id	sid	tid	token	lemma	pos
iajs-539	1	1	1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	PROPN
iajs-539	1	2	�	�	PROPN
iajs-539	1	3	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-539	1	4	:	:	PUNCT
iajs-539	1	5	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-539	1	6	©	©	PROPN
iajs-539	1	7	@ü‹26@@öü»€a@i1@‚b«@h2013	@ü‹26@@öü»€a@i1@‚b«@h2013	PROPN
iajs-539	1	8	ibn	ibn	PROPN
iajs-539	1	9	al	al	PROPN
iajs-539	1	10	-	-	PUNCT
iajs-539	1	11	haitham	haitham	PROPN
iajs-539	1	12	jour	jour	X
iajs-539	1	13	.	.	PROPN
iajs-539	1	14	for	for	ADP
iajs-539	1	15	pure	pure	ADJ
iajs-539	1	16	&	&	CCONJ
iajs-539	1	17	appl	appl	PROPN
iajs-539	1	18	.	.	PUNCT
iajs-539	2	1	sci	sci	PROPN
iajs-539	2	2	.	.	PUNCT
iajs-539	2	3	vol	vol	NOUN
iajs-539	2	4	.	.	PROPN
iajs-539	3	1	26	26	NUM
iajs-539	3	2	(	(	PUNCT
iajs-539	3	3	1	1	NUM
iajs-539	3	4	)	)	PUNCT
iajs-539	3	5	2013	2013	NUM
iajs-539	3	6	fixed	fix	VERB
iajs-539	3	7	point	point	NOUN
iajs-539	3	8	theorem	theorem	NOUN
iajs-539	3	9	for	for	ADP
iajs-539	3	10	uncommuting	uncommute	VERB
iajs-539	3	11	mappings	mapping	NOUN
iajs-539	4	1	salwa	salwa	PROPN
iajs-539	4	2	s.	s.	PROPN
iajs-539	4	3	abd	abd	PROPN
iajs-539	5	1	alaa	alaa	PROPN
iajs-539	5	2	abd	abd	PROPN
iajs-539	5	3	-	-	PROPN
iajs-539	5	4	ullah	ullah	PROPN
iajs-539	5	5	dept	dept	PROPN
iajs-539	5	6	.	.	PROPN
iajs-539	5	7	of	of	ADP
iajs-539	5	8	mathematics	mathematics	PROPN
iajs-539	5	9	/	/	SYM
iajs-539	5	10	college	college	NOUN
iajs-539	5	11	of	of	ADP
iajs-539	5	12	education	education	NOUN
iajs-539	5	13	for	for	ADP
iajs-539	5	14	pure	pure	ADJ
iajs-539	5	15	science(ibn	science(ibn	NOUN
iajs-539	5	16	alhaitham	alhaitham	NOUN
iajs-539	5	17	)	)	PUNCT
iajs-539	5	18	university	university	NOUN
iajs-539	5	19	of	of	ADP
iajs-539	5	20	baghdad	baghdad	PROPN
iajs-539	5	21	received	receive	VERB
iajs-539	5	22	in:19	in:19	PROPN
iajs-539	5	23	june	june	PROPN
iajs-539	5	24	2012	2012	NUM
iajs-539	5	25	accepted	accept	VERB
iajs-539	5	26	in:15	in:15	PROPN
iajs-539	5	27	october	october	PROPN
iajs-539	5	28	2012	2012	NUM
iajs-539	5	29	abstract	abstract	NOUN
iajs-539	5	30	in	in	ADP
iajs-539	5	31	this	this	DET
iajs-539	5	32	paper	paper	NOUN
iajs-539	5	33	we	we	PRON
iajs-539	5	34	prove	prove	VERB
iajs-539	5	35	a	a	DET
iajs-539	5	36	theorem	theorem	NOUN
iajs-539	5	37	about	about	ADP
iajs-539	5	38	the	the	DET
iajs-539	5	39	existence	existence	NOUN
iajs-539	5	40	and	and	CCONJ
iajs-539	5	41	uniqueness	uniqueness	ADJ
iajs-539	5	42	common	common	ADJ
iajs-539	5	43	fixed	fix	VERB
iajs-539	5	44	point	point	NOUN
iajs-539	5	45	for	for	ADP
iajs-539	5	46	two	two	NUM
iajs-539	5	47	uncommenting	uncommente	VERB
iajs-539	5	48	self	self	NOUN
iajs-539	5	49	-	-	PUNCT
iajs-539	5	50	mappings	mapping	NOUN
iajs-539	5	51	which	which	PRON
iajs-539	5	52	defined	define	VERB
iajs-539	5	53	on	on	ADP
iajs-539	5	54	orbitally	orbitally	ADV
iajs-539	5	55	complete	complete	VERB
iajs-539	5	56	g	g	NOUN
iajs-539	5	57	-	-	PUNCT
iajs-539	5	58	metric	metric	ADJ
iajs-539	5	59	space	space	NOUN
iajs-539	5	60	.	.	PUNCT
iajs-539	6	1	where	where	SCONJ
iajs-539	6	2	we	we	PRON
iajs-539	6	3	use	use	VERB
iajs-539	6	4	a	a	DET
iajs-539	6	5	general	general	ADJ
iajs-539	6	6	contraction	contraction	NOUN
iajs-539	6	7	condition	condition	NOUN
iajs-539	6	8	.	.	PUNCT
iajs-539	7	1	key	key	ADJ
iajs-539	7	2	words	word	NOUN
iajs-539	7	3	:	:	PUNCT
iajs-539	7	4	g	g	NOUN
iajs-539	7	5	-	-	PUNCT
iajs-539	7	6	metric	metric	ADJ
iajs-539	7	7	space	space	NOUN
iajs-539	7	8	,	,	PUNCT
iajs-539	7	9	orbitaliy	orbitaliy	ADV
iajs-539	7	10	complete	complete	ADJ
iajs-539	7	11	,	,	PUNCT
iajs-539	7	12	commuting	commuting	NOUN
iajs-539	7	13	mappings	mapping	NOUN
iajs-539	7	14	,	,	PUNCT
iajs-539	7	15	common	common	ADJ
iajs-539	7	16	fixed	fix	VERB
iajs-539	7	17	point	point	NOUN
iajs-539	7	18	.	.	PUNCT
iajs-539	8	1	312	312	NUM
iajs-539	8	2	|	|	NOUN
iajs-539	8	3	mathematics	mathematics	PROPN
iajs-539	8	4	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NOUN
iajs-539	8	5	�	�	NOUN
iajs-539	8	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-539	8	7	:	:	PUNCT
iajs-539	8	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-539	8	9	©	©	PROPN
iajs-539	8	10	@ü‹26@@öü»€a@i1@‚b«@h2013	@ü‹26@@öü»€a@i1@‚b«@h2013	PROPN
iajs-539	8	11	ibn	ibn	PROPN
iajs-539	8	12	al	al	PROPN
iajs-539	8	13	-	-	PUNCT
iajs-539	8	14	haitham	haitham	PROPN
iajs-539	8	15	jour	jour	X
iajs-539	8	16	.	.	PROPN
iajs-539	9	1	for	for	ADP
iajs-539	9	2	pure	pure	ADJ
iajs-539	9	3	&	&	CCONJ
iajs-539	9	4	appl	appl	PROPN
iajs-539	9	5	.	.	PUNCT
iajs-539	10	1	sci	sci	PROPN
iajs-539	10	2	.	.	PUNCT
iajs-539	10	3	vol	vol	NOUN
iajs-539	10	4	.	.	PROPN
iajs-539	11	1	26	26	NUM
iajs-539	11	2	(	(	PUNCT
iajs-539	11	3	1	1	NUM
iajs-539	11	4	)	)	PUNCT
iajs-539	11	5	2013	2013	NUM
iajs-539	11	6	introduction	introduction	NOUN
iajs-539	11	7	and	and	CCONJ
iajs-539	11	8	preliminaries	preliminary	NOUN
iajs-539	11	9	a	a	DET
iajs-539	11	10	number	number	NOUN
iajs-539	11	11	of	of	ADP
iajs-539	11	12	authors	author	NOUN
iajs-539	11	13	have	have	AUX
iajs-539	11	14	defined	define	VERB
iajs-539	11	15	contractive	contractive	ADJ
iajs-539	11	16	type	type	NOUN
iajs-539	11	17	mappings	mapping	NOUN
iajs-539	11	18	on	on	ADP
iajs-539	11	19	a	a	DET
iajs-539	11	20	usual	usual	ADJ
iajs-539	11	21	complete	complete	ADJ
iajs-539	11	22	metric	metric	ADJ
iajs-539	11	23	space	space	NOUN
iajs-539	11	24	x	x	PUNCT
iajs-539	11	25	which	which	PRON
iajs-539	11	26	are	be	AUX
iajs-539	11	27	generalizations	generalization	NOUN
iajs-539	11	28	of	of	ADP
iajs-539	11	29	the	the	DET
iajs-539	11	30	well	well	ADV
iajs-539	11	31	known	know	VERB
iajs-539	11	32	banach	banach	NOUN
iajs-539	11	33	’s	’s	PART
iajs-539	11	34	contraction	contraction	NOUN
iajs-539	11	35	principle	principle	NOUN
iajs-539	12	1	[	[	X
iajs-539	12	2	1	1	NUM
iajs-539	12	3	:	:	PUNCT
iajs-539	12	4	pp	pp	ADJ
iajs-539	12	5	.	.	PUNCT
iajs-539	13	1	175	175	NUM
iajs-539	13	2	-	-	SYM
iajs-539	13	3	206	206	NUM
iajs-539	13	4	]	]	PUNCT
iajs-539	13	5	,	,	PUNCT
iajs-539	13	6	and	and	CCONJ
iajs-539	14	1	which	which	PRON
iajs-539	14	2	have	have	VERB
iajs-539	14	3	the	the	DET
iajs-539	14	4	property	property	NOUN
iajs-539	14	5	that	that	PRON
iajs-539	14	6	each	each	DET
iajs-539	14	7	such	such	ADJ
iajs-539	14	8	mapping	mapping	NOUN
iajs-539	14	9	has	have	VERB
iajs-539	14	10	a	a	DET
iajs-539	14	11	unique	unique	ADJ
iajs-539	14	12	fixed	fix	VERB
iajs-539	14	13	point	point	NOUN
iajs-539	14	14	.	.	PUNCT
iajs-539	15	1	the	the	DET
iajs-539	15	2	fixed	fix	VERB
iajs-539	15	3	point	point	NOUN
iajs-539	15	4	can	can	AUX
iajs-539	15	5	always	always	ADV
iajs-539	15	6	be	be	AUX
iajs-539	15	7	found	find	VERB
iajs-539	15	8	by	by	ADP
iajs-539	15	9	using	use	VERB
iajs-539	15	10	picard	picard	NOUN
iajs-539	15	11	iteration	iteration	NOUN
iajs-539	15	12	(	(	PUNCT
iajs-539	15	13	i.e.	i.e.	X
iajs-539	15	14	iterative	iterative	NOUN
iajs-539	15	15	sequence[zidler	sequence[zidler	NOUN
iajs-539	15	16	:	:	PUNCT
iajs-539	15	17	pp.15	pp.15	PROPN
iajs-539	15	18	-	-	X
iajs-539	15	19	30	30	NUM
iajs-539	15	20	]	]	PUNCT
iajs-539	15	21	)	)	PUNCT
iajs-539	15	22	,	,	PUNCT
iajs-539	15	23	beginning	begin	VERB
iajs-539	15	24	with	with	ADP
iajs-539	15	25	some	some	DET
iajs-539	15	26	initial	initial	ADJ
iajs-539	15	27	choice	choice	NOUN
iajs-539	15	28	x0∈x	x0∈x	PROPN
iajs-539	15	29	.	.	PUNCT
iajs-539	16	1	and	and	CCONJ
iajs-539	16	2	then	then	ADV
iajs-539	16	3	many	many	ADJ
iajs-539	16	4	authors	author	NOUN
iajs-539	16	5	have	have	AUX
iajs-539	16	6	extended	extend	VERB
iajs-539	16	7	,	,	PUNCT
iajs-539	16	8	generalized	generalized	ADJ
iajs-539	16	9	and	and	CCONJ
iajs-539	16	10	improved	improve	VERB
iajs-539	16	11	banach	banach	NOUN
iajs-539	16	12	’s	’s	PART
iajs-539	16	13	contraction	contraction	NOUN
iajs-539	16	14	principle	principle	NOUN
iajs-539	16	15	in	in	ADP
iajs-539	16	16	different	different	ADJ
iajs-539	16	17	ways	way	NOUN
iajs-539	16	18	some	some	DET
iajs-539	16	19	these	these	DET
iajs-539	16	20	ways	way	NOUN
iajs-539	16	21	are	be	AUX
iajs-539	16	22	depending	depend	VERB
iajs-539	16	23	on	on	ADP
iajs-539	16	24	commuting	commuting	NOUN
iajs-539	16	25	mappings	mapping	NOUN
iajs-539	16	26	,	,	PUNCT
iajs-539	16	27	compatible	compatible	ADJ
iajs-539	16	28	mappings	mapping	NOUN
iajs-539	16	29	,	,	PUNCT
iajs-539	16	30	weakly	weakly	ADJ
iajs-539	16	31	commuting	commuting	NOUN
iajs-539	16	32	mappings	mapping	NOUN
iajs-539	16	33	,	,	PUNCT
iajs-539	16	34	…	…	PUNCT
iajs-539	17	1	ets	et	NOUN
iajs-539	17	2	(	(	PUNCT
iajs-539	17	3	such	such	ADJ
iajs-539	17	4	as	as	ADP
iajs-539	17	5	,	,	PUNCT
iajs-539	17	6	see	see	VERB
iajs-539	17	7	[	[	X
iajs-539	17	8	3,4,5,6	3,4,5,6	NUM
iajs-539	17	9	]	]	PUNCT
iajs-539	17	10	)	)	PUNCT
iajs-539	17	11	.	.	PUNCT
iajs-539	18	1	recently	recently	ADV
iajs-539	18	2	,	,	PUNCT
iajs-539	18	3	branciari	branciari	NOUN
iajs-539	18	4	[	[	X
iajs-539	18	5	7	7	X
iajs-539	18	6	]	]	PUNCT
iajs-539	18	7	introduced	introduce	VERB
iajs-539	18	8	a	a	DET
iajs-539	18	9	generalization	generalization	NOUN
iajs-539	18	10	of	of	ADP
iajs-539	18	11	metric	metric	ADJ
iajs-539	18	12	space	space	NOUN
iajs-539	18	13	and	and	CCONJ
iajs-539	18	14	proved	prove	VERB
iajs-539	18	15	a	a	DET
iajs-539	18	16	general	general	ADJ
iajs-539	18	17	version	version	NOUN
iajs-539	18	18	of	of	ADP
iajs-539	18	19	banach	banach	NOUN
iajs-539	18	20	’s	’s	PART
iajs-539	18	21	contraction	contraction	NOUN
iajs-539	18	22	principle	principle	NOUN
iajs-539	18	23	.	.	PUNCT
iajs-539	19	1	and	and	CCONJ
iajs-539	19	2	then	then	ADV
iajs-539	19	3	,	,	PUNCT
iajs-539	19	4	p.das[8	p.das[8	PROPN
iajs-539	19	5	]	]	X
iajs-539	19	6	,	,	PUNCT
iajs-539	19	7	p.das	p.da	NOUN
iajs-539	19	8	and	and	CCONJ
iajs-539	19	9	l.dey	l.dey	PROPN
iajs-539	20	1	[	[	X
iajs-539	20	2	9	9	NUM
iajs-539	20	3	]	]	PUNCT
iajs-539	20	4	,	,	PUNCT
iajs-539	20	5	s.mordi	s.mordi	X
iajs-539	21	1	[	[	X
iajs-539	21	2	10	10	NUM
iajs-539	21	3	]	]	PUNCT
iajs-539	21	4	and	and	CCONJ
iajs-539	21	5	akram	akram	PROPN
iajs-539	21	6	,	,	PUNCT
iajs-539	21	7	zafar	zafar	PROPN
iajs-539	21	8	and	and	CCONJ
iajs-539	21	9	siddiqui[11	siddiqui[11	PROPN
iajs-539	21	10	]	]	PUNCT
iajs-539	21	11	prove	prove	VERB
iajs-539	21	12	other	other	ADJ
iajs-539	21	13	results	result	NOUN
iajs-539	21	14	about	about	ADP
iajs-539	21	15	the	the	DET
iajs-539	21	16	existence	existence	NOUN
iajs-539	21	17	of	of	ADP
iajs-539	21	18	fixed	fix	VERB
iajs-539	21	19	points	point	NOUN
iajs-539	21	20	and	and	CCONJ
iajs-539	21	21	common	common	ADJ
iajs-539	21	22	fixed	fix	VERB
iajs-539	21	23	points	point	NOUN
iajs-539	21	24	for	for	ADP
iajs-539	21	25	mappings	mapping	NOUN
iajs-539	21	26	defined	define	VERB
iajs-539	21	27	on	on	ADP
iajs-539	21	28	complete	complete	ADJ
iajs-539	21	29	g	g	NOUN
iajs-539	21	30	-	-	PUNCT
iajs-539	21	31	metric	metric	ADJ
iajs-539	21	32	space	space	NOUN
iajs-539	21	33	.	.	PUNCT
iajs-539	22	1	throughout	throughout	ADP
iajs-539	22	2	this	this	DET
iajs-539	22	3	paper	paper	NOUN
iajs-539	22	4	r+	r+	NOUN
iajs-539	22	5	is	be	AUX
iajs-539	22	6	denoted	denote	VERB
iajs-539	22	7	by	by	ADP
iajs-539	22	8	non	non	ADJ
iajs-539	22	9	-	-	ADJ
iajs-539	22	10	negative	negative	ADJ
iajs-539	22	11	real	real	ADJ
iajs-539	22	12	numbers	number	NOUN
iajs-539	22	13	and	and	CCONJ
iajs-539	22	14	n	n	PRON
iajs-539	22	15	is	be	AUX
iajs-539	22	16	positive	positive	ADJ
iajs-539	22	17	integer	integer	NOUN
iajs-539	22	18	numbers	number	NOUN
iajs-539	22	19	.	.	PUNCT
iajs-539	23	1	now	now	ADV
iajs-539	23	2	we	we	PRON
iajs-539	23	3	begin	begin	VERB
iajs-539	23	4	with	with	ADP
iajs-539	23	5	the	the	DET
iajs-539	23	6	following	follow	VERB
iajs-539	23	7	definition	definition	NOUN
iajs-539	23	8	.	.	PUNCT
iajs-539	24	1	definition	definition	NOUN
iajs-539	24	2	1	1	NUM
iajs-539	24	3	.	.	PUNCT
iajs-539	25	1	1[11	1[11	NUM
iajs-539	25	2	]	]	PUNCT
iajs-539	25	3	:	:	PUNCT
iajs-539	25	4	let	let	VERB
iajs-539	25	5	x	x	PRON
iajs-539	25	6	be	be	AUX
iajs-539	25	7	a	a	DET
iajs-539	25	8	nonempty	nonempty	ADJ
iajs-539	25	9	set	set	VERB
iajs-539	25	10	.	.	PUNCT
iajs-539	26	1	suppose	suppose	VERB
iajs-539	26	2	that	that	SCONJ
iajs-539	26	3	the	the	DET
iajs-539	26	4	mapping	mapping	NOUN
iajs-539	26	5	ρ	ρ	NOUN
iajs-539	26	6	:	:	PUNCT
iajs-539	26	7	x	x	SYM
iajs-539	26	8	×	×	NOUN
iajs-539	26	9	x	x	PUNCT
iajs-539	26	10	→r+	→r+	NOUN
iajs-539	26	11	such	such	ADJ
iajs-539	26	12	that	that	PRON
iajs-539	26	13	for	for	ADP
iajs-539	26	14	all	all	DET
iajs-539	26	15	x	x	SYM
iajs-539	26	16	,	,	PUNCT
iajs-539	26	17	y	y	PROPN
iajs-539	26	18	∈	∈	PROPN
iajs-539	26	19	x	x	X
iajs-539	26	20	and	and	CCONJ
iajs-539	26	21	for	for	ADP
iajs-539	26	22	all	all	DET
iajs-539	26	23	distinct	distinct	ADJ
iajs-539	26	24	points	point	NOUN
iajs-539	26	25	z	z	NOUN
iajs-539	26	26	,	,	PUNCT
iajs-539	26	27	v	v	X
iajs-539	26	28	∈	∈	NOUN
iajs-539	26	29	x\	x\	NOUN
iajs-539	26	30	{	{	PUNCT
iajs-539	26	31	x	x	PROPN
iajs-539	26	32	,	,	PUNCT
iajs-539	26	33	y	y	PROPN
iajs-539	26	34	}	}	PUNCT
iajs-539	26	35	,	,	PUNCT
iajs-539	26	36	satisfies	satisfy	VERB
iajs-539	26	37	:	:	PUNCT
iajs-539	26	38	1	1	X
iajs-539	26	39	.	.	X
iajs-539	26	40	ρ	ρ	PROPN
iajs-539	26	41	(	(	PUNCT
iajs-539	26	42	x	x	NOUN
iajs-539	26	43	,	,	PUNCT
iajs-539	26	44	y	y	NOUN
iajs-539	26	45	)	)	PUNCT
iajs-539	26	46	=	=	SYM
iajs-539	26	47	0	0	PUNCT
iajs-539	27	1	if	if	SCONJ
iajs-539	27	2	and	and	CCONJ
iajs-539	27	3	only	only	ADV
iajs-539	27	4	if	if	SCONJ
iajs-539	27	5	x	x	X
iajs-539	27	6	=	=	SYM
iajs-539	27	7	y	y	PROPN
iajs-539	27	8	,	,	PUNCT
iajs-539	27	9	2	2	NUM
iajs-539	27	10	.	.	X
iajs-539	27	11	ρ	ρ	PROPN
iajs-539	27	12	(	(	PUNCT
iajs-539	27	13	x	x	NOUN
iajs-539	27	14	,	,	PUNCT
iajs-539	27	15	y	y	NOUN
iajs-539	27	16	)	)	PUNCT
iajs-539	27	17	=	=	SYM
iajs-539	27	18	ρ	ρ	PROPN
iajs-539	27	19	(	(	PUNCT
iajs-539	27	20	y	y	PROPN
iajs-539	27	21	,	,	PUNCT
iajs-539	27	22	x	x	NOUN
iajs-539	27	23	)	)	PUNCT
iajs-539	27	24	,	,	PUNCT
iajs-539	27	25	3	3	X
iajs-539	27	26	.	.	X
iajs-539	27	27	ρ	ρ	PROPN
iajs-539	27	28	(	(	PUNCT
iajs-539	27	29	x	x	NOUN
iajs-539	27	30	,	,	PUNCT
iajs-539	27	31	y	y	NOUN
iajs-539	27	32	)	)	PUNCT
iajs-539	27	33	≤	≤	NOUN
iajs-539	27	34	ρ	ρ	PROPN
iajs-539	27	35	(	(	PUNCT
iajs-539	27	36	x	x	X
iajs-539	27	37	,	,	PUNCT
iajs-539	27	38	z	z	NOUN
iajs-539	27	39	)	)	PUNCT
iajs-539	28	1	+	+	CCONJ
iajs-539	28	2	ρ	ρ	PROPN
iajs-539	28	3	(	(	PUNCT
iajs-539	28	4	z	z	NOUN
iajs-539	28	5	,	,	PUNCT
iajs-539	28	6	v	v	NOUN
iajs-539	28	7	)	)	PUNCT
iajs-539	29	1	+	+	NOUN
iajs-539	29	2	ρ	ρ	PROPN
iajs-539	29	3	(	(	PUNCT
iajs-539	29	4	v	v	NOUN
iajs-539	29	5	,	,	PUNCT
iajs-539	29	6	y	y	PROPN
iajs-539	29	7	)	)	PUNCT
iajs-539	29	8	,	,	PUNCT
iajs-539	29	9	(	(	PUNCT
iajs-539	29	10	rectangular	rectangular	ADJ
iajs-539	29	11	property	property	NOUN
iajs-539	29	12	)	)	PUNCT
iajs-539	29	13	,	,	PUNCT
