id	sid	tid	token	lemma	pos
ejpam-5341	1	1	european	european	PROPN
ejpam-5341	1	2	journal	journal	PROPN
ejpam-5341	1	3	of	of	ADP
ejpam-5341	1	4	pure	pure	ADJ
ejpam-5341	1	5	and	and	CCONJ
ejpam-5341	1	6	applied	apply	VERB
ejpam-5341	1	7	mathematics	mathematic	NOUN
ejpam-5341	1	8	vol	vol	NOUN
ejpam-5341	1	9	.	.	PROPN
ejpam-5341	2	1	17	17	NUM
ejpam-5341	2	2	,	,	PUNCT
ejpam-5341	2	3	no	no	INTJ
ejpam-5341	2	4	.	.	NOUN
ejpam-5341	2	5	4	4	NUM
ejpam-5341	2	6	,	,	PUNCT
ejpam-5341	2	7	2024	2024	NUM
ejpam-5341	2	8	,	,	PUNCT
ejpam-5341	2	9	2985	2985	NUM
ejpam-5341	2	10	-	-	SYM
ejpam-5341	2	11	2989	2989	NUM
ejpam-5341	2	12	issn	issn	PROPN
ejpam-5341	2	13	1307	1307	NUM
ejpam-5341	2	14	-	-	SYM
ejpam-5341	2	15	5543	5543	NUM
ejpam-5341	2	16	–	–	PUNCT
ejpam-5341	2	17	ejpam.com	ejpam.com	X
ejpam-5341	2	18	published	publish	VERB
ejpam-5341	2	19	by	by	ADP
ejpam-5341	2	20	new	new	PROPN
ejpam-5341	2	21	york	york	PROPN
ejpam-5341	2	22	business	business	NOUN
ejpam-5341	2	23	global	global	ADJ
ejpam-5341	2	24	every	every	DET
ejpam-5341	2	25	uniquely	uniquely	ADV
ejpam-5341	2	26	remotal	remotal	ADJ
ejpam-5341	2	27	set	set	NOUN
ejpam-5341	2	28	in	in	ADP
ejpam-5341	2	29	a	a	DET
ejpam-5341	2	30	hilbert	hilbert	NOUN
ejpam-5341	2	31	space	space	NOUN
ejpam-5341	2	32	is	be	AUX
ejpam-5341	2	33	a	a	DET
ejpam-5341	2	34	singleton	singleton	ADJ
ejpam-5341	2	35	roshdi	roshdi	NOUN
ejpam-5341	2	36	khalil1,∗	khalil1,∗	NOUN
ejpam-5341	2	37	,	,	PUNCT
ejpam-5341	2	38	abdelrahman	abdelrahman	NOUN
ejpam-5341	2	39	yousef2	yousef2	PROPN
ejpam-5341	2	40	,	,	PUNCT
ejpam-5341	2	41	waseem	waseem	PROPN
ejpam-5341	2	42	ghazi	ghazi	PROPN
ejpam-5341	2	43	alshanti3	alshanti3	PROPN
ejpam-5341	2	44	,	,	PUNCT
ejpam-5341	2	45	ma	ma	PROPN
ejpam-5341	2	46	′	′	NUM
ejpam-5341	2	47	mon	mon	PROPN
ejpam-5341	2	48	abu	abu	PROPN
ejpam-5341	2	49	hammad3	hammad3	PROPN
ejpam-5341	2	50	1	1	NUM
ejpam-5341	2	51	department	department	NOUN
ejpam-5341	2	52	of	of	ADP
ejpam-5341	2	53	mathematics	mathematic	NOUN
ejpam-5341	2	54	,	,	PUNCT
ejpam-5341	2	55	the	the	DET
ejpam-5341	2	56	university	university	PROPN
ejpam-5341	2	57	of	of	ADP
ejpam-5341	2	58	jordan	jordan	PROPN
ejpam-5341	2	59	,	,	PUNCT
ejpam-5341	2	60	queen	queen	PROPN
ejpam-5341	2	61	rania	rania	PROPN
ejpam-5341	2	62	st	st	PROPN
ejpam-5341	2	63	,	,	PUNCT
ejpam-5341	2	64	amman	amman	PROPN
ejpam-5341	2	65	,	,	PUNCT
ejpam-5341	2	66	11942	11942	NUM
ejpam-5341	2	67	,	,	PUNCT
ejpam-5341	2	68	jordan	jordan	PROPN
ejpam-5341	2	69	2	2	NUM
ejpam-5341	2	70	department	department	NOUN
ejpam-5341	2	71	of	of	ADP
ejpam-5341	2	72	mathematics	mathematic	NOUN
ejpam-5341	2	73	and	and	CCONJ
ejpam-5341	2	74	statistics	statistic	NOUN
ejpam-5341	2	75	,	,	PUNCT
ejpam-5341	2	76	american	american	PROPN
ejpam-5341	2	77	university	university	PROPN
ejpam-5341	2	78	of	of	ADP
ejpam-5341	2	79	sharjah	sharjah	PROPN
ejpam-5341	2	80	,	,	PUNCT
ejpam-5341	2	81	p.o.box	p.o.box	PROPN
ejpam-5341	2	82	26666	26666	NUM
ejpam-5341	2	83	,	,	PUNCT
ejpam-5341	2	84	sharjah	sharjah	PROPN
ejpam-5341	2	85	,	,	PUNCT
ejpam-5341	2	86	united	united	PROPN
ejpam-5341	2	87	arab	arab	PROPN
ejpam-5341	2	88	emirates	emirates	PROPN
ejpam-5341	2	89	3	3	NUM
ejpam-5341	2	90	department	department	NOUN
ejpam-5341	2	91	of	of	ADP
ejpam-5341	2	92	mathematics	mathematic	NOUN
ejpam-5341	2	93	,	,	PUNCT
ejpam-5341	2	94	al	al	PROPN
ejpam-5341	2	95	zaytoonah	zaytoonah	PROPN
ejpam-5341	2	96	university	university	PROPN
ejpam-5341	2	97	of	of	ADP
ejpam-5341	2	98	jordan	jordan	PROPN
ejpam-5341	2	99	,	,	PUNCT
ejpam-5341	2	100	queen	queen	PROPN
ejpam-5341	2	101	alia	alia	PROPN
ejpam-5341	2	102	airport	airport	PROPN
ejpam-5341	2	103	st	st	PROPN
ejpam-5341	2	104	594	594	NUM
ejpam-5341	2	105	,	,	PUNCT
ejpam-5341	2	106	amman	amman	PROPN
ejpam-5341	2	107	,	,	PUNCT
ejpam-5341	2	108	11733	11733	NUM
ejpam-5341	2	109	,	,	PUNCT
ejpam-5341	2	110	jordan	jordan	PROPN
ejpam-5341	2	111	abstract	abstract	PROPN
ejpam-5341	2	112	.	.	PUNCT
ejpam-5341	3	1	in	in	ADP
ejpam-5341	3	2	this	this	DET
ejpam-5341	3	3	paper	paper	NOUN
ejpam-5341	3	4	we	we	PRON
ejpam-5341	3	5	prove	prove	VERB
ejpam-5341	3	6	that	that	SCONJ
ejpam-5341	3	7	every	every	DET
ejpam-5341	3	8	uniquely	uniquely	ADV
ejpam-5341	3	9	remotal	remotal	ADJ
ejpam-5341	3	10	set	set	NOUN
ejpam-5341	3	11	in	in	ADP
ejpam-5341	3	12	a	a	DET
ejpam-5341	3	13	hilbert	hilbert	NOUN
ejpam-5341	3	14	space	space	NOUN
ejpam-5341	3	15	is	be	AUX
ejpam-5341	3	16	a	a	DET
ejpam-5341	3	17	singleton	singleton	NOUN
ejpam-5341	3	18	.	.	PUNCT
ejpam-5341	4	1	2020	2020	NUM
ejpam-5341	4	2	mathematics	mathematic	NOUN
ejpam-5341	4	3	subject	subject	NOUN
ejpam-5341	4	4	classifications	classification	NOUN
ejpam-5341	4	5	:	:	PUNCT
ejpam-5341	4	6	46b20	46b20	NUM
ejpam-5341	4	7	,	,	PUNCT
ejpam-5341	4	8	41a50	41a50	NUM
ejpam-5341	4	9	,	,	PUNCT
ejpam-5341	4	10	41a65	41a65	NUM
ejpam-5341	4	11	key	key	ADJ
ejpam-5341	4	12	words	word	NOUN
ejpam-5341	4	13	and	and	CCONJ
ejpam-5341	4	14	phrases	phrase	NOUN
ejpam-5341	4	15	:	:	PUNCT
ejpam-5341	4	16	uniquely	uniquely	ADV
ejpam-5341	4	17	remotal	remotal	ADJ
ejpam-5341	4	18	sets	set	NOUN
ejpam-5341	4	19	,	,	PUNCT
ejpam-5341	4	20	farthest	farth	ADJ
ejpam-5341	4	21	points	point	NOUN
ejpam-5341	4	22	,	,	PUNCT
ejpam-5341	4	23	uniquely	uniquely	ADV
ejpam-5341	4	24	distant	distant	ADJ
ejpam-5341	4	25	sets	set	NOUN
ejpam-5341	4	26	,	,	PUNCT
ejpam-5341	4	27	hilbert	hilbert	NOUN
ejpam-5341	4	28	space	space	NOUN
ejpam-5341	4	29	1	1	NUM
ejpam-5341	4	30	.	.	PUNCT
ejpam-5341	5	1	introduction	introduction	NOUN
ejpam-5341	5	2	let	let	VERB
ejpam-5341	5	3	h	h	PRON
ejpam-5341	5	4	be	be	AUX
ejpam-5341	5	5	a	a	DET
ejpam-5341	5	6	hilbert	hilbert	NOUN
ejpam-5341	5	7	space	space	NOUN
ejpam-5341	5	8	,	,	PUNCT
ejpam-5341	5	9	and	and	CCONJ
ejpam-5341	5	10	let	let	VERB
ejpam-5341	5	11	e	e	PRON
ejpam-5341	5	12	⊆	⊆	NUM
ejpam-5341	5	13	h	h	NOUN
ejpam-5341	5	14	be	be	AUX
ejpam-5341	5	15	a	a	DET
ejpam-5341	5	16	closed	closed	ADJ
ejpam-5341	5	17	and	and	CCONJ
ejpam-5341	5	18	bounded	bound	VERB
ejpam-5341	5	19	subset	subset	NOUN
ejpam-5341	5	20	of	of	ADP
ejpam-5341	5	21	h.	h.	PROPN
ejpam-5341	5	22	the	the	DET
ejpam-5341	5	23	real	real	ADV
ejpam-5341	5	24	-	-	PUNCT
ejpam-5341	5	25	valued	value	VERB
ejpam-5341	5	26	function	function	NOUN
ejpam-5341	5	27	d	d	X
ejpam-5341	5	28	(	(	PUNCT
ejpam-5341	5	29	·	·	PUNCT
ejpam-5341	5	30	,	,	PUNCT
ejpam-5341	5	31	e	e	NOUN
ejpam-5341	5	32	)	)	PUNCT
ejpam-5341	5	33	:	:	PUNCT
ejpam-5341	6	1	h	h	NOUN
ejpam-5341	6	2	→	→	SYM
ejpam-5341	6	3	r	r	NOUN
ejpam-5341	6	4	defined	define	VERB
ejpam-5341	6	5	by	by	ADP
ejpam-5341	6	6	d(x	d(x	PROPN
ejpam-5341	6	7	,	,	PUNCT
ejpam-5341	6	8	e	e	NOUN
ejpam-5341	6	9	)	)	PUNCT
ejpam-5341	6	10	:	:	PUNCT
ejpam-5341	7	1	=	=	SYM
ejpam-5341	7	2	sup	sup	NOUN
ejpam-5341	7	3	e∈e	e∈e	VERB
ejpam-5341	7	4	∥x−	∥x−	PRON
ejpam-5341	7	5	e∥	e∥	NOUN
ejpam-5341	7	6	,	,	PUNCT
ejpam-5341	7	7	for	for	SCONJ
ejpam-5341	7	8	x	x	PROPN
ejpam-5341	7	9	∈	∈	PROPN
ejpam-5341	7	10	h	h	NOUN
ejpam-5341	7	11	,	,	PUNCT
ejpam-5341	7	12	(	(	PUNCT
ejpam-5341	7	13	1	1	X
ejpam-5341	7	14	)	)	PUNCT
ejpam-5341	7	15	is	be	AUX
ejpam-5341	7	16	referred	refer	VERB
ejpam-5341	7	17	to	to	ADP
ejpam-5341	7	18	as	as	ADP
ejpam-5341	7	19	the	the	DET
ejpam-5341	7	20	farthest	farth	ADJ
ejpam-5341	7	21	distance	distance	NOUN
ejpam-5341	7	22	function	function	NOUN
ejpam-5341	7	23	.	.	PUNCT
ejpam-5341	8	1	the	the	DET
ejpam-5341	8	2	set	set	PROPN
ejpam-5341	8	3	e	e	NOUN
ejpam-5341	8	4	is	be	AUX
ejpam-5341	8	5	termed	term	VERB
ejpam-5341	8	6	remotal	remotal	ADJ
ejpam-5341	8	7	if	if	SCONJ
ejpam-5341	8	8	,	,	PUNCT
ejpam-5341	8	9	for	for	ADP
ejpam-5341	8	10	every	every	DET
ejpam-5341	8	11	x	x	SYM
ejpam-5341	8	12	∈	∈	PROPN
ejpam-5341	8	13	h	h	NOUN
ejpam-5341	8	14	,	,	PUNCT
ejpam-5341	8	15	there	there	PRON
ejpam-5341	8	16	exists	exist	VERB
