id	sid	tid	token	lemma	pos
iajs-812	1	1	ibn	ibn	PROPN
iajs-812	1	2	alhaitham	alhaitham	NOUN
iajs-812	1	3	j.	j.	PROPN
iajs-812	1	4	for	for	ADP
iajs-812	1	5	pure	pure	ADJ
iajs-812	1	6	&	&	CCONJ
iajs-812	1	7	appl	appl	PROPN
iajs-812	1	8	.	.	PUNCT
iajs-812	2	1	sci	sci	PROPN
iajs-812	2	2	.	.	PUNCT
iajs-812	2	3	vol.24	vol.24	NOUN
iajs-812	2	4	(	(	PUNCT
iajs-812	2	5	3	3	NUM
iajs-812	2	6	)	)	PUNCT
iajs-812	2	7	2011	2011	NUM
iajs-812	2	8	on	on	ADP
iajs-812	2	9	pairwise	pairwise	NOUN
iajs-812	2	10	semi	semi	ADJ
iajs-812	2	11	-	-	ADJ
iajs-812	2	12	p	p	ADJ
iajs-812	2	13	-	-	PUNCT
iajs-812	2	14	separation	separation	NOUN
iajs-812	2	15	axioms	axiom	NOUN
iajs-812	2	16	in	in	ADP
iajs-812	2	17	bitopological	bitopological	ADJ
iajs-812	2	18	spaces	space	NOUN
iajs-812	2	19	r.	r.	PROPN
iajs-812	2	20	n.majeed	n.majeed	VERB
iajs-812	2	21	department	department	PROPN
iajs-812	2	22	of	of	ADP
iajs-812	2	23	mathematics	mathematics	PROPN
iajs-812	2	24	,	,	PUNCT
iajs-812	2	25	college	college	NOUN
iajs-812	2	26	of	of	ADP
iajs-812	2	27	education	education	PROPN
iajs-812	2	28	ibn	ibn	PROPN
iajs-812	2	29	alhaitham	alhaitham	NOUN
iajs-812	2	30	,	,	PUNCT
iajs-812	2	31	university	university	NOUN
iajs-812	2	32	of	of	ADP
iajs-812	2	33	baghdad	baghdad	PROPN
iajs-812	2	34	received	receive	VERB
iajs-812	2	35	in	in	ADP
iajs-812	2	36	:	:	PUNCT
iajs-812	2	37	10	10	NUM
iajs-812	2	38	october	october	NOUN
iajs-812	2	39	2010	2010	NUM
iajs-812	2	40	accepted	accept	VERB
iajs-812	2	41	in	in	ADP
iajs-812	2	42	:	:	PUNCT
iajs-812	2	43	13	13	NUM
iajs-812	2	44	march	march	NOUN
iajs-812	2	45	2011	2011	NUM
iajs-812	2	46	abstract	abstract	NOUN
iajs-812	2	47	in	in	ADP
iajs-812	2	48	this	this	DET
iajs-812	2	49	paper	paper	NOUN
iajs-812	2	50	,	,	PUNCT
iajs-812	2	51	we	we	PRON
iajs-812	2	52	define	define	VERB
iajs-812	2	53	a	a	DET
iajs-812	2	54	new	new	ADJ
iajs-812	2	55	type	type	NOUN
iajs-812	2	56	of	of	ADP
iajs-812	2	57	pairwise	pairwise	NOUN
iajs-812	2	58	separation	separation	NOUN
iajs-812	2	59	axioms	axiom	NOUN
iajs-812	2	60	called	call	VERB
iajs-812	2	61	pairwise	pairwise	NOUN
iajs-812	2	62	semi	semi	ADJ
iajs-812	2	63	-	-	ADJ
iajs-812	2	64	p	p	ADJ
iajs-812	2	65	separation	separation	NOUN
iajs-812	2	66	axioms	axiom	NOUN
iajs-812	2	67	in	in	ADP
iajs-812	2	68	bitopological	bitopological	ADJ
iajs-812	2	69	spaces	space	NOUN
iajs-812	2	70	,	,	PUNCT
iajs-812	2	71	also	also	ADV
iajs-812	2	72	we	we	PRON
iajs-812	2	73	study	study	VERB
iajs-812	2	74	some	some	DET
iajs-812	2	75	properties	property	NOUN
iajs-812	2	76	of	of	ADP
iajs-812	2	77	these	these	DET
iajs-812	2	78	spaces	space	NOUN
iajs-812	2	79	and	and	CCONJ
iajs-812	2	80	relationships	relationship	NOUN
iajs-812	2	81	of	of	ADP
iajs-812	2	82	each	each	DET
iajs-812	2	83	one	one	NOUN
iajs-812	2	84	with	with	ADP
iajs-812	2	85	the	the	DET
iajs-812	2	86	ordinary	ordinary	ADJ
iajs-812	2	87	separation	separation	NOUN
iajs-812	2	88	axioms	axiom	VERB
iajs-812	2	89	in	in	ADP
iajs-812	2	90	the	the	DET
iajs-812	2	91	bitopological	bitopological	ADJ
iajs-812	2	92	spaces	space	NOUN
iajs-812	2	93	.	.	PUNCT
iajs-812	3	1	keywords	keyword	NOUN
iajs-812	3	2	:	:	PUNCT
iajs-812	3	3	bitopological	bitopological	ADJ
iajs-812	3	4	space	space	NOUN
iajs-812	3	5	,	,	PUNCT
iajs-812	3	6	pairwise	pairwise	NOUN
iajs-812	3	7	semi	semi	NOUN
iajs-812	3	8	-	-	NOUN
iajs-812	3	9	pspace	pspace	NOUN
iajs-812	3	10	,	,	PUNCT
iajs-812	3	11	pairwise	pairwise	NOUN
iajs-812	3	12	semi	semi	NOUN
iajs-812	3	13	-	-	NOUN
iajs-812	3	14	pspace	pspace	NOUN
iajs-812	3	15	,	,	PUNCT
iajs-812	3	16	pairwise	pairwise	NOUN
iajs-812	3	17	semi	semi	NOUN
iajs-812	3	18	-	-	NOUN
iajs-812	3	19	pspace	pspace	NOUN
iajs-812	3	20	,	,	PUNCT
iajs-812	3	21	pairwise	pairwise	NOUN
iajs-812	3	22	semi	semi	ADJ
iajs-812	3	23	-	-	ADJ
iajs-812	3	24	p	p	ADJ
iajs-812	3	25	space	space	NOUN
iajs-812	3	26	,	,	PUNCT
iajs-812	3	27	pairwise	pairwise	NOUN
iajs-812	3	28	semi	semi	ADJ
iajs-812	3	29	-	-	ADJ
iajs-812	3	30	p	p	ADJ
iajs-812	3	31	normal	normal	ADJ
iajs-812	3	32	space	space	NOUN
iajs-812	3	33	.	.	PUNCT
iajs-812	4	1	1	1	NUM
iajs-812	4	2	-	-	PUNCT
iajs-812	4	3	introduction	introduction	NOUN
iajs-812	4	4	the	the	DET
iajs-812	4	5	theory	theory	NOUN
iajs-812	4	6	of	of	ADP
iajs-812	4	7	bitopological	bitopological	ADJ
iajs-812	4	8	spaces	space	NOUN
iajs-812	4	9	started	start	VERB
iajs-812	4	10	with	with	ADP
iajs-812	4	11	the	the	DET
iajs-812	4	12	paper	paper	NOUN
iajs-812	4	13	of	of	ADP
iajs-812	4	14	kelly	kelly	PROPN
iajs-812	4	15	in	in	ADP
iajs-812	4	16	[	[	X
iajs-812	4	17	1	1	NUM
iajs-812	4	18	]	]	PUNCT
iajs-812	4	19	.	.	PUNCT
iajs-812	5	1	a	a	DET
iajs-812	5	2	set	set	NOUN
iajs-812	5	3	equipped	equip	VERB
iajs-812	5	4	with	with	ADP
iajs-812	5	5	two	two	NUM
iajs-812	5	6	topologies	topology	NOUN
iajs-812	5	7	is	be	AUX
iajs-812	5	8	called	call	VERB
iajs-812	5	9	a	a	DET
iajs-812	5	10	bitopological	bitopological	ADJ
iajs-812	5	11	space	space	NOUN
iajs-812	5	12	.	.	PUNCT
iajs-812	6	1	since	since	SCONJ
iajs-812	6	2	then	then	ADV
iajs-812	6	3	several	several	ADJ
iajs-812	6	4	authors	author	NOUN
iajs-812	6	5	continued	continue	VERB
iajs-812	6	6	investigating	investigate	VERB
iajs-812	6	7	such	such	ADJ
iajs-812	6	8	spaces	space	NOUN
iajs-812	6	9	.	.	PUNCT
iajs-812	7	1	furthermore	furthermore	ADV
iajs-812	7	2	,	,	PUNCT
iajs-812	7	3	kelly	kelly	PROPN
iajs-812	7	4	extended	extend	VERB
iajs-812	7	5	some	some	PRON
iajs-812	7	6	of	of	ADP
iajs-812	7	7	the	the	DET
iajs-812	7	8	standard	standard	ADJ
iajs-812	7	9	results	result	NOUN
iajs-812	7	10	of	of	ADP
iajs-812	7	11	separation	separation	NOUN
iajs-812	7	12	axioms	axiom	NOUN
iajs-812	7	13	in	in	ADP
iajs-812	7	14	a	a	DET
iajs-812	7	15	topological	topological	ADJ
iajs-812	7	16	space	space	NOUN
iajs-812	7	17	to	to	ADP
iajs-812	7	18	a	a	DET
iajs-812	7	19	bitopological	bitopological	ADJ
iajs-812	7	20	space	space	NOUN
iajs-812	7	21	,	,	PUNCT
iajs-812	7	22	such	such	ADJ
iajs-812	7	23	extensions	extension	NOUN
iajs-812	7	24	are	be	AUX
iajs-812	7	25	pairwise	pairwise	NOUN
iajs-812	7	26	regular	regular	ADJ
iajs-812	7	27	,	,	PUNCT
iajs-812	7	28	pairwise	pairwise	NOUN
iajs-812	7	29	hausdorff	hausdorff	NOUN
iajs-812	7	30	and	and	CCONJ
iajs-812	7	31	pairwise	pairwise	NOUN
iajs-812	7	32	normal	normal	ADJ
iajs-812	7	33	,	,	PUNCT
iajs-812	7	34	concepts	concept	NOUN
iajs-812	7	35	of	of	ADP
iajs-812	7	36	pairwise	pairwise	NOUN
iajs-812	7	37	and	and	CCONJ
iajs-812	7	38	pairwise	pairwise	NOUN
iajs-812	7	39	were	be	AUX
iajs-812	7	40	introduced	introduce	VERB
iajs-812	7	41	by	by	ADP
iajs-812	7	42	murdeshwar	murdeshwar	NOUN
iajs-812	7	43	and	and	CCONJ
iajs-812	7	44	naimpally	naimpally	ADV
iajs-812	7	45	in	in	ADP
iajs-812	7	46	[	[	X
iajs-812	7	47	2	2	NUM
iajs-812	7	48	]	]	PUNCT
iajs-812	7	49	.	.	PUNCT
iajs-812	8	1	the	the	DET
iajs-812	8	2	purpose	purpose	NOUN
iajs-812	8	3	of	of	ADP
iajs-812	8	4	this	this	DET
iajs-812	8	5	paper	paper	NOUN
iajs-812	8	6	is	be	AUX
iajs-812	8	7	to	to	PART
iajs-812	8	8	introduce	introduce	VERB
iajs-812	8	9	and	and	CCONJ
iajs-812	8	10	investigate	investigate	VERB
iajs-812	8	11	the	the	DET
iajs-812	8	12	notion	notion	NOUN
iajs-812	8	13	of	of	ADP
iajs-812	8	14	pairwise	pairwise	NOUN
iajs-812	8	15	semip	semip	NOUN
iajs-812	8	16	separation	separation	NOUN
iajs-812	8	17	axioms	axiom	NOUN
iajs-812	8	18	in	in	ADP
iajs-812	8	19	bitopological	bitopological	ADJ
iajs-812	8	20	spaces	space	NOUN
iajs-812	8	21	and	and	CCONJ
iajs-812	8	22	study	study	VERB
iajs-812	8	23	some	some	DET
iajs-812	8	24	properties	property	NOUN
iajs-812	8	25	of	of	ADP
iajs-812	8	26	these	these	DET
iajs-812	8	27	spaces	space	NOUN
iajs-812	8	28	and	and	CCONJ
iajs-812	8	29	relationships	relationship	NOUN
iajs-812	8	30	of	of	ADP
iajs-812	8	31	each	each	DET
iajs-812	8	32	one	one	NOUN
iajs-812	8	33	with	with	ADP
iajs-812	8	34	the	the	DET
iajs-812	8	35	ordinary	ordinary	ADJ
iajs-812	8	36	separation	separation	NOUN
iajs-812	8	37	axioms	axiom	VERB
iajs-812	8	38	in	in	ADP
iajs-812	8	39	the	the	DET
iajs-812	8	40	bitopological	bitopological	ADJ
iajs-812	8	41	spaces	space	NOUN
iajs-812	8	42	.	.	PUNCT
iajs-812	9	1	2preliminaries	2preliminaries	NUM
iajs-812	9	2	in	in	ADP
iajs-812	9	3	this	this	DET
iajs-812	9	4	section	section	NOUN
iajs-812	9	5	,	,	PUNCT
iajs-812	9	6	we	we	PRON
iajs-812	9	7	introduce	introduce	VERB
iajs-812	9	8	some	some	DET
iajs-812	9	9	definitions	definition	NOUN
iajs-812	9	10	and	and	CCONJ
iajs-812	9	11	propositions	proposition	NOUN
iajs-812	9	12	,	,	PUNCT
iajs-812	9	13	which	which	PRON
iajs-812	9	14	is	be	AUX
iajs-812	9	15	necessary	necessary	ADJ
iajs-812	9	16	for	for	ADP
iajs-812	9	17	the	the	DET
iajs-812	9	18	paper	paper	NOUN
iajs-812	9	19	.	.	PUNCT
iajs-812	10	1	definition	definition	NOUN
iajs-812	10	2	2.1[3	2.1[3	NUM
iajs-812	10	3	]	]	X
iajs-812	10	4	:	:	PUNCT
iajs-812	10	5	a	a	DET
iajs-812	10	6	subset	subset	NOUN
iajs-812	10	7	a	a	PRON
iajs-812	10	8	of	of	ADP
iajs-812	10	9	a	a	DET
iajs-812	10	10	topological	topological	ADJ
iajs-812	10	11	space	space	NOUN
iajs-812	10	12	is	be	AUX
iajs-812	10	13	called	call	VERB
iajs-812	10	14	a	a	DET
iajs-812	10	15	pre	pre	ADJ
iajs-812	10	16	-	-	ADJ
iajs-812	10	17	open	open	ADJ
iajs-812	10	18	set	set	NOUN
iajs-812	10	19	if	if	SCONJ
iajs-812	10	20	.	.	PUNCT
iajs-812	11	1	the	the	DET
iajs-812	11	2	complement	complement	NOUN
iajs-812	11	3	of	of	ADP
iajs-812	11	4	pre	pre	ADJ
iajs-812	11	5	-	-	ADJ
iajs-812	11	6	open	open	ADJ
iajs-812	11	7	set	set	NOUN
iajs-812	11	8	is	be	AUX
iajs-812	11	9	called	call	VERB
iajs-812	11	10	pre	pre	ADJ
iajs-812	11	11	-	-	ADJ
iajs-812	11	12	closed	closed	ADJ
iajs-812	11	13	set	set	NOUN
iajs-812	11	14	.	.	PUNCT
iajs-812	12	1	the	the	DET
iajs-812	12	2	family	family	NOUN
iajs-812	12	3	of	of	ADP
iajs-812	12	4	all	all	DET
iajs-812	12	5	pre	pre	ADJ
iajs-812	12	6	-	-	ADJ
iajs-812	12	7	open	open	ADJ
iajs-812	12	8	subsets	subset	NOUN
iajs-812	12	9	of	of	ADP
iajs-812	12	10	x	x	PROPN
iajs-812	12	11	is	be	AUX
iajs-812	12	12	denoted	denote	VERB
iajs-812	12	13	by	by	ADP
iajs-812	12	14	po(x	po(x	NOUN
iajs-812	12	15	)	)	PUNCT
iajs-812	12	16	.	.	PUNCT
iajs-812	13	1	the	the	DET
iajs-812	13	2	family	family	NOUN
iajs-812	13	3	of	of	ADP
iajs-812	13	4	all	all	DET
iajs-812	13	5	p	p	PRON
iajs-812	13	6	re	re	ADJ
iajs-812	13	7	-	-	ADJ
iajs-812	13	8	closed	closed	ADJ
iajs-812	13	9	subsets	subset	NOUN
iajs-812	13	10	of	of	ADP
iajs-812	13	11	x	x	PROPN
iajs-812	13	12	is	be	AUX
iajs-812	13	13	denoted	denote	VERB
iajs-812	13	14	by	by	ADP
iajs-812	13	15	pc(x	pc(x	NOUN
iajs-812	13	16	)	)	PUNCT
iajs-812	13	17	.	.	PUNCT
iajs-812	14	1	proposition	proposition	NOUN
iajs-812	14	2	2.2	2.2	NUM
iajs-812	15	1	[	[	X
iajs-812	15	2	4	4	NUM
iajs-812	15	3	]	]	PUNCT
iajs-812	15	4	:	:	PUNCT
iajs-812	15	5	let	let	AUX
iajs-812	15	6	be	be	AUX
iajs-812	15	7	a	a	DET
iajs-812	15	8	topological	topological	ADJ
iajs-812	15	9	space	space	NOUN
iajs-812	15	10	,	,	PUNCT
iajs-812	15	11	then	then	ADV
iajs-812	15	12	:	:	PUNCT
iajs-812	15	13	1	1	NUM
iajs-812	15	14	-	-	PUNCT
iajs-812	15	15	every	every	DET
iajs-812	15	16	open	open	ADJ
iajs-812	15	17	set	set	NOUN
iajs-812	15	18	is	be	AUX
iajs-812	15	19	a	a	DET
iajs-812	15	20	pre	pre	ADJ
iajs-812	15	21	-	-	ADJ
iajs-812	15	22	open	open	ADJ
iajs-812	15	23	set	set	NOUN
iajs-812	15	24	.	.	PUNCT
iajs-812	16	1	2	2	NUM
iajs-812	16	2	-	-	NUM
iajs-812	16	3	every	every	DET
iajs-812	16	4	closed	closed	ADJ
iajs-812	16	5	set	set	NOUN
iajs-812	16	6	is	be	AUX
iajs-812	16	7	a	a	DET
iajs-812	16	8	pre	pre	ADJ
iajs-812	16	9	-	-	ADJ
iajs-812	16	10	closed	closed	ADJ
iajs-812	16	11	set	set	NOUN
iajs-812	16	12	.	.	PUNCT
iajs-812	17	1	ibn	ibn	PROPN
iajs-812	17	2	alhaitham	alhaitham	PROPN
iajs-812	17	3	j.	j.	PROPN
iajs-812	17	4	for	for	ADP
iajs-812	17	5	pure	pure	ADJ
iajs-812	17	6	&	&	CCONJ
iajs-812	17	7	appl	appl	PROPN
iajs-812	17	8	.	.	PUNCT
iajs-812	18	1	sci	sci	PROPN
iajs-812	18	2	.	.	PUNCT
iajs-812	18	3	vol.24	vol.24	NOUN
iajs-812	18	4	(	(	PUNCT
iajs-812	18	5	3	3	NUM
iajs-812	18	6	)	)	PUNCT
iajs-812	18	7	2011	2011	NUM
iajs-812	18	8	but	but	CCONJ
iajs-812	18	9	the	the	DET
iajs-812	18	10	converse	converse	NOUN
iajs-812	18	11	of	of	ADP
iajs-812	18	12	(	(	PUNCT
iajs-812	18	13	1	1	NUM
iajs-812	18	14	)	)	PUNCT
iajs-812	18	15	and	and	CCONJ
iajs-812	18	16	(	(	PUNCT
iajs-812	18	17	2	2	X
iajs-812	18	18	)	)	PUNCT
iajs-812	18	19	is	be	AUX
iajs-812	18	20	not	not	PART
iajs-812	18	21	true	true	ADJ
iajs-812	18	22	in	in	ADP
iajs-812	18	23	general	general	ADJ
iajs-812	18	24	.	.	PUNCT
iajs-812	19	1	proposition	proposition	NOUN
iajs-812	19	2	2.3	2.3	NUM
iajs-812	20	1	[	[	X
iajs-812	20	2	4	4	NUM
iajs-812	20	3	]	]	PUNCT
iajs-812	20	4	:	:	PUNCT
iajs-812	20	5	the	the	DET
iajs-812	20	6	union	union	NOUN
iajs-812	20	7	of	of	ADP
iajs-812	20	8	any	any	DET
iajs-812	20	9	family	family	NOUN
iajs-812	20	10	of	of	ADP
iajs-812	20	11	pre	pre	ADJ
iajs-812	20	12	-	-	ADJ
iajs-812	20	13	open	open	ADJ
iajs-812	20	14	sets	set	NOUN
iajs-812	20	15	is	be	AUX
iajs-812	20	16	a	a	DET
iajs-812	20	17	pre	pre	ADJ
iajs-812	20	18	-	-	ADJ
iajs-812	20	19	open	open	ADJ
iajs-812	20	20	set	set	NOUN
iajs-812	20	21	.	.	PUNCT
iajs-812	21	1	definition	definition	NOUN
iajs-812	21	2	2.4[3	2.4[3	NUM
iajs-812	21	3	]	]	X
iajs-812	21	4	:	:	PUNCT
