id	sid	tid	token	lemma	pos
iajs-826	1	1	ibn	ibn	PROPN
iajs-826	1	2	alhaitham	alhaitham	NOUN
iajs-826	1	3	j.	j.	PROPN
iajs-826	2	1	fo	fo	ADP
iajs-826	2	2	r	r	NOUN
iajs-826	2	3	pure	pure	ADJ
iajs-826	2	4	&	&	CCONJ
iajs-826	2	5	appl	appl	PROPN
iajs-826	2	6	.	.	PUNCT
iajs-826	3	1	sc	sc	PROPN
iajs-826	3	2	i.	i.	PROPN
iajs-826	3	3	vo	vo	PROPN
iajs-826	4	1	l.24	l.24	PROPN
iajs-826	4	2	(	(	PUNCT
iajs-826	4	3	1	1	NUM
iajs-826	4	4	)	)	PUNCT
iajs-826	4	5	2011	2011	NUM
iajs-826	4	6	n	n	CCONJ
iajs-826	4	7	–	–	PUNCT
iajs-826	4	8	topological	topological	ADJ
iajs-826	4	9	space	space	NOUN
iajs-826	4	10	and	and	CCONJ
iajs-826	4	11	its	its	PRON
iajs-826	4	12	applications	application	NOUN
iajs-826	4	13	in	in	ADP
iajs-826	4	14	artificial	artificial	ADJ
iajs-826	4	15	neural	neural	ADJ
iajs-826	4	16	networks	network	NOUN
iajs-826	4	17	l.n.m.tawfiq	l.n.m.tawfiq	PROPN
iajs-826	4	18	and	and	CCONJ
iajs-826	4	19	r.n.majeed	r.n.majee	VERB
iajs-826	4	20	department	department	NOUN
iajs-826	4	21	of	of	ADP
iajs-826	4	22	mathematics	mathematics	PROPN
iajs-826	4	23	,	,	PUNCT
iajs-826	4	24	college	college	NOUN
iajs-826	4	25	of	of	ADP
iajs-826	4	26	education	education	PROPN
iajs-826	4	27	-ibn	-ibn	PUNCT
iajs-826	4	28	al	al	PROPN
iajs-826	4	29	-	-	PUNCT
iajs-826	4	30	haitham	haitham	PROPN
iajs-826	4	31	,	,	PUNCT
iajs-826	4	32	baghdad	baghdad	PROPN
iajs-826	4	33	university	university	PROPN
iajs-826	4	34	.	.	PUNCT
iajs-826	5	1	received	receive	VERB
iajs-826	5	2	in	in	ADP
iajs-826	5	3	march,16,2009	march,16,2009	PROPN
iajs-826	5	4	accepted	accept	VERB
iajs-826	5	5	in	in	ADP
iajs-826	5	6	march,29,2010	march,29,2010	PROPN
iajs-826	5	7	abstract	abstract	NOUN
iajs-826	5	8	in	in	ADP
iajs-826	5	9	this	this	DET
iajs-826	5	10	paper	paper	NOUN
iajs-826	5	11	we	we	PRON
iajs-826	5	12	give	give	VERB
iajs-826	5	13	definitions	definition	NOUN
iajs-826	5	14	,	,	PUNCT
iajs-826	5	15	properties	property	NOUN
iajs-826	5	16	and	and	CCONJ
iajs-826	5	17	examples	example	NOUN
iajs-826	5	18	of	of	ADP
iajs-826	5	19	the	the	DET
iajs-826	5	20	notion	notion	NOUN
iajs-826	5	21	of	of	ADP
iajs-826	5	22	type	type	NOUN
iajs-826	5	23	ntopological	ntopological	ADJ
iajs-826	5	24	space	space	NOUN
iajs-826	5	25	.	.	PUNCT
iajs-826	6	1	throughout	throughout	ADP
iajs-826	6	2	this	this	DET
iajs-826	6	3	paper	paper	NOUN
iajs-826	6	4	n	n	NOUN
iajs-826	6	5	is	be	AUX
iajs-826	6	6	a	a	DET
iajs-826	6	7	finite	finite	ADJ
iajs-826	6	8	positive	positive	ADJ
iajs-826	6	9	number	number	NOUN
iajs-826	6	10	,	,	PUNCT
iajs-826	6	11	n	n	PRON
iajs-826	6	12	2	2	NUM
iajs-826	6	13	.	.	PUNCT
iajs-826	7	1	the	the	DET
iajs-826	7	2	task	task	NOUN
iajs-826	7	3	of	of	ADP
iajs-826	7	4	this	this	DET
iajs-826	7	5	paper	paper	NOUN
iajs-826	7	6	is	be	AUX
iajs-826	7	7	to	to	PART
iajs-826	7	8	study	study	VERB
iajs-826	7	9	and	and	CCONJ
iajs-826	7	10	investigate	investigate	VERB
iajs-826	7	11	some	some	DET
iajs-826	7	12	properties	property	NOUN
iajs-826	7	13	of	of	ADP
iajs-826	7	14	such	such	ADJ
iajs-826	7	15	spaces	space	NOUN
iajs-826	7	16	with	with	ADP
iajs-826	7	17	the	the	DET
iajs-826	7	18	existence	existence	NOUN
iajs-826	7	19	of	of	ADP
iajs-826	7	20	a	a	DET
iajs-826	7	21	relation	relation	NOUN
iajs-826	7	22	between	between	ADP
iajs-826	7	23	this	this	DET
iajs-826	7	24	space	space	NOUN
iajs-826	7	25	and	and	CCONJ
iajs-826	7	26	artificial	artificial	ADJ
iajs-826	7	27	neural	neural	ADJ
iajs-826	7	28	networks	network	NOUN
iajs-826	7	29	(	(	PUNCT
iajs-826	7	30	nn	nn	NOUN
iajs-826	7	31	's	's	PART
iajs-826	7	32	)	)	PUNCT
iajs-826	7	33	,	,	PUNCT
iajs-826	7	34	that	that	ADV
iajs-826	7	35	is	is	ADV
iajs-826	7	36	we	we	PRON
iajs-826	7	37	applied	apply	VERB
iajs-826	7	38	the	the	DET
iajs-826	7	39	definition	definition	NOUN
iajs-826	7	40	of	of	ADP
iajs-826	7	41	this	this	DET
iajs-826	7	42	space	space	NOUN
iajs-826	7	43	in	in	ADP
iajs-826	7	44	computer	computer	NOUN
iajs-826	7	45	field	field	NOUN
iajs-826	7	46	and	and	CCONJ
iajs-826	7	47	specially	specially	ADV
iajs-826	7	48	in	in	ADP
iajs-826	7	49	parallel	parallel	ADJ
iajs-826	7	50	processing	processing	NOUN
iajs-826	7	51	.	.	PUNCT
iajs-826	8	1	introduction	introduction	NOUN
iajs-826	8	2	finite	finite	PROPN
iajs-826	8	3	spaces	space	NOUN
iajs-826	8	4	were	be	AUX
iajs-826	8	5	first	first	ADV
iajs-826	8	6	studied	study	VERB
iajs-826	8	7	by	by	ADP
iajs-826	8	8	p..	p..	X
iajs-826	8	9	lexandroff	lexandroff	NOUN
iajs-826	8	10	in	in	ADP
iajs-826	8	11	1937	1937	NUM
iajs-826	8	12	.	.	PUNCT
iajs-826	9	1	ctually	ctually	ADV
iajs-826	9	2	,	,	PUNCT
iajs-826	9	3	finite	finite	PROPN
iajs-826	9	4	spaces	space	NOUN
iajs-826	9	5	had	have	AUX
iajs-826	9	6	been	be	AUX
iajs-826	9	7	more	more	ADV
iajs-826	9	8	earlier	early	ADV
iajs-826	9	9	investigated	investigate	VERB
iajs-826	9	10	by	by	ADP
iajs-826	9	11	many	many	ADJ
iajs-826	9	12	authors	author	NOUN
iajs-826	9	13	under	under	ADP
iajs-826	9	14	the	the	DET
iajs-826	9	15	name	name	NOUN
iajs-826	9	16	of	of	ADP
iajs-826	9	17	simplicial	simplicial	ADJ
iajs-826	9	18	complexes	complex	NOUN
iajs-826	9	19	.	.	PUNCT
iajs-826	10	1	there	there	PRON
iajs-826	10	2	were	be	VERB
iajs-826	10	3	several	several	ADJ
iajs-826	10	4	other	other	ADJ
iajs-826	10	5	contributions	contribution	NOUN
iajs-826	10	6	by	by	ADP
iajs-826	10	7	flachasmeyer	flachasmeyer	NOUN
iajs-826	10	8	in	in	ADP
iajs-826	10	9	1961	1961	NUM
iajs-826	10	10	,	,	PUNCT
iajs-826	10	11	stong	stong	ADJ
iajs-826	10	12	in	in	ADP
iajs-826	10	13	1966	1966	NUM
iajs-826	10	14	and	and	CCONJ
iajs-826	10	15	l.lotz	l.lotz	VERB
iajs-826	10	16	in	in	ADP
iajs-826	10	17	1970	1970	NUM
iajs-826	10	18	,	,	PUNCT
iajs-826	10	19	in	in	ADP
iajs-826	10	20	this	this	DET
iajs-826	10	21	paper	paper	NOUN
iajs-826	10	22	we	we	PRON
iajs-826	10	23	define	define	VERB
iajs-826	10	24	and	and	CCONJ
iajs-826	10	25	study	study	VERB
iajs-826	10	26	the	the	DET
iajs-826	10	27	notion	notion	NOUN
iajs-826	10	28	of	of	ADP
iajs-826	10	29	ntopological	ntopological	ADJ
iajs-826	10	30	space	space	NOUN
iajs-826	10	31	and	and	CCONJ
iajs-826	10	32	discuss	discuss	VERB
iajs-826	10	33	some	some	DET
iajs-826	10	34	properties	property	NOUN
iajs-826	10	35	of	of	ADP
iajs-826	10	36	finite	finite	ADJ
iajs-826	10	37	spaces	space	NOUN
iajs-826	10	38	.	.	PUNCT
iajs-826	11	1	however	however	ADV
iajs-826	11	2	,	,	PUNCT
iajs-826	11	3	the	the	DET
iajs-826	11	4	subject	subject	NOUN
iajs-826	11	5	has	have	AUX
iajs-826	11	6	never	never	ADV
iajs-826	11	7	been	be	AUX
iajs-826	11	8	considered	consider	VERB
iajs-826	11	9	as	as	ADP
iajs-826	11	10	a	a	DET
iajs-826	11	11	main	main	ADJ
iajs-826	11	12	field	field	NOUN
iajs-826	11	13	of	of	ADP
iajs-826	11	14	topology	topology	NOUN
iajs-826	11	15	.	.	PUNCT
iajs-826	12	1	with	with	ADP
iajs-826	12	2	the	the	DET
iajs-826	12	3	progress	progress	NOUN
iajs-826	12	4	of	of	ADP
iajs-826	12	5	computer	computer	NOUN
iajs-826	12	6	technology	technology	NOUN
iajs-826	12	7	,	,	PUNCT
iajs-826	12	8	finite	finite	PROPN
iajs-826	12	9	spaces	space	NOUN
iajs-826	12	10	have	have	AUX
iajs-826	12	11	become	become	VERB
iajs-826	12	12	more	more	ADV
iajs-826	12	13	important	important	ADJ
iajs-826	12	14	.	.	PUNCT
iajs-826	13	1	herman	herman	PROPN
iajs-826	13	2	in1990	in1990	PROPN
iajs-826	13	3	,	,	PUNCT
iajs-826	13	4	khalimsky	khalimsky	PROPN
iajs-826	13	5	and	and	CCONJ
iajs-826	13	6	et	et	PROPN
iajs-826	13	7	.	.	PUNCT
iajs-826	14	1	al	al	PROPN
iajs-826	14	2	.	.	PROPN
iajs-826	15	1	in	in	ADP
iajs-826	15	2	1990	1990	NUM
iajs-826	15	3	,	,	PUNCT
iajs-826	15	4	kong	kong	PROPN
iajs-826	15	5	and	and	CCONJ
iajs-826	15	6	kopperman	kopperman	NOUN
iajs-826	15	7	in	in	ADP
iajs-826	15	8	1991	1991	NUM
iajs-826	15	9	and	and	CCONJ
iajs-826	15	10	[	[	X
iajs-826	15	11	1	1	X
iajs-826	15	12	]	]	PUNCT
iajs-826	15	13	have	have	AUX
iajs-826	15	14	applied	apply	VERB
iajs-826	15	15	them	they	PRON
iajs-826	15	16	to	to	PART
iajs-826	15	17	model	model	VERB
iajs-826	15	18	the	the	DET
iajs-826	15	19	computer	computer	NOUN
iajs-826	15	20	screen	screen	NOUN
iajs-826	15	21	.	.	PUNCT
iajs-826	16	1	in	in	ADP
iajs-826	16	2	this	this	DET
iajs-826	16	3	paper	paper	NOUN
iajs-826	16	4	we	we	PRON
iajs-826	16	5	focus	focus	VERB
iajs-826	16	6	on	on	ADP
iajs-826	16	7	ntopological	ntopological	ADJ
iajs-826	16	8	space	space	NOUN
iajs-826	16	9	,	,	PUNCT
iajs-826	16	10	the	the	DET
iajs-826	16	11	main	main	ADJ
iajs-826	16	12	importance	importance	NOUN
iajs-826	16	13	of	of	ADP
iajs-826	16	14	study	study	NOUN
iajs-826	16	15	is	be	AUX
iajs-826	16	16	to	to	PART
iajs-826	16	17	offer	offer	VERB
iajs-826	16	18	new	new	ADJ
iajs-826	16	19	formulations	formulation	NOUN
iajs-826	16	20	for	for	ADP
iajs-826	16	21	separation	separation	NOUN
iajs-826	16	22	axioms	axiom	NOUN
iajs-826	16	23	in	in	ADP
iajs-826	16	24	ntopological	ntopological	ADJ
iajs-826	16	25	space	space	NOUN
iajs-826	16	26	.	.	PUNCT
iajs-826	17	1	we	we	PRON
iajs-826	17	2	present	present	VERB
iajs-826	17	3	and	and	CCONJ
iajs-826	17	4	study	study	VERB
iajs-826	17	5	comparisons	comparison	NOUN
iajs-826	17	6	between	between	ADP
iajs-826	17	7	ntopological	ntopological	ADJ
iajs-826	17	8	space	space	NOUN
iajs-826	17	9	and	and	CCONJ
iajs-826	17	10	nn'a	nn'a	PROPN
iajs-826	17	11	in	in	ADP
iajs-826	17	12	the	the	DET
iajs-826	17	13	case	case	NOUN
iajs-826	17	14	of	of	ADP
iajs-826	17	15	finite	finite	ADJ
iajs-826	17	16	spaces	space	NOUN
iajs-826	17	17	.	.	PUNCT
iajs-826	18	1	2	2	X
iajs-826	18	2	.	.	X
iajs-826	18	3	asic	asic	ADP
iajs-826	18	4	definition	definition	NOUN
iajs-826	18	5	of	of	ADP
iajs-826	18	6	ntopological	ntopological	ADJ
iajs-826	18	7	space	space	NOUN
iajs-826	18	8	and	and	CCONJ
iajs-826	18	9	their	their	PRON
iajs-826	18	10	properties	property	NOUN
iajs-826	18	11	in	in	ADP
iajs-826	18	12	this	this	DET
iajs-826	18	13	section	section	NOUN
iajs-826	18	14	we	we	PRON
iajs-826	18	15	introduce	introduce	VERB
iajs-826	18	16	the	the	DET
iajs-826	18	17	notion	notion	NOUN
iajs-826	18	18	of	of	ADP
iajs-826	18	19	ntopological	ntopological	ADJ
iajs-826	18	20	space	space	NOUN
iajs-826	18	21	,	,	PUNCT
iajs-826	18	22	and	and	CCONJ
iajs-826	18	23	give	give	VERB
iajs-826	18	24	its	its	PRON
iajs-826	18	25	properties	property	NOUN
iajs-826	18	26	.	.	PUNCT
iajs-826	19	1	several	several	ADJ
iajs-826	19	2	of	of	ADP
iajs-826	19	3	the	the	DET
iajs-826	19	4	classical	classical	ADJ
iajs-826	19	5	results	result	NOUN
iajs-826	19	6	[	[	X
iajs-826	19	7	2	2	NUM
iajs-826	19	8	]	]	PUNCT
iajs-826	19	9	are	be	AUX
iajs-826	19	10	extended	extend	VERB
iajs-826	19	11	by	by	ADP
iajs-826	19	12	defining	define	VERB
iajs-826	19	13	appropriate	appropriate	ADJ
iajs-826	19	14	substructures	substructure	NOUN
iajs-826	19	15	on	on	ADP
iajs-826	19	16	the	the	DET
iajs-826	19	17	ntopological	ntopological	ADJ
iajs-826	19	18	space	space	NOUN
iajs-826	19	19	.	.	PUNCT
iajs-826	20	1	examples	example	NOUN
iajs-826	20	2	are	be	AUX
iajs-826	20	3	given	give	VERB
iajs-826	20	4	to	to	PART
iajs-826	20	5	illustrate	illustrate	VERB
iajs-826	20	6	these	these	DET
iajs-826	20	7	structures	structure	NOUN
iajs-826	20	8	.	.	PUNCT
iajs-826	21	1	definition	definition	NOUN
iajs-826	21	2	2.1	2.1	NUM
iajs-826	21	3	let	let	VERB
iajs-826	21	4	(	(	PUNCT
iajs-826	21	5	x	x	NOUN
iajs-826	21	6	,	,	PUNCT
iajs-826	21	7	)	)	PUNCT
iajs-826	21	8	be	be	AUX
iajs-826	21	9	a	a	DET
iajs-826	21	10	non	non	X
iajs-826	21	11	empty	empty	ADJ
iajs-826	21	12	space	space	NOUN
iajs-826	21	13	with	with	ADP
iajs-826	21	14	n	n	CCONJ
iajs-826	21	15	different	different	ADJ
iajs-826	21	16	topology	topology	NOUN
iajs-826	21	17	.	.	PUNCT
iajs-826	22	1	{	{	PUNCT
iajs-826	22	2	x	x	X
iajs-826	22	3	,	,	PUNCT
iajs-826	22	4	}	}	PUNCT
iajs-826	22	5	is	be	AUX
iajs-826	22	6	ca	can	AUX
iajs-826	22	7	lled	lle	VERB
iajs-826	22	8	"	"	PUNCT
iajs-826	22	9	ntopological	ntopological	ADJ
iajs-826	22	10	space	space	NOUN
iajs-826	22	11	"	"	PUNCT
iajs-826	22	12	if	if	SCONJ
iajs-826	22	13	there	there	PRON
iajs-826	22	14	exists	exist	VERB
iajs-826	22	15	n	n	CCONJ
iajs-826	22	16	proper	proper	ADJ
iajs-826	22	17	subspace	subspace	NOUN
iajs-826	22	18	of	of	ADP
iajs-826	22	19	x	x	SYM
iajs-826	22	20	such	such	ADJ
iajs-826	22	21	that	that	PRON
iajs-826	22	22	:	:	PUNCT
iajs-826	22	23	ibn	ibn	PROPN
iajs-826	22	24	alhaitham	alhaitham	NOUN
iajs-826	23	1	j.	j.	PROPN
iajs-826	24	1	fo	fo	ADP
iajs-826	24	2	r	r	NOUN
iajs-826	24	3	pure	pure	ADJ
iajs-826	24	4	&	&	CCONJ
iajs-826	24	5	appl	appl	PROPN
iajs-826	24	6	.	.	PUNCT
iajs-826	25	1	sc	sc	PROPN
iajs-826	25	2	i.	i.	PROPN
iajs-826	25	3	vo	vo	PROPN
iajs-826	25	4	l.24	l.24	PROPN
iajs-826	25	5	(	(	PUNCT
iajs-826	25	6	1	1	NUM
iajs-826	25	7	)	)	PUNCT
iajs-826	25	8	2011	2011	NUM
iajs-826	25	9	1	1	NUM
iajs-826	25	10	.	.	PUNCT
iajs-826	25	11	x	x	X
iajs-826	26	1	=	=	NOUN
iajs-826	26	2	2	2	X
iajs-826	26	3	.	.	PUNCT
iajs-826	26	4	=	=	PRON
iajs-826	26	5	is	be	AUX
iajs-826	26	6	a	a	DET
iajs-826	26	7	subspace	subspace	NOUN
iajs-826	26	8	of	of	ADP
iajs-826	26	9	(	(	PUNCT
iajs-826	26	10	,	,	PUNCT
iajs-826	26	11	where	where	SCONJ
iajs-826	26	12	i	i	PRON
iajs-826	26	13	=	=	NOUN
iajs-826	26	14	1,2,	1,2,	NUM
iajs-826	26	15	…	…	SYM
iajs-826	26	16	,n	,n	PUNCT
iajs-826	26	17	.	.	PUNCT
iajs-826	26	18	example	example	NOUN
iajs-826	26	19	2.2	2.2	NUM
iajs-826	26	20	let	let	VERB
iajs-826	26	21	(	(	PUNCT
iajs-826	26	22	{	{	PUNCT
iajs-826	26	23	1	1	NUM
iajs-826	26	24	,	,	PUNCT
iajs-826	26	25	2	2	NUM
iajs-826	26	26	,	,	PUNCT
iajs-826	26	27	3	3	NUM
iajs-826	26	28	}	}	PUNCT
iajs-826	26	29	,	,	PUNCT
iajs-826	26	30	)	)	PUNCT
iajs-826	26	31	be	be	AUX
iajs-826	26	32	3	3	NUM
iajs-826	26	33	–	–	PUNCT
iajs-826	26	34	topological	topological	ADJ
iajs-826	26	35	space	space	NOUN
iajs-826	26	36	where	where	SCONJ
iajs-826	26	37	=	=	PRON
iajs-826	26	38	{	{	PUNCT
iajs-826	26	39	x	x	NOUN
iajs-826	26	40	,	,	PUNCT
iajs-826	26	41	when	when	SCONJ
iajs-826	26	42	x=	x=	X
iajs-826	26	43	{	{	PUNCT
iajs-826	26	44	1,2,3	1,2,3	NUM
iajs-826	26	45	}	}	PUNCT
iajs-826	26	46	,	,	PUNCT
iajs-826	26	47	=	=	NOUN
iajs-826	26	48	{	{	PUNCT
iajs-826	26	49	x	x	NOUN
iajs-826	26	50	,	,	PUNCT
iajs-826	26	51	{	{	PUNCT
iajs-826	26	52	1	1	NUM
iajs-826	26	53	}	}	PUNCT
iajs-826	26	54	,	,	PUNCT
iajs-826	26	55	}	}	PUNCT
iajs-826	26	56	and	and	CCONJ
iajs-826	26	57	=	=	PRON
iajs-826	26	58	{	{	PUNCT
iajs-826	26	59	x,{2	x,{2	NOUN
iajs-826	26	60	}	}	PUNCT
iajs-826	26	61	,	,	PUNCT
iajs-826	26	62	}	}	PUNCT
iajs-826	26	63	let	let	VERB
iajs-826	26	64	=	=	PRON
iajs-826	26	65	{	{	PUNCT
iajs-826	26	66	1	1	NUM
iajs-826	26	67	}	}	PUNCT
iajs-826	26	68	,	,	PUNCT
iajs-826	26	69	=	=	NOUN
iajs-826	26	70	{	{	PUNCT
iajs-826	26	71	2	2	NUM
iajs-826	26	72	}	}	PUNCT
iajs-826	26	73	and	and	CCONJ
iajs-826	26	74	=	=	NOUN
iajs-826	26	75	{	{	PUNCT
iajs-826	26	76	3}.it	3}.it	NUM
iajs-826	26	77	clear	clear	ADJ
iajs-826	26	78	that	that	SCONJ
iajs-826	26	79	x=	x=	PROPN
iajs-826	27	1	and	and	CCONJ
iajs-826	27	2	=	=	PRON
iajs-826	27	3	{	{	PUNCT
iajs-826	27	4	{	{	PUNCT
iajs-826	27	5	1	1	NUM
iajs-826	27	6	}	}	PUNCT
iajs-826	27	7	,	,	PUNCT
iajs-826	27	8	}	}	PUNCT
iajs-826	27	9	,	,	PUNCT
iajs-826	27	10	=	=	PRON
iajs-826	27	11	{	{	PUNCT
iajs-826	27	12	{	{	PUNCT
iajs-826	27	13	2	2	NUM
iajs-826	27	14	}	}	PUNCT
iajs-826	27	15	,	,	PUNCT
iajs-826	27	16	}	}	PUNCT
iajs-826	27	17	,	,	PUNCT
iajs-826	27	18	=	=	PRON
iajs-826	27	19	{	{	PUNCT
iajs-826	27	20	{	{	PUNCT
iajs-826	27	21	3	3	NUM
iajs-826	27	22	}	}	PUNCT
iajs-826	27	23	,	,	PUNCT
iajs-826	27	24	}	}	PUNCT
iajs-826	27	25	.	.	PUNCT
iajs-826	28	1	it	it	PRON
iajs-826	28	2	is	be	AUX
iajs-826	28	3	clear	clear	ADJ
iajs-826	28	4	that	that	SCONJ
iajs-826	28	5	(	(	PUNCT
iajs-826	28	6	,	,	PUNCT
iajs-826	28	7	is	be	AUX
iajs-826	28	8	a	a	DET
iajs-826	28	9	topological	topological	ADJ
iajs-826	28	10	space	space	NOUN
iajs-826	28	11	of	of	ADP
iajs-826	28	12	(	(	PUNCT
iajs-826	28	13	x	x	X
iajs-826	28	14	for	for	ADP
iajs-826	28	15	i=1,2,3	i=1,2,3	NUM
iajs-826	28	16	.	.	PUNCT
iajs-826	29	1	now	now	ADV
iajs-826	29	2	,	,	PUNCT
iajs-826	29	3	we	we	PRON
iajs-826	29	4	give	give	VERB
iajs-826	29	5	the	the	DET
iajs-826	29	6	definition	definition	NOUN
iajs-826	29	7	of	of	ADP
iajs-826	29	8	open	open	ADJ
iajs-826	29	9	set	set	NOUN
iajs-826	29	10	in	in	ADP
iajs-826	29	11	ntopological	ntopological	ADJ
iajs-826	29	12	space	space	NOUN
iajs-826	29	13	.	.	PUNCT
iajs-826	30	1	definition	definition	NOUN
iajs-826	30	2	2.3	2.3	NUM
iajs-826	30	3	a	a	DET
iajs-826	30	4	subset	subset	ADJ
iajs-826	30	5	u	u	NOUN
iajs-826	30	6	of	of	ADP
iajs-826	30	7	ntopological	ntopological	ADJ
iajs-826	30	8	space	space	NOUN
iajs-826	30	9	(	(	PUNCT
iajs-826	30	10	x	x	NOUN
iajs-826	30	11	,	,	PUNCT
iajs-826	30	12	)	)	PUNCT
iajs-826	30	13	is	be	AUX
iajs-826	30	14	said	say	VERB
iajs-826	30	15	to	to	PART
iajs-826	30	16	be	be	AUX
iajs-826	30	17	an	an	DET
iajs-826	30	18	"	"	PUNCT
iajs-826	30	19	nopen	nopen	ADJ
iajs-826	30	20	set	set	NOUN
iajs-826	30	21	"	"	PUNCT
iajs-826	30	22	if	if	SCONJ
iajs-826	30	23	and	and	CCONJ
iajs-826	30	24	only	only	ADV
iajs-826	30	25	if	if	SCONJ
iajs-826	30	26	it	it	PRON
iajs-826	30	27	is	be	AUX
iajs-826	30	28	open	open	ADJ
iajs-826	30	29	in	in	ADP
iajs-826	30	30	,	,	PUNCT
iajs-826	30	31	for	for	ADP
iajs-826	30	32	some	some	DET
iajs-826	30	33	i	i	NOUN
iajs-826	30	34	=	=	SYM
iajs-826	30	35	1,2,	1,2,	NUM
iajs-826	30	36	…	…	SYM
iajs-826	30	37	,n	,n	PUNCT
iajs-826	30	38	.	.	PUNCT
iajs-826	31	1	definition	definition	NOUN
iajs-826	31	2	2.4	2.4	NUM
iajs-826	31	3	the	the	DET
iajs-826	31	4	complement	complement	NOUN
iajs-826	31	5	of	of	ADP
iajs-826	31	6	nopen	nopen	ADJ
iajs-826	31	7	set	set	VERB
iajs-826	31	8	in	in	ADP
iajs-826	31	9	ntopological	ntopological	ADJ
iajs-826	31	10	space	space	NOUN
iajs-826	31	11	(	(	PUNCT
iajs-826	31	12	x	x	NOUN
iajs-826	31	13	,	,	PUNCT
iajs-826	31	14	)	)	PUNCT
iajs-826	31	15	is	be	AUX
iajs-826	31	16	said	say	VERB
iajs-826	31	17	to	to	PART
iajs-826	31	18	be	be	AUX
iajs-826	31	19	an	an	DET
iajs-826	31	20	"	"	PUNCT
iajs-826	31	21	n	n	CCONJ
iajs-826	31	22	-	-	PUNCT
iajs-826	31	23	closed	closed	ADJ
iajs-826	31	24	set	set	NOUN
iajs-826	31	25	"	"	PUNCT
iajs-826	31	26	.	.	PUNCT
iajs-826	32	1	remark	remark	VERB
iajs-826	32	2	2.5	2.5	NUM
iajs-826	32	3	1every	1every	NUM
iajs-826	32	4	open	open	ADJ
iajs-826	32	5	set	set	VERB
iajs-826	32	6	in	in	ADP
iajs-826	32	7	topological	topological	ADJ
iajs-826	32	8	space	space	NOUN
iajs-826	32	9	(	(	PUNCT
iajs-826	32	10	x	x	X
iajs-826	32	11	is	be	AUX
iajs-826	32	12	nopen	nopen	ADJ
iajs-826	32	13	set	set	NOUN
iajs-826	32	14	,	,	PUNCT
iajs-826	32	15	for	for	ADP
iajs-826	32	16	all	all	DET
iajs-826	32	17	i=	i=	PROPN
iajs-826	32	18	1,2,	1,2,	NUM
iajs-826	32	19	…	…	SYM
iajs-826	32	20	,n	,n	NOUN
iajs-826	32	21	,	,	PUNCT
iajs-826	32	22	but	but	CCONJ
iajs-826	32	23	the	the	DET
iajs-826	32	24	converse	converse	NOUN
iajs-826	32	25	is	be	AUX
iajs-826	32	26	not	not	PART
iajs-826	32	27	true	true	ADJ
iajs-826	32	28	,	,	PUNCT
iajs-826	32	29	(	(	PUNCT
iajs-826	32	30	see	see	VERB
iajs-826	32	31	the	the	DET
iajs-826	32	32	following	following	ADJ
iajs-826	32	33	example	example	NOUN
iajs-826	32	34	2.6	2.6	NUM
iajs-826	32	35	)	)	PUNCT
iajs-826	32	36	.	.	PUNCT
iajs-826	33	1	2every	2every	NUM
iajs-826	33	2	closed	close	VERB
iajs-826	33	3	set	set	NOUN
iajs-826	33	4	in	in	ADP
iajs-826	33	5	topological	topological	ADJ
iajs-826	33	6	space	space	NOUN
iajs-826	33	7	(	(	PUNCT
iajs-826	33	8	x	x	X
iajs-826	33	9	is	be	AUX
iajs-826	33	10	nclosed	nclose	VERB
iajs-826	33	11	set	set	VERB
iajs-826	33	12	,	,	PUNCT
iajs-826	33	13	for	for	ADP
iajs-826	33	14	all	all	DET
iajs-826	33	15	i=1,2,	i=1,2,	NOUN
iajs-826	33	16	..	..	PUNCT
iajs-826	33	17	,n	,n	PUNCT
iajs-826	33	18	but	but	CCONJ
iajs-826	33	19	the	the	DET
iajs-826	33	20	converse	converse	NOUN
iajs-826	33	21	is	be	AUX
iajs-826	33	22	not	not	PART
iajs-826	33	23	true	true	ADJ
iajs-826	33	24	,	,	PUNCT