ejpam-5341	8	17	an	an	DET
ejpam-5341	8	18	e	e	NOUN
ejpam-5341	8	19	∈	∈	NOUN
ejpam-5341	8	20	e	e	NOUN
ejpam-5341	8	21	such	such	ADJ
ejpam-5341	8	22	that	that	DET
ejpam-5341	8	23	d(x	d(x	NOUN
ejpam-5341	8	24	,	,	PUNCT
ejpam-5341	8	25	e	e	NOUN
ejpam-5341	8	26	)	)	PUNCT
ejpam-5341	9	1	=	=	SYM
ejpam-5341	9	2	∥x−	∥x−	PROPN
ejpam-5341	9	3	e∥.	e∥.	NOUN
ejpam-5341	9	4	in	in	ADP
ejpam-5341	9	5	this	this	DET
ejpam-5341	9	6	case	case	NOUN
ejpam-5341	9	7	,	,	PUNCT
ejpam-5341	9	8	the	the	DET
ejpam-5341	9	9	set	set	NOUN
ejpam-5341	9	10	p	p	X
ejpam-5341	9	11	(	(	PUNCT
ejpam-5341	9	12	x	x	X
ejpam-5341	9	13	,	,	PUNCT
ejpam-5341	9	14	e	e	NOUN
ejpam-5341	9	15	)	)	PUNCT
ejpam-5341	9	16	:	:	PUNCT
ejpam-5341	9	17	=	=	SYM
ejpam-5341	9	18	{	{	PUNCT
ejpam-5341	9	19	e	e	X
ejpam-5341	9	20	∈	∈	PROPN
ejpam-5341	9	21	e	e	NOUN
ejpam-5341	9	22	:	:	PUNCT
ejpam-5341	9	23	d(x	d(x	NOUN
ejpam-5341	9	24	,	,	PUNCT
ejpam-5341	9	25	e	e	NOUN
ejpam-5341	9	26	)	)	PUNCT
ejpam-5341	9	27	=	=	SYM
ejpam-5341	10	1	∥x−	∥x−	NUM
ejpam-5341	10	2	e∥	e∥	NOUN
ejpam-5341	10	3	}	}	PUNCT
ejpam-5341	10	4	is	be	AUX
ejpam-5341	10	5	denoted	denote	VERB
ejpam-5341	10	6	as	as	ADP
ejpam-5341	10	7	p	p	PROPN
ejpam-5341	10	8	(	(	PUNCT
ejpam-5341	10	9	x	x	X
ejpam-5341	10	10	,	,	PUNCT
ejpam-5341	10	11	e	e	NOUN
ejpam-5341	10	12	)	)	PUNCT
ejpam-5341	10	13	.	.	PUNCT
ejpam-5341	11	1	clearly	clearly	ADV
ejpam-5341	11	2	,	,	PUNCT
ejpam-5341	11	3	p	p	X
ejpam-5341	11	4	(	(	PUNCT
ejpam-5341	11	5	·	·	PUNCT
ejpam-5341	11	6	,	,	PUNCT
ejpam-5341	11	7	e	e	NOUN
ejpam-5341	11	8	)	)	PUNCT
ejpam-5341	11	9	:	:	PUNCT
ejpam-5341	11	10	h	h	NOUN
ejpam-5341	11	11	→	→	SYM
ejpam-5341	11	12	2e	2e	PROPN
ejpam-5341	11	13	is	be	AUX
ejpam-5341	11	14	a	a	DET
ejpam-5341	11	15	multi	multi	ADJ
ejpam-5341	11	16	-	-	ADJ
ejpam-5341	11	17	valued	value	VERB
ejpam-5341	11	18	function	function	NOUN
ejpam-5341	11	19	.	.	PUNCT
ejpam-5341	12	1	however	however	ADV
ejpam-5341	12	2	,	,	PUNCT
ejpam-5341	12	3	if	if	SCONJ
ejpam-5341	12	4	p	p	X
ejpam-5341	12	5	(	(	PUNCT
ejpam-5341	12	6	·	·	PUNCT
ejpam-5341	12	7	,	,	PUNCT
ejpam-5341	12	8	e	e	NOUN
ejpam-5341	12	9	)	)	PUNCT
ejpam-5341	12	10	:	:	PUNCT
ejpam-5341	12	11	h	h	NOUN
ejpam-5341	12	12	→	→	SYM
ejpam-5341	12	13	2e	2e	PROPN
ejpam-5341	12	14	is	be	AUX
ejpam-5341	12	15	single	single	ADV
ejpam-5341	12	16	-	-	PUNCT
ejpam-5341	12	17	valued	value	VERB
ejpam-5341	12	18	,	,	PUNCT
ejpam-5341	12	19	meaning	mean	VERB
ejpam-5341	12	20	p	p	X
ejpam-5341	12	21	(	(	PUNCT
ejpam-5341	12	22	x	x	X
ejpam-5341	12	23	,	,	PUNCT
ejpam-5341	12	24	e	e	NOUN
ejpam-5341	12	25	)	)	PUNCT
ejpam-5341	12	26	is	be	AUX
ejpam-5341	12	27	a	a	DET
ejpam-5341	12	28	singleton	singleton	NOUN
ejpam-5341	12	29	for	for	ADP
ejpam-5341	12	30	all	all	DET
ejpam-5341	12	31	x	x	SYM
ejpam-5341	12	32	∈	∈	PROPN
ejpam-5341	12	33	h	h	NOUN
ejpam-5341	12	34	,	,	PUNCT
ejpam-5341	12	35	then	then	ADV
ejpam-5341	12	36	e	e	PROPN
ejpam-5341	12	37	is	be	AUX
ejpam-5341	12	38	called	call	VERB
ejpam-5341	12	39	uniquely	uniquely	ADV
ejpam-5341	12	40	remotal	remotal	ADJ
ejpam-5341	12	41	.	.	PUNCT
ejpam-5341	13	1	∗corresponding	∗corresponde	VERB
ejpam-5341	13	2	author	author	NOUN
ejpam-5341	13	3	.	.	PUNCT
ejpam-5341	14	1	doi	doi	NOUN
ejpam-5341	14	2	:	:	PUNCT
ejpam-5341	14	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5341	https://doi.org/10.29020/nybg.ejpam.v17i4.5341	NOUN
ejpam-5341	14	4	email	email	NOUN
ejpam-5341	14	5	addresses	address	NOUN
ejpam-5341	14	6	:	:	PUNCT
ejpam-5341	15	1	roshdi@ju.edu.jo	roshdi@ju.edu.jo	PROPN
ejpam-5341	15	2	(	(	PUNCT
ejpam-5341	15	3	r.	r.	PROPN
ejpam-5341	15	4	khalil	khalil	PROPN
ejpam-5341	15	5	)	)	PUNCT
ejpam-5341	15	6	,	,	PUNCT
ejpam-5341	15	7	afyousef@aus.edu	afyousef@aus.edu	INTJ
ejpam-5341	15	8	(	(	PUNCT
ejpam-5341	15	9	a.	a.	PROPN
ejpam-5341	15	10	yousef	yousef	PROPN
ejpam-5341	15	11	)	)	PUNCT
ejpam-5341	15	12	,	,	PUNCT
ejpam-5341	15	13	w.alshanti@zuj.edu.jo	w.alshanti@zuj.edu.jo	PROPN
ejpam-5341	15	14	(	(	PUNCT
ejpam-5341	15	15	w.	w.	PROPN
ejpam-5341	15	16	g.	g.	PROPN
ejpam-5341	15	17	alshanti	alshanti	PROPN
ejpam-5341	15	18	)	)	PUNCT
ejpam-5341	15	19	,	,	PUNCT
ejpam-5341	15	20	m.abuhammad@zuj.edu.jo	m.abuhammad@zuj.edu.jo	NOUN
ejpam-5341	15	21	(	(	PUNCT
ejpam-5341	15	22	m.	m.	NOUN
ejpam-5341	15	23	abu	abu	PROPN
ejpam-5341	15	24	hammad	hammad	PROPN
ejpam-5341	15	25	)	)	PUNCT
ejpam-5341	15	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5341	15	27	2985	2985	NUM
ejpam-5341	16	1	copyright	copyright	NOUN
ejpam-5341	16	2	:	:	PUNCT
ejpam-5341	16	3	©	©	PROPN
ejpam-5341	16	4	2024	2024	NUM
ejpam-5341	16	5	the	the	DET
ejpam-5341	16	6	author(s	author(s	NOUN
ejpam-5341	16	7	)	)	PUNCT
ejpam-5341	16	8	.	.	PUNCT
ejpam-5341	17	1	(	(	PUNCT
ejpam-5341	17	2	cc	cc	NOUN
ejpam-5341	17	3	by	by	ADP
ejpam-5341	17	4	-	-	PUNCT
ejpam-5341	17	5	nc	nc	PROPN
ejpam-5341	17	6	4.0	4.0	NUM
ejpam-5341	17	7	)	)	PUNCT
ejpam-5341	17	8	r	r	NOUN
ejpam-5341	17	9	khalil	khalil	PROPN
ejpam-5341	17	10	et	et	PROPN
ejpam-5341	17	11	al	al	PROPN
ejpam-5341	17	12	.	.	PUNCT
ejpam-5341	17	13	/	/	SYM
ejpam-5341	17	14	eur	eur	PROPN
ejpam-5341	17	15	.	.	PUNCT
ejpam-5341	18	1	j.	j.	PROPN
ejpam-5341	18	2	pure	pure	PROPN
ejpam-5341	18	3	appl	appl	PROPN
ejpam-5341	18	4	.	.	PROPN
ejpam-5341	18	5	math	math	PROPN
ejpam-5341	18	6	,	,	PUNCT
ejpam-5341	18	7	17	17	NUM
ejpam-5341	18	8	(	(	PUNCT
ejpam-5341	18	9	4	4	NUM
ejpam-5341	18	10	)	)	PUNCT
ejpam-5341	18	11	(	(	PUNCT
ejpam-5341	18	12	2024	2024	NUM
ejpam-5341	18	13	)	)	PUNCT
ejpam-5341	18	14	,	,	PUNCT
ejpam-5341	18	15	2985	2985	NUM
ejpam-5341	18	16	-	-	SYM
ejpam-5341	18	17	2989	2989	NUM
ejpam-5341	18	18	2986	2986	NUM
ejpam-5341	18	19	the	the	DET
ejpam-5341	18	20	study	study	NOUN
ejpam-5341	18	21	of	of	ADP
ejpam-5341	18	22	remotal	remotal	ADJ
ejpam-5341	18	23	and	and	CCONJ
ejpam-5341	18	24	uniquely	uniquely	ADV
ejpam-5341	18	25	remotal	remotal	ADJ
ejpam-5341	18	26	sets	set	NOUN
ejpam-5341	18	27	has	have	AUX
ejpam-5341	18	28	garnered	garner	VERB
ejpam-5341	18	29	significant	significant	ADJ
ejpam-5341	18	30	interest	interest	NOUN
ejpam-5341	18	31	over	over	ADP
ejpam-5341	18	32	the	the	DET
ejpam-5341	18	33	past	past	ADJ
ejpam-5341	18	34	few	few	ADJ
ejpam-5341	18	35	decades	decade	NOUN
ejpam-5341	18	36	due	due	ADP
ejpam-5341	18	37	to	to	ADP
ejpam-5341	18	38	their	their	PRON
ejpam-5341	18	39	connections	connection	NOUN
ejpam-5341	18	40	with	with	ADP
ejpam-5341	18	41	the	the	DET
ejpam-5341	18	42	geometry	geometry	NOUN
ejpam-5341	18	43	of	of	ADP
ejpam-5341	18	44	hilbert	hilbert	NOUN
ejpam-5341	18	45	and	and	CCONJ
ejpam-5341	18	46	banach	banach	NOUN
ejpam-5341	18	47	spaces	space	NOUN
ejpam-5341	18	48	[	[	X
ejpam-5341	18	49	2–15	2–15	NUM
ejpam-5341	18	50	]	]	PUNCT
ejpam-5341	18	51	.	.	PUNCT
ejpam-5341	19	1	among	among	ADP
ejpam-5341	19	2	these	these	PRON
ejpam-5341	19	3	,	,	PUNCT
ejpam-5341	19	4	uniquely	uniquely	ADV
ejpam-5341	19	5	remotal	remotal	ADJ
ejpam-5341	19	6	sets	set	NOUN
ejpam-5341	19	7	hold	hold	VERB
ejpam-5341	19	8	particular	particular	ADJ
ejpam-5341	19	9	significance	significance	NOUN
ejpam-5341	19	10	.	.	PUNCT
ejpam-5341	20	1	indeed	indeed	ADV
ejpam-5341	20	2	,	,	PUNCT
ejpam-5341	20	3	one	one	NUM
ejpam-5341	20	4	of	of	ADP
ejpam-5341	20	5	the	the	DET
ejpam-5341	20	6	most	most	ADV
ejpam-5341	20	7	intriguing	intriguing	ADJ
ejpam-5341	20	8	open	open	ADJ
ejpam-5341	20	9	problems	problem	NOUN
ejpam-5341	20	10	in	in	ADP
ejpam-5341	20	11	functional	functional	ADJ
ejpam-5341	20	12	analysis	analysis	NOUN
ejpam-5341	20	13	is	be	AUX
ejpam-5341	20	14	the	the	DET
ejpam-5341	20	15	well	well	ADV
ejpam-5341	20	16	-	-	PUNCT
ejpam-5341	20	17	known	know	VERB
ejpam-5341	20	18	farthest	farth	ADJ
ejpam-5341	20	19	point	point	NOUN
ejpam-5341	20	20	problem	problem	NOUN
ejpam-5341	20	21	,	,	PUNCT
ejpam-5341	20	22	which	which	PRON
ejpam-5341	20	23	conjectures	conjecture	VERB
