNCT
ejpam-6433	90	3	h	h	NOUN
ejpam-6433	90	4	)	)	PUNCT
ejpam-6433	90	5	}	}	PUNCT
ejpam-6433	90	6	.	.	PUNCT
ejpam-6433	91	1	it	it	PRON
ejpam-6433	91	2	is	be	AUX
ejpam-6433	91	3	worth	worth	ADJ
ejpam-6433	91	4	noticing	notice	VERB
ejpam-6433	91	5	that	that	SCONJ
ejpam-6433	91	6	if	if	SCONJ
ejpam-6433	91	7	for	for	ADP
ejpam-6433	91	8	example	example	NOUN
ejpam-6433	91	9	(	(	PUNCT
ejpam-6433	91	10	g	g	NOUN
ejpam-6433	91	11	,	,	PUNCT
ejpam-6433	91	12	h	h	NOUN
ejpam-6433	91	13	)	)	PUNCT
ejpam-6433	91	14	is	be	AUX
ejpam-6433	91	15	a	a	DET
ejpam-6433	91	16	nonempty	nonempty	ADJ
ejpam-6433	91	17	,	,	PUNCT
ejpam-6433	91	18	weakly	weakly	ADV
ejpam-6433	91	19	compact	compact	ADJ
ejpam-6433	91	20	and	and	CCONJ
ejpam-6433	91	21	convex	convex	ADJ
ejpam-6433	91	22	pair	pair	NOUN
ejpam-6433	91	23	in	in	ADP
ejpam-6433	91	24	a	a	DET
ejpam-6433	91	25	banach	banach	NOUN
ejpam-6433	91	26	space	space	NOUN
ejpam-6433	91	27	x	x	NOUN
ejpam-6433	91	28	,	,	PUNCT
ejpam-6433	91	29	then	then	ADV
ejpam-6433	91	30	(	(	PUNCT
ejpam-6433	91	31	g0,h0	g0,h0	PROPN
ejpam-6433	91	32	)	)	PUNCT
ejpam-6433	91	33	∈	∈	PROPN
ejpam-6433	91	34	mg×h(t	mg×h(t	NOUN
ejpam-6433	91	35	)	)	PUNCT
ejpam-6433	91	36	(	(	PUNCT
ejpam-6433	91	37	see	see	VERB
ejpam-6433	91	38	lemmas	lemmas	PROPN
ejpam-6433	91	39	2.3	2.3	NUM
ejpam-6433	91	40	and	and	CCONJ
ejpam-6433	91	41	2.4	2.4	NUM
ejpam-6433	91	42	of	of	ADP
ejpam-6433	91	43	[	[	X
ejpam-6433	91	44	15	15	NUM
ejpam-6433	91	45	]	]	NUM
ejpam-6433	91	46	)	)	PUNCT
ejpam-6433	91	47	.	.	PUNCT
ejpam-6433	92	1	we	we	PRON
ejpam-6433	92	2	are	be	AUX
ejpam-6433	92	3	now	now	ADV
ejpam-6433	92	4	ready	ready	ADJ
ejpam-6433	92	5	to	to	PART
ejpam-6433	92	6	recall	recall	VERB
ejpam-6433	92	7	the	the	DET
ejpam-6433	92	8	concept	concept	NOUN
ejpam-6433	92	9	of	of	ADP
ejpam-6433	92	10	meir	meir	PROPN
ejpam-6433	92	11	-	-	PUNCT
ejpam-6433	92	12	keeler	keeler	PROPN
ejpam-6433	92	13	condensing	condense	VERB
ejpam-6433	92	14	operators	operator	NOUN
ejpam-6433	92	15	which	which	PRON
ejpam-6433	92	16	was	be	AUX
ejpam-6433	92	17	introduced	introduce	VERB
ejpam-6433	92	18	in	in	ADP
ejpam-6433	92	19	[	[	X
ejpam-6433	92	20	10	10	NUM
ejpam-6433	92	21	]	]	PUNCT
ejpam-6433	92	22	.	.	PUNCT
ejpam-6433	93	1	definition	definition	NOUN
ejpam-6433	93	2	3	3	X
ejpam-6433	93	3	.	.	PUNCT
ejpam-6433	94	1	let	let	VERB
ejpam-6433	94	2	(	(	PUNCT
ejpam-6433	94	3	g	g	NOUN
ejpam-6433	94	4	,	,	PUNCT
ejpam-6433	94	5	h	h	NOUN
ejpam-6433	94	6	)	)	PUNCT
ejpam-6433	94	7	be	be	VERB
ejpam-6433	94	8	a	a	DET
ejpam-6433	94	9	nonempty	nonempty	ADJ
ejpam-6433	94	10	and	and	CCONJ
ejpam-6433	94	11	convex	convex	ADJ
ejpam-6433	94	12	pair	pair	NOUN
ejpam-6433	94	13	in	in	ADP
ejpam-6433	94	14	a	a	DET
ejpam-6433	94	15	banach	banach	NOUN
ejpam-6433	94	16	space	space	NOUN
ejpam-6433	94	17	x	x	NOUN
ejpam-6433	94	18	and	and	CCONJ
ejpam-6433	94	19	ℵ	ℵ	X
ejpam-6433	94	20	be	be	VERB
ejpam-6433	94	21	an	an	DET
ejpam-6433	94	22	mnc	mnc	PROPN
ejpam-6433	94	23	on	on	ADP
ejpam-6433	94	24	x.	x.	PROPN
ejpam-6433	94	25	a	a	DET
ejpam-6433	94	26	mapping	mapping	NOUN
ejpam-6433	94	27	t	t	NOUN
ejpam-6433	94	28	:	:	PUNCT
ejpam-6433	94	29	g	g	PROPN
ejpam-6433	94	30	∪	∪	ADJ
ejpam-6433	94	31	h	h	NOUN
ejpam-6433	94	32	→	→	SYM
ejpam-6433	94	33	g	g	NOUN
ejpam-6433	94	34	∪	∪	ADJ
ejpam-6433	94	35	h	h	NOUN
ejpam-6433	94	36	is	be	AUX
ejpam-6433	94	37	said	say	VERB
ejpam-6433	94	38	to	to	PART
ejpam-6433	94	39	be	be	AUX
ejpam-6433	94	40	a	a	DET
ejpam-6433	94	41	meir	meir	ADJ
ejpam-6433	94	42	-	-	PUNCT
ejpam-6433	94	43	keeler	keeler	NOUN
ejpam-6433	94	44	condensing	condense	VERB
ejpam-6433	94	45	operator	operator	NOUN
ejpam-6433	94	46	if	if	SCONJ
ejpam-6433	94	47	t	t	PROPN
ejpam-6433	94	48	is	be	AUX
ejpam-6433	94	49	cyclic	cyclic	ADJ
ejpam-6433	94	50	(	(	PUNCT
ejpam-6433	94	51	noncyclic	noncyclic	NOUN
ejpam-6433	94	52	)	)	PUNCT
ejpam-6433	94	53	and	and	CCONJ
ejpam-6433	94	54	for	for	ADP
ejpam-6433	94	55	any	any	DET
ejpam-6433	94	56	ε	ε	PROPN
ejpam-6433	94	57	>	>	X
ejpam-6433	94	58	0	0	PUNCT
ejpam-6433	95	1	there	there	PRON
ejpam-6433	95	2	exists	exist	VERB
ejpam-6433	95	3	δ	δ	X
ejpam-6433	95	4	=	=	PUNCT
ejpam-6433	95	5	δ(ε	δ(ε	PROPN
ejpam-6433	95	6	)	)	PUNCT
ejpam-6433	95	7	>	>	X
ejpam-6433	95	8	0	0	PUNCT
ejpam-6433	95	9	such	such	ADJ
ejpam-6433	95	10	that	that	PRON
ejpam-6433	95	11	for	for	ADP
ejpam-6433	95	12	any	any	DET
ejpam-6433	95	13	(	(	PUNCT
ejpam-6433	95	14	l1,l2	l1,l2	PROPN
ejpam-6433	95	15	)	)	PUNCT
ejpam-6433	95	16	∈	∈	PROPN
ejpam-6433	95	17	mg×h(t	mg×h(t	NOUN
ejpam-6433	95	18	)	)	PUNCT
ejpam-6433	95	19	we	we	PRON
ejpam-6433	95	20	have	have	VERB
ejpam-6433	95	21	ε	ε	PROPN
ejpam-6433	95	22	≤	≤	PROPN
ejpam-6433	95	23	ℵ(l1	ℵ(l1	NOUN
ejpam-6433	95	24	∪	∪	NOUN
ejpam-6433	95	25	l2	l2	NOUN
ejpam-6433	95	26	)	)	PUNCT
ejpam-6433	95	27	<	<	X
ejpam-6433	95	28	ε+	ε+	X
ejpam-6433	95	29	δ	δ	PROPN
ejpam-6433	95	30	⇒	⇒	PROPN
ejpam-6433	95	31	ℵ	ℵ	PROPN
ejpam-6433	95	32	(	(	PUNCT
ejpam-6433	95	33	t	t	PROPN
ejpam-6433	95	34	(	(	PUNCT
ejpam-6433	95	35	l1	l1	PROPN
ejpam-6433	95	36	)	)	PUNCT
ejpam-6433	95	37	∪	∪	ADP
ejpam-6433	95	38	t	t	PROPN
ejpam-6433	95	39	(	(	PUNCT
ejpam-6433	95	40	l2	l2	PROPN
ejpam-6433	95	41	)	)	PUNCT
ejpam-6433	95	42	)	)	PUNCT
ejpam-6433	95	43	<	<	X
ejpam-6433	95	44	ε	ε	PROPN
ejpam-6433	95	45	.	.	PUNCT
ejpam-6433	96	1	the	the	DET
ejpam-6433	96	2	next	next	ADJ
ejpam-6433	96	3	best	good	ADJ
ejpam-6433	96	4	proximity	proximity	NOUN
ejpam-6433	96	5	point	point	NOUN
ejpam-6433	96	6	(	(	PUNCT
ejpam-6433	96	7	pair	pair	NOUN
ejpam-6433	96	8	)	)	PUNCT
ejpam-6433	96	9	theorems	theorem	NOUN
ejpam-6433	96	10	are	be	AUX
ejpam-6433	96	11	the	the	DET
ejpam-6433	96	12	main	main	ADJ
ejpam-6433	96	13	results	result	NOUN
ejpam-6433	96	14	of	of	ADP
ejpam-6433	96	15	[	[	X
ejpam-6433	96	16	10	10	NUM
ejpam-6433	96	17	]	]	PUNCT
ejpam-6433	96	18	.	.	PUNCT
ejpam-6433	97	1	theorem	theorem	NOUN
ejpam-6433	97	2	5	5	NUM
ejpam-6433	97	3	.	.	PUNCT
ejpam-6433	98	1	let	let	VERB
ejpam-6433	98	2	(	(	PUNCT
ejpam-6433	98	3	g	g	NOUN
ejpam-6433	98	4	,	,	PUNCT
ejpam-6433	98	5	h	h	NOUN
ejpam-6433	98	6	)	)	PUNCT
ejpam-6433	98	7	be	be	VERB
ejpam-6433	98	8	a	a	DET
ejpam-6433	98	9	nonempty	nonempty	ADJ
ejpam-6433	98	10	,	,	PUNCT
ejpam-6433	98	11	bounded	bound	VERB
ejpam-6433	98	12	,	,	PUNCT
ejpam-6433	98	13	closed	closed	ADJ
ejpam-6433	98	14	and	and	CCONJ
ejpam-6433	98	15	convex	convex	VERB
ejpam-6433	98	16	pair	pair	NOUN
ejpam-6433	98	17	in	in	ADP
ejpam-6433	98	18	a	a	DET
ejpam-6433	98	19	banach	banach	NOUN
ejpam-6433	98	20	space	space	NOUN
ejpam-6433	98	21	x	x	INTJ
ejpam-6433	98	22	such	such	ADJ
ejpam-6433	98	23	that	that	DET
ejpam-6433	98	24	g0	g0	NOUN
ejpam-6433	98	25	is	be	AUX
ejpam-6433	98	26	nonempty	nonempty	ADJ
ejpam-6433	98	27	and	and	CCONJ
ejpam-6433	98	28	ℵ	ℵ	NOUN
ejpam-6433	98	29	is	be	AUX
ejpam-6433	98	30	an	an	DET
ejpam-6433	98	31	mnc	mnc	PROPN
ejpam-6433	98	32	on	on	ADP
ejpam-6433	98	33	x.	x.	PROPN
ejpam-6433	98	34	let	let	VERB
ejpam-6433	98	35	t	t	NOUN
ejpam-6433	98	36	:	:	PUNCT
ejpam-6433	98	37	g	g	PROPN
ejpam-6433	98	38	∪	∪	ADJ
ejpam-6433	98	39	h	h	NOUN
ejpam-6433	98	40	→	→	SYM
ejpam-6433	98	41	g	g	PROPN
ejpam-6433	98	42	∪h	∪h	NUM
ejpam-6433	98	43	be	be	AUX
ejpam-6433	98	44	a	a	DET
ejpam-6433	98	45	cyclic	cyclic	ADJ
ejpam-6433	98	46	relatively	relatively	ADV
ejpam-6433	98	47	nonexpansive	nonexpansive	ADJ
ejpam-6433	98	48	mapping	mapping	NOUN
ejpam-6433	98	49	which	which	PRON
ejpam-6433	98	50	is	be	AUX
ejpam-6433	98	51	a	a	DET
ejpam-6433	98	52	meir	meir	ADJ
ejpam-6433	98	53	-	-	PUNCT
ejpam-6433	98	54	keeler	keeler	NOUN
ejpam-6433	98	55	condensing	condense	VERB
ejpam-6433	98	56	operator	operator	NOUN
ejpam-6433	98	57	.	.	PUNCT
ejpam-6433	99	1	then	then	ADV
ejpam-6433	99	2	t	t	PROPN
ejpam-6433	99	3	has	have	VERB
ejpam-6433	99	4	a	a	DET
ejpam-6433	99	5	best	good	ADJ
ejpam-6433	99	6	proximity	proximity	NOUN
ejpam-6433	99	7	point	point	NOUN
ejpam-6433	99	8	.	.	PUNCT
ejpam-6433	100	1	theorem	theorem	ADJ
ejpam-6433	100	2	6	6	NUM
ejpam-6433	100	3	.	.	PUNCT
ejpam-6433	101	1	let	let	VERB
ejpam-6433	101	2	(	(	PUNCT
ejpam-6433	101	3	g	g	NOUN
ejpam-6433	101	4	,	,	PUNCT
ejpam-6433	101	5	h	h	NOUN
ejpam-6433	101	6	)	)	PUNCT
ejpam-6433	101	7	be	be	VERB
ejpam-6433	101	8	a	a	DET
ejpam-6433	101	9	nonempty	nonempty	ADJ
ejpam-6433	101	10	,	,	PUNCT
ejpam-6433	101	11	bounded	bound	VERB
ejpam-6433	101	12	,	,	PUNCT
ejpam-6433	101	13	closed	closed	ADJ
ejpam-6433	101	14	and	and	CCONJ
ejpam-6433	101	15	convex	convex	VERB
ejpam-6433	101	16	pair	pair	NOUN
ejpam-6433	101	17	in	in	ADP
ejpam-6433	101	18	a	a	DET
ejpam-6433	101	19	strictly	strictly	ADV
ejpam-6433	101	20	convex	convex	ADJ
ejpam-6433	101	21	banach	banach	NOUN
ejpam-6433	101	22	space	space	NOUN
ejpam-6433	101	23	x	x	INTJ
ejpam-6433	101	24	such	such	ADJ
ejpam-6433	101	25	that	that	DET
ejpam-6433	101	26	g0	g0	NOUN
ejpam-6433	101	27	is	be	AUX
ejpam-6433	101	28	nonempty	nonempty	ADJ
ejpam-6433	101	29	and	and	CCONJ
ejpam-6433	101	30	ℵ	ℵ	NOUN
ejpam-6433	101	31	is	be	AUX
ejpam-6433	101	32	an	an	DET
ejpam-6433	101	33	mnc	mnc	PROPN
ejpam-6433	101	34	on	on	ADP
ejpam-6433	101	35	x.	x.	PROPN
ejpam-6433	101	36	let	let	VERB
ejpam-6433	101	37	t	t	NOUN
ejpam-6433	101	38	:	:	PUNCT
ejpam-6433	101	39	g	g	PROPN
ejpam-6433	101	40	∪	∪	ADJ
ejpam-6433	101	41	h	h	NOUN
ejpam-6433	101	42	→	→	SYM
ejpam-6433	101	43	g	g	PROPN
ejpam-6433	101	44	∪	∪	NOUN
ejpam-6433	101	45	h	h	NOUN
ejpam-6433	101	46	be	be	VERB
ejpam-6433	101	47	a	a	DET
ejpam-6433	101	48	noncyclic	noncyclic	ADJ
ejpam-6433	101	49	relatively	relatively	ADV
ejpam-6433	101	50	nonexpansive	nonexpansive	ADJ
ejpam-6433	101	51	mapping	mapping	NOUN
ejpam-6433	101	52	which	which	PRON
ejpam-6433	101	53	is	be	AUX
ejpam-6433	101	54	a	a	DET
ejpam-6433	101	55	meir	meir	ADJ
ejpam-6433	101	56	-	-	PUNCT
ejpam-6433	101	57	keeler	keeler	NOUN
ejpam-6433	101	58	condensing	condense	VERB
ejpam-6433	101	59	operator	operator	NOUN
ejpam-6433	101	60	.	.	PUNCT
ejpam-6433	102	1	then	then	ADV
ejpam-6433	102	2	t	t	PROPN
ejpam-6433	102	3	has	have	VERB
ejpam-6433	102	4	a	a	DET
ejpam-6433	102	5	best	good	ADJ
ejpam-6433	102	6	proximity	proximity	NOUN
ejpam-6433	102	7	point	point	NOUN
ejpam-6433	102	8	.	.	PUNCT
ejpam-6433	103	1	the	the	DET
ejpam-6433	103	2	main	main	ADJ
ejpam-6433	103	3	purpose	purpose	NOUN
ejpam-6433	103	4	of	of	ADP
ejpam-6433	103	5	this	this	DET
ejpam-6433	103	6	article	article	NOUN
ejpam-6433	103	7	is	be	AUX
ejpam-6433	103	8	to	to	PART
ejpam-6433	103	9	present	present	VERB
ejpam-6433	103	10	counterpart	counterpart	NOUN
ejpam-6433	103	11	results	result	NOUN
ejpam-6433	103	12	of	of	ADP
ejpam-6433	103	13	theorem	theorem	ADJ
ejpam-6433	103	14	5	5	NUM
ejpam-6433	103	15	and	and	CCONJ
ejpam-6433	103	16	6	6	NUM
ejpam-6433	103	17	in	in	ADP
ejpam-6433	103	18	the	the	DET
ejpam-6433	103	19	setting	setting	NOUN
ejpam-6433	103	20	of	of	ADP
ejpam-6433	103	21	hyperconvex	hyperconvex	ADJ
ejpam-6433	103	22	metric	metric	ADJ
ejpam-6433	103	23	spaces	space	NOUN
ejpam-6433	103	24	under	under	ADP
ejpam-6433	103	25	different	different	ADJ
ejpam-6433	103	26	conditions	condition	NOUN
ejpam-6433	103	27	.	.	PUNCT
ejpam-6433	104	1	2	2	X
ejpam-6433	104	2	.	.	X
ejpam-6433	104	3	best	good	ADJ
ejpam-6433	104	4	proximity	proximity	NOUN
ejpam-6433	104	5	version	version	NOUN
ejpam-6433	104	6	of	of	ADP
ejpam-6433	104	7	schauder	schauder	NOUN
ejpam-6433	104	8	’s	’s	PART
ejpam-6433	104	9	fixed	fix	VERB
ejpam-6433	104	10	point	point	NOUN
ejpam-6433	104	11	theorem	theorem	VERB
ejpam-6433	104	12	in	in	ADP
ejpam-6433	104	13	hyperconvex	hyperconvex	ADJ
ejpam-6433	104	14	spaces	space	NOUN
ejpam-6433	104	15	let	let	AUX
ejpam-6433	104	16	(	(	PUNCT
ejpam-6433	104	17	m	m	NOUN
ejpam-6433	104	18	,	,	PUNCT
ejpam-6433	104	19	d	d	X
ejpam-6433	104	20	)	)	PUNCT
ejpam-6433	104	21	be	be	AUX
ejpam-6433	104	22	a	a	DET
ejpam-6433	104	23	metric	metric	ADJ
ejpam-6433	104	24	space	space	NOUN
ejpam-6433	104	25	.	.	PUNCT
ejpam-6433	105	1	throughout	throughout	ADP
ejpam-6433	105	2	this	this	DET
ejpam-6433	105	3	article	article	NOUN
ejpam-6433	105	4	,	,	PUNCT
ejpam-6433	105	5	b(x	b(x	NOUN
ejpam-6433	105	6	;	;	PUNCT
ejpam-6433	105	7	r	r	X
ejpam-6433	105	8	)	)	PUNCT
ejpam-6433	105	9	displays	display	VERB
ejpam-6433	105	10	a	a	DET
ejpam-6433	105	11	closed	closed	ADJ
ejpam-6433	105	12	ball	ball	NOUN
ejpam-6433	105	13	centered	center	VERB
ejpam-6433	105	14	at	at	ADP
ejpam-6433	105	15	x	x	PROPN
ejpam-6433	105	16	∈	∈	PROPN
ejpam-6433	105	17	m	m	NOUN
ejpam-6433	105	18	with	with	ADP
ejpam-6433	105	19	radius	radius	NOUN
ejpam-6433	105	20	r	r	NOUN
ejpam-6433	105	21	>	>	X
ejpam-6433	105	22	0	0	NUM
ejpam-6433	105	23	,	,	PUNCT
ejpam-6433	105	24	that	that	ADV
ejpam-6433	105	25	is	is	ADV
ejpam-6433	105	26	,	,	PUNCT
ejpam-6433	105	27	b(x	b(x	ADJ
ejpam-6433	105	28	;	;	PUNCT
ejpam-6433	105	29	r	r	X
ejpam-6433	105	30	)	)	PUNCT
ejpam-6433	105	31	=	=	SYM
ejpam-6433	105	32	{	{	PUNCT
ejpam-6433	105	33	y	y	PROPN
ejpam-6433	105	34	∈	∈	PROPN
ejpam-6433	105	35	m	m	X
ejpam-6433	105	36	;	;	PUNCT
ejpam-6433	106	1	d(y	d(y	NOUN
ejpam-6433	106	2	,	,	PUNCT
ejpam-6433	106	3	x	x	NOUN
ejpam-6433	106	4	)	)	PUNCT
ejpam-6433	106	5	≤	≤	NOUN
ejpam-6433	106	6	r	r	NOUN
ejpam-6433	106	7	}	}	PUNCT
ejpam-6433	106	8	.	.	PUNCT
ejpam-6433	107	1	we	we	PRON
ejpam-6433	107	2	mention	mention	VERB
ejpam-6433	107	3	that	that	SCONJ
ejpam-6433	107	4	a	a	DET
ejpam-6433	107	5	multivalued	multivalue	VERB
ejpam-6433	107	6	mapping	mapping	NOUN
ejpam-6433	107	7	f	f	NOUN
ejpam-6433	107	8	:	:	PUNCT
ejpam-6433	107	9	m	m	VERB
ejpam-6433	107	10	→	→	SYM
ejpam-6433	107	11	2	2	NUM
ejpam-6433	107	12	m	m	NOUN
ejpam-6433	107	13	−	−	NOUN
ejpam-6433	107	14	{	{	PUNCT
ejpam-6433	107	15	∅	∅	NOUN
ejpam-6433	107	16	}	}	PUNCT
ejpam-6433	107	17	is	be	AUX
ejpam-6433	107	18	said	say	VERB
ejpam-6433	107	19	to	to	PART
ejpam-6433	107	20	be	be	AUX
ejpam-6433	107	21	almost	almost	ADV
ejpam-6433	107	22	lowersemicontinuous	lowersemicontinuous	ADJ
ejpam-6433	107	23	at	at	ADP
ejpam-6433	107	24	a	a	DET
ejpam-6433	107	25	point	point	NOUN
ejpam-6433	107	26	x	x	X
ejpam-6433	107	27	∈	∈	NOUN
ejpam-6433	107	28	m	m	VERB
ejpam-6433	107	29	if	if	SCONJ
ejpam-6433	107	30	for	for	ADP
ejpam-6433	107	31	each	each	DET
ejpam-6433	107	32	ε	ε	PROPN
ejpam-6433	107	33	>	>	X
ejpam-6433	107	34	0	0	PUNCT
ejpam-6433	108	1	there	there	PRON
ejpam-6433	108	2	exist	exist	VERB
ejpam-6433	108	3	an	an	DET
ejpam-6433	108	4	open	open	ADJ
ejpam-6433	108	5	neighborhood	neighborhood	NOUN
ejpam-6433	108	6	u(x	u(x	NOUN
ejpam-6433	108	7	)	)	PUNCT
ejpam-6433	108	8	of	of	ADP
ejpam-6433	108	9	x	x	X
ejpam-6433	108	10	and	and	CCONJ
ejpam-6433	108	11	a	a	DET
ejpam-6433	108	12	point	point	NOUN
ejpam-6433	108	13	z	z	NOUN
ejpam-6433	108	14	∈	∈	PROPN
ejpam-6433	108	15	fx	fx	NOUN
ejpam-6433	108	16	such	such	ADJ
ejpam-6433	108	17	that	that	SCONJ
ejpam-6433	108	18	b(z	b(z	NOUN
ejpam-6433	108	19	,	,	PUNCT
ejpam-6433	108	20	ε	ε	PROPN
ejpam-6433	108	21	)	)	PUNCT
ejpam-6433	108	22	∩	∩	ADJ
ejpam-6433	108	23	f	f	PROPN
ejpam-6433	108	24	(	(	PUNCT
ejpam-6433	108	25	y	y	NOUN
ejpam-6433	108	26	)	)	PUNCT
ejpam-6433	108	27	̸=	̸=	NOUN
ejpam-6433	108	28	∅	∅	NOUN
ejpam-6433	108	29	,	,	PUNCT
ejpam-6433	108	30	for	for	ADP
ejpam-6433	108	31	all	all	DET
ejpam-6433	108	32	y	y	PROPN
ejpam-6433	108	33	∈	∈	PROPN
ejpam-6433	108	34	u(x	u(x	PROPN
ejpam-6433	108	35	)	)	PUNCT
ejpam-6433	108	36	.	.	PUNCT
ejpam-6433	109	1	for	for	ADP
ejpam-6433	109	2	a	a	DET
ejpam-6433	109	3	given	give	VERB
ejpam-6433	109	4	ε	ε	PROPN
ejpam-6433	109	5	>	>	X
ejpam-6433	109	6	0	0	PROPN
ejpam-6433	109	7	and	and	CCONJ
ejpam-6433	109	8	g	g	PROPN
ejpam-6433	109	9	∈	∈	PROPN
ejpam-6433	109	10	bc(m	bc(m	NOUN
ejpam-6433	109	11	)	)	PUNCT
ejpam-6433	109	12	,	,	PUNCT
ejpam-6433	109	13	the	the	DET
ejpam-6433	109	14	ε	ε	PROPN
ejpam-6433	109	15	-	-	PUNCT
ejpam-6433	109	16	neighborhood	neighborhood	NOUN
ejpam-6433	109	17	of	of	ADP
ejpam-6433	109	18	g	g	NOUN
ejpam-6433	109	19	is	be	AUX
ejpam-6433	109	20	defined	define	VERB
ejpam-6433	109	21	with	with	ADP
ejpam-6433	109	22	nε(g	nε(g	NUM
ejpam-6433	109	23	)	)	PUNCT
ejpam-6433	110	1	:	:	PUNCT
ejpam-6433	110	2	=	=	SYM
ejpam-6433	110	3	{	{	PUNCT
ejpam-6433	110	4	u	u	NOUN
ejpam-6433	110	5	∈	∈	PROPN
ejpam-6433	110	6	m	m	VERB
ejpam-6433	110	7	:	:	PUNCT
ejpam-6433	111	1	d(u	d(u	PROPN
ejpam-6433	111	2	,	,	PUNCT
ejpam-6433	111	3	g	g	NOUN
ejpam-6433	111	4	)	)	PUNCT
ejpam-6433	111	5	≤	≤	NUM
ejpam-6433	111	6	ε	ε	PROPN
ejpam-6433	111	7	}	}	PUNCT
ejpam-6433	111	8	.	.	PUNCT
ejpam-6433	112	1	m.	m.	NOUN
ejpam-6433	112	2	gabeleh	gabeleh	PROPN
ejpam-6433	112	3	,	,	PUNCT
ejpam-6433	112	4	j.	j.	PROPN
ejpam-6433	112	5	markin	markin	PROPN
ejpam-6433	112	6	,	,	PUNCT
ejpam-6433	112	7	m.	m.	NOUN
ejpam-6433	112	8	aphane	aphane	PROPN
ejpam-6433	112	9	/	/	SYM
ejpam-6433	112	10	eur	eur	PROPN
ejpam-6433	112	11	.	.	PUNCT
ejpam-6433	113	1	j.	j.	PROPN
ejpam-6433	113	2	pure	pure	PROPN
ejpam-6433	113	3	appl	appl	PROPN
ejpam-6433	113	4	.	.	PROPN
ejpam-6433	113	5	math	math	PROPN
ejpam-6433	113	6	,	,	PUNCT
ejpam-6433	113	7	18	18	NUM
ejpam-6433	113	8	(	(	PUNCT
ejpam-6433	113	9	3	3	NUM
ejpam-6433	113	10	)	)	PUNCT
ejpam-6433	113	11	(	(	PUNCT
ejpam-6433	113	12	2025	2025	NUM
ejpam-6433	113	13	)	)	PUNCT
ejpam-6433	113	14	,	,	PUNCT
ejpam-6433	113	15	6433	6433	NUM
ejpam-6433	113	16	6	6	NUM
ejpam-6433	113	17	of	of	ADP
ejpam-6433	113	18	17	17	NUM
ejpam-6433	113	19	a	a	DET
ejpam-6433	113	20	concept	concept	NOUN
ejpam-6433	113	21	of	of	ADP
ejpam-6433	113	22	hyperconvexity	hyperconvexity	NOUN
ejpam-6433	113	23	is	be	AUX
ejpam-6433	113	24	based	base	VERB
ejpam-6433	113	25	on	on	ADP
ejpam-6433	113	26	a	a	DET
ejpam-6433	113	27	property	property	NOUN
ejpam-6433	113	28	of	of	ADP
ejpam-6433	113	29	closed	closed	ADJ
ejpam-6433	113	30	balls	ball	NOUN
ejpam-6433	113	31	in	in	ADP
ejpam-6433	113	32	metric	metric	ADJ
ejpam-6433	113	33	spaces	space	NOUN
ejpam-6433	113	34	which	which	PRON
ejpam-6433	113	35	was	be	AUX
ejpam-6433	113	36	introduced	introduce	VERB
ejpam-6433	113	37	by	by	ADP
ejpam-6433	113	38	aronszajn	aronszajn	PROPN
ejpam-6433	113	39	and	and	CCONJ
ejpam-6433	113	40	panitchpakdi	panitchpakdi	PROPN
ejpam-6433	113	41	(	(	PUNCT
ejpam-6433	113	42	[	[	X
ejpam-6433	113	43	16	16	NUM
ejpam-6433	113	44	]	]	PUNCT
ejpam-6433	113	45	)	)	PUNCT
ejpam-6433	113	46	in	in	ADP
ejpam-6433	113	47	1965	1965	NUM
ejpam-6433	113	48	as	as	SCONJ
ejpam-6433	113	49	follows	follow	VERB
ejpam-6433	113	50	.	.	PUNCT
ejpam-6433	114	1	definition	definition	NOUN
ejpam-6433	114	2	4	4	NUM
ejpam-6433	114	3	.	.	PUNCT
ejpam-6433	115	1	let	let	AUX
ejpam-6433	115	2	(	(	PUNCT
ejpam-6433	115	3	m	m	NOUN
ejpam-6433	115	4	,	,	PUNCT
ejpam-6433	115	5	d	d	X
ejpam-6433	115	6	)	)	PUNCT
ejpam-6433	115	7	be	be	AUX
ejpam-6433	115	8	a	a	DET
ejpam-6433	115	9	metric	metric	ADJ
ejpam-6433	115	10	space	space	NOUN
ejpam-6433	115	11	and	and	CCONJ
ejpam-6433	115	12	∅	∅	NOUN
ejpam-6433	115	13	=	=	NOUN
ejpam-6433	115	14	̸	̸	NUM
ejpam-6433	115	15	g	g	ADP
ejpam-6433	115	16	⊆	⊆	NUM
ejpam-6433	115	17	m.	m.	NOUN
ejpam-6433	115	18	then	then	ADV
ejpam-6433	115	19	g	g	PROPN
ejpam-6433	115	20	is	be	AUX
ejpam-6433	115	21	called	call	VERB
ejpam-6433	115	22	hyperconvex	hyperconvex	PROPN
ejpam-6433	115	23	if	if	SCONJ
ejpam-6433	115	24	for	for	ADP
ejpam-6433	115	25	any	any	DET
ejpam-6433	115	26	family	family	NOUN
ejpam-6433	115	27	{	{	PUNCT
ejpam-6433	115	28	xα}α∈i	xα}α∈i	NOUN
ejpam-6433	116	1	in	in	ADP
ejpam-6433	116	2	g	g	PROPN
ejpam-6433	116	3	such	such	ADJ
ejpam-6433	116	4	that	that	PRON
ejpam-6433	116	5	d(xα	d(xα	PROPN
ejpam-6433	116	6	,	,	PUNCT
ejpam-6433	116	7	xβ	xβ	NOUN
ejpam-6433	116	8	)	)	PUNCT
ejpam-6433	116	9	≤	≤	PUNCT
ejpam-6433	117	1	rα	rα	VERB
ejpam-6433	118	1	+	+	CCONJ
ejpam-6433	118	2	rβ	rβ	X
ejpam-6433	118	3	for	for	ADP
ejpam-6433	118	4	all	all	DET
ejpam-6433	118	5	α	α	NOUN
ejpam-6433	118	6	,	,	PUNCT
ejpam-6433	118	7	β	β	X
ejpam-6433	118	8	∈	∈	PROPN
ejpam-6433	119	1	i	i	PRON
ejpam-6433	119	2	,	,	PUNCT
ejpam-6433	119	3	we	we	PRON
ejpam-6433	119	4	have⋂	have⋂	ADV
ejpam-6433	119	5	α∈i	α∈i	NOUN
ejpam-6433	119	6	b(xα	b(xα	ADV
ejpam-6433	119	7	;	;	PUNCT
ejpam-6433	119	8	rα	rα	X
ejpam-6433	119	9	)	)	PUNCT
ejpam-6433	119	10	∩	∩	NOUN
ejpam-6433	119	11	g	g	PROPN
ejpam-6433	119	12	̸=	̸=	PROPN
ejpam-6433	119	13	∅.	∅.	PRON
ejpam-6433	119	14	particularly	particularly	ADV
ejpam-6433	119	15	,	,	PUNCT
ejpam-6433	119	16	if	if	SCONJ
ejpam-6433	119	17	g	g	PROPN
ejpam-6433	119	18	=	=	PROPN
ejpam-6433	119	19	m	m	PROPN
ejpam-6433	119	20	,	,	PUNCT
ejpam-6433	119	21	then	then	ADV
ejpam-6433	119	22	we	we	PRON
ejpam-6433	119	23	say	say	VERB
ejpam-6433	119	24	that	that	SCONJ
ejpam-6433	119	25	m	m	PROPN
ejpam-6433	119	26	is	be	AUX
ejpam-6433	119	27	a	a	DET
ejpam-6433	119	28	hyperconvex	hyperconvex	ADJ
ejpam-6433	119	29	metric	metric	ADJ
ejpam-6433	119	30	space	space	NOUN
ejpam-6433	119	31	.	.	PUNCT
ejpam-6433	120	1	it	it	PRON
ejpam-6433	120	2	is	be	AUX
ejpam-6433	120	3	worth	worth	ADJ
ejpam-6433	120	4	mentioning	mention	VERB
ejpam-6433	120	5	that	that	SCONJ
ejpam-6433	120	6	hyperconvex	hyperconvex	ADJ
ejpam-6433	120	7	metric	metric	ADJ
ejpam-6433	120	8	spaces	space	NOUN
ejpam-6433	120	9	are	be	AUX
ejpam-6433	120	10	complete	complete	ADJ
ejpam-6433	120	11	(	(	PUNCT
ejpam-6433	120	12	see	see	VERB
ejpam-6433	120	13	[	[	X
ejpam-6433	120	14	17	17	NUM
ejpam-6433	120	15	]	]	PUNCT
ejpam-6433	120	16	for	for	ADP
ejpam-6433	120	17	more	more	ADJ
ejpam-6433	120	18	details	detail	NOUN
ejpam-6433	120	19	)	)	PUNCT
ejpam-6433	120	20	.	.	PUNCT
ejpam-6433	121	1	in	in	ADP
ejpam-6433	121	2	order	order	NOUN
ejpam-6433	121	3	to	to	PART
ejpam-6433	121	4	give	give	VERB
ejpam-6433	121	5	a	a	DET
ejpam-6433	121	6	suitable	suitable	ADJ
ejpam-6433	121	7	characterization	characterization	NOUN
ejpam-6433	121	8	of	of	ADP
ejpam-6433	121	9	hyperconvexity	hyperconvexity	NOUN
ejpam-6433	121	10	,	,	PUNCT
ejpam-6433	121	11	we	we	PRON
ejpam-6433	121	12	need	need	VERB
ejpam-6433	121	13	to	to	PART
ejpam-6433	121	14	recall	recall	VERB
ejpam-6433	121	15	the	the	DET
ejpam-6433	121	16	following	follow	VERB
ejpam-6433	121	17	notions	notion	NOUN
ejpam-6433	121	18	.	.	PUNCT
ejpam-6433	122	1	definition	definition	NOUN
ejpam-6433	122	2	5	5	NUM
ejpam-6433	122	3	.	.	PUNCT
ejpam-6433	123	1	a	a	DET
ejpam-6433	123	2	metric	metric	ADJ
ejpam-6433	123	3	space	space	NOUN
ejpam-6433	123	4	(	(	PUNCT
ejpam-6433	123	5	m	m	PROPN
ejpam-6433	123	6	,	,	PUNCT
ejpam-6433	123	7	d	d	X
ejpam-6433	123	8	)	)	PUNCT
ejpam-6433	123	9	is	be	AUX
ejpam-6433	123	10	called	call	VERB
ejpam-6433	123	11	metrically	metrically	ADV
ejpam-6433	123	12	convex	convex	ADJ
ejpam-6433	123	13	whenever	whenever	SCONJ
ejpam-6433	123	14	for	for	ADP
ejpam-6433	123	15	any	any	DET
ejpam-6433	123	16	two	two	NUM
ejpam-6433	123	17	distinct	distinct	ADJ
ejpam-6433	123	18	points	point	NOUN
ejpam-6433	123	19	x	x	NOUN
ejpam-6433	123	20	,	,	PUNCT
ejpam-6433	123	21	y	y	PROPN
ejpam-6433	123	22	∈	∈	PROPN
ejpam-6433	123	23	m	m	VERB
ejpam-6433	123	24	there	there	PRON
ejpam-6433	123	25	exists	exist	VERB
ejpam-6433	123	26	an	an	DET
ejpam-6433	123	27	element	element	NOUN
ejpam-6433	123	28	z	z	PROPN
ejpam-6433	123	29	∈	∈	PROPN
ejpam-6433	123	30	m−	m−	PROPN
ejpam-6433	123	31	{	{	PUNCT
ejpam-6433	123	32	x	x	PROPN
ejpam-6433	123	33	,	,	PUNCT
ejpam-6433	123	34	y	y	NOUN
ejpam-6433	123	35	}	}	PUNCT
ejpam-6433	123	36	for	for	ADP
ejpam-6433	123	37	which	which	PRON
ejpam-6433	123	38	d(x	d(x	PROPN
ejpam-6433	123	39	,	,	PUNCT
ejpam-6433	123	40	y	y	NOUN
ejpam-6433	123	41	)	)	PUNCT
ejpam-6433	123	42	=	=	SYM
ejpam-6433	124	1	d(x	d(x	PROPN
ejpam-6433	124	2	,	,	PUNCT
ejpam-6433	124	3	z	z	NOUN
ejpam-6433	124	4	)	)	PUNCT
ejpam-6433	125	1	+	+	CCONJ
ejpam-6433	125	2	d(z	d(z	PROPN
ejpam-6433	125	3	,	,	PUNCT
ejpam-6433	125	4	y	y	NOUN
ejpam-6433	125	5	)	)	PUNCT
ejpam-6433	125	6	.	.	PUNCT
ejpam-6433	126	1	definition	definition	NOUN
ejpam-6433	126	2	6	6	NUM
ejpam-6433	126	3	.	.	PUNCT
ejpam-6433	127	1	a	a	DET
ejpam-6433	127	2	metric	metric	ADJ
ejpam-6433	127	3	space	space	NOUN
ejpam-6433	127	4	(	(	PUNCT
ejpam-6433	127	5	m	m	PROPN
ejpam-6433	127	6	,	,	PUNCT
ejpam-6433	127	7	d	d	X
ejpam-6433	127	8	)	)	PUNCT
ejpam-6433	127	9	is	be	AUX
ejpam-6433	127	10	said	say	VERB
ejpam-6433	127	11	to	to	PART
ejpam-6433	127	12	have	have	VERB
ejpam-6433	127	13	binary	binary	ADJ
ejpam-6433	127	14	ball	ball	NOUN
ejpam-6433	127	15	intersection	intersection	NOUN
ejpam-6433	127	16	property	property	NOUN
ejpam-6433	127	17	provided	provide	VERB
ejpam-6433	127	18	that	that	SCONJ
ejpam-6433	127	19	any	any	DET
ejpam-6433	127	20	family	family	NOUN
ejpam-6433	127	21	of	of	ADP
ejpam-6433	127	22	closed	closed	ADJ
ejpam-6433	127	23	balls	ball	NOUN
ejpam-6433	127	24	,	,	PUNCT
ejpam-6433	127	25	each	each	DET
ejpam-6433	127	26	two	two	NUM
ejpam-6433	127	27	of	of	ADP
ejpam-6433	127	28	which	which	PRON
ejpam-6433	127	29	intersect	intersect	NOUN
ejpam-6433	127	30	must	must	AUX
ejpam-6433	127	31	have	have	VERB
ejpam-6433	127	32	nonempty	nonempty	ADJ
ejpam-6433	127	33	intersection	intersection	NOUN
ejpam-6433	127	34	.	.	PUNCT
ejpam-6433	128	1	we	we	PRON
ejpam-6433	128	2	now	now	ADV
ejpam-6433	128	3	have	have	VERB
ejpam-6433	128	4	the	the	DET
ejpam-6433	128	5	following	following	ADJ
ejpam-6433	128	6	result	result	NOUN
ejpam-6433	128	7	regarding	regard	VERB
ejpam-6433	128	8	hyperconvex	hyperconvex	ADJ
ejpam-6433	128	9	spaces	space	NOUN
ejpam-6433	128	10	.	.	PUNCT
ejpam-6433	129	1	proposition	proposition	NOUN
ejpam-6433	129	2	1	1	NUM
ejpam-6433	129	3	.	.	PUNCT
ejpam-6433	130	1	(	(	PUNCT
ejpam-6433	130	2	see	see	VERB
ejpam-6433	130	3	[	[	X
ejpam-6433	130	4	17	17	NUM
ejpam-6433	130	5	]	]	PUNCT
ejpam-6433	130	6	;	;	PUNCT
ejpam-6433	130	7	p.	p.	NOUN
ejpam-6433	130	8	77	77	NUM
ejpam-6433	130	9	)	)	PUNCT
ejpam-6433	130	10	a	a	DET
ejpam-6433	130	11	complete	complete	ADJ
ejpam-6433	130	12	metric	metric	ADJ
ejpam-6433	130	13	space	space	NOUN
ejpam-6433	130	14	(	(	PUNCT
ejpam-6433	130	15	m	m	PROPN
ejpam-6433	130	16	,	,	PUNCT
ejpam-6433	130	17	d	d	X
ejpam-6433	130	18	)	)	PUNCT
ejpam-6433	130	19	is	be	AUX
ejpam-6433	130	20	hyperconvex	hyperconvex	ADJ
ejpam-6433	130	21	if	if	SCONJ
ejpam-6433	131	1	and	and	CCONJ
ejpam-6433	131	2	only	only	ADV
ejpam-6433	131	3	if	if	SCONJ
ejpam-6433	131	4	m	m	NOUN
ejpam-6433	131	5	is	be	AUX
ejpam-6433	131	6	metrically	metrically	ADV
ejpam-6433	131	7	convex	convex	ADJ
ejpam-6433	131	8	and	and	CCONJ
ejpam-6433	131	9	has	have	VERB
ejpam-6433	131	10	the	the	DET
ejpam-6433	131	11	binary	binary	PROPN
ejpam-6433	131	12	ball	ball	NOUN
ejpam-6433	131	13	intersection	intersection	NOUN
ejpam-6433	131	14	property	property	NOUN
ejpam-6433	131	15	.	.	PUNCT
ejpam-6433	132	1	using	use	VERB
ejpam-6433	132	2	proposition	proposition	NOUN
ejpam-6433	132	3	1	1	NUM
ejpam-6433	132	4	it	it	PRON
ejpam-6433	132	5	can	can	AUX
ejpam-6433	132	6	be	be	AUX
ejpam-6433	132	7	shown	show	VERB
ejpam-6433	132	8	that	that	SCONJ
ejpam-6433	132	9	the	the	DET
ejpam-6433	132	10	non	non	ADJ
ejpam-6433	132	11	-	-	ADJ
ejpam-6433	132	12	reflexive	reflexive	ADJ
ejpam-6433	132	13	banach	banach	NOUN
ejpam-6433	132	14	spaces	space	VERB
ejpam-6433	132	15	l∞	l∞	NOUN
ejpam-6433	132	16	,	,	PUNCT
ejpam-6433	132	17	l∞	l∞	NOUN
ejpam-6433	132	18	are	be	AUX
ejpam-6433	132	19	hyperconvex	hyperconvex	ADJ
ejpam-6433	132	20	.	.	PUNCT
ejpam-6433	133	1	it	it	PRON
ejpam-6433	133	2	is	be	AUX
ejpam-6433	133	3	interesting	interesting	ADJ
ejpam-6433	133	4	to	to	PART
ejpam-6433	133	5	note	note	VERB
ejpam-6433	133	6	that	that	SCONJ
ejpam-6433	133	7	hyperconvex	hyperconvex	ADJ
ejpam-6433	133	8	subsets	subset	NOUN
ejpam-6433	133	9	of	of	ADP
ejpam-6433	133	10	banach	banach	NOUN
ejpam-6433	133	11	spaces	space	NOUN
ejpam-6433	133	12	may	may	AUX
ejpam-6433	133	13	not	not	PART
ejpam-6433	133	14	be	be	AUX
ejpam-6433	133	15	convex	convex	ADJ
ejpam-6433	133	16	.	.	PUNCT
ejpam-6433	133	17	example	example	NOUN
ejpam-6433	134	1	2	2	NUM
ejpam-6433	134	2	.	.	X
ejpam-6433	134	3	in	in	ADP
ejpam-6433	134	4	the	the	DET
ejpam-6433	134	5	finite	finite	ADJ
ejpam-6433	134	6	dimensional	dimensional	ADJ
ejpam-6433	134	7	banach	banach	NOUN
ejpam-6433	134	8	space	space	NOUN
ejpam-6433	134	9	(	(	PUNCT
ejpam-6433	134	10	r2	r2	PROPN
ejpam-6433	134	11	,	,	PUNCT
ejpam-6433	134	12	∥.∥∞	∥.∥∞	NUM
ejpam-6433	134	13	)	)	PUNCT
ejpam-6433	134	14	,	,	PUNCT
ejpam-6433	134	15	suppose	suppose	VERB
ejpam-6433	134	16	g	g	PROPN
ejpam-6433	134	17	=	=	PRON
ejpam-6433	134	18	{	{	PUNCT
ejpam-6433	134	19	(	(	PUNCT
ejpam-6433	134	20	x	x	X
ejpam-6433	134	21	,	,	PUNCT
ejpam-6433	134	22	x+	x+	NUM
ejpam-6433	134	23	1	1	NUM
ejpam-6433	134	24	)	)	PUNCT
ejpam-6433	134	25	:	:	PUNCT
ejpam-6433	134	26	−1	−1	NOUN
ejpam-6433	134	27	≤	≤	NUM
ejpam-6433	134	28	x	x	SYM
ejpam-6433	134	29	≤	≤	NUM
ejpam-6433	134	30	0	0	NUM
ejpam-6433	134	31	}	}	PUNCT
ejpam-6433	134	32	⋃	⋃	NOUN
ejpam-6433	134	33	{	{	PUNCT
ejpam-6433	134	34	(	(	PUNCT
ejpam-6433	134	35	x,−x+	x,−x+	NUM
ejpam-6433	134	36	1	1	NUM
ejpam-6433	134	37	)	)	PUNCT
ejpam-6433	134	38	:	:	PUNCT
ejpam-6433	134	39	0	0	NUM
ejpam-6433	134	40	≤	≤	NUM
