id	sid	tid	token	lemma	pos
ejpam-4583	1	1	european	european	PROPN
ejpam-4583	1	2	journal	journal	PROPN
ejpam-4583	1	3	of	of	ADP
ejpam-4583	1	4	pure	pure	ADJ
ejpam-4583	1	5	and	and	CCONJ
ejpam-4583	1	6	applied	apply	VERB
ejpam-4583	1	7	mathematics	mathematic	NOUN
ejpam-4583	1	8	vol	vol	NOUN
ejpam-4583	1	9	.	.	PUNCT
ejpam-4583	2	1	16	16	NUM
ejpam-4583	2	2	,	,	PUNCT
ejpam-4583	2	3	no	no	INTJ
ejpam-4583	2	4	.	.	NOUN
ejpam-4583	2	5	2	2	NUM
ejpam-4583	2	6	,	,	PUNCT
ejpam-4583	2	7	2023	2023	NUM
ejpam-4583	2	8	,	,	PUNCT
ejpam-4583	2	9	819	819	NUM
ejpam-4583	2	10	-	-	SYM
ejpam-4583	2	11	832	832	NUM
ejpam-4583	2	12	issn	issn	PROPN
ejpam-4583	2	13	1307	1307	NUM
ejpam-4583	2	14	-	-	SYM
ejpam-4583	2	15	5543	5543	NUM
ejpam-4583	2	16	–	–	PUNCT
ejpam-4583	2	17	ejpam.com	ejpam.com	X
ejpam-4583	2	18	published	publish	VERB
ejpam-4583	2	19	by	by	ADP
ejpam-4583	2	20	new	new	PROPN
ejpam-4583	2	21	york	york	PROPN
ejpam-4583	2	22	business	business	PROPN
ejpam-4583	2	23	global	global	PROPN
ejpam-4583	2	24	f−open	f−open	PROPN
ejpam-4583	2	25	and	and	CCONJ
ejpam-4583	2	26	f−closed	f−close	VERB
ejpam-4583	2	27	sets	set	NOUN
ejpam-4583	2	28	in	in	ADP
ejpam-4583	2	29	topological	topological	ADJ
ejpam-4583	2	30	spaces	space	NOUN
ejpam-4583	2	31	mesfer	mesfer	VERB
ejpam-4583	2	32	h.	h.	PROPN
ejpam-4583	2	33	alqahtani	alqahtani	PROPN
ejpam-4583	2	34	department	department	PROPN
ejpam-4583	2	35	of	of	ADP
ejpam-4583	2	36	mathematics	mathematics	PROPN
ejpam-4583	2	37	,	,	PUNCT
ejpam-4583	2	38	university	university	NOUN
ejpam-4583	2	39	college	college	NOUN
ejpam-4583	2	40	of	of	ADP
ejpam-4583	2	41	umluj	umluj	PROPN
ejpam-4583	2	42	,	,	PUNCT
ejpam-4583	2	43	university	university	NOUN
ejpam-4583	2	44	of	of	ADP
ejpam-4583	2	45	tabuk	tabuk	PROPN
ejpam-4583	2	46	,	,	PUNCT
ejpam-4583	2	47	tabuk	tabuk	PROPN
ejpam-4583	2	48	,	,	PUNCT
ejpam-4583	2	49	saudi	saudi	PROPN
ejpam-4583	2	50	arabia	arabia	PROPN
ejpam-4583	2	51	abstract	abstract	NOUN
ejpam-4583	2	52	.	.	PUNCT
ejpam-4583	3	1	an	an	DET
ejpam-4583	3	2	open	open	ADJ
ejpam-4583	3	3	(	(	PUNCT
ejpam-4583	3	4	resp	resp	NOUN
ejpam-4583	3	5	.	.	PROPN
ejpam-4583	3	6	,	,	PUNCT
ejpam-4583	3	7	closed	closed	ADJ
ejpam-4583	3	8	)	)	PUNCT
ejpam-4583	3	9	subset	subset	VERB
ejpam-4583	3	10	a	a	PRON
ejpam-4583	3	11	of	of	ADP
ejpam-4583	3	12	a	a	DET
ejpam-4583	3	13	topological	topological	ADJ
ejpam-4583	3	14	space	space	NOUN
ejpam-4583	3	15	(	(	PUNCT
ejpam-4583	3	16	x	x	X
ejpam-4583	3	17	,	,	PUNCT
ejpam-4583	3	18	t	t	PROPN
ejpam-4583	3	19	)	)	PUNCT
ejpam-4583	3	20	is	be	AUX
ejpam-4583	3	21	called	call	VERB
ejpam-4583	3	22	f	f	PROPN
ejpam-4583	3	23	-open	-open	PROPN
ejpam-4583	3	24	(	(	PUNCT
ejpam-4583	3	25	resp	resp	NOUN
ejpam-4583	3	26	.	.	PUNCT
ejpam-4583	4	1	,	,	PUNCT
ejpam-4583	4	2	f	f	PROPN
ejpam-4583	4	3	-closed	-close	VERB
ejpam-4583	4	4	)	)	PUNCT
ejpam-4583	4	5	set	set	VERB
ejpam-4583	4	6	if	if	SCONJ
ejpam-4583	4	7	cl(a)\a	cl(a)\a	X
ejpam-4583	4	8	(	(	PUNCT
ejpam-4583	4	9	resp	resp	NOUN
ejpam-4583	4	10	.	.	PUNCT
ejpam-4583	4	11	,	,	PUNCT
ejpam-4583	5	1	a\	a\	NOUN
ejpam-4583	5	2	int(a	int(a	PROPN
ejpam-4583	5	3	)	)	PUNCT
ejpam-4583	5	4	)	)	PUNCT
ejpam-4583	5	5	is	be	AUX
ejpam-4583	5	6	finite	finite	NOUN
ejpam-4583	5	7	set	set	NOUN
ejpam-4583	5	8	.	.	PUNCT
ejpam-4583	6	1	in	in	ADP
ejpam-4583	6	2	this	this	DET
ejpam-4583	6	3	work	work	NOUN
ejpam-4583	6	4	,	,	PUNCT
ejpam-4583	6	5	we	we	PRON
ejpam-4583	6	6	study	study	VERB
ejpam-4583	6	7	the	the	DET
ejpam-4583	6	8	main	main	ADJ
ejpam-4583	6	9	properties	property	NOUN
ejpam-4583	6	10	of	of	ADP
ejpam-4583	6	11	these	these	DET
ejpam-4583	6	12	definitions	definition	NOUN
ejpam-4583	6	13	and	and	CCONJ
ejpam-4583	6	14	examine	examine	VERB
ejpam-4583	6	15	the	the	DET
ejpam-4583	6	16	relationships	relationship	NOUN
ejpam-4583	6	17	between	between	ADP
ejpam-4583	6	18	f	f	PROPN
ejpam-4583	6	19	-open	-open	PROPN
ejpam-4583	6	20	and	and	CCONJ
ejpam-4583	6	21	f	f	NOUN
ejpam-4583	6	22	-closed	-closed	ADJ
ejpam-4583	6	23	sets	set	NOUN
ejpam-4583	6	24	with	with	ADP
ejpam-4583	6	25	other	other	ADJ
ejpam-4583	6	26	kinds	kind	NOUN
ejpam-4583	6	27	such	such	ADJ
ejpam-4583	6	28	as	as	ADP
ejpam-4583	6	29	regularly	regularly	ADV
ejpam-4583	6	30	open	open	ADJ
ejpam-4583	6	31	,	,	PUNCT
ejpam-4583	6	32	regularly	regularly	ADV
ejpam-4583	6	33	closed	close	VERB
ejpam-4583	6	34	,	,	PUNCT
ejpam-4583	6	35	closed	closed	ADJ
ejpam-4583	6	36	,	,	PUNCT
ejpam-4583	6	37	and	and	CCONJ
ejpam-4583	6	38	open	open	ADJ
ejpam-4583	6	39	sets	set	NOUN
ejpam-4583	6	40	.	.	PUNCT
ejpam-4583	7	1	then	then	ADV
ejpam-4583	7	2	,	,	PUNCT
ejpam-4583	7	3	we	we	PRON
ejpam-4583	7	4	establish	establish	VERB
ejpam-4583	7	5	some	some	DET
ejpam-4583	7	6	operators	operator	NOUN
ejpam-4583	7	7	such	such	ADJ
ejpam-4583	7	8	as	as	ADP
ejpam-4583	7	9	f	f	PROPN
ejpam-4583	7	10	-interior	-interior	PROPN
ejpam-4583	7	11	,	,	PUNCT
ejpam-4583	7	12	f	f	PROPN
ejpam-4583	7	13	-closure	-closure	NOUN
ejpam-4583	7	14	,	,	PUNCT
ejpam-4583	7	15	and	and	CCONJ
ejpam-4583	7	16	f	f	PROPN
ejpam-4583	7	17	-derived	-derived	PROPN
ejpam-4583	7	18	...	...	PUNCT
ejpam-4583	7	19	etc	etc	X
ejpam-4583	7	20	.	.	X
ejpam-4583	7	21	,	,	PUNCT
ejpam-4583	7	22	using	use	VERB
ejpam-4583	7	23	f	f	PROPN
ejpam-4583	7	24	-open	-open	PROPN
ejpam-4583	7	25	and	and	CCONJ
ejpam-4583	7	26	f	f	NOUN
ejpam-4583	7	27	-closed	-close	VERB
ejpam-4583	7	28	sets	set	NOUN
ejpam-4583	7	29	.	.	PUNCT
ejpam-4583	8	1	at	at	ADP
ejpam-4583	8	2	the	the	DET
ejpam-4583	8	3	end	end	NOUN
ejpam-4583	8	4	of	of	ADP
ejpam-4583	8	5	this	this	DET
ejpam-4583	8	6	work	work	NOUN
ejpam-4583	8	7	,	,	PUNCT
ejpam-4583	8	8	we	we	PRON
ejpam-4583	8	9	introduce	introduce	VERB
ejpam-4583	8	10	definitions	definition	NOUN
ejpam-4583	8	11	of	of	ADP
ejpam-4583	8	12	f	f	PROPN
ejpam-4583	8	13	-continuous	-continuous	ADJ
ejpam-4583	8	14	function	function	NOUN
ejpam-4583	8	15	,	,	PUNCT
ejpam-4583	8	16	f	f	PROPN
ejpam-4583	8	17	-compact	-compact	PROPN
ejpam-4583	8	18	space	space	NOUN
ejpam-4583	8	19	,	,	PUNCT
ejpam-4583	8	20	and	and	CCONJ
ejpam-4583	8	21	other	other	ADJ
ejpam-4583	8	22	related	related	ADJ
ejpam-4583	8	23	properties	property	NOUN
ejpam-4583	8	24	.	.	PUNCT
ejpam-4583	9	1	2020	2020	NUM
ejpam-4583	9	2	mathematics	mathematic	NOUN
ejpam-4583	9	3	subject	subject	NOUN
ejpam-4583	9	4	classifications	classification	NOUN
ejpam-4583	9	5	:	:	PUNCT
ejpam-4583	9	6	05c99	05c99	NUM
ejpam-4583	9	7	,	,	PUNCT
ejpam-4583	9	8	54f15	54f15	NUM
ejpam-4583	9	9	key	key	ADJ
ejpam-4583	9	10	words	word	NOUN
ejpam-4583	9	11	and	and	CCONJ
ejpam-4583	9	12	phrases	phrase	NOUN
ejpam-4583	9	13	:	:	PUNCT
ejpam-4583	9	14	topological	topological	ADJ
ejpam-4583	9	15	space	space	NOUN
ejpam-4583	9	16	,	,	PUNCT
ejpam-4583	9	17	f	f	PROPN
ejpam-4583	9	18	-open	-open	PROPN
ejpam-4583	9	19	,	,	PUNCT
ejpam-4583	9	20	open	open	ADJ
ejpam-4583	9	21	domain	domain	NOUN
ejpam-4583	9	22	,	,	PUNCT
ejpam-4583	9	23	f	f	PROPN
ejpam-4583	9	24	-interior	-interior	PROPN
ejpam-4583	9	25	,	,	PUNCT
ejpam-4583	9	26	f	f	PROPN
ejpam-4583	9	27	-closure	-closure	PROPN
ejpam-4583	9	28	,	,	PUNCT
ejpam-4583	9	29	f	f	PROPN
ejpam-4583	9	30	-derived	-derived	PROPN
ejpam-4583	9	31	,	,	PUNCT
ejpam-4583	9	32	f	f	PROPN
ejpam-4583	9	33	-continuous	-continuous	PROPN
ejpam-4583	9	34	,	,	PUNCT
ejpam-4583	9	35	f	f	PROPN
ejpam-4583	9	36	-compact	-compact	PROPN
ejpam-4583	9	37	1	1	NUM
ejpam-4583	9	38	.	.	PUNCT
ejpam-4583	9	39	introduction	introduction	NOUN
ejpam-4583	9	40	in	in	ADP
ejpam-4583	9	41	the	the	DET
ejpam-4583	9	42	topological	topological	ADJ
ejpam-4583	9	43	space	space	NOUN
ejpam-4583	9	44	x	x	NOUN
ejpam-4583	9	45	,	,	PUNCT
ejpam-4583	9	46	a	a	DET
ejpam-4583	9	47	subset	subset	NOUN
ejpam-4583	9	48	b	b	NOUN
ejpam-4583	9	49	of	of	ADP
ejpam-4583	9	50	a	a	DET
ejpam-4583	9	51	space	space	NOUN
ejpam-4583	9	52	x	x	PUNCT
ejpam-4583	9	53	is	be	AUX
ejpam-4583	9	54	said	say	VERB
ejpam-4583	9	55	to	to	PART
ejpam-4583	9	56	be	be	AUX
ejpam-4583	9	57	a	a	DET
ejpam-4583	9	58	regularly	regularly	ADV
ejpam-4583	9	59	-	-	PUNCT
ejpam-4583	9	60	closed	closed	ADJ
ejpam-4583	9	61	,	,	PUNCT
ejpam-4583	9	62	called	call	VERB
ejpam-4583	9	63	also	also	ADV
ejpam-4583	9	64	closed	closed	ADJ
ejpam-4583	9	65	domain	domain	NOUN
ejpam-4583	9	66	if	if	SCONJ
ejpam-4583	9	67	b	b	NOUN
ejpam-4583	9	68	=	=	SYM
ejpam-4583	9	69	cl(int(b	cl(int(b	NOUN
ejpam-4583	9	70	)	)	PUNCT
ejpam-4583	9	71	)	)	PUNCT
ejpam-4583	9	72	.	.	PUNCT
ejpam-4583	10	1	a	a	DET
ejpam-4583	10	2	subset	subset	NOUN
ejpam-4583	10	3	b	b	NOUN
ejpam-4583	10	4	of	of	ADP
ejpam-4583	10	5	x	x	SYM
ejpam-4583	10	6	is	be	AUX
ejpam-4583	10	7	said	say	VERB
ejpam-4583	10	8	to	to	PART
ejpam-4583	10	9	be	be	AUX
ejpam-4583	10	10	a	a	DET
ejpam-4583	10	11	regularly	regularly	ADV
ejpam-4583	10	12	-	-	PUNCT
ejpam-4583	10	13	open	open	ADJ
ejpam-4583	10	14	,	,	PUNCT
ejpam-4583	10	15	called	call	VERB
ejpam-4583	10	16	also	also	ADV
ejpam-4583	10	17	open	open	ADJ
ejpam-4583	10	18	domain	domain	NOUN
ejpam-4583	10	19	if	if	SCONJ
ejpam-4583	10	20	b	b	PROPN
ejpam-4583	10	21	=	=	SYM
ejpam-4583	10	22	int(cl(b	int(cl(b	PROPN
ejpam-4583	10	23	)	)	PUNCT
ejpam-4583	10	24	)	)	PUNCT
ejpam-4583	11	1	[	[	X
ejpam-4583	11	2	2	2	NUM
ejpam-4583	11	3	]	]	PUNCT
ejpam-4583	11	4	.	.	PUNCT
ejpam-4583	12	1	in	in	ADP
ejpam-4583	12	2	this	this	DET
ejpam-4583	12	3	work	work	NOUN
ejpam-4583	12	4	,	,	PUNCT
ejpam-4583	12	5	we	we	PRON
ejpam-4583	12	6	are	be	AUX
ejpam-4583	12	7	interested	interested	ADJ
ejpam-4583	12	8	in	in	ADP
ejpam-4583	12	9	studying	study	VERB
ejpam-4583	12	10	the	the	DET
ejpam-4583	12	11	concepts	concept	NOUN
ejpam-4583	12	12	of	of	ADP
ejpam-4583	12	13	f	f	PROPN
ejpam-4583	12	14	-open	-open	PROPN
ejpam-4583	12	15	and	and	CCONJ
ejpam-4583	12	16	f	f	NOUN
ejpam-4583	12	17	-closed	-close	VERB
ejpam-4583	12	18	sets	set	NOUN
ejpam-4583	12	19	in	in	ADP
ejpam-4583	12	20	topological	topological	ADJ
ejpam-4583	12	21	spaces	space	NOUN
ejpam-4583	12	22	in	in	ADP
ejpam-4583	12	23	detail	detail	NOUN
ejpam-4583	12	24	.	.	PUNCT
ejpam-4583	13	1	we	we	PRON
ejpam-4583	13	2	organize	organize	VERB
ejpam-4583	13	3	this	this	DET
ejpam-4583	13	4	paper	paper	NOUN
ejpam-4583	13	5	as	as	SCONJ
ejpam-4583	13	6	follows	follow	VERB
ejpam-4583	13	7	.	.	PUNCT
ejpam-4583	14	1	in	in	ADP
ejpam-4583	14	2	section	section	NOUN
ejpam-4583	14	3	2	2	NUM
ejpam-4583	14	4	,	,	PUNCT
ejpam-4583	14	5	we	we	PRON
ejpam-4583	14	6	recall	recall	VERB
ejpam-4583	14	7	the	the	DET
ejpam-4583	14	8	basic	basic	ADJ
ejpam-4583	14	9	concepts	concept	NOUN
ejpam-4583	14	10	and	and	CCONJ
ejpam-4583	14	11	findings	finding	NOUN
ejpam-4583	14	12	that	that	PRON
ejpam-4583	14	13	make	make	VERB
ejpam-4583	14	14	this	this	DET
ejpam-4583	14	15	work	work	NOUN
ejpam-4583	14	16	self	self	NOUN
ejpam-4583	14	17	-	-	PUNCT
ejpam-4583	14	18	contained	contain	VERB
ejpam-4583	14	19	.	.	PUNCT
ejpam-4583	15	1	in	in	ADP
ejpam-4583	15	2	section	section	NOUN
ejpam-4583	15	3	3	3	NUM
ejpam-4583	15	4	,	,	PUNCT
ejpam-4583	15	5	we	we	PRON
ejpam-4583	15	6	introduce	introduce	VERB
ejpam-4583	15	7	definitions	definition	NOUN
ejpam-4583	15	8	of	of	ADP
ejpam-4583	15	9	f	f	PROPN
ejpam-4583	15	10	-open	-open	PROPN
ejpam-4583	15	11	and	and	CCONJ
ejpam-4583	15	12	f	f	NOUN
ejpam-4583	15	13	-closed	-close	VERB
ejpam-4583	15	14	sets	set	NOUN
ejpam-4583	15	15	and	and	CCONJ
ejpam-4583	15	16	examine	examine	VERB
ejpam-4583	15	17	the	the	DET
ejpam-4583	15	18	relationships	relationship	NOUN
ejpam-4583	15	19	between	between	ADP
ejpam-4583	15	20	them	they	PRON
ejpam-4583	15	21	and	and	CCONJ
ejpam-4583	15	22	other	other	ADJ
ejpam-4583	15	23	types	type	NOUN
ejpam-4583	15	24	such	such	ADJ
ejpam-4583	15	25	as	as	ADP
ejpam-4583	15	26	open	open	ADJ
ejpam-4583	15	27	domain	domain	NOUN
ejpam-4583	15	28	,	,	PUNCT
ejpam-4583	15	29	closed	closed	ADJ
ejpam-4583	15	30	domain	domain	NOUN
ejpam-4583	15	31	,	,	PUNCT
ejpam-4583	15	32	closed	closed	ADJ
ejpam-4583	15	33	,	,	PUNCT
ejpam-4583	15	34	and	and	CCONJ
ejpam-4583	15	35	open	open	ADJ
ejpam-4583	15	36	sets	set	NOUN
ejpam-4583	15	37	.	.	PUNCT
ejpam-4583	16	1	we	we	PRON
ejpam-4583	16	2	also	also	ADV
ejpam-4583	16	3	present	present	VERB
ejpam-4583	16	4	some	some	DET
ejpam-4583	16	5	important	important	ADJ
ejpam-4583	16	6	theorems	theorem	NOUN
ejpam-4583	16	7	.	.	PUNCT
ejpam-4583	17	1	in	in	ADP
ejpam-4583	17	2	section	section	NOUN
ejpam-4583	17	3	4	4	NUM
ejpam-4583	17	4	,	,	PUNCT
ejpam-4583	17	5	we	we	PRON
ejpam-4583	17	6	establish	establish	VERB
ejpam-4583	17	7	some	some	DET
ejpam-4583	17	8	operators	operator	NOUN
ejpam-4583	17	9	such	such	ADJ
ejpam-4583	17	10	as	as	ADP
ejpam-4583	17	11	f	f	PROPN
ejpam-4583	17	12	-interior	-interior	PROPN
ejpam-4583	17	13	,	,	PUNCT
ejpam-4583	17	14	f	f	PROPN
ejpam-4583	17	15	-closure	-closure	PROPN
ejpam-4583	17	16	,	,	PUNCT
ejpam-4583	17	17	f	f	PROPN
ejpam-4583	17	18	-border	-border	PROPN
ejpam-4583	17	19	,	,	PUNCT
ejpam-4583	17	20	f	f	PROPN
ejpam-4583	17	21	-frontier	-frontier	PROPN
ejpam-4583	17	22	,	,	PUNCT
ejpam-4583	17	23	f	f	PROPN
ejpam-4583	17	24	exterior	exterior	NOUN
ejpam-4583	17	25	,	,	PUNCT
ejpam-4583	17	26	and	and	CCONJ
ejpam-4583	17	27	f	f	PROPN
ejpam-4583	17	28	-derived	-derive	VERB
ejpam-4583	17	29	using	use	VERB
ejpam-4583	17	30	f	f	PROPN
ejpam-4583	17	31	-open	-open	PROPN
ejpam-4583	17	32	and	and	CCONJ
ejpam-4583	17	33	f	f	NOUN
ejpam-4583	17	34	-closed	-close	VERB
ejpam-4583	17	35	sets	set	NOUN
ejpam-4583	17	36	.	.	PUNCT
ejpam-4583	18	1	then	then	ADV
ejpam-4583	18	2	we	we	PRON
ejpam-4583	18	3	introduce	introduce	VERB
ejpam-4583	18	4	some	some	DET
ejpam-4583	18	5	related	relate	VERB
ejpam-4583	18	6	theorems	theorem	NOUN
ejpam-4583	18	7	.	.	PUNCT
ejpam-4583	19	1	in	in	ADP
ejpam-4583	19	2	section	section	NOUN
ejpam-4583	19	3	5	5	NUM
ejpam-4583	19	4	,	,	PUNCT
ejpam-4583	19	5	we	we	PRON
ejpam-4583	19	6	introduce	introduce	VERB
ejpam-4583	19	7	definitions	definition	NOUN
ejpam-4583	19	8	of	of	ADP
ejpam-4583	19	9	f	f	PROPN
ejpam-4583	19	10	-continuous	-continuous	PROPN
ejpam-4583	19	11	,	,	PUNCT
ejpam-4583	19	12	f	f	PROPN
ejpam-4583	19	13	-open	-open	PROPN
ejpam-4583	19	14	,	,	PUNCT
ejpam-4583	19	15	f	f	PROPN
ejpam-4583	19	16	-closed	-closed	PROPN
ejpam-4583	19	17	,	,	PUNCT
ejpam-4583	19	18	and	and	CCONJ
ejpam-4583	19	19	f	f	PROPN
ejpam-4583	19	20	-homeomorphism	-homeomorphism	NOUN
ejpam-4583	19	21	functions	function	NOUN
ejpam-4583	19	22	.	.	PUNCT
ejpam-4583	20	1	we	we	PRON
ejpam-4583	20	2	also	also	ADV
ejpam-4583	20	3	provide	provide	VERB
ejpam-4583	20	4	definitions	definition	NOUN
ejpam-4583	20	5	of	of	ADP
ejpam-4583	20	6	f	f	PROPN
ejpam-4583	20	7	-compact	-compact	PROPN
ejpam-4583	20	8	,	,	PUNCT
ejpam-4583	20	9	f	f	PROPN
ejpam-4583	20	10	-lindelöf	-lindelöf	NOUN
ejpam-4583	20	11	,	,	PUNCT
ejpam-4583	20	12	and	and	CCONJ
ejpam-4583	20	13	f	f	X
ejpam-4583	20	14	-countably	-countably	ADV
ejpam-4583	20	15	compact	compact	ADJ
ejpam-4583	20	16	spaces	space	NOUN
ejpam-4583	20	17	.	.	PUNCT
ejpam-4583	21	1	in	in	ADP
ejpam-4583	21	2	addition	addition	NOUN
ejpam-4583	21	3	,	,	PUNCT
ejpam-4583	21	4	we	we	PRON
ejpam-4583	21	5	present	present	VERB
ejpam-4583	21	6	some	some	DET
ejpam-4583	21	7	related	related	ADJ
ejpam-4583	21	8	properties	property	NOUN
ejpam-4583	21	9	.	.	PUNCT
ejpam-4583	22	1	throughout	throughout	ADP
ejpam-4583	22	2	this	this	DET
ejpam-4583	22	3	paper	paper	NOUN
ejpam-4583	22	4	,	,	PUNCT
ejpam-4583	22	5	the	the	DET
ejpam-4583	22	6	subset	subset	NOUN
ejpam-4583	22	7	b	b	PROPN
ejpam-4583	22	8	of	of	ADP
ejpam-4583	22	9	a	a	DET
ejpam-4583	22	10	topological	topological	ADJ
ejpam-4583	22	11	space	space	NOUN
ejpam-4583	22	12	(	(	PUNCT
ejpam-4583	22	13	x	x	X
ejpam-4583	22	14	,	,	PUNCT
ejpam-4583	22	15	t	t	PROPN
ejpam-4583	22	16	)	)	PUNCT
ejpam-4583	22	17	,	,	PUNCT
ejpam-4583	22	18	we	we	PRON
ejpam-4583	22	19	will	will	AUX
ejpam-4583	22	20	denote	denote	VERB
ejpam-4583	22	21	the	the	DET
ejpam-4583	22	22	complement	complement	NOUN
ejpam-4583	22	23	of	of	ADP
ejpam-4583	22	24	b	b	NOUN
ejpam-4583	22	25	in	in	ADP
ejpam-4583	22	26	(	(	PUNCT
ejpam-4583	22	27	x	x	NOUN
ejpam-4583	22	28	,	,	PUNCT
ejpam-4583	22	29	t	t	PROPN
ejpam-4583	22	30	)	)	PUNCT
ejpam-4583	22	31	by	by	ADP
ejpam-4583	22	32	x	x	PROPN
ejpam-4583	22	33	\b	\b	PROPN
ejpam-4583	22	34	,	,	PUNCT
ejpam-4583	22	35	the	the	DET
ejpam-4583	22	36	set	set	NOUN
ejpam-4583	22	37	of	of	ADP
ejpam-4583	22	38	positive	positive	ADJ
ejpam-4583	22	39	integers	integer	NOUN
ejpam-4583	22	40	by	by	ADP
ejpam-4583	22	41	n	n	CCONJ
ejpam-4583	22	42	,	,	PUNCT
ejpam-4583	22	43	the	the	DET
ejpam-4583	22	44	set	set	NOUN
ejpam-4583	22	45	of	of	ADP
ejpam-4583	22	46	integers	integer	NOUN
ejpam-4583	22	47	numbers	number	NOUN
ejpam-4583	22	48	by	by	ADP
ejpam-4583	22	49	z	z	PROPN
ejpam-4583	22	50	,	,	PUNCT
ejpam-4583	22	51	the	the	DET
ejpam-4583	22	52	set	set	NOUN
ejpam-4583	22	53	of	of	ADP
ejpam-4583	22	54	real	real	ADJ
ejpam-4583	22	55	numbers	number	NOUN
ejpam-4583	22	56	by	by	ADP
ejpam-4583	22	57	r	r	NOUN
ejpam-4583	22	58	,	,	PUNCT
ejpam-4583	22	59	and	and	CCONJ
ejpam-4583	22	60	usual	usual	ADJ
ejpam-4583	22	61	topology	topology	NOUN
ejpam-4583	22	62	in	in	ADP
ejpam-4583	22	63	r	r	NOUN
ejpam-4583	22	64	by	by	ADP
ejpam-4583	22	65	u	u	NOUN
ejpam-4583	22	66	.	.	PUNCT
ejpam-4583	23	1	unless	unless	SCONJ
ejpam-4583	23	2	or	or	CCONJ
ejpam-4583	23	3	otherwise	otherwise	ADV
ejpam-4583	23	4	mentioned	mention	VERB
ejpam-4583	23	5	,	,	PUNCT
ejpam-4583	23	6	x	x	PRON
ejpam-4583	23	7	stands	stand	VERB
ejpam-4583	23	8	for	for	ADP
ejpam-4583	23	9	the	the	DET
ejpam-4583	23	10	topological	topological	ADJ
ejpam-4583	23	11	space	space	NOUN
ejpam-4583	23	12	(	(	PUNCT
ejpam-4583	23	13	x	x	X
ejpam-4583	23	14	,	,	PUNCT
ejpam-4583	23	15	t	t	PROPN
ejpam-4583	23	16	)	)	PUNCT
ejpam-4583	23	17	.	.	PUNCT
ejpam-4583	24	1	doi	doi	NOUN
ejpam-4583	24	2	:	:	PUNCT
ejpam-4583	24	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4583	https://doi.org/10.29020/nybg.ejpam.v16i2.4583	VERB
ejpam-4583	24	4	email	email	NOUN
ejpam-4583	24	5	address	address	NOUN
ejpam-4583	24	6	:	:	PUNCT
ejpam-4583	24	7	m	m	VERB
ejpam-4583	24	8	¯	¯	PROPN
ejpam-4583	24	9	halqahtani@ut.edu.sa	halqahtani@ut.edu.sa	PROPN
ejpam-4583	24	10	(	(	PUNCT
ejpam-4583	24	11	m.	m.	PROPN
ejpam-4583	24	12	h.	h.	PROPN
ejpam-4583	24	13	alqahtani	alqahtani	PROPN
ejpam-4583	24	14	)	)	PUNCT
ejpam-4583	24	15	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4583	25	1	819	819	NUM
ejpam-4583	26	1	©	©	PROPN
ejpam-4583	26	2	2023	2023	NUM
ejpam-4583	26	3	ejpam	ejpam	NOUN
ejpam-4583	26	4	all	all	DET
ejpam-4583	26	5	rights	right	NOUN
ejpam-4583	26	6	reserved	reserve	VERB
ejpam-4583	26	7	.	.	PUNCT
ejpam-4583	27	1	m.	m.	PROPN
ejpam-4583	27	2	h.	h.	PROPN
ejpam-4583	27	3	alqahtani	alqahtani	PROPN
ejpam-4583	27	4	/	/	SYM
ejpam-4583	27	5	eur	eur	PROPN
ejpam-4583	27	6	.	.	PUNCT
ejpam-4583	28	1	j.	j.	PROPN
ejpam-4583	28	2	pure	pure	PROPN
ejpam-4583	28	3	appl	appl	PROPN
ejpam-4583	28	4	.	.	PROPN
ejpam-4583	28	5	math	math	PROPN
ejpam-4583	28	6	,	,	PUNCT
ejpam-4583	28	7	16	16	NUM
ejpam-4583	28	8	(	(	PUNCT
ejpam-4583	28	9	2	2	NUM
ejpam-4583	28	10	)	)	PUNCT
ejpam-4583	28	11	(	(	PUNCT
ejpam-4583	28	12	2023	2023	NUM
ejpam-4583	28	13	)	)	PUNCT
ejpam-4583	28	14	,	,	PUNCT
ejpam-4583	28	15	819	819	NUM
ejpam-4583	28	16	-	-	SYM
ejpam-4583	28	17	832	832	NUM
ejpam-4583	28	18	820	820	NUM
ejpam-4583	28	19	2	2	NUM
ejpam-4583	28	20	.	.	PUNCT
ejpam-4583	28	21	preliminaries	preliminary	NOUN
ejpam-4583	28	22	in	in	ADP
ejpam-4583	28	23	this	this	DET
ejpam-4583	28	24	section	section	NOUN
ejpam-4583	29	1	,	,	PUNCT
ejpam-4583	29	2	we	we	PRON
ejpam-4583	29	3	recall	recall	VERB
ejpam-4583	29	4	the	the	DET
ejpam-4583	29	5	basic	basic	ADJ
ejpam-4583	29	6	concepts	concept	NOUN
ejpam-4583	29	7	and	and	CCONJ
ejpam-4583	29	8	findings	finding	NOUN
ejpam-4583	29	9	that	that	PRON
ejpam-4583	29	10	make	make	VERB
ejpam-4583	29	11	this	this	DET
ejpam-4583	29	12	work	work	NOUN
ejpam-4583	29	13	selfcontained	selfcontaine	VERB
ejpam-4583	29	14	.	.	PUNCT
ejpam-4583	30	1	definition	definition	NOUN
ejpam-4583	30	2	1	1	NUM
ejpam-4583	30	3	.	.	PUNCT
ejpam-4583	31	1	[	[	X
ejpam-4583	31	2	1	1	X
ejpam-4583	31	3	]	]	PUNCT
ejpam-4583	31	4	let	let	VERB
ejpam-4583	31	5	k	k	PRON
ejpam-4583	31	6	be	be	AUX
ejpam-4583	31	7	a	a	DET
ejpam-4583	31	8	subset	subset	NOUN
ejpam-4583	31	9	of	of	ADP
ejpam-4583	31	10	the	the	DET
ejpam-4583	31	11	topological	topological	ADJ
ejpam-4583	31	12	space	space	NOUN
ejpam-4583	31	13	(	(	PUNCT
ejpam-4583	31	14	x	x	X
ejpam-4583	31	15	,	,	PUNCT
ejpam-4583	31	16	t	t	PROPN
ejpam-4583	31	17	)	)	PUNCT
ejpam-4583	31	18	,	,	PUNCT
ejpam-4583	31	19	then	then	ADV
ejpam-4583	31	20	the	the	DET
ejpam-4583	31	21	interior	interior	NOUN
ejpam-4583	31	22	of	of	ADP
ejpam-4583	31	23	k	k	PROPN
ejpam-4583	31	24	is	be	AUX
ejpam-4583	31	25	defined	define	VERB
ejpam-4583	31	26	as	as	ADP
ejpam-4583	31	27	the	the	DET
ejpam-4583	31	28	union	union	NOUN
ejpam-4583	31	29	of	of	ADP
ejpam-4583	31	30	all	all	DET
ejpam-4583	31	31	open	open	ADJ
ejpam-4583	31	32	subsets	subset	NOUN
ejpam-4583	31	33	of	of	ADP
ejpam-4583	31	34	k	k	PROPN
ejpam-4583	31	35	(	(	PUNCT
ejpam-4583	31	36	or	or	CCONJ
ejpam-4583	31	37	the	the	DET
ejpam-4583	31	38	largest	large	ADJ
ejpam-4583	31	39	open	open	ADJ
ejpam-4583	31	40	set	set	NOUN
ejpam-4583	31	41	contained	contain	VERB
ejpam-4583	31	42	in	in	ADP
ejpam-4583	31	43	k	k	NOUN
ejpam-4583	31	44	)	)	PUNCT
ejpam-4583	31	45	and	and	CCONJ
ejpam-4583	31	46	is	be	AUX
ejpam-4583	31	47	denoted	denote	VERB
ejpam-4583	31	48	by	by	ADP
ejpam-4583	31	49	int(k	int(k	NOUN
ejpam-4583	31	50	)	)	PUNCT
ejpam-4583	31	51	.	.	PUNCT
ejpam-4583	32	1	definition	definition	NOUN
ejpam-4583	32	2	2	2	NUM
ejpam-4583	32	3	.	.	PUNCT
ejpam-4583	33	1	[	[	X
ejpam-4583	33	2	1	1	X
ejpam-4583	33	3	]	]	PUNCT
ejpam-4583	33	4	let	let	VERB
ejpam-4583	33	5	k	k	PRON
ejpam-4583	33	6	be	be	AUX
ejpam-4583	33	7	a	a	DET
ejpam-4583	33	8	subset	subset	NOUN
ejpam-4583	33	9	of	of	ADP
ejpam-4583	33	10	the	the	DET
ejpam-4583	33	11	topological	topological	ADJ
ejpam-4583	33	12	space	space	NOUN
ejpam-4583	33	13	(	(	PUNCT
ejpam-4583	33	14	x	x	X
ejpam-4583	33	15	,	,	PUNCT
ejpam-4583	33	16	t	t	PROPN
ejpam-4583	33	17	)	)	PUNCT
ejpam-4583	33	18	,	,	PUNCT
ejpam-4583	33	19	then	then	ADV
ejpam-4583	33	20	the	the	DET
ejpam-4583	33	21	clouser	clouser	NOUN
ejpam-4583	33	22	of	of	ADP
ejpam-4583	33	23	k	k	PROPN
ejpam-4583	33	24	is	be	AUX
ejpam-4583	33	25	defined	define	VERB
ejpam-4583	33	26	as	as	ADP
ejpam-4583	33	27	the	the	DET
ejpam-4583	33	28	intersection	intersection	NOUN
ejpam-4583	33	29	of	of	ADP
ejpam-4583	33	30	all	all	DET
ejpam-4583	33	31	closed	closed	ADJ
ejpam-4583	33	32	sets	set	NOUN
ejpam-4583	33	33	containing	contain	VERB
ejpam-4583	33	34	k	k	PROPN
ejpam-4583	33	35	,	,	PUNCT
ejpam-4583	33	36	and	and	CCONJ
ejpam-4583	33	37	is	be	AUX
ejpam-4583	33	38	denoted	denote	VERB
ejpam-4583	33	39	by	by	ADP
ejpam-4583	33	40	cl(k	cl(k	NOUN
ejpam-4583	33	41	)	)	PUNCT
ejpam-4583	33	42	.	.	PUNCT
ejpam-4583	34	1	definition	definition	NOUN
ejpam-4583	34	2	3	3	NUM
ejpam-4583	34	3	.	.	PUNCT
ejpam-4583	35	1	[	[	X
ejpam-4583	35	2	1	1	X
ejpam-4583	35	3	]	]	PUNCT
ejpam-4583	35	4	let	let	VERB
ejpam-4583	35	5	k	k	PRON
ejpam-4583	35	6	be	be	AUX
ejpam-4583	35	7	a	a	DET
ejpam-4583	35	8	subset	subset	NOUN
ejpam-4583	35	9	of	of	ADP
ejpam-4583	35	10	the	the	DET
ejpam-4583	35	11	topological	topological	ADJ
ejpam-4583	35	12	space	space	NOUN
ejpam-4583	35	13	(	(	PUNCT
ejpam-4583	35	14	x	x	X
ejpam-4583	35	15	,	,	PUNCT
ejpam-4583	35	16	t	t	PROPN
ejpam-4583	35	17	)	)	PUNCT
ejpam-4583	35	18	.	.	PUNCT
ejpam-4583	36	1	a	a	DET
ejpam-4583	36	2	point	point	NOUN
ejpam-4583	36	3	x	x	X
ejpam-4583	36	4	∈	∈	NOUN
ejpam-4583	36	5	x	x	PUNCT
ejpam-4583	36	6	is	be	AUX
ejpam-4583	36	7	said	say	VERB
ejpam-4583	36	8	to	to	PART
ejpam-4583	36	9	be	be	AUX
ejpam-4583	36	10	limit	limit	NOUN
ejpam-4583	36	11	points	point	NOUN
ejpam-4583	36	12	(	(	PUNCT
ejpam-4583	36	13	or	or	CCONJ
ejpam-4583	36	14	an	an	DET
ejpam-4583	36	15	accumulation	accumulation	NOUN
ejpam-4583	36	16	point	point	NOUN
ejpam-4583	36	17	,	,	PUNCT
ejpam-4583	36	18	or	or	CCONJ
ejpam-4583	36	19	a	a	DET
ejpam-4583	36	20	cluster	cluster	NOUN
ejpam-4583	36	21	point	point	NOUN
ejpam-4583	36	22	)	)	PUNCT
ejpam-4583	36	23	of	of	ADP
ejpam-4583	36	24	k	k	PRON
ejpam-4583	36	25	if	if	SCONJ
ejpam-4583	37	1	and	and	CCONJ
ejpam-4583	37	2	only	only	ADV
ejpam-4583	37	3	if	if	SCONJ
ejpam-4583	37	4	every	every	DET
ejpam-4583	37	5	open	open	ADJ
ejpam-4583	37	6	set	set	VERB
ejpam-4583	37	7	v	v	NOUN
ejpam-4583	37	8	containing	contain	VERB
ejpam-4583	37	9	x	x	X
ejpam-4583	37	10	,	,	PUNCT
ejpam-4583	37	11	contains	contain	VERB
ejpam-4583	37	12	at	at	ADV
ejpam-4583	37	13	least	least	ADV
ejpam-4583	37	14	one	one	NUM
ejpam-4583	37	15	point	point	NOUN
ejpam-4583	37	16	of	of	ADP
ejpam-4583	37	17	k	k	PROPN
ejpam-4583	37	18	different	different	ADJ
ejpam-4583	37	19	from	from	ADP
ejpam-4583	37	20	x.	x.	NOUN
ejpam-4583	37	21	the	the	DET
ejpam-4583	37	22	set	set	NOUN
ejpam-4583	37	23	of	of	ADP
ejpam-4583	37	24	all	all	DET
ejpam-4583	37	25	limit	limit	NOUN
ejpam-4583	37	26	points	point	NOUN
ejpam-4583	37	27	of	of	ADP
ejpam-4583	37	28	k	k	PROPN
ejpam-4583	37	29	is	be	AUX
ejpam-4583	37	30	called	call	VERB
ejpam-4583	37	31	the	the	DET
ejpam-4583	37	32	derived	derive	VERB
ejpam-4583	37	33	set	set	NOUN
ejpam-4583	37	34	of	of	ADP
ejpam-4583	37	35	k	k	PROPN
ejpam-4583	37	36	and	and	CCONJ
ejpam-4583	37	37	denoted	denote	VERB
ejpam-4583	37	38	by	by	ADP
ejpam-4583	37	39	d(k	d(k	PROPN
ejpam-4583	37	40	)	)	PUNCT
ejpam-4583	37	41	.	.	PUNCT
ejpam-4583	38	1	definition	definition	NOUN
ejpam-4583	38	2	4	4	NUM
ejpam-4583	38	3	.	.	PUNCT
ejpam-4583	39	1	[	[	X
ejpam-4583	39	2	1	1	X
ejpam-4583	39	3	]	]	PUNCT
ejpam-4583	39	4	let	let	VERB
ejpam-4583	39	5	k	k	PRON
ejpam-4583	39	6	be	be	AUX
ejpam-4583	39	7	a	a	DET
ejpam-4583	39	8	subset	subset	NOUN
ejpam-4583	39	9	of	of	ADP
ejpam-4583	39	10	the	the	DET
ejpam-4583	39	11	topological	topological	ADJ
ejpam-4583	39	12	space	space	NOUN
ejpam-4583	39	13	(	(	PUNCT
ejpam-4583	39	14	x	x	X
ejpam-4583	39	15	,	,	PUNCT
ejpam-4583	39	16	t	t	PROPN
ejpam-4583	39	17	)	)	PUNCT
ejpam-4583	39	18	,	,	PUNCT
ejpam-4583	39	19	then	then	ADV
ejpam-4583	39	20	the	the	DET
ejpam-4583	39	21	border	border	NOUN
ejpam-4583	39	22	of	of	ADP
ejpam-4583	39	23	k	k	PROPN
ejpam-4583	39	24	is	be	AUX
ejpam-4583	39	25	defined	define	VERB
ejpam-4583	39	26	as	as	ADP
ejpam-4583	39	27	bd(k	bd(k	X
ejpam-4583	39	28	)	)	PUNCT
ejpam-4583	39	29	=	=	SYM
ejpam-4583	39	30	k	k	X
ejpam-4583	39	31	\	\	PROPN
ejpam-4583	39	32	int(k	int(k	PROPN
ejpam-4583	39	33	)	)	PUNCT
ejpam-4583	39	34	.	.	PUNCT
ejpam-4583	40	1	definition	definition	NOUN
ejpam-4583	40	2	5	5	NUM
ejpam-4583	40	3	.	.	PUNCT
ejpam-4583	41	1	[	[	X
ejpam-4583	41	2	1	1	X
ejpam-4583	41	3	]	]	PUNCT
ejpam-4583	41	4	let	let	VERB
ejpam-4583	41	5	k	k	PRON
ejpam-4583	41	6	be	be	AUX
ejpam-4583	41	7	a	a	DET
ejpam-4583	41	8	subset	subset	NOUN
ejpam-4583	41	9	of	of	ADP
ejpam-4583	41	10	the	the	DET
ejpam-4583	41	11	topological	topological	ADJ
ejpam-4583	41	12	space	space	NOUN
ejpam-4583	41	13	(	(	PUNCT
ejpam-4583	41	14	x	x	X
ejpam-4583	41	15	,	,	PUNCT
ejpam-4583	41	16	t	t	PROPN
ejpam-4583	41	17	)	)	PUNCT
ejpam-4583	41	18	,	,	PUNCT
ejpam-4583	41	19	then	then	ADV
ejpam-4583	41	20	the	the	DET
ejpam-4583	41	21	frontier	frontier	NOUN
ejpam-4583	41	22	of	of	ADP
ejpam-4583	41	23	k	k	PROPN
ejpam-4583	41	24	is	be	AUX
ejpam-4583	41	25	defined	define	VERB
ejpam-4583	41	26	as	as	ADP
ejpam-4583	41	27	fr(k	fr(k	NOUN
ejpam-4583	41	28	)	)	PUNCT
ejpam-4583	41	29	=	=	SYM
ejpam-4583	41	30	cl(k	cl(k	X
ejpam-4583	41	31	)	)	PUNCT
ejpam-4583	41	32	\	\	PROPN
ejpam-4583	42	1	int(k	int(k	PROPN
ejpam-4583	42	2	)	)	PUNCT
ejpam-4583	42	3	.	.	PUNCT
ejpam-4583	43	1	definition	definition	NOUN
ejpam-4583	43	2	6	6	NUM
ejpam-4583	43	3	.	.	PUNCT
ejpam-4583	44	1	[	[	X
ejpam-4583	44	2	1	1	X
ejpam-4583	44	3	]	]	PUNCT
ejpam-4583	44	4	let	let	VERB
ejpam-4583	44	5	k	k	PRON
ejpam-4583	44	6	be	be	AUX
ejpam-4583	44	7	a	a	DET
ejpam-4583	44	8	subset	subset	NOUN
ejpam-4583	44	9	of	of	ADP
ejpam-4583	44	10	the	the	DET
ejpam-4583	44	11	topological	topological	ADJ
ejpam-4583	44	12	space	space	NOUN
ejpam-4583	44	13	(	(	PUNCT
ejpam-4583	44	14	x	x	X
ejpam-4583	44	15	,	,	PUNCT
ejpam-4583	44	16	t	t	PROPN
ejpam-4583	44	17	)	)	PUNCT
ejpam-4583	44	18	,	,	PUNCT
ejpam-4583	44	19	then	then	ADV
ejpam-4583	44	20	the	the	DET
ejpam-4583	44	21	exterior	exterior	NOUN
ejpam-4583	44	22	of	of	ADP
ejpam-4583	44	23	k	k	PROPN
ejpam-4583	44	24	is	be	AUX
ejpam-4583	44	25	defined	define	VERB
ejpam-4583	44	26	as	as	ADP
ejpam-4583	44	27	ext(k	ext(k	PROPN
ejpam-4583	44	28	)	)	PUNCT
ejpam-4583	44	29	=	=	SYM
ejpam-4583	44	30	int(x	int(x	PROPN
ejpam-4583	44	31	\k	\k	NOUN
ejpam-4583	44	32	)	)	PUNCT
ejpam-4583	44	33	.	.	PUNCT
ejpam-4583	45	1	definition	definition	NOUN
ejpam-4583	45	2	7	7	NUM
ejpam-4583	45	3	.	.	PUNCT
ejpam-4583	46	1	[	[	X
ejpam-4583	46	2	1	1	X
ejpam-4583	46	3	]	]	PUNCT
ejpam-4583	46	4	a	a	DET
ejpam-4583	46	5	function	function	NOUN
ejpam-4583	46	6	h	h	NOUN
ejpam-4583	46	7	from	from	ADP
ejpam-4583	46	8	the	the	DET
ejpam-4583	46	9	topological	topological	ADJ
ejpam-4583	46	10	space	space	NOUN
ejpam-4583	46	11	(	(	PUNCT
ejpam-4583	46	12	x	x	X
ejpam-4583	46	13	,	,	PUNCT
ejpam-4583	46	14	t	t	PROPN
ejpam-4583	46	15	)	)	PUNCT
ejpam-4583	46	16	into	into	ADP
ejpam-4583	46	17	the	the	DET
ejpam-4583	46	18	topological	topological	ADJ
ejpam-4583	46	19	space	space	NOUN
ejpam-4583	46	20	(	(	PUNCT
ejpam-4583	46	21	y	y	NOUN
ejpam-4583	46	22	,	,	PUNCT
ejpam-4583	46	23	p	p	NOUN
ejpam-4583	46	24	)	)	PUNCT
ejpam-4583	46	25	is	be	AUX
ejpam-4583	46	26	said	say	VERB
ejpam-4583	46	27	to	to	PART
ejpam-4583	46	28	be	be	AUX
ejpam-4583	46	29	continuous	continuous	ADJ
ejpam-4583	46	30	if	if	SCONJ
ejpam-4583	46	31	h−1(u	h−1(u	PROPN
ejpam-4583	46	32	)	)	PUNCT
ejpam-4583	46	33	is	be	AUX
ejpam-4583	46	34	an	an	DET
ejpam-4583	46	35	open	open	ADJ
ejpam-4583	46	36	subset	subset	NOUN
ejpam-4583	46	37	in	in	ADP
ejpam-4583	46	38	x	x	PUNCT
ejpam-4583	46	39	for	for	ADP
ejpam-4583	46	40	every	every	DET
ejpam-4583	46	41	open	open	ADJ
ejpam-4583	46	42	subsets	subset	NOUN
ejpam-4583	46	43	u	u	NOUN
ejpam-4583	46	44	in	in	ADP
ejpam-4583	46	45	y.	y.	PROPN
ejpam-4583	46	46	definition	definition	NOUN
ejpam-4583	46	47	8	8	NUM
ejpam-4583	46	48	.	.	PUNCT
ejpam-4583	47	1	[	[	X
ejpam-4583	47	2	1	1	X
ejpam-4583	47	3	]	]	PUNCT
ejpam-4583	47	4	a	a	DET
ejpam-4583	47	5	function	function	NOUN
ejpam-4583	47	6	h	h	NOUN
ejpam-4583	47	7	from	from	ADP
ejpam-4583	47	8	the	the	DET
ejpam-4583	47	9	topological	topological	ADJ
ejpam-4583	47	10	space	space	NOUN
ejpam-4583	47	11	(	(	PUNCT
ejpam-4583	47	12	x	x	X
ejpam-4583	47	13	,	,	PUNCT
ejpam-4583	47	14	t	t	PROPN
ejpam-4583	47	15	)	)	PUNCT
ejpam-4583	47	16	into	into	ADP
ejpam-4583	47	17	the	the	DET
ejpam-4583	47	18	topological	topological	ADJ
ejpam-4583	47	19	space	space	NOUN
ejpam-4583	47	20	(	(	PUNCT
ejpam-4583	47	21	y	y	NOUN
ejpam-4583	47	22	,	,	PUNCT
ejpam-4583	47	23	p	p	NOUN
ejpam-4583	47	24	)	)	PUNCT
ejpam-4583	47	25	is	be	AUX
ejpam-4583	47	26	said	say	VERB
ejpam-4583	47	27	to	to	PART
ejpam-4583	47	28	be	be	AUX
ejpam-4583	47	29	open	open	ADJ
ejpam-4583	47	30	(	(	PUNCT
ejpam-4583	47	31	resp	resp	NOUN
ejpam-4583	47	32	.	.	PUNCT
ejpam-4583	48	1	closed	close	VERB
ejpam-4583	48	2	)	)	PUNCT
ejpam-4583	49	1	if	if	SCONJ
ejpam-4583	49	2	h(u	h(u	PROPN
ejpam-4583	49	3	)	)	PUNCT
ejpam-4583	49	4	is	be	AUX
ejpam-4583	49	5	an	an	DET
ejpam-4583	49	6	open	open	ADJ
ejpam-4583	49	7	(	(	PUNCT
ejpam-4583	49	8	resp	resp	NOUN
ejpam-4583	49	9	.	.	PROPN
ejpam-4583	49	10	,	,	PUNCT
ejpam-4583	49	11	closed	closed	ADJ
ejpam-4583	49	12	)	)	PUNCT
ejpam-4583	49	13	subset	subset	VERB
ejpam-4583	49	14	in	in	ADP
ejpam-4583	49	15	y	y	PROPN
ejpam-4583	49	16	for	for	ADP
ejpam-4583	49	17	every	every	DET
ejpam-4583	49	18	open	open	ADJ
ejpam-4583	49	19	(	(	PUNCT
ejpam-4583	49	20	resp	resp	NOUN
ejpam-4583	49	21	.	.	PROPN
ejpam-4583	49	22	,	,	PUNCT
ejpam-4583	49	23	closed	closed	ADJ
ejpam-4583	49	24	)	)	PUNCT
ejpam-4583	49	25	subsets	subset	VERB
ejpam-4583	49	26	u	u	NOUN
ejpam-4583	49	27	in	in	ADP
ejpam-4583	49	28	x.	x.	NOUN
ejpam-4583	49	29	definition	definition	NOUN
ejpam-4583	49	30	9	9	NUM
ejpam-4583	49	31	.	.	PUNCT
ejpam-4583	50	1	[	[	X
ejpam-4583	50	2	1	1	X
ejpam-4583	50	3	]	]	PUNCT
ejpam-4583	50	4	a	a	DET
ejpam-4583	50	5	bijection	bijection	ADJ
ejpam-4583	50	6	function	function	NOUN
ejpam-4583	50	7	h	h	NOUN
ejpam-4583	50	8	from	from	ADP
ejpam-4583	50	9	the	the	DET
ejpam-4583	50	10	topological	topological	ADJ
ejpam-4583	50	11	space	space	NOUN
ejpam-4583	50	12	(	(	PUNCT
ejpam-4583	50	13	x	x	X
ejpam-4583	50	14	,	,	PUNCT
ejpam-4583	50	15	t	t	PROPN
ejpam-4583	50	16	)	)	PUNCT
ejpam-4583	50	17	into	into	ADP
ejpam-4583	50	18	the	the	DET
ejpam-4583	50	19	topological	topological	ADJ
ejpam-4583	50	20	space	space	NOUN
ejpam-4583	50	21	(	(	PUNCT
ejpam-4583	50	22	y	y	NOUN
ejpam-4583	50	23	,	,	PUNCT
ejpam-4583	50	24	p	p	NOUN
ejpam-4583	50	25	)	)	PUNCT
ejpam-4583	50	26	is	be	AUX
ejpam-4583	50	27	said	say	VERB
ejpam-4583	50	28	to	to	PART
ejpam-4583	50	29	be	be	AUX
ejpam-4583	50	30	homeomorphism	homeomorphism	PROPN
ejpam-4583	50	31	if	if	SCONJ
ejpam-4583	50	32	and	and	CCONJ
ejpam-4583	50	33	only	only	ADV
ejpam-4583	50	34	if	if	SCONJ
ejpam-4583	50	35	h	h	NOUN
ejpam-4583	50	36	and	and	CCONJ
ejpam-4583	50	37	h−1	h−1	PROPN
ejpam-4583	50	38	are	be	AUX
ejpam-4583	50	39	continuous	continuous	ADJ
ejpam-4583	50	40	.	.	PUNCT
ejpam-4583	51	1	definition	definition	NOUN
ejpam-4583	51	2	10	10	NUM
ejpam-4583	51	3	.	.	PUNCT
ejpam-4583	52	1	[	[	X
ejpam-4583	52	2	1	1	X
ejpam-4583	52	3	]	]	X
ejpam-4583	52	4	let	let	VERB
ejpam-4583	52	5	(	(	PUNCT
ejpam-4583	52	6	x	x	X
ejpam-4583	52	7	,	,	PUNCT
ejpam-4583	52	8	t	t	PROPN
ejpam-4583	52	9	)	)	PUNCT
ejpam-4583	52	10	be	be	AUX
ejpam-4583	52	11	a	a	DET
ejpam-4583	52	12	topological	topological	ADJ
ejpam-4583	52	13	space	space	NOUN
ejpam-4583	52	14	,	,	PUNCT
ejpam-4583	52	15	then	then	ADV
ejpam-4583	52	16	(	(	PUNCT
ejpam-4583	52	17	x	x	X
ejpam-4583	52	18	,	,	PUNCT
ejpam-4583	52	19	t	t	PROPN
ejpam-4583	52	20	)	)	PUNCT
ejpam-4583	52	21	is	be	AUX
ejpam-4583	52	22	compact	compact	ADJ
ejpam-4583	52	23	(	(	PUNCT
ejpam-4583	52	24	resp	resp	NOUN
ejpam-4583	52	25	.	.	PUNCT
ejpam-4583	52	26	,	,	PUNCT
ejpam-4583	52	27	lindelöf	lindelöf	PROPN
ejpam-4583	52	28	)	)	PUNCT
ejpam-4583	52	29	if	if	SCONJ
ejpam-4583	52	30	and	and	CCONJ
ejpam-4583	52	31	only	only	ADV
ejpam-4583	52	32	if	if	SCONJ
ejpam-4583	52	33	any	any	DET
ejpam-4583	52	34	open	open	ADJ
ejpam-4583	52	35	cover	cover	NOUN
ejpam-4583	52	36	of	of	ADP
ejpam-4583	52	37	x	x	PUNCT
ejpam-4583	52	38	has	have	VERB
ejpam-4583	52	39	a	a	DET
ejpam-4583	52	40	finite	finite	NOUN
ejpam-4583	52	41	(	(	PUNCT
ejpam-4583	52	42	resp	resp	NOUN
ejpam-4583	52	43	.	.	PUNCT
ejpam-4583	52	44	,	,	PUNCT
ejpam-4583	52	45	countable	countable	ADJ
ejpam-4583	52	46	)	)	PUNCT
ejpam-4583	52	47	subcover	subcover	NOUN
ejpam-4583	52	48	of	of	ADP
ejpam-4583	52	49	open	open	ADJ
ejpam-4583	52	50	sets	set	NOUN
ejpam-4583	52	51	.	.	PUNCT
ejpam-4583	53	1	definition	definition	NOUN
ejpam-4583	53	2	11	11	NUM
ejpam-4583	53	3	.	.	PUNCT
ejpam-4583	54	1	[	[	X
ejpam-4583	54	2	1	1	X
ejpam-4583	54	3	]	]	X
ejpam-4583	54	4	let	let	VERB
ejpam-4583	54	5	(	(	PUNCT
ejpam-4583	54	6	x	x	X
ejpam-4583	54	7	,	,	PUNCT