ejpam-5341	20	24	:	:	PUNCT
ejpam-5341	20	25	”	"	PUNCT
ejpam-5341	20	26	every	every	DET
ejpam-5341	20	27	uniquely	uniquely	ADV
ejpam-5341	20	28	remotal	remotal	ADJ
ejpam-5341	20	29	set	set	NOUN
ejpam-5341	20	30	in	in	ADP
ejpam-5341	20	31	h	h	NOUN
ejpam-5341	20	32	is	be	AUX
ejpam-5341	20	33	a	a	DET
ejpam-5341	20	34	singleton	singleton	NOUN
ejpam-5341	20	35	”	"	PUNCT
ejpam-5341	20	36	.	.	PUNCT
ejpam-5341	21	1	this	this	PRON
ejpam-5341	21	2	is	be	AUX
ejpam-5341	21	3	the	the	DET
ejpam-5341	21	4	central	central	ADJ
ejpam-5341	21	5	focus	focus	NOUN
ejpam-5341	21	6	of	of	ADP
ejpam-5341	21	7	this	this	DET
ejpam-5341	21	8	paper	paper	NOUN
ejpam-5341	21	9	.	.	PUNCT
ejpam-5341	22	1	this	this	DET
ejpam-5341	22	2	problem	problem	NOUN
ejpam-5341	22	3	has	have	AUX
ejpam-5341	22	4	persisted	persist	VERB
ejpam-5341	22	5	for	for	ADP
ejpam-5341	22	6	over	over	ADP
ejpam-5341	22	7	70	70	NUM
ejpam-5341	22	8	years	year	NOUN
ejpam-5341	22	9	.	.	PUNCT
ejpam-5341	23	1	its	its	PRON
ejpam-5341	23	2	significance	significance	NOUN
ejpam-5341	23	3	was	be	AUX
ejpam-5341	23	4	further	far	ADV
ejpam-5341	23	5	highlighted	highlight	VERB
ejpam-5341	23	6	when	when	SCONJ
ejpam-5341	23	7	klee	klee	PROPN
ejpam-5341	23	8	[	[	X
ejpam-5341	23	9	9	9	NUM
ejpam-5341	23	10	]	]	PUNCT
ejpam-5341	23	11	established	establish	VERB
ejpam-5341	23	12	the	the	DET
ejpam-5341	23	13	equivalence	equivalence	NOUN
ejpam-5341	23	14	of	of	ADP
ejpam-5341	23	15	the	the	DET
ejpam-5341	23	16	following	follow	VERB
ejpam-5341	23	17	two	two	NUM
ejpam-5341	23	18	statements	statement	NOUN
ejpam-5341	23	19	:	:	PUNCT
ejpam-5341	23	20	(	(	PUNCT
ejpam-5341	23	21	i	i	NOUN
ejpam-5341	23	22	)	)	PUNCT
ejpam-5341	23	23	every	every	DET
ejpam-5341	23	24	uniquely	uniquely	ADV
ejpam-5341	23	25	remotal	remotal	ADJ
ejpam-5341	23	26	set	set	NOUN
ejpam-5341	23	27	is	be	AUX
ejpam-5341	23	28	a	a	DET
ejpam-5341	23	29	singleton	singleton	NOUN
ejpam-5341	23	30	.	.	PUNCT
ejpam-5341	24	1	(	(	PUNCT
ejpam-5341	24	2	ii	ii	NOUN
ejpam-5341	24	3	)	)	PUNCT
ejpam-5341	24	4	every	every	DET
ejpam-5341	24	5	uniquely	uniquely	ADV
ejpam-5341	24	6	proximinal	proximinal	ADJ
ejpam-5341	24	7	set	set	NOUN
ejpam-5341	24	8	in	in	ADP
ejpam-5341	24	9	a	a	DET
ejpam-5341	24	10	hilbert	hilbert	NOUN
ejpam-5341	24	11	space	space	NOUN
ejpam-5341	24	12	h	h	NOUN
ejpam-5341	24	13	is	be	AUX
ejpam-5341	24	14	convex	convex	ADJ
ejpam-5341	24	15	.	.	PUNCT
ejpam-5341	25	1	since	since	SCONJ
ejpam-5341	25	2	klee	klee	PROPN
ejpam-5341	25	3	’s	’s	PART
ejpam-5341	25	4	result	result	NOUN
ejpam-5341	25	5	,	,	PUNCT
ejpam-5341	25	6	considerable	considerable	ADJ
ejpam-5341	25	7	progress	progress	NOUN
ejpam-5341	25	8	has	have	AUX
ejpam-5341	25	9	been	be	AUX
ejpam-5341	25	10	made	make	VERB
ejpam-5341	25	11	toward	toward	ADP
ejpam-5341	25	12	resolving	resolve	VERB
ejpam-5341	25	13	this	this	DET
ejpam-5341	25	14	question	question	NOUN
ejpam-5341	25	15	,	,	PUNCT
ejpam-5341	25	16	with	with	ADP
ejpam-5341	25	17	many	many	ADJ
ejpam-5341	25	18	partial	partial	ADJ
ejpam-5341	25	19	results	result	NOUN
ejpam-5341	25	20	supporting	support	VERB
ejpam-5341	25	21	the	the	DET
ejpam-5341	25	22	conjecture	conjecture	NOUN
ejpam-5341	25	23	.	.	PUNCT
ejpam-5341	26	1	in	in	ADP
ejpam-5341	26	2	[	[	X
ejpam-5341	26	3	1	1	NUM
ejpam-5341	26	4	]	]	PUNCT
ejpam-5341	26	5	,	,	PUNCT
ejpam-5341	26	6	the	the	DET
ejpam-5341	26	7	following	follow	VERB
ejpam-5341	26	8	theorem	theorem	NOUN
ejpam-5341	26	9	was	be	AUX
ejpam-5341	26	10	established	establish	VERB
ejpam-5341	26	11	:	:	PUNCT
ejpam-5341	26	12	theorem	theorem	NOUN
ejpam-5341	26	13	1	1	NUM
ejpam-5341	26	14	(	(	PUNCT
ejpam-5341	26	15	[	[	X
ejpam-5341	26	16	1	1	NUM
ejpam-5341	26	17	]	]	NUM
ejpam-5341	26	18	)	)	PUNCT
ejpam-5341	26	19	.	.	PUNCT
ejpam-5341	27	1	every	every	DET
ejpam-5341	27	2	uniquely	uniquely	ADV
ejpam-5341	27	3	remotal	remotal	ADJ
ejpam-5341	27	4	set	set	NOUN
ejpam-5341	27	5	that	that	PRON
ejpam-5341	27	6	is	be	AUX
ejpam-5341	27	7	also	also	ADV
ejpam-5341	27	8	uniquely	uniquely	ADV
ejpam-5341	27	9	distant	distant	ADJ
ejpam-5341	27	10	is	be	AUX
ejpam-5341	27	11	a	a	DET
ejpam-5341	27	12	singleton	singleton	NOUN
ejpam-5341	27	13	.	.	PUNCT
ejpam-5341	28	1	this	this	DET
ejpam-5341	28	2	result	result	NOUN
ejpam-5341	28	3	represents	represent	VERB
ejpam-5341	28	4	the	the	DET
ejpam-5341	28	5	closest	close	ADJ
ejpam-5341	28	6	attempt	attempt	NOUN
ejpam-5341	28	7	to	to	ADP
ejpam-5341	28	8	date	date	NOUN
ejpam-5341	28	9	to	to	PART
ejpam-5341	28	10	resolve	resolve	VERB
ejpam-5341	28	11	the	the	DET
ejpam-5341	28	12	farthest	farth	ADJ
ejpam-5341	28	13	point	point	NOUN
ejpam-5341	28	14	problem	problem	NOUN
ejpam-5341	28	15	.	.	PUNCT
ejpam-5341	29	1	2	2	X
ejpam-5341	29	2	.	.	X
ejpam-5341	29	3	preliminaries	preliminary	NOUN
ejpam-5341	29	4	in	in	ADP
ejpam-5341	29	5	[	[	X
ejpam-5341	29	6	1	1	NUM
ejpam-5341	29	7	]	]	PUNCT
ejpam-5341	29	8	,	,	PUNCT
ejpam-5341	29	9	the	the	DET
ejpam-5341	29	10	following	follow	VERB
ejpam-5341	29	11	definition	definition	NOUN
ejpam-5341	29	12	and	and	CCONJ
ejpam-5341	29	13	result	result	NOUN
ejpam-5341	29	14	were	be	AUX
ejpam-5341	29	15	presented	present	VERB
ejpam-5341	29	16	:	:	PUNCT
ejpam-5341	29	17	definition	definition	NOUN
ejpam-5341	29	18	1	1	NUM
ejpam-5341	29	19	(	(	PUNCT
ejpam-5341	29	20	[	[	X
ejpam-5341	29	21	1	1	NUM
ejpam-5341	29	22	]	]	PUNCT
ejpam-5341	29	23	)	)	PUNCT
ejpam-5341	29	24	.	.	PUNCT
ejpam-5341	30	1	let	let	VERB
ejpam-5341	30	2	h	h	PRON
ejpam-5341	30	3	be	be	AUX
ejpam-5341	30	4	a	a	DET
ejpam-5341	30	5	hilbert	hilbert	NOUN
ejpam-5341	30	6	space	space	NOUN
ejpam-5341	30	7	,	,	PUNCT
ejpam-5341	30	8	and	and	CCONJ
ejpam-5341	30	9	let	let	VERB
ejpam-5341	30	10	e	e	PRON
ejpam-5341	30	11	⊆	⊆	NUM
ejpam-5341	30	12	h	h	NOUN
ejpam-5341	30	13	be	be	AUX
ejpam-5341	30	14	a	a	DET
ejpam-5341	30	15	closed	closed	ADJ
ejpam-5341	30	16	and	and	CCONJ
ejpam-5341	30	17	bounded	bound	VERB
ejpam-5341	30	18	subset	subset	NOUN
ejpam-5341	30	19	.	.	PUNCT
ejpam-5341	31	1	then	then	ADV
ejpam-5341	31	2	e	e	PROPN
ejpam-5341	31	3	is	be	AUX
ejpam-5341	31	4	said	say	VERB
ejpam-5341	31	5	to	to	PART
ejpam-5341	31	6	be	be	AUX
ejpam-5341	31	7	a	a	DET
ejpam-5341	31	8	uniquely	uniquely	ADV
ejpam-5341	31	9	distant	distant	ADJ
ejpam-5341	31	10	set	set	NOUN
ejpam-5341	31	11	in	in	ADP
ejpam-5341	31	12	h	h	NOUN
ejpam-5341	31	13	if	if	SCONJ
ejpam-5341	31	14	the	the	DET
ejpam-5341	31	15	following	follow	VERB
ejpam-5341	31	16	two	two	NUM
ejpam-5341	31	17	conditions	condition	NOUN
ejpam-5341	31	18	are	be	AUX
ejpam-5341	31	19	satisfied	satisfied	ADJ
ejpam-5341	31	20	:	:	PUNCT
ejpam-5341	31	21	(	(	PUNCT
ejpam-5341	31	22	i	i	NOUN
ejpam-5341	31	23	)	)	PUNCT
ejpam-5341	31	24	e	e	NOUN
ejpam-5341	31	25	is	be	AUX
ejpam-5341	31	26	uniquely	uniquely	ADV
ejpam-5341	31	27	remotal	remotal	ADJ
ejpam-5341	31	28	,	,	PUNCT
ejpam-5341	31	29	(	(	PUNCT
ejpam-5341	31	30	ii	ii	NOUN
ejpam-5341	31	31	)	)	PUNCT
ejpam-5341	31	32	if	if	SCONJ
ejpam-5341	31	33	x	x	SYM
ejpam-5341	31	34	∈	∈	PROPN
ejpam-5341	31	35	h	h	NOUN
ejpam-5341	31	36	and	and	CCONJ
ejpam-5341	31	37	y	y	PROPN
ejpam-5341	31	38	is	be	AUX
ejpam-5341	31	39	the	the	DET
ejpam-5341	31	40	farthest	farth	ADJ
ejpam-5341	31	41	point	point	NOUN
ejpam-5341	31	42	from	from	ADP
ejpam-5341	31	43	x	x	PROPN
ejpam-5341	31	44	∈	∈	PROPN
ejpam-5341	31	45	e	e	NOUN
ejpam-5341	31	46	,	,	PUNCT
ejpam-5341	31	47	then	then	ADV
ejpam-5341	31	48	for	for	ADP
ejpam-5341	31	49	every	every	DET
ejpam-5341	31	50	ϵ	ϵ	PROPN
ejpam-5341	31	51	>	>	X
ejpam-5341	31	52	0	0	NUM
ejpam-5341	31	53	,	,	PUNCT
ejpam-5341	31	54	there	there	PRON
ejpam-5341	31	55	exists	exist	VERB
ejpam-5341	31	56	a	a	DET
ejpam-5341	31	57	δ	δ	PROPN
ejpam-5341	31	58	>	>	X
ejpam-5341	31	59	0	0	NUM
ejpam-5341	32	1	such	such	ADJ
ejpam-5341	32	2	that	that	SCONJ
