id	sid	tid	token	lemma	pos
iajs-777	1	1	2011	2011	NUM
iajs-777	1	2	)	)	PUNCT
iajs-777	1	3	2	2	NUM
iajs-777	1	4	(	(	PUNCT
iajs-777	1	5	24مجلة	24مجلة	NUM
iajs-777	1	6	ابن	ابن	VERB
iajs-777	1	7	الهیثم	الهیثم	ADJ
iajs-777	1	8	للعلوم	للعلوم	PROPN
iajs-777	1	9	الصرفة	الصرفة	PROPN
iajs-777	1	10	والتطبیقیة	والتطبیقیة	PROPN
iajs-777	1	11	المجلد	المجلد	PROPN
iajs-777	1	12	شبه	شبه	VERB
iajs-777	1	13	المنتظمة	المنتظمة	VERB
iajs-777	1	14	المغلقة	المغلقة	PROPN
iajs-777	1	15			NOUN
iajs-777	1	16	-المجموعات	-المجموعات	ADJ
iajs-777	1	17	نادیة	نادیة	NOUN
iajs-777	1	18	فائق	فائق	VERB
iajs-777	1	19	محمد	محمد	ADJ
iajs-777	1	20	جامعة	جامعة	NOUN
iajs-777	1	21	بغداد،ابن	بغداد،ابن	PROPN
iajs-777	1	22	الهیثم	الهیثم	VERB
iajs-777	1	23	-كلیة	-كلیة	PROPN
iajs-777	1	24	التربیة،قسم	التربیة،قسم	PROPN
iajs-777	1	25	الریاضیات	الریاضیات	PROPN
iajs-777	1	26	2010،حزیران	2010،حزیران	PROPN
iajs-777	1	27	،	،	PROPN
iajs-777	1	28	23	23	NUM
iajs-777	1	29	:	:	PUNCT
iajs-777	1	30	استلم	استلم	PROPN
iajs-777	1	31	البحث	البحث	VERB
iajs-777	1	32	في	في	ADP
iajs-777	1	33	2010،ایلول	2010،ایلول	PROPN
iajs-777	1	34	،	،	NOUN
iajs-777	2	1	27	27	NUM
iajs-777	2	2	:	:	PUNCT
iajs-777	2	3	قبل	قبل	NOUN
iajs-777	2	4	البحث	البحث	VERB
iajs-777	2	5	في	في	ADP
iajs-777	2	6	الخالصة	الخالصة	NOUN
iajs-777	2	7	ـة	ـة	AUX
iajs-777	2	8	یــــدعى	یــــدعى	VERB
iajs-777	3	1	ـة	ـة	PROPN
iajs-777	3	2	فـــي	فـــي	PROPN
iajs-777	3	3	الفضـــاءات	الفضـــاءات	PROPN
iajs-777	3	4	التبولوجیــ	التبولوجیــ	PROPN
iajs-777	3	5	ــات	ــات	PROPN
iajs-777	3	6	المغلقــ	المغلقــ	PROPN
iajs-777	3	7	ـة	ـة	PROPN
iajs-777	3	8	نـــوع	نـــوع	PROPN
iajs-777	3	9	جدیـــد	جدیـــد	NOUN
iajs-777	3	10	مـــن	مـــن	PROPN
iajs-777	3	11	المجموعــ	المجموعــ	INTJ
iajs-777	3	12	ــد	ــد	INTJ
iajs-777	4	1	قمنـــا	قمنـــا	ADP
iajs-777	4	2	فـــي	فـــي	PROPN
iajs-777	4	3	هـــذا	هـــذا	PROPN
iajs-777	4	4	البحـــث	البحـــث	PROPN
iajs-777	4	5	بتقــــدیم	بتقــــدیم	VERB
iajs-777	4	6	ودراســ	ودراســ	PROPN
iajs-777	4	7	لقـ	لقـ	VERB
iajs-777	4	8			NOUN
iajs-777	4	9	-قـة	-قـة	X
iajs-777	4	10	لان	لان	PROPN
iajs-777	4	11	هذا	هذا	NOUN
iajs-777	4	12	النوع	النوع	PROPN
iajs-777	4	13	من	من	PRON
iajs-777	4	14	المجموعـات	المجموعـات	PROPN
iajs-777	4	15	المغلقـة	المغلقـة	PROPN
iajs-777	4	16	تحـوي	تحـوي	PROPN
iajs-777	4	17	مجموعـات	مجموعـات	PROPN
iajs-777	4	18	شـبه	شـبه	PROPN
iajs-777	4	19	مغ	مغ	PROPN
iajs-777	4	20	اذشبه	اذشبه	PROPN
iajs-777	4	21	المنتظمة	المنتظمة	PROPN
iajs-777	4	22	المغلقة	المغلقة	PROPN
iajs-777	4	23	،	،	PROPN
iajs-777	4	24			NUM
iajs-777	4	25	-بالمجموعات	-بالمجموعات	PROPN
iajs-777	4	26	مـن	مـن	NOUN
iajs-777	4	27	الـدوال	الـدوال	NOUN
iajs-777	4	28	المسـتمرة	المسـتمرة	NOUN
iajs-777	4	29	والمتـرددة	والمتـرددة	ADJ
iajs-777	4	30	تـدعى	تـدعى	NOUN
iajs-777	4	31	دالـة	دالـة	VERB
iajs-777	4	32	اجدیـد	اجدیـد	NOUN
iajs-777	4	33	ادمنا	ادمنا	NOUN
iajs-777	4	34	ودرسـنا	ودرسـنا	ADJ
iajs-777	4	35	نوعـوكمـا	نوعـوكمـا	PROPN
iajs-777	5	1	قـ	قـ	VERB
iajs-777	5	2	.	.	PUNCT
iajs-777	6	1	وتكـون	وتكـون	PROPN
iajs-777	6	2	محتـواه	محتـواه	PROPN
iajs-777	7	1	فـي	فـي	PROPN
iajs-777	8	1	المجموعـات	المجموعـات	PROPN
iajs-777	8	2	قبـل	قبـل	ADJ
iajs-777	8	3	شـبه	شـبه	NOUN
iajs-777	8	4	المغلقـة	المغلقـة	VERB
iajs-777	8	5	كمـا	كمـا	NOUN
iajs-777	8	6	وجـدنا	وجـدنا	NOUN
iajs-777	8	7	ان	ان	AUX
iajs-777	8	8	االسـتمراریة	االسـتمراریة	VERB
iajs-777	8	9	مـن	مـن	PROPN
iajs-777	8	10	.	.	PUNCT
iajs-777	9	1	شـبه	شـبه	PROPN
iajs-777	9	2	المنتظمـة	المنتظمـة	VERB
iajs-777	9	3	المتـرددة	المتـرددة	NOUN
iajs-777	9	4			NOUN
iajs-777	9	5	-شبه	-شبه	PUNCT
iajs-777	9	6	المنتظمة	المنتظمة	PROPN
iajs-777	9	7	المستمرة	المستمرة	ADJ
iajs-777	9	8	ودالة	ودالة	NOUN
iajs-777	9	9	من	من	DET
iajs-777	9	10	الـنمط	الـنمط	NOUN
iajs-777	9	11			X
iajs-777	9	12	-من	-من	ADP
iajs-777	9	13	النمط	النمط	NOUN
iajs-777	9	14	.شبهالمراریة	.شبهالمراریة	PUNCT
iajs-777	9	15	من	من	PRON
iajs-777	9	16	النمط	النمط	NOUN
iajs-777	9	17	قبل	قبل	PROPN
iajs-777	10	1	واالست	واالست	ADV
iajs-777	10	2			X
iajs-777	10	3	-به	-به	SYM
iajs-777	10	4	ششبه	ششبه	ADJ
iajs-777	10	5	المنتظمة	المنتظمة	PROPN
iajs-777	10	6	تكون	تكون	VERB
iajs-777	10	7	واقعة	واقعة	PROPN
iajs-777	10	8	تماماً	تماماً	PROPN
iajs-777	10	9	بین	بین	PROPN
iajs-777	10	10	االستمراریة	االستمراریة	PROPN
iajs-777	11	1	من	من	PROPN
iajs-777	11	2	النمط	النمط	PROPN
iajs-777	11	3			PUNCT
iajs-777	11	4	-النمط	-النمط	PROPN
iajs-777	11	5	،	،	NOUN
iajs-777	11	6	شـبه	شـبه	PROPN
iajs-777	11	7	المنتظمـة	المنتظمـة	NOUN
iajs-777	11	8	المسـتمرة	المسـتمرة	PROPN
iajs-777	11	9	--الدالة	--الدالة	PUNCT
iajs-777	11	10	مـن	مـن	PROPN
iajs-777	11	11	الـنمط	الـنمط	PROPN
iajs-777	11	12	،	،	PROPN
iajs-777	11	13	شبه	شبه	PROPN
iajs-777	11	14	المنتظمة	المنتظمة	PROPN
iajs-777	11	15	المغلقة	المغلقة	PROPN
iajs-777	11	16	--المجموعة	--المجموعة	PROPN
iajs-777	11	17	من	من	DET
iajs-777	11	18	النمط	النمط	NOUN
iajs-777	11	19	:	:	PUNCT
iajs-777	11	20	الكلمات	الكلمات	VERB
iajs-777	11	21	المفتاحیة	المفتاحیة	ADV
iajs-777	11	22	.شبه	.شبه	PUNCT
iajs-777	12	1	المنتظمة	المنتظمة	PROPN
iajs-777	12	2	المترددة	المترددة	VERB
iajs-777	12	3	--الدالة	--الدالة	PUNCT
iajs-777	12	4	من	من	PRON
iajs-777	12	5	النمط	النمط	PROPN
iajs-777	12	6	ibn	ibn	PROPN
iajs-777	12	7	alhaitham	alhaitham	PROPN
iajs-777	12	8	j.	j.	PROPN
iajs-777	12	9	for	for	ADP
iajs-777	12	10	pure	pure	ADJ
iajs-777	12	11	&	&	CCONJ
iajs-777	12	12	appl	appl	PROPN
iajs-777	12	13	.	.	PUNCT
iajs-777	13	1	sci	sci	PROPN
iajs-777	13	2	.	.	PUNCT
iajs-777	13	3	vol.24	vol.24	NOUN
iajs-777	13	4	(	(	PUNCT
iajs-777	13	5	2	2	NUM
iajs-777	13	6	)	)	PUNCT
iajs-777	13	7	2011	2011	NUM
iajs-777	13	8			NOUN
iajs-777	13	9	semi	semi	ADJ
iajs-777	13	10	-	-	ADJ
iajs-777	13	11	regular	regular	ADJ
iajs-777	13	12	closed	closed	ADJ
iajs-777	13	13	sets	set	NOUN
iajs-777	13	14	n.	n.	PROPN
iajs-777	13	15	f.	f.	PROPN
iajs-777	13	16	mohammed	mohammed	PROPN
iajs-777	13	17	department	department	PROPN
iajs-777	13	18	of	of	ADP
iajs-777	13	19	mathematics	mathematics	PROPN
iajs-777	13	20	,	,	PUNCT
iajs-777	13	21	college	college	NOUN
iajs-777	13	22	of	of	ADP
iajs-777	13	23	education	education	NOUN
iajs-777	13	24	,	,	PUNCT
iajs-777	13	25	-ibn	-ibn	NUM
iajs-777	13	26	-	-	PUNCT
iajs-777	13	27	al	al	PROPN
iajs-777	13	28	-	-	PUNCT
iajs-777	13	29	haitham	haitham	PROPN
iajs-777	13	30	,	,	PUNCT
iajs-777	13	31	university	university	PROPN
iajs-777	13	32	of	of	ADP
iajs-777	13	33	baghdad	baghdad	PROPN
iajs-777	13	34	received	receive	VERB
iajs-777	13	35	in	in	ADP
iajs-777	13	36	:	:	PUNCT
iajs-777	13	37	23	23	NUM
iajs-777	13	38	,	,	PUNCT
iajs-777	13	39	june	june	PROPN
iajs-777	13	40	,	,	PUNCT
iajs-777	13	41	2010	2010	NUM
iajs-777	13	42	accepted	accept	VERB
iajs-777	13	43	in	in	ADP
iajs-777	13	44	:	:	PUNCT
iajs-777	13	45	27	27	NUM
iajs-777	13	46	,	,	PUNCT
iajs-777	13	47	september	september	PROPN
iajs-777	13	48	,	,	PUNCT
iajs-777	13	49	2010	2010	NUM
iajs-777	13	50	abstract	abstract	NOUN
iajs-777	13	51	in	in	ADP
iajs-777	13	52	this	this	DET
iajs-777	13	53	paper	paper	NOUN
iajs-777	13	54	,	,	PUNCT
iajs-777	13	55	a	a	DET
iajs-777	13	56	new	new	ADJ
iajs-777	13	57	class	class	NOUN
iajs-777	13	58	of	of	ADP
iajs-777	13	59	sets	set	NOUN
iajs-777	13	60	,	,	PUNCT
iajs-777	13	61	namely	namely	ADV
iajs-777	13	62	semi	semi	NOUN
iajs-777	13	63	-	-	ADJ
iajs-777	13	64	regular	regular	ADJ
iajs-777	13	65	closed	closed	ADJ
iajs-777	13	66	sets	set	NOUN
iajs-777	13	67	is	be	AUX
iajs-777	13	68	introduced	introduce	VERB
iajs-777	13	69	and	and	CCONJ
iajs-777	13	70	studied	study	VERB
iajs-777	13	71	for	for	ADP
iajs-777	13	72	topological	topological	ADJ
iajs-777	13	73	spaces	space	NOUN
iajs-777	13	74	.	.	PUNCT
iajs-777	14	1	this	this	DET
iajs-777	14	2	class	class	NOUN
iajs-777	14	3	properly	properly	ADV
iajs-777	14	4	contains	contain	VERB
iajs-777	14	5	the	the	DET
iajs-777	14	6	class	class	NOUN
iajs-777	14	7	of	of	ADP
iajs-777	14	8	semi--closed	semi--close	VERB
iajs-777	14	9	sets	set	NOUN
iajs-777	14	10	and	and	CCONJ
iajs-777	14	11	is	be	AUX
iajs-777	14	12	property	property	NOUN
iajs-777	14	13	contained	contain	VERB
iajs-777	14	14	in	in	ADP
iajs-777	14	15	the	the	DET
iajs-777	14	16	class	class	NOUN
iajs-777	14	17	of	of	ADP
iajs-777	14	18	pre	pre	ADJ
iajs-777	14	19	-	-	ADJ
iajs-777	14	20	semi	semi	ADJ
iajs-777	14	21	-	-	ADJ
iajs-777	14	22	closed	closed	ADJ
iajs-777	14	23	sets	set	NOUN
iajs-777	14	24	.	.	PUNCT
iajs-777	15	1	also	also	ADV
iajs-777	15	2	,	,	PUNCT
iajs-777	15	3	we	we	PRON
iajs-777	15	4	introduce	introduce	VERB
iajs-777	15	5	and	and	CCONJ
iajs-777	15	6	study	study	VERB
iajs-777	15	7	srcontinuity	srcontinuity	NOUN
iajs-777	15	8	and	and	CCONJ
iajs-777	15	9	sr	sr	NOUN
iajs-777	15	10	-	-	NOUN
iajs-777	15	11	irresoleteness	irresoleteness	ADJ
iajs-777	15	12	.	.	PUNCT
iajs-777	16	1	we	we	PRON
iajs-777	16	2	showed	show	VERB
iajs-777	16	3	that	that	SCONJ
iajs-777	16	4	sr	sr	NOUN
iajs-777	16	5	-	-	PUNCT
iajs-777	16	6	continuity	continuity	NOUN
iajs-777	16	7	falls	fall	VERB
iajs-777	16	8	strictly	strictly	ADV
iajs-777	16	9	in	in	ADP
iajs-777	16	10	between	between	ADP
iajs-777	16	11	semi-continuity	semi-continuity	NOUN
iajs-777	16	12	and	and	CCONJ
iajs-777	16	13	pre	pre	ADJ
iajs-777	16	14	-	-	ADJ
iajs-777	16	15	semi	semi	ADJ
iajs-777	16	16	-	-	NOUN
iajs-777	16	17	continuity	continuity	NOUN
iajs-777	16	18	.	.	PUNCT
iajs-777	17	1	key	key	ADJ
iajs-777	17	2	words	word	NOUN
iajs-777	17	3	:	:	PUNCT
iajs-777	17	4	semi	semi	NOUN
iajs-777	17	5	-	-	ADJ
iajs-777	17	6	regular	regular	ADJ
iajs-777	17	7	closed	closed	ADJ
iajs-777	17	8	set	set	NOUN
iajs-777	17	9	,	,	PUNCT
iajs-777	17	10	semi	semi	NOUN
iajs-777	17	11	-	-	ADJ
iajs-777	17	12	regular	regular	ADJ
iajs-777	17	13	continuous	continuous	ADJ
iajs-777	17	14	,	,	PUNCT
iajs-777	17	15	semi	semi	NOUN
iajs-777	17	16	-	-	PUNCT
iajs-777	17	17	regular	regular	ADJ
iajs-777	17	18	irresolute	irresolute	NOUN
iajs-777	17	19	.	.	PUNCT
iajs-777	18	1	introduction	introduction	NOUN
iajs-777	18	2	najasted	najaste	VERB
iajs-777	19	1	[	[	X
iajs-777	19	2	1	1	X
iajs-777	19	3	]	]	PUNCT
iajs-777	19	4	and	and	CCONJ
iajs-777	19	5	levine	levine	PROPN
iajs-777	19	6	[	[	X
iajs-777	19	7	2	2	NUM
iajs-777	19	8	]	]	PUNCT
iajs-777	19	9	introduced	introduce	VERB
iajs-777	19	10	-open	-open	PROPN
iajs-777	19	11	sets	set	NOUN
iajs-777	19	12	and	and	CCONJ
iajs-777	19	13	generalized	generalize	VERB
iajs-777	19	14	closed	closed	ADJ
iajs-777	19	15	sets	set	NOUN
iajs-777	19	16	,	,	PUNCT
iajs-777	19	17	kummar	kummar	PROPN
iajs-777	19	18	introduced	introduce	VERB
iajs-777	19	19	-generalized	-generalized	ADJ
iajs-777	19	20	regular	regular	ADJ
iajs-777	19	21	closed	close	VERB
iajs-777	19	22	set	set	VERB
iajs-777	19	23	and	and	CCONJ
iajs-777	19	24	pre	pre	ADJ
iajs-777	19	25	-	-	ADJ
iajs-777	19	26	semi	semi	ADJ
iajs-777	19	27	closed	closed	ADJ
iajs-777	19	28	set	set	NOUN
iajs-777	19	29	,	,	PUNCT
iajs-777	19	30	see	see	VERB
iajs-777	19	31	[	[	X
iajs-777	19	32	3	3	X
iajs-777	19	33	]	]	PUNCT
iajs-777	19	34	and	and	CCONJ
iajs-777	19	35	[	[	X
iajs-777	19	36	4	4	NUM
iajs-777	19	37	]	]	PUNCT
iajs-777	19	38	.	.	PUNCT
iajs-777	20	1	alot	alot	NOUN
iajs-777	20	2	of	of	ADP
iajs-777	20	3	work	work	NOUN
iajs-777	20	4	was	be	AUX
iajs-777	20	5	done	do	VERB
iajs-777	20	6	in	in	ADP
iajs-777	20	7	the	the	DET
iajs-777	20	8	field	field	NOUN
iajs-777	20	9	of	of	ADP
iajs-777	20	10	generalized	generalized	ADJ
iajs-777	20	11	closed	closed	ADJ
iajs-777	20	12	sets	set	NOUN
iajs-777	20	13	.	.	PUNCT
iajs-777	21	1	in	in	ADP
iajs-777	21	2	this	this	DET
iajs-777	21	3	paper	paper	NOUN
iajs-777	21	4	we	we	PRON
iajs-777	21	5	employ	employ	VERB
iajs-777	21	6	a	a	DET
iajs-777	21	7	new	new	ADJ
iajs-777	21	8	technique	technique	NOUN
iajs-777	21	9	to	to	PART
iajs-777	21	10	obtain	obtain	VERB
iajs-777	21	11	a	a	DET
iajs-777	21	12	new	new	ADJ
iajs-777	21	13	class	class	NOUN
iajs-777	21	14	of	of	ADP
iajs-777	21	15	sets	set	NOUN
iajs-777	21	16	,	,	PUNCT
iajs-777	21	17	called	call	VERB
iajs-777	21	18	-semi	-semi	PROPN
iajs-777	21	19	-	-	PUNCT
iajs-777	21	20	regular	regular	ADJ
iajs-777	21	21	closed	closed	ADJ
iajs-777	21	22	sets	set	NOUN
iajs-777	21	23	.	.	PUNCT
iajs-777	22	1	this	this	DET
iajs-777	22	2	class	class	NOUN
iajs-777	22	3	is	be	AUX
iajs-777	22	4	obtained	obtain	VERB
iajs-777	22	5	by	by	ADP
iajs-777	22	6	semi--closed	semi--closed	ADJ
iajs-777	22	7	set	set	ADJ
iajs-777	22	8	and	and	CCONJ
iajs-777	22	9	regular	regular	ADJ
iajs-777	22	10	open	open	ADJ
iajs-777	22	11	set	set	NOUN
iajs-777	22	12	.	.	PUNCT
iajs-777	23	1	it	it	PRON
iajs-777	23	2	is	be	AUX
iajs-777	23	3	shown	show	VERB
iajs-777	23	4	that	that	SCONJ
iajs-777	23	5	the	the	DET
iajs-777	23	6	class	class	NOUN
iajs-777	23	7	of	of	ADP
iajs-777	23	8	-semiregular	-semiregular	PROPN
iajs-777	23	9	closed	closed	ADJ
iajs-777	23	10	sets	set	NOUN
iajs-777	23	11	p	p	PRON
iajs-777	23	12	roperly	roperly	ADV
iajs-777	23	13	contains	contain	VERB
iajs-777	23	14	the	the	DET
iajs-777	23	15	class	class	NOUN
iajs-777	23	16	of	of	ADP
iajs-777	23	17	semi--closed	semi--close	VERB
iajs-777	23	18	sets	set	NOUN
iajs-777	23	19	and	and	CCONJ
iajs-777	23	20	is	be	AUX
iajs-777	23	21	properly	properly	ADV
iajs-777	23	22	contained	contain	VERB
iajs-777	23	23	in	in	ADP
iajs-777	23	24	the	the	DET
iajs-777	23	25	class	class	NOUN
iajs-777	23	26	of	of	ADP
iajs-777	23	27	p	p	NOUN
iajs-777	23	28	re	re	ADJ
iajs-777	23	29	-	-	ADJ
iajs-777	23	30	semi	semi	ADJ
iajs-777	23	31	-	-	ADJ
iajs-777	23	32	closed	closed	ADJ
iajs-777	23	33	sets	set	NOUN
iajs-777	23	34	.	.	PUNCT
iajs-777	24	1	we	we	PRON
iajs-777	24	2	also	also	ADV
iajs-777	24	3	introduce	introduce	VERB
iajs-777	24	4	and	and	CCONJ
iajs-777	24	5	study	study	VERB
iajs-777	24	6	two	two	NUM
iajs-777	24	7	classes	class	NOUN
iajs-777	24	8	of	of	ADP
iajs-777	24	9	maps	map	NOUN
iajs-777	24	10	,	,	PUNCT
iajs-777	24	11	namely	namely	ADV
iajs-777	24	12	,	,	PUNCT
iajs-777	24	13	-semi	-semi	PROPN
iajs-777	24	14	-	-	PUNCT
iajs-777	24	15	regular	regular	ADJ
iajs-777	24	16	continuity	continuity	NOUN
iajs-777	24	17	and	and	CCONJ
iajs-777	24	18	-semi	-semi	PROPN
iajs-777	24	19	-	-	PUNCT
iajs-777	24	20	regular	regular	ADJ
iajs-777	24	21	irresoluteness	irresoluteness	NOUN
iajs-777	24	22	,	,	PUNCT
iajs-777	24	23	-semi	-semi	PROPN
iajs-777	24	24	-	-	PUNCT
iajs-777	24	25	regular	regular	ADJ
iajs-777	24	26	continuity	continuity	NOUN
iajs-777	24	27	falls	fall	VERB
iajs-777	24	28	strictly	strictly	ADV
iajs-777	24	29	in	in	ADP
iajs-777	24	30	between	between	ADP
iajs-777	24	31	semi--continuity	semi--continuity	PROPN
iajs-777	24	32	and	and	CCONJ
iajs-777	24	33	pre	pre	ADJ
iajs-777	24	34	-	-	ADJ
iajs-777	24	35	semi	semi	ADJ
iajs-777	24	36	-	-	NOUN
iajs-777	24	37	continuity	continuity	NOUN
iajs-777	24	38	.	.	PUNCT
iajs-777	25	1	1preliminaries	1preliminaries	NUM
iajs-777	25	2	throughout	throughout	ADP
iajs-777	25	3	this	this	DET
iajs-777	25	4	paper	paper	NOUN
iajs-777	25	5	(	(	PUNCT
iajs-777	25	6	x,	x,	PROPN
iajs-777	25	7	)	)	PUNCT
iajs-777	25	8	and	and	CCONJ
iajs-777	25	9	(	(	PUNCT
iajs-777	25	10	y,	y,	PROPN
iajs-777	25	11	'	'	PUNCT
iajs-777	25	12	)	)	PUNCT
iajs-777	25	13	represent	represent	VERB
iajs-777	25	14	non	non	ADJ
iajs-777	25	15	-	-	ADJ
iajs-777	25	16	empty	empty	ADJ
iajs-777	25	17	topological	topological	ADJ
iajs-777	25	18	spaces	space	NOUN
iajs-777	25	19	.	.	PUNCT
iajs-777	26	1	for	for	ADP
iajs-777	26	2	a	a	DET
iajs-777	26	3	subset	subset	NOUN
iajs-777	26	4	a	a	PRON
iajs-777	26	5	of	of	ADP
iajs-777	26	6	a	a	DET
iajs-777	26	7	space	space	NOUN
iajs-777	26	8	(	(	PUNCT
iajs-777	26	9	x,	x,	PROPN
iajs-777	26	10	)	)	PUNCT
iajs-777	26	11	,	,	PUNCT
iajs-777	26	12	cl(a	cl(a	NUM
iajs-777	26	13	)	)	PUNCT
iajs-777	26	14	and	and	CCONJ
iajs-777	26	15	int(a	int(a	PROPN
iajs-777	26	16	)	)	PUNCT
iajs-777	26	17	represent	represent	VERB
iajs-777	26	18	the	the	DET
iajs-777	26	19	closure	closure	NOUN
iajs-777	26	20	of	of	ADP
iajs-777	26	21	a	a	PRON
iajs-777	26	22	and	and	CCONJ
iajs-777	26	23	the	the	DET
iajs-777	26	24	interior	interior	NOUN
iajs-777	26	25	of	of	ADP
iajs-777	26	26	a	a	DET
iajs-777	26	27	respectively	respectively	ADV
iajs-777	26	28	.	.	PUNCT
iajs-777	27	1	1.1	1.1	NUM
iajs-777	27	2	definition	definition	NOUN
iajs-777	27	3	:	:	PUNCT
iajs-777	27	4	a	a	DET
iajs-777	27	5	subset	subset	NOUN
iajs-777	27	6	a	a	PRON
iajs-777	27	7	of	of	ADP
iajs-777	27	8	a	a	DET
iajs-777	27	9	space	space	NOUN
iajs-777	27	10	(	(	PUNCT
iajs-777	27	11	x,	x,	X
iajs-777	27	12	)	)	PUNCT
iajs-777	27	13	is	be	AUX
iajs-777	27	14	called	call	VERB
iajs-777	27	15	(	(	PUNCT
iajs-777	27	16	1	1	NUM
iajs-777	27	17	)	)	PUNCT
iajs-777	27	18	an	an	DET
iajs-777	27	19	-open	-open	PROPN
iajs-777	27	20	set	set	NOUN
iajs-777	27	21	[	[	X
iajs-777	27	22	1	1	NUM
iajs-777	27	23	]	]	PUNCT
iajs-777	27	24	,	,	PUNCT
iajs-777	27	25	[	[	X
iajs-777	27	26	5	5	X
iajs-777	27	27	]	]	PUNCT
iajs-777	27	28	if	if	SCONJ
iajs-777	27	29	a	a	DET
iajs-777	27	30			PROPN
iajs-777	27	31	int(cl(int(a	int(cl(int(a	PROPN
iajs-777	27	32	)	)	PUNCT
iajs-777	27	33	)	)	PUNCT
iajs-777	27	34	)	)	PUNCT
iajs-777	27	35	and	and	CCONJ
iajs-777	27	36	-closed	-close	VERB
iajs-777	27	37	if	if	SCONJ
iajs-777	27	38	cl(int(cl(a	cl(int(cl(a	NOUN
iajs-777	27	39	)	)	PUNCT
iajs-777	27	40	)	)	PUNCT
iajs-777	27	41	)	)	PUNCT
iajs-777	28	1			PROPN
iajs-777	28	2	a.	a.	NOUN
iajs-777	28	3	(	(	PUNCT
iajs-777	28	4	2	2	NUM
iajs-777	28	5	)	)	PUNCT
iajs-777	28	6	a	a	DET
iajs-777	28	7	semi--open	semi--open	PUNCT
iajs-777	28	8	set	set	NOUN
iajs-777	28	9	[	[	X
iajs-777	28	10	6	6	NUM
iajs-777	28	11	]	]	PUNCT
iajs-777	28	12	,	,	PUNCT
iajs-777	28	13	[	[	X
iajs-777	28	14	7	7	X
iajs-777	28	15	]	]	X
iajs-777	28	16	if	if	SCONJ
iajs-777	28	17	a	a	DET
iajs-777	28	18			NOUN
iajs-777	28	19	cl(int(cl(int(a	cl(int(cl(int(a	PROPN
iajs-777	28	20	)	)	PUNCT
iajs-777	28	21	)	)	PUNCT
iajs-777	28	22	)	)	PUNCT
iajs-777	28	23	)	)	PUNCT
iajs-777	28	24	and	and	CCONJ
iajs-777	28	25	semi--closed	semi--close	VERB
iajs-777	28	26	if	if	SCONJ
iajs-777	28	27	int(cl(int(cl(a	int(cl(int(cl(a	ADJ
iajs-777	28	28	)	)	PUNCT
iajs-777	28	29	)	)	PUNCT
iajs-777	28	30	)	)	PUNCT
iajs-777	28	31	)	)	PUNCT
iajs-777	29	1			PROPN
iajs-777	29	2	a.	a.	NOUN
iajs-777	29	3	(	(	PUNCT
iajs-777	29	4	3	3	X
iajs-777	29	5	)	)	PUNCT
iajs-777	29	6	a	a	DET
iajs-777	29	7	semi	semi	ADJ
iajs-777	29	8	-	-	ADJ
iajs-777	29	9	preopen	preopen	ADJ
iajs-777	29	10	set	set	NOUN
iajs-777	29	11	[	[	X
iajs-777	29	12	8	8	NUM
iajs-777	29	13	]	]	PUNCT
iajs-777	29	14	,	,	PUNCT
iajs-777	29	15	[	[	X
iajs-777	29	16	9	9	X
iajs-777	29	17	]	]	X
iajs-777	29	18	if	if	SCONJ
iajs-777	29	19	a	a	DET
iajs-777	29	20			PROPN
iajs-777	29	21	cl(int(cl(a	cl(int(cl(a	NOUN
iajs-777	29	22	)	)	PUNCT
iajs-777	29	23	)	)	PUNCT
iajs-777	29	24	)	)	PUNCT
iajs-777	29	25	and	and	CCONJ
iajs-777	29	26	semi	semi	ADV
iajs-777	29	27	-	-	ADJ
iajs-777	29	28	preclosed	preclosed	ADJ
iajs-777	29	29	if	if	SCONJ
iajs-777	29	30	int(cl(int(a	int(cl(int(a	PROPN
iajs-777	29	31	)	)	PUNCT
iajs-777	29	32	)	)	PUNCT
iajs-777	29	33	)	)	PUNCT
iajs-777	30	1			PROPN
iajs-777	30	2	a.	a.	NOUN
iajs-777	30	3	(	(	PUNCT
iajs-777	30	4	4	4	NUM
iajs-777	30	5	)	)	PUNCT
iajs-777	30	6	a	a	DET
iajs-777	30	7	regular	regular	ADJ
iajs-777	30	8	open	open	ADJ
iajs-777	30	9	set	set	NOUN
iajs-777	30	10	[	[	X
iajs-777	30	11	10	10	NUM
iajs-777	30	12	]	]	PUNCT
iajs-777	30	13	,	,	PUNCT
iajs-777	30	14	[	[	X
iajs-777	30	15	11	11	NUM
iajs-777	30	16	]	]	X
iajs-777	30	17	if	if	SCONJ
iajs-777	30	18	a	a	PRON
iajs-777	30	19	=	=	SYM
iajs-777	30	20	int(cl(a	int(cl(a	PROPN
iajs-777	30	21	)	)	PUNCT
iajs-777	30	22	)	)	PUNCT
iajs-777	30	23	and	and	CCONJ
iajs-777	30	24	regular	regular	ADJ
iajs-777	30	25	closed	close	VERB
iajs-777	30	26	if	if	SCONJ
iajs-777	30	27	a	a	DET
iajs-777	30	28	=	=	NOUN
iajs-777	30	29	cl(int(a	cl(int(a	NOUN
iajs-777	30	30	)	)	PUNCT
iajs-777	30	31	)	)	PUNCT
iajs-777	30	32	.	.	PUNCT
iajs-777	31	1	(	(	PUNCT
iajs-777	31	2	5	5	X
iajs-777	31	3	)	)	PUNCT
iajs-777	31	4	a	a	DET
iajs-777	31	5	generalized	generalize	VERB
iajs-777	31	6	closed	close	VERB
iajs-777	31	7	set	set	NOUN
iajs-777	31	8	(	(	PUNCT
iajs-777	31	9	briefly	briefly	NOUN
iajs-777	31	10	g	g	NOUN
iajs-777	31	11	-	-	PUNCT
iajs-777	31	12	closed	closed	ADJ
iajs-777	31	13	)	)	PUNCT
iajs-777	32	1	[	[	X
iajs-777	32	2	2	2	NUM
iajs-777	32	3	]	]	PUNCT
iajs-777	32	4	,	,	PUNCT
iajs-777	32	5	[	[	X
iajs-777	32	6	12	12	NUM
iajs-777	32	7	]	]	X
iajs-777	32	8	if	if	SCONJ
iajs-777	32	9	cl(a	cl(a	NUM
iajs-777	32	10	)	)	PUNCT
iajs-777	32	11			PROPN
iajs-777	32	12	u	u	PROPN
iajs-777	32	13	whenever	whenever	SCONJ
iajs-777	32	14	a	a	DET
iajs-777	32	15			PROPN
iajs-777	32	16	u	u	NOUN
iajs-777	32	17	and	and	CCONJ
iajs-777	32	18	u	u	NOUN
iajs-777	32	19	is	be	AUX
iajs-777	32	20	open	open	ADJ
iajs-777	32	21	in	in	ADP
iajs-777	32	22	(	(	PUNCT
iajs-777	32	23	x,	x,	PROPN
iajs-777	32	24	)	)	PUNCT
iajs-777	32	25	.	.	PUNCT
iajs-777	33	1	the	the	DET
iajs-777	33	2	complement	complement	NOUN
iajs-777	33	3	of	of	ADP
iajs-777	33	4	a	a	DET
iajs-777	33	5	g	g	NOUN
iajs-777	33	6	-	-	PUNCT
iajs-777	33	7	closed	close	VERB
iajs-777	33	8	set	set	NOUN
iajs-777	33	9	is	be	AUX
iajs-777	33	10	called	call	VERB
iajs-777	33	11	a	a	DET
iajs-777	33	12	g	g	NOUN
iajs-777	33	13	-	-	PUNCT
iajs-777	33	14	open	open	ADJ
