id	sid	tid	token	lemma	pos
ejpam-4136	1	1	european	european	PROPN
ejpam-4136	1	2	journal	journal	PROPN
ejpam-4136	1	3	of	of	ADP
ejpam-4136	1	4	pure	pure	ADJ
ejpam-4136	1	5	and	and	CCONJ
ejpam-4136	1	6	applied	apply	VERB
ejpam-4136	1	7	mathematics	mathematic	NOUN
ejpam-4136	1	8	vol	vol	NOUN
ejpam-4136	1	9	.	.	PUNCT
ejpam-4136	2	1	14	14	NUM
ejpam-4136	2	2	,	,	PUNCT
ejpam-4136	2	3	no	no	INTJ
ejpam-4136	2	4	.	.	NOUN
ejpam-4136	2	5	4	4	NUM
ejpam-4136	2	6	,	,	PUNCT
ejpam-4136	2	7	2021	2021	NUM
ejpam-4136	2	8	,	,	PUNCT
ejpam-4136	2	9	1148	1148	NUM
ejpam-4136	2	10	-	-	SYM
ejpam-4136	2	11	1160	1160	NUM
ejpam-4136	2	12	issn	issn	PROPN
ejpam-4136	2	13	1307	1307	NUM
ejpam-4136	2	14	-	-	SYM
ejpam-4136	2	15	5543	5543	NUM
ejpam-4136	2	16	–	–	PUNCT
ejpam-4136	2	17	ejpam.com	ejpam.com	X
ejpam-4136	2	18	published	publish	VERB
ejpam-4136	2	19	by	by	ADP
ejpam-4136	2	20	new	new	PROPN
ejpam-4136	2	21	york	york	PROPN
ejpam-4136	2	22	business	business	PROPN
ejpam-4136	2	23	global	global	VERB
ejpam-4136	2	24	some	some	DET
ejpam-4136	2	25	aspects	aspect	NOUN
ejpam-4136	2	26	of	of	ADP
ejpam-4136	2	27	b(αn	b(αn	NOUN
ejpam-4136	2	28	,	,	PUNCT
ejpam-4136	2	29	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	2	30	spaces	space	NOUN
ejpam-4136	2	31	over	over	ADP
ejpam-4136	2	32	banach	banach	NOUN
ejpam-4136	2	33	algebras	algebras	X
ejpam-4136	2	34	akbar	akbar	NOUN
ejpam-4136	2	35	dehghan	dehghan	PROPN
ejpam-4136	2	36	nezhad1,∗	nezhad1,∗	NOUN
ejpam-4136	2	37	,	,	PUNCT
ejpam-4136	2	38	stojan	stojan	ADP
ejpam-4136	2	39	radenović2	radenović2	PROPN
ejpam-4136	2	40	1	1	NUM
ejpam-4136	2	41	school	school	NOUN
ejpam-4136	2	42	of	of	ADP
ejpam-4136	2	43	mathematics	mathematic	NOUN
ejpam-4136	2	44	,	,	PUNCT
ejpam-4136	2	45	iran	iran	PROPN
ejpam-4136	2	46	university	university	PROPN
ejpam-4136	2	47	of	of	ADP
ejpam-4136	2	48	science	science	NOUN
ejpam-4136	2	49	and	and	CCONJ
ejpam-4136	2	50	technology	technology	NOUN
ejpam-4136	2	51	,	,	PUNCT
ejpam-4136	2	52	narmak	narmak	PROPN
ejpam-4136	2	53	,	,	PUNCT
ejpam-4136	2	54	tehran	tehran	PROPN
ejpam-4136	2	55	,	,	PUNCT
ejpam-4136	2	56	iran	iran	PROPN
ejpam-4136	2	57	2	2	NUM
ejpam-4136	2	58	faculty	faculty	NOUN
ejpam-4136	2	59	of	of	ADP
ejpam-4136	2	60	mechanical	mechanical	ADJ
ejpam-4136	2	61	engineering	engineering	NOUN
ejpam-4136	2	62	,	,	PUNCT
ejpam-4136	2	63	university	university	PROPN
ejpam-4136	2	64	of	of	ADP
ejpam-4136	2	65	belgrade	belgrade	PROPN
ejpam-4136	2	66	,	,	PUNCT
ejpam-4136	2	67	kraljice	kraljice	NOUN
ejpam-4136	2	68	marije	marije	PROPN
ejpam-4136	2	69	16	16	NUM
ejpam-4136	2	70	,	,	PUNCT
ejpam-4136	2	71	11120	11120	NUM
ejpam-4136	2	72	belgrad	belgrad	NOUN
ejpam-4136	2	73	35	35	NUM
ejpam-4136	2	74	,	,	PUNCT
ejpam-4136	2	75	serbia	serbia	PROPN
ejpam-4136	2	76	abstract	abstract	ADJ
ejpam-4136	2	77	.	.	PUNCT
ejpam-4136	3	1	in	in	ADP
ejpam-4136	3	2	this	this	DET
ejpam-4136	3	3	paper	paper	NOUN
ejpam-4136	3	4	,	,	PUNCT
ejpam-4136	3	5	we	we	PRON
ejpam-4136	3	6	give	give	VERB
ejpam-4136	3	7	a	a	DET
ejpam-4136	3	8	definition	definition	NOUN
ejpam-4136	3	9	of	of	ADP
ejpam-4136	3	10	a	a	DET
ejpam-4136	3	11	b(αn	b(αn	NOUN
ejpam-4136	3	12	,	,	PUNCT
ejpam-4136	3	13	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	3	14	spaces	space	NOUN
ejpam-4136	3	15	over	over	ADP
ejpam-4136	3	16	banach	banach	NOUN
ejpam-4136	3	17	algebras	algebra	NOUN
ejpam-4136	3	18	.	.	PUNCT
ejpam-4136	4	1	the	the	DET
ejpam-4136	4	2	purpose	purpose	NOUN
ejpam-4136	4	3	of	of	ADP
ejpam-4136	4	4	this	this	DET
ejpam-4136	4	5	paper	paper	NOUN
ejpam-4136	4	6	is	be	AUX
ejpam-4136	4	7	to	to	PART
ejpam-4136	4	8	prove	prove	VERB
ejpam-4136	4	9	the	the	DET
ejpam-4136	4	10	concept	concept	NOUN
ejpam-4136	4	11	of	of	ADP
ejpam-4136	4	12	extension	extension	NOUN
ejpam-4136	4	13	of	of	ADP
ejpam-4136	4	14	fixed	fix	VERB
ejpam-4136	4	15	point	point	NOUN
ejpam-4136	4	16	theorems	theorem	NOUN
ejpam-4136	4	17	in	in	ADP
ejpam-4136	4	18	b(αn	b(αn	NOUN
ejpam-4136	4	19	,	,	PUNCT
ejpam-4136	4	20	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	4	21	spaces	space	NOUN
ejpam-4136	4	22	over	over	ADP
ejpam-4136	4	23	banach	banach	NOUN
ejpam-4136	4	24	algebras	algebra	NOUN
ejpam-4136	4	25	.	.	PUNCT
ejpam-4136	5	1	2020	2020	NUM
ejpam-4136	5	2	mathematics	mathematics	PROPN
ejpam-4136	5	3	subject	subject	NOUN
ejpam-4136	5	4	classifications	classification	NOUN
ejpam-4136	5	5	:	:	PUNCT
ejpam-4136	5	6	54h25	54h25	NUM
ejpam-4136	5	7	,	,	PUNCT
ejpam-4136	5	8	47h10	47h10	NUM
ejpam-4136	5	9	,	,	PUNCT
ejpam-4136	5	10	46b20	46b20	NUM
ejpam-4136	5	11	key	key	ADJ
ejpam-4136	5	12	words	word	NOUN
ejpam-4136	5	13	and	and	CCONJ
ejpam-4136	5	14	phrases	phrase	NOUN
ejpam-4136	5	15	:	:	PUNCT
ejpam-4136	5	16	b(αn	b(αn	NOUN
ejpam-4136	5	17	,	,	PUNCT
ejpam-4136	5	18	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	5	19	spaces	space	NOUN
ejpam-4136	5	20	,	,	PUNCT
ejpam-4136	5	21	bn	bn	ADJ
ejpam-4136	5	22	-	-	PUNCT
ejpam-4136	5	23	metric	metric	ADJ
ejpam-4136	5	24	space	space	NOUN
ejpam-4136	5	25	,	,	PUNCT
ejpam-4136	5	26	fixed	fix	VERB
ejpam-4136	5	27	point	point	NOUN
ejpam-4136	5	28	.	.	PUNCT
ejpam-4136	6	1	1	1	X
ejpam-4136	6	2	.	.	X
ejpam-4136	6	3	introduction	introduction	NOUN
ejpam-4136	6	4	and	and	CCONJ
ejpam-4136	6	5	preliminaries	preliminary	NOUN
ejpam-4136	6	6	bakhtin	bakhtin	NOUN
ejpam-4136	6	7	(	(	PUNCT
ejpam-4136	6	8	1989	1989	NUM
ejpam-4136	6	9	)	)	PUNCT
ejpam-4136	6	10	,	,	PUNCT
ejpam-4136	6	11	bourbaki	bourbaki	NOUN
ejpam-4136	6	12	(	(	PUNCT
ejpam-4136	6	13	1974	1974	NUM
ejpam-4136	6	14	)	)	PUNCT
ejpam-4136	6	15	,	,	PUNCT
ejpam-4136	6	16	czerwik	czerwik	PROPN
ejpam-4136	6	17	(	(	PUNCT
ejpam-4136	6	18	1993	1993	NUM
ejpam-4136	6	19	)	)	PUNCT
ejpam-4136	6	20	and	and	CCONJ
ejpam-4136	6	21	heinonen	heinonen	PROPN
ejpam-4136	6	22	(	(	PUNCT
ejpam-4136	6	23	2001	2001	NUM
ejpam-4136	6	24	)	)	PUNCT
ejpam-4136	6	25	generalized	generalize	VERB
ejpam-4136	6	26	the	the	DET
ejpam-4136	6	27	structure	structure	NOUN
ejpam-4136	6	28	of	of	ADP
ejpam-4136	6	29	metric	metric	ADJ
ejpam-4136	6	30	space	space	NOUN
ejpam-4136	6	31	by	by	ADP
ejpam-4136	6	32	weakening	weaken	VERB
ejpam-4136	6	33	the	the	DET
ejpam-4136	6	34	triangle	triangle	NOUN
ejpam-4136	6	35	inequality	inequality	NOUN
ejpam-4136	6	36	and	and	CCONJ
ejpam-4136	6	37	called	call	VERB
ejpam-4136	6	38	it	it	PRON
ejpam-4136	6	39	the	the	DET
ejpam-4136	6	40	bmetric	bmetric	ADJ
ejpam-4136	6	41	space	space	NOUN
ejpam-4136	6	42	.	.	PUNCT
ejpam-4136	7	1	in	in	ADP
ejpam-4136	7	2	2017	2017	NUM
ejpam-4136	7	3	,	,	PUNCT
ejpam-4136	7	4	kamran	kamran	PROPN
ejpam-4136	7	5	et	et	PROPN
ejpam-4136	7	6	al	al	PROPN
ejpam-4136	7	7	.	.	PUNCT
ejpam-4136	8	1	[	[	X
ejpam-4136	8	2	8	8	NUM
ejpam-4136	8	3	]	]	PUNCT
ejpam-4136	8	4	,	,	PUNCT
ejpam-4136	8	5	introduced	introduce	VERB
ejpam-4136	8	6	the	the	DET
ejpam-4136	8	7	concept	concept	NOUN
ejpam-4136	8	8	of	of	ADP
ejpam-4136	8	9	extended	extended	ADJ
ejpam-4136	8	10	b	b	X
ejpam-4136	8	11	-	-	PUNCT
ejpam-4136	8	12	metric	metric	ADJ
ejpam-4136	8	13	space	space	NOUN
ejpam-4136	8	14	by	by	ADP
ejpam-4136	8	15	further	far	ADV
ejpam-4136	8	16	weakening	weaken	VERB
ejpam-4136	8	17	the	the	DET
ejpam-4136	8	18	triangle	triangle	NOUN
ejpam-4136	8	19	inequality	inequality	NOUN
ejpam-4136	8	20	.	.	PUNCT
ejpam-4136	9	1	the	the	DET
ejpam-4136	9	2	main	main	ADJ
ejpam-4136	9	3	purpose	purpose	NOUN
ejpam-4136	9	4	of	of	ADP
ejpam-4136	9	5	this	this	DET
ejpam-4136	9	6	paper	paper	NOUN
ejpam-4136	9	7	is	be	AUX
ejpam-4136	9	8	a	a	DET
ejpam-4136	9	9	generalization	generalization	NOUN
ejpam-4136	9	10	of	of	ADP
ejpam-4136	9	11	cone	cone	NOUN
ejpam-4136	9	12	n	n	CCONJ
ejpam-4136	9	13	-	-	PUNCT
ejpam-4136	9	14	metric	metric	ADJ
ejpam-4136	9	15	spaces	space	NOUN
ejpam-4136	9	16	into	into	ADP
ejpam-4136	9	17	b(αn	b(αn	NOUN
ejpam-4136	9	18	,	,	PUNCT
ejpam-4136	9	19	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	9	20	spaces	space	NOUN
ejpam-4136	9	21	.	.	PUNCT
ejpam-4136	10	1	in	in	ADP
ejpam-4136	10	2	this	this	DET
ejpam-4136	10	3	section	section	NOUN
ejpam-4136	10	4	,	,	PUNCT
ejpam-4136	10	5	we	we	PRON
ejpam-4136	10	6	recall	recall	VERB
ejpam-4136	10	7	some	some	DET
ejpam-4136	10	8	definitions	definition	NOUN
ejpam-4136	10	9	,	,	PUNCT
ejpam-4136	10	10	notations	notation	NOUN
ejpam-4136	10	11	and	and	CCONJ
ejpam-4136	10	12	terminologies	terminology	NOUN
ejpam-4136	10	13	which	which	PRON
ejpam-4136	10	14	will	will	AUX
ejpam-4136	10	15	be	be	AUX
ejpam-4136	10	16	used	use	VERB
ejpam-4136	10	17	to	to	PART
ejpam-4136	10	18	prove	prove	VERB
ejpam-4136	10	19	the	the	DET
ejpam-4136	10	20	main	main	ADJ
ejpam-4136	10	21	results	result	NOUN
ejpam-4136	10	22	.	.	PUNCT
ejpam-4136	11	1	when	when	SCONJ
ejpam-4136	11	2	good	good	ADJ
ejpam-4136	11	3	references	reference	NOUN
ejpam-4136	11	4	are	be	AUX
ejpam-4136	11	5	available	available	ADJ
ejpam-4136	11	6	we	we	PRON
ejpam-4136	11	7	may	may	AUX
ejpam-4136	11	8	not	not	PART
ejpam-4136	11	9	include	include	VERB
ejpam-4136	11	10	the	the	DET
ejpam-4136	11	11	details	detail	NOUN
ejpam-4136	11	12	of	of	ADP
ejpam-4136	11	13	all	all	DET
ejpam-4136	11	14	the	the	DET
ejpam-4136	11	15	introduction	introduction	NOUN
ejpam-4136	11	16	and	and	CCONJ
ejpam-4136	11	17	proofs	proof	NOUN
ejpam-4136	11	18	(	(	PUNCT
ejpam-4136	11	19	for	for	ADP
ejpam-4136	11	20	example	example	NOUN
ejpam-4136	11	21	,	,	PUNCT
ejpam-4136	11	22	[	[	X
ejpam-4136	11	23	12	12	NUM
ejpam-4136	11	24	]	]	PUNCT
ejpam-4136	11	25	,	,	PUNCT
ejpam-4136	12	1	[	[	X
ejpam-4136	12	2	11	11	NUM
ejpam-4136	12	3	]	]	PUNCT
ejpam-4136	12	4	,	,	PUNCT
ejpam-4136	12	5	[	[	X
ejpam-4136	12	6	9	9	NUM
ejpam-4136	12	7	]	]	PUNCT
ejpam-4136	12	8	,	,	PUNCT
ejpam-4136	13	1	[	[	X
ejpam-4136	13	2	5	5	NUM
ejpam-4136	13	3	]	]	PUNCT
ejpam-4136	13	4	,	,	PUNCT
ejpam-4136	13	5	[	[	X
ejpam-4136	13	6	13	13	NUM
ejpam-4136	13	7	]	]	PUNCT
ejpam-4136	13	8	,	,	PUNCT
ejpam-4136	13	9	[	[	X
ejpam-4136	13	10	10	10	NUM
ejpam-4136	13	11	]	]	PUNCT
ejpam-4136	13	12	,	,	PUNCT
ejpam-4136	14	1	[	[	X
ejpam-4136	14	2	1	1	NUM
ejpam-4136	14	3	]	]	NUM
ejpam-4136	14	4	)	)	PUNCT
ejpam-4136	14	5	.	.	PUNCT
ejpam-4136	15	1	definition	definition	NOUN
ejpam-4136	15	2	1	1	NUM
ejpam-4136	15	3	.	.	PUNCT
ejpam-4136	16	1	[	[	X
ejpam-4136	16	2	14	14	NUM
ejpam-4136	16	3	]	]	PUNCT
ejpam-4136	16	4	a	a	DET
ejpam-4136	16	5	vector	vector	NOUN
ejpam-4136	16	6	space	space	NOUN
ejpam-4136	16	7	a	a	PRON
ejpam-4136	16	8	over	over	ADP
ejpam-4136	16	9	a	a	DET
ejpam-4136	16	10	field	field	NOUN
ejpam-4136	16	11	k	k	NOUN
ejpam-4136	17	1	(	(	PUNCT
ejpam-4136	17	2	r	r	NOUN
ejpam-4136	17	3	or	or	CCONJ
ejpam-4136	17	4	c	c	NOUN
ejpam-4136	17	5	)	)	PUNCT
ejpam-4136	17	6	is	be	AUX
ejpam-4136	17	7	said	say	VERB
ejpam-4136	17	8	to	to	PART
ejpam-4136	17	9	be	be	AUX
ejpam-4136	17	10	an	an	DET
ejpam-4136	17	11	algebra	algebra	NOUN
ejpam-4136	17	12	if	if	SCONJ
ejpam-4136	17	13	it	it	PRON
ejpam-4136	17	14	is	be	AUX
ejpam-4136	17	15	closed	close	VERB
ejpam-4136	17	16	under	under	ADP
ejpam-4136	17	17	multiplication	multiplication	NOUN
ejpam-4136	17	18	(	(	PUNCT
ejpam-4136	17	19	i.e.	i.e.	X
ejpam-4136	17	20	,	,	PUNCT
ejpam-4136	17	21	for	for	ADP
ejpam-4136	17	22	all	all	DET
ejpam-4136	17	23	a	a	PRON
ejpam-4136	17	24	,	,	PUNCT
ejpam-4136	17	25	b	b	X
ejpam-4136	17	26	∈	∈	PROPN
ejpam-4136	17	27	a	a	X
ejpam-4136	17	28	,	,	PUNCT
ejpam-4136	17	29	ab	ab	PROPN
ejpam-4136	17	30	∈	∈	PROPN
ejpam-4136	17	31	a	a	PRON
ejpam-4136	17	32	)	)	PUNCT
ejpam-4136	17	33	and	and	CCONJ
ejpam-4136	17	34	(	(	PUNCT
ejpam-4136	17	35	i1	i1	PROPN
ejpam-4136	17	36	)	)	PUNCT
ejpam-4136	17	37	(	(	PUNCT
ejpam-4136	17	38	ab)c	ab)c	PROPN
ejpam-4136	17	39	=	=	SYM
ejpam-4136	17	40	a(bc	a(bc	PROPN
ejpam-4136	17	41	)	)	PUNCT
ejpam-4136	17	42	for	for	ADP
ejpam-4136	17	43	all	all	DET
ejpam-4136	17	44	a	a	DET
ejpam-4136	17	45	,	,	PUNCT
ejpam-4136	17	46	b	b	NOUN
ejpam-4136	17	47	,	,	PUNCT
ejpam-4136	17	48	c	c	PROPN
ejpam-4136	17	49	∈	∈	PROPN
ejpam-4136	17	50	a	a	DET
ejpam-4136	17	51	,	,	PUNCT
ejpam-4136	17	52	(	(	PUNCT
ejpam-4136	17	53	i2	i2	PROPN
ejpam-4136	17	54	)	)	PUNCT
ejpam-4136	17	55	a(b+	a(b+	PRON
ejpam-4136	18	1	c	c	X
ejpam-4136	18	2	)	)	PUNCT
ejpam-4136	18	3	=	=	SYM
ejpam-4136	18	4	ab+	ab+	NOUN
ejpam-4136	18	5	ac	ac	PROPN
ejpam-4136	18	6	and	and	CCONJ
ejpam-4136	18	7	(	(	PUNCT
ejpam-4136	18	8	a+	a+	X
ejpam-4136	18	9	b)c	b)c	X
ejpam-4136	18	10	=	=	SYM
ejpam-4136	18	11	ab+	ab+	NOUN
ejpam-4136	18	12	bc	bc	VERB
ejpam-4136	18	13	for	for	ADP
ejpam-4136	18	14	all	all	DET
ejpam-4136	18	15	a	a	DET
ejpam-4136	18	16	,	,	PUNCT
ejpam-4136	18	17	b	b	NOUN
ejpam-4136	18	18	,	,	PUNCT
ejpam-4136	18	19	c	c	PROPN
ejpam-4136	18	20	∈	∈	PROPN
ejpam-4136	18	21	a	a	DET
ejpam-4136	18	22	,	,	PUNCT
ejpam-4136	18	23	(	(	PUNCT
ejpam-4136	18	24	i3	i3	NOUN
ejpam-4136	18	25	)	)	PUNCT
ejpam-4136	18	26	k(ab	k(ab	PROPN
ejpam-4136	18	27	)	)	PUNCT
ejpam-4136	18	28	=	=	PUNCT
ejpam-4136	18	29	(	(	PUNCT
ejpam-4136	18	30	ka)b	ka)b	PROPN
ejpam-4136	18	31	=	=	SYM
ejpam-4136	18	32	a(kb	a(kb	X
ejpam-4136	18	33	)	)	PUNCT
ejpam-4136	18	34	for	for	ADP
ejpam-4136	18	35	all	all	DET
ejpam-4136	18	36	a	a	PRON
ejpam-4136	18	37	,	,	PUNCT
ejpam-4136	18	38	b	b	X
ejpam-4136	18	39	∈	∈	PROPN
ejpam-4136	18	40	a	a	PRON
ejpam-4136	18	41	,	,	PUNCT
ejpam-4136	18	42	for	for	ADP
ejpam-4136	18	43	all	all	DET
ejpam-4136	18	44	k	k	PROPN
ejpam-4136	18	45	∈	∈	PROPN
ejpam-4136	18	46	k.	k.	NOUN
ejpam-4136	18	47	∗corresponding	∗corresponde	VERB
ejpam-4136	18	48	author	author	NOUN
ejpam-4136	18	49	.	.	PUNCT
ejpam-4136	19	1	doi	doi	NOUN
ejpam-4136	19	2	:	:	PUNCT
ejpam-4136	19	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4136	https://doi.org/10.29020/nybg.ejpam.v14i4.4136	VERB
ejpam-4136	19	4	email	email	NOUN
ejpam-4136	19	5	addresses	address	NOUN
ejpam-4136	19	6	:	:	PUNCT
ejpam-4136	19	7	dehghannezhad@iust.ac.ir	dehghannezhad@iust.ac.ir	ADJ
ejpam-4136	19	8	(	(	PUNCT
ejpam-4136	19	9	akbar	akbar	NOUN
ejpam-4136	19	10	dehghan	dehghan	PROPN
ejpam-4136	19	11	nezhad	nezhad	VERB
ejpam-4136	19	12	)	)	PUNCT
ejpam-4136	19	13	,	,	PUNCT
ejpam-4136	20	1	radens@beotel.net	radens@beotel.net	PROPN
ejpam-4136	20	2	(	(	PUNCT
ejpam-4136	20	3	stojan	stojan	ADP
ejpam-4136	20	4	radenović	radenović	ADJ
ejpam-4136	20	5	)	)	PUNCT
ejpam-4136	20	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4136	20	7	1148	1148	NUM
ejpam-4136	20	8	©	©	PROPN
ejpam-4136	20	9	2021	2021	NUM
ejpam-4136	20	10	ejpam	ejpam	VERB
ejpam-4136	20	11	all	all	DET
ejpam-4136	20	12	rights	right	NOUN
ejpam-4136	20	13	reserved	reserve	VERB
ejpam-4136	20	14	.	.	PUNCT
ejpam-4136	21	1	a.	a.	PROPN
ejpam-4136	21	2	d.nezhad	d.nezhad	PROPN
ejpam-4136	21	3	,	,	PUNCT
ejpam-4136	21	4	s.	s.	PROPN
ejpam-4136	21	5	radenović	radenović	PROPN
ejpam-4136	21	6	/	/	SYM
ejpam-4136	21	7	eur	eur	PROPN
ejpam-4136	21	8	.	.	PUNCT
ejpam-4136	22	1	j.	j.	PROPN
ejpam-4136	22	2	pure	pure	PROPN
ejpam-4136	22	3	appl	appl	PROPN
ejpam-4136	22	4	.	.	PROPN
ejpam-4136	22	5	math	math	PROPN
ejpam-4136	22	6	,	,	PUNCT
ejpam-4136	22	7	14	14	NUM
ejpam-4136	22	8	(	(	PUNCT
ejpam-4136	22	9	4	4	NUM
ejpam-4136	22	10	)	)	PUNCT
ejpam-4136	22	11	(	(	PUNCT
ejpam-4136	22	12	2021	2021	NUM
ejpam-4136	22	13	)	)	PUNCT
ejpam-4136	22	14	,	,	PUNCT
ejpam-4136	22	15	1148	1148	NUM
ejpam-4136	22	16	-	-	SYM
ejpam-4136	22	17	1160	1160	NUM
ejpam-4136	22	18	1149	1149	NUM
ejpam-4136	22	19	a	a	DET
ejpam-4136	22	20	banach	banach	NOUN
ejpam-4136	22	21	space	space	NOUN
ejpam-4136	22	22	a	a	PRON
ejpam-4136	22	23	over	over	ADP
ejpam-4136	22	24	a	a	DET
ejpam-4136	22	25	field	field	NOUN
ejpam-4136	22	26	k	k	NOUN
ejpam-4136	23	1	(	(	PUNCT
ejpam-4136	23	2	r	r	NOUN
ejpam-4136	23	3	or	or	CCONJ
ejpam-4136	23	4	c	c	NOUN
ejpam-4136	23	5	)	)	PUNCT
ejpam-4136	23	6	is	be	AUX
ejpam-4136	23	7	said	say	VERB
ejpam-4136	23	8	to	to	PART
ejpam-4136	23	9	be	be	AUX
ejpam-4136	23	10	a	a	DET
ejpam-4136	23	11	banach	banach	NOUN
ejpam-4136	23	12	algebra	algebra	NOUN
ejpam-4136	23	13	if	if	SCONJ
ejpam-4136	23	14	(	(	PUNCT
ejpam-4136	23	15	i4	i4	PROPN
ejpam-4136	23	16	)	)	PUNCT
ejpam-4136	23	17	a	a	PRON
ejpam-4136	23	18	is	be	AUX
ejpam-4136	23	19	an	an	DET
ejpam-4136	23	20	algebra	algebra	NOUN
ejpam-4136	23	21	and	and	CCONJ
ejpam-4136	23	22	for	for	ADP
ejpam-4136	23	23	all	all	DET
ejpam-4136	23	24	a	a	DET
ejpam-4136	23	25	,	,	PUNCT
ejpam-4136	23	26	b	b	NOUN
ejpam-4136	23	27	,	,	PUNCT
ejpam-4136	23	28	c	c	PROPN
ejpam-4136	23	29	∈	∈	PROPN
ejpam-4136	23	30	a	a	DET
ejpam-4136	23	31	,	,	PUNCT
ejpam-4136	23	32	(	(	PUNCT
ejpam-4136	23	33	i5	i5	NOUN
ejpam-4136	23	34	)	)	PUNCT
ejpam-4136	23	35	∥	∥	PUNCT
ejpam-4136	24	1	ab	ab	PROPN
ejpam-4136	24	2	∥≤∥	∥≤∥	PROPN
ejpam-4136	24	3	a	a	DET
ejpam-4136	24	4	∥	∥	X
ejpam-4136	24	5	·	·	PUNCT
ejpam-4136	24	6	∥	∥	NUM
ejpam-4136	24	7	b	b	NOUN
ejpam-4136	24	8	∥	∥	NOUN
ejpam-4136	24	9	for	for	ADP
ejpam-4136	24	10	all	all	DET
ejpam-4136	24	11	a	a	DET
ejpam-4136	24	12	,	,	PUNCT
ejpam-4136	24	13	b	b	X
ejpam-4136	24	14	∈	∈	PROPN
ejpam-4136	24	15	a.	a.	NOUN
ejpam-4136	24	16	here	here	ADV
ejpam-4136	24	17	we	we	PRON
ejpam-4136	24	18	shall	shall	AUX
ejpam-4136	24	19	always	always	ADV
ejpam-4136	24	20	assume	assume	VERB
ejpam-4136	24	21	that	that	SCONJ
ejpam-4136	24	22	the	the	DET
ejpam-4136	24	23	banach	banach	NOUN
ejpam-4136	24	24	algebra	algebra	NOUN
ejpam-4136	24	25	a	a	PRON
ejpam-4136	24	26	is	be	AUX
ejpam-4136	24	27	unital	unital	ADJ
ejpam-4136	24	28	,	,	PUNCT
ejpam-4136	24	29	that	that	PRON
ejpam-4136	24	30	is	is	ADV
ejpam-4136	24	31	it	it	PRON
ejpam-4136	24	32	has	have	VERB
ejpam-4136	24	33	a	a	DET
ejpam-4136	24	34	unity	unity	NOUN
ejpam-4136	24	35	element	element	NOUN
ejpam-4136	24	36	ea	ea	ADP
ejpam-4136	25	1	such	such	ADJ
ejpam-4136	25	2	that	that	PRON
ejpam-4136	25	3	eaa	eaa	PROPN
ejpam-4136	25	4	=	=	PROPN
ejpam-4136	25	5	aea	aea	PROPN
ejpam-4136	25	6	=	=	PROPN
ejpam-4136	25	7	a	a	PROPN
ejpam-4136	25	8	,	,	PUNCT
ejpam-4136	25	9	for	for	ADP
ejpam-4136	25	10	all	all	DET
ejpam-4136	25	11	a	a	DET
ejpam-4136	25	12	∈	∈	PROPN
ejpam-4136	25	13	a.	a.	NOUN
ejpam-4136	25	14	note	note	NOUN
ejpam-4136	25	15	that	that	SCONJ
ejpam-4136	25	16	the	the	DET
ejpam-4136	25	17	unity	unity	NOUN
ejpam-4136	25	18	element	element	NOUN
ejpam-4136	25	19	of	of	ADP
ejpam-4136	25	20	a	a	DET
ejpam-4136	25	21	banach	banach	NOUN
ejpam-4136	25	22	algebra	algebra	NOUN
ejpam-4136	25	23	a	a	PRON
ejpam-4136	25	24	,	,	PUNCT
ejpam-4136	25	25	if	if	SCONJ
ejpam-4136	25	26	it	it	PRON
ejpam-4136	25	27	exists	exist	VERB
ejpam-4136	25	28	,	,	PUNCT
ejpam-4136	25	29	is	be	AUX
ejpam-4136	25	30	unique	unique	ADJ
ejpam-4136	25	31	.	.	PUNCT
ejpam-4136	26	1	a	a	DET
ejpam-4136	26	2	non	non	ADJ
ejpam-4136	26	3	-	-	ADJ
ejpam-4136	26	4	zero	zero	NUM
ejpam-4136	26	5	element	element	NOUN
ejpam-4136	26	6	b	b	PROPN
ejpam-4136	26	7	∈	∈	PROPN
ejpam-4136	26	8	a	a	PRON
ejpam-4136	26	9	is	be	AUX
ejpam-4136	26	10	said	say	VERB
ejpam-4136	26	11	to	to	PART
ejpam-4136	26	12	be	be	AUX
ejpam-4136	26	13	invertible	invertible	ADJ
ejpam-4136	26	14	if	if	SCONJ
ejpam-4136	26	15	its	its	PRON
ejpam-4136	26	16	inverse	inverse	NOUN
ejpam-4136	26	17	exists	exist	VERB
ejpam-4136	26	18	i.e.	i.e.	X
ejpam-4136	26	19	if	if	SCONJ
ejpam-4136	26	20	there	there	PRON
ejpam-4136	26	21	exists	exist	VERB
ejpam-4136	26	22	a	a	DET
ejpam-4136	26	23	non	non	ADJ
ejpam-4136	26	24	-	-	ADJ
ejpam-4136	26	25	zero	zero	ADJ
ejpam-4136	26	26	element	element	NOUN
ejpam-4136	26	27	b−1	b−1	PROPN
ejpam-4136	26	28	∈	∈	PROPN
ejpam-4136	26	29	a	a	DET
ejpam-4136	26	30	such	such	ADJ
ejpam-4136	26	31	that	that	SCONJ
ejpam-4136	26	32	bb−1	bb−1	NOUN
ejpam-4136	26	33	=	=	SYM
ejpam-4136	26	34	b−1b	b−1b	X
ejpam-4136	26	35	=	=	SYM
ejpam-4136	26	36	ea	ea	NOUN
ejpam-4136	26	37	,	,	PUNCT
ejpam-4136	26	38	we	we	PRON
ejpam-4136	26	39	call	call	VERB
ejpam-4136	26	40	b−1	b−1	PROPN
ejpam-4136	26	41	is	be	AUX
ejpam-4136	26	42	the	the	DET
ejpam-4136	26	43	inverse	inverse	NOUN
ejpam-4136	26	44	of	of	ADP
ejpam-4136	26	45	b.	b.	PROPN
ejpam-4136	26	46	one	one	PROPN
ejpam-4136	26	47	can	can	AUX
ejpam-4136	26	48	show	show	VERB
ejpam-4136	26	49	that	that	SCONJ
ejpam-4136	26	50	in	in	ADP
ejpam-4136	26	51	a	a	DET
ejpam-4136	26	52	banach	banach	NOUN
ejpam-4136	26	53	algebra	algebra	NOUN
ejpam-4136	26	54	a	a	DET
ejpam-4136	26	55	,	,	PUNCT
ejpam-4136	26	56	with	with	ADP
ejpam-4136	26	57	the	the	DET
ejpam-4136	26	58	unity	unity	NOUN
ejpam-4136	26	59	element	element	NOUN
ejpam-4136	26	60	ea	ea	ADP
ejpam-4136	26	61	the	the	DET
ejpam-4136	26	62	inverse	inverse	NOUN
ejpam-4136	26	63	of	of	ADP
ejpam-4136	26	64	an	an	DET
ejpam-4136	26	65	element	element	NOUN
ejpam-4136	26	66	is	be	AUX
ejpam-4136	26	67	unique	unique	ADJ
ejpam-4136	26	68	.	.	PUNCT
ejpam-4136	27	1	also	also	ADV
ejpam-4136	27	2	for	for	ADP
ejpam-4136	27	3	all	all	DET
ejpam-4136	27	4	a	a	PRON
ejpam-4136	27	5	,	,	PUNCT
ejpam-4136	27	6	b	b	X
ejpam-4136	27	7	∈	∈	PROPN
ejpam-4136	27	8	a	a	PRON
ejpam-4136	27	9	,	,	PUNCT
ejpam-4136	27	10	we	we	PRON
ejpam-4136	27	11	have	have	VERB
ejpam-4136	27	12	(	(	PUNCT
ejpam-4136	27	13	ab)−1	ab)−1	PROPN
ejpam-4136	27	14	=	=	NOUN
ejpam-4136	27	15	b−1a−1	b−1a−1	PROPN
ejpam-4136	27	16	and	and	CCONJ
ejpam-4136	27	17	(	(	PUNCT
ejpam-4136	27	18	a−1)−1	a−1)−1	NOUN
ejpam-4136	27	19	=	=	PUNCT
ejpam-4136	27	20	a.	a.	NOUN
ejpam-4136	27	21	definition	definition	NOUN
ejpam-4136	27	22	2	2	NUM
ejpam-4136	27	23	.	.	PUNCT
ejpam-4136	28	1	[	[	X
ejpam-4136	28	2	6	6	NUM
ejpam-4136	28	3	]	]	PUNCT
ejpam-4136	28	4	a	a	DET
ejpam-4136	28	5	subset	subset	NOUN
ejpam-4136	28	6	p	p	NOUN
ejpam-4136	28	7	of	of	ADP
ejpam-4136	28	8	a	a	DET
ejpam-4136	28	9	unital	unital	ADJ
ejpam-4136	28	10	banach	banach	NOUN
ejpam-4136	28	11	algebra	algebra	NOUN
ejpam-4136	28	12	a	a	PRON
ejpam-4136	28	13	is	be	AUX
ejpam-4136	28	14	called	call	VERB
ejpam-4136	28	15	(	(	PUNCT
ejpam-4136	28	16	p1	p1	PROPN
ejpam-4136	28	17	)	)	PUNCT
ejpam-4136	28	18	p	p	NOUN
ejpam-4136	28	19	is	be	AUX
ejpam-4136	28	20	non	non	X
ejpam-4136	28	21	empty	empty	ADJ
ejpam-4136	28	22	,	,	PUNCT
ejpam-4136	28	23	0a	0a	PROPN
ejpam-4136	28	24	,	,	PUNCT
ejpam-4136	28	25	ea	ea	X
ejpam-4136	29	1	∈	∈	PROPN
ejpam-4136	30	1	p	p	X
ejpam-4136	30	2	,	,	PUNCT
ejpam-4136	30	3	where	where	SCONJ
ejpam-4136	30	4	0a	0a	PROPN
ejpam-4136	30	5	is	be	AUX
ejpam-4136	30	6	the	the	DET
ejpam-4136	30	7	zero	zero	NUM
ejpam-4136	30	8	element	element	NOUN
ejpam-4136	30	9	of	of	ADP
ejpam-4136	30	10	a.	a.	NOUN
ejpam-4136	30	11	(	(	PUNCT
ejpam-4136	30	12	p2	p2	PROPN
ejpam-4136	30	13	)	)	PUNCT
ejpam-4136	30	14	if	if	SCONJ
ejpam-4136	30	15	a	a	PRON
ejpam-4136	30	16	,	,	PUNCT
ejpam-4136	30	17	b	b	PROPN
ejpam-4136	30	18	∈	∈	PROPN
ejpam-4136	30	19	p	p	NOUN
ejpam-4136	30	20	and	and	CCONJ
ejpam-4136	30	21	r	r	NOUN
ejpam-4136	30	22	,	,	PUNCT
ejpam-4136	30	23	s	s	X
ejpam-4136	30	24	≥	≥	NOUN
ejpam-4136	30	25	0	0	NUM
ejpam-4136	30	26	,	,	PUNCT
ejpam-4136	30	27	then	then	ADV
ejpam-4136	30	28	ra+	ra+	PROPN
ejpam-4136	30	29	sb	sb	PROPN
ejpam-4136	30	30	∈	∈	PROPN
ejpam-4136	30	31	p.	p.	PROPN
ejpam-4136	30	32	(	(	PUNCT
ejpam-4136	30	33	p3	p3	PROPN
ejpam-4136	30	34	)	)	PUNCT
ejpam-4136	30	35	a	a	PRON
ejpam-4136	30	36	,	,	PUNCT
ejpam-4136	30	37	b	b	X
ejpam-4136	30	38	∈	∈	PROPN
ejpam-4136	30	39	p	p	NOUN
ejpam-4136	30	40	implies	imply	VERB
ejpam-4136	30	41	ab	ab	PROPN
ejpam-4136	30	42	∈	∈	PROPN
ejpam-4136	30	43	k.	k.	PROPN
ejpam-4136	31	1	(	(	PUNCT
ejpam-4136	31	2	p4	p4	ADJ
ejpam-4136	31	3	)	)	PUNCT
ejpam-4136	31	4	if	if	SCONJ
ejpam-4136	31	5	a,−a	a,−a	VERB
ejpam-4136	31	6	∈	∈	PROPN
ejpam-4136	31	7	k	k	PROPN
ejpam-4136	31	8	for	for	ADP
ejpam-4136	31	9	some	some	DET
ejpam-4136	31	10	a	a	DET
ejpam-4136	31	11	∈	∈	PROPN
ejpam-4136	31	12	a	a	DET
ejpam-4136	31	13	then	then	ADV
ejpam-4136	31	14	a	a	DET
ejpam-4136	31	15	=	=	SYM
ejpam-4136	31	16	0a	0a	PROPN
ejpam-4136	31	17	,	,	PUNCT
ejpam-4136	31	18	where	where	SCONJ
ejpam-4136	31	19	0a	0a	PROPN
ejpam-4136	31	20	is	be	AUX
ejpam-4136	31	21	the	the	DET
ejpam-4136	31	22	zero	zero	NUM
ejpam-4136	31	23	element	element	NOUN
ejpam-4136	31	24	of	of	ADP
ejpam-4136	31	25	a.	a.	NOUN
ejpam-4136	31	26	a	a	DET
ejpam-4136	31	27	cone	cone	NOUN
ejpam-4136	31	28	p	p	NOUN
ejpam-4136	31	29	is	be	AUX
ejpam-4136	31	30	called	call	VERB
ejpam-4136	31	31	a	a	DET
ejpam-4136	31	32	solid	solid	ADJ
ejpam-4136	31	33	cone	cone	NOUN
ejpam-4136	31	34	if	if	SCONJ
ejpam-4136	31	35	int(p	int(p	PROPN
ejpam-4136	31	36	)	)	PUNCT
ejpam-4136	31	37	̸=	̸=	PROPN
ejpam-4136	31	38	0	0	NUM
ejpam-4136	31	39	.	.	PUNCT
ejpam-4136	32	1	each	each	DET
ejpam-4136	32	2	cone	cone	NOUN
ejpam-4136	32	3	p	p	NOUN
ejpam-4136	32	4	induces	induce	VERB
ejpam-4136	32	5	a	a	DET
ejpam-4136	32	6	partial	partial	ADJ
ejpam-4136	32	7	ordering	ordering	NOUN
ejpam-4136	32	8	⪯	⪯	NOUN
ejpam-4136	32	9	on	on	ADP
ejpam-4136	32	10	a	a	PRON
ejpam-4136	32	11	by	by	ADP
ejpam-4136	32	12	a	a	DET
ejpam-4136	32	13	⪯	⪯	NOUN
ejpam-4136	33	1	b	b	NOUN
ejpam-4136	34	1	if	if	SCONJ
ejpam-4136	35	1	and	and	CCONJ
ejpam-4136	35	2	only	only	ADV
ejpam-4136	35	3	if	if	SCONJ
ejpam-4136	35	4	a	a	DET
ejpam-4136	35	5	−	−	PROPN
ejpam-4136	35	6	b	b	PROPN
ejpam-4136	35	7	∈	∈	PROPN
ejpam-4136	35	8	p.	p.	NOUN
ejpam-4136	35	9	we	we	PRON
ejpam-4136	35	10	write	write	VERB
ejpam-4136	35	11	a	a	DET
ejpam-4136	35	12	≺	≺	NOUN
ejpam-4136	35	13	b	b	NOUN
ejpam-4136	35	14	if	if	SCONJ
ejpam-4136	35	15	a	a	DET
ejpam-4136	35	16	⪯	⪯	NOUN
ejpam-4136	35	17	b	b	PROPN
ejpam-4136	35	18	and	and	CCONJ
ejpam-4136	35	19	a	a	DET
ejpam-4136	35	20	̸=	̸=	PROPN
ejpam-4136	35	21	b.	b.	NOUN
ejpam-4136	35	22	when	when	SCONJ
ejpam-4136	35	23	the	the	DET
ejpam-4136	35	24	cone	cone	NOUN
ejpam-4136	35	25	is	be	AUX
ejpam-4136	35	26	solid	solid	ADJ
ejpam-4136	35	27	a≪	a≪	ADP
ejpam-4136	35	28	b	b	NOUN
ejpam-4136	35	29	will	will	AUX
ejpam-4136	35	30	stand	stand	VERB
ejpam-4136	35	31	for	for	ADP
ejpam-4136	35	32	a−	a−	PROPN
ejpam-4136	35	33	b	b	PROPN
ejpam-4136	35	34	∈	∈	PROPN
ejpam-4136	35	35	int(p	int(p	PROPN
ejpam-4136	35	36	)	)	PUNCT
ejpam-4136	35	37	.	.	PUNCT
ejpam-4136	36	1	the	the	DET
ejpam-4136	36	2	cone	cone	NOUN
ejpam-4136	36	3	p	p	NOUN
ejpam-4136	36	4	is	be	AUX
ejpam-4136	36	5	said	say	VERB
ejpam-4136	36	6	to	to	PART
ejpam-4136	36	7	be	be	AUX
ejpam-4136	36	8	normal	normal	ADJ
ejpam-4136	36	9	if	if	SCONJ
ejpam-4136	36	10	there	there	PRON
ejpam-4136	36	11	exists	exist	VERB
ejpam-4136	36	12	a	a	DET
ejpam-4136	36	13	number	number	NOUN
ejpam-4136	36	14	l	l	NOUN
ejpam-4136	36	15	>	>	X
ejpam-4136	36	16	0	0	NUM
ejpam-4136	36	17	such	such	ADJ
ejpam-4136	36	18	that	that	SCONJ
ejpam-4136	36	19	0a	0a	PROPN
ejpam-4136	36	20	⪯	⪯	NOUN
ejpam-4136	36	21	a	a	DET
ejpam-4136	36	22	⪯	⪯	NOUN
ejpam-4136	36	23	implies	imply	VERB
ejpam-4136	36	24	∥	∥	X
ejpam-4136	36	25	a	a	DET
ejpam-4136	36	26	∥≤	∥≤	PROPN
ejpam-4136	36	27	l	l	NOUN
ejpam-4136	36	28	∥	∥	PUNCT
ejpam-4136	36	29	b	b	NOUN
ejpam-4136	36	30	∥.	∥.	NOUN
ejpam-4136	36	31	the	the	DET
ejpam-4136	36	32	least	least	ADV
ejpam-4136	36	33	positive	positive	ADJ
ejpam-4136	36	34	number	number	NOUN
ejpam-4136	36	35	l	l	NOUN
ejpam-4136	36	36	,	,	PUNCT
ejpam-4136	36	37	which	which	PRON
ejpam-4136	36	38	satisfies	satisfy	VERB
ejpam-4136	36	39	the	the	DET
ejpam-4136	36	40	normality	normality	NOUN
ejpam-4136	36	41	condition	condition	NOUN
ejpam-4136	36	42	is	be	AUX
ejpam-4136	36	43	called	call	VERB
ejpam-4136	36	44	the	the	DET
ejpam-4136	36	45	normal	normal	ADJ
ejpam-4136	36	46	constant	constant	NOUN
ejpam-4136	36	47	of	of	ADP
ejpam-4136	36	48	p.	p.	PROPN
ejpam-4136	36	49	remark	remark	NOUN
ejpam-4136	36	50	1	1	NUM
ejpam-4136	36	51	.	.	PUNCT
ejpam-4136	37	1	an	an	DET
ejpam-4136	37	2	ordered	order	VERB
ejpam-4136	37	3	ring	ring	NOUN
ejpam-4136	37	4	is	be	AUX
ejpam-4136	37	5	a	a	DET
ejpam-4136	37	6	(	(	PUNCT
ejpam-4136	37	7	usually	usually	ADV
ejpam-4136	37	8	commutative	commutative	ADJ
ejpam-4136	37	9	)	)	PUNCT
ejpam-4136	37	10	ring	ring	NOUN
ejpam-4136	37	11	r	r	NOUN
ejpam-4136	37	12	with	with	ADP
ejpam-4136	37	13	a	a	DET
ejpam-4136	37	14	total	total	ADJ
ejpam-4136	37	15	order	order	NOUN
ejpam-4136	37	16	⪯	⪯	NOUN
ejpam-4136	37	17	such	such	ADJ
ejpam-4136	37	18	that	that	PRON
ejpam-4136	37	19	for	for	ADP
ejpam-4136	37	20	all	all	DET
ejpam-4136	37	21	a	a	DET
ejpam-4136	37	22	,	,	PUNCT
ejpam-4136	37	23	b	b	NOUN
ejpam-4136	37	24	,	,	PUNCT
ejpam-4136	37	25	and	and	CCONJ
ejpam-4136	37	26	c	c	X
ejpam-4136	37	27	in	in	ADP
ejpam-4136	37	28	r	r	NOUN
ejpam-4136	37	29	:	:	PUNCT
ejpam-4136	37	30	i	i	NOUN
ejpam-4136	37	31	)	)	PUNCT
ejpam-4136	37	32	if	if	SCONJ
ejpam-4136	37	33	a	a	DET
ejpam-4136	37	34	⪯	⪯	NOUN
ejpam-4136	37	35	b	b	NOUN
ejpam-4136	37	36	,	,	PUNCT
ejpam-4136	37	37	then	then	ADV
ejpam-4136	37	38	a+	a+	PUNCT
ejpam-4136	37	39	c	c	PROPN
ejpam-4136	37	40	⪯	⪯	NOUN
ejpam-4136	37	41	b+	b+	ADP
ejpam-4136	37	42	c	c	PROPN
ejpam-4136	37	43	ii	ii	PROPN
ejpam-4136	37	44	)	)	PUNCT
ejpam-4136	37	45	if	if	SCONJ
ejpam-4136	37	46	0	0	NUM
ejpam-4136	37	47	⪯	⪯	VERB
ejpam-4136	37	48	a	a	PRON
ejpam-4136	37	49	and	and	CCONJ
ejpam-4136	37	50	0	0	NUM
ejpam-4136	37	51	⪯	⪯	PROPN
ejpam-4136	37	52	b	b	NUM
ejpam-4136	37	53	,	,	PUNCT
ejpam-4136	37	54	then	then	ADV
ejpam-4136	37	55	0	0	NUM
ejpam-4136	37	56	⪯	⪯	VERB
ejpam-4136	37	57	a	a	DET
ejpam-4136	37	58	·	·	PUNCT
ejpam-4136	37	59	b.	b.	NOUN
ejpam-4136	38	1	we	we	PRON
ejpam-4136	38	2	denote	denote	VERB
ejpam-4136	38	3	r+	r+	PUNCT
ejpam-4136	38	4	a	a	DET
ejpam-4136	38	5	set	set	NOUN
ejpam-4136	38	6	of	of	ADP
ejpam-4136	38	7	non	non	ADJ
ejpam-4136	38	8	-	-	ADJ
ejpam-4136	38	9	negative	negative	ADJ
ejpam-4136	38	10	elements	element	NOUN
ejpam-4136	38	11	of	of	ADP
ejpam-4136	38	12	r	r	NOUN
ejpam-4136	38	13	namely	namely	ADV
ejpam-4136	38	14	r+	r+	PUNCT
ejpam-4136	38	15	=	=	PUNCT
ejpam-4136	38	16	{	{	PUNCT
ejpam-4136	38	17	g	g	PROPN
ejpam-4136	38	18	∈	∈	PROPN
ejpam-4136	38	19	r	r	NOUN
ejpam-4136	38	20	:	:	PUNCT
ejpam-4136	38	21	0	0	NUM
ejpam-4136	38	22	⪯	⪯	NOUN
ejpam-4136	38	23	g	g	NOUN
ejpam-4136	38	24	}	}	PUNCT
ejpam-4136	38	25	.	.	PUNCT
ejpam-4136	39	1	definition	definition	NOUN
ejpam-4136	39	2	3	3	NUM
ejpam-4136	39	3	.	.	PUNCT
ejpam-4136	40	1	[	[	X
ejpam-4136	40	2	7	7	X
ejpam-4136	40	3	]	]	X
ejpam-4136	40	4	let	let	VERB
ejpam-4136	40	5	x	x	PRON
ejpam-4136	40	6	be	be	AUX
ejpam-4136	40	7	a	a	DET
ejpam-4136	40	8	non	non	ADJ
ejpam-4136	40	9	-	-	ADJ
ejpam-4136	40	10	empty	empty	ADJ
ejpam-4136	40	11	set	set	NOUN
ejpam-4136	40	12	and	and	CCONJ
ejpam-4136	40	13	a	a	DET
ejpam-4136	40	14	a	a	DET
ejpam-4136	40	15	banach	banach	NOUN
ejpam-4136	40	16	algebra	algebra	NOUN
ejpam-4136	40	17	.	.	PUNCT
ejpam-4136	41	1	a	a	DET
ejpam-4136	41	2	mapping	mapping	NOUN
ejpam-4136	41	3	dc	dc	PROPN
ejpam-4136	41	4	:	:	PUNCT
ejpam-4136	41	5	x	x	X
ejpam-4136	41	6	×x	×x	VERB
ejpam-4136	41	7	−→	−→	NOUN
ejpam-4136	41	8	a	a	PRON
ejpam-4136	41	9	is	be	AUX
ejpam-4136	41	10	called	call	VERB
ejpam-4136	41	11	a	a	DET
ejpam-4136	41	12	cone	cone	NOUN
ejpam-4136	41	13	metric	metric	NOUN
ejpam-4136	41	14	if	if	SCONJ
ejpam-4136	41	15	it	it	PRON
ejpam-4136	41	16	satisfies	satisfy	VERB
ejpam-4136	41	17	the	the	DET
ejpam-4136	41	18	following	follow	VERB
ejpam-4136	41	19	conditions	condition	NOUN
