id	sid	tid	token	lemma	pos
ejpam-3133	1	1	european	european	PROPN
ejpam-3133	1	2	journal	journal	PROPN
ejpam-3133	1	3	of	of	ADP
ejpam-3133	1	4	pure	pure	ADJ
ejpam-3133	1	5	and	and	CCONJ
ejpam-3133	1	6	applied	apply	VERB
ejpam-3133	1	7	mathematics	mathematic	NOUN
ejpam-3133	1	8	vol	vol	NOUN
ejpam-3133	1	9	.	.	PUNCT
ejpam-3133	2	1	11	11	NUM
ejpam-3133	2	2	,	,	PUNCT
ejpam-3133	2	3	no	no	INTJ
ejpam-3133	2	4	.	.	NOUN
ejpam-3133	2	5	1	1	NUM
ejpam-3133	2	6	,	,	PUNCT
ejpam-3133	2	7	2018	2018	NUM
ejpam-3133	2	8	,	,	PUNCT
ejpam-3133	2	9	90	90	NUM
ejpam-3133	2	10	-	-	SYM
ejpam-3133	2	11	109	109	NUM
ejpam-3133	2	12	issn	issn	PROPN
ejpam-3133	2	13	1307	1307	NUM
ejpam-3133	2	14	-	-	SYM
ejpam-3133	2	15	5543	5543	NUM
ejpam-3133	2	16	–	–	PUNCT
ejpam-3133	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3133	2	18	published	publish	VERB
ejpam-3133	2	19	by	by	ADP
ejpam-3133	2	20	new	new	PROPN
ejpam-3133	2	21	york	york	PROPN
ejpam-3133	2	22	business	business	PROPN
ejpam-3133	2	23	global	global	VERB
ejpam-3133	2	24	some	some	DET
ejpam-3133	2	25	common	common	ADJ
ejpam-3133	2	26	fixed	fix	VERB
ejpam-3133	2	27	points	point	NOUN
ejpam-3133	2	28	of	of	ADP
ejpam-3133	2	29	six	six	NUM
ejpam-3133	2	30	mappings	mapping	NOUN
ejpam-3133	2	31	on	on	ADP
ejpam-3133	2	32	gbmetric	gbmetric	ADJ
ejpam-3133	2	33	spaces	space	NOUN
ejpam-3133	2	34	using	use	VERB
ejpam-3133	2	35	(	(	PUNCT
ejpam-3133	2	36	e.a	e.a	PROPN
ejpam-3133	2	37	)	)	PUNCT
ejpam-3133	2	38	property	property	NOUN
ejpam-3133	2	39	z.	z.	PROPN
ejpam-3133	2	40	mustafa1,∗	mustafa1,∗	PROPN
ejpam-3133	2	41	,	,	PUNCT
ejpam-3133	2	42	m.m.m	m.m.m	NOUN
ejpam-3133	2	43	.	.	PUNCT
ejpam-3133	3	1	jaradat2	jaradat2	PROPN
ejpam-3133	3	2	,	,	PUNCT
ejpam-3133	3	3	h.	h.	PROPN
ejpam-3133	3	4	aydi3,4	aydi3,4	PROPN
ejpam-3133	3	5	,	,	PUNCT
ejpam-3133	3	6	a.	a.	NOUN
ejpam-3133	3	7	alrhayyel5	alrhayyel5	NOUN
ejpam-3133	3	8	1	1	NUM
ejpam-3133	3	9	department	department	NOUN
ejpam-3133	3	10	of	of	ADP
ejpam-3133	3	11	mathematics	mathematic	NOUN
ejpam-3133	3	12	,	,	PUNCT
ejpam-3133	3	13	statistics	statistic	NOUN
ejpam-3133	3	14	and	and	CCONJ
ejpam-3133	3	15	physics	physics	PROPN
ejpam-3133	3	16	,	,	PUNCT
ejpam-3133	3	17	qatar	qatar	PROPN
ejpam-3133	3	18	university	university	PROPN
ejpam-3133	3	19	,	,	PUNCT
ejpam-3133	3	20	doha	doha	PROPN
ejpam-3133	3	21	,	,	PUNCT
ejpam-3133	3	22	qatar	qatar	PROPN
ejpam-3133	3	23	department	department	PROPN
ejpam-3133	3	24	of	of	ADP
ejpam-3133	3	25	mathematics	mathematic	NOUN
ejpam-3133	3	26	,	,	PUNCT
ejpam-3133	3	27	the	the	DET
ejpam-3133	3	28	hashemite	hashemite	PROPN
ejpam-3133	3	29	university	university	NOUN
ejpam-3133	3	30	,	,	PUNCT
ejpam-3133	3	31	zarqajordan	zarqajordan	PROPN
ejpam-3133	3	32	2	2	NUM
ejpam-3133	3	33	department	department	NOUN
ejpam-3133	3	34	of	of	ADP
ejpam-3133	3	35	mathematics	mathematic	NOUN
ejpam-3133	3	36	,	,	PUNCT
ejpam-3133	3	37	statistics	statistic	NOUN
ejpam-3133	3	38	and	and	CCONJ
ejpam-3133	3	39	physics	physics	PROPN
ejpam-3133	3	40	,	,	PUNCT
ejpam-3133	3	41	qatar	qatar	PROPN
ejpam-3133	3	42	university	university	PROPN
ejpam-3133	3	43	,	,	PUNCT
ejpam-3133	3	44	doha	doha	PROPN
ejpam-3133	3	45	,	,	PUNCT
ejpam-3133	3	46	qatar	qatar	PROPN
ejpam-3133	3	47	3	3	NUM
ejpam-3133	3	48	imam	imam	PROPN
ejpam-3133	3	49	abdulrahman	abdulrahman	PROPN
ejpam-3133	3	50	bin	bin	PROPN
ejpam-3133	3	51	faisal	faisal	PROPN
ejpam-3133	3	52	university	university	PROPN
ejpam-3133	3	53	,	,	PUNCT
ejpam-3133	3	54	department	department	NOUN
ejpam-3133	3	55	of	of	ADP
ejpam-3133	3	56	mathematics	mathematics	PROPN
ejpam-3133	3	57	,	,	PUNCT
ejpam-3133	3	58	college	college	NOUN
ejpam-3133	3	59	of	of	ADP
ejpam-3133	3	60	education	education	NOUN
ejpam-3133	3	61	of	of	ADP
ejpam-3133	3	62	jubail	jubail	PROPN
ejpam-3133	3	63	,	,	PUNCT
ejpam-3133	3	64	p.o	p.o	PROPN
ejpam-3133	3	65	:	:	PUNCT
ejpam-3133	3	66	12020	12020	NUM
ejpam-3133	3	67	,	,	PUNCT
ejpam-3133	3	68	industrial	industrial	ADJ
ejpam-3133	3	69	jubail	jubail	NOUN
ejpam-3133	3	70	31961	31961	NUM
ejpam-3133	3	71	,	,	PUNCT
ejpam-3133	3	72	saudi	saudi	PROPN
ejpam-3133	3	73	arabia	arabia	PROPN
ejpam-3133	3	74	4	4	NUM
ejpam-3133	3	75	department	department	NOUN
ejpam-3133	3	76	of	of	ADP
ejpam-3133	3	77	medical	medical	ADJ
ejpam-3133	3	78	research	research	NOUN
ejpam-3133	3	79	,	,	PUNCT
ejpam-3133	3	80	china	china	PROPN
ejpam-3133	3	81	medical	medical	PROPN
ejpam-3133	3	82	university	university	PROPN
ejpam-3133	3	83	hospital	hospital	NOUN
ejpam-3133	3	84	,	,	PUNCT
ejpam-3133	3	85	china	china	PROPN
ejpam-3133	3	86	medical	medical	PROPN
ejpam-3133	3	87	university	university	PROPN
ejpam-3133	3	88	,	,	PUNCT
ejpam-3133	3	89	taichung	taichung	PROPN
ejpam-3133	3	90	,	,	PUNCT
ejpam-3133	3	91	taiwan	taiwan	PROPN
ejpam-3133	3	92	5	5	NUM
ejpam-3133	3	93	department	department	NOUN
ejpam-3133	3	94	of	of	ADP
ejpam-3133	3	95	mathematics	mathematics	PROPN
ejpam-3133	3	96	.	.	PUNCT
ejpam-3133	4	1	faculty	faculty	NOUN
ejpam-3133	4	2	of	of	ADP
ejpam-3133	4	3	science	science	NOUN
ejpam-3133	4	4	,	,	PUNCT
ejpam-3133	4	5	yarmouk	yarmouk	CCONJ
ejpam-3133	4	6	university	university	NOUN
ejpam-3133	4	7	,	,	PUNCT
ejpam-3133	4	8	irbid	irbid	PROPN
ejpam-3133	4	9	,	,	PUNCT
ejpam-3133	4	10	jordan	jordan	PROPN
ejpam-3133	4	11	abstract	abstract	PROPN
ejpam-3133	4	12	.	.	PUNCT
ejpam-3133	5	1	the	the	DET
ejpam-3133	5	2	aim	aim	NOUN
ejpam-3133	5	3	of	of	ADP
ejpam-3133	5	4	this	this	DET
ejpam-3133	5	5	manuscript	manuscript	NOUN
ejpam-3133	5	6	is	be	AUX
ejpam-3133	5	7	to	to	PART
ejpam-3133	5	8	present	present	VERB
ejpam-3133	5	9	a	a	DET
ejpam-3133	5	10	unique	unique	ADJ
ejpam-3133	5	11	common	common	ADJ
ejpam-3133	5	12	fixed	fix	VERB
ejpam-3133	5	13	point	point	NOUN
ejpam-3133	5	14	theorem	theorem	NOUN
ejpam-3133	5	15	for	for	ADP
ejpam-3133	5	16	six	six	NUM
ejpam-3133	5	17	mappings	mapping	NOUN
ejpam-3133	5	18	satisfying	satisfying	ADJ
ejpam-3133	5	19	(	(	PUNCT
ejpam-3133	5	20	φ	φ	PROPN
ejpam-3133	5	21	,	,	PUNCT
ejpam-3133	5	22	ψ)-contractions	ψ)-contraction	NOUN
ejpam-3133	5	23	using	use	VERB
ejpam-3133	5	24	(	(	PUNCT
ejpam-3133	5	25	e.a	e.a	PROPN
ejpam-3133	5	26	)	)	PUNCT
ejpam-3133	5	27	property	property	NOUN
ejpam-3133	5	28	in	in	ADP
ejpam-3133	5	29	the	the	DET
ejpam-3133	5	30	framework	framework	NOUN
ejpam-3133	5	31	of	of	ADP
ejpam-3133	5	32	gbmetric	gbmetric	ADJ
ejpam-3133	5	33	spaces	space	NOUN
ejpam-3133	5	34	.	.	PUNCT
ejpam-3133	6	1	an	an	DET
ejpam-3133	6	2	illustrative	illustrative	ADJ
ejpam-3133	6	3	example	example	NOUN
ejpam-3133	6	4	is	be	AUX
ejpam-3133	6	5	also	also	ADV
ejpam-3133	6	6	given	give	VERB
ejpam-3133	6	7	to	to	PART
ejpam-3133	6	8	justify	justify	VERB
ejpam-3133	6	9	the	the	DET
ejpam-3133	6	10	established	establish	VERB
ejpam-3133	6	11	result	result	NOUN
ejpam-3133	6	12	.	.	PUNCT
ejpam-3133	7	1	2010	2010	NUM
ejpam-3133	7	2	mathematics	mathematic	NOUN
ejpam-3133	7	3	subject	subject	NOUN
ejpam-3133	7	4	classifications	classification	NOUN
ejpam-3133	7	5	:	:	PUNCT
ejpam-3133	7	6	47h10	47h10	NUM
ejpam-3133	7	7	,	,	PUNCT
ejpam-3133	7	8	54h25	54h25	NUM
ejpam-3133	7	9	key	key	ADJ
ejpam-3133	7	10	words	word	NOUN
ejpam-3133	7	11	and	and	CCONJ
ejpam-3133	7	12	phrases	phrase	NOUN
ejpam-3133	7	13	:	:	PUNCT
ejpam-3133	7	14	complete	complete	VERB
ejpam-3133	7	15	gb	gb	ADV
ejpam-3133	7	16	-	-	PUNCT
ejpam-3133	7	17	metric	metric	ADJ
ejpam-3133	7	18	space	space	NOUN
ejpam-3133	7	19	,	,	PUNCT
ejpam-3133	7	20	cauchy	cauchy	ADJ
ejpam-3133	7	21	sequence	sequence	NOUN
ejpam-3133	7	22	,	,	PUNCT
ejpam-3133	7	23	(	(	PUNCT
ejpam-3133	7	24	φ	φ	NOUN
ejpam-3133	7	25	,	,	PUNCT
ejpam-3133	7	26	ψ)-contraction	ψ)-contraction	PUNCT
ejpam-3133	7	27	,	,	PUNCT
ejpam-3133	7	28	(	(	PUNCT
ejpam-3133	7	29	e.a	e.a	PROPN
ejpam-3133	7	30	)	)	PUNCT
ejpam-3133	7	31	property	property	NOUN
ejpam-3133	7	32	,	,	PUNCT
ejpam-3133	7	33	common	common	ADJ
ejpam-3133	7	34	fixed	fix	VERB
ejpam-3133	7	35	point	point	NOUN
ejpam-3133	7	36	,	,	PUNCT
ejpam-3133	7	37	weakly	weakly	ADV
ejpam-3133	7	38	compatible	compatible	ADJ
ejpam-3133	7	39	.	.	PUNCT
ejpam-3133	8	1	1	1	X
ejpam-3133	8	2	.	.	X
ejpam-3133	8	3	introduction	introduction	NOUN
ejpam-3133	8	4	in	in	ADP
ejpam-3133	8	5	recent	recent	ADJ
ejpam-3133	8	6	years	year	NOUN
ejpam-3133	8	7	,	,	PUNCT
ejpam-3133	8	8	many	many	ADJ
ejpam-3133	8	9	authors	author	NOUN
ejpam-3133	8	10	studied	study	VERB
ejpam-3133	8	11	common	common	ADJ
ejpam-3133	8	12	fixed	fix	VERB
ejpam-3133	8	13	points	point	NOUN
ejpam-3133	8	14	of	of	ADP
ejpam-3133	8	15	mappings	mapping	NOUN
ejpam-3133	8	16	having	have	VERB
ejpam-3133	8	17	different	different	ADJ
ejpam-3133	8	18	contractive	contractive	ADJ
ejpam-3133	8	19	conditions	condition	NOUN
ejpam-3133	8	20	.	.	PUNCT
ejpam-3133	9	1	this	this	DET
ejpam-3133	9	2	area	area	NOUN
ejpam-3133	9	3	has	have	VERB
ejpam-3133	9	4	variety	variety	NOUN
ejpam-3133	9	5	of	of	ADP
ejpam-3133	9	6	important	important	ADJ
ejpam-3133	9	7	applications	application	NOUN
ejpam-3133	9	8	in	in	ADP
ejpam-3133	9	9	applied	apply	VERB
ejpam-3133	9	10	mathematics	mathematic	NOUN
ejpam-3133	9	11	and	and	CCONJ
ejpam-3133	9	12	sciences	science	NOUN
ejpam-3133	9	13	.	.	PUNCT
ejpam-3133	10	1	in	in	ADP
ejpam-3133	10	2	1976	1976	NUM
ejpam-3133	10	3	,	,	PUNCT
ejpam-3133	10	4	jungck	jungck	NOUN
ejpam-3133	11	1	[	[	X
ejpam-3133	11	2	17	17	NUM
ejpam-3133	11	3	]	]	PUNCT
ejpam-3133	11	4	proved	prove	VERB
ejpam-3133	11	5	a	a	DET
ejpam-3133	11	6	common	common	ADJ
ejpam-3133	11	7	fixed	fix	VERB
ejpam-3133	11	8	point	point	NOUN
ejpam-3133	11	9	theorem	theorem	NOUN
ejpam-3133	11	10	for	for	ADP
ejpam-3133	11	11	commuting	commuting	NOUN
ejpam-3133	11	12	maps	map	NOUN
ejpam-3133	11	13	under	under	ADP
ejpam-3133	11	14	the	the	DET
ejpam-3133	11	15	assumption	assumption	NOUN
ejpam-3133	11	16	that	that	SCONJ
ejpam-3133	11	17	one	one	NUM
ejpam-3133	11	18	of	of	ADP
ejpam-3133	11	19	maps	map	NOUN
ejpam-3133	11	20	must	must	AUX
ejpam-3133	11	21	be	be	AUX
ejpam-3133	11	22	continuous	continuous	ADJ
ejpam-3133	11	23	.	.	PUNCT
ejpam-3133	12	1	in	in	ADP
ejpam-3133	12	2	1982	1982	NUM
ejpam-3133	12	3	,	,	PUNCT
ejpam-3133	12	4	the	the	DET
ejpam-3133	12	5	concept	concept	NOUN
ejpam-3133	12	6	of	of	ADP
ejpam-3133	12	7	weak	weak	ADJ
ejpam-3133	12	8	commutativity	commutativity	NOUN
ejpam-3133	12	9	for	for	ADP
ejpam-3133	12	10	a	a	DET
ejpam-3133	12	11	pair	pair	NOUN
ejpam-3133	12	12	of	of	ADP
ejpam-3133	12	13	self	self	NOUN
ejpam-3133	12	14	maps	map	NOUN
ejpam-3133	12	15	was	be	AUX
ejpam-3133	12	16	introduced	introduce	VERB
ejpam-3133	12	17	by	by	ADP
ejpam-3133	12	18	sessa	sessa	NOUN
ejpam-3133	12	19	[	[	X
ejpam-3133	12	20	47	47	NUM
ejpam-3133	12	21	]	]	PUNCT
ejpam-3133	12	22	.	.	PUNCT
ejpam-3133	13	1	he	he	PRON
ejpam-3133	13	2	also	also	ADV
ejpam-3133	13	3	proved	prove	VERB
ejpam-3133	13	4	that	that	SCONJ
ejpam-3133	13	5	weakly	weakly	ADJ
ejpam-3133	13	6	commuting	commuting	NOUN
ejpam-3133	13	7	pairs	pair	NOUN
ejpam-3133	13	8	of	of	ADP
ejpam-3133	13	9	maps	map	NOUN
ejpam-3133	13	10	in	in	ADP
ejpam-3133	13	11	a	a	DET
ejpam-3133	13	12	metric	metric	ADJ
ejpam-3133	13	13	space	space	NOUN
ejpam-3133	13	14	are	be	AUX
ejpam-3133	13	15	commuting	commute	VERB
ejpam-3133	13	16	,	,	PUNCT
ejpam-3133	13	17	but	but	CCONJ
ejpam-3133	13	18	the	the	DET
ejpam-3133	13	19	converse	converse	NOUN
ejpam-3133	13	20	need	need	AUX
ejpam-3133	13	21	not	not	PART
ejpam-3133	13	22	be	be	AUX
ejpam-3133	13	23	true	true	ADJ
ejpam-3133	13	24	.	.	PUNCT
ejpam-3133	14	1	later	later	ADV
ejpam-3133	14	2	,	,	PUNCT
ejpam-3133	14	3	jungck	jungck	PROPN
ejpam-3133	15	1	[	[	X
ejpam-3133	15	2	18	18	NUM
ejpam-3133	15	3	]	]	PUNCT
ejpam-3133	15	4	introduced	introduce	VERB
ejpam-3133	15	5	the	the	DET
ejpam-3133	15	6	notion	notion	NOUN
ejpam-3133	15	7	of	of	ADP
ejpam-3133	15	8	compatible	compatible	ADJ
ejpam-3133	15	9	mappings	mapping	NOUN
ejpam-3133	15	10	in	in	ADP
ejpam-3133	15	11	order	order	NOUN
ejpam-3133	15	12	to	to	PART
ejpam-3133	15	13	generalize	generalize	VERB
ejpam-3133	15	14	the	the	DET
ejpam-3133	15	15	concepts	concept	NOUN
ejpam-3133	15	16	of	of	ADP
ejpam-3133	15	17	weak	weak	ADJ
ejpam-3133	15	18	commutativity	commutativity	NOUN
ejpam-3133	15	19	and	and	CCONJ
ejpam-3133	15	20	showed	show	VERB
ejpam-3133	15	21	that	that	SCONJ
ejpam-3133	15	22	weak	weak	ADJ
ejpam-3133	15	23	commuting	commuting	NOUN
ejpam-3133	15	24	maps	map	NOUN
ejpam-3133	15	25	are	be	AUX
ejpam-3133	15	26	compatible	compatible	ADJ
ejpam-3133	15	27	,	,	PUNCT
ejpam-3133	15	28	but	but	CCONJ
ejpam-3133	15	29	the	the	DET
ejpam-3133	15	30	reverse	reverse	ADJ
ejpam-3133	15	31	implication	implication	NOUN
ejpam-3133	15	32	may	may	AUX
ejpam-3133	15	33	not	not	PART
ejpam-3133	15	34	hold	hold	VERB
ejpam-3133	15	35	.	.	PUNCT
ejpam-3133	16	1	∗corresponding	∗corresponde	VERB
ejpam-3133	16	2	author	author	NOUN
ejpam-3133	16	3	.	.	PUNCT
ejpam-3133	17	1	email	email	NOUN
ejpam-3133	17	2	addresses	address	NOUN
ejpam-3133	17	3	:	:	PUNCT
ejpam-3133	17	4	zead@qu.edu.qa	zead@qu.edu.qa	PROPN
ejpam-3133	17	5	,	,	PUNCT
ejpam-3133	17	6	zmagablh@hu.edu.jo	zmagablh@hu.edu.jo	PROPN
ejpam-3133	17	7	(	(	PUNCT
ejpam-3133	17	8	z.	z.	PROPN
ejpam-3133	17	9	mustafa	mustafa	PROPN
ejpam-3133	17	10	)	)	PUNCT
ejpam-3133	17	11	,	,	PUNCT
ejpam-3133	17	12	mmjst4@qu.edu.qa	mmjst4@qu.edu.qa	PROPN
ejpam-3133	17	13	(	(	PUNCT
ejpam-3133	17	14	m.m.m	m.m.m	NOUN
ejpam-3133	17	15	.	.	PUNCT
ejpam-3133	17	16	jaradat	jaradat	PROPN
ejpam-3133	17	17	)	)	PUNCT
ejpam-3133	17	18	,	,	PUNCT
ejpam-3133	17	19	hmaydi@iau.edu.sa	hmaydi@iau.edu.sa	PROPN
ejpam-3133	17	20	,	,	PUNCT
ejpam-3133	17	21	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	PROPN
ejpam-3133	17	22	(	(	PUNCT
ejpam-3133	17	23	h.	h.	PROPN
ejpam-3133	17	24	aydi	aydi	VERB
ejpam-3133	17	25	)	)	PUNCT
ejpam-3133	17	26	,	,	PUNCT
ejpam-3133	17	27	al-rhayyel@yu.edu.jo	al-rhayyel@yu.edu.jo	NUM
ejpam-3133	17	28	(	(	PUNCT
ejpam-3133	17	29	a.	a.	NOUN
ejpam-3133	17	30	alrhayyel	alrhayyel	PROPN
ejpam-3133	17	31	)	)	PUNCT
ejpam-3133	17	32	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3133	18	1	90	90	NUM
ejpam-3133	18	2	c	c	NOUN
ejpam-3133	18	3	©	©	PROPN
ejpam-3133	18	4	2018	2018	NUM
ejpam-3133	18	5	ejpam	ejpam	VERB
ejpam-3133	18	6	all	all	DET
ejpam-3133	18	7	rights	right	NOUN
ejpam-3133	18	8	reserved	reserve	VERB
ejpam-3133	18	9	.	.	PUNCT
ejpam-3133	19	1	z.	z.	PROPN
ejpam-3133	19	2	mustafa	mustafa	PROPN
ejpam-3133	19	3	et	et	PROPN
ejpam-3133	19	4	al	al	PROPN
ejpam-3133	19	5	.	.	PUNCT
ejpam-3133	19	6	/	/	SYM
ejpam-3133	19	7	eur	eur	PROPN
ejpam-3133	19	8	.	.	PUNCT
ejpam-3133	20	1	j.	j.	PROPN
ejpam-3133	20	2	pure	pure	PROPN
ejpam-3133	20	3	appl	appl	PROPN
ejpam-3133	20	4	.	.	PROPN
ejpam-3133	20	5	math	math	PROPN
ejpam-3133	20	6	,	,	PUNCT
ejpam-3133	20	7	11	11	NUM
ejpam-3133	20	8	(	(	PUNCT
ejpam-3133	20	9	1	1	NUM
ejpam-3133	20	10	)	)	PUNCT
ejpam-3133	20	11	(	(	PUNCT
ejpam-3133	20	12	2018	2018	NUM
ejpam-3133	20	13	)	)	PUNCT
ejpam-3133	20	14	,	,	PUNCT
ejpam-3133	20	15	90	90	NUM
ejpam-3133	20	16	-	-	SYM
ejpam-3133	20	17	109	109	NUM
ejpam-3133	20	18	91	91	NUM
ejpam-3133	20	19	in	in	ADP
ejpam-3133	20	20	1996	1996	NUM
ejpam-3133	20	21	,	,	PUNCT
ejpam-3133	20	22	jungck	jungck	PROPN
ejpam-3133	21	1	[	[	X
ejpam-3133	21	2	20	20	NUM
ejpam-3133	21	3	]	]	PUNCT
ejpam-3133	21	4	defined	define	VERB
ejpam-3133	21	5	a	a	DET
ejpam-3133	21	6	pair	pair	NOUN
ejpam-3133	21	7	of	of	ADP
ejpam-3133	21	8	self	self	NOUN
ejpam-3133	21	9	mappings	mapping	NOUN
ejpam-3133	21	10	to	to	PART
ejpam-3133	21	11	be	be	AUX
ejpam-3133	21	12	weakly	weakly	ADV
ejpam-3133	21	13	compatible	compatible	ADJ
ejpam-3133	21	14	if	if	SCONJ
ejpam-3133	21	15	they	they	PRON
ejpam-3133	21	16	commute	commute	VERB
ejpam-3133	21	17	at	at	ADP
ejpam-3133	21	18	their	their	PRON
ejpam-3133	21	19	coincidence	coincidence	NOUN
ejpam-3133	21	20	points	point	NOUN
ejpam-3133	21	21	.	.	PUNCT
ejpam-3133	22	1	therefore	therefore	ADV
ejpam-3133	22	2	,	,	PUNCT
ejpam-3133	22	3	we	we	PRON
ejpam-3133	22	4	have	have	VERB
ejpam-3133	22	5	one	one	NUM
ejpam-3133	22	6	way	way	NOUN
ejpam-3133	22	7	implication	implication	NOUN
ejpam-3133	22	8	namely	namely	ADV
ejpam-3133	22	9	,	,	PUNCT
ejpam-3133	22	10	commuting	commute	VERB
ejpam-3133	22	11	maps⇒weakly	maps⇒weakly	ADV
ejpam-3133	22	12	commuting	commuting	NOUN
ejpam-3133	22	13	maps	map	NOUN
ejpam-3133	22	14	⇒	⇒	NOUN
ejpam-3133	22	15	compatible	compatible	ADJ
ejpam-3133	22	16	maps	map	NOUN
ejpam-3133	22	17	⇒	⇒	VERB
ejpam-3133	22	18	weakly	weakly	ADJ
ejpam-3133	22	19	compatible	compatible	ADJ
ejpam-3133	22	20	maps	map	NOUN
ejpam-3133	22	21	.	.	PUNCT
ejpam-3133	23	1	recently	recently	ADV
ejpam-3133	23	2	,	,	PUNCT
ejpam-3133	23	3	various	various	ADJ
ejpam-3133	23	4	authors	author	NOUN
ejpam-3133	23	5	have	have	AUX
ejpam-3133	23	6	introduced	introduce	VERB
ejpam-3133	23	7	a	a	DET
ejpam-3133	23	8	coincidence	coincidence	NOUN
ejpam-3133	23	9	points	point	NOUN
ejpam-3133	23	10	results	result	NOUN
ejpam-3133	23	11	for	for	ADP
ejpam-3133	23	12	various	various	ADJ
ejpam-3133	23	13	classes	class	NOUN
ejpam-3133	23	14	of	of	ADP
ejpam-3133	23	15	mappings	mapping	NOUN
ejpam-3133	23	16	on	on	ADP
ejpam-3133	23	17	metric	metric	ADJ
ejpam-3133	23	18	spaces	space	NOUN
ejpam-3133	23	19	.	.	PUNCT
ejpam-3133	24	1	for	for	ADP
ejpam-3133	24	2	more	more	ADJ
ejpam-3133	24	3	details	detail	NOUN
ejpam-3133	24	4	on	on	ADP
ejpam-3133	24	5	coincidence	coincidence	NOUN
ejpam-3133	24	6	point	point	NOUN
ejpam-3133	24	7	theory	theory	NOUN
ejpam-3133	24	8	and	and	CCONJ
ejpam-3133	24	9	related	related	ADJ
ejpam-3133	24	10	results	result	NOUN
ejpam-3133	24	11	,	,	PUNCT
ejpam-3133	24	12	see	see	VERB
ejpam-3133	24	13	[	[	X
ejpam-3133	24	14	19	19	NUM
ejpam-3133	24	15	,	,	PUNCT
ejpam-3133	24	16	21	21	NUM
ejpam-3133	24	17	,	,	PUNCT
ejpam-3133	24	18	43	43	NUM
ejpam-3133	24	19	]	]	PUNCT
ejpam-3133	24	20	.	.	PUNCT
ejpam-3133	25	1	however	however	ADV
ejpam-3133	25	2	,	,	PUNCT
ejpam-3133	25	3	the	the	DET
ejpam-3133	25	4	study	study	NOUN
ejpam-3133	25	5	of	of	ADP
ejpam-3133	25	6	common	common	ADJ
ejpam-3133	25	7	fixed	fix	VERB
ejpam-3133	25	8	points	point	NOUN
ejpam-3133	25	9	of	of	ADP
ejpam-3133	25	10	non	non	ADJ
ejpam-3133	25	11	-	-	ADJ
ejpam-3133	25	12	compatible	compatible	ADJ
ejpam-3133	25	13	mappings	mapping	NOUN
ejpam-3133	25	14	has	have	AUX
ejpam-3133	25	15	recently	recently	ADV
ejpam-3133	25	16	been	be	AUX
ejpam-3133	25	17	initiated	initiate	VERB
ejpam-3133	25	18	by	by	ADP
ejpam-3133	25	19	pant	pant	NOUN
ejpam-3133	25	20	[	[	X
ejpam-3133	25	21	44	44	NUM
ejpam-3133	25	22	]	]	PUNCT
ejpam-3133	25	23	.	.	PUNCT
ejpam-3133	26	1	in	in	ADP
ejpam-3133	26	2	2002	2002	NUM
ejpam-3133	26	3	,	,	PUNCT
ejpam-3133	26	4	amari	amari	PROPN
ejpam-3133	26	5	and	and	CCONJ
ejpam-3133	26	6	el	el	PROPN
ejpam-3133	26	7	moutawakil	moutawakil	PROPN
ejpam-3133	27	1	[	[	X
ejpam-3133	27	2	1	1	X
ejpam-3133	27	3	]	]	PUNCT
ejpam-3133	27	4	defined	define	VERB
ejpam-3133	27	5	a	a	DET
ejpam-3133	27	6	new	new	ADJ
ejpam-3133	27	7	property	property	NOUN
ejpam-3133	27	8	called	call	VERB
ejpam-3133	27	9	(	(	PUNCT
ejpam-3133	27	10	e.a	e.a	PROPN
ejpam-3133	27	11	)	)	PUNCT
ejpam-3133	27	12	property	property	NOUN
ejpam-3133	27	13	which	which	PRON
ejpam-3133	27	14	generalizes	generalize	VERB
ejpam-3133	27	15	the	the	DET
ejpam-3133	27	16	concept	concept	NOUN
ejpam-3133	27	17	of	of	ADP
ejpam-3133	27	18	non	non	ADJ
ejpam-3133	27	19	-	-	ADJ
ejpam-3133	27	20	compatible	compatible	ADJ
ejpam-3133	27	21	mappings	mapping	NOUN
ejpam-3133	27	22	and	and	CCONJ
ejpam-3133	27	23	they	they	PRON
ejpam-3133	27	24	proved	prove	VERB
ejpam-3133	27	25	some	some	DET
ejpam-3133	27	26	common	common	ADJ
ejpam-3133	27	27	fixed	fix	VERB
ejpam-3133	27	28	point	point	NOUN
ejpam-3133	27	29	theorem	theorem	VERB
ejpam-3133	27	30	.	.	PROPN
ejpam-3133	27	31	yan	yan	PROPN
ejpam-3133	27	32	et	et	PROPN
ejpam-3133	27	33	al	al	PROPN
ejpam-3133	27	34	.	.	PUNCT
ejpam-3133	28	1	[	[	X
ejpam-3133	28	2	48	48	NUM
ejpam-3133	28	3	]	]	PUNCT
ejpam-3133	28	4	gave	give	VERB
ejpam-3133	28	5	the	the	DET
ejpam-3133	28	6	idea	idea	NOUN
ejpam-3133	28	7	of	of	ADP
ejpam-3133	28	8	(	(	PUNCT
ejpam-3133	28	9	φ	φ	NOUN
ejpam-3133	28	10	,	,	PUNCT
ejpam-3133	28	11	ψ)-contractions	ψ)-contraction	NOUN
ejpam-3133	28	12	and	and	CCONJ
ejpam-3133	28	13	proved	prove	VERB
ejpam-3133	28	14	a	a	DET
ejpam-3133	28	15	fixed	fix	VERB
ejpam-3133	28	16	point	point	NOUN
ejpam-3133	28	17	theorem	theorem	NOUN
ejpam-3133	28	18	of	of	ADP
ejpam-3133	28	19	a	a	DET
ejpam-3133	28	20	contraction	contraction	NOUN
ejpam-3133	28	21	mapping	mapping	NOUN
ejpam-3133	28	22	in	in	ADP
ejpam-3133	28	23	a	a	DET
ejpam-3133	28	24	complete	complete	ADJ
ejpam-3133	28	25	metric	metric	ADJ
ejpam-3133	28	26	space	space	NOUN
ejpam-3133	28	27	endowed	endow	VERB
ejpam-3133	28	28	with	with	ADP
ejpam-3133	28	29	a	a	DET
ejpam-3133	28	30	partial	partial	ADJ
ejpam-3133	28	31	order	order	NOUN
ejpam-3133	28	32	by	by	ADP
ejpam-3133	28	33	using	use	VERB
ejpam-3133	28	34	altering	alter	VERB
ejpam-3133	28	35	distance	distance	NOUN
ejpam-3133	28	36	functions	function	NOUN
ejpam-3133	28	37	[	[	X
ejpam-3133	28	38	22	22	NUM
ejpam-3133	28	39	]	]	PUNCT
ejpam-3133	28	40	.	.	PUNCT
ejpam-3133	29	1	different	different	ADJ
ejpam-3133	29	2	authors	author	NOUN
ejpam-3133	29	3	used	use	VERB
ejpam-3133	29	4	(	(	PUNCT
ejpam-3133	29	5	φ	φ	PROPN
ejpam-3133	29	6	,	,	PUNCT
ejpam-3133	29	7	ψ)-contractions	ψ)-contraction	NOUN
ejpam-3133	29	8	to	to	PART
ejpam-3133	29	9	obtain	obtain	VERB
ejpam-3133	29	10	common	common	ADJ
ejpam-3133	29	11	fixed	fix	VERB
ejpam-3133	29	12	point	point	NOUN
ejpam-3133	29	13	results	result	NOUN
ejpam-3133	29	14	in	in	ADP
ejpam-3133	29	15	different	different	ADJ
ejpam-3133	29	16	spaces	space	NOUN
ejpam-3133	29	17	.	.	PUNCT
ejpam-3133	30	1	some	some	PRON
ejpam-3133	30	2	of	of	ADP
ejpam-3133	30	3	the	the	DET
ejpam-3133	30	4	works	work	NOUN
ejpam-3133	30	5	on	on	ADP
ejpam-3133	30	6	(	(	PUNCT
ejpam-3133	30	7	φ	φ	PROPN
ejpam-3133	30	8	,	,	PUNCT
ejpam-3133	30	9	ψ)-contractions	ψ)-contraction	NOUN
ejpam-3133	30	10	are	be	AUX
ejpam-3133	30	11	given	give	VERB
ejpam-3133	30	12	in	in	ADP
ejpam-3133	30	13	[	[	X
ejpam-3133	30	14	4	4	NUM
ejpam-3133	30	15	,	,	PUNCT
ejpam-3133	30	16	5	5	NUM
ejpam-3133	30	17	,	,	PUNCT
ejpam-3133	30	18	8	8	NUM
ejpam-3133	30	19	,	,	PUNCT
ejpam-3133	30	20	10	10	NUM
ejpam-3133	30	21	,	,	PUNCT
ejpam-3133	30	22	26	26	NUM
ejpam-3133	30	23	,	,	PUNCT
ejpam-3133	30	24	27	27	NUM
ejpam-3133	30	25	,	,	PUNCT
ejpam-3133	30	26	42	42	NUM
ejpam-3133	30	27	,	,	PUNCT
ejpam-3133	30	28	23	23	NUM
ejpam-3133	30	29	,	,	PUNCT
ejpam-3133	30	30	41	41	NUM
ejpam-3133	30	31	]	]	PUNCT
ejpam-3133	30	32	.	.	PUNCT
ejpam-3133	31	1	mustafa	mustafa	PROPN
ejpam-3133	31	2	and	and	CCONJ
ejpam-3133	31	3	sims	sim	NOUN
ejpam-3133	31	4	[	[	X
ejpam-3133	31	5	28	28	NUM
ejpam-3133	31	6	]	]	PUNCT
ejpam-3133	31	7	introduced	introduce	VERB
ejpam-3133	31	8	a	a	DET
ejpam-3133	31	9	new	new	ADJ
ejpam-3133	31	10	generalizations	generalization	NOUN
ejpam-3133	31	11	of	of	ADP
ejpam-3133	31	12	a	a	DET
ejpam-3133	31	13	metric	metric	ADJ
ejpam-3133	31	14	space	space	NOUN
ejpam-3133	31	15	by	by	ADP
ejpam-3133	31	16	assigning	assign	VERB
ejpam-3133	31	17	to	to	ADP
ejpam-3133	31	18	every	every	DET
ejpam-3133	31	19	(	(	PUNCT
ejpam-3133	31	20	x	x	NOUN
ejpam-3133	31	21	,	,	PUNCT
ejpam-3133	31	22	y	y	PROPN
ejpam-3133	31	23	,	,	PUNCT
ejpam-3133	31	24	z	z	NOUN
ejpam-3133	31	25	)	)	PUNCT
ejpam-3133	31	26	∈	∈	PROPN
ejpam-3133	31	27	x	x	X
ejpam-3133	31	28	×x	×x	X
ejpam-3133	31	29	×x	×x	VERB
ejpam-3133	31	30	a	a	DET
ejpam-3133	31	31	real	real	ADJ
ejpam-3133	31	32	number	number	NOUN
ejpam-3133	31	33	and	and	CCONJ
ejpam-3133	31	34	is	be	AUX
ejpam-3133	31	35	named	name	VERB
ejpam-3133	31	36	as	as	ADP
ejpam-3133	31	37	a	a	DET
ejpam-3133	31	38	g	g	NOUN
ejpam-3133	31	39	-	-	PUNCT
ejpam-3133	31	40	metric	metric	ADJ
ejpam-3133	31	41	space	space	NOUN
ejpam-3133	31	42	.	.	PUNCT
ejpam-3133	32	1	in	in	ADP
ejpam-3133	32	2	2008	2008	NUM
ejpam-3133	32	3	,	,	PUNCT
ejpam-3133	32	4	mustafa	mustafa	PROPN
ejpam-3133	32	5	et	et	PROPN
ejpam-3133	32	6	al	al	PROPN
ejpam-3133	32	7	.	.	PUNCT
ejpam-3133	33	1	[	[	X
ejpam-3133	33	2	29	29	NUM
ejpam-3133	33	3	]	]	PUNCT
ejpam-3133	33	4	obtained	obtain	VERB
ejpam-3133	33	5	some	some	DET
ejpam-3133	33	6	fixed	fix	VERB
ejpam-3133	33	7	point	point	NOUN
ejpam-3133	33	8	results	result	NOUN
ejpam-3133	33	9	in	in	ADP
ejpam-3133	33	10	g	g	NOUN
ejpam-3133	33	11	-	-	PUNCT
ejpam-3133	33	12	metric	metric	ADJ
ejpam-3133	33	13	spaces	space	NOUN
ejpam-3133	33	14	for	for	ADP
ejpam-3133	33	15	mappings	mapping	NOUN
ejpam-3133	33	16	satisfying	satisfy	VERB
ejpam-3133	33	17	different	different	ADJ
ejpam-3133	33	18	contractive	contractive	ADJ
ejpam-3133	33	19	conditions	condition	NOUN
ejpam-3133	33	20	.	.	PUNCT
ejpam-3133	34	1	after	after	SCONJ
ejpam-3133	34	2	that	that	PRON
ejpam-3133	34	3	several	several	ADJ
ejpam-3133	34	4	fixed	fix	VERB
ejpam-3133	34	5	point	point	NOUN
ejpam-3133	34	6	results	result	NOUN
ejpam-3133	34	7	were	be	AUX
ejpam-3133	34	8	obtained	obtain	VERB
ejpam-3133	34	9	.	.	PUNCT
ejpam-3133	35	1	among	among	ADP
ejpam-3133	35	2	these	these	DET
ejpam-3133	35	3	works	work	NOUN
ejpam-3133	35	4	,	,	PUNCT
ejpam-3133	35	5	we	we	PRON
ejpam-3133	35	6	mention	mention	VERB
ejpam-3133	35	7	(	(	PUNCT
ejpam-3133	35	8	[	[	X
ejpam-3133	35	9	6],[7],[11],[14],[15	6],[7],[11],[14],[15	X
ejpam-3133	35	10	]	]	X
ejpam-3133	35	11	,	,	PUNCT
ejpam-3133	35	12	[	[	X
ejpam-3133	35	13	16],[24]-[40	16],[24]-[40	NUM
ejpam-3133	35	14	]	]	PUNCT
ejpam-3133	35	15	)	)	PUNCT
ejpam-3133	35	16	.	.	PUNCT
ejpam-3133	36	1	in	in	ADP
ejpam-3133	36	2	2014	2014	NUM
ejpam-3133	36	3	,	,	PUNCT
ejpam-3133	36	4	aghajani	aghajani	PROPN
ejpam-3133	36	5	et	et	PROPN
ejpam-3133	36	6	al	al	PROPN
ejpam-3133	36	7	.	.	PUNCT
ejpam-3133	37	1	[	[	X
ejpam-3133	37	2	2	2	X
ejpam-3133	37	3	]	]	PUNCT
ejpam-3133	37	4	introduced	introduce	VERB
ejpam-3133	37	5	a	a	DET
ejpam-3133	37	6	new	new	ADJ
ejpam-3133	37	7	generalization	generalization	NOUN
ejpam-3133	37	8	of	of	ADP
ejpam-3133	37	9	a	a	DET
ejpam-3133	37	10	metric	metric	ADJ
ejpam-3133	37	11	space	space	NOUN
ejpam-3133	37	12	.	.	PUNCT
ejpam-3133	38	1	they	they	PRON
ejpam-3133	38	2	combined	combine	VERB
ejpam-3133	38	3	the	the	DET
ejpam-3133	38	4	definition	definition	NOUN
ejpam-3133	38	5	of	of	ADP
ejpam-3133	38	6	a	a	DET
ejpam-3133	38	7	g	g	NOUN
ejpam-3133	38	8	-	-	PUNCT
ejpam-3133	38	9	metric	metric	ADJ
ejpam-3133	38	10	and	and	CCONJ
ejpam-3133	38	11	a	a	DET
ejpam-3133	38	12	b	b	NOUN
ejpam-3133	38	13	-	-	ADJ
ejpam-3133	38	14	metric	metric	ADJ
ejpam-3133	38	15	and	and	CCONJ
ejpam-3133	38	16	generated	generate	VERB
ejpam-3133	38	17	a	a	DET
ejpam-3133	38	18	new	new	ADJ
ejpam-3133	38	19	definition	definition	NOUN
ejpam-3133	38	20	called	call	VERB
ejpam-3133	38	21	a	a	DET
ejpam-3133	38	22	gb	gb	ADV
ejpam-3133	38	23	-	-	PUNCT
ejpam-3133	38	24	metric	metric	ADJ
ejpam-3133	38	25	space	space	NOUN
ejpam-3133	38	26	.	.	PUNCT
ejpam-3133	39	1	they	they	PRON
ejpam-3133	39	2	also	also	ADV
ejpam-3133	39	3	pointed	point	VERB
ejpam-3133	39	4	out	out	ADP
ejpam-3133	39	5	that	that	SCONJ
ejpam-3133	39	6	the	the	DET
ejpam-3133	39	7	class	class	NOUN
ejpam-3133	39	8	of	of	ADP
ejpam-3133	39	9	gb	gb	ADV
ejpam-3133	39	10	-	-	PUNCT
ejpam-3133	39	11	metric	metric	ADJ
ejpam-3133	39	12	spaces	space	NOUN
ejpam-3133	39	13	is	be	AUX
ejpam-3133	39	14	effectively	effectively	ADV
ejpam-3133	39	15	larger	large	ADJ
ejpam-3133	39	16	than	than	ADP
ejpam-3133	39	17	that	that	PRON
ejpam-3133	39	18	of	of	ADP
ejpam-3133	39	19	g	g	NOUN
ejpam-3133	39	20	-	-	PUNCT
ejpam-3133	39	21	metric	metric	ADJ
ejpam-3133	39	22	spaces	space	NOUN
ejpam-3133	39	23	.	.	PUNCT
ejpam-3133	40	1	note	note	VERB
ejpam-3133	40	2	that	that	SCONJ
ejpam-3133	40	3	a	a	DET
ejpam-3133	40	4	g	g	NOUN
ejpam-3133	40	5	-	-	PUNCT
ejpam-3133	40	6	metric	metric	ADJ
ejpam-3133	40	7	space	space	NOUN
ejpam-3133	40	8	becomes	become	VERB
ejpam-3133	40	9	a	a	DET
ejpam-3133	40	10	particular	particular	ADJ
ejpam-3133	40	11	case	case	NOUN
ejpam-3133	40	12	of	of	ADP
ejpam-3133	40	13	a	a	DET
ejpam-3133	40	14	gb	gb	ADV
ejpam-3133	40	15	-	-	PUNCT
ejpam-3133	40	16	metric	metric	ADJ
ejpam-3133	40	17	space	space	NOUN
ejpam-3133	40	18	when	when	SCONJ
ejpam-3133	40	19	s	s	VERB
ejpam-3133	40	20	=	=	NOUN
ejpam-3133	40	21	1	1	X
ejpam-3133	40	22	.	.	PUNCT
ejpam-3133	40	23	further	far	ADV
ejpam-3133	40	24	,	,	PUNCT
ejpam-3133	40	25	they	they	PRON
ejpam-3133	40	26	showed	show	VERB
ejpam-3133	40	27	that	that	SCONJ
ejpam-3133	40	28	every	every	DET
ejpam-3133	40	29	gb	gb	ADV
ejpam-3133	40	30	-	-	PUNCT
ejpam-3133	40	31	metric	metric	ADJ
ejpam-3133	40	32	space	space	NOUN
ejpam-3133	40	33	is	be	AUX
ejpam-3133	40	34	equivalent	equivalent	ADJ
ejpam-3133	40	35	to	to	ADP
ejpam-3133	40	36	a	a	DET
ejpam-3133	40	37	b	b	NOUN
ejpam-3133	40	38	-	-	PUNCT
ejpam-3133	40	39	metric	metric	ADJ
ejpam-3133	40	40	space	space	NOUN
ejpam-3133	40	41	topologically	topologically	ADV
ejpam-3133	40	42	.	.	PUNCT
ejpam-3133	41	1	in	in	ADP
ejpam-3133	41	2	the	the	DET
ejpam-3133	41	3	current	current	ADJ
ejpam-3133	41	4	work	work	NOUN
ejpam-3133	41	5	,	,	PUNCT
ejpam-3133	41	6	we	we	PRON
ejpam-3133	41	7	will	will	AUX
ejpam-3133	41	8	obtain	obtain	VERB
ejpam-3133	41	9	a	a	DET
ejpam-3133	41	10	unique	unique	ADJ
ejpam-3133	41	11	common	common	ADJ
ejpam-3133	41	12	fixed	fix	VERB
ejpam-3133	41	13	point	point	NOUN
ejpam-3133	41	14	result	result	NOUN
ejpam-3133	41	15	in	in	ADP
ejpam-3133	41	16	gbmetric	gbmetric	ADJ
ejpam-3133	41	17	spaces	space	NOUN
ejpam-3133	41	18	involving	involve	VERB
ejpam-3133	41	19	(	(	PUNCT
ejpam-3133	41	20	φ	φ	NOUN
ejpam-3133	41	21	,	,	PUNCT
ejpam-3133	41	22	ψ)-contractions	ψ)-contraction	NOUN
ejpam-3133	41	23	and	and	CCONJ
ejpam-3133	41	24	using	use	VERB
ejpam-3133	41	25	the	the	DET
ejpam-3133	41	26	(	(	PUNCT
ejpam-3133	41	27	e.a	e.a	PROPN
ejpam-3133	41	28	)	)	PUNCT
ejpam-3133	41	29	property	property	NOUN
ejpam-3133	41	30	.	.	PUNCT
ejpam-3133	42	1	also	also	ADV
ejpam-3133	42	2	,	,	PUNCT
ejpam-3133	42	3	an	an	DET
ejpam-3133	42	4	example	example	NOUN
ejpam-3133	42	5	to	to	PART
ejpam-3133	42	6	illustrate	illustrate	VERB
ejpam-3133	42	7	the	the	DET
ejpam-3133	42	8	main	main	ADJ
ejpam-3133	42	9	result	result	NOUN
ejpam-3133	42	10	is	be	AUX
ejpam-3133	42	11	given	give	VERB
ejpam-3133	42	12	.	.	PUNCT
ejpam-3133	43	1	2	2	X
ejpam-3133	43	2	.	.	X
ejpam-3133	43	3	preliminaries	preliminary	NOUN
ejpam-3133	43	4	first	first	ADV
ejpam-3133	43	5	,	,	PUNCT
ejpam-3133	43	6	we	we	PRON
ejpam-3133	43	7	present	present	VERB
ejpam-3133	43	8	some	some	DET
ejpam-3133	43	9	definitions	definition	NOUN
ejpam-3133	43	10	from	from	ADP
ejpam-3133	43	11	the	the	DET
ejpam-3133	43	12	literature	literature	NOUN
ejpam-3133	43	13	.	.	PUNCT
ejpam-3133	44	1	definition	definition	NOUN
ejpam-3133	44	2	1	1	NUM
ejpam-3133	44	3	.	.	PUNCT
ejpam-3133	45	1	(	(	PUNCT
ejpam-3133	45	2	[	[	X
ejpam-3133	45	3	13	13	NUM
ejpam-3133	45	4	]	]	PUNCT
ejpam-3133	45	5	)	)	PUNCT
ejpam-3133	45	6	let	let	VERB
ejpam-3133	45	7	x	x	PRON
ejpam-3133	45	8	be	be	AUX
ejpam-3133	45	9	a	a	DET
ejpam-3133	45	10	nonempty	nonempty	ADV
ejpam-3133	45	11	set	set	VERB
ejpam-3133	45	12	and	and	CCONJ
ejpam-3133	45	13	s	s	PRON
ejpam-3133	45	14	≥	≥	NUM
ejpam-3133	45	15	1	1	NUM
ejpam-3133	45	16	be	be	AUX
ejpam-3133	45	17	a	a	DET
ejpam-3133	45	18	given	give	VERB
ejpam-3133	45	19	real	real	ADJ
ejpam-3133	45	20	number	number	NOUN
ejpam-3133	45	21	.	.	PUNCT
ejpam-3133	46	1	a	a	DET
ejpam-3133	46	2	function	function	NOUN
ejpam-3133	46	3	d	d	NOUN
ejpam-3133	46	4	:	:	PUNCT
ejpam-3133	46	5	x	x	SYM
ejpam-3133	46	6	×	×	NOUN
ejpam-3133	46	7	x	x	INTJ
ejpam-3133	46	8	→	→	X
ejpam-3133	47	1	[	[	X
ejpam-3133	47	2	0,∞	0,∞	NOUN
ejpam-3133	47	3	)	)	PUNCT
ejpam-3133	47	4	is	be	AUX
ejpam-3133	47	5	called	call	VERB
ejpam-3133	47	6	a	a	DET
ejpam-3133	47	7	b	b	NOUN
ejpam-3133	47	8	-	-	ADJ
ejpam-3133	47	9	metric	metric	ADJ
ejpam-3133	47	10	provided	provide	VERB
ejpam-3133	47	11	that	that	SCONJ
ejpam-3133	47	12	,	,	PUNCT
ejpam-3133	47	13	for	for	ADP
ejpam-3133	47	14	all	all	DET
ejpam-3133	47	15	a	a	DET
ejpam-3133	47	16	,	,	PUNCT
ejpam-3133	47	17	b	b	NOUN
ejpam-3133	47	18	,	,	PUNCT
ejpam-3133	47	19	c	c	PROPN
ejpam-3133	47	20	∈	∈	PROPN
ejpam-3133	47	21	x	x	NOUN
ejpam-3133	47	22	,	,	PUNCT
ejpam-3133	47	23	the	the	DET
ejpam-3133	47	24	following	follow	VERB
ejpam-3133	47	25	conditions	condition	NOUN
ejpam-3133	47	26	are	be	AUX
ejpam-3133	47	27	satisfied	satisfied	ADJ
ejpam-3133	47	28	:	:	PUNCT
ejpam-3133	47	29	(	(	PUNCT
ejpam-3133	47	30	b1	b1	NOUN
ejpam-3133	47	31	)	)	PUNCT
ejpam-3133	47	32	d(a	d(a	PROPN
ejpam-3133	47	33	,	,	PUNCT
ejpam-3133	47	34	b	b	NOUN
ejpam-3133	47	35	)	)	PUNCT
ejpam-3133	47	36	=	=	SYM
ejpam-3133	47	37	0	0	PUNCT
ejpam-3133	48	1	if	if	SCONJ
ejpam-3133	48	2	and	and	CCONJ
ejpam-3133	48	3	only	only	ADV
ejpam-3133	48	4	if	if	SCONJ
ejpam-3133	48	5	a	a	DET
ejpam-3133	48	6	=	=	SYM
ejpam-3133	48	7	b	b	NOUN
ejpam-3133	48	8	;	;	PUNCT
ejpam-3133	48	9	(	(	PUNCT
ejpam-3133	48	10	b2	b2	NOUN
ejpam-3133	48	11	)	)	PUNCT
ejpam-3133	48	12	d(a	d(a	PROPN
ejpam-3133	48	13	,	,	PUNCT
ejpam-3133	48	14	b	b	NOUN
ejpam-3133	48	15	)	)	PUNCT
ejpam-3133	48	16	=	=	SYM
ejpam-3133	48	17	d(b	d(b	PROPN
ejpam-3133	48	18	,	,	PUNCT
ejpam-3133	48	19	a	a	PRON
ejpam-3133	48	20	)	)	PUNCT
ejpam-3133	48	21	;	;	PUNCT
ejpam-3133	48	22	(	(	PUNCT
ejpam-3133	48	23	b3	b3	PROPN
ejpam-3133	48	24	)	)	PUNCT
ejpam-3133	48	25	d(a	d(a	PROPN
ejpam-3133	48	26	,	,	PUNCT
ejpam-3133	48	27	c	c	NOUN
ejpam-3133	48	28	)	)	PUNCT
ejpam-3133	48	29	≤	≤	PUNCT
ejpam-3133	49	1	s[d(a	s[d(a	PROPN
ejpam-3133	49	2	,	,	PUNCT
ejpam-3133	49	3	b	b	NOUN
ejpam-3133	49	4	)	)	PUNCT
ejpam-3133	49	5	+	+	CCONJ
ejpam-3133	49	6	d(b	d(b	PROPN
ejpam-3133	49	7	,	,	PUNCT
ejpam-3133	49	8	c	c	NOUN
ejpam-3133	49	9	)	)	PUNCT
ejpam-3133	49	10	]	]	PUNCT
ejpam-3133	49	11	.	.	PUNCT
ejpam-3133	50	1	the	the	DET
ejpam-3133	50	2	pair	pair	NOUN
ejpam-3133	50	3	(	(	PUNCT
ejpam-3133	50	4	x	x	X
ejpam-3133	50	5	,	,	PUNCT
ejpam-3133	50	6	d	d	NOUN
ejpam-3133	50	7	)	)	PUNCT
ejpam-3133	50	8	is	be	AUX
ejpam-3133	50	9	called	call	VERB
ejpam-3133	50	10	a	a	DET
ejpam-3133	50	11	b	b	NOUN
ejpam-3133	50	12	-	-	PUNCT
ejpam-3133	50	13	metric	metric	ADJ
ejpam-3133	50	14	space	space	NOUN
ejpam-3133	50	15	with	with	ADP
ejpam-3133	50	16	parameter	parameter	NOUN
ejpam-3133	50	17	s.	s.	PROPN
ejpam-3133	50	18	the	the	DET
ejpam-3133	50	19	following	follow	VERB
ejpam-3133	50	20	definition	definition	NOUN
ejpam-3133	50	21	was	be	AUX
ejpam-3133	50	22	given	give	VERB
ejpam-3133	50	23	by	by	ADP
ejpam-3133	50	24	mustafa	mustafa	PROPN
ejpam-3133	50	25	and	and	CCONJ
ejpam-3133	50	26	sims	sim	NOUN
ejpam-3133	50	27	[	[	X
ejpam-3133	50	28	28	28	NUM
ejpam-3133	50	29	]	]	PUNCT
ejpam-3133	50	30	z.	z.	PROPN
ejpam-3133	50	31	mustafa	mustafa	PROPN
ejpam-3133	50	32	et	et	PROPN
ejpam-3133	50	33	al	al	PROPN
ejpam-3133	50	34	.	.	PUNCT
ejpam-3133	50	35	/	/	SYM
ejpam-3133	50	36	eur	eur	PROPN
ejpam-3133	50	37	.	.	PUNCT
ejpam-3133	51	1	j.	j.	PROPN
ejpam-3133	51	2	pure	pure	PROPN
ejpam-3133	51	3	appl	appl	PROPN
ejpam-3133	51	4	.	.	PROPN
ejpam-3133	51	5	math	math	PROPN
ejpam-3133	51	6	,	,	PUNCT
ejpam-3133	51	7	11	11	NUM
ejpam-3133	51	8	(	(	PUNCT
ejpam-3133	51	9	1	1	NUM
ejpam-3133	51	10	)	)	PUNCT
ejpam-3133	51	11	(	(	PUNCT
ejpam-3133	51	12	2018	2018	NUM
ejpam-3133	51	13	)	)	PUNCT
ejpam-3133	51	14	,	,	PUNCT
ejpam-3133	51	15	90	90	NUM
ejpam-3133	51	16	-	-	SYM
ejpam-3133	51	17	109	109	NUM
ejpam-3133	51	18	92	92	NUM
ejpam-3133	51	19	definition	definition	NOUN
ejpam-3133	51	20	2	2	NUM
ejpam-3133	51	21	.	.	PUNCT
ejpam-3133	52	1	(	(	PUNCT
ejpam-3133	52	2	[	[	X
ejpam-3133	52	3	28	28	NUM
ejpam-3133	52	4	]	]	PUNCT
ejpam-3133	52	5	)	)	PUNCT
ejpam-3133	52	6	let	let	VERB
ejpam-3133	52	7	x	x	PRON
ejpam-3133	52	8	be	be	AUX
ejpam-3133	52	9	a	a	DET
ejpam-3133	52	10	nonempty	nonempty	ADV
ejpam-3133	52	11	set	set	VERB
ejpam-3133	52	12	and	and	CCONJ
ejpam-3133	52	13	g	g	NOUN
ejpam-3133	52	14	:	:	PUNCT
ejpam-3133	52	15	x	x	X
ejpam-3133	52	16	×x	×x	X
ejpam-3133	52	17	×x	×x	X
ejpam-3133	52	18	→	→	PUNCT
ejpam-3133	52	19	[	[	X
ejpam-3133	52	20	0,∞	0,∞	NOUN
ejpam-3133	52	21	)	)	PUNCT
ejpam-3133	52	22	satisfies	satisfie	NOUN
ejpam-3133	52	23	:	:	PUNCT
ejpam-3133	52	24	(	(	PUNCT
ejpam-3133	52	25	g1	g1	PROPN
ejpam-3133	52	26	)	)	PUNCT
ejpam-3133	52	27	g(a	g(a	PROPN
ejpam-3133	52	28	,	,	PUNCT
ejpam-3133	52	29	b	b	NOUN
ejpam-3133	52	30	,	,	PUNCT
ejpam-3133	52	31	c	c	NOUN
ejpam-3133	52	32	)	)	PUNCT
ejpam-3133	53	1	=	=	SYM
ejpam-3133	53	2	0	0	PUNCT
ejpam-3133	54	1	if	if	SCONJ
ejpam-3133	54	2	a	a	DET
ejpam-3133	54	3	=	=	SYM
ejpam-3133	54	4	b	b	NOUN
ejpam-3133	54	5	=	=	SYM
ejpam-3133	54	6	c	c	NOUN
ejpam-3133	54	7	;	;	PUNCT
ejpam-3133	54	8	(	(	PUNCT
ejpam-3133	54	9	g2	g2	PROPN
ejpam-3133	54	10	)	)	PUNCT
ejpam-3133	54	11	g(a	g(a	PROPN
ejpam-3133	54	12	,	,	PUNCT
ejpam-3133	54	13	a	a	DET
ejpam-3133	54	14	,	,	PUNCT
ejpam-3133	54	15	b	b	NOUN
ejpam-3133	54	16	)	)	PUNCT
ejpam-3133	54	17	>	>	X
ejpam-3133	54	18	0	0	PUNCT
ejpam-3133	55	1	for	for	ADP
ejpam-3133	55	2	all	all	DET
ejpam-3133	55	3	a	a	DET
ejpam-3133	55	4	,	,	PUNCT
ejpam-3133	55	5	b	b	X
ejpam-3133	55	6	∈	∈	PROPN
ejpam-3133	55	7	x	x	PUNCT
ejpam-3133	55	8	with	with	ADP
ejpam-3133	55	9	a	a	DET
ejpam-3133	55	10	6=	6=	NUM
ejpam-3133	55	11	b	b	NOUN
ejpam-3133	55	12	;	;	PUNCT
ejpam-3133	55	13	(	(	PUNCT
ejpam-3133	55	14	g3	g3	NOUN
ejpam-3133	55	15	)	)	PUNCT
ejpam-3133	55	16	g(a	g(a	PROPN
ejpam-3133	55	17	,	,	PUNCT
ejpam-3133	55	18	b	b	PROPN
ejpam-3133	55	19	,	,	PUNCT
ejpam-3133	55	20	b	b	NOUN
ejpam-3133	55	21	)	)	PUNCT
ejpam-3133	55	22	≤	≤	NOUN
ejpam-3133	55	23	g(a	g(a	PROPN
ejpam-3133	55	24	,	,	PUNCT
ejpam-3133	55	25	b	b	PROPN
ejpam-3133	55	26	,	,	PUNCT
ejpam-3133	55	27	c	c	NOUN
ejpam-3133	55	28	)	)	PUNCT
ejpam-3133	55	29	for	for	ADP
ejpam-3133	55	30	all	all	DET
ejpam-3133	55	31	a	a	DET
ejpam-3133	55	32	,	,	PUNCT
ejpam-3133	55	33	b	b	NOUN
ejpam-3133	55	34	,	,	PUNCT
ejpam-3133	55	35	c	c	PROPN
ejpam-3133	55	36	∈	∈	PROPN
ejpam-3133	55	37	x	x	PUNCT
ejpam-3133	55	38	with	with	ADP
ejpam-3133	55	39	a	a	DET
ejpam-3133	55	40	6=	6=	NOUN
ejpam-3133	55	41	c	c	NOUN
ejpam-3133	55	42	;	;	PUNCT
ejpam-3133	55	43	(	(	PUNCT
ejpam-3133	55	44	g4	g4	NOUN
ejpam-3133	55	45	)	)	PUNCT
ejpam-3133	55	46	g(a	g(a	PROPN
ejpam-3133	55	47	,	,	PUNCT
ejpam-3133	55	48	b	b	NOUN
ejpam-3133	55	49	,	,	PUNCT
ejpam-3133	55	50	c	c	NOUN
ejpam-3133	55	51	)	)	PUNCT
ejpam-3133	55	52	=	=	SYM
ejpam-3133	56	1	g(b	g(b	X
ejpam-3133	56	2	,	,	PUNCT
ejpam-3133	56	3	c	c	X
ejpam-3133	56	4	,	,	PUNCT
ejpam-3133	56	5	a	a	PRON
ejpam-3133	56	6	)	)	PUNCT
ejpam-3133	56	7	=	=	SYM
ejpam-3133	56	8	g(c	g(c	NOUN
ejpam-3133	56	9	,	,	PUNCT
ejpam-3133	56	10	a	a	DET
ejpam-3133	56	11	,	,	PUNCT
ejpam-3133	56	12	b	b	NOUN
ejpam-3133	56	13	)	)	PUNCT
ejpam-3133	56	14	=	=	SYM
ejpam-3133	56	15	·	·	PUNCT
ejpam-3133	56	16	·	·	PUNCT
ejpam-3133	56	17	·	·	PUNCT
ejpam-3133	56	18	(	(	PUNCT
ejpam-3133	56	19	symmetry	symmetry	NOUN
ejpam-3133	56	20	in	in	ADP
ejpam-3133	56	21	a	a	DET
ejpam-3133	56	22	,	,	PUNCT
ejpam-3133	56	23	b	b	NOUN
ejpam-3133	56	24	,	,	PUNCT
ejpam-3133	56	25	c	c	NOUN
ejpam-3133	56	26	)	)	PUNCT
ejpam-3133	56	27	;	;	PUNCT
ejpam-3133	56	28	(	(	PUNCT
ejpam-3133	56	29	g5	g5	NOUN
ejpam-3133	56	30	)	)	PUNCT
ejpam-3133	56	31	g(a	g(a	PROPN
ejpam-3133	56	32	,	,	PUNCT
ejpam-3133	56	33	b	b	NOUN
ejpam-3133	56	34	,	,	PUNCT
ejpam-3133	56	35	c	c	NOUN
ejpam-3133	56	36	)	)	PUNCT
ejpam-3133	56	37	≤	≤	NOUN
ejpam-3133	57	1	g(a	g(a	PROPN
ejpam-3133	57	2	,	,	PUNCT
ejpam-3133	57	3	d	d	X
ejpam-3133	57	4	,	,	PUNCT
ejpam-3133	57	5	d	d	NOUN
ejpam-3133	57	6	)	)	PUNCT
ejpam-3133	58	1	+	+	NOUN
ejpam-3133	58	2	g(d	g(d	PROPN
ejpam-3133	58	3	,	,	PUNCT
ejpam-3133	58	4	b	b	PROPN
ejpam-3133	58	5	,	,	PUNCT
ejpam-3133	58	6	c	c	NOUN
ejpam-3133	58	7	)	)	PUNCT
ejpam-3133	58	8	for	for	ADP
ejpam-3133	58	9	all	all	DET
ejpam-3133	58	10	a	a	DET
ejpam-3133	58	11	,	,	PUNCT
ejpam-3133	58	12	b	b	NOUN
ejpam-3133	58	13	,	,	PUNCT
ejpam-3133	58	14	c	c	NOUN
ejpam-3133	58	15	,	,	PUNCT
ejpam-3133	58	16	d	d	PROPN
ejpam-3133	58	17	∈	∈	PROPN
ejpam-3133	58	18	x.	x.	NOUN
ejpam-3133	58	19	then	then	ADV
ejpam-3133	58	20	function	function	VERB
ejpam-3133	58	21	g	g	PROPN
ejpam-3133	58	22	is	be	AUX
ejpam-3133	58	23	called	call	VERB
ejpam-3133	58	24	a	a	DET
ejpam-3133	58	25	g	g	NOUN
ejpam-3133	58	26	-	-	NOUN
ejpam-3133	58	27	metric	metric	ADJ
ejpam-3133	58	28	on	on	ADP
ejpam-3133	58	29	x	x	NOUN
ejpam-3133	58	30	,	,	PUNCT
ejpam-3133	58	31	and	and	CCONJ
ejpam-3133	58	32	the	the	DET
ejpam-3133	58	33	pair	pair	NOUN
ejpam-3133	58	34	(	(	PUNCT
ejpam-3133	58	35	x	x	NOUN
ejpam-3133	58	36	,	,	PUNCT
ejpam-3133	58	37	g	g	NOUN
ejpam-3133	58	38	)	)	PUNCT
ejpam-3133	58	39	is	be	AUX
ejpam-3133	58	40	called	call	VERB
ejpam-3133	58	41	a	a	DET
ejpam-3133	58	42	g	g	NOUN
ejpam-3133	58	43	-	-	PUNCT
ejpam-3133	58	44	metric	metric	ADJ
ejpam-3133	58	45	space	space	NOUN
ejpam-3133	58	46	.	.	PUNCT
ejpam-3133	59	1	as	as	ADP
ejpam-3133	59	2	a	a	DET
ejpam-3133	59	3	combination	combination	NOUN
ejpam-3133	59	4	of	of	ADP
ejpam-3133	59	5	the	the	DET
ejpam-3133	59	6	two	two	NUM
ejpam-3133	59	7	above	above	ADJ
ejpam-3133	59	8	definitions	definition	NOUN
ejpam-3133	59	9	,	,	PUNCT
ejpam-3133	59	10	aghajani	aghajani	PROPN