ejpam-4583	54	8	t	t	PROPN
ejpam-4583	54	9	)	)	PUNCT
ejpam-4583	54	10	be	be	AUX
ejpam-4583	54	11	a	a	DET
ejpam-4583	54	12	topological	topological	ADJ
ejpam-4583	54	13	space	space	NOUN
ejpam-4583	54	14	,	,	PUNCT
ejpam-4583	54	15	then	then	ADV
ejpam-4583	54	16	(	(	PUNCT
ejpam-4583	54	17	x	x	X
ejpam-4583	54	18	,	,	PUNCT
ejpam-4583	54	19	t	t	PROPN
ejpam-4583	54	20	)	)	PUNCT
ejpam-4583	54	21	is	be	AUX
ejpam-4583	54	22	countably	countably	ADV
ejpam-4583	54	23	compact	compact	ADJ
ejpam-4583	54	24	space	space	NOUN
ejpam-4583	55	1	if	if	SCONJ
ejpam-4583	55	2	and	and	CCONJ
ejpam-4583	55	3	only	only	ADV
ejpam-4583	55	4	if	if	SCONJ
ejpam-4583	55	5	any	any	DET
ejpam-4583	55	6	countable	countable	ADJ
ejpam-4583	55	7	open	open	ADJ
ejpam-4583	55	8	cover	cover	NOUN
ejpam-4583	55	9	of	of	ADP
ejpam-4583	55	10	x	x	PUNCT
ejpam-4583	55	11	has	have	VERB
ejpam-4583	55	12	a	a	DET
ejpam-4583	55	13	finite	finite	ADJ
ejpam-4583	55	14	subcover	subcover	NOUN
ejpam-4583	55	15	of	of	ADP
ejpam-4583	55	16	open	open	ADJ
ejpam-4583	55	17	sets	set	NOUN
ejpam-4583	55	18	.	.	PUNCT
ejpam-4583	56	1	m.	m.	NOUN
ejpam-4583	56	2	h.	h.	PROPN
ejpam-4583	56	3	alqahtani	alqahtani	PROPN
ejpam-4583	56	4	/	/	SYM
ejpam-4583	56	5	eur	eur	PROPN
ejpam-4583	56	6	.	.	PUNCT
ejpam-4583	57	1	j.	j.	PROPN
ejpam-4583	57	2	pure	pure	PROPN
ejpam-4583	57	3	appl	appl	PROPN
ejpam-4583	57	4	.	.	PROPN
ejpam-4583	57	5	math	math	PROPN
ejpam-4583	57	6	,	,	PUNCT
ejpam-4583	57	7	16	16	NUM
ejpam-4583	57	8	(	(	PUNCT
ejpam-4583	57	9	2	2	NUM
ejpam-4583	57	10	)	)	PUNCT
ejpam-4583	57	11	(	(	PUNCT
ejpam-4583	57	12	2023	2023	NUM
ejpam-4583	57	13	)	)	PUNCT
ejpam-4583	57	14	,	,	PUNCT
ejpam-4583	57	15	819	819	NUM
ejpam-4583	57	16	-	-	SYM
ejpam-4583	57	17	832	832	NUM
ejpam-4583	57	18	821	821	NUM
ejpam-4583	57	19	3	3	NUM
ejpam-4583	57	20	.	.	PUNCT
ejpam-4583	58	1	f	f	PROPN
ejpam-4583	58	2	-open	-open	PROPN
ejpam-4583	58	3	and	and	CCONJ
ejpam-4583	58	4	f	f	NOUN
ejpam-4583	58	5	-closed	-close	VERB
ejpam-4583	58	6	sets	set	NOUN
ejpam-4583	58	7	definition	definition	NOUN
ejpam-4583	58	8	12	12	NUM
ejpam-4583	58	9	.	.	PUNCT
ejpam-4583	59	1	an	an	DET
ejpam-4583	59	2	open	open	NOUN
ejpam-4583	59	3	subset	subset	VERB
ejpam-4583	59	4	a	a	PRON
ejpam-4583	59	5	of	of	ADP
ejpam-4583	59	6	a	a	DET
ejpam-4583	59	7	topological	topological	ADJ
ejpam-4583	59	8	space	space	NOUN
ejpam-4583	59	9	(	(	PUNCT
ejpam-4583	59	10	x	x	X
ejpam-4583	59	11	,	,	PUNCT
ejpam-4583	59	12	t	t	PROPN
ejpam-4583	59	13	)	)	PUNCT
ejpam-4583	59	14	is	be	AUX
ejpam-4583	59	15	called	call	VERB
ejpam-4583	59	16	f	f	PROPN
ejpam-4583	59	17	-open	-open	NOUN
ejpam-4583	59	18	set	set	VERB
ejpam-4583	59	19	if	if	SCONJ
ejpam-4583	59	20	cl(a	cl(a	NUM
ejpam-4583	59	21	)	)	PUNCT
ejpam-4583	59	22	\a	\a	VERB
ejpam-4583	59	23	is	be	AUX
ejpam-4583	59	24	finite	finite	NOUN
ejpam-4583	59	25	set	set	NOUN
ejpam-4583	59	26	.	.	PUNCT
ejpam-4583	60	1	that	that	PRON
ejpam-4583	60	2	is	is	ADV
ejpam-4583	60	3	,	,	PUNCT
ejpam-4583	60	4	a	a	PRON
ejpam-4583	60	5	is	be	AUX
ejpam-4583	60	6	an	an	DET
ejpam-4583	60	7	open	open	ADJ
ejpam-4583	60	8	set	set	NOUN
ejpam-4583	60	9	and	and	CCONJ
ejpam-4583	60	10	the	the	DET
ejpam-4583	60	11	frontier	frontier	NOUN
ejpam-4583	60	12	of	of	ADP
ejpam-4583	60	13	a	a	PRON
ejpam-4583	60	14	is	be	AUX
ejpam-4583	60	15	a	a	DET
ejpam-4583	60	16	finite	finite	ADJ
ejpam-4583	60	17	set	set	NOUN
ejpam-4583	60	18	.	.	PUNCT
ejpam-4583	61	1	definition	definition	NOUN
ejpam-4583	61	2	13	13	NUM
ejpam-4583	61	3	.	.	PUNCT
ejpam-4583	62	1	a	a	DET
ejpam-4583	62	2	closed	closed	NOUN
ejpam-4583	62	3	subset	subset	VERB
ejpam-4583	62	4	a	a	PRON
ejpam-4583	62	5	of	of	ADP
ejpam-4583	62	6	a	a	DET
ejpam-4583	62	7	topological	topological	ADJ
ejpam-4583	62	8	space	space	NOUN
ejpam-4583	62	9	(	(	PUNCT
ejpam-4583	62	10	x	x	X
ejpam-4583	62	11	,	,	PUNCT
ejpam-4583	62	12	t	t	PROPN
ejpam-4583	62	13	)	)	PUNCT
ejpam-4583	62	14	is	be	AUX
ejpam-4583	62	15	called	call	VERB
ejpam-4583	62	16	f	f	PROPN
ejpam-4583	62	17	-closed	-close	VERB
ejpam-4583	62	18	set	set	NOUN
ejpam-4583	62	19	if	if	SCONJ
ejpam-4583	62	20	a	a	DET
ejpam-4583	62	21	\	\	PUNCT
ejpam-4583	62	22	int(a	int(a	PROPN
ejpam-4583	62	23	)	)	PUNCT
ejpam-4583	62	24	is	be	AUX
ejpam-4583	62	25	finite	finite	NOUN
ejpam-4583	62	26	set	set	NOUN
ejpam-4583	62	27	.	.	PUNCT
ejpam-4583	63	1	that	that	PRON
ejpam-4583	63	2	is	is	ADV
ejpam-4583	63	3	,	,	PUNCT
ejpam-4583	63	4	a	a	PRON
ejpam-4583	63	5	is	be	AUX
ejpam-4583	63	6	a	a	DET
ejpam-4583	63	7	closed	closed	ADJ
ejpam-4583	63	8	set	set	NOUN
ejpam-4583	63	9	and	and	CCONJ
ejpam-4583	63	10	the	the	DET
ejpam-4583	63	11	frontier	frontier	NOUN
ejpam-4583	63	12	of	of	ADP
ejpam-4583	63	13	a	a	PRON
ejpam-4583	63	14	is	be	AUX
ejpam-4583	63	15	a	a	DET
ejpam-4583	63	16	finite	finite	ADJ
ejpam-4583	63	17	set	set	NOUN
ejpam-4583	63	18	.	.	PUNCT
ejpam-4583	64	1	theorem	theorem	NOUN
ejpam-4583	64	2	1	1	NUM
ejpam-4583	64	3	.	.	PUNCT
ejpam-4583	65	1	let	let	VERB
ejpam-4583	65	2	(	(	PUNCT
ejpam-4583	65	3	x	x	X
ejpam-4583	65	4	,	,	PUNCT
ejpam-4583	65	5	t	t	PROPN
ejpam-4583	65	6	)	)	PUNCT
ejpam-4583	65	7	be	be	AUX
ejpam-4583	65	8	a	a	DET
ejpam-4583	65	9	topological	topological	ADJ
ejpam-4583	65	10	space	space	NOUN
ejpam-4583	65	11	,	,	PUNCT
ejpam-4583	65	12	then	then	ADV
ejpam-4583	65	13	(	(	PUNCT
ejpam-4583	65	14	i	i	NOUN
ejpam-4583	65	15	)	)	PUNCT
ejpam-4583	65	16	the	the	DET
ejpam-4583	65	17	complement	complement	NOUN
ejpam-4583	65	18	of	of	ADP
ejpam-4583	65	19	any	any	DET
ejpam-4583	65	20	f	f	PROPN
ejpam-4583	65	21	-open	-open	PROPN
ejpam-4583	65	22	subset	subset	NOUN
ejpam-4583	65	23	of	of	ADP
ejpam-4583	65	24	x	x	SYM
ejpam-4583	65	25	is	be	AUX
ejpam-4583	65	26	a	a	DET
ejpam-4583	65	27	f	f	PROPN
ejpam-4583	65	28	-closed	-closed	PROPN
ejpam-4583	65	29	;	;	PUNCT
ejpam-4583	65	30	(	(	PUNCT
ejpam-4583	65	31	ii	ii	NOUN
ejpam-4583	65	32	)	)	PUNCT
ejpam-4583	65	33	the	the	DET
ejpam-4583	65	34	complement	complement	NOUN
ejpam-4583	65	35	of	of	ADP
ejpam-4583	65	36	any	any	DET
ejpam-4583	65	37	f	f	PROPN
ejpam-4583	65	38	-closed	-closed	PROPN
ejpam-4583	65	39	subset	subset	NOUN
ejpam-4583	65	40	of	of	ADP
ejpam-4583	65	41	x	x	SYM
ejpam-4583	65	42	is	be	AUX
ejpam-4583	65	43	a	a	DET
ejpam-4583	65	44	f	f	NOUN
ejpam-4583	65	45	-open	-open	NOUN
ejpam-4583	65	46	.	.	PUNCT
ejpam-4583	66	1	proof	proof	NOUN
ejpam-4583	66	2	.	.	PUNCT
ejpam-4583	67	1	let	let	VERB
ejpam-4583	67	2	a	a	DET
ejpam-4583	67	3	be	be	AUX
ejpam-4583	67	4	any	any	DET
ejpam-4583	67	5	f	f	PROPN
ejpam-4583	67	6	-open	-open	NOUN
ejpam-4583	67	7	subset	subset	VERB
ejpam-4583	67	8	in	in	ADP
ejpam-4583	67	9	x	x	NOUN
ejpam-4583	67	10	,	,	PUNCT
ejpam-4583	67	11	then	then	ADV
ejpam-4583	67	12	x\a	x\a	PROPN
ejpam-4583	67	13	is	be	AUX
ejpam-4583	67	14	closed	closed	ADJ
ejpam-4583	67	15	and	and	CCONJ
ejpam-4583	67	16	(	(	PUNCT
ejpam-4583	67	17	x\a)\int(x\a	x\a)\int(x\a	NUM
ejpam-4583	67	18	)	)	PUNCT
ejpam-4583	68	1	=	=	SYM
ejpam-4583	68	2	(	(	PUNCT
ejpam-4583	68	3	x	x	SYM
ejpam-4583	68	4	\a)\	\a)\	X
ejpam-4583	68	5	(	(	PUNCT
ejpam-4583	68	6	x	x	SYM
ejpam-4583	68	7	\	\	X
ejpam-4583	68	8	cl(a	cl(a	NUM
ejpam-4583	68	9	)	)	PUNCT
ejpam-4583	68	10	)	)	PUNCT
ejpam-4583	69	1	=	=	PUNCT
ejpam-4583	70	1	(	(	PUNCT
ejpam-4583	70	2	x	x	X
ejpam-4583	70	3	\a)∩	\a)∩	PROPN
ejpam-4583	70	4	cl(a	cl(a	X
ejpam-4583	70	5	)	)	PUNCT
ejpam-4583	70	6	=	=	SYM
ejpam-4583	70	7	cl(a)\a	cl(a)\a	X
ejpam-4583	70	8	is	be	AUX
ejpam-4583	70	9	finite	finite	ADJ
ejpam-4583	70	10	.	.	PUNCT
ejpam-4583	71	1	therefore	therefore	ADV
ejpam-4583	71	2	,	,	PUNCT
ejpam-4583	71	3	x	x	PUNCT
ejpam-4583	71	4	\a	\a	ADJ
ejpam-4583	71	5	is	be	AUX
ejpam-4583	71	6	a	a	DET
ejpam-4583	71	7	f	f	PROPN
ejpam-4583	71	8	-closed	-closed	PROPN
ejpam-4583	71	9	.	.	PUNCT
ejpam-4583	72	1	using	use	VERB
ejpam-4583	72	2	the	the	DET
ejpam-4583	72	3	same	same	ADJ
ejpam-4583	72	4	way	way	NOUN
ejpam-4583	72	5	to	to	PART
ejpam-4583	72	6	prove	prove	VERB
ejpam-4583	72	7	the	the	DET
ejpam-4583	72	8	complement	complement	NOUN
ejpam-4583	72	9	of	of	ADP
ejpam-4583	72	10	any	any	DET
ejpam-4583	72	11	f	f	PROPN
ejpam-4583	72	12	-closed	-closed	PROPN
ejpam-4583	72	13	subset	subset	NOUN
ejpam-4583	72	14	in	in	ADP
ejpam-4583	72	15	x	x	PROPN
ejpam-4583	72	16	is	be	AUX
ejpam-4583	72	17	a	a	DET
ejpam-4583	72	18	f	f	PROPN
ejpam-4583	72	19	-open	-open	PROPN
ejpam-4583	72	20	.	.	PUNCT
ejpam-4583	73	1	remark	remark	NOUN
ejpam-4583	73	2	1	1	NUM
ejpam-4583	73	3	.	.	PUNCT
ejpam-4583	74	1	i	i	PRON
ejpam-4583	74	2	)	)	PUNCT
ejpam-4583	75	1	any	any	DET
ejpam-4583	75	2	clopen	clopen	ADJ
ejpam-4583	75	3	(	(	PUNCT
ejpam-4583	75	4	open	open	ADJ
ejpam-4583	75	5	-	-	PUNCT
ejpam-4583	75	6	and	and	CCONJ
ejpam-4583	75	7	-	-	PUNCT
ejpam-4583	75	8	closed	closed	ADJ
ejpam-4583	75	9	)	)	PUNCT
ejpam-4583	75	10	subset	subset	NOUN
ejpam-4583	75	11	of	of	ADP
ejpam-4583	75	12	the	the	DET
ejpam-4583	75	13	topological	topological	ADJ
ejpam-4583	75	14	space	space	NOUN
ejpam-4583	75	15	(	(	PUNCT
ejpam-4583	75	16	x	x	X
ejpam-4583	75	17	,	,	PUNCT
ejpam-4583	75	18	t	t	PROPN
ejpam-4583	75	19	)	)	PUNCT
ejpam-4583	75	20	is	be	AUX
ejpam-4583	75	21	f	f	PROPN
ejpam-4583	75	22	-open	-open	PROPN
ejpam-4583	75	23	and	and	CCONJ
ejpam-4583	75	24	f	f	NOUN
ejpam-4583	75	25	-closed	-close	VERB
ejpam-4583	75	26	sets	set	NOUN
ejpam-4583	75	27	;	;	PUNCT
ejpam-4583	75	28	ii	ii	X
ejpam-4583	75	29	)	)	PUNCT
ejpam-4583	75	30	any	any	DET
ejpam-4583	75	31	finite	finite	NOUN
ejpam-4583	75	32	closed	close	VERB
ejpam-4583	75	33	subset	subset	NOUN
ejpam-4583	75	34	of	of	ADP
ejpam-4583	75	35	the	the	DET
ejpam-4583	75	36	topological	topological	ADJ
ejpam-4583	75	37	space	space	NOUN
ejpam-4583	75	38	(	(	PUNCT
ejpam-4583	75	39	x	x	X
ejpam-4583	75	40	,	,	PUNCT
ejpam-4583	75	41	t	t	PROPN
ejpam-4583	75	42	)	)	PUNCT
ejpam-4583	75	43	is	be	AUX
ejpam-4583	75	44	f	f	PROPN
ejpam-4583	75	45	-closed	-closed	PROPN
ejpam-4583	75	46	.	.	PUNCT
ejpam-4583	76	1	the	the	DET
ejpam-4583	76	2	collection	collection	NOUN
ejpam-4583	76	3	of	of	ADP
ejpam-4583	76	4	all	all	DET
ejpam-4583	76	5	f	f	PROPN
ejpam-4583	76	6	-open	-open	PROPN
ejpam-4583	76	7	(	(	PUNCT
ejpam-4583	76	8	resp	resp	NOUN
ejpam-4583	76	9	.	.	PUNCT
ejpam-4583	76	10	,	,	PUNCT
ejpam-4583	76	11	f	f	PROPN
ejpam-4583	76	12	-closed	-closed	PROPN
ejpam-4583	76	13	)	)	PUNCT
ejpam-4583	76	14	subsets	subset	NOUN
ejpam-4583	76	15	of	of	ADP
ejpam-4583	76	16	the	the	DET
ejpam-4583	76	17	topological	topological	ADJ
ejpam-4583	76	18	space	space	NOUN
ejpam-4583	76	19	(	(	PUNCT
ejpam-4583	76	20	x	x	X
ejpam-4583	76	21	,	,	PUNCT
ejpam-4583	76	22	t	t	PROPN
ejpam-4583	76	23	)	)	PUNCT
ejpam-4583	76	24	is	be	AUX
ejpam-4583	76	25	denoted	denote	VERB
ejpam-4583	76	26	by	by	ADP
ejpam-4583	76	27	fo(x	fo(x	PUNCT
ejpam-4583	76	28	)	)	PUNCT
ejpam-4583	76	29	(	(	PUNCT
ejpam-4583	76	30	resp	resp	NOUN
ejpam-4583	76	31	.	.	PUNCT
ejpam-4583	76	32	,	,	PUNCT
ejpam-4583	76	33	fc(x	fc(x	NOUN
ejpam-4583	76	34	)	)	PUNCT
ejpam-4583	76	35	)	)	PUNCT
ejpam-4583	76	36	.	.	PUNCT
ejpam-4583	77	1	example	example	NOUN
ejpam-4583	78	1	1	1	X
ejpam-4583	78	2	.	.	PUNCT
ejpam-4583	79	1	let	let	AUX
ejpam-4583	79	2	(	(	PUNCT
ejpam-4583	79	3	r	r	NOUN
ejpam-4583	79	4	,	,	PUNCT
ejpam-4583	79	5	u	u	NOUN
ejpam-4583	79	6	)	)	PUNCT
ejpam-4583	79	7	be	be	VERB
ejpam-4583	79	8	a	a	DET
ejpam-4583	79	9	topological	topological	ADJ
ejpam-4583	79	10	space	space	NOUN
ejpam-4583	79	11	,	,	PUNCT
ejpam-4583	79	12	where	where	SCONJ
ejpam-4583	79	13	u	u	NOUN
ejpam-4583	79	14	is	be	AUX
ejpam-4583	79	15	denoted	denote	VERB
ejpam-4583	79	16	for	for	ADP
ejpam-4583	79	17	the	the	DET
ejpam-4583	79	18	usual	usual	ADJ
ejpam-4583	79	19	topology	topology	NOUN
ejpam-4583	79	20	.	.	PUNCT
ejpam-4583	80	1	let	let	VERB
ejpam-4583	80	2	a	a	DET
ejpam-4583	80	3	=	=	X
ejpam-4583	80	4	(	(	PUNCT
ejpam-4583	80	5	2	2	NUM
ejpam-4583	80	6	,	,	PUNCT
ejpam-4583	80	7	100	100	NUM
ejpam-4583	80	8	)	)	PUNCT
ejpam-4583	80	9	is	be	AUX
ejpam-4583	80	10	an	an	DET
ejpam-4583	80	11	open	open	ADJ
ejpam-4583	80	12	interval	interval	NOUN
ejpam-4583	80	13	in	in	ADP
ejpam-4583	80	14	(	(	PUNCT
ejpam-4583	80	15	r	r	NOUN
ejpam-4583	80	16	,	,	PUNCT
ejpam-4583	80	17	u	u	NOUN
ejpam-4583	80	18	)	)	PUNCT
ejpam-4583	80	19	,	,	PUNCT
ejpam-4583	80	20	then	then	ADV
ejpam-4583	80	21	a	a	PRON
ejpam-4583	80	22	is	be	AUX
ejpam-4583	80	23	a	a	DET
ejpam-4583	80	24	f	f	X
ejpam-4583	80	25	-open	-open	NOUN
ejpam-4583	80	26	set	set	NOUN
ejpam-4583	80	27	,	,	PUNCT
ejpam-4583	80	28	because	because	SCONJ
ejpam-4583	80	29	,	,	PUNCT
ejpam-4583	80	30	(	(	PUNCT
ejpam-4583	80	31	2	2	NUM
ejpam-4583	80	32	,	,	PUNCT
ejpam-4583	80	33	100	100	NUM
ejpam-4583	80	34	)	)	PUNCT
ejpam-4583	80	35	∈	∈	PROPN
ejpam-4583	80	36	u	u	NOUN
ejpam-4583	80	37	and	and	CCONJ
ejpam-4583	80	38	cl(2	cl(2	NOUN
ejpam-4583	80	39	,	,	PUNCT
ejpam-4583	80	40	100)\(2	100)\(2	NUM
ejpam-4583	80	41	,	,	PUNCT
ejpam-4583	80	42	100	100	NUM
ejpam-4583	80	43	)	)	PUNCT
ejpam-4583	80	44	=	=	PUNCT
ejpam-4583	81	1	[	[	X
ejpam-4583	81	2	2	2	NUM
ejpam-4583	81	3	,	,	PUNCT
ejpam-4583	81	4	100]\(2	100]\(2	NUM
ejpam-4583	81	5	,	,	PUNCT
ejpam-4583	81	6	100	100	NUM
ejpam-4583	81	7	)	)	PUNCT
ejpam-4583	81	8	=	=	SYM
ejpam-4583	81	9	{	{	PUNCT
ejpam-4583	81	10	2	2	NUM
ejpam-4583	81	11	,	,	PUNCT
ejpam-4583	81	12	100	100	NUM
ejpam-4583	81	13	}	}	PUNCT
ejpam-4583	81	14	is	be	AUX
ejpam-4583	81	15	finite	finite	ADJ
ejpam-4583	81	16	.	.	PUNCT
ejpam-4583	82	1	any	any	DET
ejpam-4583	82	2	open	open	ADJ
ejpam-4583	82	3	intervals	interval	NOUN
ejpam-4583	82	4	of	of	ADP
ejpam-4583	82	5	(	(	PUNCT
ejpam-4583	82	6	r	r	NOUN
ejpam-4583	82	7	,	,	PUNCT
ejpam-4583	82	8	u	u	NOUN
ejpam-4583	82	9	)	)	PUNCT
ejpam-4583	82	10	is	be	AUX
ejpam-4583	82	11	a	a	DET
ejpam-4583	82	12	f	f	PROPN
ejpam-4583	82	13	-open	-open	NOUN
ejpam-4583	82	14	set	set	NOUN
ejpam-4583	82	15	.	.	PUNCT
ejpam-4583	83	1	on	on	ADP
ejpam-4583	83	2	the	the	DET
ejpam-4583	83	3	other	other	ADJ
ejpam-4583	83	4	hand	hand	NOUN
ejpam-4583	83	5	,	,	PUNCT
ejpam-4583	83	6	let	let	VERB
ejpam-4583	83	7	b	b	X
ejpam-4583	83	8	=	=	PUNCT
ejpam-4583	84	1	[	[	X
ejpam-4583	84	2	1	1	NUM
ejpam-4583	84	3	,	,	PUNCT
ejpam-4583	84	4	6	6	NUM
ejpam-4583	84	5	]	]	PUNCT
ejpam-4583	84	6	is	be	AUX
ejpam-4583	84	7	a	a	DET
ejpam-4583	84	8	closed	closed	ADJ
ejpam-4583	84	9	interval	interval	NOUN
ejpam-4583	84	10	in	in	ADP
ejpam-4583	84	11	(	(	PUNCT
ejpam-4583	84	12	r	r	NOUN
ejpam-4583	84	13	,	,	PUNCT
ejpam-4583	84	14	u	u	NOUN
ejpam-4583	84	15	)	)	PUNCT
ejpam-4583	84	16	,	,	PUNCT
ejpam-4583	84	17	then	then	ADV
ejpam-4583	84	18	b	b	X
ejpam-4583	84	19	is	be	AUX
ejpam-4583	84	20	a	a	DET
ejpam-4583	84	21	f	f	PROPN
ejpam-4583	84	22	-closed	-close	VERB
ejpam-4583	84	23	set	set	NOUN
ejpam-4583	84	24	,	,	PUNCT
ejpam-4583	84	25	because	because	SCONJ
ejpam-4583	84	26	,	,	PUNCT
ejpam-4583	84	27	[	[	X
ejpam-4583	84	28	1	1	NUM
ejpam-4583	84	29	,	,	PUNCT
ejpam-4583	84	30	6	6	NUM
ejpam-4583	84	31	]	]	PUNCT
ejpam-4583	84	32	is	be	AUX
ejpam-4583	84	33	closed	close	VERB
ejpam-4583	84	34	set	set	ADJ
ejpam-4583	84	35	and	and	CCONJ
ejpam-4583	84	36	[	[	X
ejpam-4583	84	37	1	1	NUM
ejpam-4583	84	38	,	,	PUNCT
ejpam-4583	84	39	6	6	NUM
ejpam-4583	84	40	]	]	PUNCT
ejpam-4583	84	41	\	\	PROPN
ejpam-4583	84	42	int[1	int[1	PROPN
ejpam-4583	84	43	,	,	PUNCT
ejpam-4583	84	44	6	6	NUM
ejpam-4583	84	45	]	]	PUNCT
ejpam-4583	84	46	=	=	PUNCT
ejpam-4583	85	1	[	[	X
ejpam-4583	85	2	1	1	NUM
ejpam-4583	85	3	,	,	PUNCT
ejpam-4583	85	4	6	6	NUM
ejpam-4583	85	5	]	]	PUNCT
ejpam-4583	85	6	\	\	PUNCT
ejpam-4583	85	7	(	(	PUNCT
ejpam-4583	85	8	1	1	NUM
ejpam-4583	85	9	,	,	PUNCT
ejpam-4583	85	10	6	6	NUM
ejpam-4583	85	11	)	)	PUNCT
ejpam-4583	85	12	=	=	PRON
ejpam-4583	85	13	{	{	PUNCT
ejpam-4583	85	14	1	1	NUM
ejpam-4583	85	15	,	,	PUNCT
ejpam-4583	85	16	6	6	NUM
ejpam-4583	85	17	}	}	PUNCT
ejpam-4583	85	18	is	be	AUX
ejpam-4583	85	19	finite	finite	ADJ
ejpam-4583	85	20	.	.	PUNCT
ejpam-4583	86	1	any	any	DET
ejpam-4583	86	2	closed	closed	ADJ
ejpam-4583	86	3	interval	interval	NOUN
ejpam-4583	86	4	or	or	CCONJ
ejpam-4583	86	5	finite	finite	ADJ
ejpam-4583	86	6	set	set	NOUN
ejpam-4583	86	7	of	of	ADP
ejpam-4583	86	8	(	(	PUNCT
ejpam-4583	86	9	r	r	NOUN
ejpam-4583	86	10	,	,	PUNCT
ejpam-4583	86	11	u	u	NOUN
ejpam-4583	86	12	)	)	PUNCT
ejpam-4583	86	13	is	be	AUX
ejpam-4583	86	14	a	a	DET
ejpam-4583	86	15	f	f	PROPN
ejpam-4583	86	16	-closed	-close	VERB
ejpam-4583	86	17	set	set	NOUN
ejpam-4583	86	18	.	.	PUNCT
ejpam-4583	87	1	definition	definition	NOUN
ejpam-4583	87	2	14	14	NUM
ejpam-4583	87	3	.	.	PUNCT
ejpam-4583	88	1	if	if	SCONJ
ejpam-4583	88	2	(	(	PUNCT
ejpam-4583	88	3	x	x	X
ejpam-4583	88	4	,	,	PUNCT
ejpam-4583	88	5	t	t	PROPN
ejpam-4583	88	6	)	)	PUNCT
ejpam-4583	88	7	is	be	AUX
ejpam-4583	88	8	a	a	DET
ejpam-4583	88	9	topological	topological	ADJ
ejpam-4583	88	10	space	space	NOUN
ejpam-4583	88	11	,	,	PUNCT
ejpam-4583	88	12	x	x	X
ejpam-4583	88	13	is	be	AUX
ejpam-4583	88	14	a	a	DET
ejpam-4583	88	15	point	point	NOUN
ejpam-4583	88	16	of	of	ADP
ejpam-4583	88	17	x	x	X
ejpam-4583	88	18	,	,	PUNCT
ejpam-4583	88	19	a	a	DET
ejpam-4583	88	20	f	f	PROPN
ejpam-4583	88	21	-open	-open	PROPN
ejpam-4583	88	22	neighbourhood	neighbourhood	NOUN
ejpam-4583	88	23	of	of	ADP
ejpam-4583	88	24	x	x	SYM
ejpam-4583	88	25	is	be	AUX
ejpam-4583	88	26	a	a	DET
ejpam-4583	88	27	f	f	PROPN
ejpam-4583	88	28	-open	-open	PROPN
ejpam-4583	88	29	subset	subset	NOUN
ejpam-4583	88	30	u	u	NOUN
ejpam-4583	88	31	of	of	ADP
ejpam-4583	88	32	x	x	PRON
ejpam-4583	88	33	,	,	PUNCT
ejpam-4583	88	34	which	which	PRON
ejpam-4583	88	35	is	be	AUX
ejpam-4583	88	36	containing	contain	VERB
ejpam-4583	88	37	x.	x.	PROPN
ejpam-4583	88	38	lemma	lemma	PROPN
ejpam-4583	89	1	1	1	X
ejpam-4583	89	2	.	.	PUNCT
ejpam-4583	90	1	let	let	VERB
ejpam-4583	90	2	(	(	PUNCT
ejpam-4583	90	3	x	x	X
ejpam-4583	90	4	,	,	PUNCT
ejpam-4583	90	5	t	t	PROPN
ejpam-4583	90	6	)	)	PUNCT
ejpam-4583	90	7	be	be	AUX
ejpam-4583	90	8	a	a	DET
ejpam-4583	90	9	topological	topological	ADJ
ejpam-4583	90	10	space	space	NOUN
ejpam-4583	90	11	and	and	CCONJ
ejpam-4583	90	12	∅	∅	NOUN
ejpam-4583	91	1	=	=	NOUN
ejpam-4583	91	2	̸	̸	NOUN
ejpam-4583	91	3	v	v	ADP
ejpam-4583	91	4	⊂	⊂	PROPN
ejpam-4583	91	5	x	x	X
ejpam-4583	91	6	is	be	AUX
ejpam-4583	91	7	f	f	PROPN
ejpam-4583	91	8	-open	-open	NOUN
ejpam-4583	91	9	set	set	NOUN
ejpam-4583	91	10	,	,	PUNCT
ejpam-4583	91	11	then	then	ADV
ejpam-4583	91	12	for	for	ADP
ejpam-4583	91	13	every	every	DET
ejpam-4583	91	14	x	x	SYM
ejpam-4583	91	15	∈	∈	PROPN
ejpam-4583	91	16	v	v	ADP
ejpam-4583	91	17	there	there	PRON
ejpam-4583	91	18	exists	exist	VERB
ejpam-4583	91	19	a	a	DET
ejpam-4583	91	20	f	f	NOUN
ejpam-4583	91	21	-open	-open	PROPN
ejpam-4583	91	22	neighborhood	neighborhood	NOUN
ejpam-4583	91	23	ux	ux	NOUN
ejpam-4583	91	24	of	of	ADP
ejpam-4583	91	25	the	the	DET
ejpam-4583	91	26	point	point	NOUN
ejpam-4583	91	27	x	x	PUNCT
ejpam-4583	91	28	contained	contain	VERB
ejpam-4583	91	29	in	in	ADP
ejpam-4583	91	30	v.	v.	ADP
ejpam-4583	91	31	proof	proof	NOUN
ejpam-4583	91	32	.	.	PUNCT
ejpam-4583	92	1	assume	assume	VERB
ejpam-4583	92	2	that	that	SCONJ
ejpam-4583	92	3	v	v	NOUN
ejpam-4583	92	4	is	be	AUX
ejpam-4583	92	5	f	f	PROPN
ejpam-4583	92	6	-open	-open	ADJ
ejpam-4583	92	7	and	and	CCONJ
ejpam-4583	92	8	pick	pick	VERB
ejpam-4583	92	9	x	x	PUNCT
ejpam-4583	92	10	∈	∈	PROPN
ejpam-4583	92	11	v	v	ADP
ejpam-4583	92	12	arbitrary	arbitrary	ADJ
ejpam-4583	92	13	.	.	PUNCT
ejpam-4583	93	1	let	let	VERB
ejpam-4583	93	2	ux	ux	INTJ
ejpam-4583	93	3	=	=	SYM
ejpam-4583	93	4	v	v	PROPN
ejpam-4583	93	5	.	.	PUNCT
ejpam-4583	94	1	then	then	ADV
ejpam-4583	94	2	v	v	NOUN
ejpam-4583	94	3	is	be	AUX
ejpam-4583	94	4	a	a	DET
ejpam-4583	94	5	f	f	PROPN
ejpam-4583	94	6	-open	-open	PROPN
ejpam-4583	94	7	neighborhood	neighborhood	NOUN
ejpam-4583	94	8	of	of	ADP
ejpam-4583	94	9	x	x	X
ejpam-4583	94	10	and	and	CCONJ
ejpam-4583	94	11	x	x	SYM
ejpam-4583	94	12	∈	∈	NOUN
ejpam-4583	94	13	v	v	ADP
ejpam-4583	94	14	⊆	⊆	NUM
ejpam-4583	94	15	v.	v.	ADP
ejpam-4583	94	16	the	the	DET
ejpam-4583	94	17	converse	converse	NOUN
ejpam-4583	94	18	of	of	ADP
ejpam-4583	94	19	the	the	DET
ejpam-4583	94	20	previous	previous	ADJ
ejpam-4583	94	21	lemma	lemma	PROPN
ejpam-4583	94	22	is	be	AUX
ejpam-4583	94	23	not	not	PART
ejpam-4583	94	24	true	true	ADJ
ejpam-4583	94	25	in	in	ADP
ejpam-4583	94	26	general	general	ADJ
ejpam-4583	94	27	.	.	PUNCT
ejpam-4583	95	1	we	we	PRON
ejpam-4583	95	2	have	have	VERB
ejpam-4583	95	3	the	the	DET
ejpam-4583	95	4	following	follow	VERB
ejpam-4583	95	5	example	example	NOUN
ejpam-4583	95	6	:	:	PUNCT
ejpam-4583	95	7	m.	m.	PROPN
ejpam-4583	95	8	h.	h.	PROPN
ejpam-4583	95	9	alqahtani	alqahtani	PROPN
ejpam-4583	95	10	/	/	SYM
ejpam-4583	95	11	eur	eur	PROPN
ejpam-4583	95	12	.	.	PUNCT
ejpam-4583	96	1	j.	j.	PROPN
ejpam-4583	96	2	pure	pure	PROPN
ejpam-4583	96	3	appl	appl	PROPN
ejpam-4583	96	4	.	.	PROPN
ejpam-4583	96	5	math	math	PROPN
ejpam-4583	96	6	,	,	PUNCT
ejpam-4583	96	7	16	16	NUM
ejpam-4583	96	8	(	(	PUNCT
ejpam-4583	96	9	2	2	NUM
ejpam-4583	96	10	)	)	PUNCT
ejpam-4583	96	11	(	(	PUNCT
ejpam-4583	96	12	2023	2023	NUM
ejpam-4583	96	13	)	)	PUNCT
ejpam-4583	96	14	,	,	PUNCT
ejpam-4583	96	15	819	819	NUM
ejpam-4583	96	16	-	-	SYM
ejpam-4583	96	17	832	832	NUM
ejpam-4583	96	18	822	822	NUM
ejpam-4583	96	19	example	example	NOUN
ejpam-4583	96	20	2	2	NUM
ejpam-4583	96	21	.	.	PUNCT
ejpam-4583	97	1	let	let	VERB
ejpam-4583	97	2	an	an	DET
ejpam-4583	97	3	=	=	SYM
ejpam-4583	97	4	(	(	PUNCT
ejpam-4583	97	5	n	n	CCONJ
ejpam-4583	97	6	,	,	PUNCT
ejpam-4583	97	7	n	n	PROPN
ejpam-4583	97	8	+	+	NOUN
ejpam-4583	97	9	1	1	X
ejpam-4583	97	10	)	)	PUNCT
ejpam-4583	97	11	be	be	AUX
ejpam-4583	97	12	a	a	DET
ejpam-4583	97	13	subset	subset	NOUN
ejpam-4583	97	14	of	of	ADP
ejpam-4583	97	15	(	(	PUNCT
ejpam-4583	97	16	r	r	NOUN
ejpam-4583	97	17	,	,	PUNCT
ejpam-4583	97	18	u	u	NOUN
ejpam-4583	97	19	)	)	PUNCT
ejpam-4583	97	20	,	,	PUNCT
ejpam-4583	97	21	for	for	ADP
ejpam-4583	97	22	all	all	DET
ejpam-4583	97	23	n	n	PRON
ejpam-4583	97	24	∈	∈	PROPN
ejpam-4583	97	25	z.	z.	PROPN
ejpam-4583	98	1	then	then	ADV
ejpam-4583	98	2	,	,	PUNCT
ejpam-4583	98	3	an	an	DET
ejpam-4583	98	4	=	=	X
ejpam-4583	98	5	(	(	PUNCT
ejpam-4583	98	6	n	n	CCONJ
ejpam-4583	98	7	,	,	PUNCT
ejpam-4583	98	8	n	n	PROPN
ejpam-4583	98	9	+	+	NOUN
ejpam-4583	98	10	1	1	X
ejpam-4583	98	11	)	)	PUNCT
ejpam-4583	98	12	∈	∈	PROPN
ejpam-4583	98	13	u	u	NOUN
ejpam-4583	98	14	and	and	CCONJ
ejpam-4583	98	15	cl(n	cl(n	NOUN
ejpam-4583	98	16	,	,	PUNCT
ejpam-4583	98	17	n	n	X
ejpam-4583	98	18	+	+	NOUN
ejpam-4583	98	19	1	1	NUM
ejpam-4583	98	20	)	)	PUNCT
ejpam-4583	98	21	\	\	NOUN
ejpam-4583	98	22	(	(	PUNCT
ejpam-4583	98	23	n	n	X
ejpam-4583	98	24	,	,	PUNCT
ejpam-4583	98	25	n	n	PROPN
ejpam-4583	98	26	+	+	NOUN
ejpam-4583	98	27	1	1	NUM
ejpam-4583	98	28	)	)	PUNCT
ejpam-4583	98	29	=	=	PRON
ejpam-4583	98	30	{	{	PUNCT
ejpam-4583	98	31	n	n	X
ejpam-4583	98	32	,	,	PUNCT
ejpam-4583	98	33	n	n	PROPN
ejpam-4583	98	34	+	+	NOUN
ejpam-4583	98	35	1	1	NUM
ejpam-4583	98	36	}	}	PUNCT
ejpam-4583	98	37	is	be	AUX
ejpam-4583	98	38	finite	finite	NOUN
ejpam-4583	98	39	set	set	VERB
ejpam-4583	98	40	for	for	ADP
ejpam-4583	98	41	all	all	DET
ejpam-4583	98	42	n	n	PRON
ejpam-4583	98	43	∈	∈	PROPN
ejpam-4583	98	44	z.	z.	NOUN
ejpam-4583	98	45	then	then	ADV
ejpam-4583	98	46	an	an	DET
ejpam-4583	98	47	=	=	X
ejpam-4583	98	48	(	(	PUNCT
ejpam-4583	98	49	n	n	CCONJ
ejpam-4583	98	50	,	,	PUNCT
ejpam-4583	98	51	n	n	PROPN
ejpam-4583	98	52	+	+	NOUN
ejpam-4583	98	53	1	1	NUM
ejpam-4583	98	54	)	)	PUNCT
ejpam-4583	98	55	is	be	AUX
ejpam-4583	98	56	f	f	PROPN
ejpam-4583	98	57	-open	-open	NOUN
ejpam-4583	98	58	set	set	VERB
ejpam-4583	98	59	for	for	ADP
ejpam-4583	98	60	all	all	PRON
ejpam-4583	98	61	n	n	PRON
ejpam-4583	98	62	∈	∈	NOUN
ejpam-4583	98	63	z.	z.	PROPN
ejpam-4583	98	64	let	let	VERB
ejpam-4583	98	65	b	b	NOUN
ejpam-4583	98	66	=	=	SYM
ejpam-4583	98	67	⋃	⋃	NOUN
ejpam-4583	98	68	n∈z(n	n∈z(n	NOUN
ejpam-4583	98	69	,	,	PUNCT
ejpam-4583	98	70	n	n	NOUN
ejpam-4583	98	71	+	+	NOUN
ejpam-4583	98	72	1	1	NUM
ejpam-4583	98	73	)	)	PUNCT
ejpam-4583	98	74	and	and	CCONJ
ejpam-4583	98	75	let	let	VERB
ejpam-4583	98	76	x	x	X
ejpam-4583	98	77	∈	∈	PROPN
ejpam-4583	98	78	b	b	NOUN
ejpam-4583	98	79	=	=	NOUN
ejpam-4583	98	80	⋃	⋃	NOUN
ejpam-4583	98	81	n∈z(n	n∈z(n	NOUN
ejpam-4583	98	82	,	,	PUNCT
ejpam-4583	98	83	n+	n+	X
ejpam-4583	98	84	1	1	X
ejpam-4583	98	85	)	)	PUNCT
ejpam-4583	98	86	be	be	AUX
ejpam-4583	98	87	arbitrary	arbitrary	ADJ
ejpam-4583	98	88	,	,	PUNCT
ejpam-4583	98	89	then	then	ADV
ejpam-4583	98	90	there	there	PRON
ejpam-4583	98	91	exists	exist	VERB
ejpam-4583	98	92	some	some	DET
ejpam-4583	98	93	n1	n1	NOUN
ejpam-4583	98	94	∈	∈	NOUN
ejpam-4583	98	95	z	z	NOUN
ejpam-4583	98	96	such	such	ADJ
ejpam-4583	98	97	that	that	SCONJ
ejpam-4583	98	98	x	x	SYM
ejpam-4583	98	99	∈	∈	PROPN
ejpam-4583	98	100	(	(	PUNCT
ejpam-4583	98	101	n1	n1	NOUN
ejpam-4583	98	102	,	,	PUNCT
ejpam-4583	98	103	n1	n1	PROPN
ejpam-4583	98	104	+	+	CCONJ
ejpam-4583	98	105	1	1	NUM
ejpam-4583	98	106	)	)	PUNCT
ejpam-4583	98	107	is	be	AUX
ejpam-4583	98	108	a	a	DET
ejpam-4583	98	109	f	f	PROPN
ejpam-4583	98	110	-open	-open	PROPN
ejpam-4583	98	111	neighborhood	neighborhood	NOUN
ejpam-4583	98	112	containing	contain	VERB
ejpam-4583	98	113	x	x	PUNCT
ejpam-4583	98	114	and	and	CCONJ
ejpam-4583	98	115	contained	contain	VERB
ejpam-4583	98	116	in	in	ADP
ejpam-4583	98	117	b	b	NOUN
ejpam-4583	98	118	,	,	PUNCT
ejpam-4583	98	119	that	that	PRON
ejpam-4583	98	120	is	be	AUX
ejpam-4583	98	121	mean	mean	ADJ
ejpam-4583	98	122	for	for	ADP
ejpam-4583	98	123	any	any	DET
ejpam-4583	98	124	x	x	SYM
ejpam-4583	98	125	∈	∈	PROPN
ejpam-4583	98	126	b	b	NOUN
ejpam-4583	98	127	there	there	PRON
ejpam-4583	98	128	exist	exist	VERB
ejpam-4583	98	129	a	a	DET
ejpam-4583	98	130	f	f	PROPN
ejpam-4583	98	131	-open	-open	PROPN
ejpam-4583	98	132	neighborhood	neighborhood	NOUN
ejpam-4583	98	133	containing	contain	VERB
ejpam-4583	98	134	x	x	PUNCT
ejpam-4583	98	135	and	and	CCONJ
ejpam-4583	98	136	contained	contain	VERB
ejpam-4583	98	137	in	in	ADP
ejpam-4583	98	138	b.	b.	PROPN
ejpam-4583	98	139	however	however	ADV
ejpam-4583	98	140	,	,	PUNCT
ejpam-4583	98	141	b	b	PROPN
ejpam-4583	98	142	is	be	AUX
ejpam-4583	98	143	not	not	PART
ejpam-4583	98	144	f	f	PROPN
ejpam-4583	98	145	-open	-open	NOUN
ejpam-4583	98	146	set	set	NOUN
ejpam-4583	98	147	,	,	PUNCT
ejpam-4583	98	148	because	because	SCONJ
ejpam-4583	98	149	b	b	PROPN
ejpam-4583	98	150	=	=	SYM
ejpam-4583	98	151	⋃	⋃	NOUN
ejpam-4583	98	152	n∈z(n	n∈z(n	NOUN
ejpam-4583	98	153	,	,	PUNCT
ejpam-4583	98	154	n+	n+	X
ejpam-4583	98	155	1	1	NUM
ejpam-4583	98	156	)	)	PUNCT
ejpam-4583	98	157	=	=	SYM
ejpam-4583	98	158	r	r	NOUN
ejpam-4583	98	159	\	\	NOUN
ejpam-4583	98	160	z	z	NOUN
ejpam-4583	98	161	is	be	AUX
ejpam-4583	98	162	open	open	ADJ
ejpam-4583	98	163	set	set	VERB
ejpam-4583	98	164	and	and	CCONJ
ejpam-4583	98	165	cl(b	cl(b	NOUN
ejpam-4583	98	166	)	)	PUNCT
ejpam-4583	98	167	\	\	PUNCT
ejpam-4583	99	1	(	(	PUNCT
ejpam-4583	99	2	b	b	X
ejpam-4583	99	3	)	)	PUNCT
ejpam-4583	99	4	=	=	SYM
ejpam-4583	99	5	r	r	NOUN
ejpam-4583	99	6	\	\	NOUN
ejpam-4583	99	7	(	(	PUNCT
ejpam-4583	99	8	r	r	NOUN
ejpam-4583	99	9	\	\	PROPN
ejpam-4583	99	10	z	z	NOUN
ejpam-4583	99	11	)	)	PUNCT
ejpam-4583	99	12	=	=	NOUN
ejpam-4583	99	13	z	z	NOUN
ejpam-4583	99	14	is	be	AUX
ejpam-4583	99	15	not	not	PART
ejpam-4583	99	16	finite	finite	ADJ
ejpam-4583	99	17	set	set	NOUN
ejpam-4583	99	18	.	.	PUNCT
ejpam-4583	100	1	therefore	therefore	ADV
ejpam-4583	100	2	,	,	PUNCT
ejpam-4583	100	3	b	b	X
ejpam-4583	100	4	=	=	SYM
ejpam-4583	100	5	⋃	⋃	NOUN
ejpam-4583	100	6	n∈z(n	n∈z(n	NOUN
ejpam-4583	100	7	,	,	PUNCT
ejpam-4583	100	8	n+	n+	X
ejpam-4583	100	9	1	1	NUM
ejpam-4583	100	10	)	)	PUNCT
ejpam-4583	100	11	is	be	AUX
ejpam-4583	100	12	not	not	PART
ejpam-4583	100	13	f	f	PROPN
ejpam-4583	100	14	-open	-open	NOUN
ejpam-4583	100	15	set	set	NOUN
ejpam-4583	100	16	.	.	PUNCT
ejpam-4583	101	1	it	it	PRON
ejpam-4583	101	2	is	be	AUX
ejpam-4583	101	3	clear	clear	ADJ
ejpam-4583	101	4	by	by	ADP
ejpam-4583	101	5	the	the	DET
ejpam-4583	101	6	definitions	definition	NOUN
ejpam-4583	101	7	every	every	DET
ejpam-4583	101	8	f	f	X
ejpam-4583	101	9	-open	-open	PROPN
ejpam-4583	101	10	and	and	CCONJ
ejpam-4583	101	11	f	f	NOUN
ejpam-4583	101	12	-closed	-close	VERB
ejpam-4583	101	13	sets	set	NOUN
ejpam-4583	101	14	are	be	AUX
ejpam-4583	101	15	open	open	ADJ
ejpam-4583	101	16	and	and	CCONJ
ejpam-4583	101	17	closed	closed	ADJ
ejpam-4583	101	18	,	,	PUNCT
ejpam-4583	101	19	respectively	respectively	ADV
ejpam-4583	101	20	.	.	PUNCT
ejpam-4583	102	1	however	however	ADV
ejpam-4583	102	2	,	,	PUNCT
ejpam-4583	102	3	the	the	DET
ejpam-4583	102	4	converse	converse	NOUN
ejpam-4583	102	5	is	be	AUX
ejpam-4583	102	6	not	not	PART
ejpam-4583	102	7	true	true	ADJ
ejpam-4583	102	8	in	in	ADP
ejpam-4583	102	9	general	general	ADJ
ejpam-4583	102	10	.	.	PUNCT
ejpam-4583	103	1	here	here	ADV
ejpam-4583	103	2	is	be	AUX
ejpam-4583	103	3	an	an	DET
ejpam-4583	103	4	example	example	NOUN
ejpam-4583	103	5	of	of	ADP
ejpam-4583	103	6	open	open	ADJ
ejpam-4583	103	7	(	(	PUNCT
ejpam-4583	103	8	resp	resp	NOUN
ejpam-4583	103	9	.	.	PROPN
ejpam-4583	103	10	,	,	PUNCT
ejpam-4583	103	11	closed	closed	ADJ
ejpam-4583	103	12	)	)	PUNCT
ejpam-4583	103	13	set	set	NOUN
ejpam-4583	103	14	which	which	PRON
ejpam-4583	103	15	is	be	AUX
ejpam-4583	103	16	not	not	PART
ejpam-4583	103	17	f	f	PROPN
ejpam-4583	103	18	-open	-open	NOUN
ejpam-4583	103	19	(	(	PUNCT
ejpam-4583	103	20	resp	resp	NOUN
ejpam-4583	103	21	.	.	PUNCT
ejpam-4583	103	22	,	,	PUNCT
ejpam-4583	103	23	f	f	PROPN
ejpam-4583	103	24	-closed	-closed	PROPN
ejpam-4583	103	25	)	)	PUNCT
ejpam-4583	103	26	.	.	PUNCT
ejpam-4583	104	1	example	example	NOUN
ejpam-4583	105	1	3	3	X
ejpam-4583	105	2	.	.	X
ejpam-4583	105	3	there	there	PRON
ejpam-4583	105	4	exist	exist	VERB
ejpam-4583	105	5	a	a	DET
ejpam-4583	105	6	=	=	X
ejpam-4583	105	7	r\z	r\z	NOUN
ejpam-4583	105	8	is	be	AUX
ejpam-4583	105	9	an	an	DET
ejpam-4583	105	10	open	open	ADJ
ejpam-4583	105	11	subset	subset	NOUN
ejpam-4583	105	12	of	of	ADP
ejpam-4583	105	13	(	(	PUNCT
ejpam-4583	105	14	r	r	NOUN
ejpam-4583	105	15	,	,	PUNCT
ejpam-4583	105	16	u	u	NOUN
ejpam-4583	105	17	)	)	PUNCT
ejpam-4583	105	18	.	.	PUNCT
ejpam-4583	106	1	however	however	ADV
ejpam-4583	106	2	,	,	PUNCT
ejpam-4583	106	3	cl(r\z)\(r\z	cl(r\z)\(r\z	NOUN
ejpam-4583	106	4	)	)	PUNCT
ejpam-4583	106	5	=	=	PUNCT
ejpam-4583	107	1	r\	r\	PROPN
ejpam-4583	107	2	(	(	PUNCT
ejpam-4583	107	3	r\z	r\z	NOUN
ejpam-4583	107	4	)	)	PUNCT
ejpam-4583	107	5	)	)	PUNCT
ejpam-4583	108	1	=	=	PUNCT
ejpam-4583	108	2	z	z	NOUN
ejpam-4583	108	3	is	be	AUX
ejpam-4583	108	4	not	not	PART
ejpam-4583	108	5	finite	finite	ADJ
ejpam-4583	108	6	.	.	PUNCT
ejpam-4583	109	1	hence	hence	ADV
ejpam-4583	109	2	a	a	PRON
ejpam-4583	109	3	is	be	AUX
ejpam-4583	109	4	not	not	PART
ejpam-4583	109	5	f	f	PROPN
ejpam-4583	109	6	-open	-open	NOUN
ejpam-4583	109	7	set	set	NOUN
ejpam-4583	109	8	.	.	PUNCT
ejpam-4583	110	1	also	also	ADV
ejpam-4583	110	2	,	,	PUNCT
ejpam-4583	110	3	z	z	PROPN
ejpam-4583	110	4	is	be	AUX
ejpam-4583	110	5	a	a	DET
ejpam-4583	110	6	closed	closed	ADJ
ejpam-4583	110	7	set	set	NOUN
ejpam-4583	110	8	in	in	ADP
ejpam-4583	110	9	(	(	PUNCT
ejpam-4583	110	10	r	r	NOUN
ejpam-4583	110	11	,	,	PUNCT
ejpam-4583	110	12	u	u	NOUN
ejpam-4583	110	13	)	)	PUNCT
ejpam-4583	110	14	,	,	PUNCT
ejpam-4583	110	15	but	but	CCONJ
ejpam-4583	110	16	z	z	NOUN
ejpam-4583	110	17	\	\	PROPN
ejpam-4583	110	18	int(z	int(z	PROPN
ejpam-4583	110	19	)	)	PUNCT
ejpam-4583	110	20	=	=	PUNCT
ejpam-4583	110	21	z	z	NOUN
ejpam-4583	110	22	\	\	NOUN
ejpam-4583	110	23	∅	∅	NOUN
ejpam-4583	110	24	=	=	PUNCT
ejpam-4583	110	25	z	z	NOUN
ejpam-4583	110	26	is	be	AUX
ejpam-4583	110	27	not	not	PART
ejpam-4583	110	28	finite	finite	ADJ
ejpam-4583	110	29	.	.	PUNCT
ejpam-4583	111	1	therefore	therefore	ADV
ejpam-4583	111	2	,	,	PUNCT
ejpam-4583	111	3	z	z	NOUN
ejpam-4583	111	4	is	be	AUX
ejpam-4583	111	5	not	not	PART
ejpam-4583	111	6	f	f	PROPN
ejpam-4583	111	7	-closed	-close	VERB
ejpam-4583	111	8	set	set	NOUN
ejpam-4583	111	9	.	.	PUNCT
ejpam-4583	112	1	there	there	PRON
ejpam-4583	112	2	is	be	VERB
ejpam-4583	112	3	an	an	DET
ejpam-4583	112	4	example	example	NOUN
ejpam-4583	112	5	of	of	ADP
ejpam-4583	112	6	f	f	PROPN
ejpam-4583	112	7	-open	-open	PROPN
ejpam-4583	112	8	(	(	PUNCT
ejpam-4583	112	9	resp	resp	NOUN
ejpam-4583	112	10	.	.	PUNCT
ejpam-4583	112	11	,	,	PUNCT
ejpam-4583	112	12	f	f	PROPN
ejpam-4583	112	13	-closed	-close	VERB
ejpam-4583	112	14	)	)	PUNCT
ejpam-4583	112	15	set	set	NOUN
ejpam-4583	112	16	which	which	PRON
ejpam-4583	112	17	is	be	AUX
ejpam-4583	112	18	not	not	PART
ejpam-4583	112	19	an	an	DET
ejpam-4583	112	20	open	open	ADJ
ejpam-4583	112	21	domain	domain	NOUN
ejpam-4583	112	22	(	(	PUNCT
ejpam-4583	112	23	resp	resp	NOUN
ejpam-4583	112	24	.	.	PUNCT
ejpam-4583	112	25	,	,	PUNCT
ejpam-4583	112	26	closed	closed	ADJ
ejpam-4583	112	27	domain	domain	NOUN
ejpam-4583	112	28	)	)	PUNCT
ejpam-4583	112	29	.	.	PUNCT
ejpam-4583	112	30	example	example	NOUN
ejpam-4583	113	1	4	4	X
ejpam-4583	113	2	.	.	PUNCT
ejpam-4583	113	3	let	let	VERB
ejpam-4583	113	4	a	a	PRON
ejpam-4583	113	5	=	=	X
ejpam-4583	113	6	(	(	PUNCT
ejpam-4583	113	7	2	2	NUM
ejpam-4583	113	8	,	,	PUNCT
ejpam-4583	113	9	5	5	NUM
ejpam-4583	113	10	)	)	PUNCT
ejpam-4583	113	11	∪	∪	NOUN
ejpam-4583	113	12	(	(	PUNCT
ejpam-4583	113	13	5	5	NUM
ejpam-4583	113	14	,	,	PUNCT
ejpam-4583	113	15	9	9	NUM
ejpam-4583	113	16	)	)	PUNCT
ejpam-4583	113	17	is	be	AUX
ejpam-4583	113	18	a	a	DET
ejpam-4583	113	19	f	f	PROPN
ejpam-4583	113	20	-open	-open	NOUN
ejpam-4583	113	21	subset	subset	NOUN
ejpam-4583	113	22	in	in	ADP
ejpam-4583	113	23	(	(	PUNCT
ejpam-4583	113	24	r	r	NOUN
ejpam-4583	113	25	,	,	PUNCT
ejpam-4583	113	26	u	u	NOUN
ejpam-4583	113	27	)	)	PUNCT
ejpam-4583	113	28	,	,	PUNCT
ejpam-4583	113	29	because	because	SCONJ
ejpam-4583	113	30	,	,	PUNCT
ejpam-4583	113	31	(	(	PUNCT
ejpam-4583	113	32	2	2	NUM
ejpam-4583	113	33	,	,	PUNCT
ejpam-4583	113	34	5	5	NUM
ejpam-4583	113	35	)	)	PUNCT
ejpam-4583	113	36	∪	∪	NOUN
ejpam-4583	113	37	(	(	PUNCT
ejpam-4583	113	38	5	5	NUM
ejpam-4583	113	39	,	,	PUNCT
ejpam-4583	113	40	9	9	NUM
ejpam-4583	113	41	)	)	PUNCT
ejpam-4583	113	42	is	be	AUX
ejpam-4583	113	43	open	open	ADJ
ejpam-4583	113	44	and	and	CCONJ
ejpam-4583	113	45	cl((2	cl((2	CCONJ
ejpam-4583	113	46	,	,	PUNCT
ejpam-4583	113	47	5	5	X
ejpam-4583	113	48	)	)	PUNCT
ejpam-4583	113	49	∪	∪	NOUN
ejpam-4583	113	50	(	(	PUNCT
ejpam-4583	113	51	5	5	NUM
ejpam-4583	113	52	,	,	PUNCT
ejpam-4583	113	53	9	9	NUM
ejpam-4583	113	54	)	)	PUNCT
ejpam-4583	113	55	)	)	PUNCT
ejpam-4583	113	56	\	\	PUNCT
ejpam-4583	114	1	(	(	PUNCT
ejpam-4583	114	2	(	(	PUNCT
ejpam-4583	114	3	2	2	NUM
ejpam-4583	114	4	,	,	PUNCT
ejpam-4583	114	5	5	5	NUM
ejpam-4583	114	6	)	)	PUNCT
ejpam-4583	114	7	∪	∪	NOUN
ejpam-4583	114	8	(	(	PUNCT
ejpam-4583	114	9	(	(	PUNCT
ejpam-4583	114	10	5	5	NUM
ejpam-4583	114	11	,	,	PUNCT
ejpam-4583	114	12	9	9	NUM
ejpam-4583	114	13	)	)	PUNCT
ejpam-4583	114	14	)	)	PUNCT
ejpam-4583	115	1	=	=	PUNCT
ejpam-4583	116	1	[	[	X
ejpam-4583	116	2	2	2	NUM
ejpam-4583	116	3	,	,	PUNCT
ejpam-4583	116	4	9	9	NUM
ejpam-4583	116	5	]	]	PUNCT
ejpam-4583	116	6	\	\	PUNCT
ejpam-4583	116	7	(	(	PUNCT
ejpam-4583	116	8	(	(	PUNCT
ejpam-4583	116	9	2	2	NUM
ejpam-4583	116	10	,	,	PUNCT
ejpam-4583	116	11	5	5	NUM
ejpam-4583	116	12	)	)	PUNCT
ejpam-4583	116	13	∪	∪	NOUN
ejpam-4583	116	14	(	(	PUNCT
ejpam-4583	116	15	5	5	NUM
ejpam-4583	116	16	,	,	PUNCT
ejpam-4583	116	17	9	9	NUM