iajs-826	33	25	(	(	PUNCT
iajs-826	33	26	see	see	VERB
iajs-826	33	27	the	the	DET
iajs-826	33	28	following	following	ADJ
iajs-826	33	29	example	example	NOUN
iajs-826	33	30	2.6	2.6	NUM
iajs-826	33	31	)	)	PUNCT
iajs-826	33	32	.	.	PUNCT
iajs-826	34	1	3every	3every	NUM
iajs-826	34	2	open	open	ADJ
iajs-826	34	3	set	set	VERB
iajs-826	34	4	in	in	ADP
iajs-826	34	5	subspace	subspace	NOUN
iajs-826	34	6	for	for	ADP
iajs-826	34	7	all	all	DET
iajs-826	34	8	i=	i=	PROPN
iajs-826	34	9	1,2,	1,2,	NUM
iajs-826	34	10	…	…	PUNCT
iajs-826	34	11	,n	,n	PUNCT
iajs-826	34	12	need	need	VERB
iajs-826	34	13	not	not	PART
iajs-826	34	14	to	to	PART
iajs-826	34	15	be	be	AUX
iajs-826	34	16	nopen	nopen	ADJ
iajs-826	34	17	set	set	VERB
iajs-826	34	18	in	in	ADP
iajs-826	34	19	n	n	CCONJ
iajs-826	34	20	topological	topological	ADJ
iajs-826	34	21	space	space	NOUN
iajs-826	34	22	(	(	PUNCT
iajs-826	34	23	x	x	NOUN
iajs-826	34	24	,	,	PUNCT
iajs-826	34	25	)	)	PUNCT
iajs-826	34	26	,	,	PUNCT
iajs-826	34	27	only	only	ADV
iajs-826	34	28	if	if	SCONJ
iajs-826	34	29	the	the	DET
iajs-826	34	30	subspace	subspace	NOUN
iajs-826	34	31	is	be	AUX
iajs-826	34	32	open	open	ADJ
iajs-826	34	33	in	in	ADP
iajs-826	34	34	(	(	PUNCT
iajs-826	34	35	x	x	INTJ
iajs-826	34	36	,	,	PUNCT
iajs-826	34	37	(	(	PUNCT
iajs-826	34	38	see	see	VERB
iajs-826	34	39	the	the	DET
iajs-826	34	40	following	following	ADJ
iajs-826	34	41	example	example	NOUN
iajs-826	34	42	2.6	2.6	NUM
iajs-826	34	43	)	)	PUNCT
iajs-826	34	44	.	.	PUNCT
iajs-826	35	1	example	example	NOUN
iajs-826	35	2	2.6	2.6	NUM
iajs-826	35	3	let	let	AUX
iajs-826	35	4	be	be	AUX
iajs-826	35	5	4	4	NUM
iajs-826	35	6	-	-	PUNCT
iajs-826	35	7	topological	topological	ADJ
iajs-826	35	8	space	space	NOUN
iajs-826	35	9	(	(	PUNCT
iajs-826	35	10	where	where	SCONJ
iajs-826	35	11	is	be	AUX
iajs-826	35	12	the	the	DET
iajs-826	35	13	set	set	NOUN
iajs-826	35	14	of	of	ADP
iajs-826	35	15	natural	natural	ADJ
iajs-826	35	16	numbers	number	NOUN
iajs-826	35	17	)	)	PUNCT
iajs-826	35	18	such	such	ADJ
iajs-826	35	19	that	that	PRON
iajs-826	35	20	and	and	CCONJ
iajs-826	35	21	let	let	VERB
iajs-826	35	22	x1	x1	NUM
iajs-826	35	23	,	,	PUNCT
iajs-826	35	24	x2	x2	PROPN
iajs-826	35	25	,	,	PUNCT
iajs-826	35	26	x3	x3	ADJ
iajs-826	35	27	,	,	PUNCT
iajs-826	35	28	x4	x4	PROPN
iajs-826	35	29	be	be	VERB
iajs-826	35	30	four	four	NUM
iajs-826	35	31	subspace	subspace	NOUN
iajs-826	35	32	of	of	ADP
iajs-826	35	33	x	x	SYM
iajs-826	35	34	such	such	ADJ
iajs-826	35	35	that	that	SCONJ
iajs-826	35	36	:	:	PUNCT
iajs-826	35	37	x1=	x1=	PROPN
iajs-826	35	38	{	{	PUNCT
iajs-826	35	39	1	1	NUM
iajs-826	35	40	}	}	PUNCT
iajs-826	35	41	implies	imply	VERB
iajs-826	35	42	=	=	PUNCT
iajs-826	35	43	x2=	x2=	X
iajs-826	35	44	{	{	PUNCT
iajs-826	35	45	2	2	NUM
iajs-826	35	46	}	}	PUNCT
iajs-826	35	47	implies	imply	VERB
iajs-826	35	48	=	=	PUNCT
iajs-826	35	49	x3=	x3=	X
iajs-826	35	50	{	{	PUNCT
iajs-826	35	51	3	3	NUM
iajs-826	35	52	}	}	PUNCT
iajs-826	35	53	implies	imply	VERB
iajs-826	35	54	=	=	PUNCT
iajs-826	35	55	x4=	x4=	NOUN
iajs-826	35	56	{	{	PUNCT
iajs-826	35	57	4	4	NUM
iajs-826	35	58	,	,	PUNCT
iajs-826	35	59	5	5	NUM
iajs-826	35	60	,	,	PUNCT
iajs-826	35	61	6	6	NUM
iajs-826	35	62	,	,	PUNCT
iajs-826	35	63	7	7	NUM
iajs-826	35	64	,	,	PUNCT
iajs-826	35	65	…	…	PUNCT
iajs-826	35	66	}	}	PUNCT
iajs-826	35	67	implies	imply	VERB
iajs-826	35	68	=	=	PUNCT
iajs-826	35	69	.	.	PUNCT
iajs-826	36	1	it	it	PRON
iajs-826	36	2	is	be	AUX
iajs-826	36	3	clear	clear	ADJ
iajs-826	36	4	that	that	SCONJ
iajs-826	36	5	x=	x=	PUNCT
iajs-826	37	1	x1	x1	PROPN
iajs-826	37	2	x2	x2	PROPN
iajs-826	37	3	x3	x3	PROPN
iajs-826	37	4	x4	x4	PROPN
iajs-826	37	5	now	now	ADV
iajs-826	37	6	,	,	PUNCT
iajs-826	37	7	to	to	PART
iajs-826	37	8	show	show	VERB
iajs-826	37	9	the	the	DET
iajs-826	37	10	converse	converse	NOUN
iajs-826	37	11	of	of	ADP
iajs-826	37	12	part	part	NOUN
iajs-826	37	13	(	(	PUNCT
iajs-826	37	14	1	1	NUM
iajs-826	37	15	)	)	PUNCT
iajs-826	37	16	is	be	AUX
iajs-826	37	17	not	not	PART
iajs-826	37	18	true	true	ADJ
iajs-826	37	19	,	,	PUNCT
iajs-826	37	20	let	let	VERB
iajs-826	37	21	{	{	PUNCT
iajs-826	37	22	1	1	NUM
iajs-826	37	23	}	}	PUNCT
iajs-826	37	24	is	be	AUX
iajs-826	37	25	nopen	nopen	ADJ
iajs-826	37	26	set	set	VERB
iajs-826	37	27	in	in	ADP
iajs-826	37	28	but	but	CCONJ
iajs-826	37	29	it	it	PRON
iajs-826	37	30	is	be	AUX
iajs-826	37	31	not	not	PART
iajs-826	37	32	open	open	ADJ
iajs-826	37	33	set	set	VERB
iajs-826	37	34	in	in	ADP
iajs-826	37	35	each	each	PRON
iajs-826	37	36	(	(	PUNCT
iajs-826	37	37	x	x	X
iajs-826	37	38	;	;	PUNCT
iajs-826	37	39	i=	i=	PROPN
iajs-826	37	40	1,2,	1,2,	NUM
iajs-826	37	41	…	…	SYM
iajs-826	37	42	,n	,n	NOUN
iajs-826	37	43	.	.	PUNCT
iajs-826	38	1	also	also	ADV
iajs-826	38	2	,	,	PUNCT
iajs-826	38	3	to	to	PART
iajs-826	38	4	show	show	VERB
iajs-826	38	5	the	the	DET
iajs-826	38	6	converse	converse	NOUN
iajs-826	38	7	of	of	ADP
iajs-826	38	8	part	part	NOUN
iajs-826	38	9	(	(	PUNCT
iajs-826	38	10	2	2	NUM
iajs-826	38	11	)	)	PUNCT
iajs-826	38	12	is	be	AUX
iajs-826	38	13	not	not	PART
iajs-826	38	14	true	true	ADJ
iajs-826	38	15	,	,	PUNCT
iajs-826	38	16	let	let	VERB
iajs-826	38	17	{	{	PUNCT
iajs-826	38	18	2	2	NUM
iajs-826	38	19	,	,	PUNCT
iajs-826	38	20	3	3	NUM
iajs-826	38	21	,	,	PUNCT
iajs-826	38	22	4	4	NUM
iajs-826	38	23	,	,	PUNCT
iajs-826	38	24	5	5	NUM
iajs-826	38	25	,	,	PUNCT
iajs-826	38	26	…	…	PUNCT
iajs-826	38	27	}	}	PUNCT
iajs-826	38	28	is	be	AUX
iajs-826	38	29	nclosed	nclose	VERB
iajs-826	38	30	set	set	VERB
iajs-826	39	1	but	but	CCONJ
iajs-826	39	2	it	it	PRON
iajs-826	39	3	is	be	AUX
iajs-826	39	4	not	not	PART
iajs-826	39	5	closed	close	VERB
iajs-826	39	6	set	set	VERB
iajs-826	39	7	in	in	ADP
iajs-826	39	8	each	each	PRON
iajs-826	39	9	(	(	PUNCT
iajs-826	39	10	x	x	X
iajs-826	39	11	;	;	PUNCT
iajs-826	39	12	i=	i=	PROPN
iajs-826	39	13	1,2,	1,2,	NUM
iajs-826	39	14	…	…	SYM
iajs-826	39	15	,n	,n	PUNCT
iajs-826	39	16	.	.	PUNCT
iajs-826	40	1	and	and	CCONJ
iajs-826	40	2	also	also	ADV
iajs-826	40	3	notice	notice	VERB
iajs-826	40	4	that	that	SCONJ
iajs-826	40	5	the	the	DET
iajs-826	40	6	subspace	subspace	PROPN
iajs-826	40	7	x1=	x1=	PROPN
iajs-826	40	8	{	{	PUNCT
iajs-826	40	9	1	1	NUM
iajs-826	40	10	}	}	PUNCT
iajs-826	40	11	is	be	AUX
iajs-826	40	12	open	open	ADJ
iajs-826	40	13	in	in	ADP
iajs-826	40	14	implies	implie	NOUN
iajs-826	40	15	that	that	SCONJ
iajs-826	40	16	each	each	DET
iajs-826	40	17	open	open	ADJ
iajs-826	40	18	set	set	VERB
iajs-826	40	19	in	in	ADP
iajs-826	40	20	is	be	AUX
iajs-826	40	21	nopen	nopen	ADJ
iajs-826	40	22	set	set	VERB
iajs-826	40	23	in	in	ADP
iajs-826	40	24	but	but	CCONJ
iajs-826	40	25	in	in	ADP
iajs-826	40	26	the	the	DET
iajs-826	40	27	other	other	ADJ
iajs-826	40	28	hand	hand	NOUN
iajs-826	40	29	notice	notice	NOUN
iajs-826	40	30	that	that	SCONJ
iajs-826	40	31	the	the	DET
iajs-826	40	32	subspace	subspace	NOUN
iajs-826	40	33	x3=	x3=	PUNCT
iajs-826	40	34	{	{	PUNCT
iajs-826	40	35	3	3	X
iajs-826	40	36	}	}	PUNCT
iajs-826	40	37	is	be	AUX
iajs-826	40	38	not	not	PART
iajs-826	40	39	open	open	ADJ
iajs-826	40	40	in	in	ADP
iajs-826	40	41	(	(	PUNCT
iajs-826	40	42	x3	x3	ADJ
iajs-826	40	43	,	,	PUNCT
iajs-826	40	44	implies	imply	VERB
iajs-826	40	45	that	that	SCONJ
iajs-826	40	46	each	each	DET
iajs-826	40	47	open	open	ADJ
iajs-826	40	48	set	set	NOUN
iajs-826	40	49	in	in	ADP
iajs-826	40	50	(	(	PUNCT
iajs-826	40	51	x3	x3	ADJ
iajs-826	40	52	,	,	PUNCT
iajs-826	40	53	need	need	VERB
iajs-826	40	54	not	not	PART
iajs-826	40	55	to	to	PART
iajs-826	40	56	be	be	AUX
iajs-826	40	57	nopen	nopen	ADJ
iajs-826	40	58	set	set	VERB
iajs-826	40	59	in	in	ADP
iajs-826	40	60	next	next	ADJ
iajs-826	40	61	,	,	PUNCT
iajs-826	40	62	we	we	PRON
iajs-826	40	63	give	give	VERB
iajs-826	40	64	a	a	DET
iajs-826	40	65	definition	definition	NOUN
iajs-826	40	66	about	about	ADP
iajs-826	40	67	sub	sub	NOUN
iajs-826	40	68	ntopological	ntopological	ADJ
iajs-826	40	69	space	space	NOUN
iajs-826	40	70	.	.	PUNCT
iajs-826	41	1	definition	definition	NOUN
iajs-826	41	2	2.7	2.7	NUM
iajs-826	41	3	let	let	VERB
iajs-826	41	4	(	(	PUNCT
iajs-826	41	5	x	x	NOUN
iajs-826	41	6	,	,	PUNCT
iajs-826	41	7	)	)	PUNCT
iajs-826	41	8	be	be	AUX
iajs-826	41	9	ntopological	ntopological	ADJ
iajs-826	41	10	space	space	NOUN
iajs-826	41	11	(	(	PUNCT
iajs-826	41	12	)	)	PUNCT
iajs-826	41	13	.	.	PUNCT
iajs-826	42	1	the	the	DET
iajs-826	42	2	subspace	subspace	PROPN
iajs-826	42	3	y	y	PROPN
iajs-826	42	4	(	(	PUNCT
iajs-826	42	5	)	)	PUNCT
iajs-826	42	6	of	of	ADP
iajs-826	42	7	x	x	SYM
iajs-826	42	8	is	be	AUX
iajs-826	42	9	called	call	VERB
iajs-826	42	10	a	a	DET
iajs-826	42	11	sub	sub	NOUN
iajs-826	42	12	ntopological	ntopological	ADJ
iajs-826	42	13	space	space	NOUN
iajs-826	42	14	of	of	ADP
iajs-826	42	15	x	x	PUNCT
iajs-826	42	16	if	if	SCONJ
iajs-826	42	17	and	and	CCONJ
iajs-826	42	18	only	only	ADV
iajs-826	42	19	if	if	SCONJ
iajs-826	42	20	ibn	ibn	PROPN
iajs-826	42	21	alhaitham	alhaitham	NOUN
iajs-826	43	1	j.	j.	PROPN
iajs-826	44	1	fo	fo	ADP
iajs-826	44	2	r	r	NOUN
iajs-826	44	3	pure	pure	ADJ
iajs-826	44	4	&	&	CCONJ
iajs-826	44	5	appl	appl	PROPN
iajs-826	44	6	.	.	PUNCT
iajs-826	45	1	sc	sc	PROPN
iajs-826	45	2	i.	i.	PROPN
iajs-826	45	3	vo	vo	PROPN
iajs-826	46	1	l.24	l.24	PROPN
iajs-826	46	2	(	(	PUNCT
iajs-826	46	3	1	1	NUM
iajs-826	46	4	)	)	PUNCT
iajs-826	46	5	2011	2011	NUM
iajs-826	46	6	(	(	PUNCT
iajs-826	46	7	i	i	NOUN
iajs-826	46	8	)	)	PUNCT
iajs-826	46	9	there	there	PRON
iajs-826	46	10	exists	exist	VERB
iajs-826	46	11	n	n	CCONJ
iajs-826	46	12	proper	proper	ADJ
iajs-826	46	13	subspace	subspace	NOUN
iajs-826	46	14	,	,	PUNCT
iajs-826	46	15	…	…	PUNCT
iajs-826	46	16	,	,	PUNCT
iajs-826	46	17	of	of	ADP
iajs-826	46	18	y	y	PRON
iajs-826	46	19	such	such	ADJ
iajs-826	46	20	that	that	PRON
iajs-826	46	21	and	and	CCONJ
iajs-826	46	22	(	(	PUNCT
iajs-826	46	23	y	y	NOUN
iajs-826	46	24	,	,	PUNCT
iajs-826	46	25	is	be	AUX
iajs-826	46	26	sub	sub	ADJ
iajs-826	46	27	-	-	ADJ
iajs-826	46	28	n	n	CCONJ
iajs-826	46	29	-	-	PUNCT
iajs-826	46	30	topological	topological	ADJ
iajs-826	46	31	space	space	NOUN
iajs-826	46	32	of	of	ADP
iajs-826	46	33	(	(	PUNCT
iajs-826	46	34	x	x	NOUN
iajs-826	46	35	,	,	PUNCT
iajs-826	46	36	)	)	PUNCT
iajs-826	46	37	,	,	PUNCT
iajs-826	46	38	that	that	PRON
iajs-826	46	39	is	is	ADV
iajs-826	46	40	=	=	SYM
iajs-826	46	41	y	y	PROPN
iajs-826	46	42			PUNCT
iajs-826	46	43	.	.	PUNCT
iajs-826	47	1	(	(	PUNCT
iajs-826	47	2	ii	ii	NOUN
iajs-826	47	3	)	)	PUNCT
iajs-826	47	4	=	=	VERB
iajs-826	47	5	is	be	AUX
iajs-826	47	6	subspace	subspace	NOUN
iajs-826	47	7	of	of	ADP
iajs-826	47	8	(	(	PUNCT
iajs-826	47	9	y	y	PROPN
iajs-826	47	10	,	,	PUNCT
iajs-826	47	11	eexample	eexample	NOUN
iajs-826	47	12	2.8	2.8	NUM
iajs-826	47	13	let	let	VERB
iajs-826	47	14	(	(	PUNCT
iajs-826	47	15	x	x	NOUN
iajs-826	47	16	,	,	PUNCT
iajs-826	47	17	)	)	PUNCT
iajs-826	47	18	is	be	AUX
iajs-826	47	19	3	3	NUM
iajs-826	47	20	–	–	PUNCT
iajs-826	47	21	topological	topological	ADJ
iajs-826	47	22	space	space	NOUN
iajs-826	47	23	where	where	SCONJ
iajs-826	47	24	x={1,2,3,4,5,6,7	x={1,2,3,4,5,6,7	PROPN
iajs-826	47	25	}	}	PUNCT
iajs-826	47	26	,	,	PUNCT
iajs-826	47	27	=	=	PRON
iajs-826	47	28	{	{	PUNCT
iajs-826	47	29	x	x	NOUN
iajs-826	47	30	,	,	PUNCT
iajs-826	47	31	=	=	PRON
iajs-826	47	32	{	{	PUNCT
iajs-826	47	33	x	x	NOUN
iajs-826	47	34	,	,	PUNCT
iajs-826	47	35	,	,	PUNCT
iajs-826	47	36	{	{	PUNCT
iajs-826	47	37	2,4,6	2,4,6	NUM
iajs-826	47	38	}	}	PUNCT
iajs-826	47	39	}	}	PUNCT
iajs-826	47	40	,	,	PUNCT
iajs-826	47	41	and	and	CCONJ
iajs-826	47	42	=	=	NOUN
iajs-826	47	43	{	{	PUNCT
iajs-826	47	44	x	x	NOUN
iajs-826	47	45	,	,	PUNCT
iajs-826	47	46	{	{	PUNCT
iajs-826	47	47	3,7	3,7	NUM
iajs-826	47	48	}	}	PUNCT
iajs-826	47	49	}	}	PUNCT
iajs-826	47	50	and	and	CCONJ
iajs-826	47	51	let	let	VERB
iajs-826	47	52	let	let	VERB
iajs-826	47	53	y	y	PRON
iajs-826	47	54	=	=	VERB
iajs-826	47	55	{	{	PUNCT
iajs-826	47	56	2,3,5,6	2,3,5,6	NUM
iajs-826	47	57	}	}	PUNCT
iajs-826	47	58	,	,	PUNCT
iajs-826	47	59	=	=	PUNCT
iajs-826	47	60	y	y	X
iajs-826	47	61	=	=	SYM
iajs-826	47	62	{	{	PUNCT
iajs-826	47	63	y	y	PROPN
iajs-826	47	64	,	,	PUNCT
iajs-826	47	65			ADV
iajs-826	47	66	}	}	PUNCT
iajs-826	47	67	,	,	PUNCT
iajs-826	47	68	=	=	PUNCT
iajs-826	47	69	y	y	X
iajs-826	47	70	=	=	SYM
iajs-826	47	71	{	{	PUNCT
iajs-826	47	72	y	y	PROPN
iajs-826	47	73	,	,	PUNCT
iajs-826	47	74			PROPN
iajs-826	47	75	,	,	PUNCT
iajs-826	47	76	{	{	PUNCT
iajs-826	47	77	2,6	2,6	NUM
iajs-826	47	78	}	}	PUNCT
iajs-826	47	79	}	}	PUNCT
iajs-826	47	80	,	,	PUNCT
iajs-826	47	81	=	=	PUNCT
iajs-826	47	82	y	y	X
iajs-826	47	83	=	=	SYM
iajs-826	47	84	{	{	PUNCT
iajs-826	47	85	y	y	PROPN
iajs-826	47	86	,	,	PUNCT
iajs-826	47	87			ADJ
iajs-826	47	88	,	,	PUNCT
iajs-826	47	89	{	{	PUNCT
iajs-826	47	90	3	3	NUM
iajs-826	47	91	}	}	PUNCT
iajs-826	47	92	}	}	PUNCT
iajs-826	47	93	.	.	PUNCT
iajs-826	48	1	it	it	PRON
iajs-826	48	2	is	be	AUX
iajs-826	48	3	clear	clear	ADJ
iajs-826	48	4	that	that	SCONJ
iajs-826	48	5	(	(	PUNCT
iajs-826	48	6	y	y	NOUN
iajs-826	48	7	,	,	PUNCT
iajs-826	48	8	is	be	AUX
iajs-826	48	9	sub	sub	NOUN
iajs-826	48	10	3	3	NUM
iajs-826	48	11	topological	topological	ADJ
iajs-826	48	12	space	space	NOUN
iajs-826	48	13	of	of	ADP
iajs-826	48	14	(	(	PUNCT
iajs-826	48	15	x	x	NOUN
iajs-826	48	16	,	,	PUNCT
iajs-826	48	17	)	)	PUNCT
iajs-826	48	18	where	where	SCONJ
iajs-826	48	19	,	,	PUNCT
iajs-826	48	20	=	=	NOUN
iajs-826	48	21	{	{	PUNCT
iajs-826	48	22	2,3	2,3	NUM
iajs-826	48	23	}	}	PUNCT
iajs-826	48	24	,	,	PUNCT
iajs-826	49	1	=	=	NOUN
iajs-826	49	2	{	{	PUNCT
iajs-826	49	3	5	5	NUM
iajs-826	49	4	}	}	PUNCT
iajs-826	49	5	=	=	NOUN
iajs-826	49	6	{	{	PUNCT
iajs-826	49	7	6	6	NUM
iajs-826	49	8	}	}	PUNCT
iajs-826	49	9	and	and	CCONJ
iajs-826	49	10	=	=	SYM
iajs-826	49	11	=	=	SYM
iajs-826	49	12	=	=	PUNCT
iajs-826	49	13	=	=	NOUN
iajs-826	49	14	{	{	PUNCT
iajs-826	49	15			NOUN
iajs-826	49	16	,	,	PUNCT
iajs-826	49	17	now	now	ADV
iajs-826	49	18	,	,	PUNCT
iajs-826	49	19	we	we	PRON
iajs-826	49	20	introduce	introduce	VERB
iajs-826	49	21	definitions	definition	NOUN
iajs-826	49	22	and	and	CCONJ
iajs-826	49	23	examples	example	NOUN
iajs-826	49	24	about	about	ADP
iajs-826	49	25	separation	separation	NOUN
iajs-826	49	26	axioms	axiom	NOUN
iajs-826	49	27	in	in	ADP
iajs-826	49	28	ntopological	ntopological	ADJ
iajs-826	49	29	space	space	NOUN
iajs-826	49	30	.	.	PUNCT
iajs-826	50	1	definition	definition	NOUN
iajs-826	50	2	2.9	2.9	NUM
iajs-826	50	3	an	an	DET
iajs-826	50	4	ntopological	ntopological	ADJ
iajs-826	50	5	space	space	NOUN
iajs-826	50	6	(	(	PUNCT
iajs-826	50	7	x	x	NOUN
iajs-826	50	8	,	,	PUNCT
iajs-826	50	9	)	)	PUNCT
iajs-826	50	10	is	be	AUX
iajs-826	50	11	said	say	VERB
iajs-826	50	12	to	to	PART
iajs-826	50	13	be	be	AUX
iajs-826	50	14	an	an	DET
iajs-826	50	15	"	"	PUNCT
iajs-826	50	16	n	n	CCONJ
iajs-826	50	17	-space	-space	NOUN
iajs-826	50	18	"	"	PUNCT
iajs-826	50	19	if	if	SCONJ
iajs-826	50	20	and	and	CCONJ
iajs-826	50	21	only	only	ADV
iajs-826	50	22	if	if	SCONJ
iajs-826	50	23	for	for	ADP
iajs-826	50	24	each	each	DET
iajs-826	50	25	pair	pair	NOUN
iajs-826	50	26	of	of	ADP
iajs-826	50	27	distinct	distinct	ADJ
iajs-826	50	28	points	point	NOUN
iajs-826	50	29	x	x	X
iajs-826	50	30	,	,	PUNCT
iajs-826	50	31	yx	yx	PROPN
iajs-826	50	32	,	,	PUNCT
iajs-826	50	33	there	there	PRON
iajs-826	50	34	exists	exist	VERB
iajs-826	50	35	nopen	nopen	ADJ
iajs-826	50	36	set	set	VERB
iajs-826	50	37	u	u	NOUN
iajs-826	50	38	of	of	ADP
iajs-826	50	39	x	x	SYM
iajs-826	51	1	such	such	ADJ
iajs-826	51	2	that	that	PRON
iajs-826	51	3	xu	xu	PROPN
iajs-826	51	4	and	and	CCONJ
iajs-826	51	5	yu	yu	PROPN
iajs-826	51	6	.	.	PUNCT
iajs-826	51	7	proposition	proposition	NOUN
iajs-826	51	8	2.10	2.10	NUM
iajs-826	51	9	an	an	DET
iajs-826	51	10	ntopological	ntopological	ADJ
iajs-826	51	11	space	space	NOUN
iajs-826	51	12	(	(	PUNCT
iajs-826	51	13	x	x	NOUN
iajs-826	51	14	,	,	PUNCT
iajs-826	51	15	)	)	PUNCT
iajs-826	51	16	is	be	AUX
iajs-826	51	17	n	n	PRON
iajs-826	51	18	–	–	PUNCT
iajs-826	51	19	space	space	NOUN
iajs-826	51	20	if	if	SCONJ
iajs-826	51	21	(	(	PUNCT
iajs-826	51	22	x	x	X
iajs-826	51	23	is	be	AUX
iajs-826	51	24	–	–	PUNCT
iajs-826	51	25	space	space	NOUN
iajs-826	51	26	for	for	ADP
iajs-826	51	27	some	some	DET
iajs-826	51	28	i	i	NOUN
iajs-826	51	29	=	=	SYM
iajs-826	51	30	1,2,	1,2,	NUM
iajs-826	51	31	…	…	PUNCT
iajs-826	51	32	,n	,n	NOUN
iajs-826	51	33	.	.	PUNCT
iajs-826	52	1	proof	proof	NOUN
iajs-826	52	2	to	to	PART
iajs-826	52	3	prove	prove	VERB
iajs-826	52	4	(	(	PUNCT
iajs-826	52	5	x	x	NOUN
iajs-826	52	6	,	,	PUNCT
iajs-826	52	7	)	)	PUNCT
iajs-826	52	8	is	be	AUX
iajs-826	52	9	n	n	DET
iajs-826	52	10	space	space	NOUN
iajs-826	52	11	,	,	PUNCT
iajs-826	52	12	we	we	PRON
iajs-826	52	13	must	must	AUX
iajs-826	52	14	prove	prove	VERB
iajs-826	52	15	for	for	ADP
iajs-826	52	16	any	any	DET
iajs-826	52	17	x	x	NOUN
iajs-826	52	18	,	,	PUNCT
iajs-826	52	19	yx	yx	ADP
iajs-826	52	20	such	such	ADJ
iajs-826	52	21	that	that	SCONJ
iajs-826	52	22	x≠	x≠	PROPN
iajs-826	52	23	y	y	PROPN
iajs-826	52	24	,	,	PUNCT
iajs-826	52	25	there	there	PRON
iajs-826	52	26	exists	exist	VERB
iajs-826	52	27	n	n	CCONJ
iajs-826	52	28	-	-	PUNCT
iajs-826	52	29	open	open	ADJ
iajs-826	52	30	set	set	NOUN
iajs-826	52	31	u	u	NOUN
iajs-826	52	32	of	of	ADP
iajs-826	52	33	x	x	SYM
iajs-826	52	34	such	such	ADJ
iajs-826	52	35	that	that	PRON
iajs-826	52	36	xu	xu	PROPN
iajs-826	52	37	and	and	CCONJ
iajs-826	52	38	yu	yu	PROPN
iajs-826	52	39	.	.	PUNCT
iajs-826	53	1	now	now	ADV
iajs-826	53	2	,	,	PUNCT
iajs-826	53	3	let	let	VERB
iajs-826	53	4	x	x	PRON
iajs-826	53	5	,	,	PUNCT
iajs-826	53	6	yx	yx	PROPN
iajs-826	53	7	;	;	PUNCT
iajs-826	53	8	x≠	x≠	PROPN
iajs-826	53	9	y	y	PROPN
iajs-826	53	10	since	since	SCONJ
iajs-826	53	11	there	there	PRON
iajs-826	53	12	exists	exist	VERB
iajs-826	53	13	i1,2,	i1,2,	NOUN
iajs-826	53	14	…	…	PUNCT
iajs-826	53	15	,n	,n	NOUN
iajs-826	53	16	such	such	ADJ
iajs-826	53	17	that	that	SCONJ
iajs-826	53	18	(	(	PUNCT
iajs-826	53	19	x	x	X
iajs-826	53	20	is	be	AUX
iajs-826	53	21	–	–	PUNCT
iajs-826	53	22	space	space	NOUN
iajs-826	53	23	,	,	PUNCT
iajs-826	53	24	implies	imply	VERB
iajs-826	53	25	there	there	PRON
iajs-826	53	26	exists	exist	VERB
iajs-826	53	27	open	open	ADJ
iajs-826	53	28	set	set	VERB
iajs-826	53	29	u	u	NOUN
iajs-826	53	30	in	in	ADP
iajs-826	53	31	such	such	ADJ
iajs-826	53	32	that	that	PRON
iajs-826	53	33	xu	xu	PROPN
iajs-826	53	34	and	and	CCONJ
iajs-826	53	35	yu	yu	PROPN
iajs-826	53	36	,	,	PUNCT
iajs-826	53	37	therefore	therefore	ADV
iajs-826	53	38			NUM
iajs-826	53	39	n	n	CCONJ
iajs-826	53	40	-	-	PUNCT
iajs-826	53	41	open	open	ADJ
iajs-826	53	42	set	set	NOUN
iajs-826	53	43	u	u	NOUN
iajs-826	53	44	of	of	ADP
iajs-826	53	45	x	x	SYM
iajs-826	53	46	such	such	ADJ
iajs-826	53	47	that	that	PRON
iajs-826	53	48	xu	xu	PROPN
iajs-826	54	1	and	and	CCONJ
iajs-826	54	2	yu(by	yu(by	PROPN
iajs-826	54	3	definition	definition	NOUN
iajs-826	54	4	2.3	2.3	NUM
iajs-826	54	5	)	)	PUNCT
iajs-826	54	6	.	.	PUNCT
iajs-826	55	1	thus	thus	ADV
iajs-826	55	2	(	(	PUNCT
iajs-826	55	3	x	x	X
iajs-826	55	4	,	,	PUNCT
iajs-826	55	5	)	)	PUNCT
iajs-826	55	6	is	be	AUX
iajs-826	55	7	n	n	DET
iajs-826	55	8	space	space	NOUN
iajs-826	55	9	.	.	PUNCT
iajs-826	56	1	■	■	PUNCT
iajs-826	56	2	remark	remark	VERB
iajs-826	56	3	2.11	2.11	NUM
iajs-826	56	4	the	the	DET
iajs-826	56	5	converse	converse	NOUN
iajs-826	56	6	of	of	ADP
iajs-826	56	7	(	(	PUNCT
iajs-826	56	8	proposition	proposition	NOUN
iajs-826	56	9	2.10	2.10	NUM
iajs-826	56	10	)	)	PUNCT
iajs-826	56	11	is	be	AUX
iajs-826	56	12	not	not	PART
iajs-826	56	13	true	true	ADJ
iajs-826	56	14	,	,	PUNCT
iajs-826	56	15	to	to	PART
iajs-826	56	16	see	see	VERB
iajs-826	56	17	this	this	PRON
iajs-826	56	18	,	,	PUNCT
iajs-826	56	19	let	let	VERB
iajs-826	56	20	(	(	PUNCT
iajs-826	56	21	{	{	PUNCT
iajs-826	56	22	1	1	NUM
iajs-826	56	23	,	,	PUNCT