iajs-539	29	14	then	then	ADV
iajs-539	29	15	the	the	DET
iajs-539	29	16	ordered	ordered	ADJ
iajs-539	29	17	pair	pair	NOUN
iajs-539	29	18	(	(	PUNCT
iajs-539	29	19	x	x	NOUN
iajs-539	29	20	,	,	PUNCT
iajs-539	29	21	ρ	ρ	PROPN
iajs-539	29	22	)	)	PUNCT
iajs-539	29	23	is	be	AUX
iajs-539	29	24	called	call	VERB
iajs-539	29	25	a	a	DET
iajs-539	29	26	generalized	generalize	VERB
iajs-539	29	27	metric	metric	ADJ
iajs-539	29	28	space	space	NOUN
iajs-539	29	29	(	(	PUNCT
iajs-539	29	30	or	or	CCONJ
iajs-539	29	31	shortly	shortly	ADV
iajs-539	29	32	g	g	NOUN
iajs-539	29	33	-	-	PUNCT
iajs-539	29	34	metric	metric	ADJ
iajs-539	29	35	space	space	NOUN
iajs-539	29	36	.	.	PUNCT
iajs-539	29	37	)	)	PUNCT
iajs-539	29	38	.	.	PUNCT
iajs-539	30	1	note	note	VERB
iajs-539	30	2	that	that	SCONJ
iajs-539	30	3	,	,	PUNCT
iajs-539	30	4	any	any	DET
iajs-539	30	5	metric	metric	ADJ
iajs-539	30	6	space	space	NOUN
iajs-539	30	7	is	be	AUX
iajs-539	30	8	g	g	NOUN
iajs-539	30	9	-	-	PUNCT
iajs-539	30	10	metric	metric	ADJ
iajs-539	30	11	space	space	NOUN
iajs-539	30	12	but	but	CCONJ
iajs-539	30	13	the	the	DET
iajs-539	30	14	converse	converse	NOUN
iajs-539	30	15	is	be	AUX
iajs-539	30	16	not	not	PART
iajs-539	30	17	true	true	ADJ
iajs-539	30	18	,	,	PUNCT
iajs-539	30	19	for	for	ADP
iajs-539	30	20	examples	example	NOUN
iajs-539	30	21	,	,	PUNCT
iajs-539	30	22	example1.2	example1.2	PROPN
iajs-539	30	23	:	:	PUNCT
iajs-539	30	24	let	let	VERB
iajs-539	30	25	x={a	x={a	PROPN
iajs-539	30	26	,	,	PUNCT
iajs-539	30	27	b	b	PROPN
iajs-539	30	28	,	,	PUNCT
iajs-539	30	29	c	c	X
iajs-539	30	30	,	,	PUNCT
iajs-539	30	31	d	d	NOUN
iajs-539	30	32	,	,	PUNCT
iajs-539	30	33	}	}	PUNCT
iajs-539	30	34	.	.	PUNCT
iajs-539	31	1	define	define	VERB
iajs-539	31	2	ρ	ρ	NUM
iajs-539	31	3	:x	:x	PROPN
iajs-539	31	4	×	×	NOUN
iajs-539	31	5	x	x	SYM
iajs-539	31	6	→r	→r	PUNCT
iajs-539	31	7	by	by	ADP
iajs-539	31	8	ρ	ρ	PROPN
iajs-539	31	9	(	(	PUNCT
iajs-539	31	10	a	a	PROPN
iajs-539	31	11	,	,	PUNCT
iajs-539	31	12	b)=	b)=	NOUN
iajs-539	31	13	ρ	ρ	PROPN
iajs-539	31	14	(	(	PUNCT
iajs-539	31	15	b	b	PROPN
iajs-539	31	16	,	,	PUNCT
iajs-539	31	17	a)=	a)=	PROPN
iajs-539	31	18	3	3	NUM
iajs-539	31	19	,	,	PUNCT
iajs-539	31	20	ρ	ρ	PROPN
iajs-539	31	21	(	(	PUNCT
iajs-539	31	22	b	b	NOUN
iajs-539	31	23	,	,	PUNCT
iajs-539	31	24	c)=	c)=	PROPN
iajs-539	31	25	ρ	ρ	PROPN
iajs-539	31	26	(	(	PUNCT
iajs-539	31	27	c	c	PROPN
iajs-539	31	28	,	,	PUNCT
iajs-539	31	29	b)=	b)=	NOUN
iajs-539	31	30	ρ	ρ	PROPN
iajs-539	31	31	(	(	PUNCT
iajs-539	31	32	a	a	PRON
iajs-539	31	33	,	,	PUNCT
iajs-539	31	34	c)=	c)=	PROPN
iajs-539	31	35	ρ	ρ	PROPN
iajs-539	31	36	(	(	PUNCT
iajs-539	31	37	c	c	PROPN
iajs-539	31	38	,	,	PUNCT
iajs-539	31	39	a)=1	a)=1	PROPN
iajs-539	31	40	,	,	PUNCT
iajs-539	31	41	ρ	ρ	PROPN
iajs-539	31	42	(	(	PUNCT
iajs-539	31	43	a	a	DET
iajs-539	31	44	,	,	PUNCT
iajs-539	31	45	d)=	d)=	NOUN
iajs-539	31	46	ρ	ρ	NOUN
iajs-539	31	47	(	(	PUNCT
iajs-539	31	48	d	d	PROPN
iajs-539	31	49	,	,	PUNCT
iajs-539	31	50	a)=	a)=	PROPN
iajs-539	31	51	ρ	ρ	PROPN
iajs-539	31	52	(	(	PUNCT
iajs-539	31	53	b	b	PROPN
iajs-539	31	54	,	,	PUNCT
iajs-539	31	55	d)=	d)=	NOUN
iajs-539	31	56	ρ	ρ	NOUN
iajs-539	31	57	(	(	PUNCT
iajs-539	31	58	d	d	PROPN
iajs-539	31	59	,	,	PUNCT
iajs-539	31	60	b)=	b)=	NOUN
iajs-539	31	61	ρ	ρ	PROPN
iajs-539	31	62	(	(	PUNCT
iajs-539	31	63	c	c	PROPN
iajs-539	31	64	,	,	PUNCT
iajs-539	31	65	d)=	d)=	NOUN
iajs-539	31	66	ρ	ρ	PROPN
iajs-539	31	67	(	(	PUNCT
iajs-539	31	68	d	d	NOUN
iajs-539	31	69	,	,	PUNCT
iajs-539	31	70	c)=4	c)=4	NOUN
iajs-539	31	71	.	.	PUNCT
iajs-539	32	1	it	it	PRON
iajs-539	32	2	is	be	AUX
iajs-539	32	3	easily	easily	ADV
iajs-539	32	4	to	to	PART
iajs-539	32	5	show	show	VERB
iajs-539	32	6	that	that	SCONJ
iajs-539	32	7	(	(	PUNCT
iajs-539	32	8	x	x	X
iajs-539	32	9	,	,	PUNCT
iajs-539	32	10	ρ	ρ	PROPN
iajs-539	32	11	)	)	PUNCT
iajs-539	32	12	is	be	AUX
iajs-539	32	13	g	g	NOUN
iajs-539	32	14	-	-	PUNCT
iajs-539	32	15	metric	metric	ADJ
iajs-539	32	16	space	space	NOUN
iajs-539	32	17	and	and	CCONJ
iajs-539	32	18	it	it	PRON
iajs-539	32	19	is	be	AUX
iajs-539	32	20	not	not	PART
iajs-539	32	21	metric	metric	ADJ
iajs-539	32	22	space	space	NOUN
iajs-539	32	23	,	,	PUNCT
iajs-539	32	24	since	since	SCONJ
iajs-539	32	25	ρ	ρ	PROPN
iajs-539	32	26	(	(	PUNCT
iajs-539	32	27	a	a	PRON
iajs-539	32	28	,	,	PUNCT
iajs-539	32	29	b	b	NOUN
iajs-539	32	30	)	)	PUNCT
iajs-539	32	31	ρ	ρ	NOUN
iajs-539	32	32	(	(	PUNCT
iajs-539	32	33	a	a	PROPN
iajs-539	32	34	,	,	PUNCT
iajs-539	32	35	c)+	c)+	PROPN
iajs-539	32	36	ρ	ρ	X
iajs-539	32	37	(	(	PUNCT
iajs-539	32	38	c	c	PROPN
iajs-539	32	39	,	,	PUNCT
iajs-539	32	40	b	b	NOUN
iajs-539	32	41	)	)	PUNCT
iajs-539	32	42	3	3	NUM
iajs-539	32	43	1	1	NUM
iajs-539	32	44	+	+	NUM
iajs-539	32	45	1	1	NUM
iajs-539	32	46	example1.3	example1.3	NUM
iajs-539	32	47	:	:	PUNCT
iajs-539	32	48	consider	consider	VERB
iajs-539	32	49	x	x	X
iajs-539	32	50	=	=	VERB
iajs-539	32	51	r	r	NOUN
iajs-539	32	52	,	,	PUNCT
iajs-539	32	53	µ	µ	PRON
iajs-539	32	54	:x	:x	NOUN
iajs-539	32	55	×	×	NOUN
iajs-539	32	56	x	x	SYM
iajs-539	32	57	→r	→r	X
iajs-539	32	58	and	and	CCONJ
iajs-539	32	59	µ	µ	X
iajs-539	32	60	(	(	PUNCT
iajs-539	32	61	x	x	X
iajs-539	32	62	,	,	PUNCT
iajs-539	32	63	y)=	y)=	ADJ
iajs-539	32	64	(	(	PUNCT
iajs-539	32	65	x	x	NOUN
iajs-539	32	66	-	-	PUNCT
iajs-539	32	67	y)2	y)2	NOUN
iajs-539	32	68	,	,	PUNCT
iajs-539	32	69	clearly	clearly	ADV
iajs-539	32	70	µ	µ	PRON
iajs-539	32	71	is	be	AUX
iajs-539	32	72	not	not	PART
iajs-539	32	73	g	g	NOUN
iajs-539	32	74	-	-	PUNCT
iajs-539	32	75	metric	metric	ADJ
iajs-539	32	76	space	space	NOUN
iajs-539	32	77	and	and	CCONJ
iajs-539	32	78	so	so	ADV
iajs-539	32	79	is	be	AUX
iajs-539	32	80	not	not	PART
iajs-539	32	81	metric	metric	ADJ
iajs-539	32	82	space	space	NOUN
iajs-539	32	83	since	since	SCONJ
iajs-539	32	84	,	,	PUNCT
iajs-539	32	85	for	for	ADP
iajs-539	32	86	x=2	x=2	PROPN
iajs-539	32	87	,	,	PUNCT
iajs-539	32	88	y=0	y=0	X
iajs-539	32	89	,	,	PUNCT
iajs-539	32	90	z=1	z=1	PROPN
iajs-539	32	91	and	and	CCONJ
iajs-539	32	92	w=1/2.we	w=1/2.we	PROPN
iajs-539	32	93	have	have	VERB
iajs-539	32	94	µ	µ	X
iajs-539	32	95	(	(	PUNCT
iajs-539	32	96	2,0	2,0	NUM
iajs-539	32	97	)	)	PUNCT
iajs-539	32	98	>	>	X
iajs-539	32	99	µ	µ	X
iajs-539	32	100	(	(	PUNCT
iajs-539	32	101	2,1)+	2,1)+	PROPN
iajs-539	32	102	µ	µ	X
iajs-539	32	103	(	(	PUNCT
iajs-539	32	104	1,1/2	1,1/2	NUM
iajs-539	32	105	)	)	PUNCT
iajs-539	33	1	+	+	NUM
iajs-539	33	2	µ	µ	X
iajs-539	33	3	(	(	PUNCT
iajs-539	33	4	1/2	1/2	NUM
iajs-539	33	5	,	,	PUNCT
iajs-539	33	6	0	0	NUM
iajs-539	33	7	)	)	PUNCT
iajs-539	33	8	example1.4	example1.4	NOUN
iajs-539	33	9	:	:	PUNCT
iajs-539	33	10	let	let	VERB
iajs-539	33	11	ρ	ρ	NOUN
iajs-539	33	12	:	:	PUNCT
iajs-539	33	13	r	r	NOUN
iajs-539	33	14	2	2	NUM
iajs-539	33	15	→r+	→r+	NOUN
iajs-539	33	16	be	be	VERB
iajs-539	33	17	a	a	DET
iajs-539	33	18	mapping	mapping	NOUN
iajs-539	33	19	such	such	ADJ
iajs-539	33	20	that	that	DET
iajs-539	33	21	ρ(x	ρ(x	NOUN
iajs-539	33	22	,	,	PUNCT
iajs-539	33	23	y)=max{µ	y)=max{µ	PUNCT
iajs-539	33	24	(	(	PUNCT
iajs-539	33	25	x	x	X
iajs-539	33	26	,	,	PUNCT
iajs-539	33	27	z	z	NOUN
iajs-539	33	28	)	)	PUNCT
iajs-539	33	29	,	,	PUNCT
iajs-539	33	30	µ	µ	X
iajs-539	33	31	(	(	PUNCT
iajs-539	33	32	z	z	NOUN
iajs-539	33	33	,	,	PUNCT
iajs-539	33	34	w	w	NOUN
iajs-539	33	35	)	)	PUNCT
iajs-539	33	36	,	,	PUNCT
iajs-539	33	37	µ	µ	X
iajs-539	33	38	(	(	PUNCT
iajs-539	33	39	w	w	PROPN
iajs-539	33	40	,	,	PUNCT
iajs-539	33	41	y	y	NOUN
iajs-539	33	42	)	)	PUNCT
iajs-539	33	43	}	}	PUNCT
iajs-539	33	44	,	,	PUNCT
iajs-539	33	45	whereas	whereas	SCONJ
iajs-539	33	46	in	in	ADP
iajs-539	33	47	example	example	NOUN
iajs-539	33	48	above	above	ADV
iajs-539	33	49	,	,	PUNCT
iajs-539	33	50	then	then	ADV
iajs-539	33	51	ρ	ρ	PROPN
iajs-539	33	52	is	be	AUX
iajs-539	33	53	g	g	NOUN
iajs-539	33	54	-	-	PUNCT
iajs-539	33	55	metric	metric	ADJ
iajs-539	33	56	space	space	NOUN
iajs-539	33	57	.	.	PUNCT
iajs-539	34	1	therefore	therefore	ADV
iajs-539	34	2	,	,	PUNCT
iajs-539	34	3	g	g	NOUN
iajs-539	34	4	-	-	PUNCT
iajs-539	34	5	metric	metric	ADJ
iajs-539	34	6	space	space	NOUN
iajs-539	34	7	is	be	AUX
iajs-539	34	8	a	a	DET
iajs-539	34	9	proper	proper	ADJ
iajs-539	34	10	extension	extension	NOUN
iajs-539	34	11	of	of	ADP
iajs-539	34	12	a	a	DET
iajs-539	34	13	metric	metric	ADJ
iajs-539	34	14	space	space	NOUN
iajs-539	34	15	.	.	PUNCT
iajs-539	35	1	also	also	ADV
iajs-539	35	2	,	,	PUNCT
iajs-539	35	3	one	one	PRON
iajs-539	35	4	can	can	AUX
iajs-539	35	5	generate	generate	VERB
iajs-539	35	6	many	many	ADJ
iajs-539	35	7	g	g	NOUN
iajs-539	35	8	-	-	PUNCT
iajs-539	35	9	metric	metric	ADJ
iajs-539	35	10	spaces	space	NOUN
iajs-539	35	11	by	by	ADP
iajs-539	35	12	usual	usual	ADJ
iajs-539	35	13	sense	sense	NOUN
iajs-539	35	14	,	,	PUNCT
iajs-539	35	15	such	such	ADJ
iajs-539	35	16	as	as	ADP
iajs-539	35	17	:	:	PUNCT
iajs-539	35	18	example	example	NOUN
iajs-539	35	19	1.5	1.5	NUM
iajs-539	35	20	:	:	PUNCT
iajs-539	35	21	if	if	SCONJ
iajs-539	35	22	ρ(x	ρ(x	PROPN
iajs-539	35	23	,	,	PUNCT
iajs-539	35	24	y	y	NOUN
iajs-539	35	25	)	)	PUNCT
iajs-539	35	26	g	g	NOUN
iajs-539	35	27	-	-	PUNCT
iajs-539	35	28	metric	metric	ADJ
iajs-539	35	29	space	space	NOUN
iajs-539	35	30	ρ1	ρ1	NOUN
iajs-539	35	31	(	(	PUNCT
iajs-539	35	32	x	x	X
iajs-539	35	33	,	,	PUNCT
iajs-539	35	34	y)=	y)=	ADJ
iajs-539	35	35	ρ(x	ρ(x	PROPN
iajs-539	35	36	,	,	PUNCT
iajs-539	35	37	y	y	NOUN
iajs-539	35	38	)	)	PUNCT
iajs-539	35	39	/	/	PUNCT
iajs-539	35	40	(	(	PUNCT
iajs-539	36	1	1	1	NUM
iajs-539	36	2	+	+	NUM
iajs-539	36	3	ρ(x	ρ(x	NOUN
iajs-539	36	4	,	,	PUNCT
iajs-539	36	5	y	y	NOUN
iajs-539	36	6	)	)	PUNCT
iajs-539	36	7	)	)	PUNCT
iajs-539	36	8	also	also	ADV
iajs-539	36	9	g	g	NOUN
iajs-539	36	10	-	-	PUNCT
iajs-539	36	11	metric	metric	ADJ
iajs-539	36	12	space	space	NOUN
iajs-539	36	13	.	.	PUNCT
iajs-539	37	1	remark1.6	remark1.6	PROPN
iajs-539	38	1	[	[	X
iajs-539	38	2	7	7	NUM
iajs-539	38	3	]	]	PUNCT
iajs-539	38	4	:	:	PUNCT
iajs-539	38	5	the	the	DET
iajs-539	38	6	g	g	NOUN
iajs-539	38	7	-	-	PUNCT
iajs-539	38	8	metric	metric	ADJ
iajs-539	38	9	space	space	NOUN
iajs-539	38	10	is	be	AUX
iajs-539	38	11	continues	continue	VERB
iajs-539	38	12	function	function	NOUN
iajs-539	38	13	on	on	ADP
iajs-539	38	14	x	x	SYM
iajs-539	38	15	×	×	NOUN
iajs-539	38	16	x.	x.	NOUN
iajs-539	38	17	remark1.7	remark1.7	PUNCT
iajs-539	39	1	[	[	X
iajs-539	39	2	11	11	NUM
iajs-539	39	3	]	]	SYM
iajs-539	39	4	:	:	PUNCT
iajs-539	39	5	as	as	ADP
iajs-539	39	6	in	in	ADP
iajs-539	39	7	the	the	DET
iajs-539	39	8	usual	usual	ADJ
iajs-539	39	9	metric	metric	ADJ
iajs-539	39	10	space	space	NOUN
iajs-539	39	11	settings	setting	NOUN
iajs-539	39	12	,	,	PUNCT
iajs-539	39	13	a	a	DET
iajs-539	39	14	g	g	NOUN
iajs-539	39	15	-	-	PUNCT
iajs-539	39	16	metric	metric	ADJ
iajs-539	39	17	space	space	NOUN
iajs-539	39	18	is	be	AUX
iajs-539	39	19	a	a	DET
iajs-539	39	20	topological	topological	ADJ
iajs-539	39	21	space	space	NOUN
iajs-539	39	22	with	with	ADP
iajs-539	39	23	respect	respect	NOUN
iajs-539	39	24	to	to	ADP
iajs-539	39	25	the	the	DET
iajs-539	39	26	basis	basis	NOUN
iajs-539	39	27	given	give	VERB
iajs-539	39	28	by	by	ADP
iajs-539	39	29	b={b(x	b={b(x	PROPN
iajs-539	39	30	,	,	PUNCT
iajs-539	39	31	r	r	NOUN
iajs-539	39	32	):	):	PUNCT
iajs-539	39	33	x	x	SYM
iajs-539	39	34	∈x	∈x	NOUN
iajs-539	39	35	,	,	PUNCT
iajs-539	39	36	r∈	r∈	PROPN
iajs-539	39	37	r+},where	r+},where	NOUN
iajs-539	39	38	b(x	b(x	PROPN
iajs-539	39	39	,	,	PUNCT
iajs-539	39	40	r)={y	r)={y	PROPN
iajs-539	39	41	∈x	∈x	NOUN
iajs-539	39	42	:	:	PUNCT
iajs-539	39	43	ρ	ρ	PROPN
iajs-539	39	44	(	(	PUNCT
iajs-539	39	45	x	x	NOUN
iajs-539	39	46	,	,	PUNCT
iajs-539	39	47	y	y	PROPN
iajs-539	39	48	)	)	PUNCT
iajs-539	39	49	<	<	X
iajs-539	39	50	r	r	X
iajs-539	39	51	}	}	PUNCT
iajs-539	39	52	is	be	AUX
iajs-539	39	53	open	open	ADJ
iajs-539	39	54	ball	ball	NOUN
iajs-539	39	55	centered	center	VERB
iajs-539	39	56	by	by	ADP
iajs-539	39	57	x	x	PUNCT
iajs-539	39	58	and	and	CCONJ
iajs-539	39	59	with	with	ADP
iajs-539	39	60	radius	radius	PROPN
iajs-539	39	61	r.	r.	PROPN
iajs-539	39	62	definition1.9[11	definition1.9[11	PROPN
iajs-539	39	63	]	]	PUNCT
iajs-539	39	64	:	:	PUNCT
iajs-539	39	65	let	let	VERB
iajs-539	39	66	(	(	PUNCT
iajs-539	39	67	x	x	NOUN
iajs-539	39	68	,	,	PUNCT
iajs-539	39	69	ρ	ρ	PROPN
iajs-539	39	70	)	)	PUNCT
iajs-539	39	71	be	be	AUX
iajs-539	39	72	a	a	DET
iajs-539	39	73	g	g	NOUN
iajs-539	39	74	-	-	PUNCT
iajs-539	39	75	metric	metric	ADJ
iajs-539	39	76	space	space	NOUN
iajs-539	39	77	.	.	PUNCT
iajs-539	40	1	a	a	DET
iajs-539	40	2	sequence	sequence	NOUN
iajs-539	40	3	{	{	PUNCT
iajs-539	40	4	xn	xn	NOUN
iajs-539	40	5	}	}	PUNCT
iajs-539	40	6	in	in	ADP
iajs-539	40	7	x	x	VERB
iajs-539	40	8	is	be	AUX
iajs-539	40	9	said	say	VERB
iajs-539	40	10	to	to	PART
iajs-539	40	11	to	to	PART
iajs-539	40	12	be	be	AUX
iajs-539	40	13	a	a	DET
iajs-539	40	14	cauchy	cauchy	ADJ
iajs-539	40	15	sequence	sequence	NOUN
iajs-539	40	16	if	if	SCONJ
iajs-539	40	17	for	for	ADP
iajs-539	40	18	any	any	DET
iajs-539	40	19	ε	ε	PROPN
iajs-539	40	20	>	>	X
iajs-539	40	21	0	0	PUNCT
iajs-539	40	22	there	there	PRON
iajs-539	40	23	exists	exist	VERB
iajs-539	40	24	nε	nε	PROPN
iajs-539	40	25	in	in	ADP
iajs-539	40	26	n	n	CCONJ
iajs-539	40	27	such	such	ADJ
iajs-539	40	28	that	that	PRON
iajs-539	40	29	for	for	ADP
iajs-539	40	30	all	all	DET
iajs-539	40	31	m	m	PROPN
iajs-539	40	32	,	,	PUNCT
iajs-539	40	33	n	n	PROPN
iajs-539	40	34	∈	∈	PROPN
iajs-539	40	35	n	n	NOUN
iajs-539	40	36	and	and	CCONJ
iajs-539	40	37	m	m	PROPN
iajs-539	40	38	,	,	PUNCT
iajs-539	40	39	n	n	CCONJ
iajs-539	40	40	>	>	X
iajs-539	40	41	nε	nε	PROPN
iajs-539	40	42	,	,	PUNCT
iajs-539	40	43	one	one	NUM
iajs-539	40	44	has	have	VERB
iajs-539	40	45	ρ(xn	ρ(xn	NUM
iajs-539	40	46	,	,	PUNCT
iajs-539	40	47	xn+m)<ε	xn+m)<ε	PROPN
iajs-539	40	48	.	.	PUNCT
iajs-539	41	1	313	313	NUM
iajs-539	41	2	|	|	NOUN
iajs-539	41	3	mathematics	mathematics	PROPN
iajs-539	41	4	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NOUN
iajs-539	41	5	�	�	NOUN
iajs-539	41	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-539	41	7	:	:	PUNCT
iajs-539	41	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-539	41	9	©	©	PROPN
iajs-539	41	10	@ü‹26@@öü»€a@i1@‚b«@h2013	@ü‹26@@öü»€a@i1@‚b«@h2013	PROPN
iajs-539	41	11	ibn	ibn	PROPN
iajs-539	41	12	al	al	PROPN
iajs-539	41	13	-	-	PUNCT
iajs-539	41	14	haitham	haitham	PROPN
iajs-539	41	15	jour	jour	X
iajs-539	41	16	.	.	PROPN
iajs-539	42	1	for	for	ADP
iajs-539	42	2	pure	pure	ADJ
iajs-539	42	3	&	&	CCONJ
iajs-539	42	4	appl	appl	PROPN
iajs-539	42	5	.	.	PUNCT
iajs-539	43	1	sci	sci	PROPN
iajs-539	43	2	.	.	PUNCT
iajs-539	43	3	vol	vol	NOUN
iajs-539	43	4	.	.	PROPN
iajs-539	44	1	26	26	NUM
iajs-539	44	2	(	(	PUNCT
iajs-539	44	3	1	1	NUM
iajs-539	44	4	)	)	PUNCT
iajs-539	44	5	2013	2013	NUM
iajs-539	44	6	the	the	DET
iajs-539	44	7	space	space	NOUN