ejpam-4583	116	18	)	)	PUNCT
ejpam-4583	116	19	)	)	PUNCT
ejpam-4583	117	1	=	=	PRON
ejpam-4583	117	2	{	{	PUNCT
ejpam-4583	117	3	2	2	NUM
ejpam-4583	117	4	,	,	PUNCT
ejpam-4583	117	5	5	5	NUM
ejpam-4583	117	6	,	,	PUNCT
ejpam-4583	117	7	9	9	NUM
ejpam-4583	117	8	}	}	PUNCT
ejpam-4583	117	9	is	be	AUX
ejpam-4583	117	10	finite	finite	ADJ
ejpam-4583	117	11	.	.	PUNCT
ejpam-4583	118	1	but	but	CCONJ
ejpam-4583	118	2	a	a	PRON
ejpam-4583	118	3	is	be	AUX
ejpam-4583	118	4	not	not	PART
ejpam-4583	118	5	open	open	ADJ
ejpam-4583	118	6	domain	domain	NOUN
ejpam-4583	118	7	,	,	PUNCT
ejpam-4583	118	8	because	because	SCONJ
ejpam-4583	118	9	(	(	PUNCT
ejpam-4583	118	10	2	2	NUM
ejpam-4583	118	11	,	,	PUNCT
ejpam-4583	118	12	5	5	NUM
ejpam-4583	118	13	)	)	PUNCT
ejpam-4583	118	14	∪	∪	NOUN
ejpam-4583	118	15	(	(	PUNCT
ejpam-4583	118	16	5	5	NUM
ejpam-4583	118	17	,	,	PUNCT
ejpam-4583	118	18	9	9	NUM
ejpam-4583	118	19	)	)	PUNCT
ejpam-4583	118	20	̸=	̸=	PROPN
ejpam-4583	118	21	int(cl((2	int(cl((2	PROPN
ejpam-4583	118	22	,	,	PUNCT
ejpam-4583	118	23	5	5	NUM
ejpam-4583	118	24	)	)	PUNCT
ejpam-4583	118	25	∪	∪	NOUN
ejpam-4583	118	26	(	(	PUNCT
ejpam-4583	118	27	5	5	NUM
ejpam-4583	118	28	,	,	PUNCT
ejpam-4583	118	29	9	9	NUM
ejpam-4583	118	30	)	)	PUNCT
ejpam-4583	118	31	)	)	PUNCT
ejpam-4583	118	32	)	)	PUNCT
ejpam-4583	119	1	=	=	PUNCT
ejpam-4583	119	2	(	(	PUNCT
ejpam-4583	119	3	2	2	NUM
ejpam-4583	119	4	,	,	PUNCT
ejpam-4583	119	5	9	9	NUM
ejpam-4583	119	6	)	)	PUNCT
ejpam-4583	119	7	.	.	PUNCT
ejpam-4583	120	1	moreover	moreover	ADV
ejpam-4583	120	2	,	,	PUNCT
ejpam-4583	120	3	r	r	NOUN
ejpam-4583	120	4	\	\	NOUN
ejpam-4583	120	5	a	a	PRON
ejpam-4583	120	6	is	be	AUX
ejpam-4583	120	7	f	f	PROPN
ejpam-4583	120	8	-closed	-close	VERB
ejpam-4583	120	9	set	set	NOUN
ejpam-4583	120	10	,	,	PUNCT
ejpam-4583	120	11	because	because	SCONJ
ejpam-4583	120	12	r	r	NOUN
ejpam-4583	120	13	\	\	PROPN
ejpam-4583	120	14	a	a	PRON
ejpam-4583	120	15	is	be	AUX
ejpam-4583	120	16	closed	closed	ADJ
ejpam-4583	120	17	and	and	CCONJ
ejpam-4583	120	18	(	(	PUNCT
ejpam-4583	120	19	r	r	NOUN
ejpam-4583	120	20	\	\	PROPN
ejpam-4583	120	21	a	a	PRON
ejpam-4583	120	22	)	)	PUNCT
ejpam-4583	120	23	\	\	PUNCT
ejpam-4583	121	1	int(r	int(r	PROPN
ejpam-4583	121	2	\	\	PROPN
ejpam-4583	121	3	a	a	X
ejpam-4583	121	4	)	)	PUNCT
ejpam-4583	121	5	=	=	SYM
ejpam-4583	121	6	(	(	PUNCT
ejpam-4583	121	7	(	(	PUNCT
ejpam-4583	121	8	−∞	−∞	NOUN
ejpam-4583	121	9	,	,	PUNCT
ejpam-4583	121	10	2	2	NUM
ejpam-4583	121	11	]	]	PUNCT
ejpam-4583	121	12	∪	∪	ADP
ejpam-4583	121	13	[	[	X
ejpam-4583	121	14	9,∞	9,∞	NUM
ejpam-4583	121	15	)	)	PUNCT
ejpam-4583	121	16	∪	∪	ADP
ejpam-4583	121	17	{	{	PUNCT
ejpam-4583	121	18	5	5	NUM
ejpam-4583	121	19	}	}	PUNCT
ejpam-4583	121	20	)	)	PUNCT
ejpam-4583	121	21	\	\	PUNCT
ejpam-4583	122	1	(	(	PUNCT
ejpam-4583	122	2	(	(	PUNCT
ejpam-4583	122	3	−∞	−∞	NOUN
ejpam-4583	122	4	,	,	PUNCT
ejpam-4583	122	5	2	2	NUM
ejpam-4583	122	6	)	)	PUNCT
ejpam-4583	122	7	∪	∪	NOUN
ejpam-4583	122	8	(	(	PUNCT
ejpam-4583	122	9	9,∞	9,∞	NUM
ejpam-4583	122	10	)	)	PUNCT
ejpam-4583	122	11	)	)	PUNCT
ejpam-4583	123	1	=	=	PRON
ejpam-4583	123	2	{	{	PUNCT
ejpam-4583	123	3	2	2	NUM
ejpam-4583	123	4	,	,	PUNCT
ejpam-4583	123	5	5	5	NUM
ejpam-4583	123	6	,	,	PUNCT
ejpam-4583	123	7	9	9	NUM
ejpam-4583	123	8	}	}	PUNCT
ejpam-4583	123	9	is	be	AUX
ejpam-4583	123	10	finite	finite	ADJ
ejpam-4583	123	11	.	.	PUNCT
ejpam-4583	124	1	but	but	CCONJ
ejpam-4583	124	2	r	r	NOUN
ejpam-4583	124	3	\	\	PROPN
ejpam-4583	124	4	a	a	PRON
ejpam-4583	124	5	is	be	AUX
ejpam-4583	124	6	not	not	PART
ejpam-4583	124	7	closed	closed	ADJ
ejpam-4583	124	8	domain	domain	NOUN
ejpam-4583	124	9	because	because	SCONJ
ejpam-4583	124	10	the	the	DET
ejpam-4583	124	11	complement	complement	NOUN
ejpam-4583	124	12	of	of	ADP
ejpam-4583	124	13	closed	closed	ADJ
ejpam-4583	124	14	domain	domain	NOUN
ejpam-4583	124	15	is	be	AUX
ejpam-4583	124	16	open	open	ADJ
ejpam-4583	124	17	domain	domain	NOUN
ejpam-4583	124	18	or	or	CCONJ
ejpam-4583	124	19	cl(int(r	cl(int(r	NOUN
ejpam-4583	124	20	\	\	PROPN
ejpam-4583	125	1	a	a	PRON
ejpam-4583	125	2	)	)	PUNCT
ejpam-4583	125	3	)	)	PUNCT
ejpam-4583	126	1	=	=	SYM
ejpam-4583	126	2	cl(int((−∞	cl(int((−∞	PROPN
ejpam-4583	126	3	,	,	PUNCT
ejpam-4583	126	4	2	2	NUM
ejpam-4583	126	5	]	]	PUNCT
ejpam-4583	126	6	∪	∪	ADP
ejpam-4583	126	7	[	[	X
ejpam-4583	126	8	9,∞	9,∞	NUM
ejpam-4583	126	9	)	)	PUNCT
ejpam-4583	126	10	∪	∪	ADP
ejpam-4583	126	11	{	{	PUNCT
ejpam-4583	126	12	5	5	NUM
ejpam-4583	126	13	}	}	PUNCT
ejpam-4583	126	14	)	)	PUNCT
ejpam-4583	126	15	)	)	PUNCT
ejpam-4583	127	1	=	=	PUNCT
ejpam-4583	127	2	cl((−∞	cl((−∞	NOUN
ejpam-4583	127	3	,	,	PUNCT
ejpam-4583	127	4	2	2	NUM
ejpam-4583	127	5	)	)	PUNCT
ejpam-4583	127	6	∪	∪	NOUN
ejpam-4583	127	7	(	(	PUNCT
ejpam-4583	127	8	9,∞	9,∞	NUM
ejpam-4583	127	9	)	)	PUNCT
ejpam-4583	127	10	)	)	PUNCT
ejpam-4583	128	1	=	=	PUNCT
ejpam-4583	128	2	(	(	PUNCT
ejpam-4583	128	3	(	(	PUNCT
ejpam-4583	128	4	−∞	−∞	NOUN
ejpam-4583	128	5	,	,	PUNCT
ejpam-4583	128	6	2	2	NUM
ejpam-4583	128	7	]	]	PUNCT
ejpam-4583	128	8	∪	∪	ADP
ejpam-4583	128	9	[	[	X
ejpam-4583	128	10	9,∞	9,∞	NUM
ejpam-4583	128	11	)	)	PUNCT
ejpam-4583	128	12	)	)	PUNCT
ejpam-4583	129	1	̸=	̸=	PROPN
ejpam-4583	129	2	(	(	PUNCT
ejpam-4583	129	3	r	r	NOUN
ejpam-4583	129	4	\a	\a	NUM
ejpam-4583	129	5	)	)	PUNCT
ejpam-4583	129	6	.	.	PUNCT
ejpam-4583	130	1	now	now	ADV
ejpam-4583	130	2	,	,	PUNCT
ejpam-4583	130	3	there	there	PRON
ejpam-4583	130	4	is	be	VERB
ejpam-4583	130	5	an	an	DET
ejpam-4583	130	6	example	example	NOUN
ejpam-4583	130	7	of	of	ADP
ejpam-4583	130	8	an	an	DET
ejpam-4583	130	9	open	open	ADJ
ejpam-4583	130	10	domain	domain	NOUN
ejpam-4583	130	11	(	(	PUNCT
ejpam-4583	130	12	resp	resp	NOUN
ejpam-4583	130	13	.	.	PROPN
ejpam-4583	130	14	,	,	PUNCT
ejpam-4583	130	15	closed	closed	ADJ
ejpam-4583	130	16	domain	domain	NOUN
ejpam-4583	130	17	)	)	PUNCT
ejpam-4583	130	18	set	set	NOUN
ejpam-4583	130	19	which	which	PRON
ejpam-4583	130	20	is	be	AUX
ejpam-4583	130	21	not	not	PART
ejpam-4583	130	22	f	f	PROPN
ejpam-4583	130	23	-open	-open	NOUN
ejpam-4583	130	24	(	(	PUNCT
ejpam-4583	130	25	resp	resp	NOUN
ejpam-4583	130	26	.	.	PUNCT
ejpam-4583	130	27	,	,	PUNCT
ejpam-4583	130	28	f	f	PROPN
ejpam-4583	130	29	-closed	-close	VERB
ejpam-4583	130	30	)	)	PUNCT
ejpam-4583	130	31	set	set	NOUN
ejpam-4583	130	32	.	.	PUNCT
ejpam-4583	130	33	example	example	NOUN
ejpam-4583	131	1	5	5	NUM
ejpam-4583	131	2	.	.	X
ejpam-4583	132	1	let	let	AUX
ejpam-4583	132	2	(	(	PUNCT
ejpam-4583	132	3	r	r	NOUN
ejpam-4583	132	4	,	,	PUNCT
ejpam-4583	132	5	tz	tz	NOUN
ejpam-4583	132	6	)	)	PUNCT
ejpam-4583	132	7	be	be	VERB
ejpam-4583	132	8	the	the	DET
ejpam-4583	132	9	excluded	exclude	VERB
ejpam-4583	132	10	set	set	VERB
ejpam-4583	132	11	topological	topological	ADJ
ejpam-4583	132	12	space	space	NOUN
ejpam-4583	132	13	on	on	ADP
ejpam-4583	132	14	r	r	NOUN
ejpam-4583	132	15	by	by	ADP
ejpam-4583	132	16	z.	z.	PROPN
ejpam-4583	132	17	let	let	VERB
ejpam-4583	132	18	k	k	PROPN
ejpam-4583	132	19	=	=	PUNCT
ejpam-4583	132	20	(	(	PUNCT
ejpam-4583	132	21	0	0	NUM
ejpam-4583	132	22	,	,	PUNCT
ejpam-4583	132	23	1	1	NUM
ejpam-4583	132	24	)	)	PUNCT
ejpam-4583	132	25	,	,	PUNCT
ejpam-4583	132	26	then	then	ADV
ejpam-4583	132	27	k	k	PROPN
ejpam-4583	132	28	∈	∈	PROPN
ejpam-4583	132	29	tz	tz	NOUN
ejpam-4583	132	30	and	and	CCONJ
ejpam-4583	132	31	cl(k	cl(k	NOUN
ejpam-4583	132	32	)	)	PUNCT
ejpam-4583	132	33	\k	\k	X
ejpam-4583	133	1	=	=	SYM
ejpam-4583	133	2	(	(	PUNCT
ejpam-4583	133	3	(	(	PUNCT
ejpam-4583	133	4	0	0	NUM
ejpam-4583	133	5	,	,	PUNCT
ejpam-4583	133	6	1	1	NUM
ejpam-4583	133	7	)	)	PUNCT
ejpam-4583	133	8	∪	∪	ADP
ejpam-4583	133	9	z	z	NOUN
ejpam-4583	133	10	)	)	PUNCT
ejpam-4583	133	11	\	\	PUNCT
ejpam-4583	133	12	(	(	PUNCT
ejpam-4583	133	13	0	0	NUM
ejpam-4583	133	14	,	,	PUNCT
ejpam-4583	133	15	1	1	NUM
ejpam-4583	133	16	)	)	PUNCT
ejpam-4583	133	17	=	=	NOUN
ejpam-4583	133	18	z	z	NOUN
ejpam-4583	133	19	is	be	AUX
ejpam-4583	133	20	not	not	PART
ejpam-4583	133	21	finite	finite	ADJ
ejpam-4583	133	22	,	,	PUNCT
ejpam-4583	133	23	then	then	ADV
ejpam-4583	133	24	k	k	PROPN
ejpam-4583	133	25	is	be	AUX
ejpam-4583	133	26	not	not	PART
ejpam-4583	133	27	f	f	PROPN
ejpam-4583	133	28	-open	-open	NOUN
ejpam-4583	133	29	set	set	NOUN
ejpam-4583	133	30	.	.	PUNCT
ejpam-4583	134	1	but	but	CCONJ
ejpam-4583	134	2	k	k	PROPN
ejpam-4583	134	3	=	=	SYM
ejpam-4583	134	4	int(cl(k	int(cl(k	PROPN
ejpam-4583	134	5	)	)	PUNCT
ejpam-4583	134	6	)	)	PUNCT
ejpam-4583	135	1	=	=	PUNCT
ejpam-4583	135	2	int(cl(0	int(cl(0	PROPN
ejpam-4583	135	3	,	,	PUNCT
ejpam-4583	135	4	1	1	NUM
ejpam-4583	135	5	)	)	PUNCT
ejpam-4583	135	6	)	)	PUNCT
ejpam-4583	136	1	=	=	SYM
ejpam-4583	136	2	int((0	int((0	NOUN
ejpam-4583	136	3	,	,	PUNCT
ejpam-4583	136	4	1	1	X
ejpam-4583	136	5	)	)	PUNCT
ejpam-4583	136	6	∪	∪	ADP
ejpam-4583	136	7	z	z	NOUN
ejpam-4583	136	8	)	)	PUNCT
ejpam-4583	136	9	=	=	SYM
ejpam-4583	136	10	(	(	PUNCT
ejpam-4583	136	11	0	0	NUM
ejpam-4583	136	12	,	,	PUNCT
ejpam-4583	136	13	1	1	NUM
ejpam-4583	136	14	)	)	PUNCT
ejpam-4583	136	15	=	=	SYM
ejpam-4583	137	1	k	k	NOUN
ejpam-4583	137	2	,	,	PUNCT
ejpam-4583	137	3	then	then	ADV
ejpam-4583	137	4	k	k	PROPN
ejpam-4583	137	5	is	be	AUX
ejpam-4583	137	6	open	open	ADJ
ejpam-4583	137	7	domain	domain	NOUN
ejpam-4583	137	8	.	.	PUNCT
ejpam-4583	138	1	by	by	ADP
ejpam-4583	138	2	theorem	theorem	NOUN
ejpam-4583	138	3	1	1	NUM
ejpam-4583	138	4	,	,	PUNCT
ejpam-4583	138	5	the	the	DET
ejpam-4583	138	6	complement	complement	NOUN
ejpam-4583	138	7	of	of	ADP
ejpam-4583	138	8	f	f	PROPN
ejpam-4583	138	9	-closed	-close	VERB
ejpam-4583	138	10	set	set	NOUN
ejpam-4583	138	11	is	be	AUX
ejpam-4583	138	12	f	f	PROPN
ejpam-4583	138	13	-open	-open	NOUN
ejpam-4583	138	14	set	set	VERB
ejpam-4583	138	15	and	and	CCONJ
ejpam-4583	138	16	the	the	DET
ejpam-4583	138	17	complement	complement	NOUN
ejpam-4583	138	18	of	of	ADP
ejpam-4583	138	19	open	open	ADJ
ejpam-4583	138	20	domain	domain	NOUN
ejpam-4583	138	21	is	be	AUX
ejpam-4583	138	22	closed	closed	ADJ
ejpam-4583	138	23	domain	domain	NOUN
ejpam-4583	138	24	,	,	PUNCT
ejpam-4583	138	25	then	then	ADV
ejpam-4583	138	26	x	x	X
ejpam-4583	138	27	\k	\k	X
ejpam-4583	138	28	=	=	PUNCT
ejpam-4583	138	29	x	x	SYM
ejpam-4583	138	30	\	\	X
ejpam-4583	138	31	(	(	PUNCT
ejpam-4583	138	32	0	0	NUM
ejpam-4583	138	33	,	,	PUNCT
ejpam-4583	138	34	1	1	NUM
ejpam-4583	138	35	)	)	PUNCT
ejpam-4583	138	36	is	be	AUX
ejpam-4583	138	37	an	an	DET
ejpam-4583	138	38	example	example	NOUN
ejpam-4583	138	39	of	of	ADP
ejpam-4583	138	40	closed	closed	ADJ
ejpam-4583	138	41	domain	domain	NOUN
ejpam-4583	138	42	set	set	NOUN
ejpam-4583	138	43	which	which	PRON
ejpam-4583	138	44	is	be	AUX
ejpam-4583	138	45	not	not	PART
ejpam-4583	138	46	f	f	PROPN
ejpam-4583	138	47	-closed	-closed	PROPN
ejpam-4583	138	48	.	.	PUNCT
ejpam-4583	139	1	theorem	theorem	NOUN
ejpam-4583	139	2	2	2	NUM
ejpam-4583	139	3	.	.	PUNCT
ejpam-4583	140	1	let	let	AUX
ejpam-4583	140	2	(	(	PUNCT
ejpam-4583	140	3	x	x	X
ejpam-4583	140	4	,	,	PUNCT
ejpam-4583	140	5	t	t	PROPN
ejpam-4583	140	6	)	)	PUNCT
ejpam-4583	140	7	be	be	AUX
ejpam-4583	140	8	a	a	DET
ejpam-4583	140	9	topological	topological	ADJ
ejpam-4583	140	10	space	space	NOUN
ejpam-4583	140	11	,	,	PUNCT
ejpam-4583	140	12	then	then	ADV
ejpam-4583	140	13	i	i	PRON
ejpam-4583	140	14	)	)	PUNCT
ejpam-4583	140	15	finite	finite	VERB
ejpam-4583	140	16	union	union	NOUN
ejpam-4583	140	17	of	of	ADP
ejpam-4583	140	18	f	f	PROPN
ejpam-4583	140	19	-closed	-closed	ADJ
ejpam-4583	140	20	subsets	subset	NOUN
ejpam-4583	140	21	in	in	ADP
ejpam-4583	140	22	x	x	PRON
ejpam-4583	140	23	is	be	AUX
ejpam-4583	140	24	a	a	DET
ejpam-4583	140	25	f	f	PROPN
ejpam-4583	140	26	-closed	-closed	PROPN
ejpam-4583	140	27	;	;	PUNCT
ejpam-4583	140	28	ii	ii	X
ejpam-4583	140	29	)	)	PUNCT
ejpam-4583	140	30	finite	finite	PROPN
ejpam-4583	140	31	union	union	NOUN
ejpam-4583	140	32	of	of	ADP
ejpam-4583	140	33	f	f	PROPN
ejpam-4583	140	34	-open	-open	PROPN
ejpam-4583	140	35	subsets	subset	NOUN
ejpam-4583	140	36	in	in	ADP
ejpam-4583	140	37	x	x	PRON
ejpam-4583	140	38	is	be	AUX
ejpam-4583	140	39	a	a	DET
ejpam-4583	140	40	f	f	PROPN
ejpam-4583	140	41	-open	-open	NOUN
ejpam-4583	140	42	;	;	PUNCT
ejpam-4583	140	43	iii	iii	X
ejpam-4583	140	44	)	)	PUNCT
ejpam-4583	140	45	finite	finite	ADJ
ejpam-4583	140	46	intersection	intersection	NOUN
ejpam-4583	140	47	of	of	ADP
ejpam-4583	140	48	f	f	PROPN
ejpam-4583	140	49	-open	-open	PROPN
ejpam-4583	140	50	subsets	subset	NOUN
ejpam-4583	140	51	in	in	ADP
ejpam-4583	140	52	x	x	PRON
ejpam-4583	140	53	is	be	AUX
ejpam-4583	140	54	a	a	DET
ejpam-4583	140	55	f	f	PROPN
ejpam-4583	140	56	-open	-open	NOUN
ejpam-4583	140	57	;	;	PUNCT
ejpam-4583	140	58	iv	iv	X
ejpam-4583	140	59	)	)	PUNCT
ejpam-4583	140	60	finite	finite	ADJ
ejpam-4583	140	61	intersection	intersection	NOUN
ejpam-4583	140	62	of	of	ADP
ejpam-4583	140	63	f	f	PROPN
ejpam-4583	140	64	-closed	-closed	ADJ
ejpam-4583	140	65	subsets	subset	NOUN
ejpam-4583	140	66	in	in	ADP
ejpam-4583	140	67	x	x	PRON
ejpam-4583	140	68	is	be	AUX
ejpam-4583	140	69	a	a	DET
ejpam-4583	140	70	f	f	PROPN
ejpam-4583	140	71	-closed	-closed	PROPN
ejpam-4583	140	72	.	.	PUNCT
ejpam-4583	141	1	m.	m.	PROPN
ejpam-4583	141	2	h.	h.	PROPN
ejpam-4583	141	3	alqahtani	alqahtani	PROPN
ejpam-4583	141	4	/	/	SYM
ejpam-4583	141	5	eur	eur	PROPN
ejpam-4583	141	6	.	.	PUNCT
ejpam-4583	142	1	j.	j.	PROPN
ejpam-4583	142	2	pure	pure	PROPN
ejpam-4583	142	3	appl	appl	PROPN
ejpam-4583	142	4	.	.	PROPN
ejpam-4583	142	5	math	math	PROPN
ejpam-4583	142	6	,	,	PUNCT
ejpam-4583	142	7	16	16	NUM
ejpam-4583	142	8	(	(	PUNCT
ejpam-4583	142	9	2	2	NUM
ejpam-4583	142	10	)	)	PUNCT
ejpam-4583	142	11	(	(	PUNCT
ejpam-4583	142	12	2023	2023	NUM
ejpam-4583	142	13	)	)	PUNCT
ejpam-4583	142	14	,	,	PUNCT
ejpam-4583	142	15	819	819	NUM
ejpam-4583	142	16	-	-	SYM
ejpam-4583	142	17	832	832	NUM
ejpam-4583	142	18	823	823	NUM
ejpam-4583	142	19	proof	proof	NOUN
ejpam-4583	142	20	.	.	PUNCT
ejpam-4583	143	1	i	i	PRON
ejpam-4583	143	2	)	)	PUNCT
ejpam-4583	143	3	suppose	suppose	VERB
ejpam-4583	143	4	that	that	SCONJ
ejpam-4583	143	5	ki	ki	PROPN
ejpam-4583	143	6	be	be	AUX
ejpam-4583	143	7	f	f	PROPN
ejpam-4583	143	8	-closed	-close	VERB
ejpam-4583	143	9	set	set	NOUN
ejpam-4583	143	10	for	for	ADP
ejpam-4583	143	11	all	all	PRON
ejpam-4583	143	12	i	i	PRON
ejpam-4583	143	13	∈	∈	PROPN
ejpam-4583	143	14	{	{	PUNCT
ejpam-4583	143	15	1	1	NUM
ejpam-4583	143	16	,	,	PUNCT
ejpam-4583	143	17	2	2	NUM
ejpam-4583	143	18	,	,	PUNCT
ejpam-4583	143	19	3	3	NUM
ejpam-4583	143	20	,	,	PUNCT
ejpam-4583	143	21	.	.	PUNCT
ejpam-4583	143	22	.	.	PUNCT
ejpam-4583	144	1	.	.	PUNCT
ejpam-4583	145	1	,	,	PUNCT
ejpam-4583	145	2	n	n	CCONJ
ejpam-4583	145	3	}	}	PUNCT
ejpam-4583	145	4	,	,	PUNCT
ejpam-4583	145	5	then	then	ADV
ejpam-4583	145	6	ki	ki	PROPN
ejpam-4583	145	7	is	be	AUX
ejpam-4583	145	8	a	a	DET
ejpam-4583	145	9	closed	closed	ADJ
ejpam-4583	145	10	set	set	NOUN
ejpam-4583	145	11	and	and	CCONJ
ejpam-4583	145	12	ki	ki	PROPN
ejpam-4583	145	13	\	\	PROPN
ejpam-4583	145	14	int(ki	int(ki	PROPN
ejpam-4583	145	15	)	)	PUNCT
ejpam-4583	145	16	is	be	AUX
ejpam-4583	145	17	finite	finite	ADJ
ejpam-4583	145	18	for	for	ADP
ejpam-4583	145	19	all	all	DET
ejpam-4583	145	20	i.	i.	NOUN
ejpam-4583	145	21	since	since	SCONJ
ejpam-4583	145	22	⋃n	⋃n	PROPN
ejpam-4583	145	23	i=1ki	i=1ki	X
ejpam-4583	145	24	is	be	AUX
ejpam-4583	145	25	closed	closed	ADJ
ejpam-4583	145	26	,	,	PUNCT
ejpam-4583	145	27	then	then	ADV
ejpam-4583	145	28	we	we	PRON
ejpam-4583	145	29	need	need	VERB
ejpam-4583	145	30	to	to	PART
ejpam-4583	145	31	show	show	VERB
ejpam-4583	145	32	the	the	DET
ejpam-4583	145	33	other	other	ADJ
ejpam-4583	145	34	condition	condition	NOUN
ejpam-4583	145	35	of	of	ADP
ejpam-4583	145	36	f	f	PROPN
ejpam-4583	145	37	-closed	-close	VERB
ejpam-4583	145	38	set	set	NOUN
ejpam-4583	145	39	.	.	PUNCT
ejpam-4583	146	1	claim	claim	NOUN
ejpam-4583	146	2	:	:	PUNCT
ejpam-4583	146	3	n⋃	n⋃	PROPN
ejpam-4583	146	4	i=1	i=1	PROPN
ejpam-4583	146	5	ki	ki	PROPN
ejpam-4583	146	6	\	\	PROPN
ejpam-4583	146	7	int	int	PROPN
ejpam-4583	146	8	(	(	PUNCT
ejpam-4583	146	9	n⋃	n⋃	PROPN
ejpam-4583	146	10	i=1	i=1	PROPN
ejpam-4583	146	11	ki	ki	PROPN
ejpam-4583	146	12	)	)	PUNCT
ejpam-4583	147	1	⊆	⊆	NUM
ejpam-4583	147	2	n⋃	n⋃	NOUN
ejpam-4583	147	3	i=1	i=1	PROPN
ejpam-4583	148	1	(	(	PUNCT
ejpam-4583	148	2	ki	ki	PROPN
ejpam-4583	148	3	\	\	PROPN
ejpam-4583	148	4	int(ki	int(ki	PROPN
ejpam-4583	148	5	)	)	PUNCT
ejpam-4583	148	6	)	)	PUNCT
ejpam-4583	149	1	,	,	PUNCT
ejpam-4583	149	2	let	let	VERB
ejpam-4583	149	3	x	x	SYM
ejpam-4583	149	4	∈	∈	PROPN
ejpam-4583	149	5	⋃n	⋃n	PROPN
ejpam-4583	149	6	i=1ki	i=1ki	PROPN
ejpam-4583	149	7	\	\	PROPN
ejpam-4583	149	8	int	int	PROPN
ejpam-4583	149	9	(	(	PUNCT
ejpam-4583	149	10	⋃n	⋃n	PROPN
ejpam-4583	149	11	i=1ki	i=1ki	X
ejpam-4583	149	12	)	)	PUNCT
ejpam-4583	149	13	be	be	AUX
ejpam-4583	149	14	arbitrary	arbitrary	ADJ
ejpam-4583	149	15	.	.	PUNCT
ejpam-4583	150	1	since	since	SCONJ
ejpam-4583	150	2	⋃n	⋃n	PROPN
ejpam-4583	150	3	i=1	i=1	PROPN
ejpam-4583	150	4	int(ki	int(ki	ADV
ejpam-4583	150	5	)	)	PUNCT
ejpam-4583	150	6	⊆	⊆	NUM
ejpam-4583	150	7	int	int	NOUN
ejpam-4583	150	8	(	(	PUNCT
ejpam-4583	150	9	⋃n	⋃n	PROPN
ejpam-4583	150	10	i=1ki	i=1ki	X
ejpam-4583	150	11	)	)	PUNCT
ejpam-4583	150	12	,	,	PUNCT
ejpam-4583	150	13	then	then	ADV
ejpam-4583	150	14	there	there	PRON
ejpam-4583	150	15	exists	exist	VERB
ejpam-4583	150	16	i1	i1	PROPN
ejpam-4583	150	17	∈	∈	PROPN
ejpam-4583	150	18	{	{	PUNCT
ejpam-4583	150	19	1	1	NUM
ejpam-4583	150	20	,	,	PUNCT
ejpam-4583	150	21	2	2	NUM
ejpam-4583	150	22	,	,	PUNCT
ejpam-4583	150	23	3	3	NUM
ejpam-4583	150	24	,	,	PUNCT
ejpam-4583	150	25	.	.	PUNCT
ejpam-4583	150	26	.	.	PUNCT
ejpam-4583	151	1	.	.	PUNCT
ejpam-4583	152	1	,	,	PUNCT
ejpam-4583	153	1	n	n	CCONJ
ejpam-4583	153	2	}	}	PUNCT
ejpam-4583	153	3	such	such	ADJ
ejpam-4583	153	4	that	that	SCONJ
ejpam-4583	153	5	x	x	SYM
ejpam-4583	153	6	∈	∈	PROPN
ejpam-4583	153	7	ki1	ki1	NOUN
ejpam-4583	153	8	and	and	CCONJ
ejpam-4583	153	9	x	x	PROPN
ejpam-4583	153	10	/∈	/∈	PUNCT
ejpam-4583	153	11	int(ki	int(ki	ADJ
ejpam-4583	153	12	)	)	PUNCT
ejpam-4583	153	13	for	for	ADP
ejpam-4583	153	14	all	all	PRON
ejpam-4583	153	15	i	i	PRON
ejpam-4583	153	16	∈	∈	PROPN
ejpam-4583	153	17	{	{	PUNCT
ejpam-4583	153	18	1	1	NUM
ejpam-4583	153	19	,	,	PUNCT
ejpam-4583	153	20	2	2	NUM
ejpam-4583	153	21	,	,	PUNCT
ejpam-4583	153	22	3	3	NUM
ejpam-4583	153	23	,	,	PUNCT
ejpam-4583	153	24	.	.	PUNCT
ejpam-4583	153	25	.	.	PUNCT
ejpam-4583	154	1	.	.	PUNCT
ejpam-4583	154	2	,	,	PUNCT
ejpam-4583	154	3	n	n	CCONJ
ejpam-4583	154	4	}	}	PUNCT
ejpam-4583	154	5	.	.	PUNCT
ejpam-4583	155	1	then	then	ADV
ejpam-4583	155	2	x	x	X
ejpam-4583	155	3	∈	∈	PROPN
ejpam-4583	155	4	(	(	PUNCT
ejpam-4583	155	5	ki1	ki1	NOUN
ejpam-4583	155	6	)	)	PUNCT
ejpam-4583	155	7	\	\	NOUN
ejpam-4583	155	8	int(ki1	int(ki1	NUM
ejpam-4583	155	9	)	)	PUNCT
ejpam-4583	155	10	,	,	PUNCT
ejpam-4583	155	11	then	then	ADV
ejpam-4583	155	12	x	x	PROPN
ejpam-4583	155	13	∈	∈	PROPN
ejpam-4583	155	14	⋃n	⋃n	PROPN
ejpam-4583	155	15	i=1(ki	i=1(ki	NOUN
ejpam-4583	155	16	\	\	PROPN
ejpam-4583	155	17	int(ki	int(ki	NOUN
ejpam-4583	155	18	)	)	PUNCT
ejpam-4583	155	19	)	)	PUNCT
ejpam-4583	155	20	.	.	PUNCT
ejpam-4583	156	1	claim	claim	NOUN
ejpam-4583	156	2	is	be	AUX
ejpam-4583	156	3	proved	prove	VERB
ejpam-4583	156	4	.	.	PUNCT
ejpam-4583	157	1	since	since	SCONJ
ejpam-4583	157	2	the	the	DET
ejpam-4583	157	3	finite	finite	PROPN
ejpam-4583	157	4	union	union	PROPN
ejpam-4583	157	5	of	of	ADP
ejpam-4583	157	6	finite	finite	PROPN
ejpam-4583	157	7	sets	set	NOUN
ejpam-4583	157	8	is	be	AUX
ejpam-4583	157	9	finite	finite	ADJ
ejpam-4583	157	10	.	.	PUNCT
ejpam-4583	158	1	then	then	ADV
ejpam-4583	158	2	,	,	PUNCT
ejpam-4583	158	3	⋃n	⋃n	PROPN
ejpam-4583	158	4	i=1ki	i=1ki	PROPN
ejpam-4583	158	5	\	\	PROPN
ejpam-4583	158	6	int	int	PROPN
ejpam-4583	158	7	(	(	PUNCT
ejpam-4583	158	8	⋃n	⋃n	PROPN
ejpam-4583	158	9	i=1ki	i=1ki	X
ejpam-4583	158	10	)	)	PUNCT
ejpam-4583	158	11	is	be	AUX
ejpam-4583	158	12	finite	finite	PROPN
ejpam-4583	158	13	.	.	PUNCT
ejpam-4583	159	1	therefore	therefore	ADV
ejpam-4583	159	2	,	,	PUNCT
ejpam-4583	159	3	⋃n	⋃n	PROPN
ejpam-4583	159	4	i=1ki	i=1ki	X
ejpam-4583	159	5	is	be	AUX
ejpam-4583	159	6	f	f	PROPN
ejpam-4583	159	7	-closed	-closed	PROPN
ejpam-4583	159	8	.	.	PUNCT
ejpam-4583	159	9	ii	ii	PROPN
ejpam-4583	159	10	)	)	PUNCT
ejpam-4583	159	11	suppose	suppose	VERB
ejpam-4583	159	12	that	that	SCONJ
ejpam-4583	159	13	ki	ki	PROPN
ejpam-4583	159	14	be	be	AUX
ejpam-4583	159	15	f	f	PROPN
ejpam-4583	159	16	-open	-open	NOUN
ejpam-4583	159	17	set	set	VERB
ejpam-4583	159	18	for	for	ADP
ejpam-4583	159	19	all	all	PRON
ejpam-4583	159	20	i	i	PRON
ejpam-4583	159	21	∈	∈	PROPN
ejpam-4583	159	22	{	{	PUNCT
ejpam-4583	159	23	1	1	NUM
ejpam-4583	159	24	,	,	PUNCT
ejpam-4583	159	25	2	2	NUM
ejpam-4583	159	26	,	,	PUNCT
ejpam-4583	159	27	3	3	NUM
ejpam-4583	159	28	,	,	PUNCT
ejpam-4583	159	29	.	.	PUNCT
ejpam-4583	159	30	.	.	PUNCT
ejpam-4583	160	1	.	.	PUNCT
ejpam-4583	161	1	,	,	PUNCT
ejpam-4583	161	2	n	n	CCONJ
ejpam-4583	161	3	}	}	PUNCT
ejpam-4583	161	4	,	,	PUNCT
ejpam-4583	161	5	then	then	ADV
ejpam-4583	161	6	ki	ki	PROPN
ejpam-4583	161	7	is	be	AUX
ejpam-4583	161	8	an	an	DET
ejpam-4583	161	9	open	open	ADJ
ejpam-4583	161	10	set	set	NOUN
ejpam-4583	161	11	and	and	CCONJ
ejpam-4583	161	12	cl(ki	cl(ki	PROPN
ejpam-4583	161	13	)	)	PUNCT
ejpam-4583	161	14	\ki	\ki	NOUN
ejpam-4583	161	15	is	be	AUX
ejpam-4583	161	16	finite	finite	ADJ
ejpam-4583	161	17	for	for	ADP
ejpam-4583	161	18	all	all	DET
ejpam-4583	161	19	i.	i.	NOUN
ejpam-4583	161	20	since	since	SCONJ
ejpam-4583	161	21	⋃n	⋃n	PROPN
ejpam-4583	161	22	i=1ki	i=1ki	X
ejpam-4583	161	23	is	be	AUX
ejpam-4583	161	24	open	open	ADJ
ejpam-4583	161	25	,	,	PUNCT
ejpam-4583	161	26	then	then	ADV
ejpam-4583	161	27	we	we	PRON
ejpam-4583	161	28	need	need	VERB
ejpam-4583	161	29	to	to	PART
ejpam-4583	161	30	show	show	VERB
ejpam-4583	161	31	the	the	DET
ejpam-4583	161	32	other	other	ADJ
ejpam-4583	161	33	condition	condition	NOUN
ejpam-4583	161	34	of	of	ADP
ejpam-4583	161	35	f	f	PROPN
ejpam-4583	161	36	-open	-open	PROPN
ejpam-4583	161	37	set	set	NOUN
ejpam-4583	161	38	.	.	PUNCT
ejpam-4583	162	1	claim	claim	NOUN
ejpam-4583	162	2	:	:	PUNCT
ejpam-4583	162	3	cl	cl	NOUN
ejpam-4583	162	4	(	(	PUNCT
ejpam-4583	162	5	n⋃	n⋃	NOUN
ejpam-4583	162	6	i=1	i=1	PROPN
ejpam-4583	162	7	ki	ki	PROPN
ejpam-4583	162	8	)	)	PUNCT
ejpam-4583	162	9	\	\	PROPN
ejpam-4583	162	10	n⋃	n⋃	VERB
ejpam-4583	163	1	i=1	i=1	PROPN
ejpam-4583	163	2	ki	ki	PROPN
ejpam-4583	163	3	⊆	⊆	NUM
ejpam-4583	163	4	n⋃	n⋃	NOUN
ejpam-4583	163	5	i=1	i=1	PROPN
ejpam-4583	163	6	(	(	PUNCT
ejpam-4583	163	7	cl(ki	cl(ki	ADJ
ejpam-4583	163	8	)	)	PUNCT
ejpam-4583	163	9	\ki	\ki	NOUN
ejpam-4583	163	10	)	)	PUNCT
ejpam-4583	163	11	,	,	PUNCT
ejpam-4583	163	12	let	let	VERB
ejpam-4583	163	13	x	x	X
ejpam-4583	163	14	∈	∈	PROPN
ejpam-4583	163	15	cl	cl	NOUN
ejpam-4583	163	16	(	(	PUNCT
ejpam-4583	163	17	⋃n	⋃n	PROPN
ejpam-4583	163	18	i=1ki	i=1ki	X
ejpam-4583	163	19	)	)	PUNCT
ejpam-4583	163	20	\	\	PROPN
ejpam-4583	163	21	⋃n	⋃n	PROPN
ejpam-4583	163	22	i=1ki	i=1ki	X
ejpam-4583	163	23	be	be	AUX
ejpam-4583	163	24	arbitrary	arbitrary	ADJ
ejpam-4583	163	25	.	.	PUNCT
ejpam-4583	164	1	since	since	SCONJ
ejpam-4583	164	2	cl	cl	NOUN
ejpam-4583	164	3	(	(	PUNCT
ejpam-4583	164	4	⋃n	⋃n	PROPN
ejpam-4583	164	5	i=1ki	i=1ki	X
ejpam-4583	164	6	)	)	PUNCT
ejpam-4583	164	7	=	=	SYM
ejpam-4583	164	8	⋃n	⋃n	PROPN
ejpam-4583	164	9	i=1	i=1	X
ejpam-4583	164	10	cl(ki	cl(ki	PROPN
ejpam-4583	164	11	)	)	PUNCT
ejpam-4583	164	12	,	,	PUNCT
ejpam-4583	164	13	then	then	ADV
ejpam-4583	164	14	x	x	X
ejpam-4583	164	15	∈	∈	PROPN
ejpam-4583	164	16	⋃n	⋃n	PROPN
ejpam-4583	164	17	i=1	i=1	PROPN
ejpam-4583	164	18	cl(ki	cl(ki	PROPN
ejpam-4583	164	19	)	)	PUNCT
ejpam-4583	164	20	\	\	PROPN
ejpam-4583	164	21	⋃n	⋃n	PROPN
ejpam-4583	164	22	i=1ki	i=1ki	X
ejpam-4583	164	23	,	,	PUNCT
ejpam-4583	164	24	that	that	PRON
ejpam-4583	164	25	is	is	ADV
ejpam-4583	164	26	mean	mean	VERB
ejpam-4583	164	27	there	there	PRON
ejpam-4583	164	28	exist	exist	VERB
ejpam-4583	164	29	i1	i1	PROPN
ejpam-4583	164	30	∈	∈	PROPN
ejpam-4583	164	31	{	{	PUNCT
ejpam-4583	164	32	1	1	NUM
ejpam-4583	164	33	,	,	PUNCT
ejpam-4583	164	34	2	2	NUM
ejpam-4583	164	35	,	,	PUNCT
ejpam-4583	164	36	3	3	NUM
ejpam-4583	164	37	,	,	PUNCT
ejpam-4583	164	38	.	.	PUNCT
ejpam-4583	164	39	.	.	PUNCT
ejpam-4583	165	1	.	.	PUNCT
ejpam-4583	166	1	,	,	PUNCT
ejpam-4583	167	1	n	n	CCONJ
ejpam-4583	167	2	}	}	PUNCT
ejpam-4583	167	3	such	such	ADJ
ejpam-4583	167	4	that	that	SCONJ
ejpam-4583	167	5	x	x	SYM
ejpam-4583	167	6	∈	∈	PROPN
ejpam-4583	167	7	cl(ki1	cl(ki1	NUM
ejpam-4583	167	8	)	)	PUNCT
ejpam-4583	167	9	and	and	CCONJ
ejpam-4583	167	10	x	x	X
ejpam-4583	167	11	/∈	/∈	PROPN
ejpam-4583	167	12	ki	ki	PROPN
ejpam-4583	167	13	for	for	ADP
ejpam-4583	167	14	all	all	PRON
ejpam-4583	167	15	i	i	PRON
ejpam-4583	167	16	∈	∈	PROPN
ejpam-4583	167	17	{	{	PUNCT
ejpam-4583	167	18	1	1	NUM
ejpam-4583	167	19	,	,	PUNCT
ejpam-4583	167	20	2	2	NUM
ejpam-4583	167	21	,	,	PUNCT
ejpam-4583	167	22	3	3	NUM
ejpam-4583	167	23	,	,	PUNCT
ejpam-4583	167	24	.	.	PUNCT
ejpam-4583	167	25	.	.	PUNCT
ejpam-4583	167	26	.	.	PUNCT
ejpam-4583	167	27	,	,	PUNCT
ejpam-4583	167	28	n	n	CCONJ
ejpam-4583	167	29	}	}	PUNCT
ejpam-4583	167	30	.	.	PUNCT
ejpam-4583	168	1	then	then	ADV
ejpam-4583	168	2	x	x	X
ejpam-4583	168	3	∈	∈	PROPN
ejpam-4583	168	4	(	(	PUNCT
ejpam-4583	168	5	cl(ki1	cl(ki1	NOUN
ejpam-4583	168	6	)	)	PUNCT
ejpam-4583	168	7	\ki1	\ki1	NUM
ejpam-4583	168	8	)	)	PUNCT
ejpam-4583	168	9	,	,	PUNCT
ejpam-4583	168	10	so	so	ADV
ejpam-4583	168	11	thus	thus	ADV
ejpam-4583	168	12	x	x	X
ejpam-4583	168	13	∈	∈	PROPN
ejpam-4583	168	14	⋃n	⋃n	PROPN
ejpam-4583	168	15	i=1(cl(ki	i=1(cl(ki	PROPN
ejpam-4583	168	16	)	)	PUNCT
ejpam-4583	168	17	\ki	\ki	NOUN
ejpam-4583	168	18	)	)	PUNCT
ejpam-4583	168	19	.	.	PUNCT
ejpam-4583	169	1	claim	claim	NOUN
ejpam-4583	169	2	is	be	AUX
ejpam-4583	169	3	proved	prove	VERB
ejpam-4583	169	4	.	.	PUNCT
ejpam-4583	170	1	since	since	SCONJ
ejpam-4583	170	2	the	the	DET
ejpam-4583	170	3	finite	finite	PROPN
ejpam-4583	170	4	union	union	PROPN
ejpam-4583	170	5	of	of	ADP
ejpam-4583	170	6	finite	finite	PROPN
ejpam-4583	170	7	sets	set	NOUN
ejpam-4583	170	8	is	be	AUX
ejpam-4583	170	9	finite	finite	ADJ
ejpam-4583	170	10	.	.	PUNCT
ejpam-4583	171	1	then	then	ADV
ejpam-4583	171	2	,	,	PUNCT
ejpam-4583	171	3	cl	cl	INTJ
ejpam-4583	171	4	(	(	PUNCT
ejpam-4583	171	5	⋃n	⋃n	PROPN
ejpam-4583	171	6	i=1ki	i=1ki	X
ejpam-4583	171	7	)	)	PUNCT
ejpam-4583	171	8	\	\	PROPN
ejpam-4583	171	9	⋃n	⋃n	PROPN
ejpam-4583	171	10	i=1ki	i=1ki	X
ejpam-4583	171	11	is	be	AUX
ejpam-4583	171	12	finite	finite	ADJ
ejpam-4583	171	13	.	.	PUNCT
ejpam-4583	172	1	therefore	therefore	ADV
ejpam-4583	172	2	,	,	PUNCT
ejpam-4583	172	3	⋃n	⋃n	PROPN
ejpam-4583	172	4	i=1ki	i=1ki	X
ejpam-4583	172	5	is	be	AUX
ejpam-4583	172	6	f	f	PROPN
ejpam-4583	172	7	-open	-open	PROPN
ejpam-4583	172	8	.	.	PUNCT
ejpam-4583	172	9	iii	iii	X
ejpam-4583	172	10	)	)	PUNCT
ejpam-4583	172	11	suppose	suppose	VERB
ejpam-4583	172	12	that	that	SCONJ
ejpam-4583	172	13	ki	ki	PROPN
ejpam-4583	172	14	be	be	AUX
ejpam-4583	172	15	f	f	PROPN
ejpam-4583	172	16	-open	-open	NOUN
ejpam-4583	172	17	set	set	VERB
ejpam-4583	172	18	for	for	ADP
ejpam-4583	172	19	all	all	PRON
ejpam-4583	172	20	i	i	PRON
ejpam-4583	172	21	∈	∈	PROPN
ejpam-4583	172	22	{	{	PUNCT
ejpam-4583	172	23	1	1	NUM
ejpam-4583	172	24	,	,	PUNCT
ejpam-4583	172	25	2	2	NUM
ejpam-4583	172	26	,	,	PUNCT
ejpam-4583	172	27	3	3	NUM
ejpam-4583	172	28	,	,	PUNCT
ejpam-4583	172	29	.	.	PUNCT
ejpam-4583	172	30	.	.	PUNCT
ejpam-4583	173	1	.	.	PUNCT
ejpam-4583	174	1	,	,	PUNCT
ejpam-4583	174	2	n	n	CCONJ
ejpam-4583	174	3	}	}	PUNCT
ejpam-4583	174	4	,	,	PUNCT
ejpam-4583	174	5	then	then	ADV
ejpam-4583	174	6	⋂n	⋂n	VERB
ejpam-4583	174	7	i=1ki	i=1ki	PROPN
ejpam-4583	174	8	is	be	AUX
ejpam-4583	174	9	open	open	ADJ
ejpam-4583	174	10	and	and	CCONJ
ejpam-4583	174	11	by	by	ADP
ejpam-4583	174	12	morgan	morgan	PROPN
ejpam-4583	174	13	’s	’s	PART
ejpam-4583	174	14	laws	law	NOUN
ejpam-4583	174	15	,	,	PUNCT
ejpam-4583	174	16	theorem	theorem	VERB
ejpam-4583	174	17	1	1	NUM
ejpam-4583	174	18	and	and	CCONJ
ejpam-4583	174	19	theorem	theorem	VERB
ejpam-4583	174	20	2	2	NUM
ejpam-4583	174	21	part	part	NOUN
ejpam-4583	174	22	(	(	PUNCT
ejpam-4583	174	23	i	i	NOUN
ejpam-4583	174	24	)	)	PUNCT
ejpam-4583	174	25	we	we	PRON
ejpam-4583	174	26	have	have	VERB
ejpam-4583	174	27	⋂n	⋂n	PROPN
ejpam-4583	175	1	i=1ki	i=1ki	PROPN
ejpam-4583	175	2	is	be	AUX
ejpam-4583	175	3	f	f	PROPN
ejpam-4583	175	4	-open	-open	NOUN
ejpam-4583	175	5	,	,	PUNCT
ejpam-4583	175	6	because	because	SCONJ
ejpam-4583	175	7	x	x	NUM
ejpam-4583	175	8	\	\	PROPN
ejpam-4583	175	9	⋂n	⋂n	PROPN
ejpam-4583	175	10	i=1ki	i=1ki	PROPN
ejpam-4583	175	11	=	=	SYM
ejpam-4583	175	12	⋃n	⋃n	PROPN
ejpam-4583	175	13	i=1(x	i=1(x	PROPN
ejpam-4583	175	14	\ki	\ki	NOUN
ejpam-4583	175	15	)	)	PUNCT
ejpam-4583	175	16	is	be	AUX
ejpam-4583	175	17	f	f	PROPN
ejpam-4583	175	18	-closed	-close	VERB
ejpam-4583	175	19	set	set	NOUN
ejpam-4583	175	20	.	.	PUNCT
ejpam-4583	176	1	iv	iv	X
ejpam-4583	176	2	)	)	PUNCT
ejpam-4583	176	3	suppose	suppose	VERB
ejpam-4583	176	4	that	that	SCONJ
ejpam-4583	176	5	ki	ki	PROPN
ejpam-4583	176	6	be	be	AUX
ejpam-4583	176	7	f	f	PROPN
ejpam-4583	176	8	-closed	-close	VERB
ejpam-4583	176	9	set	set	NOUN
ejpam-4583	176	10	for	for	ADP
ejpam-4583	176	11	all	all	PRON
ejpam-4583	176	12	i	i	PRON
ejpam-4583	176	13	∈	∈	PROPN
ejpam-4583	176	14	{	{	PUNCT
ejpam-4583	176	15	1	1	NUM
ejpam-4583	176	16	,	,	PUNCT
ejpam-4583	176	17	2	2	NUM
ejpam-4583	176	18	,	,	PUNCT
ejpam-4583	176	19	3	3	NUM
ejpam-4583	176	20	,	,	PUNCT
ejpam-4583	176	21	.	.	PUNCT
ejpam-4583	176	22	.	.	PUNCT
ejpam-4583	177	1	.	.	PUNCT
ejpam-4583	178	1	,	,	PUNCT
ejpam-4583	178	2	n	n	CCONJ
ejpam-4583	178	3	}	}	PUNCT
ejpam-4583	178	4	,	,	PUNCT
ejpam-4583	178	5	then	then	ADV
ejpam-4583	178	6	⋂n	⋂n	VERB
ejpam-4583	178	7	i=1ki	i=1ki	PROPN
ejpam-4583	178	8	is	be	AUX
ejpam-4583	178	9	closed	close	VERB
ejpam-4583	178	10	and	and	CCONJ
ejpam-4583	178	11	by	by	ADP
ejpam-4583	178	12	morgan	morgan	PROPN
ejpam-4583	178	13	’s	’s	PART
ejpam-4583	178	14	laws	law	NOUN
ejpam-4583	178	15	,	,	PUNCT
ejpam-4583	178	16	theorem	theorem	VERB
ejpam-4583	178	17	1	1	NUM
ejpam-4583	178	18	and	and	CCONJ
ejpam-4583	178	19	theorem	theorem	VERB
ejpam-4583	178	20	2	2	NUM
ejpam-4583	178	21	part	part	NOUN
ejpam-4583	178	22	(	(	PUNCT
ejpam-4583	178	23	ii	ii	NOUN
ejpam-4583	178	24	)	)	PUNCT
ejpam-4583	178	25	we	we	PRON
ejpam-4583	178	26	have	have	VERB
ejpam-4583	178	27	⋂n	⋂n	PROPN
ejpam-4583	178	28	i=1ki	i=1ki	PROPN
ejpam-4583	178	29	is	be	AUX
ejpam-4583	178	30	f	f	PROPN
ejpam-4583	178	31	-closed	-close	VERB
ejpam-4583	178	32	,	,	PUNCT
ejpam-4583	178	33	because	because	SCONJ
ejpam-4583	178	34	x	x	NUM
ejpam-4583	178	35	\	\	PROPN
ejpam-4583	178	36	⋂n	⋂n	PROPN
ejpam-4583	178	37	i=1ki	i=1ki	PROPN
ejpam-4583	178	38	=	=	SYM
ejpam-4583	178	39	⋃n	⋃n	PROPN
ejpam-4583	178	40	i=1(x	i=1(x	PROPN
ejpam-4583	178	41	\ki	\ki	NOUN
ejpam-4583	178	42	)	)	PUNCT
ejpam-4583	178	43	is	be	AUX
ejpam-4583	178	44	f	f	PROPN
ejpam-4583	178	45	-open	-open	NOUN
ejpam-4583	178	46	set	set	NOUN
ejpam-4583	178	47	.	.	PUNCT
ejpam-4583	179	1	in	in	ADP
ejpam-4583	179	2	general	general	ADJ
ejpam-4583	179	3	,	,	PUNCT
ejpam-4583	179	4	countable	countable	ADJ
ejpam-4583	179	5	union	union	NOUN
ejpam-4583	179	6	of	of	ADP
ejpam-4583	179	7	f	f	PROPN
ejpam-4583	179	8	-open	-open	PROPN
ejpam-4583	179	9	sets	set	NOUN
ejpam-4583	179	10	may	may	AUX
ejpam-4583	179	11	not	not	PART
ejpam-4583	179	12	be	be	AUX
ejpam-4583	179	13	f	f	PROPN
ejpam-4583	179	14	-open	-open	NOUN
ejpam-4583	179	15	set	set	NOUN
ejpam-4583	179	16	.	.	PUNCT
ejpam-4583	179	17	example	example	NOUN
ejpam-4583	180	1	6	6	NUM
ejpam-4583	180	2	.	.	PUNCT
ejpam-4583	180	3	let	let	VERB
ejpam-4583	180	4	an	an	PRON
ejpam-4583	180	5	=	=	SYM
ejpam-4583	180	6	(	(	PUNCT
ejpam-4583	180	7	n	n	CCONJ
ejpam-4583	180	8	,	,	PUNCT
ejpam-4583	180	9	n+1	n+1	X
ejpam-4583	180	10	)	)	PUNCT
ejpam-4583	180	11	be	be	VERB
ejpam-4583	180	12	a	a	DET
ejpam-4583	180	13	subset	subset	NOUN
ejpam-4583	180	14	of	of	ADP
ejpam-4583	180	15	(	(	PUNCT
ejpam-4583	180	16	r	r	NOUN
ejpam-4583	180	17	,	,	PUNCT
ejpam-4583	180	18	u	u	NOUN
ejpam-4583	180	19	)	)	PUNCT
ejpam-4583	180	20	,	,	PUNCT
ejpam-4583	180	21	for	for	ADP
ejpam-4583	180	22	all	all	DET
ejpam-4583	180	23	n	n	PRON
ejpam-4583	180	24	∈	∈	PROPN
ejpam-4583	180	25	n	n	CCONJ
ejpam-4583	180	26	,	,	PUNCT
ejpam-4583	180	27	then	then	ADV
ejpam-4583	180	28	,	,	PUNCT
ejpam-4583	180	29	an	an	DET
ejpam-4583	180	30	=	=	X
ejpam-4583	180	31	(	(	PUNCT
ejpam-4583	180	32	n	n	CCONJ
ejpam-4583	180	33	,	,	PUNCT
ejpam-4583	180	34	n+1	n+1	NOUN
ejpam-4583	180	35	)	)	PUNCT
ejpam-4583	180	36	∈	∈	PROPN
ejpam-4583	180	37	u	u	NOUN
ejpam-4583	180	38	and	and	CCONJ
ejpam-4583	180	39	cl(n	cl(n	NOUN
ejpam-4583	180	40	,	,	PUNCT
ejpam-4583	180	41	n+1)\	n+1)\	PROPN
ejpam-4583	180	42	(	(	PUNCT
ejpam-4583	180	43	n	n	CCONJ
ejpam-4583	180	44	,	,	PUNCT
ejpam-4583	180	45	n+1	n+1	PROPN
ejpam-4583	180	46	)	)	PUNCT
ejpam-4583	180	47	=	=	SYM
ejpam-4583	180	48	{	{	PUNCT
ejpam-4583	180	49	n	n	CCONJ
ejpam-4583	180	50	,	,	PUNCT
ejpam-4583	180	51	n+1	n+1	VERB
ejpam-4583	180	52	}	}	PUNCT
ejpam-4583	180	53	is	be	AUX
ejpam-4583	180	54	finite	finite	ADJ
ejpam-4583	180	55	for	for	ADP
ejpam-4583	180	56	all	all	DET
ejpam-4583	180	57	n	n	DET
ejpam-4583	180	58	∈	∈	PROPN
ejpam-4583	180	59	n.	n.	NOUN
ejpam-4583	180	60	hence	hence	ADV
ejpam-4583	180	61	,	,	PUNCT
ejpam-4583	181	1	an	an	DET
ejpam-4583	181	2	=	=	X
ejpam-4583	181	3	(	(	PUNCT
ejpam-4583	181	4	n	n	CCONJ
ejpam-4583	181	5	,	,	PUNCT
ejpam-4583	181	6	n+1	n+1	PROPN
ejpam-4583	181	7	)	)	PUNCT
ejpam-4583	181	8	is	be	AUX
ejpam-4583	181	9	f−open	f−open	VERB
ejpam-4583	181	10	set	set	VERB
ejpam-4583	181	11	for	for	ADP
ejpam-4583	181	12	all	all	PRON
ejpam-4583	181	13	n	n	DET
ejpam-4583	181	14	∈	∈	PROPN
ejpam-4583	181	15	n.	n.	NOUN
ejpam-4583	181	16	we	we	PRON
ejpam-4583	181	17	have	have	VERB
ejpam-4583	181	18	⋃	⋃	PROPN
ejpam-4583	181	19	n∈n(n	n∈n(n	PROPN
ejpam-4583	181	20	,	,	PUNCT
ejpam-4583	181	21	n+1	n+1	PROPN
ejpam-4583	181	22	)	)	PUNCT
ejpam-4583	181	23	=	=	PUNCT
ejpam-4583	182	1	[	[	X
ejpam-4583	182	2	1,∞	1,∞	NUM
ejpam-4583	182	3	)	)	PUNCT
ejpam-4583	183	1	\n	\n	PUNCT
ejpam-4583	183	2	is	be	AUX
ejpam-4583	183	3	an	an	DET
ejpam-4583	183	4	open	open	ADJ
ejpam-4583	183	5	set	set	NOUN
ejpam-4583	183	6	.	.	PUNCT
ejpam-4583	184	1	however	however	ADV
ejpam-4583	184	2	,	,	PUNCT
ejpam-4583	184	3	cl	cl	INTJ
ejpam-4583	184	4	(	(	PUNCT
ejpam-4583	184	5	⋃	⋃	PROPN
ejpam-4583	184	6	n∈n(n	n∈n(n	NOUN
ejpam-4583	184	7	,	,	PUNCT
ejpam-4583	184	8	n+1))\	n+1))\	PROPN
ejpam-4583	184	9	⋃	⋃	NOUN
ejpam-4583	184	10	n∈n(n	n∈n(n	NOUN
ejpam-4583	184	11	,	,	PUNCT
ejpam-4583	184	12	n+1	n+1	NOUN
ejpam-4583	184	13	)	)	PUNCT
ejpam-4583	184	14	=	=	SYM
ejpam-4583	184	15	cl([1,∞)\n)\([1,∞)\n	cl([1,∞)\n)\([1,∞)\n	NOUN
ejpam-4583	184	16	)	)	PUNCT
ejpam-4583	184	17	=	=	PUNCT
ejpam-4583	185	1	[	[	X
ejpam-4583	185	2	1,∞)\([1,∞)\n	1,∞)\([1,∞)\n	NUM
ejpam-4583	185	3	)	)	PUNCT
ejpam-4583	185	4	=	=	PUNCT
ejpam-4583	186	1	n	n	CCONJ
ejpam-4583	186	2	is	be	AUX
ejpam-4583	186	3	not	not	PART
ejpam-4583	186	4	finite	finite	ADJ
ejpam-4583	186	5	set	set	NOUN
ejpam-4583	186	6	.	.	PUNCT
ejpam-4583	187	1	therefore	therefore	ADV
ejpam-4583	187	2	,	,	PUNCT
ejpam-4583	187	3	⋃	⋃	PUNCT