iajs-777	33	15	set	set	NOUN
iajs-777	33	16	.	.	PUNCT
iajs-777	34	1	(	(	PUNCT
iajs-777	34	2	6	6	NUM
iajs-777	34	3	)	)	PUNCT
iajs-777	34	4	an	an	DET
iajs-777	34	5	-generalized	-generalized	PROPN
iajs-777	34	6	closed	close	VERB
iajs-777	34	7	set	set	NOUN
iajs-777	34	8	(	(	PUNCT
iajs-777	34	9	briefly	briefly	ADV
iajs-777	34	10	g	g	ADV
iajs-777	34	11	-	-	PUNCT
iajs-777	34	12	closed	closed	ADJ
iajs-777	34	13	)	)	PUNCT
iajs-777	35	1	[	[	X
iajs-777	35	2	13	13	NUM
iajs-777	35	3	]	]	PUNCT
iajs-777	35	4	if	if	SCONJ
iajs-777	35	5			NOUN
iajs-777	35	6	cl(a	cl(a	NUM
iajs-777	35	7	)	)	PUNCT
iajs-777	35	8			PROPN
iajs-777	35	9	u	u	PROPN
iajs-777	35	10	whenever	whenever	SCONJ
iajs-777	35	11	a	a	DET
iajs-777	35	12			PROPN
iajs-777	35	13	u	u	NOUN
iajs-777	35	14	and	and	CCONJ
iajs-777	35	15	u	u	NOUN
iajs-777	35	16	is	be	AUX
iajs-777	35	17	open	open	ADJ
iajs-777	35	18	in	in	ADP
iajs-777	35	19	(	(	PUNCT
iajs-777	35	20	x,	x,	X
iajs-777	35	21	)	)	PUNCT
iajs-777	35	22	.	.	PUNCT
iajs-777	36	1	(	(	PUNCT
iajs-777	36	2	7	7	X
iajs-777	36	3	)	)	PUNCT
iajs-777	36	4	a	a	DET
iajs-777	36	5	generalized	generalized	ADJ
iajs-777	36	6	-closed	-closed	ADJ
iajs-777	36	7	set	set	NOUN
iajs-777	36	8	(	(	PUNCT
iajs-777	36	9	briefly	briefly	ADV
iajs-777	36	10	g-closed	g-close	VERB
iajs-777	36	11	)	)	PUNCT
iajs-777	37	1	[	[	X
iajs-777	37	2	14	14	NUM
iajs-777	37	3	]	]	X
iajs-777	37	4	if	if	SCONJ
iajs-777	37	5	cl(a	cl(a	VERB
iajs-777	37	6	)	)	PUNCT
iajs-777	37	7			PROPN
iajs-777	37	8	u	u	PROPN
iajs-777	37	9	whenever	whenever	SCONJ
iajs-777	37	10	a	a	DET
iajs-777	37	11			PROPN
iajs-777	37	12	u	u	NOUN
iajs-777	37	13	and	and	CCONJ
iajs-777	37	14	u	u	NOUN
iajs-777	37	15	is	be	AUX
iajs-777	37	16	-open	-open	PROPN
iajs-777	37	17	in	in	ADP
iajs-777	37	18	(	(	PUNCT
iajs-777	37	19	x,	x,	X
iajs-777	37	20	)	)	PUNCT
iajs-777	37	21	.	.	PUNCT
iajs-777	38	1	(	(	PUNCT
iajs-777	38	2	8)	8)	NUM
iajs-777	38	3	a	a	DET
iajs-777	38	4	generalized	generalized	ADJ
iajs-777	38	5	*-closed	*-close	VERB
iajs-777	38	6	set	set	NOUN
iajs-777	38	7	(	(	PUNCT
iajs-777	38	8	briefly	briefly	ADV
iajs-777	38	9	g*-closed	g*-close	VERB
iajs-777	38	10	)	)	PUNCT
iajs-777	39	1	[	[	X
iajs-777	39	2	14	14	NUM
iajs-777	39	3	]	]	X
iajs-777	39	4	if	if	SCONJ
iajs-777	39	5	cl(a	cl(a	VERB
iajs-777	39	6	)	)	PUNCT
iajs-777	39	7			PROPN
iajs-777	39	8	int(u	int(u	PROPN
iajs-777	39	9	)	)	PUNCT
iajs-777	39	10	whenever	whenever	SCONJ
iajs-777	39	11	a	a	DET
iajs-777	39	12			PROPN
iajs-777	39	13	u	u	NOUN
iajs-777	39	14	and	and	CCONJ
iajs-777	39	15	u	u	NOUN
iajs-777	39	16	is	be	AUX
iajs-777	39	17	-open	-open	PROPN
iajs-777	39	18	in	in	ADP
iajs-777	39	19	(	(	PUNCT
iajs-777	39	20	x,	x,	X
iajs-777	39	21	)	)	PUNCT
iajs-777	39	22	.	.	PUNCT
iajs-777	40	1	ibn	ibn	PROPN
iajs-777	40	2	alhaitham	alhaitham	PROPN
iajs-777	40	3	j.	j.	PROPN
iajs-777	40	4	for	for	ADP
iajs-777	40	5	pure	pure	ADJ
iajs-777	40	6	&	&	CCONJ
iajs-777	40	7	appl	appl	PROPN
iajs-777	40	8	.	.	PUNCT
iajs-777	41	1	sci	sci	PROPN
iajs-777	41	2	.	.	PUNCT
iajs-777	41	3	vol.24	vol.24	NOUN
iajs-777	41	4	(	(	PUNCT
iajs-777	41	5	2	2	NUM
iajs-777	41	6	)	)	PUNCT
iajs-777	41	7	2011	2011	NUM
iajs-777	41	8	(	(	PUNCT
iajs-777	41	9	9	9	NUM
iajs-777	41	10	)	)	PUNCT
iajs-777	41	11	an	an	DET
iajs-777	41	12	**-generalized	**-generalize	VERB
iajs-777	41	13	closed	closed	ADJ
iajs-777	41	14	set	set	NOUN
iajs-777	41	15	(	(	PUNCT
iajs-777	41	16	briefly	briefly	ADV
iajs-777	41	17	**g	**g	NOUN
iajs-777	41	18	-	-	PUNCT
iajs-777	41	19	closed	closed	ADJ
iajs-777	41	20	)	)	PUNCT
iajs-777	42	1	[	[	X
iajs-777	42	2	14	14	NUM
iajs-777	42	3	]	]	X
iajs-777	42	4	if	if	SCONJ
iajs-777	42	5			NOUN
iajs-777	42	6	cl(a	cl(a	NUM
iajs-777	42	7	)	)	PUNCT
iajs-777	42	8			PROPN
iajs-777	42	9	int(cl(u	int(cl(u	PROPN
iajs-777	42	10	)	)	PUNCT
iajs-777	42	11	)	)	PUNCT
iajs-777	43	1	whenever	whenever	SCONJ
iajs-777	43	2	a	a	DET
iajs-777	43	3			PROPN
iajs-777	43	4	u	u	NOUN
iajs-777	43	5	and	and	CCONJ
iajs-777	43	6	u	u	NOUN
iajs-777	43	7	is	be	AUX
iajs-777	43	8	open	open	ADJ
iajs-777	43	9	in	in	ADP
iajs-777	43	10	(	(	PUNCT
iajs-777	43	11	x,	x,	X
iajs-777	43	12	)	)	PUNCT
iajs-777	43	13	.	.	PUNCT
iajs-777	44	1	(	(	PUNCT
iajs-777	44	2	10	10	NUM
iajs-777	44	3	)	)	PUNCT
iajs-777	44	4	a	a	DET
iajs-777	44	5	generalized	generalize	VERB
iajs-777	44	6	**-closed	**-close	VERB
iajs-777	44	7	set	set	NOUN
iajs-777	44	8	(	(	PUNCT
iajs-777	44	9	briefly	briefly	ADV
iajs-777	44	10	g**-closed	g**-close	VERB
iajs-777	44	11	)	)	PUNCT
iajs-777	45	1	[	[	X
iajs-777	45	2	14	14	NUM
iajs-777	45	3	]	]	X
iajs-777	45	4	if	if	SCONJ
iajs-777	45	5	cl(a	cl(a	VERB
iajs-777	45	6	)	)	PUNCT
iajs-777	45	7			PROPN
iajs-777	45	8	int(cl(u	int(cl(u	PROPN
iajs-777	45	9	)	)	PUNCT
iajs-777	45	10	)	)	PUNCT
iajs-777	46	1	whenever	whenever	SCONJ
iajs-777	46	2	a	a	DET
iajs-777	46	3			PROPN
iajs-777	46	4	u	u	NOUN
iajs-777	46	5	and	and	CCONJ
iajs-777	46	6	u	u	NOUN
iajs-777	46	7	is	be	AUX
iajs-777	46	8	-open	-open	PROPN
iajs-777	46	9	in	in	ADP
iajs-777	46	10	(	(	PUNCT
iajs-777	46	11	x,	x,	X
iajs-777	46	12	)	)	PUNCT
iajs-777	46	13	.	.	PUNCT
iajs-777	47	1	(	(	PUNCT
iajs-777	47	2	11	11	NUM
iajs-777	47	3	)	)	PUNCT
iajs-777	47	4	a	a	DET
iajs-777	47	5	regular	regular	ADJ
iajs-777	47	6	generalized	generalize	VERB
iajs-777	47	7	closed	close	VERB
iajs-777	47	8	set	set	NOUN
iajs-777	47	9	(	(	PUNCT
iajs-777	47	10	briefly	briefly	NOUN
iajs-777	47	11	rg	rg	NOUN
iajs-777	47	12	-	-	PUNCT
iajs-777	47	13	closed	closed	ADJ
iajs-777	47	14	)	)	PUNCT
iajs-777	48	1	[	[	X
iajs-777	48	2	15	15	NUM
iajs-777	48	3	]	]	X
iajs-777	48	4	if	if	SCONJ
iajs-777	48	5	cl(a	cl(a	NUM
iajs-777	48	6	)	)	PUNCT
iajs-777	48	7			PROPN
iajs-777	48	8	u	u	PROPN
iajs-777	48	9	whenever	whenever	SCONJ
iajs-777	48	10	a	a	DET
iajs-777	48	11			PROPN
iajs-777	48	12	u	u	NOUN
iajs-777	48	13	and	and	CCONJ
iajs-777	48	14	u	u	NOUN
iajs-777	48	15	is	be	AUX
iajs-777	48	16	regular	regular	ADJ
iajs-777	48	17	open	open	ADJ
iajs-777	48	18	in	in	ADP
iajs-777	48	19	(	(	PUNCT
iajs-777	48	20	x,	x,	X
iajs-777	48	21	)	)	PUNCT
iajs-777	48	22	.	.	PUNCT
iajs-777	49	1	(	(	PUNCT
iajs-777	49	2	12	12	NUM
iajs-777	49	3	)	)	PUNCT
iajs-777	49	4	an	an	DET
iajs-777	49	5	-generalized	-generalized	ADJ
iajs-777	49	6	regular	regular	ADJ
iajs-777	49	7	closed	close	VERB
iajs-777	49	8	set	set	NOUN
iajs-777	49	9	(	(	PUNCT
iajs-777	49	10	briefly	briefly	ADV
iajs-777	49	11	gr	gr	ADV
iajs-777	49	12	-	-	PUNCT
iajs-777	49	13	closed	closed	ADJ
iajs-777	49	14	)	)	PUNCT
iajs-777	50	1	[	[	X
iajs-777	50	2	3	3	X
iajs-777	50	3	]	]	PUNCT
iajs-777	50	4	if	if	SCONJ
iajs-777	50	5	cl(a	cl(a	VERB
iajs-777	50	6	)	)	PUNCT
iajs-777	50	7			PROPN
iajs-777	50	8	u	u	PROPN
iajs-777	50	9	whenever	whenever	SCONJ
iajs-777	50	10	a	a	DET
iajs-777	50	11			PROPN
iajs-777	50	12	u	u	NOUN
iajs-777	50	13	and	and	CCONJ
iajs-777	50	14	u	u	NOUN
iajs-777	50	15	is	be	AUX
iajs-777	50	16	regular	regular	ADJ
iajs-777	50	17	open	open	ADJ
iajs-777	50	18	in	in	ADP
iajs-777	50	19	(	(	PUNCT
iajs-777	50	20	x,	x,	X
iajs-777	50	21	)	)	PUNCT
iajs-777	50	22	.	.	PUNCT
iajs-777	51	1	(	(	PUNCT
iajs-777	51	2	13	13	NUM
iajs-777	51	3	)	)	PUNCT
iajs-777	51	4	a	a	DET
iajs-777	51	5	generalized	generalized	ADJ
iajs-777	51	6	semi	semi	ADJ
iajs-777	51	7	-	-	ADJ
iajs-777	51	8	preclosed	preclosed	ADJ
iajs-777	51	9	set	set	NOUN
iajs-777	51	10	(	(	PUNCT
iajs-777	51	11	briefly	briefly	ADV
iajs-777	51	12	gsp	gsp	VERB
iajs-777	51	13	-	-	PUNCT
iajs-777	51	14	closed	close	VERB
iajs-777	51	15	)	)	PUNCT
iajs-777	52	1	[	[	X
iajs-777	52	2	16	16	NUM
iajs-777	52	3	]	]	X
iajs-777	52	4	if	if	SCONJ
iajs-777	52	5	spcl(a	spcl(a	NUM
iajs-777	52	6	)	)	PUNCT
iajs-777	52	7			PROPN
iajs-777	52	8	u	u	PROPN
iajs-777	52	9	whenever	whenever	SCONJ
iajs-777	52	10	a	a	DET
iajs-777	52	11			PROPN
iajs-777	52	12	u	u	NOUN
iajs-777	52	13	and	and	CCONJ
iajs-777	52	14	u	u	NOUN
iajs-777	52	15	is	be	AUX
iajs-777	52	16	open	open	ADJ
iajs-777	52	17	in	in	ADP
iajs-777	52	18	(	(	PUNCT
iajs-777	52	19	x,	x,	X
iajs-777	52	20	)	)	PUNCT
iajs-777	52	21	.	.	PUNCT
iajs-777	53	1	(	(	PUNCT
iajs-777	53	2	14	14	NUM
iajs-777	53	3	)	)	PUNCT
iajs-777	53	4	a	a	DET
iajs-777	53	5	pre	pre	ADJ
iajs-777	53	6	-	-	ADJ
iajs-777	53	7	semi	semi	ADJ
iajs-777	53	8	-	-	ADJ
iajs-777	53	9	closed	closed	ADJ
iajs-777	53	10	set	set	NOUN
iajs-777	53	11	[	[	X
iajs-777	53	12	4	4	X
iajs-777	53	13	]	]	PUNCT
iajs-777	53	14	if	if	SCONJ
iajs-777	53	15	spcl(a	spcl(a	NUM
iajs-777	53	16	)	)	PUNCT
iajs-777	53	17			PROPN
iajs-777	53	18	u	u	PROPN
iajs-777	53	19	whenever	whenever	SCONJ
iajs-777	53	20	a	a	DET
iajs-777	53	21			PROPN
iajs-777	53	22	u	u	NOUN
iajs-777	53	23	and	and	CCONJ
iajs-777	53	24	u	u	NOUN
iajs-777	53	25	is	be	AUX
iajs-777	53	26	g	g	NOUN
iajs-777	53	27	-	-	PUNCT
iajs-777	53	28	open	open	ADJ
iajs-777	53	29	in	in	ADP
iajs-777	53	30	(	(	PUNCT
iajs-777	53	31	x,	x,	PROPN
iajs-777	53	32	)	)	PUNCT
iajs-777	53	33	.	.	PUNCT
iajs-777	54	1	the	the	DET
iajs-777	54	2	semi--closure	semi--closure	PROPN
iajs-777	54	3	(	(	PUNCT
iajs-777	54	4	resp	resp	NOUN
iajs-777	54	5	.	.	PUNCT
iajs-777	55	1	-closure	-closure	NOUN
iajs-777	55	2	,	,	PUNCT
iajs-777	55	3	semi	semi	ADJ
iajs-777	55	4	-	-	ADJ
iajs-777	55	5	pre	pre	ADJ
iajs-777	55	6	-	-	NOUN
iajs-777	55	7	closure	closure	NOUN
iajs-777	55	8	)	)	PUNCT
iajs-777	55	9	of	of	ADP
iajs-777	55	10	a	a	DET
iajs-777	55	11	in	in	ADP
iajs-777	55	12	(	(	PUNCT
iajs-777	55	13	x,	x,	X
iajs-777	55	14	)	)	PUNCT
iajs-777	55	15	is	be	AUX
iajs-777	55	16	the	the	DET
iajs-777	55	17	intersection	intersection	NOUN
iajs-777	55	18	of	of	ADP
iajs-777	55	19	all	all	DET
iajs-777	55	20	semi--closed	semi--closed	ADJ
iajs-777	55	21	(	(	PUNCT
iajs-777	55	22	resp	resp	NOUN
iajs-777	55	23	.	.	PUNCT
iajs-777	56	1	-closure	-closure	NOUN
iajs-777	56	2	,	,	PUNCT
iajs-777	56	3	semi	semi	ADJ
iajs-777	56	4	-	-	ADJ
iajs-777	56	5	pre	pre	ADJ
iajs-777	56	6	-	-	ADJ
iajs-777	56	7	closure	closure	ADJ
iajs-777	56	8	)	)	PUNCT
iajs-777	56	9	sets	set	NOUN
iajs-777	56	10	of	of	ADP
iajs-777	56	11	(	(	PUNCT
iajs-777	56	12	x,	x,	X
iajs-777	56	13	)	)	PUNCT
iajs-777	56	14	that	that	PRON
iajs-777	56	15	contain	contain	VERB
iajs-777	56	16	a	a	PRON
iajs-777	56	17	and	and	CCONJ
iajs-777	56	18	is	be	AUX
iajs-777	56	19	denoted	denote	VERB
iajs-777	56	20	by	by	ADP
iajs-777	56	21	scl(a	scl(a	NOUN
iajs-777	56	22	)	)	PUNCT
iajs-777	56	23	(	(	PUNCT
iajs-777	56	24	resp	resp	NOUN
iajs-777	56	25	.	.	PUNCT
iajs-777	57	1	cl(a	cl(a	PROPN
iajs-777	57	2	)	)	PUNCT
iajs-777	57	3	,	,	PUNCT
iajs-777	57	4	spcl(a	spcl(a	NUM
iajs-777	57	5	)	)	PUNCT
iajs-777	57	6	)	)	PUNCT
iajs-777	57	7	.	.	PUNCT
iajs-777	58	1	1.2	1.2	NUM
iajs-777	58	2	proposition	proposition	NOUN
iajs-777	58	3	:	:	PUNCT
iajs-777	58	4	(	(	PUNCT
iajs-777	58	5	1	1	X
iajs-777	58	6	)	)	PUNCT
iajs-777	58	7	every	every	DET
iajs-777	58	8	-closed	-closed	ADJ
iajs-777	58	9	set	set	NOUN
iajs-777	58	10	is	be	AUX
iajs-777	58	11	semi--closed	semi--close	VERB
iajs-777	58	12	set	set	ADJ
iajs-777	58	13	,	,	PUNCT
iajs-777	58	14	not	not	PART
iajs-777	58	15	conversely	conversely	ADV
iajs-777	58	16	,	,	PUNCT
iajs-777	59	1	[	[	X
iajs-777	59	2	6	6	NUM
iajs-777	59	3	]	]	PUNCT
iajs-777	59	4	.	.	PUNCT
iajs-777	60	1	(	(	PUNCT
iajs-777	60	2	2	2	X
iajs-777	60	3	)	)	PUNCT
iajs-777	60	4	every	every	DET
iajs-777	60	5	closed	closed	ADJ
iajs-777	60	6	set	set	NOUN
iajs-777	60	7	is	be	AUX
iajs-777	60	8	-closed	-close	VERB
iajs-777	60	9	set	set	NOUN
iajs-777	60	10	,	,	PUNCT
iajs-777	60	11	so	so	CCONJ
iajs-777	60	12	it	it	PRON
iajs-777	60	13	is	be	AUX
iajs-777	60	14	semi--closed	semi--close	VERB
iajs-777	60	15	set	set	ADJ
iajs-777	60	16	,	,	PUNCT
iajs-777	60	17	not	not	PART
iajs-777	60	18	conversely	conversely	ADV
iajs-777	60	19	,	,	PUNCT
iajs-777	60	20	[	[	X
iajs-777	60	21	6	6	NUM
iajs-777	60	22	]	]	PUNCT
iajs-777	60	23	.	.	PUNCT
iajs-777	61	1	(	(	PUNCT
iajs-777	61	2	3	3	X
iajs-777	61	3	)	)	PUNCT
iajs-777	61	4	every	every	DET
iajs-777	61	5	closed	closed	ADJ
iajs-777	61	6	(	(	PUNCT
iajs-777	61	7	resp	resp	NOUN
iajs-777	61	8	.	.	PUNCT
iajs-777	62	1	-closed	-closed	ADJ
iajs-777	62	2	,	,	PUNCT
iajs-777	62	3	g	g	NOUN
iajs-777	62	4	-	-	PUNCT
iajs-777	62	5	closed	closed	ADJ
iajs-777	62	6	,	,	PUNCT
iajs-777	62	7	g-closed	g-close	VERB
iajs-777	62	8	)	)	PUNCT
iajs-777	62	9	set	set	NOUN
iajs-777	62	10	is	be	AUX
iajs-777	62	11	an	an	DET
iajs-777	62	12	gr	gr	ADV
iajs-777	62	13	-	-	PUNCT
iajs-777	62	14	closed	closed	ADJ
iajs-777	62	15	set	set	NOUN
iajs-777	62	16	,	,	PUNCT
iajs-777	62	17	[	[	X
iajs-777	62	18	3	3	NUM
iajs-777	62	19	]	]	PUNCT
iajs-777	62	20	.	.	PUNCT
iajs-777	63	1	(	(	PUNCT
iajs-777	63	2	4	4	X
iajs-777	63	3	)	)	PUNCT
iajs-777	63	4	every	every	DET
iajs-777	63	5	g*-closed	g*-closed	PROPN
iajs-777	63	6	(	(	PUNCT
iajs-777	63	7	resp	resp	NOUN
iajs-777	63	8	.	.	PUNCT
iajs-777	64	1	**g	**g	NOUN
iajs-777	64	2	-	-	PUNCT
iajs-777	64	3	closed	closed	ADJ
iajs-777	64	4	,	,	PUNCT
iajs-777	64	5	g**-closed	g**-close	VERB
iajs-777	64	6	set	set	NOUN
iajs-777	64	7	is	be	AUX
iajs-777	64	8	an	an	DET
iajs-777	64	9	gr	gr	ADV
iajs-777	64	10	-	-	PUNCT
iajs-777	64	11	closed	closed	ADJ
iajs-777	64	12	set	set	NOUN
iajs-777	64	13	,	,	PUNCT
iajs-777	64	14	[	[	X
iajs-777	64	15	3	3	NUM
iajs-777	64	16	]	]	PUNCT
iajs-777	64	17	.	.	PUNCT
iajs-777	65	1	(	(	PUNCT
iajs-777	65	2	5	5	X
iajs-777	65	3	)	)	PUNCT
iajs-777	65	4	every	every	DET
iajs-777	65	5	pre	pre	ADJ
iajs-777	65	6	-	-	ADJ
iajs-777	65	7	semi	semi	ADJ
iajs-777	65	8	-	-	ADJ
iajs-777	65	9	closed	closed	ADJ
iajs-777	65	10	set	set	VERB
iajs-777	65	11	ia	ia	PROPN
iajs-777	65	12	gsp	gsp	PROPN
iajs-777	65	13	-	-	PUNCT
iajs-777	65	14	closed	close	VERB
iajs-777	65	15	set	set	NOUN
iajs-777	65	16	[	[	X
iajs-777	65	17	4	4	NUM
iajs-777	65	18	]	]	PUNCT
iajs-777	65	19	.	.	PUNCT
iajs-777	66	1	(	(	PUNCT
iajs-777	66	2	6	6	X
iajs-777	66	3	)	)	PUNCT
iajs-777	66	4	every	every	DET
iajs-777	66	5	semi--closed	semi--closed	ADJ
iajs-777	66	6	set	set	NOUN
iajs-777	66	7	is	be	AUX
iajs-777	66	8	semi	semi	ADJ
iajs-777	66	9	-	-	ADJ
iajs-777	66	10	pre	pre	ADJ
iajs-777	66	11	-	-	ADJ
iajs-777	66	12	closed	closed	ADJ
iajs-777	66	13	set	set	NOUN
iajs-777	66	14	(	(	PUNCT
iajs-777	66	15	the	the	DET
iajs-777	66	16	proof	proof	NOUN
iajs-777	66	17	follows	follow	VERB
iajs-777	66	18	directly	directly	ADV
iajs-777	66	19	from	from	ADP
iajs-777	66	20	the	the	DET
iajs-777	66	21	definitions	definition	NOUN
iajs-777	66	22	)	)	PUNCT
iajs-777	66	23	.	.	PUNCT
iajs-777	67	1	1.3	1.3	NUM
iajs-777	67	2	remark	remark	NOUN
iajs-777	67	3	:	:	PUNCT
iajs-777	67	4	[	[	X
iajs-777	67	5	6	6	NUM
iajs-777	67	6	]	]	PUNCT
iajs-777	67	7	let	let	VERB
iajs-777	67	8	x	x	PRON
iajs-777	67	9	be	be	AUX
iajs-777	67	10	a	a	DET
iajs-777	67	11	topological	topological	ADJ
iajs-777	67	12	space	space	NOUN
iajs-777	67	13	,	,	PUNCT
iajs-777	67	14	a	a	PRON
iajs-777	67	15	and	and	CCONJ
iajs-777	67	16	b	b	NOUN
iajs-777	67	17	be	be	AUX
iajs-777	67	18	two	two	NUM
iajs-777	67	19	subsets	subset	NOUN
iajs-777	67	20	of	of	ADP
iajs-777	67	21	x	x	NOUN
iajs-777	67	22	,	,	PUNCT
iajs-777	67	23	then	then	ADV
iajs-777	67	24	(	(	PUNCT
iajs-777	67	25	1	1	X
iajs-777	67	26	)	)	PUNCT
iajs-777	67	27	a	a	PRON
iajs-777	67	28	is	be	AUX
iajs-777	67	29	semi--closed	semi--closed	AUX
iajs-777	67	30	set	set	VERB
iajs-777	67	31	if	if	SCONJ
iajs-777	67	32	and	and	CCONJ
iajs-777	67	33	only	only	ADV
iajs-777	67	34	if	if	SCONJ
iajs-777	67	35	a	a	DET
iajs-777	67	36	=	=	SYM
iajs-777	67	37	scl(a	scl(a	NOUN
iajs-777	67	38	)	)	PUNCT
iajs-777	67	39	.	.	PUNCT
iajs-777	68	1	(	(	PUNCT
iajs-777	68	2	2	2	X
iajs-777	68	3	)	)	PUNCT
iajs-777	68	4	a	a	DET
iajs-777	68	5			PROPN
iajs-777	68	6	scl(a	scl(a	PROPN
iajs-777	68	7	)	)	PUNCT
iajs-777	68	8			PROPN
iajs-777	68	9	cl(a	cl(a	PROPN
iajs-777	68	10	)	)	PUNCT
iajs-777	68	11			NOUN
iajs-777	68	12	cl(a	cl(a	NUM
iajs-777	68	13	)	)	PUNCT
iajs-777	68	14	.	.	PUNCT
iajs-777	69	1	(	(	PUNCT
iajs-777	69	2	3	3	X
iajs-777	69	3	)	)	PUNCT
iajs-777	69	4	scl(a	scl(a	ADJ
iajs-777	69	5	)	)	PUNCT
iajs-777	69	6			PROPN
iajs-777	69	7	scl(b	scl(b	PROPN
iajs-777	69	8	)	)	PUNCT
iajs-777	69	9	,	,	PUNCT
iajs-777	69	10	whenever	whenever	SCONJ
iajs-777	69	11	a	a	DET
iajs-777	69	12			PROPN
iajs-777	69	13	b.	b.	PROPN
iajs-777	69	14	1.4	1.4	NUM
iajs-777	69	15	definition	definition	NOUN
iajs-777	69	16	:	:	PUNCT
iajs-777	69	17	a	a	DET
iajs-777	69	18	function	function	NOUN
iajs-777	69	19	f:(x,	f:(x,	PROPN
iajs-777	69	20	)	)	PUNCT
iajs-777	69	21			PROPN
iajs-777	69	22	(	(	PUNCT
iajs-777	69	23	y,	y,	PROPN
iajs-777	69	24	'	'	PUNCT
iajs-777	69	25	)	)	PUNCT
iajs-777	69	26	is	be	AUX
iajs-777	69	27	said	say	VERB
iajs-777	69	28	to	to	PART
iajs-777	69	29	be	be	AUX
iajs-777	69	30	:	:	PUNCT
iajs-777	69	31	(	(	PUNCT
iajs-777	69	32	1	1	X
iajs-777	69	33	)	)	PUNCT
iajs-777	69	34	semi--continuous	semi--continuous	ADJ
iajs-777	70	1	[	[	X
iajs-777	70	2	6	6	NUM
iajs-777	70	3	]	]	PUNCT
iajs-777	70	4	,	,	PUNCT
iajs-777	70	5	[	[	X
iajs-777	70	6	7	7	X
iajs-777	70	7	]	]	X
iajs-777	70	8	if	if	SCONJ
iajs-777	70	9	f	f	X
iajs-777	70	10	–	–	PUNCT
iajs-777	70	11	1(v	1(v	NUM
iajs-777	70	12	)	)	PUNCT
iajs-777	70	13	is	be	AUX
iajs-777	70	14	a	a	DET
iajs-777	70	15	semi--closed	semi--closed	ADJ
iajs-777	70	16	set	set	NOUN
iajs-777	70	17	in	in	ADP
iajs-777	70	18	(	(	PUNCT
iajs-777	70	19	x,	x,	X
iajs-777	70	20	)	)	PUNCT
iajs-777	70	21	for	for	ADP
iajs-777	70	22	every	every	DET
iajs-777	70	23	closed	close	VERB
iajs-777	70	24	set	set	VERB
iajs-777	70	25	v	v	NOUN
iajs-777	70	26	of	of	ADP
iajs-777	70	27	(	(	PUNCT
iajs-777	70	28	y,	y,	PROPN
iajs-777	70	29	'	'	PUNCT
iajs-777	70	30	)	)	PUNCT
iajs-777	70	31	.	.	PUNCT
iajs-777	71	1	(	(	PUNCT
iajs-777	71	2	2	2	X
iajs-777	71	3	)	)	PUNCT
iajs-777	71	4	g	g	NOUN
iajs-777	71	5	-	-	PUNCT
iajs-777	71	6	continuous	continuous	ADJ
iajs-777	71	7	[	[	X
iajs-777	71	8	17	17	NUM
iajs-777	71	9	]	]	PUNCT
iajs-777	71	10	if	if	SCONJ
iajs-777	71	11	f	f	PROPN
iajs-777	71	12	–	–	PUNCT
iajs-777	71	13	1	1	NUM
iajs-777	71	14	(	(	PUNCT
iajs-777	71	15	v	v	NOUN
iajs-777	71	16	)	)	PUNCT
iajs-777	71	17	is	be	AUX
iajs-777	71	18	a	a	DET
iajs-777	71	19	g	g	NOUN
iajs-777	71	20	-	-	PUNCT
iajs-777	71	21	closed	close	VERB
iajs-777	71	22	set	set	NOUN
iajs-777	71	23	in	in	ADP
iajs-777	71	24	(	(	PUNCT
iajs-777	71	25	x,	x,	X
iajs-777	71	26	)	)	PUNCT
iajs-777	71	27	for	for	ADP
iajs-777	71	28	every	every	DET
iajs-777	71	29	closed	close	VERB
iajs-777	71	30	set	set	VERB
iajs-777	71	31	v	v	NOUN
iajs-777	71	32	of	of	ADP
iajs-777	71	33	(	(	PUNCT
iajs-777	71	34	y,	y,	PROPN
iajs-777	71	35	'	'	PUNCT
iajs-777	71	36	)	)	PUNCT
iajs-777	71	37	.	.	PUNCT
iajs-777	72	1	(	(	PUNCT
iajs-777	72	2	3	3	X
iajs-777	72	3	)	)	PUNCT
iajs-777	72	4	g	g	ADV
iajs-777	72	5	-	-	ADJ
iajs-777	72	6	continuous	continuous	ADJ
iajs-777	72	7	[	[	X
iajs-777	72	8	18	18	NUM
iajs-777	72	9	]	]	PUNCT
iajs-777	72	10	if	if	SCONJ
iajs-777	72	11	f	f	PROPN
iajs-777	72	12	–	–	PUNCT
iajs-777	72	13	1	1	NUM
iajs-777	72	14	(	(	PUNCT
iajs-777	72	15	v	v	NOUN
iajs-777	72	16	)	)	PUNCT
iajs-777	72	17	is	be	AUX
iajs-777	72	18	an	an	DET
iajs-777	72	19	g	g	ADV
iajs-777	72	20	-	-	PUNCT
iajs-777	72	21	closed	closed	ADJ
iajs-777	72	22	set	set	NOUN
iajs-777	72	23	in	in	ADP
iajs-777	72	24	(	(	PUNCT
iajs-777	72	25	x,	x,	X
iajs-777	72	26	)	)	PUNCT
iajs-777	72	27	for	for	ADP
iajs-777	72	28	every	every	DET
iajs-777	72	29	closed	close	VERB
iajs-777	72	30	set	set	VERB
iajs-777	72	31	v	v	NOUN
iajs-777	72	32	of	of	ADP
iajs-777	72	33	(	(	PUNCT
iajs-777	72	34	y,	y,	PROPN
iajs-777	72	35	'	'	PUNCT
iajs-777	72	36	)	)	PUNCT
iajs-777	72	37	.	.	PUNCT
iajs-777	73	1	(	(	PUNCT
iajs-777	73	2	4	4	X
iajs-777	73	3	)	)	PUNCT
iajs-777	73	4	g	g	NOUN
iajs-777	73	5	-continuous	-continuous	ADJ
iajs-777	73	6	[	[	X
iajs-777	73	7	14	14	NUM
iajs-777	73	8	]	]	PUNCT
iajs-777	73	9	if	if	SCONJ
iajs-777	73	10	f	f	PROPN
iajs-777	73	11	–	–	PUNCT
iajs-777	73	12	1	1	NUM
iajs-777	73	13	(	(	PUNCT
iajs-777	73	14	v	v	NOUN
iajs-777	73	15	)	)	PUNCT
iajs-777	73	16	is	be	AUX
iajs-777	73	17	a	a	DET
iajs-777	73	18	g-closed	g-close	VERB
iajs-777	73	19	set	set	NOUN
iajs-777	73	20	in	in	ADP
iajs-777	73	21	(	(	PUNCT
iajs-777	73	22	x,	x,	X
iajs-777	73	23	)	)	PUNCT
iajs-777	73	24	for	for	ADP
iajs-777	73	25	every	every	DET
iajs-777	73	26	closed	close	VERB
iajs-777	73	27	set	set	VERB
iajs-777	73	28	v	v	NOUN
iajs-777	73	29	of	of	ADP
iajs-777	73	30	(	(	PUNCT
iajs-777	73	31	y,	y,	PROPN
iajs-777	73	32	'	'	PUNCT
iajs-777	73	33	)	)	PUNCT
iajs-777	73	34	.	.	PUNCT
iajs-777	74	1	(	(	PUNCT
iajs-777	74	2	5	5	NUM
iajs-777	74	3	)	)	PUNCT
iajs-777	74	4	gr	gr	ADJ
iajs-777	74	5	-	-	ADJ
iajs-777	74	6	continuous	continuous	ADJ
iajs-777	74	7	[	[	X
iajs-777	74	8	3	3	NUM
iajs-777	74	9	]	]	PUNCT
iajs-777	74	10	if	if	SCONJ
iajs-777	74	11	f	f	X
iajs-777	74	12	–	–	PUNCT
iajs-777	74	13	1(v	1(v	NUM
iajs-777	74	14	)	)	PUNCT
iajs-777	74	15	is	be	AUX
iajs-777	74	16	an	an	DET
iajs-777	74	17	gr	gr	ADV
iajs-777	74	18	-	-	PUNCT
iajs-777	74	19	closed	closed	ADJ
iajs-777	74	20	set	set	NOUN
iajs-777	74	21	in	in	ADP
iajs-777	74	22	(	(	PUNCT
iajs-777	74	23	x,	x,	X
iajs-777	74	24	)	)	PUNCT
iajs-777	74	25	for	for	ADP
iajs-777	74	26	every	every	DET
iajs-777	74	27	closed	close	VERB
iajs-777	74	28	set	set	VERB
iajs-777	74	29	v	v	NOUN
iajs-777	74	30	of	of	ADP