ejpam-6433	134	41	x	x	SYM
ejpam-6433	134	42	≤	≤	NUM
ejpam-6433	134	43	1	1	NUM
ejpam-6433	134	44	}	}	PUNCT
ejpam-6433	134	45	.	.	PUNCT
ejpam-6433	135	1	then	then	ADV
ejpam-6433	135	2	g	g	PROPN
ejpam-6433	135	3	is	be	AUX
ejpam-6433	135	4	metrically	metrically	ADV
ejpam-6433	135	5	convex	convex	ADJ
ejpam-6433	135	6	and	and	CCONJ
ejpam-6433	135	7	has	have	VERB
ejpam-6433	135	8	binary	binary	ADJ
ejpam-6433	135	9	intersection	intersection	NOUN
ejpam-6433	135	10	property	property	NOUN
ejpam-6433	135	11	,	,	PUNCT
ejpam-6433	135	12	which	which	PRON
ejpam-6433	135	13	means	mean	VERB
ejpam-6433	135	14	that	that	SCONJ
ejpam-6433	135	15	g	g	PROPN
ejpam-6433	135	16	is	be	AUX
ejpam-6433	135	17	a	a	DET
ejpam-6433	135	18	hyperconvex	hyperconvex	NOUN
ejpam-6433	135	19	subset	subset	NOUN
ejpam-6433	135	20	of	of	ADP
ejpam-6433	135	21	(	(	PUNCT
ejpam-6433	135	22	r2	r2	PROPN
ejpam-6433	135	23	,	,	PUNCT
ejpam-6433	135	24	∥.∥∞	∥.∥∞	NUM
ejpam-6433	135	25	)	)	PUNCT
ejpam-6433	135	26	,	,	PUNCT
ejpam-6433	135	27	but	but	CCONJ
ejpam-6433	135	28	clearly	clearly	ADV
ejpam-6433	135	29	g	g	PROPN
ejpam-6433	135	30	is	be	AUX
ejpam-6433	135	31	not	not	PART
ejpam-6433	135	32	convex	convex	ADJ
ejpam-6433	135	33	.	.	PUNCT
ejpam-6433	136	1	the	the	DET
ejpam-6433	136	2	next	next	ADJ
ejpam-6433	136	3	result	result	NOUN
ejpam-6433	136	4	give	give	VERB
ejpam-6433	136	5	us	we	PRON
ejpam-6433	136	6	an	an	DET
ejpam-6433	136	7	appropriate	appropriate	ADJ
ejpam-6433	136	8	condition	condition	NOUN
ejpam-6433	136	9	for	for	ADP
ejpam-6433	136	10	convexity	convexity	NOUN
ejpam-6433	136	11	of	of	ADP
ejpam-6433	136	12	hyperconvex	hyperconvex	ADJ
ejpam-6433	136	13	subsets	subset	NOUN
ejpam-6433	136	14	of	of	ADP
ejpam-6433	136	15	a	a	DET
ejpam-6433	136	16	banach	banach	NOUN
ejpam-6433	136	17	space	space	NOUN
ejpam-6433	136	18	.	.	PUNCT
ejpam-6433	137	1	proposition	proposition	NOUN
ejpam-6433	137	2	2	2	NUM
ejpam-6433	137	3	.	.	PUNCT
ejpam-6433	138	1	(	(	PUNCT
ejpam-6433	138	2	see	see	VERB
ejpam-6433	138	3	corollary	corollary	ADJ
ejpam-6433	138	4	4.5.18	4.5.18	NUM
ejpam-6433	138	5	of	of	ADP
ejpam-6433	138	6	[	[	X
ejpam-6433	138	7	18	18	NUM
ejpam-6433	138	8	]	]	PUNCT
ejpam-6433	138	9	)	)	PUNCT
ejpam-6433	138	10	let	let	VERB
ejpam-6433	138	11	x	x	PRON
ejpam-6433	138	12	be	be	AUX
ejpam-6433	138	13	a	a	DET
ejpam-6433	138	14	banach	banach	NOUN
ejpam-6433	138	15	space	space	NOUN
ejpam-6433	138	16	.	.	PUNCT
ejpam-6433	139	1	then	then	ADV
ejpam-6433	139	2	the	the	DET
ejpam-6433	139	3	following	follow	VERB
ejpam-6433	139	4	statements	statement	NOUN
ejpam-6433	139	5	are	be	AUX
ejpam-6433	139	6	equivalent	equivalent	ADJ
ejpam-6433	139	7	:	:	PUNCT
ejpam-6433	139	8	(	(	PUNCT
ejpam-6433	139	9	i	i	NOUN
ejpam-6433	139	10	)	)	PUNCT
ejpam-6433	139	11	x	x	VERB
ejpam-6433	139	12	is	be	AUX
ejpam-6433	139	13	strictly	strictly	ADV
ejpam-6433	139	14	convex	convex	ADJ
ejpam-6433	139	15	;	;	PUNCT
ejpam-6433	139	16	(	(	PUNCT
ejpam-6433	139	17	ii	ii	NOUN
ejpam-6433	139	18	)	)	PUNCT
ejpam-6433	139	19	every	every	PRON
ejpam-6433	139	20	nonempty	nonempty	ADJ
ejpam-6433	139	21	and	and	CCONJ
ejpam-6433	139	22	hyperconvex	hyperconvex	NOUN
ejpam-6433	139	23	subset	subset	NOUN
ejpam-6433	139	24	of	of	ADP
ejpam-6433	139	25	x	x	PUNCT
ejpam-6433	139	26	is	be	AUX
ejpam-6433	139	27	convex	convex	PROPN
ejpam-6433	139	28	.	.	PUNCT
ejpam-6433	140	1	m.	m.	NOUN
ejpam-6433	140	2	gabeleh	gabeleh	PROPN
ejpam-6433	140	3	,	,	PUNCT
ejpam-6433	140	4	j.	j.	PROPN
ejpam-6433	140	5	markin	markin	PROPN
ejpam-6433	140	6	,	,	PUNCT
ejpam-6433	140	7	m.	m.	NOUN
ejpam-6433	140	8	aphane	aphane	PROPN
ejpam-6433	140	9	/	/	SYM
ejpam-6433	140	10	eur	eur	PROPN
ejpam-6433	140	11	.	.	PUNCT
ejpam-6433	141	1	j.	j.	PROPN
ejpam-6433	141	2	pure	pure	PROPN
ejpam-6433	141	3	appl	appl	PROPN
ejpam-6433	141	4	.	.	PROPN
ejpam-6433	141	5	math	math	PROPN
ejpam-6433	141	6	,	,	PUNCT
ejpam-6433	141	7	18	18	NUM
ejpam-6433	141	8	(	(	PUNCT
ejpam-6433	141	9	3	3	NUM
ejpam-6433	141	10	)	)	PUNCT
ejpam-6433	141	11	(	(	PUNCT
ejpam-6433	141	12	2025	2025	NUM
ejpam-6433	141	13	)	)	PUNCT
ejpam-6433	141	14	,	,	PUNCT
ejpam-6433	141	15	6433	6433	NUM
ejpam-6433	141	16	7	7	NUM
ejpam-6433	141	17	of	of	ADP
ejpam-6433	141	18	17	17	NUM
ejpam-6433	141	19	to	to	PART
ejpam-6433	141	20	state	state	VERB
ejpam-6433	141	21	another	another	DET
ejpam-6433	141	22	useful	useful	ADJ
ejpam-6433	141	23	characterization	characterization	NOUN
ejpam-6433	141	24	of	of	ADP
ejpam-6433	141	25	convexity	convexity	NOUN
ejpam-6433	141	26	of	of	ADP
ejpam-6433	141	27	hyperconvex	hyperconvex	ADJ
ejpam-6433	141	28	subspaces	subspace	NOUN
ejpam-6433	141	29	of	of	ADP
ejpam-6433	141	30	a	a	DET
ejpam-6433	141	31	banach	banach	NOUN
ejpam-6433	141	32	space	space	NOUN
ejpam-6433	141	33	x	x	NOUN
ejpam-6433	141	34	,	,	PUNCT
ejpam-6433	141	35	we	we	PRON
ejpam-6433	141	36	recall	recall	VERB
ejpam-6433	141	37	the	the	DET
ejpam-6433	141	38	following	follow	VERB
ejpam-6433	141	39	geometric	geometric	ADJ
ejpam-6433	141	40	concept	concept	NOUN
ejpam-6433	141	41	.	.	PUNCT
ejpam-6433	142	1	definition	definition	NOUN
ejpam-6433	142	2	7	7	NUM
ejpam-6433	142	3	.	.	PUNCT
ejpam-6433	143	1	(	(	PUNCT
ejpam-6433	143	2	[	[	X
ejpam-6433	143	3	19	19	NUM
ejpam-6433	143	4	]	]	PUNCT
ejpam-6433	143	5	)	)	PUNCT
ejpam-6433	143	6	let	let	VERB
ejpam-6433	143	7	(	(	PUNCT
ejpam-6433	143	8	g	g	NOUN
ejpam-6433	143	9	,	,	PUNCT
ejpam-6433	143	10	h	h	NOUN
ejpam-6433	143	11	)	)	PUNCT
ejpam-6433	143	12	be	be	VERB
ejpam-6433	143	13	a	a	DET
ejpam-6433	143	14	nonempty	nonempty	ADJ
ejpam-6433	143	15	pair	pair	NOUN
ejpam-6433	143	16	in	in	ADP
ejpam-6433	143	17	a	a	DET
ejpam-6433	143	18	metric	metric	ADJ
ejpam-6433	143	19	space	space	NOUN
ejpam-6433	143	20	(	(	PUNCT
ejpam-6433	143	21	m	m	PROPN
ejpam-6433	143	22	,	,	PUNCT
ejpam-6433	143	23	d	d	NOUN
ejpam-6433	143	24	)	)	PUNCT
ejpam-6433	143	25	with	with	ADP
ejpam-6433	143	26	g0	g0	ADJ
ejpam-6433	143	27	̸=	̸=	PROPN
ejpam-6433	143	28	∅.	∅.	ADP
ejpam-6433	143	29	the	the	DET
ejpam-6433	143	30	pair	pair	NOUN
ejpam-6433	143	31	(	(	PUNCT
ejpam-6433	143	32	g	g	NOUN
ejpam-6433	143	33	,	,	PUNCT
ejpam-6433	143	34	h	h	NOUN
ejpam-6433	143	35	)	)	PUNCT
ejpam-6433	143	36	is	be	AUX
ejpam-6433	143	37	said	say	VERB
ejpam-6433	143	38	to	to	PART
ejpam-6433	143	39	have	have	VERB
ejpam-6433	143	40	the	the	DET
ejpam-6433	143	41	p	p	NOUN
ejpam-6433	143	42	-	-	PUNCT
ejpam-6433	143	43	property	property	NOUN
ejpam-6433	143	44	if	if	NOUN
ejpam-6433	143	45	and	and	CCONJ
ejpam-6433	143	46	only	only	ADV
ejpam-6433	143	47	if	if	SCONJ
ejpam-6433	143	48	{	{	PUNCT
ejpam-6433	143	49	d(x1	d(x1	NOUN
ejpam-6433	143	50	,	,	PUNCT
ejpam-6433	143	51	y1	y1	NOUN
ejpam-6433	143	52	)	)	PUNCT
ejpam-6433	143	53	=	=	SYM
ejpam-6433	143	54	d(g	d(g	PROPN
ejpam-6433	143	55	,	,	PUNCT
ejpam-6433	143	56	h	h	NOUN
ejpam-6433	143	57	)	)	PUNCT
ejpam-6433	143	58	d(x2	d(x2	NOUN
ejpam-6433	143	59	,	,	PUNCT
ejpam-6433	143	60	y2	y2	PROPN
ejpam-6433	143	61	)	)	PUNCT
ejpam-6433	143	62	=	=	SYM
ejpam-6433	143	63	d(g	d(g	PROPN
ejpam-6433	143	64	,	,	PUNCT
ejpam-6433	143	65	h	h	NOUN
ejpam-6433	143	66	)	)	PUNCT
ejpam-6433	143	67	⇒	⇒	NOUN
ejpam-6433	143	68	d(x1	d(x1	NOUN
ejpam-6433	143	69	,	,	PUNCT
ejpam-6433	143	70	x2	x2	NUM
ejpam-6433	143	71	)	)	PUNCT
ejpam-6433	143	72	=	=	SYM
ejpam-6433	143	73	d(y1	d(y1	NOUN
ejpam-6433	143	74	,	,	PUNCT
ejpam-6433	143	75	y2	y2	PROPN
ejpam-6433	143	76	)	)	PUNCT
ejpam-6433	143	77	,	,	PUNCT
ejpam-6433	143	78	where	where	SCONJ
ejpam-6433	143	79	x1	x1	X
ejpam-6433	143	80	,	,	PUNCT
ejpam-6433	143	81	x2	x2	PROPN
ejpam-6433	143	82	∈	∈	PROPN
ejpam-6433	143	83	g0	g0	NOUN
ejpam-6433	143	84	and	and	CCONJ
ejpam-6433	143	85	y1	y1	PROPN
ejpam-6433	143	86	,	,	PUNCT
ejpam-6433	143	87	y2	y2	PROPN
ejpam-6433	143	88	∈	∈	PROPN
ejpam-6433	143	89	h0	h0	PROPN
ejpam-6433	143	90	.	.	PUNCT
ejpam-6433	144	1	we	we	PRON
ejpam-6433	144	2	now	now	ADV
ejpam-6433	144	3	conclude	conclude	VERB
ejpam-6433	144	4	the	the	DET
ejpam-6433	144	5	following	follow	VERB
ejpam-6433	144	6	result	result	NOUN
ejpam-6433	144	7	.	.	PUNCT
ejpam-6433	145	1	proposition	proposition	NOUN
ejpam-6433	145	2	3	3	X
ejpam-6433	145	3	.	.	PUNCT
ejpam-6433	146	1	let	let	VERB
ejpam-6433	146	2	x	x	PRON
ejpam-6433	146	3	be	be	AUX
ejpam-6433	146	4	a	a	DET
ejpam-6433	146	5	banach	banach	NOUN
ejpam-6433	146	6	space	space	NOUN
ejpam-6433	146	7	.	.	PUNCT
ejpam-6433	147	1	then	then	ADV
ejpam-6433	147	2	the	the	DET
ejpam-6433	147	3	following	follow	VERB
ejpam-6433	147	4	statements	statement	NOUN
ejpam-6433	147	5	are	be	AUX
ejpam-6433	147	6	equivalent	equivalent	ADJ
ejpam-6433	147	7	:	:	PUNCT
ejpam-6433	147	8	(	(	PUNCT
ejpam-6433	147	9	i	i	NOUN
ejpam-6433	147	10	)	)	PUNCT
ejpam-6433	147	11	ever	ever	ADV
ejpam-6433	147	12	pair	pair	NOUN
ejpam-6433	147	13	of	of	ADP
ejpam-6433	147	14	nonempty	nonempty	ADJ
ejpam-6433	147	15	,	,	PUNCT
ejpam-6433	147	16	closed	closed	ADJ
ejpam-6433	147	17	and	and	CCONJ
ejpam-6433	147	18	convex	convex	ADJ
ejpam-6433	147	19	subsets	subset	NOUN
ejpam-6433	147	20	of	of	ADP
ejpam-6433	147	21	x	x	PUNCT
ejpam-6433	147	22	has	have	VERB
ejpam-6433	147	23	the	the	DET
ejpam-6433	147	24	p	p	NOUN
ejpam-6433	147	25	-	-	PUNCT
ejpam-6433	147	26	property	property	NOUN
ejpam-6433	147	27	;	;	PUNCT
ejpam-6433	147	28	(	(	PUNCT
ejpam-6433	147	29	ii	ii	NOUN
ejpam-6433	147	30	)	)	PUNCT
ejpam-6433	147	31	every	every	PRON
ejpam-6433	147	32	nonempty	nonempty	ADJ
ejpam-6433	147	33	and	and	CCONJ
ejpam-6433	147	34	hyperconvex	hyperconvex	NOUN
ejpam-6433	147	35	subset	subset	NOUN
ejpam-6433	147	36	of	of	ADP
ejpam-6433	147	37	x	x	PUNCT
ejpam-6433	147	38	is	be	AUX
ejpam-6433	147	39	convex	convex	NOUN
ejpam-6433	147	40	.	.	PUNCT
ejpam-6433	148	1	proof	proof	NOUN
ejpam-6433	148	2	.	.	PUNCT
ejpam-6433	149	1	it	it	PRON
ejpam-6433	149	2	is	be	AUX
ejpam-6433	149	3	sufficient	sufficient	ADJ
ejpam-6433	149	4	to	to	PART
ejpam-6433	149	5	note	note	VERB
ejpam-6433	149	6	that	that	SCONJ
ejpam-6433	149	7	by	by	ADP
ejpam-6433	149	8	theorem	theorem	NOUN
ejpam-6433	149	9	3.1	3.1	NUM
ejpam-6433	149	10	of	of	ADP
ejpam-6433	149	11	[	[	X
ejpam-6433	149	12	20	20	NUM
ejpam-6433	149	13	]	]	PUNCT
ejpam-6433	149	14	,	,	PUNCT
ejpam-6433	149	15	every	every	DET
ejpam-6433	149	16	pair	pair	NOUN
ejpam-6433	149	17	of	of	ADP
ejpam-6433	149	18	nonempty	nonempty	NOUN
ejpam-6433	149	19	,	,	PUNCT
ejpam-6433	149	20	closed	closed	ADJ
ejpam-6433	149	21	and	and	CCONJ
ejpam-6433	149	22	convex	convex	ADJ
ejpam-6433	149	23	subsets	subset	NOUN
ejpam-6433	149	24	of	of	ADP
ejpam-6433	149	25	x	x	PUNCT
ejpam-6433	149	26	has	have	VERB
ejpam-6433	149	27	the	the	DET
ejpam-6433	149	28	p	p	NOUN
ejpam-6433	149	29	-	-	PUNCT
ejpam-6433	149	30	property	property	NOUN
ejpam-6433	149	31	if	if	NOUN
ejpam-6433	149	32	and	and	CCONJ
ejpam-6433	149	33	only	only	ADV
ejpam-6433	149	34	if	if	SCONJ
ejpam-6433	149	35	x	x	PRON
ejpam-6433	149	36	is	be	AUX
ejpam-6433	149	37	strictly	strictly	ADV
ejpam-6433	149	38	convex	convex	ADJ
ejpam-6433	149	39	.	.	PUNCT
ejpam-6433	150	1	now	now	ADV
ejpam-6433	150	2	the	the	DET
ejpam-6433	150	3	result	result	NOUN
ejpam-6433	150	4	follows	follow	VERB
ejpam-6433	150	5	from	from	ADP
ejpam-6433	150	6	proposition	proposition	NOUN
ejpam-6433	150	7	2	2	NUM
ejpam-6433	150	8	.	.	PUNCT
ejpam-6433	150	9	definition	definition	NOUN
ejpam-6433	150	10	8	8	NUM
ejpam-6433	150	11	.	.	PUNCT
ejpam-6433	151	1	a	a	DET
ejpam-6433	151	2	subset	subset	NOUN
ejpam-6433	151	3	g	g	NOUN
ejpam-6433	151	4	of	of	ADP
ejpam-6433	151	5	a	a	DET
ejpam-6433	151	6	hyperconvex	hyperconvex	ADJ
ejpam-6433	151	7	metric	metric	ADJ
ejpam-6433	151	8	space	space	NOUN
ejpam-6433	151	9	(	(	PUNCT
ejpam-6433	151	10	m	m	PROPN
ejpam-6433	151	11	,	,	PUNCT
ejpam-6433	151	12	d	d	X
ejpam-6433	151	13	)	)	PUNCT
ejpam-6433	151	14	is	be	AUX
ejpam-6433	151	15	called	call	VERB
ejpam-6433	151	16	admissible	admissible	ADJ
ejpam-6433	151	17	if	if	SCONJ
ejpam-6433	151	18	g	g	PROPN
ejpam-6433	151	19	is	be	AUX
ejpam-6433	151	20	the	the	DET
ejpam-6433	151	21	nonempty	nonempty	ADJ
ejpam-6433	151	22	intersection	intersection	NOUN
ejpam-6433	151	23	of	of	ADP
ejpam-6433	151	24	a	a	DET
ejpam-6433	151	25	family	family	NOUN
ejpam-6433	151	26	of	of	ADP
ejpam-6433	151	27	closed	closed	ADJ
ejpam-6433	151	28	balls	ball	NOUN
ejpam-6433	151	29	.	.	PUNCT
ejpam-6433	152	1	the	the	DET
ejpam-6433	152	2	set	set	NOUN
ejpam-6433	152	3	of	of	ADP
ejpam-6433	152	4	all	all	DET
ejpam-6433	152	5	admissible	admissible	ADJ
ejpam-6433	152	6	subsets	subset	NOUN
ejpam-6433	152	7	of	of	ADP
ejpam-6433	152	8	a	a	DET
ejpam-6433	152	9	hyperconvex	hyperconvex	ADJ
ejpam-6433	152	10	space	space	NOUN
ejpam-6433	152	11	m	m	PROPN
ejpam-6433	152	12	will	will	AUX
ejpam-6433	152	13	be	be	AUX
ejpam-6433	152	14	denoted	denote	VERB
ejpam-6433	152	15	by	by	ADP
ejpam-6433	152	16	a(m	a(m	NOUN
ejpam-6433	152	17	)	)	PUNCT
ejpam-6433	152	18	.	.	PUNCT
ejpam-6433	153	1	it	it	PRON
ejpam-6433	153	2	is	be	AUX
ejpam-6433	153	3	well	well	ADV
ejpam-6433	153	4	-	-	PUNCT
ejpam-6433	153	5	known	know	VERB
ejpam-6433	153	6	that	that	SCONJ
ejpam-6433	153	7	if	if	SCONJ
ejpam-6433	153	8	(	(	PUNCT
ejpam-6433	153	9	m	m	NOUN
ejpam-6433	153	10	,	,	PUNCT
ejpam-6433	153	11	d	d	X
ejpam-6433	153	12	)	)	PUNCT
ejpam-6433	153	13	is	be	AUX
ejpam-6433	153	14	a	a	DET
ejpam-6433	153	15	hyperconvex	hyperconvex	ADJ
ejpam-6433	153	16	space	space	NOUN
ejpam-6433	153	17	,	,	PUNCT
ejpam-6433	153	18	then	then	ADV
ejpam-6433	153	19	every	every	DET
ejpam-6433	153	20	admissible	admissible	ADJ
ejpam-6433	153	21	subset	subset	NOUN
ejpam-6433	153	22	of	of	ADP
ejpam-6433	153	23	m	m	PROPN
ejpam-6433	153	24	is	be	AUX
ejpam-6433	153	25	also	also	ADV
ejpam-6433	153	26	hyperconvex	hyperconvex	ADJ
ejpam-6433	153	27	.	.	PUNCT
ejpam-6433	154	1	for	for	ADP
ejpam-6433	154	2	a	a	DET
ejpam-6433	154	3	nonempty	nonempty	ADJ
ejpam-6433	154	4	and	and	CCONJ
ejpam-6433	154	5	bounded	bound	VERB
ejpam-6433	154	6	subset	subset	VERB
ejpam-6433	154	7	g	g	NOUN
ejpam-6433	154	8	of	of	ADP
ejpam-6433	154	9	a	a	DET
ejpam-6433	154	10	hyperconvex	hyperconvex	ADJ
ejpam-6433	154	11	space	space	NOUN
ejpam-6433	154	12	m	m	VERB
ejpam-6433	154	13	the	the	DET
ejpam-6433	154	14	cover	cover	NOUN
ejpam-6433	154	15	of	of	ADP
ejpam-6433	154	16	g	g	PROPN
ejpam-6433	154	17	is	be	AUX
ejpam-6433	154	18	defined	define	VERB
ejpam-6433	154	19	with	with	ADP
ejpam-6433	154	20	cov(g	cov(g	PROPN
ejpam-6433	154	21	)	)	PUNCT
ejpam-6433	154	22	=	=	SYM
ejpam-6433	154	23	⋂	⋂	PROPN
ejpam-6433	154	24	{	{	PUNCT
ejpam-6433	154	25	b	b	NOUN
ejpam-6433	154	26	⊆	⊆	NUM
ejpam-6433	154	27	m	m	PRON
ejpam-6433	154	28	:	:	PUNCT
ejpam-6433	154	29	b	b	X
ejpam-6433	154	30	is	be	AUX
ejpam-6433	154	31	a	a	DET
ejpam-6433	154	32	closed	closed	ADJ
ejpam-6433	154	33	ball	ball	NOUN
ejpam-6433	154	34	containing	contain	VERB
ejpam-6433	154	35	g	g	NOUN
ejpam-6433	154	36	}	}	PUNCT
ejpam-6433	154	37	.	.	PUNCT
ejpam-6433	155	1	also	also	ADV
ejpam-6433	155	2	,	,	PUNCT
ejpam-6433	155	3	we	we	PRON
ejpam-6433	155	4	set	set	VERB
ejpam-6433	155	5	δx(g	δx(g	PUNCT
ejpam-6433	155	6	)	)	PUNCT
ejpam-6433	155	7	:	:	PUNCT
ejpam-6433	156	1	=	=	SYM
ejpam-6433	156	2	sup	sup	NOUN
ejpam-6433	156	3	y∈g	y∈g	NOUN
ejpam-6433	156	4	{	{	PUNCT
ejpam-6433	156	5	d(x	d(x	PROPN
ejpam-6433	156	6	,	,	PUNCT
ejpam-6433	156	7	y	y	PROPN
ejpam-6433	156	8	)	)	PUNCT
ejpam-6433	156	9	:	:	PUNCT
ejpam-6433	157	1	y	y	PROPN
ejpam-6433	157	2	∈	∈	PROPN
ejpam-6433	157	3	g	g	PROPN
ejpam-6433	157	4	}	}	PUNCT
ejpam-6433	157	5	,	,	PUNCT
ejpam-6433	157	6	for	for	ADP
ejpam-6433	157	7	all	all	PRON
ejpam-6433	157	8	x	x	SYM
ejpam-6433	157	9	∈	∈	PROPN
ejpam-6433	157	10	m.	m.	NOUN
ejpam-6433	157	11	definition	definition	NOUN
ejpam-6433	157	12	9	9	NUM
ejpam-6433	157	13	.	.	PUNCT
ejpam-6433	158	1	a	a	DET
ejpam-6433	158	2	set	set	NOUN
ejpam-6433	158	3	g	g	NOUN
ejpam-6433	158	4	in	in	ADP
ejpam-6433	158	5	a	a	DET
ejpam-6433	158	6	hyperconvex	hyperconvex	ADJ
ejpam-6433	158	7	metric	metric	ADJ
ejpam-6433	158	8	space	space	NOUN
ejpam-6433	158	9	(	(	PUNCT
ejpam-6433	158	10	m	m	PROPN
ejpam-6433	158	11	,	,	PUNCT
ejpam-6433	158	12	d	d	X
ejpam-6433	158	13	)	)	PUNCT
ejpam-6433	158	14	is	be	AUX
ejpam-6433	158	15	said	say	VERB
ejpam-6433	158	16	to	to	PART
ejpam-6433	158	17	be	be	AUX
ejpam-6433	158	18	sub	sub	ADJ
ejpam-6433	158	19	-	-	ADJ
ejpam-6433	158	20	admissible	admissible	ADJ
ejpam-6433	158	21	provided	provide	VERB
ejpam-6433	158	22	that	that	SCONJ
ejpam-6433	158	23	for	for	ADP
ejpam-6433	158	24	any	any	DET
ejpam-6433	158	25	finite	finite	NOUN
ejpam-6433	158	26	subset	subset	NOUN
ejpam-6433	158	27	e	e	NOUN
ejpam-6433	158	28	of	of	ADP
ejpam-6433	158	29	g	g	PROPN
ejpam-6433	158	30	we	we	PRON
ejpam-6433	158	31	have	have	VERB
ejpam-6433	158	32	cov(e	cov(e	PROPN
ejpam-6433	158	33	)	)	PUNCT
ejpam-6433	158	34	⊆	⊆	NUM
ejpam-6433	158	35	g.	g.	NOUN
ejpam-6433	158	36	the	the	DET
ejpam-6433	158	37	hyperconvex	hyperconvex	ADJ
ejpam-6433	158	38	version	version	NOUN
ejpam-6433	158	39	of	of	ADP
ejpam-6433	158	40	schauder	schauder	NOUN
ejpam-6433	158	41	’s	’s	PART
ejpam-6433	158	42	fixed	fix	VERB
ejpam-6433	158	43	problem	problem	NOUN
ejpam-6433	158	44	was	be	AUX
ejpam-6433	158	45	presented	present	VERB
ejpam-6433	158	46	by	by	ADP
ejpam-6433	158	47	r.	r.	PROPN
ejpam-6433	158	48	espinola	espinola	PROPN
ejpam-6433	158	49	as	as	SCONJ
ejpam-6433	158	50	follows	follow	VERB
ejpam-6433	158	51	.	.	PUNCT
ejpam-6433	159	1	theorem	theorem	ADJ
ejpam-6433	159	2	7	7	NUM
ejpam-6433	159	3	.	.	PUNCT
ejpam-6433	160	1	(	(	PUNCT
ejpam-6433	160	2	lemma	lemma	PROPN
ejpam-6433	160	3	3	3	NUM
ejpam-6433	160	4	of	of	ADP
ejpam-6433	160	5	[	[	X
ejpam-6433	160	6	2	2	NUM
ejpam-6433	160	7	]	]	PUNCT
ejpam-6433	160	8	)	)	PUNCT
ejpam-6433	160	9	let	let	VERB
ejpam-6433	160	10	(	(	PUNCT
ejpam-6433	160	11	m	m	NOUN
ejpam-6433	160	12	,	,	PUNCT
ejpam-6433	160	13	d	d	X
ejpam-6433	160	14	)	)	PUNCT
ejpam-6433	160	15	be	be	AUX
ejpam-6433	160	16	a	a	DET
ejpam-6433	160	17	compact	compact	ADJ
ejpam-6433	160	18	and	and	CCONJ
ejpam-6433	160	19	hyperconvex	hyperconvex	ADJ
ejpam-6433	160	20	metric	metric	ADJ
ejpam-6433	160	21	space	space	NOUN
ejpam-6433	160	22	.	.	PUNCT
ejpam-6433	161	1	if	if	SCONJ
ejpam-6433	161	2	t	t	NOUN
ejpam-6433	161	3	:	:	PUNCT
ejpam-6433	161	4	m	m	VERB
ejpam-6433	161	5	→	→	NOUN
ejpam-6433	161	6	m	m	VERB
ejpam-6433	161	7	is	be	AUX
ejpam-6433	161	8	continuous	continuous	ADJ
ejpam-6433	161	9	,	,	PUNCT
ejpam-6433	161	10	then	then	ADV
ejpam-6433	161	11	t	t	PROPN
ejpam-6433	161	12	has	have	VERB
ejpam-6433	161	13	a	a	DET
ejpam-6433	161	14	fixed	fix	VERB
ejpam-6433	161	15	point	point	NOUN
ejpam-6433	161	16	.	.	PUNCT
ejpam-6433	162	1	m.	m.	NOUN
ejpam-6433	162	2	gabeleh	gabeleh	PROPN
ejpam-6433	162	3	,	,	PUNCT
ejpam-6433	162	4	j.	j.	PROPN
ejpam-6433	162	5	markin	markin	PROPN
ejpam-6433	162	6	,	,	PUNCT
ejpam-6433	162	7	m.	m.	NOUN
ejpam-6433	162	8	aphane	aphane	PROPN
ejpam-6433	162	9	/	/	SYM
ejpam-6433	162	10	eur	eur	PROPN
ejpam-6433	162	11	.	.	PUNCT
ejpam-6433	163	1	j.	j.	PROPN
ejpam-6433	163	2	pure	pure	PROPN
ejpam-6433	163	3	appl	appl	PROPN
ejpam-6433	163	4	.	.	PROPN
ejpam-6433	163	5	math	math	PROPN
ejpam-6433	163	6	,	,	PUNCT
ejpam-6433	163	7	18	18	NUM
ejpam-6433	163	8	(	(	PUNCT
ejpam-6433	163	9	3	3	NUM
ejpam-6433	163	10	)	)	PUNCT
ejpam-6433	163	11	(	(	PUNCT
ejpam-6433	163	12	2025	2025	NUM
ejpam-6433	163	13	)	)	PUNCT
ejpam-6433	163	14	,	,	PUNCT
ejpam-6433	163	15	6433	6433	NUM
ejpam-6433	163	16	8	8	NUM
ejpam-6433	163	17	of	of	ADP
ejpam-6433	163	18	17	17	NUM
ejpam-6433	163	19	an	an	DET
ejpam-6433	163	20	important	important	ADJ
ejpam-6433	163	21	observation	observation	NOUN
ejpam-6433	163	22	about	about	ADP
ejpam-6433	163	23	theorem	theorem	VERB
ejpam-6433	163	24	7	7	NUM
ejpam-6433	163	25	is	be	AUX
ejpam-6433	163	26	that	that	SCONJ
ejpam-6433	163	27	if	if	SCONJ
ejpam-6433	163	28	m	m	NOUN
ejpam-6433	163	29	is	be	AUX
ejpam-6433	163	30	a	a	DET
ejpam-6433	163	31	hyperconvex	hyperconvex	NOUN
ejpam-6433	163	32	subset	subset	NOUN
ejpam-6433	163	33	of	of	ADP
ejpam-6433	163	34	a	a	DET
ejpam-6433	163	35	banach	banach	NOUN
ejpam-6433	163	36	space	space	NOUN
ejpam-6433	163	37	x	x	NOUN
ejpam-6433	163	38	,	,	PUNCT
ejpam-6433	163	39	then	then	ADV
ejpam-6433	163	40	m	m	NOUN
ejpam-6433	163	41	may	may	AUX
ejpam-6433	163	42	not	not	PART
ejpam-6433	163	43	be	be	AUX
ejpam-6433	163	44	convex	convex	ADJ
ejpam-6433	163	45	and	and	CCONJ
ejpam-6433	163	46	so	so	ADV
ejpam-6433	163	47	the	the	DET
ejpam-6433	163	48	existence	existence	NOUN
ejpam-6433	163	49	of	of	ADP
ejpam-6433	163	50	a	a	DET
ejpam-6433	163	51	fixed	fix	VERB
ejpam-6433	163	52	point	point	NOUN
ejpam-6433	163	53	for	for	ADP
ejpam-6433	163	54	the	the	DET
ejpam-6433	163	55	continuous	continuous	ADJ
ejpam-6433	163	56	mapping	mapping	NOUN
ejpam-6433	163	57	t	t	NOUN
ejpam-6433	163	58	can	can	AUX
ejpam-6433	163	59	not	not	PART
ejpam-6433	163	60	be	be	AUX
ejpam-6433	163	61	obtained	obtain	VERB
ejpam-6433	163	62	from	from	ADP
ejpam-6433	163	63	the	the	DET
ejpam-6433	163	64	schauder	schauder	NOUN
ejpam-6433	163	65	’s	’s	PART
ejpam-6433	163	66	fixed	fix	VERB
ejpam-6433	163	67	point	point	NOUN
ejpam-6433	163	68	theorem	theorem	VERB
ejpam-6433	163	69	.	.	PUNCT
ejpam-6433	164	1	we	we	PRON
ejpam-6433	164	2	are	be	AUX
ejpam-6433	164	3	now	now	ADV
ejpam-6433	164	4	in	in	ADP
ejpam-6433	164	5	position	position	NOUN
ejpam-6433	164	6	to	to	PART
ejpam-6433	164	7	state	state	VERB
ejpam-6433	164	8	the	the	DET
ejpam-6433	164	9	first	first	ADJ
ejpam-6433	164	10	existence	existence	NOUN
ejpam-6433	164	11	result	result	NOUN
ejpam-6433	164	12	of	of	ADP
ejpam-6433	164	13	this	this	DET
ejpam-6433	164	14	paper	paper	NOUN
ejpam-6433	164	15	which	which	PRON
ejpam-6433	164	16	is	be	AUX
ejpam-6433	164	17	not	not	PART
ejpam-6433	164	18	only	only	ADV
ejpam-6433	164	19	a	a	DET
ejpam-6433	164	20	different	different	ADJ
ejpam-6433	164	21	version	version	NOUN
ejpam-6433	164	22	of	of	ADP
ejpam-6433	164	23	theorem	theorem	NOUN
ejpam-6433	164	24	1	1	NUM
ejpam-6433	164	25	in	in	ADP
ejpam-6433	164	26	the	the	DET
ejpam-6433	164	27	framework	framework	NOUN
ejpam-6433	164	28	of	of	ADP
ejpam-6433	164	29	hyperconvex	hyperconvex	ADJ
ejpam-6433	164	30	spaces	space	NOUN
ejpam-6433	164	31	,	,	PUNCT
ejpam-6433	164	32	but	but	CCONJ
ejpam-6433	164	33	also	also	ADV
ejpam-6433	164	34	is	be	AUX
ejpam-6433	164	35	a	a	DET
ejpam-6433	164	36	generalization	generalization	NOUN
ejpam-6433	164	37	of	of	ADP
ejpam-6433	164	38	theorem	theorem	ADJ
ejpam-6433	164	39	7	7	NUM
ejpam-6433	164	40	.	.	PUNCT
ejpam-6433	164	41	theorem	theorem	NOUN
ejpam-6433	164	42	8	8	NUM
ejpam-6433	164	43	.	.	PUNCT
ejpam-6433	165	1	(	(	PUNCT
ejpam-6433	165	2	compare	compare	VERB
ejpam-6433	165	3	to	to	ADP
ejpam-6433	165	4	theorem	theorem	ADJ
ejpam-6433	165	5	1	1	NUM
ejpam-6433	165	6	and	and	CCONJ
ejpam-6433	165	7	theorem	theorem	VERB
ejpam-6433	165	8	7	7	NUM
ejpam-6433	165	9	)	)	PUNCT
ejpam-6433	165	10	let	let	NOUN
ejpam-6433	165	11	(	(	PUNCT
ejpam-6433	165	12	m	m	NOUN
ejpam-6433	165	13	,	,	PUNCT
ejpam-6433	165	14	d	d	X
ejpam-6433	165	15	)	)	PUNCT
ejpam-6433	165	16	be	be	AUX
ejpam-6433	165	17	a	a	DET
ejpam-6433	165	18	hyperconvex	hyperconvex	ADJ
ejpam-6433	165	19	metric	metric	ADJ
ejpam-6433	165	20	space	space	NOUN
ejpam-6433	165	21	and	and	CCONJ
ejpam-6433	165	22	(	(	PUNCT
ejpam-6433	165	23	g	g	NOUN
ejpam-6433	165	24	,	,	PUNCT
ejpam-6433	165	25	h	h	NOUN
ejpam-6433	165	26	)	)	PUNCT
ejpam-6433	165	27	be	be	AUX
ejpam-6433	165	28	a	a	DET
ejpam-6433	165	29	nonempty	nonempty	ADJ
ejpam-6433	165	30	,	,	PUNCT
ejpam-6433	165	31	compact	compact	ADJ
ejpam-6433	165	32	and	and	CCONJ
ejpam-6433	165	33	hyperconvex	hyperconvex	ADJ
ejpam-6433	165	34	pair	pair	NOUN
ejpam-6433	165	35	in	in	ADP
ejpam-6433	165	36	m.	m.	NOUN
ejpam-6433	165	37	if	if	SCONJ
ejpam-6433	165	38	t	t	NOUN
ejpam-6433	165	39	:	:	PUNCT
ejpam-6433	165	40	g∪h	g∪h	NOUN
ejpam-6433	165	41	→	→	SYM
ejpam-6433	165	42	g∪h	g∪h	NOUN
ejpam-6433	165	43	is	be	AUX
ejpam-6433	165	44	a	a	DET
ejpam-6433	165	45	cyclic	cyclic	ADJ
ejpam-6433	165	46	relatively	relatively	ADV
ejpam-6433	165	47	u	u	ADJ
ejpam-6433	165	48	-	-	ADJ
ejpam-6433	165	49	continuous	continuous	ADJ
ejpam-6433	165	50	mapping	mapping	NOUN
ejpam-6433	165	51	,	,	PUNCT
ejpam-6433	165	52	then	then	ADV
ejpam-6433	165	53	t	t	PROPN
ejpam-6433	165	54	has	have	VERB
ejpam-6433	165	55	a	a	DET
ejpam-6433	165	56	best	good	ADJ
ejpam-6433	165	57	proximity	proximity	NOUN
ejpam-6433	165	58	point	point	NOUN
ejpam-6433	165	59	.	.	PUNCT
ejpam-6433	166	1	proof	proof	NOUN
ejpam-6433	166	2	.	.	PUNCT
ejpam-6433	167	1	by	by	ADP
ejpam-6433	167	2	statement	statement	NOUN
ejpam-6433	167	3	(	(	PUNCT
ejpam-6433	167	4	ii	ii	NOUN
ejpam-6433	167	5	)	)	PUNCT
ejpam-6433	167	6	on	on	ADP
ejpam-6433	167	7	page	page	NOUN
ejpam-6433	167	8	4	4	NUM
ejpam-6433	167	9	,	,	PUNCT
ejpam-6433	167	10	the	the	DET
ejpam-6433	167	11	proximal	proximal	ADJ
ejpam-6433	167	12	pair	pair	NOUN
ejpam-6433	167	13	(	(	PUNCT
ejpam-6433	167	14	g0,h0	g0,h0	PROPN
ejpam-6433	167	15	)	)	PUNCT
ejpam-6433	167	16	is	be	AUX
ejpam-6433	167	17	nonempty	nonempty	ADJ
ejpam-6433	167	18	.	.	PUNCT
ejpam-6433	168	1	to	to	PART
ejpam-6433	168	2	see	see	VERB
ejpam-6433	168	3	that	that	SCONJ
ejpam-6433	168	4	both	both	DET
ejpam-6433	168	5	sets	set	NOUN
ejpam-6433	168	6	are	be	AUX
ejpam-6433	168	7	compact	compact	ADJ
ejpam-6433	168	8	,	,	PUNCT
ejpam-6433	168	9	assume	assume	VERB
ejpam-6433	168	10	that	that	SCONJ
ejpam-6433	168	11	{	{	PUNCT
ejpam-6433	168	12	xn	xn	X
ejpam-6433	168	13	}	}	PUNCT
ejpam-6433	168	14	is	be	AUX
ejpam-6433	168	15	a	a	DET
ejpam-6433	168	16	sequence	sequence	NOUN
ejpam-6433	168	17	in	in	ADP
ejpam-6433	168	18	g0	g0	ADJ
ejpam-6433	168	19	converging	converge	VERB
ejpam-6433	168	20	to	to	ADP
ejpam-6433	168	21	a	a	DET
ejpam-6433	168	22	point	point	NOUN
ejpam-6433	168	23	p	p	X
ejpam-6433	168	24	∈	∈	PROPN
ejpam-6433	168	25	g.	g.	NOUN
ejpam-6433	168	26	then	then	ADV
ejpam-6433	168	27	,	,	PUNCT
ejpam-6433	168	28	there	there	PRON
ejpam-6433	168	29	exists	exist	VERB
ejpam-6433	168	30	a	a	DET
ejpam-6433	168	31	corresponding	correspond	VERB
ejpam-6433	168	32	sequence	sequence	NOUN
ejpam-6433	168	33	{	{	PUNCT
ejpam-6433	168	34	yn	yn	NOUN
ejpam-6433	168	35	}	}	PUNCT
ejpam-6433	168	36	in	in	ADP
ejpam-6433	168	37	h	h	NOUN
ejpam-6433	168	38	such	such	ADJ
ejpam-6433	168	39	that	that	SCONJ
ejpam-6433	168	40	d(xn	d(xn	PROPN
ejpam-6433	168	41	,	,	PUNCT
ejpam-6433	168	42	yn	yn	PROPN
ejpam-6433	168	43	)	)	PUNCT
ejpam-6433	168	44	=	=	SYM
ejpam-6433	168	45	d(g	d(g	PROPN
ejpam-6433	168	46	,	,	PUNCT
ejpam-6433	168	47	h	h	NOUN
ejpam-6433	168	48	)	)	PUNCT
ejpam-6433	168	49	.	.	PUNCT
ejpam-6433	169	1	by	by	ADP
ejpam-6433	169	2	compactness	compactness	NOUN
ejpam-6433	169	3	of	of	ADP
ejpam-6433	169	4	h	h	NOUN
ejpam-6433	169	5	,	,	PUNCT
ejpam-6433	169	6	{	{	PUNCT
ejpam-6433	169	7	yn	yn	NOUN
ejpam-6433	169	8	}	}	PUNCT
ejpam-6433	169	9	has	have	VERB
ejpam-6433	169	10	a	a	DET
ejpam-6433	169	11	convergent	convergent	NOUN
ejpam-6433	169	12	subsequence	subsequence	NOUN
ejpam-6433	169	13	,	,	PUNCT
ejpam-6433	169	14	also	also	ADV
ejpam-6433	169	15	labeled	label	VERB
ejpam-6433	169	16	as	as	ADP
ejpam-6433	169	17	{	{	PUNCT
ejpam-6433	169	18	yn	yn	NOUN
ejpam-6433	169	19	}	}	PUNCT
ejpam-6433	169	20	,	,	PUNCT
ejpam-6433	169	21	with	with	ADP
ejpam-6433	169	22	limit	limit	NOUN
ejpam-6433	169	23	q	q	X
ejpam-6433	169	24	,	,	PUNCT
ejpam-6433	169	25	such	such	ADJ
ejpam-6433	169	26	that	that	PRON
ejpam-6433	169	27	limn→+∞	limn→+∞	VERB
ejpam-6433	169	28	d(xn	d(xn	PROPN
ejpam-6433	169	29	,	,	PUNCT
ejpam-6433	169	30	yn	yn	PROPN
ejpam-6433	169	31	)	)	PUNCT
ejpam-6433	169	32	=	=	SYM
ejpam-6433	169	33	d(p	d(p	PROPN
ejpam-6433	169	34	,	,	PUNCT
ejpam-6433	169	35	q	q	NOUN
ejpam-6433	169	36	)	)	PUNCT
ejpam-6433	169	37	=	=	SYM
ejpam-6433	169	38	d(g	d(g	PROPN
ejpam-6433	169	39	,	,	PUNCT
ejpam-6433	169	40	h	h	NOUN
ejpam-6433	169	41	)	)	PUNCT
ejpam-6433	169	42	.	.	PUNCT
ejpam-6433	170	1	therefore	therefore	ADV
ejpam-6433	170	2	,	,	PUNCT
ejpam-6433	170	3	g0	g0	PROPN
ejpam-6433	170	4	and	and	CCONJ
ejpam-6433	170	5	h0	h0	NOUN
ejpam-6433	170	6	are	be	AUX
ejpam-6433	170	7	closed	close	VERB
ejpam-6433	170	8	subsets	subset	NOUN
ejpam-6433	170	9	of	of	ADP
ejpam-6433	170	10	compact	compact	ADJ
ejpam-6433	170	11	sets	set	NOUN
ejpam-6433	170	12	,	,	PUNCT
ejpam-6433	170	13	hence	hence	ADV
ejpam-6433	170	14	both	both	PRON
ejpam-6433	170	15	are	be	AUX
ejpam-6433	170	16	compact	compact	ADJ
ejpam-6433	170	17	.	.	PUNCT
ejpam-6433	171	1	to	to	PART
ejpam-6433	171	2	prove	prove	VERB
ejpam-6433	171	3	hyperconvexity	hyperconvexity	NOUN
ejpam-6433	171	4	of	of	ADP
ejpam-6433	171	5	the	the	DET
ejpam-6433	171	6	pair	pair	NOUN
ejpam-6433	171	7	(	(	PUNCT
ejpam-6433	171	8	g0,h0	g0,h0	PROPN
ejpam-6433	171	9	)	)	PUNCT
ejpam-6433	171	10	,	,	PUNCT
ejpam-6433	171	11	choose	choose	VERB
ejpam-6433	171	12	points	point	NOUN
ejpam-6433	171	13	{	{	PUNCT
ejpam-6433	171	14	xi	xi	NOUN
ejpam-6433	171	15	}	}	PUNCT
ejpam-6433	171	16	in	in	ADP
ejpam-6433	171	17	g0	g0	PROPN
