id	sid	tid	token	lemma	pos
iajs-1184	1	1	2009	2009	NUM
iajs-1184	1	2	)	)	PUNCT
iajs-1184	1	3	3	3	NUM
iajs-1184	1	4	(	(	PUNCT
iajs-1184	1	5	22مجلة	22مجلة	NUM
iajs-1184	1	6	ابن	ابن	PROPN
iajs-1184	1	7	الھیثم	الھیثم	PROPN
iajs-1184	1	8	للعلوم	للعلوم	PROPN
iajs-1184	1	9	الصرفة	الصرفة	PROPN
iajs-1184	1	10	والتطبیقیة	والتطبیقیة	PROPN
iajs-1184	1	11	المجلد	المجلد	VERB
iajs-1184	1	12	قبل	قبل	PROPN
iajs-1184	1	13	المفتوحة	المفتوحة	PROPN
iajs-1184	1	14	شبه	شبه	VERB
iajs-1184	1	15	المجموعاتبعض	المجموعاتبعض	PROPN
iajs-1184	1	16	النتائج	النتائج	PROPN
iajs-1184	1	17	حول	حول	PROPN
iajs-1184	1	18	احمد	احمد	PROPN
iajs-1184	1	19	إبراهیم	إبراهیم	PROPN
iajs-1184	1	20	ناصررشا	ناصررشا	PROPN
iajs-1184	1	21	ناصر	ناصر	NOUN
iajs-1184	1	22	مجید	مجید	PROPN
iajs-1184	1	23	،	،	PROPN
iajs-1184	2	1	د	د	PROPN
iajs-1184	2	2	الهیثم	الهیثم	ADJ
iajs-1184	2	3	،	،	ADJ
iajs-1184	2	4	أبن	أبن	NOUN
iajs-1184	2	5	-كلیة	-كلیة	NOUN
iajs-1184	2	6	التربیة	التربیة	NOUN
iajs-1184	2	7	سم	سم	PRON
iajs-1184	2	8	الریاضیات،ق	الریاضیات،ق	PUNCT
iajs-1184	2	9	جامعة	جامعة	PROPN
iajs-1184	2	10	بغدا	بغدا	PROPN
iajs-1184	2	11	خالصةال	خالصةال	PROPN
iajs-1184	2	12	x)اذا	x)اذا	PROPN
iajs-1184	2	13	كان	كان	PROPN
iajs-1184	2	14	"	"	PUNCT
iajs-1184	2	15	عرفها	عرفها	NOUN
iajs-1184	2	16	بالشكل	بالشكل	PROPN
iajs-1184	2	17	اذ	اذ	PROPN
iajs-1184	2	18	،	،	NOUN
iajs-1184	2	19	إن	إن	X
iajs-1184	2	20	أول	أول	NOUN
iajs-1184	2	21	من	من	INTJ
iajs-1184	2	22	قدم	قدم	NOUN
iajs-1184	2	23	تعریف	تعریف	VERB
iajs-1184	2	24	المجموعة	المجموعة	PROPN
iajs-1184	2	25	شبه	شبه	NOUN
iajs-1184	2	26	قبل	قبل	PROPN
iajs-1184	2	27	المفتوحة	المفتوحة	PROPN
iajs-1184	2	28	هو	هو	PROPN
iajs-1184	2	29	الریاضي	الریاضي	PROPN
iajs-1184	2	30	اندرجفك	اندرجفك	PROPN
iajs-1184	2	31	,	,	PUNCT
iajs-1184	2	32			NOUN
iajs-1184	2	33	)	)	PUNCT
iajs-1184	2	34	فضاء	فضاء	NOUN
iajs-1184	2	35	تبولوجي	تبولوجي	NOUN
iajs-1184	2	36	وa	وa	PROPN
iajs-1184	2	37	مجموعة	مجموعة	PROPN
iajs-1184	2	38	جزئیة	جزئیة	PROPN
iajs-1184	2	39	منx	منx	X
iajs-1184	2	40	فأنa	فأنa	NOUN
iajs-1184	2	41	ان	ان	PROPN
iajs-1184	2	42	تسمى	تسمى	PROPN
iajs-1184	2	43	مجموعة	مجموعة	PROPN
iajs-1184	2	44	شبه	شبه	PROPN
iajs-1184	2	45	قبل	قبل	PROPN
iajs-1184	2	46	المفتوحة	المفتوحة	PROPN
iajs-1184	2	47	اذا	اذا	PROPN
iajs-1184	2	48	ك	ك	X
iajs-1184	2	49	�	�	PROPN
iajs-1184	2	50	⊆	⊆	NUM
iajs-1184	2	51	�	�	PROPN
iajs-1184	2	52	∘	∘	NOUN
iajs-1184	2	53	�	�	PROPN
iajs-1184	2	54	�	�	PROPN
iajs-1184	2	55	�	�	PROPN
iajs-1184	2	56	.	.	PUNCT
iajs-1184	2	57	"	"	PUNCT
iajs-1184	3	1	أعالهلقد	أعالهلقد	NOUN
iajs-1184	3	2	قمنا	قمنا	ADV
iajs-1184	3	3	في	في	SCONJ
iajs-1184	3	4	هذا	هذا	NOUN
iajs-1184	3	5	البحث	البحث	NOUN
iajs-1184	3	6	بدراسة	بدراسة	PROPN
iajs-1184	3	7	خواص	خواص	ADV
iajs-1184	3	8	المجموعات	المجموعات	NOUN
iajs-1184	3	9	شبه	شبه	VERB
iajs-1184	3	10	قبل	قبل	PROPN
iajs-1184	3	11	المفتوحة	المفتوحة	PROPN
iajs-1184	3	12	ولكن	ولكن	PROPN
iajs-1184	3	13	لیس	لیس	NOUN
iajs-1184	3	14	عن	عن	NOUN
iajs-1184	3	15	طریق	طریق	NOUN
iajs-1184	3	16	التعریف	التعریف	PROPN
iajs-1184	3	17	تعریف	تعریف	VERB
iajs-1184	3	18	ثاني	ثاني	PROPN
iajs-1184	3	19	مكافئ	مكافئ	PROPN
iajs-1184	3	20	لتعریفها	لتعریفها	PROPN
iajs-1184	3	21	وكذلك	وكذلك	PROPN
iajs-1184	3	22	درسنا	درسنا	PROPN
iajs-1184	3	23	العالقة	العالقة	PROPN
iajs-1184	3	24	بینها	بینها	NOUN
iajs-1184	3	25	وبین	وبین	VERB
iajs-1184	3	26	أنواع	أنواع	NOUN
iajs-1184	3	27	أخرى	أخرى	PROPN
iajs-1184	3	28	من	من	PROPN
iajs-1184	3	29	المجامیع	المجامیع	PROPN
iajs-1184	4	1	طة	طة	AUX
iajs-1184	4	2	ابواسانما	ابواسانما	NOUN
iajs-1184	4	3	.المفتوحة	.المفتوحة	VERB
iajs-1184	4	4	الضعیفة	الضعیفة	VERB
iajs-1184	4	5	ibn	ibn	PROPN
iajs-1184	4	6	alhaitham	alhaitham	NOUN
iajs-1184	4	7	j.	j.	PROPN
iajs-1184	5	1	fo	fo	ADP
iajs-1184	5	2	r	r	NOUN
iajs-1184	5	3	pure	pure	ADJ
iajs-1184	5	4	&	&	CCONJ
iajs-1184	5	5	appl	appl	PROPN
iajs-1184	5	6	.	.	PUNCT
iajs-1184	6	1	sc	sc	PROPN
iajs-1184	7	1	i	i	PRON
iajs-1184	7	2	vo	vo	INTJ
iajs-1184	7	3	l.22	l.22	X
iajs-1184	7	4	(	(	PUNCT
iajs-1184	7	5	3	3	NUM
iajs-1184	7	6	)	)	PUNCT
iajs-1184	7	7	2009	2009	NUM
iajs-1184	7	8	some	some	DET
iajs-1184	7	9	results	result	VERB
iajs-1184	7	10	on	on	ADP
iajs-1184	7	11	semi	semi	ADJ
iajs-1184	7	12	-	-	ADJ
iajs-1184	7	13	preopen	preopen	ADJ
iajs-1184	7	14	sets	set	NOUN
iajs-1184	7	15	r.	r.	PROPN
iajs-1184	7	16	n.	n.	PROPN
iajs-1184	7	17	majeed	majeed	PROPN
iajs-1184	7	18	,	,	PUNCT
iajs-1184	7	19	a.	a.	PROPN
iajs-1184	7	20	i.	i.	PROPN
iajs-1184	7	21	nasir	nasir	PROPN
iajs-1184	7	22	department	department	PROPN
iajs-1184	7	23	of	of	ADP
iajs-1184	7	24	mathematics	mathematics	PROPN
iajs-1184	7	25	,	,	PUNCT
iajs-1184	7	26	college	college	NOUN
iajs-1184	7	27	of	of	ADP
iajs-1184	7	28	education	education	NOUN
iajs-1184	7	29	–	–	PUNCT
iajs-1184	7	30	ibn	ibn	PROPN
iajs-1184	7	31	alhaitham	alhaitham	NOUN
iajs-1184	7	32	,	,	PUNCT
iajs-1184	7	33	university	university	NOUN
iajs-1184	7	34	of	of	ADP
iajs-1184	7	35	baghdad	baghdad	PROPN
iajs-1184	7	36	abstract	abstract	ADJ
iajs-1184	7	37	the	the	DET
iajs-1184	7	38	definition	definition	NOUN
iajs-1184	7	39	of	of	ADP
iajs-1184	7	40	semi	semi	ADJ
iajs-1184	7	41	-	-	ADJ
iajs-1184	7	42	preopen	preopen	ADJ
iajs-1184	7	43	sets	set	NOUN
iajs-1184	7	44	were	be	AUX
iajs-1184	7	45	first	first	ADV
iajs-1184	7	46	introduced	introduce	VERB
iajs-1184	7	47	by	by	ADP
iajs-1184	7	48	"	"	PUNCT
iajs-1184	7	49	andrijevic	andrijevic	ADJ
iajs-1184	7	50	"	"	PUNCT
iajs-1184	7	51	as	as	SCONJ
iajs-1184	7	52	were	be	AUX
iajs-1184	7	53	is	be	AUX
iajs-1184	7	54	defined	define	VERB
iajs-1184	7	55	by	by	ADP
iajs-1184	7	56	:	:	PUNCT
iajs-1184	7	57	let	let	VERB
iajs-1184	7	58	(	(	PUNCT
iajs-1184	7	59	x	x	X
iajs-1184	7	60	,	,	PUNCT
iajs-1184	7	61			PROPN
iajs-1184	7	62	)	)	PUNCT
iajs-1184	7	63	be	be	AUX
iajs-1184	7	64	a	a	DET
iajs-1184	7	65	topological	topological	ADJ
iajs-1184	7	66	space	space	NOUN
iajs-1184	7	67	,	,	PUNCT
iajs-1184	7	68	and	and	CCONJ
iajs-1184	7	69	let	let	VERB
iajs-1184	7	70	a	a	DET
iajs-1184	7	71	⊆	⊆	NUM
iajs-1184	7	72	�	�	NOUN
iajs-1184	7	73	,	,	PUNCT
iajs-1184	7	74	then	then	ADV
iajs-1184	7	75	a	a	PRON
iajs-1184	7	76	is	be	AUX
iajs-1184	7	77	called	call	VERB
iajs-1184	7	78	semi	semi	ADJ
iajs-1184	7	79	-	-	ADJ
iajs-1184	7	80	preopen	preopen	ADJ
iajs-1184	7	81	set	set	VERB
iajs-1184	7	82	if	if	SCONJ
iajs-1184	7	83	�	�	PROPN
iajs-1184	7	84	⊆	⊆	NUM
iajs-1184	7	85	�	�	PROPN
iajs-1184	7	86	∘	∘	NOUN
iajs-1184	7	87	�	�	PROPN
iajs-1184	7	88	�	�	PROPN
iajs-1184	7	89	�	�	PROPN
iajs-1184	7	90	.	.	PUNCT
iajs-1184	8	1	in	in	ADP
iajs-1184	8	2	this	this	DET
iajs-1184	8	3	paper	paper	NOUN
iajs-1184	8	4	,	,	PUNCT
iajs-1184	8	5	we	we	PRON
iajs-1184	8	6	study	study	VERB
iajs-1184	8	7	the	the	DET
iajs-1184	8	8	properties	property	NOUN
iajs-1184	8	9	of	of	ADP
iajs-1184	8	10	semi	semi	ADJ
iajs-1184	8	11	-	-	ADJ
iajs-1184	8	12	preopen	preopen	ADJ
iajs-1184	8	13	sets	set	NOUN
iajs-1184	8	14	but	but	CCONJ
iajs-1184	8	15	by	by	ADP
iajs-1184	8	16	another	another	DET
iajs-1184	8	17	definition	definition	NOUN
iajs-1184	8	18	which	which	PRON
iajs-1184	8	19	is	be	AUX
iajs-1184	8	20	equivalent	equivalent	ADJ
iajs-1184	8	21	to	to	ADP
iajs-1184	8	22	the	the	DET
iajs-1184	8	23	first	first	ADJ
iajs-1184	8	24	definition	definition	NOUN
iajs-1184	8	25	and	and	CCONJ
iajs-1184	8	26	we	we	PRON
iajs-1184	8	27	also	also	ADV
iajs-1184	8	28	study	study	VERB
iajs-1184	8	29	the	the	DET
iajs-1184	8	30	relationships	relationship	NOUN
iajs-1184	8	31	among	among	ADP
iajs-1184	8	32	it	it	PRON
iajs-1184	8	33	and	and	CCONJ
iajs-1184	8	34	(	(	PUNCT
iajs-1184	8	35	open	open	ADJ
iajs-1184	8	36	,	,	PUNCT
iajs-1184	8	37	α	α	NOUN
iajs-1184	8	38	-	-	ADJ
iajs-1184	8	39	open	open	ADJ
iajs-1184	8	40	,	,	PUNCT
iajs-1184	8	41	preopen	preopen	ADJ
iajs-1184	8	42	and	and	CCONJ
iajs-1184	8	43	semi	semi	ADJ
iajs-1184	8	44	-	-	ADJ
iajs-1184	8	45	p	p	ADJ
iajs-1184	8	46	-	-	PUNCT
iajs-1184	8	47	open	open	ADJ
iajs-1184	8	48	)	)	PUNCT
iajs-1184	8	49	sets	set	NOUN
iajs-1184	8	50	.	.	PUNCT
iajs-1184	9	1	1.preliminaries	1.preliminaries	NUM
iajs-1184	9	2	definition	definition	NOUN
iajs-1184	9	3	1.1	1.1	NUM
iajs-1184	9	4	(	(	PUNCT
iajs-1184	9	5	1)(4	1)(4	NUM
iajs-1184	9	6	):	):	PUNCT
iajs-1184	9	7	a	a	DET
iajs-1184	9	8	subset	subset	NOUN
iajs-1184	9	9	a	a	PRON
iajs-1184	9	10	of	of	ADP
iajs-1184	9	11	a	a	DET
iajs-1184	9	12	topological	topological	ADJ
iajs-1184	9	13	space	space	NOUN
iajs-1184	9	14	(	(	PUNCT
iajs-1184	9	15	x	x	X
iajs-1184	9	16	,	,	PUNCT
iajs-1184	9	17			PROPN
iajs-1184	9	18	)	)	PUNCT
iajs-1184	9	19	is	be	AUX
iajs-1184	9	20	called	call	VERB
iajs-1184	9	21	α	α	PRON
iajs-1184	9	22	–	–	PUNCT
iajs-1184	9	23	open	open	ADJ
iajs-1184	9	24	set	set	VERB
iajs-1184	9	25	if	if	SCONJ
iajs-1184	9	26	and	and	CCONJ
iajs-1184	9	27	only	only	ADV
iajs-1184	9	28	if	if	SCONJ
iajs-1184	9	29	a	a	DET
iajs-1184	9	30	ح	ح	PROPN
iajs-1184	9	31	�	�	PROPN
iajs-1184	9	32	°	°	SYM
iajs-1184	9	33	�	�	PROPN
iajs-1184	9	34	�	�	PROPN
iajs-1184	9	35	�	�	PROPN
iajs-1184	9	36	�	�	PROPN
iajs-1184	9	37	�	�	PROPN
iajs-1184	9	38	°	°	PROPN
iajs-1184	9	39	the	the	DET
iajs-1184	9	40	family	family	NOUN
iajs-1184	9	41	of	of	ADP
iajs-1184	9	42	all	all	DET
iajs-1184	9	43	α	α	NOUN
iajs-1184	9	44	–	–	PUNCT
iajs-1184	9	45	open	open	ADJ
iajs-1184	9	46	sets	set	NOUN
iajs-1184	9	47	is	be	AUX
iajs-1184	9	48	denoted	denote	VERB
iajs-1184	9	49	by	by	ADP
iajs-1184	9	50	α	α	PROPN
iajs-1184	9	51	.	.	PUNCT
iajs-1184	10	1	definition	definition	NOUN
iajs-1184	10	2	1.2	1.2	NUM
iajs-1184	10	3	(	(	PUNCT
iajs-1184	10	4	1)(5	1)(5	NUM
iajs-1184	10	5	)	)	PUNCT
iajs-1184	10	6	:	:	PUNCT
iajs-1184	10	7	a	a	DET
iajs-1184	10	8	subset	subset	NOUN
iajs-1184	10	9	a	a	PRON
iajs-1184	10	10	of	of	ADP
iajs-1184	10	11	a	a	DET
iajs-1184	10	12	topological	topological	ADJ
iajs-1184	10	13	space	space	NOUN
iajs-1184	10	14	(	(	PUNCT
iajs-1184	10	15	x	x	X
iajs-1184	10	16	,	,	PUNCT
iajs-1184	10	17			PROPN
iajs-1184	10	18	)	)	PUNCT
iajs-1184	10	19	is	be	AUX
iajs-1184	10	20	called	call	VERB
iajs-1184	10	21	a	a	DET
iajs-1184	10	22	preopen	preopen	ADJ
iajs-1184	10	23	set	set	VERB
iajs-1184	10	24	if	if	SCONJ
iajs-1184	10	25	a	a	DET
iajs-1184	10	26	ح	ح	PROPN
iajs-1184	10	27	�	�	PROPN
iajs-1184	10	28	�	�	PROPN
iajs-1184	10	29	°	°	NOUN
iajs-1184	10	30	the	the	DET
iajs-1184	10	31	complement	complement	NOUN
iajs-1184	10	32	of	of	ADP
iajs-1184	10	33	a	a	DET
iajs-1184	10	34	preopen	preopen	ADJ
iajs-1184	10	35	set	set	NOUN
iajs-1184	10	36	is	be	AUX
iajs-1184	10	37	called	call	VERB
iajs-1184	10	38	preclosed	preclose	VERB
iajs-1184	10	39	set	set	NOUN
iajs-1184	10	40	.	.	PUNCT
iajs-1184	11	1	the	the	DET
iajs-1184	11	2	family	family	NOUN
iajs-1184	11	3	of	of	ADP
iajs-1184	11	4	all	all	DET
iajs-1184	11	5	preopen	preopen	ADJ
iajs-1184	11	6	sets	set	NOUN
iajs-1184	11	7	of	of	ADP
iajs-1184	11	8	x	x	SYM
iajs-1184	11	9	is	be	AUX
iajs-1184	11	10	denoted	denote	VERB
iajs-1184	11	11	by	by	ADP
iajs-1184	11	12	po(x	po(x	NOUN
iajs-1184	11	13	)	)	PUNCT
iajs-1184	11	14	.	.	PUNCT
iajs-1184	12	1	the	the	DET
iajs-1184	12	2	family	family	NOUN
iajs-1184	12	3	of	of	ADP
iajs-1184	12	4	all	all	DET
iajs-1184	12	5	preclosed	preclose	VERB
iajs-1184	12	6	sets	set	NOUN
iajs-1184	12	7	of	of	ADP
iajs-1184	12	8	x	x	SYM
iajs-1184	12	9	is	be	AUX
iajs-1184	12	10	denoted	denote	VERB
iajs-1184	12	11	by	by	ADP
iajs-1184	12	12	pc(x	pc(x	NOUN
iajs-1184	12	13	)	)	PUNCT
iajs-1184	12	14	.	.	PUNCT
iajs-1184	13	1	theorem	theorem	VERB
iajs-1184	13	2	1.3	1.3	NUM
iajs-1184	13	3	(	(	PUNCT
iajs-1184	13	4	2	2	NUM
iajs-1184	13	5	)	)	PUNCT
iajs-1184	13	6	:	:	PUNCT
iajs-1184	13	7	the	the	DET
iajs-1184	13	8	union	union	NOUN
iajs-1184	13	9	of	of	ADP
iajs-1184	13	10	any	any	DET
iajs-1184	13	11	family	family	NOUN
iajs-1184	13	12	of	of	ADP
iajs-1184	13	13	preopen	preopen	ADJ
iajs-1184	13	14	sets	set	NOUN
iajs-1184	13	15	is	be	AUX
iajs-1184	13	16	a	a	DET
iajs-1184	13	17	preopen	preopen	ADJ
iajs-1184	13	18	set	set	NOUN
iajs-1184	13	19	.	.	PUNCT
iajs-1184	14	1	definition	definition	NOUN
iajs-1184	14	2	1.4	1.4	NUM
iajs-1184	14	3	(	(	PUNCT
iajs-1184	14	4	1	1	NUM
iajs-1184	14	5	)	)	PUNCT
iajs-1184	14	6	:	:	PUNCT
iajs-1184	14	7	the	the	DET
iajs-1184	14	8	intersection	intersection	NOUN
iajs-1184	14	9	of	of	ADP
iajs-1184	14	10	all	all	DET
iajs-1184	14	11	preclosed	preclose	VERB
iajs-1184	14	12	sets	set	NOUN
iajs-1184	14	13	containing	contain	VERB
iajs-1184	14	14	a	a	PRON
iajs-1184	14	15	is	be	AUX
iajs-1184	14	16	called	call	VERB
iajs-1184	14	17	the	the	DET
iajs-1184	14	18	preclosure	preclosure	NOUN
iajs-1184	14	19	of	of	ADP
iajs-1184	14	20	a	a	PRON
iajs-1184	14	21	,	,	PUNCT
iajs-1184	14	22	denoted	denote	VERB
iajs-1184	14	23	by	by	ADP
iajs-1184	14	24	pre	pre	ADJ
iajs-1184	14	25	-	-	ADJ
iajs-1184	14	26	cl	cl	ADJ
iajs-1184	14	27	a.	a.	NOUN
iajs-1184	14	28	definition	definition	NOUN
iajs-1184	14	29	1.5	1.5	NUM
iajs-1184	14	30	(	(	PUNCT
iajs-1184	14	31	1	1	NUM
iajs-1184	14	32	)	)	PUNCT
iajs-1184	14	33	:	:	PUNCT
iajs-1184	14	34	a	a	DET
iajs-1184	14	35	subset	subset	NOUN
iajs-1184	14	36	a	a	PRON
iajs-1184	14	37	of	of	ADP
iajs-1184	14	38	a	a	DET
iajs-1184	14	39	topological	topological	ADJ
iajs-1184	14	40	space	space	NOUN
iajs-1184	14	41	(	(	PUNCT
iajs-1184	14	42	x	x	X
iajs-1184	14	43	,	,	PUNCT
iajs-1184	14	44			PROPN
iajs-1184	14	45	)	)	PUNCT
iajs-1184	14	46	is	be	AUX