ejpam-4583	187	4	n∈n(n	n∈n(n	PROPN
ejpam-4583	187	5	,	,	PUNCT
ejpam-4583	187	6	n+	n+	NUM
ejpam-4583	187	7	1	1	NUM
ejpam-4583	187	8	)	)	PUNCT
ejpam-4583	187	9	is	be	AUX
ejpam-4583	187	10	not	not	PART
ejpam-4583	187	11	f	f	PROPN
ejpam-4583	187	12	-open	-open	NOUN
ejpam-4583	187	13	set	set	NOUN
ejpam-4583	187	14	.	.	PUNCT
ejpam-4583	188	1	m.	m.	PROPN
ejpam-4583	188	2	h.	h.	PROPN
ejpam-4583	188	3	alqahtani	alqahtani	PROPN
ejpam-4583	188	4	/	/	SYM
ejpam-4583	188	5	eur	eur	PROPN
ejpam-4583	188	6	.	.	PUNCT
ejpam-4583	189	1	j.	j.	PROPN
ejpam-4583	189	2	pure	pure	PROPN
ejpam-4583	189	3	appl	appl	PROPN
ejpam-4583	189	4	.	.	PROPN
ejpam-4583	189	5	math	math	PROPN
ejpam-4583	189	6	,	,	PUNCT
ejpam-4583	189	7	16	16	NUM
ejpam-4583	189	8	(	(	PUNCT
ejpam-4583	189	9	2	2	NUM
ejpam-4583	189	10	)	)	PUNCT
ejpam-4583	189	11	(	(	PUNCT
ejpam-4583	189	12	2023	2023	NUM
ejpam-4583	189	13	)	)	PUNCT
ejpam-4583	189	14	,	,	PUNCT
ejpam-4583	189	15	819	819	NUM
ejpam-4583	189	16	-	-	SYM
ejpam-4583	189	17	832	832	NUM
ejpam-4583	189	18	824	824	NUM
ejpam-4583	189	19	in	in	ADP
ejpam-4583	189	20	general	general	ADJ
ejpam-4583	189	21	countable	countable	ADJ
ejpam-4583	189	22	intersection	intersection	NOUN
ejpam-4583	189	23	of	of	ADP
ejpam-4583	189	24	f	f	PROPN
ejpam-4583	189	25	-closed	-close	VERB
ejpam-4583	189	26	sets	set	NOUN
ejpam-4583	189	27	may	may	AUX
ejpam-4583	189	28	not	not	PART
ejpam-4583	189	29	be	be	AUX
ejpam-4583	189	30	f	f	PROPN
ejpam-4583	189	31	-closed	-close	VERB
ejpam-4583	189	32	set	set	NOUN
ejpam-4583	189	33	.	.	PUNCT
ejpam-4583	189	34	example	example	NOUN
ejpam-4583	190	1	7	7	NUM
ejpam-4583	190	2	.	.	PUNCT
ejpam-4583	190	3	by	by	ADP
ejpam-4583	190	4	theorem	theorem	NOUN
ejpam-4583	190	5	1	1	NUM
ejpam-4583	190	6	and	and	CCONJ
ejpam-4583	190	7	example	example	NOUN
ejpam-4583	190	8	6	6	NUM
ejpam-4583	190	9	,	,	PUNCT
ejpam-4583	190	10	we	we	PRON
ejpam-4583	190	11	have	have	VERB
ejpam-4583	190	12	r	r	NOUN
ejpam-4583	190	13	\	\	NOUN
ejpam-4583	190	14	(	(	PUNCT
ejpam-4583	190	15	⋃	⋃	PUNCT
ejpam-4583	190	16	n∈n(n	n∈n(n	PROPN
ejpam-4583	190	17	,	,	PUNCT
ejpam-4583	190	18	n	n	PROPN
ejpam-4583	190	19	+	+	NOUN
ejpam-4583	190	20	1	1	NUM
ejpam-4583	190	21	)	)	PUNCT
ejpam-4583	190	22	)	)	PUNCT
ejpam-4583	191	1	=	=	SYM
ejpam-4583	191	2	⋂	⋂	PROPN
ejpam-4583	191	3	n∈n(r	n∈n(r	NOUN
ejpam-4583	191	4	\	\	PUNCT
ejpam-4583	191	5	(	(	PUNCT
ejpam-4583	191	6	n	n	X
ejpam-4583	191	7	,	,	PUNCT
ejpam-4583	191	8	n	n	PROPN
ejpam-4583	191	9	+	+	NOUN
ejpam-4583	191	10	1	1	NUM
ejpam-4583	191	11	)	)	PUNCT
ejpam-4583	191	12	)	)	PUNCT
ejpam-4583	191	13	is	be	AUX
ejpam-4583	191	14	countable	countable	ADJ
ejpam-4583	191	15	intersection	intersection	NOUN
ejpam-4583	191	16	of	of	ADP
ejpam-4583	191	17	f	f	PROPN
ejpam-4583	191	18	-closed	-close	VERB
ejpam-4583	191	19	sets	set	NOUN
ejpam-4583	191	20	which	which	PRON
ejpam-4583	191	21	is	be	AUX
ejpam-4583	191	22	not	not	PART
ejpam-4583	191	23	f	f	PROPN
ejpam-4583	191	24	-closed	-close	VERB
ejpam-4583	191	25	set	set	NOUN
ejpam-4583	191	26	or	or	CCONJ
ejpam-4583	191	27	v	v	NOUN
ejpam-4583	191	28	=	=	SYM
ejpam-4583	191	29	r	r	NOUN
ejpam-4583	191	30	\	\	NOUN
ejpam-4583	191	31	(	(	PUNCT
ejpam-4583	191	32	n	n	CCONJ
ejpam-4583	191	33	,	,	PUNCT
ejpam-4583	191	34	n+	n+	X
ejpam-4583	191	35	1	1	NUM
ejpam-4583	191	36	)	)	PUNCT
ejpam-4583	191	37	=	=	SYM
ejpam-4583	191	38	(	(	PUNCT
ejpam-4583	191	39	−∞	−∞	NOUN
ejpam-4583	191	40	,	,	PUNCT
ejpam-4583	191	41	n	n	CCONJ
ejpam-4583	191	42	]	]	PUNCT
ejpam-4583	191	43	∪	∪	X
ejpam-4583	191	44	[	[	X
ejpam-4583	191	45	n+	n+	NOUN
ejpam-4583	191	46	1,∞	1,∞	NUM
ejpam-4583	191	47	)	)	PUNCT
ejpam-4583	191	48	is	be	AUX
ejpam-4583	191	49	closed	close	VERB
ejpam-4583	191	50	for	for	ADP
ejpam-4583	191	51	all	all	PRON
ejpam-4583	191	52	n	n	PRON
ejpam-4583	191	53	∈	∈	NOUN
ejpam-4583	191	54	n	n	CCONJ
ejpam-4583	191	55	,	,	PUNCT
ejpam-4583	191	56	and	and	CCONJ
ejpam-4583	191	57	(	(	PUNCT
ejpam-4583	191	58	(	(	PUNCT
ejpam-4583	191	59	−∞	−∞	NOUN
ejpam-4583	191	60	,	,	PUNCT
ejpam-4583	191	61	n	n	CCONJ
ejpam-4583	191	62	]	]	PUNCT
ejpam-4583	191	63	∪	∪	X
ejpam-4583	191	64	[	[	X
ejpam-4583	191	65	n+	n+	NOUN
ejpam-4583	191	66	1,∞	1,∞	NUM
ejpam-4583	191	67	)	)	PUNCT
ejpam-4583	191	68	)	)	PUNCT
ejpam-4583	191	69	\	\	PROPN
ejpam-4583	192	1	int((−∞	int((−∞	PROPN
ejpam-4583	192	2	,	,	PUNCT
ejpam-4583	192	3	n]∪[n+1,∞	n]∪[n+1,∞	NOUN
ejpam-4583	192	4	)	)	PUNCT
ejpam-4583	192	5	)	)	PUNCT
ejpam-4583	193	1	=	=	PRON
ejpam-4583	193	2	{	{	PUNCT
ejpam-4583	193	3	n	n	CCONJ
ejpam-4583	193	4	,	,	PUNCT
ejpam-4583	193	5	n+1	n+1	VERB
ejpam-4583	193	6	}	}	PUNCT
ejpam-4583	193	7	is	be	AUX
ejpam-4583	193	8	finite	finite	NOUN
ejpam-4583	193	9	set	set	VERB
ejpam-4583	193	10	for	for	ADP
ejpam-4583	193	11	all	all	DET
ejpam-4583	193	12	n	n	PRON
ejpam-4583	193	13	∈	∈	PROPN
ejpam-4583	193	14	n.	n.	NOUN
ejpam-4583	193	15	then	then	ADV
ejpam-4583	193	16	v	v	NOUN
ejpam-4583	193	17	is	be	AUX
ejpam-4583	193	18	a	a	DET
ejpam-4583	193	19	f	f	NOUN
ejpam-4583	193	20	-closed	-close	VERB
ejpam-4583	193	21	set	set	NOUN
ejpam-4583	193	22	for	for	ADP
ejpam-4583	193	23	all	all	DET
ejpam-4583	193	24	n	n	DET
ejpam-4583	193	25	∈	∈	PROPN
ejpam-4583	193	26	n.	n.	NOUN
ejpam-4583	193	27	since	since	SCONJ
ejpam-4583	193	28	⋂	⋂	PROPN
ejpam-4583	193	29	n∈n((−∞	n∈n((−∞	NUM
ejpam-4583	193	30	,	,	PUNCT
ejpam-4583	193	31	n]∪	n]∪	PROPN
ejpam-4583	193	32	[	[	X
ejpam-4583	193	33	n+1,∞	n+1,∞	ADJ
ejpam-4583	193	34	)	)	PUNCT
ejpam-4583	193	35	)	)	PUNCT
ejpam-4583	194	1	=	=	SYM
ejpam-4583	194	2	(	(	PUNCT
ejpam-4583	194	3	−∞	−∞	NOUN
ejpam-4583	194	4	,	,	PUNCT
ejpam-4583	194	5	1)∪n	1)∪n	PRON
ejpam-4583	194	6	is	be	AUX
ejpam-4583	194	7	closed	closed	ADJ
ejpam-4583	194	8	,	,	PUNCT
ejpam-4583	194	9	then	then	ADV
ejpam-4583	194	10	we	we	PRON
ejpam-4583	194	11	need	need	VERB
ejpam-4583	194	12	to	to	PART
ejpam-4583	194	13	show	show	VERB
ejpam-4583	194	14	the	the	DET
ejpam-4583	194	15	other	other	ADJ
ejpam-4583	194	16	condition	condition	NOUN
ejpam-4583	194	17	of	of	ADP
ejpam-4583	194	18	f	f	PROPN
ejpam-4583	194	19	-closed	-close	VERB
ejpam-4583	194	20	set	set	NOUN
ejpam-4583	194	21	.	.	PUNCT
ejpam-4583	195	1	let	let	VERB
ejpam-4583	195	2	⋂	⋂	PROPN
ejpam-4583	195	3	n∈n((−∞	n∈n((−∞	NUM
ejpam-4583	195	4	,	,	PUNCT
ejpam-4583	195	5	n]∪	n]∪	PROPN
ejpam-4583	195	6	[	[	X
ejpam-4583	195	7	n+1,∞	n+1,∞	ADJ
ejpam-4583	195	8	)	)	PUNCT
ejpam-4583	195	9	)	)	PUNCT
ejpam-4583	196	1	\	\	PROPN
ejpam-4583	196	2	int	int	NOUN
ejpam-4583	196	3	(	(	PUNCT
ejpam-4583	196	4	⋂	⋂	PROPN
ejpam-4583	196	5	n∈n((−∞	n∈n((−∞	NUM
ejpam-4583	196	6	,	,	PUNCT
ejpam-4583	196	7	n]∪	n]∪	X
ejpam-4583	196	8	[	[	X
ejpam-4583	196	9	n	n	X
ejpam-4583	196	10	+	+	NOUN
ejpam-4583	196	11	1,∞	1,∞	NUM
ejpam-4583	196	12	)	)	PUNCT
ejpam-4583	196	13	)	)	PUNCT
ejpam-4583	196	14	)	)	PUNCT
ejpam-4583	197	1	=	=	PUNCT
ejpam-4583	197	2	(	(	PUNCT
ejpam-4583	197	3	(	(	PUNCT
ejpam-4583	197	4	−∞	−∞	NOUN
ejpam-4583	197	5	,	,	PUNCT
ejpam-4583	197	6	1	1	NUM
ejpam-4583	197	7	)	)	PUNCT
ejpam-4583	197	8	∪	∪	NOUN
ejpam-4583	197	9	n	n	CCONJ
ejpam-4583	197	10	)	)	PUNCT
ejpam-4583	197	11	\	\	PROPN
ejpam-4583	197	12	int((−∞	int((−∞	PROPN
ejpam-4583	197	13	,	,	PUNCT
ejpam-4583	197	14	1	1	NUM
ejpam-4583	197	15	)	)	PUNCT
ejpam-4583	197	16	∪	∪	NOUN
ejpam-4583	197	17	n	n	CCONJ
ejpam-4583	197	18	)	)	PUNCT
ejpam-4583	197	19	=	=	SYM
ejpam-4583	197	20	(	(	PUNCT
ejpam-4583	197	21	(	(	PUNCT
ejpam-4583	197	22	−∞	−∞	NOUN
ejpam-4583	197	23	,	,	PUNCT
ejpam-4583	197	24	1	1	NUM
ejpam-4583	197	25	)	)	PUNCT
ejpam-4583	197	26	∪	∪	ADP
ejpam-4583	197	27	n	n	CCONJ
ejpam-4583	197	28	)	)	PUNCT
ejpam-4583	197	29	\	\	NOUN
ejpam-4583	197	30	(	(	PUNCT
ejpam-4583	197	31	−∞	−∞	NOUN
ejpam-4583	197	32	,	,	PUNCT
ejpam-4583	197	33	1	1	NUM
ejpam-4583	197	34	)	)	PUNCT
ejpam-4583	197	35	=	=	PRON
ejpam-4583	198	1	n	n	PROPN
ejpam-4583	198	2	is	be	AUX
ejpam-4583	198	3	not	not	PART
ejpam-4583	198	4	finite	finite	ADJ
ejpam-4583	198	5	set	set	NOUN
ejpam-4583	198	6	.	.	PUNCT
ejpam-4583	199	1	therefore	therefore	ADV
ejpam-4583	199	2	,	,	PUNCT
ejpam-4583	199	3	⋂	⋂	PROPN
ejpam-4583	199	4	n∈n(r	n∈n(r	PROPN
ejpam-4583	199	5	\	\	PUNCT
ejpam-4583	199	6	(	(	PUNCT
ejpam-4583	199	7	n	n	CCONJ
ejpam-4583	199	8	,	,	PUNCT
ejpam-4583	199	9	n+	n+	X
ejpam-4583	199	10	1	1	NUM
ejpam-4583	199	11	)	)	PUNCT
ejpam-4583	199	12	)	)	PUNCT
ejpam-4583	199	13	is	be	AUX
ejpam-4583	199	14	not	not	PART
ejpam-4583	199	15	f	f	PROPN
ejpam-4583	199	16	-closed	-close	VERB
ejpam-4583	199	17	set	set	NOUN
ejpam-4583	199	18	.	.	PUNCT
ejpam-4583	200	1	in	in	ADP
ejpam-4583	200	2	general	general	ADJ
ejpam-4583	200	3	countable	countable	ADJ
ejpam-4583	200	4	union	union	NOUN
ejpam-4583	200	5	of	of	ADP
ejpam-4583	200	6	f	f	PROPN
ejpam-4583	200	7	-closed	-close	VERB
ejpam-4583	200	8	sets	set	NOUN
ejpam-4583	200	9	may	may	AUX
ejpam-4583	200	10	not	not	PART
ejpam-4583	200	11	be	be	AUX
ejpam-4583	200	12	f	f	PROPN
ejpam-4583	200	13	-closed	-close	VERB
ejpam-4583	200	14	set	set	NOUN
ejpam-4583	200	15	.	.	PUNCT
ejpam-4583	200	16	example	example	NOUN
ejpam-4583	201	1	8	8	NUM
ejpam-4583	201	2	.	.	PUNCT
ejpam-4583	202	1	let	let	VERB
ejpam-4583	202	2	kn	kn	PROPN
ejpam-4583	202	3	=	=	PUNCT
ejpam-4583	202	4	{	{	PUNCT
ejpam-4583	202	5	1	1	NUM
ejpam-4583	202	6	n	n	CCONJ
ejpam-4583	202	7	}	}	PUNCT
ejpam-4583	202	8	is	be	AUX
ejpam-4583	202	9	a	a	DET
ejpam-4583	202	10	f−closed	f−close	VERB
ejpam-4583	202	11	set	set	NOUN
ejpam-4583	202	12	in	in	ADP
ejpam-4583	202	13	(	(	PUNCT
ejpam-4583	202	14	r	r	NOUN
ejpam-4583	202	15	,	,	PUNCT
ejpam-4583	202	16	u	u	NOUN
ejpam-4583	202	17	)	)	PUNCT
ejpam-4583	202	18	for	for	ADP
ejpam-4583	202	19	all	all	PRON
ejpam-4583	202	20	n	n	PRON
ejpam-4583	202	21	∈	∈	NOUN
ejpam-4583	202	22	n	n	CCONJ
ejpam-4583	202	23	,	,	PUNCT
ejpam-4583	202	24	because	because	SCONJ
ejpam-4583	202	25	{	{	PUNCT
ejpam-4583	202	26	1	1	NUM
ejpam-4583	202	27	n	n	CCONJ
ejpam-4583	202	28	}	}	PUNCT
ejpam-4583	202	29	is	be	AUX
ejpam-4583	202	30	closed	close	VERB
ejpam-4583	202	31	for	for	ADP
ejpam-4583	202	32	all	all	PRON
ejpam-4583	202	33	n	n	PRON
ejpam-4583	202	34	∈	∈	NOUN
ejpam-4583	202	35	n	n	CCONJ
ejpam-4583	202	36	,	,	PUNCT
ejpam-4583	202	37	and	and	CCONJ
ejpam-4583	202	38	{	{	PUNCT
ejpam-4583	202	39	1	1	NUM
ejpam-4583	202	40	n	n	CCONJ
ejpam-4583	202	41	}	}	PUNCT
ejpam-4583	202	42	\	\	NOUN
ejpam-4583	202	43	int	int	NOUN
ejpam-4583	202	44	(	(	PUNCT
ejpam-4583	202	45	{	{	PUNCT
ejpam-4583	202	46	1	1	NUM
ejpam-4583	202	47	n	n	CCONJ
ejpam-4583	202	48	}	}	PUNCT
ejpam-4583	202	49	)	)	PUNCT
ejpam-4583	203	1	=	=	PRON
ejpam-4583	203	2	{	{	PUNCT
ejpam-4583	203	3	1	1	NUM
ejpam-4583	203	4	n	n	CCONJ
ejpam-4583	203	5	}	}	PUNCT
ejpam-4583	203	6	\	\	NOUN
ejpam-4583	203	7	∅	∅	NOUN
ejpam-4583	203	8	=	=	SYM
ejpam-4583	203	9	{	{	PUNCT
ejpam-4583	203	10	1	1	NUM
ejpam-4583	203	11	n	n	CCONJ
ejpam-4583	203	12	}	}	PUNCT
ejpam-4583	203	13	is	be	AUX
ejpam-4583	203	14	finite	finite	ADJ
ejpam-4583	203	15	for	for	ADP
ejpam-4583	203	16	all	all	DET
ejpam-4583	203	17	n	n	DET
ejpam-4583	203	18	∈	∈	PROPN
ejpam-4583	203	19	n.	n.	NOUN
ejpam-4583	203	20	however,⋃	however,⋃	PROPN
ejpam-4583	203	21	n∈n	n∈n	ADV
ejpam-4583	203	22	{	{	PUNCT
ejpam-4583	203	23	1	1	NUM
ejpam-4583	203	24	n	n	CCONJ
ejpam-4583	203	25	}	}	PUNCT
ejpam-4583	203	26	is	be	AUX
ejpam-4583	203	27	not	not	PART
ejpam-4583	203	28	a	a	DET
ejpam-4583	203	29	closed	closed	ADJ
ejpam-4583	203	30	set	set	NOUN
ejpam-4583	203	31	.	.	PUNCT
ejpam-4583	204	1	hence	hence	ADV
ejpam-4583	204	2	is	be	AUX
ejpam-4583	204	3	not	not	PART
ejpam-4583	204	4	a	a	DET
ejpam-4583	204	5	f	f	NOUN
ejpam-4583	204	6	-closed	-close	VERB
ejpam-4583	204	7	set	set	NOUN
ejpam-4583	204	8	.	.	PUNCT
ejpam-4583	205	1	in	in	ADP
ejpam-4583	205	2	general	general	ADJ
ejpam-4583	205	3	countable	countable	ADJ
ejpam-4583	205	4	intersection	intersection	NOUN
ejpam-4583	205	5	of	of	ADP
ejpam-4583	205	6	f	f	PROPN
ejpam-4583	205	7	-open	-open	PROPN
ejpam-4583	205	8	sets	set	NOUN
ejpam-4583	205	9	may	may	AUX
ejpam-4583	205	10	not	not	PART
ejpam-4583	205	11	be	be	AUX
ejpam-4583	205	12	f	f	PROPN
ejpam-4583	205	13	-open	-open	NOUN
ejpam-4583	205	14	set	set	NOUN
ejpam-4583	205	15	.	.	PUNCT
ejpam-4583	205	16	example	example	NOUN
ejpam-4583	206	1	9	9	NUM
ejpam-4583	206	2	.	.	X
ejpam-4583	207	1	we	we	PRON
ejpam-4583	207	2	have	have	VERB
ejpam-4583	207	3	(	(	PUNCT
ejpam-4583	207	4	−1	−1	NOUN
ejpam-4583	207	5	n	n	CCONJ
ejpam-4583	207	6	,	,	PUNCT
ejpam-4583	207	7	1	1	NUM
ejpam-4583	207	8	n	n	CCONJ
ejpam-4583	207	9	)	)	PUNCT
ejpam-4583	207	10	is	be	AUX
ejpam-4583	207	11	a	a	DET
ejpam-4583	207	12	f	f	PROPN
ejpam-4583	207	13	-open	-open	NOUN
ejpam-4583	207	14	set	set	VERB
ejpam-4583	207	15	in	in	ADP
ejpam-4583	207	16	(	(	PUNCT
ejpam-4583	207	17	r	r	NOUN
ejpam-4583	207	18	,	,	PUNCT
ejpam-4583	207	19	u	u	NOUN
ejpam-4583	207	20	)	)	PUNCT
ejpam-4583	207	21	for	for	ADP
ejpam-4583	207	22	all	all	DET
ejpam-4583	207	23	n	n	DET
ejpam-4583	207	24	∈	∈	PROPN
ejpam-4583	207	25	n.	n.	NOUN
ejpam-4583	207	26	but	but	CCONJ
ejpam-4583	207	27	⋂	⋂	PROPN
ejpam-4583	207	28	n∈n	n∈n	PROPN
ejpam-4583	207	29	(	(	PUNCT
ejpam-4583	207	30	−1	−1	NOUN
ejpam-4583	207	31	n	n	CCONJ
ejpam-4583	207	32	,	,	PUNCT
ejpam-4583	207	33	1	1	NUM
ejpam-4583	207	34	n	n	CCONJ
ejpam-4583	207	35	)	)	PUNCT
ejpam-4583	207	36	=	=	PRON
ejpam-4583	207	37	{	{	PUNCT
ejpam-4583	207	38	0	0	NUM
ejpam-4583	207	39	}	}	PUNCT
ejpam-4583	207	40	is	be	AUX
ejpam-4583	207	41	not	not	PART
ejpam-4583	207	42	open	open	ADJ
ejpam-4583	207	43	set	set	NOUN
ejpam-4583	207	44	,	,	PUNCT
ejpam-4583	207	45	then	then	ADV
ejpam-4583	207	46	is	be	AUX
ejpam-4583	207	47	not	not	PART
ejpam-4583	207	48	f	f	PROPN
ejpam-4583	207	49	-open	-open	NOUN
ejpam-4583	207	50	set	set	NOUN
ejpam-4583	207	51	.	.	PUNCT
ejpam-4583	208	1	4	4	X
ejpam-4583	208	2	.	.	X
ejpam-4583	209	1	some	some	DET
ejpam-4583	209	2	topological	topological	ADJ
ejpam-4583	209	3	properties	property	NOUN
ejpam-4583	209	4	definition	definition	NOUN
ejpam-4583	209	5	15	15	NUM
ejpam-4583	209	6	.	.	PUNCT
ejpam-4583	210	1	let	let	VERB
ejpam-4583	210	2	k	k	PRON
ejpam-4583	210	3	be	be	AUX
ejpam-4583	210	4	a	a	DET
ejpam-4583	210	5	subset	subset	NOUN
ejpam-4583	210	6	of	of	ADP
ejpam-4583	210	7	the	the	DET
ejpam-4583	210	8	topological	topological	ADJ
ejpam-4583	210	9	space	space	NOUN
ejpam-4583	210	10	(	(	PUNCT
ejpam-4583	210	11	x	x	X
ejpam-4583	210	12	,	,	PUNCT
ejpam-4583	210	13	t	t	PROPN
ejpam-4583	210	14	)	)	PUNCT
ejpam-4583	210	15	.	.	PUNCT
ejpam-4583	211	1	then	then	ADV
ejpam-4583	211	2	,	,	PUNCT
ejpam-4583	211	3	i	i	PROPN
ejpam-4583	211	4	)	)	PUNCT
ejpam-4583	211	5	the	the	DET
ejpam-4583	211	6	f	f	PROPN
ejpam-4583	211	7	-interior	-interior	NOUN
ejpam-4583	211	8	of	of	ADP
ejpam-4583	211	9	k	k	PROPN
ejpam-4583	211	10	is	be	AUX
ejpam-4583	211	11	defined	define	VERB
ejpam-4583	211	12	as	as	ADP
ejpam-4583	211	13	the	the	DET
ejpam-4583	211	14	union	union	NOUN
ejpam-4583	211	15	of	of	ADP
ejpam-4583	211	16	all	all	DET
ejpam-4583	211	17	f	f	PROPN
ejpam-4583	211	18	-open	-open	PROPN
ejpam-4583	211	19	subsets	subset	NOUN
ejpam-4583	211	20	of	of	ADP
ejpam-4583	211	21	k	k	PROPN
ejpam-4583	211	22	(	(	PUNCT
ejpam-4583	211	23	or	or	CCONJ
ejpam-4583	211	24	the	the	DET
ejpam-4583	211	25	largest	large	ADJ
ejpam-4583	211	26	f	f	NOUN
ejpam-4583	211	27	-open	-open	ADJ
ejpam-4583	211	28	set	set	NOUN
ejpam-4583	211	29	contained	contain	VERB
ejpam-4583	211	30	in	in	ADP
ejpam-4583	211	31	k	k	NOUN
ejpam-4583	211	32	)	)	PUNCT
ejpam-4583	211	33	and	and	CCONJ
ejpam-4583	211	34	is	be	AUX
ejpam-4583	211	35	denoted	denote	VERB
ejpam-4583	211	36	by	by	ADP
ejpam-4583	211	37	intf	intf	PROPN
ejpam-4583	211	38	(	(	PUNCT
ejpam-4583	211	39	k	k	NOUN
ejpam-4583	211	40	)	)	PUNCT
ejpam-4583	211	41	.	.	PUNCT
ejpam-4583	212	1	ii	ii	X
ejpam-4583	212	2	)	)	PUNCT
ejpam-4583	212	3	the	the	DET
ejpam-4583	212	4	f	f	PROPN
ejpam-4583	212	5	-clouser	-clouser	PROPN
ejpam-4583	212	6	of	of	ADP
ejpam-4583	212	7	k	k	PROPN
ejpam-4583	212	8	is	be	AUX
ejpam-4583	212	9	defined	define	VERB
ejpam-4583	212	10	as	as	ADP
ejpam-4583	212	11	the	the	DET
ejpam-4583	212	12	intersection	intersection	NOUN
ejpam-4583	212	13	of	of	ADP
ejpam-4583	212	14	all	all	DET
ejpam-4583	212	15	f	f	PROPN
ejpam-4583	212	16	-closed	-closed	ADJ
ejpam-4583	212	17	sets	set	NOUN
ejpam-4583	212	18	containing	contain	VERB
ejpam-4583	212	19	k	k	PROPN
ejpam-4583	212	20	,	,	PUNCT
ejpam-4583	212	21	and	and	CCONJ
ejpam-4583	212	22	is	be	AUX
ejpam-4583	212	23	denoted	denote	VERB
ejpam-4583	212	24	by	by	ADP
ejpam-4583	212	25	clf	clf	PROPN
ejpam-4583	212	26	(	(	PUNCT
ejpam-4583	212	27	k	k	NOUN
ejpam-4583	212	28	)	)	PUNCT
ejpam-4583	212	29	.	.	PUNCT
ejpam-4583	213	1	definition	definition	NOUN
ejpam-4583	213	2	16	16	NUM
ejpam-4583	213	3	.	.	PUNCT
ejpam-4583	214	1	let	let	VERB
ejpam-4583	214	2	x	x	SYM
ejpam-4583	214	3	∈	∈	PROPN
ejpam-4583	214	4	intf	intf	PROPN
ejpam-4583	214	5	(	(	PUNCT
ejpam-4583	214	6	k	k	NOUN
ejpam-4583	214	7	)	)	PUNCT
ejpam-4583	215	1	if	if	SCONJ
ejpam-4583	216	1	and	and	CCONJ
ejpam-4583	216	2	only	only	ADV
ejpam-4583	216	3	if	if	SCONJ
ejpam-4583	216	4	there	there	PRON
ejpam-4583	216	5	exist	exist	VERB
ejpam-4583	216	6	a	a	DET
ejpam-4583	216	7	f	f	NOUN
ejpam-4583	216	8	-open	-open	NOUN
ejpam-4583	216	9	set	set	VERB
ejpam-4583	216	10	u	u	PRON
ejpam-4583	216	11	such	such	ADJ
ejpam-4583	216	12	that	that	SCONJ
ejpam-4583	216	13	x	x	SYM
ejpam-4583	216	14	∈	∈	PROPN
ejpam-4583	216	15	u	u	NOUN
ejpam-4583	216	16	⊆	⊆	PROPN
ejpam-4583	216	17	k.	k.	NOUN
ejpam-4583	216	18	theorem	theorem	PROPN
ejpam-4583	216	19	3	3	X
ejpam-4583	216	20	.	.	PUNCT
ejpam-4583	217	1	let	let	VERB
ejpam-4583	217	2	k	k	PRON
ejpam-4583	217	3	be	be	AUX
ejpam-4583	217	4	a	a	DET
ejpam-4583	217	5	subset	subset	NOUN
ejpam-4583	217	6	of	of	ADP
ejpam-4583	217	7	the	the	DET
ejpam-4583	217	8	topological	topological	ADJ
ejpam-4583	217	9	space	space	NOUN
ejpam-4583	217	10	(	(	PUNCT
ejpam-4583	217	11	x	x	X
ejpam-4583	217	12	,	,	PUNCT
ejpam-4583	217	13	t	t	PROPN
ejpam-4583	217	14	)	)	PUNCT
ejpam-4583	217	15	.	.	PUNCT
ejpam-4583	218	1	then	then	ADV
ejpam-4583	218	2	,	,	PUNCT
ejpam-4583	218	3	i	i	PROPN
ejpam-4583	218	4	)	)	PUNCT
ejpam-4583	218	5	intf	intf	PROPN
ejpam-4583	218	6	(	(	PUNCT
ejpam-4583	218	7	k	k	NOUN
ejpam-4583	218	8	)	)	PUNCT
ejpam-4583	218	9	⊆	⊆	NUM
ejpam-4583	218	10	int(k	int(k	NUM
ejpam-4583	218	11	)	)	PUNCT
ejpam-4583	218	12	⊆	⊆	PROPN
ejpam-4583	218	13	k.	k.	PROPN
ejpam-4583	218	14	ii	ii	PROPN
ejpam-4583	218	15	)	)	PUNCT
ejpam-4583	219	1	k	k	PROPN
ejpam-4583	219	2	⊆	⊆	NUM
ejpam-4583	219	3	cl(k	cl(k	NUM
ejpam-4583	219	4	)	)	PUNCT
ejpam-4583	219	5	⊆	⊆	NUM
ejpam-4583	219	6	clf	clf	PROPN
ejpam-4583	219	7	(	(	PUNCT
ejpam-4583	219	8	k	k	NOUN
ejpam-4583	219	9	)	)	PUNCT
ejpam-4583	219	10	.	.	PUNCT
ejpam-4583	220	1	proof	proof	NOUN
ejpam-4583	220	2	.	.	PUNCT
ejpam-4583	221	1	i	i	PRON
ejpam-4583	221	2	)	)	PUNCT
ejpam-4583	221	3	let	let	VERB
ejpam-4583	221	4	x	x	X
ejpam-4583	221	5	∈	∈	PROPN
ejpam-4583	221	6	intf	intf	PROPN
ejpam-4583	221	7	(	(	PUNCT
ejpam-4583	221	8	k	k	NOUN
ejpam-4583	221	9	)	)	PUNCT
ejpam-4583	221	10	be	be	AUX
ejpam-4583	221	11	arbitrary	arbitrary	ADJ
ejpam-4583	221	12	,	,	PUNCT
ejpam-4583	221	13	then	then	ADV
ejpam-4583	221	14	there	there	PRON
ejpam-4583	221	15	exist	exist	VERB
ejpam-4583	221	16	a	a	DET
ejpam-4583	221	17	f	f	NOUN
ejpam-4583	221	18	-open	-open	NOUN
ejpam-4583	221	19	set	set	VERB
ejpam-4583	221	20	u	u	PRON
ejpam-4583	221	21	such	such	ADJ
ejpam-4583	221	22	that	that	SCONJ
ejpam-4583	221	23	x	x	SYM
ejpam-4583	221	24	∈	∈	PROPN
ejpam-4583	221	25	u	u	NOUN
ejpam-4583	221	26	⊆	⊆	NUM
ejpam-4583	221	27	k.	k.	NOUN
ejpam-4583	221	28	since	since	SCONJ
ejpam-4583	221	29	any	any	DET
ejpam-4583	221	30	f	f	PROPN
ejpam-4583	221	31	-open	-open	NOUN
ejpam-4583	221	32	set	set	NOUN
ejpam-4583	221	33	is	be	AUX
ejpam-4583	221	34	open	open	ADJ
ejpam-4583	221	35	,	,	PUNCT
ejpam-4583	221	36	then	then	ADV
ejpam-4583	221	37	x	x	PART
ejpam-4583	221	38	∈	∈	PROPN
ejpam-4583	221	39	int(k	int(k	PROPN
ejpam-4583	221	40	)	)	PUNCT
ejpam-4583	221	41	.	.	PUNCT
ejpam-4583	222	1	hence	hence	ADV
ejpam-4583	222	2	,	,	PUNCT
ejpam-4583	222	3	intf	intf	PROPN
ejpam-4583	222	4	(	(	PUNCT
ejpam-4583	222	5	k	k	NOUN
ejpam-4583	222	6	)	)	PUNCT
ejpam-4583	222	7	⊆	⊆	NUM
ejpam-4583	222	8	int(k	int(k	NUM
ejpam-4583	222	9	)	)	PUNCT
ejpam-4583	222	10	.	.	PUNCT
ejpam-4583	223	1	also	also	ADV
ejpam-4583	223	2	by	by	ADP
ejpam-4583	223	3	the	the	DET
ejpam-4583	223	4	interior	interior	ADJ
ejpam-4583	223	5	definition	definition	NOUN
ejpam-4583	223	6	ofk	ofk	NOUN
ejpam-4583	223	7	,	,	PUNCT
ejpam-4583	223	8	we	we	PRON
ejpam-4583	223	9	have	have	VERB
ejpam-4583	223	10	int(k	int(k	NOUN
ejpam-4583	223	11	)	)	PUNCT
ejpam-4583	223	12	⊆	⊆	NUM
ejpam-4583	223	13	k.	k.	NOUN
ejpam-4583	223	14	therefore	therefore	ADV
ejpam-4583	223	15	,	,	PUNCT
ejpam-4583	223	16	intf	intf	PROPN
ejpam-4583	223	17	(	(	PUNCT
ejpam-4583	223	18	k	k	NOUN
ejpam-4583	223	19	)	)	PUNCT
ejpam-4583	223	20	⊆	⊆	NUM
ejpam-4583	223	21	int(k	int(k	NUM
ejpam-4583	223	22	)	)	PUNCT
ejpam-4583	223	23	⊆	⊆	PROPN
ejpam-4583	223	24	k.	k.	PROPN
ejpam-4583	223	25	m.	m.	PROPN
ejpam-4583	223	26	h.	h.	PROPN
ejpam-4583	223	27	alqahtani	alqahtani	PROPN
ejpam-4583	223	28	/	/	SYM
ejpam-4583	223	29	eur	eur	PROPN
ejpam-4583	223	30	.	.	PUNCT
ejpam-4583	224	1	j.	j.	PROPN
ejpam-4583	224	2	pure	pure	PROPN
ejpam-4583	224	3	appl	appl	PROPN
ejpam-4583	224	4	.	.	PROPN
ejpam-4583	224	5	math	math	PROPN
ejpam-4583	224	6	,	,	PUNCT
ejpam-4583	224	7	16	16	NUM
ejpam-4583	224	8	(	(	PUNCT
ejpam-4583	224	9	2	2	NUM
ejpam-4583	224	10	)	)	PUNCT
ejpam-4583	224	11	(	(	PUNCT
ejpam-4583	224	12	2023	2023	NUM
ejpam-4583	224	13	)	)	PUNCT
ejpam-4583	224	14	,	,	PUNCT
ejpam-4583	224	15	819	819	NUM
ejpam-4583	224	16	-	-	SYM
ejpam-4583	224	17	832	832	NUM
ejpam-4583	224	18	825	825	NUM
ejpam-4583	224	19	ii	ii	NOUN
ejpam-4583	224	20	)	)	PUNCT
ejpam-4583	224	21	by	by	ADP
ejpam-4583	224	22	the	the	DET
ejpam-4583	224	23	closure	closure	NOUN
ejpam-4583	224	24	definition	definition	NOUN
ejpam-4583	225	1	,	,	PUNCT
ejpam-4583	225	2	we	we	PRON
ejpam-4583	225	3	have	have	VERB
ejpam-4583	225	4	k	k	NOUN
ejpam-4583	225	5	⊆	⊆	NUM
ejpam-4583	225	6	cl(k	cl(k	NOUN
ejpam-4583	225	7	)	)	PUNCT
ejpam-4583	225	8	.	.	PUNCT
ejpam-4583	226	1	let	let	VERB
ejpam-4583	226	2	cl(k	cl(k	PUNCT
ejpam-4583	226	3	)	)	PUNCT
ejpam-4583	227	1	=	=	PUNCT
ejpam-4583	227	2	f	f	X
ejpam-4583	227	3	be	be	AUX
ejpam-4583	227	4	the	the	DET
ejpam-4583	227	5	smallest	small	ADJ
ejpam-4583	227	6	closed	close	VERB
ejpam-4583	227	7	set	set	VERB
ejpam-4583	227	8	such	such	ADJ
ejpam-4583	227	9	that	that	SCONJ
ejpam-4583	227	10	k	k	PROPN
ejpam-4583	227	11	⊆	⊆	NUM
ejpam-4583	227	12	f.	f.	NOUN
ejpam-4583	227	13	since	since	SCONJ
ejpam-4583	227	14	any	any	DET
ejpam-4583	227	15	f	f	PROPN
ejpam-4583	227	16	-closed	-close	VERB
ejpam-4583	227	17	set	set	NOUN
ejpam-4583	227	18	is	be	AUX
ejpam-4583	227	19	closed	closed	ADJ
ejpam-4583	227	20	,	,	PUNCT
ejpam-4583	227	21	then	then	ADV
ejpam-4583	227	22	f	f	PROPN
ejpam-4583	227	23	⊆	⊆	NUM
ejpam-4583	227	24	clf	clf	PROPN
ejpam-4583	227	25	(	(	PUNCT
ejpam-4583	227	26	k	k	NOUN
ejpam-4583	227	27	)	)	PUNCT
ejpam-4583	227	28	.	.	PUNCT
ejpam-4583	228	1	therefore	therefore	ADV
ejpam-4583	228	2	,	,	PUNCT
ejpam-4583	228	3	k	k	PROPN
ejpam-4583	228	4	⊆	⊆	NUM
ejpam-4583	228	5	cl(k	cl(k	NUM
ejpam-4583	228	6	)	)	PUNCT
ejpam-4583	228	7	⊆	⊆	NUM
ejpam-4583	228	8	clf	clf	PROPN
ejpam-4583	228	9	(	(	PUNCT
ejpam-4583	228	10	k	k	NOUN
ejpam-4583	228	11	)	)	PUNCT
ejpam-4583	228	12	.	.	PUNCT
ejpam-4583	229	1	in	in	ADP
ejpam-4583	229	2	general	general	PROPN
ejpam-4583	229	3	int(k	int(k	PROPN
ejpam-4583	229	4	)	)	PUNCT
ejpam-4583	229	5	⊈	⊈	PROPN
ejpam-4583	229	6	intf	intf	NOUN
ejpam-4583	229	7	(	(	PUNCT
ejpam-4583	229	8	k	k	NOUN
ejpam-4583	229	9	)	)	PUNCT
ejpam-4583	229	10	and	and	CCONJ
ejpam-4583	229	11	clf	clf	PROPN
ejpam-4583	229	12	(	(	PUNCT
ejpam-4583	229	13	k	k	NOUN
ejpam-4583	229	14	)	)	PUNCT
ejpam-4583	229	15	⊈	⊈	PROPN
ejpam-4583	229	16	cl(k	cl(k	NOUN
ejpam-4583	229	17	)	)	PUNCT
ejpam-4583	229	18	.	.	PUNCT
ejpam-4583	230	1	for	for	ADP
ejpam-4583	230	2	example	example	NOUN
ejpam-4583	230	3	:	:	PUNCT
ejpam-4583	230	4	example	example	NOUN
ejpam-4583	230	5	10	10	NUM
ejpam-4583	230	6	.	.	PUNCT
ejpam-4583	231	1	let	let	VERB
ejpam-4583	231	2	k	k	NOUN
ejpam-4583	231	3	=	=	PUNCT
ejpam-4583	231	4	r	r	NOUN
ejpam-4583	231	5	\	\	NOUN
ejpam-4583	231	6	z	z	NOUN
ejpam-4583	231	7	be	be	VERB
ejpam-4583	231	8	a	a	DET
ejpam-4583	231	9	subset	subset	NOUN
ejpam-4583	231	10	of	of	ADP
ejpam-4583	231	11	the	the	DET
ejpam-4583	231	12	usual	usual	ADJ
ejpam-4583	231	13	topological	topological	ADJ
ejpam-4583	231	14	space	space	NOUN
ejpam-4583	231	15	(	(	PUNCT
ejpam-4583	231	16	r	r	NOUN
ejpam-4583	231	17	,	,	PUNCT
ejpam-4583	231	18	u	u	NOUN
ejpam-4583	231	19	)	)	PUNCT
ejpam-4583	231	20	.	.	PUNCT
ejpam-4583	232	1	then	then	ADV
ejpam-4583	232	2	int(k	int(k	X
ejpam-4583	232	3	)	)	PUNCT
ejpam-4583	232	4	=	=	SYM
ejpam-4583	232	5	r	r	NOUN
ejpam-4583	232	6	\	\	PROPN
ejpam-4583	232	7	z.	z.	PROPN
ejpam-4583	232	8	however	however	ADV
ejpam-4583	232	9	,	,	PUNCT
ejpam-4583	232	10	r	r	NOUN
ejpam-4583	232	11	\	\	PROPN
ejpam-4583	232	12	z	z	NOUN
ejpam-4583	232	13	is	be	AUX
ejpam-4583	232	14	not	not	PART
ejpam-4583	232	15	f	f	PROPN
ejpam-4583	232	16	-open	-open	NOUN
ejpam-4583	232	17	,	,	PUNCT
ejpam-4583	232	18	then	then	ADV
ejpam-4583	232	19	the	the	DET
ejpam-4583	232	20	largest	large	ADJ
ejpam-4583	232	21	f	f	X
ejpam-4583	232	22	-open	-open	NOUN
ejpam-4583	232	23	subset	subset	NOUN
ejpam-4583	232	24	of	of	ADP
ejpam-4583	232	25	r	r	NOUN
ejpam-4583	232	26	\	\	PROPN
ejpam-4583	232	27	z	z	NOUN
ejpam-4583	232	28	is	be	AUX
ejpam-4583	232	29	not	not	PART
ejpam-4583	232	30	equal	equal	ADJ
ejpam-4583	233	1	r	r	NOUN
ejpam-4583	233	2	\	\	PROPN
ejpam-4583	233	3	z.	z.	PROPN
ejpam-4583	233	4	therefore	therefore	ADV
ejpam-4583	233	5	,	,	PUNCT
ejpam-4583	233	6	int(k	int(k	PROPN
ejpam-4583	233	7	)	)	PUNCT
ejpam-4583	233	8	⊈	⊈	PROPN
ejpam-4583	233	9	intf	intf	NOUN
ejpam-4583	233	10	(	(	PUNCT
ejpam-4583	233	11	k	k	NOUN
ejpam-4583	233	12	)	)	PUNCT
ejpam-4583	233	13	.	.	PUNCT
ejpam-4583	234	1	let	let	VERB
ejpam-4583	234	2	h	h	NOUN
ejpam-4583	235	1	=	=	PUNCT
ejpam-4583	235	2	z	z	AUX
ejpam-4583	235	3	be	be	AUX
ejpam-4583	235	4	a	a	DET
ejpam-4583	235	5	subset	subset	NOUN
ejpam-4583	235	6	of	of	ADP
ejpam-4583	235	7	the	the	DET
ejpam-4583	235	8	usual	usual	ADJ
ejpam-4583	235	9	topological	topological	ADJ
ejpam-4583	235	10	space	space	NOUN
ejpam-4583	235	11	(	(	PUNCT
ejpam-4583	235	12	r	r	NOUN
ejpam-4583	235	13	,	,	PUNCT
ejpam-4583	235	14	u	u	NOUN
ejpam-4583	235	15	)	)	PUNCT
ejpam-4583	235	16	,	,	PUNCT
ejpam-4583	235	17	then	then	ADV
ejpam-4583	235	18	h	h	NOUN
ejpam-4583	236	1	=	=	PUNCT
ejpam-4583	236	2	z	z	NOUN
ejpam-4583	236	3	is	be	AUX
ejpam-4583	236	4	closed	close	VERB
ejpam-4583	236	5	in	in	ADP
ejpam-4583	236	6	(	(	PUNCT
ejpam-4583	236	7	r	r	NOUN
ejpam-4583	236	8	,	,	PUNCT
ejpam-4583	236	9	u	u	NOUN
ejpam-4583	236	10	)	)	PUNCT
ejpam-4583	236	11	,	,	PUNCT
ejpam-4583	236	12	so	so	ADV
ejpam-4583	236	13	thus	thus	ADV
ejpam-4583	236	14	cl(z	cl(z	NOUN
ejpam-4583	236	15	)	)	PUNCT
ejpam-4583	236	16	=	=	SYM
ejpam-4583	237	1	z.	z.	PROPN
ejpam-4583	237	2	however	however	ADV
ejpam-4583	237	3	,	,	PUNCT
ejpam-4583	237	4	z	z	PROPN
ejpam-4583	237	5	is	be	AUX
ejpam-4583	237	6	not	not	PART
ejpam-4583	237	7	f	f	PROPN
ejpam-4583	237	8	-closed	-closed	PROPN
ejpam-4583	237	9	,	,	PUNCT
ejpam-4583	237	10	then	then	ADV
ejpam-4583	237	11	z	z	PROPN
ejpam-4583	237	12	⊂	⊂	PROPN
ejpam-4583	237	13	clf	clf	PROPN
ejpam-4583	237	14	(	(	PUNCT
ejpam-4583	237	15	z	z	NOUN
ejpam-4583	237	16	)	)	PUNCT
ejpam-4583	237	17	.	.	PUNCT
ejpam-4583	238	1	therefore	therefore	ADV
ejpam-4583	238	2	,	,	PUNCT
ejpam-4583	238	3	clf	clf	PROPN
ejpam-4583	238	4	(	(	PUNCT
ejpam-4583	238	5	h	h	NOUN
ejpam-4583	238	6	)	)	PUNCT
ejpam-4583	238	7	⊈	⊈	PROPN
ejpam-4583	238	8	cl(h	cl(h	PRON
ejpam-4583	238	9	)	)	PUNCT
ejpam-4583	238	10	.	.	PUNCT
ejpam-4583	239	1	corollary	corollary	ADJ
ejpam-4583	239	2	1	1	NUM
ejpam-4583	239	3	.	.	PUNCT
ejpam-4583	240	1	if	if	SCONJ
ejpam-4583	240	2	u	u	NOUN
ejpam-4583	240	3	is	be	AUX
ejpam-4583	240	4	f	f	PROPN
ejpam-4583	240	5	-open	-open	NOUN
ejpam-4583	240	6	set	set	ADJ
ejpam-4583	240	7	and	and	CCONJ
ejpam-4583	240	8	u	u	NOUN
ejpam-4583	240	9	∩	∩	NOUN
ejpam-4583	240	10	v	v	NOUN
ejpam-4583	240	11	=	=	SYM
ejpam-4583	240	12	∅	∅	NOUN
ejpam-4583	240	13	,	,	PUNCT
ejpam-4583	240	14	then	then	ADV
ejpam-4583	240	15	u	u	PROPN
ejpam-4583	240	16	∩	∩	PROPN
ejpam-4583	240	17	clf	clf	PROPN
ejpam-4583	240	18	(	(	PUNCT
ejpam-4583	240	19	v	v	NOUN
ejpam-4583	240	20	)	)	PUNCT
ejpam-4583	240	21	=	=	PUNCT
ejpam-4583	240	22	∅.	∅.	NOUN
ejpam-4583	240	23	in	in	ADP
ejpam-4583	240	24	particular	particular	ADJ
ejpam-4583	240	25	,	,	PUNCT
ejpam-4583	240	26	if	if	SCONJ
ejpam-4583	240	27	u	u	NOUN
ejpam-4583	240	28	and	and	CCONJ
ejpam-4583	240	29	v	v	NOUN
ejpam-4583	240	30	are	be	AUX
ejpam-4583	240	31	disjoint	disjoint	NOUN
ejpam-4583	240	32	f	f	PROPN
ejpam-4583	240	33	-open	-open	PROPN
ejpam-4583	240	34	sets	set	NOUN
ejpam-4583	240	35	,	,	PUNCT
ejpam-4583	240	36	then	then	ADV
ejpam-4583	240	37	u	u	PROPN
ejpam-4583	240	38	∩	∩	PROPN
ejpam-4583	240	39	clf	clf	PROPN
ejpam-4583	240	40	(	(	PUNCT
ejpam-4583	240	41	v	v	NOUN
ejpam-4583	240	42	)	)	PUNCT
ejpam-4583	240	43	=	=	NOUN
ejpam-4583	240	44	∅	∅	NOUN
ejpam-4583	240	45	=	=	SYM
ejpam-4583	240	46	clf	clf	PROPN
ejpam-4583	240	47	(	(	PUNCT
ejpam-4583	240	48	u	u	NOUN
ejpam-4583	240	49	)	)	PUNCT
ejpam-4583	240	50	∩	∩	ADJ
ejpam-4583	240	51	v	v	NOUN
ejpam-4583	240	52	.	.	PUNCT
ejpam-4583	241	1	proof	proof	NOUN
ejpam-4583	241	2	.	.	PUNCT
ejpam-4583	242	1	since	since	SCONJ
ejpam-4583	242	2	u	u	NOUN
ejpam-4583	242	3	∩	∩	NOUN
ejpam-4583	242	4	v	v	NOUN
ejpam-4583	242	5	=	=	SYM
ejpam-4583	242	6	∅	∅	NOUN
ejpam-4583	242	7	,	,	PUNCT
ejpam-4583	242	8	then	then	ADV
ejpam-4583	242	9	v	v	VERB
ejpam-4583	242	10	⊆	⊆	NUM
ejpam-4583	242	11	x	x	SYM
ejpam-4583	242	12	\	\	PROPN
ejpam-4583	242	13	u	u	NOUN
ejpam-4583	242	14	,	,	PUNCT
ejpam-4583	242	15	so	so	ADV
ejpam-4583	242	16	thus	thus	ADV
ejpam-4583	242	17	clf	clf	PROPN
ejpam-4583	242	18	(	(	PUNCT
ejpam-4583	242	19	v	v	NOUN
ejpam-4583	242	20	)	)	PUNCT
ejpam-4583	242	21	⊆	⊆	NUM
ejpam-4583	242	22	clf	clf	PROPN
ejpam-4583	242	23	(	(	PUNCT
ejpam-4583	242	24	x	x	SYM
ejpam-4583	242	25	\	\	PROPN
ejpam-4583	242	26	u	u	NOUN
ejpam-4583	242	27	)	)	PUNCT
ejpam-4583	242	28	.	.	PUNCT
ejpam-4583	243	1	however	however	ADV
ejpam-4583	243	2	,	,	PUNCT
ejpam-4583	243	3	u	u	PROPN
ejpam-4583	243	4	is	be	AUX
ejpam-4583	243	5	f	f	PROPN
ejpam-4583	243	6	-open	-open	PROPN
ejpam-4583	243	7	,	,	PUNCT
ejpam-4583	243	8	then	then	ADV
ejpam-4583	243	9	x	x	SYM
ejpam-4583	243	10	\	\	PROPN
ejpam-4583	243	11	u	u	PROPN
ejpam-4583	243	12	is	be	AUX
ejpam-4583	243	13	f	f	PROPN
ejpam-4583	243	14	-closed	-closed	PROPN
ejpam-4583	243	15	.	.	PUNCT
ejpam-4583	244	1	hence	hence	ADV
ejpam-4583	244	2	,	,	PUNCT
ejpam-4583	244	3	x	x	SYM
ejpam-4583	244	4	\	\	PROPN
ejpam-4583	244	5	u	u	PROPN
ejpam-4583	244	6	=	=	PROPN
ejpam-4583	244	7	clf	clf	PROPN
ejpam-4583	244	8	(	(	PUNCT
ejpam-4583	244	9	x	x	SYM
ejpam-4583	244	10	\	\	PROPN
ejpam-4583	244	11	u	u	NOUN
ejpam-4583	244	12	)	)	PUNCT
ejpam-4583	244	13	,	,	PUNCT
ejpam-4583	244	14	so	so	ADV
ejpam-4583	244	15	thus	thus	ADV
ejpam-4583	244	16	clf	clf	PROPN
ejpam-4583	244	17	(	(	PUNCT
ejpam-4583	244	18	v	v	NOUN
ejpam-4583	244	19	)	)	PUNCT
ejpam-4583	244	20	⊆	⊆	NUM
ejpam-4583	244	21	x	x	SYM
ejpam-4583	244	22	\	\	PROPN
ejpam-4583	244	23	u.	u.	PROPN
ejpam-4583	244	24	therefore	therefore	ADV
ejpam-4583	244	25	,	,	PUNCT
ejpam-4583	244	26	u	u	PROPN
ejpam-4583	244	27	∩	∩	PROPN
ejpam-4583	244	28	clf	clf	PROPN
ejpam-4583	244	29	(	(	PUNCT
ejpam-4583	244	30	v	v	NOUN
ejpam-4583	244	31	)	)	PUNCT
ejpam-4583	244	32	=	=	PUNCT
ejpam-4583	244	33	∅.	∅.	PRON
ejpam-4583	244	34	definition	definition	NOUN
ejpam-4583	244	35	17	17	NUM
ejpam-4583	244	36	.	.	PUNCT
ejpam-4583	245	1	let	let	VERB
ejpam-4583	245	2	k	k	PRON
ejpam-4583	245	3	be	be	AUX
ejpam-4583	245	4	a	a	DET
ejpam-4583	245	5	subset	subset	NOUN
ejpam-4583	245	6	of	of	ADP
ejpam-4583	245	7	the	the	DET
ejpam-4583	245	8	topological	topological	ADJ
ejpam-4583	245	9	space	space	NOUN
ejpam-4583	245	10	(	(	PUNCT
ejpam-4583	245	11	x	x	X
ejpam-4583	245	12	,	,	PUNCT
ejpam-4583	245	13	t	t	PROPN
ejpam-4583	245	14	)	)	PUNCT
ejpam-4583	245	15	.	.	PUNCT
ejpam-4583	246	1	a	a	DET
ejpam-4583	246	2	point	point	NOUN
ejpam-4583	246	3	x	x	X
ejpam-4583	246	4	∈	∈	NOUN
ejpam-4583	246	5	x	x	PUNCT
ejpam-4583	246	6	is	be	AUX
ejpam-4583	246	7	said	say	VERB
ejpam-4583	246	8	to	to	PART
ejpam-4583	246	9	be	be	AUX
ejpam-4583	246	10	f	f	PROPN
ejpam-4583	246	11	-limit	-limit	PROPN
ejpam-4583	246	12	points	point	NOUN
ejpam-4583	246	13	(	(	PUNCT
ejpam-4583	246	14	or	or	CCONJ
ejpam-4583	246	15	an	an	DET
ejpam-4583	246	16	f	f	PROPN
ejpam-4583	246	17	-accumulation	-accumulation	NOUN
ejpam-4583	246	18	point	point	NOUN
ejpam-4583	246	19	,	,	PUNCT
ejpam-4583	246	20	or	or	CCONJ
ejpam-4583	246	21	a	a	DET
ejpam-4583	246	22	f	f	NOUN
ejpam-4583	246	23	-cluster	-cluster	NOUN
ejpam-4583	246	24	point	point	NOUN
ejpam-4583	246	25	)	)	PUNCT
ejpam-4583	246	26	of	of	ADP
ejpam-4583	246	27	k	k	PRON
ejpam-4583	246	28	if	if	SCONJ
ejpam-4583	247	1	and	and	CCONJ
ejpam-4583	247	2	only	only	ADV
ejpam-4583	247	3	if	if	SCONJ
ejpam-4583	247	4	for	for	ADP
ejpam-4583	247	5	any	any	DET
ejpam-4583	247	6	f	f	PROPN
ejpam-4583	247	7	-open	-open	NOUN
ejpam-4583	247	8	set	set	VERB
ejpam-4583	247	9	v	v	NOUN
ejpam-4583	247	10	containing	contain	VERB
ejpam-4583	247	11	x	x	X
ejpam-4583	247	12	,	,	PUNCT
ejpam-4583	247	13	we	we	PRON
ejpam-4583	247	14	have	have	VERB
ejpam-4583	247	15	(	(	PUNCT
ejpam-4583	247	16	v	v	NOUN
ejpam-4583	247	17	\	\	X
ejpam-4583	247	18	{	{	PUNCT
ejpam-4583	247	19	x	x	NOUN
ejpam-4583	247	20	}	}	PUNCT
ejpam-4583	247	21	)	)	PUNCT
ejpam-4583	247	22	∩k	∩k	PROPN
ejpam-4583	247	23	̸=	̸=	PROPN
ejpam-4583	247	24	∅.	∅.	ADP
ejpam-4583	247	25	the	the	DET
ejpam-4583	247	26	set	set	NOUN
ejpam-4583	247	27	of	of	ADP
ejpam-4583	247	28	all	all	DET
ejpam-4583	247	29	f	f	PROPN
ejpam-4583	247	30	-limit	-limit	PROPN
ejpam-4583	247	31	points	point	NOUN
ejpam-4583	247	32	of	of	ADP
ejpam-4583	247	33	k	k	PROPN
ejpam-4583	247	34	is	be	AUX
ejpam-4583	247	35	called	call	VERB
ejpam-4583	247	36	the	the	DET
ejpam-4583	247	37	f	f	PROPN
ejpam-4583	247	38	-derived	-derived	PROPN
ejpam-4583	247	39	set	set	PROPN
ejpam-4583	247	40	of	of	ADP
ejpam-4583	247	41	k	k	PROPN
ejpam-4583	247	42	and	and	CCONJ
ejpam-4583	247	43	denoted	denote	VERB
ejpam-4583	247	44	by	by	ADP
ejpam-4583	247	45	df	df	PROPN
ejpam-4583	247	46	(	(	PUNCT
ejpam-4583	247	47	k	k	NOUN
ejpam-4583	247	48	)	)	PUNCT
ejpam-4583	247	49	.	.	PUNCT
ejpam-4583	248	1	theorem	theorem	ADJ
ejpam-4583	248	2	4	4	NUM
ejpam-4583	248	3	.	.	PUNCT
ejpam-4583	249	1	let	let	VERB
ejpam-4583	249	2	k	k	NOUN
ejpam-4583	249	3	and	and	CCONJ
ejpam-4583	249	4	h	h	PROPN
ejpam-4583	249	5	be	be	VERB
ejpam-4583	249	6	subsets	subset	NOUN
ejpam-4583	249	7	of	of	ADP
ejpam-4583	249	8	a	a	DET
ejpam-4583	249	9	topological	topological	ADJ
ejpam-4583	249	10	space	space	NOUN
ejpam-4583	249	11	(	(	PUNCT
ejpam-4583	249	12	x	x	X
ejpam-4583	249	13	,	,	PUNCT
ejpam-4583	249	14	t	t	PROPN
ejpam-4583	249	15	)	)	PUNCT