ejpam-4136	41	20	:	:	PUNCT
ejpam-4136	41	21	(	(	PUNCT
ejpam-4136	41	22	b1	b1	NOUN
ejpam-4136	41	23	)	)	PUNCT
ejpam-4136	41	24	0a	0a	PROPN
ejpam-4136	41	25	⪯	⪯	PROPN
ejpam-4136	41	26	dc(x	dc(x	NOUN
ejpam-4136	41	27	,	,	PUNCT
ejpam-4136	41	28	y	y	NOUN
ejpam-4136	41	29	)	)	PUNCT
ejpam-4136	41	30	,	,	PUNCT
ejpam-4136	41	31	for	for	ADP
ejpam-4136	41	32	all	all	DET
ejpam-4136	41	33	x	x	NOUN
ejpam-4136	41	34	,	,	PUNCT
ejpam-4136	41	35	y	y	PROPN
ejpam-4136	41	36	∈	∈	PROPN
ejpam-4136	41	37	x	x	PROPN
ejpam-4136	41	38	,	,	PUNCT
ejpam-4136	41	39	dc(x	dc(x	NOUN
ejpam-4136	41	40	,	,	PUNCT
ejpam-4136	41	41	y	y	NOUN
ejpam-4136	41	42	)	)	PUNCT
ejpam-4136	41	43	=	=	SYM
ejpam-4136	41	44	0a	0a	PROPN
ejpam-4136	41	45	if	if	SCONJ
ejpam-4136	41	46	and	and	CCONJ
ejpam-4136	41	47	only	only	ADV
ejpam-4136	41	48	if	if	SCONJ
ejpam-4136	41	49	x	x	X
ejpam-4136	41	50	=	=	SYM
ejpam-4136	41	51	y	y	PROPN
ejpam-4136	41	52	,	,	PUNCT
ejpam-4136	41	53	(	(	PUNCT
ejpam-4136	41	54	b2	b2	NOUN
ejpam-4136	41	55	)	)	PUNCT
ejpam-4136	41	56	dc(x	dc(x	NOUN
ejpam-4136	41	57	,	,	PUNCT
ejpam-4136	41	58	y	y	NOUN
ejpam-4136	41	59	)	)	PUNCT
ejpam-4136	41	60	=	=	SYM
ejpam-4136	41	61	dc(y	dc(y	NOUN
ejpam-4136	41	62	,	,	PUNCT
ejpam-4136	41	63	x	x	NOUN
ejpam-4136	41	64	)	)	PUNCT
ejpam-4136	41	65	,	,	PUNCT
ejpam-4136	41	66	for	for	ADP
ejpam-4136	41	67	all	all	DET
ejpam-4136	41	68	x	x	NOUN
ejpam-4136	41	69	,	,	PUNCT
ejpam-4136	41	70	y	y	PROPN
ejpam-4136	41	71	∈	∈	PROPN
ejpam-4136	41	72	x	x	X
ejpam-4136	41	73	,	,	PUNCT
ejpam-4136	41	74	(	(	PUNCT
ejpam-4136	41	75	b3	b3	PROPN
ejpam-4136	41	76	)	)	PUNCT
ejpam-4136	41	77	dc(x	dc(x	NOUN
ejpam-4136	41	78	,	,	PUNCT
ejpam-4136	41	79	y	y	NOUN
ejpam-4136	41	80	)	)	PUNCT
ejpam-4136	41	81	⪯	⪯	PROPN
ejpam-4136	41	82	dc(x	dc(x	NOUN
ejpam-4136	41	83	,	,	PUNCT
ejpam-4136	41	84	z	z	NOUN
ejpam-4136	41	85	)	)	PUNCT
ejpam-4136	41	86	+	+	NUM
ejpam-4136	41	87	dc(z	dc(z	NOUN
ejpam-4136	41	88	,	,	PUNCT
ejpam-4136	41	89	y	y	NOUN
ejpam-4136	41	90	)	)	PUNCT
ejpam-4136	41	91	for	for	ADP
ejpam-4136	41	92	all	all	DET
ejpam-4136	41	93	x	x	NOUN
ejpam-4136	41	94	,	,	PUNCT
ejpam-4136	41	95	y	y	PROPN
ejpam-4136	41	96	,	,	PUNCT
ejpam-4136	41	97	z	z	NOUN
ejpam-4136	41	98	∈	∈	PROPN
ejpam-4136	41	99	x.	x.	NOUN
ejpam-4136	41	100	in	in	ADP
ejpam-4136	41	101	this	this	DET
ejpam-4136	41	102	case	case	NOUN
ejpam-4136	41	103	,	,	PUNCT
ejpam-4136	41	104	the	the	DET
ejpam-4136	41	105	pair	pair	NOUN
ejpam-4136	41	106	(	(	PUNCT
ejpam-4136	41	107	x	x	NOUN
ejpam-4136	41	108	,	,	PUNCT
ejpam-4136	41	109	db	db	PROPN
ejpam-4136	41	110	)	)	PUNCT
ejpam-4136	41	111	is	be	AUX
ejpam-4136	41	112	called	call	VERB
ejpam-4136	41	113	a	a	DET
ejpam-4136	41	114	cone	cone	NOUN
ejpam-4136	41	115	metric	metric	ADJ
ejpam-4136	41	116	space	space	NOUN
ejpam-4136	41	117	over	over	ADP
ejpam-4136	41	118	banach	banach	NOUN
ejpam-4136	41	119	algebra	algebra	NOUN
ejpam-4136	41	120	.	.	PUNCT
ejpam-4136	42	1	the	the	DET
ejpam-4136	42	2	concept	concept	NOUN
ejpam-4136	42	3	of	of	ADP
ejpam-4136	42	4	a	a	DET
ejpam-4136	42	5	b	b	NOUN
ejpam-4136	42	6	-	-	PUNCT
ejpam-4136	42	7	metric	metric	ADJ
ejpam-4136	42	8	space	space	NOUN
ejpam-4136	42	9	is	be	AUX
ejpam-4136	42	10	initiated	initiate	VERB
ejpam-4136	42	11	by	by	ADP
ejpam-4136	42	12	bakhtin	bakhtin	NOUN
ejpam-4136	42	13	[	[	X
ejpam-4136	42	14	2	2	NUM
ejpam-4136	42	15	]	]	PUNCT
ejpam-4136	42	16	and	and	CCONJ
ejpam-4136	42	17	thereafter	thereafter	ADV
ejpam-4136	42	18	used	use	VERB
ejpam-4136	42	19	by	by	ADP
ejpam-4136	42	20	czerwick	czerwick	NOUN
ejpam-4136	42	21	[	[	X
ejpam-4136	42	22	4	4	NUM
ejpam-4136	42	23	]	]	PUNCT
ejpam-4136	42	24	.	.	PUNCT
ejpam-4136	43	1	a.	a.	PROPN
ejpam-4136	43	2	d.nezhad	d.nezhad	PROPN
ejpam-4136	43	3	,	,	PUNCT
ejpam-4136	43	4	s.	s.	PROPN
ejpam-4136	43	5	radenović	radenović	PROPN
ejpam-4136	43	6	/	/	SYM
ejpam-4136	43	7	eur	eur	PROPN
ejpam-4136	43	8	.	.	PUNCT
ejpam-4136	44	1	j.	j.	PROPN
ejpam-4136	44	2	pure	pure	PROPN
ejpam-4136	44	3	appl	appl	PROPN
ejpam-4136	44	4	.	.	PROPN
ejpam-4136	44	5	math	math	PROPN
ejpam-4136	44	6	,	,	PUNCT
ejpam-4136	44	7	14	14	NUM
ejpam-4136	44	8	(	(	PUNCT
ejpam-4136	44	9	4	4	NUM
ejpam-4136	44	10	)	)	PUNCT
ejpam-4136	44	11	(	(	PUNCT
ejpam-4136	44	12	2021	2021	NUM
ejpam-4136	44	13	)	)	PUNCT
ejpam-4136	44	14	,	,	PUNCT
ejpam-4136	44	15	1148	1148	NUM
ejpam-4136	44	16	-	-	SYM
ejpam-4136	44	17	1160	1160	NUM
ejpam-4136	44	18	1150	1150	NUM
ejpam-4136	44	19	definition	definition	NOUN
ejpam-4136	44	20	4	4	NUM
ejpam-4136	44	21	.	.	PUNCT
ejpam-4136	45	1	[	[	X
ejpam-4136	45	2	4	4	X
ejpam-4136	45	3	]	]	PUNCT
ejpam-4136	45	4	let	let	VERB
ejpam-4136	45	5	x	x	PRON
ejpam-4136	45	6	be	be	AUX
ejpam-4136	45	7	a	a	DET
ejpam-4136	45	8	non	non	ADJ
ejpam-4136	45	9	-	-	ADJ
ejpam-4136	45	10	empty	empty	ADJ
ejpam-4136	45	11	set	set	NOUN
ejpam-4136	45	12	and	and	CCONJ
ejpam-4136	45	13	db	db	VERB
ejpam-4136	45	14	:	:	PUNCT
ejpam-4136	45	15	x	x	PUNCT
ejpam-4136	45	16	×	×	NOUN
ejpam-4136	45	17	x	x	PUNCT
ejpam-4136	45	18	−→	−→	NOUN
ejpam-4136	45	19	[	[	X
ejpam-4136	45	20	0,+∞	0,+∞	NUM
ejpam-4136	45	21	)	)	PUNCT
ejpam-4136	45	22	be	be	AUX
ejpam-4136	45	23	a	a	DET
ejpam-4136	45	24	function	function	NOUN
ejpam-4136	45	25	satisfying	satisfy	VERB
ejpam-4136	45	26	the	the	DET
ejpam-4136	45	27	following	follow	VERB
ejpam-4136	45	28	conditions	condition	NOUN
ejpam-4136	45	29	:	:	PUNCT
ejpam-4136	45	30	(	(	PUNCT
ejpam-4136	45	31	b1	b1	NOUN
ejpam-4136	45	32	)	)	PUNCT
ejpam-4136	45	33	db(x	db(x	PROPN
ejpam-4136	45	34	,	,	PUNCT
ejpam-4136	45	35	y	y	NOUN
ejpam-4136	45	36	)	)	PUNCT
ejpam-4136	46	1	=	=	SYM
ejpam-4136	46	2	0	0	PUNCT
ejpam-4136	47	1	if	if	SCONJ
ejpam-4136	47	2	and	and	CCONJ
ejpam-4136	47	3	only	only	ADV
ejpam-4136	47	4	if	if	SCONJ
ejpam-4136	47	5	x	x	X
ejpam-4136	47	6	=	=	SYM
ejpam-4136	47	7	y	y	PROPN
ejpam-4136	47	8	,	,	PUNCT
ejpam-4136	47	9	(	(	PUNCT
ejpam-4136	47	10	b2	b2	NOUN
ejpam-4136	47	11	)	)	PUNCT
ejpam-4136	47	12	db(x	db(x	PROPN
ejpam-4136	47	13	,	,	PUNCT
ejpam-4136	47	14	y	y	NOUN
ejpam-4136	47	15	)	)	PUNCT
ejpam-4136	47	16	=	=	PUNCT
ejpam-4136	47	17	db(y	db(y	ADJ
ejpam-4136	47	18	,	,	PUNCT
ejpam-4136	47	19	x	x	NOUN
ejpam-4136	47	20	)	)	PUNCT
ejpam-4136	47	21	,	,	PUNCT
ejpam-4136	47	22	for	for	ADP
ejpam-4136	47	23	all	all	DET
ejpam-4136	47	24	x	x	NOUN
ejpam-4136	47	25	,	,	PUNCT
ejpam-4136	47	26	y	y	PROPN
ejpam-4136	47	27	∈	∈	PROPN
ejpam-4136	47	28	x	x	X
ejpam-4136	47	29	,	,	PUNCT
ejpam-4136	47	30	(	(	PUNCT
ejpam-4136	47	31	b3	b3	PROPN
ejpam-4136	47	32	)	)	PUNCT
ejpam-4136	47	33	db(x	db(x	PROPN
ejpam-4136	47	34	,	,	PUNCT
ejpam-4136	47	35	y	y	NOUN
ejpam-4136	47	36	)	)	PUNCT
ejpam-4136	47	37	≤	≤	NOUN
ejpam-4136	47	38	s(db(x	s(db(x	PROPN
ejpam-4136	47	39	,	,	PUNCT
ejpam-4136	47	40	z	z	NOUN
ejpam-4136	47	41	)	)	PUNCT
ejpam-4136	47	42	+	+	CCONJ
ejpam-4136	47	43	db(z	db(z	PROPN
ejpam-4136	47	44	,	,	PUNCT
ejpam-4136	47	45	y	y	NOUN
ejpam-4136	47	46	)	)	PUNCT
ejpam-4136	47	47	)	)	PUNCT
ejpam-4136	47	48	for	for	ADP
ejpam-4136	47	49	all	all	DET
ejpam-4136	47	50	x	x	PROPN
ejpam-4136	47	51	,	,	PUNCT
ejpam-4136	47	52	y	y	PROPN
ejpam-4136	47	53	,	,	PUNCT
ejpam-4136	47	54	z	z	PROPN
ejpam-4136	47	55	∈	∈	PROPN
ejpam-4136	47	56	x	x	NOUN
ejpam-4136	47	57	,	,	PUNCT
ejpam-4136	47	58	where	where	SCONJ
ejpam-4136	47	59	s	s	VERB
ejpam-4136	47	60	≥	≥	NOUN
ejpam-4136	47	61	1	1	NUM
ejpam-4136	47	62	.	.	PUNCT
ejpam-4136	48	1	the	the	DET
ejpam-4136	48	2	function	function	NOUN
ejpam-4136	48	3	db	db	PROPN
ejpam-4136	48	4	is	be	AUX
ejpam-4136	48	5	called	call	VERB
ejpam-4136	48	6	a	a	DET
ejpam-4136	48	7	b	b	NOUN
ejpam-4136	48	8	-	-	ADJ
ejpam-4136	48	9	metric	metric	ADJ
ejpam-4136	48	10	and	and	CCONJ
ejpam-4136	48	11	the	the	DET
ejpam-4136	48	12	pair	pair	NOUN
ejpam-4136	48	13	(	(	PUNCT
ejpam-4136	48	14	x	x	NOUN
ejpam-4136	48	15	,	,	PUNCT
ejpam-4136	48	16	db	db	PROPN
ejpam-4136	48	17	)	)	PUNCT
ejpam-4136	48	18	is	be	AUX
ejpam-4136	48	19	called	call	VERB
ejpam-4136	48	20	a	a	DET
ejpam-4136	48	21	b	b	NOUN
ejpam-4136	48	22	-	-	PUNCT
ejpam-4136	48	23	metric	metric	ADJ
ejpam-4136	48	24	space	space	NOUN
ejpam-4136	48	25	.	.	PUNCT
ejpam-4136	48	26	example	example	NOUN
ejpam-4136	49	1	1	1	NUM
ejpam-4136	49	2	.	.	PUNCT
ejpam-4136	50	1	[	[	X
ejpam-4136	50	2	3	3	X
ejpam-4136	50	3	]	]	X
ejpam-4136	50	4	let	let	VERB
ejpam-4136	50	5	x	x	SYM
ejpam-4136	50	6	=	=	SYM
ejpam-4136	50	7	lp[0	lp[0	PROPN
ejpam-4136	50	8	,	,	PUNCT
ejpam-4136	50	9	1	1	NUM
ejpam-4136	50	10	]	]	PUNCT
ejpam-4136	50	11	be	be	AUX
ejpam-4136	50	12	the	the	DET
ejpam-4136	50	13	space	space	NOUN
ejpam-4136	50	14	of	of	ADP
ejpam-4136	50	15	all	all	DET
ejpam-4136	50	16	real	real	ADJ
ejpam-4136	50	17	functions	function	NOUN
ejpam-4136	50	18	ϕ(t	ϕ(t	NUM
ejpam-4136	50	19	)	)	PUNCT
ejpam-4136	50	20	with	with	ADP
ejpam-4136	50	21	t	t	PROPN
ejpam-4136	50	22	∈	∈	PROPN
ejpam-4136	51	1	[	[	X
ejpam-4136	51	2	0	0	NUM
ejpam-4136	51	3	,	,	PUNCT
ejpam-4136	51	4	1	1	NUM
ejpam-4136	51	5	]	]	PUNCT
ejpam-4136	51	6	such	such	ADJ
ejpam-4136	51	7	that	that	SCONJ
ejpam-4136	51	8	∫	∫	PROPN
ejpam-4136	51	9	1	1	NUM
ejpam-4136	51	10	0	0	NUM
ejpam-4136	51	11	|ϕ(t)|p	|ϕ(t)|p	NOUN
ejpam-4136	51	12	<	<	X
ejpam-4136	51	13	∞	∞	NOUN
ejpam-4136	51	14	with	with	ADP
ejpam-4136	51	15	0	0	NUM
ejpam-4136	51	16	<	<	X
ejpam-4136	51	17	p	p	X
ejpam-4136	51	18	<	<	X
ejpam-4136	51	19	1	1	NUM
ejpam-4136	51	20	.	.	PUNCT
ejpam-4136	51	21	define	define	VERB
ejpam-4136	51	22	db	db	PROPN
ejpam-4136	51	23	:	:	PUNCT
ejpam-4136	51	24	x	x	X
ejpam-4136	51	25	×x	×x	VERB
ejpam-4136	51	26	−→	−→	NOUN
ejpam-4136	51	27	[	[	X
ejpam-4136	51	28	0,+∞	0,+∞	NUM
ejpam-4136	51	29	)	)	PUNCT
ejpam-4136	51	30	as	as	ADP
ejpam-4136	51	31	:	:	PUNCT
ejpam-4136	51	32	db(ϕ	db(ϕ	NUM
ejpam-4136	51	33	,	,	PUNCT
ejpam-4136	51	34	ψ	ψ	NOUN
ejpam-4136	51	35	)	)	PUNCT
ejpam-4136	51	36	=)	=)	PROPN
ejpam-4136	51	37	∫	∫	PROPN
ejpam-4136	51	38	1	1	NUM
ejpam-4136	51	39	0	0	NUM
ejpam-4136	51	40	|ϕ(t)−	|ϕ(t)−	PROPN
ejpam-4136	51	41	ψ(t)|pdt	ψ(t)|pdt	NOUN
ejpam-4136	51	42	)	)	PUNCT
ejpam-4136	51	43	1	1	NUM
ejpam-4136	51	44	p	p	NOUN
ejpam-4136	51	45	.	.	PUNCT
ejpam-4136	52	1	therefore	therefore	ADV
ejpam-4136	52	2	(	(	PUNCT
ejpam-4136	52	3	x	x	NOUN
ejpam-4136	52	4	,	,	PUNCT
ejpam-4136	52	5	db	db	PROPN
ejpam-4136	52	6	)	)	PUNCT
ejpam-4136	52	7	is	be	AUX
ejpam-4136	52	8	a	a	DET
ejpam-4136	52	9	b	b	NOUN
ejpam-4136	52	10	-	-	PUNCT
ejpam-4136	52	11	metric	metric	ADJ
ejpam-4136	52	12	space	space	NOUN
ejpam-4136	52	13	with	with	ADP
ejpam-4136	52	14	s	s	NOUN
ejpam-4136	52	15	=	=	SYM
ejpam-4136	52	16	2	2	NUM
ejpam-4136	52	17	1	1	NUM
ejpam-4136	52	18	p	p	NOUN
ejpam-4136	52	19	.	.	PUNCT
ejpam-4136	53	1	remark	remark	PROPN
ejpam-4136	53	2	2	2	NUM
ejpam-4136	53	3	.	.	PUNCT
ejpam-4136	54	1	[	[	X
ejpam-4136	54	2	4	4	X
ejpam-4136	54	3	]	]	PUNCT
ejpam-4136	54	4	the	the	DET
ejpam-4136	54	5	class	class	NOUN
ejpam-4136	54	6	of	of	ADP
ejpam-4136	54	7	b	b	NOUN
ejpam-4136	54	8	-	-	PUNCT
ejpam-4136	54	9	metric	metric	ADJ
ejpam-4136	54	10	space	space	NOUN
ejpam-4136	54	11	is	be	AUX
ejpam-4136	54	12	larger	large	ADJ
ejpam-4136	54	13	than	than	ADP
ejpam-4136	54	14	the	the	DET
ejpam-4136	54	15	class	class	NOUN
ejpam-4136	54	16	of	of	ADP
ejpam-4136	54	17	metric	metric	ADJ
ejpam-4136	54	18	space	space	NOUN
ejpam-4136	54	19	.	.	PUNCT
ejpam-4136	55	1	when	when	SCONJ
ejpam-4136	55	2	s	s	AUX
ejpam-4136	55	3	=	=	SYM
ejpam-4136	55	4	1	1	NUM
ejpam-4136	55	5	the	the	DET
ejpam-4136	55	6	concept	concept	NOUN
ejpam-4136	55	7	of	of	ADP
ejpam-4136	55	8	b	b	NOUN
ejpam-4136	55	9	-	-	PUNCT
ejpam-4136	55	10	metric	metric	ADJ
ejpam-4136	55	11	space	space	NOUN
ejpam-4136	55	12	coincides	coincide	VERB
ejpam-4136	55	13	with	with	ADP
ejpam-4136	55	14	the	the	DET
ejpam-4136	55	15	concept	concept	NOUN
ejpam-4136	55	16	of	of	ADP
ejpam-4136	55	17	metric	metric	ADJ
ejpam-4136	55	18	space	space	NOUN
ejpam-4136	55	19	.	.	PUNCT
ejpam-4136	56	1	in	in	ADP
ejpam-4136	56	2	the	the	DET
ejpam-4136	56	3	following	following	NOUN
ejpam-4136	56	4	we	we	PRON
ejpam-4136	56	5	recall	recall	VERB
ejpam-4136	56	6	the	the	DET
ejpam-4136	56	7	definition	definition	NOUN
ejpam-4136	56	8	of	of	ADP
ejpam-4136	56	9	the	the	DET
ejpam-4136	56	10	extended	extended	ADJ
ejpam-4136	56	11	b	b	X
ejpam-4136	56	12	-	-	PUNCT
ejpam-4136	56	13	metric	metric	ADJ
ejpam-4136	56	14	space	space	NOUN
ejpam-4136	56	15	.	.	PUNCT
ejpam-4136	57	1	definition	definition	NOUN
ejpam-4136	57	2	5	5	NUM
ejpam-4136	57	3	.	.	PUNCT
ejpam-4136	58	1	[	[	X
ejpam-4136	58	2	8	8	NUM
ejpam-4136	58	3	]	]	PUNCT
ejpam-4136	58	4	let	let	VERB
ejpam-4136	58	5	x	x	PRON
ejpam-4136	58	6	be	be	AUX
ejpam-4136	58	7	a	a	DET
ejpam-4136	58	8	non	non	ADJ
ejpam-4136	58	9	-	-	ADJ
ejpam-4136	58	10	empty	empty	ADJ
ejpam-4136	58	11	set	set	NOUN
ejpam-4136	58	12	and	and	CCONJ
ejpam-4136	58	13	α	α	NOUN
ejpam-4136	58	14	:	:	PUNCT
ejpam-4136	58	15	x	x	SYM
ejpam-4136	58	16	×	×	NOUN
ejpam-4136	58	17	x	x	PUNCT
ejpam-4136	58	18	−→	−→	NOUN
ejpam-4136	58	19	[	[	X
ejpam-4136	58	20	1,+∞	1,+∞	NUM
ejpam-4136	58	21	)	)	PUNCT
ejpam-4136	58	22	.	.	PUNCT
ejpam-4136	59	1	a	a	DET
ejpam-4136	59	2	function	function	NOUN
ejpam-4136	59	3	dα	dα	VERB
ejpam-4136	59	4	:	:	PUNCT
ejpam-4136	59	5	x	x	X
ejpam-4136	59	6	×x	×x	VERB
ejpam-4136	59	7	−→	−→	NOUN
ejpam-4136	59	8	[	[	X
ejpam-4136	59	9	0,+∞	0,+∞	NUM
ejpam-4136	59	10	)	)	PUNCT
ejpam-4136	59	11	is	be	AUX
ejpam-4136	59	12	called	call	VERB
ejpam-4136	59	13	an	an	DET
ejpam-4136	59	14	extended	extended	ADJ
ejpam-4136	59	15	b	b	NOUN
ejpam-4136	59	16	-	-	ADJ
ejpam-4136	59	17	metric	metric	ADJ
ejpam-4136	59	18	if	if	SCONJ
ejpam-4136	59	19	for	for	ADP
ejpam-4136	59	20	all	all	DET
ejpam-4136	59	21	x	x	NOUN
ejpam-4136	59	22	,	,	PUNCT
ejpam-4136	59	23	y	y	PROPN
ejpam-4136	59	24	,	,	PUNCT
ejpam-4136	59	25	z	z	NOUN
ejpam-4136	59	26	∈	∈	PROPN
ejpam-4136	59	27	x	x	PUNCT
ejpam-4136	59	28	it	it	PRON
ejpam-4136	59	29	satisfies	satisfy	VERB
ejpam-4136	59	30	the	the	DET
ejpam-4136	59	31	following	follow	VERB
ejpam-4136	59	32	conditions	condition	NOUN
ejpam-4136	59	33	:	:	PUNCT
ejpam-4136	59	34	(	(	PUNCT
ejpam-4136	59	35	b1	b1	NOUN
ejpam-4136	59	36	)	)	PUNCT
ejpam-4136	59	37	dα(x	dα(x	NOUN
ejpam-4136	59	38	,	,	PUNCT
ejpam-4136	59	39	y	y	NOUN
ejpam-4136	59	40	)	)	PUNCT
ejpam-4136	59	41	=	=	SYM
ejpam-4136	59	42	0	0	PUNCT
ejpam-4136	60	1	if	if	SCONJ
ejpam-4136	60	2	and	and	CCONJ
ejpam-4136	60	3	only	only	ADV
ejpam-4136	60	4	if	if	SCONJ
ejpam-4136	60	5	x	x	X
ejpam-4136	60	6	=	=	SYM
ejpam-4136	60	7	y	y	PROPN
ejpam-4136	60	8	,	,	PUNCT
ejpam-4136	60	9	(	(	PUNCT
ejpam-4136	60	10	b2	b2	NOUN
ejpam-4136	60	11	)	)	PUNCT
ejpam-4136	60	12	dα(x	dα(x	NOUN
ejpam-4136	60	13	,	,	PUNCT
ejpam-4136	60	14	y	y	NOUN
ejpam-4136	60	15	)	)	PUNCT
ejpam-4136	60	16	=	=	NOUN
ejpam-4136	61	1	dα(y	dα(y	NOUN
ejpam-4136	61	2	,	,	PUNCT
ejpam-4136	61	3	x	x	NOUN
ejpam-4136	61	4	)	)	PUNCT
ejpam-4136	61	5	,	,	PUNCT
ejpam-4136	61	6	(	(	PUNCT
ejpam-4136	61	7	b3	b3	NOUN
ejpam-4136	61	8	)	)	PUNCT
ejpam-4136	61	9	dα(x	dα(x	NOUN
ejpam-4136	61	10	,	,	PUNCT
ejpam-4136	61	11	y	y	NOUN
ejpam-4136	61	12	)	)	PUNCT
ejpam-4136	61	13	≤	≤	ADJ
ejpam-4136	61	14	α(x	α(x	NOUN
ejpam-4136	61	15	,	,	PUNCT
ejpam-4136	61	16	y)(dα(x	y)(dα(x	NOUN
ejpam-4136	61	17	,	,	PUNCT
ejpam-4136	61	18	z	z	NOUN
ejpam-4136	61	19	)	)	PUNCT
ejpam-4136	62	1	+	+	CCONJ
ejpam-4136	62	2	dα(z	dα(z	NOUN
ejpam-4136	62	3	,	,	PUNCT
ejpam-4136	62	4	y	y	NOUN
ejpam-4136	62	5	)	)	PUNCT
ejpam-4136	62	6	)	)	PUNCT
ejpam-4136	62	7	.	.	PUNCT
ejpam-4136	63	1	the	the	DET
ejpam-4136	63	2	pair	pair	NOUN
ejpam-4136	63	3	(	(	PUNCT
ejpam-4136	63	4	x	x	NOUN
ejpam-4136	63	5	,	,	PUNCT
ejpam-4136	63	6	dα	dα	NOUN
ejpam-4136	63	7	)	)	PUNCT
ejpam-4136	63	8	is	be	AUX
ejpam-4136	63	9	called	call	VERB
ejpam-4136	63	10	extended	extended	ADJ
ejpam-4136	63	11	b	b	X
ejpam-4136	63	12	-	-	PUNCT
ejpam-4136	63	13	metric	metric	ADJ
ejpam-4136	63	14	space	space	NOUN
ejpam-4136	63	15	.	.	PUNCT
ejpam-4136	64	1	for	for	ADP
ejpam-4136	64	2	simplicity	simplicity	NOUN
ejpam-4136	64	3	of	of	ADP
ejpam-4136	64	4	notation	notation	NOUN
ejpam-4136	64	5	,	,	PUNCT
ejpam-4136	64	6	r	r	NOUN
ejpam-4136	64	7	,	,	PUNCT
ejpam-4136	64	8	n	n	PRON
ejpam-4136	64	9	denotes	denote	VERB
ejpam-4136	64	10	the	the	DET
ejpam-4136	64	11	set	set	NOUN
ejpam-4136	64	12	of	of	ADP
ejpam-4136	64	13	real	real	ADJ
ejpam-4136	64	14	numbers	number	NOUN
ejpam-4136	64	15	and	and	CCONJ
ejpam-4136	64	16	natural	natural	ADJ
ejpam-4136	64	17	numbers	number	NOUN
ejpam-4136	64	18	respectively	respectively	ADV
ejpam-4136	64	19	.	.	PUNCT
ejpam-4136	65	1	r>0	r>0	PROPN
ejpam-4136	65	2	stands	stand	VERB
ejpam-4136	65	3	for	for	ADP
ejpam-4136	65	4	positive	positive	ADJ
ejpam-4136	65	5	reals	real	NOUN
ejpam-4136	65	6	.	.	PUNCT
ejpam-4136	66	1	here	here	ADV
ejpam-4136	66	2	and	and	CCONJ
ejpam-4136	66	3	subsequently	subsequently	ADV
ejpam-4136	66	4	,	,	PUNCT
ejpam-4136	66	5	for	for	ADP
ejpam-4136	66	6	n	n	PRON
ejpam-4136	66	7	≥	≥	NUM
ejpam-4136	66	8	2	2	NUM
ejpam-4136	66	9	,	,	PUNCT
ejpam-4136	66	10	let	let	VERB
ejpam-4136	66	11	xn	xn	PROPN
ejpam-4136	66	12	denotes	denote	VERB
ejpam-4136	66	13	the	the	DET
ejpam-4136	66	14	n	n	NUM
ejpam-4136	66	15	-	-	PUNCT
ejpam-4136	66	16	times	time	NOUN
ejpam-4136	66	17	cartesian	cartesian	ADJ
ejpam-4136	66	18	product	product	NOUN
ejpam-4136	66	19	x	x	X
ejpam-4136	66	20	×	×	NOUN
ejpam-4136	66	21	.	.	PUNCT
ejpam-4136	66	22	.	.	PUNCT
ejpam-4136	67	1	.×x︸	.×x︸	PUNCT
ejpam-4136	68	1	︷︷	︷︷	PROPN
ejpam-4136	68	2	︸	︸	PRON
ejpam-4136	68	3	n−times	n−time	NOUN
ejpam-4136	68	4	.	.	PUNCT
ejpam-4136	69	1	in	in	ADP
ejpam-4136	69	2	what	what	PRON
ejpam-4136	69	3	follows	follow	VERB
ejpam-4136	69	4	int(k	int(k	NOUN
ejpam-4136	69	5	)	)	PUNCT
ejpam-4136	69	6	and	and	CCONJ
ejpam-4136	69	7	∂k	∂k	PROPN
ejpam-4136	69	8	denote	denote	NOUN
ejpam-4136	69	9	,	,	PUNCT
ejpam-4136	69	10	respectively	respectively	ADV
ejpam-4136	69	11	,	,	PUNCT
ejpam-4136	69	12	the	the	DET
ejpam-4136	69	13	interior	interior	ADJ
ejpam-4136	69	14	and	and	CCONJ
ejpam-4136	69	15	boundary	boundary	NOUN
ejpam-4136	69	16	of	of	ADP
ejpam-4136	69	17	k.	k.	PROPN
ejpam-4136	69	18	to	to	PART
ejpam-4136	69	19	simplify	simplify	VERB
ejpam-4136	69	20	,	,	PUNCT
ejpam-4136	69	21	we	we	PRON
ejpam-4136	69	22	let	let	VERB
ejpam-4136	69	23	(	(	PUNCT
ejpam-4136	69	24	xi	xi	NOUN
ejpam-4136	69	25	)	)	PUNCT
ejpam-4136	69	26	n	n	CCONJ
ejpam-4136	69	27	i=1	i=1	PROPN
ejpam-4136	70	1	and	and	CCONJ
ejpam-4136	70	2	(	(	PUNCT
ejpam-4136	70	3	x)n1	x)n1	PROPN
ejpam-4136	70	4	stand	stand	VERB
ejpam-4136	70	5	for	for	ADP
ejpam-4136	70	6	(	(	PUNCT
ejpam-4136	70	7	x1	x1	PROPN
ejpam-4136	70	8	,	,	PUNCT
ejpam-4136	70	9	...	...	PUNCT
ejpam-4136	70	10	,	,	PUNCT
ejpam-4136	70	11	xn	xn	PROPN
ejpam-4136	70	12	)	)	PUNCT
ejpam-4136	70	13	and	and	CCONJ
ejpam-4136	70	14	(	(	PUNCT
ejpam-4136	70	15	x)ni=1	x)ni=1	X
ejpam-4136	70	16	respectively	respectively	ADV
ejpam-4136	70	17	.	.	PUNCT
ejpam-4136	71	1	let	let	VERB
ejpam-4136	71	2	t	t	NOUN
ejpam-4136	71	3	be	be	AUX
ejpam-4136	71	4	a	a	DET
ejpam-4136	71	5	mapping	mapping	NOUN
ejpam-4136	71	6	,	,	PUNCT
ejpam-4136	71	7	for	for	ADP
ejpam-4136	71	8	abbreviation	abbreviation	NOUN
ejpam-4136	71	9	,	,	PUNCT
ejpam-4136	71	10	we	we	PRON
ejpam-4136	71	11	write	write	VERB
ejpam-4136	71	12	tx	tx	PROPN
ejpam-4136	71	13	instead	instead	ADV
ejpam-4136	71	14	of	of	ADP
ejpam-4136	71	15	t	t	PROPN
ejpam-4136	71	16	(	(	PUNCT
ejpam-4136	71	17	x	x	NOUN
ejpam-4136	71	18	)	)	PUNCT
ejpam-4136	71	19	.	.	PUNCT
ejpam-4136	72	1	2	2	X
ejpam-4136	72	2	.	.	X
ejpam-4136	72	3	main	main	ADJ
ejpam-4136	72	4	results	result	NOUN
ejpam-4136	72	5	the	the	DET
ejpam-4136	72	6	goal	goal	NOUN
ejpam-4136	72	7	of	of	ADP
ejpam-4136	72	8	this	this	DET
ejpam-4136	72	9	section	section	NOUN
ejpam-4136	72	10	is	be	AUX
ejpam-4136	72	11	to	to	PART
ejpam-4136	72	12	describe	describe	VERB
ejpam-4136	72	13	a	a	DET
ejpam-4136	72	14	few	few	ADJ
ejpam-4136	72	15	properties	property	NOUN
ejpam-4136	72	16	and	and	CCONJ
ejpam-4136	72	17	results	result	NOUN
ejpam-4136	72	18	of	of	ADP
ejpam-4136	72	19	the	the	DET
ejpam-4136	72	20	b(αn	b(αn	NOUN
ejpam-4136	72	21	,	,	PUNCT
ejpam-4136	72	22	βn)hypermetric	βn)hypermetric	NOUN
ejpam-4136	72	23	spaces	space	NOUN
ejpam-4136	72	24	of	of	ADP
ejpam-4136	72	25	dimension	dimension	PROPN
ejpam-4136	72	26	n.	n.	PROPN
ejpam-4136	72	27	a.	a.	PROPN
ejpam-4136	72	28	d.nezhad	d.nezhad	PROPN
ejpam-4136	72	29	,	,	PUNCT
ejpam-4136	72	30	s.	s.	PROPN
ejpam-4136	72	31	radenović	radenović	PROPN
ejpam-4136	72	32	/	/	SYM
ejpam-4136	72	33	eur	eur	PROPN
ejpam-4136	72	34	.	.	PUNCT
ejpam-4136	73	1	j.	j.	PROPN
ejpam-4136	73	2	pure	pure	PROPN
ejpam-4136	73	3	appl	appl	PROPN
ejpam-4136	73	4	.	.	PROPN
ejpam-4136	73	5	math	math	PROPN
ejpam-4136	73	6	,	,	PUNCT
ejpam-4136	73	7	14	14	NUM
ejpam-4136	73	8	(	(	PUNCT
ejpam-4136	73	9	4	4	NUM
ejpam-4136	73	10	)	)	PUNCT
ejpam-4136	73	11	(	(	PUNCT
ejpam-4136	73	12	2021	2021	NUM
ejpam-4136	73	13	)	)	PUNCT
ejpam-4136	73	14	,	,	PUNCT
ejpam-4136	73	15	1148	1148	NUM
ejpam-4136	73	16	-	-	SYM
ejpam-4136	73	17	1160	1160	NUM
ejpam-4136	73	18	1151	1151	NUM
ejpam-4136	73	19	2.1	2.1	NUM
ejpam-4136	73	20	.	.	PUNCT
ejpam-4136	74	1	b(αn	b(αn	NOUN
ejpam-4136	74	2	,	,	PUNCT
ejpam-4136	74	3	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	74	4	spaces	space	NOUN
ejpam-4136	74	5	of	of	ADP
ejpam-4136	74	6	dimension	dimension	NOUN
ejpam-4136	74	7	n	n	CCONJ
ejpam-4136	74	8	in	in	ADP
ejpam-4136	74	9	this	this	DET
ejpam-4136	74	10	section	section	NOUN
ejpam-4136	74	11	,	,	PUNCT
ejpam-4136	74	12	we	we	PRON
ejpam-4136	74	13	will	will	AUX
ejpam-4136	74	14	present	present	VERB
ejpam-4136	74	15	some	some	DET
ejpam-4136	74	16	fixed	fix	VERB
ejpam-4136	74	17	point	point	NOUN
ejpam-4136	74	18	theorems	theorem	NOUN
ejpam-4136	74	19	in	in	ADP
ejpam-4136	74	20	set	set	NOUN
ejpam-4136	74	21	-	-	PUNCT
ejpam-4136	74	22	valued	value	VERB
ejpam-4136	74	23	metric	metric	ADJ
ejpam-4136	74	24	spaces	space	NOUN
ejpam-4136	74	25	over	over	ADP
ejpam-4136	74	26	banach	banach	NOUN
ejpam-4136	74	27	algebra	algebra	NOUN
ejpam-4136	74	28	a.	a.	NOUN
ejpam-4136	74	29	furthermore	furthermore	ADV
ejpam-4136	74	30	,	,	PUNCT
ejpam-4136	74	31	we	we	PRON
ejpam-4136	74	32	will	will	AUX
ejpam-4136	74	33	give	give	VERB
ejpam-4136	74	34	examples	example	NOUN
ejpam-4136	74	35	and	and	CCONJ
ejpam-4136	74	36	application	application	NOUN
ejpam-4136	74	37	to	to	ADP
ejpam-4136	74	38	our	our	PRON
ejpam-4136	74	39	main	main	ADJ
ejpam-4136	74	40	results	result	NOUN
ejpam-4136	74	41	.	.	PUNCT
ejpam-4136	75	1	the	the	DET
ejpam-4136	75	2	first	first	ADJ
ejpam-4136	75	3	result	result	NOUN
ejpam-4136	75	4	in	in	ADP
ejpam-4136	75	5	this	this	DET
ejpam-4136	75	6	work	work	NOUN
ejpam-4136	75	7	is	be	AUX
ejpam-4136	75	8	the	the	DET
ejpam-4136	75	9	following	follow	VERB
ejpam-4136	75	10	definition	definition	NOUN
ejpam-4136	75	11	.	.	PUNCT
ejpam-4136	76	1	for	for	ADP
ejpam-4136	76	2	n	n	PRON
ejpam-4136	76	3	≥	≥	NUM
ejpam-4136	76	4	2	2	NUM
ejpam-4136	76	5	,	,	PUNCT
ejpam-4136	76	6	let	let	VERB
ejpam-4136	76	7	xn	xn	PROPN
ejpam-4136	76	8	denotes	denote	VERB
ejpam-4136	76	9	the	the	DET
ejpam-4136	76	10	n	n	NUM
ejpam-4136	76	11	-	-	PUNCT
ejpam-4136	76	12	times	time	NOUN
ejpam-4136	76	13	cartesian	cartesian	ADJ
ejpam-4136	76	14	product	product	NOUN
ejpam-4136	76	15	x	x	X
ejpam-4136	76	16	×	×	NOUN
ejpam-4136	76	17	.	.	PUNCT
ejpam-4136	76	18	.	.	PUNCT
ejpam-4136	77	1	.×x︸	.×x︸	PUNCT
ejpam-4136	78	1	︷︷	︷︷	PROPN
ejpam-4136	78	2	︸	︸	PRON
ejpam-4136	78	3	n−times	n−time	NOUN
ejpam-4136	78	4	and	and	CCONJ
ejpam-4136	78	5	a	a	DET
ejpam-4136	78	6	be	be	AUX
ejpam-4136	78	7	a	a	DET
ejpam-4136	78	8	banach	banach	NOUN
ejpam-4136	78	9	algebras	algebra	VERB
ejpam-4136	78	10	.	.	PUNCT
ejpam-4136	79	1	let	let	VERB
ejpam-4136	79	2	p	p	NOUN
ejpam-4136	79	3	∗(a	∗(a	PROPN
ejpam-4136	79	4	)	)	PUNCT
ejpam-4136	79	5	denote	denote	VERB
ejpam-4136	79	6	the	the	DET
ejpam-4136	79	7	family	family	NOUN
ejpam-4136	79	8	of	of	ADP
ejpam-4136	79	9	all	all	DET
ejpam-4136	79	10	non	non	ADJ
ejpam-4136	79	11	-	-	ADJ
ejpam-4136	79	12	empty	empty	ADJ
ejpam-4136	79	13	subsets	subset	NOUN
ejpam-4136	79	14	of	of	ADP
ejpam-4136	79	15	a.	a.	NOUN
ejpam-4136	79	16	we	we	PRON
ejpam-4136	79	17	begin	begin	VERB
ejpam-4136	79	18	with	with	ADP
ejpam-4136	79	19	the	the	DET
ejpam-4136	79	20	following	follow	VERB
ejpam-4136	79	21	definition	definition	NOUN
ejpam-4136	79	22	.	.	PUNCT
ejpam-4136	80	1	definition	definition	NOUN
ejpam-4136	80	2	6	6	NUM
ejpam-4136	80	3	.	.	PUNCT
ejpam-4136	81	1	let	let	VERB
ejpam-4136	81	2	x	x	PRON
ejpam-4136	81	3	be	be	AUX
ejpam-4136	81	4	a	a	DET
ejpam-4136	81	5	non	non	ADJ
ejpam-4136	81	6	-	-	ADJ
ejpam-4136	81	7	empty	empty	ADJ
ejpam-4136	81	8	set	set	NOUN
ejpam-4136	81	9	and	and	CCONJ
ejpam-4136	81	10	αn	αn	VERB
ejpam-4136	81	11	,	,	PUNCT
ejpam-4136	81	12	βn	βn	PUNCT
ejpam-4136	81	13	:	:	PUNCT
ejpam-4136	81	14	xn	xn	PUNCT
ejpam-4136	81	15	−→	−→	NOUN
ejpam-4136	81	16	a.	a.	NOUN
ejpam-4136	81	17	let	let	VERB
ejpam-4136	81	18	γ(αn	γ(αn	VERB
ejpam-4136	81	19	,	,	PUNCT
ejpam-4136	81	20	βn	βn	NOUN
ejpam-4136	81	21	)	)	PUNCT
ejpam-4136	81	22	:	:	PUNCT
ejpam-4136	82	1	x	x	X
ejpam-4136	82	2	n	n	X
ejpam-4136	82	3	−→	−→	NOUN
ejpam-4136	82	4	p	p	ADJ
ejpam-4136	82	5	∗(a	∗(a	PROPN
ejpam-4136	82	6	)	)	PUNCT
ejpam-4136	82	7	be	be	AUX
ejpam-4136	82	8	a	a	DET
ejpam-4136	82	9	mapping	mapping	NOUN
ejpam-4136	82	10	(	(	PUNCT
ejpam-4136	82	11	called	call	VERB
ejpam-4136	82	12	the	the	DET
ejpam-4136	82	13	b(αn	b(αn	NOUN
ejpam-4136	82	14	,	,	PUNCT
ejpam-4136	82	15	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	82	16	over	over	ADP
ejpam-4136	82	17	banach	banach	NOUN
ejpam-4136	82	18	algebra	algebra	NOUN
ejpam-4136	82	19	a	a	PRON
ejpam-4136	82	20	)	)	PUNCT
ejpam-4136	82	21	satisfiying	satisfiye	VERB
ejpam-4136	82	22	for	for	ADP
ejpam-4136	82	23	all	all	DET
ejpam-4136	82	24	n	n	PRON
ejpam-4136	82	25	-	-	PUNCT
ejpam-4136	82	26	tuples	tuple	NOUN
ejpam-4136	82	27	(	(	PUNCT
ejpam-4136	82	28	xi	xi	NOUN
ejpam-4136	82	29	)	)	PUNCT
ejpam-4136	82	30	n	n	CCONJ
ejpam-4136	82	31	i=1	i=1	NOUN
ejpam-4136	82	32	x	x	X
ejpam-4136	82	33	n	n	CCONJ
ejpam-4136	82	34	in	in	ADP
ejpam-4136	82	35	the	the	DET
ejpam-4136	82	36	following	following	ADJ
ejpam-4136	82	37	conditions	condition	NOUN
ejpam-4136	82	38	:	:	PUNCT
ejpam-4136	82	39	(	(	PUNCT
ejpam-4136	82	40	g0	g0	PROPN
ejpam-4136	82	41	)	)	PUNCT
ejpam-4136	82	42	0a	0a	PROPN
ejpam-4136	82	43	⪯	⪯	NOUN
ejpam-4136	82	44	γ(αn	γ(αn	VERB
ejpam-4136	82	45	,	,	PUNCT
ejpam-4136	82	46	βn)(xi	βn)(xi	PUNCT
ejpam-4136	82	47	)	)	PUNCT
ejpam-4136	82	48	n	n	CCONJ
ejpam-4136	82	49	i=1	i=1	PROPN
ejpam-4136	82	50	,	,	PUNCT
ejpam-4136	82	51	(	(	PUNCT
ejpam-4136	82	52	g1	g1	X
ejpam-4136	82	53	)	)	PUNCT
ejpam-4136	82	54	γ(αn	γ(αn	VERB
ejpam-4136	82	55	,	,	PUNCT
ejpam-4136	82	56	βn)(xi	βn)(xi	PUNCT
ejpam-4136	82	57	)	)	PUNCT
ejpam-4136	82	58	n	n	PRON
ejpam-4136	82	59	i=1	i=1	PROPN
ejpam-4136	82	60	=	=	X
ejpam-4136	82	61	{	{	PUNCT
ejpam-4136	82	62	0a	0a	PROPN
ejpam-4136	82	63	}	}	PUNCT
ejpam-4136	82	64	,	,	PUNCT
ejpam-4136	82	65	if	if	SCONJ
ejpam-4136	82	66	x1	x1	PROPN
ejpam-4136	82	67	=	=	X
ejpam-4136	82	68	.	.	PUNCT
ejpam-4136	82	69	.	.	PUNCT
ejpam-4136	82	70	.	.	PUNCT
ejpam-4136	83	1	=	=	PUNCT
ejpam-4136	83	2	xn	xn	PROPN
ejpam-4136	83	3	,	,	PUNCT
ejpam-4136	83	4	(	(	PUNCT
ejpam-4136	83	5	g2	g2	PROPN
ejpam-4136	83	6	)	)	PUNCT
ejpam-4136	83	7	γ(αn	γ(αn	PROPN
ejpam-4136	83	8	,	,	PUNCT
ejpam-4136	83	9	βn)(xi	βn)(xi	PUNCT
ejpam-4136	83	10	)	)	PUNCT
ejpam-4136	83	11	n	n	CCONJ
ejpam-4136	83	12	i=1	i=1	PROPN
ejpam-4136	83	13	⊇	⊇	X
ejpam-4136	83	14	{	{	PUNCT
ejpam-4136	83	15	0a	0a	PROPN
ejpam-4136	83	16	}	}	PUNCT
ejpam-4136	83	17	,	,	PUNCT
ejpam-4136	83	18	for	for	ADP
ejpam-4136	83	19	all	all	DET
ejpam-4136	83	20	x1	x1	PROPN
ejpam-4136	83	21	,	,	PUNCT
ejpam-4136	83	22	...	...	PUNCT
ejpam-4136	83	23	,	,	PUNCT
ejpam-4136	83	24	xn	xn	PROPN
ejpam-4136	83	25	with	with	ADP
ejpam-4136	83	26	xi	xi	PROPN
ejpam-4136	83	27	̸=	̸=	PROPN
ejpam-4136	83	28	xj	xj	PROPN
ejpam-4136	83	29	,	,	PUNCT
ejpam-4136	83	30	for	for	ADP
ejpam-4136	83	31	some	some	DET
ejpam-4136	83	32	i	i	PROPN
ejpam-4136	83	33	,	,	PUNCT
ejpam-4136	83	34	j	j	PROPN
ejpam-4136	83	35	∈	∈	PROPN
ejpam-4136	83	36	{	{	PUNCT
ejpam-4136	83	37	1	1	NUM
ejpam-4136	83	38	,	,	PUNCT
ejpam-4136	83	39	...	...	PUNCT
ejpam-4136	83	40	,	,	PUNCT
ejpam-4136	83	41	n	n	CCONJ
ejpam-4136	83	42	}	}	PUNCT
ejpam-4136	83	43	,	,	PUNCT
ejpam-4136	83	44	(	(	PUNCT
ejpam-4136	83	45	g3	g3	NOUN
ejpam-4136	83	46	)	)	PUNCT
ejpam-4136	83	47	γ(αn	γ(αn	PROPN
ejpam-4136	83	48	,	,	PUNCT
ejpam-4136	83	49	βn)(xi	βn)(xi	PUNCT
ejpam-4136	83	50	)	)	PUNCT
ejpam-4136	83	51	n	n	PRON
ejpam-4136	83	52	i=1	i=1	PROPN
ejpam-4136	83	53	=	=	PUNCT
ejpam-4136	83	54	γ(αn	γ(αn	PROPN
ejpam-4136	83	55	,	,	PUNCT
ejpam-4136	83	56	βn)(xπi	βn)(xπi	NUM
ejpam-4136	83	57	)	)	PUNCT
ejpam-4136	83	58	n	n	CCONJ
ejpam-4136	83	59	i=1	i=1	PROPN
ejpam-4136	83	60	,	,	PUNCT
ejpam-4136	83	61	for	for	ADP
ejpam-4136	83	62	every	every	DET
ejpam-4136	83	63	permutation	permutation	NOUN
ejpam-4136	83	64	(	(	PUNCT
ejpam-4136	83	65	π(1	π(1	NOUN
ejpam-4136	83	66	)	)	PUNCT
ejpam-4136	83	67	,	,	PUNCT
ejpam-4136	83	68	...	...	PUNCT
ejpam-4136	83	69	,	,	PUNCT
ejpam-4136	83	70	π(n	π(n	PROPN
ejpam-4136	83	71	)	)	PUNCT
ejpam-4136	83	72	)	)	PUNCT
ejpam-4136	83	73	of	of	ADP
ejpam-4136	83	74	(	(	PUNCT
ejpam-4136	83	75	1	1	NUM
ejpam-4136	83	76	,	,	PUNCT
ejpam-4136	83	77	2	2	NUM
ejpam-4136	83	78	,	,	PUNCT
ejpam-4136	83	79	...	...	PUNCT
ejpam-4136	83	80	,	,	PUNCT
ejpam-4136	83	81	n	n	CCONJ
ejpam-4136	83	82	)	)	PUNCT
ejpam-4136	83	83	,	,	PUNCT
ejpam-4136	83	84	(	(	PUNCT
ejpam-4136	83	85	g4	g4	NOUN
ejpam-4136	83	86	)	)	PUNCT
ejpam-4136	83	87	γ(αn	γ(αn	PROPN
ejpam-4136	83	88	,	,	PUNCT
ejpam-4136	83	89	βn)((xi	βn)((xi	PROPN
ejpam-4136	83	90	)	)	PUNCT
ejpam-4136	84	1	n−1	n−1	PROPN
ejpam-4136	84	2	i=1	i=1	PROPN
ejpam-4136	84	3	,	,	PUNCT
ejpam-4136	84	4	xn−1	xn−1	PROPN
ejpam-4136	84	5	)	)	PUNCT
ejpam-4136	84	6	⊆	⊆	NUM
ejpam-4136	84	7	γ(αn	γ(αn	PROPN
ejpam-4136	84	8	,	,	PUNCT
ejpam-4136	84	9	βn)(xi	βn)(xi	PUNCT
ejpam-4136	84	10	)	)	PUNCT
ejpam-4136	84	11	n	n	CCONJ
ejpam-4136	84	12	i=1	i=1	PROPN
ejpam-4136	84	13	,	,	PUNCT
ejpam-4136	84	14	for	for	ADP
ejpam-4136	84	15	all	all	DET
ejpam-4136	84	16	x1	x1	PROPN
ejpam-4136	84	17	,	,	PUNCT
ejpam-4136	84	18	.	.	PUNCT
ejpam-4136	84	19	.	.	PUNCT
ejpam-4136	84	20	.	.	PUNCT
ejpam-4136	85	1	,	,	PUNCT
ejpam-4136	85	2	xn	xn	PUNCT
ejpam-4136	85	3	∈	∈	PROPN
ejpam-4136	85	4	x	x	X
ejpam-4136	85	5	,	,	PUNCT
ejpam-4136	85	6	(	(	PUNCT
ejpam-4136	85	7	g5	g5	NOUN
ejpam-4136	85	8	)	)	PUNCT
ejpam-4136	85	9	γ(αn	γ(αn	PROPN
ejpam-4136	85	10	,	,	PUNCT
ejpam-4136	85	11	βn)(xi	βn)(xi	PUNCT
ejpam-4136	85	12	)	)	PUNCT
ejpam-4136	85	13	n	n	CCONJ
ejpam-4136	85	14	i=1	i=1	PROPN
ejpam-4136	85	15	⊆	⊆	NUM
ejpam-4136	85	16	αn(xi	αn(xi	PROPN
ejpam-4136	85	17	)	)	PUNCT
ejpam-4136	85	18	n	n	CCONJ
ejpam-4136	85	19	i=1	i=1	PRON
ejpam-4136	85	20	·	·	PUNCT
ejpam-4136	85	21	γ(αn	γ(αn	VERB
ejpam-4136	85	22	,	,	PUNCT
ejpam-4136	85	23	βn)(x1	βn)(x1	NOUN
ejpam-4136	85	24	,	,	PUNCT
ejpam-4136	85	25	(	(	PUNCT