iajs-826	56	24	2	2	NUM
iajs-826	56	25	,	,	PUNCT
iajs-826	56	26	3	3	NUM
iajs-826	56	27	}	}	PUNCT
iajs-826	56	28	,	,	PUNCT
iajs-826	56	29	be	be	AUX
iajs-826	56	30	3topological	3topological	ADJ
iajs-826	56	31	space	space	NOUN
iajs-826	56	32	in	in	ADP
iajs-826	56	33	(	(	PUNCT
iajs-826	56	34	example	example	NOUN
iajs-826	56	35	2.2	2.2	NUM
iajs-826	56	36	)	)	PUNCT
iajs-826	56	37	,	,	PUNCT
iajs-826	56	38	then	then	ADV
iajs-826	56	39	the	the	DET
iajs-826	56	40	space	space	NOUN
iajs-826	56	41	(	(	PUNCT
iajs-826	56	42	{	{	PUNCT
iajs-826	56	43	1,2,3	1,2,3	NUM
iajs-826	56	44	}	}	PUNCT
iajs-826	56	45	,	,	PUNCT
iajs-826	56	46	is	be	AUX
iajs-826	56	47	3	3	NUM
iajs-826	56	48	–	–	PUNCT
iajs-826	56	49	space	space	NOUN
iajs-826	56	50	,	,	PUNCT
iajs-826	56	51	but	but	CCONJ
iajs-826	56	52	each	each	PRON
iajs-826	56	53	(	(	PUNCT
iajs-826	56	54	x	x	X
iajs-826	56	55	is	be	AUX
iajs-826	56	56	not	not	PART
iajs-826	56	57	space	space	NOUN
iajs-826	56	58	.	.	PUNCT
iajs-826	57	1	remark	remark	VERB
iajs-826	57	2	2.12	2.12	NUM
iajs-826	57	3	if	if	SCONJ
iajs-826	57	4	(	(	PUNCT
iajs-826	57	5	x	x	NOUN
iajs-826	57	6	,	,	PUNCT
iajs-826	57	7	)	)	PUNCT
iajs-826	57	8	is	be	AUX
iajs-826	57	9	n	n	DET
iajs-826	57	10	space	space	NOUN
iajs-826	57	11	then	then	ADV
iajs-826	57	12	need	need	VERB
iajs-826	57	13	not	not	PART
iajs-826	57	14	to	to	PART
iajs-826	57	15	be	be	AUX
iajs-826	57	16	space	space	NOUN
iajs-826	57	17	for	for	ADP
iajs-826	57	18	all	all	DET
iajs-826	57	19	i=	i=	PROPN
iajs-826	57	20	1,2,	1,2,	NUM
iajs-826	57	21	…	…	SYM
iajs-826	57	22	,n	,n	NOUN
iajs-826	57	23	,	,	PUNCT
iajs-826	57	24	only	only	ADV
iajs-826	57	25	if	if	SCONJ
iajs-826	57	26	(	(	PUNCT
iajs-826	57	27	x	x	X
iajs-826	57	28	is	be	AUX
iajs-826	57	29	space	space	NOUN
iajs-826	57	30	.	.	PUNCT
iajs-826	58	1	theorem	theorem	NOUN
iajs-826	58	2	2.13	2.13	NUM
iajs-826	58	3	let	let	VERB
iajs-826	58	4	(	(	PUNCT
iajs-826	58	5	x	x	NOUN
iajs-826	58	6	,	,	PUNCT
iajs-826	58	7	)	)	PUNCT
iajs-826	58	8	is	be	AUX
iajs-826	58	9	n	n	DET
iajs-826	58	10	space	space	NOUN
iajs-826	58	11	and	and	CCONJ
iajs-826	58	12	(	(	PUNCT
iajs-826	58	13	y	y	PROPN
iajs-826	58	14	,	,	PUNCT
iajs-826	58	15	is	be	AUX
iajs-826	58	16	a	a	DET
iajs-826	58	17	sub	sub	NOUN
iajs-826	58	18	ntopological	ntopological	ADJ
iajs-826	58	19	space	space	NOUN
iajs-826	58	20	of	of	ADP
iajs-826	58	21	the	the	DET
iajs-826	58	22	ntopological	ntopological	ADJ
iajs-826	58	23	space	space	NOUN
iajs-826	58	24	(	(	PUNCT
iajs-826	58	25	x	x	NOUN
iajs-826	58	26	,	,	PUNCT
iajs-826	58	27	)	)	PUNCT
iajs-826	58	28	.	.	PUNCT
iajs-826	59	1	then(y	then(y	INTJ
iajs-826	59	2	,	,	PUNCT
iajs-826	59	3	is	be	AUX
iajs-826	59	4	also	also	ADV
iajs-826	59	5	n	n	DET
iajs-826	59	6	space	space	NOUN
iajs-826	59	7	.	.	PUNCT
iajs-826	60	1	proof	proof	NOUN
iajs-826	60	2	to	to	PART
iajs-826	60	3	prove	prove	VERB
iajs-826	60	4	(	(	PUNCT
iajs-826	60	5	y	y	PROPN
iajs-826	60	6	,	,	PUNCT
iajs-826	60	7	is	be	AUX
iajs-826	60	8	n	n	DET
iajs-826	60	9	space	space	NOUN
iajs-826	60	10	,	,	PUNCT
iajs-826	60	11	we	we	PRON
iajs-826	60	12	must	must	AUX
iajs-826	60	13	prove	prove	VERB
iajs-826	60	14	:	:	PUNCT
iajs-826	60	15	x	x	ADV
iajs-826	60	16	,	,	PUNCT
iajs-826	60	17	y	y	PROPN
iajs-826	60	18	y	y	PROPN
iajs-826	60	19	,	,	PUNCT
iajs-826	60	20	x≠	x≠	PROPN
iajs-826	60	21	y	y	PROPN
iajs-826	60	22	,	,	PUNCT
iajs-826	60	23	u	u	NOUN
iajs-826	60	24	for	for	ADP
iajs-826	60	25	some	some	DET
iajs-826	60	26	i	i	PRON
iajs-826	60	27	,	,	PUNCT
iajs-826	60	28	such	such	ADJ
iajs-826	60	29	that	that	PRON
iajs-826	60	30	xu	xu	PROPN
iajs-826	60	31	and	and	CCONJ
iajs-826	60	32	yu	yu	PROPN
iajs-826	60	33	.	.	PUNCT
iajs-826	61	1	ibn	ibn	PROPN
iajs-826	61	2	alhaitham	alhaitham	PROPN
iajs-826	62	1	j.	j.	PROPN
iajs-826	63	1	fo	fo	ADP
iajs-826	63	2	r	r	NOUN
iajs-826	63	3	pure	pure	ADJ
iajs-826	63	4	&	&	CCONJ
iajs-826	63	5	appl	appl	PROPN
iajs-826	63	6	.	.	PUNCT
iajs-826	64	1	sc	sc	PROPN
iajs-826	64	2	i.	i.	PROPN
iajs-826	64	3	vo	vo	PROPN
iajs-826	65	1	l.24	l.24	PROPN
iajs-826	65	2	(	(	PUNCT
iajs-826	65	3	1	1	NUM
iajs-826	65	4	)	)	PUNCT
iajs-826	65	5	2011	2011	NUM
iajs-826	65	6	now	now	ADV
iajs-826	65	7	,	,	PUNCT
iajs-826	65	8	let	let	VERB
iajs-826	65	9	x	x	PRON
iajs-826	65	10	,	,	PUNCT
iajs-826	65	11	y	y	PROPN
iajs-826	65	12	y	y	PROPN
iajs-826	65	13	,	,	PUNCT
iajs-826	65	14	x≠	x≠	PROPN
iajs-826	65	15	y	y	PROPN
iajs-826	65	16	implies	imply	VERB
iajs-826	65	17	x	x	X
iajs-826	65	18	,	,	PUNCT
iajs-826	65	19	y	y	PROPN
iajs-826	65	20	x	x	NUM
iajs-826	65	21	.	.	PUNCT
iajs-826	66	1	then	then	ADV
iajs-826	66	2	,	,	PUNCT
iajs-826	66	3	there	there	PRON
iajs-826	66	4	exists	exist	VERB
iajs-826	66	5	w	w	ADV
iajs-826	66	6	for	for	ADP
iajs-826	66	7	some	some	DET
iajs-826	66	8	i	i	PRON
iajs-826	66	9	,	,	PUNCT
iajs-826	66	10	such	such	ADJ
iajs-826	66	11	that	that	SCONJ
iajs-826	66	12	(	(	PUNCT
iajs-826	66	13	x	x	SYM
iajs-826	66	14	w	w	VERB
iajs-826	66	15			PROPN
iajs-826	66	16	y	y	PROPN
iajs-826	66	17	w	w	PROPN
iajs-826	66	18	)	)	PUNCT
iajs-826	66	19	or	or	CCONJ
iajs-826	66	20	(	(	PUNCT
iajs-826	66	21	x	x	X
iajs-826	66	22	w	w	PUNCT
iajs-826	66	23			PROPN
iajs-826	66	24	y	y	PROPN
iajs-826	66	25	w	w	NOUN
iajs-826	66	26	)	)	PUNCT
iajs-826	66	27	since	since	SCONJ
iajs-826	66	28	(	(	PUNCT
iajs-826	66	29	x	x	X
iajs-826	66	30	,	,	PUNCT
iajs-826	66	31	)	)	PUNCT
iajs-826	66	32	is	be	AUX
iajs-826	66	33	n	n	PRON
iajs-826	66	34	–	–	PUNCT
iajs-826	66	35	space	space	NOUN
iajs-826	66	36	.	.	PUNCT
iajs-826	67	1	then	then	ADV
iajs-826	67	2	y	y	PRON
iajs-826	67	3	w	w	NOUN
iajs-826	67	4	for	for	ADP
iajs-826	67	5	some	some	DET
iajs-826	67	6	i	i	NOUN
iajs-826	67	7	(	(	PUNCT
iajs-826	67	8	by	by	ADP
iajs-826	67	9	definition	definition	NOUN
iajs-826	67	10	of	of	ADP
iajs-826	67	11	so	so	ADV
iajs-826	67	12	,	,	PUNCT
iajs-826	67	13	xyw	xyw	PROPN
iajs-826	67	14	x	x	PROPN
iajs-826	68	1			NOUN
iajs-826	68	2	y	y	PROPN
iajs-826	68	3	w	w	PROPN
iajs-826	68	4	and	and	CCONJ
iajs-826	68	5	yw	yw	NOUN
iajs-826	69	1	y	y	PROPN
iajs-826	69	2	y	y	PROPN
iajs-826	69	3	w	w	PROPN
iajs-826	69	4	or	or	CCONJ
iajs-826	69	5	x	x	PUNCT
iajs-826	69	6	w	w	PROPN
iajs-826	69	7			NOUN
iajs-826	69	8	x	x	X
iajs-826	69	9			NOUN
iajs-826	69	10	y	y	NUM
iajs-826	69	11	w	w	PROPN
iajs-826	69	12	and	and	CCONJ
iajs-826	69	13	y	y	PROPN
iajs-826	69	14	yw	yw	PROPN
iajs-826	69	15			NOUN
iajs-826	70	1	y	y	PROPN
iajs-826	70	2			PROPN
iajs-826	70	3	y	y	PROPN
iajs-826	71	1	w	w	ADP
iajs-826	71	2	then	then	ADV
iajs-826	71	3	(	(	PUNCT
iajs-826	71	4	y	y	PROPN
iajs-826	71	5	,	,	PUNCT
iajs-826	71	6	)	)	PUNCT
iajs-826	71	7	is	be	AUX
iajs-826	71	8	space	space	NOUN
iajs-826	71	9	.	.	PUNCT
iajs-826	72	1	then	then	ADV
iajs-826	72	2	(	(	PUNCT
iajs-826	72	3	y	y	NOUN
iajs-826	72	4	,	,	PUNCT
iajs-826	72	5	is	be	AUX
iajs-826	72	6	n	n	DET
iajs-826	72	7	space	space	NOUN
iajs-826	72	8	.	.	PUNCT
iajs-826	73	1	■	■	PUNCT
iajs-826	73	2	example	example	NOUN
iajs-826	73	3	2.14	2.14	NUM
iajs-826	73	4	let	let	VERB
iajs-826	73	5	(	(	PUNCT
iajs-826	73	6	{	{	PUNCT
iajs-826	73	7	1	1	NUM
iajs-826	73	8	,	,	PUNCT
iajs-826	73	9	2	2	NUM
iajs-826	73	10	,	,	PUNCT
iajs-826	73	11	3	3	NUM
iajs-826	73	12	,	,	PUNCT
iajs-826	73	13	4	4	NUM
iajs-826	73	14	}	}	PUNCT
iajs-826	73	15	,	,	PUNCT
iajs-826	73	16	)	)	PUNCT
iajs-826	73	17	is	be	AUX
iajs-826	73	18	3space	3space	NUM
iajs-826	73	19	where	where	SCONJ
iajs-826	73	20	=	=	PRON
iajs-826	73	21	{	{	PUNCT
iajs-826	73	22	x	x	NOUN
iajs-826	73	23	,	,	PUNCT
iajs-826	73	24	,	,	PUNCT
iajs-826	73	25	=	=	PRON
iajs-826	73	26	{	{	PUNCT
iajs-826	73	27	x	x	NOUN
iajs-826	73	28	,	,	PUNCT
iajs-826	73	29	,	,	PUNCT
iajs-826	73	30	{	{	PUNCT
iajs-826	73	31	2	2	NUM
iajs-826	73	32	}	}	PUNCT
iajs-826	73	33	,	,	PUNCT
iajs-826	73	34	{	{	PUNCT
iajs-826	73	35	4},{2,4	4},{2,4	NUM
iajs-826	73	36	}	}	PUNCT
iajs-826	73	37	}	}	PUNCT
iajs-826	73	38	and	and	CCONJ
iajs-826	73	39	=	=	PRON
iajs-826	73	40	{	{	PUNCT
iajs-826	73	41	x	x	NOUN
iajs-826	73	42	,	,	PUNCT
iajs-826	73	43	{	{	PUNCT
iajs-826	73	44	2,4},{3,4},{4},{2,3,4	2,4},{3,4},{4},{2,3,4	NUM
iajs-826	73	45	}	}	PUNCT
iajs-826	73	46	}	}	PUNCT
iajs-826	73	47	.	.	PUNCT
iajs-826	74	1	and	and	CCONJ
iajs-826	74	2	let	let	VERB
iajs-826	74	3	y	y	PRON
iajs-826	74	4	=	=	PRON
iajs-826	74	5	{	{	PUNCT
iajs-826	74	6	1,3,4}x	1,3,4}x	NUM
iajs-826	74	7	,	,	PUNCT
iajs-826	74	8	then	then	ADV
iajs-826	74	9	(	(	PUNCT
iajs-826	74	10	y	y	NOUN
iajs-826	74	11	,	,	PUNCT
iajs-826	74	12	is	be	AUX
iajs-826	74	13	sub	sub	NOUN
iajs-826	74	14	3space	3space	NUM
iajs-826	74	15	where	where	SCONJ
iajs-826	74	16	=	=	PRON
iajs-826	74	17	{	{	PUNCT
iajs-826	74	18	y	y	NOUN
iajs-826	74	19	,	,	PUNCT
iajs-826	74	20			ADV
iajs-826	74	21	}	}	PUNCT
iajs-826	74	22	,	,	PUNCT
iajs-826	74	23	=	=	PRON
iajs-826	74	24	{	{	PUNCT
iajs-826	74	25	y	y	PROPN
iajs-826	74	26	,	,	PUNCT
iajs-826	74	27			ADJ
iajs-826	74	28	,	,	PUNCT
iajs-826	74	29	{	{	PUNCT
iajs-826	74	30	4	4	NUM
iajs-826	74	31	}	}	PUNCT
iajs-826	74	32	}	}	PUNCT
iajs-826	74	33	,	,	PUNCT
iajs-826	74	34	=	=	PRON
iajs-826	74	35	{	{	PUNCT
iajs-826	74	36	y	y	PROPN
iajs-826	74	37	,	,	PUNCT
iajs-826	74	38			ADJ
iajs-826	74	39	,	,	PUNCT
iajs-826	74	40	{	{	PUNCT
iajs-826	74	41	4},{3,4	4},{3,4	NUM
iajs-826	74	42	}	}	PUNCT
iajs-826	74	43	}	}	PUNCT
iajs-826	74	44	.	.	PUNCT
iajs-826	75	1	definition	definition	NOUN
iajs-826	75	2	2.15	2.15	NUM
iajs-826	75	3	an	an	DET
iajs-826	75	4	ntopological	ntopological	ADJ
iajs-826	75	5	space	space	NOUN
iajs-826	75	6	(	(	PUNCT
iajs-826	75	7	x	x	NOUN
iajs-826	75	8	,	,	PUNCT
iajs-826	75	9	)	)	PUNCT
iajs-826	75	10	is	be	AUX
iajs-826	75	11	said	say	VERB
iajs-826	75	12	to	to	PART
iajs-826	75	13	be	be	AUX
iajs-826	75	14	an	an	DET
iajs-826	75	15	"	"	PUNCT
iajs-826	75	16	n	n	CCONJ
iajs-826	75	17	-space	-space	NOUN
iajs-826	75	18	"	"	PUNCT
iajs-826	75	19	if	if	SCONJ
iajs-826	75	20	and	and	CCONJ
iajs-826	75	21	if	if	SCONJ
iajs-826	75	22	for	for	ADP
iajs-826	75	23	each	each	DET
iajs-826	75	24	pair	pair	NOUN
iajs-826	75	25	of	of	ADP
iajs-826	75	26	distinct	distinct	ADJ
iajs-826	75	27	points	point	NOUN
iajs-826	75	28	x	x	X
iajs-826	75	29	,	,	PUNCT
iajs-826	75	30	yx	yx	PROPN
iajs-826	75	31	,	,	PUNCT
iajs-826	75	32	there	there	PRON
iajs-826	75	33	exists	exist	VERB
iajs-826	75	34	two	two	NUM
iajs-826	75	35	nopen	nopen	ADJ
iajs-826	75	36	sets	set	NOUN
iajs-826	75	37	u	u	NOUN
iajs-826	75	38	and	and	CCONJ
iajs-826	75	39	v	v	NOUN
iajs-826	75	40	of	of	ADP
iajs-826	75	41	x	x	PUNCT
iajs-826	75	42	such	such	ADJ
iajs-826	75	43	that	that	PRON
iajs-826	75	44	xu	xu	PUNCT
iajs-826	76	1			PROPN
iajs-826	76	2	yu	yu	PROPN
iajs-826	76	3	and	and	CCONJ
iajs-826	76	4	xv	xv	PROPN
iajs-826	76	5			PROPN
iajs-826	76	6	yv	yv	PROPN
iajs-826	76	7	.	.	PUNCT
iajs-826	76	8	proposition	proposition	NOUN
iajs-826	76	9	2.16	2.16	NUM
iajs-826	76	10	an	an	DET
iajs-826	76	11	ntopological	ntopological	ADJ
iajs-826	76	12	space	space	NOUN
iajs-826	76	13	(	(	PUNCT
iajs-826	76	14	x	x	NOUN
iajs-826	76	15	,	,	PUNCT
iajs-826	76	16	)	)	PUNCT
iajs-826	76	17	is	be	AUX
iajs-826	76	18	n	n	PRON
iajs-826	76	19	-space	-space	NOUN
iajs-826	76	20	if	if	SCONJ
iajs-826	76	21	(	(	PUNCT
iajs-826	76	22	x	x	X
iajs-826	76	23	is	be	AUX
iajs-826	76	24	–	–	PUNCT
iajs-826	76	25	space	space	NOUN
iajs-826	76	26	for	for	ADP
iajs-826	76	27	some	some	DET
iajs-826	76	28	i	i	NOUN
iajs-826	76	29	=	=	SYM
iajs-826	76	30	1,2,	1,2,	NUM
iajs-826	76	31	…	…	PUNCT
iajs-826	76	32	,n	,n	NOUN
iajs-826	76	33	.	.	PUNCT
iajs-826	77	1	proof	proof	NOUN
iajs-826	77	2	to	to	PART
iajs-826	77	3	prove	prove	VERB
iajs-826	77	4	(	(	PUNCT
iajs-826	77	5	x	x	NOUN
iajs-826	77	6	,	,	PUNCT
iajs-826	77	7	)	)	PUNCT
iajs-826	77	8	is	be	AUX
iajs-826	77	9	n	n	DET
iajs-826	77	10	space	space	NOUN
iajs-826	77	11	,	,	PUNCT
iajs-826	77	12	we	we	PRON
iajs-826	77	13	must	must	AUX
iajs-826	77	14	prove	prove	VERB
iajs-826	77	15	for	for	ADP
iajs-826	77	16	any	any	DET
iajs-826	77	17	x	x	NOUN
iajs-826	77	18	,	,	PUNCT
iajs-826	77	19	yx	yx	ADP
iajs-826	77	20	such	such	ADJ
iajs-826	77	21	that	that	SCONJ
iajs-826	77	22	x≠	x≠	PROPN
iajs-826	77	23	y	y	PROPN
iajs-826	77	24	,	,	PUNCT
iajs-826	77	25	there	there	PRON
iajs-826	77	26	exists	exist	VERB
iajs-826	77	27	two	two	NUM
iajs-826	77	28	n	n	ADV
iajs-826	77	29	-	-	PUNCT
iajs-826	77	30	open	open	ADJ
iajs-826	77	31	sets	set	VERB
iajs-826	77	32	u	u	NOUN
iajs-826	77	33	and	and	CCONJ
iajs-826	77	34	v	v	NOUN
iajs-826	77	35	of	of	ADP
iajs-826	77	36	x	x	PUNCT
iajs-826	77	37	such	such	ADJ
iajs-826	77	38	that	that	PRON
iajs-826	77	39	xu	xu	PUNCT
iajs-826	78	1			PROPN
iajs-826	78	2	yu	yu	PROPN
iajs-826	78	3	and	and	CCONJ
iajs-826	78	4	xv	xv	PROPN
iajs-826	78	5			PROPN
iajs-826	78	6	yv	yv	PROPN
iajs-826	78	7	.	.	PUNCT
iajs-826	79	1	now	now	ADV
iajs-826	79	2	,	,	PUNCT
iajs-826	79	3	let	let	VERB
iajs-826	79	4	x	x	PRON
iajs-826	79	5	,	,	PUNCT
iajs-826	79	6	yx	yx	PROPN
iajs-826	79	7	;	;	PUNCT
iajs-826	79	8	x≠	x≠	PROPN
iajs-826	79	9	y	y	PROPN
iajs-826	79	10	since	since	SCONJ
iajs-826	79	11	there	there	PRON
iajs-826	79	12	exists	exist	VERB
iajs-826	79	13	i1,2,	i1,2,	NOUN
iajs-826	79	14	…	…	PUNCT
iajs-826	79	15	,n	,n	NOUN
iajs-826	79	16	such	such	ADJ
iajs-826	79	17	that	that	SCONJ
iajs-826	79	18	(	(	PUNCT
iajs-826	79	19	x	x	X
iajs-826	79	20	is	be	AUX
iajs-826	79	21	–	–	PUNCT
iajs-826	79	22	space	space	NOUN
iajs-826	79	23	,	,	PUNCT
iajs-826	79	24	implies	imply	VERB
iajs-826	79	25	there	there	PRON
iajs-826	79	26	exists	exist	VERB
iajs-826	79	27	two	two	NUM
iajs-826	79	28	open	open	ADJ
iajs-826	79	29	sets	set	NOUN
iajs-826	79	30	u	u	NOUN
iajs-826	79	31	and	and	CCONJ
iajs-826	79	32	v	v	NOUN
iajs-826	79	33	in	in	ADP
iajs-826	79	34	such	such	ADJ
iajs-826	79	35	that	that	PRON
iajs-826	79	36	xu	xu	PUNCT
iajs-826	80	1			PROPN
iajs-826	80	2	yu	yu	PROPN
iajs-826	80	3	and	and	CCONJ
iajs-826	80	4	xv	xv	PROPN
iajs-826	80	5			PROPN
iajs-826	80	6	yv	yv	PROPN
iajs-826	80	7	,	,	PUNCT
iajs-826	80	8	therefore	therefore	ADV
iajs-826	80	9	there	there	PRON
iajs-826	80	10	exists	exist	VERB
iajs-826	80	11	two	two	NUM
iajs-826	80	12	open	open	ADJ
iajs-826	80	13	sets	set	NOUN
iajs-826	80	14	u	u	NOUN
iajs-826	80	15	and	and	CCONJ
iajs-826	80	16	v	v	NOUN
iajs-826	80	17	of	of	ADP
iajs-826	80	18	x	x	PUNCT
iajs-826	80	19	such	such	ADJ
iajs-826	80	20	that	that	PRON
iajs-826	80	21	xu	xu	PUNCT
iajs-826	81	1			PROPN
iajs-826	81	2	yu	yu	PROPN
iajs-826	81	3	and	and	CCONJ
iajs-826	81	4	xv	xv	PROPN
iajs-826	81	5			PROPN
iajs-826	81	6	yv	yv	PROPN
iajs-826	81	7	(	(	PUNCT
iajs-826	81	8	by	by	ADP
iajs-826	81	9	definition	definition	NOUN
iajs-826	81	10	2.3	2.3	NUM
iajs-826	81	11	)	)	PUNCT
iajs-826	81	12	.	.	PUNCT
iajs-826	82	1	thus	thus	ADV
iajs-826	82	2	(	(	PUNCT
iajs-826	82	3	x	x	X
iajs-826	82	4	,	,	PUNCT
iajs-826	82	5	)	)	PUNCT
iajs-826	82	6	is	be	AUX
iajs-826	82	7	n	n	PRON
iajs-826	82	8	–	–	PUNCT
iajs-826	82	9	space	space	NOUN
iajs-826	82	10	.	.	PUNCT
iajs-826	83	1	■	■	PUNCT
iajs-826	83	2	remark	remark	VERB
iajs-826	83	3	2.17	2.17	NUM
iajs-826	83	4	the	the	DET
iajs-826	83	5	converse	converse	NOUN
iajs-826	83	6	of	of	ADP
iajs-826	83	7	(	(	PUNCT
iajs-826	83	8	proposition	proposition	NOUN
iajs-826	83	9	2.16	2.16	NUM
iajs-826	83	10	)	)	PUNCT
iajs-826	83	11	is	be	AUX
iajs-826	83	12	not	not	PART
iajs-826	83	13	true	true	ADJ
iajs-826	83	14	,	,	PUNCT
iajs-826	83	15	as	as	ADP
iajs-826	83	16	the	the	DET
iajs-826	83	17	following	follow	VERB
iajs-826	83	18	example	example	NOUN
iajs-826	83	19	:	:	PUNCT
iajs-826	83	20	example	example	NOUN
iajs-826	83	21	2.18	2.18	NUM
iajs-826	83	22	let	let	VERB
iajs-826	83	23	x=	x=	PUNCT
iajs-826	83	24	{	{	PUNCT
iajs-826	83	25	1,2,3,	1,2,3,	NUM
iajs-826	83	26	…	…	X
iajs-826	83	27	,n	,n	NOUN
iajs-826	83	28	}	}	PUNCT
iajs-826	83	29	;	;	PUNCT
iajs-826	83	30	n	n	CCONJ
iajs-826	83	31	and	and	CCONJ
iajs-826	83	32	let	let	VERB
iajs-826	83	33	=	=	PRON
iajs-826	83	34	{	{	PUNCT
iajs-826	83	35	x	x	NOUN
iajs-826	83	36	,	,	PUNCT
iajs-826	83	37	;	;	PUNCT
iajs-826	83	38	i=1,2,3,	i=1,2,3,	NOUN
iajs-826	83	39	…	…	PUNCT
iajs-826	83	40	,n	,n	NOUN
iajs-826	83	41	,	,	PUNCT
iajs-826	83	42	then	then	ADV
iajs-826	83	43	the	the	DET
iajs-826	83	44	space	space	NOUN
iajs-826	83	45	(	(	PUNCT
iajs-826	83	46	x	x	NOUN
iajs-826	83	47	,	,	PUNCT
iajs-826	83	48	)	)	PUNCT
iajs-826	83	49	is	be	AUX
iajs-826	83	50	n	n	CCONJ
iajs-826	83	51	-	-	PUNCT
iajs-826	83	52	topological	topological	ADJ
iajs-826	83	53	space	space	NOUN
iajs-826	83	54	,	,	PUNCT
iajs-826	83	55	notice	notice	VERB
iajs-826	83	56	that	that	SCONJ
iajs-826	83	57	(	(	PUNCT
iajs-826	83	58	x	x	NOUN
iajs-826	83	59	,	,	PUNCT
iajs-826	83	60	)	)	PUNCT
iajs-826	83	61	is	be	AUX
iajs-826	83	62	n	n	PRON
iajs-826	83	63	-space	-space	NOUN
iajs-826	83	64	but	but	CCONJ
iajs-826	83	65	each	each	DET
iajs-826	83	66	(	(	PUNCT
iajs-826	83	67	x	x	X
iajs-826	83	68	,	,	PUNCT
iajs-826	83	69	is	be	AUX
iajs-826	83	70	not	not	PART
iajs-826	83	71	–	–	PUNCT
iajs-826	83	72	space	space	NOUN
iajs-826	83	73	,	,	PUNCT
iajs-826	83	74	for	for	ADP
iajs-826	83	75	all	all	DET
iajs-826	83	76	i.	i.	NOUN
iajs-826	83	77	note	note	NOUN
iajs-826	83	78	1	1	X
iajs-826	83	79	.	.	PUNCT
iajs-826	84	1	it	it	PRON
iajs-826	84	2	is	be	AUX
iajs-826	84	3	clear	clear	ADJ
iajs-826	84	4	that	that	SCONJ
iajs-826	84	5	each	each	DET
iajs-826	84	6	nspace	nspace	NOUN
iajs-826	84	7	is	be	AUX
iajs-826	84	8	also	also	ADV
iajs-826	84	9	,	,	PUNCT
iajs-826	84	10	nspace	nspace	NOUN
iajs-826	84	11	but	but	CCONJ
iajs-826	84	12	the	the	DET
iajs-826	84	13	converse	converse	NOUN
iajs-826	84	14	is	be	AUX
iajs-826	84	15	not	not	PART
iajs-826	84	16	true	true	ADJ
iajs-826	84	17	see	see	NOUN
iajs-826	84	18	(	(	PUNCT
iajs-826	84	19	example	example	NOUN
iajs-826	84	20	2.14	2.14	NUM
iajs-826	84	21	)	)	PUNCT
iajs-826	84	22	,	,	PUNCT
iajs-826	84	23	the	the	DET
iajs-826	84	24	space	space	NOUN
iajs-826	84	25	is	be	AUX
iajs-826	84	26	3space	3space	NUM
iajs-826	84	27	but	but	CCONJ
iajs-826	84	28	not	not	PART
iajs-826	84	29	3space	3space	NUM
iajs-826	84	30	.	.	PUNCT
iajs-826	85	1	2	2	NUM
iajs-826	85	2	.	.	X
iajs-826	86	1	if	if	SCONJ
iajs-826	86	2	ntopological	ntopological	ADJ
iajs-826	86	3	space	space	NOUN
iajs-826	86	4	is	be	AUX
iajs-826	86	5	not	not	PART
iajs-826	86	6	n	n	DET
iajs-826	86	7	space	space	NOUN
iajs-826	86	8	,	,	PUNCT
iajs-826	86	9	then	then	ADV
iajs-826	86	10	it	it	PRON
iajs-826	86	11	is	be	AUX
iajs-826	86	12	not	not	PART
iajs-826	86	13	n	n	PRON
iajs-826	86	14	space	space	NOUN
iajs-826	86	15	.	.	PUNCT
iajs-826	87	1	theorem	theorem	VERB
iajs-826	87	2	2.19	2.19	NUM
iajs-826	87	3	let	let	VERB
iajs-826	87	4	(	(	PUNCT
iajs-826	87	5	x	x	NOUN
iajs-826	87	6	,	,	PUNCT
iajs-826	87	7	)	)	PUNCT
iajs-826	87	8	is	be	AUX
iajs-826	87	9	n	n	DET
iajs-826	87	10	space	space	NOUN
iajs-826	87	11	and	and	CCONJ
iajs-826	87	12	(	(	PUNCT
iajs-826	87	13	y	y	NOUN
iajs-826	87	14	,	,	PUNCT
iajs-826	87	15	is	be	AUX
iajs-826	87	16	sub	sub	ADJ
iajs-826	87	17	ntopological	ntopological	ADJ
iajs-826	87	18	space	space	NOUN
iajs-826	87	19	of	of	ADP
iajs-826	87	20	(	(	PUNCT
iajs-826	87	21	x	x	NOUN
iajs-826	87	22	,	,	PUNCT
iajs-826	87	23	)	)	PUNCT
iajs-826	87	24	.	.	PUNCT
iajs-826	88	1	then(y	then(y	INTJ
iajs-826	88	2	,	,	PUNCT
iajs-826	88	3	is	be	AUX
iajs-826	88	4	nspace	nspace	NOUN
iajs-826	88	5	.	.	PUNCT
iajs-826	89	1	proof	proof	NOUN
iajs-826	89	2	to	to	PART
iajs-826	89	3	prove	prove	VERB
iajs-826	89	4	(	(	PUNCT
iajs-826	89	5	y	y	PROPN
iajs-826	89	6	,	,	PUNCT
iajs-826	89	7	is	be	AUX
iajs-826	89	8	n	n	DET
iajs-826	89	9	space	space	NOUN
iajs-826	89	10	,	,	PUNCT
iajs-826	89	11	we	we	PRON
iajs-826	89	12	must	must	AUX
iajs-826	89	13	prove	prove	VERB
iajs-826	89	14	:	:	PUNCT
iajs-826	89	15	x	x	ADV
iajs-826	89	16	,	,	PUNCT
iajs-826	89	17	y	y	PROPN
iajs-826	89	18	y	y	PROPN
iajs-826	89	19	,	,	PUNCT
iajs-826	89	20	x≠	x≠	PROPN
iajs-826	89	21	y	y	PROPN
iajs-826	89	22	,	,	PUNCT