ejpam-6433	171	18	and	and	CCONJ
ejpam-6433	171	19	{	{	PUNCT
ejpam-6433	171	20	yi	yi	NOUN
ejpam-6433	171	21	}	}	PUNCT
ejpam-6433	171	22	in	in	ADP
ejpam-6433	171	23	h0	h0	PROPN
ejpam-6433	171	24	such	such	ADJ
ejpam-6433	171	25	that	that	SCONJ
ejpam-6433	171	26	d(xi	d(xi	PROPN
ejpam-6433	171	27	,	,	PUNCT
ejpam-6433	171	28	yi	yi	NOUN
ejpam-6433	171	29	)	)	PUNCT
ejpam-6433	171	30	=	=	SYM
ejpam-6433	172	1	d(g	d(g	PROPN
ejpam-6433	172	2	,	,	PUNCT
ejpam-6433	172	3	h	h	NOUN
ejpam-6433	172	4	)	)	PUNCT
ejpam-6433	172	5	.	.	PUNCT
ejpam-6433	173	1	consider	consider	VERB
ejpam-6433	173	2	the	the	DET
ejpam-6433	173	3	collection	collection	NOUN
ejpam-6433	173	4	of	of	ADP
ejpam-6433	173	5	balls	ball	NOUN
ejpam-6433	173	6	{	{	PUNCT
ejpam-6433	173	7	b(xi	b(xi	PROPN
ejpam-6433	173	8	;	;	PUNCT
ejpam-6433	173	9	ri	ri	X
ejpam-6433	173	10	)	)	PUNCT
ejpam-6433	173	11	}	}	PUNCT
ejpam-6433	173	12	and	and	CCONJ
ejpam-6433	173	13	{	{	PUNCT
ejpam-6433	173	14	b(yi	b(yi	NUM
ejpam-6433	173	15	;	;	PUNCT
ejpam-6433	173	16	ri	ri	X
ejpam-6433	173	17	)	)	PUNCT
ejpam-6433	173	18	}	}	PUNCT
ejpam-6433	173	19	such	such	ADJ
ejpam-6433	173	20	that	that	SCONJ
ejpam-6433	173	21	d(xi	d(xi	PROPN
ejpam-6433	173	22	,	,	PUNCT
ejpam-6433	173	23	xj	xj	PROPN
ejpam-6433	173	24	)	)	PUNCT
ejpam-6433	173	25	≤	≤	NUM
ejpam-6433	173	26	ri+	ri+	PROPN
ejpam-6433	173	27	rj	rj	PROPN
ejpam-6433	173	28	and	and	CCONJ
ejpam-6433	173	29	d(yi	d(yi	PROPN
ejpam-6433	173	30	,	,	PUNCT
ejpam-6433	173	31	yj	yj	PROPN
ejpam-6433	173	32	)	)	PUNCT
ejpam-6433	173	33	≤	≤	PROPN
ejpam-6433	173	34	ri	ri	PROPN
ejpam-6433	173	35	+	+	CCONJ
ejpam-6433	173	36	rj	rj	PROPN
ejpam-6433	173	37	.	.	PUNCT
ejpam-6433	174	1	by	by	ADP
ejpam-6433	174	2	a	a	DET
ejpam-6433	174	3	result	result	NOUN
ejpam-6433	174	4	of	of	ADP
ejpam-6433	174	5	khamsi	khamsi	NOUN
ejpam-6433	174	6	et	et	PROPN
ejpam-6433	174	7	al	al	PROPN
ejpam-6433	174	8	.	.	PUNCT
ejpam-6433	175	1	[	[	X
ejpam-6433	175	2	21	21	NUM
ejpam-6433	175	3	]	]	PUNCT
ejpam-6433	175	4	,	,	PUNCT
ejpam-6433	175	5	dh	dh	INTJ
ejpam-6433	175	6	(	(	PUNCT
ejpam-6433	175	7	⋂	⋂	PROPN
ejpam-6433	175	8	i	i	PRON
ejpam-6433	175	9	b(xi	b(xi	VERB
ejpam-6433	175	10	;	;	PUNCT
ejpam-6433	175	11	ri	ri	X
ejpam-6433	175	12	)	)	PUNCT
ejpam-6433	175	13	,	,	PUNCT
ejpam-6433	175	14	⋂	⋂	PROPN
ejpam-6433	175	15	i	i	PROPN
ejpam-6433	175	16	b(yi	b(yi	NUM
ejpam-6433	175	17	;	;	PUNCT
ejpam-6433	175	18	ri	ri	NOUN
ejpam-6433	175	19	)	)	PUNCT
ejpam-6433	175	20	)	)	PUNCT
ejpam-6433	176	1	≤	≤	NUM
ejpam-6433	177	1	sup	sup	NOUN
ejpam-6433	177	2	i	i	PRON
ejpam-6433	177	3	d(xi	d(xi	PROPN
ejpam-6433	177	4	,	,	PUNCT
ejpam-6433	177	5	yi	yi	NOUN
ejpam-6433	177	6	)	)	PUNCT
ejpam-6433	177	7	=	=	SYM
ejpam-6433	178	1	d(g	d(g	PROPN
ejpam-6433	178	2	,	,	PUNCT
ejpam-6433	178	3	h	h	NOUN
ejpam-6433	178	4	)	)	PUNCT
ejpam-6433	178	5	,	,	PUNCT
ejpam-6433	178	6	where	where	SCONJ
ejpam-6433	178	7	dh	dh	NOUN
ejpam-6433	178	8	is	be	AUX
ejpam-6433	178	9	the	the	DET
ejpam-6433	178	10	hausdorff	hausdorff	NOUN
ejpam-6433	178	11	metric	metric	NOUN
ejpam-6433	178	12	derived	derive	VERB
ejpam-6433	178	13	from	from	ADP
ejpam-6433	178	14	the	the	DET
ejpam-6433	178	15	metric	metric	ADJ
ejpam-6433	178	16	d.	d.	PROPN
ejpam-6433	178	17	this	this	PRON
ejpam-6433	178	18	shows	show	VERB
ejpam-6433	178	19	that	that	SCONJ
ejpam-6433	178	20	b(xi	b(xi	VERB
ejpam-6433	178	21	;	;	PUNCT
ejpam-6433	178	22	ri	ri	X
ejpam-6433	178	23	)	)	PUNCT
ejpam-6433	178	24	∩	∩	PROPN
ejpam-6433	178	25	g0	g0	ADJ
ejpam-6433	178	26	̸=	̸=	PROPN
ejpam-6433	178	27	∅	∅	NOUN
ejpam-6433	178	28	,	,	PUNCT
ejpam-6433	178	29	implying	imply	VERB
ejpam-6433	178	30	that	that	SCONJ
ejpam-6433	178	31	g0	g0	NOUN
ejpam-6433	178	32	is	be	AUX
ejpam-6433	178	33	hyperconvex	hyperconvex	ADJ
ejpam-6433	178	34	,	,	PUNCT
ejpam-6433	178	35	and	and	CCONJ
ejpam-6433	178	36	similarly	similarly	ADV
ejpam-6433	178	37	that	that	DET
ejpam-6433	178	38	h0	h0	NOUN
ejpam-6433	178	39	is	be	AUX
ejpam-6433	178	40	hyperconvex	hyperconvex	ADJ
ejpam-6433	178	41	.	.	PUNCT
ejpam-6433	179	1	using	use	VERB
ejpam-6433	179	2	the	the	DET
ejpam-6433	179	3	fact	fact	NOUN
ejpam-6433	179	4	that	that	SCONJ
ejpam-6433	179	5	t	t	PROPN
ejpam-6433	179	6	is	be	AUX
ejpam-6433	179	7	relatively	relatively	ADV
ejpam-6433	179	8	u	u	NOUN
ejpam-6433	179	9	-	-	ADJ
ejpam-6433	179	10	continuous	continuous	ADJ
ejpam-6433	179	11	,	,	PUNCT
ejpam-6433	179	12	(	(	PUNCT
ejpam-6433	179	13	g0,h0	g0,h0	PROPN
ejpam-6433	179	14	)	)	PUNCT
ejpam-6433	179	15	is	be	AUX
ejpam-6433	179	16	t	t	PROPN
ejpam-6433	179	17	-invariant	-invariant	PROPN
ejpam-6433	179	18	.	.	PUNCT
ejpam-6433	180	1	define	define	VERB
ejpam-6433	180	2	a	a	DET
ejpam-6433	180	3	multivalued	multivalue	VERB
ejpam-6433	180	4	mapping	mapping	NOUN
ejpam-6433	180	5	f	f	NOUN
ejpam-6433	180	6	:	:	PUNCT
ejpam-6433	180	7	g0	g0	PROPN
ejpam-6433	180	8	→	→	SYM
ejpam-6433	180	9	2g0	2g0	NOUN
ejpam-6433	180	10	by	by	ADP
ejpam-6433	180	11	f	f	PROPN
ejpam-6433	180	12	(	(	PUNCT
ejpam-6433	180	13	v	v	NOUN
ejpam-6433	180	14	)	)	PUNCT
ejpam-6433	181	1	:	:	PUNCT
ejpam-6433	181	2	=	=	SYM
ejpam-6433	181	3	b	b	X
ejpam-6433	181	4	(	(	PUNCT
ejpam-6433	181	5	tv	tv	NOUN
ejpam-6433	181	6	;	;	PUNCT
ejpam-6433	181	7	d(g	d(g	PROPN
ejpam-6433	181	8	,	,	PUNCT
ejpam-6433	181	9	h	h	NOUN
ejpam-6433	181	10	)	)	PUNCT
ejpam-6433	181	11	)	)	PUNCT
ejpam-6433	182	1	⋂	⋂	PROPN
ejpam-6433	182	2	g0	g0	NOUN
ejpam-6433	182	3	,	,	PUNCT
ejpam-6433	182	4	for	for	ADP
ejpam-6433	182	5	all	all	DET
ejpam-6433	182	6	v	v	PRON
ejpam-6433	182	7	∈	∈	PROPN
ejpam-6433	182	8	g0	g0	PROPN
ejpam-6433	182	9	.	.	PUNCT
ejpam-6433	182	10	note	note	VERB
ejpam-6433	182	11	that	that	SCONJ
ejpam-6433	182	12	the	the	DET
ejpam-6433	182	13	values	value	NOUN
ejpam-6433	182	14	of	of	ADP
ejpam-6433	182	15	f	f	PROPN
ejpam-6433	182	16	are	be	AUX
ejpam-6433	182	17	nonempty	nonempty	ADJ
ejpam-6433	182	18	.	.	PUNCT
ejpam-6433	183	1	indeed	indeed	ADV
ejpam-6433	183	2	,	,	PUNCT
ejpam-6433	183	3	for	for	ADP
ejpam-6433	183	4	any	any	DET
ejpam-6433	183	5	v	v	PROPN
ejpam-6433	183	6	∈	∈	PROPN
ejpam-6433	183	7	g0	g0	NOUN
ejpam-6433	183	8	,	,	PUNCT
ejpam-6433	183	9	there	there	PRON
ejpam-6433	183	10	exists	exist	VERB
ejpam-6433	183	11	y	y	PROPN
ejpam-6433	183	12	∈	∈	PROPN
ejpam-6433	183	13	h0	h0	NOUN
ejpam-6433	184	1	such	such	ADJ
ejpam-6433	184	2	that	that	SCONJ
ejpam-6433	184	3	d(v	d(v	PROPN
ejpam-6433	184	4	,	,	PUNCT
ejpam-6433	184	5	y	y	NOUN
ejpam-6433	184	6	)	)	PUNCT
ejpam-6433	184	7	=	=	SYM
ejpam-6433	184	8	d(g	d(g	PROPN
ejpam-6433	184	9	,	,	PUNCT
ejpam-6433	184	10	h	h	NOUN
ejpam-6433	184	11	)	)	PUNCT
ejpam-6433	184	12	and	and	CCONJ
ejpam-6433	184	13	again	again	ADV
ejpam-6433	184	14	using	use	VERB
ejpam-6433	184	15	the	the	DET
ejpam-6433	184	16	relatively	relatively	ADV
ejpam-6433	184	17	u	u	NOUN
ejpam-6433	184	18	-	-	NOUN
ejpam-6433	184	19	continuity	continuity	NOUN
ejpam-6433	184	20	of	of	ADP
ejpam-6433	184	21	t	t	PROPN
ejpam-6433	184	22	,	,	PUNCT
ejpam-6433	184	23	d(tv	d(tv	PROPN
ejpam-6433	184	24	,	,	PUNCT
ejpam-6433	184	25	ty	ty	INTJ
ejpam-6433	184	26	)	)	PUNCT
ejpam-6433	184	27	=	=	SYM
ejpam-6433	185	1	d(g	d(g	PROPN
ejpam-6433	185	2	,	,	PUNCT
ejpam-6433	185	3	h	h	NOUN
ejpam-6433	185	4	)	)	PUNCT
ejpam-6433	185	5	and	and	CCONJ
ejpam-6433	185	6	so	so	ADV
ejpam-6433	185	7	,	,	PUNCT
ejpam-6433	185	8	ty	ty	NUM
ejpam-6433	185	9	∈	∈	PROPN
ejpam-6433	185	10	b	b	PROPN
ejpam-6433	185	11	(	(	PUNCT
ejpam-6433	185	12	tv	tv	NOUN
ejpam-6433	185	13	;	;	PUNCT
ejpam-6433	185	14	d(g	d(g	PROPN
ejpam-6433	185	15	,	,	PUNCT
ejpam-6433	185	16	h	h	NOUN
ejpam-6433	185	17	)	)	PUNCT
ejpam-6433	185	18	)	)	PUNCT
ejpam-6433	186	1	⋂	⋂	PROPN
ejpam-6433	186	2	g0	g0	PROPN
ejpam-6433	186	3	.	.	PUNCT
ejpam-6433	187	1	we	we	PRON
ejpam-6433	187	2	claim	claim	VERB
ejpam-6433	187	3	that	that	SCONJ
ejpam-6433	187	4	f	f	PROPN
ejpam-6433	187	5	is	be	AUX
ejpam-6433	187	6	almost	almost	ADV
ejpam-6433	187	7	lower	low	ADJ
ejpam-6433	187	8	-	-	PUNCT
ejpam-6433	187	9	semicontinuous	semicontinuous	ADJ
ejpam-6433	187	10	.	.	PUNCT
ejpam-6433	188	1	let	let	VERB
ejpam-6433	188	2	x0	x0	PROPN
ejpam-6433	188	3	∈	∈	PROPN
ejpam-6433	188	4	g0	g0	PROPN
ejpam-6433	188	5	.	.	PUNCT
ejpam-6433	189	1	then	then	ADV
ejpam-6433	189	2	there	there	PRON
ejpam-6433	189	3	is	be	VERB
ejpam-6433	189	4	an	an	DET
ejpam-6433	189	5	element	element	NOUN
ejpam-6433	189	6	y0	y0	PROPN
ejpam-6433	189	7	∈	∈	NOUN
ejpam-6433	189	8	h0	h0	NOUN
ejpam-6433	189	9	such	such	ADJ
ejpam-6433	189	10	that	that	DET
ejpam-6433	189	11	d(x0	d(x0	NOUN
ejpam-6433	189	12	,	,	PUNCT
ejpam-6433	189	13	y0	y0	PROPN
ejpam-6433	189	14	)	)	PUNCT
ejpam-6433	189	15	=	=	SYM
ejpam-6433	189	16	d(g	d(g	PROPN
ejpam-6433	189	17	,	,	PUNCT
ejpam-6433	189	18	h	h	NOUN
ejpam-6433	189	19	)	)	PUNCT
ejpam-6433	189	20	.	.	PUNCT
ejpam-6433	190	1	now	now	ADV
ejpam-6433	190	2	for	for	ADP
ejpam-6433	190	3	given	give	VERB
ejpam-6433	190	4	ε	ε	PROPN
ejpam-6433	190	5	>	>	X
ejpam-6433	190	6	0	0	PUNCT
ejpam-6433	191	1	there	there	PRON
ejpam-6433	191	2	exists	exist	VERB
ejpam-6433	191	3	δ	δ	PROPN
ejpam-6433	191	4	>	>	X
ejpam-6433	191	5	0	0	NUM
ejpam-6433	192	1	such	such	ADJ
ejpam-6433	192	2	that	that	SCONJ
ejpam-6433	192	3	if	if	SCONJ
ejpam-6433	192	4	z	z	PROPN
ejpam-6433	192	5	∈	∈	VERB
ejpam-6433	192	6	g	g	NOUN
ejpam-6433	192	7	with	with	ADP
ejpam-6433	192	8	d(z	d(z	NOUN
ejpam-6433	192	9	,	,	PUNCT
ejpam-6433	192	10	y0	y0	PROPN
ejpam-6433	192	11	)	)	PUNCT
ejpam-6433	192	12	<	<	X
ejpam-6433	192	13	δ	δ	PROPN
ejpam-6433	192	14	+	+	PROPN
ejpam-6433	192	15	d(g	d(g	PROPN
ejpam-6433	192	16	,	,	PUNCT
ejpam-6433	192	17	h	h	NOUN
ejpam-6433	192	18	)	)	PUNCT
ejpam-6433	192	19	,	,	PUNCT
ejpam-6433	192	20	then	then	ADV
ejpam-6433	192	21	d(tz	d(tz	NUM
ejpam-6433	192	22	,	,	PUNCT
ejpam-6433	192	23	ty	ty	INTJ
ejpam-6433	192	24	)	)	PUNCT
ejpam-6433	192	25	<	<	X
ejpam-6433	192	26	ε+d(g	ε+d(g	SYM
ejpam-6433	192	27	,	,	PUNCT
ejpam-6433	192	28	h	h	NOUN
ejpam-6433	192	29	)	)	PUNCT
ejpam-6433	192	30	.	.	PUNCT
ejpam-6433	193	1	set	set	PROPN
ejpam-6433	193	2	u(x0	u(x0	PROPN
ejpam-6433	193	3	,	,	PUNCT
ejpam-6433	193	4	δ	δ	PROPN
ejpam-6433	193	5	)	)	PUNCT
ejpam-6433	193	6	:	:	PUNCT
ejpam-6433	194	1	=	=	SYM
ejpam-6433	194	2	{	{	PUNCT
ejpam-6433	194	3	u	u	PROPN
ejpam-6433	194	4	∈	∈	PROPN
ejpam-6433	194	5	g0	g0	NOUN
ejpam-6433	194	6	:	:	PUNCT
ejpam-6433	194	7	d(u	d(u	PROPN
ejpam-6433	194	8	,	,	PUNCT
ejpam-6433	194	9	x0	x0	PROPN
ejpam-6433	194	10	)	)	PUNCT
ejpam-6433	194	11	<	<	X
ejpam-6433	194	12	δ	δ	PROPN
ejpam-6433	194	13	}	}	PUNCT
ejpam-6433	194	14	.	.	PUNCT
ejpam-6433	195	1	then	then	ADV
ejpam-6433	195	2	for	for	ADP
ejpam-6433	195	3	any	any	DET
ejpam-6433	195	4	u	u	PROPN
ejpam-6433	195	5	∈	∈	PROPN
ejpam-6433	195	6	u(x0	u(x0	NOUN
ejpam-6433	195	7	,	,	PUNCT
ejpam-6433	195	8	δ	δ	PROPN
ejpam-6433	195	9	)	)	PUNCT
ejpam-6433	195	10	we	we	PRON
ejpam-6433	195	11	have	have	VERB
ejpam-6433	195	12	d(u	d(u	PROPN
ejpam-6433	195	13	,	,	PUNCT
ejpam-6433	195	14	y0	y0	NOUN
ejpam-6433	195	15	)	)	PUNCT
ejpam-6433	195	16	≤	≤	PUNCT
ejpam-6433	196	1	d(u	d(u	PROPN
ejpam-6433	196	2	,	,	PUNCT
ejpam-6433	196	3	x0	x0	PROPN
ejpam-6433	196	4	)	)	PUNCT
ejpam-6433	197	1	+	+	NUM
ejpam-6433	197	2	d(x0	d(x0	NOUN
ejpam-6433	197	3	,	,	PUNCT
ejpam-6433	197	4	y0	y0	PROPN
ejpam-6433	197	5	)	)	PUNCT
ejpam-6433	198	1	<	<	X
ejpam-6433	198	2	δ	δ	PROPN
ejpam-6433	198	3	+	+	PROPN
ejpam-6433	198	4	d(g	d(g	PROPN
ejpam-6433	198	5	,	,	PUNCT
ejpam-6433	198	6	h	h	NOUN
ejpam-6433	198	7	)	)	PUNCT
ejpam-6433	198	8	,	,	PUNCT
ejpam-6433	198	9	and	and	CCONJ
ejpam-6433	198	10	hence	hence	ADV
ejpam-6433	198	11	,	,	PUNCT
ejpam-6433	198	12	d(tu	d(tu	PROPN
ejpam-6433	198	13	,	,	PUNCT
ejpam-6433	198	14	ty0	ty0	NOUN
ejpam-6433	198	15	)	)	PUNCT
ejpam-6433	198	16	<	<	X
ejpam-6433	198	17	ε+d(g	ε+d(g	SYM
ejpam-6433	198	18	,	,	PUNCT
ejpam-6433	198	19	h	h	NOUN
ejpam-6433	198	20	)	)	PUNCT
ejpam-6433	198	21	.	.	PUNCT
ejpam-6433	199	1	(	(	PUNCT
ejpam-6433	199	2	1	1	X
ejpam-6433	199	3	)	)	PUNCT
ejpam-6433	199	4	m.	m.	NOUN
ejpam-6433	199	5	gabeleh	gabeleh	NOUN
ejpam-6433	199	6	,	,	PUNCT
ejpam-6433	199	7	j.	j.	PROPN
ejpam-6433	199	8	markin	markin	PROPN
ejpam-6433	199	9	,	,	PUNCT
ejpam-6433	199	10	m.	m.	NOUN
ejpam-6433	199	11	aphane	aphane	PROPN
ejpam-6433	199	12	/	/	SYM
ejpam-6433	199	13	eur	eur	PROPN
ejpam-6433	199	14	.	.	PUNCT
ejpam-6433	200	1	j.	j.	PROPN
ejpam-6433	200	2	pure	pure	PROPN
ejpam-6433	200	3	appl	appl	PROPN
ejpam-6433	200	4	.	.	PROPN
ejpam-6433	200	5	math	math	PROPN
ejpam-6433	200	6	,	,	PUNCT
ejpam-6433	200	7	18	18	NUM
ejpam-6433	200	8	(	(	PUNCT
ejpam-6433	200	9	3	3	NUM
ejpam-6433	200	10	)	)	PUNCT
ejpam-6433	200	11	(	(	PUNCT
ejpam-6433	200	12	2025	2025	NUM
ejpam-6433	200	13	)	)	PUNCT
ejpam-6433	200	14	,	,	PUNCT
ejpam-6433	200	15	6433	6433	NUM
ejpam-6433	200	16	9	9	NUM
ejpam-6433	200	17	of	of	ADP
ejpam-6433	200	18	17	17	NUM
ejpam-6433	200	19	we	we	PRON
ejpam-6433	200	20	claim	claim	VERB
ejpam-6433	200	21	that	that	SCONJ
ejpam-6433	200	22	b(ty0	b(ty0	NOUN
ejpam-6433	200	23	;	;	PUNCT
ejpam-6433	200	24	ε	ε	PROPN
ejpam-6433	200	25	)	)	PUNCT
ejpam-6433	200	26	∩	∩	ADJ
ejpam-6433	200	27	fu	fu	NOUN
ejpam-6433	200	28	̸=	̸=	PROPN
ejpam-6433	200	29	∅	∅	NOUN
ejpam-6433	200	30	for	for	ADP
ejpam-6433	200	31	u	u	PROPN
ejpam-6433	200	32	∈	∈	PROPN
ejpam-6433	200	33	u(x0	u(x0	NOUN
ejpam-6433	200	34	,	,	PUNCT
ejpam-6433	200	35	δ	δ	PROPN
ejpam-6433	200	36	)	)	PUNCT
ejpam-6433	200	37	.	.	PUNCT
ejpam-6433	201	1	by	by	ADP
ejpam-6433	201	2	(	(	PUNCT
ejpam-6433	201	3	1	1	X
ejpam-6433	201	4	)	)	PUNCT
ejpam-6433	201	5	b(ty0	b(ty0	NOUN
ejpam-6433	201	6	;	;	PUNCT
ejpam-6433	201	7	ε	ε	PROPN
ejpam-6433	201	8	)	)	PUNCT
ejpam-6433	201	9	∩	∩	PROPN
ejpam-6433	201	10	b	b	X
ejpam-6433	201	11	(	(	PUNCT
ejpam-6433	201	12	tu	tu	PROPN
ejpam-6433	201	13	,	,	PUNCT
ejpam-6433	201	14	d(g	d(g	PROPN
ejpam-6433	201	15	,	,	PUNCT
ejpam-6433	201	16	h	h	NOUN
ejpam-6433	201	17	)	)	PUNCT
ejpam-6433	201	18	)	)	PUNCT
ejpam-6433	202	1	̸=	̸=	PROPN
ejpam-6433	202	2	∅.	∅.	AUX
ejpam-6433	202	3	consider	consider	VERB
ejpam-6433	202	4	cov(p	cov(p	PROPN
ejpam-6433	202	5	,	,	PUNCT
ejpam-6433	202	6	q	q	NOUN
ejpam-6433	202	7	)	)	PUNCT
ejpam-6433	202	8	,	,	PUNCT
ejpam-6433	202	9	where	where	SCONJ
ejpam-6433	202	10	p	p	PROPN
ejpam-6433	202	11	∈	∈	PROPN
ejpam-6433	202	12	b(ty0	b(ty0	PROPN
ejpam-6433	202	13	,	,	PUNCT
ejpam-6433	202	14	ε	ε	PROPN
ejpam-6433	202	15	)	)	PUNCT
ejpam-6433	202	16	∩	∩	ADJ
ejpam-6433	202	17	g0	g0	PROPN
ejpam-6433	202	18	,	,	PUNCT
ejpam-6433	202	19	and	and	CCONJ
ejpam-6433	202	20	q	q	PROPN
ejpam-6433	202	21	∈	∈	PROPN
ejpam-6433	202	22	fu	fu	NOUN
ejpam-6433	202	23	.	.	PUNCT
ejpam-6433	203	1	since	since	SCONJ
ejpam-6433	203	2	g0	g0	PROPN
ejpam-6433	203	3	is	be	AUX
ejpam-6433	203	4	hyperconvex	hyperconvex	ADJ
ejpam-6433	203	5	,	,	PUNCT
ejpam-6433	203	6	cov(p	cov(p	PROPN
ejpam-6433	203	7	,	,	PUNCT
ejpam-6433	203	8	q	q	NOUN
ejpam-6433	203	9	)	)	PUNCT
ejpam-6433	203	10	⊆	⊆	NUM
ejpam-6433	203	11	g0	g0	NOUN
ejpam-6433	203	12	.	.	PUNCT
ejpam-6433	204	1	then	then	ADV
ejpam-6433	204	2	,	,	PUNCT
ejpam-6433	204	3	as	as	ADP
ejpam-6433	204	4	an	an	DET
ejpam-6433	204	5	intersection	intersection	NOUN
ejpam-6433	204	6	of	of	ADP
ejpam-6433	204	7	admissible	admissible	ADJ
ejpam-6433	204	8	sets	set	NOUN
ejpam-6433	204	9	with	with	ADP
ejpam-6433	204	10	pairwise	pairwise	NOUN
ejpam-6433	204	11	nonempty	nonempty	ADJ
ejpam-6433	204	12	intersections	intersection	NOUN
ejpam-6433	204	13	,	,	PUNCT
ejpam-6433	204	14	b(ty0	b(ty0	PROPN
ejpam-6433	204	15	;	;	PUNCT
ejpam-6433	204	16	ε	ε	PROPN
ejpam-6433	204	17	)	)	PUNCT
ejpam-6433	204	18	∩	∩	X
ejpam-6433	204	19	cov(p	cov(p	PROPN
ejpam-6433	204	20	,	,	PUNCT
ejpam-6433	204	21	q	q	ADJ
ejpam-6433	204	22	)	)	PUNCT
ejpam-6433	204	23	∩	∩	ADJ
ejpam-6433	204	24	b	b	X
ejpam-6433	204	25	(	(	PUNCT
ejpam-6433	204	26	tu	tu	PROPN
ejpam-6433	204	27	,	,	PUNCT
ejpam-6433	204	28	d(g	d(g	PROPN
ejpam-6433	204	29	,	,	PUNCT
ejpam-6433	204	30	h	h	NOUN
ejpam-6433	204	31	)	)	PUNCT
ejpam-6433	204	32	)	)	PUNCT
ejpam-6433	205	1	̸=	̸=	PROPN
ejpam-6433	205	2	∅.	∅.	ADP
ejpam-6433	205	3	this	this	PRON
ejpam-6433	205	4	shows	show	VERB
ejpam-6433	205	5	that	that	SCONJ
ejpam-6433	205	6	b(ty0	b(ty0	NOUN
ejpam-6433	205	7	;	;	PUNCT
ejpam-6433	205	8	ε)∩	ε)∩	NOUN
ejpam-6433	205	9	fu	fu	NOUN
ejpam-6433	205	10	̸=	̸=	PROPN
ejpam-6433	205	11	∅	∅	NOUN
ejpam-6433	205	12	and	and	CCONJ
ejpam-6433	205	13	therefore	therefore	ADV
ejpam-6433	205	14	,	,	PUNCT
ejpam-6433	205	15	that	that	SCONJ
ejpam-6433	205	16	f	f	PROPN
ejpam-6433	205	17	is	be	AUX
ejpam-6433	205	18	almost	almost	ADV
ejpam-6433	205	19	lower	lower	ADV
ejpam-6433	205	20	-	-	PUNCT
ejpam-6433	205	21	semicontinuous	semicontinuous	ADJ
ejpam-6433	205	22	at	at	ADP
ejpam-6433	205	23	the	the	DET
ejpam-6433	205	24	point	point	NOUN
ejpam-6433	205	25	x0	x0	PROPN
ejpam-6433	205	26	.	.	PUNCT
ejpam-6433	206	1	to	to	PART
ejpam-6433	206	2	see	see	VERB
ejpam-6433	206	3	that	that	SCONJ
ejpam-6433	206	4	values	value	NOUN
ejpam-6433	206	5	of	of	ADP
ejpam-6433	206	6	f	f	PROPN
ejpam-6433	206	7	are	be	AUX
ejpam-6433	206	8	sub	sub	ADJ
ejpam-6433	206	9	-	-	ADJ
ejpam-6433	206	10	admissible	admissible	ADJ
ejpam-6433	206	11	sets	set	NOUN
ejpam-6433	206	12	,	,	PUNCT
ejpam-6433	206	13	let	let	VERB
ejpam-6433	206	14	{	{	PUNCT
ejpam-6433	206	15	xi	xi	PART
ejpam-6433	206	16	}	}	PUNCT
ejpam-6433	206	17	be	be	AUX
ejpam-6433	206	18	a	a	DET
ejpam-6433	206	19	collection	collection	NOUN
ejpam-6433	206	20	of	of	ADP
ejpam-6433	206	21	points	point	NOUN
ejpam-6433	206	22	in	in	ADP
ejpam-6433	206	23	f	f	PROPN
ejpam-6433	206	24	(	(	PUNCT
ejpam-6433	206	25	v	v	NOUN
ejpam-6433	206	26	)	)	PUNCT
ejpam-6433	206	27	and	and	CCONJ
ejpam-6433	206	28	consider	consider	VERB
ejpam-6433	206	29	the	the	DET
ejpam-6433	206	30	set	set	NOUN
ejpam-6433	206	31	cov({xi	cov({xi	PROPN
ejpam-6433	206	32	}	}	PUNCT
ejpam-6433	206	33	)	)	PUNCT
ejpam-6433	206	34	.	.	PUNCT
ejpam-6433	207	1	hyperconvexity	hyperconvexity	NOUN
ejpam-6433	207	2	of	of	ADP
ejpam-6433	207	3	g0	g0	PROPN
ejpam-6433	207	4	implies	imply	VERB
ejpam-6433	207	5	that	that	SCONJ
ejpam-6433	207	6	cov({xi	cov({xi	NOUN
ejpam-6433	207	7	}	}	PUNCT
ejpam-6433	207	8	)	)	PUNCT
ejpam-6433	207	9	⊆	⊆	NUM
ejpam-6433	207	10	g0	g0	NOUN
ejpam-6433	207	11	,	,	PUNCT
ejpam-6433	207	12	and	and	CCONJ
ejpam-6433	207	13	the	the	DET
ejpam-6433	207	14	relation	relation	NOUN
ejpam-6433	207	15	δcov({xi})(tv	δcov({xi})(tv	PROPN
ejpam-6433	207	16	)	)	PUNCT
ejpam-6433	207	17	=	=	SYM
ejpam-6433	207	18	δ{xi}(tv	δ{xi}(tv	NOUN
ejpam-6433	207	19	)	)	PUNCT
ejpam-6433	207	20	,	,	PUNCT
ejpam-6433	207	21	deduces	deduce	VERB
ejpam-6433	207	22	that	that	DET
ejpam-6433	207	23	cov({xi	cov({xi	NOUN
ejpam-6433	207	24	}	}	PUNCT
ejpam-6433	207	25	)	)	PUNCT
ejpam-6433	208	1	⊆	⊆	NUM
ejpam-6433	208	2	f	f	X
ejpam-6433	208	3	(	(	PUNCT
ejpam-6433	208	4	v	v	NOUN
ejpam-6433	208	5	)	)	PUNCT
ejpam-6433	208	6	,	,	PUNCT
ejpam-6433	208	7	concluding	conclude	VERB
ejpam-6433	208	8	that	that	SCONJ
ejpam-6433	208	9	f	f	PROPN
ejpam-6433	208	10	(	(	PUNCT
ejpam-6433	208	11	v	v	NOUN
ejpam-6433	208	12	)	)	PUNCT
ejpam-6433	208	13	is	be	AUX
ejpam-6433	208	14	sub	sub	ADJ
ejpam-6433	208	15	-	-	ADJ
ejpam-6433	208	16	admissible	admissible	ADJ
ejpam-6433	208	17	.	.	PUNCT
ejpam-6433	209	1	by	by	ADP
ejpam-6433	209	2	theorem	theorem	NOUN
ejpam-6433	209	3	1	1	NUM
ejpam-6433	209	4	of	of	ADP
ejpam-6433	209	5	[	[	X
ejpam-6433	209	6	22	22	NUM
ejpam-6433	209	7	]	]	PUNCT
ejpam-6433	209	8	,	,	PUNCT
ejpam-6433	209	9	as	as	ADP
ejpam-6433	209	10	an	an	DET
ejpam-6433	209	11	almost	almost	ADV
ejpam-6433	209	12	lowersemicontinuous	lowersemicontinuous	ADJ
ejpam-6433	209	13	mapping	mapping	NOUN
ejpam-6433	209	14	with	with	ADP
ejpam-6433	209	15	sub	sub	ADJ
ejpam-6433	209	16	-	-	ADJ
ejpam-6433	209	17	admissible	admissible	ADJ
ejpam-6433	209	18	values	value	NOUN
ejpam-6433	209	19	,	,	PUNCT
ejpam-6433	209	20	the	the	DET
ejpam-6433	209	21	mapping	mapping	NOUN
ejpam-6433	209	22	f	f	X
ejpam-6433	209	23	has	have	VERB
ejpam-6433	209	24	a	a	DET
ejpam-6433	209	25	continuous	continuous	ADJ
ejpam-6433	209	26	selection	selection	NOUN
ejpam-6433	209	27	ℏ	ℏ	PROPN
ejpam-6433	209	28	:	:	PUNCT
ejpam-6433	209	29	g0	g0	PROPN
ejpam-6433	209	30	→	→	SYM
ejpam-6433	209	31	g0	g0	NOUN
ejpam-6433	209	32	such	such	ADJ
ejpam-6433	209	33	that	that	SCONJ
ejpam-6433	209	34	ℏv	ℏv	PROPN
ejpam-6433	209	35	∈	∈	PROPN
ejpam-6433	209	36	fv	fv	PROPN
ejpam-6433	209	37	for	for	ADP
ejpam-6433	209	38	v	v	PROPN
ejpam-6433	209	39	∈	∈	PROPN
ejpam-6433	209	40	g0	g0	NOUN
ejpam-6433	209	41	.	.	PUNCT
ejpam-6433	210	1	by	by	ADP
ejpam-6433	210	2	using	use	VERB
ejpam-6433	210	3	theorem	theorem	NOUN
ejpam-6433	210	4	7	7	NUM
ejpam-6433	210	5	,	,	PUNCT
ejpam-6433	210	6	the	the	DET
ejpam-6433	210	7	continuous	continuous	ADJ
ejpam-6433	210	8	self	self	NOUN
ejpam-6433	210	9	map	map	NOUN
ejpam-6433	210	10	ℏ	ℏ	PROPN
ejpam-6433	210	11	on	on	ADP
ejpam-6433	210	12	the	the	DET
ejpam-6433	210	13	compact	compact	ADJ
ejpam-6433	210	14	hyperconvex	hyperconvex	NOUN
ejpam-6433	210	15	space	space	NOUN
ejpam-6433	210	16	g0	g0	PROPN
ejpam-6433	210	17	has	have	VERB
ejpam-6433	210	18	a	a	DET
ejpam-6433	210	19	fixed	fix	VERB
ejpam-6433	210	20	point	point	NOUN
ejpam-6433	210	21	x∗.	x∗.	PUNCT
ejpam-6433	211	1	the	the	DET
ejpam-6433	211	2	definition	definition	NOUN
ejpam-6433	211	3	of	of	ADP
ejpam-6433	211	4	the	the	DET
ejpam-6433	211	5	mapping	mapping	NOUN
ejpam-6433	211	6	f	f	PROPN
ejpam-6433	211	7	implies	imply	VERB
ejpam-6433	211	8	d(x∗	d(x∗	ADV
ejpam-6433	211	9	,	,	PUNCT
ejpam-6433	211	10	tx∗	tx∗	NOUN
ejpam-6433	211	11	)	)	PUNCT
ejpam-6433	212	1	=	=	SYM
ejpam-6433	212	2	d(g	d(g	PROPN
ejpam-6433	212	3	,	,	PUNCT
ejpam-6433	212	4	h	h	NOUN
ejpam-6433	212	5	)	)	PUNCT
ejpam-6433	212	6	and	and	CCONJ
ejpam-6433	212	7	the	the	DET
ejpam-6433	212	8	proof	proof	NOUN
ejpam-6433	212	9	is	be	AUX
ejpam-6433	212	10	completed	complete	VERB
ejpam-6433	212	11	.	.	PUNCT
ejpam-6433	213	1	the	the	DET
ejpam-6433	213	2	next	next	ADJ
ejpam-6433	213	3	result	result	NOUN
ejpam-6433	213	4	is	be	AUX
ejpam-6433	213	5	a	a	DET
ejpam-6433	213	6	consequence	consequence	NOUN
ejpam-6433	213	7	of	of	ADP
ejpam-6433	213	8	theorem	theorem	ADJ
ejpam-6433	213	9	8	8	NUM
ejpam-6433	213	10	.	.	PUNCT
ejpam-6433	213	11	corollary	corollary	ADJ
ejpam-6433	213	12	1	1	NUM
ejpam-6433	213	13	.	.	PUNCT
ejpam-6433	214	1	(	(	PUNCT
ejpam-6433	214	2	theorem	theorem	VERB
ejpam-6433	214	3	15	15	NUM
ejpam-6433	214	4	of	of	ADP
ejpam-6433	214	5	[	[	X
ejpam-6433	214	6	23	23	NUM
ejpam-6433	214	7	]	]	PUNCT
ejpam-6433	214	8	)	)	PUNCT
ejpam-6433	214	9	let	let	VERB
ejpam-6433	214	10	(	(	PUNCT
ejpam-6433	214	11	g	g	NOUN
ejpam-6433	214	12	,	,	PUNCT
ejpam-6433	214	13	h	h	NOUN
ejpam-6433	214	14	)	)	PUNCT
ejpam-6433	214	15	be	be	VERB
ejpam-6433	214	16	a	a	DET
ejpam-6433	214	17	nonempty	nonempty	ADJ
ejpam-6433	214	18	and	and	CCONJ
ejpam-6433	214	19	admissible	admissible	ADJ
ejpam-6433	214	20	pair	pair	NOUN
ejpam-6433	214	21	in	in	ADP
ejpam-6433	214	22	a	a	DET
ejpam-6433	214	23	hyperconvex	hyperconvex	ADJ
ejpam-6433	214	24	metric	metric	ADJ
ejpam-6433	214	25	space	space	NOUN
ejpam-6433	214	26	(	(	PUNCT
ejpam-6433	214	27	m	m	PROPN
ejpam-6433	214	28	,	,	PUNCT
ejpam-6433	214	29	d	d	NOUN
ejpam-6433	214	30	)	)	PUNCT
ejpam-6433	214	31	such	such	ADJ
ejpam-6433	214	32	that	that	DET
ejpam-6433	214	33	g0	g0	NOUN
ejpam-6433	214	34	is	be	AUX
ejpam-6433	214	35	compact	compact	ADJ
ejpam-6433	214	36	.	.	PUNCT
ejpam-6433	215	1	let	let	VERB
ejpam-6433	215	2	t	t	NOUN
ejpam-6433	215	3	:	:	PUNCT
ejpam-6433	215	4	g	g	PROPN
ejpam-6433	215	5	∪	∪	ADJ
ejpam-6433	215	6	h	h	NOUN
ejpam-6433	215	7	→	→	SYM
ejpam-6433	215	8	g	g	PROPN
ejpam-6433	215	9	∪	∪	NOUN
ejpam-6433	215	10	h	h	NOUN
ejpam-6433	215	11	be	be	VERB
ejpam-6433	215	12	a	a	DET
ejpam-6433	215	13	cyclic	cyclic	ADJ
ejpam-6433	215	14	relatively	relatively	ADV
ejpam-6433	215	15	u	u	ADJ
ejpam-6433	215	16	-	-	ADJ
ejpam-6433	215	17	continuous	continuous	ADJ
ejpam-6433	215	18	mapping	mapping	NOUN
ejpam-6433	215	19	.	.	PUNCT
ejpam-6433	216	1	then	then	ADV
ejpam-6433	216	2	t	t	PROPN
ejpam-6433	216	3	has	have	VERB
ejpam-6433	216	4	a	a	DET
ejpam-6433	216	5	best	good	ADJ
ejpam-6433	216	6	proximity	proximity	NOUN
ejpam-6433	216	7	point	point	NOUN
ejpam-6433	216	8	.	.	PUNCT
ejpam-6433	217	1	proof	proof	NOUN
ejpam-6433	217	2	.	.	PUNCT
ejpam-6433	218	1	by	by	ADP
ejpam-6433	218	2	lemma	lemma	PROPN
ejpam-6433	218	3	2.5	2.5	NUM
ejpam-6433	218	4	of	of	ADP
ejpam-6433	218	5	[	[	X
ejpam-6433	218	6	14	14	NUM
ejpam-6433	218	7	]	]	PUNCT
ejpam-6433	218	8	,	,	PUNCT
ejpam-6433	218	9	since	since	SCONJ
ejpam-6433	218	10	(	(	PUNCT
ejpam-6433	218	11	g	g	NOUN
ejpam-6433	218	12	,	,	PUNCT
ejpam-6433	218	13	h	h	NOUN
ejpam-6433	218	14	)	)	PUNCT
ejpam-6433	218	15	is	be	AUX
ejpam-6433	218	16	an	an	DET
ejpam-6433	218	17	admissible	admissible	ADJ
ejpam-6433	218	18	pair	pair	NOUN
ejpam-6433	218	19	in	in	ADP
ejpam-6433	218	20	a	a	DET
ejpam-6433	218	21	hyperconvex	hyperconvex	ADJ
ejpam-6433	218	22	space	space	NOUN
ejpam-6433	218	23	m	m	VERB
ejpam-6433	218	24	the	the	DET
ejpam-6433	218	25	proximal	proximal	ADJ
ejpam-6433	218	26	pair	pair	NOUN
ejpam-6433	218	27	(	(	PUNCT
ejpam-6433	218	28	g0,h0	g0,h0	PROPN
ejpam-6433	218	29	)	)	PUNCT
ejpam-6433	218	30	is	be	AUX
ejpam-6433	218	31	nonempty	nonempty	ADJ
ejpam-6433	218	32	and	and	CCONJ
ejpam-6433	218	33	admissible	admissible	ADJ
ejpam-6433	218	34	too	too	ADV
ejpam-6433	218	35	,	,	PUNCT
ejpam-6433	218	36	which	which	PRON
ejpam-6433	218	37	ensures	ensure	VERB
ejpam-6433	218	38	that	that	SCONJ
ejpam-6433	218	39	g0	g0	NOUN
ejpam-6433	218	40	is	be	AUX
ejpam-6433	218	41	hyperconvex	hyperconvex	ADJ
ejpam-6433	218	42	.	.	PUNCT
ejpam-6433	219	1	now	now	ADV
ejpam-6433	219	2	the	the	DET
ejpam-6433	219	3	result	result	NOUN
ejpam-6433	219	4	follows	follow	VERB
ejpam-6433	219	5	from	from	ADP
ejpam-6433	219	6	theorem	theorem	ADJ
ejpam-6433	219	7	8	8	NUM
ejpam-6433	219	8	,	,	PUNCT
ejpam-6433	219	9	immediately	immediately	ADV
ejpam-6433	219	10	.	.	PUNCT
ejpam-6433	220	1	the	the	DET
ejpam-6433	220	2	next	next	ADJ
ejpam-6433	220	3	example	example	NOUN
ejpam-6433	220	4	shows	show	VERB
ejpam-6433	220	5	the	the	DET
ejpam-6433	220	6	useability	useability	NOUN
ejpam-6433	220	7	of	of	ADP
ejpam-6433	220	8	theorem	theorem	ADJ
ejpam-6433	220	9	8	8	NUM
ejpam-6433	220	10	w.r.t	w.r.t	NOUN
ejpam-6433	220	11	.	.	PUNCT
ejpam-6433	221	1	theorem	theorem	VERB
ejpam-6433	221	2	3	3	NUM
ejpam-6433	221	3	.	.	NOUN
ejpam-6433	221	4	example	example	NOUN
ejpam-6433	221	5	3	3	X
ejpam-6433	221	6	.	.	X
ejpam-6433	221	7	consider	consider	VERB
ejpam-6433	221	8	the	the	DET
ejpam-6433	221	9	hyperconvex	hyperconvex	ADJ
ejpam-6433	221	10	space	space	NOUN
ejpam-6433	221	11	ℓ∞	ℓ∞	PROPN
ejpam-6433	221	12	consists	consist	VERB
ejpam-6433	221	13	of	of	ADP
ejpam-6433	221	14	all	all	DET
ejpam-6433	221	15	real	real	ADJ
ejpam-6433	221	16	bounded	bounded	ADJ
ejpam-6433	221	17	sequences	sequence	NOUN
ejpam-6433	221	18	equipped	equip	VERB
ejpam-6433	221	19	with	with	ADP
ejpam-6433	221	20	the	the	DET
ejpam-6433	221	21	supremum	supremum	ADJ
ejpam-6433	221	22	norm	norm	NOUN
ejpam-6433	221	23	and	and	CCONJ
ejpam-6433	221	24	let	let	VERB
ejpam-6433	221	25	{	{	PUNCT
ejpam-6433	221	26	en}n∈n	en}n∈n	VERB
ejpam-6433	221	27	be	be	AUX
ejpam-6433	221	28	the	the	DET
ejpam-6433	221	29	canonical	canonical	ADJ
ejpam-6433	221	30	basis	basis	NOUN
ejpam-6433	221	31	of	of	ADP
ejpam-6433	221	32	ℓ∞.	ℓ∞.	PROPN
ejpam-6433	221	33	set	set	NOUN
ejpam-6433	221	34	g	g	PROPN
ejpam-6433	221	35	=	=	PUNCT
ejpam-6433	221	36	{	{	PUNCT
ejpam-6433	221	37	te1	te1	PROPN
ejpam-6433	221	38	+	+	CCONJ
ejpam-6433	221	39	e2	e2	PROPN
ejpam-6433	221	40	;	;	PUNCT
ejpam-6433	221	41	t	t	PROPN
ejpam-6433	221	42	∈	∈	PROPN
ejpam-6433	222	1	[	[	X
ejpam-6433	222	2	0	0	NUM
ejpam-6433	222	3	,	,	PUNCT
ejpam-6433	222	4	1	1	NUM
ejpam-6433	222	5	]	]	PUNCT
ejpam-6433	222	6	}	}	PUNCT
ejpam-6433	222	7	h	h	NOUN
ejpam-6433	222	8	=	=	PRON
ejpam-6433	222	9	{	{	PUNCT
ejpam-6433	222	10	se1	se1	NOUN
ejpam-6433	222	11	+	+	CCONJ
ejpam-6433	222	12	e3	e3	NOUN
ejpam-6433	222	13	;	;	PUNCT
ejpam-6433	222	14	s	s	X
ejpam-6433	222	15	∈	∈	X
ejpam-6433	223	1	[	[	X
ejpam-6433	223	2	0	0	NUM
ejpam-6433	223	3	,	,	PUNCT
ejpam-6433	223	4	1	1	NUM
ejpam-6433	223	5	]	]	PUNCT
ejpam-6433	223	6	}	}	PUNCT
ejpam-6433	223	7	.	.	PUNCT
ejpam-6433	224	1	then	then	ADV
ejpam-6433	224	2	(	(	PUNCT
ejpam-6433	224	3	g	g	NOUN
ejpam-6433	224	4	,	,	PUNCT
ejpam-6433	224	5	h	h	NOUN
ejpam-6433	224	6	)	)	PUNCT
ejpam-6433	224	7	is	be	AUX
ejpam-6433	224	8	a	a	DET
ejpam-6433	224	9	compact	compact	ADJ
ejpam-6433	224	10	,	,	PUNCT
ejpam-6433	224	11	convex	convex	NOUN
ejpam-6433	224	12	,	,	PUNCT
ejpam-6433	224	13	proximinal	proximinal	ADJ
ejpam-6433	224	14	and	and	CCONJ
ejpam-6433	224	15	hyperconvex	hyperconvex	ADJ
ejpam-6433	224	16	pair	pair	NOUN
ejpam-6433	224	17	in	in	ADP
ejpam-6433	224	18	ℓ∞	ℓ∞	PROPN
ejpam-6433	224	19	with	with	ADP
ejpam-6433	224	20	d(g	d(g	PROPN
ejpam-6433	224	21	,	,	PUNCT
ejpam-6433	224	22	h	h	NOUN