ejpam-4136	85	26	a	a	X
ejpam-4136	85	27	)	)	PUNCT
ejpam-4136	85	28	n	n	PRON
ejpam-4136	85	29	2	2	NUM
ejpam-4136	85	30	)	)	PUNCT
ejpam-4136	86	1	+	+	CCONJ
ejpam-4136	86	2	βn(xi	βn(xi	ADJ
ejpam-4136	86	3	)	)	PUNCT
ejpam-4136	86	4	n	n	CCONJ
ejpam-4136	86	5	i=1	i=1	PRON
ejpam-4136	86	6	·	·	PUNCT
ejpam-4136	86	7	γ(αn	γ(αn	VERB
ejpam-4136	86	8	,	,	PUNCT
ejpam-4136	86	9	βn)(a	βn)(a	PROPN
ejpam-4136	86	10	,	,	PUNCT
ejpam-4136	86	11	(	(	PUNCT
ejpam-4136	86	12	xi	xi	NOUN
ejpam-4136	86	13	)	)	PUNCT
ejpam-4136	86	14	n	n	PRON
ejpam-4136	86	15	i=2	i=2	PROPN
ejpam-4136	86	16	)	)	PUNCT
ejpam-4136	86	17	,	,	PUNCT
ejpam-4136	86	18	for	for	ADP
ejpam-4136	86	19	all	all	DET
ejpam-4136	86	20	x1	x1	PROPN
ejpam-4136	86	21	,	,	PUNCT
ejpam-4136	86	22	.	.	PUNCT
ejpam-4136	86	23	.	.	PUNCT
ejpam-4136	86	24	.	.	PUNCT
ejpam-4136	87	1	,	,	PUNCT
ejpam-4136	87	2	xn	xn	PROPN
ejpam-4136	87	3	,	,	PUNCT
ejpam-4136	87	4	a	a	DET
ejpam-4136	87	5	∈	∈	NOUN
ejpam-4136	87	6	x.	x.	NOUN
ejpam-4136	88	1	we	we	PRON
ejpam-4136	88	2	denote	denote	VERB
ejpam-4136	88	3	a+	a+	PUNCT
ejpam-4136	88	4	a	a	DET
ejpam-4136	88	5	set	set	NOUN
ejpam-4136	88	6	of	of	ADP
ejpam-4136	88	7	non	non	ADJ
ejpam-4136	88	8	-	-	ADJ
ejpam-4136	88	9	negative	negative	ADJ
ejpam-4136	88	10	elements	element	NOUN
ejpam-4136	88	11	of	of	ADP
ejpam-4136	88	12	a	a	DET
ejpam-4136	88	13	namely	namely	ADV
ejpam-4136	88	14	a+	a+	PUNCT
ejpam-4136	88	15	=	=	PUNCT
ejpam-4136	88	16	{	{	PUNCT
ejpam-4136	88	17	a	a	PRON
ejpam-4136	88	18	∈	∈	PROPN
ejpam-4136	88	19	a	a	PRON
ejpam-4136	88	20	:	:	PUNCT
ejpam-4136	88	21	0a	0a	PROPN
ejpam-4136	88	22	⪯	⪯	NOUN
ejpam-4136	88	23	a	a	PRON
ejpam-4136	88	24	}	}	PUNCT
ejpam-4136	88	25	.	.	PUNCT
ejpam-4136	89	1	let	let	VERB
ejpam-4136	89	2	ai	ai	VERB
ejpam-4136	89	3	subsets	subset	NOUN
ejpam-4136	89	4	of	of	ADP
ejpam-4136	89	5	x	x	PRON
ejpam-4136	89	6	,	,	PUNCT
ejpam-4136	89	7	(	(	PUNCT
ejpam-4136	89	8	i	i	NOUN
ejpam-4136	89	9	=	=	NOUN
ejpam-4136	89	10	1	1	NUM
ejpam-4136	89	11	,	,	PUNCT
ejpam-4136	89	12	.	.	PUNCT
ejpam-4136	89	13	.	.	PUNCT
ejpam-4136	90	1	.	.	PUNCT
ejpam-4136	90	2	,	,	PUNCT
ejpam-4136	90	3	n	n	CCONJ
ejpam-4136	90	4	)	)	PUNCT
ejpam-4136	91	1	,	,	PUNCT
ejpam-4136	91	2	for	for	ADP
ejpam-4136	91	3	any	any	DET
ejpam-4136	91	4	b	b	NOUN
ejpam-4136	91	5	,	,	PUNCT
ejpam-4136	91	6	b′	b′	NUM
ejpam-4136	91	7	∈	∈	NOUN
ejpam-4136	91	8	p	p	NOUN
ejpam-4136	91	9	∗(a+	∗(a+	NOUN
ejpam-4136	91	10	)	)	PUNCT
ejpam-4136	91	11	and	and	CCONJ
ejpam-4136	91	12	α	α	PRON
ejpam-4136	91	13	∈	∈	PROPN
ejpam-4136	91	14	a+	a+	PUNCT
ejpam-4136	91	15	.	.	PUNCT
ejpam-4136	91	16	we	we	PRON
ejpam-4136	91	17	define	define	VERB
ejpam-4136	91	18	γ(αn	γ(αn	PROPN
ejpam-4136	91	19	,	,	PUNCT
ejpam-4136	91	20	βn)(ai	βn)(ai	PUNCT
ejpam-4136	91	21	)	)	PUNCT
ejpam-4136	91	22	n	n	PRON
ejpam-4136	91	23	i=1	i=1	NOUN
ejpam-4136	91	24	=	=	PUNCT
ejpam-4136	91	25	⋃	⋃	NOUN
ejpam-4136	91	26	{	{	PUNCT
ejpam-4136	91	27	γn(xi	γn(xi	PROPN
ejpam-4136	91	28	)	)	PUNCT
ejpam-4136	92	1	n	n	CCONJ
ejpam-4136	92	2	i=1	i=1	PROPN
ejpam-4136	93	1	|	|	ADV
ejpam-4136	93	2	xi	xi	X
ejpam-4136	93	3	∈	∈	PROPN
ejpam-4136	93	4	ai	ai	VERB
ejpam-4136	93	5	,	,	PUNCT
ejpam-4136	93	6	i	i	NOUN
ejpam-4136	93	7	=	=	NOUN
ejpam-4136	93	8	1	1	NUM
ejpam-4136	93	9	,	,	PUNCT
ejpam-4136	93	10	.	.	PUNCT
ejpam-4136	93	11	.	.	PUNCT
ejpam-4136	93	12	.	.	PUNCT
ejpam-4136	94	1	,	,	PUNCT
ejpam-4136	94	2	n	n	CCONJ
ejpam-4136	94	3	}	}	PUNCT
ejpam-4136	94	4	,	,	PUNCT
ejpam-4136	94	5	b	b	X
ejpam-4136	95	1	+	+	NOUN
ejpam-4136	95	2	b′	b′	NOUN
ejpam-4136	95	3	=	=	PUNCT
ejpam-4136	95	4	{	{	PUNCT
ejpam-4136	95	5	b+	b+	X
ejpam-4136	95	6	b′	b′	NUM
ejpam-4136	95	7	|	|	ADV
ejpam-4136	95	8	∈	∈	PROPN
ejpam-4136	95	9	b	b	PROPN
ejpam-4136	95	10	,	,	PUNCT
ejpam-4136	95	11	b′	b′	NUM
ejpam-4136	95	12	∈	∈	PROPN
ejpam-4136	95	13	b′	b′	NOUN
ejpam-4136	95	14	}	}	PUNCT
ejpam-4136	95	15	and	and	CCONJ
ejpam-4136	95	16	α	α	PRON
ejpam-4136	95	17	·	·	SYM
ejpam-4136	95	18	b	b	X
ejpam-4136	95	19	=	=	SYM
ejpam-4136	95	20	{	{	PUNCT
ejpam-4136	95	21	α	α	NOUN
ejpam-4136	95	22	·	·	PUNCT
ejpam-4136	95	23	b	b	X
ejpam-4136	95	24	|	|	NOUN
ejpam-4136	95	25	b	b	PROPN
ejpam-4136	95	26	∈	∈	PROPN
ejpam-4136	95	27	b	b	PROPN
ejpam-4136	95	28	,	,	PUNCT
ejpam-4136	95	29	α	α	PROPN
ejpam-4136	95	30	∈	∈	PROPN
ejpam-4136	95	31	a+	a+	PUNCT
ejpam-4136	95	32	}	}	PUNCT
ejpam-4136	95	33	.	.	PUNCT
ejpam-4136	96	1	we	we	PRON
ejpam-4136	96	2	shall	shall	AUX
ejpam-4136	96	3	use	use	VERB
ejpam-4136	96	4	the	the	DET
ejpam-4136	96	5	following	follow	VERB
ejpam-4136	96	6	abbreviated	abbreviate	VERB
ejpam-4136	96	7	notation	notation	NOUN
ejpam-4136	96	8	:	:	PUNCT
ejpam-4136	96	9	the	the	DET
ejpam-4136	96	10	function	function	NOUN
ejpam-4136	96	11	γn	γn	NOUN
ejpam-4136	96	12	is	be	AUX
ejpam-4136	96	13	called	call	VERB
ejpam-4136	96	14	a	a	DET
ejpam-4136	96	15	ordered	order	VERB
ejpam-4136	96	16	b(αn	b(αn	NOUN
ejpam-4136	96	17	,	,	PUNCT
ejpam-4136	96	18	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	96	19	over	over	ADP
ejpam-4136	96	20	banach	banach	NOUN
ejpam-4136	96	21	algebra	algebra	NOUN
ejpam-4136	96	22	a	a	PRON
ejpam-4136	96	23	of	of	ADP
ejpam-4136	96	24	dimension	dimension	NOUN
ejpam-4136	96	25	n	n	CCONJ
ejpam-4136	96	26	,	,	PUNCT
ejpam-4136	96	27	or	or	CCONJ
ejpam-4136	96	28	more	more	ADV
ejpam-4136	96	29	specifically	specifically	ADV
ejpam-4136	96	30	a	a	DET
ejpam-4136	96	31	b(αn	b(αn	NOUN
ejpam-4136	96	32	,	,	PUNCT
ejpam-4136	96	33	βn)hypermetric	βn)hypermetric	NOUN
ejpam-4136	96	34	onx	onx	PROPN
ejpam-4136	96	35	over	over	ADP
ejpam-4136	96	36	banach	banach	NOUN
ejpam-4136	96	37	algebraa	algebraa	NOUN
ejpam-4136	96	38	.	.	PUNCT
ejpam-4136	97	1	the	the	DET
ejpam-4136	97	2	pair	pair	NOUN
ejpam-4136	97	3	(	(	PUNCT
ejpam-4136	97	4	x	x	NOUN
ejpam-4136	97	5	,	,	PUNCT
ejpam-4136	97	6	γn	γn	NUM
ejpam-4136	97	7	)	)	PUNCT
ejpam-4136	97	8	is	be	AUX
ejpam-4136	97	9	called	call	VERB
ejpam-4136	97	10	an	an	DET
ejpam-4136	97	11	b(αn	b(αn	NOUN
ejpam-4136	97	12	,	,	PUNCT
ejpam-4136	97	13	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	97	14	space	space	NOUN
ejpam-4136	97	15	over	over	ADP
ejpam-4136	97	16	banach	banach	NOUN
ejpam-4136	97	17	algebra	algebra	NOUN
ejpam-4136	97	18	a.	a.	NOUN
ejpam-4136	97	19	for	for	ADP
ejpam-4136	97	20	example	example	NOUN
ejpam-4136	97	21	,	,	PUNCT
ejpam-4136	97	22	we	we	PRON
ejpam-4136	97	23	can	can	AUX
ejpam-4136	97	24	place	place	VERB
ejpam-4136	97	25	a+	a+	PUNCT
ejpam-4136	97	26	=	=	PUNCT
ejpam-4136	97	27	z0	z0	PROPN
ejpam-4136	97	28	+	+	CCONJ
ejpam-4136	97	29	or	or	CCONJ
ejpam-4136	97	30	r0	r0	NOUN
ejpam-4136	97	31	+	+	NOUN
ejpam-4136	97	32	,	,	PUNCT
ejpam-4136	97	33	where	where	SCONJ
ejpam-4136	97	34	z0	z0	PROPN
ejpam-4136	97	35	+	+	CCONJ
ejpam-4136	97	36	:	:	PUNCT
ejpam-4136	97	37	=	=	SYM
ejpam-4136	97	38	n	n	CCONJ
ejpam-4136	97	39	∪	∪	X
ejpam-4136	97	40	{	{	PUNCT
ejpam-4136	97	41	0	0	NUM
ejpam-4136	97	42	}	}	PUNCT
ejpam-4136	97	43	=	=	SYM
ejpam-4136	97	44	{	{	PUNCT
ejpam-4136	97	45	0	0	NUM
ejpam-4136	97	46	,	,	PUNCT
ejpam-4136	97	47	1	1	NUM
ejpam-4136	97	48	,	,	PUNCT
ejpam-4136	97	49	2	2	NUM
ejpam-4136	97	50	,	,	PUNCT
ejpam-4136	97	51	.	.	PUNCT
ejpam-4136	97	52	.	.	PUNCT
ejpam-4136	97	53	.	.	PUNCT
ejpam-4136	98	1	}	}	PUNCT
ejpam-4136	99	1	and	and	CCONJ
ejpam-4136	99	2	r0	r0	VERB
ejpam-4136	99	3	+	+	CCONJ
ejpam-4136	99	4	:	:	PUNCT
ejpam-4136	99	5	=	=	X
ejpam-4136	100	1	[	[	X
ejpam-4136	100	2	0,+∞	0,+∞	NUM
ejpam-4136	100	3	)	)	PUNCT
ejpam-4136	100	4	.	.	PUNCT
ejpam-4136	101	1	here	here	ADV
ejpam-4136	101	2	,	,	PUNCT
ejpam-4136	101	3	for	for	ADP
ejpam-4136	101	4	simplicity	simplicity	NOUN
ejpam-4136	101	5	we	we	PRON
ejpam-4136	101	6	assume	assume	VERB
ejpam-4136	101	7	that	that	SCONJ
ejpam-4136	101	8	a+	a+	PUNCT
ejpam-4136	101	9	=	=	SYM
ejpam-4136	101	10	r0	r0	NOUN
ejpam-4136	101	11	+	+	PROPN
ejpam-4136	101	12	.	.	PUNCT
ejpam-4136	102	1	the	the	DET
ejpam-4136	102	2	following	follow	VERB
ejpam-4136	102	3	useful	useful	ADJ
ejpam-4136	102	4	properties	property	NOUN
ejpam-4136	102	5	of	of	ADP
ejpam-4136	102	6	a	a	DET
ejpam-4136	102	7	bn	bn	NOUN
ejpam-4136	102	8	-	-	PUNCT
ejpam-4136	102	9	hypermetric	hypermetric	NOUN
ejpam-4136	102	10	are	be	AUX
ejpam-4136	102	11	easily	easily	ADV
ejpam-4136	102	12	derived	derive	VERB
ejpam-4136	102	13	from	from	ADP
ejpam-4136	102	14	the	the	DET
ejpam-4136	102	15	axioms	axiom	NOUN
ejpam-4136	102	16	.	.	PUNCT
ejpam-4136	103	1	remark	remark	NOUN
ejpam-4136	103	2	3	3	NUM
ejpam-4136	103	3	.	.	PUNCT
ejpam-4136	104	1	if	if	SCONJ
ejpam-4136	104	2	αn(xi	αn(xi	PROPN
ejpam-4136	104	3	)	)	PUNCT
ejpam-4136	105	1	n	n	CCONJ
ejpam-4136	105	2	i=1	i=1	PROPN
ejpam-4136	105	3	=	=	SYM
ejpam-4136	105	4	βn(xi	βn(xi	PROPN
ejpam-4136	105	5	)	)	PUNCT
ejpam-4136	106	1	n	n	CCONJ
ejpam-4136	106	2	i=1	i=1	PROPN
ejpam-4136	106	3	=	=	PUNCT
ejpam-4136	106	4	c	c	PROPN
ejpam-4136	106	5	for	for	ADP
ejpam-4136	106	6	c	c	PROPN
ejpam-4136	106	7	≥	≥	NUM
ejpam-4136	106	8	1	1	NUM
ejpam-4136	106	9	and	and	CCONJ
ejpam-4136	106	10	n	n	CCONJ
ejpam-4136	106	11	=	=	SYM
ejpam-4136	106	12	1	1	NUM
ejpam-4136	106	13	,	,	PUNCT
ejpam-4136	106	14	then	then	ADV
ejpam-4136	106	15	we	we	PRON
ejpam-4136	106	16	obtain	obtain	VERB
ejpam-4136	106	17	the	the	DET
ejpam-4136	106	18	definition	definition	NOUN
ejpam-4136	106	19	of	of	ADP
ejpam-4136	106	20	b	b	NOUN
ejpam-4136	106	21	-	-	PUNCT
ejpam-4136	106	22	metric	metric	ADJ
ejpam-4136	106	23	space	space	NOUN
ejpam-4136	106	24	(	(	PUNCT
ejpam-4136	106	25	czerwik	czerwik	PROPN
ejpam-4136	106	26	[	[	X
ejpam-4136	106	27	4	4	NUM
ejpam-4136	106	28	]	]	NUM
ejpam-4136	106	29	)	)	PUNCT
ejpam-4136	106	30	.	.	PUNCT
ejpam-4136	107	1	it	it	PRON
ejpam-4136	107	2	is	be	AUX
ejpam-4136	107	3	clear	clear	ADJ
ejpam-4136	107	4	that	that	SCONJ
ejpam-4136	107	5	for	for	ADP
ejpam-4136	107	6	c	c	NOUN
ejpam-4136	107	7	=	=	SYM
ejpam-4136	107	8	1	1	NUM
ejpam-4136	107	9	,	,	PUNCT
ejpam-4136	107	10	this	this	DET
ejpam-4136	107	11	b	b	X
ejpam-4136	107	12	-	-	ADJ
ejpam-4136	107	13	metric	metric	ADJ
ejpam-4136	107	14	becomes	become	VERB
ejpam-4136	107	15	a	a	DET
ejpam-4136	107	16	usual	usual	ADJ
ejpam-4136	107	17	metric	metric	NOUN
ejpam-4136	107	18	.	.	PUNCT
ejpam-4136	108	1	a.	a.	PROPN
ejpam-4136	108	2	d.nezhad	d.nezhad	PROPN
ejpam-4136	108	3	,	,	PUNCT
ejpam-4136	108	4	s.	s.	PROPN
ejpam-4136	108	5	radenović	radenović	PROPN
ejpam-4136	108	6	/	/	SYM
ejpam-4136	108	7	eur	eur	PROPN
ejpam-4136	108	8	.	.	PUNCT
ejpam-4136	109	1	j.	j.	PROPN
ejpam-4136	109	2	pure	pure	PROPN
ejpam-4136	109	3	appl	appl	PROPN
ejpam-4136	109	4	.	.	PROPN
ejpam-4136	109	5	math	math	PROPN
ejpam-4136	109	6	,	,	PUNCT
ejpam-4136	109	7	14	14	NUM
ejpam-4136	109	8	(	(	PUNCT
ejpam-4136	109	9	4	4	NUM
ejpam-4136	109	10	)	)	PUNCT
ejpam-4136	109	11	(	(	PUNCT
ejpam-4136	109	12	2021	2021	NUM
ejpam-4136	109	13	)	)	PUNCT
ejpam-4136	109	14	,	,	PUNCT
ejpam-4136	109	15	1148	1148	NUM
ejpam-4136	109	16	-	-	SYM
ejpam-4136	109	17	1160	1160	NUM
ejpam-4136	109	18	1152	1152	NUM
ejpam-4136	109	19	proposition	proposition	NOUN
ejpam-4136	109	20	1	1	NUM
ejpam-4136	109	21	.	.	PUNCT
ejpam-4136	110	1	(	(	PUNCT
ejpam-4136	110	2	example	example	NOUN
ejpam-4136	110	3	)	)	PUNCT
ejpam-4136	110	4	we	we	PRON
ejpam-4136	110	5	assume	assume	VERB
ejpam-4136	110	6	that	that	SCONJ
ejpam-4136	110	7	a+	a+	PUNCT
ejpam-4136	110	8	=	=	SYM
ejpam-4136	110	9	r0	r0	NOUN
ejpam-4136	110	10	+	+	PROPN
ejpam-4136	110	11	.	.	PUNCT
ejpam-4136	111	1	let	let	VERB
ejpam-4136	111	2	x	x	PUNCT
ejpam-4136	111	3	=	=	PUNCT
ejpam-4136	112	1	[	[	X
ejpam-4136	112	2	0	0	NUM
ejpam-4136	112	3	,	,	PUNCT
ejpam-4136	112	4	1	1	NUM
ejpam-4136	112	5	]	]	PUNCT
ejpam-4136	112	6	and	and	CCONJ
ejpam-4136	112	7	α2	α2	ADJ
ejpam-4136	112	8	,	,	PUNCT
ejpam-4136	112	9	β2	β2	VERB
ejpam-4136	112	10	:	:	PUNCT
ejpam-4136	112	11	x	x	PROPN
ejpam-4136	112	12	×x	×x	VERB
ejpam-4136	112	13	−→	−→	NOUN
ejpam-4136	112	14	[	[	X
ejpam-4136	112	15	1,+∞	1,+∞	NUM
ejpam-4136	112	16	)	)	PUNCT
ejpam-4136	112	17	,	,	PUNCT
ejpam-4136	112	18	with	with	ADP
ejpam-4136	112	19	α2(x	α2(x	PROPN
ejpam-4136	112	20	,	,	PUNCT
ejpam-4136	112	21	y	y	NOUN
ejpam-4136	112	22	)	)	PUNCT
ejpam-4136	112	23	=	=	SYM
ejpam-4136	113	1	1	1	NUM
ejpam-4136	113	2	+	+	NUM
ejpam-4136	113	3	1	1	NUM
ejpam-4136	113	4	x+y	x+y	NUM
ejpam-4136	113	5	,	,	PUNCT
ejpam-4136	113	6	β2(x	β2(x	NUM
ejpam-4136	113	7	,	,	PUNCT
ejpam-4136	113	8	y	y	NOUN
ejpam-4136	113	9	)	)	PUNCT
ejpam-4136	113	10	=	=	SYM
ejpam-4136	114	1	1	1	NUM
ejpam-4136	114	2	+	+	NUM
ejpam-4136	114	3	2	2	NUM
ejpam-4136	114	4	x+y	x+y	NUM
ejpam-4136	114	5	.	.	PUNCT
ejpam-4136	115	1	define	define	VERB
ejpam-4136	115	2	ωα2,β2	ωα2,β2	NOUN
ejpam-4136	115	3	:	:	PUNCT
ejpam-4136	115	4	x	x	X
ejpam-4136	115	5	×x	×x	ADP
ejpam-4136	115	6	→	→	SYM
ejpam-4136	115	7	p	p	NOUN
ejpam-4136	115	8	∗(r0	∗(r0	ADJ
ejpam-4136	115	9	+	+	NOUN
ejpam-4136	115	10	)	)	PUNCT
ejpam-4136	115	11	with	with	ADP
ejpam-4136	115	12	,	,	PUNCT
ejpam-4136	115	13	ω(α2,β2)(x	ω(α2,β2)(x	PROPN
ejpam-4136	115	14	,	,	PUNCT
ejpam-4136	115	15	y	y	NOUN
ejpam-4136	115	16	)	)	PUNCT
ejpam-4136	115	17	=	=	PUNCT
ejpam-4136	116	1			PUNCT
ejpam-4136	116	2	[	[	X
ejpam-4136	116	3	1	1	NUM
ejpam-4136	116	4	,	,	PUNCT
ejpam-4136	116	5	1	1	NUM
ejpam-4136	116	6	xy	xy	NOUN
ejpam-4136	116	7	)	)	PUNCT
ejpam-4136	116	8	;	;	PUNCT
ejpam-4136	116	9	x	x	X
ejpam-4136	116	10	,	,	PUNCT
ejpam-4136	116	11	y	y	PROPN
ejpam-4136	116	12	∈	∈	PROPN
ejpam-4136	116	13	(	(	PUNCT
ejpam-4136	116	14	0	0	NUM
ejpam-4136	116	15	,	,	PUNCT
ejpam-4136	116	16	1	1	NUM
ejpam-4136	116	17	]	]	PUNCT
ejpam-4136	116	18	,	,	PUNCT
ejpam-4136	116	19	x	x	PUNCT
ejpam-4136	116	20	̸=	̸=	PROPN
ejpam-4136	116	21	y	y	PROPN
ejpam-4136	116	22	{	{	PUNCT
ejpam-4136	116	23	0	0	NUM
ejpam-4136	116	24	}	}	PUNCT
ejpam-4136	116	25	;	;	PUNCT
ejpam-4136	116	26	x	x	X
ejpam-4136	116	27	,	,	PUNCT
ejpam-4136	116	28	y	y	PROPN
ejpam-4136	116	29	∈	∈	PROPN
ejpam-4136	117	1	[	[	X
ejpam-4136	117	2	0	0	NUM
ejpam-4136	117	3	,	,	PUNCT
ejpam-4136	117	4	1	1	NUM
ejpam-4136	117	5	]	]	PUNCT
ejpam-4136	117	6	,	,	PUNCT
ejpam-4136	117	7	x	x	PUNCT
ejpam-4136	117	8	=	=	VERB
ejpam-4136	117	9	y	y	PROPN
ejpam-4136	117	10	ω(α2,β2)(y	ω(α2,β2)(y	PROPN
ejpam-4136	117	11	,	,	PUNCT
ejpam-4136	117	12	x	x	X
ejpam-4136	117	13	)	)	PUNCT
ejpam-4136	117	14	=	=	PUNCT
ejpam-4136	118	1	[	[	X
ejpam-4136	118	2	1	1	NUM
ejpam-4136	118	3	,	,	PUNCT
ejpam-4136	118	4	1x	1x	NUM
ejpam-4136	118	5	)	)	PUNCT
ejpam-4136	118	6	;	;	PUNCT
ejpam-4136	119	1	y	y	PROPN
ejpam-4136	119	2	=	=	SYM
ejpam-4136	119	3	0	0	PROPN
ejpam-4136	119	4	,	,	PUNCT
ejpam-4136	119	5	x	x	SYM
ejpam-4136	119	6	∈	∈	PROPN
ejpam-4136	119	7	(	(	PUNCT
ejpam-4136	119	8	0	0	NUM
ejpam-4136	119	9	,	,	PUNCT
ejpam-4136	119	10	1	1	NUM
ejpam-4136	119	11	]	]	PUNCT
ejpam-4136	119	12	(	(	PUNCT
ejpam-4136	119	13	1	1	X
ejpam-4136	119	14	)	)	PUNCT
ejpam-4136	119	15	and	and	CCONJ
ejpam-4136	119	16	also	also	ADV
ejpam-4136	119	17	assume	assume	VERB
ejpam-4136	119	18	a+b	a+b	NUM
ejpam-4136	119	19	=	=	X
ejpam-4136	119	20	a	a	DET
ejpam-4136	119	21	∪b	∪b	NOUN
ejpam-4136	119	22	,	,	PUNCT
ejpam-4136	119	23	for	for	ADP
ejpam-4136	119	24	all	all	DET
ejpam-4136	119	25	a	a	DET
ejpam-4136	119	26	,	,	PUNCT
ejpam-4136	119	27	b	b	X
ejpam-4136	119	28	∈	∈	PROPN
ejpam-4136	119	29	p	p	NOUN
ejpam-4136	119	30	∗(r0	∗(r0	PRON
ejpam-4136	119	31	+	+	NOUN
ejpam-4136	119	32	)	)	PUNCT
ejpam-4136	119	33	.	.	PUNCT
ejpam-4136	120	1	then	then	ADV
ejpam-4136	120	2	(	(	PUNCT
ejpam-4136	120	3	x	x	NOUN
ejpam-4136	120	4	,	,	PUNCT
ejpam-4136	120	5	ω(α2,β2	ω(α2,β2	NUM
ejpam-4136	120	6	)	)	PUNCT
ejpam-4136	120	7	)	)	PUNCT
ejpam-4136	120	8	is	be	AUX
ejpam-4136	120	9	a	a	DET
ejpam-4136	120	10	b(α2,β2)hypermetric	b(α2,β2)hypermetric	ADJ
ejpam-4136	120	11	space	space	NOUN
ejpam-4136	120	12	.	.	PUNCT
ejpam-4136	121	1	proof	proof	NOUN
ejpam-4136	121	2	.	.	PUNCT
ejpam-4136	122	1	it	it	PRON
ejpam-4136	122	2	is	be	AUX
ejpam-4136	122	3	sufficient	sufficient	ADJ
ejpam-4136	122	4	to	to	PART
ejpam-4136	122	5	show	show	VERB
ejpam-4136	122	6	that	that	PRON
ejpam-4136	122	7	ω(α2,β2	ω(α2,β2	NOUN
ejpam-4136	122	8	)	)	PUNCT
ejpam-4136	122	9	is	be	AUX
ejpam-4136	122	10	satisfied	satisfied	ADJ
ejpam-4136	122	11	in	in	ADP
ejpam-4136	122	12	all	all	DET
ejpam-4136	122	13	properties	property	NOUN
ejpam-4136	122	14	[	[	X
ejpam-4136	122	15	(	(	PUNCT
ejpam-4136	122	16	g0	g0	NOUN
ejpam-4136	122	17	)	)	PUNCT
ejpam-4136	122	18	]	]	PUNCT
ejpam-4136	122	19	,	,	PUNCT
ejpam-4136	122	20	[	[	X
ejpam-4136	122	21	(	(	PUNCT
ejpam-4136	122	22	g1	g1	PROPN
ejpam-4136	122	23	)	)	PUNCT
ejpam-4136	122	24	]	]	PUNCT
ejpam-4136	122	25	,	,	PUNCT
ejpam-4136	122	26	[	[	X
ejpam-4136	122	27	(	(	PUNCT
ejpam-4136	122	28	g2	g2	PROPN
ejpam-4136	122	29	)	)	PUNCT
ejpam-4136	122	30	]	]	PUNCT
ejpam-4136	122	31	,	,	PUNCT
ejpam-4136	122	32	.	.	PUNCT
ejpam-4136	122	33	.	.	PUNCT
ejpam-4136	122	34	.	.	PUNCT
ejpam-4136	123	1	,	,	PUNCT
ejpam-4136	124	1	[	[	X
ejpam-4136	124	2	(	(	PUNCT
ejpam-4136	124	3	g5	g5	NOUN
ejpam-4136	124	4	)	)	PUNCT
ejpam-4136	124	5	]	]	PUNCT
ejpam-4136	124	6	.	.	PUNCT
ejpam-4136	125	1	the	the	DET
ejpam-4136	125	2	proofs	proof	NOUN
ejpam-4136	125	3	of	of	ADP
ejpam-4136	125	4	[	[	X
ejpam-4136	125	5	(	(	PUNCT
ejpam-4136	125	6	g0	g0	NOUN
ejpam-4136	125	7	)	)	PUNCT
ejpam-4136	125	8	]	]	PUNCT
ejpam-4136	125	9	,	,	PUNCT
ejpam-4136	125	10	[	[	X
ejpam-4136	125	11	(	(	PUNCT
ejpam-4136	125	12	g1	g1	PROPN
ejpam-4136	125	13	)	)	PUNCT
ejpam-4136	125	14	]	]	PUNCT
ejpam-4136	125	15	,	,	PUNCT
ejpam-4136	125	16	.	.	PUNCT
ejpam-4136	125	17	.	.	PUNCT
ejpam-4136	125	18	.	.	PUNCT
ejpam-4136	126	1	,	,	PUNCT
ejpam-4136	127	1	[	[	X
ejpam-4136	127	2	(	(	PUNCT
ejpam-4136	127	3	g4	g4	NOUN
ejpam-4136	127	4	)	)	PUNCT
ejpam-4136	127	5	]	]	PUNCT
ejpam-4136	127	6	,	,	PUNCT
ejpam-4136	127	7	are	be	AUX
ejpam-4136	127	8	immediate	immediate	ADJ
ejpam-4136	127	9	from	from	ADP
ejpam-4136	127	10	the	the	DET
ejpam-4136	127	11	definition	definition	NOUN
ejpam-4136	127	12	of	of	ADP
ejpam-4136	127	13	ω(α2,β2	ω(α2,β2	NUM
ejpam-4136	127	14	)	)	PUNCT
ejpam-4136	127	15	.	.	PUNCT
ejpam-4136	128	1	we	we	PRON
ejpam-4136	128	2	only	only	ADV
ejpam-4136	128	3	need	need	VERB
ejpam-4136	128	4	to	to	PART
ejpam-4136	128	5	show	show	VERB
ejpam-4136	128	6	that	that	PRON
ejpam-4136	128	7	ω(α2,β2	ω(α2,β2	NOUN
ejpam-4136	128	8	)	)	PUNCT
ejpam-4136	128	9	is	be	AUX
ejpam-4136	128	10	satisfied	satisfied	ADJ
ejpam-4136	128	11	in	in	ADP
ejpam-4136	128	12	ω(α2,β2)(x	ω(α2,β2)(x	PROPN
ejpam-4136	128	13	,	,	PUNCT
ejpam-4136	128	14	y	y	PROPN
ejpam-4136	128	15	)	)	PUNCT
ejpam-4136	128	16	⊆	⊆	NUM
ejpam-4136	128	17	α2(x	α2(x	PROPN
ejpam-4136	128	18	,	,	PUNCT
ejpam-4136	128	19	y).ω(α2,β2)(x	y).ω(α2,β2)(x	PROPN
ejpam-4136	128	20	,	,	PUNCT
ejpam-4136	128	21	z	z	NOUN
ejpam-4136	128	22	)	)	PUNCT
ejpam-4136	128	23	+	+	CCONJ
ejpam-4136	129	1	β2(x	β2(x	NUM
ejpam-4136	129	2	,	,	PUNCT
ejpam-4136	129	3	y).ω(α2,β2)(z	y).ω(α2,β2)(z	PROPN
ejpam-4136	129	4	,	,	PUNCT
ejpam-4136	129	5	y	y	NOUN
ejpam-4136	129	6	)	)	PUNCT
ejpam-4136	129	7	,	,	PUNCT
ejpam-4136	129	8	for	for	ADP
ejpam-4136	129	9	all	all	DET
ejpam-4136	129	10	x	x	NOUN
ejpam-4136	129	11	,	,	PUNCT
ejpam-4136	129	12	y	y	PROPN
ejpam-4136	129	13	,	,	PUNCT
ejpam-4136	129	14	z	z	NOUN
ejpam-4136	129	15	∈	∈	PROPN
ejpam-4136	129	16	x.	x.	NOUN
ejpam-4136	129	17	we	we	PRON
ejpam-4136	129	18	distinguish	distinguish	VERB
ejpam-4136	129	19	the	the	DET
ejpam-4136	129	20	following	follow	VERB
ejpam-4136	129	21	cases	case	NOUN
ejpam-4136	129	22	:	:	PUNCT
ejpam-4136	129	23	(	(	PUNCT
ejpam-4136	129	24	i	i	NOUN
ejpam-4136	129	25	)	)	PUNCT
ejpam-4136	129	26	let	let	VERB
ejpam-4136	129	27	x	x	PRON
ejpam-4136	129	28	,	,	PUNCT
ejpam-4136	129	29	y	y	PROPN
ejpam-4136	129	30	∈	∈	PROPN
ejpam-4136	129	31	(	(	PUNCT
ejpam-4136	129	32	0	0	NUM
ejpam-4136	129	33	,	,	PUNCT
ejpam-4136	129	34	1	1	NUM
ejpam-4136	129	35	]	]	PUNCT
ejpam-4136	129	36	for	for	ADP
ejpam-4136	129	37	z	z	PROPN
ejpam-4136	129	38	∈	∈	PROPN
ejpam-4136	129	39	(	(	PUNCT
ejpam-4136	129	40	0	0	NUM
ejpam-4136	129	41	,	,	PUNCT
ejpam-4136	129	42	1	1	NUM
ejpam-4136	129	43	]	]	PUNCT
ejpam-4136	129	44	,	,	PUNCT
ejpam-4136	129	45	we	we	PRON
ejpam-4136	129	46	have	have	VERB
ejpam-4136	129	47	ω(α2,β2)(x	ω(α2,β2)(x	PROPN
ejpam-4136	129	48	,	,	PUNCT
ejpam-4136	129	49	y	y	PROPN
ejpam-4136	129	50	)	)	PUNCT
ejpam-4136	129	51	⊆	⊆	NUM
ejpam-4136	129	52	α2(x	α2(x	PROPN
ejpam-4136	129	53	,	,	PUNCT
ejpam-4136	129	54	y).ω(α2,β2)(x	y).ω(α2,β2)(x	PROPN
ejpam-4136	129	55	,	,	PUNCT
ejpam-4136	129	56	z	z	NOUN
ejpam-4136	129	57	)	)	PUNCT
ejpam-4136	129	58	+	+	CCONJ
ejpam-4136	129	59	β2(x	β2(x	NUM
ejpam-4136	129	60	,	,	PUNCT
ejpam-4136	129	61	y).ω(α2,β2)(z	y).ω(α2,β2)(z	NOUN
ejpam-4136	129	62	,	,	PUNCT
ejpam-4136	129	63	y	y	NOUN
ejpam-4136	129	64	)	)	PUNCT
ejpam-4136	129	65	if	if	SCONJ
ejpam-4136	129	66	and	and	CCONJ
ejpam-4136	129	67	only	only	ADV
ejpam-4136	129	68	if	if	SCONJ
ejpam-4136	129	69	[	[	X
ejpam-4136	129	70	1	1	NUM
ejpam-4136	129	71	,	,	PUNCT
ejpam-4136	129	72	1	1	NUM
ejpam-4136	129	73	xy	xy	NOUN
ejpam-4136	129	74	)	)	PUNCT
ejpam-4136	130	1	⊆	⊆	NUM
ejpam-4136	130	2	(	(	PUNCT
ejpam-4136	130	3	1	1	NUM
ejpam-4136	130	4	+	+	NUM
ejpam-4136	130	5	1	1	NUM
ejpam-4136	130	6	x+y	x+y	NUM
ejpam-4136	130	7	)	)	PUNCT
ejpam-4136	131	1	[	[	X
ejpam-4136	131	2	0	0	NUM
ejpam-4136	131	3	,	,	PUNCT
ejpam-4136	131	4	1	1	NUM
ejpam-4136	131	5	xz	xz	NOUN
ejpam-4136	131	6	)	)	PUNCT
ejpam-4136	132	1	+	+	PROPN
ejpam-4136	132	2	(	(	PUNCT
ejpam-4136	132	3	1	1	NUM
ejpam-4136	132	4	+	+	NUM
ejpam-4136	132	5	2	2	NUM
ejpam-4136	132	6	x+y	x+y	NUM
ejpam-4136	132	7	)	)	PUNCT
ejpam-4136	133	1	[	[	X
ejpam-4136	133	2	0	0	NUM
ejpam-4136	133	3	,	,	PUNCT
ejpam-4136	133	4	1	1	NUM
ejpam-4136	133	5	zy	zy	NOUN
ejpam-4136	133	6	)	)	PUNCT
ejpam-4136	134	1	if	if	SCONJ
ejpam-4136	135	1	and	and	CCONJ
ejpam-4136	135	2	only	only	ADV
ejpam-4136	135	3	if	if	SCONJ
ejpam-4136	135	4	[	[	X
ejpam-4136	135	5	1	1	NUM
ejpam-4136	135	6	,	,	PUNCT
ejpam-4136	135	7	1	1	NUM
ejpam-4136	135	8	xy	xy	NOUN
ejpam-4136	135	9	)	)	PUNCT
ejpam-4136	136	1	⊆	⊆	NUM
ejpam-4136	136	2	(	(	PUNCT
ejpam-4136	136	3	1	1	NUM
ejpam-4136	136	4	+	+	NUM
ejpam-4136	136	5	2	2	NUM
ejpam-4136	136	6	x+y	x+y	NUM
ejpam-4136	136	7	)	)	PUNCT
ejpam-4136	136	8	(	(	PUNCT
ejpam-4136	136	9	[	[	X
ejpam-4136	136	10	0	0	NUM
ejpam-4136	136	11	,	,	PUNCT
ejpam-4136	136	12	1	1	NUM
ejpam-4136	136	13	xz	xz	NOUN
ejpam-4136	136	14	)	)	PUNCT
ejpam-4136	137	1	+	+	CCONJ
ejpam-4136	138	1	[	[	X
ejpam-4136	138	2	0	0	NUM
ejpam-4136	138	3	,	,	PUNCT
ejpam-4136	138	4	1	1	NUM
ejpam-4136	138	5	zy	zy	NOUN
ejpam-4136	138	6	)	)	PUNCT
ejpam-4136	138	7	)	)	PUNCT
ejpam-4136	139	1	if	if	SCONJ
ejpam-4136	139	2	and	and	CCONJ
ejpam-4136	139	3	only	only	ADV
ejpam-4136	139	4	if	if	SCONJ
ejpam-4136	139	5	[	[	X
ejpam-4136	139	6	1	1	NUM
ejpam-4136	139	7	,	,	PUNCT
ejpam-4136	139	8	1	1	NUM
ejpam-4136	139	9	xy	xy	NOUN
ejpam-4136	139	10	)	)	PUNCT
ejpam-4136	139	11	⊆	⊆	NUM
ejpam-4136	139	12	(	(	PUNCT
ejpam-4136	139	13	x+y+2	x+y+2	PROPN
ejpam-4136	139	14	x+y	x+y	NUM
ejpam-4136	139	15	)	)	PUNCT
ejpam-4136	140	1	[	[	X
ejpam-4136	140	2	0	0	NUM
ejpam-4136	140	3	,	,	PUNCT
ejpam-4136	140	4	x+y	x+y	NUM
ejpam-4136	140	5	xyz	xyz	PROPN
ejpam-4136	140	6	)	)	PUNCT
ejpam-4136	141	1	if	if	SCONJ
ejpam-4136	141	2	and	and	CCONJ
ejpam-4136	141	3	only	only	ADV
ejpam-4136	141	4	if	if	SCONJ
ejpam-4136	141	5	z	z	NOUN
ejpam-4136	141	6	≤	≤	NOUN
ejpam-4136	141	7	2	2	NUM
ejpam-4136	141	8	+	+	CCONJ
ejpam-4136	141	9	x+	x+	ADJ
ejpam-4136	141	10	y.	y.	NOUN
ejpam-4136	141	11	if	if	SCONJ
ejpam-4136	141	12	z	z	NOUN
ejpam-4136	141	13	=	=	SYM
ejpam-4136	141	14	0	0	NUM
ejpam-4136	141	15	,	,	PUNCT
ejpam-4136	141	16	then	then	ADV
ejpam-4136	141	17	ω(α2,β2)(x	ω(α2,β2)(x	PROPN
ejpam-4136	141	18	,	,	PUNCT
ejpam-4136	141	19	y	y	PROPN
ejpam-4136	141	20	)	)	PUNCT
ejpam-4136	141	21	⊆	⊆	NUM
ejpam-4136	141	22	α2(x	α2(x	PROPN
ejpam-4136	141	23	,	,	PUNCT
ejpam-4136	141	24	y).ω(α2,β2)(x	y).ω(α2,β2)(x	PROPN
ejpam-4136	141	25	,	,	PUNCT
ejpam-4136	141	26	0	0	NUM
ejpam-4136	141	27	)	)	PUNCT
ejpam-4136	141	28	+	+	CCONJ
ejpam-4136	141	29	β2(x	β2(x	PUNCT
ejpam-4136	141	30	,	,	PUNCT
ejpam-4136	141	31	y).ω(α2,β2)(0	y).ω(α2,β2)(0	PROPN
ejpam-4136	141	32	,	,	PUNCT
ejpam-4136	141	33	y	y	NOUN
ejpam-4136	141	34	)	)	PUNCT
ejpam-4136	141	35	if	if	SCONJ
ejpam-4136	141	36	and	and	CCONJ
ejpam-4136	141	37	only	only	ADV
ejpam-4136	141	38	if	if	SCONJ
ejpam-4136	141	39	[	[	X
ejpam-4136	141	40	1	1	NUM
ejpam-4136	141	41	,	,	PUNCT
ejpam-4136	141	42	1	1	NUM
ejpam-4136	141	43	xy	xy	NOUN
ejpam-4136	141	44	)	)	PUNCT
ejpam-4136	142	1	⊆	⊆	NUM
ejpam-4136	142	2	(	(	PUNCT
ejpam-4136	142	3	1	1	NUM
ejpam-4136	142	4	+	+	NUM
ejpam-4136	142	5	1	1	NUM
ejpam-4136	142	6	x+y	x+y	NUM
ejpam-4136	142	7	)	)	PUNCT
ejpam-4136	143	1	[	[	X
ejpam-4136	143	2	0	0	NUM
ejpam-4136	143	3	,	,	PUNCT
ejpam-4136	143	4	1	1	NUM
ejpam-4136	143	5	x	x	NOUN
ejpam-4136	143	6	)	)	PUNCT
ejpam-4136	144	1	+	+	CCONJ
ejpam-4136	144	2	(	(	PUNCT
ejpam-4136	144	3	1	1	NUM
ejpam-4136	144	4	+	+	SYM
ejpam-4136	144	5	2	2	NUM
ejpam-4136	144	6	x+y	x+y	NUM
ejpam-4136	144	7	)	)	PUNCT
ejpam-4136	145	1	[	[	X
ejpam-4136	145	2	0	0	NUM
ejpam-4136	145	3	,	,	PUNCT
ejpam-4136	145	4	1	1	NUM
ejpam-4136	145	5	y	y	NOUN
ejpam-4136	145	6	)	)	PUNCT
ejpam-4136	146	1	if	if	SCONJ
ejpam-4136	146	2	and	and	CCONJ
ejpam-4136	146	3	only	only	ADV
ejpam-4136	146	4	if	if	SCONJ
ejpam-4136	146	5	[	[	X
ejpam-4136	146	6	1	1	NUM
ejpam-4136	146	7	,	,	PUNCT
ejpam-4136	146	8	1	1	NUM
ejpam-4136	146	9	xy	xy	NOUN
ejpam-4136	146	10	)	)	PUNCT
ejpam-4136	146	11	⊆	⊆	NUM
ejpam-4136	146	12	(	(	PUNCT
ejpam-4136	146	13	1	1	NUM
ejpam-4136	146	14	+	+	NUM
ejpam-4136	146	15	2	2	NUM
ejpam-4136	146	16	x+y	x+y	NUM
ejpam-4136	146	17	)	)	PUNCT
ejpam-4136	146	18	(	(	PUNCT
ejpam-4136	146	19	[	[	X
ejpam-4136	146	20	0	0	NUM
ejpam-4136	146	21	,	,	PUNCT
ejpam-4136	146	22	1	1	NUM
ejpam-4136	146	23	x)+[0	x)+[0	PROPN
ejpam-4136	146	24	,	,	PUNCT
ejpam-4136	146	25	1y	1y	NOUN
ejpam-4136	146	26	)	)	PUNCT
ejpam-4136	146	27	)	)	PUNCT
ejpam-4136	147	1	if	if	SCONJ
ejpam-4136	147	2	and	and	CCONJ
ejpam-4136	147	3	only	only	ADV
ejpam-4136	147	4	if	if	SCONJ
ejpam-4136	147	5	[	[	X
ejpam-4136	147	6	1	1	NUM
ejpam-4136	147	7	,	,	PUNCT
ejpam-4136	147	8	1	1	NUM
ejpam-4136	147	9	xy	xy	NOUN
ejpam-4136	147	10	)	)	PUNCT
ejpam-4136	147	11	⊆	⊆	NUM
ejpam-4136	147	12	(	(	PUNCT
ejpam-4136	147	13	x+y+2	x+y+2	PROPN
ejpam-4136	147	14	x+y	x+y	NUM
ejpam-4136	147	15	)	)	PUNCT
ejpam-4136	148	1	[	[	X
ejpam-4136	148	2	0	0	NUM
ejpam-4136	148	3	,	,	PUNCT
ejpam-4136	148	4	x+y	x+y	NUM
ejpam-4136	148	5	xy	xy	X
ejpam-4136	148	6	)	)	PUNCT
ejpam-4136	149	1	if	if	SCONJ
ejpam-4136	149	2	and	and	CCONJ
ejpam-4136	149	3	only	only	ADV
ejpam-4136	149	4	if	if	SCONJ
ejpam-4136	149	5	2	2	NUM
ejpam-4136	149	6	≤	≤	NUM
ejpam-4136	149	7	2+x+y	2+x+y	NUM
ejpam-4136	149	8	.	.	PUNCT
ejpam-4136	149	9	(	(	PUNCT
ejpam-4136	149	10	ii	ii	NOUN
ejpam-4136	149	11	)	)	PUNCT
ejpam-4136	149	12	for	for	ADP
ejpam-4136	149	13	x	x	PROPN
ejpam-4136	149	14	∈	∈	PROPN
ejpam-4136	149	15	(	(	PUNCT
ejpam-4136	149	16	0	0	NUM
ejpam-4136	149	17	,	,	PUNCT
ejpam-4136	149	18	1	1	NUM
ejpam-4136	149	19	]	]	PUNCT
ejpam-4136	149	20	and	and	CCONJ
ejpam-4136	149	21	y	y	PROPN
ejpam-4136	149	22	=	=	SYM
ejpam-4136	149	23	0	0	PROPN
ejpam-4136	149	24	,	,	PUNCT
ejpam-4136	149	25	let	let	VERB
ejpam-4136	149	26	z	z	NOUN
ejpam-4136	149	27	∈	∈	PROPN
ejpam-4136	149	28	(	(	PUNCT
ejpam-4136	149	29	0	0	NUM
ejpam-4136	149	30	,	,	PUNCT
ejpam-4136	149	31	1	1	NUM
ejpam-4136	149	32	]	]	PUNCT
ejpam-4136	149	33	,	,	PUNCT
ejpam-4136	149	34	ω(α2,β2)(x	ω(α2,β2)(x	PROPN
ejpam-4136	149	35	,	,	PUNCT
ejpam-4136	149	36	0	0	NUM
ejpam-4136	149	37	)	)	PUNCT
ejpam-4136	149	38	⊆	⊆	NUM
ejpam-4136	149	39	α2(x	α2(x	PROPN
ejpam-4136	149	40	,	,	PUNCT
ejpam-4136	149	41	0).ω(α2,β2)(x	0).ω(α2,β2)(x	NUM
ejpam-4136	149	42	,	,	PUNCT
ejpam-4136	149	43	z	z	NOUN
ejpam-4136	149	44	)	)	PUNCT
ejpam-4136	150	1	+	+	CCONJ
ejpam-4136	150	2	β2(x	β2(x	NUM
ejpam-4136	150	3	,	,	PUNCT
ejpam-4136	150	4	0).ω(α2,β2)(z	0).ω(α2,β2)(z	NUM
ejpam-4136	150	5	,	,	PUNCT
ejpam-4136	150	6	0	0	NUM
ejpam-4136	150	7	)	)	PUNCT
ejpam-4136	150	8	if	if	SCONJ
ejpam-4136	150	9	and	and	CCONJ
ejpam-4136	150	10	only	only	ADV
ejpam-4136	150	11	if	if	SCONJ
ejpam-4136	150	12	[	[	X
ejpam-4136	150	13	1	1	NUM
ejpam-4136	150	14	,	,	PUNCT
ejpam-4136	150	15	1x	1x	NUM
ejpam-4136	150	16	)	)	PUNCT
ejpam-4136	151	1	⊆	⊆	NUM
ejpam-4136	151	2	(	(	PUNCT
ejpam-4136	151	3	1+x	1+x	NUM
ejpam-4136	151	4	x	x	SYM
ejpam-4136	151	5	)	)	PUNCT
ejpam-4136	152	1	[	[	X
ejpam-4136	152	2	0	0	NUM
ejpam-4136	152	3	,	,	PUNCT
ejpam-4136	152	4	1	1	NUM
ejpam-4136	152	5	xz	xz	NOUN
ejpam-4136	152	6	)	)	PUNCT
ejpam-4136	153	1	+	+	CCONJ
ejpam-4136	153	2	(	(	PUNCT
ejpam-4136	153	3	2+x	2+x	NUM
ejpam-4136	153	4	x	x	X
ejpam-4136	153	5	)	)	PUNCT
ejpam-4136	154	1	[	[	X
ejpam-4136	154	2	0	0	NUM
ejpam-4136	154	3	,	,	PUNCT
ejpam-4136	154	4	1z	1z	NOUN
ejpam-4136	154	5	)	)	PUNCT
ejpam-4136	155	1	if	if	SCONJ
ejpam-4136	155	2	and	and	CCONJ
ejpam-4136	155	3	only	only	ADV
ejpam-4136	155	4	if	if	SCONJ
ejpam-4136	155	5	[	[	X
ejpam-4136	155	6	1	1	NUM
ejpam-4136	155	7	,	,	PUNCT
ejpam-4136	155	8	1x	1x	NUM
ejpam-4136	155	9	)	)	PUNCT
ejpam-4136	156	1	⊆	⊆	NUM
ejpam-4136	156	2	(	(	PUNCT
ejpam-4136	156	3	2+x	2+x	NUM
ejpam-4136	156	4	x	x	X
ejpam-4136	156	5	)	)	PUNCT
ejpam-4136	156	6	(	(	PUNCT
ejpam-4136	156	7	[	[	X
ejpam-4136	156	8	0	0	NUM
ejpam-4136	156	9	,	,	PUNCT
ejpam-4136	156	10	1	1	NUM
ejpam-4136	156	11	xz	xz	NOUN
ejpam-4136	156	12	)	)	PUNCT
ejpam-4136	157	1	+	+	CCONJ
ejpam-4136	158	1	[	[	X
ejpam-4136	158	2	0	0	NUM
ejpam-4136	158	3	,	,	PUNCT
ejpam-4136	158	4	1z	1z	NUM
ejpam-4136	158	5	)	)	PUNCT
ejpam-4136	158	6	)	)	PUNCT
ejpam-4136	159	1	if	if	SCONJ
ejpam-4136	159	2	and	and	CCONJ
ejpam-4136	159	3	only	only	ADV
ejpam-4136	159	4	if	if	SCONJ
ejpam-4136	159	5	[	[	X
ejpam-4136	159	6	1	1	NUM
ejpam-4136	159	7	,	,	PUNCT
ejpam-4136	159	8	1x	1x	NUM
ejpam-4136	159	9	)	)	PUNCT
ejpam-4136	160	1	⊆	⊆	NUM
ejpam-4136	160	2	(	(	PUNCT
ejpam-4136	160	3	x+2	x+2	NUM
ejpam-4136	160	4	x	x	SYM
ejpam-4136	160	5	)	)	PUNCT
ejpam-4136	161	1	[	[	X
ejpam-4136	161	2	0	0	NUM
ejpam-4136	161	3	,	,	PUNCT
ejpam-4136	161	4	x+1	x+1	PROPN
ejpam-4136	161	5	xz	xz	PROPN
ejpam-4136	161	6	)	)	PUNCT
ejpam-4136	162	1	if	if	SCONJ
ejpam-4136	162	2	and	and	CCONJ
ejpam-4136	162	3	only	only	ADV
ejpam-4136	162	4	if	if	SCONJ
ejpam-4136	162	5	xz	xz	PROPN
ejpam-4136	162	6	≤	≤	X
ejpam-4136	162	7	(	(	PUNCT
ejpam-4136	162	8	x+	x+	PROPN
ejpam-4136	162	9	1)(x+	1)(x+	NUM
ejpam-4136	162	10	2	2	NUM
ejpam-4136	162	11	)	)	PUNCT
ejpam-4136	162	12	.	.	PUNCT
ejpam-4136	163	1	(	(	PUNCT
ejpam-4136	163	2	iii	iii	X
ejpam-4136	163	3	)	)	PUNCT
ejpam-4136	163	4	let	let	VERB
ejpam-4136	163	5	x	x	PRON
ejpam-4136	163	6	,	,	PUNCT
ejpam-4136	163	7	y	y	PROPN
ejpam-4136	163	8	∈	∈	PROPN
ejpam-4136	164	1	[	[	X
ejpam-4136	164	2	0	0	NUM
ejpam-4136	164	3	,	,	PUNCT
ejpam-4136	164	4	1	1	NUM
ejpam-4136	164	5	]	]	PUNCT
ejpam-4136	164	6	,	,	PUNCT
ejpam-4136	164	7	x	x	PUNCT
ejpam-4136	164	8	=	=	PUNCT
ejpam-4136	164	9	y.	y.	PROPN
ejpam-4136	164	10	obviously	obviously	ADV