iajs-826	89	23	u	u	PROPN
iajs-826	89	24	,	,	PUNCT
iajs-826	89	25	v	v	NOUN
iajs-826	89	26	for	for	ADP
iajs-826	89	27	some	some	DET
iajs-826	89	28	i	i	PRON
iajs-826	89	29	,	,	PUNCT
iajs-826	89	30	such	such	ADJ
iajs-826	89	31	that	that	SCONJ
iajs-826	89	32	xu	xu	PROPN
iajs-826	89	33	yu	yu	PROPN
iajs-826	89	34	and	and	CCONJ
iajs-826	89	35	x	x	ADJ
iajs-826	89	36			PROPN
iajs-826	89	37	v	v	PROPN
iajs-826	89	38	yv	yv	PROPN
iajs-826	89	39	.	.	PUNCT
iajs-826	90	1	ibn	ibn	PROPN
iajs-826	90	2	alhaitham	alhaitham	PROPN
iajs-826	91	1	j.	j.	PROPN
iajs-826	92	1	fo	fo	ADP
iajs-826	92	2	r	r	NOUN
iajs-826	92	3	pure	pure	ADJ
iajs-826	92	4	&	&	CCONJ
iajs-826	92	5	appl	appl	PROPN
iajs-826	92	6	.	.	PUNCT
iajs-826	93	1	sc	sc	PROPN
iajs-826	93	2	i.	i.	PROPN
iajs-826	93	3	vo	vo	PROPN
iajs-826	94	1	l.24	l.24	PROPN
iajs-826	94	2	(	(	PUNCT
iajs-826	94	3	1	1	NUM
iajs-826	94	4	)	)	PUNCT
iajs-826	94	5	2011	2011	NUM
iajs-826	94	6	now	now	ADV
iajs-826	94	7	,	,	PUNCT
iajs-826	94	8	since	since	SCONJ
iajs-826	94	9	y	y	PROPN
iajs-826	94	10	x	x	NOUN
iajs-826	94	11	,	,	PUNCT
iajs-826	94	12	then	then	ADV
iajs-826	94	13	x	x	X
iajs-826	94	14	,	,	PUNCT
iajs-826	94	15	y	y	PROPN
iajs-826	94	16	x	x	PROPN
iajs-826	94	17	and	and	CCONJ
iajs-826	94	18	x	x	X
iajs-826	94	19	is	be	AUX
iajs-826	94	20	n	n	PRON
iajs-826	94	21	space	space	NOUN
iajs-826	94	22	,	,	PUNCT
iajs-826	94	23	then	then	ADV
iajs-826	94	24			VERB
iajs-826	94	25			NOUN
iajs-826	94	26	for	for	ADP
iajs-826	94	27	some	some	DET
iajs-826	94	28	i	i	PRON
iajs-826	94	29	,	,	PUNCT
iajs-826	94	30	such	such	ADJ
iajs-826	94	31	that	that	SCONJ
iajs-826	94	32	x	x	PROPN
iajs-826	94	33			PROPN
iajs-826	94	34	y	y	PROPN
iajs-826	94	35	and	and	CCONJ
iajs-826	94	36	x	x	PROPN
iajs-826	94	37			PROPN
iajs-826	94	38	y	y	PROPN
iajs-826	94	39	.	.	PUNCT
iajs-826	95	1	then	then	ADV
iajs-826	95	2	y	y	PROPN
iajs-826	95	3	,	,	PUNCT
iajs-826	95	4	y	y	PROPN
iajs-826	95	5	for	for	ADP
iajs-826	95	6	some	some	DET
iajs-826	95	7	i	i	PRON
iajs-826	95	8	,	,	PUNCT
iajs-826	95	9	(	(	PUNCT
iajs-826	95	10	by	by	ADP
iajs-826	95	11	definition	definition	NOUN
iajs-826	95	12	of	of	ADP
iajs-826	95	13	.	.	PUNCT
iajs-826	96	1	so	so	ADV
iajs-826	96	2	x	x	PROPN
iajs-826	96	3	y	y	PROPN
iajs-826	96	4			PROPN
iajs-826	96	5	y	y	PROPN
iajs-826	96	6	y	y	PROPN
iajs-826	96	7	and	and	CCONJ
iajs-826	96	8	x	x	PROPN
iajs-826	96	9	y	y	PROPN
iajs-826	97	1			PROPN
iajs-826	97	2	y	y	PROPN
iajs-826	97	3	y	y	PROPN
iajs-826	97	4	.	.	PUNCT
iajs-826	98	1	then	then	ADV
iajs-826	98	2	(	(	PUNCT
iajs-826	98	3	y	y	PROPN
iajs-826	98	4	,	,	PUNCT
iajs-826	98	5	)	)	PUNCT
iajs-826	98	6	is	be	AUX
iajs-826	98	7	space	space	NOUN
iajs-826	98	8	for	for	ADP
iajs-826	98	9	some	some	DET
iajs-826	98	10	i	i	PRON
iajs-826	98	11	,	,	PUNCT
iajs-826	98	12	then	then	ADV
iajs-826	98	13	(	(	PUNCT
iajs-826	98	14	y	y	NOUN
iajs-826	98	15	,	,	PUNCT
iajs-826	98	16	is	be	AUX
iajs-826	98	17	n	n	DET
iajs-826	98	18	space	space	NOUN
iajs-826	98	19	.	.	PUNCT
iajs-826	99	1	■	■	PUNCT
iajs-826	99	2	definition	definition	NOUN
iajs-826	99	3	2.20	2.20	NUM
iajs-826	99	4	an	an	DET
iajs-826	99	5	ntopological	ntopological	ADJ
iajs-826	99	6	space	space	NOUN
iajs-826	99	7	(	(	PUNCT
iajs-826	99	8	x	x	NOUN
iajs-826	99	9	,	,	PUNCT
iajs-826	99	10	)	)	PUNCT
iajs-826	99	11	is	be	AUX
iajs-826	99	12	said	say	VERB
iajs-826	99	13	to	to	PART
iajs-826	99	14	be	be	AUX
iajs-826	99	15	an	an	DET
iajs-826	99	16	"	"	PUNCT
iajs-826	99	17	n	n	CCONJ
iajs-826	99	18	-space	-space	NOUN
iajs-826	99	19	"	"	PUNCT
iajs-826	99	20	if	if	SCONJ
iajs-826	99	21	and	and	CCONJ
iajs-826	99	22	if	if	SCONJ
iajs-826	99	23	x	x	NOUN
iajs-826	99	24	,	,	PUNCT
iajs-826	99	25	y	y	PROPN
iajs-826	99	26	x	x	ADV
iajs-826	99	27	x≠	x≠	PROPN
iajs-826	99	28	y	y	PROPN
iajs-826	99	29	,	,	PUNCT
iajs-826	99	30	u	u	PROPN
iajs-826	99	31	,	,	PUNCT
iajs-826	99	32	v	v	NOUN
iajs-826	99	33	n	n	CCONJ
iajs-826	99	34	-	-	PUNCT
iajs-826	99	35	open	open	ADJ
iajs-826	99	36	sets	set	NOUN
iajs-826	99	37	of	of	ADP
iajs-826	99	38	x	x	NOUN
iajs-826	99	39	,	,	PUNCT
iajs-826	99	40	such	such	ADJ
iajs-826	99	41	that	that	SCONJ
iajs-826	99	42	uv=	uv=	PROPN
iajs-826	99	43	,	,	PUNCT
iajs-826	99	44	xu	xu	PUNCT
iajs-826	100	1			PROPN
iajs-826	100	2	y	y	PROPN
iajs-826	100	3	v.	v.	ADP
iajs-826	100	4	proposition	proposition	NOUN
iajs-826	100	5	2.21	2.21	NUM
iajs-826	100	6	an	an	DET
iajs-826	100	7	ntopological	ntopological	ADJ
iajs-826	100	8	space	space	NOUN
iajs-826	100	9	(	(	PUNCT
iajs-826	100	10	x	x	NOUN
iajs-826	100	11	,	,	PUNCT
iajs-826	100	12	)	)	PUNCT
iajs-826	100	13	is	be	AUX
iajs-826	100	14	n	n	PRON
iajs-826	100	15	-space	-space	NOUN
iajs-826	100	16	if	if	SCONJ
iajs-826	100	17	(	(	PUNCT
iajs-826	100	18	x	x	X
iajs-826	100	19	is	be	AUX
iajs-826	100	20	–	–	PUNCT
iajs-826	100	21	space	space	NOUN
iajs-826	100	22	for	for	ADP
iajs-826	100	23	some	some	DET
iajs-826	100	24	i	i	NOUN
iajs-826	100	25	=	=	NOUN
iajs-826	100	26	1	1	NUM
iajs-826	100	27	,	,	PUNCT
iajs-826	100	28	2	2	NUM
iajs-826	100	29	,	,	PUNCT
iajs-826	100	30	…	…	PUNCT
iajs-826	100	31	,	,	PUNCT
iajs-826	100	32	n.	n.	NOUN
iajs-826	100	33	proof	proof	NOUN
iajs-826	100	34	to	to	PART
iajs-826	100	35	prove	prove	VERB
iajs-826	100	36	(	(	PUNCT
iajs-826	100	37	x	x	NOUN
iajs-826	100	38	,	,	PUNCT
iajs-826	100	39	)	)	PUNCT
iajs-826	100	40	is	be	AUX
iajs-826	100	41	n	n	DET
iajs-826	100	42	space	space	NOUN
iajs-826	100	43	,	,	PUNCT
iajs-826	100	44	we	we	PRON
iajs-826	100	45	must	must	AUX
iajs-826	100	46	prove	prove	VERB
iajs-826	100	47	for	for	ADP
iajs-826	100	48	any	any	DET
iajs-826	100	49	x	x	NOUN
iajs-826	100	50	,	,	PUNCT
iajs-826	100	51	yx	yx	ADP
iajs-826	100	52	such	such	ADJ
iajs-826	100	53	that	that	SCONJ
iajs-826	100	54	x≠	x≠	PROPN
iajs-826	100	55	y	y	PROPN
iajs-826	100	56	,	,	PUNCT
iajs-826	100	57	there	there	PRON
iajs-826	100	58	exists	exist	VERB
iajs-826	100	59	two	two	NUM
iajs-826	100	60	n	n	ADV
iajs-826	100	61	-	-	PUNCT
iajs-826	100	62	open	open	ADJ
iajs-826	100	63	sets	set	VERB
iajs-826	100	64	u	u	NOUN
iajs-826	100	65	and	and	CCONJ
iajs-826	100	66	v	v	NOUN
iajs-826	100	67	of	of	ADP
iajs-826	100	68	x	x	PUNCT
iajs-826	100	69	such	such	ADJ
iajs-826	100	70	that	that	PRON
iajs-826	100	71	uv=	uv=	PROPN
iajs-826	100	72	,	,	PUNCT
iajs-826	100	73	xu	xu	PUNCT
iajs-826	101	1			PROPN
iajs-826	101	2	y	y	PROPN
iajs-826	101	3	v.	v.	CCONJ
iajs-826	101	4	now	now	ADV
iajs-826	101	5	,	,	PUNCT
iajs-826	101	6	let	let	VERB
iajs-826	101	7	x	x	PRON
iajs-826	101	8	,	,	PUNCT
iajs-826	101	9	yx	yx	PROPN
iajs-826	101	10	;	;	PUNCT
iajs-826	101	11	x≠	x≠	PROPN
iajs-826	101	12	y	y	PROPN
iajs-826	101	13	since	since	SCONJ
iajs-826	101	14	there	there	PRON
iajs-826	101	15	exists	exist	VERB
iajs-826	101	16	i1,2,	i1,2,	NOUN
iajs-826	101	17	…	…	PUNCT
iajs-826	101	18	,n	,n	NOUN
iajs-826	101	19	such	such	ADJ
iajs-826	101	20	that	that	SCONJ
iajs-826	101	21	(	(	PUNCT
iajs-826	101	22	x	x	X
iajs-826	101	23	is	be	AUX
iajs-826	101	24	–	–	PUNCT
iajs-826	101	25	space	space	NOUN
iajs-826	101	26	,	,	PUNCT
iajs-826	101	27	implies	imply	VERB
iajs-826	101	28	there	there	PRON
iajs-826	101	29	exists	exist	VERB
iajs-826	101	30	two	two	NUM
iajs-826	101	31	open	open	ADJ
iajs-826	101	32	sets	set	NOUN
iajs-826	101	33	u	u	NOUN
iajs-826	101	34	and	and	CCONJ
iajs-826	101	35	v	v	NOUN
iajs-826	101	36	in	in	ADP
iajs-826	101	37	such	such	ADJ
iajs-826	101	38	that	that	DET
iajs-826	101	39	uv=	uv=	PROPN
iajs-826	101	40	,	,	PUNCT
iajs-826	101	41	xu	xu	PUNCT
iajs-826	102	1			PROPN
iajs-826	102	2	y	y	PROPN
iajs-826	102	3	v	v	NOUN
iajs-826	102	4	,	,	PUNCT
iajs-826	102	5	therefore	therefore	ADV
iajs-826	102	6	there	there	PRON
iajs-826	102	7	exists	exist	VERB
iajs-826	102	8	two	two	NUM
iajs-826	102	9	open	open	ADJ
iajs-826	102	10	sets	set	NOUN
iajs-826	102	11	u	u	NOUN
iajs-826	102	12	and	and	CCONJ
iajs-826	102	13	v	v	NOUN
iajs-826	102	14	of	of	ADP
iajs-826	102	15	x	x	PUNCT
iajs-826	102	16	such	such	ADJ
iajs-826	102	17	that	that	PRON
iajs-826	102	18	uv=	uv=	PROPN
iajs-826	102	19	,	,	PUNCT
iajs-826	102	20	xu	xu	PUNCT
iajs-826	103	1			PROPN
iajs-826	103	2	y	y	PROPN
iajs-826	103	3	v(by	v(by	PROPN
iajs-826	103	4	definition	definition	NOUN
iajs-826	103	5	2.3	2.3	NUM
iajs-826	103	6	)	)	PUNCT
iajs-826	103	7	.	.	PUNCT
iajs-826	104	1	thus	thus	ADV
iajs-826	104	2	(	(	PUNCT
iajs-826	104	3	x	x	X
iajs-826	104	4	,	,	PUNCT
iajs-826	104	5	)	)	PUNCT
iajs-826	104	6	is	be	AUX
iajs-826	104	7	n	n	PRON
iajs-826	104	8	–	–	PUNCT
iajs-826	104	9	space	space	NOUN
iajs-826	104	10	.	.	PUNCT
iajs-826	105	1	■	■	PUNCT
iajs-826	105	2	remark	remark	VERB
iajs-826	105	3	2.22	2.22	NUM
iajs-826	105	4	the	the	DET
iajs-826	105	5	converse	converse	NOUN
iajs-826	105	6	of	of	ADP
iajs-826	105	7	(	(	PUNCT
iajs-826	105	8	proposition	proposition	NOUN
iajs-826	105	9	2.21	2.21	NUM
iajs-826	105	10	)	)	PUNCT
iajs-826	105	11	is	be	AUX
iajs-826	105	12	not	not	PART
iajs-826	105	13	true	true	ADJ
iajs-826	105	14	,	,	PUNCT
iajs-826	105	15	to	to	PART
iajs-826	105	16	see	see	VERB
iajs-826	105	17	that	that	PRON
iajs-826	105	18	consider	consider	VERB
iajs-826	105	19	the	the	DET
iajs-826	105	20	n	n	CCONJ
iajs-826	105	21	-	-	PUNCT
iajs-826	105	22	topological	topological	ADJ
iajs-826	105	23	space	space	NOUN
iajs-826	105	24	(	(	PUNCT
iajs-826	105	25	x	x	NOUN
iajs-826	105	26	,	,	PUNCT
iajs-826	105	27	)	)	PUNCT
iajs-826	105	28	in	in	ADP
iajs-826	105	29	(	(	PUNCT
iajs-826	105	30	example	example	NOUN
iajs-826	105	31	2.18	2.18	NUM
iajs-826	105	32	)	)	PUNCT
iajs-826	105	33	,	,	PUNCT
iajs-826	105	34	which	which	PRON
iajs-826	105	35	is	be	AUX
iajs-826	105	36	n	n	PRON
iajs-826	105	37	-space	-space	NOUN
iajs-826	105	38	but	but	CCONJ
iajs-826	105	39	each	each	DET
iajs-826	105	40	(	(	PUNCT
iajs-826	105	41	x	x	X
iajs-826	105	42	,	,	PUNCT
iajs-826	105	43	is	be	AUX
iajs-826	105	44	not	not	PART
iajs-826	105	45	–	–	PUNCT
iajs-826	105	46	space	space	NOUN
iajs-826	105	47	,	,	PUNCT
iajs-826	105	48	for	for	ADP
iajs-826	105	49	all	all	DET
iajs-826	105	50	i.	i.	NOUN
iajs-826	105	51	note	note	NOUN
iajs-826	105	52	1	1	X
iajs-826	105	53	.	.	PUNCT
iajs-826	106	1	it	it	PRON
iajs-826	106	2	is	be	AUX
iajs-826	106	3	clear	clear	ADJ
iajs-826	106	4	that	that	SCONJ
iajs-826	106	5	each	each	DET
iajs-826	106	6	n	n	PRON
iajs-826	106	7	space	space	NOUN
iajs-826	106	8	is	be	AUX
iajs-826	106	9	also	also	ADV
iajs-826	106	10	,	,	PUNCT
iajs-826	106	11	nspace	nspace	NOUN
iajs-826	106	12	,	,	PUNCT
iajs-826	106	13	so	so	ADV
iajs-826	106	14	is	be	AUX
iajs-826	106	15	n	n	DET
iajs-826	106	16	space	space	NOUN
iajs-826	106	17	but	but	CCONJ
iajs-826	106	18	the	the	DET
iajs-826	106	19	converse	converse	NOUN
iajs-826	106	20	is	be	AUX
iajs-826	106	21	not	not	PART
iajs-826	106	22	true	true	ADJ
iajs-826	106	23	.	.	PUNCT
iajs-826	107	1	2	2	X
iajs-826	107	2	.	.	X
iajs-826	107	3	if	if	SCONJ
iajs-826	107	4	ntopological	ntopological	ADJ
iajs-826	107	5	space	space	NOUN
iajs-826	107	6	is	be	AUX
iajs-826	107	7	not	not	PART
iajs-826	107	8	n	n	DET
iajs-826	107	9	space	space	NOUN
iajs-826	107	10	,	,	PUNCT
iajs-826	107	11	then	then	ADV
iajs-826	107	12	it	it	PRON
iajs-826	107	13	is	be	AUX
iajs-826	107	14	not	not	PART
iajs-826	107	15	n	n	DET
iajs-826	107	16	space	space	NOUN
iajs-826	107	17	,	,	PUNCT
iajs-826	107	18	then	then	ADV
iajs-826	107	19	it	it	PRON
iajs-826	107	20	is	be	AUX
iajs-826	107	21	not	not	PART
iajs-826	107	22	n	n	PRON
iajs-826	107	23	space	space	NOUN
iajs-826	107	24	.	.	PUNCT
iajs-826	108	1	theorem	theorem	VERB
iajs-826	108	2	2.23	2.23	NUM
iajs-826	108	3	let	let	VERB
iajs-826	108	4	(	(	PUNCT
iajs-826	108	5	x	x	NOUN
iajs-826	108	6	,	,	PUNCT
iajs-826	108	7	)	)	PUNCT
iajs-826	108	8	is	be	AUX
iajs-826	108	9	n	n	DET
iajs-826	108	10	space	space	NOUN
iajs-826	108	11	and	and	CCONJ
iajs-826	108	12	(	(	PUNCT
iajs-826	108	13	y	y	NOUN
iajs-826	108	14	,	,	PUNCT
iajs-826	108	15	is	be	AUX
iajs-826	108	16	sub	sub	ADJ
iajs-826	108	17	ntopological	ntopological	ADJ
iajs-826	108	18	space	space	NOUN
iajs-826	108	19	of	of	ADP
iajs-826	108	20	(	(	PUNCT
iajs-826	108	21	x	x	NOUN
iajs-826	108	22	,	,	PUNCT
iajs-826	108	23	)	)	PUNCT
iajs-826	108	24	.	.	PUNCT
iajs-826	109	1	then	then	ADV
iajs-826	109	2	(	(	PUNCT
iajs-826	109	3	y	y	NOUN
iajs-826	109	4	,	,	PUNCT
iajs-826	109	5	is	be	AUX
iajs-826	109	6	n	n	DET
iajs-826	109	7	space	space	NOUN
iajs-826	109	8	.	.	PUNCT
iajs-826	110	1	proof	proof	NOUN
iajs-826	110	2	the	the	DET
iajs-826	110	3	proof	proof	NOUN
iajs-826	110	4	of	of	ADP
iajs-826	110	5	this	this	DET
iajs-826	110	6	theorem	theorem	NOUN
iajs-826	110	7	is	be	AUX
iajs-826	110	8	similar	similar	ADJ
iajs-826	110	9	of	of	ADP
iajs-826	110	10	the	the	DET
iajs-826	110	11	proof	proof	NOUN
iajs-826	110	12	of	of	ADP
iajs-826	110	13	theorem	theorem	ADJ
iajs-826	110	14	2.19	2.19	NUM
iajs-826	110	15	■	■	SYM
iajs-826	110	16	3	3	X
iajs-826	110	17	.	.	PUNCT
iajs-826	110	18	application	application	NOUN
iajs-826	110	19	of	of	ADP
iajs-826	110	20	ntopological	ntopological	ADJ
iajs-826	110	21	space	space	NOUN
iajs-826	110	22	in	in	ADP
iajs-826	110	23	nn	nn	NOUN
iajs-826	110	24	's	's	PART
iajs-826	110	25	3.1	3.1	NUM
iajs-826	110	26	.	.	PUNCT
iajs-826	111	1	what	what	PRON
iajs-826	111	2	are	be	AUX
iajs-826	111	3	artificial	artificial	ADJ
iajs-826	111	4	neural	neural	ADJ
iajs-826	111	5	networks	network	NOUN
iajs-826	111	6	?	?	PUNCT
iajs-826	112	1	an	an	DET
iajs-826	112	2	artificial	artificial	ADJ
iajs-826	112	3	neural	neural	ADJ
iajs-826	112	4	network	network	NOUN
iajs-826	112	5	(	(	PUNCT
iajs-826	112	6	ann	ann	PROPN
iajs-826	112	7	)	)	PUNCT
iajs-826	112	8	is	be	AUX
iajs-826	112	9	an	an	DET
iajs-826	112	10	information	information	NOUN
iajs-826	112	11	processing	processing	NOUN
iajs-826	112	12	paradigm	paradigm	NOUN
iajs-826	112	13	that	that	PRON
iajs-826	112	14	is	be	AUX
iajs-826	112	15	inspired	inspire	VERB
iajs-826	112	16	by	by	ADP
iajs-826	112	17	the	the	DET
iajs-826	112	18	way	way	NOUN
iajs-826	112	19	biological	biological	ADJ
iajs-826	112	20	nervous	nervous	ADJ
iajs-826	112	21	systems	system	NOUN
iajs-826	112	22	,	,	PUNCT
iajs-826	112	23	such	such	ADJ
iajs-826	112	24	as	as	ADP
iajs-826	112	25	the	the	DET
iajs-826	112	26	brain	brain	NOUN
iajs-826	112	27	,	,	PUNCT
iajs-826	112	28	process	process	NOUN
iajs-826	112	29	information	information	NOUN
iajs-826	112	30	.	.	PUNCT
iajs-826	113	1	the	the	DET
iajs-826	113	2	key	key	ADJ
iajs-826	113	3	element	element	NOUN
iajs-826	113	4	of	of	ADP
iajs-826	113	5	this	this	DET
iajs-826	113	6	paradigm	paradigm	NOUN
iajs-826	113	7	is	be	AUX
iajs-826	113	8	the	the	DET
iajs-826	113	9	novel	novel	ADJ
iajs-826	113	10	structure	structure	NOUN
iajs-826	113	11	of	of	ADP
iajs-826	113	12	the	the	DET
iajs-826	113	13	information	information	NOUN
iajs-826	113	14	processing	processing	NOUN
iajs-826	113	15	system	system	NOUN
iajs-826	113	16	.	.	PUNCT
iajs-826	114	1	it	it	PRON
iajs-826	114	2	is	be	AUX
iajs-826	114	3	composed	compose	VERB
iajs-826	114	4	of	of	ADP
iajs-826	114	5	a	a	DET
iajs-826	114	6	large	large	ADJ
iajs-826	114	7	number	number	NOUN
iajs-826	114	8	of	of	ADP
iajs-826	114	9	highly	highly	ADV
iajs-826	114	10	interconnected	interconnected	ADJ
iajs-826	114	11	processing	processing	NOUN
iajs-826	114	12	elements	element	NOUN
iajs-826	114	13	(	(	PUNCT
iajs-826	114	14	neurons	neuron	NOUN
iajs-826	114	15	)	)	PUNCT
iajs-826	114	16	working	work	VERB
iajs-826	114	17	in	in	ADP
iajs-826	114	18	unison	unison	NOUN
iajs-826	114	19	to	to	PART
iajs-826	114	20	solve	solve	VERB
iajs-826	114	21	specific	specific	ADJ
iajs-826	114	22	problems	problem	NOUN
iajs-826	114	23	.	.	PUNCT
iajs-826	115	1	ann	ann	PROPN
iajs-826	115	2	's	's	PART
iajs-826	115	3	,	,	PUNCT
iajs-826	115	4	like	like	ADP
iajs-826	115	5	people	people	NOUN
iajs-826	115	6	,	,	PUNCT
iajs-826	115	7	learn	learn	VERB
iajs-826	115	8	by	by	ADP
iajs-826	115	9	example	example	NOUN
iajs-826	115	10	.	.	PUNCT
iajs-826	116	1	an	an	DET
iajs-826	116	2	ann	ann	PROPN
iajs-826	116	3	is	be	AUX
iajs-826	116	4	configured	configure	VERB
iajs-826	116	5	for	for	ADP
iajs-826	116	6	a	a	DET
iajs-826	116	7	specific	specific	ADJ
iajs-826	116	8	application	application	NOUN
iajs-826	116	9	,	,	PUNCT
iajs-826	116	10	such	such	ADJ
iajs-826	116	11	as	as	ADP
iajs-826	116	12	pattern	pattern	NOUN
iajs-826	116	13	recognition	recognition	NOUN
iajs-826	116	14	or	or	CCONJ
iajs-826	116	15	data	datum	NOUN
iajs-826	116	16	classification	classification	NOUN
iajs-826	116	17	,	,	PUNCT
iajs-826	116	18	through	through	ADP
iajs-826	116	19	a	a	DET
iajs-826	116	20	learning	learning	NOUN
iajs-826	116	21	process	process	NOUN
iajs-826	116	22	.	.	PUNCT
iajs-826	117	1	learning	learn	VERB
iajs-826	117	2	in	in	ADP
iajs-826	117	3	biological	biological	ADJ
iajs-826	117	4	systems	system	NOUN
iajs-826	117	5	involves	involve	VERB
iajs-826	117	6	adjustments	adjustment	NOUN
iajs-826	117	7	to	to	ADP
iajs-826	117	8	the	the	DET
iajs-826	117	9	synaptic	synaptic	ADJ
iajs-826	117	10	connections	connection	NOUN
iajs-826	117	11	that	that	PRON
iajs-826	117	12	exist	exist	VERB
iajs-826	117	13	between	between	ADP
iajs-826	117	14	the	the	DET
iajs-826	117	15	neurons	neuron	NOUN
iajs-826	117	16	.	.	PUNCT
iajs-826	118	1	this	this	PRON
iajs-826	118	2	is	be	AUX
iajs-826	118	3	true	true	ADJ
iajs-826	118	4	of	of	ADP
iajs-826	118	5	ann	ann	PROPN
iajs-826	118	6	's	's	PART
iajs-826	118	7	as	as	ADP
iajs-826	118	8	well.[3	well.[3	NOUN
iajs-826	118	9	]	]	PUNCT
iajs-826	118	10	that	that	PRON
iajs-826	118	11	is	be	AUX
iajs-826	118	12	artificial	artificial	ADJ
iajs-826	118	13	neural	neural	ADJ
iajs-826	118	14	networks	network	NOUN
iajs-826	118	15	are	be	AUX
iajs-826	118	16	relatively	relatively	ADV
iajs-826	118	17	crude	crude	ADJ
iajs-826	118	18	electronic	electronic	ADJ
iajs-826	118	19	models	model	NOUN
iajs-826	118	20	based	base	VERB
iajs-826	118	21	on	on	ADP
iajs-826	118	22	the	the	DET
iajs-826	118	23	neural	neural	ADJ
iajs-826	118	24	ibn	ibn	PROPN
iajs-826	118	25	alhaitham	alhaitham	NOUN
iajs-826	119	1	j.	j.	PROPN
iajs-826	120	1	fo	fo	ADP
iajs-826	120	2	r	r	NOUN
iajs-826	120	3	pure	pure	ADJ
iajs-826	120	4	&	&	CCONJ
iajs-826	120	5	appl	appl	PROPN
iajs-826	120	6	.	.	PUNCT
iajs-826	121	1	sc	sc	PROPN
iajs-826	121	2	i.	i.	PROPN
iajs-826	121	3	vo	vo	PROPN
iajs-826	121	4	l.24	l.24	PROPN
iajs-826	121	5	(	(	PUNCT
iajs-826	121	6	1	1	NUM
iajs-826	121	7	)	)	PUNCT
iajs-826	121	8	2011	2011	NUM
iajs-826	121	9	structure	structure	NOUN
iajs-826	121	10	of	of	ADP
iajs-826	121	11	the	the	DET
iajs-826	121	12	brain	brain	NOUN
iajs-826	121	13	.	.	PUNCT
iajs-826	122	1	the	the	DET
iajs-826	122	2	brain	brain	NOUN
iajs-826	122	3	basically	basically	ADV
iajs-826	122	4	learns	learn	VERB
iajs-826	122	5	from	from	ADP
iajs-826	122	6	experience	experience	NOUN
iajs-826	122	7	.	.	PUNCT
iajs-826	123	1	it	it	PRON
iajs-826	123	2	is	be	AUX
iajs-826	123	3	natural	natural	ADJ
iajs-826	123	4	proof	proof	NOUN
iajs-826	123	5	that	that	SCONJ
iajs-826	123	6	some	some	DET
iajs-826	123	7	problems	problem	NOUN
iajs-826	123	8	that	that	PRON
iajs-826	123	9	are	be	AUX
iajs-826	123	10	beyond	beyond	ADP
iajs-826	123	11	the	the	DET
iajs-826	123	12	scope	scope	NOUN
iajs-826	123	13	of	of	ADP
iajs-826	123	14	current	current	ADJ
iajs-826	123	15	computers	computer	NOUN
iajs-826	123	16	are	be	AUX
iajs-826	123	17	indeed	indeed	ADV
iajs-826	123	18	solvable	solvable	ADJ
iajs-826	123	19	by	by	ADP
iajs-826	123	20	small	small	ADJ
iajs-826	123	21	energy	energy	NOUN
iajs-826	123	22	efficient	efficient	ADJ
iajs-826	123	23	packages	package	NOUN
iajs-826	123	24	.	.	PUNCT
iajs-826	124	1	this	this	DET
iajs-826	124	2	brain	brain	NOUN
iajs-826	124	3	modeling	modeling	NOUN
iajs-826	124	4	also	also	ADV
iajs-826	124	5	promises	promise	VERB
iajs-826	124	6	a	a	DET
iajs-826	124	7	less	less	ADV
iajs-826	124	8	technical	technical	ADJ
iajs-826	124	9	way	way	NOUN
iajs-826	124	10	to	to	PART
