id	sid	tid	token	lemma	pos
ejpam-4171	1	1	european	european	PROPN
ejpam-4171	1	2	journal	journal	PROPN
ejpam-4171	1	3	of	of	ADP
ejpam-4171	1	4	pure	pure	ADJ
ejpam-4171	1	5	and	and	CCONJ
ejpam-4171	1	6	applied	apply	VERB
ejpam-4171	1	7	mathematics	mathematic	NOUN
ejpam-4171	1	8	vol	vol	NOUN
ejpam-4171	1	9	.	.	PROPN
ejpam-4171	2	1	15	15	NUM
ejpam-4171	2	2	,	,	PUNCT
ejpam-4171	2	3	no	no	INTJ
ejpam-4171	2	4	.	.	NOUN
ejpam-4171	2	5	1	1	NUM
ejpam-4171	2	6	,	,	PUNCT
ejpam-4171	2	7	2022	2022	NUM
ejpam-4171	2	8	,	,	PUNCT
ejpam-4171	2	9	135	135	NUM
ejpam-4171	2	10	-	-	SYM
ejpam-4171	2	11	143	143	NUM
ejpam-4171	2	12	issn	issn	PROPN
ejpam-4171	2	13	1307	1307	NUM
ejpam-4171	2	14	-	-	SYM
ejpam-4171	2	15	5543	5543	NUM
ejpam-4171	2	16	–	–	PUNCT
ejpam-4171	3	1	ejpam.com	ejpam.com	X
ejpam-4171	3	2	published	publish	VERB
ejpam-4171	3	3	by	by	ADP
ejpam-4171	3	4	new	new	PROPN
ejpam-4171	3	5	york	york	PROPN
ejpam-4171	3	6	business	business	PROPN
ejpam-4171	3	7	global	global	PROPN
ejpam-4171	3	8	quadruple	quadruple	PROPN
ejpam-4171	3	9	g	g	ADV
ejpam-4171	3	10	-	-	PUNCT
ejpam-4171	3	11	best	good	ADJ
ejpam-4171	3	12	proximity	proximity	NOUN
ejpam-4171	3	13	point	point	NOUN
ejpam-4171	3	14	for	for	ADP
ejpam-4171	3	15	new	new	ADJ
ejpam-4171	3	16	contraction	contraction	NOUN
ejpam-4171	3	17	in	in	ADP
ejpam-4171	3	18	complete	complete	ADJ
ejpam-4171	3	19	metric	metric	ADJ
ejpam-4171	3	20	space	space	NOUN
ejpam-4171	3	21	savita	savita	PROPN
ejpam-4171	3	22	rathee1	rathee1	PROPN
ejpam-4171	3	23	,	,	PUNCT
ejpam-4171	3	24	monika	monika	PROPN
ejpam-4171	3	25	swami1,∗	swami1,∗	PROPN
ejpam-4171	3	26	1	1	NUM
ejpam-4171	3	27	department	department	NOUN
ejpam-4171	3	28	of	of	ADP
ejpam-4171	3	29	mathematics	mathematics	PROPN
ejpam-4171	3	30	,	,	PUNCT
ejpam-4171	3	31	maharshi	maharshi	PROPN
ejpam-4171	3	32	dayanand	dayanand	PROPN
ejpam-4171	3	33	university	university	PROPN
ejpam-4171	3	34	,	,	PUNCT
ejpam-4171	3	35	rohtak	rohtak	PROPN
ejpam-4171	3	36	,	,	PUNCT
ejpam-4171	3	37	india	india	PROPN
ejpam-4171	3	38	abstract	abstract	NOUN
ejpam-4171	3	39	.	.	PUNCT
ejpam-4171	4	1	the	the	DET
ejpam-4171	4	2	aim	aim	NOUN
ejpam-4171	4	3	of	of	ADP
ejpam-4171	4	4	this	this	DET
ejpam-4171	4	5	manuscript	manuscript	NOUN
ejpam-4171	4	6	is	be	AUX
ejpam-4171	4	7	to	to	PART
ejpam-4171	4	8	propose	propose	VERB
ejpam-4171	4	9	a	a	DET
ejpam-4171	4	10	contraction	contraction	NOUN
ejpam-4171	4	11	to	to	PART
ejpam-4171	4	12	pursue	pursue	VERB
ejpam-4171	4	13	the	the	DET
ejpam-4171	4	14	existence	existence	NOUN
ejpam-4171	4	15	of	of	ADP
ejpam-4171	4	16	g	g	NOUN
ejpam-4171	4	17	-	-	PUNCT
ejpam-4171	4	18	best	good	ADJ
ejpam-4171	4	19	proximity	proximity	NOUN
ejpam-4171	4	20	point	point	NOUN
ejpam-4171	4	21	results	result	NOUN
ejpam-4171	4	22	.	.	PUNCT
ejpam-4171	5	1	the	the	DET
ejpam-4171	5	2	finding	finding	NOUN
ejpam-4171	5	3	of	of	ADP
ejpam-4171	5	4	this	this	DET
ejpam-4171	5	5	manuscript	manuscript	NOUN
ejpam-4171	5	6	generalize	generalize	VERB
ejpam-4171	5	7	and	and	CCONJ
ejpam-4171	5	8	unify	unify	VERB
ejpam-4171	5	9	the	the	DET
ejpam-4171	5	10	results	result	NOUN
ejpam-4171	5	11	of	of	ADP
ejpam-4171	5	12	rohen	rohen	NOUN
ejpam-4171	5	13	and	and	CCONJ
ejpam-4171	5	14	mlaiki	mlaiki	NOUN
ejpam-4171	5	15	by	by	ADP
ejpam-4171	5	16	using	use	VERB
ejpam-4171	5	17	the	the	DET
ejpam-4171	5	18	new	new	ADJ
ejpam-4171	5	19	contraction	contraction	NOUN
ejpam-4171	5	20	with	with	ADP
ejpam-4171	5	21	p	p	NOUN
ejpam-4171	5	22	-	-	PUNCT
ejpam-4171	5	23	property	property	NOUN
ejpam-4171	5	24	and	and	CCONJ
ejpam-4171	5	25	prove	prove	VERB
ejpam-4171	5	26	the	the	DET
ejpam-4171	5	27	existence	existence	NOUN
ejpam-4171	5	28	and	and	CCONJ
ejpam-4171	5	29	uniqueness	uniqueness	NOUN
ejpam-4171	5	30	of	of	ADP
ejpam-4171	5	31	quadruple	quadruple	NOUN
ejpam-4171	5	32	best	good	ADJ
ejpam-4171	5	33	proximity	proximity	NOUN
ejpam-4171	5	34	point	point	NOUN
ejpam-4171	5	35	alongwith	alongwith	NOUN
ejpam-4171	5	36	an	an	DET
ejpam-4171	5	37	example	example	NOUN
ejpam-4171	5	38	.	.	PUNCT
ejpam-4171	6	1	2020	2020	NUM
ejpam-4171	6	2	mathematics	mathematic	NOUN
ejpam-4171	6	3	subject	subject	NOUN
ejpam-4171	6	4	classifications	classification	NOUN
ejpam-4171	6	5	:	:	PUNCT
ejpam-4171	6	6	47h10	47h10	NUM
ejpam-4171	6	7	,	,	PUNCT
ejpam-4171	6	8	54h25	54h25	NUM
ejpam-4171	6	9	key	key	ADJ
ejpam-4171	6	10	words	word	NOUN
ejpam-4171	6	11	and	and	CCONJ
ejpam-4171	6	12	phrases	phrase	NOUN
ejpam-4171	6	13	:	:	PUNCT
ejpam-4171	6	14	best	good	ADJ
ejpam-4171	6	15	proximity	proximity	NOUN
ejpam-4171	6	16	point	point	NOUN
ejpam-4171	6	17	,	,	PUNCT
ejpam-4171	6	18	quadruple	quadruple	X
ejpam-4171	6	19	best	good	ADJ
ejpam-4171	6	20	proximity	proximity	NOUN
ejpam-4171	6	21	point	point	NOUN
ejpam-4171	6	22	,	,	PUNCT
ejpam-4171	6	23	metric	metric	ADJ
ejpam-4171	6	24	space	space	NOUN
ejpam-4171	6	25	,	,	PUNCT
ejpam-4171	6	26	contraction	contraction	NOUN
ejpam-4171	6	27	1	1	NUM
ejpam-4171	6	28	.	.	PUNCT
ejpam-4171	7	1	introduction	introduction	NOUN
ejpam-4171	7	2	fixed	fix	VERB
ejpam-4171	7	3	point	point	NOUN
ejpam-4171	7	4	theory	theory	NOUN
ejpam-4171	7	5	is	be	AUX
ejpam-4171	7	6	a	a	DET
ejpam-4171	7	7	flourished	flourish	VERB
ejpam-4171	7	8	theory	theory	NOUN
ejpam-4171	7	9	due	due	ADP
ejpam-4171	7	10	to	to	ADP
ejpam-4171	7	11	its	its	PRON
ejpam-4171	7	12	functioning	functioning	NOUN
ejpam-4171	7	13	in	in	ADP
ejpam-4171	7	14	physics	physics	NOUN
ejpam-4171	7	15	,	,	PUNCT
ejpam-4171	7	16	computer	computer	NOUN
ejpam-4171	7	17	science	science	NOUN
ejpam-4171	7	18	,	,	PUNCT
ejpam-4171	7	19	engineering	engineering	NOUN
ejpam-4171	7	20	etc	etc	X
ejpam-4171	7	21	.	.	X
ejpam-4171	7	22	as	as	SCONJ
ejpam-4171	7	23	always	always	ADV
ejpam-4171	7	24	it	it	PRON
ejpam-4171	7	25	is	be	AUX
ejpam-4171	7	26	not	not	PART
ejpam-4171	7	27	possible	possible	ADJ
ejpam-4171	7	28	to	to	PART
ejpam-4171	7	29	find	find	VERB
ejpam-4171	7	30	fixed	fix	VERB
ejpam-4171	7	31	point	point	NOUN
ejpam-4171	7	32	for	for	ADP
ejpam-4171	7	33	every	every	DET
ejpam-4171	7	34	selfcontractive	selfcontractive	ADJ
ejpam-4171	7	35	mappings	mapping	NOUN
ejpam-4171	7	36	,	,	PUNCT
ejpam-4171	7	37	then	then	ADV
ejpam-4171	7	38	there	there	PRON
ejpam-4171	7	39	is	be	VERB
ejpam-4171	7	40	possibility	possibility	NOUN
ejpam-4171	7	41	of	of	ADP
ejpam-4171	7	42	existence	existence	NOUN
ejpam-4171	7	43	of	of	ADP
ejpam-4171	7	44	a	a	DET
ejpam-4171	7	45	point	point	NOUN
ejpam-4171	7	46	with	with	ADP
ejpam-4171	7	47	minimum	minimum	ADJ
ejpam-4171	7	48	distance	distance	NOUN
ejpam-4171	7	49	between	between	ADP
ejpam-4171	7	50	the	the	DET
ejpam-4171	7	51	point	point	NOUN
ejpam-4171	7	52	and	and	CCONJ
ejpam-4171	7	53	its	its	PRON
ejpam-4171	7	54	image	image	NOUN
ejpam-4171	7	55	.	.	PUNCT
ejpam-4171	8	1	this	this	DET
ejpam-4171	8	2	point	point	NOUN
ejpam-4171	8	3	is	be	AUX
ejpam-4171	8	4	known	know	VERB
ejpam-4171	8	5	as	as	ADP
ejpam-4171	8	6	best	good	ADJ
ejpam-4171	8	7	proximity	proximity	NOUN
ejpam-4171	8	8	point	point	NOUN
ejpam-4171	8	9	which	which	PRON
ejpam-4171	8	10	was	be	AUX
ejpam-4171	8	11	introduced	introduce	VERB
ejpam-4171	8	12	by	by	ADP
ejpam-4171	8	13	fan	fan	NOUN
ejpam-4171	8	14	[	[	X
ejpam-4171	8	15	8	8	NUM
ejpam-4171	8	16	]	]	PUNCT
ejpam-4171	8	17	and	and	CCONJ
ejpam-4171	8	18	extended	extend	VERB
ejpam-4171	8	19	by	by	ADP
ejpam-4171	8	20	basha	basha	PROPN
ejpam-4171	9	1	[	[	X
ejpam-4171	9	2	5	5	NUM
ejpam-4171	9	3	]	]	PUNCT
ejpam-4171	9	4	and	and	CCONJ
ejpam-4171	9	5	many	many	ADJ
ejpam-4171	9	6	more	more	ADJ
ejpam-4171	9	7	researchers	researcher	NOUN
ejpam-4171	9	8	.	.	PUNCT
ejpam-4171	10	1	in	in	ADP
ejpam-4171	10	2	1987	1987	NUM
ejpam-4171	10	3	,	,	PUNCT
ejpam-4171	10	4	guo	guo	PROPN
ejpam-4171	10	5	and	and	CCONJ
ejpam-4171	10	6	lakshmikantham	lakshmikantham	VERB
ejpam-4171	10	7	[	[	X
ejpam-4171	10	8	10	10	NUM
ejpam-4171	10	9	]	]	PUNCT
ejpam-4171	10	10	,	,	PUNCT
ejpam-4171	10	11	introduced	introduce	VERB
ejpam-4171	10	12	coupled	couple	VERB
ejpam-4171	10	13	fixed	fix	VERB
ejpam-4171	10	14	point	point	NOUN
ejpam-4171	10	15	and	and	CCONJ
ejpam-4171	10	16	proved	prove	VERB
ejpam-4171	10	17	its	its	PRON
ejpam-4171	10	18	related	related	ADJ
ejpam-4171	10	19	fixed	fix	VERB
ejpam-4171	10	20	point	point	NOUN
ejpam-4171	10	21	theorems	theorem	NOUN
ejpam-4171	10	22	under	under	ADP
ejpam-4171	10	23	appropriate	appropriate	ADJ
ejpam-4171	10	24	conditions	condition	NOUN
ejpam-4171	10	25	.	.	PUNCT
ejpam-4171	11	1	after	after	ADP
ejpam-4171	11	2	that	that	PRON
ejpam-4171	11	3	,	,	PUNCT
ejpam-4171	11	4	lakshmikantham	lakshmikantham	ADJ
ejpam-4171	11	5	and	and	CCONJ
ejpam-4171	11	6	ciric	ciric	ADJ
ejpam-4171	11	7	in	in	ADP
ejpam-4171	11	8	[	[	X
ejpam-4171	11	9	13	13	NUM
ejpam-4171	11	10	]	]	PUNCT
ejpam-4171	11	11	extend	extend	VERB
ejpam-4171	11	12	these	these	DET
ejpam-4171	11	13	results	result	NOUN
ejpam-4171	11	14	by	by	ADP
ejpam-4171	11	15	defining	define	VERB
ejpam-4171	11	16	the	the	DET
ejpam-4171	11	17	g	g	NOUN
ejpam-4171	11	18	-	-	PUNCT
ejpam-4171	11	19	monotone	monotone	NOUN
ejpam-4171	11	20	property	property	NOUN
ejpam-4171	11	21	.	.	PUNCT
ejpam-4171	12	1	the	the	DET
ejpam-4171	12	2	results	result	NOUN
ejpam-4171	12	3	of	of	ADP
ejpam-4171	12	4	[	[	X
ejpam-4171	12	5	10	10	NUM
ejpam-4171	12	6	]	]	PUNCT
ejpam-4171	12	7	leads	lead	VERB
ejpam-4171	12	8	to	to	ADP
ejpam-4171	12	9	the	the	DET
ejpam-4171	12	10	development	development	NOUN
ejpam-4171	12	11	of	of	ADP
ejpam-4171	12	12	tripled	triple	VERB
ejpam-4171	12	13	fixed	fix	VERB
ejpam-4171	12	14	point	point	NOUN
ejpam-4171	12	15	by	by	ADP
ejpam-4171	12	16	berinde	berinde	NOUN
ejpam-4171	12	17	and	and	CCONJ
ejpam-4171	12	18	borcut	borcut	VERB
ejpam-4171	12	19	[	[	X
ejpam-4171	12	20	7	7	NUM
ejpam-4171	12	21	]	]	PUNCT
ejpam-4171	12	22	.	.	PUNCT
ejpam-4171	13	1	in	in	ADP
ejpam-4171	13	2	[	[	X
ejpam-4171	13	3	7	7	NUM
ejpam-4171	13	4	]	]	PUNCT
ejpam-4171	13	5	,	,	PUNCT
ejpam-4171	13	6	they	they	PRON
ejpam-4171	13	7	proved	prove	VERB
ejpam-4171	13	8	the	the	DET
ejpam-4171	13	9	existence	existence	NOUN
ejpam-4171	13	10	and	and	CCONJ
ejpam-4171	13	11	uniqueness	uniqueness	NOUN
ejpam-4171	13	12	of	of	ADP
ejpam-4171	13	13	the	the	DET
ejpam-4171	13	14	introduced	introduce	VERB
ejpam-4171	13	15	tripled	triple	VERB
ejpam-4171	13	16	fixed	fix	VERB
ejpam-4171	13	17	point	point	NOUN
ejpam-4171	13	18	for	for	ADP
ejpam-4171	13	19	non	non	ADJ
ejpam-4171	13	20	-	-	ADJ
ejpam-4171	13	21	linear	linear	ADJ
ejpam-4171	13	22	mappings	mapping	NOUN
ejpam-4171	13	23	in	in	ADP
ejpam-4171	13	24	partially	partially	ADV
ejpam-4171	13	25	ordered	order	VERB
ejpam-4171	13	26	complete	complete	ADJ
ejpam-4171	13	27	metric	metric	ADJ
ejpam-4171	13	28	space	space	NOUN
ejpam-4171	13	29	and	and	CCONJ
ejpam-4171	13	30	later	later	ADV
ejpam-4171	13	31	on	on	ADP
ejpam-4171	13	32	many	many	ADJ
ejpam-4171	13	33	results	result	NOUN
ejpam-4171	13	34	exists	exist	VERB
ejpam-4171	13	35	between	between	ADP
ejpam-4171	13	36	coupled	couple	VERB
ejpam-4171	13	37	and	and	CCONJ
ejpam-4171	13	38	tripled	triple	VERB
ejpam-4171	13	39	fixed	fix	VERB
ejpam-4171	13	40	points	point	NOUN
ejpam-4171	13	41	on	on	ADP
ejpam-4171	13	42	different	different	ADJ
ejpam-4171	13	43	spaces	space	NOUN
ejpam-4171	13	44	under	under	ADP
ejpam-4171	13	45	different	different	ADJ
ejpam-4171	13	46	contractions	contraction	NOUN
ejpam-4171	13	47	.	.	PUNCT
ejpam-4171	14	1	in	in	ADP
ejpam-4171	14	2	2012	2012	NUM
ejpam-4171	14	3	,	,	PUNCT
ejpam-4171	14	4	tripled	triple	VERB
ejpam-4171	14	5	fixed	fix	VERB
ejpam-4171	14	6	point	point	NOUN
ejpam-4171	14	7	was	be	AUX
ejpam-4171	14	8	extended	extend	VERB
ejpam-4171	14	9	to	to	PART
ejpam-4171	14	10	quadruple	quadruple	VERB
ejpam-4171	14	11	fixed	fix	VERB
ejpam-4171	14	12	point	point	NOUN
ejpam-4171	14	13	by	by	ADP
ejpam-4171	14	14	karapinar	karapinar	NOUN
ejpam-4171	14	15	and	and	CCONJ
ejpam-4171	14	16	luong	luong	PROPN
ejpam-4171	15	1	[	[	X
ejpam-4171	15	2	11	11	NUM
ejpam-4171	15	3	]	]	PUNCT
ejpam-4171	15	4	in	in	ADP
ejpam-4171	15	5	complete	complete	ADJ
ejpam-4171	15	6	metric	metric	ADJ
ejpam-4171	15	7	space	space	NOUN
ejpam-4171	15	8	.	.	PUNCT
ejpam-4171	16	1	motivated	motivate	VERB
ejpam-4171	16	2	from	from	ADP
ejpam-4171	16	3	[	[	X
ejpam-4171	16	4	18	18	NUM
ejpam-4171	16	5	]	]	PUNCT
ejpam-4171	16	6	,	,	PUNCT
ejpam-4171	16	7	rohen	rohen	NOUN
ejpam-4171	16	8	and	and	CCONJ
ejpam-4171	16	9	maliki	maliki	PROPN
ejpam-4171	17	1	[	[	X
ejpam-4171	17	2	17	17	NUM
ejpam-4171	17	3	]	]	PUNCT
ejpam-4171	17	4	gave	give	VERB
ejpam-4171	17	5	the	the	DET
ejpam-4171	17	6	notion	notion	NOUN
ejpam-4171	17	7	of	of	ADP
ejpam-4171	17	8	tripled	triple	VERB
ejpam-4171	17	9	best	good	ADJ
ejpam-4171	17	10	proximity	proximity	NOUN
ejpam-4171	17	11	points	point	NOUN
ejpam-4171	17	12	theorem	theorem	VERB
ejpam-4171	17	13	graced	graced	ADJ
ejpam-4171	17	14	with	with	ADP
ejpam-4171	17	15	p	p	NOUN
ejpam-4171	17	16	-	-	PUNCT
ejpam-4171	17	17	property	property	NOUN
ejpam-4171	17	18	and	and	CCONJ
ejpam-4171	17	19	the	the	DET
ejpam-4171	17	20	developed	developed	ADJ
ejpam-4171	17	21	contraction	contraction	NOUN
ejpam-4171	17	22	.	.	PUNCT
ejpam-4171	18	1	see	see	VERB
ejpam-4171	18	2	references	reference	NOUN
ejpam-4171	18	3	[	[	X
ejpam-4171	18	4	15	15	NUM
ejpam-4171	18	5	]	]	PUNCT
ejpam-4171	18	6	,	,	PUNCT
ejpam-4171	18	7	[	[	X
ejpam-4171	18	8	2	2	NUM
ejpam-4171	18	9	]	]	PUNCT
ejpam-4171	18	10	,	,	PUNCT
ejpam-4171	18	11	[	[	X
ejpam-4171	18	12	9	9	NUM
ejpam-4171	18	13	]	]	PUNCT
ejpam-4171	18	14	,	,	PUNCT
ejpam-4171	18	15	[	[	X
ejpam-4171	18	16	14	14	NUM
ejpam-4171	18	17	]	]	PUNCT
ejpam-4171	18	18	for	for	ADP
ejpam-4171	18	19	further	further	ADJ
ejpam-4171	18	20	research	research	NOUN
ejpam-4171	18	21	in	in	ADP
ejpam-4171	18	22	coupled	couple	VERB
ejpam-4171	18	23	best	good	ADJ
ejpam-4171	18	24	proximity	proximity	NOUN
ejpam-4171	18	25	point	point	NOUN
ejpam-4171	18	26	results	result	NOUN
ejpam-4171	18	27	.	.	PUNCT
ejpam-4171	19	1	∗corresponding	∗corresponde	VERB
ejpam-4171	19	2	author	author	NOUN
ejpam-4171	19	3	.	.	PUNCT
ejpam-4171	20	1	doi	doi	NOUN
ejpam-4171	20	2	:	:	PUNCT
ejpam-4171	20	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4171	https://doi.org/10.29020/nybg.ejpam.v15i1.4171	PROPN
ejpam-4171	20	4	email	email	NOUN
ejpam-4171	20	5	addresses	address	NOUN
ejpam-4171	20	6	:	:	PUNCT
ejpam-4171	20	7	dr.savitarathee@gmail.com	dr.savitarathee@gmail.com	PROPN
ejpam-4171	20	8	(	(	PUNCT
ejpam-4171	20	9	s.	s.	PROPN
ejpam-4171	20	10	rathee	rathee	PROPN
ejpam-4171	20	11	)	)	PUNCT
ejpam-4171	20	12	,	,	PUNCT
ejpam-4171	20	13	monikaswami06@gmail.com	monikaswami06@gmail.com	X
ejpam-4171	20	14	(	(	PUNCT
ejpam-4171	20	15	m.	m.	NOUN
ejpam-4171	20	16	swami	swami	PROPN
ejpam-4171	20	17	)	)	PUNCT
ejpam-4171	20	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4171	21	1	135	135	NUM
ejpam-4171	21	2	©	©	PROPN
ejpam-4171	21	3	2022	2022	NUM
ejpam-4171	21	4	ejpam	ejpam	VERB
ejpam-4171	21	5	all	all	DET
ejpam-4171	21	6	rights	right	NOUN
ejpam-4171	21	7	reserved	reserve	VERB
ejpam-4171	21	8	.	.	PUNCT
ejpam-4171	22	1	s.	s.	PROPN
ejpam-4171	22	2	rathee	rathee	PROPN
ejpam-4171	22	3	,	,	PUNCT
ejpam-4171	22	4	m.	m.	NOUN
ejpam-4171	22	5	swami	swami	PROPN
ejpam-4171	22	6	,	,	PUNCT
ejpam-4171	22	7	/	/	SYM
ejpam-4171	22	8	eur	eur	NOUN
ejpam-4171	22	9	.	.	PUNCT
ejpam-4171	23	1	j.	j.	PROPN
ejpam-4171	23	2	pure	pure	PROPN
ejpam-4171	23	3	appl	appl	PROPN
ejpam-4171	23	4	.	.	PROPN
ejpam-4171	23	5	math	math	PROPN
ejpam-4171	23	6	,	,	PUNCT
ejpam-4171	23	7	15	15	NUM
ejpam-4171	23	8	(	(	PUNCT
ejpam-4171	23	9	1	1	NUM
ejpam-4171	23	10	)	)	PUNCT
ejpam-4171	23	11	(	(	PUNCT
ejpam-4171	23	12	2022	2022	NUM
ejpam-4171	23	13	)	)	PUNCT
ejpam-4171	23	14	,	,	PUNCT
ejpam-4171	23	15	135	135	NUM
ejpam-4171	23	16	-	-	SYM
ejpam-4171	23	17	143	143	NUM
ejpam-4171	23	18	136	136	NUM
ejpam-4171	23	19	rohen	rohen	NOUN
ejpam-4171	23	20	and	and	CCONJ
ejpam-4171	23	21	maliki	maliki	PROPN
ejpam-4171	24	1	[	[	X
ejpam-4171	24	2	17	17	NUM
ejpam-4171	24	3	]	]	PUNCT
ejpam-4171	24	4	and	and	CCONJ
ejpam-4171	24	5	karapinar	karapinar	NOUN
ejpam-4171	24	6	and	and	CCONJ
ejpam-4171	24	7	luong	luong	PROPN
ejpam-4171	25	1	[	[	X
ejpam-4171	25	2	11	11	NUM
ejpam-4171	25	3	]	]	PUNCT
ejpam-4171	25	4	,	,	PUNCT
ejpam-4171	25	5	motivated	motivate	VERB
ejpam-4171	25	6	us	we	PRON
ejpam-4171	25	7	,	,	PUNCT
ejpam-4171	25	8	in	in	ADP
ejpam-4171	25	9	the	the	DET
ejpam-4171	25	10	direction	direction	NOUN
ejpam-4171	25	11	to	to	PART
ejpam-4171	25	12	precede	precede	VERB
ejpam-4171	25	13	the	the	DET
ejpam-4171	25	14	quadruple	quadruple	ADJ
ejpam-4171	25	15	best	good	ADJ
ejpam-4171	25	16	proximity	proximity	NOUN
ejpam-4171	25	17	point	point	NOUN
ejpam-4171	25	18	.	.	PUNCT
ejpam-4171	26	1	we	we	PRON
ejpam-4171	26	2	propose	propose	VERB
ejpam-4171	26	3	the	the	DET
ejpam-4171	26	4	quadruple	quadruple	ADJ
ejpam-4171	26	5	best	good	ADJ
ejpam-4171	26	6	proximity	proximity	NOUN
ejpam-4171	26	7	point	point	NOUN
ejpam-4171	26	8	results	result	NOUN
ejpam-4171	26	9	with	with	ADP
ejpam-4171	26	10	p	p	NOUN
ejpam-4171	26	11	-	-	PUNCT
ejpam-4171	26	12	property	property	NOUN
ejpam-4171	26	13	and	and	CCONJ
ejpam-4171	26	14	the	the	DET
ejpam-4171	26	15	newly	newly	ADV
ejpam-4171	26	16	introduce	introduce	ADJ
ejpam-4171	26	17	contraction	contraction	NOUN
ejpam-4171	26	18	.	.	PUNCT
ejpam-4171	27	1	also	also	ADV
ejpam-4171	27	2	,	,	PUNCT
ejpam-4171	27	3	examples	example	NOUN
ejpam-4171	27	4	are	be	AUX
ejpam-4171	27	5	supplied	supply	VERB
ejpam-4171	27	6	in	in	ADP
ejpam-4171	27	7	favour	favour	NOUN
ejpam-4171	27	8	of	of	ADP
ejpam-4171	27	9	our	our	PRON
ejpam-4171	27	10	results	result	NOUN
ejpam-4171	27	11	.	.	PUNCT
ejpam-4171	28	1	2	2	X
ejpam-4171	28	2	.	.	X
ejpam-4171	28	3	preliminaries	preliminary	NOUN
ejpam-4171	28	4	definition	definition	NOUN
ejpam-4171	28	5	1	1	NUM
ejpam-4171	28	6	.	.	PUNCT
ejpam-4171	29	1	[	[	X
ejpam-4171	29	2	3	3	X
ejpam-4171	29	3	]	]	X
ejpam-4171	29	4	let	let	VERB
ejpam-4171	29	5	(	(	PUNCT
ejpam-4171	29	6	x	x	NOUN
ejpam-4171	29	7	,	,	PUNCT
ejpam-4171	29	8	d	d	NOUN
ejpam-4171	29	9	)	)	PUNCT
ejpam-4171	29	10	be	be	AUX
ejpam-4171	29	11	metric	metric	ADJ
ejpam-4171	29	12	space	space	NOUN
ejpam-4171	29	13	,	,	PUNCT
ejpam-4171	29	14	q	q	PUNCT
ejpam-4171	29	15	and	and	CCONJ
ejpam-4171	29	16	r	r	NOUN
ejpam-4171	29	17	be	be	AUX
ejpam-4171	29	18	two	two	NUM
ejpam-4171	29	19	non	non	ADJ
ejpam-4171	29	20	-	-	ADJ
ejpam-4171	29	21	empty	empty	ADJ
ejpam-4171	29	22	subset	subset	NOUN
ejpam-4171	29	23	of	of	ADP
ejpam-4171	29	24	x.	x.	NOUN
ejpam-4171	29	25	define	define	VERB
ejpam-4171	29	26	d(q	d(q	PROPN
ejpam-4171	29	27	,	,	PUNCT
ejpam-4171	29	28	r	r	NOUN
ejpam-4171	29	29	)	)	PUNCT
ejpam-4171	29	30	=	=	PUNCT
ejpam-4171	29	31	inf{d(x	inf{d(x	PROPN
ejpam-4171	29	32	,	,	PUNCT
ejpam-4171	29	33	y	y	PROPN
ejpam-4171	29	34	)	)	PUNCT
ejpam-4171	29	35	:	:	PUNCT
ejpam-4171	30	1	x	x	PUNCT
ejpam-4171	30	2	∈	∈	PROPN
ejpam-4171	30	3	q	q	NOUN
ejpam-4171	30	4	,	,	PUNCT
ejpam-4171	30	5	y	y	PROPN
ejpam-4171	30	6	∈	∈	PROPN
ejpam-4171	30	7	r	r	NOUN
ejpam-4171	30	8	}	}	PUNCT
ejpam-4171	30	9	,	,	PUNCT
ejpam-4171	30	10	q0	q0	PROPN
ejpam-4171	30	11	=	=	SYM
ejpam-4171	30	12	{	{	PUNCT
ejpam-4171	30	13	x	x	PUNCT
ejpam-4171	30	14	∈	∈	PROPN
ejpam-4171	30	15	q	q	NOUN
ejpam-4171	30	16	:	:	PUNCT
ejpam-4171	30	17	there	there	PRON
ejpam-4171	30	18	exists	exist	VERB
ejpam-4171	30	19	some	some	DET
ejpam-4171	30	20	y	y	PROPN
ejpam-4171	30	21	∈	∈	PROPN
ejpam-4171	30	22	r	r	NOUN
ejpam-4171	30	23	such	such	ADJ
ejpam-4171	30	24	that	that	DET
ejpam-4171	30	25	d(x	d(x	PROPN
ejpam-4171	30	26	,	,	PUNCT
ejpam-4171	30	27	y	y	NOUN
ejpam-4171	30	28	)	)	PUNCT
ejpam-4171	30	29	=	=	SYM
ejpam-4171	31	1	d(q	d(q	PROPN
ejpam-4171	31	2	,	,	PUNCT
ejpam-4171	31	3	r	r	NOUN
ejpam-4171	31	4	)	)	PUNCT
ejpam-4171	31	5	}	}	PUNCT
ejpam-4171	31	6	,	,	PUNCT
ejpam-4171	31	7	r0	r0	NOUN
ejpam-4171	31	8	=	=	PUNCT
ejpam-4171	31	9	{	{	PUNCT
ejpam-4171	31	10	y	y	PROPN
ejpam-4171	31	11	∈	∈	PROPN
ejpam-4171	31	12	r	r	NOUN
ejpam-4171	31	13	:	:	PUNCT
ejpam-4171	31	14	there	there	PRON
ejpam-4171	31	15	exists	exist	VERB
ejpam-4171	31	16	some	some	DET
ejpam-4171	31	17	x	x	SYM
ejpam-4171	31	18	∈	∈	PROPN
ejpam-4171	31	19	q	q	NOUN
ejpam-4171	31	20	such	such	ADJ
ejpam-4171	31	21	that	that	DET
ejpam-4171	31	22	d(x	d(x	PROPN
ejpam-4171	31	23	,	,	PUNCT
ejpam-4171	31	24	y	y	NOUN
ejpam-4171	31	25	)	)	PUNCT
ejpam-4171	31	26	=	=	SYM
ejpam-4171	32	1	d(q	d(q	PROPN
ejpam-4171	32	2	,	,	PUNCT
ejpam-4171	32	3	r	r	NOUN
ejpam-4171	32	4	)	)	PUNCT
ejpam-4171	32	5	}	}	PUNCT
ejpam-4171	32	6	.	.	PUNCT
ejpam-4171	33	1	in	in	ADP
ejpam-4171	33	2	2011	2011	NUM
ejpam-4171	33	3	,	,	PUNCT
ejpam-4171	33	4	basha	basha	PROPN
ejpam-4171	33	5	[	[	X
ejpam-4171	33	6	4	4	NUM
ejpam-4171	33	7	]	]	PUNCT
ejpam-4171	33	8	proved	prove	VERB
ejpam-4171	33	9	sufficient	sufficient	ADJ
ejpam-4171	33	10	conditions	condition	NOUN
ejpam-4171	33	11	when	when	SCONJ
ejpam-4171	33	12	q0	q0	PROPN
ejpam-4171	33	13	and	and	CCONJ
ejpam-4171	33	14	r0	r0	NOUN
ejpam-4171	33	15	are	be	AUX
ejpam-4171	33	16	non	non	ADJ
ejpam-4171	33	17	-	-	ADJ
ejpam-4171	33	18	empty	empty	ADJ
ejpam-4171	33	19	.	.	PUNCT
ejpam-4171	34	1	definition	definition	NOUN
ejpam-4171	34	2	2	2	NUM
ejpam-4171	34	3	.	.	PUNCT
ejpam-4171	35	1	[	[	X
ejpam-4171	35	2	6	6	NUM
ejpam-4171	35	3	]	]	PUNCT
ejpam-4171	35	4	let	let	VERB
ejpam-4171	35	5	(	(	PUNCT
ejpam-4171	35	6	x	x	NOUN
ejpam-4171	35	7	,	,	PUNCT
ejpam-4171	35	8	d	d	NOUN
ejpam-4171	35	9	)	)	PUNCT
ejpam-4171	35	10	be	be	AUX
ejpam-4171	35	11	metric	metric	ADJ
ejpam-4171	35	12	space	space	NOUN
ejpam-4171	35	13	and	and	CCONJ
ejpam-4171	36	1	q	q	NOUN
ejpam-4171	36	2	=	=	NOUN
ejpam-4171	36	3	̸	̸	PUNCT
ejpam-4171	36	4	ϕ,r	ϕ,r	NOUN
ejpam-4171	36	5	=	=	NOUN
ejpam-4171	36	6	̸	̸	NUM
ejpam-4171	36	7	ϕ	ϕ	NOUN
ejpam-4171	36	8	are	be	AUX
ejpam-4171	36	9	subsets	subset	NOUN
ejpam-4171	36	10	of	of	ADP
ejpam-4171	36	11	x.	x.	NOUN
ejpam-4171	36	12	let	let	VERB
ejpam-4171	36	13	g	g	NOUN
ejpam-4171	36	14	:	:	PUNCT
ejpam-4171	36	15	q	q	X
ejpam-4171	36	16	→	→	PUNCT
ejpam-4171	36	17	r	r	NOUN
ejpam-4171	36	18	be	be	AUX
ejpam-4171	36	19	a	a	DET
ejpam-4171	36	20	mapping	mapping	NOUN
ejpam-4171	36	21	.	.	PUNCT
ejpam-4171	37	1	then	then	ADV
ejpam-4171	37	2	x	x	SYM
ejpam-4171	37	3	∈	∈	PROPN
ejpam-4171	37	4	q	q	NOUN
ejpam-4171	37	5	is	be	AUX
ejpam-4171	37	6	said	say	VERB
ejpam-4171	37	7	to	to	PART
ejpam-4171	37	8	be	be	AUX
ejpam-4171	37	9	best	good	ADJ