ejpam-4136	164	11	,	,	PUNCT
ejpam-4136	164	12	ω(α2,β2	ω(α2,β2	X
ejpam-4136	164	13	)	)	PUNCT
ejpam-4136	164	14	is	be	AUX
ejpam-4136	164	15	satisfied	satisfied	ADJ
ejpam-4136	164	16	in	in	ADP
ejpam-4136	164	17	the	the	DET
ejpam-4136	164	18	(	(	PUNCT
ejpam-4136	164	19	g5	g5	NOUN
ejpam-4136	164	20	)	)	PUNCT
ejpam-4136	164	21	.	.	PUNCT
ejpam-4136	165	1	hence	hence	ADV
ejpam-4136	165	2	(	(	PUNCT
ejpam-4136	165	3	x	x	NOUN
ejpam-4136	165	4	,	,	PUNCT
ejpam-4136	165	5	ω(α2,β2	ω(α2,β2	NUM
ejpam-4136	165	6	)	)	PUNCT
ejpam-4136	165	7	)	)	PUNCT
ejpam-4136	165	8	is	be	AUX
ejpam-4136	165	9	a	a	DET
ejpam-4136	165	10	b(α2,β2)-hypermetric	b(α2,β2)-hypermetric	ADJ
ejpam-4136	165	11	space	space	NOUN
ejpam-4136	165	12	.	.	PUNCT
ejpam-4136	166	1	proposition	proposition	NOUN
ejpam-4136	166	2	2	2	NUM
ejpam-4136	166	3	.	.	PUNCT
ejpam-4136	167	1	let	let	AUX
ejpam-4136	167	2	(	(	PUNCT
ejpam-4136	167	3	x	x	X
ejpam-4136	167	4	,	,	PUNCT
ejpam-4136	167	5	γ(αn	γ(αn	VERB
ejpam-4136	167	6	,	,	PUNCT
ejpam-4136	167	7	βn	βn	NOUN
ejpam-4136	167	8	)	)	PUNCT
ejpam-4136	167	9	)	)	PUNCT
ejpam-4136	167	10	be	be	AUX
ejpam-4136	167	11	a	a	DET
ejpam-4136	167	12	b(αn	b(αn	NOUN
ejpam-4136	167	13	,	,	PUNCT
ejpam-4136	167	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	167	15	space	space	NOUN
ejpam-4136	167	16	over	over	ADP
ejpam-4136	167	17	banach	banach	NOUN
ejpam-4136	167	18	algebra	algebra	NOUN
ejpam-4136	167	19	a.	a.	NOUN
ejpam-4136	167	20	then	then	ADV
ejpam-4136	167	21	for	for	ADP
ejpam-4136	167	22	any	any	DET
ejpam-4136	167	23	x1	x1	PROPN
ejpam-4136	167	24	,	,	PUNCT
ejpam-4136	167	25	...	...	PUNCT
ejpam-4136	167	26	,	,	PUNCT
ejpam-4136	167	27	xn	xn	PROPN
ejpam-4136	167	28	,	,	PUNCT
ejpam-4136	167	29	a	a	DET
ejpam-4136	167	30	∈	∈	NOUN
ejpam-4136	167	31	x	x	PRON
ejpam-4136	167	32	it	it	PRON
ejpam-4136	167	33	follows	follow	VERB
ejpam-4136	167	34	that	that	SCONJ
ejpam-4136	167	35	:	:	PUNCT
ejpam-4136	167	36	(	(	PUNCT
ejpam-4136	167	37	1	1	X
ejpam-4136	167	38	)	)	PUNCT
ejpam-4136	167	39	if	if	SCONJ
ejpam-4136	167	40	γ(αn	γ(αn	VERB
ejpam-4136	167	41	,	,	PUNCT
ejpam-4136	167	42	βn)(xi	βn)(xi	PUNCT
ejpam-4136	167	43	)	)	PUNCT
ejpam-4136	167	44	n	n	PRON
ejpam-4136	167	45	i=1	i=1	PROPN
ejpam-4136	168	1	=	=	X
ejpam-4136	168	2	{	{	PUNCT
ejpam-4136	168	3	0a	0a	PROPN
ejpam-4136	168	4	}	}	PUNCT
ejpam-4136	168	5	,	,	PUNCT
ejpam-4136	168	6	then	then	ADV
ejpam-4136	168	7	x1	x1	PROPN
ejpam-4136	168	8	=	=	PUNCT
ejpam-4136	168	9	...	...	PUNCT
ejpam-4136	169	1	=	=	SYM
ejpam-4136	169	2	xn	xn	PROPN
ejpam-4136	169	3	,	,	PUNCT
ejpam-4136	169	4	(	(	PUNCT
ejpam-4136	169	5	2	2	X
ejpam-4136	169	6	)	)	PUNCT
ejpam-4136	169	7	γ(αn	γ(αn	PROPN
ejpam-4136	169	8	,	,	PUNCT
ejpam-4136	169	9	βn)(xi	βn)(xi	PUNCT
ejpam-4136	169	10	)	)	PUNCT
ejpam-4136	169	11	n	n	CCONJ
ejpam-4136	169	12	i=1	i=1	PROPN
ejpam-4136	169	13	⊆	⊆	NUM
ejpam-4136	169	14	∑n	∑n	PROPN
ejpam-4136	169	15	j=2	j=2	PROPN
ejpam-4136	169	16	γ(αn	γ(αn	PROPN
ejpam-4136	169	17	,	,	PUNCT
ejpam-4136	169	18	βn)((x1	βn)((x1	ADJ
ejpam-4136	169	19	)	)	PUNCT
ejpam-4136	169	20	n−1	n−1	PROPN
ejpam-4136	169	21	1	1	NUM
ejpam-4136	169	22	,	,	PUNCT
ejpam-4136	169	23	xj	xj	PROPN
ejpam-4136	169	24	)	)	PUNCT
ejpam-4136	169	25	,	,	PUNCT
ejpam-4136	169	26	(	(	PUNCT
ejpam-4136	169	27	3	3	X
ejpam-4136	169	28	)	)	PUNCT
ejpam-4136	169	29	γ(αn	γ(αn	PROPN
ejpam-4136	169	30	,	,	PUNCT
ejpam-4136	169	31	βn)(xi	βn)(xi	PUNCT
ejpam-4136	169	32	)	)	PUNCT
ejpam-4136	169	33	n	n	CCONJ
ejpam-4136	169	34	i=1	i=1	PROPN
ejpam-4136	169	35	⊆	⊆	NUM
ejpam-4136	169	36	∑n	∑n	PROPN
ejpam-4136	169	37	j=1	j=1	PROPN
ejpam-4136	169	38	γ(αn	γ(αn	PROPN
ejpam-4136	169	39	,	,	PUNCT
ejpam-4136	169	40	βn)(xj	βn)(xj	PUNCT
ejpam-4136	169	41	,	,	PUNCT
ejpam-4136	169	42	(	(	PUNCT
ejpam-4136	169	43	a	a	X
ejpam-4136	169	44	)	)	PUNCT
ejpam-4136	169	45	n	n	PRON
ejpam-4136	169	46	2	2	NUM
ejpam-4136	169	47	)	)	PUNCT
ejpam-4136	169	48	,	,	PUNCT
ejpam-4136	169	49	(	(	PUNCT
ejpam-4136	169	50	4	4	X
ejpam-4136	169	51	)	)	PUNCT
ejpam-4136	169	52	γ(αn	γ(αn	PROPN
ejpam-4136	169	53	,	,	PUNCT
ejpam-4136	169	54	βn)(x1	βn)(x1	NOUN
ejpam-4136	169	55	,	,	PUNCT
ejpam-4136	169	56	(	(	PUNCT
ejpam-4136	169	57	x2	x2	PROPN
ejpam-4136	169	58	)	)	PUNCT
ejpam-4136	169	59	n	n	PRON
ejpam-4136	169	60	2	2	NUM
ejpam-4136	169	61	)	)	PUNCT
ejpam-4136	169	62	⊆	⊆	NUM
ejpam-4136	169	63	(	(	PUNCT
ejpam-4136	169	64	n−	n−	NOUN
ejpam-4136	169	65	1)γ(αn	1)γ(αn	NUM
ejpam-4136	169	66	,	,	PUNCT
ejpam-4136	169	67	βn)((x1	βn)((x1	ADJ
ejpam-4136	169	68	)	)	PUNCT
ejpam-4136	169	69	n−2	n−2	PROPN
ejpam-4136	169	70	1	1	NUM
ejpam-4136	169	71	,	,	PUNCT
ejpam-4136	169	72	x2	x2	PROPN
ejpam-4136	169	73	)	)	PUNCT
ejpam-4136	169	74	.	.	PUNCT
ejpam-4136	170	1	a.	a.	PROPN
ejpam-4136	170	2	d.nezhad	d.nezhad	PROPN
ejpam-4136	170	3	,	,	PUNCT
ejpam-4136	170	4	s.	s.	PROPN
ejpam-4136	170	5	radenović	radenović	PROPN
ejpam-4136	170	6	/	/	SYM
ejpam-4136	170	7	eur	eur	PROPN
ejpam-4136	170	8	.	.	PUNCT
ejpam-4136	171	1	j.	j.	PROPN
ejpam-4136	171	2	pure	pure	PROPN
ejpam-4136	171	3	appl	appl	PROPN
ejpam-4136	171	4	.	.	PROPN
ejpam-4136	171	5	math	math	PROPN
ejpam-4136	171	6	,	,	PUNCT
ejpam-4136	171	7	14	14	NUM
ejpam-4136	171	8	(	(	PUNCT
ejpam-4136	171	9	4	4	NUM
ejpam-4136	171	10	)	)	PUNCT
ejpam-4136	171	11	(	(	PUNCT
ejpam-4136	171	12	2021	2021	NUM
ejpam-4136	171	13	)	)	PUNCT
ejpam-4136	171	14	,	,	PUNCT
ejpam-4136	171	15	1148	1148	NUM
ejpam-4136	171	16	-	-	SYM
ejpam-4136	171	17	1160	1160	NUM
ejpam-4136	171	18	1153	1153	NUM
ejpam-4136	171	19	proposition	proposition	NOUN
ejpam-4136	171	20	3	3	NUM
ejpam-4136	171	21	.	.	PUNCT
ejpam-4136	172	1	let	let	AUX
ejpam-4136	172	2	(	(	PUNCT
ejpam-4136	172	3	x	x	X
ejpam-4136	172	4	,	,	PUNCT
ejpam-4136	172	5	γ(αn	γ(αn	VERB
ejpam-4136	172	6	,	,	PUNCT
ejpam-4136	172	7	βn	βn	NOUN
ejpam-4136	172	8	)	)	PUNCT
ejpam-4136	172	9	)	)	PUNCT
ejpam-4136	172	10	be	be	AUX
ejpam-4136	172	11	a	a	DET
ejpam-4136	172	12	b(αn	b(αn	NOUN
ejpam-4136	172	13	,	,	PUNCT
ejpam-4136	172	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	172	15	space	space	NOUN
ejpam-4136	172	16	over	over	ADP
ejpam-4136	172	17	banach	banach	NOUN
ejpam-4136	172	18	algebra	algebra	NOUN
ejpam-4136	172	19	a.	a.	NOUN
ejpam-4136	172	20	then	then	ADV
ejpam-4136	172	21	{	{	PUNCT
ejpam-4136	172	22	0a	0a	PROPN
ejpam-4136	172	23	}	}	PUNCT
ejpam-4136	172	24	⊆	⊆	NUM
ejpam-4136	172	25	γ(αn	γ(αn	NUM
ejpam-4136	172	26	,	,	PUNCT
ejpam-4136	172	27	βn)(xi	βn)(xi	PUNCT
ejpam-4136	172	28	)	)	PUNCT
ejpam-4136	172	29	n	n	CCONJ
ejpam-4136	172	30	i=1	i=1	PROPN
ejpam-4136	172	31	for	for	ADP
ejpam-4136	172	32	every	every	DET
ejpam-4136	172	33	x1	x1	PROPN
ejpam-4136	172	34	,	,	PUNCT
ejpam-4136	172	35	...	...	PUNCT
ejpam-4136	172	36	,	,	PUNCT
ejpam-4136	172	37	xn	xn	PROPN
ejpam-4136	172	38	∈	∈	PROPN
ejpam-4136	172	39	x.	x.	NOUN
ejpam-4136	172	40	proof	proof	NOUN
ejpam-4136	172	41	.	.	PUNCT
ejpam-4136	173	1	by	by	ADP
ejpam-4136	173	2	the	the	DET
ejpam-4136	173	3	condition	condition	NOUN
ejpam-4136	173	4	(	(	PUNCT
ejpam-4136	173	5	g4	g4	NOUN
ejpam-4136	173	6	)	)	PUNCT
ejpam-4136	173	7	of	of	ADP
ejpam-4136	173	8	definition	definition	NOUN
ejpam-4136	173	9	of	of	ADP
ejpam-4136	173	10	b(αn	b(αn	NOUN
ejpam-4136	173	11	,	,	PUNCT
ejpam-4136	173	12	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	173	13	space	space	NOUN
ejpam-4136	173	14	,	,	PUNCT
ejpam-4136	173	15	we	we	PRON
ejpam-4136	173	16	have	have	VERB
ejpam-4136	173	17	{	{	PUNCT
ejpam-4136	173	18	0a	0a	NUM
ejpam-4136	173	19	}	}	PUNCT
ejpam-4136	173	20	=	=	SYM
ejpam-4136	173	21	γ(αn	γ(αn	PROPN
ejpam-4136	173	22	,	,	PUNCT
ejpam-4136	173	23	βn)(x1	βn)(x1	NUM
ejpam-4136	173	24	)	)	PUNCT
ejpam-4136	173	25	n	n	CCONJ
ejpam-4136	173	26	1	1	NUM
ejpam-4136	173	27	⊆	⊆	NUM
ejpam-4136	173	28	γ(αn	γ(αn	NUM
ejpam-4136	173	29	,	,	PUNCT
ejpam-4136	173	30	βn)(xi	βn)(xi	PUNCT
ejpam-4136	173	31	)	)	PUNCT
ejpam-4136	173	32	n	n	PRON
ejpam-4136	173	33	i=1	i=1	PROPN
ejpam-4136	173	34	.	.	PUNCT
ejpam-4136	174	1	proposition	proposition	NOUN
ejpam-4136	174	2	4	4	NUM
ejpam-4136	174	3	.	.	PUNCT
ejpam-4136	175	1	every	every	DET
ejpam-4136	175	2	b(αn	b(αn	NOUN
ejpam-4136	175	3	,	,	PUNCT
ejpam-4136	175	4	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	175	5	space	space	NOUN
ejpam-4136	175	6	(	(	PUNCT
ejpam-4136	175	7	x	x	X
ejpam-4136	175	8	,	,	PUNCT
ejpam-4136	175	9	γ(αn	γ(αn	VERB
ejpam-4136	175	10	,	,	PUNCT
ejpam-4136	175	11	βn	βn	NOUN
ejpam-4136	175	12	)	)	PUNCT
ejpam-4136	175	13	)	)	PUNCT
ejpam-4136	175	14	over	over	ADP
ejpam-4136	175	15	banach	banach	NOUN
ejpam-4136	175	16	algebra	algebra	NOUN
ejpam-4136	175	17	a	a	DET
ejpam-4136	175	18	defines	define	NOUN
ejpam-4136	175	19	a	a	DET
ejpam-4136	175	20	b(α2,β2)-hypermetric	b(α2,β2)-hypermetric	ADJ
ejpam-4136	175	21	space	space	NOUN
ejpam-4136	175	22	(	(	PUNCT
ejpam-4136	175	23	x	x	NOUN
ejpam-4136	175	24	,	,	PUNCT
ejpam-4136	175	25	γ(α2,β2	γ(α2,β2	NOUN
ejpam-4136	175	26	)	)	PUNCT
ejpam-4136	175	27	)	)	PUNCT
ejpam-4136	175	28	over	over	ADP
ejpam-4136	175	29	banach	banach	NOUN
ejpam-4136	175	30	algebra	algebra	NOUN
ejpam-4136	175	31	a	a	PRON
ejpam-4136	175	32	as	as	SCONJ
ejpam-4136	175	33	follows	follow	VERB
ejpam-4136	175	34	:	:	PUNCT
ejpam-4136	175	35	γ(α2,β2)(x	γ(α2,β2)(x	PROPN
ejpam-4136	175	36	,	,	PUNCT
ejpam-4136	175	37	y	y	NOUN
ejpam-4136	175	38	)	)	PUNCT
ejpam-4136	175	39	=	=	SYM
ejpam-4136	175	40	γ(αn	γ(αn	PROPN
ejpam-4136	175	41	,	,	PUNCT
ejpam-4136	175	42	βn)(x	βn)(x	PROPN
ejpam-4136	175	43	,	,	PUNCT
ejpam-4136	175	44	(	(	PUNCT
ejpam-4136	175	45	y	y	NOUN
ejpam-4136	175	46	)	)	PUNCT
ejpam-4136	175	47	n	n	PRON
ejpam-4136	175	48	2	2	NUM
ejpam-4136	175	49	)	)	PUNCT
ejpam-4136	176	1	+	+	CCONJ
ejpam-4136	176	2	γ(αn	γ(αn	PROPN
ejpam-4136	176	3	,	,	PUNCT
ejpam-4136	176	4	βn)(y	βn)(y	NUM
ejpam-4136	176	5	,	,	PUNCT
ejpam-4136	176	6	(	(	PUNCT
ejpam-4136	176	7	x	x	X
ejpam-4136	176	8	)	)	PUNCT
ejpam-4136	176	9	n	n	PRON
ejpam-4136	176	10	2	2	NUM
ejpam-4136	176	11	)	)	PUNCT
ejpam-4136	176	12	,	,	PUNCT
ejpam-4136	176	13	for	for	ADP
ejpam-4136	176	14	all	all	DET
ejpam-4136	176	15	x	x	NOUN
ejpam-4136	176	16	,	,	PUNCT
ejpam-4136	176	17	y	y	PROPN
ejpam-4136	176	18	∈	∈	PROPN
ejpam-4136	176	19	x	x	NOUN
ejpam-4136	176	20	,	,	PUNCT
ejpam-4136	176	21	where	where	SCONJ
ejpam-4136	176	22	α2(x	α2(x	PROPN
ejpam-4136	176	23	,	,	PUNCT
ejpam-4136	176	24	y	y	NOUN
ejpam-4136	176	25	)	)	PUNCT
ejpam-4136	176	26	=	=	SYM
ejpam-4136	176	27	max{αn(x	max{αn(x	PROPN
ejpam-4136	176	28	,	,	PUNCT
ejpam-4136	176	29	(	(	PUNCT
ejpam-4136	176	30	y	y	NOUN
ejpam-4136	176	31	)	)	PUNCT
ejpam-4136	176	32	n	n	PRON
ejpam-4136	176	33	2	2	NUM
ejpam-4136	176	34	)	)	PUNCT
ejpam-4136	176	35	,	,	PUNCT
ejpam-4136	176	36	αn(y	αn(y	NUM
ejpam-4136	176	37	,	,	PUNCT
ejpam-4136	176	38	(	(	PUNCT
ejpam-4136	176	39	x	x	X
ejpam-4136	176	40	)	)	PUNCT
ejpam-4136	176	41	n	n	PRON
ejpam-4136	176	42	2	2	NUM
ejpam-4136	176	43	)	)	PUNCT
ejpam-4136	176	44	}	}	PUNCT
ejpam-4136	176	45	and	and	CCONJ
ejpam-4136	176	46	β2(x	β2(x	NUM
ejpam-4136	176	47	,	,	PUNCT
ejpam-4136	176	48	y	y	NOUN
ejpam-4136	176	49	)	)	PUNCT
ejpam-4136	176	50	=	=	SYM
ejpam-4136	176	51	max{βn(x	max{βn(x	X
ejpam-4136	176	52	,	,	PUNCT
ejpam-4136	176	53	(	(	PUNCT
ejpam-4136	176	54	y)n2	y)n2	PROPN
ejpam-4136	176	55	)	)	PUNCT
ejpam-4136	176	56	,	,	PUNCT
ejpam-4136	176	57	βn(y	βn(y	PRON
ejpam-4136	176	58	,	,	PUNCT
ejpam-4136	176	59	(	(	PUNCT
ejpam-4136	176	60	x)n2	x)n2	PROPN
ejpam-4136	176	61	)	)	PUNCT
ejpam-4136	176	62	}	}	PUNCT
ejpam-4136	176	63	.	.	PUNCT
ejpam-4136	177	1	proof	proof	NOUN
ejpam-4136	177	2	.	.	PUNCT
ejpam-4136	178	1	note	note	VERB
ejpam-4136	178	2	that	that	SCONJ
ejpam-4136	179	1	[	[	X
ejpam-4136	179	2	(	(	PUNCT
ejpam-4136	179	3	g0	g0	NOUN
ejpam-4136	179	4	)	)	PUNCT
ejpam-4136	179	5	]	]	PUNCT
ejpam-4136	179	6	,	,	PUNCT
ejpam-4136	179	7	.	.	PUNCT
ejpam-4136	179	8	.	.	PUNCT
ejpam-4136	179	9	.	.	PUNCT
ejpam-4136	180	1	,	,	PUNCT
ejpam-4136	181	1	[	[	X
ejpam-4136	181	2	(	(	PUNCT
ejpam-4136	181	3	g4	g4	NOUN
ejpam-4136	181	4	)	)	PUNCT
ejpam-4136	181	5	]	]	PUNCT
ejpam-4136	181	6	trivially	trivially	ADV
ejpam-4136	181	7	hold	hold	VERB
ejpam-4136	181	8	.	.	PUNCT
ejpam-4136	182	1	we	we	PRON
ejpam-4136	182	2	only	only	ADV
ejpam-4136	182	3	need	need	VERB
ejpam-4136	182	4	to	to	PART
ejpam-4136	182	5	show	show	VERB
ejpam-4136	182	6	that	that	SCONJ
ejpam-4136	182	7	γ(α2,β2	γ(α2,β2	NOUN
ejpam-4136	182	8	)	)	PUNCT
ejpam-4136	182	9	is	be	AUX
ejpam-4136	182	10	satisfied	satisfied	ADJ
ejpam-4136	182	11	in	in	ADP
ejpam-4136	182	12	γ(α2,β2)(x	γ(α2,β2)(x	PROPN
ejpam-4136	182	13	,	,	PUNCT
ejpam-4136	182	14	y	y	PROPN
ejpam-4136	182	15	)	)	PUNCT
ejpam-4136	182	16	⊆	⊆	NUM
ejpam-4136	182	17	α2(x	α2(x	PROPN
ejpam-4136	182	18	,	,	PUNCT
ejpam-4136	182	19	y	y	NOUN
ejpam-4136	182	20	)	)	PUNCT
ejpam-4136	182	21	·	·	PUNCT
ejpam-4136	183	1	γ(α2,β2)(x	γ(α2,β2)(x	PROPN
ejpam-4136	183	2	,	,	PUNCT
ejpam-4136	183	3	z	z	NOUN
ejpam-4136	183	4	)	)	PUNCT
ejpam-4136	184	1	+	+	CCONJ
ejpam-4136	184	2	β2(x	β2(x	NUM
ejpam-4136	184	3	,	,	PUNCT
ejpam-4136	184	4	y	y	PROPN
ejpam-4136	184	5	)	)	PUNCT
ejpam-4136	184	6	·	·	PUNCT
ejpam-4136	185	1	γ(α2,β2)(z	γ(α2,β2)(z	PROPN
ejpam-4136	185	2	,	,	PUNCT
ejpam-4136	185	3	y	y	NOUN
ejpam-4136	185	4	)	)	PUNCT
ejpam-4136	185	5	,	,	PUNCT
ejpam-4136	185	6	for	for	ADP
ejpam-4136	185	7	all	all	DET
ejpam-4136	185	8	x	x	NOUN
ejpam-4136	185	9	,	,	PUNCT
ejpam-4136	185	10	y	y	PROPN
ejpam-4136	185	11	,	,	PUNCT
ejpam-4136	185	12	z	z	PROPN
ejpam-4136	185	13	∈	∈	PROPN
ejpam-4136	185	14	x.	x.	NOUN
ejpam-4136	186	1	the	the	DET
ejpam-4136	186	2	proof	proof	NOUN
ejpam-4136	186	3	is	be	AUX
ejpam-4136	186	4	straightforward	straightforward	ADJ
ejpam-4136	186	5	,	,	PUNCT
ejpam-4136	186	6	by	by	ADP
ejpam-4136	186	7	setting	set	VERB
ejpam-4136	186	8	α2(x	α2(x	PROPN
ejpam-4136	186	9	,	,	PUNCT
ejpam-4136	186	10	y	y	NOUN
ejpam-4136	186	11	)	)	PUNCT
ejpam-4136	186	12	=	=	SYM
ejpam-4136	186	13	max{αn(x	max{αn(x	PROPN
ejpam-4136	186	14	,	,	PUNCT
ejpam-4136	186	15	(	(	PUNCT
ejpam-4136	186	16	y	y	NOUN
ejpam-4136	186	17	)	)	PUNCT
ejpam-4136	186	18	n	n	PRON
ejpam-4136	186	19	2	2	NUM
ejpam-4136	186	20	)	)	PUNCT
ejpam-4136	186	21	,	,	PUNCT
ejpam-4136	186	22	αn(y	αn(y	NUM
ejpam-4136	186	23	,	,	PUNCT
ejpam-4136	186	24	(	(	PUNCT
ejpam-4136	186	25	x	x	X
ejpam-4136	186	26	)	)	PUNCT
ejpam-4136	186	27	n	n	PRON
ejpam-4136	186	28	2	2	NUM
ejpam-4136	186	29	)	)	PUNCT
ejpam-4136	186	30	}	}	PUNCT
ejpam-4136	186	31	and	and	CCONJ
ejpam-4136	186	32	β2(x	β2(x	NUM
ejpam-4136	186	33	,	,	PUNCT
ejpam-4136	186	34	y	y	NOUN
ejpam-4136	186	35	)	)	PUNCT
ejpam-4136	186	36	=	=	SYM
ejpam-4136	186	37	max{βn(x	max{βn(x	X
ejpam-4136	186	38	,	,	PUNCT
ejpam-4136	186	39	(	(	PUNCT
ejpam-4136	186	40	y)n2	y)n2	PROPN
ejpam-4136	186	41	)	)	PUNCT
ejpam-4136	186	42	,	,	PUNCT
ejpam-4136	186	43	βn(y	βn(y	PRON
ejpam-4136	186	44	,	,	PUNCT
ejpam-4136	186	45	(	(	PUNCT
ejpam-4136	186	46	x)n2	x)n2	PROPN
ejpam-4136	186	47	)	)	PUNCT
ejpam-4136	186	48	}	}	PUNCT
ejpam-4136	186	49	and	and	CCONJ
ejpam-4136	186	50	the	the	DET
ejpam-4136	186	51	condition	condition	NOUN
ejpam-4136	186	52	(	(	PUNCT
ejpam-4136	186	53	g5	g5	NOUN
ejpam-4136	186	54	)	)	PUNCT
ejpam-4136	186	55	of	of	ADP
ejpam-4136	186	56	definition	definition	NOUN
ejpam-4136	186	57	of	of	ADP
ejpam-4136	186	58	b(αn	b(αn	NOUN
ejpam-4136	186	59	,	,	PUNCT
ejpam-4136	186	60	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	186	61	space	space	NOUN
ejpam-4136	186	62	over	over	ADP
ejpam-4136	186	63	banach	banach	NOUN
ejpam-4136	186	64	algebra	algebra	NOUN
ejpam-4136	186	65	a.	a.	NOUN
ejpam-4136	186	66	proposition	proposition	NOUN
ejpam-4136	186	67	5	5	NUM
ejpam-4136	186	68	.	.	PUNCT
ejpam-4136	187	1	let	let	VERB
ejpam-4136	187	2	e	e	PRON
ejpam-4136	187	3	be	be	AUX
ejpam-4136	187	4	an	an	DET
ejpam-4136	187	5	arbitrary	arbitrary	ADJ
ejpam-4136	187	6	positive	positive	ADJ
ejpam-4136	187	7	real	real	ADJ
ejpam-4136	187	8	value	value	NOUN
ejpam-4136	187	9	number	number	NOUN
ejpam-4136	187	10	,	,	PUNCT
ejpam-4136	187	11	and	and	CCONJ
ejpam-4136	187	12	(	(	PUNCT
ejpam-4136	187	13	x	x	X
ejpam-4136	187	14	,	,	PUNCT
ejpam-4136	187	15	d	d	NOUN
ejpam-4136	187	16	)	)	PUNCT
ejpam-4136	187	17	be	be	AUX
ejpam-4136	187	18	a	a	DET
ejpam-4136	187	19	metric	metric	ADJ
ejpam-4136	187	20	space	space	NOUN
ejpam-4136	187	21	.	.	PUNCT
ejpam-4136	188	1	we	we	PRON
ejpam-4136	188	2	define	define	VERB
ejpam-4136	188	3	an	an	DET
ejpam-4136	188	4	induced	induced	ADJ
ejpam-4136	188	5	b(α2,β2)-hypermetric	b(α2,β2)-hypermetric	ADJ
ejpam-4136	188	6	over	over	ADP
ejpam-4136	188	7	banach	banach	NOUN
ejpam-4136	188	8	algebra	algebra	PROPN
ejpam-4136	188	9	r.	r.	PROPN
ejpam-4136	188	10	γe	γe	PROPN
ejpam-4136	188	11	(	(	PUNCT
ejpam-4136	188	12	α2,β2	α2,β2	PROPN
ejpam-4136	188	13	)	)	PUNCT
ejpam-4136	188	14	:	:	PUNCT
ejpam-4136	188	15	x	x	X
ejpam-4136	188	16	×x	×x	VERB
ejpam-4136	188	17	→	→	SYM
ejpam-4136	188	18	p	p	NOUN
ejpam-4136	188	19	∗(r0	∗(r0	ADJ
ejpam-4136	188	20	+	+	NOUN
ejpam-4136	188	21	)	)	PUNCT
ejpam-4136	188	22	(	(	PUNCT
ejpam-4136	188	23	2	2	X
ejpam-4136	188	24	)	)	PUNCT
ejpam-4136	188	25	γe	γe	NOUN
ejpam-4136	188	26	(	(	PUNCT
ejpam-4136	188	27	α2,β2	α2,β2	PROPN
ejpam-4136	188	28	)	)	PUNCT
ejpam-4136	188	29	(	(	PUNCT
ejpam-4136	188	30	x	x	X
ejpam-4136	188	31	,	,	PUNCT
ejpam-4136	188	32	y	y	NOUN
ejpam-4136	188	33	)	)	PUNCT
ejpam-4136	188	34	=	=	PUNCT
ejpam-4136	189	1			PUNCT
ejpam-4136	189	2	(	(	PUNCT
ejpam-4136	189	3	d(x	d(x	PROPN
ejpam-4136	189	4	,	,	PUNCT
ejpam-4136	189	5	y)−	y)−	PROPN
ejpam-4136	189	6	e	e	NOUN
ejpam-4136	189	7	,	,	PUNCT
ejpam-4136	189	8	d(x	d(x	PROPN
ejpam-4136	189	9	,	,	PUNCT
ejpam-4136	189	10	y	y	NOUN
ejpam-4136	189	11	)	)	PUNCT
ejpam-4136	190	1	+	+	NUM
ejpam-4136	190	2	e	e	X
ejpam-4136	190	3	)	)	PUNCT
ejpam-4136	190	4	∪	∪	ADP
ejpam-4136	190	5	{	{	PUNCT
ejpam-4136	190	6	0	0	NUM
ejpam-4136	190	7	}	}	PUNCT
ejpam-4136	190	8	;	;	PUNCT
ejpam-4136	190	9	x	x	X
ejpam-4136	190	10	̸=	̸=	PROPN
ejpam-4136	190	11	y	y	PROPN
ejpam-4136	190	12	,	,	PUNCT
ejpam-4136	190	13	d(x	d(x	PROPN
ejpam-4136	190	14	,	,	PUNCT
ejpam-4136	190	15	y	y	PROPN
ejpam-4136	190	16	)	)	PUNCT
ejpam-4136	190	17	>	>	X
ejpam-4136	191	1	e	e	X
ejpam-4136	191	2	(	(	PUNCT
ejpam-4136	191	3	d(x	d(x	PROPN
ejpam-4136	191	4	,	,	PUNCT
ejpam-4136	191	5	y)−	y)−	PROPN
ejpam-4136	191	6	e	e	NOUN
ejpam-4136	191	7	,	,	PUNCT
ejpam-4136	191	8	d(x	d(x	PROPN
ejpam-4136	191	9	,	,	PUNCT
ejpam-4136	191	10	y	y	NOUN
ejpam-4136	191	11	)	)	PUNCT
ejpam-4136	191	12	+	+	NUM
ejpam-4136	191	13	e	e	X
ejpam-4136	191	14	)	)	PUNCT
ejpam-4136	191	15	∩	∩	ADJ
ejpam-4136	191	16	r0	r0	NOUN
ejpam-4136	191	17	+	+	X
ejpam-4136	191	18	;	;	PUNCT
ejpam-4136	191	19	x	x	X
ejpam-4136	191	20	̸=	̸=	PROPN
ejpam-4136	191	21	y	y	PROPN
ejpam-4136	191	22	,	,	PUNCT
ejpam-4136	191	23	d(x	d(x	PROPN
ejpam-4136	191	24	,	,	PUNCT
ejpam-4136	191	25	y	y	NOUN
ejpam-4136	191	26	)	)	PUNCT
ejpam-4136	191	27	<	<	X
ejpam-4136	191	28	e	e	X
ejpam-4136	191	29	{	{	PUNCT
ejpam-4136	191	30	0	0	NUM
ejpam-4136	191	31	}	}	PUNCT
ejpam-4136	191	32	;	;	PUNCT
ejpam-4136	191	33	x	x	SYM
ejpam-4136	191	34	=	=	SYM
ejpam-4136	191	35	y	y	PROPN
ejpam-4136	191	36	ot	ot	NOUN
ejpam-4136	191	37	d(x	d(x	PROPN
ejpam-4136	191	38	,	,	PUNCT
ejpam-4136	191	39	y	y	NOUN
ejpam-4136	191	40	)	)	PUNCT
ejpam-4136	191	41	=	=	SYM
ejpam-4136	192	1	e.	e.	PROPN
ejpam-4136	192	2	(	(	PUNCT
ejpam-4136	192	3	3	3	NUM
ejpam-4136	192	4	)	)	PUNCT
ejpam-4136	192	5	then	then	ADV
ejpam-4136	192	6	(	(	PUNCT
ejpam-4136	192	7	x	x	X
ejpam-4136	192	8	,	,	PUNCT
ejpam-4136	192	9	γe	γe	INTJ
ejpam-4136	192	10	(	(	PUNCT
ejpam-4136	192	11	α2,β2	α2,β2	PROPN
ejpam-4136	192	12	)	)	PUNCT
ejpam-4136	192	13	)	)	PUNCT
ejpam-4136	192	14	is	be	AUX
ejpam-4136	192	15	a	a	DET
ejpam-4136	192	16	b(α2,β2)-hypermetric	b(α2,β2)-hypermetric	ADJ
ejpam-4136	192	17	space	space	NOUN
ejpam-4136	192	18	over	over	ADP
ejpam-4136	192	19	banach	banach	NOUN
ejpam-4136	192	20	algebra	algebra	PROPN
ejpam-4136	192	21	r.	r.	PROPN
ejpam-4136	192	22	2.2	2.2	NUM
ejpam-4136	192	23	.	.	PUNCT
ejpam-4136	193	1	quotient	quotient	PROPN
ejpam-4136	193	2	b(αn	b(αn	PROPN
ejpam-4136	193	3	,	,	PUNCT
ejpam-4136	193	4	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	193	5	space	space	NOUN
ejpam-4136	193	6	over	over	ADP
ejpam-4136	193	7	banach	banach	NOUN
ejpam-4136	193	8	algebra	algebra	NOUN
ejpam-4136	193	9	a	a	DET
ejpam-4136	193	10	let	let	NOUN
ejpam-4136	193	11	(	(	PUNCT
ejpam-4136	193	12	x	x	X
ejpam-4136	193	13	,	,	PUNCT
ejpam-4136	193	14	γ(αn	γ(αn	VERB
ejpam-4136	193	15	,	,	PUNCT
ejpam-4136	193	16	βn	βn	NOUN
ejpam-4136	193	17	)	)	PUNCT
ejpam-4136	193	18	)	)	PUNCT
ejpam-4136	193	19	be	be	AUX
ejpam-4136	193	20	a	a	DET
ejpam-4136	193	21	b(αn	b(αn	NOUN
ejpam-4136	193	22	,	,	PUNCT
ejpam-4136	193	23	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	193	24	space	space	NOUN
ejpam-4136	193	25	over	over	ADP
ejpam-4136	193	26	banach	banach	NOUN
ejpam-4136	193	27	algebra	algebra	NOUN
ejpam-4136	193	28	a	a	PRON
ejpam-4136	194	1	and	and	CCONJ
ejpam-4136	194	2	x̃	x̃	PROPN
ejpam-4136	194	3	be	be	AUX
ejpam-4136	194	4	a	a	DET
ejpam-4136	194	5	partition	partition	NOUN
ejpam-4136	194	6	of	of	ADP
ejpam-4136	194	7	x.	x.	NOUN
ejpam-4136	194	8	for	for	ADP
ejpam-4136	194	9	each	each	DET
ejpam-4136	194	10	point	point	NOUN
ejpam-4136	194	11	p	p	X
ejpam-4136	194	12	∈	∈	PROPN
ejpam-4136	194	13	x	x	NOUN
ejpam-4136	194	14	,	,	PUNCT
ejpam-4136	194	15	we	we	PRON
ejpam-4136	194	16	denote	denote	VERB
ejpam-4136	194	17	p̃	p̃	PROPN
ejpam-4136	194	18	a	a	DET
ejpam-4136	194	19	point	point	NOUN
ejpam-4136	194	20	in	in	ADP
ejpam-4136	194	21	x̃	x̃	PROPN
ejpam-4136	194	22	containing	contain	VERB
ejpam-4136	194	23	p	p	X
ejpam-4136	194	24	,	,	PUNCT
ejpam-4136	194	25	and	and	CCONJ
ejpam-4136	194	26	we	we	PRON
ejpam-4136	194	27	denote	denote	VERB
ejpam-4136	194	28	the	the	DET
ejpam-4136	194	29	equivalent	equivalent	ADJ
ejpam-4136	194	30	relation	relation	NOUN
ejpam-4136	194	31	induced	induce	VERB
ejpam-4136	194	32	by	by	ADP
ejpam-4136	194	33	the	the	DET
ejpam-4136	194	34	relation	relation	NOUN
ejpam-4136	194	35	by	by	ADP
ejpam-4136	194	36	∼.	∼.	ADJ
ejpam-4136	194	37	definition	definition	NOUN
ejpam-4136	194	38	7	7	NUM
ejpam-4136	194	39	.	.	PUNCT
ejpam-4136	195	1	let	let	AUX
ejpam-4136	195	2	(	(	PUNCT
ejpam-4136	195	3	x	x	X
ejpam-4136	195	4	,	,	PUNCT
ejpam-4136	195	5	γ(αn	γ(αn	VERB
ejpam-4136	195	6	,	,	PUNCT
ejpam-4136	195	7	βn	βn	NOUN
ejpam-4136	195	8	)	)	PUNCT
ejpam-4136	195	9	)	)	PUNCT
ejpam-4136	195	10	be	be	AUX
ejpam-4136	195	11	a	a	DET
ejpam-4136	195	12	b(αn	b(αn	NOUN
ejpam-4136	195	13	,	,	PUNCT
ejpam-4136	195	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	195	15	space	space	NOUN
ejpam-4136	195	16	over	over	ADP
ejpam-4136	195	17	banach	banach	NOUN
ejpam-4136	195	18	algebra	algebra	NOUN
ejpam-4136	195	19	a.	a.	NOUN
ejpam-4136	195	20	let	let	VERB
ejpam-4136	195	21	p1	p1	PROPN
ejpam-4136	195	22	,	,	PUNCT
ejpam-4136	195	23	.	.	PUNCT
ejpam-4136	195	24	.	.	PUNCT
ejpam-4136	196	1	.	.	PUNCT
ejpam-4136	197	1	,	,	PUNCT
ejpam-4136	197	2	pn	pn	PROPN
ejpam-4136	197	3	∈	∈	PROPN
ejpam-4136	197	4	x	x	X
ejpam-4136	197	5	,	,	PUNCT
ejpam-4136	197	6	and	and	CCONJ
ejpam-4136	197	7	consider	consider	VERB
ejpam-4136	197	8	p̃1	p̃1	PROPN
ejpam-4136	197	9	,	,	PUNCT
ejpam-4136	197	10	.	.	PUNCT
ejpam-4136	197	11	.	.	PUNCT
ejpam-4136	198	1	.	.	PUNCT
ejpam-4136	199	1	,	,	PUNCT
ejpam-4136	199	2	p̃n	p̃n	NOUN
ejpam-4136	199	3	∈	∈	NOUN
ejpam-4136	199	4	x̃.	x̃.	ADV
ejpam-4136	199	5	a	a	DET
ejpam-4136	199	6	quotient	quotient	NOUN
ejpam-4136	199	7	b(αn	b(αn	NOUN
ejpam-4136	199	8	,	,	PUNCT
ejpam-4136	199	9	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	199	10	of	of	ADP
ejpam-4136	199	11	points	point	NOUN
ejpam-4136	199	12	of	of	ADP
ejpam-4136	199	13	x̃	x̃	PROPN
ejpam-4136	199	14	induced	induce	VERB
ejpam-4136	199	15	by	by	ADP
ejpam-4136	199	16	γ(αn	γ(αn	PROPN
ejpam-4136	199	17	,	,	PUNCT
ejpam-4136	199	18	βn	βn	NOUN
ejpam-4136	199	19	)	)	PUNCT
ejpam-4136	199	20	is	be	AUX
ejpam-4136	199	21	the	the	DET
ejpam-4136	199	22	function	function	NOUN
ejpam-4136	199	23	γ̃(αn	γ̃(αn	NOUN
ejpam-4136	199	24	,	,	PUNCT
ejpam-4136	199	25	βn	βn	NOUN
ejpam-4136	199	26	)	)	PUNCT
ejpam-4136	199	27	:	:	PUNCT
ejpam-4136	200	1	x̃	x̃	PROPN
ejpam-4136	200	2	n	n	PRON
ejpam-4136	200	3	−→	−→	VERB
ejpam-4136	200	4	p	p	ADJ
ejpam-4136	200	5	∗(a+	∗(a+	NOUN
ejpam-4136	200	6	)	)	PUNCT
ejpam-4136	200	7	given	give	VERB
ejpam-4136	200	8	by	by	ADP
ejpam-4136	200	9	γ̃(αn	γ̃(αn	ADJ
ejpam-4136	200	10	,	,	PUNCT
ejpam-4136	200	11	βn)(p̃i	βn)(p̃i	PROPN
ejpam-4136	200	12	)	)	PUNCT
ejpam-4136	200	13	n	n	CCONJ
ejpam-4136	200	14	i=1	i=1	PROPN
ejpam-4136	200	15	=	=	SYM
ejpam-4136	200	16	⋂	⋂	PROPN
ejpam-4136	200	17	pi∈p̃i	pi∈p̃i	PROPN
ejpam-4136	200	18	γ(αn	γ(αn	VERB
ejpam-4136	200	19	,	,	PUNCT
ejpam-4136	200	20	βn)(pi	βn)(pi	NOUN
ejpam-4136	200	21	)	)	PUNCT
ejpam-4136	200	22	n	n	PRON
ejpam-4136	200	23	i=1	i=1	NOUN
ejpam-4136	200	24	.	.	PUNCT
ejpam-4136	200	25	a.	a.	PROPN
ejpam-4136	200	26	d.nezhad	d.nezhad	PROPN
ejpam-4136	200	27	,	,	PUNCT
ejpam-4136	200	28	s.	s.	PROPN
ejpam-4136	200	29	radenović	radenović	PROPN
ejpam-4136	200	30	/	/	SYM
ejpam-4136	200	31	eur	eur	PROPN
ejpam-4136	200	32	.	.	PUNCT
ejpam-4136	201	1	j.	j.	PROPN
ejpam-4136	201	2	pure	pure	PROPN
ejpam-4136	201	3	appl	appl	PROPN
ejpam-4136	201	4	.	.	PROPN
ejpam-4136	201	5	math	math	PROPN
ejpam-4136	201	6	,	,	PUNCT
ejpam-4136	201	7	14	14	NUM
ejpam-4136	201	8	(	(	PUNCT
ejpam-4136	201	9	4	4	NUM
ejpam-4136	201	10	)	)	PUNCT
ejpam-4136	201	11	(	(	PUNCT
ejpam-4136	201	12	2021	2021	NUM
ejpam-4136	201	13	)	)	PUNCT
ejpam-4136	201	14	,	,	PUNCT
ejpam-4136	201	15	1148	1148	NUM
ejpam-4136	201	16	-	-	SYM
ejpam-4136	201	17	1160	1160	NUM
ejpam-4136	201	18	1154	1154	NUM
ejpam-4136	201	19	proposition	proposition	NOUN
ejpam-4136	201	20	6	6	NUM
ejpam-4136	201	21	.	.	PUNCT
ejpam-4136	202	1	the	the	DET
ejpam-4136	202	2	quotient	quotient	NOUN
ejpam-4136	202	3	b(αn	b(αn	NOUN
ejpam-4136	202	4	,	,	PUNCT
ejpam-4136	202	5	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	202	6	over	over	ADP
ejpam-4136	202	7	banach	banach	NOUN
ejpam-4136	202	8	algebra	algebra	NOUN
ejpam-4136	202	9	a	a	DET
ejpam-4136	202	10	induced	induce	VERB
ejpam-4136	202	11	by	by	ADP
ejpam-4136	202	12	γ(αn	γ(αn	PROPN
ejpam-4136	202	13	,	,	PUNCT
ejpam-4136	202	14	βn	βn	NOUN
ejpam-4136	202	15	)	)	PUNCT
ejpam-4136	202	16	is	be	AUX
ejpam-4136	202	17	well	well	ADV
ejpam-4136	202	18	-	-	PUNCT
ejpam-4136	202	19	defined	define	VERB
ejpam-4136	202	20	and	and	CCONJ
ejpam-4136	202	21	is	be	AUX
ejpam-4136	202	22	a	a	DET
ejpam-4136	202	23	b(αn	b(αn	NOUN
ejpam-4136	202	24	,	,	PUNCT
ejpam-4136	202	25	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	202	26	on	on	ADP
ejpam-4136	202	27	x̃	x̃	PROPN
ejpam-4136	202	28	over	over	ADP
ejpam-4136	202	29	banach	banach	NOUN
ejpam-4136	202	30	algebra	algebra	NOUN
ejpam-4136	202	31	a.	a.	NOUN
ejpam-4136	202	32	proof	proof	NOUN
ejpam-4136	202	33	.	.	PUNCT
ejpam-4136	203	1	γ̃(αn	γ̃(αn	ADJ
ejpam-4136	203	2	,	,	PUNCT
ejpam-4136	203	3	βn	βn	NOUN
ejpam-4136	203	4	)	)	PUNCT
ejpam-4136	203	5	is	be	AUX
ejpam-4136	203	6	satisfied	satisfied	ADJ
ejpam-4136	203	7	in	in	ADP
ejpam-4136	203	8	all	all	DET
ejpam-4136	203	9	properties	property	NOUN
ejpam-4136	203	10	(	(	PUNCT
ejpam-4136	203	11	g0	g0	NOUN
ejpam-4136	203	12	)	)	PUNCT
ejpam-4136	203	13	,	,	PUNCT
ejpam-4136	203	14	till	till	SCONJ
ejpam-4136	203	15	(	(	PUNCT
ejpam-4136	203	16	g4	g4	NOUN
ejpam-4136	203	17	)	)	PUNCT
ejpam-4136	203	18	.	.	PUNCT
ejpam-4136	204	1	γ̃(αn	γ̃(αn	ADJ
ejpam-4136	204	2	,	,	PUNCT
ejpam-4136	204	3	βn)(p̃i	βn)(p̃i	PROPN
ejpam-4136	204	4	)	)	PUNCT
ejpam-4136	204	5	n	n	CCONJ
ejpam-4136	204	6	i=1	i=1	PROPN
ejpam-4136	204	7	⊆	⊆	NUM
ejpam-4136	204	8	γ̃(αn	γ̃(αn	ADJ
ejpam-4136	204	9	,	,	PUNCT
ejpam-4136	204	10	βn)(p̃1	βn)(p̃1	PROPN
ejpam-4136	204	11	,	,	PUNCT
ejpam-4136	204	12	(	(	PUNCT
ejpam-4136	204	13	q̃	q̃	PROPN
ejpam-4136	204	14	)	)	PUNCT
ejpam-4136	204	15	n	n	PRON
ejpam-4136	204	16	2	2	NUM
ejpam-4136	204	17	)	)	PUNCT
ejpam-4136	204	18	+	+	CCONJ
ejpam-4136	204	19	γ(αn	γ(αn	PROPN
ejpam-4136	204	20	,	,	PUNCT
ejpam-4136	204	21	βn)(q̃	βn)(q̃	PROPN
ejpam-4136	204	22	,	,	PUNCT
ejpam-4136	204	23	(	(	PUNCT
ejpam-4136	204	24	p̃i	p̃i	NOUN
ejpam-4136	204	25	)	)	PUNCT
ejpam-4136	204	26	n	n	PRON
ejpam-4136	204	27	i=2	i=2	PROPN
ejpam-4136	204	28	)	)	PUNCT
ejpam-4136	204	29	(	(	PUNCT
ejpam-4136	204	30	4)⋂	4)⋂	NUM
ejpam-4136	204	31	pi∈p̃i	pi∈p̃i	X
ejpam-4136	204	32	γ(αn	γ(αn	VERB
ejpam-4136	204	33	,	,	PUNCT
ejpam-4136	204	34	βn)(pi	βn)(pi	NOUN
ejpam-4136	204	35	)	)	PUNCT
ejpam-4136	204	36	n	n	CCONJ
ejpam-4136	204	37	i=1	i=1	PROPN
ejpam-4136	204	38	⊆	⊆	NUM
ejpam-4136	204	39	⋂	⋂	PROPN
ejpam-4136	204	40	pi∈p̃i	pi∈p̃i	PROPN
ejpam-4136	204	41	q∈q̃	q∈q̃	PUNCT
ejpam-4136	205	1	(	(	PUNCT
ejpam-4136	205	2	γ(αn	γ(αn	VERB
ejpam-4136	205	3	,	,	PUNCT
ejpam-4136	205	4	βn)(p1	βn)(p1	NOUN
ejpam-4136	205	5	,	,	PUNCT
ejpam-4136	205	6	(	(	PUNCT
ejpam-4136	205	7	q	q	X
ejpam-4136	205	8	)	)	PUNCT
ejpam-4136	205	9	n	n	PRON
ejpam-4136	205	10	2	2	NUM
ejpam-4136	205	11	)	)	PUNCT
ejpam-4136	206	1	+	+	CCONJ
ejpam-4136	206	2	γ(αn	γ(αn	PROPN
ejpam-4136	206	3	,	,	PUNCT
ejpam-4136	206	4	βn)(q	βn)(q	PROPN
ejpam-4136	206	5	,	,	PUNCT
ejpam-4136	206	6	(	(	PUNCT
ejpam-4136	206	7	pi	pi	NOUN
ejpam-4136	206	8	)	)	PUNCT
ejpam-4136	206	9	n	n	PRON
ejpam-4136	206	10	i=2	i=2	PROPN
ejpam-4136	206	11	)	)	PUNCT
ejpam-4136	206	12	)	)	PUNCT
ejpam-4136	207	1	⋂	⋂	PROPN
ejpam-4136	207	2	pi∈p̃i	pi∈p̃i	PROPN
ejpam-4136	207	3	q∈q̃	q∈q̃	X
ejpam-4136	208	1	γ(αn	γ(αn	PROPN
ejpam-4136	208	2	,	,	PUNCT
ejpam-4136	208	3	βn)(p1	βn)(p1	NOUN
ejpam-4136	208	4	,	,	PUNCT
ejpam-4136	208	5	(	(	PUNCT
ejpam-4136	208	6	q	q	X
ejpam-4136	208	7	)	)	PUNCT
ejpam-4136	208	8	n	n	PRON
ejpam-4136	208	9	2	2	NUM
ejpam-4136	208	10	)	)	PUNCT
ejpam-4136	209	1	+	+	CCONJ
ejpam-4136	209	2	⋂	⋂	PROPN
ejpam-4136	209	3	pi∈p̃i	pi∈p̃i	PROPN
ejpam-4136	209	4	q∈q̃	q∈q̃	PUNCT
ejpam-4136	209	5	γ(αn	γ(αn	PROPN
ejpam-4136	209	6	,	,	PUNCT
ejpam-4136	209	7	βn)(q	βn)(q	PROPN
ejpam-4136	209	8	,	,	PUNCT
ejpam-4136	209	9	(	(	PUNCT
ejpam-4136	209	10	pi	pi	NOUN
ejpam-4136	209	11	)	)	PUNCT
ejpam-4136	209	12	n	n	PRON
ejpam-4136	209	13	i=2	i=2	PROPN
ejpam-4136	209	14	)	)	PUNCT
ejpam-4136	209	15	=	=	SYM
ejpam-4136	210	1	⋂	⋂	PROPN
ejpam-4136	210	2	pi∈p̃i	pi∈p̃i	PROPN
ejpam-4136	210	3	q∈q̃	q∈q̃	PUNCT
ejpam-4136	211	1	(	(	PUNCT
ejpam-4136	211	2	γ(αn	γ(αn	VERB
ejpam-4136	211	3	,	,	PUNCT
ejpam-4136	211	4	βn)(p1	βn)(p1	NOUN
ejpam-4136	211	5	,	,	PUNCT
ejpam-4136	211	6	(	(	PUNCT
ejpam-4136	211	7	q	q	X
ejpam-4136	211	8	)	)	PUNCT
ejpam-4136	211	9	n	n	PRON
ejpam-4136	211	10	2	2	NUM
ejpam-4136	211	11	)	)	PUNCT
ejpam-4136	212	1	+	+	CCONJ
ejpam-4136	212	2	γ(αn	γ(αn	PROPN
ejpam-4136	212	3	,	,	PUNCT
ejpam-4136	212	4	βn)(q	βn)(q	PROPN
ejpam-4136	212	5	,	,	PUNCT
ejpam-4136	212	6	(	(	PUNCT
ejpam-4136	212	7	pi	pi	NOUN
ejpam-4136	212	8	)	)	PUNCT
ejpam-4136	212	9	n	n	PRON
ejpam-4136	212	10	i=2	i=2	PROPN
ejpam-4136	212	11	)	)	PUNCT
ejpam-4136	212	12	)	)	PUNCT
ejpam-4136	213	1	(	(	PUNCT
ejpam-4136	213	2	5	5	X