ejpam-5341	32	3	d(x	d(x	PROPN
ejpam-5341	32	4	,	,	PUNCT
ejpam-5341	32	5	e	e	PROPN
ejpam-5341	32	6	\b(y	\b(y	PROPN
ejpam-5341	32	7	,	,	PUNCT
ejpam-5341	32	8	δ	δ	PROPN
ejpam-5341	32	9	)	)	PUNCT
ejpam-5341	32	10	)	)	PUNCT
ejpam-5341	32	11	≤	≤	NUM
ejpam-5341	32	12	d(x	d(x	NOUN
ejpam-5341	32	13	,	,	PUNCT
ejpam-5341	32	14	e)−	e)−	PROPN
ejpam-5341	32	15	ϵ.	ϵ.	NOUN
ejpam-5341	32	16	the	the	DET
ejpam-5341	32	17	main	main	ADJ
ejpam-5341	32	18	result	result	NOUN
ejpam-5341	32	19	in	in	ADP
ejpam-5341	32	20	[	[	X
ejpam-5341	32	21	1	1	NUM
ejpam-5341	32	22	]	]	PUNCT
ejpam-5341	32	23	was	be	AUX
ejpam-5341	32	24	as	as	SCONJ
ejpam-5341	32	25	follows	follow	VERB
ejpam-5341	32	26	:	:	PUNCT
ejpam-5341	32	27	theorem	theorem	NOUN
ejpam-5341	32	28	2	2	NUM
ejpam-5341	32	29	(	(	PUNCT
ejpam-5341	32	30	[	[	X
ejpam-5341	32	31	1	1	NUM
ejpam-5341	32	32	]	]	NUM
ejpam-5341	32	33	)	)	PUNCT
ejpam-5341	32	34	.	.	PUNCT
ejpam-5341	33	1	every	every	DET
ejpam-5341	33	2	uniquely	uniquely	ADV
ejpam-5341	33	3	distant	distant	ADJ
ejpam-5341	33	4	set	set	NOUN
ejpam-5341	33	5	in	in	ADP
ejpam-5341	33	6	h	h	NOUN
ejpam-5341	33	7	is	be	AUX
ejpam-5341	33	8	a	a	DET
ejpam-5341	33	9	singleton	singleton	NOUN
ejpam-5341	33	10	.	.	PUNCT
ejpam-5341	34	1	in	in	ADP
ejpam-5341	34	2	this	this	DET
ejpam-5341	34	3	paper	paper	NOUN
ejpam-5341	34	4	,	,	PUNCT
ejpam-5341	34	5	we	we	PRON
ejpam-5341	34	6	prove	prove	VERB
ejpam-5341	34	7	that	that	SCONJ
ejpam-5341	34	8	theorem	theorem	VERB
ejpam-5341	34	9	2	2	NUM
ejpam-5341	34	10	holds	hold	VERB
ejpam-5341	34	11	true	true	ADJ
ejpam-5341	34	12	for	for	ADP
ejpam-5341	34	13	uniquely	uniquely	ADV
ejpam-5341	34	14	remotal	remotal	ADJ
ejpam-5341	34	15	sets	set	NOUN
ejpam-5341	34	16	in	in	ADP
ejpam-5341	34	17	h	h	NOUN
ejpam-5341	34	18	,	,	PUNCT
ejpam-5341	34	19	without	without	ADP
ejpam-5341	34	20	requiring	require	VERB
ejpam-5341	34	21	condition	condition	NOUN
ejpam-5341	34	22	(	(	PUNCT
ejpam-5341	34	23	ii	ii	NOUN
ejpam-5341	34	24	)	)	PUNCT
ejpam-5341	34	25	in	in	ADP
ejpam-5341	34	26	definition	definition	NOUN
ejpam-5341	34	27	1	1	NUM
ejpam-5341	34	28	.	.	PUNCT
ejpam-5341	35	1	this	this	PRON
ejpam-5341	35	2	effectively	effectively	ADV
ejpam-5341	35	3	proves	prove	VERB
ejpam-5341	35	4	the	the	DET
ejpam-5341	35	5	farthest	farth	ADJ
ejpam-5341	35	6	point	point	NOUN
ejpam-5341	35	7	conjecture	conjecture	NOUN
ejpam-5341	35	8	.	.	PUNCT
ejpam-5341	36	1	r	r	NOUN
ejpam-5341	36	2	khalil	khalil	PROPN
ejpam-5341	36	3	et	et	PROPN
ejpam-5341	36	4	al	al	PROPN
ejpam-5341	36	5	.	.	PUNCT
ejpam-5341	36	6	/	/	SYM
ejpam-5341	36	7	eur	eur	PROPN
ejpam-5341	36	8	.	.	PUNCT
ejpam-5341	37	1	j.	j.	PROPN
ejpam-5341	37	2	pure	pure	PROPN
ejpam-5341	37	3	appl	appl	PROPN
ejpam-5341	37	4	.	.	PROPN
ejpam-5341	37	5	math	math	PROPN
ejpam-5341	37	6	,	,	PUNCT
ejpam-5341	37	7	17	17	NUM
ejpam-5341	37	8	(	(	PUNCT
ejpam-5341	37	9	4	4	NUM
ejpam-5341	37	10	)	)	PUNCT
ejpam-5341	37	11	(	(	PUNCT
ejpam-5341	37	12	2024	2024	NUM
ejpam-5341	37	13	)	)	PUNCT
ejpam-5341	37	14	,	,	PUNCT
ejpam-5341	37	15	2985	2985	NUM
ejpam-5341	37	16	-	-	SYM
ejpam-5341	37	17	2989	2989	NUM
ejpam-5341	37	18	2987	2987	NUM
ejpam-5341	37	19	3	3	NUM
ejpam-5341	37	20	.	.	PUNCT
ejpam-5341	37	21	main	main	ADJ
ejpam-5341	37	22	result	result	NOUN
ejpam-5341	37	23	in	in	ADP
ejpam-5341	37	24	this	this	DET
ejpam-5341	37	25	section	section	NOUN
ejpam-5341	37	26	,	,	PUNCT
ejpam-5341	37	27	using	use	VERB
ejpam-5341	37	28	the	the	DET
ejpam-5341	37	29	result	result	NOUN
ejpam-5341	37	30	from	from	ADP
ejpam-5341	37	31	[	[	X
ejpam-5341	37	32	1	1	NUM
ejpam-5341	37	33	]	]	PUNCT
ejpam-5341	37	34	,	,	PUNCT
ejpam-5341	37	35	we	we	PRON
ejpam-5341	37	36	prove	prove	VERB
ejpam-5341	37	37	the	the	DET
ejpam-5341	37	38	following	following	NOUN
ejpam-5341	37	39	:	:	PUNCT
ejpam-5341	37	40	every	every	DET
ejpam-5341	37	41	uniquely	uniquely	ADV
ejpam-5341	37	42	remotal	remotal	ADJ
ejpam-5341	37	43	set	set	NOUN
ejpam-5341	37	44	in	in	ADP
ejpam-5341	37	45	h	h	NOUN
ejpam-5341	37	46	is	be	AUX
ejpam-5341	37	47	a	a	DET
ejpam-5341	37	48	singleton	singleton	NOUN
ejpam-5341	37	49	.	.	PUNCT
ejpam-5341	38	1	consequently	consequently	ADV
ejpam-5341	38	2	,	,	PUNCT
ejpam-5341	38	3	by	by	ADP
ejpam-5341	38	4	klee	klee	PROPN
ejpam-5341	38	5	’s	’s	PART
ejpam-5341	38	6	result	result	NOUN
ejpam-5341	38	7	[	[	X
ejpam-5341	38	8	14	14	NUM
ejpam-5341	38	9	]	]	PUNCT
ejpam-5341	38	10	,	,	PUNCT
ejpam-5341	38	11	we	we	PRON
ejpam-5341	38	12	also	also	ADV
ejpam-5341	38	13	obtain	obtain	VERB
ejpam-5341	38	14	the	the	DET
ejpam-5341	38	15	result	result	NOUN
ejpam-5341	38	16	:	:	PUNCT
ejpam-5341	38	17	every	every	DET
ejpam-5341	38	18	uniquely	uniquely	ADV
ejpam-5341	38	19	proximinal	proximinal	ADJ
ejpam-5341	38	20	set	set	NOUN
ejpam-5341	38	21	in	in	ADP
ejpam-5341	38	22	a	a	DET
ejpam-5341	38	23	hilbert	hilbert	NOUN
ejpam-5341	38	24	space	space	NOUN
ejpam-5341	38	25	is	be	AUX
ejpam-5341	38	26	convex	convex	PROPN
ejpam-5341	38	27	.	.	PUNCT
ejpam-5341	39	1	theorem	theorem	NOUN
ejpam-5341	39	2	3	3	NUM
ejpam-5341	39	3	.	.	PUNCT
ejpam-5341	40	1	every	every	DET
ejpam-5341	40	2	convex	convex	NOUN
ejpam-5341	40	3	uniquely	uniquely	ADV
ejpam-5341	40	4	remotal	remotal	ADJ
ejpam-5341	40	5	set	set	NOUN
ejpam-5341	40	6	in	in	ADP
ejpam-5341	40	7	a	a	DET
ejpam-5341	40	8	hilbert	hilbert	NOUN
ejpam-5341	40	9	space	space	NOUN
ejpam-5341	40	10	h	h	NOUN
ejpam-5341	40	11	is	be	AUX
ejpam-5341	40	12	uniquely	uniquely	ADV
ejpam-5341	40	13	distant	distant	ADJ
ejpam-5341	40	14	.	.	PUNCT
ejpam-5341	41	1	proof	proof	NOUN
ejpam-5341	41	2	.	.	PUNCT
ejpam-5341	42	1	consider	consider	VERB
ejpam-5341	42	2	the	the	DET
ejpam-5341	42	3	statement	statement	NOUN
ejpam-5341	42	4	q	q	NOUN
ejpam-5341	42	5	:	:	PUNCT
ejpam-5341	42	6	”	"	PUNCT
ejpam-5341	42	7	for	for	ADP
ejpam-5341	42	8	every	every	DET
ejpam-5341	42	9	ϵ	ϵ	PROPN
ejpam-5341	42	10	>	>	X
ejpam-5341	42	11	0	0	NUM
ejpam-5341	42	12	,	,	PUNCT
ejpam-5341	42	13	there	there	PRON
ejpam-5341	42	14	exists	exist	VERB
ejpam-5341	42	15	a	a	DET
ejpam-5341	42	16	δ	δ	PROPN
ejpam-5341	42	17	>	>	X
ejpam-5341	42	18	0	0	NUM
ejpam-5341	42	19	such	such	ADJ
ejpam-5341	42	20	that	that	SCONJ
ejpam-5341	42	21	d(x	d(x	PROPN
ejpam-5341	42	22	,	,	PUNCT
ejpam-5341	43	1	e	e	PROPN
ejpam-5341	43	2	\b(y	\b(y	PROPN
ejpam-5341	43	3	,	,	PUNCT
ejpam-5341	43	4	δ	δ	PROPN
ejpam-5341	43	5	)	)	PUNCT
ejpam-5341	43	6	)	)	PUNCT
ejpam-5341	43	7	≤	≤	NUM
ejpam-5341	43	8	d(x	d(x	NOUN
ejpam-5341	43	9	,	,	PUNCT
ejpam-5341	43	10	e)−	e)−	PROPN
ejpam-5341	43	11	ϵ.	ϵ.	NOUN
ejpam-5341	43	12	”	"	PUNCT
ejpam-5341	43	13	here	here	ADV
ejpam-5341	43	14	,	,	PUNCT
ejpam-5341	43	15	x	x	PROPN
ejpam-5341	43	16	∈	∈	PROPN
ejpam-5341	43	17	h	h	NOUN
ejpam-5341	43	18	and	and	CCONJ
ejpam-5341	43	19	y	y	PROPN
ejpam-5341	43	20	=	=	SYM
ejpam-5341	43	21	p	p	X
ejpam-5341	43	22	(	(	PUNCT
ejpam-5341	43	23	x	x	X
ejpam-5341	43	24	,	,	PUNCT
ejpam-5341	43	25	e	e	NOUN
ejpam-5341	43	26	)	)	PUNCT
ejpam-5341	43	27	.	.	PUNCT
ejpam-5341	44	1	to	to	PART
ejpam-5341	44	2	prove	prove	VERB
ejpam-5341	44	3	the	the	DET
ejpam-5341	44	4	theorem	theorem	NOUN
ejpam-5341	44	5	,	,	PUNCT
ejpam-5341	44	6	we	we	PRON
ejpam-5341	44	7	show	show	VERB
ejpam-5341	44	8	that	that	SCONJ
ejpam-5341	44	9	q	q	PROPN
ejpam-5341	44	10	holds	hold	VERB
ejpam-5341	44	11	for	for	ADP
ejpam-5341	44	12	any	any	DET
ejpam-5341	44	13	uniquely	uniquely	ADV
ejpam-5341	44	14	remotal	remotal	ADJ
ejpam-5341	44	15	set	set	NOUN
ejpam-5341	44	16	e	e	PROPN
ejpam-5341	44	17	⊂	⊂	PROPN
ejpam-5341	44	18	h.	h.	PROPN
ejpam-5341	44	19	this	this	PRON
ejpam-5341	44	20	is	be	AUX
ejpam-5341	44	21	achieved	achieve	VERB
ejpam-5341	44	22	by	by	ADP
ejpam-5341	44	23	demonstrating	demonstrate	VERB
ejpam-5341	44	24	that	that	SCONJ
ejpam-5341	44	25	the	the	DET
ejpam-5341	44	26	negation	negation	NOUN
ejpam-5341	44	27	of	of	ADP
ejpam-5341	44	28	q	q	NOUN