iajs-826	124	11	develop	develop	VERB
iajs-826	124	12	machine	machine	NOUN
iajs-826	124	13	solutions	solution	NOUN
iajs-826	124	14	.	.	PUNCT
iajs-826	125	1	this	this	DET
iajs-826	125	2	new	new	ADJ
iajs-826	125	3	approach	approach	NOUN
iajs-826	125	4	to	to	ADP
iajs-826	125	5	computing	computing	NOUN
iajs-826	125	6	also	also	ADV
iajs-826	125	7	provides	provide	VERB
iajs-826	125	8	a	a	DET
iajs-826	125	9	more	more	ADV
iajs-826	125	10	graceful	graceful	ADJ
iajs-826	125	11	degradation	degradation	NOUN
iajs-826	125	12	during	during	ADP
iajs-826	125	13	system	system	NOUN
iajs-826	125	14	overload	overload	NOUN
iajs-826	125	15	than	than	ADP
iajs-826	125	16	its	its	PRON
iajs-826	125	17	more	more	ADV
iajs-826	125	18	traditional	traditional	ADJ
iajs-826	125	19	counterparts	counterpart	NOUN
iajs-826	125	20	.	.	PUNCT
iajs-826	126	1	these	these	DET
iajs-826	126	2	biologically	biologically	ADV
iajs-826	126	3	inspired	inspire	VERB
iajs-826	126	4	methods	method	NOUN
iajs-826	126	5	of	of	ADP
iajs-826	126	6	computing	computing	NOUN
iajs-826	126	7	are	be	AUX
iajs-826	126	8	thought	think	VERB
iajs-826	126	9	to	to	PART
iajs-826	126	10	be	be	AUX
iajs-826	126	11	the	the	DET
iajs-826	126	12	next	next	ADJ
iajs-826	126	13	major	major	ADJ
iajs-826	126	14	advancement	advancement	NOUN
iajs-826	126	15	in	in	ADP
iajs-826	126	16	the	the	DET
iajs-826	126	17	computing	computing	NOUN
iajs-826	126	18	industry	industry	NOUN
iajs-826	126	19	.	.	PUNCT
iajs-826	127	1	even	even	ADV
iajs-826	127	2	simple	simple	ADJ
iajs-826	127	3	animal	animal	NOUN
iajs-826	127	4	brains	brain	NOUN
iajs-826	127	5	are	be	AUX
iajs-826	127	6	capable	capable	ADJ
iajs-826	127	7	of	of	ADP
iajs-826	127	8	functions	function	NOUN
iajs-826	127	9	that	that	PRON
iajs-826	127	10	are	be	AUX
iajs-826	127	11	currently	currently	ADV
iajs-826	127	12	impossible	impossible	ADJ
iajs-826	127	13	for	for	ADP
iajs-826	127	14	computers	computer	NOUN
iajs-826	127	15	.	.	PUNCT
iajs-826	128	1	computers	computer	NOUN
iajs-826	128	2	do	do	AUX
iajs-826	128	3	rote	rote	VERB
iajs-826	128	4	things	thing	NOUN
iajs-826	128	5	well	well	ADV
iajs-826	128	6	,	,	PUNCT
iajs-826	128	7	like	like	ADP
iajs-826	128	8	keeping	keep	VERB
iajs-826	128	9	ledgers	ledger	NOUN
iajs-826	128	10	or	or	CCONJ
iajs-826	128	11	performing	perform	VERB
iajs-826	128	12	complex	complex	ADJ
iajs-826	128	13	math	math	NOUN
iajs-826	128	14	.	.	PUNCT
iajs-826	129	1	but	but	CCONJ
iajs-826	129	2	computers	computer	NOUN
iajs-826	129	3	have	have	VERB
iajs-826	129	4	trouble	trouble	NOUN
iajs-826	129	5	recognizing	recognize	VERB
iajs-826	129	6	even	even	ADV
iajs-826	129	7	simple	simple	ADJ
iajs-826	129	8	patterns	pattern	NOUN
iajs-826	129	9	much	much	ADV
iajs-826	129	10	less	less	ADV
iajs-826	129	11	generalizing	generalize	VERB
iajs-826	129	12	those	those	DET
iajs-826	129	13	patterns	pattern	NOUN
iajs-826	129	14	of	of	ADP
iajs-826	129	15	the	the	DET
iajs-826	129	16	past	past	NOUN
iajs-826	129	17	into	into	ADP
iajs-826	129	18	actions	action	NOUN
iajs-826	129	19	of	of	ADP
iajs-826	129	20	the	the	DET
iajs-826	129	21	future	future	NOUN
iajs-826	129	22	.	.	PUNCT
iajs-826	130	1	3.2	3.2	NUM
iajs-826	130	2	.	.	PUNCT
iajs-826	130	3	artificial	artificial	ADJ
iajs-826	130	4	network	network	NOUN
iajs-826	130	5	operations	operation	NOUN
iajs-826	130	6	the	the	DET
iajs-826	130	7	other	other	ADJ
iajs-826	130	8	part	part	NOUN
iajs-826	130	9	of	of	ADP
iajs-826	130	10	the	the	DET
iajs-826	130	11	"	"	PUNCT
iajs-826	130	12	art	art	NOUN
iajs-826	130	13	"	"	PUNCT
iajs-826	130	14	of	of	ADP
iajs-826	130	15	using	use	VERB
iajs-826	130	16	neural	neural	ADJ
iajs-826	130	17	networks	network	NOUN
iajs-826	130	18	revolves	revolve	VERB
iajs-826	130	19	around	around	ADP
iajs-826	130	20	the	the	DET
iajs-826	130	21	myriad	myriad	NOUN
iajs-826	130	22	of	of	ADP
iajs-826	130	23	ways	way	NOUN
iajs-826	130	24	these	these	DET
iajs-826	130	25	individual	individual	ADJ
iajs-826	130	26	neurons	neuron	NOUN
iajs-826	130	27	can	can	AUX
iajs-826	130	28	be	be	AUX
iajs-826	130	29	clustered	cluster	VERB
iajs-826	130	30	together	together	ADV
iajs-826	130	31	.	.	PUNCT
iajs-826	131	1	this	this	DET
iajs-826	131	2	clustering	clustering	NOUN
iajs-826	131	3	occurs	occur	VERB
iajs-826	131	4	in	in	ADP
iajs-826	131	5	the	the	DET
iajs-826	131	6	human	human	ADJ
iajs-826	131	7	mind	mind	NOUN
iajs-826	131	8	in	in	ADP
iajs-826	131	9	such	such	DET
iajs-826	131	10	a	a	DET
iajs-826	131	11	way	way	NOUN
iajs-826	131	12	that	that	PRON
iajs-826	131	13	information	information	NOUN
iajs-826	131	14	can	can	AUX
iajs-826	131	15	be	be	AUX
iajs-826	131	16	processed	process	VERB
iajs-826	131	17	in	in	ADP
iajs-826	131	18	a	a	DET
iajs-826	131	19	dynamic	dynamic	ADJ
iajs-826	131	20	,	,	PUNCT
iajs-826	131	21	interactive	interactive	ADJ
iajs-826	131	22	,	,	PUNCT
iajs-826	131	23	and	and	CCONJ
iajs-826	131	24	self	self	NOUN
iajs-826	131	25	-	-	PUNCT
iajs-826	131	26	organizing	organize	VERB
iajs-826	131	27	way	way	NOUN
iajs-826	131	28	.	.	PUNCT
iajs-826	132	1	biologically	biologically	ADV
iajs-826	132	2	,	,	PUNCT
iajs-826	132	3	neural	neural	ADJ
iajs-826	132	4	networks	network	NOUN
iajs-826	132	5	are	be	AUX
iajs-826	132	6	constructed	construct	VERB
iajs-826	132	7	in	in	ADP
iajs-826	132	8	a	a	DET
iajs-826	132	9	three	three	NUM
iajs-826	132	10	-	-	PUNCT
iajs-826	132	11	dimensional	dimensional	ADJ
iajs-826	132	12	world	world	NOUN
iajs-826	132	13	from	from	ADP
iajs-826	132	14	microscopic	microscopic	ADJ
iajs-826	132	15	components	component	NOUN
iajs-826	132	16	.	.	PUNCT
iajs-826	133	1	these	these	DET
iajs-826	133	2	neurons	neuron	NOUN
iajs-826	133	3	seem	seem	VERB
iajs-826	133	4	capable	capable	ADJ
iajs-826	133	5	of	of	ADP
iajs-826	133	6	nearly	nearly	ADV
iajs-826	133	7	unrestricted	unrestricted	ADJ
iajs-826	133	8	interconnections	interconnection	NOUN
iajs-826	133	9	.	.	PUNCT
iajs-826	134	1	that	that	PRON
iajs-826	134	2	is	be	AUX
iajs-826	134	3	not	not	PART
iajs-826	134	4	true	true	ADJ
iajs-826	134	5	of	of	ADP
iajs-826	134	6	any	any	DET
iajs-826	134	7	proposed	propose	VERB
iajs-826	134	8	,	,	PUNCT
iajs-826	134	9	or	or	CCONJ
iajs-826	134	10	existing	exist	VERB
iajs-826	134	11	,	,	PUNCT
iajs-826	134	12	man	man	NOUN
iajs-826	134	13	-	-	PUNCT
iajs-826	134	14	made	make	VERB
iajs-826	134	15	network	network	NOUN
iajs-826	134	16	.	.	PUNCT
iajs-826	135	1	integrated	integrate	VERB
iajs-826	135	2	circuits	circuit	NOUN
iajs-826	135	3	,	,	PUNCT
iajs-826	135	4	using	use	VERB
iajs-826	135	5	current	current	ADJ
iajs-826	135	6	technology	technology	NOUN
iajs-826	135	7	,	,	PUNCT
iajs-826	135	8	are	be	AUX
iajs-826	135	9	two	two	NUM
iajs-826	135	10	-	-	PUNCT
iajs-826	135	11	dimensional	dimensional	ADJ
iajs-826	135	12	devices	device	NOUN
iajs-826	135	13	with	with	ADP
iajs-826	135	14	a	a	DET
iajs-826	135	15	limited	limited	ADJ
iajs-826	135	16	number	number	NOUN
iajs-826	135	17	of	of	ADP
iajs-826	135	18	layers	layer	NOUN
iajs-826	135	19	for	for	ADP
iajs-826	135	20	interconnection	interconnection	NOUN
iajs-826	135	21	.	.	PUNCT
iajs-826	136	1	this	this	DET
iajs-826	136	2	physical	physical	ADJ
iajs-826	136	3	reality	reality	NOUN
iajs-826	136	4	restrains	restrain	VERB
iajs-826	136	5	the	the	DET
iajs-826	136	6	types	type	NOUN
iajs-826	136	7	,	,	PUNCT
iajs-826	136	8	and	and	CCONJ
iajs-826	136	9	scope	scope	NOUN
iajs-826	136	10	,	,	PUNCT
iajs-826	136	11	of	of	ADP
iajs-826	136	12	artificial	artificial	ADJ
iajs-826	136	13	neural	neural	ADJ
iajs-826	136	14	networks	network	NOUN
iajs-826	136	15	that	that	PRON
iajs-826	136	16	can	can	AUX
iajs-826	136	17	be	be	AUX
iajs-826	136	18	implemented	implement	VERB
iajs-826	136	19	in	in	ADP
iajs-826	136	20	silicon.[3	silicon.[3	PROPN
iajs-826	136	21	]	]	PUNCT
iajs-826	136	22	currently	currently	ADV
iajs-826	136	23	,	,	PUNCT
iajs-826	136	24	neural	neural	ADJ
iajs-826	136	25	networks	network	NOUN
iajs-826	136	26	are	be	AUX
iajs-826	136	27	the	the	DET
iajs-826	136	28	simple	simple	ADJ
iajs-826	136	29	clustering	clustering	NOUN
iajs-826	136	30	of	of	ADP
iajs-826	136	31	the	the	DET
iajs-826	136	32	primitive	primitive	ADJ
iajs-826	136	33	artificial	artificial	ADJ
iajs-826	136	34	neurons	neuron	NOUN
iajs-826	136	35	.	.	PUNCT
iajs-826	137	1	this	this	DET
iajs-826	137	2	clustering	clustering	NOUN
iajs-826	137	3	occurs	occur	VERB
iajs-826	137	4	by	by	ADP
iajs-826	137	5	creating	create	VERB
iajs-826	137	6	layers	layer	NOUN
iajs-826	137	7	which	which	PRON
iajs-826	137	8	are	be	AUX
iajs-826	137	9	then	then	ADV
iajs-826	137	10	connected	connect	VERB
iajs-826	137	11	to	to	ADP
iajs-826	137	12	one	one	NUM
iajs-826	137	13	another	another	DET
iajs-826	137	14	.	.	PUNCT
iajs-826	138	1	how	how	SCONJ
iajs-826	138	2	these	these	DET
iajs-826	138	3	layers	layer	NOUN
iajs-826	138	4	connect	connect	VERB
iajs-826	138	5	is	be	AUX
iajs-826	138	6	the	the	DET
iajs-826	138	7	other	other	ADJ
iajs-826	138	8	part	part	NOUN
iajs-826	138	9	of	of	ADP
iajs-826	138	10	the	the	DET
iajs-826	138	11	"	"	PUNCT
iajs-826	138	12	art	art	NOUN
iajs-826	138	13	"	"	PUNCT
iajs-826	138	14	of	of	ADP
iajs-826	138	15	engineering	engineering	NOUN
iajs-826	138	16	networks	network	NOUN
iajs-826	138	17	to	to	PART
iajs-826	138	18	resolve	resolve	VERB
iajs-826	138	19	real	real	ADJ
iajs-826	138	20	world	world	NOUN
iajs-826	138	21	problems	problem	NOUN
iajs-826	138	22	.	.	PUNCT
iajs-826	139	1	basically	basically	ADV
iajs-826	139	2	,	,	PUNCT
iajs-826	139	3	all	all	DET
iajs-826	139	4	artificial	artificial	ADJ
iajs-826	139	5	neural	neural	ADJ
iajs-826	139	6	networks	network	NOUN
iajs-826	139	7	have	have	VERB
iajs-826	139	8	a	a	DET
iajs-826	139	9	similar	similar	ADJ
iajs-826	139	10	structure	structure	NOUN
iajs-826	139	11	or	or	CCONJ
iajs-826	139	12	topology	topology	NOUN
iajs-826	139	13	as	as	SCONJ
iajs-826	139	14	shown	show	VERB
iajs-826	139	15	in	in	ADP
iajs-826	139	16	figure	figure	NOUN
iajs-826	139	17	(	(	PUNCT
iajs-826	139	18	1	1	NUM
iajs-826	139	19	)	)	PUNCT
iajs-826	139	20	.	.	PUNCT
iajs-826	140	1	in	in	ADP
iajs-826	140	2	that	that	DET
iajs-826	140	3	structure	structure	NOUN
iajs-826	140	4	some	some	PRON
iajs-826	140	5	of	of	ADP
iajs-826	140	6	the	the	DET
iajs-826	140	7	neurons	neuron	NOUN
iajs-826	140	8	interfaces	interface	NOUN
iajs-826	140	9	to	to	ADP
iajs-826	140	10	the	the	DET
iajs-826	140	11	real	real	ADJ
iajs-826	140	12	world	world	NOUN
iajs-826	140	13	to	to	PART
iajs-826	140	14	receive	receive	VERB
iajs-826	140	15	its	its	PRON
iajs-826	140	16	inputs	input	NOUN
iajs-826	140	17	.	.	PUNCT
iajs-826	141	1	other	other	ADJ
iajs-826	141	2	neurons	neuron	NOUN
iajs-826	141	3	provide	provide	VERB
iajs-826	141	4	the	the	DET
iajs-826	141	5	real	real	ADJ
iajs-826	141	6	world	world	NOUN
iajs-826	141	7	with	with	ADP
iajs-826	141	8	the	the	DET
iajs-826	141	9	networks	network	NOUN
iajs-826	141	10	outputs	output	NOUN
iajs-826	141	11	.	.	PUNCT
iajs-826	142	1	this	this	DET
iajs-826	142	2	output	output	NOUN
iajs-826	142	3	might	might	AUX
iajs-826	142	4	be	be	AUX
iajs-826	142	5	the	the	DET
iajs-826	142	6	particular	particular	ADJ
iajs-826	142	7	character	character	NOUN
iajs-826	142	8	that	that	SCONJ
iajs-826	142	9	the	the	DET
iajs-826	142	10	network	network	NOUN
iajs-826	142	11	thinks	think	VERB
iajs-826	142	12	that	that	SCONJ
iajs-826	142	13	it	it	PRON
iajs-826	142	14	has	have	AUX
iajs-826	142	15	scanned	scan	VERB
iajs-826	142	16	or	or	CCONJ
iajs-826	142	17	the	the	DET
iajs-826	142	18	particular	particular	ADJ
iajs-826	142	19	image	image	NOUN
iajs-826	142	20	it	it	PRON
iajs-826	142	21	thinks	think	VERB
iajs-826	142	22	is	be	AUX
iajs-826	142	23	being	be	AUX
iajs-826	142	24	viewed	view	VERB
iajs-826	142	25	.	.	PUNCT
iajs-826	143	1	all	all	DET
iajs-826	143	2	the	the	DET
iajs-826	143	3	rest	rest	NOUN
iajs-826	143	4	of	of	ADP
iajs-826	143	5	the	the	DET
iajs-826	143	6	neurons	neuron	NOUN
iajs-826	143	7	are	be	AUX
iajs-826	143	8	hidden	hide	VERB
iajs-826	143	9	from	from	ADP
iajs-826	143	10	view	view	NOUN
iajs-826	143	11	.	.	PUNCT
iajs-826	144	1	but	but	CCONJ
iajs-826	144	2	a	a	DET
iajs-826	144	3	neural	neural	ADJ
iajs-826	144	4	network	network	NOUN
iajs-826	144	5	is	be	AUX
iajs-826	144	6	more	more	ADJ
iajs-826	144	7	than	than	ADP
iajs-826	144	8	a	a	DET
iajs-826	144	9	bunch	bunch	NOUN
iajs-826	144	10	of	of	ADP
iajs-826	144	11	neurons	neuron	NOUN
iajs-826	144	12	.	.	PUNCT
iajs-826	145	1	some	some	DET
iajs-826	145	2	early	early	ADJ
iajs-826	145	3	researchers	researcher	NOUN
iajs-826	145	4	tried	try	VERB
iajs-826	145	5	to	to	PART
iajs-826	145	6	simply	simply	ADV
iajs-826	145	7	connect	connect	VERB
iajs-826	145	8	neurons	neuron	NOUN
iajs-826	145	9	in	in	ADP
iajs-826	145	10	a	a	DET
iajs-826	145	11	random	random	ADJ
iajs-826	145	12	manner	manner	NOUN
iajs-826	145	13	,	,	PUNCT
iajs-826	145	14	without	without	ADP
iajs-826	145	15	much	much	ADJ
iajs-826	145	16	success	success	NOUN
iajs-826	145	17	.	.	PUNCT
iajs-826	146	1	now	now	ADV
iajs-826	146	2	,	,	PUNCT
iajs-826	146	3	it	it	PRON
iajs-826	146	4	is	be	AUX
iajs-826	146	5	known	know	VERB
iajs-826	146	6	that	that	SCONJ
iajs-826	146	7	even	even	ADV
iajs-826	146	8	the	the	DET
iajs-826	146	9	brains	brain	NOUN
iajs-826	146	10	of	of	ADP
iajs-826	146	11	snails	snail	NOUN
iajs-826	146	12	are	be	AUX
iajs-826	146	13	structured	structured	ADJ
iajs-826	146	14	devices	device	NOUN
iajs-826	146	15	.	.	PUNCT
iajs-826	147	1	one	one	NUM
iajs-826	147	2	of	of	ADP
iajs-826	147	3	the	the	DET
iajs-826	147	4	easiest	easy	ADJ
iajs-826	147	5	ways	way	NOUN
iajs-826	147	6	to	to	PART
iajs-826	147	7	design	design	VERB
iajs-826	147	8	a	a	DET
iajs-826	147	9	structure	structure	NOUN
iajs-826	147	10	is	be	AUX
iajs-826	147	11	to	to	PART
iajs-826	147	12	create	create	VERB
iajs-826	147	13	layers	layer	NOUN
iajs-826	147	14	of	of	ADP
iajs-826	147	15	elements	element	NOUN
iajs-826	147	16	.	.	PUNCT
iajs-826	148	1	it	it	PRON
iajs-826	148	2	is	be	AUX
iajs-826	148	3	the	the	DET
iajs-826	148	4	grouping	grouping	NOUN
iajs-826	148	5	of	of	ADP
iajs-826	148	6	these	these	DET
iajs-826	148	7	neurons	neuron	NOUN
iajs-826	148	8	into	into	ADP
iajs-826	148	9	layers	layer	NOUN
iajs-826	148	10	,	,	PUNCT
iajs-826	148	11	the	the	DET
iajs-826	148	12	connections	connection	NOUN
iajs-826	148	13	between	between	ADP
iajs-826	148	14	these	these	DET
iajs-826	148	15	layers	layer	NOUN
iajs-826	148	16	,	,	PUNCT
iajs-826	148	17	and	and	CCONJ
iajs-826	148	18	the	the	DET
iajs-826	148	19	summation	summation	NOUN
iajs-826	148	20	and	and	CCONJ
iajs-826	148	21	transfer	transfer	NOUN
iajs-826	148	22	functions	function	NOUN
iajs-826	148	23	that	that	PRON
iajs-826	148	24	comprise	comprise	VERB
iajs-826	148	25	a	a	DET
iajs-826	148	26	functioning	function	VERB
iajs-826	148	27	neural	neural	ADJ
iajs-826	148	28	network	network	NOUN
iajs-826	148	29	.	.	PUNCT
iajs-826	149	1	the	the	DET
iajs-826	149	2	general	general	ADJ
iajs-826	149	3	terms	term	NOUN
iajs-826	149	4	used	use	VERB
iajs-826	149	5	to	to	PART
iajs-826	149	6	describe	describe	VERB
iajs-826	149	7	these	these	DET
iajs-826	149	8	characteristics	characteristic	NOUN
iajs-826	149	9	are	be	AUX
iajs-826	149	10	common	common	ADJ
iajs-826	149	11	to	to	ADP
iajs-826	149	12	all	all	DET
iajs-826	149	13	networks	network	NOUN
iajs-826	149	14	.	.	PUNCT
iajs-826	150	1	although	although	SCONJ
iajs-826	150	2	there	there	PRON
iajs-826	150	3	are	be	VERB
iajs-826	150	4	useful	useful	ADJ
iajs-826	150	5	networks	network	NOUN
iajs-826	150	6	which	which	PRON
iajs-826	150	7	contain	contain	VERB
iajs-826	150	8	only	only	ADV
iajs-826	150	9	one	one	NUM
iajs-826	150	10	layer	layer	NOUN
iajs-826	150	11	,	,	PUNCT
iajs-826	150	12	or	or	CCONJ
iajs-826	150	13	even	even	ADV
iajs-826	150	14	one	one	NUM
iajs-826	150	15	element	element	NOUN
iajs-826	150	16	,	,	PUNCT
iajs-826	150	17	most	most	ADJ
iajs-826	150	18	applications	application	NOUN
iajs-826	150	19	require	require	VERB
iajs-826	150	20	networks	network	NOUN
iajs-826	150	21	that	that	PRON
iajs-826	150	22	contain	contain	VERB
iajs-826	150	23	at	at	ADP
iajs-826	150	24	least	least	ADJ
iajs-826	150	25	the	the	DET
iajs-826	150	26	three	three	NUM
iajs-826	150	27	normal	normal	ADJ
iajs-826	150	28	types	type	NOUN
iajs-826	150	29	of	of	ADP
iajs-826	150	30	layers	layer	NOUN
iajs-826	150	31	input	input	NOUN
iajs-826	150	32	,	,	PUNCT
iajs-826	150	33	hidden	hide	VERB
iajs-826	150	34	,	,	PUNCT
iajs-826	150	35	and	and	CCONJ
iajs-826	150	36	output	output	NOUN
iajs-826	150	37	.	.	PUNCT
iajs-826	151	1	the	the	DET
iajs-826	151	2	layer	layer	NOUN
iajs-826	151	3	of	of	ADP
iajs-826	151	4	input	input	NOUN
iajs-826	151	5	neurons	neuron	NOUN
iajs-826	151	6	receives	receive	VERB
iajs-826	151	7	the	the	DET
iajs-826	151	8	data	datum	NOUN
iajs-826	151	9	either	either	CCONJ
iajs-826	151	10	from	from	ADP
iajs-826	151	11	input	input	NOUN
iajs-826	151	12	files	file	NOUN
iajs-826	151	13	or	or	CCONJ
iajs-826	151	14	directly	directly	ADV
iajs-826	151	15	from	from	ADP
iajs-826	151	16	electronic	electronic	ADJ
iajs-826	151	17	sensors	sensor	NOUN
iajs-826	151	18	in	in	ADP
iajs-826	151	19	real	real	ADJ
iajs-826	151	20	-	-	PUNCT
iajs-826	151	21	time	time	NOUN
iajs-826	151	22	applications	application	NOUN
iajs-826	151	23	.	.	PUNCT
iajs-826	152	1	ibn	ibn	PROPN
iajs-826	152	2	alhaitham	alhaitham	PROPN
iajs-826	153	1	j.	j.	PROPN
iajs-826	154	1	fo	fo	ADP
iajs-826	154	2	r	r	NOUN
iajs-826	154	3	pure	pure	ADJ
iajs-826	154	4	&	&	CCONJ
iajs-826	154	5	appl	appl	PROPN
iajs-826	154	6	.	.	PUNCT
iajs-826	155	1	sc	sc	PROPN
iajs-826	155	2	i.	i.	PROPN
iajs-826	155	3	vo	vo	PROPN
iajs-826	156	1	l.24	l.24	PROPN
iajs-826	156	2	(	(	PUNCT
iajs-826	156	3	1	1	NUM
iajs-826	156	4	)	)	PUNCT
iajs-826	156	5	2011	2011	NUM
iajs-826	156	6	the	the	DET
iajs-826	156	7	output	output	NOUN
iajs-826	156	8	layer	layer	NOUN
iajs-826	156	9	sends	send	VERB
iajs-826	156	10	information	information	NOUN
iajs-826	156	11	directly	directly	ADV
iajs-826	156	12	to	to	ADP
iajs-826	156	13	the	the	DET
iajs-826	156	14	outside	outside	ADJ
iajs-826	156	15	world	world	NOUN
iajs-826	156	16	,	,	PUNCT
iajs-826	156	17	to	to	ADP
iajs-826	156	18	a	a	DET
iajs-826	156	19	secondary	secondary	ADJ
iajs-826	156	20	computer	computer	NOUN
iajs-826	156	21	process	process	NOUN
iajs-826	156	22	,	,	PUNCT
iajs-826	156	23	or	or	CCONJ
iajs-826	156	24	to	to	ADP
iajs-826	156	25	other	other	ADJ
iajs-826	156	26	devices	device	NOUN
iajs-826	156	27	such	such	ADJ
iajs-826	156	28	as	as	ADP
iajs-826	156	29	a	a	DET
iajs-826	156	30	mechanical	mechanical	ADJ
iajs-826	156	31	control	control	NOUN
iajs-826	156	32	system	system	NOUN
iajs-826	156	33	.	.	PUNCT
iajs-826	157	1	between	between	ADP
iajs-826	157	2	these	these	DET
iajs-826	157	3	two	two	NUM
iajs-826	157	4	layers	layer	NOUN
iajs-826	157	5	,	,	PUNCT
iajs-826	157	6	there	there	PRON
iajs-826	157	7	can	can	AUX
iajs-826	157	8	be	be	AUX
iajs-826	157	9	many	many	ADJ
iajs-826	157	10	hidden	hidden	ADJ
iajs-826	157	11	layers	layer	NOUN
iajs-826	157	12	.	.	PUNCT
iajs-826	158	1	these	these	DET
iajs-826	158	2	internal	internal	ADJ
iajs-826	158	3	layers	layer	NOUN
iajs-826	158	4	contain	contain	VERB
iajs-826	158	5	many	many	ADJ
iajs-826	158	6	of	of	ADP
iajs-826	158	7	the	the	DET
iajs-826	158	8	neurons	neuron	NOUN
iajs-826	158	9	in	in	ADP
iajs-826	158	10	various	various	ADJ
iajs-826	158	11	interconnected	interconnected	ADJ
iajs-826	158	12	structures	structure	NOUN
iajs-826	158	13	.	.	PUNCT
iajs-826	159	1	the	the	DET
iajs-826	159	2	inputs	input	NOUN
iajs-826	159	3	and	and	CCONJ
iajs-826	159	4	outputs	output	NOUN
iajs-826	159	5	of	of	ADP
iajs-826	159	6	each	each	PRON
iajs-826	159	7	of	of	ADP
iajs-826	159	8	these	these	DET
iajs-826	159	9	hidden	hide	VERB
iajs-826	159	10	neurons	neuron	NOUN
iajs-826	159	11	simply	simply	ADV
iajs-826	159	12	go	go	VERB
iajs-826	159	13	to	to	ADP