iajs-812	21	5	the	the	DET
iajs-812	21	6	union	union	NOUN
iajs-812	21	7	of	of	ADP
iajs-812	21	8	all	all	DET
iajs-812	21	9	per	per	ADP
iajs-812	21	10	-	-	PUNCT
iajs-812	21	11	open	open	ADJ
iajs-812	21	12	sets	set	NOUN
iajs-812	21	13	contained	contain	VERB
iajs-812	21	14	in	in	ADP
iajs-812	21	15	a	a	PRON
iajs-812	21	16	is	be	AUX
iajs-812	21	17	called	call	VERB
iajs-812	21	18	the	the	DET
iajs-812	21	19	pre	pre	NOUN
iajs-812	21	20	-	-	NOUN
iajs-812	21	21	interior	interior	ADJ
iajs-812	21	22	of	of	ADP
iajs-812	21	23	a	a	PRON
iajs-812	21	24	,	,	PUNCT
iajs-812	21	25	denoted	denote	VERB
iajs-812	21	26	by	by	ADP
iajs-812	21	27	pre	pre	ADJ
iajs-812	21	28	-	-	ADJ
iajs-812	21	29	int	int	ADJ
iajs-812	21	30	a.	a.	NOUN
iajs-812	21	31	the	the	DET
iajs-812	21	32	intersection	intersection	NOUN
iajs-812	21	33	of	of	ADP
iajs-812	21	34	all	all	DET
iajs-812	21	35	pre	pre	ADJ
iajs-812	21	36	-	-	ADJ
iajs-812	21	37	closed	closed	ADJ
iajs-812	21	38	sets	set	NOUN
iajs-812	21	39	containing	contain	VERB
iajs-812	21	40	a	a	PRON
iajs-812	21	41	is	be	AUX
iajs-812	21	42	called	call	VERB
iajs-812	21	43	the	the	DET
iajs-812	21	44	per	per	NOUN
iajs-812	21	45	-	-	PUNCT
iajs-812	21	46	closure	closure	NOUN
iajs-812	21	47	of	of	ADP
iajs-812	21	48	a	a	PRON
iajs-812	21	49	,	,	PUNCT
iajs-812	21	50	and	and	CCONJ
iajs-812	21	51	is	be	AUX
iajs-812	21	52	denoted	denote	VERB
iajs-812	21	53	by	by	ADP
iajs-812	21	54	pre	pre	ADJ
iajs-812	21	55	-	-	ADJ
iajs-812	21	56	cl	cl	ADJ
iajs-812	21	57	a.	a.	NOUN
iajs-812	21	58	proposition	proposition	NOUN
iajs-812	21	59	2.5	2.5	NUM
iajs-812	22	1	[	[	X
iajs-812	22	2	4	4	NUM
iajs-812	22	3	]	]	PUNCT
iajs-812	22	4	:	:	PUNCT
iajs-812	22	5	let	let	AUX
iajs-812	22	6	be	be	AUX
iajs-812	22	7	a	a	DET
iajs-812	22	8	topological	topological	ADJ
iajs-812	22	9	space	space	NOUN
iajs-812	22	10	and	and	CCONJ
iajs-812	22	11	a	a	DET
iajs-812	22	12	,	,	PUNCT
iajs-812	22	13	b	b	NOUN
iajs-812	22	14	be	be	AUX
iajs-812	22	15	any	any	DET
iajs-812	22	16	two	two	NUM
iajs-812	22	17	subsets	subset	NOUN
iajs-812	22	18	of	of	ADP
iajs-812	22	19	x	x	NOUN
iajs-812	22	20	,	,	PUNCT
iajs-812	22	21	then	then	ADV
iajs-812	22	22	:	:	PUNCT
iajs-812	22	23	pre	pre	ADJ
iajs-812	22	24	-	-	NOUN
iajs-812	22	25	cl	cl	VERB
iajs-812	22	26	a	a	DET
iajs-812	22	27	definition	definition	NOUN
iajs-812	22	28	2.6	2.6	NUM
iajs-812	23	1	[	[	X
iajs-812	23	2	4	4	NUM
iajs-812	23	3	]	]	X
iajs-812	23	4	:	:	PUNCT
iajs-812	23	5	a	a	DET
iajs-812	23	6	subset	subset	NOUN
iajs-812	23	7	a	a	PRON
iajs-812	23	8	of	of	ADP
iajs-812	23	9	a	a	DET
iajs-812	23	10	topological	topological	ADJ
iajs-812	23	11	space	space	NOUN
iajs-812	23	12	is	be	AUX
iajs-812	23	13	said	say	VERB
iajs-812	23	14	to	to	PART
iajs-812	23	15	be	be	AUX
iajs-812	23	16	semi	semi	ADJ
iajs-812	23	17	-	-	ADJ
iajs-812	23	18	p	p	ADJ
iajs-812	23	19	-	-	PUNCT
iajs-812	23	20	open	open	NOUN
iajs-812	23	21	set	set	NOUN
iajs-812	23	22	if	if	SCONJ
iajs-812	23	23	and	and	CCONJ
iajs-812	23	24	only	only	ADV
iajs-812	23	25	if	if	SCONJ
iajs-812	23	26	there	there	PRON
iajs-812	23	27	exists	exist	VERB
iajs-812	23	28	a	a	DET
iajs-812	23	29	pre	pre	ADJ
iajs-812	23	30	-	-	ADJ
iajs-812	23	31	open	open	ADJ
iajs-812	23	32	set	set	NOUN
iajs-812	23	33	in	in	ADP
iajs-812	23	34	x	x	NOUN
iajs-812	23	35	,	,	PUNCT
iajs-812	23	36	say	say	VERB
iajs-812	23	37	u	u	NOUN
iajs-812	23	38	,	,	PUNCT
iajs-812	23	39	such	such	ADJ
iajs-812	23	40	that	that	SCONJ
iajs-812	23	41	the	the	DET
iajs-812	23	42	family	family	NOUN
iajs-812	23	43	of	of	ADP
iajs-812	23	44	all	all	DET
iajs-812	23	45	semi	semi	ADJ
iajs-812	23	46	-	-	ADJ
iajs-812	23	47	p	p	ADJ
iajs-812	23	48	-	-	PUNCT
iajs-812	23	49	open	open	ADJ
iajs-812	23	50	sets	set	NOUN
iajs-812	23	51	of	of	ADP
iajs-812	23	52	x	x	SYM
iajs-812	23	53	is	be	AUX
iajs-812	23	54	denoted	denote	VERB
iajs-812	23	55	by	by	ADP
iajs-812	23	56	s	s	NOUN
iajs-812	23	57	-	-	PUNCT
iajs-812	23	58	p(x	p(x	NOUN
iajs-812	23	59	)	)	PUNCT
iajs-812	23	60	.	.	PUNCT
iajs-812	24	1	the	the	DET
iajs-812	24	2	complement	complement	NOUN
iajs-812	24	3	of	of	ADP
iajs-812	24	4	semi	semi	ADJ
iajs-812	24	5	-	-	ADJ
iajs-812	24	6	p	p	ADJ
iajs-812	24	7	-	-	PUNCT
iajs-812	24	8	open	open	ADJ
iajs-812	24	9	set	set	NOUN
iajs-812	24	10	is	be	AUX
iajs-812	24	11	called	call	VERB
iajs-812	24	12	semi	semi	ADJ
iajs-812	24	13	-	-	ADJ
iajs-812	24	14	p	p	ADJ
iajs-812	24	15	-	-	PUNCT
iajs-812	24	16	closed	close	VERB
iajs-812	24	17	set	set	NOUN
iajs-812	24	18	.	.	PUNCT
iajs-812	25	1	the	the	DET
iajs-812	25	2	family	family	NOUN
iajs-812	25	3	of	of	ADP
iajs-812	25	4	all	all	DET
iajs-812	25	5	semi	semi	ADJ
iajs-812	25	6	-	-	ADJ
iajs-812	25	7	p	p	ADJ
iajs-812	25	8	-	-	PUNCT
iajs-812	25	9	closed	close	VERB
iajs-812	25	10	sets	set	NOUN
iajs-812	25	11	of	of	ADP
iajs-812	25	12	x	x	SYM
iajs-812	25	13	is	be	AUX
iajs-812	25	14	denoted	denote	VERB
iajs-812	25	15	by	by	ADP
iajs-812	25	16	s	s	NOUN
iajs-812	25	17	-	-	PUNCT
iajs-812	25	18	p	p	NOUN
iajs-812	25	19	-	-	PUNCT
iajs-812	25	20	c(x	c(x	NOUN
iajs-812	25	21	)	)	PUNCT
iajs-812	25	22	.	.	PUNCT
iajs-812	26	1	proposition	proposition	NOUN
iajs-812	26	2	2.7	2.7	NUM
iajs-812	27	1	[	[	X
iajs-812	27	2	4	4	NUM
iajs-812	27	3	]	]	PUNCT
iajs-812	27	4	:	:	PUNCT
iajs-812	27	5	1every	1every	NUM
iajs-812	27	6	open	open	ADJ
iajs-812	27	7	(	(	PUNCT
iajs-812	27	8	closed	closed	ADJ
iajs-812	27	9	)	)	PUNCT
iajs-812	27	10	set	set	NOUN
iajs-812	27	11	is	be	AUX
iajs-812	27	12	semi	semi	ADJ
iajs-812	27	13	-	-	ADJ
iajs-812	27	14	p	p	ADJ
iajs-812	27	15	-	-	PUNCT
iajs-812	27	16	open	open	ADJ
iajs-812	27	17	(	(	PUNCT
iajs-812	27	18	closed	closed	ADJ
iajs-812	27	19	)	)	PUNCT
iajs-812	27	20	set	set	VERB
iajs-812	27	21	respectively	respectively	ADV
iajs-812	27	22	.	.	PUNCT
iajs-812	28	1	2every	2every	NUM
iajs-812	28	2	pre	pre	ADJ
iajs-812	28	3	-	-	ADJ
iajs-812	28	4	open	open	ADJ
iajs-812	28	5	(	(	PUNCT
iajs-812	28	6	pre	pre	ADJ
iajs-812	28	7	-	-	ADJ
iajs-812	28	8	closed	closed	ADJ
iajs-812	28	9	)	)	PUNCT
iajs-812	28	10	set	set	NOUN
iajs-812	28	11	is	be	AUX
iajs-812	28	12	semi	semi	ADJ
iajs-812	28	13	-	-	ADJ
iajs-812	28	14	p	p	ADJ
iajs-812	28	15	-	-	PUNCT
iajs-812	28	16	open	open	ADJ
iajs-812	28	17	(	(	PUNCT
iajs-812	28	18	semi	semi	ADJ
iajs-812	28	19	-	-	ADJ
iajs-812	28	20	p	p	ADJ
iajs-812	28	21	-	-	PUNCT
iajs-812	28	22	closed	closed	ADJ
iajs-812	28	23	)	)	PUNCT
iajs-812	28	24	set	set	VERB
iajs-812	28	25	respectively	respectively	ADV
iajs-812	28	26	.	.	PUNCT
iajs-812	29	1	also	also	ADV
iajs-812	29	2	,	,	PUNCT
iajs-812	29	3	the	the	DET
iajs-812	29	4	converse	converse	NOUN
iajs-812	29	5	of	of	ADP
iajs-812	29	6	(	(	PUNCT
iajs-812	29	7	1	1	NUM
iajs-812	29	8	)	)	PUNCT
iajs-812	29	9	and	and	CCONJ
iajs-812	29	10	(	(	PUNCT
iajs-812	29	11	2	2	X
iajs-812	29	12	)	)	PUNCT
iajs-812	29	13	is	be	AUX
iajs-812	29	14	not	not	PART
iajs-812	29	15	true	true	ADJ
iajs-812	29	16	in	in	ADP
iajs-812	29	17	general	general	ADJ
iajs-812	29	18	.	.	PUNCT
iajs-812	30	1	proposition	proposition	NOUN
iajs-812	30	2	2.8	2.8	NUM
iajs-812	30	3	:	:	PUNCT
iajs-812	30	4	the	the	DET
iajs-812	30	5	union	union	NOUN
iajs-812	30	6	of	of	ADP
iajs-812	30	7	any	any	DET
iajs-812	30	8	family	family	NOUN
iajs-812	30	9	of	of	ADP
iajs-812	30	10	semi	semi	ADJ
iajs-812	30	11	-	-	ADJ
iajs-812	30	12	p	p	ADJ
iajs-812	30	13	-	-	PUNCT
iajs-812	30	14	open	open	ADJ
iajs-812	30	15	sets	set	NOUN
iajs-812	30	16	is	be	AUX
iajs-812	30	17	semi	semi	ADJ
iajs-812	30	18	-	-	ADJ
iajs-812	30	19	p	p	ADJ
iajs-812	30	20	-	-	PUNCT
iajs-812	30	21	open	open	ADJ
iajs-812	30	22	set	set	NOUN
iajs-812	30	23	.	.	PUNCT
iajs-812	31	1	proof	proof	NOUN
iajs-812	31	2	:	:	PUNCT
iajs-812	31	3	let	let	AUX
iajs-812	31	4	be	be	AUX
iajs-812	31	5	any	any	DET
iajs-812	31	6	family	family	NOUN
iajs-812	31	7	of	of	ADP
iajs-812	31	8	semi	semi	ADJ
iajs-812	31	9	-	-	ADJ
iajs-812	31	10	p	p	ADJ
iajs-812	31	11	-	-	PUNCT
iajs-812	31	12	open	open	ADJ
iajs-812	31	13	sets	set	NOUN
iajs-812	31	14	in	in	ADP
iajs-812	31	15	x	x	NOUN
iajs-812	31	16	,	,	PUNCT
iajs-812	31	17	we	we	PRON
iajs-812	31	18	must	must	AUX
iajs-812	31	19	prove	prove	VERB
iajs-812	31	20	is	be	AUX
iajs-812	31	21	a	a	DET
iajs-812	31	22	semi	semi	ADJ
iajs-812	31	23	-	-	ADJ
iajs-812	31	24	p	p	ADJ
iajs-812	31	25	-	-	PUNCT
iajs-812	31	26	open	open	NOUN
iajs-812	31	27	set	set	NOUN
iajs-812	31	28	,	,	PUNCT
iajs-812	31	29	since	since	SCONJ
iajs-812	31	30	is	be	AUX
iajs-812	31	31	semi	semi	ADJ
iajs-812	31	32	-	-	ADJ
iajs-812	31	33	p	p	ADJ
iajs-812	31	34	-	-	PUNCT
iajs-812	31	35	open	open	NOUN
iajs-812	31	36	set	set	NOUN
iajs-812	31	37	,	,	PUNCT
iajs-812	31	38	for	for	ADP
iajs-812	31	39	all	all	PRON
iajs-812	31	40	,	,	PUNCT
iajs-812	31	41	which	which	PRON
iajs-812	31	42	implies	imply	VERB
iajs-812	31	43	there	there	PRON
iajs-812	31	44	exists	exist	VERB
iajs-812	31	45	a	a	DET
iajs-812	31	46	preopen	preopen	NOUN
iajs-812	31	47	set	set	NOUN
iajs-812	31	48	such	such	ADJ
iajs-812	31	49	that	that	PRON
iajs-812	31	50	.	.	PUNCT
iajs-812	32	1	thus	thus	ADV
iajs-812	32	2	and	and	CCONJ
iajs-812	32	3	from	from	ADP
iajs-812	32	4	(	(	PUNCT
iajs-812	32	5	proposition	proposition	NOUN
iajs-812	32	6	2.3	2.3	NUM
iajs-812	32	7	and	and	CCONJ
iajs-812	32	8	2.5	2.5	NUM
iajs-812	32	9	)	)	PUNCT
iajs-812	32	10	we	we	PRON
iajs-812	32	11	have	have	VERB
iajs-812	32	12	a	a	DET
iajs-812	32	13	pre	pre	ADJ
iajs-812	32	14	-	-	ADJ
iajs-812	32	15	open	open	ADJ
iajs-812	32	16	set	set	NOUN
iajs-812	32	17	such	such	ADJ
iajs-812	32	18	that	that	SCONJ
iajs-812	32	19	hence	hence	ADV
iajs-812	32	20	is	be	AUX
iajs-812	32	21	a	a	DET
iajs-812	32	22	semip	semip	NOUN
iajs-812	32	23	-	-	PUNCT
iajs-812	32	24	open	open	ADJ
iajs-812	32	25	set	set	NOUN
iajs-812	32	26	.	.	PUNCT
iajs-812	33	1	■	■	PUNCT
iajs-812	33	2	definition	definition	NOUN
iajs-812	33	3	2.9	2.9	NUM
iajs-812	34	1	[	[	NOUN
iajs-812	34	2	4	4	NUM
iajs-812	34	3	]	]	PUNCT
iajs-812	34	4	:	:	PUNCT
iajs-812	34	5	let	let	AUX
iajs-812	34	6	be	be	AUX
iajs-812	34	7	a	a	DET
iajs-812	34	8	topological	topological	ADJ
iajs-812	34	9	space	space	NOUN
iajs-812	34	10	and	and	CCONJ
iajs-812	34	11	let	let	VERB
iajs-812	34	12	a	a	PRON
iajs-812	34	13	be	be	AUX
iajs-812	34	14	any	any	DET
iajs-812	34	15	subset	subset	NOUN
iajs-812	34	16	of	of	ADP
iajs-812	34	17	x	x	PRON
iajs-812	34	18	,	,	PUNCT
iajs-812	34	19	then	then	ADV
iajs-812	34	20	:	:	PUNCT
iajs-812	34	21	1the	1the	PROPN
iajs-812	34	22	union	union	NOUN
iajs-812	34	23	of	of	ADP
iajs-812	34	24	all	all	DET
iajs-812	34	25	semi	semi	ADJ
iajs-812	34	26	-	-	ADJ
iajs-812	34	27	p	p	ADJ
iajs-812	34	28	-	-	PUNCT
iajs-812	34	29	open	open	ADJ
iajs-812	34	30	sets	set	NOUN
iajs-812	34	31	contained	contain	VERB
iajs-812	34	32	in	in	ADP
iajs-812	34	33	a	a	PRON
iajs-812	34	34	is	be	AUX
iajs-812	34	35	called	call	VERB
iajs-812	34	36	the	the	DET
iajs-812	34	37	semi	semi	ADJ
iajs-812	34	38	-	-	ADJ
iajs-812	34	39	p	p	ADJ
iajs-812	34	40	-	-	NOUN
iajs-812	34	41	interior	interior	NOUN
iajs-812	34	42	of	of	ADP
iajs-812	34	43	a	a	PRON
iajs-812	34	44	,	,	PUNCT
iajs-812	34	45	denoted	denote	VERB
iajs-812	34	46	by	by	ADP
iajs-812	34	47	semi	semi	ADJ
iajs-812	34	48	-	-	ADJ
iajs-812	34	49	p	p	ADJ
iajs-812	34	50	-	-	PUNCT
iajs-812	34	51	int	int	NOUN
iajs-812	34	52	a.	a.	NOUN
iajs-812	34	53	2the	2the	NUM
iajs-812	34	54	intersection	intersection	NOUN
iajs-812	34	55	of	of	ADP
iajs-812	34	56	all	all	DET
iajs-812	34	57	semi	semi	ADJ
iajs-812	34	58	-	-	ADJ
iajs-812	34	59	p	p	ADJ
iajs-812	34	60	-	-	PUNCT
iajs-812	34	61	closed	close	VERB
iajs-812	34	62	sets	set	NOUN
iajs-812	34	63	containing	contain	VERB
iajs-812	34	64	a	a	PRON
iajs-812	34	65	is	be	AUX
iajs-812	34	66	called	call	VERB
iajs-812	34	67	the	the	DET
iajs-812	34	68	semi	semi	ADJ
iajs-812	34	69	-	-	ADJ
iajs-812	34	70	p	p	ADJ
iajs-812	34	71	-	-	PUNCT
iajs-812	34	72	closure	closure	NOUN
iajs-812	34	73	of	of	ADP
iajs-812	34	74	a	a	PRON
iajs-812	34	75	,	,	PUNCT
iajs-812	34	76	and	and	CCONJ
iajs-812	34	77	denoted	denote	VERB
iajs-812	34	78	by	by	ADP
iajs-812	34	79	semi	semi	ADJ
iajs-812	34	80	-	-	ADJ
iajs-812	34	81	p	p	ADJ
iajs-812	34	82	-	-	PUNCT
iajs-812	34	83	cl	cl	NOUN
iajs-812	34	84	a.	a.	NOUN
iajs-812	34	85	definition	definition	NOUN
iajs-812	34	86	2.10	2.10	NUM
iajs-812	34	87	[	[	NOUN
iajs-812	34	88	4	4	NUM
iajs-812	34	89	]	]	PUNCT
iajs-812	34	90	:	:	PUNCT
iajs-812	34	91	let	let	AUX
iajs-812	34	92	be	be	AUX
iajs-812	34	93	a	a	DET
iajs-812	34	94	topological	topological	ADJ
iajs-812	34	95	space	space	NOUN
iajs-812	34	96	and	and	CCONJ
iajs-812	34	97	let	let	VERB
iajs-812	34	98	.	.	PUNCT
iajs-812	35	1	a	a	DET
iajs-812	35	2	subset	subset	NOUN
iajs-812	35	3	n	n	NOUN
iajs-812	35	4	of	of	ADP
iajs-812	35	5	x	x	VERB
iajs-812	35	6	is	be	AUX
iajs-812	35	7	said	say	VERB
iajs-812	35	8	to	to	PART
iajs-812	35	9	be	be	AUX
iajs-812	35	10	semi	semi	ADJ
iajs-812	35	11	-	-	ADJ
iajs-812	35	12	pneighborhood	pneighborhood	ADJ
iajs-812	35	13	of	of	ADP
iajs-812	35	14	x	x	PRON
iajs-812	35	15	if	if	SCONJ
iajs-812	35	16	and	and	CCONJ
iajs-812	35	17	only	only	ADV
iajs-812	35	18	if	if	SCONJ
iajs-812	35	19	there	there	PRON
iajs-812	35	20	exists	exist	VERB
iajs-812	35	21	a	a	DET
iajs-812	35	22	semi	semi	ADJ
iajs-812	35	23	-	-	ADJ
iajs-812	35	24	p	p	ADJ
iajs-812	35	25	-	-	PUNCT