iajs-777	74	31	(	(	PUNCT
iajs-777	74	32	y,	y,	PROPN
iajs-777	74	33	'	'	PUNCT
iajs-777	74	34	)	)	PUNCT
iajs-777	74	35	.	.	PUNCT
iajs-777	75	1	(	(	PUNCT
iajs-777	75	2	6	6	NUM
iajs-777	75	3	)	)	PUNCT
iajs-777	75	4	pre	pre	ADJ
iajs-777	75	5	-	-	ADJ
iajs-777	75	6	semi	semi	ADJ
iajs-777	75	7	-	-	ADJ
iajs-777	75	8	continuous	continuous	ADJ
iajs-777	75	9	[	[	X
iajs-777	75	10	4	4	NUM
iajs-777	75	11	]	]	X
iajs-777	75	12	if	if	SCONJ
iajs-777	75	13	f	f	X
iajs-777	75	14	–	–	PUNCT
iajs-777	75	15	1(v	1(v	NUM
iajs-777	75	16	)	)	PUNCT
iajs-777	75	17	is	be	AUX
iajs-777	75	18	a	a	DET
iajs-777	75	19	pre	pre	ADJ
iajs-777	75	20	-	-	ADJ
iajs-777	75	21	semi	semi	ADJ
iajs-777	75	22	-	-	ADJ
iajs-777	75	23	closed	closed	ADJ
iajs-777	75	24	set	set	NOUN
iajs-777	75	25	in	in	ADP
iajs-777	75	26	(	(	PUNCT
iajs-777	75	27	x,	x,	X
iajs-777	75	28	)	)	PUNCT
iajs-777	75	29	for	for	ADP
iajs-777	75	30	every	every	DET
iajs-777	75	31	closed	close	VERB
iajs-777	75	32	set	set	VERB
iajs-777	75	33	v	v	NOUN
iajs-777	75	34	of	of	ADP
iajs-777	75	35	(	(	PUNCT
iajs-777	75	36	y,	y,	PROPN
iajs-777	75	37	'	'	PUNCT
iajs-777	75	38	)	)	PUNCT
iajs-777	75	39	.	.	PUNCT
iajs-777	76	1	(	(	PUNCT
iajs-777	76	2	7	7	X
iajs-777	76	3	)	)	PUNCT
iajs-777	76	4	gsp	gsp	NOUN
iajs-777	76	5	-	-	PUNCT
iajs-777	76	6	continuous	continuous	ADJ
iajs-777	76	7	[	[	X
iajs-777	76	8	16	16	NUM
iajs-777	76	9	]	]	PUNCT
iajs-777	76	10	if	if	SCONJ
iajs-777	76	11	f	f	X
iajs-777	76	12	–	–	PUNCT
iajs-777	76	13	1(v	1(v	NUM
iajs-777	76	14	)	)	PUNCT
iajs-777	76	15	is	be	AUX
iajs-777	76	16	a	a	DET
iajs-777	76	17	gsp	gsp	NOUN
iajs-777	76	18	-	-	PUNCT
iajs-777	76	19	closed	close	VERB
iajs-777	76	20	set	set	NOUN
iajs-777	76	21	in	in	ADP
iajs-777	76	22	(	(	PUNCT
iajs-777	76	23	x,	x,	X
iajs-777	76	24	)	)	PUNCT
iajs-777	76	25	for	for	ADP
iajs-777	76	26	every	every	DET
iajs-777	76	27	closed	close	VERB
iajs-777	76	28	set	set	VERB
iajs-777	76	29	v	v	NOUN
iajs-777	76	30	of	of	ADP
iajs-777	76	31	(	(	PUNCT
iajs-777	76	32	y,	y,	PROPN
iajs-777	76	33	'	'	PUNCT
iajs-777	76	34	)	)	PUNCT
iajs-777	76	35	.	.	PUNCT
iajs-777	77	1	(	(	PUNCT
iajs-777	77	2	8)	8)	NUM
iajs-777	77	3	semi--irresolute	semi--irresolute	ADJ
iajs-777	77	4	[	[	X
iajs-777	77	5	6	6	NUM
iajs-777	77	6	]	]	PUNCT
iajs-777	77	7	if	if	SCONJ
iajs-777	77	8	f	f	X
iajs-777	77	9	–	–	PUNCT
iajs-777	77	10	1(v	1(v	NUM
iajs-777	77	11	)	)	PUNCT
iajs-777	77	12	is	be	AUX
iajs-777	77	13	a	a	DET
iajs-777	77	14	semi--closed	semi--closed	ADJ
iajs-777	77	15	set	set	NOUN
iajs-777	77	16	in	in	ADP
iajs-777	77	17	(	(	PUNCT
iajs-777	77	18	x,	x,	X
iajs-777	77	19	)	)	PUNCT
iajs-777	77	20	for	for	ADP
iajs-777	77	21	every	every	DET
iajs-777	77	22	semi--closed	semi--close	VERB
iajs-777	77	23	set	set	NOUN
iajs-777	77	24	v	v	NOUN
iajs-777	77	25	of	of	ADP
iajs-777	77	26	(	(	PUNCT
iajs-777	77	27	y,	y,	PROPN
iajs-777	77	28	'	'	PUNCT
iajs-777	77	29	)	)	PUNCT
iajs-777	77	30	.	.	PUNCT
iajs-777	78	1	(	(	PUNCT
iajs-777	78	2	9	9	X
iajs-777	78	3	)	)	PUNCT
iajs-777	78	4	gr	gr	ADJ
iajs-777	78	5	-	-	PUNCT
iajs-777	78	6	irresolute	irresolute	ADJ
iajs-777	78	7	[	[	X
iajs-777	78	8	3	3	X
iajs-777	78	9	]	]	PUNCT
iajs-777	78	10	if	if	SCONJ
iajs-777	78	11	f	f	X
iajs-777	78	12	–	–	PUNCT
iajs-777	78	13	1(v	1(v	NUM
iajs-777	78	14	)	)	PUNCT
iajs-777	78	15	is	be	AUX
iajs-777	78	16	an	an	DET
iajs-777	78	17	gr	gr	ADV
iajs-777	78	18	-	-	PUNCT
iajs-777	78	19	closed	closed	ADJ
iajs-777	78	20	set	set	NOUN
iajs-777	78	21	in	in	ADP
iajs-777	78	22	(	(	PUNCT
iajs-777	78	23	x,	x,	X
iajs-777	78	24	)	)	PUNCT
iajs-777	78	25	for	for	ADP
iajs-777	78	26	every	every	DET
iajs-777	78	27	gr	gr	ADV
iajs-777	78	28	-	-	PUNCT
iajs-777	78	29	closed	closed	ADJ
iajs-777	78	30	set	set	ADJ
iajs-777	78	31	v	v	NOUN
iajs-777	78	32	of	of	ADP
iajs-777	78	33	(	(	PUNCT
iajs-777	78	34	y,	y,	PROPN
iajs-777	78	35	'	'	PUNCT
iajs-777	78	36	)	)	PUNCT
iajs-777	78	37	.	.	PUNCT
iajs-777	79	1	(	(	PUNCT
iajs-777	79	2	10	10	NUM
iajs-777	79	3	)	)	PUNCT
iajs-777	79	4	regular	regular	ADJ
iajs-777	79	5	irresolute	irresolute	NOUN
iajs-777	79	6	[	[	X
iajs-777	79	7	19	19	NUM
iajs-777	79	8	]	]	X
iajs-777	79	9	if	if	SCONJ
iajs-777	79	10	f	f	PROPN
iajs-777	79	11	–	–	PUNCT
iajs-777	79	12	1	1	NUM
iajs-777	79	13	(	(	PUNCT
iajs-777	79	14	v	v	NOUN
iajs-777	79	15	)	)	PUNCT
iajs-777	79	16	is	be	AUX
iajs-777	79	17	a	a	DET
iajs-777	79	18	regular	regular	ADJ
iajs-777	79	19	open	open	ADJ
iajs-777	79	20	set	set	NOUN
iajs-777	79	21	in	in	ADP
iajs-777	79	22	(	(	PUNCT
iajs-777	79	23	x,	x,	X
iajs-777	79	24	)	)	PUNCT
iajs-777	79	25	for	for	ADP
iajs-777	79	26	every	every	DET
iajs-777	79	27	regular	regular	ADJ
iajs-777	79	28	open	open	ADJ
iajs-777	79	29	set	set	NOUN
iajs-777	79	30	v	v	NOUN
iajs-777	79	31	of	of	ADP
iajs-777	79	32	(	(	PUNCT
iajs-777	79	33	y,	y,	PROPN
iajs-777	79	34	'	'	PUNCT
iajs-777	79	35	)	)	PUNCT
iajs-777	79	36	.	.	PUNCT
iajs-777	80	1	(	(	PUNCT
iajs-777	80	2	11	11	NUM
iajs-777	80	3	)	)	PUNCT
iajs-777	80	4	semi-*-closed	semi-*-close	VERB
iajs-777	81	1	[	[	X
iajs-777	81	2	6	6	NUM
iajs-777	81	3	]	]	PUNCT
iajs-777	81	4	if	if	SCONJ
iajs-777	81	5	f	f	PROPN
iajs-777	81	6	(	(	PUNCT
iajs-777	81	7	u	u	NOUN
iajs-777	81	8	)	)	PUNCT
iajs-777	81	9	is	be	AUX
iajs-777	81	10	a	a	DET
iajs-777	81	11	semi--closed	semi--closed	ADJ
iajs-777	81	12	set	set	NOUN
iajs-777	81	13	in	in	ADP
iajs-777	81	14	(	(	PUNCT
iajs-777	81	15	y,	y,	PROPN
iajs-777	81	16	'	'	PUNCT
iajs-777	81	17	)	)	PUNCT
iajs-777	81	18	for	for	ADP
iajs-777	81	19	every	every	DET
iajs-777	81	20	semi--closed	semi--close	VERB
iajs-777	81	21	set	set	VERB
iajs-777	81	22	u	u	NOUN
iajs-777	81	23	in	in	ADP
iajs-777	81	24	(	(	PUNCT
iajs-777	81	25	x,	x,	PROPN
iajs-777	81	26	)	)	PUNCT
iajs-777	81	27	.	.	PUNCT
iajs-777	82	1	1.5	1.5	NUM
iajs-777	82	2	proposition	proposition	NOUN
iajs-777	82	3	:	:	PUNCT
iajs-777	82	4	(	(	PUNCT
iajs-777	82	5	1	1	X
iajs-777	82	6	)	)	PUNCT
iajs-777	82	7	every	every	DET
iajs-777	82	8	g	g	NUM
iajs-777	82	9	-	-	ADJ
iajs-777	82	10	continuous	continuous	ADJ
iajs-777	82	11	map	map	NOUN
iajs-777	82	12	is	be	AUX
iajs-777	82	13	gr	gr	ADJ
iajs-777	82	14	-	-	ADJ
iajs-777	82	15	continuous	continuous	ADJ
iajs-777	82	16	map	map	NOUN
iajs-777	82	17	[	[	X
iajs-777	82	18	3	3	NUM
iajs-777	82	19	]	]	PUNCT
iajs-777	82	20	.	.	PUNCT
iajs-777	83	1	(	(	PUNCT
iajs-777	83	2	2	2	X
iajs-777	83	3	)	)	PUNCT
iajs-777	83	4	every	every	DET
iajs-777	83	5	g	g	NOUN
iajs-777	83	6	-	-	PUNCT
iajs-777	83	7	continuous	continuous	ADJ
iajs-777	83	8	(	(	PUNCT
iajs-777	83	9	resp	resp	NOUN
iajs-777	83	10	.g-continuous	.g-continuous	PUNCT
iajs-777	83	11	)	)	PUNCT
iajs-777	83	12	map	map	NOUN
iajs-777	83	13	is	be	AUX
iajs-777	83	14	an	an	DET
iajs-777	83	15	gr	gr	ADJ
iajs-777	83	16	-	-	ADJ
iajs-777	83	17	continuous	continuous	ADJ
iajs-777	83	18	map	map	NOUN
iajs-777	84	1	[	[	X
iajs-777	84	2	3	3	NUM
iajs-777	84	3	]	]	PUNCT
iajs-777	84	4	.	.	PUNCT
iajs-777	85	1	(	(	PUNCT
iajs-777	85	2	3	3	X
iajs-777	85	3	)	)	PUNCT
iajs-777	85	4	every	every	DET
iajs-777	85	5	pre	pre	ADJ
iajs-777	85	6	-	-	ADJ
iajs-777	85	7	semi	semi	ADJ
iajs-777	85	8	-	-	ADJ
iajs-777	85	9	continuous	continuous	ADJ
iajs-777	85	10	map	map	NOUN
iajs-777	85	11	is	be	AUX
iajs-777	85	12	gsp	gsp	VERB
iajs-777	85	13	-	-	PUNCT
iajs-777	85	14	continuous	continuous	ADJ
iajs-777	85	15	map	map	NOUN
iajs-777	85	16	[	[	X
iajs-777	85	17	4	4	NUM
iajs-777	85	18	]	]	PUNCT
iajs-777	85	19	.	.	PUNCT
iajs-777	86	1	ibn	ibn	PROPN
iajs-777	86	2	alhaitham	alhaitham	PROPN
iajs-777	86	3	j.	j.	PROPN
iajs-777	86	4	for	for	ADP
iajs-777	86	5	pure	pure	ADJ
iajs-777	86	6	&	&	CCONJ
iajs-777	86	7	appl	appl	PROPN
iajs-777	86	8	.	.	PUNCT
iajs-777	87	1	sci	sci	PROPN
iajs-777	87	2	.	.	PUNCT
iajs-777	87	3	vol.24	vol.24	NOUN
iajs-777	87	4	(	(	PUNCT
iajs-777	87	5	2	2	NUM
iajs-777	87	6	)	)	PUNCT
iajs-777	87	7	2011	2011	NUM
iajs-777	87	8	(	(	PUNCT
iajs-777	87	9	4	4	X
iajs-777	87	10	)	)	PUNCT
iajs-777	87	11	every	every	DET
iajs-777	87	12	gr	gr	ADJ
iajs-777	87	13	-	-	PUNCT
iajs-777	87	14	irresolut	irresolut	NOUN
iajs-777	87	15	map	map	NOUN
iajs-777	87	16	is	be	AUX
iajs-777	87	17	gr	gr	ADJ
iajs-777	87	18	-	-	ADJ
iajs-777	87	19	continuous	continuous	ADJ
iajs-777	87	20	map	map	NOUN
iajs-777	88	1	[	[	X
iajs-777	88	2	3	3	NUM
iajs-777	88	3	]	]	PUNCT
iajs-777	88	4	.	.	PUNCT
iajs-777	89	1	(	(	PUNCT
iajs-777	89	2	5	5	X
iajs-777	89	3	)	)	PUNCT
iajs-777	89	4	every	every	DET
iajs-777	89	5	continuous	continuous	ADJ
iajs-777	89	6	and	and	CCONJ
iajs-777	89	7	open	open	ADJ
iajs-777	89	8	map	map	NOUN
iajs-777	89	9	is	be	AUX
iajs-777	89	10	semi--irresolute	semi--irresolute	ADJ
iajs-777	89	11	map	map	NOUN
iajs-777	89	12	[	[	X
iajs-777	89	13	20	20	NUM
iajs-777	89	14	]	]	PUNCT
iajs-777	89	15	.	.	PUNCT
iajs-777	90	1	2	2	PROPN
iajs-777	90	2	-semi	-semi	PROPN
iajs-777	90	3	-	-	PUNCT
iajs-777	90	4	regular	regular	ADJ
iajs-777	90	5	closed	closed	ADJ
iajs-777	90	6	sets	set	NOUN
iajs-777	90	7	in	in	ADP
iajs-777	90	8	this	this	DET
iajs-777	90	9	section	section	NOUN
iajs-777	90	10	we	we	PRON
iajs-777	90	11	introduce	introduce	VERB
iajs-777	90	12	the	the	DET
iajs-777	90	13	class	class	NOUN
iajs-777	90	14	of	of	ADP
iajs-777	90	15	-semi	-semi	PROPN
iajs-777	90	16	-	-	PUNCT
iajs-777	90	17	regular	regular	ADJ
iajs-777	90	18	closed	closed	ADJ
iajs-777	90	19	sets	set	NOUN
iajs-777	90	20	and	and	CCONJ
iajs-777	90	21	study	study	VERB
iajs-777	90	22	some	some	PRON
iajs-777	90	23	of	of	ADP
iajs-777	90	24	it	it	PRON
iajs-777	90	25	's	be	AUX
iajs-777	90	26	basic	basic	ADJ
iajs-777	90	27	properties	property	NOUN
iajs-777	90	28	.	.	PUNCT
iajs-777	91	1	2.1	2.1	NUM
iajs-777	91	2	definition	definition	NOUN
iajs-777	91	3	:	:	PUNCT
iajs-777	91	4	a	a	DET
iajs-777	91	5	subset	subset	NOUN
iajs-777	91	6	a	a	PRON
iajs-777	91	7	of	of	ADP
iajs-777	91	8	(	(	PUNCT
iajs-777	91	9	x,	x,	X
iajs-777	91	10	)	)	PUNCT
iajs-777	91	11	is	be	AUX
iajs-777	91	12	called	call	VERB
iajs-777	91	13	-semi	-semi	PROPN
iajs-777	91	14	-	-	PUNCT
iajs-777	91	15	regular	regular	ADJ
iajs-777	91	16	closed	closed	ADJ
iajs-777	91	17	set	set	NOUN
iajs-777	91	18	(	(	PUNCT
iajs-777	91	19	briefly	briefly	ADV
iajs-777	91	20	sr	sr	ADV
iajs-777	91	21	-	-	PUNCT
iajs-777	91	22	closed	closed	ADJ
iajs-777	91	23	)	)	PUNCT
iajs-777	91	24	if	if	SCONJ
iajs-777	91	25	scl(a)u	scl(a)u	NOUN
iajs-777	91	26	whenever	whenever	SCONJ
iajs-777	91	27	a	a	DET
iajs-777	91	28			PROPN
iajs-777	91	29	u	u	NOUN
iajs-777	91	30	and	and	CCONJ
iajs-777	91	31	u	u	NOUN
iajs-777	91	32	is	be	AUX
iajs-777	91	33	regular	regular	ADJ
iajs-777	91	34	open	open	ADJ
iajs-777	91	35	in	in	ADP
iajs-777	91	36	(	(	PUNCT
iajs-777	91	37	x,	x,	PROPN
iajs-777	91	38	)	)	PUNCT
iajs-777	91	39	.	.	PUNCT
iajs-777	92	1	src(x	src(x	NUM
iajs-777	92	2	)	)	PUNCT
iajs-777	92	3	denotes	denote	VERB
iajs-777	92	4	the	the	DET
iajs-777	92	5	collection	collection	NOUN
iajs-777	92	6	of	of	ADP
iajs-777	92	7	all	all	DET
iajs-777	92	8	sr	sr	NOUN
iajs-777	92	9	-	-	PUNCT
iajs-777	92	10	closed	closed	ADJ
iajs-777	92	11	subset	subset	NOUN
iajs-777	92	12	of	of	ADP
iajs-777	92	13	(	(	PUNCT
iajs-777	92	14	x,	x,	X
iajs-777	92	15	)	)	PUNCT
iajs-777	93	1	2.2.proposition	2.2.proposition	NUM
iajs-777	93	2	:	:	PUNCT
iajs-777	93	3	every	every	DET
iajs-777	93	4	semi--closed	semi--closed	ADJ
iajs-777	93	5	set	set	NOUN
iajs-777	93	6	is	be	AUX
iajs-777	93	7	an	an	DET
iajs-777	93	8	sr	sr	ADV
iajs-777	93	9	-	-	PUNCT
iajs-777	93	10	closed	closed	ADJ
iajs-777	93	11	set	set	NOUN
iajs-777	93	12	.	.	PUNCT
iajs-777	94	1	proof	proof	NOUN
iajs-777	94	2	:	:	PUNCT
iajs-777	94	3	let	let	VERB
iajs-777	94	4	a	a	PRON
iajs-777	94	5	be	be	AUX
iajs-777	94	6	a	a	DET
iajs-777	94	7	semi--closed	semi--closed	ADJ
iajs-777	94	8	set	set	NOUN
iajs-777	94	9	,	,	PUNCT
iajs-777	94	10	let	let	VERB
iajs-777	94	11	u	u	PRON
iajs-777	94	12	be	be	AUX
iajs-777	94	13	a	a	DET
iajs-777	94	14	regular	regular	ADJ
iajs-777	94	15	open	open	ADJ
iajs-777	94	16	set	set	NOUN
iajs-777	94	17	of	of	ADP
iajs-777	94	18	(	(	PUNCT
iajs-777	94	19	x,	x,	X
iajs-777	94	20	)	)	PUNCT
iajs-777	94	21	such	such	ADJ
iajs-777	94	22	that	that	SCONJ
iajs-777	94	23	a	a	DET
iajs-777	94	24			PROPN
iajs-777	94	25	u.	u.	PROPN
iajs-777	94	26	since	since	SCONJ
iajs-777	94	27	scl(a	scl(a	X
iajs-777	94	28	)	)	PUNCT
iajs-777	94	29	=	=	SYM
iajs-777	94	30	a	a	PRON
iajs-777	94	31	for	for	ADP
iajs-777	94	32	any	any	DET
iajs-777	94	33	semi--closed	semi--closed	ADJ
iajs-777	94	34	set	set	NOUN
iajs-777	94	35	(	(	PUNCT
iajs-777	94	36	by	by	ADP
iajs-777	94	37	part	part	NOUN
iajs-777	94	38	1	1	NUM
iajs-777	94	39	of	of	ADP
iajs-777	94	40	remark	remark	NOUN
iajs-777	94	41	1.3	1.3	NUM
iajs-777	94	42	)	)	PUNCT
iajs-777	94	43	,	,	PUNCT
iajs-777	94	44	then	then	ADV
iajs-777	94	45	scl(a	scl(a	X
iajs-777	94	46	)	)	PUNCT
iajs-777	94	47			PROPN
iajs-777	94	48	u.	u.	PROPN
iajs-777	94	49	therefore	therefore	ADV
iajs-777	94	50	a	a	PRON
iajs-777	94	51	is	be	AUX
iajs-777	94	52	also	also	ADV
iajs-777	94	53	an	an	DET
iajs-777	94	54	sr	sr	ADV
iajs-777	94	55	-	-	PUNCT
iajs-777	94	56	closed	closed	ADJ
iajs-777	94	57	set	set	NOUN
iajs-777	94	58	.	.	PUNCT
iajs-777	95	1	the	the	DET
iajs-777	95	2	following	follow	VERB
iajs-777	95	3	example	example	NOUN
iajs-777	95	4	shows	show	VERB
iajs-777	95	5	that	that	SCONJ
iajs-777	95	6	the	the	DET
iajs-777	95	7	converse	converse	NOUN
iajs-777	95	8	of	of	ADP
iajs-777	95	9	the	the	DET
iajs-777	95	10	above	above	ADJ
iajs-777	95	11	proposition	proposition	NOUN
iajs-777	95	12	is	be	AUX
iajs-777	95	13	not	not	PART
iajs-777	95	14	true	true	ADJ
iajs-777	95	15	in	in	ADP
iajs-777	95	16	general	general	ADJ
iajs-777	95	17	.	.	PUNCT
iajs-777	96	1	2.3	2.3	NUM
iajs-777	96	2	example	example	NOUN
iajs-777	96	3	:	:	PUNCT
iajs-777	96	4	let	let	VERB
iajs-777	96	5	x={a	x={a	PROPN
iajs-777	96	6	,	,	PUNCT
iajs-777	96	7	b	b	PROPN
iajs-777	96	8	,	,	PUNCT
iajs-777	96	9	c	c	NOUN
iajs-777	96	10	}	}	PUNCT
iajs-777	96	11	and	and	CCONJ
iajs-777	96	12	={x,,{a},{c},{a	={x,,{a},{c},{a	NUM
iajs-777	96	13	,	,	PUNCT
iajs-777	96	14	c	c	NOUN
iajs-777	96	15	}	}	PUNCT
iajs-777	96	16	}	}	PUNCT
iajs-777	96	17	.	.	PUNCT
iajs-777	97	1	let	let	VERB
iajs-777	97	2	a={a	a={a	NOUN
iajs-777	97	3	,	,	PUNCT
iajs-777	97	4	c	c	NOUN
iajs-777	97	5	}	}	PUNCT
iajs-777	97	6	,	,	PUNCT
iajs-777	97	7	x	x	X
iajs-777	97	8	is	be	AUX
iajs-777	97	9	the	the	DET
iajs-777	97	10	only	only	ADJ
iajs-777	97	11	regular	regular	ADJ
iajs-777	97	12	open	open	ADJ
iajs-777	97	13	set	set	NOUN
iajs-777	97	14	containing	contain	VERB
iajs-777	97	15	a.	a.	NOUN
iajs-777	97	16	it	it	PRON
iajs-777	97	17	is	be	AUX
iajs-777	97	18	clear	clear	ADJ
iajs-777	97	19	a	a	PRON
iajs-777	97	20	is	be	AUX
iajs-777	97	21	an	an	DET
iajs-777	97	22	sr	sr	ADV
iajs-777	97	23	-	-	PUNCT
iajs-777	97	24	closed	closed	ADJ
iajs-777	97	25	set	set	NOUN
iajs-777	97	26	.	.	PUNCT
iajs-777	98	1	but	but	CCONJ
iajs-777	98	2	a	a	PRON
iajs-777	98	3	is	be	AUX
iajs-777	98	4	not	not	PART
iajs-777	98	5	semi--closed	semi--close	VERB
iajs-777	98	6	set	set	VERB
iajs-777	98	7	since	since	SCONJ
iajs-777	98	8	scl({a	scl({a	PROPN
iajs-777	98	9	,	,	PUNCT
iajs-777	98	10	c	c	NOUN
iajs-777	98	11	}	}	PUNCT
iajs-777	98	12	)	)	PUNCT
iajs-777	99	1	=	=	SYM
iajs-777	99	2	x	x	SYM
iajs-777	99	3			NOUN
iajs-777	99	4	{	{	PUNCT
iajs-777	99	5	a	a	PRON
iajs-777	99	6	,	,	PUNCT
iajs-777	99	7	c	c	NOUN
iajs-777	99	8	}	}	PUNCT
iajs-777	99	9	.	.	PUNCT
iajs-777	100	1	thus	thus	ADV
iajs-777	100	2	the	the	DET
iajs-777	100	3	class	class	NOUN
iajs-777	100	4	of	of	ADP
iajs-777	100	5	sr	sr	NOUN
iajs-777	100	6	-	-	PUNCT
iajs-777	100	7	closed	closed	ADJ
iajs-777	100	8	set	set	NOUN
iajs-777	100	9	p	p	NOUN
iajs-777	100	10	roperly	roperly	ADV
iajs-777	100	11	contains	contain	VERB
iajs-777	100	12	the	the	DET
iajs-777	100	13	class	class	NOUN
iajs-777	100	14	of	of	ADP
iajs-777	100	15	semi--closed	semi--close	VERB
iajs-777	100	16	sets	set	NOUN
iajs-777	100	17	.	.	PUNCT
iajs-777	101	1	2.4	2.4	NUM
iajs-777	101	2	proposition	proposition	NOUN
iajs-777	101	3	:	:	PUNCT
iajs-777	101	4	every	every	DET
iajs-777	101	5	gr	gr	ADV
iajs-777	101	6	-	-	PUNCT
iajs-777	101	7	closed	closed	ADJ
iajs-777	101	8	set	set	NOUN
iajs-777	101	9	is	be	AUX
iajs-777	101	10	an	an	DET
iajs-777	101	11	sr	sr	ADV
iajs-777	101	12	-	-	PUNCT
iajs-777	101	13	closed	closed	ADJ
iajs-777	101	14	set	set	NOUN
iajs-777	101	15	.	.	PUNCT
iajs-777	102	1	proof	proof	NOUN
iajs-777	102	2	:	:	PUNCT
iajs-777	102	3	let	let	VERB
iajs-777	102	4	a	a	PRON
iajs-777	102	5	be	be	AUX
iajs-777	102	6	an	an	DET
iajs-777	102	7	gr	gr	ADV
iajs-777	102	8	-	-	PUNCT
iajs-777	102	9	closed	closed	ADJ
iajs-777	102	10	set	set	NOUN
iajs-777	102	11	,	,	PUNCT
iajs-777	102	12	let	let	VERB
iajs-777	102	13	u	u	PRON
iajs-777	102	14	be	be	AUX
iajs-777	102	15	a	a	DET
iajs-777	102	16	regular	regular	ADJ
iajs-777	102	17	open	open	ADJ
iajs-777	102	18	set	set	NOUN
iajs-777	102	19	of	of	ADP
iajs-777	102	20	(	(	PUNCT
iajs-777	102	21	x,	x,	X
iajs-777	102	22	)	)	PUNCT
iajs-777	103	1	such	such	ADJ
iajs-777	103	2	that	that	SCONJ
iajs-777	103	3	a	a	DET
iajs-777	103	4			PROPN
iajs-777	103	5	u.	u.	PROPN
iajs-777	103	6	since	since	SCONJ
iajs-777	103	7	a	a	DET
iajs-777	103	8	is	be	AUX
iajs-777	103	9	gr	gr	ADV
iajs-777	103	10	-	-	PUNCT
iajs-777	103	11	closed	closed	ADJ
iajs-777	103	12	set	set	NOUN
iajs-777	103	13	and	and	CCONJ
iajs-777	103	14	scl(a	scl(a	ADJ
iajs-777	103	15	)	)	PUNCT
iajs-777	103	16			PROPN
iajs-777	103	17	cl(a	cl(a	PROPN
iajs-777	103	18	)	)	PUNCT
iajs-777	103	19	(	(	PUNCT
iajs-777	103	20	by	by	ADP
iajs-777	103	21	part	part	NOUN
iajs-777	103	22	(	(	PUNCT
iajs-777	103	23	2	2	NUM
iajs-777	103	24	)	)	PUNCT
iajs-777	103	25	of	of	ADP
iajs-777	103	26	remark	remark	NOUN
iajs-777	103	27	1.3	1.3	NUM
iajs-777	103	28	)	)	PUNCT
iajs-777	103	29	,	,	PUNCT
iajs-777	103	30	then	then	ADV
iajs-777	103	31	scl(a	scl(a	X
iajs-777	103	32	)	)	PUNCT
iajs-777	103	33			PROPN
iajs-777	103	34	u.	u.	PROPN
iajs-777	103	35	therefore	therefore	ADV
iajs-777	103	36	a	a	PRON
iajs-777	103	37	is	be	AUX
iajs-777	103	38	also	also	ADV
iajs-777	103	39	an	an	DET
iajs-777	103	40	sr	sr	ADV
iajs-777	103	41	-	-	PUNCT
iajs-777	103	42	closed	closed	ADJ
iajs-777	103	43	set	set	NOUN
iajs-777	103	44	.	.	PUNCT
iajs-777	104	1	the	the	DET
iajs-777	104	2	following	follow	VERB
iajs-777	104	3	example	example	NOUN
iajs-777	104	4	shows	show	VERB
iajs-777	104	5	that	that	SCONJ
iajs-777	104	6	the	the	DET
iajs-777	104	7	sr	sr	ADV
iajs-777	104	8	-	-	PUNCT
iajs-777	104	9	closed	closed	ADJ
iajs-777	104	10	set	set	NOUN
iajs-777	104	11	need	need	AUX
iajs-777	104	12	not	not	PART
iajs-777	104	13	to	to	PART
iajs-777	104	14	be	be	AUX
iajs-777	104	15	an	an	DET
iajs-777	104	16	gr	gr	ADV
iajs-777	104	17	-	-	PUNCT
iajs-777	104	18	closed	closed	ADJ
iajs-777	104	19	set	set	NOUN
iajs-777	104	20	.	.	PUNCT
iajs-777	105	1	2.5	2.5	NUM
iajs-777	105	2	example	example	NOUN
iajs-777	105	3	:	:	PUNCT
iajs-777	105	4	let	let	VERB
iajs-777	105	5	x={a	x={a	PROPN
iajs-777	105	6	,	,	PUNCT
iajs-777	105	7	b	b	PROPN
iajs-777	105	8	,	,	PUNCT
iajs-777	105	9	c	c	NOUN
iajs-777	105	10	}	}	PUNCT
iajs-777	105	11	and	and	CCONJ
iajs-777	105	12	={x,,{a},{b},{a	={x,,{a},{b},{a	NUM
iajs-777	105	13	,	,	PUNCT
iajs-777	105	14	b	b	NOUN
iajs-777	105	15	}	}	PUNCT
iajs-777	105	16	}	}	PUNCT
iajs-777	105	17	.	.	PUNCT
iajs-777	106	1	let	let	VERB
iajs-777	106	2	a={b	a={b	ADV
iajs-777	106	3	}	}	PUNCT
iajs-777	106	4	,	,	PUNCT
iajs-777	106	5	let	let	VERB
iajs-777	106	6	{	{	PUNCT
iajs-777	106	7	b	b	NOUN
iajs-777	106	8	}	}	PUNCT
iajs-777	106	9	is	be	AUX
iajs-777	106	10	the	the	DET
iajs-777	106	11	regular	regular	ADJ
iajs-777	106	12	open	open	ADJ
iajs-777	106	13	set	set	NOUN
iajs-777	106	14	containing	contain	VERB
iajs-777	106	15	a.	a.	NOUN
iajs-777	106	16	trivially	trivially	ADV
iajs-777	106	17	a	a	PRON
iajs-777	106	18	is	be	AUX
iajs-777	106	19	an	an	DET
iajs-777	106	20	sr	sr	ADV
iajs-777	106	21	-	-	PUNCT
iajs-777	106	22	closed	closed	ADJ
iajs-777	106	23	set	set	NOUN
iajs-777	106	24	since	since	SCONJ
iajs-777	106	25	scl(a)={b	scl(a)={b	ADV
iajs-777	106	26	}	}	PUNCT
iajs-777	106	27			PROPN
iajs-777	106	28	{	{	PUNCT
iajs-777	106	29	b	b	NOUN
iajs-777	106	30	}	}	PUNCT
iajs-777	106	31	.	.	PUNCT
iajs-777	107	1	but	but	CCONJ
iajs-777	107	2	a	a	PRON
iajs-777	107	3	is	be	AUX
iajs-777	107	4	not	not	PART
iajs-777	107	5	grclosed	grclose	VERB
iajs-777	107	6	set	set	VERB
iajs-777	107	7	since	since	SCONJ
iajs-777	107	8	cl(a)={b	cl(a)={b	PROPN
iajs-777	107	9	,	,	PUNCT
iajs-777	107	10	c	c	NOUN
iajs-777	107	11	}	}	PUNCT
iajs-777	107	12			PROPN
iajs-777	107	13	{	{	PUNCT
iajs-777	107	14	b	b	NOUN
iajs-777	107	15	}	}	PUNCT
iajs-777	107	16	.	.	PUNCT
iajs-777	108	1	2.6	2.6	NUM
iajs-777	108	2	corollary	corollary	NOUN
iajs-777	108	3	:	:	PUNCT
iajs-777	108	4	every	every	DET
iajs-777	108	5	closed	closed	ADJ
iajs-777	108	6	(	(	PUNCT
iajs-777	108	7	resp	resp	NOUN
iajs-777	108	8	.	.	PUNCT
iajs-777	109	1	-closed	-closed	ADJ
iajs-777	109	2	,	,	PUNCT
iajs-777	109	3	g	g	NOUN
iajs-777	109	4	-	-	PUNCT
iajs-777	109	5	closed	closed	ADJ
iajs-777	109	6	,	,	PUNCT
iajs-777	109	7	g-closed	g-close	VERB
iajs-777	109	8	)	)	PUNCT
iajs-777	109	9	set	set	NOUN
iajs-777	109	10	is	be	AUX
iajs-777	109	11	an	an	DET
iajs-777	109	12	sr	sr	ADV