ejpam-4583	249	16	.	.	PUNCT
ejpam-4583	250	1	then	then	ADV
ejpam-4583	250	2	we	we	PRON
ejpam-4583	250	3	have	have	VERB
ejpam-4583	250	4	the	the	DET
ejpam-4583	250	5	following	follow	VERB
ejpam-4583	250	6	properties	property	NOUN
ejpam-4583	250	7	:	:	PUNCT
ejpam-4583	250	8	(	(	PUNCT
ejpam-4583	250	9	i	i	NOUN
ejpam-4583	250	10	)	)	PUNCT
ejpam-4583	250	11	d(k	d(k	PROPN
ejpam-4583	250	12	)	)	PUNCT
ejpam-4583	251	1	⊂	⊂	PROPN
ejpam-4583	251	2	df	df	PROPN
ejpam-4583	251	3	(	(	PUNCT
ejpam-4583	251	4	k	k	NOUN
ejpam-4583	251	5	)	)	PUNCT
ejpam-4583	251	6	,	,	PUNCT
ejpam-4583	251	7	where	where	SCONJ
ejpam-4583	251	8	d(k	d(k	PROPN
ejpam-4583	251	9	)	)	PUNCT
ejpam-4583	251	10	is	be	AUX
ejpam-4583	251	11	the	the	DET
ejpam-4583	251	12	derived	derive	VERB
ejpam-4583	251	13	set	set	NOUN
ejpam-4583	251	14	of	of	ADP
ejpam-4583	251	15	k.	k.	PROPN
ejpam-4583	251	16	(	(	PUNCT
ejpam-4583	251	17	ii	ii	PROPN
ejpam-4583	251	18	)	)	PUNCT
ejpam-4583	251	19	if	if	SCONJ
ejpam-4583	251	20	k	k	PROPN
ejpam-4583	251	21	⊆	⊆	NUM
ejpam-4583	251	22	h	h	NOUN
ejpam-4583	251	23	,	,	PUNCT
ejpam-4583	251	24	then	then	ADV
ejpam-4583	251	25	df	df	PROPN
ejpam-4583	251	26	(	(	PUNCT
ejpam-4583	251	27	k	k	NOUN
ejpam-4583	251	28	)	)	PUNCT
ejpam-4583	251	29	⊆	⊆	NUM
ejpam-4583	251	30	df	df	NOUN
ejpam-4583	251	31	(	(	PUNCT
ejpam-4583	251	32	h	h	NOUN
ejpam-4583	251	33	)	)	PUNCT
ejpam-4583	251	34	.	.	PUNCT
ejpam-4583	252	1	(	(	PUNCT
ejpam-4583	252	2	iii	iii	X
ejpam-4583	252	3	)	)	PUNCT
ejpam-4583	252	4	df	df	NOUN
ejpam-4583	252	5	(	(	PUNCT
ejpam-4583	252	6	k	k	NOUN
ejpam-4583	252	7	)	)	PUNCT
ejpam-4583	252	8	∪df	∪df	NOUN
ejpam-4583	252	9	(	(	PUNCT
ejpam-4583	252	10	h	h	NOUN
ejpam-4583	252	11	)	)	PUNCT
ejpam-4583	252	12	=	=	SYM
ejpam-4583	252	13	df	df	PROPN
ejpam-4583	252	14	(	(	PUNCT
ejpam-4583	252	15	k	k	NOUN
ejpam-4583	252	16	∪h	∪h	NUM
ejpam-4583	252	17	)	)	PUNCT
ejpam-4583	252	18	and	and	CCONJ
ejpam-4583	252	19	df	df	PROPN
ejpam-4583	252	20	(	(	PUNCT
ejpam-4583	252	21	k	k	PROPN
ejpam-4583	252	22	∩h	∩h	PROPN
ejpam-4583	252	23	)	)	PUNCT
ejpam-4583	253	1	⊂	⊂	PROPN
ejpam-4583	253	2	df	df	PROPN
ejpam-4583	253	3	(	(	PUNCT
ejpam-4583	253	4	k	k	NOUN
ejpam-4583	253	5	)	)	PUNCT
ejpam-4583	253	6	∩df	∩df	NOUN
ejpam-4583	253	7	(	(	PUNCT
ejpam-4583	253	8	h	h	NOUN
ejpam-4583	253	9	)	)	PUNCT
ejpam-4583	253	10	.	.	PUNCT
ejpam-4583	254	1	proof	proof	NOUN
ejpam-4583	254	2	.	.	PUNCT
ejpam-4583	255	1	for	for	ADP
ejpam-4583	255	2	(	(	PUNCT
ejpam-4583	255	3	i	i	NOUN
ejpam-4583	255	4	)	)	PUNCT
ejpam-4583	255	5	it	it	PRON
ejpam-4583	255	6	suffices	suffice	VERB
ejpam-4583	255	7	to	to	PART
ejpam-4583	255	8	observe	observe	VERB
ejpam-4583	255	9	that	that	SCONJ
ejpam-4583	255	10	every	every	DET
ejpam-4583	255	11	f	f	PROPN
ejpam-4583	255	12	-open	-open	NOUN
ejpam-4583	255	13	is	be	AUX
ejpam-4583	255	14	open	open	ADJ
ejpam-4583	255	15	.	.	PUNCT
ejpam-4583	256	1	for	for	ADP
ejpam-4583	256	2	(	(	PUNCT
ejpam-4583	256	3	ii	ii	NOUN
ejpam-4583	256	4	)	)	PUNCT
ejpam-4583	256	5	follow	follow	VERB
ejpam-4583	256	6	from	from	ADP
ejpam-4583	256	7	definition	definition	NOUN
ejpam-4583	256	8	17	17	NUM
ejpam-4583	256	9	.	.	PUNCT
ejpam-4583	257	1	for	for	ADP
ejpam-4583	257	2	(	(	PUNCT
ejpam-4583	257	3	iii	iii	NOUN
ejpam-4583	257	4	)	)	PUNCT
ejpam-4583	257	5	is	be	AUX
ejpam-4583	257	6	a	a	DET
ejpam-4583	257	7	modification	modification	NOUN
ejpam-4583	257	8	of	of	ADP
ejpam-4583	257	9	the	the	DET
ejpam-4583	257	10	standard	standard	ADJ
ejpam-4583	257	11	proof	proof	NOUN
ejpam-4583	257	12	for	for	ADP
ejpam-4583	257	13	d.	d.	PROPN
ejpam-4583	257	14	in	in	ADP
ejpam-4583	257	15	general	general	ADJ
ejpam-4583	257	16	df	df	PROPN
ejpam-4583	257	17	(	(	PUNCT
ejpam-4583	257	18	k	k	NOUN
ejpam-4583	257	19	)	)	PUNCT
ejpam-4583	257	20	⊈	⊈	PROPN
ejpam-4583	258	1	d(k	d(k	PROPN
ejpam-4583	258	2	)	)	PUNCT
ejpam-4583	258	3	.	.	PUNCT
ejpam-4583	259	1	for	for	ADP
ejpam-4583	259	2	example	example	NOUN
ejpam-4583	259	3	:	:	PUNCT
ejpam-4583	259	4	example	example	NOUN
ejpam-4583	259	5	11	11	NUM
ejpam-4583	259	6	.	.	PUNCT
ejpam-4583	260	1	let	let	AUX
ejpam-4583	260	2	(	(	PUNCT
ejpam-4583	260	3	r	r	NOUN
ejpam-4583	260	4	,	,	PUNCT
ejpam-4583	260	5	t	t	NOUN
ejpam-4583	260	6	1	1	NUM
ejpam-4583	260	7	2	2	NUM
ejpam-4583	260	8	)	)	PUNCT
ejpam-4583	260	9	be	be	AUX
ejpam-4583	260	10	a	a	DET
ejpam-4583	260	11	topological	topological	ADJ
ejpam-4583	260	12	space	space	NOUN
ejpam-4583	260	13	,	,	PUNCT
ejpam-4583	260	14	where	where	SCONJ
ejpam-4583	260	15	t	t	PROPN
ejpam-4583	260	16	1	1	NUM
ejpam-4583	260	17	2	2	NUM
ejpam-4583	260	18	is	be	AUX
ejpam-4583	260	19	the	the	DET
ejpam-4583	260	20	particular	particular	ADJ
ejpam-4583	260	21	point	point	NOUN
ejpam-4583	260	22	topology	topology	NOUN
ejpam-4583	260	23	at	at	ADP
ejpam-4583	260	24	1	1	NUM
ejpam-4583	260	25	2	2	NUM
ejpam-4583	260	26	.	.	PUNCT
ejpam-4583	261	1	let	let	VERB
ejpam-4583	261	2	k	k	NOUN
ejpam-4583	261	3	=	=	SYM
ejpam-4583	261	4	z	z	PROPN
ejpam-4583	261	5	,	,	PUNCT
ejpam-4583	261	6	then	then	ADV
ejpam-4583	261	7	d(z	d(z	PROPN
ejpam-4583	261	8	)	)	PUNCT
ejpam-4583	262	1	=	=	SYM
ejpam-4583	262	2	∅	∅	NOUN
ejpam-4583	262	3	,	,	PUNCT
ejpam-4583	262	4	because	because	SCONJ
ejpam-4583	262	5	{	{	PUNCT
ejpam-4583	262	6	1	1	NUM
ejpam-4583	262	7	2	2	NUM
ejpam-4583	262	8	,	,	PUNCT
ejpam-4583	262	9	x	x	NOUN
ejpam-4583	262	10	}	}	PUNCT
ejpam-4583	262	11	for	for	ADP
ejpam-4583	262	12	any	any	DET
ejpam-4583	262	13	x	x	SYM
ejpam-4583	262	14	∈	∈	NOUN
ejpam-4583	262	15	r	r	NOUN
ejpam-4583	262	16	is	be	AUX
ejpam-4583	262	17	an	an	DET
ejpam-4583	262	18	open	open	ADJ
ejpam-4583	262	19	set	set	NOUN
ejpam-4583	262	20	containing	contain	VERB
ejpam-4583	262	21	x	x	PUNCT
ejpam-4583	262	22	and	and	CCONJ
ejpam-4583	262	23	(	(	PUNCT
ejpam-4583	262	24	{	{	PUNCT
ejpam-4583	262	25	1	1	NUM
ejpam-4583	262	26	2	2	NUM
ejpam-4583	262	27	,	,	PUNCT
ejpam-4583	262	28	x	x	NOUN
ejpam-4583	262	29	}	}	PUNCT
ejpam-4583	262	30	\	\	NOUN
ejpam-4583	262	31	{	{	PUNCT
ejpam-4583	262	32	x	x	NOUN
ejpam-4583	262	33	}	}	PUNCT
ejpam-4583	262	34	)	)	PUNCT
ejpam-4583	262	35	∩	∩	NOUN
ejpam-4583	262	36	z	z	NOUN
ejpam-4583	262	37	=	=	PUNCT
ejpam-4583	262	38	∅.	∅.	NOUN
ejpam-4583	262	39	let	let	VERB
ejpam-4583	262	40	v	v	PART
ejpam-4583	262	41	be	be	AUX
ejpam-4583	262	42	any	any	DET
ejpam-4583	262	43	f	f	PROPN
ejpam-4583	262	44	-open	-open	NOUN
ejpam-4583	262	45	subset	subset	NOUN
ejpam-4583	262	46	of	of	ADP
ejpam-4583	262	47	r	r	NOUN
ejpam-4583	262	48	,	,	PUNCT
ejpam-4583	262	49	then	then	ADV
ejpam-4583	262	50	we	we	PRON
ejpam-4583	262	51	have	have	VERB
ejpam-4583	262	52	1	1	NUM
ejpam-4583	262	53	2	2	NUM
ejpam-4583	262	54	∈	∈	NOUN
ejpam-4583	262	55	v	v	NOUN
ejpam-4583	262	56	,	,	PUNCT
ejpam-4583	262	57	and	and	CCONJ
ejpam-4583	262	58	cl(v	cl(v	X
ejpam-4583	262	59	)	)	PUNCT
ejpam-4583	262	60	\	\	PROPN
ejpam-4583	262	61	v	v	NOUN
ejpam-4583	262	62	is	be	AUX
ejpam-4583	262	63	finite	finite	ADJ
ejpam-4583	262	64	.	.	PUNCT
ejpam-4583	263	1	hence	hence	ADV
ejpam-4583	263	2	,	,	PUNCT
ejpam-4583	263	3	v	v	NOUN
ejpam-4583	263	4	=	=	SYM
ejpam-4583	263	5	r	r	NOUN
ejpam-4583	263	6	\h	\h	NOUN
ejpam-4583	263	7	where	where	SCONJ
ejpam-4583	263	8	h	h	NOUN
ejpam-4583	263	9	is	be	AUX
ejpam-4583	263	10	finite	finite	ADJ
ejpam-4583	263	11	.	.	PUNCT
ejpam-4583	263	12	suppose	suppose	VERB
ejpam-4583	263	13	not	not	PART
ejpam-4583	263	14	,	,	PUNCT
ejpam-4583	263	15	h	h	NOUN
ejpam-4583	263	16	is	be	AUX
ejpam-4583	263	17	infinite	infinite	ADJ
ejpam-4583	263	18	,	,	PUNCT
ejpam-4583	263	19	then	then	ADV
ejpam-4583	263	20	cl(v	cl(v	X
ejpam-4583	263	21	)	)	PUNCT
ejpam-4583	263	22	\v	\v	PUNCT
ejpam-4583	264	1	=	=	SYM
ejpam-4583	264	2	r	r	NOUN
ejpam-4583	264	3	\r	\r	PUNCT
ejpam-4583	264	4	\h	\h	X
ejpam-4583	265	1	=	=	PUNCT
ejpam-4583	266	1	h	h	PROPN
ejpam-4583	266	2	is	be	AUX
ejpam-4583	266	3	infinite	infinite	ADJ
ejpam-4583	266	4	.	.	PUNCT
ejpam-4583	267	1	hence	hence	ADV
ejpam-4583	267	2	,	,	PUNCT
ejpam-4583	267	3	v	v	PRON
ejpam-4583	267	4	is	be	AUX
ejpam-4583	267	5	not	not	PART
ejpam-4583	267	6	f	f	PROPN
ejpam-4583	267	7	-open	-open	NOUN
ejpam-4583	267	8	set	set	NOUN
ejpam-4583	267	9	.	.	PUNCT
ejpam-4583	268	1	let	let	VERB
ejpam-4583	268	2	x	x	PUNCT
ejpam-4583	268	3	∈	∈	NOUN
ejpam-4583	268	4	r	r	NOUN
ejpam-4583	268	5	be	be	VERB
ejpam-4583	268	6	arbitrary	arbitrary	ADJ
ejpam-4583	268	7	,	,	PUNCT
ejpam-4583	268	8	then	then	ADV
ejpam-4583	268	9	for	for	ADP
ejpam-4583	268	10	any	any	DET
ejpam-4583	268	11	f	f	PROPN
ejpam-4583	268	12	-open	-open	NOUN
ejpam-4583	268	13	set	set	VERB
ejpam-4583	268	14	v	v	NOUN
ejpam-4583	268	15	containing	contain	VERB
ejpam-4583	268	16	x	x	PUNCT
ejpam-4583	268	17	we	we	PRON
ejpam-4583	268	18	have	have	VERB
ejpam-4583	268	19	v	v	NUM
ejpam-4583	268	20	∩	∩	NOUN
ejpam-4583	268	21	z	z	PROPN
ejpam-4583	268	22	̸=	̸=	PROPN
ejpam-4583	268	23	∅.	∅.	PRON
ejpam-4583	268	24	hence	hence	ADV
ejpam-4583	268	25	,	,	PUNCT
ejpam-4583	268	26	df	df	PROPN
ejpam-4583	268	27	(	(	PUNCT
ejpam-4583	268	28	z	z	NOUN
ejpam-4583	268	29	)	)	PUNCT
ejpam-4583	269	1	=	=	SYM
ejpam-4583	269	2	r	r	NOUN
ejpam-4583	269	3	,	,	PUNCT
ejpam-4583	269	4	so	so	ADV
ejpam-4583	269	5	thus	thus	ADV
ejpam-4583	269	6	df	df	X
ejpam-4583	269	7	(	(	PUNCT
ejpam-4583	269	8	z	z	NOUN
ejpam-4583	269	9	)	)	PUNCT
ejpam-4583	269	10	⊈	⊈	PROPN
ejpam-4583	269	11	d(z	d(z	PROPN
ejpam-4583	269	12	)	)	PUNCT
ejpam-4583	269	13	.	.	PUNCT
ejpam-4583	270	1	therefore	therefore	ADV
ejpam-4583	270	2	,	,	PUNCT
ejpam-4583	270	3	df	df	PROPN
ejpam-4583	270	4	(	(	PUNCT
ejpam-4583	270	5	k	k	NOUN
ejpam-4583	270	6	)	)	PUNCT
ejpam-4583	270	7	⊈	⊈	PROPN
ejpam-4583	270	8	d(k	d(k	PROPN
ejpam-4583	270	9	)	)	PUNCT
ejpam-4583	270	10	.	.	PUNCT
ejpam-4583	271	1	in	in	ADP
ejpam-4583	271	2	general	general	ADJ
ejpam-4583	271	3	df	df	PROPN
ejpam-4583	271	4	(	(	PUNCT
ejpam-4583	271	5	k	k	PROPN
ejpam-4583	271	6	∩h	∩h	PROPN
ejpam-4583	271	7	)	)	PUNCT
ejpam-4583	272	1	⊉	⊉	PROPN
ejpam-4583	272	2	df	df	PROPN
ejpam-4583	272	3	(	(	PUNCT
ejpam-4583	272	4	k	k	NOUN
ejpam-4583	272	5	)	)	PUNCT
ejpam-4583	272	6	∩df	∩df	NOUN
ejpam-4583	272	7	(	(	PUNCT
ejpam-4583	272	8	h	h	NOUN
ejpam-4583	272	9	)	)	PUNCT
ejpam-4583	272	10	.	.	PUNCT
ejpam-4583	273	1	for	for	ADP
ejpam-4583	273	2	example	example	NOUN
ejpam-4583	273	3	:	:	PUNCT
ejpam-4583	273	4	m.	m.	PROPN
ejpam-4583	273	5	h.	h.	PROPN
ejpam-4583	273	6	alqahtani	alqahtani	PROPN
ejpam-4583	273	7	/	/	SYM
ejpam-4583	273	8	eur	eur	PROPN
ejpam-4583	273	9	.	.	PUNCT
ejpam-4583	274	1	j.	j.	PROPN
ejpam-4583	274	2	pure	pure	PROPN
ejpam-4583	274	3	appl	appl	PROPN
ejpam-4583	274	4	.	.	PROPN
ejpam-4583	274	5	math	math	PROPN
ejpam-4583	274	6	,	,	PUNCT
ejpam-4583	274	7	16	16	NUM
ejpam-4583	274	8	(	(	PUNCT
ejpam-4583	274	9	2	2	NUM
ejpam-4583	274	10	)	)	PUNCT
ejpam-4583	274	11	(	(	PUNCT
ejpam-4583	274	12	2023	2023	NUM
ejpam-4583	274	13	)	)	PUNCT
ejpam-4583	274	14	,	,	PUNCT
ejpam-4583	274	15	819	819	NUM
ejpam-4583	274	16	-	-	SYM
ejpam-4583	274	17	832	832	NUM
ejpam-4583	274	18	826	826	NUM
ejpam-4583	274	19	example	example	NOUN
ejpam-4583	274	20	12	12	NUM
ejpam-4583	274	21	.	.	PUNCT
ejpam-4583	275	1	there	there	PRON
ejpam-4583	275	2	exists	exist	VERB
ejpam-4583	275	3	k	k	PROPN
ejpam-4583	275	4	=	=	PUNCT
ejpam-4583	275	5	(	(	PUNCT
ejpam-4583	275	6	1	1	NUM
ejpam-4583	275	7	,	,	PUNCT
ejpam-4583	275	8	2	2	NUM
ejpam-4583	275	9	)	)	PUNCT
ejpam-4583	275	10	and	and	CCONJ
ejpam-4583	275	11	h	h	NOUN
ejpam-4583	275	12	=	=	SYM
ejpam-4583	275	13	(	(	PUNCT
ejpam-4583	275	14	2	2	NUM
ejpam-4583	275	15	,	,	PUNCT
ejpam-4583	275	16	3	3	NUM
ejpam-4583	275	17	)	)	PUNCT
ejpam-4583	275	18	are	be	AUX
ejpam-4583	275	19	f	f	PROPN
ejpam-4583	275	20	-open	-open	PROPN
ejpam-4583	275	21	subsets	subset	NOUN
ejpam-4583	275	22	of	of	ADP
ejpam-4583	275	23	the	the	DET
ejpam-4583	275	24	usual	usual	ADJ
ejpam-4583	275	25	topological	topological	ADJ
ejpam-4583	275	26	space	space	NOUN
ejpam-4583	275	27	(	(	PUNCT
ejpam-4583	275	28	r	r	NOUN
ejpam-4583	275	29	,	,	PUNCT
ejpam-4583	275	30	u	u	NOUN
ejpam-4583	275	31	)	)	PUNCT
ejpam-4583	275	32	such	such	ADJ
ejpam-4583	275	33	that	that	DET
ejpam-4583	275	34	df	df	PROPN
ejpam-4583	275	35	(	(	PUNCT
ejpam-4583	275	36	k	k	X
ejpam-4583	275	37	∩	∩	ADJ
ejpam-4583	275	38	h	h	NOUN
ejpam-4583	275	39	)	)	PUNCT
ejpam-4583	276	1	=	=	SYM
ejpam-4583	276	2	df	df	NOUN
ejpam-4583	276	3	(	(	PUNCT
ejpam-4583	276	4	(	(	PUNCT
ejpam-4583	276	5	1	1	NUM
ejpam-4583	276	6	,	,	PUNCT
ejpam-4583	276	7	2	2	NUM
ejpam-4583	276	8	)	)	PUNCT
ejpam-4583	276	9	∩	∩	NOUN
ejpam-4583	276	10	(	(	PUNCT
ejpam-4583	276	11	2	2	NUM
ejpam-4583	276	12	,	,	PUNCT
ejpam-4583	276	13	3	3	NUM
ejpam-4583	276	14	)	)	PUNCT
ejpam-4583	276	15	)	)	PUNCT
ejpam-4583	277	1	=	=	SYM
ejpam-4583	277	2	df	df	NOUN
ejpam-4583	277	3	(	(	PUNCT
ejpam-4583	277	4	∅	∅	NOUN
ejpam-4583	277	5	)	)	PUNCT
ejpam-4583	277	6	=	=	NOUN
ejpam-4583	277	7	∅	∅	NOUN
ejpam-4583	277	8	and	and	CCONJ
ejpam-4583	277	9	df	df	PROPN
ejpam-4583	277	10	(	(	PUNCT
ejpam-4583	277	11	k)∩df	k)∩df	PROPN
ejpam-4583	277	12	(	(	PUNCT
ejpam-4583	277	13	h	h	NOUN
ejpam-4583	277	14	)	)	PUNCT
ejpam-4583	277	15	=	=	SYM
ejpam-4583	277	16	df	df	NOUN
ejpam-4583	277	17	(	(	PUNCT
ejpam-4583	277	18	(	(	PUNCT
ejpam-4583	277	19	1	1	NUM
ejpam-4583	277	20	,	,	PUNCT
ejpam-4583	277	21	2))∩df	2))∩df	NUM
ejpam-4583	277	22	(	(	PUNCT
ejpam-4583	277	23	(	(	PUNCT
ejpam-4583	277	24	2	2	NUM
ejpam-4583	277	25	,	,	PUNCT
ejpam-4583	277	26	3	3	NUM
ejpam-4583	277	27	)	)	PUNCT
ejpam-4583	277	28	)	)	PUNCT
ejpam-4583	277	29	=	=	PUNCT
ejpam-4583	278	1	[	[	X
ejpam-4583	278	2	1	1	NUM
ejpam-4583	278	3	,	,	PUNCT
ejpam-4583	278	4	2]∩	2]∩	NUM
ejpam-4583	278	5	[	[	X
ejpam-4583	278	6	2	2	NUM
ejpam-4583	278	7	,	,	PUNCT
ejpam-4583	278	8	3	3	NUM
ejpam-4583	278	9	]	]	PUNCT
ejpam-4583	278	10	=	=	PUNCT
ejpam-4583	278	11	{	{	PUNCT
ejpam-4583	278	12	2	2	NUM
ejpam-4583	278	13	}	}	PUNCT
ejpam-4583	278	14	.	.	PUNCT
ejpam-4583	279	1	therefore	therefore	ADV
ejpam-4583	279	2	,	,	PUNCT
ejpam-4583	279	3	df	df	PROPN
ejpam-4583	279	4	(	(	PUNCT
ejpam-4583	279	5	k∩h	k∩h	PROPN
ejpam-4583	279	6	)	)	PUNCT
ejpam-4583	279	7	⊉	⊉	PROPN
ejpam-4583	279	8	df	df	NOUN
ejpam-4583	279	9	(	(	PUNCT
ejpam-4583	279	10	k	k	NOUN
ejpam-4583	279	11	)	)	PUNCT
ejpam-4583	279	12	∩df	∩df	NOUN
ejpam-4583	279	13	(	(	PUNCT
ejpam-4583	279	14	h	h	NOUN
ejpam-4583	279	15	)	)	PUNCT
ejpam-4583	279	16	.	.	PUNCT
ejpam-4583	279	17	theorem	theorem	NOUN
ejpam-4583	279	18	5	5	NUM
ejpam-4583	279	19	.	.	PUNCT
ejpam-4583	280	1	let	let	VERB
ejpam-4583	280	2	k	k	NOUN
ejpam-4583	280	3	and	and	CCONJ
ejpam-4583	280	4	h	h	PROPN
ejpam-4583	280	5	be	be	VERB
ejpam-4583	280	6	subsets	subset	NOUN
ejpam-4583	280	7	of	of	ADP
ejpam-4583	280	8	a	a	DET
ejpam-4583	280	9	topological	topological	ADJ
ejpam-4583	280	10	space	space	NOUN
ejpam-4583	280	11	(	(	PUNCT
ejpam-4583	280	12	x	x	X
ejpam-4583	280	13	,	,	PUNCT
ejpam-4583	280	14	t	t	PROPN
ejpam-4583	280	15	)	)	PUNCT
ejpam-4583	280	16	.	.	PUNCT
ejpam-4583	281	1	then	then	ADV
ejpam-4583	281	2	we	we	PRON
ejpam-4583	281	3	have	have	VERB
ejpam-4583	281	4	the	the	DET
ejpam-4583	281	5	following	follow	VERB
ejpam-4583	281	6	properties	property	NOUN
ejpam-4583	281	7	:	:	PUNCT
ejpam-4583	281	8	(	(	PUNCT
ejpam-4583	281	9	i	i	NOUN
ejpam-4583	281	10	)	)	PUNCT
ejpam-4583	281	11	intf	intf	PROPN
ejpam-4583	281	12	(	(	PUNCT
ejpam-4583	281	13	x	x	NOUN
ejpam-4583	281	14	)	)	PUNCT
ejpam-4583	281	15	=	=	SYM
ejpam-4583	281	16	x.	x.	NOUN
ejpam-4583	281	17	(	(	PUNCT
ejpam-4583	281	18	ii	ii	PROPN
ejpam-4583	281	19	)	)	PUNCT
ejpam-4583	281	20	intf	intf	NOUN
ejpam-4583	281	21	(	(	PUNCT
ejpam-4583	281	22	k	k	NOUN
ejpam-4583	281	23	)	)	PUNCT
ejpam-4583	281	24	⊆	⊆	NUM
ejpam-4583	281	25	k.	k.	NOUN
ejpam-4583	281	26	(	(	PUNCT
ejpam-4583	281	27	iii	iii	NOUN
ejpam-4583	281	28	)	)	PUNCT
ejpam-4583	281	29	if	if	SCONJ
ejpam-4583	281	30	k	k	PROPN
ejpam-4583	281	31	⊆	⊆	NUM
ejpam-4583	281	32	h	h	NOUN
ejpam-4583	281	33	,	,	PUNCT
ejpam-4583	281	34	then	then	ADV
ejpam-4583	281	35	intf	intf	PROPN
ejpam-4583	281	36	(	(	PUNCT
ejpam-4583	281	37	k	k	NOUN
ejpam-4583	281	38	)	)	PUNCT
ejpam-4583	281	39	⊆	⊆	NUM
ejpam-4583	281	40	intf	intf	NOUN
ejpam-4583	281	41	(	(	PUNCT
ejpam-4583	281	42	h	h	NOUN
ejpam-4583	281	43	)	)	PUNCT
ejpam-4583	281	44	.	.	PUNCT
ejpam-4583	282	1	(	(	PUNCT
ejpam-4583	282	2	iv	iv	X
ejpam-4583	282	3	)	)	PUNCT
ejpam-4583	282	4	intf	intf	PROPN
ejpam-4583	282	5	(	(	PUNCT
ejpam-4583	282	6	intf	intf	PROPN
ejpam-4583	282	7	(	(	PUNCT
ejpam-4583	282	8	k	k	NOUN
ejpam-4583	282	9	)	)	PUNCT
ejpam-4583	282	10	)	)	PUNCT
ejpam-4583	283	1	=	=	SYM
ejpam-4583	283	2	intf	intf	X
ejpam-4583	283	3	(	(	PUNCT
ejpam-4583	283	4	k	k	NOUN
ejpam-4583	283	5	)	)	PUNCT
ejpam-4583	283	6	.	.	PUNCT
ejpam-4583	284	1	(	(	PUNCT
ejpam-4583	284	2	v	v	NOUN
ejpam-4583	284	3	)	)	PUNCT
ejpam-4583	284	4	intf	intf	NOUN
ejpam-4583	284	5	(	(	PUNCT
ejpam-4583	284	6	k	k	PROPN
ejpam-4583	284	7	∩h	∩h	PROPN
ejpam-4583	284	8	)	)	PUNCT
ejpam-4583	285	1	=	=	SYM
ejpam-4583	285	2	intf	intf	X
ejpam-4583	285	3	(	(	PUNCT
ejpam-4583	285	4	k	k	NOUN
ejpam-4583	285	5	)	)	PUNCT
ejpam-4583	285	6	∩	∩	ADJ
ejpam-4583	285	7	intf	intf	X
ejpam-4583	285	8	(	(	PUNCT
ejpam-4583	285	9	h	h	NOUN
ejpam-4583	285	10	)	)	PUNCT
ejpam-4583	285	11	.	.	PUNCT
ejpam-4583	286	1	(	(	PUNCT
ejpam-4583	286	2	vi	vi	NOUN
ejpam-4583	286	3	)	)	PUNCT
ejpam-4583	286	4	intf	intf	NOUN
ejpam-4583	286	5	(	(	PUNCT
ejpam-4583	286	6	k	k	NOUN
ejpam-4583	286	7	)	)	PUNCT
ejpam-4583	286	8	∪	∪	NOUN
ejpam-4583	286	9	intf	intf	PROPN
ejpam-4583	286	10	(	(	PUNCT
ejpam-4583	286	11	h	h	NOUN
ejpam-4583	286	12	)	)	PUNCT
ejpam-4583	286	13	⊆	⊆	NUM
ejpam-4583	286	14	intf	intf	NOUN
ejpam-4583	286	15	(	(	PUNCT
ejpam-4583	286	16	k	k	NOUN
ejpam-4583	286	17	∪h	∪h	NUM
ejpam-4583	286	18	)	)	PUNCT
ejpam-4583	286	19	.	.	PUNCT
ejpam-4583	287	1	proof	proof	NOUN
ejpam-4583	287	2	.	.	PUNCT
ejpam-4583	288	1	the	the	DET
ejpam-4583	288	2	properties	property	NOUN
ejpam-4583	288	3	(	(	PUNCT
ejpam-4583	288	4	i	i	NOUN
ejpam-4583	288	5	)	)	PUNCT
ejpam-4583	288	6	,	,	PUNCT
ejpam-4583	288	7	(	(	PUNCT
ejpam-4583	288	8	ii	ii	NOUN
ejpam-4583	288	9	)	)	PUNCT
ejpam-4583	288	10	,	,	PUNCT
ejpam-4583	288	11	(	(	PUNCT
ejpam-4583	288	12	iii	iii	NOUN
ejpam-4583	288	13	)	)	PUNCT
ejpam-4583	288	14	and	and	CCONJ
ejpam-4583	288	15	(	(	PUNCT
ejpam-4583	288	16	iv	iv	X
ejpam-4583	288	17	)	)	PUNCT
ejpam-4583	288	18	follow	follow	VERB
ejpam-4583	288	19	from	from	ADP
ejpam-4583	288	20	definitions	definition	NOUN
ejpam-4583	288	21	12	12	NUM
ejpam-4583	288	22	and	and	CCONJ
ejpam-4583	288	23	definition	definition	NOUN
ejpam-4583	288	24	15	15	NUM
ejpam-4583	288	25	.	.	PUNCT
ejpam-4583	288	26	to	to	PART
ejpam-4583	288	27	prove	prove	VERB
ejpam-4583	288	28	(	(	PUNCT
ejpam-4583	288	29	v	v	NOUN
ejpam-4583	288	30	)	)	PUNCT
ejpam-4583	288	31	,	,	PUNCT
ejpam-4583	288	32	by	by	ADP
ejpam-4583	288	33	property	property	NOUN
ejpam-4583	288	34	(	(	PUNCT
ejpam-4583	288	35	ii	ii	NOUN
ejpam-4583	288	36	)	)	PUNCT
ejpam-4583	288	37	we	we	PRON
ejpam-4583	288	38	have	have	VERB
ejpam-4583	288	39	intf	intf	X
ejpam-4583	288	40	(	(	PUNCT
ejpam-4583	288	41	k	k	NOUN
ejpam-4583	288	42	)	)	PUNCT
ejpam-4583	288	43	⊆	⊆	NUM
ejpam-4583	288	44	k	k	PROPN
ejpam-4583	288	45	and	and	CCONJ
ejpam-4583	288	46	intf	intf	PROPN
ejpam-4583	288	47	(	(	PUNCT
ejpam-4583	288	48	h	h	NOUN
ejpam-4583	288	49	)	)	PUNCT
ejpam-4583	288	50	⊆	⊆	NUM
ejpam-4583	288	51	h	h	NOUN
ejpam-4583	288	52	,	,	PUNCT
ejpam-4583	288	53	then	then	ADV
ejpam-4583	288	54	intf	intf	PROPN
ejpam-4583	288	55	(	(	PUNCT
ejpam-4583	288	56	k)∩	k)∩	PROPN
ejpam-4583	288	57	intf	intf	PROPN
ejpam-4583	288	58	(	(	PUNCT
ejpam-4583	288	59	h	h	NOUN
ejpam-4583	288	60	)	)	PUNCT
ejpam-4583	288	61	⊆	⊆	NUM
ejpam-4583	288	62	k	k	PROPN
ejpam-4583	288	63	∩h	∩h	PROPN
ejpam-4583	288	64	.	.	PUNCT
ejpam-4583	289	1	as	as	SCONJ
ejpam-4583	289	2	intf	intf	PROPN
ejpam-4583	289	3	(	(	PUNCT
ejpam-4583	289	4	k	k	NOUN
ejpam-4583	289	5	)	)	PUNCT
ejpam-4583	289	6	∩	∩	ADJ
ejpam-4583	289	7	intf	intf	X
ejpam-4583	289	8	(	(	PUNCT
ejpam-4583	289	9	h	h	NOUN
ejpam-4583	289	10	)	)	PUNCT
ejpam-4583	289	11	is	be	AUX
ejpam-4583	289	12	f	f	PROPN
ejpam-4583	289	13	-open	-open	PROPN
ejpam-4583	289	14	,	,	PUNCT
ejpam-4583	289	15	then	then	ADV
ejpam-4583	289	16	we	we	PRON
ejpam-4583	289	17	have	have	VERB
ejpam-4583	289	18	intf	intf	X
ejpam-4583	289	19	(	(	PUNCT
ejpam-4583	289	20	k	k	NOUN
ejpam-4583	289	21	)	)	PUNCT
ejpam-4583	289	22	∩	∩	ADJ
ejpam-4583	289	23	intf	intf	X
ejpam-4583	289	24	(	(	PUNCT
ejpam-4583	289	25	h	h	NOUN
ejpam-4583	289	26	)	)	PUNCT
ejpam-4583	289	27	⊆	⊆	NUM
ejpam-4583	289	28	intf	intf	NOUN
ejpam-4583	289	29	(	(	PUNCT
ejpam-4583	289	30	k∩h	k∩h	PROPN
ejpam-4583	289	31	)	)	PUNCT
ejpam-4583	289	32	,	,	PUNCT
ejpam-4583	289	33	because	because	SCONJ
ejpam-4583	289	34	intf	intf	PROPN
ejpam-4583	289	35	(	(	PUNCT
ejpam-4583	289	36	k)∩intf	k)∩intf	PROPN
ejpam-4583	289	37	(	(	PUNCT
ejpam-4583	289	38	h	h	NOUN
ejpam-4583	289	39	)	)	PUNCT
ejpam-4583	289	40	is	be	AUX
ejpam-4583	289	41	f	f	PROPN
ejpam-4583	289	42	-open	-open	PROPN
ejpam-4583	289	43	and	and	CCONJ
ejpam-4583	289	44	intf	intf	PROPN
ejpam-4583	289	45	(	(	PUNCT
ejpam-4583	289	46	k∩h	k∩h	PROPN
ejpam-4583	289	47	)	)	PUNCT
ejpam-4583	289	48	is	be	AUX
ejpam-4583	289	49	the	the	DET
ejpam-4583	289	50	largest	large	ADJ
ejpam-4583	289	51	f	f	NOUN
ejpam-4583	289	52	-open	-open	ADJ
ejpam-4583	289	53	set	set	NOUN
ejpam-4583	289	54	contained	contain	VERB
ejpam-4583	289	55	in	in	ADP
ejpam-4583	289	56	k	k	PROPN
ejpam-4583	289	57	∩h	∩h	PROPN
ejpam-4583	289	58	.	.	PUNCT
ejpam-4583	290	1	conversely	conversely	ADV
ejpam-4583	290	2	,	,	PUNCT
ejpam-4583	290	3	(	(	PUNCT
ejpam-4583	290	4	k	k	PROPN
ejpam-4583	290	5	∩h	∩h	PROPN
ejpam-4583	290	6	)	)	PUNCT
ejpam-4583	291	1	⊆	⊆	NUM
ejpam-4583	291	2	k	k	PROPN
ejpam-4583	291	3	and	and	CCONJ
ejpam-4583	291	4	(	(	PUNCT
ejpam-4583	291	5	k	k	PROPN
ejpam-4583	291	6	∩h	∩h	PROPN
ejpam-4583	291	7	)	)	PUNCT
ejpam-4583	291	8	⊆	⊆	NUM
ejpam-4583	291	9	h	h	NOUN
ejpam-4583	291	10	,	,	PUNCT
ejpam-4583	291	11	by	by	ADP
ejpam-4583	291	12	property	property	NOUN
ejpam-4583	291	13	(	(	PUNCT
ejpam-4583	291	14	iii	iii	X
ejpam-4583	291	15	)	)	PUNCT
ejpam-4583	291	16	we	we	PRON
ejpam-4583	291	17	have	have	VERB
ejpam-4583	291	18	intf	intf	X
ejpam-4583	291	19	(	(	PUNCT
ejpam-4583	291	20	k	k	X
ejpam-4583	291	21	∩	∩	ADJ
ejpam-4583	291	22	h	h	NOUN
ejpam-4583	291	23	)	)	PUNCT
ejpam-4583	291	24	⊆	⊆	NUM
ejpam-4583	291	25	intf	intf	NOUN
ejpam-4583	291	26	(	(	PUNCT
ejpam-4583	291	27	k	k	NOUN
ejpam-4583	291	28	)	)	PUNCT
ejpam-4583	291	29	and	and	CCONJ
ejpam-4583	291	30	intf	intf	PROPN
ejpam-4583	291	31	(	(	PUNCT
ejpam-4583	291	32	k	k	X
ejpam-4583	291	33	∩	∩	ADJ
ejpam-4583	291	34	h	h	NOUN
ejpam-4583	291	35	)	)	PUNCT
ejpam-4583	291	36	⊆	⊆	NUM
ejpam-4583	291	37	intf	intf	NOUN
ejpam-4583	291	38	(	(	PUNCT
ejpam-4583	291	39	h	h	NOUN
ejpam-4583	291	40	)	)	PUNCT
ejpam-4583	291	41	.	.	PUNCT
ejpam-4583	292	1	hence	hence	ADV
ejpam-4583	292	2	,	,	PUNCT
ejpam-4583	292	3	intf	intf	PROPN
ejpam-4583	292	4	(	(	PUNCT
ejpam-4583	292	5	k	k	X
ejpam-4583	292	6	∩	∩	ADJ
ejpam-4583	292	7	h	h	NOUN
ejpam-4583	292	8	)	)	PUNCT
ejpam-4583	292	9	⊆	⊆	NUM
ejpam-4583	292	10	intf	intf	NOUN
ejpam-4583	292	11	(	(	PUNCT
ejpam-4583	292	12	k	k	NOUN
ejpam-4583	292	13	)	)	PUNCT
ejpam-4583	292	14	∩	∩	ADJ
ejpam-4583	292	15	intf	intf	X
ejpam-4583	292	16	(	(	PUNCT
ejpam-4583	292	17	h	h	NOUN
ejpam-4583	292	18	)	)	PUNCT
ejpam-4583	292	19	.	.	PUNCT
ejpam-4583	293	1	therefore	therefore	ADV
ejpam-4583	293	2	,	,	PUNCT
ejpam-4583	293	3	intf	intf	PROPN
ejpam-4583	293	4	(	(	PUNCT
ejpam-4583	293	5	k	k	PROPN
ejpam-4583	293	6	∩h	∩h	PROPN
ejpam-4583	293	7	)	)	PUNCT
ejpam-4583	294	1	=	=	SYM
ejpam-4583	294	2	intf	intf	X
ejpam-4583	294	3	(	(	PUNCT
ejpam-4583	294	4	k	k	NOUN
ejpam-4583	294	5	)	)	PUNCT
ejpam-4583	294	6	∩	∩	ADJ
ejpam-4583	294	7	intf	intf	X
ejpam-4583	294	8	(	(	PUNCT
ejpam-4583	294	9	h	h	NOUN
ejpam-4583	294	10	)	)	PUNCT
ejpam-4583	294	11	.	.	PUNCT
ejpam-4583	295	1	to	to	PART
ejpam-4583	295	2	prove	prove	VERB
ejpam-4583	295	3	(	(	PUNCT
ejpam-4583	295	4	vi	vi	NOUN
ejpam-4583	295	5	)	)	PUNCT
ejpam-4583	295	6	,	,	PUNCT
ejpam-4583	295	7	since	since	SCONJ
ejpam-4583	295	8	k	k	PROPN
ejpam-4583	295	9	⊆	⊆	X
ejpam-4583	295	10	(	(	PUNCT
ejpam-4583	295	11	k	k	PROPN
ejpam-4583	295	12	∪	∪	PROPN
ejpam-4583	295	13	h	h	NOUN
ejpam-4583	295	14	)	)	PUNCT
ejpam-4583	295	15	and	and	CCONJ
ejpam-4583	295	16	h	h	NOUN
ejpam-4583	295	17	⊆	⊆	NUM
ejpam-4583	295	18	(	(	PUNCT
ejpam-4583	295	19	k	k	PROPN
ejpam-4583	295	20	∪	∪	PROPN
ejpam-4583	295	21	h	h	NOUN
ejpam-4583	295	22	)	)	PUNCT
ejpam-4583	295	23	,	,	PUNCT
ejpam-4583	295	24	from	from	ADP
ejpam-4583	295	25	property	property	NOUN
ejpam-4583	295	26	(	(	PUNCT
ejpam-4583	295	27	iii	iii	X
ejpam-4583	295	28	)	)	PUNCT
ejpam-4583	295	29	we	we	PRON
ejpam-4583	295	30	have	have	VERB
ejpam-4583	295	31	intf	intf	X
ejpam-4583	295	32	(	(	PUNCT
ejpam-4583	295	33	k	k	NOUN
ejpam-4583	295	34	)	)	PUNCT
ejpam-4583	295	35	⊆	⊆	NUM
ejpam-4583	295	36	intf	intf	NOUN
ejpam-4583	295	37	(	(	PUNCT
ejpam-4583	295	38	k	k	PROPN
ejpam-4583	295	39	∪	∪	PROPN
ejpam-4583	295	40	h	h	NOUN
ejpam-4583	295	41	)	)	PUNCT
ejpam-4583	295	42	and	and	CCONJ
ejpam-4583	295	43	intf	intf	PROPN
ejpam-4583	295	44	(	(	PUNCT
ejpam-4583	295	45	h	h	NOUN
ejpam-4583	295	46	)	)	PUNCT
ejpam-4583	295	47	⊆	⊆	NUM
ejpam-4583	295	48	intf	intf	NOUN
ejpam-4583	295	49	(	(	PUNCT
ejpam-4583	295	50	k	k	PROPN
ejpam-4583	295	51	∪h	∪h	NUM
ejpam-4583	295	52	)	)	PUNCT
ejpam-4583	295	53	.	.	PUNCT
ejpam-4583	296	1	therefore	therefore	ADV
ejpam-4583	296	2	,	,	PUNCT
ejpam-4583	296	3	intf	intf	PROPN
ejpam-4583	296	4	(	(	PUNCT
ejpam-4583	296	5	k	k	NOUN
ejpam-4583	296	6	)	)	PUNCT
ejpam-4583	296	7	∪	∪	NOUN
ejpam-4583	296	8	intf	intf	PROPN
ejpam-4583	296	9	(	(	PUNCT
ejpam-4583	296	10	h	h	NOUN
ejpam-4583	296	11	)	)	PUNCT
ejpam-4583	296	12	⊆	⊆	NUM
ejpam-4583	296	13	intf	intf	NOUN
ejpam-4583	296	14	(	(	PUNCT
ejpam-4583	296	15	k	k	PROPN
ejpam-4583	296	16	∪h	∪h	NUM
ejpam-4583	296	17	)	)	PUNCT
ejpam-4583	296	18	.	.	PUNCT
ejpam-4583	297	1	in	in	ADP
ejpam-4583	297	2	general	general	ADJ
ejpam-4583	297	3	,	,	PUNCT
ejpam-4583	297	4	intf	intf	PROPN
ejpam-4583	297	5	(	(	PUNCT
ejpam-4583	297	6	k	k	NOUN
ejpam-4583	297	7	∪h	∪h	NUM
ejpam-4583	297	8	)	)	PUNCT
ejpam-4583	297	9	⊈	⊈	PROPN
ejpam-4583	297	10	intf	intf	NOUN
ejpam-4583	297	11	(	(	PUNCT
ejpam-4583	297	12	k	k	NOUN
ejpam-4583	297	13	)	)	PUNCT
ejpam-4583	297	14	∪	∪	NOUN
ejpam-4583	297	15	intf	intf	PROPN
ejpam-4583	297	16	(	(	PUNCT
ejpam-4583	297	17	h	h	NOUN
ejpam-4583	297	18	)	)	PUNCT
ejpam-4583	297	19	.	.	PUNCT
ejpam-4583	298	1	for	for	ADP
ejpam-4583	298	2	example	example	NOUN
ejpam-4583	298	3	:	:	PUNCT
ejpam-4583	298	4	example	example	NOUN
ejpam-4583	298	5	13	13	NUM
ejpam-4583	298	6	.	.	PUNCT
ejpam-4583	299	1	let	let	VERB
ejpam-4583	299	2	k	k	NOUN
ejpam-4583	299	3	=	=	PRON
ejpam-4583	299	4	r\n	r\n	ADJ
ejpam-4583	299	5	and	and	CCONJ
ejpam-4583	299	6	h	h	NOUN
ejpam-4583	299	7	=	=	PUNCT
ejpam-4583	300	1	n	n	X
ejpam-4583	300	2	be	be	VERB
ejpam-4583	300	3	a	a	DET
ejpam-4583	300	4	subsets	subset	NOUN
ejpam-4583	300	5	of	of	ADP
ejpam-4583	300	6	the	the	DET
ejpam-4583	300	7	usual	usual	ADJ
ejpam-4583	300	8	topological	topological	ADJ
ejpam-4583	300	9	space	space	NOUN
ejpam-4583	300	10	(	(	PUNCT
ejpam-4583	300	11	r	r	NOUN
ejpam-4583	300	12	,	,	PUNCT
ejpam-4583	300	13	u	u	NOUN
ejpam-4583	300	14	)	)	PUNCT
ejpam-4583	300	15	,	,	PUNCT
ejpam-4583	300	16	where	where	SCONJ
ejpam-4583	300	17	n	n	ADV
ejpam-4583	300	18	=	=	SYM
ejpam-4583	300	19	{	{	PUNCT
ejpam-4583	300	20	1	1	NUM
ejpam-4583	300	21	,	,	PUNCT
ejpam-4583	300	22	2	2	NUM
ejpam-4583	300	23	,	,	PUNCT
ejpam-4583	300	24	3	3	NUM
ejpam-4583	300	25	,	,	PUNCT
ejpam-4583	300	26	.	.	PUNCT
ejpam-4583	300	27	.	.	PUNCT
ejpam-4583	300	28	.	.	PUNCT
ejpam-4583	301	1	}	}	PUNCT
ejpam-4583	301	2	.	.	PUNCT
ejpam-4583	302	1	then	then	ADV
ejpam-4583	302	2	intf	intf	PROPN
ejpam-4583	302	3	(	(	PUNCT
ejpam-4583	302	4	k	k	NOUN
ejpam-4583	302	5	∪h	∪h	NUM
ejpam-4583	302	6	)	)	PUNCT
ejpam-4583	302	7	=	=	VERB
ejpam-4583	302	8	r.	r.	PROPN
ejpam-4583	302	9	however	however	ADV
ejpam-4583	302	10	,	,	PUNCT
ejpam-4583	302	11	r	r	NOUN
ejpam-4583	302	12	\n	\n	PROPN
ejpam-4583	302	13	is	be	AUX
ejpam-4583	302	14	not	not	PART
ejpam-4583	302	15	f	f	PROPN
ejpam-4583	302	16	-open	-open	NOUN
ejpam-4583	302	17	set	set	NOUN
ejpam-4583	302	18	,	,	PUNCT
ejpam-4583	302	19	then	then	ADV
ejpam-4583	302	20	intf	intf	PROPN
ejpam-4583	302	21	(	(	PUNCT
ejpam-4583	302	22	r	r	NOUN
ejpam-4583	302	23	\	\	PROPN
ejpam-4583	302	24	n	n	CCONJ
ejpam-4583	302	25	)	)	PUNCT
ejpam-4583	303	1	⊂	⊂	PROPN
ejpam-4583	303	2	r	r	NOUN
ejpam-4583	303	3	\	\	PROPN
ejpam-4583	303	4	n	n	PROPN
ejpam-4583	303	5	and	and	CCONJ
ejpam-4583	303	6	intf	intf	PROPN
ejpam-4583	303	7	(	(	PUNCT
ejpam-4583	303	8	h	h	NOUN
ejpam-4583	303	9	)	)	PUNCT
ejpam-4583	303	10	=	=	PUNCT
ejpam-4583	303	11	∅.	∅.	VERB
ejpam-4583	303	12	therefore	therefore	ADV
ejpam-4583	303	13	,	,	PUNCT
ejpam-4583	303	14	intf	intf	PROPN
ejpam-4583	303	15	(	(	PUNCT
ejpam-4583	303	16	k	k	NOUN
ejpam-4583	303	17	∪h	∪h	NUM
ejpam-4583	303	18	)	)	PUNCT
ejpam-4583	303	19	⊈	⊈	PROPN
ejpam-4583	304	1	intf	intf	NOUN
ejpam-4583	304	2	(	(	PUNCT
ejpam-4583	304	3	k	k	NOUN
ejpam-4583	304	4	)	)	PUNCT
ejpam-4583	304	5	∪	∪	NOUN
ejpam-4583	304	6	intf	intf	PROPN
ejpam-4583	304	7	(	(	PUNCT
ejpam-4583	304	8	h	h	NOUN
ejpam-4583	304	9	)	)	PUNCT
ejpam-4583	304	10	.	.	PUNCT
ejpam-4583	305	1	theorem	theorem	ADJ
ejpam-4583	305	2	6	6	NUM
ejpam-4583	305	3	.	.	PUNCT
ejpam-4583	306	1	let	let	VERB
ejpam-4583	306	2	k	k	NOUN
ejpam-4583	306	3	and	and	CCONJ
ejpam-4583	306	4	h	h	PROPN
ejpam-4583	306	5	be	be	VERB
ejpam-4583	306	6	subsets	subset	NOUN
ejpam-4583	306	7	of	of	ADP
ejpam-4583	306	8	a	a	DET
ejpam-4583	306	9	topological	topological	ADJ
ejpam-4583	306	10	space	space	NOUN
ejpam-4583	306	11	(	(	PUNCT
ejpam-4583	306	12	x	x	X
ejpam-4583	306	13	,	,	PUNCT
ejpam-4583	306	14	t	t	PROPN
ejpam-4583	306	15	)	)	PUNCT
ejpam-4583	306	16	.	.	PUNCT
ejpam-4583	307	1	then	then	ADV
ejpam-4583	307	2	we	we	PRON
ejpam-4583	307	3	have	have	VERB
ejpam-4583	307	4	the	the	DET
ejpam-4583	307	5	following	follow	VERB
ejpam-4583	307	6	properties	property	NOUN
ejpam-4583	307	7	:	:	PUNCT
ejpam-4583	307	8	(	(	PUNCT
ejpam-4583	307	9	i	i	NOUN
ejpam-4583	307	10	)	)	PUNCT
ejpam-4583	307	11	clf	clf	PROPN
ejpam-4583	307	12	(	(	PUNCT
ejpam-4583	307	13	∅	∅	NOUN
ejpam-4583	307	14	)	)	PUNCT
ejpam-4583	307	15	=	=	PUNCT
ejpam-4583	307	16	∅.	∅.	PRON
ejpam-4583	307	17	(	(	PUNCT
ejpam-4583	307	18	ii	ii	NOUN
ejpam-4583	307	19	)	)	PUNCT
ejpam-4583	307	20	k	k	PROPN
ejpam-4583	308	1	⊆	⊆	NUM
ejpam-4583	308	2	clf	clf	PROPN
ejpam-4583	308	3	(	(	PUNCT
ejpam-4583	308	4	k	k	NOUN
ejpam-4583	308	5	)	)	PUNCT
ejpam-4583	308	6	.	.	PUNCT
ejpam-4583	309	1	(	(	PUNCT
ejpam-4583	309	2	iii	iii	X
ejpam-4583	309	3	)	)	PUNCT
ejpam-4583	309	4	if	if	SCONJ
ejpam-4583	309	5	k	k	PROPN
ejpam-4583	309	6	⊆	⊆	NUM
ejpam-4583	309	7	h	h	NOUN
ejpam-4583	309	8	,	,	PUNCT
ejpam-4583	309	9	then	then	ADV
ejpam-4583	309	10	clf	clf	PROPN
ejpam-4583	309	11	(	(	PUNCT
ejpam-4583	309	12	k	k	PROPN
ejpam-4583	309	13	)	)	PUNCT
ejpam-4583	309	14	⊆	⊆	NUM
ejpam-4583	309	15	clf	clf	PROPN
ejpam-4583	309	16	(	(	PUNCT
ejpam-4583	309	17	h	h	NOUN
ejpam-4583	309	18	)	)	PUNCT
ejpam-4583	309	19	.	.	PUNCT
ejpam-4583	310	1	(	(	PUNCT
ejpam-4583	310	2	iv	iv	X
ejpam-4583	310	3	)	)	PUNCT
ejpam-4583	310	4	clf	clf	PROPN
ejpam-4583	310	5	(	(	PUNCT
ejpam-4583	310	6	k	k	NOUN
ejpam-4583	310	7	∪h	∪h	NUM
ejpam-4583	310	8	)	)	PUNCT
ejpam-4583	310	9	=	=	SYM
ejpam-4583	310	10	clf	clf	PROPN
ejpam-4583	310	11	(	(	PUNCT
ejpam-4583	310	12	k	k	NOUN
ejpam-4583	310	13	)	)	PUNCT
ejpam-4583	310	14	∪	∪	ADP
ejpam-4583	310	15	clf	clf	PROPN
ejpam-4583	310	16	(	(	PUNCT
ejpam-4583	310	17	h	h	NOUN
ejpam-4583	310	18	)	)	PUNCT
ejpam-4583	310	19	.	.	PUNCT
ejpam-4583	311	1	(	(	PUNCT
ejpam-4583	311	2	v	v	NOUN
ejpam-4583	311	3	)	)	PUNCT
ejpam-4583	311	4	clf	clf	PROPN
ejpam-4583	311	5	(	(	PUNCT
ejpam-4583	311	6	clf	clf	PROPN
ejpam-4583	311	7	(	(	PUNCT
ejpam-4583	311	8	k	k	NOUN
ejpam-4583	311	9	)	)	PUNCT
ejpam-4583	311	10	)	)	PUNCT
ejpam-4583	312	1	=	=	SYM
ejpam-4583	312	2	clf	clf	PROPN
ejpam-4583	312	3	(	(	PUNCT
ejpam-4583	312	4	k	k	NOUN
ejpam-4583	312	5	)	)	PUNCT
ejpam-4583	312	6	.	.	PUNCT
ejpam-4583	313	1	m.	m.	PROPN
ejpam-4583	313	2	h.	h.	PROPN
ejpam-4583	313	3	alqahtani	alqahtani	PROPN
ejpam-4583	313	4	/	/	SYM
ejpam-4583	313	5	eur	eur	PROPN
ejpam-4583	313	6	.	.	PUNCT
ejpam-4583	314	1	j.	j.	PROPN
ejpam-4583	314	2	pure	pure	PROPN
ejpam-4583	314	3	appl	appl	PROPN
ejpam-4583	314	4	.	.	PROPN
ejpam-4583	314	5	math	math	PROPN
ejpam-4583	314	6	,	,	PUNCT
ejpam-4583	314	7	16	16	NUM
ejpam-4583	314	8	(	(	PUNCT
ejpam-4583	314	9	2	2	NUM
ejpam-4583	314	10	)	)	PUNCT
ejpam-4583	314	11	(	(	PUNCT
ejpam-4583	314	12	2023	2023	NUM
ejpam-4583	314	13	)	)	PUNCT
ejpam-4583	314	14	,	,	PUNCT
ejpam-4583	314	15	819	819	NUM
ejpam-4583	314	16	-	-	SYM
ejpam-4583	314	17	832	832	NUM
ejpam-4583	314	18	827	827	NUM
ejpam-4583	314	19	proof	proof	NOUN
ejpam-4583	314	20	.	.	PUNCT
ejpam-4583	315	1	the	the	DET
ejpam-4583	315	2	properties	property	NOUN
ejpam-4583	315	3	(	(	PUNCT
ejpam-4583	315	4	i	i	NOUN
ejpam-4583	315	5	)	)	PUNCT
ejpam-4583	315	6	,	,	PUNCT
ejpam-4583	315	7	(	(	PUNCT
ejpam-4583	315	8	ii	ii	NOUN
ejpam-4583	315	9	)	)	PUNCT
ejpam-4583	315	10	,	,	PUNCT
ejpam-4583	315	11	(	(	PUNCT
ejpam-4583	315	12	iii	iii	NOUN
ejpam-4583	315	13	)	)	PUNCT
ejpam-4583	315	14	and	and	CCONJ
ejpam-4583	315	15	(	(	PUNCT
ejpam-4583	315	16	v	v	NOUN
ejpam-4583	315	17	)	)	PUNCT
ejpam-4583	315	18	follow	follow	VERB
ejpam-4583	315	19	from	from	ADP
ejpam-4583	315	20	definition	definition	NOUN
ejpam-4583	315	21	13	13	NUM
ejpam-4583	315	22	and	and	CCONJ
ejpam-4583	315	23	definition	definition	NOUN
ejpam-4583	315	24	15	15	NUM
ejpam-4583	315	25	.	.	PUNCT
ejpam-4583	316	1	the	the	DET
ejpam-4583	316	2	property	property	NOUN
ejpam-4583	316	3	(	(	PUNCT
ejpam-4583	316	4	iv	iv	NOUN
ejpam-4583	316	5	)	)	PUNCT
ejpam-4583	316	6	,	,	PUNCT
ejpam-4583	316	7	follow	follow	VERB
ejpam-4583	316	8	from	from	ADP
ejpam-4583	316	9	property	property	NOUN
ejpam-4583	316	10	(	(	PUNCT
ejpam-4583	316	11	iii	iii	NOUN
ejpam-4583	316	12	)	)	PUNCT
ejpam-4583	316	13	,	,	PUNCT
ejpam-4583	316	14	definition	definition	NOUN
ejpam-4583	316	15	12	12	NUM
ejpam-4583	316	16	,	,	PUNCT
ejpam-4583	316	17	definition	definition	NOUN
ejpam-4583	316	18	15	15	NUM
ejpam-4583	316	19	and	and	CCONJ
ejpam-4583	316	20	using	use	VERB
ejpam-4583	316	21	set	set	VERB
ejpam-4583	316	22	theoretic	theoretic	ADJ
ejpam-4583	316	23	properties	property	NOUN
ejpam-4583	316	24	.	.	PUNCT
ejpam-4583	317	1	theorem	theorem	VERB
ejpam-4583	317	2	7	7	NUM
ejpam-4583	317	3	.	.	PUNCT
ejpam-4583	318	1	let	let	VERB
ejpam-4583	318	2	k	k	PRON
ejpam-4583	318	3	be	be	AUX
ejpam-4583	318	4	a	a	DET
ejpam-4583	318	5	subset	subset	NOUN
ejpam-4583	318	6	of	of	ADP
ejpam-4583	318	7	the	the	DET
ejpam-4583	318	8	topological	topological	ADJ
ejpam-4583	318	9	space	space	NOUN
ejpam-4583	318	10	(	(	PUNCT
ejpam-4583	318	11	x	x	X
ejpam-4583	318	12	,	,	PUNCT
ejpam-4583	318	13	t	t	PROPN
ejpam-4583	318	14	)	)	PUNCT
ejpam-4583	318	15	.	.	PUNCT
ejpam-4583	319	1	then	then	ADV
ejpam-4583	319	2	,	,	PUNCT
ejpam-4583	319	3	(	(	PUNCT
ejpam-4583	319	4	i	i	NOUN
ejpam-4583	319	5	)	)	PUNCT
ejpam-4583	319	6	intf	intf	PROPN
ejpam-4583	319	7	(	(	PUNCT
ejpam-4583	319	8	k	k	NOUN