ejpam-3133	59	11	et	et	PROPN
ejpam-3133	59	12	al	al	PROPN
ejpam-3133	59	13	.	.	PUNCT
ejpam-3133	60	1	[	[	X
ejpam-3133	60	2	2	2	NUM
ejpam-3133	60	3	]	]	PUNCT
ejpam-3133	60	4	(	(	PUNCT
ejpam-3133	60	5	see	see	VERB
ejpam-3133	60	6	also	also	ADV
ejpam-3133	60	7	[	[	X
ejpam-3133	60	8	3	3	NUM
ejpam-3133	60	9	]	]	PUNCT
ejpam-3133	60	10	)	)	PUNCT
ejpam-3133	60	11	introduced	introduce	VERB
ejpam-3133	60	12	the	the	DET
ejpam-3133	60	13	following	following	NOUN
ejpam-3133	60	14	.	.	PUNCT
ejpam-3133	61	1	definition	definition	NOUN
ejpam-3133	61	2	3	3	NUM
ejpam-3133	61	3	.	.	PUNCT
ejpam-3133	62	1	(	(	PUNCT
ejpam-3133	62	2	[	[	X
ejpam-3133	62	3	2	2	NUM
ejpam-3133	62	4	]	]	PUNCT
ejpam-3133	62	5	)	)	PUNCT
ejpam-3133	62	6	let	let	VERB
ejpam-3133	62	7	x	x	PRON
ejpam-3133	62	8	be	be	AUX
ejpam-3133	62	9	a	a	DET
ejpam-3133	62	10	nonempty	nonempty	ADV
ejpam-3133	62	11	set	set	VERB
ejpam-3133	62	12	and	and	CCONJ
ejpam-3133	62	13	s	s	PRON
ejpam-3133	62	14	≥	≥	NUM
ejpam-3133	62	15	1	1	NUM
ejpam-3133	62	16	be	be	AUX
ejpam-3133	62	17	a	a	DET
ejpam-3133	62	18	given	give	VERB
ejpam-3133	62	19	real	real	ADJ
ejpam-3133	62	20	number	number	NOUN
ejpam-3133	62	21	.	.	PUNCT
ejpam-3133	62	22	suppose	suppose	VERB
ejpam-3133	62	23	that	that	SCONJ
ejpam-3133	62	24	a	a	DET
ejpam-3133	62	25	mapping	mapping	NOUN
ejpam-3133	62	26	gb	gb	NOUN
ejpam-3133	62	27	:	:	PUNCT
ejpam-3133	62	28	x	x	PROPN
ejpam-3133	62	29	×x	×x	X
ejpam-3133	62	30	×x	×x	X
ejpam-3133	62	31	→	→	PUNCT
ejpam-3133	62	32	[	[	X
ejpam-3133	62	33	0,∞	0,∞	NOUN
ejpam-3133	62	34	)	)	PUNCT
ejpam-3133	62	35	satisfies	satisfie	NOUN
ejpam-3133	62	36	:	:	PUNCT
ejpam-3133	62	37	(	(	PUNCT
ejpam-3133	62	38	gb1	gb1	NOUN
ejpam-3133	62	39	)	)	PUNCT
ejpam-3133	62	40	gb(x	gb(x	PROPN
ejpam-3133	62	41	,	,	PUNCT
ejpam-3133	62	42	y	y	PROPN
ejpam-3133	62	43	,	,	PUNCT
ejpam-3133	62	44	z	z	NOUN
ejpam-3133	62	45	)	)	PUNCT
ejpam-3133	63	1	=	=	SYM
ejpam-3133	63	2	0	0	PUNCT
ejpam-3133	64	1	if	if	SCONJ
ejpam-3133	64	2	x	x	NOUN
ejpam-3133	64	3	=	=	PUNCT
ejpam-3133	64	4	y	y	PROPN
ejpam-3133	64	5	=	=	SYM
ejpam-3133	64	6	z	z	PROPN
ejpam-3133	64	7	;	;	PUNCT
ejpam-3133	64	8	(	(	PUNCT
ejpam-3133	64	9	gb2	gb2	PROPN
ejpam-3133	64	10	)	)	PUNCT
ejpam-3133	64	11	gb(x	gb(x	ADJ
ejpam-3133	64	12	,	,	PUNCT
ejpam-3133	64	13	x	x	NOUN
ejpam-3133	64	14	,	,	PUNCT
ejpam-3133	64	15	y	y	PROPN
ejpam-3133	64	16	)	)	PUNCT
ejpam-3133	64	17	>	>	X
ejpam-3133	64	18	0	0	PUNCT
ejpam-3133	65	1	for	for	ADP
ejpam-3133	65	2	all	all	DET
ejpam-3133	65	3	x	x	NOUN
ejpam-3133	65	4	,	,	PUNCT
ejpam-3133	65	5	y	y	PROPN
ejpam-3133	65	6	∈	∈	PROPN
ejpam-3133	65	7	x	x	PUNCT
ejpam-3133	65	8	with	with	ADP
ejpam-3133	65	9	x	x	SYM
ejpam-3133	65	10	6=	6=	PROPN
ejpam-3133	65	11	y	y	PROPN
ejpam-3133	65	12	;	;	PUNCT
ejpam-3133	65	13	(	(	PUNCT
ejpam-3133	65	14	gb3	gb3	NOUN
ejpam-3133	65	15	)	)	PUNCT
ejpam-3133	65	16	gb(x	gb(x	PROPN
ejpam-3133	65	17	,	,	PUNCT
ejpam-3133	65	18	y	y	PROPN
ejpam-3133	65	19	,	,	PUNCT
ejpam-3133	65	20	y	y	NOUN
ejpam-3133	65	21	)	)	PUNCT
ejpam-3133	65	22	≤	≤	NOUN
ejpam-3133	65	23	gb(x	gb(x	PUNCT
ejpam-3133	65	24	,	,	PUNCT
ejpam-3133	65	25	y	y	PROPN
ejpam-3133	65	26	,	,	PUNCT
ejpam-3133	65	27	z	z	NOUN
ejpam-3133	65	28	)	)	PUNCT
ejpam-3133	65	29	for	for	ADP
ejpam-3133	65	30	all	all	DET
ejpam-3133	65	31	x	x	NOUN
ejpam-3133	65	32	,	,	PUNCT
ejpam-3133	65	33	y	y	PROPN
ejpam-3133	65	34	,	,	PUNCT
ejpam-3133	65	35	z	z	NOUN
ejpam-3133	65	36	∈	∈	PROPN
ejpam-3133	65	37	x	x	PUNCT
ejpam-3133	65	38	with	with	ADP
ejpam-3133	65	39	x	x	SYM
ejpam-3133	65	40	6=	6=	PROPN
ejpam-3133	65	41	z	z	NOUN
ejpam-3133	65	42	;	;	PUNCT
ejpam-3133	65	43	(	(	PUNCT
ejpam-3133	65	44	gb4	gb4	NOUN
ejpam-3133	65	45	)	)	PUNCT
ejpam-3133	65	46	gb(x	gb(x	PROPN
ejpam-3133	65	47	,	,	PUNCT
ejpam-3133	65	48	y	y	PROPN
ejpam-3133	65	49	,	,	PUNCT
ejpam-3133	65	50	z	z	NOUN
ejpam-3133	65	51	)	)	PUNCT
ejpam-3133	65	52	=	=	SYM
ejpam-3133	65	53	gb(p{x	gb(p{x	NOUN
ejpam-3133	65	54	,	,	PUNCT
ejpam-3133	65	55	y	y	PROPN
ejpam-3133	65	56	,	,	PUNCT
ejpam-3133	65	57	z	z	NOUN
ejpam-3133	65	58	}	}	PUNCT
ejpam-3133	65	59	)	)	PUNCT
ejpam-3133	65	60	where	where	SCONJ
ejpam-3133	65	61	p	p	NOUN
ejpam-3133	65	62	is	be	AUX
ejpam-3133	65	63	a	a	DET
ejpam-3133	65	64	permutation	permutation	NOUN
ejpam-3133	65	65	of	of	ADP
ejpam-3133	65	66	x	x	PROPN
ejpam-3133	65	67	,	,	PUNCT
ejpam-3133	65	68	y	y	PROPN
ejpam-3133	65	69	,	,	PUNCT
ejpam-3133	65	70	z	z	PROPN
ejpam-3133	65	71	(	(	PUNCT
ejpam-3133	65	72	symmetry	symmetry	PROPN
ejpam-3133	65	73	)	)	PUNCT
ejpam-3133	65	74	;	;	PUNCT
ejpam-3133	65	75	(	(	PUNCT
ejpam-3133	65	76	gb5	gb5	NOUN
ejpam-3133	65	77	)	)	PUNCT
ejpam-3133	65	78	gb(x	gb(x	PROPN
ejpam-3133	65	79	,	,	PUNCT
ejpam-3133	65	80	y	y	PROPN
ejpam-3133	65	81	,	,	PUNCT
ejpam-3133	65	82	z	z	NOUN
ejpam-3133	65	83	)	)	PUNCT
ejpam-3133	65	84	≤	≤	NOUN
ejpam-3133	65	85	s(gb(x	s(gb(x	PROPN
ejpam-3133	65	86	,	,	PUNCT
ejpam-3133	65	87	a	a	PRON
ejpam-3133	65	88	,	,	PUNCT
ejpam-3133	65	89	a	a	NOUN
ejpam-3133	65	90	)	)	PUNCT
ejpam-3133	65	91	+	+	NOUN
ejpam-3133	65	92	gb(a	gb(a	NOUN
ejpam-3133	65	93	,	,	PUNCT
ejpam-3133	65	94	y	y	PROPN
ejpam-3133	65	95	,	,	PUNCT
ejpam-3133	65	96	z	z	NOUN
ejpam-3133	65	97	)	)	PUNCT
ejpam-3133	65	98	)	)	PUNCT
ejpam-3133	65	99	for	for	ADP
ejpam-3133	65	100	all	all	DET
ejpam-3133	65	101	x	x	NOUN
ejpam-3133	65	102	,	,	PUNCT
ejpam-3133	65	103	y	y	PROPN
ejpam-3133	65	104	,	,	PUNCT
ejpam-3133	65	105	z	z	PROPN
ejpam-3133	65	106	,	,	PUNCT
ejpam-3133	65	107	a	a	DET
ejpam-3133	65	108	∈	∈	NOUN
ejpam-3133	65	109	x.	x.	NOUN
ejpam-3133	65	110	then	then	ADV
ejpam-3133	65	111	gb	gb	PRON
ejpam-3133	65	112	is	be	AUX
ejpam-3133	65	113	called	call	VERB
ejpam-3133	65	114	a	a	DET
ejpam-3133	65	115	generalized	generalized	ADJ
ejpam-3133	65	116	b	b	NOUN
ejpam-3133	65	117	-	-	ADJ
ejpam-3133	65	118	metric	metric	ADJ
ejpam-3133	65	119	(	(	PUNCT
ejpam-3133	65	120	named	name	VERB
ejpam-3133	65	121	as	as	ADP
ejpam-3133	65	122	a	a	DET
ejpam-3133	65	123	gb	gb	ADV
ejpam-3133	65	124	-	-	PUNCT
ejpam-3133	65	125	metric	metric	NOUN
ejpam-3133	65	126	)	)	PUNCT
ejpam-3133	65	127	on	on	ADP
ejpam-3133	65	128	x	x	NOUN
ejpam-3133	65	129	,	,	PUNCT
ejpam-3133	65	130	and	and	CCONJ
ejpam-3133	65	131	the	the	DET
ejpam-3133	65	132	pair	pair	NOUN
ejpam-3133	65	133	(	(	PUNCT
ejpam-3133	65	134	x	x	NOUN
ejpam-3133	65	135	,	,	PUNCT
ejpam-3133	65	136	gb	gb	PRON
ejpam-3133	65	137	)	)	PUNCT
ejpam-3133	65	138	is	be	AUX
ejpam-3133	65	139	called	call	VERB
ejpam-3133	65	140	a	a	DET
ejpam-3133	65	141	gb	gb	ADV
ejpam-3133	65	142	-	-	PUNCT
ejpam-3133	65	143	metric	metric	ADJ
ejpam-3133	65	144	space	space	NOUN
ejpam-3133	65	145	.	.	PUNCT
ejpam-3133	66	1	note	note	VERB
ejpam-3133	66	2	that	that	SCONJ
ejpam-3133	66	3	every	every	DET
ejpam-3133	66	4	g	g	NOUN
ejpam-3133	66	5	-	-	PUNCT
ejpam-3133	66	6	metric	metric	ADJ
ejpam-3133	66	7	space	space	NOUN
ejpam-3133	66	8	is	be	AUX
ejpam-3133	66	9	a	a	DET
ejpam-3133	66	10	gb	gb	ADV
ejpam-3133	66	11	-	-	PUNCT
ejpam-3133	66	12	metric	metric	ADJ
ejpam-3133	66	13	space	space	NOUN
ejpam-3133	66	14	,	,	PUNCT
ejpam-3133	66	15	but	but	CCONJ
ejpam-3133	66	16	the	the	DET
ejpam-3133	66	17	converse	converse	NOUN
ejpam-3133	66	18	need	need	VERB
ejpam-3133	66	19	not	not	PART
ejpam-3133	66	20	to	to	PART
ejpam-3133	66	21	be	be	AUX
ejpam-3133	66	22	true	true	ADJ
ejpam-3133	66	23	as	as	ADP
ejpam-3133	66	24	its	its	PRON
ejpam-3133	66	25	clear	clear	ADJ
ejpam-3133	66	26	from	from	ADP
ejpam-3133	66	27	the	the	DET
ejpam-3133	66	28	following	follow	VERB
ejpam-3133	66	29	example	example	NOUN
ejpam-3133	66	30	.	.	PUNCT
ejpam-3133	67	1	example	example	NOUN
ejpam-3133	68	1	1	1	NUM
ejpam-3133	68	2	.	.	PUNCT
ejpam-3133	69	1	(	(	PUNCT
ejpam-3133	69	2	[	[	X
ejpam-3133	69	3	46	46	NUM
ejpam-3133	69	4	]	]	PUNCT
ejpam-3133	69	5	)	)	PUNCT
ejpam-3133	69	6	let	let	VERB
ejpam-3133	69	7	x={1	x={1	ADJ
ejpam-3133	69	8	,	,	PUNCT
ejpam-3133	69	9	2	2	NUM
ejpam-3133	69	10	,	,	PUNCT
ejpam-3133	69	11	3	3	NUM
ejpam-3133	69	12	,	,	PUNCT
ejpam-3133	69	13	4	4	NUM
ejpam-3133	69	14	}	}	PUNCT
ejpam-3133	69	15	.	.	PUNCT
ejpam-3133	70	1	define	define	VERB
ejpam-3133	70	2	gb	gb	PRON
ejpam-3133	70	3	:	:	PUNCT
ejpam-3133	70	4	x	x	PROPN
ejpam-3133	70	5	×x	×x	X
ejpam-3133	70	6	×x	×x	X
ejpam-3133	70	7	→	→	PUNCT
ejpam-3133	70	8	[	[	X
ejpam-3133	70	9	0,∞	0,∞	NOUN
ejpam-3133	70	10	)	)	PUNCT
ejpam-3133	70	11	by	by	ADP
ejpam-3133	70	12	gb(1	gb(1	PROPN
ejpam-3133	70	13	,	,	PUNCT
ejpam-3133	70	14	1	1	NUM
ejpam-3133	70	15	,	,	PUNCT
ejpam-3133	70	16	1	1	NUM
ejpam-3133	70	17	)	)	PUNCT
ejpam-3133	70	18	=	=	SYM
ejpam-3133	71	1	gb(2	gb(2	PROPN
ejpam-3133	71	2	,	,	PUNCT
ejpam-3133	71	3	2	2	NUM
ejpam-3133	71	4	,	,	PUNCT
ejpam-3133	71	5	2	2	NUM
ejpam-3133	71	6	)	)	PUNCT
ejpam-3133	71	7	=	=	SYM
ejpam-3133	72	1	gb(3	gb(3	NOUN
ejpam-3133	72	2	,	,	PUNCT
ejpam-3133	72	3	3	3	NUM
ejpam-3133	72	4	,	,	PUNCT
ejpam-3133	72	5	3	3	NUM
ejpam-3133	72	6	)	)	PUNCT
ejpam-3133	72	7	=	=	SYM
ejpam-3133	73	1	gb(4	gb(4	PROPN
ejpam-3133	73	2	,	,	PUNCT
ejpam-3133	73	3	4	4	NUM
ejpam-3133	73	4	,	,	PUNCT
ejpam-3133	73	5	4	4	NUM
ejpam-3133	73	6	)	)	PUNCT
ejpam-3133	73	7	=	=	SYM
ejpam-3133	73	8	0	0	NUM
ejpam-3133	73	9	,	,	PUNCT
ejpam-3133	73	10	gb(1	gb(1	PROPN
ejpam-3133	73	11	,	,	PUNCT
ejpam-3133	73	12	1	1	NUM
ejpam-3133	73	13	,	,	PUNCT
ejpam-3133	73	14	2	2	NUM
ejpam-3133	73	15	)	)	PUNCT
ejpam-3133	73	16	=	=	SYM
ejpam-3133	73	17	gb(1	gb(1	PROPN
ejpam-3133	73	18	,	,	PUNCT
ejpam-3133	73	19	2	2	NUM
ejpam-3133	73	20	,	,	PUNCT
ejpam-3133	73	21	2	2	NUM
ejpam-3133	73	22	)	)	PUNCT
ejpam-3133	73	23	=	=	SYM
ejpam-3133	73	24	gb(1	gb(1	PROPN
ejpam-3133	73	25	,	,	PUNCT
ejpam-3133	73	26	1	1	NUM
ejpam-3133	73	27	,	,	PUNCT
ejpam-3133	73	28	3	3	NUM
ejpam-3133	73	29	)	)	PUNCT
ejpam-3133	73	30	=	=	SYM
ejpam-3133	73	31	gb(1	gb(1	PROPN
ejpam-3133	73	32	,	,	PUNCT
ejpam-3133	73	33	3	3	NUM
ejpam-3133	73	34	,	,	PUNCT
ejpam-3133	73	35	3	3	NUM
ejpam-3133	73	36	)	)	PUNCT
ejpam-3133	73	37	=	=	SYM
ejpam-3133	73	38	gb(1	gb(1	PROPN
ejpam-3133	73	39	,	,	PUNCT
ejpam-3133	73	40	1	1	NUM
ejpam-3133	73	41	,	,	PUNCT
ejpam-3133	73	42	4	4	NUM
ejpam-3133	73	43	)	)	PUNCT
ejpam-3133	73	44	=	=	SYM
ejpam-3133	73	45	gb(1	gb(1	PROPN
ejpam-3133	73	46	,	,	PUNCT
ejpam-3133	73	47	4	4	NUM
ejpam-3133	73	48	,	,	PUNCT
ejpam-3133	73	49	4	4	NUM
ejpam-3133	73	50	)	)	PUNCT
ejpam-3133	73	51	=	=	SYM
ejpam-3133	73	52	1	1	NUM
ejpam-3133	73	53	,	,	PUNCT
ejpam-3133	73	54	gb(2	gb(2	NOUN
ejpam-3133	73	55	,	,	PUNCT
ejpam-3133	73	56	2	2	NUM
ejpam-3133	73	57	,	,	PUNCT
ejpam-3133	73	58	3	3	NUM
ejpam-3133	73	59	)	)	PUNCT
ejpam-3133	73	60	=	=	SYM
ejpam-3133	73	61	gb(2	gb(2	PROPN
ejpam-3133	73	62	,	,	PUNCT
ejpam-3133	73	63	3	3	NUM
ejpam-3133	73	64	,	,	PUNCT
ejpam-3133	73	65	3	3	NUM
ejpam-3133	73	66	)	)	PUNCT
ejpam-3133	73	67	=	=	SYM
ejpam-3133	73	68	gb(2	gb(2	PROPN
ejpam-3133	73	69	,	,	PUNCT
ejpam-3133	73	70	4	4	NUM
ejpam-3133	73	71	,	,	PUNCT
ejpam-3133	73	72	4	4	NUM
ejpam-3133	73	73	)	)	PUNCT
ejpam-3133	73	74	=	=	SYM
ejpam-3133	73	75	gb(2	gb(2	PROPN
ejpam-3133	73	76	,	,	PUNCT
ejpam-3133	73	77	2	2	NUM
ejpam-3133	73	78	,	,	PUNCT
ejpam-3133	73	79	4	4	NUM
ejpam-3133	73	80	)	)	PUNCT
ejpam-3133	73	81	=	=	SYM
ejpam-3133	73	82	2	2	NUM
ejpam-3133	73	83	,	,	PUNCT
ejpam-3133	73	84	gb(3	gb(3	NOUN
ejpam-3133	73	85	,	,	PUNCT
ejpam-3133	73	86	4	4	NUM
ejpam-3133	73	87	,	,	PUNCT
ejpam-3133	73	88	4	4	NUM
ejpam-3133	73	89	)	)	PUNCT
ejpam-3133	73	90	=	=	SYM
ejpam-3133	74	1	gb(3	gb(3	NOUN
ejpam-3133	74	2	,	,	PUNCT
ejpam-3133	74	3	3	3	NUM
ejpam-3133	74	4	,	,	PUNCT
ejpam-3133	74	5	4	4	NUM
ejpam-3133	74	6	)	)	PUNCT
ejpam-3133	74	7	=	=	SYM
ejpam-3133	74	8	3	3	NUM
ejpam-3133	74	9	,	,	PUNCT
ejpam-3133	74	10	gb(1	gb(1	PROPN
ejpam-3133	74	11	,	,	PUNCT
ejpam-3133	74	12	2	2	NUM
ejpam-3133	74	13	,	,	PUNCT
ejpam-3133	74	14	3	3	NUM
ejpam-3133	74	15	)	)	PUNCT
ejpam-3133	74	16	=	=	SYM
ejpam-3133	74	17	4	4	NUM
ejpam-3133	74	18	,	,	PUNCT
ejpam-3133	74	19	gb(1	gb(1	PROPN
ejpam-3133	74	20	,	,	PUNCT
ejpam-3133	74	21	3	3	NUM
ejpam-3133	74	22	,	,	PUNCT
ejpam-3133	74	23	4	4	NUM
ejpam-3133	74	24	)	)	PUNCT
ejpam-3133	74	25	=	=	SYM
ejpam-3133	74	26	5	5	NUM
ejpam-3133	74	27	,	,	PUNCT
ejpam-3133	74	28	gb(1	gb(1	PROPN
ejpam-3133	74	29	,	,	PUNCT
ejpam-3133	74	30	2	2	NUM
ejpam-3133	74	31	,	,	PUNCT
ejpam-3133	74	32	4	4	NUM
ejpam-3133	74	33	)	)	PUNCT
ejpam-3133	74	34	=	=	SYM
ejpam-3133	74	35	6	6	NUM
ejpam-3133	74	36	,	,	PUNCT
ejpam-3133	74	37	gb(2	gb(2	NOUN
ejpam-3133	74	38	,	,	PUNCT
ejpam-3133	74	39	3	3	NUM
ejpam-3133	74	40	,	,	PUNCT
ejpam-3133	74	41	4	4	NUM
ejpam-3133	74	42	)	)	PUNCT
ejpam-3133	74	43	=	=	SYM
ejpam-3133	74	44	7	7	X
ejpam-3133	74	45	.	.	X
ejpam-3133	74	46	evidently	evidently	ADV
ejpam-3133	74	47	,	,	PUNCT
ejpam-3133	74	48	the	the	DET
ejpam-3133	74	49	above	above	ADJ
ejpam-3133	74	50	is	be	AUX
ejpam-3133	74	51	a	a	DET
ejpam-3133	74	52	gb	gb	NOUN
ejpam-3133	74	53	-	-	PUNCT
ejpam-3133	74	54	metric	metric	ADJ
ejpam-3133	74	55	on	on	ADP
ejpam-3133	74	56	x	x	PUNCT
ejpam-3133	74	57	with	with	ADP
ejpam-3133	74	58	s	s	NOUN
ejpam-3133	74	59	=	=	NOUN
ejpam-3133	74	60	7	7	NUM
ejpam-3133	74	61	5	5	NUM
ejpam-3133	74	62	,	,	PUNCT
ejpam-3133	74	63	but	but	CCONJ
ejpam-3133	74	64	not	not	PART
ejpam-3133	74	65	a	a	DET
ejpam-3133	74	66	g	g	NOUN
ejpam-3133	74	67	-	-	PUNCT
ejpam-3133	74	68	metric	metric	ADJ
ejpam-3133	74	69	.	.	PUNCT
ejpam-3133	75	1	in	in	ADP
ejpam-3133	75	2	fact	fact	NOUN
ejpam-3133	75	3	,	,	PUNCT
ejpam-3133	75	4	the	the	DET
ejpam-3133	75	5	rectangle	rectangle	NOUN
ejpam-3133	75	6	inequality	inequality	NOUN
ejpam-3133	75	7	is	be	AUX
ejpam-3133	75	8	violated	violate	VERB
ejpam-3133	75	9	,	,	PUNCT
ejpam-3133	75	10	for	for	ADP
ejpam-3133	75	11	instant	instant	NOUN
ejpam-3133	75	12	7	7	NUM
ejpam-3133	75	13	=	=	SYM
ejpam-3133	75	14	gb(2	gb(2	PROPN
ejpam-3133	75	15	,	,	PUNCT
ejpam-3133	75	16	3	3	NUM
ejpam-3133	75	17	,	,	PUNCT
ejpam-3133	75	18	4	4	NUM
ejpam-3133	75	19	)	)	PUNCT
ejpam-3133	75	20	�	�	PROPN
ejpam-3133	75	21	gb(2	gb(2	PROPN
ejpam-3133	75	22	,	,	PUNCT
ejpam-3133	75	23	1	1	NUM
ejpam-3133	75	24	,	,	PUNCT
ejpam-3133	75	25	1)+gb(1	1)+gb(1	NUM
ejpam-3133	75	26	,	,	PUNCT
ejpam-3133	75	27	3	3	NUM
ejpam-3133	75	28	,	,	PUNCT
ejpam-3133	75	29	4	4	NUM
ejpam-3133	75	30	)	)	PUNCT
ejpam-3133	75	31	=	=	SYM
ejpam-3133	76	1	1	1	NUM
ejpam-3133	76	2	+	+	NOUN
ejpam-3133	76	3	5	5	NUM
ejpam-3133	76	4	.	.	PUNCT
ejpam-3133	77	1	the	the	DET
ejpam-3133	77	2	following	follow	VERB
ejpam-3133	77	3	example	example	NOUN
ejpam-3133	77	4	can	can	AUX
ejpam-3133	77	5	be	be	AUX
ejpam-3133	77	6	founded	found	VERB
ejpam-3133	77	7	in	in	ADP
ejpam-3133	77	8	[	[	X
ejpam-3133	77	9	45	45	NUM
ejpam-3133	77	10	]	]	PUNCT
ejpam-3133	77	11	.	.	PUNCT
ejpam-3133	78	1	example	example	NOUN
ejpam-3133	79	1	2	2	NUM
ejpam-3133	79	2	.	.	X
ejpam-3133	80	1	let	let	AUX
ejpam-3133	80	2	(	(	PUNCT
ejpam-3133	80	3	x	x	NOUN
ejpam-3133	80	4	,	,	PUNCT
ejpam-3133	80	5	g	g	NOUN
ejpam-3133	80	6	)	)	PUNCT
ejpam-3133	80	7	be	be	AUX
ejpam-3133	80	8	a	a	DET
ejpam-3133	80	9	g	g	NOUN
ejpam-3133	80	10	-	-	PUNCT
ejpam-3133	80	11	metric	metric	ADJ
ejpam-3133	80	12	space	space	NOUN
ejpam-3133	80	13	.	.	PUNCT
ejpam-3133	81	1	take	take	VERB
ejpam-3133	81	2	gb(x	gb(x	ADJ
ejpam-3133	81	3	,	,	PUNCT
ejpam-3133	81	4	y	y	PROPN
ejpam-3133	81	5	,	,	PUNCT
ejpam-3133	81	6	z	z	NOUN
ejpam-3133	81	7	)	)	PUNCT
ejpam-3133	81	8	=	=	SYM
ejpam-3133	81	9	gp(x	gp(x	PROPN
ejpam-3133	81	10	,	,	PUNCT
ejpam-3133	81	11	y	y	NOUN
ejpam-3133	81	12	,	,	PUNCT
ejpam-3133	81	13	z	z	NOUN
ejpam-3133	81	14	)	)	PUNCT
ejpam-3133	81	15	,	,	PUNCT
ejpam-3133	81	16	where	where	SCONJ
ejpam-3133	81	17	p	p	NOUN
ejpam-3133	81	18	>	>	X
ejpam-3133	81	19	1	1	NUM
ejpam-3133	81	20	is	be	AUX
ejpam-3133	81	21	a	a	DET
ejpam-3133	81	22	real	real	ADJ
ejpam-3133	81	23	number	number	NOUN
ejpam-3133	81	24	.	.	PUNCT
ejpam-3133	82	1	note	note	VERB
ejpam-3133	82	2	that	that	SCONJ
ejpam-3133	82	3	gb	gb	PRON
ejpam-3133	82	4	is	be	AUX
ejpam-3133	82	5	a	a	DET
ejpam-3133	82	6	gb	gb	ADV
ejpam-3133	82	7	-	-	PUNCT
ejpam-3133	82	8	metric	metric	ADJ
ejpam-3133	82	9	with	with	ADP
ejpam-3133	82	10	s	s	NOUN
ejpam-3133	82	11	=	=	NOUN
ejpam-3133	82	12	2p−1	2p−1	NUM
ejpam-3133	82	13	.	.	PUNCT
ejpam-3133	83	1	in	in	ADP
ejpam-3133	83	2	general	general	ADJ
ejpam-3133	83	3	(	(	PUNCT
ejpam-3133	83	4	x	x	NOUN
ejpam-3133	83	5	,	,	PUNCT
ejpam-3133	83	6	gb	gb	PRON
ejpam-3133	83	7	)	)	PUNCT
ejpam-3133	83	8	is	be	AUX
ejpam-3133	83	9	not	not	PART
ejpam-3133	83	10	necessary	necessary	ADJ
ejpam-3133	83	11	a	a	DET
ejpam-3133	83	12	g	g	NOUN
ejpam-3133	83	13	-	-	PUNCT
ejpam-3133	83	14	metric	metric	ADJ
ejpam-3133	83	15	space	space	NOUN
ejpam-3133	83	16	.	.	PUNCT
ejpam-3133	84	1	for	for	ADP
ejpam-3133	84	2	instant	instant	NOUN
ejpam-3133	84	3	,	,	PUNCT
ejpam-3133	84	4	let	let	VERB
ejpam-3133	84	5	x	x	PUNCT
ejpam-3133	84	6	=	=	PUNCT
ejpam-3133	84	7	r	r	NOUN
ejpam-3133	84	8	and	and	CCONJ
ejpam-3133	84	9	the	the	DET
ejpam-3133	84	10	g	g	NOUN
ejpam-3133	84	11	-	-	PUNCT
ejpam-3133	84	12	metric	metric	NOUN
ejpam-3133	84	13	be	be	AUX
ejpam-3133	84	14	defined	define	VERB
ejpam-3133	84	15	by	by	ADP
ejpam-3133	84	16	g(x	g(x	PROPN
ejpam-3133	84	17	,	,	PUNCT
ejpam-3133	84	18	y	y	PROPN
ejpam-3133	84	19	,	,	PUNCT
ejpam-3133	84	20	z	z	NOUN
ejpam-3133	84	21	)	)	PUNCT
ejpam-3133	84	22	=	=	SYM
ejpam-3133	84	23	1	1	NUM
ejpam-3133	84	24	3(|x−y|+	3(|x−y|+	NUM
ejpam-3133	84	25	|y−z|+	|y−z|+	DET
ejpam-3133	84	26	|x−z|	|x−z|	NOUN
ejpam-3133	84	27	)	)	PUNCT
ejpam-3133	84	28	for	for	ADP
ejpam-3133	84	29	all	all	DET
ejpam-3133	84	30	x	x	NOUN
ejpam-3133	84	31	,	,	PUNCT
ejpam-3133	84	32	y	y	PROPN
ejpam-3133	84	33	,	,	PUNCT
ejpam-3133	84	34	z	z	PROPN
ejpam-3133	84	35	∈	∈	PROPN
ejpam-3133	84	36	r.	r.	PROPN
ejpam-3133	84	37	then	then	ADV
ejpam-3133	84	38	gb(x	gb(x	ADJ
ejpam-3133	84	39	,	,	PUNCT
ejpam-3133	84	40	y	y	PROPN
ejpam-3133	84	41	,	,	PUNCT
ejpam-3133	84	42	z	z	NOUN
ejpam-3133	84	43	)	)	PUNCT
ejpam-3133	84	44	=	=	SYM
ejpam-3133	85	1	g2(x	g2(x	PROPN
ejpam-3133	85	2	,	,	PUNCT
ejpam-3133	85	3	y	y	PROPN
ejpam-3133	85	4	,	,	PUNCT
ejpam-3133	85	5	z	z	NOUN
ejpam-3133	85	6	)	)	PUNCT
ejpam-3133	85	7	=	=	SYM
ejpam-3133	85	8	1	1	NUM
ejpam-3133	85	9	9(|x	9(|x	NUM
ejpam-3133	85	10	−	−	NOUN
ejpam-3133	85	11	y|	y|	NOUN
ejpam-3133	85	12	+	+	CCONJ
ejpam-3133	85	13	|y	|y	VERB
ejpam-3133	85	14	−	−	PROPN
ejpam-3133	85	15	z|	z|	PROPN
ejpam-3133	85	16	+	+	PROPN
ejpam-3133	85	17	|x	|x	PROPN
ejpam-3133	85	18	−	−	PROPN
ejpam-3133	85	19	z|)2	z|)2	PROPN
ejpam-3133	85	20	is	be	AUX
ejpam-3133	85	21	a	a	DET
ejpam-3133	85	22	gb	gb	NOUN
ejpam-3133	85	23	-	-	PUNCT
ejpam-3133	85	24	metric	metric	ADJ
ejpam-3133	85	25	on	on	ADP
ejpam-3133	85	26	r	r	NOUN
ejpam-3133	85	27	with	with	ADP
ejpam-3133	85	28	s	s	NOUN
ejpam-3133	85	29	=	=	SYM
ejpam-3133	85	30	22−1	22−1	NUM
ejpam-3133	85	31	=	=	SYM
ejpam-3133	85	32	2	2	NUM
ejpam-3133	85	33	,	,	PUNCT
ejpam-3133	85	34	but	but	CCONJ
ejpam-3133	85	35	it	it	PRON
ejpam-3133	85	36	is	be	AUX
ejpam-3133	85	37	not	not	PART
ejpam-3133	85	38	a	a	DET
ejpam-3133	85	39	g	g	NOUN
ejpam-3133	85	40	-	-	PUNCT
ejpam-3133	85	41	metric	metric	ADJ
ejpam-3133	85	42	on	on	ADP
ejpam-3133	85	43	r.	r.	PROPN
ejpam-3133	85	44	example	example	NOUN
ejpam-3133	86	1	3	3	NUM
ejpam-3133	86	2	.	.	PUNCT
ejpam-3133	87	1	(	(	PUNCT
ejpam-3133	87	2	[	[	X
ejpam-3133	87	3	2	2	NUM
ejpam-3133	87	4	]	]	PUNCT
ejpam-3133	87	5	)	)	PUNCT
ejpam-3133	87	6	let	let	VERB
ejpam-3133	87	7	x	x	NOUN
ejpam-3133	87	8	=	=	SYM
ejpam-3133	87	9	r.	r.	PROPN
ejpam-3133	87	10	take	take	VERB
ejpam-3133	87	11	the	the	DET
ejpam-3133	87	12	gb	gb	ADV
ejpam-3133	87	13	-	-	PUNCT
ejpam-3133	87	14	metric	metric	NOUN
ejpam-3133	87	15	defined	define	VERB
ejpam-3133	87	16	by	by	ADP
ejpam-3133	87	17	gb(x	gb(x	PROPN
ejpam-3133	87	18	,	,	PUNCT
ejpam-3133	87	19	y	y	PROPN
ejpam-3133	87	20	,	,	PUNCT
ejpam-3133	87	21	z	z	NOUN
ejpam-3133	87	22	)	)	PUNCT
ejpam-3133	87	23	=	=	SYM
ejpam-3133	87	24	max	max	PROPN
ejpam-3133	87	25	{	{	PUNCT
ejpam-3133	87	26	|x−	|x−	PROPN
ejpam-3133	87	27	y|2	y|2	PROPN
ejpam-3133	87	28	,	,	PUNCT
ejpam-3133	87	29	|y	|y	ADJ
ejpam-3133	87	30	−	−	PROPN
ejpam-3133	87	31	z|2	z|2	PROPN
ejpam-3133	87	32	,	,	PUNCT
ejpam-3133	87	33	|z	|z	PROPN
ejpam-3133	87	34	−	−	PROPN
ejpam-3133	87	35	x|2	x|2	PROPN
ejpam-3133	87	36	}	}	PUNCT
ejpam-3133	87	37	,	,	PUNCT
ejpam-3133	87	38	∀	∀	X
ejpam-3133	87	39	x	x	NOUN
ejpam-3133	87	40	,	,	PUNCT
ejpam-3133	87	41	y	y	PROPN
ejpam-3133	87	42	,	,	PUNCT
ejpam-3133	87	43	z	z	PROPN
ejpam-3133	87	44	∈	∈	PROPN
ejpam-3133	87	45	x.	x.	NOUN
ejpam-3133	87	46	then	then	ADV
ejpam-3133	87	47	(	(	PUNCT
ejpam-3133	87	48	x	x	NOUN
ejpam-3133	87	49	,	,	PUNCT
ejpam-3133	87	50	gb	gb	PRON
ejpam-3133	87	51	)	)	PUNCT
ejpam-3133	87	52	is	be	AUX
ejpam-3133	87	53	a	a	DET
ejpam-3133	87	54	complete	complete	ADJ
ejpam-3133	87	55	gb	gb	ADV
ejpam-3133	87	56	-	-	PUNCT
ejpam-3133	87	57	metric	metric	ADJ
ejpam-3133	87	58	space	space	NOUN
ejpam-3133	87	59	with	with	ADP
ejpam-3133	87	60	s	s	NOUN
ejpam-3133	87	61	=	=	SYM
ejpam-3133	87	62	2	2	NUM
ejpam-3133	87	63	,	,	PUNCT
ejpam-3133	87	64	but	but	CCONJ
ejpam-3133	87	65	not	not	PART
ejpam-3133	87	66	a	a	DET
ejpam-3133	87	67	g	g	NOUN
ejpam-3133	87	68	-	-	PUNCT
ejpam-3133	87	69	metric	metric	ADJ
ejpam-3133	87	70	.	.	PUNCT
ejpam-3133	88	1	z.	z.	PROPN
ejpam-3133	88	2	mustafa	mustafa	PROPN
ejpam-3133	88	3	et	et	PROPN
ejpam-3133	88	4	al	al	PROPN
ejpam-3133	88	5	.	.	PUNCT
ejpam-3133	88	6	/	/	SYM
ejpam-3133	88	7	eur	eur	PROPN
ejpam-3133	88	8	.	.	PUNCT
ejpam-3133	89	1	j.	j.	PROPN
ejpam-3133	89	2	pure	pure	PROPN
ejpam-3133	89	3	appl	appl	PROPN
ejpam-3133	89	4	.	.	PROPN
ejpam-3133	89	5	math	math	PROPN
ejpam-3133	89	6	,	,	PUNCT
ejpam-3133	89	7	11	11	NUM
ejpam-3133	89	8	(	(	PUNCT
ejpam-3133	89	9	1	1	NUM
ejpam-3133	89	10	)	)	PUNCT
ejpam-3133	89	11	(	(	PUNCT
ejpam-3133	89	12	2018	2018	NUM
ejpam-3133	89	13	)	)	PUNCT
ejpam-3133	89	14	,	,	PUNCT
ejpam-3133	89	15	90	90	NUM
ejpam-3133	89	16	-	-	SYM
ejpam-3133	89	17	109	109	NUM
ejpam-3133	89	18	93	93	NUM
ejpam-3133	89	19	proposition	proposition	NOUN
ejpam-3133	89	20	1	1	NUM
ejpam-3133	89	21	.	.	PUNCT
ejpam-3133	90	1	(	(	PUNCT
ejpam-3133	90	2	[	[	X
ejpam-3133	90	3	2	2	NUM
ejpam-3133	90	4	]	]	PUNCT
ejpam-3133	90	5	)	)	PUNCT
ejpam-3133	90	6	let	let	VERB
ejpam-3133	90	7	x	x	PRON
ejpam-3133	90	8	be	be	AUX
ejpam-3133	90	9	a	a	DET
ejpam-3133	90	10	gb	gb	ADV
ejpam-3133	90	11	-	-	PUNCT
ejpam-3133	90	12	metric	metric	ADJ
ejpam-3133	90	13	space	space	NOUN
ejpam-3133	90	14	.	.	PUNCT
ejpam-3133	91	1	then	then	ADV
ejpam-3133	91	2	for	for	ADP
ejpam-3133	91	3	each	each	DET
ejpam-3133	91	4	x	x	PROPN
ejpam-3133	91	5	,	,	PUNCT
ejpam-3133	91	6	y	y	PROPN
ejpam-3133	91	7	,	,	PUNCT
ejpam-3133	91	8	z	z	PROPN
ejpam-3133	91	9	,	,	PUNCT
ejpam-3133	91	10	a	a	DET
ejpam-3133	91	11	∈	∈	PROPN
ejpam-3133	91	12	x	x	X
ejpam-3133	91	13	,	,	PUNCT
ejpam-3133	91	14	it	it	PRON
ejpam-3133	91	15	follows	follow	VERB
ejpam-3133	91	16	that	that	SCONJ
ejpam-3133	91	17	(	(	PUNCT
ejpam-3133	91	18	1	1	X
ejpam-3133	91	19	)	)	PUNCT
ejpam-3133	91	20	if	if	SCONJ
ejpam-3133	91	21	gb(x	gb(x	ADJ
ejpam-3133	91	22	,	,	PUNCT
ejpam-3133	91	23	y	y	PROPN
ejpam-3133	91	24	,	,	PUNCT
ejpam-3133	91	25	z	z	NOUN
ejpam-3133	91	26	)	)	PUNCT
ejpam-3133	91	27	=	=	SYM
ejpam-3133	91	28	0	0	NUM
ejpam-3133	91	29	,	,	PUNCT
ejpam-3133	91	30	then	then	ADV
ejpam-3133	91	31	x	x	X
ejpam-3133	91	32	=	=	PUNCT
ejpam-3133	91	33	y	y	PROPN
ejpam-3133	91	34	=	=	SYM
ejpam-3133	91	35	z	z	PROPN
ejpam-3133	91	36	,	,	PUNCT
ejpam-3133	91	37	(	(	PUNCT
ejpam-3133	91	38	2	2	NUM
ejpam-3133	91	39	)	)	PUNCT
ejpam-3133	91	40	gb(x	gb(x	PROPN
ejpam-3133	91	41	,	,	PUNCT
ejpam-3133	91	42	y	y	PROPN
ejpam-3133	91	43	,	,	PUNCT
ejpam-3133	91	44	z	z	NOUN
ejpam-3133	91	45	)	)	PUNCT
ejpam-3133	91	46	≤	≤	NOUN
ejpam-3133	91	47	s(gb(x	s(gb(x	PROPN
ejpam-3133	91	48	,	,	PUNCT
ejpam-3133	91	49	x	x	NOUN
ejpam-3133	91	50	,	,	PUNCT
ejpam-3133	91	51	y	y	PROPN
ejpam-3133	91	52	)	)	PUNCT
ejpam-3133	92	1	+	+	ADV
ejpam-3133	92	2	gb(x	gb(x	ADJ
ejpam-3133	92	3	,	,	PUNCT
ejpam-3133	92	4	x	x	NOUN
ejpam-3133	92	5	,	,	PUNCT
ejpam-3133	92	6	z	z	NOUN
ejpam-3133	92	7	)	)	PUNCT
ejpam-3133	92	8	)	)	PUNCT
ejpam-3133	92	9	,	,	PUNCT
ejpam-3133	92	10	(	(	PUNCT
ejpam-3133	92	11	3	3	X
ejpam-3133	92	12	)	)	PUNCT
ejpam-3133	92	13	gb(x	gb(x	PROPN
ejpam-3133	92	14	,	,	PUNCT
ejpam-3133	92	15	y	y	PROPN
ejpam-3133	92	16	,	,	PUNCT
ejpam-3133	92	17	y	y	NOUN
ejpam-3133	92	18	)	)	PUNCT
ejpam-3133	92	19	≤	≤	NOUN
ejpam-3133	92	20	2sgb(y	2sgb(y	NUM
ejpam-3133	92	21	,	,	PUNCT
ejpam-3133	92	22	x	x	X
ejpam-3133	92	23	,	,	PUNCT
ejpam-3133	92	24	x	x	X
ejpam-3133	92	25	)	)	PUNCT
ejpam-3133	92	26	,	,	PUNCT
ejpam-3133	92	27	(	(	PUNCT
ejpam-3133	92	28	4	4	X
ejpam-3133	92	29	)	)	PUNCT
ejpam-3133	92	30	gb(x	gb(x	PROPN
ejpam-3133	92	31	,	,	PUNCT
ejpam-3133	92	32	y	y	PROPN
ejpam-3133	92	33	,	,	PUNCT
ejpam-3133	92	34	z	z	NOUN
ejpam-3133	92	35	)	)	PUNCT
ejpam-3133	92	36	≤	≤	NOUN
ejpam-3133	92	37	s(gb(x	s(gb(x	PROPN
ejpam-3133	92	38	,	,	PUNCT
ejpam-3133	92	39	a	a	PRON
ejpam-3133	92	40	,	,	PUNCT
ejpam-3133	92	41	z	z	NOUN
ejpam-3133	92	42	)	)	PUNCT
ejpam-3133	93	1	+	+	NOUN
ejpam-3133	93	2	gb(a	gb(a	NOUN
ejpam-3133	93	3	,	,	PUNCT
ejpam-3133	93	4	y	y	PROPN
ejpam-3133	93	5	,	,	PUNCT
ejpam-3133	93	6	z	z	NOUN
ejpam-3133	93	7	)	)	PUNCT
ejpam-3133	93	8	)	)	PUNCT
ejpam-3133	93	9	.	.	PUNCT
ejpam-3133	94	1	definition	definition	NOUN
ejpam-3133	94	2	4	4	NUM
ejpam-3133	94	3	.	.	PUNCT
ejpam-3133	95	1	(	(	PUNCT
ejpam-3133	95	2	[	[	X
ejpam-3133	95	3	2	2	NUM
ejpam-3133	95	4	]	]	PUNCT
ejpam-3133	95	5	)	)	PUNCT
ejpam-3133	95	6	let	let	VERB
ejpam-3133	95	7	x	x	PRON
ejpam-3133	95	8	be	be	AUX
ejpam-3133	95	9	a	a	DET
ejpam-3133	95	10	gb	gb	ADV
ejpam-3133	95	11	-	-	PUNCT
ejpam-3133	95	12	metric	metric	ADJ
ejpam-3133	95	13	space	space	NOUN
ejpam-3133	95	14	.	.	PUNCT
ejpam-3133	96	1	a	a	DET
ejpam-3133	96	2	sequence	sequence	NOUN
ejpam-3133	96	3	{	{	PUNCT
ejpam-3133	96	4	xn	xn	NOUN
ejpam-3133	96	5	}	}	PUNCT
ejpam-3133	96	6	in	in	ADP
ejpam-3133	96	7	x	x	VERB
ejpam-3133	96	8	is	be	AUX
ejpam-3133	96	9	said	say	VERB
ejpam-3133	96	10	to	to	PART
ejpam-3133	96	11	be	be	AUX
ejpam-3133	96	12	:	:	PUNCT
ejpam-3133	96	13	(	(	PUNCT
ejpam-3133	96	14	1	1	X
ejpam-3133	96	15	)	)	PUNCT
ejpam-3133	96	16	gb	gb	NOUN
ejpam-3133	96	17	-	-	PUNCT
ejpam-3133	96	18	cauchy	cauchy	ADJ
ejpam-3133	96	19	sequence	sequence	NOUN
ejpam-3133	96	20	if	if	SCONJ
ejpam-3133	96	21	for	for	ADP
ejpam-3133	96	22	each	each	DET
ejpam-3133	96	23	ε	ε	PROPN
ejpam-3133	96	24	>	>	X
ejpam-3133	96	25	0	0	PROPN
ejpam-3133	96	26	,	,	PUNCT
ejpam-3133	96	27	there	there	PRON
ejpam-3133	96	28	exists	exist	VERB
ejpam-3133	96	29	a	a	DET
ejpam-3133	96	30	positive	positive	ADJ
ejpam-3133	96	31	integer	integer	NOUN
ejpam-3133	96	32	n0	n0	NOUN
ejpam-3133	96	33	such	such	ADJ
ejpam-3133	96	34	that	that	PRON
ejpam-3133	96	35	for	for	ADP
ejpam-3133	96	36	all	all	DET
ejpam-3133	96	37	m	m	PROPN
ejpam-3133	96	38	,	,	PUNCT
ejpam-3133	96	39	n	n	CCONJ
ejpam-3133	96	40	,	,	PUNCT
ejpam-3133	96	41	l	l	PROPN
ejpam-3133	96	42	≥	≥	NUM
ejpam-3133	96	43	n0	n0	NUM
ejpam-3133	96	44	,	,	PUNCT
ejpam-3133	96	45	gb(xn	gb(xn	PROPN
ejpam-3133	96	46	,	,	PUNCT
ejpam-3133	96	47	xm	xm	PROPN
ejpam-3133	96	48	,	,	PUNCT
ejpam-3133	96	49	xl	xl	PROPN
ejpam-3133	96	50	)	)	PUNCT
ejpam-3133	96	51	<	<	AUX
ejpam-3133	96	52	ε	ε	PROPN
ejpam-3133	96	53	;	;	PUNCT
ejpam-3133	96	54	(	(	PUNCT
ejpam-3133	96	55	2	2	X
ejpam-3133	96	56	)	)	PUNCT
ejpam-3133	96	57	gb	gb	NOUN
ejpam-3133	96	58	-	-	PUNCT
ejpam-3133	96	59	convergent	convergent	NOUN
ejpam-3133	96	60	to	to	ADP
ejpam-3133	96	61	a	a	DET
ejpam-3133	96	62	point	point	NOUN
ejpam-3133	96	63	x	x	SYM
ejpam-3133	96	64	∈	∈	NOUN
ejpam-3133	96	65	x	x	INTJ
ejpam-3133	96	66	if	if	SCONJ
ejpam-3133	96	67	for	for	ADP
ejpam-3133	96	68	each	each	DET
ejpam-3133	96	69	ε	ε	PROPN
ejpam-3133	96	70	>	>	X
ejpam-3133	96	71	0	0	PROPN
ejpam-3133	96	72	,	,	PUNCT
ejpam-3133	96	73	there	there	PRON
ejpam-3133	96	74	exists	exist	VERB
ejpam-3133	96	75	a	a	DET
ejpam-3133	96	76	positive	positive	ADJ
ejpam-3133	96	77	integer	integer	NOUN
ejpam-3133	96	78	n0	n0	NOUN
ejpam-3133	96	79	such	such	ADJ
ejpam-3133	96	80	that	that	SCONJ
ejpam-3133	96	81	,	,	PUNCT
ejpam-3133	96	82	for	for	ADP
ejpam-3133	96	83	all	all	DET
ejpam-3133	96	84	m	m	PROPN
ejpam-3133	96	85	,	,	PUNCT
ejpam-3133	96	86	n	n	PRON
ejpam-3133	96	87	≥	≥	NOUN
ejpam-3133	96	88	n0	n0	NUM
ejpam-3133	96	89	,	,	PUNCT
ejpam-3133	96	90	gb(xn	gb(xn	PROPN
ejpam-3133	96	91	,	,	PUNCT
ejpam-3133	96	92	xm	xm	PROPN
ejpam-3133	96	93	,	,	PUNCT
ejpam-3133	96	94	x	x	X
ejpam-3133	96	95	)	)	PUNCT
ejpam-3133	96	96	<	<	X
ejpam-3133	96	97	ε	ε	PROPN
ejpam-3133	96	98	.	.	PUNCT
ejpam-3133	96	99	proposition	proposition	NOUN
ejpam-3133	96	100	2	2	NUM
ejpam-3133	96	101	.	.	PUNCT
ejpam-3133	97	1	(	(	PUNCT
ejpam-3133	97	2	[	[	X
ejpam-3133	97	3	2	2	NUM
ejpam-3133	97	4	,	,	PUNCT
ejpam-3133	97	5	9	9	NUM
ejpam-3133	97	6	]	]	PUNCT
ejpam-3133	97	7	)	)	PUNCT
ejpam-3133	97	8	let	let	VERB
ejpam-3133	97	9	x	x	PRON
ejpam-3133	97	10	be	be	AUX
ejpam-3133	97	11	a	a	DET
ejpam-3133	97	12	gb	gb	ADV
ejpam-3133	97	13	-	-	PUNCT
ejpam-3133	97	14	metric	metric	ADJ
ejpam-3133	97	15	space	space	NOUN
ejpam-3133	97	16	.	.	PUNCT
ejpam-3133	98	1	the	the	DET
ejpam-3133	98	2	following	follow	VERB
ejpam-3133	98	3	are	be	AUX
ejpam-3133	98	4	equivalent	equivalent	ADJ
ejpam-3133	98	5	:	:	PUNCT
ejpam-3133	98	6	(	(	PUNCT
ejpam-3133	98	7	1	1	X
ejpam-3133	98	8	)	)	PUNCT
ejpam-3133	98	9	{	{	PUNCT
ejpam-3133	98	10	xn	xn	X
ejpam-3133	98	11	}	}	PUNCT
ejpam-3133	98	12	is	be	AUX
ejpam-3133	98	13	gb	gb	NOUN
ejpam-3133	98	14	-	-	PUNCT
ejpam-3133	98	15	convergent	convergent	NOUN
ejpam-3133	98	16	to	to	PART
ejpam-3133	98	17	x	x	PRON
ejpam-3133	98	18	;	;	PUNCT
ejpam-3133	98	19	(	(	PUNCT
ejpam-3133	98	20	2	2	X
ejpam-3133	98	21	)	)	PUNCT
ejpam-3133	98	22	gb(xn	gb(xn	NOUN
ejpam-3133	98	23	,	,	PUNCT
ejpam-3133	98	24	xn	xn	PROPN
ejpam-3133	98	25	,	,	PUNCT
ejpam-3133	98	26	x)→	x)→	PROPN
ejpam-3133	98	27	0	0	PUNCT
ejpam-3133	98	28	as	as	ADP
ejpam-3133	98	29	n→∞	n→∞	NUM
ejpam-3133	98	30	;	;	PUNCT
ejpam-3133	98	31	(	(	PUNCT
ejpam-3133	98	32	3	3	X
ejpam-3133	98	33	)	)	PUNCT
ejpam-3133	98	34	gb(xn	gb(xn	NOUN
ejpam-3133	98	35	,	,	PUNCT
ejpam-3133	98	36	x	x	X
ejpam-3133	98	37	,	,	PUNCT
ejpam-3133	98	38	x)→	x)→	PROPN
ejpam-3133	98	39	0	0	PUNCT
ejpam-3133	99	1	as	as	ADP
ejpam-3133	99	2	n→∞.	n→∞.	ADJ
ejpam-3133	99	3	definition	definition	NOUN
ejpam-3133	99	4	5	5	NUM
ejpam-3133	99	5	.	.	PUNCT
ejpam-3133	100	1	(	(	PUNCT
ejpam-3133	100	2	[	[	X
ejpam-3133	100	3	2	2	NUM
ejpam-3133	100	4	]	]	PUNCT
ejpam-3133	100	5	)	)	PUNCT
ejpam-3133	100	6	a	a	DET
ejpam-3133	100	7	gb	gb	ADV
ejpam-3133	100	8	-	-	PUNCT
ejpam-3133	100	9	metric	metric	ADJ
ejpam-3133	100	10	space	space	NOUN
ejpam-3133	100	11	x	x	PUNCT
ejpam-3133	100	12	is	be	AUX
ejpam-3133	100	13	called	call	VERB
ejpam-3133	100	14	gb	gb	ADV
ejpam-3133	100	15	-	-	PUNCT
ejpam-3133	100	16	complete	complete	ADJ
ejpam-3133	100	17	if	if	SCONJ
ejpam-3133	100	18	every	every	DET
ejpam-3133	100	19	gb	gb	NOUN
ejpam-3133	100	20	-	-	PUNCT
ejpam-3133	100	21	cauchy	cauchy	ADJ
ejpam-3133	100	22	sequence	sequence	NOUN
ejpam-3133	100	23	is	be	AUX
ejpam-3133	100	24	gb	gb	NOUN
ejpam-3133	100	25	-	-	PUNCT
ejpam-3133	100	26	convergent	convergent	NOUN
ejpam-3133	100	27	in	in	ADP
ejpam-3133	100	28	x.	x.	NOUN
ejpam-3133	100	29	the	the	DET
ejpam-3133	100	30	following	follow	VERB
ejpam-3133	100	31	definition	definition	NOUN
ejpam-3133	100	32	was	be	AUX
ejpam-3133	100	33	given	give	VERB
ejpam-3133	100	34	by	by	ADP
ejpam-3133	100	35	jungck	jungck	NOUN
ejpam-3133	100	36	[	[	X
ejpam-3133	100	37	19	19	NUM
ejpam-3133	100	38	]	]	PUNCT
ejpam-3133	100	39	.	.	PUNCT
ejpam-3133	101	1	definition	definition	NOUN
ejpam-3133	101	2	6	6	NUM
ejpam-3133	101	3	.	.	PUNCT
ejpam-3133	102	1	(	(	PUNCT
ejpam-3133	102	2	[	[	X
ejpam-3133	102	3	19	19	NUM
ejpam-3133	102	4	]	]	SYM
ejpam-3133	102	5	)	)	PUNCT
ejpam-3133	102	6	two	two	NUM
ejpam-3133	102	7	maps	map	NOUN
ejpam-3133	102	8	f	f	PROPN
ejpam-3133	102	9	and	and	CCONJ
ejpam-3133	102	10	g	g	PROPN
ejpam-3133	102	11	are	be	AUX
ejpam-3133	102	12	said	say	VERB
ejpam-3133	102	13	to	to	PART
ejpam-3133	102	14	be	be	AUX
ejpam-3133	102	15	weakly	weakly	ADV
ejpam-3133	102	16	compatible	compatible	ADJ
ejpam-3133	102	17	if	if	SCONJ
ejpam-3133	102	18	they	they	PRON
ejpam-3133	102	19	commute	commute	VERB
ejpam-3133	102	20	at	at	ADP
ejpam-3133	102	21	their	their	PRON
ejpam-3133	102	22	coincidence	coincidence	NOUN
ejpam-3133	102	23	points	point	NOUN
ejpam-3133	102	24	,	,	PUNCT
ejpam-3133	102	25	that	that	PRON
ejpam-3133	102	26	is	be	AUX
ejpam-3133	102	27	if	if	SCONJ
ejpam-3133	102	28	f(x	f(x	PROPN
ejpam-3133	102	29	)	)	PUNCT
ejpam-3133	103	1	=	=	PUNCT
ejpam-3133	104	1	g(x	g(x	NOUN
ejpam-3133	104	2	)	)	PUNCT
ejpam-3133	104	3	for	for	ADP
ejpam-3133	104	4	some	some	DET
ejpam-3133	104	5	x	x	SYM
ejpam-3133	104	6	∈	∈	PROPN
ejpam-3133	104	7	x	x	NOUN
ejpam-3133	104	8	,	,	PUNCT
ejpam-3133	104	9	then	then	ADV
ejpam-3133	104	10	f(g(x	f(g(x	NOUN
ejpam-3133	104	11	)	)	PUNCT
ejpam-3133	104	12	)	)	PUNCT
ejpam-3133	105	1	=	=	SYM
ejpam-3133	105	2	g(f(x	g(f(x	PROPN
ejpam-3133	105	3	)	)	PUNCT
ejpam-3133	105	4	)	)	PUNCT
ejpam-3133	105	5	.	.	PUNCT
ejpam-3133	106	1	the	the	DET
ejpam-3133	106	2	following	follow	VERB
ejpam-3133	106	3	definition	definition	NOUN
ejpam-3133	106	4	was	be	AUX
ejpam-3133	106	5	introduced	introduce	VERB
ejpam-3133	106	6	by	by	ADP
ejpam-3133	106	7	amari	amari	PROPN
ejpam-3133	106	8	and	and	CCONJ
ejpam-3133	106	9	el	el	PROPN
ejpam-3133	106	10	moutawakil	moutawakil	PROPN
ejpam-3133	107	1	[	[	X
ejpam-3133	107	2	1	1	X
ejpam-3133	107	3	]	]	PUNCT
ejpam-3133	107	4	in	in	ADP
ejpam-3133	107	5	2002	2002	NUM
ejpam-3133	107	6	.	.	PUNCT
ejpam-3133	108	1	definition	definition	NOUN
ejpam-3133	108	2	7	7	NUM
ejpam-3133	108	3	.	.	PUNCT
ejpam-3133	109	1	(	(	PUNCT
ejpam-3133	109	2	[	[	X
ejpam-3133	109	3	1	1	NUM
ejpam-3133	109	4	]	]	PUNCT
ejpam-3133	109	5	)	)	PUNCT
ejpam-3133	109	6	two	two	NUM
ejpam-3133	109	7	self	self	NOUN
ejpam-3133	109	8	mappings	mapping	NOUN
ejpam-3133	109	9	s	s	PART
ejpam-3133	109	10	and	and	CCONJ
ejpam-3133	109	11	t	t	PROPN
ejpam-3133	109	12	of	of	ADP
ejpam-3133	109	13	a	a	DET
ejpam-3133	109	14	metric	metric	ADJ
ejpam-3133	109	15	space	space	NOUN
ejpam-3133	109	16	(	(	PUNCT
ejpam-3133	109	17	x	x	X
ejpam-3133	109	18	,	,	PUNCT
ejpam-3133	109	19	d	d	NOUN
ejpam-3133	109	20	)	)	PUNCT
ejpam-3133	109	21	are	be	AUX
ejpam-3133	109	22	said	say	VERB
ejpam-3133	109	23	to	to	PART
ejpam-3133	109	24	satisfy	satisfy	VERB
ejpam-3133	109	25	an	an	DET
ejpam-3133	109	26	(	(	PUNCT
ejpam-3133	109	27	e.a	e.a	PROPN
ejpam-3133	109	28	)	)	PUNCT
ejpam-3133	109	29	property	property	NOUN
ejpam-3133	109	30	if	if	SCONJ
ejpam-3133	109	31	there	there	PRON
ejpam-3133	109	32	exists	exist	VERB
ejpam-3133	109	33	a	a	DET
ejpam-3133	109	34	sequence	sequence	NOUN
ejpam-3133	109	35	{	{	PUNCT
ejpam-3133	109	36	xn	xn	NOUN
ejpam-3133	109	37	}	}	PUNCT
ejpam-3133	109	38	in	in	ADP
ejpam-3133	109	39	x	x	SYM
ejpam-3133	109	40	such	such	ADJ
ejpam-3133	109	41	that	that	SCONJ
ejpam-3133	109	42	lim	lim	PROPN
ejpam-3133	109	43	n→∞	n→∞	NUM
ejpam-3133	109	44	sxn	sxn	NOUN
ejpam-3133	109	45	=	=	PROPN
ejpam-3133	109	46	lim	lim	PROPN
ejpam-3133	109	47	n→∞	n→∞	X
ejpam-3133	110	1	txn	txn	NOUN
ejpam-3133	110	2	=	=	SYM
ejpam-3133	110	3	r	r	NOUN
ejpam-3133	110	4	for	for	ADP
ejpam-3133	110	5	some	some	DET
ejpam-3133	110	6	r	r	NOUN
ejpam-3133	110	7	∈	∈	NOUN
ejpam-3133	110	8	x.	x.	NOUN
ejpam-3133	111	1	this	this	DET
ejpam-3133	111	2	concept	concept	NOUN
ejpam-3133	111	3	was	be	AUX
ejpam-3133	111	4	extended	extend	VERB
ejpam-3133	111	5	to	to	ADP
ejpam-3133	111	6	g	g	NOUN
ejpam-3133	111	7	-	-	PUNCT
ejpam-3133	111	8	metric	metric	ADJ
ejpam-3133	111	9	spaces	space	NOUN
ejpam-3133	111	10	in	in	ADP
ejpam-3133	111	11	[	[	X
ejpam-3133	111	12	24	24	NUM
ejpam-3133	111	13	]	]	PUNCT
ejpam-3133	111	14	.	.	PUNCT
ejpam-3133	112	1	the	the	DET
ejpam-3133	112	2	following	follow	VERB
ejpam-3133	112	3	lemma	lemma	PROPN
ejpam-3133	112	4	is	be	AUX
ejpam-3133	112	5	useful	useful	ADJ
ejpam-3133	112	6	in	in	ADP
ejpam-3133	112	7	the	the	DET
ejpam-3133	112	8	proof	proof	NOUN
ejpam-3133	112	9	of	of	ADP
ejpam-3133	112	10	our	our	PRON
ejpam-3133	112	11	main	main	ADJ
ejpam-3133	112	12	result	result	NOUN
ejpam-3133	112	13	.	.	PUNCT
ejpam-3133	113	1	lemma	lemma	PROPN
ejpam-3133	113	2	1	1	NUM
ejpam-3133	113	3	.	.	PUNCT
ejpam-3133	114	1	(	(	PUNCT
ejpam-3133	114	2	[	[	X
ejpam-3133	114	3	45	45	NUM
ejpam-3133	114	4	]	]	PUNCT
ejpam-3133	114	5	)	)	PUNCT
ejpam-3133	114	6	let	let	AUX
ejpam-3133	114	7	(	(	PUNCT
ejpam-3133	114	8	x	x	NOUN
ejpam-3133	114	9	,	,	PUNCT
ejpam-3133	114	10	gb	gb	PRON
ejpam-3133	114	11	)	)	PUNCT
ejpam-3133	114	12	be	be	AUX
ejpam-3133	114	13	a	a	DET
ejpam-3133	114	14	gb	gb	ADV
ejpam-3133	114	15	-	-	PUNCT
ejpam-3133	114	16	metric	metric	ADJ
ejpam-3133	114	17	space	space	NOUN
ejpam-3133	114	18	with	with	ADP
ejpam-3133	114	19	s	s	PRON
ejpam-3133	114	20	>	>	X
ejpam-3133	114	21	1	1	X
ejpam-3133	114	22	.	.	PUNCT
ejpam-3133	114	23	suppose	suppose	VERB
ejpam-3133	114	24	that	that	SCONJ
ejpam-3133	114	25	{	{	PUNCT
ejpam-3133	114	26	xn	xn	X
ejpam-3133	114	27	}	}	PUNCT
ejpam-3133	114	28	,	,	PUNCT
ejpam-3133	114	29	{	{	PUNCT
ejpam-3133	114	30	yn	yn	X
ejpam-3133	114	31	}	}	PUNCT
ejpam-3133	114	32	and	and	CCONJ
ejpam-3133	114	33	{	{	PUNCT
ejpam-3133	114	34	zn	zn	X
ejpam-3133	114	35	}	}	PUNCT
ejpam-3133	114	36	are	be	AUX
ejpam-3133	114	37	gb	gb	ADV
ejpam-3133	114	38	-	-	PUNCT
ejpam-3133	114	39	convergent	convergent	NOUN
ejpam-3133	114	40	sequences	sequence	NOUN
ejpam-3133	114	41	to	to	ADP
ejpam-3133	114	42	x	x	PRON
ejpam-3133	114	43	,	,	PUNCT
ejpam-3133	114	44	y	y	PROPN
ejpam-3133	114	45	and	and	CCONJ
ejpam-3133	114	46	z	z	PROPN
ejpam-3133	114	47	,	,	PUNCT
ejpam-3133	114	48	respectively	respectively	ADV
ejpam-3133	114	49	.	.	PUNCT
ejpam-3133	115	1	then	then	ADV
ejpam-3133	115	2	we	we	PRON
ejpam-3133	115	3	have	have	VERB
ejpam-3133	115	4	(	(	PUNCT
ejpam-3133	115	5	i	i	NOUN
ejpam-3133	115	6	)	)	PUNCT
ejpam-3133	115	7	1	1	NUM
ejpam-3133	115	8	s3	s3	PROPN
ejpam-3133	115	9	gb(x	gb(x	PROPN
ejpam-3133	115	10	,	,	PUNCT
ejpam-3133	115	11	y	y	PROPN
ejpam-3133	115	12	,	,	PUNCT
ejpam-3133	115	13	z	z	NOUN
ejpam-3133	115	14	)	)	PUNCT
ejpam-3133	115	15	≤	≤	NOUN
ejpam-3133	115	16	lim	lim	PROPN
ejpam-3133	115	17	inf	inf	PROPN
ejpam-3133	115	18	n→∞	n→∞	X
ejpam-3133	115	19	gb(xn	gb(xn	PROPN
ejpam-3133	115	20	,	,	PUNCT
ejpam-3133	115	21	yn	yn	PROPN
ejpam-3133	115	22	,	,	PUNCT
ejpam-3133	115	23	zn	zn	PROPN
ejpam-3133	115	24	)	)	PUNCT
ejpam-3133	115	25	≤	≤	NOUN
ejpam-3133	116	1	lim	lim	PROPN
ejpam-3133	116	2	sup	sup	VERB
ejpam-3133	116	3	n→∞	n→∞	NUM
ejpam-3133	116	4	gb(xn	gb(xn	NOUN
ejpam-3133	116	5	,	,	PUNCT
ejpam-3133	116	6	yn	yn	PROPN
ejpam-3133	116	7	,	,	PUNCT
ejpam-3133	116	8	zn	zn	PROPN
ejpam-3133	116	9	)	)	PUNCT
ejpam-3133	116	10	≤	≤	PROPN
ejpam-3133	116	11	s3gb(x	s3gb(x	PROPN
ejpam-3133	116	12	,	,	PUNCT
ejpam-3133	116	13	y	y	PROPN
ejpam-3133	116	14	,	,	PUNCT
ejpam-3133	116	15	z	z	NOUN
ejpam-3133	116	16	)	)	PUNCT
ejpam-3133	116	17	.	.	PUNCT
ejpam-3133	117	1	(	(	PUNCT
ejpam-3133	117	2	ii	ii	NOUN
ejpam-3133	117	3	)	)	PUNCT
ejpam-3133	117	4	if	if	SCONJ
ejpam-3133	117	5	{	{	PUNCT
ejpam-3133	117	6	zn	zn	NOUN
ejpam-3133	117	7	}	}	PUNCT
ejpam-3133	117	8	=	=	PUNCT
ejpam-3133	117	9	c	c	NOUN
ejpam-3133	117	10	is	be	AUX
ejpam-3133	117	11	constant	constant	ADJ
ejpam-3133	117	12	,	,	PUNCT
ejpam-3133	117	13	then	then	ADV
ejpam-3133	117	14	1	1	NUM
ejpam-3133	117	15	s2	s2	PROPN
ejpam-3133	117	16	gb(x	gb(x	PROPN
ejpam-3133	117	17	,	,	PUNCT
ejpam-3133	117	18	y	y	PROPN
ejpam-3133	117	19	,	,	PUNCT
ejpam-3133	117	20	c	c	NOUN
ejpam-3133	117	21	)	)	PUNCT
ejpam-3133	117	22	≤	≤	NOUN
ejpam-3133	117	23	lim	lim	PROPN
ejpam-3133	117	24	inf	inf	PROPN
ejpam-3133	117	25	n→∞	n→∞	X
ejpam-3133	117	26	gb(xn	gb(xn	PROPN
ejpam-3133	117	27	,	,	PUNCT
ejpam-3133	117	28	yn	yn	PROPN
ejpam-3133	117	29	,	,	PUNCT
ejpam-3133	117	30	c	c	NOUN
ejpam-3133	117	31	)	)	PUNCT
ejpam-3133	118	1	≤	≤	NOUN
ejpam-3133	118	2	lim	lim	PROPN
ejpam-3133	118	3	sup	sup	VERB
ejpam-3133	118	4	n→∞	n→∞	NUM
ejpam-3133	118	5	gb(xn	gb(xn	NOUN
ejpam-3133	118	6	,	,	PUNCT
ejpam-3133	118	7	ync	ync	PROPN
ejpam-3133	118	8	)	)	PUNCT
ejpam-3133	118	9	≤	≤	NOUN
ejpam-3133	119	1	s2gb(x	s2gb(x	PROPN
ejpam-3133	119	2	,	,	PUNCT
ejpam-3133	119	3	y	y	PROPN
ejpam-3133	119	4	,	,	PUNCT
ejpam-3133	119	5	c	c	NOUN
ejpam-3133	119	6	)	)	PUNCT
ejpam-3133	119	7	.	.	PUNCT
ejpam-3133	120	1	z.	z.	PROPN
ejpam-3133	120	2	mustafa	mustafa	PROPN
ejpam-3133	120	3	et	et	PROPN
ejpam-3133	120	4	al	al	PROPN
ejpam-3133	120	5	.	.	PUNCT
ejpam-3133	120	6	/	/	SYM
ejpam-3133	120	7	eur	eur	PROPN
ejpam-3133	120	8	.	.	PUNCT
ejpam-3133	121	1	j.	j.	PROPN
ejpam-3133	121	2	pure	pure	PROPN
ejpam-3133	121	3	appl	appl	PROPN
ejpam-3133	121	4	.	.	PROPN
ejpam-3133	121	5	math	math	PROPN
ejpam-3133	121	6	,	,	PUNCT
ejpam-3133	121	7	11	11	NUM
ejpam-3133	121	8	(	(	PUNCT
ejpam-3133	121	9	1	1	NUM
ejpam-3133	121	10	)	)	PUNCT
ejpam-3133	121	11	(	(	PUNCT
ejpam-3133	121	12	2018	2018	NUM
ejpam-3133	121	13	)	)	PUNCT
ejpam-3133	121	14	,	,	PUNCT
ejpam-3133	121	15	90	90	NUM
ejpam-3133	121	16	-	-	SYM
ejpam-3133	121	17	109	109	NUM
ejpam-3133	121	18	94	94	NUM
ejpam-3133	121	19	(	(	PUNCT