iajs-826	159	14	other	other	ADJ
iajs-826	159	15	neurons	neuron	NOUN
iajs-826	159	16	.	.	PUNCT
iajs-826	160	1	in	in	ADP
iajs-826	160	2	most	most	ADJ
iajs-826	160	3	networks	network	NOUN
iajs-826	160	4	each	each	DET
iajs-826	160	5	neuron	neuron	NOUN
iajs-826	160	6	in	in	ADP
iajs-826	160	7	a	a	DET
iajs-826	160	8	hidden	hide	VERB
iajs-826	160	9	layer	layer	NOUN
iajs-826	160	10	receives	receive	VERB
iajs-826	160	11	the	the	DET
iajs-826	160	12	signals	signal	NOUN
iajs-826	160	13	from	from	ADP
iajs-826	160	14	all	all	PRON
iajs-826	160	15	of	of	ADP
iajs-826	160	16	the	the	DET
iajs-826	160	17	neurons	neuron	NOUN
iajs-826	160	18	in	in	ADP
iajs-826	160	19	a	a	DET
iajs-826	160	20	layer	layer	NOUN
iajs-826	160	21	above	above	ADP
iajs-826	160	22	it	it	PRON
iajs-826	160	23	,	,	PUNCT
iajs-826	160	24	typically	typically	ADV
iajs-826	160	25	an	an	DET
iajs-826	160	26	input	input	NOUN
iajs-826	160	27	layer	layer	NOUN
iajs-826	160	28	.	.	PUNCT
iajs-826	161	1	after	after	SCONJ
iajs-826	161	2	a	a	DET
iajs-826	161	3	neuron	neuron	NOUN
iajs-826	161	4	performs	perform	VERB
iajs-826	161	5	its	its	PRON
iajs-826	161	6	function	function	NOUN
iajs-826	161	7	it	it	PRON
iajs-826	161	8	passes	pass	VERB
iajs-826	161	9	its	its	PRON
iajs-826	161	10	output	output	NOUN
iajs-826	161	11	to	to	ADP
iajs-826	161	12	all	all	PRON
iajs-826	161	13	of	of	ADP
iajs-826	161	14	the	the	DET
iajs-826	161	15	neurons	neuron	NOUN
iajs-826	161	16	in	in	ADP
iajs-826	161	17	the	the	DET
iajs-826	161	18	layer	layer	NOUN
iajs-826	161	19	below	below	ADP
iajs-826	161	20	it	it	PRON
iajs-826	161	21	,	,	PUNCT
iajs-826	161	22	providing	provide	VERB
iajs-826	161	23	a	a	DET
iajs-826	161	24	feed	feed	NOUN
iajs-826	161	25	forward	forward	ADV
iajs-826	161	26	path	path	NOUN
iajs-826	161	27	to	to	ADP
iajs-826	161	28	the	the	DET
iajs-826	161	29	output	output	NOUN
iajs-826	161	30	.	.	PUNCT
iajs-826	162	1	these	these	DET
iajs-826	162	2	lines	line	NOUN
iajs-826	162	3	of	of	ADP
iajs-826	162	4	communication	communication	NOUN
iajs-826	162	5	from	from	ADP
iajs-826	162	6	one	one	NUM
iajs-826	162	7	neuron	neuron	NOUN
iajs-826	162	8	to	to	ADP
iajs-826	162	9	another	another	PRON
iajs-826	162	10	are	be	AUX
iajs-826	162	11	important	important	ADJ
iajs-826	162	12	aspects	aspect	NOUN
iajs-826	162	13	of	of	ADP
iajs-826	162	14	neural	neural	ADJ
iajs-826	162	15	networks	network	NOUN
iajs-826	162	16	.	.	PUNCT
iajs-826	163	1	they	they	PRON
iajs-826	163	2	are	be	AUX
iajs-826	163	3	the	the	DET
iajs-826	163	4	glue	glue	NOUN
iajs-826	163	5	to	to	ADP
iajs-826	163	6	the	the	DET
iajs-826	163	7	system	system	NOUN
iajs-826	163	8	.	.	PUNCT
iajs-826	164	1	they	they	PRON
iajs-826	164	2	are	be	AUX
iajs-826	164	3	the	the	DET
iajs-826	164	4	connections	connection	NOUN
iajs-826	164	5	which	which	PRON
iajs-826	164	6	provide	provide	VERB
iajs-826	164	7	a	a	DET
iajs-826	164	8	variable	variable	ADJ
iajs-826	164	9	strength	strength	NOUN
iajs-826	164	10	to	to	ADP
iajs-826	164	11	an	an	DET
iajs-826	164	12	input	input	NOUN
iajs-826	164	13	.	.	PUNCT
iajs-826	165	1	there	there	PRON
iajs-826	165	2	are	be	VERB
iajs-826	165	3	two	two	NUM
iajs-826	165	4	types	type	NOUN
iajs-826	165	5	of	of	ADP
iajs-826	165	6	these	these	DET
iajs-826	165	7	connections	connection	NOUN
iajs-826	165	8	.	.	PUNCT
iajs-826	166	1	one	one	NUM
iajs-826	166	2	causes	cause	VERB
iajs-826	166	3	the	the	DET
iajs-826	166	4	summing	sum	VERB
iajs-826	166	5	mechanism	mechanism	NOUN
iajs-826	166	6	of	of	ADP
iajs-826	166	7	the	the	DET
iajs-826	166	8	next	next	ADJ
iajs-826	166	9	neuron	neuron	NOUN
iajs-826	166	10	to	to	PART
iajs-826	166	11	add	add	VERB
iajs-826	166	12	while	while	SCONJ
iajs-826	166	13	the	the	DET
iajs-826	166	14	other	other	ADJ
iajs-826	166	15	causes	cause	VERB
iajs-826	166	16	it	it	PRON
iajs-826	166	17	to	to	PART
iajs-826	166	18	subtract	subtract	VERB
iajs-826	166	19	.	.	PUNCT
iajs-826	167	1	in	in	ADP
iajs-826	167	2	more	more	ADJ
iajs-826	167	3	human	human	ADJ
iajs-826	167	4	terms	term	NOUN
iajs-826	167	5	one	one	NUM
iajs-826	167	6	excites	excite	VERB
iajs-826	167	7	while	while	SCONJ
iajs-826	167	8	the	the	DET
iajs-826	167	9	other	other	ADJ
iajs-826	167	10	inhibits	inhibit	VERB
iajs-826	167	11	.	.	PUNCT
iajs-826	168	1	some	some	DET
iajs-826	168	2	networks	network	NOUN
iajs-826	168	3	want	want	VERB
iajs-826	168	4	a	a	DET
iajs-826	168	5	neuron	neuron	NOUN
iajs-826	168	6	to	to	PART
iajs-826	168	7	inhibit	inhibit	VERB
iajs-826	168	8	the	the	DET
iajs-826	168	9	other	other	ADJ
iajs-826	168	10	neurons	neuron	NOUN
iajs-826	168	11	in	in	ADP
iajs-826	168	12	the	the	DET
iajs-826	168	13	same	same	ADJ
iajs-826	168	14	layer	layer	NOUN
iajs-826	168	15	.	.	PUNCT
iajs-826	169	1	this	this	PRON
iajs-826	169	2	is	be	AUX
iajs-826	169	3	called	call	VERB
iajs-826	169	4	lateral	lateral	ADJ
iajs-826	169	5	inhibition	inhibition	NOUN
iajs-826	169	6	.	.	PUNCT
iajs-826	170	1	the	the	DET
iajs-826	170	2	most	most	ADV
iajs-826	170	3	common	common	ADJ
iajs-826	170	4	use	use	NOUN
iajs-826	170	5	of	of	ADP
iajs-826	170	6	this	this	PRON
iajs-826	170	7	is	be	AUX
iajs-826	170	8	in	in	ADP
iajs-826	170	9	the	the	DET
iajs-826	170	10	output	output	NOUN
iajs-826	170	11	layer	layer	NOUN
iajs-826	170	12	.	.	PUNCT
iajs-826	171	1	for	for	ADP
iajs-826	171	2	example	example	NOUN
iajs-826	171	3	in	in	ADP
iajs-826	171	4	text	text	NOUN
iajs-826	171	5	recognition	recognition	NOUN
iajs-826	171	6	if	if	SCONJ
iajs-826	171	7	the	the	DET
iajs-826	171	8	probability	probability	NOUN
iajs-826	171	9	of	of	ADP
iajs-826	171	10	a	a	DET
iajs-826	171	11	character	character	NOUN
iajs-826	171	12	being	be	AUX
iajs-826	171	13	a	a	DET
iajs-826	171	14	"	"	PUNCT
iajs-826	171	15	p	p	NOUN
iajs-826	171	16	"	"	PUNCT
iajs-826	171	17	is	be	AUX
iajs-826	171	18	.85	.85	NUM
iajs-826	171	19	and	and	CCONJ
iajs-826	171	20	the	the	DET
iajs-826	171	21	probability	probability	NOUN
iajs-826	171	22	of	of	ADP
iajs-826	171	23	the	the	DET
iajs-826	171	24	character	character	NOUN
iajs-826	171	25	being	be	AUX
iajs-826	171	26	an	an	DET
iajs-826	171	27	"	"	PUNCT
iajs-826	171	28	f	f	NOUN
iajs-826	171	29	"	"	PUNCT
iajs-826	171	30	is	be	AUX
iajs-826	171	31	.65	.65	NUM
iajs-826	171	32	,	,	PUNCT
iajs-826	171	33	the	the	DET
iajs-826	171	34	network	network	NOUN
iajs-826	171	35	wants	want	VERB
iajs-826	171	36	to	to	PART
iajs-826	171	37	choose	choose	VERB
iajs-826	171	38	the	the	DET
iajs-826	171	39	highest	high	ADJ
iajs-826	171	40	probability	probability	NOUN
iajs-826	171	41	and	and	CCONJ
iajs-826	171	42	inhibit	inhibit	VERB
iajs-826	171	43	all	all	DET
iajs-826	171	44	the	the	DET
iajs-826	171	45	others	other	NOUN
iajs-826	171	46	.	.	PUNCT
iajs-826	172	1	it	it	PRON
iajs-826	172	2	can	can	AUX
iajs-826	172	3	do	do	VERB
iajs-826	172	4	that	that	PRON
iajs-826	172	5	with	with	ADP
iajs-826	172	6	lateral	lateral	ADJ
iajs-826	172	7	inhibition	inhibition	NOUN
iajs-826	172	8	.	.	PUNCT
iajs-826	173	1	this	this	DET
iajs-826	173	2	concept	concept	NOUN
iajs-826	173	3	is	be	AUX
iajs-826	173	4	also	also	ADV
iajs-826	173	5	called	call	VERB
iajs-826	173	6	competition	competition	NOUN
iajs-826	173	7	.	.	PUNCT
iajs-826	174	1	3.3	3.3	NUM
iajs-826	174	2	.	.	PUNCT
iajs-826	175	1	a	a	DET
iajs-826	175	2	relation	relation	NOUN
iajs-826	175	3	between	between	ADP
iajs-826	175	4	ann	ann	PROPN
iajs-826	175	5	's	's	PART
iajs-826	175	6	and	and	CCONJ
iajs-826	175	7	ntopological	ntopological	ADJ
iajs-826	175	8	space	space	NOUN
iajs-826	175	9	nn	nn	PROPN
iajs-826	175	10	's	's	PART
iajs-826	175	11	have	have	AUX
iajs-826	175	12	been	be	AUX
iajs-826	175	13	developed	develop	VERB
iajs-826	175	14	as	as	ADP
iajs-826	175	15	generalizations	generalization	NOUN
iajs-826	175	16	of	of	ADP
iajs-826	175	17	mathematical	mathematical	ADJ
iajs-826	175	18	models	model	NOUN
iajs-826	175	19	of	of	ADP
iajs-826	175	20	human	human	ADJ
iajs-826	175	21	cognition	cognition	NOUN
iajs-826	175	22	or	or	CCONJ
iajs-826	175	23	neural	neural	ADJ
iajs-826	175	24	biology	biology	NOUN
iajs-826	175	25	,	,	PUNCT
iajs-826	175	26	and	and	CCONJ
iajs-826	175	27	is	be	AUX
iajs-826	175	28	characterized	characterize	VERB
iajs-826	175	29	by	by	ADP
iajs-826	175	30	:	:	PUNCT
iajs-826	175	31	1	1	X
iajs-826	175	32	.	.	X
iajs-826	176	1	it	it	PRON
iajs-826	176	2	is	be	AUX
iajs-826	176	3	a	a	DET
iajs-826	176	4	pattern	pattern	NOUN
iajs-826	176	5	of	of	ADP
iajs-826	176	6	connections	connection	NOUN
iajs-826	176	7	between	between	ADP
iajs-826	176	8	the	the	DET
iajs-826	176	9	neurons	neuron	NOUN
iajs-826	176	10	and	and	CCONJ
iajs-826	176	11	the	the	DET
iajs-826	176	12	layers	layer	NOUN
iajs-826	176	13	(	(	PUNCT
iajs-826	176	14	called	call	VERB
iajs-826	176	15	topology	topology	NOUN
iajs-826	176	16	of	of	ADP
iajs-826	176	17	network	network	NOUN
iajs-826	176	18	)	)	PUNCT
iajs-826	176	19	.	.	PUNCT
iajs-826	177	1	2	2	X
iajs-826	177	2	.	.	X
iajs-826	177	3	it	it	PRON
iajs-826	177	4	is	be	AUX
iajs-826	177	5	a	a	DET
iajs-826	177	6	method	method	NOUN
iajs-826	177	7	of	of	ADP
iajs-826	177	8	determining	determine	VERB
iajs-826	177	9	the	the	DET
iajs-826	177	10	weights	weight	NOUN
iajs-826	177	11	on	on	ADP
iajs-826	177	12	the	the	DET
iajs-826	177	13	connections	connection	NOUN
iajs-826	177	14	(	(	PUNCT
iajs-826	177	15	called	call	VERB
iajs-826	177	16	it	it	PRON
iajs-826	177	17	's	be	AUX
iajs-826	177	18	training	training	NOUN
iajs-826	177	19	,	,	PUNCT
iajs-826	177	20	or	or	CCONJ
iajs-826	177	21	learning	learn	VERB
iajs-826	177	22	algorithm	algorithm	NOUN
iajs-826	177	23	)	)	PUNCT
iajs-826	177	24	.	.	PUNCT
iajs-826	178	1	3	3	X
iajs-826	178	2	.	.	X
iajs-826	179	1	it	it	PRON
iajs-826	179	2	is	be	AUX
iajs-826	179	3	activation	activation	NOUN
iajs-826	179	4	function	function	NOUN
iajs-826	179	5	.	.	PUNCT
iajs-826	180	1			PROPN
iajs-826	180	2	neural	neural	ADJ
iajs-826	180	3	network	network	NOUN
iajs-826	180	4	consists	consist	VERB
iajs-826	180	5	of	of	ADP
iajs-826	180	6	a	a	DET
iajs-826	180	7	number	number	NOUN
iajs-826	180	8	of	of	ADP
iajs-826	180	9	simple	simple	ADJ
iajs-826	180	10	processing	processing	NOUN
iajs-826	180	11	elements	element	NOUN
iajs-826	180	12	called	call	VERB
iajs-826	180	13	neurons	neuron	NOUN
iajs-826	180	14	,	,	PUNCT
iajs-826	180	15	these	these	DET
iajs-826	180	16	neurons	neuron	NOUN
iajs-826	180	17	consist	consist	VERB
iajs-826	180	18	in	in	ADP
iajs-826	180	19	many	many	ADJ
iajs-826	180	20	layer	layer	NOUN
iajs-826	180	21	.	.	PUNCT
iajs-826	181	1	the	the	DET
iajs-826	181	2	numbers	number	NOUN
iajs-826	181	3	of	of	ADP
iajs-826	181	4	neurons	neuron	NOUN
iajs-826	181	5	and	and	CCONJ
iajs-826	181	6	layers	layer	NOUN
iajs-826	181	7	in	in	ADP
iajs-826	181	8	the	the	DET
iajs-826	181	9	nn	nn	NOUN
iajs-826	181	10	's	's	PART
iajs-826	181	11	differ	differ	VERB
iajs-826	181	12	from	from	ADP
iajs-826	181	13	not	not	PART
iajs-826	181	14	work	work	NOUN
iajs-826	181	15	to	to	ADP
iajs-826	181	16	network	network	NOUN
iajs-826	181	17	and	and	CCONJ
iajs-826	181	18	this	this	PRON
iajs-826	181	19	is	be	AUX
iajs-826	181	20	called	call	VERB
iajs-826	181	21	the	the	DET
iajs-826	181	22	topology	topology	NOUN
iajs-826	181	23	of	of	ADP
iajs-826	181	24	the	the	DET
iajs-826	181	25	network	network	NOUN
iajs-826	181	26	.	.	PUNCT
iajs-826	182	1	the	the	DET
iajs-826	182	2	nn	nn	NOUN
iajs-826	182	3	's	's	PART
iajs-826	182	4	with	with	ADP
iajs-826	182	5	multilayer	multilayer	NOUN
iajs-826	182	6	is	be	AUX
iajs-826	182	7	not	not	PART
iajs-826	182	8	well	well	ADV
iajs-826	182	9	understood	understand	VERB
iajs-826	182	10	[	[	X
iajs-826	182	11	4	4	NUM
iajs-826	182	12	]	]	PUNCT
iajs-826	182	13	.	.	PUNCT
iajs-826	183	1	some	some	DET
iajs-826	183	2	authors	author	NOUN
iajs-826	183	3	[	[	X
iajs-826	183	4	5	5	NUM
iajs-826	183	5	]	]	PUNCT
iajs-826	183	6	see	see	VERB
iajs-826	183	7	that	that	SCONJ
iajs-826	183	8	little	little	ADJ
iajs-826	183	9	theoretical	theoretical	ADJ
iajs-826	183	10	gain	gain	NOUN
iajs-826	183	11	in	in	ADP
iajs-826	183	12	using	use	VERB
iajs-826	183	13	more	more	ADJ
iajs-826	183	14	than	than	ADP
iajs-826	183	15	one	one	NUM
iajs-826	183	16	hidden	hide	VERB
iajs-826	183	17	layer	layer	NOUN
iajs-826	183	18	since	since	SCONJ
iajs-826	183	19	a	a	DET
iajs-826	183	20	single	single	ADJ
iajs-826	183	21	hidden	hide	VERB
iajs-826	183	22	layer	layer	NOUN
iajs-826	183	23	model	model	NOUN
iajs-826	183	24	suffices	suffice	NOUN
iajs-826	183	25	for	for	ADP
iajs-826	183	26	density	density	NOUN
iajs-826	183	27	.	.	PUNCT
iajs-826	184	1	in	in	ADP
iajs-826	184	2	this	this	DET
iajs-826	184	3	paper	paper	NOUN
iajs-826	184	4	,	,	PUNCT
iajs-826	184	5	we	we	PRON
iajs-826	184	6	introduce	introduce	VERB
iajs-826	184	7	the	the	DET
iajs-826	184	8	definition	definition	NOUN
iajs-826	184	9	and	and	CCONJ
iajs-826	184	10	properties	property	NOUN
iajs-826	184	11	of	of	ADP
iajs-826	184	12	ntopological	ntopological	ADJ
iajs-826	184	13	space	space	NOUN
iajs-826	184	14	which	which	PRON
iajs-826	184	15	can	can	AUX
iajs-826	184	16	be	be	AUX
iajs-826	184	17	applied	apply	VERB
iajs-826	184	18	to	to	ADP
iajs-826	184	19	nn	nn	NOUN
iajs-826	184	20	's	's	PART
iajs-826	184	21	with	with	ADP
iajs-826	184	22	more	more	ADJ
iajs-826	184	23	than	than	ADP
iajs-826	184	24	one	one	NUM
iajs-826	184	25	hidden	hide	VERB
iajs-826	184	26	layer	layer	NOUN
iajs-826	184	27	.	.	PUNCT
iajs-826	185	1	one	one	NUM
iajs-826	185	2	important	important	ADJ
iajs-826	185	3	advantage	advantage	NOUN
iajs-826	185	4	of	of	ADP
iajs-826	185	5	the	the	DET
iajs-826	185	6	multiple	multiple	ADJ
iajs-826	185	7	layer	layer	NOUN
iajs-826	185	8	model	model	NOUN
iajs-826	185	9	(	(	PUNCT
iajs-826	185	10	ntopological	ntopological	ADJ
iajs-826	185	11	space	space	NOUN
iajs-826	185	12	(	(	PUNCT
iajs-826	185	13	see	see	VERB
iajs-826	185	14	figure	figure	NOUN
iajs-826	185	15	(	(	PUNCT
iajs-826	185	16	2	2	NUM
iajs-826	185	17	)	)	PUNCT
iajs-826	185	18	)	)	PUNCT
iajs-826	185	19	has	have	VERB
iajs-826	185	20	to	to	PART
iajs-826	185	21	do	do	VERB
iajs-826	185	22	with	with	ADP
iajs-826	185	23	the	the	DET
iajs-826	185	24	existence	existence	NOUN
iajs-826	185	25	of	of	ADP
iajs-826	185	26	locally	locally	ADV
iajs-826	185	27	supported	support	VERB
iajs-826	185	28	functions	function	NOUN
iajs-826	185	29	in	in	ADP
iajs-826	185	30	the	the	DET
iajs-826	185	31	two	two	NUM
iajs-826	185	32	hidden	hide	VERB
iajs-826	185	33	layer	layer	NOUN
iajs-826	185	34	model	model	NOUN
iajs-826	185	35	(	(	PUNCT
iajs-826	185	36	4topological	4topological	NUM
iajs-826	185	37	space	space	NOUN
iajs-826	185	38	)	)	PUNCT
iajs-826	185	39	since	since	SCONJ
iajs-826	185	40	for	for	ADP
iajs-826	185	41	any	any	DET
iajs-826	185	42	activation	activation	NOUN
iajs-826	185	43	function	function	NOUN
iajs-826	185	44	for	for	ADP
iajs-826	185	45	every	every	PRON
iajs-826	185	46	and	and	CCONJ
iajs-826	185	47	thus	thus	ADV
iajs-826	185	48	g(x	g(x	NOUN
iajs-826	185	49	)	)	PUNCT
iajs-826	185	50	defined	define	VERB
iajs-826	185	51	above	above	ADV
iajs-826	185	52	has	have	VERB
iajs-826	185	53	no	no	DET
iajs-826	185	54	compact	compact	ADJ
iajs-826	185	55	support.(see	support.(see	NOUN
iajs-826	186	1	[	[	X
iajs-826	186	2	6	6	NUM
iajs-826	186	3	]	]	PUNCT
iajs-826	186	4	,	,	PUNCT
iajs-826	186	5	[	[	X
iajs-826	186	6	7	7	X
iajs-826	186	7	]	]	PUNCT
iajs-826	186	8	for	for	ADP
iajs-826	186	9	amore	amore	NOUN
iajs-826	186	10	detailed	detailed	ADJ
iajs-826	186	11	discussion	discussion	NOUN
iajs-826	186	12	)	)	PUNCT
iajs-826	186	13	.	.	PUNCT
iajs-826	187	1	nother	nother	ADP
iajs-826	187	2	advantage	advantage	NOUN
iajs-826	187	3	of	of	ADP
iajs-826	187	4	the	the	DET
iajs-826	187	5	multilayer	multilayer	ADJ
iajs-826	187	6	model	model	NOUN
iajs-826	187	7	(	(	PUNCT
iajs-826	187	8	ntopological	ntopological	ADJ
iajs-826	187	9	space	space	NOUN
iajs-826	187	10	)	)	PUNCT
iajs-826	187	11	,	,	PUNCT
iajs-826	187	12	there	there	PRON
iajs-826	187	13	is	be	VERB
iajs-826	187	14	a	a	DET
iajs-826	187	15	lower	low	ADJ
iajs-826	187	16	bound	bind	VERB
iajs-826	187	17	on	on	ADP
iajs-826	187	18	the	the	DET
iajs-826	187	19	degree	degree	NOUN
iajs-826	187	20	to	to	PART
iajs-826	187	21	which	which	PRON
iajs-826	187	22	the	the	DET
iajs-826	187	23	single	single	ADJ
iajs-826	187	24	hidden	hide	VERB
iajs-826	187	25	layer	layer	NOUN
iajs-826	187	26	model	model	NOUN
iajs-826	187	27	(	(	PUNCT
iajs-826	187	28	3topological	3topological	ADJ
iajs-826	187	29	space	space	NOUN
iajs-826	187	30	)	)	PUNCT
iajs-826	187	31	with	with	ADP
iajs-826	187	32	r	r	NOUN
iajs-826	187	33	neuron	neuron	NOUN
iajs-826	187	34	units	unit	NOUN
iajs-826	187	35	in	in	ADP
iajs-826	187	36	the	the	DET
iajs-826	187	37	hidden	hide	VERB
iajs-826	187	38	layer	layer	NOUN
iajs-826	187	39	can	can	AUX
iajs-826	187	40	approximate	approximate	VERB
iajs-826	187	41	any	any	DET
iajs-826	187	42	function	function	NOUN
iajs-826	187	43	.	.	PUNCT
iajs-826	188	1	it	it	PRON
iajs-826	188	2	is	be	AUX
iajs-826	188	3	given	give	VERB
iajs-826	188	4	by	by	ADP
iajs-826	188	5	the	the	DET
iajs-826	188	6	extent	extent	NOUN
iajs-826	188	7	to	to	PART
iajs-826	188	8	which	which	PRON
iajs-826	188	9	a	a	DET
iajs-826	188	10	linear	linear	ADJ
iajs-826	188	11	combination	combination	NOUN
iajs-826	188	12	of	of	ADP
iajs-826	188	13	r	r	NOUN
iajs-826	188	14	activation	activation	NOUN
iajs-826	188	15	function	function	NOUN
iajs-826	188	16	can	can	AUX
iajs-826	188	17	approximate	approximate	VERB
iajs-826	188	18	this	this	DET
iajs-826	188	19	same	same	ADJ
iajs-826	188	20	function	function	NOUN
iajs-826	188	21	,	,	PUNCT
iajs-826	188	22	and	and	CCONJ
iajs-826	188	23	,	,	PUNCT
iajs-826	188	24	more	more	ADV
iajs-826	188	25	importantly	importantly	ADV
iajs-826	188	26	,	,	PUNCT
iajs-826	188	27	activation	activation	NOUN
iajs-826	188	28	function	function	NOUN
iajs-826	188	29	approximate	approximate	VERB
iajs-826	188	30	itself	itself	PRON
iajs-826	188	31	is	be	AUX
iajs-826	188	32	bounded	bound	VERB
iajs-826	188	33	below	below	ADV
iajs-826	188	34	(	(	PUNCT
iajs-826	188	35	a	a	DET
iajs-826	188	36	way	way	NOUN
iajs-826	188	37	from	from	ADP
iajs-826	188	38	zero	zero	NUM
iajs-826	188	39	)	)	PUNCT
iajs-826	188	40	with	with	SCONJ
iajs-826	188	41	some	some	DET
iajs-826	188	42	nontrifling	nontrifle	VERB
iajs-826	188	43	dependence	dependence	NOUN
iajs-826	188	44	on	on	ADP
iajs-826	188	45	r	r	NOUN
iajs-826	188	46	and	and	CCONJ
iajs-826	188	47	on	on	ADP
iajs-826	188	48	the	the	DET
iajs-826	188	49	set	set	NOUN
iajs-826	188	50	to	to	PART
iajs-826	188	51	be	be	AUX
iajs-826	188	52	approximated	approximate	VERB
iajs-826	188	53	.	.	PUNCT
iajs-826	189	1	in	in	ADP
iajs-826	189	2	the	the	DET
iajs-826	189	3	single	single	ADJ
iajs-826	189	4	hidden	hide	VERB
iajs-826	189	5	layer	layer	NOUN
iajs-826	189	6	model	model	NOUN
iajs-826	189	7	(	(	PUNCT
iajs-826	189	8	3topological	3topological	ADJ
iajs-826	189	9	space	space	NOUN
iajs-826	189	10	)	)	PUNCT
iajs-826	189	11	there	there	PRON
iajs-826	189	12	is	be	VERB
iajs-826	189	13	an	an	DET
iajs-826	189	14	intrinsic	intrinsic	ADJ
iajs-826	189	15	lower	low	ADJ
iajs-826	189	16	bound	bind	VERB
iajs-826	189	17	on	on	ADP
iajs-826	189	18	the	the	DET
iajs-826	189	19	degree	degree	NOUN
iajs-826	189	20	of	of	ADP
iajs-826	189	21	ibn	ibn	PROPN
iajs-826	189	22	alhaitham	alhaitham	NOUN
iajs-826	189	23	j.	j.	PROPN
iajs-826	190	1	fo	fo	ADP
iajs-826	190	2	r	r	NOUN
iajs-826	190	3	pure	pure	ADJ
iajs-826	190	4	&	&	CCONJ
iajs-826	190	5	appl	appl	PROPN
iajs-826	190	6	.	.	PUNCT
iajs-826	191	1	sc	sc	PROPN
iajs-826	191	2	i.	i.	PROPN
iajs-826	191	3	vo	vo	PROPN
iajs-826	191	4	l.24	l.24	PROPN
iajs-826	191	5	(	(	PUNCT
iajs-826	191	6	1	1	NUM
iajs-826	191	7	)	)	PUNCT
iajs-826	191	8	2011	2011	NUM
iajs-826	191	9	approximation	approximation	NOUN
iajs-826	191	10	depending	depend	VERB
iajs-826	191	11	on	on	ADP
iajs-826	191	12	the	the	DET
iajs-826	191	13	number	number	NOUN