iajs-1184	14	47	said	say	VERB
iajs-1184	14	48	to	to	PART
iajs-1184	14	49	be	be	AUX
iajs-1184	14	50	semi	semi	ADJ
iajs-1184	14	51	-	-	ADJ
iajs-1184	14	52	p	p	ADJ
iajs-1184	14	53	-	-	PUNCT
iajs-1184	14	54	open	open	NOUN
iajs-1184	14	55	set	set	NOUN
iajs-1184	14	56	,	,	PUNCT
iajs-1184	14	57	if	if	SCONJ
iajs-1184	14	58	there	there	PRON
iajs-1184	14	59	exists	exist	VERB
iajs-1184	14	60	a	a	DET
iajs-1184	14	61	preopen	preopen	ADJ
iajs-1184	14	62	set	set	NOUN
iajs-1184	14	63	in	in	ADP
iajs-1184	14	64	x	x	PART
iajs-1184	14	65	say	say	VERB
iajs-1184	14	66	u	u	NOUN
iajs-1184	14	67	such	such	ADJ
iajs-1184	14	68	that	that	SCONJ
iajs-1184	14	69	uح	uح	PROPN
iajs-1184	14	70	a	a	DET
iajs-1184	14	71	ح	ح	ADJ
iajs-1184	14	72	pre	pre	NOUN
iajs-1184	14	73	-	-	NOUN
iajs-1184	14	74	cl	cl	ADJ
iajs-1184	14	75	u.	u.	NOUN
iajs-1184	14	76	the	the	DET
iajs-1184	14	77	complement	complement	NOUN
iajs-1184	14	78	of	of	ADP
iajs-1184	14	79	a	a	DET
iajs-1184	14	80	semi	semi	ADJ
iajs-1184	14	81	-	-	ADJ
iajs-1184	14	82	p	p	ADJ
iajs-1184	14	83	-	-	PUNCT
iajs-1184	14	84	open	open	ADJ
iajs-1184	14	85	set	set	NOUN
iajs-1184	14	86	is	be	AUX
iajs-1184	14	87	called	call	VERB
iajs-1184	14	88	semi	semi	ADJ
iajs-1184	14	89	-	-	ADJ
iajs-1184	14	90	p	p	ADJ
iajs-1184	14	91	-	-	PUNCT
iajs-1184	14	92	closed	close	VERB
iajs-1184	14	93	set	set	NOUN
iajs-1184	14	94	.	.	PUNCT
iajs-1184	15	1	the	the	DET
iajs-1184	15	2	family	family	NOUN
iajs-1184	15	3	of	of	ADP
iajs-1184	15	4	all	all	DET
iajs-1184	15	5	semi	semi	ADJ
iajs-1184	15	6	-	-	ADJ
iajs-1184	15	7	p	p	ADJ
iajs-1184	15	8	-	-	PUNCT
iajs-1184	15	9	open	open	ADJ
iajs-1184	15	10	sets	set	NOUN
iajs-1184	15	11	of	of	ADP
iajs-1184	15	12	x	x	SYM
iajs-1184	15	13	is	be	AUX
iajs-1184	15	14	denoted	denote	VERB
iajs-1184	15	15	by	by	ADP
iajs-1184	15	16	s	s	NOUN
iajs-1184	15	17	-	-	PUNCT
iajs-1184	15	18	p(x	p(x	NOUN
iajs-1184	15	19	)	)	PUNCT
iajs-1184	15	20	.	.	PUNCT
iajs-1184	16	1	the	the	DET
iajs-1184	16	2	family	family	NOUN
iajs-1184	16	3	of	of	ADP
iajs-1184	16	4	all	all	DET
iajs-1184	16	5	semip	semip	NOUN
iajs-1184	16	6	-	-	PUNCT
iajs-1184	16	7	closed	close	VERB
iajs-1184	16	8	sets	set	NOUN
iajs-1184	16	9	of	of	ADP
iajs-1184	16	10	x	x	SYM
iajs-1184	16	11	is	be	AUX
iajs-1184	16	12	denoted	denote	VERB
iajs-1184	16	13	by	by	ADP
iajs-1184	16	14	s	s	NOUN
iajs-1184	16	15	-	-	NOUN
iajs-1184	16	16	pc(x	pc(x	NOUN
iajs-1184	16	17	)	)	PUNCT
iajs-1184	16	18	.	.	PUNCT
iajs-1184	17	1	proposition	proposition	NOUN
iajs-1184	17	2	1.6	1.6	NUM
iajs-1184	17	3	(	(	PUNCT
iajs-1184	17	4	2	2	NUM
iajs-1184	17	5	):	):	PUNCT
iajs-1184	17	6	for	for	ADP
iajs-1184	17	7	any	any	DET
iajs-1184	17	8	subset	subset	NOUN
iajs-1184	17	9	a	a	PRON
iajs-1184	17	10	of	of	ADP
iajs-1184	17	11	a	a	DET
iajs-1184	17	12	topological	topological	ADJ
iajs-1184	17	13	space	space	NOUN
iajs-1184	17	14	(	(	PUNCT
iajs-1184	17	15	x	x	NOUN
iajs-1184	17	16	,	,	PUNCT
iajs-1184	17	17			PROPN
iajs-1184	17	18	)	)	PUNCT
iajs-1184	17	19	,	,	PUNCT
iajs-1184	17	20	pre	pre	ADJ
iajs-1184	17	21	-	-	NOUN
iajs-1184	17	22	cl	cl	VERB
iajs-1184	17	23	a	a	DET
iajs-1184	17	24	ح	ح	NOUN
iajs-1184	17	25	a	a	DET
iajs-1184	17	26	�	�	PROPN
iajs-1184	17	27	and	and	CCONJ
iajs-1184	17	28	the	the	DET
iajs-1184	17	29	converse	converse	NOUN
iajs-1184	17	30	is	be	AUX
iajs-1184	17	31	not	not	PART
iajs-1184	17	32	true	true	ADJ
iajs-1184	17	33	.	.	PUNCT
iajs-1184	18	1	ibn	ibn	PROPN
iajs-1184	18	2	alhaitham	alhaitham	NOUN
iajs-1184	19	1	j.	j.	PROPN
iajs-1184	20	1	fo	fo	ADP
iajs-1184	20	2	r	r	NOUN
iajs-1184	20	3	pure	pure	ADJ
iajs-1184	20	4	&	&	CCONJ
iajs-1184	20	5	appl	appl	PROPN
iajs-1184	20	6	.	.	PUNCT
iajs-1184	21	1	sc	sc	PROPN
iajs-1184	22	1	i	i	PRON
iajs-1184	22	2	vo	vo	INTJ
iajs-1184	22	3	l.22	l.22	X
iajs-1184	22	4	(	(	PUNCT
iajs-1184	22	5	3	3	NUM
iajs-1184	22	6	)	)	PUNCT
iajs-1184	22	7	2009	2009	NUM
iajs-1184	22	8	2	2	NUM
iajs-1184	22	9	.	.	PUNCT
iajs-1184	22	10	semi	semi	ADJ
iajs-1184	22	11	–	–	PUNCT
iajs-1184	22	12	preopen	preopen	ADJ
iajs-1184	22	13	sets	set	NOUN
iajs-1184	22	14	definition	definition	NOUN
iajs-1184	22	15	2.1(6	2.1(6	NUM
iajs-1184	22	16	):	):	PUNCT
iajs-1184	22	17	a	a	DET
iajs-1184	22	18	subset	subset	NOUN
iajs-1184	22	19	a	a	PRON
iajs-1184	22	20	of	of	ADP
iajs-1184	22	21	a	a	DET
iajs-1184	22	22	topological	topological	ADJ
iajs-1184	22	23	space	space	NOUN
iajs-1184	22	24	(	(	PUNCT
iajs-1184	22	25	x	x	X
iajs-1184	22	26	,	,	PUNCT
iajs-1184	22	27			PROPN
iajs-1184	22	28	)	)	PUNCT
iajs-1184	22	29	is	be	AUX
iajs-1184	22	30	said	say	VERB
iajs-1184	22	31	to	to	PART
iajs-1184	22	32	be	be	AUX
iajs-1184	22	33	semi	semi	ADJ
iajs-1184	22	34	-	-	ADJ
iajs-1184	22	35	preopen	preopen	ADJ
iajs-1184	22	36	set	set	NOUN
iajs-1184	22	37	,	,	PUNCT
iajs-1184	22	38	if	if	SCONJ
iajs-1184	22	39	and	and	CCONJ
iajs-1184	22	40	only	only	ADV
iajs-1184	22	41	if	if	SCONJ
iajs-1184	22	42	there	there	PRON
iajs-1184	22	43	exists	exist	VERB
iajs-1184	22	44	a	a	DET
iajs-1184	22	45	preopen	preopen	ADJ
iajs-1184	22	46	set	set	NOUN
iajs-1184	22	47	in	in	ADP
iajs-1184	22	48	x	x	PART
iajs-1184	22	49	say	say	VERB
iajs-1184	22	50	u	u	NOUN
iajs-1184	22	51	such	such	ADJ
iajs-1184	22	52	that	that	SCONJ
iajs-1184	22	53	u	u	PRON
iajs-1184	22	54	ح	ح	VERB
iajs-1184	22	55	a	a	DET
iajs-1184	22	56	ح	ح	PROPN
iajs-1184	22	57	�	�	PROPN
iajs-1184	22	58	�	�	PROPN
iajs-1184	22	59	the	the	DET
iajs-1184	22	60	complement	complement	NOUN
iajs-1184	22	61	of	of	ADP
iajs-1184	22	62	semi	semi	ADJ
iajs-1184	22	63	-	-	ADJ
iajs-1184	22	64	preopen	preopen	ADJ
iajs-1184	22	65	set	set	NOUN
iajs-1184	22	66	is	be	AUX
iajs-1184	22	67	called	call	VERB
iajs-1184	22	68	semipreclosed	semipreclose	VERB
iajs-1184	22	69	set	set	NOUN
iajs-1184	22	70	.	.	PUNCT
iajs-1184	23	1	the	the	DET
iajs-1184	23	2	family	family	NOUN
iajs-1184	23	3	of	of	ADP
iajs-1184	23	4	all	all	DET
iajs-1184	23	5	semi	semi	ADJ
iajs-1184	23	6	-	-	ADJ
iajs-1184	23	7	preopen	preopen	ADJ
iajs-1184	23	8	sets	set	NOUN
iajs-1184	23	9	of	of	ADP
iajs-1184	23	10	x	x	SYM
iajs-1184	23	11	is	be	AUX
iajs-1184	23	12	denoted	denote	VERB
iajs-1184	23	13	by	by	ADP
iajs-1184	23	14	spo(x	spo(x	PROPN
iajs-1184	23	15	)	)	PUNCT
iajs-1184	23	16	.	.	PUNCT
iajs-1184	24	1	the	the	DET
iajs-1184	24	2	family	family	NOUN
iajs-1184	24	3	of	of	ADP
iajs-1184	24	4	all	all	DET
iajs-1184	24	5	semi	semi	ADJ
iajs-1184	24	6	-	-	ADJ
iajs-1184	24	7	preclosed	preclosed	ADJ
iajs-1184	24	8	sets	set	NOUN
iajs-1184	24	9	of	of	ADP
iajs-1184	24	10	x	x	SYM
iajs-1184	24	11	is	be	AUX
iajs-1184	24	12	denoted	denote	VERB
iajs-1184	24	13	by	by	ADP
iajs-1184	24	14	spc(x	spc(x	PROPN
iajs-1184	24	15	)	)	PUNCT
iajs-1184	24	16	.	.	PUNCT
iajs-1184	25	1	definition	definition	NOUN
iajs-1184	25	2	2.2	2.2	NUM
iajs-1184	25	3	:	:	PUNCT
iajs-1184	25	4	let	let	VERB
iajs-1184	25	5	(	(	PUNCT
iajs-1184	25	6	x	x	X
iajs-1184	25	7	,	,	PUNCT
iajs-1184	25	8			PROPN
iajs-1184	25	9	)	)	PUNCT
iajs-1184	25	10	be	be	AUX
iajs-1184	25	11	a	a	DET
iajs-1184	25	12	topological	topological	ADJ
iajs-1184	25	13	space	space	NOUN
iajs-1184	25	14	and	and	CCONJ
iajs-1184	25	15	aح	aح	ADP
iajs-1184	25	16	x	x	NOUN
iajs-1184	25	17	,	,	PUNCT
iajs-1184	25	18	a	a	PRON
iajs-1184	25	19	is	be	AUX
iajs-1184	25	20	called	call	VERB
iajs-1184	25	21	semi	semi	ADJ
iajs-1184	25	22	-	-	ADJ
iajs-1184	25	23	preneighborhood	preneighborhood	NOUN
iajs-1184	25	24	of	of	ADP
iajs-1184	25	25	a	a	DET
iajs-1184	25	26	point	point	NOUN
iajs-1184	25	27	x	x	PUNCT
iajs-1184	25	28	in	in	ADP
iajs-1184	25	29	x	x	SYM
iajs-1184	25	30	,	,	PUNCT
iajs-1184	25	31	if	if	SCONJ
iajs-1184	25	32	there	there	PRON
iajs-1184	25	33	exists	exist	VERB
iajs-1184	25	34	semi	semi	ADJ
iajs-1184	25	35	-	-	ADJ
iajs-1184	25	36	preopen	preopen	ADJ
iajs-1184	25	37	set	set	VERB
iajs-1184	25	38	u	u	NOUN
iajs-1184	25	39	in	in	ADP
iajs-1184	25	40	x	x	SYM
iajs-1184	25	41	such	such	ADJ
iajs-1184	25	42	that	that	SCONJ
iajs-1184	25	43	xخ	xخ	PROPN
iajs-1184	26	1	u	u	PROPN
iajs-1184	26	2	ح	ح	NOUN
iajs-1184	26	3	a	a	PRON
iajs-1184	26	4	.	.	PUNCT
iajs-1184	27	1	theorem	theorem	ADJ
iajs-1184	27	2	2.3	2.3	NUM
iajs-1184	27	3	:	:	PUNCT
iajs-1184	27	4	the	the	DET
iajs-1184	27	5	union	union	NOUN
iajs-1184	27	6	of	of	ADP
iajs-1184	27	7	any	any	DET
iajs-1184	27	8	family	family	NOUN
iajs-1184	27	9	of	of	ADP
iajs-1184	27	10	semipreopen	semipreopen	ADJ
iajs-1184	27	11	sets	set	NOUN
iajs-1184	27	12	is	be	AUX
iajs-1184	27	13	semipreopen	semipreopen	ADJ
iajs-1184	27	14	set	set	VERB
iajs-1184	27	15	.	.	PUNCT
iajs-1184	28	1	proof	proof	NOUN
iajs-1184	28	2	:	:	PUNCT
iajs-1184	28	3	let	let	VERB
iajs-1184	28	4	{	{	PUNCT
iajs-1184	28	5	aα	aα	NOUN
iajs-1184	28	6	}	}	PUNCT
iajs-1184	28	7	;	;	PUNCT
iajs-1184	28	8	α	α	PROPN
iajs-1184	28	9	خl	خl	AUX
iajs-1184	28	10	be	be	AUX
iajs-1184	28	11	any	any	DET
iajs-1184	28	12	family	family	NOUN
iajs-1184	28	13	of	of	ADP
iajs-1184	28	14	semi	semi	ADJ
iajs-1184	28	15	-	-	ADJ
iajs-1184	28	16	preopen	preopen	ADJ
iajs-1184	28	17	sets	set	NOUN
iajs-1184	28	18	,	,	PUNCT
iajs-1184	28	19	we	we	PRON
iajs-1184	28	20	must	must	AUX
iajs-1184	28	21	prove	prove	VERB
iajs-1184	28	22	⋃	⋃	PROPN
iajs-1184	28	23	�	�	PROPN
iajs-1184	28	24	�	�	PROPN
iajs-1184	28	25	�	�	PROPN
iajs-1184	28	26	∈	∈	PROPN
iajs-1184	28	27	�	�	PROPN
iajs-1184	28	28	is	be	AUX
iajs-1184	28	29	semi	semi	ADJ
iajs-1184	28	30	-	-	ADJ
iajs-1184	28	31	preopen	preopen	ADJ
iajs-1184	28	32	set	set	NOUN
iajs-1184	28	33	.	.	PUNCT
iajs-1184	29	1	this	this	PRON
iajs-1184	29	2	means	mean	VERB
iajs-1184	29	3	we	we	PRON
iajs-1184	29	4	must	must	AUX
iajs-1184	29	5	prove	prove	VERB
iajs-1184	29	6	there	there	PRON
iajs-1184	29	7	exists	exist	VERB
iajs-1184	29	8	uخpo(x	uخpo(x	ADP
iajs-1184	29	9	)	)	PUNCT
iajs-1184	29	10	such	such	ADJ
iajs-1184	29	11	that	that	SCONJ
iajs-1184	29	12	u	u	PROPN
iajs-1184	29	13	⋃	⋃	PROPN
iajs-1184	29	14	ح	ح	NOUN
iajs-1184	29	15	�	�	NOUN
iajs-1184	29	16	∈	∈	PROPN
iajs-1184	29	17	�	�	PROPN
iajs-1184	29	18	�	�	PROPN
iajs-1184	29	19	�	�	PROPN
iajs-1184	29	20	.	.	PUNCT
iajs-1184	30	1	�	�	PROPN
iajs-1184	30	2	�	�	PROPN
iajs-1184	30	3	ح	ح	PROPN
iajs-1184	30	4	since	since	SCONJ
iajs-1184	30	5	for	for	ADP
iajs-1184	30	6	all	all	DET
iajs-1184	30	7	αخl	αخl	NOUN
iajs-1184	30	8	,	,	PUNCT
iajs-1184	30	9	aα	aα	PROPN
iajs-1184	30	10	is	be	AUX
iajs-1184	30	11	semipreopen	semipreopen	ADJ
iajs-1184	30	12	,	,	PUNCT
iajs-1184	30	13	therefore	therefore	ADV
iajs-1184	30	14	there	there	PRON
iajs-1184	30	15	exists	exist	VERB
iajs-1184	30	16	uα	uα	PROPN
iajs-1184	30	17	خpo(x	خpo(x	NUM
iajs-1184	30	18	)	)	PUNCT
iajs-1184	30	19	such	such	ADJ
iajs-1184	30	20	that	that	SCONJ
iajs-1184	30	21	�	�	PROPN
iajs-1184	30	22	�	�	PROPN
iajs-1184	30	23	ح	ح	PROPN
iajs-1184	30	24	�	�	PROPN
iajs-1184	30	25	�	�	PROPN
iajs-1184	30	26	ح	ح	PROPN
iajs-1184	30	27	�	�	PROPN
iajs-1184	30	28	�	�	PROPN
iajs-1184	30	29	�	�	PROPN
iajs-1184	30	30	,	,	PUNCT
iajs-1184	30	31	and	and	CCONJ
iajs-1184	30	32	since	since	SCONJ
iajs-1184	30	33	⋃	⋃	PROPN
iajs-1184	30	34	�	�	PROPN
iajs-1184	30	35	�	�	PROPN
iajs-1184	30	36	�	�	PROPN
iajs-1184	30	37	∈	∈	PROPN
iajs-1184	30	38	�	�	PROPN
iajs-1184	30	39	is	be	AUX
iajs-1184	30	40	a	a	DET
iajs-1184	30	41	preopen	preopen	ADJ
iajs-1184	30	42	set	set	NOUN
iajs-1184	30	43	(	(	PUNCT
iajs-1184	30	44	by	by	ADP
iajs-1184	30	45	theorem	theorem	NOUN
iajs-1184	30	46	1.3	1.3	NUM
iajs-1184	30	47	)	)	PUNCT
iajs-1184	30	48	,	,	PUNCT
iajs-1184	30	49	therefore	therefore	ADV
iajs-1184	30	50	let	let	VERB
iajs-1184	30	51	u	u	PRON
iajs-1184	30	52	=	=	NOUN
iajs-1184	30	53	⋃	⋃	PROPN
iajs-1184	30	54	�	�	PROPN
iajs-1184	30	55	�	�	PROPN
iajs-1184	30	56	�	�	PROPN
iajs-1184	30	57	∈	∈	PROPN
iajs-1184	30	58	�	�	PROPN
iajs-1184	30	59	,	,	PUNCT
iajs-1184	30	60	then	then	ADV
iajs-1184	30	61	we	we	PRON
iajs-1184	30	62	get	get	VERB
iajs-1184	30	63	u	u	PRON
iajs-1184	30	64	ح	ح	NOUN
iajs-1184	30	65	⋃	⋃	PROPN
iajs-1184	30	66	�	�	PROPN
iajs-1184	30	67	�	�	PROPN
iajs-1184	30	68	�	�	PROPN
iajs-1184	30	69	∈	∈	PROPN
iajs-1184	30	70	�	�	PROPN
iajs-1184	30	71	…	…	PUNCT
iajs-1184	30	72	…	…	SYM
iajs-1184	30	73	……	……	X
iajs-1184	30	74	(	(	PUNCT
iajs-1184	30	75	1	1	X
iajs-1184	30	76	)	)	PUNCT
iajs-1184	30	77	now	now	ADV
iajs-1184	30	78	since	since	SCONJ
iajs-1184	30	79	�	�	PROPN
iajs-1184	30	80	�	�	PROPN
iajs-1184	30	81	ح	ح	PROPN
iajs-1184	30	82	�	�	PROPN
iajs-1184	30	83	�	�	PROPN
iajs-1184	30	84	�	�	PROPN
iajs-1184	30	85	for	for	ADP
iajs-1184	30	86	all	all	DET
iajs-1184	30	87	αخl	αخl	NOUN
iajs-1184	30	88	,	,	PUNCT
iajs-1184	30	89	therefore	therefore	ADV
iajs-1184	30	90	⋃	⋃	PROPN
iajs-1184	30	91	�	�	PROPN
iajs-1184	30	92	�	�	PROPN
iajs-1184	30	93	�	�	PROPN
iajs-1184	30	94	∈	∈	PROPN
iajs-1184	30	95	�	�	PROPN
iajs-1184	30	96	⋃	⋃	PROPN
iajs-1184	30	97	ح	ح	PROPN
iajs-1184	30	98	lخ	lخ	PROPN
iajs-1184	30	99	�	�	PROPN
iajs-1184	30	100	�	�	PROPN
iajs-1184	30	101	�	�	PROPN
iajs-1184	30	102	�	�	PROPN
iajs-1184	30	103	for	for	ADP
iajs-1184	30	104	all	all	DET
iajs-1184	30	105	αخl	αخl	NOUN
iajs-1184	30	106	,	,	PUNCT
iajs-1184	30	107	implies	imply	VERB
iajs-1184	30	108	⋃	⋃	PROPN
iajs-1184	30	109	lخ	lخ	PROPN
iajs-1184	30	110	�	�	PROPN
iajs-1184	30	111	�	�	PROPN
iajs-1184	30	112	�	�	PROPN
iajs-1184	30	113	⋃	⋃	PROPN
iajs-1184	30	114	ح	ح	PROPN
iajs-1184	30	115	lخ	lخ	PROPN
iajs-1184	30	116	�	�	PROPN
iajs-1184	30	117	�	�	PROPN