ejpam-5341	44	29	,	,	PUNCT
ejpam-5341	44	30	denoted	denote	VERB
ejpam-5341	44	31	∼	∼	NOUN
ejpam-5341	44	32	q	q	NOUN
ejpam-5341	44	33	,	,	PUNCT
ejpam-5341	44	34	is	be	AUX
ejpam-5341	44	35	false	false	ADJ
ejpam-5341	44	36	for	for	ADP
ejpam-5341	44	37	any	any	DET
ejpam-5341	44	38	uniquely	uniquely	ADV
ejpam-5341	44	39	remotal	remotal	ADJ
ejpam-5341	44	40	set	set	NOUN
ejpam-5341	44	41	in	in	ADP
ejpam-5341	44	42	h.	h.	PROPN
ejpam-5341	44	43	let	let	VERB
ejpam-5341	44	44	e	e	PRON
ejpam-5341	44	45	⊆	⊆	NUM
ejpam-5341	44	46	h	h	NOUN
ejpam-5341	44	47	be	be	AUX
ejpam-5341	44	48	a	a	DET
ejpam-5341	44	49	closed	closed	ADJ
ejpam-5341	44	50	,	,	PUNCT
ejpam-5341	44	51	convex	convex	NOUN
ejpam-5341	44	52	,	,	PUNCT
ejpam-5341	44	53	and	and	CCONJ
ejpam-5341	44	54	bounded	bound	VERB
ejpam-5341	44	55	subset	subset	NOUN
ejpam-5341	44	56	that	that	PRON
ejpam-5341	44	57	is	be	AUX
ejpam-5341	44	58	uniquely	uniquely	ADV
ejpam-5341	44	59	remotal	remotal	ADJ
ejpam-5341	44	60	.	.	PUNCT
ejpam-5341	45	1	by	by	ADP
ejpam-5341	45	2	definition	definition	NOUN
ejpam-5341	45	3	1	1	NUM
ejpam-5341	45	4	,	,	PUNCT
ejpam-5341	45	5	uniquely	uniquely	ADV
ejpam-5341	45	6	distant	distant	ADJ
ejpam-5341	45	7	implies	imply	VERB
ejpam-5341	45	8	that	that	SCONJ
ejpam-5341	45	9	if	if	SCONJ
ejpam-5341	45	10	x	x	PROPN
ejpam-5341	45	11	∈	∈	PROPN
ejpam-5341	45	12	h	h	NOUN
ejpam-5341	45	13	,	,	PUNCT
ejpam-5341	45	14	and	and	CCONJ
ejpam-5341	45	15	y	y	PROPN
ejpam-5341	45	16	is	be	AUX
ejpam-5341	45	17	the	the	DET
ejpam-5341	45	18	farthest	farth	ADJ
ejpam-5341	45	19	point	point	NOUN
ejpam-5341	45	20	from	from	ADP
ejpam-5341	45	21	x	x	PUNCT
ejpam-5341	45	22	in	in	ADP
ejpam-5341	45	23	e	e	NOUN
ejpam-5341	45	24	,	,	PUNCT
ejpam-5341	45	25	then	then	ADV
ejpam-5341	45	26	d(x	d(x	PROPN
ejpam-5341	45	27	,	,	PUNCT
ejpam-5341	45	28	e	e	NOUN
ejpam-5341	45	29	)	)	PUNCT
ejpam-5341	45	30	=	=	SYM
ejpam-5341	45	31	r	r	NOUN
ejpam-5341	45	32	=	=	PUNCT
ejpam-5341	45	33	∥x−	∥x−	PROPN
ejpam-5341	45	34	y∥	y∥	NOUN
ejpam-5341	45	35	.	.	PUNCT
ejpam-5341	46	1	(	(	PUNCT
ejpam-5341	46	2	2	2	X
ejpam-5341	46	3	)	)	PUNCT
ejpam-5341	46	4	moreover	moreover	ADV
ejpam-5341	46	5	,	,	PUNCT
ejpam-5341	46	6	for	for	ADP
ejpam-5341	46	7	every	every	DET
ejpam-5341	46	8	ϵ	ϵ	X
ejpam-5341	46	9	>	>	X
ejpam-5341	46	10	0	0	NUM
ejpam-5341	46	11	,	,	PUNCT
ejpam-5341	46	12	there	there	PRON
ejpam-5341	46	13	exists	exist	VERB
ejpam-5341	46	14	a	a	DET
ejpam-5341	46	15	δ	δ	PROPN
ejpam-5341	46	16	>	>	X
ejpam-5341	46	17	0	0	NUM
ejpam-5341	46	18	such	such	ADJ
ejpam-5341	46	19	that	that	SCONJ
ejpam-5341	46	20	d(x	d(x	PROPN
ejpam-5341	46	21	,	,	PUNCT
ejpam-5341	47	1	e	e	PROPN
ejpam-5341	47	2	\b(y	\b(y	PROPN
ejpam-5341	47	3	,	,	PUNCT
ejpam-5341	47	4	δ	δ	PROPN
ejpam-5341	47	5	)	)	PUNCT
ejpam-5341	47	6	)	)	PUNCT
ejpam-5341	47	7	≤	≤	NUM
ejpam-5341	47	8	d(x	d(x	NOUN
ejpam-5341	47	9	,	,	PUNCT
ejpam-5341	47	10	e)−	e)−	PROPN
ejpam-5341	47	11	ϵ	ϵ	NOUN
ejpam-5341	47	12	=	=	PUNCT
ejpam-5341	47	13	r	r	NOUN
ejpam-5341	47	14	−	−	NOUN
ejpam-5341	48	1	ϵ.	ϵ.	NOUN
ejpam-5341	48	2	now	now	ADV
ejpam-5341	48	3	,	,	PUNCT
ejpam-5341	48	4	∼	∼	NOUN
ejpam-5341	48	5	q	q	NOUN
ejpam-5341	48	6	states	state	NOUN
ejpam-5341	48	7	that	that	SCONJ
ejpam-5341	48	8	there	there	PRON
ejpam-5341	48	9	exists	exist	VERB
ejpam-5341	48	10	an	an	DET
ejpam-5341	48	11	ϵ	ϵ	NOUN
ejpam-5341	48	12	,	,	PUNCT
ejpam-5341	48	13	with	with	ADP
ejpam-5341	48	14	0	0	NUM
ejpam-5341	48	15	<	<	X
ejpam-5341	48	16	ϵ	ϵ	X
ejpam-5341	48	17	<	<	X
ejpam-5341	48	18	r	r	NOUN
ejpam-5341	48	19	,	,	PUNCT
ejpam-5341	48	20	such	such	ADJ
ejpam-5341	48	21	that	that	PRON
ejpam-5341	48	22	for	for	ADP
ejpam-5341	48	23	every	every	DET
ejpam-5341	48	24	δ	δ	PROPN
ejpam-5341	48	25	>	>	X
ejpam-5341	48	26	0	0	PROPN
ejpam-5341	48	27	,	,	PUNCT
ejpam-5341	48	28	one	one	NUM
ejpam-5341	48	29	has	have	VERB
ejpam-5341	48	30	d(x	d(x	PROPN
ejpam-5341	48	31	,	,	PUNCT
ejpam-5341	48	32	e	e	PROPN
ejpam-5341	48	33	\b(y	\b(y	PROPN
ejpam-5341	48	34	,	,	PUNCT
ejpam-5341	48	35	δ	δ	PROPN
ejpam-5341	48	36	)	)	PUNCT
ejpam-5341	48	37	)	)	PUNCT
ejpam-5341	48	38	>	>	PUNCT
ejpam-5341	49	1	r	r	NOUN
ejpam-5341	49	2	−	−	NOUN
ejpam-5341	49	3	ϵ.	ϵ.	NOUN
ejpam-5341	49	4	assume	assume	VERB
ejpam-5341	49	5	without	without	ADP
ejpam-5341	49	6	loss	loss	NOUN
ejpam-5341	49	7	of	of	ADP
ejpam-5341	49	8	generality	generality	NOUN
ejpam-5341	49	9	that	that	PRON
ejpam-5341	49	10	x	x	PUNCT
ejpam-5341	49	11	belongs	belong	VERB
ejpam-5341	49	12	to	to	ADP
ejpam-5341	49	13	the	the	DET
ejpam-5341	49	14	boundary	boundary	NOUN
ejpam-5341	49	15	of	of	ADP
ejpam-5341	49	16	e	e	NOUN
ejpam-5341	49	17	,	,	PUNCT
ejpam-5341	49	18	and	and	CCONJ
ejpam-5341	49	19	let	let	VERB
ejpam-5341	49	20	d(y	d(y	NOUN
ejpam-5341	49	21	,	,	PUNCT
ejpam-5341	49	22	e	e	NOUN
ejpam-5341	49	23	)	)	PUNCT
ejpam-5341	49	24	=	=	SYM
ejpam-5341	50	1	s.	s.	PROPN
ejpam-5341	50	2	then	then	ADV
ejpam-5341	50	3	,	,	PUNCT
ejpam-5341	50	4	clearly	clearly	ADV
ejpam-5341	50	5	s	s	VERB
ejpam-5341	50	6	≥	≥	PROPN
ejpam-5341	50	7	r.	r.	NOUN
ejpam-5341	50	8	define	define	VERB
ejpam-5341	50	9	δn	δn	PROPN
ejpam-5341	50	10	=	=	SYM
ejpam-5341	50	11	s	s	PART
ejpam-5341	50	12	−	−	PROPN
ejpam-5341	50	13	1	1	NUM
ejpam-5341	50	14	n	n	NOUN
ejpam-5341	50	15	,	,	PUNCT
ejpam-5341	50	16	and	and	CCONJ
ejpam-5341	50	17	set	set	VERB
ejpam-5341	50	18	bn	bn	NOUN
ejpam-5341	50	19	=	=	SYM
ejpam-5341	50	20	b(y	b(y	PROPN
ejpam-5341	50	21	,	,	PUNCT
ejpam-5341	50	22	δn	δn	NOUN
ejpam-5341	50	23	)	)	PUNCT
ejpam-5341	50	24	.	.	PUNCT
ejpam-5341	51	1	let	let	VERB
ejpam-5341	51	2	en	en	X
ejpam-5341	51	3	=	=	SYM
ejpam-5341	51	4	e	e	PROPN
ejpam-5341	51	5	\bn	\bn	PROPN
ejpam-5341	51	6	.	.	PUNCT
ejpam-5341	52	1	then	then	ADV
ejpam-5341	52	2	,	,	PUNCT
ejpam-5341	52	3	it	it	PRON
ejpam-5341	52	4	is	be	AUX
ejpam-5341	52	5	evident	evident	ADJ
ejpam-5341	52	6	that	that	SCONJ
ejpam-5341	52	7	:	:	PUNCT
ejpam-5341	52	8	b1	b1	VERB
ejpam-5341	52	9	⊆	⊆	NUM
ejpam-5341	52	10	b2	b2	NOUN
ejpam-5341	52	11	⊆	⊆	NUM
ejpam-5341	52	12	.	.	PUNCT
ejpam-5341	52	13	.	.	PUNCT
ejpam-5341	52	14	.	.	PUNCT
ejpam-5341	53	1	⊆	⊆	NUM
ejpam-5341	53	2	bn	bn	NUM
ejpam-5341	53	3	⊆	⊆	NUM
ejpam-5341	53	4	.	.	PUNCT
ejpam-5341	53	5	.	.	PUNCT
ejpam-5341	54	1	.	.	PUNCT
ejpam-5341	55	1	and	and	CCONJ
ejpam-5341	55	2	e1	e1	PROPN
ejpam-5341	55	3	⊇	⊇	PROPN
ejpam-5341	55	4	e2	e2	PROPN
ejpam-5341	55	5	⊇	⊇	PROPN
ejpam-5341	55	6	.	.	PUNCT
ejpam-5341	55	7	.	.	PUNCT
ejpam-5341	55	8	.	.	PUNCT
ejpam-5341	56	1	⊇	⊇	PROPN
ejpam-5341	56	2	en	en	PROPN
ejpam-5341	56	3	⊇	⊇	PROPN
ejpam-5341	56	4	.	.	PUNCT
ejpam-5341	56	5	.	.	PUNCT
ejpam-5341	56	6	.	.	PUNCT
ejpam-5341	57	1	further	far	ADV
ejpam-5341	57	2	,	,	PUNCT
ejpam-5341	57	3	we	we	PRON
ejpam-5341	57	4	have	have	VERB
ejpam-5341	57	5	:	:	PUNCT
ejpam-5341	58	1	∪bn	∪bn	PROPN
ejpam-5341	58	2	=	=	SYM
ejpam-5341	58	3	b(y	b(y	PROPN
ejpam-5341	58	4	,	,	PUNCT
ejpam-5341	58	5	s	s	PART
ejpam-5341	58	6	)	)	PUNCT
ejpam-5341	58	7	and	and	CCONJ
ejpam-5341	58	8	∩	∩	PROPN
ejpam-5341	58	9	en	en	X
ejpam-5341	58	10	=	=	NOUN
ejpam-5341	58	11	∅	∅	NOUN
ejpam-5341	58	12	(	(	PUNCT
ejpam-5341	58	13	3	3	X
ejpam-5341	58	14	)	)	PUNCT
ejpam-5341	58	15	now	now	ADV
ejpam-5341	58	16	,	,	PUNCT
ejpam-5341	58	17	d(x	d(x	PROPN
ejpam-5341	58	18	,	,	PUNCT
ejpam-5341	58	19	en	en	X
ejpam-5341	58	20	)	)	PUNCT
ejpam-5341	58	21	≥	≥	NOUN
ejpam-5341	58	22	d(x	d(x	PROPN
ejpam-5341	58	23	,	,	PUNCT
ejpam-5341	58	24	en+1	en+1	NUM
ejpam-5341	58	25	)	)	PUNCT
ejpam-5341	58	26	for	for	ADP
ejpam-5341	58	27	all	all	DET
ejpam-5341	58	28	n.	n.	NOUN
ejpam-5341	58	29	thus	thus	ADV
ejpam-5341	58	30	,	,	PUNCT
ejpam-5341	58	31	by	by	ADP
ejpam-5341	58	32	(	(	PUNCT
ejpam-5341	58	33	3	3	NUM
ejpam-5341	58	34	)	)	PUNCT
ejpam-5341	58	35	,	,	PUNCT
ejpam-5341	58	36	we	we	PRON
ejpam-5341	58	37	have	have	VERB
ejpam-5341	58	38	d(x	d(x	NOUN