iajs-539	44	8	(	(	PUNCT
iajs-539	44	9	x	x	X
iajs-539	44	10	,	,	PUNCT
iajs-539	44	11	ρ	ρ	PROPN
iajs-539	44	12	)	)	PUNCT
iajs-539	44	13	is	be	AUX
iajs-539	44	14	called	call	VERB
iajs-539	44	15	complete	complete	ADJ
iajs-539	44	16	if	if	SCONJ
iajs-539	44	17	every	every	DET
iajs-539	44	18	cauchy	cauchy	ADJ
iajs-539	44	19	sequence	sequence	NOUN
iajs-539	44	20	in	in	ADP
iajs-539	44	21	x	x	PROPN
iajs-539	44	22	is	be	AUX
iajs-539	44	23	convergent	convergent	ADJ
iajs-539	44	24	.	.	PUNCT
iajs-539	45	1	definition1.10	definition1.10	NOUN
iajs-539	45	2	:	:	PUNCT
iajs-539	45	3	let	let	VERB
iajs-539	45	4	t	t	NOUN
iajs-539	45	5	be	be	AUX
iajs-539	45	6	a	a	DET
iajs-539	45	7	self	self	NOUN
iajs-539	45	8	mapping	mapping	NOUN
iajs-539	45	9	on	on	ADP
iajs-539	45	10	x.	x.	NOUN
iajs-539	45	11	let	let	VERB
iajs-539	45	12	x0∈	x0∈	PROPN
iajs-539	45	13	x.	x.	PROPN
iajs-539	45	14	a	a	DET
iajs-539	45	15	sequence	sequence	NOUN
iajs-539	45	16	{	{	PUNCT
iajs-539	45	17	tnx	tnx	NOUN
iajs-539	45	18	}	}	PUNCT
iajs-539	45	19	in	in	ADP
iajs-539	45	20	x	x	PROPN
iajs-539	45	21	is	be	AUX
iajs-539	45	22	said	say	VERB
iajs-539	45	23	to	to	PART
iajs-539	45	24	be	be	AUX
iajs-539	45	25	an	an	DET
iajs-539	45	26	orbit	orbit	NOUN
iajs-539	45	27	of	of	ADP
iajs-539	45	28	x	x	PUNCT
iajs-539	45	29	by	by	ADP
iajs-539	45	30	t	t	NOUN
iajs-539	45	31	and	and	CCONJ
iajs-539	45	32	denoted	denote	VERB
iajs-539	45	33	by	by	ADP
iajs-539	45	34	o(x	o(x	PROPN
iajs-539	45	35	,	,	PUNCT
iajs-539	45	36	n)=	n)=	NOUN
iajs-539	45	37	{	{	PUNCT
iajs-539	45	38	x	x	NOUN
iajs-539	45	39	,	,	PUNCT
iajs-539	45	40	tx	tx	PROPN
iajs-539	45	41	,	,	PUNCT
iajs-539	45	42	t2x,	t2x,	PROPN
iajs-539	45	43	…	…	PUNCT
iajs-539	45	44	,tnx	,tnx	NOUN
iajs-539	45	45	}	}	PUNCT
iajs-539	45	46	,	,	PUNCT
iajs-539	45	47	for	for	ADP
iajs-539	45	48	all	all	DET
iajs-539	45	49	n	n	DET
iajs-539	45	50	∈	∈	PROPN
iajs-539	45	51	n.	n.	NOUN
iajs-539	45	52	also	also	ADV
iajs-539	45	53	,	,	PUNCT
iajs-539	45	54	o	o	X
iajs-539	45	55	(	(	PUNCT
iajs-539	45	56	x	x	X
iajs-539	45	57	,	,	PUNCT
iajs-539	45	58	∞	∞	PROPN
iajs-539	45	59	)	)	PUNCT
iajs-539	46	1	=	=	NOUN
iajs-539	46	2	{	{	PUNCT
iajs-539	46	3	x	x	NOUN
iajs-539	46	4	,	,	PUNCT
iajs-539	46	5	tx	tx	PROPN
iajs-539	46	6	,	,	PUNCT
iajs-539	46	7	t2x	t2x	ADJ
iajs-539	46	8	,	,	PUNCT
iajs-539	46	9	…	…	PUNCT
iajs-539	46	10	}	}	PUNCT
iajs-539	46	11	.	.	PUNCT
iajs-539	47	1	definition	definition	NOUN
iajs-539	47	2	1.11[9	1.11[9	NUM
iajs-539	47	3	]	]	X
iajs-539	47	4	:	:	PUNCT
iajs-539	47	5	let	let	VERB
iajs-539	47	6	t	t	PROPN
iajs-539	47	7	be	be	AUX
iajs-539	47	8	mapping	map	VERB
iajs-539	47	9	on	on	ADP
iajs-539	47	10	a	a	DET
iajs-539	47	11	g	g	NOUN
iajs-539	47	12	-	-	PUNCT
iajs-539	47	13	metric	metric	ADJ
iajs-539	47	14	space	space	NOUN
iajs-539	47	15	(	(	PUNCT
iajs-539	47	16	x	x	X
iajs-539	47	17	,	,	PUNCT
iajs-539	47	18	ρ	ρ	PROPN
iajs-539	47	19	)	)	PUNCT
iajs-539	47	20	into	into	ADP
iajs-539	47	21	itself	itself	PRON
iajs-539	47	22	.	.	PUNCT
iajs-539	48	1	(	(	PUNCT
iajs-539	48	2	x	x	X
iajs-539	48	3	,	,	PUNCT
iajs-539	48	4	ρ	ρ	PROPN
iajs-539	48	5	)	)	PUNCT
iajs-539	48	6	is	be	AUX
iajs-539	48	7	said	say	VERB
iajs-539	48	8	to	to	PART
iajs-539	48	9	be	be	AUX
iajs-539	48	10	t	t	NOUN
iajs-539	48	11	-	-	PUNCT
iajs-539	48	12	orbitally	orbitally	ADV
iajs-539	48	13	complete	complete	ADJ
iajs-539	48	14	if	if	SCONJ
iajs-539	48	15	and	and	CCONJ
iajs-539	48	16	only	only	ADV
iajs-539	48	17	if	if	SCONJ
iajs-539	48	18	every	every	DET
iajs-539	48	19	cauchy	cauchy	ADJ
iajs-539	48	20	sequence	sequence	NOUN
iajs-539	48	21	in	in	ADP
iajs-539	48	22	o	o	PROPN
iajs-539	48	23	(	(	PUNCT
iajs-539	48	24	x	x	X
iajs-539	48	25	,	,	PUNCT
iajs-539	48	26	∞	∞	PROPN
iajs-539	48	27	)	)	PUNCT
iajs-539	48	28	converges	converge	VERB
iajs-539	48	29	in	in	ADP
iajs-539	48	30	x	x	PRON
iajs-539	48	31	,	,	PUNCT
iajs-539	48	32	for	for	ADP
iajs-539	48	33	some	some	DET
iajs-539	48	34	x	x	SYM
iajs-539	48	35	∈	∈	PROPN
iajs-539	48	36	x.	x.	NOUN
iajs-539	49	1	now	now	ADV
iajs-539	49	2	we	we	PRON
iajs-539	49	3	introduced	introduce	VERB
iajs-539	49	4	the	the	DET
iajs-539	49	5	following	follow	VERB
iajs-539	49	6	concept	concept	NOUN
iajs-539	49	7	definition	definition	NOUN
iajs-539	49	8	1.12	1.12	NUM
iajs-539	49	9	:	:	PUNCT
iajs-539	49	10	let	let	VERB
iajs-539	49	11	t1s	t1s	PRON
iajs-539	49	12	be	be	AUX
iajs-539	49	13	two	two	NUM
iajs-539	49	14	self	self	NOUN
iajs-539	49	15	mappings	mapping	NOUN
iajs-539	49	16	on	on	ADP
iajs-539	49	17	a	a	DET
iajs-539	49	18	g	g	NOUN
iajs-539	49	19	-	-	PUNCT
iajs-539	49	20	metric	metric	ADJ
iajs-539	49	21	space	space	NOUN
iajs-539	49	22	x.	x.	NOUN
iajs-539	49	23	x	x	PROPN
iajs-539	49	24	is	be	AUX
iajs-539	49	25	called	call	VERB
iajs-539	49	26	st	st	NOUN
iajs-539	49	27	-	-	PUNCT
iajs-539	49	28	orbitally	orbitally	ADV
iajs-539	49	29	complete	complete	ADJ
iajs-539	49	30	if	if	SCONJ
iajs-539	49	31	for	for	ADP
iajs-539	49	32	x0∈x	x0∈x	DET
iajs-539	49	33	the	the	DET
iajs-539	49	34	sequence	sequence	NOUN
iajs-539	49	35	{	{	PUNCT
iajs-539	49	36	x0,tx0,stx0,tstx0	x0,tx0,stx0,tstx0	NOUN
iajs-539	49	37	,	,	PUNCT
iajs-539	49	38	…	…	PUNCT
iajs-539	49	39	.	.	PUNCT
iajs-539	49	40	}	}	PUNCT
iajs-539	49	41	converges	converge	VERB
iajs-539	49	42	to	to	ADP
iajs-539	49	43	a	a	DET
iajs-539	49	44	point	point	NOUN
iajs-539	49	45	in	in	ADP
iajs-539	49	46	x.	x.	NOUN
iajs-539	49	47	or	or	CCONJ
iajs-539	49	48	the	the	DET
iajs-539	49	49	sequence	sequence	NOUN
iajs-539	49	50	{	{	PUNCT
iajs-539	49	51	xn	xn	NOUN
iajs-539	49	52	}	}	PUNCT
iajs-539	49	53	converges	converge	NOUN
iajs-539	49	54	to	to	ADP
iajs-539	49	55	a	a	DET
iajs-539	49	56	point	point	NOUN
iajs-539	49	57	in	in	ADP
iajs-539	49	58	x	x	PUNCT
iajs-539	49	59	where	where	SCONJ
iajs-539	49	60	x0∈x	x0∈x	NOUN
iajs-539	49	61	,	,	PUNCT
iajs-539	49	62	x2n+1	x2n+1	PROPN
iajs-539	49	63	=	=	SYM
iajs-539	49	64	tx2n	tx2n	PROPN
iajs-539	49	65	,	,	PUNCT
iajs-539	49	66	x2n+2	x2n+2	X
iajs-539	49	67	=	=	NOUN
iajs-539	49	68	sx2n+1	sx2n+1	ADJ
iajs-539	49	69	…	…	PUNCT
iajs-539	49	70	(	(	PUNCT
iajs-539	49	71	1	1	NUM
iajs-539	49	72	)	)	PUNCT
iajs-539	49	73	for	for	ADP
iajs-539	49	74	all	all	DET
iajs-539	49	75	n∈n	n∈n	NOUN
iajs-539	49	76	{	{	PUNCT
iajs-539	49	77	0	0	NUM
iajs-539	49	78	}	}	PUNCT
iajs-539	49	79	.	.	PUNCT
iajs-539	50	1	definition1.13	definition1.13	NOUN
iajs-539	50	2	:	:	PUNCT
iajs-539	50	3	a	a	DET
iajs-539	50	4	point	point	NOUN
iajs-539	50	5	x	x	PUNCT
iajs-539	50	6	in	in	ADP
iajs-539	50	7	x	x	PROPN
iajs-539	50	8	is	be	AUX
iajs-539	50	9	a	a	DET
iajs-539	50	10	common	common	ADJ
iajs-539	50	11	fixed	fix	VERB
iajs-539	50	12	point	point	NOUN
iajs-539	50	13	of	of	ADP
iajs-539	50	14	two	two	NUM
iajs-539	50	15	self	self	NOUN
iajs-539	50	16	-	-	PUNCT
iajs-539	50	17	mappings	mapping	NOUN
iajs-539	50	18	on	on	ADP
iajs-539	50	19	g	g	NOUN
iajs-539	50	20	-	-	PUNCT
iajs-539	50	21	metric	metric	ADJ
iajs-539	50	22	space	space	NOUN
iajs-539	50	23	x	x	INTJ
iajs-539	50	24	if	if	SCONJ
iajs-539	50	25	tx	tx	VERB
iajs-539	50	26	=	=	PUNCT
iajs-539	50	27	sx	sx	PROPN
iajs-539	50	28	=	=	PUNCT
iajs-539	50	29	x.	x.	NOUN
iajs-539	50	30	definition1.14	definition1.14	PROPN
iajs-539	50	31	:	:	PUNCT
iajs-539	50	32	let	let	VERB
iajs-539	50	33	t	t	NOUN
iajs-539	50	34	and	and	CCONJ
iajs-539	50	35	s	s	AUX
iajs-539	50	36	be	be	AUX
iajs-539	50	37	self	self	NOUN
iajs-539	50	38	mappings	mapping	NOUN
iajs-539	50	39	on	on	ADP
iajs-539	50	40	g	g	NOUN
iajs-539	50	41	-	-	PUNCT
iajs-539	50	42	metric	metric	ADJ
iajs-539	50	43	space	space	NOUN
iajs-539	50	44	x.	x.	NOUN
iajs-539	50	45	t	t	PROPN
iajs-539	50	46	and	and	CCONJ
iajs-539	50	47	s	s	VERB
iajs-539	50	48	are	be	AUX
iajs-539	50	49	commuting	commute	VERB
iajs-539	50	50	mappings	mapping	NOUN
iajs-539	50	51	if	if	SCONJ
iajs-539	50	52	there	there	PRON
iajs-539	50	53	exists	exist	VERB
iajs-539	50	54	a	a	DET
iajs-539	50	55	point	point	NOUN
iajs-539	50	56	x	x	PUNCT
iajs-539	50	57	in	in	ADP
iajs-539	50	58	x	x	X
iajs-539	50	59	such	such	ADJ
iajs-539	50	60	that	that	DET
iajs-539	50	61	t	t	NOUN
iajs-539	50	62	x	x	PUNCT
iajs-539	51	1	=	=	SYM
iajs-539	51	2	s	s	X
iajs-539	51	3	x	x	X
iajs-539	51	4	and	and	CCONJ
iajs-539	51	5	t	t	NOUN
iajs-539	51	6	s	s	PART
iajs-539	51	7	x	x	X
iajs-539	51	8	=	=	SYM
iajs-539	51	9	s	s	PROPN
iajs-539	51	10	t	t	NOUN
iajs-539	51	11	x	x	X
iajs-539	51	12	..	..	PUNCT
iajs-539	51	13	main	main	ADJ
iajs-539	51	14	results	result	NOUN
iajs-539	51	15	let	let	VERB
iajs-539	51	16	φ	φ	PROPN
iajs-539	51	17	be	be	AUX
iajs-539	51	18	a	a	DET
iajs-539	51	19	family	family	NOUN
iajs-539	51	20	of	of	ADP
iajs-539	51	21	functions	function	NOUN
iajs-539	51	22	such	such	ADJ
iajs-539	51	23	that	that	SCONJ
iajs-539	51	24	ϕ	ϕ	PROPN
iajs-539	51	25	∈	∈	PROPN
iajs-539	51	26	φ	φ	X
iajs-539	51	27	mean	mean	VERB
iajs-539	51	28	that	that	SCONJ
iajs-539	51	29	ϕ	ϕ	X
iajs-539	51	30	:	:	PUNCT
iajs-539	51	31	r+→r+	r+→r+	NOUN
iajs-539	51	32	is	be	AUX
iajs-539	51	33	continuous	continuous	ADJ
iajs-539	51	34	from	from	ADP
iajs-539	51	35	the	the	DET
iajs-539	51	36	right	right	NOUN
iajs-539	51	37	,	,	PUNCT
iajs-539	51	38	non	non	ADJ
iajs-539	51	39	-	-	ADJ
iajs-539	51	40	decreasing	decrease	VERB
iajs-539	51	41	and	and	CCONJ
iajs-539	51	42	satisfy	satisfy	VERB
iajs-539	51	43	the	the	DET
iajs-539	51	44	condition	condition	NOUN
iajs-539	51	45	φ(t	φ(t	PROPN
iajs-539	51	46	)	)	PUNCT
iajs-539	51	47	<	<	X
iajs-539	51	48	t	t	PROPN
iajs-539	51	49	for	for	ADP
iajs-539	51	50	t	t	PROPN
iajs-539	51	51	>	>	X
iajs-539	51	52	0	0	PUNCT
iajs-539	51	53	and	and	CCONJ
iajs-539	51	54	φ(0)=0	φ(0)=0	PROPN
iajs-539	51	55	.	.	PUNCT
iajs-539	52	1	it	it	PRON
iajs-539	52	2	is	be	AUX
iajs-539	52	3	easy	easy	ADJ
iajs-539	52	4	to	to	PART
iajs-539	52	5	have	have	VERB
iajs-539	52	6	the	the	DET
iajs-539	52	7	following	follow	VERB
iajs-539	52	8	lemma	lemma	PROPN
iajs-539	52	9	lemma2.1	lemma2.1	PROPN
iajs-539	52	10	:	:	PUNCT
iajs-539	52	11	if	if	SCONJ
iajs-539	52	12	ϕ1	ϕ1	NOUN
iajs-539	52	13	,	,	PUNCT
iajs-539	52	14	ϕ2	ϕ2	ADV
iajs-539	52	15	∈	∈	PROPN
iajs-539	52	16	φ	φ	NOUN
iajs-539	52	17	,	,	PUNCT
iajs-539	52	18	then	then	ADV
iajs-539	52	19	there	there	PRON
iajs-539	52	20	is	be	VERB
iajs-539	52	21	some	some	DET
iajs-539	52	22	ϕ3	ϕ3	PROPN
iajs-539	52	23	∈	∈	PROPN
iajs-539	52	24	φ	φ	NOUN
iajs-539	52	25	such	such	ADJ
iajs-539	52	26	that	that	SCONJ
iajs-539	52	27	max	max	PROPN
iajs-539	52	28	{	{	PUNCT
iajs-539	52	29	ϕ1(t	ϕ1(t	PROPN
iajs-539	52	30	)	)	PUNCT
iajs-539	52	31	,	,	PUNCT
iajs-539	52	32	ϕ2(t	ϕ2(t	PROPN
iajs-539	52	33	)	)	PUNCT
iajs-539	52	34	}	}	PUNCT
iajs-539	52	35	≤	≤	NUM
iajs-539	52	36	ϕ3	ϕ3	PROPN
iajs-539	52	37	(	(	PUNCT
iajs-539	52	38	t	t	PROPN
iajs-539	52	39	)	)	PUNCT
iajs-539	52	40	for	for	ADP
iajs-539	52	41	all	all	DET
iajs-539	52	42	t	t	PROPN
iajs-539	52	43	>	>	X
iajs-539	52	44	0	0	X
iajs-539	52	45	.	.	PUNCT
iajs-539	53	1	proof	proof	NOUN
iajs-539	53	2	:	:	PUNCT
iajs-539	53	3	we	we	PRON
iajs-539	53	4	can	can	AUX
iajs-539	53	5	see	see	VERB
iajs-539	53	6	ϕ3	ϕ3	PROPN
iajs-539	53	7	as	as	ADP
iajs-539	53	8	ϕ1	ϕ1	NOUN
iajs-539	53	9	+	+	X
iajs-539	53	10	ϕ2	ϕ2	ADV
iajs-539	53	11	.	.	PUNCT
iajs-539	54	1	lemma	lemma	PROPN
iajs-539	54	2	2.1[12	2.1[12	PROPN
iajs-539	54	3	]	]	X
iajs-539	54	4	:	:	PUNCT
iajs-539	54	5	let	let	VERB
iajs-539	54	6	φ	φ	PROPN
iajs-539	54	7	∈	∈	PROPN
iajs-539	54	8	φ	φ	PROPN
iajs-539	54	9	,	,	PUNCT
iajs-539	54	10	then	then	ADV
iajs-539	54	11	φ	φ	PROPN
iajs-539	54	12	n(t	n(t	PROPN
iajs-539	54	13	)	)	PUNCT
iajs-539	54	14	→	→	SYM
iajs-539	54	15	0	0	NUM
iajs-539	54	16	as	as	ADP
iajs-539	54	17	n	n	NUM
iajs-539	54	18	→+∞	→+∞	ADV
iajs-539	54	19	for	for	ADP
iajs-539	54	20	every	every	DET
iajs-539	54	21	t	t	PROPN
iajs-539	54	22	>	>	X
iajs-539	54	23	0	0	NUM
iajs-539	54	24	.	.	PUNCT
iajs-539	55	1	proposition2.3	proposition2.3	PROPN
iajs-539	55	2	:	:	PUNCT
iajs-539	55	3	let	let	VERB
iajs-539	55	4	(	(	PUNCT
iajs-539	55	5	x	x	NOUN
iajs-539	55	6	,	,	PUNCT
iajs-539	55	7	ρ	ρ	PROPN
iajs-539	55	8	)	)	PUNCT
iajs-539	55	9	be	be	VERB
iajs-539	55	10	a	a	DET
iajs-539	55	11	g	g	NOUN
iajs-539	55	12	-	-	PUNCT
iajs-539	55	13	metric	metric	ADJ
iajs-539	55	14	space	space	NOUN
iajs-539	55	15	.	.	PUNCT
iajs-539	56	1	let	let	VERB
iajs-539	56	2	s	s	NOUN
iajs-539	56	3	,	,	PUNCT
iajs-539	56	4	t	t	NOUN
iajs-539	56	5	:	:	PUNCT
iajs-539	56	6	x	x	PUNCT
iajs-539	56	7	→x	→x	PUNCT
iajs-539	56	8	be	be	AUX
iajs-539	56	9	mappings	mapping	NOUN
iajs-539	56	10	.	.	PUNCT
iajs-539	57	1	if	if	SCONJ
iajs-539	57	2	for	for	ADP
iajs-539	57	3	each	each	DET
iajs-539	57	4	x	x	NOUN
iajs-539	57	5	,	,	PUNCT
iajs-539	57	6	y	y	PROPN
iajs-539	57	7	in	in	ADP
iajs-539	57	8	x	x	PROPN
iajs-539	57	9	and	and	CCONJ
iajs-539	57	10	t	t	PROPN
iajs-539	57	11	and	and	CCONJ
iajs-539	57	12	s	s	AUX
iajs-539	57	13	satisfy	satisfy	VERB
iajs-539	57	14	the	the	DET
iajs-539	57	15	condition	condition	NOUN
iajs-539	57	16	:	:	PUNCT
iajs-539	57	17	ρ(stx	ρ(stx	VERB
iajs-539	57	18	,	,	PUNCT
iajs-539	57	19	tsy)≤	tsy)≤	ADJ
iajs-539	57	20	max{ϕ1(1/2[ρ(x	max{ϕ1(1/2[ρ(x	PROPN
iajs-539	57	21	,	,	PUNCT
iajs-539	57	22	sy)+	sy)+	VERB
iajs-539	57	23	ρ(y	ρ(y	NOUN
iajs-539	57	24	,	,	PUNCT
iajs-539	57	25	tx	tx	PROPN
iajs-539	57	26	)	)	PUNCT
iajs-539	57	27	]	]	PUNCT
iajs-539	57	28	)	)	PUNCT
iajs-539	57	29	,	,	PUNCT
iajs-539	57	30	ϕ2(ρ(x	ϕ2(ρ(x	PROPN
iajs-539	57	31	,	,	PUNCT
iajs-539	57	32	tx	tx	PROPN
iajs-539	57	33	)	)	PUNCT
iajs-539	57	34	)	)	PUNCT
iajs-539	57	35	,	,	PUNCT
iajs-539	57	36	ϕ3(ρ(y	ϕ3(ρ(y	PROPN
iajs-539	57	37	,	,	PUNCT
iajs-539	57	38	sy	sy	NOUN
iajs-539	57	39	)	)	PUNCT
iajs-539	57	40	)	)	PUNCT
iajs-539	57	41	,	,	PUNCT
iajs-539	57	42	ϕ4(ρ(x	ϕ4(ρ(x	PROPN
iajs-539	57	43	,	,	PUNCT
iajs-539	57	44	y	y	PROPN
iajs-539	57	45	)	)	PUNCT
iajs-539	57	46	)	)	PUNCT
iajs-539	57	47	}	}	PUNCT
iajs-539	57	48	for	for	ADP
iajs-539	57	49	all	all	DET
iajs-539	57	50	x	x	NOUN
iajs-539	57	51	,	,	PUNCT
iajs-539	57	52	y	y	PROPN
iajs-539	57	53	∈	∈	PROPN
iajs-539	57	54	x	x	NOUN
iajs-539	57	55	,	,	PUNCT
iajs-539	57	56	where	where	SCONJ
iajs-539	57	57	ϕi	ϕi	ADP
iajs-539	57	58	∈	∈	PROPN
iajs-539	57	59	φ	φ	X
iajs-539	57	60	(	(	PUNCT
iajs-539	57	61	i	i	NOUN
iajs-539	57	62	=	=	NOUN
iajs-539	57	63	1,2,3,4	1,2,3,4	NUM
iajs-539	57	64	)	)	PUNCT
iajs-539	57	65	..	..	PUNCT
iajs-539	58	1	(	(	PUNCT
iajs-539	58	2	2	2	X
iajs-539	58	3	)	)	PUNCT
iajs-539	58	4	then	then	ADV
iajs-539	58	5	the	the	DET
iajs-539	58	6	sequence	sequence	NOUN
iajs-539	58	7	{	{	PUNCT
iajs-539	58	8	xn	xn	NOUN
iajs-539	58	9	}	}	PUNCT
iajs-539	58	10	defined	define	VERB
iajs-539	58	11	by	by	ADP
iajs-539	58	12	(	(	PUNCT
iajs-539	58	13	1	1	X
iajs-539	58	14	)	)	PUNCT
iajs-539	58	15	is	be	AUX
iajs-539	58	16	a	a	DET
iajs-539	58	17	cauchy	cauchy	ADJ
iajs-539	58	18	sequence	sequence	NOUN
iajs-539	58	19	.	.	PUNCT
iajs-539	59	1	proof	proof	NOUN
iajs-539	59	2	:	:	PUNCT
iajs-539	59	3	let	let	VERB