ejpam-6433	224	23	)	)	PUNCT
ejpam-6433	224	24	=	=	SYM
ejpam-6433	224	25	1	1	X
ejpam-6433	224	26	.	.	X
ejpam-6433	224	27	define	define	VERB
ejpam-6433	224	28	a	a	DET
ejpam-6433	224	29	mapping	mapping	NOUN
ejpam-6433	224	30	t	t	NOUN
ejpam-6433	224	31	:	:	PUNCT
ejpam-6433	224	32	g	g	PROPN
ejpam-6433	224	33	∪	∪	ADJ
ejpam-6433	224	34	h	h	NOUN
ejpam-6433	224	35	→	→	SYM
ejpam-6433	224	36	g	g	PROPN
ejpam-6433	224	37	∪h	∪h	NUM
ejpam-6433	224	38	with	with	ADP
ejpam-6433	224	39	t	t	PROPN
ejpam-6433	224	40	(	(	PUNCT
ejpam-6433	224	41	te1	te1	PROPN
ejpam-6433	224	42	+	+	CCONJ
ejpam-6433	224	43	e2	e2	PROPN
ejpam-6433	224	44	)	)	PUNCT
ejpam-6433	225	1	=	=	SYM
ejpam-6433	225	2	te1	te1	NOUN
ejpam-6433	225	3	+	+	CCONJ
ejpam-6433	225	4	e3	e3	NOUN
ejpam-6433	225	5	,	,	PUNCT
ejpam-6433	225	6	t	t	PROPN
ejpam-6433	225	7	(	(	PUNCT
ejpam-6433	225	8	se1	se1	PROPN
ejpam-6433	225	9	+	+	CCONJ
ejpam-6433	225	10	e3	e3	NOUN
ejpam-6433	225	11	)	)	PUNCT
ejpam-6433	225	12	=	=	SYM
ejpam-6433	226	1	se1	se1	PROPN
ejpam-6433	226	2	+	+	CCONJ
ejpam-6433	226	3	e2	e2	PROPN
ejpam-6433	226	4	,	,	PUNCT
ejpam-6433	226	5	for	for	ADP
ejpam-6433	226	6	all	all	DET
ejpam-6433	226	7	t	t	PROPN
ejpam-6433	226	8	,	,	PUNCT
ejpam-6433	226	9	s	s	PART
ejpam-6433	226	10	∈	∈	PROPN
ejpam-6433	227	1	[	[	X
ejpam-6433	227	2	0	0	NUM
ejpam-6433	227	3	,	,	PUNCT
ejpam-6433	227	4	1	1	NUM
ejpam-6433	227	5	]	]	PUNCT
ejpam-6433	227	6	.	.	PUNCT
ejpam-6433	228	1	then	then	ADV
ejpam-6433	228	2	t	t	PROPN
ejpam-6433	228	3	is	be	AUX
ejpam-6433	228	4	cyclic	cyclic	ADJ
ejpam-6433	228	5	and	and	CCONJ
ejpam-6433	228	6	for	for	ADP
ejpam-6433	228	7	any	any	DET
ejpam-6433	228	8	x	x	SYM
ejpam-6433	228	9	=	=	PUNCT
ejpam-6433	228	10	te1	te1	PROPN
ejpam-6433	228	11	+	+	CCONJ
ejpam-6433	228	12	e2	e2	PROPN
ejpam-6433	228	13	∈	∈	PROPN
ejpam-6433	228	14	g	g	PROPN
ejpam-6433	228	15	and	and	CCONJ
ejpam-6433	229	1	y	y	PROPN
ejpam-6433	229	2	=	=	SYM
ejpam-6433	229	3	se1	se1	PROPN
ejpam-6433	229	4	+	+	CCONJ
ejpam-6433	229	5	e3	e3	VERB
ejpam-6433	229	6	we	we	PRON
ejpam-6433	229	7	have	have	VERB
ejpam-6433	229	8	∥tx−	∥tx−	ADV
ejpam-6433	229	9	ty∥∞	ty∥∞	ADJ
ejpam-6433	229	10	=	=	SYM
ejpam-6433	229	11	1	1	NUM
ejpam-6433	229	12	=	=	SYM
ejpam-6433	229	13	∥x−	∥x−	NUM
ejpam-6433	229	14	y∥∞	y∥∞	PROPN
ejpam-6433	229	15	,	,	PUNCT
ejpam-6433	229	16	m.	m.	NOUN
ejpam-6433	229	17	gabeleh	gabeleh	PROPN
ejpam-6433	229	18	,	,	PUNCT
ejpam-6433	229	19	j.	j.	PROPN
ejpam-6433	229	20	markin	markin	PROPN
ejpam-6433	229	21	,	,	PUNCT
ejpam-6433	229	22	m.	m.	NOUN
ejpam-6433	229	23	aphane	aphane	PROPN
ejpam-6433	229	24	/	/	SYM
ejpam-6433	229	25	eur	eur	PROPN
ejpam-6433	229	26	.	.	PUNCT
ejpam-6433	230	1	j.	j.	PROPN
ejpam-6433	230	2	pure	pure	PROPN
ejpam-6433	230	3	appl	appl	PROPN
ejpam-6433	230	4	.	.	PROPN
ejpam-6433	230	5	math	math	PROPN
ejpam-6433	230	6	,	,	PUNCT
ejpam-6433	230	7	18	18	NUM
ejpam-6433	230	8	(	(	PUNCT
ejpam-6433	230	9	3	3	NUM
ejpam-6433	230	10	)	)	PUNCT
ejpam-6433	230	11	(	(	PUNCT
ejpam-6433	230	12	2025	2025	NUM
ejpam-6433	230	13	)	)	PUNCT
ejpam-6433	230	14	,	,	PUNCT
ejpam-6433	230	15	6433	6433	NUM
ejpam-6433	230	16	10	10	NUM
ejpam-6433	230	17	of	of	ADP
ejpam-6433	230	18	17	17	NUM
ejpam-6433	230	19	which	which	PRON
ejpam-6433	230	20	implies	imply	VERB
ejpam-6433	230	21	that	that	SCONJ
ejpam-6433	230	22	t	t	PROPN
ejpam-6433	230	23	is	be	AUX
ejpam-6433	230	24	relatively	relatively	ADV
ejpam-6433	230	25	u	u	NOUN
ejpam-6433	230	26	-	-	ADJ
ejpam-6433	230	27	continuous	continuous	ADJ
ejpam-6433	230	28	.	.	PUNCT
ejpam-6433	231	1	it	it	PRON
ejpam-6433	231	2	now	now	ADV
ejpam-6433	231	3	follows	follow	VERB
ejpam-6433	231	4	from	from	ADP
ejpam-6433	231	5	theorem	theorem	ADJ
ejpam-6433	231	6	8	8	NUM
ejpam-6433	231	7	that	that	SCONJ
ejpam-6433	231	8	t	t	PROPN
ejpam-6433	231	9	has	have	VERB
ejpam-6433	231	10	a	a	DET
ejpam-6433	231	11	best	good	ADJ
ejpam-6433	231	12	proximity	proximity	NOUN
ejpam-6433	231	13	point	point	NOUN
ejpam-6433	231	14	,	,	PUNCT
ejpam-6433	231	15	indeed	indeed	ADV
ejpam-6433	231	16	,	,	PUNCT
ejpam-6433	231	17	every	every	DET
ejpam-6433	231	18	point	point	NOUN
ejpam-6433	231	19	of	of	ADP
ejpam-6433	231	20	g	g	PROPN
ejpam-6433	231	21	is	be	AUX
ejpam-6433	231	22	a	a	DET
ejpam-6433	231	23	best	good	ADJ
ejpam-6433	231	24	proximity	proximity	NOUN
ejpam-6433	231	25	point	point	NOUN
ejpam-6433	231	26	of	of	ADP
ejpam-6433	231	27	t	t	PROPN
ejpam-6433	231	28	.	.	PUNCT
ejpam-6433	232	1	note	note	VERB
ejpam-6433	232	2	that	that	SCONJ
ejpam-6433	232	3	the	the	DET
ejpam-6433	232	4	banach	banach	NOUN
ejpam-6433	232	5	space	space	NOUN
ejpam-6433	232	6	ℓ∞	ℓ∞	PROPN
ejpam-6433	232	7	is	be	AUX
ejpam-6433	232	8	not	not	PART
ejpam-6433	232	9	strictly	strictly	ADV
ejpam-6433	232	10	convex	convex	ADJ
ejpam-6433	232	11	and	and	CCONJ
ejpam-6433	232	12	so	so	ADV
ejpam-6433	232	13	the	the	DET
ejpam-6433	232	14	existence	existence	NOUN
ejpam-6433	232	15	of	of	ADP
ejpam-6433	232	16	a	a	DET
ejpam-6433	232	17	best	good	ADJ
ejpam-6433	232	18	proximity	proximity	NOUN
ejpam-6433	232	19	point	point	NOUN
ejpam-6433	232	20	of	of	ADP
ejpam-6433	232	21	t	t	NOUN
ejpam-6433	232	22	can	can	AUX
ejpam-6433	232	23	not	not	PART
ejpam-6433	232	24	be	be	AUX
ejpam-6433	232	25	concluded	conclude	VERB
ejpam-6433	232	26	from	from	ADP
ejpam-6433	232	27	theorem	theorem	ADJ
ejpam-6433	232	28	3	3	X
ejpam-6433	232	29	.	.	PUNCT
ejpam-6433	233	1	it	it	PRON
ejpam-6433	233	2	is	be	AUX
ejpam-6433	233	3	worth	worth	ADJ
ejpam-6433	233	4	noticing	notice	VERB
ejpam-6433	233	5	that	that	SCONJ
ejpam-6433	233	6	the	the	DET
ejpam-6433	233	7	noncyclic	noncyclic	ADJ
ejpam-6433	233	8	version	version	NOUN
ejpam-6433	233	9	of	of	ADP
ejpam-6433	233	10	theorem	theorem	ADJ
ejpam-6433	233	11	8	8	NUM
ejpam-6433	233	12	holds	hold	VERB
ejpam-6433	233	13	by	by	ADP
ejpam-6433	233	14	adding	add	VERB
ejpam-6433	233	15	a	a	DET
ejpam-6433	233	16	geometric	geometric	ADJ
ejpam-6433	233	17	property	property	NOUN
ejpam-6433	233	18	which	which	PRON
ejpam-6433	233	19	is	be	AUX
ejpam-6433	233	20	inspired	inspire	VERB
ejpam-6433	233	21	from	from	ADP
ejpam-6433	233	22	strictly	strictly	ADV
ejpam-6433	233	23	convex	convex	VERB
ejpam-6433	233	24	banach	banach	NOUN
ejpam-6433	233	25	spaces	space	NOUN
ejpam-6433	233	26	.	.	PUNCT
ejpam-6433	234	1	definition	definition	NOUN
ejpam-6433	234	2	10	10	NUM
ejpam-6433	234	3	.	.	PUNCT
ejpam-6433	235	1	(	(	PUNCT
ejpam-6433	235	2	[	[	X
ejpam-6433	235	3	6	6	NUM
ejpam-6433	235	4	]	]	PUNCT
ejpam-6433	235	5	)	)	PUNCT
ejpam-6433	235	6	a	a	DET
ejpam-6433	235	7	nonempty	nonempty	ADJ
ejpam-6433	235	8	pair	pair	NOUN
ejpam-6433	235	9	(	(	PUNCT
ejpam-6433	235	10	g	g	NOUN
ejpam-6433	235	11	,	,	PUNCT
ejpam-6433	235	12	h	h	NOUN
ejpam-6433	235	13	)	)	PUNCT
ejpam-6433	235	14	in	in	ADP
ejpam-6433	235	15	a	a	DET
ejpam-6433	235	16	metric	metric	ADJ
ejpam-6433	235	17	space	space	NOUN
ejpam-6433	235	18	(	(	PUNCT
ejpam-6433	235	19	m	m	PROPN
ejpam-6433	235	20	,	,	PUNCT
ejpam-6433	235	21	d	d	X
ejpam-6433	235	22	)	)	PUNCT
ejpam-6433	235	23	is	be	AUX
ejpam-6433	235	24	said	say	VERB
ejpam-6433	235	25	to	to	PART
ejpam-6433	235	26	be	be	AUX
ejpam-6433	235	27	a	a	DET
ejpam-6433	235	28	semi	semi	ADJ
ejpam-6433	235	29	-	-	ADJ
ejpam-6433	235	30	sharp	sharp	ADJ
ejpam-6433	235	31	proximinal	proximinal	ADJ
ejpam-6433	235	32	pair	pair	NOUN
ejpam-6433	235	33	provided	provide	VERB
ejpam-6433	235	34	that	that	SCONJ
ejpam-6433	235	35	for	for	ADP
ejpam-6433	235	36	any	any	DET
ejpam-6433	235	37	(	(	PUNCT
ejpam-6433	235	38	x	x	NOUN
ejpam-6433	235	39	,	,	PUNCT
ejpam-6433	235	40	y	y	NOUN
ejpam-6433	235	41	)	)	PUNCT
ejpam-6433	235	42	∈	∈	PROPN
ejpam-6433	235	43	g	g	NOUN
ejpam-6433	235	44	×	×	PROPN
ejpam-6433	235	45	h	h	NOUN
ejpam-6433	235	46	there	there	ADV
ejpam-6433	235	47	exists	exist	VERB
ejpam-6433	235	48	at	at	ADP
ejpam-6433	235	49	most	most	ADV
ejpam-6433	235	50	one	one	NUM
ejpam-6433	235	51	point	point	NOUN
ejpam-6433	235	52	(	(	PUNCT
ejpam-6433	235	53	x′	x′	NUM
ejpam-6433	235	54	,	,	PUNCT
ejpam-6433	235	55	y′	y′	NUM
ejpam-6433	235	56	)	)	PUNCT
ejpam-6433	236	1	∈	∈	PROPN
ejpam-6433	236	2	g	g	PROPN
ejpam-6433	236	3	×h	×h	PROPN
ejpam-6433	236	4	for	for	ADP
ejpam-6433	236	5	which	which	PRON
ejpam-6433	236	6	d(x	d(x	NOUN
ejpam-6433	236	7	,	,	PUNCT
ejpam-6433	236	8	y′	y′	NUM
ejpam-6433	236	9	)	)	PUNCT
ejpam-6433	236	10	=	=	SYM
ejpam-6433	236	11	d(x′	d(x′	PROPN
ejpam-6433	236	12	,	,	PUNCT
ejpam-6433	236	13	y	y	NOUN
ejpam-6433	236	14	)	)	PUNCT
ejpam-6433	236	15	=	=	SYM
ejpam-6433	236	16	d(g	d(g	PROPN
ejpam-6433	236	17	,	,	PUNCT
ejpam-6433	236	18	h	h	NOUN
ejpam-6433	236	19	)	)	PUNCT
ejpam-6433	236	20	.	.	PUNCT
ejpam-6433	237	1	it	it	PRON
ejpam-6433	237	2	is	be	AUX
ejpam-6433	237	3	worth	worth	ADJ
ejpam-6433	237	4	noticing	notice	VERB
ejpam-6433	237	5	that	that	SCONJ
ejpam-6433	237	6	every	every	DET
ejpam-6433	237	7	nonempty	nonempty	ADJ
ejpam-6433	237	8	and	and	CCONJ
ejpam-6433	237	9	convex	convex	ADJ
ejpam-6433	237	10	pair	pair	NOUN
ejpam-6433	237	11	in	in	ADP
ejpam-6433	237	12	a	a	DET
ejpam-6433	237	13	strictly	strictly	ADV
ejpam-6433	237	14	convex	convex	ADJ
ejpam-6433	237	15	banach	banach	NOUN
ejpam-6433	237	16	space	space	NOUN
ejpam-6433	237	17	x	x	PUNCT
ejpam-6433	237	18	is	be	AUX
ejpam-6433	237	19	a	a	DET
ejpam-6433	237	20	semi	semi	ADJ
ejpam-6433	237	21	-	-	ADJ
ejpam-6433	237	22	sharp	sharp	ADJ
ejpam-6433	237	23	proximinal	proximinal	ADJ
ejpam-6433	237	24	pair	pair	NOUN
ejpam-6433	237	25	(	(	PUNCT
ejpam-6433	237	26	see	see	VERB
ejpam-6433	237	27	[	[	X
ejpam-6433	237	28	6	6	NUM
ejpam-6433	237	29	]	]	NUM
ejpam-6433	237	30	)	)	PUNCT
ejpam-6433	237	31	.	.	PUNCT
ejpam-6433	238	1	the	the	DET
ejpam-6433	238	2	next	next	ADJ
ejpam-6433	238	3	example	example	NOUN
ejpam-6433	238	4	shows	show	VERB
ejpam-6433	238	5	that	that	SCONJ
ejpam-6433	238	6	strict	strict	ADJ
ejpam-6433	238	7	convexity	convexity	NOUN
ejpam-6433	238	8	assumption	assumption	NOUN
ejpam-6433	238	9	of	of	ADP
ejpam-6433	238	10	a	a	DET
ejpam-6433	238	11	banach	banach	NOUN
ejpam-6433	238	12	space	space	NOUN
ejpam-6433	238	13	x	x	PUNCT
ejpam-6433	238	14	is	be	AUX
ejpam-6433	238	15	not	not	PART
ejpam-6433	238	16	an	an	DET
ejpam-6433	238	17	essential	essential	ADJ
ejpam-6433	238	18	condition	condition	NOUN
ejpam-6433	238	19	for	for	ADP
ejpam-6433	238	20	semi	semi	ADJ
ejpam-6433	238	21	-	-	ADJ
ejpam-6433	238	22	sharp	sharp	ADJ
ejpam-6433	238	23	proximinality	proximinality	NOUN
ejpam-6433	238	24	of	of	ADP
ejpam-6433	238	25	convex	convex	ADJ
ejpam-6433	238	26	pairs	pair	NOUN
ejpam-6433	238	27	.	.	PUNCT
ejpam-6433	239	1	example	example	NOUN
ejpam-6433	239	2	4	4	NUM
ejpam-6433	239	3	.	.	PUNCT
ejpam-6433	240	1	in	in	ADP
ejpam-6433	240	2	the	the	DET
ejpam-6433	240	3	hyperconvex	hyperconvex	NOUN
ejpam-6433	240	4	space	space	NOUN
ejpam-6433	240	5	ℓ∞	ℓ∞	PROPN
ejpam-6433	240	6	,	,	PUNCT
ejpam-6433	240	7	put	put	VERB
ejpam-6433	240	8	g	g	NOUN
ejpam-6433	240	9	=	=	PUNCT
ejpam-6433	240	10	con	con	X
ejpam-6433	240	11	(	(	PUNCT
ejpam-6433	240	12	{	{	PUNCT
ejpam-6433	240	13	e2n−1	e2n−1	PROPN
ejpam-6433	240	14	+	+	CCONJ
ejpam-6433	240	15	e2n	e2n	X
ejpam-6433	240	16	;	;	PUNCT
ejpam-6433	240	17	n	n	CCONJ
ejpam-6433	240	18	∈	∈	PROPN
ejpam-6433	240	19	n	n	NOUN
ejpam-6433	240	20	}	}	PUNCT
ejpam-6433	240	21	)	)	PUNCT
ejpam-6433	241	1	h	h	NOUN
ejpam-6433	242	1	=	=	PUNCT
ejpam-6433	242	2	con	con	X
ejpam-6433	242	3	(	(	PUNCT
ejpam-6433	242	4	{	{	PUNCT
ejpam-6433	242	5	2e2n	2e2n	ADJ
ejpam-6433	242	6	+	+	CCONJ
ejpam-6433	242	7	e2n+1	e2n+1	ADJ
ejpam-6433	242	8	;	;	PUNCT
ejpam-6433	242	9	n	n	CCONJ
ejpam-6433	242	10	∈	∈	PROPN
ejpam-6433	242	11	n	n	NOUN
ejpam-6433	242	12	}	}	PUNCT
ejpam-6433	242	13	)	)	PUNCT
ejpam-6433	242	14	,	,	PUNCT
ejpam-6433	242	15	where	where	SCONJ
ejpam-6433	242	16	con(a	con(a	X
ejpam-6433	242	17	)	)	PUNCT
ejpam-6433	242	18	denotes	denote	VERB
ejpam-6433	242	19	the	the	DET
ejpam-6433	242	20	closed	closed	ADJ
ejpam-6433	242	21	convex	convex	NOUN
ejpam-6433	242	22	hull	hull	NOUN
ejpam-6433	242	23	of	of	ADP
ejpam-6433	242	24	the	the	DET
ejpam-6433	242	25	set	set	NOUN
ejpam-6433	242	26	a	a	DET
ejpam-6433	242	27	⊆	⊆	NUM
ejpam-6433	242	28	ℓ∞.	ℓ∞.	NOUN
ejpam-6433	242	29	clearly	clearly	ADV
ejpam-6433	242	30	,	,	PUNCT
ejpam-6433	242	31	d(g	d(g	PROPN
ejpam-6433	242	32	,	,	PUNCT
ejpam-6433	242	33	h	h	NOUN
ejpam-6433	242	34	)	)	PUNCT
ejpam-6433	242	35	=	=	SYM
ejpam-6433	242	36	1	1	NUM
ejpam-6433	242	37	,	,	PUNCT
ejpam-6433	242	38	g0	g0	NOUN
ejpam-6433	242	39	=	=	SYM
ejpam-6433	242	40	g	g	PROPN
ejpam-6433	242	41	,	,	PUNCT
ejpam-6433	242	42	h0	h0	NOUN
ejpam-6433	242	43	=	=	SYM
ejpam-6433	242	44	h	h	PROPN
ejpam-6433	242	45	,	,	PUNCT
ejpam-6433	242	46	and	and	CCONJ
ejpam-6433	242	47	that	that	SCONJ
ejpam-6433	242	48	(	(	PUNCT
ejpam-6433	242	49	g	g	NOUN
ejpam-6433	242	50	,	,	PUNCT
ejpam-6433	242	51	h	h	NOUN
ejpam-6433	242	52	)	)	PUNCT
ejpam-6433	242	53	is	be	AUX
ejpam-6433	242	54	a	a	DET
ejpam-6433	242	55	semi	semi	ADJ
ejpam-6433	242	56	-	-	ADJ
ejpam-6433	242	57	sharp	sharp	ADJ
ejpam-6433	242	58	proximinal	proximinal	ADJ
ejpam-6433	242	59	pair	pair	NOUN
ejpam-6433	242	60	.	.	PUNCT
ejpam-6433	243	1	theorem	theorem	NOUN
ejpam-6433	243	2	9	9	NUM
ejpam-6433	243	3	.	.	PUNCT
ejpam-6433	244	1	(	(	PUNCT
ejpam-6433	244	2	compare	compare	VERB
ejpam-6433	244	3	to	to	ADP
ejpam-6433	244	4	theorem	theorem	VERB
ejpam-6433	244	5	4	4	NUM
ejpam-6433	244	6	)	)	PUNCT
ejpam-6433	244	7	let	let	VERB
ejpam-6433	244	8	(	(	PUNCT
ejpam-6433	244	9	g	g	NOUN
ejpam-6433	244	10	,	,	PUNCT
ejpam-6433	244	11	h	h	NOUN
ejpam-6433	244	12	)	)	PUNCT
ejpam-6433	244	13	be	be	AUX
ejpam-6433	244	14	a	a	DET
ejpam-6433	244	15	nonempty	nonempty	ADJ
ejpam-6433	244	16	,	,	PUNCT
ejpam-6433	244	17	compact	compact	ADJ
ejpam-6433	244	18	and	and	CCONJ
ejpam-6433	244	19	hyperconvex	hyperconvex	ADJ
ejpam-6433	244	20	pair	pair	NOUN
ejpam-6433	244	21	in	in	ADP
ejpam-6433	244	22	a	a	DET
ejpam-6433	244	23	hyperconvex	hyperconvex	ADJ
ejpam-6433	244	24	metric	metric	ADJ
ejpam-6433	244	25	space	space	NOUN
ejpam-6433	244	26	(	(	PUNCT
ejpam-6433	244	27	m	m	PROPN
ejpam-6433	244	28	,	,	PUNCT
ejpam-6433	244	29	d	d	NOUN
ejpam-6433	244	30	)	)	PUNCT
ejpam-6433	244	31	which	which	PRON
ejpam-6433	244	32	is	be	AUX
ejpam-6433	244	33	a	a	DET
ejpam-6433	244	34	semi	semi	ADJ
ejpam-6433	244	35	-	-	ADJ
ejpam-6433	244	36	sharp	sharp	ADJ
ejpam-6433	244	37	proximinal	proximinal	ADJ
ejpam-6433	244	38	pair	pair	NOUN
ejpam-6433	244	39	.	.	PUNCT
ejpam-6433	245	1	if	if	SCONJ
ejpam-6433	245	2	t	t	NOUN
ejpam-6433	245	3	:	:	PUNCT
ejpam-6433	245	4	g	g	PROPN
ejpam-6433	245	5	∪	∪	ADJ
ejpam-6433	245	6	h	h	NOUN
ejpam-6433	245	7	→	→	SYM
ejpam-6433	245	8	g	g	PROPN
ejpam-6433	245	9	∪	∪	NOUN
ejpam-6433	245	10	h	h	NOUN
ejpam-6433	245	11	is	be	AUX
ejpam-6433	245	12	a	a	DET
ejpam-6433	245	13	noncyclic	noncyclic	ADJ
ejpam-6433	245	14	relatively	relatively	ADV
ejpam-6433	245	15	u	u	ADJ
ejpam-6433	245	16	-	-	ADJ
ejpam-6433	245	17	continuous	continuous	ADJ
ejpam-6433	245	18	mapping	mapping	NOUN
ejpam-6433	245	19	,	,	PUNCT
ejpam-6433	245	20	then	then	ADV
ejpam-6433	245	21	t	t	PROPN
ejpam-6433	245	22	has	have	VERB
ejpam-6433	245	23	a	a	DET
ejpam-6433	245	24	best	good	ADJ
ejpam-6433	245	25	proximity	proximity	NOUN
ejpam-6433	245	26	pair	pair	NOUN
ejpam-6433	245	27	.	.	PUNCT
ejpam-6433	246	1	proof	proof	NOUN
ejpam-6433	246	2	.	.	PUNCT
ejpam-6433	247	1	as	as	ADP
ejpam-6433	247	2	in	in	ADP
ejpam-6433	247	3	the	the	DET
ejpam-6433	247	4	proof	proof	NOUN
ejpam-6433	247	5	of	of	ADP
ejpam-6433	247	6	theorem	theorem	ADJ
ejpam-6433	247	7	8	8	NUM
ejpam-6433	247	8	,	,	PUNCT
ejpam-6433	247	9	(	(	PUNCT
ejpam-6433	247	10	g0,h0	g0,h0	PROPN
ejpam-6433	247	11	)	)	PUNCT
ejpam-6433	247	12	is	be	AUX
ejpam-6433	247	13	nonempty	nonempty	ADJ
ejpam-6433	247	14	and	and	CCONJ
ejpam-6433	247	15	hyperconvex	hyperconvex	ADJ
ejpam-6433	247	16	.	.	PUNCT
ejpam-6433	248	1	t	t	PROPN
ejpam-6433	248	2	invariance	invariance	NOUN
ejpam-6433	248	3	of	of	ADP
ejpam-6433	248	4	these	these	DET
ejpam-6433	248	5	sets	set	NOUN
ejpam-6433	248	6	follows	follow	VERB
ejpam-6433	248	7	from	from	ADP
ejpam-6433	248	8	relatively	relatively	ADV
ejpam-6433	248	9	u	u	NOUN
ejpam-6433	248	10	-	-	NOUN
ejpam-6433	248	11	continuity	continuity	NOUN
ejpam-6433	248	12	of	of	ADP
ejpam-6433	248	13	t	t	NOUN
ejpam-6433	248	14	,	,	PUNCT
ejpam-6433	248	15	that	that	ADV
ejpam-6433	248	16	is	is	ADV
ejpam-6433	248	17	,	,	PUNCT
ejpam-6433	248	18	for	for	ADP
ejpam-6433	248	19	any	any	DET
ejpam-6433	248	20	pair	pair	NOUN
ejpam-6433	248	21	(	(	PUNCT
ejpam-6433	248	22	x	x	NOUN
ejpam-6433	248	23	,	,	PUNCT
ejpam-6433	248	24	y	y	NOUN
ejpam-6433	248	25	)	)	PUNCT
ejpam-6433	248	26	∈	∈	PROPN
ejpam-6433	248	27	g0×h0	g0×h0	NOUN
ejpam-6433	248	28	,	,	PUNCT
ejpam-6433	248	29	if	if	SCONJ
ejpam-6433	248	30	d(x	d(x	PROPN
ejpam-6433	248	31	,	,	PUNCT
ejpam-6433	248	32	y	y	NOUN
ejpam-6433	248	33	)	)	PUNCT
ejpam-6433	248	34	=	=	SYM
ejpam-6433	249	1	d(g	d(g	PROPN
ejpam-6433	249	2	,	,	PUNCT
ejpam-6433	249	3	h	h	NOUN
ejpam-6433	249	4	)	)	PUNCT
ejpam-6433	249	5	,	,	PUNCT
ejpam-6433	249	6	then	then	ADV
ejpam-6433	249	7	d(tx	d(tx	PROPN
ejpam-6433	249	8	,	,	PUNCT
ejpam-6433	249	9	ty	ty	INTJ
ejpam-6433	249	10	)	)	PUNCT
ejpam-6433	249	11	=	=	SYM
ejpam-6433	250	1	d(g	d(g	PROPN
ejpam-6433	250	2	,	,	PUNCT
ejpam-6433	250	3	h	h	NOUN
ejpam-6433	250	4	)	)	PUNCT
ejpam-6433	250	5	,	,	PUNCT
ejpam-6433	250	6	implying	imply	VERB
ejpam-6433	250	7	that	that	SCONJ
ejpam-6433	250	8	(	(	PUNCT
ejpam-6433	250	9	tx	tx	PROPN
ejpam-6433	250	10	,	,	PUNCT
ejpam-6433	250	11	ty	ty	INTJ
ejpam-6433	250	12	)	)	PUNCT
ejpam-6433	250	13	∈	∈	PROPN
ejpam-6433	250	14	(	(	PUNCT
ejpam-6433	250	15	g0,h0	g0,h0	PROPN
ejpam-6433	250	16	)	)	PUNCT
ejpam-6433	250	17	.	.	PUNCT
ejpam-6433	251	1	choose	choose	VERB
ejpam-6433	251	2	x0	x0	PROPN
ejpam-6433	251	3	∈	∈	PROPN
ejpam-6433	251	4	g0	g0	PROPN
ejpam-6433	251	5	and	and	CCONJ
ejpam-6433	251	6	y0	y0	PROPN
ejpam-6433	251	7	∈	∈	PROPN
ejpam-6433	251	8	h0	h0	NOUN
ejpam-6433	251	9	such	such	ADJ
ejpam-6433	251	10	that	that	DET
ejpam-6433	251	11	d(x0	d(x0	NOUN
ejpam-6433	251	12	,	,	PUNCT
ejpam-6433	251	13	y0	y0	PROPN
ejpam-6433	251	14	)	)	PUNCT
ejpam-6433	251	15	=	=	SYM
ejpam-6433	251	16	d(g	d(g	PROPN
ejpam-6433	251	17	,	,	PUNCT
ejpam-6433	251	18	h	h	NOUN
ejpam-6433	251	19	)	)	PUNCT
ejpam-6433	251	20	.	.	PUNCT
ejpam-6433	252	1	then	then	ADV
ejpam-6433	252	2	by	by	ADP
ejpam-6433	252	3	relatively	relatively	ADV
ejpam-6433	252	4	ucontinuity	ucontinuity	NOUN
ejpam-6433	252	5	of	of	ADP
ejpam-6433	252	6	t	t	NOUN
ejpam-6433	252	7	we	we	PRON
ejpam-6433	252	8	have	have	VERB
ejpam-6433	252	9	d(tx0	d(tx0	PROPN
ejpam-6433	252	10	,	,	PUNCT
ejpam-6433	252	11	ty0	ty0	NOUN
ejpam-6433	252	12	)	)	PUNCT
ejpam-6433	253	1	=	=	SYM
ejpam-6433	253	2	d(g	d(g	PROPN
ejpam-6433	253	3	,	,	PUNCT
ejpam-6433	253	4	h	h	NOUN
ejpam-6433	253	5	)	)	PUNCT
ejpam-6433	253	6	.	.	PUNCT
ejpam-6433	254	1	given	give	VERB
ejpam-6433	254	2	ε	ε	PROPN
ejpam-6433	254	3	>	>	X
ejpam-6433	254	4	0	0	PROPN
ejpam-6433	254	5	,	,	PUNCT
ejpam-6433	254	6	define	define	VERB
ejpam-6433	254	7	an	an	DET
ejpam-6433	254	8	open	open	ADJ
ejpam-6433	254	9	neighborhood	neighborhood	NOUN
ejpam-6433	254	10	of	of	ADP
ejpam-6433	254	11	x0	x0	PROPN
ejpam-6433	254	12	by	by	ADP
ejpam-6433	254	13	u(x0	u(x0	PROPN
ejpam-6433	254	14	,	,	PUNCT
ejpam-6433	254	15	δ	δ	PROPN
ejpam-6433	254	16	)	)	PUNCT
ejpam-6433	254	17	:	:	PUNCT
ejpam-6433	255	1	=	=	SYM
ejpam-6433	255	2	{	{	PUNCT
ejpam-6433	255	3	u	u	NOUN
ejpam-6433	255	4	∈	∈	PROPN
ejpam-6433	255	5	g0	g0	NOUN
ejpam-6433	255	6	:	:	PUNCT
ejpam-6433	255	7	d(u	d(u	PROPN
ejpam-6433	255	8	,	,	PUNCT
ejpam-6433	255	9	x0	x0	PROPN
ejpam-6433	255	10	)	)	PUNCT
ejpam-6433	255	11	<	<	X
ejpam-6433	255	12	δ	δ	X
ejpam-6433	255	13	}	}	PUNCT
ejpam-6433	255	14	.	.	PUNCT
ejpam-6433	256	1	then	then	ADV
ejpam-6433	256	2	u	u	PROPN
ejpam-6433	256	3	∈	∈	PROPN
ejpam-6433	256	4	u(x0	u(x0	NOUN
ejpam-6433	256	5	,	,	PUNCT
ejpam-6433	256	6	δ	δ	PROPN
ejpam-6433	256	7	)	)	PUNCT
ejpam-6433	256	8	implies	imply	VERB
ejpam-6433	256	9	that	that	SCONJ
ejpam-6433	256	10	d(u	d(u	PROPN
ejpam-6433	256	11	,	,	PUNCT
ejpam-6433	256	12	y0	y0	PROPN
ejpam-6433	256	13	)	)	PUNCT
ejpam-6433	256	14	<	<	X
ejpam-6433	256	15	d(u	d(u	PROPN
ejpam-6433	256	16	,	,	PUNCT
ejpam-6433	256	17	x0	x0	PROPN
ejpam-6433	256	18	)	)	PUNCT
ejpam-6433	256	19	+	+	NUM
ejpam-6433	256	20	d(x0	d(x0	NOUN
ejpam-6433	256	21	,	,	PUNCT
ejpam-6433	256	22	y0	y0	PROPN
ejpam-6433	256	23	)	)	PUNCT
ejpam-6433	256	24	<	<	X
ejpam-6433	256	25	δ	δ	PROPN
ejpam-6433	256	26	+	+	PROPN
ejpam-6433	256	27	d(g	d(g	PROPN
ejpam-6433	256	28	,	,	PUNCT
ejpam-6433	256	29	h	h	NOUN
ejpam-6433	256	30	)	)	PUNCT
ejpam-6433	256	31	,	,	PUNCT
ejpam-6433	256	32	m.	m.	NOUN
ejpam-6433	256	33	gabeleh	gabeleh	PROPN
ejpam-6433	256	34	,	,	PUNCT
ejpam-6433	256	35	j.	j.	PROPN
ejpam-6433	256	36	markin	markin	PROPN
ejpam-6433	256	37	,	,	PUNCT
ejpam-6433	256	38	m.	m.	NOUN
ejpam-6433	256	39	aphane	aphane	PROPN
ejpam-6433	256	40	/	/	SYM
ejpam-6433	256	41	eur	eur	PROPN
ejpam-6433	256	42	.	.	PUNCT
ejpam-6433	257	1	j.	j.	PROPN
ejpam-6433	257	2	pure	pure	PROPN
ejpam-6433	257	3	appl	appl	PROPN
ejpam-6433	257	4	.	.	PROPN
ejpam-6433	257	5	math	math	PROPN
ejpam-6433	257	6	,	,	PUNCT
ejpam-6433	257	7	18	18	NUM
ejpam-6433	257	8	(	(	PUNCT
ejpam-6433	257	9	3	3	NUM
ejpam-6433	257	10	)	)	PUNCT
ejpam-6433	257	11	(	(	PUNCT
ejpam-6433	257	12	2025	2025	NUM
ejpam-6433	257	13	)	)	PUNCT
ejpam-6433	257	14	,	,	PUNCT
ejpam-6433	257	15	6433	6433	NUM
ejpam-6433	257	16	11	11	NUM
ejpam-6433	257	17	of	of	ADP
ejpam-6433	257	18	17	17	NUM
ejpam-6433	257	19	and	and	CCONJ
ejpam-6433	257	20	therefore	therefore	ADV
ejpam-6433	257	21	,	,	PUNCT
ejpam-6433	257	22	by	by	ADP
ejpam-6433	257	23	relatively	relatively	ADV
ejpam-6433	257	24	u	u	NOUN
ejpam-6433	257	25	-	-	NOUN
ejpam-6433	257	26	continuity	continuity	NOUN
ejpam-6433	257	27	of	of	ADP
ejpam-6433	257	28	t	t	PROPN
ejpam-6433	257	29	,	,	PUNCT
ejpam-6433	257	30	d(tu	d(tu	PROPN
ejpam-6433	257	31	,	,	PUNCT
ejpam-6433	257	32	ty0	ty0	NOUN
ejpam-6433	257	33	)	)	PUNCT
ejpam-6433	257	34	<	<	X
ejpam-6433	257	35	ε+d(g	ε+d(g	SYM
ejpam-6433	257	36	,	,	PUNCT
ejpam-6433	257	37	h	h	NOUN
ejpam-6433	257	38	)	)	PUNCT
ejpam-6433	257	39	.	.	PUNCT
ejpam-6433	258	1	now	now	ADV
ejpam-6433	258	2	define	define	VERB
ejpam-6433	258	3	a	a	DET
ejpam-6433	258	4	multivalued	multivalue	VERB
ejpam-6433	258	5	map	map	NOUN
ejpam-6433	258	6	f	f	NOUN
ejpam-6433	258	7	:	:	PUNCT
ejpam-6433	258	8	g0	g0	PROPN
ejpam-6433	258	9	→	→	SYM
ejpam-6433	258	10	2h0	2h0	NUM
ejpam-6433	258	11	by	by	ADP
ejpam-6433	258	12	f	f	PROPN
ejpam-6433	258	13	(	(	PUNCT
ejpam-6433	258	14	u	u	NOUN
ejpam-6433	258	15	)	)	PUNCT
ejpam-6433	259	1	=	=	SYM
ejpam-6433	259	2	b	b	PROPN
ejpam-6433	259	3	(	(	PUNCT
ejpam-6433	259	4	tu	tu	PROPN
ejpam-6433	259	5	;	;	PUNCT
ejpam-6433	259	6	d(g	d(g	PROPN
ejpam-6433	259	7	,	,	PUNCT
ejpam-6433	259	8	h	h	NOUN
ejpam-6433	259	9	)	)	PUNCT
ejpam-6433	259	10	)	)	PUNCT
ejpam-6433	260	1	⋂	⋂	PROPN
ejpam-6433	260	2	h0	h0	PROPN
ejpam-6433	260	3	,	,	PUNCT
ejpam-6433	260	4	for	for	ADP
ejpam-6433	260	5	u	u	PROPN
ejpam-6433	260	6	∈	∈	PROPN
ejpam-6433	260	7	g0	g0	PROPN
ejpam-6433	260	8	.	.	PUNCT
ejpam-6433	261	1	by	by	ADP
ejpam-6433	261	2	analogous	analogous	ADJ
ejpam-6433	261	3	arguments	argument	NOUN
ejpam-6433	261	4	to	to	ADP
ejpam-6433	261	5	those	those	PRON
ejpam-6433	261	6	in	in	ADP
ejpam-6433	261	7	the	the	DET
ejpam-6433	261	8	proof	proof	NOUN
ejpam-6433	261	9	of	of	ADP
ejpam-6433	261	10	theorem	theorem	NOUN
ejpam-6433	261	11	8	8	NUM
ejpam-6433	261	12	,	,	PUNCT
ejpam-6433	261	13	f	f	PROPN
ejpam-6433	261	14	is	be	AUX
ejpam-6433	261	15	an	an	DET
ejpam-6433	261	16	almost	almost	ADV
ejpam-6433	261	17	lower	low	ADJ
ejpam-6433	261	18	-	-	PUNCT
ejpam-6433	261	19	semicontinuous	semicontinuous	ADJ
ejpam-6433	261	20	mapping	mapping	NOUN
ejpam-6433	261	21	with	with	ADP
ejpam-6433	261	22	subadmissible	subadmissible	ADJ
ejpam-6433	261	23	values	value	NOUN
ejpam-6433	261	24	.	.	PUNCT
ejpam-6433	262	1	then	then	ADV
ejpam-6433	262	2	,	,	PUNCT
ejpam-6433	262	3	as	as	ADP
ejpam-6433	262	4	above	above	ADV
ejpam-6433	262	5	,	,	PUNCT
ejpam-6433	262	6	f	f	PROPN
ejpam-6433	262	7	has	have	VERB
ejpam-6433	262	8	a	a	DET
ejpam-6433	262	9	continuous	continuous	ADJ
ejpam-6433	262	10	selection	selection	NOUN
ejpam-6433	262	11	h	h	NOUN
ejpam-6433	262	12	:	:	PUNCT
ejpam-6433	262	13	g0	g0	PROPN
ejpam-6433	262	14	→	→	SYM
ejpam-6433	262	15	h0	h0	PROPN
ejpam-6433	262	16	.	.	PROPN
ejpam-6433	263	1	by	by	ADP
ejpam-6433	263	2	semi	semi	ADJ
ejpam-6433	263	3	-	-	ADJ
ejpam-6433	263	4	sharp	sharp	ADJ
ejpam-6433	263	5	proximinality	proximinality	NOUN
ejpam-6433	263	6	of	of	ADP
ejpam-6433	263	7	the	the	DET
ejpam-6433	263	8	pair	pair	NOUN
ejpam-6433	263	9	(	(	PUNCT
ejpam-6433	263	10	g	g	NOUN
ejpam-6433	263	11	,	,	PUNCT
ejpam-6433	263	12	h	h	NOUN
ejpam-6433	263	13	)	)	PUNCT
ejpam-6433	263	14	,	,	PUNCT
ejpam-6433	263	15	we	we	PRON
ejpam-6433	263	16	can	can	AUX
ejpam-6433	263	17	define	define	VERB
ejpam-6433	263	18	a	a	DET
ejpam-6433	263	19	mapping	mapping	NOUN
ejpam-6433	263	20	p	p	NOUN
ejpam-6433	263	21	:	:	PUNCT
ejpam-6433	263	22	h0	h0	PROPN
ejpam-6433	263	23	→	→	SYM
ejpam-6433	263	24	g0	g0	PROPN
ejpam-6433	263	25	as	as	ADP
ejpam-6433	263	26	a	a	DET
ejpam-6433	263	27	projection	projection	NOUN
ejpam-6433	263	28	map	map	NOUN
ejpam-6433	263	29	that	that	PRON
ejpam-6433	263	30	associates	associate	NOUN
ejpam-6433	263	31	to	to	ADP
ejpam-6433	263	32	each	each	DET
ejpam-6433	263	33	point	point	NOUN
ejpam-6433	263	34	p	p	NOUN
ejpam-6433	263	35	in	in	ADP
ejpam-6433	263	36	h0	h0	NOUN
ejpam-6433	263	37	the	the	DET
ejpam-6433	263	38	unique	unique	ADJ
ejpam-6433	263	39	point	point	NOUN
ejpam-6433	263	40	q	q	PUNCT
ejpam-6433	263	41	in	in	ADP
ejpam-6433	263	42	g0	g0	NOUN
ejpam-6433	263	43	such	such	ADJ
ejpam-6433	263	44	that	that	SCONJ
ejpam-6433	263	45	d(p	d(p	PROPN
ejpam-6433	263	46	,	,	PUNCT
ejpam-6433	263	47	q	q	NOUN
ejpam-6433	263	48	)	)	PUNCT
ejpam-6433	263	49	=	=	SYM
ejpam-6433	263	50	d(g	d(g	PROPN
ejpam-6433	263	51	,	,	PUNCT
ejpam-6433	263	52	h	h	NOUN
ejpam-6433	263	53	)	)	PUNCT
ejpam-6433	263	54	.	.	PUNCT
ejpam-6433	264	1	we	we	PRON
ejpam-6433	264	2	claim	claim	VERB
ejpam-6433	264	3	that	that	SCONJ
ejpam-6433	264	4	this	this	DET
ejpam-6433	264	5	correspondence	correspondence	NOUN
ejpam-6433	264	6	is	be	AUX
ejpam-6433	264	7	a	a	DET
ejpam-6433	264	8	continuous	continuous	ADJ
ejpam-6433	264	9	mapping	mapping	NOUN
ejpam-6433	264	10	.	.	PUNCT
ejpam-6433	265	1	assume	assume	VERB
ejpam-6433	265	2	that	that	SCONJ
ejpam-6433	265	3	a	a	DET
ejpam-6433	265	4	sequence	sequence	NOUN
ejpam-6433	265	5	{	{	PUNCT
ejpam-6433	265	6	pn	pn	NOUN
ejpam-6433	265	7	}	}	PUNCT
ejpam-6433	265	8	in	in	ADP
ejpam-6433	265	9	h0	h0	NOUN
ejpam-6433	265	10	converges	converge	NOUN
ejpam-6433	265	11	to	to	ADP
ejpam-6433	265	12	a	a	DET
ejpam-6433	265	13	point	point	NOUN
ejpam-6433	265	14	p	p	X
ejpam-6433	265	15	∈	∈	PROPN
ejpam-6433	265	16	h	h	NOUN
ejpam-6433	265	17	,	,	PUNCT
ejpam-6433	265	18	and	and	CCONJ
ejpam-6433	265	19	by	by	ADP
ejpam-6433	265	20	contrary	contrary	ADJ
ejpam-6433	265	21	assume	assume	VERB
ejpam-6433	265	22	that	that	SCONJ
ejpam-6433	265	23	{	{	PUNCT
ejpam-6433	265	24	p(pn	p(pn	NOUN
ejpam-6433	265	25	)	)	PUNCT
ejpam-6433	265	26	}	}	PUNCT
ejpam-6433	265	27	does	do	AUX
ejpam-6433	265	28	not	not	PART
ejpam-6433	265	29	converge	converge	VERB
ejpam-6433	265	30	to	to	ADP
ejpam-6433	265	31	p(p	p(p	NOUN
ejpam-6433	265	32	)	)	PUNCT
ejpam-6433	265	33	.	.	PUNCT
ejpam-6433	266	1	by	by	ADP
ejpam-6433	266	2	compactness	compactness	NOUN
ejpam-6433	266	3	of	of	ADP
ejpam-6433	266	4	the	the	DET
ejpam-6433	266	5	set	set	ADJ
ejpam-6433	266	6	g0	g0	NOUN
ejpam-6433	266	7	,	,	PUNCT
ejpam-6433	266	8	{	{	PUNCT
ejpam-6433	266	9	p(pn	p(pn	NOUN
ejpam-6433	266	10	)	)	PUNCT
ejpam-6433	266	11	}	}	PUNCT
ejpam-6433	266	12	has	have	VERB
ejpam-6433	266	13	a	a	DET
ejpam-6433	266	14	convergent	convergent	ADJ
ejpam-6433	266	15	subsequence	subsequence	NOUN
ejpam-6433	266	16	{	{	PUNCT
ejpam-6433	266	17	qn	qn	NOUN
ejpam-6433	266	18	}	}	PUNCT
ejpam-6433	266	19	that	that	PRON
ejpam-6433	266	20	converges	converge	VERB
ejpam-6433	266	21	to	to	ADP
ejpam-6433	266	22	a	a	DET
ejpam-6433	266	23	point	point	NOUN
ejpam-6433	266	24	q.	q.	NOUN
ejpam-6433	266	25	then	then	ADV
ejpam-6433	266	26	,	,	PUNCT
ejpam-6433	266	27	limn→+∞	limn→+∞	VERB
ejpam-6433	266	28	d(pn	d(pn	PROPN
ejpam-6433	266	29	,	,	PUNCT
ejpam-6433	266	30	qn	qn	NOUN
ejpam-6433	266	31	)	)	PUNCT
ejpam-6433	266	32	=	=	SYM
ejpam-6433	266	33	d(p	d(p	PROPN
ejpam-6433	266	34	,	,	PUNCT
ejpam-6433	266	35	q	q	NOUN
ejpam-6433	266	36	)	)	PUNCT
ejpam-6433	266	37	=	=	SYM
ejpam-6433	267	1	d(g	d(g	PROPN
ejpam-6433	267	2	,	,	PUNCT
ejpam-6433	267	3	h	h	NOUN
ejpam-6433	267	4	)	)	PUNCT
ejpam-6433	267	5	,	,	PUNCT
ejpam-6433	267	6	where	where	SCONJ
ejpam-6433	267	7	q	q	PROPN
ejpam-6433	267	8	̸=	̸=	PROPN
ejpam-6433	267	9	p(p	p(p	NOUN
ejpam-6433	267	10	)	)	PUNCT
ejpam-6433	267	11	,	,	PUNCT