ejpam-3133	121	20	iii	iii	NOUN
ejpam-3133	121	21	)	)	PUNCT
ejpam-3133	122	1	if	if	SCONJ
ejpam-3133	122	2	{	{	PUNCT
ejpam-3133	122	3	zn	zn	NOUN
ejpam-3133	122	4	}	}	PUNCT
ejpam-3133	122	5	=	=	SYM
ejpam-3133	122	6	c	c	NOUN
ejpam-3133	122	7	and	and	CCONJ
ejpam-3133	122	8	{	{	PUNCT
ejpam-3133	122	9	yn	yn	NOUN
ejpam-3133	122	10	}	}	PUNCT
ejpam-3133	122	11	=	=	SYM
ejpam-3133	123	1	b	b	NOUN
ejpam-3133	123	2	are	be	AUX
ejpam-3133	123	3	constant	constant	ADJ
ejpam-3133	123	4	,	,	PUNCT
ejpam-3133	123	5	then	then	ADV
ejpam-3133	123	6	1	1	NUM
ejpam-3133	123	7	s	s	VERB
ejpam-3133	123	8	gb(x	gb(x	ADJ
ejpam-3133	123	9	,	,	PUNCT
ejpam-3133	123	10	b	b	NOUN
ejpam-3133	123	11	,	,	PUNCT
ejpam-3133	123	12	c	c	NOUN
ejpam-3133	123	13	)	)	PUNCT
ejpam-3133	123	14	≤	≤	NOUN
ejpam-3133	123	15	lim	lim	PROPN
ejpam-3133	123	16	inf	inf	PROPN
ejpam-3133	123	17	n→∞	n→∞	X
ejpam-3133	123	18	gb(xn	gb(xn	PROPN
ejpam-3133	123	19	,	,	PUNCT
ejpam-3133	123	20	b	b	PROPN
ejpam-3133	123	21	,	,	PUNCT
ejpam-3133	123	22	c	c	NOUN
ejpam-3133	123	23	)	)	PUNCT
ejpam-3133	123	24	≤	≤	NOUN
ejpam-3133	123	25	lim	lim	PROPN
ejpam-3133	123	26	sup	sup	VERB
ejpam-3133	123	27	n→∞	n→∞	NUM
ejpam-3133	123	28	gb(xn	gb(xn	NOUN
ejpam-3133	123	29	,	,	PUNCT
ejpam-3133	123	30	b	b	PROPN
ejpam-3133	123	31	,	,	PUNCT
ejpam-3133	123	32	c	c	NOUN
ejpam-3133	123	33	)	)	PUNCT
ejpam-3133	123	34	≤	≤	NOUN
ejpam-3133	124	1	sgb(x	sgb(x	PROPN
ejpam-3133	124	2	,	,	PUNCT
ejpam-3133	124	3	b	b	NOUN
ejpam-3133	124	4	,	,	PUNCT
ejpam-3133	124	5	c	c	NOUN
ejpam-3133	124	6	)	)	PUNCT
ejpam-3133	124	7	.	.	PUNCT
ejpam-3133	125	1	in	in	ADP
ejpam-3133	125	2	particular	particular	ADJ
ejpam-3133	125	3	,	,	PUNCT
ejpam-3133	125	4	if	if	SCONJ
ejpam-3133	125	5	x	x	ADP
ejpam-3133	125	6	=	=	PUNCT
ejpam-3133	125	7	y	y	PROPN
ejpam-3133	125	8	=	=	SYM
ejpam-3133	125	9	z	z	PROPN
ejpam-3133	125	10	,	,	PUNCT
ejpam-3133	125	11	then	then	ADV
ejpam-3133	125	12	we	we	PRON
ejpam-3133	125	13	have	have	AUX
ejpam-3133	125	14	limn→∞gb(xn	limn→∞gb(xn	PROPN
ejpam-3133	125	15	,	,	PUNCT
ejpam-3133	125	16	yn	yn	PROPN
ejpam-3133	125	17	,	,	PUNCT
ejpam-3133	125	18	zn	zn	PROPN
ejpam-3133	125	19	)	)	PUNCT
ejpam-3133	125	20	=	=	PUNCT
ejpam-3133	126	1	0	0	NUM
ejpam-3133	126	2	.	.	NOUN
ejpam-3133	126	3	3	3	X
ejpam-3133	126	4	.	.	X
ejpam-3133	126	5	main	main	ADJ
ejpam-3133	126	6	results	result	NOUN
ejpam-3133	126	7	we	we	PRON
ejpam-3133	126	8	start	start	VERB
ejpam-3133	126	9	this	this	DET
ejpam-3133	126	10	section	section	NOUN
ejpam-3133	126	11	with	with	ADP
ejpam-3133	126	12	the	the	DET
ejpam-3133	126	13	following	follow	VERB
ejpam-3133	126	14	definition	definition	NOUN
ejpam-3133	126	15	and	and	CCONJ
ejpam-3133	126	16	lemma	lemma	PROPN
ejpam-3133	126	17	which	which	PRON
ejpam-3133	126	18	will	will	AUX
ejpam-3133	126	19	play	play	VERB
ejpam-3133	126	20	a	a	DET
ejpam-3133	126	21	major	major	ADJ
ejpam-3133	126	22	role	role	NOUN
ejpam-3133	126	23	in	in	ADP
ejpam-3133	126	24	our	our	PRON
ejpam-3133	126	25	main	main	ADJ
ejpam-3133	126	26	result	result	NOUN
ejpam-3133	126	27	.	.	PUNCT
ejpam-3133	127	1	lemma	lemma	PROPN
ejpam-3133	127	2	2	2	X
ejpam-3133	127	3	.	.	PUNCT
ejpam-3133	128	1	let	let	AUX
ejpam-3133	128	2	(	(	PUNCT
ejpam-3133	128	3	x	x	NOUN
ejpam-3133	128	4	,	,	PUNCT
ejpam-3133	128	5	gb	gb	PRON
ejpam-3133	128	6	)	)	PUNCT
ejpam-3133	128	7	be	be	AUX
ejpam-3133	128	8	a	a	DET
ejpam-3133	128	9	gb	gb	ADV
ejpam-3133	128	10	-	-	PUNCT
ejpam-3133	128	11	metric	metric	ADJ
ejpam-3133	128	12	space	space	NOUN
ejpam-3133	128	13	with	with	ADP
ejpam-3133	128	14	s	s	PRON
ejpam-3133	128	15	>	>	X
ejpam-3133	128	16	1	1	X
ejpam-3133	128	17	.	.	PUNCT
ejpam-3133	128	18	suppose	suppose	VERB
ejpam-3133	128	19	that	that	SCONJ
ejpam-3133	128	20	{	{	PUNCT
ejpam-3133	128	21	xn	xn	X
ejpam-3133	128	22	}	}	PUNCT
ejpam-3133	128	23	is	be	AUX
ejpam-3133	128	24	a	a	DET
ejpam-3133	128	25	gbconvergent	gbconvergent	NOUN
ejpam-3133	128	26	sequence	sequence	NOUN
ejpam-3133	128	27	to	to	PART
ejpam-3133	128	28	x.	x.	VERB
ejpam-3133	128	29	then	then	ADV
ejpam-3133	128	30	for	for	ADP
ejpam-3133	128	31	y	y	PROPN
ejpam-3133	128	32	∈	∈	PROPN
ejpam-3133	128	33	x	x	INTJ
ejpam-3133	128	34	we	we	PRON
ejpam-3133	128	35	have	have	VERB
ejpam-3133	128	36	1	1	NUM
ejpam-3133	128	37	s	s	NOUN
ejpam-3133	128	38	gb(y	gb(y	ADJ
ejpam-3133	128	39	,	,	PUNCT
ejpam-3133	128	40	x	x	X
ejpam-3133	128	41	,	,	PUNCT
ejpam-3133	128	42	x	x	NOUN
ejpam-3133	128	43	)	)	PUNCT
ejpam-3133	128	44	≤	≤	NOUN
ejpam-3133	128	45	lim	lim	PROPN
ejpam-3133	128	46	inf	inf	PROPN
ejpam-3133	128	47	n→∞	n→∞	X
ejpam-3133	128	48	gb(y	gb(y	PUNCT
ejpam-3133	128	49	,	,	PUNCT
ejpam-3133	128	50	xn	xn	PROPN
ejpam-3133	128	51	,	,	PUNCT
ejpam-3133	128	52	xn	xn	PROPN
ejpam-3133	128	53	)	)	PUNCT
ejpam-3133	128	54	≤	≤	NOUN
ejpam-3133	128	55	lim	lim	PROPN
ejpam-3133	128	56	sup	sup	PROPN
ejpam-3133	128	57	n→∞	n→∞	NUM
ejpam-3133	128	58	gb(y	gb(y	PUNCT
ejpam-3133	128	59	,	,	PUNCT
ejpam-3133	128	60	xn	xn	PROPN
ejpam-3133	128	61	,	,	PUNCT
ejpam-3133	128	62	xn	xn	PROPN
ejpam-3133	128	63	)	)	PUNCT
ejpam-3133	128	64	≤	≤	NOUN
ejpam-3133	128	65	sgb(y	sgb(y	PROPN
ejpam-3133	128	66	,	,	PUNCT
ejpam-3133	128	67	x	x	X
ejpam-3133	128	68	,	,	PUNCT
ejpam-3133	128	69	x	x	NOUN
ejpam-3133	128	70	)	)	PUNCT
ejpam-3133	128	71	.	.	PUNCT
ejpam-3133	129	1	proof	proof	NOUN
ejpam-3133	129	2	.	.	PUNCT
ejpam-3133	130	1	using	use	VERB
ejpam-3133	130	2	the	the	DET
ejpam-3133	130	3	rectangle	rectangle	NOUN
ejpam-3133	130	4	inequality	inequality	NOUN
ejpam-3133	130	5	for	for	ADP
ejpam-3133	130	6	the	the	DET
ejpam-3133	130	7	gb	gb	NOUN
ejpam-3133	130	8	-	-	PUNCT
ejpam-3133	130	9	metric	metric	ADJ
ejpam-3133	130	10	,	,	PUNCT
ejpam-3133	130	11	we	we	PRON
ejpam-3133	130	12	obtain	obtain	VERB
ejpam-3133	130	13	that	that	PRON
ejpam-3133	130	14	gb(y	gb(y	ADV
ejpam-3133	131	1	,	,	PUNCT
ejpam-3133	131	2	x	x	X
ejpam-3133	131	3	,	,	PUNCT
ejpam-3133	131	4	x	x	X
ejpam-3133	131	5	)	)	PUNCT
ejpam-3133	131	6	≤	≤	NOUN
ejpam-3133	131	7	s[gb(y	s[gb(y	PROPN
ejpam-3133	131	8	,	,	PUNCT
ejpam-3133	131	9	xn	xn	PROPN
ejpam-3133	131	10	,	,	PUNCT
ejpam-3133	131	11	xn	xn	PUNCT
ejpam-3133	131	12	)	)	PUNCT
ejpam-3133	132	1	+	+	NOUN
ejpam-3133	132	2	gb(xn	gb(xn	PROPN
ejpam-3133	132	3	,	,	PUNCT
ejpam-3133	132	4	x	x	X
ejpam-3133	132	5	,	,	PUNCT
ejpam-3133	132	6	x	x	X
ejpam-3133	132	7	)	)	PUNCT
ejpam-3133	132	8	]	]	PUNCT
ejpam-3133	132	9	(	(	PUNCT
ejpam-3133	132	10	1	1	X
ejpam-3133	132	11	)	)	PUNCT
ejpam-3133	132	12	and	and	CCONJ
ejpam-3133	132	13	gb(y	gb(y	ADV
ejpam-3133	132	14	,	,	PUNCT
ejpam-3133	132	15	xn	xn	PROPN
ejpam-3133	132	16	,	,	PUNCT
ejpam-3133	132	17	xn	xn	PROPN
ejpam-3133	132	18	)	)	PUNCT
ejpam-3133	133	1	≤	≤	NOUN
ejpam-3133	133	2	s[gb(y	s[gb(y	PROPN
ejpam-3133	133	3	,	,	PUNCT
ejpam-3133	133	4	x	x	X
ejpam-3133	133	5	,	,	PUNCT
ejpam-3133	133	6	x	x	X
ejpam-3133	133	7	)	)	PUNCT
ejpam-3133	133	8	+	+	ADV
ejpam-3133	133	9	gb(x	gb(x	ADJ
ejpam-3133	133	10	,	,	PUNCT
ejpam-3133	133	11	xn	xn	PROPN
ejpam-3133	133	12	,	,	PUNCT
ejpam-3133	133	13	xn	xn	PROPN
ejpam-3133	133	14	)	)	PUNCT
ejpam-3133	133	15	]	]	PUNCT
ejpam-3133	133	16	.	.	PUNCT
ejpam-3133	134	1	(	(	PUNCT
ejpam-3133	134	2	2	2	X
ejpam-3133	134	3	)	)	PUNCT
ejpam-3133	134	4	taking	take	VERB
ejpam-3133	134	5	the	the	DET
ejpam-3133	134	6	limit	limit	NOUN
ejpam-3133	134	7	inferior	inferior	ADJ
ejpam-3133	134	8	as	as	ADP
ejpam-3133	134	9	n	n	PROPN
ejpam-3133	134	10	→	→	SYM
ejpam-3133	134	11	∞	∞	NUM
ejpam-3133	134	12	in	in	ADP
ejpam-3133	134	13	(	(	PUNCT
ejpam-3133	134	14	1	1	NUM
ejpam-3133	134	15	)	)	PUNCT
ejpam-3133	134	16	and	and	CCONJ
ejpam-3133	134	17	the	the	DET
ejpam-3133	134	18	limit	limit	NOUN
ejpam-3133	134	19	superior	superior	ADJ
ejpam-3133	134	20	as	as	ADP
ejpam-3133	134	21	n	n	PROPN
ejpam-3133	134	22	→	→	SYM
ejpam-3133	134	23	∞	∞	NUM
ejpam-3133	134	24	in	in	ADP
ejpam-3133	134	25	(	(	PUNCT
ejpam-3133	134	26	2	2	NUM
ejpam-3133	134	27	)	)	PUNCT
ejpam-3133	134	28	,	,	PUNCT
ejpam-3133	134	29	the	the	DET
ejpam-3133	134	30	proof	proof	NOUN
ejpam-3133	134	31	is	be	AUX
ejpam-3133	134	32	completed	complete	VERB
ejpam-3133	134	33	.	.	PUNCT
ejpam-3133	135	1	definition	definition	NOUN
ejpam-3133	135	2	8	8	NUM
ejpam-3133	135	3	.	.	PUNCT
ejpam-3133	136	1	a	a	DET
ejpam-3133	136	2	mapping	mapping	NOUN
ejpam-3133	136	3	ψ	ψ	X
ejpam-3133	136	4	:	:	PUNCT
ejpam-3133	137	1	[	[	X
ejpam-3133	137	2	0,∞)→	0,∞)→	NOUN
ejpam-3133	137	3	[	[	X
ejpam-3133	137	4	0,∞	0,∞	NOUN
ejpam-3133	137	5	)	)	PUNCT
ejpam-3133	137	6	is	be	AUX
ejpam-3133	137	7	called	call	VERB
ejpam-3133	137	8	a	a	DET
ejpam-3133	137	9	super	super	ADV
ejpam-3133	137	10	-	-	ADJ
ejpam-3133	137	11	altering	alter	VERB
ejpam-3133	137	12	distance	distance	NOUN
ejpam-3133	137	13	function	function	NOUN
ejpam-3133	137	14	if	if	SCONJ
ejpam-3133	137	15	the	the	DET
ejpam-3133	137	16	following	follow	VERB
ejpam-3133	137	17	properties	property	NOUN
ejpam-3133	137	18	are	be	AUX
ejpam-3133	137	19	satisfied	satisfied	ADJ
ejpam-3133	137	20	:	:	PUNCT
ejpam-3133	137	21	1	1	X
ejpam-3133	137	22	.	.	X
ejpam-3133	137	23	ψ	ψ	NOUN
ejpam-3133	137	24	is	be	AUX
ejpam-3133	137	25	continuous	continuous	ADJ
ejpam-3133	137	26	and	and	CCONJ
ejpam-3133	137	27	increasing	increase	VERB
ejpam-3133	137	28	.	.	PUNCT
ejpam-3133	138	1	2	2	X
ejpam-3133	138	2	.	.	X
ejpam-3133	138	3	ψ(t	ψ(t	PROPN
ejpam-3133	138	4	)	)	PUNCT
ejpam-3133	139	1	=	=	SYM
ejpam-3133	139	2	0	0	PUNCT
ejpam-3133	140	1	if	if	SCONJ
ejpam-3133	140	2	and	and	CCONJ
ejpam-3133	140	3	only	only	ADV
ejpam-3133	140	4	if	if	SCONJ
ejpam-3133	140	5	t	t	PROPN
ejpam-3133	140	6	=	=	SYM
ejpam-3133	140	7	0	0	X
ejpam-3133	140	8	.	.	PUNCT
ejpam-3133	141	1	we	we	PRON
ejpam-3133	141	2	denoted	denote	VERB
ejpam-3133	141	3	by	by	ADP
ejpam-3133	141	4	ψ	ψ	NOUN
ejpam-3133	141	5	to	to	PART
ejpam-3133	141	6	be	be	AUX
ejpam-3133	141	7	the	the	DET
ejpam-3133	141	8	set	set	NOUN
ejpam-3133	141	9	of	of	ADP
ejpam-3133	141	10	all	all	DET
ejpam-3133	141	11	super	super	ADJ
ejpam-3133	141	12	-	-	ADJ
ejpam-3133	141	13	altering	alter	VERB
ejpam-3133	141	14	distance	distance	NOUN
ejpam-3133	141	15	functions	function	NOUN
ejpam-3133	141	16	.	.	PUNCT
ejpam-3133	142	1	note	note	VERB
ejpam-3133	142	2	that	that	SCONJ
ejpam-3133	142	3	the	the	DET
ejpam-3133	142	4	class	class	NOUN
ejpam-3133	142	5	of	of	ADP
ejpam-3133	142	6	altering	alter	VERB
ejpam-3133	142	7	distance	distance	NOUN
ejpam-3133	142	8	functions	function	NOUN
ejpam-3133	142	9	was	be	AUX
ejpam-3133	142	10	defined	define	VERB
ejpam-3133	142	11	in	in	ADP
ejpam-3133	142	12	[	[	X
ejpam-3133	142	13	22	22	NUM
ejpam-3133	142	14	]	]	PUNCT
ejpam-3133	142	15	,	,	PUNCT
ejpam-3133	142	16	where	where	SCONJ
ejpam-3133	142	17	ψ	ψ	NOUN
ejpam-3133	142	18	is	be	AUX
ejpam-3133	142	19	considered	consider	VERB
ejpam-3133	142	20	nondecreasing	nondecrease	VERB
ejpam-3133	142	21	(	(	PUNCT
ejpam-3133	142	22	not	not	PART
ejpam-3133	142	23	necessarily	necessarily	ADV
ejpam-3133	142	24	increasing	increase	VERB
ejpam-3133	142	25	)	)	PUNCT
ejpam-3133	142	26	.	.	PUNCT
ejpam-3133	143	1	any	any	DET
ejpam-3133	143	2	super	super	ADV
ejpam-3133	143	3	-	-	ADJ
ejpam-3133	143	4	altering	alter	VERB
ejpam-3133	143	5	distance	distance	NOUN
ejpam-3133	143	6	function	function	NOUN
ejpam-3133	143	7	is	be	AUX
ejpam-3133	143	8	of	of	ADP
ejpam-3133	143	9	course	course	NOUN
ejpam-3133	143	10	a	a	DET
ejpam-3133	143	11	function	function	NOUN
ejpam-3133	143	12	in	in	ADP
ejpam-3133	143	13	the	the	DET
ejpam-3133	143	14	sense	sense	NOUN
ejpam-3133	143	15	of	of	ADP
ejpam-3133	143	16	[	[	X
ejpam-3133	143	17	22	22	NUM
ejpam-3133	143	18	]	]	PUNCT
ejpam-3133	143	19	.	.	PUNCT
ejpam-3133	144	1	in	in	ADP
ejpam-3133	144	2	the	the	DET
ejpam-3133	144	3	following	follow	VERB
ejpam-3133	144	4	example	example	NOUN
ejpam-3133	144	5	,	,	PUNCT
ejpam-3133	144	6	the	the	DET
ejpam-3133	144	7	given	give	VERB
ejpam-3133	144	8	mapping	mapping	NOUN
ejpam-3133	144	9	is	be	AUX
ejpam-3133	144	10	just	just	ADV
ejpam-3133	144	11	an	an	DET
ejpam-3133	144	12	altering	alter	VERB
ejpam-3133	144	13	distance	distance	NOUN
ejpam-3133	144	14	function	function	NOUN
ejpam-3133	144	15	,	,	PUNCT
ejpam-3133	144	16	but	but	CCONJ
ejpam-3133	144	17	not	not	PART
ejpam-3133	144	18	in	in	ADP
ejpam-3133	144	19	ψ	ψ	PROPN
ejpam-3133	144	20	.	.	PUNCT
ejpam-3133	144	21	example	example	NOUN
ejpam-3133	145	1	4	4	NUM
ejpam-3133	145	2	.	.	PUNCT
ejpam-3133	145	3	let	let	VERB
ejpam-3133	145	4	ψ	ψ	X
ejpam-3133	145	5	:	:	PUNCT
ejpam-3133	146	1	[	[	X
ejpam-3133	146	2	0,∞)→	0,∞)→	NOUN
ejpam-3133	146	3	[	[	X
ejpam-3133	146	4	0,∞	0,∞	X
ejpam-3133	146	5	)	)	PUNCT
ejpam-3133	146	6	be	be	VERB
ejpam-3133	146	7	such	such	ADJ
ejpam-3133	146	8	that	that	SCONJ
ejpam-3133	146	9	{	{	PUNCT
ejpam-3133	146	10	ψ(t	ψ(t	PROPN
ejpam-3133	146	11	)	)	PUNCT
ejpam-3133	146	12	=	=	SYM
ejpam-3133	146	13	t	t	NOUN
ejpam-3133	146	14	if	if	SCONJ
ejpam-3133	146	15	t	t	PROPN
ejpam-3133	146	16	∈	∈	PROPN
ejpam-3133	147	1	[	[	X
ejpam-3133	147	2	0	0	NUM
ejpam-3133	147	3	,	,	PUNCT
ejpam-3133	147	4	1	1	NUM
ejpam-3133	147	5	]	]	PUNCT
ejpam-3133	147	6	ψ(t	ψ(t	PROPN
ejpam-3133	147	7	)	)	PUNCT
ejpam-3133	147	8	=	=	SYM
ejpam-3133	147	9	1	1	NUM
ejpam-3133	147	10	if	if	SCONJ
ejpam-3133	147	11	t	t	PROPN
ejpam-3133	147	12	≥	≥	NUM
ejpam-3133	147	13	1	1	NUM
ejpam-3133	147	14	.	.	PUNCT
ejpam-3133	147	15	theorem	theorem	NOUN
ejpam-3133	147	16	1	1	NUM
ejpam-3133	147	17	.	.	PUNCT
ejpam-3133	148	1	let	let	AUX
ejpam-3133	148	2	(	(	PUNCT
ejpam-3133	148	3	x	x	NOUN
ejpam-3133	148	4	,	,	PUNCT
ejpam-3133	148	5	gb	gb	PRON
ejpam-3133	148	6	)	)	PUNCT
ejpam-3133	148	7	be	be	AUX
ejpam-3133	148	8	a	a	DET
ejpam-3133	148	9	complete	complete	ADJ
ejpam-3133	148	10	gb	gb	ADV
ejpam-3133	148	11	-	-	PUNCT
ejpam-3133	148	12	metric	metric	ADJ
ejpam-3133	148	13	space	space	NOUN
ejpam-3133	148	14	and	and	CCONJ
ejpam-3133	148	15	let	let	VERB
ejpam-3133	148	16	f	f	X
ejpam-3133	148	17	,	,	PUNCT
ejpam-3133	148	18	g	g	PROPN
ejpam-3133	148	19	,	,	PUNCT
ejpam-3133	148	20	h	h	NOUN
ejpam-3133	148	21	,	,	PUNCT
ejpam-3133	148	22	r	r	NOUN
ejpam-3133	148	23	,	,	PUNCT
ejpam-3133	148	24	s	s	PROPN
ejpam-3133	148	25	,	,	PUNCT
ejpam-3133	148	26	t	t	NOUN
ejpam-3133	148	27	:	:	PUNCT
ejpam-3133	148	28	x	x	X
ejpam-3133	148	29	→	→	PUNCT
ejpam-3133	148	30	x	x	PART
ejpam-3133	148	31	be	be	AUX
ejpam-3133	148	32	self	self	NOUN
ejpam-3133	148	33	mappings	mapping	NOUN
ejpam-3133	148	34	such	such	ADJ
ejpam-3133	148	35	that	that	SCONJ
ejpam-3133	148	36	z.	z.	PROPN
ejpam-3133	148	37	mustafa	mustafa	PROPN
ejpam-3133	148	38	et	et	PROPN
ejpam-3133	148	39	al	al	PROPN
ejpam-3133	148	40	.	.	PUNCT
ejpam-3133	148	41	/	/	SYM
ejpam-3133	148	42	eur	eur	PROPN
ejpam-3133	148	43	.	.	PUNCT
ejpam-3133	149	1	j.	j.	PROPN
ejpam-3133	149	2	pure	pure	PROPN
ejpam-3133	149	3	appl	appl	PROPN
ejpam-3133	149	4	.	.	PROPN
ejpam-3133	149	5	math	math	PROPN
ejpam-3133	149	6	,	,	PUNCT
ejpam-3133	149	7	11	11	NUM
ejpam-3133	149	8	(	(	PUNCT
ejpam-3133	149	9	1	1	NUM
ejpam-3133	149	10	)	)	PUNCT
ejpam-3133	149	11	(	(	PUNCT
ejpam-3133	149	12	2018	2018	NUM
ejpam-3133	149	13	)	)	PUNCT
ejpam-3133	149	14	,	,	PUNCT
ejpam-3133	149	15	90	90	NUM
ejpam-3133	149	16	-	-	SYM
ejpam-3133	149	17	109	109	NUM
ejpam-3133	149	18	95	95	NUM
ejpam-3133	149	19	(	(	PUNCT
ejpam-3133	149	20	i	i	NOUN
ejpam-3133	149	21	)	)	PUNCT
ejpam-3133	149	22	(	(	PUNCT
ejpam-3133	149	23	f	f	X
ejpam-3133	149	24	,	,	PUNCT
ejpam-3133	149	25	s	s	PART
ejpam-3133	149	26	)	)	PUNCT
ejpam-3133	149	27	and	and	CCONJ
ejpam-3133	149	28	(	(	PUNCT
ejpam-3133	149	29	g	g	NOUN
ejpam-3133	149	30	,	,	PUNCT
ejpam-3133	149	31	r	r	NOUN
ejpam-3133	149	32	)	)	PUNCT
ejpam-3133	149	33	satisfy	satisfy	NOUN
ejpam-3133	149	34	the	the	DET
ejpam-3133	149	35	(	(	PUNCT
ejpam-3133	149	36	e.a	e.a	PROPN
ejpam-3133	149	37	)	)	PUNCT
ejpam-3133	149	38	property	property	NOUN
ejpam-3133	149	39	;	;	PUNCT
ejpam-3133	149	40	(	(	PUNCT
ejpam-3133	149	41	ii	ii	NOUN
ejpam-3133	149	42	)	)	PUNCT
ejpam-3133	149	43	f(x	f(x	PROPN
ejpam-3133	149	44	)	)	PUNCT
ejpam-3133	149	45	⊆	⊆	NUM
ejpam-3133	149	46	t	t	NOUN
ejpam-3133	149	47	(	(	PUNCT
ejpam-3133	149	48	x	x	NOUN
ejpam-3133	149	49	)	)	PUNCT
ejpam-3133	149	50	,	,	PUNCT
ejpam-3133	149	51	g(x	g(x	NOUN
ejpam-3133	149	52	)	)	PUNCT
ejpam-3133	149	53	⊆	⊆	NUM
ejpam-3133	149	54	s(x	s(x	NOUN
ejpam-3133	149	55	)	)	PUNCT
ejpam-3133	149	56	and	and	CCONJ
ejpam-3133	149	57	h(x	h(x	PROPN
ejpam-3133	149	58	)	)	PUNCT
ejpam-3133	149	59	⊆	⊆	NUM
ejpam-3133	149	60	r(x	r(x	PROPN
ejpam-3133	149	61	)	)	PUNCT
ejpam-3133	149	62	;	;	PUNCT
ejpam-3133	149	63	(	(	PUNCT
ejpam-3133	149	64	iii	iii	X
ejpam-3133	149	65	)	)	PUNCT
ejpam-3133	149	66	r(x	r(x	PROPN
ejpam-3133	149	67	)	)	PUNCT
ejpam-3133	149	68	is	be	AUX
ejpam-3133	149	69	a	a	DET
ejpam-3133	149	70	closed	closed	ADJ
ejpam-3133	149	71	subspace	subspace	NOUN
ejpam-3133	149	72	of	of	ADP
ejpam-3133	149	73	x	x	PRON
ejpam-3133	149	74	;	;	PUNCT
ejpam-3133	149	75	(	(	PUNCT
ejpam-3133	149	76	iv	iv	X
ejpam-3133	149	77	)	)	PUNCT
ejpam-3133	149	78	(	(	PUNCT
ejpam-3133	149	79	f	f	X
ejpam-3133	149	80	,	,	PUNCT
ejpam-3133	149	81	s	s	PART
ejpam-3133	149	82	)	)	PUNCT
ejpam-3133	149	83	,	,	PUNCT
ejpam-3133	149	84	(	(	PUNCT
ejpam-3133	149	85	g	g	NOUN
ejpam-3133	149	86	,	,	PUNCT
ejpam-3133	149	87	r	r	NOUN
ejpam-3133	149	88	)	)	PUNCT
ejpam-3133	149	89	and	and	CCONJ
ejpam-3133	149	90	(	(	PUNCT
ejpam-3133	149	91	h	h	NOUN
ejpam-3133	149	92	,	,	PUNCT
ejpam-3133	149	93	t	t	PROPN
ejpam-3133	149	94	)	)	PUNCT
ejpam-3133	149	95	are	be	AUX
ejpam-3133	149	96	weakly	weakly	ADV
ejpam-3133	149	97	compatible	compatible	ADJ
ejpam-3133	149	98	pairs	pair	NOUN
ejpam-3133	149	99	of	of	ADP
ejpam-3133	149	100	mappings	mapping	NOUN
ejpam-3133	149	101	;	;	PUNCT
ejpam-3133	149	102	(	(	PUNCT
ejpam-3133	149	103	v	v	NOUN
ejpam-3133	149	104	)	)	PUNCT
ejpam-3133	149	105	ψ	ψ	NOUN
ejpam-3133	149	106	(	(	PUNCT
ejpam-3133	149	107	s2gb(fx	s2gb(fx	NOUN
ejpam-3133	149	108	,	,	PUNCT
ejpam-3133	149	109	gy	gy	NOUN
ejpam-3133	149	110	,	,	PUNCT
ejpam-3133	149	111	hz	hz	NOUN
ejpam-3133	149	112	)	)	PUNCT
ejpam-3133	149	113	)	)	PUNCT
ejpam-3133	150	1	≤	≤	NUM
ejpam-3133	150	2	ψ	ψ	X
ejpam-3133	150	3	(	(	PUNCT
ejpam-3133	150	4	m(x	m(x	PROPN
ejpam-3133	150	5	,	,	PUNCT
ejpam-3133	150	6	y	y	PROPN
ejpam-3133	150	7	,	,	PUNCT
ejpam-3133	150	8	z	z	NOUN
ejpam-3133	150	9	)	)	PUNCT
ejpam-3133	150	10	)	)	PUNCT
ejpam-3133	151	1	−	−	PROPN
ejpam-3133	151	2	φ	φ	PROPN
ejpam-3133	151	3	(	(	PUNCT
ejpam-3133	151	4	m(x	m(x	PROPN
ejpam-3133	151	5	,	,	PUNCT
ejpam-3133	151	6	y	y	PROPN
ejpam-3133	151	7	,	,	PUNCT
ejpam-3133	151	8	z	z	NOUN
ejpam-3133	151	9	)	)	PUNCT
ejpam-3133	151	10	)	)	PUNCT
ejpam-3133	151	11	,	,	PUNCT
ejpam-3133	151	12	∀x	∀x	X
ejpam-3133	151	13	,	,	PUNCT
ejpam-3133	151	14	y	y	PROPN
ejpam-3133	151	15	,	,	PUNCT
ejpam-3133	151	16	z	z	NOUN
ejpam-3133	151	17	∈	∈	PROPN
ejpam-3133	151	18	x	x	X
ejpam-3133	151	19	(	(	PUNCT
ejpam-3133	151	20	3	3	NUM
ejpam-3133	151	21	)	)	PUNCT
ejpam-3133	151	22	where	where	SCONJ
ejpam-3133	151	23	ψ	ψ	X
ejpam-3133	151	24	,	,	PUNCT
ejpam-3133	151	25	φ	φ	PROPN
ejpam-3133	151	26	∈	∈	PROPN
ejpam-3133	151	27	ψ	ψ	X
ejpam-3133	151	28	and	and	CCONJ
ejpam-3133	151	29	m(x	m(x	PROPN
ejpam-3133	151	30	,	,	PUNCT
ejpam-3133	151	31	y	y	PROPN
ejpam-3133	151	32	,	,	PUNCT
ejpam-3133	151	33	z	z	NOUN
ejpam-3133	151	34	)	)	PUNCT
ejpam-3133	151	35	=	=	SYM
ejpam-3133	151	36	max	max	PROPN
ejpam-3133	151	37	{	{	PUNCT
ejpam-3133	151	38	gb(fx	gb(fx	PROPN
ejpam-3133	151	39	,	,	PUNCT
ejpam-3133	151	40	sx	sx	PROPN
ejpam-3133	151	41	,	,	PUNCT
ejpam-3133	151	42	tz	tz	PROPN
ejpam-3133	151	43	)	)	PUNCT
ejpam-3133	151	44	,	,	PUNCT
ejpam-3133	151	45	gb(gy	gb(gy	PROPN
ejpam-3133	151	46	,	,	PUNCT
ejpam-3133	151	47	ry	ry	NOUN
ejpam-3133	151	48	,	,	PUNCT
ejpam-3133	151	49	ry	ry	NOUN
ejpam-3133	151	50	)	)	PUNCT
ejpam-3133	151	51	,	,	PUNCT
ejpam-3133	151	52	gb(fx	gb(fx	PROPN
ejpam-3133	151	53	,	,	PUNCT
ejpam-3133	151	54	fx	fx	PROPN
ejpam-3133	151	55	,	,	PUNCT
ejpam-3133	151	56	hz	hz	PROPN
ejpam-3133	151	57	)	)	PUNCT
ejpam-3133	151	58	,	,	PUNCT
ejpam-3133	151	59	gb(tz	gb(tz	PROPN
ejpam-3133	151	60	,	,	PUNCT
ejpam-3133	151	61	tz	tz	PROPN
ejpam-3133	151	62	,	,	PUNCT
ejpam-3133	151	63	hz	hz	X
ejpam-3133	151	64	)	)	PUNCT
ejpam-3133	151	65	+	+	PROPN
ejpam-3133	151	66	gb(fx	gb(fx	PROPN
ejpam-3133	151	67	,	,	PUNCT
ejpam-3133	151	68	sx	sx	PROPN
ejpam-3133	151	69	,	,	PUNCT
ejpam-3133	151	70	sx	sx	PROPN
ejpam-3133	151	71	)	)	PUNCT
ejpam-3133	151	72	2s	2s	PROPN
ejpam-3133	151	73	}	}	PUNCT
ejpam-3133	151	74	.	.	PUNCT
ejpam-3133	152	1	then	then	ADV
ejpam-3133	152	2	f	f	X
ejpam-3133	152	3	,	,	PUNCT
ejpam-3133	152	4	g	g	PROPN
ejpam-3133	152	5	,	,	PUNCT
ejpam-3133	152	6	h	h	NOUN
ejpam-3133	152	7	,	,	PUNCT
ejpam-3133	152	8	r	r	NOUN
ejpam-3133	152	9	,	,	PUNCT
ejpam-3133	152	10	s	s	PART
ejpam-3133	152	11	and	and	CCONJ
ejpam-3133	152	12	t	t	PROPN
ejpam-3133	152	13	have	have	VERB
ejpam-3133	152	14	a	a	DET
ejpam-3133	152	15	unique	unique	ADJ
ejpam-3133	152	16	common	common	ADJ
ejpam-3133	152	17	fixed	fix	VERB
ejpam-3133	152	18	point	point	NOUN
ejpam-3133	152	19	in	in	ADP
ejpam-3133	152	20	x.	x.	NOUN
ejpam-3133	152	21	proof	proof	NOUN
ejpam-3133	152	22	.	.	PUNCT
ejpam-3133	153	1	since	since	SCONJ
ejpam-3133	153	2	the	the	DET
ejpam-3133	153	3	pair	pair	NOUN
ejpam-3133	153	4	(	(	PUNCT
ejpam-3133	153	5	f	f	X
ejpam-3133	153	6	,	,	PUNCT
ejpam-3133	153	7	s	s	PART
ejpam-3133	153	8	)	)	PUNCT
ejpam-3133	153	9	satisfies	satisfy	VERB
ejpam-3133	153	10	the	the	DET
ejpam-3133	153	11	(	(	PUNCT
ejpam-3133	153	12	e.a	e.a	PROPN
ejpam-3133	153	13	)	)	PUNCT
ejpam-3133	153	14	property	property	NOUN
ejpam-3133	153	15	,	,	PUNCT
ejpam-3133	153	16	there	there	PRON
ejpam-3133	153	17	exists	exist	VERB
ejpam-3133	153	18	a	a	DET
ejpam-3133	153	19	sequence	sequence	NOUN
ejpam-3133	153	20	{	{	PUNCT
ejpam-3133	153	21	xn	xn	NOUN
ejpam-3133	153	22	}	}	PUNCT
ejpam-3133	153	23	such	such	ADJ
ejpam-3133	153	24	that	that	SCONJ
ejpam-3133	153	25	lim	lim	PROPN
ejpam-3133	153	26	n→∞	n→∞	PRON
ejpam-3133	153	27	fxn	fxn	PROPN
ejpam-3133	153	28	=	=	PUNCT
ejpam-3133	153	29	lim	lim	PROPN
ejpam-3133	153	30	n→∞	n→∞	NUM
ejpam-3133	153	31	sxn	sxn	NOUN
ejpam-3133	153	32	=	=	SYM
ejpam-3133	153	33	q1	q1	PROPN
ejpam-3133	153	34	,	,	PUNCT
ejpam-3133	153	35	for	for	ADP
ejpam-3133	153	36	some	some	DET
ejpam-3133	153	37	q1	q1	PROPN
ejpam-3133	153	38	∈	∈	PROPN
ejpam-3133	153	39	x.	x.	NOUN
ejpam-3133	153	40	as	as	ADP
ejpam-3133	153	41	f(x	f(x	PROPN
ejpam-3133	153	42	)	)	PUNCT
ejpam-3133	153	43	⊆	⊆	NUM
ejpam-3133	153	44	t	t	NOUN
ejpam-3133	153	45	(	(	PUNCT
ejpam-3133	153	46	x	x	NOUN
ejpam-3133	153	47	)	)	PUNCT
ejpam-3133	153	48	,	,	PUNCT
ejpam-3133	153	49	there	there	PRON
ejpam-3133	153	50	exists	exist	VERB
ejpam-3133	153	51	a	a	DET
ejpam-3133	153	52	sequence	sequence	NOUN
ejpam-3133	153	53	{	{	PUNCT
ejpam-3133	153	54	zn	zn	NOUN
ejpam-3133	153	55	}	}	PUNCT
ejpam-3133	153	56	∈	∈	PROPN
ejpam-3133	153	57	x	x	NOUN
ejpam-3133	153	58	such	such	ADJ
ejpam-3133	153	59	that	that	DET
ejpam-3133	153	60	fxn	fxn	NOUN
ejpam-3133	153	61	=	=	PUNCT
ejpam-3133	153	62	tzn	tzn	NOUN
ejpam-3133	153	63	and	and	CCONJ
ejpam-3133	153	64	lim	lim	PROPN
ejpam-3133	153	65	n→∞	n→∞	NUM
ejpam-3133	153	66	fxn	fxn	PROPN
ejpam-3133	153	67	=	=	PUNCT
ejpam-3133	153	68	lim	lim	PROPN
ejpam-3133	153	69	n→∞	n→∞	NUM
ejpam-3133	154	1	tzn	tzn	PROPN
ejpam-3133	154	2	=	=	PUNCT
ejpam-3133	155	1	lim	lim	PROPN
ejpam-3133	155	2	n→∞	n→∞	NUM
ejpam-3133	155	3	sxn	sxn	NOUN
ejpam-3133	155	4	=	=	PROPN
ejpam-3133	155	5	q1	q1	PROPN
ejpam-3133	155	6	.	.	PUNCT
ejpam-3133	156	1	(	(	PUNCT
ejpam-3133	156	2	4	4	X
ejpam-3133	156	3	)	)	PUNCT
ejpam-3133	156	4	again	again	ADV
ejpam-3133	156	5	the	the	DET
ejpam-3133	156	6	pair	pair	NOUN
ejpam-3133	156	7	(	(	PUNCT
ejpam-3133	156	8	g	g	NOUN
ejpam-3133	156	9	,	,	PUNCT
ejpam-3133	156	10	r	r	NOUN
ejpam-3133	156	11	)	)	PUNCT
ejpam-3133	156	12	satisfies	satisfy	VERB
ejpam-3133	156	13	the	the	DET
ejpam-3133	156	14	(	(	PUNCT
ejpam-3133	156	15	e.a	e.a	PROPN
ejpam-3133	156	16	)	)	PUNCT
ejpam-3133	156	17	property	property	NOUN
ejpam-3133	156	18	,	,	PUNCT
ejpam-3133	156	19	so	so	SCONJ
ejpam-3133	156	20	there	there	PRON
ejpam-3133	156	21	exists	exist	VERB
ejpam-3133	156	22	a	a	DET
ejpam-3133	156	23	sequence	sequence	NOUN
ejpam-3133	156	24	{	{	PUNCT
ejpam-3133	156	25	yn	yn	NOUN
ejpam-3133	156	26	}	}	PUNCT
ejpam-3133	156	27	such	such	ADJ
ejpam-3133	156	28	that	that	SCONJ
ejpam-3133	156	29	lim	lim	PROPN
ejpam-3133	156	30	n→∞	n→∞	NUM
ejpam-3133	156	31	gyn	gyn	PROPN
ejpam-3133	156	32	=	=	SYM
ejpam-3133	156	33	lim	lim	PROPN
ejpam-3133	156	34	n→∞	n→∞	NUM
ejpam-3133	156	35	ryn	ryn	PROPN
ejpam-3133	156	36	=	=	PROPN
ejpam-3133	156	37	q2	q2	PROPN
ejpam-3133	156	38	,	,	PUNCT
ejpam-3133	156	39	for	for	ADP
ejpam-3133	156	40	some	some	DET
ejpam-3133	156	41	q2	q2	NOUN
ejpam-3133	156	42	∈	∈	PROPN
ejpam-3133	156	43	x.	x.	NOUN
ejpam-3133	156	44	(	(	PUNCT
ejpam-3133	156	45	5	5	NUM
ejpam-3133	156	46	)	)	PUNCT
ejpam-3133	156	47	but	but	CCONJ
ejpam-3133	156	48	g(x	g(x	NOUN
ejpam-3133	156	49	)	)	PUNCT
ejpam-3133	156	50	⊆	⊆	NUM
ejpam-3133	156	51	s(x	s(x	NOUN
ejpam-3133	156	52	)	)	PUNCT
ejpam-3133	156	53	,	,	PUNCT
ejpam-3133	156	54	so	so	CCONJ
ejpam-3133	156	55	there	there	PRON
ejpam-3133	156	56	exists	exist	VERB
ejpam-3133	156	57	a	a	DET
ejpam-3133	156	58	sequence	sequence	NOUN
ejpam-3133	156	59	{	{	PUNCT
ejpam-3133	156	60	αn	αn	NOUN
ejpam-3133	156	61	}	}	PUNCT
ejpam-3133	156	62	∈	∈	PROPN
ejpam-3133	156	63	x	x	NOUN
ejpam-3133	156	64	such	such	ADJ
ejpam-3133	156	65	that	that	DET
ejpam-3133	156	66	gyn	gyn	NOUN
ejpam-3133	156	67	=	=	SYM
ejpam-3133	156	68	sαn	sαn	NOUN
ejpam-3133	156	69	,	,	PUNCT
ejpam-3133	156	70	and	and	CCONJ
ejpam-3133	156	71	lim	lim	PROPN
ejpam-3133	156	72	n→∞	n→∞	NUM
ejpam-3133	156	73	gyn	gyn	PROPN
ejpam-3133	156	74	=	=	SYM
ejpam-3133	156	75	lim	lim	PROPN
ejpam-3133	156	76	n→∞	n→∞	NUM
ejpam-3133	156	77	sαn	sαn	NOUN
ejpam-3133	156	78	=	=	PROPN
ejpam-3133	156	79	lim	lim	PROPN
ejpam-3133	156	80	n→∞	n→∞	NUM
ejpam-3133	156	81	ryn	ryn	PROPN
ejpam-3133	156	82	=	=	PROPN
ejpam-3133	156	83	q2	q2	PROPN
ejpam-3133	156	84	.	.	PUNCT
ejpam-3133	157	1	(	(	PUNCT
ejpam-3133	157	2	6	6	NUM
ejpam-3133	157	3	)	)	PUNCT
ejpam-3133	157	4	now	now	ADV
ejpam-3133	157	5	,	,	PUNCT
ejpam-3133	157	6	we	we	PRON
ejpam-3133	157	7	shall	shall	AUX
ejpam-3133	157	8	show	show	VERB
ejpam-3133	157	9	that	that	SCONJ
ejpam-3133	157	10	lim	lim	PROPN
ejpam-3133	157	11	n→∞	n→∞	PRON
ejpam-3133	157	12	hzn	hzn	PROPN
ejpam-3133	157	13	=	=	PROPN
ejpam-3133	157	14	q1	q1	PROPN
ejpam-3133	157	15	.	.	PUNCT
ejpam-3133	158	1	from	from	ADP
ejpam-3133	158	2	(	(	PUNCT
ejpam-3133	158	3	3	3	NUM
ejpam-3133	158	4	)	)	PUNCT
ejpam-3133	158	5	,	,	PUNCT
ejpam-3133	158	6	(	(	PUNCT
ejpam-3133	158	7	gb3	gb3	NOUN
ejpam-3133	158	8	)	)	PUNCT
ejpam-3133	158	9	and	and	CCONJ
ejpam-3133	158	10	the	the	DET
ejpam-3133	158	11	fact	fact	NOUN
ejpam-3133	158	12	that	that	SCONJ
ejpam-3133	158	13	ψ	ψ	NOUN
ejpam-3133	158	14	is	be	AUX
ejpam-3133	158	15	an	an	DET
ejpam-3133	158	16	increasing	increase	VERB
ejpam-3133	158	17	mapping	mapping	NOUN
ejpam-3133	158	18	,	,	PUNCT
ejpam-3133	158	19	we	we	PRON
ejpam-3133	158	20	have	have	VERB
ejpam-3133	158	21	ψ	ψ	X
ejpam-3133	158	22	(	(	PUNCT
ejpam-3133	158	23	sgb(fxn	sgb(fxn	PROPN
ejpam-3133	158	24	,	,	PUNCT
ejpam-3133	158	25	fxn	fxn	NOUN
ejpam-3133	158	26	,	,	PUNCT
ejpam-3133	158	27	hzn	hzn	NOUN
ejpam-3133	158	28	)	)	PUNCT
ejpam-3133	158	29	)	)	PUNCT
ejpam-3133	159	1	≤	≤	NUM
ejpam-3133	159	2	ψ	ψ	X
ejpam-3133	159	3	(	(	PUNCT
ejpam-3133	159	4	s2gb(fxn	s2gb(fxn	PROPN
ejpam-3133	159	5	,	,	PUNCT
ejpam-3133	159	6	gyn	gyn	NOUN
ejpam-3133	159	7	,	,	PUNCT
ejpam-3133	159	8	hzn	hzn	NOUN
ejpam-3133	159	9	)	)	PUNCT
ejpam-3133	159	10	)	)	PUNCT
ejpam-3133	159	11	≤	≤	NUM
ejpam-3133	159	12	ψ	ψ	X
ejpam-3133	159	13	(	(	PUNCT
ejpam-3133	159	14	m(xn	m(xn	PROPN
ejpam-3133	159	15	,	,	PUNCT
ejpam-3133	159	16	yn	yn	PROPN
ejpam-3133	159	17	,	,	PUNCT
ejpam-3133	159	18	zn	zn	PROPN
ejpam-3133	159	19	)	)	PUNCT
ejpam-3133	159	20	)	)	PUNCT
ejpam-3133	160	1	−	−	PROPN
ejpam-3133	161	1	φ	φ	PROPN
ejpam-3133	161	2	(	(	PUNCT
ejpam-3133	161	3	m(xn	m(xn	PROPN
ejpam-3133	161	4	,	,	PUNCT
ejpam-3133	161	5	yn	yn	PROPN
ejpam-3133	161	6	,	,	PUNCT
ejpam-3133	161	7	zn	zn	PROPN
ejpam-3133	161	8	)	)	PUNCT
ejpam-3133	161	9	)	)	PUNCT
ejpam-3133	161	10	(	(	PUNCT
ejpam-3133	161	11	7	7	X
ejpam-3133	161	12	)	)	PUNCT
ejpam-3133	161	13	where	where	SCONJ
ejpam-3133	161	14	,	,	PUNCT
ejpam-3133	161	15	m(xn	m(xn	PROPN
ejpam-3133	161	16	,	,	PUNCT
ejpam-3133	161	17	yn	yn	PROPN
ejpam-3133	161	18	,	,	PUNCT
ejpam-3133	161	19	zn	zn	PROPN
ejpam-3133	161	20	)	)	PUNCT
ejpam-3133	161	21	=	=	SYM
ejpam-3133	161	22	max	max	PROPN
ejpam-3133	161	23	{	{	PUNCT
ejpam-3133	161	24	gb(fxn	gb(fxn	PROPN
ejpam-3133	161	25	,	,	PUNCT
ejpam-3133	161	26	sxn	sxn	PROPN
ejpam-3133	161	27	,	,	PUNCT
ejpam-3133	161	28	t	t	PROPN
ejpam-3133	161	29	zn	zn	NUM
ejpam-3133	161	30	)	)	PUNCT
ejpam-3133	161	31	,	,	PUNCT
ejpam-3133	161	32	gb(gyn	gb(gyn	PROPN
ejpam-3133	161	33	,	,	PUNCT
ejpam-3133	161	34	ryn	ryn	PROPN
ejpam-3133	161	35	,	,	PUNCT
ejpam-3133	161	36	ryn	ryn	PROPN
ejpam-3133	161	37	)	)	PUNCT
ejpam-3133	161	38	,	,	PUNCT
ejpam-3133	161	39	gb(fxn	gb(fxn	PROPN
ejpam-3133	161	40	,	,	PUNCT
ejpam-3133	161	41	fxn	fxn	NOUN
ejpam-3133	161	42	,	,	PUNCT
ejpam-3133	161	43	hzn	hzn	NOUN
ejpam-3133	161	44	)	)	PUNCT
ejpam-3133	161	45	,	,	PUNCT
ejpam-3133	161	46	gb(tzn	gb(tzn	PROPN
ejpam-3133	161	47	,	,	PUNCT
ejpam-3133	161	48	t	t	PROPN
ejpam-3133	161	49	zn	zn	NUM
ejpam-3133	161	50	,	,	PUNCT
ejpam-3133	161	51	hzn	hzn	PROPN
ejpam-3133	161	52	)	)	PUNCT
ejpam-3133	162	1	+	+	PROPN
ejpam-3133	162	2	gb(fxn	gb(fxn	ADJ
ejpam-3133	162	3	,	,	PUNCT
ejpam-3133	162	4	sxn	sxn	NOUN
ejpam-3133	162	5	,	,	PUNCT
ejpam-3133	162	6	sxn	sxn	NOUN
ejpam-3133	162	7	)	)	PUNCT
ejpam-3133	162	8	2s	2s	PROPN
ejpam-3133	162	9	}	}	PUNCT
ejpam-3133	162	10	,	,	PUNCT
ejpam-3133	162	11	z.	z.	PROPN
ejpam-3133	162	12	mustafa	mustafa	PROPN
ejpam-3133	162	13	et	et	PROPN
ejpam-3133	162	14	al	al	PROPN
ejpam-3133	162	15	.	.	PUNCT
ejpam-3133	162	16	/	/	SYM
ejpam-3133	162	17	eur	eur	PROPN
ejpam-3133	162	18	.	.	PUNCT
ejpam-3133	163	1	j.	j.	PROPN
ejpam-3133	163	2	pure	pure	PROPN
ejpam-3133	163	3	appl	appl	PROPN
ejpam-3133	163	4	.	.	PROPN
ejpam-3133	163	5	math	math	PROPN
ejpam-3133	163	6	,	,	PUNCT
ejpam-3133	163	7	11	11	NUM
ejpam-3133	163	8	(	(	PUNCT
ejpam-3133	163	9	1	1	NUM
ejpam-3133	163	10	)	)	PUNCT
ejpam-3133	163	11	(	(	PUNCT
ejpam-3133	163	12	2018	2018	NUM
ejpam-3133	163	13	)	)	PUNCT
ejpam-3133	163	14	,	,	PUNCT
ejpam-3133	163	15	90	90	NUM
ejpam-3133	163	16	-	-	SYM
ejpam-3133	163	17	109	109	NUM
ejpam-3133	163	18	96	96	NUM
ejpam-3133	163	19	=	=	SYM
ejpam-3133	163	20	max	max	PROPN
ejpam-3133	163	21	{	{	PUNCT
ejpam-3133	163	22	gb(fxn	gb(fxn	PROPN
ejpam-3133	163	23	,	,	PUNCT
ejpam-3133	163	24	sxn	sxn	NOUN
ejpam-3133	163	25	,	,	PUNCT
ejpam-3133	163	26	fxn	fxn	NOUN
ejpam-3133	163	27	)	)	PUNCT
ejpam-3133	163	28	,	,	PUNCT
ejpam-3133	163	29	gb(gyn	gb(gyn	PROPN
ejpam-3133	163	30	,	,	PUNCT
ejpam-3133	163	31	ryn	ryn	PROPN
ejpam-3133	163	32	,	,	PUNCT
ejpam-3133	163	33	ryn	ryn	PROPN
ejpam-3133	163	34	)	)	PUNCT
ejpam-3133	163	35	,	,	PUNCT
ejpam-3133	163	36	gb(fxn	gb(fxn	PROPN
ejpam-3133	163	37	,	,	PUNCT
ejpam-3133	163	38	fxn	fxn	NOUN
ejpam-3133	163	39	,	,	PUNCT
ejpam-3133	163	40	hzn	hzn	NOUN
ejpam-3133	163	41	)	)	PUNCT
ejpam-3133	163	42	,	,	PUNCT
ejpam-3133	163	43	gb(fxn	gb(fxn	PROPN
ejpam-3133	163	44	,	,	PUNCT
ejpam-3133	163	45	fxn	fxn	NOUN
ejpam-3133	163	46	,	,	PUNCT
ejpam-3133	163	47	hzn	hzn	NOUN
ejpam-3133	163	48	)	)	PUNCT
ejpam-3133	164	1	+	+	PROPN
ejpam-3133	164	2	gb(fxn	gb(fxn	ADJ
ejpam-3133	164	3	,	,	PUNCT
ejpam-3133	164	4	sxn	sxn	NOUN
ejpam-3133	164	5	,	,	PUNCT
ejpam-3133	164	6	sxn	sxn	NOUN
ejpam-3133	164	7	)	)	PUNCT
ejpam-3133	164	8	2s	2s	PROPN
ejpam-3133	164	9	}	}	PUNCT
ejpam-3133	164	10	.	.	PUNCT
ejpam-3133	165	1	taking	take	VERB
ejpam-3133	165	2	lim	lim	PROPN
ejpam-3133	165	3	supn→∞	supn→∞	PROPN
ejpam-3133	165	4	and	and	CCONJ
ejpam-3133	165	5	using	use	VERB
ejpam-3133	165	6	(	(	PUNCT
ejpam-3133	165	7	4	4	NUM
ejpam-3133	165	8	)	)	PUNCT
ejpam-3133	165	9	together	together	ADV
ejpam-3133	165	10	with	with	ADP
ejpam-3133	165	11	(	(	PUNCT
ejpam-3133	165	12	6	6	NUM
ejpam-3133	165	13	)	)	PUNCT
ejpam-3133	165	14	,	,	PUNCT
ejpam-3133	165	15	we	we	PRON
ejpam-3133	165	16	obtain	obtain	VERB
ejpam-3133	165	17	lim	lim	PROPN
ejpam-3133	165	18	sup	sup	VERB
ejpam-3133	165	19	n→∞	n→∞	NUM
ejpam-3133	165	20	m(xn	m(xn	PROPN
ejpam-3133	165	21	,	,	PUNCT
ejpam-3133	165	22	yn	yn	PROPN
ejpam-3133	165	23	,	,	PUNCT
ejpam-3133	165	24	zn	zn	PROPN
ejpam-3133	165	25	)	)	PUNCT
ejpam-3133	166	1	=	=	SYM
ejpam-3133	166	2	lim	lim	PROPN
ejpam-3133	166	3	sup	sup	PROPN
ejpam-3133	166	4	n→∞	n→∞	NUM
ejpam-3133	166	5	gb(fxn	gb(fxn	PROPN
ejpam-3133	166	6	,	,	PUNCT
ejpam-3133	166	7	fxn	fxn	NOUN
ejpam-3133	166	8	,	,	PUNCT
ejpam-3133	166	9	hzn	hzn	NOUN
ejpam-3133	166	10	)	)	PUNCT
ejpam-3133	166	11	.	.	PUNCT
ejpam-3133	167	1	(	(	PUNCT
ejpam-3133	167	2	8)	8)	NUM
ejpam-3133	167	3	taking	take	VERB
ejpam-3133	167	4	again	again	ADV
ejpam-3133	167	5	lim	lim	PROPN
ejpam-3133	167	6	supn→∞	supn→∞	PROPN
ejpam-3133	167	7	in	in	ADP
ejpam-3133	167	8	(	(	PUNCT
ejpam-3133	167	9	7	7	NUM
ejpam-3133	167	10	)	)	PUNCT
ejpam-3133	167	11	and	and	CCONJ
ejpam-3133	167	12	substituting	substitute	VERB
ejpam-3133	167	13	(	(	PUNCT
ejpam-3133	167	14	8)	8)	NUM
ejpam-3133	167	15	,	,	PUNCT
ejpam-3133	167	16	we	we	PRON
ejpam-3133	167	17	get	get	VERB
ejpam-3133	167	18	ψ	ψ	X
ejpam-3133	167	19	(	(	PUNCT
ejpam-3133	167	20	lim	lim	PROPN
ejpam-3133	167	21	sup	sup	PROPN
ejpam-3133	167	22	n→∞	n→∞	NUM
ejpam-3133	167	23	sgb(fxn	sgb(fxn	PROPN
ejpam-3133	167	24	,	,	PUNCT
ejpam-3133	167	25	fxn	fxn	NOUN
ejpam-3133	167	26	,	,	PUNCT
ejpam-3133	167	27	hzn	hzn	NOUN
ejpam-3133	167	28	)	)	PUNCT
ejpam-3133	167	29	)	)	PUNCT
ejpam-3133	168	1	≤	≤	NUM
ejpam-3133	168	2	ψ	ψ	X
ejpam-3133	168	3	(	(	PUNCT
ejpam-3133	168	4	lim	lim	PROPN
ejpam-3133	168	5	sup	sup	PROPN
ejpam-3133	168	6	n→∞	n→∞	NUM
ejpam-3133	169	1	s2gb(fxn	s2gb(fxn	PROPN
ejpam-3133	169	2	,	,	PUNCT
ejpam-3133	169	3	gyn	gyn	NOUN
ejpam-3133	169	4	,	,	PUNCT
ejpam-3133	169	5	hzn	hzn	NOUN
ejpam-3133	169	6	)	)	PUNCT
ejpam-3133	169	7	)	)	PUNCT
ejpam-3133	170	1	≤	≤	NUM
ejpam-3133	170	2	ψ	ψ	X
ejpam-3133	170	3	(	(	PUNCT
ejpam-3133	170	4	lim	lim	PROPN
ejpam-3133	170	5	sup	sup	PROPN
ejpam-3133	170	6	n→∞	n→∞	NUM
ejpam-3133	170	7	gb(fxn	gb(fxn	PROPN
ejpam-3133	170	8	,	,	PUNCT
ejpam-3133	170	9	fxn	fxn	NOUN
ejpam-3133	170	10	,	,	PUNCT
ejpam-3133	170	11	hzn	hzn	NOUN
ejpam-3133	170	12	)	)	PUNCT
ejpam-3133	170	13	)	)	PUNCT
ejpam-3133	171	1	−	−	PROPN
ejpam-3133	171	2	φ	φ	PROPN
ejpam-3133	171	3	(	(	PUNCT
ejpam-3133	171	4	lim	lim	PROPN
ejpam-3133	171	5	inf	inf	PROPN
ejpam-3133	171	6	n→∞	n→∞	NUM
ejpam-3133	171	7	m(xn	m(xn	PROPN
ejpam-3133	171	8	,	,	PUNCT
ejpam-3133	171	9	yn	yn	PROPN
ejpam-3133	171	10	,	,	PUNCT
ejpam-3133	171	11	zn	zn	PROPN
ejpam-3133	171	12	)	)	PUNCT
ejpam-3133	171	13	)	)	PUNCT
ejpam-3133	171	14	.	.	PUNCT
ejpam-3133	172	1	≤	≤	NUM
ejpam-3133	172	2	ψ	ψ	X
ejpam-3133	172	3	(	(	PUNCT
ejpam-3133	172	4	lim	lim	PROPN
ejpam-3133	172	5	sup	sup	PROPN
ejpam-3133	172	6	n→∞	n→∞	NUM
ejpam-3133	172	7	gb(fxn	gb(fxn	PROPN
ejpam-3133	172	8	,	,	PUNCT
ejpam-3133	172	9	fxn	fxn	NOUN
ejpam-3133	172	10	,	,	PUNCT
ejpam-3133	172	11	hzn	hzn	NOUN
ejpam-3133	172	12	)	)	PUNCT
ejpam-3133	172	13	)	)	PUNCT
ejpam-3133	172	14	.	.	PUNCT
ejpam-3133	173	1	(	(	PUNCT
ejpam-3133	173	2	9	9	X
ejpam-3133	173	3	)	)	PUNCT
ejpam-3133	173	4	since	since	SCONJ
ejpam-3133	173	5	s	s	PROPN
ejpam-3133	173	6	>	>	X
ejpam-3133	173	7	1	1	NUM
ejpam-3133	173	8	and	and	CCONJ
ejpam-3133	173	9	being	be	AUX
ejpam-3133	173	10	ψ	ψ	NOUN
ejpam-3133	173	11	is	be	AUX
ejpam-3133	173	12	an	an	DET
ejpam-3133	173	13	increasing	increase	VERB
ejpam-3133	173	14	mapping	mapping	NOUN
ejpam-3133	173	15	,	,	PUNCT
ejpam-3133	173	16	we	we	PRON
ejpam-3133	173	17	deduce	deduce	VERB
ejpam-3133	173	18	from	from	ADP
ejpam-3133	173	19	(	(	PUNCT
ejpam-3133	173	20	9	9	NUM
ejpam-3133	173	21	)	)	PUNCT
ejpam-3133	173	22	that	that	PRON
ejpam-3133	173	23	lim	lim	PROPN
ejpam-3133	173	24	sup	sup	PROPN
ejpam-3133	173	25	n→∞	n→∞	NUM
ejpam-3133	173	26	gb(fxn	gb(fxn	PROPN
ejpam-3133	173	27	,	,	PUNCT
ejpam-3133	173	28	fxn	fxn	NOUN
ejpam-3133	173	29	,	,	PUNCT
ejpam-3133	173	30	hzn	hzn	NOUN
ejpam-3133	173	31	)	)	PUNCT
ejpam-3133	173	32	=	=	SYM
ejpam-3133	174	1	0	0	NUM
ejpam-3133	174	2	,	,	PUNCT
ejpam-3133	174	3	which	which	PRON
ejpam-3133	174	4	implies	imply	VERB
ejpam-3133	174	5	that	that	SCONJ
ejpam-3133	174	6	lim	lim	PROPN
ejpam-3133	174	7	n→∞	n→∞	PRON
ejpam-3133	174	8	gb(fxn	gb(fxn	PROPN
ejpam-3133	174	9	,	,	PUNCT
ejpam-3133	174	10	fxn	fxn	NOUN
ejpam-3133	174	11	,	,	PUNCT
ejpam-3133	174	12	hzn	hzn	NOUN
ejpam-3133	174	13	)	)	PUNCT
ejpam-3133	174	14	=	=	SYM
ejpam-3133	174	15	0	0	NUM
ejpam-3133	174	16	,	,	PUNCT
ejpam-3133	174	17	(	(	PUNCT
ejpam-3133	174	18	10	10	NUM
ejpam-3133	174	19	)	)	PUNCT
ejpam-3133	174	20	and	and	CCONJ
ejpam-3133	174	21	so	so	ADV
ejpam-3133	174	22	by	by	ADP
ejpam-3133	174	23	(	(	PUNCT
ejpam-3133	174	24	8)	8)	NUM
ejpam-3133	174	25	,	,	PUNCT
ejpam-3133	174	26	we	we	PRON
ejpam-3133	174	27	conclude	conclude	VERB
ejpam-3133	174	28	that	that	SCONJ
ejpam-3133	174	29	lim	lim	PROPN
ejpam-3133	174	30	n→∞	n→∞	NUM
ejpam-3133	174	31	m(xn	m(xn	PROPN
ejpam-3133	174	32	,	,	PUNCT
ejpam-3133	174	33	yn	yn	PROPN
ejpam-3133	174	34	,	,	PUNCT
ejpam-3133	174	35	zn	zn	PROPN
ejpam-3133	174	36	)	)	PUNCT
ejpam-3133	174	37	=	=	SYM
ejpam-3133	175	1	0	0	X
ejpam-3133	175	2	.	.	PUNCT
ejpam-3133	176	1	(	(	PUNCT
ejpam-3133	176	2	11	11	NUM
ejpam-3133	176	3	)	)	PUNCT
ejpam-3133	176	4	now	now	ADV
ejpam-3133	176	5	,	,	PUNCT
ejpam-3133	176	6	by	by	ADP
ejpam-3133	176	7	(	(	PUNCT
ejpam-3133	176	8	gb4	gb4	NOUN
ejpam-3133	176	9	)	)	PUNCT
ejpam-3133	176	10	,	,	PUNCT
ejpam-3133	176	11	(	(	PUNCT
ejpam-3133	176	12	10	10	NUM
ejpam-3133	176	13	)	)	PUNCT
ejpam-3133	176	14	and	and	CCONJ
ejpam-3133	176	15	(	(	PUNCT
ejpam-3133	176	16	4	4	NUM
ejpam-3133	176	17	)	)	PUNCT
ejpam-3133	176	18	,	,	PUNCT
ejpam-3133	176	19	we	we	PRON
ejpam-3133	176	20	have	have	VERB
ejpam-3133	176	21	gb(hzn	gb(hzn	PROPN
ejpam-3133	176	22	,	,	PUNCT
ejpam-3133	176	23	q1	q1	PROPN
ejpam-3133	176	24	,	,	PUNCT
ejpam-3133	176	25	q1	q1	PROPN
ejpam-3133	176	26	)	)	PUNCT
ejpam-3133	177	1	≤	≤	PROPN
ejpam-3133	177	2	s	s	PART
ejpam-3133	177	3	[	[	PUNCT
ejpam-3133	177	4	gb(hzn	gb(hzn	PROPN
ejpam-3133	177	5	,	,	PUNCT
ejpam-3133	177	6	fxn	fxn	NOUN
ejpam-3133	177	7	,	,	PUNCT
ejpam-3133	177	8	fxn	fxn	NOUN
ejpam-3133	177	9	)	)	PUNCT
ejpam-3133	178	1	+	+	PROPN
ejpam-3133	178	2	gb(fxn	gb(fxn	PROPN
ejpam-3133	178	3	,	,	PUNCT
ejpam-3133	178	4	q1	q1	PROPN
ejpam-3133	178	5	,	,	PUNCT
ejpam-3133	178	6	q1	q1	PROPN
ejpam-3133	178	7	)	)	PUNCT
ejpam-3133	178	8	]	]	PUNCT
ejpam-3133	178	9	→	→	SYM
ejpam-3133	178	10	0	0	NUM
ejpam-3133	178	11	as	as	ADP
ejpam-3133	178	12	n→∞.	n→∞.	PROPN
ejpam-3133	178	13	(	(	PUNCT
ejpam-3133	178	14	12	12	NUM
ejpam-3133	178	15	)	)	PUNCT
ejpam-3133	178	16	thus	thus	ADV
ejpam-3133	178	17	,	,	PUNCT
ejpam-3133	178	18	lim	lim	PROPN
ejpam-3133	178	19	n→∞	n→∞	NUM
ejpam-3133	178	20	gb(hzn	gb(hzn	PROPN
ejpam-3133	178	21	,	,	PUNCT
ejpam-3133	178	22	q1	q1	PROPN
ejpam-3133	178	23	,	,	PUNCT
ejpam-3133	178	24	q1	q1	PROPN
ejpam-3133	178	25	)	)	PUNCT
ejpam-3133	178	26	=	=	SYM
ejpam-3133	178	27	0	0	NUM
ejpam-3133	178	28	which	which	PRON
ejpam-3133	178	29	gives	give	VERB
ejpam-3133	178	30	that	that	DET
ejpam-3133	178	31	limhzn	limhzn	PROPN
ejpam-3133	178	32	=	=	PROPN
ejpam-3133	178	33	q1	q1	PROPN
ejpam-3133	178	34	as	as	ADP
ejpam-3133	178	35	n	n	NUM
ejpam-3133	178	36	→	→	SYM
ejpam-3133	178	37	∞.	∞.	PROPN
ejpam-3133	178	38	now	now	ADV
ejpam-3133	178	39	,	,	PUNCT
ejpam-3133	178	40	we	we	PRON
ejpam-3133	178	41	shall	shall	AUX
ejpam-3133	178	42	prove	prove	VERB
ejpam-3133	178	43	that	that	DET
ejpam-3133	178	44	q1	q1	PROPN
ejpam-3133	178	45	=	=	SYM
ejpam-3133	178	46	q2	q2	NOUN
ejpam-3133	178	47	.	.	PUNCT
ejpam-3133	179	1	by	by	ADP
ejpam-3133	179	2	applying	apply	VERB
ejpam-3133	179	3	(	(	PUNCT
ejpam-3133	179	4	3	3	NUM
ejpam-3133	179	5	)	)	PUNCT
ejpam-3133	179	6	and	and	CCONJ
ejpam-3133	179	7	using	use	VERB
ejpam-3133	179	8	(	(	PUNCT
ejpam-3133	179	9	gb3	gb3	NOUN
ejpam-3133	179	10	)	)	PUNCT
ejpam-3133	179	11	,	,	PUNCT
ejpam-3133	179	12	we	we	PRON
ejpam-3133	179	13	find	find	VERB
ejpam-3133	179	14	that	that	SCONJ
ejpam-3133	179	15	ψ	ψ	X
ejpam-3133	179	16	(	(	PUNCT
ejpam-3133	179	17	sgb(fxn	sgb(fxn	PROPN
ejpam-3133	179	18	,	,	PUNCT
ejpam-3133	179	19	gyn	gyn	NOUN
ejpam-3133	179	20	,	,	PUNCT
ejpam-3133	179	21	gyn	gyn	NOUN
ejpam-3133	179	22	)	)	PUNCT
ejpam-3133	179	23	)	)	PUNCT
ejpam-3133	180	1	≤	≤	NUM
ejpam-3133	181	1	ψ	ψ	X
ejpam-3133	181	2	(	(	PUNCT
ejpam-3133	181	3	s2gb(fxn	s2gb(fxn	PROPN
ejpam-3133	181	4	,	,	PUNCT
ejpam-3133	181	5	gyn	gyn	NOUN
ejpam-3133	181	6	,	,	PUNCT
ejpam-3133	181	7	hzn	hzn	NOUN
ejpam-3133	181	8	)	)	PUNCT
ejpam-3133	181	9	)	)	PUNCT
ejpam-3133	182	1	≤	≤	NUM
ejpam-3133	182	2	ψ	ψ	X
ejpam-3133	182	3	(	(	PUNCT
ejpam-3133	182	4	m(xn	m(xn	PROPN
ejpam-3133	182	5	,	,	PUNCT
ejpam-3133	182	6	yn	yn	PROPN
ejpam-3133	182	7	,	,	PUNCT
ejpam-3133	182	8	zn	zn	PROPN
ejpam-3133	182	9	)	)	PUNCT