iajs-1184	30	118	�	�	PROPN
iajs-1184	30	119	�	�	PROPN
iajs-1184	30	120	�	�	PROPN
iajs-1184	30	121	�	�	PROPN
iajs-1184	30	122	�	�	PROPN
iajs-1184	30	123	�	�	PROPN
iajs-1184	30	124	�	�	PROPN
iajs-1184	30	125	�	�	PROPN
iajs-1184	30	126	�	�	PROPN
iajs-1184	30	127	�	�	PROPN
iajs-1184	30	128	�	�	PROPN
iajs-1184	30	129	�	�	PROPN
iajs-1184	30	130	for	for	ADP
iajs-1184	30	131	all	all	DET
iajs-1184	30	132	αخl	αخl	NOUN
iajs-1184	30	133	,	,	PUNCT
iajs-1184	30	134	thus	thus	ADV
iajs-1184	30	135	⋃	⋃	PUNCT
iajs-1184	30	136	lخ	lخ	PROPN
iajs-1184	30	137	�	�	PROPN
iajs-1184	30	138	�	�	PROPN
iajs-1184	30	139	�	�	PROPN
iajs-1184	30	140	�	�	PROPN
iajs-1184	30	141	�	�	PROPN
iajs-1184	30	142	ح	ح	NOUN
iajs-1184	31	1	=	=	PUNCT
iajs-1184	31	2	⋃	⋃	PROPN
iajs-1184	31	3	lخ	lخ	PROPN
iajs-1184	31	4	�	�	PROPN
iajs-1184	31	5	�	�	PROPN
iajs-1184	31	6	�	�	PROPN
iajs-1184	31	7	�	�	PROPN
iajs-1184	31	8	�	�	PROPN
iajs-1184	31	9	�	�	PROPN
iajs-1184	31	10	�	�	PROPN
iajs-1184	31	11	�	�	PROPN
iajs-1184	31	12	�	�	PROPN
iajs-1184	31	13	�	�	PROPN
iajs-1184	31	14	�	�	PROPN
iajs-1184	31	15	�	�	PROPN
iajs-1184	31	16	�	�	PROPN
iajs-1184	31	17	�	�	PROPN
iajs-1184	31	18	…	…	PUNCT
iajs-1184	31	19	..	..	PUNCT
iajs-1184	31	20	(	(	PUNCT
iajs-1184	31	21	2	2	X
iajs-1184	31	22	)	)	PUNCT
iajs-1184	31	23	and	and	CCONJ
iajs-1184	31	24	from	from	ADP
iajs-1184	31	25	(	(	PUNCT
iajs-1184	31	26	1	1	NUM
iajs-1184	31	27	)	)	PUNCT
iajs-1184	31	28	and	and	CCONJ
iajs-1184	31	29	(	(	PUNCT
iajs-1184	31	30	2	2	X
iajs-1184	31	31	)	)	PUNCT
iajs-1184	31	32	we	we	PRON
iajs-1184	31	33	get	get	VERB
iajs-1184	31	34	,	,	PUNCT
iajs-1184	31	35	there	there	PRON
iajs-1184	31	36	exists	exist	VERB
iajs-1184	31	37	uخpo(x	uخpo(x	ADP
iajs-1184	31	38	)	)	PUNCT
iajs-1184	31	39	such	such	ADJ
iajs-1184	31	40	that	that	SCONJ
iajs-1184	31	41	u	u	PROPN
iajs-1184	31	42	ح	ح	PROPN
iajs-1184	31	43	⋃	⋃	PROPN
iajs-1184	31	44	�	�	PROPN
iajs-1184	31	45	�	�	PROPN
iajs-1184	31	46	�	�	PROPN
iajs-1184	31	47	∈	∈	PROPN
iajs-1184	31	48	�	�	PROPN
iajs-1184	31	49	⋃	⋃	PROPN
iajs-1184	31	50	therefore	therefore	ADV
iajs-1184	31	51	,	,	PUNCT
iajs-1184	31	52	�	�	PROPN
iajs-1184	31	53	�	�	PROPN
iajs-1184	31	54	ح	ح	PROPN
iajs-1184	31	55	�	�	PROPN
iajs-1184	31	56	∈	∈	PROPN
iajs-1184	31	57	�	�	PROPN
iajs-1184	31	58	�	�	PROPN
iajs-1184	31	59	�	�	PROPN
iajs-1184	31	60	is	be	AUX
iajs-1184	31	61	semi	semi	ADJ
iajs-1184	31	62	-	-	ADJ
iajs-1184	31	63	preopen	preopen	ADJ
iajs-1184	31	64	set	set	NOUN
iajs-1184	31	65	.	.	PUNCT
iajs-1184	32	1	■	■	PUNCT
iajs-1184	32	2	corollary	corollary	ADJ
iajs-1184	32	3	2.4	2.4	NUM
iajs-1184	32	4	:	:	PUNCT
iajs-1184	32	5	the	the	DET
iajs-1184	32	6	intersection	intersection	NOUN
iajs-1184	32	7	of	of	ADP
iajs-1184	32	8	any	any	DET
iajs-1184	32	9	family	family	NOUN
iajs-1184	32	10	of	of	ADP
iajs-1184	32	11	semi	semi	ADJ
iajs-1184	32	12	-	-	ADJ
iajs-1184	32	13	preclosed	preclosed	ADJ
iajs-1184	32	14	sets	set	NOUN
iajs-1184	32	15	is	be	AUX
iajs-1184	32	16	semi	semi	ADJ
iajs-1184	32	17	-	-	ADJ
iajs-1184	32	18	preclosed	preclosed	ADJ
iajs-1184	32	19	set	set	NOUN
iajs-1184	32	20	.	.	PUNCT
iajs-1184	33	1	proof	proof	NOUN
iajs-1184	33	2	:	:	PUNCT
iajs-1184	33	3	let	let	VERB
iajs-1184	33	4	{	{	PUNCT
iajs-1184	33	5	fα	fα	ADP
iajs-1184	33	6	}	}	PUNCT
iajs-1184	33	7	;	;	PUNCT
iajs-1184	33	8	α	α	PROPN
iajs-1184	33	9	خl	خl	AUX
iajs-1184	33	10	be	be	AUX
iajs-1184	33	11	any	any	DET
iajs-1184	33	12	family	family	NOUN
iajs-1184	33	13	of	of	ADP
iajs-1184	33	14	semi	semi	ADJ
iajs-1184	33	15	-	-	ADJ
iajs-1184	33	16	preclosed	preclose	VERB
iajs-1184	33	17	sets	set	NOUN
iajs-1184	33	18	,	,	PUNCT
iajs-1184	33	19	we	we	PRON
iajs-1184	33	20	must	must	AUX
iajs-1184	33	21	prove	prove	VERB
iajs-1184	33	22	⋂	⋂	PROPN
iajs-1184	33	23	�	�	PROPN
iajs-1184	33	24	�	�	PROPN
iajs-1184	33	25	�	�	PROPN
iajs-1184	33	26	∈	∈	PROPN
iajs-1184	33	27	�	�	PROPN
iajs-1184	33	28	is	be	AUX
iajs-1184	33	29	semipreclosed	semipreclose	VERB
iajs-1184	33	30	this	this	PRON
iajs-1184	33	31	means	mean	VERB
iajs-1184	33	32	we	we	PRON
iajs-1184	33	33	must	must	AUX
iajs-1184	33	34	prove	prove	VERB
iajs-1184	33	35	(	(	PUNCT
iajs-1184	33	36	⋂	⋂	PROPN
iajs-1184	33	37	�	�	PROPN
iajs-1184	33	38	�	�	PROPN
iajs-1184	33	39	�	�	PROPN
iajs-1184	33	40	∈	∈	PROPN
iajs-1184	33	41	�	�	PROPN
iajs-1184	33	42	)	)	PUNCT
iajs-1184	33	43	�	�	PROPN
iajs-1184	33	44	is	be	AUX
iajs-1184	33	45	semi	semi	ADJ
iajs-1184	33	46	-	-	ADJ
iajs-1184	33	47	preopen	preopen	ADJ
iajs-1184	33	48	set	set	NOUN
iajs-1184	33	49	.	.	PUNCT
iajs-1184	34	1	since	since	SCONJ
iajs-1184	34	2	for	for	ADP
iajs-1184	34	3	all	all	DET
iajs-1184	34	4	αخl	αخl	NOUN
iajs-1184	34	5	,	,	PUNCT
iajs-1184	34	6	�	�	PROPN
iajs-1184	34	7	�	�	PROPN
iajs-1184	34	8	�	�	PROPN
iajs-1184	34	9	is	be	AUX
iajs-1184	34	10	semi	semi	ADJ
iajs-1184	34	11	-	-	ADJ
iajs-1184	34	12	preopen	preopen	ADJ
iajs-1184	34	13	set	set	NOUN
iajs-1184	34	14	(	(	PUNCT
iajs-1184	34	15	by	by	ADP
iajs-1184	34	16	definition	definition	NOUN
iajs-1184	34	17	2.1	2.1	NUM
iajs-1184	34	18	)	)	PUNCT
iajs-1184	34	19	,	,	PUNCT
iajs-1184	34	20	therefore	therefore	ADV
iajs-1184	34	21	⋃	⋃	PUNCT
iajs-1184	34	22	�	�	PROPN
iajs-1184	34	23	�	�	PROPN
iajs-1184	34	24	�	�	PROPN
iajs-1184	34	25	�	�	PROPN
iajs-1184	34	26	∈	∈	PROPN
iajs-1184	34	27	�	�	PROPN
iajs-1184	34	28	is	be	AUX
iajs-1184	34	29	semi	semi	ADJ
iajs-1184	34	30	-	-	ADJ
iajs-1184	34	31	preopen	preopen	ADJ
iajs-1184	34	32	set	set	NOUN
iajs-1184	34	33	(	(	PUNCT
iajs-1184	34	34	by	by	ADP
iajs-1184	34	35	theorem	theorem	NOUN
iajs-1184	34	36	2.3	2.3	NUM
iajs-1184	34	37	)	)	PUNCT
iajs-1184	34	38	,	,	PUNCT
iajs-1184	34	39	implies	imply	VERB
iajs-1184	34	40	there	there	PRON
iajs-1184	34	41	exists	exist	VERB
iajs-1184	34	42	u	u	NOUN
iajs-1184	34	43	po(x	po(x	PUNCT
iajs-1184	34	44	)	)	PUNCT
iajs-1184	34	45	such	such	ADJ
iajs-1184	34	46	that	that	SCONJ
iajs-1184	34	47	u	u	PROPN
iajs-1184	34	48	ح	ح	PROPN
iajs-1184	34	49	⋃	⋃	PROPN
iajs-1184	34	50	�	�	PROPN
iajs-1184	34	51	�	�	PROPN
iajs-1184	34	52	�	�	PROPN
iajs-1184	34	53	�	�	PROPN
iajs-1184	34	54	∈	∈	PROPN
iajs-1184	34	55	�	�	PROPN
iajs-1184	34	56	⋃	⋃	PROPN
iajs-1184	34	57	and	and	CCONJ
iajs-1184	34	58	since	since	SCONJ
iajs-1184	34	59	,	,	PUNCT
iajs-1184	34	60	�	�	PROPN
iajs-1184	34	61	�	�	PROPN
iajs-1184	34	62	ح	ح	PROPN
iajs-1184	34	63	�	�	PROPN
iajs-1184	34	64	�	�	PROPN
iajs-1184	34	65	�	�	PROPN
iajs-1184	34	66	�	�	PROPN
iajs-1184	34	67	∈	∈	PROPN
iajs-1184	34	68	�	�	PROPN
iajs-1184	34	69	=	=	SYM
iajs-1184	34	70	(	(	PUNCT
iajs-1184	34	71	⋂	⋂	PROPN
iajs-1184	34	72	�	�	PROPN
iajs-1184	34	73	�	�	PROPN
iajs-1184	34	74	�	�	PROPN
iajs-1184	34	75	∈	∈	PROPN
iajs-1184	34	76	�	�	PROPN
iajs-1184	34	77	)	)	PUNCT
iajs-1184	34	78	�	�	PROPN
iajs-1184	34	79	,	,	PUNCT
iajs-1184	34	80	therefore	therefore	ADV
iajs-1184	34	81	u	u	PROPN
iajs-1184	34	82	ح	ح	PROPN
iajs-1184	34	83	(	(	PUNCT
iajs-1184	34	84	⋂	⋂	PROPN
iajs-1184	34	85	�	�	PROPN
iajs-1184	34	86	�	�	PROPN
iajs-1184	34	87	�	�	PROPN
iajs-1184	34	88	∈	∈	PROPN
iajs-1184	34	89	�	�	PROPN
iajs-1184	34	90	thus	thus	ADV
iajs-1184	34	91	.	.	PUNCT
iajs-1184	35	1	�	�	PROPN
iajs-1184	35	2	�	�	PROPN
iajs-1184	35	3	ح	ح	PROPN
iajs-1184	35	4	�	�	PROPN
iajs-1184	35	5	(	(	PUNCT
iajs-1184	35	6	(	(	PUNCT
iajs-1184	35	7	⋂	⋂	PROPN
iajs-1184	35	8	�	�	PROPN
iajs-1184	35	9	�	�	PROPN
iajs-1184	35	10	�	�	PROPN
iajs-1184	35	11	∈	∈	PROPN
iajs-1184	35	12	�	�	PROPN
iajs-1184	35	13	)	)	PUNCT
iajs-1184	35	14	�	�	PROPN
iajs-1184	35	15	is	be	AUX
iajs-1184	35	16	semi	semi	ADJ
iajs-1184	35	17	-	-	ADJ
iajs-1184	35	18	preopen	preopen	ADJ
iajs-1184	35	19	set	set	NOUN
iajs-1184	35	20	,	,	PUNCT
iajs-1184	35	21	implies	imply	VERB
iajs-1184	35	22	⋂	⋂	PROPN
iajs-1184	35	23	�	�	PROPN
iajs-1184	35	24	�	�	PROPN
iajs-1184	35	25	�	�	PROPN
iajs-1184	35	26	∈	∈	PROPN
iajs-1184	35	27	�	�	PROPN
iajs-1184	35	28	is	be	AUX
iajs-1184	35	29	semi	semi	ADJ
iajs-1184	35	30	-	-	ADJ
iajs-1184	35	31	preclosed	preclosed	ADJ
iajs-1184	35	32	set	set	NOUN
iajs-1184	35	33	.	.	PUNCT
iajs-1184	36	1	■	■	PUNCT
iajs-1184	36	2	remark	remark	VERB
iajs-1184	36	3	2.5	2.5	NUM
iajs-1184	36	4	:	:	PUNCT
iajs-1184	36	5	the	the	DET
iajs-1184	36	6	intersection	intersection	NOUN
iajs-1184	36	7	of	of	ADP
iajs-1184	36	8	two	two	NUM
iajs-1184	36	9	semi	semi	ADJ
iajs-1184	36	10	-	-	ADJ
iajs-1184	36	11	preopen	preopen	ADJ
iajs-1184	36	12	sets	set	NOUN
iajs-1184	36	13	need	need	VERB
iajs-1184	36	14	not	not	PART
iajs-1184	36	15	to	to	PART
iajs-1184	36	16	be	be	AUX
iajs-1184	36	17	semi	semi	ADJ
iajs-1184	36	18	-	-	ADJ
iajs-1184	36	19	preopen	preopen	ADJ
iajs-1184	36	20	set	set	NOUN
iajs-1184	36	21	,	,	PUNCT
iajs-1184	36	22	as	as	SCONJ
iajs-1184	36	23	the	the	DET
iajs-1184	36	24	following	follow	VERB
iajs-1184	36	25	example	example	NOUN
iajs-1184	36	26	shows	show	VERB
iajs-1184	36	27	:	:	PUNCT
iajs-1184	36	28	example	example	NOUN
iajs-1184	36	29	1	1	NUM
iajs-1184	36	30	:	:	PUNCT
iajs-1184	36	31	let	let	VERB
iajs-1184	36	32	x={1,2,3	x={1,2,3	VERB
iajs-1184	36	33	}	}	PUNCT
iajs-1184	36	34	,	,	PUNCT
iajs-1184	36	35			NOUN
iajs-1184	36	36	=	=	PRON
iajs-1184	36	37	{	{	PUNCT
iajs-1184	36	38	x,	x,	PROPN
iajs-1184	36	39	,	,	PUNCT
iajs-1184	36	40	{	{	PUNCT
iajs-1184	36	41	1,2	1,2	NUM
iajs-1184	36	42	}	}	PUNCT
iajs-1184	36	43	}	}	PUNCT
iajs-1184	36	44	po(x	po(x	NUM
iajs-1184	36	45	)	)	PUNCT
iajs-1184	36	46	=	=	SYM
iajs-1184	36	47			PROPN
iajs-1184	36	48			NOUN
iajs-1184	36	49	{	{	PUNCT
iajs-1184	36	50	{	{	PUNCT
iajs-1184	36	51	1},{2},{1,3},{2,3	1},{2},{1,3},{2,3	NUM
iajs-1184	36	52	}	}	PUNCT
iajs-1184	36	53	}	}	PUNCT
iajs-1184	36	54	,	,	PUNCT
iajs-1184	36	55	spo(x	spo(x	X
iajs-1184	36	56	)	)	PUNCT
iajs-1184	36	57	=	=	NOUN
iajs-1184	36	58	po(x	po(x	X
iajs-1184	36	59	)	)	PUNCT
iajs-1184	36	60	let	let	VERB
iajs-1184	36	61	a=	a=	VERB
iajs-1184	36	62	{	{	PUNCT
iajs-1184	36	63	1,3	1,3	NUM
iajs-1184	36	64	}	}	PUNCT
iajs-1184	36	65	and	and	CCONJ
iajs-1184	36	66	b={2,3	b={2,3	NOUN
iajs-1184	36	67	}	}	PUNCT
iajs-1184	36	68	are	be	AUX
iajs-1184	36	69	both	both	PRON
iajs-1184	36	70	semi	semi	ADJ
iajs-1184	36	71	-	-	ADJ
iajs-1184	36	72	preopen	preopen	ADJ
iajs-1184	36	73	sets	set	NOUN
iajs-1184	36	74	,	,	PUNCT
iajs-1184	36	75	but	but	CCONJ
iajs-1184	36	76	a	a	DET
iajs-1184	36	77			ADJ
iajs-1184	36	78	b={3	b={3	NOUN
iajs-1184	36	79	}	}	PUNCT
iajs-1184	36	80	is	be	AUX
iajs-1184	36	81	not	not	PART
iajs-1184	36	82	semi	semi	ADJ
iajs-1184	36	83	-	-	ADJ
iajs-1184	36	84	preopen	preopen	ADJ
iajs-1184	36	85	set	set	NOUN
iajs-1184	36	86	.	.	PUNCT
iajs-1184	37	1	remark	remark	VERB
iajs-1184	37	2	2.6	2.6	NUM
iajs-1184	37	3	:	:	PUNCT
iajs-1184	37	4	the	the	DET
iajs-1184	37	5	union	union	NOUN
iajs-1184	37	6	of	of	ADP
iajs-1184	37	7	two	two	NUM
iajs-1184	37	8	semi	semi	ADJ
iajs-1184	37	9	-	-	ADJ
iajs-1184	37	10	preclosed	preclose	VERB
iajs-1184	37	11	sets	set	NOUN
iajs-1184	37	12	need	need	VERB
iajs-1184	37	13	not	not	PART
iajs-1184	37	14	to	to	PART
iajs-1184	37	15	be	be	AUX
iajs-1184	37	16	semi	semi	ADJ
iajs-1184	37	17	-	-	ADJ
iajs-1184	37	18	preclosed	preclosed	ADJ
iajs-1184	37	19	set	set	NOUN
iajs-1184	37	20	,	,	PUNCT
iajs-1184	37	21	as	as	SCONJ
iajs-1184	37	22	the	the	DET
iajs-1184	37	23	example	example	NOUN
iajs-1184	37	24	1	1	NUM
iajs-1184	37	25	,	,	PUNCT
iajs-1184	37	26	let	let	VERB
iajs-1184	37	27	x={1,2,3	x={1,2,3	NUM
iajs-1184	37	28	}	}	PUNCT
iajs-1184	37	29	,	,	PUNCT
iajs-1184	37	30			NOUN
iajs-1184	37	31	=	=	PRON
iajs-1184	37	32	{	{	PUNCT
iajs-1184	37	33	x,	x,	PROPN
iajs-1184	37	34	,	,	PUNCT
iajs-1184	37	35	{	{	PUNCT
iajs-1184	37	36	1,2}}then	1,2}}then	NOUN
iajs-1184	37	37	{	{	PUNCT
iajs-1184	37	38	1	1	NUM
iajs-1184	37	39	}	}	PUNCT
iajs-1184	37	40	and	and	CCONJ
iajs-1184	37	41	{	{	PUNCT
iajs-1184	37	42	2	2	NUM
iajs-1184	37	43	}	}	PUNCT
iajs-1184	37	44	are	be	AUX
iajs-1184	37	45	two	two	NUM
iajs-1184	37	46	semi	semi	ADJ
iajs-1184	37	47	-	-	ADJ
iajs-1184	37	48	preclosed	preclosed	ADJ
iajs-1184	37	49	sets	set	NOUN
iajs-1184	37	50	since	since	SCONJ
iajs-1184	37	51	x-{1}={2,3	x-{1}={2,3	PROPN
iajs-1184	37	52	}	}	PUNCT
iajs-1184	37	53	and	and	CCONJ
iajs-1184	37	54	x-{2}={1,3	x-{2}={1,3	PROPN
iajs-1184	37	55	}	}	PUNCT
iajs-1184	37	56	are	be	AUX
iajs-1184	37	57	two	two	NUM
iajs-1184	37	58	semi	semi	ADJ
iajs-1184	37	59	-	-	ADJ
iajs-1184	37	60	preopen	preopen	ADJ
iajs-1184	37	61	sets	set	NOUN
iajs-1184	37	62	,	,	PUNCT
iajs-1184	37	63	but	but	CCONJ
iajs-1184	37	64	{	{	PUNCT
iajs-1184	37	65	1}{2}={1,2	1}{2}={1,2	X
iajs-1184	37	66	}	}	PUNCT
iajs-1184	37	67	is	be	AUX
iajs-1184	37	68	not	not	PART
iajs-1184	37	69	semi	semi	ADV
iajs-1184	37	70	-	-	ADJ
iajs-1184	37	71	preclosed	preclosed	ADJ
iajs-1184	37	72	set	set	NOUN
iajs-1184	37	73	since	since	SCONJ
iajs-1184	37	74	x{1,2}={3	x{1,2}={3	PROPN
iajs-1184	37	75	}	}	PUNCT
iajs-1184	37	76	is	be	AUX
iajs-1184	37	77	not	not	PART
iajs-1184	37	78	semi	semi	ADJ
iajs-1184	37	79	-	-	ADJ
iajs-1184	37	80	preopen	preopen	ADJ
iajs-1184	37	81	set	set	NOUN
iajs-1184	37	82	.	.	PUNCT
iajs-1184	38	1	definition	definition	NOUN
iajs-1184	38	2	2.7	2.7	NUM
iajs-1184	38	3	:	:	PUNCT
iajs-1184	38	4	the	the	DET
iajs-1184	38	5	union	union	NOUN
iajs-1184	38	6	of	of	ADP
iajs-1184	38	7	all	all	DET
iajs-1184	38	8	semi	semi	ADJ
iajs-1184	38	9	-	-	ADJ
iajs-1184	38	10	preopen	preopen	ADJ
iajs-1184	38	11	sets	set	NOUN