ejpam-6433	267	12	contradicting	contradict	VERB
ejpam-6433	267	13	uniqueness	uniqueness	NOUN
ejpam-6433	267	14	of	of	ADP
ejpam-6433	267	15	the	the	DET
ejpam-6433	267	16	proximal	proximal	ADJ
ejpam-6433	267	17	point	point	NOUN
ejpam-6433	267	18	.	.	PUNCT
ejpam-6433	268	1	therefore	therefore	ADV
ejpam-6433	268	2	,	,	PUNCT
ejpam-6433	268	3	p	p	PRON
ejpam-6433	268	4	is	be	AUX
ejpam-6433	268	5	a	a	DET
ejpam-6433	268	6	continuous	continuous	ADJ
ejpam-6433	268	7	mapping	mapping	NOUN
ejpam-6433	268	8	.	.	PUNCT
ejpam-6433	269	1	as	as	ADP
ejpam-6433	269	2	a	a	DET
ejpam-6433	269	3	continuous	continuous	ADJ
ejpam-6433	269	4	self	self	NOUN
ejpam-6433	269	5	mapping	mapping	NOUN
ejpam-6433	269	6	on	on	ADP
ejpam-6433	269	7	a	a	DET
ejpam-6433	269	8	compact	compact	ADJ
ejpam-6433	269	9	hyperconvex	hyperconvex	NOUN
ejpam-6433	269	10	set	set	NOUN
ejpam-6433	269	11	,	,	PUNCT
ejpam-6433	269	12	the	the	DET
ejpam-6433	269	13	mapping	mapping	NOUN
ejpam-6433	269	14	poh	poh	NOUN
ejpam-6433	269	15	:	:	PUNCT
ejpam-6433	269	16	g0	g0	PROPN
ejpam-6433	269	17	→	→	SYM
ejpam-6433	269	18	g0	g0	PROPN
ejpam-6433	269	19	has	have	VERB
ejpam-6433	269	20	a	a	DET
ejpam-6433	269	21	fixed	fix	VERB
ejpam-6433	269	22	point	point	NOUN
ejpam-6433	269	23	z	z	PROPN
ejpam-6433	269	24	∈	∈	PROPN
ejpam-6433	269	25	g0	g0	PROPN
ejpam-6433	269	26	.	.	PUNCT
ejpam-6433	270	1	by	by	ADP
ejpam-6433	270	2	definition	definition	NOUN
ejpam-6433	270	3	of	of	ADP
ejpam-6433	270	4	this	this	DET
ejpam-6433	270	5	mapping	mapping	NOUN
ejpam-6433	270	6	,	,	PUNCT
ejpam-6433	270	7	z	z	PROPN
ejpam-6433	270	8	=	=	SYM
ejpam-6433	270	9	tz	tz	NOUN
ejpam-6433	270	10	,	,	PUNCT
ejpam-6433	270	11	and	and	CCONJ
ejpam-6433	270	12	if	if	SCONJ
ejpam-6433	270	13	w	w	NOUN
ejpam-6433	270	14	is	be	AUX
ejpam-6433	270	15	the	the	DET
ejpam-6433	270	16	unique	unique	ADJ
ejpam-6433	270	17	point	point	NOUN
ejpam-6433	270	18	in	in	ADP
ejpam-6433	270	19	h0	h0	PROPN
ejpam-6433	270	20	such	such	ADJ
ejpam-6433	270	21	that	that	SCONJ
ejpam-6433	270	22	d(z	d(z	PROPN
ejpam-6433	270	23	,	,	PUNCT
ejpam-6433	270	24	w	w	NOUN
ejpam-6433	270	25	)	)	PUNCT
ejpam-6433	270	26	=	=	SYM
ejpam-6433	270	27	d(g	d(g	PROPN
ejpam-6433	270	28	,	,	PUNCT
ejpam-6433	270	29	h	h	NOUN
ejpam-6433	270	30	)	)	PUNCT
ejpam-6433	270	31	,	,	PUNCT
ejpam-6433	270	32	it	it	PRON
ejpam-6433	270	33	follows	follow	VERB
ejpam-6433	270	34	from	from	ADP
ejpam-6433	270	35	relatively	relatively	ADV
ejpam-6433	270	36	u	u	NOUN
ejpam-6433	270	37	-	-	NOUN
ejpam-6433	270	38	continuity	continuity	NOUN
ejpam-6433	270	39	of	of	ADP
ejpam-6433	270	40	t	t	NOUN
ejpam-6433	270	41	that	that	PRON
ejpam-6433	270	42	w	w	PROPN
ejpam-6433	270	43	=	=	PUNCT
ejpam-6433	270	44	tw	tw	NOUN
ejpam-6433	270	45	and	and	CCONJ
ejpam-6433	270	46	the	the	DET
ejpam-6433	270	47	proof	proof	NOUN
ejpam-6433	270	48	is	be	AUX
ejpam-6433	270	49	completed	complete	VERB
ejpam-6433	270	50	.	.	PUNCT
ejpam-6433	271	1	the	the	DET
ejpam-6433	271	2	next	next	ADJ
ejpam-6433	271	3	example	example	NOUN
ejpam-6433	271	4	guarantees	guarantee	VERB
ejpam-6433	271	5	that	that	SCONJ
ejpam-6433	271	6	the	the	DET
ejpam-6433	271	7	semi	semi	ADJ
ejpam-6433	271	8	-	-	ADJ
ejpam-6433	271	9	sharp	sharp	ADJ
ejpam-6433	271	10	proximinality	proximinality	NOUN
ejpam-6433	271	11	of	of	ADP
ejpam-6433	271	12	the	the	DET
ejpam-6433	271	13	pair	pair	NOUN
ejpam-6433	271	14	(	(	PUNCT
ejpam-6433	271	15	g	g	NOUN
ejpam-6433	271	16	,	,	PUNCT
ejpam-6433	271	17	h	h	NOUN
ejpam-6433	271	18	)	)	PUNCT
ejpam-6433	271	19	in	in	ADP
ejpam-6433	271	20	theorem	theorem	NOUN
ejpam-6433	271	21	9	9	NUM
ejpam-6433	271	22	is	be	AUX
ejpam-6433	271	23	essential	essential	ADJ
ejpam-6433	271	24	.	.	PUNCT
ejpam-6433	272	1	example	example	NOUN
ejpam-6433	272	2	5	5	NUM
ejpam-6433	272	3	.	.	X
ejpam-6433	273	1	consider	consider	VERB
ejpam-6433	273	2	the	the	DET
ejpam-6433	273	3	hyperconvex	hyperconvex	ADJ
ejpam-6433	273	4	space	space	NOUN
ejpam-6433	273	5	ℓ∞	ℓ∞	PROPN
ejpam-6433	273	6	with	with	ADP
ejpam-6433	273	7	the	the	DET
ejpam-6433	273	8	canonical	canonical	ADJ
ejpam-6433	273	9	basis	basis	NOUN
ejpam-6433	273	10	{	{	PUNCT
ejpam-6433	273	11	en}n∈n	en}n∈n	PUNCT
ejpam-6433	273	12	and	and	CCONJ
ejpam-6433	273	13	let	let	VERB
ejpam-6433	273	14	g	g	NOUN
ejpam-6433	273	15	=	=	PUNCT
ejpam-6433	273	16	{	{	PUNCT
ejpam-6433	273	17	te1	te1	NOUN
ejpam-6433	274	1	+	+	CCONJ
ejpam-6433	274	2	2e2	2e2	NUM
ejpam-6433	274	3	:	:	PUNCT
ejpam-6433	274	4	0	0	NUM
ejpam-6433	274	5	≤	≤	NUM
ejpam-6433	274	6	t	t	NOUN
ejpam-6433	274	7	≤	≤	NUM
ejpam-6433	274	8	1	1	NUM
ejpam-6433	274	9	}	}	PUNCT
ejpam-6433	274	10	,	,	PUNCT
ejpam-6433	274	11	h	h	NOUN
ejpam-6433	274	12	=	=	PRON
ejpam-6433	274	13	{	{	PUNCT
ejpam-6433	274	14	te3	te3	NOUN
ejpam-6433	274	15	:	:	PUNCT
ejpam-6433	275	1	0	0	NUM
ejpam-6433	275	2	≤	≤	NUM
ejpam-6433	275	3	t	t	NOUN
ejpam-6433	275	4	≤	≤	NUM
ejpam-6433	275	5	1	1	NUM
ejpam-6433	275	6	}	}	PUNCT
ejpam-6433	275	7	.	.	PUNCT
ejpam-6433	276	1	then	then	ADV
ejpam-6433	276	2	(	(	PUNCT
ejpam-6433	276	3	g	g	NOUN
ejpam-6433	276	4	,	,	PUNCT
ejpam-6433	276	5	h	h	NOUN
ejpam-6433	276	6	)	)	PUNCT
ejpam-6433	276	7	is	be	AUX
ejpam-6433	276	8	a	a	DET
ejpam-6433	276	9	compact	compact	ADJ
ejpam-6433	276	10	and	and	CCONJ
ejpam-6433	276	11	hyperconvex	hyperconvex	ADJ
ejpam-6433	276	12	pair	pair	NOUN
ejpam-6433	276	13	with	with	ADP
ejpam-6433	276	14	d(g	d(g	PROPN
ejpam-6433	276	15	,	,	PUNCT
ejpam-6433	276	16	h	h	NOUN
ejpam-6433	276	17	)	)	PUNCT
ejpam-6433	276	18	=	=	SYM
ejpam-6433	276	19	2	2	X
ejpam-6433	276	20	.	.	PUNCT
ejpam-6433	276	21	clearly	clearly	ADV
ejpam-6433	276	22	,	,	PUNCT
ejpam-6433	276	23	(	(	PUNCT
ejpam-6433	276	24	g	g	NOUN
ejpam-6433	276	25	,	,	PUNCT
ejpam-6433	276	26	h	h	NOUN
ejpam-6433	276	27	)	)	PUNCT
ejpam-6433	276	28	is	be	AUX
ejpam-6433	276	29	not	not	PART
ejpam-6433	276	30	a	a	DET
ejpam-6433	276	31	semi	semi	ADJ
ejpam-6433	276	32	-	-	ADJ
ejpam-6433	276	33	sharp	sharp	ADJ
ejpam-6433	276	34	proximinal	proximinal	ADJ
ejpam-6433	276	35	pair	pair	NOUN
ejpam-6433	276	36	.	.	PUNCT
ejpam-6433	277	1	define	define	VERB
ejpam-6433	277	2	t	t	NOUN
ejpam-6433	277	3	:	:	PUNCT
ejpam-6433	277	4	g	g	PROPN
ejpam-6433	277	5	∪	∪	ADJ
ejpam-6433	277	6	h	h	NOUN
ejpam-6433	277	7	→	→	SYM
ejpam-6433	277	8	g	g	PROPN
ejpam-6433	277	9	∪h	∪h	NUM
ejpam-6433	277	10	by	by	ADP
ejpam-6433	277	11	t	t	PROPN
ejpam-6433	277	12	(	(	PUNCT
ejpam-6433	277	13	te1	te1	PROPN
ejpam-6433	277	14	+	+	CCONJ
ejpam-6433	277	15	2e2	2e2	NUM
ejpam-6433	277	16	)	)	PUNCT
ejpam-6433	277	17	=	=	SYM
ejpam-6433	278	1	√	√	NUM
ejpam-6433	278	2	te1	te1	NOUN
ejpam-6433	278	3	+	+	CCONJ
ejpam-6433	278	4	2e2	2e2	PROPN
ejpam-6433	278	5	,	,	PUNCT
ejpam-6433	278	6	for	for	ADP
ejpam-6433	278	7	all	all	DET
ejpam-6433	278	8	t	t	NOUN
ejpam-6433	278	9	∈	∈	PROPN
ejpam-6433	279	1	[	[	X
ejpam-6433	279	2	0	0	NUM
ejpam-6433	279	3	,	,	PUNCT
ejpam-6433	279	4	1	1	NUM
ejpam-6433	279	5	]	]	PUNCT
ejpam-6433	279	6	,	,	PUNCT
ejpam-6433	279	7	t	t	PROPN
ejpam-6433	279	8	(	(	PUNCT
ejpam-6433	279	9	te3	te3	PROPN
ejpam-6433	279	10	)	)	PUNCT
ejpam-6433	279	11	=	=	PRON
ejpam-6433	279	12	{	{	PUNCT
ejpam-6433	279	13	0	0	NUM
ejpam-6433	279	14	,	,	PUNCT
ejpam-6433	279	15	if	if	SCONJ
ejpam-6433	279	16	t	t	PROPN
ejpam-6433	279	17	̸=	̸=	PROPN
ejpam-6433	279	18	0	0	NUM
ejpam-6433	279	19	,	,	PUNCT
ejpam-6433	279	20	e3	e3	NOUN
ejpam-6433	279	21	,	,	PUNCT
ejpam-6433	279	22	if	if	SCONJ
ejpam-6433	279	23	t	t	PROPN
ejpam-6433	279	24	=	=	SYM
ejpam-6433	279	25	0	0	PROPN
ejpam-6433	279	26	.	.	PUNCT
ejpam-6433	280	1	then	then	ADV
ejpam-6433	280	2	d∞(tx	d∞(tx	NOUN
ejpam-6433	280	3	,	,	PUNCT
ejpam-6433	280	4	ty	ty	INTJ
ejpam-6433	280	5	)	)	PUNCT
ejpam-6433	280	6	=	=	SYM
ejpam-6433	280	7	2	2	NUM
ejpam-6433	280	8	=	=	SYM
ejpam-6433	280	9	d∞(x	d∞(x	X
ejpam-6433	280	10	,	,	PUNCT
ejpam-6433	280	11	y	y	NOUN
ejpam-6433	280	12	)	)	PUNCT
ejpam-6433	280	13	,	,	PUNCT
ejpam-6433	280	14	for	for	ADP
ejpam-6433	280	15	all	all	DET
ejpam-6433	280	16	(	(	PUNCT
ejpam-6433	280	17	x	x	NOUN
ejpam-6433	280	18	,	,	PUNCT
ejpam-6433	280	19	y	y	PROPN
ejpam-6433	280	20	)	)	PUNCT
ejpam-6433	280	21	∈	∈	PROPN
ejpam-6433	280	22	g	g	PROPN
ejpam-6433	280	23	×h	×h	PROPN
ejpam-6433	280	24	,	,	PUNCT
ejpam-6433	280	25	which	which	PRON
ejpam-6433	280	26	deduces	deduce	VERB
ejpam-6433	280	27	that	that	PRON
ejpam-6433	280	28	t	t	PROPN
ejpam-6433	280	29	is	be	AUX
ejpam-6433	280	30	a	a	DET
ejpam-6433	280	31	noncyclic	noncyclic	ADJ
ejpam-6433	280	32	relatively	relatively	ADV
ejpam-6433	280	33	u	u	NOUN
ejpam-6433	280	34	-	-	ADJ
ejpam-6433	280	35	continuous	continuous	ADJ
ejpam-6433	280	36	.	.	PUNCT
ejpam-6433	281	1	note	note	NOUN
ejpam-6433	281	2	that	that	SCONJ
ejpam-6433	281	3	t	t	PROPN
ejpam-6433	281	4	does	do	AUX
ejpam-6433	281	5	not	not	PART
ejpam-6433	281	6	possess	possess	VERB
ejpam-6433	281	7	any	any	DET
ejpam-6433	281	8	best	good	ADJ
ejpam-6433	281	9	proximity	proximity	NOUN
ejpam-6433	281	10	pair	pair	NOUN
ejpam-6433	281	11	.	.	PUNCT
ejpam-6433	282	1	m.	m.	NOUN
ejpam-6433	282	2	gabeleh	gabeleh	PROPN
ejpam-6433	282	3	,	,	PUNCT
ejpam-6433	282	4	j.	j.	PROPN
ejpam-6433	282	5	markin	markin	PROPN
ejpam-6433	282	6	,	,	PUNCT
ejpam-6433	282	7	m.	m.	NOUN
ejpam-6433	282	8	aphane	aphane	PROPN
ejpam-6433	282	9	/	/	SYM
ejpam-6433	282	10	eur	eur	PROPN
ejpam-6433	282	11	.	.	PUNCT
ejpam-6433	283	1	j.	j.	PROPN
ejpam-6433	283	2	pure	pure	PROPN
ejpam-6433	283	3	appl	appl	PROPN
ejpam-6433	283	4	.	.	PROPN
ejpam-6433	283	5	math	math	PROPN
ejpam-6433	283	6	,	,	PUNCT
ejpam-6433	283	7	18	18	NUM
ejpam-6433	283	8	(	(	PUNCT
ejpam-6433	283	9	3	3	NUM
ejpam-6433	283	10	)	)	PUNCT
ejpam-6433	283	11	(	(	PUNCT
ejpam-6433	283	12	2025	2025	NUM
ejpam-6433	283	13	)	)	PUNCT
ejpam-6433	283	14	,	,	PUNCT
ejpam-6433	283	15	6433	6433	NUM
ejpam-6433	283	16	12	12	NUM
ejpam-6433	283	17	of	of	ADP
ejpam-6433	283	18	17	17	NUM
ejpam-6433	283	19	3	3	NUM
ejpam-6433	283	20	.	.	PUNCT
ejpam-6433	284	1	hyperconvex	hyperconvex	NOUN
ejpam-6433	284	2	spaces	space	NOUN
ejpam-6433	284	3	equipped	equip	VERB
ejpam-6433	284	4	with	with	ADP
ejpam-6433	284	5	a	a	DET
ejpam-6433	284	6	suitable	suitable	ADJ
ejpam-6433	284	7	mnc	mnc	NOUN
ejpam-6433	284	8	in	in	ADP
ejpam-6433	284	9	this	this	DET
ejpam-6433	284	10	section	section	NOUN
ejpam-6433	284	11	,	,	PUNCT
ejpam-6433	284	12	we	we	PRON
ejpam-6433	284	13	extend	extend	VERB
ejpam-6433	284	14	theorem	theorem	ADJ
ejpam-6433	284	15	8	8	NUM
ejpam-6433	284	16	and	and	CCONJ
ejpam-6433	284	17	theorem	theorem	VERB
ejpam-6433	284	18	9	9	NUM
ejpam-6433	284	19	by	by	ADP
ejpam-6433	284	20	relaxing	relax	VERB
ejpam-6433	284	21	the	the	DET
ejpam-6433	284	22	compactness	compactness	NOUN
ejpam-6433	284	23	assumption	assumption	NOUN
ejpam-6433	284	24	of	of	ADP
ejpam-6433	284	25	the	the	DET
ejpam-6433	284	26	hyperconvex	hyperconvex	ADJ
ejpam-6433	284	27	space	space	NOUN
ejpam-6433	284	28	m	m	VERB
ejpam-6433	284	29	and	and	CCONJ
ejpam-6433	284	30	replacing	replace	VERB
ejpam-6433	284	31	a	a	DET
ejpam-6433	284	32	suitable	suitable	ADJ
ejpam-6433	284	33	mnc	mnc	NOUN
ejpam-6433	284	34	on	on	ADP
ejpam-6433	284	35	m.	m.	NOUN
ejpam-6433	284	36	for	for	ADP
ejpam-6433	284	37	this	this	DET
ejpam-6433	284	38	purpose	purpose	NOUN
ejpam-6433	284	39	,	,	PUNCT
ejpam-6433	284	40	we	we	PRON
ejpam-6433	284	41	need	need	VERB
ejpam-6433	284	42	to	to	PART
ejpam-6433	284	43	recall	recall	VERB
ejpam-6433	284	44	the	the	DET
ejpam-6433	284	45	following	follow	VERB
ejpam-6433	284	46	useful	useful	ADJ
ejpam-6433	284	47	tools	tool	NOUN
ejpam-6433	284	48	of	of	ADP
ejpam-6433	284	49	hyperconvex	hyperconvex	ADJ
ejpam-6433	284	50	spaces	space	NOUN
ejpam-6433	284	51	which	which	PRON
ejpam-6433	284	52	were	be	AUX
ejpam-6433	284	53	presented	present	VERB
ejpam-6433	284	54	by	by	ADP
ejpam-6433	284	55	m.a	m.a	PROPN
ejpam-6433	284	56	.	.	PROPN
ejpam-6433	284	57	khamsi	khamsi	PROPN
ejpam-6433	284	58	in	in	ADP
ejpam-6433	284	59	[	[	X
ejpam-6433	284	60	24	24	NUM
ejpam-6433	284	61	]	]	PUNCT
ejpam-6433	284	62	.	.	PUNCT
ejpam-6433	285	1	definition	definition	NOUN
ejpam-6433	285	2	11	11	NUM
ejpam-6433	285	3	.	.	PUNCT
ejpam-6433	286	1	let	let	VERB
ejpam-6433	286	2	g	g	PRON
ejpam-6433	286	3	be	be	AUX
ejpam-6433	286	4	a	a	DET
ejpam-6433	286	5	nonempty	nonempty	ADJ
ejpam-6433	286	6	subset	subset	NOUN
ejpam-6433	286	7	of	of	ADP
ejpam-6433	286	8	a	a	DET
ejpam-6433	286	9	metric	metric	ADJ
ejpam-6433	286	10	space	space	NOUN
ejpam-6433	286	11	(	(	PUNCT
ejpam-6433	286	12	m	m	PROPN
ejpam-6433	286	13	,	,	PUNCT
ejpam-6433	286	14	d	d	NOUN
ejpam-6433	286	15	)	)	PUNCT
ejpam-6433	286	16	.	.	PUNCT
ejpam-6433	287	1	we	we	PRON
ejpam-6433	287	2	say	say	VERB
ejpam-6433	287	3	that	that	SCONJ
ejpam-6433	287	4	g	g	PROPN
ejpam-6433	287	5	is	be	AUX
ejpam-6433	287	6	a	a	DET
ejpam-6433	287	7	nonexpansive	nonexpansive	ADJ
ejpam-6433	287	8	retract	retract	NOUN
ejpam-6433	287	9	of	of	ADP
ejpam-6433	287	10	m	m	PRON
ejpam-6433	287	11	if	if	SCONJ
ejpam-6433	287	12	there	there	PRON
ejpam-6433	287	13	exists	exist	VERB
ejpam-6433	287	14	a	a	DET
ejpam-6433	287	15	nonexpansive	nonexpansive	ADJ
ejpam-6433	287	16	mapping	mapping	NOUN
ejpam-6433	287	17	r	r	NOUN
ejpam-6433	287	18	:	:	PUNCT
ejpam-6433	287	19	m	m	VERB
ejpam-6433	287	20	→	→	SYM
ejpam-6433	287	21	g	g	NOUN
ejpam-6433	287	22	such	such	ADJ
ejpam-6433	287	23	that	that	PRON
ejpam-6433	287	24	rx	rx	NOUN
ejpam-6433	287	25	=	=	NOUN
ejpam-6433	287	26	x	x	PROPN
ejpam-6433	287	27	for	for	ADP
ejpam-6433	287	28	any	any	DET
ejpam-6433	287	29	x	x	SYM
ejpam-6433	287	30	∈	∈	PROPN
ejpam-6433	287	31	g.	g.	NOUN
ejpam-6433	287	32	proposition	proposition	NOUN
ejpam-6433	287	33	4	4	NUM
ejpam-6433	287	34	.	.	PUNCT
ejpam-6433	288	1	(	(	PUNCT
ejpam-6433	288	2	proposition	proposition	NOUN
ejpam-6433	288	3	1	1	NUM
ejpam-6433	288	4	of	of	ADP
ejpam-6433	288	5	[	[	X
ejpam-6433	288	6	24	24	NUM
ejpam-6433	288	7	]	]	PUNCT
ejpam-6433	288	8	)	)	PUNCT
ejpam-6433	288	9	a	a	DET
ejpam-6433	288	10	metric	metric	ADJ
ejpam-6433	288	11	space	space	NOUN
ejpam-6433	288	12	(	(	PUNCT
ejpam-6433	288	13	m	m	PROPN
ejpam-6433	288	14	,	,	PUNCT
ejpam-6433	288	15	d	d	X
ejpam-6433	288	16	)	)	PUNCT
ejpam-6433	288	17	is	be	AUX
ejpam-6433	288	18	hyperconvex	hyperconvex	PROPN
ejpam-6433	288	19	iff	iff	PROPN
ejpam-6433	288	20	for	for	ADP
ejpam-6433	288	21	any	any	DET
ejpam-6433	288	22	metric	metric	ADJ
ejpam-6433	288	23	space	space	NOUN
ejpam-6433	288	24	(	(	PUNCT
ejpam-6433	288	25	n	n	X
ejpam-6433	288	26	,	,	PUNCT
ejpam-6433	288	27	ρ	ρ	PROPN
ejpam-6433	288	28	)	)	PUNCT
ejpam-6433	288	29	which	which	PRON
ejpam-6433	288	30	contains	contain	VERB
ejpam-6433	288	31	isometrically	isometrically	PROPN
ejpam-6433	288	32	m	m	PROPN
ejpam-6433	288	33	,	,	PUNCT
ejpam-6433	288	34	there	there	PRON
ejpam-6433	288	35	exists	exist	VERB
ejpam-6433	288	36	a	a	DET
ejpam-6433	288	37	nonexpansive	nonexpansive	ADJ
ejpam-6433	288	38	retract	retract	NOUN
ejpam-6433	288	39	r	r	NOUN
ejpam-6433	288	40	:	:	PUNCT
ejpam-6433	288	41	n	n	X
ejpam-6433	288	42	→	→	PUNCT
ejpam-6433	288	43	m.	m.	NOUN
ejpam-6433	288	44	now	now	ADV
ejpam-6433	288	45	for	for	ADP
ejpam-6433	288	46	a	a	DET
ejpam-6433	288	47	metric	metric	ADJ
ejpam-6433	288	48	space	space	NOUN
ejpam-6433	288	49	(	(	PUNCT
ejpam-6433	288	50	m	m	PROPN
ejpam-6433	288	51	,	,	PUNCT
ejpam-6433	288	52	d	d	X
ejpam-6433	288	53	)	)	PUNCT
ejpam-6433	288	54	we	we	PRON
ejpam-6433	288	55	define	define	VERB
ejpam-6433	288	56	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	288	57	)	)	PUNCT
ejpam-6433	289	1	=	=	PRON
ejpam-6433	289	2	{	{	PUNCT
ejpam-6433	289	3	(	(	PUNCT
ejpam-6433	289	4	xj)j∈m	xj)j∈m	NUM
ejpam-6433	289	5	⊆	⊆	NUM
ejpam-6433	289	6	r	r	NOUN
ejpam-6433	289	7	:	:	PUNCT
ejpam-6433	289	8	sup	sup	NOUN
ejpam-6433	289	9	j∈m	j∈m	NOUN
ejpam-6433	289	10	|xj	|xj	NUM
ejpam-6433	290	1	|	|	ADV
ejpam-6433	290	2	<	<	X
ejpam-6433	290	3	+	+	NOUN
ejpam-6433	290	4	∞	∞	NUM
ejpam-6433	290	5	}	}	PUNCT
ejpam-6433	290	6	,	,	PUNCT
ejpam-6433	290	7	and	and	CCONJ
ejpam-6433	290	8	let	let	VERB
ejpam-6433	290	9	d∞	d∞	PROPN
ejpam-6433	290	10	(	(	PUNCT
ejpam-6433	290	11	(	(	PUNCT
ejpam-6433	290	12	xj	xj	NOUN
ejpam-6433	290	13	)	)	PUNCT
ejpam-6433	290	14	,	,	PUNCT
ejpam-6433	290	15	(	(	PUNCT
ejpam-6433	290	16	yj	yj	PROPN
ejpam-6433	290	17	)	)	PUNCT
ejpam-6433	290	18	)	)	PUNCT
ejpam-6433	290	19	:	:	PUNCT
ejpam-6433	291	1	=	=	NOUN
ejpam-6433	291	2	sup	sup	NOUN
ejpam-6433	291	3	j∈m	j∈m	NOUN
ejpam-6433	291	4	|xj	|xj	NUM
ejpam-6433	291	5	−	−	PROPN
ejpam-6433	291	6	yj	yj	PROPN
ejpam-6433	291	7	|	|	NOUN
ejpam-6433	291	8	,	,	PUNCT
ejpam-6433	291	9	for	for	ADP
ejpam-6433	291	10	all	all	PRON
ejpam-6433	291	11	(	(	PUNCT
ejpam-6433	291	12	xj	xj	PROPN
ejpam-6433	291	13	)	)	PUNCT
ejpam-6433	291	14	,	,	PUNCT
ejpam-6433	291	15	(	(	PUNCT
ejpam-6433	291	16	yj	yj	PROPN
ejpam-6433	291	17	)	)	PUNCT
ejpam-6433	291	18	∈	∈	PROPN
ejpam-6433	291	19	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	291	20	)	)	PUNCT
ejpam-6433	291	21	.	.	PUNCT
ejpam-6433	292	1	then	then	ADV
ejpam-6433	292	2	(	(	PUNCT
ejpam-6433	292	3	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	292	4	)	)	PUNCT
ejpam-6433	292	5	,	,	PUNCT
ejpam-6433	292	6	d∞	d∞	PROPN
ejpam-6433	292	7	)	)	PUNCT
ejpam-6433	292	8	is	be	AUX
ejpam-6433	292	9	a	a	DET
ejpam-6433	292	10	hyperconvex	hyperconvex	ADJ
ejpam-6433	292	11	metric	metric	ADJ
ejpam-6433	292	12	space	space	NOUN
ejpam-6433	292	13	.	.	PUNCT
ejpam-6433	293	1	let	let	VERB
ejpam-6433	293	2	x0	x0	PROPN
ejpam-6433	293	3	∈	∈	PROPN
ejpam-6433	293	4	m	m	AUX
ejpam-6433	293	5	be	be	VERB
ejpam-6433	293	6	a	a	DET
ejpam-6433	293	7	fixed	fix	VERB
ejpam-6433	293	8	element	element	NOUN
ejpam-6433	293	9	and	and	CCONJ
ejpam-6433	293	10	define	define	VERB
ejpam-6433	293	11	the	the	DET
ejpam-6433	293	12	natural	natural	ADJ
ejpam-6433	293	13	isometric	isometric	ADJ
ejpam-6433	293	14	embedding	embed	VERB
ejpam-6433	293	15	η	η	PROPN
ejpam-6433	293	16	:	:	PUNCT
ejpam-6433	293	17	m	m	PROPN
ejpam-6433	293	18	→	→	SYM
ejpam-6433	293	19	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	293	20	)	)	PUNCT
ejpam-6433	293	21	as	as	SCONJ
ejpam-6433	293	22	follows	follow	VERB
ejpam-6433	293	23	:	:	PUNCT
ejpam-6433	293	24	η(x	η(x	X
ejpam-6433	293	25	)	)	PUNCT
ejpam-6433	293	26	=	=	SYM
ejpam-6433	293	27	(	(	PUNCT
ejpam-6433	293	28	d(x	d(x	PROPN
ejpam-6433	293	29	,	,	PUNCT
ejpam-6433	293	30	y)−	y)−	PROPN
ejpam-6433	293	31	d(x0	d(x0	NOUN
ejpam-6433	293	32	,	,	PUNCT
ejpam-6433	293	33	y	y	PROPN
ejpam-6433	293	34	)	)	PUNCT
ejpam-6433	293	35	)	)	PUNCT
ejpam-6433	294	1	y∈m	y∈m	PROPN
ejpam-6433	294	2	.	.	PUNCT
ejpam-6433	295	1	notice	notice	VERB
ejpam-6433	295	2	that	that	SCONJ
ejpam-6433	295	3	for	for	ADP
ejpam-6433	295	4	any	any	DET
ejpam-6433	295	5	y	y	PROPN
ejpam-6433	295	6	∈	∈	PROPN
ejpam-6433	295	7	m	m	VERB
ejpam-6433	295	8	we	we	PRON
ejpam-6433	295	9	have	have	VERB
ejpam-6433	295	10	supy∈m	supy∈m	PROPN
ejpam-6433	295	11	|d(x	|d(x	PROPN
ejpam-6433	295	12	,	,	PUNCT
ejpam-6433	295	13	y	y	NOUN
ejpam-6433	295	14	)	)	PUNCT
ejpam-6433	295	15	−	−	NOUN
ejpam-6433	295	16	d(x0	d(x0	NOUN
ejpam-6433	295	17	,	,	PUNCT
ejpam-6433	295	18	y)|	y)|	PROPN
ejpam-6433	295	19	≤	≤	NOUN
ejpam-6433	295	20	d(x	d(x	PROPN
ejpam-6433	295	21	,	,	PUNCT
ejpam-6433	295	22	x0	x0	PROPN
ejpam-6433	295	23	)	)	PUNCT
ejpam-6433	295	24	and	and	CCONJ
ejpam-6433	295	25	so	so	ADV
ejpam-6433	295	26	,	,	PUNCT
ejpam-6433	295	27	η	η	PROPN
ejpam-6433	295	28	is	be	AUX
ejpam-6433	295	29	well	well	ADV
ejpam-6433	295	30	-	-	PUNCT
ejpam-6433	295	31	defined	define	VERB
ejpam-6433	295	32	.	.	PUNCT
ejpam-6433	296	1	also	also	ADV
ejpam-6433	296	2	,	,	PUNCT
ejpam-6433	296	3	d∞	d∞	PROPN
ejpam-6433	296	4	(	(	PUNCT
ejpam-6433	296	5	η(x	η(x	NOUN
ejpam-6433	296	6	)	)	PUNCT
ejpam-6433	296	7	,	,	PUNCT
ejpam-6433	296	8	η(z	η(z	PROPN
ejpam-6433	296	9	)	)	PUNCT
ejpam-6433	296	10	)	)	PUNCT
ejpam-6433	296	11	=	=	PUNCT
ejpam-6433	296	12	sup	sup	NOUN
ejpam-6433	296	13	y∈m	y∈m	NOUN
ejpam-6433	296	14	|d(x	|d(x	PROPN
ejpam-6433	296	15	,	,	PUNCT
ejpam-6433	296	16	y)−	y)−	PROPN
ejpam-6433	296	17	d(z	d(z	PROPN
ejpam-6433	296	18	,	,	PUNCT
ejpam-6433	296	19	y)|	y)|	PROPN
ejpam-6433	296	20	=	=	PUNCT
ejpam-6433	296	21	d(x	d(x	PROPN
ejpam-6433	296	22	,	,	PUNCT
ejpam-6433	296	23	z	z	NOUN
ejpam-6433	296	24	)	)	PUNCT
ejpam-6433	296	25	,	,	PUNCT
ejpam-6433	296	26	for	for	ADP
ejpam-6433	296	27	all	all	DET
ejpam-6433	296	28	x	x	NOUN
ejpam-6433	296	29	,	,	PUNCT
ejpam-6433	296	30	z	z	PROPN
ejpam-6433	296	31	∈	∈	PROPN
ejpam-6433	296	32	m	m	PROPN
ejpam-6433	296	33	,	,	PUNCT
ejpam-6433	296	34	which	which	PRON
ejpam-6433	296	35	implies	imply	VERB
ejpam-6433	296	36	that	that	SCONJ
ejpam-6433	296	37	the	the	DET
ejpam-6433	296	38	metric	metric	ADJ
ejpam-6433	296	39	space	space	NOUN
ejpam-6433	296	40	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	296	41	)	)	PUNCT
ejpam-6433	296	42	contains	contain	VERB
ejpam-6433	296	43	an	an	DET
ejpam-6433	296	44	isometric	isometric	ADJ
ejpam-6433	296	45	copy	copy	NOUN
ejpam-6433	296	46	m.	m.	NOUN
ejpam-6433	296	47	if	if	SCONJ
ejpam-6433	296	48	m	m	NOUN
ejpam-6433	296	49	is	be	AUX
ejpam-6433	296	50	a	a	DET
ejpam-6433	296	51	hyperconvex	hyperconvex	ADJ
ejpam-6433	296	52	space	space	NOUN
ejpam-6433	296	53	,	,	PUNCT
ejpam-6433	296	54	then	then	ADV
ejpam-6433	296	55	η(m	η(m	ADV
ejpam-6433	296	56	)	)	PUNCT
ejpam-6433	296	57	is	be	AUX
ejpam-6433	296	58	an	an	DET
ejpam-6433	296	59	isometric	isometric	ADJ
ejpam-6433	296	60	copy	copy	NOUN
ejpam-6433	296	61	of	of	ADP
ejpam-6433	296	62	m	m	PROPN
ejpam-6433	296	63	in	in	ADP
ejpam-6433	296	64	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	296	65	)	)	PUNCT
ejpam-6433	296	66	and	and	CCONJ
ejpam-6433	296	67	is	be	AUX
ejpam-6433	296	68	,	,	PUNCT
ejpam-6433	296	69	therefore	therefore	ADV
ejpam-6433	296	70	,	,	PUNCT
ejpam-6433	296	71	a	a	DET
ejpam-6433	296	72	hyperconvex	hyperconvex	NOUN
ejpam-6433	296	73	set	set	NOUN
ejpam-6433	296	74	.	.	PUNCT
ejpam-6433	297	1	throughout	throughout	ADP
ejpam-6433	297	2	this	this	DET
ejpam-6433	297	3	work	work	NOUN
ejpam-6433	297	4	we	we	PRON
ejpam-6433	297	5	will	will	AUX
ejpam-6433	297	6	use	use	VERB
ejpam-6433	297	7	m	m	PROPN
ejpam-6433	297	8	instead	instead	ADV
ejpam-6433	297	9	of	of	ADP
ejpam-6433	297	10	η(m	η(m	NOUN
ejpam-6433	297	11	)	)	PUNCT
ejpam-6433	297	12	.	.	PUNCT
ejpam-6433	298	1	similarly	similarly	ADV
ejpam-6433	298	2	,	,	PUNCT
ejpam-6433	298	3	for	for	ADP
ejpam-6433	298	4	any	any	DET
ejpam-6433	298	5	hyperconvex	hyperconvex	NOUN
ejpam-6433	298	6	subset	subset	NOUN
ejpam-6433	298	7	g	g	PROPN
ejpam-6433	298	8	of	of	ADP
ejpam-6433	298	9	m	m	VERB
ejpam-6433	298	10	we	we	PRON
ejpam-6433	298	11	use	use	VERB
ejpam-6433	298	12	g	g	NOUN
ejpam-6433	298	13	instead	instead	ADV
ejpam-6433	298	14	of	of	ADP
ejpam-6433	298	15	η(g	η(g	NUM
ejpam-6433	298	16	)	)	PUNCT
ejpam-6433	298	17	.	.	PUNCT
ejpam-6433	299	1	for	for	ADP
ejpam-6433	299	2	m	m	PRON
ejpam-6433	299	3	or	or	CCONJ
ejpam-6433	299	4	any	any	DET
ejpam-6433	299	5	hyperconvex	hyperconvex	NOUN
ejpam-6433	299	6	subset	subset	NOUN
ejpam-6433	299	7	g	g	PROPN
ejpam-6433	299	8	of	of	ADP
ejpam-6433	299	9	m	m	PROPN
ejpam-6433	299	10	,	,	PUNCT
ejpam-6433	299	11	we	we	PRON
ejpam-6433	299	12	define	define	VERB
ejpam-6433	299	13	m∞	m∞	NOUN
ejpam-6433	299	14	=	=	SYM
ejpam-6433	299	15	cov(m	cov(m	PROPN
ejpam-6433	299	16	)	)	PUNCT
ejpam-6433	299	17	or	or	CCONJ
ejpam-6433	299	18	g∞	g∞	X
ejpam-6433	299	19	=	=	SYM
ejpam-6433	299	20	cov(g	cov(g	PROPN
ejpam-6433	299	21	)	)	PUNCT
ejpam-6433	299	22	in	in	ADP
ejpam-6433	299	23	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	299	24	)	)	PUNCT
ejpam-6433	299	25	.	.	PUNCT
ejpam-6433	300	1	clearly	clearly	ADV
ejpam-6433	300	2	,	,	PUNCT
ejpam-6433	300	3	m∞	m∞	PUNCT
ejpam-6433	300	4	and	and	CCONJ
ejpam-6433	300	5	g∞	g∞	PROPN
ejpam-6433	300	6	are	be	AUX
ejpam-6433	300	7	hyperconvex	hyperconvex	ADJ
ejpam-6433	300	8	subsets	subset	NOUN
ejpam-6433	300	9	of	of	ADP
ejpam-6433	300	10	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	300	11	)	)	PUNCT
ejpam-6433	300	12	and	and	CCONJ
ejpam-6433	300	13	are	be	AUX
ejpam-6433	300	14	convex	convex	ADJ
ejpam-6433	300	15	.	.	PUNCT
ejpam-6433	301	1	it	it	PRON
ejpam-6433	301	2	is	be	AUX
ejpam-6433	301	3	worth	worth	ADJ
ejpam-6433	301	4	noticing	notice	VERB
ejpam-6433	301	5	that	that	PRON
ejpam-6433	301	6	for	for	ADP
ejpam-6433	301	7	any	any	DET
ejpam-6433	301	8	hyperconvex	hyperconvex	ADJ
ejpam-6433	301	9	space	space	NOUN
ejpam-6433	301	10	m	m	VERB
ejpam-6433	301	11	there	there	PRON
ejpam-6433	301	12	is	be	VERB
ejpam-6433	301	13	a	a	DET
ejpam-6433	301	14	nonexpansive	nonexpansive	ADJ
ejpam-6433	301	15	retraction	retraction	NOUN
ejpam-6433	301	16	r	r	NOUN
ejpam-6433	301	17	of	of	ADP
ejpam-6433	301	18	m∞	m∞	PROPN
ejpam-6433	301	19	onto	onto	ADP
ejpam-6433	301	20	m	m	PROPN
ejpam-6433	301	21	,	,	PUNCT
ejpam-6433	301	22	and	and	CCONJ
ejpam-6433	301	23	for	for	ADP
ejpam-6433	301	24	any	any	DET
ejpam-6433	301	25	hyperconvex	hyperconvex	NOUN
ejpam-6433	301	26	subset	subset	NOUN
ejpam-6433	301	27	g	g	NOUN
ejpam-6433	301	28	of	of	ADP
ejpam-6433	301	29	m	m	PROPN
ejpam-6433	301	30	,	,	PUNCT
ejpam-6433	301	31	r(g∞	r(g∞	NOUN
ejpam-6433	301	32	)	)	PUNCT
ejpam-6433	301	33	=	=	SYM
ejpam-6433	301	34	g	g	NOUN
ejpam-6433	301	35	(	(	PUNCT
ejpam-6433	301	36	see	see	VERB
ejpam-6433	301	37	[	[	X
ejpam-6433	301	38	17	17	NUM
ejpam-6433	301	39	]	]	NUM
ejpam-6433	301	40	)	)	PUNCT
ejpam-6433	301	41	.	.	PUNCT
ejpam-6433	302	1	we	we	PRON
ejpam-6433	302	2	are	be	AUX
ejpam-6433	302	3	now	now	ADV
ejpam-6433	302	4	able	able	ADJ
ejpam-6433	302	5	to	to	PART
ejpam-6433	302	6	define	define	VERB
ejpam-6433	302	7	a	a	DET
ejpam-6433	302	8	suitable	suitable	ADJ
ejpam-6433	302	9	mnc	mnc	NOUN
ejpam-6433	302	10	on	on	ADP
ejpam-6433	302	11	the	the	DET
ejpam-6433	302	12	hyperconvex	hyperconvex	ADJ
ejpam-6433	302	13	space	space	NOUN
ejpam-6433	302	14	m∞.	m∞.	PROPN
ejpam-6433	302	15	lemma	lemma	PROPN
ejpam-6433	303	1	1	1	X
ejpam-6433	303	2	.	.	PUNCT
ejpam-6433	304	1	let	let	AUX
ejpam-6433	304	2	(	(	PUNCT
ejpam-6433	304	3	m	m	NOUN
ejpam-6433	304	4	,	,	PUNCT
ejpam-6433	304	5	d	d	X
ejpam-6433	304	6	)	)	PUNCT
ejpam-6433	304	7	be	be	AUX
ejpam-6433	304	8	a	a	DET
ejpam-6433	304	9	hyperconvex	hyperconvex	ADJ
ejpam-6433	304	10	metric	metric	ADJ
ejpam-6433	304	11	space	space	NOUN
ejpam-6433	304	12	and	and	CCONJ
ejpam-6433	304	13	r	r	NOUN
ejpam-6433	304	14	be	be	VERB
ejpam-6433	304	15	a	a	DET
ejpam-6433	304	16	nonexpansive	nonexpansive	ADJ
ejpam-6433	304	17	retract	retract	NOUN
ejpam-6433	304	18	from	from	ADP
ejpam-6433	304	19	m∞	m∞	PROPN
ejpam-6433	304	20	onto	onto	ADP
ejpam-6433	304	21	m.	m.	NOUN
ejpam-6433	304	22	suppose	suppose	VERB
ejpam-6433	304	23	ℵ	ℵ	NOUN
ejpam-6433	304	24	is	be	AUX
ejpam-6433	304	25	an	an	DET
ejpam-6433	304	26	mnc	mnc	PROPN
ejpam-6433	304	27	on	on	ADP
ejpam-6433	304	28	m	m	PRON
ejpam-6433	304	29	and	and	CCONJ
ejpam-6433	304	30	define	define	VERB
ejpam-6433	304	31	a	a	DET
ejpam-6433	304	32	function	function	NOUN
ejpam-6433	304	33	ℵr	ℵr	ADP
ejpam-6433	304	34	:	:	PUNCT
ejpam-6433	304	35	b(m∞	b(m∞	NUM
ejpam-6433	304	36	)	)	PUNCT
ejpam-6433	304	37	→	→	PUNCT
ejpam-6433	305	1	[	[	X
ejpam-6433	305	2	0,∞	0,∞	NOUN
ejpam-6433	305	3	)	)	PUNCT
ejpam-6433	305	4	as	as	ADP
ejpam-6433	305	5	ℵr(g	ℵr(g	PUNCT
ejpam-6433	305	6	)	)	PUNCT
ejpam-6433	305	7	:	:	PUNCT
ejpam-6433	305	8	=	=	SYM
ejpam-6433	305	9	ℵ	ℵ	X
ejpam-6433	305	10	(	(	PUNCT
ejpam-6433	305	11	r(g	r(g	NUM
ejpam-6433	305	12	)	)	PUNCT
ejpam-6433	305	13	)	)	PUNCT
ejpam-6433	305	14	,	,	PUNCT
ejpam-6433	305	15	for	for	ADP
ejpam-6433	305	16	all	all	DET
ejpam-6433	305	17	g	g	PROPN
ejpam-6433	305	18	∈	∈	PROPN
ejpam-6433	305	19	b(m∞	b(m∞	NOUN
ejpam-6433	305	20	)	)	PUNCT
ejpam-6433	305	21	.	.	PUNCT
ejpam-6433	306	1	then	then	ADV
ejpam-6433	306	2	ℵr	ℵr	X
ejpam-6433	306	3	is	be	AUX
ejpam-6433	306	4	an	an	DET
ejpam-6433	306	5	mnc	mnc	PROPN
ejpam-6433	306	6	on	on	ADP
ejpam-6433	306	7	m∞.	m∞.	PROPN
ejpam-6433	306	8	m.	m.	NOUN
ejpam-6433	306	9	gabeleh	gabeleh	PROPN
ejpam-6433	306	10	,	,	PUNCT
ejpam-6433	306	11	j.	j.	PROPN
ejpam-6433	306	12	markin	markin	PROPN
ejpam-6433	306	13	,	,	PUNCT
ejpam-6433	306	14	m.	m.	NOUN
ejpam-6433	306	15	aphane	aphane	PROPN
ejpam-6433	306	16	/	/	SYM
ejpam-6433	306	17	eur	eur	PROPN
ejpam-6433	306	18	.	.	PUNCT
ejpam-6433	307	1	j.	j.	PROPN
ejpam-6433	307	2	pure	pure	PROPN
ejpam-6433	307	3	appl	appl	PROPN
ejpam-6433	307	4	.	.	PROPN
ejpam-6433	307	5	math	math	PROPN
ejpam-6433	307	6	,	,	PUNCT
ejpam-6433	307	7	18	18	NUM
ejpam-6433	307	8	(	(	PUNCT
ejpam-6433	307	9	3	3	NUM
ejpam-6433	307	10	)	)	PUNCT
ejpam-6433	307	11	(	(	PUNCT
ejpam-6433	307	12	2025	2025	NUM
ejpam-6433	307	13	)	)	PUNCT
ejpam-6433	307	14	,	,	PUNCT
ejpam-6433	307	15	6433	6433	NUM
ejpam-6433	307	16	13	13	NUM
ejpam-6433	307	17	of	of	ADP
ejpam-6433	307	18	17	17	NUM
ejpam-6433	307	19	proof	proof	NOUN
ejpam-6433	307	20	.	.	PUNCT
ejpam-6433	308	1	the	the	DET
ejpam-6433	308	2	proof	proof	NOUN
ejpam-6433	308	3	is	be	AUX
ejpam-6433	308	4	trivial	trivial	ADJ
ejpam-6433	308	5	.	.	PUNCT
ejpam-6433	309	1	the	the	DET