ejpam-4583	319	9	)	)	PUNCT
ejpam-4583	319	10	=	=	PUNCT
ejpam-4583	319	11	x	x	SYM
ejpam-4583	319	12	\	\	PROPN
ejpam-4583	319	13	clf	clf	PROPN
ejpam-4583	319	14	(	(	PUNCT
ejpam-4583	319	15	x	x	NOUN
ejpam-4583	319	16	\k	\k	NOUN
ejpam-4583	319	17	)	)	PUNCT
ejpam-4583	319	18	.	.	PUNCT
ejpam-4583	320	1	(	(	PUNCT
ejpam-4583	320	2	ii	ii	X
ejpam-4583	320	3	)	)	PUNCT
ejpam-4583	320	4	clf	clf	PROPN
ejpam-4583	320	5	(	(	PUNCT
ejpam-4583	320	6	k	k	NOUN
ejpam-4583	320	7	)	)	PUNCT
ejpam-4583	320	8	=	=	PUNCT
ejpam-4583	321	1	x	x	SYM
ejpam-4583	321	2	\	\	PROPN
ejpam-4583	321	3	intf	intf	PROPN
ejpam-4583	321	4	(	(	PUNCT
ejpam-4583	321	5	x	x	NOUN
ejpam-4583	321	6	\k	\k	NOUN
ejpam-4583	321	7	)	)	PUNCT
ejpam-4583	321	8	.	.	PUNCT
ejpam-4583	322	1	proof	proof	NOUN
ejpam-4583	322	2	.	.	PUNCT
ejpam-4583	323	1	(	(	PUNCT
ejpam-4583	323	2	i	i	NOUN
ejpam-4583	323	3	)	)	PUNCT
ejpam-4583	323	4	we	we	PRON
ejpam-4583	323	5	have	have	VERB
ejpam-4583	323	6	intf	intf	X
ejpam-4583	323	7	(	(	PUNCT
ejpam-4583	323	8	k	k	NOUN
ejpam-4583	323	9	)	)	PUNCT
ejpam-4583	323	10	=	=	PUNCT
ejpam-4583	324	1	x	x	SYM
ejpam-4583	324	2	\	\	PROPN
ejpam-4583	324	3	clf	clf	PROPN
ejpam-4583	324	4	(	(	PUNCT
ejpam-4583	324	5	x	x	NOUN
ejpam-4583	324	6	\k	\k	NOUN
ejpam-4583	324	7	)	)	PUNCT
ejpam-4583	324	8	,	,	PUNCT
ejpam-4583	324	9	then	then	ADV
ejpam-4583	324	10	x	x	PUNCT
ejpam-4583	324	11	\k	\k	PROPN
ejpam-4583	324	12	⊆	⊆	NUM
ejpam-4583	324	13	clf	clf	PROPN
ejpam-4583	324	14	(	(	PUNCT
ejpam-4583	324	15	x	x	NOUN
ejpam-4583	324	16	\k	\k	NOUN
ejpam-4583	324	17	)	)	PUNCT
ejpam-4583	324	18	,	,	PUNCT
ejpam-4583	324	19	thus	thus	ADV
ejpam-4583	324	20	x	x	ADP
ejpam-4583	324	21	\	\	PROPN
ejpam-4583	324	22	clf	clf	PROPN
ejpam-4583	324	23	(	(	PUNCT
ejpam-4583	324	24	x	x	SYM
ejpam-4583	324	25	\	\	PROPN
ejpam-4583	324	26	k	k	X
ejpam-4583	324	27	)	)	PUNCT
ejpam-4583	324	28	⊆	⊆	NUM
ejpam-4583	324	29	k.	k.	NOUN
ejpam-4583	324	30	since	since	SCONJ
ejpam-4583	324	31	x	x	PROPN
ejpam-4583	324	32	\	\	PROPN
ejpam-4583	324	33	clf	clf	PROPN
ejpam-4583	324	34	(	(	PUNCT
ejpam-4583	324	35	x	x	SYM
ejpam-4583	324	36	\	\	PROPN
ejpam-4583	324	37	k	k	X
ejpam-4583	324	38	)	)	PUNCT
ejpam-4583	324	39	is	be	AUX
ejpam-4583	324	40	f	f	PROPN
ejpam-4583	324	41	-open	-open	PROPN
ejpam-4583	324	42	,	,	PUNCT
ejpam-4583	324	43	then	then	ADV
ejpam-4583	324	44	x	x	ADP
ejpam-4583	324	45	\	\	PROPN
ejpam-4583	324	46	clf	clf	PROPN
ejpam-4583	324	47	(	(	PUNCT
ejpam-4583	324	48	x	x	SYM
ejpam-4583	324	49	\	\	PROPN
ejpam-4583	324	50	k	k	X
ejpam-4583	324	51	)	)	PUNCT
ejpam-4583	324	52	⊆	⊆	NUM
ejpam-4583	324	53	intf	intf	NOUN
ejpam-4583	324	54	(	(	PUNCT
ejpam-4583	324	55	k)	k)	PROPN
ejpam-4583	324	56	...	...	X
ejpam-4583	324	57	(1	(1	NUM
ejpam-4583	324	58	)	)	PUNCT
ejpam-4583	324	59	.	.	PUNCT
ejpam-4583	325	1	now	now	ADV
ejpam-4583	325	2	,	,	PUNCT
ejpam-4583	325	3	let	let	VERB
ejpam-4583	325	4	v	v	PART
ejpam-4583	325	5	be	be	AUX
ejpam-4583	325	6	any	any	DET
ejpam-4583	325	7	f	f	PROPN
ejpam-4583	325	8	-open	-open	PROPN
ejpam-4583	325	9	set	set	NOUN
ejpam-4583	325	10	contained	contain	VERB
ejpam-4583	325	11	in	in	ADP
ejpam-4583	325	12	k	k	PROPN
ejpam-4583	325	13	,	,	PUNCT
ejpam-4583	325	14	i.e.	i.e.	X
ejpam-4583	325	15	,	,	PUNCT
ejpam-4583	325	16	v	v	ADP
ejpam-4583	325	17	⊆	⊆	NUM
ejpam-4583	325	18	k	k	NOUN
ejpam-4583	325	19	and	and	CCONJ
ejpam-4583	325	20	v	v	NOUN
ejpam-4583	325	21	is	be	AUX
ejpam-4583	325	22	f	f	PROPN
ejpam-4583	325	23	-open	-open	PROPN
ejpam-4583	325	24	,	,	PUNCT
ejpam-4583	325	25	then	then	ADV
ejpam-4583	325	26	x	x	PUNCT
ejpam-4583	325	27	\k	\k	NOUN
ejpam-4583	325	28	⊆	⊆	NUM
ejpam-4583	325	29	x	x	SYM
ejpam-4583	325	30	\v	\v	PROPN
ejpam-4583	325	31	=	=	SYM
ejpam-4583	325	32	clf	clf	PROPN
ejpam-4583	325	33	(	(	PUNCT
ejpam-4583	325	34	x	x	PROPN
ejpam-4583	325	35	\v	\v	X
ejpam-4583	325	36	)	)	PUNCT
ejpam-4583	325	37	.	.	PUNCT
ejpam-4583	326	1	then	then	ADV
ejpam-4583	326	2	clf	clf	PROPN
ejpam-4583	326	3	(	(	PUNCT
ejpam-4583	326	4	x	x	SYM
ejpam-4583	326	5	\k	\k	NOUN
ejpam-4583	326	6	)	)	PUNCT
ejpam-4583	326	7	⊆	⊆	NUM
ejpam-4583	326	8	x	x	SYM
ejpam-4583	326	9	\v	\v	NOUN
ejpam-4583	326	10	,	,	PUNCT
ejpam-4583	326	11	hence	hence	ADV
ejpam-4583	326	12	v	v	VERB
ejpam-4583	326	13	⊆	⊆	NUM
ejpam-4583	326	14	x	x	SYM
ejpam-4583	326	15	\	\	PROPN
ejpam-4583	326	16	clf	clf	PROPN
ejpam-4583	326	17	(	(	PUNCT
ejpam-4583	326	18	x	x	NOUN
ejpam-4583	326	19	\k	\k	NOUN
ejpam-4583	326	20	)	)	PUNCT
ejpam-4583	326	21	.	.	PUNCT
ejpam-4583	327	1	that	that	PRON
ejpam-4583	327	2	is	be	AUX
ejpam-4583	327	3	,	,	PUNCT
ejpam-4583	327	4	any	any	DET
ejpam-4583	327	5	f	f	PROPN
ejpam-4583	327	6	-open	-open	PROPN
ejpam-4583	327	7	set	set	NOUN
ejpam-4583	327	8	contained	contain	VERB
ejpam-4583	327	9	in	in	ADP
ejpam-4583	327	10	k	k	PROPN
ejpam-4583	327	11	is	be	AUX
ejpam-4583	327	12	contained	contain	VERB
ejpam-4583	327	13	in	in	ADP
ejpam-4583	327	14	x	x	SYM
ejpam-4583	327	15	\	\	PROPN
ejpam-4583	327	16	clf	clf	PROPN
ejpam-4583	327	17	(	(	PUNCT
ejpam-4583	327	18	x	x	NOUN
ejpam-4583	327	19	\k	\k	NOUN
ejpam-4583	327	20	)	)	PUNCT
ejpam-4583	327	21	,	,	PUNCT
ejpam-4583	327	22	which	which	PRON
ejpam-4583	327	23	means	mean	VERB
ejpam-4583	327	24	that	that	SCONJ
ejpam-4583	327	25	intf	intf	PROPN
ejpam-4583	327	26	(	(	PUNCT
ejpam-4583	327	27	k	k	NOUN
ejpam-4583	327	28	)	)	PUNCT
ejpam-4583	327	29	⊆	⊆	NUM
ejpam-4583	327	30	x	x	SYM
ejpam-4583	327	31	\	\	PROPN
ejpam-4583	327	32	clf	clf	PROPN
ejpam-4583	327	33	(	(	PUNCT
ejpam-4583	327	34	x	x	SYM
ejpam-4583	327	35	\k	\k	NOUN
ejpam-4583	327	36	)	)	PUNCT
ejpam-4583	327	37	...	...	PUNCT
ejpam-4583	327	38	(	(	PUNCT
ejpam-4583	327	39	2	2	NUM
ejpam-4583	327	40	)	)	PUNCT
ejpam-4583	327	41	.	.	PUNCT
ejpam-4583	328	1	from	from	ADP
ejpam-4583	328	2	(	(	PUNCT
ejpam-4583	328	3	1	1	NUM
ejpam-4583	328	4	)	)	PUNCT
ejpam-4583	328	5	and	and	CCONJ
ejpam-4583	328	6	(	(	PUNCT
ejpam-4583	328	7	2	2	X
ejpam-4583	328	8	)	)	PUNCT
ejpam-4583	328	9	equality	equality	NOUN
ejpam-4583	328	10	holds	hold	VERB
ejpam-4583	328	11	.	.	PUNCT
ejpam-4583	329	1	(	(	PUNCT
ejpam-4583	329	2	ii	ii	NOUN
ejpam-4583	329	3	)	)	PUNCT
ejpam-4583	329	4	can	can	AUX
ejpam-4583	329	5	be	be	AUX
ejpam-4583	329	6	proved	prove	VERB
ejpam-4583	329	7	by	by	ADP
ejpam-4583	329	8	replacing	replace	VERB
ejpam-4583	329	9	k	k	PROPN
ejpam-4583	329	10	and	and	CCONJ
ejpam-4583	329	11	x	x	SYM
ejpam-4583	329	12	\k	\k	NOUN
ejpam-4583	329	13	by	by	ADP
ejpam-4583	329	14	x	x	PROPN
ejpam-4583	329	15	\k	\k	NOUN
ejpam-4583	329	16	and	and	CCONJ
ejpam-4583	329	17	k	k	NOUN
ejpam-4583	329	18	,	,	PUNCT
ejpam-4583	329	19	respectively	respectively	ADV
ejpam-4583	329	20	in	in	ADP
ejpam-4583	329	21	(	(	PUNCT
ejpam-4583	329	22	i	i	NOUN
ejpam-4583	329	23	)	)	PUNCT
ejpam-4583	329	24	and	and	CCONJ
ejpam-4583	329	25	using	use	VERB
ejpam-4583	329	26	set	set	VERB
ejpam-4583	329	27	theoretic	theoretic	ADJ
ejpam-4583	329	28	properties	property	NOUN
ejpam-4583	329	29	.	.	PUNCT
ejpam-4583	330	1	definition	definition	NOUN
ejpam-4583	330	2	18	18	NUM
ejpam-4583	330	3	.	.	PUNCT
ejpam-4583	331	1	let	let	VERB
ejpam-4583	331	2	k	k	PRON
ejpam-4583	331	3	be	be	AUX
ejpam-4583	331	4	a	a	DET
ejpam-4583	331	5	subset	subset	NOUN
ejpam-4583	331	6	of	of	ADP
ejpam-4583	331	7	the	the	DET
ejpam-4583	331	8	topological	topological	ADJ
ejpam-4583	331	9	space	space	NOUN
ejpam-4583	331	10	x.	x.	NOUN
ejpam-4583	332	1	then	then	ADV
ejpam-4583	332	2	f	f	PROPN
ejpam-4583	332	3	-border	-border	PROPN
ejpam-4583	332	4	of	of	ADP
ejpam-4583	332	5	k	k	PROPN
ejpam-4583	332	6	is	be	AUX
ejpam-4583	332	7	defined	define	VERB
ejpam-4583	332	8	as	as	ADP
ejpam-4583	332	9	bdf	bdf	NOUN
ejpam-4583	332	10	(	(	PUNCT
ejpam-4583	332	11	k	k	NOUN
ejpam-4583	332	12	)	)	PUNCT
ejpam-4583	332	13	=	=	SYM
ejpam-4583	333	1	k	k	PROPN
ejpam-4583	333	2	\	\	PROPN
ejpam-4583	333	3	intf	intf	PROPN
ejpam-4583	333	4	(	(	PUNCT
ejpam-4583	333	5	k	k	NOUN
ejpam-4583	333	6	)	)	PUNCT
ejpam-4583	333	7	.	.	PUNCT
ejpam-4583	334	1	theorem	theorem	ADJ
ejpam-4583	334	2	8	8	NUM
ejpam-4583	334	3	.	.	PUNCT
ejpam-4583	335	1	let	let	VERB
ejpam-4583	335	2	k	k	PRON
ejpam-4583	335	3	be	be	AUX
ejpam-4583	335	4	a	a	DET
ejpam-4583	335	5	subset	subset	NOUN
ejpam-4583	335	6	of	of	ADP
ejpam-4583	335	7	the	the	DET
ejpam-4583	335	8	topological	topological	ADJ
ejpam-4583	335	9	space	space	NOUN
ejpam-4583	335	10	(	(	PUNCT
ejpam-4583	335	11	x	x	X
ejpam-4583	335	12	,	,	PUNCT
ejpam-4583	335	13	t	t	PROPN
ejpam-4583	335	14	)	)	PUNCT
ejpam-4583	335	15	.	.	PUNCT
ejpam-4583	336	1	then	then	ADV
ejpam-4583	336	2	we	we	PRON
ejpam-4583	336	3	have	have	VERB
ejpam-4583	336	4	the	the	DET
ejpam-4583	336	5	following	follow	VERB
ejpam-4583	336	6	properties	property	NOUN
ejpam-4583	336	7	:	:	PUNCT
ejpam-4583	336	8	(	(	PUNCT
ejpam-4583	336	9	i	i	NOUN
ejpam-4583	336	10	)	)	PUNCT
ejpam-4583	336	11	bd(k	bd(k	X
ejpam-4583	336	12	)	)	PUNCT
ejpam-4583	337	1	⊂	⊂	PROPN
ejpam-4583	337	2	bdf	bdf	NOUN
ejpam-4583	337	3	(	(	PUNCT
ejpam-4583	337	4	k	k	NOUN
ejpam-4583	337	5	)	)	PUNCT
ejpam-4583	337	6	,	,	PUNCT
ejpam-4583	337	7	where	where	SCONJ
ejpam-4583	337	8	bd(k	bd(k	X
ejpam-4583	337	9	)	)	PUNCT
ejpam-4583	337	10	denotes	denote	VERB
ejpam-4583	337	11	the	the	DET
ejpam-4583	337	12	border	border	NOUN
ejpam-4583	337	13	of	of	ADP
ejpam-4583	337	14	k.	k.	PROPN
ejpam-4583	337	15	(	(	PUNCT
ejpam-4583	337	16	ii	ii	PROPN
ejpam-4583	337	17	)	)	PUNCT
ejpam-4583	337	18	k	k	PROPN
ejpam-4583	338	1	=	=	PUNCT
ejpam-4583	338	2	intf	intf	PROPN
ejpam-4583	338	3	(	(	PUNCT
ejpam-4583	338	4	k	k	NOUN
ejpam-4583	338	5	)	)	PUNCT
ejpam-4583	338	6	∪bdf	∪bdf	PROPN
ejpam-4583	338	7	(	(	PUNCT
ejpam-4583	338	8	k	k	NOUN
ejpam-4583	338	9	)	)	PUNCT
ejpam-4583	338	10	.	.	PUNCT
ejpam-4583	339	1	(	(	PUNCT
ejpam-4583	339	2	iii	iii	X
ejpam-4583	339	3	)	)	PUNCT
ejpam-4583	339	4	intf	intf	NOUN
ejpam-4583	339	5	(	(	PUNCT
ejpam-4583	339	6	k	k	NOUN
ejpam-4583	339	7	)	)	PUNCT
ejpam-4583	339	8	∩bdf	∩bdf	NOUN
ejpam-4583	339	9	(	(	PUNCT
ejpam-4583	339	10	k	k	X
ejpam-4583	339	11	)	)	PUNCT
ejpam-4583	339	12	=	=	SYM
ejpam-4583	339	13	∅.	∅.	X
ejpam-4583	339	14	(	(	PUNCT
ejpam-4583	339	15	iv	iv	X
ejpam-4583	339	16	)	)	PUNCT
ejpam-4583	339	17	k	k	X
ejpam-4583	339	18	is	be	AUX
ejpam-4583	339	19	a	a	DET
ejpam-4583	339	20	f−open	f−open	NOUN
ejpam-4583	339	21	set	set	VERB
ejpam-4583	339	22	if	if	SCONJ
ejpam-4583	339	23	and	and	CCONJ
ejpam-4583	339	24	only	only	ADV
ejpam-4583	339	25	if	if	SCONJ
ejpam-4583	339	26	bdf	bdf	NOUN
ejpam-4583	339	27	(	(	PUNCT
ejpam-4583	339	28	k	k	NOUN
ejpam-4583	339	29	)	)	PUNCT
ejpam-4583	339	30	=	=	SYM
ejpam-4583	339	31	∅.	∅.	X
ejpam-4583	339	32	(	(	PUNCT
ejpam-4583	339	33	v	v	NOUN
ejpam-4583	339	34	)	)	PUNCT
ejpam-4583	339	35	intf	intf	NOUN
ejpam-4583	339	36	(	(	PUNCT
ejpam-4583	339	37	bdf	bdf	NOUN
ejpam-4583	339	38	(	(	PUNCT
ejpam-4583	339	39	k	k	NOUN
ejpam-4583	339	40	)	)	PUNCT
ejpam-4583	339	41	)	)	PUNCT
ejpam-4583	340	1	=	=	SYM
ejpam-4583	340	2	∅.	∅.	X
ejpam-4583	340	3	(	(	PUNCT
ejpam-4583	340	4	vi	vi	NOUN
ejpam-4583	340	5	)	)	PUNCT
ejpam-4583	340	6	bdf	bdf	NOUN
ejpam-4583	340	7	(	(	PUNCT
ejpam-4583	340	8	bdf	bdf	NOUN
ejpam-4583	340	9	(	(	PUNCT
ejpam-4583	340	10	k	k	NOUN
ejpam-4583	340	11	)	)	PUNCT
ejpam-4583	340	12	)	)	PUNCT
ejpam-4583	341	1	=	=	SYM
ejpam-4583	341	2	bdf	bdf	NOUN
ejpam-4583	341	3	(	(	PUNCT
ejpam-4583	341	4	k	k	NOUN
ejpam-4583	341	5	)	)	PUNCT
ejpam-4583	341	6	.	.	PUNCT
ejpam-4583	342	1	(	(	PUNCT
ejpam-4583	342	2	vii	vii	PROPN
ejpam-4583	342	3	)	)	PUNCT
ejpam-4583	342	4	bdf	bdf	NOUN
ejpam-4583	342	5	(	(	PUNCT
ejpam-4583	342	6	k	k	NOUN
ejpam-4583	342	7	)	)	PUNCT
ejpam-4583	342	8	=	=	SYM
ejpam-4583	343	1	k	k	PROPN
ejpam-4583	343	2	∩	∩	PROPN
ejpam-4583	343	3	clf	clf	PROPN
ejpam-4583	343	4	(	(	PUNCT
ejpam-4583	343	5	x	x	NOUN
ejpam-4583	343	6	\k	\k	NOUN
ejpam-4583	343	7	)	)	PUNCT
ejpam-4583	343	8	.	.	PUNCT
ejpam-4583	344	1	proof	proof	NOUN
ejpam-4583	344	2	.	.	PUNCT
ejpam-4583	345	1	to	to	PART
ejpam-4583	345	2	prove	prove	VERB
ejpam-4583	345	3	(	(	PUNCT
ejpam-4583	345	4	i	i	NOUN
ejpam-4583	345	5	)	)	PUNCT
ejpam-4583	345	6	,	,	PUNCT
ejpam-4583	345	7	let	let	VERB
ejpam-4583	345	8	x	x	PUNCT
ejpam-4583	345	9	∈	∈	PROPN
ejpam-4583	345	10	bd(k	bd(k	X
ejpam-4583	345	11	)	)	PUNCT
ejpam-4583	345	12	be	be	AUX
ejpam-4583	345	13	arbitrary	arbitrary	ADJ
ejpam-4583	345	14	,	,	PUNCT
ejpam-4583	345	15	then	then	ADV
ejpam-4583	345	16	x	x	SYM
ejpam-4583	345	17	∈	∈	PROPN
ejpam-4583	345	18	k	k	PROPN
ejpam-4583	345	19	\	\	PROPN
ejpam-4583	345	20	int(k	int(k	PROPN
ejpam-4583	345	21	)	)	PUNCT
ejpam-4583	345	22	,	,	PUNCT
ejpam-4583	345	23	so	so	ADV
ejpam-4583	345	24	thus	thus	ADV
ejpam-4583	345	25	x	x	X
ejpam-4583	345	26	/∈	/∈	PUNCT
ejpam-4583	345	27	int(k	int(k	PROPN
ejpam-4583	345	28	)	)	PUNCT
ejpam-4583	345	29	.	.	PUNCT
ejpam-4583	346	1	by	by	ADP
ejpam-4583	346	2	theorem	theorem	NOUN
ejpam-4583	346	3	3	3	NUM
ejpam-4583	346	4	part	part	NOUN
ejpam-4583	346	5	(	(	PUNCT
ejpam-4583	346	6	i	i	NOUN
ejpam-4583	346	7	)	)	PUNCT
ejpam-4583	346	8	we	we	PRON
ejpam-4583	346	9	have	have	VERB
ejpam-4583	346	10	intf	intf	X
ejpam-4583	346	11	(	(	PUNCT
ejpam-4583	346	12	k	k	NOUN
ejpam-4583	346	13	)	)	PUNCT
ejpam-4583	346	14	⊆	⊆	NUM
ejpam-4583	346	15	int(k	int(k	NUM
ejpam-4583	346	16	)	)	PUNCT
ejpam-4583	346	17	⊆	⊆	NUM
ejpam-4583	346	18	k	k	NOUN
ejpam-4583	346	19	,	,	PUNCT
ejpam-4583	346	20	then	then	ADV
ejpam-4583	346	21	x	x	PROPN
ejpam-4583	346	22	/∈	/∈	PUNCT
ejpam-4583	347	1	intf	intf	PROPN
ejpam-4583	347	2	(	(	PUNCT
ejpam-4583	347	3	k	k	NOUN
ejpam-4583	347	4	)	)	PUNCT
ejpam-4583	347	5	.	.	PUNCT
ejpam-4583	348	1	hence	hence	ADV
ejpam-4583	348	2	x	x	X
ejpam-4583	348	3	∈	∈	PROPN
ejpam-4583	348	4	(	(	PUNCT
ejpam-4583	348	5	k	k	PROPN
ejpam-4583	348	6	\	\	PROPN
ejpam-4583	348	7	intf	intf	PROPN
ejpam-4583	348	8	(	(	PUNCT
ejpam-4583	348	9	k	k	NOUN
ejpam-4583	348	10	)	)	PUNCT
ejpam-4583	348	11	)	)	PUNCT
ejpam-4583	349	1	=	=	SYM
ejpam-4583	349	2	bdf	bdf	NOUN
ejpam-4583	349	3	(	(	PUNCT
ejpam-4583	349	4	k	k	NOUN
ejpam-4583	349	5	)	)	PUNCT
ejpam-4583	349	6	.	.	PUNCT
ejpam-4583	350	1	therefore	therefore	ADV
ejpam-4583	350	2	,	,	PUNCT
ejpam-4583	350	3	bd(k	bd(k	X
ejpam-4583	350	4	)	)	PUNCT
ejpam-4583	350	5	⊆	⊆	NUM
ejpam-4583	350	6	bdf	bdf	NOUN
ejpam-4583	350	7	(	(	PUNCT
ejpam-4583	350	8	k	k	NOUN
ejpam-4583	350	9	)	)	PUNCT
ejpam-4583	350	10	.	.	PUNCT
ejpam-4583	351	1	the	the	DET
ejpam-4583	351	2	properties	property	NOUN
ejpam-4583	351	3	(	(	PUNCT
ejpam-4583	351	4	ii	ii	NOUN
ejpam-4583	351	5	)	)	PUNCT
ejpam-4583	351	6	,	,	PUNCT
ejpam-4583	351	7	(	(	PUNCT
ejpam-4583	351	8	iii	iii	NOUN
ejpam-4583	351	9	)	)	PUNCT
ejpam-4583	351	10	and	and	CCONJ
ejpam-4583	351	11	(	(	PUNCT
ejpam-4583	351	12	iv	iv	X
ejpam-4583	351	13	)	)	PUNCT
ejpam-4583	351	14	follow	follow	VERB
ejpam-4583	351	15	from	from	ADP
ejpam-4583	351	16	definition	definition	NOUN
ejpam-4583	351	17	18	18	NUM
ejpam-4583	351	18	.	.	PUNCT
ejpam-4583	351	19	to	to	PART
ejpam-4583	351	20	prove	prove	VERB
ejpam-4583	351	21	(	(	PUNCT
ejpam-4583	351	22	v	v	NOUN
ejpam-4583	351	23	)	)	PUNCT
ejpam-4583	351	24	,	,	PUNCT
ejpam-4583	351	25	let	let	VERB
ejpam-4583	351	26	x	x	X
ejpam-4583	351	27	∈	∈	PROPN
ejpam-4583	351	28	intf	intf	PROPN
ejpam-4583	351	29	(	(	PUNCT
ejpam-4583	351	30	bdf	bdf	NOUN
ejpam-4583	351	31	(	(	PUNCT
ejpam-4583	351	32	k	k	NOUN
ejpam-4583	351	33	)	)	PUNCT
ejpam-4583	351	34	)	)	PUNCT
ejpam-4583	351	35	be	be	AUX
ejpam-4583	351	36	arbitrary	arbitrary	ADJ
ejpam-4583	351	37	,	,	PUNCT
ejpam-4583	351	38	then	then	ADV
ejpam-4583	351	39	x	x	PART
ejpam-4583	351	40	∈	∈	PROPN
ejpam-4583	351	41	bdf	bdf	NOUN
ejpam-4583	351	42	(	(	PUNCT
ejpam-4583	351	43	k	k	NOUN
ejpam-4583	351	44	)	)	PUNCT
ejpam-4583	351	45	.	.	PUNCT
ejpam-4583	352	1	since	since	SCONJ
ejpam-4583	352	2	bdf	bdf	NOUN
ejpam-4583	352	3	(	(	PUNCT
ejpam-4583	352	4	k	k	NOUN
ejpam-4583	352	5	)	)	PUNCT
ejpam-4583	352	6	⊆	⊆	NUM
ejpam-4583	352	7	k	k	NOUN
ejpam-4583	352	8	,	,	PUNCT
ejpam-4583	352	9	then	then	ADV
ejpam-4583	352	10	x	x	PART
ejpam-4583	352	11	∈	∈	PROPN
ejpam-4583	352	12	intf	intf	PROPN
ejpam-4583	352	13	(	(	PUNCT
ejpam-4583	352	14	bdf	bdf	NOUN
ejpam-4583	352	15	(	(	PUNCT
ejpam-4583	352	16	k	k	NOUN
ejpam-4583	352	17	)	)	PUNCT
ejpam-4583	352	18	)	)	PUNCT
ejpam-4583	352	19	⊆	⊆	NUM
ejpam-4583	352	20	intf	intf	NOUN
ejpam-4583	352	21	(	(	PUNCT
ejpam-4583	352	22	k	k	NOUN
ejpam-4583	352	23	)	)	PUNCT
ejpam-4583	352	24	,	,	PUNCT
ejpam-4583	352	25	m.	m.	PROPN
ejpam-4583	352	26	h.	h.	PROPN
ejpam-4583	352	27	alqahtani	alqahtani	PROPN
ejpam-4583	352	28	/	/	SYM
ejpam-4583	352	29	eur	eur	PROPN
ejpam-4583	352	30	.	.	PUNCT
ejpam-4583	353	1	j.	j.	PROPN
ejpam-4583	353	2	pure	pure	PROPN
ejpam-4583	353	3	appl	appl	PROPN
ejpam-4583	353	4	.	.	PROPN
ejpam-4583	353	5	math	math	PROPN
ejpam-4583	353	6	,	,	PUNCT
ejpam-4583	353	7	16	16	NUM
ejpam-4583	353	8	(	(	PUNCT
ejpam-4583	353	9	2	2	NUM
ejpam-4583	353	10	)	)	PUNCT
ejpam-4583	353	11	(	(	PUNCT
ejpam-4583	353	12	2023	2023	NUM
ejpam-4583	353	13	)	)	PUNCT
ejpam-4583	353	14	,	,	PUNCT
ejpam-4583	353	15	819	819	NUM
ejpam-4583	353	16	-	-	SYM
ejpam-4583	353	17	832	832	NUM
ejpam-4583	353	18	828	828	NUM
ejpam-4583	353	19	so	so	ADV
ejpam-4583	353	20	thus	thus	ADV
ejpam-4583	353	21	x	x	X
ejpam-4583	353	22	∈	∈	PROPN
ejpam-4583	353	23	intf	intf	NOUN
ejpam-4583	353	24	(	(	PUNCT
ejpam-4583	353	25	k	k	NOUN
ejpam-4583	353	26	)	)	PUNCT
ejpam-4583	353	27	∩	∩	ADJ
ejpam-4583	353	28	bdf	bdf	NOUN
ejpam-4583	353	29	(	(	PUNCT
ejpam-4583	353	30	k	k	NOUN
ejpam-4583	353	31	)	)	PUNCT
ejpam-4583	353	32	which	which	PRON
ejpam-4583	353	33	contradicts	contradict	VERB
ejpam-4583	353	34	(	(	PUNCT
ejpam-4583	353	35	iii	iii	NOUN
ejpam-4583	353	36	)	)	PUNCT
ejpam-4583	353	37	.	.	PUNCT
ejpam-4583	354	1	for	for	ADP
ejpam-4583	354	2	(	(	PUNCT
ejpam-4583	354	3	vi	vi	NOUN
ejpam-4583	354	4	)	)	PUNCT
ejpam-4583	354	5	from	from	ADP
ejpam-4583	354	6	definition	definition	NOUN
ejpam-4583	354	7	18	18	NUM
ejpam-4583	354	8	and	and	CCONJ
ejpam-4583	354	9	property	property	NOUN
ejpam-4583	354	10	(	(	PUNCT
ejpam-4583	354	11	v	v	NOUN
ejpam-4583	354	12	)	)	PUNCT
ejpam-4583	354	13	we	we	PRON
ejpam-4583	354	14	have	have	VERB
ejpam-4583	354	15	bdf	bdf	NOUN
ejpam-4583	354	16	(	(	PUNCT
ejpam-4583	354	17	bdf	bdf	NOUN
ejpam-4583	354	18	(	(	PUNCT
ejpam-4583	354	19	k	k	NOUN
ejpam-4583	354	20	)	)	PUNCT
ejpam-4583	354	21	)	)	PUNCT
ejpam-4583	355	1	=	=	SYM
ejpam-4583	355	2	bdf	bdf	NOUN
ejpam-4583	355	3	(	(	PUNCT
ejpam-4583	355	4	k)\intf	k)\intf	X
ejpam-4583	355	5	(	(	PUNCT
ejpam-4583	355	6	bdf	bdf	NOUN
ejpam-4583	355	7	(	(	PUNCT
ejpam-4583	355	8	k	k	NOUN
ejpam-4583	355	9	)	)	PUNCT
ejpam-4583	355	10	)	)	PUNCT
ejpam-4583	356	1	=	=	SYM
ejpam-4583	356	2	bdf	bdf	NOUN
ejpam-4583	356	3	(	(	PUNCT
ejpam-4583	356	4	k)\∅	k)\∅	NOUN
ejpam-4583	356	5	=	=	SYM
ejpam-4583	356	6	bdf	bdf	NOUN
ejpam-4583	356	7	(	(	PUNCT
ejpam-4583	356	8	k	k	NOUN
ejpam-4583	356	9	)	)	PUNCT
ejpam-4583	356	10	.	.	PUNCT
ejpam-4583	357	1	the	the	DET
ejpam-4583	357	2	property	property	NOUN
ejpam-4583	357	3	(	(	PUNCT
ejpam-4583	357	4	vii	vii	PROPN
ejpam-4583	357	5	)	)	PUNCT
ejpam-4583	357	6	follow	follow	VERB
ejpam-4583	357	7	from	from	ADP
ejpam-4583	357	8	theorem	theorem	ADJ
ejpam-4583	357	9	7	7	NUM
ejpam-4583	357	10	part	part	NOUN
ejpam-4583	357	11	(	(	PUNCT
ejpam-4583	357	12	i	i	NOUN
ejpam-4583	357	13	)	)	PUNCT
ejpam-4583	357	14	and	and	CCONJ
ejpam-4583	357	15	definition	definition	NOUN
ejpam-4583	357	16	18	18	NUM
ejpam-4583	357	17	.	.	PUNCT
ejpam-4583	358	1	in	in	ADP
ejpam-4583	358	2	general	general	ADJ
ejpam-4583	358	3	bdf	bdf	NOUN
ejpam-4583	358	4	(	(	PUNCT
ejpam-4583	358	5	k	k	NOUN
ejpam-4583	358	6	)	)	PUNCT
ejpam-4583	358	7	⊈	⊈	PROPN
ejpam-4583	358	8	bd(k	bd(k	NOUN
ejpam-4583	358	9	)	)	PUNCT
ejpam-4583	358	10	.	.	PUNCT
ejpam-4583	359	1	for	for	ADP
ejpam-4583	359	2	example	example	NOUN
ejpam-4583	359	3	:	:	PUNCT
ejpam-4583	359	4	example	example	NOUN
ejpam-4583	359	5	14	14	NUM
ejpam-4583	359	6	.	.	PUNCT
ejpam-4583	360	1	let	let	VERB
ejpam-4583	360	2	k	k	NOUN
ejpam-4583	360	3	=	=	PUNCT
ejpam-4583	360	4	r	r	NOUN
ejpam-4583	360	5	\	\	NOUN
ejpam-4583	360	6	n	n	CCONJ
ejpam-4583	360	7	be	be	AUX
ejpam-4583	360	8	a	a	DET
ejpam-4583	360	9	subset	subset	NOUN
ejpam-4583	360	10	of	of	ADP
ejpam-4583	360	11	the	the	DET
ejpam-4583	360	12	usual	usual	ADJ
ejpam-4583	360	13	topological	topological	ADJ
ejpam-4583	360	14	space	space	NOUN
ejpam-4583	360	15	(	(	PUNCT
ejpam-4583	360	16	r	r	NOUN
ejpam-4583	360	17	,	,	PUNCT
ejpam-4583	360	18	u	u	NOUN
ejpam-4583	360	19	)	)	PUNCT
ejpam-4583	360	20	,	,	PUNCT
ejpam-4583	360	21	where	where	SCONJ
ejpam-4583	360	22	n	n	ADV
ejpam-4583	360	23	=	=	SYM
ejpam-4583	360	24	{	{	PUNCT
ejpam-4583	360	25	1	1	NUM
ejpam-4583	360	26	,	,	PUNCT
ejpam-4583	360	27	2	2	NUM
ejpam-4583	360	28	,	,	PUNCT
ejpam-4583	360	29	3	3	NUM
ejpam-4583	360	30	,	,	PUNCT
ejpam-4583	360	31	.	.	PUNCT
ejpam-4583	360	32	.	.	PUNCT
ejpam-4583	360	33	.	.	PUNCT
ejpam-4583	361	1	}	}	PUNCT
ejpam-4583	361	2	.	.	PUNCT
ejpam-4583	362	1	then	then	ADV
ejpam-4583	362	2	bd(k	bd(k	X
ejpam-4583	362	3	)	)	PUNCT
ejpam-4583	363	1	=	=	PUNCT
ejpam-4583	363	2	∅.	∅.	NOUN
ejpam-4583	363	3	since	since	SCONJ
ejpam-4583	363	4	r\n	r\n	ADJ
ejpam-4583	363	5	is	be	AUX
ejpam-4583	363	6	not	not	PART
ejpam-4583	363	7	f	f	PROPN
ejpam-4583	363	8	-open	-open	NOUN
ejpam-4583	363	9	set	set	NOUN
ejpam-4583	363	10	,	,	PUNCT
ejpam-4583	363	11	then	then	ADV
ejpam-4583	363	12	intf	intf	PROPN
ejpam-4583	363	13	(	(	PUNCT
ejpam-4583	363	14	r\n	r\n	PROPN
ejpam-4583	363	15	)	)	PUNCT
ejpam-4583	363	16	⊂	⊂	PRON
ejpam-4583	363	17	r\n	r\n	PROPN
ejpam-4583	363	18	.	.	PUNCT
ejpam-4583	364	1	hence	hence	ADV
ejpam-4583	364	2	,	,	PUNCT
ejpam-4583	364	3	(	(	PUNCT
ejpam-4583	364	4	(	(	PUNCT
ejpam-4583	364	5	r	r	NOUN
ejpam-4583	364	6	\	\	NOUN
ejpam-4583	364	7	n	n	CCONJ
ejpam-4583	364	8	)	)	PUNCT
ejpam-4583	364	9	\	\	PROPN
ejpam-4583	364	10	intf	intf	PROPN
ejpam-4583	364	11	(	(	PUNCT
ejpam-4583	364	12	r	r	NOUN
ejpam-4583	364	13	\	\	PROPN
ejpam-4583	364	14	n	n	CCONJ
ejpam-4583	364	15	)	)	PUNCT
ejpam-4583	364	16	)	)	PUNCT
ejpam-4583	365	1	̸=	̸=	PROPN
ejpam-4583	365	2	∅.	∅.	PRON
ejpam-4583	365	3	therefore	therefore	ADV
ejpam-4583	365	4	,	,	PUNCT
ejpam-4583	365	5	bdf	bdf	NOUN
ejpam-4583	365	6	(	(	PUNCT
ejpam-4583	365	7	k	k	NOUN
ejpam-4583	365	8	)	)	PUNCT
ejpam-4583	365	9	⊈	⊈	PROPN
ejpam-4583	365	10	bd(k	bd(k	NOUN
ejpam-4583	365	11	)	)	PUNCT
ejpam-4583	365	12	.	.	PUNCT
ejpam-4583	366	1	definition	definition	NOUN
ejpam-4583	366	2	19	19	NUM
ejpam-4583	366	3	.	.	PUNCT
ejpam-4583	367	1	let	let	VERB
ejpam-4583	367	2	k	k	PRON
ejpam-4583	367	3	be	be	AUX
ejpam-4583	367	4	a	a	DET
ejpam-4583	367	5	subset	subset	NOUN
ejpam-4583	367	6	of	of	ADP
ejpam-4583	367	7	the	the	DET
ejpam-4583	367	8	topological	topological	ADJ
ejpam-4583	367	9	space	space	NOUN
ejpam-4583	367	10	x.	x.	NOUN
ejpam-4583	368	1	then	then	ADV
ejpam-4583	368	2	f	f	PROPN
ejpam-4583	368	3	-frontier	-frontier	PROPN
ejpam-4583	368	4	of	of	ADP
ejpam-4583	368	5	k	k	PROPN
ejpam-4583	368	6	is	be	AUX
ejpam-4583	368	7	defined	define	VERB
ejpam-4583	368	8	as	as	ADP
ejpam-4583	368	9	frf	frf	PROPN
ejpam-4583	368	10	(	(	PUNCT
ejpam-4583	368	11	k	k	NOUN
ejpam-4583	368	12	)	)	PUNCT
ejpam-4583	368	13	=	=	SYM
ejpam-4583	368	14	clf	clf	PROPN
ejpam-4583	368	15	(	(	PUNCT
ejpam-4583	368	16	k	k	NOUN
ejpam-4583	368	17	)	)	PUNCT
ejpam-4583	368	18	\	\	PROPN
ejpam-4583	368	19	intf	intf	PROPN
ejpam-4583	368	20	(	(	PUNCT
ejpam-4583	368	21	k	k	NOUN
ejpam-4583	368	22	)	)	PUNCT
ejpam-4583	368	23	.	.	PUNCT
ejpam-4583	369	1	theorem	theorem	NOUN
ejpam-4583	369	2	9	9	NUM
ejpam-4583	369	3	.	.	PUNCT
ejpam-4583	370	1	let	let	VERB
ejpam-4583	370	2	k	k	PRON
ejpam-4583	370	3	be	be	AUX
ejpam-4583	370	4	a	a	DET
ejpam-4583	370	5	subset	subset	NOUN
ejpam-4583	370	6	of	of	ADP
ejpam-4583	370	7	the	the	DET
ejpam-4583	370	8	topological	topological	ADJ
ejpam-4583	370	9	space	space	NOUN
ejpam-4583	370	10	(	(	PUNCT
ejpam-4583	370	11	x	x	X
ejpam-4583	370	12	,	,	PUNCT
ejpam-4583	370	13	t	t	PROPN
ejpam-4583	370	14	)	)	PUNCT
ejpam-4583	370	15	.	.	PUNCT
ejpam-4583	371	1	then	then	ADV
ejpam-4583	371	2	we	we	PRON
ejpam-4583	371	3	have	have	VERB
ejpam-4583	371	4	the	the	DET
ejpam-4583	371	5	following	follow	VERB
ejpam-4583	371	6	properties	property	NOUN
ejpam-4583	371	7	:	:	PUNCT
ejpam-4583	371	8	(	(	PUNCT
ejpam-4583	371	9	i	i	NOUN
ejpam-4583	371	10	)	)	PUNCT
ejpam-4583	371	11	fr(k	fr(k	NOUN
ejpam-4583	371	12	)	)	PUNCT
ejpam-4583	372	1	⊂	⊂	PROPN
ejpam-4583	372	2	frf	frf	PROPN
ejpam-4583	372	3	(	(	PUNCT
ejpam-4583	372	4	k	k	NOUN
ejpam-4583	372	5	)	)	PUNCT
ejpam-4583	372	6	,	,	PUNCT
ejpam-4583	372	7	where	where	SCONJ
ejpam-4583	372	8	fr(k	fr(k	NOUN
ejpam-4583	372	9	)	)	PUNCT
ejpam-4583	372	10	denotes	denote	VERB
ejpam-4583	372	11	the	the	DET
ejpam-4583	372	12	frontier	frontier	NOUN
ejpam-4583	372	13	of	of	ADP
ejpam-4583	372	14	k.	k.	PROPN
ejpam-4583	372	15	(	(	PUNCT
ejpam-4583	372	16	ii	ii	PROPN
ejpam-4583	372	17	)	)	PUNCT
ejpam-4583	372	18	clf	clf	PROPN
ejpam-4583	372	19	(	(	PUNCT
ejpam-4583	372	20	k	k	NOUN
ejpam-4583	372	21	)	)	PUNCT
ejpam-4583	373	1	=	=	SYM
ejpam-4583	373	2	intf	intf	NOUN
ejpam-4583	373	3	(	(	PUNCT
ejpam-4583	373	4	k	k	NOUN
ejpam-4583	373	5	)	)	PUNCT
ejpam-4583	373	6	∪	∪	NOUN
ejpam-4583	373	7	frf	frf	PROPN
ejpam-4583	373	8	(	(	PUNCT
ejpam-4583	373	9	k	k	NOUN
ejpam-4583	373	10	)	)	PUNCT
ejpam-4583	373	11	.	.	PUNCT
ejpam-4583	374	1	(	(	PUNCT
ejpam-4583	374	2	iii	iii	X
ejpam-4583	374	3	)	)	PUNCT
ejpam-4583	374	4	intf	intf	NOUN
ejpam-4583	374	5	(	(	PUNCT
ejpam-4583	374	6	k	k	NOUN
ejpam-4583	374	7	)	)	PUNCT
ejpam-4583	374	8	∩	∩	ADJ
ejpam-4583	374	9	frf	frf	X
ejpam-4583	374	10	(	(	PUNCT
ejpam-4583	374	11	k	k	NOUN
ejpam-4583	374	12	)	)	PUNCT
ejpam-4583	374	13	=	=	SYM
ejpam-4583	374	14	∅.	∅.	X
ejpam-4583	374	15	(	(	PUNCT
ejpam-4583	374	16	iv	iv	X
ejpam-4583	374	17	)	)	PUNCT
ejpam-4583	374	18	bdf	bdf	NOUN
ejpam-4583	374	19	(	(	PUNCT
ejpam-4583	374	20	k	k	NOUN
ejpam-4583	374	21	)	)	PUNCT
ejpam-4583	374	22	⊂	⊂	PROPN
ejpam-4583	375	1	frf	frf	PROPN
ejpam-4583	375	2	(	(	PUNCT
ejpam-4583	375	3	k	k	NOUN
ejpam-4583	375	4	)	)	PUNCT
ejpam-4583	375	5	.	.	PUNCT
ejpam-4583	376	1	(	(	PUNCT
ejpam-4583	376	2	v	v	NOUN
ejpam-4583	376	3	)	)	PUNCT
ejpam-4583	376	4	frf	frf	PROPN
ejpam-4583	376	5	(	(	PUNCT
ejpam-4583	376	6	k	k	NOUN
ejpam-4583	376	7	)	)	PUNCT
ejpam-4583	376	8	=	=	SYM
ejpam-4583	376	9	clf	clf	PROPN
ejpam-4583	376	10	(	(	PUNCT
ejpam-4583	376	11	k	k	NOUN
ejpam-4583	376	12	)	)	PUNCT
ejpam-4583	376	13	∩	∩	PROPN
ejpam-4583	376	14	clf	clf	PROPN
ejpam-4583	376	15	(	(	PUNCT
ejpam-4583	376	16	x	x	NOUN
ejpam-4583	376	17	\k	\k	NOUN
ejpam-4583	376	18	)	)	PUNCT
ejpam-4583	376	19	.	.	PUNCT
ejpam-4583	377	1	(	(	PUNCT
ejpam-4583	377	2	vi	vi	X
ejpam-4583	377	3	)	)	PUNCT
ejpam-4583	377	4	frf	frf	NOUN
ejpam-4583	377	5	(	(	PUNCT
ejpam-4583	377	6	k	k	NOUN
ejpam-4583	377	7	)	)	PUNCT
ejpam-4583	377	8	=	=	SYM
ejpam-4583	377	9	frf	frf	PROPN
ejpam-4583	377	10	(	(	PUNCT
ejpam-4583	377	11	x	x	NOUN
ejpam-4583	377	12	\k	\k	NOUN
ejpam-4583	377	13	)	)	PUNCT
ejpam-4583	377	14	.	.	PUNCT
ejpam-4583	378	1	(	(	PUNCT
ejpam-4583	378	2	viii	viii	NOUN
ejpam-4583	378	3	)	)	PUNCT
ejpam-4583	378	4	intf	intf	NOUN
ejpam-4583	378	5	(	(	PUNCT
ejpam-4583	378	6	k	k	NOUN
ejpam-4583	378	7	)	)	PUNCT
ejpam-4583	378	8	=	=	SYM
ejpam-4583	379	1	k	k	PROPN
ejpam-4583	379	2	\	\	PROPN
ejpam-4583	379	3	frf	frf	PROPN
ejpam-4583	379	4	(	(	PUNCT
ejpam-4583	379	5	k	k	NOUN
ejpam-4583	379	6	)	)	PUNCT
ejpam-4583	379	7	.	.	PUNCT
ejpam-4583	380	1	proof	proof	NOUN
ejpam-4583	380	2	.	.	PUNCT
ejpam-4583	381	1	the	the	DET
ejpam-4583	381	2	property	property	NOUN
ejpam-4583	381	3	(	(	PUNCT
ejpam-4583	381	4	i	i	NOUN
ejpam-4583	381	5	)	)	PUNCT
ejpam-4583	381	6	,	,	PUNCT
ejpam-4583	381	7	by	by	ADP
ejpam-4583	381	8	theorem	theorem	NOUN
ejpam-4583	381	9	3	3	NUM
ejpam-4583	381	10	and	and	CCONJ
ejpam-4583	381	11	definition	definition	NOUN
ejpam-4583	381	12	19	19	NUM
ejpam-4583	381	13	,	,	PUNCT
ejpam-4583	381	14	we	we	PRON
ejpam-4583	381	15	have	have	VERB
ejpam-4583	381	16	intf	intf	X
ejpam-4583	381	17	(	(	PUNCT
ejpam-4583	381	18	k	k	NOUN
ejpam-4583	381	19	)	)	PUNCT
ejpam-4583	381	20	⊆	⊆	NUM
ejpam-4583	381	21	int(k	int(k	NUM
ejpam-4583	381	22	)	)	PUNCT
ejpam-4583	381	23	and	and	CCONJ
ejpam-4583	381	24	cl(k	cl(k	NUM
ejpam-4583	381	25	)	)	PUNCT
ejpam-4583	381	26	⊆	⊆	NUM
ejpam-4583	381	27	clf	clf	PROPN
ejpam-4583	381	28	(	(	PUNCT
ejpam-4583	381	29	k	k	NOUN
ejpam-4583	381	30	)	)	PUNCT
ejpam-4583	381	31	,	,	PUNCT
ejpam-4583	381	32	then	then	ADV
ejpam-4583	381	33	fr(k	fr(k	NOUN
ejpam-4583	381	34	)	)	PUNCT
ejpam-4583	381	35	=	=	SYM
ejpam-4583	381	36	(	(	PUNCT
ejpam-4583	381	37	cl(k	cl(k	NOUN
ejpam-4583	381	38	)	)	PUNCT
ejpam-4583	381	39	\	\	PROPN
ejpam-4583	381	40	int(k	int(k	PROPN
ejpam-4583	381	41	)	)	PUNCT
ejpam-4583	381	42	)	)	PUNCT
ejpam-4583	382	1	⊆	⊆	NUM
ejpam-4583	382	2	clf	clf	PROPN
ejpam-4583	382	3	(	(	PUNCT
ejpam-4583	382	4	k	k	NOUN
ejpam-4583	382	5	)	)	PUNCT
ejpam-4583	382	6	\	\	PROPN
ejpam-4583	382	7	intf	intf	PROPN
ejpam-4583	382	8	(	(	PUNCT
ejpam-4583	382	9	k	k	NOUN
ejpam-4583	382	10	)	)	PUNCT
ejpam-4583	382	11	=	=	SYM
ejpam-4583	382	12	frf	frf	PROPN
ejpam-4583	382	13	(	(	PUNCT
ejpam-4583	382	14	k	k	NOUN
ejpam-4583	382	15	)	)	PUNCT
ejpam-4583	382	16	.	.	PUNCT
ejpam-4583	383	1	the	the	DET
ejpam-4583	383	2	properties	property	NOUN
ejpam-4583	383	3	(	(	PUNCT
ejpam-4583	383	4	ii	ii	NOUN
ejpam-4583	383	5	)	)	PUNCT
ejpam-4583	383	6	and	and	CCONJ
ejpam-4583	383	7	(	(	PUNCT
ejpam-4583	383	8	iii	iii	X
ejpam-4583	383	9	)	)	PUNCT
ejpam-4583	383	10	follow	follow	VERB
ejpam-4583	383	11	from	from	ADP
ejpam-4583	383	12	definition	definition	NOUN
ejpam-4583	383	13	19	19	NUM
ejpam-4583	383	14	.	.	PUNCT
ejpam-4583	384	1	for	for	ADP
ejpam-4583	384	2	(	(	PUNCT
ejpam-4583	384	3	iv	iv	NOUN
ejpam-4583	384	4	)	)	PUNCT
ejpam-4583	384	5	,	,	PUNCT
ejpam-4583	384	6	since	since	SCONJ
ejpam-4583	384	7	k	k	PROPN
ejpam-4583	384	8	⊆	⊆	NUM
ejpam-4583	384	9	clf	clf	PROPN
ejpam-4583	384	10	(	(	PUNCT
ejpam-4583	384	11	k	k	NOUN
ejpam-4583	384	12	)	)	PUNCT
ejpam-4583	384	13	,	,	PUNCT
ejpam-4583	384	14	then	then	ADV
ejpam-4583	384	15	bdf	bdf	NOUN
ejpam-4583	384	16	(	(	PUNCT
ejpam-4583	384	17	k	k	NOUN
ejpam-4583	384	18	)	)	PUNCT
ejpam-4583	384	19	=	=	SYM
ejpam-4583	384	20	(	(	PUNCT
ejpam-4583	384	21	k	k	PROPN
ejpam-4583	384	22	\	\	PROPN
ejpam-4583	384	23	intf	intf	PROPN
ejpam-4583	384	24	(	(	PUNCT
ejpam-4583	384	25	k	k	NOUN
ejpam-4583	384	26	)	)	PUNCT
ejpam-4583	384	27	)	)	PUNCT
ejpam-4583	384	28	⊆	⊆	X
ejpam-4583	385	1	(	(	PUNCT
ejpam-4583	385	2	clf	clf	PROPN
ejpam-4583	385	3	(	(	PUNCT
ejpam-4583	385	4	k	k	NOUN
ejpam-4583	385	5	)	)	PUNCT
ejpam-4583	385	6	\	\	PROPN
ejpam-4583	385	7	intf	intf	PROPN
ejpam-4583	385	8	(	(	PUNCT
ejpam-4583	385	9	k	k	NOUN
ejpam-4583	385	10	)	)	PUNCT
ejpam-4583	385	11	)	)	PUNCT
ejpam-4583	386	1	=	=	SYM
ejpam-4583	386	2	frf	frf	X
ejpam-4583	386	3	(	(	PUNCT
ejpam-4583	386	4	k	k	NOUN
ejpam-4583	386	5	)	)	PUNCT
ejpam-4583	386	6	.	.	PUNCT
ejpam-4583	387	1	the	the	DET
ejpam-4583	387	2	property	property	NOUN
ejpam-4583	387	3	(	(	PUNCT
ejpam-4583	387	4	v	v	NOUN
ejpam-4583	387	5	)	)	PUNCT
ejpam-4583	387	6	follow	follow	VERB
ejpam-4583	387	7	from	from	ADP
ejpam-4583	387	8	theorem	theorem	ADJ
ejpam-4583	387	9	7	7	NUM
ejpam-4583	387	10	and	and	CCONJ
ejpam-4583	387	11	definition	definition	NOUN
ejpam-4583	387	12	19	19	NUM
ejpam-4583	387	13	.	.	PUNCT
ejpam-4583	388	1	the	the	DET
ejpam-4583	388	2	property	property	NOUN
ejpam-4583	388	3	(	(	PUNCT
ejpam-4583	388	4	vi	vi	NOUN
ejpam-4583	388	5	)	)	PUNCT
ejpam-4583	388	6	follow	follow	VERB
ejpam-4583	388	7	from	from	ADP
ejpam-4583	388	8	property	property	NOUN
ejpam-4583	388	9	(	(	PUNCT
ejpam-4583	388	10	v	v	NOUN
ejpam-4583	388	11	)	)	PUNCT
ejpam-4583	388	12	and	and	CCONJ
ejpam-4583	388	13	definition	definition	NOUN
ejpam-4583	388	14	19	19	NUM
ejpam-4583	388	15	.	.	PUNCT
ejpam-4583	389	1	the	the	DET
ejpam-4583	389	2	property	property	NOUN
ejpam-4583	389	3	(	(	PUNCT
ejpam-4583	389	4	vii	vii	PROPN
ejpam-4583	389	5	)	)	PUNCT
ejpam-4583	389	6	follow	follow	VERB
ejpam-4583	389	7	from	from	ADP
ejpam-4583	389	8	definition	definition	NOUN
ejpam-4583	389	9	19	19	NUM
ejpam-4583	389	10	.	.	PUNCT
ejpam-4583	390	1	in	in	ADP
ejpam-4583	390	2	general	general	ADJ
ejpam-4583	390	3	frf	frf	PROPN
ejpam-4583	390	4	(	(	PUNCT
ejpam-4583	390	5	k	k	NOUN
ejpam-4583	390	6	)	)	PUNCT
ejpam-4583	390	7	⊈	⊈	PROPN
ejpam-4583	390	8	fr(k	fr(k	NOUN
ejpam-4583	390	9	)	)	PUNCT
ejpam-4583	390	10	and	and	CCONJ
ejpam-4583	390	11	frf	frf	NUM
ejpam-4583	390	12	(	(	PUNCT
ejpam-4583	390	13	k	k	NOUN
ejpam-4583	390	14	)	)	PUNCT
ejpam-4583	390	15	⊈	⊈	PROPN
ejpam-4583	390	16	bdf	bdf	NOUN
ejpam-4583	390	17	(	(	PUNCT
ejpam-4583	390	18	k	k	NOUN
ejpam-4583	390	19	)	)	PUNCT
ejpam-4583	390	20	.	.	PUNCT
ejpam-4583	391	1	for	for	ADP
ejpam-4583	391	2	example	example	NOUN
ejpam-4583	391	3	:	:	PUNCT
ejpam-4583	391	4	example	example	NOUN
ejpam-4583	391	5	15	15	NUM
ejpam-4583	391	6	.	.	PUNCT
ejpam-4583	392	1	let	let	VERB
ejpam-4583	392	2	k	k	NOUN
ejpam-4583	392	3	=	=	PUNCT
ejpam-4583	392	4	n	n	PART
ejpam-4583	392	5	be	be	AUX
ejpam-4583	392	6	a	a	DET
ejpam-4583	392	7	subset	subset	NOUN
ejpam-4583	392	8	of	of	ADP
ejpam-4583	392	9	the	the	DET
ejpam-4583	392	10	usual	usual	ADJ
ejpam-4583	392	11	topological	topological	ADJ
ejpam-4583	392	12	space	space	NOUN
ejpam-4583	392	13	(	(	PUNCT
ejpam-4583	392	14	r	r	NOUN
ejpam-4583	392	15	,	,	PUNCT
ejpam-4583	392	16	u	u	NOUN
ejpam-4583	392	17	)	)	PUNCT
ejpam-4583	392	18	,	,	PUNCT
ejpam-4583	392	19	where	where	SCONJ
ejpam-4583	392	20	n	n	ADV
ejpam-4583	392	21	=	=	SYM
ejpam-4583	392	22	{	{	PUNCT
ejpam-4583	392	23	1	1	NUM
ejpam-4583	392	24	,	,	PUNCT
ejpam-4583	392	25	2	2	NUM
ejpam-4583	392	26	,	,	PUNCT
ejpam-4583	392	27	3	3	NUM
ejpam-4583	392	28	,	,	PUNCT
ejpam-4583	392	29	.	.	PUNCT
ejpam-4583	392	30	.	.	PUNCT
ejpam-4583	392	31	.	.	PUNCT
ejpam-4583	393	1	}	}	PUNCT
ejpam-4583	393	2	.	.	PUNCT
ejpam-4583	394	1	then	then	ADV
ejpam-4583	394	2	fr(k	fr(k	NOUN
ejpam-4583	394	3	)	)	PUNCT
ejpam-4583	394	4	=	=	VERB
ejpam-4583	394	5	n.	n.	NOUN
ejpam-4583	394	6	without	without	ADP
ejpam-4583	394	7	loss	loss	NOUN
ejpam-4583	394	8	of	of	ADP
ejpam-4583	394	9	generality	generality	NOUN
ejpam-4583	394	10	,	,	PUNCT
ejpam-4583	394	11	we	we	PRON
ejpam-4583	394	12	assume	assume	VERB
ejpam-4583	394	13	that	that	SCONJ
ejpam-4583	394	14	,	,	PUNCT
ejpam-4583	394	15	clf	clf	PROPN
ejpam-4583	394	16	(	(	PUNCT
ejpam-4583	394	17	k	k	NOUN
ejpam-4583	394	18	)	)	PUNCT
ejpam-4583	394	19	=	=	SYM
ejpam-4583	394	20	{	{	PUNCT
ejpam-4583	394	21	1	1	NUM
ejpam-4583	394	22	,	,	PUNCT
ejpam-4583	394	23	2	2	NUM
ejpam-4583	394	24	,	,	PUNCT
ejpam-4583	394	25	3	3	NUM
ejpam-4583	394	26	,	,	PUNCT
ejpam-4583	394	27	.	.	PUNCT
ejpam-4583	394	28	.	.	PUNCT
ejpam-4583	395	1	.	.	PUNCT
ejpam-4583	396	1	,	,	PUNCT
ejpam-4583	396	2	n}∪[n,∞	n}∪[n,∞	PROPN
ejpam-4583	396	3	)	)	PUNCT
ejpam-4583	396	4	,	,	PUNCT
ejpam-4583	396	5	for	for	ADP
ejpam-4583	396	6	some	some	DET
ejpam-4583	396	7	n	n	PRON
ejpam-4583	396	8	∈	∈	PROPN
ejpam-4583	396	9	n	n	CCONJ
ejpam-4583	396	10	,	,	PUNCT
ejpam-4583	396	11	then	then	ADV
ejpam-4583	396	12	frf	frf	PROPN
ejpam-4583	396	13	(	(	PUNCT
ejpam-4583	396	14	k	k	NOUN
ejpam-4583	396	15	)	)	PUNCT
ejpam-4583	396	16	=	=	SYM
ejpam-4583	396	17	clf	clf	PROPN
ejpam-4583	396	18	(	(	PUNCT
ejpam-4583	396	19	k)\intf	k)\intf	X
ejpam-4583	396	20	(	(	PUNCT
ejpam-4583	396	21	k	k	NOUN