iajs-1184	38	12	contained	contain	VERB
iajs-1184	38	13	in	in	ADP
iajs-1184	38	14	a	a	PRON
iajs-1184	38	15	is	be	AUX
iajs-1184	38	16	called	call	VERB
iajs-1184	38	17	the	the	DET
iajs-1184	38	18	semi	semi	ADJ
iajs-1184	38	19	-	-	NOUN
iajs-1184	38	20	preinterior	preinterior	ADJ
iajs-1184	38	21	of	of	ADP
iajs-1184	38	22	a	a	PRON
iajs-1184	38	23	,	,	PUNCT
iajs-1184	38	24	denoted	denote	VERB
iajs-1184	38	25	by	by	ADP
iajs-1184	38	26	s	s	NOUN
iajs-1184	38	27	-	-	PUNCT
iajs-1184	38	28	pre	pre	NOUN
iajs-1184	38	29	-	-	NOUN
iajs-1184	38	30	int	int	ADJ
iajs-1184	38	31	a	a	PRON
iajs-1184	38	32	.	.	PUNCT
iajs-1184	39	1	definition	definition	NOUN
iajs-1184	39	2	2.8	2.8	NUM
iajs-1184	39	3	:	:	PUNCT
iajs-1184	39	4	the	the	DET
iajs-1184	39	5	intersection	intersection	NOUN
iajs-1184	39	6	of	of	ADP
iajs-1184	39	7	all	all	DET
iajs-1184	39	8	semi	semi	ADJ
iajs-1184	39	9	-	-	ADJ
iajs-1184	39	10	preclosed	preclosed	ADJ
iajs-1184	39	11	sets	set	NOUN
iajs-1184	39	12	containing	contain	VERB
iajs-1184	39	13	a	a	PRON
iajs-1184	39	14	is	be	AUX
iajs-1184	39	15	called	call	VERB
iajs-1184	39	16	the	the	DET
iajs-1184	39	17	semi	semi	ADJ
iajs-1184	39	18	-	-	ADJ
iajs-1184	39	19	preclosure	preclosure	ADJ
iajs-1184	39	20	of	of	ADP
iajs-1184	39	21	a	a	PRON
iajs-1184	39	22	,	,	PUNCT
iajs-1184	39	23	denoted	denote	VERB
iajs-1184	39	24	by	by	ADP
iajs-1184	39	25	s	s	NOUN
iajs-1184	39	26	-	-	PUNCT
iajs-1184	39	27	pre	pre	NOUN
iajs-1184	39	28	-	-	NOUN
iajs-1184	39	29	cl	cl	ADJ
iajs-1184	39	30	a	a	PRON
iajs-1184	39	31	.	.	PUNCT
iajs-1184	40	1	proposition	proposition	NOUN
iajs-1184	40	2	2.9	2.9	NUM
iajs-1184	40	3	:	:	SYM
iajs-1184	40	4	1	1	X
iajs-1184	40	5	.	.	X
iajs-1184	41	1	if	if	SCONJ
iajs-1184	41	2	aح	aح	VERB
iajs-1184	41	3	b	b	NOUN
iajs-1184	41	4	,	,	PUNCT
iajs-1184	41	5	then	then	ADV
iajs-1184	41	6	s	s	NOUN
iajs-1184	41	7	-	-	PUNCT
iajs-1184	41	8	pre	pre	NOUN
iajs-1184	41	9	-	-	NOUN
iajs-1184	41	10	int	int	ADJ
iajs-1184	41	11	a	a	DET
iajs-1184	41	12	ح	ح	NOUN
iajs-1184	41	13	s	s	NOUN
iajs-1184	41	14	-	-	PUNCT
iajs-1184	41	15	pre	pre	ADJ
iajs-1184	41	16	-	-	ADJ
iajs-1184	41	17	int	int	ADJ
iajs-1184	41	18	b.	b.	PROPN
iajs-1184	41	19	.a	.a	PROPN
iajs-1184	41	20	.	.	PUNCT
iajs-1184	42	1	s	s	X
iajs-1184	42	2	-	-	PUNCT
iajs-1184	42	3	pre	pre	NOUN
iajs-1184	42	4	-	-	NOUN
iajs-1184	42	5	int	int	ADJ
iajs-1184	42	6	a	a	DET
iajs-1184	42	7	2	2	NUM
iajs-1184	42	8	ح	ح	NOUN
iajs-1184	42	9	3	3	NUM
iajs-1184	42	10	.	.	PUNCT
iajs-1184	43	1	s	s	X
iajs-1184	43	2	-	-	PUNCT
iajs-1184	43	3	pre	pre	NOUN
iajs-1184	43	4	-	-	ADJ
iajs-1184	43	5	int	int	ADJ
iajs-1184	43	6	a	a	DET
iajs-1184	43	7			NOUN
iajs-1184	43	8	s	s	NOUN
iajs-1184	43	9	-	-	PUNCT
iajs-1184	43	10	pre	pre	ADJ
iajs-1184	43	11	-	-	ADJ
iajs-1184	43	12	int	int	ADJ
iajs-1184	43	13	b	b	PROPN
iajs-1184	43	14	ح	ح	NOUN
iajs-1184	43	15	s	s	NOUN
iajs-1184	43	16	-	-	PUNCT
iajs-1184	43	17	pre	pre	NOUN
iajs-1184	43	18	-	-	ADJ
iajs-1184	43	19	int	int	ADJ
iajs-1184	43	20	(	(	PUNCT
iajs-1184	43	21	a	a	DET
iajs-1184	43	22			NOUN
iajs-1184	43	23	b	b	PROPN
iajs-1184	43	24	)	)	PUNCT
iajs-1184	43	25	.	.	PUNCT
iajs-1184	44	1	4	4	X
iajs-1184	44	2	.	.	X
iajs-1184	44	3	s	s	X
iajs-1184	44	4	-	-	PUNCT
iajs-1184	44	5	pre	pre	NOUN
iajs-1184	44	6	-	-	ADJ
iajs-1184	44	7	int	int	ADJ
iajs-1184	44	8	(	(	PUNCT
iajs-1184	44	9	a	a	DET
iajs-1184	44	10			ADJ
iajs-1184	44	11	b	b	NOUN
iajs-1184	44	12	)	)	PUNCT
iajs-1184	44	13	ح	ح	NOUN
iajs-1184	44	14	s	s	NOUN
iajs-1184	44	15	-	-	PUNCT
iajs-1184	44	16	pre	pre	NOUN
iajs-1184	44	17	-	-	ADJ
iajs-1184	44	18	int	int	ADJ
iajs-1184	44	19	a	a	DET
iajs-1184	44	20			NOUN
iajs-1184	44	21	s	s	NOUN
iajs-1184	44	22	-	-	PUNCT
iajs-1184	44	23	pre	pre	ADJ
iajs-1184	44	24	-	-	ADJ
iajs-1184	44	25	int	int	ADJ
iajs-1184	44	26	b.	b.	NOUN
iajs-1184	44	27	proof	proof	NOUN
iajs-1184	44	28	:	:	PUNCT
iajs-1184	44	29	the	the	DET
iajs-1184	44	30	proof	proof	NOUN
iajs-1184	44	31	of	of	ADP
iajs-1184	44	32	(	(	PUNCT
iajs-1184	44	33	1	1	NUM
iajs-1184	44	34	)	)	PUNCT
iajs-1184	44	35	and	and	CCONJ
iajs-1184	44	36	(	(	PUNCT
iajs-1184	44	37	2	2	X
iajs-1184	44	38	)	)	PUNCT
iajs-1184	44	39	is	be	AUX
iajs-1184	44	40	direct	direct	ADJ
iajs-1184	44	41	by	by	ADP
iajs-1184	44	42	the	the	DET
iajs-1184	44	43	definition	definition	NOUN
iajs-1184	44	44	of	of	ADP
iajs-1184	44	45	subsets	subset	NOUN
iajs-1184	44	46	and	and	CCONJ
iajs-1184	44	47	s	s	NOUN
iajs-1184	44	48	-	-	PUNCT
iajs-1184	44	49	pre	pre	NOUN
iajs-1184	44	50	-	-	NOUN
iajs-1184	44	51	int	int	ADJ
iajs-1184	44	52	a	a	PRON
iajs-1184	44	53	.	.	PUNCT
iajs-1184	45	1	ibn	ibn	PROPN
iajs-1184	45	2	alhaitham	alhaitham	NOUN
iajs-1184	46	1	j.	j.	PROPN
iajs-1184	47	1	fo	fo	ADP
iajs-1184	47	2	r	r	NOUN
iajs-1184	47	3	pure	pure	ADJ
iajs-1184	47	4	&	&	CCONJ
iajs-1184	47	5	appl	appl	PROPN
iajs-1184	47	6	.	.	PUNCT
iajs-1184	48	1	sc	sc	PROPN
iajs-1184	49	1	i	i	PRON
iajs-1184	49	2	vo	vo	INTJ
iajs-1184	49	3	l.22	l.22	X
iajs-1184	49	4	(	(	PUNCT
iajs-1184	49	5	3	3	NUM
iajs-1184	49	6	)	)	PUNCT
iajs-1184	49	7	2009	2009	NUM
iajs-1184	49	8	3	3	NUM
iajs-1184	49	9	.	.	PUNCT
iajs-1184	50	1	since	since	SCONJ
iajs-1184	50	2	aح	aح	ADP
iajs-1184	50	3	a	a	PROPN
iajs-1184	50	4	,	,	PUNCT
iajs-1184	50	5	therefore	therefore	ADV
iajs-1184	50	6	s	s	NOUN
iajs-1184	50	7	-	-	PUNCT
iajs-1184	50	8	pre	pre	NOUN
iajs-1184	50	9	-	-	NOUN
iajs-1184	50	10	int	int	ADJ
iajs-1184	50	11	aح	aح	PROPN
iajs-1184	50	12	s	s	NOUN
iajs-1184	50	13	-	-	PUNCT
iajs-1184	50	14	pre	pre	NOUN
iajs-1184	50	15	-	-	ADJ
iajs-1184	50	16	int	int	ADJ
iajs-1184	50	17	(	(	PUNCT
iajs-1184	50	18	a	a	DET
iajs-1184	50	19			PROPN
iajs-1184	50	20	b	b	PROPN
iajs-1184	50	21	)	)	PUNCT
iajs-1184	50	22	(	(	PUNCT
iajs-1184	50	23	by	by	ADP
iajs-1184	50	24	part	part	NOUN
iajs-1184	50	25	1	1	NUM
iajs-1184	50	26	)	)	PUNCT
iajs-1184	50	27	,	,	PUNCT
iajs-1184	50	28	and	and	CCONJ
iajs-1184	50	29	since	since	SCONJ
iajs-1184	50	30	ح	ح	PROPN
iajs-1184	50	31	a	a	PROPN
iajs-1184	50	32	,	,	PUNCT
iajs-1184	50	33	therefore	therefore	ADV
iajs-1184	50	34	s	s	NOUN
iajs-1184	50	35	-	-	PUNCT
iajs-1184	50	36	pre	pre	ADJ
iajs-1184	50	37	-	-	ADJ
iajs-1184	50	38	int	int	ADJ
iajs-1184	50	39	ح	ح	NOUN
iajs-1184	50	40	s	s	NOUN
iajs-1184	50	41	-	-	PUNCT
iajs-1184	50	42	pre	pre	NOUN
iajs-1184	50	43	-	-	ADJ
iajs-1184	50	44	int	int	ADJ
iajs-1184	50	45	(	(	PUNCT
iajs-1184	50	46	a	a	DET
iajs-1184	50	47			PROPN
iajs-1184	50	48	b	b	PROPN
iajs-1184	50	49	)	)	PUNCT
iajs-1184	50	50	(	(	PUNCT
iajs-1184	50	51	by	by	ADP
iajs-1184	50	52	part	part	NOUN
iajs-1184	50	53	1	1	NUM
iajs-1184	50	54	)	)	PUNCT
iajs-1184	50	55	,	,	PUNCT
iajs-1184	50	56	implies	imply	VERB
iajs-1184	50	57	s	s	NOUN
iajs-1184	50	58	-	-	PUNCT
iajs-1184	50	59	pre	pre	NOUN
iajs-1184	50	60	-	-	ADJ
iajs-1184	50	61	int	int	ADJ
iajs-1184	50	62	a	a	DET
iajs-1184	50	63			NOUN
iajs-1184	50	64	s	s	NOUN
iajs-1184	50	65	-	-	NOUN
iajs-1184	50	66	preint	preint	NOUN
iajs-1184	50	67	b	b	PROPN
iajs-1184	50	68	ح	ح	NOUN
iajs-1184	50	69	s	s	NOUN
iajs-1184	50	70	-	-	PUNCT
iajs-1184	50	71	pre	pre	NOUN
iajs-1184	50	72	-	-	ADJ
iajs-1184	50	73	int	int	ADJ
iajs-1184	50	74	(	(	PUNCT
iajs-1184	50	75	a	a	DET
iajs-1184	50	76			NOUN
iajs-1184	50	77	b	b	PROPN
iajs-1184	50	78	)	)	PUNCT
iajs-1184	50	79	.	.	PUNCT
iajs-1184	51	1	the	the	DET
iajs-1184	51	2	converse	converse	NOUN
iajs-1184	51	3	is	be	AUX
iajs-1184	51	4	not	not	PART
iajs-1184	51	5	true	true	ADJ
iajs-1184	51	6	in	in	ADP
iajs-1184	51	7	general	general	ADJ
iajs-1184	51	8	,	,	PUNCT
iajs-1184	51	9	as	as	SCONJ
iajs-1184	51	10	the	the	DET
iajs-1184	51	11	following	following	NOUN
iajs-1184	51	12	of	of	ADP
iajs-1184	51	13	example	example	NOUN
iajs-1184	51	14	(	(	PUNCT
iajs-1184	51	15	1	1	NUM
iajs-1184	51	16	):	):	PUNCT
iajs-1184	51	17	let	let	VERB
iajs-1184	51	18	a={2	a={2	PROPN
iajs-1184	51	19	}	}	PUNCT
iajs-1184	51	20	,	,	PUNCT
iajs-1184	51	21	={3	={3	X
iajs-1184	51	22	}	}	PUNCT
iajs-1184	51	23	and	and	CCONJ
iajs-1184	51	24	a={2,3	a={2,3	NUM
iajs-1184	51	25	}	}	PUNCT
iajs-1184	51	26	,	,	PUNCT
iajs-1184	51	27	then	then	ADV
iajs-1184	51	28	:	:	PUNCT
iajs-1184	51	29	s	s	X
iajs-1184	51	30	-	-	PUNCT
iajs-1184	51	31	pre	pre	NOUN
iajs-1184	51	32	-	-	NOUN
iajs-1184	51	33	int{2}={2	int{2}={2	NOUN
iajs-1184	51	34	}	}	PUNCT
iajs-1184	51	35	,	,	PUNCT
iajs-1184	51	36	s	s	X
iajs-1184	51	37	-	-	PUNCT
iajs-1184	51	38	pre	pre	ADJ
iajs-1184	51	39	-	-	ADJ
iajs-1184	51	40	int{3}=	int{3}=	ADJ
iajs-1184	51	41			NOUN
iajs-1184	51	42	and	and	CCONJ
iajs-1184	51	43	s	s	NOUN
iajs-1184	51	44	-	-	PUNCT
iajs-1184	51	45	pre	pre	NOUN
iajs-1184	51	46	-	-	ADJ
iajs-1184	51	47	int{2,3}={2,3	int{2,3}={2,3	ADJ
iajs-1184	51	48	}	}	PUNCT
iajs-1184	51	49	.	.	PUNCT
iajs-1184	51	50	ut	ut	PROPN
iajs-1184	52	1	s	s	X
iajs-1184	52	2	-	-	PUNCT
iajs-1184	52	3	pre	pre	NOUN
iajs-1184	52	4	-	-	ADJ
iajs-1184	52	5	int	int	ADJ
iajs-1184	52	6	(	(	PUNCT
iajs-1184	52	7	a	a	DET
iajs-1184	52	8			NOUN
iajs-1184	52	9	b	b	NOUN
iajs-1184	52	10	)	)	PUNCT
iajs-1184	53	1	=	=	NOUN
iajs-1184	53	2	{	{	PUNCT
iajs-1184	53	3	2,3}	2,3}	NUM
iajs-1184	53	4	{	{	PUNCT
iajs-1184	53	5	2}=	2}=	PROPN
iajs-1184	53	6	s	s	PROPN
iajs-1184	53	7	-	-	PUNCT
iajs-1184	53	8	pre	pre	NOUN
iajs-1184	53	9	-	-	ADJ
iajs-1184	53	10	int	int	ADJ
iajs-1184	53	11	a	a	DET
iajs-1184	53	12			NOUN
iajs-1184	53	13	s	s	NOUN
iajs-1184	53	14	-	-	PUNCT
iajs-1184	53	15	pre	pre	ADJ
iajs-1184	53	16	-	-	ADJ
iajs-1184	53	17	int	int	ADJ
iajs-1184	53	18	b.	b.	NOUN
iajs-1184	53	19	4	4	X
iajs-1184	53	20	.	.	PUNCT
iajs-1184	54	1	a	a	PROPN
iajs-1184	54	2	ح	ح	VERB
iajs-1184	54	3	a	a	PRON
iajs-1184	54	4	,	,	PUNCT
iajs-1184	54	5	then	then	ADV
iajs-1184	54	6	this	this	PRON
iajs-1184	54	7	implies	imply	VERB
iajs-1184	54	8	that	that	SCONJ
iajs-1184	54	9	s	s	NOUN
iajs-1184	54	10	-	-	PUNCT
iajs-1184	54	11	pre	pre	NOUN
iajs-1184	54	12	-	-	ADJ
iajs-1184	54	13	int	int	ADJ
iajs-1184	54	14	(	(	PUNCT
iajs-1184	54	15	a	a	DET
iajs-1184	54	16			ADJ
iajs-1184	54	17	b	b	NOUN
iajs-1184	54	18	)	)	PUNCT
iajs-1184	54	19	ح	ح	NOUN
iajs-1184	54	20	s	s	NOUN
iajs-1184	54	21	-	-	PUNCT
iajs-1184	54	22	pre	pre	NOUN
iajs-1184	54	23	-	-	NOUN
iajs-1184	54	24	int	int	ADJ
iajs-1184	54	25	a	a	PRON
iajs-1184	54	26	(	(	PUNCT
iajs-1184	54	27	by	by	ADP
iajs-1184	54	28	part	part	NOUN
iajs-1184	54	29	1	1	NUM
iajs-1184	54	30	)	)	PUNCT
iajs-1184	54	31	,	,	PUNCT
iajs-1184	54	32	and	and	CCONJ
iajs-1184	54	33	a	a	PROPN
iajs-1184	54	34	s	s	PROPN
iajs-1184	54	35	-	-	PUNCT
iajs-1184	54	36	pre	pre	ADJ
iajs-1184	54	37	-	-	ADJ
iajs-1184	54	38	int	int	ADJ
iajs-1184	54	39			NOUN
iajs-1184	54	40	(	(	PUNCT
iajs-1184	54	41	by	by	ADP
iajs-1184	54	42	part	part	NOUN
iajs-1184	54	43	1	1	NUM
iajs-1184	54	44	)	)	PUNCT
iajs-1184	54	45	,	,	PUNCT
iajs-1184	54	46	therefore	therefore	ADV
iajs-1184	54	47	s	s	NOUN
iajs-1184	54	48	-	-	PUNCT
iajs-1184	54	49	pre	pre	NOUN
iajs-1184	54	50	-	-	ADJ
iajs-1184	54	51	int	int	ADJ
iajs-1184	54	52	(	(	PUNCT
iajs-1184	54	53	a	a	DET
iajs-1184	54	54			NUM
iajs-1184	54	55	ح	ح	NOUN
iajs-1184	54	56			NOUN
iajs-1184	54	57	,	,	PUNCT
iajs-1184	54	58	then	then	ADV
iajs-1184	54	59	s	s	NOUN
iajs-1184	54	60	-	-	PUNCT
iajs-1184	54	61	pre	pre	NOUN
iajs-1184	54	62	-	-	ADJ
iajs-1184	54	63	int	int	ADJ
iajs-1184	54	64	(	(	PUNCT
iajs-1184	54	65	a	a	DET
iajs-1184	54	66			ADJ
iajs-1184	54	67	b	b	NOUN
iajs-1184	54	68	)	)	PUNCT
iajs-1184	54	69	ح	ح	PROPN
iajs-1184	54	70	b	b	X
iajs-1184	54	71	)	)	PUNCT
iajs-1184	54	72	ح	ح	PROPN
iajs-1184	54	73	s	s	PROPN
iajs-1184	54	74	-	-	PUNCT
iajs-1184	54	75	pre	pre	NOUN
iajs-1184	54	76	-	-	ADJ
iajs-1184	54	77	int	int	ADJ
iajs-1184	54	78	a	a	DET
iajs-1184	54	79			NOUN
iajs-1184	54	80	s	s	NOUN
iajs-1184	54	81	-	-	PUNCT
iajs-1184	54	82	pre	pre	ADJ
iajs-1184	54	83	-	-	ADJ
iajs-1184	54	84	int	int	ADJ
iajs-1184	54	85	b.	b.	NOUN
iajs-1184	54	86	but	but	CCONJ
iajs-1184	54	87	s	s	NOUN
iajs-1184	54	88	-	-	PUNCT
iajs-1184	54	89	pre	pre	NOUN
iajs-1184	54	90	-	-	ADJ
iajs-1184	54	91	int	int	ADJ
iajs-1184	54	92	a	a	DET
iajs-1184	54	93			NOUN
iajs-1184	54	94	s	s	NOUN
iajs-1184	54	95	-	-	PUNCT
iajs-1184	54	96	pre	pre	ADJ
iajs-1184	54	97	-	-	ADJ
iajs-1184	54	98	int	int	ADJ
iajs-1184	54	99	b	b	PROPN
iajs-1184	54	100			PROPN
iajs-1184	54	101	s	s	NOUN
iajs-1184	54	102	-	-	PUNCT
iajs-1184	54	103	pre	pre	NOUN
iajs-1184	54	104	-	-	ADJ
iajs-1184	54	105	int	int	ADJ
iajs-1184	54	106	(	(	PUNCT
iajs-1184	54	107	a	a	DET
iajs-1184	54	108			ADJ
iajs-1184	54	109	b	b	NOUN
iajs-1184	54	110	)	)	PUNCT
iajs-1184	54	111	,	,	PUNCT
iajs-1184	54	112	as	as	SCONJ
iajs-1184	54	113	the	the	DET
iajs-1184	54	114	following	follow	VERB
iajs-1184	54	115	example	example	NOUN
iajs-1184	54	116	shows	show	VERB
iajs-1184	54	117	:	:	PUNCT
iajs-1184	54	118	example	example	NOUN
iajs-1184	54	119	2	2	NUM
iajs-1184	54	120	:	:	PUNCT
iajs-1184	54	121	let	let	VERB
iajs-1184	54	122	x={1,2,3,4	x={1,2,3,4	NOUN
iajs-1184	54	123	}	}	PUNCT
iajs-1184	54	124	,	,	PUNCT
iajs-1184	54	125	={x,	={x,	PUNCT
iajs-1184	54	126	,	,	PUNCT
iajs-1184	54	127	{	{	PUNCT
iajs-1184	54	128	1},{2},{1,2	1},{2},{1,2	NUM
iajs-1184	54	129	}	}	PUNCT
iajs-1184	54	130	}	}	PUNCT
iajs-1184	54	131	po(x	po(x	NUM
iajs-1184	54	132	)	)	PUNCT
iajs-1184	54	133	=	=	SYM
iajs-1184	54	134			PROPN
iajs-1184	54	135			NOUN
iajs-1184	54	136	{	{	PUNCT
iajs-1184	54	137	{	{	PUNCT
iajs-1184	54	138	1,2,3},{1,2,4	1,2,3},{1,2,4	NUM