iajs-812	35	26	open	open	NOUN
iajs-812	35	27	set	set	NOUN
iajs-812	35	28	g	g	NOUN
iajs-812	35	29	,	,	PUNCT
iajs-812	35	30	such	such	ADJ
iajs-812	35	31	that	that	SCONJ
iajs-812	35	32	we	we	PRON
iajs-812	35	33	shall	shall	AUX
iajs-812	35	34	use	use	VERB
iajs-812	35	35	the	the	DET
iajs-812	35	36	symbol	symbol	NOUN
iajs-812	35	37	nbd	nbd	PROPN
iajs-812	35	38	.	.	PUNCT
iajs-812	36	1	instead	instead	ADV
iajs-812	36	2	of	of	ADP
iajs-812	36	3	the	the	DET
iajs-812	36	4	word	word	NOUN
iajs-812	36	5	neighborhood	neighborhood	NOUN
iajs-812	36	6	.	.	PUNCT
iajs-812	37	1	if	if	SCONJ
iajs-812	37	2	n	n	NOUN
iajs-812	37	3	is	be	AUX
iajs-812	37	4	semi	semi	ADJ
iajs-812	37	5	-	-	ADJ
iajs-812	37	6	p	p	ADJ
iajs-812	37	7	-	-	PUNCT
iajs-812	37	8	open	open	ADJ
iajs-812	37	9	subset	subset	NOUN
iajs-812	37	10	of	of	ADP
iajs-812	37	11	x	x	PRON
iajs-812	37	12	,	,	PUNCT
iajs-812	37	13	then	then	ADV
iajs-812	37	14	n	n	PRON
iajs-812	37	15	is	be	AUX
iajs-812	37	16	a	a	DET
iajs-812	37	17	semi	semi	ADJ
iajs-812	37	18	-	-	ADJ
iajs-812	37	19	p	p	ADJ
iajs-812	37	20	-	-	PUNCT
iajs-812	37	21	open	open	ADJ
iajs-812	37	22	nbd	nbd	PROPN
iajs-812	37	23	of	of	ADP
iajs-812	37	24	x.	x.	PROPN
iajs-812	37	25	ibn	ibn	PROPN
iajs-812	37	26	alhaitham	alhaitham	PROPN
iajs-812	37	27	j.	j.	PROPN
iajs-812	37	28	for	for	ADP
iajs-812	37	29	pure	pure	ADJ
iajs-812	37	30	&	&	CCONJ
iajs-812	37	31	appl	appl	PROPN
iajs-812	37	32	.	.	PUNCT
iajs-812	38	1	sci	sci	PROPN
iajs-812	38	2	.	.	PUNCT
iajs-812	38	3	vol.24	vol.24	NOUN
iajs-812	38	4	(	(	PUNCT
iajs-812	38	5	3	3	NUM
iajs-812	38	6	)	)	PUNCT
iajs-812	38	7	2011	2011	NUM
iajs-812	38	8	proposition	proposition	NOUN
iajs-812	38	9	2.11	2.11	NUM
iajs-812	38	10	:	:	PUNCT
iajs-812	38	11	let	let	AUX
iajs-812	38	12	be	be	AUX
iajs-812	38	13	a	a	DET
iajs-812	38	14	topological	topological	ADJ
iajs-812	38	15	space	space	NOUN
iajs-812	38	16	,	,	PUNCT
iajs-812	38	17	then	then	ADV
iajs-812	38	18	every	every	DET
iajs-812	38	19	semi	semi	ADJ
iajs-812	38	20	-	-	ADJ
iajs-812	38	21	p	p	ADJ
iajs-812	38	22	-	-	PUNCT
iajs-812	38	23	nbd	nbd	PROPN
iajs-812	38	24	is	be	AUX
iajs-812	38	25	a	a	DET
iajs-812	38	26	semi	semi	ADJ
iajs-812	38	27	-	-	ADJ
iajs-812	38	28	p	p	ADJ
iajs-812	38	29	-	-	PUNCT
iajs-812	38	30	open	open	ADJ
iajs-812	38	31	set	set	NOUN
iajs-812	38	32	.	.	PUNCT
iajs-812	39	1	proof	proof	NOUN
iajs-812	39	2	:	:	PUNCT
iajs-812	39	3	let	let	VERB
iajs-812	39	4	n	n	PRON
iajs-812	39	5	be	be	AUX
iajs-812	39	6	any	any	DET
iajs-812	39	7	semi	semi	ADJ
iajs-812	39	8	-	-	ADJ
iajs-812	39	9	p	p	ADJ
iajs-812	39	10	-	-	PUNCT
iajs-812	39	11	nbds	nbds	NOUN
iajs-812	39	12	for	for	ADP
iajs-812	39	13	each	each	PRON
iajs-812	39	14	of	of	ADP
iajs-812	39	15	its	its	PRON
iajs-812	39	16	points	point	NOUN
iajs-812	39	17	,	,	PUNCT
iajs-812	39	18	that	that	PRON
iajs-812	39	19	is	be	AUX
iajs-812	39	20	means	mean	NOUN
iajs-812	39	21	for	for	ADP
iajs-812	39	22	each	each	PRON
iajs-812	39	23	,	,	PUNCT
iajs-812	39	24	there	there	PRON
iajs-812	39	25	exists	exist	VERB
iajs-812	39	26	a	a	DET
iajs-812	39	27	semi	semi	ADJ
iajs-812	39	28	-	-	ADJ
iajs-812	39	29	popen	popen	ADJ
iajs-812	39	30	set	set	NOUN
iajs-812	39	31	g	g	PROPN
iajs-812	39	32	such	such	ADJ
iajs-812	39	33	that	that	SCONJ
iajs-812	39	34	now	now	ADV
iajs-812	39	35	we	we	PRON
iajs-812	39	36	must	must	AUX
iajs-812	39	37	prove	prove	VERB
iajs-812	39	38	n	n	PRON
iajs-812	39	39	is	be	AUX
iajs-812	39	40	a	a	DET
iajs-812	39	41	semi	semi	ADJ
iajs-812	39	42	-	-	ADJ
iajs-812	39	43	p	p	ADJ
iajs-812	39	44	-	-	PUNCT
iajs-812	39	45	open	open	NOUN
iajs-812	39	46	set	set	NOUN
iajs-812	39	47	,	,	PUNCT
iajs-812	39	48	since	since	SCONJ
iajs-812	39	49	and	and	CCONJ
iajs-812	39	50	since	since	SCONJ
iajs-812	39	51	n	n	PRON
iajs-812	39	52	is	be	AUX
iajs-812	39	53	a	a	DET
iajs-812	39	54	semi	semi	ADJ
iajs-812	39	55	-	-	NOUN
iajs-812	39	56	pnbd	pnbd	NOUN
iajs-812	39	57	for	for	ADP
iajs-812	39	58	all	all	PRON
iajs-812	39	59	.	.	PUNCT
iajs-812	40	1	thus	thus	ADV
iajs-812	40	2	,	,	PUNCT
iajs-812	40	3	and	and	CCONJ
iajs-812	40	4	from	from	ADP
iajs-812	40	5	(	(	PUNCT
iajs-812	40	6	proposition	proposition	NOUN
iajs-812	40	7	2.8	2.8	NUM
iajs-812	40	8	)	)	PUNCT
iajs-812	40	9	we	we	PRON
iajs-812	40	10	have	have	VERB
iajs-812	40	11	n	n	PROPN
iajs-812	40	12	is	be	AUX
iajs-812	40	13	a	a	DET
iajs-812	40	14	semi	semi	ADJ
iajs-812	40	15	-	-	ADJ
iajs-812	40	16	p	p	ADJ
iajs-812	40	17	-	-	PUNCT
iajs-812	40	18	open	open	ADJ
iajs-812	40	19	set	set	NOUN
iajs-812	40	20	.	.	PUNCT
iajs-812	41	1	■	■	PUNCT
iajs-812	41	2	definition	definition	NOUN
iajs-812	41	3	2.12	2.12	NUM
iajs-812	41	4	[	[	X
iajs-812	41	5	1	1	NUM
iajs-812	41	6	]	]	PUNCT
iajs-812	41	7	:	:	PUNCT
iajs-812	41	8	let	let	VERB
iajs-812	41	9	x	x	PRON
iajs-812	41	10	be	be	AUX
iajs-812	41	11	a	a	DET
iajs-812	41	12	non	non	ADJ
iajs-812	41	13	-	-	ADJ
iajs-812	41	14	empty	empty	ADJ
iajs-812	41	15	set	set	NOUN
iajs-812	41	16	,	,	PUNCT
iajs-812	41	17	let	let	VERB
iajs-812	41	18	be	be	AUX
iajs-812	41	19	any	any	DET
iajs-812	41	20	two	two	NUM
iajs-812	41	21	topologies	topology	NOUN
iajs-812	41	22	on	on	ADP
iajs-812	41	23	x	x	NOUN
iajs-812	41	24	,	,	PUNCT
iajs-812	41	25	then	then	ADV
iajs-812	41	26	is	be	AUX
iajs-812	41	27	called	call	VERB
iajs-812	41	28	a	a	DET
iajs-812	41	29	bitopological	bitopological	ADJ
iajs-812	41	30	space	space	NOUN
iajs-812	41	31	.	.	PUNCT
iajs-812	42	1	note	note	VERB
iajs-812	42	2	2.13	2.13	NUM
iajs-812	42	3	:	:	PUNCT
iajs-812	42	4	in	in	ADP
iajs-812	42	5	the	the	DET
iajs-812	42	6	space	space	NOUN
iajs-812	42	7	,	,	PUNCT
iajs-812	42	8	we	we	PRON
iajs-812	42	9	shall	shall	AUX
iajs-812	42	10	denote	denote	VERB
iajs-812	42	11	to	to	ADP
iajs-812	42	12	the	the	DET
iajs-812	42	13	set	set	NOUN
iajs-812	42	14	of	of	ADP
iajs-812	42	15	all	all	DET
iajs-812	42	16	semi	semi	ADJ
iajs-812	42	17	-	-	ADJ
iajs-812	42	18	popen	popen	ADJ
iajs-812	42	19	sets	set	NOUN
iajs-812	42	20	in	in	ADP
iajs-812	42	21	)	)	PUNCT
iajs-812	42	22	by	by	ADP
iajs-812	42	23	s	s	NOUN
iajs-812	42	24	-	-	PUNCT
iajs-812	42	25	p(x	p(x	NOUN
iajs-812	42	26	,	,	PUNCT
iajs-812	42	27	(	(	PUNCT
iajs-812	42	28	s	s	NOUN
iajs-812	42	29	-	-	PUNCT
iajs-812	42	30	p(x	p(x	NOUN
iajs-812	42	31	,	,	PUNCT
iajs-812	42	32	)	)	PUNCT
iajs-812	42	33	)	)	PUNCT
iajs-812	42	34	respectively	respectively	ADV
iajs-812	42	35	.	.	PUNCT
iajs-812	43	1	definition	definition	NOUN
iajs-812	43	2	2.14	2.14	NUM
iajs-812	43	3	[	[	X
iajs-812	43	4	2	2	NUM
iajs-812	43	5	]	]	PUNCT
iajs-812	43	6	:	:	PUNCT
iajs-812	43	7	a	a	DET
iajs-812	43	8	bitopological	bitopological	ADJ
iajs-812	43	9	space	space	NOUN
iajs-812	43	10	is	be	AUX
iajs-812	43	11	said	say	VERB
iajs-812	43	12	to	to	PART
iajs-812	43	13	be	be	AUX
iajs-812	43	14	:	:	PUNCT
iajs-812	43	15	1pairwise	1pairwise	NUM
iajs-812	43	16	if	if	SCONJ
iajs-812	43	17	for	for	ADP
iajs-812	43	18	every	every	DET
iajs-812	43	19	pair	pair	NOUN
iajs-812	43	20	of	of	ADP
iajs-812	43	21	points	point	NOUN
iajs-812	43	22	x	x	PUNCT
iajs-812	43	23	and	and	CCONJ
iajs-812	43	24	y	y	PROPN
iajs-812	43	25	in	in	ADP
iajs-812	43	26	x	x	PUNCT
iajs-812	43	27	such	such	ADJ
iajs-812	43	28	that	that	SCONJ
iajs-812	43	29	there	there	PRON
iajs-812	43	30	exists	exist	VERB
iajs-812	43	31	a	a	DET
iajs-812	43	32	-open	-open	ADJ
iajs-812	43	33	set	set	NOUN
iajs-812	43	34	containing	contain	VERB
iajs-812	43	35	x	x	PUNCT
iajs-812	43	36	but	but	CCONJ
iajs-812	43	37	not	not	PART
iajs-812	43	38	y	y	PROPN
iajs-812	43	39	or	or	CCONJ
iajs-812	43	40	y	y	PROPN
iajs-812	43	41	but	but	CCONJ
iajs-812	43	42	not	not	PART
iajs-812	43	43	x	x	X
iajs-812	43	44	or	or	CCONJ
iajs-812	43	45	a	a	DET
iajs-812	43	46	-open	-open	ADJ
iajs-812	43	47	set	set	NOUN
iajs-812	43	48	containing	contain	VERB
iajs-812	43	49	y	y	PROPN
iajs-812	43	50	but	but	CCONJ
iajs-812	43	51	not	not	PART
iajs-812	43	52	x	x	PUNCT
iajs-812	43	53	or	or	CCONJ
iajs-812	43	54	x	x	NOUN
iajs-812	43	55	but	but	CCONJ
iajs-812	43	56	not	not	PART
iajs-812	43	57	y.	y.	NOUN
iajs-812	43	58	2pairwise	2pairwise	NUM
iajs-812	43	59	if	if	SCONJ
iajs-812	43	60	for	for	ADP
iajs-812	43	61	every	every	DET
iajs-812	43	62	pair	pair	NOUN
iajs-812	43	63	of	of	ADP
iajs-812	43	64	points	point	NOUN
iajs-812	43	65	x	x	PUNCT
iajs-812	43	66	and	and	CCONJ
iajs-812	43	67	y	y	PROPN
iajs-812	43	68	in	in	ADP
iajs-812	43	69	x	x	PUNCT
iajs-812	43	70	such	such	ADJ
iajs-812	43	71	that	that	SCONJ
iajs-812	43	72	there	there	PRON
iajs-812	43	73	exists	exist	VERB
iajs-812	43	74	a	a	DET
iajs-812	43	75	-open	-open	ADJ
iajs-812	43	76	set	set	VERB
iajs-812	43	77	u	u	NOUN
iajs-812	43	78	and	and	CCONJ
iajs-812	43	79	a	a	DET
iajs-812	43	80	-open	-open	NOUN
iajs-812	43	81	set	set	VERB
iajs-812	43	82	v	v	ADP
iajs-812	43	83	such	such	DET
iajs-812	43	84	that	that	DET
iajs-812	43	85	definition	definition	NOUN
iajs-812	43	86	2.15[1	2.15[1	NUM
iajs-812	43	87	]	]	X
iajs-812	43	88	:	:	PUNCT
iajs-812	43	89	a	a	DET
iajs-812	43	90	bitopological	bitopological	ADJ
iajs-812	43	91	space	space	NOUN
iajs-812	43	92	is	be	AUX
iajs-812	43	93	said	say	VERB
iajs-812	43	94	to	to	PART
iajs-812	43	95	be	be	AUX
iajs-812	43	96	:	:	PUNCT
iajs-812	43	97	1pairwise	1pairwise	NUM
iajs-812	43	98	if	if	SCONJ
iajs-812	43	99	every	every	DET
iajs-812	43	100	two	two	NUM
iajs-812	43	101	distinct	distinct	ADJ
iajs-812	43	102	points	point	NOUN
iajs-812	43	103	in	in	ADP
iajs-812	43	104	x	x	PRON
iajs-812	43	105	can	can	AUX
iajs-812	43	106	be	be	AUX
iajs-812	43	107	separated	separate	VERB
iajs-812	43	108	by	by	ADP
iajs-812	43	109	disjoint	disjoint	NOUN
iajs-812	43	110	open	open	ADJ
iajs-812	43	111	set	set	VERB
iajs-812	43	112	and	and	CCONJ
iajs-812	43	113	-open	-open	ADJ
iajs-812	43	114	sets	set	NOUN
iajs-812	43	115	.	.	PUNCT
iajs-812	44	1	2pairwise	2pairwise	NUM
iajs-812	44	2	regular	regular	ADJ
iajs-812	44	3	space	space	NOUN
iajs-812	44	4	,	,	PUNCT
iajs-812	44	5	if	if	SCONJ
iajs-812	44	6	for	for	ADP
iajs-812	44	7	each	each	DET
iajs-812	44	8	point	point	NOUN
iajs-812	44	9	and	and	CCONJ
iajs-812	44	10	each	each	PRON
iajs-812	44	11	-closed	-close	VERB
iajs-812	44	12	set	set	NOUN
iajs-812	44	13	f	f	NOUN
iajs-812	44	14	not	not	PART
iajs-812	44	15	containing	contain	VERB
iajs-812	44	16	x	x	X
iajs-812	44	17	,	,	PUNCT
iajs-812	44	18	there	there	PRON
iajs-812	44	19	exists	exist	VERB
iajs-812	44	20	a	a	DET
iajs-812	44	21	-open	-open	ADJ
iajs-812	44	22	set	set	VERB
iajs-812	44	23	u	u	NOUN
iajs-812	44	24	and	and	CCONJ
iajs-812	44	25	-open	-open	NOUN
iajs-812	44	26	set	set	VERB
iajs-812	44	27	v	v	ADP
iajs-812	44	28	such	such	ADJ
iajs-812	44	29	that	that	SCONJ
iajs-812	44	30	where	where	SCONJ
iajs-812	44	31	3pairwise	3pairwise	NUM
iajs-812	44	32	normal	normal	ADJ
iajs-812	44	33	space	space	NOUN
iajs-812	44	34	,	,	PUNCT
iajs-812	44	35	if	if	SCONJ
iajs-812	44	36	for	for	ADP
iajs-812	44	37	each	each	DET
iajs-812	44	38	-closed	-close	VERB
iajs-812	44	39	set	set	VERB
iajs-812	44	40	a	a	DET
iajs-812	44	41	and	and	CCONJ
iajs-812	44	42	-closed	-closed	ADJ
iajs-812	44	43	set	set	NOUN
iajs-812	44	44	b	b	NOUN
iajs-812	44	45	such	such	ADJ
iajs-812	44	46	that	that	SCONJ
iajs-812	44	47	there	there	PRON
iajs-812	44	48	exist	exist	VERB
iajs-812	44	49	sets	set	NOUN
iajs-812	44	50	u	u	NOUN
iajs-812	44	51	and	and	CCONJ
iajs-812	44	52	v	v	ADP
iajs-812	44	53	such	such	ADJ
iajs-812	44	54	that	that	SCONJ
iajs-812	44	55	u	u	NOUN
iajs-812	44	56	is	be	AUX
iajs-812	44	57	-open	-open	ADJ
iajs-812	44	58	,	,	PUNCT
iajs-812	44	59	v	v	NOUN
iajs-812	44	60	is	be	AUX
iajs-812	44	61	-open	-open	ADJ
iajs-812	44	62	,	,	PUNCT
iajs-812	44	63	3	3	NUM
iajs-812	44	64	-	-	PUNCT
iajs-812	44	65	pairwise	pairwise	NOUN
iajs-812	44	66	semi	semi	ADJ
iajs-812	44	67	-	-	ADJ
iajs-812	44	68	p	p	ADJ
iajs-812	44	69	-	-	PUNCT
iajs-812	44	70	separation	separation	NOUN
iajs-812	44	71	axioms	axiom	NOUN
iajs-812	44	72	we	we	PRON
iajs-812	44	73	begin	begin	VERB
iajs-812	44	74	with	with	ADP
iajs-812	44	75	the	the	DET
iajs-812	44	76	definition	definition	NOUN
iajs-812	44	77	of	of	ADP
iajs-812	44	78	pairwise	pairwise	PROPN
iajs-812	44	79	semi	semi	NOUN
iajs-812	44	80	-	-	NOUN
iajs-812	44	81	pspaces	pspace	NOUN
iajs-812	44	82	.	.	PUNCT
iajs-812	45	1	definition	definition	NOUN
iajs-812	45	2	3.1	3.1	NUM
iajs-812	45	3	:	:	PUNCT
iajs-812	45	4	a	a	DET
iajs-812	45	5	space	space	NOUN
iajs-812	45	6	is	be	AUX
iajs-812	45	7	called	call	VERB
iajs-812	45	8	pairwise	pairwise	NOUN
iajs-812	45	9	semi	semi	NOUN
iajs-812	45	10	-	-	NOUN
iajs-812	45	11	pspace	pspace	NOUN
iajs-812	45	12	if	if	SCONJ
iajs-812	45	13	for	for	ADP
iajs-812	45	14	any	any	DET
iajs-812	45	15	pair	pair	NOUN
iajs-812	45	16	of	of	ADP
iajs-812	45	17	distinct	distinct	ADJ
iajs-812	45	18	points	point	NOUN
iajs-812	45	19	x	x	PUNCT
iajs-812	45	20	and	and	CCONJ
iajs-812	45	21	y	y	PROPN
iajs-812	45	22	in	in	ADP
iajs-812	45	23	x	x	SYM
iajs-812	45	24	,	,	PUNCT
iajs-812	45	25	there	there	PRON
iajs-812	45	26	exists	exist	VERB
iajs-812	45	27	a	a	DET
iajs-812	45	28	-semi	-semi	NOUN
iajs-812	45	29	-	-	PUNCT
iajs-812	45	30	p	p	NOUN
iajs-812	45	31	-	-	PUNCT
iajs-812	45	32	open	open	NOUN
iajs-812	45	33	set	set	NOUN
iajs-812	45	34	or	or	CCONJ
iajs-812	45	35	-semi	-semi	NOUN
iajs-812	45	36	-	-	PUNCT
iajs-812	45	37	p	p	X
iajs-812	45	38	-	-	PUNCT