ejpam-4583	396	22	)	)	PUNCT
ejpam-4583	396	23	=	=	SYM
ejpam-4583	396	24	{	{	PUNCT
ejpam-4583	396	25	1	1	NUM
ejpam-4583	396	26	,	,	PUNCT
ejpam-4583	396	27	2	2	NUM
ejpam-4583	396	28	,	,	PUNCT
ejpam-4583	396	29	3	3	NUM
ejpam-4583	396	30	,	,	PUNCT
ejpam-4583	396	31	.	.	PUNCT
ejpam-4583	396	32	.	.	PUNCT
ejpam-4583	396	33	.	.	PUNCT
ejpam-4583	397	1	,	,	PUNCT
ejpam-4583	397	2	n}∪	n}∪	X
ejpam-4583	398	1	[	[	X
ejpam-4583	398	2	n,∞	n,∞	NOUN
ejpam-4583	398	3	)	)	PUNCT
ejpam-4583	398	4	\	\	NOUN
ejpam-4583	398	5	∅	∅	NOUN
ejpam-4583	398	6	=	=	SYM
ejpam-4583	398	7	{	{	PUNCT
ejpam-4583	398	8	1	1	NUM
ejpam-4583	398	9	,	,	PUNCT
ejpam-4583	398	10	2	2	NUM
ejpam-4583	398	11	,	,	PUNCT
ejpam-4583	398	12	3	3	NUM
ejpam-4583	398	13	,	,	PUNCT
ejpam-4583	398	14	.	.	PUNCT
ejpam-4583	398	15	.	.	PUNCT
ejpam-4583	399	1	.	.	PUNCT
ejpam-4583	400	1	,	,	PUNCT
ejpam-4583	400	2	n	n	CCONJ
ejpam-4583	400	3	}	}	PUNCT
ejpam-4583	400	4	∪	∪	VERB
ejpam-4583	400	5	[	[	X
ejpam-4583	400	6	n,∞	n,∞	NOUN
ejpam-4583	400	7	)	)	PUNCT
ejpam-4583	400	8	.	.	PUNCT
ejpam-4583	401	1	hence	hence	ADV
ejpam-4583	401	2	,	,	PUNCT
ejpam-4583	401	3	frf	frf	PROPN
ejpam-4583	401	4	(	(	PUNCT
ejpam-4583	401	5	k	k	NOUN
ejpam-4583	401	6	)	)	PUNCT
ejpam-4583	401	7	⊈	⊈	PROPN
ejpam-4583	401	8	fr(k	fr(k	NOUN
ejpam-4583	401	9	)	)	PUNCT
ejpam-4583	401	10	.	.	PUNCT
ejpam-4583	402	1	for	for	ADP
ejpam-4583	402	2	frf	frf	PROPN
ejpam-4583	402	3	(	(	PUNCT
ejpam-4583	402	4	k	k	NOUN
ejpam-4583	402	5	)	)	PUNCT
ejpam-4583	402	6	⊈	⊈	PROPN
ejpam-4583	402	7	bdf	bdf	NOUN
ejpam-4583	402	8	(	(	PUNCT
ejpam-4583	402	9	k	k	NOUN
ejpam-4583	402	10	)	)	PUNCT
ejpam-4583	402	11	,	,	PUNCT
ejpam-4583	402	12	let	let	VERB
ejpam-4583	402	13	k	k	PROPN
ejpam-4583	402	14	=	=	PUNCT
ejpam-4583	402	15	(	(	PUNCT
ejpam-4583	402	16	1	1	NUM
ejpam-4583	402	17	,	,	PUNCT
ejpam-4583	402	18	2	2	NUM
ejpam-4583	402	19	]	]	PUNCT
ejpam-4583	402	20	be	be	AUX
ejpam-4583	402	21	a	a	DET
ejpam-4583	402	22	subsets	subset	NOUN
ejpam-4583	402	23	in	in	ADP
ejpam-4583	402	24	(	(	PUNCT
ejpam-4583	402	25	r	r	NOUN
ejpam-4583	402	26	,	,	PUNCT
ejpam-4583	402	27	u	u	NOUN
ejpam-4583	402	28	)	)	PUNCT
ejpam-4583	402	29	,	,	PUNCT
ejpam-4583	402	30	then	then	ADV
ejpam-4583	402	31	bdf	bdf	NOUN
ejpam-4583	402	32	(	(	PUNCT
ejpam-4583	402	33	k	k	NOUN
ejpam-4583	402	34	)	)	PUNCT
ejpam-4583	402	35	=	=	SYM
ejpam-4583	402	36	{	{	PUNCT
ejpam-4583	402	37	2	2	NUM
ejpam-4583	402	38	}	}	PUNCT
ejpam-4583	402	39	and	and	CCONJ
ejpam-4583	402	40	frf	frf	NUM
ejpam-4583	402	41	(	(	PUNCT
ejpam-4583	402	42	k	k	NOUN
ejpam-4583	402	43	)	)	PUNCT
ejpam-4583	402	44	=	=	SYM
ejpam-4583	402	45	{	{	PUNCT
ejpam-4583	402	46	1	1	NUM
ejpam-4583	402	47	,	,	PUNCT
ejpam-4583	402	48	2	2	NUM
ejpam-4583	402	49	}	}	PUNCT
ejpam-4583	402	50	.	.	PUNCT
ejpam-4583	403	1	hence	hence	ADV
ejpam-4583	403	2	,	,	PUNCT
ejpam-4583	403	3	frf	frf	PROPN
ejpam-4583	403	4	(	(	PUNCT
ejpam-4583	403	5	k	k	NOUN
ejpam-4583	403	6	)	)	PUNCT
ejpam-4583	403	7	⊈	⊈	PROPN
ejpam-4583	403	8	bdf	bdf	NOUN
ejpam-4583	403	9	(	(	PUNCT
ejpam-4583	403	10	k	k	NOUN
ejpam-4583	403	11	)	)	PUNCT
ejpam-4583	403	12	.	.	PUNCT
ejpam-4583	404	1	definition	definition	NOUN
ejpam-4583	404	2	20	20	NUM
ejpam-4583	404	3	.	.	PUNCT
ejpam-4583	405	1	let	let	VERB
ejpam-4583	405	2	k	k	PRON
ejpam-4583	405	3	be	be	AUX
ejpam-4583	405	4	a	a	DET
ejpam-4583	405	5	subset	subset	NOUN
ejpam-4583	405	6	of	of	ADP
ejpam-4583	405	7	the	the	DET
ejpam-4583	405	8	topological	topological	ADJ
ejpam-4583	405	9	space	space	NOUN
ejpam-4583	405	10	x.	x.	NOUN
ejpam-4583	406	1	then	then	ADV
ejpam-4583	406	2	f	f	PROPN
ejpam-4583	406	3	-exterior	-exterior	PROPN
ejpam-4583	406	4	of	of	ADP
ejpam-4583	406	5	k	k	PROPN
ejpam-4583	406	6	is	be	AUX
ejpam-4583	406	7	defined	define	VERB
ejpam-4583	406	8	as	as	ADP
ejpam-4583	406	9	extf	extf	ADJ
ejpam-4583	406	10	(	(	PUNCT
ejpam-4583	406	11	k	k	NOUN
ejpam-4583	406	12	)	)	PUNCT
ejpam-4583	407	1	=	=	SYM
ejpam-4583	407	2	intf	intf	PROPN
ejpam-4583	407	3	(	(	PUNCT
ejpam-4583	407	4	x	x	NOUN
ejpam-4583	407	5	\k	\k	NOUN
ejpam-4583	407	6	)	)	PUNCT
ejpam-4583	407	7	.	.	PUNCT
ejpam-4583	408	1	m.	m.	PROPN
ejpam-4583	408	2	h.	h.	PROPN
ejpam-4583	408	3	alqahtani	alqahtani	PROPN
ejpam-4583	408	4	/	/	SYM
ejpam-4583	408	5	eur	eur	PROPN
ejpam-4583	408	6	.	.	PUNCT
ejpam-4583	409	1	j.	j.	PROPN
ejpam-4583	409	2	pure	pure	PROPN
ejpam-4583	409	3	appl	appl	PROPN
ejpam-4583	409	4	.	.	PROPN
ejpam-4583	409	5	math	math	PROPN
ejpam-4583	409	6	,	,	PUNCT
ejpam-4583	409	7	16	16	NUM
ejpam-4583	409	8	(	(	PUNCT
ejpam-4583	409	9	2	2	NUM
ejpam-4583	409	10	)	)	PUNCT
ejpam-4583	409	11	(	(	PUNCT
ejpam-4583	409	12	2023	2023	NUM
ejpam-4583	409	13	)	)	PUNCT
ejpam-4583	409	14	,	,	PUNCT
ejpam-4583	409	15	819	819	NUM
ejpam-4583	409	16	-	-	SYM
ejpam-4583	409	17	832	832	NUM
ejpam-4583	409	18	829	829	NUM
ejpam-4583	409	19	theorem	theorem	VERB
ejpam-4583	409	20	10	10	NUM
ejpam-4583	409	21	.	.	PUNCT
ejpam-4583	410	1	let	let	VERB
ejpam-4583	410	2	k	k	PRON
ejpam-4583	410	3	be	be	AUX
ejpam-4583	410	4	a	a	DET
ejpam-4583	410	5	subset	subset	NOUN
ejpam-4583	410	6	of	of	ADP
ejpam-4583	410	7	the	the	DET
ejpam-4583	410	8	topological	topological	ADJ
ejpam-4583	410	9	space	space	NOUN
ejpam-4583	410	10	(	(	PUNCT
ejpam-4583	410	11	x	x	X
ejpam-4583	410	12	,	,	PUNCT
ejpam-4583	410	13	t	t	PROPN
ejpam-4583	410	14	)	)	PUNCT
ejpam-4583	410	15	.	.	PUNCT
ejpam-4583	411	1	then	then	ADV
ejpam-4583	411	2	we	we	PRON
ejpam-4583	411	3	have	have	VERB
ejpam-4583	411	4	the	the	DET
ejpam-4583	411	5	following	follow	VERB
ejpam-4583	411	6	properties	property	NOUN
ejpam-4583	411	7	:	:	PUNCT
ejpam-4583	411	8	(	(	PUNCT
ejpam-4583	411	9	i	i	NOUN
ejpam-4583	411	10	)	)	PUNCT
ejpam-4583	411	11	extf	extf	PROPN
ejpam-4583	411	12	(	(	PUNCT
ejpam-4583	411	13	k	k	X
ejpam-4583	411	14	)	)	PUNCT
ejpam-4583	411	15	⊂	⊂	PROPN
ejpam-4583	411	16	ext(k	ext(k	PROPN
ejpam-4583	411	17	)	)	PUNCT
ejpam-4583	411	18	,	,	PUNCT
ejpam-4583	411	19	where	where	SCONJ
ejpam-4583	411	20	ext(k	ext(k	NOUN
ejpam-4583	411	21	)	)	PUNCT
ejpam-4583	411	22	denotes	denote	VERB
ejpam-4583	411	23	the	the	DET
ejpam-4583	411	24	exterior	exterior	NOUN
ejpam-4583	411	25	of	of	ADP
ejpam-4583	411	26	k.	k.	PROPN
ejpam-4583	411	27	(	(	PUNCT
ejpam-4583	411	28	ii	ii	PROPN
ejpam-4583	411	29	)	)	PUNCT
ejpam-4583	411	30	extf	extf	NOUN
ejpam-4583	411	31	(	(	PUNCT
ejpam-4583	411	32	k	k	X
ejpam-4583	411	33	)	)	PUNCT
ejpam-4583	411	34	is	be	AUX
ejpam-4583	411	35	open	open	ADJ
ejpam-4583	411	36	.	.	PUNCT
ejpam-4583	412	1	(	(	PUNCT
ejpam-4583	412	2	iii	iii	X
ejpam-4583	412	3	)	)	PUNCT
ejpam-4583	412	4	extf	extf	NOUN
ejpam-4583	412	5	(	(	PUNCT
ejpam-4583	412	6	k	k	NOUN
ejpam-4583	412	7	)	)	PUNCT
ejpam-4583	412	8	=	=	PUNCT
ejpam-4583	413	1	x	x	SYM
ejpam-4583	413	2	\	\	PROPN
ejpam-4583	413	3	clf	clf	PROPN
ejpam-4583	413	4	(	(	PUNCT
ejpam-4583	413	5	k	k	NOUN
ejpam-4583	413	6	)	)	PUNCT
ejpam-4583	413	7	.	.	PUNCT
ejpam-4583	414	1	(	(	PUNCT
ejpam-4583	414	2	iv	iv	X
ejpam-4583	414	3	)	)	PUNCT
ejpam-4583	414	4	extf	extf	NOUN
ejpam-4583	414	5	(	(	PUNCT
ejpam-4583	414	6	extf	extf	ADJ
ejpam-4583	414	7	(	(	PUNCT
ejpam-4583	414	8	k	k	NOUN
ejpam-4583	414	9	)	)	PUNCT
ejpam-4583	414	10	)	)	PUNCT
ejpam-4583	415	1	=	=	SYM
ejpam-4583	415	2	intf	intf	PROPN
ejpam-4583	415	3	(	(	PUNCT
ejpam-4583	415	4	clf	clf	PROPN
ejpam-4583	415	5	(	(	PUNCT
ejpam-4583	415	6	k	k	NOUN
ejpam-4583	415	7	)	)	PUNCT
ejpam-4583	415	8	)	)	PUNCT
ejpam-4583	415	9	.	.	PUNCT
ejpam-4583	416	1	(	(	PUNCT
ejpam-4583	416	2	v	v	NOUN
ejpam-4583	416	3	)	)	PUNCT
ejpam-4583	416	4	if	if	SCONJ
ejpam-4583	416	5	k	k	PROPN
ejpam-4583	416	6	⊆	⊆	NUM
ejpam-4583	416	7	h	h	NOUN
ejpam-4583	416	8	,	,	PUNCT
ejpam-4583	416	9	then	then	ADV
ejpam-4583	416	10	extf	extf	ADJ
ejpam-4583	416	11	(	(	PUNCT
ejpam-4583	416	12	h	h	NOUN
ejpam-4583	416	13	)	)	PUNCT
ejpam-4583	416	14	⊆	⊆	NUM
ejpam-4583	416	15	extf	extf	NOUN
ejpam-4583	416	16	(	(	PUNCT
ejpam-4583	416	17	k	k	NOUN
ejpam-4583	416	18	)	)	PUNCT
ejpam-4583	416	19	.	.	PUNCT
ejpam-4583	417	1	(	(	PUNCT
ejpam-4583	417	2	vi	vi	X
ejpam-4583	417	3	)	)	PUNCT
ejpam-4583	417	4	extf	extf	NOUN
ejpam-4583	417	5	(	(	PUNCT
ejpam-4583	417	6	x	x	SYM
ejpam-4583	417	7	\	\	PROPN
ejpam-4583	417	8	extf	extf	NOUN
ejpam-4583	417	9	(	(	PUNCT
ejpam-4583	417	10	k	k	NOUN
ejpam-4583	417	11	)	)	PUNCT
ejpam-4583	417	12	)	)	PUNCT
ejpam-4583	418	1	=	=	PRON
ejpam-4583	418	2	extf	extf	ADJ
ejpam-4583	418	3	(	(	PUNCT
ejpam-4583	418	4	k	k	NOUN
ejpam-4583	418	5	)	)	PUNCT
ejpam-4583	418	6	.	.	PUNCT
ejpam-4583	419	1	(	(	PUNCT
ejpam-4583	419	2	vii	vii	PROPN
ejpam-4583	419	3	)	)	PUNCT
ejpam-4583	419	4	intf	intf	PROPN
ejpam-4583	419	5	(	(	PUNCT
ejpam-4583	419	6	k	k	NOUN
ejpam-4583	419	7	)	)	PUNCT
ejpam-4583	419	8	⊂	⊂	PROPN
ejpam-4583	419	9	extf	extf	PROPN
ejpam-4583	419	10	(	(	PUNCT
ejpam-4583	419	11	extf	extf	ADJ
ejpam-4583	419	12	(	(	PUNCT
ejpam-4583	419	13	k	k	NOUN
ejpam-4583	419	14	)	)	PUNCT
ejpam-4583	419	15	)	)	PUNCT
ejpam-4583	419	16	.	.	PUNCT
ejpam-4583	420	1	(	(	PUNCT
ejpam-4583	420	2	viii	viii	NOUN
ejpam-4583	420	3	)	)	PUNCT
ejpam-4583	420	4	extf	extf	NOUN
ejpam-4583	420	5	(	(	PUNCT
ejpam-4583	420	6	k	k	X
ejpam-4583	420	7	∪h	∪h	NUM
ejpam-4583	420	8	)	)	PUNCT
ejpam-4583	421	1	⊂	⊂	PROPN
ejpam-4583	421	2	extf	extf	ADJ
ejpam-4583	421	3	(	(	PUNCT
ejpam-4583	421	4	k	k	NOUN
ejpam-4583	421	5	)	)	PUNCT
ejpam-4583	421	6	∪	∪	ADJ
ejpam-4583	421	7	extf	extf	ADJ
ejpam-4583	421	8	(	(	PUNCT
ejpam-4583	421	9	h	h	NOUN
ejpam-4583	421	10	)	)	PUNCT
ejpam-4583	421	11	.	.	PUNCT
ejpam-4583	422	1	(	(	PUNCT
ejpam-4583	422	2	ix	ix	CCONJ
ejpam-4583	422	3	)	)	PUNCT
ejpam-4583	422	4	extf	extf	NOUN
ejpam-4583	422	5	(	(	PUNCT
ejpam-4583	423	1	k	k	PROPN
ejpam-4583	423	2	∩h	∩h	PROPN
ejpam-4583	423	3	)	)	PUNCT
ejpam-4583	423	4	⊃	⊃	PROPN
ejpam-4583	423	5	extf	extf	ADJ
ejpam-4583	423	6	(	(	PUNCT
ejpam-4583	423	7	k	k	NOUN
ejpam-4583	423	8	)	)	PUNCT
ejpam-4583	423	9	∩	∩	ADJ
ejpam-4583	423	10	extf	extf	ADJ
ejpam-4583	423	11	(	(	PUNCT
ejpam-4583	423	12	h	h	NOUN
ejpam-4583	423	13	)	)	PUNCT
ejpam-4583	423	14	.	.	PUNCT
ejpam-4583	424	1	(	(	PUNCT
ejpam-4583	424	2	x	x	X
ejpam-4583	424	3	)	)	PUNCT
ejpam-4583	424	4	x	x	X
ejpam-4583	424	5	=	=	SYM
ejpam-4583	424	6	intf	intf	X
ejpam-4583	424	7	(	(	PUNCT
ejpam-4583	424	8	k	k	NOUN
ejpam-4583	424	9	)	)	PUNCT
ejpam-4583	424	10	∪	∪	ADJ
ejpam-4583	424	11	extf	extf	ADJ
ejpam-4583	424	12	(	(	PUNCT
ejpam-4583	424	13	k	k	NOUN
ejpam-4583	424	14	)	)	PUNCT
ejpam-4583	424	15	∪	∪	NOUN
ejpam-4583	424	16	frf	frf	PROPN
ejpam-4583	424	17	(	(	PUNCT
ejpam-4583	424	18	k	k	NOUN
ejpam-4583	424	19	)	)	PUNCT
ejpam-4583	424	20	.	.	PUNCT
ejpam-4583	425	1	proof	proof	NOUN
ejpam-4583	425	2	.	.	PUNCT
ejpam-4583	426	1	the	the	DET
ejpam-4583	426	2	property	property	NOUN
ejpam-4583	426	3	(	(	PUNCT
ejpam-4583	426	4	i	i	NOUN
ejpam-4583	426	5	)	)	PUNCT
ejpam-4583	426	6	,	,	PUNCT
ejpam-4583	426	7	follow	follow	VERB
ejpam-4583	426	8	from	from	ADP
ejpam-4583	426	9	definition	definition	NOUN
ejpam-4583	426	10	20	20	NUM
ejpam-4583	426	11	and	and	CCONJ
ejpam-4583	426	12	theorem	theorem	VERB
ejpam-4583	426	13	3	3	NUM
ejpam-4583	426	14	.	.	PUNCT
ejpam-4583	427	1	the	the	DET
ejpam-4583	427	2	property	property	NOUN
ejpam-4583	427	3	(	(	PUNCT
ejpam-4583	427	4	ii	ii	NOUN
ejpam-4583	427	5	)	)	PUNCT
ejpam-4583	427	6	,	,	PUNCT
ejpam-4583	427	7	follow	follow	VERB
ejpam-4583	427	8	from	from	ADP
ejpam-4583	427	9	definition	definition	NOUN
ejpam-4583	427	10	15	15	NUM
ejpam-4583	427	11	.	.	PUNCT
ejpam-4583	428	1	the	the	DET
ejpam-4583	428	2	property	property	NOUN
ejpam-4583	428	3	(	(	PUNCT
ejpam-4583	428	4	iii	iii	NOUN
ejpam-4583	428	5	)	)	PUNCT
ejpam-4583	428	6	,	,	PUNCT
ejpam-4583	428	7	follow	follow	VERB
ejpam-4583	428	8	from	from	ADP
ejpam-4583	428	9	theorem	theorem	ADJ
ejpam-4583	428	10	7	7	NUM
ejpam-4583	428	11	and	and	CCONJ
ejpam-4583	428	12	definition	definition	NOUN
ejpam-4583	428	13	20	20	NUM
ejpam-4583	428	14	.	.	PUNCT
ejpam-4583	428	15	to	to	PART
ejpam-4583	428	16	prove	prove	VERB
ejpam-4583	428	17	(	(	PUNCT
ejpam-4583	428	18	iv	iv	X
ejpam-4583	428	19	)	)	PUNCT
ejpam-4583	428	20	extf	extf	NOUN
ejpam-4583	428	21	(	(	PUNCT
ejpam-4583	428	22	extf	extf	ADJ
ejpam-4583	428	23	(	(	PUNCT
ejpam-4583	428	24	k	k	NOUN
ejpam-4583	428	25	)	)	PUNCT
ejpam-4583	428	26	)	)	PUNCT
ejpam-4583	429	1	=	=	PRON
ejpam-4583	429	2	extf	extf	ADJ
ejpam-4583	429	3	(	(	PUNCT
ejpam-4583	429	4	intf	intf	PROPN
ejpam-4583	429	5	(	(	PUNCT
ejpam-4583	429	6	x	x	SYM
ejpam-4583	429	7	\	\	PROPN
ejpam-4583	429	8	k	k	NOUN
ejpam-4583	429	9	)	)	PUNCT
ejpam-4583	429	10	)	)	PUNCT
ejpam-4583	430	1	=	=	PRON
ejpam-4583	430	2	extf	extf	ADJ
ejpam-4583	430	3	(	(	PUNCT
ejpam-4583	430	4	x	x	SYM
ejpam-4583	430	5	\	\	PROPN
ejpam-4583	430	6	clf	clf	PROPN
ejpam-4583	430	7	(	(	PUNCT
ejpam-4583	430	8	k	k	NOUN
ejpam-4583	430	9	)	)	PUNCT
ejpam-4583	430	10	)	)	PUNCT
ejpam-4583	431	1	=	=	SYM
ejpam-4583	431	2	intf	intf	NOUN
ejpam-4583	431	3	(	(	PUNCT
ejpam-4583	431	4	x	x	SYM
ejpam-4583	431	5	\	\	PROPN
ejpam-4583	431	6	(	(	PUNCT
ejpam-4583	431	7	x	x	SYM
ejpam-4583	431	8	\	\	PROPN
ejpam-4583	431	9	clf	clf	PROPN
ejpam-4583	431	10	(	(	PUNCT
ejpam-4583	431	11	k	k	NOUN
ejpam-4583	431	12	)	)	PUNCT
ejpam-4583	431	13	)	)	PUNCT
ejpam-4583	431	14	)	)	PUNCT
ejpam-4583	432	1	=	=	PRON
ejpam-4583	432	2	intf	intf	PROPN
ejpam-4583	432	3	(	(	PUNCT
ejpam-4583	432	4	clf	clf	PROPN
ejpam-4583	432	5	(	(	PUNCT
ejpam-4583	432	6	k	k	NOUN
ejpam-4583	432	7	)	)	PUNCT
ejpam-4583	432	8	)	)	PUNCT
ejpam-4583	432	9	.	.	PUNCT
ejpam-4583	433	1	to	to	PART
ejpam-4583	433	2	prove	prove	VERB
ejpam-4583	433	3	(	(	PUNCT
ejpam-4583	433	4	v	v	NOUN
ejpam-4583	433	5	)	)	PUNCT
ejpam-4583	433	6	since	since	SCONJ
ejpam-4583	433	7	k	k	PROPN
ejpam-4583	433	8	⊆	⊆	NUM
ejpam-4583	433	9	h	h	NOUN
ejpam-4583	433	10	,	,	PUNCT
ejpam-4583	433	11	then	then	ADV
ejpam-4583	433	12	x	x	SYM
ejpam-4583	433	13	\	\	PROPN
ejpam-4583	433	14	h	h	NOUN
ejpam-4583	433	15	⊆	⊆	NUM
ejpam-4583	433	16	x	x	SYM
ejpam-4583	433	17	\	\	NOUN
ejpam-4583	434	1	k	k	NOUN
ejpam-4583	434	2	,	,	PUNCT
ejpam-4583	434	3	then	then	ADV
ejpam-4583	434	4	intf	intf	PROPN
ejpam-4583	434	5	(	(	PUNCT
ejpam-4583	434	6	x\h	x\h	PROPN
ejpam-4583	434	7	)	)	PUNCT
ejpam-4583	434	8	⊆	⊆	NUM
ejpam-4583	434	9	intf	intf	NOUN
ejpam-4583	434	10	(	(	PUNCT
ejpam-4583	434	11	x\k	x\k	NOUN
ejpam-4583	434	12	)	)	PUNCT
ejpam-4583	434	13	,	,	PUNCT
ejpam-4583	434	14	hence	hence	ADV
ejpam-4583	434	15	,	,	PUNCT
ejpam-4583	434	16	extf	extf	ADJ
ejpam-4583	434	17	(	(	PUNCT
ejpam-4583	434	18	h	h	NOUN
ejpam-4583	434	19	)	)	PUNCT
ejpam-4583	434	20	⊆	⊆	NUM
ejpam-4583	434	21	extf	extf	NOUN
ejpam-4583	434	22	(	(	PUNCT
ejpam-4583	434	23	k	k	NOUN
ejpam-4583	434	24	)	)	PUNCT
ejpam-4583	434	25	.	.	PUNCT
ejpam-4583	435	1	for	for	ADP
ejpam-4583	435	2	(	(	PUNCT
ejpam-4583	435	3	vi	vi	NOUN
ejpam-4583	435	4	)	)	PUNCT
ejpam-4583	435	5	,	,	PUNCT
ejpam-4583	435	6	extf	extf	ADJ
ejpam-4583	435	7	(	(	PUNCT
ejpam-4583	435	8	x\extf	x\extf	PROPN
ejpam-4583	435	9	(	(	PUNCT
ejpam-4583	435	10	k	k	NOUN
ejpam-4583	435	11	)	)	PUNCT
ejpam-4583	435	12	)	)	PUNCT
ejpam-4583	436	1	=	=	PRON
ejpam-4583	436	2	extf	extf	ADJ
ejpam-4583	436	3	(	(	PUNCT
ejpam-4583	436	4	x\intf	x\intf	PROPN
ejpam-4583	436	5	(	(	PUNCT
ejpam-4583	436	6	x\k	x\k	NOUN
ejpam-4583	436	7	)	)	PUNCT
ejpam-4583	436	8	)	)	PUNCT
ejpam-4583	437	1	=	=	SYM
ejpam-4583	437	2	intf	intf	PROPN
ejpam-4583	437	3	(	(	PUNCT
ejpam-4583	437	4	x\(x\intf	x\(x\intf	PROPN
ejpam-4583	437	5	(	(	PUNCT
ejpam-4583	437	6	x\k	x\k	NOUN
ejpam-4583	437	7	)	)	PUNCT
ejpam-4583	437	8	)	)	PUNCT
ejpam-4583	437	9	)	)	PUNCT
ejpam-4583	438	1	=	=	X
ejpam-4583	438	2	intf	intf	PROPN
ejpam-4583	438	3	(	(	PUNCT
ejpam-4583	438	4	intf	intf	PROPN
ejpam-4583	438	5	(	(	PUNCT
ejpam-4583	438	6	x\k	x\k	NOUN
ejpam-4583	438	7	)	)	PUNCT
ejpam-4583	438	8	)	)	PUNCT
ejpam-4583	439	1	=	=	SYM
ejpam-4583	439	2	intf	intf	X
ejpam-4583	439	3	(	(	PUNCT
ejpam-4583	439	4	x\k	x\k	NOUN
ejpam-4583	439	5	)	)	PUNCT
ejpam-4583	439	6	=	=	PRON
ejpam-4583	439	7	extf	extf	ADJ
ejpam-4583	439	8	(	(	PUNCT
ejpam-4583	439	9	k	k	NOUN
ejpam-4583	439	10	)	)	PUNCT
ejpam-4583	439	11	.	.	PUNCT
ejpam-4583	440	1	for	for	ADP
ejpam-4583	440	2	(	(	PUNCT
ejpam-4583	440	3	vii	vii	PROPN
ejpam-4583	440	4	)	)	PUNCT
ejpam-4583	440	5	,	,	PUNCT
ejpam-4583	440	6	intf	intf	PROPN
ejpam-4583	440	7	(	(	PUNCT
ejpam-4583	440	8	k	k	NOUN
ejpam-4583	440	9	)	)	PUNCT
ejpam-4583	440	10	⊆	⊆	NUM
ejpam-4583	440	11	intf	intf	NOUN
ejpam-4583	440	12	(	(	PUNCT
ejpam-4583	440	13	clf	clf	PROPN
ejpam-4583	440	14	(	(	PUNCT
ejpam-4583	440	15	k	k	NOUN
ejpam-4583	440	16	)	)	PUNCT
ejpam-4583	440	17	)	)	PUNCT
ejpam-4583	441	1	⊆	⊆	NUM
ejpam-4583	441	2	intf	intf	NOUN
ejpam-4583	441	3	(	(	PUNCT
ejpam-4583	441	4	x	x	SYM
ejpam-4583	441	5	\	\	PROPN
ejpam-4583	441	6	intf	intf	PROPN
ejpam-4583	441	7	(	(	PUNCT
ejpam-4583	441	8	x	x	SYM
ejpam-4583	441	9	\	\	PROPN
ejpam-4583	441	10	k	k	NOUN
ejpam-4583	441	11	)	)	PUNCT
ejpam-4583	441	12	)	)	PUNCT
ejpam-4583	442	1	=	=	SYM
ejpam-4583	442	2	intf	intf	NOUN
ejpam-4583	442	3	(	(	PUNCT
ejpam-4583	442	4	x	x	SYM
ejpam-4583	442	5	\	\	PROPN
ejpam-4583	442	6	extf	extf	NOUN
ejpam-4583	442	7	(	(	PUNCT
ejpam-4583	442	8	k	k	NOUN
ejpam-4583	442	9	)	)	PUNCT
ejpam-4583	442	10	)	)	PUNCT
ejpam-4583	443	1	=	=	PRON
ejpam-4583	443	2	extf	extf	ADJ
ejpam-4583	443	3	(	(	PUNCT
ejpam-4583	443	4	extf	extf	ADJ
ejpam-4583	443	5	(	(	PUNCT
ejpam-4583	443	6	k	k	NOUN
ejpam-4583	443	7	)	)	PUNCT
ejpam-4583	443	8	)	)	PUNCT
ejpam-4583	443	9	.	.	PUNCT
ejpam-4583	444	1	the	the	DET
ejpam-4583	444	2	property	property	NOUN
ejpam-4583	444	3	(	(	PUNCT
ejpam-4583	444	4	viii	viii	NOUN
ejpam-4583	444	5	)	)	PUNCT
ejpam-4583	444	6	extf	extf	NOUN
ejpam-4583	444	7	(	(	PUNCT
ejpam-4583	444	8	k	k	NOUN
ejpam-4583	444	9	∪h	∪h	NUM
ejpam-4583	444	10	)	)	PUNCT
ejpam-4583	445	1	=	=	VERB
ejpam-4583	445	2	intf	intf	NOUN
ejpam-4583	445	3	(	(	PUNCT
ejpam-4583	445	4	x	x	SYM
ejpam-4583	445	5	\	\	PROPN
ejpam-4583	445	6	(	(	PUNCT
ejpam-4583	445	7	k	k	NOUN
ejpam-4583	445	8	∪h	∪h	NUM
ejpam-4583	445	9	)	)	PUNCT
ejpam-4583	445	10	)	)	PUNCT
ejpam-4583	446	1	=	=	PUNCT
ejpam-4583	446	2	(	(	PUNCT
ejpam-4583	446	3	x\clf	x\clf	X
ejpam-4583	446	4	(	(	PUNCT
ejpam-4583	446	5	k∪h	k∪h	NOUN
ejpam-4583	446	6	)	)	PUNCT
ejpam-4583	446	7	)	)	PUNCT
ejpam-4583	447	1	=	=	PRON
ejpam-4583	448	1	(	(	PUNCT
ejpam-4583	448	2	x\(clf	x\(clf	X
ejpam-4583	448	3	(	(	PUNCT
ejpam-4583	448	4	k)∪clf	k)∪clf	X
ejpam-4583	448	5	(	(	PUNCT
ejpam-4583	448	6	h	h	NOUN
ejpam-4583	448	7	)	)	PUNCT
ejpam-4583	448	8	)	)	PUNCT
ejpam-4583	448	9	)	)	PUNCT
ejpam-4583	449	1	⊂	⊂	PROPN
ejpam-4583	449	2	x\clf	x\clf	PUNCT
ejpam-4583	450	1	(	(	PUNCT
ejpam-4583	450	2	k)∪x\clf	k)∪x\clf	PROPN
ejpam-4583	450	3	(	(	PUNCT
ejpam-4583	450	4	h	h	NOUN
ejpam-4583	450	5	)	)	PUNCT
ejpam-4583	450	6	=	=	SYM
ejpam-4583	451	1	(	(	PUNCT
ejpam-4583	451	2	x\clf	x\clf	X
ejpam-4583	451	3	(	(	PUNCT
ejpam-4583	451	4	k))∩(x\	k))∩(x\	PROPN
ejpam-4583	451	5	clf	clf	PROPN
ejpam-4583	451	6	(	(	PUNCT
ejpam-4583	451	7	h	h	NOUN
ejpam-4583	451	8	)	)	PUNCT
ejpam-4583	451	9	)	)	PUNCT
ejpam-4583	451	10	)	)	PUNCT
ejpam-4583	451	11	=	=	PRON
ejpam-4583	451	12	extf	extf	ADJ
ejpam-4583	451	13	(	(	PUNCT
ejpam-4583	451	14	k	k	NOUN
ejpam-4583	451	15	)	)	PUNCT
ejpam-4583	451	16	∩	∩	ADJ
ejpam-4583	451	17	extf	extf	NOUN
ejpam-4583	451	18	(	(	PUNCT
ejpam-4583	451	19	h	h	NOUN
ejpam-4583	451	20	)	)	PUNCT
ejpam-4583	451	21	⊂	⊂	PROPN
ejpam-4583	451	22	extf	extf	ADJ
ejpam-4583	451	23	(	(	PUNCT
ejpam-4583	451	24	k	k	NOUN
ejpam-4583	451	25	)	)	PUNCT
ejpam-4583	451	26	∪	∪	ADJ
ejpam-4583	451	27	extf	extf	ADJ
ejpam-4583	451	28	(	(	PUNCT
ejpam-4583	451	29	h	h	NOUN
ejpam-4583	451	30	)	)	PUNCT
ejpam-4583	451	31	.	.	PUNCT
ejpam-4583	452	1	the	the	DET
ejpam-4583	452	2	property	property	NOUN
ejpam-4583	452	3	(	(	PUNCT
ejpam-4583	452	4	ix	ix	ADV
ejpam-4583	452	5	):	):	PUNCT
ejpam-4583	452	6	extf	extf	PROPN
ejpam-4583	452	7	(	(	PUNCT
ejpam-4583	452	8	k	k	X
ejpam-4583	452	9	∩	∩	ADJ
ejpam-4583	452	10	h	h	NOUN
ejpam-4583	452	11	)	)	PUNCT
ejpam-4583	452	12	=	=	VERB
ejpam-4583	452	13	intf	intf	NOUN
ejpam-4583	452	14	(	(	PUNCT
ejpam-4583	452	15	x	x	SYM
ejpam-4583	452	16	\	\	PROPN
ejpam-4583	452	17	(	(	PUNCT
ejpam-4583	452	18	k	k	PROPN
ejpam-4583	452	19	∩h	∩h	PROPN
ejpam-4583	452	20	)	)	PUNCT
ejpam-4583	452	21	)	)	PUNCT
ejpam-4583	453	1	=	=	PUNCT
ejpam-4583	453	2	(	(	PUNCT
ejpam-4583	453	3	x	x	SYM
ejpam-4583	453	4	\	\	PROPN
ejpam-4583	453	5	clf	clf	PROPN
ejpam-4583	453	6	(	(	PUNCT
ejpam-4583	453	7	k	k	PROPN
ejpam-4583	453	8	∩h	∩h	PROPN
ejpam-4583	453	9	)	)	PUNCT
ejpam-4583	453	10	)	)	PUNCT
ejpam-4583	454	1	⊃	⊃	PROPN
ejpam-4583	454	2	(	(	PUNCT
ejpam-4583	454	3	x	x	SYM
ejpam-4583	454	4	\	\	PROPN
ejpam-4583	454	5	(	(	PUNCT
ejpam-4583	454	6	clf	clf	PROPN
ejpam-4583	454	7	(	(	PUNCT
ejpam-4583	454	8	k)∩	k)∩	PROPN
ejpam-4583	454	9	clf	clf	PROPN
ejpam-4583	454	10	(	(	PUNCT
ejpam-4583	454	11	h	h	NOUN
ejpam-4583	454	12	)	)	PUNCT
ejpam-4583	454	13	)	)	PUNCT
ejpam-4583	454	14	)	)	PUNCT
ejpam-4583	455	1	=	=	PUNCT
ejpam-4583	455	2	(	(	PUNCT
ejpam-4583	455	3	x	x	SYM
ejpam-4583	455	4	\	\	PROPN
ejpam-4583	455	5	clf	clf	PROPN
ejpam-4583	455	6	(	(	PUNCT
ejpam-4583	455	7	k))∪	k))∪	PROPN
ejpam-4583	455	8	(	(	PUNCT
ejpam-4583	455	9	x	x	SYM
ejpam-4583	455	10	\	\	PROPN
ejpam-4583	455	11	clf	clf	PROPN
ejpam-4583	455	12	(	(	PUNCT
ejpam-4583	455	13	h	h	NOUN
ejpam-4583	455	14	)	)	PUNCT
ejpam-4583	455	15	)	)	PUNCT
ejpam-4583	455	16	)	)	PUNCT
ejpam-4583	456	1	=	=	PRON
ejpam-4583	456	2	extf	extf	ADJ
ejpam-4583	456	3	(	(	PUNCT
ejpam-4583	456	4	k	k	NOUN
ejpam-4583	456	5	)	)	PUNCT
ejpam-4583	456	6	∪	∪	ADJ
ejpam-4583	456	7	extf	extf	ADJ
ejpam-4583	456	8	(	(	PUNCT
ejpam-4583	456	9	h	h	NOUN
ejpam-4583	456	10	)	)	PUNCT
ejpam-4583	456	11	⊃	⊃	PROPN
ejpam-4583	456	12	extf	extf	ADJ
ejpam-4583	456	13	(	(	PUNCT
ejpam-4583	456	14	k	k	NOUN
ejpam-4583	456	15	)	)	PUNCT
ejpam-4583	456	16	∩	∩	ADJ
ejpam-4583	456	17	extf	extf	ADJ
ejpam-4583	456	18	(	(	PUNCT
ejpam-4583	456	19	h	h	NOUN
ejpam-4583	456	20	)	)	PUNCT
ejpam-4583	456	21	.	.	PUNCT
ejpam-4583	457	1	the	the	DET
ejpam-4583	457	2	property	property	NOUN
ejpam-4583	457	3	(	(	PUNCT
ejpam-4583	457	4	x	x	X
ejpam-4583	457	5	)	)	PUNCT
ejpam-4583	457	6	follow	follow	VERB
ejpam-4583	457	7	from	from	ADP
ejpam-4583	457	8	the	the	DET
ejpam-4583	457	9	definitions	definition	NOUN
ejpam-4583	457	10	19	19	NUM
ejpam-4583	457	11	and	and	CCONJ
ejpam-4583	457	12	20	20	NUM
ejpam-4583	457	13	.	.	PUNCT
ejpam-4583	458	1	in	in	ADP
ejpam-4583	458	2	general	general	ADJ
ejpam-4583	458	3	ext(k	ext(k	PROPN
ejpam-4583	458	4	)	)	PUNCT
ejpam-4583	458	5	⊈	⊈	PROPN
ejpam-4583	458	6	extf	extf	NOUN
ejpam-4583	458	7	(	(	PUNCT
ejpam-4583	458	8	k	k	NOUN
ejpam-4583	458	9	)	)	PUNCT
ejpam-4583	458	10	,	,	PUNCT
ejpam-4583	458	11	extf	extf	NOUN
ejpam-4583	458	12	(	(	PUNCT
ejpam-4583	458	13	k	k	X
ejpam-4583	458	14	∪h	∪h	NUM
ejpam-4583	458	15	)	)	PUNCT
ejpam-4583	458	16	⊉	⊉	PROPN
ejpam-4583	458	17	extf	extf	ADJ
ejpam-4583	458	18	(	(	PUNCT
ejpam-4583	458	19	k)∪extf	k)∪extf	PROPN
ejpam-4583	458	20	(	(	PUNCT
ejpam-4583	458	21	h	h	NOUN
ejpam-4583	458	22	)	)	PUNCT
ejpam-4583	458	23	and	and	CCONJ
ejpam-4583	458	24	extf	extf	ADJ
ejpam-4583	458	25	(	(	PUNCT
ejpam-4583	458	26	k	k	X
ejpam-4583	458	27	∩	∩	ADJ
ejpam-4583	458	28	h	h	NOUN
ejpam-4583	458	29	)	)	PUNCT
ejpam-4583	458	30	⊈	⊈	PROPN
ejpam-4583	458	31	extf	extf	NOUN
ejpam-4583	458	32	(	(	PUNCT
ejpam-4583	458	33	k	k	NOUN
ejpam-4583	458	34	)	)	PUNCT
ejpam-4583	458	35	∩	∩	ADJ
ejpam-4583	458	36	extf	extf	ADJ
ejpam-4583	458	37	(	(	PUNCT
ejpam-4583	458	38	h	h	NOUN
ejpam-4583	458	39	)	)	PUNCT
ejpam-4583	458	40	.	.	PUNCT
ejpam-4583	459	1	for	for	ADP
ejpam-4583	459	2	example	example	NOUN
ejpam-4583	459	3	:	:	PUNCT
ejpam-4583	459	4	example	example	NOUN
ejpam-4583	459	5	16	16	NUM
ejpam-4583	459	6	.	.	PUNCT
ejpam-4583	460	1	let	let	VERB
ejpam-4583	460	2	k	k	NOUN
ejpam-4583	460	3	=	=	PUNCT
ejpam-4583	460	4	z	z	AUX
ejpam-4583	460	5	be	be	AUX
ejpam-4583	460	6	a	a	DET
ejpam-4583	460	7	subset	subset	NOUN
ejpam-4583	460	8	of	of	ADP
ejpam-4583	460	9	the	the	DET
ejpam-4583	460	10	usual	usual	ADJ
ejpam-4583	460	11	topological	topological	ADJ
ejpam-4583	460	12	space	space	NOUN
ejpam-4583	460	13	(	(	PUNCT
ejpam-4583	460	14	r	r	NOUN
ejpam-4583	460	15	,	,	PUNCT
ejpam-4583	460	16	u	u	NOUN
ejpam-4583	460	17	)	)	PUNCT
ejpam-4583	460	18	.	.	PUNCT
ejpam-4583	461	1	then	then	ADV
ejpam-4583	461	2	ext(k	ext(k	X
ejpam-4583	461	3	)	)	PUNCT
ejpam-4583	461	4	=	=	SYM
ejpam-4583	461	5	int(r\z	int(r\z	PROPN
ejpam-4583	461	6	)	)	PUNCT
ejpam-4583	461	7	=	=	SYM
ejpam-4583	461	8	r\z	r\z	NOUN
ejpam-4583	461	9	.	.	PUNCT
ejpam-4583	462	1	but	but	CCONJ
ejpam-4583	462	2	r\z	r\z	NOUN
ejpam-4583	462	3	is	be	AUX
ejpam-4583	462	4	not	not	PART
ejpam-4583	462	5	f	f	PROPN
ejpam-4583	462	6	-open	-open	NOUN
ejpam-4583	462	7	,	,	PUNCT
ejpam-4583	462	8	then	then	ADV
ejpam-4583	462	9	extf	extf	ADJ
ejpam-4583	462	10	(	(	PUNCT
ejpam-4583	462	11	(	(	PUNCT
ejpam-4583	462	12	k	k	X
ejpam-4583	462	13	)	)	PUNCT
ejpam-4583	463	1	=	=	SYM
ejpam-4583	463	2	intf	intf	NOUN
ejpam-4583	463	3	(	(	PUNCT
ejpam-4583	463	4	(	(	PUNCT
ejpam-4583	463	5	r\z	r\z	NOUN
ejpam-4583	463	6	)	)	PUNCT
ejpam-4583	463	7	⊂	⊂	PROPN
ejpam-4583	463	8	r\z	r\z	NOUN
ejpam-4583	463	9	.	.	PUNCT
ejpam-4583	464	1	hence	hence	ADV
ejpam-4583	464	2	,	,	PUNCT
ejpam-4583	464	3	ext(k	ext(k	PROPN
ejpam-4583	464	4	)	)	PUNCT
ejpam-4583	464	5	⊈	⊈	PROPN
ejpam-4583	464	6	extf	extf	NOUN
ejpam-4583	464	7	(	(	PUNCT
ejpam-4583	464	8	k	k	NOUN
ejpam-4583	464	9	)	)	PUNCT
ejpam-4583	464	10	.	.	PUNCT
ejpam-4583	465	1	for	for	ADP
ejpam-4583	465	2	extf	extf	NOUN
ejpam-4583	465	3	(	(	PUNCT
ejpam-4583	465	4	k∪h	k∪h	ADJ
ejpam-4583	465	5	)	)	PUNCT
ejpam-4583	465	6	⊉	⊉	PROPN
ejpam-4583	465	7	extf	extf	ADJ
ejpam-4583	465	8	(	(	PUNCT
ejpam-4583	465	9	k)∪extf	k)∪extf	PROPN
ejpam-4583	465	10	(	(	PUNCT
ejpam-4583	465	11	h	h	NOUN
ejpam-4583	465	12	)	)	PUNCT
ejpam-4583	465	13	,	,	PUNCT
ejpam-4583	465	14	let	let	VERB
ejpam-4583	465	15	k	k	PROPN
ejpam-4583	465	16	=	=	SYM
ejpam-4583	465	17	(	(	PUNCT
ejpam-4583	465	18	−∞	−∞	NOUN
ejpam-4583	465	19	,	,	PUNCT
ejpam-4583	465	20	2	2	NUM
ejpam-4583	465	21	)	)	PUNCT
ejpam-4583	465	22	and	and	CCONJ
ejpam-4583	465	23	h	h	NOUN
ejpam-4583	465	24	=	=	SYM
ejpam-4583	465	25	(	(	PUNCT
ejpam-4583	465	26	0,∞	0,∞	NUM
ejpam-4583	465	27	)	)	PUNCT
ejpam-4583	465	28	,	,	PUNCT
ejpam-4583	465	29	then	then	ADV
ejpam-4583	465	30	extf	extf	VERB
ejpam-4583	465	31	(	(	PUNCT
ejpam-4583	465	32	k	k	NOUN
ejpam-4583	465	33	∪h	∪h	NUM
ejpam-4583	465	34	)	)	PUNCT
ejpam-4583	466	1	=	=	PRON
ejpam-4583	466	2	extf	extf	ADJ
ejpam-4583	466	3	(	(	PUNCT
ejpam-4583	466	4	r	r	NOUN
ejpam-4583	466	5	)	)	PUNCT
ejpam-4583	466	6	=	=	NOUN
ejpam-4583	466	7	∅	∅	NOUN
ejpam-4583	466	8	and	and	CCONJ
ejpam-4583	466	9	extf	extf	ADJ
ejpam-4583	466	10	(	(	PUNCT
ejpam-4583	466	11	k)∪extf	k)∪extf	PROPN
ejpam-4583	466	12	(	(	PUNCT
ejpam-4583	466	13	h	h	NOUN
ejpam-4583	466	14	)	)	PUNCT
ejpam-4583	466	15	=	=	SYM
ejpam-4583	467	1	(	(	PUNCT
ejpam-4583	467	2	2,∞)∪	2,∞)∪	NUM
ejpam-4583	467	3	(	(	PUNCT
ejpam-4583	467	4	−∞	−∞	NOUN
ejpam-4583	467	5	,	,	PUNCT
ejpam-4583	467	6	0	0	NUM
ejpam-4583	467	7	)	)	PUNCT
ejpam-4583	467	8	.	.	PUNCT
ejpam-4583	468	1	hence	hence	ADV
ejpam-4583	468	2	,	,	PUNCT
ejpam-4583	468	3	extf	extf	ADJ
ejpam-4583	468	4	(	(	PUNCT
ejpam-4583	468	5	k	k	X
ejpam-4583	468	6	∪h	∪h	NUM
ejpam-4583	468	7	)	)	PUNCT
ejpam-4583	468	8	⊉	⊉	PROPN
ejpam-4583	468	9	extf	extf	ADJ
ejpam-4583	468	10	(	(	PUNCT
ejpam-4583	468	11	k)∪extf	k)∪extf	PROPN
ejpam-4583	468	12	(	(	PUNCT
ejpam-4583	468	13	h	h	NOUN
ejpam-4583	468	14	)	)	PUNCT
ejpam-4583	468	15	.	.	PUNCT
ejpam-4583	469	1	for	for	ADP
ejpam-4583	469	2	extf	extf	NOUN
ejpam-4583	469	3	(	(	PUNCT
ejpam-4583	469	4	k	k	PROPN
ejpam-4583	469	5	∩h	∩h	PROPN
ejpam-4583	469	6	)	)	PUNCT
ejpam-4583	469	7	⊈	⊈	PROPN
ejpam-4583	469	8	extf	extf	NOUN
ejpam-4583	469	9	(	(	PUNCT
ejpam-4583	469	10	k)∩extf	k)∩extf	X
ejpam-4583	469	11	(	(	PUNCT
ejpam-4583	469	12	h	h	NOUN
ejpam-4583	469	13	)	)	PUNCT
ejpam-4583	469	14	,	,	PUNCT
ejpam-4583	469	15	let	let	VERB
ejpam-4583	469	16	k	k	PROPN
ejpam-4583	469	17	=	=	SYM
ejpam-4583	469	18	(	(	PUNCT
ejpam-4583	469	19	−∞	−∞	NOUN
ejpam-4583	469	20	,	,	PUNCT
ejpam-4583	469	21	2	2	NUM
ejpam-4583	469	22	]	]	PUNCT
ejpam-4583	469	23	and	and	CCONJ
ejpam-4583	469	24	h	h	NOUN
ejpam-4583	469	25	=	=	PUNCT
ejpam-4583	470	1	[	[	X
ejpam-4583	470	2	2,∞	2,∞	NUM
ejpam-4583	470	3	)	)	PUNCT
ejpam-4583	470	4	,	,	PUNCT
ejpam-4583	470	5	then	then	ADV
ejpam-4583	470	6	extf	extf	VERB
ejpam-4583	470	7	(	(	PUNCT
ejpam-4583	470	8	k	k	X
ejpam-4583	470	9	∩	∩	ADJ
ejpam-4583	470	10	h	h	NOUN
ejpam-4583	470	11	)	)	PUNCT
ejpam-4583	470	12	=	=	PRON
ejpam-4583	470	13	extf	extf	ADJ
ejpam-4583	470	14	(	(	PUNCT
ejpam-4583	470	15	{	{	PUNCT
ejpam-4583	470	16	2	2	NUM
ejpam-4583	470	17	}	}	PUNCT
ejpam-4583	470	18	)	)	PUNCT
ejpam-4583	471	1	=	=	SYM
ejpam-4583	471	2	r	r	NOUN
ejpam-4583	471	3	\	\	NOUN
ejpam-4583	471	4	{	{	PUNCT
ejpam-4583	471	5	2	2	NUM
ejpam-4583	471	6	}	}	PUNCT
ejpam-4583	471	7	and	and	CCONJ
ejpam-4583	471	8	extf	extf	ADJ
ejpam-4583	471	9	(	(	PUNCT
ejpam-4583	471	10	k)∩extf	k)∩extf	X
ejpam-4583	471	11	(	(	PUNCT
ejpam-4583	471	12	h	h	NOUN
ejpam-4583	471	13	)	)	PUNCT
ejpam-4583	471	14	=	=	SYM
ejpam-4583	471	15	(	(	PUNCT
ejpam-4583	471	16	2,∞)∩(−∞	2,∞)∩(−∞	NUM
ejpam-4583	471	17	,	,	PUNCT
ejpam-4583	471	18	2	2	NUM
ejpam-4583	471	19	)	)	PUNCT
ejpam-4583	471	20	=	=	NOUN
ejpam-4583	471	21	∅.	∅.	VERB
ejpam-4583	471	22	hence	hence	ADV
ejpam-4583	471	23	,	,	PUNCT
ejpam-4583	471	24	extf	extf	ADJ
ejpam-4583	471	25	(	(	PUNCT
ejpam-4583	471	26	k∩h	k∩h	PROPN
ejpam-4583	471	27	)	)	PUNCT
ejpam-4583	471	28	⊈	⊈	PROPN
ejpam-4583	471	29	extf	extf	NOUN
ejpam-4583	471	30	(	(	PUNCT
ejpam-4583	471	31	k)∩extf	k)∩extf	X
ejpam-4583	471	32	(	(	PUNCT
ejpam-4583	471	33	h	h	NOUN
ejpam-4583	471	34	)	)	PUNCT
ejpam-4583	471	35	.	.	PUNCT
ejpam-4583	472	1	m.	m.	PROPN
ejpam-4583	472	2	h.	h.	PROPN
ejpam-4583	472	3	alqahtani	alqahtani	PROPN
ejpam-4583	472	4	/	/	SYM
ejpam-4583	472	5	eur	eur	PROPN
ejpam-4583	472	6	.	.	PUNCT
ejpam-4583	473	1	j.	j.	PROPN
ejpam-4583	473	2	pure	pure	PROPN
ejpam-4583	473	3	appl	appl	PROPN
ejpam-4583	473	4	.	.	PROPN
ejpam-4583	473	5	math	math	PROPN
ejpam-4583	473	6	,	,	PUNCT
ejpam-4583	473	7	16	16	NUM
ejpam-4583	473	8	(	(	PUNCT
ejpam-4583	473	9	2	2	NUM
ejpam-4583	473	10	)	)	PUNCT
ejpam-4583	473	11	(	(	PUNCT
ejpam-4583	473	12	2023	2023	NUM
ejpam-4583	473	13	)	)	PUNCT
ejpam-4583	473	14	,	,	PUNCT
ejpam-4583	473	15	819	819	NUM
ejpam-4583	473	16	-	-	SYM
ejpam-4583	473	17	832	832	NUM
ejpam-4583	473	18	830	830	NUM
ejpam-4583	473	19	5	5	NUM
ejpam-4583	473	20	.	.	PUNCT
ejpam-4583	474	1	f	f	PROPN
ejpam-4583	474	2	-continuity	-continuity	PROPN
ejpam-4583	474	3	and	and	CCONJ
ejpam-4583	474	4	f	f	PROPN
ejpam-4583	474	5	-compactness	-compactness	NOUN
ejpam-4583	474	6	definition	definition	NOUN
ejpam-4583	474	7	21	21	NUM
ejpam-4583	474	8	.	.	PUNCT
ejpam-4583	475	1	a	a	DET
ejpam-4583	475	2	function	function	NOUN
ejpam-4583	475	3	h	h	NOUN
ejpam-4583	475	4	:	:	PUNCT
ejpam-4583	475	5	(	(	PUNCT
ejpam-4583	475	6	x	x	X
ejpam-4583	475	7	,	,	PUNCT
ejpam-4583	475	8	t	t	PROPN
ejpam-4583	475	9	)	)	PUNCT
ejpam-4583	475	10	→	→	SYM
ejpam-4583	475	11	(	(	PUNCT
ejpam-4583	475	12	y	y	PROPN
ejpam-4583	475	13	,	,	PUNCT
ejpam-4583	475	14	p	p	NOUN
ejpam-4583	475	15	)	)	PUNCT
ejpam-4583	475	16	is	be	AUX
ejpam-4583	475	17	said	say	VERB
ejpam-4583	475	18	to	to	PART
ejpam-4583	475	19	be	be	AUX
ejpam-4583	475	20	f	f	X
ejpam-4583	475	21	-continuous	-continuous	ADJ
ejpam-4583	475	22	if	if	SCONJ
ejpam-4583	475	23	h−1(u	h−1(u	PROPN
ejpam-4583	475	24	)	)	PUNCT
ejpam-4583	475	25	is	be	AUX
ejpam-4583	475	26	a	a	DET
ejpam-4583	475	27	f	f	NOUN
ejpam-4583	475	28	-open	-open	NOUN
ejpam-4583	475	29	set	set	VERB
ejpam-4583	475	30	in	in	ADP
ejpam-4583	475	31	x	x	PUNCT
ejpam-4583	475	32	for	for	ADP
ejpam-4583	475	33	every	every	DET
ejpam-4583	475	34	open	open	ADJ
ejpam-4583	475	35	sets	set	VERB
ejpam-4583	475	36	u	u	NOUN
ejpam-4583	475	37	in	in	ADP
ejpam-4583	475	38	y.	y.	PROPN
ejpam-4583	475	39	definition	definition	NOUN
ejpam-4583	475	40	22	22	NUM
ejpam-4583	475	41	.	.	PUNCT
ejpam-4583	476	1	a	a	DET
ejpam-4583	476	2	function	function	NOUN
ejpam-4583	476	3	h	h	NOUN
ejpam-4583	476	4	:	:	PUNCT
ejpam-4583	476	5	(	(	PUNCT
ejpam-4583	476	6	x	x	X
ejpam-4583	476	7	,	,	PUNCT
ejpam-4583	476	8	t	t	PROPN
ejpam-4583	476	9	)	)	PUNCT
ejpam-4583	476	10	→	→	SYM
ejpam-4583	476	11	(	(	PUNCT
ejpam-4583	476	12	y	y	PROPN
ejpam-4583	476	13	,	,	PUNCT
ejpam-4583	476	14	p	p	NOUN
ejpam-4583	476	15	)	)	PUNCT
ejpam-4583	476	16	is	be	AUX
ejpam-4583	476	17	said	say	VERB
ejpam-4583	476	18	to	to	PART
ejpam-4583	476	19	be	be	AUX
ejpam-4583	476	20	f−open	f−open	PROPN
ejpam-4583	476	21	if	if	SCONJ
ejpam-4583	476	22	h(u	h(u	PROPN
ejpam-4583	476	23	)	)	PUNCT
ejpam-4583	476	24	is	be	AUX
ejpam-4583	476	25	f−open	f−open	PROPN
ejpam-4583	476	26	in	in	ADP
ejpam-4583	476	27	y	y	PROPN
ejpam-4583	476	28	for	for	ADP
ejpam-4583	476	29	every	every	DET
ejpam-4583	476	30	open	open	ADJ
ejpam-4583	476	31	sets	set	VERB
ejpam-4583	476	32	u	u	NOUN
ejpam-4583	476	33	in	in	ADP
ejpam-4583	476	34	x.	x.	NOUN
ejpam-4583	476	35	definition	definition	NOUN
ejpam-4583	476	36	23	23	NUM
ejpam-4583	476	37	.	.	PUNCT
ejpam-4583	477	1	a	a	DET
ejpam-4583	477	2	function	function	NOUN
ejpam-4583	477	3	h	h	NOUN
ejpam-4583	477	4	:	:	PUNCT
ejpam-4583	477	5	(	(	PUNCT
ejpam-4583	477	6	x	x	X
ejpam-4583	477	7	,	,	PUNCT
ejpam-4583	477	8	t	t	PROPN
ejpam-4583	477	9	)	)	PUNCT
ejpam-4583	477	10	→	→	SYM
ejpam-4583	477	11	(	(	PUNCT
ejpam-4583	477	12	y	y	PROPN
ejpam-4583	477	13	,	,	PUNCT
ejpam-4583	477	14	p	p	NOUN
ejpam-4583	477	15	)	)	PUNCT
ejpam-4583	477	16	is	be	AUX
ejpam-4583	477	17	said	say	VERB
ejpam-4583	477	18	to	to	PART
ejpam-4583	477	19	be	be	AUX
ejpam-4583	477	20	f	f	PROPN
ejpam-4583	477	21	-closed	-close	VERB
ejpam-4583	477	22	if	if	SCONJ
ejpam-4583	477	23	h(u	h(u	PROPN
ejpam-4583	477	24	)	)	PUNCT
ejpam-4583	477	25	is	be	AUX
ejpam-4583	477	26	f	f	PROPN
ejpam-4583	477	27	-closed	-close	VERB
ejpam-4583	477	28	in	in	ADP
ejpam-4583	477	29	y	y	PROPN
ejpam-4583	477	30	for	for	ADP
ejpam-4583	477	31	every	every	DET
ejpam-4583	477	32	closed	close	VERB
ejpam-4583	477	33	sets	set	NOUN
ejpam-4583	477	34	u	u	NOUN
ejpam-4583	477	35	in	in	ADP
ejpam-4583	477	36	x.	x.	NOUN
ejpam-4583	477	37	definition	definition	NOUN
ejpam-4583	477	38	24	24	NUM
ejpam-4583	477	39	.	.	PUNCT
ejpam-4583	478	1	a	a	DET
ejpam-4583	478	2	bijection	bijection	ADJ
ejpam-4583	478	3	function	function	NOUN
ejpam-4583	478	4	h	h	NOUN
ejpam-4583	478	5	:	:	PUNCT
ejpam-4583	478	6	(	(	PUNCT
ejpam-4583	478	7	x	x	X
ejpam-4583	478	8	,	,	PUNCT
ejpam-4583	478	9	t	t	PROPN
ejpam-4583	478	10	)	)	PUNCT
ejpam-4583	478	11	→	→	SYM
ejpam-4583	478	12	(	(	PUNCT
ejpam-4583	478	13	y	y	PROPN
ejpam-4583	478	14	,	,	PUNCT
ejpam-4583	478	15	p	p	NOUN
ejpam-4583	478	16	)	)	PUNCT
ejpam-4583	478	17	is	be	AUX
ejpam-4583	478	18	said	say	VERB
ejpam-4583	478	19	to	to	PART
ejpam-4583	478	20	be	be	AUX
ejpam-4583	478	21	f−hmoeomrphism	f−hmoeomrphism	NOUN
ejpam-4583	478	22	if	if	SCONJ
ejpam-4583	478	23	and	and	CCONJ
ejpam-4583	478	24	only	only	ADV
ejpam-4583	478	25	if	if	SCONJ
ejpam-4583	478	26	h	h	NOUN
ejpam-4583	478	27	and	and	CCONJ
ejpam-4583	478	28	h−1	h−1	PROPN
ejpam-4583	478	29	are	be	AUX
ejpam-4583	478	30	f	f	PROPN
ejpam-4583	478	31	-continuous	-continuous	ADJ
ejpam-4583	478	32	.	.	PUNCT