iajs-539	59	4	x0∈x	x0∈x	PROPN
iajs-539	59	5	and	and	CCONJ
iajs-539	59	6	{	{	PUNCT
iajs-539	59	7	xn	xn	NOUN
iajs-539	59	8	}	}	PUNCT
iajs-539	59	9	be	be	AUX
iajs-539	59	10	a	a	DET
iajs-539	59	11	sequence	sequence	NOUN
iajs-539	59	12	as	as	ADP
iajs-539	59	13	in	in	ADP
iajs-539	59	14	(	(	PUNCT
iajs-539	59	15	1).the	1).the	DET
iajs-539	59	16	proof	proof	NOUN
iajs-539	59	17	includes	include	VERB
iajs-539	59	18	two	two	NUM
iajs-539	59	19	steps	step	NOUN
iajs-539	59	20	:	:	PUNCT
iajs-539	59	21	step	step	NOUN
iajs-539	59	22	1	1	NUM
iajs-539	59	23	:	:	PUNCT
iajs-539	59	24	to	to	PART
iajs-539	59	25	show	show	VERB
iajs-539	59	26	that	that	SCONJ
iajs-539	59	27	limn→∞	limn→∞	PROPN
iajs-539	59	28	ρ(xn	ρ(xn	NUM
iajs-539	59	29	,	,	PUNCT
iajs-539	59	30	xn+1)=0	xn+1)=0	NUM
iajs-539	59	31	,	,	PUNCT
iajs-539	59	32	let	let	VERB
iajs-539	59	33	x1,x2∈{xn	x1,x2∈{xn	NOUN
iajs-539	59	34	}	}	PUNCT
iajs-539	59	35	and	and	CCONJ
iajs-539	59	36	m	m	PROPN
iajs-539	59	37	=	=	ADJ
iajs-539	59	38	max	max	PROPN
iajs-539	59	39	{	{	PUNCT
iajs-539	59	40	ρ(x0,x1	ρ(x0,x1	ADJ
iajs-539	59	41	)	)	PUNCT
iajs-539	59	42	,	,	PUNCT
iajs-539	59	43	ρ(x1,x2	ρ(x1,x2	NOUN
iajs-539	59	44	)	)	PUNCT
iajs-539	59	45	}	}	PUNCT
iajs-539	59	46	.	.	PUNCT
iajs-539	60	1	since	since	SCONJ
iajs-539	60	2	all	all	DET
iajs-539	60	3	ϕ	ϕ	NOUN
iajs-539	60	4	i	i	PRON
iajs-539	60	5	are	be	AUX
iajs-539	60	6	non	non	ADJ
iajs-539	60	7	-	-	ADJ
iajs-539	60	8	decreasing	decrease	VERB
iajs-539	60	9	functions	function	NOUN
iajs-539	60	10	by	by	ADP
iajs-539	60	11	(	(	PUNCT
iajs-539	60	12	2	2	NUM
iajs-539	60	13	)	)	PUNCT
iajs-539	60	14	,	,	PUNCT
iajs-539	60	15	ρ(x2,x3)=ρ(stx0,tsx1	ρ(x2,x3)=ρ(stx0,tsx1	NOUN
iajs-539	60	16	)	)	PUNCT
iajs-539	60	17	≤	≤	PUNCT
iajs-539	60	18	max{ϕ1(1/2[ρ(x0,sx1)+ρ(x1,tx0)]),ϕ2(ρ(x0,tx0)),ϕ3(ρ(x1,sx1)),ϕ4(ρ(x0,x1	max{ϕ1(1/2[ρ(x0,sx1)+ρ(x1,tx0)]),ϕ2(ρ(x0,tx0)),ϕ3(ρ(x1,sx1)),ϕ4(ρ(x0,x1	ADV
iajs-539	60	19	)	)	PUNCT
iajs-539	60	20	)	)	PUNCT
iajs-539	60	21	}	}	PUNCT
iajs-539	60	22	≤	≤	NUM
iajs-539	60	23	max{ϕ1(m	max{ϕ1(m	PROPN
iajs-539	60	24	)	)	PUNCT
iajs-539	60	25	,	,	PUNCT
iajs-539	60	26	ϕ2(m),ϕ3(m),ϕ4(m	ϕ2(m),ϕ3(m),ϕ4(m	NUM
iajs-539	60	27	)	)	PUNCT
iajs-539	60	28	}	}	PUNCT
iajs-539	60	29	≤	≤	NUM
iajs-539	60	30	ϕ	ϕ	X
iajs-539	60	31	(	(	PUNCT
iajs-539	60	32	m	m	PROPN
iajs-539	60	33	)	)	PUNCT
iajs-539	60	34	…	…	PUNCT
iajs-539	60	35	(	(	PUNCT
iajs-539	60	36	3	3	X
iajs-539	60	37	)	)	PUNCT
iajs-539	60	38	where	where	SCONJ
iajs-539	60	39	ϕ	ϕ	PROPN
iajs-539	60	40	∈	∈	PROPN
iajs-539	60	41	φ	φ	PROPN
iajs-539	60	42	.	.	PUNCT
iajs-539	61	1	therefore	therefore	ADV
iajs-539	61	2	,	,	PUNCT
iajs-539	61	3	we	we	PRON
iajs-539	61	4	have	have	VERB
iajs-539	61	5	ρ(x3,x4)=	ρ(x3,x4)=	PROPN
iajs-539	61	6	ρ(stx1,tsx2	ρ(stx1,tsx2	NUM
iajs-539	61	7	)	)	PUNCT
iajs-539	61	8	≤	≤	NUM
iajs-539	61	9	max{ϕ1(1/2[ρ(x1,sx2)+ρ(x2,tx1)]),ϕ2(ρ(x1,tx1)),ϕ3(ρ(x2,sx2)),ϕ4(ρ(x1,x2	max{ϕ1(1/2[ρ(x1,sx2)+ρ(x2,tx1)]),ϕ2(ρ(x1,tx1)),ϕ3(ρ(x2,sx2)),ϕ4(ρ(x1,x2	PROPN
iajs-539	61	10	)	)	PUNCT
iajs-539	61	11	)	)	PUNCT
iajs-539	61	12	}	}	PUNCT
iajs-539	62	1	≤	≤	NUM
iajs-539	62	2	max	max	PROPN
iajs-539	62	3	{	{	PUNCT
iajs-539	62	4	ϕ1(m	ϕ1(m	PROPN
iajs-539	62	5	)	)	PUNCT
iajs-539	62	6	,	,	PUNCT
iajs-539	62	7	ϕ2(ϕ	ϕ2(ϕ	PUNCT
iajs-539	62	8	(	(	PUNCT
iajs-539	62	9	m	m	NOUN
iajs-539	62	10	)	)	PUNCT
iajs-539	62	11	)	)	PUNCT
iajs-539	62	12	,	,	PUNCT
iajs-539	62	13	ϕ3(m),ϕ4(m)}≤	ϕ3(m),ϕ4(m)}≤	PROPN
iajs-539	62	14	ϕ	ϕ	X
iajs-539	62	15	(	(	PUNCT
iajs-539	62	16	m	m	NOUN
iajs-539	62	17	)	)	PUNCT
iajs-539	62	18	,	,	PUNCT
iajs-539	62	19	…	…	PUNCT
iajs-539	62	20	(	(	PUNCT
iajs-539	62	21	4	4	X
iajs-539	62	22	)	)	PUNCT
iajs-539	62	23	314	314	NUM
iajs-539	62	24	|	|	ADV
iajs-539	62	25	mathematics	mathematics	PROPN
iajs-539	62	26	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NOUN
iajs-539	62	27	�	�	NOUN
iajs-539	62	28	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-539	62	29	:	:	PUNCT
iajs-539	62	30	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-539	62	31	©	©	PROPN
iajs-539	62	32	@ü‹26@@öü»€a@i1@‚b«@h2013	@ü‹26@@öü»€a@i1@‚b«@h2013	PROPN
iajs-539	62	33	ibn	ibn	PROPN
iajs-539	62	34	al	al	PROPN
iajs-539	62	35	-	-	PUNCT
iajs-539	62	36	haitham	haitham	PROPN
iajs-539	62	37	jour	jour	X
iajs-539	62	38	.	.	PROPN
iajs-539	63	1	for	for	ADP
iajs-539	63	2	pure	pure	ADJ
iajs-539	63	3	&	&	CCONJ
iajs-539	63	4	appl	appl	PROPN
iajs-539	63	5	.	.	PUNCT
iajs-539	64	1	sci	sci	PROPN
iajs-539	64	2	.	.	PUNCT
iajs-539	64	3	vol	vol	NOUN
iajs-539	64	4	.	.	PROPN
iajs-539	65	1	26	26	NUM
iajs-539	65	2	(	(	PUNCT
iajs-539	65	3	1	1	NUM
iajs-539	65	4	)	)	PUNCT
iajs-539	65	5	2013	2013	NUM
iajs-539	65	6	using	use	VERB
iajs-539	65	7	(	(	PUNCT
iajs-539	65	8	2),(3	2),(3	NOUN
iajs-539	65	9	)	)	PUNCT
iajs-539	65	10	and	and	CCONJ
iajs-539	65	11	(	(	PUNCT
iajs-539	65	12	4),we	4),we	NUM
iajs-539	65	13	get	get	VERB
iajs-539	65	14	ρ(x4,x5)=ρ(stx2,tsx3	ρ(x4,x5)=ρ(stx2,tsx3	NOUN
iajs-539	65	15	)	)	PUNCT
iajs-539	65	16	≤	≤	ADJ
iajs-539	65	17	max{ϕ1(1/2[ρ(x3,sx2)+ρ(x2,tx3)]),ϕ2(ρ(x2,tx2),ϕ3(ρ(x3,sx3),ϕ4(ρ(x2,x3	max{ϕ1(1/2[ρ(x3,sx2)+ρ(x2,tx3)]),ϕ2(ρ(x2,tx2),ϕ3(ρ(x3,sx3),ϕ4(ρ(x2,x3	PROPN
iajs-539	65	18	)	)	PUNCT
iajs-539	65	19	}	}	PUNCT
iajs-539	65	20	≤	≤	NUM
iajs-539	65	21	max	max	PROPN
iajs-539	65	22	{	{	PUNCT
iajs-539	65	23	ϕ1(ϕ	ϕ1(ϕ	PROPN
iajs-539	65	24	(	(	PUNCT
iajs-539	65	25	m	m	NOUN
iajs-539	65	26	)	)	PUNCT
iajs-539	65	27	)	)	PUNCT
iajs-539	65	28	,	,	PUNCT
iajs-539	65	29	ϕ2(ϕ	ϕ2(ϕ	PUNCT
iajs-539	65	30	(	(	PUNCT
iajs-539	65	31	m	m	NOUN
iajs-539	65	32	)	)	PUNCT
iajs-539	65	33	)	)	PUNCT
iajs-539	65	34	,	,	PUNCT
iajs-539	65	35	ϕ3(ϕ	ϕ3(ϕ	PROPN
iajs-539	65	36	(	(	PUNCT
iajs-539	65	37	m	m	NOUN
iajs-539	65	38	)	)	PUNCT
iajs-539	65	39	)	)	PUNCT
iajs-539	65	40	,	,	PUNCT
iajs-539	65	41	ϕ4(ϕ	ϕ4(ϕ	PROPN
iajs-539	65	42	(	(	PUNCT
iajs-539	65	43	m	m	NOUN
iajs-539	65	44	)	)	PUNCT
iajs-539	65	45	)	)	PUNCT
iajs-539	65	46	}	}	PUNCT
iajs-539	65	47	≤	≤	NOUN
iajs-539	65	48	ϕ2(m	ϕ2(m	X
iajs-539	65	49	)	)	PUNCT
iajs-539	65	50	…	…	PUNCT
iajs-539	65	51	(	(	PUNCT
iajs-539	65	52	5	5	NUM
iajs-539	65	53	)	)	PUNCT
iajs-539	65	54	again	again	ADV
iajs-539	65	55	from	from	ADP
iajs-539	65	56	(	(	PUNCT
iajs-539	65	57	2),(4	2),(4	NUM
iajs-539	65	58	)	)	PUNCT
iajs-539	65	59	and	and	CCONJ
iajs-539	65	60	(	(	PUNCT
iajs-539	65	61	5	5	NUM
iajs-539	65	62	)	)	PUNCT
iajs-539	65	63	,	,	PUNCT
iajs-539	65	64	we	we	PRON
iajs-539	65	65	get	get	VERB
iajs-539	65	66	ρ(x5,x6)=ρ(stx3,tsx4	ρ(x5,x6)=ρ(stx3,tsx4	NOUN
iajs-539	65	67	)	)	PUNCT
iajs-539	65	68	≤	≤	NUM
iajs-539	65	69	max{ϕ1(1/2[ρ(x3,sx4)+	max{ϕ1(1/2[ρ(x3,sx4)+	PROPN
iajs-539	65	70	ρ(x4,tx3	ρ(x4,tx3	PROPN
iajs-539	65	71	)	)	PUNCT
iajs-539	65	72	]	]	PUNCT
iajs-539	65	73	)	)	PUNCT
iajs-539	65	74	,	,	PUNCT
iajs-539	65	75	ϕ2	ϕ2	ADV
iajs-539	65	76	(	(	PUNCT
iajs-539	65	77	ρ(x3,tx3	ρ(x3,tx3	PROPN
iajs-539	65	78	)	)	PUNCT
iajs-539	65	79	)	)	PUNCT
iajs-539	65	80	,	,	PUNCT
iajs-539	65	81	ϕ3	ϕ3	PROPN
iajs-539	65	82	(	(	PUNCT
iajs-539	65	83	ρ(x4,sx4	ρ(x4,sx4	NOUN
iajs-539	65	84	)	)	PUNCT
iajs-539	65	85	)	)	PUNCT
iajs-539	65	86	,	,	PUNCT
iajs-539	65	87	ϕ4(ρ(x3,x4	ϕ4(ρ(x3,x4	PROPN
iajs-539	65	88	)	)	PUNCT
iajs-539	65	89	)	)	PUNCT
iajs-539	65	90	}	}	PUNCT
iajs-539	65	91	≤	≤	NUM
iajs-539	65	92	max	max	PROPN
iajs-539	65	93	{	{	PUNCT
iajs-539	65	94	ϕ1(ϕ	ϕ1(ϕ	PROPN
iajs-539	65	95	(	(	PUNCT
iajs-539	65	96	m	m	NOUN
iajs-539	65	97	)	)	PUNCT
iajs-539	65	98	)	)	PUNCT
iajs-539	65	99	,	,	PUNCT
iajs-539	65	100	ϕ2(ϕ	ϕ2(ϕ	NUM
iajs-539	65	101	2(m	2(m	NUM
iajs-539	65	102	)	)	PUNCT
iajs-539	65	103	)	)	PUNCT
iajs-539	65	104	,	,	PUNCT
iajs-539	65	105	ϕ3(ϕ	ϕ3(ϕ	PROPN
iajs-539	65	106	(	(	PUNCT
iajs-539	65	107	m	m	NOUN
iajs-539	65	108	)	)	PUNCT
iajs-539	65	109	)	)	PUNCT
iajs-539	65	110	,	,	PUNCT
iajs-539	65	111	ϕ4(ϕ	ϕ4(ϕ	PROPN
iajs-539	65	112	(	(	PUNCT
iajs-539	65	113	m))}≤	m))}≤	X
iajs-539	65	114	ϕ	ϕ	PROPN
iajs-539	65	115	2(m	2(m	NUM
iajs-539	65	116	)	)	PUNCT
iajs-539	65	117	,	,	PUNCT
iajs-539	65	118	...	...	PUNCT
iajs-539	65	119	(	(	PUNCT
iajs-539	65	120	6	6	NUM
iajs-539	65	121	)	)	PUNCT
iajs-539	65	122	in	in	ADP
iajs-539	65	123	general	general	ADJ
iajs-539	65	124	,	,	PUNCT
iajs-539	65	125	by	by	ADP
iajs-539	65	126	induction	induction	NOUN
iajs-539	65	127	,	,	PUNCT
iajs-539	65	128	we	we	PRON
iajs-539	65	129	get	get	VERB
iajs-539	65	130	ρ(xn	ρ(xn	NUM
iajs-539	65	131	,	,	PUNCT
iajs-539	65	132	xn+1)≤	xn+1)≤	PUNCT
iajs-539	65	133	ϕ[n/2](m	ϕ[n/2](m	NUM
iajs-539	65	134	)	)	PUNCT
iajs-539	65	135	for	for	ADP
iajs-539	65	136	n	n	X
iajs-539	65	137	≥	≥	NUM
iajs-539	65	138	2	2	NUM
iajs-539	65	139	,	,	PUNCT
iajs-539	65	140	where	where	SCONJ
iajs-539	65	141	[	[	X
iajs-539	65	142	n/2	n/2	X
iajs-539	65	143	]	]	PUNCT
iajs-539	65	144	stands	stand	VERB
iajs-539	65	145	for	for	ADP
iajs-539	65	146	the	the	DET
iajs-539	65	147	greatest	great	ADJ
iajs-539	65	148	integer	integer	NOUN
iajs-539	65	149	not	not	PART
iajs-539	65	150	exceeding	exceed	VERB
iajs-539	65	151	n/2	n/2	NOUN
iajs-539	65	152	.	.	PUNCT
iajs-539	66	1	since	since	SCONJ
iajs-539	66	2	ϕ	ϕ	PROPN
iajs-539	66	3	∈	∈	PROPN
iajs-539	66	4	φ	φ	PROPN
iajs-539	66	5	,	,	PUNCT
iajs-539	66	6	by	by	ADP
iajs-539	66	7	lemma2.2	lemma2.2	NOUN
iajs-539	66	8	it	it	PRON
iajs-539	66	9	follows	follow	VERB
iajs-539	66	10	that	that	SCONJ
iajs-539	66	11	ϕ	ϕ	PROPN
iajs-539	66	12	n(m	n(m	PROPN
iajs-539	66	13	)	)	PUNCT
iajs-539	66	14	→	→	SYM
iajs-539	66	15	0	0	NUM
iajs-539	66	16	as	as	ADP
iajs-539	66	17	n	n	NOUN
iajs-539	66	18	→	→	SYM
iajs-539	66	19	+	+	NOUN
iajs-539	66	20	∞	∞	PROPN
iajs-539	66	21	for	for	ADP
iajs-539	66	22	every	every	DET
iajs-539	66	23	m	m	NOUN
iajs-539	66	24	>	>	X
iajs-539	66	25	0	0	NUM
iajs-539	66	26	.	.	PUNCT
iajs-539	67	1	thus	thus	ADV
iajs-539	67	2	,	,	PUNCT
iajs-539	67	3	we	we	PRON
iajs-539	67	4	obtain	obtain	VERB
iajs-539	67	5	ρ(xn	ρ(xn	NUM
iajs-539	67	6	,	,	PUNCT
iajs-539	67	7	xn+1)→0	xn+1)→0	VERB
iajs-539	67	8	as	as	ADP
iajs-539	67	9	n	n	X
iajs-539	67	10	→∞.	→∞.	NUM
iajs-539	67	11	…	…	PUNCT
iajs-539	67	12	(	(	PUNCT
iajs-539	67	13	7	7	X
iajs-539	67	14	)	)	PUNCT
iajs-539	67	15	step2	step2	PROPN
iajs-539	67	16	:	:	PUNCT
iajs-539	67	17	suppose	suppose	VERB
iajs-539	67	18	that	that	SCONJ
iajs-539	67	19	proposition	proposition	NOUN
iajs-539	67	20	is	be	AUX
iajs-539	67	21	not	not	PART
iajs-539	67	22	true	true	ADJ
iajs-539	67	23	.	.	PUNCT
iajs-539	68	1	then	then	ADV
iajs-539	68	2	there	there	PRON
iajs-539	68	3	exists	exist	VERB
iajs-539	68	4	an	an	DET
iajs-539	68	5	ε	ε	PROPN
iajs-539	68	6	>	>	X
iajs-539	68	7	0	0	NUM
iajs-539	68	8	such	such	ADJ
iajs-539	68	9	that	that	PRON
iajs-539	68	10	for	for	ADP
iajs-539	68	11	each	each	DET
iajs-539	68	12	i∈	i∈	NOUN
iajs-539	68	13	n	n	CCONJ
iajs-539	68	14	,	,	PUNCT
iajs-539	68	15	there	there	PRON
iajs-539	68	16	exist	exist	VERB
iajs-539	68	17	positive	positive	ADJ
iajs-539	68	18	integers	integer	NOUN
iajs-539	68	19	ni	ni	PROPN
iajs-539	68	20	,	,	PUNCT
iajs-539	68	21	mi	mi	PROPN
iajs-539	68	22	,	,	PUNCT
iajs-539	68	23	with	with	SCONJ
iajs-539	68	24	i	i	PROPN
iajs-539	68	25	≤	≤	X
iajs-539	68	26	ni	ni	PROPN
iajs-539	68	27	<	<	X
iajs-539	68	28	mi	mi	PROPN
iajs-539	68	29	,	,	PUNCT
iajs-539	68	30	satisfying	satisfying	ADJ
iajs-539	68	31	ε	ε	PROPN
iajs-539	68	32	≤	≤	PROPN
iajs-539	68	33	ρ(xni	ρ(xni	PROPN
iajs-539	68	34	,	,	PUNCT
iajs-539	68	35	xmi	xmi	PROPN
iajs-539	68	36	)	)	PUNCT
iajs-539	68	37	≤	≤	NUM
iajs-539	68	38	ρ(xni	ρ(xni	PROPN
iajs-539	68	39	,	,	PUNCT
iajs-539	68	40	xmi+1	xmi+1	PROPN
iajs-539	68	41	)	)	PUNCT
iajs-539	68	42	ρ(xni	ρ(xni	PROPN
iajs-539	68	43	,	,	PUNCT
iajs-539	68	44	xmi−1	xmi−1	PROPN
iajs-539	68	45	)	)	PUNCT
iajs-539	68	46	<	<	X
iajs-539	68	47	ε	ε	PROPN
iajs-539	68	48	for	for	ADP
iajs-539	68	49	i	i	PROPN
iajs-539	68	50	=	=	SYM
iajs-539	68	51	1,2	1,2	NUM
iajs-539	68	52	,	,	PUNCT
iajs-539	68	53	..	..	PUNCT
iajs-539	68	54	...	...	PUNCT
iajs-539	69	1	(	(	PUNCT
iajs-539	69	2	8)	8)	NUM
iajs-539	69	3	set	set	NOUN
iajs-539	69	4	,	,	PUNCT
iajs-539	69	5	εi=	εi=	PROPN
iajs-539	69	6	ρ(xni	ρ(xni	PROPN
iajs-539	69	7	,	,	PUNCT
iajs-539	69	8	xmi+1	xmi+1	PROPN
iajs-539	69	9	)	)	PUNCT
iajs-539	69	10	ρi	ρi	NOUN
iajs-539	69	11	=	=	SYM
iajs-539	69	12	ρ(xi	ρ(xi	PROPN
iajs-539	69	13	,	,	PUNCT
iajs-539	69	14	xi+1)for	xi+1)for	PUNCT
iajs-539	70	1	i	i	NOUN
iajs-539	70	2	=	=	SYM
iajs-539	70	3	1,2	1,2	NUM
iajs-539	70	4	,	,	PUNCT
iajs-539	70	5	...	...	PUNCT
iajs-539	70	6	,	,	PUNCT
iajs-539	70	7	,	,	PUNCT
iajs-539	70	8	.	.	PUNCT
iajs-539	71	1	(	(	PUNCT
iajs-539	71	2	9	9	NUM
iajs-539	71	3	)	)	PUNCT
iajs-539	71	4	then	then	ADV
iajs-539	71	5	we	we	PRON
iajs-539	71	6	have	have	VERB
iajs-539	71	7	ε	ε	PROPN
iajs-539	71	8	≤	≤	NUM
iajs-539	71	9	εi	εi	VERB
iajs-539	71	10	=	=	SYM
iajs-539	71	11	ρ(xni	ρ(xni	PROPN
iajs-539	71	12	,	,	PUNCT
iajs-539	71	13	xmi+1	xmi+1	PROPN
iajs-539	71	14	)	)	PUNCT
iajs-539	71	15	≤	≤	NUM
iajs-539	71	16	ρ(xni	ρ(xni	PROPN
iajs-539	71	17	,	,	PUNCT
iajs-539	71	18	xmi−1)+	xmi−1)+	PROPN
iajs-539	71	19	ρ(xmi−1,xmi	ρ(xmi−1,xmi	NUM
iajs-539	71	20	)	)	PUNCT
iajs-539	72	1	+	+	X
iajs-539	73	1	ρ(xmi	ρ(xmi	X
iajs-539	73	2	,	,	PUNCT
iajs-539	73	3	xmi−1	xmi−1	PROPN
iajs-539	73	4	)	)	PUNCT
iajs-539	73	5	<	<	X
iajs-539	73	6	ε+ρmi−1+ρmi	ε+ρmi−1+ρmi	AUX
iajs-539	73	7	,	,	PUNCT
iajs-539	73	8	i=	i=	PROPN
iajs-539	73	9	1,2	1,2	NUM
iajs-539	73	10	,	,	PUNCT
iajs-539	73	11	...	...	PUNCT
iajs-539	73	12	...	...	PUNCT
iajs-539	74	1	(	(	PUNCT
iajs-539	74	2	10	10	X
iajs-539	74	3	)	)	PUNCT
iajs-539	74	4	taking	take	VERB
iajs-539	74	5	the	the	DET
iajs-539	74	6	limit	limit	NOUN
iajs-539	74	7	as	as	ADP
iajs-539	74	8	i→+∞	i→+∞	PROPN
iajs-539	74	9	,	,	PUNCT
iajs-539	74	10	we	we	PRON
iajs-539	74	11	get	get	VERB
iajs-539	74	12	lim	lim	PROPN
iajs-539	74	13	εi	εi	VERB
iajs-539	74	14	=	=	SYM
iajs-539	74	15	ε	ε	PROPN
iajs-539	74	16	.	.	PROPN
iajs-539	75	1	on	on	ADP
iajs-539	75	2	the	the	DET
iajs-539	75	3	other	other	ADJ
iajs-539	75	4	hand	hand	NOUN
iajs-539	75	5	,	,	PUNCT
iajs-539	75	6	by	by	ADP
iajs-539	75	7	(	(	PUNCT
iajs-539	75	8	2	2	NUM
iajs-539	75	9	)	)	PUNCT
iajs-539	75	10	,	,	PUNCT
iajs-539	75	11	εi	εi	VERB
iajs-539	75	12	=	=	SYM
iajs-539	75	13	ρ(xni	ρ(xni	PROPN
iajs-539	75	14	,	,	PUNCT
iajs-539	75	15	xmi	xmi	PROPN
iajs-539	75	16	)	)	PUNCT
iajs-539	75	17	≤	≤	NUM
iajs-539	75	18	ρ(xni	ρ(xni	PROPN
iajs-539	75	19	,	,	PUNCT
iajs-539	75	20	xni+1)+	xni+1)+	PROPN
iajs-539	76	1	ρ(xni+1,xni+2	ρ(xni+1,xni+2	PROPN
iajs-539	76	2	)	)	PUNCT
iajs-539	77	1	+	+	CCONJ
iajs-539	78	1	ρ(xni+2	ρ(xni+2	NUM
iajs-539	78	2	,	,	PUNCT
iajs-539	78	3	xmi+2)+	xmi+2)+	PROPN
iajs-539	78	4	ρ(xmi+2,xmi+1	ρ(xmi+2,xmi+1	PROPN
iajs-539	78	5	)	)	PUNCT
iajs-539	79	1	+	+	NUM
iajs-539	79	2	ρ(xmi+1,xmi	ρ(xmi+1,xmi	X
iajs-539	79	3	)	)	PUNCT
iajs-539	80	1	=	=	PUNCT
iajs-539	81	1	ρni+ρni+1	ρni+ρni+1	PROPN
iajs-539	81	2	+	+	NOUN
iajs-539	81	3	ρ(xni+2	ρ(xni+2	NUM
iajs-539	81	4	,	,	PUNCT