iajs-812	45	39	open	open	ADJ
iajs-812	45	40	set	set	NOUN
iajs-812	45	41	which	which	PRON
iajs-812	45	42	contains	contain	VERB
iajs-812	45	43	one	one	NUM
iajs-812	45	44	of	of	ADP
iajs-812	45	45	them	they	PRON
iajs-812	45	46	but	but	CCONJ
iajs-812	45	47	not	not	PART
iajs-812	45	48	the	the	DET
iajs-812	45	49	other	other	ADJ
iajs-812	45	50	.	.	PUNCT
iajs-812	46	1	ibn	ibn	PROPN
iajs-812	46	2	alhaitham	alhaitham	PROPN
iajs-812	46	3	j.	j.	PROPN
iajs-812	46	4	for	for	ADP
iajs-812	46	5	pure	pure	ADJ
iajs-812	46	6	&	&	CCONJ
iajs-812	46	7	appl	appl	PROPN
iajs-812	46	8	.	.	PUNCT
iajs-812	47	1	sci	sci	PROPN
iajs-812	47	2	.	.	PUNCT
iajs-812	47	3	vol.24	vol.24	NOUN
iajs-812	47	4	(	(	PUNCT
iajs-812	47	5	3	3	NUM
iajs-812	47	6	)	)	PUNCT
iajs-812	47	7	2011	2011	NUM
iajs-812	47	8	proposition	proposition	NOUN
iajs-812	47	9	3.2	3.2	NUM
iajs-812	47	10	:	:	PUNCT
iajs-812	47	11	if	if	SCONJ
iajs-812	47	12	a	a	DET
iajs-812	47	13	space	space	NOUN
iajs-812	47	14	is	be	AUX
iajs-812	47	15	pairwise	pairwise	NOUN
iajs-812	47	16	space	space	NOUN
iajs-812	47	17	,	,	PUNCT
iajs-812	47	18	then	then	ADV
iajs-812	47	19	is	be	AUX
iajs-812	47	20	pairwise	pairwise	NOUN
iajs-812	47	21	semi	semi	ADJ
iajs-812	47	22	-	-	NOUN
iajs-812	47	23	pspace	pspace	NOUN
iajs-812	47	24	.	.	PUNCT
iajs-812	48	1	proof	proof	NOUN
iajs-812	48	2	:	:	PUNCT
iajs-812	48	3	for	for	ADP
iajs-812	48	4	any	any	DET
iajs-812	48	5	such	such	ADJ
iajs-812	48	6	that	that	PRON
iajs-812	48	7	,	,	PUNCT
iajs-812	48	8	we	we	PRON
iajs-812	48	9	must	must	AUX
iajs-812	48	10	prove	prove	VERB
iajs-812	48	11	there	there	PRON
iajs-812	48	12	exists	exist	VERB
iajs-812	48	13	a	a	DET
iajs-812	48	14	semi	semi	ADJ
iajs-812	48	15	-	-	ADJ
iajs-812	48	16	p	p	ADJ
iajs-812	48	17	-	-	PUNCT
iajs-812	48	18	open	open	ADJ
iajs-812	48	19	in	in	ADP
iajs-812	48	20	which	which	PRON
iajs-812	48	21	contains	contain	VERB
iajs-812	48	22	one	one	NUM
iajs-812	48	23	of	of	ADP
iajs-812	48	24	them	they	PRON
iajs-812	48	25	but	but	CCONJ
iajs-812	48	26	not	not	PART
iajs-812	48	27	the	the	DET
iajs-812	48	28	other	other	ADJ
iajs-812	48	29	.	.	PUNCT
iajs-812	49	1	now	now	ADV
iajs-812	49	2	,	,	PUNCT
iajs-812	49	3	let	let	VERB
iajs-812	49	4	in	in	ADP
iajs-812	49	5	x	x	PRON
iajs-812	49	6	,	,	PUNCT
iajs-812	49	7	since	since	SCONJ
iajs-812	49	8	is	be	AUX
iajs-812	49	9	pairwise	pairwise	NOUN
iajs-812	49	10	space	space	NOUN
iajs-812	49	11	,	,	PUNCT
iajs-812	49	12	then	then	ADV
iajs-812	49	13	there	there	PRON
iajs-812	49	14	exists	exist	VERB
iajs-812	49	15	open	open	ADJ
iajs-812	49	16	set	set	VERB
iajs-812	49	17	u	u	NOUN
iajs-812	49	18	in	in	ADP
iajs-812	49	19	such	such	ADJ
iajs-812	49	20	that	that	PRON
iajs-812	49	21	but	but	CCONJ
iajs-812	49	22	from	from	ADP
iajs-812	49	23	(	(	PUNCT
iajs-812	49	24	proposition	proposition	NOUN
iajs-812	49	25	2.7	2.7	NUM
iajs-812	49	26	part	part	NOUN
iajs-812	49	27	(	(	PUNCT
iajs-812	49	28	1	1	NUM
iajs-812	49	29	)	)	PUNCT
iajs-812	49	30	)	)	PUNCT
iajs-812	50	1	there	there	PRON
iajs-812	50	2	exists	exist	VERB
iajs-812	50	3	semi	semi	ADJ
iajs-812	50	4	-	-	ADJ
iajs-812	50	5	popen	popen	ADJ
iajs-812	50	6	set	set	NOUN
iajs-812	50	7	u	u	PRON
iajs-812	50	8	such	such	ADJ
iajs-812	50	9	that	that	SCONJ
iajs-812	50	10	thus	thus	ADV
iajs-812	50	11	is	be	AUX
iajs-812	50	12	pairwise	pairwise	NOUN
iajs-812	50	13	semi	semi	ADJ
iajs-812	50	14	-	-	NOUN
iajs-812	50	15	pspace	pspace	NOUN
iajs-812	50	16	.	.	PUNCT
iajs-812	51	1	■	■	PUNCT
iajs-812	51	2	remark	remark	VERB
iajs-812	51	3	3.3	3.3	NUM
iajs-812	51	4	:	:	PUNCT
iajs-812	51	5	the	the	DET
iajs-812	51	6	converse	converse	NOUN
iajs-812	51	7	of	of	ADP
iajs-812	51	8	(	(	PUNCT
iajs-812	51	9	proposition	proposition	NOUN
iajs-812	51	10	3.2	3.2	NUM
iajs-812	51	11	)	)	PUNCT
iajs-812	51	12	is	be	AUX
iajs-812	51	13	not	not	PART
iajs-812	51	14	true	true	ADJ
iajs-812	51	15	in	in	ADP
iajs-812	51	16	general	general	ADJ
iajs-812	51	17	,	,	PUNCT
iajs-812	51	18	as	as	SCONJ
iajs-812	51	19	the	the	DET
iajs-812	51	20	following	follow	VERB
iajs-812	51	21	example	example	NOUN
iajs-812	51	22	shows	show	VERB
iajs-812	51	23	:	:	PUNCT
iajs-812	51	24	example	example	NOUN
iajs-812	51	25	1	1	NUM
iajs-812	51	26	:	:	PUNCT
iajs-812	51	27	let	let	VERB
iajs-812	51	28	x={1	x={1	ADJ
iajs-812	51	29	,	,	PUNCT
iajs-812	51	30	2	2	NUM
iajs-812	51	31	,	,	PUNCT
iajs-812	51	32	3	3	NUM
iajs-812	51	33	}	}	PUNCT
iajs-812	51	34	,	,	PUNCT
iajs-812	51	35	,	,	PUNCT
iajs-812	51	36	po(x	po(x	X
iajs-812	51	37	,	,	PUNCT
iajs-812	51	38	=	=	SYM
iajs-812	51	39	s	s	X
iajs-812	51	40	-	-	PUNCT
iajs-812	51	41	p(x	p(x	NOUN
iajs-812	51	42	,	,	PUNCT
iajs-812	51	43	=	=	PRON
iajs-812	51	44	{	{	PUNCT
iajs-812	51	45	,	,	PUNCT
iajs-812	51	46	po(x	po(x	ADJ
iajs-812	51	47	,	,	PUNCT
iajs-812	51	48	=	=	SYM
iajs-812	51	49	s	s	X
iajs-812	51	50	-	-	PUNCT
iajs-812	51	51	p(x	p(x	NOUN
iajs-812	51	52	,	,	PUNCT
iajs-812	51	53	=	=	PRON
iajs-812	51	54	{	{	PUNCT
iajs-812	51	55	.	.	PUNCT
iajs-812	52	1	then	then	ADV
iajs-812	52	2	,	,	PUNCT
iajs-812	52	3	clearly	clearly	ADV
iajs-812	52	4	the	the	DET
iajs-812	52	5	space	space	NOUN
iajs-812	52	6	is	be	AUX
iajs-812	52	7	pairwise	pairwise	NOUN
iajs-812	52	8	semi	semi	ADJ
iajs-812	52	9	-	-	NOUN
iajs-812	52	10	pspace	pspace	NOUN
iajs-812	52	11	,	,	PUNCT
iajs-812	52	12	but	but	CCONJ
iajs-812	52	13	not	not	PART
iajs-812	52	14	pairwise	pairwise	NOUN
iajs-812	52	15	space	space	NOUN
iajs-812	52	16	,	,	PUNCT
iajs-812	52	17	since	since	SCONJ
iajs-812	52	18	2	2	NUM
iajs-812	52	19	in	in	ADP
iajs-812	52	20	x	x	PUNCT
iajs-812	53	1	but	but	CCONJ
iajs-812	53	2	there	there	PRON
iajs-812	53	3	is	be	VERB
iajs-812	53	4	no	no	DET
iajs-812	53	5	open	open	ADJ
iajs-812	53	6	set	set	NOUN
iajs-812	53	7	u	u	NOUN
iajs-812	53	8	or	or	CCONJ
iajs-812	53	9	u	u	NOUN
iajs-812	53	10	such	such	ADJ
iajs-812	53	11	that	that	SCONJ
iajs-812	53	12	2	2	NUM
iajs-812	53	13	theorem	theorem	VERB
iajs-812	53	14	3.4	3.4	NUM
iajs-812	53	15	:	:	PUNCT
iajs-812	53	16	for	for	ADP
iajs-812	53	17	a	a	DET
iajs-812	53	18	space	space	NOUN
iajs-812	53	19	,	,	PUNCT
iajs-812	53	20	the	the	DET
iajs-812	53	21	following	follow	VERB
iajs-812	53	22	are	be	AUX
iajs-812	53	23	equivalent	equivalent	ADJ
iajs-812	53	24	:	:	PUNCT
iajs-812	53	25	(	(	PUNCT
iajs-812	53	26	1	1	X
iajs-812	53	27	)	)	PUNCT
iajs-812	53	28	is	be	AUX
iajs-812	53	29	pairwise	pairwise	NOUN
iajs-812	53	30	semi	semi	ADJ
iajs-812	53	31	-	-	ADJ
iajs-812	53	32	p	p	ADJ
iajs-812	53	33	space	space	NOUN
iajs-812	53	34	.	.	PUNCT
iajs-812	54	1	(	(	PUNCT
iajs-812	54	2	2	2	X
iajs-812	54	3	)	)	PUNCT
iajs-812	54	4	for	for	ADP
iajs-812	54	5	every	every	DET
iajs-812	54	6	(	(	PUNCT
iajs-812	54	7	3	3	NUM
iajs-812	54	8	)	)	PUNCT
iajs-812	54	9	for	for	ADP
iajs-812	54	10	every	every	DET
iajs-812	54	11	the	the	DET
iajs-812	54	12	intersection	intersection	NOUN
iajs-812	54	13	of	of	ADP
iajs-812	54	14	all	all	PRON
iajs-812	54	15	and	and	CCONJ
iajs-812	54	16	all	all	PRON
iajs-812	54	17	is	be	AUX
iajs-812	54	18	{	{	PUNCT
iajs-812	54	19	x	x	NOUN
iajs-812	54	20	}	}	PUNCT
iajs-812	54	21	.	.	PUNCT
iajs-812	55	1	proof	proof	NOUN
iajs-812	55	2	:	:	PUNCT
iajs-812	55	3	suppose	suppose	VERB
iajs-812	55	4	x≠	x≠	PROPN
iajs-812	55	5	y	y	PROPN
iajs-812	55	6	in	in	ADP
iajs-812	55	7	x	x	SYM
iajs-812	55	8	,	,	PUNCT
iajs-812	55	9	there	there	PRON
iajs-812	55	10	exists	exist	VERB
iajs-812	55	11	a	a	DET
iajs-812	55	12	-semi	-semi	NOUN
iajs-812	55	13	-	-	PUNCT
iajs-812	55	14	p	p	NOUN
iajs-812	55	15	-	-	PUNCT
iajs-812	55	16	open	open	NOUN
iajs-812	55	17	set	set	NOUN
iajs-812	55	18	u	u	NOUN
iajs-812	55	19	containing	contain	VERB
iajs-812	55	20	x	x	PUNCT
iajs-812	55	21	but	but	CCONJ
iajs-812	55	22	not	not	PART
iajs-812	55	23	y	y	PROPN
iajs-812	55	24	or	or	CCONJ
iajs-812	55	25	a	a	DET
iajs-812	55	26	semi	semi	ADJ
iajs-812	55	27	-	-	ADJ
iajs-812	55	28	p	p	ADJ
iajs-812	55	29	-	-	PUNCT
iajs-812	55	30	open	open	NOUN
iajs-812	55	31	set	set	NOUN
iajs-812	55	32	v	v	NOUN
iajs-812	55	33	containing	contain	VERB
iajs-812	55	34	y	y	NOUN
iajs-812	55	35	but	but	CCONJ
iajs-812	55	36	not	not	PART
iajs-812	56	1	x	x	X
iajs-812	56	2	.that	.that	PRON
iajs-812	56	3	means	mean	VERB
iajs-812	56	4	mean	mean	VERB
iajs-812	56	5	either	either	ADV
iajs-812	56	6	or	or	CCONJ
iajs-812	56	7	hence	hence	ADV
iajs-812	56	8	for	for	ADP
iajs-812	56	9	a	a	DET
iajs-812	56	10	point	point	NOUN
iajs-812	56	11	x	x	NOUN
iajs-812	56	12	,	,	PUNCT
iajs-812	56	13	y	y	PROPN
iajs-812	56	14	.thus	.thus	PRON
iajs-812	56	15	{	{	PUNCT
iajs-812	56	16	x	x	X
iajs-812	56	17	}	}	PUNCT
iajs-812	56	18	.	.	PUNCT
iajs-812	57	1	suppose	suppose	VERB
iajs-812	57	2	there	there	PRON
iajs-812	57	3	exists	exist	VERB
iajs-812	57	4	y	y	PROPN
iajs-812	57	5	≠	≠	PROPN
iajs-812	57	6	x	x	PUNCT
iajs-812	57	7	such	such	ADJ
iajs-812	57	8	that	that	SCONJ
iajs-812	57	9	y	y	PROPN
iajs-812	57	10	belongs	belong	VERB
iajs-812	57	11	to	to	ADP
iajs-812	57	12	the	the	DET
iajs-812	57	13	intersection	intersection	NOUN
iajs-812	57	14	of	of	ADP
iajs-812	57	15	all	all	PRON
iajs-812	57	16	and	and	CCONJ
iajs-812	57	17	all	all	PRON
iajs-812	57	18	.hence	.hence	VERB
iajs-812	57	19	is	be	AUX
iajs-812	57	20	not	not	PART
iajs-812	57	21	pairwise	pairwise	NOUN
iajs-812	57	22	semi	semi	ADJ
iajs-812	57	23	-	-	NOUN
iajs-812	57	24	pspace	pspace	NOUN
iajs-812	57	25	,	,	PUNCT
iajs-812	57	26	implies	imply	VERB
iajs-812	57	27	semi	semi	ADV
iajs-812	57	28	pcl	pcl	PROPN
iajs-812	57	29	{	{	PUNCT
iajs-812	57	30	x	x	NOUN
iajs-812	57	31	}	}	PUNCT
iajs-812	57	32	which	which	PRON
iajs-812	57	33	is	be	AUX
iajs-812	57	34	a	a	DET
iajs-812	57	35	contradiction	contradiction	NOUN
iajs-812	57	36	,	,	PUNCT
iajs-812	57	37	thus	thus	ADV
iajs-812	57	38	the	the	DET
iajs-812	57	39	intersection	intersection	NOUN
iajs-812	57	40	of	of	ADP
iajs-812	57	41	all	all	PRON
iajs-812	57	42	and	and	CCONJ
iajs-812	57	43	all	all	PRON
iajs-812	57	44	let	let	VERB
iajs-812	57	45	x	x	SYM
iajs-812	57	46	≠	≠	PROPN
iajs-812	57	47	y	y	PROPN
iajs-812	57	48	in	in	ADP
iajs-812	57	49	x	x	PRON
iajs-812	57	50	,	,	PUNCT
iajs-812	57	51	since	since	SCONJ
iajs-812	57	52	{	{	PUNCT
iajs-812	57	53	x	x	NOUN
iajs-812	57	54	}	}	PUNCT
iajs-812	57	55	=	=	PUNCT
iajs-812	57	56	the	the	DET
iajs-812	57	57	intersection	intersection	NOUN
iajs-812	57	58	of	of	ADP
iajs-812	57	59	all	all	PRON
iajs-812	57	60	and	and	CCONJ
iajs-812	57	61	hence	hence	ADV
iajs-812	57	62	,	,	PUNCT
iajs-812	57	63	there	there	PRON
iajs-812	57	64	exists	exist	VERB
iajs-812	57	65	either	either	CCONJ
iajs-812	57	66	on	on	ADP
iajs-812	57	67	not	not	PART
iajs-812	57	68	containing	contain	VERB
iajs-812	57	69	x	x	PUNCT
iajs-812	57	70	or	or	CCONJ
iajs-812	57	71	a	a	PRON
iajs-812	57	72	not	not	PART
iajs-812	57	73	containing	contain	VERB
iajs-812	57	74	x	x	X
iajs-812	57	75	.therefore	.therefore	X
iajs-812	57	76	is	be	AUX
iajs-812	57	77	pairwise	pairwise	NOUN
iajs-812	57	78	semi	semi	ADJ
iajs-812	57	79	-	-	ADJ
iajs-812	57	80	p	p	ADJ
iajs-812	57	81	space	space	NOUN
iajs-812	57	82	.	.	PUNCT
iajs-812	58	1	■	■	PUNCT
iajs-812	58	2	ibn	ibn	PROPN
iajs-812	58	3	alhaitham	alhaitham	NOUN
iajs-812	58	4	j.	j.	PROPN
iajs-812	58	5	for	for	ADP
iajs-812	58	6	pure	pure	ADJ
iajs-812	58	7	&	&	CCONJ
iajs-812	58	8	appl	appl	PROPN
iajs-812	58	9	.	.	PUNCT
iajs-812	59	1	sci	sci	PROPN
iajs-812	59	2	.	.	PUNCT
iajs-812	59	3	vol.24	vol.24	NOUN
iajs-812	59	4	(	(	PUNCT
iajs-812	59	5	3	3	NUM
iajs-812	59	6	)	)	PUNCT
iajs-812	59	7	2011	2011	NUM
iajs-812	59	8	theorem	theorem	VERB
iajs-812	59	9	3.5	3.5	NUM
iajs-812	59	10	:	:	PUNCT
iajs-812	59	11	the	the	DET
iajs-812	59	12	product	product	NOUN
iajs-812	59	13	of	of	ADP
iajs-812	59	14	an	an	DET
iajs-812	59	15	arbitrary	arbitrary	ADJ
iajs-812	59	16	family	family	NOUN
iajs-812	59	17	of	of	ADP
iajs-812	59	18	pairwise	pairwise	NOUN
iajs-812	59	19	semi	semi	ADV
iajs-812	59	20	-pspaces	-pspace	NOUN
iajs-812	59	21	is	be	AUX
iajs-812	59	22	pairwise	pairwise	NOUN
iajs-812	59	23	semi	semi	ADV
iajs-812	59	24	p	p	NOUN
iajs-812	59	25	space	space	NOUN
iajs-812	59	26	.	.	PUNCT
iajs-812	60	1	proof	proof	NOUN
iajs-812	60	2	:	:	PUNCT
iajs-812	60	3	let	let	AUX
iajs-812	60	4	be	be	AUX
iajs-812	60	5	the	the	DET
iajs-812	60	6	product	product	NOUN
iajs-812	60	7	of	of	ADP
iajs-812	60	8	an	an	DET
iajs-812	60	9	arbitrary	arbitrary	ADJ
iajs-812	60	10	family	family	NOUN
iajs-812	60	11	of	of	ADP
iajs-812	60	12	pairwise	pairwise	PROPN
iajs-812	60	13	semi	semi	ADV
iajs-812	60	14	-pspaces	-pspace	NOUN
iajs-812	60	15	,	,	PUNCT
iajs-812	60	16	where	where	SCONJ
iajs-812	60	17	and	and	CCONJ
iajs-812	60	18	are	be	AUX
iajs-812	60	19	the	the	DET
iajs-812	60	20	product	product	NOUN
iajs-812	60	21	topologies	topology	NOUN
iajs-812	60	22	on	on	ADP
iajs-812	60	23	x	x	PUNCT
iajs-812	60	24	generated	generate	VERB
iajs-812	60	25	by	by	ADP
iajs-812	60	26	respectively	respectively	ADV
iajs-812	60	27	and	and	CCONJ
iajs-812	60	28	x	x	SYM
iajs-812	60	29	=	=	PUNCT
iajs-812	60	30	.	.	PUNCT
iajs-812	61	1	let	let	VERB
iajs-812	61	2	and	and	CCONJ
iajs-812	61	3	be	be	AUX
iajs-812	61	4	two	two	NUM
iajs-812	61	5	distinct	distinct	ADJ
iajs-812	61	6	points	point	NOUN
iajs-812	61	7	of	of	ADP
iajs-812	61	8	x.	x.	NOUN
iajs-812	61	9	hence	hence	ADV
iajs-812	61	10	for	for	ADP
iajs-812	61	11	some	some	PRON
iajs-812	61	12	.	.	PUNCT