ejpam-4171	37	10	proximity	proximity	NOUN
ejpam-4171	37	11	point	point	NOUN
ejpam-4171	37	12	if	if	SCONJ
ejpam-4171	37	13	and	and	CCONJ
ejpam-4171	37	14	only	only	ADV
ejpam-4171	37	15	if	if	SCONJ
ejpam-4171	37	16	d(x	d(x	PROPN
ejpam-4171	37	17	,	,	PUNCT
ejpam-4171	37	18	gx	gx	PROPN
ejpam-4171	37	19	)	)	PUNCT
ejpam-4171	37	20	=	=	SYM
ejpam-4171	37	21	d(q	d(q	PROPN
ejpam-4171	37	22	,	,	PUNCT
ejpam-4171	37	23	r	r	NOUN
ejpam-4171	37	24	)	)	PUNCT
ejpam-4171	37	25	.	.	PUNCT
ejpam-4171	38	1	definition	definition	NOUN
ejpam-4171	38	2	3	3	NUM
ejpam-4171	38	3	.	.	PUNCT
ejpam-4171	39	1	[	[	X
ejpam-4171	39	2	7	7	X
ejpam-4171	39	3	]	]	X
ejpam-4171	39	4	let	let	VERB
ejpam-4171	39	5	g	g	NOUN
ejpam-4171	39	6	:	:	PUNCT
ejpam-4171	39	7	x	x	PROPN
ejpam-4171	39	8	×x	×x	X
ejpam-4171	39	9	×x	×x	X
ejpam-4171	39	10	→	→	SYM
ejpam-4171	39	11	x.	x.	NOUN
ejpam-4171	39	12	an	an	DET
ejpam-4171	39	13	element	element	NOUN
ejpam-4171	39	14	(	(	PUNCT
ejpam-4171	39	15	x	x	X
ejpam-4171	39	16	,	,	PUNCT
ejpam-4171	39	17	y	y	PROPN
ejpam-4171	39	18	,	,	PUNCT
ejpam-4171	39	19	z	z	NOUN
ejpam-4171	39	20	)	)	PUNCT
ejpam-4171	39	21	is	be	AUX
ejpam-4171	39	22	said	say	VERB
ejpam-4171	39	23	to	to	PART
ejpam-4171	39	24	be	be	AUX
ejpam-4171	39	25	tripled	triple	VERB
ejpam-4171	39	26	fixed	fix	VERB
ejpam-4171	39	27	point	point	NOUN
ejpam-4171	39	28	of	of	ADP
ejpam-4171	39	29	g	g	PROPN
ejpam-4171	39	30	if	if	SCONJ
ejpam-4171	39	31	g(x	g(x	PROPN
ejpam-4171	39	32	,	,	PUNCT
ejpam-4171	39	33	y	y	PROPN
ejpam-4171	39	34	,	,	PUNCT
ejpam-4171	39	35	z	z	NOUN
ejpam-4171	39	36	)	)	PUNCT
ejpam-4171	39	37	=	=	SYM
ejpam-4171	39	38	x	x	NOUN
ejpam-4171	39	39	,	,	PUNCT
ejpam-4171	39	40	g(y	g(y	PROPN
ejpam-4171	39	41	,	,	PUNCT
ejpam-4171	39	42	x	x	X
ejpam-4171	39	43	,	,	PUNCT
ejpam-4171	39	44	z	z	NOUN
ejpam-4171	39	45	)	)	PUNCT
ejpam-4171	39	46	=	=	SYM
ejpam-4171	39	47	y	y	PROPN
ejpam-4171	39	48	and	and	CCONJ
ejpam-4171	39	49	g(z	g(z	PROPN
ejpam-4171	39	50	,	,	PUNCT
ejpam-4171	39	51	y	y	PROPN
ejpam-4171	39	52	,	,	PUNCT
ejpam-4171	39	53	x	x	NOUN
ejpam-4171	39	54	)	)	PUNCT
ejpam-4171	39	55	=	=	PUNCT
ejpam-4171	39	56	z.	z.	PROPN
ejpam-4171	39	57	definition	definition	NOUN
ejpam-4171	39	58	4	4	NUM
ejpam-4171	39	59	.	.	PUNCT
ejpam-4171	40	1	[	[	X
ejpam-4171	40	2	11	11	NUM
ejpam-4171	40	3	]	]	PUNCT
ejpam-4171	40	4	let	let	VERB
ejpam-4171	40	5	g	g	NOUN
ejpam-4171	40	6	:	:	PUNCT
ejpam-4171	40	7	x×x×x×x	x×x×x×x	PROPN
ejpam-4171	40	8	→	→	SYM
ejpam-4171	40	9	x.	x.	NOUN
ejpam-4171	40	10	an	an	DET
ejpam-4171	40	11	element	element	NOUN
ejpam-4171	40	12	(	(	PUNCT
ejpam-4171	40	13	x	x	X
ejpam-4171	40	14	,	,	PUNCT
ejpam-4171	40	15	y	y	PROPN
ejpam-4171	40	16	,	,	PUNCT
ejpam-4171	40	17	z	z	PROPN
ejpam-4171	40	18	,	,	PUNCT
ejpam-4171	40	19	t	t	PROPN
ejpam-4171	40	20	)	)	PUNCT
ejpam-4171	40	21	is	be	AUX
ejpam-4171	40	22	said	say	VERB
ejpam-4171	40	23	to	to	PART
ejpam-4171	40	24	be	be	AUX
ejpam-4171	40	25	quadruple	quadruple	ADV
ejpam-4171	40	26	fixed	fix	VERB
ejpam-4171	40	27	point	point	NOUN
ejpam-4171	40	28	of	of	ADP
ejpam-4171	40	29	g	g	PROPN
ejpam-4171	40	30	if	if	SCONJ
ejpam-4171	40	31	g(x	g(x	PROPN
ejpam-4171	40	32	,	,	PUNCT
ejpam-4171	40	33	y	y	PROPN
ejpam-4171	40	34	,	,	PUNCT
ejpam-4171	40	35	z	z	PROPN
ejpam-4171	40	36	,	,	PUNCT
ejpam-4171	40	37	t	t	PROPN
ejpam-4171	40	38	)	)	PUNCT
ejpam-4171	40	39	=	=	SYM
ejpam-4171	41	1	x	x	NOUN
ejpam-4171	41	2	,	,	PUNCT
ejpam-4171	41	3	g(y	g(y	PROPN
ejpam-4171	41	4	,	,	PUNCT
ejpam-4171	41	5	x	x	X
ejpam-4171	41	6	,	,	PUNCT
ejpam-4171	41	7	z	z	PROPN
ejpam-4171	41	8	,	,	PUNCT
ejpam-4171	41	9	t	t	PROPN
ejpam-4171	41	10	)	)	PUNCT
ejpam-4171	41	11	=	=	SYM
ejpam-4171	41	12	y	y	PROPN
ejpam-4171	41	13	,	,	PUNCT
ejpam-4171	41	14	g(z	g(z	PROPN
ejpam-4171	41	15	,	,	PUNCT
ejpam-4171	41	16	y	y	PROPN
ejpam-4171	41	17	,	,	PUNCT
ejpam-4171	41	18	x	x	PROPN
ejpam-4171	41	19	,	,	PUNCT
ejpam-4171	41	20	t	t	PROPN
ejpam-4171	41	21	)	)	PUNCT
ejpam-4171	41	22	=	=	SYM
ejpam-4171	41	23	z	z	PROPN
ejpam-4171	41	24	and	and	CCONJ
ejpam-4171	41	25	g(t	g(t	PROPN
ejpam-4171	41	26	,	,	PUNCT
ejpam-4171	41	27	y	y	PROPN
ejpam-4171	41	28	,	,	PUNCT
ejpam-4171	41	29	z	z	PROPN
ejpam-4171	41	30	,	,	PUNCT
ejpam-4171	41	31	x	x	NOUN
ejpam-4171	41	32	)	)	PUNCT
ejpam-4171	41	33	=	=	SYM
ejpam-4171	41	34	t.	t.	NOUN
ejpam-4171	41	35	definition	definition	NOUN
ejpam-4171	41	36	5	5	NUM
ejpam-4171	41	37	.	.	PUNCT
ejpam-4171	42	1	[	[	X
ejpam-4171	42	2	16	16	NUM
ejpam-4171	42	3	]	]	X
ejpam-4171	42	4	let	let	AUX
ejpam-4171	42	5	(	(	PUNCT
ejpam-4171	42	6	q	q	NOUN
ejpam-4171	42	7	,	,	PUNCT
ejpam-4171	42	8	r	r	NOUN
ejpam-4171	42	9	)	)	PUNCT
ejpam-4171	42	10	be	be	AUX
ejpam-4171	42	11	non	non	ADJ
ejpam-4171	42	12	-	-	ADJ
ejpam-4171	42	13	empty	empty	ADJ
ejpam-4171	42	14	pair	pair	NOUN
ejpam-4171	42	15	of	of	ADP
ejpam-4171	42	16	subsets	subset	NOUN
ejpam-4171	42	17	of	of	ADP
ejpam-4171	42	18	mertic	mertic	ADJ
ejpam-4171	42	19	space	space	NOUN
ejpam-4171	42	20	(	(	PUNCT
ejpam-4171	42	21	x	x	X
ejpam-4171	42	22	,	,	PUNCT
ejpam-4171	42	23	d	d	NOUN
ejpam-4171	42	24	)	)	PUNCT
ejpam-4171	42	25	with	with	ADP
ejpam-4171	42	26	q0	q0	PROPN
ejpam-4171	42	27	̸=	̸=	PROPN
ejpam-4171	42	28	ϕ	ϕ	NOUN
ejpam-4171	42	29	,	,	PUNCT
ejpam-4171	42	30	then	then	ADV
ejpam-4171	42	31	the	the	DET
ejpam-4171	42	32	pair	pair	NOUN
ejpam-4171	42	33	(	(	PUNCT
ejpam-4171	42	34	q	q	NOUN
ejpam-4171	42	35	,	,	PUNCT
ejpam-4171	42	36	r	r	NOUN
ejpam-4171	42	37	)	)	PUNCT
ejpam-4171	42	38	has	have	VERB
ejpam-4171	42	39	p	p	NOUN
ejpam-4171	42	40	-	-	PUNCT
ejpam-4171	42	41	property	property	NOUN
ejpam-4171	42	42	if	if	NOUN
ejpam-4171	42	43	and	and	CCONJ
ejpam-4171	42	44	only	only	ADV
ejpam-4171	42	45	if	if	SCONJ
ejpam-4171	42	46	{	{	PUNCT
ejpam-4171	42	47	d(x1	d(x1	NOUN
ejpam-4171	42	48	,	,	PUNCT
ejpam-4171	42	49	y1	y1	NOUN
ejpam-4171	42	50	)	)	PUNCT
ejpam-4171	42	51	=	=	SYM
ejpam-4171	42	52	d(q	d(q	PROPN
ejpam-4171	42	53	,	,	PUNCT
ejpam-4171	42	54	r	r	NOUN
ejpam-4171	42	55	)	)	PUNCT
ejpam-4171	42	56	d(x2	d(x2	NOUN
ejpam-4171	42	57	,	,	PUNCT
ejpam-4171	42	58	y2	y2	PROPN
ejpam-4171	42	59	)	)	PUNCT
ejpam-4171	43	1	=	=	SYM
ejpam-4171	43	2	d(q	d(q	PROPN
ejpam-4171	43	3	,	,	PUNCT
ejpam-4171	43	4	r	r	NOUN
ejpam-4171	43	5	)	)	PUNCT
ejpam-4171	43	6	=	=	NOUN
ejpam-4171	43	7	⇒	⇒	NOUN
ejpam-4171	43	8	d(x1	d(x1	NOUN
ejpam-4171	43	9	,	,	PUNCT
ejpam-4171	43	10	x2	x2	NUM
ejpam-4171	43	11	)	)	PUNCT
ejpam-4171	43	12	=	=	SYM
ejpam-4171	43	13	d(y1	d(y1	NOUN
ejpam-4171	43	14	,	,	PUNCT
ejpam-4171	43	15	y2	y2	PROPN
ejpam-4171	43	16	)	)	PUNCT
ejpam-4171	43	17	,	,	PUNCT
ejpam-4171	43	18	where	where	SCONJ
ejpam-4171	43	19	x1	x1	X
ejpam-4171	43	20	,	,	PUNCT
ejpam-4171	43	21	x2	x2	PROPN
ejpam-4171	43	22	∈	∈	PROPN
ejpam-4171	43	23	q	q	NOUN
ejpam-4171	43	24	and	and	CCONJ
ejpam-4171	43	25	y1	y1	ADJ
ejpam-4171	43	26	,	,	PUNCT
ejpam-4171	43	27	y2	y2	PROPN
ejpam-4171	43	28	∈	∈	PROPN
ejpam-4171	43	29	r.	r.	PROPN
ejpam-4171	43	30	definition	definition	NOUN
ejpam-4171	43	31	6	6	NUM
ejpam-4171	43	32	.	.	PUNCT
ejpam-4171	44	1	[	[	X
ejpam-4171	44	2	12	12	NUM
ejpam-4171	44	3	]	]	X
ejpam-4171	44	4	let	let	AUX
ejpam-4171	44	5	(	(	PUNCT
ejpam-4171	44	6	q	q	NOUN
ejpam-4171	44	7	,	,	PUNCT
ejpam-4171	44	8	r	r	NOUN
ejpam-4171	44	9	)	)	PUNCT
ejpam-4171	44	10	be	be	AUX
ejpam-4171	44	11	non	non	ADJ
ejpam-4171	44	12	-	-	ADJ
ejpam-4171	44	13	empty	empty	ADJ
ejpam-4171	44	14	pair	pair	NOUN
ejpam-4171	44	15	of	of	ADP
ejpam-4171	44	16	subsets	subset	NOUN
ejpam-4171	44	17	of	of	ADP
ejpam-4171	44	18	mertic	mertic	ADJ
ejpam-4171	44	19	space	space	NOUN
ejpam-4171	44	20	(	(	PUNCT
ejpam-4171	44	21	x	x	X
ejpam-4171	44	22	,	,	PUNCT
ejpam-4171	44	23	d	d	NOUN
ejpam-4171	44	24	)	)	PUNCT
ejpam-4171	44	25	.	.	PUNCT
ejpam-4171	45	1	consider	consider	VERB
ejpam-4171	45	2	g	g	NOUN
ejpam-4171	45	3	:	:	PUNCT
ejpam-4171	45	4	q	q	X
ejpam-4171	45	5	→	→	X
ejpam-4171	45	6	q	q	X
ejpam-4171	45	7	and	and	CCONJ
ejpam-4171	45	8	g	g	NOUN
ejpam-4171	45	9	:	:	PUNCT
ejpam-4171	45	10	q	q	X
ejpam-4171	45	11	→	→	PUNCT
ejpam-4171	45	12	r	r	AUX
ejpam-4171	45	13	be	be	NOUN
ejpam-4171	45	14	mappings	mapping	NOUN
ejpam-4171	45	15	then	then	ADV
ejpam-4171	45	16	a	a	DET
ejpam-4171	45	17	point	point	NOUN
ejpam-4171	45	18	x	x	X
ejpam-4171	45	19	∈	∈	PROPN
ejpam-4171	45	20	q	q	NOUN
ejpam-4171	45	21	is	be	AUX
ejpam-4171	45	22	a	a	DET
ejpam-4171	45	23	best	good	ADJ
ejpam-4171	45	24	proximity	proximity	NOUN
ejpam-4171	45	25	gpoint	gpoint	NOUN
ejpam-4171	45	26	of	of	ADP
ejpam-4171	45	27	the	the	DET
ejpam-4171	45	28	pair	pair	NOUN
ejpam-4171	45	29	(	(	PUNCT
ejpam-4171	45	30	g	g	NOUN
ejpam-4171	45	31	,	,	PUNCT
ejpam-4171	45	32	g	g	NOUN
ejpam-4171	45	33	)	)	PUNCT
ejpam-4171	45	34	if	if	SCONJ
ejpam-4171	45	35	d(gx	d(gx	PROPN
ejpam-4171	45	36	,	,	PUNCT
ejpam-4171	45	37	gx	gx	PROPN
ejpam-4171	45	38	)	)	PUNCT
ejpam-4171	46	1	=	=	SYM
ejpam-4171	46	2	d(q	d(q	PROPN
ejpam-4171	46	3	,	,	PUNCT
ejpam-4171	46	4	r	r	NOUN
ejpam-4171	46	5	)	)	PUNCT
ejpam-4171	46	6	.	.	PUNCT
ejpam-4171	47	1	definition	definition	NOUN
ejpam-4171	47	2	7	7	NUM
ejpam-4171	47	3	.	.	PUNCT
ejpam-4171	48	1	[	[	X
ejpam-4171	48	2	1	1	X
ejpam-4171	48	3	]	]	PUNCT
ejpam-4171	48	4	let	let	VERB
ejpam-4171	48	5	ψ	ψ	PART
ejpam-4171	48	6	represent	represent	VERB
ejpam-4171	48	7	the	the	DET
ejpam-4171	48	8	family	family	NOUN
ejpam-4171	48	9	of	of	ADP
ejpam-4171	48	10	functions	function	NOUN
ejpam-4171	48	11	ψ	ψ	VERB
ejpam-4171	48	12	such	such	ADJ
ejpam-4171	48	13	that	that	DET
ejpam-4171	48	14	ψ	ψ	X
ejpam-4171	48	15	:	:	PUNCT
ejpam-4171	48	16	[	[	X
ejpam-4171	48	17	0,∞	0,∞	NOUN
ejpam-4171	48	18	)	)	PUNCT
ejpam-4171	48	19	→	→	PUNCT
ejpam-4171	49	1	[	[	X
ejpam-4171	49	2	0,∞	0,∞	NOUN
ejpam-4171	49	3	)	)	PUNCT
ejpam-4171	49	4	which	which	PRON
ejpam-4171	49	5	satisfy	satisfy	VERB
ejpam-4171	49	6	(	(	PUNCT
ejpam-4171	49	7	i	i	NOUN
ejpam-4171	49	8	)	)	PUNCT
ejpam-4171	49	9	ψ(x	ψ(x	PROPN
ejpam-4171	49	10	)	)	PUNCT
ejpam-4171	50	1	=	=	SYM
ejpam-4171	50	2	0	0	PUNCT
ejpam-4171	51	1	if	if	SCONJ
ejpam-4171	51	2	and	and	CCONJ
ejpam-4171	51	3	only	only	ADV
ejpam-4171	51	4	if	if	SCONJ
ejpam-4171	51	5	x	x	PROPN
ejpam-4171	51	6	=	=	NOUN
ejpam-4171	51	7	0	0	NUM
ejpam-4171	51	8	.	.	PUNCT
ejpam-4171	51	9	(	(	PUNCT
ejpam-4171	51	10	ii	ii	NOUN
ejpam-4171	51	11	)	)	PUNCT
ejpam-4171	51	12	ψ(x	ψ(x	PROPN
ejpam-4171	51	13	)	)	PUNCT
ejpam-4171	51	14	is	be	AUX
ejpam-4171	51	15	continuous	continuous	ADJ
ejpam-4171	51	16	and	and	CCONJ
ejpam-4171	51	17	non	non	ADJ
ejpam-4171	51	18	-	-	ADJ
ejpam-4171	51	19	decreasing	decrease	VERB
ejpam-4171	51	20	.	.	PUNCT
ejpam-4171	52	1	s.	s.	PROPN
ejpam-4171	52	2	rathee	rathee	PROPN
ejpam-4171	52	3	,	,	PUNCT
ejpam-4171	52	4	m.	m.	NOUN
ejpam-4171	52	5	swami	swami	PROPN
ejpam-4171	52	6	,	,	PUNCT
ejpam-4171	52	7	/	/	SYM
ejpam-4171	52	8	eur	eur	NOUN
ejpam-4171	52	9	.	.	PUNCT
ejpam-4171	53	1	j.	j.	PROPN
ejpam-4171	53	2	pure	pure	PROPN
ejpam-4171	53	3	appl	appl	PROPN
ejpam-4171	53	4	.	.	PROPN
ejpam-4171	53	5	math	math	PROPN
ejpam-4171	53	6	,	,	PUNCT
ejpam-4171	53	7	15	15	NUM
ejpam-4171	53	8	(	(	PUNCT
ejpam-4171	53	9	1	1	NUM
ejpam-4171	53	10	)	)	PUNCT
ejpam-4171	53	11	(	(	PUNCT
ejpam-4171	53	12	2022	2022	NUM
ejpam-4171	53	13	)	)	PUNCT
ejpam-4171	53	14	,	,	PUNCT
ejpam-4171	53	15	135	135	NUM
ejpam-4171	53	16	-	-	SYM
ejpam-4171	53	17	143	143	NUM
ejpam-4171	53	18	137	137	NUM
ejpam-4171	53	19	let	let	VERB
ejpam-4171	53	20	θ	θ	NOUN
ejpam-4171	53	21	signify	signify	VERB
ejpam-4171	53	22	the	the	DET
ejpam-4171	53	23	collection	collection	NOUN
ejpam-4171	53	24	of	of	ADP
ejpam-4171	53	25	functions	function	NOUN
ejpam-4171	53	26	of	of	ADP
ejpam-4171	53	27	type	type	NOUN
ejpam-4171	53	28	θ	θ	NOUN
ejpam-4171	53	29	:	:	PUNCT
ejpam-4171	54	1	[	[	X
ejpam-4171	54	2	0,∞)8	0,∞)8	X
ejpam-4171	54	3	→	→	SYM
ejpam-4171	54	4	[	[	X
ejpam-4171	54	5	0,∞	0,∞	NUM
ejpam-4171	54	6	)	)	PUNCT
ejpam-4171	54	7	such	such	ADJ
ejpam-4171	54	8	that	that	SCONJ
ejpam-4171	54	9	θ(x	θ(x	PROPN
ejpam-4171	54	10	,	,	PUNCT
ejpam-4171	54	11	y	y	PROPN
ejpam-4171	54	12	,	,	PUNCT
ejpam-4171	54	13	z	z	PROPN
ejpam-4171	54	14	,	,	PUNCT
ejpam-4171	54	15	t	t	PROPN
ejpam-4171	54	16	,	,	PUNCT
ejpam-4171	54	17	a	a	DET
ejpam-4171	54	18	,	,	PUNCT
ejpam-4171	54	19	b	b	NOUN
ejpam-4171	54	20	,	,	PUNCT
ejpam-4171	54	21	c	c	X
ejpam-4171	54	22	,	,	PUNCT
ejpam-4171	54	23	u	u	NOUN
ejpam-4171	54	24	)	)	PUNCT
ejpam-4171	54	25	=	=	SYM
ejpam-4171	54	26	min{x	min{x	PROPN
ejpam-4171	54	27	,	,	PUNCT
ejpam-4171	54	28	y	y	PROPN
ejpam-4171	54	29	,	,	PUNCT
ejpam-4171	54	30	z	z	PROPN
ejpam-4171	54	31	,	,	PUNCT
ejpam-4171	54	32	t	t	PROPN
ejpam-4171	54	33	,	,	PUNCT
ejpam-4171	54	34	a	a	DET
ejpam-4171	54	35	,	,	PUNCT
ejpam-4171	54	36	b	b	NOUN
ejpam-4171	54	37	,	,	PUNCT
ejpam-4171	54	38	c	c	X
ejpam-4171	54	39	,	,	PUNCT
ejpam-4171	54	40	u	u	NOUN
ejpam-4171	54	41	}	}	PUNCT
ejpam-4171	54	42	for	for	ADP
ejpam-4171	54	43	all	all	DET
ejpam-4171	54	44	x	x	NOUN
ejpam-4171	54	45	,	,	PUNCT
ejpam-4171	54	46	y	y	PROPN
ejpam-4171	54	47	,	,	PUNCT
ejpam-4171	54	48	z	z	PROPN
ejpam-4171	54	49	,	,	PUNCT
ejpam-4171	54	50	t	t	PROPN
ejpam-4171	54	51	,	,	PUNCT
ejpam-4171	54	52	a	a	DET
ejpam-4171	54	53	,	,	PUNCT
ejpam-4171	54	54	b	b	NOUN
ejpam-4171	54	55	,	,	PUNCT
ejpam-4171	54	56	c	c	X
ejpam-4171	54	57	,	,	PUNCT
ejpam-4171	54	58	u	u	NOUN
ejpam-4171	54	59	∈	∈	PROPN
ejpam-4171	55	1	[	[	X
ejpam-4171	55	2	0,∞	0,∞	NOUN
ejpam-4171	55	3	)	)	PUNCT
ejpam-4171	55	4	.	.	PUNCT
ejpam-4171	56	1	definition	definition	NOUN
ejpam-4171	56	2	8	8	NUM
ejpam-4171	56	3	.	.	PUNCT
ejpam-4171	57	1	[	[	X
ejpam-4171	57	2	17	17	NUM
ejpam-4171	57	3	]	]	X
ejpam-4171	57	4	let	let	AUX
ejpam-4171	57	5	(	(	PUNCT
ejpam-4171	57	6	x	x	NOUN
ejpam-4171	57	7	,	,	PUNCT
ejpam-4171	57	8	d	d	NOUN
ejpam-4171	57	9	)	)	PUNCT
ejpam-4171	57	10	be	be	AUX
ejpam-4171	57	11	a	a	DET
ejpam-4171	57	12	complete	complete	ADJ
ejpam-4171	57	13	metric	metric	ADJ
ejpam-4171	57	14	space	space	NOUN
ejpam-4171	57	15	and	and	CCONJ
ejpam-4171	57	16	q	q	NOUN
ejpam-4171	57	17	̸=	̸=	PROPN
ejpam-4171	57	18	ϕ	ϕ	NOUN
ejpam-4171	57	19	and	and	CCONJ
ejpam-4171	57	20	r	r	PROPN
ejpam-4171	57	21	̸=	̸=	PROPN
ejpam-4171	57	22	ϕ	ϕ	NOUN
ejpam-4171	57	23	are	be	AUX
ejpam-4171	57	24	closed	closed	ADJ
ejpam-4171	57	25	subsets	subset	NOUN
ejpam-4171	57	26	.	.	PUNCT
ejpam-4171	58	1	an	an	DET
ejpam-4171	58	2	element	element	NOUN
ejpam-4171	58	3	(	(	PUNCT
ejpam-4171	58	4	x	x	X
ejpam-4171	58	5	,	,	PUNCT
ejpam-4171	58	6	y	y	PROPN
ejpam-4171	58	7	,	,	PUNCT
ejpam-4171	58	8	z	z	NOUN
ejpam-4171	58	9	)	)	PUNCT
ejpam-4171	58	10	∈	∈	PROPN
ejpam-4171	58	11	x	x	X
ejpam-4171	58	12	×	×	NOUN
ejpam-4171	58	13	x	x	SYM
ejpam-4171	58	14	×	×	NOUN
ejpam-4171	58	15	x	x	VERB
ejpam-4171	58	16	is	be	AUX
ejpam-4171	58	17	said	say	VERB
ejpam-4171	58	18	to	to	PART
ejpam-4171	58	19	be	be	AUX
ejpam-4171	58	20	a	a	DET
ejpam-4171	58	21	tripled	triple	VERB
ejpam-4171	58	22	best	good	ADJ
ejpam-4171	58	23	proximity	proximity	NOUN
ejpam-4171	58	24	point	point	NOUN
ejpam-4171	58	25	of	of	ADP
ejpam-4171	58	26	g	g	NOUN
ejpam-4171	58	27	:	:	PUNCT
ejpam-4171	58	28	x	x	SYM
ejpam-4171	59	1	×	×	NOUN
ejpam-4171	59	2	x	x	SYM
ejpam-4171	59	3	×	×	NOUN
ejpam-4171	59	4	x	x	INTJ
ejpam-4171	59	5	→	→	SYM
ejpam-4171	59	6	x	x	X
ejpam-4171	59	7	if	if	SCONJ
ejpam-4171	59	8	x	x	X
ejpam-4171	59	9	,	,	PUNCT
ejpam-4171	59	10	z	z	PROPN
ejpam-4171	59	11	∈	∈	PROPN
ejpam-4171	59	12	q	q	NOUN
ejpam-4171	59	13	and	and	CCONJ
ejpam-4171	59	14	y	y	PROPN
ejpam-4171	59	15	∈	∈	PROPN
ejpam-4171	59	16	r	r	NOUN
ejpam-4171	59	17	such	such	ADJ
ejpam-4171	59	18	that	that	DET
ejpam-4171	59	19	d(x	d(x	NOUN
ejpam-4171	59	20	,	,	PUNCT
ejpam-4171	59	21	g(x	g(x	PROPN
ejpam-4171	59	22	,	,	PUNCT
ejpam-4171	59	23	y	y	PROPN
ejpam-4171	59	24	,	,	PUNCT
ejpam-4171	59	25	z	z	NOUN
ejpam-4171	59	26	)	)	PUNCT
ejpam-4171	59	27	)	)	PUNCT
ejpam-4171	60	1	=	=	SYM
ejpam-4171	60	2	d(q	d(q	PROPN
ejpam-4171	60	3	,	,	PUNCT
ejpam-4171	60	4	r	r	NOUN
ejpam-4171	60	5	)	)	PUNCT
ejpam-4171	60	6	,	,	PUNCT
ejpam-4171	60	7	d(y	d(y	NOUN
ejpam-4171	60	8	,	,	PUNCT
ejpam-4171	60	9	g(y	g(y	PROPN
ejpam-4171	60	10	,	,	PUNCT
ejpam-4171	60	11	x	x	X
ejpam-4171	60	12	,	,	PUNCT
ejpam-4171	60	13	y	y	NOUN
ejpam-4171	60	14	)	)	PUNCT
ejpam-4171	60	15	)	)	PUNCT
ejpam-4171	61	1	=	=	SYM
ejpam-4171	61	2	d(q	d(q	PROPN
ejpam-4171	61	3	,	,	PUNCT
ejpam-4171	61	4	r	r	NOUN
ejpam-4171	61	5	)	)	PUNCT
ejpam-4171	61	6	and	and	CCONJ
ejpam-4171	61	7	d(z	d(z	PROPN
ejpam-4171	61	8	,	,	PUNCT
ejpam-4171	61	9	g(z	g(z	PROPN
ejpam-4171	61	10	,	,	PUNCT
ejpam-4171	61	11	y	y	PROPN
ejpam-4171	61	12	,	,	PUNCT
ejpam-4171	61	13	x	x	NOUN
ejpam-4171	61	14	)	)	PUNCT
ejpam-4171	61	15	)	)	PUNCT
ejpam-4171	62	1	=	=	SYM
ejpam-4171	62	2	d(q	d(q	PROPN
ejpam-4171	62	3	,	,	PUNCT
ejpam-4171	62	4	r	r	NOUN
ejpam-4171	62	5	)	)	PUNCT
ejpam-4171	62	6	.	.	PUNCT
ejpam-4171	63	1	3	3	X
ejpam-4171	63	2	.	.	X
ejpam-4171	63	3	main	main	ADJ
ejpam-4171	63	4	results	result	NOUN
ejpam-4171	63	5	definition	definition	NOUN
ejpam-4171	63	6	9	9	NUM
ejpam-4171	63	7	.	.	PUNCT
ejpam-4171	64	1	let	let	AUX
ejpam-4171	64	2	(	(	PUNCT
ejpam-4171	64	3	x	x	NOUN
ejpam-4171	64	4	,	,	PUNCT
ejpam-4171	64	5	d	d	NOUN
ejpam-4171	64	6	)	)	PUNCT
ejpam-4171	64	7	be	be	AUX
ejpam-4171	64	8	a	a	DET
ejpam-4171	64	9	complete	complete	ADJ
ejpam-4171	64	10	metric	metric	ADJ
ejpam-4171	64	11	space	space	NOUN
ejpam-4171	64	12	and	and	CCONJ
ejpam-4171	64	13	(	(	PUNCT
ejpam-4171	64	14	q	q	ADJ
ejpam-4171	64	15	,	,	PUNCT
ejpam-4171	64	16	r	r	NOUN
ejpam-4171	64	17	)	)	PUNCT
ejpam-4171	64	18	be	be	AUX
ejpam-4171	64	19	a	a	DET
ejpam-4171	64	20	pair	pair	NOUN
ejpam-4171	64	21	of	of	ADP
ejpam-4171	64	22	non	non	ADJ
ejpam-4171	64	23	-	-	ADJ
ejpam-4171	64	24	empty	empty	ADJ
ejpam-4171	64	25	subset	subset	NOUN
ejpam-4171	64	26	of	of	ADP
ejpam-4171	64	27	x	x	SYM
ejpam-4171	64	28	such	such	ADJ
ejpam-4171	64	29	that	that	SCONJ
ejpam-4171	64	30	q0	q0	PROPN
ejpam-4171	64	31	is	be	AUX
ejpam-4171	64	32	non	non	ADJ
ejpam-4171	64	33	-	-	ADJ
ejpam-4171	64	34	empty	empty	ADJ
ejpam-4171	64	35	.	.	PUNCT
ejpam-4171	65	1	consider	consider	VERB
ejpam-4171	65	2	g	g	NOUN
ejpam-4171	65	3	:	:	PUNCT
ejpam-4171	65	4	x	x	SYM
ejpam-4171	65	5	→	→	SYM
ejpam-4171	65	6	x	x	X
ejpam-4171	65	7	and	and	CCONJ
ejpam-4171	65	8	g	g	PROPN
ejpam-4171	65	9	:	:	PUNCT
ejpam-4171	65	10	x4	x4	PROPN
ejpam-4171	65	11	→	→	PUNCT
ejpam-4171	65	12	x	x	X
ejpam-4171	65	13	be	be	AUX
ejpam-4171	65	14	two	two	NUM
ejpam-4171	65	15	mappings	mapping	NOUN
ejpam-4171	65	16	,	,	PUNCT
ejpam-4171	65	17	then	then	ADV
ejpam-4171	65	18	(	(	PUNCT
ejpam-4171	65	19	x	x	X
ejpam-4171	65	20	,	,	PUNCT
ejpam-4171	65	21	y	y	PROPN
ejpam-4171	65	22	,	,	PUNCT
ejpam-4171	65	23	z	z	PROPN
ejpam-4171	65	24	,	,	PUNCT
ejpam-4171	65	25	t	t	PROPN
ejpam-4171	65	26	)	)	PUNCT
ejpam-4171	65	27	is	be	AUX
ejpam-4171	65	28	said	say	VERB
ejpam-4171	65	29	to	to	PART
ejpam-4171	65	30	be	be	AUX
ejpam-4171	65	31	quadruple	quadruple	NOUN
ejpam-4171	65	32	g	g	ADV
ejpam-4171	65	33	-	-	PUNCT
ejpam-4171	65	34	best	good	ADJ
ejpam-4171	65	35	proximity	proximity	NOUN
ejpam-4171	65	36	point	point	NOUN
ejpam-4171	65	37	of	of	ADP
ejpam-4171	65	38	g	g	PROPN
ejpam-4171	65	39	and	and	CCONJ
ejpam-4171	65	40	g	g	NOUN
ejpam-4171	65	41	if	if	SCONJ
ejpam-4171	65	42	d(gx	d(gx	PROPN
ejpam-4171	65	43	,	,	PUNCT
ejpam-4171	65	44	g(x	g(x	PROPN
ejpam-4171	65	45	,	,	PUNCT
ejpam-4171	65	46	y	y	PROPN
ejpam-4171	65	47	,	,	PUNCT
ejpam-4171	65	48	z	z	PROPN
ejpam-4171	65	49	,	,	PUNCT
ejpam-4171	65	50	t	t	PROPN
ejpam-4171	65	51	)	)	PUNCT
ejpam-4171	65	52	)	)	PUNCT
ejpam-4171	66	1	=	=	PUNCT
ejpam-4171	66	2	d(q	d(q	PROPN
ejpam-4171	66	3	,	,	PUNCT
ejpam-4171	66	4	r	r	NOUN
ejpam-4171	66	5	)	)	PUNCT
ejpam-4171	66	6	,	,	PUNCT
ejpam-4171	66	7	d(gy	d(gy	PROPN
ejpam-4171	66	8	,	,	PUNCT
ejpam-4171	66	9	g(y	g(y	PROPN
ejpam-4171	66	10	,	,	PUNCT
ejpam-4171	66	11	x	x	X
ejpam-4171	66	12	,	,	PUNCT
ejpam-4171	66	13	z	z	PROPN
ejpam-4171	66	14	,	,	PUNCT
ejpam-4171	66	15	t	t	PROPN
ejpam-4171	66	16	)	)	PUNCT
ejpam-4171	66	17	)	)	PUNCT
ejpam-4171	67	1	=	=	PUNCT
ejpam-4171	67	2	d(q	d(q	PROPN
ejpam-4171	67	3	,	,	PUNCT
ejpam-4171	67	4	r	r	NOUN
ejpam-4171	67	5	)	)	PUNCT
ejpam-4171	67	6	,	,	PUNCT
ejpam-4171	67	7	d(gz	d(gz	PROPN
ejpam-4171	67	8	,	,	PUNCT
ejpam-4171	67	9	g(z	g(z	PROPN
ejpam-4171	67	10	,	,	PUNCT
ejpam-4171	67	11	y	y	PROPN
ejpam-4171	67	12	,	,	PUNCT
ejpam-4171	67	13	x	x	PROPN
ejpam-4171	67	14	,	,	PUNCT
ejpam-4171	67	15	t	t	PROPN
ejpam-4171	67	16	)	)	PUNCT
ejpam-4171	67	17	)	)	PUNCT
ejpam-4171	68	1	=	=	PUNCT
ejpam-4171	68	2	d(q	d(q	PROPN
ejpam-4171	68	3	,	,	PUNCT
ejpam-4171	68	4	r	r	NOUN
ejpam-4171	68	5	)	)	PUNCT
ejpam-4171	68	6	and	and	CCONJ
ejpam-4171	68	7	d(gt	d(gt	PROPN
ejpam-4171	68	8	,	,	PUNCT
ejpam-4171	68	9	g(t	g(t	PROPN
ejpam-4171	68	10	,	,	PUNCT
ejpam-4171	68	11	y	y	PROPN
ejpam-4171	68	12	,	,	PUNCT
ejpam-4171	68	13	z	z	PROPN
ejpam-4171	68	14	,	,	PUNCT
ejpam-4171	68	15	x	x	NOUN
ejpam-4171	68	16	)	)	PUNCT
ejpam-4171	68	17	)	)	PUNCT
ejpam-4171	69	1	=	=	SYM
ejpam-4171	69	2	d(q	d(q	PROPN
ejpam-4171	69	3	,	,	PUNCT
ejpam-4171	69	4	r	r	NOUN
ejpam-4171	69	5	)	)	PUNCT
ejpam-4171	69	6	for	for	ADP
ejpam-4171	69	7	all	all	DET
ejpam-4171	69	8	x	x	NOUN
ejpam-4171	69	9	,	,	PUNCT
ejpam-4171	69	10	z	z	PROPN
ejpam-4171	69	11	∈	∈	PROPN
ejpam-4171	69	12	q	q	NOUN
ejpam-4171	69	13	and	and	CCONJ
ejpam-4171	69	14	y	y	PROPN
ejpam-4171	69	15	,	,	PUNCT
ejpam-4171	69	16	t	t	PROPN
ejpam-4171	69	17	∈	∈	PROPN
ejpam-4171	69	18	r.	r.	PROPN
ejpam-4171	69	19	if	if	SCONJ
ejpam-4171	69	20	g	g	PROPN
ejpam-4171	69	21	=	=	VERB
ejpam-4171	69	22	i	i	PROPN
ejpam-4171	69	23	(	(	PUNCT
ejpam-4171	69	24	identity	identity	NOUN
ejpam-4171	69	25	mapping	mapping	NOUN
ejpam-4171	69	26	)	)	PUNCT
ejpam-4171	69	27	then	then	ADV
ejpam-4171	69	28	(	(	PUNCT
ejpam-4171	69	29	x	x	X
ejpam-4171	69	30	,	,	PUNCT
ejpam-4171	69	31	y	y	PROPN
ejpam-4171	69	32	,	,	PUNCT
ejpam-4171	69	33	z	z	PROPN
ejpam-4171	69	34	,	,	PUNCT
ejpam-4171	69	35	t	t	PROPN
ejpam-4171	69	36	)	)	PUNCT
ejpam-4171	69	37	is	be	AUX
ejpam-4171	69	38	said	say	VERB
ejpam-4171	69	39	to	to	PART
ejpam-4171	69	40	be	be	AUX
ejpam-4171	69	41	quadruple	quadruple	ADV
ejpam-4171	69	42	best	good	ADJ
ejpam-4171	69	43	proximity	proximity	NOUN
ejpam-4171	69	44	point	point	NOUN
ejpam-4171	69	45	of	of	ADP
ejpam-4171	69	46	g	g	PROPN
ejpam-4171	69	47	if	if	SCONJ
ejpam-4171	69	48	d(x	d(x	NOUN
ejpam-4171	69	49	,	,	PUNCT
ejpam-4171	69	50	g(x	g(x	PROPN
ejpam-4171	69	51	,	,	PUNCT
ejpam-4171	69	52	y	y	PROPN
ejpam-4171	69	53	,	,	PUNCT
ejpam-4171	69	54	z	z	PROPN
ejpam-4171	69	55	,	,	PUNCT
ejpam-4171	69	56	t	t	PROPN