iajs-539	81	5	xmi+2)+ρmi+1+ρmi	xmi+2)+ρmi+1+ρmi	PROPN
iajs-539	81	6	,	,	PUNCT
iajs-539	81	7	i=	i=	PROPN
iajs-539	81	8	1,2	1,2	NUM
iajs-539	81	9	,	,	PUNCT
iajs-539	81	10	...	...	PUNCT
iajs-539	81	11	...	...	PUNCT
iajs-539	82	1	(	(	PUNCT
iajs-539	82	2	11	11	X
iajs-539	82	3	)	)	PUNCT
iajs-539	82	4	we	we	PRON
iajs-539	82	5	will	will	AUX
iajs-539	82	6	now	now	ADV
iajs-539	82	7	analyze	analyze	VERB
iajs-539	82	8	the	the	DET
iajs-539	82	9	term	term	NOUN
iajs-539	82	10	ρ(xni+2	ρ(xni+2	X
iajs-539	82	11	,	,	PUNCT
iajs-539	82	12	xmi+2	xmi+2	PROPN
iajs-539	82	13	)	)	PUNCT
iajs-539	82	14	ρ(xni+2	ρ(xni+2	NUM
iajs-539	82	15	,	,	PUNCT
iajs-539	82	16	xmi+2)=	xmi+2)=	PROPN
iajs-539	82	17	ρ(stxni	ρ(stxni	NOUN
iajs-539	82	18	,	,	PUNCT
iajs-539	82	19	tsxmi	tsxmi	NOUN
iajs-539	82	20	)	)	PUNCT
iajs-539	82	21	≤	≤	NUM
iajs-539	82	22	max{ϕ1(1/2[ρ(xni	max{ϕ1(1/2[ρ(xni	NOUN
iajs-539	82	23	,	,	PUNCT
iajs-539	82	24	sxmi)+	sxmi)+	NOUN
iajs-539	82	25	ρ(xmi	ρ(xmi	NOUN
iajs-539	82	26	,	,	PUNCT
iajs-539	82	27	txni	txni	NOUN
iajs-539	82	28	)	)	PUNCT
iajs-539	82	29	]	]	PUNCT
iajs-539	82	30	)	)	PUNCT
iajs-539	82	31	,	,	PUNCT
iajs-539	82	32	ϕ2	ϕ2	ADV
iajs-539	82	33	(	(	PUNCT
iajs-539	82	34	ρ(xni	ρ(xni	NOUN
iajs-539	82	35	,	,	PUNCT
iajs-539	82	36	txni	txni	NOUN
iajs-539	82	37	)	)	PUNCT
iajs-539	82	38	)	)	PUNCT
iajs-539	82	39	,	,	PUNCT
iajs-539	82	40	ϕ3	ϕ3	PROPN
iajs-539	82	41	(	(	PUNCT
iajs-539	82	42	ρ(xmi	ρ(xmi	PROPN
iajs-539	82	43	,	,	PUNCT
iajs-539	82	44	sxmi	sxmi	NOUN
iajs-539	82	45	)	)	PUNCT
iajs-539	82	46	)	)	PUNCT
iajs-539	82	47	,	,	PUNCT
iajs-539	82	48	ϕ4	ϕ4	PROPN
iajs-539	82	49	(	(	PUNCT
iajs-539	82	50	ρ(xni	ρ(xni	PROPN
iajs-539	82	51	,	,	PUNCT
iajs-539	82	52	xmi	xmi	PROPN
iajs-539	82	53	)	)	PUNCT
iajs-539	82	54	)	)	PUNCT
iajs-539	82	55	}	}	PUNCT
iajs-539	82	56	315	315	NUM
iajs-539	82	57	|	|	ADV
iajs-539	82	58	mathematics	mathematics	PROPN
iajs-539	82	59	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NOUN
iajs-539	82	60	�	�	NOUN
iajs-539	82	61	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-539	82	62	:	:	PUNCT
iajs-539	82	63	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-539	83	1	©	©	PROPN
iajs-539	83	2	@ü‹26@@öü»€a@i1@‚b«@h2013	@ü‹26@@öü»€a@i1@‚b«@h2013	PROPN
iajs-539	83	3	ibn	ibn	PROPN
iajs-539	83	4	al	al	PROPN
iajs-539	83	5	-	-	PUNCT
iajs-539	83	6	haitham	haitham	PROPN
iajs-539	83	7	jour	jour	X
iajs-539	83	8	.	.	PROPN
iajs-539	84	1	for	for	ADP
iajs-539	84	2	pure	pure	ADJ
iajs-539	84	3	&	&	CCONJ
iajs-539	84	4	appl	appl	PROPN
iajs-539	84	5	.	.	PUNCT
iajs-539	85	1	sci	sci	PROPN
iajs-539	85	2	.	.	PUNCT
iajs-539	85	3	vol	vol	NOUN
iajs-539	85	4	.	.	PROPN
iajs-539	86	1	26	26	NUM
iajs-539	86	2	(	(	PUNCT
iajs-539	86	3	1	1	NUM
iajs-539	86	4	)	)	PUNCT
iajs-539	86	5	2013	2013	NUM
iajs-539	86	6	≤	≤	NUM
iajs-539	86	7	max{ϕ1(1/2[ρ(xni	max{ϕ1(1/2[ρ(xni	NOUN
iajs-539	86	8	,	,	PUNCT
iajs-539	86	9	xmi+1)+	xmi+1)+	PROPN
iajs-539	86	10	ρ(xmi	ρ(xmi	PROPN
iajs-539	86	11	,	,	PUNCT
iajs-539	86	12	xni+1)]),ϕ2(ρ(xni	xni+1)]),ϕ2(ρ(xni	NOUN
iajs-539	86	13	,	,	PUNCT
iajs-539	86	14	xni+1)),ϕ3(ρ(xmi	xni+1)),ϕ3(ρ(xmi	ADV
iajs-539	86	15	,	,	PUNCT
iajs-539	86	16	xmi+1	xmi+1	PROPN
iajs-539	86	17	)	)	PUNCT
iajs-539	86	18	)	)	PUNCT
iajs-539	86	19	,	,	PUNCT
iajs-539	86	20	ϕ4	ϕ4	PROPN
iajs-539	86	21	(	(	PUNCT
iajs-539	86	22	ρ(xni	ρ(xni	PROPN
iajs-539	86	23	,	,	PUNCT
iajs-539	86	24	xmi	xmi	PROPN
iajs-539	86	25	)	)	PUNCT
iajs-539	86	26	)	)	PUNCT
iajs-539	86	27	}	}	PUNCT
iajs-539	86	28	≤	≤	NUM
iajs-539	86	29	max{ϕ1(1/2[εi	max{ϕ1(1/2[εi	NOUN
iajs-539	86	30	+	+	CCONJ
iajs-539	86	31	(	(	PUNCT
iajs-539	86	32	εi	εi	VERB
iajs-539	86	33	+	+	NOUN
iajs-539	86	34	ρni-1+ρni	ρni-1+ρni	NOUN
iajs-539	86	35	)	)	PUNCT
iajs-539	86	36	]	]	PUNCT
iajs-539	86	37	)	)	PUNCT
iajs-539	86	38	,	,	PUNCT
iajs-539	86	39	ϕ2(ρni	ϕ2(ρni	NOUN
iajs-539	86	40	)	)	PUNCT
iajs-539	86	41	,	,	PUNCT
iajs-539	86	42	ϕ3(ρmi	ϕ3(ρmi	NOUN
iajs-539	86	43	)	)	PUNCT
iajs-539	86	44	,	,	PUNCT
iajs-539	86	45	ϕ4(εi	ϕ4(εi	PROPN
iajs-539	86	46	)	)	PUNCT
iajs-539	86	47	}	}	PUNCT
iajs-539	86	48	≤	≤	NUM
iajs-539	86	49	ϕ	ϕ	NOUN
iajs-539	86	50	(	(	PUNCT
iajs-539	86	51	εi	εi	VERB
iajs-539	86	52	+	+	NOUN
iajs-539	86	53	ρni-1	ρni-1	X
iajs-539	86	54	+	+	CCONJ
iajs-539	86	55	ρmi+	ρmi+	PROPN
iajs-539	86	56	ρni)=	ρni)=	PROPN
iajs-539	86	57	ϕ	ϕ	PROPN
iajs-539	86	58	(	(	PUNCT
iajs-539	86	59	ki	ki	PROPN
iajs-539	86	60	)	)	PUNCT
iajs-539	86	61	…	…	PUNCT
iajs-539	86	62	(	(	PUNCT
iajs-539	86	63	12	12	NUM
iajs-539	86	64	)	)	PUNCT
iajs-539	86	65	where	where	SCONJ
iajs-539	86	66	ki	ki	PROPN
iajs-539	86	67	=	=	PUNCT
iajs-539	86	68	εi	εi	VERB
iajs-539	86	69	+	+	ADV
iajs-539	86	70	ρni-1	ρni-1	X
iajs-539	86	71	+	+	ADJ
iajs-539	86	72	ρmi+	ρmi+	PROPN
iajs-539	86	73	ρni	ρni	PROPN
iajs-539	86	74	.	.	PUNCT
iajs-539	87	1	substituting	substitute	VERB
iajs-539	87	2	(	(	PUNCT
iajs-539	87	3	11	11	NUM
iajs-539	87	4	)	)	PUNCT
iajs-539	87	5	into	into	ADP
iajs-539	87	6	(	(	PUNCT
iajs-539	87	7	10	10	NUM
iajs-539	87	8	)	)	PUNCT
iajs-539	87	9	,	,	PUNCT
iajs-539	87	10	taking	take	VERB
iajs-539	87	11	the	the	DET
iajs-539	87	12	limit	limit	NOUN
iajs-539	87	13	as	as	ADP
iajs-539	87	14	i→+∞	i→+∞	PROPN
iajs-539	87	15	,	,	PUNCT
iajs-539	87	16	and	and	CCONJ
iajs-539	87	17	using	use	VERB
iajs-539	87	18	the	the	DET
iajs-539	87	19	right	right	ADJ
iajs-539	87	20	continuity	continuity	NOUN
iajs-539	87	21	of	of	ADP
iajs-539	87	22	ϕ	ϕ	NOUN
iajs-539	87	23	,	,	PUNCT
iajs-539	87	24	we	we	PRON
iajs-539	87	25	get	get	VERB
iajs-539	87	26	ε	ε	PROPN
iajs-539	87	27	=	=	SYM
iajs-539	87	28	limi→∞εi	limi→∞εi	PROPN
iajs-539	87	29	≤	≤	NUM
iajs-539	87	30	limki→ε+	limki→ε+	VERB
iajs-539	87	31	ϕ(ki)=	ϕ(ki)=	PROPN
iajs-539	87	32	ϕ	ϕ	PROPN
iajs-539	87	33	(	(	PUNCT
iajs-539	87	34	ε	ε	PROPN
iajs-539	87	35	)	)	PUNCT
iajs-539	87	36	<	<	X
iajs-539	87	37	ε	ε	PROPN
iajs-539	87	38	,	,	PUNCT
iajs-539	87	39	…	…	PUNCT
iajs-539	87	40	(	(	PUNCT
iajs-539	87	41	13	13	NUM
iajs-539	87	42	)	)	PUNCT
iajs-539	87	43	which	which	PRON
iajs-539	87	44	is	be	AUX
iajs-539	87	45	a	a	DET
iajs-539	87	46	contradiction	contradiction	NOUN
iajs-539	87	47	.	.	PUNCT
iajs-539	88	1	limn→∞	limn→∞	PROPN
iajs-539	88	2	ρ(xn	ρ(xn	NUM
iajs-539	88	3	,	,	PUNCT
iajs-539	88	4	xm	xm	PROPN
iajs-539	88	5	)	)	PUNCT
iajs-539	88	6	=	=	SYM
iajs-539	88	7	0	0	X
iajs-539	88	8	.	.	PUNCT
iajs-539	89	1	thus	thus	ADV
iajs-539	89	2	{	{	PUNCT
iajs-539	89	3	xn	xn	X
iajs-539	89	4	}	}	PUNCT
iajs-539	89	5	is	be	AUX
iajs-539	89	6	a	a	DET
iajs-539	89	7	cauchy	cauchy	ADJ
iajs-539	89	8	sequence	sequence	NOUN
iajs-539	89	9	.	.	PUNCT
iajs-539	90	1	now	now	ADV
iajs-539	90	2	we	we	PRON
iajs-539	90	3	prove	prove	VERB
iajs-539	90	4	our	our	PRON
iajs-539	90	5	results	result	NOUN
iajs-539	90	6	:	:	PUNCT
iajs-539	90	7	theorem	theorem	VERB
iajs-539	90	8	2.4	2.4	NUM
iajs-539	90	9	:	:	PUNCT
iajs-539	90	10	let	let	VERB
iajs-539	90	11	(	(	PUNCT
iajs-539	90	12	x	x	NOUN
iajs-539	90	13	,	,	PUNCT
iajs-539	90	14	ρ	ρ	PROPN
iajs-539	90	15	)	)	PUNCT
iajs-539	90	16	be	be	VERB
iajs-539	90	17	a	a	DET
iajs-539	90	18	g	g	NOUN
iajs-539	90	19	-	-	PUNCT
iajs-539	90	20	metric	metric	ADJ
iajs-539	90	21	space	space	NOUN
iajs-539	90	22	.	.	PUNCT
iajs-539	91	1	let	let	VERB
iajs-539	91	2	s	s	PRON
iajs-539	91	3	and	and	CCONJ
iajs-539	91	4	t	t	PROPN
iajs-539	91	5	be	be	AUX
iajs-539	91	6	self	self	NOUN
iajs-539	91	7	mappings	mapping	NOUN
iajs-539	91	8	on	on	ADP
iajs-539	91	9	x	x	PUNCT
iajs-539	91	10	satisfying	satisfy	VERB
iajs-539	91	11	(	(	PUNCT
iajs-539	91	12	2	2	NUM
iajs-539	91	13	)	)	PUNCT
iajs-539	91	14	of	of	ADP
iajs-539	91	15	proposition	proposition	NOUN
iajs-539	91	16	2.3	2.3	NUM
iajs-539	91	17	if	if	SCONJ
iajs-539	91	18	s	s	PRON
iajs-539	91	19	or	or	CCONJ
iajs-539	91	20	t	t	PROPN
iajs-539	91	21	is	be	AUX
iajs-539	91	22	continuous	continuous	ADJ
iajs-539	91	23	and	and	CCONJ
iajs-539	91	24	x	x	VERB
iajs-539	91	25	is	be	AUX
iajs-539	91	26	st	st	NOUN
iajs-539	91	27	-	-	PUNCT
iajs-539	91	28	orbitally	orbitally	ADV
iajs-539	91	29	complete	complete	ADJ
iajs-539	91	30	,	,	PUNCT
iajs-539	91	31	then	then	ADV
iajs-539	91	32	s	s	PRON
iajs-539	91	33	and	and	CCONJ
iajs-539	91	34	t	t	PROPN
iajs-539	91	35	have	have	VERB
iajs-539	91	36	a	a	DET
iajs-539	91	37	unique	unique	ADJ
iajs-539	91	38	common	common	ADJ
iajs-539	91	39	fixed	fix	VERB
iajs-539	91	40	point	point	NOUN
iajs-539	91	41	.	.	PUNCT
iajs-539	92	1	proof	proof	NOUN
iajs-539	92	2	:	:	PUNCT
iajs-539	92	3	let	let	VERB
iajs-539	92	4	x0	x0	PROPN
iajs-539	92	5	∈	∈	PROPN
iajs-539	92	6	x	x	PUNCT
iajs-539	92	7	and	and	CCONJ
iajs-539	92	8	define	define	VERB
iajs-539	92	9	{	{	PUNCT
iajs-539	92	10	xn	xn	NOUN
iajs-539	92	11	}	}	PUNCT
iajs-539	92	12	as	as	ADP
iajs-539	92	13	in	in	ADP
iajs-539	92	14	(	(	PUNCT
iajs-539	92	15	1	1	NUM
iajs-539	92	16	)	)	PUNCT
iajs-539	92	17	.	.	PUNCT
iajs-539	93	1	then	then	ADV
iajs-539	93	2	,	,	PUNCT
iajs-539	93	3	by	by	ADP
iajs-539	93	4	proposition	proposition	NOUN
iajs-539	93	5	2.3	2.3	NUM
iajs-539	93	6	,	,	PUNCT
iajs-539	93	7	it	it	PRON
iajs-539	93	8	follows	follow	VERB
iajs-539	93	9	that	that	SCONJ
iajs-539	93	10	{	{	PUNCT
iajs-539	93	11	xn	xn	X
iajs-539	93	12	}	}	PUNCT
iajs-539	93	13	is	be	AUX
iajs-539	93	14	a	a	DET
iajs-539	93	15	cauchy	cauchy	ADJ
iajs-539	93	16	sequence	sequence	NOUN
iajs-539	93	17	.	.	PUNCT
iajs-539	94	1	since	since	SCONJ
iajs-539	94	2	x	x	PRON
iajs-539	94	3	is	be	AUX
iajs-539	94	4	a	a	DET
iajs-539	94	5	st	st	NOUN
iajs-539	94	6	-	-	PUNCT
iajs-539	94	7	orbitally	orbitally	ADV
iajs-539	94	8	complete	complete	ADJ
iajs-539	94	9	g	g	NOUN
iajs-539	94	10	-	-	PUNCT
iajs-539	94	11	metric	metric	ADJ
iajs-539	94	12	space	space	NOUN
iajs-539	94	13	,	,	PUNCT
iajs-539	94	14	{	{	PUNCT
iajs-539	94	15	xn	xn	X
iajs-539	94	16	}	}	PUNCT
iajs-539	94	17	is	be	AUX
iajs-539	94	18	convergent	convergent	ADJ
iajs-539	94	19	to	to	ADP
iajs-539	94	20	a	a	DET
iajs-539	94	21	limit	limit	NOUN
iajs-539	94	22	u	u	NOUN
iajs-539	94	23	in	in	ADP
iajs-539	94	24	x.	x.	NOUN
iajs-539	94	25	suppose	suppose	VERB
iajs-539	94	26	that	that	SCONJ
iajs-539	94	27	s	s	VERB
iajs-539	94	28	is	be	AUX
iajs-539	94	29	continuous	continuous	ADJ
iajs-539	94	30	.	.	PUNCT
iajs-539	95	1	then	then	ADV
iajs-539	95	2	u	u	X
iajs-539	95	3	=	=	PROPN
iajs-539	95	4	limn→∞	limn→∞	PROPN
iajs-539	95	5	x2n+2	x2n+2	PUNCT
iajs-539	96	1	=	=	NOUN
iajs-539	96	2	limn→∞sx2n+1	limn→∞sx2n+1	PROPN
iajs-539	96	3	=	=	SYM
iajs-539	96	4	s	s	PART
iajs-539	96	5	limn→∞x2n+1=	limn→∞x2n+1=	PROPN
iajs-539	96	6	su	su	PROPN
iajs-539	96	7	.	.	PROPN
iajs-539	96	8	…	…	PUNCT
iajs-539	96	9	(	(	PUNCT
iajs-539	96	10	14	14	NUM
iajs-539	96	11	)	)	PUNCT
iajs-539	96	12	this	this	PRON
iajs-539	96	13	implies	imply	VERB
iajs-539	96	14	that	that	SCONJ
iajs-539	96	15	u	u	NOUN
iajs-539	96	16	is	be	AUX
iajs-539	96	17	a	a	DET
iajs-539	96	18	fixed	fix	VERB
iajs-539	96	19	point	point	NOUN
iajs-539	96	20	of	of	ADP
iajs-539	96	21	s.	s.	PROPN
iajs-539	96	22	from	from	ADP
iajs-539	96	23	(	(	PUNCT
iajs-539	96	24	2	2	NUM
iajs-539	96	25	)	)	PUNCT
iajs-539	96	26	,	,	PUNCT
iajs-539	96	27	we	we	PRON
iajs-539	96	28	get	get	VERB
iajs-539	96	29	ρ(u	ρ(u	PROPN
iajs-539	96	30	,	,	PUNCT
iajs-539	96	31	su	su	PROPN
iajs-539	96	32	)	)	PUNCT
iajs-539	96	33	=	=	SYM
iajs-539	96	34	0	0	NUM
iajs-539	96	35	and	and	CCONJ
iajs-539	96	36	ρ(u	ρ(u	PROPN
iajs-539	96	37	,	,	PUNCT
iajs-539	96	38	tu)=	tu)=	PROPN
iajs-539	96	39	ρ(u	ρ(u	PROPN
iajs-539	96	40	,	,	PUNCT
iajs-539	96	41	tsu	tsu	PROPN
iajs-539	96	42	)	)	PUNCT
iajs-539	96	43	≤	≤	NOUN
iajs-539	96	44	ρ(u	ρ(u	PROPN
iajs-539	96	45	,	,	PUNCT
iajs-539	96	46	x2n+1)+	x2n+1)+	PROPN
iajs-539	96	47	ρ(x2n+1,x2n+2)+	ρ(x2n+1,x2n+2)+	PROPN
iajs-539	96	48	ρ(stx2n	ρ(stx2n	PROPN
iajs-539	96	49	,	,	PUNCT
iajs-539	96	50	tsu	tsu	NOUN
iajs-539	96	51	)	)	PUNCT
iajs-539	96	52	≤	≤	NOUN
iajs-539	97	1	ρ(u	ρ(u	PROPN
iajs-539	97	2	,	,	PUNCT
iajs-539	97	3	x2n+1)+ρ(x2n+1,x2n+2)+	x2n+1)+ρ(x2n+1,x2n+2)+	PROPN
iajs-539	97	4	max{ϕ1(1/2[ρ(x2n	max{ϕ1(1/2[ρ(x2n	PROPN
iajs-539	97	5	,	,	PUNCT
iajs-539	97	6	su)+ρ(u	su)+ρ(u	NOUN
iajs-539	97	7	,	,	PUNCT
iajs-539	97	8	tx2n	tx2n	NOUN
iajs-539	97	9	)	)	PUNCT
iajs-539	97	10	]	]	PUNCT
iajs-539	97	11	)	)	PUNCT
iajs-539	97	12	,	,	PUNCT
iajs-539	97	13	ϕ2(ρ(x2n	ϕ2(ρ(x2n	NOUN
iajs-539	97	14	,	,	PUNCT
iajs-539	97	15	tx2n)),ϕ3	tx2n)),ϕ3	PROPN
iajs-539	97	16	(	(	PUNCT
iajs-539	97	17	ρ(u	ρ(u	PROPN
iajs-539	97	18	,	,	PUNCT
iajs-539	97	19	su)),ϕ4	su)),ϕ4	PROPN
iajs-539	97	20	(	(	PUNCT
iajs-539	97	21	ρ(x2n	ρ(x2n	NOUN
iajs-539	97	22	,	,	PUNCT
iajs-539	97	23	u	u	NOUN
iajs-539	97	24	)	)	PUNCT
iajs-539	97	25	)	)	PUNCT
iajs-539	97	26	}	}	PUNCT
iajs-539	97	27	…	…	PUNCT
iajs-539	97	28	(	(	PUNCT
iajs-539	97	29	15	15	NUM
iajs-539	97	30	)	)	PUNCT
iajs-539	97	31	when	when	SCONJ
iajs-539	97	32	n→∞	n→∞	X
iajs-539	97	33	,	,	PUNCT
iajs-539	97	34	we	we	PRON
iajs-539	97	35	get	get	VERB
iajs-539	97	36	ρ(u	ρ(u	PROPN
iajs-539	97	37	,	,	PUNCT
iajs-539	97	38	tu)=	tu)=	PROPN
iajs-539	97	39	0	0	NUM
iajs-539	97	40	.	.	PUNCT
iajs-539	98	1	thus	thus	ADV
iajs-539	98	2	,	,	PUNCT
iajs-539	98	3	we	we	PRON
iajs-539	98	4	have	have	VERB
iajs-539	98	5	u	u	NOUN
iajs-539	98	6	=	=	PROPN
iajs-539	98	7	su	su	PROPN
iajs-539	98	8	=	=	PROPN
iajs-539	98	9	tu	tu	PROPN
iajs-539	98	10	.	.	PUNCT
iajs-539	99	1	therefore	therefore	ADV
iajs-539	99	2	,	,	PUNCT
iajs-539	99	3	u	u	NOUN
iajs-539	99	4	is	be	AUX
iajs-539	99	5	the	the	DET
iajs-539	99	6	common	common	ADJ
iajs-539	99	7	fixed	fix	VERB
iajs-539	99	8	point	point	NOUN
iajs-539	99	9	of	of	ADP
iajs-539	99	10	s	s	PRON
iajs-539	99	11	and	and	CCONJ
iajs-539	99	12	t.	t.	NOUN
iajs-539	99	13	the	the	DET
iajs-539	99	14	proof	proof	NOUN
iajs-539	99	15	for	for	ADP
iajs-539	99	16	t	t	PROPN
iajs-539	99	17	continuous	continuous	ADJ
iajs-539	99	18	is	be	AUX
iajs-539	99	19	similar	similar	ADJ
iajs-539	99	20	.	.	PUNCT
iajs-539	100	1	we	we	PRON
iajs-539	100	2	will	will	AUX
iajs-539	100	3	now	now	ADV
iajs-539	100	4	show	show	VERB
iajs-539	100	5	that	that	SCONJ
iajs-539	100	6	u	u	PRON
iajs-539	100	7	is	be	AUX
iajs-539	100	8	unique	unique	ADJ
iajs-539	100	9	.	.	PUNCT
iajs-539	101	1	suppose	suppose	VERB
iajs-539	101	2	that	that	SCONJ
iajs-539	101	3	v	v	NOUN
iajs-539	101	4	is	be	AUX
iajs-539	101	5	also	also	ADV
iajs-539	101	6	a	a	DET
iajs-539	101	7	common	common	ADJ
iajs-539	101	8	fixed	fix	VERB
iajs-539	101	9	point	point	NOUN
iajs-539	101	10	of	of	ADP
iajs-539	101	11	s	s	PRON
iajs-539	101	12	and	and	CCONJ
iajs-539	101	13	t.	t.	PROPN
iajs-539	101	14	then	then	ADV
iajs-539	101	15	,	,	PUNCT
iajs-539	101	16	from	from	ADP
iajs-539	101	17	(	(	PUNCT
iajs-539	101	18	2	2	NUM
iajs-539	101	19	)	)	PUNCT
iajs-539	101	20	,	,	PUNCT
iajs-539	101	21	ρ(u	ρ(u	PROPN
iajs-539	101	22	,	,	PUNCT
iajs-539	101	23	v)=	v)=	PROPN
iajs-539	101	24	ρ(stu	ρ(stu	PROPN
iajs-539	101	25	,	,	PUNCT
iajs-539	101	26	tsv	tsv	NOUN
iajs-539	101	27	)	)	PUNCT
iajs-539	101	28	≤	≤	PROPN