iajs-812	62	1	but	but	CCONJ
iajs-812	62	2	is	be	AUX
iajs-812	62	3	pairwise	pairwise	NOUN
iajs-812	62	4	semi	semi	ADV
iajs-812	62	5	-p	-p	ADP
iajs-812	62	6	space	space	NOUN
iajs-812	62	7	,	,	PUNCT
iajs-812	62	8	therefore	therefore	ADV
iajs-812	62	9	,	,	PUNCT
iajs-812	62	10	there	there	PRON
iajs-812	62	11	exists	exist	VERB
iajs-812	62	12	either	either	CCONJ
iajs-812	62	13	a	a	DET
iajs-812	62	14	-semi	-semi	NOUN
iajs-812	62	15	-	-	PUNCT
iajs-812	62	16	p	p	NOUN
iajs-812	62	17	-	-	PUNCT
iajs-812	62	18	open	open	ADJ
iajs-812	62	19	set	set	NOUN
iajs-812	62	20	containing	contain	VERB
iajs-812	62	21	but	but	CCONJ
iajs-812	62	22	not	not	PART
iajs-812	62	23	or	or	CCONJ
iajs-812	62	24	a	a	DET
iajs-812	62	25	-semi	-semi	NOUN
iajs-812	62	26	-	-	PUNCT
iajs-812	62	27	p	p	NOUN
iajs-812	62	28	-	-	PUNCT
iajs-812	62	29	open	open	ADJ
iajs-812	62	30	set	set	NOUN
iajs-812	62	31	containing	contain	VERB
iajs-812	62	32	but	but	CCONJ
iajs-812	62	33	not	not	PART
iajs-812	62	34	.	.	PUNCT
iajs-812	63	1	define	define	VERB
iajs-812	63	2	and	and	CCONJ
iajs-812	63	3	then	then	ADV
iajs-812	63	4	u	u	NOUN
iajs-812	63	5	is	be	AUX
iajs-812	63	6	a	a	DET
iajs-812	63	7	semi	semi	ADJ
iajs-812	63	8	-	-	ADJ
iajs-812	63	9	p	p	ADJ
iajs-812	63	10	-	-	PUNCT
iajs-812	63	11	open	open	NOUN
iajs-812	63	12	set	set	NOUN
iajs-812	63	13	and	and	CCONJ
iajs-812	63	14	v	v	NOUN
iajs-812	63	15	is	be	AUX
iajs-812	63	16	semi	semi	ADJ
iajs-812	63	17	-	-	ADJ
iajs-812	63	18	p	p	ADJ
iajs-812	63	19	-	-	PUNCT
iajs-812	63	20	open	open	NOUN
iajs-812	63	21	set	set	NOUN
iajs-812	63	22	,	,	PUNCT
iajs-812	63	23	also	also	ADV
iajs-812	63	24	,	,	PUNCT
iajs-812	63	25	u	u	NOUN
iajs-812	63	26	contains	contain	VERB
iajs-812	63	27	x	x	PUNCT
iajs-812	63	28	but	but	CCONJ
iajs-812	63	29	not	not	PART
iajs-812	63	30	y.	y.	PROPN
iajs-812	63	31	hence	hence	ADV
iajs-812	63	32	is	be	AUX
iajs-812	63	33	pairwise	pairwise	NOUN
iajs-812	63	34	semi	semi	ADV
iajs-812	63	35	p	p	NOUN
iajs-812	63	36	space	space	NOUN
iajs-812	63	37	.	.	PUNCT
iajs-812	64	1	■	■	PUNCT
iajs-812	64	2	definition	definition	NOUN
iajs-812	64	3	3.6	3.6	NUM
iajs-812	64	4	:	:	PUNCT
iajs-812	64	5	a	a	DET
iajs-812	64	6	space	space	NOUN
iajs-812	64	7	is	be	AUX
iajs-812	64	8	called	call	VERB
iajs-812	64	9	pairwise	pairwise	NOUN
iajs-812	64	10	semi	semi	NOUN
iajs-812	64	11	-	-	NOUN
iajs-812	64	12	pspace	pspace	ADJ
iajs-812	64	13	,	,	PUNCT
iajs-812	64	14	if	if	SCONJ
iajs-812	64	15	for	for	ADP
iajs-812	64	16	any	any	DET
iajs-812	64	17	pair	pair	NOUN
iajs-812	64	18	of	of	ADP
iajs-812	64	19	distinct	distinct	ADJ
iajs-812	64	20	points	point	NOUN
iajs-812	64	21	x	x	PUNCT
iajs-812	64	22	and	and	CCONJ
iajs-812	64	23	y	y	PROPN
iajs-812	64	24	in	in	ADP
iajs-812	64	25	x	x	SYM
iajs-812	64	26	,	,	PUNCT
iajs-812	64	27	there	there	PRON
iajs-812	64	28	exists	exist	VERB
iajs-812	64	29	a	a	DET
iajs-812	64	30	-semi	-semi	NOUN
iajs-812	64	31	-	-	PUNCT
iajs-812	64	32	p	p	NOUN
iajs-812	64	33	-	-	PUNCT
iajs-812	64	34	open	open	ADJ
iajs-812	64	35	set	set	NOUN
iajs-812	64	36	u	u	NOUN
iajs-812	64	37	and	and	CCONJ
iajs-812	64	38	-semi	-semi	NOUN
iajs-812	64	39	-	-	PUNCT
iajs-812	64	40	p	p	X
iajs-812	64	41	-	-	PUNCT
iajs-812	64	42	open	open	NOUN
iajs-812	64	43	set	set	NOUN
iajs-812	64	44	v	v	ADP
iajs-812	64	45	such	such	ADJ
iajs-812	64	46	that	that	PRON
iajs-812	64	47	and	and	CCONJ
iajs-812	64	48	proposition	proposition	NOUN
iajs-812	64	49	3.7	3.7	NUM
iajs-812	64	50	:	:	PUNCT
iajs-812	64	51	if	if	SCONJ
iajs-812	64	52	a	a	DET
iajs-812	64	53	space	space	NOUN
iajs-812	64	54	is	be	AUX
iajs-812	64	55	pairwise	pairwise	NOUN
iajs-812	64	56	space	space	NOUN
iajs-812	64	57	,	,	PUNCT
iajs-812	64	58	then	then	ADV
iajs-812	64	59	is	be	AUX
iajs-812	64	60	pairwise	pairwise	NOUN
iajs-812	64	61	semi	semi	ADJ
iajs-812	64	62	-	-	NOUN
iajs-812	64	63	pspace	pspace	NOUN
iajs-812	64	64	.	.	PUNCT
iajs-812	65	1	proof	proof	NOUN
iajs-812	65	2	:	:	PUNCT
iajs-812	65	3	for	for	ADP
iajs-812	65	4	any	any	PRON
iajs-812	65	5	in	in	ADP
iajs-812	65	6	x	x	PRON
iajs-812	65	7	,	,	PUNCT
iajs-812	65	8	since	since	SCONJ
iajs-812	65	9	is	be	AUX
iajs-812	65	10	pairwise	pairwise	NOUN
iajs-812	65	11	space	space	NOUN
iajs-812	65	12	,	,	PUNCT
iajs-812	65	13	then	then	ADV
iajs-812	65	14	there	there	PRON
iajs-812	65	15	exists	exist	VERB
iajs-812	65	16	-open	-open	PROPN
iajs-812	65	17	set	set	VERB
iajs-812	65	18	u	u	NOUN
iajs-812	65	19	and	and	CCONJ
iajs-812	65	20	-open	-open	NOUN
iajs-812	65	21	set	set	VERB
iajs-812	65	22	v	v	ADP
iajs-812	65	23	such	such	ADJ
iajs-812	65	24	that	that	PRON
iajs-812	65	25	and	and	CCONJ
iajs-812	65	26	and	and	CCONJ
iajs-812	65	27	since	since	SCONJ
iajs-812	65	28	every	every	DET
iajs-812	65	29	open	open	ADJ
iajs-812	65	30	set	set	NOUN
iajs-812	65	31	is	be	AUX
iajs-812	65	32	semi	semi	ADJ
iajs-812	65	33	-	-	ADJ
iajs-812	65	34	p	p	ADJ
iajs-812	65	35	-	-	PUNCT
iajs-812	65	36	open	open	ADJ
iajs-812	65	37	set	set	NOUN
iajs-812	65	38	(	(	PUNCT
iajs-812	65	39	by	by	ADP
iajs-812	65	40	proposition	proposition	NOUN
iajs-812	65	41	2.7	2.7	NUM
iajs-812	65	42	part	part	NOUN
iajs-812	65	43	(	(	PUNCT
iajs-812	65	44	1	1	NUM
iajs-812	65	45	)	)	PUNCT
iajs-812	65	46	)	)	PUNCT
iajs-812	65	47	,	,	PUNCT
iajs-812	65	48	which	which	PRON
iajs-812	65	49	implies	imply	VERB
iajs-812	65	50	u	u	NOUN
iajs-812	65	51	is	be	AUX
iajs-812	65	52	semi	semi	ADJ
iajs-812	65	53	-	-	ADJ
iajs-812	65	54	p	p	ADJ
iajs-812	65	55	-	-	PUNCT
iajs-812	65	56	open	open	NOUN
iajs-812	65	57	set	set	NOUN
iajs-812	65	58	in	in	ADP
iajs-812	65	59	containing	contain	VERB
iajs-812	65	60	x	x	PUNCT
iajs-812	65	61	but	but	CCONJ
iajs-812	65	62	not	not	PART
iajs-812	65	63	y	y	PROPN
iajs-812	65	64	and	and	CCONJ
iajs-812	65	65	v	v	NOUN
iajs-812	65	66	is	be	AUX
iajs-812	65	67	semi	semi	ADJ
iajs-812	65	68	-	-	ADJ
iajs-812	65	69	p	p	ADJ
iajs-812	65	70	-	-	PUNCT
iajs-812	65	71	open	open	NOUN
iajs-812	65	72	set	set	NOUN
iajs-812	65	73	in	in	ADP
iajs-812	65	74	containing	contain	VERB
iajs-812	65	75	y	y	PROPN
iajs-812	65	76	but	but	CCONJ
iajs-812	65	77	not	not	PART
iajs-812	65	78	x.	x.	NOUN
iajs-812	65	79	hence	hence	ADV
iajs-812	65	80	is	be	AUX
iajs-812	65	81	pairwise	pairwise	NOUN
iajs-812	65	82	semi	semi	ADJ
iajs-812	65	83	-	-	NOUN
iajs-812	65	84	pspace	pspace	NOUN
iajs-812	65	85	.	.	PUNCT
iajs-812	66	1	■	■	PUNCT
iajs-812	66	2	remark	remark	VERB
iajs-812	66	3	3.8	3.8	NUM
iajs-812	66	4	:	:	PUNCT
iajs-812	66	5	the	the	DET
iajs-812	66	6	converse	converse	NOUN
iajs-812	66	7	of	of	ADP
iajs-812	66	8	(	(	PUNCT
iajs-812	66	9	proposition	proposition	NOUN
iajs-812	66	10	3.7	3.7	NUM
iajs-812	66	11	)	)	PUNCT
iajs-812	66	12	is	be	AUX
iajs-812	66	13	not	not	PART
iajs-812	66	14	true	true	ADJ
iajs-812	66	15	in	in	ADP
iajs-812	66	16	general	general	ADJ
iajs-812	66	17	as	as	SCONJ
iajs-812	66	18	the	the	DET
iajs-812	66	19	following	follow	VERB
iajs-812	66	20	example	example	NOUN
iajs-812	66	21	shows	show	VERB
iajs-812	66	22	:	:	PUNCT
iajs-812	66	23	consider	consider	VERB
iajs-812	66	24	example	example	NOUN
iajs-812	66	25	1	1	NUM
iajs-812	66	26	,	,	PUNCT
iajs-812	66	27	where	where	SCONJ
iajs-812	66	28	:	:	PUNCT
iajs-812	67	1	x={1	x={1	ADJ
iajs-812	67	2	,	,	PUNCT
iajs-812	67	3	2	2	NUM
iajs-812	67	4	,	,	PUNCT
iajs-812	67	5	3	3	NUM
iajs-812	67	6	}	}	PUNCT
iajs-812	67	7	,	,	PUNCT
iajs-812	67	8	,	,	PUNCT
iajs-812	67	9	po(x	po(x	X
iajs-812	67	10	,	,	PUNCT
iajs-812	67	11	=	=	SYM
iajs-812	67	12	s	s	X
iajs-812	67	13	-	-	PUNCT
iajs-812	67	14	p(x	p(x	NOUN
iajs-812	67	15	,	,	PUNCT
iajs-812	67	16	=	=	PRON
iajs-812	67	17	{	{	PUNCT
iajs-812	67	18	,	,	PUNCT
iajs-812	67	19	po(x	po(x	ADJ
iajs-812	67	20	,	,	PUNCT
iajs-812	67	21	=	=	SYM
iajs-812	67	22	s	s	X
iajs-812	67	23	-	-	PUNCT
iajs-812	67	24	p(x	p(x	NOUN
iajs-812	67	25	,	,	PUNCT
iajs-812	67	26	=	=	PRON
iajs-812	67	27	{	{	PUNCT
iajs-812	67	28	.	.	PUNCT
iajs-812	68	1	then	then	ADV
iajs-812	68	2	,	,	PUNCT
iajs-812	68	3	clearly	clearly	ADV
iajs-812	68	4	that	that	SCONJ
iajs-812	68	5	the	the	DET
iajs-812	68	6	space	space	NOUN
iajs-812	68	7	is	be	AUX
iajs-812	68	8	pairwise	pairwise	NOUN
iajs-812	68	9	semi	semi	ADJ
iajs-812	68	10	-	-	NOUN
iajs-812	68	11	pspace	pspace	NOUN
iajs-812	68	12	,	,	PUNCT
iajs-812	68	13	but	but	CCONJ
iajs-812	68	14	not	not	PART
iajs-812	68	15	pairwise	pairwise	NOUN
iajs-812	68	16	space	space	NOUN
iajs-812	68	17	,	,	PUNCT
iajs-812	68	18	since	since	SCONJ
iajs-812	68	19	in	in	ADP
iajs-812	68	20	x	x	NOUN
iajs-812	68	21	,	,	PUNCT
iajs-812	68	22	but	but	CCONJ
iajs-812	68	23	there	there	PRON
iajs-812	68	24	is	be	VERB
iajs-812	68	25	no	no	DET
iajs-812	68	26	-open	-open	ADJ
iajs-812	68	27	set	set	NOUN
iajs-812	68	28	containing	contain	VERB
iajs-812	68	29	2	2	NUM
iajs-812	68	30	but	but	CCONJ
iajs-812	68	31	not	not	PART
iajs-812	68	32	containing	contain	VERB
iajs-812	68	33	3	3	NUM
iajs-812	68	34	and	and	CCONJ
iajs-812	68	35	there	there	PRON
iajs-812	68	36	is	be	VERB
iajs-812	68	37	no	no	DET
iajs-812	68	38	-open	-open	ADJ
iajs-812	68	39	set	set	NOUN
iajs-812	68	40	containing	contain	VERB
iajs-812	68	41	3	3	NUM
iajs-812	68	42	but	but	CCONJ
iajs-812	68	43	not	not	PART
iajs-812	68	44	2	2	NUM
iajs-812	68	45	.	.	X
iajs-812	68	46	theorem	theorem	VERB
iajs-812	68	47	3.9	3.9	NUM
iajs-812	68	48	:	:	PUNCT
iajs-812	68	49	the	the	DET
iajs-812	68	50	product	product	NOUN
iajs-812	68	51	of	of	ADP
iajs-812	68	52	an	an	DET
iajs-812	68	53	arbitrary	arbitrary	ADJ
iajs-812	68	54	family	family	NOUN
iajs-812	68	55	of	of	ADP
iajs-812	68	56	pairwise	pairwise	NOUN
iajs-812	68	57	semi	semi	ADV
iajs-812	68	58	-pspaces	-pspace	NOUN
iajs-812	68	59	is	be	AUX
iajs-812	68	60	pairwise	pairwise	NOUN
iajs-812	68	61	semi	semi	ADV
iajs-812	68	62	p	p	NOUN
iajs-812	68	63	space	space	NOUN
iajs-812	68	64	.	.	PUNCT
iajs-812	69	1	proof	proof	NOUN
iajs-812	69	2	:	:	PUNCT
iajs-812	69	3	similar	similar	ADJ
iajs-812	69	4	to	to	ADP
iajs-812	69	5	the	the	DET
iajs-812	69	6	proof	proof	NOUN
iajs-812	69	7	of	of	ADP
iajs-812	69	8	(	(	PUNCT
iajs-812	69	9	theorem	theorem	ADJ
iajs-812	69	10	3.5	3.5	NUM
iajs-812	69	11	)	)	PUNCT
iajs-812	69	12	.	.	PUNCT
iajs-812	70	1	■	■	PUNCT
iajs-812	70	2	ibn	ibn	NOUN
iajs-812	70	3	alhaitham	alhaitham	NOUN
iajs-812	70	4	j.	j.	PROPN
iajs-812	70	5	for	for	ADP
iajs-812	70	6	pure	pure	ADJ
iajs-812	70	7	&	&	CCONJ
iajs-812	70	8	appl	appl	PROPN
iajs-812	70	9	.	.	PUNCT
iajs-812	71	1	sci	sci	PROPN
iajs-812	71	2	.	.	PUNCT
iajs-812	71	3	vol.24	vol.24	NOUN
iajs-812	71	4	(	(	PUNCT
iajs-812	71	5	3	3	NUM
iajs-812	71	6	)	)	PUNCT
iajs-812	71	7	2011	2011	NUM
iajs-812	71	8	definition	definition	NOUN
iajs-812	71	9	3.10	3.10	NUM
iajs-812	71	10	:	:	PUNCT
iajs-812	71	11	a	a	DET
iajs-812	71	12	space	space	NOUN
iajs-812	71	13	is	be	AUX
iajs-812	71	14	called	call	VERB
iajs-812	71	15	pairwise	pairwise	NOUN
iajs-812	71	16	semi	semi	NOUN
iajs-812	71	17	-	-	NOUN
iajs-812	71	18	pspace	pspace	ADJ
iajs-812	71	19	,	,	PUNCT
iajs-812	71	20	if	if	SCONJ
iajs-812	71	21	for	for	ADP
iajs-812	71	22	any	any	DET
iajs-812	71	23	pair	pair	NOUN
iajs-812	71	24	of	of	ADP
iajs-812	71	25	distinct	distinct	ADJ
iajs-812	71	26	points	point	NOUN
iajs-812	71	27	x	x	PUNCT
iajs-812	71	28	and	and	CCONJ
iajs-812	71	29	y	y	PROPN
iajs-812	71	30	in	in	ADP
iajs-812	71	31	x	x	SYM
iajs-812	71	32	,	,	PUNCT
iajs-812	71	33	there	there	PRON
iajs-812	71	34	exists	exist	VERB
iajs-812	71	35	a	a	DET
iajs-812	71	36	-semi	-semi	NOUN
iajs-812	71	37	-	-	PUNCT
iajs-812	71	38	p	p	NOUN
iajs-812	71	39	-	-	PUNCT
iajs-812	71	40	open	open	ADJ
iajs-812	71	41	set	set	NOUN
iajs-812	71	42	u	u	NOUN
iajs-812	71	43	and	and	CCONJ
iajs-812	71	44	-semi	-semi	NOUN
iajs-812	71	45	-	-	PUNCT
iajs-812	71	46	p	p	X
iajs-812	71	47	-	-	PUNCT
iajs-812	71	48	open	open	NOUN
iajs-812	71	49	set	set	NOUN
iajs-812	71	50	v	v	ADP
iajs-812	71	51	such	such	ADJ
iajs-812	71	52	that	that	PRON
iajs-812	71	53	and	and	CCONJ
iajs-812	71	54	.	.	PUNCT
iajs-812	72	1	proposition	proposition	NOUN
iajs-812	72	2	3.11	3.11	NUM
iajs-812	72	3	:	:	PUNCT
iajs-812	72	4	if	if	SCONJ
iajs-812	72	5	a	a	DET
iajs-812	72	6	space	space	NOUN
iajs-812	72	7	is	be	AUX
iajs-812	72	8	pairwise	pairwise	NOUN
iajs-812	72	9	space	space	NOUN
iajs-812	72	10	,	,	PUNCT
iajs-812	72	11	then	then	ADV
iajs-812	72	12	is	be	AUX
iajs-812	72	13	pairwise	pairwise	NOUN
iajs-812	72	14	semi	semi	ADJ
iajs-812	72	15	-	-	NOUN
iajs-812	72	16	pspace	pspace	NOUN
iajs-812	72	17	.	.	PUNCT
iajs-812	73	1	proof	proof	NOUN
iajs-812	73	2	:	:	PUNCT
iajs-812	73	3	similar	similar	ADJ
iajs-812	73	4	of	of	ADP
iajs-812	73	5	the	the	DET
iajs-812	73	6	proof	proof	NOUN
iajs-812	73	7	of	of	ADP
iajs-812	73	8	(	(	PUNCT
iajs-812	73	9	proposition	proposition	NOUN
iajs-812	73	10	3.7	3.7	NUM
iajs-812	73	11	)	)	PUNCT
iajs-812	73	12	.	.	PUNCT
iajs-812	74	1	■	■	PUNCT
iajs-812	74	2	remark	remark	VERB
iajs-812	74	3	3.12	3.12	NUM
iajs-812	74	4	:	:	PUNCT
iajs-812	74	5	the	the	DET
iajs-812	74	6	converse	converse	NOUN
iajs-812	74	7	of	of	ADP
iajs-812	74	8	(	(	PUNCT
iajs-812	74	9	proposition	proposition	NOUN
iajs-812	74	10	3.11	3.11	NUM
iajs-812	74	11	)	)	PUNCT
iajs-812	74	12	is	be	AUX
iajs-812	74	13	not	not	PART
iajs-812	74	14	true	true	ADJ
iajs-812	74	15	in	in	ADP
iajs-812	74	16	general	general	ADJ
iajs-812	74	17	;	;	PUNCT
iajs-812	74	18	consider	consider	VERB