ejpam-4171	69	57	)	)	PUNCT
ejpam-4171	69	58	)	)	PUNCT
ejpam-4171	70	1	=	=	PUNCT
ejpam-4171	70	2	d(q	d(q	PROPN
ejpam-4171	70	3	,	,	PUNCT
ejpam-4171	70	4	r	r	NOUN
ejpam-4171	70	5	)	)	PUNCT
ejpam-4171	70	6	,	,	PUNCT
ejpam-4171	70	7	d(y	d(y	NOUN
ejpam-4171	70	8	,	,	PUNCT
ejpam-4171	70	9	g(y	g(y	PROPN
ejpam-4171	70	10	,	,	PUNCT
ejpam-4171	70	11	x	x	X
ejpam-4171	70	12	,	,	PUNCT
ejpam-4171	70	13	z	z	PROPN
ejpam-4171	70	14	,	,	PUNCT
ejpam-4171	70	15	t	t	PROPN
ejpam-4171	70	16	)	)	PUNCT
ejpam-4171	70	17	)	)	PUNCT
ejpam-4171	71	1	=	=	PUNCT
ejpam-4171	71	2	d(q	d(q	PROPN
ejpam-4171	71	3	,	,	PUNCT
ejpam-4171	71	4	r	r	NOUN
ejpam-4171	71	5	)	)	PUNCT
ejpam-4171	71	6	,	,	PUNCT
ejpam-4171	71	7	d(z	d(z	PROPN
ejpam-4171	71	8	,	,	PUNCT
ejpam-4171	71	9	g(z	g(z	PROPN
ejpam-4171	71	10	,	,	PUNCT
ejpam-4171	71	11	y	y	PROPN
ejpam-4171	71	12	,	,	PUNCT
ejpam-4171	71	13	x	x	PROPN
ejpam-4171	71	14	,	,	PUNCT
ejpam-4171	71	15	t	t	PROPN
ejpam-4171	71	16	)	)	PUNCT
ejpam-4171	71	17	)	)	PUNCT
ejpam-4171	72	1	=	=	PUNCT
ejpam-4171	72	2	d(q	d(q	PROPN
ejpam-4171	72	3	,	,	PUNCT
ejpam-4171	72	4	r	r	NOUN
ejpam-4171	72	5	)	)	PUNCT
ejpam-4171	72	6	and	and	CCONJ
ejpam-4171	72	7	d(t	d(t	PROPN
ejpam-4171	72	8	,	,	PUNCT
ejpam-4171	72	9	g(t	g(t	PROPN
ejpam-4171	72	10	,	,	PUNCT
ejpam-4171	72	11	y	y	PROPN
ejpam-4171	72	12	,	,	PUNCT
ejpam-4171	72	13	z	z	PROPN
ejpam-4171	72	14	,	,	PUNCT
ejpam-4171	72	15	x	x	NOUN
ejpam-4171	72	16	)	)	PUNCT
ejpam-4171	72	17	)	)	PUNCT
ejpam-4171	73	1	=	=	SYM
ejpam-4171	73	2	d(q	d(q	PROPN
ejpam-4171	73	3	,	,	PUNCT
ejpam-4171	73	4	r	r	NOUN
ejpam-4171	73	5	)	)	PUNCT
ejpam-4171	73	6	for	for	ADP
ejpam-4171	73	7	all	all	DET
ejpam-4171	73	8	x	x	NOUN
ejpam-4171	73	9	,	,	PUNCT
ejpam-4171	73	10	z	z	PROPN
ejpam-4171	73	11	∈	∈	PROPN
ejpam-4171	73	12	q	q	NOUN
ejpam-4171	73	13	and	and	CCONJ
ejpam-4171	73	14	y	y	PROPN
ejpam-4171	73	15	,	,	PUNCT
ejpam-4171	73	16	t	t	PROPN
ejpam-4171	73	17	∈	∈	PROPN
ejpam-4171	73	18	r.	r.	PROPN
ejpam-4171	73	19	theorem	theorem	NOUN
ejpam-4171	73	20	1	1	X
ejpam-4171	73	21	.	.	PUNCT
ejpam-4171	74	1	let	let	VERB
ejpam-4171	74	2	q	q	NOUN
ejpam-4171	74	3	and	and	CCONJ
ejpam-4171	74	4	r	r	NOUN
ejpam-4171	74	5	be	be	AUX
ejpam-4171	74	6	non	non	ADJ
ejpam-4171	74	7	-	-	ADJ
ejpam-4171	74	8	empty	empty	ADJ
ejpam-4171	74	9	subset	subset	NOUN
ejpam-4171	74	10	of	of	ADP
ejpam-4171	74	11	complete	complete	ADJ
ejpam-4171	74	12	metric	metric	ADJ
ejpam-4171	74	13	space	space	NOUN
ejpam-4171	74	14	(	(	PUNCT
ejpam-4171	74	15	x	x	X
ejpam-4171	74	16	,	,	PUNCT
ejpam-4171	74	17	d	d	NOUN
ejpam-4171	74	18	)	)	PUNCT
ejpam-4171	74	19	such	such	ADJ
ejpam-4171	74	20	that	that	SCONJ
ejpam-4171	74	21	q0	q0	PROPN
ejpam-4171	74	22	and	and	CCONJ
ejpam-4171	74	23	r0	r0	NOUN
ejpam-4171	74	24	are	be	AUX
ejpam-4171	74	25	non	non	ADJ
ejpam-4171	74	26	-	-	ADJ
ejpam-4171	74	27	empty	empty	ADJ
ejpam-4171	74	28	and	and	CCONJ
ejpam-4171	74	29	g	g	NOUN
ejpam-4171	74	30	:	:	PUNCT
ejpam-4171	74	31	x	x	SYM
ejpam-4171	74	32	→	→	PUNCT
ejpam-4171	74	33	x	x	X
ejpam-4171	74	34	is	be	AUX
ejpam-4171	74	35	an	an	DET
ejpam-4171	74	36	isometry	isometry	NOUN
ejpam-4171	74	37	such	such	ADJ
ejpam-4171	74	38	that	that	SCONJ
ejpam-4171	74	39	q0	q0	VERB
ejpam-4171	74	40	⊆	⊆	NUM
ejpam-4171	74	41	g(q0	g(q0	NOUN
ejpam-4171	74	42	)	)	PUNCT
ejpam-4171	74	43	and	and	CCONJ
ejpam-4171	74	44	r0	r0	VERB
ejpam-4171	74	45	⊆	⊆	NUM
ejpam-4171	74	46	g(r0	g(r0	NOUN
ejpam-4171	74	47	)	)	PUNCT
ejpam-4171	74	48	,	,	PUNCT
ejpam-4171	74	49	let	let	VERB
ejpam-4171	74	50	g	g	NOUN
ejpam-4171	74	51	:	:	PUNCT
ejpam-4171	74	52	x4	x4	PROPN
ejpam-4171	74	53	→	→	PUNCT
ejpam-4171	74	54	x	x	X
ejpam-4171	74	55	be	be	AUX
ejpam-4171	74	56	continuous	continuous	ADJ
ejpam-4171	74	57	mapping	mapping	NOUN
ejpam-4171	74	58	and	and	CCONJ
ejpam-4171	74	59	ψ	ψ	NOUN
ejpam-4171	74	60	,	,	PUNCT
ejpam-4171	74	61	ζ	ζ	PROPN
ejpam-4171	74	62	∈	∈	NOUN
ejpam-4171	74	63	ψ	ψ	NOUN
ejpam-4171	74	64	and	and	CCONJ
ejpam-4171	74	65	θ	θ	PROPN
ejpam-4171	74	66	∈	∈	PROPN
ejpam-4171	74	67	θ	θ	PROPN
ejpam-4171	74	68	,	,	PUNCT
ejpam-4171	74	69	satisfies	satisfy	VERB
ejpam-4171	74	70	the	the	DET
ejpam-4171	74	71	preceeding	preceede	VERB
ejpam-4171	74	72	conditions	condition	NOUN
ejpam-4171	74	73	:	:	PUNCT
ejpam-4171	74	74	(	(	PUNCT
ejpam-4171	74	75	i	i	NOUN
ejpam-4171	74	76	)	)	PUNCT
ejpam-4171	74	77	for	for	ADP
ejpam-4171	74	78	every	every	DET
ejpam-4171	74	79	x	x	PROPN
ejpam-4171	74	80	,	,	PUNCT
ejpam-4171	74	81	y	y	PROPN
ejpam-4171	74	82	,	,	PUNCT
ejpam-4171	74	83	z	z	PROPN
ejpam-4171	74	84	,	,	PUNCT
ejpam-4171	74	85	t	t	PROPN
ejpam-4171	74	86	,	,	PUNCT
ejpam-4171	74	87	a	a	DET
ejpam-4171	74	88	,	,	PUNCT
ejpam-4171	74	89	b	b	NOUN
ejpam-4171	74	90	,	,	PUNCT
ejpam-4171	74	91	c	c	X
ejpam-4171	74	92	,	,	PUNCT
ejpam-4171	74	93	u	u	NOUN
ejpam-4171	74	94	∈	∈	PROPN
ejpam-4171	74	95	x	x	INTJ
ejpam-4171	74	96	ψ(d(gx	ψ(d(gx	PROPN
ejpam-4171	74	97	,	,	PUNCT
ejpam-4171	74	98	ga	ga	PROPN
ejpam-4171	74	99	)	)	PUNCT
ejpam-4171	74	100	)	)	PUNCT
ejpam-4171	75	1	=	=	SYM
ejpam-4171	75	2	ψ(d(g(x	ψ(d(g(x	PROPN
ejpam-4171	75	3	,	,	PUNCT
ejpam-4171	75	4	y	y	PROPN
ejpam-4171	75	5	,	,	PUNCT
ejpam-4171	75	6	z	z	PROPN
ejpam-4171	75	7	,	,	PUNCT
ejpam-4171	75	8	t	t	PROPN
ejpam-4171	75	9	)	)	PUNCT
ejpam-4171	75	10	,	,	PUNCT
ejpam-4171	75	11	g(a	g(a	PROPN
ejpam-4171	75	12	,	,	PUNCT
ejpam-4171	75	13	b	b	PROPN
ejpam-4171	75	14	,	,	PUNCT
ejpam-4171	75	15	c	c	X
ejpam-4171	75	16	,	,	PUNCT
ejpam-4171	75	17	u	u	NOUN
ejpam-4171	75	18	)	)	PUNCT
ejpam-4171	75	19	)	)	PUNCT
ejpam-4171	75	20	)	)	PUNCT
ejpam-4171	75	21	≤ψ{max(d(x	≤ψ{max(d(x	NOUN
ejpam-4171	75	22	,	,	PUNCT
ejpam-4171	75	23	a	a	PRON
ejpam-4171	75	24	)	)	PUNCT
ejpam-4171	75	25	,	,	PUNCT
ejpam-4171	75	26	d(y	d(y	PROPN
ejpam-4171	75	27	,	,	PUNCT
ejpam-4171	75	28	b	b	NOUN
ejpam-4171	75	29	)	)	PUNCT
ejpam-4171	75	30	,	,	PUNCT
ejpam-4171	75	31	d(z	d(z	PROPN
ejpam-4171	75	32	,	,	PUNCT
ejpam-4171	75	33	c	c	NOUN
ejpam-4171	75	34	)	)	PUNCT
ejpam-4171	75	35	,	,	PUNCT
ejpam-4171	75	36	d(t	d(t	PROPN
ejpam-4171	75	37	,	,	PUNCT
ejpam-4171	75	38	u	u	NOUN
ejpam-4171	75	39	)	)	PUNCT
ejpam-4171	75	40	)	)	PUNCT
ejpam-4171	75	41	}	}	PUNCT
ejpam-4171	75	42	−	−	ADP
ejpam-4171	75	43	ζ{max(d(x	ζ{max(d(x	NOUN
ejpam-4171	75	44	,	,	PUNCT
ejpam-4171	75	45	a	a	PRON
ejpam-4171	75	46	)	)	PUNCT
ejpam-4171	75	47	,	,	PUNCT
ejpam-4171	75	48	d(y	d(y	PROPN
ejpam-4171	75	49	,	,	PUNCT
ejpam-4171	75	50	b	b	NOUN
ejpam-4171	75	51	)	)	PUNCT
ejpam-4171	75	52	,	,	PUNCT
ejpam-4171	75	53	d(z	d(z	PROPN
ejpam-4171	75	54	,	,	PUNCT
ejpam-4171	75	55	c	c	NOUN
ejpam-4171	75	56	)	)	PUNCT
ejpam-4171	75	57	,	,	PUNCT
ejpam-4171	75	58	d(t	d(t	PROPN
ejpam-4171	75	59	,	,	PUNCT
ejpam-4171	75	60	u	u	NOUN
ejpam-4171	75	61	)	)	PUNCT
ejpam-4171	75	62	)	)	PUNCT
ejpam-4171	75	63	}	}	PUNCT
ejpam-4171	75	64	+	+	CCONJ
ejpam-4171	75	65	θ[d(ga	θ[d(ga	ADJ
ejpam-4171	75	66	,	,	PUNCT
ejpam-4171	75	67	g(x	g(x	PROPN
ejpam-4171	75	68	,	,	PUNCT
ejpam-4171	75	69	y	y	PROPN
ejpam-4171	75	70	,	,	PUNCT
ejpam-4171	75	71	z	z	PROPN
ejpam-4171	75	72	,	,	PUNCT
ejpam-4171	75	73	t))−	t))−	PROPN
ejpam-4171	75	74	d(q	d(q	PROPN
ejpam-4171	75	75	,	,	PUNCT
ejpam-4171	75	76	r	r	NOUN
ejpam-4171	75	77	)	)	PUNCT
ejpam-4171	75	78	,	,	PUNCT
ejpam-4171	75	79	d(gb	d(gb	NOUN
ejpam-4171	75	80	,	,	PUNCT
ejpam-4171	75	81	g(y	g(y	PROPN
ejpam-4171	75	82	,	,	PUNCT
ejpam-4171	75	83	x	x	X
ejpam-4171	75	84	,	,	PUNCT
ejpam-4171	75	85	z	z	PROPN
ejpam-4171	75	86	,	,	PUNCT
ejpam-4171	75	87	t))−	t))−	PROPN
ejpam-4171	75	88	d(q	d(q	PROPN
ejpam-4171	75	89	,	,	PUNCT
ejpam-4171	75	90	r	r	NOUN
ejpam-4171	75	91	)	)	PUNCT
ejpam-4171	75	92	,	,	PUNCT
ejpam-4171	75	93	d(gc	d(gc	PROPN
ejpam-4171	75	94	,	,	PUNCT
ejpam-4171	75	95	g(z	g(z	PROPN
ejpam-4171	75	96	,	,	PUNCT
ejpam-4171	75	97	y	y	PROPN
ejpam-4171	75	98	,	,	PUNCT
ejpam-4171	75	99	x	x	NOUN
ejpam-4171	75	100	,	,	PUNCT
ejpam-4171	75	101	t))−	t))−	PROPN
ejpam-4171	75	102	d(q	d(q	PROPN
ejpam-4171	75	103	,	,	PUNCT
ejpam-4171	75	104	r	r	NOUN
ejpam-4171	75	105	)	)	PUNCT
ejpam-4171	75	106	,	,	PUNCT
ejpam-4171	75	107	d(gu	d(gu	PROPN
ejpam-4171	75	108	,	,	PUNCT
ejpam-4171	75	109	g(t	g(t	PROPN
ejpam-4171	75	110	,	,	PUNCT
ejpam-4171	75	111	y	y	PROPN
ejpam-4171	75	112	,	,	PUNCT
ejpam-4171	75	113	z	z	PROPN
ejpam-4171	75	114	,	,	PUNCT
ejpam-4171	75	115	x))−	x))−	PROPN
ejpam-4171	75	116	d(q	d(q	PROPN
ejpam-4171	75	117	,	,	PUNCT
ejpam-4171	75	118	r	r	NOUN
ejpam-4171	75	119	)	)	PUNCT
ejpam-4171	75	120	,	,	PUNCT
ejpam-4171	75	121	d(gx	d(gx	PROPN
ejpam-4171	75	122	,	,	PUNCT
ejpam-4171	75	123	g(x	g(x	PROPN
ejpam-4171	75	124	,	,	PUNCT
ejpam-4171	75	125	y	y	PROPN
ejpam-4171	75	126	,	,	PUNCT
ejpam-4171	75	127	z	z	PROPN
ejpam-4171	75	128	,	,	PUNCT
ejpam-4171	75	129	t))−	t))−	PROPN
ejpam-4171	75	130	d(q	d(q	PROPN
ejpam-4171	75	131	,	,	PUNCT
ejpam-4171	75	132	r	r	NOUN
ejpam-4171	75	133	)	)	PUNCT
ejpam-4171	75	134	,	,	PUNCT
ejpam-4171	75	135	d(gy	d(gy	PROPN
ejpam-4171	75	136	,	,	PUNCT
ejpam-4171	75	137	g(y	g(y	PROPN
ejpam-4171	75	138	,	,	PUNCT
ejpam-4171	75	139	x	x	X
ejpam-4171	75	140	,	,	PUNCT
ejpam-4171	75	141	z	z	PROPN
ejpam-4171	75	142	,	,	PUNCT
ejpam-4171	75	143	t))−	t))−	PROPN
ejpam-4171	75	144	d(q	d(q	PROPN
ejpam-4171	75	145	,	,	PUNCT
ejpam-4171	75	146	r	r	NOUN
ejpam-4171	75	147	)	)	PUNCT
ejpam-4171	75	148	,	,	PUNCT
ejpam-4171	75	149	d(gz	d(gz	PROPN
ejpam-4171	75	150	,	,	PUNCT
ejpam-4171	75	151	g(z	g(z	PROPN
ejpam-4171	75	152	,	,	PUNCT
ejpam-4171	75	153	y	y	PROPN
ejpam-4171	75	154	,	,	PUNCT
ejpam-4171	75	155	x	x	NOUN
ejpam-4171	75	156	,	,	PUNCT
ejpam-4171	75	157	t))−	t))−	PROPN
ejpam-4171	75	158	d(q	d(q	PROPN
ejpam-4171	75	159	,	,	PUNCT
ejpam-4171	75	160	r	r	NOUN
ejpam-4171	75	161	)	)	PUNCT
ejpam-4171	75	162	,	,	PUNCT
ejpam-4171	75	163	d(gt	d(gt	PROPN
ejpam-4171	75	164	,	,	PUNCT
ejpam-4171	75	165	g(t	g(t	PROPN
ejpam-4171	75	166	,	,	PUNCT
ejpam-4171	75	167	y	y	PROPN
ejpam-4171	75	168	,	,	PUNCT
ejpam-4171	75	169	z	z	PROPN
ejpam-4171	75	170	,	,	PUNCT
ejpam-4171	75	171	x))−	x))−	PROPN
ejpam-4171	75	172	d(q	d(q	PROPN
ejpam-4171	75	173	,	,	PUNCT
ejpam-4171	75	174	r	r	NOUN
ejpam-4171	75	175	)	)	PUNCT
ejpam-4171	75	176	]	]	PUNCT
ejpam-4171	75	177	(	(	PUNCT
ejpam-4171	75	178	1	1	X
ejpam-4171	75	179	)	)	PUNCT
ejpam-4171	75	180	(	(	PUNCT
ejpam-4171	75	181	ii	ii	NOUN
ejpam-4171	75	182	)	)	PUNCT
ejpam-4171	75	183	g(q0,r0,q0,r0	g(q0,r0,q0,r0	X
ejpam-4171	75	184	)	)	PUNCT
ejpam-4171	75	185	⊆	⊆	NUM
ejpam-4171	75	186	r0	r0	NOUN
ejpam-4171	75	187	(	(	PUNCT
ejpam-4171	75	188	iii	iii	NOUN
ejpam-4171	75	189	)	)	PUNCT
ejpam-4171	75	190	g(r0,q0,r0,q0	g(r0,q0,r0,q0	NOUN
ejpam-4171	75	191	)	)	PUNCT
ejpam-4171	75	192	⊆	⊆	NUM
ejpam-4171	75	193	q0	q0	PROPN
ejpam-4171	75	194	(	(	PUNCT
ejpam-4171	75	195	iv	iv	NOUN
ejpam-4171	75	196	)	)	PUNCT
ejpam-4171	75	197	pair	pair	NOUN
ejpam-4171	75	198	(	(	PUNCT
ejpam-4171	75	199	q	q	NOUN
ejpam-4171	75	200	,	,	PUNCT
ejpam-4171	75	201	r	r	NOUN
ejpam-4171	75	202	)	)	PUNCT
ejpam-4171	75	203	has	have	VERB
ejpam-4171	75	204	p	p	NOUN
ejpam-4171	75	205	-	-	PUNCT
ejpam-4171	75	206	property	property	NOUN
ejpam-4171	75	207	then	then	ADV
ejpam-4171	75	208	(	(	PUNCT
ejpam-4171	75	209	a	a	DET
ejpam-4171	75	210	,	,	PUNCT
ejpam-4171	75	211	a	a	PRON
ejpam-4171	75	212	,	,	PUNCT
ejpam-4171	75	213	a	a	DET
ejpam-4171	75	214	,	,	PUNCT
ejpam-4171	75	215	a	a	PRON
ejpam-4171	75	216	)	)	PUNCT
ejpam-4171	75	217	is	be	AUX
ejpam-4171	75	218	the	the	DET
ejpam-4171	75	219	unique	unique	ADJ
ejpam-4171	75	220	quadruple	quadruple	NOUN
ejpam-4171	75	221	g	g	NOUN
ejpam-4171	75	222	-	-	PUNCT
ejpam-4171	75	223	best	good	ADJ
ejpam-4171	75	224	proximity	proximity	NOUN
ejpam-4171	75	225	point	point	NOUN
ejpam-4171	75	226	of	of	ADP
ejpam-4171	75	227	the	the	DET
ejpam-4171	75	228	pair	pair	NOUN
ejpam-4171	75	229	(	(	PUNCT
ejpam-4171	75	230	g	g	NOUN
ejpam-4171	75	231	,	,	PUNCT
ejpam-4171	75	232	g	g	NOUN
ejpam-4171	75	233	)	)	PUNCT
ejpam-4171	75	234	.	.	PUNCT
ejpam-4171	76	1	proof	proof	NOUN
ejpam-4171	76	2	.	.	PUNCT
ejpam-4171	77	1	choose	choose	VERB
ejpam-4171	77	2	x0	x0	PROPN
ejpam-4171	77	3	,	,	PUNCT
ejpam-4171	77	4	z0	z0	PROPN
ejpam-4171	77	5	∈	∈	PROPN
ejpam-4171	77	6	q0	q0	NOUN
ejpam-4171	77	7	and	and	CCONJ
ejpam-4171	77	8	y0	y0	PROPN
ejpam-4171	77	9	,	,	PUNCT
ejpam-4171	77	10	t0	t0	PROPN
ejpam-4171	77	11	∈	∈	PROPN
ejpam-4171	77	12	r0	r0	NOUN
ejpam-4171	77	13	.	.	PUNCT
ejpam-4171	78	1	since	since	SCONJ
ejpam-4171	78	2	g(x0	g(x0	NOUN
ejpam-4171	78	3	,	,	PUNCT
ejpam-4171	78	4	y0	y0	PROPN
ejpam-4171	78	5	,	,	PUNCT
ejpam-4171	78	6	z0	z0	PROPN
ejpam-4171	78	7	,	,	PUNCT
ejpam-4171	78	8	t0	t0	PROPN
ejpam-4171	78	9	)	)	PUNCT
ejpam-4171	78	10	,	,	PUNCT
ejpam-4171	78	11	g(z0	g(z0	NOUN
ejpam-4171	78	12	,	,	PUNCT
ejpam-4171	78	13	y0	y0	PROPN
ejpam-4171	78	14	,	,	PUNCT
ejpam-4171	78	15	x0	x0	PROPN
ejpam-4171	78	16	,	,	PUNCT
ejpam-4171	78	17	t0	t0	PROPN
ejpam-4171	78	18	)	)	PUNCT
ejpam-4171	78	19	∈	∈	PROPN
ejpam-4171	78	20	r0	r0	NOUN
ejpam-4171	78	21	and	and	CCONJ
ejpam-4171	78	22	g(y0	g(y0	NOUN
ejpam-4171	78	23	,	,	PUNCT
ejpam-4171	78	24	x0	x0	PROPN
ejpam-4171	78	25	,	,	PUNCT
ejpam-4171	78	26	t0	t0	PROPN
ejpam-4171	78	27	,	,	PUNCT
ejpam-4171	78	28	z0	z0	PROPN
ejpam-4171	78	29	)	)	PUNCT
ejpam-4171	78	30	,	,	PUNCT
ejpam-4171	78	31	g(t0	g(t0	NOUN
ejpam-4171	78	32	,	,	PUNCT
ejpam-4171	78	33	z0	z0	PROPN
ejpam-4171	78	34	,	,	PUNCT
ejpam-4171	78	35	y0	y0	PROPN
ejpam-4171	78	36	,	,	PUNCT
ejpam-4171	78	37	x0	x0	PROPN
ejpam-4171	78	38	)	)	PUNCT
ejpam-4171	78	39	∈	∈	PROPN
ejpam-4171	78	40	q0	q0	NOUN
ejpam-4171	78	41	,	,	PUNCT
ejpam-4171	78	42	there	there	PRON
ejpam-4171	78	43	exist	exist	VERB
ejpam-4171	78	44	x1	x1	PROPN
ejpam-4171	78	45	,	,	PUNCT
ejpam-4171	78	46	z1	z1	PROPN
ejpam-4171	78	47	∈	∈	PROPN
ejpam-4171	78	48	q	q	X
ejpam-4171	78	49	and	and	CCONJ
ejpam-4171	78	50	y1	y1	PROPN
ejpam-4171	78	51	,	,	PUNCT
ejpam-4171	78	52	t1	t1	NOUN
ejpam-4171	78	53	∈	∈	PROPN
ejpam-4171	79	1	r	r	NOUN
ejpam-4171	79	2	such	such	ADJ
ejpam-4171	79	3	that	that	DET
ejpam-4171	79	4	d(gx1	d(gx1	PROPN
ejpam-4171	79	5	,	,	PUNCT
ejpam-4171	79	6	g(x0	g(x0	NOUN
ejpam-4171	79	7	,	,	PUNCT
ejpam-4171	79	8	y0	y0	PROPN
ejpam-4171	79	9	,	,	PUNCT
ejpam-4171	79	10	z0	z0	PROPN
ejpam-4171	79	11	,	,	PUNCT
ejpam-4171	79	12	t0	t0	PROPN
ejpam-4171	79	13	)	)	PUNCT
ejpam-4171	79	14	)	)	PUNCT
ejpam-4171	80	1	=	=	SYM
ejpam-4171	80	2	d(gy1	d(gy1	PROPN
ejpam-4171	80	3	,	,	PUNCT
ejpam-4171	80	4	g(y0	g(y0	NOUN
ejpam-4171	80	5	,	,	PUNCT
ejpam-4171	80	6	x0	x0	PROPN
ejpam-4171	80	7	,	,	PUNCT
ejpam-4171	80	8	z0	z0	PROPN
ejpam-4171	80	9	,	,	PUNCT
ejpam-4171	80	10	t0	t0	PROPN
ejpam-4171	80	11	)	)	PUNCT
ejpam-4171	80	12	)	)	PUNCT
ejpam-4171	81	1	=	=	SYM
ejpam-4171	81	2	d(gz1	d(gz1	ADJ
ejpam-4171	81	3	,	,	PUNCT
ejpam-4171	81	4	g(z0	g(z0	NOUN
ejpam-4171	81	5	,	,	PUNCT
ejpam-4171	81	6	y0	y0	PROPN
ejpam-4171	81	7	,	,	PUNCT
ejpam-4171	81	8	x0	x0	PROPN
ejpam-4171	81	9	,	,	PUNCT
ejpam-4171	81	10	t0	t0	PROPN
ejpam-4171	81	11	)	)	PUNCT
ejpam-4171	81	12	)	)	PUNCT
ejpam-4171	82	1	=	=	PUNCT
ejpam-4171	82	2	s.	s.	PROPN
ejpam-4171	82	3	rathee	rathee	PROPN
ejpam-4171	82	4	,	,	PUNCT
ejpam-4171	82	5	m.	m.	NOUN
ejpam-4171	82	6	swami	swami	PROPN
ejpam-4171	82	7	,	,	PUNCT
ejpam-4171	82	8	/	/	SYM
ejpam-4171	82	9	eur	eur	NOUN
ejpam-4171	82	10	.	.	PUNCT
ejpam-4171	83	1	j.	j.	PROPN
ejpam-4171	83	2	pure	pure	PROPN
ejpam-4171	83	3	appl	appl	PROPN
ejpam-4171	83	4	.	.	PROPN
ejpam-4171	83	5	math	math	PROPN
ejpam-4171	83	6	,	,	PUNCT
ejpam-4171	83	7	15	15	NUM
ejpam-4171	83	8	(	(	PUNCT
ejpam-4171	83	9	1	1	NUM
ejpam-4171	83	10	)	)	PUNCT
ejpam-4171	83	11	(	(	PUNCT
ejpam-4171	83	12	2022	2022	NUM
ejpam-4171	83	13	)	)	PUNCT
ejpam-4171	83	14	,	,	PUNCT
ejpam-4171	83	15	135	135	NUM
ejpam-4171	83	16	-	-	SYM
ejpam-4171	83	17	143	143	NUM
ejpam-4171	83	18	138	138	NUM
ejpam-4171	83	19	d(gt1	d(gt1	PROPN
ejpam-4171	83	20	,	,	PUNCT
ejpam-4171	83	21	g(t0	g(t0	NOUN
ejpam-4171	83	22	,	,	PUNCT
ejpam-4171	83	23	z0	z0	PROPN
ejpam-4171	83	24	,	,	PUNCT
ejpam-4171	83	25	y0	y0	PROPN
ejpam-4171	83	26	,	,	PUNCT
ejpam-4171	83	27	x0	x0	PROPN
ejpam-4171	83	28	)	)	PUNCT
ejpam-4171	83	29	)	)	PUNCT
ejpam-4171	84	1	=	=	PUNCT
ejpam-4171	84	2	d(q	d(q	PROPN
ejpam-4171	84	3	,	,	PUNCT
ejpam-4171	84	4	r	r	NOUN
ejpam-4171	84	5	)	)	PUNCT
ejpam-4171	84	6	.	.	PUNCT
ejpam-4171	85	1	continuing	continue	VERB
ejpam-4171	85	2	like	like	ADP
ejpam-4171	85	3	this	this	PRON
ejpam-4171	85	4	,	,	PUNCT
ejpam-4171	85	5	we	we	PRON
ejpam-4171	85	6	get	get	VERB
ejpam-4171	85	7	a	a	DET
ejpam-4171	85	8	sequence	sequence	NOUN
ejpam-4171	85	9	of	of	ADP
ejpam-4171	85	10	{	{	PUNCT
ejpam-4171	85	11	gxn	gxn	PROPN
ejpam-4171	85	12	}	}	PUNCT
ejpam-4171	85	13	,	,	PUNCT
ejpam-4171	85	14	{	{	PUNCT
ejpam-4171	85	15	gzn	gzn	NOUN
ejpam-4171	85	16	}	}	PUNCT
ejpam-4171	85	17	∈	∈	PROPN
ejpam-4171	85	18	q	q	X
ejpam-4171	85	19	and	and	CCONJ
ejpam-4171	85	20	{	{	PUNCT
ejpam-4171	85	21	gyn	gyn	NOUN
ejpam-4171	85	22	}	}	PUNCT
ejpam-4171	85	23	,	,	PUNCT
ejpam-4171	85	24	{	{	PUNCT
ejpam-4171	85	25	gtn	gtn	PROPN
ejpam-4171	85	26	}	}	PUNCT
ejpam-4171	85	27	∈	∈	PROPN
ejpam-4171	85	28	r	r	NOUN
ejpam-4171	85	29	such	such	ADJ
ejpam-4171	85	30	that	that	DET
ejpam-4171	85	31	d(gxn+1	d(gxn+1	NOUN
ejpam-4171	85	32	,	,	PUNCT
ejpam-4171	85	33	g(xn	g(xn	X
ejpam-4171	85	34	,	,	PUNCT
ejpam-4171	85	35	yn	yn	PROPN
ejpam-4171	85	36	,	,	PUNCT
ejpam-4171	85	37	zn	zn	PROPN
ejpam-4171	85	38	,	,	PUNCT
ejpam-4171	85	39	tn	tn	PROPN
ejpam-4171	85	40	)	)	PUNCT
ejpam-4171	85	41	)	)	PUNCT
ejpam-4171	86	1	=	=	SYM
ejpam-4171	86	2	d(q	d(q	PROPN
ejpam-4171	86	3	,	,	PUNCT
ejpam-4171	86	4	r	r	NOUN
ejpam-4171	86	5	)	)	PUNCT
ejpam-4171	86	6	d(gyn+1	d(gyn+1	PROPN
ejpam-4171	86	7	,	,	PUNCT
ejpam-4171	86	8	g(yn	g(yn	PROPN
ejpam-4171	86	9	,	,	PUNCT
ejpam-4171	86	10	xn	xn	PROPN
ejpam-4171	86	11	,	,	PUNCT
ejpam-4171	86	12	tn	tn	PROPN
ejpam-4171	86	13	,	,	PUNCT
ejpam-4171	86	14	zn	zn	NOUN
ejpam-4171	86	15	)	)	PUNCT
ejpam-4171	86	16	)	)	PUNCT
ejpam-4171	87	1	=	=	SYM
ejpam-4171	87	2	d(q	d(q	PROPN
ejpam-4171	87	3	,	,	PUNCT
ejpam-4171	87	4	r	r	NOUN
ejpam-4171	87	5	)	)	PUNCT
ejpam-4171	87	6	d(gzn+1	d(gzn+1	PROPN
ejpam-4171	87	7	,	,	PUNCT
ejpam-4171	87	8	g(zn	g(zn	PROPN
ejpam-4171	87	9	,	,	PUNCT
ejpam-4171	87	10	yn	yn	PROPN
ejpam-4171	87	11	,	,	PUNCT
ejpam-4171	87	12	xn	xn	PROPN
ejpam-4171	87	13	,	,	PUNCT
ejpam-4171	87	14	tn	tn	PROPN
ejpam-4171	87	15	)	)	PUNCT
ejpam-4171	87	16	)	)	PUNCT
ejpam-4171	88	1	=	=	SYM
ejpam-4171	88	2	d(q	d(q	PROPN
ejpam-4171	88	3	,	,	PUNCT
ejpam-4171	88	4	r	r	NOUN
ejpam-4171	88	5	)	)	PUNCT
ejpam-4171	88	6	d(gtn+1	d(gtn+1	NOUN
ejpam-4171	88	7	,	,	PUNCT
ejpam-4171	88	8	g(tn	g(tn	NOUN
ejpam-4171	88	9	,	,	PUNCT
ejpam-4171	88	10	zn	zn	PROPN
ejpam-4171	88	11	,	,	PUNCT
ejpam-4171	88	12	yn	yn	PROPN
ejpam-4171	88	13	,	,	PUNCT
ejpam-4171	88	14	xn	xn	PROPN
ejpam-4171	88	15	)	)	PUNCT
ejpam-4171	88	16	)	)	PUNCT
ejpam-4171	89	1	=	=	SYM
ejpam-4171	89	2	d(q	d(q	PROPN
ejpam-4171	89	3	,	,	PUNCT
ejpam-4171	89	4	r	r	NOUN
ejpam-4171	89	5	)	)	PUNCT
ejpam-4171	89	6	for	for	ADP
ejpam-4171	89	7	all	all	PRON
ejpam-4171	89	8	n	n	DET
ejpam-4171	89	9	∈	∈	NOUN
ejpam-4171	89	10	in	in	ADP
ejpam-4171	89	11	∪	∪	ADJ
ejpam-4171	89	12	{	{	PUNCT
ejpam-4171	89	13	0	0	NUM
ejpam-4171	89	14	}	}	PUNCT
ejpam-4171	89	15	(	(	PUNCT
ejpam-4171	89	16	2	2	X
ejpam-4171	89	17	)	)	PUNCT
ejpam-4171	89	18	if	if	SCONJ
ejpam-4171	89	19	d(gxn	d(gxn	PROPN
ejpam-4171	89	20	,	,	PUNCT
ejpam-4171	89	21	gxn+1	gxn+1	NOUN
ejpam-4171	89	22	)	)	PUNCT
ejpam-4171	89	23	=	=	SYM
ejpam-4171	89	24	d(gyn	d(gyn	PROPN
ejpam-4171	89	25	,	,	PUNCT
ejpam-4171	89	26	gyn+1	gyn+1	NOUN
ejpam-4171	89	27	)	)	PUNCT
ejpam-4171	89	28	=	=	SYM
ejpam-4171	89	29	d(gzn	d(gzn	PROPN
ejpam-4171	89	30	,	,	PUNCT
ejpam-4171	89	31	gzn+1	gzn+1	PROPN
ejpam-4171	89	32	)	)	PUNCT
ejpam-4171	89	33	=	=	SYM
ejpam-4171	89	34	d(gtn	d(gtn	PROPN
ejpam-4171	89	35	,	,	PUNCT
ejpam-4171	89	36	gtn+1	gtn+1	NOUN
ejpam-4171	89	37	)	)	PUNCT
ejpam-4171	89	38	=	=	SYM
ejpam-4171	89	39	0	0	NUM
ejpam-4171	89	40	for	for	ADP
ejpam-4171	89	41	all	all	PRON
ejpam-4171	89	42	n	n	DET
ejpam-4171	89	43	∈	∈	NOUN
ejpam-4171	89	44	in	in	ADP
ejpam-4171	89	45	∪	∪	ADJ
ejpam-4171	89	46	{	{	PUNCT
ejpam-4171	89	47	0	0	NUM
ejpam-4171	89	48	}	}	PUNCT
ejpam-4171	89	49	then	then	ADV
ejpam-4171	89	50	nothing	nothing	PRON
ejpam-4171	89	51	to	to	PART
ejpam-4171	89	52	prove	prove	VERB
ejpam-4171	89	53	.	.	PUNCT
ejpam-4171	90	1	suppose	suppose	VERB
ejpam-4171	90	2	d(gxn	d(gxn	PROPN
ejpam-4171	90	3	,	,	PUNCT
ejpam-4171	90	4	gxn+1	gxn+1	PROPN
ejpam-4171	90	5	)	)	PUNCT
ejpam-4171	90	6	>	>	X
ejpam-4171	90	7	0	0	PUNCT
ejpam-4171	90	8	or	or	CCONJ
ejpam-4171	90	9	d(gyn	d(gyn	PROPN
ejpam-4171	90	10	,	,	PUNCT
ejpam-4171	90	11	gyn+1	gyn+1	NOUN
ejpam-4171	90	12	)	)	PUNCT
ejpam-4171	90	13	>	>	X
ejpam-4171	90	14	0	0	PUNCT
ejpam-4171	90	15	or	or	CCONJ
ejpam-4171	90	16	d(gzn	d(gzn	PROPN
ejpam-4171	90	17	,	,	PUNCT
ejpam-4171	90	18	gzn+1	gzn+1	PROPN
ejpam-4171	90	19	)	)	PUNCT
ejpam-4171	90	20	>	>	X
ejpam-4171	90	21	0	0	PUNCT
ejpam-4171	90	22	or	or	CCONJ
ejpam-4171	90	23	d(gtn	d(gtn	PROPN
ejpam-4171	90	24	,	,	PUNCT
ejpam-4171	90	25	gtn+1	gtn+1	PROPN
ejpam-4171	90	26	)	)	PUNCT
ejpam-4171	90	27	>	>	X
ejpam-4171	91	1	0	0	X
ejpam-4171	91	2	.	.	PUNCT
ejpam-4171	92	1	from(1	from(1	NOUN
ejpam-4171	92	2	)	)	PUNCT
ejpam-4171	92	3	,	,	PUNCT
ejpam-4171	92	4	p	p	NOUN
ejpam-4171	92	5	-	-	PUNCT
ejpam-4171	92	6	property	property	NOUN
ejpam-4171	92	7	,	,	PUNCT
ejpam-4171	92	8	and	and	CCONJ
ejpam-4171	92	9	d(gxn+1	d(gxn+1	NOUN
ejpam-4171	92	10	,	,	PUNCT
ejpam-4171	92	11	g(xn	g(xn	X
ejpam-4171	92	12	,	,	PUNCT
ejpam-4171	92	13	yn	yn	PROPN
ejpam-4171	92	14	,	,	PUNCT
ejpam-4171	92	15	zn	zn	PROPN
ejpam-4171	92	16	,	,	PUNCT
ejpam-4171	92	17	tn	tn	PROPN
ejpam-4171	92	18	)	)	PUNCT
ejpam-4171	92	19	)	)	PUNCT
ejpam-4171	93	1	=	=	SYM
ejpam-4171	93	2	d(q	d(q	PROPN
ejpam-4171	93	3	,	,	PUNCT
ejpam-4171	93	4	r	r	NOUN
ejpam-4171	93	5	)	)	PUNCT
ejpam-4171	93	6	,	,	PUNCT
ejpam-4171	93	7	d(gxn	d(gxn	PROPN
ejpam-4171	93	8	,	,	PUNCT
ejpam-4171	93	9	g(xn−1	g(xn−1	ADJ
ejpam-4171	93	10	,	,	PUNCT
ejpam-4171	93	11	yn−1	yn−1	ADJ
ejpam-4171	93	12	,	,	PUNCT
ejpam-4171	93	13	zn−1	zn−1	PROPN
ejpam-4171	93	14	,	,	PUNCT
ejpam-4171	93	15	tn−1	tn−1	ADJ
ejpam-4171	93	16	)	)	PUNCT
ejpam-4171	93	17	)	)	PUNCT
ejpam-4171	94	1	=	=	SYM
ejpam-4171	94	2	d(q	d(q	PROPN
ejpam-4171	94	3	,	,	PUNCT
ejpam-4171	94	4	r	r	NOUN
ejpam-4171	94	5	)	)	PUNCT
ejpam-4171	94	6	,	,	PUNCT
ejpam-4171	94	7	we	we	PRON
ejpam-4171	94	8	have	have	AUX
ejpam-4171	94	9	d(gxn	d(gxn	PROPN
ejpam-4171	94	10	,	,	PUNCT