iajs-1184	54	139	}	}	PUNCT
iajs-1184	54	140	}	}	PUNCT
iajs-1184	54	141	spo(x	spo(x	PROPN
iajs-1184	54	142	)	)	PUNCT
iajs-1184	54	143	=	=	SYM
iajs-1184	54	144	po(x	po(x	X
iajs-1184	54	145	)	)	PUNCT
iajs-1184	54	146			NOUN
iajs-1184	54	147	{	{	PUNCT
iajs-1184	54	148	{	{	PUNCT
iajs-1184	54	149	1,3},{1,4},{1,3,4},{2,3},{2,4},{2,3,4	1,3},{1,4},{1,3,4},{2,3},{2,4},{2,3,4	NUM
iajs-1184	54	150	}	}	PUNCT
iajs-1184	54	151	}	}	PUNCT
iajs-1184	54	152	let	let	VERB
iajs-1184	54	153	a	a	DET
iajs-1184	54	154	=	=	NOUN
iajs-1184	54	155	{	{	PUNCT
iajs-1184	54	156	2,3,4	2,3,4	NUM
iajs-1184	54	157	}	}	PUNCT
iajs-1184	54	158	,	,	PUNCT
iajs-1184	54	159	b	b	X
iajs-1184	54	160	=	=	X
iajs-1184	54	161	{	{	PUNCT
iajs-1184	54	162	1,3,4	1,3,4	NUM
iajs-1184	54	163	}	}	PUNCT
iajs-1184	54	164	and	and	CCONJ
iajs-1184	54	165	a	a	DET
iajs-1184	54	166			NOUN
iajs-1184	54	167	b=	b=	NOUN
iajs-1184	54	168	{	{	PUNCT
iajs-1184	54	169	3,4},then	3,4},then	NUM
iajs-1184	54	170	:	:	PUNCT
iajs-1184	54	171	s	s	X
iajs-1184	54	172	-	-	PUNCT
iajs-1184	54	173	pre	pre	NOUN
iajs-1184	54	174	-	-	ADJ
iajs-1184	54	175	int	int	ADJ
iajs-1184	54	176	{	{	PUNCT
iajs-1184	54	177	2,3,4}={2,3,4	2,3,4}={2,3,4	NUM
iajs-1184	54	178	}	}	PUNCT
iajs-1184	54	179	,	,	PUNCT
iajs-1184	54	180	s	s	X
iajs-1184	54	181	-	-	PUNCT
iajs-1184	54	182	pre	pre	NOUN
iajs-1184	54	183	-	-	ADJ
iajs-1184	54	184	int	int	ADJ
iajs-1184	54	185	{	{	PUNCT
iajs-1184	54	186	1,3,4}=	1,3,4}=	NUM
iajs-1184	54	187	{	{	PUNCT
iajs-1184	54	188	1,3,4	1,3,4	NUM
iajs-1184	54	189	}	}	PUNCT
iajs-1184	54	190	and	and	CCONJ
iajs-1184	54	191	s	s	NOUN
iajs-1184	54	192	-	-	PUNCT
iajs-1184	54	193	pre	pre	NOUN
iajs-1184	54	194	-	-	ADJ
iajs-1184	54	195	int	int	ADJ
iajs-1184	54	196	(	(	PUNCT
iajs-1184	54	197	a	a	DET
iajs-1184	54	198			ADJ
iajs-1184	54	199	b	b	NOUN
iajs-1184	54	200	)	)	PUNCT
iajs-1184	54	201	=	=	VERB
iajs-1184	55	1			ADJ
iajs-1184	55	2	.but	.but	PUNCT
iajs-1184	56	1	s	s	X
iajs-1184	56	2	-	-	PUNCT
iajs-1184	56	3	pre	pre	NOUN
iajs-1184	56	4	-	-	ADJ
iajs-1184	56	5	int	int	ADJ
iajs-1184	56	6	a	a	DET
iajs-1184	56	7			NOUN
iajs-1184	56	8	s	s	NOUN
iajs-1184	56	9	-	-	PUNCT
iajs-1184	56	10	pre	pre	ADJ
iajs-1184	56	11	-	-	ADJ
iajs-1184	56	12	int	int	ADJ
iajs-1184	56	13	b	b	NOUN
iajs-1184	56	14	=	=	PUNCT
iajs-1184	56	15	{	{	PUNCT
iajs-1184	56	16	3,4	3,4	NUM
iajs-1184	56	17	}	}	PUNCT
iajs-1184	56	18			PROPN
iajs-1184	56	19			NOUN
iajs-1184	56	20	=	=	SYM
iajs-1184	56	21	s	s	NOUN
iajs-1184	56	22	-	-	PUNCT
iajs-1184	56	23	pre	pre	NOUN
iajs-1184	56	24	-	-	ADJ
iajs-1184	56	25	int	int	ADJ
iajs-1184	56	26	(	(	PUNCT
iajs-1184	56	27	a	a	DET
iajs-1184	56	28			ADJ
iajs-1184	56	29	b	b	NOUN
iajs-1184	56	30	)	)	PUNCT
iajs-1184	56	31	.	.	PUNCT
iajs-1184	57	1	proposition	proposition	NOUN
iajs-1184	57	2	2.10	2.10	NUM
iajs-1184	57	3	:	:	SYM
iajs-1184	58	1	1	1	X
iajs-1184	58	2	.	.	X
iajs-1184	59	1	if	if	SCONJ
iajs-1184	59	2	aح	aح	VERB
iajs-1184	59	3	b	b	NOUN
iajs-1184	59	4	,	,	PUNCT
iajs-1184	59	5	then	then	ADV
iajs-1184	59	6	s	s	NOUN
iajs-1184	59	7	-	-	PUNCT
iajs-1184	59	8	pre	pre	NOUN
iajs-1184	59	9	-	-	NOUN
iajs-1184	59	10	cl	cl	VERB
iajs-1184	59	11	a	a	DET
iajs-1184	59	12	ح	ح	NOUN
iajs-1184	59	13	s	s	NOUN
iajs-1184	59	14	-	-	PUNCT
iajs-1184	59	15	pre	pre	ADJ
iajs-1184	59	16	-	-	ADJ
iajs-1184	59	17	cl	cl	ADJ
iajs-1184	59	18	b.	b.	NOUN
iajs-1184	59	19	2	2	NUM
iajs-1184	59	20	.	.	PUNCT
iajs-1184	60	1	a	a	DET
iajs-1184	60	2	ح	ح	NOUN
iajs-1184	60	3	s	s	NOUN
iajs-1184	60	4	-	-	PUNCT
iajs-1184	60	5	pre	pre	ADJ
iajs-1184	60	6	-	-	NOUN
iajs-1184	60	7	cl	cl	ADJ
iajs-1184	60	8	a.	a.	NOUN
iajs-1184	60	9	3	3	NUM
iajs-1184	60	10	.	.	PUNCT
iajs-1184	61	1	s	s	X
iajs-1184	61	2	-	-	PUNCT
iajs-1184	61	3	pre	pre	ADJ
iajs-1184	61	4	-	-	ADJ
iajs-1184	61	5	cl	cl	ADJ
iajs-1184	61	6			NOUN
iajs-1184	61	7	=	=	PUNCT
iajs-1184	61	8			ADJ
iajs-1184	61	9	,	,	PUNCT
iajs-1184	61	10	s	s	NOUN
iajs-1184	61	11	-	-	PUNCT
iajs-1184	61	12	pre	pre	NOUN
iajs-1184	61	13	-	-	NOUN
iajs-1184	61	14	cl	cl	ADJ
iajs-1184	61	15	x	x	PUNCT
iajs-1184	62	1	=	=	PUNCT
iajs-1184	62	2	x.	x.	NOUN
iajs-1184	62	3	4	4	NUM
iajs-1184	62	4	.	.	X
iajs-1184	63	1	s	s	X
iajs-1184	63	2	-	-	PUNCT
iajs-1184	63	3	pre	pre	NOUN
iajs-1184	63	4	-	-	NOUN
iajs-1184	63	5	cl	cl	VERB
iajs-1184	63	6	a	a	DET
iajs-1184	63	7			NOUN
iajs-1184	63	8	s	s	NOUN
iajs-1184	63	9	-	-	PUNCT
iajs-1184	63	10	pre	pre	NOUN
iajs-1184	63	11	-	-	NOUN
iajs-1184	63	12	cl	cl	ADJ
iajs-1184	63	13	b	b	NOUN
iajs-1184	63	14	ح	ح	NOUN
iajs-1184	63	15	s	s	NOUN
iajs-1184	63	16	-	-	PUNCT
iajs-1184	63	17	pre	pre	NOUN
iajs-1184	63	18	-	-	NOUN
iajs-1184	63	19	cl	cl	ADJ
iajs-1184	63	20	(	(	PUNCT
iajs-1184	63	21	a	a	DET
iajs-1184	63	22			NOUN
iajs-1184	63	23	b	b	PROPN
iajs-1184	63	24	)	)	PUNCT
iajs-1184	63	25	.	.	PUNCT
iajs-1184	64	1	5	5	X
iajs-1184	64	2	.	.	X
iajs-1184	64	3	s	s	X
iajs-1184	64	4	-	-	PUNCT
iajs-1184	64	5	pre	pre	NOUN
iajs-1184	64	6	-	-	NOUN
iajs-1184	64	7	cl	cl	ADJ
iajs-1184	64	8	(	(	PUNCT
iajs-1184	64	9	a	a	DET
iajs-1184	64	10			ADJ
iajs-1184	64	11	b	b	NOUN
iajs-1184	64	12	)	)	PUNCT
iajs-1184	64	13	ح	ح	NOUN
iajs-1184	64	14	s	s	NOUN
iajs-1184	64	15	-	-	PUNCT
iajs-1184	64	16	pre	pre	NOUN
iajs-1184	64	17	-	-	NOUN
iajs-1184	64	18	cl	cl	ADJ
iajs-1184	64	19	a	a	DET
iajs-1184	64	20			NOUN
iajs-1184	64	21	s	s	NOUN
iajs-1184	64	22	-	-	PUNCT
iajs-1184	64	23	pre	pre	ADJ
iajs-1184	64	24	-	-	ADJ
iajs-1184	64	25	cl	cl	ADJ
iajs-1184	64	26	b.	b.	NOUN
iajs-1184	64	27	proof	proof	NOUN
iajs-1184	64	28	:	:	PUNCT
iajs-1184	64	29	1	1	X
iajs-1184	64	30	.	.	X
iajs-1184	65	1	let	let	VERB
iajs-1184	65	2	x	x	PRON
iajs-1184	65	3	be	be	AUX
iajs-1184	65	4	any	any	DET
iajs-1184	65	5	element	element	NOUN
iajs-1184	65	6	in	in	ADP
iajs-1184	65	7	x	x	NOUN
iajs-1184	65	8	,	,	PUNCT
iajs-1184	65	9	such	such	ADJ
iajs-1184	65	10	that	that	SCONJ
iajs-1184	65	11	x	x	PUNCT
iajs-1184	65	12	s	s	X
iajs-1184	65	13	-	-	PUNCT
iajs-1184	65	14	pre	pre	NOUN
iajs-1184	65	15	-	-	ADJ
iajs-1184	65	16	cl	cl	ADJ
iajs-1184	65	17	b	b	NOUN
iajs-1184	65	18	,	,	PUNCT
iajs-1184	65	19	which	which	PRON
iajs-1184	65	20	implies	imply	VERB
iajs-1184	65	21	there	there	PRON
iajs-1184	65	22	existence	existence	NOUN
iajs-1184	65	23	of	of	ADP
iajs-1184	65	24	a	a	DET
iajs-1184	65	25	semi	semi	ADJ
iajs-1184	65	26	-	-	ADJ
iajs-1184	65	27	preclosed	preclosed	ADJ
iajs-1184	65	28	set	set	NOUN
iajs-1184	65	29	f	f	PROPN
iajs-1184	65	30	such	such	ADJ
iajs-1184	65	31	that	that	SCONJ
iajs-1184	65	32	�	�	PROPN
iajs-1184	65	33	⊆	⊆	NUM
iajs-1184	65	34	�	�	PROPN
iajs-1184	65	35	and	and	CCONJ
iajs-1184	65	36	x	x	SYM
iajs-1184	65	37	f	f	NOUN
iajs-1184	65	38	,	,	PUNCT
iajs-1184	65	39	but	but	CCONJ
iajs-1184	65	40	�	�	PROPN
iajs-1184	65	41	⊆	⊆	NUM
iajs-1184	65	42	�	�	PROPN
iajs-1184	65	43	so	so	ADV
iajs-1184	65	44	�	�	PROPN
iajs-1184	65	45	⊆	⊆	NUM
iajs-1184	65	46	�	�	PROPN
iajs-1184	65	47	and	and	CCONJ
iajs-1184	65	48	x	x	PROPN
iajs-1184	65	49	f	f	PROPN
iajs-1184	65	50	,	,	PUNCT
iajs-1184	65	51	hence	hence	ADV
iajs-1184	65	52	x	x	SYM
iajs-1184	65	53	spre	spre	ADJ
iajs-1184	65	54	-	-	NOUN
iajs-1184	65	55	cl	cl	ADJ
iajs-1184	65	56	a.	a.	NOUN
iajs-1184	65	57	2	2	NUM
iajs-1184	65	58	.	.	PUNCT
iajs-1184	66	1	since	since	SCONJ
iajs-1184	66	2	s	s	NOUN
iajs-1184	66	3	-	-	PUNCT
iajs-1184	66	4	pre	pre	NOUN
iajs-1184	66	5	-	-	NOUN
iajs-1184	66	6	cl	cl	ADJ
iajs-1184	66	7	a	a	PRON
iajs-1184	66	8	is	be	AUX
iajs-1184	66	9	the	the	DET
iajs-1184	66	10	intersection	intersection	NOUN
iajs-1184	66	11	of	of	ADP
iajs-1184	66	12	all	all	DET
iajs-1184	66	13	semi	semi	ADJ
iajs-1184	66	14	-	-	ADJ
iajs-1184	66	15	preclosed	preclosed	ADJ
iajs-1184	66	16	sets	set	NOUN
iajs-1184	66	17	containing	contain	VERB
iajs-1184	66	18	a	a	PRON
iajs-1184	66	19	,	,	PUNCT
iajs-1184	66	20	we	we	PRON
iajs-1184	66	21	have	have	VERB
iajs-1184	66	22	a	a	DET
iajs-1184	66	23	ح	ح	ADJ
iajs-1184	66	24	spre	spre	ADJ
iajs-1184	66	25	-	-	NOUN
iajs-1184	66	26	cl	cl	ADJ
iajs-1184	66	27	a.	a.	NOUN
iajs-1184	66	28	3	3	NUM
iajs-1184	66	29	.	.	PUNCT
iajs-1184	67	1			NOUN
iajs-1184	67	2	and	and	CCONJ
iajs-1184	67	3	x	x	NOUN
iajs-1184	67	4	are	be	AUX
iajs-1184	67	5	semi	semi	ADJ
iajs-1184	67	6	-	-	ADJ
iajs-1184	67	7	preopen	preopen	ADJ
iajs-1184	67	8	sets	set	NOUN
iajs-1184	67	9	(	(	PUNCT
iajs-1184	67	10	by	by	ADP
iajs-1184	67	11	being	be	AUX
iajs-1184	67	12	open	open	ADJ
iajs-1184	67	13	set	set	NOUN
iajs-1184	67	14	)	)	PUNCT
iajs-1184	67	15	,	,	PUNCT
iajs-1184	67	16	thus	thus	ADV
iajs-1184	67	17	s	s	NOUN
iajs-1184	67	18	-	-	PUNCT
iajs-1184	67	19	pre	pre	ADJ
iajs-1184	67	20	-	-	ADJ
iajs-1184	67	21	cl	cl	ADJ
iajs-1184	67	22			NOUN
iajs-1184	67	23	=	=	SYM
iajs-1184	67	24			NOUN
iajs-1184	67	25	and	and	CCONJ
iajs-1184	67	26	s	s	NOUN
iajs-1184	67	27	-	-	PUNCT
iajs-1184	67	28	pre	pre	NOUN
iajs-1184	67	29	-	-	NOUN
iajs-1184	67	30	cl	cl	ADJ
iajs-1184	67	31	x	x	PUNCT
iajs-1184	67	32	=	=	PUNCT
iajs-1184	67	33	x.	x.	NOUN
iajs-1184	67	34	4	4	X
iajs-1184	67	35	.	.	PUNCT
iajs-1184	68	1	since	since	SCONJ
iajs-1184	68	2	a	a	DET
iajs-1184	68	3	ح	ح	PROPN
iajs-1184	68	4	a	a	SYM
iajs-1184	68	5	b	b	NOUN
iajs-1184	68	6	,	,	PUNCT
iajs-1184	68	7	therefore	therefore	ADV
iajs-1184	68	8	s	s	NOUN
iajs-1184	68	9	-	-	PUNCT
iajs-1184	68	10	pre	pre	NOUN
iajs-1184	68	11	-	-	NOUN
iajs-1184	68	12	cl	cl	VERB
iajs-1184	68	13	a	a	DET
iajs-1184	68	14	ح	ح	NOUN
iajs-1184	68	15	s	s	NOUN
iajs-1184	68	16	-	-	PUNCT
iajs-1184	68	17	pre	pre	NOUN
iajs-1184	68	18	-	-	NOUN
iajs-1184	68	19	cl	cl	ADJ
iajs-1184	68	20	(	(	PUNCT
iajs-1184	68	21	a	a	DET
iajs-1184	68	22			PROPN
iajs-1184	68	23	b	b	PROPN
iajs-1184	68	24	)	)	PUNCT
iajs-1184	68	25	(	(	PUNCT
iajs-1184	68	26	by	by	ADP
iajs-1184	68	27	part	part	NOUN
iajs-1184	68	28	1	1	NUM
iajs-1184	68	29	)	)	PUNCT
iajs-1184	68	30	,	,	PUNCT
iajs-1184	68	31	and	and	CCONJ
iajs-1184	68	32	since	since	SCONJ
iajs-1184	68	33	b	b	PROPN
iajs-1184	68	34	ح	ح	PROPN
iajs-1184	68	35	a	a	PROPN
iajs-1184	68	36	b	b	PROPN
iajs-1184	68	37	,	,	PUNCT
iajs-1184	68	38	therefore	therefore	ADV
iajs-1184	68	39	s	s	NOUN
iajs-1184	68	40	-	-	PUNCT
iajs-1184	68	41	pre	pre	NOUN
iajs-1184	68	42	-	-	NOUN
iajs-1184	68	43	cl	cl	ADJ
iajs-1184	68	44	b	b	NOUN
iajs-1184	68	45	ح	ح	NOUN
iajs-1184	68	46	s	s	NOUN
iajs-1184	68	47	-	-	PUNCT
iajs-1184	68	48	pre	pre	NOUN
iajs-1184	68	49	-	-	NOUN
iajs-1184	68	50	cl	cl	ADJ
iajs-1184	68	51	(	(	PUNCT
iajs-1184	68	52	a	a	DET
iajs-1184	68	53			PROPN
iajs-1184	68	54	b	b	PROPN
iajs-1184	68	55	)	)	PUNCT
iajs-1184	68	56	(	(	PUNCT
iajs-1184	68	57	by	by	ADP
iajs-1184	68	58	part	part	NOUN
iajs-1184	68	59	1	1	NUM
iajs-1184	68	60	)	)	PUNCT
iajs-1184	68	61	,	,	PUNCT
iajs-1184	68	62	implies	imply	VERB
iajs-1184	68	63	s	s	NOUN
iajs-1184	68	64	-	-	PUNCT
iajs-1184	68	65	pre	pre	NOUN
iajs-1184	68	66	-	-	NOUN
iajs-1184	68	67	cl	cl	VERB
iajs-1184	68	68	a	a	DET
iajs-1184	68	69			NOUN
iajs-1184	68	70	s	s	NOUN
iajs-1184	68	71	-	-	PUNCT
iajs-1184	68	72	pre	pre	NOUN
iajs-1184	68	73	-	-	NOUN
iajs-1184	68	74	cl	cl	ADJ
iajs-1184	68	75	b	b	NOUN
iajs-1184	68	76	ح	ح	NOUN
iajs-1184	68	77	s	s	NOUN
iajs-1184	68	78	-	-	PUNCT
iajs-1184	68	79	pre	pre	NOUN
iajs-1184	68	80	-	-	NOUN
iajs-1184	68	81	cl	cl	ADJ
iajs-1184	68	82	(	(	PUNCT
iajs-1184	68	83	a	a	DET
iajs-1184	68	84			NOUN
iajs-1184	68	85	b	b	PROPN
iajs-1184	68	86	)	)	PUNCT
iajs-1184	68	87	.	.	PUNCT
iajs-1184	69	1	5	5	X
iajs-1184	69	2	.	.	X
iajs-1184	69	3	since	since	SCONJ
iajs-1184	69	4	a	a	DET
iajs-1184	69	5			NOUN
iajs-1184	69	6	b	b	PROPN
iajs-1184	69	7	ح	ح	NOUN
iajs-1184	69	8	a	a	PRON
iajs-1184	69	9	,	,	PUNCT
iajs-1184	69	10	then	then	ADV
iajs-1184	69	11	this	this	PRON
iajs-1184	69	12	implies	imply	VERB
iajs-1184	69	13	that	that	SCONJ
iajs-1184	69	14	s	s	NOUN
iajs-1184	69	15	-	-	PUNCT
iajs-1184	69	16	pre	pre	NOUN
iajs-1184	69	17	-	-	NOUN
iajs-1184	69	18	cl	cl	ADJ
iajs-1184	69	19	(	(	PUNCT
iajs-1184	69	20	a	a	DET
iajs-1184	69	21			ADJ
iajs-1184	69	22	b	b	NOUN
iajs-1184	69	23	)	)	PUNCT
iajs-1184	69	24	ح	ح	NOUN
iajs-1184	69	25	s	s	NOUN
iajs-1184	69	26	-	-	PUNCT
iajs-1184	69	27	pre	pre	NOUN
iajs-1184	69	28	-	-	NOUN
iajs-1184	69	29	cl	cl	ADJ
iajs-1184	69	30	a	a	PRON
iajs-1184	69	31	(	(	PUNCT
iajs-1184	69	32	by	by	ADP
iajs-1184	69	33	part	part	NOUN
iajs-1184	69	34	1	1	NUM
iajs-1184	69	35	)	)	PUNCT
iajs-1184	69	36	,	,	PUNCT
iajs-1184	69	37	and	and	CCONJ
iajs-1184	69	38	since	since	SCONJ
iajs-1184	69	39	a	a	DET
iajs-1184	69	40			NOUN
iajs-1184	69	41	b	b	PROPN
iajs-1184	69	42	ح	ح	PROPN
iajs-1184	69	43	b	b	NOUN
iajs-1184	69	44	,	,	PUNCT
iajs-1184	69	45	therefore	therefore	ADV
iajs-1184	69	46	s	s	NOUN
iajs-1184	69	47	-	-	PUNCT
iajs-1184	69	48	pre	pre	NOUN
iajs-1184	69	49	-	-	NOUN
iajs-1184	69	50	cl	cl	ADJ
iajs-1184	69	51	(	(	PUNCT
iajs-1184	69	52	a	a	DET
iajs-1184	69	53			ADJ
iajs-1184	69	54	b	b	NOUN
iajs-1184	69	55	)	)	PUNCT
iajs-1184	69	56	ح	ح	NOUN
iajs-1184	69	57	s	s	NOUN
iajs-1184	69	58	-	-	PUNCT
iajs-1184	69	59	pre	pre	ADJ
iajs-1184	69	60	-	-	ADJ
iajs-1184	69	61	cl	cl	ADJ
iajs-1184	69	62	b	b	NOUN
iajs-1184	69	63	(	(	PUNCT
iajs-1184	69	64	by	by	ADP
iajs-1184	69	65	part	part	NOUN
iajs-1184	69	66	1	1	NUM
iajs-1184	69	67	)	)	PUNCT
iajs-1184	69	68	,	,	PUNCT
iajs-1184	69	69	therefore	therefore	ADV
iajs-1184	69	70	s	s	NOUN
iajs-1184	69	71	-	-	PUNCT
iajs-1184	69	72	pre	pre	NOUN
iajs-1184	69	73	-	-	NOUN
iajs-1184	69	74	cl	cl	ADJ
iajs-1184	69	75	(	(	PUNCT