iajs-777	109	13	-	-	PUNCT
iajs-777	109	14	closed	closed	ADJ
iajs-777	109	15	set	set	NOUN
iajs-777	109	16	.	.	PUNCT
iajs-777	110	1	proof	proof	NOUN
iajs-777	110	2	:	:	PUNCT
iajs-777	110	3	since	since	SCONJ
iajs-777	110	4	every	every	DET
iajs-777	110	5	gr	gr	ADV
iajs-777	110	6	-	-	PUNCT
iajs-777	110	7	closed	closed	ADJ
iajs-777	110	8	set	set	NOUN
iajs-777	110	9	is	be	AUX
iajs-777	110	10	an	an	DET
iajs-777	110	11	sr	sr	ADV
iajs-777	110	12	-	-	PUNCT
iajs-777	110	13	closed	closed	ADJ
iajs-777	110	14	set	set	NOUN
iajs-777	110	15	,	,	PUNCT
iajs-777	110	16	then	then	ADV
iajs-777	110	17	in	in	ADP
iajs-777	110	18	vitue	vitue	NOUN
iajs-777	110	19	of	of	ADP
iajs-777	110	20	proposition	proposition	NOUN
iajs-777	110	21	1.2	1.2	NUM
iajs-777	110	22	part	part	NOUN
iajs-777	110	23	(	(	PUNCT
iajs-777	110	24	2	2	NUM
iajs-777	110	25	)	)	PUNCT
iajs-777	110	26	the	the	DET
iajs-777	110	27	proof	proof	NOUN
iajs-777	110	28	is	be	AUX
iajs-777	110	29	over	over	ADV
iajs-777	110	30	.	.	PUNCT
iajs-777	111	1	the	the	DET
iajs-777	111	2	following	follow	VERB
iajs-777	111	3	example	example	NOUN
iajs-777	111	4	shows	show	VERB
iajs-777	111	5	that	that	SCONJ
iajs-777	111	6	the	the	PRON
iajs-777	111	7	reveres	revere	VERB
iajs-777	111	8	implications	implication	NOUN
iajs-777	111	9	in	in	ADP
iajs-777	111	10	the	the	DET
iajs-777	111	11	above	above	ADJ
iajs-777	111	12	corollary	corollary	NOUN
iajs-777	111	13	are	be	AUX
iajs-777	111	14	not	not	PART
iajs-777	111	15	true	true	ADJ
iajs-777	111	16	in	in	ADP
iajs-777	111	17	general	general	ADJ
iajs-777	111	18	.	.	PUNCT
iajs-777	112	1	2.7	2.7	NUM
iajs-777	112	2	example	example	NOUN
iajs-777	112	3	:	:	PUNCT
iajs-777	112	4	let	let	VERB
iajs-777	112	5	x	x	PRON
iajs-777	112	6	,	,	PUNCT
iajs-777	112	7			PROPN
iajs-777	112	8	and	and	CCONJ
iajs-777	112	9	a	a	DET
iajs-777	112	10	be	be	NOUN
iajs-777	112	11	as	as	ADP
iajs-777	112	12	in	in	ADP
iajs-777	112	13	example	example	NOUN
iajs-777	112	14	2.3	2.3	NUM
iajs-777	112	15	.	.	PUNCT
iajs-777	113	1	a	a	PRON
iajs-777	113	2	is	be	AUX
iajs-777	113	3	neither	neither	CCONJ
iajs-777	113	4	closed	closed	ADJ
iajs-777	113	5	(	(	PUNCT
iajs-777	113	6	since	since	SCONJ
iajs-777	113	7	cl(a	cl(a	NUM
iajs-777	113	8	)	)	PUNCT
iajs-777	113	9	=	=	SYM
iajs-777	113	10	x	x	PUNCT
iajs-777	113	11			PROPN
iajs-777	113	12	a	a	NOUN
iajs-777	113	13	)	)	PUNCT
iajs-777	113	14	nor	nor	CCONJ
iajs-777	113	15	-closed	-closed	ADJ
iajs-777	113	16	(	(	PUNCT
iajs-777	113	17	since	since	SCONJ
iajs-777	113	18	cl(a	cl(a	VERB
iajs-777	113	19	)	)	PUNCT
iajs-777	113	20	=	=	SYM
iajs-777	114	1	x	x	PUNCT
iajs-777	114	2			PROPN
iajs-777	114	3	a	a	NOUN
iajs-777	114	4	)	)	PUNCT
iajs-777	114	5	and	and	CCONJ
iajs-777	114	6	also	also	ADV
iajs-777	114	7	it	it	PRON
iajs-777	114	8	is	be	AUX
iajs-777	114	9	neither	neither	CCONJ
iajs-777	114	10	g	g	NOUN
iajs-777	114	11	-	-	PUNCT
iajs-777	114	12	closed	closed	ADJ
iajs-777	114	13	(	(	PUNCT
iajs-777	114	14	since	since	SCONJ
iajs-777	114	15	a={a	a={a	NOUN
iajs-777	114	16	,	,	PUNCT
iajs-777	114	17	c	c	NOUN
iajs-777	114	18	}	}	PUNCT
iajs-777	114	19			PROPN
iajs-777	114	20	{	{	PUNCT
iajs-777	114	21	a	a	NOUN
iajs-777	114	22	,	,	PUNCT
iajs-777	114	23	c	c	NOUN
iajs-777	114	24	}	}	PUNCT
iajs-777	114	25	whenever	whenever	SCONJ
iajs-777	114	26	{	{	PUNCT
iajs-777	114	27	a	a	PRON
iajs-777	114	28	,	,	PUNCT
iajs-777	114	29	c	c	NOUN
iajs-777	114	30	}	}	PUNCT
iajs-777	114	31			NOUN
iajs-777	114	32			NOUN
iajs-777	114	33	,	,	PUNCT
iajs-777	114	34	but	but	CCONJ
iajs-777	114	35	cl(a	cl(a	X
iajs-777	114	36	)	)	PUNCT
iajs-777	114	37	=	=	SYM
iajs-777	115	1	x	x	X
iajs-777	115	2			PROPN
iajs-777	115	3	{	{	PUNCT
iajs-777	115	4	a	a	NOUN
iajs-777	115	5	,	,	PUNCT
iajs-777	115	6	c	c	NOUN
iajs-777	115	7	}	}	PUNCT
iajs-777	115	8	)	)	PUNCT
iajs-777	115	9	nor	nor	CCONJ
iajs-777	115	10	g-closed	g-close	VERB
iajs-777	115	11	(	(	PUNCT
iajs-777	115	12	since	since	SCONJ
iajs-777	115	13	a={a	a={a	NOUN
iajs-777	115	14	,	,	PUNCT
iajs-777	115	15	c	c	NOUN
iajs-777	115	16	}	}	PUNCT
iajs-777	115	17			PROPN
iajs-777	115	18	{	{	PUNCT
iajs-777	115	19	a	a	NOUN
iajs-777	115	20	,	,	PUNCT
iajs-777	115	21	c	c	NOUN
iajs-777	115	22	}	}	PUNCT
iajs-777	115	23	whenever	whenever	SCONJ
iajs-777	115	24	{	{	PUNCT
iajs-777	115	25	a	a	PRON
iajs-777	115	26	,	,	PUNCT
iajs-777	115	27	c	c	NOUN
iajs-777	115	28	}	}	PUNCT
iajs-777	115	29			NOUN
iajs-777	115	30	o(x	o(x	NUM
iajs-777	115	31	)	)	PUNCT
iajs-777	115	32	,	,	PUNCT
iajs-777	115	33	but	but	CCONJ
iajs-777	115	34	cl(a	cl(a	ADJ
iajs-777	115	35	)	)	PUNCT
iajs-777	115	36	=	=	SYM
iajs-777	116	1	x	x	X
iajs-777	116	2			PROPN
iajs-777	116	3	{	{	PUNCT
iajs-777	116	4	a	a	PRON
iajs-777	116	5	,	,	PUNCT
iajs-777	116	6	c	c	NOUN
iajs-777	116	7	}	}	PUNCT
iajs-777	116	8	)	)	PUNCT
iajs-777	116	9	.	.	PUNCT
iajs-777	117	1	2.8	2.8	NUM
iajs-777	117	2	corollary	corollary	NOUN
iajs-777	117	3	:	:	PUNCT
iajs-777	117	4	every	every	DET
iajs-777	117	5	g*-closed	g*-closed	PROPN
iajs-777	117	6	(	(	PUNCT
iajs-777	117	7	resp	resp	NOUN
iajs-777	117	8	.	.	PUNCT
iajs-777	118	1	**g	**g	NOUN
iajs-777	118	2	-	-	PUNCT
iajs-777	118	3	closed	closed	ADJ
iajs-777	118	4	,	,	PUNCT
iajs-777	118	5	g**-closed	g**-close	VERB
iajs-777	118	6	)	)	PUNCT
iajs-777	118	7	set	set	NOUN
iajs-777	118	8	is	be	AUX
iajs-777	118	9	an	an	DET
iajs-777	118	10	sr	sr	ADV
iajs-777	118	11	-	-	PUNCT
iajs-777	118	12	closed	closed	ADJ
iajs-777	118	13	set	set	NOUN
iajs-777	118	14	.	.	PUNCT
iajs-777	119	1	proof	proof	NOUN
iajs-777	119	2	:	:	PUNCT
iajs-777	119	3	since	since	SCONJ
iajs-777	119	4	every	every	DET
iajs-777	119	5	gr	gr	ADV
iajs-777	119	6	-	-	PUNCT
iajs-777	119	7	closed	closed	ADJ
iajs-777	119	8	set	set	NOUN
iajs-777	119	9	is	be	AUX
iajs-777	119	10	an	an	DET
iajs-777	119	11	sr	sr	ADV
iajs-777	119	12	-	-	PUNCT
iajs-777	119	13	closed	closed	ADJ
iajs-777	119	14	set	set	NOUN
iajs-777	119	15	,	,	PUNCT
iajs-777	119	16	part	part	NOUN
iajs-777	119	17	(	(	PUNCT
iajs-777	119	18	4	4	NUM
iajs-777	119	19	)	)	PUNCT
iajs-777	119	20	of	of	ADP
iajs-777	119	21	proposition	proposition	NOUN
iajs-777	119	22	1.2	1.2	NUM
iajs-777	119	23	is	be	AUX
iajs-777	119	24	applicable	applicable	ADJ
iajs-777	119	25	.	.	PUNCT
iajs-777	120	1	the	the	DET
iajs-777	120	2	following	follow	VERB
iajs-777	120	3	example	example	NOUN
iajs-777	120	4	shows	show	VERB
iajs-777	120	5	that	that	SCONJ
iajs-777	120	6	an	an	DET
iajs-777	120	7	sr	sr	ADV
iajs-777	120	8	-	-	PUNCT
iajs-777	120	9	closed	closed	ADJ
iajs-777	120	10	set	set	NOUN
iajs-777	120	11	needs	need	VERB
iajs-777	120	12	not	not	PART
iajs-777	120	13	to	to	PART
iajs-777	120	14	be	be	AUX
iajs-777	120	15	a	a	DET
iajs-777	120	16	g*-closed	g*-closed	PROPN
iajs-777	120	17	set	set	NOUN
iajs-777	120	18	.	.	PUNCT
iajs-777	121	1	ibn	ibn	PROPN
iajs-777	121	2	alhaitham	alhaitham	PROPN
iajs-777	121	3	j.	j.	PROPN
iajs-777	121	4	for	for	ADP
iajs-777	121	5	pure	pure	ADJ
iajs-777	121	6	&	&	CCONJ
iajs-777	121	7	appl	appl	PROPN
iajs-777	121	8	.	.	PUNCT
iajs-777	122	1	sci	sci	PROPN
iajs-777	122	2	.	.	PUNCT
iajs-777	122	3	vol.24	vol.24	NOUN
iajs-777	122	4	(	(	PUNCT
iajs-777	122	5	2	2	NUM
iajs-777	122	6	)	)	PUNCT
iajs-777	122	7	2011	2011	NUM
iajs-777	122	8	2.9	2.9	NUM
iajs-777	122	9	example	example	NOUN
iajs-777	122	10	:	:	PUNCT
iajs-777	122	11	let	let	VERB
iajs-777	122	12	x=	x=	PROPN
iajs-777	122	13	�	�	PROPN
iajs-777	122	14	and	and	CCONJ
iajs-777	122	15			PROPN
iajs-777	122	16	=	=	NOUN
iajs-777	123	1	u	u	NOUN
iajs-777	123	2	,	,	PUNCT
iajs-777	123	3	let	let	VERB
iajs-777	123	4	a=(a	a=(a	NOUN
iajs-777	123	5	,	,	PUNCT
iajs-777	123	6	b	b	NOUN
iajs-777	123	7	)	)	PUNCT
iajs-777	123	8	is	be	AUX
iajs-777	123	9	sr	sr	NOUN
iajs-777	123	10	-	-	PUNCT
iajs-777	123	11	closed	closed	ADJ
iajs-777	123	12	set	set	NOUN
iajs-777	123	13	but	but	CCONJ
iajs-777	123	14	not	not	PART
iajs-777	123	15	a	a	DET
iajs-777	123	16	g*-closed	g*-closed	PROPN
iajs-777	123	17	set	set	NOUN
iajs-777	123	18	,	,	PUNCT
iajs-777	123	19	since	since	SCONJ
iajs-777	123	20	(	(	PUNCT
iajs-777	123	21	a	a	DET
iajs-777	123	22	,	,	PUNCT
iajs-777	123	23	b	b	NOUN
iajs-777	123	24	)	)	PUNCT
iajs-777	123	25			PROPN
iajs-777	123	26	(	(	PUNCT
iajs-777	123	27	a	a	DET
iajs-777	123	28	,	,	PUNCT
iajs-777	123	29	b	b	NOUN
iajs-777	123	30	)	)	PUNCT
iajs-777	123	31	and	and	CCONJ
iajs-777	123	32	(	(	PUNCT
iajs-777	123	33	a	a	DET
iajs-777	123	34	,	,	PUNCT
iajs-777	123	35	b	b	NOUN
iajs-777	123	36	)	)	PUNCT
iajs-777	123	37	is	be	AUX
iajs-777	123	38	-open	-open	PROPN
iajs-777	123	39	set	set	VERB
iajs-777	123	40	in	in	ADP
iajs-777	123	41	(	(	PUNCT
iajs-777	123	42	�	�	PROPN
iajs-777	123	43	,	,	PUNCT
iajs-777	123	44	u	u	NOUN
iajs-777	123	45	)	)	PUNCT
iajs-777	123	46	,	,	PUNCT
iajs-777	123	47	but	but	CCONJ
iajs-777	123	48	cl(a	cl(a	ADJ
iajs-777	123	49	)	)	PUNCT
iajs-777	123	50	=	=	PUNCT
iajs-777	124	1	[	[	X
iajs-777	124	2	a	a	DET
iajs-777	124	3	,	,	PUNCT
iajs-777	124	4	b	b	NOUN
iajs-777	124	5	]	]	X
iajs-777	124	6			PROPN
iajs-777	124	7	(	(	PUNCT
iajs-777	124	8	a	a	DET
iajs-777	124	9	,	,	PUNCT
iajs-777	124	10	b	b	NOUN
iajs-777	124	11	)	)	PUNCT
iajs-777	124	12	.	.	PUNCT
iajs-777	125	1	2.10	2.10	NUM
iajs-777	125	2	proposition	proposition	NOUN
iajs-777	125	3	:	:	PUNCT
iajs-777	125	4	every	every	DET
iajs-777	125	5	r	r	NOUN
iajs-777	125	6	-	-	PUNCT
iajs-777	125	7	gclosed	gclose	VERB
iajs-777	125	8	is	be	AUX
iajs-777	125	9	an	an	DET
iajs-777	125	10	sr	sr	ADV
iajs-777	125	11	-	-	PUNCT
iajs-777	125	12	closed	closed	ADJ
iajs-777	125	13	set	set	NOUN
iajs-777	125	14	.	.	PUNCT
iajs-777	126	1	proof	proof	NOUN
iajs-777	126	2	:	:	PUNCT
iajs-777	126	3	let	let	VERB
iajs-777	126	4	a	a	PRON
iajs-777	126	5	be	be	AUX
iajs-777	126	6	a	a	DET
iajs-777	126	7	regular	regular	ADJ
iajs-777	126	8	generalized	generalize	VERB
iajs-777	126	9	closed	close	VERB
iajs-777	126	10	set	set	NOUN
iajs-777	126	11	of	of	ADP
iajs-777	126	12	(	(	PUNCT
iajs-777	126	13	x,	x,	PROPN
iajs-777	126	14	)	)	PUNCT
iajs-777	126	15	.	.	PUNCT
iajs-777	127	1	let	let	VERB
iajs-777	127	2	u	u	PRON
iajs-777	127	3	be	be	AUX
iajs-777	127	4	a	a	DET
iajs-777	127	5	regular	regular	ADJ
iajs-777	127	6	open	open	ADJ
iajs-777	127	7	set	set	NOUN
iajs-777	127	8	of	of	ADP
iajs-777	127	9	(	(	PUNCT
iajs-777	127	10	x,	x,	X
iajs-777	127	11	)	)	PUNCT
iajs-777	127	12	such	such	ADJ
iajs-777	127	13	that	that	SCONJ
iajs-777	127	14	a	a	DET
iajs-777	127	15			PROPN
iajs-777	127	16	u.	u.	PROPN
iajs-777	127	17	then	then	ADV
iajs-777	127	18	cl(a	cl(a	PUNCT
iajs-777	127	19	)	)	PUNCT
iajs-777	127	20			PROPN
iajs-777	127	21	u	u	PROPN
iajs-777	127	22	since	since	SCONJ
iajs-777	127	23	a	a	PRON
iajs-777	127	24	is	be	AUX
iajs-777	127	25	r	r	NOUN
iajs-777	127	26	-	-	PUNCT
iajs-777	127	27	g	g	NOUN
iajs-777	127	28	closed	close	VERB
iajs-777	127	29	set	set	NOUN
iajs-777	127	30	.	.	PUNCT
iajs-777	128	1	since	since	SCONJ
iajs-777	128	2	every	every	DET
iajs-777	128	3	closed	closed	ADJ
iajs-777	128	4	set	set	NOUN
iajs-777	128	5	is	be	AUX
iajs-777	128	6	semi-closed	semi-close	VERB
iajs-777	128	7	set	set	NOUN
iajs-777	128	8	,	,	PUNCT
iajs-777	128	9	then	then	ADV
iajs-777	128	10	scl	scl	NOUN
iajs-777	128	11			PROPN
iajs-777	128	12	cl(a	cl(a	X
iajs-777	128	13	)	)	PUNCT
iajs-777	128	14	(	(	PUNCT
iajs-777	128	15	part	part	NOUN
iajs-777	128	16	2	2	NUM
iajs-777	128	17	of	of	ADP
iajs-777	128	18	remark	remark	NOUN
iajs-777	128	19	1.3	1.3	NUM
iajs-777	128	20	)	)	PUNCT
iajs-777	128	21	.	.	PUNCT
iajs-777	129	1	thus	thus	ADV
iajs-777	129	2	scl(a	scl(a	X
iajs-777	129	3	)	)	PUNCT
iajs-777	129	4			PROPN
iajs-777	129	5	u	u	PROPN
iajs-777	129	6	,	,	PUNCT
iajs-777	129	7	therefore	therefore	ADV
iajs-777	129	8	a	a	PRON
iajs-777	129	9	is	be	AUX
iajs-777	129	10	an	an	DET
iajs-777	129	11	srclosed	srclose	VERB
iajs-777	129	12	set	set	NOUN
iajs-777	129	13	.	.	PUNCT
iajs-777	130	1	the	the	DET
iajs-777	130	2	converse	converse	NOUN
iajs-777	130	3	of	of	ADP
iajs-777	130	4	above	above	ADJ
iajs-777	130	5	proposition	proposition	NOUN
iajs-777	130	6	is	be	AUX
iajs-777	130	7	not	not	PART
iajs-777	130	8	always	always	ADV
iajs-777	130	9	true	true	ADJ
iajs-777	130	10	as	as	SCONJ
iajs-777	130	11	the	the	DET
iajs-777	130	12	following	follow	VERB
iajs-777	130	13	example	example	NOUN
iajs-777	130	14	shows	show	VERB
iajs-777	130	15	.	.	PUNCT
iajs-777	131	1	2.11	2.11	NUM
iajs-777	131	2	example	example	NOUN
iajs-777	131	3	:	:	PUNCT
iajs-777	131	4	let	let	VERB
iajs-777	131	5	x	x	PRON
iajs-777	131	6	and	and	CCONJ
iajs-777	131	7			NOUN
iajs-777	131	8	be	be	VERB
iajs-777	131	9	as	as	ADP
iajs-777	131	10	in	in	ADP
iajs-777	131	11	example	example	NOUN
iajs-777	131	12	2.3	2.3	NUM
iajs-777	131	13	,	,	PUNCT
iajs-777	131	14	let	let	VERB
iajs-777	131	15	a={c	a={c	NOUN
iajs-777	131	16	}	}	PUNCT
iajs-777	131	17	and	and	CCONJ
iajs-777	131	18	u={c	u={c	PROPN
iajs-777	131	19	}	}	PUNCT
iajs-777	131	20	is	be	AUX
iajs-777	131	21	regular	regular	ADJ
iajs-777	131	22	open	open	ADJ
iajs-777	131	23	set	set	NOUN
iajs-777	131	24	containing	contain	VERB
iajs-777	131	25	a.	a.	NOUN
iajs-777	131	26	it	it	PRON
iajs-777	131	27	is	be	AUX
iajs-777	131	28	clear	clear	ADJ
iajs-777	131	29	a	a	PRON
iajs-777	131	30	is	be	AUX
iajs-777	131	31	an	an	DET
iajs-777	131	32	sr	sr	ADV
iajs-777	131	33	-	-	PUNCT
iajs-777	131	34	closed	closed	ADJ
iajs-777	131	35	set	set	NOUN
iajs-777	131	36	since	since	SCONJ
iajs-777	131	37	scl(a	scl(a	NOUN
iajs-777	131	38	)	)	PUNCT
iajs-777	131	39	=	=	SYM
iajs-777	131	40	{	{	PUNCT
iajs-777	131	41	c	c	NOUN
iajs-777	131	42	}	}	PUNCT
iajs-777	131	43			PROPN
iajs-777	131	44	{	{	PUNCT
iajs-777	131	45	c	c	NOUN
iajs-777	131	46	}	}	PUNCT
iajs-777	131	47	.	.	PUNCT
iajs-777	132	1	but	but	CCONJ
iajs-777	132	2	is	be	AUX
iajs-777	132	3	not	not	PART
iajs-777	132	4	r	r	NOUN
iajs-777	132	5	-	-	PUNCT
iajs-777	132	6	g	g	NOUN
iajs-777	132	7	closed	close	VERB
iajs-777	132	8	set	set	VERB
iajs-777	132	9	since	since	SCONJ
iajs-777	132	10	cl(a	cl(a	VERB
iajs-777	132	11	)	)	PUNCT
iajs-777	133	1	=	=	SYM
iajs-777	133	2	{	{	PUNCT
iajs-777	133	3	b	b	NOUN
iajs-777	133	4	,	,	PUNCT
iajs-777	133	5	c	c	NOUN
iajs-777	133	6	}	}	PUNCT
iajs-777	133	7			PROPN
iajs-777	133	8	{	{	PUNCT
iajs-777	133	9	c	c	NOUN
iajs-777	133	10	}	}	PUNCT
iajs-777	133	11	.	.	PUNCT
iajs-777	134	1	2.12	2.12	NUM
iajs-777	134	2	proposition	proposition	NOUN
iajs-777	134	3	:	:	PUNCT
iajs-777	134	4	every	every	DET
iajs-777	134	5	g	g	ADV
iajs-777	134	6	-	-	PUNCT
iajs-777	134	7	closed	closed	ADJ
iajs-777	134	8	set	set	NOUN
iajs-777	134	9	is	be	AUX
iajs-777	134	10	an	an	DET
iajs-777	134	11	sr	sr	ADV
iajs-777	134	12	-	-	PUNCT
iajs-777	134	13	closed	closed	ADJ
iajs-777	134	14	set	set	ADJ
iajs-777	134	15	proof	proof	NOUN
iajs-777	134	16	:	:	PUNCT
iajs-777	134	17	let	let	VERB
iajs-777	134	18	a	a	PRON
iajs-777	134	19	be	be	AUX
iajs-777	134	20	an	an	DET
iajs-777	134	21	g	g	ADV
iajs-777	134	22	-	-	PUNCT
iajs-777	134	23	closed	closed	ADJ
iajs-777	134	24	set	set	NOUN
iajs-777	134	25	,	,	PUNCT
iajs-777	134	26	let	let	VERB
iajs-777	134	27	u	u	PRON
iajs-777	134	28	be	be	AUX
iajs-777	134	29	a	a	DET
iajs-777	134	30	regular	regular	ADJ
iajs-777	134	31	open	open	ADJ
iajs-777	134	32	set	set	NOUN
iajs-777	134	33	of	of	ADP
iajs-777	134	34	(	(	PUNCT
iajs-777	134	35	x,	x,	X
iajs-777	134	36	)	)	PUNCT
iajs-777	134	37	such	such	ADJ
iajs-777	134	38	that	that	SCONJ
iajs-777	134	39	a	a	DET
iajs-777	134	40			PROPN
iajs-777	134	41	u.	u.	PROPN
iajs-777	134	42	since	since	SCONJ
iajs-777	134	43	a	a	PRON
iajs-777	134	44	is	is	ADJ
iajs-777	134	45	g	g	ADV
iajs-777	134	46	-	-	PUNCT
iajs-777	134	47	closed	closed	ADJ
iajs-777	134	48	and	and	CCONJ
iajs-777	134	49	every	every	DET
iajs-777	134	50	regular	regular	ADJ
iajs-777	134	51	open	open	ADJ
iajs-777	134	52	set	set	NOUN
iajs-777	134	53	is	be	AUX
iajs-777	134	54	an	an	DET
iajs-777	134	55	open	open	ADJ
iajs-777	134	56	set	set	NOUN
iajs-777	134	57	,	,	PUNCT
iajs-777	134	58	then	then	ADV
iajs-777	134	59	cl(a	cl(a	ADJ
iajs-777	134	60	)	)	PUNCT
iajs-777	134	61			PROPN
iajs-777	134	62	u.	u.	PROPN
iajs-777	134	63	but	but	CCONJ
iajs-777	134	64	scl(a	scl(a	ADJ
iajs-777	134	65	)	)	PUNCT
iajs-777	134	66			PROPN
iajs-777	134	67			X
iajs-777	134	68	cl(a	cl(a	NUM
iajs-777	134	69	)	)	PUNCT
iajs-777	134	70	since	since	SCONJ
iajs-777	134	71	every	every	DET
iajs-777	134	72	-closed	-closed	ADJ
iajs-777	134	73	set	set	NOUN
iajs-777	134	74	is	be	AUX
iajs-777	134	75	semi--closed	semi--close	VERB
iajs-777	134	76	set	set	VERB
iajs-777	134	77	.	.	PUNCT
iajs-777	135	1	therefore	therefore	ADV
iajs-777	135	2	a	a	PRON
iajs-777	135	3	is	be	AUX
iajs-777	135	4	also	also	ADV
iajs-777	135	5	an	an	DET
iajs-777	135	6	sr	sr	ADV
iajs-777	135	7	-	-	PUNCT
iajs-777	135	8	closed	closed	ADJ
iajs-777	135	9	set	set	NOUN
iajs-777	135	10	.	.	PUNCT
iajs-777	136	1	the	the	DET
iajs-777	136	2	converse	converse	NOUN
iajs-777	136	3	in	in	ADP
iajs-777	136	4	the	the	DET
iajs-777	136	5	above	above	ADJ
iajs-777	136	6	proposition	proposition	NOUN
iajs-777	136	7	is	be	AUX
iajs-777	136	8	not	not	PART
iajs-777	136	9	true	true	ADJ
iajs-777	136	10	as	as	SCONJ
iajs-777	136	11	it	it	PRON
iajs-777	136	12	can	can	AUX
iajs-777	136	13	be	be	AUX
iajs-777	136	14	seen	see	VERB
iajs-777	136	15	from	from	ADP
iajs-777	136	16	the	the	DET
iajs-777	136	17	following	follow	VERB
iajs-777	136	18	example	example	NOUN
iajs-777	136	19	.	.	PUNCT
iajs-777	137	1	2.13	2.13	NUM
iajs-777	137	2	example	example	NOUN
iajs-777	137	3	:	:	PUNCT
iajs-777	137	4	in	in	ADP
iajs-777	137	5	example	example	NOUN
iajs-777	137	6	2.3	2.3	NUM
iajs-777	137	7	cl(a	cl(a	NOUN
iajs-777	137	8	)	)	PUNCT
iajs-777	137	9	=	=	SYM
iajs-777	138	1	x	x	X
iajs-777	138	2			PROPN
iajs-777	138	3	{	{	PUNCT
iajs-777	138	4	a	a	NOUN
iajs-777	138	5	,	,	PUNCT
iajs-777	138	6	c	c	NOUN
iajs-777	138	7	}	}	PUNCT
iajs-777	138	8	.	.	PUNCT
iajs-777	139	1	thus	thus	ADV
iajs-777	139	2	a	a	PRON
iajs-777	139	3	is	be	AUX
iajs-777	139	4	not	not	PART
iajs-777	139	5	g	g	ADV
iajs-777	139	6	-	-	PUNCT
iajs-777	139	7	closed	closed	ADJ
iajs-777	139	8	set	set	NOUN
iajs-777	139	9	,	,	PUNCT
iajs-777	139	10	but	but	CCONJ
iajs-777	139	11	it	it	PRON
iajs-777	139	12	is	be	AUX
iajs-777	139	13	sr	sr	NOUN
iajs-777	139	14	-	-	PUNCT
iajs-777	139	15	closed	closed	ADJ
iajs-777	139	16	set	set	NOUN
iajs-777	139	17	.	.	PUNCT
iajs-777	140	1	2.14	2.14	NUM
iajs-777	140	2	proposition	proposition	NOUN
iajs-777	140	3	:	:	PUNCT
iajs-777	140	4	let	let	VERB
iajs-777	140	5	a	a	PRON
iajs-777	140	6	be	be	AUX
iajs-777	140	7	an	an	DET
iajs-777	140	8	sr	sr	ADV
iajs-777	140	9	-	-	PUNCT
iajs-777	140	10	closed	closed	ADJ
iajs-777	140	11	set	set	NOUN
iajs-777	140	12	of	of	ADP
iajs-777	140	13	(	(	PUNCT
iajs-777	140	14	x,	x,	PROPN
iajs-777	140	15	)	)	PUNCT
iajs-777	140	16	.	.	PUNCT
iajs-777	141	1	then	then	ADV
iajs-777	141	2	scl(a)-a	scl(a)-a	PROPN
iajs-777	141	3	does	do	AUX
iajs-777	141	4	contain	contain	VERB
iajs-777	141	5	any	any	DET
iajs-777	141	6	non	non	ADJ
iajs-777	141	7	-	-	ADJ
iajs-777	141	8	empty	empty	ADJ
iajs-777	141	9	regular	regular	ADJ
iajs-777	141	10	closed	closed	ADJ
iajs-777	141	11	set	set	NOUN
iajs-777	141	12	.	.	PUNCT
iajs-777	142	1	proof	proof	NOUN
iajs-777	142	2	:	:	PUNCT
iajs-777	142	3	let	let	VERB
iajs-777	142	4	f	f	PRON
iajs-777	142	5	be	be	AUX
iajs-777	142	6	any	any	DET
iajs-777	142	7	regular	regular	ADJ
iajs-777	142	8	closed	closed	ADJ
iajs-777	142	9	set	set	NOUN
iajs-777	142	10	of	of	ADP
iajs-777	142	11	(	(	PUNCT
iajs-777	142	12	x,	x,	X
iajs-777	142	13	)	)	PUNCT
iajs-777	142	14	such	such	ADJ
iajs-777	142	15	that	that	SCONJ
iajs-777	142	16	f	f	PROPN
iajs-777	142	17			PROPN
iajs-777	142	18	scl(a	scl(a	PROPN
iajs-777	142	19	)	)	PUNCT
iajs-777	142	20	–	–	PUNCT
iajs-777	142	21	a.	a.	NOUN
iajs-777	143	1	then	then	ADV
iajs-777	143	2	f	f	PROPN
iajs-777	143	3			PROPN
iajs-777	143	4	x	x	INTJ
iajs-777	143	5	–	–	PUNCT
iajs-777	143	6	a	a	PRON
iajs-777	143	7	implies	imply	VERB
iajs-777	143	8	that	that	SCONJ
iajs-777	143	9	a	a	DET
iajs-777	143	10			PROPN
iajs-777	143	11	x	x	INTJ
iajs-777	143	12	–	–	PUNCT
iajs-777	143	13	f.	f.	PROPN
iajs-777	143	14	since	since	SCONJ
iajs-777	143	15	a	a	PRON
iajs-777	143	16	is	be	AUX
iajs-777	143	17	sr	sr	NOUN
iajs-777	143	18	-	-	PUNCT
iajs-777	143	19	closed	closed	ADJ
iajs-777	143	20	and	and	CCONJ
iajs-777	143	21	x	x	X
iajs-777	143	22	–	–	PUNCT
iajs-777	143	23	f	f	PROPN
iajs-777	143	24	is	be	AUX
iajs-777	143	25	a	a	DET
iajs-777	143	26	regular	regular	ADJ
iajs-777	143	27	open	open	ADJ
iajs-777	143	28	set	set	NOUN
iajs-777	143	29	of	of	ADP
iajs-777	143	30	(	(	PUNCT
iajs-777	143	31	x,	x,	PROPN
iajs-777	143	32	)	)	PUNCT
iajs-777	143	33	,	,	PUNCT
iajs-777	143	34	then	then	ADV
iajs-777	143	35	scl(a	scl(a	X
iajs-777	143	36	)	)	PUNCT
iajs-777	143	37			PROPN
iajs-777	143	38	x	x	INTJ
iajs-777	143	39	–	–	PUNCT
iajs-777	143	40	f	f	X
iajs-777	143	41	,	,	PUNCT
iajs-777	143	42	so	so	ADV
iajs-777	143	43	f	f	PROPN
iajs-777	143	44			PROPN
iajs-777	143	45	x	x	X
iajs-777	143	46	scl(a	scl(a	PROPN
iajs-777	143	47	)	)	PUNCT
iajs-777	143	48	.	.	PUNCT
iajs-777	144	1	therefore	therefore	ADV
iajs-777	144	2	f	f	PROPN
iajs-777	144	3			PROPN
iajs-777	144	4	scl(a	scl(a	PROPN
iajs-777	144	5	)	)	PUNCT
iajs-777	144	6			NOUN
iajs-777	144	7	(	(	PUNCT