ejpam-4171	94	11	gxn+1	gxn+1	NOUN
ejpam-4171	94	12	)	)	PUNCT
ejpam-4171	94	13	=	=	SYM
ejpam-4171	95	1	d(g(xn−1	d(g(xn−1	PROPN
ejpam-4171	95	2	,	,	PUNCT
ejpam-4171	95	3	yn−1	yn−1	PROPN
ejpam-4171	95	4	,	,	PUNCT
ejpam-4171	95	5	zn−1	zn−1	PROPN
ejpam-4171	95	6	,	,	PUNCT
ejpam-4171	95	7	tn−1	tn−1	PROPN
ejpam-4171	95	8	)	)	PUNCT
ejpam-4171	95	9	,	,	PUNCT
ejpam-4171	95	10	g(xn	g(xn	X
ejpam-4171	95	11	,	,	PUNCT
ejpam-4171	95	12	yn	yn	PROPN
ejpam-4171	95	13	,	,	PUNCT
ejpam-4171	95	14	zn	zn	PROPN
ejpam-4171	95	15	,	,	PUNCT
ejpam-4171	95	16	tn	tn	PROPN
ejpam-4171	95	17	)	)	PUNCT
ejpam-4171	95	18	)	)	PUNCT
ejpam-4171	95	19	ψ(d(gxn	ψ(d(gxn	VERB
ejpam-4171	95	20	,	,	PUNCT
ejpam-4171	95	21	gxn+1	gxn+1	NOUN
ejpam-4171	95	22	)	)	PUNCT
ejpam-4171	95	23	)	)	PUNCT
ejpam-4171	96	1	=	=	PUNCT
ejpam-4171	96	2	ψ(d(g(xn−1	ψ(d(g(xn−1	ADJ
ejpam-4171	96	3	,	,	PUNCT
ejpam-4171	96	4	yn−1	yn−1	PROPN
ejpam-4171	96	5	,	,	PUNCT
ejpam-4171	96	6	zn−1	zn−1	PROPN
ejpam-4171	96	7	,	,	PUNCT
ejpam-4171	96	8	tn−1	tn−1	PROPN
ejpam-4171	96	9	)	)	PUNCT
ejpam-4171	96	10	,	,	PUNCT
ejpam-4171	96	11	g(xn	g(xn	X
ejpam-4171	96	12	,	,	PUNCT
ejpam-4171	96	13	yn	yn	PROPN
ejpam-4171	96	14	,	,	PUNCT
ejpam-4171	96	15	zn	zn	PROPN
ejpam-4171	96	16	,	,	PUNCT
ejpam-4171	96	17	tn	tn	PROPN
ejpam-4171	96	18	)	)	PUNCT
ejpam-4171	96	19	)	)	PUNCT
ejpam-4171	96	20	)	)	PUNCT
ejpam-4171	96	21	≤ψ{max(d(xn−1	≤ψ{max(d(xn−1	NUM
ejpam-4171	96	22	,	,	PUNCT
ejpam-4171	96	23	xn	xn	PROPN
ejpam-4171	96	24	)	)	PUNCT
ejpam-4171	96	25	,	,	PUNCT
ejpam-4171	96	26	d(yn−1	d(yn−1	PROPN
ejpam-4171	96	27	,	,	PUNCT
ejpam-4171	96	28	yn	yn	PROPN
ejpam-4171	96	29	)	)	PUNCT
ejpam-4171	96	30	,	,	PUNCT
ejpam-4171	96	31	d(zn−1	d(zn−1	PROPN
ejpam-4171	96	32	,	,	PUNCT
ejpam-4171	96	33	zn	zn	PROPN
ejpam-4171	96	34	)	)	PUNCT
ejpam-4171	96	35	,	,	PUNCT
ejpam-4171	96	36	d(tn−1	d(tn−1	PROPN
ejpam-4171	96	37	,	,	PUNCT
ejpam-4171	96	38	tn	tn	NOUN
ejpam-4171	96	39	)	)	PUNCT
ejpam-4171	96	40	)	)	PUNCT
ejpam-4171	96	41	}	}	PUNCT
ejpam-4171	96	42	−	−	ADP
ejpam-4171	96	43	ζ{max(d(xn−1	ζ{max(d(xn−1	ADJ
ejpam-4171	96	44	,	,	PUNCT
ejpam-4171	96	45	xn	xn	NUM
ejpam-4171	96	46	)	)	PUNCT
ejpam-4171	96	47	,	,	PUNCT
ejpam-4171	96	48	d(yn−1	d(yn−1	PROPN
ejpam-4171	96	49	,	,	PUNCT
ejpam-4171	96	50	yn	yn	PROPN
ejpam-4171	96	51	)	)	PUNCT
ejpam-4171	96	52	,	,	PUNCT
ejpam-4171	96	53	d(zn−1	d(zn−1	PROPN
ejpam-4171	96	54	,	,	PUNCT
ejpam-4171	96	55	zn	zn	PROPN
ejpam-4171	96	56	)	)	PUNCT
ejpam-4171	96	57	,	,	PUNCT
ejpam-4171	96	58	d(tn−1	d(tn−1	PROPN
ejpam-4171	96	59	,	,	PUNCT
ejpam-4171	96	60	tn	tn	NOUN
ejpam-4171	96	61	)	)	PUNCT
ejpam-4171	96	62	)	)	PUNCT
ejpam-4171	96	63	}	}	PUNCT
ejpam-4171	96	64	+	+	CCONJ
ejpam-4171	96	65	θ[d(gxn	θ[d(gxn	NOUN
ejpam-4171	96	66	,	,	PUNCT
ejpam-4171	96	67	g(xn−1	g(xn−1	ADJ
ejpam-4171	96	68	,	,	PUNCT
ejpam-4171	96	69	yn−1	yn−1	ADJ
ejpam-4171	96	70	,	,	PUNCT
ejpam-4171	96	71	zn−1	zn−1	PROPN
ejpam-4171	96	72	,	,	PUNCT
ejpam-4171	96	73	tn−1)−	tn−1)−	PROPN
ejpam-4171	96	74	d(q	d(q	PROPN
ejpam-4171	96	75	,	,	PUNCT
ejpam-4171	96	76	r	r	NOUN
ejpam-4171	96	77	)	)	PUNCT
ejpam-4171	96	78	,	,	PUNCT
ejpam-4171	96	79	d(gyn	d(gyn	PROPN
ejpam-4171	96	80	,	,	PUNCT
ejpam-4171	96	81	g(yn−1	g(yn−1	ADJ
ejpam-4171	96	82	,	,	PUNCT
ejpam-4171	96	83	xn−1	xn−1	PROPN
ejpam-4171	96	84	,	,	PUNCT
ejpam-4171	96	85	tn−1	tn−1	ADJ
ejpam-4171	96	86	,	,	PUNCT
ejpam-4171	96	87	zn−1)−	zn−1)−	PROPN
ejpam-4171	96	88	d(q	d(q	PROPN
ejpam-4171	96	89	,	,	PUNCT
ejpam-4171	96	90	r	r	NOUN
ejpam-4171	96	91	)	)	PUNCT
ejpam-4171	96	92	,	,	PUNCT
ejpam-4171	96	93	d(gzn	d(gzn	PROPN
ejpam-4171	96	94	,	,	PUNCT
ejpam-4171	96	95	g(zn−1	g(zn−1	PROPN
ejpam-4171	96	96	,	,	PUNCT
ejpam-4171	96	97	yn−1	yn−1	PROPN
ejpam-4171	96	98	,	,	PUNCT
ejpam-4171	96	99	xn−1	xn−1	PROPN
ejpam-4171	96	100	,	,	PUNCT
ejpam-4171	96	101	tn−1)−	tn−1)−	PROPN
ejpam-4171	96	102	d(q	d(q	PROPN
ejpam-4171	96	103	,	,	PUNCT
ejpam-4171	96	104	r	r	NOUN
ejpam-4171	96	105	)	)	PUNCT
ejpam-4171	96	106	,	,	PUNCT
ejpam-4171	96	107	d(gtn	d(gtn	PROPN
ejpam-4171	96	108	,	,	PUNCT
ejpam-4171	96	109	g(tn−1	g(tn−1	NOUN
ejpam-4171	96	110	,	,	PUNCT
ejpam-4171	96	111	zn−1	zn−1	PROPN
ejpam-4171	96	112	,	,	PUNCT
ejpam-4171	96	113	yn−1	yn−1	PROPN
ejpam-4171	96	114	,	,	PUNCT
ejpam-4171	96	115	xn−1)−	xn−1)−	PROPN
ejpam-4171	96	116	d(q	d(q	PROPN
ejpam-4171	96	117	,	,	PUNCT
ejpam-4171	96	118	r	r	NOUN
ejpam-4171	96	119	)	)	PUNCT
ejpam-4171	96	120	,	,	PUNCT
ejpam-4171	96	121	d(gxn−1	d(gxn−1	PROPN
ejpam-4171	96	122	,	,	PUNCT
ejpam-4171	96	123	g(xn−1	g(xn−1	ADJ
ejpam-4171	96	124	,	,	PUNCT
ejpam-4171	96	125	yn−1	yn−1	PROPN
ejpam-4171	96	126	,	,	PUNCT
ejpam-4171	96	127	zn−1	zn−1	PROPN
ejpam-4171	96	128	,	,	PUNCT
ejpam-4171	96	129	tn−1)−	tn−1)−	PROPN
ejpam-4171	96	130	d(q	d(q	PROPN
ejpam-4171	96	131	,	,	PUNCT
ejpam-4171	96	132	r	r	NOUN
ejpam-4171	96	133	)	)	PUNCT
ejpam-4171	96	134	,	,	PUNCT
ejpam-4171	96	135	d(gyn−1	d(gyn−1	X
ejpam-4171	96	136	,	,	PUNCT
ejpam-4171	96	137	g(yn−1	g(yn−1	ADJ
ejpam-4171	96	138	,	,	PUNCT
ejpam-4171	96	139	xn−1	xn−1	PROPN
ejpam-4171	96	140	,	,	PUNCT
ejpam-4171	96	141	tn−1	tn−1	ADJ
ejpam-4171	96	142	,	,	PUNCT
ejpam-4171	96	143	zn−1)−	zn−1)−	PROPN
ejpam-4171	96	144	d(q	d(q	PROPN
ejpam-4171	96	145	,	,	PUNCT
ejpam-4171	96	146	r	r	NOUN
ejpam-4171	96	147	)	)	PUNCT
ejpam-4171	96	148	,	,	PUNCT
ejpam-4171	96	149	d(gzn−1	d(gzn−1	PROPN
ejpam-4171	96	150	,	,	PUNCT
ejpam-4171	96	151	g(zn−1	g(zn−1	ADJ
ejpam-4171	96	152	,	,	PUNCT
ejpam-4171	96	153	yn−1	yn−1	PROPN
ejpam-4171	96	154	,	,	PUNCT
ejpam-4171	96	155	xn−1	xn−1	PROPN
ejpam-4171	96	156	,	,	PUNCT
ejpam-4171	96	157	tn−1)−	tn−1)−	PROPN
ejpam-4171	96	158	d(q	d(q	PROPN
ejpam-4171	96	159	,	,	PUNCT
ejpam-4171	96	160	r	r	NOUN
ejpam-4171	96	161	)	)	PUNCT
ejpam-4171	96	162	,	,	PUNCT
ejpam-4171	96	163	d(gtn−1	d(gtn−1	PROPN
ejpam-4171	96	164	,	,	PUNCT
ejpam-4171	96	165	g(tn−1	g(tn−1	NOUN
ejpam-4171	96	166	,	,	PUNCT
ejpam-4171	96	167	zn−1	zn−1	PROPN
ejpam-4171	96	168	,	,	PUNCT
ejpam-4171	96	169	yn−1	yn−1	PROPN
ejpam-4171	96	170	,	,	PUNCT
ejpam-4171	96	171	xn−1)−	xn−1)−	PROPN
ejpam-4171	96	172	d(q	d(q	PROPN
ejpam-4171	96	173	,	,	PUNCT
ejpam-4171	96	174	r	r	NOUN
ejpam-4171	96	175	)	)	PUNCT
ejpam-4171	96	176	]	]	PUNCT
ejpam-4171	96	177	=	=	PUNCT
ejpam-4171	96	178	ψ{max(d(xn−1	ψ{max(d(xn−1	X
ejpam-4171	96	179	,	,	PUNCT
ejpam-4171	96	180	xn	xn	PROPN
ejpam-4171	96	181	)	)	PUNCT
ejpam-4171	96	182	,	,	PUNCT
ejpam-4171	96	183	d(yn−1	d(yn−1	PROPN
ejpam-4171	96	184	,	,	PUNCT
ejpam-4171	96	185	yn	yn	PROPN
ejpam-4171	96	186	)	)	PUNCT
ejpam-4171	96	187	,	,	PUNCT
ejpam-4171	96	188	d(zn−1	d(zn−1	PROPN
ejpam-4171	96	189	,	,	PUNCT
ejpam-4171	96	190	zn	zn	PROPN
ejpam-4171	96	191	)	)	PUNCT
ejpam-4171	96	192	,	,	PUNCT
ejpam-4171	96	193	d(tn−1	d(tn−1	PROPN
ejpam-4171	96	194	,	,	PUNCT
ejpam-4171	96	195	tn	tn	NOUN
ejpam-4171	96	196	)	)	PUNCT
ejpam-4171	96	197	)	)	PUNCT
ejpam-4171	96	198	}	}	PUNCT
ejpam-4171	96	199	−	−	ADP
ejpam-4171	96	200	ζ{max(d(xn−1	ζ{max(d(xn−1	ADJ
ejpam-4171	96	201	,	,	PUNCT
ejpam-4171	96	202	xn	xn	NUM
ejpam-4171	96	203	)	)	PUNCT
ejpam-4171	96	204	,	,	PUNCT
ejpam-4171	96	205	d(yn−1	d(yn−1	PROPN
ejpam-4171	96	206	,	,	PUNCT
ejpam-4171	96	207	yn	yn	PROPN
ejpam-4171	96	208	)	)	PUNCT
ejpam-4171	96	209	,	,	PUNCT
ejpam-4171	96	210	d(zn−1	d(zn−1	PROPN
ejpam-4171	96	211	,	,	PUNCT
ejpam-4171	96	212	zn	zn	PROPN
ejpam-4171	96	213	)	)	PUNCT
ejpam-4171	96	214	,	,	PUNCT
ejpam-4171	96	215	d(tn−1	d(tn−1	PROPN
ejpam-4171	96	216	,	,	PUNCT
ejpam-4171	96	217	tn	tn	NOUN
ejpam-4171	96	218	)	)	PUNCT
ejpam-4171	96	219	)	)	PUNCT
ejpam-4171	96	220	}	}	PUNCT
ejpam-4171	96	221	(	(	PUNCT
ejpam-4171	96	222	3	3	X
ejpam-4171	96	223	)	)	PUNCT
ejpam-4171	96	224	similarly	similarly	ADV
ejpam-4171	96	225	for	for	ADP
ejpam-4171	96	226	d(gyn+1	d(gyn+1	NOUN
ejpam-4171	96	227	,	,	PUNCT
ejpam-4171	96	228	g(yn	g(yn	PROPN
ejpam-4171	96	229	,	,	PUNCT
ejpam-4171	96	230	xn	xn	PROPN
ejpam-4171	96	231	,	,	PUNCT
ejpam-4171	96	232	tn	tn	PROPN
ejpam-4171	96	233	,	,	PUNCT
ejpam-4171	96	234	zn	zn	NOUN
ejpam-4171	96	235	)	)	PUNCT
ejpam-4171	96	236	)	)	PUNCT
ejpam-4171	96	237	=	=	PUNCT
ejpam-4171	97	1	d(q	d(q	PROPN
ejpam-4171	97	2	,	,	PUNCT
ejpam-4171	97	3	r	r	NOUN
ejpam-4171	97	4	)	)	PUNCT
ejpam-4171	97	5	,	,	PUNCT
ejpam-4171	97	6	d(gyn	d(gyn	PROPN
ejpam-4171	97	7	,	,	PUNCT
ejpam-4171	97	8	g(yn−1	g(yn−1	ADJ
ejpam-4171	97	9	,	,	PUNCT
ejpam-4171	97	10	xn−1	xn−1	PROPN
ejpam-4171	97	11	,	,	PUNCT
ejpam-4171	97	12	tn−1	tn−1	ADJ
ejpam-4171	97	13	,	,	PUNCT
ejpam-4171	97	14	zn−1	zn−1	PROPN
ejpam-4171	97	15	)	)	PUNCT
ejpam-4171	97	16	)	)	PUNCT
ejpam-4171	98	1	=	=	PUNCT
ejpam-4171	98	2	d(q	d(q	PROPN
ejpam-4171	98	3	,	,	PUNCT
ejpam-4171	98	4	r	r	NOUN
ejpam-4171	98	5	)	)	PUNCT
ejpam-4171	98	6	,	,	PUNCT
ejpam-4171	98	7	d(gzn+1	d(gzn+1	PROPN
ejpam-4171	98	8	,	,	PUNCT
ejpam-4171	98	9	g(zn	g(zn	PROPN
ejpam-4171	98	10	,	,	PUNCT
ejpam-4171	98	11	yn	yn	PROPN
ejpam-4171	98	12	,	,	PUNCT
ejpam-4171	98	13	xn	xn	PROPN
ejpam-4171	98	14	,	,	PUNCT
ejpam-4171	98	15	tn	tn	PROPN
ejpam-4171	98	16	)	)	PUNCT
ejpam-4171	98	17	)	)	PUNCT
ejpam-4171	99	1	=	=	SYM
ejpam-4171	99	2	d(q	d(q	PROPN
ejpam-4171	99	3	,	,	PUNCT
ejpam-4171	99	4	r	r	NOUN
ejpam-4171	99	5	)	)	PUNCT
ejpam-4171	99	6	,	,	PUNCT
ejpam-4171	99	7	d(gzn	d(gzn	PROPN
ejpam-4171	99	8	,	,	PUNCT
ejpam-4171	99	9	g(zn−1	g(zn−1	PROPN
ejpam-4171	99	10	,	,	PUNCT
ejpam-4171	99	11	yn−1	yn−1	PROPN
ejpam-4171	99	12	,	,	PUNCT
ejpam-4171	99	13	xn−1	xn−1	PROPN
ejpam-4171	99	14	,	,	PUNCT
ejpam-4171	99	15	tn−1	tn−1	ADJ
ejpam-4171	99	16	)	)	PUNCT
ejpam-4171	99	17	)	)	PUNCT
ejpam-4171	100	1	=	=	SYM
ejpam-4171	100	2	d(q	d(q	PROPN
ejpam-4171	100	3	,	,	PUNCT
ejpam-4171	100	4	r	r	NOUN
ejpam-4171	100	5	)	)	PUNCT
ejpam-4171	100	6	and	and	CCONJ
ejpam-4171	100	7	d(gtn+1	d(gtn+1	NOUN
ejpam-4171	100	8	,	,	PUNCT
ejpam-4171	100	9	g(tn	g(tn	NOUN
ejpam-4171	100	10	,	,	PUNCT
ejpam-4171	100	11	zn	zn	PROPN
ejpam-4171	100	12	,	,	PUNCT
ejpam-4171	100	13	yn	yn	PROPN
ejpam-4171	100	14	,	,	PUNCT
ejpam-4171	100	15	xn	xn	PROPN
ejpam-4171	100	16	)	)	PUNCT
ejpam-4171	100	17	)	)	PUNCT
ejpam-4171	101	1	=	=	SYM
ejpam-4171	101	2	d(q	d(q	PROPN
ejpam-4171	101	3	,	,	PUNCT
ejpam-4171	101	4	r	r	NOUN
ejpam-4171	101	5	)	)	PUNCT
ejpam-4171	101	6	,	,	PUNCT
ejpam-4171	101	7	d(gtn	d(gtn	PROPN
ejpam-4171	101	8	,	,	PUNCT
ejpam-4171	101	9	g(tn−1	g(tn−1	NOUN
ejpam-4171	101	10	,	,	PUNCT
ejpam-4171	101	11	zn−1	zn−1	PROPN
ejpam-4171	101	12	,	,	PUNCT
ejpam-4171	101	13	yn−1	yn−1	PROPN
ejpam-4171	101	14	,	,	PUNCT
ejpam-4171	101	15	xn−1	xn−1	PROPN
ejpam-4171	101	16	)	)	PUNCT
ejpam-4171	101	17	)	)	PUNCT
ejpam-4171	102	1	=	=	PUNCT
ejpam-4171	102	2	d(q	d(q	PROPN
ejpam-4171	102	3	,	,	PUNCT
ejpam-4171	102	4	r	r	NOUN
ejpam-4171	102	5	)	)	PUNCT
ejpam-4171	102	6	,	,	PUNCT
ejpam-4171	102	7	we	we	PRON
ejpam-4171	102	8	have	have	VERB
ejpam-4171	102	9	ψ(d(gyn	ψ(d(gyn	NOUN
ejpam-4171	102	10	,	,	PUNCT
ejpam-4171	102	11	gyn+1	gyn+1	NOUN
ejpam-4171	102	12	)	)	PUNCT
ejpam-4171	102	13	)	)	PUNCT
ejpam-4171	103	1	≤ψ{max(d(yn−1	≤ψ{max(d(yn−1	PROPN
ejpam-4171	103	2	,	,	PUNCT
ejpam-4171	103	3	yn	yn	PROPN
ejpam-4171	103	4	)	)	PUNCT
ejpam-4171	103	5	,	,	PUNCT
ejpam-4171	103	6	d(xn−1	d(xn−1	PROPN
ejpam-4171	103	7	,	,	PUNCT
ejpam-4171	103	8	xn	xn	PROPN
ejpam-4171	103	9	)	)	PUNCT
ejpam-4171	103	10	,	,	PUNCT
ejpam-4171	103	11	d(zn−1	d(zn−1	PROPN
ejpam-4171	103	12	,	,	PUNCT
ejpam-4171	103	13	zn	zn	PROPN
ejpam-4171	103	14	)	)	PUNCT
ejpam-4171	103	15	,	,	PUNCT
ejpam-4171	103	16	d(tn−1	d(tn−1	PROPN
ejpam-4171	103	17	,	,	PUNCT
ejpam-4171	103	18	tn	tn	NOUN
ejpam-4171	103	19	)	)	PUNCT
ejpam-4171	103	20	)	)	PUNCT
ejpam-4171	103	21	}	}	PUNCT
ejpam-4171	104	1	−	−	ADP
ejpam-4171	104	2	ζ{max(d(yn−1	ζ{max(d(yn−1	PROPN
ejpam-4171	104	3	,	,	PUNCT
ejpam-4171	104	4	yn	yn	PROPN
ejpam-4171	104	5	)	)	PUNCT
ejpam-4171	104	6	,	,	PUNCT
ejpam-4171	104	7	d(xn−1	d(xn−1	PROPN
ejpam-4171	104	8	,	,	PUNCT
ejpam-4171	104	9	xn	xn	PROPN
ejpam-4171	104	10	)	)	PUNCT
ejpam-4171	104	11	,	,	PUNCT
ejpam-4171	104	12	d(zn−1	d(zn−1	PROPN
ejpam-4171	104	13	,	,	PUNCT
ejpam-4171	104	14	zn	zn	PROPN
ejpam-4171	104	15	)	)	PUNCT
ejpam-4171	104	16	,	,	PUNCT
ejpam-4171	104	17	d(tn−1	d(tn−1	PROPN
ejpam-4171	104	18	,	,	PUNCT
ejpam-4171	104	19	tn	tn	NOUN
ejpam-4171	104	20	)	)	PUNCT
ejpam-4171	104	21	)	)	PUNCT
ejpam-4171	104	22	}	}	PUNCT
ejpam-4171	104	23	(	(	PUNCT
ejpam-4171	104	24	4	4	X
ejpam-4171	104	25	)	)	PUNCT
ejpam-4171	104	26	ψ(d(gzn	ψ(d(gzn	NOUN
ejpam-4171	104	27	,	,	PUNCT
ejpam-4171	104	28	gzn+1	gzn+1	NOUN
ejpam-4171	104	29	)	)	PUNCT
ejpam-4171	104	30	)	)	PUNCT
ejpam-4171	104	31	≤ψ{max(d(zn−1	≤ψ{max(d(zn−1	PROPN
ejpam-4171	104	32	,	,	PUNCT
ejpam-4171	104	33	zn	zn	NOUN
ejpam-4171	104	34	)	)	PUNCT
ejpam-4171	104	35	,	,	PUNCT
ejpam-4171	104	36	d(yn−1	d(yn−1	PROPN
ejpam-4171	104	37	,	,	PUNCT
ejpam-4171	104	38	yn	yn	PROPN
ejpam-4171	104	39	)	)	PUNCT
ejpam-4171	104	40	,	,	PUNCT
ejpam-4171	104	41	d(xn−1	d(xn−1	PROPN
ejpam-4171	104	42	,	,	PUNCT
ejpam-4171	104	43	xn	xn	PROPN
ejpam-4171	104	44	)	)	PUNCT
ejpam-4171	104	45	,	,	PUNCT
ejpam-4171	104	46	d(tn−1	d(tn−1	PROPN
ejpam-4171	104	47	,	,	PUNCT
ejpam-4171	104	48	tn	tn	NOUN
ejpam-4171	104	49	)	)	PUNCT
ejpam-4171	104	50	)	)	PUNCT
ejpam-4171	104	51	}	}	PUNCT
ejpam-4171	105	1	−	−	ADP
ejpam-4171	105	2	ζ{max(d(zn−1	ζ{max(d(zn−1	PROPN
ejpam-4171	105	3	,	,	PUNCT
ejpam-4171	105	4	zn	zn	PROPN
ejpam-4171	105	5	)	)	PUNCT
ejpam-4171	105	6	,	,	PUNCT
ejpam-4171	105	7	d(yn−1	d(yn−1	PROPN
ejpam-4171	105	8	,	,	PUNCT
ejpam-4171	105	9	yn	yn	PROPN
ejpam-4171	105	10	)	)	PUNCT
ejpam-4171	105	11	,	,	PUNCT
ejpam-4171	105	12	d(xn−1	d(xn−1	PROPN
ejpam-4171	105	13	,	,	PUNCT
ejpam-4171	105	14	xn	xn	PROPN
ejpam-4171	105	15	)	)	PUNCT
ejpam-4171	105	16	,	,	PUNCT
ejpam-4171	105	17	d(tn−1	d(tn−1	PROPN
ejpam-4171	105	18	,	,	PUNCT
ejpam-4171	105	19	tn	tn	NOUN
ejpam-4171	105	20	)	)	PUNCT
ejpam-4171	105	21	)	)	PUNCT
ejpam-4171	105	22	}	}	PUNCT
ejpam-4171	105	23	(	(	PUNCT
ejpam-4171	105	24	5	5	X
ejpam-4171	105	25	)	)	PUNCT
ejpam-4171	105	26	ψ(d(gtn	ψ(d(gtn	SYM
ejpam-4171	105	27	,	,	PUNCT
ejpam-4171	105	28	gtn+1	gtn+1	NOUN
ejpam-4171	105	29	)	)	PUNCT
ejpam-4171	105	30	)	)	PUNCT
ejpam-4171	105	31	≤ψ{max(d(tn−1	≤ψ{max(d(tn−1	NUM
ejpam-4171	105	32	,	,	PUNCT
ejpam-4171	105	33	tn	tn	PROPN
ejpam-4171	105	34	)	)	PUNCT
ejpam-4171	105	35	,	,	PUNCT
ejpam-4171	105	36	d(yn−1	d(yn−1	PROPN
ejpam-4171	105	37	,	,	PUNCT
ejpam-4171	105	38	yn	yn	PROPN
ejpam-4171	105	39	)	)	PUNCT
ejpam-4171	105	40	,	,	PUNCT
ejpam-4171	105	41	d(zn−1	d(zn−1	PROPN
ejpam-4171	105	42	,	,	PUNCT
ejpam-4171	105	43	zn	zn	PROPN
ejpam-4171	105	44	)	)	PUNCT
ejpam-4171	105	45	,	,	PUNCT
ejpam-4171	105	46	d(xn−1	d(xn−1	PROPN
ejpam-4171	105	47	,	,	PUNCT
ejpam-4171	105	48	xn	xn	PROPN
ejpam-4171	105	49	)	)	PUNCT
ejpam-4171	105	50	)	)	PUNCT
ejpam-4171	105	51	}	}	PUNCT
ejpam-4171	105	52	−	−	ADP
ejpam-4171	105	53	ζ{max(d(tn−1	ζ{max(d(tn−1	PROPN
ejpam-4171	105	54	,	,	PUNCT
ejpam-4171	105	55	tn	tn	PROPN
ejpam-4171	105	56	)	)	PUNCT
ejpam-4171	105	57	,	,	PUNCT
ejpam-4171	105	58	d(yn−1	d(yn−1	PROPN
ejpam-4171	105	59	,	,	PUNCT
ejpam-4171	105	60	yn	yn	PROPN
ejpam-4171	105	61	)	)	PUNCT
ejpam-4171	105	62	,	,	PUNCT
ejpam-4171	105	63	d(zn−1	d(zn−1	PROPN
ejpam-4171	105	64	,	,	PUNCT
ejpam-4171	105	65	zn	zn	PROPN
ejpam-4171	105	66	)	)	PUNCT
ejpam-4171	105	67	,	,	PUNCT
ejpam-4171	105	68	d(xn−1	d(xn−1	PROPN
ejpam-4171	105	69	,	,	PUNCT
ejpam-4171	105	70	xn	xn	PROPN
ejpam-4171	105	71	)	)	PUNCT
ejpam-4171	105	72	)	)	PUNCT
ejpam-4171	105	73	}	}	PUNCT
ejpam-4171	105	74	(	(	PUNCT
ejpam-4171	105	75	6	6	NUM
ejpam-4171	105	76	)	)	PUNCT
ejpam-4171	105	77	from	from	ADP
ejpam-4171	105	78	(	(	PUNCT
ejpam-4171	105	79	3	3	NUM
ejpam-4171	105	80	)	)	PUNCT
ejpam-4171	105	81	,	,	PUNCT
ejpam-4171	105	82	(	(	PUNCT
ejpam-4171	105	83	4	4	NUM
ejpam-4171	105	84	)	)	PUNCT
ejpam-4171	105	85	,	,	PUNCT
ejpam-4171	105	86	(	(	PUNCT
ejpam-4171	105	87	5	5	NUM
ejpam-4171	105	88	)	)	PUNCT
ejpam-4171	105	89	and	and	CCONJ
ejpam-4171	105	90	(	(	PUNCT
ejpam-4171	105	91	6	6	NUM
ejpam-4171	105	92	)	)	PUNCT
ejpam-4171	105	93	,	,	PUNCT
ejpam-4171	105	94	we	we	PRON
ejpam-4171	105	95	obtain	obtain	VERB
ejpam-4171	105	96	ψ[max{d(gxn	ψ[max{d(gxn	ADP
ejpam-4171	105	97	,	,	PUNCT
ejpam-4171	105	98	gxn+1),d(gyn	gxn+1),d(gyn	NOUN
ejpam-4171	105	99	,	,	PUNCT
ejpam-4171	105	100	gyn+1	gyn+1	NOUN
ejpam-4171	105	101	)	)	PUNCT
ejpam-4171	105	102	,	,	PUNCT
ejpam-4171	105	103	d(gzn	d(gzn	PROPN
ejpam-4171	105	104	,	,	PUNCT
ejpam-4171	105	105	gzn+1	gzn+1	PROPN
ejpam-4171	105	106	)	)	PUNCT
ejpam-4171	105	107	,	,	PUNCT
ejpam-4171	105	108	d(gtn	d(gtn	PROPN
ejpam-4171	105	109	,	,	PUNCT
ejpam-4171	105	110	gtn+1	gtn+1	NOUN
ejpam-4171	105	111	)	)	PUNCT
ejpam-4171	105	112	}	}	PUNCT
ejpam-4171	105	113	]	]	PUNCT
ejpam-4171	106	1	s.	s.	PROPN
ejpam-4171	106	2	rathee	rathee	PROPN
ejpam-4171	106	3	,	,	PUNCT
ejpam-4171	106	4	m.	m.	NOUN
ejpam-4171	106	5	swami	swami	PROPN
ejpam-4171	106	6	,	,	PUNCT
ejpam-4171	106	7	/	/	SYM
ejpam-4171	106	8	eur	eur	NOUN
ejpam-4171	106	9	.	.	PUNCT
ejpam-4171	107	1	j.	j.	PROPN
ejpam-4171	107	2	pure	pure	PROPN
ejpam-4171	107	3	appl	appl	PROPN
ejpam-4171	107	4	.	.	PROPN
ejpam-4171	107	5	math	math	PROPN
ejpam-4171	107	6	,	,	PUNCT
ejpam-4171	107	7	15	15	NUM
ejpam-4171	107	8	(	(	PUNCT
ejpam-4171	107	9	1	1	NUM
ejpam-4171	107	10	)	)	PUNCT
ejpam-4171	107	11	(	(	PUNCT
ejpam-4171	107	12	2022	2022	NUM
ejpam-4171	107	13	)	)	PUNCT
ejpam-4171	107	14	,	,	PUNCT
ejpam-4171	107	15	135	135	NUM
ejpam-4171	107	16	-	-	SYM
ejpam-4171	107	17	143	143	NUM
ejpam-4171	107	18	139	139	NUM
ejpam-4171	107	19	≤	≤	NOUN
ejpam-4171	107	20	ψ[max{d(xn−1	ψ[max{d(xn−1	PROPN
ejpam-4171	107	21	,	,	PUNCT
ejpam-4171	107	22	xn	xn	PROPN
ejpam-4171	107	23	)	)	PUNCT
ejpam-4171	107	24	,	,	PUNCT
ejpam-4171	107	25	d(yn−1	d(yn−1	PROPN
ejpam-4171	107	26	,	,	PUNCT
ejpam-4171	107	27	yn	yn	PROPN
ejpam-4171	107	28	)	)	PUNCT
ejpam-4171	107	29	,	,	PUNCT
ejpam-4171	107	30	d(zn−1	d(zn−1	PROPN
ejpam-4171	107	31	,	,	PUNCT
ejpam-4171	107	32	zn	zn	PROPN
ejpam-4171	107	33	)	)	PUNCT
ejpam-4171	107	34	,	,	PUNCT
ejpam-4171	107	35	d(tn−1	d(tn−1	PROPN
ejpam-4171	107	36	,	,	PUNCT
ejpam-4171	107	37	tn	tn	NOUN
ejpam-4171	107	38	)	)	PUNCT
ejpam-4171	107	39	}	}	PUNCT
ejpam-4171	107	40	]	]	PUNCT
ejpam-4171	108	1	−	−	PROPN
ejpam-4171	108	2	ζ[max{d(xn−1	ζ[max{d(xn−1	NOUN
ejpam-4171	108	3	,	,	PUNCT
ejpam-4171	108	4	xn	xn	PROPN
ejpam-4171	108	5	)	)	PUNCT
ejpam-4171	108	6	,	,	PUNCT
ejpam-4171	108	7	d(yn−1	d(yn−1	PROPN
ejpam-4171	108	8	,	,	PUNCT
ejpam-4171	108	9	yn	yn	PROPN
ejpam-4171	108	10	)	)	PUNCT
ejpam-4171	108	11	,	,	PUNCT
ejpam-4171	108	12	d(zn−1	d(zn−1	PROPN
ejpam-4171	108	13	,	,	PUNCT
ejpam-4171	108	14	zn	zn	PROPN
ejpam-4171	108	15	)	)	PUNCT
ejpam-4171	108	16	,	,	PUNCT
ejpam-4171	108	17	d(tn−1	d(tn−1	PROPN
ejpam-4171	108	18	,	,	PUNCT
ejpam-4171	108	19	tn	tn	NOUN
ejpam-4171	108	20	)	)	PUNCT
ejpam-4171	108	21	}	}	PUNCT
ejpam-4171	108	22	]	]	PUNCT
ejpam-4171	108	23	=	=	PUNCT
ejpam-4171	108	24	ψ[max{d(gxn−1	ψ[max{d(gxn−1	PROPN
ejpam-4171	108	25	,	,	PUNCT
ejpam-4171	108	26	gxn	gxn	PROPN
ejpam-4171	108	27	)	)	PUNCT
ejpam-4171	108	28	,	,	PUNCT
ejpam-4171	108	29	d(gyn−1	d(gyn−1	PROPN
ejpam-4171	108	30	,	,	PUNCT
ejpam-4171	108	31	gyn	gyn	NOUN
ejpam-4171	108	32	)	)	PUNCT
ejpam-4171	108	33	,	,	PUNCT
ejpam-4171	108	34	d(gzn−1	d(gzn−1	PROPN
ejpam-4171	108	35	,	,	PUNCT
ejpam-4171	108	36	gzn	gzn	NOUN
ejpam-4171	108	37	)	)	PUNCT
ejpam-4171	108	38	,	,	PUNCT
ejpam-4171	108	39	d(gtn−1	d(gtn−1	PROPN
ejpam-4171	108	40	,	,	PUNCT
ejpam-4171	108	41	gtn	gtn	PROPN
ejpam-4171	108	42	)	)	PUNCT
ejpam-4171	108	43	}	}	PUNCT
ejpam-4171	108	44	]	]	PUNCT
ejpam-4171	108	45	−	−	PROPN
ejpam-4171	108	46	ζ[max{d(gxn−1	ζ[max{d(gxn−1	PROPN
ejpam-4171	108	47	,	,	PUNCT
ejpam-4171	108	48	gxn	gxn	PROPN
ejpam-4171	108	49	)	)	PUNCT
ejpam-4171	108	50	,	,	PUNCT
ejpam-4171	108	51	d(gyn−1	d(gyn−1	PROPN
ejpam-4171	108	52	,	,	PUNCT
ejpam-4171	108	53	gyn	gyn	NOUN
ejpam-4171	108	54	)	)	PUNCT
ejpam-4171	108	55	,	,	PUNCT
ejpam-4171	108	56	d(gzn−1	d(gzn−1	PROPN
ejpam-4171	108	57	,	,	PUNCT
ejpam-4171	108	58	gzn	gzn	NOUN
ejpam-4171	108	59	)	)	PUNCT
ejpam-4171	108	60	,	,	PUNCT
ejpam-4171	108	61	d(gtn−1	d(gtn−1	PROPN
ejpam-4171	108	62	,	,	PUNCT
ejpam-4171	108	63	gtn	gtn	PROPN
ejpam-4171	108	64	)	)	PUNCT
ejpam-4171	108	65	}	}	PUNCT
ejpam-4171	108	66	]	]	PUNCT
ejpam-4171	108	67	(	(	PUNCT
ejpam-4171	108	68	7	7	X
ejpam-4171	108	69	)	)	PUNCT
ejpam-4171	108	70	≤	≤	NOUN
ejpam-4171	108	71	ψ[max{d(gxn−1	ψ[max{d(gxn−1	PROPN
ejpam-4171	108	72	,	,	PUNCT
ejpam-4171	108	73	gxn	gxn	PROPN
ejpam-4171	108	74	)	)	PUNCT
ejpam-4171	108	75	,	,	PUNCT
ejpam-4171	108	76	d(gyn−1	d(gyn−1	PROPN
ejpam-4171	108	77	,	,	PUNCT
ejpam-4171	108	78	gyn	gyn	NOUN
ejpam-4171	108	79	)	)	PUNCT
ejpam-4171	108	80	,	,	PUNCT
ejpam-4171	108	81	d(gzn−1	d(gzn−1	PROPN
ejpam-4171	108	82	,	,	PUNCT
ejpam-4171	108	83	gzn	gzn	NOUN
ejpam-4171	108	84	)	)	PUNCT
ejpam-4171	108	85	,	,	PUNCT
ejpam-4171	108	86	d(gtn−1	d(gtn−1	PROPN
ejpam-4171	108	87	,	,	PUNCT
ejpam-4171	108	88	gtn	gtn	PROPN
ejpam-4171	108	89	)	)	PUNCT
ejpam-4171	108	90	}	}	PUNCT
ejpam-4171	108	91	]	]	PUNCT
ejpam-4171	108	92	as	as	SCONJ
ejpam-4171	108	93	ψ	ψ	PROPN
ejpam-4171	108	94	is	be	AUX
ejpam-4171	108	95	continuous	continuous	ADJ
ejpam-4171	108	96	function	function	NOUN
ejpam-4171	108	97	,	,	PUNCT
ejpam-4171	108	98	therefore	therefore	ADV
ejpam-4171	108	99	,	,	PUNCT
ejpam-4171	108	100	max{d(gxn	max{d(gxn	NOUN
ejpam-4171	108	101	,	,	PUNCT
ejpam-4171	108	102	gxn+1),d(gyn	gxn+1),d(gyn	NOUN
ejpam-4171	108	103	,	,	PUNCT
ejpam-4171	108	104	gyn+1	gyn+1	NOUN
ejpam-4171	108	105	)	)	PUNCT
ejpam-4171	108	106	,	,	PUNCT
ejpam-4171	108	107	d(gzn	d(gzn	PROPN
ejpam-4171	108	108	,	,	PUNCT
ejpam-4171	108	109	gzn+1	gzn+1	PROPN
ejpam-4171	108	110	)	)	PUNCT
ejpam-4171	108	111	,	,	PUNCT
ejpam-4171	108	112	d(gtn	d(gtn	PROPN
ejpam-4171	108	113	,	,	PUNCT
ejpam-4171	108	114	gtn+1	gtn+1	NOUN
ejpam-4171	108	115	)	)	PUNCT
ejpam-4171	108	116	}	}	PUNCT
ejpam-4171	108	117	≤	≤	NUM
ejpam-4171	108	118	max{d(gxn−1	max{d(gxn−1	PROPN
ejpam-4171	108	119	,	,	PUNCT
ejpam-4171	108	120	gxn	gxn	PROPN
ejpam-4171	108	121	)	)	PUNCT
ejpam-4171	108	122	,	,	PUNCT
ejpam-4171	108	123	d(gyn−1	d(gyn−1	PROPN
ejpam-4171	108	124	,	,	PUNCT
ejpam-4171	108	125	gyn	gyn	NOUN
ejpam-4171	108	126	)	)	PUNCT
ejpam-4171	108	127	,	,	PUNCT
ejpam-4171	108	128	d(gzn−1	d(gzn−1	PROPN
ejpam-4171	108	129	,	,	PUNCT
ejpam-4171	108	130	gzn	gzn	NOUN
ejpam-4171	108	131	)	)	PUNCT
ejpam-4171	108	132	,	,	PUNCT
ejpam-4171	108	133	d(gtn−1	d(gtn−1	PROPN