iajs-1184	69	76	a	a	DET
iajs-1184	69	77			ADJ
iajs-1184	69	78	b	b	NOUN
iajs-1184	69	79	)	)	PUNCT
iajs-1184	69	80	ح	ح	NOUN
iajs-1184	69	81	s	s	NOUN
iajs-1184	69	82	-	-	PUNCT
iajs-1184	69	83	pre	pre	NOUN
iajs-1184	69	84	-	-	NOUN
iajs-1184	69	85	cl	cl	ADJ
iajs-1184	69	86	a	a	DET
iajs-1184	69	87			NOUN
iajs-1184	69	88	s	s	NOUN
iajs-1184	69	89	-	-	PUNCT
iajs-1184	69	90	pre	pre	ADJ
iajs-1184	69	91	-	-	ADJ
iajs-1184	69	92	cl	cl	ADJ
iajs-1184	69	93	b.	b.	NOUN
iajs-1184	70	1	but	but	CCONJ
iajs-1184	70	2	the	the	DET
iajs-1184	70	3	converse	converse	NOUN
iajs-1184	70	4	of	of	ADP
iajs-1184	70	5	part	part	NOUN
iajs-1184	70	6	(	(	PUNCT
iajs-1184	70	7	4	4	NUM
iajs-1184	70	8	)	)	PUNCT
iajs-1184	70	9	is	be	AUX
iajs-1184	70	10	not	not	PART
iajs-1184	70	11	true	true	ADJ
iajs-1184	70	12	to	to	PART
iajs-1184	70	13	see	see	VERB
iajs-1184	70	14	this	this	PRON
iajs-1184	70	15	,	,	PUNCT
iajs-1184	70	16	let	let	VERB
iajs-1184	70	17	a={1},b={2	a={1},b={2	NOUN
iajs-1184	70	18	}	}	PUNCT
iajs-1184	70	19	and	and	CCONJ
iajs-1184	70	20	a	a	X
iajs-1184	70	21	b={1,2	b={1,2	NOUN
iajs-1184	70	22	}	}	PUNCT
iajs-1184	70	23	in	in	ADP
iajs-1184	70	24	the	the	DET
iajs-1184	70	25	example	example	NOUN
iajs-1184	70	26	2	2	NUM
iajs-1184	70	27	,	,	PUNCT
iajs-1184	70	28	then	then	ADV
iajs-1184	70	29	:	:	PUNCT
iajs-1184	70	30	spc	spc	PROPN
iajs-1184	70	31	(	(	PUNCT
iajs-1184	70	32	x	x	NOUN
iajs-1184	70	33	)	)	PUNCT
iajs-1184	70	34	=	=	NOUN
iajs-1184	70	35	{	{	PUNCT
iajs-1184	70	36	x,	x,	PROPN
iajs-1184	70	37	,	,	PUNCT
iajs-1184	70	38	{	{	PUNCT
iajs-1184	70	39	,3,4},{1,3,4},{3,4},{4},{3},{2,4},{2,3},{2},{1,4},{1,3},{1	,3,4},{1,3,4},{3,4},{4},{3},{2,4},{2,3},{2},{1,4},{1,3},{1	NOUN
iajs-1184	70	40	}	}	PUNCT
iajs-1184	70	41	}	}	PUNCT
iajs-1184	70	42	s	s	NOUN
iajs-1184	70	43	-	-	PUNCT
iajs-1184	70	44	pre	pre	NOUN
iajs-1184	70	45	-	-	NOUN
iajs-1184	70	46	cl	cl	ADJ
iajs-1184	70	47	{	{	PUNCT
iajs-1184	70	48	1}={1	1}={1	NUM
iajs-1184	70	49	}	}	PUNCT
iajs-1184	70	50	,	,	PUNCT
iajs-1184	70	51	s	s	X
iajs-1184	70	52	-	-	PUNCT
iajs-1184	70	53	pre	pre	NOUN
iajs-1184	70	54	-	-	NOUN
iajs-1184	70	55	cl	cl	ADJ
iajs-1184	70	56	{	{	PUNCT
iajs-1184	70	57	2}={2}and	2}={2}and	NUM
iajs-1184	70	58	s	s	NOUN
iajs-1184	70	59	-	-	PUNCT
iajs-1184	70	60	pre	pre	NOUN
iajs-1184	70	61	-	-	NOUN
iajs-1184	70	62	cl	cl	ADJ
iajs-1184	70	63	{	{	PUNCT
iajs-1184	70	64	1}	1}	NUM
iajs-1184	70	65	s	s	PROPN
iajs-1184	70	66	-	-	PUNCT
iajs-1184	70	67	pre	pre	NOUN
iajs-1184	70	68	-	-	NOUN
iajs-1184	70	69	cl	cl	ADJ
iajs-1184	70	70	{	{	PUNCT
iajs-1184	70	71	2}={1,2	2}={1,2	NOUN
iajs-1184	70	72	}	}	PUNCT
iajs-1184	70	73	but	but	CCONJ
iajs-1184	70	74	s	s	X
iajs-1184	70	75	-	-	PUNCT
iajs-1184	70	76	pre	pre	NOUN
iajs-1184	70	77	-	-	NOUN
iajs-1184	70	78	cl	cl	ADJ
iajs-1184	70	79	(	(	PUNCT
iajs-1184	70	80	{	{	PUNCT
iajs-1184	70	81	1}{2	1}{2	NUM
iajs-1184	70	82	}	}	PUNCT
iajs-1184	70	83	)	)	PUNCT
iajs-1184	71	1	=	=	SYM
iajs-1184	71	2	x	x	NOUN
iajs-1184	71	3	,	,	PUNCT
iajs-1184	71	4	which	which	PRON
iajs-1184	71	5	shows	show	VERB
iajs-1184	71	6	s	s	NOUN
iajs-1184	71	7	-	-	PUNCT
iajs-1184	71	8	pre	pre	NOUN
iajs-1184	71	9	-	-	NOUN
iajs-1184	71	10	cl	cl	ADJ
iajs-1184	71	11	(	(	PUNCT
iajs-1184	71	12	a	a	DET
iajs-1184	71	13			PROPN
iajs-1184	71	14	b	b	PROPN
iajs-1184	71	15	)	)	PUNCT
iajs-1184	71	16			PROPN
iajs-1184	71	17	s	s	NOUN
iajs-1184	71	18	-	-	PUNCT
iajs-1184	71	19	pre	pre	NOUN
iajs-1184	71	20	-	-	NOUN
iajs-1184	71	21	cl	cl	VERB
iajs-1184	71	22	a	a	DET
iajs-1184	71	23			NOUN
iajs-1184	71	24	s	s	NOUN
iajs-1184	71	25	-	-	PUNCT
iajs-1184	71	26	pre	pre	NOUN
iajs-1184	71	27	-	-	NOUN
iajs-1184	71	28	cl	cl	ADJ
iajs-1184	71	29	b	b	NOUN
iajs-1184	71	30	and	and	CCONJ
iajs-1184	71	31	also	also	ADV
iajs-1184	71	32	,	,	PUNCT
iajs-1184	71	33	the	the	DET
iajs-1184	71	34	converse	converse	NOUN
iajs-1184	71	35	of	of	ADP
iajs-1184	71	36	part	part	NOUN
iajs-1184	71	37	(	(	PUNCT
iajs-1184	71	38	5	5	NUM
iajs-1184	71	39	)	)	PUNCT
iajs-1184	71	40	is	be	AUX
iajs-1184	71	41	not	not	PART
iajs-1184	71	42	true	true	ADJ
iajs-1184	71	43	to	to	PART
iajs-1184	71	44	see	see	VERB
iajs-1184	71	45	this	this	PRON
iajs-1184	71	46	,	,	PUNCT
iajs-1184	71	47	let	let	VERB
iajs-1184	71	48	a={1,2,3	a={1,2,3	NOUN
iajs-1184	71	49	}	}	PUNCT
iajs-1184	71	50	,	,	PUNCT
iajs-1184	71	51	b={1,3,4	b={1,3,4	ADJ
iajs-1184	71	52	}	}	PUNCT
iajs-1184	71	53	and	and	CCONJ
iajs-1184	71	54	a	a	DET
iajs-1184	71	55			NOUN
iajs-1184	71	56	b	b	NOUN
iajs-1184	71	57	=	=	SYM
iajs-1184	71	58	{	{	PUNCT
iajs-1184	71	59	1,3	1,3	NUM
iajs-1184	71	60	}	}	PUNCT
iajs-1184	71	61	in	in	ADP
iajs-1184	71	62	the	the	DET
iajs-1184	71	63	example	example	NOUN
iajs-1184	71	64	2	2	NUM
iajs-1184	71	65	,	,	PUNCT
iajs-1184	71	66	then	then	ADV
iajs-1184	71	67	:	:	PUNCT
iajs-1184	71	68	s	s	X
iajs-1184	71	69	pc	pc	NOUN
iajs-1184	71	70	(	(	PUNCT
iajs-1184	71	71	x	x	NOUN
iajs-1184	71	72	)	)	PUNCT
iajs-1184	71	73	=	=	NOUN
iajs-1184	71	74	{	{	PUNCT
iajs-1184	71	75	x,	x,	PROPN
iajs-1184	71	76	,	,	PUNCT
iajs-1184	71	77	{	{	PUNCT
iajs-1184	71	78	,3,4},{1,3,4},{3,4},{4},{3},{2,4},{2,3},{2},{1,4},{1,3},{1	,3,4},{1,3,4},{3,4},{4},{3},{2,4},{2,3},{2},{1,4},{1,3},{1	ADV
iajs-1184	71	79	}	}	PUNCT
iajs-1184	71	80	}	}	PUNCT
iajs-1184	71	81	sprecl	sprecl	PROPN
iajs-1184	71	82	{	{	PUNCT
iajs-1184	71	83	1,2,3}=x	1,2,3}=x	NUM
iajs-1184	71	84	,	,	PUNCT
iajs-1184	71	85	s	s	NOUN
iajs-1184	71	86	-	-	PUNCT
iajs-1184	71	87	pre	pre	NOUN
iajs-1184	71	88	-	-	NOUN
iajs-1184	71	89	cl	cl	ADJ
iajs-1184	71	90	{	{	PUNCT
iajs-1184	71	91	1,3,4}={1,3,4	1,3,4}={1,3,4	PROPN
iajs-1184	71	92	}	}	PUNCT
iajs-1184	71	93	and	and	CCONJ
iajs-1184	71	94	s	s	NOUN
iajs-1184	71	95	-	-	PUNCT
iajs-1184	71	96	pre	pre	NOUN
iajs-1184	71	97	-	-	NOUN
iajs-1184	71	98	cl	cl	ADJ
iajs-1184	71	99	{	{	PUNCT
iajs-1184	71	100	1,2,3}	1,2,3}	NUM
iajs-1184	71	101	s	s	NOUN
iajs-1184	71	102	-	-	PUNCT
iajs-1184	71	103	pre	pre	NOUN
iajs-1184	71	104	-	-	ADJ
iajs-1184	71	105	cl{1,3,4}={1,3,4	cl{1,3,4}={1,3,4	ADJ
iajs-1184	71	106	}	}	PUNCT
iajs-1184	71	107	but	but	CCONJ
iajs-1184	71	108	s	s	X
iajs-1184	71	109	-	-	PUNCT
iajs-1184	71	110	pre	pre	NOUN
iajs-1184	71	111	-	-	NOUN
iajs-1184	71	112	cl	cl	ADJ
iajs-1184	71	113	(	(	PUNCT
iajs-1184	71	114	{	{	PUNCT
iajs-1184	71	115	1,2,3}	1,2,3}	NUM
iajs-1184	71	116	{	{	PUNCT
iajs-1184	71	117	1,3,4	1,3,4	NUM
iajs-1184	71	118	}	}	PUNCT
iajs-1184	71	119	)	)	PUNCT
iajs-1184	72	1	=	=	NOUN
iajs-1184	72	2	{	{	PUNCT
iajs-1184	72	3	1,3	1,3	NUM
iajs-1184	72	4	}	}	PUNCT
iajs-1184	72	5	which	which	PRON
iajs-1184	72	6	shows	show	VERB
iajs-1184	72	7	s	s	NOUN
iajs-1184	72	8	-	-	PUNCT
iajs-1184	72	9	pre	pre	NOUN
iajs-1184	72	10	-	-	NOUN
iajs-1184	72	11	cl	cl	ADJ
iajs-1184	72	12	a	a	DET
iajs-1184	72	13			NOUN
iajs-1184	72	14	s	s	NOUN
iajs-1184	72	15	-	-	PUNCT
iajs-1184	72	16	pre	pre	NOUN
iajs-1184	72	17	-	-	NOUN
iajs-1184	72	18	cl	cl	ADJ
iajs-1184	72	19	b	b	PROPN
iajs-1184	72	20			PROPN
iajs-1184	72	21	s	s	NOUN
iajs-1184	72	22	-	-	PUNCT
iajs-1184	72	23	pre	pre	NOUN
iajs-1184	72	24	-	-	NOUN
iajs-1184	72	25	cl	cl	ADJ
iajs-1184	72	26	(	(	PUNCT
iajs-1184	72	27	a	a	DET
iajs-1184	72	28			ADJ
iajs-1184	72	29	b	b	NOUN
iajs-1184	72	30	)	)	PUNCT
iajs-1184	72	31	.	.	PUNCT
iajs-1184	73	1	proposition	proposition	NOUN
iajs-1184	73	2	2.11	2.11	NUM
iajs-1184	73	3	:	:	PUNCT
iajs-1184	73	4	a	a	PRON
iajs-1184	73	5	is	be	AUX
iajs-1184	73	6	semi	semi	ADJ
iajs-1184	73	7	-	-	ADJ
iajs-1184	73	8	preclosed	preclosed	ADJ
iajs-1184	73	9	set	set	NOUN
iajs-1184	73	10	,	,	PUNCT
iajs-1184	73	11	if	if	SCONJ
iajs-1184	73	12	and	and	CCONJ
iajs-1184	73	13	only	only	ADV
iajs-1184	73	14	if	if	SCONJ
iajs-1184	73	15	a=	a=	ADJ
iajs-1184	73	16	s	s	X
iajs-1184	73	17	-	-	PUNCT
iajs-1184	73	18	pre	pre	ADJ
iajs-1184	73	19	-	-	ADJ
iajs-1184	73	20	cl	cl	ADJ
iajs-1184	73	21	a.	a.	NOUN
iajs-1184	73	22	proof	proof	NOUN
iajs-1184	73	23	:	:	PUNCT
iajs-1184	73	24	(	(	PUNCT
iajs-1184	73	25	)	)	PUNCT
iajs-1184	73	26	if	if	SCONJ
iajs-1184	73	27	a	a	PRON
iajs-1184	73	28	is	be	AUX
iajs-1184	73	29	semi	semi	ADJ
iajs-1184	73	30	-	-	ADJ
iajs-1184	73	31	preclosed	preclosed	ADJ
iajs-1184	73	32	set	set	NOUN
iajs-1184	73	33	,	,	PUNCT
iajs-1184	73	34	we	we	PRON
iajs-1184	73	35	must	must	AUX
iajs-1184	73	36	prove	prove	VERB
iajs-1184	73	37	a=	a=	ADJ
iajs-1184	73	38	s	s	NOUN
iajs-1184	73	39	-	-	PUNCT
iajs-1184	73	40	pre	pre	NOUN
iajs-1184	73	41	-	-	NOUN
iajs-1184	73	42	cl	cl	NOUN
iajs-1184	73	43	a	a	NOUN
iajs-1184	73	44	,	,	PUNCT
iajs-1184	73	45	that	that	PRON
iajs-1184	73	46	is	is	ADV
iajs-1184	73	47	mean	mean	VERB
iajs-1184	73	48	we	we	PRON
iajs-1184	73	49	must	must	AUX
iajs-1184	73	50	prove	prove	VERB
iajs-1184	73	51	a	a	DET
iajs-1184	73	52	ح	ح	NOUN
iajs-1184	73	53	s	s	NOUN
iajs-1184	73	54	-	-	PUNCT
iajs-1184	73	55	pre	pre	NOUN
iajs-1184	73	56	-	-	NOUN
iajs-1184	73	57	cl	cl	NOUN
iajs-1184	73	58	a	a	DET
iajs-1184	73	59	and	and	CCONJ
iajs-1184	73	60	s	s	NOUN
iajs-1184	73	61	-	-	PUNCT
iajs-1184	73	62	pre	pre	NOUN
iajs-1184	73	63	-	-	NOUN
iajs-1184	73	64	cl	cl	VERB
iajs-1184	73	65	a	a	DET
iajs-1184	73	66	ح	ح	NOUN
iajs-1184	73	67	a.	a.	NOUN
iajs-1184	73	68	now	now	ADV
iajs-1184	73	69	,	,	PUNCT
iajs-1184	73	70	to	to	PART
iajs-1184	73	71	prove	prove	VERB
iajs-1184	73	72	s	s	NOUN
iajs-1184	73	73	-	-	PUNCT
iajs-1184	73	74	pre	pre	NOUN
iajs-1184	73	75	-	-	NOUN
iajs-1184	73	76	cl	cl	VERB
iajs-1184	73	77	a	a	DET
iajs-1184	73	78	ح	ح	NOUN
iajs-1184	73	79	a	a	ADP
iajs-1184	73	80	,	,	PUNCT
iajs-1184	73	81	since	since	SCONJ
iajs-1184	73	82	s	s	NOUN
iajs-1184	73	83	-	-	PUNCT
iajs-1184	73	84	pre	pre	NOUN
iajs-1184	73	85	-	-	NOUN
iajs-1184	73	86	cl	cl	ADJ
iajs-1184	73	87	a	a	PRON
iajs-1184	73	88	is	be	AUX
iajs-1184	73	89	the	the	DET
iajs-1184	73	90	intersection	intersection	NOUN
iajs-1184	73	91	of	of	ADP
iajs-1184	73	92	all	all	DET
iajs-1184	73	93	semipreclosed	semipreclose	VERB
iajs-1184	73	94	sets	set	NOUN
iajs-1184	73	95	containing	contain	VERB
iajs-1184	73	96	a	a	PRON
iajs-1184	73	97	,	,	PUNCT
iajs-1184	73	98	and	and	CCONJ
iajs-1184	73	99	since	since	SCONJ
iajs-1184	73	100	a	a	PRON
iajs-1184	73	101	is	be	AUX
iajs-1184	73	102	semi	semi	ADJ
iajs-1184	73	103	-	-	ADJ
iajs-1184	73	104	preclosed	preclosed	ADJ
iajs-1184	73	105	set	set	NOUN
iajs-1184	73	106	,	,	PUNCT
iajs-1184	73	107	and	and	CCONJ
iajs-1184	73	108	aح	aح	ADP
iajs-1184	73	109	a	a	PRON
iajs-1184	73	110	,	,	PUNCT
iajs-1184	73	111	implies	imply	VERB
iajs-1184	73	112	s	s	PART
iajs-1184	73	113	-	-	PUNCT
iajs-1184	73	114	pre	pre	NOUN
iajs-1184	73	115	-	-	NOUN
iajs-1184	73	116	cl	cl	VERB
iajs-1184	73	117	a	a	DET
iajs-1184	73	118	ح	ح	NOUN
iajs-1184	73	119	a.	a.	NOUN
iajs-1184	73	120	now	now	ADV
iajs-1184	73	121	,	,	PUNCT
iajs-1184	73	122	to	to	PART
iajs-1184	73	123	prove	prove	VERB
iajs-1184	73	124	a	a	DET
iajs-1184	73	125	ح	ح	NOUN
iajs-1184	73	126	s	s	NOUN
iajs-1184	73	127	-	-	PUNCT
iajs-1184	73	128	pre	pre	NOUN
iajs-1184	73	129	-	-	NOUN
iajs-1184	73	130	cl	cl	NOUN
iajs-1184	73	131	a	a	NOUN
iajs-1184	73	132	,	,	PUNCT
iajs-1184	73	133	let	let	VERB
iajs-1184	73	134	x	x	PRON
iajs-1184	73	135	be	be	AUX
iajs-1184	73	136	any	any	DET
iajs-1184	73	137	element	element	NOUN
iajs-1184	73	138	in	in	ADP
iajs-1184	73	139	x	x	NOUN
iajs-1184	73	140	,	,	PUNCT
iajs-1184	73	141	such	such	ADJ
iajs-1184	73	142	that	that	SCONJ
iajs-1184	73	143	x	x	PUNCT
iajs-1184	73	144	s	s	X
iajs-1184	73	145	-	-	PUNCT
iajs-1184	73	146	pre	pre	NOUN
iajs-1184	73	147	-	-	NOUN
iajs-1184	73	148	cl	cl	NOUN
iajs-1184	73	149	a	a	PRON
iajs-1184	73	150	,	,	PUNCT
iajs-1184	73	151	which	which	PRON
iajs-1184	73	152	implies	imply	VERB
iajs-1184	73	153	there	there	PRON
iajs-1184	73	154	existence	existence	NOUN
iajs-1184	73	155	of	of	ADP
iajs-1184	73	156	a	a	DET
iajs-1184	73	157	semi	semi	ADJ
iajs-1184	73	158	-	-	ADJ
iajs-1184	73	159	preclosed	preclosed	ADJ
iajs-1184	73	160	set	set	NOUN
iajs-1184	73	161	f	f	PROPN
iajs-1184	73	162	such	such	ADJ
iajs-1184	73	163	that	that	SCONJ
iajs-1184	74	1	x∉	x∉	PROPN
iajs-1184	74	2	f	f	X
iajs-1184	74	3	,	,	PUNCT
iajs-1184	74	4	but	but	CCONJ
iajs-1184	74	5	a	a	DET
iajs-1184	74	6	ح	ح	NOUN
iajs-1184	74	7	f	f	NOUN
iajs-1184	74	8	,	,	PUNCT
iajs-1184	74	9	hence	hence	ADV
iajs-1184	74	10	x∉	x∉	PROPN
iajs-1184	74	11	a.	a.	NOUN
iajs-1184	74	12	thus	thus	ADV
iajs-1184	74	13	a	a	DET
iajs-1184	74	14	ح	ح	NOUN
iajs-1184	74	15	s	s	NOUN
iajs-1184	74	16	-	-	PUNCT
iajs-1184	74	17	pre	pre	NOUN
iajs-1184	74	18	-	-	NOUN
iajs-1184	74	19	cl	cl	NOUN
iajs-1184	74	20	a	a	NOUN
iajs-1184	74	21	,	,	PUNCT
iajs-1184	74	22	which	which	PRON
iajs-1184	74	23	implies	imply	VERB
iajs-1184	74	24	a=	a=	ADJ
iajs-1184	74	25	s	s	X
iajs-1184	74	26	-	-	PUNCT
iajs-1184	74	27	pre	pre	ADJ
iajs-1184	74	28	-	-	ADJ
iajs-1184	74	29	cl	cl	ADJ
iajs-1184	74	30	a.	a.	NOUN
iajs-1184	74	31	(	(	PUNCT
iajs-1184	74	32	⟸	⟸	ADV
iajs-1184	74	33	)	)	PUNCT
iajs-1184	74	34	the	the	DET
iajs-1184	74	35	prove	prove	NOUN
iajs-1184	74	36	is	be	AUX
iajs-1184	74	37	direct	direct	ADJ
iajs-1184	74	38	(	(	PUNCT
iajs-1184	74	39	by	by	ADP
iajs-1184	74	40	corollary	corollary	ADJ
iajs-1184	74	41	2.4	2.4	NUM
iajs-1184	74	42	)	)	PUNCT
iajs-1184	74	43	.	.	PUNCT
iajs-1184	75	1	■	■	PUNCT
iajs-1184	75	2	corollary	corollary	ADJ
iajs-1184	75	3	2.12	2.12	NUM
iajs-1184	75	4	:	:	PUNCT
iajs-1184	75	5	s	s	X
iajs-1184	75	6	-	-	PUNCT