iajs-777	144	8	x	x	X
iajs-777	144	9	–	–	PUNCT
iajs-777	144	10	scl(a	scl(a	NOUN
iajs-777	144	11	)	)	PUNCT
iajs-777	144	12	)	)	PUNCT
iajs-777	144	13	=	=	PUNCT
iajs-777	144	14	.	.	PUNCT
iajs-777	144	15	hence	hence	ADV
iajs-777	144	16	scl(a	scl(a	X
iajs-777	144	17	)	)	PUNCT
iajs-777	144	18	–	–	PUNCT
iajs-777	144	19	a	a	PRON
iajs-777	144	20	does	do	AUX
iajs-777	144	21	not	not	PART
iajs-777	144	22	contain	contain	VERB
iajs-777	144	23	any	any	DET
iajs-777	144	24	non	non	ADJ
iajs-777	144	25	-	-	ADJ
iajs-777	144	26	empty	empty	ADJ
iajs-777	144	27	regular	regular	ADJ
iajs-777	144	28	closed	closed	ADJ
iajs-777	144	29	set	set	NOUN
iajs-777	144	30	.	.	PUNCT
iajs-777	145	1	2.15	2.15	NUM
iajs-777	145	2	proposition	proposition	NOUN
iajs-777	145	3	:	:	PUNCT
iajs-777	145	4	every	every	DET
iajs-777	145	5	sr	sr	ADV
iajs-777	145	6	-	-	PUNCT
iajs-777	145	7	closed	closed	ADJ
iajs-777	145	8	set	set	NOUN
iajs-777	145	9	is	be	AUX
iajs-777	145	10	a	a	DET
iajs-777	145	11	pre	pre	ADJ
iajs-777	145	12	-	-	ADJ
iajs-777	145	13	semi	semi	ADJ
iajs-777	145	14	-	-	ADJ
iajs-777	145	15	closed	closed	ADJ
iajs-777	145	16	set	set	NOUN
iajs-777	145	17	.	.	PUNCT
iajs-777	146	1	proof	proof	NOUN
iajs-777	146	2	:	:	PUNCT
iajs-777	146	3	let	let	VERB
iajs-777	146	4	a	a	PRON
iajs-777	146	5	be	be	AUX
iajs-777	146	6	an	an	DET
iajs-777	146	7	sr	sr	ADV
iajs-777	146	8	-	-	PUNCT
iajs-777	146	9	closed	closed	ADJ
iajs-777	146	10	set	set	NOUN
iajs-777	146	11	of	of	ADP
iajs-777	146	12	(	(	PUNCT
iajs-777	146	13	x,	x,	PROPN
iajs-777	146	14	)	)	PUNCT
iajs-777	146	15	,	,	PUNCT
iajs-777	146	16	let	let	VERB
iajs-777	146	17	u	u	PRON
iajs-777	146	18	be	be	AUX
iajs-777	146	19	a	a	DET
iajs-777	146	20	regular	regular	ADJ
iajs-777	146	21	open	open	ADJ
iajs-777	146	22	set	set	NOUN
iajs-777	146	23	of	of	ADP
iajs-777	146	24	(	(	PUNCT
iajs-777	146	25	x,	x,	X
iajs-777	146	26	)	)	PUNCT
iajs-777	146	27	such	such	ADJ
iajs-777	146	28	that	that	SCONJ
iajs-777	146	29	a	a	DET
iajs-777	146	30			PROPN
iajs-777	146	31	u.	u.	PROPN
iajs-777	146	32	then	then	ADV
iajs-777	146	33	scl(a	scl(a	ADJ
iajs-777	146	34	)	)	PUNCT
iajs-777	146	35			PROPN
iajs-777	146	36	u	u	PROPN
iajs-777	146	37	since	since	SCONJ
iajs-777	146	38	a	a	DET
iajs-777	146	39	is	be	AUX
iajs-777	146	40	sr	sr	NOUN
iajs-777	146	41	-	-	PUNCT
iajs-777	146	42	closed	closed	ADJ
iajs-777	146	43	set	set	NOUN
iajs-777	146	44	.	.	PUNCT
iajs-777	147	1	since	since	SCONJ
iajs-777	147	2	every	every	DET
iajs-777	147	3	semi--closed	semi--close	VERB
iajs-777	147	4	set	set	NOUN
iajs-777	147	5	is	be	AUX
iajs-777	147	6	semipre	semipre	VERB
iajs-777	147	7	-	-	PUNCT
iajs-777	147	8	closed	close	VERB
iajs-777	147	9	set	set	NOUN
iajs-777	147	10	(	(	PUNCT
iajs-777	147	11	by	by	ADP
iajs-777	147	12	part	part	NOUN
iajs-777	147	13	6	6	NUM
iajs-777	147	14	of	of	ADP
iajs-777	147	15	proposition	proposition	NOUN
iajs-777	147	16	1.2	1.2	NUM
iajs-777	147	17	)	)	PUNCT
iajs-777	147	18	,	,	PUNCT
iajs-777	147	19	then	then	ADV
iajs-777	147	20	spcl(a	spcl(a	ADJ
iajs-777	147	21	)	)	PUNCT
iajs-777	147	22			PROPN
iajs-777	147	23	scl(a	scl(a	PROPN
iajs-777	147	24	)	)	PUNCT
iajs-777	147	25	and	and	CCONJ
iajs-777	147	26	every	every	DET
iajs-777	147	27	regular	regular	ADJ
iajs-777	147	28	open	open	ADJ
iajs-777	147	29	set	set	NOUN
iajs-777	147	30	is	be	AUX
iajs-777	147	31	g	g	NOUN
iajs-777	147	32	-	-	PUNCT
iajs-777	147	33	open	open	ADJ
iajs-777	147	34	set	set	NOUN
iajs-777	147	35	.	.	PUNCT
iajs-777	148	1	thus	thus	ADV
iajs-777	148	2	a	a	PRON
iajs-777	148	3	is	be	AUX
iajs-777	148	4	pre	pre	ADJ
iajs-777	148	5	-	-	ADJ
iajs-777	148	6	semi	semi	ADJ
iajs-777	148	7	-	-	ADJ
iajs-777	148	8	closed	closed	ADJ
iajs-777	148	9	set	set	NOUN
iajs-777	148	10	.	.	PUNCT
iajs-777	149	1	thus	thus	ADV
iajs-777	149	2	the	the	DET
iajs-777	149	3	class	class	NOUN
iajs-777	149	4	of	of	ADP
iajs-777	149	5	sr	sr	NOUN
iajs-777	149	6	-	-	PUNCT
iajs-777	149	7	closed	closed	ADJ
iajs-777	149	8	set	set	NOUN
iajs-777	149	9	properly	properly	ADV
iajs-777	149	10	contained	contain	VERB
iajs-777	149	11	in	in	ADP
iajs-777	149	12	the	the	DET
iajs-777	149	13	class	class	NOUN
iajs-777	149	14	of	of	ADP
iajs-777	149	15	p	p	NOUN
iajs-777	149	16	re	re	ADJ
iajs-777	149	17	-	-	ADJ
iajs-777	149	18	semi	semi	ADJ
iajs-777	149	19	-	-	ADJ
iajs-777	149	20	closed	closed	ADJ
iajs-777	149	21	sets	set	NOUN
iajs-777	149	22	.	.	PUNCT
iajs-777	150	1	2.16	2.16	NUM
iajs-777	150	2	corollary	corollary	NOUN
iajs-777	150	3	:	:	PUNCT
iajs-777	150	4	every	every	DET
iajs-777	150	5	sr	sr	ADV
iajs-777	150	6	-	-	PUNCT
iajs-777	150	7	closed	closed	ADJ
iajs-777	150	8	set	set	NOUN
iajs-777	150	9	is	be	AUX
iajs-777	150	10	gsp	gsp	VERB
iajs-777	150	11	-	-	PUNCT
iajs-777	150	12	closed	close	VERB
iajs-777	150	13	set	set	NOUN
iajs-777	150	14	.	.	PUNCT
iajs-777	151	1	proof	proof	NOUN
iajs-777	151	2	:	:	PUNCT
iajs-777	151	3	follows	follow	VERB
iajs-777	151	4	the	the	DET
iajs-777	151	5	above	above	ADJ
iajs-777	151	6	proposition	proposition	NOUN
iajs-777	151	7	and	and	CCONJ
iajs-777	151	8	part	part	NOUN
iajs-777	151	9	(	(	PUNCT
iajs-777	151	10	5	5	NUM
iajs-777	151	11	)	)	PUNCT
iajs-777	151	12	of	of	ADP
iajs-777	151	13	p	p	PROPN
iajs-777	151	14	roposition	roposition	NOUN
iajs-777	151	15	1.2	1.2	NUM
iajs-777	151	16	.	.	PUNCT
iajs-777	152	1	2.17	2.17	NUM
iajs-777	152	2	corollary	corollary	NOUN
iajs-777	152	3	:	:	PUNCT
iajs-777	152	4	every	every	DET
iajs-777	152	5	gr	gr	ADV
iajs-777	152	6	-	-	PUNCT
iajs-777	152	7	closed	closed	ADJ
iajs-777	152	8	set	set	NOUN
iajs-777	152	9	is	be	AUX
iajs-777	152	10	pre	pre	ADJ
iajs-777	152	11	-	-	ADJ
iajs-777	152	12	semi	semi	ADJ
iajs-777	152	13	-	-	ADJ
iajs-777	152	14	closed	closed	ADJ
iajs-777	152	15	set	set	NOUN
iajs-777	152	16	.	.	PUNCT
iajs-777	153	1	proof	proof	NOUN
iajs-777	153	2	:	:	PUNCT
iajs-777	153	3	follows	follow	VERB
iajs-777	153	4	from	from	ADP
iajs-777	153	5	the	the	DET
iajs-777	153	6	fact	fact	NOUN
iajs-777	153	7	every	every	DET
iajs-777	153	8	gr	gr	ADV
iajs-777	153	9	-	-	PUNCT
iajs-777	153	10	closed	closed	ADJ
iajs-777	153	11	set	set	NOUN
iajs-777	153	12	is	be	AUX
iajs-777	153	13	sr	sr	NOUN
iajs-777	153	14	-	-	PUNCT
iajs-777	153	15	closed	closed	ADJ
iajs-777	153	16	and	and	CCONJ
iajs-777	153	17	proposition	proposition	NOUN
iajs-777	153	18	2.15	2.15	NUM
iajs-777	153	19	.	.	PUNCT
iajs-777	154	1	2.18	2.18	NUM
iajs-777	154	2	proposition	proposition	NOUN
iajs-777	154	3	:	:	PUNCT
iajs-777	154	4	if	if	SCONJ
iajs-777	154	5	a	a	PRON
iajs-777	154	6	is	be	AUX
iajs-777	154	7	regular	regular	ADJ
iajs-777	154	8	open	open	ADJ
iajs-777	154	9	and	and	CCONJ
iajs-777	154	10	sr	sr	NOUN
iajs-777	154	11	-	-	PUNCT
iajs-777	154	12	closed	closed	ADJ
iajs-777	154	13	set	set	NOUN
iajs-777	154	14	then	then	ADV
iajs-777	154	15	a	a	PRON
iajs-777	154	16	is	be	AUX
iajs-777	154	17	semi--closed	semi--close	VERB
iajs-777	154	18	set	set	NOUN
iajs-777	154	19	.	.	PUNCT
iajs-777	155	1	proof	proof	NOUN
iajs-777	155	2	:	:	PUNCT
iajs-777	155	3	it	it	PRON
iajs-777	155	4	is	be	AUX
iajs-777	155	5	clear	clear	ADJ
iajs-777	155	6	.	.	PUNCT
iajs-777	156	1	2.19	2.19	NUM
iajs-777	156	2	proposition	proposition	NOUN
iajs-777	156	3	:	:	PUNCT
iajs-777	156	4	let	let	VERB
iajs-777	156	5	a	a	PRON
iajs-777	156	6	be	be	AUX
iajs-777	156	7	an	an	DET
iajs-777	156	8	sr	sr	ADV
iajs-777	156	9	-	-	PUNCT
iajs-777	156	10	closed	closed	ADJ
iajs-777	156	11	subset	subset	NOUN
iajs-777	156	12	of	of	ADP
iajs-777	156	13	(	(	PUNCT
iajs-777	156	14	x,	x,	PROPN
iajs-777	156	15	)	)	PUNCT
iajs-777	156	16	.	.	PUNCT
iajs-777	157	1	if	if	SCONJ
iajs-777	157	2	b	b	PROPN
iajs-777	157	3			PROPN
iajs-777	157	4	x	x	PUNCT
iajs-777	157	5	such	such	ADJ
iajs-777	157	6	that	that	SCONJ
iajs-777	157	7	a	a	DET
iajs-777	157	8			PROPN
iajs-777	157	9	b	b	PROPN
iajs-777	157	10			PROPN
iajs-777	157	11	scl(a	scl(a	PROPN
iajs-777	157	12	)	)	PUNCT
iajs-777	157	13	,	,	PUNCT
iajs-777	157	14	then	then	ADV
iajs-777	157	15	b	b	PROPN
iajs-777	157	16	is	be	AUX
iajs-777	157	17	sr	sr	NOUN
iajs-777	157	18	-	-	PUNCT
iajs-777	157	19	closed	closed	ADJ
iajs-777	157	20	set	set	NOUN
iajs-777	157	21	.	.	PUNCT
iajs-777	158	1	ibn	ibn	PROPN
iajs-777	158	2	alhaitham	alhaitham	PROPN
iajs-777	158	3	j.	j.	PROPN
iajs-777	158	4	for	for	ADP
iajs-777	158	5	pure	pure	ADJ
iajs-777	158	6	&	&	CCONJ
iajs-777	158	7	appl	appl	PROPN
iajs-777	158	8	.	.	PUNCT
iajs-777	159	1	sci	sci	PROPN
iajs-777	159	2	.	.	PUNCT
iajs-777	159	3	vol.24	vol.24	NOUN
iajs-777	159	4	(	(	PUNCT
iajs-777	159	5	2	2	NUM
iajs-777	159	6	)	)	PUNCT
iajs-777	159	7	2011	2011	NUM
iajs-777	159	8	proof	proof	NOUN
iajs-777	159	9	:	:	PUNCT
iajs-777	159	10	let	let	VERB
iajs-777	159	11	u	u	PRON
iajs-777	159	12	be	be	AUX
iajs-777	159	13	a	a	DET
iajs-777	159	14	regular	regular	ADJ
iajs-777	159	15	open	open	ADJ
iajs-777	159	16	set	set	NOUN
iajs-777	159	17	of	of	ADP
iajs-777	159	18	(	(	PUNCT
iajs-777	159	19	x,	x,	X
iajs-777	159	20	)	)	PUNCT
iajs-777	160	1	such	such	ADJ
iajs-777	160	2	that	that	DET
iajs-777	160	3	b	b	PROPN
iajs-777	160	4			PROPN
iajs-777	160	5	u.	u.	PROPN
iajs-777	160	6	then	then	ADV
iajs-777	160	7	a	a	DET
iajs-777	160	8			PROPN
iajs-777	160	9	u	u	NOUN
iajs-777	160	10	,	,	PUNCT
iajs-777	160	11	since	since	SCONJ
iajs-777	160	12	a	a	PRON
iajs-777	160	13	is	be	AUX
iajs-777	160	14	srclosed	srclose	VERB
iajs-777	160	15	set	set	NOUN
iajs-777	160	16	,	,	PUNCT
iajs-777	160	17	scl(a	scl(a	X
iajs-777	160	18	)	)	PUNCT
iajs-777	160	19			PROPN
iajs-777	160	20	u.	u.	PROPN
iajs-777	160	21	now	now	ADV
iajs-777	160	22	,	,	PUNCT
iajs-777	160	23	scl(b	scl(b	NOUN
iajs-777	160	24	)	)	PUNCT
iajs-777	160	25			PROPN
iajs-777	160	26	scl(scl(a	scl(scl(a	PROPN
iajs-777	160	27	)	)	PUNCT
iajs-777	160	28	)	)	PUNCT
iajs-777	161	1	=	=	SYM
iajs-777	161	2	scl(a	scl(a	X
iajs-777	161	3	)	)	PUNCT
iajs-777	161	4			PROPN
iajs-777	161	5	u.	u.	PROPN
iajs-777	161	6	therefore	therefore	ADV
iajs-777	161	7	b	b	PROPN
iajs-777	161	8	is	be	AUX
iajs-777	161	9	also	also	ADV
iajs-777	161	10	an	an	DET
iajs-777	161	11	sr	sr	ADV
iajs-777	161	12	-	-	PUNCT
iajs-777	161	13	closed	closed	ADJ
iajs-777	161	14	set	set	NOUN
iajs-777	161	15	.	.	PUNCT
iajs-777	162	1	fig	fig	NOUN
iajs-777	162	2	.	.	PUNCT
iajs-777	163	1	(	(	PUNCT
iajs-777	163	2	1	1	X
iajs-777	163	3	)	)	PUNCT
iajs-777	163	4	shows	show	VERB
iajs-777	163	5	the	the	DET
iajs-777	163	6	relations	relation	NOUN
iajs-777	163	7	among	among	ADP
iajs-777	163	8	the	the	DET
iajs-777	163	9	different	different	ADJ
iajs-777	163	10	types	type	NOUN
iajs-777	163	11	of	of	ADP
iajs-777	163	12	weakly	weakly	ADJ
iajs-777	163	13	closed	closed	ADJ
iajs-777	163	14	sets	set	NOUN
iajs-777	163	15	that	that	PRON
iajs-777	163	16	were	be	AUX
iajs-777	163	17	studied	study	VERB
iajs-777	163	18	in	in	ADP
iajs-777	163	19	this	this	DET
iajs-777	163	20	section	section	NOUN
iajs-777	163	21	.	.	PUNCT
iajs-777	164	1	3	3	ADJ
iajs-777	164	2	-semi	-semi	NOUN
iajs-777	164	3	regular	regular	ADJ
iajs-777	164	4	continuous	continuous	ADJ
iajs-777	164	5	maps	map	NOUN
iajs-777	164	6	and	and	CCONJ
iajs-777	164	7			NOUN
iajs-777	164	8	-semi	-semi	NOUN
iajs-777	164	9	-	-	PUNCT
iajs-777	164	10	regular	regular	ADJ
iajs-777	164	11	-	-	PUNCT
iajs-777	164	12	irresolute	irresolute	ADJ
iajs-777	164	13	maps	map	NOUN
iajs-777	164	14	3.1	3.1	NUM
iajs-777	164	15	definition	definition	NOUN
iajs-777	164	16	:	:	PUNCT
iajs-777	164	17	a	a	DET
iajs-777	164	18	function	function	NOUN
iajs-777	164	19	f:(x,	f:(x,	PROPN
iajs-777	164	20	)	)	PUNCT
iajs-777	164	21			PROPN
iajs-777	164	22	(	(	PUNCT
iajs-777	164	23	y,	y,	PROPN
iajs-777	164	24	'	'	PUNCT
iajs-777	164	25	)	)	PUNCT
iajs-777	164	26	is	be	AUX
iajs-777	164	27	called	call	VERB
iajs-777	164	28	an	an	DET
iajs-777	164	29	-semi	-semi	PROPN
iajs-777	164	30	-	-	PUNCT
iajs-777	164	31	regular	regular	ADJ
iajs-777	164	32	continuous	continuous	ADJ
iajs-777	164	33	map	map	NOUN
iajs-777	164	34	(	(	PUNCT
iajs-777	164	35	briefly	briefly	ADV
iajs-777	164	36	srcontinuous	srcontinuous	ADJ
iajs-777	164	37	if	if	SCONJ
iajs-777	164	38	f	f	X
iajs-777	164	39	–	–	PUNCT
iajs-777	164	40	1(v	1(v	NUM
iajs-777	164	41	)	)	PUNCT
iajs-777	164	42	is	be	AUX
iajs-777	164	43	an	an	DET
iajs-777	164	44	sr	sr	ADV
iajs-777	164	45	-	-	PUNCT
iajs-777	164	46	closed	closed	ADJ
iajs-777	164	47	set	set	NOUN
iajs-777	164	48	of	of	ADP
iajs-777	164	49	(	(	PUNCT
iajs-777	164	50	x,	x,	PROPN
iajs-777	164	51	)	)	PUNCT
iajs-777	164	52	for	for	ADP
iajs-777	164	53	every	every	DET
iajs-777	164	54	closed	close	VERB
iajs-777	164	55	set	set	VERB
iajs-777	164	56	v	v	NOUN
iajs-777	164	57	of	of	ADP
iajs-777	164	58	(	(	PUNCT
iajs-777	164	59	y,	y,	PROPN
iajs-777	164	60	'	'	PUNCT
iajs-777	164	61	)	)	PUNCT
iajs-777	164	62	.	.	PUNCT
iajs-777	165	1	3.2	3.2	NUM
iajs-777	165	2	proposition	proposition	NOUN
iajs-777	165	3	:	:	PUNCT
iajs-777	165	4	every	every	DET
iajs-777	165	5	semi--continuous	semi--continuous	ADJ
iajs-777	165	6	map	map	NOUN
iajs-777	165	7	is	be	AUX
iajs-777	165	8	sr	sr	NOUN
iajs-777	165	9	-	-	ADJ
iajs-777	165	10	continuous	continuous	ADJ
iajs-777	165	11	.	.	PUNCT
iajs-777	166	1	proof	proof	NOUN
iajs-777	166	2	:	:	PUNCT
iajs-777	166	3	follows	follow	VERB
iajs-777	166	4	from	from	ADP
iajs-777	166	5	proposition	proposition	NOUN
iajs-777	166	6	2.2	2.2	NUM
iajs-777	166	7	.	.	PUNCT
iajs-777	167	1	we	we	PRON
iajs-777	167	2	show	show	VERB
iajs-777	167	3	that	that	SCONJ
iajs-777	167	4	the	the	DET
iajs-777	167	5	class	class	NOUN
iajs-777	167	6	of	of	ADP
iajs-777	167	7	sr	sr	NOUN
iajs-777	167	8	-	-	ADJ
iajs-777	167	9	continuous	continuous	ADJ
iajs-777	167	10	maps	map	NOUN
iajs-777	167	11	properly	properly	ADV
iajs-777	167	12	contains	contain	VERB
iajs-777	167	13	the	the	DET
iajs-777	167	14	class	class	NOUN
iajs-777	167	15	of	of	ADP
iajs-777	167	16	grcontinuous	grcontinuous	ADJ
iajs-777	167	17	maps	map	NOUN
iajs-777	167	18	.	.	PUNCT
iajs-777	168	1	3.3	3.3	NUM
iajs-777	168	2	proposition	proposition	NOUN
iajs-777	168	3	:	:	PUNCT
iajs-777	168	4	let	let	VERB
iajs-777	168	5	f:(x,	f:(x,	PROPN
iajs-777	168	6	)	)	PUNCT
iajs-777	168	7			PROPN
iajs-777	168	8	(	(	PUNCT
iajs-777	168	9	y,	y,	PROPN
iajs-777	168	10	'	'	PUNCT
iajs-777	168	11	)	)	PUNCT
iajs-777	168	12	be	be	AUX
iajs-777	168	13	an	an	DET
iajs-777	168	14	gr	gr	ADJ
iajs-777	168	15	-	-	ADJ
iajs-777	168	16	continuous	continuous	ADJ
iajs-777	168	17	map	map	NOUN
iajs-777	168	18	.	.	PUNCT
iajs-777	169	1	then	then	ADV
iajs-777	169	2	f	f	PROPN
iajs-777	169	3	is	be	AUX
iajs-777	169	4	an	an	DET
iajs-777	169	5	sr	sr	ADV
iajs-777	169	6	-	-	PUNCT
iajs-777	169	7	continuous	continuous	ADJ
iajs-777	169	8	map	map	NOUN
iajs-777	169	9	.	.	PUNCT
iajs-777	170	1	proof	proof	NOUN
iajs-777	170	2	:	:	PUNCT
iajs-777	170	3	let	let	VERB
iajs-777	170	4	v	v	PART
iajs-777	170	5	be	be	AUX
iajs-777	170	6	a	a	DET
iajs-777	170	7	closed	closed	ADJ
iajs-777	170	8	set	set	NOUN
iajs-777	170	9	of	of	ADP
iajs-777	170	10	(	(	PUNCT
iajs-777	170	11	y,	y,	PROPN
iajs-777	170	12	'	'	PUNCT
iajs-777	170	13	)	)	PUNCT
iajs-777	170	14	.	.	PUNCT
iajs-777	171	1	since	since	SCONJ
iajs-777	171	2	f	f	PROPN
iajs-777	171	3	is	be	AUX
iajs-777	171	4	an	an	DET
iajs-777	171	5	gr	gr	ADJ
iajs-777	171	6	-	-	ADJ
iajs-777	171	7	continuous	continuous	ADJ
iajs-777	171	8	map	map	NOUN
iajs-777	171	9	,	,	PUNCT
iajs-777	171	10	then	then	ADV
iajs-777	171	11	f	f	PROPN
iajs-777	171	12	–	–	PUNCT
iajs-777	171	13	1(v	1(v	NUM
iajs-777	171	14	)	)	PUNCT
iajs-777	171	15	is	be	AUX
iajs-777	171	16	an	an	DET
iajs-777	171	17	gr	gr	ADV
iajs-777	171	18	-	-	PUNCT
iajs-777	171	19	closed	closed	ADJ
iajs-777	171	20	set	set	NOUN
iajs-777	171	21	of	of	ADP
iajs-777	171	22	(	(	PUNCT
iajs-777	171	23	x,	x,	PROPN
iajs-777	171	24	)	)	PUNCT
iajs-777	171	25	.	.	PUNCT
iajs-777	172	1	by	by	ADP
iajs-777	172	2	proposition	proposition	NOUN
iajs-777	172	3	2.4	2.4	NUM
iajs-777	172	4	f	f	NOUN
iajs-777	172	5	–	–	PUNCT
iajs-777	172	6	1(v	1(v	NUM
iajs-777	172	7	)	)	PUNCT
iajs-777	172	8	is	be	AUX
iajs-777	172	9	an	an	DET
iajs-777	172	10	sr	sr	ADV
iajs-777	172	11	-	-	PUNCT
iajs-777	172	12	closed	closed	ADJ
iajs-777	172	13	set	set	NOUN
iajs-777	172	14	of	of	ADP
iajs-777	172	15	(	(	PUNCT
iajs-777	172	16	x,	x,	PROPN
iajs-777	172	17	)	)	PUNCT
iajs-777	172	18	.	.	PUNCT
iajs-777	173	1	thus	thus	ADV
iajs-777	173	2	f	f	PROPN
iajs-777	173	3	is	be	AUX
iajs-777	173	4	an	an	DET
iajs-777	173	5	sr	sr	ADV
iajs-777	173	6	-	-	PUNCT
iajs-777	173	7	continuous	continuous	ADJ
iajs-777	173	8	map	map	NOUN
iajs-777	173	9	.	.	PUNCT
iajs-777	174	1	the	the	DET
iajs-777	174	2	implications	implication	NOUN
iajs-777	174	3	in	in	ADP
iajs-777	174	4	proposition	proposition	NOUN
iajs-777	174	5	3.3	3.3	NUM
iajs-777	174	6	is	be	AUX
iajs-777	174	7	not	not	PART
iajs-777	174	8	reversible	reversible	ADJ
iajs-777	174	9	.	.	PUNCT
iajs-777	175	1	follows	follow	VERB
iajs-777	175	2	from	from	ADP
iajs-777	175	3	the	the	DET
iajs-777	175	4	following	follow	VERB
iajs-777	175	5	example	example	NOUN
iajs-777	175	6	.	.	PUNCT
iajs-777	176	1	3.4	3.4	NUM
iajs-777	176	2	example	example	NOUN
iajs-777	176	3	:	:	PUNCT
iajs-777	176	4	let	let	VERB
iajs-777	176	5	x	x	PUNCT
iajs-777	176	6	=	=	PRON
iajs-777	176	7	{	{	PUNCT
iajs-777	176	8	a	a	PRON
iajs-777	176	9	,	,	PUNCT
iajs-777	176	10	b	b	NOUN
iajs-777	176	11	,	,	PUNCT
iajs-777	176	12	c	c	NOUN
iajs-777	176	13	}	}	PUNCT
iajs-777	176	14	=	=	SYM
iajs-777	176	15	y	y	PROPN
iajs-777	176	16	,	,	PUNCT
iajs-777	176	17			NOUN
iajs-777	176	18	=	=	SYM
iajs-777	176	19	{	{	PUNCT
iajs-777	176	20	x,,{a},{b},{a	x,,{a},{b},{a	PROPN
iajs-777	176	21	,	,	PUNCT
iajs-777	176	22	b	b	NOUN
iajs-777	176	23	}	}	PUNCT
iajs-777	176	24	}	}	PUNCT
iajs-777	176	25	and	and	CCONJ
iajs-777	176	26			NOUN
iajs-777	176	27	'	'	PUNCT
iajs-777	176	28	=	=	PUNCT
iajs-777	176	29	{	{	PUNCT
iajs-777	176	30	y,,{a	y,,{a	ADV
iajs-777	176	31	,	,	PUNCT
iajs-777	176	32	c	c	NOUN
iajs-777	176	33	}	}	PUNCT
iajs-777	176	34	}	}	PUNCT
iajs-777	176	35	.	.	PUNCT
iajs-777	177	1	define	define	VERB
iajs-777	177	2	f:(x,	f:(x,	PROPN
iajs-777	177	3	)	)	PUNCT
iajs-777	177	4			PROPN
iajs-777	177	5	(	(	PUNCT
iajs-777	177	6	y,	y,	PROPN
iajs-777	177	7	'	'	PUNCT
iajs-777	177	8	)	)	PUNCT
iajs-777	177	9	by	by	ADP
iajs-777	177	10	f(a	f(a	PROPN
iajs-777	177	11	)	)	PUNCT
iajs-777	178	1	=	=	SYM
iajs-777	178	2	c	c	X
iajs-777	178	3	,	,	PUNCT
iajs-777	178	4	f(b	f(b	PROPN
iajs-777	178	5	)	)	PUNCT
iajs-777	178	6	=	=	SYM
iajs-777	178	7	b	b	PROPN
iajs-777	178	8	and	and	CCONJ
iajs-777	178	9	f(c	f(c	PROPN
iajs-777	178	10	)	)	PUNCT
iajs-777	178	11	=	=	SYM
iajs-777	179	1	a	a	PRON
iajs-777	179	2	,	,	PUNCT
iajs-777	179	3	{	{	PUNCT
iajs-777	179	4	b	b	NOUN
iajs-777	179	5	}	}	PUNCT
iajs-777	179	6	is	be	AUX
iajs-777	179	7	a	a	DET
iajs-777	179	8	closed	closed	ADJ
iajs-777	179	9	set	set	NOUN
iajs-777	179	10	of	of	ADP
iajs-777	179	11	(	(	PUNCT
iajs-777	179	12	y,	y,	PROPN
iajs-777	179	13	'	'	PUNCT
iajs-777	179	14	)	)	PUNCT
iajs-777	180	1	but	but	CCONJ
iajs-777	180	2	f	f	X
iajs-777	180	3	–	–	PUNCT
iajs-777	180	4	1({b	1({b	NUM
iajs-777	180	5	}	}	PUNCT
iajs-777	180	6	)	)	PUNCT
iajs-777	180	7	=	=	PRON
iajs-777	180	8	{	{	PUNCT
iajs-777	180	9	b	b	NOUN
iajs-777	180	10	}	}	PUNCT
iajs-777	180	11	is	be	AUX
iajs-777	180	12	not	not	PART
iajs-777	180	13	gr	gr	ADV
iajs-777	180	14	-	-	PUNCT
iajs-777	180	15	closed	closed	ADJ
iajs-777	180	16	set	set	NOUN
iajs-777	180	17	of	of	ADP
iajs-777	180	18	(	(	PUNCT
iajs-777	180	19	x,	x,	PROPN
iajs-777	180	20	)	)	PUNCT
iajs-777	180	21	.	.	PUNCT
iajs-777	181	1	so	so	ADV
iajs-777	181	2	f	f	PROPN
iajs-777	181	3	is	be	AUX
iajs-777	181	4	not	not	PART
iajs-777	181	5	gr	gr	ADJ
iajs-777	181	6	-	-	ADJ
iajs-777	181	7	continuous	continuous	ADJ
iajs-777	181	8	map	map	NOUN
iajs-777	181	9	.	.	PUNCT
iajs-777	182	1	however	however	ADV
iajs-777	182	2	f	f	PROPN
iajs-777	182	3	is	be	AUX
iajs-777	182	4	an	an	DET
iajs-777	182	5	srcontinuous	srcontinuous	ADJ
iajs-777	182	6	map	map	NOUN
iajs-777	182	7	.	.	PUNCT
iajs-777	183	1	3.5	3.5	NUM
iajs-777	183	2	corollary	corollary	NOUN
iajs-777	183	3	:	:	PUNCT
iajs-777	183	4	every	every	DET
iajs-777	183	5	g	g	NUM
iajs-777	183	6	-	-	ADJ
iajs-777	183	7	continuous	continuous	ADJ
iajs-777	183	8	map	map	NOUN
iajs-777	183	9	is	be	AUX
iajs-777	183	10	sr	sr	NOUN
iajs-777	183	11	-	-	ADJ
iajs-777	183	12	continuous	continuous	ADJ
iajs-777	183	13	.	.	PUNCT
iajs-777	184	1	proof	proof	NOUN
iajs-777	184	2	:	:	PUNCT
iajs-777	184	3	follow	follow	VERB
iajs-777	184	4	from	from	ADP
iajs-777	184	5	part	part	NOUN
iajs-777	184	6	(	(	PUNCT
iajs-777	184	7	1	1	NUM
iajs-777	184	8	)	)	PUNCT
iajs-777	184	9	of	of	ADP
iajs-777	184	10	p	p	PROPN
iajs-777	184	11	roposition	roposition	NOUN
iajs-777	184	12	1.5	1.5	NUM
iajs-777	184	13	and	and	CCONJ
iajs-777	184	14	proposition	proposition	NOUN
iajs-777	184	15	3.3	3.3	NUM
iajs-777	184	16	.	.	PUNCT
iajs-777	185	1	the	the	DET
iajs-777	185	2	converse	converse	NOUN
iajs-777	185	3	of	of	ADP
iajs-777	185	4	the	the	DET
iajs-777	185	5	above	above	ADJ
iajs-777	185	6	corollary	corollary	NOUN
iajs-777	185	7	is	be	AUX
iajs-777	185	8	not	not	PART
iajs-777	185	9	true	true	ADJ
iajs-777	185	10	in	in	ADP
iajs-777	185	11	general	general	ADJ
iajs-777	185	12	as	as	SCONJ
iajs-777	185	13	we	we	PRON
iajs-777	185	14	see	see	VERB