ejpam-4171	108	134	,	,	PUNCT
ejpam-4171	108	135	gtn	gtn	PROPN
ejpam-4171	108	136	)	)	PUNCT
ejpam-4171	108	137	}	}	PUNCT
ejpam-4171	108	138	implies	imply	VERB
ejpam-4171	108	139	{	{	PUNCT
ejpam-4171	108	140	d(gxn	d(gxn	PROPN
ejpam-4171	108	141	,	,	PUNCT
ejpam-4171	108	142	gxn+1	gxn+1	PROPN
ejpam-4171	108	143	)	)	PUNCT
ejpam-4171	108	144	,	,	PUNCT
ejpam-4171	108	145	d(gyn	d(gyn	PROPN
ejpam-4171	108	146	,	,	PUNCT
ejpam-4171	108	147	gyn+1	gyn+1	NOUN
ejpam-4171	108	148	)	)	PUNCT
ejpam-4171	108	149	,	,	PUNCT
ejpam-4171	108	150	d(gzn	d(gzn	PROPN
ejpam-4171	108	151	,	,	PUNCT
ejpam-4171	108	152	gzn+1	gzn+1	PROPN
ejpam-4171	108	153	)	)	PUNCT
ejpam-4171	108	154	,	,	PUNCT
ejpam-4171	108	155	d(gtn	d(gtn	PROPN
ejpam-4171	108	156	,	,	PUNCT
ejpam-4171	108	157	gtn+1	gtn+1	NOUN
ejpam-4171	108	158	)	)	PUNCT
ejpam-4171	108	159	}	}	PUNCT
ejpam-4171	108	160	is	be	AUX
ejpam-4171	108	161	a	a	DET
ejpam-4171	108	162	non	non	ADJ
ejpam-4171	108	163	-	-	ADJ
ejpam-4171	108	164	increasing	increasing	ADJ
ejpam-4171	108	165	sequence	sequence	NOUN
ejpam-4171	108	166	of	of	ADP
ejpam-4171	108	167	positive	positive	ADJ
ejpam-4171	108	168	real	real	ADJ
ejpam-4171	108	169	number	number	NOUN
ejpam-4171	108	170	,	,	PUNCT
ejpam-4171	108	171	it	it	PRON
ejpam-4171	108	172	must	must	AUX
ejpam-4171	108	173	converge	converge	VERB
ejpam-4171	108	174	to	to	ADP
ejpam-4171	108	175	a	a	DET
ejpam-4171	108	176	positive	positive	ADJ
ejpam-4171	108	177	real	real	ADJ
ejpam-4171	108	178	number	number	NOUN
ejpam-4171	108	179	,	,	PUNCT
ejpam-4171	108	180	say	say	VERB
ejpam-4171	108	181	τ	τ	PROPN
ejpam-4171	108	182	=	=	NOUN
ejpam-4171	108	183	⇒	⇒	PROPN
ejpam-4171	108	184	lim	lim	PROPN
ejpam-4171	108	185	n→∞	n→∞	X
ejpam-4171	108	186	{	{	PUNCT
ejpam-4171	108	187	d(gxn	d(gxn	PROPN
ejpam-4171	108	188	,	,	PUNCT
ejpam-4171	108	189	gxn+1),d(gyn	gxn+1),d(gyn	NOUN
ejpam-4171	108	190	,	,	PUNCT
ejpam-4171	108	191	gyn+1	gyn+1	NOUN
ejpam-4171	108	192	)	)	PUNCT
ejpam-4171	108	193	,	,	PUNCT
ejpam-4171	108	194	d(gzn	d(gzn	PROPN
ejpam-4171	108	195	,	,	PUNCT
ejpam-4171	108	196	gzn+1	gzn+1	PROPN
ejpam-4171	108	197	)	)	PUNCT
ejpam-4171	108	198	,	,	PUNCT
ejpam-4171	108	199	d(gtn	d(gtn	PROPN
ejpam-4171	108	200	,	,	PUNCT
ejpam-4171	108	201	gtn+1	gtn+1	NOUN
ejpam-4171	108	202	)	)	PUNCT
ejpam-4171	108	203	}	}	PUNCT
ejpam-4171	109	1	=	=	SYM
ejpam-4171	109	2	τ	τ	X
ejpam-4171	109	3	.	.	PUNCT
ejpam-4171	109	4	taking	take	VERB
ejpam-4171	109	5	limit	limit	NOUN
ejpam-4171	109	6	on	on	ADP
ejpam-4171	109	7	both	both	DET
ejpam-4171	109	8	side	side	NOUN
ejpam-4171	109	9	in	in	ADP
ejpam-4171	109	10	(	(	PUNCT
ejpam-4171	109	11	7	7	NUM
ejpam-4171	109	12	)	)	PUNCT
ejpam-4171	109	13	,	,	PUNCT
ejpam-4171	109	14	we	we	PRON
ejpam-4171	109	15	have	have	VERB
ejpam-4171	109	16	ψ(τ	ψ(τ	NOUN
ejpam-4171	109	17	)	)	PUNCT
ejpam-4171	109	18	≤	≤	NOUN
ejpam-4171	109	19	ψ(τ)−	ψ(τ)−	NOUN
ejpam-4171	109	20	ζ(τ	ζ(τ	NOUN
ejpam-4171	109	21	)	)	PUNCT
ejpam-4171	110	1	=	=	VERB
ejpam-4171	110	2	⇒	⇒	NOUN
ejpam-4171	110	3	ζ(τ	ζ(τ	PROPN
ejpam-4171	110	4	)	)	PUNCT
ejpam-4171	110	5	=	=	PUNCT
ejpam-4171	110	6	0	0	NUM
ejpam-4171	110	7	τ	τ	X
ejpam-4171	110	8	=	=	SYM
ejpam-4171	110	9	0	0	PROPN
ejpam-4171	110	10	.	.	PUNCT
ejpam-4171	111	1	hence	hence	ADV
ejpam-4171	111	2	,	,	PUNCT
ejpam-4171	111	3	lim	lim	PROPN
ejpam-4171	111	4	n→∞	n→∞	NUM
ejpam-4171	111	5	d(gxn	d(gxn	PROPN
ejpam-4171	111	6	,	,	PUNCT
ejpam-4171	111	7	gxn+1	gxn+1	PROPN
ejpam-4171	111	8	)	)	PUNCT
ejpam-4171	112	1	=	=	SYM
ejpam-4171	112	2	lim	lim	PROPN
ejpam-4171	112	3	n→∞	n→∞	NUM
ejpam-4171	112	4	d(gyn	d(gyn	PUNCT
ejpam-4171	112	5	,	,	PUNCT
ejpam-4171	112	6	gyn+1	gyn+1	NOUN
ejpam-4171	112	7	)	)	PUNCT
ejpam-4171	112	8	=	=	SYM
ejpam-4171	113	1	lim	lim	PROPN
ejpam-4171	113	2	n→∞	n→∞	NUM
ejpam-4171	113	3	d(gzn	d(gzn	PROPN
ejpam-4171	113	4	,	,	PUNCT
ejpam-4171	113	5	gzn+1	gzn+1	PROPN
ejpam-4171	113	6	)	)	PUNCT
ejpam-4171	114	1	=	=	PROPN
ejpam-4171	114	2	lim	lim	PROPN
ejpam-4171	114	3	n→∞	n→∞	NUM
ejpam-4171	114	4	d(gtn	d(gtn	PROPN
ejpam-4171	114	5	,	,	PUNCT
ejpam-4171	114	6	gtn+1	gtn+1	NOUN
ejpam-4171	114	7	)	)	PUNCT
ejpam-4171	114	8	=	=	SYM
ejpam-4171	114	9	0	0	PUNCT
ejpam-4171	115	1	now	now	ADV
ejpam-4171	115	2	,	,	PUNCT
ejpam-4171	115	3	we	we	PRON
ejpam-4171	115	4	prove	prove	VERB
ejpam-4171	115	5	that	that	SCONJ
ejpam-4171	115	6	{	{	PUNCT
ejpam-4171	115	7	gxn	gxn	INTJ
ejpam-4171	115	8	}	}	PUNCT
ejpam-4171	115	9	,	,	PUNCT
ejpam-4171	115	10	{	{	PUNCT
ejpam-4171	115	11	gyn	gyn	NOUN
ejpam-4171	115	12	}	}	PUNCT
ejpam-4171	115	13	,	,	PUNCT
ejpam-4171	115	14	{	{	PUNCT
ejpam-4171	115	15	gzn	gzn	NOUN
ejpam-4171	115	16	}	}	PUNCT
ejpam-4171	115	17	and	and	CCONJ
ejpam-4171	115	18	{	{	PUNCT
ejpam-4171	115	19	gtn	gtn	PROPN
ejpam-4171	115	20	}	}	PUNCT
ejpam-4171	115	21	are	be	AUX
ejpam-4171	115	22	cauchy	cauchy	PROPN
ejpam-4171	115	23	sequences	sequence	NOUN
ejpam-4171	115	24	,	,	PUNCT
ejpam-4171	115	25	i.e.	i.e.	X
ejpam-4171	115	26	max{d(gxn(ι	max{d(gxn(ι	NOUN
ejpam-4171	115	27	)	)	PUNCT
ejpam-4171	115	28	,	,	PUNCT
ejpam-4171	115	29	gxm(ι	gxm(ι	PROPN
ejpam-4171	115	30	)	)	PUNCT
ejpam-4171	115	31	,	,	PUNCT
ejpam-4171	115	32	d(gyn(ι	d(gyn(ι	NOUN
ejpam-4171	115	33	)	)	PUNCT
ejpam-4171	115	34	,	,	PUNCT
ejpam-4171	115	35	gym(ι	gym(ι	NOUN
ejpam-4171	115	36	)	)	PUNCT
ejpam-4171	115	37	)	)	PUNCT
ejpam-4171	115	38	,	,	PUNCT
ejpam-4171	115	39	d(gzn(ι	d(gzn(ι	PROPN
ejpam-4171	115	40	)	)	PUNCT
ejpam-4171	115	41	,	,	PUNCT
ejpam-4171	115	42	gzm(ι	gzm(ι	PROPN
ejpam-4171	115	43	)	)	PUNCT
ejpam-4171	115	44	)	)	PUNCT
ejpam-4171	115	45	,	,	PUNCT
ejpam-4171	115	46	d(gtn(ι	d(gtn(ι	NOUN
ejpam-4171	115	47	)	)	PUNCT
ejpam-4171	115	48	,	,	PUNCT
ejpam-4171	115	49	tm(ι	tm(ι	NUM
ejpam-4171	115	50	)	)	PUNCT
ejpam-4171	115	51	)	)	PUNCT
ejpam-4171	115	52	}	}	PUNCT
ejpam-4171	115	53	<	<	X
ejpam-4171	115	54	ϵ	ϵ	X
ejpam-4171	115	55	∀m(ι	∀m(ι	PROPN
ejpam-4171	115	56	)	)	PUNCT
ejpam-4171	115	57	>	>	X
ejpam-4171	115	58	n(ι	n(ι	PROPN
ejpam-4171	115	59	)	)	PUNCT
ejpam-4171	115	60	>	>	X
ejpam-4171	116	1	ι	ι	X
ejpam-4171	116	2	.	.	PUNCT
ejpam-4171	117	1	let	let	VERB
ejpam-4171	117	2	if	if	SCONJ
ejpam-4171	117	3	possible	possible	ADJ
ejpam-4171	117	4	sequences	sequence	NOUN
ejpam-4171	117	5	are	be	AUX
ejpam-4171	117	6	not	not	PART
ejpam-4171	117	7	cauchy	cauchy	ADJ
ejpam-4171	117	8	then	then	ADV
ejpam-4171	117	9	there	there	PRON
ejpam-4171	117	10	exists	exist	VERB
ejpam-4171	117	11	an	an	DET
ejpam-4171	117	12	ϵ	ϵ	X
ejpam-4171	117	13	>	>	X
ejpam-4171	117	14	0	0	NUM
ejpam-4171	117	15	such	such	ADJ
ejpam-4171	117	16	that	that	PRON
ejpam-4171	117	17	for	for	ADP
ejpam-4171	117	18	all	all	DET
ejpam-4171	117	19	ι	ι	X
ejpam-4171	117	20	>	>	X
ejpam-4171	117	21	0	0	PUNCT
ejpam-4171	117	22	there	there	PRON
ejpam-4171	117	23	are	be	VERB
ejpam-4171	117	24	m(ι	m(ι	PROPN
ejpam-4171	117	25	)	)	PUNCT
ejpam-4171	117	26	>	>	X
ejpam-4171	117	27	n(ι	n(ι	PROPN
ejpam-4171	117	28	)	)	PUNCT
ejpam-4171	117	29	>	>	X
ejpam-4171	118	1	ι	ι	X
ejpam-4171	118	2	which	which	PRON
ejpam-4171	118	3	satisfies	satisfy	VERB
ejpam-4171	118	4	the	the	DET
ejpam-4171	118	5	conditions	condition	NOUN
ejpam-4171	118	6	max{d(gxn(ι	max{d(gxn(ι	NOUN
ejpam-4171	118	7	)	)	PUNCT
ejpam-4171	118	8	,	,	PUNCT
ejpam-4171	118	9	gxm(ι	gxm(ι	PROPN
ejpam-4171	118	10	)	)	PUNCT
ejpam-4171	118	11	,	,	PUNCT
ejpam-4171	118	12	d(gyn(ι	d(gyn(ι	NOUN
ejpam-4171	118	13	)	)	PUNCT
ejpam-4171	118	14	,	,	PUNCT
ejpam-4171	118	15	gym(ι	gym(ι	NOUN
ejpam-4171	118	16	)	)	PUNCT
ejpam-4171	118	17	)	)	PUNCT
ejpam-4171	118	18	,	,	PUNCT
ejpam-4171	118	19	d(gzn(ι	d(gzn(ι	PROPN
ejpam-4171	118	20	)	)	PUNCT
ejpam-4171	118	21	,	,	PUNCT
ejpam-4171	118	22	gzm(ι	gzm(ι	PROPN
ejpam-4171	118	23	)	)	PUNCT
ejpam-4171	118	24	)	)	PUNCT
ejpam-4171	118	25	,	,	PUNCT
ejpam-4171	118	26	d(gtn(ι	d(gtn(ι	NOUN
ejpam-4171	118	27	)	)	PUNCT
ejpam-4171	118	28	,	,	PUNCT
ejpam-4171	118	29	tm(ι	tm(ι	NUM
ejpam-4171	118	30	)	)	PUNCT
ejpam-4171	118	31	)	)	PUNCT
ejpam-4171	118	32	}	}	PUNCT
ejpam-4171	118	33	≥	≥	X
ejpam-4171	118	34	ϵ	ϵ	NOUN
ejpam-4171	118	35	and	and	CCONJ
ejpam-4171	118	36	max{d(gxn(ι)−1	max{d(gxn(ι)−1	NOUN
ejpam-4171	118	37	,	,	PUNCT
ejpam-4171	118	38	gxm(ι	gxm(ι	PROPN
ejpam-4171	118	39	)	)	PUNCT
ejpam-4171	118	40	,	,	PUNCT
ejpam-4171	118	41	d(gyn(ι)−1	d(gyn(ι)−1	PROPN
ejpam-4171	118	42	,	,	PUNCT
ejpam-4171	118	43	gym(ι	gym(ι	NOUN
ejpam-4171	118	44	)	)	PUNCT
ejpam-4171	118	45	)	)	PUNCT
ejpam-4171	118	46	,	,	PUNCT
ejpam-4171	118	47	d(gzn(ι)−1	d(gzn(ι)−1	NOUN
ejpam-4171	118	48	,	,	PUNCT
ejpam-4171	118	49	gzm(ι	gzm(ι	PROPN
ejpam-4171	118	50	)	)	PUNCT
ejpam-4171	118	51	)	)	PUNCT
ejpam-4171	118	52	,	,	PUNCT
ejpam-4171	118	53	d(gtn(ι)−1	d(gtn(ι)−1	NOUN
ejpam-4171	118	54	,	,	PUNCT
ejpam-4171	118	55	tm(ι	tm(ι	NUM
ejpam-4171	118	56	)	)	PUNCT
ejpam-4171	118	57	)	)	PUNCT
ejpam-4171	119	1	}	}	PUNCT
ejpam-4171	120	1	<	<	X
ejpam-4171	120	2	ϵ.	ϵ.	NOUN
ejpam-4171	120	3	then	then	ADV
ejpam-4171	120	4	,	,	PUNCT
ejpam-4171	120	5	we	we	PRON
ejpam-4171	120	6	have	have	VERB
ejpam-4171	120	7	ϵ	ϵ	DET
ejpam-4171	120	8	≤	≤	NUM
ejpam-4171	120	9	d(gxn(ι	d(gxn(ι	NOUN
ejpam-4171	120	10	)	)	PUNCT
ejpam-4171	120	11	,	,	PUNCT
ejpam-4171	120	12	gxm(ι	gxm(ι	PROPN
ejpam-4171	120	13	)	)	PUNCT
ejpam-4171	120	14	)	)	PUNCT
ejpam-4171	120	15	≤	≤	NUM
ejpam-4171	120	16	d(gxn(ι	d(gxn(ι	NOUN
ejpam-4171	120	17	)	)	PUNCT
ejpam-4171	120	18	,	,	PUNCT
ejpam-4171	120	19	gxn(ι)−1	gxn(ι)−1	NOUN
ejpam-4171	120	20	)	)	PUNCT
ejpam-4171	120	21	+	+	SYM
ejpam-4171	120	22	d(gxn(ι)−1	d(gxn(ι)−1	ADJ
ejpam-4171	120	23	,	,	PUNCT
ejpam-4171	120	24	gxm(ι	gxm(ι	NOUN
ejpam-4171	120	25	)	)	PUNCT
ejpam-4171	120	26	≤	≤	NUM
ejpam-4171	120	27	d(gxn(ι	d(gxn(ι	NOUN
ejpam-4171	120	28	)	)	PUNCT
ejpam-4171	120	29	,	,	PUNCT
ejpam-4171	120	30	gxn(ι)−1	gxn(ι)−1	NOUN
ejpam-4171	120	31	)	)	PUNCT
ejpam-4171	120	32	+	+	CCONJ
ejpam-4171	121	1	ϵ	ϵ	ADP
ejpam-4171	121	2	this	this	PRON
ejpam-4171	121	3	gives	give	VERB
ejpam-4171	121	4	us	we	PRON
ejpam-4171	121	5	ϵ	ϵ	DET
ejpam-4171	121	6	≤	≤	NUM
ejpam-4171	121	7	d(gxn(ι	d(gxn(ι	NOUN
ejpam-4171	121	8	)	)	PUNCT
ejpam-4171	121	9	,	,	PUNCT
ejpam-4171	121	10	gxn(ι)−1	gxn(ι)−1	NOUN
ejpam-4171	121	11	)	)	PUNCT
ejpam-4171	121	12	+	+	CCONJ
ejpam-4171	121	13	ϵ	ϵ	X
ejpam-4171	121	14	for	for	ADP
ejpam-4171	121	15	ι→	ι→	PUNCT
ejpam-4171	121	16	∞	∞	PROPN
ejpam-4171	121	17	,	,	PUNCT
ejpam-4171	121	18	we	we	PRON
ejpam-4171	121	19	have	have	VERB
ejpam-4171	121	20	lim	lim	PROPN
ejpam-4171	121	21	ι→∞	ι→∞	PART
ejpam-4171	121	22	d(gxn(ι	d(gxn(ι	NOUN
ejpam-4171	121	23	)	)	PUNCT
ejpam-4171	121	24	,	,	PUNCT
ejpam-4171	121	25	gxm(ι	gxm(ι	PROPN
ejpam-4171	121	26	)	)	PUNCT
ejpam-4171	121	27	)	)	PUNCT
ejpam-4171	122	1	=	=	SYM
ejpam-4171	122	2	ϵ	ϵ	X
ejpam-4171	122	3	(	(	PUNCT
ejpam-4171	122	4	8)	8)	NUM
ejpam-4171	122	5	also	also	ADV
ejpam-4171	122	6	,	,	PUNCT
ejpam-4171	122	7	from	from	ADP
ejpam-4171	122	8	triangular	triangular	NOUN
ejpam-4171	122	9	inequality	inequality	NOUN
ejpam-4171	122	10	,	,	PUNCT
ejpam-4171	122	11	we	we	PRON
ejpam-4171	122	12	find	find	VERB
ejpam-4171	122	13	d(gxn(ι)−1	d(gxn(ι)−1	NOUN
ejpam-4171	122	14	,	,	PUNCT
ejpam-4171	122	15	gxm(ι)−1	gxm(ι)−1	NOUN
ejpam-4171	122	16	)	)	PUNCT
ejpam-4171	122	17	≤	≤	NUM
ejpam-4171	122	18	d(gxn(ι)−1	d(gxn(ι)−1	NOUN
ejpam-4171	122	19	,	,	PUNCT
ejpam-4171	122	20	gxm(ι	gxm(ι	NOUN
ejpam-4171	122	21	)	)	PUNCT
ejpam-4171	122	22	)	)	PUNCT
ejpam-4171	123	1	+	+	CCONJ
ejpam-4171	123	2	d(gxm(ι	d(gxm(ι	PROPN
ejpam-4171	123	3	)	)	PUNCT
ejpam-4171	123	4	,	,	PUNCT
ejpam-4171	123	5	gxm(ι)−1	gxm(ι)−1	NOUN
ejpam-4171	123	6	)	)	PUNCT
ejpam-4171	123	7	≤	≤	NOUN
ejpam-4171	123	8	ϵ	ϵ	ADP
ejpam-4171	123	9	hence	hence	ADV
ejpam-4171	123	10	,	,	PUNCT
ejpam-4171	123	11	d(gxn(ι)−1	d(gxn(ι)−1	ADJ
ejpam-4171	123	12	,	,	PUNCT
ejpam-4171	123	13	gxm(ι)−1	gxm(ι)−1	NOUN
ejpam-4171	123	14	)	)	PUNCT
ejpam-4171	123	15	≤	≤	NUM
ejpam-4171	123	16	ϵ.	ϵ.	NOUN
ejpam-4171	123	17	(	(	PUNCT
ejpam-4171	123	18	9	9	NUM
ejpam-4171	123	19	)	)	PUNCT
ejpam-4171	123	20	since	since	SCONJ
ejpam-4171	123	21	d(gxn(ι	d(gxn(ι	NOUN
ejpam-4171	123	22	)	)	PUNCT
ejpam-4171	123	23	,	,	PUNCT
ejpam-4171	123	24	g(xn(ι)−1	g(xn(ι)−1	PROPN
ejpam-4171	123	25	,	,	PUNCT
ejpam-4171	123	26	yn(ι)−1	yn(ι)−1	NOUN
ejpam-4171	123	27	,	,	PUNCT
ejpam-4171	123	28	zn(ι)−1	zn(ι)−1	NOUN
ejpam-4171	123	29	,	,	PUNCT
ejpam-4171	123	30	tn(ι)−1	tn(ι)−1	NOUN
ejpam-4171	123	31	)	)	PUNCT
ejpam-4171	123	32	)	)	PUNCT
ejpam-4171	124	1	=	=	PUNCT
ejpam-4171	124	2	d(q	d(q	PROPN
ejpam-4171	124	3	,	,	PUNCT
ejpam-4171	124	4	r	r	NOUN
ejpam-4171	124	5	)	)	PUNCT
ejpam-4171	124	6	s.	s.	PROPN
ejpam-4171	124	7	rathee	rathee	PROPN
ejpam-4171	124	8	,	,	PUNCT
ejpam-4171	124	9	m.	m.	NOUN
ejpam-4171	124	10	swami	swami	PROPN
ejpam-4171	124	11	,	,	PUNCT
ejpam-4171	124	12	/	/	SYM
ejpam-4171	124	13	eur	eur	NOUN
ejpam-4171	124	14	.	.	PUNCT
ejpam-4171	125	1	j.	j.	PROPN
ejpam-4171	125	2	pure	pure	PROPN
ejpam-4171	125	3	appl	appl	PROPN
ejpam-4171	125	4	.	.	PROPN
ejpam-4171	125	5	math	math	PROPN
ejpam-4171	125	6	,	,	PUNCT
ejpam-4171	125	7	15	15	NUM
ejpam-4171	125	8	(	(	PUNCT
ejpam-4171	125	9	1	1	NUM
ejpam-4171	125	10	)	)	PUNCT
ejpam-4171	125	11	(	(	PUNCT
ejpam-4171	125	12	2022	2022	NUM
ejpam-4171	125	13	)	)	PUNCT
ejpam-4171	125	14	,	,	PUNCT
ejpam-4171	125	15	135	135	NUM
ejpam-4171	125	16	-	-	SYM
ejpam-4171	125	17	143	143	NUM
ejpam-4171	125	18	140	140	NUM
ejpam-4171	125	19	and	and	CCONJ
ejpam-4171	125	20	d(gxm(ι	d(gxm(ι	VERB
ejpam-4171	125	21	)	)	PUNCT
ejpam-4171	125	22	,	,	PUNCT
ejpam-4171	125	23	g(xm(ι)−1	g(xm(ι)−1	NOUN
ejpam-4171	125	24	,	,	PUNCT
ejpam-4171	125	25	ym(ι)−1	ym(ι)−1	NOUN
ejpam-4171	125	26	,	,	PUNCT
ejpam-4171	125	27	zm(ι)−1	zm(ι)−1	NOUN
ejpam-4171	125	28	,	,	PUNCT
ejpam-4171	125	29	tm(ι)−1	tm(ι)−1	NOUN
ejpam-4171	125	30	)	)	PUNCT
ejpam-4171	125	31	)	)	PUNCT
ejpam-4171	126	1	=	=	PUNCT
ejpam-4171	126	2	d(q	d(q	PROPN
ejpam-4171	126	3	,	,	PUNCT
ejpam-4171	126	4	r	r	NOUN
ejpam-4171	126	5	)	)	PUNCT
ejpam-4171	126	6	.	.	PUNCT
ejpam-4171	127	1	from	from	ADP
ejpam-4171	127	2	p	p	NOUN
ejpam-4171	127	3	-	-	PUNCT
ejpam-4171	127	4	property	property	NOUN
ejpam-4171	127	5	,	,	PUNCT
ejpam-4171	127	6	we	we	PRON
ejpam-4171	127	7	have	have	VERB
ejpam-4171	127	8	d(gxn(ι	d(gxn(ι	NOUN
ejpam-4171	127	9	)	)	PUNCT
ejpam-4171	127	10	,	,	PUNCT
ejpam-4171	127	11	gxm(ι	gxm(ι	PROPN
ejpam-4171	127	12	)	)	PUNCT
ejpam-4171	127	13	)	)	PUNCT
ejpam-4171	128	1	=	=	SYM
ejpam-4171	128	2	d(g(xn(ι)−1	d(g(xn(ι)−1	NOUN
ejpam-4171	128	3	,	,	PUNCT
ejpam-4171	128	4	yn(ι)−1	yn(ι)−1	NOUN
ejpam-4171	128	5	,	,	PUNCT
ejpam-4171	128	6	zn(ι)−1	zn(ι)−1	NOUN
ejpam-4171	128	7	,	,	PUNCT
ejpam-4171	128	8	tn(ι)−1	tn(ι)−1	NOUN
ejpam-4171	128	9	)	)	PUNCT
ejpam-4171	128	10	,	,	PUNCT
ejpam-4171	128	11	g(xm(ι)−1	g(xm(ι)−1	NOUN
ejpam-4171	128	12	,	,	PUNCT
ejpam-4171	128	13	ym(ι)−1	ym(ι)−1	NOUN
ejpam-4171	128	14	,	,	PUNCT
ejpam-4171	128	15	zm(ι)−1	zm(ι)−1	NOUN
ejpam-4171	128	16	,	,	PUNCT
ejpam-4171	128	17	tm(ι)−1	tm(ι)−1	NOUN
ejpam-4171	128	18	)	)	PUNCT
ejpam-4171	128	19	)	)	PUNCT
ejpam-4171	129	1	now	now	ADV
ejpam-4171	129	2	from	from	ADP
ejpam-4171	129	3	(	(	PUNCT
ejpam-4171	129	4	1	1	NUM
ejpam-4171	129	5	)	)	PUNCT
ejpam-4171	129	6	and	and	CCONJ
ejpam-4171	129	7	using	use	VERB
ejpam-4171	129	8	the	the	DET
ejpam-4171	129	9	continuity	continuity	NOUN
ejpam-4171	129	10	of	of	ADP
ejpam-4171	129	11	ψ	ψ	NOUN
ejpam-4171	129	12	,	,	PUNCT
ejpam-4171	129	13	we	we	PRON
ejpam-4171	129	14	obtain	obtain	VERB
ejpam-4171	129	15	ψ(d(gxn(ι),gxm(ι	ψ(d(gxn(ι),gxm(ι	NUM
ejpam-4171	129	16	)	)	PUNCT
ejpam-4171	129	17	)	)	PUNCT
ejpam-4171	129	18	)	)	PUNCT
ejpam-4171	130	1	=	=	NOUN
ejpam-4171	130	2	ψ(d(g(xn(ι)−1	ψ(d(g(xn(ι)−1	NOUN
ejpam-4171	130	3	,	,	PUNCT
ejpam-4171	130	4	yn(ι)−1	yn(ι)−1	NOUN
ejpam-4171	130	5	,	,	PUNCT
ejpam-4171	130	6	zn(ι)−1	zn(ι)−1	NOUN
ejpam-4171	130	7	,	,	PUNCT
ejpam-4171	130	8	tn(ι)−1	tn(ι)−1	NOUN
ejpam-4171	130	9	)	)	PUNCT
ejpam-4171	130	10	,	,	PUNCT
ejpam-4171	130	11	g(xm(ι)−1	g(xm(ι)−1	NOUN
ejpam-4171	130	12	,	,	PUNCT
ejpam-4171	130	13	ym(ι)−1	ym(ι)−1	NOUN
ejpam-4171	130	14	,	,	PUNCT
ejpam-4171	130	15	zm(ι)−1	zm(ι)−1	NOUN
ejpam-4171	130	16	,	,	PUNCT
ejpam-4171	130	17	tm(ι)−1	tm(ι)−1	NOUN
ejpam-4171	130	18	)	)	PUNCT
ejpam-4171	130	19	)	)	PUNCT
ejpam-4171	130	20	)	)	PUNCT
ejpam-4171	130	21	≤	≤	NUM
ejpam-4171	130	22	ψ[max{d(xn(ι)−1	ψ[max{d(xn(ι)−1	NOUN
ejpam-4171	130	23	,	,	PUNCT
ejpam-4171	130	24	xm(ι)−1	xm(ι)−1	NUM
ejpam-4171	130	25	)	)	PUNCT
ejpam-4171	130	26	,	,	PUNCT
ejpam-4171	130	27	d(yn(ι)−1	d(yn(ι)−1	PROPN
ejpam-4171	130	28	,	,	PUNCT
ejpam-4171	130	29	ym(ι)−1	ym(ι)−1	NOUN
ejpam-4171	130	30	)	)	PUNCT
ejpam-4171	130	31	,	,	PUNCT
ejpam-4171	130	32	d(zn(ι)−1	d(zn(ι)−1	PROPN
ejpam-4171	130	33	,	,	PUNCT
ejpam-4171	130	34	zm(ι)−1	zm(ι)−1	NUM
ejpam-4171	130	35	)	)	PUNCT
ejpam-4171	130	36	,	,	PUNCT
ejpam-4171	130	37	d(tn(ι)−1	d(tn(ι)−1	PROPN
ejpam-4171	130	38	,	,	PUNCT
ejpam-4171	130	39	tm(ι)−1)}]−	tm(ι)−1)}]−	ADJ
ejpam-4171	130	40	ζ[max{d(xn(ι)−1	ζ[max{d(xn(ι)−1	NOUN
ejpam-4171	130	41	,	,	PUNCT
ejpam-4171	130	42	xm(ι)−1	xm(ι)−1	NUM
ejpam-4171	130	43	)	)	PUNCT
ejpam-4171	130	44	,	,	PUNCT
ejpam-4171	130	45	d(yn(ι)−1	d(yn(ι)−1	PROPN
ejpam-4171	130	46	,	,	PUNCT
ejpam-4171	130	47	ym(ι)−1	ym(ι)−1	NOUN
ejpam-4171	130	48	)	)	PUNCT
ejpam-4171	130	49	,	,	PUNCT
ejpam-4171	130	50	d(zn(ι)−1	d(zn(ι)−1	PROPN
ejpam-4171	130	51	,	,	PUNCT
ejpam-4171	130	52	zm(ι)−1	zm(ι)−1	NUM
ejpam-4171	130	53	)	)	PUNCT
ejpam-4171	130	54	,	,	PUNCT
ejpam-4171	130	55	d(tn(ι)−1	d(tn(ι)−1	PROPN
ejpam-4171	130	56	,	,	PUNCT
ejpam-4171	130	57	tm(ι)−1	tm(ι)−1	NOUN
ejpam-4171	130	58	)	)	PUNCT
ejpam-4171	130	59	}	}	PUNCT
ejpam-4171	130	60	]	]	PUNCT
ejpam-4171	131	1	+	+	CCONJ
ejpam-4171	131	2	θ[d(gxm(ι)−1	θ[d(gxm(ι)−1	NOUN
ejpam-4171	131	3	,	,	PUNCT
ejpam-4171	131	4	g(xn(ι)−1	g(xn(ι)−1	NOUN
ejpam-4171	131	5	,	,	PUNCT
ejpam-4171	131	6	yn(ι)−1	yn(ι)−1	NOUN
ejpam-4171	131	7	,	,	PUNCT
ejpam-4171	131	8	zn(ι)−1	zn(ι)−1	NOUN
ejpam-4171	131	9	,	,	PUNCT
ejpam-4171	131	10	tn(ι)−1	tn(ι)−1	NOUN
ejpam-4171	131	11	)	)	PUNCT
ejpam-4171	131	12	)	)	PUNCT
ejpam-4171	131	13	,	,	PUNCT
ejpam-4171	131	14	d(gym(ι)−1	d(gym(ι)−1	NOUN
ejpam-4171	131	15	,	,	PUNCT
ejpam-4171	131	16	g(yn(ι)−1	g(yn(ι)−1	PROPN
ejpam-4171	131	17	,	,	PUNCT
ejpam-4171	131	18	xn(ι)−1	xn(ι)−1	NOUN
ejpam-4171	131	19	,	,	PUNCT
ejpam-4171	131	20	tn(ι)−1	tn(ι)−1	NOUN
ejpam-4171	131	21	,	,	PUNCT
ejpam-4171	131	22	zn(ι)−1	zn(ι)−1	NUM
ejpam-4171	131	23	)	)	PUNCT
ejpam-4171	131	24	)	)	PUNCT
ejpam-4171	131	25	,	,	PUNCT
ejpam-4171	131	26	d(gzm(ι)−1	d(gzm(ι)−1	NOUN
ejpam-4171	131	27	,	,	PUNCT
ejpam-4171	131	28	g(zn(ι)−1	g(zn(ι)−1	NOUN
ejpam-4171	131	29	,	,	PUNCT
ejpam-4171	131	30	yn(ι)−1	yn(ι)−1	NOUN
ejpam-4171	131	31	,	,	PUNCT
ejpam-4171	131	32	xn(ι)−1	xn(ι)−1	NOUN
ejpam-4171	131	33	,	,	PUNCT
ejpam-4171	131	34	tn(ι)−1	tn(ι)−1	NOUN
ejpam-4171	131	35	)	)	PUNCT
ejpam-4171	131	36	)	)	PUNCT
ejpam-4171	131	37	,	,	PUNCT
ejpam-4171	131	38	d(gtm(ι)−1	d(gtm(ι)−1	NOUN
ejpam-4171	131	39	,	,	PUNCT
ejpam-4171	131	40	g(tn(ι)−1	g(tn(ι)−1	NOUN
ejpam-4171	131	41	,	,	PUNCT
ejpam-4171	131	42	zn(ι)−1	zn(ι)−1	NUM
ejpam-4171	131	43	,	,	PUNCT
ejpam-4171	131	44	yn(ι)−1	yn(ι)−1	NOUN
ejpam-4171	131	45	,	,	PUNCT
ejpam-4171	131	46	xn(ι)−1	xn(ι)−1	PUNCT
ejpam-4171	131	47	)	)	PUNCT
ejpam-4171	131	48	)	)	PUNCT
ejpam-4171	131	49	,	,	PUNCT
ejpam-4171	131	50	d(gxn(ι)−1	d(gxn(ι)−1	PROPN
ejpam-4171	131	51	,	,	PUNCT
ejpam-4171	131	52	g(xn(ι)−1	g(xn(ι)−1	NOUN
ejpam-4171	131	53	,	,	PUNCT
ejpam-4171	131	54	yn(ι)−1	yn(ι)−1	NOUN
ejpam-4171	131	55	,	,	PUNCT
ejpam-4171	131	56	zn(ι)−1	zn(ι)−1	NOUN
ejpam-4171	131	57	,	,	PUNCT
ejpam-4171	131	58	tn(ι)−1	tn(ι)−1	NOUN
ejpam-4171	131	59	)	)	PUNCT
ejpam-4171	131	60	)	)	PUNCT
ejpam-4171	131	61	,	,	PUNCT
ejpam-4171	131	62	d(gyn(ι)−1	d(gyn(ι)−1	PROPN
ejpam-4171	131	63	,	,	PUNCT
ejpam-4171	131	64	g(yn(ι)−1	g(yn(ι)−1	NOUN
ejpam-4171	131	65	,	,	PUNCT
ejpam-4171	131	66	xn(ι)−1	xn(ι)−1	NOUN
ejpam-4171	131	67	,	,	PUNCT
ejpam-4171	131	68	tn(ι)−1	tn(ι)−1	NOUN
ejpam-4171	131	69	,	,	PUNCT
ejpam-4171	131	70	zn(ι)−1	zn(ι)−1	NUM
ejpam-4171	131	71	)	)	PUNCT
ejpam-4171	131	72	)	)	PUNCT
ejpam-4171	131	73	,	,	PUNCT
ejpam-4171	131	74	d(gzn(ι)−1	d(gzn(ι)−1	NOUN
ejpam-4171	131	75	,	,	PUNCT
ejpam-4171	131	76	g(zn(ι)−1	g(zn(ι)−1	NOUN
ejpam-4171	131	77	,	,	PUNCT
ejpam-4171	131	78	yn(ι)−1	yn(ι)−1	NOUN
ejpam-4171	131	79	,	,	PUNCT
ejpam-4171	131	80	xn(ι)−1	xn(ι)−1	NOUN
ejpam-4171	131	81	,	,	PUNCT
ejpam-4171	131	82	tn(ι)−1	tn(ι)−1	NOUN
ejpam-4171	131	83	)	)	PUNCT
ejpam-4171	131	84	)	)	PUNCT
ejpam-4171	131	85	,	,	PUNCT
ejpam-4171	131	86	d(gtn(ι)−1	d(gtn(ι)−1	NOUN
ejpam-4171	131	87	,	,	PUNCT
ejpam-4171	131	88	g(tn(ι)−1	g(tn(ι)−1	NOUN
ejpam-4171	131	89	,	,	PUNCT
ejpam-4171	131	90	zn(ι)−1	zn(ι)−1	NUM
ejpam-4171	131	91	,	,	PUNCT
ejpam-4171	131	92	yn(ι)−1	yn(ι)−1	NOUN
ejpam-4171	131	93	,	,	PUNCT
ejpam-4171	131	94	xn(ι)−1	xn(ι)−1	PUNCT
ejpam-4171	131	95	)	)	PUNCT
ejpam-4171	131	96	)	)	PUNCT
ejpam-4171	131	97	]	]	PUNCT
ejpam-4171	132	1	=	=	PUNCT
ejpam-4171	132	2	ψ[max{d(xn(ι)−1	ψ[max{d(xn(ι)−1	PROPN
ejpam-4171	132	3	,	,	PUNCT
ejpam-4171	132	4	xm(ι)−1	xm(ι)−1	NUM
ejpam-4171	132	5	)	)	PUNCT
ejpam-4171	132	6	,	,	PUNCT
ejpam-4171	132	7	d(yn(ι)−1	d(yn(ι)−1	PROPN
ejpam-4171	132	8	,	,	PUNCT
ejpam-4171	132	9	ym(ι)−1	ym(ι)−1	NOUN
ejpam-4171	132	10	)	)	PUNCT
ejpam-4171	132	11	,	,	PUNCT
ejpam-4171	132	12	d(zn(ι)−1	d(zn(ι)−1	PROPN
ejpam-4171	132	13	,	,	PUNCT
ejpam-4171	132	14	zm(ι)−1	zm(ι)−1	NUM
ejpam-4171	132	15	)	)	PUNCT
ejpam-4171	132	16	,	,	PUNCT
ejpam-4171	132	17	d(tn(ι)−1	d(tn(ι)−1	PROPN
ejpam-4171	132	18	,	,	PUNCT
ejpam-4171	132	19	tm(ι)−1)}]−	tm(ι)−1)}]−	ADJ
ejpam-4171	132	20	ζ[max{d(xn(ι)−1	ζ[max{d(xn(ι)−1	NOUN
ejpam-4171	132	21	,	,	PUNCT
ejpam-4171	132	22	xm(ι)−1	xm(ι)−1	NUM
ejpam-4171	132	23	)	)	PUNCT
ejpam-4171	132	24	,	,	PUNCT
ejpam-4171	132	25	d(yn(ι)−1	d(yn(ι)−1	PROPN
ejpam-4171	132	26	,	,	PUNCT
ejpam-4171	132	27	ym(ι)−1	ym(ι)−1	NOUN
ejpam-4171	132	28	)	)	PUNCT
ejpam-4171	132	29	,	,	PUNCT
ejpam-4171	132	30	d(zn(ι)−1	d(zn(ι)−1	PROPN
ejpam-4171	132	31	,	,	PUNCT
ejpam-4171	132	32	zm(ι)−1	zm(ι)−1	NUM
ejpam-4171	132	33	)	)	PUNCT
ejpam-4171	132	34	,	,	PUNCT
ejpam-4171	132	35	d(tn(ι)−1	d(tn(ι)−1	PROPN
ejpam-4171	132	36	,	,	PUNCT
ejpam-4171	132	37	tm(ι)−1	tm(ι)−1	NOUN
ejpam-4171	132	38	)	)	PUNCT
ejpam-4171	132	39	}	}	PUNCT
ejpam-4171	132	40	]	]	PUNCT
ejpam-4171	132	41	.	.	PUNCT
ejpam-4171	133	1	similary	similary	ADJ
ejpam-4171	133	2	,	,	PUNCT
ejpam-4171	133	3	from	from	ADP
ejpam-4171	133	4	the	the	DET
ejpam-4171	133	5	same	same	ADJ
ejpam-4171	133	6	techinque	techinque	NOUN