ejpam-5341	58	39	,	,	PUNCT
ejpam-5341	58	40	en	en	X
ejpam-5341	58	41	)	)	PUNCT
ejpam-5341	58	42	→	→	SYM
ejpam-5341	58	43	0	0	NUM
ejpam-5341	58	44	as	as	ADP
ejpam-5341	58	45	n	n	PROPN
ejpam-5341	58	46	→	→	SYM
ejpam-5341	58	47	∞.	∞.	PROPN
ejpam-5341	58	48	it	it	PRON
ejpam-5341	58	49	follows	follow	VERB
ejpam-5341	58	50	that	that	SCONJ
ejpam-5341	58	51	d(x	d(x	NOUN
ejpam-5341	58	52	,	,	PUNCT
ejpam-5341	58	53	e	e	PROPN
ejpam-5341	58	54	\bn(y	\bn(y	PROPN
ejpam-5341	58	55	,	,	PUNCT
ejpam-5341	58	56	δ	δ	PROPN
ejpam-5341	58	57	)	)	PUNCT
ejpam-5341	58	58	)	)	PUNCT
ejpam-5341	59	1	=	=	SYM
ejpam-5341	59	2	d(x	d(x	PROPN
ejpam-5341	59	3	,	,	PUNCT
ejpam-5341	59	4	en	en	X
ejpam-5341	59	5	)	)	PUNCT
ejpam-5341	59	6	>	>	PUNCT
ejpam-5341	60	1	r	r	NOUN
ejpam-5341	60	2	−	−	PROPN
ejpam-5341	60	3	ϵ	ϵ	X
ejpam-5341	60	4	>	>	X
ejpam-5341	60	5	0	0	NUM
ejpam-5341	60	6	,	,	PUNCT
ejpam-5341	60	7	for	for	ADP
ejpam-5341	60	8	all	all	DET
ejpam-5341	60	9	n.	n.	NOUN
ejpam-5341	60	10	(	(	PUNCT
ejpam-5341	60	11	4	4	NUM
ejpam-5341	60	12	)	)	PUNCT
ejpam-5341	60	13	hence	hence	ADV
ejpam-5341	60	14	,	,	PUNCT
ejpam-5341	60	15	lim	lim	PROPN
ejpam-5341	60	16	n→∞	n→∞	NUM
ejpam-5341	60	17	d(x	d(x	PROPN
ejpam-5341	60	18	,	,	PUNCT
ejpam-5341	60	19	en	en	X
ejpam-5341	60	20	)	)	PUNCT
ejpam-5341	60	21	>	>	PUNCT
ejpam-5341	61	1	r	r	NOUN
ejpam-5341	61	2	−	−	NOUN
ejpam-5341	61	3	ϵ	ϵ	X
ejpam-5341	61	4	>	>	X
ejpam-5341	61	5	0	0	PUNCT
ejpam-5341	62	1	so	so	ADV
ejpam-5341	62	2	,	,	PUNCT
ejpam-5341	62	3	we	we	PRON
ejpam-5341	62	4	obtain	obtain	VERB
ejpam-5341	62	5	:	:	PUNCT
ejpam-5341	62	6	references	reference	NOUN
ejpam-5341	62	7	2988	2988	NUM
ejpam-5341	62	8	limd(x	limd(x	PROPN
ejpam-5341	62	9	,	,	PUNCT
ejpam-5341	62	10	en	en	X
ejpam-5341	62	11	)	)	PUNCT
ejpam-5341	62	12	=	=	SYM
ejpam-5341	62	13	0	0	PUNCT
ejpam-5341	62	14	>	>	PUNCT
ejpam-5341	62	15	r	r	NOUN
ejpam-5341	62	16	−	−	NOUN
ejpam-5341	62	17	ϵ	ϵ	X
ejpam-5341	62	18	>	>	X
ejpam-5341	62	19	0	0	PUNCT
ejpam-5341	63	1	thus	thus	ADV
ejpam-5341	63	2	,	,	PUNCT
ejpam-5341	63	3	0	0	NUM
ejpam-5341	63	4	>	>	X
ejpam-5341	63	5	0	0	NUM
ejpam-5341	63	6	,	,	PUNCT
ejpam-5341	63	7	which	which	PRON
ejpam-5341	63	8	is	be	AUX
ejpam-5341	63	9	a	a	DET
ejpam-5341	63	10	contradiction	contradiction	NOUN
ejpam-5341	63	11	.	.	PUNCT
ejpam-5341	64	1	therefore	therefore	ADV
ejpam-5341	64	2	,	,	PUNCT
ejpam-5341	64	3	∼	∼	NOUN
ejpam-5341	64	4	q	q	NOUN
ejpam-5341	64	5	is	be	AUX
ejpam-5341	64	6	false	false	ADJ
ejpam-5341	64	7	,	,	PUNCT
ejpam-5341	64	8	and	and	CCONJ
ejpam-5341	64	9	q	q	NOUN
ejpam-5341	64	10	is	be	AUX
ejpam-5341	64	11	true	true	ADJ
ejpam-5341	64	12	.	.	PUNCT
ejpam-5341	65	1	this	this	PRON
ejpam-5341	65	2	implies	imply	VERB
ejpam-5341	65	3	that	that	SCONJ
ejpam-5341	65	4	every	every	DET
ejpam-5341	65	5	uniquely	uniquely	ADV
ejpam-5341	65	6	remotal	remotal	ADJ
ejpam-5341	65	7	set	set	NOUN
ejpam-5341	65	8	in	in	ADP
ejpam-5341	65	9	h	h	NOUN
ejpam-5341	65	10	is	be	AUX
ejpam-5341	65	11	a	a	DET
ejpam-5341	65	12	uniquely	uniquely	ADV
ejpam-5341	65	13	distant	distant	ADJ
ejpam-5341	65	14	set	set	NOUN
ejpam-5341	65	15	.	.	PUNCT
ejpam-5341	66	1	a	a	DET
ejpam-5341	66	2	key	key	ADJ
ejpam-5341	66	3	corollary	corollary	NOUN
ejpam-5341	66	4	of	of	ADP
ejpam-5341	66	5	this	this	DET
ejpam-5341	66	6	result	result	NOUN
ejpam-5341	66	7	is	be	AUX
ejpam-5341	66	8	:	:	PUNCT
ejpam-5341	66	9	corollary	corollary	ADJ
ejpam-5341	66	10	1	1	NUM
ejpam-5341	66	11	.	.	PUNCT
ejpam-5341	67	1	every	every	DET
ejpam-5341	67	2	uniquely	uniquely	ADV
ejpam-5341	67	3	remotal	remotal	ADJ
ejpam-5341	67	4	set	set	NOUN
ejpam-5341	67	5	in	in	ADP
ejpam-5341	67	6	h	h	NOUN
ejpam-5341	67	7	is	be	AUX
ejpam-5341	67	8	a	a	DET
ejpam-5341	67	9	singleton	singleton	NOUN
ejpam-5341	67	10	.	.	PUNCT
ejpam-5341	68	1	proof	proof	NOUN
ejpam-5341	68	2	.	.	PUNCT
ejpam-5341	69	1	the	the	DET
ejpam-5341	69	2	corollary	corollary	NOUN
ejpam-5341	69	3	follows	follow	VERB
ejpam-5341	69	4	directly	directly	ADV
ejpam-5341	69	5	from	from	ADP
ejpam-5341	69	6	theorem	theorem	ADJ
ejpam-5341	69	7	2	2	NUM
ejpam-5341	69	8	and	and	CCONJ
ejpam-5341	69	9	theorem	theorem	VERB
ejpam-5341	69	10	3	3	NUM
ejpam-5341	69	11	.	.	NOUN
ejpam-5341	69	12	remark	remark	NOUN
ejpam-5341	69	13	1	1	NUM
ejpam-5341	69	14	.	.	PUNCT
ejpam-5341	70	1	it	it	PRON
ejpam-5341	70	2	is	be	AUX
ejpam-5341	70	3	evident	evident	ADJ
ejpam-5341	70	4	that	that	SCONJ
ejpam-5341	70	5	constructing	construct	VERB
ejpam-5341	70	6	a	a	DET
ejpam-5341	70	7	concrete	concrete	ADJ
ejpam-5341	70	8	example	example	NOUN
ejpam-5341	70	9	where	where	SCONJ
ejpam-5341	70	10	a	a	DET
ejpam-5341	70	11	uniquely	uniquely	ADV
ejpam-5341	70	12	remotal	remotal	ADJ
ejpam-5341	70	13	set	set	NOUN
ejpam-5341	70	14	in	in	ADP
ejpam-5341	70	15	a	a	DET
ejpam-5341	70	16	hilbert	hilbert	NOUN
ejpam-5341	70	17	space	space	NOUN
ejpam-5341	70	18	is	be	AUX
ejpam-5341	70	19	a	a	DET
ejpam-5341	70	20	singleton	singleton	NOUN
ejpam-5341	70	21	is	be	AUX
ejpam-5341	70	22	challenging	challenging	ADJ
ejpam-5341	70	23	.	.	PUNCT
ejpam-5341	71	1	however	however	ADV
ejpam-5341	71	2	,	,	PUNCT
ejpam-5341	71	3	we	we	PRON
ejpam-5341	71	4	provide	provide	VERB
ejpam-5341	71	5	a	a	DET
ejpam-5341	71	6	straightforward	straightforward	ADJ
ejpam-5341	71	7	example	example	NOUN
ejpam-5341	71	8	to	to	PART
ejpam-5341	71	9	help	help	VERB
ejpam-5341	71	10	the	the	DET
ejpam-5341	71	11	reader	reader	NOUN
ejpam-5341	71	12	grasp	grasp	VERB
ejpam-5341	71	13	the	the	DET
ejpam-5341	71	14	concept	concept	NOUN
ejpam-5341	71	15	more	more	ADV
ejpam-5341	71	16	easily	easily	ADV
ejpam-5341	71	17	and	and	CCONJ
ejpam-5341	71	18	to	to	PART
ejpam-5341	71	19	illustrate	illustrate	VERB
ejpam-5341	71	20	the	the	DET
ejpam-5341	71	21	underlying	underlie	VERB
ejpam-5341	71	22	principles	principle	NOUN
ejpam-5341	71	23	.	.	PUNCT
ejpam-5341	72	1	the	the	DET
ejpam-5341	72	2	following	follow	VERB
ejpam-5341	72	3	example	example	NOUN
ejpam-5341	72	4	illustrates	illustrate	VERB
ejpam-5341	72	5	that	that	SCONJ
ejpam-5341	72	6	a	a	DET
ejpam-5341	72	7	subset	subset	NOUN
ejpam-5341	72	8	of	of	ADP
ejpam-5341	72	9	r2	r2	NOUN
ejpam-5341	72	10	containing	contain	VERB
ejpam-5341	72	11	two	two	NUM
ejpam-5341	72	12	elements	element	NOUN
ejpam-5341	72	13	can	can	AUX
ejpam-5341	72	14	not	not	PART
ejpam-5341	72	15	be	be	AUX
ejpam-5341	72	16	uniquely	uniquely	ADV
ejpam-5341	72	17	remotal	remotal	ADJ
ejpam-5341	72	18	.	.	PUNCT
ejpam-5341	72	19	example	example	NOUN
ejpam-5341	73	1	1	1	NUM
ejpam-5341	73	2	.	.	PUNCT
ejpam-5341	73	3	let	let	VERB
ejpam-5341	73	4	m	m	VERB
ejpam-5341	73	5	=	=	PRON
ejpam-5341	73	6	{	{	PUNCT
ejpam-5341	73	7	x	x	NOUN
ejpam-5341	73	8	,	,	PUNCT
ejpam-5341	73	9	y	y	PROPN
ejpam-5341	73	10	}	}	PUNCT
ejpam-5341	73	11	,	,	PUNCT
ejpam-5341	73	12	where	where	SCONJ
ejpam-5341	73	13	x	x	X
ejpam-5341	73	14	̸=	̸=	PROPN
ejpam-5341	73	15	y	y	PROPN
ejpam-5341	73	16	,	,	PUNCT
ejpam-5341	73	17	be	be	AUX
ejpam-5341	73	18	any	any	DET
ejpam-5341	73	19	arbitrary	arbitrary	ADJ
ejpam-5341	73	20	subset	subset	NOUN
ejpam-5341	73	21	of	of	ADP
ejpam-5341	73	22	the	the	DET
ejpam-5341	73	23	hilbert	hilbert	NOUN
ejpam-5341	73	24	space	space	NOUN
ejpam-5341	73	25	r2	r2	NOUN
ejpam-5341	73	26	.	.	PUNCT
ejpam-5341	74	1	if	if	SCONJ
ejpam-5341	74	2	m	m	NOUN
ejpam-5341	74	3	is	be	AUX
ejpam-5341	74	4	uniquely	uniquely	ADV
ejpam-5341	74	5	remotal	remotal	ADJ
ejpam-5341	74	6	,	,	PUNCT
ejpam-5341	74	7	then	then	ADV
ejpam-5341	74	8	for	for	ADP
ejpam-5341	74	9	z	z	NOUN
ejpam-5341	74	10	=	=	SYM
ejpam-5341	74	11	x+	x+	PUNCT
ejpam-5341	74	12	y	y	PROPN
ejpam-5341	74	13	2	2	NUM
ejpam-5341	74	14	we	we	PRON
ejpam-5341	74	15	obtain	obtain	VERB
ejpam-5341	74	16	the	the	DET
ejpam-5341	74	17	following	follow	VERB
ejpam-5341	74	18	||x−	||x−	PROPN
ejpam-5341	74	19	z||	z||	PUNCT
ejpam-5341	75	1	=	=	PUNCT
ejpam-5341	75	2	||x−	||x−	PROPN