iajs-812	74	19	example	example	NOUN
iajs-812	74	20	1	1	NUM
iajs-812	74	21	:	:	PUNCT
iajs-812	75	1	x={1	x={1	ADJ
iajs-812	75	2	,	,	PUNCT
iajs-812	75	3	2	2	NUM
iajs-812	75	4	,	,	PUNCT
iajs-812	75	5	3	3	NUM
iajs-812	75	6	}	}	PUNCT
iajs-812	75	7	,	,	PUNCT
iajs-812	75	8	,	,	PUNCT
iajs-812	75	9	po(x	po(x	X
iajs-812	75	10	,	,	PUNCT
iajs-812	75	11	=	=	SYM
iajs-812	75	12	s	s	X
iajs-812	75	13	-	-	PUNCT
iajs-812	75	14	p(x	p(x	NOUN
iajs-812	75	15	,	,	PUNCT
iajs-812	75	16	=	=	PRON
iajs-812	75	17	{	{	PUNCT
iajs-812	75	18	,	,	PUNCT
iajs-812	75	19	po(x	po(x	ADJ
iajs-812	75	20	,	,	PUNCT
iajs-812	75	21	=	=	SYM
iajs-812	75	22	s	s	X
iajs-812	75	23	-	-	PUNCT
iajs-812	75	24	p(x	p(x	NOUN
iajs-812	75	25	,	,	PUNCT
iajs-812	75	26	=	=	PRON
iajs-812	75	27	{	{	PUNCT
iajs-812	75	28	,	,	PUNCT
iajs-812	75	29	clearly	clearly	ADV
iajs-812	75	30	is	be	AUX
iajs-812	75	31	pairwise	pairwise	NOUN
iajs-812	75	32	semi	semi	ADJ
iajs-812	75	33	-	-	NOUN
iajs-812	75	34	pspace	pspace	NOUN
iajs-812	75	35	,	,	PUNCT
iajs-812	75	36	but	but	CCONJ
iajs-812	75	37	not	not	PART
iajs-812	75	38	pairwise	pairwise	NOUN
iajs-812	75	39	space	space	NOUN
iajs-812	75	40	,	,	PUNCT
iajs-812	75	41	since	since	SCONJ
iajs-812	75	42	in	in	ADP
iajs-812	75	43	x	x	NOUN
iajs-812	75	44	,	,	PUNCT
iajs-812	75	45	but	but	CCONJ
iajs-812	75	46	there	there	PRON
iajs-812	75	47	is	be	VERB
iajs-812	75	48	no	no	DET
iajs-812	75	49	two	two	NUM
iajs-812	75	50	disjoint	disjoint	ADJ
iajs-812	75	51	open	open	ADJ
iajs-812	75	52	sets	set	NOUN
iajs-812	75	53	in	in	ADP
iajs-812	75	54	and	and	CCONJ
iajs-812	75	55	,	,	PUNCT
iajs-812	75	56	which	which	PRON
iajs-812	75	57	contain	contain	VERB
iajs-812	75	58	2	2	NUM
iajs-812	75	59	and	and	CCONJ
iajs-812	75	60	3	3	NUM
iajs-812	75	61	respectively	respectively	ADV
iajs-812	75	62	.	.	PUNCT
iajs-812	76	1	theorem	theorem	VERB
iajs-812	76	2	3.13	3.13	NUM
iajs-812	76	3	:	:	PUNCT
iajs-812	76	4	for	for	ADP
iajs-812	76	5	a	a	DET
iajs-812	76	6	space	space	NOUN
iajs-812	76	7	,	,	PUNCT
iajs-812	76	8	the	the	DET
iajs-812	76	9	following	follow	VERB
iajs-812	76	10	are	be	AUX
iajs-812	76	11	equivalent	equivalent	ADJ
iajs-812	76	12	:	:	PUNCT
iajs-812	76	13	1	1	NUM
iajs-812	76	14	is	be	AUX
iajs-812	76	15	pairwise	pairwise	NOUN
iajs-812	76	16	semi	semi	ADJ
iajs-812	76	17	-	-	NOUN
iajs-812	76	18	pspace	pspace	NOUN
iajs-812	76	19	.	.	PUNCT
iajs-812	77	1	2for	2for	ADP
iajs-812	77	2	each	each	PRON
iajs-812	77	3	and	and	CCONJ
iajs-812	77	4	for	for	ADP
iajs-812	77	5	each	each	DET
iajs-812	77	6	such	such	ADJ
iajs-812	77	7	that	that	SCONJ
iajs-812	77	8	,	,	PUNCT
iajs-812	77	9	there	there	PRON
iajs-812	77	10	exists	exist	VERB
iajs-812	77	11	a	a	DET
iajs-812	77	12	-semi	-semi	NOUN
iajs-812	77	13	-	-	PUNCT
iajs-812	77	14	p	p	NOUN
iajs-812	77	15	-	-	PUNCT
iajs-812	77	16	open	open	NOUN
iajs-812	77	17	set	set	NOUN
iajs-812	77	18	u	u	NOUN
iajs-812	77	19	containing	contain	VERB
iajs-812	77	20	x	x	PUNCT
iajs-812	77	21	such	such	ADJ
iajs-812	77	22	that	that	SCONJ
iajs-812	77	23	-semi	-semi	NOUN
iajs-812	77	24	-	-	PUNCT
iajs-812	77	25	pclu	pclu	NOUN
iajs-812	77	26	.	.	PUNCT
iajs-812	78	1	3for	3for	ADP
iajs-812	78	2	each	each	DET
iajs-812	78	3	,	,	PUNCT
iajs-812	78	4	-semi	-semi	NOUN
iajs-812	78	5	-	-	PUNCT
iajs-812	78	6	pclu	pclu	NOUN
iajs-812	78	7	:	:	PUNCT
iajs-812	78	8	and	and	CCONJ
iajs-812	78	9	u	u	NOUN
iajs-812	78	10	is	be	AUX
iajs-812	78	11	-semi	-semi	NOUN
iajs-812	78	12	-	-	PUNCT
iajs-812	78	13	p	p	X
iajs-812	78	14	-	-	PUNCT
iajs-812	78	15	open	open	ADJ
iajs-812	78	16	set	set	NOUN
iajs-812	78	17	}	}	PUNCT
iajs-812	78	18	.	.	PUNCT
iajs-812	79	1	4the	4the	NUM
iajs-812	79	2	diagonal	diagonal	NOUN
iajs-812	79	3	is	be	AUX
iajs-812	79	4	a	a	DET
iajs-812	79	5	semi	semi	ADJ
iajs-812	79	6	-	-	ADJ
iajs-812	79	7	p	p	ADJ
iajs-812	79	8	-	-	PUNCT
iajs-812	79	9	closed	close	VERB
iajs-812	79	10	subset	subset	NOUN
iajs-812	79	11	of	of	ADP
iajs-812	79	12	proof	proof	NOUN
iajs-812	79	13	:	:	PUNCT
iajs-812	79	14	let	let	VERB
iajs-812	79	15	such	such	ADJ
iajs-812	79	16	that	that	PRON
iajs-812	79	17	,	,	PUNCT
iajs-812	79	18	since	since	SCONJ
iajs-812	79	19	is	be	AUX
iajs-812	79	20	pairwise	pairwise	NOUN
iajs-812	79	21	semi	semi	ADJ
iajs-812	79	22	-	-	NOUN
iajs-812	79	23	pspace	pspace	NOUN
iajs-812	79	24	,	,	PUNCT
iajs-812	79	25	there	there	PRON
iajs-812	79	26	exists	exist	VERB
iajs-812	79	27	-semi	-semi	NOUN
iajs-812	79	28	-	-	PUNCT
iajs-812	79	29	p	p	X
iajs-812	79	30	-	-	PUNCT
iajs-812	79	31	open	open	ADJ
iajs-812	79	32	set	set	NOUN
iajs-812	79	33	u	u	NOUN
iajs-812	79	34	and	and	CCONJ
iajs-812	79	35	-semi	-semi	NOUN
iajs-812	79	36	-	-	PUNCT
iajs-812	79	37	p	p	X
iajs-812	79	38	-	-	PUNCT
iajs-812	79	39	open	open	NOUN
iajs-812	79	40	set	set	NOUN
iajs-812	79	41	v	v	ADP
iajs-812	79	42	such	such	ADJ
iajs-812	79	43	that	that	PRON
iajs-812	79	44	and	and	CCONJ
iajs-812	79	45	.	.	PUNCT
iajs-812	80	1	hence	hence	ADV
iajs-812	80	2	-semi	-semi	NOUN
iajs-812	80	3	-	-	PUNCT
iajs-812	80	4	pclu	pclu	NOUN
iajs-812	80	5	,	,	PUNCT
iajs-812	80	6	since	since	SCONJ
iajs-812	80	7	we	we	PRON
iajs-812	80	8	have	have	VERB
iajs-812	80	9	a	a	DET
iajs-812	80	10	semi	semi	ADJ
iajs-812	80	11	-	-	ADJ
iajs-812	80	12	p	p	ADJ
iajs-812	80	13	-	-	PUNCT
iajs-812	80	14	open	open	NOUN
iajs-812	80	15	set	set	NOUN
iajs-812	80	16	v	v	ADP
iajs-812	80	17	such	such	ADJ
iajs-812	80	18	that	that	PRON
iajs-812	80	19	,	,	PUNCT
iajs-812	80	20	but	but	CCONJ
iajs-812	80	21	.	.	PUNCT
iajs-812	81	1	suppose	suppose	VERB
iajs-812	81	2	that	that	SCONJ
iajs-812	81	3	there	there	PRON
iajs-812	81	4	exists	exist	VERB
iajs-812	81	5	in	in	ADP
iajs-812	81	6	x	x	PRON
iajs-812	81	7	,	,	PUNCT
iajs-812	81	8	such	such	ADJ
iajs-812	81	9	that	that	SCONJ
iajs-812	81	10	-semi	-semi	NOUN
iajs-812	81	11	-	-	PUNCT
iajs-812	81	12	pclu	pclu	NOUN
iajs-812	81	13	;	;	PUNCT
iajs-812	81	14	and	and	CCONJ
iajs-812	81	15	u	u	NOUN
iajs-812	81	16	is	be	AUX
iajs-812	81	17	semi	semi	ADJ
iajs-812	81	18	-	-	ADJ
iajs-812	81	19	p	p	ADJ
iajs-812	81	20	-	-	PUNCT
iajs-812	81	21	open	open	ADJ
iajs-812	81	22	set	set	NOUN
iajs-812	81	23	}	}	PUNCT
iajs-812	81	24	;	;	PUNCT
iajs-812	81	25	implies	imply	VERB
iajs-812	81	26	-semi	-semi	NOUN
iajs-812	81	27	-	-	PUNCT
iajs-812	81	28	pclu	pclu	NOUN
iajs-812	81	29	;	;	PUNCT
iajs-812	81	30	for	for	ADP
iajs-812	81	31	all	all	DET
iajs-812	81	32	-semi	-semi	NOUN
iajs-812	81	33	-	-	PUNCT
iajs-812	81	34	p	p	X
iajs-812	81	35	-	-	PUNCT
iajs-812	81	36	open	open	ADJ
iajs-812	81	37	set	set	NOUN
iajs-812	81	38	u	u	NOUN
iajs-812	81	39	,	,	PUNCT
iajs-812	81	40	which	which	PRON
iajs-812	81	41	is	be	AUX
iajs-812	81	42	a	a	DET
iajs-812	81	43	contradiction	contradiction	NOUN
iajs-812	81	44	,	,	PUNCT
iajs-812	81	45	thus	thus	ADV
iajs-812	81	46	for	for	ADP
iajs-812	81	47	each	each	DET
iajs-812	81	48	,	,	PUNCT
iajs-812	81	49	-semi	-semi	NOUN
iajs-812	81	50	-	-	PUNCT
iajs-812	81	51	pclu	pclu	NOUN
iajs-812	81	52	:	:	PUNCT
iajs-812	81	53	and	and	CCONJ
iajs-812	81	54	u	u	NOUN
iajs-812	81	55	is	be	AUX
iajs-812	81	56	-semi	-semi	NOUN
iajs-812	81	57	-	-	PUNCT
iajs-812	81	58	p	p	X
iajs-812	81	59	-	-	PUNCT
iajs-812	81	60	open	open	ADJ
iajs-812	81	61	set	set	NOUN
iajs-812	81	62	}	}	PUNCT
iajs-812	81	63	.	.	PUNCT
iajs-812	82	1	to	to	PART
iajs-812	82	2	prove	prove	VERB
iajs-812	82	3	is	be	AUX
iajs-812	82	4	a	a	DET
iajs-812	82	5	semi	semi	ADJ
iajs-812	82	6	-	-	ADJ
iajs-812	82	7	p	p	ADJ
iajs-812	82	8	-	-	PUNCT
iajs-812	82	9	closed	close	VERB
iajs-812	82	10	subset	subset	NOUN
iajs-812	82	11	of	of	ADP
iajs-812	82	12	,	,	PUNCT
iajs-812	82	13	that	that	PRON
iajs-812	82	14	is	is	ADV
iajs-812	82	15	mean	mean	VERB
iajs-812	82	16	we	we	PRON
iajs-812	82	17	must	must	AUX
iajs-812	82	18	prove	prove	VERB
iajs-812	82	19	is	be	AUX
iajs-812	82	20	semi	semi	ADJ
iajs-812	82	21	-	-	ADJ
iajs-812	82	22	p	p	ADJ
iajs-812	82	23	-	-	PUNCT
iajs-812	82	24	open	open	ADJ
iajs-812	83	1	subset	subset	NOUN
iajs-812	83	2	of	of	ADP
iajs-812	83	3	let	let	VERB
iajs-812	83	4	,	,	PUNCT
iajs-812	83	5	which	which	PRON
iajs-812	83	6	implies	imply	VERB
iajs-812	83	7	that	that	SCONJ
iajs-812	83	8	in	in	ADP
iajs-812	83	9	view	view	NOUN
iajs-812	83	10	of	of	ADP
iajs-812	83	11	(	(	PUNCT
iajs-812	83	12	3	3	NUM
iajs-812	83	13	)	)	PUNCT
iajs-812	83	14	,	,	PUNCT
iajs-812	83	15	there	there	PRON
iajs-812	83	16	exists	exist	VERB
iajs-812	83	17	a	a	DET
iajs-812	83	18	-semi	-semi	NOUN
iajs-812	83	19	-	-	PUNCT
iajs-812	83	20	popen	popen	NOUN
iajs-812	83	21	set	set	NOUN
iajs-812	83	22	u	u	NOUN
iajs-812	83	23	containing	contain	VERB
iajs-812	83	24	x	x	PUNCT
iajs-812	83	25	and	and	CCONJ
iajs-812	83	26	-semi	-semi	NOUN
iajs-812	83	27	-	-	PUNCT
iajs-812	83	28	pclu	pclu	NOUN
iajs-812	83	29	.	.	PUNCT
iajs-812	84	1	ibn	ibn	PROPN
iajs-812	84	2	alhaitham	alhaitham	PROPN
iajs-812	84	3	j.	j.	PROPN
iajs-812	84	4	for	for	ADP
iajs-812	84	5	pure	pure	ADJ
iajs-812	84	6	&	&	CCONJ
iajs-812	84	7	appl	appl	PROPN
iajs-812	84	8	.	.	PUNCT
iajs-812	85	1	sci	sci	PROPN
iajs-812	85	2	.	.	PUNCT
iajs-812	85	3	vol.24	vol.24	NOUN
iajs-812	85	4	(	(	PUNCT
iajs-812	85	5	3	3	NUM
iajs-812	85	6	)	)	PUNCT
iajs-812	85	7	2011	2011	NUM
iajs-812	85	8	we	we	PRON
iajs-812	85	9	know	know	VERB
iajs-812	85	10	that	that	SCONJ
iajs-812	85	11	-semi	-semi	NOUN
iajs-812	85	12	-	-	PUNCT
iajs-812	85	13	pclu	pclu	NOUN
iajs-812	85	14	)	)	PUNCT
iajs-812	85	15	=	=	PUNCT
iajs-812	85	16	.	.	PUNCT
iajs-812	86	1	also	also	ADV
iajs-812	86	2	,	,	PUNCT
iajs-812	86	3	we	we	PRON
iajs-812	86	4	have	have	VERB
iajs-812	86	5	-semi	-semi	NOUN
iajs-812	86	6	-	-	PUNCT
iajs-812	86	7	pclu	pclu	NOUN
iajs-812	86	8	)	)	PUNCT
iajs-812	86	9	.	.	PUNCT
iajs-812	87	1	so	so	ADV
iajs-812	87	2	-semi	-semi	PROPN
iajs-812	87	3	-	-	PUNCT
iajs-812	87	4	pcl	pcl	NOUN
iajs-812	87	5	u	u	NOUN
iajs-812	87	6	)	)	PUNCT
iajs-812	87	7	.	.	PUNCT
iajs-812	88	1	but	but	CCONJ
iajs-812	88	2	-semi	-semi	NOUN
iajs-812	88	3	-	-	PUNCT
iajs-812	88	4	pclu	pclu	NOUN
iajs-812	88	5	)	)	PUNCT
iajs-812	88	6	is	be	AUX
iajs-812	88	7	a	a	DET
iajs-812	88	8	semi	semi	ADJ
iajs-812	88	9	-	-	ADJ
iajs-812	88	10	p	p	ADJ
iajs-812	88	11	open	open	ADJ
iajs-812	88	12	set	set	NOUN
iajs-812	88	13	,	,	PUNCT
iajs-812	88	14	so	so	ADV
iajs-812	88	15	is	be	AUX
iajs-812	88	16	a	a	DET
iajs-812	88	17	-semi	-semi	NOUN
iajs-812	88	18	-	-	PUNCT
iajs-812	88	19	p	p	NOUN
iajs-812	88	20	-	-	PUNCT
iajs-812	88	21	nbd	nbd	PROPN
iajs-812	88	22	of	of	ADP
iajs-812	88	23	each	each	PRON
iajs-812	88	24	of	of	ADP
iajs-812	88	25	its	its	PRON
iajs-812	88	26	points	point	NOUN
iajs-812	88	27	.	.	PUNCT
iajs-812	89	1	thus	thus	ADV
iajs-812	89	2	is	be	AUX
iajs-812	89	3	-semi	-semi	NOUN
iajs-812	89	4	-	-	PUNCT
iajs-812	89	5	pclosed	pclose	VERB
iajs-812	89	6	set	set	NOUN
iajs-812	89	7	.	.	PUNCT
iajs-812	90	1	let	let	VERB
iajs-812	90	2	in	in	ADP
iajs-812	90	3	x	x	NOUN
iajs-812	90	4	,	,	PUNCT
iajs-812	90	5	hence	hence	ADV
iajs-812	90	6	.	.	PUNCT
iajs-812	91	1	since	since	SCONJ
iajs-812	91	2	is	be	AUX
iajs-812	91	3	-semi	-semi	NOUN
iajs-812	91	4	-	-	PUNCT
iajs-812	91	5	p	p	ADV
iajs-812	91	6	-	-	PUNCT
iajs-812	91	7	closed	close	VERB
iajs-812	91	8	set	set	NOUN
iajs-812	91	9	,	,	PUNCT
iajs-812	91	10	is	be	AUX
iajs-812	91	11	a	a	DET
iajs-812	91	12	semi	semi	ADJ
iajs-812	91	13	-	-	ADJ
iajs-812	91	14	p	p	ADJ
iajs-812	91	15	-	-	PUNCT
iajs-812	91	16	nbd	nbd	PROPN
iajs-812	91	17	of	of	ADP
iajs-812	91	18	each	each	PRON
iajs-812	91	19	of	of	ADP
iajs-812	91	20	it	it	PRON
iajs-812	91	21	is	be	AUX
iajs-812	91	22	points	point	NOUN
iajs-812	91	23	.	.	PUNCT
iajs-812	92	1	therefore	therefore	ADV
iajs-812	92	2	,	,	PUNCT
iajs-812	92	3	there	there	PRON
iajs-812	92	4	exists	exist	VERB
iajs-812	92	5	a	a	DET
iajs-812	92	6	-semi	-semi	NOUN
iajs-812	92	7	-	-	PUNCT
iajs-812	92	8	p	p	NOUN
iajs-812	92	9	-	-	PUNCT
iajs-812	92	10	open	open	ADJ
iajs-812	92	11	set	set	NOUN
iajs-812	92	12	containing	contain	VERB
iajs-812	92	13	and	and	CCONJ
iajs-812	92	14	contained	contain	VERB
iajs-812	92	15	in	in	ADP
iajs-812	92	16	then	then	ADV
iajs-812	92	17	u	u	NOUN
iajs-812	92	18	is	be	AUX
iajs-812	92	19	-semi	-semi	NOUN
iajs-812	92	20	-	-	PUNCT
iajs-812	92	21	p	p	X
iajs-812	92	22	-	-	PUNCT
iajs-812	92	23	open	open	NOUN
iajs-812	92	24	set	set	NOUN
iajs-812	92	25	and	and	CCONJ
iajs-812	92	26	v	v	NOUN
iajs-812	92	27	is	be	AUX
iajs-812	92	28	-semi	-semi	NOUN
iajs-812	92	29	-	-	PUNCT
iajs-812	92	30	popen	popen	NOUN
iajs-812	92	31	set	set	NOUN
iajs-812	92	32	,	,	PUNCT
iajs-812	92	33	also	also	ADV
iajs-812	92	34	and	and	CCONJ
iajs-812	92	35	,	,	PUNCT
iajs-812	92	36	since	since	SCONJ
iajs-812	92	37	,	,	PUNCT
iajs-812	92	38	.	.	PUNCT
iajs-812	93	1	thus	thus	ADV
iajs-812	93	2	is	be	AUX
iajs-812	93	3	pairwise	pairwise	NOUN
iajs-812	93	4	semi	semi	ADJ
iajs-812	93	5	-	-	NOUN
iajs-812	93	6	pspace	pspace	NOUN
iajs-812	93	7	.	.	PUNCT
iajs-812	94	1	■	■	PUNCT
iajs-812	94	2	definition	definition	NOUN
iajs-812	94	3	3.14	3.14	NUM
iajs-812	94	4	:	:	PUNCT
iajs-812	94	5	a	a	DET
iajs-812	94	6	space	space	NOUN
iajs-812	94	7	is	be	AUX
iajs-812	94	8	said	say	VERB
iajs-812	94	9	to	to	PART
iajs-812	94	10	be	be	AUX
iajs-812	94	11	pairwise	pairwise	NOUN
iajs-812	94	12	semi	semi	ADJ
iajs-812	94	13	-	-	ADJ
iajs-812	94	14	p	p	ADJ
iajs-812	94	15	-	-	PUNCT
iajs-812	94	16	regularspace	regularspace	NOUN