iajs-539	102	1	max{ϕ1(1/2[ρ(u	max{ϕ1(1/2[ρ(u	PROPN
iajs-539	102	2	,	,	PUNCT
iajs-539	102	3	sv)+	sv)+	PROPN
iajs-539	102	4	ρ(v	ρ(v	PROPN
iajs-539	102	5	,	,	PUNCT
iajs-539	102	6	tu	tu	PROPN
iajs-539	102	7	)	)	PUNCT
iajs-539	102	8	]	]	PUNCT
iajs-539	102	9	)	)	PUNCT
iajs-539	102	10	,	,	PUNCT
iajs-539	102	11	ϕ2	ϕ2	ADV
iajs-539	102	12	(	(	PUNCT
iajs-539	102	13	ρ(u	ρ(u	PROPN
iajs-539	102	14	,	,	PUNCT
iajs-539	102	15	tu	tu	PROPN
iajs-539	102	16	)	)	PUNCT
iajs-539	102	17	)	)	PUNCT
iajs-539	102	18	,	,	PUNCT
iajs-539	102	19	ϕ3(ρ(v	ϕ3(ρ(v	PROPN
iajs-539	102	20	,	,	PUNCT
iajs-539	102	21	sv	sv	NOUN
iajs-539	102	22	)	)	PUNCT
iajs-539	102	23	)	)	PUNCT
iajs-539	102	24	,	,	PUNCT
iajs-539	102	25	ϕ4	ϕ4	PROPN
iajs-539	102	26	(	(	PUNCT
iajs-539	102	27	ρ(u	ρ(u	PROPN
iajs-539	102	28	,	,	PUNCT
iajs-539	102	29	v	v	NOUN
iajs-539	102	30	)	)	PUNCT
iajs-539	102	31	}	}	PUNCT
iajs-539	103	1	=	=	SYM
iajs-539	103	2	ϕ1(1/2[ρ(u	ϕ1(1/2[ρ(u	NOUN
iajs-539	103	3	,	,	PUNCT
iajs-539	103	4	v)+	v)+	NOUN
iajs-539	103	5	ρ(v	ρ(v	PROPN
iajs-539	103	6	,	,	PUNCT
iajs-539	103	7	u	u	NOUN
iajs-539	103	8	)	)	PUNCT
iajs-539	103	9	]	]	PUNCT
iajs-539	103	10	)	)	PUNCT
iajs-539	103	11	,	,	PUNCT
iajs-539	103	12	ϕ2	ϕ2	ADV
iajs-539	103	13	(	(	PUNCT
iajs-539	103	14	ρ(u	ρ(u	PROPN
iajs-539	103	15	,	,	PUNCT
iajs-539	103	16	u	u	NOUN
iajs-539	103	17	)	)	PUNCT
iajs-539	103	18	)	)	PUNCT
iajs-539	103	19	,	,	PUNCT
iajs-539	103	20	ϕ3	ϕ3	PROPN
iajs-539	103	21	(	(	PUNCT
iajs-539	103	22	ρ(v	ρ(v	PROPN
iajs-539	103	23	,	,	PUNCT
iajs-539	103	24	v	v	NOUN
iajs-539	103	25	)	)	PUNCT
iajs-539	103	26	)	)	PUNCT
iajs-539	103	27	,	,	PUNCT
iajs-539	103	28	ϕ4	ϕ4	PROPN
iajs-539	103	29	(	(	PUNCT
iajs-539	103	30	ρ(u	ρ(u	PROPN
iajs-539	103	31	,	,	PUNCT
iajs-539	103	32	v	v	NOUN
iajs-539	103	33	)	)	PUNCT
iajs-539	103	34	)	)	PUNCT
iajs-539	103	35	}	}	PUNCT
iajs-539	103	36	≤	≤	NUM
iajs-539	103	37	ϕ(ρ(u	ϕ(ρ(u	PROPN
iajs-539	103	38	,	,	PUNCT
iajs-539	103	39	v	v	NOUN
iajs-539	103	40	)	)	PUNCT
iajs-539	103	41	)	)	PUNCT
iajs-539	103	42	.	.	PUNCT
iajs-539	104	1	…	…	PUNCT
iajs-539	104	2	(	(	PUNCT
iajs-539	104	3	16	16	NUM
iajs-539	104	4	)	)	PUNCT
iajs-539	104	5	we	we	PRON
iajs-539	104	6	write	write	VERB
iajs-539	104	7	ρ(u	ρ(u	PROPN
iajs-539	104	8	,	,	PUNCT
iajs-539	104	9	v)≤	v)≤	PROPN
iajs-539	104	10	ϕ	ϕ	X
iajs-539	104	11	(	(	PUNCT
iajs-539	104	12	ρ(u	ρ(u	PROPN
iajs-539	104	13	,	,	PUNCT
iajs-539	104	14	v	v	NOUN
iajs-539	104	15	)	)	PUNCT
iajs-539	104	16	)	)	PUNCT
iajs-539	104	17	,	,	PUNCT
iajs-539	104	18	which	which	PRON
iajs-539	104	19	implies	imply	VERB
iajs-539	104	20	that	that	SCONJ
iajs-539	104	21	ρ(u	ρ(u	PROPN
iajs-539	104	22	,	,	PUNCT
iajs-539	104	23	v)=0	v)=0	PROPN
iajs-539	104	24	,	,	PUNCT
iajs-539	104	25	that	that	ADV
iajs-539	104	26	is	is	ADV
iajs-539	104	27	,	,	PUNCT
iajs-539	104	28	u	u	NOUN
iajs-539	104	29	=	=	PROPN
iajs-539	104	30	v.	v.	ADV
iajs-539	104	31	therefore	therefore	ADV
iajs-539	104	32	,	,	PUNCT
iajs-539	104	33	the	the	DET
iajs-539	104	34	common	common	ADJ
iajs-539	104	35	fixed	fix	VERB
iajs-539	104	36	point	point	NOUN
iajs-539	104	37	of	of	ADP
iajs-539	104	38	s	s	PRON
iajs-539	104	39	and	and	CCONJ
iajs-539	104	40	t	t	PROPN
iajs-539	104	41	is	be	AUX
iajs-539	104	42	unique	unique	ADJ
iajs-539	104	43	▪	▪	ADJ
iajs-539	104	44	corollary	corollary	NOUN
iajs-539	104	45	2.5	2.5	NUM
iajs-539	104	46	:	:	PUNCT
iajs-539	104	47	let	let	VERB
iajs-539	104	48	(	(	PUNCT
iajs-539	104	49	x	x	NOUN
iajs-539	104	50	,	,	PUNCT
iajs-539	104	51	ρ	ρ	PROPN
iajs-539	104	52	)	)	PUNCT
iajs-539	104	53	be	be	VERB
iajs-539	104	54	a	a	DET
iajs-539	104	55	st	st	NOUN
iajs-539	104	56	-	-	PUNCT
iajs-539	104	57	orbitally	orbitally	ADV
iajs-539	104	58	complete	complete	ADJ
iajs-539	104	59	g	g	NOUN
iajs-539	104	60	-	-	PUNCT
iajs-539	104	61	metric	metric	ADJ
iajs-539	104	62	space	space	NOUN
iajs-539	104	63	.	.	PUNCT
iajs-539	105	1	let	let	VERB
iajs-539	105	2	s	s	PRON
iajs-539	105	3	and	and	CCONJ
iajs-539	105	4	t	t	PROPN
iajs-539	105	5	be	be	AUX
iajs-539	105	6	self	self	NOUN
iajs-539	105	7	mappings	mapping	NOUN
iajs-539	105	8	on	on	ADP
iajs-539	105	9	x	x	PUNCT
iajs-539	105	10	satisfying	satisfy	VERB
iajs-539	105	11	for	for	ADP
iajs-539	105	12	all	all	DET
iajs-539	105	13	x	x	NOUN
iajs-539	105	14	,	,	PUNCT
iajs-539	105	15	y	y	PROPN
iajs-539	105	16	∈	∈	PROPN
iajs-539	105	17	x.	x.	NOUN
iajs-539	106	1	ρ(stx	ρ(stx	VERB
iajs-539	106	2	,	,	PUNCT
iajs-539	106	3	tsy)≤	tsy)≤	ADJ
iajs-539	106	4	max{1/2[ρ(x	max{1/2[ρ(x	NOUN
iajs-539	106	5	,	,	PUNCT
iajs-539	106	6	sy)+ρ(y	sy)+ρ(y	ADJ
iajs-539	106	7	,	,	PUNCT
iajs-539	106	8	tx)],ρ(x	tx)],ρ(x	NOUN
iajs-539	106	9	,	,	PUNCT
iajs-539	106	10	tx),ρ(y	tx),ρ(y	NOUN
iajs-539	106	11	,	,	PUNCT
iajs-539	106	12	sy),ρ(x	sy),ρ(x	NOUN
iajs-539	106	13	,	,	PUNCT
iajs-539	106	14	y	y	NOUN
iajs-539	106	15	)	)	PUNCT
iajs-539	106	16	}	}	PUNCT
iajs-539	106	17	for	for	ADP
iajs-539	106	18	all	all	DET
iajs-539	106	19	x	x	NOUN
iajs-539	106	20	,	,	PUNCT
iajs-539	106	21	y∈x	y∈x	NOUN
iajs-539	106	22	,	,	PUNCT
iajs-539	106	23	316	316	NUM
iajs-539	106	24	|	|	NOUN
iajs-539	106	25	mathematics	mathematics	PROPN
iajs-539	106	26	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NOUN
iajs-539	106	27	�	�	NOUN
iajs-539	106	28	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-539	106	29	:	:	PUNCT
iajs-539	106	30	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-539	106	31	©	©	PROPN
iajs-539	106	32	@ü‹26@@öü»€a@i1@‚b«@h2013	@ü‹26@@öü»€a@i1@‚b«@h2013	PROPN
iajs-539	106	33	ibn	ibn	PROPN
iajs-539	106	34	al	al	PROPN
iajs-539	106	35	-	-	PUNCT
iajs-539	106	36	haitham	haitham	PROPN
iajs-539	106	37	jour	jour	X
iajs-539	106	38	.	.	PROPN
iajs-539	107	1	for	for	ADP
iajs-539	107	2	pure	pure	ADJ
iajs-539	107	3	&	&	CCONJ
iajs-539	107	4	appl	appl	PROPN
iajs-539	107	5	.	.	PUNCT
iajs-539	108	1	sci	sci	PROPN
iajs-539	108	2	.	.	PUNCT
iajs-539	108	3	vol	vol	NOUN
iajs-539	108	4	.	.	PROPN
iajs-539	109	1	26	26	NUM
iajs-539	109	2	(	(	PUNCT
iajs-539	109	3	1	1	NUM
iajs-539	109	4	)	)	PUNCT
iajs-539	109	5	2013	2013	NUM
iajs-539	109	6	the	the	DET
iajs-539	109	7	sequence	sequence	NOUN
iajs-539	109	8	{	{	PUNCT
iajs-539	109	9	xn	xn	PROPN
iajs-539	109	10	}	}	PUNCT
iajs-539	109	11	is	be	AUX
iajs-539	109	12	defined	define	VERB
iajs-539	109	13	by	by	ADP
iajs-539	109	14	(	(	PUNCT
iajs-539	109	15	1	1	NUM
iajs-539	109	16	)	)	PUNCT
iajs-539	109	17	.	.	PUNCT
iajs-539	110	1	if	if	SCONJ
iajs-539	110	2	s	s	PRON
iajs-539	110	3	or	or	CCONJ
iajs-539	110	4	t	t	PROPN
iajs-539	110	5	is	be	AUX
iajs-539	110	6	continuous	continuous	ADJ
iajs-539	110	7	,	,	PUNCT
iajs-539	110	8	then	then	ADV
iajs-539	110	9	s	s	PRON
iajs-539	110	10	and	and	CCONJ
iajs-539	110	11	t	t	PROPN
iajs-539	110	12	have	have	VERB
iajs-539	110	13	a	a	DET
iajs-539	110	14	unique	unique	ADJ
iajs-539	110	15	common	common	ADJ
iajs-539	110	16	fixed	fix	VERB
iajs-539	110	17	point	point	NOUN
iajs-539	110	18	.	.	PUNCT
iajs-539	111	1	proof	proof	NOUN
iajs-539	111	2	.	.	PUNCT
iajs-539	112	1	the	the	DET
iajs-539	112	2	proof	proof	NOUN
iajs-539	112	3	follows	follow	VERB
iajs-539	112	4	by	by	ADP
iajs-539	112	5	taking	take	VERB
iajs-539	112	6	ϕi(t	ϕi(t	NOUN
iajs-539	112	7	)	)	PUNCT
iajs-539	113	1	=	=	SYM
iajs-539	113	2	t	t	NOUN
iajs-539	113	3	with	with	ADP
iajs-539	113	4	0	0	NUM
iajs-539	113	5	<	<	X
iajs-539	113	6	<	<	X
iajs-539	113	7	1	1	NUM
iajs-539	113	8	(	(	PUNCT
iajs-539	113	9	i	i	NOUN
iajs-539	113	10	=	=	NOUN
iajs-539	113	11	1,2,3,4	1,2,3,4	NUM
iajs-539	113	12	)	)	PUNCT
iajs-539	113	13	in	in	ADP
iajs-539	113	14	theorem2.4	theorem2.4	NOUN
iajs-539	113	15	▪	▪	NOUN
iajs-539	113	16	as	as	ADP
iajs-539	113	17	special	special	ADJ
iajs-539	113	18	case	case	NOUN
iajs-539	113	19	of	of	ADP
iajs-539	113	20	corollary2.5	corollary2.5	NOUN
iajs-539	113	21	we	we	PRON
iajs-539	113	22	have	have	VERB
iajs-539	113	23	theorem3.1	theorem3.1	VERB
iajs-539	113	24	in	in	ADP
iajs-539	113	25	[	[	X
iajs-539	113	26	9	9	NUM
iajs-539	113	27	]	]	PUNCT
iajs-539	113	28	,	,	PUNCT
iajs-539	113	29	theorem	theorem	VERB
iajs-539	113	30	2.1	2.1	NUM
iajs-539	113	31	in	in	ADP
iajs-539	113	32	[	[	X
iajs-539	113	33	7	7	NUM
iajs-539	113	34	]	]	PUNCT
iajs-539	113	35	and	and	CCONJ
iajs-539	113	36	theorem2.1	theorem2.1	NUM
iajs-539	113	37	in[10	in[10	X
iajs-539	113	38	]	]	PUNCT
iajs-539	113	39	.	.	PUNCT
iajs-539	114	1	now	now	ADV
iajs-539	114	2	we	we	PRON
iajs-539	114	3	will	will	AUX
iajs-539	114	4	prove	prove	VERB
iajs-539	114	5	the	the	DET
iajs-539	114	6	following	follow	VERB
iajs-539	114	7	corollary	corollary	NOUN
iajs-539	114	8	using	use	VERB
iajs-539	114	9	another	another	DET
iajs-539	114	10	condition	condition	NOUN
iajs-539	114	11	instead	instead	ADV
iajs-539	114	12	of	of	ADP
iajs-539	114	13	continuity	continuity	NOUN
iajs-539	114	14	in	in	ADP
iajs-539	114	15	theorem	theorem	ADJ
iajs-539	114	16	2.4	2.4	NUM
iajs-539	114	17	.	.	PUNCT
iajs-539	115	1	corollary	corollary	ADJ
iajs-539	115	2	2.6	2.6	NUM
iajs-539	116	1	:	:	PUNCT
iajs-539	116	2	let	let	VERB
iajs-539	116	3	(	(	PUNCT
iajs-539	116	4	x	x	NOUN
iajs-539	116	5	,	,	PUNCT
iajs-539	116	6	ρ	ρ	PROPN
iajs-539	116	7	)	)	PUNCT
iajs-539	116	8	be	be	VERB
iajs-539	116	9	a	a	DET
iajs-539	116	10	st	st	NOUN
iajs-539	116	11	-	-	PUNCT
iajs-539	116	12	orbitally	orbitally	ADV
iajs-539	116	13	complete	complete	ADJ
iajs-539	116	14	g	g	NOUN
iajs-539	116	15	-	-	PUNCT
iajs-539	116	16	metric	metric	ADJ
iajs-539	116	17	space	space	NOUN
iajs-539	116	18	.	.	PUNCT
iajs-539	117	1	let	let	VERB
iajs-539	117	2	s	s	PRON
iajs-539	117	3	and	and	CCONJ
iajs-539	117	4	t	t	PROPN
iajs-539	117	5	be	be	AUX
iajs-539	117	6	self	self	NOUN
iajs-539	117	7	mappings	mapping	NOUN
iajs-539	117	8	on	on	ADP
iajs-539	117	9	x	x	PUNCT
iajs-539	117	10	satisfying	satisfy	VERB
iajs-539	117	11	(	(	PUNCT
iajs-539	117	12	2	2	NUM
iajs-539	117	13	)	)	PUNCT
iajs-539	117	14	of	of	ADP
iajs-539	117	15	proposition2.3	proposition2.3	PROPN
iajs-539	117	16	,	,	PUNCT
iajs-539	117	17	and	and	CCONJ
iajs-539	117	18	,	,	PUNCT
iajs-539	117	19	for	for	ADP
iajs-539	117	20	each	each	DET
iajs-539	117	21	u	u	NOUN
iajs-539	117	22	∈	∈	PROPN
iajs-539	117	23	x	x	PUNCT
iajs-539	117	24	with	with	ADP
iajs-539	117	25	u	u	NOUN
iajs-539	117	26	≠	≠	PROPN
iajs-539	117	27	su	su	NOUN
iajs-539	117	28	or	or	CCONJ
iajs-539	117	29	u	u	PROPN
iajs-539	117	30	≠	≠	PROPN
iajs-539	117	31	tu	tu	PROPN
iajs-539	117	32	,	,	PUNCT
iajs-539	117	33	let	let	VERB
iajs-539	117	34	inf	inf	PROPN
iajs-539	117	35	{	{	PUNCT
iajs-539	117	36	ρ(x	ρ(x	NOUN
iajs-539	117	37	,	,	PUNCT
iajs-539	117	38	u)+	u)+	PROPN
iajs-539	117	39	ρ(x	ρ(x	NOUN
iajs-539	117	40	,	,	PUNCT
iajs-539	117	41	sx)+	sx)+	NOUN
iajs-539	117	42	ρ(y	ρ(y	NOUN
iajs-539	117	43	,	,	PUNCT
iajs-539	117	44	ty	ty	NUM
iajs-539	117	45	):	):	PUNCT
iajs-539	117	46	x	x	X
iajs-539	117	47	,	,	PUNCT
iajs-539	117	48	y	y	PROPN
iajs-539	117	49	∈	∈	PROPN
iajs-539	117	50	x	x	PUNCT
iajs-539	117	51	}	}	PUNCT
iajs-539	117	52	>	>	X
iajs-539	118	1	0	0	X
iajs-539	118	2	.	.	PUNCT
iajs-539	119	1	then	then	ADV
iajs-539	119	2	s	s	VERB
iajs-539	119	3	and	and	CCONJ
iajs-539	119	4	t	t	PROPN
iajs-539	119	5	have	have	VERB
iajs-539	119	6	a	a	DET
iajs-539	119	7	unique	unique	ADJ
iajs-539	119	8	common	common	ADJ
iajs-539	119	9	fixed	fix	VERB
iajs-539	119	10	point	point	NOUN
iajs-539	119	11	.	.	PUNCT
iajs-539	120	1	proof	proof	NOUN
iajs-539	120	2	:	:	PUNCT
iajs-539	120	3	let	let	VERB
iajs-539	120	4	x0	x0	PROPN
iajs-539	120	5	∈	∈	PROPN
iajs-539	120	6	x	x	X
iajs-539	120	7	and	and	CCONJ
iajs-539	120	8	{	{	PUNCT
iajs-539	120	9	xn	xn	NOUN
iajs-539	120	10	}	}	PUNCT
iajs-539	120	11	defined	define	VERB
iajs-539	120	12	by	by	ADP
iajs-539	120	13	(	(	PUNCT
iajs-539	120	14	1	1	NUM
iajs-539	120	15	)	)	PUNCT
iajs-539	120	16	.	.	PUNCT
iajs-539	121	1	from	from	ADP
iajs-539	121	2	proposition2.3	proposition2.3	PROPN
iajs-539	121	3	,	,	PUNCT
iajs-539	121	4	{	{	PUNCT
iajs-539	121	5	xn	xn	X
iajs-539	121	6	}	}	PUNCT
iajs-539	121	7	is	be	AUX
iajs-539	121	8	a	a	DET
iajs-539	121	9	cauchy	cauchy	ADJ
iajs-539	121	10	sequence	sequence	NOUN
iajs-539	121	11	.	.	PUNCT
iajs-539	122	1	since	since	SCONJ
iajs-539	122	2	x	x	PRON
iajs-539	122	3	is	be	AUX
iajs-539	122	4	a	a	DET
iajs-539	122	5	st	st	NOUN
iajs-539	122	6	-	-	PUNCT
iajs-539	122	7	orbitally	orbitally	ADV
iajs-539	122	8	complete	complete	ADJ
iajs-539	122	9	g	g	NOUN
iajs-539	122	10	-	-	PUNCT
iajs-539	122	11	metric	metric	ADJ
iajs-539	122	12	space	space	NOUN
iajs-539	122	13	,	,	PUNCT
iajs-539	122	14	there	there	PRON
iajs-539	122	15	exists	exist	VERB
iajs-539	122	16	u	u	NOUN
iajs-539	122	17	∈	∈	PROPN
iajs-539	122	18	x	x	PUNCT
iajs-539	122	19	such	such	ADJ
iajs-539	122	20	that	that	SCONJ
iajs-539	122	21	{	{	PUNCT
iajs-539	122	22	xn	xn	X
iajs-539	122	23	}	}	PUNCT
iajs-539	122	24	converges	converge	NOUN
iajs-539	122	25	to	to	PART
iajs-539	122	26	u.	u.	VERB
iajs-539	122	27	then	then	ADV
iajs-539	122	28	we	we	PRON
iajs-539	122	29	have	have	VERB
iajs-539	122	30	ρ(x2n+1,x2m+2)=ρ(tsx2n−1,stx2	ρ(x2n+1,x2m+2)=ρ(tsx2n−1,stx2	NUM
iajs-539	122	31	m	m	NOUN
iajs-539	122	32	)	)	PUNCT
iajs-539	122	33	≤	≤	PUNCT
iajs-539	123	1	max{ϕ1(1/2[ρ(x2n−1,sx2m)+ρ(x2m	max{ϕ1(1/2[ρ(x2n−1,sx2m)+ρ(x2m	PROPN
iajs-539	123	2	,	,	PUNCT
iajs-539	123	3	t2n−1)]),ϕ2(ρ(x2n−1,x2n	t2n−1)]),ϕ2(ρ(x2n−1,x2n	ADP
iajs-539	123	4	)	)	PUNCT
iajs-539	123	5	)	)	PUNCT
iajs-539	123	6	,	,	PUNCT
iajs-539	123	7	ϕ3(ρ(x2m	ϕ3(ρ(x2m	PROPN
iajs-539	123	8	,	,	PUNCT
iajs-539	123	9	x2m+1)),ϕ4	x2m+1)),ϕ4	PROPN
iajs-539	123	10	(	(	PUNCT
iajs-539	123	11	ρ(x2n−1,x2	ρ(x2n−1,x2	PROPN
iajs-539	123	12	m	m	NOUN
iajs-539	123	13	)	)	PUNCT
iajs-539	123	14	)	)	PUNCT
iajs-539	123	15	}	}	PUNCT
iajs-539	123	16	≤	≤	NUM
iajs-539	124	1	max{ϕ1(1/2[ρ(x2n−1,x2m+1)+	max{ϕ1(1/2[ρ(x2n−1,x2m+1)+	NUM
iajs-539	124	2	ρ(x2	ρ(x2	NOUN
iajs-539	124	3	m	m	PROPN
iajs-539	124	4	,	,	PUNCT
iajs-539	124	5	x	x	SYM
iajs-539	124	6	2n)]),ϕ2	2n)]),ϕ2	NOUN
iajs-539	124	7	(	(	PUNCT
iajs-539	124	8	ρ(x2n−1,x2n	ρ(x2n−1,x2n	PROPN
iajs-539	124	9	)	)	PUNCT
iajs-539	124	10	)	)	PUNCT
iajs-539	124	11	,	,	PUNCT
iajs-539	124	12	ϕ3(ρ(x2m	ϕ3(ρ(x2m	PROPN
iajs-539	124	13	,	,	PUNCT
iajs-539	124	14	x2m+1)),ϕ4	x2m+1)),ϕ4	PROPN
iajs-539	124	15	(	(	PUNCT
iajs-539	124	16	ρ(x2n−1,x2	ρ(x2n−1,x2	PROPN
iajs-539	124	17	m	m	NOUN
iajs-539	124	18	)	)	PUNCT
iajs-539	124	19	)	)	PUNCT
iajs-539	124	20	}	}	PUNCT
iajs-539	124	21	.	.	PUNCT
iajs-539	125	1	thus	thus	ADV
iajs-539	125	2	,	,	PUNCT
iajs-539	125	3	we	we	PRON
iajs-539	125	4	obtain	obtain	VERB
iajs-539	125	5	limn→∞	limn→∞	PROPN
iajs-539	125	6	ρ(x2n+1,u	ρ(x2n+1,u	NUM
iajs-539	125	7	)	)	PUNCT
iajs-539	125	8	=	=	SYM
iajs-539	126	1	0	0	X
iajs-539	126	2	.	.	PUNCT
iajs-539	126	3	assume	assume	VERB
iajs-539	126	4	that	that	SCONJ
iajs-539	126	5	u	u	PROPN
iajs-539	126	6	≠	≠	PROPN
iajs-539	126	7	su	su	NOUN
iajs-539	126	8	or	or	CCONJ
iajs-539	126	9	u	u	PROPN
iajs-539	126	10	≠	≠	PROPN
iajs-539	126	11	tu	tu	PROPN