ejpam-6433	309	2	next	next	ADJ
ejpam-6433	309	3	lemmas	lemmas	PROPN
ejpam-6433	309	4	play	play	VERB
ejpam-6433	309	5	important	important	ADJ
ejpam-6433	309	6	roles	role	NOUN
ejpam-6433	309	7	in	in	ADP
ejpam-6433	309	8	our	our	PRON
ejpam-6433	309	9	next	next	ADJ
ejpam-6433	309	10	results	result	NOUN
ejpam-6433	309	11	.	.	PUNCT
ejpam-6433	310	1	lemma	lemma	PROPN
ejpam-6433	310	2	2	2	NUM
ejpam-6433	310	3	.	.	PUNCT
ejpam-6433	311	1	(	(	PUNCT
ejpam-6433	311	2	lemma	lemma	PROPN
ejpam-6433	311	3	2.5	2.5	NUM
ejpam-6433	311	4	of	of	ADP
ejpam-6433	311	5	[	[	X
ejpam-6433	311	6	14	14	NUM
ejpam-6433	311	7	]	]	PUNCT
ejpam-6433	311	8	)	)	PUNCT
ejpam-6433	311	9	let	let	VERB
ejpam-6433	311	10	(	(	PUNCT
ejpam-6433	311	11	g	g	NOUN
ejpam-6433	311	12	,	,	PUNCT
ejpam-6433	311	13	h	h	NOUN
ejpam-6433	311	14	)	)	PUNCT
ejpam-6433	311	15	be	be	VERB
ejpam-6433	311	16	a	a	DET
ejpam-6433	311	17	nonempty	nonempty	ADJ
ejpam-6433	311	18	and	and	CCONJ
ejpam-6433	311	19	admissible	admissible	ADJ
ejpam-6433	311	20	pair	pair	NOUN
ejpam-6433	311	21	in	in	ADP
ejpam-6433	311	22	a	a	DET
ejpam-6433	311	23	hyperconvex	hyperconvex	ADJ
ejpam-6433	311	24	metric	metric	ADJ
ejpam-6433	311	25	space	space	NOUN
ejpam-6433	311	26	(	(	PUNCT
ejpam-6433	311	27	m	m	PROPN
ejpam-6433	311	28	,	,	PUNCT
ejpam-6433	311	29	d	d	NOUN
ejpam-6433	311	30	)	)	PUNCT
ejpam-6433	311	31	.	.	PUNCT
ejpam-6433	312	1	then	then	ADV
ejpam-6433	312	2	the	the	DET
ejpam-6433	312	3	proximal	proximal	ADJ
ejpam-6433	312	4	pair	pair	NOUN
ejpam-6433	312	5	(	(	PUNCT
ejpam-6433	312	6	g0,h0	g0,h0	PROPN
ejpam-6433	312	7	)	)	PUNCT
ejpam-6433	312	8	is	be	AUX
ejpam-6433	312	9	also	also	ADV
ejpam-6433	312	10	nonempty	nonempty	ADJ
ejpam-6433	312	11	and	and	CCONJ
ejpam-6433	312	12	admissible	admissible	ADJ
ejpam-6433	312	13	.	.	PUNCT
ejpam-6433	313	1	lemma	lemma	PROPN
ejpam-6433	313	2	3	3	X
ejpam-6433	313	3	.	.	PUNCT
ejpam-6433	314	1	let	let	VERB
ejpam-6433	314	2	(	(	PUNCT
ejpam-6433	314	3	g	g	NOUN
ejpam-6433	314	4	,	,	PUNCT
ejpam-6433	314	5	h	h	NOUN
ejpam-6433	314	6	)	)	PUNCT
ejpam-6433	314	7	be	be	VERB
ejpam-6433	314	8	a	a	DET
ejpam-6433	314	9	nonempty	nonempty	ADJ
ejpam-6433	314	10	and	and	CCONJ
ejpam-6433	314	11	admissible	admissible	ADJ
ejpam-6433	314	12	pair	pair	NOUN
ejpam-6433	314	13	in	in	ADP
ejpam-6433	314	14	a	a	DET
ejpam-6433	314	15	hyperconvex	hyperconvex	ADJ
ejpam-6433	314	16	metric	metric	ADJ
ejpam-6433	314	17	space	space	NOUN
ejpam-6433	314	18	(	(	PUNCT
ejpam-6433	314	19	m	m	PROPN
ejpam-6433	314	20	,	,	PUNCT
ejpam-6433	314	21	d	d	NOUN
ejpam-6433	314	22	)	)	PUNCT
ejpam-6433	314	23	.	.	PUNCT
ejpam-6433	315	1	suppose	suppose	VERB
ejpam-6433	315	2	(	(	PUNCT
ejpam-6433	315	3	e	e	NOUN
ejpam-6433	315	4	,	,	PUNCT
ejpam-6433	315	5	f	f	X
ejpam-6433	315	6	)	)	PUNCT
ejpam-6433	315	7	⊆	⊆	NUM
ejpam-6433	315	8	(	(	PUNCT
ejpam-6433	315	9	g∞,h∞	g∞,h∞	PROPN
ejpam-6433	315	10	)	)	PUNCT
ejpam-6433	315	11	is	be	AUX
ejpam-6433	315	12	a	a	DET
ejpam-6433	315	13	nonempty	nonempty	ADJ
ejpam-6433	315	14	,	,	PUNCT
ejpam-6433	315	15	bounded	bound	VERB
ejpam-6433	315	16	,	,	PUNCT
ejpam-6433	315	17	closed	closed	ADJ
ejpam-6433	315	18	,	,	PUNCT
ejpam-6433	315	19	convex	convex	NOUN
ejpam-6433	315	20	,	,	PUNCT
ejpam-6433	315	21	and	and	CCONJ
ejpam-6433	315	22	proximinal	proximinal	ADJ
ejpam-6433	315	23	pair	pair	NOUN
ejpam-6433	315	24	such	such	ADJ
ejpam-6433	315	25	that	that	SCONJ
ejpam-6433	315	26	d(e	d(e	PROPN
ejpam-6433	315	27	,	,	PUNCT
ejpam-6433	315	28	f	f	X
ejpam-6433	315	29	)	)	PUNCT
ejpam-6433	316	1	=	=	SYM
ejpam-6433	316	2	d(g	d(g	PROPN
ejpam-6433	316	3	,	,	PUNCT
ejpam-6433	316	4	h	h	NOUN
ejpam-6433	316	5	)	)	PUNCT
ejpam-6433	316	6	(	(	PUNCT
ejpam-6433	316	7	=	=	NOUN
ejpam-6433	316	8	d(g∞,h∞	d(g∞,h∞	NOUN
ejpam-6433	316	9	)	)	PUNCT
ejpam-6433	316	10	)	)	PUNCT
ejpam-6433	316	11	.	.	PUNCT
ejpam-6433	317	1	then	then	ADV
ejpam-6433	317	2	(	(	PUNCT
ejpam-6433	317	3	r(e	r(e	NOUN
ejpam-6433	317	4	)	)	PUNCT
ejpam-6433	317	5	,	,	PUNCT
ejpam-6433	317	6	r(f	r(f	PROPN
ejpam-6433	317	7	)	)	PUNCT
ejpam-6433	317	8	)	)	PUNCT
ejpam-6433	317	9	is	be	AUX
ejpam-6433	317	10	a	a	DET
ejpam-6433	317	11	nonempty	nonempty	ADJ
ejpam-6433	317	12	,	,	PUNCT
ejpam-6433	317	13	bounded	bound	VERB
ejpam-6433	317	14	,	,	PUNCT
ejpam-6433	317	15	hyperconvex	hyperconvex	INTJ
ejpam-6433	317	16	,	,	PUNCT
ejpam-6433	317	17	and	and	CCONJ
ejpam-6433	317	18	proximinal	proximinal	ADJ
ejpam-6433	317	19	pair	pair	NOUN
ejpam-6433	317	20	in	in	ADP
ejpam-6433	317	21	m	m	PROPN
ejpam-6433	317	22	with	with	ADP
ejpam-6433	317	23	d	d	PROPN
ejpam-6433	317	24	(	(	PUNCT
ejpam-6433	317	25	r(e	r(e	PROPN
ejpam-6433	317	26	)	)	PUNCT
ejpam-6433	317	27	,	,	PUNCT
ejpam-6433	317	28	r(f	r(f	PROPN
ejpam-6433	317	29	)	)	PUNCT
ejpam-6433	317	30	)	)	PUNCT
ejpam-6433	318	1	=	=	SYM
ejpam-6433	318	2	d(g	d(g	PROPN
ejpam-6433	318	3	,	,	PUNCT
ejpam-6433	318	4	h	h	NOUN
ejpam-6433	318	5	)	)	PUNCT
ejpam-6433	318	6	.	.	PUNCT
ejpam-6433	319	1	proof	proof	NOUN
ejpam-6433	319	2	.	.	PUNCT
ejpam-6433	320	1	as	as	SCONJ
ejpam-6433	320	2	we	we	PRON
ejpam-6433	320	3	know	know	VERB
ejpam-6433	320	4	,	,	PUNCT
ejpam-6433	320	5	in	in	ADP
ejpam-6433	320	6	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	320	7	)	)	PUNCT
ejpam-6433	320	8	each	each	PRON
ejpam-6433	320	9	closed	close	VERB
ejpam-6433	320	10	,	,	PUNCT
ejpam-6433	320	11	bounded	bound	VERB
ejpam-6433	320	12	and	and	CCONJ
ejpam-6433	320	13	convex	convex	PROPN
ejpam-6433	320	14	set	set	NOUN
ejpam-6433	320	15	is	be	AUX
ejpam-6433	320	16	also	also	ADV
ejpam-6433	320	17	an	an	DET
ejpam-6433	320	18	admissible	admissible	ADJ
ejpam-6433	320	19	set	set	NOUN
ejpam-6433	320	20	.	.	PUNCT
ejpam-6433	321	1	thus	thus	ADV
ejpam-6433	321	2	(	(	PUNCT
ejpam-6433	321	3	e	e	X
ejpam-6433	321	4	,	,	PUNCT
ejpam-6433	321	5	f	f	X
ejpam-6433	321	6	)	)	PUNCT
ejpam-6433	321	7	is	be	AUX
ejpam-6433	321	8	admissible	admissible	ADJ
ejpam-6433	321	9	in	in	ADP
ejpam-6433	321	10	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	321	11	)	)	PUNCT
ejpam-6433	321	12	.	.	PUNCT
ejpam-6433	322	1	since	since	SCONJ
ejpam-6433	322	2	a	a	DET
ejpam-6433	322	3	nonexpansive	nonexpansive	ADJ
ejpam-6433	322	4	retraction	retraction	NOUN
ejpam-6433	322	5	preserves	preserve	VERB
ejpam-6433	322	6	hyperconvexity	hyperconvexity	NOUN
ejpam-6433	322	7	,	,	PUNCT
ejpam-6433	322	8	(	(	PUNCT
ejpam-6433	322	9	r(e	r(e	NOUN
ejpam-6433	322	10	)	)	PUNCT
ejpam-6433	322	11	,	,	PUNCT
ejpam-6433	322	12	r(f	r(f	PROPN
ejpam-6433	322	13	)	)	PUNCT
ejpam-6433	322	14	)	)	PUNCT
ejpam-6433	322	15	is	be	AUX
ejpam-6433	322	16	a	a	DET
ejpam-6433	322	17	hyperconvex	hyperconvex	ADJ
ejpam-6433	322	18	pair	pair	NOUN
ejpam-6433	322	19	.	.	PUNCT
ejpam-6433	323	1	to	to	PART
ejpam-6433	323	2	see	see	VERB
ejpam-6433	323	3	the	the	DET
ejpam-6433	323	4	proximinality	proximinality	NOUN
ejpam-6433	323	5	of	of	ADP
ejpam-6433	323	6	the	the	DET
ejpam-6433	323	7	latter	latter	ADJ
ejpam-6433	323	8	pair	pair	NOUN
ejpam-6433	323	9	,	,	PUNCT
ejpam-6433	323	10	choose	choose	VERB
ejpam-6433	323	11	any	any	DET
ejpam-6433	323	12	point	point	NOUN
ejpam-6433	323	13	rp	rp	NOUN
ejpam-6433	323	14	∈	∈	PROPN
ejpam-6433	323	15	r(e	r(e	NOUN
ejpam-6433	323	16	)	)	PUNCT
ejpam-6433	323	17	,	,	PUNCT
ejpam-6433	323	18	where	where	SCONJ
ejpam-6433	323	19	p	p	PROPN
ejpam-6433	323	20	∈	∈	PROPN
ejpam-6433	323	21	e	e	X
ejpam-6433	323	22	.	.	PUNCT
ejpam-6433	324	1	then	then	ADV
ejpam-6433	324	2	there	there	PRON
ejpam-6433	324	3	is	be	VERB
ejpam-6433	324	4	a	a	DET
ejpam-6433	324	5	point	point	NOUN
ejpam-6433	324	6	q	q	X
ejpam-6433	324	7	∈	∈	NOUN
ejpam-6433	324	8	f	f	PROPN
ejpam-6433	324	9	such	such	ADJ
ejpam-6433	324	10	that	that	PRON
ejpam-6433	324	11	d∞(p	d∞(p	VERB
ejpam-6433	324	12	,	,	PUNCT
ejpam-6433	324	13	q	q	X
ejpam-6433	324	14	)	)	PUNCT
ejpam-6433	324	15	=	=	SYM
ejpam-6433	324	16	d(e	d(e	PROPN
ejpam-6433	324	17	,	,	PUNCT
ejpam-6433	324	18	f	f	X
ejpam-6433	324	19	)	)	PUNCT
ejpam-6433	325	1	(	(	PUNCT
ejpam-6433	325	2	=	=	SYM
ejpam-6433	325	3	d(g	d(g	PROPN
ejpam-6433	325	4	,	,	PUNCT
ejpam-6433	325	5	h	h	NOUN
ejpam-6433	325	6	)	)	PUNCT
ejpam-6433	325	7	)	)	PUNCT
ejpam-6433	326	1	,	,	PUNCT
ejpam-6433	326	2	implying	imply	VERB
ejpam-6433	326	3	that	that	SCONJ
ejpam-6433	326	4	d(rp	d(rp	NOUN
ejpam-6433	326	5	,	,	PUNCT
ejpam-6433	326	6	rq	rq	NOUN
ejpam-6433	326	7	)	)	PUNCT
ejpam-6433	326	8	≤	≤	NOUN
ejpam-6433	326	9	d(e	d(e	PROPN
ejpam-6433	326	10	,	,	PUNCT
ejpam-6433	326	11	f	f	PROPN
ejpam-6433	326	12	)	)	PUNCT
ejpam-6433	326	13	.	.	PUNCT
ejpam-6433	327	1	besides	besides	SCONJ
ejpam-6433	327	2	,	,	PUNCT
ejpam-6433	327	3	the	the	DET
ejpam-6433	327	4	relation	relation	NOUN
ejpam-6433	327	5	(	(	PUNCT
ejpam-6433	327	6	r(e	r(e	PROPN
ejpam-6433	327	7	)	)	PUNCT
ejpam-6433	327	8	,	,	PUNCT
ejpam-6433	327	9	r(f	r(f	PROPN
ejpam-6433	327	10	)	)	PUNCT
ejpam-6433	327	11	)	)	PUNCT
ejpam-6433	328	1	⊆	⊆	X
ejpam-6433	328	2	(	(	PUNCT
ejpam-6433	328	3	g	g	NOUN
ejpam-6433	328	4	,	,	PUNCT
ejpam-6433	328	5	h	h	NOUN
ejpam-6433	328	6	)	)	PUNCT
ejpam-6433	328	7	concludes	conclude	VERB
ejpam-6433	328	8	that	that	SCONJ
ejpam-6433	328	9	d(e	d(e	PROPN
ejpam-6433	328	10	,	,	PUNCT
ejpam-6433	328	11	f	f	X
ejpam-6433	328	12	)	)	PUNCT
ejpam-6433	329	1	=	=	SYM
ejpam-6433	330	1	d	d	PROPN
ejpam-6433	330	2	(	(	PUNCT
ejpam-6433	330	3	r(e	r(e	NOUN
ejpam-6433	330	4	)	)	PUNCT
ejpam-6433	330	5	,	,	PUNCT
ejpam-6433	330	6	r(f	r(f	PROPN
ejpam-6433	330	7	)	)	PUNCT
ejpam-6433	330	8	)	)	PUNCT
ejpam-6433	330	9	.	.	PUNCT
ejpam-6433	331	1	therefore	therefore	ADV
ejpam-6433	331	2	,	,	PUNCT
ejpam-6433	331	3	d(rp	d(rp	PROPN
ejpam-6433	331	4	,	,	PUNCT
ejpam-6433	331	5	rq	rq	NOUN
ejpam-6433	331	6	)	)	PUNCT
ejpam-6433	331	7	=	=	SYM
ejpam-6433	331	8	d(e	d(e	PROPN
ejpam-6433	331	9	,	,	PUNCT
ejpam-6433	331	10	f	f	X
ejpam-6433	331	11	)	)	PUNCT
ejpam-6433	331	12	and	and	CCONJ
ejpam-6433	331	13	so	so	ADV
ejpam-6433	331	14	,	,	PUNCT
ejpam-6433	331	15	(	(	PUNCT
ejpam-6433	331	16	r(e	r(e	NOUN
ejpam-6433	331	17	)	)	PUNCT
ejpam-6433	331	18	,	,	PUNCT
ejpam-6433	331	19	r(f	r(f	PROPN
ejpam-6433	331	20	)	)	PUNCT
ejpam-6433	331	21	)	)	PUNCT
ejpam-6433	331	22	is	be	AUX
ejpam-6433	331	23	a	a	DET
ejpam-6433	331	24	proximinal	proximinal	ADJ
ejpam-6433	331	25	pair	pair	NOUN
ejpam-6433	331	26	.	.	PUNCT
ejpam-6433	332	1	motivated	motivate	VERB
ejpam-6433	332	2	by	by	ADP
ejpam-6433	332	3	definition	definition	NOUN
ejpam-6433	332	4	3	3	NUM
ejpam-6433	332	5	we	we	PRON
ejpam-6433	332	6	introduce	introduce	VERB
ejpam-6433	332	7	the	the	DET
ejpam-6433	332	8	class	class	NOUN
ejpam-6433	332	9	of	of	ADP
ejpam-6433	332	10	meir	meir	PROPN
ejpam-6433	332	11	-	-	PUNCT
ejpam-6433	332	12	keeler	keeler	PROPN
ejpam-6433	332	13	condensing	condense	VERB
ejpam-6433	332	14	operators	operator	NOUN
ejpam-6433	332	15	in	in	ADP
ejpam-6433	332	16	the	the	DET
ejpam-6433	332	17	setting	setting	NOUN
ejpam-6433	332	18	of	of	ADP
ejpam-6433	332	19	hyperconvex	hyperconvex	ADJ
ejpam-6433	332	20	metric	metric	ADJ
ejpam-6433	332	21	spaces	space	NOUN
ejpam-6433	332	22	.	.	PUNCT
ejpam-6433	333	1	let	let	AUX
ejpam-6433	333	2	(	(	PUNCT
ejpam-6433	333	3	g	g	NOUN
ejpam-6433	333	4	,	,	PUNCT
ejpam-6433	333	5	h	h	NOUN
ejpam-6433	333	6	)	)	PUNCT
ejpam-6433	333	7	be	be	VERB
ejpam-6433	333	8	a	a	DET
ejpam-6433	333	9	nonempty	nonempty	ADJ
ejpam-6433	333	10	and	and	CCONJ
ejpam-6433	333	11	admissible	admissible	ADJ
ejpam-6433	333	12	pair	pair	NOUN
ejpam-6433	333	13	in	in	ADP
ejpam-6433	333	14	a	a	DET
ejpam-6433	333	15	hyperconvex	hyperconvex	ADJ
ejpam-6433	333	16	space	space	NOUN
ejpam-6433	333	17	(	(	PUNCT
ejpam-6433	333	18	m	m	PROPN
ejpam-6433	333	19	,	,	PUNCT
ejpam-6433	333	20	d	d	NOUN
ejpam-6433	333	21	)	)	PUNCT
ejpam-6433	333	22	and	and	CCONJ
ejpam-6433	333	23	let	let	VERB
ejpam-6433	333	24	t	t	NOUN
ejpam-6433	333	25	:	:	PUNCT
ejpam-6433	333	26	g	g	PROPN
ejpam-6433	333	27	∪	∪	ADJ
ejpam-6433	333	28	h	h	NOUN
ejpam-6433	333	29	→	→	SYM
ejpam-6433	333	30	g	g	PROPN
ejpam-6433	333	31	∪h	∪h	NUM
ejpam-6433	333	32	be	be	AUX
ejpam-6433	333	33	a	a	DET
ejpam-6433	333	34	cyclic	cyclic	ADJ
ejpam-6433	333	35	(	(	PUNCT
ejpam-6433	333	36	noncyclic	noncyclic	NOUN
ejpam-6433	333	37	)	)	PUNCT
ejpam-6433	333	38	relatively	relatively	ADV
ejpam-6433	333	39	u	u	ADJ
ejpam-6433	333	40	-	-	ADJ
ejpam-6433	333	41	continuous	continuous	ADJ
ejpam-6433	333	42	mapping	mapping	NOUN
ejpam-6433	333	43	.	.	PUNCT
ejpam-6433	334	1	put	put	VERB
ejpam-6433	334	2	m′	m′	NOUN
ejpam-6433	334	3	g×h(t	g×h(t	PRON
ejpam-6433	334	4	)	)	PUNCT
ejpam-6433	335	1	=	=	SYM
ejpam-6433	335	2	{	{	PUNCT
ejpam-6433	335	3	(	(	PUNCT
ejpam-6433	335	4	l1,l2	l1,l2	PROPN
ejpam-6433	335	5	)	)	PUNCT
ejpam-6433	335	6	⊆	⊆	NUM
ejpam-6433	335	7	(	(	PUNCT
ejpam-6433	335	8	g	g	NOUN
ejpam-6433	335	9	,	,	PUNCT
ejpam-6433	335	10	h	h	NOUN
ejpam-6433	335	11	)	)	PUNCT
ejpam-6433	335	12	s.t	s.t	PROPN
ejpam-6433	335	13	.	.	PUNCT
ejpam-6433	336	1	(	(	PUNCT
ejpam-6433	336	2	l1,l2	l1,l2	PROPN
ejpam-6433	336	3	)	)	PUNCT
ejpam-6433	336	4	is	be	AUX
ejpam-6433	336	5	nonempty	nonempty	X
ejpam-6433	336	6	,	,	PUNCT
ejpam-6433	336	7	bounded	bound	VERB
ejpam-6433	336	8	,	,	PUNCT
ejpam-6433	336	9	hyperconvex	hyperconvex	INTJ
ejpam-6433	336	10	,	,	PUNCT
ejpam-6433	336	11	proximinal	proximinal	ADJ
ejpam-6433	336	12	and	and	CCONJ
ejpam-6433	336	13	t	t	NOUN
ejpam-6433	336	14	−	−	PROPN
ejpam-6433	336	15	invariant	invariant	ADJ
ejpam-6433	336	16	with	with	ADP
ejpam-6433	336	17	d(l1,l2	d(l1,l2	NOUN
ejpam-6433	336	18	)	)	PUNCT
ejpam-6433	336	19	=	=	SYM
ejpam-6433	336	20	d(g	d(g	PROPN
ejpam-6433	336	21	,	,	PUNCT
ejpam-6433	336	22	h	h	NOUN
ejpam-6433	336	23	)	)	PUNCT
ejpam-6433	336	24	}	}	PUNCT
ejpam-6433	336	25	.	.	PUNCT
ejpam-6433	337	1	by	by	ADP
ejpam-6433	337	2	lemma	lemma	PROPN
ejpam-6433	337	3	2	2	NUM
ejpam-6433	337	4	,	,	PUNCT
ejpam-6433	337	5	under	under	ADP
ejpam-6433	337	6	the	the	DET
ejpam-6433	337	7	aforesaid	aforesaid	NOUN
ejpam-6433	337	8	assumptions	assumption	NOUN
ejpam-6433	337	9	,	,	PUNCT
ejpam-6433	337	10	the	the	DET
ejpam-6433	337	11	proximal	proximal	ADJ
ejpam-6433	337	12	pair	pair	NOUN
ejpam-6433	337	13	(	(	PUNCT
ejpam-6433	337	14	g0,h0	g0,h0	PROPN
ejpam-6433	337	15	)	)	PUNCT
ejpam-6433	337	16	is	be	AUX
ejpam-6433	337	17	also	also	ADV
ejpam-6433	337	18	nonempty	nonempty	ADJ
ejpam-6433	337	19	and	and	CCONJ
ejpam-6433	337	20	admissible	admissible	ADJ
ejpam-6433	337	21	.	.	PUNCT
ejpam-6433	338	1	also	also	ADV
ejpam-6433	338	2	,	,	PUNCT
ejpam-6433	338	3	by	by	ADP
ejpam-6433	338	4	the	the	DET
ejpam-6433	338	5	fact	fact	NOUN
ejpam-6433	338	6	that	that	SCONJ
ejpam-6433	338	7	t	t	PROPN
ejpam-6433	338	8	is	be	AUX
ejpam-6433	338	9	relatively	relatively	ADV
ejpam-6433	338	10	u	u	NOUN
ejpam-6433	338	11	-	-	ADJ
ejpam-6433	338	12	continuous	continuous	ADJ
ejpam-6433	338	13	,	,	PUNCT
ejpam-6433	338	14	(	(	PUNCT
ejpam-6433	338	15	g0,h0	g0,h0	PROPN
ejpam-6433	338	16	)	)	PUNCT
ejpam-6433	338	17	is	be	AUX
ejpam-6433	338	18	t	t	PROPN
ejpam-6433	338	19	-invariant	-invariant	PROPN
ejpam-6433	338	20	.	.	PUNCT
ejpam-6433	339	1	so	so	ADV
ejpam-6433	339	2	,	,	PUNCT
ejpam-6433	339	3	(	(	PUNCT
ejpam-6433	339	4	g0,h0	g0,h0	PROPN
ejpam-6433	339	5	)	)	PUNCT
ejpam-6433	339	6	∈	∈	PROPN
ejpam-6433	339	7	m′	m′	NOUN
ejpam-6433	339	8	g×h(t	g×h(t	PROPN
ejpam-6433	339	9	)	)	PUNCT
ejpam-6433	339	10	̸=	̸=	PROPN
ejpam-6433	339	11	∅.	∅.	ADP
ejpam-6433	339	12	definition	definition	NOUN
ejpam-6433	339	13	12	12	NUM
ejpam-6433	339	14	.	.	PUNCT
ejpam-6433	340	1	let	let	VERB
ejpam-6433	340	2	(	(	PUNCT
ejpam-6433	340	3	g	g	NOUN
ejpam-6433	340	4	,	,	PUNCT
ejpam-6433	340	5	h	h	NOUN
ejpam-6433	340	6	)	)	PUNCT
ejpam-6433	340	7	be	be	VERB
ejpam-6433	340	8	a	a	DET
ejpam-6433	340	9	nonempty	nonempty	ADJ
ejpam-6433	340	10	and	and	CCONJ
ejpam-6433	340	11	admissible	admissible	ADJ
ejpam-6433	340	12	pair	pair	NOUN
ejpam-6433	340	13	in	in	ADP
ejpam-6433	340	14	a	a	DET
ejpam-6433	340	15	hyperconvex	hyperconvex	ADJ
ejpam-6433	340	16	space	space	NOUN
ejpam-6433	340	17	(	(	PUNCT
ejpam-6433	340	18	m	m	PROPN
ejpam-6433	340	19	,	,	PUNCT
ejpam-6433	340	20	d	d	NOUN
ejpam-6433	340	21	)	)	PUNCT
ejpam-6433	340	22	and	and	CCONJ
ejpam-6433	340	23	ℵ	ℵ	X
ejpam-6433	340	24	be	be	AUX
ejpam-6433	340	25	an	an	DET
ejpam-6433	340	26	mnc	mnc	PROPN
ejpam-6433	340	27	on	on	ADP
ejpam-6433	340	28	m.	m.	NOUN
ejpam-6433	340	29	a	a	DET
ejpam-6433	340	30	mapping	mapping	NOUN
ejpam-6433	340	31	t	t	NOUN
ejpam-6433	340	32	:	:	PUNCT
ejpam-6433	340	33	g	g	PROPN
ejpam-6433	340	34	∪	∪	ADJ
ejpam-6433	340	35	h	h	NOUN
ejpam-6433	340	36	→	→	SYM
ejpam-6433	340	37	g	g	NOUN
ejpam-6433	340	38	∪	∪	ADJ
ejpam-6433	340	39	h	h	NOUN
ejpam-6433	340	40	is	be	AUX
ejpam-6433	340	41	said	say	VERB
ejpam-6433	340	42	to	to	PART
ejpam-6433	340	43	be	be	AUX
ejpam-6433	340	44	an	an	DET
ejpam-6433	340	45	hmeir	hmeir	ADJ
ejpam-6433	340	46	-	-	ADJ
ejpam-6433	340	47	keeler	keeler	ADJ
ejpam-6433	340	48	condensing	condense	VERB
ejpam-6433	340	49	operator	operator	NOUN
ejpam-6433	340	50	if	if	SCONJ
ejpam-6433	340	51	t	t	PROPN
ejpam-6433	340	52	is	be	AUX
ejpam-6433	340	53	cyclic	cyclic	ADJ
ejpam-6433	340	54	(	(	PUNCT
ejpam-6433	340	55	noncyclic	noncyclic	NOUN
ejpam-6433	340	56	)	)	PUNCT
ejpam-6433	340	57	and	and	CCONJ
ejpam-6433	340	58	for	for	ADP
ejpam-6433	340	59	any	any	DET
ejpam-6433	340	60	ε	ε	PROPN
ejpam-6433	340	61	>	>	X
ejpam-6433	340	62	0	0	PUNCT
ejpam-6433	341	1	there	there	PRON
ejpam-6433	341	2	exists	exist	VERB
ejpam-6433	341	3	δ	δ	X
ejpam-6433	341	4	=	=	PUNCT
ejpam-6433	341	5	δ(ε	δ(ε	PROPN
ejpam-6433	341	6	)	)	PUNCT
ejpam-6433	341	7	>	>	X
ejpam-6433	341	8	0	0	PUNCT
ejpam-6433	341	9	such	such	ADJ
ejpam-6433	341	10	that	that	PRON
ejpam-6433	341	11	for	for	ADP
ejpam-6433	341	12	any	any	DET
ejpam-6433	341	13	(	(	PUNCT
ejpam-6433	341	14	l1,l2	l1,l2	PROPN
ejpam-6433	341	15	)	)	PUNCT
ejpam-6433	341	16	∈	∈	PROPN
ejpam-6433	341	17	m′	m′	NOUN
ejpam-6433	341	18	g×h(t	g×h(t	PROPN
ejpam-6433	341	19	)	)	PUNCT
ejpam-6433	341	20	we	we	PRON
ejpam-6433	341	21	have	have	VERB
ejpam-6433	341	22	ε	ε	PROPN
ejpam-6433	341	23	≤	≤	PROPN
ejpam-6433	341	24	ℵ(l1	ℵ(l1	NOUN
ejpam-6433	341	25	∪	∪	NOUN
ejpam-6433	341	26	l2	l2	NOUN
ejpam-6433	341	27	)	)	PUNCT
ejpam-6433	341	28	<	<	X
ejpam-6433	341	29	ε+	ε+	X
ejpam-6433	341	30	δ	δ	PROPN
ejpam-6433	341	31	⇒	⇒	PROPN
ejpam-6433	341	32	ℵ	ℵ	PROPN
ejpam-6433	341	33	(	(	PUNCT
ejpam-6433	341	34	t	t	PROPN
ejpam-6433	341	35	(	(	PUNCT
ejpam-6433	341	36	l1	l1	PROPN
ejpam-6433	341	37	)	)	PUNCT
ejpam-6433	341	38	∪	∪	ADP
ejpam-6433	341	39	t	t	PROPN
ejpam-6433	341	40	(	(	PUNCT
ejpam-6433	341	41	l2	l2	PROPN
ejpam-6433	341	42	)	)	PUNCT
ejpam-6433	341	43	)	)	PUNCT
ejpam-6433	341	44	<	<	X
ejpam-6433	342	1	ε	ε	PROPN
ejpam-6433	342	2	.	.	PUNCT
ejpam-6433	342	3	let	let	VERB
ejpam-6433	342	4	us	we	PRON
ejpam-6433	342	5	illustrate	illustrate	VERB
ejpam-6433	342	6	the	the	DET
ejpam-6433	342	7	concept	concept	NOUN
ejpam-6433	342	8	of	of	ADP
ejpam-6433	342	9	h	h	NOUN
ejpam-6433	342	10	-	-	PUNCT
ejpam-6433	342	11	meir	meir	ADJ
ejpam-6433	342	12	-	-	PUNCT
ejpam-6433	342	13	keeler	keeler	NOUN
ejpam-6433	342	14	condensing	condense	VERB
ejpam-6433	342	15	operator	operator	NOUN
ejpam-6433	342	16	with	with	ADP
ejpam-6433	342	17	the	the	DET
ejpam-6433	342	18	following	follow	VERB
ejpam-6433	342	19	example	example	NOUN
ejpam-6433	342	20	.	.	PUNCT
ejpam-6433	343	1	m.	m.	NOUN
ejpam-6433	343	2	gabeleh	gabeleh	PROPN
ejpam-6433	343	3	,	,	PUNCT
ejpam-6433	343	4	j.	j.	PROPN
ejpam-6433	343	5	markin	markin	PROPN
ejpam-6433	343	6	,	,	PUNCT
ejpam-6433	343	7	m.	m.	NOUN
ejpam-6433	343	8	aphane	aphane	PROPN
ejpam-6433	343	9	/	/	SYM
ejpam-6433	343	10	eur	eur	PROPN
ejpam-6433	343	11	.	.	PUNCT
ejpam-6433	344	1	j.	j.	PROPN
ejpam-6433	344	2	pure	pure	PROPN
ejpam-6433	344	3	appl	appl	PROPN
ejpam-6433	344	4	.	.	PROPN
ejpam-6433	344	5	math	math	PROPN
ejpam-6433	344	6	,	,	PUNCT
ejpam-6433	344	7	18	18	NUM
ejpam-6433	344	8	(	(	PUNCT
ejpam-6433	344	9	3	3	NUM
ejpam-6433	344	10	)	)	PUNCT
ejpam-6433	344	11	(	(	PUNCT
ejpam-6433	344	12	2025	2025	NUM
ejpam-6433	344	13	)	)	PUNCT
ejpam-6433	344	14	,	,	PUNCT
ejpam-6433	344	15	6433	6433	NUM
ejpam-6433	344	16	14	14	NUM
ejpam-6433	344	17	of	of	ADP
ejpam-6433	344	18	17	17	NUM
ejpam-6433	344	19	example	example	NOUN
ejpam-6433	344	20	6	6	NUM
ejpam-6433	344	21	.	.	PUNCT
ejpam-6433	344	22	consider	consider	VERB
ejpam-6433	344	23	the	the	DET
ejpam-6433	344	24	hyperconvex	hyperconvex	ADJ
ejpam-6433	344	25	space	space	NOUN
ejpam-6433	344	26	ℓ∞	ℓ∞	NOUN
ejpam-6433	344	27	equipped	equip	VERB
ejpam-6433	344	28	with	with	ADP
ejpam-6433	344	29	kuratowski	kuratowski	PROPN
ejpam-6433	344	30	mnc	mnc	PROPN
ejpam-6433	344	31	α	α	PROPN
ejpam-6433	344	32	defined	define	VERB
ejpam-6433	344	33	in	in	ADP
ejpam-6433	344	34	example	example	NOUN
ejpam-6433	344	35	1	1	X
ejpam-6433	344	36	.	.	PUNCT
ejpam-6433	345	1	let	let	VERB
ejpam-6433	345	2	(	(	PUNCT
ejpam-6433	345	3	g	g	NOUN
ejpam-6433	345	4	,	,	PUNCT
ejpam-6433	345	5	h	h	NOUN
ejpam-6433	345	6	)	)	PUNCT
ejpam-6433	345	7	be	be	VERB
ejpam-6433	345	8	a	a	DET
ejpam-6433	345	9	nonempty	nonempty	ADJ
ejpam-6433	345	10	and	and	CCONJ
ejpam-6433	345	11	admissible	admissible	ADJ
ejpam-6433	345	12	pair	pair	NOUN
ejpam-6433	345	13	in	in	ADP
ejpam-6433	345	14	ℓ∞	ℓ∞	PROPN
ejpam-6433	345	15	for	for	ADP
ejpam-6433	345	16	which	which	PRON
ejpam-6433	345	17	h	h	NOUN
ejpam-6433	345	18	is	be	AUX
ejpam-6433	345	19	compact	compact	ADJ
ejpam-6433	345	20	.	.	PUNCT
ejpam-6433	346	1	suppose	suppose	VERB
ejpam-6433	346	2	that	that	SCONJ
ejpam-6433	346	3	t	t	NOUN
ejpam-6433	346	4	:	:	PUNCT
ejpam-6433	346	5	g	g	PROPN
ejpam-6433	346	6	∪	∪	ADJ
ejpam-6433	346	7	h	h	NOUN
ejpam-6433	346	8	→	→	SYM
ejpam-6433	346	9	g	g	PROPN
ejpam-6433	346	10	∪h	∪h	NUM
ejpam-6433	346	11	is	be	AUX
ejpam-6433	346	12	a	a	DET
ejpam-6433	346	13	cyclic	cyclic	ADJ
ejpam-6433	346	14	mapping	mapping	NOUN
ejpam-6433	346	15	such	such	ADJ
ejpam-6433	346	16	that	that	SCONJ
ejpam-6433	346	17	t	t	NOUN
ejpam-6433	346	18	∣∣	∣∣	NUM
ejpam-6433	346	19	h	h	NOUN
ejpam-6433	346	20	is	be	AUX
ejpam-6433	346	21	a	a	DET
ejpam-6433	346	22	contraction	contraction	NOUN
ejpam-6433	346	23	,	,	PUNCT
ejpam-6433	346	24	that	that	ADV
ejpam-6433	346	25	is	is	ADV
ejpam-6433	346	26	,	,	PUNCT
ejpam-6433	346	27	there	there	PRON
ejpam-6433	346	28	exists	exist	VERB
ejpam-6433	346	29	r	r	NOUN
ejpam-6433	346	30	∈	∈	PROPN
ejpam-6433	346	31	(	(	PUNCT
ejpam-6433	346	32	0	0	NUM
ejpam-6433	346	33	,	,	PUNCT
ejpam-6433	346	34	1	1	NUM
ejpam-6433	346	35	)	)	PUNCT
ejpam-6433	346	36	such	such	ADJ
ejpam-6433	346	37	that	that	PRON
ejpam-6433	346	38	for	for	ADP
ejpam-6433	346	39	any	any	DET
ejpam-6433	346	40	v	v	NOUN
ejpam-6433	346	41	,	,	PUNCT
ejpam-6433	346	42	y	y	PROPN
ejpam-6433	346	43	∈	∈	PROPN
ejpam-6433	346	44	h	h	PROPN
ejpam-6433	346	45	d∞(tv	d∞(tv	NOUN
ejpam-6433	346	46	,	,	PUNCT
ejpam-6433	346	47	ty	ty	NOUN
ejpam-6433	346	48	)	)	PUNCT
ejpam-6433	346	49	≤	≤	NOUN
ejpam-6433	346	50	rd∞(v	rd∞(v	NOUN
ejpam-6433	346	51	,	,	PUNCT
ejpam-6433	346	52	y	y	NOUN
ejpam-6433	346	53	)	)	PUNCT
ejpam-6433	346	54	.	.	PUNCT
ejpam-6433	347	1	then	then	ADV
ejpam-6433	347	2	for	for	ADP
ejpam-6433	347	3	any	any	DET
ejpam-6433	347	4	(	(	PUNCT
ejpam-6433	347	5	l1,l2	l1,l2	PROPN
ejpam-6433	347	6	)	)	PUNCT
ejpam-6433	347	7	∈	∈	PROPN
ejpam-6433	347	8	m′	m′	NOUN
ejpam-6433	347	9	g×h(t	g×h(t	PROPN
ejpam-6433	347	10	)	)	PUNCT
ejpam-6433	347	11	by	by	ADP
ejpam-6433	347	12	the	the	DET
ejpam-6433	347	13	compactness	compactness	NOUN
ejpam-6433	347	14	of	of	ADP
ejpam-6433	347	15	h	h	NOUN
ejpam-6433	347	16	,	,	PUNCT
ejpam-6433	347	17	α	α	PROPN
ejpam-6433	347	18	(	(	PUNCT
ejpam-6433	347	19	t	t	PROPN
ejpam-6433	347	20	(	(	PUNCT
ejpam-6433	347	21	l1	l1	PROPN
ejpam-6433	347	22	)	)	PUNCT
ejpam-6433	347	23	∪	∪	ADP
ejpam-6433	347	24	t	t	PROPN
ejpam-6433	347	25	(	(	PUNCT
ejpam-6433	347	26	l2	l2	PROPN
ejpam-6433	347	27	)	)	PUNCT
ejpam-6433	347	28	)	)	PUNCT
ejpam-6433	348	1	=	=	PUNCT
ejpam-6433	348	2	max{α	max{α	NOUN
ejpam-6433	348	3	(	(	PUNCT
ejpam-6433	348	4	t	t	PROPN
ejpam-6433	348	5	(	(	PUNCT
ejpam-6433	348	6	l1	l1	PROPN
ejpam-6433	348	7	)	)	PUNCT
ejpam-6433	348	8	)	)	PUNCT
ejpam-6433	348	9	︸	︸	X
ejpam-6433	349	1	︷︷	︷︷	NOUN
ejpam-6433	349	2	︸	︸	ADP
ejpam-6433	349	3	0	0	NUM
ejpam-6433	349	4	,	,	PUNCT
ejpam-6433	349	5	α	α	PROPN
ejpam-6433	349	6	(	(	PUNCT
ejpam-6433	349	7	t	t	PROPN
ejpam-6433	349	8	(	(	PUNCT
ejpam-6433	349	9	l2	l2	PROPN
ejpam-6433	349	10	)	)	PUNCT
ejpam-6433	349	11	)	)	PUNCT
ejpam-6433	349	12	}	}	PUNCT
ejpam-6433	350	1	=	=	SYM
ejpam-6433	350	2	α	α	PROPN
ejpam-6433	350	3	(	(	PUNCT
ejpam-6433	350	4	t	t	PROPN
ejpam-6433	350	5	(	(	PUNCT
ejpam-6433	350	6	l2	l2	PROPN
ejpam-6433	350	7	)	)	PUNCT
ejpam-6433	350	8	)	)	PUNCT
ejpam-6433	351	1	≤	≤	NUM
ejpam-6433	351	2	rα(l2	rα(l2	X
ejpam-6433	351	3	)	)	PUNCT
ejpam-6433	351	4	≤	≤	NOUN
ejpam-6433	351	5	rα(l1	rα(l1	X
ejpam-6433	351	6	∪	∪	ADJ
ejpam-6433	351	7	l2	l2	NOUN
ejpam-6433	351	8	)	)	PUNCT
ejpam-6433	351	9	,	,	PUNCT
ejpam-6433	351	10	which	which	PRON
ejpam-6433	351	11	ensures	ensure	VERB
ejpam-6433	351	12	that	that	SCONJ
ejpam-6433	351	13	t	t	PROPN
ejpam-6433	351	14	is	be	AUX
ejpam-6433	351	15	an	an	DET
ejpam-6433	351	16	h	h	PROPN
ejpam-6433	351	17	-	-	PUNCT
ejpam-6433	351	18	meir	meir	ADJ
ejpam-6433	351	19	-	-	PUNCT
ejpam-6433	351	20	keeler	keeler	NOUN
ejpam-6433	351	21	condensing	condense	VERB
ejpam-6433	351	22	operator	operator	NOUN
ejpam-6433	351	23	.	.	PUNCT
ejpam-6433	352	1	in	in	ADP
ejpam-6433	352	2	order	order	NOUN
ejpam-6433	352	3	to	to	PART
ejpam-6433	352	4	prove	prove	VERB
ejpam-6433	352	5	the	the	DET
ejpam-6433	352	6	main	main	ADJ
ejpam-6433	352	7	existence	existence	NOUN
ejpam-6433	352	8	results	result	NOUN
ejpam-6433	352	9	of	of	ADP
ejpam-6433	352	10	this	this	DET
ejpam-6433	352	11	section	section	NOUN
ejpam-6433	352	12	,	,	PUNCT
ejpam-6433	352	13	we	we	PRON
ejpam-6433	352	14	need	need	VERB
ejpam-6433	352	15	the	the	DET
ejpam-6433	352	16	following	follow	VERB
ejpam-6433	352	17	auxiliary	auxiliary	ADJ
ejpam-6433	352	18	lemmas	lemmas	PROPN
ejpam-6433	352	19	.	.	PUNCT
ejpam-6433	353	1	lemma	lemma	PROPN
ejpam-6433	353	2	4	4	X
ejpam-6433	353	3	.	.	PUNCT
ejpam-6433	354	1	let	let	VERB
ejpam-6433	354	2	(	(	PUNCT
ejpam-6433	354	3	g	g	NOUN
ejpam-6433	354	4	,	,	PUNCT
ejpam-6433	354	5	h	h	NOUN
ejpam-6433	354	6	)	)	PUNCT
ejpam-6433	354	7	be	be	VERB
ejpam-6433	354	8	a	a	DET
ejpam-6433	354	9	nonempty	nonempty	ADJ
ejpam-6433	354	10	and	and	CCONJ
ejpam-6433	354	11	admissible	admissible	ADJ
ejpam-6433	354	12	pair	pair	NOUN
ejpam-6433	354	13	in	in	ADP
ejpam-6433	354	14	a	a	DET
ejpam-6433	354	15	hyperconvex	hyperconvex	ADJ
ejpam-6433	354	16	metric	metric	ADJ
ejpam-6433	354	17	space	space	NOUN
ejpam-6433	354	18	(	(	PUNCT
ejpam-6433	354	19	m	m	PROPN
ejpam-6433	354	20	,	,	PUNCT
ejpam-6433	354	21	d	d	NOUN
ejpam-6433	354	22	)	)	PUNCT
ejpam-6433	354	23	and	and	CCONJ
ejpam-6433	354	24	ℵ	ℵ	X
ejpam-6433	354	25	be	be	AUX
ejpam-6433	354	26	an	an	DET
ejpam-6433	354	27	mnc	mnc	PROPN
ejpam-6433	354	28	on	on	ADP
ejpam-6433	354	29	m.	m.	NOUN
ejpam-6433	354	30	suppose	suppose	VERB
ejpam-6433	354	31	t	t	NOUN
ejpam-6433	354	32	:	:	PUNCT
ejpam-6433	354	33	g∪h	g∪h	NOUN
ejpam-6433	354	34	→	→	SYM
ejpam-6433	354	35	g∪h	g∪h	NOUN
ejpam-6433	354	36	is	be	AUX
ejpam-6433	354	37	cyclic	cyclic	ADJ
ejpam-6433	354	38	(	(	PUNCT
ejpam-6433	354	39	noncyclic	noncyclic	NOUN
ejpam-6433	354	40	)	)	PUNCT
ejpam-6433	354	41	relatively	relatively	ADV
ejpam-6433	354	42	u	u	ADJ
ejpam-6433	354	43	-	-	ADJ
ejpam-6433	354	44	continuous	continuous	ADJ
ejpam-6433	354	45	mapping	mapping	NOUN
ejpam-6433	354	46	which	which	PRON
ejpam-6433	354	47	is	be	AUX
ejpam-6433	354	48	an	an	DET
ejpam-6433	354	49	h	h	PROPN
ejpam-6433	354	50	-	-	PUNCT
ejpam-6433	354	51	meir	meir	ADJ
ejpam-6433	354	52	-	-	PUNCT
ejpam-6433	354	53	keeler	keeler	NOUN
ejpam-6433	354	54	condensing	condense	VERB
ejpam-6433	354	55	operator	operator	NOUN
ejpam-6433	354	56	.	.	PUNCT
ejpam-6433	355	1	then	then	ADV
ejpam-6433	355	2	tr	tr	PUNCT
ejpam-6433	355	3	:	:	PUNCT
ejpam-6433	355	4	g∞	g∞	X
ejpam-6433	355	5	∪h∞	∪h∞	NOUN
ejpam-6433	355	6	→	→	SYM
ejpam-6433	355	7	g∞	g∞	PROPN
ejpam-6433	355	8	∪h∞	∪h∞	NOUN
ejpam-6433	355	9	,	,	PUNCT
ejpam-6433	355	10	is	be	AUX
ejpam-6433	355	11	a	a	DET
ejpam-6433	355	12	cyclic	cyclic	ADJ
ejpam-6433	355	13	(	(	PUNCT
ejpam-6433	355	14	noncyclic	noncyclic	NOUN
ejpam-6433	355	15	)	)	PUNCT
ejpam-6433	355	16	relatively	relatively	ADV
ejpam-6433	355	17	u	u	ADJ
ejpam-6433	355	18	-	-	ADJ
ejpam-6433	355	19	continuous	continuous	ADJ
ejpam-6433	355	20	mapping	mapping	NOUN
ejpam-6433	355	21	which	which	PRON
ejpam-6433	355	22	a	a	DET
ejpam-6433	355	23	meir	meir	PROPN
ejpam-6433	355	24	-	-	PUNCT
ejpam-6433	355	25	keeler	keeler	NOUN
ejpam-6433	355	26	condensing	condense	VERB
ejpam-6433	355	27	operator	operator	NOUN
ejpam-6433	355	28	w.r.t	w.r.t	NOUN
ejpam-6433	355	29	.	.	PUNCT
ejpam-6433	356	1	the	the	DET
ejpam-6433	356	2	mnc	mnc	PROPN
ejpam-6433	356	3	ℵr	ℵr	PROPN
ejpam-6433	356	4	.	.	PROPN
ejpam-6433	356	5	proof	proof	NOUN
ejpam-6433	356	6	.	.	PUNCT
ejpam-6433	357	1	we	we	PRON