iajs-826	191	14	of	of	ADP
iajs-826	191	15	neuron	neuron	NOUN
iajs-826	191	16	units	unit	NOUN
iajs-826	191	17	used	use	VERB
iajs-826	191	18	.	.	PUNCT
iajs-826	192	1	this	this	PRON
iajs-826	192	2	is	be	AUX
iajs-826	192	3	not	not	PART
iajs-826	192	4	the	the	DET
iajs-826	192	5	casa	casa	PROPN
iajs-826	192	6	in	in	ADP
iajs-826	192	7	the	the	DET
iajs-826	192	8	two	two	NUM
iajs-826	192	9	hidden	hide	VERB
iajs-826	192	10	layer	layer	NOUN
iajs-826	192	11	model	model	NOUN
iajs-826	192	12	,	,	PUNCT
iajs-826	192	13	(	(	PUNCT
iajs-826	192	14	4topological	4topological	NUM
iajs-826	192	15	space	space	NOUN
iajs-826	192	16	)	)	PUNCT
iajs-826	192	17	.	.	PUNCT
iajs-826	193	1	finally	finally	ADV
iajs-826	193	2	,	,	PUNCT
iajs-826	193	3	we	we	PRON
iajs-826	193	4	can	can	AUX
iajs-826	193	5	show	show	VERB
iajs-826	193	6	,	,	PUNCT
iajs-826	193	7	using	use	VERB
iajs-826	193	8	the	the	DET
iajs-826	193	9	kolmogorov	kolmogorov	ADJ
iajs-826	193	10	super	super	ADJ
iajs-826	193	11	position	position	NOUN
iajs-826	193	12	theorem	theorem	ADJ
iajs-826	193	13	[	[	X
iajs-826	193	14	7	7	X
iajs-826	193	15	]	]	PUNCT
iajs-826	193	16	that	that	SCONJ
iajs-826	193	17	a	a	DET
iajs-826	193	18	finite	finite	ADJ
iajs-826	193	19	number	number	NOUN
iajs-826	193	20	of	of	ADP
iajs-826	193	21	units	unit	NOUN
iajs-826	193	22	in	in	ADP
iajs-826	193	23	both	both	DET
iajs-826	193	24	hidden	hidden	ADJ
iajs-826	193	25	layers	layer	NOUN
iajs-826	193	26	(	(	PUNCT
iajs-826	193	27	4topological	4topological	NUM
iajs-826	193	28	space	space	NOUN
iajs-826	193	29	)	)	PUNCT
iajs-826	193	30	is	be	AUX
iajs-826	193	31	sufficient	sufficient	ADJ
iajs-826	193	32	to	to	PART
iajs-826	193	33	approximate	approximate	VERB
iajs-826	193	34	arbitrarily	arbitrarily	ADV
iajs-826	193	35	well	well	ADV
iajs-826	193	36	any	any	DET
iajs-826	193	37	continuous	continuous	ADJ
iajs-826	193	38	function	function	NOUN
iajs-826	193	39	.	.	PUNCT
iajs-826	194	1	theorem	theorem	VERB
iajs-826	194	2	3.4	3.4	NUM
iajs-826	194	3	there	there	ADV
iajs-826	194	4	exists	exist	VERB
iajs-826	194	5	an	an	DET
iajs-826	194	6	activation	activation	NOUN
iajs-826	194	7	function	function	NOUN
iajs-826	194	8			PROPN
iajs-826	194	9	which	which	PRON
iajs-826	194	10	is	be	AUX
iajs-826	194	11	c	c	PROPN
iajs-826	194	12	,	,	PUNCT
iajs-826	194	13	strictly	strictly	ADV
iajs-826	194	14	increasing	increase	VERB
iajs-826	194	15	,	,	PUNCT
iajs-826	194	16	and	and	CCONJ
iajs-826	194	17	sigmoidal	sigmoidal	NOUN
iajs-826	194	18	,	,	PUNCT
iajs-826	194	19	and	and	CCONJ
iajs-826	194	20	has	have	VERB
iajs-826	194	21	the	the	DET
iajs-826	194	22	following	follow	VERB
iajs-826	194	23	property	property	NOUN
iajs-826	194	24	.	.	PUNCT
iajs-826	195	1	for	for	ADP
iajs-826	195	2	any	any	DET
iajs-826	195	3	f	f	PROPN
iajs-826	195	4			PROPN
iajs-826	195	5	c[0,1]n	c[0,1]n	PROPN
iajs-826	195	6	and	and	CCONJ
iajs-826	195	7			PROPN
iajs-826	195	8	>	>	X
iajs-826	195	9	0	0	NUM
iajs-826	195	10	,	,	PUNCT
iajs-826	195	11	there	there	PRON
iajs-826	195	12	exist	exist	VERB
iajs-826	195	13	constants	constant	NOUN
iajs-826	195	14	di	di	PROPN
iajs-826	195	15	,	,	PUNCT
iajs-826	195	16	cij	cij	PROPN
iajs-826	195	17	,	,	PUNCT
iajs-826	195	18	ij	ij	PROPN
iajs-826	195	19	,	,	PUNCT
iajs-826	195	20	i	i	ADJ
iajs-826	195	21	and	and	CCONJ
iajs-826	195	22	vectors	vector	NOUN
iajs-826	195	23	wij	wij	PROPN
iajs-826	195	24			PROPN
iajs-826	195	25	rn	rn	PROPN
iajs-826	195	26	,	,	PUNCT
iajs-826	195	27	for	for	ADP
iajs-826	195	28	which	which	PRON
iajs-826	195	29	:	:	PUNCT
iajs-826	196	1			X
iajs-826	196	2			PROPN
iajs-826	196	3			PRON
iajs-826	196	4			X
iajs-826	196	5			X
iajs-826	196	6			PROPN
iajs-826	196	7			PROPN
iajs-826	196	8			PROPN
iajs-826	196	9			PROPN
iajs-826	196	10			NOUN
iajs-826	196	11			PROPN
iajs-826	196	12			PROPN
iajs-826	196	13			PROPN
iajs-826	196	14			PROPN
iajs-826	196	15	12	12	NOUN
iajs-826	196	16	1	1	NUM
iajs-826	196	17	12	12	NUM
iajs-826	196	18	1	1	NUM
iajs-826	196	19	)	)	PUNCT
iajs-826	196	20	(	(	PUNCT
iajs-826	196	21	)	)	PUNCT
iajs-826	196	22	(	(	PUNCT
iajs-826	196	23	n	n	X
iajs-826	196	24	i	i	PRON
iajs-826	196	25	n	n	CCONJ
iajs-826	196	26	j	j	PROPN
iajs-826	196	27	iijxijwijcidxf	iijxijwijcidxf	PROPN
iajs-826	196	28			PROPN
iajs-826	196	29	<	<	X
iajs-826	196	30			PROPN
iajs-826	196	31	,	,	PUNCT
iajs-826	196	32	for	for	ADP
iajs-826	196	33	all	all	DET
iajs-826	196	34	x	x	PROPN
iajs-826	196	35	[0	[0	NOUN
iajs-826	196	36	,	,	PUNCT
iajs-826	196	37	1	1	NUM
iajs-826	196	38	]	]	PUNCT
iajs-826	196	39	n	n	X
iajs-826	196	40	.	.	PUNCT
iajs-826	197	1	proof	proof	NOUN
iajs-826	197	2	let	let	VERB
iajs-826	197	3	f	f	PRON
iajs-826	197	4	be	be	AUX
iajs-826	197	5	any	any	DET
iajs-826	197	6	continuous	continuous	ADJ
iajs-826	197	7	function	function	NOUN
iajs-826	197	8	on	on	ADP
iajs-826	197	9	[	[	X
iajs-826	197	10	0,1	0,1	NUM
iajs-826	197	11	]	]	PUNCT
iajs-826	197	12	n	n	CCONJ
iajs-826	197	13	,	,	PUNCT
iajs-826	197	14			PROPN
iajs-826	197	15	>	>	X
iajs-826	197	16	0	0	PUNCT
iajs-826	197	17	,	,	PUNCT
iajs-826	197	18	then	then	ADV
iajs-826	197	19	by	by	ADP
iajs-826	197	20	kolmogorov	kolmogorov	ADJ
iajs-826	197	21	superposition	superposition	NOUN
iajs-826	197	22	theorem	theorem	NOUN
iajs-826	197	23	,	,	PUNCT
iajs-826	197	24	there	there	PRON
iajs-826	197	25	exist	exist	VERB
iajs-826	197	26	constants	constant	NOUN
iajs-826	197	27	ci	ci	PROPN
iajs-826	197	28	,	,	PUNCT
iajs-826	197	29	ij	ij	PROPN
iajs-826	197	30	and	and	CCONJ
iajs-826	197	31	vectors	vector	NOUN
iajs-826	197	32	wij	wij	PROPN
iajs-826	197	33			PROPN
iajs-826	197	34	rn	rn	PROPN
iajs-826	197	35	,	,	PUNCT
iajs-826	198	1	such	such	ADJ
iajs-826	198	2	that	that	SCONJ
iajs-826	198	3			PROPN
iajs-826	198	4			X
iajs-826	198	5			PROPN
iajs-826	198	6			PROPN
iajs-826	198	7	1n2	1n2	NUM
iajs-826	198	8	1i	1i	NOUN
iajs-826	198	9	)	)	PUNCT
iajs-826	198	10	ijsxijv(φid)x(f	ijsxijv(φid)x(f	PROPN
iajs-826	198	11	<	<	X
iajs-826	198	12	/(2n+1	/(2n+1	NOUN
iajs-826	198	13	)	)	PUNCT
iajs-826	198	14	…	…	PUNCT
iajs-826	198	15	…	…	PUNCT
iajs-826	198	16	..	..	PUNCT
iajs-826	198	17	(	(	PUNCT
iajs-826	198	18	1	1	X
iajs-826	198	19	)	)	PUNCT
iajs-826	198	20	since	since	SCONJ
iajs-826	198	21	ф	ф	PROPN
iajs-826	198	22	is	be	AUX
iajs-826	198	23	continuous	continuous	ADJ
iajs-826	198	24	function	function	NOUN
iajs-826	198	25	,	,	PUNCT
iajs-826	198	26	and	and	CCONJ
iajs-826	198	27	by	by	SCONJ
iajs-826	198	28	restrict	restrict	VERB
iajs-826	198	29	ф	ф	PRON
iajs-826	198	30	in	in	ADP
iajs-826	198	31	[	[	X
iajs-826	198	32	0,1	0,1	NUM
iajs-826	198	33	]	]	PUNCT
iajs-826	198	34	n	n	PRON
iajs-826	198	35	can	can	AUX
iajs-826	198	36	represent	represent	VERB
iajs-826	198	37	ф	ф	ADP
iajs-826	198	38	such	such	ADJ
iajs-826	198	39	that	that	SCONJ
iajs-826	198	40			PROPN
iajs-826	198	41			PUNCT
iajs-826	198	42			NUM
iajs-826	198	43			ADJ
iajs-826	198	44	1n2	1n2	NUM
iajs-826	198	45	1j	1j	NUM
iajs-826	198	46	)	)	PUNCT
iajs-826	198	47	ijsxijr(ijc)x	ijsxijr(ijc)x	NOUN
iajs-826	198	48	(	(	PUNCT
iajs-826	198	49	…	…	PUNCT
iajs-826	198	50	…	…	PUNCT
iajs-826	198	51	…	…	PUNCT
iajs-826	198	52	…	…	PUNCT
iajs-826	198	53	(	(	PUNCT
iajs-826	198	54	2	2	NUM
iajs-826	198	55	)	)	PUNCT
iajs-826	198	56	by	by	ADP
iajs-826	198	57	substituting	substitute	VERB
iajs-826	198	58	(	(	PUNCT
iajs-826	198	59	2	2	NUM
iajs-826	198	60	)	)	PUNCT
iajs-826	198	61	in	in	ADP
iajs-826	198	62	(	(	PUNCT
iajs-826	198	63	1	1	NUM
iajs-826	198	64	)	)	PUNCT
iajs-826	198	65	,	,	PUNCT
iajs-826	198	66	we	we	PRON
iajs-826	198	67	obtain	obtain	VERB
iajs-826	198	68	:	:	PUNCT
iajs-826	198	69			X
iajs-826	198	70			PROPN
iajs-826	198	71			PRON
iajs-826	198	72			X
iajs-826	198	73			X
iajs-826	199	1			PROPN
iajs-826	199	2			PROPN
iajs-826	199	3			PROPN
iajs-826	200	1			PROPN
iajs-826	200	2			NOUN
iajs-826	201	1			PROPN
iajs-826	201	2			PROPN
iajs-826	201	3			PROPN
iajs-826	201	4			PROPN
iajs-826	201	5	1n2	1n2	PROPN
iajs-826	201	6	1i	1i	NOUN
iajs-826	201	7	1n2	1n2	NUM
iajs-826	201	8	1j	1j	NUM
iajs-826	201	9	)	)	PUNCT
iajs-826	202	1	ijl)ijsxijv(ijr	ijl)ijsxijv(ijr	NOUN
iajs-826	202	2	(	(	PUNCT
iajs-826	202	3	ij	ij	INTJ
iajs-826	202	4	cid)x(f	cid)x(f	PROPN
iajs-826	202	5	<	<	X
iajs-826	202	6			PROPN
iajs-826	202	7	then	then	ADV
iajs-826	202	8	,	,	PUNCT
iajs-826	202	9			PROPN
iajs-826	202	10			PROPN
iajs-826	202	11			PRON
iajs-826	202	12			X
iajs-826	202	13			PROPN
iajs-826	202	14			PROPN
iajs-826	202	15			NUM
iajs-826	202	16			PROPN
iajs-826	203	1			PROPN
iajs-826	203	2			NOUN
iajs-826	204	1			PROPN
iajs-826	204	2			PROPN
iajs-826	204	3			PROPN
iajs-826	204	4			PROPN
iajs-826	204	5	1n2	1n2	PROPN
iajs-826	204	6	1i	1i	NOUN
iajs-826	204	7	1n2	1n2	NUM
iajs-826	204	8	1j	1j	NUM
iajs-826	204	9	i)ijxijw	i)ijxijw	PROPN
iajs-826	204	10	(	(	PUNCT
iajs-826	204	11	ij	ij	INTJ
iajs-826	204	12	cid)x(f	cid)x(f	PROPN
iajs-826	204	13	<	<	X
iajs-826	204	14			PROPN
iajs-826	204	15	□	□	PUNCT
iajs-826	204	16	now	now	ADV
iajs-826	204	17	,	,	PUNCT
iajs-826	204	18	we	we	PRON
iajs-826	204	19	introduce	introduce	VERB
iajs-826	204	20	the	the	DET
iajs-826	204	21	following	follow	VERB
iajs-826	204	22	definition	definition	NOUN
iajs-826	204	23	:	:	PUNCT
iajs-826	204	24	definition	definition	NOUN
iajs-826	204	25	3.5	3.5	NUM
iajs-826	204	26	a	a	DET
iajs-826	204	27	set	set	NOUN
iajs-826	204	28	of	of	ADP
iajs-826	204	29	functions	function	NOUN
iajs-826	204	30	is	be	AUX
iajs-826	204	31	said	say	VERB
iajs-826	204	32	to	to	PART
iajs-826	204	33	be	be	AUX
iajs-826	204	34	fundamental	fundamental	ADJ
iajs-826	204	35	in	in	ADP
iajs-826	204	36	a	a	DET
iajs-826	204	37	given	give	VERB
iajs-826	204	38	space	space	NOUN
iajs-826	204	39	if	if	SCONJ
iajs-826	204	40	a	a	DET
iajs-826	204	41	linear	linear	ADJ
iajs-826	204	42	combinations	combination	NOUN
iajs-826	204	43	of	of	ADP
iajs-826	204	44	them	they	PRON
iajs-826	204	45	are	be	AUX
iajs-826	204	46	dense	dense	ADJ
iajs-826	204	47	in	in	ADP
iajs-826	204	48	that	that	DET
iajs-826	204	49	space	space	NOUN
iajs-826	204	50	.	.	PUNCT
iajs-826	205	1	theorem	theorem	VERB
iajs-826	205	2	3.6	3.6	NUM
iajs-826	205	3	let	let	VERB
iajs-826	205	4	k	k	PROPN
iajs-826	205	5	be	be	AUX
iajs-826	205	6	a	a	DET
iajs-826	205	7	compact	compact	ADJ
iajs-826	205	8	set	set	NOUN
iajs-826	205	9	in	in	ADP
iajs-826	205	10	rn	rn	PROPN
iajs-826	205	11	.	.	PUNCT
iajs-826	206	1	then	then	ADV
iajs-826	206	2	the	the	DET
iajs-826	206	3	set	set	ADJ
iajs-826	206	4	e	e	PROPN
iajs-826	206	5	of	of	ADP
iajs-826	206	6	functions	function	NOUN
iajs-826	206	7	of	of	ADP
iajs-826	206	8	the	the	DET
iajs-826	206	9	form	form	NOUN
iajs-826	206	10	(x	(x	NOUN
iajs-826	206	11	)	)	PUNCT
iajs-826	206	12			NUM
iajs-826	206	13	exp(atx	exp(atx	ADV
iajs-826	206	14	)	)	PUNCT
iajs-826	206	15	,	,	PUNCT
iajs-826	206	16	where	where	SCONJ
iajs-826	206	17	a	a	DET
iajs-826	206	18			PROPN
iajs-826	206	19	rn	rn	PROPN
iajs-826	206	20	,	,	PUNCT
iajs-826	206	21	is	be	AUX
iajs-826	206	22	fundamental	fundamental	ADJ
iajs-826	206	23	in	in	ADP
iajs-826	206	24	c(k	c(k	NOUN
iajs-826	206	25	)	)	PUNCT
iajs-826	206	26	.	.	PUNCT
iajs-826	207	1	proof	proof	NOUN
iajs-826	207	2	by	by	ADP
iajs-826	207	3	the	the	DET
iajs-826	207	4	stone	stone	NOUN
iajs-826	207	5	-	-	PUNCT
iajs-826	207	6	weierstrass	weierstrass	NOUN
iajs-826	207	7	theorem	theorem	NOUN
iajs-826	207	8	we	we	PRON
iajs-826	207	9	need	need	VERB
iajs-826	207	10	only	only	ADV
iajs-826	207	11	show	show	VERB
iajs-826	207	12	that	that	SCONJ
iajs-826	207	13	the	the	DET
iajs-826	207	14	set	set	NOUN
iajs-826	207	15	forms	form	VERB
iajs-826	207	16	an	an	DET
iajs-826	207	17	algebra	algebra	NOUN
iajs-826	207	18	and	and	CCONJ
iajs-826	207	19	separates	separate	VERB
iajs-826	207	20	points	point	NOUN
iajs-826	207	21	.	.	PUNCT
iajs-826	208	1	suppose	suppose	VERB
iajs-826	208	2	x	x	SYM
iajs-826	208	3			PROPN
iajs-826	208	4	k.	k.	PROPN
iajs-826	209	1	first	first	ADV
iajs-826	209	2	,	,	PUNCT
iajs-826	209	3	we	we	PRON
iajs-826	209	4	have	have	VERB
iajs-826	209	5	:	:	PUNCT
iajs-826	209	6	exp(atx	exp(atx	ADV
iajs-826	209	7	)	)	PUNCT
iajs-826	209	8	exp(btx	exp(btx	ADV
iajs-826	209	9	)	)	PUNCT
iajs-826	210	1			NUM
iajs-826	210	2	exp(atx	exp(atx	X
iajs-826	211	1	+	+	CCONJ
iajs-826	211	2	btx	btx	VERB
iajs-826	211	3	)	)	PUNCT
iajs-826	212	1			NUM
iajs-826	212	2	exp((at	exp((at	NOUN
iajs-826	212	3	+	+	CCONJ
iajs-826	212	4	bt	bt	NOUN
iajs-826	212	5	)	)	PUNCT
iajs-826	212	6	x	x	PUNCT
iajs-826	212	7	)	)	PUNCT
iajs-826	212	8	.	.	PUNCT
iajs-826	213	1	the	the	DET
iajs-826	213	2	set	set	NOUN
iajs-826	213	3	also	also	ADV
iajs-826	213	4	contains	contain	VERB
iajs-826	213	5	the	the	DET
iajs-826	213	6	function	function	NOUN
iajs-826	213	7	“	"	PUNCT
iajs-826	213	8	1	1	NUM
iajs-826	213	9	”	"	PUNCT
iajs-826	213	10	simply	simply	ADV
iajs-826	213	11	choose	choose	VERB
iajs-826	213	12	a	a	DET
iajs-826	213	13			NOUN
iajs-826	213	14	0	0	NUM
iajs-826	213	15	.	.	PUNCT
iajs-826	214	1	this	this	PRON
iajs-826	214	2	establishes	establish	VERB
iajs-826	214	3	that	that	SCONJ
iajs-826	214	4	e	e	NOUN
iajs-826	214	5	is	be	AUX
iajs-826	214	6	an	an	DET
iajs-826	214	7	algebra	algebra	NOUN
iajs-826	214	8	.	.	PUNCT
iajs-826	215	1	it	it	PRON
iajs-826	215	2	remains	remain	VERB
iajs-826	215	3	to	to	PART
iajs-826	215	4	show	show	VERB
iajs-826	215	5	that	that	SCONJ
iajs-826	215	6	e	e	NOUN
iajs-826	215	7	separates	separate	VERB
iajs-826	215	8	the	the	DET
iajs-826	215	9	points	point	NOUN
iajs-826	215	10	of	of	ADP
iajs-826	215	11	k.	k.	NOUN
iajs-826	216	1	so	so	ADV
iajs-826	216	2	let	let	VERB
iajs-826	216	3	x	x	PRON
iajs-826	216	4	,	,	PUNCT
iajs-826	216	5	y	y	PROPN
iajs-826	216	6			PROPN
iajs-826	216	7	k	k	PROPN
iajs-826	216	8	with	with	SCONJ
iajs-826	216	9	x	x	PROPN
iajs-826	216	10			PROPN
iajs-826	216	11	y.	y.	PROPN
iajs-826	216	12	set	set	VERB
iajs-826	216	13	a	a	DET
iajs-826	216	14			NOUN
iajs-826	216	15	(	(	PUNCT
iajs-826	216	16	x	x	PART
iajs-826	216	17			NOUN
iajs-826	216	18	y	y	NOUN
iajs-826	216	19	)	)	PUNCT
iajs-826	216	20	.	.	PUNCT
iajs-826	217	1	then	then	ADV
iajs-826	217	2	at(x	at(x	PUNCT
iajs-826	217	3			PROPN
iajs-826	217	4	y	y	NOUN
iajs-826	217	5	)	)	PUNCT
iajs-826	217	6			NOUN
iajs-826	217	7	0	0	NUM
iajs-826	217	8	,	,	PUNCT
iajs-826	217	9	so	so	ADV
iajs-826	217	10	atx	atx	PROPN
iajs-826	217	11			PROPN
iajs-826	217	12	aty	aty	PROPN
iajs-826	217	13	.	.	PUNCT
iajs-826	217	14	thus	thus	ADV
iajs-826	217	15	exp(atx	exp(atx	ADV
iajs-826	217	16	)	)	PUNCT
iajs-826	217	17			PROPN
iajs-826	217	18	exp(aty	exp(aty	PROPN
iajs-826	217	19	)	)	PUNCT
iajs-826	217	20	.	.	PUNCT
iajs-826	218	1	ibn	ibn	PROPN
iajs-826	218	2	alhaitham	alhaitham	NOUN
iajs-826	219	1	j.	j.	PROPN
iajs-826	220	1	fo	fo	ADP
iajs-826	220	2	r	r	NOUN
iajs-826	220	3	pure	pure	ADJ
iajs-826	220	4	&	&	CCONJ
iajs-826	220	5	appl	appl	PROPN
iajs-826	220	6	.	.	PUNCT
iajs-826	221	1	sc	sc	PROPN
iajs-826	221	2	i.	i.	PROPN
iajs-826	221	3	vo	vo	PROPN
iajs-826	222	1	l.24	l.24	PROPN
iajs-826	222	2	(	(	PUNCT
iajs-826	222	3	1	1	NUM
iajs-826	222	4	)	)	PUNCT
iajs-826	222	5	2011	2011	NUM
iajs-826	222	6	the	the	DET
iajs-826	222	7	proof	proof	NOUN
iajs-826	222	8	is	be	AUX
iajs-826	222	9	complete	complete	ADJ
iajs-826	222	10	.	.	PUNCT
iajs-826	223	1	before	before	ADP
iajs-826	223	2	considering	consider	VERB
iajs-826	223	3	more	more	ADV
iajs-826	223	4	constructive	constructive	ADJ
iajs-826	223	5	versions	version	NOUN
iajs-826	223	6	of	of	ADP
iajs-826	223	7	this	this	DET
iajs-826	223	8	result	result	NOUN
iajs-826	223	9	we	we	PRON
iajs-826	223	10	complete	complete	VERB
iajs-826	223	11	the	the	DET
iajs-826	223	12	density	density	NOUN
iajs-826	223	13	proof	proof	NOUN
iajs-826	223	14	.	.	PUNCT
iajs-826	224	1	theorem	theorem	VERB
iajs-826	224	2	3.7	3.7	NUM
iajs-826	224	3	let	let	VERB
iajs-826	224	4	k	k	PROPN
iajs-826	224	5	be	be	AUX
iajs-826	224	6	a	a	DET
iajs-826	224	7	compact	compact	ADJ
iajs-826	224	8	set	set	NOUN
iajs-826	224	9	in	in	ADP
iajs-826	224	10	r	r	NOUN
iajs-826	224	11	n	n	NOUN
iajs-826	224	12	.	.	PUNCT
iajs-826	225	1	then	then	ADV
iajs-826	225	2	the	the	DET
iajs-826	225	3	set	set	ADJ
iajs-826	225	4	f	f	PROPN
iajs-826	225	5	of	of	ADP
iajs-826	225	6	functions	function	NOUN
iajs-826	225	7	of	of	ADP
iajs-826	225	8	the	the	DET
iajs-826	225	9	form	form	NOUN
iajs-826	225	10	g(x	g(x	NOUN
iajs-826	225	11	)	)	PUNCT
iajs-826	225	12	,	,	PUNCT
iajs-826	225	13	defined	define	VERB
iajs-826	225	14	by	by	ADP
iajs-826	225	15	:	:	PUNCT
iajs-826	225	16	g(x	g(x	NOUN
iajs-826	225	17	)	)	PUNCT
iajs-826	225	18			NOUN
iajs-826	225	19			X
iajs-826	225	20			PUNCT
iajs-826	226	1			PROPN
iajs-826	227	1	k	k	NOUN
iajs-826	227	2	1j	1j	NUM
iajs-826	228	1	j	j	PROPN
iajs-826	228	2	t	t	PROPN
iajs-826	228	3	jj	jj	PROPN
iajs-826	228	4	)	)	PUNCT
iajs-826	228	5	cxw(v	cxw(v	PROPN
iajs-826	228	6	,	,	PUNCT
iajs-826	228	7	with	with	ADP
iajs-826	228	8			PROPN
iajs-826	228	9	as	as	ADP
iajs-826	228	10	a	a	DET
iajs-826	228	11	continuous	continuous	ADJ
iajs-826	228	12	sigmoidal	sigmoidal	NOUN
iajs-826	228	13	function	function	NOUN
iajs-826	228	14	is	be	AUX
iajs-826	228	15	dense	dense	ADJ
iajs-826	228	16	in	in	ADP
iajs-826	228	17	c(k	c(k	NOUN
iajs-826	228	18	)	)	PUNCT
iajs-826	228	19	.	.	PUNCT
iajs-826	229	1	proof	proof	NOUN
iajs-826	229	2	let	let	VERB
iajs-826	229	3	f	f	PROPN
iajs-826	229	4			PROPN
iajs-826	229	5	c(k	c(k	PROPN
iajs-826	229	6	)	)	PUNCT
iajs-826	229	7	.	.	PUNCT
iajs-826	230	1	for	for	ADP
iajs-826	230	2	any	any	DET
iajs-826	230	3			PROPN
iajs-826	230	4	>	>	X
iajs-826	230	5	0	0	NUM
iajs-826	230	6	,	,	PUNCT
iajs-826	230	7	there	there	PRON
iajs-826	230	8	exists	exist	VERB
iajs-826	230	9	(	(	PUNCT
iajs-826	230	10	by	by	ADP
iajs-826	230	11	theorem	theorem	NOUN
iajs-826	230	12	3.6	3.6	NUM
iajs-826	230	13	)	)	PUNCT
iajs-826	230	14	a	a	DET
iajs-826	230	15	finite	finite	ADJ
iajs-826	230	16	number	number	NOUN
iajs-826	230	17	m	m	PROPN
iajs-826	230	18	of	of	ADP
iajs-826	230	19	vectors	vector	NOUN
iajs-826	230	20	ai	ai	VERB
iajs-826	230	21	,	,	PUNCT
iajs-826	230	22	such	such	ADJ
iajs-826	230	23	that	that	SCONJ
iajs-826	230	24	:	:	PUNCT
iajs-826	230	25			NOUN
iajs-826	230	26			PROPN
iajs-826	230	27	2	2	NUM
iajs-826	230	28	xaexpf	xaexpf	PROPN
iajs-826	230	29	m	m	VERB
iajs-826	231	1	1i	1i	NOUN
iajs-826	231	2	t	t	NOUN
iajs-826	232	1	i	i	PRON
iajs-826	232	2			PROPN
iajs-826	232	3			NOUN
iajs-826	232	4			PUNCT
iajs-826	233	1	since	since	SCONJ
iajs-826	233	2	there	there	PRON
iajs-826	233	3	are	be	VERB
iajs-826	233	4	only	only	ADV
iajs-826	233	5	m	m	VERB
iajs-826	233	6	scalars	scalar	NOUN
iajs-826	233	7	xat	xat	PROPN
iajs-826	234	1	i	i	PRON
iajs-826	234	2	,	,	PUNCT
iajs-826	234	3	we	we	PRON
iajs-826	234	4	may	may	AUX
iajs-826	234	5	find	find	VERB
iajs-826	234	6	a	a	DET
iajs-826	234	7	finite	finite	ADJ
iajs-826	234	8	interval	interval	NOUN
iajs-826	234	9	including	include	VERB
iajs-826	234	10	all	all	PRON
iajs-826	234	11	of	of	ADP
iajs-826	234	12	them	they	PRON
iajs-826	234	13	.	.	PUNCT
iajs-826	235	1	thus	thus	ADV
iajs-826	235	2	there	there	PRON
iajs-826	235	3	exists	exist	VERB
iajs-826	235	4	a	a	DET
iajs-826	235	5	number	number	NOUN
iajs-826	235	6			VERB
iajs-826	235	7	such	such	ADJ
iajs-826	235	8	that	that	DET
iajs-826	235	9	exp	exp	NOUN
iajs-826	235	10	(	(	PUNCT
iajs-826	235	11	xat	xat	NOUN
iajs-826	235	12	i	i	NOUN
iajs-826	235	13	)	)	PUNCT
iajs-826	235	14			NUM
iajs-826	235	15	exp(y	exp(y	ADJ
iajs-826	235	16	)	)	PUNCT
iajs-826	235	17	,	,	PUNCT
iajs-826	235	18	where	where	SCONJ
iajs-826	235	19	y	y	PROPN
iajs-826	235	20			PROPN
iajs-826	235	21	(	(	PUNCT
iajs-826	235	22	xat	xat	PROPN
iajs-826	235	23	i	i	PRON
iajs-826	235	24	/	/	PUNCT
iajs-826	235	25	)	)	PUNCT
iajs-826	235	26			NOUN
iajs-826	236	1	[	[	X
iajs-826	236	2	0,1	0,1	NUM
iajs-826	236	3	]	]	PUNCT
iajs-826	236	4	.	.	PUNCT
iajs-826	237	1	then	then	ADV
iajs-826	237	2	theorem	theorem	VERB