ejpam-5341	75	3	y	y	PROPN
ejpam-5341	75	4	2	2	NUM
ejpam-5341	75	5	||	||	NOUN
ejpam-5341	75	6	and	and	CCONJ
ejpam-5341	75	7	||y	||y	ADJ
ejpam-5341	75	8	−	−	PROPN
ejpam-5341	75	9	z||	z||	PROPN
ejpam-5341	76	1	=	=	PUNCT
ejpam-5341	76	2	||x−	||x−	PROPN
ejpam-5341	76	3	y	y	PROPN
ejpam-5341	76	4	2	2	NUM
ejpam-5341	76	5	||	||	NOUN
ejpam-5341	76	6	this	this	PRON
ejpam-5341	76	7	implies	imply	VERB
ejpam-5341	76	8	that	that	SCONJ
ejpam-5341	76	9	d(z	d(z	PROPN
ejpam-5341	76	10	,	,	PUNCT
ejpam-5341	76	11	m	m	NOUN
ejpam-5341	76	12	)	)	PUNCT
ejpam-5341	76	13	=	=	SYM
ejpam-5341	76	14	||z	||z	NOUN
ejpam-5341	76	15	−	−	NOUN
ejpam-5341	76	16	x||	x||	PUNCT
ejpam-5341	77	1	=	=	PROPN
ejpam-5341	77	2	||z	||z	PROPN
ejpam-5341	77	3	−	−	PROPN
ejpam-5341	77	4	y||	y||	PROPN
ejpam-5341	77	5	,	,	PUNCT
ejpam-5341	77	6	which	which	PRON
ejpam-5341	77	7	contradicts	contradict	VERB
ejpam-5341	77	8	the	the	DET
ejpam-5341	77	9	fact	fact	NOUN
ejpam-5341	77	10	that	that	SCONJ
ejpam-5341	77	11	m	m	NOUN
ejpam-5341	77	12	is	be	AUX
ejpam-5341	77	13	uniquely	uniquely	ADV
ejpam-5341	77	14	remotal	remotal	ADJ
ejpam-5341	77	15	.	.	PUNCT
ejpam-5341	78	1	4	4	X
ejpam-5341	78	2	.	.	X
ejpam-5341	78	3	conclusion	conclusion	NOUN
ejpam-5341	78	4	this	this	DET
ejpam-5341	78	5	paper	paper	NOUN
ejpam-5341	78	6	presents	present	VERB
ejpam-5341	78	7	a	a	DET
ejpam-5341	78	8	proof	proof	NOUN
ejpam-5341	78	9	for	for	ADP
ejpam-5341	78	10	one	one	NUM
ejpam-5341	78	11	of	of	ADP
ejpam-5341	78	12	the	the	DET
ejpam-5341	78	13	well	well	ADV
ejpam-5341	78	14	-	-	PUNCT
ejpam-5341	78	15	known	know	VERB
ejpam-5341	78	16	longstanding	longstanding	ADJ
ejpam-5341	78	17	open	open	ADJ
ejpam-5341	78	18	problems	problem	NOUN
ejpam-5341	78	19	,	,	PUNCT
ejpam-5341	78	20	known	know	VERB
ejpam-5341	78	21	as	as	ADP
ejpam-5341	78	22	the	the	DET
ejpam-5341	78	23	farthest	farth	ADJ
ejpam-5341	78	24	point	point	NOUN
ejpam-5341	78	25	problem	problem	NOUN
ejpam-5341	78	26	.	.	PUNCT
ejpam-5341	79	1	we	we	PRON
ejpam-5341	79	2	have	have	AUX
ejpam-5341	79	3	shown	show	VERB
ejpam-5341	79	4	that	that	SCONJ
ejpam-5341	79	5	every	every	DET
ejpam-5341	79	6	uniquely	uniquely	ADV
ejpam-5341	79	7	remotal	remotal	ADJ
ejpam-5341	79	8	set	set	NOUN
ejpam-5341	79	9	in	in	ADP
ejpam-5341	79	10	a	a	DET
ejpam-5341	79	11	hilbert	hilbert	NOUN
ejpam-5341	79	12	space	space	NOUN
ejpam-5341	79	13	is	be	AUX
ejpam-5341	79	14	a	a	DET
ejpam-5341	79	15	singleton	singleton	NOUN
ejpam-5341	79	16	.	.	PUNCT
ejpam-5341	80	1	references	reference	NOUN
ejpam-5341	80	2	[	[	X
ejpam-5341	80	3	1	1	X
ejpam-5341	80	4	]	]	PUNCT
ejpam-5341	80	5	a	a	DET
ejpam-5341	80	6	tallafha	tallafha	NOUN
ejpam-5341	80	7	a	a	DET
ejpam-5341	80	8	yousef	yousef	PROPN
ejpam-5341	80	9	,	,	PUNCT
ejpam-5341	80	10	r	r	PROPN
ejpam-5341	80	11	khalil	khalil	PROPN
ejpam-5341	80	12	and	and	CCONJ
ejpam-5341	80	13	b	b	NOUN
ejpam-5341	80	14	mutabagani	mutabagani	NOUN
ejpam-5341	80	15	.	.	PUNCT
ejpam-5341	81	1	on	on	ADP
ejpam-5341	81	2	the	the	DET
ejpam-5341	81	3	farthest	farth	ADJ
ejpam-5341	81	4	point	point	NOUN
ejpam-5341	81	5	problem	problem	NOUN
ejpam-5341	81	6	in	in	ADP
ejpam-5341	81	7	hilbert	hilbert	PROPN
ejpam-5341	81	8	spaces	space	NOUN
ejpam-5341	81	9	.	.	PUNCT
ejpam-5341	82	1	european	european	ADJ
ejpam-5341	82	2	journal	journal	PROPN
ejpam-5341	82	3	of	of	ADP
ejpam-5341	82	4	pure	pure	ADJ
ejpam-5341	82	5	and	and	CCONJ
ejpam-5341	82	6	applied	applied	ADJ
ejpam-5341	82	7	mathematics	mathematic	NOUN
ejpam-5341	82	8	,	,	PUNCT
ejpam-5341	82	9	16(4):2397–2404	16(4):2397–2404	NUM
ejpam-5341	82	10	,	,	PUNCT
ejpam-5341	82	11	2023	2023	NUM
ejpam-5341	82	12	.	.	PUNCT
ejpam-5341	83	1	[	[	X
ejpam-5341	83	2	2	2	NUM
ejpam-5341	83	3	]	]	X
ejpam-5341	83	4	r	r	NOUN
ejpam-5341	83	5	khalil	khalil	PROPN
ejpam-5341	83	6	a	a	DET
ejpam-5341	83	7	yousef	yousef	PROPN
ejpam-5341	83	8	and	and	CCONJ
ejpam-5341	83	9	b	b	NOUN
ejpam-5341	83	10	mutabagani	mutabagani	NOUN
ejpam-5341	83	11	.	.	PUNCT
ejpam-5341	84	1	on	on	ADP
ejpam-5341	84	2	the	the	DET
ejpam-5341	84	3	farthest	farth	ADJ
ejpam-5341	84	4	point	point	NOUN
ejpam-5341	84	5	problem	problem	NOUN
ejpam-5341	84	6	in	in	ADP
ejpam-5341	84	7	banach	banach	NOUN
ejpam-5341	84	8	spaces	space	NOUN
ejpam-5341	84	9	.	.	PUNCT
ejpam-5341	85	1	journal	journal	NOUN
ejpam-5341	85	2	of	of	ADP
ejpam-5341	85	3	computational	computational	ADJ
ejpam-5341	85	4	analysis	analysis	NOUN
ejpam-5341	85	5	and	and	CCONJ
ejpam-5341	85	6	applications	application	NOUN
ejpam-5341	85	7	,	,	PUNCT
ejpam-5341	85	8	29(1):123–128	29(1):123–128	NUM
ejpam-5341	85	9	,	,	PUNCT
ejpam-5341	85	10	2020	2020	NUM
ejpam-5341	85	11	.	.	PUNCT
ejpam-5341	86	1	references	reference	NOUN
ejpam-5341	86	2	2989	2989	NUM
ejpam-5341	86	3	[	[	X
ejpam-5341	86	4	3	3	X
ejpam-5341	86	5	]	]	PUNCT
ejpam-5341	86	6	a	a	DET
ejpam-5341	86	7	r	r	NOUN
ejpam-5341	86	8	alimov	alimov	NOUN
ejpam-5341	86	9	.	.	PUNCT
ejpam-5341	87	1	solarity	solarity	NOUN
ejpam-5341	87	2	of	of	ADP
ejpam-5341	87	3	chebyshev	chebyshev	NOUN
ejpam-5341	87	4	sets	set	NOUN
ejpam-5341	87	5	in	in	ADP
ejpam-5341	87	6	dual	dual	ADJ
ejpam-5341	87	7	spaces	space	NOUN
ejpam-5341	87	8	and	and	CCONJ
ejpam-5341	87	9	uniquely	uniquely	ADV
ejpam-5341	87	10	remotal	remotal	ADJ
ejpam-5341	87	11	sets	set	NOUN
ejpam-5341	87	12	.	.	PUNCT
ejpam-5341	88	1	lobachevskii	lobachevskii	PROPN
ejpam-5341	88	2	journal	journal	PROPN
ejpam-5341	88	3	of	of	ADP
ejpam-5341	88	4	mathematics	mathematic	NOUN
ejpam-5341	88	5	,	,	PUNCT
ejpam-5341	88	6	42(4):785–790	42(4):785–790	NOUN
ejpam-5341	88	7	,	,	PUNCT
ejpam-5341	88	8	2021	2021	NUM
ejpam-5341	88	9	.	.	PUNCT
ejpam-5341	89	1	[	[	X
ejpam-5341	89	2	4	4	X
ejpam-5341	89	3	]	]	X
ejpam-5341	89	4	a	a	DET
ejpam-5341	89	5	astaneh	astaneh	NOUN
ejpam-5341	89	6	.	.	PUNCT
ejpam-5341	90	1	on	on	ADP
ejpam-5341	90	2	uniquely	uniquely	ADV
ejpam-5341	90	3	remotal	remotal	ADJ
ejpam-5341	90	4	subsets	subset	NOUN
ejpam-5341	90	5	of	of	ADP
ejpam-5341	90	6	hilbert	hilbert	PROPN
ejpam-5341	90	7	spaces	space	NOUN
ejpam-5341	90	8	.	.	PUNCT
ejpam-5341	91	1	indian	indian	ADJ
ejpam-5341	91	2	journal	journal	PROPN
ejpam-5341	91	3	of	of	ADP
ejpam-5341	91	4	pure	pure	ADJ
ejpam-5341	91	5	and	and	CCONJ
ejpam-5341	91	6	applied	applied	ADJ
ejpam-5341	91	7	mathematics	mathematic	NOUN
ejpam-5341	91	8	,	,	PUNCT
ejpam-5341	91	9	14(10):1311–1317	14(10):1311–1317	NUM
ejpam-5341	91	10	,	,	PUNCT
ejpam-5341	91	11	1983	1983	NUM
ejpam-5341	91	12	.	.	PUNCT
ejpam-5341	92	1	[	[	X
ejpam-5341	92	2	5	5	NUM
ejpam-5341	92	3	]	]	PUNCT
ejpam-5341	92	4	h	h	NOUN
ejpam-5341	92	5	deeb	deeb	PROPN
ejpam-5341	92	6	f	f	PROPN
ejpam-5341	92	7	saidi	saidi	PROPN
ejpam-5341	92	8	and	and	CCONJ
ejpam-5341	92	9	r	r	PROPN
ejpam-5341	92	10	khalil	khalil	PROPN
ejpam-5341	92	11	.	.	PUNCT
ejpam-5341	93	1	strong	strong	ADJ
ejpam-5341	93	2	proximinality	proximinality	NOUN
ejpam-5341	93	3	in	in	ADP
ejpam-5341	93	4	banach	banach	NOUN
ejpam-5341	93	5	spaces	space	NOUN
ejpam-5341	93	6	.	.	PUNCT
ejpam-5341	94	1	mathematics	mathematic	NOUN
ejpam-5341	94	2	journal	journal	PROPN
ejpam-5341	94	3	of	of	ADP
ejpam-5341	94	4	toyama	toyama	PROPN
ejpam-5341	94	5	university	university	PROPN
ejpam-5341	94	6	,	,	PUNCT
ejpam-5341	94	7	19:67–95	19:67–95	NUM
ejpam-5341	94	8	,	,	PUNCT
ejpam-5341	94	9	1996	1996	NUM
ejpam-5341	94	10	.	.	PUNCT
ejpam-5341	95	1	[	[	X
ejpam-5341	95	2	6	6	NUM
ejpam-5341	95	3	]	]	X
ejpam-5341	95	4	r	r	NOUN
ejpam-5341	95	5	khalil	khalil	PROPN
ejpam-5341	95	6	and	and	CCONJ
ejpam-5341	95	7	s	s	PROPN
ejpam-5341	95	8	al	al	PROPN
ejpam-5341	95	9	-	-	PUNCT
ejpam-5341	95	10	sharif	sharif	PROPN
ejpam-5341	95	11	.	.	PUNCT
ejpam-5341	96	1	remotal	remotal	ADJ
ejpam-5341	96	2	sets	set	NOUN
ejpam-5341	96	3	in	in	ADP
ejpam-5341	96	4	vector	vector	NOUN
ejpam-5341	96	5	valued	value	VERB
ejpam-5341	96	6	function	function	NOUN