ejpam-6433	357	2	assume	assume	VERB
ejpam-6433	357	3	that	that	SCONJ
ejpam-6433	357	4	t	t	PROPN
ejpam-6433	357	5	is	be	AUX
ejpam-6433	357	6	cyclic	cyclic	ADJ
ejpam-6433	357	7	.	.	PUNCT
ejpam-6433	358	1	then	then	ADV
ejpam-6433	358	2	tr(g∞	tr(g∞	ADV
ejpam-6433	358	3	)	)	PUNCT
ejpam-6433	359	1	=	=	SYM
ejpam-6433	359	2	t	t	PROPN
ejpam-6433	359	3	(	(	PUNCT
ejpam-6433	359	4	g	g	NOUN
ejpam-6433	359	5	)	)	PUNCT
ejpam-6433	359	6	⊆	⊆	NUM
ejpam-6433	359	7	h	h	NOUN
ejpam-6433	359	8	⊆	⊆	NUM
ejpam-6433	359	9	h∞	h∞	NOUN
ejpam-6433	359	10	,	,	PUNCT
ejpam-6433	359	11	tr(h∞	tr(h∞	PROPN
ejpam-6433	359	12	)	)	PUNCT
ejpam-6433	359	13	=	=	SYM
ejpam-6433	360	1	t	t	PROPN
ejpam-6433	360	2	(	(	PUNCT
ejpam-6433	360	3	h	h	NOUN
ejpam-6433	360	4	)	)	PUNCT
ejpam-6433	360	5	⊆	⊆	NUM
ejpam-6433	360	6	g	g	ADP
ejpam-6433	360	7	⊆	⊆	NUM
ejpam-6433	360	8	g∞	g∞	NOUN
ejpam-6433	360	9	,	,	PUNCT
ejpam-6433	360	10	that	that	ADV
ejpam-6433	360	11	is	is	ADV
ejpam-6433	360	12	,	,	PUNCT
ejpam-6433	360	13	tr	tr	VERB
ejpam-6433	360	14	is	be	AUX
ejpam-6433	360	15	also	also	ADV
ejpam-6433	360	16	cyclic	cyclic	ADJ
ejpam-6433	360	17	.	.	PUNCT
ejpam-6433	361	1	now	now	ADV
ejpam-6433	361	2	let	let	VERB
ejpam-6433	361	3	ε	ε	PROPN
ejpam-6433	361	4	>	>	X
ejpam-6433	361	5	0	0	PUNCT
ejpam-6433	361	6	be	be	AUX
ejpam-6433	361	7	given	give	VERB
ejpam-6433	361	8	.	.	PUNCT
ejpam-6433	362	1	since	since	SCONJ
ejpam-6433	362	2	t	t	PROPN
ejpam-6433	362	3	is	be	AUX
ejpam-6433	362	4	relatively	relatively	ADV
ejpam-6433	362	5	u	u	NOUN
ejpam-6433	362	6	-	-	ADJ
ejpam-6433	362	7	continuous	continuous	ADJ
ejpam-6433	362	8	,	,	PUNCT
ejpam-6433	362	9	there	there	PRON
ejpam-6433	362	10	exists	exist	VERB
ejpam-6433	362	11	δ	δ	PROPN
ejpam-6433	362	12	>	>	X
ejpam-6433	362	13	0	0	NUM
ejpam-6433	363	1	such	such	ADJ
ejpam-6433	363	2	that	that	PRON
ejpam-6433	363	3	for	for	ADP
ejpam-6433	363	4	any	any	DET
ejpam-6433	363	5	(	(	PUNCT
ejpam-6433	363	6	x	x	NOUN
ejpam-6433	363	7	,	,	PUNCT
ejpam-6433	363	8	y	y	NOUN
ejpam-6433	363	9	)	)	PUNCT
ejpam-6433	363	10	∈	∈	PROPN
ejpam-6433	363	11	g	g	ADP
ejpam-6433	363	12	×	×	PROPN
ejpam-6433	363	13	h	h	NOUN
ejpam-6433	363	14	with	with	ADP
ejpam-6433	363	15	d(x	d(x	PROPN
ejpam-6433	363	16	,	,	PUNCT
ejpam-6433	363	17	y	y	NOUN
ejpam-6433	363	18	)	)	PUNCT
ejpam-6433	363	19	<	<	X
ejpam-6433	363	20	δ	δ	PROPN
ejpam-6433	363	21	+	+	PROPN
ejpam-6433	363	22	d(g	d(g	PROPN
ejpam-6433	363	23	,	,	PUNCT
ejpam-6433	363	24	h	h	NOUN
ejpam-6433	363	25	)	)	PUNCT
ejpam-6433	363	26	we	we	PRON
ejpam-6433	363	27	have	have	VERB
ejpam-6433	363	28	d(tx	d(tx	PROPN
ejpam-6433	363	29	,	,	PUNCT
ejpam-6433	363	30	ty	ty	INTJ
ejpam-6433	363	31	)	)	PUNCT
ejpam-6433	363	32	<	<	X
ejpam-6433	363	33	ε	ε	PROPN
ejpam-6433	363	34	+	+	SYM
ejpam-6433	363	35	d(g	d(g	PROPN
ejpam-6433	363	36	,	,	PUNCT
ejpam-6433	363	37	h	h	NOUN
ejpam-6433	363	38	)	)	PUNCT
ejpam-6433	363	39	.	.	PUNCT
ejpam-6433	364	1	since	since	SCONJ
ejpam-6433	364	2	r	r	NOUN
ejpam-6433	364	3	:	:	PUNCT
ejpam-6433	364	4	m∞	m∞	PUNCT
ejpam-6433	364	5	→	→	PUNCT
ejpam-6433	364	6	m	m	NOUN
ejpam-6433	364	7	is	be	AUX
ejpam-6433	364	8	a	a	DET
ejpam-6433	364	9	nonexpansive	nonexpansive	ADJ
ejpam-6433	364	10	retract	retract	NOUN
ejpam-6433	364	11	,	,	PUNCT
ejpam-6433	364	12	for	for	ADP
ejpam-6433	364	13	any	any	DET
ejpam-6433	364	14	(	(	PUNCT
ejpam-6433	364	15	u	u	NOUN
ejpam-6433	364	16	,	,	PUNCT
ejpam-6433	364	17	v	v	NOUN
ejpam-6433	364	18	)	)	PUNCT
ejpam-6433	364	19	∈	∈	PROPN
ejpam-6433	364	20	g∞	g∞	PROPN
ejpam-6433	364	21	×h∞	×h∞	NOUN
ejpam-6433	364	22	with	with	ADP
ejpam-6433	364	23	d∞(u	d∞(u	PROPN
ejpam-6433	364	24	,	,	PUNCT
ejpam-6433	364	25	v	v	NOUN
ejpam-6433	364	26	)	)	PUNCT
ejpam-6433	364	27	<	<	X
ejpam-6433	364	28	δ	δ	PROPN
ejpam-6433	365	1	+	+	PROPN
ejpam-6433	365	2	d(g	d(g	PROPN
ejpam-6433	365	3	,	,	PUNCT
ejpam-6433	365	4	h	h	NOUN
ejpam-6433	365	5	)	)	PUNCT
ejpam-6433	365	6	we	we	PRON
ejpam-6433	365	7	have	have	VERB
ejpam-6433	365	8	d∞(ru	d∞(ru	NOUN
ejpam-6433	365	9	,	,	PUNCT
ejpam-6433	365	10	rv	rv	NOUN
ejpam-6433	365	11	)	)	PUNCT
ejpam-6433	365	12	<	<	X
ejpam-6433	365	13	δ	δ	PROPN
ejpam-6433	366	1	+	+	PROPN
ejpam-6433	366	2	d(g	d(g	PROPN
ejpam-6433	366	3	,	,	PUNCT
ejpam-6433	366	4	h	h	NOUN
ejpam-6433	366	5	)	)	PUNCT
ejpam-6433	366	6	and	and	CCONJ
ejpam-6433	366	7	therefore	therefore	ADV
ejpam-6433	366	8	,	,	PUNCT
ejpam-6433	366	9	d∞(tru	d∞(tru	PROPN
ejpam-6433	366	10	,	,	PUNCT
ejpam-6433	366	11	trv	trv	PROPN
ejpam-6433	366	12	)	)	PUNCT
ejpam-6433	366	13	<	<	X
ejpam-6433	366	14	ε+d(g	ε+d(g	SYM
ejpam-6433	366	15	,	,	PUNCT
ejpam-6433	366	16	h	h	NOUN
ejpam-6433	366	17	)	)	PUNCT
ejpam-6433	366	18	,	,	PUNCT
ejpam-6433	366	19	that	that	ADV
ejpam-6433	366	20	is	is	ADV
ejpam-6433	366	21	,	,	PUNCT
ejpam-6433	366	22	tr	tr	VERB
ejpam-6433	366	23	is	be	AUX
ejpam-6433	366	24	relatively	relatively	ADV
ejpam-6433	366	25	u	u	NOUN
ejpam-6433	366	26	-	-	ADJ
ejpam-6433	366	27	continuous	continuous	ADJ
ejpam-6433	366	28	.	.	PUNCT
ejpam-6433	367	1	to	to	PART
ejpam-6433	367	2	show	show	VERB
ejpam-6433	367	3	that	that	SCONJ
ejpam-6433	367	4	tr	tr	PRON
ejpam-6433	367	5	is	be	AUX
ejpam-6433	367	6	a	a	DET
ejpam-6433	367	7	meir	meir	ADJ
ejpam-6433	367	8	-	-	PUNCT
ejpam-6433	367	9	keeler	keeler	NOUN
ejpam-6433	367	10	condensing	condense	VERB
ejpam-6433	367	11	operator	operator	NOUN
ejpam-6433	367	12	consider	consider	VERB
ejpam-6433	367	13	ε	ε	PROPN
ejpam-6433	367	14	>	>	X
ejpam-6433	367	15	0	0	PUNCT
ejpam-6433	368	1	and	and	CCONJ
ejpam-6433	368	2	(	(	PUNCT
ejpam-6433	368	3	l	l	NOUN
ejpam-6433	368	4	,	,	PUNCT
ejpam-6433	368	5	k	k	NOUN
ejpam-6433	368	6	)	)	PUNCT
ejpam-6433	368	7	∈	∈	PROPN
ejpam-6433	368	8	mg∞×h∞(tr	mg∞×h∞(tr	PROPN
ejpam-6433	368	9	)	)	PUNCT
ejpam-6433	368	10	.	.	PUNCT
ejpam-6433	369	1	then	then	ADV
ejpam-6433	369	2	(	(	PUNCT
ejpam-6433	369	3	l	l	NOUN
ejpam-6433	369	4	,	,	PUNCT
ejpam-6433	369	5	k	k	NOUN
ejpam-6433	369	6	)	)	PUNCT
ejpam-6433	369	7	⊆	⊆	NUM
ejpam-6433	369	8	(	(	PUNCT
ejpam-6433	369	9	g∞,h∞	g∞,h∞	PROPN
ejpam-6433	369	10	)	)	PUNCT
ejpam-6433	369	11	is	be	AUX
ejpam-6433	369	12	a	a	DET
ejpam-6433	369	13	nonempty	nonempty	ADJ
ejpam-6433	369	14	,	,	PUNCT
ejpam-6433	369	15	bounded	bound	VERB
ejpam-6433	369	16	,	,	PUNCT
ejpam-6433	369	17	closed	closed	ADJ
ejpam-6433	369	18	,	,	PUNCT
ejpam-6433	369	19	convex	convex	NOUN
ejpam-6433	369	20	,	,	PUNCT
ejpam-6433	369	21	proximinal	proximinal	ADJ
ejpam-6433	369	22	and	and	CCONJ
ejpam-6433	369	23	trinvariant	trinvariant	ADJ
ejpam-6433	369	24	with	with	ADP
ejpam-6433	369	25	d(l	d(l	ADJ
ejpam-6433	369	26	,	,	PUNCT
ejpam-6433	369	27	k	k	NOUN
ejpam-6433	369	28	)	)	PUNCT
ejpam-6433	369	29	=	=	SYM
ejpam-6433	369	30	d(g∞,h∞	d(g∞,h∞	NOUN
ejpam-6433	369	31	)	)	PUNCT
ejpam-6433	369	32	.	.	PUNCT
ejpam-6433	370	1	it	it	PRON
ejpam-6433	370	2	follows	follow	VERB
ejpam-6433	370	3	from	from	ADP
ejpam-6433	370	4	lemma	lemma	PROPN
ejpam-6433	370	5	3	3	NUM
ejpam-6433	370	6	that	that	PRON
ejpam-6433	370	7	(	(	PUNCT
ejpam-6433	370	8	r(l	r(l	NOUN
ejpam-6433	370	9	)	)	PUNCT
ejpam-6433	370	10	,	,	PUNCT
ejpam-6433	370	11	r(k	r(k	PROPN
ejpam-6433	370	12	)	)	PUNCT
ejpam-6433	370	13	)	)	PUNCT
ejpam-6433	370	14	is	be	AUX
ejpam-6433	370	15	bounded	bound	VERB
ejpam-6433	370	16	,	,	PUNCT
ejpam-6433	370	17	hyperconvex	hyperconvex	ADJ
ejpam-6433	370	18	and	and	CCONJ
ejpam-6433	370	19	proximinal	proximinal	ADJ
ejpam-6433	370	20	with	with	ADP
ejpam-6433	370	21	d	d	PROPN
ejpam-6433	370	22	(	(	PUNCT
ejpam-6433	370	23	r(l	r(l	NOUN
ejpam-6433	370	24	)	)	PUNCT
ejpam-6433	370	25	,	,	PUNCT
ejpam-6433	370	26	r(k	r(k	PROPN
ejpam-6433	370	27	)	)	PUNCT
ejpam-6433	370	28	)	)	PUNCT
ejpam-6433	371	1	=	=	SYM
ejpam-6433	371	2	d(g	d(g	PROPN
ejpam-6433	371	3	,	,	PUNCT
ejpam-6433	371	4	h	h	NOUN
ejpam-6433	371	5	)	)	PUNCT
ejpam-6433	371	6	.	.	PUNCT
ejpam-6433	372	1	since	since	SCONJ
ejpam-6433	372	2	t	t	PROPN
ejpam-6433	372	3	maps	map	VERB
ejpam-6433	372	4	g	g	PROPN
ejpam-6433	372	5	into	into	ADP
ejpam-6433	372	6	h	h	PROPN
ejpam-6433	372	7	,	,	PUNCT
ejpam-6433	372	8	t	t	PROPN
ejpam-6433	372	9	(	(	PUNCT
ejpam-6433	372	10	r(k	r(k	PROPN
ejpam-6433	372	11	)	)	PUNCT
ejpam-6433	372	12	)	)	PUNCT
ejpam-6433	373	1	⊆	⊆	NUM
ejpam-6433	373	2	l	l	NOUN
ejpam-6433	373	3	∩h	∩h	NOUN
ejpam-6433	373	4	⊆	⊆	NUM
ejpam-6433	373	5	r(l	r(l	NOUN
ejpam-6433	373	6	)	)	PUNCT
ejpam-6433	373	7	.	.	PUNCT
ejpam-6433	374	1	we	we	PRON
ejpam-6433	374	2	now	now	ADV
ejpam-6433	374	3	have	have	VERB
ejpam-6433	374	4	t	t	NOUN
ejpam-6433	374	5	(	(	PUNCT
ejpam-6433	374	6	r(l	r(l	PROPN
ejpam-6433	374	7	)	)	PUNCT
ejpam-6433	374	8	)	)	PUNCT
ejpam-6433	374	9	=	=	SYM
ejpam-6433	375	1	tr(l	tr(l	X
ejpam-6433	375	2	)	)	PUNCT
ejpam-6433	375	3	⊆	⊆	NUM
ejpam-6433	375	4	r(k	r(k	NOUN
ejpam-6433	375	5	)	)	PUNCT
ejpam-6433	375	6	,	,	PUNCT
ejpam-6433	375	7	t	t	PROPN
ejpam-6433	375	8	(	(	PUNCT
ejpam-6433	375	9	r(k	r(k	PROPN
ejpam-6433	375	10	)	)	PUNCT
ejpam-6433	375	11	)	)	PUNCT
ejpam-6433	376	1	=	=	PUNCT
ejpam-6433	376	2	tr(k	tr(k	NOUN
ejpam-6433	376	3	)	)	PUNCT
ejpam-6433	376	4	⊆	⊆	NUM
ejpam-6433	376	5	r(l	r(l	NOUN
ejpam-6433	376	6	)	)	PUNCT
ejpam-6433	376	7	,	,	PUNCT
ejpam-6433	376	8	m.	m.	NOUN
ejpam-6433	376	9	gabeleh	gabeleh	PROPN
ejpam-6433	376	10	,	,	PUNCT
ejpam-6433	376	11	j.	j.	PROPN
ejpam-6433	376	12	markin	markin	PROPN
ejpam-6433	376	13	,	,	PUNCT
ejpam-6433	376	14	m.	m.	NOUN
ejpam-6433	376	15	aphane	aphane	PROPN
ejpam-6433	376	16	/	/	SYM
ejpam-6433	376	17	eur	eur	PROPN
ejpam-6433	376	18	.	.	PUNCT
ejpam-6433	377	1	j.	j.	PROPN
ejpam-6433	377	2	pure	pure	PROPN
ejpam-6433	377	3	appl	appl	PROPN
ejpam-6433	377	4	.	.	PROPN
ejpam-6433	377	5	math	math	PROPN
ejpam-6433	377	6	,	,	PUNCT
ejpam-6433	377	7	18	18	NUM
ejpam-6433	377	8	(	(	PUNCT
ejpam-6433	377	9	3	3	NUM
ejpam-6433	377	10	)	)	PUNCT
ejpam-6433	377	11	(	(	PUNCT
ejpam-6433	377	12	2025	2025	NUM
ejpam-6433	377	13	)	)	PUNCT
ejpam-6433	377	14	,	,	PUNCT
ejpam-6433	377	15	6433	6433	NUM
ejpam-6433	377	16	15	15	NUM
ejpam-6433	377	17	of	of	ADP
ejpam-6433	377	18	17	17	NUM
ejpam-6433	377	19	which	which	PRON
ejpam-6433	377	20	implies	imply	VERB
ejpam-6433	377	21	that	that	SCONJ
ejpam-6433	377	22	(	(	PUNCT
ejpam-6433	377	23	r(l	r(l	NOUN
ejpam-6433	377	24	)	)	PUNCT
ejpam-6433	377	25	,	,	PUNCT
ejpam-6433	377	26	r(k	r(k	PROPN
ejpam-6433	377	27	)	)	PUNCT
ejpam-6433	377	28	)	)	PUNCT
ejpam-6433	377	29	is	be	AUX
ejpam-6433	377	30	t	t	PROPN
ejpam-6433	377	31	-invariant	-invariant	PROPN
ejpam-6433	377	32	.	.	PUNCT
ejpam-6433	378	1	thus	thus	ADV
ejpam-6433	378	2	,	,	PUNCT
ejpam-6433	378	3	(	(	PUNCT
ejpam-6433	378	4	r(l	r(l	NOUN
ejpam-6433	378	5	)	)	PUNCT
ejpam-6433	378	6	,	,	PUNCT
ejpam-6433	378	7	r(k	r(k	PROPN
ejpam-6433	378	8	)	)	PUNCT
ejpam-6433	378	9	)	)	PUNCT
ejpam-6433	379	1	∈	∈	PROPN
ejpam-6433	379	2	m′	m′	NOUN
ejpam-6433	379	3	g×h(t	g×h(t	PROPN
ejpam-6433	379	4	)	)	PUNCT
ejpam-6433	379	5	.	.	PUNCT
ejpam-6433	380	1	in	in	ADP
ejpam-6433	380	2	view	view	NOUN
ejpam-6433	380	3	of	of	ADP
ejpam-6433	380	4	the	the	DET
ejpam-6433	380	5	fact	fact	NOUN
ejpam-6433	380	6	that	that	SCONJ
ejpam-6433	380	7	t	t	PROPN
ejpam-6433	380	8	is	be	AUX
ejpam-6433	380	9	an	an	DET
ejpam-6433	380	10	h	h	PROPN
ejpam-6433	380	11	-	-	PUNCT
ejpam-6433	380	12	meir	meir	ADJ
ejpam-6433	380	13	-	-	PUNCT
ejpam-6433	380	14	keeler	keeler	NOUN
ejpam-6433	380	15	condensing	condense	VERB
ejpam-6433	380	16	operator	operator	NOUN
ejpam-6433	380	17	,	,	PUNCT
ejpam-6433	380	18	there	there	PRON
ejpam-6433	380	19	exists	exist	VERB
ejpam-6433	380	20	δ	δ	X
ejpam-6433	380	21	=	=	PUNCT
ejpam-6433	380	22	δ(ε	δ(ε	PROPN
ejpam-6433	380	23	)	)	PUNCT
ejpam-6433	380	24	>	>	X
ejpam-6433	380	25	0	0	PUNCT
ejpam-6433	381	1	such	such	ADJ
ejpam-6433	381	2	that	that	SCONJ
ejpam-6433	381	3	ε	ε	PROPN
ejpam-6433	381	4	≤	≤	NUM
ejpam-6433	381	5	ℵ	ℵ	NOUN
ejpam-6433	381	6	(	(	PUNCT
ejpam-6433	381	7	r(l	r(l	NOUN
ejpam-6433	381	8	)	)	PUNCT
ejpam-6433	381	9	∪r(k	∪r(k	PROPN
ejpam-6433	381	10	)	)	PUNCT
ejpam-6433	381	11	)	)	PUNCT
ejpam-6433	381	12	︸	︸	X
ejpam-6433	382	1	︷︷	︷︷	NOUN
ejpam-6433	382	2	︸	︸	NOUN
ejpam-6433	383	1	=	=	ADJ
ejpam-6433	383	2	ℵ	ℵ	X
ejpam-6433	383	3	(	(	PUNCT
ejpam-6433	383	4	r(l∪k	r(l∪k	PROPN
ejpam-6433	383	5	)	)	PUNCT
ejpam-6433	383	6	)	)	PUNCT
ejpam-6433	384	1	<	<	X
ejpam-6433	384	2	ε+	ε+	X
ejpam-6433	384	3	δ	δ	PROPN
ejpam-6433	384	4	⇒	⇒	PROPN
ejpam-6433	384	5	ℵ	ℵ	PROPN
ejpam-6433	384	6	(	(	PUNCT
ejpam-6433	384	7	t	t	PROPN
ejpam-6433	384	8	(	(	PUNCT
ejpam-6433	384	9	r(l	r(l	PROPN
ejpam-6433	384	10	)	)	PUNCT
ejpam-6433	384	11	)	)	PUNCT
ejpam-6433	384	12	∪	∪	ADP
ejpam-6433	384	13	t	t	PROPN
ejpam-6433	384	14	(	(	PUNCT
ejpam-6433	384	15	(	(	PUNCT
ejpam-6433	384	16	rk	rk	NOUN
ejpam-6433	384	17	)	)	PUNCT
ejpam-6433	384	18	)	)	PUNCT
ejpam-6433	384	19	)	)	PUNCT
ejpam-6433	385	1	<	<	X
ejpam-6433	385	2	ε	ε	PROPN
ejpam-6433	385	3	.	.	PUNCT
ejpam-6433	385	4	by	by	ADP
ejpam-6433	385	5	the	the	DET
ejpam-6433	385	6	definition	definition	NOUN
ejpam-6433	385	7	of	of	ADP
ejpam-6433	385	8	ℵr	ℵr	NOUN
ejpam-6433	385	9	,	,	PUNCT
ejpam-6433	385	10	we	we	PRON
ejpam-6433	385	11	have	have	VERB
ejpam-6433	385	12	that	that	PRON
ejpam-6433	385	13	ℵr(b	ℵr(b	ADP
ejpam-6433	385	14	)	)	PUNCT
ejpam-6433	385	15	=	=	SYM
ejpam-6433	385	16	ℵ(r(b	ℵ(r(b	PROPN
ejpam-6433	385	17	)	)	PUNCT
ejpam-6433	385	18	)	)	PUNCT
ejpam-6433	386	1	=	=	PUNCT
ejpam-6433	386	2	ℵ(b	ℵ(b	NOUN
ejpam-6433	386	3	)	)	PUNCT
ejpam-6433	386	4	for	for	ADP
ejpam-6433	386	5	any	any	DET
ejpam-6433	386	6	bounded	bounded	ADJ
ejpam-6433	386	7	subset	subset	NOUN
ejpam-6433	386	8	of	of	ADP
ejpam-6433	386	9	m	m	PROPN
ejpam-6433	386	10	,	,	PUNCT
ejpam-6433	386	11	and	and	CCONJ
ejpam-6433	386	12	so	so	ADV
ejpam-6433	386	13	,	,	PUNCT
ejpam-6433	386	14	ε	ε	PROPN
ejpam-6433	386	15	≤	≤	PROPN
ejpam-6433	386	16	ℵr	ℵr	ADP
ejpam-6433	386	17	(	(	PUNCT
ejpam-6433	386	18	l	l	PROPN
ejpam-6433	386	19	∪	∪	X
ejpam-6433	386	20	k	k	PROPN
ejpam-6433	386	21	)	)	PUNCT
ejpam-6433	386	22	<	<	X
ejpam-6433	386	23	ε+	ε+	X
ejpam-6433	386	24	δ	δ	PROPN
ejpam-6433	386	25	⇒	⇒	NOUN
ejpam-6433	386	26	ℵr	ℵr	ADP
ejpam-6433	386	27	(	(	PUNCT
ejpam-6433	386	28	tr(l	tr(l	NOUN
ejpam-6433	386	29	)	)	PUNCT
ejpam-6433	386	30	∪	∪	ADP
ejpam-6433	386	31	tr(k	tr(k	NOUN
ejpam-6433	386	32	)	)	PUNCT
ejpam-6433	386	33	)	)	PUNCT
ejpam-6433	386	34	<	<	X
ejpam-6433	386	35	ε	ε	PROPN
ejpam-6433	386	36	.	.	PROPN
ejpam-6433	386	37	thereby	thereby	ADV
ejpam-6433	386	38	,	,	PUNCT
ejpam-6433	386	39	tr	tr	VERB
ejpam-6433	386	40	is	be	AUX
ejpam-6433	386	41	an	an	DET
ejpam-6433	386	42	ℵr	ℵr	ADJ
ejpam-6433	386	43	-	-	PUNCT
ejpam-6433	386	44	meir	meir	ADJ
ejpam-6433	386	45	-	-	PUNCT
ejpam-6433	386	46	keeler	keeler	NOUN
ejpam-6433	386	47	condensing	condense	VERB
ejpam-6433	386	48	operator	operator	NOUN
ejpam-6433	386	49	.	.	PUNCT
ejpam-6433	387	1	in	in	ADP
ejpam-6433	387	2	the	the	DET
ejpam-6433	387	3	case	case	NOUN
ejpam-6433	387	4	that	that	SCONJ
ejpam-6433	387	5	t	t	PROPN
ejpam-6433	387	6	is	be	AUX
ejpam-6433	387	7	noncyclic	noncyclic	ADJ
ejpam-6433	387	8	,	,	PUNCT
ejpam-6433	387	9	the	the	DET
ejpam-6433	387	10	result	result	NOUN
ejpam-6433	387	11	follows	follow	VERB
ejpam-6433	387	12	,	,	PUNCT
ejpam-6433	387	13	similarly	similarly	ADV
ejpam-6433	387	14	.	.	PUNCT
ejpam-6433	388	1	the	the	DET
ejpam-6433	388	2	next	next	ADJ
ejpam-6433	388	3	theorem	theorem	NOUN
ejpam-6433	388	4	is	be	AUX
ejpam-6433	388	5	a	a	DET
ejpam-6433	388	6	different	different	ADJ
ejpam-6433	388	7	version	version	NOUN
ejpam-6433	388	8	of	of	ADP
ejpam-6433	388	9	theorem	theorem	NOUN
ejpam-6433	388	10	5	5	NUM
ejpam-6433	388	11	in	in	ADP
ejpam-6433	388	12	hyperconvex	hyperconvex	ADJ
ejpam-6433	388	13	spaces	space	NOUN
ejpam-6433	388	14	.	.	PUNCT
ejpam-6433	389	1	theorem	theorem	ADJ
ejpam-6433	389	2	10	10	NUM
ejpam-6433	389	3	.	.	PUNCT
ejpam-6433	390	1	let	let	VERB
ejpam-6433	390	2	(	(	PUNCT
ejpam-6433	390	3	g	g	NOUN
ejpam-6433	390	4	,	,	PUNCT
ejpam-6433	390	5	h	h	NOUN
ejpam-6433	390	6	)	)	PUNCT
ejpam-6433	390	7	be	be	AUX
ejpam-6433	390	8	a	a	DET
ejpam-6433	390	9	nonempty	nonempty	ADJ
ejpam-6433	390	10	,	,	PUNCT
ejpam-6433	390	11	admissible	admissible	ADJ
ejpam-6433	390	12	pair	pair	NOUN
ejpam-6433	390	13	in	in	ADP
ejpam-6433	390	14	a	a	DET
ejpam-6433	390	15	hyperconvex	hyperconvex	ADJ
ejpam-6433	390	16	metric	metric	ADJ
ejpam-6433	390	17	space	space	NOUN
ejpam-6433	390	18	(	(	PUNCT
ejpam-6433	390	19	m	m	PROPN
ejpam-6433	390	20	,	,	PUNCT
ejpam-6433	390	21	d	d	NOUN
ejpam-6433	390	22	)	)	PUNCT
ejpam-6433	390	23	and	and	CCONJ
ejpam-6433	390	24	ℵ	ℵ	X
ejpam-6433	390	25	be	be	AUX
ejpam-6433	390	26	an	an	DET
ejpam-6433	390	27	mnc	mnc	PROPN
ejpam-6433	390	28	on	on	ADP
ejpam-6433	390	29	x.	x.	PROPN
ejpam-6433	390	30	suppose	suppose	VERB
ejpam-6433	390	31	t	t	NOUN
ejpam-6433	390	32	:	:	PUNCT
ejpam-6433	390	33	g	g	PROPN
ejpam-6433	390	34	∪	∪	ADJ
ejpam-6433	390	35	h	h	NOUN
ejpam-6433	390	36	→	→	SYM
ejpam-6433	390	37	g	g	PROPN
ejpam-6433	390	38	∪	∪	NOUN
ejpam-6433	390	39	h	h	NOUN
ejpam-6433	390	40	is	be	AUX
ejpam-6433	390	41	a	a	DET
ejpam-6433	390	42	cyclic	cyclic	ADJ
ejpam-6433	390	43	relatively	relatively	ADV
ejpam-6433	390	44	ucontinuous	ucontinuous	ADJ
ejpam-6433	390	45	mapping	mapping	NOUN
ejpam-6433	390	46	which	which	PRON
ejpam-6433	390	47	is	be	AUX
ejpam-6433	390	48	an	an	DET
ejpam-6433	390	49	h	h	PROPN
ejpam-6433	390	50	-	-	PUNCT
ejpam-6433	390	51	meir	meir	ADJ
ejpam-6433	390	52	-	-	PUNCT
ejpam-6433	390	53	keeler	keeler	NOUN
ejpam-6433	390	54	condensing	condense	VERB
ejpam-6433	390	55	operator	operator	NOUN
ejpam-6433	390	56	.	.	PUNCT
ejpam-6433	391	1	then	then	ADV
ejpam-6433	391	2	t	t	PROPN
ejpam-6433	391	3	has	have	VERB
ejpam-6433	391	4	a	a	DET
ejpam-6433	391	5	best	good	ADJ
ejpam-6433	391	6	proximity	proximity	NOUN
ejpam-6433	391	7	point	point	NOUN
ejpam-6433	391	8	.	.	PUNCT
ejpam-6433	392	1	proof	proof	NOUN
ejpam-6433	392	2	.	.	PUNCT
ejpam-6433	393	1	it	it	PRON
ejpam-6433	393	2	follows	follow	VERB
ejpam-6433	393	3	from	from	ADP
ejpam-6433	393	4	lemma	lemma	PROPN
ejpam-6433	393	5	4	4	NUM
ejpam-6433	393	6	that	that	SCONJ
ejpam-6433	393	7	the	the	DET
ejpam-6433	393	8	mapping	mapping	NOUN
ejpam-6433	393	9	tr	tr	VERB
ejpam-6433	393	10	:	:	PUNCT
ejpam-6433	393	11	g∞	g∞	X
ejpam-6433	393	12	∪	∪	ADP
ejpam-6433	393	13	h∞	h∞	X
ejpam-6433	393	14	→	→	SYM
ejpam-6433	393	15	g∞	g∞	X
ejpam-6433	393	16	∪	∪	NOUN
ejpam-6433	393	17	h∞	h∞	PROPN
ejpam-6433	393	18	is	be	AUX
ejpam-6433	393	19	a	a	DET
ejpam-6433	393	20	cyclic	cyclic	ADJ
ejpam-6433	393	21	relatively	relatively	ADV
ejpam-6433	393	22	u	u	ADJ
ejpam-6433	393	23	-	-	ADJ
ejpam-6433	393	24	continuous	continuous	ADJ
ejpam-6433	393	25	mapping	mapping	NOUN
ejpam-6433	393	26	which	which	PRON
ejpam-6433	393	27	is	be	AUX
ejpam-6433	393	28	a	a	DET
ejpam-6433	393	29	meir	meir	ADJ
ejpam-6433	393	30	-	-	PUNCT
ejpam-6433	393	31	keeler	keeler	NOUN
ejpam-6433	393	32	condensing	condense	VERB
ejpam-6433	393	33	operator	operator	NOUN
ejpam-6433	393	34	w.r.t	w.r.t	VERB
ejpam-6433	393	35	the	the	DET
ejpam-6433	393	36	mnc	mnc	PROPN
ejpam-6433	393	37	ℵr	ℵr	VERB
ejpam-6433	393	38	.	.	PUNCT
ejpam-6433	394	1	it	it	PRON
ejpam-6433	394	2	now	now	ADV
ejpam-6433	394	3	follows	follow	VERB
ejpam-6433	394	4	from	from	ADP
ejpam-6433	394	5	theorem	theorem	ADJ
ejpam-6433	394	6	5	5	NUM
ejpam-6433	394	7	that	that	PRON
ejpam-6433	394	8	tr	tr	VERB
ejpam-6433	394	9	has	have	VERB
ejpam-6433	394	10	a	a	DET
ejpam-6433	394	11	best	good	ADJ
ejpam-6433	394	12	proximity	proximity	NOUN
ejpam-6433	394	13	point	point	NOUN
ejpam-6433	394	14	,	,	PUNCT
ejpam-6433	394	15	i.e.	i.e.	X
ejpam-6433	394	16	,	,	PUNCT
ejpam-6433	394	17	there	there	PRON
ejpam-6433	394	18	exists	exist	VERB
ejpam-6433	394	19	a	a	DET
ejpam-6433	394	20	point	point	NOUN
ejpam-6433	394	21	p	p	X
ejpam-6433	394	22	∈	∈	PROPN
ejpam-6433	394	23	g∞	g∞	NOUN
ejpam-6433	394	24	∪	∪	NOUN
ejpam-6433	394	25	h∞	h∞	PRON
ejpam-6433	394	26	such	such	ADJ
ejpam-6433	394	27	that	that	PRON
ejpam-6433	394	28	d∞(p	d∞(p	PROPN
ejpam-6433	394	29	,	,	PUNCT
ejpam-6433	394	30	trp	trp	PROPN
ejpam-6433	394	31	)	)	PUNCT
ejpam-6433	394	32	=	=	SYM
ejpam-6433	394	33	d(g∞,h∞	d(g∞,h∞	NOUN
ejpam-6433	394	34	)	)	PUNCT
ejpam-6433	395	1	=	=	SYM
ejpam-6433	395	2	d(g	d(g	PROPN
ejpam-6433	395	3	,	,	PUNCT
ejpam-6433	395	4	h	h	NOUN
ejpam-6433	395	5	)	)	PUNCT
ejpam-6433	395	6	.	.	PUNCT
ejpam-6433	396	1	we	we	PRON
ejpam-6433	396	2	now	now	ADV
ejpam-6433	396	3	have	have	VERB
ejpam-6433	396	4	d	d	NOUN
ejpam-6433	396	5	(	(	PUNCT
ejpam-6433	396	6	rp	rp	NOUN
ejpam-6433	396	7	,	,	PUNCT
ejpam-6433	396	8	trp	trp	PROPN
ejpam-6433	396	9	)	)	PUNCT
ejpam-6433	396	10	≤	≤	PROPN
ejpam-6433	396	11	d∞(p	d∞(p	PROPN
ejpam-6433	396	12	,	,	PUNCT
ejpam-6433	396	13	trp	trp	PROPN
ejpam-6433	396	14	)	)	PUNCT
ejpam-6433	397	1	=	=	SYM
ejpam-6433	397	2	d(g	d(g	PROPN
ejpam-6433	397	3	,	,	PUNCT
ejpam-6433	397	4	h	h	NOUN
ejpam-6433	397	5	)	)	PUNCT
ejpam-6433	397	6	.	.	PUNCT
ejpam-6433	398	1	therefore	therefore	ADV
ejpam-6433	398	2	,	,	PUNCT
ejpam-6433	398	3	rp	rp	NOUN
ejpam-6433	398	4	is	be	AUX
ejpam-6433	398	5	a	a	DET
ejpam-6433	398	6	best	good	ADJ
ejpam-6433	398	7	proximity	proximity	NOUN
ejpam-6433	398	8	point	point	NOUN
ejpam-6433	398	9	for	for	ADP
ejpam-6433	398	10	the	the	DET
ejpam-6433	398	11	mapping	mapping	NOUN
ejpam-6433	398	12	t	t	NOUN
ejpam-6433	398	13	and	and	CCONJ
ejpam-6433	398	14	the	the	DET
ejpam-6433	398	15	proof	proof	NOUN
ejpam-6433	398	16	is	be	AUX
ejpam-6433	398	17	completed	complete	VERB
ejpam-6433	398	18	.	.	PUNCT
ejpam-6433	399	1	the	the	DET
ejpam-6433	399	2	noncyclic	noncyclic	PROPN
ejpam-6433	399	3	version	version	NOUN
ejpam-6433	399	4	of	of	ADP
ejpam-6433	399	5	theorem	theorem	NOUN
ejpam-6433	399	6	10	10	NUM
ejpam-6433	399	7	is	be	AUX
ejpam-6433	399	8	as	as	SCONJ
ejpam-6433	399	9	follows	follow	NOUN
ejpam-6433	399	10	.	.	PUNCT
ejpam-6433	400	1	theorem	theorem	ADJ
ejpam-6433	400	2	11	11	NUM
ejpam-6433	400	3	.	.	PUNCT
ejpam-6433	401	1	let	let	VERB
ejpam-6433	401	2	(	(	PUNCT
ejpam-6433	401	3	g	g	NOUN
ejpam-6433	401	4	,	,	PUNCT
ejpam-6433	401	5	h	h	NOUN
ejpam-6433	401	6	)	)	PUNCT
ejpam-6433	401	7	be	be	AUX
ejpam-6433	401	8	a	a	DET
ejpam-6433	401	9	nonempty	nonempty	ADJ
ejpam-6433	401	10	,	,	PUNCT
ejpam-6433	401	11	admissible	admissible	ADJ
ejpam-6433	401	12	and	and	CCONJ
ejpam-6433	401	13	semi	semi	ADJ
ejpam-6433	401	14	-	-	ADJ
ejpam-6433	401	15	sharp	sharp	ADJ
ejpam-6433	401	16	proximinal	proximinal	ADJ
ejpam-6433	401	17	pair	pair	NOUN
ejpam-6433	401	18	in	in	ADP
ejpam-6433	401	19	a	a	DET
ejpam-6433	401	20	hyperconvex	hyperconvex	ADJ
ejpam-6433	401	21	metric	metric	ADJ
ejpam-6433	401	22	space	space	NOUN
ejpam-6433	401	23	(	(	PUNCT
ejpam-6433	401	24	m	m	PROPN
ejpam-6433	401	25	,	,	PUNCT
ejpam-6433	401	26	d	d	NOUN
ejpam-6433	401	27	)	)	PUNCT
ejpam-6433	401	28	and	and	CCONJ
ejpam-6433	401	29	ℵ	ℵ	X
ejpam-6433	401	30	be	be	AUX
ejpam-6433	401	31	an	an	DET
ejpam-6433	401	32	mnc	mnc	PROPN
ejpam-6433	401	33	on	on	ADP
ejpam-6433	401	34	x.	x.	PROPN
ejpam-6433	401	35	suppose	suppose	VERB
ejpam-6433	401	36	t	t	NOUN
ejpam-6433	401	37	:	:	PUNCT
ejpam-6433	401	38	g∪h	g∪h	NOUN
ejpam-6433	401	39	→	→	SYM
ejpam-6433	401	40	g∪h	g∪h	NOUN
ejpam-6433	401	41	is	be	AUX
ejpam-6433	401	42	a	a	DET
ejpam-6433	401	43	noncyclic	noncyclic	ADJ
ejpam-6433	401	44	relatively	relatively	ADV
ejpam-6433	401	45	u	u	ADJ
ejpam-6433	401	46	-	-	ADJ
ejpam-6433	401	47	continuous	continuous	ADJ
ejpam-6433	401	48	mapping	mapping	NOUN
ejpam-6433	401	49	which	which	PRON
ejpam-6433	401	50	is	be	AUX
ejpam-6433	401	51	an	an	DET
ejpam-6433	401	52	h	h	PROPN
ejpam-6433	401	53	-	-	PUNCT
ejpam-6433	401	54	meir	meir	ADJ
ejpam-6433	401	55	-	-	PUNCT
ejpam-6433	401	56	keeler	keeler	NOUN
ejpam-6433	401	57	condensing	condense	VERB
ejpam-6433	401	58	operator	operator	NOUN
ejpam-6433	401	59	.	.	PUNCT
ejpam-6433	402	1	then	then	ADV
ejpam-6433	402	2	t	t	PROPN
ejpam-6433	402	3	has	have	VERB
ejpam-6433	402	4	a	a	DET
ejpam-6433	402	5	best	good	ADJ
ejpam-6433	402	6	proximity	proximity	NOUN
ejpam-6433	402	7	pair	pair	NOUN
ejpam-6433	402	8	.	.	PUNCT
ejpam-6433	403	1	proof	proof	NOUN
ejpam-6433	403	2	.	.	PUNCT
ejpam-6433	404	1	by	by	ADP
ejpam-6433	404	2	lemma	lemma	PROPN
ejpam-6433	404	3	4	4	NUM
ejpam-6433	404	4	,	,	PUNCT
ejpam-6433	404	5	the	the	DET
ejpam-6433	404	6	mapping	mapping	NOUN
ejpam-6433	404	7	tr	tr	VERB
ejpam-6433	404	8	:	:	PUNCT
ejpam-6433	404	9	g∞	g∞	X
ejpam-6433	404	10	∪h∞	∪h∞	NOUN
ejpam-6433	404	11	→	→	SYM
ejpam-6433	404	12	g∞	g∞	PROPN
ejpam-6433	404	13	∪h∞	∪h∞	NOUN
ejpam-6433	404	14	is	be	AUX
ejpam-6433	404	15	a	a	DET
ejpam-6433	404	16	noncyclic	noncyclic	ADJ
ejpam-6433	404	17	relatively	relatively	ADV
ejpam-6433	404	18	u	u	ADJ
ejpam-6433	404	19	-	-	ADJ
ejpam-6433	404	20	continuous	continuous	ADJ
ejpam-6433	404	21	mapping	mapping	NOUN
ejpam-6433	404	22	,	,	PUNCT
ejpam-6433	404	23	which	which	PRON
ejpam-6433	404	24	is	be	AUX
ejpam-6433	404	25	a	a	DET
ejpam-6433	404	26	meier	meier	PROPN
ejpam-6433	404	27	-	-	PUNCT
ejpam-6433	404	28	keeler	keeler	NOUN
ejpam-6433	404	29	condensing	condense	VERB
ejpam-6433	404	30	operator	operator	NOUN
ejpam-6433	404	31	w.r.t	w.r.t	NOUN
ejpam-6433	404	32	.	.	PUNCT
ejpam-6433	405	1	the	the	DET
ejpam-6433	405	2	mnc	mnc	PROPN
ejpam-6433	405	3	ℵr	ℵr	VERB
ejpam-6433	405	4	.	.	PROPN
ejpam-6433	406	1	as	as	ADP
ejpam-6433	406	2	a	a	DET
ejpam-6433	406	3	mapping	mapping	NOUN
ejpam-6433	406	4	defined	define	VERB
ejpam-6433	406	5	in	in	ADP
ejpam-6433	406	6	the	the	DET
ejpam-6433	406	7	banach	banach	NOUN
ejpam-6433	406	8	space	space	NOUN
ejpam-6433	406	9	ℓ∞(m	ℓ∞(m	NOUN
ejpam-6433	406	10	)	)	PUNCT
ejpam-6433	406	11	that	that	PRON
ejpam-6433	406	12	satisfies	satisfy	VERB
ejpam-6433	406	13	the	the	DET
ejpam-6433	406	14	conditions	condition	NOUN
ejpam-6433	406	15	of	of	ADP
ejpam-6433	406	16	theorem	theorem	NOUN
ejpam-6433	406	17	6	6	NUM
ejpam-6433	406	18	,	,	PUNCT
ejpam-6433	406	19	the	the	DET
ejpam-6433	406	20	mapping	mapping	NOUN
ejpam-6433	406	21	tr	tr	VERB
ejpam-6433	406	22	has	have	VERB
ejpam-6433	406	23	a	a	DET
ejpam-6433	406	24	best	good	ADJ
ejpam-6433	406	25	proximity	proximity	NOUN
ejpam-6433	406	26	pair	pair	NOUN
ejpam-6433	406	27	,	,	PUNCT
ejpam-6433	406	28	that	that	ADV
ejpam-6433	406	29	is	is	ADV
ejpam-6433	406	30	,	,	PUNCT
ejpam-6433	406	31	there	there	PRON
ejpam-6433	406	32	exists	exist	VERB
ejpam-6433	406	33	a	a	DET
ejpam-6433	406	34	pair	pair	NOUN
ejpam-6433	406	35	(	(	PUNCT
ejpam-6433	406	36	p	p	X
ejpam-6433	406	37	,	,	PUNCT
ejpam-6433	406	38	q	q	NOUN
ejpam-6433	406	39	)	)	PUNCT
ejpam-6433	406	40	∈	∈	NOUN
ejpam-6433	406	41	g∞×h∞	g∞×h∞	NOUN
ejpam-6433	406	42	such	such	ADJ
ejpam-6433	406	43	that	that	PRON
ejpam-6433	406	44	d∞(p	d∞(p	VERB
ejpam-6433	406	45	,	,	PUNCT
ejpam-6433	406	46	q	q	X
ejpam-6433	406	47	)	)	PUNCT
ejpam-6433	406	48	=	=	SYM
ejpam-6433	406	49	d(g∞,h∞	d(g∞,h∞	NOUN
ejpam-6433	406	50	)	)	PUNCT
ejpam-6433	407	1	=	=	SYM
ejpam-6433	407	2	d(g	d(g	PROPN
ejpam-6433	407	3	,	,	PUNCT
ejpam-6433	407	4	h	h	NOUN
ejpam-6433	407	5	)	)	PUNCT
ejpam-6433	407	6	,	,	PUNCT
ejpam-6433	407	7	we	we	PRON
ejpam-6433	407	8	obtain	obtain	VERB
ejpam-6433	407	9	p	p	X
ejpam-6433	407	10	=	=	PUNCT
ejpam-6433	407	11	trp	trp	PROPN
ejpam-6433	407	12	and	and	CCONJ
ejpam-6433	407	13	q	q	NOUN
ejpam-6433	407	14	=	=	NOUN
ejpam-6433	407	15	trq	trq	NOUN
ejpam-6433	407	16	.	.	PUNCT
ejpam-6433	408	1	since	since	SCONJ
ejpam-6433	408	2	trp	trp	PROPN
ejpam-6433	408	3	∈	∈	PROPN
ejpam-6433	408	4	g	g	PROPN
ejpam-6433	408	5	and	and	CCONJ
ejpam-6433	408	6	trq	trq	NOUN
ejpam-6433	408	7	∈	∈	PROPN
ejpam-6433	408	8	h	h	NOUN
ejpam-6433	408	9	,	,	PUNCT
ejpam-6433	408	10	we	we	PRON
ejpam-6433	408	11	have	have	VERB
ejpam-6433	408	12	rp	rp	NOUN
ejpam-6433	408	13	=	=	PUNCT
ejpam-6433	408	14	trp	trp	PROPN
ejpam-6433	408	15	and	and	CCONJ
ejpam-6433	408	16	rq	rq	X
ejpam-6433	408	17	=	=	PUNCT
ejpam-6433	408	18	trq	trq	NOUN
ejpam-6433	408	19	.	.	PUNCT
ejpam-6433	409	1	similarly	similarly	ADV
ejpam-6433	409	2	,	,	PUNCT
ejpam-6433	409	3	we	we	PRON
ejpam-6433	409	4	can	can	AUX
ejpam-6433	409	5	write	write	VERB
ejpam-6433	409	6	d∞(rp	d∞(rp	PROPN
ejpam-6433	409	7	,	,	PUNCT
ejpam-6433	409	8	rq	rq	NOUN
ejpam-6433	409	9	)	)	PUNCT
ejpam-6433	409	10	=	=	SYM
ejpam-6433	409	11	d(g∞	d(g∞	PROPN
ejpam-6433	409	12	,	,	PUNCT
ejpam-6433	409	13	h∞	h∞	NOUN
ejpam-6433	409	14	)	)	PUNCT
ejpam-6433	409	15	=	=	SYM
ejpam-6433	410	1	d(g	d(g	PROPN
ejpam-6433	410	2	,	,	PUNCT
ejpam-6433	410	3	h	h	NOUN
ejpam-6433	410	4	)	)	PUNCT
ejpam-6433	410	5	.	.	PUNCT
ejpam-6433	411	1	thus	thus	ADV
ejpam-6433	411	2	,	,	PUNCT
ejpam-6433	411	3	rp	rp	NOUN
ejpam-6433	411	4	and	and	CCONJ
ejpam-6433	411	5	rq	rq	NOUN
ejpam-6433	411	6	are	be	AUX
ejpam-6433	411	7	a	a	DET
ejpam-6433	411	8	best	good	ADJ
ejpam-6433	411	9	proximity	proximity	NOUN
ejpam-6433	411	10	pair	pair	NOUN
ejpam-6433	411	11	for	for	ADP
ejpam-6433	411	12	the	the	DET
ejpam-6433	411	13	noncyclic	noncyclic	PROPN
ejpam-6433	411	14	mapping	mapping	PROPN
ejpam-6433	411	15	t	t	PROPN
ejpam-6433	411	16	and	and	CCONJ
ejpam-6433	411	17	we	we	PRON
ejpam-6433	411	18	are	be	AUX