ejpam-3133	182	10	)	)	PUNCT
ejpam-3133	183	1	−	−	PROPN
ejpam-3133	183	2	φ	φ	PROPN
ejpam-3133	183	3	(	(	PUNCT
ejpam-3133	183	4	m(xn	m(xn	PROPN
ejpam-3133	183	5	,	,	PUNCT
ejpam-3133	183	6	yn	yn	PROPN
ejpam-3133	183	7	,	,	PUNCT
ejpam-3133	183	8	zn	zn	PROPN
ejpam-3133	183	9	)	)	PUNCT
ejpam-3133	183	10	)	)	PUNCT
ejpam-3133	183	11	.	.	PUNCT
ejpam-3133	184	1	(	(	PUNCT
ejpam-3133	184	2	13	13	X
ejpam-3133	184	3	)	)	PUNCT
ejpam-3133	184	4	taking	take	VERB
ejpam-3133	184	5	the	the	DET
ejpam-3133	184	6	limit	limit	NOUN
ejpam-3133	184	7	as	as	ADP
ejpam-3133	184	8	n→∞	n→∞	NUM
ejpam-3133	184	9	in	in	ADP
ejpam-3133	184	10	(	(	PUNCT
ejpam-3133	184	11	13	13	NUM
ejpam-3133	184	12	)	)	PUNCT
ejpam-3133	184	13	and	and	CCONJ
ejpam-3133	184	14	recalling	recall	VERB
ejpam-3133	184	15	(	(	PUNCT
ejpam-3133	184	16	11	11	NUM
ejpam-3133	184	17	)	)	PUNCT
ejpam-3133	184	18	,	,	PUNCT
ejpam-3133	184	19	we	we	PRON
ejpam-3133	184	20	obtain	obtain	VERB
ejpam-3133	184	21	lim	lim	PROPN
ejpam-3133	184	22	n→∞	n→∞	NUM
ejpam-3133	185	1	gb(fxn	gb(fxn	PROPN
ejpam-3133	185	2	,	,	PUNCT
ejpam-3133	185	3	gyn	gyn	NOUN
ejpam-3133	185	4	,	,	PUNCT
ejpam-3133	185	5	gyn	gyn	NOUN
ejpam-3133	185	6	)	)	PUNCT
ejpam-3133	185	7	=	=	SYM
ejpam-3133	185	8	0	0	X
ejpam-3133	185	9	.	.	PUNCT
ejpam-3133	186	1	(	(	PUNCT
ejpam-3133	186	2	14	14	NUM
ejpam-3133	186	3	)	)	PUNCT
ejpam-3133	186	4	thus	thus	ADV
ejpam-3133	186	5	,	,	PUNCT
ejpam-3133	186	6	by	by	ADP
ejpam-3133	186	7	using	use	VERB
ejpam-3133	186	8	(	(	PUNCT
ejpam-3133	186	9	gb4	gb4	NOUN
ejpam-3133	186	10	)	)	PUNCT
ejpam-3133	186	11	,	,	PUNCT
ejpam-3133	186	12	(	(	PUNCT
ejpam-3133	186	13	4	4	NUM
ejpam-3133	186	14	)	)	PUNCT
ejpam-3133	186	15	and	and	CCONJ
ejpam-3133	186	16	(	(	PUNCT
ejpam-3133	186	17	14	14	NUM
ejpam-3133	186	18	)	)	PUNCT
ejpam-3133	186	19	,	,	PUNCT
ejpam-3133	186	20	gb(q1	gb(q1	NOUN
ejpam-3133	186	21	,	,	PUNCT
ejpam-3133	186	22	sαn	sαn	PROPN
ejpam-3133	186	23	,	,	PUNCT
ejpam-3133	186	24	sαn	sαn	NOUN
ejpam-3133	186	25	)	)	PUNCT
ejpam-3133	186	26	=	=	SYM
ejpam-3133	186	27	gb(q1	gb(q1	NOUN
ejpam-3133	186	28	,	,	PUNCT
ejpam-3133	186	29	gyn	gyn	NOUN
ejpam-3133	186	30	,	,	PUNCT
ejpam-3133	186	31	gyn	gyn	NOUN
ejpam-3133	186	32	)	)	PUNCT
ejpam-3133	186	33	z.	z.	PROPN
ejpam-3133	186	34	mustafa	mustafa	PROPN
ejpam-3133	186	35	et	et	PROPN
ejpam-3133	186	36	al	al	PROPN
ejpam-3133	186	37	.	.	PUNCT
ejpam-3133	186	38	/	/	SYM
ejpam-3133	186	39	eur	eur	PROPN
ejpam-3133	186	40	.	.	PUNCT
ejpam-3133	187	1	j.	j.	PROPN
ejpam-3133	187	2	pure	pure	PROPN
ejpam-3133	187	3	appl	appl	PROPN
ejpam-3133	187	4	.	.	PROPN
ejpam-3133	187	5	math	math	PROPN
ejpam-3133	187	6	,	,	PUNCT
ejpam-3133	187	7	11	11	NUM
ejpam-3133	187	8	(	(	PUNCT
ejpam-3133	187	9	1	1	NUM
ejpam-3133	187	10	)	)	PUNCT
ejpam-3133	187	11	(	(	PUNCT
ejpam-3133	187	12	2018	2018	NUM
ejpam-3133	187	13	)	)	PUNCT
ejpam-3133	187	14	,	,	PUNCT
ejpam-3133	187	15	90	90	NUM
ejpam-3133	187	16	-	-	SYM
ejpam-3133	187	17	109	109	NUM
ejpam-3133	187	18	97	97	NUM
ejpam-3133	187	19	≤	≤	NUM
ejpam-3133	187	20	s	s	PART
ejpam-3133	187	21	[	[	PUNCT
ejpam-3133	187	22	gb(q1	gb(q1	NOUN
ejpam-3133	187	23	,	,	PUNCT
ejpam-3133	187	24	fxn	fxn	NOUN
ejpam-3133	187	25	,	,	PUNCT
ejpam-3133	187	26	fxn	fxn	NOUN
ejpam-3133	187	27	)	)	PUNCT
ejpam-3133	188	1	+	+	PROPN
ejpam-3133	188	2	gb(fxn	gb(fxn	ADJ
ejpam-3133	188	3	,	,	PUNCT
ejpam-3133	188	4	gyn	gyn	NOUN
ejpam-3133	188	5	,	,	PUNCT
ejpam-3133	188	6	gyn	gyn	NOUN
ejpam-3133	188	7	)	)	PUNCT
ejpam-3133	188	8	]	]	PUNCT
ejpam-3133	189	1	→	→	SYM
ejpam-3133	189	2	0	0	NUM
ejpam-3133	189	3	as	as	ADP
ejpam-3133	189	4	n→∞.	n→∞.	PROPN
ejpam-3133	189	5	this	this	PRON
ejpam-3133	189	6	implies	imply	VERB
ejpam-3133	189	7	that	that	SCONJ
ejpam-3133	189	8	limn→∞	limn→∞	PROPN
ejpam-3133	189	9	sαn	sαn	NOUN
ejpam-3133	189	10	=	=	SYM
ejpam-3133	189	11	q1	q1	PROPN
ejpam-3133	189	12	.	.	PUNCT
ejpam-3133	190	1	on	on	ADP
ejpam-3133	190	2	the	the	DET
ejpam-3133	190	3	other	other	ADJ
ejpam-3133	190	4	hand	hand	NOUN
ejpam-3133	190	5	,	,	PUNCT
ejpam-3133	190	6	from	from	ADP
ejpam-3133	190	7	(	(	PUNCT
ejpam-3133	190	8	6	6	NUM
ejpam-3133	190	9	)	)	PUNCT
ejpam-3133	190	10	we	we	PRON
ejpam-3133	190	11	have	have	AUX
ejpam-3133	190	12	lim	lim	PROPN
ejpam-3133	190	13	n→∞	n→∞	PRON
ejpam-3133	190	14	sαn	sαn	NOUN
ejpam-3133	190	15	=	=	SYM
ejpam-3133	190	16	q2	q2	NOUN
ejpam-3133	190	17	,	,	PUNCT
ejpam-3133	190	18	hence	hence	ADV
ejpam-3133	190	19	by	by	ADP
ejpam-3133	190	20	uniqueness	uniqueness	NOUN
ejpam-3133	190	21	of	of	ADP
ejpam-3133	190	22	limits	limit	NOUN
ejpam-3133	190	23	,	,	PUNCT
ejpam-3133	190	24	we	we	PRON
ejpam-3133	190	25	obtain	obtain	VERB
ejpam-3133	190	26	that	that	DET
ejpam-3133	190	27	q1	q1	NOUN
ejpam-3133	190	28	=	=	SYM
ejpam-3133	190	29	q2	q2	PROPN
ejpam-3133	190	30	.	.	PUNCT
ejpam-3133	191	1	therefore	therefore	ADV
ejpam-3133	191	2	lim	lim	PROPN
ejpam-3133	191	3	n→∞	n→∞	PROPN
ejpam-3133	191	4	fxn	fxn	PROPN
ejpam-3133	191	5	=	=	PUNCT
ejpam-3133	191	6	lim	lim	PROPN
ejpam-3133	191	7	n→∞	n→∞	NUM
ejpam-3133	191	8	hzn	hzn	NOUN
ejpam-3133	191	9	=	=	PROPN
ejpam-3133	191	10	lim	lim	PROPN
ejpam-3133	191	11	n→∞	n→∞	NUM
ejpam-3133	192	1	tzn	tzn	PROPN
ejpam-3133	192	2	=	=	PUNCT
ejpam-3133	193	1	lim	lim	PROPN
ejpam-3133	193	2	n→∞	n→∞	NUM
ejpam-3133	194	1	sxn	sxn	NOUN
ejpam-3133	194	2	=	=	PUNCT
ejpam-3133	194	3	lim	lim	PROPN
ejpam-3133	194	4	n→∞	n→∞	NUM
ejpam-3133	194	5	gyn	gyn	PROPN
ejpam-3133	194	6	=	=	SYM
ejpam-3133	194	7	lim	lim	PROPN
ejpam-3133	194	8	n→∞	n→∞	NUM
ejpam-3133	194	9	sαn	sαn	NOUN
ejpam-3133	194	10	=	=	PROPN
ejpam-3133	194	11	lim	lim	PROPN
ejpam-3133	194	12	n→∞	n→∞	X
ejpam-3133	195	1	ryn	ryn	PROPN
ejpam-3133	195	2	=	=	PROPN
ejpam-3133	195	3	q	q	X
ejpam-3133	195	4	(	(	PUNCT
ejpam-3133	195	5	15	15	NUM
ejpam-3133	195	6	)	)	PUNCT
ejpam-3133	195	7	for	for	ADP
ejpam-3133	195	8	some	some	DET
ejpam-3133	195	9	q	q	NOUN
ejpam-3133	195	10	∈	∈	PROPN
ejpam-3133	195	11	x.	x.	NOUN
ejpam-3133	195	12	since	since	SCONJ
ejpam-3133	195	13	r(x	r(x	PROPN
ejpam-3133	195	14	)	)	PUNCT
ejpam-3133	195	15	is	be	AUX
ejpam-3133	195	16	a	a	DET
ejpam-3133	195	17	closed	closed	ADJ
ejpam-3133	195	18	subspace	subspace	NOUN
ejpam-3133	195	19	of	of	ADP
ejpam-3133	195	20	x	x	PRON
ejpam-3133	195	21	,	,	PUNCT
ejpam-3133	195	22	there	there	PRON
ejpam-3133	195	23	exists	exist	VERB
ejpam-3133	195	24	u	u	NOUN
ejpam-3133	195	25	∈	∈	PROPN
ejpam-3133	195	26	x	x	PUNCT
ejpam-3133	195	27	such	such	ADJ
ejpam-3133	195	28	that	that	DET
ejpam-3133	195	29	ru	ru	NOUN
ejpam-3133	195	30	=	=	PUNCT
ejpam-3133	195	31	q.	q.	PROPN
ejpam-3133	196	1	now	now	ADV
ejpam-3133	196	2	we	we	PRON
ejpam-3133	196	3	shall	shall	AUX
ejpam-3133	196	4	prove	prove	VERB
ejpam-3133	196	5	that	that	PRON
ejpam-3133	196	6	gu	gu	NOUN
ejpam-3133	196	7	=	=	PUNCT
ejpam-3133	196	8	q.	q.	PROPN
ejpam-3133	196	9	observe	observe	VERB
ejpam-3133	196	10	that	that	SCONJ
ejpam-3133	196	11	m(xn	m(xn	PROPN
ejpam-3133	196	12	,	,	PUNCT
ejpam-3133	196	13	u	u	NOUN
ejpam-3133	196	14	,	,	PUNCT
ejpam-3133	196	15	zn	zn	NOUN
ejpam-3133	196	16	)	)	PUNCT
ejpam-3133	196	17	=	=	SYM
ejpam-3133	196	18	max	max	PROPN
ejpam-3133	196	19	{	{	PUNCT
ejpam-3133	196	20	gb(fxn	gb(fxn	PROPN
ejpam-3133	196	21	,	,	PUNCT
ejpam-3133	196	22	sxn	sxn	PROPN
ejpam-3133	196	23	,	,	PUNCT
ejpam-3133	196	24	t	t	PROPN
ejpam-3133	196	25	zn	zn	NUM
ejpam-3133	196	26	)	)	PUNCT
ejpam-3133	196	27	,	,	PUNCT
ejpam-3133	196	28	gb(gu	gb(gu	PROPN
ejpam-3133	196	29	,	,	PUNCT
ejpam-3133	196	30	ru	ru	PROPN
ejpam-3133	196	31	,	,	PUNCT
ejpam-3133	196	32	ru	ru	PROPN
ejpam-3133	196	33	)	)	PUNCT
ejpam-3133	196	34	,	,	PUNCT
ejpam-3133	196	35	gb(fxn	gb(fxn	PROPN
ejpam-3133	196	36	,	,	PUNCT
ejpam-3133	196	37	fxn	fxn	NOUN
ejpam-3133	196	38	,	,	PUNCT
ejpam-3133	196	39	hzn	hzn	NOUN
ejpam-3133	196	40	)	)	PUNCT
ejpam-3133	196	41	,	,	PUNCT
ejpam-3133	196	42	gb(tzn	gb(tzn	PROPN
ejpam-3133	196	43	,	,	PUNCT
ejpam-3133	196	44	t	t	PROPN
ejpam-3133	196	45	zn	zn	NUM
ejpam-3133	196	46	,	,	PUNCT
ejpam-3133	196	47	hzn	hzn	PROPN
ejpam-3133	196	48	)	)	PUNCT
ejpam-3133	197	1	+	+	PROPN
ejpam-3133	197	2	gb(fxn	gb(fxn	ADJ
ejpam-3133	197	3	,	,	PUNCT
ejpam-3133	197	4	sxn	sxn	NOUN
ejpam-3133	197	5	,	,	PUNCT
ejpam-3133	197	6	sxn	sxn	NOUN
ejpam-3133	197	7	)	)	PUNCT
ejpam-3133	197	8	2s	2s	PROPN
ejpam-3133	197	9	}	}	PUNCT
ejpam-3133	197	10	,	,	PUNCT
ejpam-3133	197	11	=	=	SYM
ejpam-3133	197	12	max	max	PROPN
ejpam-3133	197	13	{	{	PUNCT
ejpam-3133	197	14	gb(fxn	gb(fxn	PROPN
ejpam-3133	197	15	,	,	PUNCT
ejpam-3133	197	16	sxn	sxn	PROPN
ejpam-3133	197	17	,	,	PUNCT
ejpam-3133	197	18	t	t	PROPN
ejpam-3133	197	19	zn	zn	NUM
ejpam-3133	197	20	)	)	PUNCT
ejpam-3133	197	21	,	,	PUNCT
ejpam-3133	197	22	gb(gu	gb(gu	PROPN
ejpam-3133	197	23	,	,	PUNCT
ejpam-3133	197	24	ru	ru	PROPN
ejpam-3133	197	25	,	,	PUNCT
ejpam-3133	197	26	ru	ru	PROPN
ejpam-3133	197	27	)	)	PUNCT
ejpam-3133	197	28	,	,	PUNCT
ejpam-3133	197	29	gb(fxn	gb(fxn	PROPN
ejpam-3133	197	30	,	,	PUNCT
ejpam-3133	197	31	fxn	fxn	NOUN
ejpam-3133	197	32	,	,	PUNCT
ejpam-3133	197	33	hzn	hzn	NOUN
ejpam-3133	197	34	)	)	PUNCT
ejpam-3133	197	35	,	,	PUNCT
ejpam-3133	197	36	gb(fxn	gb(fxn	PROPN
ejpam-3133	197	37	,	,	PUNCT
ejpam-3133	197	38	fxn	fxn	NOUN
ejpam-3133	197	39	,	,	PUNCT
ejpam-3133	197	40	hzn	hzn	NOUN
ejpam-3133	197	41	)	)	PUNCT
ejpam-3133	198	1	+	+	PROPN
ejpam-3133	198	2	gb(fxn	gb(fxn	ADJ
ejpam-3133	198	3	,	,	PUNCT
ejpam-3133	198	4	sxn	sxn	NOUN
ejpam-3133	198	5	,	,	PUNCT
ejpam-3133	198	6	sxn	sxn	NOUN
ejpam-3133	198	7	)	)	PUNCT
ejpam-3133	198	8	2s	2s	PROPN
ejpam-3133	198	9	}	}	PUNCT
ejpam-3133	198	10	,	,	PUNCT
ejpam-3133	198	11	=	=	SYM
ejpam-3133	198	12	max	max	PROPN
ejpam-3133	198	13	{	{	PUNCT
ejpam-3133	198	14	gb(fxn	gb(fxn	PROPN
ejpam-3133	198	15	,	,	PUNCT
ejpam-3133	198	16	sxn	sxn	PROPN
ejpam-3133	198	17	,	,	PUNCT
ejpam-3133	198	18	t	t	PROPN
ejpam-3133	198	19	zn	zn	NUM
ejpam-3133	198	20	)	)	PUNCT
ejpam-3133	198	21	,	,	PUNCT
ejpam-3133	198	22	gb(gu	gb(gu	PROPN
ejpam-3133	198	23	,	,	PUNCT
ejpam-3133	198	24	q	q	NOUN
ejpam-3133	198	25	,	,	PUNCT
ejpam-3133	198	26	q	q	NOUN
ejpam-3133	198	27	)	)	PUNCT
ejpam-3133	198	28	,	,	PUNCT
ejpam-3133	198	29	gb(fxn	gb(fxn	PROPN
ejpam-3133	198	30	,	,	PUNCT
ejpam-3133	198	31	fxn	fxn	NOUN
ejpam-3133	198	32	,	,	PUNCT
ejpam-3133	198	33	hzn	hzn	NOUN
ejpam-3133	198	34	)	)	PUNCT
ejpam-3133	198	35	,	,	PUNCT
ejpam-3133	198	36	gb(fxn	gb(fxn	PROPN
ejpam-3133	198	37	,	,	PUNCT
ejpam-3133	198	38	fxn	fxn	NOUN
ejpam-3133	198	39	,	,	PUNCT
ejpam-3133	198	40	hzn	hzn	NOUN
ejpam-3133	198	41	)	)	PUNCT
ejpam-3133	199	1	+	+	PROPN
ejpam-3133	199	2	gb(fxn	gb(fxn	ADJ
ejpam-3133	199	3	,	,	PUNCT
ejpam-3133	199	4	sxn	sxn	NOUN
ejpam-3133	199	5	,	,	PUNCT
ejpam-3133	199	6	sxn	sxn	NOUN
ejpam-3133	199	7	)	)	PUNCT
ejpam-3133	199	8	2s	2s	PROPN
ejpam-3133	199	9	}	}	PUNCT
ejpam-3133	199	10	.	.	PUNCT
ejpam-3133	200	1	(	(	PUNCT
ejpam-3133	200	2	16	16	NUM
ejpam-3133	200	3	)	)	PUNCT
ejpam-3133	200	4	by	by	ADP
ejpam-3133	200	5	taking	take	VERB
ejpam-3133	200	6	limit	limit	NOUN
ejpam-3133	200	7	superior	superior	ADJ
ejpam-3133	200	8	as	as	ADP
ejpam-3133	200	9	n	n	PROPN
ejpam-3133	200	10	→	→	SYM
ejpam-3133	200	11	∞	∞	NUM
ejpam-3133	200	12	and	and	CCONJ
ejpam-3133	200	13	taking	take	VERB
ejpam-3133	200	14	into	into	ADP
ejpam-3133	200	15	account	account	NOUN
ejpam-3133	200	16	(	(	PUNCT
ejpam-3133	200	17	4	4	NUM
ejpam-3133	200	18	)	)	PUNCT
ejpam-3133	200	19	,	,	PUNCT
ejpam-3133	200	20	(	(	PUNCT
ejpam-3133	200	21	6	6	NUM
ejpam-3133	200	22	)	)	PUNCT
ejpam-3133	200	23	and	and	CCONJ
ejpam-3133	200	24	(	(	PUNCT
ejpam-3133	200	25	15	15	NUM
ejpam-3133	200	26	)	)	PUNCT
ejpam-3133	200	27	,	,	PUNCT
ejpam-3133	200	28	then	then	ADV
ejpam-3133	200	29	(	(	PUNCT
ejpam-3133	200	30	16	16	NUM
ejpam-3133	200	31	)	)	PUNCT
ejpam-3133	200	32	becomes	become	VERB
ejpam-3133	200	33	lim	lim	PROPN
ejpam-3133	200	34	sup	sup	NOUN
ejpam-3133	200	35	n→∞	n→∞	NUM
ejpam-3133	200	36	m(xn	m(xn	PROPN
ejpam-3133	200	37	,	,	PUNCT
ejpam-3133	200	38	u	u	NOUN
ejpam-3133	200	39	,	,	PUNCT
ejpam-3133	200	40	zn	zn	NOUN
ejpam-3133	200	41	)	)	PUNCT
ejpam-3133	201	1	=	=	SYM
ejpam-3133	201	2	gb(gu	gb(gu	PROPN
ejpam-3133	201	3	,	,	PUNCT
ejpam-3133	201	4	q	q	NOUN
ejpam-3133	201	5	,	,	PUNCT
ejpam-3133	201	6	q	q	NOUN
ejpam-3133	201	7	)	)	PUNCT
ejpam-3133	201	8	.	.	PUNCT
ejpam-3133	202	1	(	(	PUNCT
ejpam-3133	202	2	17	17	NUM
ejpam-3133	202	3	)	)	PUNCT
ejpam-3133	202	4	by	by	ADP
ejpam-3133	202	5	the	the	DET
ejpam-3133	202	6	help	help	NOUN
ejpam-3133	202	7	of	of	ADP
ejpam-3133	202	8	lemma	lemma	PROPN
ejpam-3133	202	9	2	2	NUM
ejpam-3133	202	10	,	,	PUNCT
ejpam-3133	202	11	we	we	PRON
ejpam-3133	202	12	obtain	obtain	VERB
ejpam-3133	202	13	that	that	SCONJ
ejpam-3133	202	14	1	1	NUM
ejpam-3133	202	15	s	s	NOUN
ejpam-3133	202	16	gb(q	gb(q	NOUN
ejpam-3133	202	17	,	,	PUNCT
ejpam-3133	202	18	gu	gu	NOUN
ejpam-3133	202	19	,	,	PUNCT
ejpam-3133	202	20	q	q	NOUN
ejpam-3133	202	21	)	)	PUNCT
ejpam-3133	202	22	≤	≤	PROPN
ejpam-3133	202	23	lim	lim	PROPN
ejpam-3133	202	24	inf	inf	PROPN
ejpam-3133	202	25	n→∞	n→∞	NUM
ejpam-3133	202	26	gb(gu	gb(gu	PROPN
ejpam-3133	202	27	,	,	PUNCT
ejpam-3133	202	28	fxn	fxn	NOUN
ejpam-3133	202	29	,	,	PUNCT
ejpam-3133	202	30	fxn	fxn	NOUN
ejpam-3133	202	31	)	)	PUNCT
ejpam-3133	202	32	≤	≤	NOUN
ejpam-3133	202	33	lim	lim	PROPN
ejpam-3133	202	34	sup	sup	VERB
ejpam-3133	202	35	n→∞	n→∞	NUM
ejpam-3133	202	36	gb(gu	gb(gu	NOUN
ejpam-3133	202	37	,	,	PUNCT
ejpam-3133	202	38	fxn	fxn	NOUN
ejpam-3133	202	39	,	,	PUNCT
ejpam-3133	202	40	fxn	fxn	NOUN
ejpam-3133	202	41	)	)	PUNCT
ejpam-3133	202	42	≤	≤	NOUN
ejpam-3133	202	43	sgb(gu	sgb(gu	NOUN
ejpam-3133	202	44	,	,	PUNCT
ejpam-3133	202	45	q	q	NOUN
ejpam-3133	202	46	,	,	PUNCT
ejpam-3133	202	47	q	q	NOUN
ejpam-3133	202	48	)	)	PUNCT
ejpam-3133	202	49	.	.	PUNCT
ejpam-3133	203	1	(	(	PUNCT
ejpam-3133	203	2	18	18	NUM
ejpam-3133	203	3	)	)	PUNCT
ejpam-3133	203	4	also	also	ADV
ejpam-3133	203	5	from	from	ADP
ejpam-3133	203	6	(	(	PUNCT
ejpam-3133	203	7	gb3	gb3	NOUN
ejpam-3133	203	8	)	)	PUNCT
ejpam-3133	203	9	,	,	PUNCT
ejpam-3133	203	10	we	we	PRON
ejpam-3133	203	11	have	have	VERB
ejpam-3133	203	12	gb(gu	gb(gu	NOUN
ejpam-3133	203	13	,	,	PUNCT
ejpam-3133	203	14	fxn	fxn	ADJ
ejpam-3133	203	15	,	,	PUNCT
ejpam-3133	203	16	fxn	fxn	NOUN
ejpam-3133	203	17	)	)	PUNCT
ejpam-3133	203	18	≤	≤	PROPN
ejpam-3133	203	19	gb(fxn	gb(fxn	PROPN
ejpam-3133	203	20	,	,	PUNCT
ejpam-3133	203	21	gu	gu	PROPN
ejpam-3133	203	22	,	,	PUNCT
ejpam-3133	203	23	hzn	hzn	NOUN
ejpam-3133	203	24	)	)	PUNCT
ejpam-3133	203	25	.	.	PUNCT
ejpam-3133	204	1	(	(	PUNCT
ejpam-3133	204	2	19	19	NUM
ejpam-3133	204	3	)	)	PUNCT
ejpam-3133	204	4	thus	thus	ADV
ejpam-3133	204	5	,	,	PUNCT
ejpam-3133	204	6	from	from	ADP
ejpam-3133	204	7	(	(	PUNCT
ejpam-3133	204	8	3	3	NUM
ejpam-3133	204	9	)	)	PUNCT
ejpam-3133	204	10	,	,	PUNCT
ejpam-3133	204	11	together	together	ADV
ejpam-3133	204	12	with	with	ADP
ejpam-3133	204	13	(	(	PUNCT
ejpam-3133	204	14	17	17	NUM
ejpam-3133	204	15	)	)	PUNCT
ejpam-3133	204	16	,	,	PUNCT
ejpam-3133	204	17	(	(	PUNCT
ejpam-3133	204	18	18	18	NUM
ejpam-3133	204	19	)	)	PUNCT
ejpam-3133	204	20	,	,	PUNCT
ejpam-3133	204	21	(	(	PUNCT
ejpam-3133	204	22	19	19	NUM
ejpam-3133	204	23	)	)	PUNCT
ejpam-3133	204	24	and	and	CCONJ
ejpam-3133	204	25	properties	property	NOUN
ejpam-3133	204	26	of	of	ADP
ejpam-3133	204	27	ψ	ψ	NOUN
ejpam-3133	204	28	,	,	PUNCT
ejpam-3133	204	29	we	we	PRON
ejpam-3133	204	30	get	get	VERB
ejpam-3133	204	31	that	that	DET
ejpam-3133	204	32	ψ	ψ	X
ejpam-3133	204	33	(	(	PUNCT
ejpam-3133	204	34	sgb(q	sgb(q	PROPN
ejpam-3133	204	35	,	,	PUNCT
ejpam-3133	204	36	gu	gu	NOUN
ejpam-3133	204	37	,	,	PUNCT
ejpam-3133	204	38	q	q	NOUN
ejpam-3133	204	39	)	)	PUNCT
ejpam-3133	204	40	)	)	PUNCT
ejpam-3133	205	1	≤	≤	NUM
ejpam-3133	205	2	ψ	ψ	X
ejpam-3133	205	3	(	(	PUNCT
ejpam-3133	205	4	lim	lim	PROPN
ejpam-3133	205	5	sup	sup	PROPN
ejpam-3133	205	6	n→∞	n→∞	X
ejpam-3133	205	7	s2gb(gu	s2gb(gu	NOUN
ejpam-3133	205	8	,	,	PUNCT
ejpam-3133	205	9	fxn	fxn	NOUN
ejpam-3133	205	10	,	,	PUNCT
ejpam-3133	205	11	fxn	fxn	NOUN
ejpam-3133	205	12	)	)	PUNCT
ejpam-3133	205	13	)	)	PUNCT
ejpam-3133	205	14	≤	≤	NUM
ejpam-3133	206	1	ψ	ψ	X
ejpam-3133	206	2	(	(	PUNCT
ejpam-3133	206	3	lim	lim	PROPN
ejpam-3133	206	4	sup	sup	PROPN
ejpam-3133	206	5	n→∞	n→∞	NUM
ejpam-3133	207	1	s2gb(fxn	s2gb(fxn	PROPN
ejpam-3133	207	2	,	,	PUNCT
ejpam-3133	207	3	gu	gu	NOUN
ejpam-3133	207	4	,	,	PUNCT
ejpam-3133	207	5	hzn	hzn	NOUN
ejpam-3133	207	6	)	)	PUNCT
ejpam-3133	207	7	)	)	PUNCT
ejpam-3133	208	1	=	=	SYM
ejpam-3133	208	2	lim	lim	PROPN
ejpam-3133	208	3	sup	sup	VERB
ejpam-3133	208	4	n→∞	n→∞	NUM
ejpam-3133	208	5	ψ	ψ	X
ejpam-3133	208	6	(	(	PUNCT
ejpam-3133	208	7	s2gb(fxn	s2gb(fxn	PROPN
ejpam-3133	208	8	,	,	PUNCT
ejpam-3133	208	9	gu	gu	NOUN
ejpam-3133	208	10	,	,	PUNCT
ejpam-3133	208	11	hzn	hzn	NOUN
ejpam-3133	208	12	)	)	PUNCT
ejpam-3133	208	13	)	)	PUNCT
ejpam-3133	209	1	≤	≤	NOUN
ejpam-3133	209	2	lim	lim	PROPN
ejpam-3133	209	3	sup	sup	VERB
ejpam-3133	209	4	n→∞	n→∞	NUM
ejpam-3133	209	5	ψ	ψ	X
ejpam-3133	209	6	(	(	PUNCT
ejpam-3133	209	7	m(xn	m(xn	PROPN
ejpam-3133	209	8	,	,	PUNCT
ejpam-3133	209	9	u	u	NOUN
ejpam-3133	209	10	,	,	PUNCT
ejpam-3133	209	11	zn	zn	PROPN
ejpam-3133	209	12	)	)	PUNCT
ejpam-3133	209	13	)	)	PUNCT
ejpam-3133	210	1	−	−	PROPN
ejpam-3133	210	2	lim	lim	PROPN
ejpam-3133	210	3	inf	inf	PROPN
ejpam-3133	210	4	n→∞	n→∞	X
ejpam-3133	210	5	φ	φ	PROPN
ejpam-3133	210	6	(	(	PUNCT
ejpam-3133	210	7	m(xn	m(xn	PROPN
ejpam-3133	210	8	,	,	PUNCT
ejpam-3133	210	9	u	u	NOUN
ejpam-3133	210	10	,	,	PUNCT
ejpam-3133	210	11	zn	zn	PROPN
ejpam-3133	210	12	)	)	PUNCT
ejpam-3133	210	13	)	)	PUNCT
ejpam-3133	210	14	,	,	PUNCT
ejpam-3133	210	15	z.	z.	PROPN
ejpam-3133	210	16	mustafa	mustafa	PROPN
ejpam-3133	210	17	et	et	PROPN
ejpam-3133	210	18	al	al	PROPN
ejpam-3133	210	19	.	.	PUNCT
ejpam-3133	210	20	/	/	SYM
ejpam-3133	210	21	eur	eur	PROPN
ejpam-3133	210	22	.	.	PUNCT
ejpam-3133	211	1	j.	j.	PROPN
ejpam-3133	211	2	pure	pure	PROPN
ejpam-3133	211	3	appl	appl	PROPN
ejpam-3133	211	4	.	.	PROPN
ejpam-3133	211	5	math	math	PROPN
ejpam-3133	211	6	,	,	PUNCT
ejpam-3133	211	7	11	11	NUM
ejpam-3133	211	8	(	(	PUNCT
ejpam-3133	211	9	1	1	NUM
ejpam-3133	211	10	)	)	PUNCT
ejpam-3133	211	11	(	(	PUNCT
ejpam-3133	211	12	2018	2018	NUM
ejpam-3133	211	13	)	)	PUNCT
ejpam-3133	211	14	,	,	PUNCT
ejpam-3133	212	1	90	90	NUM
ejpam-3133	212	2	-	-	SYM
ejpam-3133	212	3	109	109	NUM
ejpam-3133	212	4	98	98	NUM
ejpam-3133	212	5	=	=	SYM
ejpam-3133	212	6	ψ	ψ	X
ejpam-3133	212	7	(	(	PUNCT
ejpam-3133	212	8	lim	lim	PROPN
ejpam-3133	212	9	sup	sup	PROPN
ejpam-3133	212	10	n→∞	n→∞	NUM
ejpam-3133	213	1	m(xn	m(xn	PROPN
ejpam-3133	213	2	,	,	PUNCT
ejpam-3133	213	3	u	u	NOUN
ejpam-3133	213	4	,	,	PUNCT
ejpam-3133	213	5	zn	zn	PROPN
ejpam-3133	213	6	)	)	PUNCT
ejpam-3133	213	7	)	)	PUNCT
ejpam-3133	214	1	−	−	PROPN
ejpam-3133	214	2	φ	φ	PROPN
ejpam-3133	214	3	(	(	PUNCT
ejpam-3133	214	4	lim	lim	PROPN
ejpam-3133	214	5	inf	inf	PROPN
ejpam-3133	214	6	n→∞	n→∞	NUM
ejpam-3133	214	7	m(xn	m(xn	PROPN
ejpam-3133	214	8	,	,	PUNCT
ejpam-3133	214	9	u	u	NOUN
ejpam-3133	214	10	,	,	PUNCT
ejpam-3133	214	11	zn	zn	PROPN
ejpam-3133	214	12	)	)	PUNCT
ejpam-3133	214	13	)	)	PUNCT
ejpam-3133	214	14	,	,	PUNCT
ejpam-3133	214	15	≤	≤	NUM
ejpam-3133	214	16	ψ	ψ	X
ejpam-3133	214	17	(	(	PUNCT
ejpam-3133	214	18	gb(q	gb(q	PROPN
ejpam-3133	214	19	,	,	PUNCT
ejpam-3133	214	20	gu	gu	NOUN
ejpam-3133	214	21	,	,	PUNCT
ejpam-3133	214	22	q	q	NOUN
ejpam-3133	214	23	)	)	PUNCT
ejpam-3133	214	24	)	)	PUNCT
ejpam-3133	215	1	−	−	PROPN
ejpam-3133	215	2	φ	φ	PROPN
ejpam-3133	215	3	(	(	PUNCT
ejpam-3133	215	4	lim	lim	PROPN
ejpam-3133	215	5	inf	inf	PROPN
ejpam-3133	215	6	n→∞	n→∞	NUM
ejpam-3133	215	7	m(xn	m(xn	PROPN
ejpam-3133	215	8	,	,	PUNCT
ejpam-3133	215	9	u	u	NOUN
ejpam-3133	215	10	,	,	PUNCT
ejpam-3133	215	11	zn	zn	PROPN
ejpam-3133	215	12	)	)	PUNCT
ejpam-3133	215	13	)	)	PUNCT
ejpam-3133	215	14	,	,	PUNCT
ejpam-3133	215	15	≤	≤	NUM
ejpam-3133	215	16	ψ(gb(q	ψ(gb(q	PROPN
ejpam-3133	215	17	,	,	PUNCT
ejpam-3133	215	18	gu	gu	NOUN
ejpam-3133	215	19	,	,	PUNCT
ejpam-3133	215	20	q	q	NOUN
ejpam-3133	215	21	)	)	PUNCT
ejpam-3133	215	22	)	)	PUNCT
ejpam-3133	215	23	.	.	PUNCT
ejpam-3133	216	1	(	(	PUNCT
ejpam-3133	216	2	20	20	NUM
ejpam-3133	216	3	)	)	PUNCT
ejpam-3133	216	4	since	since	SCONJ
ejpam-3133	216	5	s	s	PROPN
ejpam-3133	216	6	>	>	X
ejpam-3133	216	7	1	1	NUM
ejpam-3133	216	8	and	and	CCONJ
ejpam-3133	216	9	ψ	ψ	NOUN
ejpam-3133	216	10	is	be	AUX
ejpam-3133	216	11	increasing	increase	VERB
ejpam-3133	216	12	,	,	PUNCT
ejpam-3133	216	13	the	the	DET
ejpam-3133	216	14	above	above	ADJ
ejpam-3133	216	15	inequality	inequality	NOUN
ejpam-3133	216	16	gives	give	VERB
ejpam-3133	216	17	that	that	DET
ejpam-3133	216	18	gb(q	gb(q	NOUN
ejpam-3133	216	19	,	,	PUNCT
ejpam-3133	216	20	gu	gu	NOUN
ejpam-3133	216	21	,	,	PUNCT
ejpam-3133	216	22	q	q	NOUN
ejpam-3133	216	23	)	)	PUNCT
ejpam-3133	216	24	=	=	SYM
ejpam-3133	216	25	0	0	NUM
ejpam-3133	216	26	,	,	PUNCT
ejpam-3133	216	27	which	which	PRON
ejpam-3133	216	28	implies	imply	VERB
ejpam-3133	216	29	that	that	PRON
ejpam-3133	216	30	gu	gu	NOUN
ejpam-3133	216	31	=	=	PUNCT
ejpam-3133	216	32	q.	q.	PROPN
ejpam-3133	216	33	but	but	CCONJ
ejpam-3133	216	34	g(x	g(x	NOUN
ejpam-3133	216	35	)	)	PUNCT
ejpam-3133	216	36	⊆	⊆	NUM
ejpam-3133	216	37	s(x	s(x	NOUN
ejpam-3133	216	38	)	)	PUNCT
ejpam-3133	216	39	,	,	PUNCT
ejpam-3133	216	40	so	so	CCONJ
ejpam-3133	216	41	there	there	PRON
ejpam-3133	216	42	exists	exist	VERB
ejpam-3133	216	43	a	a	DET
ejpam-3133	216	44	point	point	NOUN
ejpam-3133	216	45	p	p	X
ejpam-3133	216	46	∈	∈	PROPN
ejpam-3133	216	47	x	x	PUNCT
ejpam-3133	216	48	such	such	ADJ
ejpam-3133	216	49	that	that	DET
ejpam-3133	216	50	gu	gu	NOUN
ejpam-3133	216	51	=	=	NOUN
ejpam-3133	216	52	sp	sp	PROPN
ejpam-3133	216	53	=	=	NOUN
ejpam-3133	216	54	q.	q.	NOUN
ejpam-3133	216	55	we	we	PRON
ejpam-3133	216	56	shall	shall	AUX
ejpam-3133	216	57	show	show	VERB
ejpam-3133	216	58	that	that	SCONJ
ejpam-3133	216	59	fp	fp	PROPN
ejpam-3133	216	60	=	=	PUNCT
ejpam-3133	216	61	q.	q.	PROPN
ejpam-3133	216	62	now	now	ADV
ejpam-3133	216	63	m(p	m(p	PROPN
ejpam-3133	216	64	,	,	PUNCT
ejpam-3133	216	65	u	u	NOUN
ejpam-3133	216	66	,	,	PUNCT
ejpam-3133	216	67	zn	zn	NOUN
ejpam-3133	216	68	)	)	PUNCT
ejpam-3133	216	69	=	=	SYM
ejpam-3133	216	70	max	max	PROPN
ejpam-3133	216	71	{	{	PUNCT
ejpam-3133	216	72	gb(fp	gb(fp	PROPN
ejpam-3133	216	73	,	,	PUNCT
ejpam-3133	216	74	sp	sp	NOUN
ejpam-3133	216	75	,	,	PUNCT
ejpam-3133	216	76	tzn	tzn	PROPN
ejpam-3133	216	77	)	)	PUNCT
ejpam-3133	216	78	,	,	PUNCT
ejpam-3133	216	79	gb(gu	gb(gu	PROPN
ejpam-3133	216	80	,	,	PUNCT
ejpam-3133	216	81	ru	ru	PROPN
ejpam-3133	216	82	,	,	PUNCT
ejpam-3133	216	83	ru	ru	NOUN
ejpam-3133	216	84	)	)	PUNCT
ejpam-3133	216	85	,	,	PUNCT
ejpam-3133	216	86	gb(fp	gb(fp	PROPN
ejpam-3133	216	87	,	,	PUNCT
ejpam-3133	216	88	fp	fp	X
ejpam-3133	216	89	,	,	PUNCT
ejpam-3133	216	90	hzn	hzn	NOUN
ejpam-3133	216	91	)	)	PUNCT
ejpam-3133	216	92	,	,	PUNCT
ejpam-3133	216	93	gb(tzn	gb(tzn	PROPN
ejpam-3133	216	94	,	,	PUNCT
ejpam-3133	216	95	t	t	PROPN
ejpam-3133	216	96	zn	zn	NUM
ejpam-3133	216	97	,	,	PUNCT
ejpam-3133	216	98	hzn	hzn	NOUN
ejpam-3133	216	99	)	)	PUNCT
ejpam-3133	217	1	+	+	ADV
ejpam-3133	217	2	gb(fp	gb(fp	ADJ
ejpam-3133	217	3	,	,	PUNCT
ejpam-3133	217	4	sp	sp	NOUN
ejpam-3133	217	5	,	,	PUNCT
ejpam-3133	217	6	sp	sp	NOUN
ejpam-3133	217	7	)	)	PUNCT
ejpam-3133	217	8	2s	2s	NOUN
ejpam-3133	217	9	}	}	PUNCT
ejpam-3133	217	10	,	,	PUNCT
ejpam-3133	217	11	=	=	SYM
ejpam-3133	217	12	max	max	X
ejpam-3133	217	13	{	{	PUNCT
ejpam-3133	217	14	gb(fp	gb(fp	PROPN
ejpam-3133	217	15	,	,	PUNCT
ejpam-3133	217	16	q	q	NOUN
ejpam-3133	217	17	,	,	PUNCT
ejpam-3133	217	18	tzn	tzn	PROPN
ejpam-3133	217	19	)	)	PUNCT
ejpam-3133	217	20	,	,	PUNCT
ejpam-3133	217	21	gb(q	gb(q	PROPN
ejpam-3133	217	22	,	,	PUNCT
ejpam-3133	217	23	q	q	NOUN
ejpam-3133	217	24	,	,	PUNCT
ejpam-3133	217	25	q	q	NOUN
ejpam-3133	217	26	)	)	PUNCT
ejpam-3133	217	27	,	,	PUNCT
ejpam-3133	217	28	gb(fp	gb(fp	PROPN
ejpam-3133	217	29	,	,	PUNCT
ejpam-3133	217	30	fp	fp	X
ejpam-3133	217	31	,	,	PUNCT
ejpam-3133	217	32	hzn	hzn	NOUN
ejpam-3133	217	33	)	)	PUNCT
ejpam-3133	217	34	,	,	PUNCT
ejpam-3133	217	35	gb(tzn	gb(tzn	PROPN
ejpam-3133	217	36	,	,	PUNCT
ejpam-3133	217	37	t	t	PROPN
ejpam-3133	217	38	zn	zn	NUM
ejpam-3133	217	39	,	,	PUNCT
ejpam-3133	217	40	hzn	hzn	NOUN
ejpam-3133	217	41	)	)	PUNCT
ejpam-3133	218	1	+	+	ADV
ejpam-3133	218	2	gb(fp	gb(fp	ADJ
ejpam-3133	218	3	,	,	PUNCT
ejpam-3133	218	4	q	q	NOUN
ejpam-3133	218	5	,	,	PUNCT
ejpam-3133	218	6	q	q	X
ejpam-3133	218	7	)	)	PUNCT
ejpam-3133	218	8	2s	2s	NOUN
ejpam-3133	218	9	}	}	PUNCT
ejpam-3133	218	10	=	=	SYM
ejpam-3133	218	11	max	max	X
ejpam-3133	218	12	{	{	PUNCT
ejpam-3133	218	13	gb(fp	gb(fp	PROPN
ejpam-3133	218	14	,	,	PUNCT
ejpam-3133	218	15	q	q	NOUN
ejpam-3133	218	16	,	,	PUNCT
ejpam-3133	218	17	tzn	tzn	PROPN
ejpam-3133	218	18	)	)	PUNCT
ejpam-3133	218	19	,	,	PUNCT
ejpam-3133	218	20	gb(fp	gb(fp	PROPN
ejpam-3133	218	21	,	,	PUNCT
ejpam-3133	218	22	fp	fp	X
ejpam-3133	218	23	,	,	PUNCT
ejpam-3133	218	24	hzn	hzn	NOUN
ejpam-3133	218	25	)	)	PUNCT
ejpam-3133	218	26	,	,	PUNCT
ejpam-3133	218	27	gb(tzn	gb(tzn	PROPN
ejpam-3133	218	28	,	,	PUNCT
ejpam-3133	218	29	t	t	PROPN
ejpam-3133	218	30	zn	zn	NUM
ejpam-3133	218	31	,	,	PUNCT
ejpam-3133	218	32	hzn	hzn	NOUN
ejpam-3133	218	33	)	)	PUNCT
ejpam-3133	219	1	+	+	ADV
ejpam-3133	219	2	gb(fp	gb(fp	ADJ
ejpam-3133	219	3	,	,	PUNCT
ejpam-3133	219	4	q	q	NOUN
ejpam-3133	219	5	,	,	PUNCT
ejpam-3133	219	6	q	q	X
ejpam-3133	219	7	)	)	PUNCT
ejpam-3133	219	8	2s	2s	NOUN
ejpam-3133	219	9	}	}	PUNCT
ejpam-3133	219	10	(	(	PUNCT
ejpam-3133	219	11	21	21	NUM
ejpam-3133	219	12	)	)	PUNCT
ejpam-3133	219	13	≤	≤	NUM
ejpam-3133	219	14	max	max	NOUN
ejpam-3133	219	15	{	{	PUNCT
ejpam-3133	219	16	gb(fp	gb(fp	PROPN
ejpam-3133	219	17	,	,	PUNCT
ejpam-3133	219	18	q	q	NOUN
ejpam-3133	219	19	,	,	PUNCT
ejpam-3133	219	20	tzn	tzn	PROPN
ejpam-3133	219	21	)	)	PUNCT
ejpam-3133	219	22	,	,	PUNCT
ejpam-3133	220	1	gb(fp	gb(fp	PROPN
ejpam-3133	220	2	,	,	PUNCT
ejpam-3133	220	3	tzn	tzn	PROPN
ejpam-3133	220	4	,	,	PUNCT
ejpam-3133	220	5	hzn	hzn	NOUN
ejpam-3133	220	6	)	)	PUNCT
ejpam-3133	220	7	,	,	PUNCT
ejpam-3133	220	8	gb(fp	gb(fp	PROPN
ejpam-3133	220	9	,	,	PUNCT
ejpam-3133	220	10	tzn	tzn	PROPN
ejpam-3133	220	11	,	,	PUNCT
ejpam-3133	220	12	hzn	hzn	NOUN
ejpam-3133	220	13	)	)	PUNCT
ejpam-3133	221	1	+	+	ADV
ejpam-3133	221	2	gb(fp	gb(fp	ADJ
ejpam-3133	221	3	,	,	PUNCT
ejpam-3133	221	4	q	q	NOUN
ejpam-3133	221	5	,	,	PUNCT
ejpam-3133	221	6	tzn	tzn	ADJ
ejpam-3133	221	7	)	)	PUNCT
ejpam-3133	221	8	2s	2s	PROPN
ejpam-3133	221	9	}	}	PUNCT
ejpam-3133	221	10	,	,	PUNCT
ejpam-3133	221	11	≤	≤	NUM
ejpam-3133	221	12	max	max	X
ejpam-3133	221	13	{	{	PUNCT
ejpam-3133	221	14	gb(fp	gb(fp	PROPN
ejpam-3133	221	15	,	,	PUNCT
ejpam-3133	221	16	q	q	NOUN
ejpam-3133	221	17	,	,	PUNCT
ejpam-3133	221	18	tzn	tzn	PROPN
ejpam-3133	221	19	)	)	PUNCT
ejpam-3133	221	20	,	,	PUNCT
ejpam-3133	221	21	gb(fp	gb(fp	PROPN
ejpam-3133	221	22	,	,	PUNCT
ejpam-3133	221	23	tzn	tzn	PROPN
ejpam-3133	221	24	,	,	PUNCT
ejpam-3133	221	25	hzn	hzn	NOUN
ejpam-3133	221	26	)	)	PUNCT
ejpam-3133	221	27	}	}	PUNCT
ejpam-3133	221	28	.	.	PUNCT
ejpam-3133	222	1	(	(	PUNCT
ejpam-3133	222	2	22	22	NUM
ejpam-3133	222	3	)	)	PUNCT
ejpam-3133	222	4	now	now	ADV
ejpam-3133	222	5	,	,	PUNCT
ejpam-3133	222	6	taking	take	VERB
ejpam-3133	222	7	the	the	DET
ejpam-3133	222	8	limit	limit	NOUN
ejpam-3133	222	9	superior	superior	ADJ
ejpam-3133	222	10	in	in	ADP
ejpam-3133	222	11	(	(	PUNCT
ejpam-3133	222	12	22	22	NUM
ejpam-3133	222	13	)	)	PUNCT
ejpam-3133	222	14	as	as	ADP
ejpam-3133	222	15	n	n	PROPN
ejpam-3133	222	16	→	→	SYM
ejpam-3133	222	17	∞	∞	NUM
ejpam-3133	222	18	and	and	CCONJ
ejpam-3133	222	19	using	use	VERB
ejpam-3133	222	20	lemma	lemma	PROPN
ejpam-3133	222	21	1	1	NUM
ejpam-3133	222	22	,	,	PUNCT
ejpam-3133	222	23	parts	part	NOUN
ejpam-3133	222	24	(	(	PUNCT
ejpam-3133	222	25	2	2	NUM
ejpam-3133	222	26	)	)	PUNCT
ejpam-3133	222	27	and	and	CCONJ
ejpam-3133	222	28	(	(	PUNCT
ejpam-3133	222	29	3	3	NUM
ejpam-3133	222	30	)	)	PUNCT
ejpam-3133	222	31	,	,	PUNCT
ejpam-3133	222	32	we	we	PRON
ejpam-3133	222	33	obtain	obtain	VERB
ejpam-3133	222	34	lim	lim	PROPN
ejpam-3133	222	35	sup	sup	X
ejpam-3133	222	36	n→∞	n→∞	NUM
ejpam-3133	223	1	m(p	m(p	PROPN
ejpam-3133	223	2	,	,	PUNCT
ejpam-3133	223	3	u	u	NOUN
ejpam-3133	223	4	,	,	PUNCT
ejpam-3133	223	5	zn	zn	NOUN
ejpam-3133	223	6	)	)	PUNCT
ejpam-3133	223	7	=	=	SYM
ejpam-3133	223	8	lim	lim	PROPN
ejpam-3133	223	9	sup	sup	VERB
ejpam-3133	223	10	n→∞	n→∞	PRON
ejpam-3133	223	11	max	max	NOUN
ejpam-3133	223	12	{	{	PUNCT
ejpam-3133	223	13	gb(fp	gb(fp	PROPN
ejpam-3133	223	14	,	,	PUNCT
ejpam-3133	223	15	q	q	NOUN
ejpam-3133	223	16	,	,	PUNCT
ejpam-3133	223	17	tzn	tzn	PROPN
ejpam-3133	223	18	)	)	PUNCT
ejpam-3133	223	19	,	,	PUNCT
ejpam-3133	223	20	gb(fp	gb(fp	PROPN
ejpam-3133	223	21	,	,	PUNCT
ejpam-3133	223	22	tzn	tzn	PROPN
ejpam-3133	223	23	,	,	PUNCT
ejpam-3133	223	24	hzn	hzn	NOUN
ejpam-3133	223	25	)	)	PUNCT
ejpam-3133	223	26	}	}	PUNCT
ejpam-3133	224	1	=	=	SYM
ejpam-3133	224	2	max	max	PROPN
ejpam-3133	224	3	{	{	PUNCT
ejpam-3133	224	4	lim	lim	PROPN
ejpam-3133	224	5	sup	sup	NOUN
ejpam-3133	224	6	n→∞	n→∞	X
ejpam-3133	224	7	gb(fp	gb(fp	NOUN
ejpam-3133	224	8	,	,	PUNCT
ejpam-3133	224	9	q	q	X
ejpam-3133	224	10	,	,	PUNCT
ejpam-3133	224	11	tzn	tzn	PROPN
ejpam-3133	224	12	)	)	PUNCT
ejpam-3133	224	13	,	,	PUNCT
ejpam-3133	224	14	lim	lim	PROPN
ejpam-3133	224	15	sup	sup	VERB
ejpam-3133	224	16	n→∞	n→∞	X
ejpam-3133	224	17	gb(fp	gb(fp	NOUN
ejpam-3133	224	18	,	,	PUNCT
ejpam-3133	224	19	tzn	tzn	PROPN
ejpam-3133	224	20	,	,	PUNCT
ejpam-3133	224	21	hzn	hzn	NOUN
ejpam-3133	224	22	)	)	PUNCT
ejpam-3133	224	23	}	}	PUNCT
ejpam-3133	224	24	≤	≤	NOUN
ejpam-3133	224	25	max{sgb(fp	max{sgb(fp	NUM
ejpam-3133	224	26	,	,	PUNCT
ejpam-3133	224	27	q	q	NOUN
ejpam-3133	224	28	,	,	PUNCT
ejpam-3133	224	29	q	q	NOUN
ejpam-3133	224	30	)	)	PUNCT
ejpam-3133	224	31	,	,	PUNCT
ejpam-3133	224	32	s2gb(fp	s2gb(fp	NOUN
ejpam-3133	224	33	,	,	PUNCT
ejpam-3133	224	34	q	q	X
ejpam-3133	224	35	,	,	PUNCT
ejpam-3133	224	36	q	q	NOUN
ejpam-3133	224	37	)	)	PUNCT
ejpam-3133	224	38	}	}	PUNCT
ejpam-3133	224	39	=	=	SYM
ejpam-3133	224	40	s2gb(fp	s2gb(fp	NOUN
ejpam-3133	224	41	,	,	PUNCT
ejpam-3133	224	42	q	q	X
ejpam-3133	224	43	,	,	PUNCT
ejpam-3133	224	44	q	q	NOUN
ejpam-3133	224	45	)	)	PUNCT
ejpam-3133	224	46	.	.	PUNCT
ejpam-3133	225	1	(	(	PUNCT
ejpam-3133	225	2	23	23	NUM
ejpam-3133	225	3	)	)	PUNCT
ejpam-3133	225	4	now	now	ADV
ejpam-3133	225	5	,	,	PUNCT
ejpam-3133	225	6	taking	take	VERB
ejpam-3133	225	7	the	the	DET
ejpam-3133	225	8	limit	limit	NOUN
ejpam-3133	225	9	infimum	infimum	ADV
ejpam-3133	225	10	in	in	ADP
ejpam-3133	225	11	(	(	PUNCT
ejpam-3133	225	12	21	21	NUM
ejpam-3133	225	13	)	)	PUNCT
ejpam-3133	225	14	as	as	ADP
ejpam-3133	225	15	n	n	PROPN
ejpam-3133	225	16	→	→	SYM
ejpam-3133	225	17	∞	∞	NUM
ejpam-3133	225	18	and	and	CCONJ
ejpam-3133	225	19	using	use	VERB
ejpam-3133	225	20	lemma	lemma	PROPN
ejpam-3133	225	21	1	1	NUM
ejpam-3133	225	22	,	,	PUNCT
ejpam-3133	225	23	parts	part	NOUN
ejpam-3133	225	24	(	(	PUNCT
ejpam-3133	225	25	2	2	NUM
ejpam-3133	225	26	)	)	PUNCT
ejpam-3133	225	27	and	and	CCONJ
ejpam-3133	225	28	(	(	PUNCT
ejpam-3133	225	29	3	3	NUM
ejpam-3133	225	30	)	)	PUNCT
ejpam-3133	225	31	,	,	PUNCT
ejpam-3133	225	32	we	we	PRON
ejpam-3133	225	33	get	get	VERB
ejpam-3133	225	34	lim	lim	PROPN
ejpam-3133	225	35	inf	inf	PROPN
ejpam-3133	225	36	n→∞	n→∞	X
ejpam-3133	226	1	m(p	m(p	PROPN
ejpam-3133	226	2	,	,	PUNCT
ejpam-3133	226	3	u	u	NOUN
ejpam-3133	226	4	,	,	PUNCT
ejpam-3133	226	5	zn	zn	NOUN
ejpam-3133	226	6	)	)	PUNCT
ejpam-3133	226	7	=	=	SYM
ejpam-3133	226	8	lim	lim	PROPN
ejpam-3133	226	9	inf	inf	PROPN
ejpam-3133	226	10	n→∞	n→∞	NUM
ejpam-3133	226	11	max	max	PROPN
ejpam-3133	226	12	{	{	PUNCT
ejpam-3133	226	13	gb(fp	gb(fp	PROPN
ejpam-3133	226	14	,	,	PUNCT
ejpam-3133	226	15	q	q	NOUN
ejpam-3133	226	16	,	,	PUNCT
ejpam-3133	226	17	tzn	tzn	PROPN
ejpam-3133	226	18	)	)	PUNCT
ejpam-3133	226	19	,	,	PUNCT
ejpam-3133	226	20	gb(fp	gb(fp	PROPN
ejpam-3133	226	21	,	,	PUNCT
ejpam-3133	226	22	fp	fp	X
ejpam-3133	226	23	,	,	PUNCT
ejpam-3133	226	24	hzn	hzn	NOUN
ejpam-3133	226	25	)	)	PUNCT
ejpam-3133	226	26	,	,	PUNCT
ejpam-3133	226	27	gb(tzn	gb(tzn	PROPN
ejpam-3133	226	28	,	,	PUNCT
ejpam-3133	226	29	t	t	PROPN
ejpam-3133	226	30	zn	zn	NUM
ejpam-3133	226	31	,	,	PUNCT
ejpam-3133	226	32	hzn	hzn	NOUN
ejpam-3133	226	33	)	)	PUNCT
ejpam-3133	227	1	+	+	ADV
ejpam-3133	227	2	gb(fp	gb(fp	ADJ
ejpam-3133	227	3	,	,	PUNCT
ejpam-3133	227	4	q	q	NOUN
ejpam-3133	227	5	,	,	PUNCT
ejpam-3133	227	6	q	q	X
ejpam-3133	227	7	)	)	PUNCT
ejpam-3133	227	8	2s	2s	NOUN
ejpam-3133	227	9	}	}	PUNCT
ejpam-3133	227	10	=	=	SYM
ejpam-3133	227	11	max	max	PROPN
ejpam-3133	227	12	{	{	PUNCT
ejpam-3133	227	13	lim	lim	PROPN
ejpam-3133	227	14	inf	inf	PROPN
ejpam-3133	227	15	n→∞	n→∞	X
ejpam-3133	228	1	gb(fp	gb(fp	NOUN
ejpam-3133	228	2	,	,	PUNCT
ejpam-3133	228	3	q	q	X
ejpam-3133	228	4	,	,	PUNCT
ejpam-3133	228	5	tzn	tzn	PROPN
ejpam-3133	228	6	)	)	PUNCT
ejpam-3133	228	7	,	,	PUNCT
ejpam-3133	228	8	lim	lim	PROPN
ejpam-3133	228	9	inf	inf	PROPN
ejpam-3133	228	10	n→∞	n→∞	X
ejpam-3133	229	1	gb(fp	gb(fp	NOUN
ejpam-3133	229	2	,	,	PUNCT
ejpam-3133	229	3	fp	fp	X
ejpam-3133	229	4	,	,	PUNCT
ejpam-3133	229	5	hzn	hzn	NOUN
ejpam-3133	229	6	)	)	PUNCT
ejpam-3133	229	7	,	,	PUNCT
ejpam-3133	229	8	lim	lim	PROPN
ejpam-3133	229	9	infn→∞gb(tzn	infn→∞gb(tzn	PROPN
ejpam-3133	229	10	,	,	PUNCT
ejpam-3133	229	11	t	t	PROPN
ejpam-3133	229	12	zn	zn	NUM
ejpam-3133	229	13	,	,	PUNCT
ejpam-3133	229	14	hzn	hzn	PROPN
ejpam-3133	229	15	)	)	PUNCT
ejpam-3133	229	16	+	+	CCONJ
ejpam-3133	229	17	lim	lim	PROPN
ejpam-3133	229	18	infn→∞gb(fp	infn→∞gb(fp	PROPN
ejpam-3133	229	19	,	,	PUNCT
ejpam-3133	229	20	q	q	X
ejpam-3133	229	21	,	,	PUNCT
ejpam-3133	229	22	q	q	X
ejpam-3133	229	23	)	)	PUNCT
ejpam-3133	229	24	2s	2s	NOUN
ejpam-3133	229	25	}	}	PUNCT
ejpam-3133	229	26	z.	z.	PROPN
ejpam-3133	229	27	mustafa	mustafa	PROPN
ejpam-3133	229	28	et	et	PROPN
ejpam-3133	229	29	al	al	PROPN
ejpam-3133	229	30	.	.	PUNCT
ejpam-3133	229	31	/	/	SYM
ejpam-3133	229	32	eur	eur	PROPN
ejpam-3133	229	33	.	.	PUNCT
ejpam-3133	230	1	j.	j.	PROPN
ejpam-3133	230	2	pure	pure	PROPN
ejpam-3133	230	3	appl	appl	PROPN
ejpam-3133	230	4	.	.	PROPN
ejpam-3133	230	5	math	math	PROPN
ejpam-3133	230	6	,	,	PUNCT
ejpam-3133	230	7	11	11	NUM
ejpam-3133	230	8	(	(	PUNCT
ejpam-3133	230	9	1	1	NUM
ejpam-3133	230	10	)	)	PUNCT
ejpam-3133	230	11	(	(	PUNCT
ejpam-3133	230	12	2018	2018	NUM
ejpam-3133	230	13	)	)	PUNCT
ejpam-3133	230	14	,	,	PUNCT
ejpam-3133	230	15	90	90	NUM
ejpam-3133	230	16	-	-	SYM
ejpam-3133	230	17	109	109	NUM
ejpam-3133	230	18	99	99	NUM
ejpam-3133	230	19	≥	≥	NOUN
ejpam-3133	230	20	max{1	max{1	NOUN
ejpam-3133	230	21	s	s	PART
ejpam-3133	230	22	gb(fp	gb(fp	NOUN
ejpam-3133	230	23	,	,	PUNCT
ejpam-3133	230	24	q	q	X
ejpam-3133	230	25	,	,	PUNCT
ejpam-3133	230	26	q	q	NOUN
ejpam-3133	230	27	)	)	PUNCT
ejpam-3133	230	28	,	,	PUNCT
ejpam-3133	230	29	1	1	NUM
ejpam-3133	230	30	s	s	VERB
ejpam-3133	230	31	gb(fp	gb(fp	NOUN
ejpam-3133	230	32	,	,	PUNCT
ejpam-3133	230	33	fp	fp	NOUN
ejpam-3133	230	34	,	,	PUNCT
ejpam-3133	230	35	q	q	NOUN
ejpam-3133	230	36	)	)	PUNCT
ejpam-3133	230	37	,	,	PUNCT
ejpam-3133	230	38	gb(fp	gb(fp	PROPN
ejpam-3133	230	39	,	,	PUNCT
ejpam-3133	230	40	q	q	X
ejpam-3133	230	41	,	,	PUNCT
ejpam-3133	230	42	q	q	X
ejpam-3133	230	43	)	)	PUNCT
ejpam-3133	230	44	2s	2s	NOUN
ejpam-3133	230	45	}	}	PUNCT
ejpam-3133	230	46	=	=	SYM
ejpam-3133	230	47	max{1	max{1	NOUN
ejpam-3133	230	48	s	s	PART
ejpam-3133	230	49	gb(fp	gb(fp	NOUN
ejpam-3133	230	50	,	,	PUNCT
ejpam-3133	230	51	q	q	X
ejpam-3133	230	52	,	,	PUNCT
ejpam-3133	230	53	q	q	NOUN
ejpam-3133	230	54	)	)	PUNCT
ejpam-3133	230	55	,	,	PUNCT
ejpam-3133	230	56	1	1	NUM
ejpam-3133	230	57	s	s	VERB
ejpam-3133	230	58	gb(fp	gb(fp	NOUN
ejpam-3133	230	59	,	,	PUNCT
ejpam-3133	230	60	fp	fp	NOUN
ejpam-3133	230	61	,	,	PUNCT
ejpam-3133	230	62	q	q	NOUN
ejpam-3133	230	63	)	)	PUNCT
ejpam-3133	230	64	}	}	PUNCT
ejpam-3133	230	65	.	.	PUNCT
ejpam-3133	231	1	(	(	PUNCT
ejpam-3133	231	2	24	24	NUM
ejpam-3133	231	3	)	)	PUNCT
ejpam-3133	231	4	thus	thus	ADV
ejpam-3133	231	5	,	,	PUNCT
ejpam-3133	231	6	from	from	ADP
ejpam-3133	231	7	(	(	PUNCT
ejpam-3133	231	8	3	3	NUM
ejpam-3133	231	9	)	)	PUNCT
ejpam-3133	231	10	,	,	PUNCT
ejpam-3133	231	11	(	(	PUNCT
ejpam-3133	231	12	gb3	gb3	NOUN
ejpam-3133	231	13	)	)	PUNCT
ejpam-3133	231	14	and	and	CCONJ
ejpam-3133	231	15	the	the	DET
ejpam-3133	231	16	fact	fact	NOUN
ejpam-3133	231	17	that	that	SCONJ
ejpam-3133	231	18	ψ	ψ	PROPN
ejpam-3133	231	19	and	and	CCONJ
ejpam-3133	231	20	φ	φ	PROPN
ejpam-3133	231	21	are	be	AUX
ejpam-3133	231	22	increasing	increase	VERB
ejpam-3133	231	23	,	,	PUNCT
ejpam-3133	231	24	we	we	PRON
ejpam-3133	231	25	have	have	VERB
ejpam-3133	231	26	ψ	ψ	X
ejpam-3133	231	27	(	(	PUNCT
ejpam-3133	231	28	s2gb(fp	s2gb(fp	NOUN
ejpam-3133	231	29	,	,	PUNCT
ejpam-3133	231	30	q	q	X
ejpam-3133	231	31	,	,	PUNCT
ejpam-3133	231	32	q	q	NOUN
ejpam-3133	231	33	)	)	PUNCT
ejpam-3133	231	34	)	)	PUNCT
ejpam-3133	232	1	≤	≤	NUM
ejpam-3133	233	1	ψ	ψ	X
ejpam-3133	233	2	(	(	PUNCT
ejpam-3133	233	3	s2gb(fp	s2gb(fp	NOUN
ejpam-3133	233	4	,	,	PUNCT
ejpam-3133	233	5	q	q	NOUN
ejpam-3133	233	6	,	,	PUNCT
ejpam-3133	233	7	hzn	hzn	NOUN
ejpam-3133	233	8	)	)	PUNCT
ejpam-3133	233	9	)	)	PUNCT
ejpam-3133	234	1	=	=	SYM
ejpam-3133	234	2	ψ	ψ	X
ejpam-3133	234	3	(	(	PUNCT
ejpam-3133	234	4	s2gb(fp	s2gb(fp	PROPN
ejpam-3133	234	5	,	,	PUNCT
ejpam-3133	234	6	gu	gu	PROPN
ejpam-3133	234	7	,	,	PUNCT
ejpam-3133	234	8	hzn	hzn	NOUN
ejpam-3133	234	9	)	)	PUNCT
ejpam-3133	234	10	)	)	PUNCT
ejpam-3133	235	1	≤	≤	NUM
ejpam-3133	235	2	ψ	ψ	X
ejpam-3133	235	3	(	(	PUNCT
ejpam-3133	235	4	m(p	m(p	PROPN
ejpam-3133	235	5	,	,	PUNCT
ejpam-3133	235	6	u	u	NOUN
ejpam-3133	235	7	,	,	PUNCT
ejpam-3133	235	8	zn	zn	PROPN
ejpam-3133	235	9	)	)	PUNCT
ejpam-3133	235	10	)	)	PUNCT
ejpam-3133	236	1	−	−	PROPN
ejpam-3133	236	2	φ	φ	PROPN
ejpam-3133	236	3	(	(	PUNCT
ejpam-3133	236	4	m(p	m(p	PROPN
ejpam-3133	236	5	,	,	PUNCT
ejpam-3133	236	6	u	u	NOUN
ejpam-3133	236	7	,	,	PUNCT
ejpam-3133	236	8	zn	zn	PROPN
ejpam-3133	236	9	)	)	PUNCT
ejpam-3133	236	10	)	)	PUNCT
ejpam-3133	236	11	.	.	PUNCT
ejpam-3133	237	1	(	(	PUNCT
ejpam-3133	237	2	25	25	NUM
ejpam-3133	237	3	)	)	PUNCT
ejpam-3133	237	4	therefore	therefore	ADV
ejpam-3133	237	5	,	,	PUNCT
ejpam-3133	237	6	by	by	ADP
ejpam-3133	237	7	taking	take	VERB
ejpam-3133	237	8	the	the	DET
ejpam-3133	237	9	limit	limit	NOUN
ejpam-3133	237	10	superior	superior	ADJ
ejpam-3133	237	11	in	in	ADP
ejpam-3133	237	12	(	(	PUNCT
ejpam-3133	237	13	25	25	NUM
ejpam-3133	237	14	)	)	PUNCT
ejpam-3133	237	15	as	as	ADP
ejpam-3133	237	16	n→∞	n→∞	NUM
ejpam-3133	237	17	and	and	CCONJ
ejpam-3133	237	18	using	use	VERB
ejpam-3133	237	19	(	(	PUNCT
ejpam-3133	237	20	23	23	NUM
ejpam-3133	237	21	)	)	PUNCT
ejpam-3133	237	22	and	and	CCONJ
ejpam-3133	237	23	(	(	PUNCT
ejpam-3133	237	24	24	24	NUM
ejpam-3133	237	25	)	)	PUNCT
ejpam-3133	237	26	,	,	PUNCT
ejpam-3133	237	27	ψ	ψ	X
ejpam-3133	237	28	(	(	PUNCT
ejpam-3133	237	29	s2gb(fp	s2gb(fp	NOUN
ejpam-3133	237	30	,	,	PUNCT
ejpam-3133	237	31	q	q	X
ejpam-3133	237	32	,	,	PUNCT
ejpam-3133	237	33	q	q	NOUN
ejpam-3133	237	34	)	)	PUNCT
ejpam-3133	237	35	)	)	PUNCT
ejpam-3133	237	36	≤	≤	NUM
ejpam-3133	237	37	ψ	ψ	X
ejpam-3133	237	38	(	(	PUNCT
ejpam-3133	237	39	lim	lim	PROPN
ejpam-3133	237	40	sup	sup	NOUN
ejpam-3133	237	41	n→∞	n→∞	NUM
ejpam-3133	237	42	m(p	m(p	PROPN
ejpam-3133	237	43	,	,	PUNCT
ejpam-3133	237	44	u	u	NOUN
ejpam-3133	237	45	,	,	PUNCT
ejpam-3133	237	46	zn	zn	PROPN
ejpam-3133	237	47	)	)	PUNCT
ejpam-3133	237	48	)	)	PUNCT
ejpam-3133	238	1	−	−	PROPN
ejpam-3133	239	1	φ	φ	PROPN
ejpam-3133	239	2	(	(	PUNCT
ejpam-3133	239	3	lim	lim	PROPN
ejpam-3133	239	4	inf	inf	PROPN
ejpam-3133	239	5	n→∞	n→∞	X
ejpam-3133	240	1	m(p	m(p	PROPN
ejpam-3133	240	2	,	,	PUNCT
ejpam-3133	240	3	u	u	NOUN
ejpam-3133	240	4	,	,	PUNCT
ejpam-3133	240	5	zn	zn	PROPN
ejpam-3133	240	6	)	)	PUNCT
ejpam-3133	240	7	)	)	PUNCT
ejpam-3133	241	1	,	,	PUNCT
ejpam-3133	241	2	≤	≤	NUM
ejpam-3133	241	3	ψ	ψ	X
ejpam-3133	241	4	(	(	PUNCT
ejpam-3133	241	5	s2gb(fp	s2gb(fp	NOUN
ejpam-3133	241	6	,	,	PUNCT
ejpam-3133	241	7	q	q	X
ejpam-3133	241	8	,	,	PUNCT
ejpam-3133	241	9	q	q	NOUN
ejpam-3133	241	10	)	)	PUNCT
ejpam-3133	241	11	)	)	PUNCT
ejpam-3133	242	1	−	−	PROPN
ejpam-3133	242	2	φ	φ	PROPN
ejpam-3133	242	3	(	(	PUNCT
ejpam-3133	242	4	max{1	max{1	NOUN
ejpam-3133	242	5	s	s	PART
ejpam-3133	242	6	gb(fp	gb(fp	NOUN
ejpam-3133	242	7	,	,	PUNCT
ejpam-3133	242	8	q	q	X
ejpam-3133	242	9	,	,	PUNCT
ejpam-3133	242	10	q	q	NOUN
ejpam-3133	242	11	)	)	PUNCT
ejpam-3133	242	12	,	,	PUNCT
ejpam-3133	242	13	1	1	NUM
ejpam-3133	242	14	s	s	VERB
ejpam-3133	242	15	gb(fp	gb(fp	NOUN
ejpam-3133	242	16	,	,	PUNCT
ejpam-3133	242	17	fp	fp	NOUN
ejpam-3133	242	18	,	,	PUNCT
ejpam-3133	242	19	q	q	NOUN
ejpam-3133	242	20	)	)	PUNCT
ejpam-3133	242	21	}	}	PUNCT
ejpam-3133	242	22	)	)	PUNCT
ejpam-3133	242	23	,	,	PUNCT
ejpam-3133	242	24	.	.	PUNCT
ejpam-3133	243	1	(	(	PUNCT
ejpam-3133	243	2	26	26	NUM
ejpam-3133	243	3	)	)	PUNCT
ejpam-3133	243	4	so	so	ADV
ejpam-3133	243	5	,	,	PUNCT
ejpam-3133	243	6	φ	φ	PROPN
ejpam-3133	243	7	(	(	PUNCT
ejpam-3133	243	8	max{1	max{1	NOUN
ejpam-3133	243	9	s	s	PART
ejpam-3133	243	10	gb(fp	gb(fp	NOUN