iajs-812	94	17	,	,	PUNCT
iajs-812	94	18	if	if	SCONJ
iajs-812	94	19	for	for	ADP
iajs-812	94	20	each	each	DET
iajs-812	94	21	-closed	-close	VERB
iajs-812	94	22	set	set	VERB
iajs-812	94	23	f	f	NOUN
iajs-812	94	24	and	and	CCONJ
iajs-812	94	25	for	for	ADP
iajs-812	94	26	each	each	DET
iajs-812	94	27	point	point	NOUN
iajs-812	94	28	,	,	PUNCT
iajs-812	94	29	there	there	PRON
iajs-812	94	30	exist	exist	VERB
iajs-812	94	31	semi	semi	ADJ
iajs-812	94	32	-	-	ADJ
iajs-812	94	33	p	p	ADJ
iajs-812	94	34	-	-	PUNCT
iajs-812	94	35	open	open	ADJ
iajs-812	94	36	set	set	NOUN
iajs-812	94	37	u	u	NOUN
iajs-812	94	38	and	and	CCONJ
iajs-812	94	39	semi	semi	ADJ
iajs-812	94	40	-	-	ADJ
iajs-812	94	41	p	p	ADJ
iajs-812	94	42	-	-	PUNCT
iajs-812	94	43	open	open	NOUN
iajs-812	94	44	set	set	NOUN
iajs-812	94	45	v	v	ADP
iajs-812	94	46	such	such	ADJ
iajs-812	94	47	that	that	PRON
iajs-812	94	48	and	and	CCONJ
iajs-812	94	49	,	,	PUNCT
iajs-812	94	50	where	where	SCONJ
iajs-812	94	51	i	i	PRON
iajs-812	94	52	,	,	PUNCT
iajs-812	94	53	j=1	j=1	PROPN
iajs-812	94	54	,	,	PUNCT
iajs-812	94	55	2	2	NUM
iajs-812	94	56	,	,	PUNCT
iajs-812	94	57	.	.	PUNCT
iajs-812	95	1	proposition	proposition	NOUN
iajs-812	95	2	3.15	3.15	NUM
iajs-812	95	3	:	:	PUNCT
iajs-812	95	4	every	every	DET
iajs-812	95	5	pairwise	pairwise	NOUN
iajs-812	95	6	regular	regular	ADJ
iajs-812	95	7	space	space	NOUN
iajs-812	95	8	is	be	AUX
iajs-812	95	9	pairwise	pairwise	NOUN
iajs-812	95	10	semi	semi	ADJ
iajs-812	95	11	-	-	ADJ
iajs-812	95	12	p	p	ADJ
iajs-812	95	13	-	-	PUNCT
iajs-812	95	14	regularspace	regularspace	NOUN
iajs-812	95	15	.	.	PUNCT
iajs-812	96	1	proof	proof	NOUN
iajs-812	96	2	:	:	PUNCT
iajs-812	96	3	let	let	VERB
iajs-812	96	4	f	f	PRON
iajs-812	96	5	be	be	AUX
iajs-812	96	6	any	any	PRON
iajs-812	96	7	-closed	-close	VERB
iajs-812	96	8	set	set	NOUN
iajs-812	96	9	and	and	CCONJ
iajs-812	96	10	let	let	VERB
iajs-812	96	11	,	,	PUNCT
iajs-812	96	12	such	such	ADJ
iajs-812	96	13	that	that	SCONJ
iajs-812	96	14	,	,	PUNCT
iajs-812	96	15	since	since	SCONJ
iajs-812	96	16	is	be	AUX
iajs-812	96	17	pairwise	pairwise	VERB
iajs-812	96	18	regular	regular	ADJ
iajs-812	96	19	space	space	NOUN
iajs-812	96	20	,	,	PUNCT
iajs-812	96	21	there	there	PRON
iajs-812	96	22	exist	exist	VERB
iajs-812	96	23	open	open	ADJ
iajs-812	96	24	set	set	VERB
iajs-812	96	25	u	u	NOUN
iajs-812	96	26	and	and	CCONJ
iajs-812	96	27	open	open	ADJ
iajs-812	96	28	set	set	VERB
iajs-812	96	29	v	v	ADP
iajs-812	96	30	such	such	ADJ
iajs-812	96	31	that	that	PRON
iajs-812	96	32	and	and	CCONJ
iajs-812	96	33	.	.	PUNCT
iajs-812	97	1	and	and	CCONJ
iajs-812	97	2	from	from	ADP
iajs-812	97	3	(	(	PUNCT
iajs-812	97	4	proposition	proposition	NOUN
iajs-812	97	5	2.5	2.5	NUM
iajs-812	97	6	part	part	NOUN
iajs-812	97	7	(	(	PUNCT
iajs-812	97	8	1	1	NUM
iajs-812	97	9	)	)	PUNCT
iajs-812	97	10	)	)	PUNCT
iajs-812	97	11	,	,	PUNCT
iajs-812	97	12	we	we	PRON
iajs-812	97	13	have	have	VERB
iajs-812	97	14	semi	semi	ADJ
iajs-812	97	15	-	-	ADJ
iajs-812	97	16	p	p	ADJ
iajs-812	97	17	-	-	PUNCT
iajs-812	97	18	open	open	ADJ
iajs-812	97	19	set	set	NOUN
iajs-812	97	20	u	u	NOUN
iajs-812	97	21	and	and	CCONJ
iajs-812	97	22	semi	semi	ADJ
iajs-812	97	23	-	-	ADJ
iajs-812	97	24	p	p	ADJ
iajs-812	97	25	-	-	PUNCT
iajs-812	97	26	open	open	NOUN
iajs-812	97	27	set	set	NOUN
iajs-812	97	28	v	v	ADP
iajs-812	97	29	such	such	ADJ
iajs-812	97	30	that	that	PRON
iajs-812	97	31	and	and	CCONJ
iajs-812	97	32	.	.	PUNCT
iajs-812	98	1	hence	hence	ADV
iajs-812	98	2	is	be	AUX
iajs-812	98	3	pairwise	pairwise	NOUN
iajs-812	98	4	semi	semi	ADJ
iajs-812	98	5	-	-	ADJ
iajs-812	98	6	p	p	ADJ
iajs-812	98	7	-	-	PUNCT
iajs-812	98	8	regularspace	regularspace	NOUN
iajs-812	98	9	.	.	PUNCT
iajs-812	99	1	■	■	PUNCT
iajs-812	99	2	remark	remark	NOUN
iajs-812	99	3	3.16	3.16	NUM
iajs-812	99	4	:	:	PUNCT
iajs-812	99	5	the	the	DET
iajs-812	99	6	converse	converse	NOUN
iajs-812	99	7	of	of	ADP
iajs-812	99	8	(	(	PUNCT
iajs-812	99	9	proposition	proposition	NOUN
iajs-812	99	10	3.15	3.15	NUM
iajs-812	99	11	)	)	PUNCT
iajs-812	99	12	is	be	AUX
iajs-812	99	13	not	not	PART
iajs-812	99	14	true	true	ADJ
iajs-812	99	15	in	in	ADP
iajs-812	99	16	general	general	ADJ
iajs-812	99	17	,	,	PUNCT
iajs-812	99	18	as	as	SCONJ
iajs-812	99	19	the	the	DET
iajs-812	99	20	following	follow	VERB
iajs-812	99	21	example	example	NOUN
iajs-812	99	22	shows	show	VERB
iajs-812	99	23	:	:	PUNCT
iajs-812	99	24	let	let	VERB
iajs-812	99	25	x={1	x={1	ADJ
iajs-812	99	26	,	,	PUNCT
iajs-812	99	27	2	2	NUM
iajs-812	99	28	,	,	PUNCT
iajs-812	99	29	3	3	NUM
iajs-812	99	30	}	}	PUNCT
iajs-812	99	31	,	,	PUNCT
iajs-812	99	32	,	,	PUNCT
iajs-812	99	33	then	then	ADV
iajs-812	99	34	s	s	NOUN
iajs-812	99	35	-	-	PUNCT
iajs-812	99	36	p(x	p(x	NOUN
iajs-812	99	37	,	,	PUNCT
iajs-812	99	38	=	=	PRON
iajs-812	99	39	{	{	PUNCT
iajs-812	99	40	,	,	PUNCT
iajs-812	99	41	s	s	NOUN
iajs-812	99	42	-	-	PUNCT
iajs-812	99	43	p(x	p(x	NOUN
iajs-812	99	44	,	,	PUNCT
iajs-812	99	45	=	=	PRON
iajs-812	99	46	{	{	PUNCT
iajs-812	99	47	.	.	PUNCT
iajs-812	100	1	then	then	ADV
iajs-812	100	2	x	x	X
iajs-812	100	3	is	be	AUX
iajs-812	100	4	pairwise	pairwise	NOUN
iajs-812	100	5	semi	semi	ADJ
iajs-812	100	6	-	-	ADJ
iajs-812	100	7	p	p	ADJ
iajs-812	100	8	-	-	PUNCT
iajs-812	100	9	regular	regular	ADJ
iajs-812	100	10	space	space	NOUN
iajs-812	100	11	,	,	PUNCT
iajs-812	100	12	but	but	CCONJ
iajs-812	100	13	not	not	PART
iajs-812	100	14	pairwise	pairwise	VERB
iajs-812	100	15	regular	regular	ADJ
iajs-812	100	16	space	space	NOUN
iajs-812	100	17	since	since	SCONJ
iajs-812	100	18	{	{	PUNCT
iajs-812	100	19	3	3	X
iajs-812	100	20	}	}	PUNCT
iajs-812	100	21	is	be	AUX
iajs-812	100	22	closed	close	VERB
iajs-812	100	23	set	set	VERB
iajs-812	100	24	in	in	ADP
iajs-812	100	25	and	and	CCONJ
iajs-812	100	26	{	{	PUNCT
iajs-812	100	27	3	3	NUM
iajs-812	100	28	}	}	PUNCT
iajs-812	100	29	,	,	PUNCT
iajs-812	100	30	but	but	CCONJ
iajs-812	100	31	for	for	ADP
iajs-812	100	32	any	any	DET
iajs-812	100	33	open	open	ADJ
iajs-812	100	34	set	set	NOUN
iajs-812	100	35	containing	contain	VERB
iajs-812	100	36	1	1	NUM
iajs-812	100	37	and	and	CCONJ
iajs-812	100	38	for	for	ADP
iajs-812	100	39	any	any	DET
iajs-812	100	40	-open	-open	ADJ
iajs-812	100	41	set	set	NOUN
iajs-812	100	42	containing	contain	VERB
iajs-812	100	43	{	{	PUNCT
iajs-812	100	44	3	3	NUM
iajs-812	100	45	}	}	PUNCT
iajs-812	100	46	,	,	PUNCT
iajs-812	100	47	its	its	PRON
iajs-812	100	48	intersection	intersection	NOUN
iajs-812	100	49	is	be	AUX
iajs-812	100	50	not	not	PART
iajs-812	100	51	empty	empty	ADJ
iajs-812	100	52	.	.	PUNCT
iajs-812	101	1	theorem	theorem	VERB
iajs-812	101	2	3.17	3.17	NUM
iajs-812	101	3	:	:	PUNCT
iajs-812	101	4	a	a	DET
iajs-812	101	5	space	space	NOUN
iajs-812	101	6	is	be	AUX
iajs-812	101	7	pairwise	pairwise	NOUN
iajs-812	101	8	semi	semi	ADJ
iajs-812	101	9	-	-	ADJ
iajs-812	101	10	p	p	ADJ
iajs-812	101	11	-	-	PUNCT
iajs-812	101	12	regularspace	regularspace	NOUN
iajs-812	101	13	if	if	SCONJ
iajs-812	101	14	and	and	CCONJ
iajs-812	101	15	only	only	ADV
iajs-812	101	16	if	if	SCONJ
iajs-812	101	17	for	for	ADP
iajs-812	101	18	each	each	DET
iajs-812	101	19	point	point	NOUN
iajs-812	101	20	x	x	PUNCT
iajs-812	101	21	in	in	ADP
iajs-812	101	22	x	x	SYM
iajs-812	101	23	and	and	CCONJ
iajs-812	101	24	every	every	DET
iajs-812	101	25	closed	close	VERB
iajs-812	101	26	set	set	NOUN
iajs-812	101	27	f	f	NOUN
iajs-812	101	28	not	not	PART
iajs-812	101	29	containing	contain	VERB
iajs-812	101	30	x	x	PUNCT
iajs-812	101	31	there	there	PRON
iajs-812	101	32	is	be	VERB
iajs-812	101	33	a	a	DET
iajs-812	101	34	semi	semi	ADJ
iajs-812	101	35	-	-	ADJ
iajs-812	101	36	p	p	ADJ
iajs-812	101	37	-	-	PUNCT
iajs-812	101	38	open	open	NOUN
iajs-812	101	39	set	set	NOUN
iajs-812	101	40	u	u	PRON
iajs-812	101	41	such	such	ADJ
iajs-812	101	42	that	that	PRON
iajs-812	101	43	and	and	CCONJ
iajs-812	101	44	(	(	PUNCT
iajs-812	101	45	proof	proof	NOUN
iajs-812	101	46	:	:	PUNCT
iajs-812	101	47	suppose	suppose	VERB
iajs-812	101	48	is	be	AUX
iajs-812	101	49	pairwise	pairwise	NOUN
iajs-812	101	50	semi	semi	ADJ
iajs-812	101	51	-	-	ADJ
iajs-812	101	52	p	p	ADJ
iajs-812	101	53	-	-	PUNCT
iajs-812	101	54	regularspace	regularspace	NOUN
iajs-812	101	55	,	,	PUNCT
iajs-812	101	56	let	let	VERB
iajs-812	101	57	and	and	CCONJ
iajs-812	101	58	f	f	PROPN
iajs-812	101	59	is	be	AUX
iajs-812	101	60	any	any	DET
iajs-812	101	61	closed	closed	ADJ
iajs-812	101	62	set	set	NOUN
iajs-812	101	63	such	such	ADJ
iajs-812	101	64	that	that	PRON
iajs-812	101	65	,	,	PUNCT
iajs-812	101	66	implies	imply	VERB
iajs-812	101	67	is	be	AUX
iajs-812	101	68	-open	-open	ADJ
iajs-812	101	69	set	set	VERB
iajs-812	101	70	containing	contain	VERB
iajs-812	101	71	x	x	PUNCT
iajs-812	101	72	and	and	CCONJ
iajs-812	101	73	since	since	SCONJ
iajs-812	101	74	is	be	AUX
iajs-812	101	75	pairwise	pairwise	PROPN
iajs-812	101	76	ibn	ibn	PROPN
iajs-812	101	77	alhaitham	alhaitham	NOUN
iajs-812	101	78	j.	j.	PROPN
iajs-812	101	79	for	for	ADP
iajs-812	101	80	pure	pure	ADJ
iajs-812	101	81	&	&	CCONJ
iajs-812	101	82	appl	appl	PROPN
iajs-812	101	83	.	.	PUNCT
iajs-812	102	1	sci	sci	PROPN
iajs-812	102	2	.	.	PUNCT
iajs-812	102	3	vol.24	vol.24	NOUN
iajs-812	102	4	(	(	PUNCT
iajs-812	102	5	3	3	NUM
iajs-812	102	6	)	)	PUNCT
iajs-812	102	7	2011	2011	NUM
iajs-812	102	8	semi	semi	ADJ
iajs-812	102	9	-	-	ADJ
iajs-812	102	10	p	p	ADJ
iajs-812	102	11	-	-	PUNCT
iajs-812	102	12	regularspace	regularspace	NOUN
iajs-812	102	13	,	,	PUNCT
iajs-812	102	14	there	there	PRON
iajs-812	102	15	is	be	VERB
iajs-812	102	16	a	a	DET
iajs-812	102	17	semi	semi	ADJ
iajs-812	102	18	-	-	ADJ
iajs-812	102	19	p	p	ADJ
iajs-812	102	20	-	-	PUNCT
iajs-812	102	21	open	open	NOUN
iajs-812	102	22	set	set	NOUN
iajs-812	102	23	u	u	PRON
iajs-812	102	24	such	such	ADJ
iajs-812	102	25	that	that	SCONJ
iajs-812	102	26	hence	hence	ADV
iajs-812	102	27	(	(	PUNCT
iajs-812	102	28	conversely	conversely	ADV
iajs-812	102	29	,	,	PUNCT
iajs-812	102	30	let	let	VERB
iajs-812	102	31	f	f	PRON
iajs-812	102	32	be	be	AUX
iajs-812	102	33	any	any	DET
iajs-812	102	34	closed	closed	ADJ
iajs-812	102	35	set	set	NOUN
iajs-812	102	36	and	and	CCONJ
iajs-812	102	37	then	then	ADV
iajs-812	102	38	there	there	PRON
iajs-812	102	39	exists	exist	VERB
iajs-812	102	40	a	a	DET
iajs-812	102	41	semi	semi	ADJ
iajs-812	102	42	-	-	ADJ
iajs-812	102	43	p	p	ADJ
iajs-812	102	44	-	-	PUNCT
iajs-812	102	45	open	open	NOUN
iajs-812	102	46	set	set	NOUN
iajs-812	102	47	u	u	PRON
iajs-812	102	48	such	such	ADJ
iajs-812	102	49	that	that	PRON
iajs-812	102	50	and	and	CCONJ
iajs-812	102	51	(	(	PUNCT
iajs-812	102	52	let	let	VERB
iajs-812	102	53	v=	v=	INTJ
iajs-812	102	54	(	(	PUNCT
iajs-812	102	55	then	then	ADV
iajs-812	102	56	v	v	NOUN
iajs-812	102	57	is	be	AUX
iajs-812	102	58	-semi	-semi	NOUN
iajs-812	102	59	-	-	PUNCT
iajs-812	102	60	p	p	X
iajs-812	102	61	-	-	PUNCT
iajs-812	102	62	open	open	NOUN
iajs-812	102	63	set	set	NOUN
iajs-812	102	64	such	such	ADJ
iajs-812	102	65	that	that	PRON
iajs-812	102	66	and	and	CCONJ
iajs-812	102	67	,	,	PUNCT
iajs-812	102	68	thus	thus	ADV
iajs-812	102	69	is	be	AUX
iajs-812	102	70	pairwise	pairwise	NOUN
iajs-812	102	71	semi	semi	ADJ
iajs-812	102	72	-	-	ADJ
iajs-812	102	73	p	p	ADJ
iajs-812	102	74	-	-	PUNCT
iajs-812	102	75	regularspace	regularspace	NOUN
iajs-812	102	76	.	.	PUNCT
iajs-812	103	1	■	■	PUNCT
iajs-812	103	2	definition	definition	NOUN
iajs-812	103	3	3.18	3.18	NUM
iajs-812	103	4	:	:	PUNCT
iajs-812	103	5	a	a	DET
iajs-812	103	6	space	space	NOUN
iajs-812	103	7	is	be	AUX
iajs-812	103	8	said	say	VERB
iajs-812	103	9	to	to	PART
iajs-812	103	10	be	be	AUX
iajs-812	103	11	pairwise	pairwise	NOUN
iajs-812	103	12	semi	semi	ADJ
iajs-812	103	13	-	-	ADJ
iajs-812	103	14	p	p	ADJ
iajs-812	103	15	-	-	PUNCT
iajs-812	103	16	normalspace	normalspace	NOUN
iajs-812	103	17	,	,	PUNCT
iajs-812	103	18	if	if	SCONJ
iajs-812	103	19	for	for	ADP
iajs-812	103	20	each	each	DET
iajs-812	103	21	-closed	-close	VERB
iajs-812	103	22	set	set	VERB
iajs-812	103	23	a	a	PRON
iajs-812	103	24	and	and	CCONJ
iajs-812	103	25	closed	closed	ADJ
iajs-812	103	26	set	set	VERB
iajs-812	103	27	b	b	PROPN
iajs-812	103	28	disjoint	disjoint	NOUN
iajs-812	103	29	from	from	ADP
iajs-812	103	30	a	a	PRON
iajs-812	103	31	,	,	PUNCT
iajs-812	103	32	there	there	PRON
iajs-812	103	33	exist	exist	VERB
iajs-812	103	34	semi	semi	ADJ
iajs-812	103	35	-	-	ADJ
iajs-812	103	36	p	p	ADJ
iajs-812	103	37	-	-	PUNCT
iajs-812	103	38	open	open	ADJ
iajs-812	103	39	set	set	NOUN
iajs-812	103	40	u	u	NOUN
iajs-812	103	41	and	and	CCONJ
iajs-812	103	42	semi	semi	ADJ
iajs-812	103	43	-	-	ADJ
iajs-812	103	44	p	p	ADJ
iajs-812	103	45	-	-	PUNCT
iajs-812	103	46	open	open	NOUN
iajs-812	103	47	set	set	NOUN
iajs-812	103	48	v	v	ADP
iajs-812	103	49	such	such	ADJ
iajs-812	103	50	that	that	PRON
iajs-812	103	51	and	and	CCONJ
iajs-812	103	52	,	,	PUNCT
iajs-812	103	53	where	where	SCONJ
iajs-812	103	54	i	i	PRON
iajs-812	103	55	,	,	PUNCT
iajs-812	103	56	j=1	j=1	PROPN
iajs-812	103	57	,	,	PUNCT
iajs-812	103	58	2	2	NUM
iajs-812	103	59	,	,	PUNCT
iajs-812	103	60	.	.	PUNCT
iajs-812	104	1	proposition	proposition	NOUN
iajs-812	104	2	3.19	3.19	NUM
iajs-812	104	3	:	:	PUNCT
iajs-812	104	4	every	every	DET
iajs-812	104	5	pairwise	pairwise	NOUN