ejpam-4136	213	3	)	)	PUNCT
ejpam-4136	213	4	let	let	AUX
ejpam-4136	213	5	(	(	PUNCT
ejpam-4136	213	6	x	x	X
ejpam-4136	213	7	,	,	PUNCT
ejpam-4136	213	8	γ(αn	γ(αn	VERB
ejpam-4136	213	9	,	,	PUNCT
ejpam-4136	213	10	βn	βn	NOUN
ejpam-4136	213	11	)	)	PUNCT
ejpam-4136	213	12	)	)	PUNCT
ejpam-4136	213	13	be	be	AUX
ejpam-4136	213	14	a	a	DET
ejpam-4136	213	15	b(αn	b(αn	NOUN
ejpam-4136	213	16	,	,	PUNCT
ejpam-4136	213	17	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	213	18	space	space	NOUN
ejpam-4136	213	19	of	of	ADP
ejpam-4136	213	20	dimension	dimension	NOUN
ejpam-4136	213	21	n	n	CCONJ
ejpam-4136	213	22	>	>	X
ejpam-4136	213	23	2	2	NUM
ejpam-4136	213	24	over	over	ADP
ejpam-4136	213	25	banach	banach	NOUN
ejpam-4136	213	26	algebra	algebra	NOUN
ejpam-4136	213	27	a.	a.	NOUN
ejpam-4136	213	28	for	for	ADP
ejpam-4136	213	29	any	any	DET
ejpam-4136	213	30	arbitrary	arbitrary	ADJ
ejpam-4136	213	31	a	a	DET
ejpam-4136	213	32	in	in	ADP
ejpam-4136	213	33	x	x	NOUN
ejpam-4136	213	34	,	,	PUNCT
ejpam-4136	213	35	define	define	VERB
ejpam-4136	213	36	the	the	DET
ejpam-4136	213	37	function	function	NOUN
ejpam-4136	213	38	γ(αn−1,βn−1	γ(αn−1,βn−1	PUNCT
ejpam-4136	213	39	)	)	PUNCT
ejpam-4136	213	40	on	on	ADP
ejpam-4136	213	41	xn−1	xn−1	PROPN
ejpam-4136	213	42	by	by	ADP
ejpam-4136	213	43	γ(αn−1,βn−1)(xi	γ(αn−1,βn−1)(xi	ADJ
ejpam-4136	213	44	)	)	PUNCT
ejpam-4136	213	45	n−1	n−1	PROPN
ejpam-4136	213	46	i=1	i=1	X
ejpam-4136	213	47	:	:	PUNCT
ejpam-4136	213	48	=	=	SYM
ejpam-4136	213	49	γ(αn	γ(αn	PROPN
ejpam-4136	213	50	,	,	PUNCT
ejpam-4136	213	51	βn)((xi	βn)((xi	PROPN
ejpam-4136	213	52	)	)	PUNCT
ejpam-4136	214	1	n−1	n−1	PROPN
ejpam-4136	214	2	i=1	i=1	PROPN
ejpam-4136	214	3	,	,	PUNCT
ejpam-4136	214	4	a	a	PRON
ejpam-4136	214	5	)	)	PUNCT
ejpam-4136	214	6	.	.	PUNCT
ejpam-4136	215	1	then	then	ADV
ejpam-4136	215	2	we	we	PRON
ejpam-4136	215	3	have	have	VERB
ejpam-4136	215	4	the	the	DET
ejpam-4136	215	5	following	follow	VERB
ejpam-4136	215	6	result	result	NOUN
ejpam-4136	215	7	.	.	PUNCT
ejpam-4136	216	1	proposition	proposition	NOUN
ejpam-4136	216	2	7	7	NUM
ejpam-4136	216	3	.	.	PUNCT
ejpam-4136	217	1	the	the	DET
ejpam-4136	217	2	function	function	NOUN
ejpam-4136	217	3	γ(αn−1,βn−1	γ(αn−1,βn−1	ADV
ejpam-4136	217	4	)	)	PUNCT
ejpam-4136	217	5	define	define	VERB
ejpam-4136	217	6	a	a	DET
ejpam-4136	217	7	b(αn−1,βn−1)-hypermetric	b(αn−1,βn−1)-hypermetric	ADJ
ejpam-4136	217	8	on	on	ADP
ejpam-4136	217	9	x	x	PUNCT
ejpam-4136	217	10	over	over	ADP
ejpam-4136	217	11	banach	banach	NOUN
ejpam-4136	217	12	algebra	algebra	NOUN
ejpam-4136	217	13	a.	a.	NOUN
ejpam-4136	217	14	proof	proof	NOUN
ejpam-4136	217	15	.	.	PUNCT
ejpam-4136	218	1	we	we	PRON
ejpam-4136	218	2	will	will	AUX
ejpam-4136	218	3	verify	verify	VERB
ejpam-4136	218	4	that	that	PRON
ejpam-4136	218	5	γ(αn−1,βn−1	γ(αn−1,βn−1	PROPN
ejpam-4136	218	6	)	)	PUNCT
ejpam-4136	218	7	satisfies	satisfy	VERB
ejpam-4136	218	8	the	the	DET
ejpam-4136	218	9	five	five	NUM
ejpam-4136	218	10	properties	property	NOUN
ejpam-4136	218	11	of	of	ADP
ejpam-4136	218	12	a	a	DET
ejpam-4136	218	13	b(αn−1,βn−1)hypermetric	b(αn−1,βn−1)hypermetric	NOUN
ejpam-4136	218	14	over	over	ADP
ejpam-4136	218	15	banach	banach	NOUN
ejpam-4136	218	16	algebra	algebra	NOUN
ejpam-4136	218	17	a.	a.	NOUN
ejpam-4136	218	18	proposition	proposition	NOUN
ejpam-4136	218	19	8	8	NUM
ejpam-4136	218	20	.	.	PUNCT
ejpam-4136	219	1	let	let	VERB
ejpam-4136	219	2	π	π	NOUN
ejpam-4136	219	3	:	:	PUNCT
ejpam-4136	219	4	x	x	SYM
ejpam-4136	219	5	→	→	SYM
ejpam-4136	219	6	y	y	X
ejpam-4136	219	7	be	be	AUX
ejpam-4136	219	8	an	an	DET
ejpam-4136	219	9	injection	injection	NOUN
ejpam-4136	219	10	from	from	ADP
ejpam-4136	219	11	a	a	DET
ejpam-4136	219	12	set	set	NOUN
ejpam-4136	219	13	x	x	PUNCT
ejpam-4136	219	14	to	to	ADP
ejpam-4136	219	15	a	a	DET
ejpam-4136	219	16	set	set	NOUN
ejpam-4136	219	17	y	y	PROPN
ejpam-4136	219	18	.	.	PUNCT
ejpam-4136	220	1	if	if	SCONJ
ejpam-4136	220	2	γ(αn	γ(αn	VERB
ejpam-4136	220	3	,	,	PUNCT
ejpam-4136	220	4	βn	βn	NOUN
ejpam-4136	220	5	)	)	PUNCT
ejpam-4136	220	6	:	:	PUNCT
ejpam-4136	221	1	y	y	PROPN
ejpam-4136	221	2	n	n	PROPN
ejpam-4136	221	3	→	→	X
ejpam-4136	221	4	p	p	X
ejpam-4136	221	5	∗(a+	∗(a+	NOUN
ejpam-4136	221	6	)	)	PUNCT
ejpam-4136	221	7	is	be	AUX
ejpam-4136	221	8	a	a	DET
ejpam-4136	221	9	b(αn	b(αn	NOUN
ejpam-4136	221	10	,	,	PUNCT
ejpam-4136	221	11	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	221	12	on	on	ADP
ejpam-4136	221	13	the	the	DET
ejpam-4136	221	14	set	set	NOUN
ejpam-4136	221	15	y	y	PROPN
ejpam-4136	221	16	over	over	ADP
ejpam-4136	221	17	banach	banach	NOUN
ejpam-4136	221	18	algebra	algebra	NOUN
ejpam-4136	221	19	a.	a.	NOUN
ejpam-4136	221	20	then	then	ADV
ejpam-4136	221	21	γ(αn	γ(αn	VERB
ejpam-4136	221	22	,	,	PUNCT
ejpam-4136	221	23	βn	βn	NOUN
ejpam-4136	221	24	)	)	PUNCT
ejpam-4136	221	25	:	:	PUNCT
ejpam-4136	221	26	xn	xn	PROPN
ejpam-4136	222	1	→	→	PUNCT
ejpam-4136	222	2	p	p	X
ejpam-4136	222	3	∗(a+	∗(a+	NOUN
ejpam-4136	222	4	)	)	PUNCT
ejpam-4136	222	5	,	,	PUNCT
ejpam-4136	222	6	given	give	VERB
ejpam-4136	222	7	by	by	ADP
ejpam-4136	222	8	the	the	DET
ejpam-4136	222	9	formula	formula	NOUN
ejpam-4136	222	10	γ(αn	γ(αn	NOUN
ejpam-4136	222	11	,	,	PUNCT
ejpam-4136	222	12	βn)(xi	βn)(xi	PUNCT
ejpam-4136	222	13	)	)	PUNCT
ejpam-4136	222	14	n	n	PRON
ejpam-4136	222	15	i=1	i=1	PROPN
ejpam-4136	222	16	=	=	PUNCT
ejpam-4136	222	17	γ(αn	γ(αn	PROPN
ejpam-4136	222	18	,	,	PUNCT
ejpam-4136	222	19	βn)(πi	βn)(πi	NUM
ejpam-4136	222	20	)	)	PUNCT
ejpam-4136	222	21	n	n	CCONJ
ejpam-4136	222	22	i=1	i=1	PROPN
ejpam-4136	222	23	for	for	ADP
ejpam-4136	222	24	all	all	DET
ejpam-4136	222	25	x1	x1	PROPN
ejpam-4136	222	26	,	,	PUNCT
ejpam-4136	222	27	.	.	PUNCT
ejpam-4136	222	28	.	.	PUNCT
ejpam-4136	223	1	.	.	PUNCT
ejpam-4136	224	1	,	,	PUNCT
ejpam-4136	224	2	xn	xn	PUNCT
ejpam-4136	224	3	∈	∈	PROPN
ejpam-4136	224	4	x	x	X
ejpam-4136	224	5	,	,	PUNCT
ejpam-4136	224	6	is	be	AUX
ejpam-4136	224	7	a	a	DET
ejpam-4136	224	8	b(αn	b(αn	NOUN
ejpam-4136	224	9	,	,	PUNCT
ejpam-4136	224	10	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	224	11	on	on	ADP
ejpam-4136	224	12	the	the	DET
ejpam-4136	224	13	set	set	NOUN
ejpam-4136	224	14	x	x	PUNCT
ejpam-4136	224	15	over	over	ADP
ejpam-4136	224	16	banach	banach	NOUN
ejpam-4136	224	17	algebra	algebra	NOUN
ejpam-4136	224	18	a.	a.	NOUN
ejpam-4136	224	19	proposition	proposition	NOUN
ejpam-4136	224	20	9	9	NUM
ejpam-4136	224	21	.	.	PUNCT
ejpam-4136	225	1	let	let	VERB
ejpam-4136	225	2	(	(	PUNCT
ejpam-4136	225	3	x	x	X
ejpam-4136	225	4	,	,	PUNCT
ejpam-4136	225	5	γ(αn	γ(αn	VERB
ejpam-4136	225	6	,	,	PUNCT
ejpam-4136	225	7	βn	βn	NOUN
ejpam-4136	225	8	)	)	PUNCT
ejpam-4136	225	9	)	)	PUNCT
ejpam-4136	225	10	be	be	AUX
ejpam-4136	225	11	any	any	DET
ejpam-4136	225	12	b(αn	b(αn	NOUN
ejpam-4136	225	13	,	,	PUNCT
ejpam-4136	225	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	225	15	space	space	NOUN
ejpam-4136	225	16	over	over	ADP
ejpam-4136	225	17	banach	banach	NOUN
ejpam-4136	225	18	algebra	algebra	NOUN
ejpam-4136	226	1	a	a	PRON
ejpam-4136	226	2	and	and	CCONJ
ejpam-4136	226	3	λ	λ	X
ejpam-4136	226	4	∈	∈	NOUN
ejpam-4136	226	5	r0	r0	NOUN
ejpam-4136	226	6	+	+	PROPN
ejpam-4136	226	7	.	.	PUNCT
ejpam-4136	227	1	then	then	ADV
ejpam-4136	227	2	(	(	PUNCT
ejpam-4136	227	3	x	x	X
ejpam-4136	227	4	,	,	PUNCT
ejpam-4136	227	5	γλ	γλ	INTJ
ejpam-4136	227	6	(	(	PUNCT
ejpam-4136	227	7	αn	αn	NOUN
ejpam-4136	227	8	,	,	PUNCT
ejpam-4136	227	9	βn	βn	NOUN
ejpam-4136	227	10	)	)	PUNCT
ejpam-4136	227	11	)	)	PUNCT
ejpam-4136	227	12	is	be	AUX
ejpam-4136	227	13	also	also	ADV
ejpam-4136	227	14	a	a	DET
ejpam-4136	227	15	b(αn	b(αn	NOUN
ejpam-4136	227	16	,	,	PUNCT
ejpam-4136	227	17	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	227	18	space	space	NOUN
ejpam-4136	227	19	over	over	ADP
ejpam-4136	227	20	banach	banach	NOUN
ejpam-4136	227	21	algebra	algebra	NOUN
ejpam-4136	227	22	a	a	DET
ejpam-4136	227	23	where	where	SCONJ
ejpam-4136	227	24	γλ	γλ	INTJ
ejpam-4136	227	25	(	(	PUNCT
ejpam-4136	227	26	αn	αn	NOUN
ejpam-4136	227	27	,	,	PUNCT
ejpam-4136	227	28	βn	βn	NOUN
ejpam-4136	227	29	)	)	PUNCT
ejpam-4136	227	30	(	(	PUNCT
ejpam-4136	227	31	xi	xi	NOUN
ejpam-4136	227	32	)	)	PUNCT
ejpam-4136	227	33	n	n	ADV
ejpam-4136	227	34	i=1	i=1	PROPN
ejpam-4136	227	35	:	:	PUNCT
ejpam-4136	227	36	=	=	SYM
ejpam-4136	227	37	{	{	PUNCT
ejpam-4136	227	38	a	a	DET
ejpam-4136	227	39	∩	∩	X
ejpam-4136	227	40	{	{	PUNCT
ejpam-4136	227	41	a	a	DET
ejpam-4136	227	42	∈	∈	PROPN
ejpam-4136	227	43	a|0a	a|0a	NOUN
ejpam-4136	227	44	⪯	⪯	NOUN
ejpam-4136	227	45	a	a	DET
ejpam-4136	227	46	≺	≺	NOUN
ejpam-4136	227	47	λ}|a	λ}|a	PROPN
ejpam-4136	227	48	∈	∈	PROPN
ejpam-4136	227	49	γ(αn	γ(αn	NOUN
ejpam-4136	227	50	,	,	PUNCT
ejpam-4136	227	51	βn)(xi	βn)(xi	PUNCT
ejpam-4136	227	52	)	)	PUNCT
ejpam-4136	227	53	n	n	CCONJ
ejpam-4136	227	54	i=1	i=1	PROPN
ejpam-4136	227	55	}	}	PUNCT
ejpam-4136	227	56	.	.	PUNCT
ejpam-4136	228	1	so	so	ADV
ejpam-4136	228	2	,	,	PUNCT
ejpam-4136	228	3	on	on	ADP
ejpam-4136	228	4	the	the	DET
ejpam-4136	228	5	same	same	ADJ
ejpam-4136	228	6	x	x	NOUN
ejpam-4136	228	7	many	many	ADJ
ejpam-4136	228	8	b(αn	b(αn	NOUN
ejpam-4136	228	9	,	,	PUNCT
ejpam-4136	228	10	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	228	11	over	over	ADP
ejpam-4136	228	12	banach	banach	NOUN
ejpam-4136	228	13	algebra	algebra	NOUN
ejpam-4136	228	14	a	a	PRON
ejpam-4136	228	15	can	can	AUX
ejpam-4136	228	16	be	be	AUX
ejpam-4136	228	17	defined	define	VERB
ejpam-4136	228	18	,	,	PUNCT
ejpam-4136	228	19	as	as	ADP
ejpam-4136	228	20	a	a	DET
ejpam-4136	228	21	result	result	NOUN
ejpam-4136	228	22	of	of	ADP
ejpam-4136	228	23	which	which	PRON
ejpam-4136	228	24	the	the	DET
ejpam-4136	228	25	same	same	ADJ
ejpam-4136	228	26	set	set	NOUN
ejpam-4136	228	27	x	x	PUNCT
ejpam-4136	228	28	is	be	AUX
ejpam-4136	228	29	endowed	endow	VERB
ejpam-4136	228	30	with	with	ADP
ejpam-4136	228	31	different	different	ADJ
ejpam-4136	228	32	metric	metric	ADJ
ejpam-4136	228	33	structures	structure	NOUN
ejpam-4136	228	34	.	.	PUNCT
ejpam-4136	229	1	another	another	DET
ejpam-4136	229	2	structure	structure	NOUN
ejpam-4136	229	3	in	in	ADP
ejpam-4136	229	4	the	the	DET
ejpam-4136	229	5	next	next	ADJ
ejpam-4136	229	6	proposition	proposition	NOUN
ejpam-4136	229	7	is	be	AUX
ejpam-4136	229	8	useful	useful	ADJ
ejpam-4136	229	9	for	for	ADP
ejpam-4136	229	10	scaling	scale	VERB
ejpam-4136	229	11	the	the	DET
ejpam-4136	229	12	b(αn	b(αn	NOUN
ejpam-4136	229	13	,	,	PUNCT
ejpam-4136	229	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	229	15	over	over	ADP
ejpam-4136	229	16	banach	banach	NOUN
ejpam-4136	229	17	algebra	algebra	NOUN
ejpam-4136	229	18	a	a	PRON
ejpam-4136	229	19	,	,	PUNCT
ejpam-4136	229	20	so	so	SCONJ
ejpam-4136	229	21	we	we	PRON
ejpam-4136	229	22	need	need	VERB
ejpam-4136	229	23	the	the	DET
ejpam-4136	229	24	following	follow	VERB
ejpam-4136	229	25	explanation	explanation	NOUN
ejpam-4136	229	26	.	.	PUNCT
ejpam-4136	230	1	for	for	ADP
ejpam-4136	230	2	any	any	DET
ejpam-4136	230	3	non	non	ADJ
ejpam-4136	230	4	-	-	ADJ
ejpam-4136	230	5	empty	empty	ADJ
ejpam-4136	230	6	subset	subset	NOUN
ejpam-4136	230	7	b	b	PROPN
ejpam-4136	230	8	of	of	ADP
ejpam-4136	230	9	a+	a+	NOUN
ejpam-4136	230	10	,	,	PUNCT
ejpam-4136	230	11	and	and	CCONJ
ejpam-4136	230	12	λ	λ	X
ejpam-4136	230	13	∈	∈	PROPN
ejpam-4136	230	14	a+	a+	PUNCT
ejpam-4136	230	15	we	we	PRON
ejpam-4136	230	16	define	define	VERB
ejpam-4136	230	17	a	a	DET
ejpam-4136	230	18	set	set	ADJ
ejpam-4136	230	19	λ	λ	X
ejpam-4136	230	20	·	·	PUNCT
ejpam-4136	230	21	b	b	NOUN
ejpam-4136	230	22	to	to	PART
ejpam-4136	230	23	be	be	AUX
ejpam-4136	230	24	λ	λ	X
ejpam-4136	230	25	·	·	PUNCT
ejpam-4136	230	26	b	b	X
ejpam-4136	231	1	:	:	PUNCT
ejpam-4136	231	2	=	=	NOUN
ejpam-4136	231	3	{	{	PUNCT
ejpam-4136	231	4	λ	λ	X
ejpam-4136	231	5	·	·	PUNCT
ejpam-4136	231	6	b	b	X
ejpam-4136	231	7	|	|	NOUN
ejpam-4136	231	8	b	b	PROPN
ejpam-4136	231	9	∈	∈	PROPN
ejpam-4136	231	10	b	b	PROPN
ejpam-4136	231	11	}	}	PUNCT
ejpam-4136	231	12	.	.	PUNCT
ejpam-4136	232	1	a.	a.	PROPN
ejpam-4136	232	2	d.nezhad	d.nezhad	PROPN
ejpam-4136	232	3	,	,	PUNCT
ejpam-4136	232	4	s.	s.	PROPN
ejpam-4136	232	5	radenović	radenović	PROPN
ejpam-4136	232	6	/	/	SYM
ejpam-4136	232	7	eur	eur	PROPN
ejpam-4136	232	8	.	.	PUNCT
ejpam-4136	233	1	j.	j.	PROPN
ejpam-4136	233	2	pure	pure	PROPN
ejpam-4136	233	3	appl	appl	PROPN
ejpam-4136	233	4	.	.	PROPN
ejpam-4136	233	5	math	math	PROPN
ejpam-4136	233	6	,	,	PUNCT
ejpam-4136	233	7	14	14	NUM
ejpam-4136	233	8	(	(	PUNCT
ejpam-4136	233	9	4	4	NUM
ejpam-4136	233	10	)	)	PUNCT
ejpam-4136	233	11	(	(	PUNCT
ejpam-4136	233	12	2021	2021	NUM
ejpam-4136	233	13	)	)	PUNCT
ejpam-4136	233	14	,	,	PUNCT
ejpam-4136	233	15	1148	1148	NUM
ejpam-4136	233	16	-	-	SYM
ejpam-4136	233	17	1160	1160	NUM
ejpam-4136	233	18	1155	1155	NUM
ejpam-4136	233	19	proposition	proposition	NOUN
ejpam-4136	233	20	10	10	NUM
ejpam-4136	233	21	.	.	PUNCT
ejpam-4136	234	1	let	let	AUX
ejpam-4136	234	2	(	(	PUNCT
ejpam-4136	234	3	x	x	X
ejpam-4136	234	4	,	,	PUNCT
ejpam-4136	234	5	γ(αn	γ(αn	VERB
ejpam-4136	234	6	,	,	PUNCT
ejpam-4136	234	7	βn	βn	NOUN
ejpam-4136	234	8	)	)	PUNCT
ejpam-4136	234	9	)	)	PUNCT
ejpam-4136	234	10	be	be	AUX
ejpam-4136	234	11	any	any	DET
ejpam-4136	234	12	b(αn	b(αn	NOUN
ejpam-4136	234	13	,	,	PUNCT
ejpam-4136	234	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	234	15	space	space	NOUN
ejpam-4136	234	16	over	over	ADP
ejpam-4136	234	17	banach	banach	NOUN
ejpam-4136	234	18	algebra	algebra	NOUN
ejpam-4136	234	19	a.	a.	NOUN
ejpam-4136	234	20	let	let	VERB
ejpam-4136	234	21	λ	λ	PRON
ejpam-4136	234	22	be	be	AUX
ejpam-4136	234	23	any	any	DET
ejpam-4136	234	24	positive	positive	ADJ
ejpam-4136	234	25	real	real	ADJ
ejpam-4136	234	26	number	number	NOUN
ejpam-4136	234	27	.	.	PUNCT
ejpam-4136	235	1	we	we	PRON
ejpam-4136	235	2	define	define	VERB
ejpam-4136	235	3	γ̇λ	γ̇λ	ADP
ejpam-4136	235	4	(	(	PUNCT
ejpam-4136	235	5	αn	αn	NOUN
ejpam-4136	235	6	,	,	PUNCT
ejpam-4136	235	7	βn	βn	NOUN
ejpam-4136	235	8	)	)	PUNCT
ejpam-4136	235	9	(	(	PUNCT
ejpam-4136	235	10	xi	xi	NOUN
ejpam-4136	235	11	)	)	PUNCT
ejpam-4136	235	12	n	n	CCONJ
ejpam-4136	235	13	i=1	i=1	PROPN
ejpam-4136	235	14	=	=	PUNCT
ejpam-4136	235	15	λ	λ	X
ejpam-4136	235	16	·	·	PUNCT
ejpam-4136	235	17	γ(αn	γ(αn	NUM
ejpam-4136	235	18	,	,	PUNCT
ejpam-4136	235	19	βn)(xi	βn)(xi	PUNCT
ejpam-4136	235	20	)	)	PUNCT
ejpam-4136	235	21	n	n	CCONJ
ejpam-4136	235	22	i=1	i=1	PROPN
ejpam-4136	235	23	.	.	PUNCT
ejpam-4136	236	1	then	then	ADV
ejpam-4136	236	2	(	(	PUNCT
ejpam-4136	236	3	x	x	X
ejpam-4136	236	4	,	,	PUNCT
ejpam-4136	236	5	γ̇λ	γ̇λ	ADP
ejpam-4136	236	6	(	(	PUNCT
ejpam-4136	236	7	αn	αn	NOUN
ejpam-4136	236	8	,	,	PUNCT
ejpam-4136	236	9	βn	βn	NOUN
ejpam-4136	236	10	)	)	PUNCT
ejpam-4136	236	11	)	)	PUNCT
ejpam-4136	236	12	is	be	AUX
ejpam-4136	236	13	also	also	ADV
ejpam-4136	236	14	a	a	DET
ejpam-4136	236	15	b(αn	b(αn	NOUN
ejpam-4136	236	16	,	,	PUNCT
ejpam-4136	236	17	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	236	18	space	space	NOUN
ejpam-4136	236	19	over	over	ADP
ejpam-4136	236	20	banach	banach	NOUN
ejpam-4136	236	21	algebra	algebra	NOUN
ejpam-4136	236	22	a.	a.	NOUN
ejpam-4136	236	23	a	a	DET
ejpam-4136	236	24	sequence	sequence	NOUN
ejpam-4136	236	25	{	{	PUNCT
ejpam-4136	236	26	xm	xm	NOUN
ejpam-4136	236	27	}	}	PUNCT
ejpam-4136	236	28	in	in	ADP
ejpam-4136	236	29	a	a	DET
ejpam-4136	236	30	b(αn	b(αn	NOUN
ejpam-4136	236	31	,	,	PUNCT
ejpam-4136	236	32	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	236	33	space	space	NOUN
ejpam-4136	236	34	(	(	PUNCT
ejpam-4136	236	35	x	x	X
ejpam-4136	236	36	,	,	PUNCT
ejpam-4136	236	37	γ(αn	γ(αn	VERB
ejpam-4136	236	38	,	,	PUNCT
ejpam-4136	236	39	βn	βn	NOUN
ejpam-4136	236	40	)	)	PUNCT
ejpam-4136	236	41	)	)	PUNCT
ejpam-4136	236	42	over	over	ADP
ejpam-4136	236	43	banach	banach	NOUN
ejpam-4136	236	44	algebra	algebra	NOUN
ejpam-4136	236	45	a	a	PRON
ejpam-4136	236	46	is	be	AUX
ejpam-4136	236	47	said	say	VERB
ejpam-4136	236	48	to	to	PART
ejpam-4136	236	49	converge	converge	VERB
ejpam-4136	236	50	to	to	ADP
ejpam-4136	236	51	a	a	DET
ejpam-4136	236	52	point	point	NOUN
ejpam-4136	236	53	s	s	VERB
ejpam-4136	236	54	in	in	ADP
ejpam-4136	236	55	x	x	SYM
ejpam-4136	236	56	,	,	PUNCT
ejpam-4136	236	57	if	if	SCONJ
ejpam-4136	236	58	for	for	ADP
ejpam-4136	236	59	any	any	DET
ejpam-4136	236	60	ϵ	ϵ	PROPN
ejpam-4136	236	61	≻	≻	PROPN
ejpam-4136	236	62	0a	0a	PROPN
ejpam-4136	236	63	there	there	PRON
ejpam-4136	236	64	exists	exist	VERB
ejpam-4136	236	65	a	a	DET
ejpam-4136	236	66	natural	natural	ADJ
ejpam-4136	236	67	number	number	NOUN
ejpam-4136	236	68	n	n	ADP
ejpam-4136	236	69	such	such	ADJ
ejpam-4136	236	70	that	that	PRON
ejpam-4136	236	71	for	for	ADP
ejpam-4136	236	72	every	every	DET
ejpam-4136	236	73	m1	m1	NOUN
ejpam-4136	236	74	,	,	PUNCT
ejpam-4136	236	75	.	.	PUNCT
ejpam-4136	236	76	.	.	PUNCT
ejpam-4136	236	77	.	.	PUNCT
ejpam-4136	237	1	,	,	PUNCT
ejpam-4136	237	2	mn−1	mn−1	PROPN
ejpam-4136	237	3	≥	≥	NOUN
ejpam-4136	237	4	n	n	ADV
ejpam-4136	237	5	γ(αn	γ(αn	VERB
ejpam-4136	237	6	,	,	PUNCT
ejpam-4136	237	7	βn)((xmi	βn)((xmi	PUNCT
ejpam-4136	237	8	)	)	PUNCT
ejpam-4136	238	1	m−1	m−1	PROPN
ejpam-4136	238	2	i=1	i=1	X
ejpam-4136	238	3	,	,	PUNCT
ejpam-4136	238	4	s	s	X
ejpam-4136	238	5	)	)	PUNCT
ejpam-4136	238	6	⊆	⊆	NUM
ejpam-4136	238	7	{	{	PUNCT
ejpam-4136	238	8	a	a	DET
ejpam-4136	238	9	∈	∈	PROPN
ejpam-4136	238	10	a|0a	a|0a	NOUN
ejpam-4136	238	11	⪯	⪯	NOUN
ejpam-4136	238	12	a	a	DET
ejpam-4136	238	13	≺	≺	NOUN
ejpam-4136	238	14	ϵ	ϵ	X
ejpam-4136	238	15	}	}	PUNCT
ejpam-4136	238	16	,	,	PUNCT
ejpam-4136	238	17	then	then	ADV
ejpam-4136	238	18	we	we	PRON
ejpam-4136	238	19	shall	shall	AUX
ejpam-4136	238	20	write	write	VERB
ejpam-4136	238	21	lim	lim	PROPN
ejpam-4136	238	22	m1,	m1,	PROPN
ejpam-4136	238	23	...	...	PUNCT
ejpam-4136	238	24	,mn−1−→+∞	,mn−1−→+∞	PUNCT
ejpam-4136	238	25	γ(αn	γ(αn	VERB
ejpam-4136	238	26	,	,	PUNCT
ejpam-4136	238	27	βn)((xmi	βn)((xmi	PUNCT
ejpam-4136	238	28	)	)	PUNCT
ejpam-4136	239	1	m−1	m−1	PROPN
ejpam-4136	239	2	i=1	i=1	X
ejpam-4136	239	3	,	,	PUNCT
ejpam-4136	239	4	s	s	X
ejpam-4136	239	5	)	)	PUNCT
ejpam-4136	239	6	=	=	SYM
ejpam-4136	239	7	{	{	PUNCT
ejpam-4136	239	8	0a	0a	PROPN
ejpam-4136	239	9	}	}	PUNCT
ejpam-4136	239	10	.	.	PUNCT
ejpam-4136	240	1	we	we	PRON
ejpam-4136	240	2	shall	shall	AUX
ejpam-4136	240	3	say	say	VERB
ejpam-4136	240	4	that	that	SCONJ
ejpam-4136	240	5	a	a	DET
ejpam-4136	240	6	sequence	sequence	NOUN
ejpam-4136	240	7	{	{	PUNCT
ejpam-4136	240	8	xm	xm	NOUN
ejpam-4136	240	9	}	}	PUNCT
ejpam-4136	240	10	has	have	VERB
ejpam-4136	240	11	a	a	DET
ejpam-4136	240	12	cluster	cluster	NOUN
ejpam-4136	240	13	point	point	NOUN
ejpam-4136	240	14	x	x	PUNCT
ejpam-4136	240	15	if	if	SCONJ
ejpam-4136	240	16	there	there	PRON
ejpam-4136	240	17	exists	exist	VERB
ejpam-4136	240	18	a	a	DET
ejpam-4136	240	19	subsequence	subsequence	NOUN
ejpam-4136	240	20	{	{	PUNCT
ejpam-4136	240	21	xmk	xmk	PROPN
ejpam-4136	240	22	}	}	PUNCT
ejpam-4136	240	23	of	of	ADP
ejpam-4136	240	24	{	{	PUNCT
ejpam-4136	240	25	xm	xm	PROPN
ejpam-4136	240	26	}	}	PUNCT
ejpam-4136	240	27	that	that	PRON
ejpam-4136	240	28	converges	converge	VERB
ejpam-4136	240	29	to	to	ADP
ejpam-4136	240	30	x.	x.	NOUN
ejpam-4136	240	31	proposition	proposition	PROPN
ejpam-4136	240	32	11	11	NUM
ejpam-4136	240	33	.	.	PUNCT
ejpam-4136	241	1	let	let	VERB
ejpam-4136	241	2	(	(	PUNCT
ejpam-4136	241	3	x	x	X
ejpam-4136	241	4	,	,	PUNCT
ejpam-4136	241	5	γ(αn	γ(αn	VERB
ejpam-4136	241	6	,	,	PUNCT
ejpam-4136	241	7	βn	βn	NOUN
ejpam-4136	241	8	)	)	PUNCT
ejpam-4136	241	9	)	)	PUNCT
ejpam-4136	242	1	and	and	CCONJ
ejpam-4136	242	2	(	(	PUNCT
ejpam-4136	242	3	x	x	NOUN
ejpam-4136	242	4	′,γ	′,γ	X
ejpam-4136	242	5	′	′	NUM
ejpam-4136	242	6	(	(	PUNCT
ejpam-4136	242	7	αn	αn	NOUN
ejpam-4136	242	8	,	,	PUNCT
ejpam-4136	242	9	βn	βn	NOUN
ejpam-4136	242	10	)	)	PUNCT
ejpam-4136	242	11	)	)	PUNCT
ejpam-4136	242	12	be	be	AUX
ejpam-4136	242	13	two	two	NUM
ejpam-4136	242	14	b(αn	b(αn	NOUN
ejpam-4136	242	15	,	,	PUNCT
ejpam-4136	242	16	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	242	17	spaces	space	NOUN
ejpam-4136	242	18	over	over	ADP
ejpam-4136	242	19	banach	banach	NOUN
ejpam-4136	242	20	algebra	algebra	NOUN
ejpam-4136	242	21	a.	a.	NOUN
ejpam-4136	242	22	then	then	ADV
ejpam-4136	242	23	a	a	DET
ejpam-4136	242	24	function	function	NOUN
ejpam-4136	242	25	t	t	NOUN
ejpam-4136	242	26	:	:	PUNCT
ejpam-4136	242	27	x	x	X
ejpam-4136	242	28	→	→	SYM
ejpam-4136	242	29	x	x	SYM
ejpam-4136	242	30	′	′	NOUN
ejpam-4136	242	31	is	be	AUX
ejpam-4136	242	32	b(αn	b(αn	NOUN
ejpam-4136	242	33	,	,	PUNCT
ejpam-4136	242	34	βn)-continuous	βn)-continuous	ADJ
ejpam-4136	242	35	at	at	ADP
ejpam-4136	242	36	a	a	DET
ejpam-4136	242	37	point	point	NOUN
ejpam-4136	242	38	x	x	X
ejpam-4136	242	39	∈	∈	NOUN
ejpam-4136	242	40	x	x	X
ejpam-4136	242	41	,	,	PUNCT
ejpam-4136	242	42	if	if	SCONJ
ejpam-4136	242	43	and	and	CCONJ
ejpam-4136	242	44	only	only	ADV
ejpam-4136	242	45	if	if	SCONJ
ejpam-4136	242	46	it	it	PRON
ejpam-4136	242	47	is	be	AUX
ejpam-4136	242	48	b(αn	b(αn	NOUN
ejpam-4136	242	49	,	,	PUNCT
ejpam-4136	242	50	βn)-sequentially	βn)-sequentially	ADV
ejpam-4136	242	51	continuous	continuous	ADJ
ejpam-4136	242	52	at	at	ADP
ejpam-4136	242	53	x	x	NOUN
ejpam-4136	242	54	;	;	PUNCT
ejpam-4136	242	55	that	that	PRON
ejpam-4136	242	56	is	is	ADV
ejpam-4136	242	57	,	,	PUNCT
ejpam-4136	242	58	whenever	whenever	SCONJ
ejpam-4136	242	59	sequence	sequence	NOUN
ejpam-4136	242	60	{	{	PUNCT
ejpam-4136	242	61	xm	xm	NOUN
ejpam-4136	242	62	}	}	PUNCT
ejpam-4136	242	63	is	be	AUX
ejpam-4136	242	64	b(αn	b(αn	NOUN
ejpam-4136	242	65	,	,	PUNCT
ejpam-4136	242	66	βn)-convergent	βn)-convergent	NOUN
ejpam-4136	242	67	to	to	ADP
ejpam-4136	242	68	x	x	PROPN
ejpam-4136	242	69	one	one	PRON
ejpam-4136	242	70	has	have	AUX
ejpam-4136	242	71	{	{	PUNCT
ejpam-4136	242	72	t	t	PROPN
ejpam-4136	242	73	(	(	PUNCT
ejpam-4136	242	74	xm	xm	NOUN
ejpam-4136	242	75	)	)	PUNCT
ejpam-4136	242	76	}	}	PUNCT
ejpam-4136	242	77	is	be	AUX
ejpam-4136	242	78	u(αn	u(αn	NOUN
ejpam-4136	242	79	,	,	PUNCT
ejpam-4136	242	80	βn)-convergent	βn)-convergent	NOUN
ejpam-4136	242	81	to	to	ADP
ejpam-4136	242	82	t	t	PROPN
ejpam-4136	242	83	(	(	PUNCT
ejpam-4136	242	84	x	x	NOUN
ejpam-4136	242	85	)	)	PUNCT
ejpam-4136	242	86	.	.	PUNCT
ejpam-4136	243	1	definition	definition	NOUN
ejpam-4136	243	2	8	8	NUM
ejpam-4136	243	3	.	.	PUNCT
ejpam-4136	244	1	let	let	AUX
ejpam-4136	244	2	(	(	PUNCT
ejpam-4136	244	3	x	x	X
ejpam-4136	244	4	,	,	PUNCT
ejpam-4136	244	5	γ(αn	γ(αn	VERB
ejpam-4136	244	6	,	,	PUNCT
ejpam-4136	244	7	βn	βn	NOUN
ejpam-4136	244	8	)	)	PUNCT
ejpam-4136	244	9	)	)	PUNCT
ejpam-4136	244	10	be	be	AUX
ejpam-4136	244	11	a	a	DET
ejpam-4136	244	12	b(αn	b(αn	NOUN
ejpam-4136	244	13	,	,	PUNCT
ejpam-4136	244	14	βn)-hypermetric	βn)-hypermetric	ADV
ejpam-4136	244	15	spaceover	spaceover	AUX
ejpam-4136	244	16	banach	banach	NOUN
ejpam-4136	244	17	algebra	algebra	VERB
ejpam-4136	244	18	a	a	PRON
ejpam-4136	244	19	,	,	PUNCT
ejpam-4136	244	20	and	and	CCONJ
ejpam-4136	244	21	a	a	DET
ejpam-4136	244	22	⊆	⊆	NUM
ejpam-4136	244	23	x.	x.	NOUN
ejpam-4136	244	24	the	the	DET
ejpam-4136	244	25	set	set	NOUN
ejpam-4136	244	26	a	a	PRON
ejpam-4136	244	27	is	be	AUX
ejpam-4136	244	28	b(αn	b(αn	NOUN
ejpam-4136	244	29	,	,	PUNCT
ejpam-4136	244	30	βn)-compact	βn)-compact	VERB
ejpam-4136	244	31	if	if	SCONJ
ejpam-4136	244	32	for	for	ADP
ejpam-4136	244	33	every	every	DET
ejpam-4136	244	34	b(αn	b(αn	NOUN
ejpam-4136	244	35	,	,	PUNCT
ejpam-4136	244	36	βn)-sequence	βn)-sequence	NOUN
ejpam-4136	244	37	{	{	PUNCT
ejpam-4136	244	38	xm	xm	NOUN
ejpam-4136	244	39	}	}	PUNCT
ejpam-4136	244	40	in	in	ADP
ejpam-4136	244	41	a	a	PRON
ejpam-4136	244	42	,	,	PUNCT
ejpam-4136	244	43	there	there	PRON
ejpam-4136	244	44	exists	exist	VERB
ejpam-4136	244	45	a	a	DET
ejpam-4136	244	46	subsequence	subsequence	NOUN
ejpam-4136	244	47	{	{	PUNCT
ejpam-4136	244	48	xmk	xmk	PROPN
ejpam-4136	244	49	}	}	PUNCT
ejpam-4136	244	50	of	of	ADP
ejpam-4136	244	51	{	{	PUNCT
ejpam-4136	244	52	xm	xm	NOUN
ejpam-4136	244	53	}	}	PUNCT
ejpam-4136	244	54	such	such	ADJ
ejpam-4136	244	55	that	that	DET
ejpam-4136	244	56	b(αn	b(αn	NOUN
ejpam-4136	244	57	,	,	PUNCT
ejpam-4136	244	58	βn)-convergences	βn)-convergence	NOUN
ejpam-4136	244	59	to	to	ADP
ejpam-4136	244	60	some	some	DET
ejpam-4136	244	61	x0	x0	PROPN
ejpam-4136	244	62	∈	∈	PROPN
ejpam-4136	244	63	a.	a.	NOUN
ejpam-4136	244	64	proposition	proposition	NOUN
ejpam-4136	244	65	12	12	NUM
ejpam-4136	244	66	.	.	PUNCT
ejpam-4136	245	1	let	let	VERB
ejpam-4136	245	2	(	(	PUNCT
ejpam-4136	245	3	x	x	X
ejpam-4136	245	4	,	,	PUNCT
ejpam-4136	245	5	γ(αn	γ(αn	VERB
ejpam-4136	245	6	,	,	PUNCT
ejpam-4136	245	7	βn	βn	NOUN
ejpam-4136	245	8	)	)	PUNCT
ejpam-4136	245	9	)	)	PUNCT
ejpam-4136	246	1	and	and	CCONJ
ejpam-4136	246	2	(	(	PUNCT
ejpam-4136	246	3	x	x	NOUN
ejpam-4136	246	4	′,γ	′,γ	X
ejpam-4136	246	5	′	′	NUM
ejpam-4136	246	6	(	(	PUNCT
ejpam-4136	246	7	αn	αn	NOUN
ejpam-4136	246	8	,	,	PUNCT
ejpam-4136	246	9	βn	βn	NOUN
ejpam-4136	246	10	)	)	PUNCT
ejpam-4136	246	11	)	)	PUNCT
ejpam-4136	246	12	be	be	AUX
ejpam-4136	246	13	two	two	NUM
ejpam-4136	246	14	b(αn	b(αn	NOUN
ejpam-4136	246	15	,	,	PUNCT
ejpam-4136	246	16	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	246	17	spaces	space	NOUN
ejpam-4136	246	18	over	over	ADP
ejpam-4136	246	19	banach	banach	NOUN
ejpam-4136	246	20	algebra	algebra	NOUN
ejpam-4136	246	21	a	a	PRON
ejpam-4136	246	22	and	and	CCONJ
ejpam-4136	246	23	t	t	NOUN
ejpam-4136	246	24	:	:	PUNCT
ejpam-4136	246	25	x	x	X
ejpam-4136	246	26	→	→	SYM
ejpam-4136	246	27	x	x	SYM
ejpam-4136	246	28	′	′	NUM
ejpam-4136	246	29	a	a	DET
ejpam-4136	246	30	b(αn	b(αn	NOUN
ejpam-4136	246	31	,	,	PUNCT
ejpam-4136	246	32	βn)-continuous	βn)-continuous	ADJ
ejpam-4136	246	33	function	function	NOUN
ejpam-4136	246	34	on	on	ADP
ejpam-4136	246	35	x.	x.	NOUN
ejpam-4136	246	36	if	if	SCONJ
ejpam-4136	246	37	x	x	PRON
ejpam-4136	246	38	is	be	AUX
ejpam-4136	246	39	b(αn	b(αn	NOUN
ejpam-4136	246	40	,	,	PUNCT
ejpam-4136	246	41	βn)-compact	βn)-compact	NOUN
ejpam-4136	246	42	,	,	PUNCT
ejpam-4136	246	43	then	then	ADV
ejpam-4136	246	44	t	t	PROPN
ejpam-4136	246	45	(	(	PUNCT
ejpam-4136	246	46	x	x	X
ejpam-4136	246	47	)	)	PUNCT
ejpam-4136	246	48	is	be	AUX
ejpam-4136	246	49	b(αn	b(αn	NOUN
ejpam-4136	246	50	,	,	PUNCT
ejpam-4136	246	51	βn)-compact	βn)-compact	NOUN
ejpam-4136	246	52	.	.	PUNCT
ejpam-4136	247	1	definition	definition	NOUN
ejpam-4136	247	2	9	9	NUM
ejpam-4136	247	3	.	.	PUNCT
ejpam-4136	248	1	let	let	AUX
ejpam-4136	248	2	(	(	PUNCT
ejpam-4136	248	3	x	x	X
ejpam-4136	248	4	,	,	PUNCT
ejpam-4136	248	5	γ(αn	γ(αn	VERB
ejpam-4136	248	6	,	,	PUNCT
ejpam-4136	248	7	βn	βn	NOUN
ejpam-4136	248	8	)	)	PUNCT
ejpam-4136	248	9	)	)	PUNCT
ejpam-4136	248	10	be	be	AUX
ejpam-4136	248	11	a	a	DET
ejpam-4136	248	12	b(αn	b(αn	NOUN
ejpam-4136	248	13	,	,	PUNCT
ejpam-4136	248	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	248	15	space	space	NOUN
ejpam-4136	248	16	over	over	ADP
ejpam-4136	248	17	banach	banach	NOUN
ejpam-4136	248	18	algebra	algebra	NOUN
ejpam-4136	248	19	a.	a.	NOUN
ejpam-4136	248	20	then	then	ADV
ejpam-4136	248	21	for	for	ADP
ejpam-4136	248	22	x0	x0	PROPN
ejpam-4136	248	23	∈	∈	PROPN
ejpam-4136	248	24	x	x	PRON
ejpam-4136	248	25	,	,	PUNCT
ejpam-4136	248	26	r	r	PROPN
ejpam-4136	248	27	≻	≻	PROPN
ejpam-4136	248	28	0a	0a	PROPN
ejpam-4136	248	29	,	,	PUNCT
ejpam-4136	248	30	the	the	DET
ejpam-4136	248	31	b(αn	b(αn	NOUN
ejpam-4136	248	32	,	,	PUNCT
ejpam-4136	248	33	βn)-hyperball	βn)-hyperball	NOUN
ejpam-4136	248	34	with	with	ADP
ejpam-4136	248	35	centre	centre	NOUN
ejpam-4136	248	36	x0	x0	PROPN
ejpam-4136	248	37	and	and	CCONJ
ejpam-4136	248	38	radius	radius	NOUN
ejpam-4136	248	39	r	r	NOUN
ejpam-4136	248	40	is	be	AUX
ejpam-4136	248	41	bγ(αn	bγ(αn	ADJ
ejpam-4136	248	42	,	,	PUNCT
ejpam-4136	248	43	βn	βn	NOUN
ejpam-4136	248	44	)	)	PUNCT
ejpam-4136	248	45	(	(	PUNCT
ejpam-4136	248	46	x0	x0	PROPN
ejpam-4136	248	47	,	,	PUNCT
ejpam-4136	248	48	r	r	NOUN
ejpam-4136	248	49	)	)	PUNCT
ejpam-4136	248	50	=	=	SYM
ejpam-4136	248	51	{	{	PUNCT
ejpam-4136	248	52	y	y	PROPN
ejpam-4136	248	53	∈	∈	PROPN
ejpam-4136	248	54	x	x	X
ejpam-4136	248	55	:	:	PUNCT
ejpam-4136	248	56	γ(αn	γ(αn	VERB
ejpam-4136	248	57	,	,	PUNCT
ejpam-4136	248	58	βn)(x0	βn)(x0	PROPN
ejpam-4136	248	59	,	,	PUNCT
ejpam-4136	248	60	(	(	PUNCT
ejpam-4136	248	61	y	y	NOUN
ejpam-4136	248	62	)	)	PUNCT
ejpam-4136	248	63	n	n	PRON
ejpam-4136	248	64	2	2	NUM
ejpam-4136	248	65	)	)	PUNCT
ejpam-4136	248	66	⊆	⊆	X
ejpam-4136	248	67	{	{	PUNCT
ejpam-4136	248	68	a	a	DET
ejpam-4136	248	69	∈	∈	PROPN
ejpam-4136	248	70	a|0a	a|0a	NOUN
ejpam-4136	248	71	⪯	⪯	NOUN
ejpam-4136	248	72	a	a	DET
ejpam-4136	248	73	≺	≺	NOUN
ejpam-4136	248	74	r	r	NOUN
ejpam-4136	248	75	}	}	PUNCT
ejpam-4136	248	76	}	}	PUNCT
ejpam-4136	248	77	.	.	PUNCT
ejpam-4136	249	1	proposition	proposition	NOUN
ejpam-4136	249	2	13	13	NUM
ejpam-4136	249	3	.	.	PUNCT
ejpam-4136	250	1	let	let	AUX
ejpam-4136	250	2	(	(	PUNCT
ejpam-4136	250	3	x	x	X
ejpam-4136	250	4	,	,	PUNCT
ejpam-4136	250	5	γ(αn	γ(αn	VERB
ejpam-4136	250	6	,	,	PUNCT
ejpam-4136	250	7	βn	βn	NOUN
ejpam-4136	250	8	)	)	PUNCT
ejpam-4136	250	9	)	)	PUNCT
ejpam-4136	250	10	be	be	AUX
ejpam-4136	250	11	a	a	DET
ejpam-4136	250	12	b(αn	b(αn	NOUN
ejpam-4136	250	13	,	,	PUNCT
ejpam-4136	250	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	250	15	space	space	NOUN
ejpam-4136	250	16	over	over	ADP
ejpam-4136	250	17	banach	banach	NOUN
ejpam-4136	250	18	algebra	algebra	NOUN
ejpam-4136	250	19	a.	a.	NOUN
ejpam-4136	250	20	then	then	ADV
ejpam-4136	250	21	for	for	ADP
ejpam-4136	250	22	x0	x0	PROPN
ejpam-4136	250	23	∈	∈	PROPN
ejpam-4136	251	1	x	x	PRON
ejpam-4136	251	2	,	,	PUNCT
ejpam-4136	251	3	r	r	NOUN
ejpam-4136	251	4	≻	≻	PROPN
ejpam-4136	251	5	0a	0a	PROPN
ejpam-4136	251	6	,	,	PUNCT
ejpam-4136	251	7	(	(	PUNCT
ejpam-4136	251	8	i	i	NOUN
ejpam-4136	251	9	)	)	PUNCT
ejpam-4136	251	10	if	if	SCONJ
ejpam-4136	251	11	γ(αn	γ(αn	VERB
ejpam-4136	251	12	,	,	PUNCT
ejpam-4136	251	13	βn)(x0	βn)(x0	PROPN
ejpam-4136	251	14	,	,	PUNCT
ejpam-4136	251	15	(	(	PUNCT
ejpam-4136	251	16	xi	xi	NOUN
ejpam-4136	251	17	)	)	PUNCT
ejpam-4136	251	18	n	n	PRON
ejpam-4136	251	19	i=2	i=2	PROPN
ejpam-4136	251	20	)	)	PUNCT
ejpam-4136	251	21	⊆	⊆	NUM
ejpam-4136	251	22	{	{	PUNCT
ejpam-4136	251	23	a	a	DET
ejpam-4136	251	24	∈	∈	PROPN
ejpam-4136	251	25	a|0a	a|0a	NOUN
ejpam-4136	251	26	⪯	⪯	NOUN
ejpam-4136	251	27	a	a	DET
ejpam-4136	251	28	≺	≺	NOUN
ejpam-4136	251	29	r	r	NOUN
ejpam-4136	251	30	}	}	PUNCT
ejpam-4136	251	31	,	,	PUNCT
ejpam-4136	251	32	then	then	ADV
ejpam-4136	251	33	x2	x2	PROPN
ejpam-4136	251	34	,	,	PUNCT
ejpam-4136	251	35	...	...	PUNCT
ejpam-4136	251	36	,	,	PUNCT
ejpam-4136	251	37	xn	xn	PROPN
ejpam-4136	251	38	∈	∈	PROPN
ejpam-4136	251	39	bγ(αn	bγ(αn	NOUN
ejpam-4136	251	40	,	,	PUNCT
ejpam-4136	251	41	βn	βn	NOUN
ejpam-4136	251	42	)	)	PUNCT
ejpam-4136	251	43	(	(	PUNCT
ejpam-4136	251	44	x0	x0	PROPN
ejpam-4136	251	45	,	,	PUNCT
ejpam-4136	251	46	r	r	NOUN
ejpam-4136	251	47	)	)	PUNCT
ejpam-4136	251	48	,	,	PUNCT
ejpam-4136	251	49	(	(	PUNCT