ejpam-3133	243	11	,	,	PUNCT
ejpam-3133	243	12	q	q	X
ejpam-3133	243	13	,	,	PUNCT
ejpam-3133	243	14	q	q	NOUN
ejpam-3133	243	15	)	)	PUNCT
ejpam-3133	243	16	,	,	PUNCT
ejpam-3133	243	17	1	1	NUM
ejpam-3133	243	18	s	s	VERB
ejpam-3133	243	19	gb(fp	gb(fp	NOUN
ejpam-3133	243	20	,	,	PUNCT
ejpam-3133	243	21	fp	fp	NOUN
ejpam-3133	243	22	,	,	PUNCT
ejpam-3133	243	23	q	q	NOUN
ejpam-3133	243	24	)	)	PUNCT
ejpam-3133	243	25	}	}	PUNCT
ejpam-3133	243	26	)	)	PUNCT
ejpam-3133	244	1	=	=	SYM
ejpam-3133	244	2	0	0	NUM
ejpam-3133	244	3	,	,	PUNCT
ejpam-3133	244	4	or	or	CCONJ
ejpam-3133	244	5	equivalently	equivalently	ADV
ejpam-3133	244	6	,	,	PUNCT
ejpam-3133	244	7	max{1	max{1	NOUN
ejpam-3133	244	8	s	s	PART
ejpam-3133	244	9	gb(fp	gb(fp	NOUN
ejpam-3133	244	10	,	,	PUNCT
ejpam-3133	244	11	q	q	X
ejpam-3133	244	12	,	,	PUNCT
ejpam-3133	244	13	q	q	NOUN
ejpam-3133	244	14	)	)	PUNCT
ejpam-3133	244	15	,	,	PUNCT
ejpam-3133	244	16	1	1	NUM
ejpam-3133	244	17	s	s	VERB
ejpam-3133	244	18	gb(fp	gb(fp	NOUN
ejpam-3133	244	19	,	,	PUNCT
ejpam-3133	244	20	fp	fp	NOUN
ejpam-3133	244	21	,	,	PUNCT
ejpam-3133	244	22	q	q	NOUN
ejpam-3133	244	23	)	)	PUNCT
ejpam-3133	244	24	}	}	PUNCT
ejpam-3133	244	25	=	=	SYM
ejpam-3133	244	26	0	0	NUM
ejpam-3133	244	27	,	,	PUNCT
ejpam-3133	244	28	which	which	PRON
ejpam-3133	244	29	implies	imply	VERB
ejpam-3133	244	30	that	that	SCONJ
ejpam-3133	244	31	gb(fp	gb(fp	ADJ
ejpam-3133	244	32	,	,	PUNCT
ejpam-3133	244	33	q	q	X
ejpam-3133	244	34	,	,	PUNCT
ejpam-3133	244	35	q	q	NOUN
ejpam-3133	244	36	)	)	PUNCT
ejpam-3133	244	37	=	=	SYM
ejpam-3133	244	38	gb(fp	gb(fp	PROPN
ejpam-3133	244	39	,	,	PUNCT
ejpam-3133	244	40	fp	fp	NOUN
ejpam-3133	244	41	,	,	PUNCT
ejpam-3133	244	42	q	q	NOUN
ejpam-3133	244	43	)	)	PUNCT
ejpam-3133	244	44	=	=	SYM
ejpam-3133	244	45	0	0	X
ejpam-3133	244	46	.	.	PUNCT
ejpam-3133	245	1	hence	hence	ADV
ejpam-3133	245	2	fp	fp	X
ejpam-3133	245	3	=	=	PUNCT
ejpam-3133	245	4	sp	sp	PROPN
ejpam-3133	245	5	=	=	NOUN
ejpam-3133	245	6	q.	q.	NOUN
ejpam-3133	245	7	we	we	PRON
ejpam-3133	245	8	conclude	conclude	VERB
ejpam-3133	245	9	that	that	SCONJ
ejpam-3133	245	10	p	p	NOUN
ejpam-3133	245	11	is	be	AUX
ejpam-3133	245	12	a	a	DET
ejpam-3133	245	13	coincidence	coincidence	NOUN
ejpam-3133	245	14	point	point	NOUN
ejpam-3133	245	15	of	of	ADP
ejpam-3133	245	16	f	f	PROPN
ejpam-3133	245	17	and	and	CCONJ
ejpam-3133	245	18	s.	s.	PROPN
ejpam-3133	245	19	also	also	ADV
ejpam-3133	245	20	fp	fp	PROPN
ejpam-3133	245	21	=	=	SYM
ejpam-3133	245	22	sp	sp	PROPN
ejpam-3133	245	23	=	=	PUNCT
ejpam-3133	245	24	gu	gu	NOUN
ejpam-3133	245	25	=	=	NOUN
ejpam-3133	245	26	ru	ru	PROPN
ejpam-3133	245	27	=	=	PUNCT
ejpam-3133	245	28	q.	q.	PROPN
ejpam-3133	245	29	(	(	PUNCT
ejpam-3133	245	30	27	27	NUM
ejpam-3133	245	31	)	)	PUNCT
ejpam-3133	245	32	again	again	ADV
ejpam-3133	245	33	,	,	PUNCT
ejpam-3133	245	34	since	since	SCONJ
ejpam-3133	245	35	h(x	h(x	PROPN
ejpam-3133	245	36	)	)	PUNCT
ejpam-3133	245	37	⊆	⊆	NUM
ejpam-3133	245	38	r(x	r(x	PROPN
ejpam-3133	245	39	)	)	PUNCT
ejpam-3133	245	40	,	,	PUNCT
ejpam-3133	245	41	there	there	PRON
ejpam-3133	245	42	exists	exist	VERB
ejpam-3133	245	43	w	w	PROPN
ejpam-3133	245	44	∈	∈	PROPN
ejpam-3133	245	45	x	x	PUNCT
ejpam-3133	245	46	such	such	ADJ
ejpam-3133	245	47	that	that	SCONJ
ejpam-3133	245	48	hw	hw	NOUN
ejpam-3133	245	49	=	=	X
ejpam-3133	245	50	ru	ru	PROPN
ejpam-3133	245	51	=	=	PUNCT
ejpam-3133	245	52	q.	q.	PROPN
ejpam-3133	246	1	now	now	ADV
ejpam-3133	246	2	,	,	PUNCT
ejpam-3133	246	3	we	we	PRON
ejpam-3133	246	4	shall	shall	AUX
ejpam-3133	246	5	show	show	VERB
ejpam-3133	246	6	that	that	SCONJ
ejpam-3133	246	7	tw	tw	VERB
ejpam-3133	246	8	=	=	PUNCT
ejpam-3133	246	9	hw	hw	PROPN
ejpam-3133	246	10	.	.	PROPN
ejpam-3133	247	1	from	from	ADP
ejpam-3133	247	2	the	the	DET
ejpam-3133	247	3	definition	definition	NOUN
ejpam-3133	247	4	of	of	ADP
ejpam-3133	247	5	m(x	m(x	PROPN
ejpam-3133	247	6	,	,	PUNCT
ejpam-3133	247	7	y	y	PROPN
ejpam-3133	247	8	,	,	PUNCT
ejpam-3133	247	9	z	z	NOUN
ejpam-3133	247	10	)	)	PUNCT
ejpam-3133	247	11	and	and	CCONJ
ejpam-3133	247	12	by	by	ADP
ejpam-3133	247	13	the	the	DET
ejpam-3133	247	14	help	help	NOUN
ejpam-3133	247	15	of	of	ADP
ejpam-3133	247	16	(	(	PUNCT
ejpam-3133	247	17	27	27	NUM
ejpam-3133	247	18	)	)	PUNCT
ejpam-3133	247	19	,	,	PUNCT
ejpam-3133	247	20	we	we	PRON
ejpam-3133	247	21	get	get	VERB
ejpam-3133	247	22	m(p	m(p	PROPN
ejpam-3133	247	23	,	,	PUNCT
ejpam-3133	247	24	u	u	NOUN
ejpam-3133	247	25	,	,	PUNCT
ejpam-3133	247	26	w	w	PROPN
ejpam-3133	247	27	)	)	PUNCT
ejpam-3133	247	28	=	=	SYM
ejpam-3133	247	29	max	max	NOUN
ejpam-3133	247	30	{	{	PUNCT
ejpam-3133	247	31	gb(fp	gb(fp	PROPN
ejpam-3133	247	32	,	,	PUNCT
ejpam-3133	247	33	sp	sp	NOUN
ejpam-3133	247	34	,	,	PUNCT
ejpam-3133	247	35	tw	tw	NOUN
ejpam-3133	247	36	)	)	PUNCT
ejpam-3133	247	37	,	,	PUNCT
ejpam-3133	247	38	gb(gu	gb(gu	PROPN
ejpam-3133	247	39	,	,	PUNCT
ejpam-3133	247	40	ru	ru	PROPN
ejpam-3133	247	41	,	,	PUNCT
ejpam-3133	247	42	ru	ru	NOUN
ejpam-3133	247	43	)	)	PUNCT
ejpam-3133	247	44	,	,	PUNCT
ejpam-3133	247	45	gb(fp	gb(fp	PROPN
ejpam-3133	247	46	,	,	PUNCT
ejpam-3133	247	47	fp	fp	X
ejpam-3133	247	48	,	,	PUNCT
ejpam-3133	247	49	hw	hw	NOUN
ejpam-3133	247	50	)	)	PUNCT
ejpam-3133	247	51	,	,	PUNCT
ejpam-3133	247	52	gb(tw	gb(tw	PROPN
ejpam-3133	247	53	,	,	PUNCT
ejpam-3133	247	54	tw	tw	PROPN
ejpam-3133	247	55	,	,	PUNCT
ejpam-3133	247	56	hw	hw	X
ejpam-3133	247	57	)	)	PUNCT
ejpam-3133	248	1	+	+	ADV
ejpam-3133	248	2	gb(fp	gb(fp	ADJ
ejpam-3133	248	3	,	,	PUNCT
ejpam-3133	248	4	sp	sp	NOUN
ejpam-3133	248	5	,	,	PUNCT
ejpam-3133	248	6	sp	sp	NOUN
ejpam-3133	248	7	)	)	PUNCT
ejpam-3133	248	8	2s	2s	NOUN
ejpam-3133	248	9	}	}	PUNCT
ejpam-3133	248	10	,	,	PUNCT
ejpam-3133	248	11	=	=	SYM
ejpam-3133	248	12	max	max	X
ejpam-3133	248	13	{	{	PUNCT
ejpam-3133	248	14	gb(q	gb(q	PROPN
ejpam-3133	248	15	,	,	PUNCT
ejpam-3133	248	16	q	q	NOUN
ejpam-3133	248	17	,	,	PUNCT
ejpam-3133	248	18	tw	tw	NOUN
ejpam-3133	248	19	)	)	PUNCT
ejpam-3133	248	20	,	,	PUNCT
ejpam-3133	248	21	gb(q	gb(q	PROPN
ejpam-3133	248	22	,	,	PUNCT
ejpam-3133	248	23	q	q	NOUN
ejpam-3133	248	24	,	,	PUNCT
ejpam-3133	248	25	q	q	NOUN
ejpam-3133	248	26	)	)	PUNCT
ejpam-3133	248	27	,	,	PUNCT
ejpam-3133	248	28	gb(q	gb(q	PROPN
ejpam-3133	248	29	,	,	PUNCT
ejpam-3133	248	30	q	q	NOUN
ejpam-3133	248	31	,	,	PUNCT
ejpam-3133	248	32	q	q	NOUN
ejpam-3133	248	33	)	)	PUNCT
ejpam-3133	248	34	,	,	PUNCT
ejpam-3133	248	35	gb(tw	gb(tw	PROPN
ejpam-3133	248	36	,	,	PUNCT
ejpam-3133	248	37	tw	tw	PROPN
ejpam-3133	248	38	,	,	PUNCT
ejpam-3133	248	39	q	q	X
ejpam-3133	248	40	)	)	PUNCT
ejpam-3133	248	41	+	+	NOUN
ejpam-3133	248	42	gb(q	gb(q	NOUN
ejpam-3133	248	43	,	,	PUNCT
ejpam-3133	248	44	q	q	NOUN
ejpam-3133	248	45	,	,	PUNCT
ejpam-3133	248	46	q	q	X
ejpam-3133	248	47	)	)	PUNCT
ejpam-3133	248	48	2s	2s	NOUN
ejpam-3133	248	49	}	}	PUNCT
ejpam-3133	248	50	,	,	PUNCT
ejpam-3133	248	51	=	=	SYM
ejpam-3133	248	52	max	max	X
ejpam-3133	248	53	{	{	PUNCT
ejpam-3133	248	54	gb(q	gb(q	PROPN
ejpam-3133	248	55	,	,	PUNCT
ejpam-3133	248	56	q	q	NOUN
ejpam-3133	248	57	,	,	PUNCT
ejpam-3133	248	58	tw	tw	NOUN
ejpam-3133	248	59	)	)	PUNCT
ejpam-3133	248	60	,	,	PUNCT
ejpam-3133	248	61	gb(tw	gb(tw	PROPN
ejpam-3133	248	62	,	,	PUNCT
ejpam-3133	248	63	tw	tw	PROPN
ejpam-3133	248	64	,	,	PUNCT
ejpam-3133	248	65	q	q	X
ejpam-3133	248	66	)	)	PUNCT
ejpam-3133	248	67	2s	2s	NOUN
ejpam-3133	248	68	}	}	PUNCT
ejpam-3133	248	69	.	.	PUNCT
ejpam-3133	249	1	but	but	CCONJ
ejpam-3133	249	2	,	,	PUNCT
ejpam-3133	249	3	by	by	ADP
ejpam-3133	249	4	part	part	NOUN
ejpam-3133	249	5	3	3	NUM
ejpam-3133	249	6	of	of	ADP
ejpam-3133	249	7	proposition	proposition	NOUN
ejpam-3133	249	8	1	1	NUM
ejpam-3133	249	9	,	,	PUNCT
ejpam-3133	249	10	we	we	PRON
ejpam-3133	249	11	have	have	VERB
ejpam-3133	249	12	gb(tw	gb(tw	PROPN
ejpam-3133	249	13	,	,	PUNCT
ejpam-3133	249	14	tw	tw	PROPN
ejpam-3133	249	15	,	,	PUNCT
ejpam-3133	249	16	q	q	X
ejpam-3133	249	17	)	)	PUNCT
ejpam-3133	250	1	2s	2s	PROPN
ejpam-3133	250	2	≤	≤	PROPN
ejpam-3133	250	3	gb(q	gb(q	PROPN
ejpam-3133	250	4	,	,	PUNCT
ejpam-3133	250	5	q	q	X
ejpam-3133	250	6	,	,	PUNCT
ejpam-3133	250	7	tw	tw	NOUN
ejpam-3133	250	8	)	)	PUNCT
ejpam-3133	250	9	and	and	CCONJ
ejpam-3133	250	10	so	so	ADV
ejpam-3133	250	11	the	the	DET
ejpam-3133	250	12	above	above	ADJ
ejpam-3133	250	13	inequality	inequality	NOUN
ejpam-3133	250	14	becomes	become	VERB
ejpam-3133	250	15	m(p	m(p	PROPN
ejpam-3133	250	16	,	,	PUNCT
ejpam-3133	250	17	u	u	NOUN
ejpam-3133	250	18	,	,	PUNCT
ejpam-3133	250	19	w	w	PROPN
ejpam-3133	250	20	)	)	PUNCT
ejpam-3133	250	21	=	=	SYM
ejpam-3133	250	22	gb(q	gb(q	NOUN
ejpam-3133	250	23	,	,	PUNCT
ejpam-3133	250	24	q	q	X
ejpam-3133	250	25	,	,	PUNCT
ejpam-3133	250	26	tw	tw	NOUN
ejpam-3133	250	27	)	)	PUNCT
ejpam-3133	250	28	.	.	PUNCT
ejpam-3133	251	1	(	(	PUNCT
ejpam-3133	251	2	28	28	NUM
ejpam-3133	251	3	)	)	PUNCT
ejpam-3133	251	4	z.	z.	PROPN
ejpam-3133	251	5	mustafa	mustafa	PROPN
ejpam-3133	251	6	et	et	PROPN
ejpam-3133	251	7	al	al	PROPN
ejpam-3133	251	8	.	.	PUNCT
ejpam-3133	251	9	/	/	SYM
ejpam-3133	251	10	eur	eur	PROPN
ejpam-3133	251	11	.	.	PUNCT
ejpam-3133	252	1	j.	j.	PROPN
ejpam-3133	252	2	pure	pure	PROPN
ejpam-3133	252	3	appl	appl	PROPN
ejpam-3133	252	4	.	.	PROPN
ejpam-3133	252	5	math	math	PROPN
ejpam-3133	252	6	,	,	PUNCT
ejpam-3133	252	7	11	11	NUM
ejpam-3133	252	8	(	(	PUNCT
ejpam-3133	252	9	1	1	NUM
ejpam-3133	252	10	)	)	PUNCT
ejpam-3133	252	11	(	(	PUNCT
ejpam-3133	252	12	2018	2018	NUM
ejpam-3133	252	13	)	)	PUNCT
ejpam-3133	252	14	,	,	PUNCT
ejpam-3133	252	15	90	90	NUM
ejpam-3133	252	16	-	-	SYM
ejpam-3133	252	17	109	109	NUM
ejpam-3133	252	18	100	100	NUM
ejpam-3133	252	19	thus	thus	ADV
ejpam-3133	252	20	,	,	PUNCT
ejpam-3133	252	21	applying	apply	VERB
ejpam-3133	252	22	(	(	PUNCT
ejpam-3133	252	23	3	3	NUM
ejpam-3133	252	24	)	)	PUNCT
ejpam-3133	252	25	for	for	ADP
ejpam-3133	252	26	x	x	SYM
ejpam-3133	252	27	=	=	SYM
ejpam-3133	252	28	q	q	X
ejpam-3133	252	29	,	,	PUNCT
ejpam-3133	252	30	y	y	NOUN
ejpam-3133	252	31	=	=	PUNCT
ejpam-3133	252	32	q	q	PROPN
ejpam-3133	252	33	and	and	CCONJ
ejpam-3133	252	34	z	z	NOUN
ejpam-3133	252	35	=	=	SYM
ejpam-3133	252	36	tw	tw	NOUN
ejpam-3133	252	37	and	and	CCONJ
ejpam-3133	252	38	using	use	VERB
ejpam-3133	252	39	(	(	PUNCT
ejpam-3133	252	40	gb3	gb3	NOUN
ejpam-3133	252	41	)	)	PUNCT
ejpam-3133	252	42	,	,	PUNCT
ejpam-3133	252	43	(	(	PUNCT
ejpam-3133	252	44	28	28	NUM
ejpam-3133	252	45	)	)	PUNCT
ejpam-3133	252	46	and	and	CCONJ
ejpam-3133	252	47	properties	property	NOUN
ejpam-3133	252	48	of	of	ADP
ejpam-3133	252	49	ψ	ψ	NOUN
ejpam-3133	252	50	,	,	PUNCT
ejpam-3133	252	51	we	we	PRON
ejpam-3133	252	52	obtain	obtain	VERB
ejpam-3133	252	53	ψ	ψ	X
ejpam-3133	252	54	(	(	PUNCT
ejpam-3133	252	55	gb(q	gb(q	PROPN
ejpam-3133	252	56	,	,	PUNCT
ejpam-3133	252	57	q	q	NOUN
ejpam-3133	252	58	,	,	PUNCT
ejpam-3133	252	59	tw	tw	NOUN
ejpam-3133	252	60	)	)	PUNCT
ejpam-3133	252	61	)	)	PUNCT
ejpam-3133	253	1	≤	≤	NUM
ejpam-3133	253	2	ψ	ψ	X
ejpam-3133	253	3	(	(	PUNCT
ejpam-3133	253	4	s2gb(q	s2gb(q	PROPN
ejpam-3133	253	5	,	,	PUNCT
ejpam-3133	253	6	q	q	NOUN
ejpam-3133	253	7	,	,	PUNCT
ejpam-3133	253	8	tw	tw	NOUN
ejpam-3133	253	9	)	)	PUNCT
ejpam-3133	253	10	)	)	PUNCT
ejpam-3133	254	1	=	=	SYM
ejpam-3133	254	2	ψ	ψ	PROPN
ejpam-3133	254	3	(	(	PUNCT
ejpam-3133	254	4	s2gb(fp	s2gb(fp	PROPN
ejpam-3133	254	5	,	,	PUNCT
ejpam-3133	254	6	gu	gu	NOUN
ejpam-3133	254	7	,	,	PUNCT
ejpam-3133	254	8	tw	tw	NOUN
ejpam-3133	254	9	)	)	PUNCT
ejpam-3133	254	10	)	)	PUNCT
ejpam-3133	255	1	≤	≤	NUM
ejpam-3133	255	2	ψ	ψ	X
ejpam-3133	255	3	(	(	PUNCT
ejpam-3133	255	4	m(p	m(p	PROPN
ejpam-3133	255	5	,	,	PUNCT
ejpam-3133	255	6	u	u	NOUN
ejpam-3133	255	7	,	,	PUNCT
ejpam-3133	255	8	w	w	NOUN
ejpam-3133	255	9	)	)	PUNCT
ejpam-3133	255	10	)	)	PUNCT
ejpam-3133	256	1	−	−	PROPN
ejpam-3133	256	2	φ	φ	PROPN
ejpam-3133	256	3	(	(	PUNCT
ejpam-3133	256	4	m(p	m(p	PROPN
ejpam-3133	256	5	,	,	PUNCT
ejpam-3133	256	6	u	u	NOUN
ejpam-3133	256	7	,	,	PUNCT
ejpam-3133	256	8	w	w	NOUN
ejpam-3133	256	9	)	)	PUNCT
ejpam-3133	256	10	)	)	PUNCT
ejpam-3133	256	11	,	,	PUNCT
ejpam-3133	256	12	=	=	SYM
ejpam-3133	256	13	ψ	ψ	X
ejpam-3133	256	14	(	(	PUNCT
ejpam-3133	256	15	gb(q	gb(q	PROPN
ejpam-3133	256	16	,	,	PUNCT
ejpam-3133	256	17	q	q	NOUN
ejpam-3133	256	18	,	,	PUNCT
ejpam-3133	256	19	tw	tw	NOUN
ejpam-3133	256	20	)	)	PUNCT
ejpam-3133	256	21	)	)	PUNCT
ejpam-3133	257	1	−	−	PROPN
ejpam-3133	257	2	φ	φ	PROPN
ejpam-3133	257	3	(	(	PUNCT
ejpam-3133	257	4	gb(q	gb(q	PROPN
ejpam-3133	257	5	,	,	PUNCT
ejpam-3133	257	6	q	q	NOUN
ejpam-3133	257	7	,	,	PUNCT
ejpam-3133	257	8	tw	tw	NOUN
ejpam-3133	257	9	)	)	PUNCT
ejpam-3133	257	10	)	)	PUNCT
ejpam-3133	257	11	.	.	PUNCT
ejpam-3133	258	1	(	(	PUNCT
ejpam-3133	258	2	29	29	NUM
ejpam-3133	258	3	)	)	PUNCT
ejpam-3133	258	4	so	so	ADV
ejpam-3133	258	5	,	,	PUNCT
ejpam-3133	258	6	φ	φ	PROPN
ejpam-3133	258	7	(	(	PUNCT
ejpam-3133	258	8	gb(q	gb(q	PROPN
ejpam-3133	258	9	,	,	PUNCT
ejpam-3133	258	10	q	q	NOUN
ejpam-3133	258	11	,	,	PUNCT
ejpam-3133	258	12	tw	tw	NOUN
ejpam-3133	258	13	)	)	PUNCT
ejpam-3133	258	14	)	)	PUNCT
ejpam-3133	259	1	=	=	PUNCT
ejpam-3133	259	2	0	0	NUM
ejpam-3133	259	3	,	,	PUNCT
ejpam-3133	259	4	which	which	PRON
ejpam-3133	259	5	implies	imply	VERB
ejpam-3133	259	6	that	that	DET
ejpam-3133	259	7	gb(q	gb(q	NOUN
ejpam-3133	259	8	,	,	PUNCT
ejpam-3133	259	9	q	q	X
ejpam-3133	259	10	,	,	PUNCT
ejpam-3133	259	11	tw	tw	PRON
ejpam-3133	259	12	)	)	PUNCT
ejpam-3133	259	13	=	=	SYM
ejpam-3133	260	1	0	0	X
ejpam-3133	260	2	.	.	PUNCT
ejpam-3133	261	1	hence	hence	ADV
ejpam-3133	261	2	tw	tw	VERB
ejpam-3133	262	1	=	=	NOUN
ejpam-3133	262	2	q	q	PUNCT
ejpam-3133	263	1	=	=	PUNCT
ejpam-3133	263	2	hw	hw	NOUN
ejpam-3133	264	1	and	and	CCONJ
ejpam-3133	264	2	so	so	ADV
ejpam-3133	264	3	w	w	PROPN
ejpam-3133	264	4	is	be	AUX
ejpam-3133	264	5	a	a	DET
ejpam-3133	264	6	coincidence	coincidence	NOUN
ejpam-3133	264	7	point	point	NOUN
ejpam-3133	264	8	of	of	ADP
ejpam-3133	264	9	h	h	NOUN
ejpam-3133	264	10	and	and	CCONJ
ejpam-3133	264	11	t	t	PROPN
ejpam-3133	264	12	.	.	PUNCT
ejpam-3133	265	1	therefore	therefore	ADV
ejpam-3133	265	2	fp	fp	X
ejpam-3133	265	3	=	=	SYM
ejpam-3133	265	4	sp	sp	PROPN
ejpam-3133	265	5	=	=	PUNCT
ejpam-3133	265	6	gu	gu	NOUN
ejpam-3133	265	7	=	=	NOUN
ejpam-3133	265	8	ru	ru	PROPN
ejpam-3133	265	9	=	=	SYM
ejpam-3133	265	10	tw	tw	NOUN
ejpam-3133	265	11	=	=	NOUN
ejpam-3133	265	12	hw	hw	PROPN
ejpam-3133	265	13	=	=	PUNCT
ejpam-3133	265	14	q.	q.	PROPN
ejpam-3133	265	15	(	(	PUNCT
ejpam-3133	265	16	30	30	NUM
ejpam-3133	265	17	)	)	PUNCT
ejpam-3133	265	18	now	now	ADV
ejpam-3133	265	19	,	,	PUNCT
ejpam-3133	265	20	we	we	PRON
ejpam-3133	265	21	shall	shall	AUX
ejpam-3133	265	22	show	show	VERB
ejpam-3133	265	23	that	that	SCONJ
ejpam-3133	265	24	q	q	NOUN
ejpam-3133	265	25	is	be	AUX
ejpam-3133	265	26	a	a	DET
ejpam-3133	265	27	common	common	ADJ
ejpam-3133	265	28	fixed	fix	VERB
ejpam-3133	265	29	point	point	NOUN
ejpam-3133	265	30	of	of	ADP
ejpam-3133	265	31	f	f	PROPN
ejpam-3133	265	32	,	,	PUNCT
ejpam-3133	265	33	g	g	PROPN
ejpam-3133	265	34	,	,	PUNCT
ejpam-3133	265	35	h	h	NOUN
ejpam-3133	265	36	,	,	PUNCT
ejpam-3133	265	37	r	r	NOUN
ejpam-3133	265	38	,	,	PUNCT
ejpam-3133	265	39	s	s	PART
ejpam-3133	265	40	and	and	CCONJ
ejpam-3133	265	41	t	t	PROPN
ejpam-3133	265	42	.	.	PUNCT
ejpam-3133	266	1	since	since	SCONJ
ejpam-3133	266	2	the	the	DET
ejpam-3133	266	3	pairs	pair	NOUN
ejpam-3133	266	4	(	(	PUNCT
ejpam-3133	266	5	f	f	X
ejpam-3133	266	6	,	,	PUNCT
ejpam-3133	266	7	s	s	PART
ejpam-3133	266	8	)	)	PUNCT
ejpam-3133	266	9	,	,	PUNCT
ejpam-3133	266	10	(	(	PUNCT
ejpam-3133	266	11	g	g	NOUN
ejpam-3133	266	12	,	,	PUNCT
ejpam-3133	266	13	r	r	NOUN
ejpam-3133	266	14	)	)	PUNCT
ejpam-3133	266	15	and	and	CCONJ
ejpam-3133	266	16	(	(	PUNCT
ejpam-3133	266	17	h	h	NOUN
ejpam-3133	266	18	,	,	PUNCT
ejpam-3133	266	19	t	t	PROPN
ejpam-3133	266	20	)	)	PUNCT
ejpam-3133	266	21	are	be	AUX
ejpam-3133	266	22	weakly	weakly	ADV
ejpam-3133	266	23	compatible	compatible	ADJ
ejpam-3133	266	24	,	,	PUNCT
ejpam-3133	266	25	the	the	DET
ejpam-3133	266	26	functions	function	NOUN
ejpam-3133	266	27	of	of	ADP
ejpam-3133	266	28	each	each	DET
ejpam-3133	266	29	pair	pair	NOUN
ejpam-3133	266	30	commute	commute	NOUN
ejpam-3133	266	31	at	at	ADP
ejpam-3133	266	32	their	their	PRON
ejpam-3133	266	33	coincidence	coincidence	NOUN
ejpam-3133	266	34	point	point	NOUN
ejpam-3133	266	35	,	,	PUNCT
ejpam-3133	266	36	that	that	PRON
ejpam-3133	266	37	is	is	ADV
ejpam-3133	266	38	f(q	f(q	NOUN
ejpam-3133	266	39	)	)	PUNCT
ejpam-3133	266	40	=	=	SYM
ejpam-3133	267	1	f(sp	f(sp	X
ejpam-3133	267	2	)	)	PUNCT
ejpam-3133	267	3	=	=	SYM
ejpam-3133	267	4	s(fp	s(fp	PROPN
ejpam-3133	267	5	)	)	PUNCT
ejpam-3133	267	6	=	=	SYM
ejpam-3133	267	7	s(q	s(q	NOUN
ejpam-3133	267	8	)	)	PUNCT
ejpam-3133	267	9	,	,	PUNCT
ejpam-3133	267	10	r(q	r(q	PROPN
ejpam-3133	267	11	)	)	PUNCT
ejpam-3133	267	12	=	=	SYM
ejpam-3133	267	13	r(gu	r(gu	NOUN
ejpam-3133	267	14	)	)	PUNCT
ejpam-3133	267	15	=	=	SYM
ejpam-3133	267	16	g(ru	g(ru	PROPN
ejpam-3133	267	17	)	)	PUNCT
ejpam-3133	267	18	=	=	SYM
ejpam-3133	267	19	g(q	g(q	NOUN
ejpam-3133	267	20	)	)	PUNCT
ejpam-3133	267	21	,	,	PUNCT
ejpam-3133	267	22	t	t	PROPN
ejpam-3133	267	23	(	(	PUNCT
ejpam-3133	267	24	q	q	X
ejpam-3133	267	25	)	)	PUNCT
ejpam-3133	267	26	=	=	SYM
ejpam-3133	267	27	t	t	PROPN
ejpam-3133	267	28	(	(	PUNCT
ejpam-3133	267	29	hw	hw	NOUN
ejpam-3133	267	30	)	)	PUNCT
ejpam-3133	267	31	=	=	SYM
ejpam-3133	267	32	h(tw	h(tw	ADJ
ejpam-3133	267	33	)	)	PUNCT
ejpam-3133	267	34	=	=	PUNCT
ejpam-3133	267	35	h(q	h(q	ADV
ejpam-3133	267	36	)	)	PUNCT
ejpam-3133	267	37	.	.	PUNCT
ejpam-3133	268	1			NOUN
ejpam-3133	268	2	(	(	PUNCT
ejpam-3133	268	3	31	31	NUM
ejpam-3133	268	4	)	)	PUNCT
ejpam-3133	268	5	using	use	VERB
ejpam-3133	268	6	(	(	PUNCT
ejpam-3133	268	7	30	30	NUM
ejpam-3133	268	8	)	)	PUNCT
ejpam-3133	268	9	and	and	CCONJ
ejpam-3133	268	10	(	(	PUNCT
ejpam-3133	268	11	31	31	NUM
ejpam-3133	268	12	)	)	PUNCT
ejpam-3133	268	13	,	,	PUNCT
ejpam-3133	268	14	we	we	PRON
ejpam-3133	268	15	obtain	obtain	VERB
ejpam-3133	268	16	m(q	m(q	PROPN
ejpam-3133	268	17	,	,	PUNCT
ejpam-3133	268	18	u	u	NOUN
ejpam-3133	268	19	,	,	PUNCT
ejpam-3133	268	20	w	w	PROPN
ejpam-3133	268	21	)	)	PUNCT
ejpam-3133	268	22	=	=	SYM
ejpam-3133	268	23	max	max	PROPN
ejpam-3133	268	24	{	{	PUNCT
ejpam-3133	268	25	gb(fq	gb(fq	PROPN
ejpam-3133	268	26	,	,	PUNCT
ejpam-3133	268	27	sq	sq	PROPN
ejpam-3133	268	28	,	,	PUNCT
ejpam-3133	268	29	tw	tw	NOUN
ejpam-3133	268	30	)	)	PUNCT
ejpam-3133	268	31	,	,	PUNCT
ejpam-3133	268	32	gb(gu	gb(gu	PROPN
ejpam-3133	268	33	,	,	PUNCT
ejpam-3133	268	34	ru	ru	PROPN
ejpam-3133	268	35	,	,	PUNCT
ejpam-3133	268	36	ru	ru	PROPN
ejpam-3133	268	37	)	)	PUNCT
ejpam-3133	268	38	,	,	PUNCT
ejpam-3133	268	39	gb(fq	gb(fq	PROPN
ejpam-3133	268	40	,	,	PUNCT
ejpam-3133	268	41	fq	fq	PROPN
ejpam-3133	268	42	,	,	PUNCT
ejpam-3133	268	43	hw	hw	NOUN
ejpam-3133	268	44	)	)	PUNCT
ejpam-3133	268	45	,	,	PUNCT
ejpam-3133	268	46	gb(tw	gb(tw	PROPN
ejpam-3133	268	47	,	,	PUNCT
ejpam-3133	268	48	tw	tw	PROPN
ejpam-3133	268	49	,	,	PUNCT
ejpam-3133	268	50	hw	hw	X
ejpam-3133	268	51	)	)	PUNCT
ejpam-3133	269	1	+	+	NOUN
ejpam-3133	269	2	gb(fq	gb(fq	NOUN
ejpam-3133	269	3	,	,	PUNCT
ejpam-3133	269	4	sq	sq	ADJ
ejpam-3133	269	5	,	,	PUNCT
ejpam-3133	269	6	sq	sq	ADJ
ejpam-3133	269	7	)	)	PUNCT
ejpam-3133	269	8	2s	2s	NOUN
ejpam-3133	269	9	}	}	PUNCT
ejpam-3133	269	10	,	,	PUNCT
ejpam-3133	269	11	=	=	SYM
ejpam-3133	269	12	max	max	X
ejpam-3133	269	13	{	{	PUNCT
ejpam-3133	269	14	gb(fq	gb(fq	PROPN
ejpam-3133	269	15	,	,	PUNCT
ejpam-3133	269	16	sq	sq	PROPN
ejpam-3133	269	17	,	,	PUNCT
ejpam-3133	269	18	q	q	NOUN
ejpam-3133	269	19	)	)	PUNCT
ejpam-3133	269	20	,	,	PUNCT
ejpam-3133	269	21	0	0	NUM
ejpam-3133	269	22	,	,	PUNCT
ejpam-3133	269	23	gb(fq	gb(fq	PROPN
ejpam-3133	269	24	,	,	PUNCT
ejpam-3133	269	25	fq	fq	PROPN
ejpam-3133	269	26	,	,	PUNCT
ejpam-3133	269	27	q	q	NOUN
ejpam-3133	269	28	)	)	PUNCT
ejpam-3133	269	29	,	,	PUNCT
ejpam-3133	269	30	0	0	NUM
ejpam-3133	269	31	}	}	PUNCT
ejpam-3133	269	32	,	,	PUNCT
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ejpam-3133	269	34	gb(fq	gb(fq	PROPN
ejpam-3133	269	35	,	,	PUNCT
ejpam-3133	269	36	fq	fq	PROPN
ejpam-3133	269	37	,	,	PUNCT
ejpam-3133	269	38	q	q	NOUN
ejpam-3133	269	39	)	)	PUNCT
ejpam-3133	269	40	.	.	PUNCT
ejpam-3133	270	1	also	also	ADV
ejpam-3133	270	2	,	,	PUNCT
ejpam-3133	270	3	from	from	ADP
ejpam-3133	270	4	(	(	PUNCT
ejpam-3133	270	5	3	3	NUM
ejpam-3133	270	6	)	)	PUNCT
ejpam-3133	270	7	and	and	CCONJ
ejpam-3133	270	8	(	(	PUNCT
ejpam-3133	270	9	gb3	gb3	NOUN
ejpam-3133	270	10	)	)	PUNCT
ejpam-3133	270	11	,	,	PUNCT
ejpam-3133	270	12	we	we	PRON
ejpam-3133	270	13	get	get	VERB
ejpam-3133	270	14	ψ	ψ	X
ejpam-3133	270	15	(	(	PUNCT
ejpam-3133	270	16	s2gb(fq	s2gb(fq	PROPN
ejpam-3133	270	17	,	,	PUNCT
ejpam-3133	270	18	fq	fq	PROPN
ejpam-3133	270	19	,	,	PUNCT
ejpam-3133	270	20	q	q	NOUN
ejpam-3133	270	21	)	)	PUNCT
ejpam-3133	270	22	)	)	PUNCT
ejpam-3133	271	1	≤	≤	NUM
ejpam-3133	272	1	ψ	ψ	X
ejpam-3133	272	2	(	(	PUNCT
ejpam-3133	272	3	s2gb(fq	s2gb(fq	PROPN
ejpam-3133	272	4	,	,	PUNCT
ejpam-3133	272	5	gu	gu	NOUN
ejpam-3133	272	6	,	,	PUNCT
ejpam-3133	272	7	q	q	NOUN
ejpam-3133	272	8	)	)	PUNCT
ejpam-3133	272	9	)	)	PUNCT
ejpam-3133	273	1	=	=	SYM
ejpam-3133	273	2	ψ	ψ	X
ejpam-3133	273	3	(	(	PUNCT
ejpam-3133	273	4	s2gb(fq	s2gb(fq	PROPN
ejpam-3133	273	5	,	,	PUNCT
ejpam-3133	273	6	gu	gu	NOUN
ejpam-3133	273	7	,	,	PUNCT
ejpam-3133	273	8	hw	hw	NOUN
ejpam-3133	273	9	)	)	PUNCT
ejpam-3133	273	10	)	)	PUNCT
ejpam-3133	273	11	≤	≤	NUM
ejpam-3133	274	1	ψ	ψ	X
ejpam-3133	274	2	(	(	PUNCT
ejpam-3133	274	3	m(q	m(q	PROPN
ejpam-3133	274	4	,	,	PUNCT
ejpam-3133	274	5	u	u	NOUN
ejpam-3133	274	6	,	,	PUNCT
ejpam-3133	274	7	w	w	NOUN
ejpam-3133	274	8	)	)	PUNCT
ejpam-3133	274	9	)	)	PUNCT
ejpam-3133	275	1	−	−	PROPN
ejpam-3133	275	2	φ	φ	PROPN
ejpam-3133	275	3	(	(	PUNCT
ejpam-3133	275	4	m(q	m(q	PROPN
ejpam-3133	275	5	,	,	PUNCT
ejpam-3133	275	6	u	u	NOUN
ejpam-3133	275	7	,	,	PUNCT
ejpam-3133	275	8	w	w	NOUN
ejpam-3133	275	9	)	)	PUNCT
ejpam-3133	275	10	)	)	PUNCT
ejpam-3133	275	11	,	,	PUNCT
ejpam-3133	275	12	=	=	SYM
ejpam-3133	275	13	ψ	ψ	X
ejpam-3133	275	14	(	(	PUNCT
ejpam-3133	275	15	gb(fq	gb(fq	PROPN
ejpam-3133	275	16	,	,	PUNCT
ejpam-3133	275	17	fq	fq	PROPN
ejpam-3133	275	18	,	,	PUNCT
ejpam-3133	275	19	q	q	NOUN
ejpam-3133	275	20	)	)	PUNCT
ejpam-3133	275	21	)	)	PUNCT
ejpam-3133	275	22	)	)	PUNCT
ejpam-3133	276	1	−	−	PROPN
ejpam-3133	276	2	φ	φ	PROPN
ejpam-3133	276	3	(	(	PUNCT
ejpam-3133	276	4	gb(fq	gb(fq	PROPN
ejpam-3133	276	5	,	,	PUNCT
ejpam-3133	276	6	fq	fq	PROPN
ejpam-3133	276	7	,	,	PUNCT
ejpam-3133	276	8	q	q	NOUN
ejpam-3133	276	9	)	)	PUNCT
ejpam-3133	276	10	)	)	PUNCT
ejpam-3133	276	11	,	,	PUNCT
ejpam-3133	276	12	≤	≤	NUM
ejpam-3133	276	13	ψ	ψ	X
ejpam-3133	276	14	(	(	PUNCT
ejpam-3133	276	15	gb(fq	gb(fq	PROPN
ejpam-3133	276	16	,	,	PUNCT
ejpam-3133	276	17	fq	fq	PROPN
ejpam-3133	276	18	,	,	PUNCT
ejpam-3133	276	19	q	q	NOUN
ejpam-3133	276	20	)	)	PUNCT
ejpam-3133	276	21	)	)	PUNCT
ejpam-3133	276	22	.	.	PUNCT
ejpam-3133	277	1	(	(	PUNCT
ejpam-3133	277	2	32	32	NUM
ejpam-3133	277	3	)	)	PUNCT
ejpam-3133	277	4	since	since	SCONJ
ejpam-3133	277	5	s2	s2	VERB
ejpam-3133	277	6	>	>	X
ejpam-3133	277	7	s	s	X
ejpam-3133	277	8	>	>	X
ejpam-3133	277	9	1	1	NUM
ejpam-3133	277	10	and	and	CCONJ
ejpam-3133	277	11	ψ	ψ	NOUN
ejpam-3133	277	12	is	be	AUX
ejpam-3133	277	13	increasing	increase	VERB
ejpam-3133	277	14	,	,	PUNCT
ejpam-3133	277	15	the	the	DET
ejpam-3133	277	16	inequality	inequality	NOUN
ejpam-3133	277	17	above	above	ADP
ejpam-3133	277	18	yields	yield	NOUN
ejpam-3133	277	19	that	that	PRON
ejpam-3133	277	20	gb(fq	gb(fq	PROPN
ejpam-3133	277	21	,	,	PUNCT
ejpam-3133	277	22	fq	fq	PROPN
ejpam-3133	277	23	,	,	PUNCT
ejpam-3133	277	24	q	q	NOUN
ejpam-3133	277	25	)	)	PUNCT
ejpam-3133	277	26	=	=	SYM
ejpam-3133	277	27	0	0	PUNCT
ejpam-3133	278	1	and	and	CCONJ
ejpam-3133	278	2	so	so	ADV
ejpam-3133	278	3	fq	fq	PROPN
ejpam-3133	278	4	=	=	NOUN
ejpam-3133	278	5	q	q	X
ejpam-3133	278	6	=	=	PUNCT
ejpam-3133	278	7	sq	sq	PROPN
ejpam-3133	278	8	.	.	PUNCT
ejpam-3133	279	1	we	we	PRON
ejpam-3133	279	2	shall	shall	AUX
ejpam-3133	279	3	prove	prove	VERB
ejpam-3133	279	4	that	that	SCONJ
ejpam-3133	279	5	gq	gq	NOUN
ejpam-3133	279	6	=	=	SYM
ejpam-3133	279	7	rq	rq	X
ejpam-3133	279	8	=	=	PUNCT
ejpam-3133	279	9	q.	q.	NOUN
ejpam-3133	279	10	as	as	ADP
ejpam-3133	279	11	in	in	ADP
ejpam-3133	279	12	the	the	DET
ejpam-3133	279	13	above	above	NOUN
ejpam-3133	279	14	,	,	PUNCT
ejpam-3133	279	15	using	use	VERB
ejpam-3133	279	16	(	(	PUNCT
ejpam-3133	279	17	30	30	NUM
ejpam-3133	279	18	)	)	PUNCT
ejpam-3133	279	19	and	and	CCONJ
ejpam-3133	279	20	(	(	PUNCT
ejpam-3133	279	21	31	31	NUM
ejpam-3133	279	22	)	)	PUNCT
ejpam-3133	279	23	,	,	PUNCT
ejpam-3133	279	24	we	we	PRON
ejpam-3133	279	25	find	find	VERB
ejpam-3133	279	26	that	that	SCONJ
ejpam-3133	279	27	m(p	m(p	PROPN
ejpam-3133	279	28	,	,	PUNCT
ejpam-3133	279	29	q	q	NOUN
ejpam-3133	279	30	,	,	PUNCT
ejpam-3133	279	31	w	w	NOUN
ejpam-3133	279	32	)	)	PUNCT
ejpam-3133	279	33	=	=	SYM
ejpam-3133	279	34	max	max	NOUN
ejpam-3133	279	35	{	{	PUNCT
ejpam-3133	279	36	gb(fp	gb(fp	PROPN
ejpam-3133	279	37	,	,	PUNCT
ejpam-3133	279	38	sp	sp	NOUN
ejpam-3133	279	39	,	,	PUNCT
ejpam-3133	279	40	tw	tw	NOUN
ejpam-3133	279	41	)	)	PUNCT
ejpam-3133	279	42	,	,	PUNCT
ejpam-3133	279	43	gb(gq	gb(gq	PROPN
ejpam-3133	279	44	,	,	PUNCT
ejpam-3133	279	45	rq	rq	NOUN
ejpam-3133	279	46	,	,	PUNCT
ejpam-3133	279	47	rq	rq	NOUN
ejpam-3133	279	48	)	)	PUNCT
ejpam-3133	279	49	,	,	PUNCT
ejpam-3133	279	50	gb(fp	gb(fp	PROPN
ejpam-3133	279	51	,	,	PUNCT
ejpam-3133	279	52	fp	fp	X
ejpam-3133	279	53	,	,	PUNCT
ejpam-3133	279	54	hw	hw	NOUN
ejpam-3133	279	55	)	)	PUNCT
ejpam-3133	279	56	,	,	PUNCT
ejpam-3133	279	57	gb(tw	gb(tw	PROPN
ejpam-3133	279	58	,	,	PUNCT
ejpam-3133	279	59	tw	tw	PROPN
ejpam-3133	279	60	,	,	PUNCT
ejpam-3133	279	61	hw	hw	X
ejpam-3133	279	62	)	)	PUNCT
ejpam-3133	280	1	+	+	ADV
ejpam-3133	280	2	gb(fp	gb(fp	ADJ
ejpam-3133	280	3	,	,	PUNCT
ejpam-3133	280	4	sp	sp	NOUN
ejpam-3133	280	5	,	,	PUNCT
ejpam-3133	280	6	sp	sp	NOUN
ejpam-3133	280	7	)	)	PUNCT
ejpam-3133	280	8	2s	2s	NOUN
ejpam-3133	280	9	}	}	PUNCT
ejpam-3133	280	10	,	,	PUNCT
ejpam-3133	280	11	z.	z.	PROPN
ejpam-3133	280	12	mustafa	mustafa	PROPN
ejpam-3133	280	13	et	et	PROPN
ejpam-3133	280	14	al	al	PROPN
ejpam-3133	280	15	.	.	PUNCT
ejpam-3133	280	16	/	/	SYM
ejpam-3133	280	17	eur	eur	PROPN
ejpam-3133	280	18	.	.	PUNCT
ejpam-3133	281	1	j.	j.	PROPN
ejpam-3133	281	2	pure	pure	PROPN
ejpam-3133	281	3	appl	appl	PROPN
ejpam-3133	281	4	.	.	PROPN
ejpam-3133	281	5	math	math	PROPN
ejpam-3133	281	6	,	,	PUNCT
ejpam-3133	281	7	11	11	NUM
ejpam-3133	281	8	(	(	PUNCT
ejpam-3133	281	9	1	1	NUM
ejpam-3133	281	10	)	)	PUNCT
ejpam-3133	281	11	(	(	PUNCT
ejpam-3133	281	12	2018	2018	NUM
ejpam-3133	281	13	)	)	PUNCT
ejpam-3133	281	14	,	,	PUNCT
ejpam-3133	281	15	90	90	NUM
ejpam-3133	281	16	-	-	SYM
ejpam-3133	281	17	109	109	NUM
ejpam-3133	281	18	101	101	NUM
ejpam-3133	281	19	=	=	SYM
ejpam-3133	281	20	max	max	PROPN
ejpam-3133	281	21	{	{	PUNCT
ejpam-3133	281	22	gb(q	gb(q	PROPN
ejpam-3133	281	23	,	,	PUNCT
ejpam-3133	281	24	q	q	NOUN
ejpam-3133	281	25	,	,	PUNCT
ejpam-3133	281	26	q	q	NOUN
ejpam-3133	281	27	)	)	PUNCT
ejpam-3133	281	28	,	,	PUNCT
ejpam-3133	281	29	gb(rq	gb(rq	PROPN
ejpam-3133	281	30	,	,	PUNCT
ejpam-3133	281	31	rq	rq	NOUN
ejpam-3133	281	32	,	,	PUNCT
ejpam-3133	281	33	rq	rq	NOUN
ejpam-3133	281	34	)	)	PUNCT
ejpam-3133	281	35	,	,	PUNCT
ejpam-3133	281	36	gb(q	gb(q	PROPN
ejpam-3133	281	37	,	,	PUNCT
ejpam-3133	281	38	q	q	NOUN
ejpam-3133	281	39	,	,	PUNCT
ejpam-3133	281	40	q	q	NOUN
ejpam-3133	281	41	)	)	PUNCT
ejpam-3133	281	42	,	,	PUNCT
ejpam-3133	281	43	gb(q	gb(q	PROPN
ejpam-3133	281	44	,	,	PUNCT
ejpam-3133	281	45	q	q	NOUN
ejpam-3133	281	46	,	,	PUNCT
ejpam-3133	281	47	q	q	NOUN
ejpam-3133	281	48	)	)	PUNCT
ejpam-3133	282	1	+	+	NOUN
ejpam-3133	282	2	gb(q	gb(q	NOUN
ejpam-3133	282	3	,	,	PUNCT
ejpam-3133	282	4	q	q	NOUN
ejpam-3133	282	5	,	,	PUNCT
ejpam-3133	282	6	q	q	X
ejpam-3133	282	7	)	)	PUNCT
ejpam-3133	282	8	2s	2s	NOUN
ejpam-3133	282	9	}	}	PUNCT
ejpam-3133	282	10	,	,	PUNCT
ejpam-3133	282	11	=	=	NOUN
ejpam-3133	282	12	0	0	X
ejpam-3133	282	13	.	.	X
ejpam-3133	283	1	applying	apply	VERB
ejpam-3133	283	2	(	(	PUNCT
ejpam-3133	283	3	3	3	NUM
ejpam-3133	283	4	)	)	PUNCT
ejpam-3133	283	5	,	,	PUNCT
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ejpam-3133	283	7	(	(	PUNCT
ejpam-3133	283	8	s2gb(fp	s2gb(fp	PROPN
ejpam-3133	283	9	,	,	PUNCT
ejpam-3133	283	10	gq	gq	PROPN
ejpam-3133	283	11	,	,	PUNCT
ejpam-3133	283	12	hw	hw	NOUN
ejpam-3133	283	13	)	)	PUNCT
ejpam-3133	283	14	)	)	PUNCT
ejpam-3133	284	1	≤	≤	NUM
ejpam-3133	284	2	ψ	ψ	X
ejpam-3133	284	3	(	(	PUNCT
ejpam-3133	284	4	m(p	m(p	PROPN
ejpam-3133	284	5	,	,	PUNCT
ejpam-3133	284	6	q	q	NOUN
ejpam-3133	284	7	,	,	PUNCT
ejpam-3133	284	8	w	w	NOUN
ejpam-3133	284	9	)	)	PUNCT
ejpam-3133	284	10	)	)	PUNCT
ejpam-3133	285	1	−	−	PROPN
ejpam-3133	285	2	φ	φ	PROPN
ejpam-3133	285	3	(	(	PUNCT
ejpam-3133	285	4	m(p	m(p	PROPN
ejpam-3133	285	5	,	,	PUNCT
ejpam-3133	285	6	q	q	NOUN
ejpam-3133	285	7	,	,	PUNCT
ejpam-3133	285	8	w	w	NOUN
ejpam-3133	285	9	)	)	PUNCT
ejpam-3133	285	10	)	)	PUNCT
ejpam-3133	285	11	,	,	PUNCT
ejpam-3133	285	12	=	=	SYM
ejpam-3133	285	13	ψ	ψ	X
ejpam-3133	285	14	(	(	PUNCT
ejpam-3133	285	15	0	0	NUM
ejpam-3133	285	16	)	)	PUNCT
ejpam-3133	285	17	−	−	PROPN
ejpam-3133	286	1	φ	φ	PROPN
ejpam-3133	286	2	(	(	PUNCT
ejpam-3133	286	3	0	0	NUM
ejpam-3133	286	4	)	)	PUNCT
ejpam-3133	286	5	=	=	SYM
ejpam-3133	286	6	0	0	X
ejpam-3133	286	7	.	.	PUNCT
ejpam-3133	286	8	(	(	PUNCT
ejpam-3133	286	9	33	33	NUM
ejpam-3133	286	10	)	)	PUNCT
ejpam-3133	286	11	consequently	consequently	ADV
ejpam-3133	286	12	,	,	PUNCT
ejpam-3133	286	13	gb(fp	gb(fp	ADV
ejpam-3133	286	14	,	,	PUNCT
ejpam-3133	286	15	gq	gq	PROPN
ejpam-3133	286	16	,	,	PUNCT
ejpam-3133	286	17	hw	hw	ADJ
ejpam-3133	286	18	)	)	PUNCT
ejpam-3133	286	19	=	=	SYM
ejpam-3133	286	20	gb(q	gb(q	PROPN
ejpam-3133	286	21	,	,	PUNCT
ejpam-3133	286	22	gq	gq	PROPN
ejpam-3133	286	23	,	,	PUNCT
ejpam-3133	286	24	q	q	NOUN
ejpam-3133	286	25	)	)	PUNCT
ejpam-3133	286	26	=	=	SYM
ejpam-3133	286	27	0	0	PUNCT
ejpam-3133	287	1	and	and	CCONJ
ejpam-3133	287	2	so	so	ADV
ejpam-3133	287	3	gq	gq	PROPN
ejpam-3133	287	4	=	=	PUNCT
ejpam-3133	287	5	q.	q.	NOUN
ejpam-3133	287	6	hence	hence	ADV
ejpam-3133	287	7	gq	gq	NOUN
ejpam-3133	287	8	=	=	SYM
ejpam-3133	287	9	rq	rq	NOUN
ejpam-3133	287	10	=	=	PUNCT
ejpam-3133	287	11	q.	q.	PROPN
ejpam-3133	287	12	now	now	ADV
ejpam-3133	287	13	we	we	PRON
ejpam-3133	287	14	shall	shall	AUX
ejpam-3133	287	15	prove	prove	VERB
ejpam-3133	287	16	that	that	DET
ejpam-3133	287	17	hq	hq	NOUN
ejpam-3133	288	1	=	=	PUNCT
ejpam-3133	288	2	tq	tq	ADP
ejpam-3133	288	3	=	=	NOUN
ejpam-3133	288	4	q.	q.	PROPN
ejpam-3133	288	5	similarly	similarly	ADV
ejpam-3133	288	6	,	,	PUNCT
ejpam-3133	288	7	using	use	VERB
ejpam-3133	288	8	(	(	PUNCT
ejpam-3133	288	9	30	30	NUM
ejpam-3133	288	10	)	)	PUNCT
ejpam-3133	288	11	and	and	CCONJ
ejpam-3133	288	12	(	(	PUNCT
ejpam-3133	288	13	31	31	NUM
ejpam-3133	288	14	)	)	PUNCT
ejpam-3133	288	15	,	,	PUNCT
ejpam-3133	288	16	we	we	PRON
ejpam-3133	288	17	obtain	obtain	VERB
ejpam-3133	288	18	that	that	DET
ejpam-3133	288	19	m(p	m(p	PROPN
ejpam-3133	288	20	,	,	PUNCT
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ejpam-3133	288	22	,	,	PUNCT
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ejpam-3133	288	27	{	{	PUNCT
ejpam-3133	288	28	gb(fp	gb(fp	PROPN
ejpam-3133	288	29	,	,	PUNCT
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ejpam-3133	288	31	,	,	PUNCT
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ejpam-3133	288	36	,	,	PUNCT
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ejpam-3133	288	38	,	,	PUNCT
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ejpam-3133	288	40	)	)	PUNCT
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ejpam-3133	288	43	,	,	PUNCT
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ejpam-3133	288	45	,	,	PUNCT
ejpam-3133	288	46	hq	hq	NOUN
ejpam-3133	288	47	)	)	PUNCT
ejpam-3133	288	48	,	,	PUNCT
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ejpam-3133	288	50	,	,	PUNCT
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ejpam-3133	288	52	,	,	PUNCT
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ejpam-3133	289	3	,	,	PUNCT
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ejpam-3133	289	5	,	,	PUNCT
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ejpam-3133	289	10	,	,	PUNCT
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ejpam-3133	289	13	{	{	PUNCT
ejpam-3133	289	14	gb(q	gb(q	PROPN
ejpam-3133	289	15	,	,	PUNCT
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ejpam-3133	289	17	,	,	PUNCT
ejpam-3133	289	18	t	t	PROPN
ejpam-3133	289	19	q	q	NOUN
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ejpam-3133	289	21	,	,	PUNCT
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ejpam-3133	289	23	,	,	PUNCT
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ejpam-3133	289	25	,	,	PUNCT
ejpam-3133	289	26	q	q	NOUN
ejpam-3133	289	27	)	)	PUNCT
ejpam-3133	289	28	,	,	PUNCT
ejpam-3133	289	29	gb(q	gb(q	PROPN
ejpam-3133	289	30	,	,	PUNCT
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ejpam-3133	289	32	,	,	PUNCT
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ejpam-3133	289	35	,	,	PUNCT
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ejpam-3133	289	37	,	,	PUNCT
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ejpam-3133	289	39	,	,	PUNCT
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ejpam-3133	289	41	q	q	NOUN
ejpam-3133	289	42	)	)	PUNCT
ejpam-3133	289	43	+	+	NOUN
ejpam-3133	289	44	gb(q	gb(q	NOUN
ejpam-3133	289	45	,	,	PUNCT
ejpam-3133	289	46	q	q	NOUN
ejpam-3133	289	47	,	,	PUNCT
ejpam-3133	289	48	q	q	X
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ejpam-3133	289	54	max{gb(q	max{gb(q	PROPN
ejpam-3133	289	55	,	,	PUNCT
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ejpam-3133	289	61	,	,	PUNCT
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ejpam-3133	289	65	,	,	PUNCT
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ejpam-3133	289	67	,	,	PUNCT
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ejpam-3133	289	69	q	q	NOUN
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ejpam-3133	289	74	=	=	SYM
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ejpam-3133	289	76	,	,	PUNCT
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ejpam-3133	289	80	q	q	NOUN
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ejpam-3133	290	21	,	,	PUNCT
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ejpam-3133	293	9	)	)	PUNCT
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ejpam-3133	293	18	,	,	PUNCT
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ejpam-3133	293	21	)	)	PUNCT
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ejpam-3133	294	13	,	,	PUNCT
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ejpam-3133	294	20	,	,	PUNCT
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ejpam-3133	295	3	)	)	PUNCT
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ejpam-3133	295	5	,	,	PUNCT
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ejpam-3133	295	10	1	1	NUM
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ejpam-3133	297	9	=	=	PUNCT
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ejpam-3133	299	1	q.	q.	PROPN
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ejpam-3133	300	5	common	common	ADJ
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ejpam-3133	301	7	the	the	DET
ejpam-3133	301	8	obtained	obtain	VERB
ejpam-3133	301	9	fixed	fix	VERB
ejpam-3133	301	10	point	point	NOUN
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ejpam-3133	301	13	.	.	PUNCT
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ejpam-3133	302	5	another	another	DET
ejpam-3133	302	6	common	common	ADJ
ejpam-3133	302	7	fixed	fix	VERB
ejpam-3133	302	8	point	point	NOUN
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ejpam-3133	302	25	=	=	SYM
ejpam-3133	303	1	gv	gv	PROPN
ejpam-3133	303	2	=	=	SYM
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ejpam-3133	303	4	=	=	SYM
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ejpam-3133	303	6	=	=	PUNCT
ejpam-3133	303	7	sv	sv	PROPN
ejpam-3133	303	8	=	=	NOUN
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ejpam-3133	303	10	=	=	PUNCT
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ejpam-3133	304	9	=	=	SYM
ejpam-3133	304	10	max	max	PROPN
ejpam-3133	304	11	{	{	PUNCT
ejpam-3133	304	12	gb(fq	gb(fq	PROPN
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ejpam-3133	304	15	,	,	PUNCT
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ejpam-3133	304	17	)	)	PUNCT
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ejpam-3133	304	22	,	,	PUNCT
ejpam-3133	304	23	rq	rq	NOUN
ejpam-3133	304	24	)	)	PUNCT
ejpam-3133	304	25	,	,	PUNCT
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ejpam-3133	304	34	,	,	PUNCT
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ejpam-3133	305	10	,	,	PUNCT
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ejpam-3133	305	13	{	{	PUNCT
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ejpam-3133	305	29	,	,	PUNCT
ejpam-3133	305	30	0	0	NUM
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ejpam-3133	305	38	v	v	NOUN
ejpam-3133	305	39	)	)	PUNCT
ejpam-3133	305	40	.	.	PUNCT
ejpam-3133	306	1	from	from	ADP
ejpam-3133	306	2	(	(	PUNCT
ejpam-3133	306	3	3	3	X
ejpam-3133	306	4	)	)	PUNCT
ejpam-3133	306	5	we	we	PRON
ejpam-3133	306	6	have	have	VERB
ejpam-3133	306	7	that	that	DET
ejpam-3133	306	8	ψ	ψ	X
ejpam-3133	306	9	(	(	PUNCT
ejpam-3133	306	10	s2gb(q	s2gb(q	PROPN
ejpam-3133	306	11	,	,	PUNCT
ejpam-3133	306	12	q	q	NOUN
ejpam-3133	306	13	,	,	PUNCT
ejpam-3133	306	14	v	v	NOUN
ejpam-3133	306	15	)	)	PUNCT
ejpam-3133	306	16	)	)	PUNCT
ejpam-3133	307	1	=	=	SYM
ejpam-3133	307	2	ψ	ψ	X
ejpam-3133	307	3	(	(	PUNCT
ejpam-3133	307	4	s2gb(fq	s2gb(fq	PROPN
ejpam-3133	307	5	,	,	PUNCT
ejpam-3133	307	6	gq	gq	PROPN
ejpam-3133	307	7	,	,	PUNCT
ejpam-3133	307	8	hv	hv	PROPN
ejpam-3133	307	9	)	)	PUNCT
ejpam-3133	307	10	)	)	PUNCT
ejpam-3133	308	1	z.	z.	PROPN
ejpam-3133	308	2	mustafa	mustafa	PROPN
ejpam-3133	308	3	et	et	PROPN
ejpam-3133	308	4	al	al	PROPN
ejpam-3133	308	5	.	.	PUNCT
ejpam-3133	308	6	/	/	SYM
ejpam-3133	308	7	eur	eur	PROPN
ejpam-3133	308	8	.	.	PUNCT
ejpam-3133	309	1	j.	j.	PROPN
ejpam-3133	309	2	pure	pure	PROPN
ejpam-3133	309	3	appl	appl	PROPN
ejpam-3133	309	4	.	.	PROPN
ejpam-3133	309	5	math	math	PROPN
ejpam-3133	309	6	,	,	PUNCT
ejpam-3133	309	7	11	11	NUM
ejpam-3133	309	8	(	(	PUNCT
ejpam-3133	309	9	1	1	NUM
ejpam-3133	309	10	)	)	PUNCT
ejpam-3133	309	11	(	(	PUNCT
ejpam-3133	309	12	2018	2018	NUM
ejpam-3133	309	13	)	)	PUNCT
ejpam-3133	309	14	,	,	PUNCT
ejpam-3133	309	15	90	90	NUM
ejpam-3133	309	16	-	-	SYM
ejpam-3133	309	17	109	109	NUM
ejpam-3133	309	18	102	102	NUM
ejpam-3133	309	19	≤	≤	NOUN
ejpam-3133	309	20	ψ	ψ	X
ejpam-3133	309	21	(	(	PUNCT
ejpam-3133	309	22	m(q	m(q	PROPN
ejpam-3133	309	23	,	,	PUNCT
ejpam-3133	309	24	q	q	NOUN
ejpam-3133	309	25	,	,	PUNCT
ejpam-3133	309	26	v	v	NOUN
ejpam-3133	309	27	)	)	PUNCT
ejpam-3133	309	28	)	)	PUNCT
ejpam-3133	310	1	−	−	PROPN
ejpam-3133	310	2	φ	φ	PROPN
ejpam-3133	310	3	(	(	PUNCT
ejpam-3133	310	4	m(q	m(q	PROPN
ejpam-3133	310	5	,	,	PUNCT
ejpam-3133	310	6	q	q	NOUN
ejpam-3133	310	7	,	,	PUNCT
ejpam-3133	310	8	v	v	NOUN
ejpam-3133	310	9	)	)	PUNCT
ejpam-3133	310	10	)	)	PUNCT
ejpam-3133	310	11	,	,	PUNCT
ejpam-3133	310	12	=	=	SYM
ejpam-3133	310	13	ψ	ψ	X
ejpam-3133	310	14	(	(	PUNCT
ejpam-3133	310	15	gb(q	gb(q	PROPN
ejpam-3133	310	16	,	,	PUNCT
ejpam-3133	310	17	q	q	NOUN
ejpam-3133	310	18	,	,	PUNCT
ejpam-3133	310	19	v	v	NOUN
ejpam-3133	310	20	)	)	PUNCT
ejpam-3133	310	21	)	)	PUNCT
ejpam-3133	310	22	)	)	PUNCT
ejpam-3133	311	1	−	−	PROPN
ejpam-3133	311	2	φ	φ	PROPN
ejpam-3133	311	3	(	(	PUNCT
ejpam-3133	311	4	gb(q	gb(q	PROPN
ejpam-3133	311	5	,	,	PUNCT
ejpam-3133	311	6	q	q	NOUN
ejpam-3133	311	7	,	,	PUNCT
ejpam-3133	311	8	v	v	NOUN
ejpam-3133	311	9	)	)	PUNCT
ejpam-3133	311	10	)	)	PUNCT
ejpam-3133	311	11	)	)	PUNCT
ejpam-3133	311	12	,	,	PUNCT
ejpam-3133	311	13	≤	≤	NUM
ejpam-3133	311	14	ψ	ψ	X
ejpam-3133	311	15	(	(	PUNCT
ejpam-3133	311	16	gb(q	gb(q	PROPN
ejpam-3133	311	17	,	,	PUNCT
ejpam-3133	311	18	q	q	NOUN
ejpam-3133	311	19	,	,	PUNCT
ejpam-3133	311	20	v	v	NOUN
ejpam-3133	311	21	)	)	PUNCT
ejpam-3133	311	22	)	)	PUNCT
ejpam-3133	311	23	)	)	PUNCT
ejpam-3133	311	24	.	.	PUNCT
ejpam-3133	312	1	(	(	PUNCT
ejpam-3133	312	2	35	35	NUM
ejpam-3133	312	3	)	)	PUNCT
ejpam-3133	312	4	again	again	ADV
ejpam-3133	312	5	,	,	PUNCT
ejpam-3133	312	6	since	since	SCONJ
ejpam-3133	312	7	s2	s2	PROPN
ejpam-3133	312	8	>	>	X
ejpam-3133	312	9	s	s	X
ejpam-3133	312	10	>	>	X
ejpam-3133	312	11	1	1	NUM
ejpam-3133	312	12	and	and	CCONJ
ejpam-3133	312	13	being	be	AUX
ejpam-3133	312	14	ψ	ψ	NOUN
ejpam-3133	312	15	is	be	AUX
ejpam-3133	312	16	increasing	increase	VERB
ejpam-3133	312	17	,	,	PUNCT
ejpam-3133	312	18	the	the	DET
ejpam-3133	312	19	above	above	ADJ
ejpam-3133	312	20	inequality	inequality	NOUN
ejpam-3133	312	21	implies	imply	VERB
ejpam-3133	312	22	that	that	SCONJ
ejpam-3133	312	23	gb(q	gb(q	NOUN
ejpam-3133	312	24	,	,	PUNCT
ejpam-3133	312	25	q	q	NOUN
ejpam-3133	312	26	,	,	PUNCT
ejpam-3133	312	27	v	v	NOUN