iajs-1184	75	7	pre	pre	NOUN
iajs-1184	75	8	-	-	NOUN
iajs-1184	75	9	cl	cl	ADJ
iajs-1184	75	10	(	(	PUNCT
iajs-1184	75	11	s	s	NOUN
iajs-1184	75	12	-	-	PUNCT
iajs-1184	75	13	pre	pre	NOUN
iajs-1184	75	14	-	-	NOUN
iajs-1184	75	15	cl	cl	NOUN
iajs-1184	75	16	a	a	NOUN
iajs-1184	75	17	)	)	PUNCT
iajs-1184	75	18	=	=	SYM
iajs-1184	75	19	s	s	NOUN
iajs-1184	75	20	-	-	PUNCT
iajs-1184	75	21	pre	pre	NOUN
iajs-1184	75	22	-	-	NOUN
iajs-1184	75	23	cl	cl	NOUN
iajs-1184	75	24	a	a	PRON
iajs-1184	75	25	.	.	PUNCT
iajs-1184	76	1	proof	proof	NOUN
iajs-1184	76	2	:	:	PUNCT
iajs-1184	76	3	since	since	SCONJ
iajs-1184	76	4	s	s	NOUN
iajs-1184	76	5	-	-	PUNCT
iajs-1184	76	6	pre	pre	NOUN
iajs-1184	76	7	-	-	NOUN
iajs-1184	76	8	cl	cl	ADJ
iajs-1184	76	9	a	a	NOUN
iajs-1184	76	10	is	be	AUX
iajs-1184	76	11	semi	semi	ADJ
iajs-1184	76	12	-	-	ADJ
iajs-1184	76	13	preclosed	preclosed	ADJ
iajs-1184	76	14	set	set	NOUN
iajs-1184	76	15	(	(	PUNCT
iajs-1184	76	16	by	by	ADP
iajs-1184	76	17	corollary	corollary	ADJ
iajs-1184	76	18	2.4	2.4	NUM
iajs-1184	76	19	)	)	PUNCT
iajs-1184	76	20	,	,	PUNCT
iajs-1184	76	21	therefore	therefore	ADV
iajs-1184	76	22	s	s	NOUN
iajs-1184	76	23	-	-	PUNCT
iajs-1184	76	24	pre	pre	NOUN
iajs-1184	76	25	-	-	NOUN
iajs-1184	76	26	cl	cl	ADJ
iajs-1184	76	27	(	(	PUNCT
iajs-1184	76	28	s	s	NOUN
iajs-1184	76	29	-	-	PUNCT
iajs-1184	76	30	pre	pre	NOUN
iajs-1184	76	31	-	-	NOUN
iajs-1184	76	32	cl	cl	NOUN
iajs-1184	76	33	a	a	NOUN
iajs-1184	76	34	)	)	PUNCT
iajs-1184	76	35	=	=	SYM
iajs-1184	77	1	s	s	NOUN
iajs-1184	77	2	-	-	PUNCT
iajs-1184	77	3	pre	pre	NOUN
iajs-1184	77	4	-	-	NOUN
iajs-1184	77	5	cl	cl	ADJ
iajs-1184	77	6	a	a	PRON
iajs-1184	77	7	(	(	PUNCT
iajs-1184	77	8	by	by	ADP
iajs-1184	77	9	proposition	proposition	NOUN
iajs-1184	77	10	2.11	2.11	NUM
iajs-1184	77	11	)	)	PUNCT
iajs-1184	77	12	.	.	PUNCT
iajs-1184	78	1	■	■	PUNCT
iajs-1184	78	2	now	now	ADV
iajs-1184	78	3	,	,	PUNCT
iajs-1184	78	4	we	we	PRON
iajs-1184	78	5	give	give	VERB
iajs-1184	78	6	the	the	DET
iajs-1184	78	7	connection	connection	NOUN
iajs-1184	78	8	between	between	ADP
iajs-1184	78	9	semi	semi	ADJ
iajs-1184	78	10	-	-	ADJ
iajs-1184	78	11	preopen	preopen	ADJ
iajs-1184	78	12	sets	set	NOUN
iajs-1184	78	13	and	and	CCONJ
iajs-1184	78	14	some	some	DET
iajs-1184	78	15	other	other	ADJ
iajs-1184	78	16	kinds	kind	NOUN
iajs-1184	78	17	of	of	ADP
iajs-1184	78	18	weakly	weakly	ADJ
iajs-1184	78	19	open	open	ADJ
iajs-1184	78	20	sets	set	NOUN
iajs-1184	78	21	.	.	PUNCT
iajs-1184	79	1	3	3	X
iajs-1184	79	2	.	.	X
iajs-1184	79	3	relationship	relationship	NOUN
iajs-1184	79	4	among	among	ADP
iajs-1184	79	5	open	open	ADJ
iajs-1184	79	6	,	,	PUNCT
iajs-1184	79	7	α	α	NOUN
iajs-1184	79	8	-	-	ADJ
iajs-1184	79	9	open	open	ADJ
iajs-1184	79	10	,	,	PUNCT
iajs-1184	79	11	preopen	preopen	ADJ
iajs-1184	79	12	,	,	PUNCT
iajs-1184	79	13	semi	semi	ADJ
iajs-1184	79	14	–	–	PUNCT
iajs-1184	79	15	popen	popen	ADJ
iajs-1184	79	16	and	and	CCONJ
iajs-1184	79	17	semi	semi	ADJ
iajs-1184	79	18	-	-	ADJ
iajs-1184	79	19	preopen	preopen	ADJ
iajs-1184	79	20	sets	set	NOUN
iajs-1184	79	21	remark	remark	VERB
iajs-1184	79	22	3.1	3.1	NUM
iajs-1184	79	23	(	(	PUNCT
iajs-1184	79	24	3	3	NUM
iajs-1184	79	25	)	)	PUNCT
iajs-1184	79	26	:	:	PUNCT
iajs-1184	80	1	1	1	X
iajs-1184	80	2	.	.	X
iajs-1184	80	3	every	every	DET
iajs-1184	80	4	open	open	ADJ
iajs-1184	80	5	set	set	NOUN
iajs-1184	80	6	is	be	AUX
iajs-1184	80	7	a	a	DET
iajs-1184	80	8	preopen	preopen	ADJ
iajs-1184	80	9	set	set	NOUN
iajs-1184	80	10	,	,	PUNCT
iajs-1184	80	11	but	but	CCONJ
iajs-1184	80	12	not	not	PART
iajs-1184	80	13	conversely	conversely	ADV
iajs-1184	80	14	.	.	PUNCT
iajs-1184	81	1	2	2	X
iajs-1184	81	2	.	.	X
iajs-1184	81	3	every	every	DET
iajs-1184	81	4	closed	closed	ADJ
iajs-1184	81	5	set	set	NOUN
iajs-1184	81	6	is	be	AUX
iajs-1184	81	7	a	a	DET
iajs-1184	81	8	preclosed	preclose	VERB
iajs-1184	81	9	set	set	NOUN
iajs-1184	81	10	,	,	PUNCT
iajs-1184	81	11	but	but	CCONJ
iajs-1184	81	12	not	not	PART
iajs-1184	81	13	conversely	conversely	ADV
iajs-1184	81	14	.	.	PUNCT
iajs-1184	82	1	remark	remark	VERB
iajs-1184	82	2	3.2	3.2	NUM
iajs-1184	82	3	:	:	PUNCT
iajs-1184	82	4	every	every	DET
iajs-1184	82	5	preopen	preopen	ADJ
iajs-1184	82	6	set	set	NOUN
iajs-1184	82	7	is	be	AUX
iajs-1184	82	8	semi	semi	ADJ
iajs-1184	82	9	-	-	ADJ
iajs-1184	82	10	preopen	preopen	ADJ
iajs-1184	82	11	set	set	NOUN
iajs-1184	82	12	.	.	PUNCT
iajs-1184	83	1	proof	proof	NOUN
iajs-1184	83	2	:	:	PUNCT
iajs-1184	83	3	since	since	SCONJ
iajs-1184	83	4	a	a	PRON
iajs-1184	83	5	is	be	AUX
iajs-1184	83	6	a	a	DET
iajs-1184	83	7	preopen	preopen	ADJ
iajs-1184	83	8	set	set	NOUN
iajs-1184	83	9	and	and	CCONJ
iajs-1184	83	10	aح	aح	ADP
iajs-1184	83	11	a	a	PRON
iajs-1184	83	12	,	,	PUNCT
iajs-1184	83	13	and	and	CCONJ
iajs-1184	83	14	since	since	SCONJ
iajs-1184	83	15	for	for	ADP
iajs-1184	83	16	any	any	DET
iajs-1184	83	17	subset	subset	NOUN
iajs-1184	83	18	a	a	PRON
iajs-1184	83	19	of	of	ADP
iajs-1184	83	20	x	x	PRON
iajs-1184	83	21	,	,	PUNCT
iajs-1184	83	22	a	a	DET
iajs-1184	83	23	ح	ح	NOUN
iajs-1184	83	24	a	a	DET
iajs-1184	83	25	�	�	PROPN
iajs-1184	83	26	,	,	PUNCT
iajs-1184	83	27	therefore	therefore	ADV
iajs-1184	83	28	there	there	PRON
iajs-1184	83	29	exists	exist	VERB
iajs-1184	83	30	a	a	DET
iajs-1184	83	31	preopen	preopen	NOUN
iajs-1184	83	32	set	set	VERB
iajs-1184	83	33	a	a	DET
iajs-1184	83	34	such	such	ADJ
iajs-1184	83	35	that	that	PRON
iajs-1184	83	36	aح	aح	ADP
iajs-1184	83	37	a	a	DET
iajs-1184	83	38	ح	ح	NOUN
iajs-1184	83	39	a	a	DET
iajs-1184	83	40	�	�	PROPN
iajs-1184	83	41	.	.	PUNCT
iajs-1184	84	1	thus	thus	ADV
iajs-1184	84	2	a	a	PRON
iajs-1184	84	3	is	be	AUX
iajs-1184	84	4	semi	semi	ADJ
iajs-1184	84	5	-	-	ADJ
iajs-1184	84	6	preopen	preopen	ADJ
iajs-1184	84	7	set	set	NOUN
iajs-1184	84	8	.	.	PUNCT
iajs-1184	85	1	but	but	CCONJ
iajs-1184	85	2	the	the	DET
iajs-1184	85	3	converse	converse	NOUN
iajs-1184	85	4	need	need	VERB
iajs-1184	85	5	not	not	PART
iajs-1184	85	6	to	to	PART
iajs-1184	85	7	be	be	AUX
iajs-1184	85	8	true	true	ADJ
iajs-1184	85	9	in	in	ADP
iajs-1184	85	10	general	general	ADJ
iajs-1184	85	11	,	,	PUNCT
iajs-1184	85	12	as	as	ADP
iajs-1184	85	13	the	the	DET
iajs-1184	85	14	following	following	NOUN
iajs-1184	85	15	of	of	ADP
iajs-1184	85	16	example	example	NOUN
iajs-1184	85	17	2	2	NUM
iajs-1184	85	18	x={1,2,3,4	x={1,2,3,4	ADJ
iajs-1184	85	19	}	}	PUNCT
iajs-1184	85	20	,	,	PUNCT
iajs-1184	85	21	={x,	={x,	PUNCT
iajs-1184	85	22	,	,	PUNCT
iajs-1184	85	23	{	{	PUNCT
iajs-1184	85	24	1},{2},{1,2	1},{2},{1,2	NUM
iajs-1184	85	25	}	}	PUNCT
iajs-1184	85	26	}	}	PUNCT
iajs-1184	85	27	po(x	po(x	NUM
iajs-1184	85	28	)	)	PUNCT
iajs-1184	85	29	=	=	SYM
iajs-1184	85	30			PROPN
iajs-1184	85	31			NOUN
iajs-1184	85	32	{	{	PUNCT
iajs-1184	85	33	{	{	PUNCT
iajs-1184	85	34	1,2,3},{1,2,4	1,2,3},{1,2,4	NUM
iajs-1184	85	35	}	}	PUNCT
iajs-1184	85	36	}	}	PUNCT
iajs-1184	85	37	spo(x	spo(x	PROPN
iajs-1184	85	38	)	)	PUNCT
iajs-1184	85	39	=	=	SYM
iajs-1184	85	40	po(x	po(x	X
iajs-1184	85	41	)	)	PUNCT
iajs-1184	85	42			NOUN
iajs-1184	85	43	{	{	PUNCT
iajs-1184	85	44	{	{	PUNCT
iajs-1184	85	45	1,3},{1,4},{1,3,4},{2,3},{2,4},{2,3,4	1,3},{1,4},{1,3,4},{2,3},{2,4},{2,3,4	NUM
iajs-1184	85	46	}	}	PUNCT
iajs-1184	85	47	}	}	PUNCT
iajs-1184	85	48	it	it	PRON
iajs-1184	85	49	is	be	AUX
iajs-1184	85	50	clear	clear	ADJ
iajs-1184	85	51	that	that	SCONJ
iajs-1184	85	52	{	{	PUNCT
iajs-1184	85	53	1,3	1,3	NUM
iajs-1184	85	54	}	}	PUNCT
iajs-1184	85	55	is	be	AUX
iajs-1184	85	56	semi	semi	ADJ
iajs-1184	85	57	-	-	ADJ
iajs-1184	85	58	preopen	preopen	ADJ
iajs-1184	85	59	set	set	NOUN
iajs-1184	85	60	,	,	PUNCT
iajs-1184	85	61	but	but	CCONJ
iajs-1184	85	62	it	it	PRON
iajs-1184	85	63	is	be	AUX
iajs-1184	85	64	not	not	PART
iajs-1184	85	65	a	a	DET
iajs-1184	85	66	preopen	preopen	ADJ
iajs-1184	85	67	set	set	NOUN
iajs-1184	85	68	.	.	PUNCT
iajs-1184	86	1	from	from	ADP
iajs-1184	86	2	remark	remark	NOUN
iajs-1184	86	3	3.1	3.1	NUM
iajs-1184	86	4	and	and	CCONJ
iajs-1184	86	5	remark	remark	VERB
iajs-1184	86	6	3.2	3.2	NUM
iajs-1184	86	7	we	we	PRON
iajs-1184	86	8	obtain	obtain	VERB
iajs-1184	86	9	the	the	DET
iajs-1184	86	10	following	following	NOUN
iajs-1184	86	11	:	:	PUNCT
iajs-1184	86	12	remark	remark	VERB
iajs-1184	86	13	3.3	3.3	NUM
iajs-1184	86	14	:	:	PUNCT
iajs-1184	86	15	ibn	ibn	NOUN
iajs-1184	86	16	alhaitham	alhaitham	NOUN
iajs-1184	86	17	j.	j.	PROPN
iajs-1184	87	1	fo	fo	ADP
iajs-1184	87	2	r	r	NOUN
iajs-1184	87	3	pure	pure	ADJ
iajs-1184	87	4	&	&	CCONJ
iajs-1184	87	5	appl	appl	PROPN
iajs-1184	87	6	.	.	PUNCT
iajs-1184	88	1	sc	sc	PROPN
iajs-1184	89	1	i	i	PRON
iajs-1184	89	2	vo	vo	INTJ
iajs-1184	89	3	l.22	l.22	X
iajs-1184	89	4	(	(	PUNCT
iajs-1184	89	5	3	3	NUM
iajs-1184	89	6	)	)	PUNCT
iajs-1184	89	7	2009	2009	NUM
iajs-1184	89	8	every	every	DET
iajs-1184	89	9	open	open	ADJ
iajs-1184	89	10	set	set	NOUN
iajs-1184	89	11	is	be	AUX
iajs-1184	89	12	semi	semi	ADJ
iajs-1184	89	13	-	-	ADJ
iajs-1184	89	14	preopen	preopen	ADJ
iajs-1184	89	15	set	set	NOUN
iajs-1184	89	16	.	.	PUNCT
iajs-1184	90	1	but	but	CCONJ
iajs-1184	90	2	the	the	DET
iajs-1184	90	3	converse	converse	NOUN
iajs-1184	90	4	may	may	AUX
iajs-1184	90	5	be	be	AUX
iajs-1184	90	6	false	false	ADJ
iajs-1184	90	7	,	,	PUNCT
iajs-1184	90	8	as	as	ADP
iajs-1184	90	9	the	the	DET
iajs-1184	90	10	example	example	NOUN
iajs-1184	90	11	2	2	NUM
iajs-1184	90	12	in	in	ADP
iajs-1184	90	13	remark	remark	NOUN
iajs-1184	90	14	3.2	3.2	NUM
iajs-1184	90	15	.	.	PUNCT
iajs-1184	91	1	remark	remark	VERB
iajs-1184	91	2	3.4	3.4	NUM
iajs-1184	91	3	:	:	PUNCT
iajs-1184	91	4	every	every	DET
iajs-1184	91	5	α	α	X
iajs-1184	91	6	-	-	ADJ
iajs-1184	91	7	open	open	ADJ
iajs-1184	91	8	set	set	NOUN
iajs-1184	91	9	is	be	AUX
iajs-1184	91	10	semi	semi	ADJ
iajs-1184	91	11	-	-	ADJ
iajs-1184	91	12	preopen	preopen	ADJ
iajs-1184	91	13	set	set	NOUN
iajs-1184	91	14	.	.	PUNCT
iajs-1184	92	1	proof	proof	NOUN
iajs-1184	92	2	:	:	PUNCT
iajs-1184	92	3	since	since	SCONJ
iajs-1184	92	4	a	a	PRON
iajs-1184	92	5	is	be	AUX
iajs-1184	92	6	α	α	NOUN
iajs-1184	92	7	-	-	ADJ
iajs-1184	92	8	open	open	ADJ
iajs-1184	92	9	set	set	NOUN
iajs-1184	92	10	,	,	PUNCT
iajs-1184	92	11	therefore	therefore	ADV
iajs-1184	92	12	a	a	DET
iajs-1184	92	13	ح	ح	PROPN
iajs-1184	92	14	�	�	PROPN
iajs-1184	92	15	°	°	NOUN
iajs-1184	92	16	�	�	PROPN
iajs-1184	92	17	�	�	PROPN
iajs-1184	92	18	�	�	PROPN
iajs-1184	92	19	�	�	PROPN
iajs-1184	92	20	�	�	PROPN
iajs-1184	92	21	°	°	PROPN
iajs-1184	92	22	,	,	PUNCT
iajs-1184	92	23	and	and	CCONJ
iajs-1184	92	24	since	since	SCONJ
iajs-1184	92	25	�	�	PROPN
iajs-1184	92	26	°	°	PROPN
iajs-1184	92	27	is	be	AUX
iajs-1184	92	28	open	open	ADJ
iajs-1184	92	29	set	set	VERB
iajs-1184	92	30	this	this	PRON
iajs-1184	92	31	implies	imply	VERB
iajs-1184	92	32	�	�	PROPN
iajs-1184	92	33	°	°	PROPN
iajs-1184	92	34	is	be	AUX
iajs-1184	92	35	a	a	DET
iajs-1184	92	36	preopen	preopen	ADJ
iajs-1184	92	37	set	set	NOUN
iajs-1184	92	38	(	(	PUNCT
iajs-1184	92	39	by	by	ADP
iajs-1184	92	40	remark	remark	NOUN
iajs-1184	92	41	3.1	3.1	NUM
iajs-1184	92	42	)	)	PUNCT
iajs-1184	92	43	.	.	PUNCT
iajs-1184	93	1	and	and	CCONJ
iajs-1184	93	2	�	�	PROPN
iajs-1184	93	3	°	°	PROPN
iajs-1184	93	4	ح	ح	NOUN
iajs-1184	93	5	a	a	DET
iajs-1184	93	6	so	so	ADV
iajs-1184	93	7	�	�	NOUN
iajs-1184	93	8	°	°	NOUN
iajs-1184	93	9	ح	ح	VERB
iajs-1184	93	10	a	a	DET
iajs-1184	93	11	ح	ح	NOUN
iajs-1184	93	12	ح	ح	PROPN
iajs-1184	93	13	°	°	PROPN
iajs-1184	93	14	�	�	PROPN
iajs-1184	93	15	�	�	PROPN
iajs-1184	93	16	�	�	PROPN
iajs-1184	93	17	�	�	PROPN
iajs-1184	93	18	�	�	PROPN
iajs-1184	93	19	°	°	PROPN
iajs-1184	93	20	�	�	PROPN
iajs-1184	93	21	�	�	PROPN
iajs-1184	93	22	°	°	PROPN
iajs-1184	93	23	�	�	PROPN
iajs-1184	93	24	�	�	PROPN
iajs-1184	93	25	�	�	PROPN
iajs-1184	93	26	,	,	PUNCT
iajs-1184	93	27	hence	hence	ADV
iajs-1184	93	28	�	�	NOUN
iajs-1184	93	29	°	°	PROPN
iajs-1184	93	30	ح	ح	VERB
iajs-1184	93	31	a	a	DET
iajs-1184	93	32	ح	ح	PROPN
iajs-1184	93	33	�	�	PROPN
iajs-1184	93	34	°	°	NOUN
iajs-1184	93	35	�	�	PROPN
iajs-1184	93	36	�	�	PROPN
iajs-1184	93	37	�	�	PROPN
iajs-1184	93	38	�	�	PROPN
iajs-1184	93	39	.	.	PUNCT
iajs-1184	94	1	thus	thus	ADV
iajs-1184	94	2	,	,	PUNCT
iajs-1184	94	3	a	a	PRON
iajs-1184	94	4	is	be	AUX
iajs-1184	94	5	semi	semi	ADJ
iajs-1184	94	6	-	-	ADJ
iajs-1184	94	7	preopen	preopen	ADJ
iajs-1184	94	8	set	set	NOUN
iajs-1184	94	9	.	.	PUNCT
iajs-1184	95	1	■	■	PUNCT
iajs-1184	95	2	the	the	DET
iajs-1184	95	3	converse	converse	NOUN
iajs-1184	95	4	of	of	ADP
iajs-1184	95	5	remark	remark	NOUN
iajs-1184	95	6	3.4	3.4	NUM
iajs-1184	95	7	is	be	AUX
iajs-1184	95	8	not	not	PART
iajs-1184	95	9	true	true	ADJ
iajs-1184	95	10	,	,	PUNCT
iajs-1184	95	11	as	as	ADP
iajs-1184	95	12	the	the	DET
iajs-1184	95	13	following	following	NOUN
iajs-1184	95	14	of	of	ADP
iajs-1184	95	15	example	example	NOUN
iajs-1184	95	16	2	2	NUM
iajs-1184	95	17	:	:	PUNCT
iajs-1184	95	18	x={1,2,3,4	x={1,2,3,4	ADJ
iajs-1184	95	19	}	}	PUNCT
iajs-1184	95	20	,	,	PUNCT
iajs-1184	95	21	={x,	={x,	PUNCT
iajs-1184	95	22	,	,	PUNCT
iajs-1184	95	23	{	{	PUNCT
iajs-1184	95	24	1},{2},{1,2	1},{2},{1,2	NUM
iajs-1184	95	25	}	}	PUNCT
iajs-1184	95	26	}	}	PUNCT
iajs-1184	95	27	α	α	PROPN
iajs-1184	95	28	=	=	NOUN
iajs-1184	95	29	po(x	po(x	X
iajs-1184	95	30	)	)	PUNCT
iajs-1184	95	31	=	=	SYM
iajs-1184	95	32			PROPN