ejpam-5341	96	7	spaces	space	NOUN
ejpam-5341	96	8	.	.	PUNCT
ejpam-5341	97	1	scientiae	scientiae	PROPN
ejpam-5341	97	2	mathematicae	mathematicae	PROPN
ejpam-5341	97	3	japonicae	japonicae	PROPN
ejpam-5341	97	4	,	,	PUNCT
ejpam-5341	97	5	63(3):433–442	63(3):433–442	PROPN
ejpam-5341	97	6	,	,	PUNCT
ejpam-5341	97	7	2006	2006	NUM
ejpam-5341	97	8	.	.	PUNCT
ejpam-5341	98	1	[	[	X
ejpam-5341	98	2	7	7	NUM
ejpam-5341	98	3	]	]	X
ejpam-5341	98	4	r	r	NOUN
ejpam-5341	98	5	khalil	khalil	PROPN
ejpam-5341	98	6	and	and	CCONJ
ejpam-5341	98	7	m	m	PROPN
ejpam-5341	98	8	sababheh	sababheh	ADJ
ejpam-5341	98	9	.	.	PUNCT
ejpam-5341	99	1	a	a	DET
ejpam-5341	99	2	study	study	NOUN
ejpam-5341	99	3	of	of	ADP
ejpam-5341	99	4	uniquely	uniquely	ADV
ejpam-5341	99	5	remotal	remotal	ADJ
ejpam-5341	99	6	sets	set	NOUN
ejpam-5341	99	7	.	.	PUNCT
ejpam-5341	100	1	journal	journal	NOUN
ejpam-5341	100	2	of	of	ADP
ejpam-5341	100	3	computational	computational	ADJ
ejpam-5341	100	4	analysis	analysis	NOUN
ejpam-5341	100	5	and	and	CCONJ
ejpam-5341	100	6	applications	application	NOUN
ejpam-5341	100	7	.	.	PUNCT
ejpam-5341	100	8	,	,	PUNCT
ejpam-5341	100	9	13:1233–1239	13:1233–1239	NUM
ejpam-5341	100	10	,	,	PUNCT
ejpam-5341	100	11	2010	2010	NUM
ejpam-5341	100	12	.	.	PUNCT
ejpam-5341	101	1	[	[	X
ejpam-5341	101	2	8	8	NUM
ejpam-5341	101	3	]	]	X
ejpam-5341	101	4	r	r	NOUN
ejpam-5341	101	5	khalil	khalil	PROPN
ejpam-5341	101	6	and	and	CCONJ
ejpam-5341	101	7	m	m	PROPN
ejpam-5341	101	8	sababheh	sababheh	ADJ
ejpam-5341	101	9	.	.	PUNCT
ejpam-5341	102	1	remotal	remotal	ADJ
ejpam-5341	102	2	points	point	NOUN
ejpam-5341	102	3	and	and	CCONJ
ejpam-5341	102	4	krein	krein	NOUN
ejpam-5341	102	5	-	-	PUNCT
ejpam-5341	102	6	milman	milman	NOUN
ejpam-5341	102	7	type	type	NOUN
ejpam-5341	102	8	theorem	theorem	VERB
ejpam-5341	102	9	.	.	PROPN
ejpam-5341	102	10	journal	journal	PROPN
ejpam-5341	102	11	of	of	ADP
ejpam-5341	102	12	non	non	ADJ
ejpam-5341	102	13	-	-	ADJ
ejpam-5341	102	14	linear	linear	ADJ
ejpam-5341	102	15	convex	convex	NOUN
ejpam-5341	102	16	analysis	analysis	NOUN
ejpam-5341	102	17	,	,	PUNCT
ejpam-5341	102	18	12(2):5–15	12(2):5–15	NUM
ejpam-5341	102	19	,	,	PUNCT
ejpam-5341	102	20	2011	2011	NUM
ejpam-5341	102	21	.	.	PUNCT
ejpam-5341	103	1	[	[	X
ejpam-5341	103	2	9	9	NUM
ejpam-5341	103	3	]	]	SYM
ejpam-5341	103	4	v	v	NUM
ejpam-5341	103	5	klee	klee	PROPN
ejpam-5341	103	6	.	.	PUNCT
ejpam-5341	104	1	convexity	convexity	NOUN
ejpam-5341	104	2	of	of	ADP
ejpam-5341	104	3	chebyshev	chebyshev	NOUN
ejpam-5341	104	4	sets	set	NOUN
ejpam-5341	104	5	.	.	PUNCT
ejpam-5341	105	1	mathematische	mathematische	PROPN
ejpam-5341	105	2	annalen	annalen	PROPN
ejpam-5341	105	3	,	,	PUNCT
ejpam-5341	105	4	142(3):292–304	142(3):292–304	PROPN
ejpam-5341	105	5	,	,	PUNCT
ejpam-5341	105	6	1962	1962	NUM
ejpam-5341	105	7	.	.	PUNCT
ejpam-5341	106	1	[	[	X
ejpam-5341	106	2	10	10	NUM
ejpam-5341	106	3	]	]	X
ejpam-5341	106	4	a	a	DET
ejpam-5341	106	5	yousef	yousef	PROPN
ejpam-5341	106	6	m	m	NOUN
ejpam-5341	106	7	sababheh	sababheh	NOUN
ejpam-5341	106	8	and	and	CCONJ
ejpam-5341	106	9	r	r	NOUN
ejpam-5341	106	10	khalil	khalil	PROPN
ejpam-5341	106	11	.	.	PUNCT
ejpam-5341	107	1	uniquely	uniquely	ADV
ejpam-5341	107	2	remotal	remotal	ADJ
ejpam-5341	107	3	sets	set	NOUN
ejpam-5341	107	4	in	in	ADP
ejpam-5341	107	5	banach	banach	NOUN
ejpam-5341	107	6	spaces	space	NOUN
ejpam-5341	107	7	.	.	PUNCT
ejpam-5341	108	1	filomat	filomat	NOUN
ejpam-5341	108	2	,	,	PUNCT
ejpam-5341	108	3	31(9):2773–2777	31(9):2773–2777	NUM
ejpam-5341	108	4	,	,	PUNCT
ejpam-5341	108	5	2017	2017	NUM
ejpam-5341	108	6	.	.	PUNCT
ejpam-5341	109	1	[	[	X
ejpam-5341	109	2	11	11	NUM
ejpam-5341	109	3	]	]	PUNCT
ejpam-5341	109	4	maaden	maaden	NOUN
ejpam-5341	109	5	.	.	PUNCT
ejpam-5341	110	1	on	on	ADP
ejpam-5341	110	2	the	the	DET
ejpam-5341	110	3	c	c	NOUN
ejpam-5341	110	4	-	-	PUNCT
ejpam-5341	110	5	farthest	farth	ADJ
ejpam-5341	110	6	points	point	NOUN
ejpam-5341	110	7	.	.	PUNCT
ejpam-5341	111	1	extracta	extracta	PROPN
ejpam-5341	111	2	mathematicae	mathematicae	PROPN
ejpam-5341	111	3	,	,	PUNCT
ejpam-5341	111	4	16(2):211–222	16(2):211–222	PROPN
ejpam-5341	111	5	,	,	PUNCT
ejpam-5341	111	6	2001	2001	NUM
ejpam-5341	111	7	.	.	PUNCT
ejpam-5341	112	1	[	[	X
ejpam-5341	112	2	12	12	NUM
ejpam-5341	112	3	]	]	PUNCT
ejpam-5341	112	4	t	t	PROPN
ejpam-5341	112	5	d	d	PROPN
ejpam-5341	112	6	narang	narang	PROPN
ejpam-5341	112	7	.	.	PUNCT
ejpam-5341	113	1	on	on	ADP
ejpam-5341	113	2	singletonness	singletonness	NOUN
ejpam-5341	113	3	of	of	ADP
ejpam-5341	113	4	remotal	remotal	ADJ
ejpam-5341	113	5	and	and	CCONJ
ejpam-5341	113	6	uniquely	uniquely	ADV
ejpam-5341	113	7	remotal	remotal	ADJ
ejpam-5341	113	8	sets	set	NOUN
ejpam-5341	113	9	.	.	PUNCT
ejpam-5341	114	1	bulletin	bulletin	NOUN
ejpam-5341	114	2	of	of	ADP
ejpam-5341	114	3	the	the	DET
ejpam-5341	114	4	belgian	belgian	ADJ
ejpam-5341	114	5	mathematical	mathematical	ADJ
ejpam-5341	114	6	society	society	NOUN
ejpam-5341	114	7	-	-	PUNCT
ejpam-5341	114	8	simon	simon	PROPN
ejpam-5341	114	9	stevin	stevin	NOUN
ejpam-5341	114	10	,	,	PUNCT
ejpam-5341	114	11	18(1):113–120	18(1):113–120	PROPN
ejpam-5341	114	12	,	,	PUNCT
ejpam-5341	114	13	2011	2011	NUM
ejpam-5341	114	14	.	.	PUNCT
ejpam-5341	115	1	[	[	X
ejpam-5341	115	2	13	13	NUM
ejpam-5341	115	3	]	]	PUNCT
ejpam-5341	115	4	a	a	DET
ejpam-5341	115	5	niknam	niknam	NOUN
ejpam-5341	115	6	.	.	PUNCT
ejpam-5341	116	1	on	on	ADP
ejpam-5341	116	2	uniquely	uniquely	ADV
ejpam-5341	116	3	remotal	remotal	ADJ
ejpam-5341	116	4	sets	set	NOUN
ejpam-5341	116	5	.	.	PUNCT
ejpam-5341	117	1	indian	indian	ADJ
ejpam-5341	117	2	j.	j.	PROPN
ejpam-5341	117	3	pure	pure	PROPN
ejpam-5341	117	4	appl	appl	PROPN
ejpam-5341	117	5	.	.	PUNCT
ejpam-5341	117	6	math	math	PROPN
ejpam-5341	117	7	,	,	PUNCT
ejpam-5341	117	8	15(10):1079–1083	15(10):1079–1083	NOUN
ejpam-5341	117	9	,	,	PUNCT
ejpam-5341	117	10	1984	1984	NUM
ejpam-5341	117	11	.	.	PUNCT
ejpam-5341	118	1	[	[	X
ejpam-5341	118	2	14	14	NUM
ejpam-5341	118	3	]	]	PUNCT
ejpam-5341	118	4	m	m	VERB
ejpam-5341	118	5	sababheh	sababheh	ADJ
ejpam-5341	118	6	and	and	CCONJ
ejpam-5341	118	7	m	m	PROPN
ejpam-5341	118	8	khalil	khalil	PROPN
ejpam-5341	118	9	.	.	PUNCT
ejpam-5341	119	1	new	new	ADJ
ejpam-5341	119	2	results	result	NOUN
ejpam-5341	119	3	on	on	ADP
ejpam-5341	119	4	remotality	remotality	NOUN
ejpam-5341	119	5	in	in	ADP
ejpam-5341	119	6	banach	banach	NOUN
ejpam-5341	119	7	spaces	space	NOUN
ejpam-5341	119	8	.	.	PUNCT
ejpam-5341	120	1	italian	italian	ADJ
ejpam-5341	120	2	journal	journal	NOUN
ejpam-5341	120	3	of	of	ADP
ejpam-5341	120	4	pure	pure	ADJ
ejpam-5341	120	5	and	and	CCONJ
ejpam-5341	120	6	applied	applied	ADJ
ejpam-5341	120	7	mathematics	mathematic	NOUN
ejpam-5341	120	8	,	,	PUNCT
ejpam-5341	120	9	30:59–66	30:59–66	NUM
ejpam-5341	120	10	,	,	PUNCT
ejpam-5341	120	11	2013	2013	NUM
ejpam-5341	120	12	.	.	PUNCT
ejpam-5341	121	1	[	[	X
ejpam-5341	121	2	15	15	NUM
ejpam-5341	121	3	]	]	X
ejpam-5341	121	4	m	m	AUX
ejpam-5341	121	5	sababheh	sababheh	ADJ
ejpam-5341	121	6	and	and	CCONJ
ejpam-5341	121	7	r	r	NOUN
ejpam-5341	121	8	khalil	khalil	PROPN
ejpam-5341	121	9	.	.	PUNCT
ejpam-5341	122	1	remotality	remotality	NOUN
ejpam-5341	122	2	of	of	ADP
ejpam-5341	122	3	closed	closed	ADJ
ejpam-5341	122	4	bounded	bound	VERB
ejpam-5341	122	5	convex	convex	NOUN
ejpam-5341	122	6	sets	set	NOUN
ejpam-5341	122	7	in	in	ADP
ejpam-5341	122	8	reflexive	reflexive	ADJ
ejpam-5341	122	9	spaces	space	NOUN
ejpam-5341	122	10	.	.	PUNCT
ejpam-5341	123	1	numerical	numerical	ADJ
ejpam-5341	123	2	functional	functional	ADJ
ejpam-5341	123	3	analysis	analysis	NOUN
ejpam-5341	123	4	and	and	CCONJ
ejpam-5341	123	5	optimization	optimization	NOUN
ejpam-5341	123	6	,	,	PUNCT
ejpam-5341	123	7	29(10):1166–1170	29(10):1166–1170	NUM
ejpam-5341	123	8	,	,	PUNCT
ejpam-5341	123	9	2008	2008	NUM
ejpam-5341	123	10	.	.	PUNCT