ejpam-4136	251	50	ii	ii	NOUN
ejpam-4136	251	51	)	)	PUNCT
ejpam-4136	251	52	if	if	SCONJ
ejpam-4136	251	53	y	y	PROPN
ejpam-4136	251	54	∈	∈	PROPN
ejpam-4136	251	55	bγ(αn	bγ(αn	NOUN
ejpam-4136	251	56	,	,	PUNCT
ejpam-4136	251	57	βn	βn	NOUN
ejpam-4136	251	58	)	)	PUNCT
ejpam-4136	251	59	(	(	PUNCT
ejpam-4136	251	60	x0	x0	PROPN
ejpam-4136	251	61	,	,	PUNCT
ejpam-4136	251	62	r	r	NOUN
ejpam-4136	251	63	)	)	PUNCT
ejpam-4136	251	64	,	,	PUNCT
ejpam-4136	251	65	then	then	ADV
ejpam-4136	251	66	there	there	PRON
ejpam-4136	251	67	exists	exist	VERB
ejpam-4136	251	68	,	,	PUNCT
ejpam-4136	251	69	δ	δ	PROPN
ejpam-4136	251	70	≻	≻	PRON
ejpam-4136	251	71	0a	0a	VERB
ejpam-4136	251	72	such	such	ADJ
ejpam-4136	251	73	that	that	DET
ejpam-4136	251	74	bγ(αn	bγ(αn	NOUN
ejpam-4136	251	75	,	,	PUNCT
ejpam-4136	251	76	βn	βn	NOUN
ejpam-4136	251	77	)	)	PUNCT
ejpam-4136	251	78	(	(	PUNCT
ejpam-4136	251	79	y	y	PROPN
ejpam-4136	251	80	,	,	PUNCT
ejpam-4136	251	81	δ	δ	PROPN
ejpam-4136	251	82	)	)	PUNCT
ejpam-4136	251	83	⊆	⊆	NUM
ejpam-4136	251	84	bγ(αn	bγ(αn	NOUN
ejpam-4136	251	85	,	,	PUNCT
ejpam-4136	251	86	βn	βn	NOUN
ejpam-4136	251	87	)	)	PUNCT
ejpam-4136	251	88	(	(	PUNCT
ejpam-4136	251	89	x0	x0	PROPN
ejpam-4136	251	90	,	,	PUNCT
ejpam-4136	251	91	r	r	NOUN
ejpam-4136	251	92	)	)	PUNCT
ejpam-4136	251	93	.	.	PUNCT
ejpam-4136	252	1	proposition	proposition	NOUN
ejpam-4136	252	2	14	14	NUM
ejpam-4136	252	3	.	.	PUNCT
ejpam-4136	253	1	the	the	DET
ejpam-4136	253	2	set	set	NOUN
ejpam-4136	253	3	of	of	ADP
ejpam-4136	253	4	all	all	DET
ejpam-4136	253	5	γ(αn	γ(αn	PROPN
ejpam-4136	253	6	,	,	PUNCT
ejpam-4136	253	7	βn)-balls	βn)-ball	NOUN
ejpam-4136	253	8	,	,	PUNCT
ejpam-4136	253	9	bn	bn	NOUN
ejpam-4136	253	10	=	=	SYM
ejpam-4136	253	11	{	{	PUNCT
ejpam-4136	253	12	bγ(αn	bγ(αn	NOUN
ejpam-4136	253	13	,	,	PUNCT
ejpam-4136	253	14	βn	βn	NOUN
ejpam-4136	253	15	)	)	PUNCT
ejpam-4136	253	16	(	(	PUNCT
ejpam-4136	253	17	x	x	X
ejpam-4136	253	18	,	,	PUNCT
ejpam-4136	253	19	r	r	NOUN
ejpam-4136	253	20	)	)	PUNCT
ejpam-4136	253	21	:	:	PUNCT
ejpam-4136	254	1	x	x	PUNCT
ejpam-4136	254	2	∈	∈	NOUN
ejpam-4136	254	3	x	x	X
ejpam-4136	254	4	,	,	PUNCT
ejpam-4136	254	5	r	r	NOUN
ejpam-4136	254	6	>	>	X
ejpam-4136	254	7	0	0	NUM
ejpam-4136	254	8	}	}	PUNCT
ejpam-4136	254	9	,	,	PUNCT
ejpam-4136	254	10	forms	form	VERB
ejpam-4136	254	11	a	a	DET
ejpam-4136	254	12	basis	basis	NOUN
ejpam-4136	254	13	for	for	ADP
ejpam-4136	254	14	a	a	DET
ejpam-4136	254	15	topology	topology	NOUN
ejpam-4136	254	16	t	t	NOUN
ejpam-4136	254	17	(	(	PUNCT
ejpam-4136	254	18	γ(αn	γ(αn	VERB
ejpam-4136	254	19	,	,	PUNCT
ejpam-4136	254	20	βn	βn	NOUN
ejpam-4136	254	21	)	)	PUNCT
ejpam-4136	254	22	)	)	PUNCT
ejpam-4136	254	23	on	on	ADP
ejpam-4136	254	24	x.	x.	NOUN
ejpam-4136	254	25	definition	definition	NOUN
ejpam-4136	254	26	10	10	NUM
ejpam-4136	254	27	.	.	PUNCT
ejpam-4136	255	1	let	let	AUX
ejpam-4136	255	2	(	(	PUNCT
ejpam-4136	255	3	x	x	X
ejpam-4136	255	4	,	,	PUNCT
ejpam-4136	255	5	γ(αn	γ(αn	VERB
ejpam-4136	255	6	,	,	PUNCT
ejpam-4136	255	7	βn	βn	NOUN
ejpam-4136	255	8	)	)	PUNCT
ejpam-4136	255	9	)	)	PUNCT
ejpam-4136	255	10	be	be	AUX
ejpam-4136	255	11	a	a	DET
ejpam-4136	255	12	b(αn	b(αn	NOUN
ejpam-4136	255	13	,	,	PUNCT
ejpam-4136	255	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	255	15	space	space	NOUN
ejpam-4136	255	16	over	over	ADP
ejpam-4136	255	17	banach	banach	NOUN
ejpam-4136	255	18	algebra	algebra	NOUN
ejpam-4136	255	19	a.	a.	NOUN
ejpam-4136	255	20	the	the	DET
ejpam-4136	255	21	sequence	sequence	NOUN
ejpam-4136	255	22	{	{	PUNCT
ejpam-4136	255	23	xn	xn	NOUN
ejpam-4136	255	24	}	}	PUNCT
ejpam-4136	255	25	⊆	⊆	NUM
ejpam-4136	255	26	x	x	NOUN
ejpam-4136	255	27	is	be	AUX
ejpam-4136	255	28	b(αn	b(αn	NOUN
ejpam-4136	255	29	,	,	PUNCT
ejpam-4136	255	30	βn)-convergent	βn)-convergent	NOUN
ejpam-4136	255	31	to	to	ADP
ejpam-4136	255	32	x	x	PRON
ejpam-4136	255	33	if	if	SCONJ
ejpam-4136	255	34	it	it	PRON
ejpam-4136	255	35	b(αn	b(αn	VERB
ejpam-4136	255	36	,	,	PUNCT
ejpam-4136	255	37	βn)-converges	βn)-converge	VERB
ejpam-4136	255	38	to	to	ADP
ejpam-4136	255	39	x	x	PUNCT
ejpam-4136	255	40	in	in	ADP
ejpam-4136	255	41	the	the	DET
ejpam-4136	255	42	b(αn	b(αn	NOUN
ejpam-4136	255	43	,	,	PUNCT
ejpam-4136	255	44	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	255	45	topology	topology	NOUN
ejpam-4136	255	46	over	over	ADP
ejpam-4136	255	47	banach	banach	NOUN
ejpam-4136	255	48	algebra	algebra	NOUN
ejpam-4136	255	49	a	a	PRON
ejpam-4136	255	50	,	,	PUNCT
ejpam-4136	255	51	t	t	PROPN
ejpam-4136	255	52	(	(	PUNCT
ejpam-4136	255	53	γ(αn	γ(αn	VERB
ejpam-4136	255	54	,	,	PUNCT
ejpam-4136	255	55	βn	βn	NOUN
ejpam-4136	255	56	)	)	PUNCT
ejpam-4136	255	57	)	)	PUNCT
ejpam-4136	255	58	.	.	PUNCT
ejpam-4136	256	1	a.	a.	PROPN
ejpam-4136	256	2	d.nezhad	d.nezhad	PROPN
ejpam-4136	256	3	,	,	PUNCT
ejpam-4136	256	4	s.	s.	PROPN
ejpam-4136	256	5	radenović	radenović	PROPN
ejpam-4136	256	6	/	/	SYM
ejpam-4136	256	7	eur	eur	PROPN
ejpam-4136	256	8	.	.	PUNCT
ejpam-4136	257	1	j.	j.	PROPN
ejpam-4136	257	2	pure	pure	PROPN
ejpam-4136	257	3	appl	appl	PROPN
ejpam-4136	257	4	.	.	PROPN
ejpam-4136	257	5	math	math	PROPN
ejpam-4136	257	6	,	,	PUNCT
ejpam-4136	257	7	14	14	NUM
ejpam-4136	257	8	(	(	PUNCT
ejpam-4136	257	9	4	4	NUM
ejpam-4136	257	10	)	)	PUNCT
ejpam-4136	257	11	(	(	PUNCT
ejpam-4136	257	12	2021	2021	NUM
ejpam-4136	257	13	)	)	PUNCT
ejpam-4136	257	14	,	,	PUNCT
ejpam-4136	257	15	1148	1148	NUM
ejpam-4136	257	16	-	-	SYM
ejpam-4136	257	17	1160	1160	NUM
ejpam-4136	257	18	1156	1156	NUM
ejpam-4136	257	19	proposition	proposition	NOUN
ejpam-4136	257	20	15	15	NUM
ejpam-4136	257	21	.	.	PUNCT
ejpam-4136	258	1	let	let	AUX
ejpam-4136	258	2	(	(	PUNCT
ejpam-4136	258	3	x	x	X
ejpam-4136	258	4	,	,	PUNCT
ejpam-4136	258	5	γ(αn	γ(αn	VERB
ejpam-4136	258	6	,	,	PUNCT
ejpam-4136	258	7	βn	βn	NOUN
ejpam-4136	258	8	)	)	PUNCT
ejpam-4136	258	9	)	)	PUNCT
ejpam-4136	258	10	be	be	AUX
ejpam-4136	258	11	a	a	DET
ejpam-4136	258	12	b(αn	b(αn	NOUN
ejpam-4136	258	13	,	,	PUNCT
ejpam-4136	258	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	258	15	space	space	NOUN
ejpam-4136	258	16	over	over	ADP
ejpam-4136	258	17	banach	banach	NOUN
ejpam-4136	258	18	algebra	algebra	NOUN
ejpam-4136	258	19	a.	a.	NOUN
ejpam-4136	258	20	then	then	ADV
ejpam-4136	258	21	for	for	ADP
ejpam-4136	258	22	a	a	DET
ejpam-4136	258	23	sequence	sequence	NOUN
ejpam-4136	258	24	{	{	PUNCT
ejpam-4136	258	25	xm	xm	NOUN
ejpam-4136	258	26	}	}	PUNCT
ejpam-4136	258	27	⊆	⊆	NUM
ejpam-4136	258	28	x	x	NOUN
ejpam-4136	258	29	,	,	PUNCT
ejpam-4136	258	30	and	and	CCONJ
ejpam-4136	258	31	a	a	DET
ejpam-4136	258	32	point	point	NOUN
ejpam-4136	258	33	x	x	X
ejpam-4136	258	34	∈	∈	NOUN
ejpam-4136	258	35	x	x	PUNCT
ejpam-4136	258	36	the	the	DET
ejpam-4136	258	37	following	follow	VERB
ejpam-4136	258	38	are	be	AUX
ejpam-4136	258	39	equivalent	equivalent	ADJ
ejpam-4136	258	40	:	:	PUNCT
ejpam-4136	258	41	(	(	PUNCT
ejpam-4136	258	42	1	1	X
ejpam-4136	258	43	)	)	PUNCT
ejpam-4136	258	44	{	{	PUNCT
ejpam-4136	258	45	xm	xm	NOUN
ejpam-4136	258	46	}	}	PUNCT
ejpam-4136	258	47	is	be	AUX
ejpam-4136	258	48	γ(αn	γ(αn	PROPN
ejpam-4136	258	49	,	,	PUNCT
ejpam-4136	258	50	βn)-convergent	βn)-convergent	ADJ
ejpam-4136	258	51	to	to	ADP
ejpam-4136	258	52	x	x	PRON
ejpam-4136	258	53	,	,	PUNCT
ejpam-4136	258	54	(	(	PUNCT
ejpam-4136	258	55	2	2	X
ejpam-4136	258	56	)	)	PUNCT
ejpam-4136	258	57	γ(αn	γ(αn	PROPN
ejpam-4136	258	58	,	,	PUNCT
ejpam-4136	258	59	βn)((xm)n−1	βn)((xm)n−1	PROPN
ejpam-4136	258	60	1	1	NUM
ejpam-4136	258	61	,	,	PUNCT
ejpam-4136	258	62	x	x	NOUN
ejpam-4136	258	63	)	)	PUNCT
ejpam-4136	258	64	→	→	SYM
ejpam-4136	258	65	0	0	NUM
ejpam-4136	258	66	,	,	PUNCT
ejpam-4136	258	67	(	(	PUNCT
ejpam-4136	258	68	3	3	X
ejpam-4136	258	69	)	)	PUNCT
ejpam-4136	258	70	γ(αn	γ(αn	VERB
ejpam-4136	258	71	,	,	PUNCT
ejpam-4136	258	72	βn)(xm	βn)(xm	PRON
ejpam-4136	258	73	,	,	PUNCT
ejpam-4136	258	74	(	(	PUNCT
ejpam-4136	258	75	x	x	X
ejpam-4136	258	76	)	)	PUNCT
ejpam-4136	258	77	n	n	PRON
ejpam-4136	258	78	2	2	NUM
ejpam-4136	258	79	)	)	PUNCT
ejpam-4136	258	80	→	→	SYM
ejpam-4136	258	81	0	0	X
ejpam-4136	258	82	.	.	PUNCT
ejpam-4136	258	83	definition	definition	NOUN
ejpam-4136	258	84	11	11	NUM
ejpam-4136	258	85	.	.	PUNCT
ejpam-4136	259	1	let	let	VERB
ejpam-4136	259	2	(	(	PUNCT
ejpam-4136	259	3	x	x	X
ejpam-4136	259	4	,	,	PUNCT
ejpam-4136	259	5	γ(αn	γ(αn	VERB
ejpam-4136	259	6	,	,	PUNCT
ejpam-4136	259	7	βn	βn	NOUN
ejpam-4136	259	8	)	)	PUNCT
ejpam-4136	259	9	)	)	PUNCT
ejpam-4136	259	10	,	,	PUNCT
ejpam-4136	259	11	(	(	PUNCT
ejpam-4136	259	12	y	y	X
ejpam-4136	259	13	,	,	PUNCT
ejpam-4136	259	14	γ	γ	X
ejpam-4136	259	15	′	′	NUM
ejpam-4136	259	16	(	(	PUNCT
ejpam-4136	259	17	αm	αm	INTJ
ejpam-4136	259	18	,	,	PUNCT
ejpam-4136	259	19	βm	βm	VERB
ejpam-4136	259	20	)	)	PUNCT
ejpam-4136	259	21	)	)	PUNCT
ejpam-4136	259	22	be	be	AUX
ejpam-4136	259	23	universal	universal	ADJ
ejpam-4136	259	24	hypermetric	hypermetric	ADJ
ejpam-4136	259	25	spaces	space	NOUN
ejpam-4136	259	26	of	of	ADP
ejpam-4136	259	27	dimension	dimension	NOUN
ejpam-4136	259	28	n	n	CCONJ
ejpam-4136	259	29	,	,	PUNCT
ejpam-4136	259	30	m	m	VERB
ejpam-4136	259	31	respectively	respectively	ADV
ejpam-4136	259	32	over	over	ADP
ejpam-4136	259	33	banach	banach	NOUN
ejpam-4136	259	34	algebra	algebra	NOUN
ejpam-4136	259	35	a.	a.	NOUN
ejpam-4136	259	36	a	a	DET
ejpam-4136	259	37	function	function	NOUN
ejpam-4136	259	38	t	t	NOUN
ejpam-4136	259	39	:	:	PUNCT
ejpam-4136	259	40	x	x	PUNCT
ejpam-4136	259	41	−→	−→	NOUN
ejpam-4136	259	42	y	y	PROPN
ejpam-4136	259	43	is	be	AUX
ejpam-4136	259	44	b(αn	b(αn	NOUN
ejpam-4136	259	45	,	,	PUNCT
ejpam-4136	259	46	βn),(αm	βn),(αm	NUM
ejpam-4136	259	47	,	,	PUNCT
ejpam-4136	259	48	βm)continuous	βm)continuous	ADJ
ejpam-4136	259	49	at	at	ADP
ejpam-4136	259	50	point	point	NOUN
ejpam-4136	259	51	x0	x0	PROPN
ejpam-4136	259	52	∈	∈	PROPN
ejpam-4136	260	1	x	x	X
ejpam-4136	260	2	,	,	PUNCT
ejpam-4136	260	3	if	if	SCONJ
ejpam-4136	260	4	t−1(b	t−1(b	PROPN
ejpam-4136	260	5	γ	γ	X
ejpam-4136	260	6	′	′	NUM
ejpam-4136	260	7	(	(	PUNCT
ejpam-4136	260	8	αm	αm	INTJ
ejpam-4136	260	9	,	,	PUNCT
ejpam-4136	260	10	βm	βm	VERB
ejpam-4136	260	11	)	)	PUNCT
ejpam-4136	260	12	(	(	PUNCT
ejpam-4136	260	13	t	t	PROPN
ejpam-4136	260	14	(	(	PUNCT
ejpam-4136	260	15	x0	x0	PROPN
ejpam-4136	260	16	)	)	PUNCT
ejpam-4136	260	17	,	,	PUNCT
ejpam-4136	260	18	r	r	NOUN
ejpam-4136	260	19	)	)	PUNCT
ejpam-4136	260	20	)	)	PUNCT
ejpam-4136	261	1	∈	∈	PROPN
ejpam-4136	261	2	t	t	PROPN
ejpam-4136	261	3	(	(	PUNCT
ejpam-4136	261	4	un	un	PROPN
ejpam-4136	261	5	)	)	PUNCT
ejpam-4136	261	6	,	,	PUNCT
ejpam-4136	261	7	for	for	ADP
ejpam-4136	261	8	all	all	DET
ejpam-4136	261	9	r	r	NOUN
ejpam-4136	261	10	>	>	X
ejpam-4136	261	11	0	0	NUM
ejpam-4136	261	12	.	.	PUNCT
ejpam-4136	262	1	we	we	PRON
ejpam-4136	262	2	say	say	VERB
ejpam-4136	262	3	f	f	PROPN
ejpam-4136	262	4	is	be	AUX
ejpam-4136	262	5	b(αn	b(αn	PROPN
ejpam-4136	262	6	,	,	PUNCT
ejpam-4136	262	7	βn),(αm	βn),(αm	NUM
ejpam-4136	262	8	,	,	PUNCT
ejpam-4136	262	9	βm)-continuous	βm)-continuous	ADJ
ejpam-4136	262	10	if	if	SCONJ
ejpam-4136	262	11	it	it	PRON
ejpam-4136	262	12	is	be	AUX
ejpam-4136	262	13	b(αn	b(αn	NOUN
ejpam-4136	262	14	,	,	PUNCT
ejpam-4136	262	15	βn),(αm	βn),(αm	NUM
ejpam-4136	262	16	,	,	PUNCT
ejpam-4136	262	17	βm)-continuous	βm)-continuous	ADJ
ejpam-4136	262	18	at	at	ADP
ejpam-4136	262	19	all	all	DET
ejpam-4136	262	20	points	point	NOUN
ejpam-4136	262	21	of	of	ADP
ejpam-4136	262	22	x	x	PRON
ejpam-4136	262	23	;	;	PUNCT
ejpam-4136	262	24	that	that	PRON
ejpam-4136	262	25	is	is	ADV
ejpam-4136	262	26	,	,	PUNCT
ejpam-4136	262	27	continuous	continuous	ADJ
ejpam-4136	262	28	as	as	ADP
ejpam-4136	262	29	a	a	DET
ejpam-4136	262	30	function	function	NOUN
ejpam-4136	262	31	from	from	ADP
ejpam-4136	262	32	x	x	PUNCT
ejpam-4136	262	33	with	with	ADP
ejpam-4136	262	34	the	the	DET
ejpam-4136	262	35	t	t	NOUN
ejpam-4136	262	36	(	(	PUNCT
ejpam-4136	262	37	γ(αn	γ(αn	PROPN
ejpam-4136	262	38	,	,	PUNCT
ejpam-4136	262	39	βn))-topology	βn))-topology	NOUN
ejpam-4136	262	40	to	to	ADP
ejpam-4136	262	41	y	y	PROPN
ejpam-4136	262	42	with	with	ADP
ejpam-4136	262	43	the	the	DET
ejpam-4136	262	44	t	t	PROPN
ejpam-4136	262	45	(	(	PUNCT
ejpam-4136	262	46	γ	γ	PROPN
ejpam-4136	262	47	′	′	NUM
ejpam-4136	262	48	(	(	PUNCT
ejpam-4136	262	49	αm	αm	INTJ
ejpam-4136	262	50	,	,	PUNCT
ejpam-4136	262	51	βm))-topology	βm))-topology	NOUN
ejpam-4136	262	52	.	.	PUNCT
ejpam-4136	263	1	in	in	ADP
ejpam-4136	263	2	the	the	DET
ejpam-4136	263	3	sequel	sequel	NOUN
ejpam-4136	263	4	,	,	PUNCT
ejpam-4136	263	5	for	for	ADP
ejpam-4136	263	6	simplicity	simplicity	NOUN
ejpam-4136	263	7	we	we	PRON
ejpam-4136	263	8	have	have	AUX
ejpam-4136	263	9	assume	assume	VERB
ejpam-4136	263	10	that	that	SCONJ
ejpam-4136	263	11	n	n	NOUN
ejpam-4136	263	12	=	=	PUNCT
ejpam-4136	263	13	m.	m.	NOUN
ejpam-4136	263	14	since	since	SCONJ
ejpam-4136	263	15	b(αn	b(αn	NOUN
ejpam-4136	263	16	,	,	PUNCT
ejpam-4136	263	17	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	263	18	topologies	topology	NOUN
ejpam-4136	263	19	are	be	AUX
ejpam-4136	263	20	metric	metric	ADJ
ejpam-4136	263	21	topologies	topology	NOUN
ejpam-4136	263	22	we	we	PRON
ejpam-4136	263	23	have	have	VERB
ejpam-4136	263	24	:	:	PUNCT
ejpam-4136	263	25	definition	definition	NOUN
ejpam-4136	263	26	12	12	NUM
ejpam-4136	263	27	.	.	PUNCT
ejpam-4136	264	1	let	let	VERB
ejpam-4136	264	2	(	(	PUNCT
ejpam-4136	264	3	x	x	X
ejpam-4136	264	4	,	,	PUNCT
ejpam-4136	264	5	γ(αn	γ(αn	VERB
ejpam-4136	264	6	,	,	PUNCT
ejpam-4136	264	7	βn	βn	NOUN
ejpam-4136	264	8	)	)	PUNCT
ejpam-4136	264	9	)	)	PUNCT
ejpam-4136	265	1	and	and	CCONJ
ejpam-4136	265	2	(	(	PUNCT
ejpam-4136	265	3	y	y	PROPN
ejpam-4136	265	4	,	,	PUNCT
ejpam-4136	265	5	γ	γ	X
ejpam-4136	265	6	′	′	NUM
ejpam-4136	265	7	(	(	PUNCT
ejpam-4136	265	8	αn	αn	NOUN
ejpam-4136	265	9	,	,	PUNCT
ejpam-4136	265	10	βn	βn	NOUN
ejpam-4136	265	11	)	)	PUNCT
ejpam-4136	265	12	)	)	PUNCT
ejpam-4136	265	13	be	be	AUX
ejpam-4136	265	14	two	two	NUM
ejpam-4136	265	15	b(αn	b(αn	NOUN
ejpam-4136	265	16	,	,	PUNCT
ejpam-4136	265	17	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	265	18	spaces	space	NOUN
ejpam-4136	265	19	over	over	ADP
ejpam-4136	265	20	banach	banach	NOUN
ejpam-4136	265	21	algebra	algebra	NOUN
ejpam-4136	265	22	a	a	PRON
ejpam-4136	265	23	and	and	CCONJ
ejpam-4136	265	24	t	t	NOUN
ejpam-4136	265	25	:	:	PUNCT
ejpam-4136	265	26	(	(	PUNCT
ejpam-4136	265	27	x	x	X
ejpam-4136	265	28	,	,	PUNCT
ejpam-4136	265	29	γ(αn	γ(αn	VERB
ejpam-4136	265	30	,	,	PUNCT
ejpam-4136	265	31	βn	βn	NOUN
ejpam-4136	265	32	)	)	PUNCT
ejpam-4136	265	33	)	)	PUNCT
ejpam-4136	266	1	→	→	PUNCT
ejpam-4136	266	2	(	(	PUNCT
ejpam-4136	266	3	y	y	PROPN
ejpam-4136	266	4	,	,	PUNCT
ejpam-4136	266	5	γ	γ	X
ejpam-4136	266	6	′	′	NUM
ejpam-4136	266	7	(	(	PUNCT
ejpam-4136	266	8	αn	αn	NOUN
ejpam-4136	266	9	,	,	PUNCT
ejpam-4136	266	10	βn	βn	NOUN
ejpam-4136	266	11	)	)	PUNCT
ejpam-4136	266	12	)	)	PUNCT
ejpam-4136	266	13	be	be	AUX
ejpam-4136	266	14	a	a	DET
ejpam-4136	266	15	function	function	NOUN
ejpam-4136	266	16	.	.	PUNCT
ejpam-4136	267	1	the	the	DET
ejpam-4136	267	2	function	function	NOUN
ejpam-4136	267	3	f	f	PROPN
ejpam-4136	267	4	is	be	AUX
ejpam-4136	267	5	called	call	VERB
ejpam-4136	267	6	b(αn	b(αn	NOUN
ejpam-4136	267	7	,	,	PUNCT
ejpam-4136	267	8	βn)-continuous	βn)-continuous	ADJ
ejpam-4136	267	9	at	at	ADP
ejpam-4136	267	10	a	a	DET
ejpam-4136	267	11	point	point	NOUN
ejpam-4136	267	12	a	a	DET
ejpam-4136	267	13	∈	∈	NOUN
ejpam-4136	267	14	x	x	PUNCT
ejpam-4136	267	15	if	if	SCONJ
ejpam-4136	267	16	and	and	CCONJ
ejpam-4136	267	17	only	only	ADV
ejpam-4136	267	18	if	if	SCONJ
ejpam-4136	267	19	,	,	PUNCT
ejpam-4136	267	20	for	for	ADP
ejpam-4136	267	21	given	give	VERB
ejpam-4136	267	22	ϵ	ϵ	PROPN
ejpam-4136	267	23	≻	≻	PROPN
ejpam-4136	267	24	0a	0a	PROPN
ejpam-4136	267	25	,	,	PUNCT
ejpam-4136	267	26	there	there	PRON
ejpam-4136	267	27	exists	exist	VERB
ejpam-4136	267	28	δ	δ	PROPN
ejpam-4136	267	29	≻	≻	PUNCT
ejpam-4136	267	30	0a	0a	VERB
ejpam-4136	267	31	such	such	ADJ
ejpam-4136	267	32	that	that	SCONJ
ejpam-4136	267	33	x1	x1	PROPN
ejpam-4136	267	34	,	,	PUNCT
ejpam-4136	267	35	.	.	PUNCT
ejpam-4136	267	36	.	.	PUNCT
ejpam-4136	268	1	.	.	PUNCT
ejpam-4136	269	1	,	,	PUNCT
ejpam-4136	269	2	xn−1	xn−1	PROPN
ejpam-4136	269	3	∈	∈	PROPN
ejpam-4136	269	4	x	x	X
ejpam-4136	269	5	and	and	CCONJ
ejpam-4136	269	6	the	the	DET
ejpam-4136	269	7	subset	subset	NOUN
ejpam-4136	269	8	relation	relation	NOUN
ejpam-4136	269	9	γ(αn	γ(αn	VERB
ejpam-4136	269	10	,	,	PUNCT
ejpam-4136	269	11	βn)(a	βn)(a	PROPN
ejpam-4136	269	12	,	,	PUNCT
ejpam-4136	269	13	(	(	PUNCT
ejpam-4136	269	14	xi	xi	NOUN
ejpam-4136	269	15	)	)	PUNCT
ejpam-4136	269	16	n−1	n−1	PROPN
ejpam-4136	269	17	i=1	i=1	PROPN
ejpam-4136	269	18	)	)	PUNCT
ejpam-4136	270	1	⊆	⊆	X
ejpam-4136	270	2	{	{	PUNCT
ejpam-4136	270	3	a	a	DET
ejpam-4136	270	4	∈	∈	PROPN
ejpam-4136	270	5	a|0a	a|0a	NOUN
ejpam-4136	270	6	⪯	⪯	NOUN
ejpam-4136	270	7	a	a	DET
ejpam-4136	270	8	≺	≺	NOUN
ejpam-4136	270	9	δ	δ	PROPN
ejpam-4136	270	10	}	}	PUNCT
ejpam-4136	270	11	implies	imply	VERB
ejpam-4136	270	12	that	that	SCONJ
ejpam-4136	270	13	γ	γ	PROPN
ejpam-4136	270	14	′	′	NUM
ejpam-4136	270	15	(	(	PUNCT
ejpam-4136	270	16	αn	αn	NOUN
ejpam-4136	270	17	,	,	PUNCT
ejpam-4136	270	18	βn	βn	NOUN
ejpam-4136	270	19	)	)	PUNCT
ejpam-4136	270	20	(	(	PUNCT
ejpam-4136	270	21	t	t	PROPN
ejpam-4136	270	22	(	(	PUNCT
ejpam-4136	270	23	a	a	NOUN
ejpam-4136	270	24	)	)	PUNCT
ejpam-4136	270	25	,	,	PUNCT
ejpam-4136	270	26	(	(	PUNCT
ejpam-4136	270	27	t	t	PROPN
ejpam-4136	270	28	(	(	PUNCT
ejpam-4136	270	29	xi	xi	NOUN
ejpam-4136	270	30	)	)	PUNCT
ejpam-4136	270	31	)	)	PUNCT
ejpam-4136	271	1	n−1	n−1	PROPN
ejpam-4136	271	2	i=1	i=1	PROPN
ejpam-4136	271	3	)	)	PUNCT
ejpam-4136	272	1	⊆	⊆	X
ejpam-4136	272	2	{	{	PUNCT
ejpam-4136	272	3	a	a	DET
ejpam-4136	272	4	∈	∈	PROPN
ejpam-4136	272	5	a|0a	a|0a	NOUN
ejpam-4136	272	6	⪯	⪯	NOUN
ejpam-4136	272	7	a	a	DET
ejpam-4136	272	8	≺	≺	NOUN
ejpam-4136	272	9	ϵ	ϵ	NOUN
ejpam-4136	272	10	}	}	PUNCT
ejpam-4136	272	11	.	.	PUNCT
ejpam-4136	273	1	a	a	DET
ejpam-4136	273	2	function	function	NOUN
ejpam-4136	273	3	f	f	PROPN
ejpam-4136	273	4	is	be	AUX
ejpam-4136	273	5	b(αn	b(αn	NOUN
ejpam-4136	273	6	,	,	PUNCT
ejpam-4136	273	7	βn)-continuous	βn)-continuous	ADJ
ejpam-4136	273	8	on	on	ADP
ejpam-4136	273	9	x	x	SYM
ejpam-4136	273	10	if	if	SCONJ
ejpam-4136	273	11	and	and	CCONJ
ejpam-4136	273	12	only	only	ADV
ejpam-4136	273	13	if	if	SCONJ
ejpam-4136	273	14	it	it	PRON
ejpam-4136	273	15	is	be	AUX
ejpam-4136	273	16	b(αn	b(αn	NOUN
ejpam-4136	273	17	,	,	PUNCT
ejpam-4136	273	18	βn)-continuous	βn)-continuous	ADJ
ejpam-4136	273	19	at	at	ADP
ejpam-4136	273	20	all	all	DET
ejpam-4136	273	21	a	a	DET
ejpam-4136	273	22	∈	∈	NOUN
ejpam-4136	273	23	x	x	SYM
ejpam-4136	273	24	proposition	proposition	NOUN
ejpam-4136	273	25	16	16	NUM
ejpam-4136	273	26	.	.	PUNCT
ejpam-4136	274	1	let	let	VERB
ejpam-4136	274	2	(	(	PUNCT
ejpam-4136	274	3	x	x	X
ejpam-4136	274	4	,	,	PUNCT
ejpam-4136	274	5	γ(αn	γ(αn	VERB
ejpam-4136	274	6	,	,	PUNCT
ejpam-4136	274	7	βn	βn	NOUN
ejpam-4136	274	8	)	)	PUNCT
ejpam-4136	274	9	)	)	PUNCT
ejpam-4136	274	10	,	,	PUNCT
ejpam-4136	274	11	(	(	PUNCT
ejpam-4136	274	12	y	y	X
ejpam-4136	274	13	,	,	PUNCT
ejpam-4136	274	14	γ	γ	X
ejpam-4136	274	15	′	′	NUM
ejpam-4136	274	16	(	(	PUNCT
ejpam-4136	274	17	αn	αn	NOUN
ejpam-4136	274	18	,	,	PUNCT
ejpam-4136	274	19	βn	βn	NOUN
ejpam-4136	274	20	)	)	PUNCT
ejpam-4136	274	21	)	)	PUNCT
ejpam-4136	274	22	be	be	AUX
ejpam-4136	274	23	b(αn	b(αn	NOUN
ejpam-4136	274	24	,	,	PUNCT
ejpam-4136	274	25	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	274	26	spaces	space	NOUN
ejpam-4136	274	27	over	over	ADP
ejpam-4136	274	28	banach	banach	NOUN
ejpam-4136	274	29	algebra	algebra	NOUN
ejpam-4136	274	30	a.	a.	NOUN
ejpam-4136	274	31	a	a	DET
ejpam-4136	274	32	function	function	NOUN
ejpam-4136	274	33	t	t	NOUN
ejpam-4136	274	34	:	:	PUNCT
ejpam-4136	274	35	x	x	PUNCT
ejpam-4136	274	36	−→	−→	NOUN
ejpam-4136	274	37	y	y	PROPN
ejpam-4136	274	38	is	be	AUX
ejpam-4136	274	39	b(αn	b(αn	NOUN
ejpam-4136	274	40	,	,	PUNCT
ejpam-4136	274	41	βn)-continuous	βn)-continuous	ADJ
ejpam-4136	274	42	at	at	ADP
ejpam-4136	274	43	point	point	NOUN
ejpam-4136	274	44	x	x	SYM
ejpam-4136	274	45	∈	∈	NOUN
ejpam-4136	274	46	x	x	INTJ
ejpam-4136	274	47	if	if	SCONJ
ejpam-4136	274	48	and	and	CCONJ
ejpam-4136	274	49	only	only	ADV
ejpam-4136	274	50	if	if	SCONJ
ejpam-4136	274	51	it	it	PRON
ejpam-4136	274	52	is	be	AUX
ejpam-4136	274	53	b(αn	b(αn	NOUN
ejpam-4136	274	54	,	,	PUNCT
ejpam-4136	274	55	βn)-sequentially	βn)-sequentially	ADV
ejpam-4136	274	56	continuous	continuous	ADJ
ejpam-4136	274	57	at	at	ADP
ejpam-4136	274	58	x	x	NOUN
ejpam-4136	274	59	;	;	PUNCT
ejpam-4136	274	60	that	that	PRON
ejpam-4136	274	61	is	is	ADV
ejpam-4136	274	62	,	,	PUNCT
ejpam-4136	274	63	whenever	whenever	SCONJ
ejpam-4136	274	64	{	{	PUNCT
ejpam-4136	274	65	xn	xn	X
ejpam-4136	274	66	}	}	PUNCT
ejpam-4136	274	67	is	be	AUX
ejpam-4136	274	68	b(αn	b(αn	NOUN
ejpam-4136	274	69	,	,	PUNCT
ejpam-4136	274	70	βn)-convergent	βn)-convergent	NOUN
ejpam-4136	274	71	to	to	ADP
ejpam-4136	274	72	x	x	PROPN
ejpam-4136	274	73	we	we	PRON
ejpam-4136	274	74	have	have	VERB
ejpam-4136	274	75	(	(	PUNCT
ejpam-4136	274	76	t	t	PROPN
ejpam-4136	274	77	(	(	PUNCT
ejpam-4136	274	78	xn	xn	PROPN
ejpam-4136	274	79	)	)	PUNCT
ejpam-4136	274	80	)	)	PUNCT
ejpam-4136	274	81	is	be	AUX
ejpam-4136	274	82	b(αn	b(αn	NOUN
ejpam-4136	274	83	,	,	PUNCT
ejpam-4136	274	84	βn)-convergent	βn)-convergent	NOUN
ejpam-4136	274	85	to	to	ADP
ejpam-4136	274	86	t	t	PROPN
ejpam-4136	274	87	(	(	PUNCT
ejpam-4136	274	88	x	x	NOUN
ejpam-4136	274	89	)	)	PUNCT
ejpam-4136	274	90	.	.	PUNCT
ejpam-4136	275	1	proposition	proposition	NOUN
ejpam-4136	275	2	17	17	NUM
ejpam-4136	275	3	.	.	PUNCT
ejpam-4136	276	1	let	let	AUX
ejpam-4136	276	2	(	(	PUNCT
ejpam-4136	276	3	x	x	X
ejpam-4136	276	4	,	,	PUNCT
ejpam-4136	276	5	γ(αn	γ(αn	VERB
ejpam-4136	276	6	,	,	PUNCT
ejpam-4136	276	7	βn	βn	NOUN
ejpam-4136	276	8	)	)	PUNCT
ejpam-4136	276	9	)	)	PUNCT
ejpam-4136	276	10	be	be	AUX
ejpam-4136	276	11	a	a	DET
ejpam-4136	276	12	b(αn	b(αn	NOUN
ejpam-4136	276	13	,	,	PUNCT
ejpam-4136	276	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	276	15	space	space	NOUN
ejpam-4136	276	16	over	over	ADP
ejpam-4136	276	17	banach	banach	NOUN
ejpam-4136	276	18	algebra	algebra	NOUN
ejpam-4136	276	19	a.	a.	NOUN
ejpam-4136	276	20	then	then	ADV
ejpam-4136	276	21	the	the	DET
ejpam-4136	276	22	function	function	NOUN
ejpam-4136	276	23	γ(αn	γ(αn	VERB
ejpam-4136	276	24	,	,	PUNCT
ejpam-4136	276	25	βn)(zi	βn)(zi	PUNCT
ejpam-4136	276	26	)	)	PUNCT
ejpam-4136	276	27	n	n	CCONJ
ejpam-4136	276	28	i=1	i=1	PROPN
ejpam-4136	276	29	is	be	AUX
ejpam-4136	276	30	jointly	jointly	ADV
ejpam-4136	276	31	b(αn	b(αn	NOUN
ejpam-4136	276	32	,	,	PUNCT
ejpam-4136	276	33	βn)-continuous	βn)-continuous	ADJ
ejpam-4136	276	34	in	in	ADP
ejpam-4136	276	35	all	all	DET
ejpam-4136	276	36	n	n	PRON
ejpam-4136	276	37	of	of	ADP
ejpam-4136	276	38	its	its	PRON
ejpam-4136	276	39	variables	variable	NOUN
ejpam-4136	276	40	.	.	PUNCT
ejpam-4136	277	1	definition	definition	NOUN
ejpam-4136	277	2	13	13	NUM
ejpam-4136	277	3	.	.	PUNCT
ejpam-4136	278	1	a	a	DET
ejpam-4136	278	2	map	map	NOUN
ejpam-4136	278	3	t	t	NOUN
ejpam-4136	278	4	:	:	PUNCT
ejpam-4136	278	5	x	x	PUNCT
ejpam-4136	278	6	−→	−→	NOUN
ejpam-4136	278	7	y	y	NOUN
ejpam-4136	278	8	between	between	ADP
ejpam-4136	278	9	b(αn	b(αn	PROPN
ejpam-4136	278	10	,	,	PUNCT
ejpam-4136	278	11	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	278	12	spaces	space	NOUN
ejpam-4136	278	13	(	(	PUNCT
ejpam-4136	278	14	x	x	X
ejpam-4136	278	15	,	,	PUNCT
ejpam-4136	278	16	γ(αn	γ(αn	VERB
ejpam-4136	278	17	,	,	PUNCT
ejpam-4136	278	18	βn	βn	NOUN
ejpam-4136	278	19	)	)	PUNCT
ejpam-4136	278	20	)	)	PUNCT
ejpam-4136	278	21	and	and	CCONJ
ejpam-4136	278	22	(	(	PUNCT
ejpam-4136	278	23	y	y	PROPN
ejpam-4136	278	24	,	,	PUNCT
ejpam-4136	278	25	γ	γ	X
ejpam-4136	278	26	′	′	NUM
ejpam-4136	278	27	(	(	PUNCT
ejpam-4136	278	28	αn	αn	NOUN
ejpam-4136	278	29	,	,	PUNCT
ejpam-4136	278	30	βn	βn	NOUN
ejpam-4136	278	31	)	)	PUNCT
ejpam-4136	278	32	)	)	PUNCT
ejpam-4136	278	33	over	over	ADP
ejpam-4136	278	34	banach	banach	NOUN
ejpam-4136	278	35	algebra	algebra	NOUN
ejpam-4136	278	36	a	a	PRON
ejpam-4136	278	37	,	,	PUNCT
ejpam-4136	278	38	is	be	AUX
ejpam-4136	278	39	an	an	DET
ejpam-4136	278	40	iso	iso	NOUN
ejpam-4136	278	41	-	-	PUNCT
ejpam-4136	278	42	hypermetry	hypermetry	NOUN
ejpam-4136	278	43	when	when	SCONJ
ejpam-4136	278	44	γ(αn	γ(αn	VERB
ejpam-4136	278	45	,	,	PUNCT
ejpam-4136	278	46	βn)(xi	βn)(xi	PUNCT
ejpam-4136	278	47	)	)	PUNCT
ejpam-4136	278	48	n	n	PRON
ejpam-4136	278	49	i=1	i=1	NOUN
ejpam-4136	278	50	=	=	NOUN
ejpam-4136	278	51	γ	γ	X
ejpam-4136	278	52	′	′	NUM
ejpam-4136	278	53	(	(	PUNCT
ejpam-4136	278	54	αn	αn	NOUN
ejpam-4136	278	55	,	,	PUNCT
ejpam-4136	278	56	βn	βn	NOUN
ejpam-4136	278	57	)	)	PUNCT
ejpam-4136	278	58	(	(	PUNCT
ejpam-4136	278	59	t	t	PROPN
ejpam-4136	278	60	(	(	PUNCT
ejpam-4136	278	61	xi	xi	NOUN
ejpam-4136	278	62	)	)	PUNCT
ejpam-4136	278	63	)	)	PUNCT
ejpam-4136	279	1	n	n	CCONJ
ejpam-4136	279	2	i=1	i=1	PROPN
ejpam-4136	279	3	for	for	ADP
ejpam-4136	279	4	all	all	DET
ejpam-4136	279	5	x1	x1	PROPN
ejpam-4136	279	6	,	,	PUNCT
ejpam-4136	279	7	.	.	PUNCT
ejpam-4136	279	8	.	.	PUNCT
ejpam-4136	279	9	.	.	PUNCT
ejpam-4136	280	1	,	,	PUNCT
ejpam-4136	280	2	xn	xn	PUNCT
ejpam-4136	280	3	∈	∈	PROPN
ejpam-4136	280	4	x.	x.	NOUN
ejpam-4136	281	1	if	if	SCONJ
ejpam-4136	281	2	the	the	DET
ejpam-4136	281	3	iso	iso	NOUN
ejpam-4136	281	4	-	-	PUNCT
ejpam-4136	281	5	b(αn	b(αn	NOUN
ejpam-4136	281	6	,	,	PUNCT
ejpam-4136	281	7	βn)-hypermetry	βn)-hypermetry	NOUN
ejpam-4136	281	8	is	be	AUX
ejpam-4136	281	9	injective	injective	ADJ
ejpam-4136	281	10	,	,	PUNCT
ejpam-4136	281	11	we	we	PRON
ejpam-4136	281	12	call	call	VERB
ejpam-4136	281	13	it	it	PRON
ejpam-4136	281	14	iso	iso	NOUN
ejpam-4136	281	15	-	-	PUNCT
ejpam-4136	281	16	b(αn	b(αn	NOUN
ejpam-4136	281	17	,	,	PUNCT
ejpam-4136	281	18	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	281	19	embedding	embed	VERB
ejpam-4136	281	20	over	over	ADP
ejpam-4136	281	21	banach	banach	NOUN
ejpam-4136	281	22	algebra	algebra	NOUN
ejpam-4136	281	23	a.	a.	NOUN
ejpam-4136	281	24	a	a	DET
ejpam-4136	281	25	bijective	bijective	ADJ
ejpam-4136	281	26	iso	iso	NOUN
ejpam-4136	281	27	-	-	PUNCT
ejpam-4136	281	28	b(αn	b(αn	NOUN
ejpam-4136	281	29	,	,	PUNCT
ejpam-4136	281	30	βn)hypermetry	βn)hypermetry	NOUN
ejpam-4136	281	31	is	be	AUX
ejpam-4136	281	32	called	call	VERB
ejpam-4136	281	33	a	a	DET
ejpam-4136	281	34	b(αn	b(αn	NOUN
ejpam-4136	281	35	,	,	PUNCT
ejpam-4136	281	36	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	281	37	isomorphism	isomorphism	NOUN
ejpam-4136	281	38	over	over	ADP
ejpam-4136	281	39	banach	banach	NOUN
ejpam-4136	281	40	algebra	algebra	NOUN
ejpam-4136	281	41	a.	a.	NOUN
ejpam-4136	281	42	2.3	2.3	NUM
ejpam-4136	281	43	.	.	PUNCT
ejpam-4136	282	1	fixed	fix	VERB
ejpam-4136	282	2	point	point	NOUN
ejpam-4136	282	3	theorem	theorem	VERB
ejpam-4136	282	4	in	in	ADP
ejpam-4136	282	5	b(αn	b(αn	NOUN
ejpam-4136	282	6	,	,	PUNCT
ejpam-4136	282	7	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	282	8	spaces	space	NOUN
ejpam-4136	282	9	over	over	ADP
ejpam-4136	282	10	banach	banach	NOUN
ejpam-4136	282	11	algebra	algebra	NOUN
ejpam-4136	282	12	a	a	PRON
ejpam-4136	282	13	in	in	ADP
ejpam-4136	282	14	a	a	DET
ejpam-4136	282	15	b(αn	b(αn	NOUN
ejpam-4136	282	16	,	,	PUNCT
ejpam-4136	282	17	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	282	18	space	space	NOUN
ejpam-4136	282	19	over	over	ADP
ejpam-4136	282	20	banach	banach	NOUN
ejpam-4136	282	21	algebra	algebra	NOUN
ejpam-4136	282	22	a	a	PRON
ejpam-4136	282	23	,	,	PUNCT
ejpam-4136	282	24	the	the	DET
ejpam-4136	282	25	concepts	concept	NOUN
ejpam-4136	282	26	of	of	ADP
ejpam-4136	282	27	basic	basic	ADJ
ejpam-4136	282	28	topological	topological	ADJ
ejpam-4136	282	29	notions	notion	NOUN
ejpam-4136	282	30	,	,	PUNCT
ejpam-4136	282	31	such	such	ADJ
ejpam-4136	282	32	as	as	ADP
ejpam-4136	282	33	:	:	PUNCT
ejpam-4136	282	34	b(αn	b(αn	NOUN
ejpam-4136	282	35	,	,	PUNCT
ejpam-4136	282	36	βn)-cauchy	βn)-cauchy	ADJ
ejpam-4136	282	37	sequence	sequence	NOUN
ejpam-4136	282	38	,	,	PUNCT
ejpam-4136	282	39	b(αn	b(αn	NOUN
ejpam-4136	282	40	,	,	PUNCT
ejpam-4136	282	41	βn)-convergent	βn)-convergent	NOUN
ejpam-4136	282	42	sequence	sequence	NOUN
ejpam-4136	282	43	and	and	CCONJ
ejpam-4136	282	44	b(αn	b(αn	NOUN
ejpam-4136	282	45	,	,	PUNCT
ejpam-4136	282	46	βn)complete	βn)complete	ADJ
ejpam-4136	282	47	b(αn	b(αn	NOUN
ejpam-4136	282	48	,	,	PUNCT
ejpam-4136	282	49	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	282	50	space	space	NOUN
ejpam-4136	282	51	over	over	ADP
ejpam-4136	282	52	banach	banach	NOUN
ejpam-4136	282	53	algebraa	algebraa	NOUN
ejpam-4136	282	54	can	can	AUX
ejpam-4136	282	55	be	be	AUX
ejpam-4136	282	56	easily	easily	ADV
ejpam-4136	282	57	adopted	adopt	VERB
ejpam-4136	282	58	as	as	ADP
ejpam-4136	282	59	under	under	ADV
ejpam-4136	282	60	.	.	PUNCT
ejpam-4136	283	1	a.	a.	PROPN
ejpam-4136	283	2	d.nezhad	d.nezhad	PROPN
ejpam-4136	283	3	,	,	PUNCT
ejpam-4136	283	4	s.	s.	PROPN
ejpam-4136	283	5	radenović	radenović	PROPN
ejpam-4136	283	6	/	/	SYM
ejpam-4136	283	7	eur	eur	PROPN
ejpam-4136	283	8	.	.	PUNCT
ejpam-4136	284	1	j.	j.	PROPN
ejpam-4136	284	2	pure	pure	PROPN
ejpam-4136	284	3	appl	appl	PROPN
ejpam-4136	284	4	.	.	PROPN
ejpam-4136	284	5	math	math	PROPN
ejpam-4136	284	6	,	,	PUNCT
ejpam-4136	284	7	14	14	NUM
ejpam-4136	284	8	(	(	PUNCT
ejpam-4136	284	9	4	4	NUM
ejpam-4136	284	10	)	)	PUNCT
ejpam-4136	284	11	(	(	PUNCT
ejpam-4136	284	12	2021	2021	NUM
ejpam-4136	284	13	)	)	PUNCT
ejpam-4136	284	14	,	,	PUNCT
ejpam-4136	284	15	1148	1148	NUM
ejpam-4136	284	16	-	-	SYM
ejpam-4136	284	17	1160	1160	NUM
ejpam-4136	284	18	1157	1157	NUM
ejpam-4136	284	19	we	we	PRON
ejpam-4136	284	20	discuss	discuss	VERB
ejpam-4136	284	21	about	about	ADP
ejpam-4136	284	22	concept	concept	NOUN
ejpam-4136	284	23	b(αn	b(αn	NOUN
ejpam-4136	284	24	,	,	PUNCT
ejpam-4136	284	25	βn)-completeness	βn)-completeness	NOUN
ejpam-4136	284	26	of	of	ADP
ejpam-4136	284	27	b(αn	b(αn	NOUN
ejpam-4136	284	28	,	,	PUNCT
ejpam-4136	284	29	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	284	30	spaces	space	NOUN
ejpam-4136	284	31	over	over	ADP
ejpam-4136	284	32	banach	banach	NOUN
ejpam-4136	284	33	algebra	algebra	NOUN
ejpam-4136	284	34	a.	a.	NOUN
ejpam-4136	284	35	definition	definition	NOUN
ejpam-4136	284	36	14	14	NUM
ejpam-4136	284	37	.	.	PUNCT
ejpam-4136	285	1	let	let	AUX
ejpam-4136	285	2	(	(	PUNCT
ejpam-4136	285	3	x	x	X
ejpam-4136	285	4	,	,	PUNCT
ejpam-4136	285	5	γ(αn	γ(αn	VERB
ejpam-4136	285	6	,	,	PUNCT
ejpam-4136	285	7	βn	βn	NOUN
ejpam-4136	285	8	)	)	PUNCT
ejpam-4136	285	9	)	)	PUNCT
ejpam-4136	285	10	be	be	AUX
ejpam-4136	285	11	a	a	DET
ejpam-4136	285	12	b(αn	b(αn	NOUN
ejpam-4136	285	13	,	,	PUNCT
ejpam-4136	285	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	285	15	space	space	NOUN
ejpam-4136	285	16	over	over	ADP