ejpam-6433	411	19	finished	finish	VERB
ejpam-6433	411	20	.	.	PUNCT
ejpam-6433	412	1	m.	m.	NOUN
ejpam-6433	412	2	gabeleh	gabeleh	PROPN
ejpam-6433	412	3	,	,	PUNCT
ejpam-6433	412	4	j.	j.	PROPN
ejpam-6433	412	5	markin	markin	PROPN
ejpam-6433	412	6	,	,	PUNCT
ejpam-6433	412	7	m.	m.	NOUN
ejpam-6433	412	8	aphane	aphane	PROPN
ejpam-6433	412	9	/	/	SYM
ejpam-6433	412	10	eur	eur	PROPN
ejpam-6433	412	11	.	.	PUNCT
ejpam-6433	413	1	j.	j.	PROPN
ejpam-6433	413	2	pure	pure	PROPN
ejpam-6433	413	3	appl	appl	PROPN
ejpam-6433	413	4	.	.	PROPN
ejpam-6433	413	5	math	math	PROPN
ejpam-6433	413	6	,	,	PUNCT
ejpam-6433	413	7	18	18	NUM
ejpam-6433	413	8	(	(	PUNCT
ejpam-6433	413	9	3	3	NUM
ejpam-6433	413	10	)	)	PUNCT
ejpam-6433	413	11	(	(	PUNCT
ejpam-6433	413	12	2025	2025	NUM
ejpam-6433	413	13	)	)	PUNCT
ejpam-6433	413	14	,	,	PUNCT
ejpam-6433	413	15	6433	6433	NUM
ejpam-6433	413	16	16	16	NUM
ejpam-6433	413	17	of	of	ADP
ejpam-6433	413	18	17	17	NUM
ejpam-6433	413	19	4	4	NUM
ejpam-6433	413	20	.	.	PUNCT
ejpam-6433	413	21	conclusion	conclusion	NOUN
ejpam-6433	413	22	in	in	ADP
ejpam-6433	413	23	this	this	DET
ejpam-6433	413	24	paper	paper	NOUN
ejpam-6433	413	25	,	,	PUNCT
ejpam-6433	413	26	we	we	PRON
ejpam-6433	413	27	revisited	revisit	VERB
ejpam-6433	413	28	the	the	DET
ejpam-6433	413	29	main	main	ADJ
ejpam-6433	413	30	conclusions	conclusion	NOUN
ejpam-6433	413	31	of	of	ADP
ejpam-6433	413	32	[	[	X
ejpam-6433	413	33	10	10	NUM
ejpam-6433	413	34	]	]	PUNCT
ejpam-6433	413	35	related	relate	VERB
ejpam-6433	413	36	to	to	ADP
ejpam-6433	413	37	the	the	DET
ejpam-6433	413	38	existence	existence	NOUN
ejpam-6433	413	39	of	of	ADP
ejpam-6433	413	40	best	good	ADJ
ejpam-6433	413	41	proximity	proximity	NOUN
ejpam-6433	413	42	points	point	NOUN
ejpam-6433	413	43	(	(	PUNCT
ejpam-6433	413	44	pairs	pair	NOUN
ejpam-6433	413	45	)	)	PUNCT
ejpam-6433	413	46	for	for	ADP
ejpam-6433	413	47	cyclic	cyclic	ADJ
ejpam-6433	413	48	(	(	PUNCT
ejpam-6433	413	49	noncyclic	noncyclic	PROPN
ejpam-6433	413	50	)	)	PUNCT
ejpam-6433	413	51	meir	meir	PROPN
ejpam-6433	413	52	-	-	PUNCT
ejpam-6433	413	53	keeler	keeler	PROPN
ejpam-6433	413	54	condensing	condense	VERB
ejpam-6433	413	55	operators	operator	NOUN
ejpam-6433	413	56	and	and	CCONJ
ejpam-6433	413	57	obtained	obtain	VERB
ejpam-6433	413	58	similar	similar	ADJ
ejpam-6433	413	59	results	result	NOUN
ejpam-6433	413	60	in	in	ADP
ejpam-6433	413	61	the	the	DET
ejpam-6433	413	62	framework	framework	NOUN
ejpam-6433	413	63	of	of	ADP
ejpam-6433	413	64	hyperconvex	hyperconvex	ADJ
ejpam-6433	413	65	metric	metric	ADJ
ejpam-6433	413	66	spaces	space	NOUN
ejpam-6433	413	67	.	.	PUNCT
ejpam-6433	414	1	examples	example	NOUN
ejpam-6433	414	2	in	in	ADP
ejpam-6433	414	3	the	the	DET
ejpam-6433	414	4	banach	banach	NOUN
ejpam-6433	414	5	space	space	NOUN
ejpam-6433	414	6	ℓ∞	ℓ∞	PROPN
ejpam-6433	414	7	as	as	ADP
ejpam-6433	414	8	a	a	DET
ejpam-6433	414	9	well	well	ADV
ejpam-6433	414	10	known	know	VERB
ejpam-6433	414	11	hyperconvex	hyperconvex	NOUN
ejpam-6433	414	12	space	space	NOUN
ejpam-6433	414	13	,	,	PUNCT
ejpam-6433	414	14	guarantee	guarantee	VERB
ejpam-6433	414	15	the	the	DET
ejpam-6433	414	16	useability	useability	NOUN
ejpam-6433	414	17	of	of	ADP
ejpam-6433	414	18	our	our	PRON
ejpam-6433	414	19	corollaries	corollary	NOUN
ejpam-6433	414	20	.	.	PUNCT
ejpam-6433	415	1	references	reference	NOUN
ejpam-6433	415	2	[	[	X
ejpam-6433	415	3	1	1	NUM
ejpam-6433	415	4	]	]	PUNCT
ejpam-6433	415	5	a.	a.	NOUN
ejpam-6433	415	6	a.	a.	PROPN
ejpam-6433	415	7	eldred	eldred	PROPN
ejpam-6433	415	8	,	,	PUNCT
ejpam-6433	415	9	w.	w.	PROPN
ejpam-6433	415	10	a.	a.	PROPN
ejpam-6433	415	11	kirk	kirk	PROPN
ejpam-6433	415	12	,	,	PUNCT
ejpam-6433	415	13	and	and	CCONJ
ejpam-6433	415	14	p.	p.	PROPN
ejpam-6433	415	15	veeramani	veeramani	PROPN
ejpam-6433	415	16	.	.	PUNCT
ejpam-6433	416	1	proximal	proximal	ADJ
ejpam-6433	416	2	normal	normal	ADJ
ejpam-6433	416	3	structure	structure	NOUN
ejpam-6433	416	4	and	and	CCONJ
ejpam-6433	416	5	relatively	relatively	ADV
ejpam-6433	416	6	nonexpansive	nonexpansive	ADJ
ejpam-6433	416	7	mappings	mapping	NOUN
ejpam-6433	416	8	.	.	PUNCT
ejpam-6433	417	1	studia	studia	PROPN
ejpam-6433	417	2	mathematica	mathematica	PROPN
ejpam-6433	417	3	,	,	PUNCT
ejpam-6433	417	4	171:283–293	171:283–293	NUM
ejpam-6433	417	5	,	,	PUNCT
ejpam-6433	417	6	2005	2005	NUM
ejpam-6433	417	7	.	.	PUNCT
ejpam-6433	418	1	[	[	X
ejpam-6433	418	2	2	2	NUM
ejpam-6433	418	3	]	]	PUNCT
ejpam-6433	418	4	r.	r.	PROPN
ejpam-6433	418	5	esṕınola	esṕınola	PROPN
ejpam-6433	418	6	.	.	PUNCT
ejpam-6433	419	1	a	a	DET
ejpam-6433	419	2	new	new	ADJ
ejpam-6433	419	3	approach	approach	NOUN
ejpam-6433	419	4	to	to	ADP
ejpam-6433	419	5	relatively	relatively	ADV
ejpam-6433	419	6	nonexpansive	nonexpansive	ADJ
ejpam-6433	419	7	mappings	mapping	NOUN
ejpam-6433	419	8	.	.	PUNCT
ejpam-6433	420	1	proceedings	proceeding	NOUN
ejpam-6433	420	2	of	of	ADP
ejpam-6433	420	3	the	the	DET
ejpam-6433	420	4	american	american	PROPN
ejpam-6433	420	5	mathematical	mathematical	PROPN
ejpam-6433	420	6	society	society	NOUN
ejpam-6433	420	7	,	,	PUNCT
ejpam-6433	420	8	136:1987–1996	136:1987–1996	NUM
ejpam-6433	420	9	,	,	PUNCT
ejpam-6433	420	10	2008	2008	NUM
ejpam-6433	420	11	.	.	PUNCT
ejpam-6433	421	1	[	[	X
ejpam-6433	421	2	3	3	X
ejpam-6433	421	3	]	]	X
ejpam-6433	421	4	hatem	hatem	PROPN
ejpam-6433	421	5	aydi	aydi	PROPN
ejpam-6433	421	6	,	,	PUNCT
ejpam-6433	421	7	hossein	hossein	PROPN
ejpam-6433	421	8	lakzian	lakzian	PROPN
ejpam-6433	421	9	,	,	PUNCT
ejpam-6433	421	10	zoran	zoran	PROPN
ejpam-6433	421	11	d.	d.	PROPN
ejpam-6433	421	12	mitrović	mitrović	PROPN
ejpam-6433	421	13	,	,	PUNCT
ejpam-6433	421	14	and	and	CCONJ
ejpam-6433	421	15	slobodan	slobodan	PROPN
ejpam-6433	421	16	radenović.	radenović.	PRON
ejpam-6433	421	17	best	good	ADJ
ejpam-6433	421	18	proximity	proximity	NOUN
ejpam-6433	421	19	points	point	NOUN
ejpam-6433	421	20	of	of	ADP
ejpam-6433	421	21	mt	mt	PROPN
ejpam-6433	421	22	-cyclic	-cyclic	PROPN
ejpam-6433	421	23	contractions	contraction	NOUN
ejpam-6433	421	24	with	with	ADP
ejpam-6433	421	25	property	property	NOUN
ejpam-6433	421	26	uc	uc	PROPN
ejpam-6433	421	27	.	.	PROPN
ejpam-6433	421	28	numerical	numerical	ADJ
ejpam-6433	421	29	functional	functional	ADJ
ejpam-6433	421	30	analysis	analysis	NOUN
ejpam-6433	421	31	and	and	CCONJ
ejpam-6433	421	32	optimization	optimization	NOUN
ejpam-6433	421	33	,	,	PUNCT
ejpam-6433	421	34	41:871–882	41:871–882	PROPN
ejpam-6433	421	35	,	,	PUNCT
ejpam-6433	421	36	2020	2020	NUM
ejpam-6433	421	37	.	.	PUNCT
ejpam-6433	422	1	[	[	X
ejpam-6433	422	2	4	4	X
ejpam-6433	422	3	]	]	PUNCT
ejpam-6433	422	4	s.	s.	PROPN
ejpam-6433	423	1	radenović.	radenović.	VERB
ejpam-6433	423	2	a	a	DET
ejpam-6433	423	3	note	note	NOUN
ejpam-6433	423	4	on	on	ADP
ejpam-6433	423	5	fixed	fix	VERB
ejpam-6433	423	6	point	point	NOUN
ejpam-6433	423	7	theory	theory	NOUN
ejpam-6433	423	8	for	for	ADP
ejpam-6433	423	9	cyclic	cyclic	ADJ
ejpam-6433	423	10	φ	φ	PROPN
ejpam-6433	423	11	-	-	NOUN
ejpam-6433	423	12	contractions	contraction	NOUN
ejpam-6433	423	13	.	.	PUNCT
ejpam-6433	424	1	fixed	fix	VERB
ejpam-6433	424	2	point	point	NOUN
ejpam-6433	424	3	theory	theory	NOUN
ejpam-6433	424	4	and	and	CCONJ
ejpam-6433	424	5	applications	application	NOUN
ejpam-6433	424	6	,	,	PUNCT
ejpam-6433	424	7	page	page	NOUN
ejpam-6433	424	8	9	9	NUM
ejpam-6433	424	9	,	,	PUNCT
ejpam-6433	424	10	2015	2015	NUM
ejpam-6433	424	11	.	.	PUNCT
ejpam-6433	425	1	[	[	X
ejpam-6433	425	2	5	5	X
ejpam-6433	425	3	]	]	PUNCT
ejpam-6433	425	4	m.	m.	NOUN
ejpam-6433	425	5	gabeleh	gabeleh	NOUN
ejpam-6433	425	6	.	.	PUNCT
ejpam-6433	426	1	a	a	DET
ejpam-6433	426	2	characterization	characterization	NOUN
ejpam-6433	426	3	of	of	ADP
ejpam-6433	426	4	proximal	proximal	ADJ
ejpam-6433	426	5	normal	normal	ADJ
ejpam-6433	426	6	structure	structure	NOUN
ejpam-6433	426	7	via	via	ADP
ejpam-6433	426	8	proximal	proximal	ADJ
ejpam-6433	426	9	diametral	diametral	ADJ
ejpam-6433	426	10	sequences	sequence	NOUN
ejpam-6433	426	11	.	.	PUNCT
ejpam-6433	427	1	journal	journal	PROPN
ejpam-6433	427	2	of	of	ADP
ejpam-6433	427	3	fixed	fix	VERB
ejpam-6433	427	4	point	point	NOUN
ejpam-6433	427	5	theory	theory	NOUN
ejpam-6433	427	6	and	and	CCONJ
ejpam-6433	427	7	applications	application	NOUN
ejpam-6433	427	8	,	,	PUNCT
ejpam-6433	427	9	19:2909–2925	19:2909–2925	NUM
ejpam-6433	427	10	,	,	PUNCT
ejpam-6433	427	11	2017	2017	NUM
ejpam-6433	427	12	.	.	PUNCT
ejpam-6433	428	1	[	[	X
ejpam-6433	428	2	6	6	NUM
ejpam-6433	428	3	]	]	PUNCT
ejpam-6433	428	4	r.	r.	PROPN
ejpam-6433	428	5	esṕınola	esṕınola	PROPN
ejpam-6433	428	6	.	.	PUNCT
ejpam-6433	429	1	darbo	darbo	PROPN
ejpam-6433	429	2	–	–	PUNCT
ejpam-6433	429	3	sadovski	sadovski	PROPN
ejpam-6433	429	4	’s	’s	PART
ejpam-6433	429	5	theorem	theorem	NOUN
ejpam-6433	429	6	in	in	ADP
ejpam-6433	429	7	hyperconvex	hyperconvex	ADJ
ejpam-6433	429	8	metric	metric	ADJ
ejpam-6433	429	9	spaces	space	NOUN
ejpam-6433	429	10	.	.	PUNCT
ejpam-6433	430	1	rendiconti	rendiconti	ADJ
ejpam-6433	430	2	del	del	PROPN
ejpam-6433	430	3	circolo	circolo	PROPN
ejpam-6433	430	4	matematico	matematico	NOUN
ejpam-6433	430	5	di	di	X
ejpam-6433	430	6	palermo	palermo	NOUN
ejpam-6433	430	7	(	(	PUNCT
ejpam-6433	430	8	2	2	NUM
ejpam-6433	430	9	)	)	PUNCT
ejpam-6433	430	10	supplemento	supplemento	NOUN
ejpam-6433	430	11	,	,	PUNCT
ejpam-6433	430	12	40:129–137	40:129–137	NUM
ejpam-6433	430	13	,	,	PUNCT
ejpam-6433	430	14	1996	1996	NUM
ejpam-6433	430	15	.	.	PUNCT
ejpam-6433	431	1	[	[	X
ejpam-6433	431	2	7	7	NUM
ejpam-6433	431	3	]	]	PUNCT
ejpam-6433	431	4	a.	a.	NOUN
ejpam-6433	431	5	a.	a.	PROPN
ejpam-6433	431	6	eldred	eldred	PROPN
ejpam-6433	431	7	,	,	PUNCT
ejpam-6433	431	8	v.	v.	ADP
ejpam-6433	431	9	sankar	sankar	PROPN
ejpam-6433	431	10	raj	raj	PROPN
ejpam-6433	431	11	,	,	PUNCT
ejpam-6433	431	12	and	and	CCONJ
ejpam-6433	431	13	p.	p.	NOUN
ejpam-6433	431	14	veeramani	veeramani	NOUN
ejpam-6433	431	15	.	.	PUNCT
ejpam-6433	432	1	on	on	ADP
ejpam-6433	432	2	best	good	ADJ
ejpam-6433	432	3	proximity	proximity	NOUN
ejpam-6433	432	4	pair	pair	NOUN
ejpam-6433	432	5	theorems	theorem	NOUN
ejpam-6433	432	6	for	for	ADP
ejpam-6433	432	7	relatively	relatively	ADV
ejpam-6433	432	8	u	u	ADJ
ejpam-6433	432	9	-	-	ADJ
ejpam-6433	432	10	continuous	continuous	ADJ
ejpam-6433	432	11	mappings	mapping	NOUN
ejpam-6433	432	12	.	.	PUNCT
ejpam-6433	433	1	nonlinear	nonlinear	ADJ
ejpam-6433	433	2	anal	anal	PROPN
ejpam-6433	433	3	.	.	PUNCT
ejpam-6433	433	4	,	,	PUNCT
ejpam-6433	433	5	74:3870–3875	74:3870–3875	NUM
ejpam-6433	433	6	,	,	PUNCT
ejpam-6433	433	7	2011	2011	NUM
ejpam-6433	433	8	.	.	PUNCT
ejpam-6433	434	1	[	[	X
ejpam-6433	434	2	8	8	NUM
ejpam-6433	434	3	]	]	PUNCT
ejpam-6433	434	4	m.	m.	NOUN
ejpam-6433	434	5	gabeleh	gabeleh	NOUN
ejpam-6433	434	6	.	.	PUNCT
ejpam-6433	435	1	common	common	ADJ
ejpam-6433	435	2	best	good	ADJ
ejpam-6433	435	3	proximity	proximity	NOUN
ejpam-6433	435	4	pairs	pair	NOUN
ejpam-6433	435	5	in	in	ADP
ejpam-6433	435	6	strictly	strictly	ADV
ejpam-6433	435	7	convex	convex	ADJ
ejpam-6433	435	8	banach	banach	NOUN
ejpam-6433	435	9	spaces	space	VERB
ejpam-6433	435	10	.	.	PUNCT
ejpam-6433	436	1	georgian	georgian	PROPN
ejpam-6433	436	2	mathematical	mathematical	PROPN
ejpam-6433	436	3	journal	journal	PROPN
ejpam-6433	436	4	,	,	PUNCT
ejpam-6433	436	5	24:363–372	24:363–372	PROPN
ejpam-6433	436	6	,	,	PUNCT
ejpam-6433	436	7	2017	2017	NUM
ejpam-6433	436	8	.	.	PUNCT
ejpam-6433	437	1	[	[	X
ejpam-6433	437	2	9	9	NUM
ejpam-6433	437	3	]	]	PUNCT
ejpam-6433	437	4	m.	m.	NOUN
ejpam-6433	437	5	gabeleh	gabeleh	NOUN
ejpam-6433	437	6	and	and	CCONJ
ejpam-6433	437	7	j.	j.	PROPN
ejpam-6433	437	8	markin	markin	PROPN
ejpam-6433	437	9	.	.	PUNCT
ejpam-6433	438	1	optimum	optimum	ADJ
ejpam-6433	438	2	solutions	solution	NOUN
ejpam-6433	438	3	for	for	ADP
ejpam-6433	438	4	a	a	DET
ejpam-6433	438	5	system	system	NOUN
ejpam-6433	438	6	of	of	ADP
ejpam-6433	438	7	differential	differential	ADJ
ejpam-6433	438	8	equations	equation	NOUN
ejpam-6433	438	9	via	via	ADP
ejpam-6433	438	10	measure	measure	NOUN
ejpam-6433	438	11	of	of	ADP
ejpam-6433	438	12	noncompactness	noncompactness	ADJ
ejpam-6433	438	13	.	.	PUNCT
ejpam-6433	439	1	indagationes	indagatione	NOUN
ejpam-6433	439	2	mathematicae	mathematicae	PROPN
ejpam-6433	439	3	,	,	PUNCT
ejpam-6433	439	4	29:895–906	29:895–906	NUM
ejpam-6433	439	5	,	,	PUNCT
ejpam-6433	439	6	2018	2018	NUM
ejpam-6433	439	7	.	.	PUNCT
ejpam-6433	440	1	[	[	X
ejpam-6433	440	2	10	10	NUM
ejpam-6433	440	3	]	]	PUNCT
ejpam-6433	440	4	m.	m.	NOUN
ejpam-6433	440	5	gabeleh	gabeleh	PROPN
ejpam-6433	440	6	and	and	CCONJ
ejpam-6433	440	7	c.	c.	PROPN
ejpam-6433	440	8	vetro	vetro	PROPN
ejpam-6433	440	9	.	.	PUNCT
ejpam-6433	441	1	a	a	DET
ejpam-6433	441	2	new	new	ADJ
ejpam-6433	441	3	extension	extension	NOUN
ejpam-6433	441	4	of	of	ADP
ejpam-6433	441	5	darbo	darbo	NOUN
ejpam-6433	441	6	’s	’s	PART
ejpam-6433	441	7	fixed	fix	VERB
ejpam-6433	441	8	point	point	NOUN
ejpam-6433	441	9	theorem	theorem	ADJ
ejpam-6433	441	10	using	use	VERB
ejpam-6433	441	11	relatively	relatively	ADV
ejpam-6433	441	12	meir	meir	ADJ
ejpam-6433	441	13	-	-	PUNCT
ejpam-6433	441	14	keeler	keeler	NOUN
ejpam-6433	441	15	condensing	condense	VERB
ejpam-6433	441	16	operators	operator	NOUN
ejpam-6433	441	17	.	.	PUNCT
ejpam-6433	442	1	bulletin	bulletin	NOUN
ejpam-6433	442	2	of	of	ADP
ejpam-6433	442	3	the	the	DET
ejpam-6433	442	4	australian	australian	ADJ
ejpam-6433	442	5	mathematical	mathematical	ADJ
ejpam-6433	442	6	society	society	NOUN
ejpam-6433	442	7	,	,	PUNCT
ejpam-6433	442	8	98:286–297	98:286–297	PROPN
ejpam-6433	442	9	,	,	PUNCT
ejpam-6433	442	10	2018	2018	NUM
ejpam-6433	442	11	.	.	PUNCT
ejpam-6433	443	1	[	[	X
ejpam-6433	443	2	11	11	NUM
ejpam-6433	443	3	]	]	PUNCT
ejpam-6433	443	4	j.	j.	PROPN
ejpam-6433	443	5	m.	m.	PROPN
ejpam-6433	443	6	ayerbe	ayerbe	PROPN
ejpam-6433	443	7	toledano	toledano	PROPN
ejpam-6433	443	8	,	,	PUNCT
ejpam-6433	443	9	t.	t.	PROPN
ejpam-6433	443	10	domı́nguez	domı́nguez	PROPN
ejpam-6433	443	11	benavides	benavide	NOUN
ejpam-6433	443	12	,	,	PUNCT
ejpam-6433	443	13	and	and	CCONJ
ejpam-6433	443	14	g.	g.	PROPN
ejpam-6433	443	15	lópez	lópez	PROPN
ejpam-6433	443	16	-	-	PUNCT
ejpam-6433	443	17	acedo	acedo	NOUN
ejpam-6433	443	18	.	.	PUNCT
ejpam-6433	444	1	measures	measure	NOUN
ejpam-6433	444	2	of	of	ADP
ejpam-6433	444	3	noncompactness	noncompactness	ADJ
ejpam-6433	444	4	in	in	ADP
ejpam-6433	444	5	metric	metric	ADJ
ejpam-6433	444	6	fixed	fix	VERB
ejpam-6433	444	7	point	point	NOUN
ejpam-6433	444	8	theory	theory	NOUN
ejpam-6433	444	9	.	.	PUNCT
ejpam-6433	445	1	operator	operator	NOUN
ejpam-6433	445	2	theory	theory	NOUN
ejpam-6433	445	3	:	:	PUNCT
ejpam-6433	445	4	advances	advance	NOUN
ejpam-6433	445	5	and	and	CCONJ
ejpam-6433	445	6	applications	application	NOUN
ejpam-6433	445	7	.	.	PUNCT
ejpam-6433	446	1	birkhäuser	birkhäuser	NOUN
ejpam-6433	446	2	,	,	PUNCT
ejpam-6433	446	3	basel	basel	PROPN
ejpam-6433	446	4	,	,	PUNCT
ejpam-6433	446	5	1997	1997	NUM
ejpam-6433	446	6	.	.	PUNCT
ejpam-6433	447	1	[	[	X
ejpam-6433	447	2	12	12	NUM
ejpam-6433	447	3	]	]	PUNCT
ejpam-6433	447	4	k.	k.	PROPN
ejpam-6433	447	5	kuratowski	kuratowski	PROPN
ejpam-6433	447	6	.	.	PUNCT
ejpam-6433	448	1	introduction	introduction	NOUN
ejpam-6433	448	2	to	to	PART
ejpam-6433	448	3	set	set	VERB
ejpam-6433	448	4	theory	theory	NOUN
ejpam-6433	448	5	and	and	CCONJ
ejpam-6433	448	6	topology	topology	NOUN
ejpam-6433	448	7	.	.	PUNCT
ejpam-6433	449	1	pergamon	pergamon	PROPN
ejpam-6433	449	2	press	press	PROPN
ejpam-6433	449	3	,	,	PUNCT
ejpam-6433	449	4	1956	1956	NUM
ejpam-6433	449	5	.	.	PUNCT
ejpam-6433	450	1	[	[	X
ejpam-6433	450	2	13	13	NUM
ejpam-6433	450	3	]	]	PUNCT
ejpam-6433	450	4	a.	a.	NOUN
ejpam-6433	450	5	fernández	fernández	PROPN
ejpam-6433	450	6	-	-	PUNCT
ejpam-6433	450	7	león	león	PROPN
ejpam-6433	450	8	and	and	CCONJ
ejpam-6433	450	9	a.	a.	NOUN
ejpam-6433	450	10	nicolae	nicolae	PROPN
ejpam-6433	450	11	.	.	PROPN
ejpam-6433	450	12	best	good	ADJ
ejpam-6433	450	13	proximity	proximity	NOUN
ejpam-6433	450	14	pair	pair	NOUN
ejpam-6433	450	15	results	result	NOUN
ejpam-6433	450	16	for	for	ADP
ejpam-6433	450	17	relatively	relatively	ADV
ejpam-6433	450	18	nonexpansive	nonexpansive	ADJ
ejpam-6433	450	19	mappings	mapping	NOUN
ejpam-6433	450	20	in	in	ADP
ejpam-6433	450	21	geodesic	geodesic	ADJ
ejpam-6433	450	22	spaces	space	NOUN
ejpam-6433	450	23	.	.	PUNCT
ejpam-6433	451	1	numerical	numerical	ADJ
ejpam-6433	451	2	functional	functional	ADJ
ejpam-6433	451	3	analysis	analysis	NOUN
ejpam-6433	451	4	and	and	CCONJ
ejpam-6433	451	5	optimization	optimization	NOUN
ejpam-6433	451	6	,	,	PUNCT
ejpam-6433	451	7	35:1399–1418	35:1399–1418	NUM
ejpam-6433	451	8	,	,	PUNCT
ejpam-6433	451	9	2014	2014	NUM
ejpam-6433	451	10	.	.	PUNCT
ejpam-6433	452	1	[	[	X
ejpam-6433	452	2	14	14	NUM
ejpam-6433	452	3	]	]	PUNCT
ejpam-6433	452	4	m.	m.	NOUN
ejpam-6433	452	5	gabeleh	gabeleh	PROPN
ejpam-6433	452	6	and	and	CCONJ
ejpam-6433	452	7	j.	j.	PROPN
ejpam-6433	452	8	markin	markin	PROPN
ejpam-6433	452	9	.	.	PUNCT
ejpam-6433	453	1	proximal	proximal	ADJ
ejpam-6433	453	2	pairs	pair	NOUN
ejpam-6433	453	3	and	and	CCONJ
ejpam-6433	453	4	relatively	relatively	ADV
ejpam-6433	453	5	nonexpansive	nonexpansive	ADJ
ejpam-6433	453	6	mappings	mapping	NOUN
ejpam-6433	453	7	in	in	ADP
ejpam-6433	453	8	hyperconvex	hyperconvex	ADJ
ejpam-6433	453	9	spaces	space	NOUN
ejpam-6433	453	10	.	.	PUNCT
ejpam-6433	454	1	journal	journal	NOUN
ejpam-6433	454	2	of	of	ADP
ejpam-6433	454	3	fixed	fix	VERB
ejpam-6433	454	4	point	point	NOUN
ejpam-6433	454	5	theory	theory	NOUN
ejpam-6433	454	6	and	and	CCONJ
ejpam-6433	454	7	applications	application	NOUN
ejpam-6433	454	8	,	,	PUNCT
ejpam-6433	454	9	27:19	27:19	NUM
ejpam-6433	454	10	,	,	PUNCT
ejpam-6433	454	11	2025	2025	NUM
ejpam-6433	454	12	.	.	PUNCT
ejpam-6433	455	1	[	[	X
ejpam-6433	455	2	15	15	NUM
ejpam-6433	455	3	]	]	X
ejpam-6433	455	4	r.	r.	PROPN
ejpam-6433	455	5	esṕınola	esṕınola	PROPN
ejpam-6433	455	6	and	and	CCONJ
ejpam-6433	455	7	m.	m.	NOUN
ejpam-6433	455	8	gabeleh	gabeleh	NOUN
ejpam-6433	455	9	.	.	PUNCT
ejpam-6433	456	1	on	on	ADP
ejpam-6433	456	2	the	the	DET
ejpam-6433	456	3	structure	structure	NOUN
ejpam-6433	456	4	of	of	ADP
ejpam-6433	456	5	minimal	minimal	ADJ
ejpam-6433	456	6	sets	set	NOUN
ejpam-6433	456	7	of	of	ADP
ejpam-6433	456	8	relatively	relatively	ADV
ejpam-6433	456	9	nonm	nonm	NOUN
ejpam-6433	456	10	.	.	PUNCT
ejpam-6433	457	1	gabeleh	gabeleh	NOUN
ejpam-6433	457	2	,	,	PUNCT
ejpam-6433	457	3	j.	j.	PROPN
ejpam-6433	457	4	markin	markin	PROPN
ejpam-6433	457	5	,	,	PUNCT
ejpam-6433	457	6	m.	m.	NOUN
ejpam-6433	457	7	aphane	aphane	PROPN
ejpam-6433	457	8	/	/	SYM
ejpam-6433	457	9	eur	eur	PROPN
ejpam-6433	457	10	.	.	PUNCT
ejpam-6433	458	1	j.	j.	PROPN
ejpam-6433	458	2	pure	pure	PROPN
ejpam-6433	458	3	appl	appl	PROPN
ejpam-6433	458	4	.	.	PROPN
ejpam-6433	458	5	math	math	PROPN
ejpam-6433	458	6	,	,	PUNCT
ejpam-6433	458	7	18	18	NUM
ejpam-6433	458	8	(	(	PUNCT
ejpam-6433	458	9	3	3	NUM
ejpam-6433	458	10	)	)	PUNCT
ejpam-6433	458	11	(	(	PUNCT
ejpam-6433	458	12	2025	2025	NUM
ejpam-6433	458	13	)	)	PUNCT
ejpam-6433	458	14	,	,	PUNCT
ejpam-6433	458	15	6433	6433	NUM
ejpam-6433	458	16	17	17	NUM
ejpam-6433	458	17	of	of	ADP
ejpam-6433	458	18	17	17	NUM
ejpam-6433	458	19	expansive	expansive	ADJ
ejpam-6433	458	20	mappings	mapping	NOUN
ejpam-6433	458	21	.	.	PUNCT
ejpam-6433	459	1	numerical	numerical	ADJ
ejpam-6433	459	2	functional	functional	ADJ
ejpam-6433	459	3	analysis	analysis	NOUN
ejpam-6433	459	4	and	and	CCONJ
ejpam-6433	459	5	optimization	optimization	NOUN
ejpam-6433	459	6	,	,	PUNCT
ejpam-6433	459	7	34:845–860	34:845–860	PROPN
ejpam-6433	459	8	,	,	PUNCT
ejpam-6433	459	9	2013	2013	NUM
ejpam-6433	459	10	.	.	PUNCT
ejpam-6433	460	1	[	[	X
ejpam-6433	460	2	16	16	NUM
ejpam-6433	460	3	]	]	X
ejpam-6433	460	4	n.	n.	NOUN
ejpam-6433	460	5	aronszajn	aronszajn	PROPN
ejpam-6433	460	6	and	and	CCONJ
ejpam-6433	460	7	p.	p.	PROPN
ejpam-6433	460	8	panitchpakdi	panitchpakdi	PROPN
ejpam-6433	460	9	.	.	PUNCT
ejpam-6433	461	1	extensions	extension	NOUN
ejpam-6433	461	2	of	of	ADP
ejpam-6433	461	3	uniformly	uniformly	ADV
ejpam-6433	461	4	continuous	continuous	ADJ
ejpam-6433	461	5	transformations	transformation	NOUN
ejpam-6433	461	6	and	and	CCONJ
ejpam-6433	461	7	hyperconvex	hyperconvex	ADJ
ejpam-6433	461	8	metric	metric	ADJ
ejpam-6433	461	9	spaces	space	NOUN
ejpam-6433	461	10	.	.	PUNCT
ejpam-6433	462	1	pacific	pacific	PROPN
ejpam-6433	462	2	journal	journal	PROPN
ejpam-6433	462	3	of	of	ADP
ejpam-6433	462	4	mathematics	mathematic	NOUN
ejpam-6433	462	5	,	,	PUNCT
ejpam-6433	462	6	6:405–439	6:405–439	NOUN
ejpam-6433	462	7	,	,	PUNCT
ejpam-6433	462	8	1956	1956	NUM
ejpam-6433	462	9	.	.	PUNCT
ejpam-6433	463	1	[	[	X
ejpam-6433	463	2	17	17	NUM
ejpam-6433	463	3	]	]	PUNCT
ejpam-6433	463	4	m.	m.	NOUN
ejpam-6433	463	5	a.	a.	NOUN
ejpam-6433	463	6	khamsi	khamsi	PROPN
ejpam-6433	463	7	and	and	CCONJ
ejpam-6433	463	8	w.	w.	PROPN
ejpam-6433	463	9	a.	a.	PROPN
ejpam-6433	463	10	kirk	kirk	PROPN
ejpam-6433	463	11	.	.	PUNCT
ejpam-6433	464	1	an	an	DET
ejpam-6433	464	2	introduction	introduction	NOUN
ejpam-6433	464	3	to	to	ADP
ejpam-6433	464	4	metric	metric	ADJ
ejpam-6433	464	5	spaces	space	NOUN
ejpam-6433	464	6	and	and	CCONJ
ejpam-6433	464	7	fixed	fix	VERB
ejpam-6433	464	8	point	point	NOUN
ejpam-6433	464	9	theory	theory	NOUN
ejpam-6433	464	10	.	.	PUNCT
ejpam-6433	465	1	pure	pure	ADJ
ejpam-6433	465	2	and	and	CCONJ
ejpam-6433	465	3	applied	applied	ADJ
ejpam-6433	465	4	mathematics	mathematic	NOUN
ejpam-6433	465	5	.	.	PUNCT
ejpam-6433	466	1	wiley	wiley	PROPN
ejpam-6433	466	2	-	-	PUNCT
ejpam-6433	466	3	interscience	interscience	PROPN
ejpam-6433	466	4	,	,	PUNCT
ejpam-6433	466	5	new	new	PROPN
ejpam-6433	466	6	york	york	PROPN
ejpam-6433	466	7	,	,	PUNCT
ejpam-6433	466	8	usa	usa	PROPN
ejpam-6433	466	9	,	,	PUNCT
ejpam-6433	466	10	2001	2001	NUM
ejpam-6433	466	11	.	.	PUNCT
ejpam-6433	467	1	[	[	X
ejpam-6433	467	2	18	18	NUM
ejpam-6433	467	3	]	]	PUNCT
ejpam-6433	467	4	m.	m.	NOUN
ejpam-6433	467	5	borkowski	borkowski	PROPN
ejpam-6433	467	6	.	.	PUNCT
ejpam-6433	467	7	theory	theory	NOUN
ejpam-6433	467	8	of	of	ADP
ejpam-6433	467	9	hyperconvex	hyperconvex	ADJ
ejpam-6433	467	10	metric	metric	ADJ
ejpam-6433	467	11	spaces	space	NOUN
ejpam-6433	467	12	.	.	PUNCT
ejpam-6433	468	1	juliusz	juliusz	PROPN
ejpam-6433	468	2	schauder	schauder	PROPN
ejpam-6433	468	3	university	university	PROPN
ejpam-6433	468	4	centre	centre	NOUN
ejpam-6433	468	5	for	for	ADP
ejpam-6433	468	6	nonlinear	nonlinear	ADJ
ejpam-6433	468	7	studies	study	NOUN
ejpam-6433	468	8	,	,	PUNCT
ejpam-6433	468	9	nicolaus	nicolaus	PROPN
ejpam-6433	468	10	copernicus	copernicus	PROPN
ejpam-6433	468	11	university	university	PROPN
ejpam-6433	468	12	,	,	PUNCT
ejpam-6433	468	13	2015	2015	NUM
ejpam-6433	468	14	.	.	PUNCT
ejpam-6433	469	1	[	[	X
ejpam-6433	469	2	19	19	NUM
ejpam-6433	469	3	]	]	PUNCT
ejpam-6433	469	4	v.	v.	ADP
ejpam-6433	469	5	sankar	sankar	PROPN
ejpam-6433	469	6	raj	raj	PROPN
ejpam-6433	469	7	.	.	PUNCT
ejpam-6433	470	1	a	a	DET
ejpam-6433	470	2	best	good	ADJ
ejpam-6433	470	3	proximity	proximity	NOUN
ejpam-6433	470	4	point	point	NOUN
ejpam-6433	470	5	theorem	theorem	NOUN
ejpam-6433	470	6	for	for	ADP
ejpam-6433	470	7	weakly	weakly	ADJ
ejpam-6433	470	8	contractive	contractive	ADJ
ejpam-6433	470	9	non	non	ADJ
ejpam-6433	470	10	-	-	NOUN
ejpam-6433	470	11	selfmappings	selfmapping	NOUN
ejpam-6433	470	12	.	.	PUNCT
ejpam-6433	471	1	nonlinear	nonlinear	ADJ
ejpam-6433	471	2	analysis	analysis	NOUN
ejpam-6433	471	3	,	,	PUNCT
ejpam-6433	471	4	74:4804–4808	74:4804–4808	NUM
ejpam-6433	471	5	,	,	PUNCT
ejpam-6433	471	6	2011	2011	NUM
ejpam-6433	471	7	.	.	PUNCT
ejpam-6433	472	1	[	[	X
ejpam-6433	472	2	20	20	NUM
ejpam-6433	472	3	]	]	PUNCT
ejpam-6433	472	4	v.	v.	ADP
ejpam-6433	472	5	sankar	sankar	PROPN
ejpam-6433	472	6	raj	raj	PROPN
ejpam-6433	472	7	and	and	CCONJ
ejpam-6433	472	8	a.	a.	NOUN
ejpam-6433	472	9	a.	a.	PROPN
ejpam-6433	472	10	eldred	eldred	PROPN
ejpam-6433	472	11	.	.	PUNCT
ejpam-6433	473	1	a	a	DET
ejpam-6433	473	2	characterization	characterization	NOUN
ejpam-6433	473	3	of	of	ADP
ejpam-6433	473	4	strictly	strictly	ADV
ejpam-6433	473	5	convex	convex	ADJ
ejpam-6433	473	6	spaces	space	NOUN
ejpam-6433	473	7	and	and	CCONJ
ejpam-6433	473	8	applications	application	NOUN
ejpam-6433	473	9	.	.	PUNCT
ejpam-6433	474	1	journal	journal	NOUN
ejpam-6433	474	2	of	of	ADP
ejpam-6433	474	3	optimization	optimization	NOUN
ejpam-6433	474	4	theory	theory	NOUN
ejpam-6433	474	5	and	and	CCONJ
ejpam-6433	474	6	applications	application	NOUN
ejpam-6433	474	7	,	,	PUNCT
ejpam-6433	474	8	160:703–710	160:703–710	NUM
ejpam-6433	474	9	,	,	PUNCT
ejpam-6433	474	10	2014	2014	NUM
ejpam-6433	474	11	.	.	PUNCT
ejpam-6433	475	1	[	[	X
ejpam-6433	475	2	21	21	NUM
ejpam-6433	475	3	]	]	PUNCT
ejpam-6433	475	4	m.	m.	NOUN
ejpam-6433	475	5	a.	a.	NOUN
ejpam-6433	475	6	khamsi	khamsi	PROPN
ejpam-6433	475	7	,	,	PUNCT
ejpam-6433	475	8	w.	w.	PROPN
ejpam-6433	475	9	a.	a.	PROPN
ejpam-6433	475	10	kirk	kirk	PROPN
ejpam-6433	475	11	,	,	PUNCT
ejpam-6433	475	12	and	and	CCONJ
ejpam-6433	475	13	c.	c.	PROPN
ejpam-6433	475	14	yanez	yanez	PROPN
ejpam-6433	475	15	.	.	PUNCT
ejpam-6433	476	1	fixed	fix	VERB
ejpam-6433	476	2	points	point	NOUN
ejpam-6433	476	3	and	and	CCONJ
ejpam-6433	476	4	selection	selection	NOUN
ejpam-6433	476	5	theorems	theorem	NOUN
ejpam-6433	476	6	in	in	ADP
ejpam-6433	476	7	hyperconvex	hyperconvex	ADJ
ejpam-6433	476	8	spaces	space	NOUN
ejpam-6433	476	9	.	.	PUNCT
ejpam-6433	477	1	proceedings	proceeding	NOUN
ejpam-6433	477	2	of	of	ADP
ejpam-6433	477	3	the	the	DET
ejpam-6433	477	4	american	american	PROPN
ejpam-6433	477	5	mathematical	mathematical	PROPN
ejpam-6433	477	6	society	society	NOUN
ejpam-6433	477	7	,	,	PUNCT
ejpam-6433	477	8	128:3275	128:3275	NUM
ejpam-6433	477	9	–	–	PUNCT
ejpam-6433	477	10	3283	3283	NUM
ejpam-6433	477	11	,	,	PUNCT
ejpam-6433	477	12	2000	2000	NUM
ejpam-6433	477	13	.	.	PUNCT
ejpam-6433	478	1	[	[	X
ejpam-6433	478	2	22	22	NUM
ejpam-6433	478	3	]	]	PUNCT
ejpam-6433	478	4	j.	j.	PROPN
ejpam-6433	478	5	markin	markin	PROPN
ejpam-6433	478	6	.	.	PUNCT
ejpam-6433	479	1	a	a	DET
ejpam-6433	479	2	selection	selection	NOUN
ejpam-6433	479	3	theorem	theorem	VERB
ejpam-6433	479	4	for	for	ADP
ejpam-6433	479	5	quasi	quasi	ADJ
ejpam-6433	479	6	-	-	ADJ
ejpam-6433	479	7	lower	low	ADJ
ejpam-6433	479	8	semicontinuous	semicontinuous	ADJ
ejpam-6433	479	9	mappings	mapping	NOUN
ejpam-6433	479	10	in	in	ADP
ejpam-6433	479	11	hyperconvex	hyperconvex	ADJ
ejpam-6433	479	12	spaces	space	NOUN
ejpam-6433	479	13	.	.	PUNCT
ejpam-6433	480	1	journal	journal	PROPN
ejpam-6433	480	2	of	of	ADP
ejpam-6433	480	3	mathematical	mathematical	ADJ
ejpam-6433	480	4	analysis	analysis	NOUN
ejpam-6433	480	5	and	and	CCONJ
ejpam-6433	480	6	applications	application	NOUN
ejpam-6433	480	7	,	,	PUNCT
ejpam-6433	480	8	321:862–866	321:862–866	NUM
ejpam-6433	480	9	,	,	PUNCT
ejpam-6433	480	10	2006	2006	NUM
ejpam-6433	480	11	.	.	PUNCT
ejpam-6433	481	1	[	[	X
ejpam-6433	481	2	23	23	NUM
ejpam-6433	481	3	]	]	PUNCT
ejpam-6433	481	4	j.	j.	PROPN
ejpam-6433	481	5	markin	markin	PROPN
ejpam-6433	481	6	and	and	CCONJ
ejpam-6433	481	7	n.	n.	PROPN
ejpam-6433	481	8	shahzad	shahzad	PROPN
ejpam-6433	481	9	.	.	PUNCT
ejpam-6433	482	1	best	good	ADJ
ejpam-6433	482	2	proximity	proximity	NOUN
ejpam-6433	482	3	points	point	NOUN
ejpam-6433	482	4	for	for	ADP
ejpam-6433	482	5	relatively	relatively	ADV
ejpam-6433	482	6	u	u	ADJ
ejpam-6433	482	7	-	-	ADJ
ejpam-6433	482	8	continuous	continuous	ADJ
ejpam-6433	482	9	mappings	mapping	NOUN
ejpam-6433	482	10	in	in	ADP
ejpam-6433	482	11	banach	banach	NOUN
ejpam-6433	482	12	and	and	CCONJ
ejpam-6433	482	13	hyperconvex	hyperconvex	ADJ
ejpam-6433	482	14	spaces	space	NOUN
ejpam-6433	482	15	.	.	PUNCT
ejpam-6433	483	1	abstract	abstract	ADJ
ejpam-6433	483	2	and	and	CCONJ
ejpam-6433	483	3	applied	apply	VERB
ejpam-6433	483	4	analysis	analysis	NOUN
ejpam-6433	483	5	,	,	PUNCT
ejpam-6433	483	6	page	page	NOUN
ejpam-6433	483	7	5	5	NUM
ejpam-6433	483	8	,	,	PUNCT
ejpam-6433	483	9	2013	2013	NUM
ejpam-6433	483	10	.	.	PUNCT
ejpam-6433	484	1	[	[	X
ejpam-6433	484	2	24	24	NUM
ejpam-6433	484	3	]	]	PUNCT
ejpam-6433	484	4	m.	m.	NOUN
ejpam-6433	484	5	a.	a.	NOUN
ejpam-6433	484	6	khamsi	khamsi	PROPN
ejpam-6433	484	7	.	.	PUNCT
ejpam-6433	485	1	kkm	kkm	PROPN
ejpam-6433	485	2	and	and	CCONJ
ejpam-6433	485	3	ky	ky	PROPN
ejpam-6433	485	4	fan	fan	PROPN
ejpam-6433	485	5	theorems	theorem	NOUN
ejpam-6433	485	6	in	in	ADP
ejpam-6433	485	7	hyperconvex	hyperconvex	ADJ
ejpam-6433	485	8	metric	metric	ADJ
ejpam-6433	485	9	spaces	space	NOUN
ejpam-6433	485	10	.	.	PUNCT
ejpam-6433	486	1	journal	journal	PROPN
ejpam-6433	486	2	of	of	ADP
ejpam-6433	486	3	mathematical	mathematical	ADJ
ejpam-6433	486	4	analysis	analysis	NOUN
ejpam-6433	486	5	and	and	CCONJ
ejpam-6433	486	6	applications	application	NOUN
ejpam-6433	486	7	,	,	PUNCT
ejpam-6433	486	8	204:298–306	204:298–306	NUM
ejpam-6433	486	9	,	,	PUNCT
ejpam-6433	486	10	1996	1996	NUM
ejpam-6433	486	11	.	.	PUNCT