iajs-812	104	6	normal	normal	ADJ
iajs-812	104	7	space	space	NOUN
iajs-812	104	8	is	be	AUX
iajs-812	104	9	pairwise	pairwise	NOUN
iajs-812	104	10	semi	semi	ADJ
iajs-812	104	11	-	-	ADJ
iajs-812	104	12	p	p	ADJ
iajs-812	104	13	-	-	PUNCT
iajs-812	104	14	normalspace	normalspace	NOUN
iajs-812	104	15	.	.	PUNCT
iajs-812	105	1	proof	proof	NOUN
iajs-812	105	2	:	:	PUNCT
iajs-812	105	3	let	let	VERB
iajs-812	105	4	a	a	DET
iajs-812	105	5	,	,	PUNCT
iajs-812	105	6	b	b	NOUN
iajs-812	105	7	be	be	AUX
iajs-812	105	8	two	two	NUM
iajs-812	105	9	closed	closed	ADJ
iajs-812	105	10	disjoint	disjoint	NOUN
iajs-812	105	11	sets	set	NOUN
iajs-812	105	12	in	in	ADP
iajs-812	105	13	(	(	PUNCT
iajs-812	105	14	respectively	respectively	ADV
iajs-812	105	15	)	)	PUNCT
iajs-812	105	16	,	,	PUNCT
iajs-812	105	17	since	since	SCONJ
iajs-812	105	18	x	x	PRON
iajs-812	105	19	is	be	AUX
iajs-812	105	20	pairwise	pairwise	NOUN
iajs-812	105	21	normal	normal	ADJ
iajs-812	105	22	space	space	NOUN
iajs-812	105	23	,	,	PUNCT
iajs-812	105	24	there	there	PRON
iajs-812	105	25	exist	exist	VERB
iajs-812	105	26	open	open	ADJ
iajs-812	105	27	set	set	VERB
iajs-812	105	28	u	u	NOUN
iajs-812	105	29	and	and	CCONJ
iajs-812	105	30	open	open	ADJ
iajs-812	105	31	set	set	VERB
iajs-812	105	32	v	v	ADP
iajs-812	105	33	such	such	ADJ
iajs-812	105	34	that	that	PRON
iajs-812	105	35	and	and	CCONJ
iajs-812	105	36	but	but	CCONJ
iajs-812	105	37	from	from	ADP
iajs-812	105	38	(	(	PUNCT
iajs-812	105	39	proposition	proposition	NOUN
iajs-812	105	40	2.4	2.4	NUM
iajs-812	105	41	part	part	NOUN
iajs-812	105	42	(	(	PUNCT
iajs-812	105	43	1	1	NUM
iajs-812	105	44	)	)	PUNCT
iajs-812	105	45	)	)	PUNCT
iajs-812	105	46	u	u	NOUN
iajs-812	105	47	,	,	PUNCT
iajs-812	105	48	v	v	ADP
iajs-812	105	49	semi	semi	ADJ
iajs-812	105	50	-	-	ADJ
iajs-812	105	51	p	p	ADJ
iajs-812	105	52	-	-	PUNCT
iajs-812	105	53	open	open	ADJ
iajs-812	105	54	sets	set	NOUN
iajs-812	105	55	which	which	PRON
iajs-812	105	56	contains	contain	VERB
iajs-812	105	57	a	a	PRON
iajs-812	105	58	and	and	CCONJ
iajs-812	105	59	b	b	NOUN
iajs-812	105	60	respectively	respectively	ADV
iajs-812	105	61	.	.	PUNCT
iajs-812	106	1	thus	thus	ADV
iajs-812	106	2	is	be	AUX
iajs-812	106	3	pairwise	pairwise	NOUN
iajs-812	106	4	semi	semi	ADJ
iajs-812	106	5	-	-	ADJ
iajs-812	106	6	p	p	ADJ
iajs-812	106	7	-	-	PUNCT
iajs-812	106	8	normalspace	normalspace	NOUN
iajs-812	106	9	.	.	PUNCT
iajs-812	107	1	■	■	PUNCT
iajs-812	107	2	remark	remark	VERB
iajs-812	107	3	3.20	3.20	NUM
iajs-812	107	4	:	:	PUNCT
iajs-812	107	5	the	the	DET
iajs-812	107	6	converse	converse	NOUN
iajs-812	107	7	of	of	ADP
iajs-812	107	8	proposition	proposition	NOUN
iajs-812	107	9	3.19	3.19	NUM
iajs-812	107	10	is	be	AUX
iajs-812	107	11	not	not	PART
iajs-812	107	12	true	true	ADJ
iajs-812	107	13	in	in	ADP
iajs-812	107	14	general	general	ADJ
iajs-812	107	15	,	,	PUNCT
iajs-812	107	16	as	as	SCONJ
iajs-812	107	17	the	the	DET
iajs-812	107	18	following	follow	VERB
iajs-812	107	19	example	example	NOUN
iajs-812	107	20	shows	show	VERB
iajs-812	107	21	:	:	PUNCT
iajs-812	107	22	consider	consider	VERB
iajs-812	107	23	example	example	NOUN
iajs-812	107	24	2	2	NUM
iajs-812	107	25	,	,	PUNCT
iajs-812	107	26	where	where	SCONJ
iajs-812	107	27	:	:	PUNCT
iajs-812	108	1	x={1	x={1	ADJ
iajs-812	108	2	,	,	PUNCT
iajs-812	108	3	2	2	NUM
iajs-812	108	4	,	,	PUNCT
iajs-812	108	5	3	3	NUM
iajs-812	108	6	}	}	PUNCT
iajs-812	108	7	,	,	PUNCT
iajs-812	108	8	,	,	PUNCT
iajs-812	108	9	s	s	X
iajs-812	108	10	-	-	PUNCT
iajs-812	108	11	p(x	p(x	NOUN
iajs-812	108	12	,	,	PUNCT
iajs-812	108	13	=	=	PRON
iajs-812	108	14	{	{	PUNCT
iajs-812	108	15	,	,	PUNCT
iajs-812	108	16	s	s	NOUN
iajs-812	108	17	-	-	PUNCT
iajs-812	108	18	p(x	p(x	NOUN
iajs-812	108	19	,	,	PUNCT
iajs-812	108	20	=	=	PRON
iajs-812	108	21	{	{	PUNCT
iajs-812	108	22	.	.	PUNCT
iajs-812	109	1	then	then	ADV
iajs-812	109	2	is	be	AUX
iajs-812	109	3	pairwise	pairwise	NOUN
iajs-812	109	4	semi	semi	ADJ
iajs-812	109	5	-	-	ADJ
iajs-812	109	6	p	p	ADJ
iajs-812	109	7	-	-	PUNCT
iajs-812	109	8	normalspace	normalspace	NOUN
iajs-812	109	9	,	,	PUNCT
iajs-812	109	10	but	but	CCONJ
iajs-812	109	11	not	not	PART
iajs-812	109	12	pairwise	pairwise	VERB
iajs-812	109	13	normal	normal	ADJ
iajs-812	109	14	space	space	NOUN
iajs-812	109	15	,	,	PUNCT
iajs-812	109	16	since	since	SCONJ
iajs-812	109	17	{	{	PUNCT
iajs-812	109	18	3	3	NUM
iajs-812	109	19	}	}	PUNCT
iajs-812	109	20	and	and	CCONJ
iajs-812	109	21	{	{	PUNCT
iajs-812	109	22	2	2	X
iajs-812	109	23	}	}	PUNCT
iajs-812	109	24	are	be	AUX
iajs-812	109	25	closed	close	VERB
iajs-812	109	26	disjoint	disjoint	NOUN
iajs-812	109	27	sets	set	NOUN
iajs-812	109	28	in	in	ADP
iajs-812	109	29	respectively	respectively	ADV
iajs-812	109	30	but	but	CCONJ
iajs-812	109	31	for	for	ADP
iajs-812	109	32	any	any	DET
iajs-812	109	33	open	open	ADJ
iajs-812	109	34	set	set	NOUN
iajs-812	109	35	in	in	ADP
iajs-812	109	36	which	which	PRON
iajs-812	109	37	containing	contain	VERB
iajs-812	109	38	{	{	PUNCT
iajs-812	109	39	3	3	NUM
iajs-812	109	40	}	}	PUNCT
iajs-812	109	41	and	and	CCONJ
iajs-812	109	42	any	any	DET
iajs-812	109	43	open	open	ADJ
iajs-812	109	44	set	set	NOUN
iajs-812	109	45	in	in	ADP
iajs-812	109	46	which	which	PRON
iajs-812	109	47	containing	contain	VERB
iajs-812	109	48	{	{	PUNCT
iajs-812	109	49	2	2	NUM
iajs-812	109	50	}	}	PUNCT
iajs-812	109	51	,	,	PUNCT
iajs-812	109	52	its	its	PRON
iajs-812	109	53	intersection	intersection	NOUN
iajs-812	109	54	is	be	AUX
iajs-812	109	55	not	not	PART
iajs-812	109	56	empty	empty	ADJ
iajs-812	109	57	.	.	PUNCT
iajs-812	110	1	references	reference	NOUN
iajs-812	110	2	1	1	NUM
iajs-812	110	3	.	.	PUNCT
iajs-812	111	1	kelly	kelly	PROPN
iajs-812	111	2	,	,	PUNCT
iajs-812	111	3	j.	j.	PROPN
iajs-812	111	4	c.	c.	PROPN
iajs-812	111	5	(	(	PUNCT
iajs-812	111	6	1963	1963	NUM
iajs-812	111	7	)	)	PUNCT
iajs-812	111	8	,	,	PUNCT
iajs-812	111	9	bitopological	bitopological	ADJ
iajs-812	111	10	spaces	space	NOUN
iajs-812	111	11	,	,	PUNCT
iajs-812	111	12	proc	proc	NOUN
iajs-812	111	13	.	.	PUNCT
iajs-812	112	1	london	london	PROPN
iajs-812	112	2	math	math	PROPN
iajs-812	112	3	.	.	PUNCT
iajs-812	113	1	soc	soc	PROPN
iajs-812	113	2	.	.	PUNCT
iajs-812	114	1	13	13	NUM
iajs-812	114	2	:	:	SYM
iajs-812	114	3	71	71	NUM
iajs-812	114	4	-	-	SYM
iajs-812	114	5	89	89	NUM
iajs-812	114	6	.	.	NOUN
iajs-812	115	1	2	2	NUM
iajs-812	115	2	.	.	X
iajs-812	115	3	murdeshwar	murdeshwar	NOUN
iajs-812	115	4	,	,	PUNCT
iajs-812	115	5	n.	n.	PROPN
iajs-812	115	6	g.	g.	PROPN
iajs-812	115	7	and	and	CCONJ
iajs-812	115	8	naimpally	naimpally	ADV
iajs-812	115	9	,	,	PUNCT
iajs-812	115	10	s.	s.	PROPN
iajs-812	115	11	a.	a.	PROPN
iajs-812	115	12	(	(	PUNCT
iajs-812	115	13	1966	1966	NUM
iajs-812	115	14	)	)	PUNCT
iajs-812	115	15	,	,	PUNCT
iajs-812	115	16	quasi	quasi	ADJ
iajs-812	115	17	-	-	ADJ
iajs-812	115	18	uniform	uniform	ADJ
iajs-812	115	19	compact	compact	ADJ
iajs-812	115	20	spaces	space	NOUN
iajs-812	115	21	,	,	PUNCT
iajs-812	115	22	p.	p.	NOUN
iajs-812	115	23	noordhoff	noordhoff	PROPN
iajs-812	115	24	,	,	PUNCT
iajs-812	115	25	groningen	groningen	PROPN
iajs-812	115	26	.	.	PROPN
iajs-812	116	1	3	3	NUM
iajs-812	116	2	.	.	X
iajs-812	116	3	nour	nour	PROPN
iajs-812	116	4	,	,	PUNCT
iajs-812	116	5	t.	t.	PROPN
iajs-812	116	6	m.	m.	NOUN
iajs-812	116	7	(	(	PUNCT
iajs-812	116	8	1995	1995	NUM
iajs-812	116	9	)	)	PUNCT
iajs-812	116	10	,	,	PUNCT
iajs-812	116	11	a	a	DET
iajs-812	116	12	note	note	NOUN
iajs-812	116	13	on	on	ADP
iajs-812	116	14	five	five	NUM
iajs-812	116	15	separation	separation	NOUN
iajs-812	116	16	axioms	axiom	NOUN
iajs-812	116	17	in	in	ADP
iajs-812	116	18	bitopological	bitopological	ADJ
iajs-812	116	19	spaces	space	NOUN
iajs-812	116	20	,	,	PUNCT
iajs-812	116	21	indian	indian	ADJ
iajs-812	116	22	j.	j.	PROPN
iajs-812	116	23	pure	pure	PROPN
iajs-812	116	24	appl	appl	PROPN
iajs-812	116	25	.	.	PUNCT
iajs-812	116	26	math	math	PROPN
iajs-812	116	27	.	.	PUNCT
iajs-812	116	28	,	,	PUNCT
iajs-812	116	29	26(7	26(7	NUM
iajs-812	116	30	):	):	PUNCT
iajs-812	116	31	669	669	NUM
iajs-812	116	32	-	-	SYM
iajs-812	116	33	674	674	NUM
iajs-812	116	34	.	.	PUNCT
iajs-812	117	1	4	4	X
iajs-812	117	2	.	.	X
iajs-812	117	3	al	al	PROPN
iajs-812	117	4	-	-	PUNCT
iajs-812	117	5	kazragi	kazragi	PROPN
iajs-812	117	6	,	,	PUNCT
iajs-812	117	7	r.	r.	PROPN
iajs-812	117	8	b.	b.	PROPN
iajs-812	117	9	(	(	PUNCT
iajs-812	117	10	2004	2004	NUM
iajs-812	117	11	)	)	PUNCT
iajs-812	117	12	,	,	PUNCT
iajs-812	117	13	on	on	ADP
iajs-812	117	14	semi	semi	ADJ
iajs-812	117	15	-	-	ADJ
iajs-812	117	16	p	p	ADJ
iajs-812	117	17	-	-	PUNCT
iajs-812	117	18	open	open	ADJ
iajs-812	117	19	sets	set	NOUN
iajs-812	117	20	,	,	PUNCT
iajs-812	117	21	m.	m.	PROPN
iajs-812	117	22	sc	sc	PROPN
iajs-812	117	23	.	.	PUNCT
iajs-812	118	1	thesis	thesis	PROPN
iajs-812	118	2	,	,	PUNCT
iajs-812	118	3	university	university	NOUN
iajs-812	118	4	of	of	ADP
iajs-812	118	5	baghdad	baghdad	PROPN
iajs-812	118	6	,	,	PUNCT
iajs-812	118	7	college	college	NOUN
iajs-812	118	8	of	of	ADP
iajs-812	118	9	education	education	PROPN
iajs-812	118	10	ibn	ibn	NOUN
iajs-812	118	11	-	-	PUNCT
iajs-812	118	12	alhaitham	alhaitham	NOUN
iajs-812	118	13	.	.	PUNCT
iajs-812	119	1	2011	2011	NUM
iajs-812	119	2	)	)	PUNCT
iajs-812	119	3	3	3	NUM
iajs-812	119	4	(	(	PUNCT
iajs-812	119	5	24مجلة	24مجلة	NUM
iajs-812	119	6	ابن	ابن	VERB
iajs-812	119	7	الهیثم	الهیثم	ADJ
iajs-812	119	8	للعلوم	للعلوم	PROPN
iajs-812	119	9	الصرفة	الصرفة	PROPN
iajs-812	119	10	والتطبیقیة	والتطبیقیة	PROPN
iajs-812	119	11	المجلد	المجلد	VERB
iajs-812	119	12	على	على	PROPN
iajs-812	119	13	الفضاءات	الفضاءات	PROPN
iajs-812	119	14	التبولوجیة	التبولوجیة	NOUN
iajs-812	119	15	–	–	PUNCT
iajs-812	119	16	p	p	NOUN
iajs-812	119	17	–	–	PUNCT
iajs-812	119	18	حول	حول	PROPN
iajs-812	119	19	بدیھیات	بدیھیات	PROPN
iajs-812	119	20	الفصل	الفصل	PROPN
iajs-812	120	1	شبھ	شبھ	PROPN
iajs-812	120	2	الثنائیة	الثنائیة	ADV
iajs-812	120	3	رشا	رشا	PROPN
iajs-812	120	4	ناصر	ناصر	NOUN
iajs-812	120	5	مجید	مجید	PROPN
iajs-812	120	6	جامعة	جامعة	PROPN
iajs-812	120	7	بغداد	بغداد	PROPN
iajs-812	120	8	،	،	PROPN
iajs-812	120	9	ابن	ابن	PROPN
iajs-812	120	10	الھیثم	الھیثم	PROPN
iajs-812	120	11	–	–	PUNCT
iajs-812	120	12	قسم	قسم	PRON
iajs-812	120	13	الریاضیا	الریاضیا	PROPN
iajs-812	120	14	ت	ت	X
iajs-812	120	15	،	،	X
iajs-812	120	16	كلیة	كلیة	PROPN
iajs-812	120	17	التربیة	التربیة	NOUN
iajs-812	120	18	2010تشرین	2010تشرین	NUM
iajs-812	120	19	االول	االول	VERB
iajs-812	120	20	10	10	NUM
iajs-812	120	21	:	:	PUNCT
iajs-812	120	22	استلم	استلم	PROPN
iajs-812	120	23	البحث	البحث	VERB
iajs-812	120	24	في	في	ADP
iajs-812	120	25	2011	2011	NUM
iajs-812	120	26	اذار	اذار	NOUN
iajs-812	120	27	13	13	NUM
iajs-812	120	28	:	:	PUNCT
iajs-812	120	29	في	في	SCONJ
iajs-812	120	30	قبل	قبل	PROPN
iajs-812	120	31	البحث	البحث	PROPN
iajs-812	120	32	خالصةال	خالصةال	PROPN
iajs-812	120	33	في	في	ADP
iajs-812	120	34	هذا	هذا	NOUN
iajs-812	120	35	البحث	البحث	NOUN
iajs-812	120	36	قمنا	قمنا	ADV
iajs-812	120	37	بتعریف	بتعریف	VERB
iajs-812	120	38	نوع	نوع	PROPN
iajs-812	120	39	جدید	جدید	PROPN
iajs-812	120	40	من	من	PROPN
iajs-812	120	41	بدیهیات	بدیهیات	PROPN
iajs-812	120	42	الفصل	الفصل	PROPN
iajs-812	120	43	على	على	NOUN
iajs-812	120	44	الفضاءات	الفضاءات	NOUN
iajs-812	120	45	التبولوجیة	التبولوجیة	NOUN
iajs-812	120	46	الثنائیة	الثنائیة	PROPN
iajs-812	120	47	التي	التي	PROPN
iajs-812	120	48	اسمیناها	اسمیناها	PROPN
iajs-812	120	49	بدیهیات	بدیهیات	PROPN
iajs-812	120	50	كل	كل	PROPN
iajs-812	120	51	نوع	نوع	PROPN
iajs-812	120	52	مع	مع	PROPN
iajs-812	120	53	بدیهیات	بدیهیات	PROPN
iajs-812	120	54	الفصل	الفصل	PROPN
iajs-812	120	55	االعتیادیة	االعتیادیة	NOUN
iajs-812	120	56	في	في	ADP
iajs-812	120	57	سنا	سنا	NOUN
iajs-812	120	58	بعض	بعض	NOUN
iajs-812	120	59	خواص	خواص	ADV
iajs-812	120	60	هذه	هذه	PROPN
iajs-812	120	61	الفضاءات	الفضاءات	PROPN
iajs-812	120	62	وعالقاتكذلك	وعالقاتكذلك	PROPN
iajs-812	120	63	در	در	PROPN
iajs-812	120	64	،	،	PROPN
iajs-812	121	1	p	p	PROPN
iajs-812	121	2	–	–	PUNCT
iajs-812	121	3	الفصل	الفصل	PROPN
iajs-812	121	4	شبه	شبه	NOUN
iajs-812	121	5	.	.	PUNCT
iajs-812	122	1	ات	ات	ADP
iajs-812	122	2	التبولوجیة	التبولوجیة	NOUN
iajs-812	122	3	الثنائیةالفضاء	الثنائیةالفضاء	VERB
iajs-812	122	4	p	p	ADJ
iajs-812	122	5	–	–	PUNCT
iajs-812	122	6	الفضاء	الفضاء	NOUN
iajs-812	122	7	شبه	شبه	VERB
iajs-812	122	8	،	،	NOUN
iajs-812	122	9	p	p	PROPN
iajs-812	122	10	–	–	PUNCT
iajs-812	122	11	الفضاء	الفضاء	NOUN
iajs-812	122	12	شبه	شبه	VERB
iajs-812	122	13	،	،	NOUN
iajs-812	122	14	p	p	PROPN
iajs-812	122	15	–	–	PUNCT
iajs-812	122	16	الفضاء	الفضاء	ADJ
iajs-812	122	17	التبولوجي	التبولوجي	NOUN
iajs-812	122	18	الثنائي	الثنائي	PROPN
iajs-812	122	19	،	،	PROPN
iajs-812	122	20	الفضاء	الفضاء	PROPN
iajs-812	122	21	شبه	شبه	NOUN
iajs-812	122	22	:	:	PUNCT
iajs-812	122	23	یةفتاحالكلمات	یةفتاحالكلمات	NOUN
iajs-812	122	24	الم	الم	VERB
iajs-812	122	25	.االعتیادي	.االعتیادي	NOUN
iajs-812	122	26	–	–	PUNCT
iajs-812	122	27	p	p	X
iajs-812	122	28	–	–	PUNCT
iajs-812	122	29	الفضاء	الفضاء	NOUN
iajs-812	122	30	شبه	شبه	VERB
iajs-812	122	31	القیاسي	القیاسي	PROPN
iajs-812	122	32	،	،	PROPN
iajs-812	122	33	–	–	PUNCT
iajs-812	122	34	p	p	X
iajs-812	122	35	–	–	PUNCT
iajs-812	122	36	الفضاء	الفضاء	NOUN
iajs-812	122	37	شبه	شبه	X
iajs-812	122	38	،	،	NOUN