ejpam-4136	285	17	banach	banach	NOUN
ejpam-4136	285	18	algebra	algebra	NOUN
ejpam-4136	285	19	a.	a.	NOUN
ejpam-4136	285	20	then	then	ADV
ejpam-4136	285	21	a	a	DET
ejpam-4136	285	22	sequence	sequence	NOUN
ejpam-4136	285	23	{	{	PUNCT
ejpam-4136	285	24	xm	xm	NOUN
ejpam-4136	285	25	}	}	PUNCT
ejpam-4136	285	26	⊆	⊆	NUM
ejpam-4136	285	27	x	x	NUM
ejpam-4136	285	28	is	be	AUX
ejpam-4136	285	29	called	call	VERB
ejpam-4136	285	30	b(αn	b(αn	NOUN
ejpam-4136	285	31	,	,	PUNCT
ejpam-4136	285	32	βn)-cauchy	βn)-cauchy	VERB
ejpam-4136	285	33	if	if	SCONJ
ejpam-4136	285	34	for	for	ADP
ejpam-4136	285	35	every	every	DET
ejpam-4136	285	36	ε	ε	PROPN
ejpam-4136	285	37	≻	≻	PROPN
ejpam-4136	285	38	0a	0a	PROPN
ejpam-4136	285	39	,	,	PUNCT
ejpam-4136	285	40	there	there	PRON
ejpam-4136	285	41	exists	exist	VERB
ejpam-4136	285	42	n	n	PRON
ejpam-4136	285	43	∈	∈	PROPN
ejpam-4136	285	44	n	n	PRON
ejpam-4136	285	45	such	such	ADJ
ejpam-4136	285	46	that	that	SCONJ
ejpam-4136	285	47	γ(αn	γ(αn	VERB
ejpam-4136	285	48	,	,	PUNCT
ejpam-4136	285	49	βn)(xmi	βn)(xmi	PUNCT
ejpam-4136	285	50	)	)	PUNCT
ejpam-4136	286	1	n	n	CCONJ
ejpam-4136	286	2	i=1	i=1	PROPN
ejpam-4136	286	3	≺	≺	NOUN
ejpam-4136	286	4	ε	ε	PROPN
ejpam-4136	286	5	for	for	ADP
ejpam-4136	286	6	all	all	DET
ejpam-4136	286	7	m1,m2	m1,m2	PROPN
ejpam-4136	286	8	,	,	PUNCT
ejpam-4136	286	9	...	...	PUNCT
ejpam-4136	286	10	,	,	PUNCT
ejpam-4136	286	11	mn	mn	PROPN
ejpam-4136	286	12	≥	≥	PROPN
ejpam-4136	286	13	n	n	ADV
ejpam-4136	286	14	.	.	PUNCT
ejpam-4136	287	1	the	the	DET
ejpam-4136	287	2	next	next	ADJ
ejpam-4136	287	3	proposition	proposition	NOUN
ejpam-4136	287	4	follow	follow	VERB
ejpam-4136	287	5	directly	directly	ADV
ejpam-4136	287	6	from	from	ADP
ejpam-4136	287	7	the	the	DET
ejpam-4136	287	8	definitions	definition	NOUN
ejpam-4136	287	9	.	.	PUNCT
ejpam-4136	288	1	proposition	proposition	NOUN
ejpam-4136	288	2	18	18	NUM
ejpam-4136	288	3	.	.	PUNCT
ejpam-4136	289	1	in	in	ADP
ejpam-4136	289	2	a	a	DET
ejpam-4136	289	3	b(αn	b(αn	NOUN
ejpam-4136	289	4	,	,	PUNCT
ejpam-4136	289	5	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	289	6	space	space	NOUN
ejpam-4136	289	7	,	,	PUNCT
ejpam-4136	289	8	(	(	PUNCT
ejpam-4136	289	9	x	x	X
ejpam-4136	289	10	,	,	PUNCT
ejpam-4136	289	11	γ(αn	γ(αn	VERB
ejpam-4136	289	12	,	,	PUNCT
ejpam-4136	289	13	βn	βn	NOUN
ejpam-4136	289	14	)	)	PUNCT
ejpam-4136	289	15	)	)	PUNCT
ejpam-4136	289	16	over	over	ADP
ejpam-4136	289	17	banach	banach	NOUN
ejpam-4136	289	18	algebra	algebra	NOUN
ejpam-4136	289	19	a	a	PRON
ejpam-4136	289	20	,	,	PUNCT
ejpam-4136	289	21	the	the	DET
ejpam-4136	289	22	following	follow	VERB
ejpam-4136	289	23	are	be	AUX
ejpam-4136	289	24	equivalent	equivalent	ADJ
ejpam-4136	289	25	.	.	PUNCT
ejpam-4136	290	1	(	(	PUNCT
ejpam-4136	290	2	i	i	NOUN
ejpam-4136	290	3	)	)	PUNCT
ejpam-4136	290	4	the	the	DET
ejpam-4136	290	5	sequence	sequence	NOUN
ejpam-4136	290	6	{	{	PUNCT
ejpam-4136	290	7	xm	xm	NOUN
ejpam-4136	290	8	}	}	PUNCT
ejpam-4136	290	9	is	be	AUX
ejpam-4136	290	10	b(αn	b(αn	NOUN
ejpam-4136	290	11	,	,	PUNCT
ejpam-4136	290	12	βn)-cauchy	βn)-cauchy	NOUN
ejpam-4136	290	13	.	.	PUNCT
ejpam-4136	291	1	(	(	PUNCT
ejpam-4136	291	2	ii	ii	NOUN
ejpam-4136	291	3	)	)	PUNCT
ejpam-4136	291	4	for	for	ADP
ejpam-4136	291	5	every	every	DET
ejpam-4136	291	6	ε	ε	PROPN
ejpam-4136	291	7	≻	≻	PROPN
ejpam-4136	291	8	0a	0a	PROPN
ejpam-4136	291	9	,	,	PUNCT
ejpam-4136	291	10	there	there	PRON
ejpam-4136	291	11	exists	exist	VERB
ejpam-4136	291	12	n	n	PRON
ejpam-4136	291	13	∈	∈	PROPN
ejpam-4136	291	14	n	n	PRON
ejpam-4136	291	15	such	such	ADJ
ejpam-4136	291	16	that	that	SCONJ
ejpam-4136	291	17	γ(αn	γ(αn	VERB
ejpam-4136	291	18	,	,	PUNCT
ejpam-4136	291	19	βn)(xl	βn)(xl	NOUN
ejpam-4136	291	20	,	,	PUNCT
ejpam-4136	291	21	(	(	PUNCT
ejpam-4136	291	22	xm)n2	xm)n2	PROPN
ejpam-4136	291	23	)	)	PUNCT
ejpam-4136	291	24	≺	≺	NOUN
ejpam-4136	291	25	ε	ε	PROPN
ejpam-4136	291	26	,	,	PUNCT
ejpam-4136	291	27	for	for	ADP
ejpam-4136	291	28	every	every	DET
ejpam-4136	291	29	l	l	NOUN
ejpam-4136	291	30	,	,	PUNCT
ejpam-4136	291	31	m	m	VERB
ejpam-4136	291	32	≥	≥	NOUN
ejpam-4136	291	33	n	n	ADV
ejpam-4136	291	34	.	.	PUNCT
ejpam-4136	292	1	(	(	PUNCT
ejpam-4136	292	2	iii	iii	NOUN
ejpam-4136	292	3	)	)	PUNCT
ejpam-4136	292	4	{	{	PUNCT
ejpam-4136	292	5	xm	xm	NOUN
ejpam-4136	292	6	}	}	PUNCT
ejpam-4136	292	7	is	be	AUX
ejpam-4136	292	8	a	a	DET
ejpam-4136	292	9	cauchy	cauchy	ADJ
ejpam-4136	292	10	sequence	sequence	NOUN
ejpam-4136	292	11	in	in	ADP
ejpam-4136	292	12	the	the	DET
ejpam-4136	292	13	metric	metric	ADJ
ejpam-4136	292	14	space	space	NOUN
ejpam-4136	292	15	(	(	PUNCT
ejpam-4136	292	16	x	x	NOUN
ejpam-4136	292	17	,	,	PUNCT
ejpam-4136	292	18	dγ(αn	dγ(αn	NOUN
ejpam-4136	292	19	,	,	PUNCT
ejpam-4136	292	20	βn	βn	NOUN
ejpam-4136	292	21	)	)	PUNCT
ejpam-4136	292	22	)	)	PUNCT
ejpam-4136	292	23	.	.	PUNCT
ejpam-4136	293	1	corollary	corollary	ADJ
ejpam-4136	293	2	1	1	NUM
ejpam-4136	293	3	.	.	PUNCT
ejpam-4136	294	1	(	(	PUNCT
ejpam-4136	294	2	i	i	NOUN
ejpam-4136	294	3	)	)	PUNCT
ejpam-4136	294	4	every	every	DET
ejpam-4136	294	5	b(αn	b(αn	NOUN
ejpam-4136	294	6	,	,	PUNCT
ejpam-4136	294	7	βn)-convergent	βn)-convergent	ADJ
ejpam-4136	294	8	sequence	sequence	NOUN
ejpam-4136	294	9	in	in	ADP
ejpam-4136	294	10	a	a	DET
ejpam-4136	294	11	b(αn	b(αn	NOUN
ejpam-4136	294	12	,	,	PUNCT
ejpam-4136	294	13	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	294	14	space	space	NOUN
ejpam-4136	294	15	over	over	ADP
ejpam-4136	294	16	banach	banach	NOUN
ejpam-4136	294	17	algebra	algebra	NOUN
ejpam-4136	294	18	a	a	PRON
ejpam-4136	294	19	is	be	AUX
ejpam-4136	294	20	b(αn	b(αn	NOUN
ejpam-4136	294	21	,	,	PUNCT
ejpam-4136	294	22	βn)-cauchy	βn)-cauchy	NOUN
ejpam-4136	294	23	.	.	PUNCT
ejpam-4136	295	1	(	(	PUNCT
ejpam-4136	295	2	ii	ii	NOUN
ejpam-4136	295	3	)	)	PUNCT
ejpam-4136	295	4	if	if	SCONJ
ejpam-4136	295	5	a	a	DET
ejpam-4136	295	6	b(αn	b(αn	NOUN
ejpam-4136	295	7	,	,	PUNCT
ejpam-4136	295	8	βn)-cauchy	βn)-cauchy	ADJ
ejpam-4136	295	9	sequence	sequence	NOUN
ejpam-4136	295	10	in	in	ADP
ejpam-4136	295	11	a	a	DET
ejpam-4136	295	12	b(αn	b(αn	NOUN
ejpam-4136	295	13	,	,	PUNCT
ejpam-4136	295	14	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	295	15	space	space	NOUN
ejpam-4136	295	16	(	(	PUNCT
ejpam-4136	295	17	x	x	X
ejpam-4136	295	18	,	,	PUNCT
ejpam-4136	295	19	γ(αn	γ(αn	VERB
ejpam-4136	295	20	,	,	PUNCT
ejpam-4136	295	21	βn	βn	NOUN
ejpam-4136	295	22	)	)	PUNCT
ejpam-4136	295	23	)	)	PUNCT
ejpam-4136	295	24	over	over	ADP
ejpam-4136	295	25	banach	banach	NOUN
ejpam-4136	295	26	algebra	algebra	NOUN
ejpam-4136	295	27	a	a	PRON
ejpam-4136	295	28	contains	contain	VERB
ejpam-4136	295	29	a	a	DET
ejpam-4136	295	30	b(αn	b(αn	NOUN
ejpam-4136	295	31	,	,	PUNCT
ejpam-4136	295	32	βn)-convergent	βn)-convergent	PROPN
ejpam-4136	295	33	subsequence	subsequence	NOUN
ejpam-4136	295	34	,	,	PUNCT
ejpam-4136	295	35	then	then	ADV
ejpam-4136	295	36	the	the	DET
ejpam-4136	295	37	sequence	sequence	NOUN
ejpam-4136	295	38	itself	itself	PRON
ejpam-4136	295	39	is	be	AUX
ejpam-4136	295	40	b(αn	b(αn	NOUN
ejpam-4136	295	41	,	,	PUNCT
ejpam-4136	295	42	βn)convergent	βn)convergent	NOUN
ejpam-4136	295	43	.	.	PUNCT
ejpam-4136	296	1	definition	definition	NOUN
ejpam-4136	296	2	15	15	NUM
ejpam-4136	296	3	.	.	PUNCT
ejpam-4136	297	1	a	a	DET
ejpam-4136	297	2	b(αn	b(αn	NOUN
ejpam-4136	297	3	,	,	PUNCT
ejpam-4136	297	4	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	297	5	space	space	NOUN
ejpam-4136	297	6	(	(	PUNCT
ejpam-4136	297	7	x	x	X
ejpam-4136	297	8	,	,	PUNCT
ejpam-4136	297	9	γ(αn	γ(αn	VERB
ejpam-4136	297	10	,	,	PUNCT
ejpam-4136	297	11	βn	βn	NOUN
ejpam-4136	297	12	)	)	PUNCT
ejpam-4136	297	13	)	)	PUNCT
ejpam-4136	297	14	over	over	ADP
ejpam-4136	297	15	banach	banach	NOUN
ejpam-4136	297	16	algebra	algebra	NOUN
ejpam-4136	297	17	a	a	PRON
ejpam-4136	297	18	is	be	AUX
ejpam-4136	297	19	called	call	VERB
ejpam-4136	297	20	b(αn	b(αn	NOUN
ejpam-4136	297	21	,	,	PUNCT
ejpam-4136	297	22	βn)-complete	βn)-complete	VERB
ejpam-4136	297	23	if	if	SCONJ
ejpam-4136	297	24	every	every	DET
ejpam-4136	297	25	b(αn	b(αn	NOUN
ejpam-4136	297	26	,	,	PUNCT
ejpam-4136	297	27	βn)-cauchy	βn)-cauchy	ADJ
ejpam-4136	297	28	sequence	sequence	NOUN
ejpam-4136	297	29	in	in	ADP
ejpam-4136	297	30	(	(	PUNCT
ejpam-4136	297	31	x	x	NOUN
ejpam-4136	297	32	,	,	PUNCT
ejpam-4136	297	33	γ(αn	γ(αn	VERB
ejpam-4136	297	34	,	,	PUNCT
ejpam-4136	297	35	βn	βn	NOUN
ejpam-4136	297	36	)	)	PUNCT
ejpam-4136	297	37	)	)	PUNCT
ejpam-4136	297	38	is	be	AUX
ejpam-4136	297	39	b(αn	b(αn	NOUN
ejpam-4136	297	40	,	,	PUNCT
ejpam-4136	297	41	βn)-convergent	βn)-convergent	NOUN
ejpam-4136	297	42	in	in	ADP
ejpam-4136	297	43	(	(	PUNCT
ejpam-4136	297	44	x	x	NOUN
ejpam-4136	297	45	,	,	PUNCT
ejpam-4136	297	46	γ(αn	γ(αn	VERB
ejpam-4136	297	47	,	,	PUNCT
ejpam-4136	297	48	βn	βn	NOUN
ejpam-4136	297	49	)	)	PUNCT
ejpam-4136	297	50	)	)	PUNCT
ejpam-4136	297	51	.	.	PUNCT
ejpam-4136	298	1	proposition	proposition	NOUN
ejpam-4136	298	2	19	19	NUM
ejpam-4136	298	3	.	.	PUNCT
ejpam-4136	299	1	a	a	DET
ejpam-4136	299	2	b(αn	b(αn	NOUN
ejpam-4136	299	3	,	,	PUNCT
ejpam-4136	299	4	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	299	5	space	space	NOUN
ejpam-4136	299	6	(	(	PUNCT
ejpam-4136	299	7	x	x	X
ejpam-4136	299	8	,	,	PUNCT
ejpam-4136	299	9	γ(αn	γ(αn	VERB
ejpam-4136	299	10	,	,	PUNCT
ejpam-4136	299	11	βn	βn	NOUN
ejpam-4136	299	12	)	)	PUNCT
ejpam-4136	299	13	)	)	PUNCT
ejpam-4136	299	14	over	over	ADP
ejpam-4136	299	15	banach	banach	NOUN
ejpam-4136	299	16	algebra	algebra	NOUN
ejpam-4136	299	17	a	a	PRON
ejpam-4136	299	18	is	be	AUX
ejpam-4136	299	19	b(αn	b(αn	NOUN
ejpam-4136	299	20	,	,	PUNCT
ejpam-4136	299	21	βn)-complete	βn)-complete	VERB
ejpam-4136	299	22	if	if	SCONJ
ejpam-4136	299	23	and	and	CCONJ
ejpam-4136	299	24	only	only	ADV
ejpam-4136	299	25	if	if	SCONJ
ejpam-4136	299	26	(	(	PUNCT
ejpam-4136	299	27	x	x	NOUN
ejpam-4136	299	28	,	,	PUNCT
ejpam-4136	299	29	dγ(αn	dγ(αn	NOUN
ejpam-4136	299	30	,	,	PUNCT
ejpam-4136	299	31	βn	βn	NOUN
ejpam-4136	299	32	)	)	PUNCT
ejpam-4136	299	33	)	)	PUNCT
ejpam-4136	299	34	is	be	AUX
ejpam-4136	299	35	a	a	DET
ejpam-4136	299	36	complete	complete	ADJ
ejpam-4136	299	37	metric	metric	ADJ
ejpam-4136	299	38	space	space	NOUN
ejpam-4136	299	39	.	.	PUNCT
ejpam-4136	300	1	definition	definition	NOUN
ejpam-4136	300	2	16	16	NUM
ejpam-4136	300	3	.	.	PUNCT
ejpam-4136	301	1	let	let	VERB
ejpam-4136	301	2	(	(	PUNCT
ejpam-4136	301	3	x	x	X
ejpam-4136	301	4	,	,	PUNCT
ejpam-4136	301	5	γ(αn	γ(αn	VERB
ejpam-4136	301	6	,	,	PUNCT
ejpam-4136	301	7	βn	βn	NOUN
ejpam-4136	301	8	)	)	PUNCT
ejpam-4136	301	9	)	)	PUNCT
ejpam-4136	302	1	and	and	CCONJ
ejpam-4136	302	2	(	(	PUNCT
ejpam-4136	302	3	y	y	PROPN
ejpam-4136	302	4	,	,	PUNCT
ejpam-4136	302	5	γ	γ	X
ejpam-4136	302	6	′	′	NUM
ejpam-4136	302	7	(	(	PUNCT
ejpam-4136	302	8	αn	αn	NOUN
ejpam-4136	302	9	,	,	PUNCT
ejpam-4136	302	10	βn	βn	NOUN
ejpam-4136	302	11	)	)	PUNCT
ejpam-4136	302	12	)	)	PUNCT
ejpam-4136	302	13	be	be	AUX
ejpam-4136	302	14	two	two	NUM
ejpam-4136	302	15	b(αn	b(αn	NOUN
ejpam-4136	302	16	,	,	PUNCT
ejpam-4136	302	17	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	302	18	spaces	space	NOUN
ejpam-4136	302	19	over	over	ADP
ejpam-4136	302	20	banach	banach	NOUN
ejpam-4136	302	21	algebra	algebra	NOUN
ejpam-4136	302	22	a.	a.	NOUN
ejpam-4136	302	23	a	a	DET
ejpam-4136	302	24	function	function	NOUN
ejpam-4136	303	1	f	f	NOUN
ejpam-4136	303	2	:	:	PUNCT
ejpam-4136	303	3	x	x	PUNCT
ejpam-4136	303	4	−→	−→	NOUN
ejpam-4136	303	5	y	y	PROPN
ejpam-4136	303	6	is	be	AUX
ejpam-4136	303	7	called	call	VERB
ejpam-4136	303	8	a	a	DET
ejpam-4136	303	9	b(αn	b(αn	NOUN
ejpam-4136	303	10	,	,	PUNCT
ejpam-4136	303	11	βn)-contraction	βn)-contraction	NOUN
ejpam-4136	303	12	if	if	SCONJ
ejpam-4136	303	13	there	there	PRON
ejpam-4136	303	14	exists	exist	VERB
ejpam-4136	303	15	a	a	DET
ejpam-4136	303	16	constant	constant	ADJ
ejpam-4136	303	17	k	k	PROPN
ejpam-4136	303	18	∈	∈	PROPN
ejpam-4136	303	19	{	{	PUNCT
ejpam-4136	303	20	a	a	DET
ejpam-4136	303	21	∈	∈	PROPN
ejpam-4136	303	22	a|0a	a|0a	NOUN
ejpam-4136	303	23	⪯	⪯	NOUN
ejpam-4136	303	24	a	a	DET
ejpam-4136	303	25	≺	≺	NOUN
ejpam-4136	303	26	ea	ea	NOUN
ejpam-4136	303	27	}	}	PUNCT
ejpam-4136	303	28	such	such	ADJ
ejpam-4136	303	29	that	that	SCONJ
ejpam-4136	303	30	γ	γ	PROPN
ejpam-4136	303	31	′	′	NUM
ejpam-4136	303	32	(	(	PUNCT
ejpam-4136	303	33	αn	αn	NOUN
ejpam-4136	303	34	,	,	PUNCT
ejpam-4136	303	35	βn	βn	NOUN
ejpam-4136	303	36	)	)	PUNCT
ejpam-4136	303	37	(	(	PUNCT
ejpam-4136	303	38	f(xi	f(xi	NOUN
ejpam-4136	303	39	)	)	PUNCT
ejpam-4136	303	40	)	)	PUNCT
ejpam-4136	303	41	n	n	CCONJ
ejpam-4136	303	42	i=1	i=1	PROPN
ejpam-4136	303	43	⊆	⊆	NUM
ejpam-4136	303	44	kγ(αn	kγ(αn	PROPN
ejpam-4136	303	45	,	,	PUNCT
ejpam-4136	303	46	βn)(xi	βn)(xi	PUNCT
ejpam-4136	303	47	)	)	PUNCT
ejpam-4136	303	48	n	n	CCONJ
ejpam-4136	303	49	i=1	i=1	PROPN
ejpam-4136	303	50	for	for	ADP
ejpam-4136	303	51	all	all	DET
ejpam-4136	303	52	x1	x1	PROPN
ejpam-4136	303	53	,	,	PUNCT
ejpam-4136	303	54	.	.	PUNCT
ejpam-4136	303	55	.	.	PUNCT
ejpam-4136	304	1	.	.	PUNCT
ejpam-4136	305	1	,	,	PUNCT
ejpam-4136	305	2	xn	xn	PUNCT
ejpam-4136	305	3	∈	∈	PROPN
ejpam-4136	305	4	x.	x.	NOUN
ejpam-4136	306	1	it	it	PRON
ejpam-4136	306	2	follows	follow	VERB
ejpam-4136	306	3	that	that	SCONJ
ejpam-4136	306	4	f	f	PROPN
ejpam-4136	306	5	is	be	AUX
ejpam-4136	306	6	b(αn	b(αn	NOUN
ejpam-4136	306	7	,	,	PUNCT
ejpam-4136	306	8	βn)-continuous	βn)-continuous	ADJ
ejpam-4136	306	9	because	because	SCONJ
ejpam-4136	306	10	;	;	PUNCT
ejpam-4136	306	11	γ(αn	γ(αn	PROPN
ejpam-4136	306	12	,	,	PUNCT
ejpam-4136	306	13	βn)(xi	βn)(xi	PUNCT
ejpam-4136	306	14	)	)	PUNCT
ejpam-4136	306	15	n	n	CCONJ
ejpam-4136	306	16	i=1	i=1	PROPN
ejpam-4136	306	17	⊆	⊆	NUM
ejpam-4136	306	18	{	{	PUNCT
ejpam-4136	306	19	a	a	DET
ejpam-4136	306	20	∈	∈	PROPN
ejpam-4136	306	21	a|0a	a|0a	NOUN
ejpam-4136	306	22	⪯	⪯	NOUN
ejpam-4136	306	23	a	a	DET
ejpam-4136	306	24	≺	≺	NOUN
ejpam-4136	306	25	δ	δ	PROPN
ejpam-4136	306	26	}	}	PUNCT
ejpam-4136	306	27	with	with	ADP
ejpam-4136	306	28	k	k	PROPN
ejpam-4136	306	29	̸=	̸=	PROPN
ejpam-4136	306	30	0	0	NUM
ejpam-4136	306	31	and	and	CCONJ
ejpam-4136	306	32	δ	δ	NOUN
ejpam-4136	306	33	:	:	PUNCT
ejpam-4136	306	34	=	=	PUNCT
ejpam-4136	306	35	ϵk−1	ϵk−1	NOUN
ejpam-4136	306	36	implies	imply	VERB
ejpam-4136	306	37	γ	γ	X
ejpam-4136	306	38	′	′	NUM
ejpam-4136	306	39	(	(	PUNCT
ejpam-4136	306	40	αn	αn	NOUN
ejpam-4136	306	41	,	,	PUNCT
ejpam-4136	306	42	βn	βn	NOUN
ejpam-4136	306	43	)	)	PUNCT
ejpam-4136	306	44	(	(	PUNCT
ejpam-4136	306	45	f(xi	f(xi	NOUN
ejpam-4136	306	46	)	)	PUNCT
ejpam-4136	306	47	)	)	PUNCT
ejpam-4136	306	48	n	n	CCONJ
ejpam-4136	306	49	i=1	i=1	PROPN
ejpam-4136	306	50	⊆	⊆	NUM
ejpam-4136	306	51	{	{	PUNCT
ejpam-4136	306	52	a	a	DET
ejpam-4136	306	53	∈	∈	PROPN
ejpam-4136	306	54	a|0a	a|0a	NOUN
ejpam-4136	306	55	⪯	⪯	NOUN
ejpam-4136	306	56	a	a	DET
ejpam-4136	306	57	≺	≺	NOUN
ejpam-4136	306	58	ϵ	ϵ	NOUN
ejpam-4136	306	59	}	}	PUNCT
ejpam-4136	306	60	.	.	PUNCT
ejpam-4136	307	1	theorem	theorem	NOUN
ejpam-4136	307	2	1	1	NUM
ejpam-4136	307	3	.	.	PUNCT
ejpam-4136	308	1	let	let	AUX
ejpam-4136	308	2	(	(	PUNCT
ejpam-4136	308	3	x	x	X
ejpam-4136	308	4	,	,	PUNCT
ejpam-4136	308	5	γ(αn	γ(αn	VERB
ejpam-4136	308	6	,	,	PUNCT
ejpam-4136	308	7	βn	βn	NOUN
ejpam-4136	308	8	)	)	PUNCT
ejpam-4136	308	9	)	)	PUNCT
ejpam-4136	308	10	be	be	AUX
ejpam-4136	308	11	a	a	DET
ejpam-4136	308	12	b(αn	b(αn	NOUN
ejpam-4136	308	13	,	,	PUNCT
ejpam-4136	308	14	βn)-complete	βn)-complete	ADJ
ejpam-4136	308	15	space	space	NOUN
ejpam-4136	308	16	and	and	CCONJ
ejpam-4136	308	17	let	let	VERB
ejpam-4136	308	18	t	t	NOUN
ejpam-4136	308	19	:	:	PUNCT
ejpam-4136	308	20	x	x	X
ejpam-4136	308	21	→	→	PUNCT
ejpam-4136	308	22	x	x	PUNCT
ejpam-4136	308	23	be	be	AUX
ejpam-4136	308	24	a	a	DET
ejpam-4136	308	25	b(αn	b(αn	NOUN
ejpam-4136	308	26	,	,	PUNCT
ejpam-4136	308	27	βn)-contraction	βn)-contraction	NOUN
ejpam-4136	308	28	map	map	NOUN
ejpam-4136	308	29	.	.	PUNCT
ejpam-4136	309	1	then	then	ADV
ejpam-4136	309	2	t	t	PROPN
ejpam-4136	309	3	has	have	VERB
ejpam-4136	309	4	a	a	DET
ejpam-4136	309	5	unique	unique	ADJ
ejpam-4136	309	6	fixed	fix	VERB
ejpam-4136	309	7	point	point	NOUN
ejpam-4136	309	8	t	t	PROPN
ejpam-4136	309	9	(	(	PUNCT
ejpam-4136	309	10	x	x	X
ejpam-4136	309	11	)	)	PUNCT
ejpam-4136	309	12	=	=	SYM
ejpam-4136	309	13	x.	x.	NOUN
ejpam-4136	309	14	proof	proof	NOUN
ejpam-4136	309	15	.	.	PUNCT
ejpam-4136	310	1	we	we	PRON
ejpam-4136	310	2	consider	consider	VERB
ejpam-4136	310	3	xm+1	xm+1	PROPN
ejpam-4136	310	4	=	=	SYM
ejpam-4136	310	5	t	t	PROPN
ejpam-4136	310	6	(	(	PUNCT
ejpam-4136	310	7	xm	xm	PROPN
ejpam-4136	310	8	)	)	PUNCT
ejpam-4136	310	9	,	,	PUNCT
ejpam-4136	310	10	with	with	ADP
ejpam-4136	310	11	x0	x0	PROPN
ejpam-4136	310	12	being	be	AUX
ejpam-4136	310	13	any	any	DET
ejpam-4136	310	14	point	point	NOUN
ejpam-4136	310	15	inx	inx	NOUN
ejpam-4136	310	16	.	.	PUNCT
ejpam-4136	311	1	we	we	PRON
ejpam-4136	311	2	have	have	VERB
ejpam-4136	311	3	by	by	ADP
ejpam-4136	311	4	repeated	repeat	VERB
ejpam-4136	311	5	use	use	NOUN
ejpam-4136	311	6	of	of	ADP
ejpam-4136	311	7	the	the	DET
ejpam-4136	311	8	(	(	PUNCT
ejpam-4136	311	9	αn	αn	NOUN
ejpam-4136	311	10	,	,	PUNCT
ejpam-4136	311	11	βn)-rectangle	βn)-rectangle	NOUN
ejpam-4136	311	12	inequality	inequality	NOUN
ejpam-4136	311	13	and	and	CCONJ
ejpam-4136	311	14	application	application	NOUN
ejpam-4136	311	15	of	of	ADP
ejpam-4136	311	16	contraction	contraction	NOUN
ejpam-4136	311	17	property	property	NOUN
ejpam-4136	311	18	,	,	PUNCT
ejpam-4136	311	19	we	we	PRON
ejpam-4136	311	20	obtain	obtain	VERB
ejpam-4136	311	21	γ(αn	γ(αn	PROPN
ejpam-4136	311	22	,	,	PUNCT
ejpam-4136	311	23	βn)(xm	βn)(xm	PRON
ejpam-4136	311	24	,	,	PUNCT
ejpam-4136	311	25	(	(	PUNCT
ejpam-4136	311	26	xm+1	xm+1	NUM
ejpam-4136	311	27	)	)	PUNCT
ejpam-4136	311	28	n	n	DET
ejpam-4136	311	29	2	2	NUM
ejpam-4136	311	30	)	)	PUNCT
ejpam-4136	311	31	⊆	⊆	NUM
ejpam-4136	311	32	kmγ(αn	kmγ(αn	NOUN
ejpam-4136	311	33	,	,	PUNCT
ejpam-4136	311	34	βn)(x0	βn)(x0	PROPN
ejpam-4136	311	35	,	,	PUNCT
ejpam-4136	311	36	(	(	PUNCT
ejpam-4136	311	37	x1	x1	PROPN
ejpam-4136	311	38	)	)	PUNCT
ejpam-4136	311	39	n	n	PRON
ejpam-4136	311	40	1	1	NUM
ejpam-4136	311	41	)	)	PUNCT
ejpam-4136	311	42	a.	a.	NOUN
ejpam-4136	311	43	d.nezhad	d.nezhad	PROPN
ejpam-4136	311	44	,	,	PUNCT
ejpam-4136	311	45	s.	s.	PROPN
ejpam-4136	311	46	radenović	radenović	PROPN
ejpam-4136	311	47	/	/	SYM
ejpam-4136	311	48	eur	eur	PROPN
ejpam-4136	311	49	.	.	PUNCT
ejpam-4136	312	1	j.	j.	PROPN
ejpam-4136	312	2	pure	pure	PROPN
ejpam-4136	312	3	appl	appl	PROPN
ejpam-4136	312	4	.	.	PROPN
ejpam-4136	312	5	math	math	PROPN
ejpam-4136	312	6	,	,	PUNCT
ejpam-4136	312	7	14	14	NUM
ejpam-4136	312	8	(	(	PUNCT
ejpam-4136	312	9	4	4	NUM
ejpam-4136	312	10	)	)	PUNCT
ejpam-4136	312	11	(	(	PUNCT
ejpam-4136	312	12	2021	2021	NUM
ejpam-4136	312	13	)	)	PUNCT
ejpam-4136	312	14	,	,	PUNCT
ejpam-4136	312	15	1148	1148	NUM
ejpam-4136	312	16	-	-	SYM
ejpam-4136	312	17	1160	1160	NUM
ejpam-4136	312	18	1158	1158	NUM
ejpam-4136	312	19	for	for	ADP
ejpam-4136	312	20	all	all	DET
ejpam-4136	312	21	m	m	PROPN
ejpam-4136	312	22	,	,	PUNCT
ejpam-4136	312	23	s1	s1	PROPN
ejpam-4136	312	24	∈	∈	PROPN
ejpam-4136	312	25	n	n	X
ejpam-4136	312	26	which	which	PRON
ejpam-4136	312	27	m	m	VERB
ejpam-4136	312	28	<	<	X
ejpam-4136	312	29	s1	s1	PROPN
ejpam-4136	312	30	and	and	CCONJ
ejpam-4136	312	31	k	k	PROPN
ejpam-4136	312	32	∈	∈	PROPN
ejpam-4136	312	33	{	{	PUNCT
ejpam-4136	312	34	a	a	DET
ejpam-4136	312	35	∈	∈	PROPN
ejpam-4136	312	36	a|0a	a|0a	NOUN
ejpam-4136	312	37	⪯	⪯	NOUN
ejpam-4136	312	38	a	a	DET
ejpam-4136	312	39	≺	≺	NOUN
ejpam-4136	312	40	ea	ea	NOUN
ejpam-4136	312	41	}	}	PUNCT
ejpam-4136	312	42	.	.	PUNCT
ejpam-4136	313	1	from	from	ADP
ejpam-4136	313	2	the	the	DET
ejpam-4136	313	3	above	above	ADV
ejpam-4136	313	4	it	it	PRON
ejpam-4136	313	5	follows	follow	VERB
ejpam-4136	313	6	that	that	SCONJ
ejpam-4136	313	7	γ(αn	γ(αn	VERB
ejpam-4136	313	8	,	,	PUNCT
ejpam-4136	313	9	βn)(xm	βn)(xm	PRON
ejpam-4136	313	10	,	,	PUNCT
ejpam-4136	313	11	(	(	PUNCT
ejpam-4136	313	12	xs−1	xs−1	NOUN
ejpam-4136	313	13	)	)	PUNCT
ejpam-4136	313	14	n	n	PRON
ejpam-4136	313	15	2	2	NUM
ejpam-4136	313	16	)	)	PUNCT
ejpam-4136	313	17	⊆	⊆	NUM
ejpam-4136	313	18	ξ1γ(αn	ξ1γ(αn	NOUN
ejpam-4136	313	19	,	,	PUNCT
ejpam-4136	313	20	βn)(xm	βn)(xm	PRON
ejpam-4136	313	21	,	,	PUNCT
ejpam-4136	313	22	(	(	PUNCT
ejpam-4136	313	23	xm+1	xm+1	NUM
ejpam-4136	313	24	)	)	PUNCT
ejpam-4136	313	25	n	n	PRON
ejpam-4136	313	26	2	2	NUM
ejpam-4136	313	27	)	)	PUNCT
ejpam-4136	314	1	+	+	CCONJ
ejpam-4136	314	2	ξ2γ(αn	ξ2γ(αn	NOUN
ejpam-4136	314	3	,	,	PUNCT
ejpam-4136	314	4	βn)(xm+1	βn)(xm+1	PROPN
ejpam-4136	314	5	,	,	PUNCT
ejpam-4136	314	6	(	(	PUNCT
ejpam-4136	314	7	xm+2	xm+2	X
ejpam-4136	314	8	)	)	PUNCT
ejpam-4136	314	9	n	n	PRON
ejpam-4136	314	10	2	2	NUM
ejpam-4136	314	11	)	)	PUNCT
ejpam-4136	315	1	+	+	CCONJ
ejpam-4136	315	2	ξ3γ(αn	ξ3γ(αn	NOUN
ejpam-4136	315	3	,	,	PUNCT
ejpam-4136	315	4	βn)(xm+2	βn)(xm+2	NOUN
ejpam-4136	315	5	,	,	PUNCT
ejpam-4136	315	6	(	(	PUNCT
ejpam-4136	315	7	xm+3	xm+3	X
ejpam-4136	315	8	)	)	PUNCT
ejpam-4136	315	9	n	n	PRON
ejpam-4136	315	10	2	2	NUM
ejpam-4136	315	11	)	)	PUNCT
ejpam-4136	315	12	+	+	CCONJ
ejpam-4136	315	13	...	...	PUNCT
ejpam-4136	315	14	...	...	PUNCT
ejpam-4136	315	15	...	...	PUNCT
ejpam-4136	315	16	...	...	PUNCT
ejpam-4136	315	17	...	...	PUNCT
ejpam-4136	316	1	+	+	CCONJ
ejpam-4136	316	2	ξs1−mγ(αn	ξs1−mγ(αn	NOUN
ejpam-4136	316	3	,	,	PUNCT
ejpam-4136	316	4	βn)(xs1−1	βn)(xs1−1	ADJ
ejpam-4136	316	5	,	,	PUNCT
ejpam-4136	316	6	(	(	PUNCT
ejpam-4136	316	7	xs1	xs1	PROPN
ejpam-4136	316	8	)	)	PUNCT
ejpam-4136	316	9	n	n	PRON
ejpam-4136	316	10	2	2	NUM
ejpam-4136	316	11	)	)	PUNCT
ejpam-4136	316	12	⊆	⊆	NUM
ejpam-4136	316	13	ξ(km	ξ(km	NOUN
ejpam-4136	316	14	+	+	CCONJ
ejpam-4136	316	15	km+1	km+1	PROPN
ejpam-4136	316	16	+	+	CCONJ
ejpam-4136	316	17	.	.	PUNCT
ejpam-4136	316	18	.	.	PUNCT
ejpam-4136	317	1	.+	.+	NOUN
ejpam-4136	317	2	ks1−1)γ(αn	ks1−1)γ(αn	PROPN
ejpam-4136	317	3	,	,	PUNCT
ejpam-4136	317	4	βn)(x0	βn)(x0	PROPN
ejpam-4136	317	5	,	,	PUNCT
ejpam-4136	317	6	(	(	PUNCT
ejpam-4136	317	7	x1	x1	PROPN
ejpam-4136	317	8	)	)	PUNCT
ejpam-4136	317	9	n	n	PRON
ejpam-4136	317	10	2	2	NUM
ejpam-4136	317	11	)	)	PUNCT
ejpam-4136	317	12	=	=	NOUN
ejpam-4136	317	13	ξkm(ea	ξkm(ea	NOUN
ejpam-4136	317	14	−	−	PROPN
ejpam-4136	317	15	ks1−m)(ea	ks1−m)(ea	PROPN
ejpam-4136	317	16	−	−	PROPN
ejpam-4136	317	17	k)−1γ(αn	k)−1γ(αn	PROPN
ejpam-4136	317	18	,	,	PUNCT
ejpam-4136	317	19	βn)(x0	βn)(x0	PROPN
ejpam-4136	317	20	,	,	PUNCT
ejpam-4136	317	21	(	(	PUNCT
ejpam-4136	317	22	x1	x1	PROPN
ejpam-4136	317	23	)	)	PUNCT
ejpam-4136	317	24	n	n	PRON
ejpam-4136	317	25	2	2	NUM
ejpam-4136	317	26	)	)	PUNCT
ejpam-4136	317	27	.	.	PUNCT
ejpam-4136	318	1	(	(	PUNCT
ejpam-4136	318	2	6	6	NUM
ejpam-4136	318	3	)	)	PUNCT
ejpam-4136	318	4	where	where	SCONJ
ejpam-4136	318	5	ξ1	ξ1	PROPN
ejpam-4136	318	6	=	=	SYM
ejpam-4136	318	7	αn(xm	αn(xm	PROPN
ejpam-4136	318	8	,	,	PUNCT
ejpam-4136	318	9	(	(	PUNCT
ejpam-4136	318	10	xs1	xs1	PROPN
ejpam-4136	318	11	)	)	PUNCT
ejpam-4136	318	12	n	n	PRON
ejpam-4136	318	13	2	2	NUM
ejpam-4136	318	14	)	)	PUNCT
ejpam-4136	318	15	,	,	PUNCT
ejpam-4136	318	16	ξ2	ξ2	NOUN
ejpam-4136	318	17	=	=	SYM
ejpam-4136	318	18	βn(xm	βn(xm	PROPN
ejpam-4136	318	19	,	,	PUNCT
ejpam-4136	318	20	(	(	PUNCT
ejpam-4136	318	21	xs1	xs1	PROPN
ejpam-4136	318	22	)	)	PUNCT
ejpam-4136	318	23	n	n	PRON
ejpam-4136	318	24	2	2	NUM
ejpam-4136	318	25	)	)	PUNCT
ejpam-4136	318	26	.αn(xm	.αn(xm	PROPN
ejpam-4136	318	27	,	,	PUNCT
ejpam-4136	318	28	(	(	PUNCT
ejpam-4136	318	29	xm+1	xm+1	X
ejpam-4136	318	30	)	)	PUNCT
ejpam-4136	318	31	n	n	PRON
ejpam-4136	318	32	2	2	NUM
ejpam-4136	318	33	)	)	PUNCT
ejpam-4136	318	34	,	,	PUNCT
ejpam-4136	318	35	...	...	PUNCT
ejpam-4136	318	36	and	and	CCONJ
ejpam-4136	318	37	ξ	ξ	X
ejpam-4136	318	38	=	=	SYM
ejpam-4136	318	39	max{ξ1	max{ξ1	PROPN
ejpam-4136	318	40	,	,	PUNCT
ejpam-4136	318	41	ξ2	ξ2	NOUN
ejpam-4136	318	42	,	,	PUNCT
ejpam-4136	318	43	...	...	PUNCT
ejpam-4136	318	44	,	,	PUNCT
ejpam-4136	318	45	ξs1−m	ξs1−m	VERB
ejpam-4136	318	46	}	}	PUNCT
ejpam-4136	318	47	for	for	ADP
ejpam-4136	318	48	all	all	DET
ejpam-4136	318	49	xm	xm	PROPN
ejpam-4136	318	50	,	,	PUNCT
ejpam-4136	318	51	...	...	PUNCT
ejpam-4136	318	52	,	,	PUNCT
ejpam-4136	318	53	xs1	xs1	PROPN
ejpam-4136	318	54	∈	∈	PROPN
ejpam-4136	318	55	bγ(αn	bγ(αn	NOUN
ejpam-4136	318	56	,	,	PUNCT
ejpam-4136	318	57	βn	βn	NOUN
ejpam-4136	318	58	)	)	PUNCT
ejpam-4136	318	59	(	(	PUNCT
ejpam-4136	318	60	x0	x0	PROPN
ejpam-4136	318	61	,	,	PUNCT
ejpam-4136	318	62	r	r	NOUN
ejpam-4136	318	63	)	)	PUNCT
ejpam-4136	318	64	.	.	PUNCT
ejpam-4136	319	1	then	then	ADV
ejpam-4136	319	2	we	we	PRON
ejpam-4136	319	3	have	have	VERB
ejpam-4136	319	4	lim	lim	PROPN
ejpam-4136	319	5	m	m	PROPN
ejpam-4136	319	6	,	,	PUNCT
ejpam-4136	319	7	s1	s1	PROPN
ejpam-4136	319	8	→+∞	→+∞	ADP
ejpam-4136	319	9	γ(αn	γ(αn	PROPN
ejpam-4136	319	10	,	,	PUNCT
ejpam-4136	319	11	βn)(xm	βn)(xm	PRON
ejpam-4136	319	12	,	,	PUNCT
ejpam-4136	319	13	(	(	PUNCT
ejpam-4136	319	14	xs1	xs1	PROPN
ejpam-4136	319	15	)	)	PUNCT
ejpam-4136	319	16	n	n	PRON
ejpam-4136	319	17	2	2	NUM
ejpam-4136	319	18	)	)	PUNCT
ejpam-4136	319	19	=	=	PRON
ejpam-4136	319	20	{	{	PUNCT
ejpam-4136	319	21	0a	0a	PROPN
ejpam-4136	319	22	}	}	PUNCT
ejpam-4136	319	23	(	(	PUNCT
ejpam-4136	319	24	7	7	NUM
ejpam-4136	319	25	)	)	PUNCT
ejpam-4136	319	26	since	since	SCONJ
ejpam-4136	319	27	lim	lim	PROPN
ejpam-4136	319	28	m	m	PROPN
ejpam-4136	319	29	,	,	PUNCT
ejpam-4136	319	30	s1	s1	PROPN
ejpam-4136	319	31	→+∞	→+∞	PUNCT
ejpam-4136	319	32	ξkm(ea	ξkm(ea	X
ejpam-4136	319	33	−	−	PROPN
ejpam-4136	319	34	ks1−m)(ea	ks1−m)(ea	PROPN
ejpam-4136	319	35	−	−	PROPN
ejpam-4136	319	36	k)−1γ(αn	k)−1γ(αn	PROPN
ejpam-4136	319	37	,	,	PUNCT
ejpam-4136	319	38	βn)(x0	βn)(x0	PROPN
ejpam-4136	319	39	,	,	PUNCT
ejpam-4136	319	40	(	(	PUNCT
ejpam-4136	319	41	x1	x1	PROPN
ejpam-4136	319	42	)	)	PUNCT
ejpam-4136	319	43	n	n	PRON
ejpam-4136	319	44	2	2	NUM
ejpam-4136	319	45	)	)	PUNCT
ejpam-4136	319	46	=	=	PRON
ejpam-4136	319	47	{	{	PUNCT
ejpam-4136	319	48	0a	0a	PROPN
ejpam-4136	319	49	}	}	PUNCT
ejpam-4136	319	50	.	.	PUNCT
ejpam-4136	320	1	(	(	PUNCT
ejpam-4136	320	2	8)	8)	NUM
ejpam-4136	320	3	for	for	ADP
ejpam-4136	320	4	m	m	PROPN
ejpam-4136	320	5	≤	≤	NOUN
ejpam-4136	320	6	s1	s1	NOUN
ejpam-4136	320	7	≤	≤	NUM
ejpam-4136	320	8	s2	s2	NOUN
ejpam-4136	320	9	∈	∈	PROPN
ejpam-4136	320	10	n	n	NOUN
ejpam-4136	320	11	and	and	CCONJ
ejpam-4136	320	12	(	(	PUNCT
ejpam-4136	320	13	g5	g5	NOUN
ejpam-4136	320	14	)	)	PUNCT
ejpam-4136	320	15	implies	imply	VERB
ejpam-4136	320	16	that	that	SCONJ
ejpam-4136	320	17	γ(αn	γ(αn	VERB
ejpam-4136	320	18	,	,	PUNCT
ejpam-4136	320	19	βn)(xm	βn)(xm	PROPN
ejpam-4136	320	20	,	,	PUNCT
ejpam-4136	320	21	xs1	xs1	PROPN
ejpam-4136	320	22	,	,	PUNCT
ejpam-4136	320	23	(	(	PUNCT
ejpam-4136	320	24	xs2	xs2	PROPN
ejpam-4136	320	25	)	)	PUNCT
ejpam-4136	320	26	n	n	PRON
ejpam-4136	320	27	3	3	NUM
ejpam-4136	320	28	)	)	PUNCT
ejpam-4136	320	29	⊆	⊆	NUM
ejpam-4136	320	30	αn(xm	αn(xm	PROPN
ejpam-4136	320	31	,	,	PUNCT
ejpam-4136	320	32	xs1	xs1	PROPN
ejpam-4136	320	33	,	,	PUNCT
ejpam-4136	320	34	(	(	PUNCT
ejpam-4136	320	35	xs2	xs2	PROPN
ejpam-4136	320	36	)	)	PUNCT
ejpam-4136	320	37	n	n	PRON
ejpam-4136	320	38	3	3	NUM
ejpam-4136	320	39	)	)	PUNCT
ejpam-4136	320	40	γ(αn	γ(αn	VERB
ejpam-4136	320	41	,	,	PUNCT
ejpam-4136	320	42	βn)(xm	βn)(xm	PRON
ejpam-4136	320	43	,	,	PUNCT
ejpam-4136	320	44	(	(	PUNCT
ejpam-4136	320	45	xs1	xs1	PROPN
ejpam-4136	320	46	)	)	PUNCT
ejpam-4136	320	47	n	n	PRON
ejpam-4136	320	48	2	2	NUM
ejpam-4136	320	49	)	)	PUNCT
ejpam-4136	320	50	+	+	CCONJ
ejpam-4136	321	1	βn(xm	βn(xm	PROPN
ejpam-4136	321	2	,	,	PUNCT
ejpam-4136	321	3	xs1	xs1	PROPN
ejpam-4136	321	4	,	,	PUNCT
ejpam-4136	321	5	(	(	PUNCT
ejpam-4136	321	6	xs2	xs2	PROPN
ejpam-4136	321	7	)	)	PUNCT
ejpam-4136	321	8	n	n	PRON
ejpam-4136	321	9	3	3	NUM
ejpam-4136	321	10	)	)	PUNCT
ejpam-4136	321	11	γ(αn	γ(αn	PROPN
ejpam-4136	321	12	,	,	PUNCT
ejpam-4136	321	13	βn)(xs1	βn)(xs1	NOUN
ejpam-4136	321	14	,	,	PUNCT
ejpam-4136	321	15	(	(	PUNCT
ejpam-4136	321	16	xs2	xs2	PROPN
ejpam-4136	321	17	)	)	PUNCT
ejpam-4136	321	18	n	n	PRON
ejpam-4136	321	19	2	2	NUM
ejpam-4136	321	20	)	)	PUNCT
ejpam-4136	321	21	,	,	PUNCT
ejpam-4136	321	22	(	(	PUNCT
ejpam-4136	321	23	9	9	X
ejpam-4136	321	24	)	)	PUNCT
ejpam-4136	321	25	now	now	ADV
ejpam-4136	321	26	taking	take	VERB
ejpam-4136	321	27	limit	limit	NOUN
ejpam-4136	321	28	as	as	ADP
ejpam-4136	321	29	m	m	PROPN
ejpam-4136	321	30	,	,	PUNCT
ejpam-4136	321	31	s1	s1	NOUN
ejpam-4136	321	32	,	,	PUNCT
ejpam-4136	321	33	s2	s2	X
ejpam-4136	321	34	→	→	SYM
ejpam-4136	321	35	+	+	NOUN
ejpam-4136	321	36	∞	∞	PROPN
ejpam-4136	321	37	,	,	PUNCT
ejpam-4136	321	38	we	we	PRON
ejpam-4136	321	39	get	get	VERB
ejpam-4136	321	40	γ(αn	γ(αn	VERB
ejpam-4136	321	41	,	,	PUNCT
ejpam-4136	321	42	βn)(xm	βn)(xm	PROPN
ejpam-4136	321	43	,	,	PUNCT
ejpam-4136	321	44	xs1	xs1	PROPN
ejpam-4136	321	45	,	,	PUNCT
ejpam-4136	321	46	(	(	PUNCT
ejpam-4136	321	47	xs2	xs2	PROPN
ejpam-4136	321	48	)	)	PUNCT
ejpam-4136	321	49	n	n	PRON
ejpam-4136	322	1	3	3	NUM
ejpam-4136	322	2	)	)	PUNCT
ejpam-4136	322	3	→	→	SYM
ejpam-4136	322	4	{	{	PUNCT
ejpam-4136	322	5	0a	0a	PROPN
ejpam-4136	322	6	}	}	PUNCT
ejpam-4136	322	7	.	.	PUNCT
ejpam-4136	323	1	now	now	ADV
ejpam-4136	323	2	for	for	ADP
ejpam-4136	323	3	m	m	PROPN
ejpam-4136	323	4	≤	≤	NOUN
ejpam-4136	323	5	s1	s1	NOUN
ejpam-4136	323	6	≤	≤	NUM
ejpam-4136	323	7	s2	s2	NOUN
ejpam-4136	323	8	≤	≤	NOUN
ejpam-4136	323	9	.	.	PUNCT
ejpam-4136	323	10	.	.	PUNCT
ejpam-4136	323	11	.	.	PUNCT
ejpam-4136	324	1	≤	≤	NUM
ejpam-4136	324	2	sn−1	sn−1	PROPN
ejpam-4136	324	3	∈	∈	PROPN
ejpam-4136	324	4	n	n	CCONJ
ejpam-4136	324	5	,	,	PUNCT
ejpam-4136	324	6	we	we	PRON
ejpam-4136	324	7	will	will	AUX
ejpam-4136	324	8	have	have	AUX
ejpam-4136	324	9	γ(αn	γ(αn	VERB
ejpam-4136	324	10	,	,	PUNCT
ejpam-4136	324	11	βn)(xm	βn)(xm	PRON
ejpam-4136	324	12	,	,	PUNCT
ejpam-4136	324	13	(	(	PUNCT
ejpam-4136	324	14	xsi	xsi	PROPN
ejpam-4136	324	15	)	)	PUNCT
ejpam-4136	324	16	n−1	n−1	PROPN
ejpam-4136	324	17	i=1	i=1	PROPN
ejpam-4136	324	18	)	)	PUNCT
ejpam-4136	325	1	→	→	PUNCT
ejpam-4136	325	2	{	{	PUNCT
ejpam-4136	325	3	0a	0a	PROPN
ejpam-4136	325	4	}	}	PUNCT
ejpam-4136	325	5	;	;	PUNCT
ejpam-4136	325	6	whenever	whenever	SCONJ
ejpam-4136	325	7	,	,	PUNCT
ejpam-4136	325	8	m	m	PROPN
ejpam-4136	325	9	,	,	PUNCT
ejpam-4136	325	10	s1	s1	NOUN
ejpam-4136	325	11	,	,	PUNCT
ejpam-4136	325	12	.	.	PUNCT
ejpam-4136	325	13	.	.	PUNCT
ejpam-4136	325	14	.	.	PUNCT
ejpam-4136	326	1	,	,	PUNCT
ejpam-4136	326	2	sn−1	sn−1	PROPN
ejpam-4136	326	3	→	→	SYM
ejpam-4136	326	4	+	+	PROPN
ejpam-4136	326	5	∞	∞	PROPN
ejpam-4136	326	6	,	,	PUNCT
ejpam-4136	326	7	(	(	PUNCT
ejpam-4136	326	8	10	10	NUM
ejpam-4136	326	9	)	)	PUNCT
ejpam-4136	326	10	then	then	ADV
ejpam-4136	326	11	{	{	PUNCT
ejpam-4136	326	12	xm	xm	NOUN
ejpam-4136	326	13	}	}	PUNCT
ejpam-4136	326	14	is	be	AUX
ejpam-4136	326	15	a	a	DET
ejpam-4136	326	16	cauchy	cauchy	ADJ