ejpam-3133	312	28	)	)	PUNCT
ejpam-3133	312	29	=	=	SYM
ejpam-3133	312	30	0	0	PUNCT
ejpam-3133	313	1	and	and	CCONJ
ejpam-3133	313	2	so	so	ADV
ejpam-3133	313	3	q	q	NOUN
ejpam-3133	314	1	=	=	PUNCT
ejpam-3133	314	2	v.	v.	CCONJ
ejpam-3133	314	3	that	that	PRON
ejpam-3133	314	4	is	be	AUX
ejpam-3133	314	5	,	,	PUNCT
ejpam-3133	314	6	q	q	X
ejpam-3133	314	7	is	be	AUX
ejpam-3133	314	8	the	the	DET
ejpam-3133	314	9	unique	unique	ADJ
ejpam-3133	314	10	common	common	ADJ
ejpam-3133	314	11	fixed	fix	VERB
ejpam-3133	314	12	point	point	NOUN
ejpam-3133	314	13	for	for	ADP
ejpam-3133	314	14	f	f	PROPN
ejpam-3133	314	15	,	,	PUNCT
ejpam-3133	314	16	g	g	PROPN
ejpam-3133	314	17	,	,	PUNCT
ejpam-3133	314	18	h	h	NOUN
ejpam-3133	314	19	,	,	PUNCT
ejpam-3133	314	20	s	s	X
ejpam-3133	314	21	,	,	PUNCT
ejpam-3133	314	22	r	r	NOUN
ejpam-3133	314	23	and	and	CCONJ
ejpam-3133	314	24	t	t	PROPN
ejpam-3133	314	25	.	.	PUNCT
ejpam-3133	315	1	the	the	DET
ejpam-3133	315	2	following	following	ADJ
ejpam-3133	315	3	result	result	NOUN
ejpam-3133	315	4	is	be	AUX
ejpam-3133	315	5	an	an	DET
ejpam-3133	315	6	immediate	immediate	ADJ
ejpam-3133	315	7	consequence	consequence	NOUN
ejpam-3133	315	8	of	of	ADP
ejpam-3133	315	9	theorem	theorem	NOUN
ejpam-3133	315	10	1	1	NUM
ejpam-3133	315	11	by	by	ADP
ejpam-3133	315	12	taking	take	VERB
ejpam-3133	315	13	φ(t	φ(t	PROPN
ejpam-3133	315	14	)	)	PUNCT
ejpam-3133	315	15	=	=	SYM
ejpam-3133	315	16	t.	t.	NOUN
ejpam-3133	315	17	corollary	corollary	NOUN
ejpam-3133	315	18	1	1	NUM
ejpam-3133	315	19	.	.	PUNCT
ejpam-3133	316	1	let	let	AUX
ejpam-3133	316	2	(	(	PUNCT
ejpam-3133	316	3	x	x	NOUN
ejpam-3133	316	4	,	,	PUNCT
ejpam-3133	316	5	gb	gb	PRON
ejpam-3133	316	6	)	)	PUNCT
ejpam-3133	316	7	be	be	AUX
ejpam-3133	316	8	a	a	DET
ejpam-3133	316	9	complete	complete	ADJ
ejpam-3133	316	10	gb	gb	ADV
ejpam-3133	316	11	-	-	PUNCT
ejpam-3133	316	12	metric	metric	ADJ
ejpam-3133	316	13	space	space	NOUN
ejpam-3133	316	14	and	and	CCONJ
ejpam-3133	316	15	let	let	VERB
ejpam-3133	316	16	f	f	X
ejpam-3133	316	17	,	,	PUNCT
ejpam-3133	316	18	g	g	PROPN
ejpam-3133	316	19	,	,	PUNCT
ejpam-3133	316	20	h	h	NOUN
ejpam-3133	316	21	,	,	PUNCT
ejpam-3133	316	22	r	r	NOUN
ejpam-3133	316	23	,	,	PUNCT
ejpam-3133	316	24	s	s	PROPN
ejpam-3133	316	25	,	,	PUNCT
ejpam-3133	316	26	t	t	NOUN
ejpam-3133	316	27	:	:	PUNCT
ejpam-3133	316	28	x	x	X
ejpam-3133	316	29	→	→	PUNCT
ejpam-3133	316	30	x	x	PART
ejpam-3133	316	31	be	be	AUX
ejpam-3133	316	32	self	self	NOUN
ejpam-3133	316	33	mappings	mapping	NOUN
ejpam-3133	316	34	such	such	ADJ
ejpam-3133	316	35	that	that	SCONJ
ejpam-3133	316	36	(	(	PUNCT
ejpam-3133	316	37	1	1	NUM
ejpam-3133	316	38	)	)	PUNCT
ejpam-3133	316	39	(	(	PUNCT
ejpam-3133	316	40	f	f	X
ejpam-3133	316	41	,	,	PUNCT
ejpam-3133	316	42	s	s	PART
ejpam-3133	316	43	)	)	PUNCT
ejpam-3133	316	44	and	and	CCONJ
ejpam-3133	316	45	(	(	PUNCT
ejpam-3133	316	46	g	g	NOUN
ejpam-3133	316	47	,	,	PUNCT
ejpam-3133	316	48	r	r	NOUN
ejpam-3133	316	49	)	)	PUNCT
ejpam-3133	316	50	satisfy	satisfy	NOUN
ejpam-3133	316	51	the	the	DET
ejpam-3133	316	52	(	(	PUNCT
ejpam-3133	316	53	e.a	e.a	PROPN
ejpam-3133	316	54	)	)	PUNCT
ejpam-3133	316	55	property	property	NOUN
ejpam-3133	316	56	;	;	PUNCT
ejpam-3133	316	57	(	(	PUNCT
ejpam-3133	316	58	2	2	X
ejpam-3133	316	59	)	)	PUNCT
ejpam-3133	316	60	f(x	f(x	PROPN
ejpam-3133	316	61	)	)	PUNCT
ejpam-3133	316	62	⊆	⊆	NUM
ejpam-3133	316	63	t	t	NOUN
ejpam-3133	316	64	(	(	PUNCT
ejpam-3133	316	65	x	x	NOUN
ejpam-3133	316	66	)	)	PUNCT
ejpam-3133	316	67	,	,	PUNCT
ejpam-3133	316	68	g(x	g(x	NOUN
ejpam-3133	316	69	)	)	PUNCT
ejpam-3133	316	70	⊆	⊆	NUM
ejpam-3133	316	71	s(x	s(x	NOUN
ejpam-3133	316	72	)	)	PUNCT
ejpam-3133	316	73	and	and	CCONJ
ejpam-3133	316	74	h(x	h(x	PROPN
ejpam-3133	316	75	)	)	PUNCT
ejpam-3133	316	76	⊆	⊆	NUM
ejpam-3133	316	77	r(x	r(x	PROPN
ejpam-3133	316	78	)	)	PUNCT
ejpam-3133	316	79	;	;	PUNCT
ejpam-3133	316	80	(	(	PUNCT
ejpam-3133	316	81	3	3	X
ejpam-3133	316	82	)	)	PUNCT
ejpam-3133	316	83	r(x	r(x	PROPN
ejpam-3133	316	84	)	)	PUNCT
ejpam-3133	316	85	is	be	AUX
ejpam-3133	316	86	a	a	DET
ejpam-3133	316	87	closed	closed	ADJ
ejpam-3133	316	88	subspace	subspace	NOUN
ejpam-3133	316	89	of	of	ADP
ejpam-3133	316	90	x	x	PRON
ejpam-3133	316	91	;	;	PUNCT
ejpam-3133	316	92	(	(	PUNCT
ejpam-3133	316	93	4	4	NUM
ejpam-3133	316	94	)	)	PUNCT
ejpam-3133	316	95	(	(	PUNCT
ejpam-3133	316	96	f	f	X
ejpam-3133	316	97	,	,	PUNCT
ejpam-3133	316	98	s	s	PART
ejpam-3133	316	99	)	)	PUNCT
ejpam-3133	316	100	,	,	PUNCT
ejpam-3133	316	101	(	(	PUNCT
ejpam-3133	316	102	g	g	NOUN
ejpam-3133	316	103	,	,	PUNCT
ejpam-3133	316	104	r	r	NOUN
ejpam-3133	316	105	)	)	PUNCT
ejpam-3133	316	106	and	and	CCONJ
ejpam-3133	316	107	(	(	PUNCT
ejpam-3133	316	108	h	h	NOUN
ejpam-3133	316	109	,	,	PUNCT
ejpam-3133	316	110	t	t	PROPN
ejpam-3133	316	111	)	)	PUNCT
ejpam-3133	316	112	are	be	AUX
ejpam-3133	316	113	weakly	weakly	ADV
ejpam-3133	316	114	compatible	compatible	ADJ
ejpam-3133	316	115	pairs	pair	NOUN
ejpam-3133	316	116	of	of	ADP
ejpam-3133	316	117	mappings	mapping	NOUN
ejpam-3133	316	118	;	;	PUNCT
ejpam-3133	316	119	(	(	PUNCT
ejpam-3133	316	120	5	5	X
ejpam-3133	316	121	)	)	PUNCT
ejpam-3133	316	122	ψ	ψ	NOUN
ejpam-3133	316	123	(	(	PUNCT
ejpam-3133	316	124	s2gb(fx	s2gb(fx	NOUN
ejpam-3133	316	125	,	,	PUNCT
ejpam-3133	316	126	gy	gy	NOUN
ejpam-3133	316	127	,	,	PUNCT
ejpam-3133	316	128	hz	hz	NOUN
ejpam-3133	316	129	)	)	PUNCT
ejpam-3133	316	130	)	)	PUNCT
ejpam-3133	317	1	≤	≤	NUM
ejpam-3133	317	2	ψ	ψ	X
ejpam-3133	317	3	(	(	PUNCT
ejpam-3133	317	4	m(x	m(x	PROPN
ejpam-3133	317	5	,	,	PUNCT
ejpam-3133	317	6	y	y	PROPN
ejpam-3133	317	7	,	,	PUNCT
ejpam-3133	317	8	z	z	NOUN
ejpam-3133	317	9	)	)	PUNCT
ejpam-3133	317	10	)	)	PUNCT
ejpam-3133	318	1	−m(x	−m(x	PROPN
ejpam-3133	318	2	,	,	PUNCT
ejpam-3133	318	3	y	y	PROPN
ejpam-3133	318	4	,	,	PUNCT
ejpam-3133	318	5	z	z	NOUN
ejpam-3133	318	6	)	)	PUNCT
ejpam-3133	318	7	for	for	ADP
ejpam-3133	318	8	all	all	DET
ejpam-3133	318	9	x	x	NOUN
ejpam-3133	318	10	,	,	PUNCT
ejpam-3133	318	11	y	y	PROPN
ejpam-3133	318	12	,	,	PUNCT
ejpam-3133	318	13	z	z	NOUN
ejpam-3133	318	14	∈	∈	PROPN
ejpam-3133	318	15	x	x	SYM
ejpam-3133	318	16	where	where	SCONJ
ejpam-3133	318	17	ψ	ψ	VERB
ejpam-3133	318	18	∈	∈	PROPN
ejpam-3133	318	19	ψ	ψ	X
ejpam-3133	318	20	and	and	CCONJ
ejpam-3133	318	21	m(x	m(x	PROPN
ejpam-3133	318	22	,	,	PUNCT
ejpam-3133	318	23	y	y	PROPN
ejpam-3133	318	24	,	,	PUNCT
ejpam-3133	318	25	z	z	NOUN
ejpam-3133	318	26	)	)	PUNCT
ejpam-3133	318	27	=	=	SYM
ejpam-3133	318	28	max	max	PROPN
ejpam-3133	318	29	{	{	PUNCT
ejpam-3133	318	30	gb(fx	gb(fx	PROPN
ejpam-3133	318	31	,	,	PUNCT
ejpam-3133	318	32	sy	sy	PROPN
ejpam-3133	318	33	,	,	PUNCT
ejpam-3133	318	34	tz	tz	PROPN
ejpam-3133	318	35	)	)	PUNCT
ejpam-3133	318	36	,	,	PUNCT
ejpam-3133	318	37	gb(gy	gb(gy	PROPN
ejpam-3133	318	38	,	,	PUNCT
ejpam-3133	318	39	ry	ry	NOUN
ejpam-3133	318	40	,	,	PUNCT
ejpam-3133	318	41	ry	ry	NOUN
ejpam-3133	318	42	)	)	PUNCT
ejpam-3133	318	43	,	,	PUNCT
ejpam-3133	318	44	gb(fx	gb(fx	PROPN
ejpam-3133	318	45	,	,	PUNCT
ejpam-3133	318	46	fx	fx	PROPN
ejpam-3133	318	47	,	,	PUNCT
ejpam-3133	318	48	hz	hz	PROPN
ejpam-3133	318	49	)	)	PUNCT
ejpam-3133	318	50	,	,	PUNCT
ejpam-3133	318	51	gb(tz	gb(tz	PROPN
ejpam-3133	318	52	,	,	PUNCT
ejpam-3133	318	53	tz	tz	PROPN
ejpam-3133	318	54	,	,	PUNCT
ejpam-3133	318	55	hz	hz	X
ejpam-3133	318	56	)	)	PUNCT
ejpam-3133	318	57	+	+	PROPN
ejpam-3133	318	58	gb(fx	gb(fx	PROPN
ejpam-3133	318	59	,	,	PUNCT
ejpam-3133	318	60	sx	sx	PROPN
ejpam-3133	318	61	,	,	PUNCT
ejpam-3133	318	62	sx	sx	PROPN
ejpam-3133	318	63	)	)	PUNCT
ejpam-3133	318	64	2s	2s	PROPN
ejpam-3133	318	65	}	}	PUNCT
ejpam-3133	318	66	.	.	PUNCT
ejpam-3133	319	1	then	then	ADV
ejpam-3133	319	2	f	f	X
ejpam-3133	319	3	,	,	PUNCT
ejpam-3133	319	4	g	g	PROPN
ejpam-3133	319	5	,	,	PUNCT
ejpam-3133	319	6	h	h	NOUN
ejpam-3133	319	7	,	,	PUNCT
ejpam-3133	319	8	r	r	NOUN
ejpam-3133	319	9	,	,	PUNCT
ejpam-3133	319	10	s	s	PART
ejpam-3133	319	11	and	and	CCONJ
ejpam-3133	319	12	t	t	PROPN
ejpam-3133	319	13	have	have	VERB
ejpam-3133	319	14	a	a	DET
ejpam-3133	319	15	unique	unique	ADJ
ejpam-3133	319	16	common	common	ADJ
ejpam-3133	319	17	fixed	fix	VERB
ejpam-3133	319	18	point	point	NOUN
ejpam-3133	319	19	in	in	ADP
ejpam-3133	319	20	x.	x.	NOUN
ejpam-3133	319	21	as	as	ADP
ejpam-3133	319	22	in	in	ADP
ejpam-3133	319	23	the	the	DET
ejpam-3133	319	24	above	above	ADJ
ejpam-3133	319	25	corollary	corollary	NOUN
ejpam-3133	319	26	,	,	PUNCT
ejpam-3133	319	27	the	the	DET
ejpam-3133	319	28	following	following	ADJ
ejpam-3133	319	29	result	result	NOUN
ejpam-3133	319	30	follows	follow	VERB
ejpam-3133	319	31	from	from	ADP
ejpam-3133	319	32	theorem	theorem	NOUN
ejpam-3133	319	33	1	1	NUM
ejpam-3133	319	34	by	by	ADP
ejpam-3133	319	35	taking	take	VERB
ejpam-3133	319	36	ψ(t	ψ(t	PROPN
ejpam-3133	319	37	)	)	PUNCT
ejpam-3133	319	38	=	=	SYM
ejpam-3133	320	1	t.	t.	NOUN
ejpam-3133	320	2	corollary	corollary	NOUN
ejpam-3133	320	3	2	2	NUM
ejpam-3133	320	4	.	.	PUNCT
ejpam-3133	321	1	let	let	AUX
ejpam-3133	321	2	(	(	PUNCT
ejpam-3133	321	3	x	x	NOUN
ejpam-3133	321	4	,	,	PUNCT
ejpam-3133	321	5	gb	gb	PRON
ejpam-3133	321	6	)	)	PUNCT
ejpam-3133	321	7	be	be	AUX
ejpam-3133	321	8	a	a	DET
ejpam-3133	321	9	complete	complete	ADJ
ejpam-3133	321	10	gb	gb	ADV
ejpam-3133	321	11	-	-	PUNCT
ejpam-3133	321	12	metric	metric	ADJ
ejpam-3133	321	13	space	space	NOUN
ejpam-3133	321	14	and	and	CCONJ
ejpam-3133	321	15	let	let	VERB
ejpam-3133	321	16	f	f	X
ejpam-3133	321	17	,	,	PUNCT
ejpam-3133	321	18	g	g	PROPN
ejpam-3133	321	19	,	,	PUNCT
ejpam-3133	321	20	h	h	NOUN
ejpam-3133	321	21	,	,	PUNCT
ejpam-3133	321	22	r	r	NOUN
ejpam-3133	321	23	,	,	PUNCT
ejpam-3133	321	24	s	s	PROPN
ejpam-3133	321	25	,	,	PUNCT
ejpam-3133	321	26	t	t	NOUN
ejpam-3133	321	27	:	:	PUNCT
ejpam-3133	321	28	x	x	X
ejpam-3133	321	29	→	→	PUNCT
ejpam-3133	321	30	x	x	PART
ejpam-3133	321	31	be	be	AUX
ejpam-3133	321	32	self	self	NOUN
ejpam-3133	321	33	mappings	mapping	NOUN
ejpam-3133	321	34	such	such	ADJ
ejpam-3133	321	35	that	that	SCONJ
ejpam-3133	321	36	(	(	PUNCT
ejpam-3133	321	37	1	1	NUM
ejpam-3133	321	38	)	)	PUNCT
ejpam-3133	321	39	(	(	PUNCT
ejpam-3133	321	40	f	f	X
ejpam-3133	321	41	,	,	PUNCT
ejpam-3133	321	42	s	s	PART
ejpam-3133	321	43	)	)	PUNCT
ejpam-3133	321	44	and	and	CCONJ
ejpam-3133	321	45	(	(	PUNCT
ejpam-3133	321	46	g	g	NOUN
ejpam-3133	321	47	,	,	PUNCT
ejpam-3133	321	48	r	r	NOUN
ejpam-3133	321	49	)	)	PUNCT
ejpam-3133	321	50	satisfy	satisfy	NOUN
ejpam-3133	321	51	the	the	DET
ejpam-3133	321	52	(	(	PUNCT
ejpam-3133	321	53	e.a	e.a	PROPN
ejpam-3133	321	54	)	)	PUNCT
ejpam-3133	321	55	property	property	NOUN
ejpam-3133	321	56	;	;	PUNCT
ejpam-3133	321	57	(	(	PUNCT
ejpam-3133	321	58	2	2	X
ejpam-3133	321	59	)	)	PUNCT
ejpam-3133	321	60	f(x	f(x	PROPN
ejpam-3133	321	61	)	)	PUNCT
ejpam-3133	321	62	⊆	⊆	NUM
ejpam-3133	321	63	t	t	NOUN
ejpam-3133	321	64	(	(	PUNCT
ejpam-3133	321	65	x	x	NOUN
ejpam-3133	321	66	)	)	PUNCT
ejpam-3133	321	67	,	,	PUNCT
ejpam-3133	321	68	g(x	g(x	NOUN
ejpam-3133	321	69	)	)	PUNCT
ejpam-3133	321	70	⊆	⊆	NUM
ejpam-3133	321	71	s(x	s(x	NOUN
ejpam-3133	321	72	)	)	PUNCT
ejpam-3133	321	73	and	and	CCONJ
ejpam-3133	321	74	h(x	h(x	PROPN
ejpam-3133	321	75	)	)	PUNCT
ejpam-3133	321	76	⊆	⊆	NUM
ejpam-3133	321	77	r(x	r(x	PROPN
ejpam-3133	321	78	)	)	PUNCT
ejpam-3133	321	79	;	;	PUNCT
ejpam-3133	321	80	(	(	PUNCT
ejpam-3133	321	81	3	3	X
ejpam-3133	321	82	)	)	PUNCT
ejpam-3133	321	83	r(x	r(x	PROPN
ejpam-3133	321	84	)	)	PUNCT
ejpam-3133	321	85	is	be	AUX
ejpam-3133	321	86	a	a	DET
ejpam-3133	321	87	closed	closed	ADJ
ejpam-3133	321	88	subspace	subspace	NOUN
ejpam-3133	321	89	of	of	ADP
ejpam-3133	321	90	x	x	PRON
ejpam-3133	321	91	;	;	PUNCT
ejpam-3133	321	92	(	(	PUNCT
ejpam-3133	321	93	4	4	NUM
ejpam-3133	321	94	)	)	PUNCT
ejpam-3133	321	95	(	(	PUNCT
ejpam-3133	321	96	f	f	X
ejpam-3133	321	97	,	,	PUNCT
ejpam-3133	321	98	s	s	PART
ejpam-3133	321	99	)	)	PUNCT
ejpam-3133	321	100	,	,	PUNCT
ejpam-3133	321	101	(	(	PUNCT
ejpam-3133	321	102	g	g	NOUN
ejpam-3133	321	103	,	,	PUNCT
ejpam-3133	321	104	r	r	NOUN
ejpam-3133	321	105	)	)	PUNCT
ejpam-3133	321	106	and	and	CCONJ
ejpam-3133	321	107	(	(	PUNCT
ejpam-3133	321	108	h	h	NOUN
ejpam-3133	321	109	,	,	PUNCT
ejpam-3133	321	110	t	t	PROPN
ejpam-3133	321	111	)	)	PUNCT
ejpam-3133	321	112	are	be	AUX
ejpam-3133	321	113	weakly	weakly	ADV
ejpam-3133	321	114	compatible	compatible	ADJ
ejpam-3133	321	115	pairs	pair	NOUN
ejpam-3133	321	116	of	of	ADP
ejpam-3133	321	117	mappings	mapping	NOUN
ejpam-3133	321	118	;	;	PUNCT
ejpam-3133	321	119	(	(	PUNCT
ejpam-3133	321	120	5	5	X
ejpam-3133	321	121	)	)	PUNCT
ejpam-3133	321	122	s2gb(fx	s2gb(fx	PROPN
ejpam-3133	321	123	,	,	PUNCT
ejpam-3133	321	124	gy	gy	NOUN
ejpam-3133	321	125	,	,	PUNCT
ejpam-3133	321	126	hz	hz	PROPN
ejpam-3133	321	127	)	)	PUNCT
ejpam-3133	321	128	≤m(x	≤m(x	PROPN
ejpam-3133	321	129	,	,	PUNCT
ejpam-3133	321	130	y	y	PROPN
ejpam-3133	321	131	,	,	PUNCT
ejpam-3133	321	132	z)−φ	z)−φ	PROPN
ejpam-3133	321	133	(	(	PUNCT
ejpam-3133	321	134	m(x	m(x	PROPN
ejpam-3133	321	135	,	,	PUNCT
ejpam-3133	321	136	y	y	PROPN
ejpam-3133	321	137	,	,	PUNCT
ejpam-3133	321	138	z	z	NOUN
ejpam-3133	321	139	)	)	PUNCT
ejpam-3133	321	140	)	)	PUNCT
ejpam-3133	321	141	for	for	ADP
ejpam-3133	321	142	each	each	DET
ejpam-3133	321	143	x	x	PROPN
ejpam-3133	321	144	,	,	PUNCT
ejpam-3133	321	145	y	y	PROPN
ejpam-3133	321	146	,	,	PUNCT
ejpam-3133	321	147	z	z	NOUN
ejpam-3133	321	148	∈	∈	PROPN
ejpam-3133	321	149	x	x	SYM
ejpam-3133	321	150	where	where	SCONJ
ejpam-3133	321	151	φ	φ	PROPN
ejpam-3133	321	152	∈	∈	PROPN
ejpam-3133	321	153	ψ	ψ	X
ejpam-3133	321	154	and	and	CCONJ
ejpam-3133	321	155	m(x	m(x	PROPN
ejpam-3133	321	156	,	,	PUNCT
ejpam-3133	321	157	y	y	PROPN
ejpam-3133	321	158	,	,	PUNCT
ejpam-3133	321	159	z	z	NOUN
ejpam-3133	321	160	)	)	PUNCT
ejpam-3133	321	161	=	=	SYM
ejpam-3133	321	162	max	max	PROPN
ejpam-3133	321	163	{	{	PUNCT
ejpam-3133	321	164	gb(fx	gb(fx	PROPN
ejpam-3133	321	165	,	,	PUNCT
ejpam-3133	321	166	sy	sy	PROPN
ejpam-3133	321	167	,	,	PUNCT
ejpam-3133	321	168	tz	tz	PROPN
ejpam-3133	321	169	)	)	PUNCT
ejpam-3133	321	170	,	,	PUNCT
ejpam-3133	321	171	gb(gy	gb(gy	PROPN
ejpam-3133	321	172	,	,	PUNCT
ejpam-3133	321	173	ry	ry	NOUN
ejpam-3133	321	174	,	,	PUNCT
ejpam-3133	321	175	ry	ry	NOUN
ejpam-3133	321	176	)	)	PUNCT
ejpam-3133	321	177	,	,	PUNCT
ejpam-3133	321	178	gb(fx	gb(fx	PROPN
ejpam-3133	321	179	,	,	PUNCT
ejpam-3133	321	180	fx	fx	PROPN
ejpam-3133	321	181	,	,	PUNCT
ejpam-3133	321	182	hz	hz	PROPN
ejpam-3133	321	183	)	)	PUNCT
ejpam-3133	321	184	,	,	PUNCT
ejpam-3133	321	185	gb(tz	gb(tz	PROPN
ejpam-3133	321	186	,	,	PUNCT
ejpam-3133	321	187	tz	tz	PROPN
ejpam-3133	321	188	,	,	PUNCT
ejpam-3133	321	189	hz	hz	X
ejpam-3133	321	190	)	)	PUNCT
ejpam-3133	321	191	+	+	PROPN
ejpam-3133	321	192	gb(fx	gb(fx	PROPN
ejpam-3133	321	193	,	,	PUNCT
ejpam-3133	321	194	sx	sx	PROPN
ejpam-3133	321	195	,	,	PUNCT
ejpam-3133	321	196	sx	sx	PROPN
ejpam-3133	321	197	)	)	PUNCT
ejpam-3133	321	198	2s	2s	PROPN
ejpam-3133	321	199	}	}	PUNCT
ejpam-3133	321	200	.	.	PUNCT
ejpam-3133	322	1	then	then	ADV
ejpam-3133	322	2	f	f	X
ejpam-3133	322	3	,	,	PUNCT
ejpam-3133	322	4	g	g	PROPN
ejpam-3133	322	5	,	,	PUNCT
ejpam-3133	322	6	h	h	NOUN
ejpam-3133	322	7	,	,	PUNCT
ejpam-3133	322	8	r	r	NOUN
ejpam-3133	322	9	,	,	PUNCT
ejpam-3133	322	10	s	s	PART
ejpam-3133	322	11	and	and	CCONJ
ejpam-3133	322	12	t	t	PROPN
ejpam-3133	322	13	have	have	VERB
ejpam-3133	322	14	a	a	DET
ejpam-3133	322	15	unique	unique	ADJ
ejpam-3133	322	16	common	common	ADJ
ejpam-3133	322	17	fixed	fix	VERB
ejpam-3133	322	18	point	point	NOUN
ejpam-3133	322	19	in	in	ADP
ejpam-3133	322	20	x.	x.	NOUN
ejpam-3133	322	21	by	by	ADP
ejpam-3133	322	22	specifying	specify	VERB
ejpam-3133	322	23	ψ(t	ψ(t	PROPN
ejpam-3133	322	24	)	)	PUNCT
ejpam-3133	322	25	=	=	SYM
ejpam-3133	322	26	t	t	PROPN
ejpam-3133	322	27	and	and	CCONJ
ejpam-3133	322	28	φ(t	φ(t	PROPN
ejpam-3133	322	29	)	)	PUNCT
ejpam-3133	323	1	=	=	SYM
ejpam-3133	323	2	t	t	PROPN
ejpam-3133	323	3	k	k	NOUN
ejpam-3133	323	4	with	with	ADP
ejpam-3133	323	5	k	k	PROPN
ejpam-3133	323	6	>	>	X
ejpam-3133	323	7	1	1	NUM
ejpam-3133	323	8	in	in	ADP
ejpam-3133	323	9	theorem	theorem	NOUN
ejpam-3133	323	10	1	1	NUM
ejpam-3133	323	11	,	,	PUNCT
ejpam-3133	323	12	we	we	PRON
ejpam-3133	323	13	get	get	VERB
ejpam-3133	323	14	the	the	DET
ejpam-3133	323	15	following	follow	VERB
ejpam-3133	323	16	corollary	corollary	NOUN
ejpam-3133	323	17	.	.	PUNCT
ejpam-3133	324	1	z.	z.	PROPN
ejpam-3133	324	2	mustafa	mustafa	PROPN
ejpam-3133	324	3	et	et	PROPN
ejpam-3133	324	4	al	al	PROPN
ejpam-3133	324	5	.	.	PUNCT
ejpam-3133	324	6	/	/	SYM
ejpam-3133	324	7	eur	eur	PROPN
ejpam-3133	324	8	.	.	PUNCT
ejpam-3133	325	1	j.	j.	PROPN
ejpam-3133	325	2	pure	pure	PROPN
ejpam-3133	325	3	appl	appl	PROPN
ejpam-3133	325	4	.	.	PROPN
ejpam-3133	325	5	math	math	PROPN
ejpam-3133	325	6	,	,	PUNCT
ejpam-3133	325	7	11	11	NUM
ejpam-3133	325	8	(	(	PUNCT
ejpam-3133	325	9	1	1	NUM
ejpam-3133	325	10	)	)	PUNCT
ejpam-3133	325	11	(	(	PUNCT
ejpam-3133	325	12	2018	2018	NUM
ejpam-3133	325	13	)	)	PUNCT
ejpam-3133	325	14	,	,	PUNCT
ejpam-3133	325	15	90	90	NUM
ejpam-3133	325	16	-	-	SYM
ejpam-3133	325	17	109	109	NUM
ejpam-3133	325	18	103	103	NUM
ejpam-3133	325	19	corollary	corollary	NOUN
ejpam-3133	325	20	3	3	NUM
ejpam-3133	325	21	.	.	PUNCT
ejpam-3133	326	1	let	let	AUX
ejpam-3133	326	2	(	(	PUNCT
ejpam-3133	326	3	x	x	NOUN
ejpam-3133	326	4	,	,	PUNCT
ejpam-3133	326	5	gb	gb	PRON
ejpam-3133	326	6	)	)	PUNCT
ejpam-3133	326	7	be	be	AUX
ejpam-3133	326	8	a	a	DET
ejpam-3133	326	9	complete	complete	ADJ
ejpam-3133	326	10	gb	gb	ADV
ejpam-3133	326	11	-	-	PUNCT
ejpam-3133	326	12	metric	metric	ADJ
ejpam-3133	326	13	space	space	NOUN
ejpam-3133	326	14	and	and	CCONJ
ejpam-3133	326	15	let	let	VERB
ejpam-3133	326	16	f	f	X
ejpam-3133	326	17	,	,	PUNCT
ejpam-3133	326	18	g	g	PROPN
ejpam-3133	326	19	,	,	PUNCT
ejpam-3133	326	20	h	h	NOUN
ejpam-3133	326	21	,	,	PUNCT
ejpam-3133	326	22	r	r	NOUN
ejpam-3133	326	23	,	,	PUNCT
ejpam-3133	326	24	s	s	PROPN
ejpam-3133	326	25	,	,	PUNCT
ejpam-3133	326	26	t	t	NOUN
ejpam-3133	326	27	:	:	PUNCT
ejpam-3133	326	28	x	x	X
ejpam-3133	327	1	→	→	PUNCT
ejpam-3133	327	2	x	x	X
ejpam-3133	327	3	are	be	AUX
ejpam-3133	327	4	self	self	NOUN
ejpam-3133	327	5	mappings	mapping	NOUN
ejpam-3133	327	6	such	such	ADJ
ejpam-3133	327	7	that	that	SCONJ
ejpam-3133	327	8	(	(	PUNCT
ejpam-3133	327	9	1	1	NUM
ejpam-3133	327	10	)	)	PUNCT
ejpam-3133	327	11	(	(	PUNCT
ejpam-3133	327	12	f	f	X
ejpam-3133	327	13	,	,	PUNCT
ejpam-3133	327	14	s	s	PART
ejpam-3133	327	15	)	)	PUNCT
ejpam-3133	327	16	and	and	CCONJ
ejpam-3133	327	17	(	(	PUNCT
ejpam-3133	327	18	g	g	NOUN
ejpam-3133	327	19	,	,	PUNCT
ejpam-3133	327	20	r	r	NOUN
ejpam-3133	327	21	)	)	PUNCT
ejpam-3133	327	22	satisfy	satisfy	NOUN
ejpam-3133	327	23	the	the	DET
ejpam-3133	327	24	(	(	PUNCT
ejpam-3133	327	25	e.a	e.a	PROPN
ejpam-3133	327	26	)	)	PUNCT
ejpam-3133	327	27	property	property	NOUN
ejpam-3133	327	28	;	;	PUNCT
ejpam-3133	327	29	(	(	PUNCT
ejpam-3133	327	30	2	2	X
ejpam-3133	327	31	)	)	PUNCT
ejpam-3133	327	32	f(x	f(x	PROPN
ejpam-3133	327	33	)	)	PUNCT
ejpam-3133	327	34	⊆	⊆	NUM
ejpam-3133	327	35	t	t	NOUN
ejpam-3133	327	36	(	(	PUNCT
ejpam-3133	327	37	x	x	NOUN
ejpam-3133	327	38	)	)	PUNCT
ejpam-3133	327	39	,	,	PUNCT
ejpam-3133	327	40	g(x	g(x	NOUN
ejpam-3133	327	41	)	)	PUNCT
ejpam-3133	327	42	⊆	⊆	NUM
ejpam-3133	327	43	s(x	s(x	NOUN
ejpam-3133	327	44	)	)	PUNCT
ejpam-3133	327	45	and	and	CCONJ
ejpam-3133	327	46	h(x	h(x	PROPN
ejpam-3133	327	47	)	)	PUNCT
ejpam-3133	327	48	⊆	⊆	NUM
ejpam-3133	327	49	r(x	r(x	PROPN
ejpam-3133	327	50	)	)	PUNCT
ejpam-3133	327	51	;	;	PUNCT
ejpam-3133	327	52	(	(	PUNCT
ejpam-3133	327	53	3	3	X
ejpam-3133	327	54	)	)	PUNCT
ejpam-3133	327	55	r(x	r(x	PROPN
ejpam-3133	327	56	)	)	PUNCT
ejpam-3133	327	57	is	be	AUX
ejpam-3133	327	58	a	a	DET
ejpam-3133	327	59	closed	closed	ADJ
ejpam-3133	327	60	subspace	subspace	NOUN
ejpam-3133	327	61	of	of	ADP
ejpam-3133	327	62	x	x	PRON
ejpam-3133	327	63	;	;	PUNCT
ejpam-3133	327	64	(	(	PUNCT
ejpam-3133	327	65	4	4	NUM
ejpam-3133	327	66	)	)	PUNCT
ejpam-3133	327	67	(	(	PUNCT
ejpam-3133	327	68	f	f	X
ejpam-3133	327	69	,	,	PUNCT
ejpam-3133	327	70	s	s	PART
ejpam-3133	327	71	)	)	PUNCT
ejpam-3133	327	72	,	,	PUNCT
ejpam-3133	327	73	(	(	PUNCT
ejpam-3133	327	74	g	g	NOUN
ejpam-3133	327	75	,	,	PUNCT
ejpam-3133	327	76	r	r	NOUN
ejpam-3133	327	77	)	)	PUNCT
ejpam-3133	327	78	and	and	CCONJ
ejpam-3133	327	79	(	(	PUNCT
ejpam-3133	327	80	h	h	NOUN
ejpam-3133	327	81	,	,	PUNCT
ejpam-3133	327	82	t	t	PROPN
ejpam-3133	327	83	)	)	PUNCT
ejpam-3133	327	84	are	be	AUX
ejpam-3133	327	85	weakly	weakly	ADV
ejpam-3133	327	86	compatible	compatible	ADJ
ejpam-3133	327	87	pairs	pair	NOUN
ejpam-3133	327	88	of	of	ADP
ejpam-3133	327	89	mappings	mapping	NOUN
ejpam-3133	327	90	;	;	PUNCT
ejpam-3133	327	91	(	(	PUNCT
ejpam-3133	327	92	5	5	X
ejpam-3133	327	93	)	)	PUNCT
ejpam-3133	327	94	ψ	ψ	NOUN
ejpam-3133	327	95	(	(	PUNCT
ejpam-3133	327	96	s2gb(fx	s2gb(fx	NOUN
ejpam-3133	327	97	,	,	PUNCT
ejpam-3133	327	98	gy	gy	NOUN
ejpam-3133	327	99	,	,	PUNCT
ejpam-3133	327	100	hz	hz	PROPN
ejpam-3133	327	101	)	)	PUNCT
ejpam-3133	327	102	)	)	PUNCT
ejpam-3133	327	103	≤	≤	PUNCT
ejpam-3133	328	1	k−1	k−1	PROPN
ejpam-3133	328	2	k	k	PROPN
ejpam-3133	328	3	m(x	m(x	PROPN
ejpam-3133	328	4	,	,	PUNCT
ejpam-3133	328	5	y	y	PROPN
ejpam-3133	328	6	,	,	PUNCT
ejpam-3133	328	7	z	z	NOUN
ejpam-3133	328	8	)	)	PUNCT
ejpam-3133	328	9	for	for	ADP
ejpam-3133	328	10	each	each	DET
ejpam-3133	328	11	x	x	PROPN
ejpam-3133	328	12	,	,	PUNCT
ejpam-3133	328	13	y	y	PROPN
ejpam-3133	328	14	,	,	PUNCT
ejpam-3133	328	15	z	z	NOUN
ejpam-3133	328	16	∈	∈	PROPN
ejpam-3133	328	17	x	x	PUNCT
ejpam-3133	328	18	where	where	SCONJ
ejpam-3133	328	19	k	k	PROPN
ejpam-3133	328	20	is	be	AUX
ejpam-3133	328	21	a	a	DET
ejpam-3133	328	22	positive	positive	ADJ
ejpam-3133	328	23	integer	integer	NOUN
ejpam-3133	328	24	and	and	CCONJ
ejpam-3133	328	25	m(x	m(x	PROPN
ejpam-3133	328	26	,	,	PUNCT
ejpam-3133	328	27	y	y	PROPN
ejpam-3133	328	28	,	,	PUNCT
ejpam-3133	328	29	z	z	NOUN
ejpam-3133	328	30	)	)	PUNCT
ejpam-3133	328	31	=	=	SYM
ejpam-3133	328	32	max	max	PROPN
ejpam-3133	328	33	{	{	PUNCT
ejpam-3133	328	34	gb(fx	gb(fx	PROPN
ejpam-3133	328	35	,	,	PUNCT
ejpam-3133	328	36	sy	sy	PROPN
ejpam-3133	328	37	,	,	PUNCT
ejpam-3133	328	38	tz	tz	PROPN
ejpam-3133	328	39	)	)	PUNCT
ejpam-3133	328	40	,	,	PUNCT
ejpam-3133	328	41	gb(gy	gb(gy	PROPN
ejpam-3133	328	42	,	,	PUNCT
ejpam-3133	328	43	ry	ry	NOUN
ejpam-3133	328	44	,	,	PUNCT
ejpam-3133	328	45	ry	ry	NOUN
ejpam-3133	328	46	)	)	PUNCT
ejpam-3133	328	47	,	,	PUNCT
ejpam-3133	328	48	gb(fx	gb(fx	PROPN
ejpam-3133	328	49	,	,	PUNCT
ejpam-3133	328	50	fx	fx	PROPN
ejpam-3133	328	51	,	,	PUNCT
ejpam-3133	328	52	hz	hz	PROPN
ejpam-3133	328	53	)	)	PUNCT
ejpam-3133	328	54	,	,	PUNCT
ejpam-3133	328	55	gb(tz	gb(tz	PROPN
ejpam-3133	328	56	,	,	PUNCT
ejpam-3133	328	57	tz	tz	PROPN
ejpam-3133	328	58	,	,	PUNCT
ejpam-3133	328	59	hz	hz	X
ejpam-3133	328	60	)	)	PUNCT
ejpam-3133	328	61	+	+	PROPN
ejpam-3133	328	62	gb(fx	gb(fx	PROPN
ejpam-3133	328	63	,	,	PUNCT
ejpam-3133	328	64	sx	sx	PROPN
ejpam-3133	328	65	,	,	PUNCT
ejpam-3133	328	66	sx	sx	PROPN
ejpam-3133	328	67	)	)	PUNCT
ejpam-3133	328	68	2s	2s	PROPN
ejpam-3133	328	69	}	}	PUNCT
ejpam-3133	328	70	.	.	PUNCT
ejpam-3133	329	1	then	then	ADV
ejpam-3133	329	2	f	f	X
ejpam-3133	329	3	,	,	PUNCT
ejpam-3133	329	4	g	g	PROPN
ejpam-3133	329	5	,	,	PUNCT
ejpam-3133	329	6	h	h	NOUN
ejpam-3133	329	7	,	,	PUNCT
ejpam-3133	329	8	r	r	NOUN
ejpam-3133	329	9	,	,	PUNCT
ejpam-3133	329	10	s	s	PART
ejpam-3133	329	11	and	and	CCONJ
ejpam-3133	329	12	t	t	PROPN
ejpam-3133	329	13	have	have	VERB
ejpam-3133	329	14	a	a	DET
ejpam-3133	329	15	unique	unique	ADJ
ejpam-3133	329	16	common	common	ADJ
ejpam-3133	329	17	fixed	fix	VERB
ejpam-3133	329	18	point	point	NOUN
ejpam-3133	329	19	in	in	ADP
ejpam-3133	329	20	x.	x.	NOUN
ejpam-3133	329	21	by	by	ADP
ejpam-3133	329	22	taking	take	VERB
ejpam-3133	329	23	f	f	PROPN
ejpam-3133	329	24	=	=	SYM
ejpam-3133	329	25	g	g	PROPN
ejpam-3133	329	26	and	and	CCONJ
ejpam-3133	329	27	r	r	NOUN
ejpam-3133	329	28	=	=	SYM
ejpam-3133	329	29	s	s	PROPN
ejpam-3133	329	30	in	in	ADP
ejpam-3133	329	31	theorem	theorem	NOUN
ejpam-3133	329	32	1	1	NUM
ejpam-3133	329	33	,	,	PUNCT
ejpam-3133	329	34	we	we	PRON
ejpam-3133	329	35	get	get	VERB
ejpam-3133	329	36	the	the	DET
ejpam-3133	329	37	following	follow	VERB
ejpam-3133	329	38	result	result	NOUN
ejpam-3133	329	39	.	.	PUNCT
ejpam-3133	330	1	corollary	corollary	ADJ
ejpam-3133	330	2	4	4	NUM
ejpam-3133	330	3	.	.	PUNCT
ejpam-3133	331	1	let	let	AUX
ejpam-3133	331	2	(	(	PUNCT
ejpam-3133	331	3	x	x	NOUN
ejpam-3133	331	4	,	,	PUNCT
ejpam-3133	331	5	gb	gb	PRON
ejpam-3133	331	6	)	)	PUNCT
ejpam-3133	331	7	be	be	AUX
ejpam-3133	331	8	a	a	DET
ejpam-3133	331	9	complete	complete	ADJ
ejpam-3133	331	10	gb	gb	ADV
ejpam-3133	331	11	-	-	PUNCT
ejpam-3133	331	12	metric	metric	ADJ
ejpam-3133	331	13	space	space	NOUN
ejpam-3133	331	14	and	and	CCONJ
ejpam-3133	331	15	let	let	VERB
ejpam-3133	331	16	f	f	X
ejpam-3133	331	17	,	,	PUNCT
ejpam-3133	331	18	g	g	PROPN
ejpam-3133	331	19	,	,	PUNCT
ejpam-3133	331	20	h	h	NOUN
ejpam-3133	331	21	,	,	PUNCT
ejpam-3133	331	22	r	r	NOUN
ejpam-3133	331	23	,	,	PUNCT
ejpam-3133	331	24	s	s	PROPN
ejpam-3133	331	25	,	,	PUNCT
ejpam-3133	331	26	t	t	NOUN
ejpam-3133	331	27	:	:	PUNCT
ejpam-3133	331	28	x	x	X
ejpam-3133	331	29	→	→	PUNCT
ejpam-3133	331	30	x	x	PART
ejpam-3133	331	31	be	be	AUX
ejpam-3133	331	32	self	self	NOUN
ejpam-3133	331	33	mappings	mapping	NOUN
ejpam-3133	331	34	such	such	ADJ
ejpam-3133	331	35	that	that	SCONJ
ejpam-3133	331	36	(	(	PUNCT
ejpam-3133	331	37	1	1	NUM
ejpam-3133	331	38	)	)	PUNCT
ejpam-3133	331	39	(	(	PUNCT
ejpam-3133	331	40	g	g	PROPN
ejpam-3133	331	41	,	,	PUNCT
ejpam-3133	331	42	s	s	PART
ejpam-3133	331	43	)	)	PUNCT
ejpam-3133	331	44	satisfies	satisfy	VERB
ejpam-3133	331	45	the	the	DET
ejpam-3133	331	46	(	(	PUNCT
ejpam-3133	331	47	e.a	e.a	PROPN
ejpam-3133	331	48	)	)	PUNCT
ejpam-3133	331	49	property	property	NOUN
ejpam-3133	331	50	;	;	PUNCT
ejpam-3133	331	51	(	(	PUNCT
ejpam-3133	331	52	2	2	X
ejpam-3133	331	53	)	)	PUNCT
ejpam-3133	331	54	g(x	g(x	NOUN
ejpam-3133	331	55	)	)	PUNCT
ejpam-3133	331	56	⊆	⊆	NUM
ejpam-3133	331	57	t	t	NOUN
ejpam-3133	331	58	(	(	PUNCT
ejpam-3133	331	59	x	x	NOUN
ejpam-3133	331	60	)	)	PUNCT
ejpam-3133	331	61	,	,	PUNCT
ejpam-3133	331	62	g(x	g(x	NOUN
ejpam-3133	331	63	)	)	PUNCT
ejpam-3133	331	64	⊆	⊆	NUM
ejpam-3133	331	65	s(x	s(x	NOUN
ejpam-3133	331	66	)	)	PUNCT
ejpam-3133	331	67	and	and	CCONJ
ejpam-3133	331	68	h(x	h(x	PROPN
ejpam-3133	331	69	)	)	PUNCT
ejpam-3133	331	70	⊆	⊆	NUM
ejpam-3133	331	71	s(x	s(x	NOUN
ejpam-3133	331	72	)	)	PUNCT
ejpam-3133	331	73	;	;	PUNCT
ejpam-3133	331	74	(	(	PUNCT
ejpam-3133	331	75	3	3	X
ejpam-3133	331	76	)	)	PUNCT
ejpam-3133	331	77	s(x	s(x	PROPN
ejpam-3133	331	78	)	)	PUNCT
ejpam-3133	331	79	is	be	AUX
ejpam-3133	331	80	a	a	DET
ejpam-3133	331	81	closed	closed	ADJ
ejpam-3133	331	82	subspace	subspace	NOUN
ejpam-3133	331	83	of	of	ADP
ejpam-3133	331	84	x	x	PRON
ejpam-3133	331	85	;	;	PUNCT
ejpam-3133	331	86	(	(	PUNCT
ejpam-3133	331	87	4	4	NUM
ejpam-3133	331	88	)	)	PUNCT
ejpam-3133	331	89	(	(	PUNCT
ejpam-3133	331	90	g	g	PROPN
ejpam-3133	331	91	,	,	PUNCT
ejpam-3133	331	92	s	s	PROPN
ejpam-3133	331	93	)	)	PUNCT
ejpam-3133	331	94	and	and	CCONJ
ejpam-3133	331	95	(	(	PUNCT
ejpam-3133	331	96	h	h	NOUN
ejpam-3133	331	97	,	,	PUNCT
ejpam-3133	331	98	t	t	PROPN
ejpam-3133	331	99	)	)	PUNCT
ejpam-3133	331	100	are	be	AUX
ejpam-3133	331	101	weakly	weakly	ADV
ejpam-3133	331	102	compatible	compatible	ADJ
ejpam-3133	331	103	pairs	pair	NOUN
ejpam-3133	331	104	of	of	ADP
ejpam-3133	331	105	mappings	mapping	NOUN
ejpam-3133	331	106	;	;	PUNCT
ejpam-3133	331	107	(	(	PUNCT
ejpam-3133	331	108	5	5	X
ejpam-3133	331	109	)	)	PUNCT
ejpam-3133	331	110	ψ	ψ	NOUN
ejpam-3133	331	111	(	(	PUNCT
ejpam-3133	331	112	s2gb(gx	s2gb(gx	PROPN
ejpam-3133	331	113	,	,	PUNCT
ejpam-3133	331	114	gy	gy	PROPN
ejpam-3133	331	115	,	,	PUNCT
ejpam-3133	331	116	hz	hz	PROPN
ejpam-3133	331	117	)	)	PUNCT
ejpam-3133	331	118	)	)	PUNCT
ejpam-3133	332	1	≤	≤	NUM
ejpam-3133	333	1	ψ	ψ	X
ejpam-3133	333	2	(	(	PUNCT
ejpam-3133	333	3	m(x	m(x	PROPN
ejpam-3133	333	4	,	,	PUNCT
ejpam-3133	333	5	y	y	PROPN
ejpam-3133	333	6	,	,	PUNCT
ejpam-3133	333	7	z	z	NOUN
ejpam-3133	333	8	)	)	PUNCT
ejpam-3133	333	9	)	)	PUNCT
ejpam-3133	334	1	−	−	PROPN
ejpam-3133	334	2	φ	φ	PROPN
ejpam-3133	334	3	(	(	PUNCT
ejpam-3133	334	4	m(x	m(x	PROPN
ejpam-3133	334	5	,	,	PUNCT
ejpam-3133	334	6	y	y	PROPN
ejpam-3133	334	7	,	,	PUNCT
ejpam-3133	334	8	z	z	NOUN
ejpam-3133	334	9	)	)	PUNCT
ejpam-3133	334	10	)	)	PUNCT
ejpam-3133	334	11	for	for	ADP
ejpam-3133	334	12	each	each	DET
ejpam-3133	334	13	x	x	PROPN
ejpam-3133	334	14	,	,	PUNCT
ejpam-3133	334	15	y	y	PROPN
ejpam-3133	334	16	,	,	PUNCT
ejpam-3133	334	17	z	z	NOUN
ejpam-3133	334	18	∈	∈	PROPN
ejpam-3133	334	19	x	x	SYM
ejpam-3133	334	20	where	where	SCONJ
ejpam-3133	334	21	φ	φ	PROPN
ejpam-3133	334	22	∈	∈	PROPN
ejpam-3133	334	23	ψ	ψ	X
ejpam-3133	334	24	and	and	CCONJ
ejpam-3133	334	25	m(x	m(x	PROPN
ejpam-3133	334	26	,	,	PUNCT
ejpam-3133	334	27	y	y	PROPN
ejpam-3133	334	28	,	,	PUNCT
ejpam-3133	334	29	z	z	NOUN
ejpam-3133	334	30	)	)	PUNCT
ejpam-3133	334	31	=	=	SYM
ejpam-3133	334	32	max	max	PROPN
ejpam-3133	334	33	{	{	PUNCT
ejpam-3133	334	34	gb(gx	gb(gx	PROPN
ejpam-3133	334	35	,	,	PUNCT
ejpam-3133	334	36	sy	sy	PROPN
ejpam-3133	334	37	,	,	PUNCT
ejpam-3133	334	38	tz	tz	PROPN
ejpam-3133	334	39	)	)	PUNCT
ejpam-3133	334	40	,	,	PUNCT
ejpam-3133	334	41	gb(gy	gb(gy	PROPN
ejpam-3133	334	42	,	,	PUNCT
ejpam-3133	334	43	sy	sy	PROPN
ejpam-3133	334	44	,	,	PUNCT
ejpam-3133	334	45	sy	sy	PROPN
ejpam-3133	334	46	)	)	PUNCT
ejpam-3133	334	47	,	,	PUNCT
ejpam-3133	334	48	gb(gx	gb(gx	PROPN
ejpam-3133	334	49	,	,	PUNCT
ejpam-3133	334	50	gx	gx	PROPN
ejpam-3133	334	51	,	,	PUNCT
ejpam-3133	334	52	hz	hz	PROPN
ejpam-3133	334	53	)	)	PUNCT
ejpam-3133	334	54	,	,	PUNCT
ejpam-3133	334	55	gb(tz	gb(tz	PROPN
ejpam-3133	334	56	,	,	PUNCT
ejpam-3133	334	57	tz	tz	PROPN
ejpam-3133	334	58	,	,	PUNCT
ejpam-3133	334	59	hz	hz	X
ejpam-3133	334	60	)	)	PUNCT
ejpam-3133	334	61	+	+	NOUN
ejpam-3133	334	62	gb(gx	gb(gx	PROPN
ejpam-3133	334	63	,	,	PUNCT
ejpam-3133	334	64	sx	sx	PROPN
ejpam-3133	334	65	,	,	PUNCT
ejpam-3133	334	66	sx	sx	PROPN
ejpam-3133	334	67	)	)	PUNCT
ejpam-3133	334	68	2s	2s	PROPN
ejpam-3133	334	69	}	}	PUNCT
ejpam-3133	334	70	.	.	PUNCT
ejpam-3133	335	1	then	then	ADV
ejpam-3133	335	2	g	g	PROPN
ejpam-3133	335	3	,	,	PUNCT
ejpam-3133	335	4	h	h	NOUN
ejpam-3133	335	5	,	,	PUNCT
ejpam-3133	335	6	s	s	PART
ejpam-3133	335	7	and	and	CCONJ
ejpam-3133	335	8	t	t	PROPN
ejpam-3133	335	9	have	have	VERB
ejpam-3133	335	10	a	a	DET
ejpam-3133	335	11	unique	unique	ADJ
ejpam-3133	335	12	common	common	ADJ
ejpam-3133	335	13	fixed	fix	VERB
ejpam-3133	335	14	point	point	NOUN
ejpam-3133	335	15	in	in	ADP
ejpam-3133	335	16	x.	x.	NOUN
ejpam-3133	335	17	the	the	DET
ejpam-3133	335	18	following	follow	VERB
ejpam-3133	335	19	example	example	NOUN
ejpam-3133	335	20	is	be	AUX
ejpam-3133	335	21	to	to	PART
ejpam-3133	335	22	illustrate	illustrate	VERB
ejpam-3133	335	23	theorem	theorem	NOUN
ejpam-3133	335	24	1	1	NUM
ejpam-3133	335	25	.	.	NOUN
ejpam-3133	335	26	example	example	NOUN
ejpam-3133	336	1	5	5	NUM
ejpam-3133	336	2	.	.	PUNCT
ejpam-3133	336	3	let	let	VERB
ejpam-3133	336	4	x	x	PUNCT
ejpam-3133	336	5	=	=	PUNCT
ejpam-3133	337	1	[	[	X
ejpam-3133	337	2	0,∞	0,∞	NUM
ejpam-3133	337	3	)	)	PUNCT
ejpam-3133	337	4	and	and	CCONJ
ejpam-3133	337	5	g	g	NOUN
ejpam-3133	337	6	:	:	PUNCT
ejpam-3133	337	7	x	x	PUNCT
ejpam-3133	338	1	×	×	NOUN
ejpam-3133	338	2	x	x	SYM
ejpam-3133	338	3	×	×	NOUN
ejpam-3133	338	4	x	x	INTJ
ejpam-3133	338	5	→	→	X
ejpam-3133	338	6	[	[	X
ejpam-3133	338	7	0,∞	0,∞	NOUN
ejpam-3133	338	8	)	)	PUNCT
ejpam-3133	338	9	be	be	VERB
ejpam-3133	338	10	the	the	DET
ejpam-3133	338	11	complete	complete	ADJ
ejpam-3133	338	12	g	g	NOUN
ejpam-3133	338	13	-	-	PUNCT
ejpam-3133	338	14	metric	metric	ADJ
ejpam-3133	338	15	which	which	PRON
ejpam-3133	338	16	is	be	AUX
ejpam-3133	338	17	defined	define	VERB
ejpam-3133	338	18	by	by	ADP
ejpam-3133	338	19	g(x	g(x	PROPN
ejpam-3133	338	20	,	,	PUNCT
ejpam-3133	338	21	y	y	PROPN
ejpam-3133	338	22	,	,	PUNCT
ejpam-3133	338	23	z	z	NOUN
ejpam-3133	338	24	)	)	PUNCT
ejpam-3133	338	25	=	=	PRON
ejpam-3133	338	26	{	{	PUNCT
ejpam-3133	338	27	0	0	NUM
ejpam-3133	338	28	,	,	PUNCT
ejpam-3133	338	29	if	if	SCONJ
ejpam-3133	338	30	x	x	ADP
ejpam-3133	338	31	=	=	PUNCT
ejpam-3133	338	32	y	y	PROPN
ejpam-3133	338	33	=	=	SYM
ejpam-3133	338	34	z	z	PROPN
ejpam-3133	338	35	,	,	PUNCT
ejpam-3133	338	36	max{x	max{x	PROPN
ejpam-3133	338	37	,	,	PUNCT
ejpam-3133	338	38	y	y	PROPN
ejpam-3133	338	39	,	,	PUNCT
ejpam-3133	338	40	z	z	NOUN
ejpam-3133	338	41	}	}	PUNCT
ejpam-3133	338	42	,	,	PUNCT
ejpam-3133	338	43	otherwise	otherwise	ADV
ejpam-3133	338	44	.	.	PUNCT
ejpam-3133	339	1	define	define	VERB
ejpam-3133	339	2	the	the	DET
ejpam-3133	339	3	gb	gb	NOUN
ejpam-3133	339	4	metric	metric	ADJ
ejpam-3133	339	5	by	by	ADP
ejpam-3133	339	6	gb(x	gb(x	PROPN
ejpam-3133	339	7	,	,	PUNCT
ejpam-3133	339	8	y	y	PROPN
ejpam-3133	339	9	,	,	PUNCT
ejpam-3133	339	10	z	z	NOUN
ejpam-3133	339	11	)	)	PUNCT
ejpam-3133	339	12	=	=	SYM
ejpam-3133	339	13	(	(	PUNCT
ejpam-3133	339	14	g(x	g(x	PROPN
ejpam-3133	339	15	,	,	PUNCT
ejpam-3133	339	16	y	y	PROPN
ejpam-3133	339	17	,	,	PUNCT
ejpam-3133	339	18	z))2	z))2	PROPN
ejpam-3133	339	19	.	.	PUNCT
ejpam-3133	340	1	then	then	ADV
ejpam-3133	340	2	it	it	PRON
ejpam-3133	340	3	is	be	AUX
ejpam-3133	340	4	clear	clear	ADJ
ejpam-3133	340	5	that	that	SCONJ
ejpam-3133	340	6	(	(	PUNCT
ejpam-3133	340	7	x	x	NOUN
ejpam-3133	340	8	,	,	PUNCT
ejpam-3133	340	9	gb	gb	PRON
ejpam-3133	340	10	)	)	PUNCT
ejpam-3133	340	11	is	be	AUX
ejpam-3133	340	12	a	a	DET
ejpam-3133	340	13	complete	complete	ADJ
ejpam-3133	340	14	gb	gb	NOUN
ejpam-3133	340	15	-	-	PUNCT
ejpam-3133	340	16	metric	metric	ADJ
ejpam-3133	340	17	with	with	ADP
ejpam-3133	340	18	s	s	NOUN
ejpam-3133	340	19	=	=	SYM
ejpam-3133	340	20	2	2	NUM
ejpam-3133	340	21	.	.	PUNCT
ejpam-3133	340	22	also	also	ADV
ejpam-3133	340	23	,	,	PUNCT
ejpam-3133	340	24	define	define	VERB
ejpam-3133	340	25	the	the	DET
ejpam-3133	340	26	mappings	mapping	NOUN
ejpam-3133	341	1	f	f	X
ejpam-3133	341	2	,	,	PUNCT
ejpam-3133	341	3	g	g	PROPN
ejpam-3133	341	4	,	,	PUNCT
ejpam-3133	341	5	h	h	NOUN
ejpam-3133	341	6	,	,	PUNCT
ejpam-3133	341	7	r	r	NOUN
ejpam-3133	341	8	,	,	PUNCT
ejpam-3133	341	9	s	s	PART
ejpam-3133	341	10	and	and	CCONJ
ejpam-3133	341	11	t	t	PROPN
ejpam-3133	341	12	by	by	ADP
ejpam-3133	341	13	fx	fx	NOUN
ejpam-3133	341	14	=	=	PUNCT
ejpam-3133	341	15	x	x	SYM
ejpam-3133	341	16	32	32	NUM
ejpam-3133	341	17	,	,	PUNCT
ejpam-3133	341	18	g(x	g(x	NOUN
ejpam-3133	341	19	)	)	PUNCT
ejpam-3133	342	1	=	=	PUNCT
ejpam-3133	342	2	x	x	SYM
ejpam-3133	342	3	36	36	NUM
ejpam-3133	342	4	,	,	PUNCT
ejpam-3133	342	5	h(x	h(x	PROPN
ejpam-3133	342	6	)	)	PUNCT
ejpam-3133	343	1	=	=	PUNCT
ejpam-3133	344	1	x	x	X
ejpam-3133	344	2	48	48	NUM
ejpam-3133	344	3	,	,	PUNCT
ejpam-3133	344	4	z.	z.	PROPN
ejpam-3133	344	5	mustafa	mustafa	PROPN
ejpam-3133	344	6	et	et	PROPN
ejpam-3133	344	7	al	al	PROPN
ejpam-3133	344	8	.	.	PUNCT
ejpam-3133	344	9	/	/	SYM
ejpam-3133	344	10	eur	eur	PROPN
ejpam-3133	344	11	.	.	PUNCT
ejpam-3133	345	1	j.	j.	PROPN
ejpam-3133	345	2	pure	pure	PROPN
ejpam-3133	345	3	appl	appl	PROPN
ejpam-3133	345	4	.	.	PROPN
ejpam-3133	345	5	math	math	PROPN
ejpam-3133	345	6	,	,	PUNCT
ejpam-3133	345	7	11	11	NUM
ejpam-3133	345	8	(	(	PUNCT
ejpam-3133	345	9	1	1	NUM
ejpam-3133	345	10	)	)	PUNCT
ejpam-3133	345	11	(	(	PUNCT
ejpam-3133	345	12	2018	2018	NUM
ejpam-3133	345	13	)	)	PUNCT
ejpam-3133	345	14	,	,	PUNCT
ejpam-3133	345	15	90	90	NUM
ejpam-3133	345	16	-	-	SYM
ejpam-3133	345	17	109	109	NUM
ejpam-3133	345	18	104	104	NUM
ejpam-3133	345	19	and	and	CCONJ
ejpam-3133	345	20	r(x	r(x	PROPN
ejpam-3133	345	21	)	)	PUNCT
ejpam-3133	346	1	=	=	SYM
ejpam-3133	347	1	4x	4x	NUM
ejpam-3133	347	2	9	9	NUM
ejpam-3133	347	3	,	,	PUNCT
ejpam-3133	347	4	s(x	s(x	NOUN
ejpam-3133	347	5	)	)	PUNCT
ejpam-3133	347	6	=	=	PUNCT
ejpam-3133	348	1	x	x	SYM
ejpam-3133	348	2	2	2	NUM
ejpam-3133	348	3	,	,	PUNCT
ejpam-3133	348	4	and	and	CCONJ
ejpam-3133	348	5	t	t	PROPN
ejpam-3133	348	6	(	(	PUNCT
ejpam-3133	348	7	x	x	X
ejpam-3133	348	8	)	)	PUNCT
ejpam-3133	349	1	=	=	SYM
ejpam-3133	349	2	x	x	SYM
ejpam-3133	349	3	3	3	NUM
ejpam-3133	349	4	for	for	ADP
ejpam-3133	349	5	all	all	DET
ejpam-3133	349	6	x	x	SYM
ejpam-3133	349	7	∈	∈	NOUN
ejpam-3133	349	8	x.	x.	NOUN
ejpam-3133	349	9	further	far	ADV
ejpam-3133	349	10	,	,	PUNCT
ejpam-3133	349	11	define	define	VERB
ejpam-3133	349	12	ψ(t	ψ(t	PROPN
ejpam-3133	349	13	)	)	PUNCT
ejpam-3133	349	14	=	=	SYM
ejpam-3133	350	1	4	4	NUM
ejpam-3133	350	2	√	√	NOUN
ejpam-3133	350	3	t	t	PROPN
ejpam-3133	350	4	and	and	CCONJ
ejpam-3133	350	5	φ(t	φ(t	PROPN
ejpam-3133	350	6	)	)	PUNCT
ejpam-3133	350	7	=	=	PUNCT
ejpam-3133	351	1	√	√	PROPN
ejpam-3133	351	2	t	t	NOUN
ejpam-3133	351	3	3	3	NUM
ejpam-3133	351	4	for	for	ADP
ejpam-3133	351	5	all	all	DET
ejpam-3133	351	6	t	t	NOUN
ejpam-3133	351	7	∈	∈	PROPN
ejpam-3133	352	1	[	[	X
ejpam-3133	352	2	0,∞	0,∞	NOUN
ejpam-3133	352	3	)	)	PUNCT
ejpam-3133	352	4	.	.	PUNCT
ejpam-3133	353	1	then	then	ADV
ejpam-3133	353	2	f	f	X
ejpam-3133	353	3	,	,	PUNCT
ejpam-3133	353	4	g	g	PROPN
ejpam-3133	353	5	,	,	PUNCT
ejpam-3133	353	6	h	h	NOUN
ejpam-3133	353	7	,	,	PUNCT
ejpam-3133	353	8	r	r	NOUN
ejpam-3133	353	9	,	,	PUNCT
ejpam-3133	353	10	s	s	PART
ejpam-3133	353	11	and	and	CCONJ
ejpam-3133	353	12	t	t	PROPN
ejpam-3133	353	13	have	have	VERB
ejpam-3133	353	14	a	a	DET
ejpam-3133	353	15	unique	unique	ADJ
ejpam-3133	353	16	common	common	ADJ
ejpam-3133	353	17	fixed	fix	VERB
ejpam-3133	353	18	point	point	NOUN
ejpam-3133	353	19	.	.	PUNCT
ejpam-3133	354	1	proof	proof	NOUN
ejpam-3133	354	2	.	.	PUNCT
ejpam-3133	355	1	(	(	PUNCT
ejpam-3133	355	2	1	1	X
ejpam-3133	355	3	)	)	PUNCT
ejpam-3133	355	4	(	(	PUNCT
ejpam-3133	355	5	f	f	X
ejpam-3133	355	6	,	,	PUNCT
ejpam-3133	355	7	s	s	PART
ejpam-3133	355	8	)	)	PUNCT
ejpam-3133	355	9	and	and	CCONJ
ejpam-3133	355	10	(	(	PUNCT
ejpam-3133	355	11	g	g	NOUN
ejpam-3133	355	12	,	,	PUNCT
ejpam-3133	355	13	r	r	NOUN
ejpam-3133	355	14	)	)	PUNCT
ejpam-3133	355	15	satisfy	satisfy	NOUN
ejpam-3133	355	16	the	the	DET
ejpam-3133	355	17	(	(	PUNCT
ejpam-3133	355	18	e.a	e.a	PROPN
ejpam-3133	355	19	)	)	PUNCT
ejpam-3133	355	20	property	property	NOUN
ejpam-3133	355	21	with	with	ADP
ejpam-3133	355	22	xn	xn	PROPN
ejpam-3133	356	1	=	=	SYM
ejpam-3133	356	2	1	1	NUM
ejpam-3133	356	3	n	n	NOUN
ejpam-3133	356	4	.	.	PUNCT
ejpam-3133	357	1	(	(	PUNCT
ejpam-3133	357	2	2	2	X
ejpam-3133	357	3	)	)	PUNCT
ejpam-3133	357	4	f(x	f(x	PROPN
ejpam-3133	357	5	)	)	PUNCT
ejpam-3133	357	6	⊆	⊆	NUM
ejpam-3133	357	7	t	t	NOUN
ejpam-3133	357	8	(	(	PUNCT
ejpam-3133	357	9	x	x	NOUN
ejpam-3133	357	10	)	)	PUNCT
ejpam-3133	357	11	,	,	PUNCT
ejpam-3133	357	12	g(x	g(x	NOUN
ejpam-3133	357	13	)	)	PUNCT
ejpam-3133	357	14	⊆	⊆	NUM
ejpam-3133	357	15	s(x	s(x	NOUN
ejpam-3133	357	16	)	)	PUNCT
ejpam-3133	357	17	and	and	CCONJ
ejpam-3133	357	18	h(x	h(x	PROPN
ejpam-3133	357	19	)	)	PUNCT
ejpam-3133	357	20	⊆	⊆	NUM
ejpam-3133	357	21	r(x	r(x	PROPN
ejpam-3133	357	22	)	)	PUNCT
ejpam-3133	357	23	.	.	PUNCT
ejpam-3133	358	1	in	in	ADP
ejpam-3133	358	2	fact	fact	NOUN
ejpam-3133	358	3	,	,	PUNCT
ejpam-3133	358	4	f(x	f(x	PROPN
ejpam-3133	358	5	)	)	PUNCT
ejpam-3133	358	6	=	=	PUNCT
ejpam-3133	359	1	g(x	g(x	NOUN
ejpam-3133	359	2	)	)	PUNCT
ejpam-3133	359	3	=	=	SYM
ejpam-3133	359	4	s(x	s(x	PROPN
ejpam-3133	359	5	)	)	PUNCT
ejpam-3133	359	6	=	=	SYM
ejpam-3133	359	7	r(x	r(x	PROPN
ejpam-3133	359	8	)	)	PUNCT
ejpam-3133	359	9	=	=	SYM
ejpam-3133	359	10	t	t	PROPN
ejpam-3133	359	11	(	(	PUNCT
ejpam-3133	359	12	x	x	NOUN
ejpam-3133	359	13	)	)	PUNCT
ejpam-3133	359	14	=	=	NOUN
ejpam-3133	360	1	[	[	X
ejpam-3133	360	2	0,∞	0,∞	NOUN
ejpam-3133	360	3	)	)	PUNCT
ejpam-3133	360	4	.	.	PUNCT
ejpam-3133	361	1	(	(	PUNCT
ejpam-3133	361	2	3	3	X
ejpam-3133	361	3	)	)	PUNCT
ejpam-3133	361	4	r(x	r(x	NOUN
ejpam-3133	361	5	)	)	PUNCT
ejpam-3133	361	6	=	=	PUNCT
ejpam-3133	362	1	[	[	X
ejpam-3133	362	2	0,∞	0,∞	NOUN
ejpam-3133	362	3	)	)	PUNCT
ejpam-3133	362	4	is	be	AUX
ejpam-3133	362	5	a	a	DET
ejpam-3133	362	6	closed	closed	ADJ
ejpam-3133	362	7	subspace	subspace	NOUN
ejpam-3133	362	8	of	of	ADP
ejpam-3133	362	9	x.	x.	PROPN
ejpam-3133	362	10	(	(	PUNCT
ejpam-3133	362	11	4	4	NUM
ejpam-3133	362	12	)	)	PUNCT
ejpam-3133	362	13	(	(	PUNCT
ejpam-3133	362	14	f	f	X
ejpam-3133	362	15	,	,	PUNCT
ejpam-3133	362	16	s	s	PART
ejpam-3133	362	17	)	)	PUNCT
ejpam-3133	362	18	,	,	PUNCT
ejpam-3133	362	19	(	(	PUNCT
ejpam-3133	362	20	g	g	NOUN
ejpam-3133	362	21	,	,	PUNCT
ejpam-3133	362	22	r	r	NOUN
ejpam-3133	362	23	)	)	PUNCT
ejpam-3133	362	24	and	and	CCONJ
ejpam-3133	362	25	(	(	PUNCT
ejpam-3133	362	26	h	h	NOUN
ejpam-3133	362	27	,	,	PUNCT
ejpam-3133	362	28	t	t	PROPN
ejpam-3133	362	29	)	)	PUNCT
ejpam-3133	362	30	are	be	AUX
ejpam-3133	362	31	weakly	weakly	ADV
ejpam-3133	362	32	compatible	compatible	ADJ
ejpam-3133	362	33	pairs	pair	NOUN
ejpam-3133	362	34	of	of	ADP
ejpam-3133	362	35	mappings	mapping	NOUN
ejpam-3133	362	36	.	.	PUNCT
ejpam-3133	363	1	in	in	ADP
ejpam-3133	363	2	fact	fact	NOUN
ejpam-3133	363	3	,	,	PUNCT
ejpam-3133	363	4	the	the	DET