ejpam-4171	133	7	,	,	PUNCT
ejpam-4171	133	8	we	we	PRON
ejpam-4171	133	9	obtain	obtain	VERB
ejpam-4171	133	10	ψ[max{d(gxn(ι	ψ[max{d(gxn(ι	NOUN
ejpam-4171	133	11	)	)	PUNCT
ejpam-4171	133	12	,	,	PUNCT
ejpam-4171	133	13	gxm(ι	gxm(ι	PROPN
ejpam-4171	133	14	)	)	PUNCT
ejpam-4171	133	15	)	)	PUNCT
ejpam-4171	133	16	,	,	PUNCT
ejpam-4171	133	17	d(gyn(ι	d(gyn(ι	NOUN
ejpam-4171	133	18	)	)	PUNCT
ejpam-4171	133	19	,	,	PUNCT
ejpam-4171	133	20	gym(ι	gym(ι	NOUN
ejpam-4171	133	21	)	)	PUNCT
ejpam-4171	133	22	)	)	PUNCT
ejpam-4171	133	23	,	,	PUNCT
ejpam-4171	133	24	d(gzn(ι	d(gzn(ι	PROPN
ejpam-4171	133	25	)	)	PUNCT
ejpam-4171	133	26	,	,	PUNCT
ejpam-4171	133	27	gzm(ι	gzm(ι	PROPN
ejpam-4171	133	28	)	)	PUNCT
ejpam-4171	133	29	)	)	PUNCT
ejpam-4171	133	30	,	,	PUNCT
ejpam-4171	133	31	d(gtn(ι	d(gtn(ι	NOUN
ejpam-4171	133	32	)	)	PUNCT
ejpam-4171	133	33	,	,	PUNCT
ejpam-4171	133	34	gtm(ι	gtm(ι	PROPN
ejpam-4171	133	35	)	)	PUNCT
ejpam-4171	133	36	)	)	PUNCT
ejpam-4171	133	37	}	}	PUNCT
ejpam-4171	133	38	]	]	PUNCT
ejpam-4171	133	39	≤	≤	NUM
ejpam-4171	133	40	ψ[max{d(gxn(ι)−1	ψ[max{d(gxn(ι)−1	NOUN
ejpam-4171	133	41	,	,	PUNCT
ejpam-4171	133	42	gxm(ι)−1	gxm(ι)−1	NOUN
ejpam-4171	133	43	)	)	PUNCT
ejpam-4171	133	44	,	,	PUNCT
ejpam-4171	133	45	d(gyn(ι)−1	d(gyn(ι)−1	NOUN
ejpam-4171	133	46	,	,	PUNCT
ejpam-4171	133	47	gym(ι)−1	gym(ι)−1	NOUN
ejpam-4171	133	48	)	)	PUNCT
ejpam-4171	133	49	,	,	PUNCT
ejpam-4171	133	50	d(gzn(ι)−1	d(gzn(ι)−1	NOUN
ejpam-4171	133	51	,	,	PUNCT
ejpam-4171	133	52	gzm(ι)−1	gzm(ι)−1	NOUN
ejpam-4171	133	53	)	)	PUNCT
ejpam-4171	133	54	,	,	PUNCT
ejpam-4171	133	55	d(gtn(ι)−1	d(gtn(ι)−1	NOUN
ejpam-4171	133	56	,	,	PUNCT
ejpam-4171	133	57	gtm(ι)−1)}]−	gtm(ι)−1)}]−	NOUN
ejpam-4171	133	58	ζ[max{d(gxn(ι)−1	ζ[max{d(gxn(ι)−1	NOUN
ejpam-4171	133	59	,	,	PUNCT
ejpam-4171	133	60	gxm(ι)−1	gxm(ι)−1	NOUN
ejpam-4171	133	61	)	)	PUNCT
ejpam-4171	133	62	,	,	PUNCT
ejpam-4171	133	63	d(gyn(ι)−1	d(gyn(ι)−1	NOUN
ejpam-4171	133	64	,	,	PUNCT
ejpam-4171	133	65	gym(ι)−1	gym(ι)−1	NOUN
ejpam-4171	133	66	)	)	PUNCT
ejpam-4171	133	67	,	,	PUNCT
ejpam-4171	133	68	d(gzn(ι)−1	d(gzn(ι)−1	NOUN
ejpam-4171	133	69	,	,	PUNCT
ejpam-4171	133	70	gzm(ι)−1	gzm(ι)−1	NOUN
ejpam-4171	133	71	)	)	PUNCT
ejpam-4171	133	72	,	,	PUNCT
ejpam-4171	133	73	d(gtn(ι)−1	d(gtn(ι)−1	NOUN
ejpam-4171	133	74	,	,	PUNCT
ejpam-4171	133	75	gtm(ι)−1	gtm(ι)−1	NOUN
ejpam-4171	133	76	)	)	PUNCT
ejpam-4171	133	77	}	}	PUNCT
ejpam-4171	133	78	]	]	PUNCT
ejpam-4171	133	79	.	.	PUNCT
ejpam-4171	134	1	now	now	ADV
ejpam-4171	134	2	,	,	PUNCT
ejpam-4171	134	3	from	from	ADP
ejpam-4171	134	4	(	(	PUNCT
ejpam-4171	134	5	8)	8)	NUM
ejpam-4171	134	6	and	and	CCONJ
ejpam-4171	134	7	(	(	PUNCT
ejpam-4171	134	8	9	9	NUM
ejpam-4171	134	9	)	)	PUNCT
ejpam-4171	134	10	,	,	PUNCT
ejpam-4171	134	11	we	we	PRON
ejpam-4171	134	12	get	get	VERB
ejpam-4171	134	13	ψ(ϵ	ψ(ϵ	ADP
ejpam-4171	134	14	)	)	PUNCT
ejpam-4171	134	15	≤	≤	NUM
ejpam-4171	134	16	ψ(ϵ)−	ψ(ϵ)−	VERB
ejpam-4171	134	17	ζ(ϵ	ζ(ϵ	NOUN
ejpam-4171	134	18	)	)	PUNCT
ejpam-4171	134	19	ζ(ϵ	ζ(ϵ	NOUN
ejpam-4171	134	20	)	)	PUNCT
ejpam-4171	135	1	=	=	SYM
ejpam-4171	135	2	0	0	PUNCT
ejpam-4171	136	1	=	=	NOUN
ejpam-4171	136	2	⇒	⇒	VERB
ejpam-4171	136	3	ϵ	ϵ	X
ejpam-4171	136	4	=	=	SYM
ejpam-4171	136	5	0	0	PROPN
ejpam-4171	136	6	.	.	PUNCT
ejpam-4171	137	1	thus	thus	ADV
ejpam-4171	137	2	,	,	PUNCT
ejpam-4171	137	3	for	for	ADP
ejpam-4171	137	4	ι	ι	PROPN
ejpam-4171	137	5	tends	tend	VERB
ejpam-4171	137	6	to	to	PART
ejpam-4171	137	7	infinity	infinity	VERB
ejpam-4171	137	8	,	,	PUNCT
ejpam-4171	137	9	it	it	PRON
ejpam-4171	137	10	gives	give	VERB
ejpam-4171	137	11	us	we	PRON
ejpam-4171	137	12	lim	lim	PROPN
ejpam-4171	137	13	ι→∞	ι→∞	NUM
ejpam-4171	137	14	{	{	PUNCT
ejpam-4171	137	15	d(gxn(ι	d(gxn(ι	NOUN
ejpam-4171	137	16	)	)	PUNCT
ejpam-4171	137	17	,	,	PUNCT
ejpam-4171	137	18	gxm(ι	gxm(ι	PROPN
ejpam-4171	137	19	)	)	PUNCT
ejpam-4171	137	20	)	)	PUNCT
ejpam-4171	137	21	,	,	PUNCT
ejpam-4171	137	22	d(gyn(ι	d(gyn(ι	NOUN
ejpam-4171	137	23	)	)	PUNCT
ejpam-4171	137	24	,	,	PUNCT
ejpam-4171	137	25	gym(ι	gym(ι	NOUN
ejpam-4171	137	26	)	)	PUNCT
ejpam-4171	137	27	)	)	PUNCT
ejpam-4171	137	28	,	,	PUNCT
ejpam-4171	137	29	d(gzn(ι	d(gzn(ι	PROPN
ejpam-4171	137	30	)	)	PUNCT
ejpam-4171	137	31	,	,	PUNCT
ejpam-4171	137	32	gzm(ι	gzm(ι	PROPN
ejpam-4171	137	33	)	)	PUNCT
ejpam-4171	137	34	)	)	PUNCT
ejpam-4171	137	35	,	,	PUNCT
ejpam-4171	137	36	d(gtn(ι	d(gtn(ι	NOUN
ejpam-4171	137	37	)	)	PUNCT
ejpam-4171	137	38	,	,	PUNCT
ejpam-4171	137	39	gtm(ι	gtm(ι	PROPN
ejpam-4171	137	40	)	)	PUNCT
ejpam-4171	137	41	)	)	PUNCT
ejpam-4171	137	42	}	}	PUNCT
ejpam-4171	138	1	=	=	SYM
ejpam-4171	138	2	0	0	NUM
ejpam-4171	138	3	,	,	PUNCT
ejpam-4171	138	4	which	which	PRON
ejpam-4171	138	5	is	be	AUX
ejpam-4171	138	6	contradiction	contradiction	NOUN
ejpam-4171	138	7	to	to	ADP
ejpam-4171	138	8	our	our	PRON
ejpam-4171	138	9	suppostion	suppostion	NOUN
ejpam-4171	138	10	that	that	SCONJ
ejpam-4171	138	11	ϵ	ϵ	X
ejpam-4171	138	12	>	>	X
ejpam-4171	138	13	0	0	NUM
ejpam-4171	138	14	.	.	PUNCT
ejpam-4171	139	1	hence	hence	ADV
ejpam-4171	139	2	,	,	PUNCT
ejpam-4171	139	3	{	{	PUNCT
ejpam-4171	139	4	gxn	gxn	INTJ
ejpam-4171	139	5	}	}	PUNCT
ejpam-4171	139	6	,	,	PUNCT
ejpam-4171	139	7	{	{	PUNCT
ejpam-4171	139	8	gzn	gzn	NOUN
ejpam-4171	139	9	}	}	PUNCT
ejpam-4171	139	10	are	be	AUX
ejpam-4171	139	11	cauchy	cauchy	ADJ
ejpam-4171	139	12	sequences	sequence	NOUN
ejpam-4171	139	13	in	in	ADP
ejpam-4171	139	14	q	q	PROPN
ejpam-4171	139	15	and	and	CCONJ
ejpam-4171	139	16	{	{	PUNCT
ejpam-4171	139	17	gyn	gyn	NOUN
ejpam-4171	139	18	}	}	PUNCT
ejpam-4171	139	19	,	,	PUNCT
ejpam-4171	139	20	{	{	PUNCT
ejpam-4171	139	21	gtn	gtn	X
ejpam-4171	139	22	}	}	PUNCT
ejpam-4171	139	23	in	in	ADP
ejpam-4171	139	24	r.	r.	PROPN
ejpam-4171	139	25	since	since	SCONJ
ejpam-4171	139	26	(	(	PUNCT
ejpam-4171	139	27	x	x	X
ejpam-4171	139	28	,	,	PUNCT
ejpam-4171	139	29	d	d	NOUN
ejpam-4171	139	30	)	)	PUNCT
ejpam-4171	139	31	is	be	AUX
ejpam-4171	139	32	complete	complete	ADJ
ejpam-4171	139	33	metric	metric	ADJ
ejpam-4171	139	34	space	space	NOUN
ejpam-4171	139	35	,	,	PUNCT
ejpam-4171	139	36	then	then	ADV
ejpam-4171	139	37	there	there	PRON
ejpam-4171	139	38	exist	exist	VERB
ejpam-4171	139	39	,	,	PUNCT
ejpam-4171	139	40	a	a	DET
ejpam-4171	139	41	,	,	PUNCT
ejpam-4171	139	42	b	b	NOUN
ejpam-4171	139	43	,	,	PUNCT
ejpam-4171	139	44	c	c	X
ejpam-4171	139	45	,	,	PUNCT
ejpam-4171	139	46	u	u	NOUN
ejpam-4171	139	47	∈	∈	PROPN
ejpam-4171	139	48	x	x	PUNCT
ejpam-4171	139	49	such	such	ADJ
ejpam-4171	139	50	that	that	SCONJ
ejpam-4171	139	51	lim	lim	PROPN
ejpam-4171	139	52	n→∞	n→∞	PRON
ejpam-4171	139	53	gxn	gxn	PROPN
ejpam-4171	139	54	=	=	SYM
ejpam-4171	139	55	a	a	PROPN
ejpam-4171	139	56	,	,	PUNCT
ejpam-4171	139	57	lim	lim	PROPN
ejpam-4171	139	58	n→∞	n→∞	NUM
ejpam-4171	139	59	gyn	gyn	PROPN
ejpam-4171	139	60	=	=	SYM
ejpam-4171	139	61	b	b	PROPN
ejpam-4171	139	62	,	,	PUNCT
ejpam-4171	139	63	lim	lim	PROPN
ejpam-4171	139	64	n→∞	n→∞	NUM
ejpam-4171	139	65	gzn	gzn	NOUN
ejpam-4171	139	66	=	=	PUNCT
ejpam-4171	139	67	c	c	PROPN
ejpam-4171	139	68	and	and	CCONJ
ejpam-4171	139	69	lim	lim	PROPN
ejpam-4171	139	70	n→∞	n→∞	PROPN
ejpam-4171	139	71	gtn	gtn	PROPN
ejpam-4171	139	72	=	=	PUNCT
ejpam-4171	139	73	u.	u.	PROPN
ejpam-4171	139	74	as	as	ADP
ejpam-4171	139	75	q	q	PROPN
ejpam-4171	139	76	,	,	PUNCT
ejpam-4171	139	77	r	r	NOUN
ejpam-4171	139	78	are	be	AUX
ejpam-4171	139	79	closed	close	VERB
ejpam-4171	139	80	subset	subset	NOUN
ejpam-4171	139	81	of	of	ADP
ejpam-4171	139	82	x	x	PRON
ejpam-4171	139	83	,	,	PUNCT
ejpam-4171	139	84	then	then	ADV
ejpam-4171	139	85	a	a	PRON
ejpam-4171	139	86	,	,	PUNCT
ejpam-4171	139	87	c	c	PROPN
ejpam-4171	139	88	∈	∈	PROPN
ejpam-4171	139	89	q	q	X
ejpam-4171	139	90	and	and	CCONJ
ejpam-4171	139	91	b	b	NOUN
ejpam-4171	139	92	,	,	PUNCT
ejpam-4171	139	93	u	u	PROPN
ejpam-4171	139	94	∈	∈	PROPN
ejpam-4171	139	95	r.	r.	NOUN
ejpam-4171	139	96	since	since	SCONJ
ejpam-4171	139	97	g	g	PROPN
ejpam-4171	139	98	is	be	AUX
ejpam-4171	139	99	continuous	continuous	ADJ
ejpam-4171	139	100	,	,	PUNCT
ejpam-4171	139	101	then	then	ADV
ejpam-4171	139	102	lim	lim	PROPN
ejpam-4171	139	103	n→∞	n→∞	PRON
ejpam-4171	139	104	d(gxn	d(gxn	PROPN
ejpam-4171	139	105	,	,	PUNCT
ejpam-4171	139	106	g(xn	g(xn	X
ejpam-4171	139	107	,	,	PUNCT
ejpam-4171	139	108	yn	yn	PROPN
ejpam-4171	139	109	,	,	PUNCT
ejpam-4171	139	110	zn	zn	PROPN
ejpam-4171	139	111	,	,	PUNCT
ejpam-4171	139	112	tn	tn	PROPN
ejpam-4171	139	113	)	)	PUNCT
ejpam-4171	139	114	)	)	PUNCT
ejpam-4171	140	1	=	=	SYM
ejpam-4171	140	2	d(q	d(q	PROPN
ejpam-4171	140	3	,	,	PUNCT
ejpam-4171	140	4	r	r	NOUN
ejpam-4171	140	5	)	)	PUNCT
ejpam-4171	140	6	=	=	NOUN
ejpam-4171	140	7	⇒	⇒	NOUN
ejpam-4171	140	8	d(ga	d(ga	NOUN
ejpam-4171	140	9	,	,	PUNCT
ejpam-4171	140	10	g(a	g(a	PROPN
ejpam-4171	140	11	,	,	PUNCT
ejpam-4171	140	12	b	b	PROPN
ejpam-4171	140	13	,	,	PUNCT
ejpam-4171	140	14	c	c	X
ejpam-4171	140	15	,	,	PUNCT
ejpam-4171	140	16	u	u	NOUN
ejpam-4171	140	17	)	)	PUNCT
ejpam-4171	140	18	)	)	PUNCT
ejpam-4171	141	1	=	=	SYM
ejpam-4171	141	2	d(q	d(q	PROPN
ejpam-4171	141	3	,	,	PUNCT
ejpam-4171	141	4	r	r	NOUN
ejpam-4171	141	5	)	)	PUNCT
ejpam-4171	141	6	.	.	PUNCT
ejpam-4171	142	1	s.	s.	PROPN
ejpam-4171	142	2	rathee	rathee	PROPN
ejpam-4171	142	3	,	,	PUNCT
ejpam-4171	142	4	m.	m.	NOUN
ejpam-4171	142	5	swami	swami	PROPN
ejpam-4171	142	6	,	,	PUNCT
ejpam-4171	142	7	/	/	SYM
ejpam-4171	142	8	eur	eur	NOUN
ejpam-4171	142	9	.	.	PUNCT
ejpam-4171	143	1	j.	j.	PROPN
ejpam-4171	143	2	pure	pure	PROPN
ejpam-4171	143	3	appl	appl	PROPN
ejpam-4171	143	4	.	.	PROPN
ejpam-4171	143	5	math	math	PROPN
ejpam-4171	143	6	,	,	PUNCT
ejpam-4171	143	7	15	15	NUM
ejpam-4171	143	8	(	(	PUNCT
ejpam-4171	143	9	1	1	NUM
ejpam-4171	143	10	)	)	PUNCT
ejpam-4171	143	11	(	(	PUNCT
ejpam-4171	143	12	2022	2022	NUM
ejpam-4171	143	13	)	)	PUNCT
ejpam-4171	143	14	,	,	PUNCT
ejpam-4171	143	15	135	135	NUM
ejpam-4171	143	16	-	-	SYM
ejpam-4171	143	17	143	143	NUM
ejpam-4171	143	18	141	141	NUM
ejpam-4171	143	19	similarly	similarly	ADV
ejpam-4171	143	20	,	,	PUNCT
ejpam-4171	143	21	d(gb	d(gb	NOUN
ejpam-4171	143	22	,	,	PUNCT
ejpam-4171	143	23	g(b	g(b	PROPN
ejpam-4171	143	24	,	,	PUNCT
ejpam-4171	143	25	a	a	DET
ejpam-4171	143	26	,	,	PUNCT
ejpam-4171	143	27	c	c	NOUN
ejpam-4171	143	28	,	,	PUNCT
ejpam-4171	143	29	u	u	NOUN
ejpam-4171	143	30	)	)	PUNCT
ejpam-4171	143	31	)	)	PUNCT
ejpam-4171	144	1	=	=	SYM
ejpam-4171	144	2	d(q	d(q	PROPN
ejpam-4171	144	3	,	,	PUNCT
ejpam-4171	144	4	r	r	NOUN
ejpam-4171	144	5	)	)	PUNCT
ejpam-4171	144	6	,	,	PUNCT
ejpam-4171	144	7	d(gc	d(gc	PROPN
ejpam-4171	144	8	,	,	PUNCT
ejpam-4171	144	9	g(c	g(c	NOUN
ejpam-4171	144	10	,	,	PUNCT
ejpam-4171	144	11	b	b	NOUN
ejpam-4171	144	12	,	,	PUNCT
ejpam-4171	144	13	a	a	DET
ejpam-4171	144	14	,	,	PUNCT
ejpam-4171	144	15	u	u	NOUN
ejpam-4171	144	16	)	)	PUNCT
ejpam-4171	144	17	)	)	PUNCT
ejpam-4171	145	1	=	=	SYM
ejpam-4171	145	2	d(q	d(q	PROPN
ejpam-4171	145	3	,	,	PUNCT
ejpam-4171	145	4	r	r	NOUN
ejpam-4171	145	5	)	)	PUNCT
ejpam-4171	145	6	and	and	CCONJ
ejpam-4171	145	7	d(gu	d(gu	PROPN
ejpam-4171	145	8	,	,	PUNCT
ejpam-4171	145	9	g(u	g(u	PROPN
ejpam-4171	145	10	,	,	PUNCT
ejpam-4171	145	11	b	b	PROPN
ejpam-4171	145	12	,	,	PUNCT
ejpam-4171	145	13	c	c	NOUN
ejpam-4171	145	14	,	,	PUNCT
ejpam-4171	145	15	a	a	PRON
ejpam-4171	145	16	)	)	PUNCT
ejpam-4171	145	17	)	)	PUNCT
ejpam-4171	146	1	=	=	SYM
ejpam-4171	146	2	d(q	d(q	PROPN
ejpam-4171	146	3	,	,	PUNCT
ejpam-4171	146	4	r	r	NOUN
ejpam-4171	146	5	)	)	PUNCT
ejpam-4171	146	6	.	.	PUNCT
ejpam-4171	147	1	thus	thus	ADV
ejpam-4171	147	2	,	,	PUNCT
ejpam-4171	147	3	(	(	PUNCT
ejpam-4171	147	4	a	a	DET
ejpam-4171	147	5	,	,	PUNCT
ejpam-4171	147	6	b	b	NOUN
ejpam-4171	147	7	,	,	PUNCT
ejpam-4171	147	8	c	c	X
ejpam-4171	147	9	,	,	PUNCT
ejpam-4171	147	10	u	u	NOUN
ejpam-4171	147	11	)	)	PUNCT
ejpam-4171	147	12	is	be	AUX
ejpam-4171	147	13	quadruple	quadruple	NOUN
ejpam-4171	147	14	g	g	NOUN
ejpam-4171	147	15	-	-	PUNCT
ejpam-4171	147	16	best	good	ADJ
ejpam-4171	147	17	proximity	proximity	NOUN
ejpam-4171	147	18	point	point	NOUN
ejpam-4171	147	19	of	of	ADP
ejpam-4171	147	20	the	the	DET
ejpam-4171	147	21	pair	pair	NOUN
ejpam-4171	147	22	(	(	PUNCT
ejpam-4171	147	23	g	g	NOUN
ejpam-4171	147	24	,	,	PUNCT
ejpam-4171	147	25	g	g	NOUN
ejpam-4171	147	26	)	)	PUNCT
ejpam-4171	147	27	.	.	PUNCT
ejpam-4171	148	1	now	now	ADV
ejpam-4171	148	2	,	,	PUNCT
ejpam-4171	148	3	we	we	PRON
ejpam-4171	148	4	show	show	VERB
ejpam-4171	148	5	that	that	SCONJ
ejpam-4171	148	6	ga	ga	PROPN
ejpam-4171	148	7	=	=	NOUN
ejpam-4171	148	8	gb	gb	PROPN
ejpam-4171	148	9	=	=	SYM
ejpam-4171	148	10	gc	gc	PROPN
ejpam-4171	148	11	=	=	SYM
ejpam-4171	148	12	gu	gu	PROPN
ejpam-4171	148	13	.	.	PROPN
ejpam-4171	148	14	again	again	ADV
ejpam-4171	148	15	from	from	ADP
ejpam-4171	148	16	p	p	NOUN
ejpam-4171	148	17	-	-	PUNCT
ejpam-4171	148	18	property	property	NOUN
ejpam-4171	148	19	,	,	PUNCT
ejpam-4171	148	20	g	g	NOUN
ejpam-4171	148	21	-	-	PUNCT
ejpam-4171	148	22	isometry	isometry	NOUN
ejpam-4171	148	23	and	and	CCONJ
ejpam-4171	148	24	condition	condition	NOUN
ejpam-4171	148	25	(	(	PUNCT
ejpam-4171	148	26	1	1	NUM
ejpam-4171	148	27	)	)	PUNCT
ejpam-4171	148	28	,	,	PUNCT
ejpam-4171	148	29	we	we	PRON
ejpam-4171	148	30	calculate	calculate	VERB
ejpam-4171	148	31	d(ga	d(ga	NOUN
ejpam-4171	148	32	,	,	PUNCT
ejpam-4171	148	33	gc	gc	PROPN
ejpam-4171	148	34	)	)	PUNCT
ejpam-4171	149	1	=	=	SYM
ejpam-4171	149	2	d(g(a	d(g(a	PROPN
ejpam-4171	149	3	,	,	PUNCT
ejpam-4171	149	4	b	b	NOUN
ejpam-4171	149	5	,	,	PUNCT
ejpam-4171	149	6	c	c	X
ejpam-4171	149	7	,	,	PUNCT
ejpam-4171	149	8	u	u	NOUN
ejpam-4171	149	9	)	)	PUNCT
ejpam-4171	149	10	,	,	PUNCT
ejpam-4171	149	11	g(c	g(c	PROPN
ejpam-4171	149	12	,	,	PUNCT
ejpam-4171	149	13	b	b	NOUN
ejpam-4171	149	14	,	,	PUNCT
ejpam-4171	149	15	a	a	DET
ejpam-4171	149	16	,	,	PUNCT
ejpam-4171	149	17	u	u	NOUN
ejpam-4171	149	18	)	)	PUNCT
ejpam-4171	149	19	)	)	PUNCT
ejpam-4171	150	1	ψ(d(ga	ψ(d(ga	NOUN
ejpam-4171	150	2	,	,	PUNCT
ejpam-4171	150	3	gc	gc	PROPN
ejpam-4171	150	4	)	)	PUNCT
ejpam-4171	150	5	)	)	PUNCT
ejpam-4171	151	1	=	=	SYM
ejpam-4171	151	2	ψ(d(g(a	ψ(d(g(a	PROPN
ejpam-4171	151	3	,	,	PUNCT
ejpam-4171	151	4	b	b	PROPN
ejpam-4171	151	5	,	,	PUNCT
ejpam-4171	151	6	c	c	X
ejpam-4171	151	7	,	,	PUNCT
ejpam-4171	151	8	u	u	NOUN
ejpam-4171	151	9	)	)	PUNCT
ejpam-4171	151	10	,	,	PUNCT
ejpam-4171	151	11	g(c	g(c	PROPN
ejpam-4171	151	12	,	,	PUNCT
ejpam-4171	151	13	b	b	NOUN
ejpam-4171	151	14	,	,	PUNCT
ejpam-4171	151	15	a	a	DET
ejpam-4171	151	16	,	,	PUNCT
ejpam-4171	151	17	u	u	NOUN
ejpam-4171	151	18	)	)	PUNCT
ejpam-4171	151	19	)	)	PUNCT
ejpam-4171	151	20	)	)	PUNCT
ejpam-4171	151	21	≤	≤	PROPN
ejpam-4171	152	1	ψ(d(a	ψ(d(a	PROPN
ejpam-4171	152	2	,	,	PUNCT
ejpam-4171	152	3	c	c	NOUN
ejpam-4171	152	4	)	)	PUNCT
ejpam-4171	152	5	)	)	PUNCT
ejpam-4171	153	1	=	=	PUNCT
ejpam-4171	153	2	ψ(d(ga	ψ(d(ga	X
ejpam-4171	153	3	,	,	PUNCT
ejpam-4171	153	4	gc	gc	PROPN
ejpam-4171	153	5	)	)	PUNCT
ejpam-4171	153	6	)	)	PUNCT
ejpam-4171	154	1	=	=	PRON
ejpam-4171	154	2	⇒	⇒	VERB
ejpam-4171	154	3	a	a	DET
ejpam-4171	154	4	=	=	X
ejpam-4171	154	5	c.	c.	PROPN
ejpam-4171	154	6	therefore	therefore	ADV
ejpam-4171	154	7	,	,	PUNCT
ejpam-4171	154	8	ga	ga	PROPN
ejpam-4171	154	9	=	=	SYM
ejpam-4171	154	10	gb	gb	PROPN
ejpam-4171	154	11	=	=	SYM
ejpam-4171	154	12	gc	gc	PROPN
ejpam-4171	154	13	=	=	PUNCT
ejpam-4171	154	14	gu	gu	PROPN
ejpam-4171	154	15	.	.	PUNCT
ejpam-4171	154	16	to	to	PART
ejpam-4171	154	17	prove	prove	VERB
ejpam-4171	154	18	the	the	DET
ejpam-4171	154	19	uniqueness	uniqueness	NOUN
ejpam-4171	154	20	of	of	ADP
ejpam-4171	154	21	quadruple	quadruple	NOUN
ejpam-4171	154	22	g	g	NOUN
ejpam-4171	154	23	-	-	PUNCT
ejpam-4171	154	24	best	good	ADJ
ejpam-4171	154	25	proximity	proximity	NOUN
ejpam-4171	154	26	point	point	NOUN
ejpam-4171	154	27	,	,	PUNCT
ejpam-4171	154	28	consider	consider	VERB
ejpam-4171	154	29	q	q	NOUN
ejpam-4171	154	30	as	as	ADP
ejpam-4171	154	31	another	another	DET
ejpam-4171	154	32	point	point	NOUN
ejpam-4171	154	33	.	.	PUNCT
ejpam-4171	155	1	now	now	ADV
ejpam-4171	155	2	d(ga	d(ga	NOUN
ejpam-4171	155	3	,	,	PUNCT
ejpam-4171	155	4	gq	gq	PROPN
ejpam-4171	155	5	)	)	PUNCT
ejpam-4171	155	6	=	=	SYM
ejpam-4171	155	7	d(g(a	d(g(a	PROPN
ejpam-4171	155	8	,	,	PUNCT
ejpam-4171	155	9	a	a	PRON
ejpam-4171	155	10	,	,	PUNCT
ejpam-4171	155	11	a	a	PRON
ejpam-4171	155	12	,	,	PUNCT
ejpam-4171	155	13	a	a	NOUN
ejpam-4171	155	14	)	)	PUNCT
ejpam-4171	155	15	,	,	PUNCT
ejpam-4171	155	16	g(q	g(q	X
ejpam-4171	155	17	,	,	PUNCT
ejpam-4171	155	18	q	q	NOUN
ejpam-4171	155	19	,	,	PUNCT
ejpam-4171	155	20	q	q	ADJ
ejpam-4171	155	21	,	,	PUNCT
ejpam-4171	155	22	q	q	NOUN
ejpam-4171	155	23	)	)	PUNCT
ejpam-4171	155	24	)	)	PUNCT
ejpam-4171	156	1	ψ(d(ga	ψ(d(ga	NOUN
ejpam-4171	156	2	,	,	PUNCT
ejpam-4171	156	3	gq	gq	PROPN
ejpam-4171	156	4	)	)	PUNCT
ejpam-4171	156	5	)	)	PUNCT
ejpam-4171	157	1	=	=	SYM
ejpam-4171	157	2	ψ(d(g(a	ψ(d(g(a	PROPN
ejpam-4171	157	3	,	,	PUNCT
ejpam-4171	157	4	a	a	PRON
ejpam-4171	157	5	,	,	PUNCT
ejpam-4171	157	6	a	a	PRON
ejpam-4171	157	7	,	,	PUNCT
ejpam-4171	157	8	a	a	NOUN
ejpam-4171	157	9	)	)	PUNCT
ejpam-4171	157	10	,	,	PUNCT
ejpam-4171	157	11	g(q	g(q	X
ejpam-4171	157	12	,	,	PUNCT
ejpam-4171	157	13	q	q	NOUN
ejpam-4171	157	14	,	,	PUNCT
ejpam-4171	157	15	q	q	ADJ
ejpam-4171	157	16	,	,	PUNCT
ejpam-4171	157	17	q	q	NOUN
ejpam-4171	157	18	)	)	PUNCT
ejpam-4171	157	19	)	)	PUNCT
ejpam-4171	157	20	)	)	PUNCT
ejpam-4171	157	21	≤	≤	PROPN
ejpam-4171	158	1	ψ(d(a	ψ(d(a	PROPN
ejpam-4171	158	2	,	,	PUNCT
ejpam-4171	158	3	q	q	NOUN
ejpam-4171	158	4	)	)	PUNCT
ejpam-4171	158	5	)	)	PUNCT
ejpam-4171	159	1	=	=	PUNCT
ejpam-4171	159	2	ψ(d(ga	ψ(d(ga	X
ejpam-4171	159	3	,	,	PUNCT
ejpam-4171	159	4	gq	gq	PROPN
ejpam-4171	159	5	)	)	PUNCT
ejpam-4171	159	6	)	)	PUNCT
ejpam-4171	160	1	=	=	PRON
ejpam-4171	160	2	⇒	⇒	VERB
ejpam-4171	160	3	a	a	DET
ejpam-4171	160	4	=	=	NOUN
ejpam-4171	160	5	q.	q.	NOUN
ejpam-4171	160	6	hence	hence	ADV
ejpam-4171	160	7	,	,	PUNCT
ejpam-4171	160	8	the	the	DET
ejpam-4171	160	9	result	result	NOUN
ejpam-4171	160	10	.	.	PUNCT
ejpam-4171	161	1	theorem	theorem	NOUN
ejpam-4171	161	2	2	2	NUM
ejpam-4171	161	3	.	.	PUNCT
ejpam-4171	162	1	let	let	VERB
ejpam-4171	162	2	q	q	NOUN
ejpam-4171	162	3	and	and	CCONJ
ejpam-4171	162	4	r	r	NOUN
ejpam-4171	162	5	be	be	AUX
ejpam-4171	162	6	non	non	ADJ
ejpam-4171	162	7	-	-	ADJ
ejpam-4171	162	8	empty	empty	ADJ
ejpam-4171	162	9	subset	subset	NOUN
ejpam-4171	162	10	of	of	ADP
ejpam-4171	162	11	complete	complete	ADJ
ejpam-4171	162	12	metric	metric	ADJ
ejpam-4171	162	13	space	space	NOUN
ejpam-4171	162	14	(	(	PUNCT
ejpam-4171	162	15	x	x	X
ejpam-4171	162	16	,	,	PUNCT
ejpam-4171	162	17	d	d	NOUN
ejpam-4171	162	18	)	)	PUNCT
ejpam-4171	162	19	such	such	ADJ
ejpam-4171	162	20	that	that	SCONJ
ejpam-4171	162	21	q0	q0	PROPN
ejpam-4171	162	22	and	and	CCONJ
ejpam-4171	162	23	r0	r0	NOUN
ejpam-4171	162	24	are	be	AUX
ejpam-4171	162	25	non	non	ADJ
ejpam-4171	162	26	-	-	ADJ
ejpam-4171	162	27	empty	empty	ADJ
ejpam-4171	162	28	and	and	CCONJ
ejpam-4171	162	29	g	g	NOUN
ejpam-4171	162	30	:	:	PUNCT
ejpam-4171	162	31	x	x	SYM
ejpam-4171	162	32	→	→	PUNCT
ejpam-4171	162	33	x	x	X
ejpam-4171	162	34	is	be	AUX
ejpam-4171	162	35	an	an	DET
ejpam-4171	162	36	isometry	isometry	NOUN
ejpam-4171	163	1	such	such	ADJ
ejpam-4171	163	2	that	that	SCONJ
ejpam-4171	163	3	q0	q0	VERB
ejpam-4171	163	4	⊆	⊆	NUM
ejpam-4171	163	5	g(q0	g(q0	NOUN
ejpam-4171	163	6	)	)	PUNCT
ejpam-4171	163	7	and	and	CCONJ
ejpam-4171	163	8	r0	r0	VERB
ejpam-4171	163	9	⊆	⊆	NUM
ejpam-4171	163	10	g(r0	g(r0	NOUN
ejpam-4171	163	11	)	)	PUNCT
ejpam-4171	163	12	,	,	PUNCT
ejpam-4171	163	13	let	let	VERB
ejpam-4171	163	14	g	g	NOUN
ejpam-4171	163	15	:	:	PUNCT
ejpam-4171	163	16	x4	x4	PROPN
ejpam-4171	163	17	→	→	PUNCT
ejpam-4171	163	18	x	x	X
ejpam-4171	163	19	be	be	AUX
ejpam-4171	163	20	continuous	continuous	ADJ
ejpam-4171	163	21	mapping	mapping	NOUN
ejpam-4171	163	22	and	and	CCONJ
ejpam-4171	163	23	ψ	ψ	NOUN
ejpam-4171	163	24	,	,	PUNCT
ejpam-4171	163	25	ζ	ζ	PROPN
ejpam-4171	163	26	∈	∈	NOUN
ejpam-4171	163	27	ψ	ψ	NOUN
ejpam-4171	163	28	and	and	CCONJ
ejpam-4171	163	29	θ	θ	PROPN
ejpam-4171	163	30	∈	∈	PROPN
ejpam-4171	163	31	θ	θ	PROPN
ejpam-4171	163	32	,	,	PUNCT
ejpam-4171	163	33	satisfies	satisfy	VERB
ejpam-4171	163	34	the	the	DET
ejpam-4171	163	35	preceeding	preceede	VERB
ejpam-4171	163	36	conditions	condition	NOUN
ejpam-4171	163	37	:	:	PUNCT
ejpam-4171	163	38	(	(	PUNCT
ejpam-4171	163	39	i	i	NOUN
ejpam-4171	163	40	)	)	PUNCT
ejpam-4171	163	41	for	for	ADP
ejpam-4171	163	42	every	every	DET
ejpam-4171	163	43	x	x	PROPN
ejpam-4171	163	44	,	,	PUNCT
ejpam-4171	163	45	y	y	PROPN
ejpam-4171	163	46	,	,	PUNCT
ejpam-4171	163	47	z	z	PROPN
ejpam-4171	163	48	,	,	PUNCT
ejpam-4171	163	49	t	t	PROPN
ejpam-4171	163	50	,	,	PUNCT
ejpam-4171	163	51	a	a	DET
ejpam-4171	163	52	,	,	PUNCT
ejpam-4171	163	53	b	b	NOUN
ejpam-4171	163	54	,	,	PUNCT
ejpam-4171	163	55	c	c	X
ejpam-4171	163	56	,	,	PUNCT
ejpam-4171	163	57	u	u	NOUN
ejpam-4171	163	58	∈	∈	PROPN
ejpam-4171	163	59	x	x	INTJ
ejpam-4171	163	60	ψ(d(gx	ψ(d(gx	PROPN
ejpam-4171	163	61	,	,	PUNCT
ejpam-4171	163	62	ga	ga	PROPN
ejpam-4171	163	63	)	)	PUNCT
ejpam-4171	163	64	)	)	PUNCT
ejpam-4171	164	1	=	=	SYM
ejpam-4171	164	2	ψ(d(g(x	ψ(d(g(x	PROPN
ejpam-4171	164	3	,	,	PUNCT
ejpam-4171	164	4	y	y	PROPN
ejpam-4171	164	5	,	,	PUNCT
ejpam-4171	164	6	z	z	PROPN
ejpam-4171	164	7	,	,	PUNCT
ejpam-4171	164	8	t	t	PROPN
ejpam-4171	164	9	)	)	PUNCT
ejpam-4171	164	10	,	,	PUNCT
ejpam-4171	164	11	g(a	g(a	PROPN
ejpam-4171	164	12	,	,	PUNCT
ejpam-4171	164	13	b	b	PROPN
ejpam-4171	164	14	,	,	PUNCT
ejpam-4171	164	15	c	c	X
ejpam-4171	164	16	,	,	PUNCT
ejpam-4171	164	17	u	u	NOUN
ejpam-4171	164	18	)	)	PUNCT
ejpam-4171	164	19	)	)	PUNCT
ejpam-4171	164	20	)	)	PUNCT
ejpam-4171	164	21	≤ψ{max(d(x	≤ψ{max(d(x	NOUN
ejpam-4171	164	22	,	,	PUNCT
ejpam-4171	164	23	a	a	PRON
ejpam-4171	164	24	)	)	PUNCT
ejpam-4171	164	25	,	,	PUNCT
ejpam-4171	164	26	d(y	d(y	PROPN
ejpam-4171	164	27	,	,	PUNCT
ejpam-4171	164	28	b	b	NOUN
ejpam-4171	164	29	)	)	PUNCT
ejpam-4171	164	30	,	,	PUNCT
ejpam-4171	164	31	d(z	d(z	PROPN
ejpam-4171	164	32	,	,	PUNCT
ejpam-4171	164	33	c	c	NOUN
ejpam-4171	164	34	)	)	PUNCT
ejpam-4171	164	35	,	,	PUNCT
ejpam-4171	164	36	d(t	d(t	PROPN
ejpam-4171	164	37	,	,	PUNCT
ejpam-4171	164	38	u	u	NOUN
ejpam-4171	164	39	)	)	PUNCT
ejpam-4171	164	40	)	)	PUNCT
ejpam-4171	164	41	}	}	PUNCT
ejpam-4171	164	42	−	−	ADP
ejpam-4171	164	43	ζ{max(d(x	ζ{max(d(x	NOUN
ejpam-4171	164	44	,	,	PUNCT
ejpam-4171	164	45	a	a	PRON
ejpam-4171	164	46	)	)	PUNCT