iajs-539	126	12	.	.	PUNCT
iajs-539	126	13	then	then	ADV
iajs-539	126	14	,	,	PUNCT
iajs-539	126	15	by	by	ADP
iajs-539	126	16	hypothesis	hypothesis	NOUN
iajs-539	126	17	,	,	PUNCT
iajs-539	126	18	we	we	PRON
iajs-539	126	19	have	have	VERB
iajs-539	126	20	0	0	NUM
iajs-539	126	21	<	<	X
iajs-539	126	22	inf	inf	PROPN
iajs-539	126	23	{	{	PUNCT
iajs-539	126	24	ρ(x	ρ(x	PROPN
iajs-539	126	25	,	,	PUNCT
iajs-539	126	26	u)+	u)+	PROPN
iajs-539	126	27	ρ(x	ρ(x	NOUN
iajs-539	126	28	,	,	PUNCT
iajs-539	126	29	sx)+	sx)+	NOUN
iajs-539	126	30	ρ(y	ρ(y	NOUN
iajs-539	126	31	,	,	PUNCT
iajs-539	126	32	ty	ty	NUM
iajs-539	126	33	):	):	PUNCT
iajs-539	126	34	x	x	X
iajs-539	126	35	,	,	PUNCT
iajs-539	126	36	y	y	PROPN
iajs-539	126	37	∈	∈	PROPN
iajs-539	126	38	x	x	PUNCT
iajs-539	126	39	}	}	PUNCT
iajs-539	126	40	=	=	SYM
iajs-539	126	41	inf	inf	NOUN
iajs-539	126	42	{	{	PUNCT
iajs-539	126	43	ρ(x2n+1,u)+	ρ(x2n+1,u)+	PROPN
iajs-539	126	44	ρ(x2n+1,sx2n+1)+ρ(x2n+2,tx2n+2	ρ(x2n+1,sx2n+1)+ρ(x2n+2,tx2n+2	PROPN
iajs-539	126	45	):	):	PUNCT
iajs-539	126	46	n	n	PRON
iajs-539	126	47	∈	∈	PROPN
iajs-539	126	48	n	n	CCONJ
iajs-539	126	49	}	}	PUNCT
iajs-539	126	50	=	=	SYM
iajs-539	126	51	inf	inf	NOUN
iajs-539	126	52	{	{	PUNCT
iajs-539	126	53	ρ(x2n+1,u)+	ρ(x2n+1,u)+	PROPN
iajs-539	126	54	ρ(x2n+1,x2n+2)+	ρ(x2n+1,x2n+2)+	VERB
iajs-539	126	55	ρ(x2n+2	ρ(x2n+2	NOUN
iajs-539	126	56	,	,	PUNCT
iajs-539	126	57	x2n+3	x2n+3	PROPN
iajs-539	126	58	):	):	PUNCT
iajs-539	126	59	n	n	CCONJ
iajs-539	126	60	∈	∈	NOUN
iajs-539	126	61	n	n	NOUN
iajs-539	126	62	}	}	PUNCT
iajs-539	126	63	=	=	SYM
iajs-539	126	64	0	0	X
iajs-539	126	65	.	.	PUNCT
iajs-539	127	1	this	this	PRON
iajs-539	127	2	is	be	AUX
iajs-539	127	3	a	a	DET
iajs-539	127	4	contradiction	contradiction	NOUN
iajs-539	127	5	.	.	PUNCT
iajs-539	128	1	therefore	therefore	ADV
iajs-539	128	2	,	,	PUNCT
iajs-539	128	3	we	we	PRON
iajs-539	128	4	have	have	VERB
iajs-539	128	5	u	u	NOUN
iajs-539	128	6	=	=	PROPN
iajs-539	128	7	su	su	PROPN
iajs-539	128	8	=	=	PROPN
iajs-539	128	9	tu.on	tu.on	VERB
iajs-539	128	10	the	the	DET
iajs-539	128	11	other	other	ADJ
iajs-539	128	12	hand	hand	NOUN
iajs-539	128	13	,	,	PUNCT
iajs-539	128	14	we	we	PRON
iajs-539	128	15	can	can	AUX
iajs-539	128	16	prove	prove	VERB
iajs-539	128	17	the	the	DET
iajs-539	128	18	existence	existence	NOUN
iajs-539	128	19	of	of	ADP
iajs-539	128	20	a	a	DET
iajs-539	128	21	unique	unique	ADJ
iajs-539	128	22	common	common	ADJ
iajs-539	128	23	fixed	fix	VERB
iajs-539	128	24	point	point	NOUN
iajs-539	128	25	of	of	ADP
iajs-539	128	26	s	s	PRON
iajs-539	128	27	and	and	CCONJ
iajs-539	128	28	t	t	PROPN
iajs-539	128	29	by	by	ADP
iajs-539	128	30	a	a	DET
iajs-539	128	31	method	method	NOUN
iajs-539	128	32	similar	similar	ADJ
iajs-539	128	33	to	to	ADP
iajs-539	128	34	that	that	PRON
iajs-539	128	35	of	of	ADP
iajs-539	128	36	theorem	theorem	ADJ
iajs-539	128	37	2.4	2.4	NUM
iajs-539	128	38	.	.	PUNCT
iajs-539	129	1	we	we	PRON
iajs-539	129	2	can	can	AUX
iajs-539	129	3	prove	prove	VERB
iajs-539	129	4	the	the	DET
iajs-539	129	5	following	follow	VERB
iajs-539	129	6	corollary	corollary	ADJ
iajs-539	129	7	taking	take	VERB
iajs-539	129	8	t=	t=	ADJ
iajs-539	129	9	i	i	PRON
iajs-539	129	10	,	,	PUNCT
iajs-539	129	11	the	the	DET
iajs-539	129	12	identity	identity	NOUN
iajs-539	129	13	mapping	mapping	NOUN
iajs-539	129	14	,	,	PUNCT
iajs-539	129	15	in	in	ADP
iajs-539	129	16	theorem	theorem	ADJ
iajs-539	129	17	2.4	2.4	NUM
iajs-539	129	18	.	.	PUNCT
iajs-539	130	1	corollary	corollary	ADJ
iajs-539	130	2	2.7	2.7	NUM
iajs-539	130	3	:	:	PUNCT
iajs-539	130	4	let	let	VERB
iajs-539	130	5	(	(	PUNCT
iajs-539	130	6	x	x	NOUN
iajs-539	130	7	,	,	PUNCT
iajs-539	130	8	ρ	ρ	PROPN
iajs-539	130	9	)	)	PUNCT
iajs-539	130	10	be	be	VERB
iajs-539	130	11	a	a	DET
iajs-539	130	12	st	st	NOUN
iajs-539	130	13	-	-	PUNCT
iajs-539	130	14	orbitally	orbitally	ADV
iajs-539	130	15	complete	complete	ADJ
iajs-539	130	16	g	g	NOUN
iajs-539	130	17	-	-	PUNCT
iajs-539	130	18	metric	metric	ADJ
iajs-539	130	19	space	space	NOUN
iajs-539	130	20	.	.	PUNCT
iajs-539	131	1	let	let	VERB
iajs-539	131	2	s	s	PRON
iajs-539	131	3	and	and	CCONJ
iajs-539	131	4	t	t	PROPN
iajs-539	131	5	be	be	AUX
iajs-539	131	6	self	self	NOUN
iajs-539	131	7	mappings	mapping	NOUN
iajs-539	131	8	on	on	ADP
iajs-539	131	9	x	x	PUNCT
iajs-539	131	10	satisfying	satisfy	VERB
iajs-539	131	11	ρ(sx	ρ(sx	NOUN
iajs-539	131	12	,	,	PUNCT
iajs-539	131	13	sy)≤	sy)≤	ADJ
iajs-539	131	14	max{ϕ1(1/2[ρ(x	max{ϕ1(1/2[ρ(x	NOUN
iajs-539	131	15	,	,	PUNCT
iajs-539	131	16	sy)+	sy)+	VERB
iajs-539	131	17	ρ(y	ρ(y	NOUN
iajs-539	131	18	,	,	PUNCT
iajs-539	131	19	x	x	NOUN
iajs-539	131	20	)	)	PUNCT
iajs-539	131	21	]	]	PUNCT
iajs-539	131	22	)	)	PUNCT
iajs-539	131	23	,	,	PUNCT
iajs-539	131	24	ϕ3(ρ(y	ϕ3(ρ(y	PROPN
iajs-539	131	25	,	,	PUNCT
iajs-539	131	26	sy	sy	NOUN
iajs-539	131	27	)	)	PUNCT
iajs-539	131	28	)	)	PUNCT
iajs-539	131	29	,	,	PUNCT
iajs-539	131	30	ϕ4(ρ(x	ϕ4(ρ(x	PROPN
iajs-539	131	31	,	,	PUNCT
iajs-539	131	32	y	y	PROPN
iajs-539	131	33	)	)	PUNCT
iajs-539	131	34	)	)	PUNCT
iajs-539	131	35	}	}	PUNCT
iajs-539	131	36	for	for	ADP
iajs-539	131	37	all	all	DET
iajs-539	131	38	x	x	NOUN
iajs-539	131	39	,	,	PUNCT
iajs-539	131	40	y	y	PROPN
iajs-539	131	41	∈	∈	PROPN
iajs-539	131	42	x	x	NOUN
iajs-539	131	43	,	,	PUNCT
iajs-539	131	44	where	where	SCONJ
iajs-539	131	45	ϕi	ϕi	ADP
iajs-539	131	46	∈	∈	PROPN
iajs-539	131	47	φ	φ	X
iajs-539	131	48	(	(	PUNCT
iajs-539	131	49	i	i	NOUN
iajs-539	131	50	=	=	NOUN
iajs-539	131	51	1,3,4	1,3,4	NUM
iajs-539	131	52	)	)	PUNCT
iajs-539	131	53	.	.	PUNCT
iajs-539	132	1	if	if	SCONJ
iajs-539	132	2	s	s	NOUN
iajs-539	132	3	is	be	AUX
iajs-539	132	4	a	a	DET
iajs-539	132	5	continuous	continuous	ADJ
iajs-539	132	6	,	,	PUNCT
iajs-539	132	7	then	then	ADV
iajs-539	132	8	s	s	VERB
iajs-539	132	9	has	have	VERB
iajs-539	132	10	a	a	DET
iajs-539	132	11	unique	unique	ADJ
iajs-539	132	12	fixed	fix	VERB
iajs-539	132	13	point	point	NOUN
iajs-539	132	14	.	.	PUNCT
iajs-539	133	1	we	we	PRON
iajs-539	133	2	can	can	AUX
iajs-539	133	3	prove	prove	VERB
iajs-539	133	4	the	the	DET
iajs-539	133	5	following	follow	VERB
iajs-539	133	6	corollary	corollary	ADJ
iajs-539	133	7	taking	take	VERB
iajs-539	133	8	t=	t=	ADJ
iajs-539	133	9	i	i	PRON
iajs-539	133	10	,	,	PUNCT
iajs-539	133	11	the	the	DET
iajs-539	133	12	identity	identity	NOUN
iajs-539	133	13	mapping	mapping	NOUN
iajs-539	133	14	,	,	PUNCT
iajs-539	133	15	in	in	ADP
iajs-539	133	16	corollary	corollary	ADJ
iajs-539	133	17	2.5	2.5	NUM
iajs-539	133	18	.	.	PUNCT
iajs-539	134	1	corollary	corollary	ADJ
iajs-539	134	2	2.8	2.8	NUM
iajs-539	134	3	:	:	PUNCT
iajs-539	134	4	let	let	VERB
iajs-539	134	5	(	(	PUNCT
iajs-539	134	6	x	x	NOUN
iajs-539	134	7	,	,	PUNCT
iajs-539	134	8	ρ	ρ	PROPN
iajs-539	134	9	)	)	PUNCT
iajs-539	134	10	be	be	VERB
iajs-539	134	11	a	a	DET
iajs-539	134	12	st	st	NOUN
iajs-539	134	13	-	-	PUNCT
iajs-539	134	14	orbitally	orbitally	ADV
iajs-539	134	15	complete	complete	ADJ
iajs-539	134	16	g	g	NOUN
iajs-539	134	17	-	-	PUNCT
iajs-539	134	18	metric	metric	ADJ
iajs-539	134	19	space	space	NOUN
iajs-539	134	20	.	.	PUNCT
iajs-539	135	1	let	let	VERB
iajs-539	135	2	s	s	PRON
iajs-539	135	3	be	be	AUX
iajs-539	135	4	self	self	NOUN
iajs-539	135	5	mapping	mapping	NOUN
iajs-539	135	6	on	on	ADP
iajs-539	135	7	x	x	PUNCT
iajs-539	135	8	satisfying	satisfy	VERB
iajs-539	135	9	ρ(sx	ρ(sx	NOUN
iajs-539	135	10	,	,	PUNCT
iajs-539	135	11	sy)≤	sy)≤	VERB
iajs-539	135	12	α	α	PRON
iajs-539	135	13	max{1/2[ρ(x	max{1/2[ρ(x	NOUN
iajs-539	135	14	,	,	PUNCT
iajs-539	135	15	sy)+ρ(y	sy)+ρ(y	ADV
iajs-539	135	16	,	,	PUNCT
iajs-539	135	17	x)],ρ(y	x)],ρ(y	ADV
iajs-539	135	18	,	,	PUNCT
iajs-539	135	19	sy),ρ(x	sy),ρ(x	NOUN
iajs-539	135	20	,	,	PUNCT
iajs-539	135	21	y	y	NOUN
iajs-539	135	22	)	)	PUNCT
iajs-539	135	23	}	}	PUNCT
iajs-539	135	24	for	for	ADP
iajs-539	135	25	all	all	DET
iajs-539	135	26	x	x	NOUN
iajs-539	135	27	,	,	PUNCT
iajs-539	135	28	y∈x	y∈x	NOUN
iajs-539	135	29	,	,	PUNCT
iajs-539	135	30	for	for	SCONJ
iajs-539	135	31	all	all	DET
iajs-539	135	32	x	x	NOUN
iajs-539	135	33	,	,	PUNCT
iajs-539	135	34	y	y	PROPN
iajs-539	135	35	∈	∈	PROPN
iajs-539	135	36	x.	x.	NOUN
iajs-539	136	1	the	the	DET
iajs-539	136	2	sequence	sequence	NOUN
iajs-539	136	3	{	{	PUNCT
iajs-539	136	4	xn	xn	PUNCT
iajs-539	136	5	}	}	PUNCT
iajs-539	136	6	is	be	AUX
iajs-539	136	7	defined	define	VERB
iajs-539	136	8	by	by	ADP
iajs-539	136	9	x0	x0	PROPN
iajs-539	136	10	∈	∈	PROPN
iajs-539	136	11	x	x	X
iajs-539	136	12	,	,	PUNCT
iajs-539	136	13	xn+1	xn+1	PROPN
iajs-539	137	1	=	=	SYM
iajs-539	137	2	s	s	PROPN
iajs-539	137	3	xn	xn	NOUN
iajs-539	137	4	.	.	PUNCT
iajs-539	138	1	if	if	SCONJ
iajs-539	138	2	s	s	NOUN
iajs-539	138	3	is	be	AUX
iajs-539	138	4	continuous	continuous	ADJ
iajs-539	138	5	,	,	PUNCT
iajs-539	138	6	then	then	ADV
iajs-539	138	7	s	s	VERB
iajs-539	138	8	has	have	VERB
iajs-539	138	9	a	a	DET
iajs-539	138	10	unique	unique	ADJ
iajs-539	138	11	fixed	fix	VERB
iajs-539	138	12	point	point	NOUN
iajs-539	138	13	.	.	PUNCT
iajs-539	139	1	we	we	PRON
iajs-539	139	2	can	can	AUX
iajs-539	139	3	prove	prove	VERB
iajs-539	139	4	the	the	DET
iajs-539	139	5	following	follow	VERB
iajs-539	139	6	corollary	corollary	ADJ
iajs-539	139	7	taking	take	VERB
iajs-539	139	8	t=	t=	ADJ
iajs-539	139	9	i	i	PRON
iajs-539	139	10	,	,	PUNCT
iajs-539	139	11	the	the	DET
iajs-539	139	12	identity	identity	NOUN
iajs-539	139	13	mapping	mapping	NOUN
iajs-539	139	14	,	,	PUNCT
iajs-539	139	15	in	in	ADP
iajs-539	139	16	corollary	corollary	ADJ
iajs-539	139	17	2.6	2.6	NUM
iajs-539	139	18	.	.	PUNCT
iajs-539	140	1	317	317	NUM
iajs-539	140	2	|	|	ADV
iajs-539	140	3	mathematics	mathematics	PROPN
iajs-539	140	4	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NOUN
iajs-539	140	5	�	�	NOUN
iajs-539	140	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-539	140	7	:	:	PUNCT
iajs-539	140	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-539	140	9	©	©	PROPN
iajs-539	140	10	@ü‹26@@öü»€a@i1@‚b«@h2013	@ü‹26@@öü»€a@i1@‚b«@h2013	PROPN
iajs-539	140	11	ibn	ibn	PROPN
iajs-539	140	12	al	al	PROPN
iajs-539	140	13	-	-	PUNCT
iajs-539	140	14	haitham	haitham	PROPN
iajs-539	140	15	jour	jour	X
iajs-539	140	16	.	.	PROPN
iajs-539	141	1	for	for	ADP
iajs-539	141	2	pure	pure	ADJ
iajs-539	141	3	&	&	CCONJ
iajs-539	141	4	appl	appl	PROPN
iajs-539	141	5	.	.	PUNCT
iajs-539	142	1	sci	sci	PROPN
iajs-539	142	2	.	.	PUNCT
iajs-539	142	3	vol	vol	NOUN
iajs-539	142	4	.	.	PROPN
iajs-539	143	1	26	26	NUM
iajs-539	143	2	(	(	PUNCT
iajs-539	143	3	1	1	NUM
iajs-539	143	4	)	)	PUNCT
iajs-539	143	5	2013	2013	NUM
iajs-539	143	6	corollary	corollary	NOUN
iajs-539	143	7	2.9	2.9	NUM
iajs-539	143	8	:	:	PUNCT
iajs-539	143	9	let	let	VERB
iajs-539	143	10	(	(	PUNCT
iajs-539	143	11	x	x	NOUN
iajs-539	143	12	,	,	PUNCT
iajs-539	143	13	ρ	ρ	PROPN
iajs-539	143	14	)	)	PUNCT
iajs-539	143	15	be	be	VERB
iajs-539	143	16	a	a	DET
iajs-539	143	17	st	st	NOUN
iajs-539	143	18	-	-	PUNCT
iajs-539	143	19	orbitally	orbitally	ADV
iajs-539	143	20	complete	complete	ADJ
iajs-539	143	21	g	g	NOUN
iajs-539	143	22	-	-	PUNCT
iajs-539	143	23	metric	metric	ADJ
iajs-539	143	24	space	space	NOUN
iajs-539	143	25	.	.	PUNCT
iajs-539	144	1	let	let	VERB
iajs-539	144	2	s	s	PRON
iajs-539	144	3	be	be	AUX
iajs-539	144	4	self	self	NOUN
iajs-539	144	5	mapping	mapping	NOUN
iajs-539	144	6	on	on	ADP
iajs-539	144	7	x	x	PUNCT
iajs-539	144	8	satisfying	satisfy	VERB
iajs-539	144	9	(	(	PUNCT
iajs-539	144	10	2	2	NUM
iajs-539	144	11	)	)	PUNCT
iajs-539	144	12	of	of	ADP
iajs-539	144	13	proposition	proposition	NOUN
iajs-539	144	14	2.3	2.3	NUM
iajs-539	144	15	,	,	PUNCT
iajs-539	144	16	and	and	CCONJ
iajs-539	144	17	,	,	PUNCT
iajs-539	144	18	for	for	ADP
iajs-539	144	19	each	each	DET
iajs-539	144	20	u	u	NOUN
iajs-539	144	21	∈	∈	PROPN
iajs-539	144	22	x	x	PUNCT
iajs-539	144	23	with	with	ADP
iajs-539	144	24	u	u	NOUN
iajs-539	144	25	≠	≠	PROPN
iajs-539	144	26	su	su	NOUN
iajs-539	144	27	,	,	PUNCT
iajs-539	144	28	let	let	VERB
iajs-539	144	29	inf	inf	PROPN
iajs-539	144	30	{	{	PUNCT
iajs-539	144	31	ρ(x	ρ(x	NOUN
iajs-539	144	32	,	,	PUNCT
iajs-539	144	33	u)+	u)+	PROPN
iajs-539	144	34	ρ(x	ρ(x	NOUN
iajs-539	144	35	,	,	PUNCT
iajs-539	144	36	sx	sx	PROPN
iajs-539	144	37	)	)	PUNCT
iajs-539	144	38	:	:	PUNCT
iajs-539	145	1	x	x	X
iajs-539	145	2	,	,	PUNCT
iajs-539	145	3	y	y	PROPN
iajs-539	145	4	∈	∈	PROPN
iajs-539	145	5	x	x	PUNCT
iajs-539	145	6	}	}	PUNCT
iajs-539	145	7	>	>	X
iajs-539	145	8	0	0	X
iajs-539	145	9	.	.	PUNCT
iajs-539	146	1	then	then	ADV
iajs-539	146	2	s	s	AUX
iajs-539	146	3	have	have	VERB
iajs-539	146	4	a	a	DET
iajs-539	146	5	unique	unique	ADJ
iajs-539	146	6	fixed	fix	VERB
iajs-539	146	7	point	point	NOUN
iajs-539	146	8	.	.	PUNCT
iajs-539	147	1	references	reference	NOUN
iajs-539	147	2	1	1	NUM
iajs-539	147	3	.	.	PUNCT
iajs-539	148	1	agarwal	agarwal	PROPN
iajs-539	148	2	r.	r.	PROPN
iajs-539	148	3	p.;’regan	p.;’regan	PROPN
iajs-539	148	4	d.	d.	PROPN
iajs-539	148	5	o	o	PROPN
iajs-539	148	6	and	and	CCONJ
iajs-539	148	7	sahu	sahu	PROPN
iajs-539	148	8	d.r	d.r	PROPN
iajs-539	148	9	.	.	PROPN
iajs-539	148	10	,	,	PUNCT
iajs-539	148	11	(	(	PUNCT
iajs-539	148	12	2009	2009	NUM
iajs-539	148	13	)	)	PUNCT
iajs-539	148	14	,	,	PUNCT
iajs-539	148	15	fixed	fix	VERB
iajs-539	148	16	point	point	NOUN
iajs-539	148	17	theory	theory	NOUN
iajs-539	148	18	for	for	ADP
iajs-539	148	19	lipschitzian	lipschitzian	ADJ
iajs-539	148	20	type	type	NOUN
iajs-539	148	21	mappings	mapping	NOUN
iajs-539	148	22	with	with	ADP
iajs-539	148	23	applications	application	NOUN
iajs-539	148	24	,	,	PUNCT
iajs-539	148	25	springer	springer	NOUN
iajs-539	148	26	verlag	verlag	PROPN
iajs-539	148	27	,	,	PUNCT
iajs-539	148	28	new	new	PROPN
iajs-539	148	29	york	york	PROPN
iajs-539	148	30	.	.	PUNCT
iajs-539	149	1	2	2	X
iajs-539	149	2	.	.	X
iajs-539	149	3	zidler	zidler	PROPN
iajs-539	149	4	e.	e.	PROPN
iajs-539	150	1	(	(	PUNCT
iajs-539	150	2	1986),”non	1986),”non	NUM
iajs-539	150	3	linear	linear	ADJ
iajs-539	150	4	functional	functional	ADJ
iajs-539	150	5	analysis	analysis	NOUN
iajs-539	150	6	and	and	CCONJ
iajs-539	150	7	application	application	NOUN
iajs-539	150	8	,	,	PUNCT
iajs-539	150	9	(	(	PUNCT
iajs-539	150	10	i	i	NOUN
iajs-539	150	11	-	-	PUNCT
iajs-539	150	12	fixed	fix	VERB
iajs-539	150	13	point	point	NOUN
iajs-539	150	14	theorems	theorem	NOUN
iajs-539	150	15	)	)	PUNCT
iajs-539	150	16	,	,	PUNCT
iajs-539	150	17	springer	springer	NOUN
iajs-539	150	18	verlag	verlag	PROPN
iajs-539	150	19	,	,	PUNCT
iajs-539	150	20	new	new	PROPN
iajs-539	150	21	york	york	PROPN
iajs-539	150	22	.	.	PUNCT
iajs-539	151	1	3	3	X
iajs-539	151	2	.	.	X
iajs-539	151	3	jungck	jungck	PROPN
iajs-539	151	4	n.	n.	PROPN
iajs-539	151	5	(	(	PUNCT
iajs-539	151	6	1988	1988	NUM
iajs-539	151	7	)	)	PUNCT
iajs-539	151	8	,	,	PUNCT
iajs-539	151	9	common	common	ADJ