iajs-826	237	3	3.6	3.6	NUM
iajs-826	237	4	tells	tell	VERB
iajs-826	237	5	us	we	PRON
iajs-826	237	6	that	that	SCONJ
iajs-826	237	7	the	the	DET
iajs-826	237	8	function	function	NOUN
iajs-826	237	9	exp	exp	NOUN
iajs-826	237	10	(	(	PUNCT
iajs-826	237	11	y	y	PROPN
iajs-826	237	12	)	)	PUNCT
iajs-826	237	13	can	can	AUX
iajs-826	237	14	be	be	AUX
iajs-826	237	15	approximated	approximate	VERB
iajs-826	237	16	by	by	ADP
iajs-826	237	17	linear	linear	PROPN
iajs-826	237	18	combinations	combination	NOUN
iajs-826	237	19	functions	function	NOUN
iajs-826	237	20	of	of	ADP
iajs-826	237	21	the	the	DET
iajs-826	237	22	form	form	NOUN
iajs-826	237	23			X
iajs-826	237	24	(	(	PUNCT
iajs-826	237	25	t	t	PROPN
iajs-826	237	26	jw	jw	PROPN
iajs-826	237	27	x	x	PROPN
iajs-826	238	1	+	+	NUM
iajs-826	238	2	cj	cj	NOUN
iajs-826	238	3	)	)	PUNCT
iajs-826	238	4	with	with	ADP
iajs-826	238	5	a	a	DET
iajs-826	238	6	uniform	uniform	ADJ
iajs-826	238	7	error	error	NOUN
iajs-826	238	8	less	less	ADJ
iajs-826	238	9	than	than	ADP
iajs-826	238	10	/2	/2	NOUN
iajs-826	238	11	m	m	PROPN
iajs-826	238	12	,	,	PUNCT
iajs-826	238	13	from	from	ADP
iajs-826	238	14	which	which	PRON
iajs-826	238	15	the	the	DET
iajs-826	238	16	desired	desire	VERB
iajs-826	238	17	result	result	NOUN
iajs-826	238	18	easily	easily	ADV
iajs-826	238	19	follows	follow	VERB
iajs-826	238	20	.	.	PUNCT
iajs-826	239	1	■	■	PUNCT
iajs-826	239	2	remarks	remark	VERB
iajs-826	239	3	1	1	NUM
iajs-826	239	4	.	.	PUNCT
iajs-826	239	5	theorem	theorem	NOUN
iajs-826	239	6	3.6	3.6	NUM
iajs-826	239	7	tells	tell	VERB
iajs-826	239	8	us	we	PRON
iajs-826	239	9	one	one	NUM
iajs-826	239	10	hidden	hide	VERB
iajs-826	239	11	layer	layer	NOUN
iajs-826	239	12	is	be	AUX
iajs-826	239	13	sufficient	sufficient	ADJ
iajs-826	239	14	to	to	PART
iajs-826	239	15	approximate	approximate	VERB
iajs-826	239	16	any	any	DET
iajs-826	239	17	continuous	continuous	ADJ
iajs-826	239	18	function	function	NOUN
iajs-826	239	19	to	to	ADP
iajs-826	239	20	any	any	DET
iajs-826	239	21	required	required	ADJ
iajs-826	239	22	accuracy	accuracy	NOUN
iajs-826	239	23	.	.	PUNCT
iajs-826	240	1	2	2	X
iajs-826	240	2	.	.	PUNCT
iajs-826	240	3			VERB
iajs-826	240	4	in	in	ADP
iajs-826	240	5	the	the	DET
iajs-826	240	6	proof	proof	NOUN
iajs-826	240	7	of	of	ADP
iajs-826	240	8	theorem	theorem	ADJ
iajs-826	240	9	3.7	3.7	NUM
iajs-826	240	10	can	can	AUX
iajs-826	240	11	be	be	AUX
iajs-826	240	12	chosen	choose	VERB
iajs-826	240	13	to	to	PART
iajs-826	240	14	be	be	AUX
iajs-826	240	15	an	an	DET
iajs-826	240	16	integer	integer	NOUN
iajs-826	240	17	.	.	PUNCT
iajs-826	241	1	3	3	X
iajs-826	241	2	.	.	X
iajs-826	241	3	the	the	DET
iajs-826	241	4	question	question	NOUN
iajs-826	241	5	of	of	ADP
iajs-826	241	6	rate	rate	NOUN
iajs-826	241	7	of	of	ADP
iajs-826	241	8	convergence	convergence	NOUN
iajs-826	241	9	of	of	ADP
iajs-826	241	10	approximations	approximation	NOUN
iajs-826	241	11	is	be	AUX
iajs-826	241	12	obviously	obviously	ADV
iajs-826	241	13	of	of	ADP
iajs-826	241	14	considerable	considerable	ADJ
iajs-826	241	15	importance	importance	NOUN
iajs-826	241	16	.	.	PUNCT
iajs-826	242	1	if	if	SCONJ
iajs-826	242	2	f	f	PROPN
iajs-826	242	3	is	be	AUX
iajs-826	242	4	smooth	smooth	ADJ
iajs-826	242	5	and	and	CCONJ
iajs-826	242	6	we	we	PRON
iajs-826	242	7	use	use	VERB
iajs-826	242	8	smooth	smooth	ADJ
iajs-826	242	9	approximating	approximate	VERB
iajs-826	242	10	functions	function	NOUN
iajs-826	242	11	we	we	PRON
iajs-826	242	12	might	might	AUX
iajs-826	242	13	hope	hope	VERB
iajs-826	242	14	to	to	PART
iajs-826	242	15	get	get	VERB
iajs-826	242	16	better	well	ADJ
iajs-826	242	17	convergence	convergence	NOUN
iajs-826	242	18	than	than	ADP
iajs-826	242	19	the	the	DET
iajs-826	242	20	simple	simple	ADJ
iajs-826	242	21	o(1	o(1	NOUN
iajs-826	242	22	/	/	SYM
iajs-826	242	23	n	n	CCONJ
iajs-826	242	24	)	)	PUNCT
iajs-826	242	25	.	.	PUNCT
iajs-826	243	1	4	4	X
iajs-826	243	2	.	.	X
iajs-826	243	3	conclusions	conclusion	NOUN
iajs-826	243	4	1	1	X
iajs-826	243	5	.	.	PUNCT
iajs-826	244	1	we	we	PRON
iajs-826	244	2	define	define	VERB
iajs-826	244	3	ntopological	ntopological	ADJ
iajs-826	244	4	space	space	NOUN
iajs-826	244	5	and	and	CCONJ
iajs-826	244	6	give	give	VERB
iajs-826	244	7	some	some	DET
iajs-826	244	8	examples	example	NOUN
iajs-826	244	9	and	and	CCONJ
iajs-826	244	10	properties	property	NOUN
iajs-826	244	11	about	about	ADP
iajs-826	244	12	this	this	DET
iajs-826	244	13	notion	notion	NOUN
iajs-826	244	14	.	.	PUNCT
iajs-826	245	1	2	2	X
iajs-826	245	2	.	.	X
iajs-826	245	3	we	we	PRON
iajs-826	245	4	give	give	VERB
iajs-826	245	5	application	application	NOUN
iajs-826	245	6	of	of	ADP
iajs-826	245	7	ntopological	ntopological	ADJ
iajs-826	245	8	space	space	NOUN
iajs-826	245	9	in	in	ADP
iajs-826	245	10	nn	nn	PROPN
iajs-826	245	11	's	's	PART
iajs-826	245	12	,	,	PUNCT
iajs-826	245	13	then	then	ADV
iajs-826	245	14	we	we	PRON
iajs-826	245	15	obtain	obtain	VERB
iajs-826	245	16	:	:	PUNCT
iajs-826	245	17	(	(	PUNCT
iajs-826	245	18	i	i	NOUN
iajs-826	245	19	)	)	PUNCT
iajs-826	245	20	increasing	increase	VERB
iajs-826	245	21	number	number	NOUN
iajs-826	245	22	of	of	ADP
iajs-826	245	23	hidden	hide	VERB
iajs-826	245	24	units	unit	NOUN
iajs-826	245	25	leads	lead	VERB
iajs-826	245	26	to	to	ADP
iajs-826	245	27	decreasing	decrease	VERB
iajs-826	245	28	number	number	NOUN
iajs-826	245	29	of	of	ADP
iajs-826	245	30	epoch	epoch	NOUN
iajs-826	245	31	of	of	ADP
iajs-826	245	32	training	training	NOUN
iajs-826	245	33	.	.	PUNCT
iajs-826	246	1	(	(	PUNCT
iajs-826	246	2	ii	ii	X
iajs-826	246	3	)	)	PUNCT
iajs-826	246	4	large	large	ADJ
iajs-826	246	5	number	number	NOUN
iajs-826	246	6	of	of	ADP
iajs-826	246	7	hidden	hide	VERB
iajs-826	246	8	units	unit	NOUN
iajs-826	246	9	leads	lead	VERB
iajs-826	246	10	to	to	ADP
iajs-826	246	11	a	a	DET
iajs-826	246	12	small	small	ADJ
iajs-826	246	13	error	error	NOUN
iajs-826	246	14	on	on	ADP
iajs-826	246	15	the	the	DET
iajs-826	246	16	training	training	NOUN
iajs-826	246	17	set	set	NOUN
iajs-826	246	18	but	but	CCONJ
iajs-826	246	19	not	not	PART
iajs-826	246	20	necessarily	necessarily	ADV
iajs-826	246	21	leads	lead	VERB
iajs-826	246	22	to	to	ADP
iajs-826	246	23	a	a	DET
iajs-826	246	24	small	small	ADJ
iajs-826	246	25	error	error	NOUN
iajs-826	246	26	on	on	ADP
iajs-826	246	27	the	the	DET
iajs-826	246	28	test	test	NOUN
iajs-826	246	29	set	set	NOUN
iajs-826	246	30	.	.	PUNCT
iajs-826	247	1	(	(	PUNCT
iajs-826	247	2	iii	iii	X
iajs-826	247	3	)	)	PUNCT
iajs-826	247	4	if	if	SCONJ
iajs-826	247	5	we	we	PRON
iajs-826	247	6	fix	fix	VERB
iajs-826	247	7	the	the	DET
iajs-826	247	8	number	number	NOUN
iajs-826	247	9	of	of	ADP
iajs-826	247	10	basis	basis	NOUN
iajs-826	247	11	functions	function	NOUN
iajs-826	247	12	and	and	CCONJ
iajs-826	247	13	increase	increase	VERB
iajs-826	247	14	the	the	DET
iajs-826	247	15	number	number	NOUN
iajs-826	247	16	of	of	ADP
iajs-826	247	17	the	the	DET
iajs-826	247	18	layers	layer	NOUN
iajs-826	247	19	of	of	ADP
iajs-826	247	20	the	the	DET
iajs-826	247	21	nn	nn	NOUN
iajs-826	247	22	's	's	PART
iajs-826	247	23	(	(	PUNCT
iajs-826	247	24	that	that	PRON
iajs-826	247	25	's	be	AUX
iajs-826	247	26	increase	increase	NOUN
iajs-826	247	27	n	n	CCONJ
iajs-826	247	28	in	in	ADP
iajs-826	247	29	the	the	DET
iajs-826	247	30	ntopological	ntopological	ADJ
iajs-826	247	31	space	space	NOUN
iajs-826	247	32	)	)	PUNCT
iajs-826	247	33	,	,	PUNCT
iajs-826	247	34	then	then	ADV
iajs-826	247	35	we	we	PRON
iajs-826	247	36	get	get	VERB
iajs-826	247	37	an	an	DET
iajs-826	247	38	accurate	accurate	ADJ
iajs-826	247	39	numerical	numerical	ADJ
iajs-826	247	40	solution	solution	NOUN
iajs-826	247	41	.	.	PUNCT
iajs-826	248	1	references	reference	NOUN
iajs-826	248	2	1	1	NUM
iajs-826	248	3	.	.	PUNCT
iajs-826	249	1	el	el	PROPN
iajs-826	249	2	–	–	PUNCT
iajs-826	249	3	fattah	fattah	PROPN
iajs-826	249	4	eltik	eltik	PROPN
iajs-826	249	5	,	,	PUNCT
iajs-826	249	6	.	.	PROPN
iajs-826	249	7	;	;	PUNCT
iajs-826	249	8	bd	bd	PROPN
iajs-826	249	9	el-onasef	el-onasef	PROPN
iajs-826	249	10	,	,	PUNCT
iajs-826	249	11	.	.	PROPN
iajs-826	249	12	e.	e.	PROPN
iajs-826	249	13	and	and	CCONJ
iajs-826	249	14	lashin	lashin	PROPN
iajs-826	249	15	,	,	PUNCT
iajs-826	249	16	e.i	e.i	PROPN
iajs-826	249	17	.	.	PROPN
iajs-826	249	18	(	(	PUNCT
iajs-826	249	19	2002	2002	NUM
iajs-826	249	20	)	)	PUNCT
iajs-826	249	21	"	"	PUNCT
iajs-826	249	22	on	on	ADP
iajs-826	249	23	finite	finite	NOUN
iajs-826	249	24	to	to	ADP
iajs-826	249	25	topological	topological	ADJ
iajs-826	249	26	aspaces	aspace	NOUN
iajs-826	249	27	,	,	PUNCT
iajs-826	249	28	ninth	ninth	ADJ
iajs-826	249	29	prague	prague	PROPN
iajs-826	249	30	topological	topological	PROPN
iajs-826	249	31	symposium	symposium	NOUN
iajs-826	249	32	,	,	PUNCT
iajs-826	249	33	topology	topology	PROPN
iajs-826	249	34	atlas	atlas	PROPN
iajs-826	249	35	,	,	PUNCT
iajs-826	249	36	toronto	toronto	PROPN
iajs-826	249	37	,	,	PUNCT
iajs-826	249	38	pp.7590	pp.7590	PROPN
iajs-826	249	39	.	.	PROPN
iajs-826	250	1	2	2	NUM
iajs-826	250	2	.	.	X
iajs-826	250	3	wilkins	wilkins	PROPN
iajs-826	250	4	,	,	PUNCT
iajs-826	250	5	d.r	d.r	PROPN
iajs-826	250	6	.	.	PROPN
iajs-826	250	7	(	(	PUNCT
iajs-826	250	8	1998	1998	NUM
iajs-826	250	9	-	-	SYM
iajs-826	250	10	1999	1999	NUM
iajs-826	250	11	)	)	PUNCT
iajs-826	250	12	,	,	PUNCT
iajs-826	250	13	"	"	PUNCT
iajs-826	250	14	topological	topological	ADJ
iajs-826	250	15	space	space	NOUN
iajs-826	250	16	"	"	PUNCT
iajs-826	250	17	,	,	PUNCT
iajs-826	250	18	cademic	cademic	ADJ
iajs-826	250	19	year	year	NOUN
iajs-826	250	20	.	.	PUNCT
iajs-826	251	1	3	3	X
iajs-826	251	2	.	.	X
iajs-826	251	3	stergiou	stergiou	PROPN
iajs-826	251	4	,	,	PUNCT
iajs-826	251	5	c.	c.	PROPN
iajs-826	251	6	and	and	CCONJ
iajs-826	251	7	siganos	siganos	PROPN
iajs-826	251	8	,	,	PUNCT
iajs-826	251	9	d.	d.	PROPN
iajs-826	251	10	(	(	PUNCT
iajs-826	251	11	2008	2008	NUM
iajs-826	251	12	)	)	PUNCT
iajs-826	251	13	neural	neural	ADJ
iajs-826	251	14	networks	network	NOUN
iajs-826	251	15	,	,	PUNCT
iajs-826	251	16	ieee	ieee	NOUN
iajs-826	251	17	neural	neural	PROPN
iajs-826	251	18	networks	networks	PROPN
iajs-826	251	19	council	council	PROPN
iajs-826	251	20	ibn	ibn	PROPN
iajs-826	251	21	alhaitham	alhaitham	PROPN
iajs-826	252	1	j.	j.	PROPN
iajs-826	253	1	fo	fo	ADP
iajs-826	253	2	r	r	NOUN
iajs-826	253	3	pure	pure	ADJ
iajs-826	253	4	&	&	CCONJ
iajs-826	253	5	appl	appl	PROPN
iajs-826	253	6	.	.	PUNCT
iajs-826	254	1	sc	sc	PROPN
iajs-826	254	2	i.	i.	PROPN
iajs-826	254	3	vo	vo	PROPN
iajs-826	255	1	l.24	l.24	PROPN
iajs-826	255	2	(	(	PUNCT
iajs-826	255	3	1	1	NUM
iajs-826	255	4	)	)	PUNCT
iajs-826	255	5	2011	2011	NUM
iajs-826	255	6	4	4	NUM
iajs-826	255	7	.	.	PUNCT
iajs-826	255	8	tawfiq	tawfiq	PROPN
iajs-826	255	9	,	,	PUNCT
iajs-826	255	10	l.n.m	l.n.m	NOUN
iajs-826	255	11	.	.	PUNCT
iajs-826	256	1	(	(	PUNCT
iajs-826	256	2	2007	2007	NUM
iajs-826	256	3	)	)	PUNCT
iajs-826	256	4	,	,	PUNCT
iajs-826	256	5	density	density	NOUN
iajs-826	256	6	and	and	CCONJ
iajs-826	256	7	approximation	approximation	NOUN
iajs-826	256	8	by	by	ADP
iajs-826	256	9	using	use	VERB
iajs-826	256	10	feed	feed	NOUN
iajs-826	256	11	forward	forward	ADV
iajs-826	256	12	artificial	artificial	ADJ
iajs-826	256	13	neural	neural	ADJ
iajs-826	256	14	networks	network	NOUN
iajs-826	256	15	,	,	PUNCT
iajs-826	256	16	ibn	ibn	PROPN
iajs-826	256	17	al	al	PROPN
iajs-826	256	18	–	–	PUNCT
iajs-826	256	19	haithem	haithem	PROPN
iajs-826	256	20	journal	journal	NOUN
iajs-826	256	21	for	for	ADP
iajs-826	256	22	applied	applied	ADJ
iajs-826	256	23	and	and	CCONJ
iajs-826	256	24	pure	pure	ADJ
iajs-826	256	25	science,.20	science,.20	PROPN
iajs-826	256	26	,	,	PUNCT
iajs-826	256	27	1	1	NUM
iajs-826	256	28	.	.	NOUN
iajs-826	256	29	5	5	NUM
iajs-826	256	30	.	.	X
iajs-826	256	31	dijkstra	dijkstra	PROPN
iajs-826	256	32	,	,	PUNCT
iajs-826	256	33	e.w	e.w	PROPN
iajs-826	256	34	.	.	PROPN
iajs-826	256	35	(	(	PUNCT
iajs-826	256	36	2001	2001	NUM
iajs-826	256	37	)	)	PUNCT
iajs-826	256	38	"	"	PUNCT
iajs-826	256	39	pproximation	pproximation	NOUN
iajs-826	256	40	with	with	ADP
iajs-826	256	41	rtificial	rtificial	ADJ
iajs-826	256	42	networks	network	NOUN
iajs-826	256	43	"	"	PUNCT
iajs-826	256	44	,	,	PUNCT
iajs-826	256	45	sc	sc	ADV
iajs-826	256	46	thesis	thesis	NOUN
iajs-826	256	47	,	,	PUNCT
iajs-826	256	48	faculty	faculty	NOUN
iajs-826	256	49	of	of	ADP
iajs-826	256	50	mathematics	mathematic	NOUN
iajs-826	256	51	and	and	CCONJ
iajs-826	256	52	computing	compute	VERB
iajs-826	256	53	science	science	NOUN
iajs-826	256	54	eindhoven	eindhoven	PROPN
iajs-826	256	55	university	university	PROPN
iajs-826	256	56	of	of	ADP
iajs-826	256	57	technology	technology	NOUN
iajs-826	256	58	,	,	PUNCT
iajs-826	256	59	the	the	DET
iajs-826	256	60	netherlands	netherlands	PROPN
iajs-826	256	61	.	.	PUNCT
iajs-826	257	1	6	6	NUM
iajs-826	257	2	.	.	X
iajs-826	258	1	.ason	.ason	PROPN
iajs-826	258	2	,	,	PUNCT
iajs-826	258	3	j.c	j.c	PROPN
iajs-826	258	4	.	.	PROPN
iajs-826	258	5	and	and	CCONJ
iajs-826	258	6	parks	park	NOUN
iajs-826	258	7	,	,	PUNCT
iajs-826	258	8	p.c	p.c	PROPN
iajs-826	258	9	.	.	PROPN
iajs-826	258	10	(	(	PUNCT
iajs-826	258	11	2004	2004	NUM
iajs-826	258	12	)	)	PUNCT
iajs-826	258	13	"	"	PUNCT
iajs-826	258	14	selection	selection	NOUN
iajs-826	258	15	of	of	ADP
iajs-826	258	16	neural	neural	ADJ
iajs-826	258	17	network	network	NOUN
iajs-826	258	18	structures	structure	VERB
iajs-826	258	19	some	some	DET
iajs-826	258	20	approximation	approximation	NOUN
iajs-826	258	21	theory	theory	NOUN
iajs-826	258	22	guidelines	guideline	NOUN
iajs-826	258	23	,	,	PUNCT
iajs-826	258	24	iee	iee	PROPN
iajs-826	258	25	control	control	PROPN
iajs-826	258	26	engineering	engineering	PROPN
iajs-826	258	27	series	series	NOUN
iajs-826	258	28	,	,	PUNCT
iajs-826	258	29	46:151	46:151	NUM
iajs-826	258	30	-	-	SYM
iajs-826	258	31	180	180	NUM
iajs-826	258	32	.	.	NOUN
iajs-826	258	33	7	7	X
iajs-826	258	34	.	.	X
iajs-826	258	35	ellacott	ellacott	PROPN
iajs-826	258	36	,	,	PUNCT
iajs-826	258	37	s.w	s.w	PROPN
iajs-826	258	38	.	.	PROPN
iajs-826	258	39	(	(	PUNCT
iajs-826	258	40	1994	1994	NUM
iajs-826	258	41	)	)	PUNCT
iajs-826	258	42	,	,	PUNCT
iajs-826	258	43	"	"	PUNCT
iajs-826	258	44	spects	spect	NOUN
iajs-826	258	45	of	of	ADP
iajs-826	258	46	the	the	DET
iajs-826	258	47	numerical	numerical	ADJ
iajs-826	258	48	analysis	analysis	NOUN
iajs-826	258	49	of	of	ADP
iajs-826	258	50	neural	neural	ADJ
iajs-826	258	51	networks	network	NOUN
iajs-826	258	52	"	"	PUNCT
iajs-826	258	53	,	,	PUNCT
iajs-826	258	54	cta	cta	PROPN
iajs-826	258	55	numerical	numerical	ADJ
iajs-826	258	56	,	,	PUNCT
iajs-826	258	57	145	145	NUM
iajs-826	258	58	-	-	SYM
iajs-826	258	59	202	202	NUM
iajs-826	258	60	.	.	NOUN
iajs-826	258	61	8	8	NUM
iajs-826	258	62	.	.	X
iajs-826	259	1	kurkova	kurkova	PROPN
iajs-826	259	2	,	,	PUNCT
iajs-826	259	3	v.	v.	PROPN
iajs-826	259	4	(	(	PUNCT
iajs-826	259	5	1991)"kolmogorov	1991)"kolmogorov	NUM
iajs-826	259	6	's	's	PART
iajs-826	259	7	theorem	theorem	NOUN
iajs-826	259	8	is	be	AUX
iajs-826	259	9	relevant	relevant	ADJ
iajs-826	259	10	,	,	PUNCT
iajs-826	259	11	1	1	NUM
iajs-826	259	12	,	,	PUNCT
iajs-826	259	13	"	"	PUNCT
iajs-826	259	14	neural	neural	ADJ
iajs-826	259	15	computation	computation	NOUN
iajs-826	259	16	3	3	NUM
iajs-826	259	17	:	:	SYM
iajs-826	259	18	617622	617622	NUM
iajs-826	259	19	.	.	PUNCT
iajs-826	260	1	fig	fig	NOUN
iajs-826	260	2	.	.	PUNCT
iajs-826	261	1	(	(	PUNCT
iajs-826	261	2	1	1	X
iajs-826	261	3	)	)	PUNCT
iajs-826	261	4	a	a	DET
iajs-826	261	5	simple	simple	ADJ
iajs-826	261	6	neural	neural	ADJ
iajs-826	261	7	network	network	NOUN
iajs-826	261	8	diagram	diagram	PROPN
iajs-826	261	9	.	.	PUNCT
iajs-826	262	1	fig	fig	NOUN
iajs-826	262	2	.	.	PUNCT
iajs-826	263	1	(	(	PUNCT
iajs-826	263	2	2	2	X
iajs-826	263	3	)	)	PUNCT
iajs-826	263	4	graph	graph	NOUN
iajs-826	263	5	of	of	ADP
iajs-826	263	6	a	a	DET
iajs-826	263	7	multilayer(n	multilayer(n	PROPN
iajs-826	263	8	-	-	ADJ
iajs-826	263	9	topological	topological	ADJ
iajs-826	263	10	space)neural	space)neural	ADJ
iajs-826	263	11	network	network	NOUN
iajs-826	263	12	with	with	ADP
iajs-826	263	13	sequential	sequential	ADJ
iajs-826	263	14	connections	connection	NOUN
iajs-826	263	15	2011	2011	NUM
iajs-826	263	16	)	)	PUNCT
iajs-826	263	17	1	1	NUM
iajs-826	263	18	(	(	PUNCT
iajs-826	263	19	24مجلة	24مجلة	NUM
iajs-826	263	20	ابن	ابن	PROPN
iajs-826	263	21	الھیثم	الھیثم	PROPN
iajs-826	263	22	للعلوم	للعلوم	PROPN
iajs-826	263	23	الصرفة	الصرفة	PROPN
iajs-826	263	24	والتطبیقیة	والتطبیقیة	PROPN
iajs-826	263	25	المجلد	المجلد	PROPN
iajs-826	263	26	وتطبیقاتها	وتطبیقاتها	NOUN
iajs-826	263	27	في	في	SCONJ
iajs-826	263	28	الشبكات	الشبكات	PROPN
iajs-826	263	29	العصبیة	العصبیة	NOUN
iajs-826	263	30	الصناعیة	الصناعیة	VERB
iajs-826	263	31	nالفضاءات	nالفضاءات	ADJ
iajs-826	263	32	التبولوجیة	التبولوجیة	PROPN
iajs-826	263	33	ــ	ــ	PROPN
iajs-826	263	34	رشا	رشا	PROPN
iajs-826	263	35	ناصر	ناصر	NOUN
iajs-826	263	36	مجید	مجید	PROPN
iajs-826	263	37	لمى	لمى	PROPN
iajs-826	263	38	ناجي	ناجي	PROPN
iajs-826	263	39	محمد	محمد	ADJ
iajs-826	263	40	توفیق	توفیق	NOUN
iajs-826	263	41	و	و	X
iajs-826	263	42	جامعـة	جامعـة	PROPN
iajs-826	263	43	بغـداد،أبن	بغـداد،أبن	PROPN
iajs-826	263	44	الهیثم	الهیثم	PROPN
iajs-826	263	45	-كلیة	-كلیة	PROPN
iajs-826	263	46	التربیة،قسم	التربیة،قسم	PROPN
iajs-826	263	47	الریاضیات	الریاضیات	NOUN
iajs-826	263	48	2009	2009	NUM
iajs-826	263	49	آذار	آذار	NOUN
iajs-826	263	50	16استلم	16استلم	NUM
iajs-826	263	51	البحث	البحث	NOUN
iajs-826	263	52	في	في	ADP
iajs-826	263	53	2010	2010	NUM
iajs-826	263	54	آذار	آذار	NOUN
iajs-826	263	55	29قبل	29قبل	NOUN
iajs-826	263	56	البحث	البحث	VERB
iajs-826	263	57	في	في	ADP
iajs-826	263	58	الخالصة	الخالصة	PROPN
iajs-826	264	1	ة	ة	PRON
iajs-826	264	2	مـن	مـن	PROPN
iajs-826	264	3	النـوع	النـوع	PROPN
iajs-826	264	4	ـ	ـ	X
iajs-826	264	5	في	في	ADP
iajs-826	264	6	هذا	هذا	NOUN
iajs-826	264	7	البحث	البحث	NOUN
iajs-826	264	8	أعطینا	أعطینا	NOUN
iajs-826	264	9	تعار	تعار	PROPN
iajs-826	264	10	یف	یف	PROPN
iajs-826	264	11	فـي	فـي	PROPN
iajs-826	264	12	،	،	PROPN
iajs-826	264	13	n	n	ADV
iajs-826	264	14	إن	إن	ADV
iajs-826	264	15	إذا	إذا	VERB
iajs-826	264	16	.	.	PUNCT
iajs-826	265	1	nخواص	nخواص	PROPN
iajs-826	265	2	وأمثلة	وأمثلة	PROPN
iajs-826	265	3	حـول	حـول	NOUN
iajs-826	265	4	مصـطلح	مصـطلح	ADJ
iajs-826	265	5	الفضـاءات	الفضـاءات	NOUN
iajs-826	265	6	التبولوجیـ	التبولوجیـ	VERB
iajs-826	265	7	إن	إن	ADP
iajs-826	265	8	فكــرة	فكــرة	ADJ
iajs-826	265	9	هـذا	هـذا	NOUN
iajs-826	265	10	البحـث	البحـث	VERB
iajs-826	265	11	هـو	هـو	ADJ
iajs-826	265	12	دراســة	دراســة	ADJ
iajs-826	265	13	وتقـدیم	وتقـدیم	X
iajs-826	265	14	بعـض	بعـض	NOUN
iajs-826	265	15	خــواص	خــواص	PROPN
iajs-826	265	16	هـذه	هـذه	ADJ
iajs-826	265	17	الفضـاءات	الفضـاءات	NOUN
iajs-826	265	18	مــع	مــع	ADJ
iajs-826	265	19	.	.	PUNCT
iajs-826	266	1	،	،	PROPN
iajs-826	266	2	هـذا	هـذا	NOUN
iajs-826	266	3	البحـث	البحـث	VERB
iajs-826	266	4	هـو	هـو	ADJ
iajs-826	266	5	عــدد	عــدد	PROPN
iajs-826	266	6	منتهـي	منتهـي	PROPN
iajs-826	266	7	موجـب	موجـب	PROPN
iajs-826	266	8	دراسة	دراسة	PROPN
iajs-826	266	9	العالقة	العالقة	PROPN
iajs-826	266	10	بین	بین	PROPN
iajs-826	266	11	هذه	هذه	PROPN
iajs-826	266	12	الفضاءات	الفضاءات	PROPN
iajs-826	266	13	والشبكات	والشبكات	PROPN
iajs-826	266	14	العصـبیة	العصـبیة	NOUN
iajs-826	266	15	الصـناعیة	الصـناعیة	VERB
iajs-826	266	16	وهـذا	وهـذا	NOUN
iajs-826	266	17	یعنـي	یعنـي	NOUN
iajs-826	266	18	تطبیـق	تطبیـق	ADJ
iajs-826	266	19	تعریـف	تعریـف	ADV
iajs-826	266	20	هـذا	هـذا	NOUN
iajs-826	266	21	الفضـاء	الفضـاء	VERB
iajs-826	266	22	فـي	فـي	NOUN
iajs-826	266	23	حقـل	حقـل	PROPN
iajs-826	266	24	الكومبیـوتر	الكومبیـوتر	NOUN
iajs-826	266	25	.في	.في	PUNCT
iajs-826	267	1	مجال	مجال	ADJ
iajs-826	267	2	المعالجات	المعالجات	NOUN
iajs-826	267	3	المتوازیة	المتوازیة	PROPN
iajs-826	267	4	السیماو	السیماو	AUX