ejpam-4171	164	47	,	,	PUNCT
ejpam-4171	164	48	d(y	d(y	PROPN
ejpam-4171	164	49	,	,	PUNCT
ejpam-4171	164	50	b	b	NOUN
ejpam-4171	164	51	)	)	PUNCT
ejpam-4171	164	52	,	,	PUNCT
ejpam-4171	164	53	d(z	d(z	PROPN
ejpam-4171	164	54	,	,	PUNCT
ejpam-4171	164	55	c	c	NOUN
ejpam-4171	164	56	)	)	PUNCT
ejpam-4171	164	57	,	,	PUNCT
ejpam-4171	164	58	d(t	d(t	PROPN
ejpam-4171	164	59	,	,	PUNCT
ejpam-4171	164	60	u	u	NOUN
ejpam-4171	164	61	)	)	PUNCT
ejpam-4171	164	62	)	)	PUNCT
ejpam-4171	164	63	}	}	PUNCT
ejpam-4171	164	64	+	+	CCONJ
ejpam-4171	164	65	θ[d(ga	θ[d(ga	ADJ
ejpam-4171	164	66	,	,	PUNCT
ejpam-4171	164	67	g(x	g(x	PROPN
ejpam-4171	164	68	,	,	PUNCT
ejpam-4171	164	69	y	y	PROPN
ejpam-4171	164	70	,	,	PUNCT
ejpam-4171	164	71	z	z	PROPN
ejpam-4171	164	72	,	,	PUNCT
ejpam-4171	164	73	t))−	t))−	PROPN
ejpam-4171	164	74	d(q	d(q	PROPN
ejpam-4171	164	75	,	,	PUNCT
ejpam-4171	164	76	r	r	NOUN
ejpam-4171	164	77	)	)	PUNCT
ejpam-4171	164	78	,	,	PUNCT
ejpam-4171	164	79	d(gb	d(gb	NOUN
ejpam-4171	164	80	,	,	PUNCT
ejpam-4171	164	81	g(y	g(y	PROPN
ejpam-4171	164	82	,	,	PUNCT
ejpam-4171	164	83	x	x	X
ejpam-4171	164	84	,	,	PUNCT
ejpam-4171	164	85	z	z	PROPN
ejpam-4171	164	86	,	,	PUNCT
ejpam-4171	164	87	t))−	t))−	PROPN
ejpam-4171	164	88	d(q	d(q	PROPN
ejpam-4171	164	89	,	,	PUNCT
ejpam-4171	164	90	r	r	NOUN
ejpam-4171	164	91	)	)	PUNCT
ejpam-4171	164	92	,	,	PUNCT
ejpam-4171	164	93	d(gc	d(gc	PROPN
ejpam-4171	164	94	,	,	PUNCT
ejpam-4171	164	95	g(z	g(z	PROPN
ejpam-4171	164	96	,	,	PUNCT
ejpam-4171	164	97	y	y	PROPN
ejpam-4171	164	98	,	,	PUNCT
ejpam-4171	164	99	x	x	NOUN
ejpam-4171	164	100	,	,	PUNCT
ejpam-4171	164	101	t))−	t))−	PROPN
ejpam-4171	164	102	d(q	d(q	PROPN
ejpam-4171	164	103	,	,	PUNCT
ejpam-4171	164	104	r	r	NOUN
ejpam-4171	164	105	)	)	PUNCT
ejpam-4171	164	106	,	,	PUNCT
ejpam-4171	164	107	d(gu	d(gu	PROPN
ejpam-4171	164	108	,	,	PUNCT
ejpam-4171	164	109	g(t	g(t	PROPN
ejpam-4171	164	110	,	,	PUNCT
ejpam-4171	164	111	y	y	PROPN
ejpam-4171	164	112	,	,	PUNCT
ejpam-4171	164	113	z	z	PROPN
ejpam-4171	164	114	,	,	PUNCT
ejpam-4171	164	115	x))−	x))−	PROPN
ejpam-4171	164	116	d(q	d(q	PROPN
ejpam-4171	164	117	,	,	PUNCT
ejpam-4171	164	118	r	r	NOUN
ejpam-4171	164	119	)	)	PUNCT
ejpam-4171	164	120	,	,	PUNCT
ejpam-4171	164	121	d(gx	d(gx	PROPN
ejpam-4171	164	122	,	,	PUNCT
ejpam-4171	164	123	g(x	g(x	PROPN
ejpam-4171	164	124	,	,	PUNCT
ejpam-4171	164	125	y	y	PROPN
ejpam-4171	164	126	,	,	PUNCT
ejpam-4171	164	127	z	z	PROPN
ejpam-4171	164	128	,	,	PUNCT
ejpam-4171	164	129	t))−	t))−	PROPN
ejpam-4171	164	130	d(q	d(q	PROPN
ejpam-4171	164	131	,	,	PUNCT
ejpam-4171	164	132	r	r	NOUN
ejpam-4171	164	133	)	)	PUNCT
ejpam-4171	164	134	,	,	PUNCT
ejpam-4171	164	135	d(gy	d(gy	PROPN
ejpam-4171	164	136	,	,	PUNCT
ejpam-4171	164	137	g(y	g(y	PROPN
ejpam-4171	164	138	,	,	PUNCT
ejpam-4171	164	139	x	x	X
ejpam-4171	164	140	,	,	PUNCT
ejpam-4171	164	141	z	z	PROPN
ejpam-4171	164	142	,	,	PUNCT
ejpam-4171	164	143	t))−	t))−	PROPN
ejpam-4171	164	144	d(q	d(q	PROPN
ejpam-4171	164	145	,	,	PUNCT
ejpam-4171	164	146	r	r	NOUN
ejpam-4171	164	147	)	)	PUNCT
ejpam-4171	164	148	,	,	PUNCT
ejpam-4171	164	149	d(gz	d(gz	PROPN
ejpam-4171	164	150	,	,	PUNCT
ejpam-4171	164	151	g(z	g(z	PROPN
ejpam-4171	164	152	,	,	PUNCT
ejpam-4171	164	153	y	y	PROPN
ejpam-4171	164	154	,	,	PUNCT
ejpam-4171	164	155	x	x	NOUN
ejpam-4171	164	156	,	,	PUNCT
ejpam-4171	164	157	t))−	t))−	PROPN
ejpam-4171	164	158	d(q	d(q	PROPN
ejpam-4171	164	159	,	,	PUNCT
ejpam-4171	164	160	r	r	NOUN
ejpam-4171	164	161	)	)	PUNCT
ejpam-4171	164	162	,	,	PUNCT
ejpam-4171	164	163	d(gt	d(gt	PROPN
ejpam-4171	164	164	,	,	PUNCT
ejpam-4171	164	165	g(t	g(t	PROPN
ejpam-4171	164	166	,	,	PUNCT
ejpam-4171	164	167	y	y	PROPN
ejpam-4171	164	168	,	,	PUNCT
ejpam-4171	164	169	z	z	PROPN
ejpam-4171	164	170	,	,	PUNCT
ejpam-4171	164	171	x))−	x))−	PROPN
ejpam-4171	164	172	d(q	d(q	PROPN
ejpam-4171	164	173	,	,	PUNCT
ejpam-4171	164	174	r	r	NOUN
ejpam-4171	164	175	)	)	PUNCT
ejpam-4171	164	176	]	]	PUNCT
ejpam-4171	164	177	(	(	PUNCT
ejpam-4171	164	178	10	10	NUM
ejpam-4171	164	179	)	)	PUNCT
ejpam-4171	164	180	(	(	PUNCT
ejpam-4171	164	181	ii	ii	NOUN
ejpam-4171	164	182	)	)	PUNCT
ejpam-4171	164	183	g(q0,q0,q0,q0	g(q0,q0,q0,q0	ADP
ejpam-4171	164	184	)	)	PUNCT
ejpam-4171	164	185	⊆	⊆	X
ejpam-4171	164	186	r0	r0	NOUN
ejpam-4171	164	187	(	(	PUNCT
ejpam-4171	164	188	iii	iii	NOUN
ejpam-4171	164	189	)	)	PUNCT
ejpam-4171	164	190	g(r0,r0,r0,r0	g(r0,r0,r0,r0	NOUN
ejpam-4171	164	191	)	)	PUNCT
ejpam-4171	164	192	⊆	⊆	NUM
ejpam-4171	164	193	q0	q0	PROPN
ejpam-4171	164	194	(	(	PUNCT
ejpam-4171	164	195	iv	iv	NOUN
ejpam-4171	164	196	)	)	PUNCT
ejpam-4171	164	197	pair	pair	NOUN
ejpam-4171	164	198	(	(	PUNCT
ejpam-4171	164	199	q	q	NOUN
ejpam-4171	164	200	,	,	PUNCT
ejpam-4171	164	201	r	r	NOUN
ejpam-4171	164	202	)	)	PUNCT
ejpam-4171	164	203	has	have	VERB
ejpam-4171	164	204	p	p	NOUN
ejpam-4171	164	205	-	-	PUNCT
ejpam-4171	164	206	property	property	NOUN
ejpam-4171	164	207	then	then	ADV
ejpam-4171	164	208	(	(	PUNCT
ejpam-4171	164	209	a	a	DET
ejpam-4171	164	210	,	,	PUNCT
ejpam-4171	164	211	a	a	PRON
ejpam-4171	164	212	,	,	PUNCT
ejpam-4171	164	213	a	a	DET
ejpam-4171	164	214	,	,	PUNCT
ejpam-4171	164	215	a	a	PRON
ejpam-4171	164	216	)	)	PUNCT
ejpam-4171	164	217	is	be	AUX
ejpam-4171	164	218	the	the	DET
ejpam-4171	164	219	unique	unique	ADJ
ejpam-4171	164	220	quadruple	quadruple	NOUN
ejpam-4171	164	221	g	g	NOUN
ejpam-4171	164	222	-	-	PUNCT
ejpam-4171	164	223	best	good	ADJ
ejpam-4171	164	224	proximity	proximity	NOUN
ejpam-4171	164	225	point	point	NOUN
ejpam-4171	164	226	of	of	ADP
ejpam-4171	164	227	the	the	DET
ejpam-4171	164	228	pair	pair	NOUN
ejpam-4171	164	229	(	(	PUNCT
ejpam-4171	164	230	g	g	NOUN
ejpam-4171	164	231	,	,	PUNCT
ejpam-4171	164	232	g	g	NOUN
ejpam-4171	164	233	)	)	PUNCT
ejpam-4171	164	234	.	.	PUNCT
ejpam-4171	165	1	proof	proof	NOUN
ejpam-4171	165	2	.	.	PUNCT
ejpam-4171	166	1	consider	consider	VERB
ejpam-4171	166	2	x0	x0	PROPN
ejpam-4171	166	3	,	,	PUNCT
ejpam-4171	166	4	y0	y0	PROPN
ejpam-4171	166	5	,	,	PUNCT
ejpam-4171	166	6	z0	z0	PROPN
ejpam-4171	166	7	,	,	PUNCT
ejpam-4171	166	8	t0	t0	PROPN
ejpam-4171	166	9	∈	∈	PROPN
ejpam-4171	166	10	q0	q0	PROPN
ejpam-4171	166	11	theng(x0	theng(x0	NOUN
ejpam-4171	166	12	,	,	PUNCT
ejpam-4171	166	13	y0	y0	PROPN
ejpam-4171	166	14	,	,	PUNCT
ejpam-4171	166	15	z0	z0	PROPN
ejpam-4171	166	16	,	,	PUNCT
ejpam-4171	166	17	t0	t0	PROPN
ejpam-4171	166	18	)	)	PUNCT
ejpam-4171	166	19	,	,	PUNCT
ejpam-4171	166	20	g(y0	g(y0	NOUN
ejpam-4171	166	21	,	,	PUNCT
ejpam-4171	166	22	x0	x0	PROPN
ejpam-4171	166	23	,	,	PUNCT
ejpam-4171	166	24	z0	z0	PROPN
ejpam-4171	166	25	,	,	PUNCT
ejpam-4171	166	26	t0	t0	PROPN
ejpam-4171	166	27	)	)	PUNCT
ejpam-4171	166	28	,	,	PUNCT
ejpam-4171	166	29	g(z0	g(z0	NOUN
ejpam-4171	166	30	,	,	PUNCT
ejpam-4171	166	31	y0	y0	PROPN
ejpam-4171	166	32	,	,	PUNCT
ejpam-4171	166	33	x0	x0	PROPN
ejpam-4171	166	34	,	,	PUNCT
ejpam-4171	166	35	t0	t0	PROPN
ejpam-4171	166	36	)	)	PUNCT
ejpam-4171	166	37	and	and	CCONJ
ejpam-4171	166	38	g(t0	g(t0	NOUN
ejpam-4171	166	39	,	,	PUNCT
ejpam-4171	166	40	y0	y0	PROPN
ejpam-4171	166	41	,	,	PUNCT
ejpam-4171	166	42	z0	z0	PROPN
ejpam-4171	166	43	,	,	PUNCT
ejpam-4171	166	44	x0	x0	PROPN
ejpam-4171	166	45	)	)	PUNCT
ejpam-4171	166	46	∈	∈	PROPN
ejpam-4171	166	47	r0	r0	NOUN
ejpam-4171	166	48	.	.	PUNCT
ejpam-4171	167	1	then	then	ADV
ejpam-4171	167	2	by	by	ADP
ejpam-4171	167	3	the	the	DET
ejpam-4171	167	4	same	same	ADJ
ejpam-4171	167	5	process	process	NOUN
ejpam-4171	167	6	as	as	ADP
ejpam-4171	167	7	in	in	ADP
ejpam-4171	167	8	theorem	theorem	NOUN
ejpam-4171	167	9	(	(	PUNCT
ejpam-4171	167	10	1	1	NUM
ejpam-4171	167	11	)	)	PUNCT
ejpam-4171	167	12	,	,	PUNCT
ejpam-4171	167	13	we	we	PRON
ejpam-4171	167	14	obtain	obtain	VERB
ejpam-4171	167	15	(	(	PUNCT
ejpam-4171	167	16	a	a	PRON
ejpam-4171	167	17	,	,	PUNCT
ejpam-4171	167	18	a	a	PRON
ejpam-4171	167	19	,	,	PUNCT
ejpam-4171	167	20	a	a	PRON
ejpam-4171	167	21	,	,	PUNCT
ejpam-4171	167	22	a	a	NOUN
ejpam-4171	167	23	)	)	PUNCT
ejpam-4171	167	24	as	as	ADP
ejpam-4171	167	25	the	the	DET
ejpam-4171	167	26	unique	unique	ADJ
ejpam-4171	167	27	quadruple	quadruple	NOUN
ejpam-4171	167	28	g	g	NOUN
ejpam-4171	167	29	-	-	PUNCT
ejpam-4171	167	30	best	good	ADJ
ejpam-4171	167	31	proximity	proximity	NOUN
ejpam-4171	167	32	point	point	NOUN
ejpam-4171	167	33	of	of	ADP
ejpam-4171	167	34	the	the	DET
ejpam-4171	167	35	pair	pair	NOUN
ejpam-4171	167	36	(	(	PUNCT
ejpam-4171	167	37	g	g	NOUN
ejpam-4171	167	38	,	,	PUNCT
ejpam-4171	167	39	g	g	NOUN
ejpam-4171	167	40	)	)	PUNCT
ejpam-4171	167	41	.	.	PUNCT
ejpam-4171	168	1	references	reference	VERB
ejpam-4171	168	2	142	142	NUM
ejpam-4171	168	3	corollary	corollary	ADJ
ejpam-4171	168	4	1	1	NUM
ejpam-4171	168	5	.	.	PUNCT
ejpam-4171	169	1	let	let	VERB
ejpam-4171	169	2	q	q	PART
ejpam-4171	169	3	be	be	AUX
ejpam-4171	169	4	non	non	ADJ
ejpam-4171	169	5	-	-	ADJ
ejpam-4171	169	6	empty	empty	ADJ
ejpam-4171	169	7	subset	subset	NOUN
ejpam-4171	169	8	of	of	ADP
ejpam-4171	169	9	complete	complete	ADJ
ejpam-4171	169	10	metric	metric	ADJ
ejpam-4171	169	11	space	space	NOUN
ejpam-4171	169	12	(	(	PUNCT
ejpam-4171	169	13	x	x	X
ejpam-4171	169	14	,	,	PUNCT
ejpam-4171	169	15	d	d	NOUN
ejpam-4171	169	16	)	)	PUNCT
ejpam-4171	169	17	such	such	ADJ
ejpam-4171	169	18	that	that	SCONJ
ejpam-4171	169	19	q0	q0	PROPN
ejpam-4171	169	20	is	be	AUX
ejpam-4171	169	21	non	non	ADJ
ejpam-4171	169	22	-	-	ADJ
ejpam-4171	169	23	empty	empty	ADJ
ejpam-4171	169	24	and	and	CCONJ
ejpam-4171	169	25	g	g	NOUN
ejpam-4171	169	26	:	:	PUNCT
ejpam-4171	169	27	x	x	SYM
ejpam-4171	169	28	→	→	PUNCT
ejpam-4171	169	29	x	x	PART
ejpam-4171	169	30	be	be	AUX
ejpam-4171	169	31	mapping	map	VERB
ejpam-4171	169	32	such	such	ADJ
ejpam-4171	169	33	that	that	PRON
ejpam-4171	169	34	q	q	PROPN
ejpam-4171	169	35	⊆	⊆	NUM
ejpam-4171	169	36	g(q	g(q	NOUN
ejpam-4171	169	37	)	)	PUNCT
ejpam-4171	169	38	and	and	CCONJ
ejpam-4171	169	39	r	r	NOUN
ejpam-4171	169	40	⊆	⊆	NUM
ejpam-4171	169	41	g(r	g(r	NOUN
ejpam-4171	169	42	)	)	PUNCT
ejpam-4171	169	43	,	,	PUNCT
ejpam-4171	169	44	let	let	VERB
ejpam-4171	169	45	g	g	NOUN
ejpam-4171	169	46	:	:	PUNCT
ejpam-4171	169	47	x4	x4	PROPN
ejpam-4171	169	48	→	→	PUNCT
ejpam-4171	169	49	x	x	X
ejpam-4171	169	50	be	be	AUX
ejpam-4171	169	51	continuous	continuous	ADJ
ejpam-4171	169	52	mapping	mapping	NOUN
ejpam-4171	169	53	and	and	CCONJ
ejpam-4171	169	54	ψ	ψ	NOUN
ejpam-4171	169	55	,	,	PUNCT
ejpam-4171	169	56	ζ	ζ	PROPN
ejpam-4171	169	57	∈	∈	NOUN
ejpam-4171	169	58	ψ	ψ	NOUN
ejpam-4171	169	59	and	and	CCONJ
ejpam-4171	169	60	θ	θ	PROPN
ejpam-4171	169	61	∈	∈	PROPN
ejpam-4171	169	62	θ	θ	PROPN
ejpam-4171	169	63	,	,	PUNCT
ejpam-4171	169	64	satisfies	satisfy	VERB
ejpam-4171	169	65	the	the	DET
ejpam-4171	169	66	preceeding	preceede	VERB
ejpam-4171	169	67	conditions	condition	NOUN
ejpam-4171	169	68	:	:	PUNCT
ejpam-4171	169	69	(	(	PUNCT
ejpam-4171	169	70	i	i	NOUN
ejpam-4171	169	71	)	)	PUNCT
ejpam-4171	169	72	for	for	ADP
ejpam-4171	169	73	every	every	DET
ejpam-4171	169	74	x	x	PROPN
ejpam-4171	169	75	,	,	PUNCT
ejpam-4171	169	76	y	y	PROPN
ejpam-4171	169	77	,	,	PUNCT
ejpam-4171	169	78	z	z	PROPN
ejpam-4171	169	79	,	,	PUNCT
ejpam-4171	169	80	t	t	PROPN
ejpam-4171	169	81	,	,	PUNCT
ejpam-4171	169	82	a	a	DET
ejpam-4171	169	83	,	,	PUNCT
ejpam-4171	169	84	b	b	NOUN
ejpam-4171	169	85	,	,	PUNCT
ejpam-4171	169	86	c	c	X
ejpam-4171	169	87	,	,	PUNCT
ejpam-4171	169	88	u	u	NOUN
ejpam-4171	169	89	∈	∈	PROPN
ejpam-4171	169	90	x	x	INTJ
ejpam-4171	169	91	ψ(d(gx	ψ(d(gx	PROPN
ejpam-4171	169	92	,	,	PUNCT
ejpam-4171	169	93	ga	ga	PROPN
ejpam-4171	169	94	)	)	PUNCT
ejpam-4171	169	95	)	)	PUNCT
ejpam-4171	170	1	=	=	SYM
ejpam-4171	170	2	ψ(d(g(x	ψ(d(g(x	PROPN
ejpam-4171	170	3	,	,	PUNCT
ejpam-4171	170	4	y	y	PROPN
ejpam-4171	170	5	,	,	PUNCT
ejpam-4171	170	6	z	z	PROPN
ejpam-4171	170	7	,	,	PUNCT
ejpam-4171	170	8	t	t	PROPN
ejpam-4171	170	9	)	)	PUNCT
ejpam-4171	170	10	,	,	PUNCT
ejpam-4171	170	11	g(a	g(a	PROPN
ejpam-4171	170	12	,	,	PUNCT
ejpam-4171	170	13	b	b	PROPN
ejpam-4171	170	14	,	,	PUNCT
ejpam-4171	170	15	c	c	X
ejpam-4171	170	16	,	,	PUNCT
ejpam-4171	170	17	u	u	NOUN
ejpam-4171	170	18	)	)	PUNCT
ejpam-4171	170	19	)	)	PUNCT
ejpam-4171	170	20	)	)	PUNCT
ejpam-4171	170	21	≤ψ{max(d(x	≤ψ{max(d(x	NOUN
ejpam-4171	170	22	,	,	PUNCT
ejpam-4171	170	23	a	a	PRON
ejpam-4171	170	24	)	)	PUNCT
ejpam-4171	170	25	,	,	PUNCT
ejpam-4171	170	26	d(y	d(y	PROPN
ejpam-4171	170	27	,	,	PUNCT
ejpam-4171	170	28	b	b	NOUN
ejpam-4171	170	29	)	)	PUNCT
ejpam-4171	170	30	,	,	PUNCT
ejpam-4171	170	31	d(z	d(z	PROPN
ejpam-4171	170	32	,	,	PUNCT
ejpam-4171	170	33	c	c	NOUN
ejpam-4171	170	34	)	)	PUNCT
ejpam-4171	170	35	,	,	PUNCT
ejpam-4171	170	36	d(t	d(t	PROPN
ejpam-4171	170	37	,	,	PUNCT
ejpam-4171	170	38	u	u	NOUN
ejpam-4171	170	39	)	)	PUNCT
ejpam-4171	170	40	)	)	PUNCT
ejpam-4171	170	41	}	}	PUNCT
ejpam-4171	170	42	−	−	ADP
ejpam-4171	170	43	ζ{max(d(x	ζ{max(d(x	NOUN
ejpam-4171	170	44	,	,	PUNCT
ejpam-4171	170	45	a	a	PRON
ejpam-4171	170	46	)	)	PUNCT
ejpam-4171	170	47	,	,	PUNCT
ejpam-4171	170	48	d(y	d(y	PROPN
ejpam-4171	170	49	,	,	PUNCT
ejpam-4171	170	50	b	b	NOUN
ejpam-4171	170	51	)	)	PUNCT
ejpam-4171	170	52	,	,	PUNCT
ejpam-4171	170	53	d(z	d(z	PROPN
ejpam-4171	170	54	,	,	PUNCT
ejpam-4171	170	55	c	c	NOUN
ejpam-4171	170	56	)	)	PUNCT
ejpam-4171	170	57	,	,	PUNCT
ejpam-4171	170	58	d(t	d(t	PROPN
ejpam-4171	170	59	,	,	PUNCT
ejpam-4171	170	60	u	u	NOUN
ejpam-4171	170	61	)	)	PUNCT
ejpam-4171	170	62	)	)	PUNCT
ejpam-4171	170	63	}	}	PUNCT
ejpam-4171	170	64	+	+	CCONJ
ejpam-4171	170	65	θ[d(ga	θ[d(ga	ADJ
ejpam-4171	170	66	,	,	PUNCT
ejpam-4171	170	67	g(x	g(x	PROPN
ejpam-4171	170	68	,	,	PUNCT
ejpam-4171	170	69	y	y	PROPN
ejpam-4171	170	70	,	,	PUNCT
ejpam-4171	170	71	z	z	PROPN
ejpam-4171	170	72	,	,	PUNCT
ejpam-4171	170	73	t))−	t))−	PROPN
ejpam-4171	170	74	d(q	d(q	PROPN
ejpam-4171	170	75	,	,	PUNCT
ejpam-4171	170	76	r	r	NOUN
ejpam-4171	170	77	)	)	PUNCT
ejpam-4171	170	78	,	,	PUNCT
ejpam-4171	170	79	d(gb	d(gb	NOUN
ejpam-4171	170	80	,	,	PUNCT
ejpam-4171	170	81	g(y	g(y	PROPN
ejpam-4171	170	82	,	,	PUNCT
ejpam-4171	170	83	x	x	X
ejpam-4171	170	84	,	,	PUNCT
ejpam-4171	170	85	z	z	PROPN
ejpam-4171	170	86	,	,	PUNCT
ejpam-4171	170	87	t))−	t))−	PROPN
ejpam-4171	170	88	d(q	d(q	PROPN
ejpam-4171	170	89	,	,	PUNCT
ejpam-4171	170	90	r	r	NOUN
ejpam-4171	170	91	)	)	PUNCT
ejpam-4171	170	92	,	,	PUNCT
ejpam-4171	170	93	d(gc	d(gc	PROPN
ejpam-4171	170	94	,	,	PUNCT
ejpam-4171	170	95	g(z	g(z	PROPN
ejpam-4171	170	96	,	,	PUNCT
ejpam-4171	170	97	y	y	PROPN
ejpam-4171	170	98	,	,	PUNCT
ejpam-4171	170	99	x	x	NOUN
ejpam-4171	170	100	,	,	PUNCT
ejpam-4171	170	101	t))−	t))−	PROPN
ejpam-4171	170	102	d(q	d(q	PROPN
ejpam-4171	170	103	,	,	PUNCT
ejpam-4171	170	104	r	r	NOUN
ejpam-4171	170	105	)	)	PUNCT
ejpam-4171	170	106	,	,	PUNCT
ejpam-4171	170	107	d(gu	d(gu	PROPN
ejpam-4171	170	108	,	,	PUNCT
ejpam-4171	170	109	g(t	g(t	PROPN
ejpam-4171	170	110	,	,	PUNCT
ejpam-4171	170	111	y	y	PROPN
ejpam-4171	170	112	,	,	PUNCT
ejpam-4171	170	113	z	z	PROPN
ejpam-4171	170	114	,	,	PUNCT
ejpam-4171	170	115	x))−	x))−	PROPN
ejpam-4171	170	116	d(q	d(q	PROPN
ejpam-4171	170	117	,	,	PUNCT
ejpam-4171	170	118	r	r	NOUN
ejpam-4171	170	119	)	)	PUNCT
ejpam-4171	170	120	,	,	PUNCT
ejpam-4171	170	121	d(gx	d(gx	PROPN
ejpam-4171	170	122	,	,	PUNCT
ejpam-4171	170	123	g(x	g(x	PROPN
ejpam-4171	170	124	,	,	PUNCT
ejpam-4171	170	125	y	y	PROPN
ejpam-4171	170	126	,	,	PUNCT
ejpam-4171	170	127	z	z	PROPN
ejpam-4171	170	128	,	,	PUNCT
ejpam-4171	170	129	t))−	t))−	PROPN
ejpam-4171	170	130	d(q	d(q	PROPN
ejpam-4171	170	131	,	,	PUNCT
ejpam-4171	170	132	r	r	NOUN
ejpam-4171	170	133	)	)	PUNCT
ejpam-4171	170	134	,	,	PUNCT
ejpam-4171	170	135	d(gy	d(gy	PROPN
ejpam-4171	170	136	,	,	PUNCT
ejpam-4171	170	137	g(y	g(y	PROPN
ejpam-4171	170	138	,	,	PUNCT
ejpam-4171	170	139	x	x	X
ejpam-4171	170	140	,	,	PUNCT
ejpam-4171	170	141	z	z	PROPN
ejpam-4171	170	142	,	,	PUNCT
ejpam-4171	170	143	t))−	t))−	PROPN
ejpam-4171	170	144	d(q	d(q	PROPN
ejpam-4171	170	145	,	,	PUNCT
ejpam-4171	170	146	r	r	NOUN
ejpam-4171	170	147	)	)	PUNCT
ejpam-4171	170	148	,	,	PUNCT
ejpam-4171	170	149	d(gz	d(gz	PROPN
ejpam-4171	170	150	,	,	PUNCT
ejpam-4171	170	151	g(z	g(z	PROPN
ejpam-4171	170	152	,	,	PUNCT
ejpam-4171	170	153	y	y	PROPN
ejpam-4171	170	154	,	,	PUNCT
ejpam-4171	170	155	x	x	NOUN
ejpam-4171	170	156	,	,	PUNCT
ejpam-4171	170	157	t))−	t))−	PROPN
ejpam-4171	170	158	d(q	d(q	PROPN
ejpam-4171	170	159	,	,	PUNCT
ejpam-4171	170	160	r	r	NOUN
ejpam-4171	170	161	)	)	PUNCT
ejpam-4171	170	162	,	,	PUNCT
ejpam-4171	170	163	d(gt	d(gt	PROPN
ejpam-4171	170	164	,	,	PUNCT
ejpam-4171	170	165	g(t	g(t	PROPN
ejpam-4171	170	166	,	,	PUNCT
ejpam-4171	170	167	y	y	PROPN
ejpam-4171	170	168	,	,	PUNCT
ejpam-4171	170	169	z	z	PROPN
ejpam-4171	170	170	,	,	PUNCT
ejpam-4171	170	171	x))−	x))−	PROPN
ejpam-4171	170	172	d(q	d(q	PROPN
ejpam-4171	170	173	,	,	PUNCT
ejpam-4171	170	174	r	r	NOUN
ejpam-4171	170	175	)	)	PUNCT
ejpam-4171	170	176	]	]	PUNCT
ejpam-4171	170	177	(	(	PUNCT
ejpam-4171	170	178	11	11	NUM
ejpam-4171	170	179	)	)	PUNCT
ejpam-4171	170	180	(	(	PUNCT
ejpam-4171	170	181	ii	ii	NOUN
ejpam-4171	170	182	)	)	PUNCT
ejpam-4171	170	183	g(q	g(q	NOUN
ejpam-4171	170	184	,	,	PUNCT
ejpam-4171	170	185	q	q	NOUN
ejpam-4171	170	186	,	,	PUNCT
ejpam-4171	170	187	q	q	NOUN
ejpam-4171	170	188	,	,	PUNCT
ejpam-4171	170	189	q	q	NOUN
ejpam-4171	170	190	)	)	PUNCT
ejpam-4171	170	191	⊆	⊆	NUM
ejpam-4171	170	192	q	q	X
ejpam-4171	170	193	(	(	PUNCT
ejpam-4171	170	194	iii	iii	NOUN
ejpam-4171	170	195	)	)	PUNCT
ejpam-4171	170	196	g	g	NOUN
ejpam-4171	170	197	is	be	AUX
ejpam-4171	170	198	an	an	DET
ejpam-4171	170	199	isometry	isometry	NOUN
ejpam-4171	170	200	then	then	ADV
ejpam-4171	170	201	(	(	PUNCT
ejpam-4171	170	202	a	a	DET
ejpam-4171	170	203	,	,	PUNCT
ejpam-4171	170	204	a	a	PRON
ejpam-4171	170	205	,	,	PUNCT
ejpam-4171	170	206	a	a	DET
ejpam-4171	170	207	,	,	PUNCT
ejpam-4171	170	208	a	a	PRON
ejpam-4171	170	209	)	)	PUNCT
ejpam-4171	170	210	is	be	AUX
ejpam-4171	170	211	the	the	DET
ejpam-4171	170	212	unique	unique	ADJ
ejpam-4171	170	213	quadruple	quadruple	NOUN
ejpam-4171	170	214	g	g	NOUN
ejpam-4171	170	215	-	-	PUNCT
ejpam-4171	170	216	fixed	fix	VERB
ejpam-4171	170	217	point	point	NOUN
ejpam-4171	170	218	of	of	ADP
ejpam-4171	170	219	the	the	DET
ejpam-4171	170	220	pair	pair	NOUN
ejpam-4171	170	221	(	(	PUNCT
ejpam-4171	170	222	g	g	NOUN
ejpam-4171	170	223	,	,	PUNCT
ejpam-4171	170	224	g	g	NOUN
ejpam-4171	170	225	)	)	PUNCT
ejpam-4171	170	226	.	.	PUNCT
ejpam-4171	171	1	proof	proof	NOUN
ejpam-4171	171	2	.	.	PUNCT
ejpam-4171	172	1	by	by	ADP
ejpam-4171	172	2	taking	take	VERB
ejpam-4171	172	3	q	q	NOUN
ejpam-4171	172	4	=	=	NOUN
ejpam-4171	172	5	r	r	NOUN
ejpam-4171	172	6	in	in	ADP
ejpam-4171	172	7	theorem	theorem	NOUN
ejpam-4171	172	8	(	(	PUNCT
ejpam-4171	172	9	1	1	NUM
ejpam-4171	172	10	)	)	PUNCT
ejpam-4171	172	11	,	,	PUNCT
ejpam-4171	172	12	we	we	PRON
ejpam-4171	172	13	have	have	VERB
ejpam-4171	172	14	the	the	DET
ejpam-4171	172	15	desired	desire	VERB
ejpam-4171	172	16	result	result	NOUN
ejpam-4171	172	17	.	.	PUNCT
ejpam-4171	173	1	example	example	NOUN
ejpam-4171	173	2	1	1	X
ejpam-4171	173	3	.	.	X
ejpam-4171	174	1	consider	consider	VERB
ejpam-4171	174	2	x	x	PUNCT
ejpam-4171	174	3	=	=	PUNCT
ejpam-4171	175	1	[	[	X
ejpam-4171	175	2	1	1	NUM
ejpam-4171	175	3	,	,	PUNCT
ejpam-4171	175	4	5	5	NUM
ejpam-4171	175	5	]	]	PUNCT
ejpam-4171	175	6	with	with	ADP
ejpam-4171	175	7	d(x	d(x	PROPN
ejpam-4171	175	8	,	,	PUNCT
ejpam-4171	175	9	y	y	NOUN
ejpam-4171	175	10	)	)	PUNCT
ejpam-4171	175	11	=	=	PUNCT
ejpam-4171	176	1	∥x	∥x	PROPN
ejpam-4171	176	2	−	−	NUM
ejpam-4171	177	1	y∥for	y∥for	ADP
ejpam-4171	177	2	all	all	DET
ejpam-4171	177	3	x	x	NOUN
ejpam-4171	177	4	,	,	PUNCT
ejpam-4171	177	5	y	y	PROPN
ejpam-4171	177	6	∈	∈	PROPN
ejpam-4171	177	7	x.	x.	NOUN
ejpam-4171	177	8	let	let	VERB
ejpam-4171	177	9	q	q	NOUN
ejpam-4171	177	10	=	=	PUNCT
ejpam-4171	178	1	[	[	X
ejpam-4171	178	2	2	2	NUM
ejpam-4171	178	3	,	,	PUNCT
ejpam-4171	178	4	3	3	NUM
ejpam-4171	178	5	]	]	PUNCT
ejpam-4171	178	6	and	and	CCONJ
ejpam-4171	178	7	r	r	NOUN
ejpam-4171	178	8	=	=	SYM
ejpam-4171	179	1	[	[	X
ejpam-4171	179	2	3	3	NUM
ejpam-4171	179	3	,	,	PUNCT
ejpam-4171	179	4	4	4	NUM
ejpam-4171	179	5	]	]	PUNCT
ejpam-4171	179	6	be	be	AUX
ejpam-4171	179	7	subsets	subset	NOUN
ejpam-4171	179	8	of	of	ADP
ejpam-4171	179	9	x	x	X
ejpam-4171	179	10	and	and	CCONJ
ejpam-4171	179	11	g	g	PROPN
ejpam-4171	179	12	:	:	PUNCT
ejpam-4171	179	13	x4	x4	PROPN
ejpam-4171	179	14	→	→	SYM
ejpam-4171	179	15	x	x	SYM
ejpam-4171	179	16	,	,	PUNCT
ejpam-4171	179	17	g	g	NOUN
ejpam-4171	179	18	:	:	PUNCT
ejpam-4171	179	19	q	q	X
ejpam-4171	179	20	→	→	PUNCT
ejpam-4171	179	21	q	q	X
ejpam-4171	179	22	both	both	PRON
ejpam-4171	179	23	are	be	AUX
ejpam-4171	179	24	continuous	continuous	ADJ
ejpam-4171	179	25	mappings	mapping	NOUN
ejpam-4171	179	26	given	give	VERB
ejpam-4171	179	27	by	by	ADP
ejpam-4171	179	28	g(x	g(x	PROPN
ejpam-4171	179	29	,	,	PUNCT
ejpam-4171	179	30	y	y	PROPN
ejpam-4171	179	31	,	,	PUNCT
ejpam-4171	179	32	z	z	PROPN
ejpam-4171	179	33	,	,	PUNCT
ejpam-4171	179	34	t	t	PROPN
ejpam-4171	179	35	)	)	PUNCT
ejpam-4171	179	36	=	=	PUNCT
ejpam-4171	180	1	1	1	NUM
ejpam-4171	180	2	2(x	2(x	NUM
ejpam-4171	180	3	−	−	PROPN
ejpam-4171	180	4	y	y	PROPN
ejpam-4171	181	1	+	+	NOUN
ejpam-4171	181	2	z	z	PROPN
ejpam-4171	181	3	+	+	NUM
ejpam-4171	181	4	t	t	PROPN
ejpam-4171	181	5	)	)	PUNCT
ejpam-4171	181	6	and	and	CCONJ
ejpam-4171	181	7	g(x	g(x	NOUN
ejpam-4171	181	8	)	)	PUNCT
ejpam-4171	182	1	=	=	PUNCT
ejpam-4171	182	2	x	x	PUNCT
ejpam-4171	182	3	respectively	respectively	ADV
ejpam-4171	182	4	for	for	ADP
ejpam-4171	182	5	all	all	DET
ejpam-4171	182	6	x	x	NOUN
ejpam-4171	182	7	,	,	PUNCT
ejpam-4171	182	8	y	y	PROPN
ejpam-4171	182	9	,	,	PUNCT
ejpam-4171	182	10	z	z	PROPN
ejpam-4171	182	11	,	,	PUNCT
ejpam-4171	182	12	t	t	PROPN
ejpam-4171	182	13	∈	∈	PROPN
ejpam-4171	182	14	x.	x.	NOUN
ejpam-4171	182	15	consider	consider	VERB
ejpam-4171	182	16	θ	θ	X
ejpam-4171	182	17	:	:	PUNCT
ejpam-4171	183	1	[	[	X
ejpam-4171	183	2	0,∞)8	0,∞)8	X
ejpam-4171	183	3	→	→	SYM
ejpam-4171	183	4	[	[	X
ejpam-4171	183	5	0,∞	0,∞	NOUN
ejpam-4171	183	6	)	)	PUNCT
ejpam-4171	183	7	defined	define	VERB
ejpam-4171	183	8	by	by	ADP
ejpam-4171	183	9	θ(x	θ(x	PROPN
ejpam-4171	183	10	,	,	PUNCT
ejpam-4171	183	11	y	y	PROPN
ejpam-4171	183	12	,	,	PUNCT
ejpam-4171	183	13	z	z	PROPN
ejpam-4171	183	14	,	,	PUNCT
ejpam-4171	183	15	t	t	PROPN
ejpam-4171	183	16	,	,	PUNCT
ejpam-4171	183	17	a	a	DET
ejpam-4171	183	18	,	,	PUNCT
ejpam-4171	183	19	b	b	NOUN