iajs-777	185	15	in	in	ADP
iajs-777	185	16	the	the	DET
iajs-777	185	17	following	follow	VERB
iajs-777	185	18	example	example	NOUN
iajs-777	185	19	.	.	PUNCT
iajs-777	186	1	3.6	3.6	NUM
iajs-777	186	2	example	example	NOUN
iajs-777	186	3	:	:	PUNCT
iajs-777	186	4	let	let	VERB
iajs-777	186	5	x	x	PRON
iajs-777	186	6	,	,	PUNCT
iajs-777	186	7	y	y	PROPN
iajs-777	186	8	,	,	PUNCT
iajs-777	186	9			PROPN
iajs-777	186	10	and	and	CCONJ
iajs-777	186	11	the	the	DET
iajs-777	186	12	definition	definition	NOUN
iajs-777	186	13	of	of	ADP
iajs-777	186	14	f	f	PROPN
iajs-777	186	15	as	as	ADP
iajs-777	186	16	in	in	ADP
iajs-777	186	17	example	example	NOUN
iajs-777	186	18	3.4	3.4	NUM
iajs-777	186	19	,	,	PUNCT
iajs-777	186	20	let	let	VERB
iajs-777	186	21			NOUN
iajs-777	186	22	'	'	PUNCT
iajs-777	186	23	=	=	SYM
iajs-777	186	24	{	{	PUNCT
iajs-777	186	25	y,,{a},{b	y,,{a},{b	NOUN
iajs-777	186	26	,	,	PUNCT
iajs-777	186	27	c	c	NOUN
iajs-777	186	28	}	}	PUNCT
iajs-777	186	29	}	}	PUNCT
iajs-777	186	30	.	.	PUNCT
iajs-777	187	1	f	f	PROPN
iajs-777	187	2	is	be	AUX
iajs-777	187	3	not	not	PART
iajs-777	187	4	gcontinuous	gcontinuous	ADJ
iajs-777	187	5	map	map	NOUN
iajs-777	187	6	since	since	SCONJ
iajs-777	187	7	{	{	PUNCT
iajs-777	187	8	b	b	NOUN
iajs-777	187	9	,	,	PUNCT
iajs-777	187	10	c	c	NOUN
iajs-777	187	11	}	}	PUNCT
iajs-777	187	12	is	be	AUX
iajs-777	187	13	a	a	DET
iajs-777	187	14	closed	closed	ADJ
iajs-777	187	15	set	set	NOUN
iajs-777	187	16	of	of	ADP
iajs-777	187	17	(	(	PUNCT
iajs-777	187	18	y,	y,	PROPN
iajs-777	187	19	'	'	PUNCT
iajs-777	187	20	)	)	PUNCT
iajs-777	188	1	but	but	CCONJ
iajs-777	188	2	f	f	X
iajs-777	188	3	–	–	PUNCT
iajs-777	188	4	1	1	NUM
iajs-777	188	5	(	(	PUNCT
iajs-777	188	6	{	{	PUNCT
iajs-777	188	7	b	b	NOUN
iajs-777	188	8	,	,	PUNCT
iajs-777	188	9	c	c	NOUN
iajs-777	188	10	}	}	PUNCT
iajs-777	188	11	)	)	PUNCT
iajs-777	188	12	=	=	PRON
iajs-777	188	13	{	{	PUNCT
iajs-777	188	14	a	a	DET
iajs-777	188	15	,	,	PUNCT
iajs-777	188	16	b	b	NOUN
iajs-777	188	17	}	}	PUNCT
iajs-777	188	18	is	be	AUX
iajs-777	188	19	not	not	PART
iajs-777	188	20	g	g	ADV
iajs-777	188	21	-	-	PUNCT
iajs-777	188	22	closed	closed	ADJ
iajs-777	188	23	set	set	NOUN
iajs-777	188	24	of	of	ADP
iajs-777	188	25	(	(	PUNCT
iajs-777	188	26	x,	x,	PROPN
iajs-777	188	27	)	)	PUNCT
iajs-777	188	28	.	.	PUNCT
iajs-777	189	1	however	however	ADV
iajs-777	189	2	f	f	PROPN
iajs-777	189	3	is	be	AUX
iajs-777	189	4	an	an	DET
iajs-777	189	5	sr	sr	ADV
iajs-777	189	6	-	-	PUNCT
iajs-777	189	7	continuous	continuous	ADJ
iajs-777	189	8	map	map	NOUN
iajs-777	189	9	.	.	PUNCT
iajs-777	190	1	3.7	3.7	NUM
iajs-777	190	2	corollary	corollary	NOUN
iajs-777	190	3	:	:	PUNCT
iajs-777	190	4	every	every	DET
iajs-777	190	5	g	g	NOUN
iajs-777	190	6	-	-	PUNCT
iajs-777	190	7	continuous	continuous	ADJ
iajs-777	190	8	(	(	PUNCT
iajs-777	190	9	resp	resp	NOUN
iajs-777	190	10	.	.	PUNCT
iajs-777	191	1	g-continuous	g-continuous	ADJ
iajs-777	191	2	)	)	PUNCT
iajs-777	191	3	is	be	AUX
iajs-777	191	4	an	an	DET
iajs-777	191	5	sr	sr	ADV
iajs-777	191	6	-	-	ADJ
iajs-777	191	7	continuous	continuous	ADJ
iajs-777	191	8	.	.	PUNCT
iajs-777	192	1	proof	proof	NOUN
iajs-777	192	2	:	:	PUNCT
iajs-777	192	3	follows	follow	VERB
iajs-777	192	4	from	from	ADP
iajs-777	192	5	part	part	NOUN
iajs-777	192	6	(	(	PUNCT
iajs-777	192	7	2	2	NUM
iajs-777	192	8	)	)	PUNCT
iajs-777	192	9	of	of	ADP
iajs-777	192	10	p	p	PROPN
iajs-777	192	11	roposition	roposition	NOUN
iajs-777	192	12	1.5	1.5	NUM
iajs-777	192	13	and	and	CCONJ
iajs-777	192	14	proposition	proposition	NOUN
iajs-777	192	15	3.3	3.3	NUM
iajs-777	192	16	.	.	PUNCT
iajs-777	193	1	the	the	DET
iajs-777	193	2	converse	converse	NOUN
iajs-777	193	3	of	of	ADP
iajs-777	193	4	the	the	DET
iajs-777	193	5	above	above	ADJ
iajs-777	193	6	corollary	corollary	NOUN
iajs-777	193	7	is	be	AUX
iajs-777	193	8	not	not	PART
iajs-777	193	9	true	true	ADJ
iajs-777	193	10	in	in	ADP
iajs-777	193	11	general	general	ADJ
iajs-777	193	12	as	as	SCONJ
iajs-777	193	13	we	we	PRON
iajs-777	193	14	see	see	VERB
iajs-777	193	15	in	in	ADP
iajs-777	193	16	the	the	DET
iajs-777	193	17	following	follow	VERB
iajs-777	193	18	example	example	NOUN
iajs-777	193	19	.	.	PUNCT
iajs-777	194	1	3.8	3.8	NUM
iajs-777	194	2	example	example	NOUN
iajs-777	194	3	:	:	PUNCT
iajs-777	194	4	see	see	VERB
iajs-777	194	5	example	example	NOUN
iajs-777	194	6	3.4	3.4	NUM
iajs-777	194	7	f	f	NOUN
iajs-777	194	8	is	be	AUX
iajs-777	194	9	sr	sr	NOUN
iajs-777	194	10	-	-	ADJ
iajs-777	194	11	continuous	continuous	ADJ
iajs-777	194	12	map	map	NOUN
iajs-777	194	13	but	but	CCONJ
iajs-777	194	14	not	not	PART
iajs-777	194	15	g	g	NOUN
iajs-777	194	16	-	-	PUNCT
iajs-777	194	17	continuous	continuous	ADJ
iajs-777	194	18	map	map	NOUN
iajs-777	194	19	.	.	PUNCT
iajs-777	195	1	3.9	3.9	NUM
iajs-777	195	2	corollary	corollary	NOUN
iajs-777	195	3	:	:	PUNCT
iajs-777	195	4	every	every	DET
iajs-777	195	5	gr	gr	ADJ
iajs-777	195	6	-	-	PUNCT
iajs-777	195	7	irresolute	irresolute	ADJ
iajs-777	195	8	map	map	NOUN
iajs-777	195	9	is	be	AUX
iajs-777	195	10	an	an	DET
iajs-777	195	11	sr	sr	ADV
iajs-777	195	12	-	-	ADJ
iajs-777	195	13	continuous	continuous	ADJ
iajs-777	195	14	.	.	PUNCT
iajs-777	196	1	proof	proof	NOUN
iajs-777	196	2	:	:	PUNCT
iajs-777	196	3	necessity	necessity	NOUN
iajs-777	196	4	follows	follow	VERB
iajs-777	196	5	from	from	ADP
iajs-777	196	6	part	part	NOUN
iajs-777	196	7	(	(	PUNCT
iajs-777	196	8	4	4	NUM
iajs-777	196	9	)	)	PUNCT
iajs-777	196	10	of	of	ADP
iajs-777	196	11	p	p	PROPN
iajs-777	196	12	roposition	roposition	NOUN
iajs-777	196	13	1.5	1.5	NUM
iajs-777	196	14	and	and	CCONJ
iajs-777	196	15	proposition	proposition	NOUN
iajs-777	196	16	3.3	3.3	NUM
iajs-777	196	17	.	.	PUNCT
iajs-777	197	1	the	the	DET
iajs-777	197	2	converse	converse	NOUN
iajs-777	197	3	of	of	ADP
iajs-777	197	4	the	the	DET
iajs-777	197	5	above	above	ADJ
iajs-777	197	6	corollary	corollary	NOUN
iajs-777	197	7	is	be	AUX
iajs-777	197	8	not	not	PART
iajs-777	197	9	true	true	ADJ
iajs-777	197	10	in	in	ADP
iajs-777	197	11	general	general	ADJ
iajs-777	197	12	as	as	SCONJ
iajs-777	197	13	we	we	PRON
iajs-777	197	14	see	see	VERB
iajs-777	197	15	in	in	ADP
iajs-777	197	16	the	the	DET
iajs-777	197	17	following	follow	VERB
iajs-777	197	18	example	example	NOUN
iajs-777	197	19	ibn	ibn	PROPN
iajs-777	197	20	alhaitham	alhaitham	PROPN
iajs-777	197	21	j.	j.	PROPN
iajs-777	197	22	for	for	ADP
iajs-777	197	23	pure	pure	ADJ
iajs-777	197	24	&	&	CCONJ
iajs-777	197	25	appl	appl	PROPN
iajs-777	197	26	.	.	PUNCT
iajs-777	198	1	sci	sci	PROPN
iajs-777	198	2	.	.	PUNCT
iajs-777	198	3	vol.24	vol.24	NOUN
iajs-777	198	4	(	(	PUNCT
iajs-777	198	5	2	2	NUM
iajs-777	198	6	)	)	PUNCT
iajs-777	198	7	2011	2011	NUM
iajs-777	198	8	3.10	3.10	NUM
iajs-777	198	9	example	example	NOUN
iajs-777	198	10	:	:	PUNCT
iajs-777	198	11	let	let	VERB
iajs-777	198	12	x	x	PUNCT
iajs-777	198	13	=	=	PRON
iajs-777	198	14	{	{	PUNCT
iajs-777	198	15	a	a	PRON
iajs-777	198	16	,	,	PUNCT
iajs-777	198	17	b	b	NOUN
iajs-777	198	18	,	,	PUNCT
iajs-777	198	19	c	c	NOUN
iajs-777	198	20	}	}	PUNCT
iajs-777	198	21	=	=	SYM
iajs-777	198	22	y	y	PROPN
iajs-777	198	23	,	,	PUNCT
iajs-777	198	24			NOUN
iajs-777	198	25	=	=	SYM
iajs-777	198	26	{	{	PUNCT
iajs-777	198	27	x,,{a},{b},{a	x,,{a},{b},{a	PROPN
iajs-777	198	28	,	,	PUNCT
iajs-777	198	29	b	b	NOUN
iajs-777	198	30	}	}	PUNCT
iajs-777	198	31	}	}	PUNCT
iajs-777	198	32	and	and	CCONJ
iajs-777	198	33	'=i	'=i	ADJ
iajs-777	198	34	.	.	X
iajs-777	199	1	define	define	VERB
iajs-777	199	2	f	f	PROPN
iajs-777	199	3	:x	:x	PROPN
iajs-777	199	4			PROPN
iajs-777	199	5	y	y	PROPN
iajs-777	199	6	by	by	ADP
iajs-777	199	7	f(a	f(a	PROPN
iajs-777	199	8	)	)	PUNCT
iajs-777	200	1	=	=	SYM
iajs-777	200	2	c	c	X
iajs-777	200	3	,	,	PUNCT
iajs-777	200	4	f(b	f(b	PROPN
iajs-777	200	5	)	)	PUNCT
iajs-777	200	6	=	=	SYM
iajs-777	200	7	b	b	PROPN
iajs-777	200	8	and	and	CCONJ
iajs-777	200	9	f(c	f(c	PROPN
iajs-777	200	10	)	)	PUNCT
iajs-777	200	11	=	=	SYM
iajs-777	201	1	a	a	PRON
iajs-777	201	2	,	,	PUNCT
iajs-777	201	3	{	{	PUNCT
iajs-777	201	4	b	b	NOUN
iajs-777	201	5	}	}	PUNCT
iajs-777	201	6	is	be	AUX
iajs-777	201	7	an	an	DET
iajs-777	201	8	sr	sr	ADV
iajs-777	201	9	-	-	PUNCT
iajs-777	201	10	closed	closed	ADJ
iajs-777	201	11	set	set	NOUN
iajs-777	201	12	of	of	ADP
iajs-777	201	13	(	(	PUNCT
iajs-777	201	14	y,	y,	PROPN
iajs-777	201	15	'	'	PUNCT
iajs-777	201	16	)	)	PUNCT
iajs-777	202	1	but	but	CCONJ
iajs-777	202	2	f	f	X
iajs-777	202	3	–	–	PUNCT
iajs-777	202	4	1({b	1({b	NUM
iajs-777	202	5	}	}	PUNCT
iajs-777	202	6	)	)	PUNCT
iajs-777	202	7	=	=	PRON
iajs-777	202	8	{	{	PUNCT
iajs-777	202	9	b	b	NOUN
iajs-777	202	10	}	}	PUNCT
iajs-777	202	11	is	be	AUX
iajs-777	202	12	not	not	PART
iajs-777	202	13	gr	gr	ADV
iajs-777	202	14	-	-	PUNCT
iajs-777	202	15	closed	closed	ADJ
iajs-777	202	16	set	set	NOUN
iajs-777	202	17	of	of	ADP
iajs-777	202	18	(	(	PUNCT
iajs-777	202	19	x,	x,	PROPN
iajs-777	202	20	)	)	PUNCT
iajs-777	202	21	.	.	PUNCT
iajs-777	203	1	so	so	ADV
iajs-777	203	2	f	f	PROPN
iajs-777	203	3	is	be	AUX
iajs-777	203	4	not	not	PART
iajs-777	203	5	gr	gr	ADJ
iajs-777	203	6	-	-	PUNCT
iajs-777	203	7	irresolute	irresolute	ADJ
iajs-777	203	8	map	map	NOUN
iajs-777	203	9	.	.	PUNCT
iajs-777	204	1	however	however	ADV
iajs-777	204	2	f	f	PROPN
iajs-777	204	3	is	be	AUX
iajs-777	204	4	an	an	DET
iajs-777	204	5	sr	sr	ADV
iajs-777	204	6	-	-	PUNCT
iajs-777	204	7	continuous	continuous	ADJ
iajs-777	204	8	map	map	NOUN
iajs-777	204	9	.	.	PUNCT
iajs-777	205	1	3.11	3.11	NUM
iajs-777	205	2	theorem	theorem	VERB
iajs-777	205	3	:	:	PUNCT
iajs-777	205	4	let	let	VERB
iajs-777	205	5	f:(x,	f:(x,	PROPN
iajs-777	205	6	)	)	PUNCT
iajs-777	205	7			PROPN
iajs-777	205	8	(	(	PUNCT
iajs-777	205	9	y,	y,	PROPN
iajs-777	205	10	'	'	PUNCT
iajs-777	205	11	)	)	PUNCT
iajs-777	205	12	be	be	AUX
iajs-777	205	13	an	an	DET
iajs-777	205	14	sr	sr	ADV
iajs-777	205	15	-	-	PUNCT
iajs-777	205	16	continuous	continuous	ADJ
iajs-777	205	17	map	map	NOUN
iajs-777	205	18	.	.	PUNCT
iajs-777	206	1	then	then	ADV
iajs-777	206	2	f	f	PROPN
iajs-777	206	3	is	be	AUX
iajs-777	206	4	a	a	DET
iajs-777	206	5	pre	pre	ADJ
iajs-777	206	6	-	-	ADJ
iajs-777	206	7	semi	semi	ADJ
iajs-777	206	8	-	-	ADJ
iajs-777	206	9	continuous	continuous	ADJ
iajs-777	206	10	map	map	NOUN
iajs-777	206	11	.	.	PUNCT
iajs-777	207	1	proof	proof	NOUN
iajs-777	207	2	:	:	PUNCT
iajs-777	207	3	let	let	VERB
iajs-777	207	4	v	v	PART
iajs-777	207	5	be	be	AUX
iajs-777	207	6	a	a	DET
iajs-777	207	7	closed	closed	ADJ
iajs-777	207	8	set	set	NOUN
iajs-777	207	9	of	of	ADP
iajs-777	207	10	(	(	PUNCT
iajs-777	207	11	y,	y,	PROPN
iajs-777	207	12	'	'	PUNCT
iajs-777	207	13	)	)	PUNCT
iajs-777	207	14	.	.	PUNCT
iajs-777	208	1	since	since	SCONJ
iajs-777	208	2	f	f	PROPN
iajs-777	208	3	is	be	AUX
iajs-777	208	4	sr	sr	NOUN
iajs-777	208	5	-	-	PUNCT
iajs-777	208	6	continuous	continuous	ADJ
iajs-777	208	7	map	map	NOUN
iajs-777	208	8	,	,	PUNCT
iajs-777	208	9	then	then	ADV
iajs-777	208	10	f	f	PROPN
iajs-777	208	11	–	–	PUNCT
iajs-777	208	12	1(v	1(v	NUM
iajs-777	208	13	)	)	PUNCT
iajs-777	208	14	is	be	AUX
iajs-777	208	15	an	an	DET
iajs-777	208	16	sr	sr	ADV
iajs-777	208	17	-	-	PUNCT
iajs-777	208	18	closed	closed	ADJ
iajs-777	208	19	set	set	NOUN
iajs-777	208	20	of	of	ADP
iajs-777	208	21	(	(	PUNCT
iajs-777	208	22	x,	x,	PROPN
iajs-777	208	23	)	)	PUNCT
iajs-777	208	24	.	.	PUNCT
iajs-777	209	1	by	by	ADP
iajs-777	209	2	proposition	proposition	NOUN
iajs-777	209	3	(	(	PUNCT
iajs-777	209	4	2.15	2.15	NUM
iajs-777	209	5	)	)	PUNCT
iajs-777	209	6	f	f	NOUN
iajs-777	209	7	–	–	PUNCT
iajs-777	209	8	1(v	1(v	NUM
iajs-777	209	9	)	)	PUNCT
iajs-777	209	10	is	be	AUX
iajs-777	209	11	a	a	DET
iajs-777	209	12	pre	pre	ADJ
iajs-777	209	13	-	-	ADJ
iajs-777	209	14	semi	semi	ADJ
iajs-777	209	15	-	-	ADJ
iajs-777	209	16	closed	closed	ADJ
iajs-777	209	17	set	set	NOUN
iajs-777	209	18	of	of	ADP
iajs-777	209	19	(	(	PUNCT
iajs-777	209	20	x,	x,	PROPN
iajs-777	209	21	)	)	PUNCT
iajs-777	209	22	.	.	PUNCT
iajs-777	210	1	thus	thus	ADV
iajs-777	210	2	f	f	PROPN
iajs-777	210	3	is	be	AUX
iajs-777	210	4	a	a	DET
iajs-777	210	5	pre	pre	ADJ
iajs-777	210	6	-	-	ADJ
iajs-777	210	7	semi	semi	ADJ
iajs-777	210	8	-	-	ADJ
iajs-777	210	9	continuous	continuous	ADJ
iajs-777	210	10	map	map	NOUN
iajs-777	210	11	.	.	PUNCT
iajs-777	211	1	3.12	3.12	NUM
iajs-777	211	2	corollary	corollary	NOUN
iajs-777	211	3	:	:	PUNCT
iajs-777	211	4	every	every	DET
iajs-777	211	5	sr	sr	ADV
iajs-777	211	6	-	-	ADJ
iajs-777	211	7	continuous	continuous	ADJ
iajs-777	211	8	map	map	NOUN
iajs-777	211	9	is	be	AUX
iajs-777	211	10	gsp	gsp	VERB
iajs-777	211	11	-	-	PUNCT
iajs-777	211	12	continuous	continuous	ADJ
iajs-777	211	13	.	.	PUNCT
iajs-777	212	1	proof	proof	NOUN
iajs-777	212	2	:	:	PUNCT
iajs-777	212	3	follows	follow	VERB
iajs-777	212	4	from	from	ADP
iajs-777	212	5	the	the	DET
iajs-777	212	6	above	above	ADJ
iajs-777	212	7	proposition	proposition	NOUN
iajs-777	212	8	and	and	CCONJ
iajs-777	212	9	part	part	NOUN
iajs-777	212	10	(	(	PUNCT
iajs-777	212	11	3	3	NUM
iajs-777	212	12	)	)	PUNCT
iajs-777	212	13	of	of	ADP
iajs-777	212	14	p	p	PROPN
iajs-777	212	15	roposition	roposition	NOUN
iajs-777	212	16	1.5	1.5	NUM
iajs-777	212	17	.	.	PUNCT
iajs-777	213	1	3.13	3.13	NUM
iajs-777	213	2	definition	definition	NOUN
iajs-777	213	3	:	:	PUNCT
iajs-777	213	4	a	a	DET
iajs-777	213	5	function	function	NOUN
iajs-777	213	6	f:(x,	f:(x,	PROPN
iajs-777	213	7	)	)	PUNCT
iajs-777	213	8			PROPN
iajs-777	213	9	(	(	PUNCT
iajs-777	213	10	y,	y,	PROPN
iajs-777	213	11	'	'	PUNCT
iajs-777	213	12	)	)	PUNCT
iajs-777	213	13	is	be	AUX
iajs-777	213	14	called	call	VERB
iajs-777	213	15	an	an	DET
iajs-777	213	16	-semi	-semi	PROPN
iajs-777	213	17	-	-	PUNCT
iajs-777	213	18	regular	regular	ADJ
iajs-777	213	19	irresolute	irresolute	ADJ
iajs-777	213	20	(	(	PUNCT
iajs-777	213	21	briefly	briefly	NOUN
iajs-777	213	22	srirresolute	srirresolute	NOUN
iajs-777	213	23	)	)	PUNCT
iajs-777	213	24	if	if	SCONJ
iajs-777	213	25	f	f	PROPN
iajs-777	213	26	–	–	PUNCT
iajs-777	213	27	1(v	1(v	NUM
iajs-777	213	28	)	)	PUNCT
iajs-777	213	29	is	be	AUX
iajs-777	213	30	an	an	DET
iajs-777	213	31	sr	sr	ADV
iajs-777	213	32	-	-	PUNCT
iajs-777	213	33	closed	closed	ADJ
iajs-777	213	34	set	set	NOUN
iajs-777	213	35	of	of	ADP
iajs-777	213	36	(	(	PUNCT
iajs-777	213	37	x,	x,	PROPN
iajs-777	213	38	)	)	PUNCT
iajs-777	213	39	for	for	ADP
iajs-777	213	40	every	every	DET
iajs-777	213	41	srclosed	srclose	VERB
iajs-777	213	42	set	set	NOUN
iajs-777	213	43	of	of	ADP
iajs-777	213	44	(	(	PUNCT
iajs-777	213	45	y,	y,	PROPN
iajs-777	213	46	'	'	PUNCT
iajs-777	213	47	)	)	PUNCT
iajs-777	213	48	.	.	PUNCT
iajs-777	214	1	3.14	3.14	NUM
iajs-777	214	2	proposition	proposition	NOUN
iajs-777	214	3	:	:	PUNCT
iajs-777	214	4	let	let	VERB
iajs-777	214	5	f:(x,	f:(x,	PROPN
iajs-777	214	6	)	)	PUNCT
iajs-777	214	7			PROPN
iajs-777	214	8	(	(	PUNCT
iajs-777	214	9	y,	y,	PROPN
iajs-777	214	10	'	'	PUNCT
iajs-777	214	11	)	)	PUNCT
iajs-777	214	12	be	be	AUX
iajs-777	214	13	an	an	DET
iajs-777	214	14	sr	sr	PRON
iajs-777	214	15	-	-	PUNCT
iajs-777	214	16	irresolute	irresolute	ADJ
iajs-777	214	17	map	map	NOUN
iajs-777	214	18	.	.	PUNCT
iajs-777	215	1	then	then	ADV
iajs-777	215	2	f	f	PROPN
iajs-777	215	3	is	be	AUX
iajs-777	215	4	an	an	DET
iajs-777	215	5	sr	sr	ADV
iajs-777	215	6	-	-	PUNCT
iajs-777	215	7	continuous	continuous	ADJ
iajs-777	215	8	map	map	NOUN
iajs-777	215	9	.	.	PUNCT
iajs-777	216	1	proof	proof	NOUN
iajs-777	216	2	:	:	PUNCT
iajs-777	216	3	let	let	VERB
iajs-777	216	4	v	v	PART
iajs-777	216	5	be	be	AUX
iajs-777	216	6	a	a	DET
iajs-777	216	7	closed	closed	ADJ
iajs-777	216	8	set	set	NOUN
iajs-777	216	9	of	of	ADP
iajs-777	216	10	(	(	PUNCT
iajs-777	216	11	y,	y,	PROPN
iajs-777	216	12	'	'	PUNCT
iajs-777	216	13	)	)	PUNCT
iajs-777	216	14	.	.	PUNCT
iajs-777	217	1	by	by	ADP
iajs-777	217	2	corollary	corollary	ADJ
iajs-777	217	3	2.6	2.6	NUM
iajs-777	217	4	v	v	NOUN
iajs-777	217	5	is	be	AUX
iajs-777	217	6	an	an	DET
iajs-777	217	7	sr	sr	ADV
iajs-777	217	8	-	-	PUNCT
iajs-777	217	9	closed	closed	ADJ
iajs-777	217	10	set	set	NOUN
iajs-777	217	11	of	of	ADP
iajs-777	217	12	(	(	PUNCT
iajs-777	217	13	y,	y,	PROPN
iajs-777	217	14	'	'	PUNCT
iajs-777	217	15	)	)	PUNCT
iajs-777	217	16	.	.	PUNCT
iajs-777	218	1	since	since	SCONJ
iajs-777	218	2	f	f	PROPN
iajs-777	218	3	is	be	AUX
iajs-777	218	4	an	an	DET
iajs-777	218	5	sr	sr	PRON
iajs-777	218	6	-	-	PUNCT
iajs-777	218	7	irresolute	irresolute	ADJ
iajs-777	218	8	map	map	NOUN
iajs-777	218	9	,	,	PUNCT
iajs-777	218	10	f	f	PROPN
iajs-777	218	11	–	–	PUNCT
iajs-777	218	12	1	1	NUM
iajs-777	218	13	(	(	PUNCT
iajs-777	218	14	v	v	NOUN
iajs-777	218	15	)	)	PUNCT
iajs-777	218	16	is	be	AUX
iajs-777	218	17	an	an	DET
iajs-777	218	18	sr	sr	ADV
iajs-777	218	19	-	-	PUNCT
iajs-777	218	20	closed	closed	ADJ
iajs-777	218	21	set	set	NOUN
iajs-777	218	22	of	of	ADP
iajs-777	218	23	(	(	PUNCT
iajs-777	218	24	x,	x,	PROPN
iajs-777	218	25	)	)	PUNCT
iajs-777	218	26	.	.	PUNCT
iajs-777	219	1	therefore	therefore	ADV
iajs-777	219	2	f	f	PROPN
iajs-777	219	3	is	be	AUX
iajs-777	219	4	an	an	DET
iajs-777	219	5	sr	sr	ADV
iajs-777	219	6	-	-	PUNCT
iajs-777	219	7	continuous	continuous	ADJ
iajs-777	219	8	map	map	NOUN
iajs-777	219	9	.	.	PUNCT
iajs-777	220	1	thus	thus	ADV
iajs-777	220	2	the	the	DET
iajs-777	220	3	class	class	NOUN
iajs-777	220	4	of	of	ADP
iajs-777	220	5	sr	sr	NOUN
iajs-777	220	6	-	-	ADJ
iajs-777	220	7	continuous	continuous	ADJ
iajs-777	220	8	maps	map	NOUN
iajs-777	220	9	property	property	NOUN
iajs-777	220	10	continuous	continuous	ADJ
iajs-777	220	11	the	the	DET
iajs-777	220	12	class	class	NOUN
iajs-777	220	13	of	of	ADP
iajs-777	220	14	sr	sr	NOUN
iajs-777	220	15	-	-	PUNCT
iajs-777	220	16	irresolute	irresolute	ADJ
iajs-777	220	17	map	map	NOUN
iajs-777	220	18	.	.	PUNCT
iajs-777	221	1	3.15	3.15	NUM
iajs-777	221	2	corollary	corollary	NOUN
iajs-777	221	3	:	:	PUNCT
iajs-777	221	4	every	every	DET
iajs-777	221	5	sr	sr	NOUN
iajs-777	221	6	-	-	PUNCT
iajs-777	221	7	irresolute	irresolute	ADJ
iajs-777	221	8	map	map	NOUN
iajs-777	221	9	is	be	AUX
iajs-777	221	10	a	a	DET
iajs-777	221	11	pre	pre	ADJ
iajs-777	221	12	-	-	ADJ
iajs-777	221	13	semi	semi	ADJ
iajs-777	221	14	-	-	ADJ
iajs-777	221	15	continuous	continuous	ADJ
iajs-777	221	16	.	.	PUNCT
iajs-777	222	1	proof	proof	NOUN
iajs-777	222	2	:	:	PUNCT
iajs-777	222	3	follows	follow	VERB
iajs-777	222	4	from	from	ADP
iajs-777	222	5	the	the	DET
iajs-777	222	6	above	above	ADJ
iajs-777	222	7	proposition	proposition	NOUN
iajs-777	222	8	and	and	CCONJ
iajs-777	222	9	proposition	proposition	NOUN
iajs-777	222	10	3.11	3.11	NUM
iajs-777	222	11	.	.	PUNCT
iajs-777	223	1	3.16	3.16	NUM
iajs-777	223	2	corollary	corollary	NOUN
iajs-777	223	3	:	:	PUNCT
iajs-777	223	4	every	every	DET
iajs-777	223	5	sr	sr	NOUN
iajs-777	223	6	-	-	PUNCT
iajs-777	223	7	irresolute	irresolute	ADJ
iajs-777	223	8	is	be	AUX
iajs-777	223	9	a	a	DET
iajs-777	223	10	gspcontinuous	gspcontinuous	NOUN
iajs-777	223	11	.	.	PUNCT
iajs-777	224	1	proof	proof	NOUN
iajs-777	224	2	:	:	PUNCT
iajs-777	224	3	follows	follow	VERB
iajs-777	224	4	from	from	ADP
iajs-777	224	5	proposition	proposition	NOUN
iajs-777	224	6	3.14	3.14	NUM
iajs-777	224	7	and	and	CCONJ
iajs-777	224	8	corollary	corollary	ADJ
iajs-777	224	9	3.12	3.12	NUM
iajs-777	224	10	.	.	PUNCT
iajs-777	225	1	3.17	3.17	NUM
iajs-777	225	2	theorem	theorem	NOUN
iajs-777	225	3	:	:	PUNCT
iajs-777	225	4	let	let	VERB
iajs-777	225	5	f:(x,	f:(x,	PROPN
iajs-777	225	6	)	)	PUNCT
iajs-777	225	7			PROPN
iajs-777	225	8	(	(	PUNCT
iajs-777	225	9	y,	y,	PROPN
iajs-777	225	10	'	'	PUNCT
iajs-777	225	11	)	)	PUNCT
iajs-777	225	12	be	be	AUX
iajs-777	225	13	a	a	DET
iajs-777	225	14	regular	regular	ADJ
iajs-777	225	15	irresolute	irresolute	ADJ
iajs-777	225	16	and	and	CCONJ
iajs-777	225	17	semi--irresolute	semi--irresolute	ADJ
iajs-777	225	18	map	map	NOUN
iajs-777	225	19	.	.	PUNCT
iajs-777	226	1	then	then	ADV
iajs-777	226	2	f	f	PROPN
iajs-777	226	3	is	be	AUX
iajs-777	226	4	srirresolute	srirresolute	NOUN
iajs-777	226	5	map	map	NOUN
iajs-777	226	6	.	.	PUNCT
iajs-777	227	1	proof	proof	NOUN
iajs-777	227	2	:	:	PUNCT
iajs-777	227	3	let	let	VERB
iajs-777	227	4	a	a	PRON
iajs-777	227	5	be	be	AUX
iajs-777	227	6	an	an	DET
iajs-777	227	7	sr	sr	ADV
iajs-777	227	8	-	-	PUNCT
iajs-777	227	9	closed	closed	ADJ
iajs-777	227	10	set	set	NOUN
iajs-777	227	11	of	of	ADP
iajs-777	227	12	(	(	PUNCT
iajs-777	227	13	y,	y,	PROPN
iajs-777	227	14	'	'	PUNCT
iajs-777	227	15	)	)	PUNCT
iajs-777	227	16	,	,	PUNCT
iajs-777	227	17	then	then	ADV
iajs-777	227	18	there	there	PRON
iajs-777	227	19	exists	exist	VERB
iajs-777	227	20	a	a	DET
iajs-777	227	21	regular	regular	ADJ
iajs-777	227	22	open	open	ADJ
iajs-777	227	23	set	set	NOUN
iajs-777	227	24	u	u	NOUN
iajs-777	227	25	of	of	ADP
iajs-777	227	26	y	y	PRON
iajs-777	227	27	such	such	ADJ
iajs-777	227	28	that	that	SCONJ
iajs-777	227	29	scl(a	scl(a	NOUN
iajs-777	227	30	)	)	PUNCT
iajs-777	227	31			PROPN
iajs-777	227	32	u	u	PROPN
iajs-777	227	33	whenever	whenever	SCONJ
iajs-777	227	34	a	a	DET
iajs-777	227	35			PROPN
iajs-777	227	36	u.	u.	NOUN
iajs-777	227	37	by	by	ADP
iajs-777	227	38	taking	take	VERB
iajs-777	227	39	the	the	DET
iajs-777	227	40	inverse	inverse	NOUN