ejpam-3133	363	5	only	only	ADJ
ejpam-3133	363	6	coincident	coincident	ADJ
ejpam-3133	363	7	point	point	NOUN
ejpam-3133	363	8	for	for	ADP
ejpam-3133	363	9	f	f	PROPN
ejpam-3133	363	10	and	and	CCONJ
ejpam-3133	363	11	r	r	NOUN
ejpam-3133	363	12	is	be	AUX
ejpam-3133	363	13	0	0	NUM
ejpam-3133	363	14	and	and	CCONJ
ejpam-3133	363	15	f(r(0	f(r(0	NUM
ejpam-3133	363	16	)	)	PUNCT
ejpam-3133	363	17	)	)	PUNCT
ejpam-3133	364	1	=	=	PUNCT
ejpam-3133	364	2	r(f(0	r(f(0	NOUN
ejpam-3133	364	3	)	)	PUNCT
ejpam-3133	364	4	)	)	PUNCT
ejpam-3133	365	1	=	=	PUNCT
ejpam-3133	365	2	0	0	X
ejpam-3133	365	3	.	.	PUNCT
ejpam-3133	365	4	similarly	similarly	ADV
ejpam-3133	365	5	for	for	ADP
ejpam-3133	365	6	the	the	DET
ejpam-3133	365	7	other	other	ADJ
ejpam-3133	365	8	two	two	NUM
ejpam-3133	365	9	pairs	pair	NOUN
ejpam-3133	365	10	.	.	PUNCT
ejpam-3133	366	1	(	(	PUNCT
ejpam-3133	366	2	5	5	X
ejpam-3133	366	3	)	)	PUNCT
ejpam-3133	366	4	we	we	PRON
ejpam-3133	366	5	shall	shall	AUX
ejpam-3133	366	6	show	show	VERB
ejpam-3133	366	7	that	that	SCONJ
ejpam-3133	366	8	the	the	DET
ejpam-3133	366	9	above	above	ADJ
ejpam-3133	366	10	mappings	mapping	NOUN
ejpam-3133	366	11	satisfy	satisfy	VERB
ejpam-3133	366	12	the	the	DET
ejpam-3133	366	13	contractive	contractive	ADJ
ejpam-3133	366	14	condition	condition	NOUN
ejpam-3133	366	15	(	(	PUNCT
ejpam-3133	366	16	3	3	NUM
ejpam-3133	366	17	)	)	PUNCT
ejpam-3133	366	18	.	.	PUNCT
ejpam-3133	367	1	on	on	ADP
ejpam-3133	367	2	one	one	NUM
ejpam-3133	367	3	hand	hand	NOUN
ejpam-3133	367	4	,	,	PUNCT
ejpam-3133	367	5	we	we	PRON
ejpam-3133	367	6	observe	observe	VERB
ejpam-3133	367	7	that	that	SCONJ
ejpam-3133	367	8	ψ(s2gb(fx	ψ(s2gb(fx	PROPN
ejpam-3133	367	9	,	,	PUNCT
ejpam-3133	367	10	gy	gy	PROPN
ejpam-3133	367	11	,	,	PUNCT
ejpam-3133	367	12	hz	hz	NOUN
ejpam-3133	367	13	)	)	PUNCT
ejpam-3133	367	14	)	)	PUNCT
ejpam-3133	367	15	=	=	PUNCT
ejpam-3133	367	16	ψ(4(max	ψ(4(max	X
ejpam-3133	367	17	{	{	PUNCT
ejpam-3133	367	18	x	x	PROPN
ejpam-3133	367	19	32	32	NUM
ejpam-3133	367	20	,	,	PUNCT
ejpam-3133	367	21	y	y	PROPN
ejpam-3133	367	22	36	36	NUM
ejpam-3133	367	23	,	,	PUNCT
ejpam-3133	367	24	z	z	NOUN
ejpam-3133	367	25	48	48	NUM
ejpam-3133	367	26	}	}	PUNCT
ejpam-3133	367	27	)	)	PUNCT
ejpam-3133	367	28	2	2	X
ejpam-3133	367	29	)	)	PUNCT
ejpam-3133	367	30	=	=	VERB
ejpam-3133	367	31	ψ(4(max	ψ(4(max	X
ejpam-3133	367	32	{	{	PUNCT
ejpam-3133	367	33	(	(	PUNCT
ejpam-3133	367	34	x	x	SYM
ejpam-3133	367	35	32	32	NUM
ejpam-3133	367	36	)	)	PUNCT
ejpam-3133	367	37	2	2	NUM
ejpam-3133	367	38	,	,	PUNCT
ejpam-3133	367	39	(	(	PUNCT
ejpam-3133	367	40	y	y	PROPN
ejpam-3133	367	41	36	36	NUM
ejpam-3133	367	42	)	)	PUNCT
ejpam-3133	367	43	2	2	NUM
ejpam-3133	367	44	,	,	PUNCT
ejpam-3133	367	45	(	(	PUNCT
ejpam-3133	367	46	z	z	NOUN
ejpam-3133	367	47	48	48	NUM
ejpam-3133	367	48	)	)	PUNCT
ejpam-3133	367	49	2	2	NUM
ejpam-3133	367	50	}	}	PUNCT
ejpam-3133	367	51	)	)	PUNCT
ejpam-3133	367	52	=	=	VERB
ejpam-3133	368	1	ψ(max{(2x	ψ(max{(2x	VERB
ejpam-3133	368	2	32	32	NUM
ejpam-3133	368	3	)	)	PUNCT
ejpam-3133	368	4	2	2	NUM
ejpam-3133	368	5	,	,	PUNCT
ejpam-3133	368	6	(	(	PUNCT
ejpam-3133	368	7	2y	2y	NUM
ejpam-3133	368	8	36	36	NUM
ejpam-3133	368	9	)	)	SYM
ejpam-3133	368	10	2	2	NUM
ejpam-3133	368	11	,	,	PUNCT
ejpam-3133	368	12	(	(	PUNCT
ejpam-3133	368	13	2z	2z	NUM
ejpam-3133	368	14	48	48	NUM
ejpam-3133	368	15	)	)	SYM
ejpam-3133	368	16	2	2	NUM
ejpam-3133	368	17	}	}	PUNCT
ejpam-3133	368	18	)	)	PUNCT
ejpam-3133	369	1	=	=	SYM
ejpam-3133	369	2	ψ(max	ψ(max	NOUN
ejpam-3133	369	3	{	{	PUNCT
ejpam-3133	369	4	(	(	PUNCT
ejpam-3133	369	5	x	x	SYM
ejpam-3133	369	6	16	16	NUM
ejpam-3133	369	7	)	)	PUNCT
ejpam-3133	369	8	2	2	NUM
ejpam-3133	369	9	,	,	PUNCT
ejpam-3133	369	10	(	(	PUNCT
ejpam-3133	369	11	y	y	PROPN
ejpam-3133	369	12	18	18	NUM
ejpam-3133	369	13	)	)	PUNCT
ejpam-3133	369	14	2	2	NUM
ejpam-3133	369	15	,	,	PUNCT
ejpam-3133	369	16	(	(	PUNCT
ejpam-3133	369	17	z	z	NOUN
ejpam-3133	369	18	24	24	NUM
ejpam-3133	369	19	)	)	PUNCT
ejpam-3133	369	20	2	2	NUM
ejpam-3133	369	21	}	}	PUNCT
ejpam-3133	369	22	)	)	PUNCT
ejpam-3133	369	23	=	=	SYM
ejpam-3133	369	24	4	4	NUM
ejpam-3133	369	25	max	max	NOUN
ejpam-3133	369	26	{	{	PUNCT
ejpam-3133	369	27	(	(	PUNCT
ejpam-3133	369	28	x	x	PROPN
ejpam-3133	369	29	16	16	NUM
ejpam-3133	369	30	)	)	PUNCT
ejpam-3133	369	31	,	,	PUNCT
ejpam-3133	369	32	y	y	PROPN
ejpam-3133	369	33	18	18	NUM
ejpam-3133	369	34	,	,	PUNCT
ejpam-3133	369	35	z	z	NOUN
ejpam-3133	369	36	24	24	NUM
ejpam-3133	369	37	}	}	PUNCT
ejpam-3133	369	38	=	=	SYM
ejpam-3133	369	39	max{x	max{x	NOUN
ejpam-3133	369	40	4	4	NUM
ejpam-3133	369	41	,	,	PUNCT
ejpam-3133	369	42	2y	2y	NUM
ejpam-3133	369	43	9	9	NUM
ejpam-3133	369	44	,	,	PUNCT
ejpam-3133	369	45	z	z	NOUN
ejpam-3133	369	46	6	6	NUM
ejpam-3133	369	47	}	}	PUNCT
ejpam-3133	369	48	.	.	PUNCT
ejpam-3133	370	1	(	(	PUNCT
ejpam-3133	370	2	36	36	NUM
ejpam-3133	370	3	)	)	PUNCT
ejpam-3133	370	4	on	on	ADP
ejpam-3133	370	5	the	the	DET
ejpam-3133	370	6	other	other	ADJ
ejpam-3133	370	7	hand	hand	NOUN
ejpam-3133	370	8	,	,	PUNCT
ejpam-3133	370	9	m(x	m(x	PROPN
ejpam-3133	370	10	,	,	PUNCT
ejpam-3133	370	11	y	y	PROPN
ejpam-3133	370	12	,	,	PUNCT
ejpam-3133	370	13	z	z	NOUN
ejpam-3133	370	14	)	)	PUNCT
ejpam-3133	370	15	=	=	SYM
ejpam-3133	370	16	max	max	PROPN
ejpam-3133	370	17	{	{	PUNCT
ejpam-3133	370	18	max	max	PROPN
ejpam-3133	370	19	{	{	PUNCT
ejpam-3133	370	20	(	(	PUNCT
ejpam-3133	370	21	x32)2	x32)2	PROPN
ejpam-3133	370	22	,	,	PUNCT
ejpam-3133	370	23	(	(	PUNCT
ejpam-3133	370	24	y2	y2	INTJ
ejpam-3133	370	25	)	)	PUNCT
ejpam-3133	370	26	2	2	NUM
ejpam-3133	370	27	,	,	PUNCT
ejpam-3133	370	28	(	(	PUNCT
ejpam-3133	370	29	z3)2},max	z3)2},max	X
ejpam-3133	370	30	{	{	PUNCT
ejpam-3133	370	31	(	(	PUNCT
ejpam-3133	370	32	y36)2	y36)2	PROPN
ejpam-3133	370	33	,	,	PUNCT
ejpam-3133	370	34	(	(	PUNCT
ejpam-3133	370	35	4y9	4y9	NUM
ejpam-3133	370	36	)	)	PUNCT
ejpam-3133	370	37	2	2	NUM
ejpam-3133	370	38	}	}	PUNCT
ejpam-3133	370	39	max	max	PROPN
ejpam-3133	370	40	{	{	PUNCT
ejpam-3133	370	41	(	(	PUNCT
ejpam-3133	370	42	x32)2	x32)2	PROPN
ejpam-3133	370	43	,	,	PUNCT
ejpam-3133	370	44	(	(	PUNCT
ejpam-3133	370	45	z48)2	z48)2	NOUN
ejpam-3133	370	46	}	}	PUNCT
ejpam-3133	370	47	,	,	PUNCT
ejpam-3133	370	48	max	max	PROPN
ejpam-3133	370	49	{	{	PUNCT
ejpam-3133	370	50	(	(	PUNCT
ejpam-3133	370	51	z	z	NOUN
ejpam-3133	370	52	3	3	NUM
ejpam-3133	370	53	)	)	PUNCT
ejpam-3133	370	54	2	2	NUM
ejpam-3133	370	55	,	,	PUNCT
ejpam-3133	370	56	(	(	PUNCT
ejpam-3133	370	57	z	z	NOUN
ejpam-3133	370	58	48	48	NUM
ejpam-3133	370	59	)	)	PUNCT
ejpam-3133	370	60	2}+max	2}+max	NUM
ejpam-3133	370	61	{	{	PUNCT
ejpam-3133	370	62	(	(	PUNCT
ejpam-3133	370	63	x	x	X
ejpam-3133	370	64	32	32	NUM
ejpam-3133	370	65	)	)	PUNCT
ejpam-3133	370	66	2,(x	2,(x	NOUN
ejpam-3133	370	67	2	2	NUM
ejpam-3133	370	68	)	)	PUNCT
ejpam-3133	370	69	2	2	NUM
ejpam-3133	370	70	}	}	SYM
ejpam-3133	370	71	4	4	NUM
ejpam-3133	370	72	}	}	PUNCT
ejpam-3133	370	73	=	=	SYM
ejpam-3133	370	74	max	max	PROPN
ejpam-3133	370	75	{	{	PUNCT
ejpam-3133	370	76	max	max	PROPN
ejpam-3133	370	77	{	{	PUNCT
ejpam-3133	370	78	(	(	PUNCT
ejpam-3133	370	79	x32)2	x32)2	PROPN
ejpam-3133	370	80	,	,	PUNCT
ejpam-3133	370	81	(	(	PUNCT
ejpam-3133	370	82	y2	y2	INTJ
ejpam-3133	370	83	)	)	PUNCT
ejpam-3133	370	84	2	2	NUM
ejpam-3133	370	85	,	,	PUNCT
ejpam-3133	370	86	(	(	PUNCT
ejpam-3133	370	87	z3)2},max	z3)2},max	X
ejpam-3133	370	88	{	{	PUNCT
ejpam-3133	370	89	(	(	PUNCT
ejpam-3133	370	90	y36)2	y36)2	PROPN
ejpam-3133	370	91	,	,	PUNCT
ejpam-3133	370	92	(	(	PUNCT
ejpam-3133	370	93	4y9	4y9	NUM
ejpam-3133	370	94	)	)	PUNCT
ejpam-3133	370	95	2	2	NUM
ejpam-3133	370	96	}	}	PUNCT
ejpam-3133	370	97	,	,	PUNCT
ejpam-3133	370	98	max	max	PROPN
ejpam-3133	370	99	{	{	PUNCT
ejpam-3133	370	100	(	(	PUNCT
ejpam-3133	370	101	x32)2	x32)2	PROPN
ejpam-3133	370	102	,	,	PUNCT
ejpam-3133	370	103	(	(	PUNCT
ejpam-3133	370	104	z48)2	z48)2	NOUN
ejpam-3133	370	105	}	}	PUNCT
ejpam-3133	370	106	,	,	PUNCT
ejpam-3133	370	107	(	(	PUNCT
ejpam-3133	370	108	z	z	NOUN
ejpam-3133	370	109	3	3	NUM
ejpam-3133	370	110	)	)	PUNCT
ejpam-3133	370	111	2+(x	2+(x	NUM
ejpam-3133	370	112	2	2	NUM
ejpam-3133	370	113	)	)	PUNCT
ejpam-3133	370	114	2	2	NUM
ejpam-3133	370	115	4	4	NUM
ejpam-3133	370	116	.	.	PUNCT
ejpam-3133	370	117	}	}	PUNCT
ejpam-3133	370	118	=	=	SYM
ejpam-3133	370	119	max	max	PROPN
ejpam-3133	370	120	{	{	PUNCT
ejpam-3133	370	121	max	max	PROPN
ejpam-3133	370	122	{	{	PUNCT
ejpam-3133	370	123	(	(	PUNCT
ejpam-3133	370	124	x32)2	x32)2	PROPN
ejpam-3133	370	125	,	,	PUNCT
ejpam-3133	370	126	(	(	PUNCT
ejpam-3133	370	127	y2	y2	INTJ
ejpam-3133	370	128	)	)	PUNCT
ejpam-3133	370	129	2	2	NUM
ejpam-3133	370	130	,	,	PUNCT
ejpam-3133	370	131	(	(	PUNCT
ejpam-3133	370	132	z3)2	z3)2	ADV
ejpam-3133	370	133	}	}	PUNCT
ejpam-3133	370	134	,	,	PUNCT
ejpam-3133	370	135	(	(	PUNCT
ejpam-3133	370	136	4y9	4y9	NUM
ejpam-3133	370	137	)	)	PUNCT
ejpam-3133	370	138	2	2	NUM
ejpam-3133	370	139	,	,	PUNCT
ejpam-3133	370	140	(	(	PUNCT
ejpam-3133	370	141	z	z	NOUN
ejpam-3133	370	142	3	3	NUM
ejpam-3133	370	143	)	)	PUNCT
ejpam-3133	370	144	2+(x	2+(x	NUM
ejpam-3133	370	145	2	2	NUM
ejpam-3133	370	146	)	)	PUNCT
ejpam-3133	370	147	2	2	NUM
ejpam-3133	370	148	4	4	NUM
ejpam-3133	370	149	.	.	PUNCT
ejpam-3133	370	150	}	}	PUNCT
ejpam-3133	370	151	=	=	SYM
ejpam-3133	370	152	max	max	X
ejpam-3133	370	153	{	{	PUNCT
ejpam-3133	370	154	(	(	PUNCT
ejpam-3133	370	155	x32)2	x32)2	ADV
ejpam-3133	370	156	,	,	PUNCT
ejpam-3133	370	157	(	(	PUNCT
ejpam-3133	370	158	z3)2	z3)2	ADV
ejpam-3133	370	159	,	,	PUNCT
ejpam-3133	370	160	(	(	PUNCT
ejpam-3133	370	161	y2	y2	INTJ
ejpam-3133	370	162	)	)	PUNCT
ejpam-3133	370	163	2	2	NUM
ejpam-3133	370	164	,	,	PUNCT
ejpam-3133	370	165	(	(	PUNCT
ejpam-3133	370	166	z	z	NOUN
ejpam-3133	370	167	3	3	NUM
ejpam-3133	370	168	)	)	PUNCT
ejpam-3133	370	169	2+(x	2+(x	NUM
ejpam-3133	370	170	2	2	NUM
ejpam-3133	370	171	)	)	PUNCT
ejpam-3133	370	172	2	2	NUM
ejpam-3133	370	173	4	4	NUM
ejpam-3133	370	174	.	.	PUNCT
ejpam-3133	370	175	}	}	PUNCT
ejpam-3133	371	1	=	=	SYM
ejpam-3133	371	2	max	max	X
ejpam-3133	371	3	{	{	PUNCT
ejpam-3133	371	4	(	(	PUNCT
ejpam-3133	371	5	y	y	PROPN
ejpam-3133	371	6	2	2	NUM
ejpam-3133	371	7	)	)	PUNCT
ejpam-3133	371	8	2	2	NUM
ejpam-3133	371	9	,	,	PUNCT
ejpam-3133	371	10	(	(	PUNCT
ejpam-3133	371	11	z	z	NOUN
ejpam-3133	371	12	3	3	NUM
ejpam-3133	371	13	)	)	PUNCT
ejpam-3133	371	14	2	2	NUM
ejpam-3133	371	15	,	,	PUNCT
ejpam-3133	371	16	(	(	PUNCT
ejpam-3133	371	17	z3)2	z3)2	X
ejpam-3133	371	18	+	+	CCONJ
ejpam-3133	371	19	(	(	PUNCT
ejpam-3133	371	20	x2	x2	ADJ
ejpam-3133	371	21	)	)	PUNCT
ejpam-3133	371	22	2	2	NUM
ejpam-3133	371	23	4	4	NUM
ejpam-3133	371	24	}	}	PUNCT
ejpam-3133	371	25	references	reference	VERB
ejpam-3133	371	26	105	105	NUM
ejpam-3133	371	27	=	=	SYM
ejpam-3133	371	28	max	max	NOUN
ejpam-3133	371	29	{	{	PUNCT
ejpam-3133	371	30	(	(	PUNCT
ejpam-3133	371	31	y	y	PROPN
ejpam-3133	371	32	2	2	NUM
ejpam-3133	371	33	)	)	PUNCT
ejpam-3133	371	34	2	2	NUM
ejpam-3133	371	35	,	,	PUNCT
ejpam-3133	371	36	(	(	PUNCT
ejpam-3133	371	37	z	z	NOUN
ejpam-3133	371	38	3	3	NUM
ejpam-3133	371	39	)	)	PUNCT
ejpam-3133	371	40	2	2	NUM
ejpam-3133	371	41	,	,	PUNCT
ejpam-3133	371	42	(	(	PUNCT
ejpam-3133	371	43	z	z	NOUN
ejpam-3133	371	44	6	6	NUM
ejpam-3133	371	45	)	)	SYM
ejpam-3133	371	46	2	2	NUM
ejpam-3133	371	47	+	+	CCONJ
ejpam-3133	371	48	(	(	PUNCT
ejpam-3133	371	49	x	x	SYM
ejpam-3133	371	50	4	4	X
ejpam-3133	371	51	)	)	SYM
ejpam-3133	371	52	2	2	NUM
ejpam-3133	371	53	}	}	PUNCT
ejpam-3133	371	54	,	,	PUNCT
ejpam-3133	371	55	and	and	CCONJ
ejpam-3133	371	56	so	so	ADV
ejpam-3133	371	57	,	,	PUNCT
ejpam-3133	371	58	ψ(m(x	ψ(m(x	PROPN
ejpam-3133	371	59	,	,	PUNCT
ejpam-3133	371	60	y	y	PROPN
ejpam-3133	371	61	,	,	PUNCT
ejpam-3133	371	62	z))−	z))−	PROPN
ejpam-3133	371	63	φ(m(x	φ(m(x	PROPN
ejpam-3133	371	64	,	,	PUNCT
ejpam-3133	371	65	y	y	PROPN
ejpam-3133	371	66	,	,	PUNCT
ejpam-3133	371	67	z	z	NOUN
ejpam-3133	371	68	)	)	PUNCT
ejpam-3133	371	69	)	)	PUNCT
ejpam-3133	372	1	=	=	SYM
ejpam-3133	372	2	4	4	NUM
ejpam-3133	372	3	max	max	NOUN
ejpam-3133	372	4	{	{	PUNCT
ejpam-3133	372	5	y	y	PROPN
ejpam-3133	372	6	2	2	NUM
ejpam-3133	372	7	,	,	PUNCT
ejpam-3133	372	8	z	z	NOUN
ejpam-3133	372	9	3	3	NUM
ejpam-3133	372	10	,	,	PUNCT
ejpam-3133	372	11	√	√	PROPN
ejpam-3133	372	12	(	(	PUNCT
ejpam-3133	372	13	z	z	NOUN
ejpam-3133	372	14	6	6	NUM
ejpam-3133	372	15	)	)	SYM
ejpam-3133	372	16	2	2	NUM
ejpam-3133	372	17	+	+	CCONJ
ejpam-3133	372	18	(	(	PUNCT
ejpam-3133	372	19	x	x	SYM
ejpam-3133	372	20	4	4	X
ejpam-3133	372	21	)	)	SYM
ejpam-3133	372	22	2	2	NUM
ejpam-3133	372	23	}	}	PUNCT
ejpam-3133	372	24	−	−	PROPN
ejpam-3133	372	25	1	1	NUM
ejpam-3133	372	26	3	3	NUM
ejpam-3133	372	27	max	max	PROPN
ejpam-3133	372	28	{	{	PUNCT
ejpam-3133	372	29	y	y	PROPN
ejpam-3133	372	30	2	2	NUM
ejpam-3133	372	31	,	,	PUNCT
ejpam-3133	372	32	z	z	NOUN
ejpam-3133	372	33	3	3	NUM
ejpam-3133	372	34	,	,	PUNCT
ejpam-3133	372	35	√	√	PROPN
ejpam-3133	372	36	(	(	PUNCT
ejpam-3133	372	37	z	z	NOUN
ejpam-3133	372	38	6	6	NUM
ejpam-3133	372	39	)	)	SYM
ejpam-3133	372	40	2	2	NUM
ejpam-3133	372	41	+	+	CCONJ
ejpam-3133	372	42	(	(	PUNCT
ejpam-3133	372	43	x	x	SYM
ejpam-3133	372	44	4	4	X
ejpam-3133	372	45	)	)	SYM
ejpam-3133	372	46	2	2	NUM
ejpam-3133	372	47	}	}	PUNCT
ejpam-3133	372	48	=	=	SYM
ejpam-3133	372	49	max	max	X
ejpam-3133	372	50	{	{	PUNCT
ejpam-3133	372	51	11y	11y	PROPN
ejpam-3133	372	52	6	6	NUM
ejpam-3133	372	53	,	,	PUNCT
ejpam-3133	372	54	11z	11z	NOUN
ejpam-3133	372	55	9	9	NUM
ejpam-3133	372	56	,	,	PUNCT
ejpam-3133	372	57	11	11	NUM
ejpam-3133	372	58	3	3	NUM
ejpam-3133	372	59	√	√	PROPN
ejpam-3133	372	60	(	(	PUNCT
ejpam-3133	372	61	z	z	NOUN
ejpam-3133	372	62	6	6	NUM
ejpam-3133	372	63	)	)	SYM
ejpam-3133	372	64	2	2	NUM
ejpam-3133	372	65	+	+	CCONJ
ejpam-3133	372	66	(	(	PUNCT
ejpam-3133	372	67	x	x	SYM
ejpam-3133	372	68	4	4	NUM
ejpam-3133	372	69	)	)	SYM
ejpam-3133	372	70	2	2	NUM
ejpam-3133	372	71	}	}	PUNCT
ejpam-3133	372	72	.	.	PUNCT
ejpam-3133	373	1	(	(	PUNCT
ejpam-3133	373	2	37	37	X
ejpam-3133	373	3	)	)	PUNCT
ejpam-3133	373	4	combining	combine	VERB
ejpam-3133	373	5	(	(	PUNCT
ejpam-3133	373	6	36	36	NUM
ejpam-3133	373	7	)	)	PUNCT
ejpam-3133	373	8	and	and	CCONJ
ejpam-3133	373	9	(	(	PUNCT
ejpam-3133	373	10	37	37	NUM
ejpam-3133	373	11	)	)	PUNCT
ejpam-3133	373	12	,	,	PUNCT
ejpam-3133	373	13	it	it	PRON
ejpam-3133	373	14	is	be	AUX
ejpam-3133	373	15	clear	clear	ADJ
ejpam-3133	373	16	to	to	PART
ejpam-3133	373	17	see	see	VERB
ejpam-3133	373	18	that	that	SCONJ
ejpam-3133	373	19	ψ(s2gb(fx	ψ(s2gb(fx	PROPN
ejpam-3133	373	20	,	,	PUNCT
ejpam-3133	373	21	gy	gy	PROPN
ejpam-3133	373	22	,	,	PUNCT
ejpam-3133	373	23	hz	hz	NOUN
ejpam-3133	373	24	)	)	PUNCT
ejpam-3133	373	25	)	)	PUNCT
ejpam-3133	374	1	=	=	PUNCT
ejpam-3133	374	2	max{x	max{x	NOUN
ejpam-3133	374	3	4	4	NUM
ejpam-3133	374	4	,	,	PUNCT
ejpam-3133	374	5	2y	2y	NUM
ejpam-3133	374	6	9	9	NUM
ejpam-3133	374	7	,	,	PUNCT
ejpam-3133	374	8	z	z	NOUN
ejpam-3133	374	9	6	6	NUM
ejpam-3133	374	10	}	}	PUNCT
ejpam-3133	374	11	≤	≤	NUM
ejpam-3133	374	12	max	max	PROPN
ejpam-3133	374	13	{	{	PUNCT
ejpam-3133	374	14	11y	11y	PROPN
ejpam-3133	374	15	6	6	NUM
ejpam-3133	374	16	,	,	PUNCT
ejpam-3133	374	17	11z	11z	NOUN
ejpam-3133	374	18	9	9	NUM
ejpam-3133	374	19	,	,	PUNCT
ejpam-3133	374	20	11	11	NUM
ejpam-3133	374	21	3	3	NUM
ejpam-3133	374	22	√	√	PROPN
ejpam-3133	374	23	(	(	PUNCT
ejpam-3133	374	24	z	z	NOUN
ejpam-3133	374	25	6	6	NUM
ejpam-3133	374	26	)	)	SYM
ejpam-3133	374	27	2	2	NUM
ejpam-3133	375	1	+	+	CCONJ
ejpam-3133	375	2	(	(	PUNCT
ejpam-3133	375	3	x	x	SYM
ejpam-3133	375	4	4	4	X
ejpam-3133	375	5	)	)	SYM
ejpam-3133	375	6	2	2	NUM
ejpam-3133	375	7	}	}	PUNCT
ejpam-3133	375	8	=	=	SYM
ejpam-3133	375	9	ψ(m(x	ψ(m(x	PROPN
ejpam-3133	375	10	,	,	PUNCT
ejpam-3133	375	11	y	y	PROPN
ejpam-3133	375	12	,	,	PUNCT
ejpam-3133	375	13	z))−	z))−	PROPN
ejpam-3133	375	14	φ(m(x	φ(m(x	PROPN
ejpam-3133	375	15	,	,	PUNCT
ejpam-3133	375	16	y	y	PROPN
ejpam-3133	375	17	,	,	PUNCT
ejpam-3133	375	18	z	z	NOUN
ejpam-3133	375	19	)	)	PUNCT
ejpam-3133	375	20	)	)	PUNCT
ejpam-3133	375	21	.	.	PUNCT
ejpam-3133	376	1	therefore	therefore	ADV
ejpam-3133	376	2	,	,	PUNCT
ejpam-3133	376	3	all	all	DET
ejpam-3133	376	4	conditions	condition	NOUN
ejpam-3133	376	5	of	of	ADP
ejpam-3133	376	6	theorem	theorem	NOUN
ejpam-3133	376	7	1	1	NUM
ejpam-3133	376	8	are	be	AUX
ejpam-3133	376	9	satisfied	satisfied	ADJ
ejpam-3133	376	10	,	,	PUNCT
ejpam-3133	376	11	and	and	CCONJ
ejpam-3133	376	12	x	x	X
ejpam-3133	376	13	=	=	SYM
ejpam-3133	376	14	0	0	NUM
ejpam-3133	376	15	is	be	AUX
ejpam-3133	376	16	the	the	DET
ejpam-3133	376	17	unique	unique	ADJ
ejpam-3133	376	18	common	common	ADJ
ejpam-3133	376	19	fixed	fix	VERB
ejpam-3133	376	20	point	point	NOUN
ejpam-3133	376	21	of	of	ADP
ejpam-3133	376	22	f	f	PROPN
ejpam-3133	376	23	,	,	PUNCT
ejpam-3133	376	24	g	g	PROPN
ejpam-3133	376	25	,	,	PUNCT
ejpam-3133	376	26	h	h	NOUN
ejpam-3133	376	27	,	,	PUNCT
ejpam-3133	376	28	r	r	NOUN
ejpam-3133	376	29	,	,	PUNCT
ejpam-3133	376	30	s	s	PART
ejpam-3133	376	31	and	and	CCONJ
ejpam-3133	376	32	t	t	PROPN
ejpam-3133	376	33	.	.	PUNCT
ejpam-3133	377	1	4	4	X
ejpam-3133	377	2	.	.	X
ejpam-3133	377	3	conclusion	conclusion	NOUN
ejpam-3133	377	4	as	as	SCONJ
ejpam-3133	377	5	it	it	PRON
ejpam-3133	377	6	known	know	VERB
ejpam-3133	377	7	well	well	ADV
ejpam-3133	377	8	,	,	PUNCT
ejpam-3133	377	9	a	a	DET
ejpam-3133	377	10	g	g	NOUN
ejpam-3133	377	11	-	-	PUNCT
ejpam-3133	377	12	metric	metric	ADJ
ejpam-3133	377	13	space	space	NOUN
ejpam-3133	377	14	satisfies	satisfy	VERB
ejpam-3133	377	15	all	all	DET
ejpam-3133	377	16	conditions	condition	NOUN
ejpam-3133	377	17	of	of	ADP
ejpam-3133	377	18	the	the	DET
ejpam-3133	377	19	notion	notion	NOUN
ejpam-3133	377	20	of	of	ADP
ejpam-3133	377	21	a	a	DET
ejpam-3133	377	22	gb	gb	ADV
ejpam-3133	377	23	-	-	PUNCT
ejpam-3133	377	24	metric	metric	ADJ
ejpam-3133	377	25	space	space	NOUN
ejpam-3133	377	26	when	when	SCONJ
ejpam-3133	377	27	s	s	VERB
ejpam-3133	377	28	=	=	NOUN
ejpam-3133	377	29	1	1	NUM
ejpam-3133	377	30	.	.	PUNCT
ejpam-3133	378	1	but	but	CCONJ
ejpam-3133	378	2	,	,	PUNCT
ejpam-3133	378	3	if	if	SCONJ
ejpam-3133	378	4	s	s	VERB
ejpam-3133	378	5	>	>	X
ejpam-3133	378	6	1	1	NUM
ejpam-3133	378	7	,	,	PUNCT
ejpam-3133	378	8	the	the	DET
ejpam-3133	378	9	converse	converse	NOUN
ejpam-3133	378	10	need	need	AUX
ejpam-3133	378	11	not	not	PART
ejpam-3133	378	12	be	be	AUX
ejpam-3133	378	13	true	true	ADJ
ejpam-3133	378	14	.	.	PUNCT
ejpam-3133	379	1	hence	hence	ADV
ejpam-3133	379	2	,	,	PUNCT
ejpam-3133	379	3	the	the	DET
ejpam-3133	379	4	observed	observe	VERB
ejpam-3133	379	5	common	common	ADJ
ejpam-3133	379	6	fixed	fix	VERB
ejpam-3133	379	7	point	point	NOUN
ejpam-3133	379	8	results	result	NOUN
ejpam-3133	379	9	for	for	ADP
ejpam-3133	379	10	six	six	NUM
ejpam-3133	379	11	mappings	mapping	NOUN
ejpam-3133	379	12	of	of	ADP
ejpam-3133	379	13	this	this	DET
ejpam-3133	379	14	paper	paper	NOUN
ejpam-3133	379	15	,	,	PUNCT
ejpam-3133	379	16	can	can	AUX
ejpam-3133	379	17	be	be	AUX
ejpam-3133	379	18	re	re	VERB
ejpam-3133	379	19	-	-	VERB
ejpam-3133	379	20	stated	state	VERB
ejpam-3133	379	21	in	in	ADP
ejpam-3133	379	22	the	the	DET
ejpam-3133	379	23	setting	setting	NOUN
ejpam-3133	379	24	of	of	ADP
ejpam-3133	379	25	g	g	NOUN
ejpam-3133	379	26	-	-	PUNCT
ejpam-3133	379	27	metric	metric	ADJ
ejpam-3133	379	28	spaces	space	NOUN
ejpam-3133	379	29	by	by	ADP
ejpam-3133	379	30	taking	take	VERB
ejpam-3133	379	31	s	s	PART
ejpam-3133	379	32	=	=	SYM
ejpam-3133	379	33	1	1	NUM
ejpam-3133	380	1	.	.	PUNCT
ejpam-3133	380	2	references	reference	NOUN
ejpam-3133	380	3	[	[	X
ejpam-3133	380	4	1	1	NUM
ejpam-3133	380	5	]	]	PUNCT
ejpam-3133	380	6	m.	m.	NOUN
ejpam-3133	380	7	aamri	aamri	PROPN
ejpam-3133	380	8	,	,	PUNCT
ejpam-3133	380	9	d.	d.	PROPN
ejpam-3133	380	10	elmoutawakil	elmoutawakil	PROPN
ejpam-3133	380	11	,	,	PUNCT
ejpam-3133	380	12	some	some	DET
ejpam-3133	380	13	new	new	ADJ
ejpam-3133	380	14	common	common	ADJ
ejpam-3133	380	15	fixed	fix	VERB
ejpam-3133	380	16	point	point	NOUN
ejpam-3133	380	17	theorems	theorem	NOUN
ejpam-3133	380	18	under	under	ADP
ejpam-3133	380	19	strict	strict	ADJ
ejpam-3133	380	20	contractive	contractive	ADJ
ejpam-3133	380	21	conditions	condition	NOUN
ejpam-3133	380	22	,	,	PUNCT
ejpam-3133	380	23	j.	j.	PROPN
ejpam-3133	380	24	math	math	PROPN
ejpam-3133	380	25	.	.	PUNCT
ejpam-3133	381	1	anal	anal	PROPN
ejpam-3133	381	2	.	.	PUNCT
ejpam-3133	382	1	appl	appl	PROPN
ejpam-3133	382	2	.	.	PROPN
ejpam-3133	383	1	270	270	NUM
ejpam-3133	383	2	(	(	PUNCT
ejpam-3133	383	3	2002	2002	NUM
ejpam-3133	383	4	)	)	PUNCT
ejpam-3133	383	5	,	,	PUNCT
ejpam-3133	383	6	181	181	NUM
ejpam-3133	383	7	-	-	SYM
ejpam-3133	383	8	188	188	NUM
ejpam-3133	383	9	.	.	PUNCT
ejpam-3133	384	1	[	[	X
ejpam-3133	384	2	2	2	NUM
ejpam-3133	384	3	]	]	PUNCT
ejpam-3133	384	4	a.	a.	NOUN
ejpam-3133	384	5	aghajani	aghajani	PROPN
ejpam-3133	384	6	,	,	PUNCT
ejpam-3133	384	7	m.	m.	NOUN
ejpam-3133	384	8	abbas	abbas	PROPN
ejpam-3133	384	9	,	,	PUNCT
ejpam-3133	384	10	j.r	j.r	PROPN
ejpam-3133	384	11	.	.	PROPN
ejpam-3133	384	12	roshan	roshan	PROPN
ejpam-3133	384	13	,	,	PUNCT
ejpam-3133	384	14	common	common	ADJ
ejpam-3133	384	15	fixed	fix	VERB
ejpam-3133	384	16	point	point	NOUN
ejpam-3133	384	17	of	of	ADP
ejpam-3133	384	18	generalized	generalized	ADJ
ejpam-3133	384	19	weak	weak	ADJ
ejpam-3133	384	20	contractive	contractive	ADJ
ejpam-3133	384	21	mappings	mapping	NOUN
ejpam-3133	384	22	in	in	ADP
ejpam-3133	384	23	partially	partially	ADV
ejpam-3133	384	24	ordered	order	VERB
ejpam-3133	384	25	gb	gb	ADV
ejpam-3133	384	26	-	-	PUNCT
ejpam-3133	384	27	metric	metric	ADJ
ejpam-3133	384	28	spaces	space	NOUN
ejpam-3133	384	29	,	,	PUNCT
ejpam-3133	384	30	filomat	filomat	NOUN
ejpam-3133	384	31	,	,	PUNCT
ejpam-3133	384	32	8	8	NUM
ejpam-3133	384	33	(	(	PUNCT
ejpam-3133	384	34	6	6	NUM
ejpam-3133	384	35	)	)	PUNCT
ejpam-3133	384	36	(	(	PUNCT
ejpam-3133	384	37	2014	2014	NUM
ejpam-3133	384	38	)	)	PUNCT
ejpam-3133	384	39	,	,	PUNCT
ejpam-3133	384	40	10871101	10871101	NUM
ejpam-3133	384	41	.	.	PUNCT
ejpam-3133	385	1	[	[	X
ejpam-3133	385	2	3	3	X
ejpam-3133	385	3	]	]	X
ejpam-3133	385	4	a.e	a.e	PROPN
ejpam-3133	385	5	.	.	PROPN
ejpam-3133	385	6	al	al	PROPN
ejpam-3133	385	7	-	-	PUNCT
ejpam-3133	385	8	mazrooei	mazrooei	PROPN
ejpam-3133	385	9	,	,	PUNCT
ejpam-3133	385	10	j	j	PROPN
ejpam-3133	385	11	ahmad	ahmad	PROPN
ejpam-3133	385	12	,	,	PUNCT
ejpam-3133	385	13	fixed	fix	VERB
ejpam-3133	385	14	point	point	NOUN
ejpam-3133	385	15	results	result	NOUN
ejpam-3133	385	16	for	for	ADP
ejpam-3133	385	17	multivalued	multivalued	ADJ
ejpam-3133	385	18	mappings	mapping	NOUN
ejpam-3133	385	19	in	in	ADP
ejpam-3133	385	20	gbcone	gbcone	NOUN
ejpam-3133	385	21	metric	metric	ADJ
ejpam-3133	385	22	spaces	space	NOUN
ejpam-3133	385	23	,	,	PUNCT
ejpam-3133	385	24	j.	j.	PROPN
ejpam-3133	385	25	nonlinear	nonlinear	PROPN
ejpam-3133	385	26	sci	sci	PROPN
ejpam-3133	385	27	.	.	PUNCT
ejpam-3133	385	28	appl	appl	PROPN
ejpam-3133	385	29	.	.	PROPN
ejpam-3133	386	1	10	10	NUM
ejpam-3133	386	2	(	(	PUNCT
ejpam-3133	386	3	9	9	NUM
ejpam-3133	386	4	)	)	PUNCT
ejpam-3133	386	5	(	(	PUNCT
ejpam-3133	386	6	2017	2017	NUM
ejpam-3133	386	7	)	)	PUNCT
ejpam-3133	386	8	,	,	PUNCT
ejpam-3133	386	9	4866	4866	NUM
ejpam-3133	386	10	-	-	SYM
ejpam-3133	386	11	4875	4875	NUM
ejpam-3133	386	12	.	.	PUNCT
ejpam-3133	387	1	[	[	X
ejpam-3133	387	2	4	4	X
ejpam-3133	387	3	]	]	PUNCT
ejpam-3133	387	4	a.	a.	PROPN
ejpam-3133	387	5	al	al	PROPN
ejpam-3133	387	6	-	-	PUNCT
ejpam-3133	387	7	rawashdeh	rawashdeh	PROPN
ejpam-3133	387	8	,	,	PUNCT
ejpam-3133	387	9	h.	h.	PROPN
ejpam-3133	387	10	aydi	aydi	PROPN
ejpam-3133	387	11	,	,	PUNCT
ejpam-3133	387	12	a.	a.	PROPN
ejpam-3133	387	13	felhi	felhi	PROPN
ejpam-3133	387	14	,	,	PUNCT
ejpam-3133	387	15	s.	s.	PROPN
ejpam-3133	387	16	sahmim	sahmim	PROPN
ejpam-3133	387	17	,	,	PUNCT
ejpam-3133	387	18	w.	w.	PROPN
ejpam-3133	387	19	shatanawi	shatanawi	PROPN
ejpam-3133	387	20	,	,	PUNCT
ejpam-3133	387	21	on	on	ADP
ejpam-3133	387	22	common	common	ADJ
ejpam-3133	387	23	fixed	fix	VERB
ejpam-3133	387	24	points	point	NOUN
ejpam-3133	387	25	for	for	ADP
ejpam-3133	387	26	α−	α−	ADP
ejpam-3133	387	27	f	f	PROPN
ejpam-3133	387	28	-contractions	-contraction	NOUN
ejpam-3133	387	29	and	and	CCONJ
ejpam-3133	387	30	applications	application	NOUN
ejpam-3133	387	31	,	,	PUNCT
ejpam-3133	387	32	j.	j.	PROPN
ejpam-3133	387	33	nonlinear	nonlinear	PROPN
ejpam-3133	387	34	sci	sci	PROPN
ejpam-3133	387	35	.	.	PUNCT
ejpam-3133	387	36	appl	appl	PROPN
ejpam-3133	387	37	.	.	PROPN
ejpam-3133	387	38	9	9	NUM
ejpam-3133	387	39	(	(	PUNCT
ejpam-3133	387	40	5	5	NUM
ejpam-3133	387	41	)	)	PUNCT
ejpam-3133	387	42	(	(	PUNCT
ejpam-3133	387	43	2016	2016	NUM
ejpam-3133	387	44	)	)	PUNCT
ejpam-3133	387	45	,	,	PUNCT
ejpam-3133	387	46	3445–3458	3445–3458	NUM
ejpam-3133	387	47	references	reference	NOUN
ejpam-3133	387	48	106	106	NUM
ejpam-3133	388	1	[	[	X
ejpam-3133	388	2	5	5	NUM
ejpam-3133	388	3	]	]	X
ejpam-3133	388	4	h.	h.	PROPN
ejpam-3133	388	5	aydi	aydi	VERB
ejpam-3133	388	6	,	,	PUNCT
ejpam-3133	388	7	on	on	ADP
ejpam-3133	388	8	common	common	ADJ
ejpam-3133	388	9	fixed	fix	VERB
ejpam-3133	388	10	point	point	NOUN
ejpam-3133	388	11	theorems	theorem	NOUN
ejpam-3133	388	12	for	for	ADP
ejpam-3133	388	13	(	(	PUNCT
ejpam-3133	388	14	ψ,ϕ)-generalized	ψ,ϕ)-generalize	VERB
ejpam-3133	388	15	f	f	NOUN
ejpam-3133	388	16	-	-	ADJ
ejpam-3133	388	17	weakly	weakly	ADJ
ejpam-3133	388	18	contractive	contractive	ADJ
ejpam-3133	388	19	mappings	mapping	NOUN
ejpam-3133	388	20	,	,	PUNCT
ejpam-3133	388	21	miskolc	miskolc	ADJ
ejpam-3133	388	22	mathematical	mathematical	ADJ
ejpam-3133	388	23	notes	note	NOUN
ejpam-3133	388	24	,	,	PUNCT
ejpam-3133	388	25	14	14	NUM
ejpam-3133	388	26	(	(	PUNCT
ejpam-3133	388	27	1	1	NUM
ejpam-3133	388	28	)	)	PUNCT
ejpam-3133	388	29	(	(	PUNCT
ejpam-3133	388	30	2013	2013	NUM
ejpam-3133	388	31	)	)	PUNCT
ejpam-3133	388	32	,	,	PUNCT
ejpam-3133	388	33	19	19	NUM
ejpam-3133	388	34	-	-	SYM
ejpam-3133	388	35	30	30	NUM
ejpam-3133	388	36	.	.	PUNCT
ejpam-3133	389	1	[	[	X
ejpam-3133	389	2	6	6	NUM
ejpam-3133	389	3	]	]	X
ejpam-3133	389	4	h.	h.	PROPN
ejpam-3133	389	5	aydi	aydi	PROPN
ejpam-3133	389	6	,	,	PUNCT
ejpam-3133	389	7	b.	b.	PROPN
ejpam-3133	389	8	damjanovic	damjanovic	PROPN
ejpam-3133	389	9	,	,	PUNCT
ejpam-3133	389	10	b.	b.	PROPN
ejpam-3133	389	11	samet	samet	PROPN
ejpam-3133	389	12	,	,	PUNCT
ejpam-3133	389	13	w.	w.	PROPN
ejpam-3133	389	14	shatanawi	shatanawi	PROPN
ejpam-3133	389	15	,	,	PUNCT
ejpam-3133	389	16	coupled	couple	VERB
ejpam-3133	389	17	fixed	fix	VERB
ejpam-3133	389	18	point	point	NOUN
ejpam-3133	389	19	theorems	theorem	NOUN
ejpam-3133	389	20	for	for	ADP
ejpam-3133	389	21	nonlinear	nonlinear	ADJ
ejpam-3133	389	22	contractions	contraction	NOUN
ejpam-3133	389	23	in	in	ADP
ejpam-3133	389	24	partially	partially	ADV
ejpam-3133	389	25	ordered	order	VERB
ejpam-3133	389	26	g	g	NOUN
ejpam-3133	389	27	-	-	PUNCT
ejpam-3133	389	28	metric	metric	ADJ
ejpam-3133	389	29	spaces	space	NOUN
ejpam-3133	389	30	,	,	PUNCT
ejpam-3133	389	31	mathematical	mathematical	ADJ
ejpam-3133	389	32	and	and	CCONJ
ejpam-3133	389	33	computer	computer	NOUN
ejpam-3133	389	34	modelling	modelling	NOUN
ejpam-3133	389	35	,	,	PUNCT
ejpam-3133	389	36	54	54	NUM
ejpam-3133	389	37	(	(	PUNCT
ejpam-3133	389	38	2011	2011	NUM
ejpam-3133	389	39	)	)	PUNCT
ejpam-3133	389	40	,	,	PUNCT
ejpam-3133	389	41	2443	2443	NUM
ejpam-3133	389	42	-	-	SYM
ejpam-3133	389	43	2450	2450	NUM
ejpam-3133	389	44	.	.	PUNCT
ejpam-3133	390	1	[	[	X
ejpam-3133	390	2	7	7	X
ejpam-3133	390	3	]	]	X
ejpam-3133	390	4	h.	h.	PROPN
ejpam-3133	390	5	aydi	aydi	PROPN
ejpam-3133	390	6	,	,	PUNCT
ejpam-3133	390	7	a.	a.	PROPN
ejpam-3133	390	8	felhi	felhi	PROPN
ejpam-3133	390	9	,	,	PUNCT
ejpam-3133	390	10	s.	s.	PROPN
ejpam-3133	390	11	sahmim	sahmim	PROPN
ejpam-3133	390	12	,	,	PUNCT
ejpam-3133	390	13	related	relate	VERB
ejpam-3133	390	14	fixed	fix	VERB
ejpam-3133	390	15	point	point	NOUN
ejpam-3133	390	16	results	result	NOUN
ejpam-3133	390	17	for	for	ADP
ejpam-3133	390	18	cyclic	cyclic	ADJ
ejpam-3133	390	19	contractions	contraction	NOUN
ejpam-3133	390	20	on	on	ADP
ejpam-3133	390	21	g	g	NOUN
ejpam-3133	390	22	-	-	PUNCT
ejpam-3133	390	23	metric	metric	ADJ
ejpam-3133	390	24	spaces	space	NOUN
ejpam-3133	390	25	and	and	CCONJ
ejpam-3133	390	26	applications	application	NOUN
ejpam-3133	390	27	,	,	PUNCT
ejpam-3133	390	28	filomat	filomat	NOUN
ejpam-3133	390	29	,	,	PUNCT
ejpam-3133	390	30	31	31	NUM
ejpam-3133	390	31	(	(	PUNCT
ejpam-3133	390	32	3	3	NUM
ejpam-3133	390	33	)	)	PUNCT
ejpam-3133	390	34	(	(	PUNCT
ejpam-3133	390	35	2017	2017	NUM
ejpam-3133	390	36	)	)	PUNCT
ejpam-3133	390	37	,	,	PUNCT
ejpam-3133	390	38	853–869	853–869	NUM
ejpam-3133	390	39	.	.	PUNCT
ejpam-3133	391	1	[	[	X
ejpam-3133	391	2	8	8	NUM
ejpam-3133	391	3	]	]	X
ejpam-3133	391	4	h.	h.	PROPN
ejpam-3133	391	5	aydi	aydi	PROPN
ejpam-3133	391	6	,	,	PUNCT
ejpam-3133	391	7	e.	e.	PROPN
ejpam-3133	391	8	karapinar	karapinar	PROPN
ejpam-3133	391	9	,	,	PUNCT
ejpam-3133	391	10	w.	w.	PROPN
ejpam-3133	391	11	shatanawi	shatanawi	PROPN
ejpam-3133	391	12	,	,	PUNCT
ejpam-3133	391	13	coupled	couple	VERB
ejpam-3133	391	14	fixed	fix	VERB
ejpam-3133	391	15	point	point	NOUN
ejpam-3133	391	16	results	result	NOUN
ejpam-3133	391	17	for	for	ADP
ejpam-3133	391	18	(	(	PUNCT
ejpam-3133	391	19	ψ	ψ	NOUN
ejpam-3133	391	20	,	,	PUNCT
ejpam-3133	391	21	φ)-weakly	φ)-weakly	VERB
ejpam-3133	391	22	contractive	contractive	ADJ
ejpam-3133	391	23	condition	condition	NOUN
ejpam-3133	391	24	in	in	ADP
ejpam-3133	391	25	ordered	order	VERB
ejpam-3133	391	26	partial	partial	ADJ
ejpam-3133	391	27	metric	metric	ADJ
ejpam-3133	391	28	spaces	space	NOUN
ejpam-3133	391	29	,	,	PUNCT
ejpam-3133	391	30	comput	comput	NOUN
ejpam-3133	391	31	.	.	PUNCT
ejpam-3133	392	1	math	math	NOUN
ejpam-3133	392	2	.	.	PUNCT
ejpam-3133	393	1	appl	appl	PROPN
ejpam-3133	393	2	.	.	PUNCT
ejpam-3133	394	1	62	62	NUM
ejpam-3133	394	2	(	(	PUNCT
ejpam-3133	394	3	2011	2011	NUM
ejpam-3133	394	4	)	)	PUNCT
ejpam-3133	394	5	,	,	PUNCT
ejpam-3133	394	6	4449	4449	NUM
ejpam-3133	394	7	-	-	SYM
ejpam-3133	394	8	4460	4460	NUM
ejpam-3133	394	9	.	.	PUNCT
ejpam-3133	395	1	[	[	X
ejpam-3133	395	2	9	9	NUM
ejpam-3133	395	3	]	]	X
ejpam-3133	395	4	h.	h.	PROPN
ejpam-3133	395	5	aydi	aydi	PROPN
ejpam-3133	395	6	,	,	PUNCT
ejpam-3133	395	7	e.	e.	PROPN
ejpam-3133	395	8	karapinar	karapinar	PROPN
ejpam-3133	395	9	,	,	PUNCT
ejpam-3133	395	10	p.	p.	PROPN
ejpam-3133	395	11	salimi	salimi	PROPN
ejpam-3133	395	12	,	,	PUNCT
ejpam-3133	395	13	some	some	DET
ejpam-3133	395	14	fixed	fix	VERB
ejpam-3133	395	15	point	point	NOUN
ejpam-3133	395	16	results	result	NOUN
ejpam-3133	395	17	in	in	ADP
ejpam-3133	395	18	gp	gp	ADJ
ejpam-3133	395	19	-	-	ADJ
ejpam-3133	395	20	metric	metric	ADJ
ejpam-3133	395	21	spaces	space	NOUN
ejpam-3133	395	22	,	,	PUNCT
ejpam-3133	395	23	journal	journal	NOUN
ejpam-3133	395	24	of	of	ADP
ejpam-3133	395	25	applied	apply	VERB
ejpam-3133	395	26	mathematics	mathematic	NOUN
ejpam-3133	395	27	,	,	PUNCT
ejpam-3133	395	28	volume	volume	NOUN
ejpam-3133	395	29	2012	2012	NUM
ejpam-3133	395	30	,	,	PUNCT
ejpam-3133	395	31	article	article	NOUN
ejpam-3133	395	32	i	i	PROPN
ejpam-3133	395	33	d	d	PROPN
ejpam-3133	395	34	891713	891713	NUM
ejpam-3133	395	35	,	,	PUNCT
ejpam-3133	395	36	15	15	NUM
ejpam-3133	395	37	pages	page	NOUN
ejpam-3133	395	38	.	.	PUNCT
ejpam-3133	396	1	[	[	X
ejpam-3133	396	2	10	10	NUM
ejpam-3133	396	3	]	]	X
ejpam-3133	396	4	h.	h.	PROPN
ejpam-3133	396	5	aydi	aydi	PROPN
ejpam-3133	396	6	,	,	PUNCT
ejpam-3133	396	7	w.	w.	PROPN
ejpam-3133	396	8	shatanawi	shatanawi	PROPN
ejpam-3133	396	9	,	,	PUNCT
ejpam-3133	396	10	m.	m.	NOUN
ejpam-3133	396	11	postolache	postolache	PROPN
ejpam-3133	396	12	,	,	PUNCT
ejpam-3133	396	13	coupled	couple	VERB
ejpam-3133	396	14	fixed	fix	VERB
ejpam-3133	396	15	point	point	NOUN
ejpam-3133	396	16	results	result	NOUN
ejpam-3133	396	17	for	for	ADP
ejpam-3133	396	18	(	(	PUNCT
ejpam-3133	396	19	ψ	ψ	NOUN
ejpam-3133	396	20	,	,	PUNCT
ejpam-3133	396	21	φ)-weakly	φ)-weakly	VERB
ejpam-3133	396	22	contractive	contractive	ADJ
ejpam-3133	396	23	mappings	mapping	NOUN
ejpam-3133	396	24	in	in	ADP
ejpam-3133	396	25	ordered	order	VERB
ejpam-3133	396	26	g	g	NOUN
ejpam-3133	396	27	-	-	PUNCT
ejpam-3133	396	28	metric	metric	ADJ
ejpam-3133	396	29	spaces	space	NOUN
ejpam-3133	396	30	,	,	PUNCT
ejpam-3133	396	31	comput	comput	NOUN
ejpam-3133	396	32	.	.	PUNCT
ejpam-3133	397	1	math	math	NOUN
ejpam-3133	397	2	.	.	PUNCT
ejpam-3133	398	1	appl	appl	PROPN
ejpam-3133	398	2	.	.	PROPN
ejpam-3133	399	1	63	63	NUM
ejpam-3133	399	2	(	(	PUNCT
ejpam-3133	399	3	2012	2012	NUM
ejpam-3133	399	4	)	)	PUNCT
ejpam-3133	399	5	,	,	PUNCT
ejpam-3133	399	6	298	298	NUM
ejpam-3133	399	7	-	-	SYM
ejpam-3133	399	8	309	309	NUM
ejpam-3133	399	9	.	.	PUNCT
ejpam-3133	400	1	[	[	X
ejpam-3133	400	2	11	11	NUM
ejpam-3133	400	3	]	]	X
ejpam-3133	400	4	h.	h.	PROPN
ejpam-3133	400	5	aydi	aydi	PROPN
ejpam-3133	400	6	,	,	PUNCT
ejpam-3133	400	7	w.	w.	PROPN
ejpam-3133	400	8	shatanawi	shatanawi	PROPN
ejpam-3133	400	9	,	,	PUNCT
ejpam-3133	400	10	c.	c.	PROPN
ejpam-3133	400	11	vetro	vetro	PROPN
ejpam-3133	400	12	,	,	PUNCT
ejpam-3133	400	13	on	on	ADP
ejpam-3133	400	14	generalized	generalized	ADJ
ejpam-3133	400	15	weakly	weakly	ADJ
ejpam-3133	400	16	g	g	NOUN
ejpam-3133	400	17	-	-	PUNCT
ejpam-3133	400	18	contraction	contraction	NOUN
ejpam-3133	400	19	mapping	mapping	NOUN
ejpam-3133	400	20	in	in	ADP
ejpam-3133	400	21	g	g	NOUN
ejpam-3133	400	22	-	-	PUNCT
ejpam-3133	400	23	metric	metric	ADJ
ejpam-3133	400	24	spaces	space	NOUN
ejpam-3133	400	25	,	,	PUNCT
ejpam-3133	400	26	comput	comput	NOUN
ejpam-3133	400	27	.	.	PUNCT
ejpam-3133	401	1	math	math	NOUN
ejpam-3133	401	2	.	.	PUNCT
ejpam-3133	402	1	appl	appl	PROPN
ejpam-3133	402	2	.	.	PUNCT
ejpam-3133	403	1	62	62	NUM
ejpam-3133	403	2	(	(	PUNCT
ejpam-3133	403	3	2011	2011	NUM
ejpam-3133	403	4	)	)	PUNCT
ejpam-3133	403	5	,	,	PUNCT
ejpam-3133	403	6	4222	4222	NUM
ejpam-3133	403	7	-	-	SYM
ejpam-3133	403	8	4229	4229	NUM
ejpam-3133	403	9	.	.	PUNCT
ejpam-3133	404	1	[	[	X
ejpam-3133	404	2	12	12	NUM
ejpam-3133	404	3	]	]	X
ejpam-3133	404	4	s.	s.	PROPN
ejpam-3133	404	5	banach	banach	PROPN
ejpam-3133	404	6	,	,	PUNCT
ejpam-3133	404	7	sur	sur	PROPN
ejpam-3133	404	8	les	les	X
ejpam-3133	404	9	opérations	opération	NOUN
ejpam-3133	404	10	dans	dan	NOUN
ejpam-3133	404	11	les	les	X
ejpam-3133	404	12	ensembles	ensemble	NOUN
ejpam-3133	404	13	abstraits	abstrait	NOUN
ejpam-3133	404	14	et	et	PROPN
ejpam-3133	404	15	leur	leur	X
ejpam-3133	404	16	application	application	PROPN
ejpam-3133	404	17	aux	aux	PROPN
ejpam-3133	404	18	équations	équations	PROPN
ejpam-3133	404	19	integrals	integral	NOUN
ejpam-3133	404	20	,	,	PUNCT
ejpam-3133	404	21	fund	fund	NOUN
ejpam-3133	404	22	.	.	PUNCT
ejpam-3133	405	1	math	math	NOUN
ejpam-3133	405	2	.	.	PUNCT
ejpam-3133	406	1	3	3	NUM
ejpam-3133	406	2	(	(	PUNCT
ejpam-3133	406	3	1922	1922	NUM
ejpam-3133	406	4	)	)	PUNCT
ejpam-3133	406	5	,	,	PUNCT
ejpam-3133	406	6	133	133	NUM
ejpam-3133	406	7	-	-	SYM
ejpam-3133	406	8	181	181	NUM
ejpam-3133	406	9	.	.	PUNCT
ejpam-3133	407	1	[	[	X
ejpam-3133	407	2	13	13	NUM
ejpam-3133	407	3	]	]	X
ejpam-3133	407	4	s.	s.	PROPN
ejpam-3133	407	5	czerwik	czerwik	PROPN
ejpam-3133	407	6	,	,	PUNCT
ejpam-3133	407	7	contraction	contraction	NOUN
ejpam-3133	407	8	mappings	mapping	NOUN
ejpam-3133	407	9	in	in	ADP
ejpam-3133	407	10	b	b	NOUN
ejpam-3133	407	11	-	-	ADJ
ejpam-3133	407	12	metric	metric	ADJ
ejpam-3133	407	13	spaces	space	NOUN
ejpam-3133	407	14	,	,	PUNCT
ejpam-3133	407	15	acta	acta	PROPN
ejpam-3133	407	16	math	math	PROPN
ejpam-3133	407	17	.	.	PUNCT
ejpam-3133	408	1	inform	inform	NOUN
ejpam-3133	408	2	.	.	PUNCT
ejpam-3133	409	1	univ	univ	PROPN
ejpam-3133	409	2	.	.	PUNCT
ejpam-3133	409	3	ostraviensis	ostraviensis	NOUN
ejpam-3133	409	4	,	,	PUNCT
ejpam-3133	409	5	1	1	NUM
ejpam-3133	409	6	(	(	PUNCT
ejpam-3133	409	7	1993	1993	NUM
ejpam-3133	409	8	)	)	PUNCT
ejpam-3133	409	9	,	,	PUNCT
ejpam-3133	409	10	5	5	NUM
ejpam-3133	409	11	-	-	SYM
ejpam-3133	409	12	11	11	NUM
ejpam-3133	409	13	.	.	PUNCT
ejpam-3133	410	1	[	[	X
ejpam-3133	410	2	14	14	NUM
ejpam-3133	410	3	]	]	X
ejpam-3133	410	4	m.m.m	m.m.m	NOUN
ejpam-3133	410	5	.	.	PUNCT
ejpam-3133	410	6	jaradat	jaradat	PROPN
ejpam-3133	410	7	,	,	PUNCT
ejpam-3133	410	8	z.	z.	PROPN
ejpam-3133	410	9	mustafa	mustafa	PROPN
ejpam-3133	410	10	,	,	PUNCT
ejpam-3133	410	11	a.	a.	PROPN
ejpam-3133	410	12	h.	h.	PROPN
ejpam-3133	410	13	ansari	ansari	PROPN
ejpam-3133	410	14	,	,	PUNCT
ejpam-3133	410	15	p.	p.	PROPN
ejpam-3133	410	16	s.	s.	PROPN
ejpam-3133	410	17	kumari	kumari	PROPN
ejpam-3133	410	18	,	,	PUNCT
ejpam-3133	410	19	d.	d.	PROPN
ejpam-3133	410	20	dolicanin	dolicanin	PROPN
ejpam-3133	410	21	-	-	PUNCT
ejpam-3133	410	22	djekic	djekic	PROPN
ejpam-3133	410	23	and	and	CCONJ
ejpam-3133	410	24	h.m	h.m	PROPN
ejpam-3133	410	25	.	.	PROPN
ejpam-3133	410	26	jaradat	jaradat	PROPN
ejpam-3133	410	27	,	,	PUNCT
ejpam-3133	410	28	some	some	DET
ejpam-3133	410	29	fixed	fix	VERB
ejpam-3133	410	30	point	point	NOUN
ejpam-3133	410	31	results	result	NOUN
ejpam-3133	410	32	for	for	ADP
ejpam-3133	410	33	fα−ωϕ-generalized	fα−ωϕ-generalize	VERB
ejpam-3133	410	34	cyclic	cyclic	ADJ
ejpam-3133	410	35	contractions	contraction	NOUN
ejpam-3133	410	36	on	on	ADP
ejpam-3133	410	37	metric	metric	ADJ
ejpam-3133	410	38	-	-	PUNCT
ejpam-3133	410	39	like	like	ADJ
ejpam-3133	410	40	space	space	NOUN
ejpam-3133	410	41	with	with	ADP
ejpam-3133	410	42	applications	application	NOUN
ejpam-3133	410	43	to	to	PART
ejpam-3133	410	44	graphs	graph	NOUN
ejpam-3133	410	45	and	and	CCONJ
ejpam-3133	410	46	integral	integral	ADJ
ejpam-3133	410	47	equations	equation	NOUN
ejpam-3133	410	48	,	,	PUNCT
ejpam-3133	410	49	j.	j.	PROPN
ejpam-3133	410	50	math	math	PROPN
ejpam-3133	410	51	.	.	PUNCT
ejpam-3133	411	1	analysis	analysis	NOUN
ejpam-3133	411	2	,	,	PUNCT
ejpam-3133	411	3	8(1	8(1	NOUN
ejpam-3133	411	4	)	)	PUNCT
ejpam-3133	411	5	(	(	PUNCT
ejpam-3133	411	6	2017	2017	NUM
ejpam-3133	411	7	)	)	PUNCT
ejpam-3133	411	8	28–45	28–45	NUM
ejpam-3133	411	9	.	.	PUNCT
ejpam-3133	412	1	[	[	X
ejpam-3133	412	2	15	15	NUM
ejpam-3133	412	3	]	]	X
ejpam-3133	412	4	m.m.m	m.m.m	NOUN
ejpam-3133	412	5	.	.	PUNCT
ejpam-3133	412	6	jaradat	jaradat	PROPN
ejpam-3133	412	7	,	,	PUNCT
ejpam-3133	412	8	z.	z.	PROPN
ejpam-3133	412	9	mustafa	mustafa	PROPN
ejpam-3133	412	10	,	,	PUNCT
ejpam-3133	412	11	a.	a.	PROPN
ejpam-3133	412	12	h.	h.	PROPN
ejpam-3133	412	13	ansari	ansari	PROPN
ejpam-3133	412	14	,	,	PUNCT
ejpam-3133	412	15	s.	s.	PROPN
ejpam-3133	412	16	chandok	chandok	PROPN
ejpam-3133	412	17	,	,	PUNCT
ejpam-3133	412	18	c.	c.	PROPN
ejpam-3133	412	19	dolicanin	dolicanin	PROPN
ejpam-3133	412	20	,	,	PUNCT
ejpam-3133	412	21	some	some	DET
ejpam-3133	412	22	approximate	approximate	ADJ
ejpam-3133	412	23	xed	xed	PROPN
ejpam-3133	412	24	point	point	NOUN
ejpam-3133	412	25	results	result	NOUN
ejpam-3133	412	26	and	and	CCONJ
ejpam-3133	412	27	application	application	NOUN
ejpam-3133	412	28	on	on	ADP
ejpam-3133	412	29	graph	graph	NOUN
ejpam-3133	412	30	theory	theory	NOUN
ejpam-3133	412	31	for	for	ADP
ejpam-3133	412	32	partial	partial	ADJ
ejpam-3133	412	33	(	(	PUNCT
ejpam-3133	412	34	hf	hf	ADJ
ejpam-3133	412	35	)	)	PUNCT
ejpam-3133	412	36	-generalized	-generalized	ADJ
ejpam-3133	412	37	convex	convex	ADJ
ejpam-3133	412	38	contraction	contraction	NOUN
ejpam-3133	412	39	mappings	mapping	NOUN
ejpam-3133	412	40	with	with	ADP
ejpam-3133	412	41	special	special	ADJ
ejpam-3133	412	42	class	class	NOUN
ejpam-3133	412	43	of	of	ADP
ejpam-3133	412	44	functions	function	NOUN
ejpam-3133	412	45	on	on	ADP
ejpam-3133	412	46	complete	complete	ADJ
ejpam-3133	412	47	metric	metric	ADJ
ejpam-3133	412	48	space	space	NOUN
ejpam-3133	412	49	,	,	PUNCT
ejpam-3133	412	50	j.	j.	PROPN
ejpam-3133	412	51	nonlinear	nonlinear	PROPN
ejpam-3133	412	52	sci	sci	PROPN
ejpam-3133	412	53	.	.	PUNCT
ejpam-3133	412	54	appl	appl	PROPN
ejpam-3133	412	55	.	.	PROPN
ejpam-3133	413	1	10	10	NUM
ejpam-3133	413	2	(	(	PUNCT
ejpam-3133	413	3	4	4	NUM
ejpam-3133	413	4	)	)	PUNCT
ejpam-3133	413	5	(	(	PUNCT
ejpam-3133	413	6	2017	2017	NUM
ejpam-3133	413	7	)	)	PUNCT
ejpam-3133	413	8	1695	1695	NUM
ejpam-3133	413	9	-	-	SYM
ejpam-3133	413	10	1708	1708	NUM
ejpam-3133	413	11	.	.	PUNCT
ejpam-3133	414	1	[	[	X
ejpam-3133	414	2	16	16	NUM
ejpam-3133	414	3	]	]	X
ejpam-3133	414	4	m.m.m	m.m.m	NOUN
ejpam-3133	414	5	.	.	PUNCT
ejpam-3133	414	6	jaradat	jaradat	PROPN
ejpam-3133	414	7	,	,	PUNCT
ejpam-3133	414	8	z.	z.	PROPN
ejpam-3133	414	9	mustafa	mustafa	PROPN
ejpam-3133	414	10	,	,	PUNCT
ejpam-3133	414	11	m.	m.	PROPN
ejpam-3133	414	12	arshad	arshad	PROPN
ejpam-3133	414	13	,	,	PUNCT
ejpam-3133	414	14	s.	s.	PROPN
ejpam-3133	414	15	ullah	ullah	PROPN
ejpam-3133	414	16	khan	khan	PROPN
ejpam-3133	414	17	,	,	PUNCT
ejpam-3133	414	18	j.	j.	PROPN
ejpam-3133	414	19	ahmad	ahmad	PROPN
ejpam-3133	414	20	,	,	PUNCT
ejpam-3133	414	21	some	some	DET
ejpam-3133	414	22	fixed	fix	VERB
ejpam-3133	414	23	point	point	NOUN
ejpam-3133	414	24	results	result	NOUN
ejpam-3133	414	25	on	on	ADP
ejpam-3133	414	26	g	g	NOUN
ejpam-3133	414	27	-	-	PUNCT
ejpam-3133	414	28	metric	metric	ADJ
ejpam-3133	414	29	and	and	CCONJ
ejpam-3133	414	30	gb	gb	ADV
ejpam-3133	414	31	-	-	PUNCT