ejpam-4171	183	20	,	,	PUNCT
ejpam-4171	183	21	c	c	X
ejpam-4171	183	22	,	,	PUNCT
ejpam-4171	183	23	u	u	NOUN
ejpam-4171	183	24	)	)	PUNCT
ejpam-4171	183	25	=	=	SYM
ejpam-4171	183	26	min{x	min{x	PROPN
ejpam-4171	183	27	,	,	PUNCT
ejpam-4171	183	28	y	y	PROPN
ejpam-4171	183	29	,	,	PUNCT
ejpam-4171	183	30	z	z	PROPN
ejpam-4171	183	31	,	,	PUNCT
ejpam-4171	183	32	t	t	PROPN
ejpam-4171	183	33	,	,	PUNCT
ejpam-4171	183	34	a	a	DET
ejpam-4171	183	35	,	,	PUNCT
ejpam-4171	183	36	b	b	NOUN
ejpam-4171	183	37	,	,	PUNCT
ejpam-4171	183	38	c	c	X
ejpam-4171	183	39	,	,	PUNCT
ejpam-4171	183	40	u	u	NOUN
ejpam-4171	183	41	}	}	PUNCT
ejpam-4171	183	42	and	and	CCONJ
ejpam-4171	183	43	ψ	ψ	NOUN
ejpam-4171	183	44	,	,	PUNCT
ejpam-4171	183	45	ζ	ζ	NOUN
ejpam-4171	183	46	:	:	PUNCT
ejpam-4171	184	1	[	[	X
ejpam-4171	184	2	0,∞	0,∞	NOUN
ejpam-4171	184	3	)	)	PUNCT
ejpam-4171	184	4	→	→	PUNCT
ejpam-4171	185	1	[	[	X
ejpam-4171	185	2	0,∞	0,∞	NOUN
ejpam-4171	185	3	)	)	PUNCT
ejpam-4171	185	4	are	be	AUX
ejpam-4171	185	5	given	give	VERB
ejpam-4171	185	6	by	by	ADP
ejpam-4171	185	7	ψ(q	ψ(q	NOUN
ejpam-4171	185	8	)	)	PUNCT
ejpam-4171	185	9	=	=	SYM
ejpam-4171	185	10	1	1	NUM
ejpam-4171	185	11	2q	2q	NUM
ejpam-4171	185	12	,	,	PUNCT
ejpam-4171	185	13	ζ(q	ζ(q	PROPN
ejpam-4171	185	14	)	)	PUNCT
ejpam-4171	185	15	=	=	NOUN
ejpam-4171	185	16	1	1	NUM
ejpam-4171	185	17	3q	3q	NUM
ejpam-4171	185	18	.	.	PUNCT
ejpam-4171	186	1	here	here	ADV
ejpam-4171	186	2	q0	q0	PROPN
ejpam-4171	186	3	=	=	PUNCT
ejpam-4171	186	4	{	{	PUNCT
ejpam-4171	186	5	3	3	NUM
ejpam-4171	186	6	}	}	PUNCT
ejpam-4171	186	7	and	and	CCONJ
ejpam-4171	186	8	r0	r0	NOUN
ejpam-4171	186	9	=	=	PUNCT
ejpam-4171	186	10	{	{	PUNCT
ejpam-4171	186	11	3	3	NUM
ejpam-4171	186	12	}	}	PUNCT
ejpam-4171	186	13	with	with	ADP
ejpam-4171	186	14	d(q	d(q	PROPN
ejpam-4171	186	15	,	,	PUNCT
ejpam-4171	186	16	r	r	NOUN
ejpam-4171	186	17	)	)	PUNCT
ejpam-4171	186	18	=	=	SYM
ejpam-4171	186	19	0	0	X
ejpam-4171	186	20	.	.	PUNCT
ejpam-4171	187	1	taking	take	VERB
ejpam-4171	187	2	x0	x0	PROPN
ejpam-4171	187	3	,	,	PUNCT
ejpam-4171	187	4	z0	z0	PROPN
ejpam-4171	187	5	∈	∈	PROPN
ejpam-4171	187	6	q0	q0	NOUN
ejpam-4171	187	7	and	and	CCONJ
ejpam-4171	187	8	y0	y0	PROPN
ejpam-4171	187	9	,	,	PUNCT
ejpam-4171	187	10	t0	t0	PROPN
ejpam-4171	187	11	∈	∈	PROPN
ejpam-4171	187	12	r0	r0	NOUN
ejpam-4171	187	13	,	,	PUNCT
ejpam-4171	187	14	then	then	ADV
ejpam-4171	187	15	g(q0,r0,q0,r0	g(q0,r0,q0,r0	X
ejpam-4171	187	16	)	)	PUNCT
ejpam-4171	187	17	⊆	⊆	NUM
ejpam-4171	187	18	r0	r0	NOUN
ejpam-4171	187	19	,	,	PUNCT
ejpam-4171	187	20	g(r0,q0,r0,q0	g(r0,q0,r0,q0	NOUN
ejpam-4171	187	21	)	)	PUNCT
ejpam-4171	187	22	⊆	⊆	NUM
ejpam-4171	187	23	q0	q0	NOUN
ejpam-4171	187	24	.	.	PUNCT
ejpam-4171	188	1	also	also	ADV
ejpam-4171	188	2	,	,	PUNCT
ejpam-4171	188	3	the	the	DET
ejpam-4171	188	4	remaining	remain	VERB
ejpam-4171	188	5	conditions	condition	NOUN
ejpam-4171	188	6	of	of	ADP
ejpam-4171	188	7	the	the	DET
ejpam-4171	188	8	theorem	theorem	NOUN
ejpam-4171	188	9	are	be	AUX
ejpam-4171	188	10	satisfied	satisfied	ADJ
ejpam-4171	188	11	.	.	PUNCT
ejpam-4171	189	1	hence	hence	ADV
ejpam-4171	189	2	by	by	ADP
ejpam-4171	189	3	the	the	DET
ejpam-4171	189	4	theorem	theorem	NOUN
ejpam-4171	189	5	(	(	PUNCT
ejpam-4171	189	6	1	1	NUM
ejpam-4171	189	7	)	)	PUNCT
ejpam-4171	189	8	,	,	PUNCT
ejpam-4171	189	9	(	(	PUNCT
ejpam-4171	189	10	3	3	NUM
ejpam-4171	189	11	,	,	PUNCT
ejpam-4171	189	12	3	3	NUM
ejpam-4171	189	13	,	,	PUNCT
ejpam-4171	189	14	3	3	NUM
ejpam-4171	189	15	,	,	PUNCT
ejpam-4171	189	16	3	3	NUM
ejpam-4171	189	17	)	)	PUNCT
ejpam-4171	189	18	is	be	AUX
ejpam-4171	189	19	the	the	DET
ejpam-4171	189	20	quadruple	quadruple	NOUN
ejpam-4171	189	21	g	g	NOUN
ejpam-4171	189	22	-	-	PUNCT
ejpam-4171	189	23	best	good	ADJ
ejpam-4171	189	24	proximity	proximity	NOUN
ejpam-4171	189	25	point	point	NOUN
ejpam-4171	189	26	of	of	ADP
ejpam-4171	189	27	g	g	PROPN
ejpam-4171	189	28	and	and	CCONJ
ejpam-4171	189	29	g.	g.	PROPN
ejpam-4171	189	30	acknowledgements	acknowledgement	NOUN
ejpam-4171	189	31	special	special	ADJ
ejpam-4171	189	32	thanks	thank	NOUN
ejpam-4171	189	33	to	to	ADP
ejpam-4171	189	34	csir	csir	PROPN
ejpam-4171	189	35	to	to	PART
ejpam-4171	189	36	fund	fund	VERB
ejpam-4171	189	37	phd	phd	NOUN
ejpam-4171	189	38	through	through	ADP
ejpam-4171	189	39	file	file	NOUN
ejpam-4171	189	40	number	number	NOUN
ejpam-4171	189	41	09/382(0187)/2017	09/382(0187)/2017	NOUN
ejpam-4171	189	42	-	-	PUNCT
ejpam-4171	189	43	emr-1	emr-1	NUM
ejpam-4171	189	44	references	reference	NOUN
ejpam-4171	189	45	[	[	X
ejpam-4171	189	46	1	1	NUM
ejpam-4171	189	47	]	]	PUNCT
ejpam-4171	189	48	a	a	DET
ejpam-4171	189	49	a	a	DET
ejpam-4171	189	50	aserkar	aserkar	NOUN
ejpam-4171	189	51	and	and	CCONJ
ejpam-4171	189	52	m	m	PROPN
ejpam-4171	189	53	p	p	NOUN
ejpam-4171	189	54	gandhi	gandhi	PROPN
ejpam-4171	189	55	.	.	PUNCT
ejpam-4171	190	1	quadruple	quadruple	PROPN
ejpam-4171	190	2	fixed	fix	VERB
ejpam-4171	190	3	point	point	NOUN
ejpam-4171	190	4	theorem	theorem	VERB
ejpam-4171	190	5	for	for	ADP
ejpam-4171	190	6	four	four	NUM
ejpam-4171	190	7	mappings	mapping	NOUN
ejpam-4171	190	8	.	.	PUNCT
ejpam-4171	191	1	gen	gen	PROPN
ejpam-4171	191	2	.	.	PROPN
ejpam-4171	191	3	math	math	PROPN
ejpam-4171	191	4	.	.	PUNCT
ejpam-4171	192	1	notes	note	NOUN
ejpam-4171	192	2	,	,	PUNCT
ejpam-4171	192	3	25(2):95–109	25(2):95–109	NUM
ejpam-4171	192	4	,	,	PUNCT
ejpam-4171	192	5	2014	2014	NUM
ejpam-4171	192	6	.	.	PUNCT
ejpam-4171	193	1	[	[	X
ejpam-4171	193	2	2	2	NUM
ejpam-4171	193	3	]	]	PUNCT
ejpam-4171	193	4	m	m	VERB
ejpam-4171	193	5	postolache	postolache	PROPN
ejpam-4171	193	6	b	b	PROPN
ejpam-4171	193	7	s	s	PROPN
ejpam-4171	193	8	choudhury	choudhury	PROPN
ejpam-4171	193	9	,	,	PUNCT
ejpam-4171	193	10	n	n	PRON
ejpam-4171	193	11	metiya	metiya	NOUN
ejpam-4171	193	12	and	and	CCONJ
ejpam-4171	193	13	p	p	NOUN
ejpam-4171	193	14	konar	konar	NOUN
ejpam-4171	193	15	.	.	PUNCT
ejpam-4171	194	1	a	a	DET
ejpam-4171	194	2	discussion	discussion	NOUN
ejpam-4171	194	3	on	on	ADP
ejpam-4171	194	4	best	good	ADJ
ejpam-4171	194	5	proximity	proximity	NOUN
ejpam-4171	194	6	point	point	NOUN
ejpam-4171	194	7	and	and	CCONJ
ejpam-4171	194	8	coupled	couple	VERB
ejpam-4171	194	9	best	good	ADJ
ejpam-4171	194	10	proximity	proximity	NOUN
ejpam-4171	194	11	point	point	NOUN
ejpam-4171	194	12	in	in	ADP
ejpam-4171	194	13	partially	partially	ADV
ejpam-4171	194	14	ordered	order	VERB
ejpam-4171	194	15	metric	metric	ADJ
ejpam-4171	194	16	spaces	space	NOUN
ejpam-4171	194	17	.	.	PUNCT
ejpam-4171	195	1	fixed	fix	VERB
ejpam-4171	195	2	point	point	NOUN
ejpam-4171	195	3	theory	theory	NOUN
ejpam-4171	195	4	and	and	CCONJ
ejpam-4171	195	5	applications	application	NOUN
ejpam-4171	195	6	,	,	PUNCT
ejpam-4171	195	7	170:17	170:17	NUM
ejpam-4171	195	8	pages	page	NOUN
ejpam-4171	195	9	,	,	PUNCT
ejpam-4171	195	10	2015	2015	NUM
ejpam-4171	195	11	.	.	PUNCT
ejpam-4171	196	1	references	reference	NOUN
ejpam-4171	196	2	143	143	NUM
ejpam-4171	197	1	[	[	X
ejpam-4171	197	2	3	3	NUM
ejpam-4171	197	3	]	]	SYM
ejpam-4171	197	4	s	s	PART
ejpam-4171	197	5	s	s	PROPN
ejpam-4171	197	6	basha	basha	PROPN
ejpam-4171	197	7	.	.	PUNCT
ejpam-4171	197	8	extensions	extension	NOUN
ejpam-4171	197	9	of	of	ADP
ejpam-4171	197	10	banachs	banachs	PROPN
ejpam-4171	197	11	contraction	contraction	PROPN
ejpam-4171	197	12	principle	principle	PROPN
ejpam-4171	197	13	.	.	PUNCT
ejpam-4171	198	1	numerical	numerical	ADJ
ejpam-4171	198	2	functional	functional	ADJ
ejpam-4171	198	3	analysis	analysis	NOUN
ejpam-4171	198	4	and	and	CCONJ
ejpam-4171	198	5	optimization	optimization	NOUN
ejpam-4171	198	6	,	,	PUNCT
ejpam-4171	198	7	31:569–576	31:569–576	NUM
ejpam-4171	198	8	,	,	PUNCT
ejpam-4171	198	9	2010	2010	NUM
ejpam-4171	198	10	.	.	PUNCT
ejpam-4171	199	1	[	[	X
ejpam-4171	199	2	4	4	NUM
ejpam-4171	199	3	]	]	SYM
ejpam-4171	199	4	s	s	PART
ejpam-4171	199	5	s	s	PROPN
ejpam-4171	199	6	basha	basha	PROPN
ejpam-4171	199	7	.	.	PUNCT
ejpam-4171	200	1	best	good	ADJ
ejpam-4171	200	2	proximity	proximity	NOUN
ejpam-4171	200	3	point	point	NOUN
ejpam-4171	200	4	theorems	theorem	NOUN
ejpam-4171	200	5	generalizing	generalize	VERB
ejpam-4171	200	6	the	the	DET
ejpam-4171	200	7	contraction	contraction	NOUN
ejpam-4171	200	8	principle	principle	NOUN
ejpam-4171	200	9	.	.	PUNCT
ejpam-4171	201	1	nonlinear	nonlinear	ADJ
ejpam-4171	201	2	analysis	analysis	NOUN
ejpam-4171	201	3	,	,	PUNCT
ejpam-4171	201	4	74:5844–5850	74:5844–5850	NOUN
ejpam-4171	201	5	,	,	PUNCT
ejpam-4171	201	6	2011	2011	NUM
ejpam-4171	201	7	.	.	PUNCT
ejpam-4171	202	1	[	[	X
ejpam-4171	202	2	5	5	NUM
ejpam-4171	202	3	]	]	SYM
ejpam-4171	202	4	s	s	PART
ejpam-4171	202	5	s	s	PROPN
ejpam-4171	202	6	basha	basha	PROPN
ejpam-4171	202	7	.	.	PUNCT
ejpam-4171	203	1	best	good	ADJ
ejpam-4171	203	2	proximity	proximity	NOUN
ejpam-4171	203	3	points	point	NOUN
ejpam-4171	203	4	:	:	PUNCT
ejpam-4171	203	5	global	global	ADJ
ejpam-4171	203	6	optimal	optimal	ADJ
ejpam-4171	203	7	approximate	approximate	ADJ
ejpam-4171	203	8	solution	solution	NOUN
ejpam-4171	203	9	.	.	PUNCT
ejpam-4171	204	1	journal	journal	NOUN
ejpam-4171	204	2	of	of	ADP
ejpam-4171	204	3	global	global	ADJ
ejpam-4171	204	4	optimization	optimization	NOUN
ejpam-4171	204	5	,	,	PUNCT
ejpam-4171	204	6	49:15–21	49:15–21	NUM
ejpam-4171	204	7	,	,	PUNCT
ejpam-4171	204	8	2011	2011	NUM
ejpam-4171	204	9	.	.	PUNCT
ejpam-4171	205	1	[	[	X
ejpam-4171	205	2	6	6	NUM
ejpam-4171	205	3	]	]	SYM
ejpam-4171	205	4	s	s	PART
ejpam-4171	205	5	s	s	X
ejpam-4171	205	6	basha	basha	PROPN
ejpam-4171	205	7	and	and	CCONJ
ejpam-4171	205	8	p	p	PROPN
ejpam-4171	205	9	veeramani	veeramani	NOUN
ejpam-4171	205	10	.	.	PUNCT
ejpam-4171	206	1	best	good	ADJ
ejpam-4171	206	2	proximity	proximity	NOUN
ejpam-4171	206	3	pair	pair	NOUN
ejpam-4171	206	4	theorems	theorem	NOUN
ejpam-4171	206	5	for	for	ADP
ejpam-4171	206	6	multifunctions	multifunction	NOUN
ejpam-4171	206	7	with	with	ADP
ejpam-4171	206	8	open	open	ADJ
ejpam-4171	206	9	fibres	fibre	NOUN
ejpam-4171	206	10	.	.	PUNCT
ejpam-4171	207	1	journal	journal	NOUN
ejpam-4171	207	2	of	of	ADP
ejpam-4171	207	3	approximation	approximation	NOUN
ejpam-4171	207	4	theory	theory	NOUN
ejpam-4171	207	5	,	,	PUNCT
ejpam-4171	207	6	103:119–129	103:119–129	NUM
ejpam-4171	207	7	,	,	PUNCT
ejpam-4171	207	8	2000	2000	NUM
ejpam-4171	207	9	.	.	PUNCT
ejpam-4171	208	1	[	[	X
ejpam-4171	208	2	7	7	X
ejpam-4171	208	3	]	]	SYM
ejpam-4171	208	4	v	v	NOUN
ejpam-4171	208	5	berinde	berinde	NOUN
ejpam-4171	208	6	and	and	CCONJ
ejpam-4171	208	7	m	m	AUX
ejpam-4171	208	8	borcut	borcut	VERB
ejpam-4171	208	9	.	.	PUNCT
ejpam-4171	209	1	tripled	triple	VERB
ejpam-4171	209	2	fixed	fix	VERB
ejpam-4171	209	3	point	point	NOUN
ejpam-4171	209	4	theorems	theorem	NOUN
ejpam-4171	209	5	for	for	ADP
ejpam-4171	209	6	contractive	contractive	ADJ
ejpam-4171	209	7	type	type	NOUN
ejpam-4171	209	8	mappings	mapping	NOUN
ejpam-4171	209	9	in	in	ADP
ejpam-4171	209	10	partially	partially	ADV
ejpam-4171	209	11	ordered	order	VERB
ejpam-4171	209	12	metric	metric	ADJ
ejpam-4171	209	13	spaces	space	NOUN
ejpam-4171	209	14	.	.	PUNCT
ejpam-4171	210	1	nonlinear	nonlinear	ADJ
ejpam-4171	210	2	anal	anal	PROPN
ejpam-4171	210	3	.	.	PUNCT
ejpam-4171	210	4	,	,	PUNCT
ejpam-4171	210	5	74(15):4889–4897	74(15):4889–4897	NUM
ejpam-4171	210	6	,	,	PUNCT
ejpam-4171	210	7	2011	2011	NUM
ejpam-4171	210	8	.	.	PUNCT
ejpam-4171	211	1	[	[	X
ejpam-4171	211	2	8	8	NUM
ejpam-4171	211	3	]	]	X
ejpam-4171	211	4	k	k	PROPN
ejpam-4171	211	5	fan	fan	PROPN
ejpam-4171	211	6	.	.	PUNCT
ejpam-4171	212	1	extensions	extension	NOUN
ejpam-4171	212	2	of	of	ADP
ejpam-4171	212	3	two	two	NUM
ejpam-4171	212	4	fixed	fix	VERB
ejpam-4171	212	5	point	point	NOUN
ejpam-4171	212	6	theorems	theorem	NOUN
ejpam-4171	212	7	of	of	ADP
ejpam-4171	212	8	f.	f.	PROPN
ejpam-4171	212	9	e.	e.	PROPN
ejpam-4171	212	10	browder	browder	PROPN
ejpam-4171	212	11	.	.	PUNCT
ejpam-4171	213	1	mathematische	mathematische	PROPN
ejpam-4171	213	2	zeitschrift	zeitschrift	PROPN
ejpam-4171	213	3	,	,	PUNCT
ejpam-4171	213	4	112:234–240	112:234–240	NUM
ejpam-4171	213	5	,	,	PUNCT
ejpam-4171	213	6	1969	1969	NUM
ejpam-4171	213	7	.	.	PUNCT
ejpam-4171	214	1	[	[	X
ejpam-4171	214	2	9	9	NUM
ejpam-4171	214	3	]	]	SYM
ejpam-4171	214	4	m	m	VERB
ejpam-4171	214	5	marudai	marudai	PROPN
ejpam-4171	214	6	g	g	PROPN
ejpam-4171	214	7	k	k	PROPN
ejpam-4171	214	8	jacob	jacob	PROPN
ejpam-4171	214	9	,	,	PUNCT
ejpam-4171	214	10	m	m	PROPN
ejpam-4171	214	11	postolache	postolache	NOUN
ejpam-4171	214	12	and	and	CCONJ
ejpam-4171	214	13	v	v	ADP
ejpam-4171	214	14	raja	raja	PROPN
ejpam-4171	214	15	.	.	PUNCT
ejpam-4171	215	1	norm	norm	NOUN
ejpam-4171	215	2	convergence	convergence	NOUN
ejpam-4171	215	3	iterations	iteration	NOUN
ejpam-4171	215	4	for	for	ADP
ejpam-4171	215	5	best	good	ADJ
ejpam-4171	215	6	proximity	proximity	NOUN
ejpam-4171	215	7	points	point	NOUN
ejpam-4171	215	8	of	of	ADP
ejpam-4171	215	9	non	non	ADJ
ejpam-4171	215	10	-	-	ADJ
ejpam-4171	215	11	self	self	ADJ
ejpam-4171	215	12	non	non	ADJ
ejpam-4171	215	13	-	-	ADJ
ejpam-4171	215	14	expansive	expansive	ADJ
ejpam-4171	215	15	mappings	mapping	NOUN
ejpam-4171	215	16	.	.	PUNCT
ejpam-4171	216	1	u.	u.	PROPN
ejpam-4171	216	2	politeh	politeh	PROPN
ejpam-4171	216	3	.	.	PUNCT
ejpam-4171	217	1	buch	buch	PROPN
ejpam-4171	217	2	.	.	PUNCT
ejpam-4171	218	1	ser	ser	PROPN
ejpam-4171	218	2	.	.	PROPN
ejpam-4171	218	3	,	,	PUNCT
ejpam-4171	218	4	79:49–56	79:49–56	NUM
ejpam-4171	218	5	,	,	PUNCT
ejpam-4171	218	6	2017	2017	NUM
ejpam-4171	218	7	.	.	PUNCT
ejpam-4171	219	1	[	[	X
ejpam-4171	219	2	10	10	NUM
ejpam-4171	219	3	]	]	X
ejpam-4171	219	4	d	d	X
ejpam-4171	219	5	guo	guo	PROPN
ejpam-4171	219	6	and	and	CCONJ
ejpam-4171	219	7	v	v	NOUN
ejpam-4171	219	8	lakshmikantham	lakshmikantham	NOUN
ejpam-4171	219	9	.	.	PUNCT
ejpam-4171	220	1	coupled	couple	VERB
ejpam-4171	220	2	fixed	fix	VERB
ejpam-4171	220	3	points	point	NOUN
ejpam-4171	220	4	of	of	ADP
ejpam-4171	220	5	nonlinear	nonlinear	ADJ
ejpam-4171	220	6	operators	operator	NOUN
ejpam-4171	220	7	with	with	ADP
ejpam-4171	220	8	applications	application	NOUN
ejpam-4171	220	9	.	.	PUNCT
ejpam-4171	221	1	nonlinear	nonlinear	ADJ
ejpam-4171	221	2	anal	anal	PROPN
ejpam-4171	221	3	.	.	PUNCT
ejpam-4171	221	4	,	,	PUNCT
ejpam-4171	221	5	11:623–632	11:623–632	NUM
ejpam-4171	221	6	,	,	PUNCT
ejpam-4171	221	7	1987	1987	NUM
ejpam-4171	221	8	.	.	PUNCT
ejpam-4171	222	1	[	[	X
ejpam-4171	222	2	11	11	NUM
ejpam-4171	222	3	]	]	PUNCT
ejpam-4171	222	4	e	e	X
ejpam-4171	222	5	karapinar	karapinar	NOUN
ejpam-4171	222	6	and	and	CCONJ
ejpam-4171	222	7	n	n	PRON
ejpam-4171	222	8	v	v	ADP
ejpam-4171	222	9	luong	luong	PROPN
ejpam-4171	222	10	.	.	PUNCT
ejpam-4171	223	1	quadruple	quadruple	PROPN
ejpam-4171	223	2	fixed	fix	VERB
ejpam-4171	223	3	point	point	NOUN
ejpam-4171	223	4	theorems	theorem	NOUN
ejpam-4171	223	5	for	for	ADP
ejpam-4171	223	6	nonlinear	nonlinear	ADJ
ejpam-4171	223	7	contractions	contraction	NOUN
ejpam-4171	223	8	.	.	PUNCT
ejpam-4171	224	1	computer	computer	NOUN
ejpam-4171	224	2	and	and	CCONJ
ejpam-4171	224	3	mathematics	mathematic	NOUN
ejpam-4171	224	4	with	with	ADP
ejpam-4171	224	5	applications	application	NOUN
ejpam-4171	224	6	,	,	PUNCT
ejpam-4171	224	7	64:1839–1848	64:1839–1848	NUM
ejpam-4171	224	8	,	,	PUNCT
ejpam-4171	224	9	2012	2012	NUM
ejpam-4171	224	10	.	.	PUNCT
ejpam-4171	225	1	[	[	X
ejpam-4171	225	2	12	12	NUM
ejpam-4171	225	3	]	]	X
ejpam-4171	225	4	p	p	X
ejpam-4171	225	5	kumam	kumam	NOUN
ejpam-4171	225	6	and	and	CCONJ
ejpam-4171	225	7	a	a	DET
ejpam-4171	225	8	f	f	NOUN
ejpam-4171	225	9	r	r	NOUN
ejpam-4171	225	10	l	l	NOUN
ejpam-4171	225	11	de	de	X
ejpam-4171	225	12	hierro	hierro	PROPN
ejpam-4171	225	13	.	.	PROPN
ejpam-4171	225	14	on	on	ADP
ejpam-4171	225	15	existence	existence	NOUN
ejpam-4171	225	16	and	and	CCONJ
ejpam-4171	225	17	uniqueness	uniqueness	NOUN
ejpam-4171	225	18	of	of	ADP
ejpam-4171	225	19	g	g	NOUN
ejpam-4171	225	20	-	-	PUNCT
ejpam-4171	225	21	proximity	proximity	NOUN
ejpam-4171	225	22	points	point	NOUN
ejpam-4171	225	23	under	under	ADP
ejpam-4171	225	24	(	(	PUNCT
ejpam-4171	225	25	φ	φ	PROPN
ejpam-4171	225	26	,	,	PUNCT
ejpam-4171	225	27	θ	θ	PROPN
ejpam-4171	225	28	,	,	PUNCT
ejpam-4171	225	29	a	a	PRON
ejpam-4171	225	30	,	,	PUNCT
ejpam-4171	225	31	g)-contractivity	g)-contractivity	NOUN
ejpam-4171	225	32	conditions	condition	NOUN
ejpam-4171	225	33	and	and	CCONJ
ejpam-4171	225	34	consequences	consequence	NOUN
ejpam-4171	225	35	.	.	PUNCT
ejpam-4171	226	1	abstract	abstract	ADJ
ejpam-4171	226	2	and	and	CCONJ
ejpam-4171	226	3	applied	apply	VERB
ejpam-4171	226	4	analysis	analysis	NOUN
ejpam-4171	226	5	,	,	PUNCT
ejpam-4171	226	6	2014:14	2014:14	NUM
ejpam-4171	226	7	pages	page	NOUN
ejpam-4171	226	8	,	,	PUNCT
ejpam-4171	226	9	2014	2014	NUM
ejpam-4171	226	10	.	.	PUNCT
ejpam-4171	227	1	[	[	X
ejpam-4171	227	2	13	13	NUM
ejpam-4171	227	3	]	]	SYM
ejpam-4171	227	4	v	v	X
ejpam-4171	227	5	lakshmikantham	lakshmikantham	NOUN
ejpam-4171	227	6	and	and	CCONJ
ejpam-4171	227	7	l	l	NOUN
ejpam-4171	227	8	ciric	ciric	NOUN
ejpam-4171	227	9	.	.	PUNCT
ejpam-4171	228	1	coupled	couple	VERB
ejpam-4171	228	2	fixed	fix	VERB
ejpam-4171	228	3	point	point	NOUN
ejpam-4171	228	4	theorems	theorem	NOUN
ejpam-4171	228	5	for	for	ADP
ejpam-4171	228	6	non	non	ADJ
ejpam-4171	228	7	-	-	ADJ
ejpam-4171	228	8	linear	linear	ADJ
ejpam-4171	228	9	contractions	contraction	NOUN
ejpam-4171	228	10	in	in	ADP
ejpam-4171	228	11	partially	partially	ADV
ejpam-4171	228	12	ordered	order	VERB
ejpam-4171	228	13	metric	metric	ADJ
ejpam-4171	228	14	spaces	space	NOUN
ejpam-4171	228	15	.	.	PUNCT
ejpam-4171	229	1	nonlinear	nonlinear	ADJ
ejpam-4171	229	2	anal	anal	PROPN
ejpam-4171	229	3	.	.	PUNCT
ejpam-4171	229	4	,	,	PUNCT
ejpam-4171	229	5	70:4341–4349	70:4341–4349	NUM
ejpam-4171	229	6	,	,	PUNCT
ejpam-4171	229	7	2009	2009	NUM
ejpam-4171	229	8	.	.	PUNCT
ejpam-4171	230	1	[	[	X
ejpam-4171	230	2	14	14	NUM
ejpam-4171	230	3	]	]	X
ejpam-4171	230	4	d	d	PROPN
ejpam-4171	230	5	nedelcheva	nedelcheva	PROPN
ejpam-4171	230	6	m	m	PROPN
ejpam-4171	230	7	hristov	hristov	ADJ
ejpam-4171	230	8	,	,	PUNCT
ejpam-4171	230	9	a	a	DET
ejpam-4171	230	10	llchev	llchev	NOUN
ejpam-4171	230	11	and	and	CCONJ
ejpam-4171	230	12	b	b	PROPN
ejpam-4171	230	13	zlatanov	zlatanov	PROPN
ejpam-4171	230	14	.	.	PROPN
ejpam-4171	230	15	existence	existence	NOUN
ejpam-4171	230	16	of	of	ADP
ejpam-4171	230	17	coupled	couple	VERB
ejpam-4171	230	18	best	good	ADJ
ejpam-4171	230	19	proximity	proximity	NOUN
ejpam-4171	230	20	points	point	NOUN
ejpam-4171	230	21	of	of	ADP
ejpam-4171	230	22	p	p	NOUN
ejpam-4171	230	23	-	-	PUNCT
ejpam-4171	230	24	cyclic	cyclic	ADJ
ejpam-4171	230	25	contractions	contraction	NOUN
ejpam-4171	230	26	.	.	PUNCT
ejpam-4171	231	1	theory	theory	NOUN
ejpam-4171	231	2	and	and	CCONJ
ejpam-4171	231	3	application	application	NOUN
ejpam-4171	231	4	of	of	ADP
ejpam-4171	231	5	fixed	fix	VERB
ejpam-4171	231	6	point	point	NOUN
ejpam-4171	231	7	,	,	PUNCT
ejpam-4171	231	8	10(1):14	10(1):14	NUM
ejpam-4171	231	9	pages	page	NOUN
ejpam-4171	231	10	,	,	PUNCT
ejpam-4171	231	11	2021	2021	NUM
ejpam-4171	231	12	.	.	PUNCT
ejpam-4171	232	1	[	[	X
ejpam-4171	232	2	15	15	NUM
ejpam-4171	232	3	]	]	X
ejpam-4171	232	4	a	a	DET
ejpam-4171	232	5	pitea	pitea	NOUN
ejpam-4171	232	6	.	.	PUNCT
ejpam-4171	233	1	best	good	ADJ
ejpam-4171	233	2	proximity	proximity	NOUN
ejpam-4171	233	3	results	result	NOUN
ejpam-4171	233	4	on	on	ADP
ejpam-4171	233	5	dualistic	dualistic	ADJ
ejpam-4171	233	6	metric	metric	ADJ
ejpam-4171	233	7	spaces	space	NOUN
ejpam-4171	233	8	.	.	PUNCT
ejpam-4171	234	1	symmetry	symmetry	NOUN
ejpam-4171	234	2	,	,	PUNCT
ejpam-4171	234	3	11:14	11:14	NUM
ejpam-4171	234	4	pages	page	NOUN
ejpam-4171	234	5	,	,	PUNCT
ejpam-4171	234	6	2019	2019	NUM
ejpam-4171	234	7	.	.	PUNCT
ejpam-4171	235	1	[	[	X
ejpam-4171	235	2	16	16	NUM
ejpam-4171	235	3	]	]	SYM
ejpam-4171	235	4	v	v	X
ejpam-4171	235	5	s	s	X
ejpam-4171	235	6	raj	raj	NOUN
ejpam-4171	235	7	.	.	PUNCT
ejpam-4171	236	1	best	good	ADJ
ejpam-4171	236	2	proximity	proximity	NOUN
ejpam-4171	236	3	point	point	NOUN
ejpam-4171	236	4	theorem	theorem	NOUN
ejpam-4171	236	5	for	for	ADP
ejpam-4171	236	6	weakly	weakly	ADJ
ejpam-4171	236	7	contractive	contractive	ADJ
ejpam-4171	236	8	non	non	ADJ
ejpam-4171	236	9	-	-	ADJ
ejpam-4171	236	10	self	self	ADJ
ejpam-4171	236	11	mappings	mapping	NOUN
ejpam-4171	236	12	.	.	PUNCT
ejpam-4171	237	1	nonlinear	nonlinear	ADJ
ejpam-4171	237	2	anal	anal	PROPN
ejpam-4171	237	3	.	.	PUNCT
ejpam-4171	237	4	,	,	PUNCT
ejpam-4171	237	5	74:4804–4808	74:4804–4808	NUM
ejpam-4171	237	6	,	,	PUNCT
ejpam-4171	237	7	2011	2011	NUM
ejpam-4171	237	8	.	.	PUNCT
ejpam-4171	238	1	[	[	X
ejpam-4171	238	2	17	17	NUM
ejpam-4171	238	3	]	]	X
ejpam-4171	238	4	y	y	NOUN
ejpam-4171	238	5	rohen	rohen	VERB
ejpam-4171	238	6	and	and	CCONJ
ejpam-4171	238	7	n	n	DET
ejpam-4171	238	8	mlaiki	mlaiki	PROPN
ejpam-4171	238	9	.	.	PUNCT
ejpam-4171	239	1	tripled	triple	VERB
ejpam-4171	239	2	best	good	ADJ
ejpam-4171	239	3	proximity	proximity	NOUN
ejpam-4171	239	4	point	point	NOUN
ejpam-4171	239	5	in	in	ADP
ejpam-4171	239	6	complete	complete	ADJ
ejpam-4171	239	7	metric	metric	ADJ
ejpam-4171	239	8	spaces	space	NOUN
ejpam-4171	239	9	.	.	PUNCT
ejpam-4171	240	1	open	open	ADJ
ejpam-4171	240	2	mathematics	mathematic	NOUN
ejpam-4171	240	3	,	,	PUNCT
ejpam-4171	240	4	18:204–210	18:204–210	NUM
ejpam-4171	240	5	,	,	PUNCT
ejpam-4171	240	6	2020	2020	NUM
ejpam-4171	240	7	.	.	PUNCT
ejpam-4171	241	1	[	[	X
ejpam-4171	241	2	18	18	NUM
ejpam-4171	241	3	]	]	X
ejpam-4171	241	4	w	w	NOUN
ejpam-4171	241	5	shantanawi	shantanawi	PROPN
ejpam-4171	241	6	and	and	CCONJ
ejpam-4171	241	7	a	a	DET
ejpam-4171	241	8	pitea	pitea	NOUN
ejpam-4171	241	9	.	.	PUNCT
ejpam-4171	242	1	best	good	ADJ
ejpam-4171	242	2	proximity	proximity	NOUN
ejpam-4171	242	3	point	point	NOUN
ejpam-4171	242	4	and	and	CCONJ
ejpam-4171	242	5	best	good	ADJ
ejpam-4171	242	6	proximity	proximity	NOUN
ejpam-4171	242	7	coupled	couple	VERB
ejpam-4171	242	8	point	point	NOUN
ejpam-4171	242	9	in	in	ADP
ejpam-4171	242	10	a	a	DET
ejpam-4171	242	11	complete	complete	ADJ
ejpam-4171	242	12	metric	metric	ADJ
ejpam-4171	242	13	space	space	NOUN
ejpam-4171	242	14	with	with	ADP
ejpam-4171	242	15	(	(	PUNCT
ejpam-4171	242	16	p)-property	p)-property	NOUN
ejpam-4171	242	17	.	.	PUNCT
ejpam-4171	243	1	filomat	filomat	PROPN
ejpam-4171	243	2	,	,	PUNCT
ejpam-4171	243	3	29(1):63–74	29(1):63–74	NUM
ejpam-4171	243	4	,	,	PUNCT
ejpam-4171	243	5	2015	2015	NUM
ejpam-4171	243	6	.	.	PUNCT