iajs-777	227	41	image	image	NOUN
iajs-777	227	42	we	we	PRON
iajs-777	227	43	get	get	VERB
iajs-777	227	44	f	f	PROPN
iajs-777	227	45	–	–	PUNCT
iajs-777	227	46	1(scl(a	1(scl(a	NUM
iajs-777	227	47	)	)	PUNCT
iajs-777	227	48	)	)	PUNCT
iajs-777	228	1			PROPN
iajs-777	228	2	f	f	PROPN
iajs-777	228	3	–	–	PUNCT
iajs-777	228	4	1(u	1(u	NUM
iajs-777	228	5	)	)	PUNCT
iajs-777	228	6	.	.	PUNCT
iajs-777	229	1	since	since	SCONJ
iajs-777	229	2	f	f	PROPN
iajs-777	229	3	is	be	AUX
iajs-777	229	4	regular	regular	ADJ
iajs-777	229	5	irresolute	irresolute	ADJ
iajs-777	229	6	map	map	NOUN
iajs-777	229	7	,	,	PUNCT
iajs-777	229	8	then	then	ADV
iajs-777	229	9	f	f	PROPN
iajs-777	229	10	–	–	PUNCT
iajs-777	229	11	1(u	1(u	NUM
iajs-777	229	12	)	)	PUNCT
iajs-777	229	13	is	be	AUX
iajs-777	229	14	regular	regular	ADJ
iajs-777	229	15	open	open	ADJ
iajs-777	229	16	subset	subset	NOUN
iajs-777	229	17	of	of	ADP
iajs-777	229	18	x.	x.	NOUN
iajs-777	229	19	since	since	SCONJ
iajs-777	229	20	f	f	PROPN
iajs-777	229	21	is	be	AUX
iajs-777	229	22	semi--irresolute	semi--irresolute	ADJ
iajs-777	229	23	map	map	NOUN
iajs-777	229	24	,	,	PUNCT
iajs-777	229	25	then	then	ADV
iajs-777	229	26	f	f	PROPN
iajs-777	229	27	–	–	PUNCT
iajs-777	229	28	1	1	NUM
iajs-777	229	29	(	(	PUNCT
iajs-777	229	30	scl(a	scl(a	NOUN
iajs-777	229	31	)	)	PUNCT
iajs-777	229	32	)	)	PUNCT
iajs-777	229	33	is	be	AUX
iajs-777	229	34	semi--closed	semi--close	VERB
iajs-777	229	35	subset	subset	NOUN
iajs-777	229	36	of	of	ADP
iajs-777	229	37	x.	x.	NOUN
iajs-777	229	38	this	this	PRON
iajs-777	229	39	implies	imply	VERB
iajs-777	229	40	scl(f	scl(f	PROPN
iajs-777	229	41	–	–	PUNCT
iajs-777	229	42	1	1	NUM
iajs-777	229	43	(	(	PUNCT
iajs-777	229	44	scl(a)))=	scl(a)))=	PROPN
iajs-777	229	45	f	f	PROPN
iajs-777	229	46	–	–	PUNCT
iajs-777	229	47	1	1	NUM
iajs-777	229	48	(	(	PUNCT
iajs-777	229	49	scl(a	scl(a	NOUN
iajs-777	229	50	)	)	PUNCT
iajs-777	229	51	)	)	PUNCT
iajs-777	229	52	(	(	PUNCT
iajs-777	229	53	by	by	ADP
iajs-777	229	54	part	part	NOUN
iajs-777	229	55	(	(	PUNCT
iajs-777	229	56	1	1	NUM
iajs-777	229	57	)	)	PUNCT
iajs-777	229	58	of	of	ADP
iajs-777	229	59	remark	remark	NOUN
iajs-777	229	60	1.3	1.3	NUM
iajs-777	229	61	)	)	PUNCT
iajs-777	229	62	,	,	PUNCT
iajs-777	229	63	then	then	ADV
iajs-777	229	64	sclf	sclf	X
iajs-777	229	65	–	–	PUNCT
iajs-777	229	66	1	1	NUM
iajs-777	229	67	(	(	PUNCT
iajs-777	229	68	a	a	NOUN
iajs-777	229	69	)	)	PUNCT
iajs-777	229	70			PROPN
iajs-777	229	71	scl	scl	NOUN
iajs-777	229	72	(	(	PUNCT
iajs-777	229	73	f	f	X
iajs-777	229	74	–	–	PUNCT
iajs-777	229	75	1	1	NUM
iajs-777	229	76	(	(	PUNCT
iajs-777	229	77	scl(a	scl(a	NOUN
iajs-777	229	78	)	)	PUNCT
iajs-777	229	79	)	)	PUNCT
iajs-777	229	80	.	.	PUNCT
iajs-777	230	1	thus	thus	ADV
iajs-777	230	2	sclf	sclf	X
iajs-777	230	3	–	–	PUNCT
iajs-777	230	4	1	1	NUM
iajs-777	230	5	(	(	PUNCT
iajs-777	230	6	a	a	NOUN
iajs-777	230	7	)	)	PUNCT
iajs-777	230	8			PROPN
iajs-777	230	9	f	f	PROPN
iajs-777	230	10	–	–	PUNCT
iajs-777	230	11	1	1	NUM
iajs-777	230	12	(	(	PUNCT
iajs-777	230	13	u	u	NOUN
iajs-777	230	14	)	)	PUNCT
iajs-777	230	15	.	.	PUNCT
iajs-777	231	1	therefore	therefore	ADV
iajs-777	231	2	f	f	PROPN
iajs-777	231	3	–	–	PUNCT
iajs-777	231	4	1	1	NUM
iajs-777	231	5	(	(	PUNCT
iajs-777	231	6	a	a	NOUN
iajs-777	231	7	)	)	PUNCT
iajs-777	231	8	is	be	AUX
iajs-777	231	9	sr	sr	NOUN
iajs-777	231	10	-	-	PUNCT
iajs-777	231	11	closed	closed	ADJ
iajs-777	231	12	set	set	NOUN
iajs-777	231	13	in	in	ADP
iajs-777	231	14	x.	x.	NOUN
iajs-777	231	15	therefore	therefore	ADV
iajs-777	231	16	f	f	PROPN
iajs-777	231	17	is	be	AUX
iajs-777	231	18	sr	sr	NOUN
iajs-777	231	19	-	-	PUNCT
iajs-777	231	20	irresolute	irresolute	ADJ
iajs-777	231	21	map	map	NOUN
iajs-777	231	22	.	.	PUNCT
iajs-777	232	1	3.18	3.18	NUM
iajs-777	232	2	corollary	corollary	NOUN
iajs-777	232	3	:	:	PUNCT
iajs-777	232	4	every	every	DET
iajs-777	232	5	continuous	continuous	ADJ
iajs-777	232	6	,	,	PUNCT
iajs-777	232	7	open	open	ADJ
iajs-777	232	8	and	and	CCONJ
iajs-777	232	9	regular	regular	ADJ
iajs-777	232	10	irresolute	irresolute	ADJ
iajs-777	232	11	map	map	NOUN
iajs-777	232	12	is	be	AUX
iajs-777	232	13	sr	sr	NOUN
iajs-777	232	14	-	-	PUNCT
iajs-777	232	15	irresolute	irresolute	ADJ
iajs-777	232	16	.	.	PUNCT
iajs-777	233	1	proof	proof	NOUN
iajs-777	233	2	:	:	PUNCT
iajs-777	233	3	it	it	PRON
iajs-777	233	4	is	be	AUX
iajs-777	233	5	clear	clear	ADJ
iajs-777	233	6	by	by	ADP
iajs-777	233	7	part	part	NOUN
iajs-777	233	8	(	(	PUNCT
iajs-777	233	9	5	5	NUM
iajs-777	233	10	)	)	PUNCT
iajs-777	233	11	of	of	ADP
iajs-777	233	12	p	p	PROPN
iajs-777	233	13	roposition	roposition	NOUN
iajs-777	233	14	1.5	1.5	NUM
iajs-777	233	15	and	and	CCONJ
iajs-777	233	16	the	the	DET
iajs-777	233	17	above	above	ADJ
iajs-777	233	18	theorem	theorem	NOUN
iajs-777	233	19	.	.	PROPN
iajs-777	233	20	3.19	3.19	NUM
iajs-777	233	21	definition	definition	NOUN
iajs-777	233	22	:	:	PUNCT
iajs-777	233	23	let	let	VERB
iajs-777	233	24	f:(x,	f:(x,	PROPN
iajs-777	233	25	)	)	PUNCT
iajs-777	233	26			PROPN
iajs-777	233	27	(	(	PUNCT
iajs-777	233	28	y,	y,	PROPN
iajs-777	233	29	'	'	PUNCT
iajs-777	233	30	)	)	PUNCT
iajs-777	233	31	be	be	AUX
iajs-777	233	32	a	a	DET
iajs-777	233	33	function	function	NOUN
iajs-777	233	34	,	,	PUNCT
iajs-777	233	35	then	then	ADV
iajs-777	233	36	f	f	PROPN
iajs-777	233	37	is	be	AUX
iajs-777	233	38	said	say	VERB
iajs-777	233	39	to	to	PART
iajs-777	233	40	be	be	AUX
iajs-777	233	41	:	:	PUNCT
iajs-777	233	42	(	(	PUNCT
iajs-777	233	43	1)-semi	1)-semi	NUM
iajs-777	233	44	-	-	ADJ
iajs-777	233	45	regular	regular	ADJ
iajs-777	233	46	closed	closed	ADJ
iajs-777	233	47	(	(	PUNCT
iajs-777	233	48	briefly	briefly	ADV
iajs-777	233	49	sr	sr	ADV
iajs-777	233	50	-	-	PUNCT
iajs-777	233	51	closed	closed	ADJ
iajs-777	233	52	)	)	PUNCT
iajs-777	233	53	if	if	SCONJ
iajs-777	233	54	f(a	f(a	PROPN
iajs-777	233	55	)	)	PUNCT
iajs-777	233	56	is	be	AUX
iajs-777	233	57	an	an	DET
iajs-777	233	58	sr	sr	ADV
iajs-777	233	59	-	-	PUNCT
iajs-777	233	60	closed	closed	ADJ
iajs-777	233	61	set	set	NOUN
iajs-777	233	62	of	of	ADP
iajs-777	233	63	(	(	PUNCT
iajs-777	233	64	y,	y,	PROPN
iajs-777	233	65	'	'	PUNCT
iajs-777	233	66	)	)	PUNCT
iajs-777	233	67	for	for	ADP
iajs-777	233	68	every	every	DET
iajs-777	233	69	closed	close	VERB
iajs-777	233	70	set	set	VERB
iajs-777	233	71	a	a	PRON
iajs-777	233	72	of	of	ADP
iajs-777	233	73	(	(	PUNCT
iajs-777	233	74	x,	x,	PROPN
iajs-777	233	75	)	)	PUNCT
iajs-777	233	76	.	.	PUNCT
iajs-777	234	1	(	(	PUNCT
iajs-777	234	2	2	2	X
iajs-777	234	3	)	)	PUNCT
iajs-777	234	4	*-semi	*-semi	PROPN
iajs-777	234	5	-	-	ADJ
iajs-777	234	6	regular	regular	ADJ
iajs-777	234	7	closed	closed	ADJ
iajs-777	234	8	(	(	PUNCT
iajs-777	234	9	briefly	briefly	ADV
iajs-777	234	10	*sr	*sr	ADV
iajs-777	234	11	-	-	PUNCT
iajs-777	234	12	closed	closed	ADJ
iajs-777	234	13	)	)	PUNCT
iajs-777	234	14	if	if	SCONJ
iajs-777	234	15	f(a	f(a	PROPN
iajs-777	234	16	)	)	PUNCT
iajs-777	234	17	is	be	AUX
iajs-777	234	18	an	an	DET
iajs-777	234	19	sr	sr	ADV
iajs-777	234	20	-	-	PUNCT
iajs-777	234	21	closed	closed	ADJ
iajs-777	234	22	set	set	NOUN
iajs-777	234	23	of	of	ADP
iajs-777	234	24	(	(	PUNCT
iajs-777	234	25	y,	y,	PROPN
iajs-777	234	26	'	'	PUNCT
iajs-777	234	27	)	)	PUNCT
iajs-777	234	28	for	for	ADP
iajs-777	234	29	every	every	DET
iajs-777	234	30	sr	sr	NOUN
iajs-777	234	31	-	-	PUNCT
iajs-777	234	32	closed	closed	ADJ
iajs-777	234	33	set	set	NOUN
iajs-777	234	34	a	a	PRON
iajs-777	234	35	of	of	ADP
iajs-777	234	36	(	(	PUNCT
iajs-777	234	37	x,	x,	PROPN
iajs-777	234	38	)	)	PUNCT
iajs-777	234	39	.	.	PUNCT
iajs-777	235	1	3.20	3.20	NUM
iajs-777	235	2	remark	remark	NOUN
iajs-777	235	3	:	:	PUNCT
iajs-777	235	4	it	it	PRON
iajs-777	235	5	is	be	AUX
iajs-777	235	6	clear	clear	ADJ
iajs-777	235	7	that	that	SCONJ
iajs-777	235	8	every	every	DET
iajs-777	235	9	closed	closed	ADJ
iajs-777	235	10	function	function	NOUN
iajs-777	235	11	is	be	AUX
iajs-777	235	12	-semi	-semi	PROPN
iajs-777	235	13	-	-	PUNCT
iajs-777	235	14	closed	closed	ADJ
iajs-777	235	15	function	function	NOUN
iajs-777	235	16	,	,	PUNCT
iajs-777	235	17	but	but	CCONJ
iajs-777	235	18	the	the	DET
iajs-777	235	19	converse	converse	NOUN
iajs-777	235	20	is	be	AUX
iajs-777	235	21	not	not	PART
iajs-777	235	22	true	true	ADJ
iajs-777	235	23	in	in	ADP
iajs-777	235	24	general	general	ADJ
iajs-777	235	25	as	as	SCONJ
iajs-777	235	26	the	the	DET
iajs-777	235	27	following	follow	VERB
iajs-777	235	28	example	example	NOUN
iajs-777	235	29	shows	show	VERB
iajs-777	235	30	:	:	PUNCT
iajs-777	235	31	ibn	ibn	PROPN
iajs-777	235	32	alhaitham	alhaitham	NOUN
iajs-777	235	33	j.	j.	PROPN
iajs-777	235	34	for	for	ADP
iajs-777	235	35	pure	pure	ADJ
iajs-777	235	36	&	&	CCONJ
iajs-777	235	37	appl	appl	PROPN
iajs-777	235	38	.	.	PUNCT
iajs-777	236	1	sci	sci	PROPN
iajs-777	236	2	.	.	PUNCT
iajs-777	236	3	vol.24	vol.24	NOUN
iajs-777	236	4	(	(	PUNCT
iajs-777	236	5	2	2	NUM
iajs-777	236	6	)	)	PUNCT
iajs-777	236	7	2011	2011	NUM
iajs-777	236	8	3.21	3.21	NUM
iajs-777	236	9	example	example	NOUN
iajs-777	236	10	:	:	PUNCT
iajs-777	236	11	let	let	VERB
iajs-777	236	12	x={a	x={a	PROPN
iajs-777	236	13	,	,	PUNCT
iajs-777	236	14	b	b	PROPN
iajs-777	236	15	,	,	PUNCT
iajs-777	236	16	c	c	X
iajs-777	236	17	,	,	PUNCT
iajs-777	236	18	d	d	NOUN
iajs-777	236	19	}	}	PUNCT
iajs-777	236	20	,	,	PUNCT
iajs-777	236	21			NOUN
iajs-777	236	22	=	=	SYM
iajs-777	236	23	{	{	PUNCT
iajs-777	236	24	x,,{a},{b},{a	x,,{a},{b},{a	PROPN
iajs-777	236	25	,	,	PUNCT
iajs-777	236	26	b},{a	b},{a	ADV
iajs-777	236	27	,	,	PUNCT
iajs-777	236	28	b	b	NOUN
iajs-777	236	29	,	,	PUNCT
iajs-777	236	30	c	c	NOUN
iajs-777	236	31	}	}	PUNCT
iajs-777	236	32	}	}	PUNCT
iajs-777	236	33	.	.	PUNCT
iajs-777	237	1	define	define	VERB
iajs-777	237	2	f:(x,	f:(x,	PROPN
iajs-777	237	3	)	)	PUNCT
iajs-777	237	4			PROPN
iajs-777	237	5	(	(	PUNCT
iajs-777	237	6	x,	x,	PROPN
iajs-777	237	7	)	)	PUNCT
iajs-777	237	8	by	by	ADP
iajs-777	237	9	f(a	f(a	PROPN
iajs-777	237	10	)	)	PUNCT
iajs-777	237	11	=	=	SYM
iajs-777	238	1	a	a	PRON
iajs-777	238	2	,	,	PUNCT
iajs-777	238	3	f(b	f(b	PROPN
iajs-777	238	4	)	)	PUNCT
iajs-777	238	5	=	=	SYM
iajs-777	238	6	b	b	PROPN
iajs-777	238	7	,	,	PUNCT
iajs-777	238	8	f(c	f(c	PROPN
iajs-777	238	9	)	)	PUNCT
iajs-777	238	10	=	=	SYM
iajs-777	238	11	f(d	f(d	PROPN
iajs-777	238	12	)	)	PUNCT
iajs-777	238	13	=	=	PUNCT
iajs-777	239	1	d	d	NOUN
iajs-777	239	2	we	we	PRON
iajs-777	239	3	observe	observe	VERB
iajs-777	239	4	f	f	PROPN
iajs-777	239	5	is	be	AUX
iajs-777	239	6	-semi	-semi	PROPN
iajs-777	239	7	-	-	PUNCT
iajs-777	239	8	regular	regular	ADJ
iajs-777	239	9	closed	closed	ADJ
iajs-777	239	10	function	function	NOUN
iajs-777	239	11	which	which	PRON
iajs-777	239	12	is	be	AUX
iajs-777	239	13	not	not	PART
iajs-777	239	14	closed	close	VERB
iajs-777	239	15	function	function	NOUN
iajs-777	239	16	since	since	SCONJ
iajs-777	239	17	{	{	PUNCT
iajs-777	239	18	a	a	DET
iajs-777	239	19	,	,	PUNCT
iajs-777	239	20	c	c	NOUN
iajs-777	239	21	,	,	PUNCT
iajs-777	239	22	d	d	NOUN
iajs-777	239	23	}	}	PUNCT
iajs-777	239	24	is	be	AUX
iajs-777	239	25	closed	close	VERB
iajs-777	239	26	set	set	VERB
iajs-777	239	27	in	in	ADP
iajs-777	239	28	x	x	NOUN
iajs-777	239	29	,	,	PUNCT
iajs-777	239	30	but	but	CCONJ
iajs-777	239	31	f({a	f({a	PROPN
iajs-777	239	32	,	,	PUNCT
iajs-777	239	33	c	c	X
iajs-777	239	34	,	,	PUNCT
iajs-777	239	35	d	d	NOUN
iajs-777	239	36	}	}	PUNCT
iajs-777	239	37	)	)	PUNCT
iajs-777	239	38	=	=	PRON
iajs-777	239	39	{	{	PUNCT
iajs-777	239	40	a	a	PRON
iajs-777	239	41	,	,	PUNCT
iajs-777	239	42	d	d	NOUN
iajs-777	239	43	}	}	PUNCT
iajs-777	239	44	is	be	AUX
iajs-777	239	45	not	not	PART
iajs-777	239	46	closed	close	VERB
iajs-777	239	47	set	set	VERB
iajs-777	239	48	in	in	ADP
iajs-777	239	49	x.	x.	NOUN
iajs-777	239	50	hence	hence	PROPN
iajs-777	239	51	f	f	PROPN
iajs-777	239	52	is	be	AUX
iajs-777	239	53	-semi	-semi	PROPN
iajs-777	239	54	-	-	PUNCT
iajs-777	239	55	regular	regular	ADJ
iajs-777	239	56	closed	closed	ADJ
iajs-777	239	57	function	function	NOUN
iajs-777	239	58	,	,	PUNCT
iajs-777	239	59	which	which	PRON
iajs-777	239	60	is	be	AUX
iajs-777	239	61	not	not	PART
iajs-777	239	62	closed	closed	ADJ
iajs-777	239	63	function	function	NOUN
iajs-777	239	64	.	.	PUNCT
iajs-777	240	1	finally	finally	ADV
iajs-777	240	2	,	,	PUNCT
iajs-777	240	3	we	we	PRON
iajs-777	240	4	prove	prove	VERB
iajs-777	240	5	the	the	DET
iajs-777	240	6	following	follow	VERB
iajs-777	240	7	theorem	theorem	VERB
iajs-777	240	8	.	.	PROPN
iajs-777	241	1	3.22	3.22	NUM
iajs-777	241	2	theorem	theorem	NOUN
iajs-777	241	3	:	:	PUNCT
iajs-777	241	4	let	let	VERB
iajs-777	241	5	f:(x,	f:(x,	PROPN
iajs-777	241	6	)	)	PUNCT
iajs-777	241	7			PROPN
iajs-777	241	8	(	(	PUNCT
iajs-777	241	9	y,	y,	PROPN
iajs-777	241	10	'	'	PUNCT
iajs-777	241	11	)	)	PUNCT
iajs-777	241	12	be	be	AUX
iajs-777	241	13	a	a	DET
iajs-777	241	14	regular	regular	ADJ
iajs-777	241	15	irresolute	irresolute	ADJ
iajs-777	241	16	and	and	CCONJ
iajs-777	241	17	semi-*-closed	semi-*-close	VERB
iajs-777	241	18	map	map	NOUN
iajs-777	241	19	.	.	PUNCT
iajs-777	242	1	then	then	ADV
iajs-777	242	2	f	f	PROPN
iajs-777	242	3	is	be	AUX
iajs-777	242	4	*-semi	*-semi	PROPN
iajs-777	242	5	-	-	ADJ
iajs-777	242	6	regular	regular	ADJ
iajs-777	242	7	closed	closed	ADJ
iajs-777	242	8	map	map	NOUN
iajs-777	242	9	.	.	PUNCT
iajs-777	243	1	proof	proof	NOUN
iajs-777	243	2	:	:	PUNCT
iajs-777	243	3	let	let	VERB
iajs-777	243	4	a	a	PRON
iajs-777	243	5	be	be	AUX
iajs-777	243	6	an	an	DET
iajs-777	243	7	sr	sr	ADV
iajs-777	243	8	-	-	PUNCT
iajs-777	243	9	closed	closed	ADJ
iajs-777	243	10	set	set	NOUN
iajs-777	243	11	of	of	ADP
iajs-777	243	12	(	(	PUNCT
iajs-777	243	13	x,	x,	PROPN
iajs-777	243	14	)	)	PUNCT
iajs-777	243	15	,	,	PUNCT
iajs-777	243	16	let	let	VERB
iajs-777	243	17	u	u	PRON
iajs-777	243	18	be	be	AUX
iajs-777	243	19	a	a	DET
iajs-777	243	20	regular	regular	ADJ
iajs-777	243	21	open	open	ADJ
iajs-777	243	22	set	set	NOUN
iajs-777	243	23	of	of	ADP
iajs-777	243	24	(	(	PUNCT
iajs-777	243	25	y,	y,	PROPN
iajs-777	243	26	'	'	PUNCT
iajs-777	243	27	)	)	PUNCT
iajs-777	243	28	such	such	ADJ
iajs-777	243	29	that	that	DET
iajs-777	243	30	f(a	f(a	NOUN
iajs-777	243	31	)	)	PUNCT
iajs-777	243	32			PROPN
iajs-777	243	33	u.	u.	PROPN
iajs-777	243	34	since	since	SCONJ
iajs-777	243	35	f	f	PROPN
iajs-777	243	36	is	be	AUX
iajs-777	243	37	regular	regular	ADJ
iajs-777	243	38	irresolute	irresolute	ADJ
iajs-777	243	39	,	,	PUNCT
iajs-777	243	40	then	then	ADV
iajs-777	243	41	f	f	PROPN
iajs-777	243	42	–	–	PUNCT
iajs-777	243	43	1(u	1(u	NUM
iajs-777	243	44	)	)	PUNCT
iajs-777	243	45	is	be	AUX
iajs-777	243	46	a	a	DET
iajs-777	243	47	regular	regular	ADJ
iajs-777	243	48	open	open	ADJ
iajs-777	243	49	set	set	NOUN
iajs-777	243	50	of	of	ADP
iajs-777	243	51	(	(	PUNCT
iajs-777	243	52	x,	x,	PROPN
iajs-777	243	53	)	)	PUNCT
iajs-777	243	54	.	.	PUNCT
iajs-777	244	1	since	since	SCONJ
iajs-777	244	2	a	a	DET
iajs-777	244	3			PROPN
iajs-777	244	4	f	f	PROPN
iajs-777	244	5	–	–	PUNCT
iajs-777	244	6	1(u	1(u	NUM
iajs-777	244	7	)	)	PUNCT
iajs-777	244	8	and	and	CCONJ
iajs-777	244	9	a	a	PRON
iajs-777	244	10	is	be	AUX
iajs-777	244	11	an	an	DET
iajs-777	244	12	sr	sr	ADV
iajs-777	244	13	-	-	PUNCT
iajs-777	244	14	closed	closed	ADJ
iajs-777	244	15	,	,	PUNCT
iajs-777	244	16	then	then	ADV
iajs-777	244	17	scl(a	scl(a	X
iajs-777	244	18	)	)	PUNCT
iajs-777	244	19			PROPN
iajs-777	244	20	f	f	PROPN
iajs-777	244	21	–	–	PUNCT
iajs-777	244	22	1(u	1(u	NUM
iajs-777	244	23	)	)	PUNCT
iajs-777	244	24	.	.	PUNCT
iajs-777	245	1	this	this	PRON
iajs-777	245	2	implies	imply	VERB
iajs-777	245	3	f(scl(a	f(scl(a	NOUN
iajs-777	245	4	)	)	PUNCT
iajs-777	245	5	)	)	PUNCT
iajs-777	246	1			PROPN
iajs-777	246	2	u.	u.	PROPN
iajs-777	246	3	since	since	SCONJ
iajs-777	246	4	f	f	PROPN
iajs-777	246	5	is	be	AUX
iajs-777	246	6	semi-*-closed	semi-*-close	VERB
iajs-777	246	7	map	map	NOUN
iajs-777	246	8	,	,	PUNCT
iajs-777	246	9	then	then	ADV
iajs-777	246	10	f(scl(a	f(scl(a	VERB
iajs-777	246	11	)	)	PUNCT
iajs-777	246	12	)	)	PUNCT
iajs-777	247	1	=	=	SYM
iajs-777	247	2	scl	scl	X
iajs-777	247	3	(	(	PUNCT
iajs-777	247	4	f(scl(a	f(scl(a	PROPN
iajs-777	247	5	)	)	PUNCT
iajs-777	247	6	)	)	PUNCT
iajs-777	247	7	)	)	PUNCT
iajs-777	247	8	.	.	PUNCT
iajs-777	248	1	so	so	ADV
iajs-777	248	2	scl(f(a	scl(f(a	PROPN
iajs-777	248	3	)	)	PUNCT
iajs-777	248	4	)	)	PUNCT
iajs-777	249	1			PROPN
iajs-777	249	2	scl(f(scl(a	scl(f(scl(a	PROPN
iajs-777	249	3	)	)	PUNCT
iajs-777	249	4	)	)	PUNCT
iajs-777	249	5	)	)	PUNCT
iajs-777	250	1	=	=	PRON
iajs-777	250	2	f(scl(a	f(scl(a	PROPN
iajs-777	250	3	)	)	PUNCT
iajs-777	250	4	)	)	PUNCT
iajs-777	250	5	)	)	PUNCT
iajs-777	251	1			PROPN
iajs-777	251	2	u.	u.	PROPN
iajs-777	251	3	therefore	therefore	ADV
iajs-777	251	4	f(a	f(a	PROPN
iajs-777	251	5	)	)	PUNCT
iajs-777	251	6	is	be	AUX
iajs-777	251	7	an	an	DET
iajs-777	251	8	sr	sr	ADV
iajs-777	251	9	-	-	PUNCT
iajs-777	251	10	closed	closed	ADJ
iajs-777	251	11	set	set	NOUN
iajs-777	251	12	of	of	ADP
iajs-777	251	13	(	(	PUNCT
iajs-777	251	14	y,	y,	PROPN
iajs-777	251	15	'	'	PUNCT
iajs-777	251	16	)	)	PUNCT
iajs-777	251	17	.	.	PUNCT
iajs-777	252	1	3.23	3.23	NUM
iajs-777	252	2	corollary	corollary	NOUN
iajs-777	252	3	:	:	PUNCT
iajs-777	252	4	let	let	VERB
iajs-777	252	5	f:(x,	f:(x,	PROPN
iajs-777	252	6	)	)	PUNCT
iajs-777	252	7			PROPN
iajs-777	252	8	(	(	PUNCT
iajs-777	252	9	y,	y,	PROPN
iajs-777	252	10	'	'	PUNCT
iajs-777	252	11	)	)	PUNCT
iajs-777	252	12	be	be	AUX
iajs-777	252	13	a	a	DET
iajs-777	252	14	regular	regular	ADJ
iajs-777	252	15	irresolute	irresolute	ADJ
iajs-777	252	16	and	and	CCONJ
iajs-777	252	17	semi-*-closed	semi-*-close	VERB
iajs-777	252	18	map	map	NOUN
iajs-777	252	19	.	.	PUNCT
iajs-777	253	1	then	then	ADV
iajs-777	253	2	f(a	f(a	PROPN
iajs-777	253	3	)	)	PUNCT
iajs-777	253	4	is	be	AUX
iajs-777	253	5	a	a	DET
iajs-777	253	6	pre	pre	ADJ
iajs-777	253	7	-	-	ADJ
iajs-777	253	8	semi	semi	ADJ
iajs-777	253	9	-	-	ADJ
iajs-777	253	10	closed	closed	ADJ
iajs-777	253	11	set	set	NOUN
iajs-777	253	12	of	of	ADP
iajs-777	253	13	(	(	PUNCT
iajs-777	253	14	y,	y,	PROPN
iajs-777	253	15	'	'	PUNCT
iajs-777	253	16	)	)	PUNCT
iajs-777	253	17	for	for	ADP
iajs-777	253	18	every	every	DET
iajs-777	253	19	sr	sr	NOUN
iajs-777	253	20	-	-	PUNCT
iajs-777	253	21	closed	closed	ADJ
iajs-777	253	22	set	set	NOUN
iajs-777	253	23	of	of	ADP
iajs-777	253	24	(	(	PUNCT
iajs-777	253	25	x,	x,	PROPN
iajs-777	253	26	)	)	PUNCT
iajs-777	253	27	.	.	PUNCT
iajs-777	254	1	proof	proof	NOUN
iajs-777	254	2	:	:	PUNCT
iajs-777	254	3	it	it	PRON
iajs-777	254	4	is	be	AUX
iajs-777	254	5	clear	clear	ADJ
iajs-777	254	6	.	.	PUNCT
iajs-777	255	1	fig	fig	NOUN
iajs-777	255	2	.	.	PUNCT
iajs-777	256	1	(	(	PUNCT
iajs-777	256	2	2	2	X
iajs-777	256	3	)	)	PUNCT
iajs-777	256	4	explains	explain	VERB
iajs-777	256	5	the	the	DET
iajs-777	256	6	relationships	relationship	NOUN
iajs-777	256	7	among	among	ADP
iajs-777	256	8	the	the	DET
iajs-777	256	9	different	different	ADJ
iajs-777	256	10	types	type	NOUN
iajs-777	256	11	of	of	ADP
iajs-777	256	12	weakly	weakly	ADJ
iajs-777	256	13	continuous	continuous	ADJ
iajs-777	256	14	function	function	NOUN
iajs-777	256	15	.	.	PUNCT
iajs-777	257	1	references	reference	NOUN
iajs-777	257	2	1	1	NUM
iajs-777	257	3	.	.	PUNCT
iajs-777	258	1	njasted	njaste	VERB
iajs-777	258	2	,	,	PUNCT
iajs-777	258	3	olav	olav	PROPN
iajs-777	258	4	,	,	PUNCT
iajs-777	258	5	(	(	PUNCT
iajs-777	258	6	1965	1965	NUM
iajs-777	258	7	)	)	PUNCT
iajs-777	258	8	,	,	PUNCT
iajs-777	258	9	on	on	ADP
iajs-777	258	10	some	some	DET
iajs-777	258	11	classes	class	NOUN
iajs-777	258	12	of	of	ADP
iajs-777	258	13	nearly	nearly	ADV
iajs-777	258	14	open	open	ADJ
iajs-777	258	15	sets	set	NOUN
iajs-777	258	16	,	,	PUNCT
iajs-777	258	17	pacific	pacific	PROPN
iajs-777	258	18	j.	j.	PROPN
iajs-777	258	19	math	math	PROPN
iajs-777	258	20	.	.	PUNCT
iajs-777	259	1	,	,	PUNCT
iajs-777	259	2	15	15	NUM
iajs-777	259	3	(	(	PUNCT
iajs-777	259	4	3	3	NUM
iajs-777	259	5	):	):	PUNCT
iajs-777	259	6	961	961	NUM
iajs-777	259	7	-	-	SYM
iajs-777	259	8	970	970	NUM
iajs-777	259	9	.	.	NOUN
iajs-777	259	10	2	2	NUM
iajs-777	259	11	.	.	X
iajs-777	259	12	levine	levine	PROPN
iajs-777	259	13	,	,	PUNCT
iajs-777	259	14	n.	n.	PROPN
iajs-777	259	15	(	(	PUNCT
iajs-777	259	16	1970	1970	NUM
iajs-777	259	17	)	)	PUNCT
iajs-777	259	18	,	,	PUNCT
iajs-777	259	19	generalized	generalize	VERB
iajs-777	259	20	closed	closed	ADJ
iajs-777	259	21	sets	set	NOUN
iajs-777	259	22	in	in	ADP
iajs-777	259	23	topology	topology	NOUN
iajs-777	259	24	rend	rend	VERB
iajs-777	259	25	.	.	PUNCT
iajs-777	260	1	cire	cire	PROPN
iajs-777	260	2	.	.	PUNCT
iajs-777	261	1	math	math	NOUN
iajs-777	261	2	.	.	PUNCT
iajs-777	262	1	palermo	palermo	PROPN
iajs-777	262	2	,	,	PUNCT
iajs-777	262	3	19(2	19(2	NUM
iajs-777	262	4	):	):	PUNCT
iajs-777	262	5	89	89	NUM
iajs-777	262	6	-	-	SYM
iajs-777	262	7	96	96	NUM
iajs-777	262	8	.	.	PUNCT
iajs-777	263	1	3	3	X
iajs-777	263	2	.	.	X
iajs-777	263	3	kumar	kumar	PROPN
iajs-777	263	4	,	,	PUNCT
iajs-777	263	5	m.	m.	PROPN
iajs-777	263	6	k.	k.	PROPN
iajs-777	263	7	r.	r.	PROPN
iajs-777	263	8	s.	s.	PROPN
iajs-777	263	9	veera	veera	PROPN
iajs-777	263	10	,	,	PUNCT
iajs-777	263	11	(	(	PUNCT