ejpam-4136	326	17	sequence	sequence	NOUN
ejpam-4136	326	18	.	.	PUNCT
ejpam-4136	327	1	by	by	ADP
ejpam-4136	327	2	completeness	completeness	NOUN
ejpam-4136	327	3	of	of	ADP
ejpam-4136	327	4	(	(	PUNCT
ejpam-4136	327	5	x	x	NOUN
ejpam-4136	327	6	,	,	PUNCT
ejpam-4136	327	7	γ(αn	γ(αn	VERB
ejpam-4136	327	8	,	,	PUNCT
ejpam-4136	327	9	βn	βn	NOUN
ejpam-4136	327	10	)	)	PUNCT
ejpam-4136	327	11	)	)	PUNCT
ejpam-4136	327	12	,	,	PUNCT
ejpam-4136	327	13	there	there	PRON
ejpam-4136	327	14	exists	exist	VERB
ejpam-4136	327	15	a	a	DET
ejpam-4136	327	16	∈	∈	NOUN
ejpam-4136	327	17	x	x	PUNCT
ejpam-4136	327	18	such	such	ADJ
ejpam-4136	327	19	that	that	SCONJ
ejpam-4136	327	20	{	{	PUNCT
ejpam-4136	327	21	xn	xn	X
ejpam-4136	327	22	}	}	PUNCT
ejpam-4136	327	23	is	be	AUX
ejpam-4136	327	24	b(αn	b(αn	NOUN
ejpam-4136	327	25	,	,	PUNCT
ejpam-4136	327	26	βn)-convergent	βn)-convergent	NOUN
ejpam-4136	327	27	to	to	PART
ejpam-4136	327	28	a.	a.	NOUN
ejpam-4136	327	29	it	it	PRON
ejpam-4136	327	30	follows	follow	VERB
ejpam-4136	327	31	that	that	SCONJ
ejpam-4136	327	32	the	the	DET
ejpam-4136	327	33	limit	limit	NOUN
ejpam-4136	327	34	xm	xm	PROPN
ejpam-4136	327	35	is	be	AUX
ejpam-4136	327	36	a	a	DET
ejpam-4136	327	37	fixed	fix	VERB
ejpam-4136	327	38	point	point	NOUN
ejpam-4136	327	39	of	of	ADP
ejpam-4136	327	40	t	t	PROPN
ejpam-4136	327	41	follows	follow	VERB
ejpam-4136	327	42	the	the	DET
ejpam-4136	327	43	b(αn	b(αn	NOUN
ejpam-4136	327	44	,	,	PUNCT
ejpam-4136	327	45	βn)-continuity	βn)-continuity	NOUN
ejpam-4136	327	46	of	of	ADP
ejpam-4136	327	47	t	t	PROPN
ejpam-4136	327	48	,	,	PUNCT
ejpam-4136	327	49	and	and	CCONJ
ejpam-4136	327	50	ta	ta	X
ejpam-4136	328	1	=	=	SYM
ejpam-4136	328	2	t	t	PROPN
ejpam-4136	328	3	lim	lim	PROPN
ejpam-4136	328	4	m→+∞	m→+∞	PROPN
ejpam-4136	328	5	xm	xm	PROPN
ejpam-4136	329	1	=	=	SYM
ejpam-4136	329	2	lim	lim	PROPN
ejpam-4136	329	3	m→+∞	m→+∞	PROPN
ejpam-4136	329	4	txm	txm	PROPN
ejpam-4136	329	5	=	=	PROPN
ejpam-4136	329	6	lim	lim	PROPN
ejpam-4136	329	7	m→+∞	m→+∞	PROPN
ejpam-4136	329	8	xm+1	xm+1	PROPN
ejpam-4136	329	9	=	=	PUNCT
ejpam-4136	329	10	a.	a.	NOUN
ejpam-4136	329	11	(	(	PUNCT
ejpam-4136	329	12	11	11	NUM
ejpam-4136	329	13	)	)	PUNCT
ejpam-4136	329	14	finally	finally	ADV
ejpam-4136	329	15	,	,	PUNCT
ejpam-4136	329	16	if	if	SCONJ
ejpam-4136	329	17	a	a	PRON
ejpam-4136	329	18	and	and	CCONJ
ejpam-4136	329	19	b	b	NOUN
ejpam-4136	329	20	are	be	AUX
ejpam-4136	329	21	two	two	NUM
ejpam-4136	329	22	fixed	fix	VERB
ejpam-4136	329	23	points	point	NOUN
ejpam-4136	329	24	,	,	PUNCT
ejpam-4136	329	25	then	then	ADV
ejpam-4136	329	26	{	{	PUNCT
ejpam-4136	329	27	0a	0a	PROPN
ejpam-4136	329	28	}	}	PUNCT
ejpam-4136	329	29	⊆	⊆	NUM
ejpam-4136	329	30	γ(αn	γ(αn	NOUN
ejpam-4136	329	31	,	,	PUNCT
ejpam-4136	329	32	βn)(a	βn)(a	PROPN
ejpam-4136	329	33	,	,	PUNCT
ejpam-4136	329	34	(	(	PUNCT
ejpam-4136	329	35	b	b	NOUN
ejpam-4136	329	36	)	)	PUNCT
ejpam-4136	329	37	n	n	DET
ejpam-4136	329	38	2	2	NUM
ejpam-4136	329	39	)	)	PUNCT
ejpam-4136	329	40	=	=	SYM
ejpam-4136	329	41	γ(αn	γ(αn	PROPN
ejpam-4136	329	42	,	,	PUNCT
ejpam-4136	329	43	βn	βn	NOUN
ejpam-4136	329	44	)	)	PUNCT
ejpam-4136	329	45	(	(	PUNCT
ejpam-4136	329	46	t	t	PROPN
ejpam-4136	329	47	(	(	PUNCT
ejpam-4136	329	48	a	a	NOUN
ejpam-4136	329	49	)	)	PUNCT
ejpam-4136	329	50	,	,	PUNCT
ejpam-4136	329	51	(	(	PUNCT
ejpam-4136	329	52	t	t	PROPN
ejpam-4136	329	53	(	(	PUNCT
ejpam-4136	329	54	b))n2	b))n2	NUM
ejpam-4136	329	55	)	)	PUNCT
ejpam-4136	330	1	⊆	⊆	NUM
ejpam-4136	330	2	kγ(αn	kγ(αn	NOUN
ejpam-4136	330	3	,	,	PUNCT
ejpam-4136	330	4	βn)(a	βn)(a	PROPN
ejpam-4136	330	5	,	,	PUNCT
ejpam-4136	330	6	(	(	PUNCT
ejpam-4136	330	7	b	b	NOUN
ejpam-4136	330	8	)	)	PUNCT
ejpam-4136	330	9	n	n	PRON
ejpam-4136	330	10	2	2	NUM
ejpam-4136	330	11	)	)	PUNCT
ejpam-4136	330	12	.	.	PUNCT
ejpam-4136	331	1	(	(	PUNCT
ejpam-4136	331	2	12	12	NUM
ejpam-4136	331	3	)	)	PUNCT
ejpam-4136	331	4	we	we	PRON
ejpam-4136	331	5	conclude	conclude	VERB
ejpam-4136	331	6	from	from	ADP
ejpam-4136	331	7	k	k	PROPN
ejpam-4136	331	8	≺	≺	NOUN
ejpam-4136	331	9	ea	ea	CCONJ
ejpam-4136	331	10	that	that	PRON
ejpam-4136	331	11	γn(a	γn(a	ADP
ejpam-4136	331	12	,	,	PUNCT
ejpam-4136	331	13	(	(	PUNCT
ejpam-4136	331	14	b	b	NOUN
ejpam-4136	331	15	)	)	PUNCT
ejpam-4136	331	16	n	n	PRON
ejpam-4136	331	17	2	2	NUM
ejpam-4136	331	18	)	)	PUNCT
ejpam-4136	331	19	=	=	PRON
ejpam-4136	331	20	{	{	PUNCT
ejpam-4136	331	21	0a	0a	PROPN
ejpam-4136	331	22	}	}	PUNCT
ejpam-4136	331	23	.	.	PUNCT
ejpam-4136	332	1	consequently	consequently	ADV
ejpam-4136	332	2	a	a	DET
ejpam-4136	332	3	=	=	SYM
ejpam-4136	332	4	b	b	NOUN
ejpam-4136	332	5	and	and	CCONJ
ejpam-4136	332	6	the	the	DET
ejpam-4136	332	7	fixed	fix	VERB
ejpam-4136	332	8	point	point	NOUN
ejpam-4136	332	9	is	be	AUX
ejpam-4136	332	10	unique	unique	ADJ
ejpam-4136	332	11	.	.	PUNCT
ejpam-4136	333	1	references	reference	NOUN
ejpam-4136	333	2	1159	1159	NUM
ejpam-4136	333	3	proposition	proposition	NOUN
ejpam-4136	333	4	20	20	NUM
ejpam-4136	333	5	.	.	PUNCT
ejpam-4136	334	1	the	the	DET
ejpam-4136	334	2	equation	equation	NOUN
ejpam-4136	334	3	x	x	PUNCT
ejpam-4136	334	4	l	l	NOUN
ejpam-4136	334	5	+	+	NOUN
ejpam-4136	334	6	1	1	NUM
ejpam-4136	334	7	=	=	SYM
ejpam-4136	334	8	(	(	PUNCT
ejpam-4136	334	9	l2	l2	NOUN
ejpam-4136	334	10	−	−	PROPN
ejpam-4136	334	11	1)xl+1	1)xl+1	PROPN
ejpam-4136	334	12	+	+	PUNCT
ejpam-4136	334	13	l2x	l2x	PROPN
ejpam-4136	334	14	,	,	PUNCT
ejpam-4136	334	15	for	for	ADP
ejpam-4136	334	16	each	each	DET
ejpam-4136	334	17	natural	natural	ADJ
ejpam-4136	334	18	nuber	nuber	PROPN
ejpam-4136	334	19	l	l	PROPN
ejpam-4136	334	20	>	>	X
ejpam-4136	334	21	1	1	NUM
ejpam-4136	334	22	,	,	PUNCT
ejpam-4136	334	23	has	have	VERB
ejpam-4136	334	24	a	a	DET
ejpam-4136	334	25	unique	unique	ADJ
ejpam-4136	334	26	real	real	ADJ
ejpam-4136	334	27	solution	solution	NOUN
ejpam-4136	334	28	.	.	PUNCT
ejpam-4136	335	1	proof	proof	NOUN
ejpam-4136	335	2	.	.	PUNCT
ejpam-4136	336	1	on	on	ADP
ejpam-4136	336	2	can	can	AUX
ejpam-4136	336	3	check	check	VERB
ejpam-4136	336	4	that	that	SCONJ
ejpam-4136	336	5	if	if	SCONJ
ejpam-4136	336	6	x	x	X
ejpam-4136	336	7	∈	∈	NOUN
ejpam-4136	336	8	r	r	NOUN
ejpam-4136	336	9	with	with	ADP
ejpam-4136	336	10	|x|	|x|	PROPN
ejpam-4136	336	11	>	>	SYM
ejpam-4136	336	12	1	1	NUM
ejpam-4136	336	13	,	,	PUNCT
ejpam-4136	336	14	then	then	ADV
ejpam-4136	336	15	x	x	PUNCT
ejpam-4136	336	16	is	be	AUX
ejpam-4136	336	17	not	not	PART
ejpam-4136	336	18	a	a	DET
ejpam-4136	336	19	solution	solution	NOUN
ejpam-4136	336	20	for	for	ADP
ejpam-4136	336	21	the	the	DET
ejpam-4136	336	22	above	above	ADJ
ejpam-4136	336	23	equation	equation	NOUN
ejpam-4136	336	24	.	.	PUNCT
ejpam-4136	337	1	now	now	ADV
ejpam-4136	337	2	let	let	VERB
ejpam-4136	337	3	x	x	PUNCT
ejpam-4136	337	4	=	=	PUNCT
ejpam-4136	338	1	[	[	X
ejpam-4136	338	2	−1	−1	NOUN
ejpam-4136	338	3	,	,	PUNCT
ejpam-4136	338	4	1	1	NUM
ejpam-4136	338	5	]	]	PUNCT
ejpam-4136	338	6	.	.	PUNCT
ejpam-4136	339	1	define	define	VERB
ejpam-4136	339	2	ωα2,β2	ωα2,β2	NOUN
ejpam-4136	339	3	:	:	PUNCT
ejpam-4136	339	4	x	x	PUNCT
ejpam-4136	339	5	×	×	NOUN
ejpam-4136	339	6	x	x	INTJ
ejpam-4136	339	7	→	→	X
ejpam-4136	339	8	p	p	X
ejpam-4136	339	9	∗(r0	∗(r0	VERB
ejpam-4136	339	10	+	+	NOUN
ejpam-4136	339	11	)	)	PUNCT
ejpam-4136	339	12	with	with	ADP
ejpam-4136	339	13	,	,	PUNCT
ejpam-4136	339	14	ωα2,β2(x	ωα2,β2(x	PROPN
ejpam-4136	339	15	,	,	PUNCT
ejpam-4136	339	16	y	y	PROPN
ejpam-4136	339	17	)	)	PUNCT
ejpam-4136	339	18	=	=	PUNCT
ejpam-4136	340	1	[	[	X
ejpam-4136	340	2	0	0	NUM
ejpam-4136	340	3	,	,	PUNCT
ejpam-4136	340	4	|x−y|	|x−y|	NOUN
ejpam-4136	340	5	]	]	PUNCT
ejpam-4136	340	6	and	and	CCONJ
ejpam-4136	340	7	α2	α2	ADJ
ejpam-4136	340	8	,	,	PUNCT
ejpam-4136	340	9	β2	β2	VERB
ejpam-4136	340	10	:	:	PUNCT
ejpam-4136	340	11	x×x	x×x	PROPN
ejpam-4136	340	12	−→	−→	NOUN
ejpam-4136	340	13	[	[	X
ejpam-4136	340	14	1,+∞	1,+∞	NUM
ejpam-4136	340	15	)	)	PUNCT
ejpam-4136	340	16	,	,	PUNCT
ejpam-4136	340	17	with	with	ADP
ejpam-4136	340	18	α2(x	α2(x	PROPN
ejpam-4136	340	19	,	,	PUNCT
ejpam-4136	340	20	y	y	NOUN
ejpam-4136	340	21	)	)	PUNCT
ejpam-4136	340	22	=	=	SYM
ejpam-4136	340	23	1+|x|+|y|	1+|x|+|y|	NUM
ejpam-4136	340	24	,	,	PUNCT
ejpam-4136	340	25	β2(x	β2(x	NUM
ejpam-4136	340	26	,	,	PUNCT
ejpam-4136	340	27	y	y	NOUN
ejpam-4136	340	28	)	)	PUNCT
ejpam-4136	340	29	=	=	SYM
ejpam-4136	341	1	2+|x|+|y|	2+|x|+|y|	NUM
ejpam-4136	341	2	.	.	PUNCT
ejpam-4136	342	1	then	then	ADV
ejpam-4136	342	2	(	(	PUNCT
ejpam-4136	342	3	x	x	NOUN
ejpam-4136	342	4	,	,	PUNCT
ejpam-4136	342	5	ω(α2,β2	ω(α2,β2	NUM
ejpam-4136	342	6	)	)	PUNCT
ejpam-4136	342	7	)	)	PUNCT
ejpam-4136	342	8	is	be	AUX
ejpam-4136	342	9	a	a	DET
ejpam-4136	342	10	complete	complete	ADJ
ejpam-4136	342	11	b(α2,β2)-hypermetric	b(α2,β2)-hypermetric	ADJ
ejpam-4136	342	12	space	space	NOUN
ejpam-4136	342	13	over	over	ADP
ejpam-4136	342	14	banach	banach	NOUN
ejpam-4136	342	15	algebra	algebra	NOUN
ejpam-4136	342	16	r	r	NOUN
ejpam-4136	342	17	.	.	PUNCT
ejpam-4136	343	1	also	also	ADV
ejpam-4136	343	2	,	,	PUNCT
ejpam-4136	343	3	define	define	VERB
ejpam-4136	343	4	the	the	DET
ejpam-4136	343	5	mapping	mapping	NOUN
ejpam-4136	343	6	t	t	NOUN
ejpam-4136	343	7	:	:	PUNCT
ejpam-4136	343	8	x	x	X
ejpam-4136	343	9	→	→	SYM
ejpam-4136	343	10	x	x	PUNCT
ejpam-4136	343	11	by	by	ADP
ejpam-4136	343	12	tx	tx	PROPN
ejpam-4136	343	13	=	=	PUNCT
ejpam-4136	343	14	xl	xl	PROPN
ejpam-4136	344	1	+	+	NUM
ejpam-4136	344	2	1	1	NUM
ejpam-4136	344	3	(	(	PUNCT
ejpam-4136	344	4	l2	l2	NOUN
ejpam-4136	344	5	−	−	PROPN
ejpam-4136	344	6	1)xl	1)xl	PROPN
ejpam-4136	344	7	+	+	NUM
ejpam-4136	344	8	l2	l2	NOUN
ejpam-4136	344	9	.	.	PUNCT
ejpam-4136	345	1	now	now	ADV
ejpam-4136	345	2	,	,	PUNCT
ejpam-4136	345	3	we	we	PRON
ejpam-4136	345	4	study	study	VERB
ejpam-4136	345	5	the	the	DET
ejpam-4136	345	6	following	following	ADJ
ejpam-4136	345	7	cases	case	NOUN
ejpam-4136	345	8	:	:	PUNCT
ejpam-4136	345	9	case	case	NOUN
ejpam-4136	346	1	i	i	PRON
ejpam-4136	346	2	:	:	PUNCT
ejpam-4136	346	3	if	if	SCONJ
ejpam-4136	346	4	x	x	X
ejpam-4136	346	5	=	=	PUNCT
ejpam-4136	346	6	y.	y.	NOUN
ejpam-4136	346	7	then	then	ADV
ejpam-4136	346	8	ω(α2,β2)(t	ω(α2,β2)(t	PROPN
ejpam-4136	346	9	(	(	PUNCT
ejpam-4136	346	10	x	x	NOUN
ejpam-4136	346	11	)	)	PUNCT
ejpam-4136	346	12	,	,	PUNCT
ejpam-4136	346	13	t	t	PROPN
ejpam-4136	346	14	(	(	PUNCT
ejpam-4136	346	15	y	y	NOUN
ejpam-4136	346	16	)	)	PUNCT
ejpam-4136	346	17	)	)	PUNCT
ejpam-4136	347	1	=	=	SYM
ejpam-4136	347	2	ω(α2,β2)(t	ω(α2,β2)(t	X
ejpam-4136	347	3	(	(	PUNCT
ejpam-4136	347	4	x	x	NOUN
ejpam-4136	347	5	)	)	PUNCT
ejpam-4136	347	6	,	,	PUNCT
ejpam-4136	347	7	t	t	PROPN
ejpam-4136	347	8	(	(	PUNCT
ejpam-4136	347	9	x	x	NOUN
ejpam-4136	347	10	)	)	PUNCT
ejpam-4136	347	11	)	)	PUNCT
ejpam-4136	347	12	=	=	PRON
ejpam-4136	347	13	{	{	PUNCT
ejpam-4136	347	14	0	0	NUM
ejpam-4136	347	15	}	}	NUM
ejpam-4136	347	16	⊆	⊆	NUM
ejpam-4136	347	17	1	1	NUM
ejpam-4136	347	18	l3	l3	NOUN
ejpam-4136	347	19	ω(α2,β2)(x	ω(α2,β2)(x	PROPN
ejpam-4136	347	20	,	,	PUNCT
ejpam-4136	347	21	y	y	PROPN
ejpam-4136	347	22	)	)	PUNCT
ejpam-4136	347	23	=	=	PRON
ejpam-4136	347	24	{	{	PUNCT
ejpam-4136	347	25	0	0	NUM
ejpam-4136	347	26	}	}	PUNCT
ejpam-4136	347	27	.	.	PUNCT
ejpam-4136	348	1	case	case	NOUN
ejpam-4136	348	2	ii	ii	NOUN
ejpam-4136	348	3	:	:	PUNCT
ejpam-4136	348	4	if	if	SCONJ
ejpam-4136	348	5	x	x	PROPN
ejpam-4136	348	6	̸=	̸=	PROPN
ejpam-4136	348	7	y.	y.	NOUN
ejpam-4136	348	8	then	then	ADV
ejpam-4136	348	9	ω(α2,β2)(t	ω(α2,β2)(t	PROPN
ejpam-4136	348	10	(	(	PUNCT
ejpam-4136	348	11	x	x	NOUN
ejpam-4136	348	12	)	)	PUNCT
ejpam-4136	348	13	,	,	PUNCT
ejpam-4136	348	14	t	t	PROPN
ejpam-4136	348	15	(	(	PUNCT
ejpam-4136	348	16	y	y	NOUN
ejpam-4136	348	17	)	)	PUNCT
ejpam-4136	348	18	)	)	PUNCT
ejpam-4136	348	19	=	=	SYM
ejpam-4136	348	20	ω(α2,β2	ω(α2,β2	X
ejpam-4136	348	21	)	)	PUNCT
ejpam-4136	348	22	(	(	PUNCT
ejpam-4136	348	23	xl	xl	PROPN
ejpam-4136	348	24	+	+	NUM
ejpam-4136	348	25	1	1	NUM
ejpam-4136	348	26	(	(	PUNCT
ejpam-4136	348	27	l2	l2	NOUN
ejpam-4136	348	28	−	−	PROPN
ejpam-4136	348	29	1)xl	1)xl	PROPN
ejpam-4136	348	30	+	+	NUM
ejpam-4136	348	31	l2	l2	NOUN
ejpam-4136	348	32	,	,	PUNCT
ejpam-4136	348	33	yl	yl	NOUN
ejpam-4136	348	34	+	+	CCONJ
ejpam-4136	348	35	1	1	NUM
ejpam-4136	348	36	(	(	PUNCT
ejpam-4136	348	37	l2	l2	NOUN
ejpam-4136	348	38	−	−	ADP
ejpam-4136	348	39	1)yl	1)yl	NUM
ejpam-4136	348	40	+	+	NUM
ejpam-4136	348	41	l2	l2	NOUN
ejpam-4136	348	42	)	)	PUNCT
ejpam-4136	348	43	=	=	PUNCT
ejpam-4136	349	1	[	[	X
ejpam-4136	349	2	0	0	NUM
ejpam-4136	349	3	,	,	PUNCT
ejpam-4136	349	4	xl	xl	PROPN
ejpam-4136	349	5	+	+	CCONJ
ejpam-4136	349	6	1	1	NUM
ejpam-4136	349	7	(	(	PUNCT
ejpam-4136	349	8	l2	l2	NOUN
ejpam-4136	349	9	−	−	PROPN
ejpam-4136	349	10	1)xl	1)xl	PROPN
ejpam-4136	349	11	+	+	NUM
ejpam-4136	349	12	l2	l2	NOUN
ejpam-4136	349	13	−	−	NOUN
ejpam-4136	349	14	yl	yl	NOUN
ejpam-4136	349	15	+	+	CCONJ
ejpam-4136	349	16	1	1	NUM
ejpam-4136	349	17	(	(	PUNCT
ejpam-4136	349	18	l2	l2	NOUN
ejpam-4136	349	19	−	−	ADP
ejpam-4136	349	20	1)yl	1)yl	NUM
ejpam-4136	349	21	+	+	NUM
ejpam-4136	349	22	l2	l2	NOUN
ejpam-4136	349	23	]	]	PUNCT
ejpam-4136	349	24	=	=	PUNCT
ejpam-4136	350	1	[	[	X
ejpam-4136	350	2	0	0	NUM
ejpam-4136	350	3	,	,	PUNCT
ejpam-4136	350	4	|xl	|xl	X
ejpam-4136	350	5	−	−	PUNCT
ejpam-4136	350	6	yl|	yl|	PROPN
ejpam-4136	350	7	(	(	PUNCT
ejpam-4136	350	8	(	(	PUNCT
ejpam-4136	350	9	l2	l2	VERB
ejpam-4136	350	10	−	−	PROPN
ejpam-4136	350	11	1)xl	1)xl	PROPN
ejpam-4136	350	12	+	+	CCONJ
ejpam-4136	350	13	l2)((l2	l2)((l2	NUM
ejpam-4136	350	14	−	−	PROPN
ejpam-4136	351	1	1)yl	1)yl	NUM
ejpam-4136	351	2	+	+	NUM
ejpam-4136	351	3	l2	l2	NOUN
ejpam-4136	351	4	)	)	PUNCT
ejpam-4136	351	5	]	]	PUNCT
ejpam-4136	352	1	⊆	⊆	NUM
ejpam-4136	352	2	1	1	NUM
ejpam-4136	352	3	l3	l3	NOUN
ejpam-4136	352	4	|x−	|x−	NOUN
ejpam-4136	352	5	y|	y|	NOUN
ejpam-4136	352	6	⊆	⊆	SYM
ejpam-4136	352	7	1	1	NUM
ejpam-4136	352	8	l3	l3	NOUN
ejpam-4136	352	9	ω(α2,β2)(x	ω(α2,β2)(x	PROPN
ejpam-4136	352	10	,	,	PUNCT
ejpam-4136	352	11	y	y	PROPN
ejpam-4136	352	12	)	)	PUNCT
ejpam-4136	352	13	,	,	PUNCT
ejpam-4136	352	14	where	where	SCONJ
ejpam-4136	352	15	we	we	PRON
ejpam-4136	352	16	choose	choose	VERB
ejpam-4136	352	17	k	k	NOUN
ejpam-4136	352	18	=	=	SYM
ejpam-4136	352	19	1	1	NUM
ejpam-4136	352	20	l3	l3	X
ejpam-4136	352	21	<	<	X
ejpam-4136	352	22	1	1	NUM
ejpam-4136	352	23	.	.	PUNCT
ejpam-4136	352	24	thus	thus	ADV
ejpam-4136	352	25	,	,	PUNCT
ejpam-4136	352	26	t	t	PROPN
ejpam-4136	352	27	satisfies	satisfy	VERB
ejpam-4136	352	28	all	all	DET
ejpam-4136	352	29	conditions	condition	NOUN
ejpam-4136	352	30	of	of	ADP
ejpam-4136	352	31	theorem	theorem	NOUN
ejpam-4136	352	32	2.32	2.32	NUM
ejpam-4136	352	33	.	.	PUNCT
ejpam-4136	353	1	therefore	therefore	ADV
ejpam-4136	353	2	,	,	PUNCT
ejpam-4136	353	3	t	t	PROPN
ejpam-4136	353	4	has	have	VERB
ejpam-4136	353	5	a	a	DET
ejpam-4136	353	6	unique	unique	ADJ
ejpam-4136	353	7	fixed	fix	VERB
ejpam-4136	353	8	point	point	NOUN
ejpam-4136	353	9	.	.	PUNCT
ejpam-4136	354	1	note	note	VERB
ejpam-4136	354	2	that	that	SCONJ
ejpam-4136	354	3	the	the	DET
ejpam-4136	354	4	unique	unique	ADJ
ejpam-4136	354	5	fixed	fix	VERB
ejpam-4136	354	6	point	point	NOUN
ejpam-4136	354	7	of	of	ADP
ejpam-4136	354	8	t	t	PROPN
ejpam-4136	354	9	is	be	AUX
ejpam-4136	354	10	the	the	DET
ejpam-4136	354	11	unique	unique	ADJ
ejpam-4136	354	12	solution	solution	NOUN
ejpam-4136	354	13	of	of	ADP
ejpam-4136	354	14	the	the	DET
ejpam-4136	354	15	equation	equation	NOUN
ejpam-4136	354	16	.	.	PUNCT
ejpam-4136	355	1	3	3	X
ejpam-4136	355	2	.	.	X
ejpam-4136	355	3	conclusion	conclusion	NOUN
ejpam-4136	355	4	the	the	DET
ejpam-4136	355	5	objective	objective	NOUN
ejpam-4136	355	6	of	of	ADP
ejpam-4136	355	7	this	this	DET
ejpam-4136	355	8	paper	paper	NOUN
ejpam-4136	355	9	is	be	AUX
ejpam-4136	355	10	to	to	PART
ejpam-4136	355	11	study	study	VERB
ejpam-4136	355	12	about	about	ADP
ejpam-4136	355	13	b(αn	b(αn	NOUN
ejpam-4136	355	14	,	,	PUNCT
ejpam-4136	355	15	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	355	16	spaces	space	NOUN
ejpam-4136	355	17	and	and	CCONJ
ejpam-4136	355	18	introduced	introduce	VERB
ejpam-4136	355	19	certain	certain	ADJ
ejpam-4136	355	20	fixed	fix	VERB
ejpam-4136	355	21	point	point	NOUN
ejpam-4136	355	22	results	result	NOUN
ejpam-4136	355	23	of	of	ADP
ejpam-4136	355	24	mappings	mapping	NOUN
ejpam-4136	355	25	in	in	ADP
ejpam-4136	355	26	the	the	DET
ejpam-4136	355	27	setting	setting	NOUN
ejpam-4136	355	28	of	of	ADP
ejpam-4136	355	29	b(αn	b(αn	NOUN
ejpam-4136	355	30	,	,	PUNCT
ejpam-4136	355	31	βn)-hypermetric	βn)-hypermetric	ADJ
ejpam-4136	355	32	spaces	space	NOUN
ejpam-4136	355	33	.	.	PUNCT
ejpam-4136	356	1	this	this	DET
ejpam-4136	356	2	study	study	NOUN
ejpam-4136	356	3	is	be	AUX
ejpam-4136	356	4	a	a	DET
ejpam-4136	356	5	candidate	candidate	NOUN
ejpam-4136	356	6	of	of	ADP
ejpam-4136	356	7	a	a	DET
ejpam-4136	356	8	pioneer	pioneer	NOUN
ejpam-4136	356	9	result	result	NOUN
ejpam-4136	356	10	and	and	CCONJ
ejpam-4136	356	11	many	many	ADJ
ejpam-4136	356	12	refined	refined	ADJ
ejpam-4136	356	13	results	result	NOUN
ejpam-4136	356	14	can	can	AUX
ejpam-4136	356	15	be	be	AUX
ejpam-4136	356	16	derived	derive	VERB
ejpam-4136	356	17	in	in	ADP
ejpam-4136	356	18	the	the	DET
ejpam-4136	356	19	near	near	ADJ
ejpam-4136	356	20	future	future	NOUN
ejpam-4136	356	21	.	.	PUNCT
ejpam-4136	357	1	the	the	DET
ejpam-4136	357	2	purpose	purpose	NOUN
ejpam-4136	357	3	definition	definition	NOUN
ejpam-4136	357	4	is	be	AUX
ejpam-4136	357	5	applicable	applicable	ADJ
ejpam-4136	357	6	for	for	ADP
ejpam-4136	357	7	engineering	engineering	NOUN
ejpam-4136	357	8	science	science	NOUN
ejpam-4136	357	9	.	.	PUNCT
ejpam-4136	358	1	references	reference	NOUN
ejpam-4136	358	2	[	[	X
ejpam-4136	358	3	1	1	X
ejpam-4136	358	4	]	]	PUNCT
ejpam-4136	358	5	s.	s.	PROPN
ejpam-4136	358	6	radenović	radenović	PROPN
ejpam-4136	358	7	and	and	CCONJ
ejpam-4136	358	8	b.	b.	PROPN
ejpam-4136	358	9	e.	e.	PROPN
ejpam-4136	358	10	rhoadesb	rhoadesb	PROPN
ejpam-4136	358	11	.	.	PUNCT
ejpam-4136	359	1	fixed	fix	VERB
ejpam-4136	359	2	point	point	NOUN
ejpam-4136	359	3	theorem	theorem	VERB
ejpam-4136	359	4	for	for	ADP
ejpam-4136	359	5	two	two	NUM
ejpam-4136	359	6	non	non	ADJ
ejpam-4136	359	7	-	-	ADJ
ejpam-4136	359	8	self	self	ADJ
ejpam-4136	359	9	mappings	mapping	NOUN
ejpam-4136	359	10	in	in	ADP
ejpam-4136	359	11	cone	cone	NOUN
ejpam-4136	359	12	metric	metric	ADJ
ejpam-4136	359	13	spaces	space	NOUN
ejpam-4136	359	14	.	.	PUNCT
ejpam-4136	360	1	computers	computer	NOUN
ejpam-4136	360	2	and	and	CCONJ
ejpam-4136	360	3	mathematics	mathematic	NOUN
ejpam-4136	360	4	with	with	ADP
ejpam-4136	360	5	applications	application	NOUN
ejpam-4136	360	6	,	,	PUNCT
ejpam-4136	360	7	57:1701–1707	57:1701–1707	NUM
ejpam-4136	360	8	,	,	PUNCT
ejpam-4136	360	9	2009	2009	NUM
ejpam-4136	360	10	.	.	PUNCT
ejpam-4136	361	1	references	reference	NOUN
ejpam-4136	361	2	1160	1160	NUM
ejpam-4136	361	3	[	[	X
ejpam-4136	361	4	2	2	NUM
ejpam-4136	361	5	]	]	PUNCT
ejpam-4136	361	6	i.	i.	NOUN
ejpam-4136	361	7	bakhtin	bakhtin	PROPN
ejpam-4136	361	8	.	.	PUNCT
ejpam-4136	362	1	the	the	DET
ejpam-4136	362	2	contraction	contraction	NOUN
ejpam-4136	362	3	mapping	map	VERB
ejpam-4136	362	4	principle	principle	NOUN
ejpam-4136	362	5	in	in	ADP
ejpam-4136	362	6	quasimetric	quasimetric	ADJ
ejpam-4136	362	7	spaces	space	NOUN
ejpam-4136	362	8	.	.	PUNCT
ejpam-4136	363	1	func	func	PROPN
ejpam-4136	363	2	.	.	PUNCT
ejpam-4136	364	1	an	an	DET
ejpam-4136	364	2	.	.	PROPN
ejpam-4136	364	3	,	,	PUNCT
ejpam-4136	364	4	gos	gos	PROPN
ejpam-4136	364	5	.	.	PUNCT
ejpam-4136	364	6	ped	ped	PROPN
ejpam-4136	364	7	.	.	PROPN
ejpam-4136	364	8	inst	inst	PROPN
ejpam-4136	364	9	.	.	PUNCT
ejpam-4136	365	1	unianowsk	unianowsk	PROPN
ejpam-4136	365	2	,	,	PUNCT
ejpam-4136	365	3	30:26–37	30:26–37	PROPN
ejpam-4136	365	4	,	,	PUNCT
ejpam-4136	365	5	1989	1989	NUM
ejpam-4136	365	6	.	.	PUNCT
ejpam-4136	366	1	[	[	X
ejpam-4136	366	2	3	3	X
ejpam-4136	366	3	]	]	PUNCT
ejpam-4136	366	4	v.	v.	CCONJ
ejpam-4136	366	5	berinde	berinde	NOUN
ejpam-4136	366	6	.	.	PUNCT
ejpam-4136	367	1	generalized	generalized	ADJ
ejpam-4136	367	2	contractions	contraction	NOUN
ejpam-4136	367	3	in	in	ADP
ejpam-4136	367	4	quasimetric	quasimetric	ADJ
ejpam-4136	367	5	spaces	space	NOUN
ejpam-4136	367	6	.	.	PUNCT
ejpam-4136	368	1	seminar	seminar	NOUN
ejpam-4136	368	2	on	on	ADP
ejpam-4136	368	3	fixed	fix	VERB
ejpam-4136	368	4	point	point	NOUN
ejpam-4136	368	5	theory	theory	NOUN
ejpam-4136	368	6	,	,	PUNCT
ejpam-4136	368	7	babes	babes	NOUN
ejpam-4136	368	8	-	-	PUNCT
ejpam-4136	368	9	bolyai	bolyai	NOUN
ejpam-4136	368	10	,	,	PUNCT
ejpam-4136	368	11	university	university	NOUN
ejpam-4136	368	12	,	,	PUNCT
ejpam-4136	368	13	3(9):3–9	3(9):3–9	NUM
ejpam-4136	368	14	,	,	PUNCT
ejpam-4136	368	15	1993	1993	NUM
ejpam-4136	368	16	.	.	PUNCT
ejpam-4136	369	1	[	[	X
ejpam-4136	369	2	4	4	X
ejpam-4136	369	3	]	]	X
ejpam-4136	369	4	s.	s.	PROPN
ejpam-4136	369	5	czerwik	czerwik	PROPN
ejpam-4136	369	6	.	.	PUNCT
ejpam-4136	370	1	contraction	contraction	NOUN
ejpam-4136	370	2	mappings	mapping	NOUN
ejpam-4136	370	3	in	in	ADP
ejpam-4136	370	4	b	b	NOUN
ejpam-4136	370	5	-	-	ADJ
ejpam-4136	370	6	metric	metric	ADJ
ejpam-4136	370	7	spaces	space	NOUN
ejpam-4136	370	8	.	.	PUNCT
ejpam-4136	371	1	acta	acta	PROPN
ejpam-4136	371	2	math	math	PROPN
ejpam-4136	371	3	.	.	PUNCT
ejpam-4136	372	1	inform	inform	NOUN
ejpam-4136	372	2	.	.	PUNCT
ejpam-4136	373	1	univ	univ	PROPN
ejpam-4136	373	2	.	.	PROPN
ejpam-4136	374	1	ostrav	ostrav	PROPN
ejpam-4136	374	2	,	,	PUNCT
ejpam-4136	374	3	1:5–11	1:5–11	NUM
ejpam-4136	374	4	,	,	PUNCT
ejpam-4136	374	5	1993	1993	NUM
ejpam-4136	374	6	.	.	PUNCT
ejpam-4136	375	1	[	[	X
ejpam-4136	375	2	5	5	NUM
ejpam-4136	375	3	]	]	PUNCT
ejpam-4136	375	4	k.	k.	NOUN
ejpam-4136	375	5	deimling	deimling	PROPN
ejpam-4136	375	6	.	.	PUNCT
ejpam-4136	376	1	nonlinear	nonlinear	ADJ
ejpam-4136	376	2	functional	functional	ADJ
ejpam-4136	376	3	analysis	analysis	NOUN
ejpam-4136	376	4	.	.	PUNCT
ejpam-4136	377	1	springer	springer	NOUN
ejpam-4136	377	2	-	-	PUNCT
ejpam-4136	377	3	verlag	verlag	PROPN
ejpam-4136	377	4	,	,	PUNCT
ejpam-4136	377	5	newyork	newyork	PROPN
ejpam-4136	377	6	,	,	PUNCT
ejpam-4136	377	7	1985	1985	NUM
ejpam-4136	377	8	.	.	PUNCT
ejpam-4136	378	1	[	[	X
ejpam-4136	378	2	6	6	NUM
ejpam-4136	378	3	]	]	PUNCT
ejpam-4136	378	4	j.	j.	PROPN
ejpam-4136	378	5	fernandez	fernandez	PROPN
ejpam-4136	378	6	,	,	PUNCT
ejpam-4136	378	7	n.	n.	PROPN
ejpam-4136	378	8	malviya	malviya	PROPN
ejpam-4136	378	9	,	,	PUNCT
ejpam-4136	378	10	s.	s.	PROPN
ejpam-4136	378	11	radenoviµc	radenoviµc	PROPN
ejpam-4136	378	12	,	,	PUNCT
ejpam-4136	378	13	and	and	CCONJ
ejpam-4136	378	14	k.	k.	PROPN
ejpam-4136	378	15	saxena	saxena	PROPN
ejpam-4136	378	16	.	.	PUNCT
ejpam-4136	379	1	f	f	X
ejpam-4136	379	2	-	-	PUNCT
ejpam-4136	379	3	cone	cone	NOUN
ejpam-4136	379	4	metric	metric	ADJ
ejpam-4136	379	5	spaces	space	NOUN
ejpam-4136	379	6	over	over	ADP
ejpam-4136	379	7	banach	banach	NOUN
ejpam-4136	379	8	algebra	algebra	NOUN
ejpam-4136	379	9	.	.	PUNCT
ejpam-4136	380	1	fixed	fix	VERB
ejpam-4136	380	2	point	point	NOUN
ejpam-4136	380	3	theory	theory	NOUN
ejpam-4136	380	4	appl	appl	NOUN
ejpam-4136	380	5	,	,	PUNCT
ejpam-4136	380	6	7:18	7:18	NUM
ejpam-4136	380	7	pp	pp	NOUN
ejpam-4136	380	8	.	.	PUNCT
ejpam-4136	380	9	,	,	PUNCT
ejpam-4136	380	10	2017	2017	NUM
ejpam-4136	380	11	.	.	PUNCT
ejpam-4136	381	1	[	[	X
ejpam-4136	381	2	7	7	X
ejpam-4136	381	3	]	]	X
ejpam-4136	381	4	l.	l.	PROPN
ejpam-4136	381	5	huang	huang	PROPN
ejpam-4136	381	6	and	and	CCONJ
ejpam-4136	381	7	zhang	zhang	PROPN
ejpam-4136	381	8	x.	x.	PROPN
ejpam-4136	381	9	cone	cone	PROPN
ejpam-4136	381	10	metric	metric	ADJ
ejpam-4136	381	11	spaces	space	NOUN
ejpam-4136	381	12	and	and	CCONJ
ejpam-4136	381	13	fixed	fix	VERB
ejpam-4136	381	14	point	point	NOUN
ejpam-4136	381	15	theorems	theorem	NOUN
ejpam-4136	381	16	of	of	ADP
ejpam-4136	381	17	contractive	contractive	ADJ
ejpam-4136	381	18	mappings	mapping	NOUN
ejpam-4136	381	19	.	.	PUNCT
ejpam-4136	382	1	j.	j.	PROPN
ejpam-4136	382	2	math	math	PROPN
ejpam-4136	382	3	.	.	PUNCT
ejpam-4136	383	1	anal	anal	PROPN
ejpam-4136	383	2	.	.	PUNCT
ejpam-4136	384	1	appl	appl	PROPN
ejpam-4136	384	2	.	.	PROPN
ejpam-4136	384	3	,	,	PUNCT
ejpam-4136	384	4	332(2):1468–1476	332(2):1468–1476	PROPN
ejpam-4136	384	5	,	,	PUNCT
ejpam-4136	384	6	2007	2007	NUM
ejpam-4136	384	7	.	.	PUNCT
ejpam-4136	385	1	[	[	X
ejpam-4136	385	2	8	8	X
ejpam-4136	385	3	]	]	PUNCT
ejpam-4136	385	4	t.	t.	PROPN
ejpam-4136	385	5	kamran	kamran	PROPN
ejpam-4136	385	6	,	,	PUNCT
ejpam-4136	385	7	m.	m.	NOUN
ejpam-4136	385	8	samreen	samreen	PROPN
ejpam-4136	385	9	,	,	PUNCT
ejpam-4136	385	10	and	and	CCONJ
ejpam-4136	385	11	q.	q.	PROPN
ejpam-4136	385	12	ul	ul	INTJ
ejpam-4136	385	13	.	.	PUNCT
ejpam-4136	385	14	ain	ain	PROPN
ejpam-4136	385	15	.	.	PUNCT
ejpam-4136	386	1	a	a	DET
ejpam-4136	386	2	generalization	generalization	NOUN
ejpam-4136	386	3	of	of	ADP
ejpam-4136	386	4	b	b	NOUN
ejpam-4136	386	5	-	-	PUNCT
ejpam-4136	386	6	metric	metric	ADJ
ejpam-4136	386	7	space	space	NOUN
ejpam-4136	386	8	and	and	CCONJ
ejpam-4136	386	9	some	some	DET
ejpam-4136	386	10	fixed	fix	VERB
ejpam-4136	386	11	point	point	NOUN
ejpam-4136	386	12	theorems	theorem	NOUN
ejpam-4136	386	13	.	.	PUNCT
ejpam-4136	387	1	mathematics	mathematic	NOUN
ejpam-4136	387	2	,	,	PUNCT
ejpam-4136	387	3	5:1–7	5:1–7	NUM
ejpam-4136	387	4	,	,	PUNCT
ejpam-4136	387	5	2017	2017	NUM
ejpam-4136	387	6	.	.	PUNCT
ejpam-4136	388	1	[	[	X
ejpam-4136	388	2	9	9	NUM
ejpam-4136	388	3	]	]	PUNCT
ejpam-4136	388	4	r.	r.	PROPN
ejpam-4136	388	5	kannan	kannan	PROPN
ejpam-4136	388	6	.	.	PUNCT
ejpam-4136	389	1	some	some	DET
ejpam-4136	389	2	results	result	NOUN
ejpam-4136	389	3	on	on	ADP
ejpam-4136	389	4	fixed	fix	VERB
ejpam-4136	389	5	points	point	NOUN
ejpam-4136	389	6	.	.	PUNCT
ejpam-4136	390	1	am	be	AUX
ejpam-4136	390	2	.	.	PUNCT
ejpam-4136	391	1	math	math	NOUN
ejpam-4136	391	2	.	.	PUNCT
ejpam-4136	392	1	monthly	monthly	ADJ
ejpam-4136	392	2	,	,	PUNCT
ejpam-4136	392	3	79:405–408	79:405–408	PROPN
ejpam-4136	392	4	,	,	PUNCT
ejpam-4136	392	5	1969	1969	NUM
ejpam-4136	392	6	.	.	PUNCT
ejpam-4136	393	1	[	[	X
ejpam-4136	393	2	10	10	NUM
ejpam-4136	393	3	]	]	PUNCT
ejpam-4136	393	4	k.	k.	PROPN
ejpam-4136	393	5	a.	a.	PROPN
ejpam-4136	393	6	khan	khan	PROPN
ejpam-4136	393	7	.	.	PUNCT
ejpam-4136	394	1	on	on	ADP
ejpam-4136	394	2	the	the	DET
ejpam-4136	394	3	possibitity	possibitity	NOUN
ejpam-4136	394	4	of	of	ADP
ejpam-4136	394	5	n	n	CCONJ
ejpam-4136	394	6	-	-	PUNCT
ejpam-4136	394	7	topological	topological	ADJ
ejpam-4136	394	8	spaces	space	NOUN
ejpam-4136	394	9	.	.	PUNCT
ejpam-4136	395	1	internatial	internatial	ADJ
ejpam-4136	395	2	journal	journal	PROPN
ejpam-4136	395	3	of	of	ADP
ejpam-4136	395	4	mathematical	mathematical	ADJ
ejpam-4136	395	5	archive	archive	NOUN
ejpam-4136	395	6	,	,	PUNCT
ejpam-4136	395	7	3(6):2520–2523	3(6):2520–2523	NOUN
ejpam-4136	395	8	,	,	PUNCT
ejpam-4136	395	9	2012	2012	NUM
ejpam-4136	395	10	.	.	PUNCT
ejpam-4136	396	1	[	[	X
ejpam-4136	396	2	11	11	NUM
ejpam-4136	396	3	]	]	PUNCT
ejpam-4136	396	4	k.	k.	PROPN
ejpam-4136	396	5	a.	a.	PROPN
ejpam-4136	396	6	khan	khan	PROPN
ejpam-4136	396	7	.	.	PUNCT
ejpam-4136	397	1	generalized	generalized	ADJ
ejpam-4136	397	2	n	n	CCONJ
ejpam-4136	397	3	-	-	PUNCT
ejpam-4136	397	4	metric	metric	ADJ
ejpam-4136	397	5	spaces	space	NOUN
ejpam-4136	397	6	and	and	CCONJ
ejpam-4136	397	7	fixed	fix	VERB
ejpam-4136	397	8	point	point	NOUN
ejpam-4136	397	9	theorems	theorem	NOUN
ejpam-4136	397	10	.	.	PUNCT
ejpam-4136	398	1	journal	journal	PROPN
ejpam-4136	398	2	of	of	ADP
ejpam-4136	398	3	nonlinear	nonlinear	ADJ
ejpam-4136	398	4	and	and	CCONJ
ejpam-4136	398	5	convex	convex	ADJ
ejpam-4136	398	6	analysis	analysis	NOUN
ejpam-4136	398	7	,	,	PUNCT
ejpam-4136	398	8	15(6):1221–1229	15(6):1221–1229	NUM
ejpam-4136	398	9	,	,	PUNCT
ejpam-4136	398	10	2014	2014	NUM
ejpam-4136	398	11	.	.	PUNCT
ejpam-4136	399	1	[	[	X
ejpam-4136	399	2	12	12	NUM
ejpam-4136	399	3	]	]	PUNCT
ejpam-4136	399	4	a.	a.	NOUN
ejpam-4136	399	5	dehghan	dehghan	PROPN
ejpam-4136	399	6	nezhad	nezhad	VERB
ejpam-4136	399	7	,	,	PUNCT
ejpam-4136	399	8	ahmad	ahmad	PROPN
ejpam-4136	399	9	reza	reza	PROPN
ejpam-4136	399	10	forough	forough	PROPN
ejpam-4136	399	11	,	,	PUNCT
ejpam-4136	399	12	nikola	nikola	PROPN
ejpam-4136	399	13	mirkov	mirkov	PROPN
ejpam-4136	399	14	,	,	PUNCT
ejpam-4136	399	15	and	and	CCONJ
ejpam-4136	399	16	stojan	stojan	ADP
ejpam-4136	399	17	radenović.	radenović.	PROPN
ejpam-4136	399	18	a	a	DET
ejpam-4136	399	19	new	new	ADJ
ejpam-4136	399	20	version	version	NOUN
ejpam-4136	399	21	of	of	ADP
ejpam-4136	399	22	un	un	ADJ
ejpam-4136	399	23	-	-	ADJ
ejpam-4136	399	24	hypermetric	hypermetric	ADJ
ejpam-4136	399	25	space	space	NOUN
ejpam-4136	399	26	results	result	NOUN
ejpam-4136	399	27	.	.	PUNCT
ejpam-4136	400	1	vojnotehnički	vojnotehnički	PROPN
ejpam-4136	400	2	glasnik	glasnik	PROPN
ejpam-4136	400	3	/	/	SYM
ejpam-4136	400	4	military	military	ADJ
ejpam-4136	400	5	technical	technical	ADJ
ejpam-4136	400	6	courier	courier	NOUN
ejpam-4136	400	7	,	,	PUNCT
ejpam-4136	400	8	69(3):562–577	69(3):562–577	PROPN
ejpam-4136	400	9	,	,	PUNCT
ejpam-4136	400	10	2012	2012	NUM
ejpam-4136	400	11	.	.	PUNCT
ejpam-4136	401	1	[	[	X
ejpam-4136	401	2	13	13	NUM
ejpam-4136	401	3	]	]	SYM
ejpam-4136	401	4	sh	sh	PROPN
ejpam-4136	401	5	.	.	PROPN
ejpam-4136	401	6	rezapour	rezapour	PROPN
ejpam-4136	401	7	.	.	PUNCT
ejpam-4136	402	1	a	a	DET
ejpam-4136	402	2	review	review	NOUN
ejpam-4136	402	3	on	on	ADP
ejpam-4136	402	4	topological	topological	ADJ
ejpam-4136	402	5	properties	property	NOUN
ejpam-4136	402	6	of	of	ADP
ejpam-4136	402	7	cone	cone	NOUN
ejpam-4136	402	8	metric	metric	ADJ
ejpam-4136	402	9	spaces	space	NOUN
ejpam-4136	402	10	.	.	PUNCT
ejpam-4136	403	1	analysis	analysis	NOUN
ejpam-4136	403	2	,	,	PUNCT
ejpam-4136	403	3	topology	topology	NOUN
ejpam-4136	403	4	and	and	CCONJ
ejpam-4136	403	5	applications	application	NOUN
ejpam-4136	403	6	2008	2008	NUM
ejpam-4136	403	7	,	,	PUNCT
ejpam-4136	403	8	vrnja£ka	vrnja£ka	PROPN
ejpam-4136	403	9	banja	banja	PROPN
ejpam-4136	403	10	,	,	PUNCT
ejpam-4136	403	11	serbia	serbia	PROPN
ejpam-4136	403	12	,	,	PUNCT
ejpam-4136	403	13	from	from	ADP
ejpam-4136	403	14	may	may	PROPN
ejpam-4136	403	15	30	30	NUM
ejpam-4136	403	16	to	to	ADP
ejpam-4136	403	17	june	june	PROPN
ejpam-4136	403	18	4	4	NUM
ejpam-4136	403	19	,	,	PUNCT
ejpam-4136	403	20	2008	2008	NUM
ejpam-4136	403	21	.	.	PUNCT
ejpam-4136	404	1	[	[	X
ejpam-4136	404	2	14	14	NUM
ejpam-4136	404	3	]	]	X
ejpam-4136	404	4	w.	w.	PROPN
ejpam-4136	404	5	rudin	rudin	PROPN
ejpam-4136	404	6	.	.	PUNCT
ejpam-4136	405	1	functional	functional	ADJ
ejpam-4136	405	2	analysis	analysis	NOUN
ejpam-4136	405	3	.	.	PUNCT
ejpam-4136	406	1	2nd	2nd	ADJ
ejpam-4136	406	2	edn	edn	PROPN
ejpam-4136	406	3	.	.	PUNCT
ejpam-4136	407	1	mcgraw	mcgraw	PROPN
ejpam-4136	407	2	-	-	PUNCT
ejpam-4136	407	3	hill	hill	PROPN
ejpam-4136	407	4	,	,	PUNCT
ejpam-4136	407	5	newyork	newyork	PROPN
ejpam-4136	407	6	,	,	PUNCT
ejpam-4136	407	7	1991	1991	NUM
ejpam-4136	407	8	.	.	PUNCT