iajs-1184	95	33			NOUN
iajs-1184	95	34	{	{	PUNCT
iajs-1184	95	35	{	{	PUNCT
iajs-1184	95	36	1,2,3},{1,2,4	1,2,3},{1,2,4	NUM
iajs-1184	95	37	}	}	PUNCT
iajs-1184	95	38	}	}	PUNCT
iajs-1184	95	39	spo(x	spo(x	PROPN
iajs-1184	95	40	)	)	PUNCT
iajs-1184	95	41	=	=	SYM
iajs-1184	95	42	po(x	po(x	X
iajs-1184	95	43	)	)	PUNCT
iajs-1184	95	44			NOUN
iajs-1184	95	45	{	{	PUNCT
iajs-1184	95	46	{	{	PUNCT
iajs-1184	95	47	1,3},{1,4},{1,3,4},{2,3},{2,4},{2,3,4	1,3},{1,4},{1,3,4},{2,3},{2,4},{2,3,4	NUM
iajs-1184	95	48	}	}	PUNCT
iajs-1184	95	49	}	}	PUNCT
iajs-1184	95	50	.	.	PUNCT
iajs-1184	96	1	remark	remark	VERB
iajs-1184	96	2	3.5	3.5	NUM
iajs-1184	96	3	:	:	PUNCT
iajs-1184	96	4	every	every	DET
iajs-1184	96	5	semi	semi	ADJ
iajs-1184	96	6	-	-	ADJ
iajs-1184	96	7	p	p	ADJ
iajs-1184	96	8	-	-	PUNCT
iajs-1184	96	9	open	open	ADJ
iajs-1184	96	10	set	set	NOUN
iajs-1184	96	11	is	be	AUX
iajs-1184	96	12	semi	semi	ADJ
iajs-1184	96	13	-	-	ADJ
iajs-1184	96	14	preopen	preopen	ADJ
iajs-1184	96	15	set	set	NOUN
iajs-1184	96	16	.	.	PUNCT
iajs-1184	97	1	proof	proof	NOUN
iajs-1184	97	2	:	:	PUNCT
iajs-1184	97	3	let	let	VERB
iajs-1184	97	4	a	a	PRON
iajs-1184	97	5	be	be	AUX
iajs-1184	97	6	any	any	DET
iajs-1184	97	7	semi	semi	ADJ
iajs-1184	97	8	-	-	ADJ
iajs-1184	97	9	p	p	ADJ
iajs-1184	97	10	-	-	PUNCT
iajs-1184	97	11	open	open	ADJ
iajs-1184	97	12	set	set	NOUN
iajs-1184	97	13	,	,	PUNCT
iajs-1184	97	14	this	this	PRON
iajs-1184	97	15	means	mean	VERB
iajs-1184	97	16	there	there	PRON
iajs-1184	97	17	exists	exist	VERB
iajs-1184	97	18	a	a	DET
iajs-1184	97	19	preopen	preopen	ADJ
iajs-1184	97	20	set	set	NOUN
iajs-1184	97	21	in	in	ADP
iajs-1184	97	22	x	x	PART
iajs-1184	97	23	say	say	VERB
iajs-1184	97	24	u	u	NOUN
iajs-1184	97	25	such	such	ADJ
iajs-1184	97	26	that	that	SCONJ
iajs-1184	97	27	u	u	PRON
iajs-1184	97	28	ح	ح	VERB
iajs-1184	97	29	a	a	DET
iajs-1184	97	30	ح	ح	ADJ
iajs-1184	97	31	pre	pre	ADJ
iajs-1184	97	32	-	-	ADJ
iajs-1184	97	33	cl	cl	ADJ
iajs-1184	97	34	u	u	NOUN
iajs-1184	97	35	,	,	PUNCT
iajs-1184	97	36	and	and	CCONJ
iajs-1184	97	37	since	since	SCONJ
iajs-1184	97	38	pre	pre	ADJ
iajs-1184	97	39	-	-	ADJ
iajs-1184	97	40	cl	cl	ADJ
iajs-1184	97	41	u	u	PROPN
iajs-1184	97	42	ح	ح	PROPN
iajs-1184	97	43	�	�	PROPN
iajs-1184	97	44	�	�	PROPN
iajs-1184	97	45	(	(	PUNCT
iajs-1184	97	46	by	by	ADP
iajs-1184	97	47	proposition	proposition	NOUN
iajs-1184	97	48	1.6	1.6	NUM
iajs-1184	97	49	)	)	PUNCT
iajs-1184	97	50	,	,	PUNCT
iajs-1184	97	51	therefore	therefore	ADV
iajs-1184	97	52	u	u	PRON
iajs-1184	97	53	ح	ح	VERB
iajs-1184	97	54	a	a	DET
iajs-1184	97	55	ح	ح	PROPN
iajs-1184	97	56	�	�	PROPN
iajs-1184	97	57	�	�	PROPN
iajs-1184	97	58	.	.	PUNCT
iajs-1184	98	1	thus	thus	ADV
iajs-1184	98	2	a	a	PRON
iajs-1184	98	3	is	be	AUX
iajs-1184	98	4	semi	semi	ADJ
iajs-1184	98	5	-	-	ADJ
iajs-1184	98	6	preopen	preopen	ADJ
iajs-1184	98	7	set	set	NOUN
iajs-1184	98	8	.	.	PUNCT
iajs-1184	99	1	■	■	PUNCT
iajs-1184	99	2	ut	ut	NOUN
iajs-1184	99	3	the	the	DET
iajs-1184	99	4	converse	converse	NOUN
iajs-1184	99	5	is	be	AUX
iajs-1184	99	6	not	not	PART
iajs-1184	99	7	true	true	ADJ
iajs-1184	99	8	,	,	PUNCT
iajs-1184	99	9	as	as	SCONJ
iajs-1184	99	10	the	the	DET
iajs-1184	99	11	following	follow	VERB
iajs-1184	99	12	example	example	NOUN
iajs-1184	99	13	show	show	NOUN
iajs-1184	99	14	:	:	PUNCT
iajs-1184	99	15	example	example	NOUN
iajs-1184	99	16	3	3	NUM
iajs-1184	99	17	:	:	PUNCT
iajs-1184	99	18	let	let	VERB
iajs-1184	99	19	x=	x=	PUNCT
iajs-1184	99	20	{	{	PUNCT
iajs-1184	99	21	1,2,3,4	1,2,3,4	NUM
iajs-1184	99	22	}	}	PUNCT
iajs-1184	99	23	,	,	PUNCT
iajs-1184	99	24	={	={	INTJ
iajs-1184	99	25	,	,	PUNCT
iajs-1184	99	26	x	x	X
iajs-1184	99	27	,	,	PUNCT
iajs-1184	99	28	{	{	PUNCT
iajs-1184	99	29	1,2	1,2	NUM
iajs-1184	99	30	}	}	PUNCT
iajs-1184	99	31	,	,	PUNCT
iajs-1184	99	32	{	{	PUNCT
iajs-1184	99	33	3	3	NUM
iajs-1184	99	34	}	}	PUNCT
iajs-1184	99	35	,	,	PUNCT
iajs-1184	99	36	{	{	PUNCT
iajs-1184	99	37	1,2,3	1,2,3	NOUN
iajs-1184	99	38	}	}	PUNCT
iajs-1184	99	39	}	}	PUNCT
iajs-1184	99	40	,	,	PUNCT
iajs-1184	99	41	�	�	PROPN
iajs-1184	99	42	=	=	PRON
iajs-1184	99	43	{	{	PUNCT
iajs-1184	99	44	x	x	NOUN
iajs-1184	99	45	,	,	PUNCT
iajs-1184	99	46			PROPN
iajs-1184	99	47	,	,	PUNCT
iajs-1184	99	48	{	{	PUNCT
iajs-1184	99	49	1,2,4},{3,4},{4	1,2,4},{3,4},{4	NOUN
iajs-1184	99	50	}	}	PUNCT
iajs-1184	99	51	}	}	PUNCT
iajs-1184	99	52	(x	(x	NOUN
iajs-1184	99	53	)	)	PUNCT
iajs-1184	99	54	=	=	SYM
iajs-1184	99	55			PROPN
iajs-1184	99	56			NOUN
iajs-1184	99	57	{	{	PUNCT
iajs-1184	99	58	{	{	PUNCT
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iajs-1184	99	61	}	}	PUNCT
iajs-1184	99	62	c(x	c(x	PROPN
iajs-1184	99	63	)	)	PUNCT
iajs-1184	99	64	=	=	PROPN
iajs-1184	99	65	�	�	PROPN
iajs-1184	99	66			PROPN
iajs-1184	99	67	{	{	PUNCT
iajs-1184	99	68	{	{	PUNCT
iajs-1184	99	69	2,3,4},{1,3,4},{2,4},{1,4},{2},{1	2,3,4},{1,3,4},{2,4},{1,4},{2},{1	NOUN
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iajs-1184	99	72	s(x	s(x	NOUN
iajs-1184	99	73	)	)	PUNCT
iajs-1184	99	74	=	=	SYM
iajs-1184	99	75	(x	(x	NOUN
iajs-1184	99	76	)	)	PUNCT
iajs-1184	99	77			NOUN
iajs-1184	99	78	{	{	PUNCT
iajs-1184	99	79	{	{	PUNCT
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iajs-1184	99	82	}	}	PUNCT
iajs-1184	99	83	now	now	ADV
iajs-1184	99	84	{	{	PUNCT
iajs-1184	99	85	1,4}خ	1,4}خ	NUM
iajs-1184	99	86	s(x	s(x	NOUN
iajs-1184	99	87	)	)	PUNCT
iajs-1184	99	88	,	,	PUNCT
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iajs-1184	99	90	{	{	PUNCT
iajs-1184	99	91	1}{1,4	1}{1,4	ADV
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iajs-1184	99	94	pre	pre	ADJ
iajs-1184	99	95	-	-	NOUN
iajs-1184	99	96	cl	cl	ADJ
iajs-1184	99	97	{	{	PUNCT
iajs-1184	99	98	1}={1},thus	1}={1},thus	NUM
iajs-1184	99	99	{	{	PUNCT
iajs-1184	99	100	1,4	1,4	NUM
iajs-1184	99	101	}	}	PUNCT
iajs-1184	99	102	is	be	AUX
iajs-1184	99	103	not	not	PART
iajs-1184	99	104	semi	semi	ADJ
iajs-1184	99	105	-	-	ADJ
iajs-1184	99	106	p	p	ADJ
iajs-1184	99	107	-	-	PUNCT
iajs-1184	99	108	open	open	ADJ
iajs-1184	99	109	set	set	NOUN
iajs-1184	99	110	.	.	PUNCT
iajs-1184	100	1	conclusion	conclusion	NOUN
iajs-1184	100	2	1	1	NUM
iajs-1184	100	3	.	.	PUNCT
iajs-1184	101	1	the	the	DET
iajs-1184	101	2	union	union	NOUN
iajs-1184	101	3	of	of	ADP
iajs-1184	101	4	any	any	DET
iajs-1184	101	5	family	family	NOUN
iajs-1184	101	6	of	of	ADP
iajs-1184	101	7	semipreopen	semipreopen	ADJ
iajs-1184	101	8	sets	set	NOUN
iajs-1184	101	9	is	be	AUX
iajs-1184	101	10	semipreopen	semipreopen	ADJ
iajs-1184	101	11	set	set	VERB
iajs-1184	101	12	.	.	PUNCT
iajs-1184	102	1	2	2	X
iajs-1184	102	2	.	.	X
iajs-1184	102	3	the	the	DET
iajs-1184	102	4	intersection	intersection	NOUN
iajs-1184	102	5	of	of	ADP
iajs-1184	102	6	any	any	DET
iajs-1184	102	7	family	family	NOUN
iajs-1184	102	8	of	of	ADP
iajs-1184	102	9	semi	semi	ADJ
iajs-1184	102	10	-	-	ADJ
iajs-1184	102	11	preclosed	preclosed	ADJ
iajs-1184	102	12	sets	set	NOUN
iajs-1184	102	13	is	be	AUX
iajs-1184	102	14	semi	semi	ADJ
iajs-1184	102	15	-	-	ADJ
iajs-1184	102	16	preclosed	preclosed	ADJ
iajs-1184	102	17	set	set	NOUN
iajs-1184	102	18	.	.	PUNCT
iajs-1184	103	1	3	3	X
iajs-1184	103	2	.	.	X
iajs-1184	103	3	every	every	DET
iajs-1184	103	4	preopen	preopen	ADJ
iajs-1184	103	5	set	set	NOUN
iajs-1184	103	6	is	be	AUX
iajs-1184	103	7	semi	semi	ADJ
iajs-1184	103	8	-	-	ADJ
iajs-1184	103	9	preopen	preopen	ADJ
iajs-1184	103	10	set	set	NOUN
iajs-1184	103	11	.	.	PUNCT
iajs-1184	104	1	4	4	X
iajs-1184	104	2	.	.	X
iajs-1184	104	3	every	every	DET
iajs-1184	104	4	open	open	ADJ
iajs-1184	104	5	set	set	NOUN
iajs-1184	104	6	is	be	AUX
iajs-1184	104	7	semi	semi	ADJ
iajs-1184	104	8	-	-	ADJ
iajs-1184	104	9	preopen	preopen	ADJ
iajs-1184	104	10	set	set	NOUN
iajs-1184	104	11	.	.	PUNCT
iajs-1184	105	1	5	5	X
iajs-1184	105	2	.	.	X
iajs-1184	105	3	every	every	DET
iajs-1184	105	4	semi	semi	ADJ
iajs-1184	105	5	-	-	ADJ
iajs-1184	105	6	p	p	ADJ
iajs-1184	105	7	-	-	PUNCT
iajs-1184	105	8	open	open	ADJ
iajs-1184	105	9	set	set	NOUN
iajs-1184	105	10	is	be	AUX
iajs-1184	105	11	semi	semi	ADJ
iajs-1184	105	12	-	-	ADJ
iajs-1184	105	13	preopen	preopen	ADJ
iajs-1184	105	14	set	set	NOUN
iajs-1184	105	15	.	.	PUNCT
iajs-1184	106	1	references	reference	NOUN
iajs-1184	106	2	1	1	NUM
iajs-1184	106	3	.	.	PUNCT
iajs-1184	106	4	navalagi	navalagi	ADJ
iajs-1184	106	5	,	,	PUNCT
iajs-1184	106	6	g.b	g.b	PROPN
iajs-1184	106	7	.	.	PUNCT
iajs-1184	107	1	(	(	PUNCT
iajs-1184	107	2	2000	2000	NUM
iajs-1184	107	3	)	)	PUNCT
iajs-1184	107	4	,	,	PUNCT
iajs-1184	107	5	"	"	PUNCT
iajs-1184	107	6	definition	definition	NOUN
iajs-1184	107	7	bank	bank	NOUN
iajs-1184	107	8	in	in	ADP
iajs-1184	107	9	general	general	ADJ
iajs-1184	107	10	topology	topology	NOUN
iajs-1184	107	11	"	"	PUNCT
iajs-1184	107	12	,	,	PUNCT
iajs-1184	107	13	internet	internet	NOUN
iajs-1184	107	14	.	.	PUNCT
iajs-1184	108	1	2	2	NUM
iajs-1184	108	2	.	.	X
iajs-1184	108	3	esmaeel	esmaeel	VERB
iajs-1184	108	4	,	,	PUNCT
iajs-1184	108	5	r.b	r.b	NOUN
iajs-1184	108	6	.	.	PROPN
iajs-1184	109	1	(	(	PUNCT
iajs-1184	109	2	2004	2004	NUM
iajs-1184	109	3	)	)	PUNCT
iajs-1184	109	4	"	"	PUNCT
iajs-1184	109	5	on	on	ADP
iajs-1184	109	6	semi	semi	ADJ
iajs-1184	109	7	-	-	ADJ
iajs-1184	109	8	p	p	ADJ
iajs-1184	109	9	-	-	PUNCT
iajs-1184	109	10	open	open	ADJ
iajs-1184	109	11	sets	set	NOUN
iajs-1184	109	12	"	"	PUNCT
iajs-1184	109	13	,	,	PUNCT
iajs-1184	109	14	m.sc	m.sc	PROPN
iajs-1184	109	15	.	.	PUNCT
iajs-1184	110	1	thesis	thesis	NOUN
iajs-1184	110	2	,	,	PUNCT
iajs-1184	110	3	university	university	NOUN
iajs-1184	110	4	of	of	ADP
iajs-1184	110	5	baghdad	baghdad	PROPN
iajs-1184	110	6	.	.	PUNCT
iajs-1184	111	1	301	301	NUM
iajs-1184	111	2	,	,	PUNCT
iajs-1184	111	3	-4	-4	PROPN
iajs-1184	111	4	)	)	PUNCT
iajs-1184	111	5	,	,	PUNCT
iajs-1184	111	6	299-(356math	299-(356math	NUM
iajs-1184	111	7	.	.	PUNCT
iajs-1184	112	1	hungarica	hungarica	ADJ
iajs-1184	112	2	,	,	PUNCT
iajs-1184	112	3	ganster	ganster	NOUN
iajs-1184	112	4	and	and	CCONJ
iajs-1184	112	5	ivan	ivan	PROPN
iajs-1184	112	6	rrilly	rrilly	PROPN
iajs-1184	112	7	,	,	PUNCT
iajs-1184	112	8	(	(	PUNCT
iajs-1184	112	9	1990	1990	NUM
iajs-1184	112	10	)	)	PUNCT
iajs-1184	112	11	,	,	PUNCT
iajs-1184	112	12	acta	acta	PROPN
iajs-1184	112	13	maximum	maximum	PROPN
iajs-1184	113	1	3	3	NUM
iajs-1184	113	2	.	.	PUNCT
iajs-1184	113	3	internet	internet	NOUN
iajs-1184	113	4	.	.	PUNCT
iajs-1184	114	1	4	4	X
iajs-1184	114	2	.	.	X
iajs-1184	114	3	olav	olav	PROPN
iajs-1184	114	4	njastad	njastad	PROPN
iajs-1184	114	5	,	,	PUNCT
iajs-1184	114	6	(	(	PUNCT
iajs-1184	114	7	1965	1965	NUM
iajs-1184	114	8	)	)	PUNCT
iajs-1184	114	9	,	,	PUNCT
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iajs-1184	114	11	journal	journal	PROPN
iajs-1184	114	12	of	of	ADP
iajs-1184	114	13	mathematics	mathematic	NOUN
iajs-1184	114	14	,	,	PUNCT
iajs-1184	114	15	15:3	15:3	NUM
iajs-1184	114	16	.	.	NOUN
iajs-1184	114	17	5	5	NUM
iajs-1184	114	18	.	.	PUNCT
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iajs-1184	115	2	,	,	PUNCT
iajs-1184	115	3	a.s	a.s	PROPN
iajs-1184	115	4	.	.	PROPN
iajs-1184	115	5	abd	abd	PROPN
iajs-1184	115	6	el	el	PROPN
iajs-1184	115	7	-	-	PUNCT
iajs-1184	115	8	monsef	monsef	PROPN
iajs-1184	115	9	m.e	m.e	PROPN
iajs-1184	115	10	.	.	PROPN
iajs-1184	115	11	and	and	CCONJ
iajs-1184	115	12	el	el	PROPN
iajs-1184	115	13	-	-	PUNCT
iajs-1184	115	14	deeb	deeb	PROPN
iajs-1184	115	15	,	,	PUNCT
iajs-1184	115	16	s.n	s.n	PROPN
iajs-1184	115	17	.	.	PROPN
iajs-1184	115	18	(	(	PUNCT
iajs-1184	115	19	1981	1981	NUM
iajs-1184	115	20	)	)	PUNCT
iajs-1184	115	21	.	.	PUNCT
iajs-1184	116	1	p	p	X
iajs-1184	116	2	roc.math	roc.math	PROPN
iajs-1184	116	3	.	.	PUNCT
iajs-1184	117	1	and	and	CCONJ
iajs-1184	117	2	phys.soc.egypt	phys.soc.egypt	PROPN
iajs-1184	117	3	51	51	NUM
iajs-1184	117	4	.	.	NOUN
iajs-1184	118	1	6	6	NUM
iajs-1184	118	2	.	.	X
iajs-1184	118	3	dontchev	dontchev	PROPN
iajs-1184	118	4	,	,	PUNCT
iajs-1184	118	5	j.	j.	PROPN
iajs-1184	118	6	(	(	PUNCT
iajs-1184	118	7	1994	1994	NUM
iajs-1184	118	8	)	)	PUNCT
iajs-1184	118	9	,	,	PUNCT
iajs-1184	118	10	helsinki	helsinki	PROPN
iajs-1184	118	11	unv	unv	PROPN
iajs-1184	118	12	.	.	PROPN
iajs-1184	118	13	,	,	PUNCT
iajs-1184	118	14	j.	j.	PROPN
iajs-1184	118	15	pure	pure	PROPN
iajs-1184	118	16	appl	appl	PROPN
iajs-1184	118	17	.	.	PUNCT
iajs-1184	118	18	math	math	PROPN
iajs-1184	118	19	.	.	PUNCT
iajs-1184	118	20	,	,	PUNCT
iajs-1184	118	21	25(9	25(9	NUM
iajs-1184	118	22	)	)	PUNCT
iajs-1184	118	23	.	.	PUNCT
iajs-1184	119	1	7	7	X
iajs-1184	119	2	.	.	X
iajs-1184	119	3	navalagi	navalagi	ADJ
iajs-1184	119	4	,	,	PUNCT
iajs-1184	119	5	g.b	g.b	PROPN
iajs-1184	119	6	.	.	PUNCT
iajs-1184	119	7	(	(	PUNCT
iajs-1184	119	8	2000	2000	NUM
iajs-1184	119	9	)	)	PUNCT
iajs-1184	119	10	.	.	PUNCT
iajs-1184	120	1	definition	definition	NOUN
iajs-1184	120	2	bank	bank	PROPN
iajs-1184	120	3	in	in	ADP
iajs-1184	120	4	general	general	ADJ
iajs-1184	120	5	topology	topology	NOUN
iajs-1184	120	6	,	,	PUNCT
iajs-1184	120	7	department	department	NOUN
iajs-1184	120	8	of	of	ADP
iajs-1184	120	9	mathematics	mathematics	PROPN
iajs-1184	120	10	,	,	PUNCT
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iajs-1184	120	12	,	,	PUNCT
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iajs-1184	120	14	,	,	PUNCT
iajs-1184	120	15	india	india	PROPN