iajs-777	263	12	2002	2002	NUM
iajs-777	263	13	)	)	PUNCT
iajs-777	263	14	,	,	PUNCT
iajs-777	263	15	-generalized	-generalize	VERB
iajs-777	263	16	regular	regular	ADJ
iajs-777	263	17	closed	closed	ADJ
iajs-777	263	18	sets	set	NOUN
iajs-777	263	19	,	,	PUNCT
iajs-777	263	20	acta	acta	PROPN
iajs-777	263	21	ciencia	ciencia	PROPN
iajs-777	263	22	indica	indica	PROPN
iajs-777	263	23	,	,	PUNCT
iajs-777	263	24	xxviiim(2	xxviiim(2	PROPN
iajs-777	263	25	)	)	PUNCT
iajs-777	263	26	,	,	PUNCT
iajs-777	263	27	279	279	NUM
iajs-777	263	28	.	.	PUNCT
iajs-777	264	1	4	4	X
iajs-777	264	2	.	.	X
iajs-777	264	3	kummar	kummar	NOUN
iajs-777	264	4	,	,	PUNCT
iajs-777	264	5	m.	m.	PROPN
iajs-777	264	6	k.	k.	PROPN
iajs-777	264	7	r.s	r.s	PROPN
iajs-777	264	8	.	.	PROPN
iajs-777	264	9	veera	veera	PROPN
iajs-777	264	10	,	,	PUNCT
iajs-777	264	11	(	(	PUNCT
iajs-777	264	12	2002	2002	NUM
iajs-777	264	13	)	)	PUNCT
iajs-777	264	14	,	,	PUNCT
iajs-777	264	15	pre	pre	ADJ
iajs-777	264	16	-	-	ADJ
iajs-777	264	17	semi	semi	ADJ
iajs-777	264	18	-	-	ADJ
iajs-777	264	19	closed	closed	ADJ
iajs-777	264	20	sets	set	NOUN
iajs-777	264	21	,	,	PUNCT
iajs-777	264	22	indian	indian	ADJ
iajs-777	264	23	journal	journal	NOUN
iajs-777	264	24	of	of	ADP
iajs-777	264	25	math	math	NOUN
iajs-777	264	26	.	.	PUNCT
iajs-777	264	27	,	,	PUNCT
iajs-777	265	1	44(2	44(2	NUM
iajs-777	265	2	):	):	PUNCT
iajs-777	265	3	165	165	NUM
iajs-777	265	4	-	-	SYM
iajs-777	265	5	181	181	NUM
iajs-777	265	6	.	.	PUNCT
iajs-777	266	1	5	5	NUM
iajs-777	266	2	.	.	X
iajs-777	266	3	popa	popa	ADJ
iajs-777	266	4	,	,	PUNCT
iajs-777	266	5	valeriu	valeriu	NOUN
iajs-777	266	6	and	and	CCONJ
iajs-777	266	7	noiri	noiri	PROPN
iajs-777	266	8	,	,	PUNCT
iajs-777	266	9	taleashi	taleashi	PRON
iajs-777	266	10	,	,	PUNCT
iajs-777	266	11	(	(	PUNCT
iajs-777	266	12	2000	2000	NUM
iajs-777	266	13	)	)	PUNCT
iajs-777	266	14	,	,	PUNCT
iajs-777	266	15	some	some	DET
iajs-777	266	16	properties	property	NOUN
iajs-777	266	17	of	of	ADP
iajs-777	266	18	-irresolute	-irresolute	ADJ
iajs-777	266	19	multifunctions	multifunction	NOUN
iajs-777	266	20	,	,	PUNCT
iajs-777	266	21	arab	arab	ADJ
iajs-777	266	22	j.m	j.m	PROPN
iajs-777	266	23	ath	ath	NOUN
iajs-777	266	24	.	.	PUNCT
iajs-777	267	1	sc	sc	PROPN
iajs-777	267	2	.	.	PROPN
iajs-777	267	3	,	,	PUNCT
iajs-777	267	4	6(2):17	6(2):17	NUM
iajs-777	267	5	-	-	SYM
iajs-777	267	6	26	26	NUM
iajs-777	267	7	.	.	PUNCT
iajs-777	268	1	6	6	NUM
iajs-777	268	2	.	.	X
iajs-777	268	3	al	al	PROPN
iajs-777	268	4	-	-	PUNCT
iajs-777	268	5	tabatabai	tabatabai	PROPN
iajs-777	268	6	,	,	PUNCT
iajs-777	268	7	nadia	nadia	PROPN
iajs-777	268	8	m.ali	m.ali	PROPN
iajs-777	268	9	,	,	PUNCT
iajs-777	268	10	(	(	PUNCT
iajs-777	268	11	2004	2004	NUM
iajs-777	268	12	)	)	PUNCT
iajs-777	268	13	,	,	PUNCT
iajs-777	268	14	on	on	ADP
iajs-777	268	15	new	new	ADJ
iajs-777	268	16	types	type	NOUN
iajs-777	268	17	of	of	ADP
iajs-777	268	18	weakly	weakly	ADJ
iajs-777	268	19	open	open	ADJ
iajs-777	268	20	sets	set	NOUN
iajs-777	268	21	-open	-open	PROPN
iajs-777	268	22	and	and	CCONJ
iajs-777	268	23	semi--open	semi--open	PUNCT
iajs-777	268	24	sets	set	NOUN
iajs-777	268	25	,	,	PUNCT
iajs-777	268	26	m.sc	m.sc	PROPN
iajs-777	268	27	.	.	PUNCT
iajs-777	269	1	thesis	thesis	NOUN
iajs-777	269	2	,	,	PUNCT
iajs-777	269	3	university	university	NOUN
iajs-777	269	4	of	of	ADP
iajs-777	269	5	baghdad	baghdad	PROPN
iajs-777	269	6	.	.	PUNCT
iajs-777	270	1	7	7	X
iajs-777	270	2	.	.	X
iajs-777	271	1	nasir	nasir	PROPN
iajs-777	271	2	,	,	PUNCT
iajs-777	271	3	ahmed	ahmed	PROPN
iajs-777	271	4	,	,	PUNCT
iajs-777	271	5	ibrahem	ibrahem	NOUN
iajs-777	271	6	,	,	PUNCT
iajs-777	271	7	(	(	PUNCT
iajs-777	271	8	2005	2005	NUM
iajs-777	271	9	)	)	PUNCT
iajs-777	271	10	,	,	PUNCT
iajs-777	271	11	some	some	DET
iajs-777	271	12	kind	kind	NOUN
iajs-777	271	13	of	of	ADP
iajs-777	271	14	strongly	strongly	ADV
iajs-777	271	15	compact	compact	ADJ
iajs-777	271	16	and	and	CCONJ
iajs-777	271	17	pair	pair	NOUN
iajs-777	271	18	-	-	PUNCT
iajs-777	271	19	wise	wise	ADJ
iajs-777	271	20	compact	compact	ADJ
iajs-777	271	21	spaces	space	NOUN
iajs-777	271	22	,	,	PUNCT
iajs-777	271	23	m.sc	m.sc	PROPN
iajs-777	271	24	.	.	PUNCT
iajs-777	272	1	thesis	thesis	NOUN
iajs-777	272	2	,	,	PUNCT
iajs-777	272	3	university	university	NOUN
iajs-777	272	4	of	of	ADP
iajs-777	272	5	baghdad	baghdad	PROPN
iajs-777	272	6	.	.	PUNCT
iajs-777	273	1	8	8	NUM
iajs-777	273	2	.	.	X
iajs-777	273	3	andrijevic	andrijevic	PROPN
iajs-777	273	4	,	,	PUNCT
iajs-777	273	5	d.	d.	PROPN
iajs-777	273	6	(	(	PUNCT
iajs-777	273	7	1986	1986	NUM
iajs-777	273	8	)	)	PUNCT
iajs-777	273	9	,	,	PUNCT
iajs-777	273	10	semi	semi	ADJ
iajs-777	273	11	-	-	ADJ
iajs-777	273	12	pere	pere	ADJ
iajs-777	273	13	sets	set	NOUN
iajs-777	273	14	,	,	PUNCT
iajs-777	273	15	math	math	NOUN
iajs-777	273	16	.	.	PUNCT
iajs-777	274	1	vesnik	vesnik	PROPN
iajs-777	274	2	,	,	PUNCT
iajs-777	274	3	38(1	38(1	NUM
iajs-777	274	4	):	):	PUNCT
iajs-777	274	5	24	24	NUM
iajs-777	274	6	-	-	SYM
iajs-777	274	7	32	32	NUM
iajs-777	274	8	.	.	PUNCT
iajs-777	275	1	9	9	NUM
iajs-777	275	2	.	.	X
iajs-777	275	3	al	al	PROPN
iajs-777	275	4	-	-	PUNCT
iajs-777	275	5	maliki	maliki	PROPN
iajs-777	275	6	,	,	PUNCT
iajs-777	275	7	najlaa	najlaa	PROPN
iajs-777	275	8	jabbar	jabbar	PROPN
iajs-777	275	9	,	,	PUNCT
iajs-777	275	10	(	(	PUNCT
iajs-777	275	11	2005	2005	NUM
iajs-777	275	12	)	)	PUNCT
iajs-777	275	13	,	,	PUNCT
iajs-777	275	14	some	some	DET
iajs-777	275	15	kinds	kind	NOUN
iajs-777	275	16	of	of	ADP
iajs-777	275	17	weakly	weakly	ADV
iajs-777	275	18	connected	connect	VERB
iajs-777	275	19	and	and	CCONJ
iajs-777	275	20	pairwis	pairwis	VERB
iajs-777	275	21	connected	connected	ADJ
iajs-777	275	22	space	space	NOUN
iajs-777	275	23	,	,	PUNCT
iajs-777	275	24	m.sc	m.sc	PROPN
iajs-777	275	25	.	.	PUNCT
iajs-777	276	1	thesis	thesis	NOUN
iajs-777	276	2	,	,	PUNCT
iajs-777	276	3	university	university	NOUN
iajs-777	276	4	of	of	ADP
iajs-777	276	5	baghdad	baghdad	PROPN
iajs-777	276	6	.	.	PUNCT
iajs-777	277	1	10	10	NUM
iajs-777	277	2	.	.	X
iajs-777	277	3	adams	adams	PROPN
iajs-777	277	4	,	,	PUNCT
iajs-777	277	5	colin	colin	PROPN
iajs-777	277	6	and	and	CCONJ
iajs-777	277	7	franzosa	franzosa	PROPN
iajs-777	277	8	,	,	PUNCT
iajs-777	277	9	robert	robert	PROPN
iajs-777	277	10	,	,	PUNCT
iajs-777	277	11	(	(	PUNCT
iajs-777	277	12	2008	2008	NUM
iajs-777	277	13	)	)	PUNCT
iajs-777	277	14	,	,	PUNCT
iajs-777	277	15	introduction	introduction	NOUN
iajs-777	277	16	to	to	ADP
iajs-777	277	17	topology	topology	NOUN
iajs-777	277	18	pure	pure	ADJ
iajs-777	277	19	and	and	CCONJ
iajs-777	277	20	applied	apply	VERB
iajs-777	277	21	,	,	PUNCT
iajs-777	277	22	upper	upper	ADJ
iajs-777	277	23	saddle	saddle	NOUN
iajs-777	277	24	river	river	NOUN
iajs-777	277	25	,	,	PUNCT
iajs-777	277	26	njo4458	njo4458	NOUN
iajs-777	277	27	.	.	PUNCT
iajs-777	278	1	11	11	NUM
iajs-777	278	2	.	.	X
iajs-777	279	1	popa	popa	ADJ
iajs-777	279	2	,	,	PUNCT
iajs-777	279	3	valeriu	valeriu	NOUN
iajs-777	279	4	and	and	CCONJ
iajs-777	279	5	noiri	noiri	PROPN
iajs-777	279	6	,	,	PUNCT
iajs-777	279	7	tokashi	tokashi	PRON
iajs-777	279	8	,	,	PUNCT
iajs-777	279	9	(	(	PUNCT
iajs-777	279	10	2001	2001	NUM
iajs-777	279	11	)	)	PUNCT
iajs-777	279	12	,	,	PUNCT
iajs-777	279	13	on	on	ADP
iajs-777	279	14	the	the	DET
iajs-777	279	15	definitions	definition	NOUN
iajs-777	279	16	of	of	ADP
iajs-777	279	17	some	some	DET
iajs-777	279	18	generalized	generalized	ADJ
iajs-777	279	19	forms	form	NOUN
iajs-777	279	20	of	of	ADP
iajs-777	279	21	continuty	continuty	NOUN
iajs-777	279	22	under	under	ADP
iajs-777	279	23	minimal	minimal	ADJ
iajs-777	279	24	conditions	condition	NOUN
iajs-777	279	25	,	,	PUNCT
iajs-777	279	26	mem	mem	PROPN
iajs-777	279	27	.	.	PUNCT
iajs-777	279	28	fac	fac	PROPN
iajs-777	279	29	.	.	PUNCT
iajs-777	280	1	sci	sci	PROPN
iajs-777	280	2	.	.	PROPN
iajs-777	280	3	,	,	PUNCT
iajs-777	280	4	kochi	kochi	VERB
iajs-777	280	5	univ.(math	univ.(math	PRON
iajs-777	280	6	.	.	PUNCT
iajs-777	280	7	)	)	PUNCT
iajs-777	280	8	,	,	PUNCT
iajs-777	280	9	22:9	22:9	NUM
iajs-777	280	10	-	-	SYM
iajs-777	280	11	18	18	NUM
iajs-777	280	12	.	.	NOUN
iajs-777	280	13	12	12	NUM
iajs-777	280	14	.	.	PUNCT
iajs-777	281	1	nagata	nagata	PROPN
iajs-777	281	2	,	,	PUNCT
iajs-777	281	3	j.	j.	PROPN
iajs-777	281	4	,	,	PUNCT
iajs-777	281	5	(	(	PUNCT
iajs-777	281	6	2002	2002	NUM
iajs-777	281	7	)	)	PUNCT
iajs-777	281	8	,	,	PUNCT
iajs-777	281	9	on	on	ADP
iajs-777	281	10	preclosed	preclose	VERB
iajs-777	281	11	sets	set	NOUN
iajs-777	281	12	and	and	CCONJ
iajs-777	281	13	their	their	PRON
iajs-777	281	14	generalizations	generalization	NOUN
iajs-777	281	15	,	,	PUNCT
iajs-777	281	16	houston	houston	PROPN
iajs-777	281	17	journal	journal	PROPN
iajs-777	281	18	of	of	ADP
iajs-777	281	19	math	math	NOUN
iajs-777	281	20	.	.	PUNCT
iajs-777	281	21	,	,	PUNCT
iajs-777	281	22	28(4	28(4	NUM
iajs-777	281	23	)	)	PUNCT
iajs-777	281	24	.	.	PUNCT
iajs-777	282	1	13	13	NUM
iajs-777	282	2	.	.	PUNCT
iajs-777	282	3	maki	maki	PROPN
iajs-777	282	4	,	,	PUNCT
iajs-777	282	5	h.	h.	PROPN
iajs-777	282	6	;	;	PUNCT
iajs-777	282	7	devi	devi	PROPN
iajs-777	282	8	,	,	PUNCT
iajs-777	282	9	r.	r.	PROPN
iajs-777	282	10	and	and	CCONJ
iajs-777	282	11	balachandran	balachandran	PROPN
iajs-777	282	12	,	,	PUNCT
iajs-777	282	13	k.	k.	PROPN
iajs-777	282	14	(	(	PUNCT
iajs-777	282	15	1994	1994	NUM
iajs-777	282	16	)	)	PUNCT
iajs-777	282	17	,	,	PUNCT
iajs-777	282	18	associated	associate	VERB
iajs-777	282	19	topologies	topology	NOUN
iajs-777	282	20	of	of	ADP
iajs-777	282	21	generalized	generalized	ADJ
iajs-777	282	22	-closed	-closed	ADJ
iajs-777	282	23	sets	set	NOUN
iajs-777	282	24	and	and	CCONJ
iajs-777	282	25	-generalized	-generalized	ADJ
iajs-777	282	26	closed	close	VERB
iajs-777	282	27	sets	set	NOUN
iajs-777	282	28	,	,	PUNCT
iajs-777	282	29	mem.fac	mem.fac	NOUN
iajs-777	282	30	.	.	PUNCT
iajs-777	283	1	sci	sci	PROPN
iajs-777	283	2	.	.	PUNCT
iajs-777	283	3	kohi	kohi	PROPN
iajs-777	283	4	.	.	PROPN
iajs-777	283	5	,	,	PUNCT
iajs-777	284	1	univ	univ	PROPN
iajs-777	284	2	.	.	PUNCT
iajs-777	284	3	ser	ser	PROPN
iajs-777	284	4	.	.	PUNCT
iajs-777	284	5	a.	a.	PROPN
iajs-777	284	6	math	math	PROPN
iajs-777	284	7	.	.	PUNCT
iajs-777	284	8	,	,	PUNCT
iajs-777	284	9	15:51	15:51	NUM
iajs-777	284	10	-	-	SYM
iajs-777	284	11	63	63	NUM
iajs-777	284	12	.	.	PUNCT
iajs-777	285	1	14	14	NUM
iajs-777	285	2	.	.	PUNCT
iajs-777	286	1	maki	maki	PROPN
iajs-777	286	2	,	,	PUNCT
iajs-777	286	3	h.	h.	PROPN
iajs-777	286	4	;	;	PUNCT
iajs-777	286	5	devi	devi	PROPN
iajs-777	286	6	,	,	PUNCT
iajs-777	286	7	r.	r.	PROPN
iajs-777	286	8	and	and	CCONJ
iajs-777	286	9	balachdran	balachdran	PROPN
iajs-777	286	10	,	,	PUNCT
iajs-777	286	11	k.	k.	PROPN
iajs-777	286	12	91993	91993	NUM
iajs-777	286	13	)	)	PUNCT
iajs-777	286	14	,	,	PUNCT
iajs-777	286	15	generalized	generalize	VERB
iajs-777	286	16	-closed	-closed	ADJ
iajs-777	286	17	sets	set	NOUN
iajs-777	286	18	in	in	ADP
iajs-777	286	19	topology	topology	NOUN
iajs-777	286	20	,	,	PUNCT
iajs-777	286	21	bull	bull	NOUN
iajs-777	286	22	.	.	PUNCT
iajs-777	287	1	fukuoka	fukuoka	PROPN
iajs-777	287	2	univ	univ	PROPN
iajs-777	287	3	.	.	PUNCT
iajs-777	288	1	ed	ed	NOUN
iajs-777	288	2	.	.	PUNCT
iajs-777	289	1	part	part	PROPN
iajs-777	289	2	iii	iii	PROPN
iajs-777	289	3	,	,	PUNCT
iajs-777	289	4	42:13	42:13	NUM
iajs-777	289	5	-	-	SYM
iajs-777	289	6	21	21	NUM
iajs-777	289	7	.	.	PUNCT
iajs-777	290	1	ibn	ibn	PROPN
iajs-777	290	2	alhaitham	alhaitham	PROPN
iajs-777	290	3	j.	j.	PROPN
iajs-777	290	4	for	for	ADP
iajs-777	290	5	pure	pure	ADJ
iajs-777	290	6	&	&	CCONJ
iajs-777	290	7	appl	appl	PROPN
iajs-777	290	8	.	.	PUNCT
iajs-777	291	1	sci	sci	PROPN
iajs-777	291	2	.	.	PUNCT
iajs-777	291	3	vol.24	vol.24	NOUN
iajs-777	291	4	(	(	PUNCT
iajs-777	291	5	2	2	NUM
iajs-777	291	6	)	)	PUNCT
iajs-777	291	7	2011	2011	NUM
iajs-777	291	8	15	15	NUM
iajs-777	291	9	.	.	PUNCT
iajs-777	292	1	sundaram	sundaram	PROPN
iajs-777	292	2	,	,	PUNCT
iajs-777	292	3	p.	p.	PROPN
iajs-777	292	4	;	;	PUNCT
iajs-777	292	5	maki	maki	PROPN
iajs-777	292	6	,	,	PUNCT
iajs-777	292	7	h.	h.	PROPN
iajs-777	292	8	and	and	CCONJ
iajs-777	292	9	balachandran	balachandran	PROPN
iajs-777	292	10	,	,	PUNCT
iajs-777	292	11	k.	k.	PROPN
iajs-777	292	12	(	(	PUNCT
iajs-777	292	13	1991	1991	NUM
iajs-777	292	14	)	)	PUNCT
iajs-777	292	15	,	,	PUNCT
iajs-777	292	16	semi	semi	ADJ
iajs-777	292	17	-	-	ADJ
iajs-777	292	18	generalized	generalized	ADJ
iajs-777	292	19	continuous	continuous	ADJ
iajs-777	292	20	map	map	NOUN
iajs-777	292	21	and	and	CCONJ
iajs-777	292	22	semi	semi	ADJ
iajs-777	292	23	-	-	ADJ
iajs-777	292	24	t1/2	t1/2	ADJ
iajs-777	292	25	space	space	NOUN
iajs-777	292	26	,	,	PUNCT
iajs-777	292	27	bull	bull	NOUN
iajs-777	292	28	.	.	PUNCT
iajs-777	293	1	fukuoka	fukuoka	PROPN
iajs-777	293	2	univ	univ	PROPN
iajs-777	293	3	.	.	PUNCT
iajs-777	294	1	fd	fd	PROPN
iajs-777	294	2	.	.	PUNCT
iajs-777	295	1	part	part	PROPN
iajs-777	295	2	iii	iii	PROPN
iajs-777	295	3	,	,	PUNCT
iajs-777	295	4	40:33	40:33	NUM
iajs-777	295	5	-	-	SYM
iajs-777	295	6	40	40	NUM
iajs-777	295	7	.	.	PUNCT
iajs-777	296	1	16	16	NUM
iajs-777	296	2	.	.	PUNCT
iajs-777	297	1	dontchev	dontchev	PROPN
iajs-777	297	2	,	,	PUNCT
iajs-777	297	3	j.	j.	PROPN
iajs-777	297	4	(	(	PUNCT
iajs-777	297	5	1995	1995	NUM
iajs-777	297	6	)	)	PUNCT
iajs-777	297	7	,	,	PUNCT
iajs-777	297	8	on	on	ADP
iajs-777	297	9	generalized	generalized	ADJ
iajs-777	297	10	semi	semi	ADJ
iajs-777	297	11	-	-	ADJ
iajs-777	297	12	preopen	preopen	ADJ
iajs-777	297	13	sets	set	NOUN
iajs-777	297	14	,	,	PUNCT
iajs-777	297	15	mem	mem	X
iajs-777	297	16	.	.	PUNCT
iajs-777	298	1	fac.sci.kochi.univ.ser	fac.sci.kochi.univ.ser	PROPN
iajs-777	298	2	.	.	PROPN
iajs-777	299	1	a.m	a.m	PROPN
iajs-777	299	2	ath	ath	PROPN
iajs-777	299	3	.	.	PROPN
iajs-777	299	4	,	,	PUNCT
iajs-777	299	5	16:35	16:35	NUM
iajs-777	299	6	-	-	SYM
iajs-777	299	7	48	48	NUM
iajs-777	299	8	.	.	PUNCT
iajs-777	299	9	17	17	NUM
iajs-777	299	10	.	.	X
iajs-777	300	1	balachandran	balachandran	PROPN
iajs-777	300	2	,	,	PUNCT
iajs-777	300	3	k.	k.	PROPN
iajs-777	300	4	;	;	PUNCT
iajs-777	300	5	sundaram	sundaram	PROPN
iajs-777	300	6	,	,	PUNCT
iajs-777	300	7	p.	p.	NOUN
iajs-777	300	8	and	and	CCONJ
iajs-777	300	9	maki	maki	PROPN
iajs-777	300	10	,	,	PUNCT
iajs-777	300	11	h.	h.	PROPN
iajs-777	300	12	(	(	PUNCT
iajs-777	300	13	1991	1991	NUM
iajs-777	300	14	)	)	PUNCT
iajs-777	300	15	,	,	PUNCT
iajs-777	300	16	on	on	ADP
iajs-777	300	17	generalized	generalized	ADJ
iajs-777	300	18	continuous	continuous	ADJ
iajs-777	300	19	maps	map	NOUN
iajs-777	300	20	in	in	ADP
iajs-777	300	21	toplogical	toplogical	ADJ
iajs-777	300	22	spaces	space	NOUN
iajs-777	300	23	,	,	PUNCT
iajs-777	300	24	mem.fac.sci.kochi	mem.fac.sci.kochi	PROPN
iajs-777	300	25	.	.	PUNCT
iajs-777	301	1	univ	univ	PROPN
iajs-777	301	2	.	.	PUNCT
iajs-777	301	3	ser.a.math	ser.a.math	NOUN
iajs-777	301	4	.	.	PUNCT
iajs-777	302	1	,	,	PUNCT
iajs-777	302	2	1	1	NUM
iajs-777	302	3	:	:	SYM
iajs-777	302	4	5	5	NUM
iajs-777	302	5	-	-	SYM
iajs-777	302	6	13	13	NUM
iajs-777	302	7	.	.	PUNCT
iajs-777	302	8	18	18	NUM
iajs-777	302	9	.	.	PUNCT
iajs-777	303	1	gnanambal	gnanambal	PROPN
iajs-777	303	2	,	,	PUNCT
iajs-777	303	3	y.	y.	PROPN
iajs-777	303	4	(	(	PUNCT
iajs-777	303	5	1997	1997	NUM
iajs-777	303	6	)	)	PUNCT
iajs-777	303	7	on	on	ADP
iajs-777	303	8	generalized	generalize	VERB
iajs-777	303	9	preregular	preregular	ADJ
iajs-777	303	10	closed	close	VERB
iajs-777	303	11	sets	set	NOUN
iajs-777	303	12	in	in	ADP
iajs-777	303	13	topological	topological	ADJ
iajs-777	303	14	spaces	space	NOUN
iajs-777	303	15	,	,	PUNCT
iajs-777	303	16	indian	indian	PROPN
iajs-777	303	17	j.	j.	PROPN
iajs-777	303	18	pure	pure	PROPN
iajs-777	303	19	appl	appl	PROPN
iajs-777	303	20	.	.	PUNCT
iajs-777	303	21	math	math	PROPN
iajs-777	303	22	.	.	PUNCT
iajs-777	304	1	,	,	PUNCT
iajs-777	304	2	28(3):351	28(3):351	NOUN
iajs-777	304	3	-	-	SYM
iajs-777	304	4	360	360	NUM
iajs-777	304	5	.	.	PUNCT
iajs-777	304	6	19	19	NUM
iajs-777	304	7	.	.	X
iajs-777	305	1	palanreppan	palanreppan	NOUN
iajs-777	305	2	,	,	PUNCT
iajs-777	305	3	n.	n.	PROPN
iajs-777	305	4	and	and	CCONJ
iajs-777	305	5	k.	k.	PROPN
iajs-777	305	6	c.	c.	PROPN
iajs-777	305	7	roo	roo	PROPN
iajs-777	305	8	,	,	PUNCT
iajs-777	305	9	(	(	PUNCT
iajs-777	305	10	1993	1993	NUM
iajs-777	305	11	)	)	PUNCT
iajs-777	305	12	,	,	PUNCT
iajs-777	305	13	regular	regular	ADJ
iajs-777	305	14	generalized	generalize	VERB
iajs-777	305	15	closed	close	VERB
iajs-777	305	16	sets	set	NOUN
iajs-777	305	17	,	,	PUNCT
iajs-777	305	18	kyung	kyung	PROPN
iajs-777	305	19	pook	pook	PROPN
iajs-777	305	20	math	math	PROPN
iajs-777	305	21	.	.	PUNCT
iajs-777	306	1	j.	j.	PROPN
iajs-777	306	2	,	,	PUNCT
iajs-777	306	3	33(2	33(2	NUM
iajs-777	306	4	):	):	PUNCT
iajs-777	306	5	211	211	NUM
iajs-777	306	6	-	-	SYM
iajs-777	306	7	219	219	NUM
iajs-777	306	8	.	.	PUNCT
iajs-777	306	9	20	20	NUM
iajs-777	306	10	.	.	PUNCT
iajs-777	307	1	mohammed	mohammed	PROPN
iajs-777	307	2	,	,	PUNCT
iajs-777	307	3	nadia	nadia	PROPN
iajs-777	307	4	,	,	PUNCT
iajs-777	307	5	faiq	faiq	PROPN
iajs-777	307	6	,	,	PUNCT
iajs-777	307	7	(	(	PUNCT
iajs-777	307	8	2010	2010	NUM
iajs-777	307	9	)	)	PUNCT
iajs-777	307	10	,	,	PUNCT
iajs-777	307	11	on	on	ADP
iajs-777	307	12	semi--connected	semi--connecte	VERB
iajs-777	307	13	subspaces	subspace	NOUN
iajs-777	307	14	,	,	PUNCT
iajs-777	307	15	baghdad	baghdad	PROPN
iajs-777	307	16	science	science	PROPN
iajs-777	307	17	journal	journal	PROPN
iajs-777	307	18	(	(	PUNCT
iajs-777	307	19	physics	physics	NOUN
iajs-777	307	20	and	and	CCONJ
iajs-777	307	21	mathematics	mathematic	NOUN
iajs-777	307	22	)	)	PUNCT
iajs-777	307	23	,	,	PUNCT
iajs-777	307	24	7(1	7(1	NUM
iajs-777	307	25	)	)	PUNCT
iajs-777	307	26	,	,	PUNCT
iajs-777	307	27	issn:1815	issn:1815	NOUN
iajs-777	307	28	-	-	PUNCT
iajs-777	307	29	4808	4808	NUM
iajs-777	307	30	.	.	PUNCT
iajs-777	308	1	closed	close	VERB
iajs-777	308	2			PROPN
iajs-777	308	3	g	g	NOUN
iajs-777	308	4	-	-	PUNCT
iajs-777	308	5	closed	close	VERB
iajs-777	308	6			NOUN
iajs-777	308	7	rg	rg	NOUN
iajs-777	308	8	-	-	PUNCT
iajs-777	308	9	closed	closed	ADJ
iajs-777	308	10	g	g	ADV
iajs-777	308	11	-	-	PUNCT
iajs-777	308	12	closed	closed	ADJ
iajs-777	308	13			NOUN
iajs-777	308	14	gr	gr	ADV
iajs-777	308	15	-	-	PUNCT
iajs-777	308	16	closed	closed	ADJ
iajs-777	308	17	-closed	-close	VERB
iajs-777	308	18	g-closed	g-close	VERB
iajs-777	308	19	**g	**g	NOUN
iajs-777	308	20	-	-	PUNCT
iajs-777	308	21	closed	close	VERB
iajs-777	308	22	g*-closed	g*-close	VERB
iajs-777	308	23	g**-closed	g**-close	VERB
iajs-777	308	24	semi--closed	semi--closed	ADJ
iajs-777	308	25			ADJ
iajs-777	308	26	sr	sr	ADV
iajs-777	308	27	-	-	PUNCT
iajs-777	308	28	closed	close	VERB
iajs-777	308	29			NOUN
iajs-777	308	30	pre	pre	ADJ
iajs-777	308	31	-	-	ADJ
iajs-777	308	32	semi	semi	ADJ
iajs-777	308	33	-	-	ADJ
iajs-777	308	34	closed	closed	ADJ
iajs-777	308	35	regular	regular	ADJ
iajs-777	308	36	open	open	ADJ
iajs-777	308	37	gsp	gsp	NOUN
iajs-777	308	38	-	-	PUNCT
iajs-777	308	39	closed	close	VERB
iajs-777	308	40	fig	fig	NOUN
iajs-777	308	41	.	.	PUNCT
iajs-777	309	1	(	(	PUNCT
iajs-777	309	2	1	1	X
iajs-777	309	3	)	)	PUNCT
iajs-777	309	4	the	the	DET
iajs-777	309	5	relations	relation	NOUN
iajs-777	309	6	among	among	ADP
iajs-777	309	7	the	the	DET
iajs-777	309	8	different	different	ADJ
iajs-777	309	9	types	type	NOUN
iajs-777	309	10	of	of	ADP
iajs-777	309	11	weakly	weakly	ADJ
iajs-777	309	12	closed	closed	ADJ
iajs-777	309	13	sets	set	NOUN
iajs-777	309	14	continuous	continuous	ADJ
iajs-777	309	15	open	open	NUM
iajs-777	309	16	semi--irresolute	semi--irresolute	ADJ
iajs-777	309	17	regular	regular	ADJ
iajs-777	309	18	irresolutesr	irresolutesr	NOUN
iajs-777	309	19	-	-	PUNCT
iajs-777	309	20	irresolute	irresolute	ADJ
iajs-777	309	21	g	g	NOUN
iajs-777	309	22	-	-	PUNCT
iajs-777	309	23	continuous	continuous	ADJ
iajs-777	309	24			ADJ
iajs-777	309	25	g	g	PROPN
iajs-777	309	26	-	-	ADJ
iajs-777	309	27	continuous	continuous	ADJ
iajs-777	309	28			ADJ
iajs-777	309	29	gr	gr	ADJ
iajs-777	309	30	-	-	ADJ
iajs-777	309	31	continuous	continuous	ADJ
iajs-777	309	32			ADJ
iajs-777	309	33	sr	sr	NOUN
iajs-777	309	34	-	-	ADJ
iajs-777	309	35	continuous	continuous	ADJ
iajs-777	309	36	g-continuous	g-continuous	ADJ
iajs-777	309	37			ADJ
iajs-777	309	38	gr	gr	PROPN
iajs-777	309	39	-	-	PUNCT
iajs-777	309	40	irresolute	irresolute	ADJ
iajs-777	309	41			ADJ
iajs-777	309	42	pre	pre	ADJ
iajs-777	309	43	-	-	ADJ
iajs-777	309	44	semi	semi	ADJ
iajs-777	309	45	-	-	ADJ
iajs-777	309	46	continuous	continuous	ADJ
iajs-777	309	47	gsp	gsp	NOUN
iajs-777	309	48	-	-	PUNCT
iajs-777	309	49	continuous	continuous	ADJ
iajs-777	309	50	fig	fig	NOUN
iajs-777	309	51	.	.	PUNCT
iajs-777	310	1	(	(	PUNCT
iajs-777	310	2	2	2	X
iajs-777	310	3	)	)	PUNCT
iajs-777	310	4	the	the	DET
iajs-777	310	5	relationships	relationship	NOUN
iajs-777	310	6	among	among	ADP
iajs-777	310	7	the	the	DET
iajs-777	310	8	different	different	ADJ
iajs-777	310	9	types	type	NOUN
iajs-777	310	10	of	of	ADP
iajs-777	310	11	weakly	weakly	ADJ
iajs-777	310	12	continuous	continuous	ADJ
iajs-777	310	13	function	function	NOUN
iajs-777	310	14	.	.	PUNCT