ejpam-3133	414	32	metric	metric	ADJ
ejpam-3133	414	33	spaces	space	NOUN
ejpam-3133	414	34	,	,	PUNCT
ejpam-3133	414	35	demonstratio	demonstratio	PROPN
ejpam-3133	414	36	mathematica	mathematica	PROPN
ejpam-3133	414	37	,	,	PUNCT
ejpam-3133	414	38	50	50	NUM
ejpam-3133	414	39	(	(	PUNCT
ejpam-3133	414	40	2017	2017	NUM
ejpam-3133	414	41	)	)	PUNCT
ejpam-3133	414	42	190	190	NUM
ejpam-3133	414	43	–	–	PUNCT
ejpam-3133	414	44	207	207	NUM
ejpam-3133	414	45	.	.	PUNCT
ejpam-3133	415	1	[	[	X
ejpam-3133	415	2	17	17	NUM
ejpam-3133	415	3	]	]	X
ejpam-3133	415	4	g.	g.	PROPN
ejpam-3133	415	5	jungk	jungk	PROPN
ejpam-3133	415	6	,	,	PUNCT
ejpam-3133	415	7	commuting	commuting	NOUN
ejpam-3133	415	8	maps	map	NOUN
ejpam-3133	415	9	and	and	CCONJ
ejpam-3133	415	10	fixed	fix	VERB
ejpam-3133	415	11	points	point	NOUN
ejpam-3133	415	12	,	,	PUNCT
ejpam-3133	415	13	am	be	AUX
ejpam-3133	415	14	.	.	PUNCT
ejpam-3133	415	15	math	math	NOUN
ejpam-3133	415	16	.	.	PUNCT
ejpam-3133	416	1	monthly	monthly	ADJ
ejpam-3133	416	2	,	,	PUNCT
ejpam-3133	416	3	83	83	NUM
ejpam-3133	416	4	(	(	PUNCT
ejpam-3133	416	5	1976	1976	NUM
ejpam-3133	416	6	)	)	PUNCT
ejpam-3133	416	7	,	,	PUNCT
ejpam-3133	416	8	261	261	NUM
ejpam-3133	416	9	-	-	SYM
ejpam-3133	416	10	263	263	NUM
ejpam-3133	416	11	.	.	PUNCT
ejpam-3133	417	1	[	[	X
ejpam-3133	417	2	18	18	NUM
ejpam-3133	417	3	]	]	X
ejpam-3133	417	4	g.	g.	PROPN
ejpam-3133	417	5	jungk	jungk	PROPN
ejpam-3133	417	6	,	,	PUNCT
ejpam-3133	417	7	compatible	compatible	ADJ
ejpam-3133	417	8	mappings	mapping	NOUN
ejpam-3133	417	9	and	and	CCONJ
ejpam-3133	417	10	common	common	ADJ
ejpam-3133	417	11	fixed	fix	VERB
ejpam-3133	417	12	points	point	NOUN
ejpam-3133	417	13	,	,	PUNCT
ejpam-3133	417	14	int.j	int.j	PROPN
ejpam-3133	417	15	.	.	PROPN
ejpam-3133	417	16	math	math	NOUN
ejpam-3133	417	17	.	.	PUNCT
ejpam-3133	418	1	sci	sci	PROPN
ejpam-3133	418	2	.	.	PROPN
ejpam-3133	418	3	,	,	PUNCT
ejpam-3133	418	4	9(4)(1986	9(4)(1986	NUM
ejpam-3133	418	5	)	)	PUNCT
ejpam-3133	418	6	,	,	PUNCT
ejpam-3133	418	7	771	771	NUM
ejpam-3133	418	8	-	-	SYM
ejpam-3133	418	9	779	779	NUM
ejpam-3133	418	10	.	.	PUNCT
ejpam-3133	418	11	references	reference	NOUN
ejpam-3133	418	12	107	107	NUM
ejpam-3133	419	1	[	[	X
ejpam-3133	419	2	19	19	NUM
ejpam-3133	419	3	]	]	PUNCT
ejpam-3133	419	4	g.	g.	PROPN
ejpam-3133	419	5	jungk	jungk	PROPN
ejpam-3133	419	6	,	,	PUNCT
ejpam-3133	419	7	common	common	ADJ
ejpam-3133	419	8	fixed	fix	VERB
ejpam-3133	419	9	points	point	NOUN
ejpam-3133	419	10	for	for	ADP
ejpam-3133	419	11	commuting	commute	VERB
ejpam-3133	419	12	and	and	CCONJ
ejpam-3133	419	13	compatible	compatible	ADJ
ejpam-3133	419	14	maps	map	NOUN
ejpam-3133	419	15	on	on	ADP
ejpam-3133	419	16	compacta	compacta	NOUN
ejpam-3133	419	17	,	,	PUNCT
ejpam-3133	419	18	pro	pro	ADJ
ejpam-3133	419	19	.	.	PUNCT
ejpam-3133	419	20	am	be	AUX
ejpam-3133	419	21	.	.	PUNCT
ejpam-3133	420	1	math	math	NOUN
ejpam-3133	420	2	.	.	PUNCT
ejpam-3133	421	1	soc	soc	PROPN
ejpam-3133	421	2	.	.	PUNCT
ejpam-3133	422	1	103	103	NUM
ejpam-3133	422	2	(	(	PUNCT
ejpam-3133	422	3	1988	1988	NUM
ejpam-3133	422	4	)	)	PUNCT
ejpam-3133	422	5	,	,	PUNCT
ejpam-3133	422	6	977	977	NUM
ejpam-3133	422	7	-	-	SYM
ejpam-3133	422	8	983	983	NUM
ejpam-3133	422	9	.	.	PUNCT
ejpam-3133	423	1	[	[	X
ejpam-3133	423	2	20	20	NUM
ejpam-3133	423	3	]	]	PUNCT
ejpam-3133	423	4	g.	g.	PROPN
ejpam-3133	423	5	jungk	jungk	PROPN
ejpam-3133	423	6	,	,	PUNCT
ejpam-3133	423	7	common	common	ADJ
ejpam-3133	423	8	fixed	fix	VERB
ejpam-3133	423	9	points	point	NOUN
ejpam-3133	423	10	for	for	ADP
ejpam-3133	423	11	noncontinuous	noncontinuous	ADJ
ejpam-3133	423	12	nonself	nonself	PROPN
ejpam-3133	423	13	maps	map	NOUN
ejpam-3133	423	14	on	on	ADP
ejpam-3133	423	15	nonmetric	nonmetric	ADJ
ejpam-3133	423	16	spaces	space	NOUN
ejpam-3133	423	17	,	,	PUNCT
ejpam-3133	423	18	far	far	PROPN
ejpam-3133	423	19	east	east	PROPN
ejpam-3133	423	20	j.	j.	PROPN
ejpam-3133	423	21	math	math	PROPN
ejpam-3133	423	22	.	.	PUNCT
ejpam-3133	424	1	sci	sci	PROPN
ejpam-3133	424	2	.	.	PROPN
ejpam-3133	424	3	4	4	NUM
ejpam-3133	424	4	(	(	PUNCT
ejpam-3133	424	5	1996	1996	NUM
ejpam-3133	424	6	)	)	PUNCT
ejpam-3133	424	7	,	,	PUNCT
ejpam-3133	424	8	199	199	NUM
ejpam-3133	424	9	-	-	SYM
ejpam-3133	424	10	215	215	NUM
ejpam-3133	424	11	.	.	PUNCT
ejpam-3133	425	1	[	[	X
ejpam-3133	425	2	21	21	NUM
ejpam-3133	425	3	]	]	X
ejpam-3133	425	4	g.	g.	PROPN
ejpam-3133	425	5	jungk	jungk	PROPN
ejpam-3133	425	6	,	,	PUNCT
ejpam-3133	425	7	n.	n.	PROPN
ejpam-3133	425	8	hussain	hussain	PROPN
ejpam-3133	425	9	,	,	PUNCT
ejpam-3133	425	10	compatible	compatible	ADJ
ejpam-3133	425	11	maps	map	NOUN
ejpam-3133	425	12	and	and	CCONJ
ejpam-3133	425	13	invariant	invariant	ADJ
ejpam-3133	425	14	approximation	approximation	NOUN
ejpam-3133	425	15	,	,	PUNCT
ejpam-3133	425	16	j.	j.	PROPN
ejpam-3133	425	17	math	math	PROPN
ejpam-3133	425	18	.	.	PUNCT
ejpam-3133	426	1	anal	anal	PROPN
ejpam-3133	426	2	.	.	PUNCT
ejpam-3133	427	1	appl	appl	PROPN
ejpam-3133	427	2	.	.	PUNCT
ejpam-3133	428	1	325(2)(2007	325(2)(2007	NUM
ejpam-3133	428	2	)	)	PUNCT
ejpam-3133	428	3	,	,	PUNCT
ejpam-3133	428	4	1003	1003	NUM
ejpam-3133	428	5	-	-	SYM
ejpam-3133	428	6	1012	1012	NUM
ejpam-3133	428	7	.	.	PUNCT
ejpam-3133	429	1	[	[	X
ejpam-3133	429	2	22	22	NUM
ejpam-3133	429	3	]	]	X
ejpam-3133	429	4	m.s	m.s	PROPN
ejpam-3133	429	5	.	.	PROPN
ejpam-3133	429	6	khan	khan	PROPN
ejpam-3133	429	7	,	,	PUNCT
ejpam-3133	429	8	m.	m.	NOUN
ejpam-3133	429	9	swalesh	swalesh	PROPN
ejpam-3133	429	10	,	,	PUNCT
ejpam-3133	429	11	s.	s.	PROPN
ejpam-3133	429	12	sessa	sessa	PROPN
ejpam-3133	429	13	,	,	PUNCT
ejpam-3133	429	14	fixed	fix	VERB
ejpam-3133	429	15	points	point	NOUN
ejpam-3133	429	16	theorems	theorem	NOUN
ejpam-3133	429	17	by	by	ADP
ejpam-3133	429	18	altering	alter	VERB
ejpam-3133	429	19	distances	distance	NOUN
ejpam-3133	429	20	between	between	ADP
ejpam-3133	429	21	the	the	DET
ejpam-3133	429	22	points	point	NOUN
ejpam-3133	429	23	,	,	PUNCT
ejpam-3133	429	24	bull	bull	NOUN
ejpam-3133	429	25	.	.	PUNCT
ejpam-3133	430	1	aust	aust	PROPN
ejpam-3133	430	2	.	.	PUNCT
ejpam-3133	430	3	math	math	PROPN
ejpam-3133	430	4	.	.	PUNCT
ejpam-3133	431	1	soc	soc	PROPN
ejpam-3133	431	2	.	.	PUNCT
ejpam-3133	432	1	30	30	NUM
ejpam-3133	432	2	(	(	PUNCT
ejpam-3133	432	3	1984	1984	NUM
ejpam-3133	432	4	)	)	PUNCT
ejpam-3133	432	5	,	,	PUNCT
ejpam-3133	432	6	1	1	NUM
ejpam-3133	432	7	-	-	SYM
ejpam-3133	432	8	9	9	NUM
ejpam-3133	432	9	.	.	PUNCT
ejpam-3133	433	1	[	[	X
ejpam-3133	433	2	23	23	NUM
ejpam-3133	433	3	]	]	X
ejpam-3133	433	4	d.	d.	PROPN
ejpam-3133	433	5	lateef	lateef	PROPN
ejpam-3133	433	6	,	,	PUNCT
ejpam-3133	433	7	j.	j.	PROPN
ejpam-3133	433	8	ahmad	ahmad	PROPN
ejpam-3133	433	9	,	,	PUNCT
ejpam-3133	433	10	a.e	a.e	PROPN
ejpam-3133	433	11	.	.	PROPN
ejpam-3133	433	12	al	al	PROPN
ejpam-3133	433	13	-	-	PUNCT
ejpam-3133	433	14	mazrooei	mazrooei	ADJ
ejpam-3133	433	15	,	,	PUNCT
ejpam-3133	433	16	common	common	ADJ
ejpam-3133	433	17	fixed	fix	VERB
ejpam-3133	433	18	point	point	NOUN
ejpam-3133	433	19	theorems	theorem	NOUN
ejpam-3133	433	20	for	for	ADP
ejpam-3133	433	21	generalized	generalized	ADJ
ejpam-3133	433	22	contractions	contraction	NOUN
ejpam-3133	433	23	,	,	PUNCT
ejpam-3133	433	24	journal	journal	NOUN
ejpam-3133	433	25	of	of	ADP
ejpam-3133	433	26	mathematical	mathematical	ADJ
ejpam-3133	433	27	analysis	analysis	NOUN
ejpam-3133	433	28	,	,	PUNCT
ejpam-3133	433	29	8	8	NUM
ejpam-3133	433	30	(	(	PUNCT
ejpam-3133	433	31	3	3	NUM
ejpam-3133	433	32	)	)	PUNCT
ejpam-3133	433	33	(	(	PUNCT
ejpam-3133	433	34	2017	2017	NUM
ejpam-3133	433	35	)	)	PUNCT
ejpam-3133	433	36	,	,	PUNCT
ejpam-3133	433	37	157	157	NUM
ejpam-3133	433	38	-	-	SYM
ejpam-3133	433	39	166	166	NUM
ejpam-3133	433	40	.	.	PUNCT
ejpam-3133	434	1	[	[	X
ejpam-3133	434	2	24	24	NUM
ejpam-3133	434	3	]	]	PUNCT
ejpam-3133	434	4	z.	z.	PROPN
ejpam-3133	434	5	mustafa	mustafa	PROPN
ejpam-3133	434	6	,	,	PUNCT
ejpam-3133	434	7	h.	h.	PROPN
ejpam-3133	434	8	aydi	aydi	PROPN
ejpam-3133	434	9	,	,	PUNCT
ejpam-3133	434	10	e.	e.	PROPN
ejpam-3133	434	11	karapinar	karapinar	PROPN
ejpam-3133	434	12	,	,	PUNCT
ejpam-3133	434	13	on	on	ADP
ejpam-3133	434	14	common	common	ADJ
ejpam-3133	434	15	fixed	fix	VERB
ejpam-3133	434	16	points	point	NOUN
ejpam-3133	434	17	in	in	ADP
ejpam-3133	434	18	g	g	NOUN
ejpam-3133	434	19	-	-	PUNCT
ejpam-3133	434	20	metric	metric	ADJ
ejpam-3133	434	21	spaces	space	NOUN
ejpam-3133	434	22	using	use	VERB
ejpam-3133	434	23	(	(	PUNCT
ejpam-3133	434	24	e.a	e.a	PROPN
ejpam-3133	434	25	)	)	PUNCT
ejpam-3133	434	26	property	property	NOUN
ejpam-3133	434	27	,	,	PUNCT
ejpam-3133	434	28	comput	comput	NOUN
ejpam-3133	434	29	.	.	PUNCT
ejpam-3133	435	1	math	math	NOUN
ejpam-3133	435	2	.	.	PUNCT
ejpam-3133	436	1	appl	appl	PROPN
ejpam-3133	436	2	.	.	PROPN
ejpam-3133	437	1	6	6	NUM
ejpam-3133	437	2	(	(	PUNCT
ejpam-3133	437	3	6	6	NUM
ejpam-3133	437	4	)	)	PUNCT
ejpam-3133	437	5	(	(	PUNCT
ejpam-3133	437	6	2012	2012	NUM
ejpam-3133	437	7	)	)	PUNCT
ejpam-3133	437	8	,	,	PUNCT
ejpam-3133	437	9	1944	1944	NUM
ejpam-3133	437	10	-	-	SYM
ejpam-3133	437	11	1956	1956	NUM
ejpam-3133	437	12	.	.	PUNCT
ejpam-3133	438	1	[	[	X
ejpam-3133	438	2	25	25	NUM
ejpam-3133	438	3	]	]	PUNCT
ejpam-3133	438	4	z.	z.	PROPN
ejpam-3133	438	5	mustafa	mustafa	PROPN
ejpam-3133	438	6	,	,	PUNCT
ejpam-3133	438	7	h.	h.	PROPN
ejpam-3133	438	8	aydi	aydi	PROPN
ejpam-3133	438	9	,	,	PUNCT
ejpam-3133	438	10	e.	e.	PROPN
ejpam-3133	438	11	karapinar	karapinar	PROPN
ejpam-3133	438	12	,	,	PUNCT
ejpam-3133	438	13	generalized	generalized	ADJ
ejpam-3133	438	14	meir	meir	PROPN
ejpam-3133	438	15	-	-	PUNCT
ejpam-3133	438	16	keeler	keeler	PROPN
ejpam-3133	438	17	type	type	NOUN
ejpam-3133	438	18	contractions	contraction	NOUN
ejpam-3133	438	19	on	on	ADP
ejpam-3133	438	20	g	g	NOUN
ejpam-3133	438	21	-	-	PUNCT
ejpam-3133	438	22	metric	metric	ADJ
ejpam-3133	438	23	spaces	space	NOUN
ejpam-3133	438	24	,	,	PUNCT
ejpam-3133	438	25	appl	appl	PROPN
ejpam-3133	438	26	.	.	PROPN
ejpam-3133	438	27	math	math	PROPN
ejpam-3133	438	28	.	.	PUNCT
ejpam-3133	439	1	comput	comput	NOUN
ejpam-3133	439	2	.	.	PUNCT
ejpam-3133	440	1	219	219	NUM
ejpam-3133	440	2	(	(	PUNCT
ejpam-3133	440	3	2013	2013	NUM
ejpam-3133	440	4	)	)	PUNCT
ejpam-3133	440	5	,	,	PUNCT
ejpam-3133	440	6	10441	10441	NUM
ejpam-3133	440	7	-	-	SYM
ejpam-3133	440	8	10447	10447	NUM
ejpam-3133	440	9	.	.	PUNCT
ejpam-3133	441	1	[	[	X
ejpam-3133	441	2	26	26	NUM
ejpam-3133	441	3	]	]	PUNCT
ejpam-3133	441	4	z.	z.	PROPN
ejpam-3133	441	5	mustafa	mustafa	PROPN
ejpam-3133	441	6	,	,	PUNCT
ejpam-3133	441	7	j.r	j.r	PROPN
ejpam-3133	441	8	.	.	PROPN
ejpam-3133	441	9	roshan	roshan	PROPN
ejpam-3133	441	10	,	,	PUNCT
ejpam-3133	441	11	v.	v.	CCONJ
ejpam-3133	441	12	parvaneh	parvaneh	NOUN
ejpam-3133	441	13	,	,	PUNCT
ejpam-3133	441	14	coupled	couple	VERB
ejpam-3133	441	15	coincidence	coincidence	NOUN
ejpam-3133	441	16	point	point	NOUN
ejpam-3133	441	17	results	result	NOUN
ejpam-3133	441	18	for	for	ADP
ejpam-3133	441	19	(	(	PUNCT
ejpam-3133	441	20	ψ	ψ	X
ejpam-3133	441	21	,	,	PUNCT
ejpam-3133	441	22	φ	φ	NUM
ejpam-3133	441	23	)	)	PUNCT
ejpam-3133	441	24	-weakly	-weakly	ADJ
ejpam-3133	441	25	contractive	contractive	ADJ
ejpam-3133	441	26	mappings	mapping	NOUN
ejpam-3133	441	27	in	in	ADP
ejpam-3133	441	28	partially	partially	ADV
ejpam-3133	441	29	ordered	order	VERB
ejpam-3133	441	30	gb	gb	ADV
ejpam-3133	441	31	-	-	PUNCT
ejpam-3133	441	32	metric	metric	ADJ
ejpam-3133	441	33	spaces	space	NOUN
ejpam-3133	441	34	,	,	PUNCT
ejpam-3133	441	35	fixed	fix	VERB
ejpam-3133	441	36	point	point	NOUN
ejpam-3133	441	37	theory	theory	NOUN
ejpam-3133	441	38	appl	appl	NOUN
ejpam-3133	441	39	.	.	PUNCT
ejpam-3133	442	1	2013:206	2013:206	NUM
ejpam-3133	442	2	,	,	PUNCT
ejpam-3133	442	3	(	(	PUNCT
ejpam-3133	442	4	2013	2013	NUM
ejpam-3133	442	5	)	)	PUNCT
ejpam-3133	442	6	.	.	PUNCT
ejpam-3133	443	1	[	[	X
ejpam-3133	443	2	27	27	NUM
ejpam-3133	443	3	]	]	PUNCT
ejpam-3133	443	4	z.	z.	PROPN
ejpam-3133	443	5	mustafa	mustafa	PROPN
ejpam-3133	443	6	,	,	PUNCT
ejpam-3133	443	7	j.r	j.r	PROPN
ejpam-3133	443	8	.	.	PROPN
ejpam-3133	443	9	roshan	roshan	PROPN
ejpam-3133	443	10	,	,	PUNCT
ejpam-3133	443	11	v.	v.	CCONJ
ejpam-3133	443	12	parvaneh	parvaneh	NOUN
ejpam-3133	443	13	,	,	PUNCT
ejpam-3133	443	14	existence	existence	NOUN
ejpam-3133	443	15	of	of	ADP
ejpam-3133	443	16	a	a	DET
ejpam-3133	443	17	tripled	triple	VERB
ejpam-3133	443	18	coincidence	coincidence	NOUN
ejpam-3133	443	19	point	point	NOUN
ejpam-3133	443	20	in	in	ADP
ejpam-3133	443	21	ordered	order	VERB
ejpam-3133	443	22	gb	gb	ADV
ejpam-3133	443	23	-	-	PUNCT
ejpam-3133	443	24	metric	metric	ADJ
ejpam-3133	443	25	spaces	space	NOUN
ejpam-3133	443	26	and	and	CCONJ
ejpam-3133	443	27	applications	application	NOUN
ejpam-3133	443	28	to	to	ADP
ejpam-3133	443	29	a	a	DET
ejpam-3133	443	30	system	system	NOUN
ejpam-3133	443	31	of	of	ADP
ejpam-3133	443	32	integral	integral	ADJ
ejpam-3133	443	33	equations	equation	NOUN
ejpam-3133	443	34	,	,	PUNCT
ejpam-3133	443	35	journal	journal	NOUN
ejpam-3133	443	36	of	of	ADP
ejpam-3133	443	37	inequalities	inequality	NOUN
ejpam-3133	443	38	and	and	CCONJ
ejpam-3133	443	39	applications	application	NOUN
ejpam-3133	443	40	,	,	PUNCT
ejpam-3133	443	41	2013	2013	NUM
ejpam-3133	443	42	,	,	PUNCT
ejpam-3133	443	43	2013:453	2013:453	NUM
ejpam-3133	443	44	[	[	X
ejpam-3133	443	45	28	28	NUM
ejpam-3133	443	46	]	]	PUNCT
ejpam-3133	443	47	z.	z.	PROPN
ejpam-3133	443	48	mustafa	mustafa	PROPN
ejpam-3133	443	49	,	,	PUNCT
ejpam-3133	443	50	b.	b.	PROPN
ejpam-3133	443	51	sims	sims	PROPN
ejpam-3133	443	52	,	,	PUNCT
ejpam-3133	443	53	a	a	DET
ejpam-3133	443	54	new	new	ADJ
ejpam-3133	443	55	approach	approach	NOUN
ejpam-3133	443	56	to	to	ADP
ejpam-3133	443	57	generalized	generalize	VERB
ejpam-3133	443	58	metric	metric	ADJ
ejpam-3133	443	59	spaces	space	NOUN
ejpam-3133	443	60	,	,	PUNCT
ejpam-3133	443	61	j.	j.	PROPN
ejpam-3133	443	62	nonlinear	nonlinear	PROPN
ejpam-3133	443	63	and	and	CCONJ
ejpam-3133	443	64	convex	convex	ADJ
ejpam-3133	443	65	analysis	analysis	NOUN
ejpam-3133	443	66	,	,	PUNCT
ejpam-3133	443	67	7	7	NUM
ejpam-3133	443	68	(	(	PUNCT
ejpam-3133	443	69	2006	2006	NUM
ejpam-3133	443	70	)	)	PUNCT
ejpam-3133	443	71	,	,	PUNCT
ejpam-3133	443	72	289	289	NUM
ejpam-3133	443	73	-	-	SYM
ejpam-3133	443	74	297	297	NUM
ejpam-3133	443	75	.	.	PUNCT
ejpam-3133	444	1	[	[	X
ejpam-3133	444	2	29	29	NUM
ejpam-3133	444	3	]	]	PUNCT
ejpam-3133	444	4	z.	z.	PROPN
ejpam-3133	444	5	mustafa	mustafa	PROPN
ejpam-3133	444	6	,	,	PUNCT
ejpam-3133	444	7	h.	h.	PROPN
ejpam-3133	444	8	obiedat	obiedat	PROPN
ejpam-3133	444	9	,	,	PUNCT
ejpam-3133	444	10	f.	f.	PROPN
ejpam-3133	444	11	awawdeh	awawdeh	PROPN
ejpam-3133	444	12	,	,	PUNCT
ejpam-3133	444	13	some	some	DET
ejpam-3133	444	14	common	common	ADJ
ejpam-3133	444	15	fixed	fix	VERB
ejpam-3133	444	16	point	point	NOUN
ejpam-3133	444	17	theorems	theorem	NOUN
ejpam-3133	444	18	for	for	ADP
ejpam-3133	444	19	mapping	mapping	NOUN
ejpam-3133	444	20	on	on	ADP
ejpam-3133	444	21	complete	complete	ADJ
ejpam-3133	444	22	g	g	NOUN
ejpam-3133	444	23	-	-	PUNCT
ejpam-3133	444	24	metric	metric	ADJ
ejpam-3133	444	25	spaces	space	NOUN
ejpam-3133	444	26	,	,	PUNCT
ejpam-3133	444	27	fixed	fix	VERB
ejpam-3133	444	28	point	point	NOUN
ejpam-3133	444	29	theory	theory	NOUN
ejpam-3133	444	30	appl	appl	NOUN
ejpam-3133	444	31	,	,	PUNCT
ejpam-3133	444	32	2008	2008	NUM
ejpam-3133	444	33	,	,	PUNCT
ejpam-3133	444	34	article	article	NOUN
ejpam-3133	444	35	i	i	PROPN
ejpam-3133	444	36	d	d	PROPN
ejpam-3133	444	37	189870	189870	NUM
ejpam-3133	444	38	.	.	PUNCT
ejpam-3133	445	1	[	[	X
ejpam-3133	445	2	30	30	NUM
ejpam-3133	445	3	]	]	PUNCT
ejpam-3133	445	4	z.	z.	PROPN
ejpam-3133	445	5	mustafa	mustafa	PROPN
ejpam-3133	445	6	,	,	PUNCT
ejpam-3133	445	7	j.	j.	PROPN
ejpam-3133	445	8	r.	r.	PROPN
ejpam-3133	445	9	roshan	roshan	PROPN
ejpam-3133	445	10	,	,	PUNCT
ejpam-3133	445	11	v.	v.	ADP
ejpam-3133	445	12	parvaneh	parvaneh	NOUN
ejpam-3133	445	13	and	and	CCONJ
ejpam-3133	445	14	z.	z.	PROPN
ejpam-3133	445	15	kadelburg	kadelburg	PROPN
ejpam-3133	445	16	.	.	PUNCT
ejpam-3133	446	1	some	some	DET
ejpam-3133	446	2	common	common	ADJ
ejpam-3133	446	3	fixed	fix	VERB
ejpam-3133	446	4	point	point	NOUN
ejpam-3133	446	5	results	result	NOUN
ejpam-3133	446	6	in	in	ADP
ejpam-3133	446	7	ordered	order	VERB
ejpam-3133	446	8	partial	partial	ADJ
ejpam-3133	446	9	b	b	NOUN
ejpam-3133	446	10	-	-	PUNCT
ejpam-3133	446	11	metric	metric	ADJ
ejpam-3133	446	12	space	space	NOUN
ejpam-3133	446	13	,	,	PUNCT
ejpam-3133	446	14	j.	j.	PROPN
ejpam-3133	446	15	inequalities	inequalities	PROPN
ejpam-3133	446	16	and	and	CCONJ
ejpam-3133	446	17	applications	application	NOUN
ejpam-3133	446	18	2013:562	2013:562	NUM
ejpam-3133	446	19	(	(	PUNCT
ejpam-3133	446	20	2013	2013	NUM
ejpam-3133	446	21	)	)	PUNCT
ejpam-3133	446	22	26	26	NUM
ejpam-3133	446	23	pages	page	NOUN
ejpam-3133	446	24	.	.	PUNCT
ejpam-3133	447	1	[	[	X
ejpam-3133	447	2	31	31	NUM
ejpam-3133	447	3	]	]	PUNCT
ejpam-3133	447	4	z.	z.	PROPN
ejpam-3133	447	5	mustafa	mustafa	PROPN
ejpam-3133	447	6	,	,	PUNCT
ejpam-3133	447	7	t.	t.	PROPN
ejpam-3133	447	8	v.	v.	ADP
ejpam-3133	447	9	an	an	PRON
ejpam-3133	447	10	and	and	CCONJ
ejpam-3133	447	11	n.	n.	NOUN
ejpam-3133	447	12	v.	v.	ADP
ejpam-3133	447	13	dung	dung	NOUN
ejpam-3133	447	14	,	,	PUNCT
ejpam-3133	447	15	two	two	NUM
ejpam-3133	447	16	fixed	fix	VERB
ejpam-3133	447	17	point	point	NOUN
ejpam-3133	447	18	theorems	theorem	NOUN
ejpam-3133	447	19	for	for	ADP
ejpam-3133	447	20	maps	map	NOUN
ejpam-3133	447	21	on	on	ADP
ejpam-3133	447	22	incomplete	incomplete	ADJ
ejpam-3133	447	23	g	g	NOUN
ejpam-3133	447	24	-	-	PUNCT
ejpam-3133	447	25	metric	metric	ADJ
ejpam-3133	447	26	spaces	space	NOUN
ejpam-3133	447	27	,	,	PUNCT
ejpam-3133	447	28	applied	apply	VERB
ejpam-3133	447	29	mathematical	mathematical	ADJ
ejpam-3133	447	30	sciences	science	NOUN
ejpam-3133	447	31	,	,	PUNCT
ejpam-3133	447	32	7	7	NUM
ejpam-3133	447	33	46	46	NUM
ejpam-3133	447	34	(	(	PUNCT
ejpam-3133	447	35	2013	2013	NUM
ejpam-3133	447	36	)	)	PUNCT
ejpam-3133	447	37	2271	2271	NUM
ejpam-3133	447	38	2281	2281	NUM
ejpam-3133	447	39	.	.	PUNCT
ejpam-3133	448	1	[	[	X
ejpam-3133	448	2	32	32	NUM
ejpam-3133	448	3	]	]	PUNCT
ejpam-3133	448	4	z.	z.	PROPN
ejpam-3133	448	5	mustafa	mustafa	PROPN
ejpam-3133	448	6	,	,	PUNCT
ejpam-3133	448	7	j.	j.	PROPN
ejpam-3133	448	8	r.	r.	PROPN
ejpam-3133	448	9	roshan	roshan	PROPN
ejpam-3133	448	10	,	,	PUNCT
ejpam-3133	448	11	v.	v.	ADP
ejpam-3133	448	12	parvaneh	parvaneh	NOUN
ejpam-3133	448	13	and	and	CCONJ
ejpam-3133	448	14	z.	z.	PROPN
ejpam-3133	448	15	kadelburg	kadelburg	PROPN
ejpam-3133	448	16	.	.	PUNCT
ejpam-3133	449	1	fixed	fix	VERB
ejpam-3133	449	2	point	point	NOUN
ejpam-3133	449	3	theorems	theorem	NOUN
ejpam-3133	449	4	for	for	ADP
ejpam-3133	449	5	weakly	weakly	ADJ
ejpam-3133	449	6	t	t	PROPN
ejpam-3133	449	7	-	-	PUNCT
ejpam-3133	449	8	chatterjea	chatterjea	PROPN
ejpam-3133	449	9	and	and	CCONJ
ejpam-3133	449	10	weakly	weakly	ADJ
ejpam-3133	449	11	t	t	PROPN
ejpam-3133	449	12	-	-	PUNCT
ejpam-3133	449	13	kannan	kannan	PROPN
ejpam-3133	449	14	contractions	contraction	NOUN
ejpam-3133	449	15	in	in	ADP
ejpam-3133	449	16	b	b	NOUN
ejpam-3133	449	17	-	-	ADJ
ejpam-3133	449	18	metric	metric	ADJ
ejpam-3133	449	19	spaces	space	NOUN
ejpam-3133	449	20	,	,	PUNCT
ejpam-3133	449	21	j.	j.	PROPN
ejpam-3133	449	22	of	of	ADP
ejpam-3133	449	23	inequalities	inequality	NOUN
ejpam-3133	449	24	and	and	CCONJ
ejpam-3133	449	25	applications	application	NOUN
ejpam-3133	449	26	(	(	PUNCT
ejpam-3133	449	27	2014	2014	NUM
ejpam-3133	449	28	)	)	PUNCT
ejpam-3133	449	29	46	46	NUM
ejpam-3133	449	30	..	..	PUNCT
ejpam-3133	450	1	[	[	X
ejpam-3133	450	2	33	33	NUM
ejpam-3133	450	3	]	]	PUNCT
ejpam-3133	450	4	z.	z.	PROPN
ejpam-3133	450	5	mustafa	mustafa	PROPN
ejpam-3133	450	6	,	,	PUNCT
ejpam-3133	450	7	m.	m.	PROPN
ejpam-3133	450	8	jaradat	jaradat	PROPN
ejpam-3133	450	9	,	,	PUNCT
ejpam-3133	450	10	a.	a.	NOUN
ejpam-3133	450	11	ansari	ansari	PROPN
ejpam-3133	450	12	,	,	PUNCT
ejpam-3133	450	13	b.	b.	PROPN
ejpam-3133	450	14	z.	z.	PROPN
ejpam-3133	450	15	popovi	popovi	PROPN
ejpam-3133	450	16	and	and	CCONJ
ejpam-3133	450	17	h.	h.	PROPN
ejpam-3133	450	18	jaradat	jaradat	PROPN
ejpam-3133	450	19	,	,	PUNCT
ejpam-3133	450	20	c	c	NOUN
ejpam-3133	450	21	-	-	PUNCT
ejpam-3133	450	22	class	class	NOUN
ejpam-3133	450	23	functions	function	NOUN
ejpam-3133	450	24	with	with	ADP
ejpam-3133	450	25	new	new	ADJ
ejpam-3133	450	26	approach	approach	NOUN
ejpam-3133	450	27	on	on	ADP
ejpam-3133	450	28	coincidence	coincidence	NOUN
ejpam-3133	450	29	point	point	NOUN
ejpam-3133	450	30	results	result	NOUN
ejpam-3133	450	31	for	for	ADP
ejpam-3133	450	32	generalized	generalized	ADJ
ejpam-3133	450	33	(	(	PUNCT
ejpam-3133	450	34	ψ,ϕ	ψ,ϕ	ADJ
ejpam-3133	450	35	)	)	PUNCT
ejpam-3133	450	36	-weakly	-weakly	NOUN
ejpam-3133	450	37	contractions	contraction	NOUN
ejpam-3133	450	38	in	in	ADP
ejpam-3133	450	39	ordered	order	VERB
ejpam-3133	450	40	bmetric	bmetric	ADJ
ejpam-3133	450	41	spaces	space	NOUN
ejpam-3133	450	42	,	,	PUNCT
ejpam-3133	450	43	springerplus	springerplus	NOUN
ejpam-3133	450	44	(	(	PUNCT
ejpam-3133	450	45	2016	2016	NUM
ejpam-3133	450	46	)	)	PUNCT
ejpam-3133	450	47	5:802	5:802	NUM
ejpam-3133	450	48	,	,	PUNCT
ejpam-3133	450	49	18	18	NUM
ejpam-3133	450	50	pages	page	NOUN
ejpam-3133	450	51	.	.	PUNCT
ejpam-3133	451	1	references	reference	NOUN
ejpam-3133	451	2	108	108	NUM
ejpam-3133	452	1	[	[	X
ejpam-3133	452	2	34	34	NUM
ejpam-3133	452	3	]	]	PUNCT
ejpam-3133	452	4	z.	z.	PROPN
ejpam-3133	452	5	mustafa	mustafa	PROPN
ejpam-3133	452	6	,	,	PUNCT
ejpam-3133	452	7	m.	m.	NOUN
ejpam-3133	452	8	m.	m.	PROPN
ejpam-3133	452	9	m.	m.	PROPN
ejpam-3133	452	10	jaradatat	jaradatat	PROPN
ejpam-3133	452	11	,	,	PUNCT
ejpam-3133	452	12	h.	h.	PROPN
ejpam-3133	452	13	m.	m.	PROPN
ejpam-3133	452	14	jaradat	jaradat	PROPN
ejpam-3133	452	15	,	,	PUNCT
ejpam-3133	452	16	some	some	DET
ejpam-3133	452	17	common	common	ADJ
ejpam-3133	452	18	fixed	fix	VERB
ejpam-3133	452	19	point	point	NOUN
ejpam-3133	452	20	results	result	NOUN
ejpam-3133	452	21	of	of	ADP
ejpam-3133	452	22	graphs	graph	NOUN
ejpam-3133	452	23	on	on	ADP
ejpam-3133	452	24	b−	b−	PROPN
ejpam-3133	452	25	metric	metric	ADJ
ejpam-3133	452	26	space	space	NOUN
ejpam-3133	452	27	,	,	PUNCT
ejpam-3133	452	28	j.	j.	PROPN
ejpam-3133	452	29	of	of	ADP
ejpam-3133	452	30	nonlinear	nonlinear	PROPN
ejpam-3133	452	31	sci	sci	PROPN
ejpam-3133	452	32	.	.	PROPN
ejpam-3133	452	33	and	and	CCONJ
ejpam-3133	452	34	appl	appl	PROPN
ejpam-3133	452	35	.	.	PROPN
ejpam-3133	452	36	,	,	PUNCT
ejpam-3133	452	37	9(6	9(6	NUM
ejpam-3133	452	38	)	)	PUNCT
ejpam-3133	452	39	(	(	PUNCT
ejpam-3133	452	40	2016	2016	NUM
ejpam-3133	452	41	)	)	PUNCT
ejpam-3133	452	42	4838	4838	NUM
ejpam-3133	452	43	-	-	SYM
ejpam-3133	452	44	4851	4851	NUM
ejpam-3133	452	45	.	.	PUNCT
ejpam-3133	453	1	[	[	X
ejpam-3133	453	2	35	35	NUM
ejpam-3133	453	3	]	]	PUNCT
ejpam-3133	453	4	z.	z.	PROPN
ejpam-3133	453	5	mustafa	mustafa	PROPN
ejpam-3133	453	6	,	,	PUNCT
ejpam-3133	453	7	m.	m.	PROPN
ejpam-3133	453	8	m.m	m.m	PROPN
ejpam-3133	453	9	.	.	PROPN
ejpam-3133	453	10	jaradat	jaradat	PROPN
ejpam-3133	453	11	and	and	CCONJ
ejpam-3133	453	12	h.m	h.m	PROPN
ejpam-3133	453	13	.	.	PROPN
ejpam-3133	453	14	jaradat	jaradat	PROPN
ejpam-3133	453	15	,	,	PUNCT
ejpam-3133	453	16	a	a	DET
ejpam-3133	453	17	remarks	remark	NOUN
ejpam-3133	453	18	on	on	ADP
ejpam-3133	453	19	the	the	DET
ejpam-3133	453	20	paper	paper	NOUN
ejpam-3133	453	21	“	"	PUNCT
ejpam-3133	453	22	some	some	DET
ejpam-3133	453	23	fixed	fix	VERB
ejpam-3133	453	24	point	point	NOUN
ejpam-3133	453	25	theorems	theorem	NOUN
ejpam-3133	453	26	for	for	ADP
ejpam-3133	453	27	generalized	generalized	ADJ
ejpam-3133	453	28	contractive	contractive	ADJ
ejpam-3133	453	29	mappings	mapping	NOUN
ejpam-3133	453	30	in	in	ADP
ejpam-3133	453	31	complete	complete	ADJ
ejpam-3133	453	32	metric	metric	ADJ
ejpam-3133	453	33	spaces	space	NOUN
ejpam-3133	453	34	”	"	PUNCT
ejpam-3133	453	35	.	.	PUNCT
ejpam-3133	454	1	j.	j.	PROPN
ejpam-3133	454	2	of	of	ADP
ejpam-3133	454	3	mathematical	mathematical	ADJ
ejpam-3133	454	4	analysis	analysis	NOUN
ejpam-3133	454	5	,	,	PUNCT
ejpam-3133	454	6	8(2	8(2	NUM
ejpam-3133	454	7	)	)	PUNCT
ejpam-3133	454	8	(	(	PUNCT
ejpam-3133	454	9	2017	2017	NUM
ejpam-3133	454	10	)	)	PUNCT
ejpam-3133	454	11	17	17	NUM
ejpam-3133	454	12	-	-	SYM
ejpam-3133	454	13	22	22	NUM
ejpam-3133	454	14	.	.	PUNCT
ejpam-3133	455	1	[	[	X
ejpam-3133	455	2	36	36	NUM
ejpam-3133	455	3	]	]	PUNCT
ejpam-3133	455	4	z.	z.	PROPN
ejpam-3133	455	5	mustafa	mustafa	PROPN
ejpam-3133	455	6	,	,	PUNCT
ejpam-3133	455	7	m.m.m	m.m.m	PROPN
ejpam-3133	455	8	.	.	PUNCT
ejpam-3133	455	9	jaradat	jaradat	PROPN
ejpam-3133	455	10	,	,	PUNCT
ejpam-3133	455	11	e.	e.	PROPN
ejpam-3133	455	12	karapnar	karapnar	PROPN
ejpam-3133	455	13	,	,	PUNCT
ejpam-3133	455	14	a	a	DET
ejpam-3133	455	15	new	new	ADJ
ejpam-3133	455	16	xed	xed	PROPN
ejpam-3133	455	17	point	point	NOUN
ejpam-3133	455	18	result	result	NOUN
ejpam-3133	455	19	via	via	ADP
ejpam-3133	455	20	property	property	NOUN
ejpam-3133	455	21	p	p	NOUN
ejpam-3133	455	22	with	with	ADP
ejpam-3133	455	23	an	an	DET
ejpam-3133	455	24	application	application	NOUN
ejpam-3133	455	25	,	,	PUNCT
ejpam-3133	455	26	j.	j.	PROPN
ejpam-3133	455	27	of	of	ADP
ejpam-3133	455	28	nonlinear	nonlinear	PROPN
ejpam-3133	455	29	sci	sci	PROPN
ejpam-3133	455	30	.	.	PROPN
ejpam-3133	455	31	and	and	CCONJ
ejpam-3133	455	32	appl	appl	PROPN
ejpam-3133	455	33	.	.	PROPN
ejpam-3133	455	34	,	,	PUNCT
ejpam-3133	455	35	10	10	NUM
ejpam-3133	455	36	(	(	PUNCT
ejpam-3133	455	37	2017	2017	NUM
ejpam-3133	455	38	)	)	PUNCT
ejpam-3133	455	39	2066	2066	NUM
ejpam-3133	455	40	-	-	SYM
ejpam-3133	455	41	2078	2078	NUM
ejpam-3133	455	42	.	.	PUNCT
ejpam-3133	456	1	[	[	X
ejpam-3133	456	2	37	37	NUM
ejpam-3133	456	3	]	]	PUNCT
ejpam-3133	456	4	z.	z.	PROPN
ejpam-3133	456	5	mustafa	mustafa	PROPN
ejpam-3133	456	6	,	,	PUNCT
ejpam-3133	456	7	m.	m.	PROPN
ejpam-3133	456	8	arshad	arshad	PROPN
ejpam-3133	456	9	,	,	PUNCT
ejpam-3133	456	10	s.	s.	PROPN
ejpam-3133	456	11	u.	u.	PROPN
ejpam-3133	456	12	khan	khan	PROPN
ejpam-3133	456	13	,	,	PUNCT
ejpam-3133	456	14	j.	j.	PROPN
ejpam-3133	456	15	ahmad	ahmad	PROPN
ejpam-3133	456	16	,	,	PUNCT
ejpam-3133	456	17	m.m.m	m.m.m	PROPN
ejpam-3133	456	18	.	.	PUNCT
ejpam-3133	456	19	jaradat	jaradat	PROPN
ejpam-3133	456	20	,	,	PUNCT
ejpam-3133	456	21	common	common	ADJ
ejpam-3133	456	22	fixed	fix	VERB
ejpam-3133	456	23	points	point	NOUN
ejpam-3133	456	24	for	for	ADP
ejpam-3133	456	25	multivalued	multivalued	ADJ
ejpam-3133	456	26	mappings	mapping	NOUN
ejpam-3133	456	27	in	in	ADP
ejpam-3133	456	28	g	g	NOUN
ejpam-3133	456	29	-	-	PUNCT
ejpam-3133	456	30	metric	metric	ADJ
ejpam-3133	456	31	spaces	space	NOUN
ejpam-3133	456	32	with	with	ADP
ejpam-3133	456	33	applications	application	NOUN
ejpam-3133	456	34	,	,	PUNCT
ejpam-3133	456	35	j.	j.	PROPN
ejpam-3133	456	36	nonlinear	nonlinear	PROPN
ejpam-3133	456	37	sci	sci	PROPN
ejpam-3133	456	38	.	.	PROPN
ejpam-3133	456	39	and	and	CCONJ
ejpam-3133	456	40	appl	appl	PROPN
ejpam-3133	456	41	.	.	PROPN
ejpam-3133	456	42	,	,	PUNCT
ejpam-3133	456	43	10	10	NUM
ejpam-3133	456	44	(	(	PUNCT
ejpam-3133	456	45	2017	2017	NUM
ejpam-3133	456	46	)	)	PUNCT
ejpam-3133	456	47	2550	2550	NUM
ejpam-3133	456	48	-	-	SYM
ejpam-3133	456	49	2564	2564	NUM
ejpam-3133	456	50	.	.	PUNCT
ejpam-3133	457	1	[	[	X
ejpam-3133	457	2	38	38	NUM
ejpam-3133	457	3	]	]	X
ejpam-3133	457	4	abdullah	abdullah	PROPN
ejpam-3133	457	5	,	,	PUNCT
ejpam-3133	457	6	m.	m.	NOUN
ejpam-3133	457	7	sarwar	sarwar	PROPN
ejpam-3133	457	8	,	,	PUNCT
ejpam-3133	457	9	z.	z.	PROPN
ejpam-3133	457	10	mustafa	mustafa	PROPN
ejpam-3133	457	11	,	,	PUNCT
ejpam-3133	457	12	and	and	CCONJ
ejpam-3133	457	13	m.m.m	m.m.m	INTJ
ejpam-3133	457	14	.	.	PUNCT
ejpam-3133	457	15	jaradat	jaradat	PROPN
ejpam-3133	457	16	,	,	PUNCT
ejpam-3133	457	17	common	common	ADJ
ejpam-3133	457	18	fixed	fix	VERB
ejpam-3133	457	19	points	point	NOUN
ejpam-3133	457	20	of	of	ADP
ejpam-3133	457	21	(	(	PUNCT
ejpam-3133	457	22	φ	φ	PROPN
ejpam-3133	457	23	,	,	PUNCT
ejpam-3133	457	24	ψ)-contraction	ψ)-contraction	PUNCT
ejpam-3133	457	25	on	on	ADP
ejpam-3133	457	26	gmetric	gmetric	ADJ
ejpam-3133	457	27	space	space	NOUN
ejpam-3133	457	28	using	use	VERB
ejpam-3133	457	29	e.a	e.a	PROPN
ejpam-3133	457	30	property	property	NOUN
ejpam-3133	457	31	,	,	PUNCT
ejpam-3133	457	32	j.	j.	PROPN
ejpam-3133	457	33	of	of	ADP
ejpam-3133	457	34	mathematical	mathematical	ADJ
ejpam-3133	457	35	analysis	analysis	NOUN
ejpam-3133	457	36	,	,	PUNCT
ejpam-3133	457	37	8(4	8(4	NUM
ejpam-3133	457	38	)	)	PUNCT
ejpam-3133	457	39	(	(	PUNCT
ejpam-3133	457	40	2017	2017	NUM
ejpam-3133	457	41	)	)	PUNCT
ejpam-3133	457	42	136–146	136–146	NUM
ejpam-3133	457	43	.	.	PUNCT
ejpam-3133	458	1	[	[	X
ejpam-3133	458	2	39	39	NUM
ejpam-3133	458	3	]	]	PUNCT
ejpam-3133	458	4	z.	z.	PROPN
ejpam-3133	458	5	mustafa	mustafa	PROPN
ejpam-3133	458	6	,	,	PUNCT
ejpam-3133	458	7	h.	h.	PROPN
ejpam-3133	458	8	aydi	aydi	PROPN
ejpam-3133	458	9	and	and	CCONJ
ejpam-3133	458	10	e.	e.	PROPN
ejpam-3133	458	11	karapinar	karapinar	PROPN
ejpam-3133	458	12	,	,	PUNCT
ejpam-3133	458	13	on	on	ADP
ejpam-3133	458	14	common	common	ADJ
ejpam-3133	458	15	fixed	fix	VERB
ejpam-3133	458	16	points	point	NOUN
ejpam-3133	458	17	in	in	ADP
ejpam-3133	458	18	g	g	NOUN
ejpam-3133	458	19	-	-	PUNCT
ejpam-3133	458	20	metric	metric	ADJ
ejpam-3133	458	21	spaces	space	NOUN
ejpam-3133	458	22	using	use	VERB
ejpam-3133	458	23	(	(	PUNCT
ejpam-3133	458	24	e.a	e.a	PROPN
ejpam-3133	458	25	)	)	PUNCT
ejpam-3133	458	26	property	property	NOUN
ejpam-3133	458	27	,	,	PUNCT
ejpam-3133	458	28	computer	computer	NOUN
ejpam-3133	458	29	and	and	CCONJ
ejpam-3133	458	30	mathematics	mathematic	NOUN
ejpam-3133	458	31	with	with	ADP
ejpam-3133	458	32	apllication	apllication	NOUN
ejpam-3133	458	33	.	.	PUNCT
ejpam-3133	459	1	64	64	NUM
ejpam-3133	459	2	(	(	PUNCT
ejpam-3133	459	3	2012	2012	NUM
ejpam-3133	459	4	)	)	PUNCT
ejpam-3133	459	5	1944	1944	NUM
ejpam-3133	459	6	–	–	PUNCT
ejpam-3133	459	7	1956	1956	NUM
ejpam-3133	459	8	.	.	PUNCT
ejpam-3133	460	1	[	[	X
ejpam-3133	460	2	40	40	NUM
ejpam-3133	460	3	]	]	PUNCT
ejpam-3133	461	1	z.	z.	PROPN
ejpam-3133	461	2	mustafa	mustafa	PROPN
ejpam-3133	461	3	,	,	PUNCT
ejpam-3133	461	4	common	common	ADJ
ejpam-3133	461	5	fixed	fix	VERB
ejpam-3133	461	6	points	point	NOUN
ejpam-3133	461	7	of	of	ADP
ejpam-3133	461	8	weakly	weakly	ADJ
ejpam-3133	461	9	compatible	compatible	ADJ
ejpam-3133	461	10	mappings	mapping	NOUN
ejpam-3133	461	11	in	in	ADP
ejpam-3133	461	12	g	g	NOUN
ejpam-3133	461	13	-	-	PUNCT
ejpam-3133	461	14	metric	metric	ADJ
ejpam-3133	461	15	spaces	space	NOUN
ejpam-3133	461	16	,	,	PUNCT
ejpam-3133	461	17	appl	appl	PROPN
ejpam-3133	461	18	.	.	PROPN
ejpam-3133	461	19	mathematical	mathematical	PROPN
ejpam-3133	461	20	sci	sci	PROPN
ejpam-3133	461	21	.	.	PROPN
ejpam-3133	461	22	,	,	PUNCT
ejpam-3133	461	23	6(92	6(92	NUM
ejpam-3133	461	24	)	)	PUNCT
ejpam-3133	461	25	(	(	PUNCT
ejpam-3133	461	26	2012	2012	NUM
ejpam-3133	461	27	)	)	PUNCT
ejpam-3133	461	28	4589–4600	4589–4600	NUM
ejpam-3133	461	29	.	.	PUNCT
ejpam-3133	462	1	[	[	X
ejpam-3133	462	2	41	41	NUM
ejpam-3133	462	3	]	]	X
ejpam-3133	462	4	b.	b.	PROPN
ejpam-3133	462	5	moeini	moeini	PROPN
ejpam-3133	462	6	,	,	PUNCT
ejpam-3133	462	7	a.h	a.h	PROPN
ejpam-3133	462	8	.	.	PROPN
ejpam-3133	462	9	ansari	ansari	PROPN
ejpam-3133	462	10	,	,	PUNCT
ejpam-3133	462	11	h.	h.	PROPN
ejpam-3133	462	12	aydi	aydi	PROPN
ejpam-3133	462	13	,	,	PUNCT
ejpam-3133	462	14	some	some	DET
ejpam-3133	462	15	common	common	ADJ
ejpam-3133	462	16	fixed	fix	VERB
ejpam-3133	462	17	point	point	NOUN
ejpam-3133	462	18	theorems	theorem	NOUN
ejpam-3133	462	19	without	without	ADP
ejpam-3133	462	20	orbital	orbital	ADJ
ejpam-3133	462	21	continuity	continuity	NOUN
ejpam-3133	462	22	via	via	ADP
ejpam-3133	462	23	c	c	NOUN
ejpam-3133	462	24	-	-	PUNCT
ejpam-3133	462	25	class	class	NOUN
ejpam-3133	462	26	functions	function	NOUN
ejpam-3133	462	27	and	and	CCONJ
ejpam-3133	462	28	an	an	DET
ejpam-3133	462	29	application	application	NOUN
ejpam-3133	462	30	,	,	PUNCT
ejpam-3133	462	31	journal	journal	NOUN
ejpam-3133	462	32	of	of	ADP
ejpam-3133	462	33	mathematical	mathematical	ADJ
ejpam-3133	462	34	analysis	analysis	NOUN
ejpam-3133	462	35	,	,	PUNCT
ejpam-3133	462	36	8	8	NUM
ejpam-3133	462	37	(	(	PUNCT
ejpam-3133	462	38	4	4	NUM
ejpam-3133	462	39	)	)	PUNCT
ejpam-3133	462	40	(	(	PUNCT
ejpam-3133	462	41	2017	2017	NUM
ejpam-3133	462	42	)	)	PUNCT
ejpam-3133	462	43	,	,	PUNCT
ejpam-3133	462	44	46–55	46–55	NUM
ejpam-3133	462	45	.	.	PUNCT
ejpam-3133	463	1	[	[	X
ejpam-3133	463	2	42	42	NUM
ejpam-3133	463	3	]	]	X
ejpam-3133	463	4	h.k	h.k	PROPN
ejpam-3133	463	5	.	.	PROPN
ejpam-3133	463	6	nashine	nashine	PROPN
ejpam-3133	463	7	,	,	PUNCT
ejpam-3133	463	8	b.	b.	PROPN
ejpam-3133	463	9	samet	samet	PROPN
ejpam-3133	463	10	,	,	PUNCT
ejpam-3133	463	11	fixed	fix	VERB
ejpam-3133	463	12	point	point	NOUN
ejpam-3133	463	13	results	result	NOUN
ejpam-3133	463	14	for	for	ADP
ejpam-3133	463	15	mappings	mapping	NOUN
ejpam-3133	463	16	satisfying	satisfy	VERB
ejpam-3133	463	17	(	(	PUNCT
ejpam-3133	463	18	ψ	ψ	NOUN
ejpam-3133	463	19	,	,	PUNCT
ejpam-3133	463	20	φ)-weakly	φ)-weakly	VERB
ejpam-3133	463	21	contractive	contractive	ADJ
ejpam-3133	463	22	condition	condition	NOUN
ejpam-3133	463	23	in	in	ADP
ejpam-3133	463	24	partially	partially	ADV
ejpam-3133	463	25	ordered	order	VERB
ejpam-3133	463	26	metric	metric	ADJ
ejpam-3133	463	27	spaces	space	NOUN
ejpam-3133	463	28	,	,	PUNCT
ejpam-3133	463	29	nonlinear	nonlinear	ADJ
ejpam-3133	463	30	anal	anal	NOUN
ejpam-3133	463	31	.	.	PUNCT
ejpam-3133	464	1	74	74	NUM
ejpam-3133	464	2	(	(	PUNCT
ejpam-3133	464	3	2011	2011	NUM
ejpam-3133	464	4	)	)	PUNCT
ejpam-3133	464	5	,	,	PUNCT
ejpam-3133	464	6	2201	2201	NUM
ejpam-3133	464	7	-	-	SYM
ejpam-3133	464	8	2209	2209	NUM
ejpam-3133	464	9	.	.	PUNCT
ejpam-3133	465	1	[	[	X
ejpam-3133	465	2	43	43	NUM
ejpam-3133	465	3	]	]	X
ejpam-3133	465	4	r.p	r.p	PROPN
ejpam-3133	465	5	.	.	PROPN
ejpam-3133	465	6	pant	pant	NOUN
ejpam-3133	465	7	,	,	PUNCT
ejpam-3133	465	8	common	common	ADJ
ejpam-3133	465	9	fixed	fix	VERB
ejpam-3133	465	10	points	point	NOUN
ejpam-3133	465	11	of	of	ADP
ejpam-3133	465	12	noncommuting	noncommute	VERB
ejpam-3133	465	13	mappings	mapping	NOUN
ejpam-3133	465	14	,	,	PUNCT
ejpam-3133	465	15	j.	j.	PROPN
ejpam-3133	465	16	math	math	PROPN
ejpam-3133	465	17	.	.	PUNCT
ejpam-3133	466	1	anal	anal	PROPN
ejpam-3133	466	2	.	.	PUNCT
ejpam-3133	467	1	appl	appl	PROPN
ejpam-3133	467	2	.	.	PUNCT
ejpam-3133	468	1	188	188	NUM
ejpam-3133	468	2	(	(	PUNCT
ejpam-3133	468	3	1994	1994	NUM
ejpam-3133	468	4	)	)	PUNCT
ejpam-3133	468	5	,	,	PUNCT
ejpam-3133	468	6	436	436	NUM
ejpam-3133	468	7	-	-	SYM
ejpam-3133	468	8	440	440	NUM
ejpam-3133	468	9	.	.	PUNCT
ejpam-3133	469	1	[	[	X
ejpam-3133	469	2	44	44	NUM
ejpam-3133	469	3	]	]	X
ejpam-3133	469	4	r.p	r.p	PROPN
ejpam-3133	469	5	.	.	PROPN
ejpam-3133	469	6	pant	pant	NOUN
ejpam-3133	469	7	,	,	PUNCT
ejpam-3133	469	8	common	common	ADJ
ejpam-3133	469	9	fixed	fix	VERB
ejpam-3133	469	10	point	point	NOUN
ejpam-3133	469	11	of	of	ADP
ejpam-3133	469	12	contractive	contractive	ADJ
ejpam-3133	469	13	maps	map	NOUN
ejpam-3133	469	14	,	,	PUNCT
ejpam-3133	469	15	j.	j.	PROPN
ejpam-3133	469	16	math	math	PROPN
ejpam-3133	469	17	.	.	PUNCT
ejpam-3133	470	1	anal	anal	PROPN
ejpam-3133	470	2	.	.	PUNCT
ejpam-3133	470	3	appl	appl	PROPN
ejpam-3133	470	4	.	.	PUNCT
ejpam-3133	471	1	226	226	NUM
ejpam-3133	471	2	(	(	PUNCT
ejpam-3133	471	3	1998	1998	NUM
ejpam-3133	471	4	)	)	PUNCT
ejpam-3133	471	5	,	,	PUNCT
ejpam-3133	471	6	251	251	NUM
ejpam-3133	471	7	-	-	SYM
ejpam-3133	471	8	258	258	NUM
ejpam-3133	471	9	.	.	PUNCT
ejpam-3133	472	1	[	[	X
ejpam-3133	472	2	45	45	NUM
ejpam-3133	472	3	]	]	X
ejpam-3133	472	4	j.r	j.r	PROPN
ejpam-3133	472	5	.	.	PROPN
ejpam-3133	472	6	roshan	roshan	PROPN
ejpam-3133	472	7	,	,	PUNCT
ejpam-3133	472	8	n.	n.	PROPN
ejpam-3133	472	9	shobkolaei	shobkolaei	PROPN
ejpam-3133	472	10	,	,	PUNCT
ejpam-3133	472	11	s.	s.	PROPN
ejpam-3133	472	12	sedghi	sedghi	PROPN
ejpam-3133	472	13	,	,	PUNCT
ejpam-3133	472	14	v.	v.	ADP
ejpam-3133	472	15	parvaneh	parvaneh	PROPN
ejpam-3133	472	16	,	,	PUNCT
ejpam-3133	472	17	s.	s.	PROPN
ejpam-3133	472	18	radenović	radenović	VERB
ejpam-3133	472	19	,	,	PUNCT
ejpam-3133	472	20	common	common	ADJ
ejpam-3133	472	21	fixed	fix	VERB
ejpam-3133	472	22	point	point	NOUN
ejpam-3133	472	23	theorems	theorem	NOUN
ejpam-3133	472	24	for	for	ADP
ejpam-3133	472	25	three	three	NUM
ejpam-3133	472	26	maps	map	NOUN
ejpam-3133	472	27	in	in	ADP
ejpam-3133	472	28	discontinuous	discontinuous	ADJ
ejpam-3133	472	29	gb	gb	ADV
ejpam-3133	472	30	-	-	PUNCT
ejpam-3133	472	31	metric	metric	ADJ
ejpam-3133	472	32	spaces	space	NOUN
ejpam-3133	472	33	,	,	PUNCT
ejpam-3133	472	34	acta	acta	PROPN
ejpam-3133	472	35	mathematica	mathematica	PROPN
ejpam-3133	472	36	scientia	scientia	PROPN
ejpam-3133	472	37	,	,	PUNCT
ejpam-3133	472	38	34	34	NUM
ejpam-3133	472	39	(	(	PUNCT
ejpam-3133	472	40	5	5	NUM
ejpam-3133	472	41	)	)	PUNCT
ejpam-3133	472	42	(	(	PUNCT
ejpam-3133	472	43	2015	2015	NUM
ejpam-3133	472	44	)	)	PUNCT
ejpam-3133	472	45	,	,	PUNCT
ejpam-3133	472	46	1643	1643	NUM
ejpam-3133	472	47	-	-	SYM
ejpam-3133	472	48	1654	1654	NUM
ejpam-3133	472	49	.	.	PUNCT
ejpam-3133	473	1	[	[	X
ejpam-3133	473	2	46	46	NUM
ejpam-3133	473	3	]	]	X
ejpam-3133	473	4	m.	m.	NOUN
ejpam-3133	473	5	sarwar	sarwar	PROPN
ejpam-3133	473	6	,	,	PUNCT
ejpam-3133	473	7	s.	s.	PROPN
ejpam-3133	473	8	abdullah	abdullah	PROPN
ejpam-3133	473	9	,	,	PUNCT
ejpam-3133	473	10	i.a	i.a	PROPN
ejpam-3133	473	11	.	.	PROPN
ejpam-3133	473	12	shah	shah	PROPN
ejpam-3133	473	13	,	,	PUNCT
ejpam-3133	473	14	fixed	fix	VERB
ejpam-3133	473	15	point	point	NOUN
ejpam-3133	473	16	theorem	theorem	VERB
ejpam-3133	473	17	satisfying	satisfy	VERB
ejpam-3133	473	18	some	some	DET
ejpam-3133	473	19	rational	rational	ADJ
ejpam-3133	473	20	type	type	NOUN
ejpam-3133	473	21	contraction	contraction	NOUN
ejpam-3133	473	22	in	in	ADP
ejpam-3133	473	23	gb	gb	ADV
ejpam-3133	473	24	-	-	PUNCT
ejpam-3133	473	25	metric	metric	ADJ
ejpam-3133	473	26	spaces	space	NOUN
ejpam-3133	473	27	,	,	PUNCT
ejpam-3133	473	28	j.	j.	PROPN
ejpam-3133	473	29	adv	adv	PROPN
ejpam-3133	473	30	.	.	PUNCT
ejpam-3133	473	31	math	math	PROPN
ejpam-3133	473	32	.	.	PUNCT
ejpam-3133	474	1	stud	stud	PROPN
ejpam-3133	474	2	.	.	PUNCT
ejpam-3133	475	1	9	9	NUM
ejpam-3133	475	2	(	(	PUNCT
ejpam-3133	475	3	2	2	NUM
ejpam-3133	475	4	)	)	PUNCT
ejpam-3133	475	5	(	(	PUNCT
ejpam-3133	475	6	2016	2016	NUM
ejpam-3133	475	7	)	)	PUNCT
ejpam-3133	475	8	,	,	PUNCT
ejpam-3133	475	9	320	320	NUM
ejpam-3133	475	10	-	-	SYM
ejpam-3133	475	11	329	329	NUM
ejpam-3133	475	12	.	.	PUNCT
ejpam-3133	476	1	[	[	X
ejpam-3133	476	2	47	47	NUM
ejpam-3133	476	3	]	]	PUNCT
ejpam-3133	476	4	s.	s.	PROPN
ejpam-3133	476	5	sessa	sessa	PROPN
ejpam-3133	476	6	,	,	PUNCT
ejpam-3133	476	7	on	on	ADP
ejpam-3133	476	8	a	a	DET
ejpam-3133	476	9	weak	weak	ADJ
ejpam-3133	476	10	commutativity	commutativity	NOUN
ejpam-3133	476	11	condition	condition	NOUN
ejpam-3133	476	12	of	of	ADP
ejpam-3133	476	13	mappings	mapping	NOUN
ejpam-3133	476	14	in	in	ADP
ejpam-3133	476	15	fixed	fix	VERB
ejpam-3133	476	16	point	point	NOUN
ejpam-3133	476	17	consideration	consideration	NOUN
ejpam-3133	476	18	,	,	PUNCT
ejpam-3133	476	19	publ	publ	NOUN
ejpam-3133	476	20	.	.	PUNCT
ejpam-3133	477	1	inst	inst	PROPN
ejpam-3133	477	2	.	.	PUNCT
ejpam-3133	478	1	math	math	NOUN
ejpam-3133	478	2	.	.	PUNCT
ejpam-3133	479	1	soc	soc	PROPN
ejpam-3133	479	2	.	.	PUNCT
ejpam-3133	480	1	32	32	NUM
ejpam-3133	480	2	(	(	PUNCT
ejpam-3133	480	3	1982	1982	NUM
ejpam-3133	480	4	)	)	PUNCT
ejpam-3133	480	5	,	,	PUNCT
ejpam-3133	480	6	149	149	NUM
ejpam-3133	480	7	-	-	SYM
ejpam-3133	480	8	153	153	NUM
ejpam-3133	480	9	.	.	PUNCT
ejpam-3133	481	1	references	reference	NOUN
ejpam-3133	481	2	109	109	NUM
ejpam-3133	481	3	[	[	SYM
ejpam-3133	481	4	48	48	NUM
ejpam-3133	481	5	]	]	PUNCT
ejpam-3133	481	6	f.	f.	PROPN
ejpam-3133	481	7	yan	yan	PROPN
ejpam-3133	481	8	,	,	PUNCT
ejpam-3133	481	9	y.	y.	PROPN
ejpam-3133	481	10	su	su	PROPN
ejpam-3133	481	11	,	,	PUNCT
ejpam-3133	481	12	q.	q.	PROPN
ejpam-3133	481	13	feng	feng	PROPN
ejpam-3133	481	14	,	,	PUNCT
ejpam-3133	481	15	a	a	DET
ejpam-3133	481	16	new	new	ADJ
ejpam-3133	481	17	contraction	contraction	NOUN
ejpam-3133	481	18	mapping	mapping	NOUN
ejpam-3133	481	19	principle	principle	NOUN
ejpam-3133	481	20	in	in	ADP
ejpam-3133	481	21	partially	partially	ADV
ejpam-3133	481	22	ordered	order	VERB
ejpam-3133	481	23	metric	metric	ADJ
ejpam-3133	481	24	spaces	space	NOUN
ejpam-3133	481	25	and	and	CCONJ
ejpam-3133	481	26	applications	application	NOUN
ejpam-3133	481	27	to	to	ADP
ejpam-3133	481	28	ordinary	ordinary	ADJ
ejpam-3133	481	29	differential	differential	ADJ
ejpam-3133	481	30	equations	equation	NOUN
ejpam-3133	481	31	.	.	PUNCT
ejpam-3133	482	1	fixed	fix	VERB
ejpam-3133	482	2	point	point	NOUN
ejpam-3133	482	3	theory	theory	NOUN
ejpam-3133	482	4	appl	appl	PROPN
ejpam-3133	482	5	.	.	PROPN
ejpam-3133	483	1	2012	2012	NUM
ejpam-3133	483	2	,	,	PUNCT
ejpam-3133	483	3	2012:152	2012:152	NUM
ejpam-3133	483	4	.	.	PUNCT