iajs-539	151	10	fixed	fix	VERB
iajs-539	151	11	point	point	NOUN
iajs-539	151	12	for	for	ADP
iajs-539	151	13	commuting	commute	VERB
iajs-539	151	14	and	and	CCONJ
iajs-539	151	15	compatible	compatible	ADJ
iajs-539	151	16	maps	map	NOUN
iajs-539	151	17	on	on	ADP
iajs-539	151	18	compacta	compacta	NOUN
iajs-539	151	19	proc	proc	PROPN
iajs-539	151	20	.	.	PUNCT
iajs-539	152	1	amer	amer	PROPN
iajs-539	152	2	.	.	PUNCT
iajs-539	152	3	math	math	PROPN
iajs-539	152	4	.	.	PUNCT
iajs-539	153	1	soc	soc	PROPN
iajs-539	153	2	.	.	PUNCT
iajs-539	153	3	,	,	PUNCT
iajs-539	153	4	103:(3	103:(3	NUM
iajs-539	153	5	)	)	PUNCT
iajs-539	153	6	,	,	PUNCT
iajs-539	153	7	977	977	NUM
iajs-539	153	8	-	-	SYM
iajs-539	153	9	983	983	NUM
iajs-539	153	10	.	.	PUNCT
iajs-539	154	1	4	4	X
iajs-539	154	2	.	.	PUNCT
iajs-539	154	3	joshi	joshi	PROPN
iajs-539	154	4	m.	m.	PROPN
iajs-539	154	5	l.	l.	PROPN
iajs-539	154	6	and	and	CCONJ
iajs-539	154	7	mehta	mehta	PROPN
iajs-539	154	8	j.	j.	PROPN
iajs-539	154	9	g.	g.	PROPN
iajs-539	154	10	(	(	PUNCT
iajs-539	154	11	2010	2010	NUM
iajs-539	154	12	)	)	PUNCT
iajs-539	154	13	,	,	PUNCT
iajs-539	154	14	common	common	ADJ
iajs-539	154	15	fixed	fix	VERB
iajs-539	154	16	point	point	NOUN
iajs-539	154	17	for	for	ADP
iajs-539	154	18	weakly	weakly	ADJ
iajs-539	154	19	compatible	compatible	ADJ
iajs-539	154	20	maps	map	NOUN
iajs-539	154	21	in	in	ADP
iajs-539	154	22	complete	complete	ADJ
iajs-539	154	23	metric	metric	ADJ
iajs-539	154	24	spaces	space	NOUN
iajs-539	154	25	,	,	PUNCT
iajs-539	154	26	int	int	NOUN
iajs-539	154	27	.	.	PUNCT
iajs-539	155	1	j	j	PROPN
iajs-539	155	2	of	of	ADP
iajs-539	155	3	computer	computer	NOUN
iajs-539	155	4	appl	appl	PROPN
iajs-539	155	5	.	.	PROPN
iajs-539	155	6	,	,	PUNCT
iajs-539	155	7	11:(4	11:(4	NUM
iajs-539	155	8	)	)	PUNCT
iajs-539	155	9	,	,	PUNCT
iajs-539	155	10	451	451	NUM
iajs-539	155	11	-	-	SYM
iajs-539	155	12	459	459	NUM
iajs-539	155	13	.	.	PUNCT
iajs-539	156	1	5	5	X
iajs-539	156	2	.	.	X
iajs-539	156	3	singh	singh	PROPN
iajs-539	156	4	s.	s.	PROPN
iajs-539	156	5	l.	l.	PROPN
iajs-539	156	6	;	;	PUNCT
iajs-539	156	7	hematulin	hematulin	PROPN
iajs-539	156	8	a.	a.	PROPN
iajs-539	156	9	and	and	CCONJ
iajs-539	156	10	r.	r.	PROPN
iajs-539	156	11	pant	pant	PROPN
iajs-539	156	12	,	,	PUNCT
iajs-539	156	13	(	(	PUNCT
iajs-539	156	14	2009	2009	NUM
iajs-539	156	15	)	)	PUNCT
iajs-539	156	16	,	,	PUNCT
iajs-539	156	17	new	new	ADJ
iajs-539	156	18	coincidence	coincidence	NOUN
iajs-539	156	19	common	common	ADJ
iajs-539	156	20	fixed	fix	VERB
iajs-539	156	21	point	point	NOUN
iajs-539	156	22	theorems	theorem	NOUN
iajs-539	156	23	,	,	PUNCT
iajs-539	156	24	applied	apply	VERB
iajs-539	156	25	general	general	ADJ
iajs-539	156	26	topology	topology	NOUN
iajs-539	156	27	,	,	PUNCT
iajs-539	156	28	10:(1	10:(1	NUM
iajs-539	156	29	)	)	PUNCT
iajs-539	156	30	,	,	PUNCT
iajs-539	156	31	121	121	NUM
iajs-539	156	32	-	-	SYM
iajs-539	156	33	130	130	NUM
iajs-539	156	34	.	.	PUNCT
iajs-539	157	1	6	6	NUM
iajs-539	157	2	.	.	X
iajs-539	157	3	tiwary	tiwary	PROPN
iajs-539	157	4	k.	k.	PROPN
iajs-539	157	5	;	;	PUNCT
iajs-539	157	6	basu	basu	PROPN
iajs-539	157	7	t.	t.	PROPN
iajs-539	157	8	and	and	CCONJ
iajs-539	157	9	sen	sen	PROPN
iajs-539	157	10	s.	s.	PROPN
iajs-539	157	11	(	(	PUNCT
iajs-539	157	12	1995	1995	NUM
iajs-539	157	13	)	)	PUNCT
iajs-539	157	14	,	,	PUNCT
iajs-539	157	15	some	some	DET
iajs-539	157	16	common	common	ADJ
iajs-539	157	17	fixed	fix	VERB
iajs-539	157	18	point	point	NOUN
iajs-539	157	19	theorems	theorem	NOUN
iajs-539	157	20	in	in	ADP
iajs-539	157	21	complete	complete	ADJ
iajs-539	157	22	metric	metric	ADJ
iajs-539	157	23	space	space	NOUN
iajs-539	157	24	,	,	PUNCT
iajs-539	157	25	soochow	soochow	PROPN
iajs-539	157	26	journal	journal	PROPN
iajs-539	157	27	of	of	ADP
iajs-539	157	28	mathematics	mathematic	NOUN
iajs-539	157	29	,	,	PUNCT
iajs-539	157	30	21:(4	21:(4	NUM
iajs-539	157	31	)	)	PUNCT
iajs-539	157	32	,	,	PUNCT
iajs-539	157	33	32	32	NUM
iajs-539	157	34	-	-	SYM
iajs-539	157	35	34	34	NUM
iajs-539	157	36	.	.	PUNCT
iajs-539	158	1	7	7	X
iajs-539	158	2	.	.	X
iajs-539	158	3	branciari	branciari	PROPN
iajs-539	158	4	a.	a.	PROPN
iajs-539	158	5	(	(	PUNCT
iajs-539	158	6	2000	2000	NUM
iajs-539	158	7	)	)	PUNCT
iajs-539	158	8	,	,	PUNCT
iajs-539	158	9	a	a	DET
iajs-539	158	10	fixed	fix	VERB
iajs-539	158	11	point	point	NOUN
iajs-539	158	12	theorem	theorem	NOUN
iajs-539	158	13	of	of	ADP
iajs-539	158	14	banach	banach	NOUN
iajs-539	158	15	-	-	PUNCT
iajs-539	158	16	caccioppoli	caccioppoli	NOUN
iajs-539	158	17	type	type	NOUN
iajs-539	158	18	on	on	ADP
iajs-539	158	19	a	a	DET
iajs-539	158	20	class	class	NOUN
iajs-539	158	21	of	of	ADP
iajs-539	158	22	generalized	generalized	ADJ
iajs-539	158	23	metric	metric	ADJ
iajs-539	158	24	spaces	space	NOUN
iajs-539	158	25	,	,	PUNCT
iajs-539	158	26	publ	publ	PROPN
iajs-539	158	27	.	.	PUNCT
iajs-539	159	1	math	math	NOUN
iajs-539	159	2	.	.	PUNCT
iajs-539	160	1	debrecen	debrecen	PROPN
iajs-539	160	2	,	,	PUNCT
iajs-539	160	3	57:(1	57:(1	PROPN
iajs-539	160	4	-	-	SYM
iajs-539	160	5	2	2	NUM
iajs-539	160	6	)	)	PUNCT
iajs-539	160	7	,	,	PUNCT
iajs-539	160	8	31	31	NUM
iajs-539	160	9	-	-	SYM
iajs-539	160	10	37	37	NUM
iajs-539	160	11	.	.	NOUN
iajs-539	160	12	8	8	NUM
iajs-539	160	13	.	.	PUNCT
iajs-539	161	1	das	das	PROPN
iajs-539	161	2	p.	p.	PROPN
iajs-539	161	3	(	(	PUNCT
iajs-539	161	4	2002	2002	NUM
iajs-539	161	5	)	)	PUNCT
iajs-539	161	6	,	,	PUNCT
iajs-539	161	7	a	a	DET
iajs-539	161	8	fixed	fix	VERB
iajs-539	161	9	point	point	NOUN
iajs-539	161	10	theorem	theorem	VERB
iajs-539	161	11	on	on	ADP
iajs-539	161	12	a	a	DET
iajs-539	161	13	class	class	NOUN
iajs-539	161	14	of	of	ADP
iajs-539	161	15	generalized	generalized	ADJ
iajs-539	161	16	metric	metric	ADJ
iajs-539	161	17	spaces	space	NOUN
iajs-539	161	18	,	,	PUNCT
iajs-539	161	19	korean	korean	PROPN
iajs-539	161	20	j.	j.	PROPN
iajs-539	161	21	math	math	PROPN
iajs-539	161	22	.	.	PUNCT
iajs-539	162	1	sc	sc	PROPN
iajs-539	162	2	.	.	PROPN
iajs-539	162	3	,	,	PUNCT
iajs-539	162	4	9:(1	9:(1	NUM
iajs-539	162	5	)	)	PUNCT
iajs-539	162	6	,	,	PUNCT
iajs-539	162	7	29	29	NUM
iajs-539	162	8	-	-	SYM
iajs-539	162	9	33	33	NUM
iajs-539	162	10	.	.	NOUN
iajs-539	163	1	9	9	NUM
iajs-539	163	2	.	.	PUNCT
iajs-539	164	1	das	das	PROPN
iajs-539	164	2	p.	p.	PROPN
iajs-539	164	3	and	and	CCONJ
iajs-539	164	4	dey	dey	PROPN
iajs-539	164	5	l.k	l.k	PROPN
iajs-539	164	6	.	.	PROPN
iajs-539	164	7	(	(	PUNCT
iajs-539	164	8	2007	2007	NUM
iajs-539	164	9	)	)	PUNCT
iajs-539	164	10	,	,	PUNCT
iajs-539	164	11	a	a	DET
iajs-539	164	12	fixed	fix	VERB
iajs-539	164	13	point	point	NOUN
iajs-539	164	14	theorem	theorem	VERB
iajs-539	164	15	in	in	ADP
iajs-539	164	16	generalized	generalized	ADJ
iajs-539	164	17	metric	metric	ADJ
iajs-539	164	18	space	space	NOUN
iajs-539	164	19	,	,	PUNCT
iajs-539	164	20	soochow	soochow	PROPN
iajs-539	164	21	j.	j.	PROPN
iajs-539	164	22	math	math	PROPN
iajs-539	164	23	.	.	PUNCT
iajs-539	164	24	,	,	PUNCT
iajs-539	164	25	33:(1	33:(1	NUM
iajs-539	164	26	)	)	PUNCT
iajs-539	164	27	,	,	PUNCT
iajs-539	164	28	33	33	NUM
iajs-539	164	29	-	-	SYM
iajs-539	164	30	39	39	NUM
iajs-539	164	31	.	.	PUNCT
iajs-539	165	1	10	10	NUM
iajs-539	165	2	.	.	PUNCT
iajs-539	165	3	moradi	moradi	PROPN
iajs-539	165	4	s.	s.	PROPN
iajs-539	165	5	,(2000	,(2000	PROPN
iajs-539	165	6	)	)	PUNCT
iajs-539	165	7	,	,	PUNCT
iajs-539	165	8	kannan	kannan	PROPN
iajs-539	165	9	fixed	fix	VERB
iajs-539	165	10	-	-	PUNCT
iajs-539	165	11	point	point	NOUN
iajs-539	165	12	theorem	theorem	NOUN
iajs-539	165	13	on	on	ADP
iajs-539	165	14	complete	complete	ADJ
iajs-539	165	15	metric	metric	ADJ
iajs-539	165	16	spaces	space	NOUN
iajs-539	165	17	and	and	CCONJ
iajs-539	165	18	on	on	ADP
iajs-539	165	19	generalized	generalized	ADJ
iajs-539	165	20	metric	metric	ADJ
iajs-539	165	21	spaces	space	NOUN
iajs-539	165	22	depended	depend	VERB
iajs-539	165	23	an	an	DET
iajs-539	165	24	another	another	DET
iajs-539	165	25	function	function	NOUN
iajs-539	165	26	,	,	PUNCT
iajs-539	165	27	mathematics	mathematic	NOUN
iajs-539	165	28	subject	subject	ADJ
iajs-539	165	29	classification	classification	NOUN
iajs-539	165	30	,	,	PUNCT
iajs-539	165	31	primary	primary	ADJ
iajs-539	165	32	46j10	46j10	NOUN
iajs-539	165	33	,	,	PUNCT
iajs-539	165	34	46j15	46j15	NUM
iajs-539	165	35	,	,	PUNCT
iajs-539	165	36	47h10	47h10	NUM
iajs-539	165	37	,	,	PUNCT
iajs-539	165	38	16	16	NUM
iajs-539	165	39	.	.	PUNCT
iajs-539	166	1	11	11	NUM
iajs-539	166	2	.	.	PUNCT
iajs-539	167	1	akram	akram	PROPN
iajs-539	167	2	m.	m.	PROPN
iajs-539	167	3	,	,	PUNCT
iajs-539	167	4	zafar	zafar	PROPN
iajs-539	167	5	a.	a.	PROPN
iajs-539	167	6	a.	a.	PROPN
iajs-539	167	7	,	,	PUNCT
iajs-539	167	8	.	.	PUNCT
iajs-539	168	1	siddiqui	siddiqui	PROPN
iajs-539	168	2	a.	a.	PROPN
iajs-539	168	3	a	a	PRON
iajs-539	168	4	,	,	PUNCT
iajs-539	168	5	(	(	PUNCT
iajs-539	168	6	2011	2011	NUM
iajs-539	168	7	)	)	PUNCT
iajs-539	168	8	,	,	PUNCT
iajs-539	168	9	common	common	ADJ
iajs-539	168	10	fixed	fix	VERB
iajs-539	168	11	point	point	NOUN
iajs-539	168	12	theorems	theorem	NOUN
iajs-539	168	13	for	for	ADP
iajs-539	168	14	self	self	NOUN
iajs-539	168	15	maps	map	NOUN
iajs-539	168	16	of	of	ADP
iajs-539	168	17	a	a	DET
iajs-539	168	18	generalized	generalize	VERB
iajs-539	168	19	metric	metric	ADJ
iajs-539	168	20	space	space	NOUN
iajs-539	168	21	satisfying	satisfy	VERB
iajs-539	168	22	a	a	DET
iajs-539	168	23	-	-	PUNCT
iajs-539	168	24	contraction	contraction	NOUN
iajs-539	168	25	type	type	NOUN
iajs-539	168	26	condition	condition	NOUN
iajs-539	168	27	,	,	PUNCT
iajs-539	168	28	int	int	NOUN
iajs-539	168	29	.	.	PUNCT
iajs-539	169	1	j.	j.	PROPN
iajs-539	169	2	math	math	PROPN
iajs-539	169	3	.	.	PROPN
iajs-539	169	4	,	,	PUNCT
iajs-539	169	5	5:(16	5:(16	NUM
iajs-539	169	6	)	)	PUNCT
iajs-539	169	7	,	,	PUNCT
iajs-539	169	8	757	757	PROPN
iajs-539	169	9	-	-	SYM
iajs-539	169	10	763	763	NUM
iajs-539	169	11	.	.	PUNCT
iajs-539	170	1	12	12	NUM
iajs-539	170	2	.	.	PUNCT
iajs-539	170	3	a.	a.	PROPN
iajs-539	170	4	razani	razani	PROPN
iajs-539	170	5	,	,	PUNCT
iajs-539	170	6	z.	z.	PROPN
iajs-539	170	7	mazlumi	mazlumi	PROPN
iajs-539	170	8	nezhad	nezhad	VERB
iajs-539	170	9	and	and	CCONJ
iajs-539	170	10	m.	m.	NOUN
iajs-539	170	11	boujary	boujary	PROPN
iajs-539	170	12	,	,	PUNCT
iajs-539	170	13	(	(	PUNCT
iajs-539	170	14	2009	2009	NUM
iajs-539	170	15	)	)	PUNCT
iajs-539	170	16	,	,	PUNCT
iajs-539	170	17	a	a	DET
iajs-539	170	18	fxed	fxe	VERB
iajs-539	170	19	point	point	NOUN
iajs-539	170	20	theorem	theorem	NOUN
iajs-539	170	21	for	for	ADP
iajs-539	170	22	wdistance	wdistance	NOUN
iajs-539	170	23	,	,	PUNCT
iajs-539	170	24	applied	apply	VERB
iajs-539	170	25	sciences	science	NOUN
iajs-539	170	26	,	,	PUNCT
iajs-539	170	27	(	(	PUNCT
iajs-539	170	28	11	11	NUM
iajs-539	170	29	):	):	PUNCT
iajs-539	170	30	114	114	NUM
iajs-539	170	31	-	-	SYM
iajs-539	170	32	117	117	NUM
iajs-539	170	33	.	.	NOUN
iajs-539	170	34	318	318	NUM
iajs-539	171	1	|	|	ADV
iajs-539	171	2	mathematics	mathematics	PROPN
iajs-539	171	3	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NOUN
iajs-539	171	4	�	�	NOUN
iajs-539	171	5	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-539	171	6	:	:	PUNCT
iajs-539	171	7	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-539	171	8	©	©	PROPN
iajs-539	171	9	@ü‹26@@öü»€a@i1@‚b«@h2013	@ü‹26@@öü»€a@i1@‚b«@h2013	PROPN
iajs-539	171	10	ibn	ibn	PROPN
iajs-539	171	11	al	al	PROPN
iajs-539	171	12	-	-	PUNCT
iajs-539	171	13	haitham	haitham	PROPN
iajs-539	171	14	jour	jour	X
iajs-539	171	15	.	.	PROPN
iajs-539	172	1	for	for	ADP
iajs-539	172	2	pure	pure	ADJ
iajs-539	172	3	&	&	CCONJ
iajs-539	172	4	appl	appl	PROPN
iajs-539	172	5	.	.	PUNCT
iajs-539	173	1	sci	sci	PROPN
iajs-539	173	2	.	.	PUNCT
iajs-539	173	3	vol	vol	NOUN
iajs-539	173	4	.	.	PROPN
iajs-539	174	1	26	26	NUM
iajs-539	174	2	(	(	PUNCT
iajs-539	174	3	1	1	NUM
iajs-539	174	4	)	)	PUNCT
iajs-539	174	5	2013	2013	NUM
iajs-539	174	6	حول	حول	X
iajs-539	174	7	النقطة	النقطة	PROPN
iajs-539	174	8	الصامدة	الصامدة	PROPN
iajs-539	174	9	لتطبیقین	لتطبیقین	PROPN
iajs-539	174	10	غیر	غیر	PROPN
iajs-539	174	11	متبادلین	متبادلین	PROPN
iajs-539	174	12	مبرھنة	مبرھنة	VERB
iajs-539	174	13	سلوى	سلوى	X
iajs-539	174	14	سلمان	سلمان	NOUN
iajs-539	174	15	عبد	عبد	ADJ
iajs-539	174	16	الء	الء	NOUN
iajs-539	174	17	عبد	عبد	PROPN
iajs-539	174	18	هللاآ	هللاآ	PROPN
iajs-539	174	19	جامعة	جامعة	NOUN
iajs-539	174	20	بغداد	بغداد	PROPN
iajs-539	174	21	/	/	SYM
iajs-539	174	22	)	)	PUNCT
iajs-539	174	23	ابن	ابن	PROPN
iajs-539	174	24	الھیثم(كلیة	الھیثم(كلیة	PROPN
iajs-539	174	25	التربیة	التربیة	NOUN
iajs-539	174	26	للعلوم	للعلوم	NOUN
iajs-539	174	27	الصرفة	الصرفة	NOUN
iajs-539	174	28	/الریاضیات	/الریاضیات	PUNCT
iajs-539	175	1	علوم	علوم	PROPN
iajs-539	175	2	قسم	قسم	PROPN
iajs-539	175	3	2012تشرین	2012تشرین	NUM
iajs-539	175	4	االول	االول	NOUN
iajs-539	175	5	15قبل	15قبل	NUM
iajs-539	175	6	البحث	البحث	NOUN
iajs-539	175	7	في	في	PROPN
iajs-539	175	8	:	:	PUNCT
iajs-539	175	9	،	،	NOUN
iajs-539	175	10	2012حزیران	2012حزیران	NUM
iajs-539	175	11	19استلم	19استلم	NUM
iajs-539	175	12	البحث	البحث	NOUN
iajs-539	175	13	في	في	NOUN
iajs-539	175	14	:	:	PUNCT
iajs-539	175	15	الخالصة	الخالصة	NOUN
iajs-539	175	16	في	في	SCONJ
iajs-539	175	17	ھذا	ھذا	NOUN
iajs-539	175	18	البحث	البحث	PROPN
iajs-539	175	19	برھنا	برھنا	VERB
iajs-539	175	20	نتیجة	نتیجة	PROPN
iajs-539	175	21	حول	حول	PROPN
iajs-539	175	22	وجود	وجود	PROPN
iajs-539	175	23	ووحدانیة	ووحدانیة	PROPN
iajs-539	175	24	نقطة	نقطة	PROPN
iajs-539	175	25	صامدة	صامدة	NOUN
iajs-539	175	26	مشتركة	مشتركة	PROPN
iajs-539	175	27	ةلتطبیقین	ةلتطبیقین	PROPN
iajs-539	176	1	غیر	غیر	PROPN
iajs-539	176	2	متبادلین	متبادلین	PROPN
iajs-539	176	3	معرفین	معرفین	PROPN
iajs-539	176	4	على	على	NOUN
iajs-539	176	5	فضاء	فضاء	NOUN
iajs-539	176	6	g	g	NOUN
iajs-539	176	7	–	–	PUNCT
iajs-539	176	8	.	.	PUNCT
iajs-539	177	1	متري	متري	NOUN
iajs-539	177	2	كامل	كامل	PROPN
iajs-539	177	3	مساریا	مساریا	PROPN
iajs-539	177	4	،	،	PROPN
iajs-539	177	5	إذ	إذ	PROPN
iajs-539	177	6	استخدمنا	استخدمنا	PROPN
iajs-539	177	7	تطبیق	تطبیق	PROPN
iajs-539	177	8	انكماشي	انكماشي	PROPN
iajs-539	177	9	معمم	معمم	PROPN
iajs-539	177	10	متري	متري	PROPN
iajs-539	177	11	،	،	PROPN
iajs-539	177	12	كامل	كامل	PROPN
iajs-539	177	13	مساریا	مساریا	PROPN
iajs-539	177	14	،	،	PROPN
iajs-539	177	15	تطبیقات	تطبیقات	PROPN
iajs-539	177	16	غیر	غیر	PROPN
iajs-539	177	17	متبادلة	متبادلة	PROPN
iajs-539	177	18	،	،	X
iajs-539	177	19	نقطة	نقطة	PROPN
iajs-539	177	20	صامدة	صامدة	NOUN
iajs-539	177	21	مشتركة	مشتركة	PROPN
iajs-539	177	22	.	.	PUNCT
iajs-539	178	1	–	–	PUNCT
iajs-539	178	2	gفضاء	gفضاء	NOUN
iajs-539	178	3	:	:	PUNCT
iajs-539	178	4	الكلمات	الكلمات	VERB
iajs-539	178	5	المفتاحیة	المفتاحیة	ADJ
iajs-539	179	1	319	319	NUM
iajs-539	180	1	|	|	NOUN
iajs-539	180	2	mathematics	mathematic	NOUN