ejpam-4583	479	1	theorem	theorem	NOUN
ejpam-4583	479	2	11	11	NUM
ejpam-4583	479	3	.	.	PUNCT
ejpam-4583	480	1	let	let	VERB
ejpam-4583	480	2	h	h	NOUN
ejpam-4583	480	3	:	:	PUNCT
ejpam-4583	480	4	(	(	PUNCT
ejpam-4583	480	5	x	x	X
ejpam-4583	480	6	,	,	PUNCT
ejpam-4583	480	7	t	t	PROPN
ejpam-4583	480	8	)	)	PUNCT
ejpam-4583	480	9	→	→	SYM
ejpam-4583	480	10	(	(	PUNCT
ejpam-4583	480	11	y	y	PROPN
ejpam-4583	480	12	,	,	PUNCT
ejpam-4583	480	13	p	p	NOUN
ejpam-4583	480	14	)	)	PUNCT
ejpam-4583	480	15	be	be	AUX
ejpam-4583	480	16	a	a	DET
ejpam-4583	480	17	f	f	NUM
ejpam-4583	480	18	-continuous	-continuous	ADJ
ejpam-4583	480	19	function	function	NOUN
ejpam-4583	480	20	,	,	PUNCT
ejpam-4583	480	21	then	then	ADV
ejpam-4583	480	22	h	h	NOUN
ejpam-4583	480	23	is	be	AUX
ejpam-4583	480	24	continuous	continuous	ADJ
ejpam-4583	480	25	function	function	NOUN
ejpam-4583	480	26	.	.	PUNCT
ejpam-4583	481	1	proof	proof	NOUN
ejpam-4583	481	2	.	.	PUNCT
ejpam-4583	482	1	let	let	VERB
ejpam-4583	482	2	u	u	PRON
ejpam-4583	482	3	be	be	AUX
ejpam-4583	482	4	any	any	DET
ejpam-4583	482	5	open	open	ADJ
ejpam-4583	482	6	set	set	NOUN
ejpam-4583	482	7	in	in	ADP
ejpam-4583	482	8	y	y	PROPN
ejpam-4583	482	9	,	,	PUNCT
ejpam-4583	482	10	then	then	ADV
ejpam-4583	482	11	by	by	ADP
ejpam-4583	482	12	f	f	PROPN
ejpam-4583	482	13	-continuity	-continuity	PROPN
ejpam-4583	482	14	h−1(u	h−1(u	PROPN
ejpam-4583	482	15	)	)	PUNCT
ejpam-4583	482	16	is	be	AUX
ejpam-4583	482	17	f	f	PROPN
ejpam-4583	482	18	-open	-open	NOUN
ejpam-4583	482	19	set	set	VERB
ejpam-4583	482	20	in	in	ADP
ejpam-4583	482	21	x.	x.	NOUN
ejpam-4583	482	22	since	since	SCONJ
ejpam-4583	482	23	any	any	DET
ejpam-4583	482	24	f	f	PROPN
ejpam-4583	482	25	-open	-open	NOUN
ejpam-4583	482	26	set	set	NOUN
ejpam-4583	482	27	is	be	AUX
ejpam-4583	482	28	open	open	ADJ
ejpam-4583	482	29	,	,	PUNCT
ejpam-4583	482	30	then	then	ADV
ejpam-4583	482	31	h−1(u	h−1(u	PROPN
ejpam-4583	482	32	)	)	PUNCT
ejpam-4583	482	33	is	be	AUX
ejpam-4583	482	34	open	open	ADJ
ejpam-4583	482	35	set	set	VERB
ejpam-4583	482	36	in	in	ADP
ejpam-4583	482	37	x.	x.	NOUN
ejpam-4583	482	38	in	in	ADP
ejpam-4583	482	39	general	general	ADJ
ejpam-4583	482	40	,	,	PUNCT
ejpam-4583	482	41	the	the	DET
ejpam-4583	482	42	converse	converse	NOUN
ejpam-4583	482	43	of	of	ADP
ejpam-4583	482	44	the	the	DET
ejpam-4583	482	45	previous	previous	ADJ
ejpam-4583	482	46	theorem	theorem	NOUN
ejpam-4583	482	47	is	be	AUX
ejpam-4583	482	48	not	not	PART
ejpam-4583	482	49	true	true	ADJ
ejpam-4583	482	50	.	.	PUNCT
ejpam-4583	483	1	there	there	PRON
ejpam-4583	483	2	is	be	VERB
ejpam-4583	483	3	an	an	DET
ejpam-4583	483	4	example	example	NOUN
ejpam-4583	483	5	of	of	ADP
ejpam-4583	483	6	continuous	continuous	ADJ
ejpam-4583	483	7	function	function	NOUN
ejpam-4583	483	8	which	which	PRON
ejpam-4583	483	9	is	be	AUX
ejpam-4583	483	10	not	not	PART
ejpam-4583	483	11	f−continuous	f−continuous	ADJ
ejpam-4583	483	12	function	function	NOUN
ejpam-4583	483	13	.	.	PUNCT
ejpam-4583	483	14	example	example	NOUN
ejpam-4583	484	1	17	17	NUM
ejpam-4583	484	2	.	.	PUNCT
ejpam-4583	485	1	the	the	DET
ejpam-4583	485	2	identity	identity	NOUN
ejpam-4583	485	3	function	function	NOUN
ejpam-4583	485	4	i	i	NOUN
ejpam-4583	485	5	d	d	PROPN
ejpam-4583	485	6	:	:	PUNCT
ejpam-4583	485	7	(	(	PUNCT
ejpam-4583	485	8	r	r	NOUN
ejpam-4583	485	9	,	,	PUNCT
ejpam-4583	485	10	u	u	NOUN
ejpam-4583	485	11	)	)	PUNCT
ejpam-4583	485	12	→	→	SYM
ejpam-4583	485	13	(	(	PUNCT
ejpam-4583	485	14	r	r	NOUN
ejpam-4583	485	15	,	,	PUNCT
ejpam-4583	485	16	u	u	NOUN
ejpam-4583	485	17	)	)	PUNCT
ejpam-4583	485	18	is	be	AUX
ejpam-4583	485	19	a	a	DET
ejpam-4583	485	20	continuous	continuous	ADJ
ejpam-4583	485	21	function	function	NOUN
ejpam-4583	485	22	.	.	PUNCT
ejpam-4583	486	1	however	however	ADV
ejpam-4583	486	2	,	,	PUNCT
ejpam-4583	486	3	there	there	PRON
ejpam-4583	486	4	exist	exist	VERB
ejpam-4583	486	5	(	(	PUNCT
ejpam-4583	486	6	r	r	NOUN
ejpam-4583	486	7	\	\	PROPN
ejpam-4583	486	8	z	z	X
ejpam-4583	486	9	)	)	PUNCT
ejpam-4583	486	10	∈	∈	PROPN
ejpam-4583	486	11	u	u	NOUN
ejpam-4583	486	12	and	and	CCONJ
ejpam-4583	486	13	id−1(r	id−1(r	ADJ
ejpam-4583	486	14	\	\	PUNCT
ejpam-4583	487	1	z	z	X
ejpam-4583	487	2	)	)	PUNCT
ejpam-4583	487	3	=	=	SYM
ejpam-4583	487	4	r	r	NOUN
ejpam-4583	487	5	\	\	NOUN
ejpam-4583	487	6	z	z	NOUN
ejpam-4583	487	7	is	be	AUX
ejpam-4583	487	8	not	not	PART
ejpam-4583	487	9	f−open	f−open	ADV
ejpam-4583	487	10	set	set	VERB
ejpam-4583	487	11	,	,	PUNCT
ejpam-4583	487	12	because	because	SCONJ
ejpam-4583	487	13	cl(r	cl(r	NOUN
ejpam-4583	487	14	\	\	PROPN
ejpam-4583	487	15	z	z	X
ejpam-4583	487	16	)	)	PUNCT
ejpam-4583	487	17	\	\	PUNCT
ejpam-4583	488	1	(	(	PUNCT
ejpam-4583	488	2	r	r	NOUN
ejpam-4583	488	3	\	\	PROPN
ejpam-4583	488	4	z	z	NOUN
ejpam-4583	488	5	)	)	PUNCT
ejpam-4583	488	6	=	=	NOUN
ejpam-4583	488	7	z	z	NOUN
ejpam-4583	488	8	is	be	AUX
ejpam-4583	488	9	not	not	PART
ejpam-4583	488	10	finite	finite	ADJ
ejpam-4583	488	11	.	.	PUNCT
ejpam-4583	489	1	definition	definition	NOUN
ejpam-4583	489	2	25	25	NUM
ejpam-4583	489	3	.	.	PUNCT
ejpam-4583	490	1	let	let	VERB
ejpam-4583	490	2	(	(	PUNCT
ejpam-4583	490	3	x	x	X
ejpam-4583	490	4	,	,	PUNCT
ejpam-4583	490	5	t	t	PROPN
ejpam-4583	490	6	)	)	PUNCT
ejpam-4583	490	7	be	be	AUX
ejpam-4583	490	8	a	a	DET
ejpam-4583	490	9	topological	topological	ADJ
ejpam-4583	490	10	space	space	NOUN
ejpam-4583	490	11	.	.	PUNCT
ejpam-4583	491	1	then	then	ADV
ejpam-4583	491	2	(	(	PUNCT
ejpam-4583	491	3	x	x	X
ejpam-4583	491	4	,	,	PUNCT
ejpam-4583	491	5	t	t	PROPN
ejpam-4583	491	6	)	)	PUNCT
ejpam-4583	491	7	is	be	AUX
ejpam-4583	491	8	a	a	DET
ejpam-4583	491	9	f	f	PROPN
ejpam-4583	491	10	-compact	-compact	PROPN
ejpam-4583	491	11	(	(	PUNCT
ejpam-4583	491	12	resp	resp	NOUN
ejpam-4583	491	13	.	.	PUNCT
ejpam-4583	491	14	,	,	PUNCT
ejpam-4583	491	15	f	f	PROPN
ejpam-4583	491	16	lindelöf	lindelöf	PROPN
ejpam-4583	491	17	)	)	PUNCT
ejpam-4583	491	18	space	space	NOUN
ejpam-4583	491	19	if	if	SCONJ
ejpam-4583	492	1	and	and	CCONJ
ejpam-4583	492	2	only	only	ADV
ejpam-4583	492	3	if	if	SCONJ
ejpam-4583	492	4	any	any	DET
ejpam-4583	492	5	open	open	ADJ
ejpam-4583	492	6	cover	cover	NOUN
ejpam-4583	492	7	of	of	ADP
ejpam-4583	492	8	x	x	PUNCT
ejpam-4583	492	9	has	have	VERB
ejpam-4583	492	10	a	a	DET
ejpam-4583	492	11	finite	finite	NOUN
ejpam-4583	492	12	(	(	PUNCT
ejpam-4583	492	13	resp	resp	NOUN
ejpam-4583	492	14	.	.	PUNCT
ejpam-4583	492	15	,	,	PUNCT
ejpam-4583	492	16	countable	countable	ADJ
ejpam-4583	492	17	)	)	PUNCT
ejpam-4583	492	18	subcover	subcover	NOUN
ejpam-4583	492	19	of	of	ADP
ejpam-4583	492	20	f	f	PROPN
ejpam-4583	492	21	-open	-open	PROPN
ejpam-4583	492	22	sets	set	NOUN
ejpam-4583	492	23	.	.	PUNCT
ejpam-4583	493	1	definition	definition	NOUN
ejpam-4583	493	2	26	26	NUM
ejpam-4583	493	3	.	.	PUNCT
ejpam-4583	494	1	let	let	VERB
ejpam-4583	494	2	(	(	PUNCT
ejpam-4583	494	3	x	x	X
ejpam-4583	494	4	,	,	PUNCT
ejpam-4583	494	5	t	t	PROPN
ejpam-4583	494	6	)	)	PUNCT
ejpam-4583	494	7	be	be	AUX
ejpam-4583	494	8	a	a	DET
ejpam-4583	494	9	topological	topological	ADJ
ejpam-4583	494	10	space	space	NOUN
ejpam-4583	494	11	.	.	PUNCT
ejpam-4583	495	1	then	then	ADV
ejpam-4583	495	2	(	(	PUNCT
ejpam-4583	495	3	x	x	X
ejpam-4583	495	4	,	,	PUNCT
ejpam-4583	495	5	t	t	PROPN
ejpam-4583	495	6	)	)	PUNCT
ejpam-4583	495	7	is	be	AUX
ejpam-4583	495	8	a	a	DET
ejpam-4583	495	9	f	f	NOUN
ejpam-4583	495	10	-countably	-countably	ADV
ejpam-4583	495	11	compact	compact	ADJ
ejpam-4583	495	12	space	space	NOUN
ejpam-4583	495	13	if	if	SCONJ
ejpam-4583	496	1	and	and	CCONJ
ejpam-4583	496	2	only	only	ADV
ejpam-4583	496	3	if	if	SCONJ
ejpam-4583	496	4	any	any	DET
ejpam-4583	496	5	countable	countable	ADJ
ejpam-4583	496	6	open	open	ADJ
ejpam-4583	496	7	cover	cover	NOUN
ejpam-4583	496	8	of	of	ADP
ejpam-4583	496	9	x	x	PUNCT
ejpam-4583	496	10	has	have	VERB
ejpam-4583	496	11	a	a	DET
ejpam-4583	496	12	finite	finite	ADJ
ejpam-4583	496	13	subcover	subcover	NOUN
ejpam-4583	496	14	of	of	ADP
ejpam-4583	496	15	f	f	PROPN
ejpam-4583	496	16	-open	-open	PROPN
ejpam-4583	496	17	sets	set	NOUN
ejpam-4583	496	18	.	.	PUNCT
ejpam-4583	497	1	theorem	theorem	NOUN
ejpam-4583	497	2	12	12	NUM
ejpam-4583	497	3	.	.	PUNCT
ejpam-4583	498	1	any	any	DET
ejpam-4583	498	2	f	f	PROPN
ejpam-4583	498	3	-compact	-compact	PROPN
ejpam-4583	498	4	space	space	NOUN
ejpam-4583	498	5	is	be	AUX
ejpam-4583	498	6	compact	compact	ADJ
ejpam-4583	498	7	.	.	PUNCT
ejpam-4583	499	1	proof	proof	NOUN
ejpam-4583	499	2	.	.	PUNCT
ejpam-4583	500	1	obvious	obvious	ADJ
ejpam-4583	500	2	,	,	PUNCT
ejpam-4583	500	3	because	because	SCONJ
ejpam-4583	500	4	any	any	DET
ejpam-4583	500	5	f	f	PROPN
ejpam-4583	500	6	-open	-open	NOUN
ejpam-4583	500	7	set	set	NOUN
ejpam-4583	500	8	is	be	AUX
ejpam-4583	500	9	open	open	ADJ
ejpam-4583	500	10	.	.	PUNCT
ejpam-4583	501	1	here	here	ADV
ejpam-4583	501	2	an	an	DET
ejpam-4583	501	3	example	example	NOUN
ejpam-4583	501	4	of	of	ADP
ejpam-4583	501	5	compact	compact	ADJ
ejpam-4583	501	6	space	space	NOUN
ejpam-4583	501	7	which	which	PRON
ejpam-4583	501	8	is	be	AUX
ejpam-4583	501	9	not	not	PART
ejpam-4583	501	10	f	f	PROPN
ejpam-4583	501	11	-compact	-compact	PROPN
ejpam-4583	501	12	space	space	NOUN
ejpam-4583	501	13	.	.	PUNCT
ejpam-4583	502	1	example	example	NOUN
ejpam-4583	502	2	18	18	NUM
ejpam-4583	502	3	.	.	PUNCT
ejpam-4583	502	4	overlapping	overlap	VERB
ejpam-4583	502	5	interval	interval	NOUN
ejpam-4583	502	6	topology	topology	NOUN
ejpam-4583	503	1	[	[	X
ejpam-4583	503	2	3	3	NUM
ejpam-4583	503	3	]	]	PUNCT
ejpam-4583	503	4	.	.	PUNCT
ejpam-4583	504	1	on	on	ADP
ejpam-4583	504	2	the	the	DET
ejpam-4583	504	3	set	set	NOUN
ejpam-4583	504	4	x	x	PUNCT
ejpam-4583	504	5	=	=	PUNCT
ejpam-4583	505	1	[	[	X
ejpam-4583	505	2	−1	−1	NOUN
ejpam-4583	505	3	,	,	PUNCT
ejpam-4583	505	4	1	1	X
ejpam-4583	505	5	]	]	PUNCT
ejpam-4583	505	6	we	we	PRON
ejpam-4583	505	7	generate	generate	VERB
ejpam-4583	505	8	a	a	DET
ejpam-4583	505	9	topology	topology	NOUN
ejpam-4583	505	10	from	from	ADP
ejpam-4583	505	11	sets	set	NOUN
ejpam-4583	505	12	of	of	ADP
ejpam-4583	505	13	the	the	DET
ejpam-4583	505	14	form	form	NOUN
ejpam-4583	505	15	[	[	X
ejpam-4583	505	16	−1	−1	NOUN
ejpam-4583	505	17	,	,	PUNCT
ejpam-4583	505	18	b	b	NOUN
ejpam-4583	505	19	)	)	PUNCT
ejpam-4583	505	20	for	for	ADP
ejpam-4583	505	21	b	b	PROPN
ejpam-4583	505	22	>	>	X
ejpam-4583	505	23	0	0	PROPN
ejpam-4583	506	1	and	and	CCONJ
ejpam-4583	506	2	(	(	PUNCT
ejpam-4583	506	3	a	a	PRON
ejpam-4583	506	4	,	,	PUNCT
ejpam-4583	506	5	1	1	NUM
ejpam-4583	506	6	]	]	PUNCT
ejpam-4583	506	7	for	for	ADP
ejpam-4583	506	8	a	a	DET
ejpam-4583	506	9	<	<	X
ejpam-4583	506	10	0	0	NUM
ejpam-4583	506	11	.	.	PUNCT
ejpam-4583	507	1	then	then	ADV
ejpam-4583	507	2	all	all	DET
ejpam-4583	507	3	sets	set	NOUN
ejpam-4583	507	4	of	of	ADP
ejpam-4583	507	5	the	the	DET
ejpam-4583	507	6	form	form	NOUN
ejpam-4583	507	7	(	(	PUNCT
ejpam-4583	507	8	a	a	DET
ejpam-4583	507	9	,	,	PUNCT
ejpam-4583	507	10	b	b	NOUN
ejpam-4583	507	11	)	)	PUNCT
ejpam-4583	507	12	are	be	AUX
ejpam-4583	507	13	also	also	ADV
ejpam-4583	507	14	open	open	ADJ
ejpam-4583	507	15	.	.	PUNCT
ejpam-4583	508	1	we	we	PRON
ejpam-4583	508	2	have	have	VERB
ejpam-4583	508	3	x	x	NOUN
ejpam-4583	508	4	is	be	AUX
ejpam-4583	508	5	a	a	DET
ejpam-4583	508	6	compact	compact	ADJ
ejpam-4583	508	7	space	space	NOUN
ejpam-4583	508	8	,	,	PUNCT
ejpam-4583	508	9	since	since	SCONJ
ejpam-4583	508	10	in	in	ADP
ejpam-4583	508	11	any	any	DET
ejpam-4583	508	12	open	open	ADJ
ejpam-4583	508	13	covering	covering	NOUN
ejpam-4583	508	14	,	,	PUNCT
ejpam-4583	508	15	the	the	DET
ejpam-4583	508	16	two	two	NUM
ejpam-4583	508	17	sets	set	NOUN
ejpam-4583	508	18	which	which	PRON
ejpam-4583	508	19	include	include	VERB
ejpam-4583	508	20	1	1	NUM
ejpam-4583	508	21	and	and	CCONJ
ejpam-4583	508	22	−1	−1	NOUN
ejpam-4583	508	23	will	will	AUX
ejpam-4583	508	24	cover	cover	VERB
ejpam-4583	508	25	x.	x.	NOUN
ejpam-4583	508	26	the	the	DET
ejpam-4583	508	27	space	space	NOUN
ejpam-4583	508	28	x	x	PUNCT
ejpam-4583	508	29	is	be	AUX
ejpam-4583	508	30	not	not	PART
ejpam-4583	508	31	f	f	PROPN
ejpam-4583	508	32	-compact	-compact	PROPN
ejpam-4583	508	33	space	space	NOUN
ejpam-4583	508	34	,	,	PUNCT
ejpam-4583	508	35	because	because	SCONJ
ejpam-4583	508	36	there	there	PRON
ejpam-4583	508	37	exists	exist	VERB
ejpam-4583	508	38	{	{	PUNCT
ejpam-4583	508	39	[	[	X
ejpam-4583	508	40	−1	−1	NOUN
ejpam-4583	508	41	,	,	PUNCT
ejpam-4583	508	42	0.5	0.5	NUM
ejpam-4583	508	43	)	)	PUNCT
ejpam-4583	508	44	,	,	PUNCT
ejpam-4583	508	45	(	(	PUNCT
ejpam-4583	508	46	−0.5	−0.5	VERB
ejpam-4583	508	47	,	,	PUNCT
ejpam-4583	508	48	1	1	NUM
ejpam-4583	508	49	]	]	PUNCT
ejpam-4583	508	50	}	}	PUNCT
ejpam-4583	508	51	open	open	ADJ
ejpam-4583	508	52	cover	cover	NOUN
ejpam-4583	508	53	for	for	ADP
ejpam-4583	508	54	x	x	PUNCT
ejpam-4583	508	55	has	have	VERB
ejpam-4583	508	56	no	no	DET
ejpam-4583	508	57	finite	finite	NOUN
ejpam-4583	508	58	subcover	subcover	NOUN
ejpam-4583	508	59	of	of	ADP
ejpam-4583	508	60	f	f	PROPN
ejpam-4583	508	61	-open	-open	PROPN
ejpam-4583	508	62	sets	set	NOUN
ejpam-4583	508	63	,	,	PUNCT
ejpam-4583	508	64	because	because	SCONJ
ejpam-4583	508	65	[	[	X
ejpam-4583	508	66	−1	−1	NOUN
ejpam-4583	508	67	,	,	PUNCT
ejpam-4583	508	68	0.5	0.5	NUM
ejpam-4583	508	69	)	)	PUNCT
ejpam-4583	508	70	and	and	CCONJ
ejpam-4583	508	71	(	(	PUNCT
ejpam-4583	508	72	−0.5	−0.5	PROPN
ejpam-4583	508	73	,	,	PUNCT
ejpam-4583	508	74	1	1	NUM
ejpam-4583	508	75	]	]	PUNCT
ejpam-4583	508	76	are	be	AUX
ejpam-4583	508	77	not	not	PART
ejpam-4583	508	78	f−open	f−open	PROPN
ejpam-4583	508	79	sets	set	NOUN
ejpam-4583	508	80	(	(	PUNCT
ejpam-4583	508	81	cl[−1	cl[−1	NUM
ejpam-4583	508	82	,	,	PUNCT
ejpam-4583	508	83	0.5	0.5	NUM
ejpam-4583	508	84	)	)	PUNCT
ejpam-4583	508	85	\	\	PUNCT
ejpam-4583	509	1	[	[	X
ejpam-4583	509	2	−1	−1	NOUN
ejpam-4583	509	3	,	,	PUNCT
ejpam-4583	509	4	0.5	0.5	NUM
ejpam-4583	509	5	)	)	PUNCT
ejpam-4583	509	6	=	=	PUNCT
ejpam-4583	510	1	[	[	X
ejpam-4583	510	2	−1	−1	NOUN
ejpam-4583	510	3	,	,	PUNCT
ejpam-4583	510	4	1	1	NUM
ejpam-4583	510	5	]	]	PUNCT
ejpam-4583	510	6	\	\	PUNCT
ejpam-4583	511	1	[	[	X
ejpam-4583	511	2	−1	−1	NOUN
ejpam-4583	511	3	,	,	PUNCT
ejpam-4583	511	4	0.5	0.5	NUM
ejpam-4583	511	5	)	)	PUNCT
ejpam-4583	511	6	=	=	NOUN
ejpam-4583	512	1	[	[	X
ejpam-4583	512	2	0.5	0.5	NUM
ejpam-4583	512	3	,	,	PUNCT
ejpam-4583	512	4	1	1	NUM
ejpam-4583	512	5	]	]	PUNCT
ejpam-4583	512	6	is	be	AUX
ejpam-4583	512	7	not	not	PART
ejpam-4583	512	8	finite	finite	ADJ
ejpam-4583	512	9	set	set	NOUN
ejpam-4583	512	10	and	and	CCONJ
ejpam-4583	512	11	cl(−0.5	cl(−0.5	NUM
ejpam-4583	512	12	,	,	PUNCT
ejpam-4583	512	13	1	1	NUM
ejpam-4583	512	14	]	]	PUNCT
ejpam-4583	512	15	\	\	PUNCT
ejpam-4583	512	16	(	(	PUNCT
ejpam-4583	512	17	−0.5	−0.5	PROPN
ejpam-4583	512	18	,	,	PUNCT
ejpam-4583	512	19	1	1	NUM
ejpam-4583	512	20	]	]	PUNCT
ejpam-4583	512	21	=	=	PUNCT
ejpam-4583	513	1	[	[	X
ejpam-4583	513	2	−1	−1	NOUN
ejpam-4583	513	3	,	,	PUNCT
ejpam-4583	513	4	1	1	NUM
ejpam-4583	513	5	]	]	PUNCT
ejpam-4583	513	6	\	\	PUNCT
ejpam-4583	513	7	(	(	PUNCT
ejpam-4583	513	8	−0.5	−0.5	PROPN
ejpam-4583	513	9	,	,	PUNCT
ejpam-4583	513	10	1	1	NUM
ejpam-4583	513	11	]	]	PUNCT
ejpam-4583	513	12	=	=	PUNCT
ejpam-4583	514	1	[	[	X
ejpam-4583	514	2	−1,−0.5	−1,−0.5	X
ejpam-4583	514	3	]	]	X
ejpam-4583	514	4	is	be	AUX
ejpam-4583	514	5	not	not	PART
ejpam-4583	514	6	finite	finite	ADJ
ejpam-4583	514	7	set	set	NOUN
ejpam-4583	514	8	)	)	PUNCT
ejpam-4583	514	9	.	.	PUNCT
ejpam-4583	515	1	m.	m.	PROPN
ejpam-4583	515	2	h.	h.	PROPN
ejpam-4583	515	3	alqahtani	alqahtani	PROPN
ejpam-4583	515	4	/	/	SYM
ejpam-4583	515	5	eur	eur	PROPN
ejpam-4583	515	6	.	.	PUNCT
ejpam-4583	516	1	j.	j.	PROPN
ejpam-4583	516	2	pure	pure	PROPN
ejpam-4583	516	3	appl	appl	PROPN
ejpam-4583	516	4	.	.	PROPN
ejpam-4583	516	5	math	math	PROPN
ejpam-4583	516	6	,	,	PUNCT
ejpam-4583	516	7	16	16	NUM
ejpam-4583	516	8	(	(	PUNCT
ejpam-4583	516	9	2	2	NUM
ejpam-4583	516	10	)	)	PUNCT
ejpam-4583	516	11	(	(	PUNCT
ejpam-4583	516	12	2023	2023	NUM
ejpam-4583	516	13	)	)	PUNCT
ejpam-4583	516	14	,	,	PUNCT
ejpam-4583	516	15	819	819	NUM
ejpam-4583	516	16	-	-	SYM
ejpam-4583	516	17	832	832	NUM
ejpam-4583	516	18	831	831	NUM
ejpam-4583	516	19	corollary	corollary	ADJ
ejpam-4583	516	20	2	2	NUM
ejpam-4583	516	21	.	.	PUNCT
ejpam-4583	517	1	any	any	DET
ejpam-4583	517	2	f	f	PROPN
ejpam-4583	517	3	-lindelöf	-lindelöf	NUM
ejpam-4583	517	4	(	(	PUNCT
ejpam-4583	517	5	resp	resp	NOUN
ejpam-4583	517	6	.	.	PUNCT
ejpam-4583	517	7	,	,	PUNCT
ejpam-4583	517	8	f	f	PROPN
ejpam-4583	517	9	-countably	-countably	ADV
ejpam-4583	517	10	compact	compact	ADJ
ejpam-4583	517	11	)	)	PUNCT
ejpam-4583	517	12	space	space	NOUN
ejpam-4583	517	13	is	be	AUX
ejpam-4583	517	14	lindelöf	lindelöf	NOUN
ejpam-4583	517	15	(	(	PUNCT
ejpam-4583	517	16	resp	resp	PROPN
ejpam-4583	517	17	.	.	PUNCT
ejpam-4583	517	18	,	,	PUNCT
ejpam-4583	517	19	countably	countably	ADV
ejpam-4583	517	20	compact	compact	ADJ
ejpam-4583	517	21	)	)	PUNCT
ejpam-4583	517	22	.	.	PUNCT
ejpam-4583	518	1	theorem	theorem	VERB
ejpam-4583	518	2	13	13	NUM
ejpam-4583	518	3	.	.	PUNCT
ejpam-4583	519	1	if	if	SCONJ
ejpam-4583	519	2	there	there	PRON
ejpam-4583	519	3	exists	exist	VERB
ejpam-4583	519	4	a	a	DET
ejpam-4583	519	5	f	f	NOUN
ejpam-4583	519	6	-open	-open	PROPN
ejpam-4583	519	7	f	f	PROPN
ejpam-4583	519	8	-continuous	-continuous	ADJ
ejpam-4583	519	9	function	function	NOUN
ejpam-4583	519	10	h	h	NOUN
ejpam-4583	519	11	from	from	ADP
ejpam-4583	519	12	f	f	PROPN
ejpam-4583	519	13	-compact	-compact	PROPN
ejpam-4583	519	14	space	space	NOUN
ejpam-4583	519	15	(	(	PUNCT
ejpam-4583	519	16	x	x	NOUN
ejpam-4583	519	17	,	,	PUNCT
ejpam-4583	519	18	t	t	PROPN
ejpam-4583	519	19	)	)	PUNCT
ejpam-4583	519	20	onto	onto	ADP
ejpam-4583	519	21	a	a	DET
ejpam-4583	519	22	topological	topological	ADJ
ejpam-4583	519	23	space	space	NOUN
ejpam-4583	519	24	(	(	PUNCT
ejpam-4583	519	25	y	y	NOUN
ejpam-4583	519	26	,	,	PUNCT
ejpam-4583	519	27	p	p	NOUN
ejpam-4583	519	28	)	)	PUNCT
ejpam-4583	519	29	,	,	PUNCT
ejpam-4583	519	30	then	then	ADV
ejpam-4583	519	31	(	(	PUNCT
ejpam-4583	519	32	y	y	NOUN
ejpam-4583	519	33	,	,	PUNCT
ejpam-4583	519	34	p	p	NOUN
ejpam-4583	519	35	)	)	PUNCT
ejpam-4583	519	36	is	be	AUX
ejpam-4583	519	37	a	a	DET
ejpam-4583	519	38	f	f	PROPN
ejpam-4583	519	39	-compact	-compact	PROPN
ejpam-4583	519	40	space	space	NOUN
ejpam-4583	519	41	.	.	PUNCT
ejpam-4583	520	1	proof	proof	NOUN
ejpam-4583	520	2	.	.	PUNCT
ejpam-4583	521	1	let	let	VERB
ejpam-4583	521	2	{	{	PUNCT
ejpam-4583	521	3	vα	vα	X
ejpam-4583	521	4	:	:	PUNCT
ejpam-4583	521	5	α	α	PROPN
ejpam-4583	521	6	∈	∈	PROPN
ejpam-4583	521	7	λ	λ	NOUN
ejpam-4583	521	8	}	}	PUNCT
ejpam-4583	521	9	be	be	VERB
ejpam-4583	521	10	any	any	DET
ejpam-4583	521	11	open	open	ADJ
ejpam-4583	521	12	cover	cover	NOUN
ejpam-4583	521	13	of	of	ADP
ejpam-4583	521	14	y	y	PROPN
ejpam-4583	521	15	.	.	PUNCT
ejpam-4583	522	1	since	since	SCONJ
ejpam-4583	522	2	h	h	PROPN
ejpam-4583	522	3	is	be	AUX
ejpam-4583	522	4	f	f	PROPN
ejpam-4583	522	5	-continuous	-continuous	ADJ
ejpam-4583	522	6	,	,	PUNCT
ejpam-4583	522	7	then	then	ADV
ejpam-4583	522	8	h−1(vα	h−1(vα	VERB
ejpam-4583	522	9	)	)	PUNCT
ejpam-4583	522	10	is	be	AUX
ejpam-4583	522	11	f	f	PROPN
ejpam-4583	522	12	-open	-open	ADJ
ejpam-4583	522	13	in	in	ADP
ejpam-4583	522	14	x	x	PUNCT
ejpam-4583	522	15	for	for	ADP
ejpam-4583	522	16	each	each	DET
ejpam-4583	522	17	α	α	PRON
ejpam-4583	522	18	∈	∈	PROPN
ejpam-4583	522	19	λ	λ	PROPN
ejpam-4583	522	20	.	.	PUNCT
ejpam-4583	523	1	since	since	SCONJ
ejpam-4583	523	2	y	y	PROPN
ejpam-4583	523	3	⊆	⊆	NUM
ejpam-4583	523	4	⋃	⋃	NOUN
ejpam-4583	523	5	α∈λ	α∈λ	NOUN
ejpam-4583	523	6	vα	vα	NOUN
ejpam-4583	523	7	,	,	PUNCT
ejpam-4583	523	8	then	then	ADV
ejpam-4583	523	9	x	x	X
ejpam-4583	523	10	=	=	PUNCT
ejpam-4583	523	11	h−1(y	h−1(y	PROPN
ejpam-4583	523	12	)	)	PUNCT
ejpam-4583	524	1	⊆	⊆	X
ejpam-4583	524	2	h−1	h−1	X
ejpam-4583	524	3	(	(	PUNCT
ejpam-4583	524	4	⋃	⋃	NOUN
ejpam-4583	524	5	α∈λ	α∈λ	NOUN
ejpam-4583	524	6	vα	vα	NOUN
ejpam-4583	524	7	)	)	PUNCT
ejpam-4583	524	8	=	=	SYM
ejpam-4583	524	9	⋃	⋃	NOUN
ejpam-4583	524	10	α∈λ	α∈λ	NOUN
ejpam-4583	524	11	h−1(vα	h−1(vα	VERB
ejpam-4583	524	12	)	)	PUNCT
ejpam-4583	524	13	)	)	PUNCT
ejpam-4583	524	14	,	,	PUNCT
ejpam-4583	524	15	that	that	PRON
ejpam-4583	524	16	is	be	AUX
ejpam-4583	524	17	means	mean	VERB
ejpam-4583	524	18	{	{	PUNCT
ejpam-4583	524	19	h−1(vα	h−1(vα	PROPN
ejpam-4583	524	20	)	)	PUNCT
ejpam-4583	524	21	:	:	PUNCT
ejpam-4583	524	22	α	α	PROPN
ejpam-4583	524	23	∈	∈	PROPN
ejpam-4583	524	24	λ	λ	PROPN
ejpam-4583	524	25	}	}	PUNCT
ejpam-4583	524	26	is	be	AUX
ejpam-4583	524	27	an	an	DET
ejpam-4583	524	28	open	open	ADJ
ejpam-4583	524	29	cover	cover	NOUN
ejpam-4583	524	30	of	of	ADP
ejpam-4583	524	31	x	x	X
ejpam-4583	524	32	(	(	PUNCT
ejpam-4583	524	33	because	because	SCONJ
ejpam-4583	524	34	any	any	DET
ejpam-4583	524	35	f	f	PROPN
ejpam-4583	524	36	-open	-open	NOUN
ejpam-4583	524	37	set	set	NOUN
ejpam-4583	524	38	is	be	AUX
ejpam-4583	524	39	open	open	ADJ
ejpam-4583	524	40	)	)	PUNCT
ejpam-4583	524	41	.	.	PUNCT
ejpam-4583	525	1	then	then	ADV
ejpam-4583	525	2	,	,	PUNCT
ejpam-4583	525	3	by	by	ADP
ejpam-4583	525	4	the	the	DET
ejpam-4583	525	5	f	f	PROPN
ejpam-4583	525	6	-compactness	-compactness	PROPN
ejpam-4583	525	7	of	of	ADP
ejpam-4583	525	8	x	x	NOUN
ejpam-4583	525	9	,	,	PUNCT
ejpam-4583	525	10	there	there	PRON
ejpam-4583	525	11	exist	exist	VERB
ejpam-4583	525	12	α1	α1	NOUN
ejpam-4583	525	13	,	,	PUNCT
ejpam-4583	525	14	α2	α2	ADJ
ejpam-4583	525	15	,	,	PUNCT
ejpam-4583	525	16	·	·	PUNCT
ejpam-4583	525	17	·	·	PUNCT
ejpam-4583	526	1	·	·	PUNCT
ejpam-4583	526	2	αn	αn	NOUN
ejpam-4583	526	3	∈	∈	PROPN
ejpam-4583	526	4	λ	λ	NOUN
ejpam-4583	526	5	such	such	ADJ
ejpam-4583	526	6	that	that	SCONJ
ejpam-4583	527	1	h−1(vα1)∪	h−1(vα1)∪	PRON
ejpam-4583	527	2	h−1(vα2)∪	h−1(vα2)∪	NOUN
ejpam-4583	527	3	·	·	PUNCT
ejpam-4583	527	4	·	·	PUNCT
ejpam-4583	527	5	·	·	PUNCT
ejpam-4583	527	6	∪	∪	ADP
ejpam-4583	527	7	h−1(vαn	h−1(vαn	NOUN
ejpam-4583	527	8	)	)	PUNCT
ejpam-4583	527	9	=	=	SYM
ejpam-4583	528	1	x	x	NOUN
ejpam-4583	528	2	,	,	PUNCT
ejpam-4583	528	3	then	then	ADV
ejpam-4583	528	4	h[h−1(vα1)∪	h[h−1(vα1)∪	VERB
ejpam-4583	528	5	h−1(vα2)∪	h−1(vα2)∪	PROPN
ejpam-4583	528	6	·	·	SYM
ejpam-4583	528	7	·	·	PUNCT
ejpam-4583	528	8	·	·	PUNCT
ejpam-4583	528	9	∪h−1(vαn	∪h−1(vαn	NUM
ejpam-4583	528	10	)	)	PUNCT
ejpam-4583	528	11	]	]	PUNCT
ejpam-4583	529	1	=	=	SYM
ejpam-4583	529	2	h(x	h(x	PROPN
ejpam-4583	529	3	)	)	PUNCT
ejpam-4583	529	4	,	,	PUNCT
ejpam-4583	529	5	then	then	ADV
ejpam-4583	529	6	h(h−1(vα1))∪h(h−1(vα2))∪	h(h−1(vα1))∪h(h−1(vα2))∪	PROPN
ejpam-4583	529	7	·	·	PUNCT
ejpam-4583	529	8	·	·	PUNCT
ejpam-4583	529	9	·	·	PUNCT
ejpam-4583	529	10	∪h(h−1(vαn	∪h(h−1(vαn	NUM
ejpam-4583	529	11	)	)	PUNCT
ejpam-4583	529	12	)	)	PUNCT
ejpam-4583	530	1	=	=	SYM
ejpam-4583	530	2	y	y	PROPN
ejpam-4583	530	3	,	,	PUNCT
ejpam-4583	530	4	then	then	ADV
ejpam-4583	530	5	vα1	vα1	NOUN
ejpam-4583	530	6	∪	∪	ADJ
ejpam-4583	530	7	vα2	vα2	NOUN
ejpam-4583	530	8	∪	∪	X
ejpam-4583	530	9	·	·	PUNCT
ejpam-4583	530	10	·	·	PUNCT
ejpam-4583	530	11	·	·	PUNCT
ejpam-4583	530	12	∪	∪	ADP
ejpam-4583	530	13	vαn	vαn	NOUN
ejpam-4583	530	14	=	=	SYM
ejpam-4583	530	15	y	y	PROPN
ejpam-4583	530	16	.	.	PUNCT
ejpam-4583	531	1	since	since	SCONJ
ejpam-4583	531	2	h	h	PROPN
ejpam-4583	531	3	is	be	AUX
ejpam-4583	531	4	f	f	PROPN
ejpam-4583	531	5	-open	-open	PROPN
ejpam-4583	531	6	,	,	PUNCT
ejpam-4583	531	7	then	then	ADV
ejpam-4583	531	8	{	{	PUNCT
ejpam-4583	531	9	vα1	vα1	NOUN
ejpam-4583	531	10	∪	∪	ADJ
ejpam-4583	531	11	vα2	vα2	NOUN
ejpam-4583	531	12	∪	∪	X
ejpam-4583	531	13	·	·	PUNCT
ejpam-4583	531	14	·	·	PUNCT
ejpam-4583	531	15	·	·	PUNCT
ejpam-4583	531	16	∪	∪	ADP
ejpam-4583	531	17	vαn	vαn	NOUN
ejpam-4583	531	18	}	}	PUNCT
ejpam-4583	531	19	is	be	AUX
ejpam-4583	531	20	a	a	DET
ejpam-4583	531	21	finite	finite	ADJ
ejpam-4583	531	22	subcover	subcover	NOUN
ejpam-4583	531	23	of	of	ADP
ejpam-4583	531	24	f	f	PROPN
ejpam-4583	531	25	-open	-open	PROPN
ejpam-4583	531	26	sets	set	NOUN
ejpam-4583	531	27	for	for	ADP
ejpam-4583	531	28	y	y	PROPN
ejpam-4583	531	29	.	.	PUNCT
ejpam-4583	532	1	therefore	therefore	ADV
ejpam-4583	532	2	,	,	PUNCT
ejpam-4583	532	3	(	(	PUNCT
ejpam-4583	532	4	y	y	NOUN
ejpam-4583	532	5	,	,	PUNCT
ejpam-4583	532	6	p	p	NOUN
ejpam-4583	532	7	)	)	PUNCT
ejpam-4583	532	8	is	be	AUX
ejpam-4583	532	9	a	a	DET
ejpam-4583	532	10	f	f	PROPN
ejpam-4583	532	11	-compact	-compact	PROPN
ejpam-4583	532	12	space	space	NOUN
ejpam-4583	532	13	.	.	PUNCT
ejpam-4583	533	1	a	a	DET
ejpam-4583	533	2	subset	subset	NOUN
ejpam-4583	533	3	b	b	NOUN
ejpam-4583	533	4	of	of	ADP
ejpam-4583	533	5	a	a	DET
ejpam-4583	533	6	space	space	NOUN
ejpam-4583	533	7	x	x	PUNCT
ejpam-4583	533	8	is	be	AUX
ejpam-4583	533	9	f	f	PROPN
ejpam-4583	533	10	-compact	-compact	PROPN
ejpam-4583	533	11	if	if	SCONJ
ejpam-4583	533	12	and	and	CCONJ
ejpam-4583	533	13	only	only	ADV
ejpam-4583	533	14	if	if	SCONJ
ejpam-4583	533	15	b	b	NOUN
ejpam-4583	533	16	is	be	AUX
ejpam-4583	533	17	a	a	DET
ejpam-4583	533	18	f	f	PROPN
ejpam-4583	533	19	-compact	-compact	PROPN
ejpam-4583	533	20	topological	topological	ADJ
ejpam-4583	533	21	space	space	NOUN
ejpam-4583	533	22	with	with	ADP
ejpam-4583	533	23	the	the	DET
ejpam-4583	533	24	subspace	subspace	NOUN
ejpam-4583	533	25	topology	topology	NOUN
ejpam-4583	533	26	.	.	PUNCT
ejpam-4583	534	1	theorem	theorem	VERB
ejpam-4583	534	2	14	14	NUM
ejpam-4583	534	3	.	.	PUNCT
ejpam-4583	535	1	if	if	SCONJ
ejpam-4583	535	2	there	there	PRON
ejpam-4583	535	3	exists	exist	VERB
ejpam-4583	535	4	a	a	DET
ejpam-4583	535	5	f	f	NUM
ejpam-4583	535	6	-continuous	-continuous	ADJ
ejpam-4583	535	7	function	function	NOUN
ejpam-4583	535	8	h	h	NOUN
ejpam-4583	535	9	from	from	ADP
ejpam-4583	535	10	f	f	PROPN
ejpam-4583	535	11	-compact	-compact	PROPN
ejpam-4583	535	12	space	space	NOUN
ejpam-4583	535	13	(	(	PUNCT
ejpam-4583	535	14	x	x	NOUN
ejpam-4583	535	15	,	,	PUNCT
ejpam-4583	535	16	t	t	PROPN
ejpam-4583	535	17	)	)	PUNCT
ejpam-4583	535	18	onto	onto	ADP
ejpam-4583	535	19	a	a	DET
ejpam-4583	535	20	topological	topological	ADJ
ejpam-4583	535	21	space	space	NOUN
ejpam-4583	535	22	(	(	PUNCT
ejpam-4583	535	23	y	y	NOUN
ejpam-4583	535	24	,	,	PUNCT
ejpam-4583	535	25	p	p	NOUN
ejpam-4583	535	26	)	)	PUNCT
ejpam-4583	535	27	,	,	PUNCT
ejpam-4583	535	28	then	then	ADV
ejpam-4583	535	29	(	(	PUNCT
ejpam-4583	535	30	y	y	NOUN
ejpam-4583	535	31	,	,	PUNCT
ejpam-4583	535	32	p	p	NOUN
ejpam-4583	535	33	)	)	PUNCT
ejpam-4583	535	34	is	be	AUX
ejpam-4583	535	35	compact	compact	ADJ
ejpam-4583	535	36	.	.	PUNCT
ejpam-4583	536	1	proof	proof	NOUN
ejpam-4583	536	2	.	.	PUNCT
ejpam-4583	537	1	using	use	VERB
ejpam-4583	537	2	the	the	DET
ejpam-4583	537	3	same	same	ADJ
ejpam-4583	537	4	proof	proof	NOUN
ejpam-4583	537	5	of	of	ADP
ejpam-4583	537	6	theorem	theorem	ADJ
ejpam-4583	537	7	13	13	NUM
ejpam-4583	537	8	.	.	PUNCT
ejpam-4583	537	9	theorem	theorem	NOUN
ejpam-4583	537	10	15	15	NUM
ejpam-4583	537	11	.	.	PUNCT
ejpam-4583	538	1	if	if	SCONJ
ejpam-4583	538	2	there	there	PRON
ejpam-4583	538	3	exists	exist	VERB
ejpam-4583	538	4	a	a	DET
ejpam-4583	538	5	f	f	NOUN
ejpam-4583	538	6	-open	-open	PROPN
ejpam-4583	538	7	f	f	PROPN
ejpam-4583	538	8	-continuous	-continuous	ADJ
ejpam-4583	538	9	function	function	NOUN
ejpam-4583	538	10	h	h	NOUN
ejpam-4583	538	11	from	from	ADP
ejpam-4583	538	12	a	a	DET
ejpam-4583	538	13	f	f	NOUN
ejpam-4583	538	14	-lindelöf	-lindelöf	NUM
ejpam-4583	538	15	(	(	PUNCT
ejpam-4583	538	16	resp	resp	NOUN
ejpam-4583	538	17	.	.	PUNCT
ejpam-4583	538	18	,	,	PUNCT
ejpam-4583	538	19	f	f	PROPN
ejpam-4583	538	20	-countably	-countably	ADV
ejpam-4583	538	21	compact	compact	ADJ
ejpam-4583	538	22	)	)	PUNCT
ejpam-4583	538	23	space	space	NOUN
ejpam-4583	538	24	(	(	PUNCT
ejpam-4583	538	25	x	x	X
ejpam-4583	538	26	,	,	PUNCT
ejpam-4583	538	27	t	t	PROPN
ejpam-4583	538	28	)	)	PUNCT
ejpam-4583	538	29	onto	onto	ADP
ejpam-4583	538	30	a	a	DET
ejpam-4583	538	31	topological	topological	ADJ
ejpam-4583	538	32	space	space	NOUN
ejpam-4583	538	33	(	(	PUNCT
ejpam-4583	538	34	y	y	NOUN
ejpam-4583	538	35	,	,	PUNCT
ejpam-4583	538	36	p	p	NOUN
ejpam-4583	538	37	)	)	PUNCT
ejpam-4583	538	38	,	,	PUNCT
ejpam-4583	538	39	then	then	ADV
ejpam-4583	538	40	(	(	PUNCT
ejpam-4583	538	41	y	y	NOUN
ejpam-4583	538	42	,	,	PUNCT
ejpam-4583	538	43	p	p	NOUN
ejpam-4583	538	44	)	)	PUNCT
ejpam-4583	538	45	is	be	AUX
ejpam-4583	538	46	f	f	PROPN
ejpam-4583	538	47	lindelöf	lindelöf	PROPN
ejpam-4583	538	48	(	(	PUNCT
ejpam-4583	538	49	resp	resp	PROPN
ejpam-4583	538	50	.	.	PUNCT
ejpam-4583	538	51	,	,	PUNCT
ejpam-4583	538	52	f	f	PROPN
ejpam-4583	538	53	-countably	-countably	ADV
ejpam-4583	538	54	compact	compact	ADJ
ejpam-4583	538	55	)	)	PUNCT
ejpam-4583	538	56	.	.	PUNCT
ejpam-4583	539	1	proof	proof	NOUN
ejpam-4583	539	2	.	.	PUNCT
ejpam-4583	540	1	using	use	VERB
ejpam-4583	540	2	the	the	DET
ejpam-4583	540	3	same	same	ADJ
ejpam-4583	540	4	proof	proof	NOUN
ejpam-4583	540	5	of	of	ADP
ejpam-4583	540	6	theorem	theorem	ADJ
ejpam-4583	540	7	13	13	NUM
ejpam-4583	540	8	.	.	PUNCT
ejpam-4583	540	9	theorem	theorem	VERB
ejpam-4583	540	10	16	16	NUM
ejpam-4583	540	11	.	.	PUNCT
ejpam-4583	541	1	if	if	SCONJ
ejpam-4583	541	2	there	there	PRON
ejpam-4583	541	3	exists	exist	VERB
ejpam-4583	541	4	a	a	DET
ejpam-4583	541	5	f	f	NUM
ejpam-4583	541	6	-continuous	-continuous	ADJ
ejpam-4583	541	7	function	function	NOUN
ejpam-4583	541	8	h	h	NOUN
ejpam-4583	541	9	from	from	ADP
ejpam-4583	541	10	a	a	DET
ejpam-4583	541	11	f	f	NOUN
ejpam-4583	541	12	-lindelöf	-lindelöf	ADJ
ejpam-4583	541	13	space	space	NOUN
ejpam-4583	541	14	(	(	PUNCT
ejpam-4583	541	15	x	x	X
ejpam-4583	541	16	,	,	PUNCT
ejpam-4583	541	17	t	t	PROPN
ejpam-4583	541	18	)	)	PUNCT
ejpam-4583	541	19	onto	onto	ADP
ejpam-4583	541	20	a	a	DET
ejpam-4583	541	21	topological	topological	ADJ
ejpam-4583	541	22	space	space	NOUN
ejpam-4583	541	23	(	(	PUNCT
ejpam-4583	541	24	y	y	NOUN
ejpam-4583	541	25	,	,	PUNCT
ejpam-4583	541	26	p	p	NOUN
ejpam-4583	541	27	)	)	PUNCT
ejpam-4583	541	28	,	,	PUNCT
ejpam-4583	541	29	then	then	ADV
ejpam-4583	541	30	(	(	PUNCT
ejpam-4583	541	31	y	y	NOUN
ejpam-4583	541	32	,	,	PUNCT
ejpam-4583	541	33	p	p	NOUN
ejpam-4583	541	34	)	)	PUNCT
ejpam-4583	541	35	is	be	AUX
ejpam-4583	541	36	lindelöf	lindelöf	NOUN
ejpam-4583	541	37	.	.	PUNCT
ejpam-4583	542	1	proof	proof	NOUN
ejpam-4583	542	2	.	.	PUNCT
ejpam-4583	543	1	let	let	VERB
ejpam-4583	543	2	{	{	PUNCT
ejpam-4583	543	3	vα	vα	X
ejpam-4583	543	4	:	:	PUNCT
ejpam-4583	543	5	α	α	PROPN
ejpam-4583	543	6	∈	∈	PROPN
ejpam-4583	543	7	λ	λ	NOUN
ejpam-4583	543	8	}	}	PUNCT
ejpam-4583	543	9	be	be	VERB
ejpam-4583	543	10	any	any	DET
ejpam-4583	543	11	open	open	ADJ
ejpam-4583	543	12	cover	cover	NOUN
ejpam-4583	543	13	of	of	ADP
ejpam-4583	543	14	y	y	PROPN
ejpam-4583	543	15	.	.	PUNCT
ejpam-4583	544	1	since	since	SCONJ
ejpam-4583	544	2	h	h	PROPN
ejpam-4583	544	3	is	be	AUX
ejpam-4583	544	4	f	f	PROPN
ejpam-4583	544	5	-continuous	-continuous	ADJ
ejpam-4583	544	6	,	,	PUNCT
ejpam-4583	544	7	then	then	ADV
ejpam-4583	544	8	h−1(vα	h−1(vα	VERB
ejpam-4583	544	9	)	)	PUNCT
ejpam-4583	544	10	is	be	AUX
ejpam-4583	544	11	f	f	PROPN
ejpam-4583	544	12	-open	-open	PROPN
ejpam-4583	544	13	subsets	subset	NOUN
ejpam-4583	544	14	in	in	ADP
ejpam-4583	544	15	x	x	PUNCT
ejpam-4583	544	16	for	for	ADP
ejpam-4583	544	17	each	each	DET
ejpam-4583	544	18	α	α	PRON
ejpam-4583	544	19	∈	∈	PROPN
ejpam-4583	544	20	λ	λ	PROPN
ejpam-4583	544	21	.	.	PUNCT
ejpam-4583	545	1	since	since	SCONJ
ejpam-4583	545	2	y	y	PROPN
ejpam-4583	545	3	⊆	⊆	NUM
ejpam-4583	545	4	⋃	⋃	NOUN
ejpam-4583	545	5	α∈λ	α∈λ	NOUN
ejpam-4583	545	6	vα	vα	NOUN
ejpam-4583	545	7	,	,	PUNCT
ejpam-4583	545	8	then	then	ADV
ejpam-4583	545	9	x	x	X
ejpam-4583	545	10	=	=	PUNCT
ejpam-4583	545	11	h−1(y	h−1(y	PROPN
ejpam-4583	545	12	)	)	PUNCT
ejpam-4583	546	1	⊆	⊆	X
ejpam-4583	546	2	h−1	h−1	X
ejpam-4583	546	3	(	(	PUNCT
ejpam-4583	546	4	⋃	⋃	NOUN
ejpam-4583	546	5	α∈λ	α∈λ	NOUN
ejpam-4583	546	6	vα	vα	NOUN
ejpam-4583	546	7	)	)	PUNCT
ejpam-4583	546	8	=	=	SYM
ejpam-4583	546	9	⋃	⋃	NOUN
ejpam-4583	546	10	α∈λ	α∈λ	NOUN
ejpam-4583	546	11	h−1(vα	h−1(vα	VERB
ejpam-4583	546	12	)	)	PUNCT
ejpam-4583	546	13	)	)	PUNCT
ejpam-4583	546	14	,	,	PUNCT
ejpam-4583	546	15	that	that	PRON
ejpam-4583	546	16	is	be	AUX
ejpam-4583	546	17	means	mean	VERB
ejpam-4583	546	18	{	{	PUNCT
ejpam-4583	546	19	h−1(vα	h−1(vα	PROPN
ejpam-4583	546	20	)	)	PUNCT
ejpam-4583	546	21	:	:	PUNCT
ejpam-4583	546	22	α	α	PROPN
ejpam-4583	546	23	∈	∈	PROPN
ejpam-4583	546	24	λ	λ	PROPN
ejpam-4583	546	25	}	}	PUNCT
ejpam-4583	546	26	is	be	AUX
ejpam-4583	546	27	an	an	DET
ejpam-4583	546	28	open	open	ADJ
ejpam-4583	546	29	cover	cover	NOUN
ejpam-4583	546	30	of	of	ADP
ejpam-4583	546	31	x	x	X
ejpam-4583	546	32	(	(	PUNCT
ejpam-4583	546	33	because	because	SCONJ
ejpam-4583	546	34	any	any	DET
ejpam-4583	546	35	f	f	PROPN
ejpam-4583	546	36	-open	-open	NOUN
ejpam-4583	546	37	set	set	NOUN
ejpam-4583	546	38	is	be	AUX
ejpam-4583	546	39	open	open	ADJ
ejpam-4583	546	40	)	)	PUNCT
ejpam-4583	546	41	.	.	PUNCT
ejpam-4583	547	1	then	then	ADV
ejpam-4583	547	2	,	,	PUNCT
ejpam-4583	547	3	by	by	ADP
ejpam-4583	547	4	the	the	DET
ejpam-4583	547	5	f	f	PROPN
ejpam-4583	547	6	-lindelöfness	-lindelöfness	PROPN
ejpam-4583	547	7	ofx	ofx	PROPN
ejpam-4583	547	8	,	,	PUNCT
ejpam-4583	547	9	there	there	PRON
ejpam-4583	547	10	exists	exist	VERB
ejpam-4583	547	11	α1	α1	PROPN
ejpam-4583	547	12	,	,	PUNCT
ejpam-4583	547	13	α2	α2	ADJ
ejpam-4583	547	14	,	,	PUNCT
ejpam-4583	547	15	·	·	PUNCT
ejpam-4583	547	16	·	·	PUNCT
ejpam-4583	547	17	·	·	PUNCT
ejpam-4583	548	1	such	such	ADJ
ejpam-4583	548	2	that	that	SCONJ
ejpam-4583	548	3	h−1(vα1)∪	h−1(vα1)∪	PRON
ejpam-4583	548	4	h−1(vα2)∪	h−1(vα2)∪	NOUN
ejpam-4583	548	5	·	·	PUNCT
ejpam-4583	548	6	·	·	PUNCT
ejpam-4583	548	7	·	·	PUNCT
ejpam-4583	549	1	=	=	PUNCT
ejpam-4583	549	2	x	x	X
ejpam-4583	549	3	,	,	PUNCT
ejpam-4583	549	4	then	then	ADV
ejpam-4583	549	5	h[h−1(vα1)∪	h[h−1(vα1)∪	VERB
ejpam-4583	549	6	h−1(vα2)∪	h−1(vα2)∪	NOUN
ejpam-4583	549	7	.	.	PUNCT
ejpam-4583	549	8	.	.	PUNCT
ejpam-4583	549	9	.	.	PUNCT
ejpam-4583	550	1	]	]	PUNCT
ejpam-4583	551	1	=	=	PUNCT
ejpam-4583	551	2	h(x	h(x	PROPN
ejpam-4583	551	3	)	)	PUNCT
ejpam-4583	551	4	,	,	PUNCT
ejpam-4583	551	5	then	then	ADV
ejpam-4583	551	6	h(h−1(vα1	h(h−1(vα1	NUM
ejpam-4583	551	7	)	)	PUNCT
ejpam-4583	551	8	)	)	PUNCT
ejpam-4583	551	9	∪	∪	ADP
ejpam-4583	551	10	h(h−1(vα2	h(h−1(vα2	NUM
ejpam-4583	551	11	)	)	PUNCT
ejpam-4583	551	12	)	)	PUNCT
ejpam-4583	551	13	∪	∪	ADP
ejpam-4583	551	14	·	·	PUNCT
ejpam-4583	551	15	·	·	PUNCT
ejpam-4583	551	16	·	·	PUNCT
ejpam-4583	552	1	=	=	SYM
ejpam-4583	552	2	y	y	PROPN
ejpam-4583	552	3	,	,	PUNCT
ejpam-4583	552	4	then	then	ADV
ejpam-4583	552	5	vα1	vα1	NOUN
ejpam-4583	552	6	∪	∪	ADJ
ejpam-4583	552	7	vα2	vα2	NOUN
ejpam-4583	552	8	∪	∪	X
ejpam-4583	552	9	·	·	PUNCT
ejpam-4583	552	10	·	·	PUNCT
ejpam-4583	552	11	·	·	PUNCT
ejpam-4583	553	1	=	=	PUNCT
ejpam-4583	553	2	y	y	PROPN
ejpam-4583	553	3	.	.	PUNCT
ejpam-4583	554	1	hence	hence	ADV
ejpam-4583	554	2	,	,	PUNCT
ejpam-4583	554	3	{	{	PUNCT
ejpam-4583	554	4	vα1	vα1	NOUN
ejpam-4583	554	5	∪	∪	ADJ
ejpam-4583	554	6	vα2	vα2	NOUN
ejpam-4583	554	7	∪	∪	ADV
ejpam-4583	554	8	.	.	PUNCT
ejpam-4583	554	9	.	.	PUNCT
ejpam-4583	554	10	.	.	PUNCT
ejpam-4583	555	1	}	}	PUNCT
ejpam-4583	555	2	is	be	AUX
ejpam-4583	555	3	a	a	DET
ejpam-4583	555	4	countable	countable	ADJ
ejpam-4583	555	5	subcover	subcover	NOUN
ejpam-4583	555	6	of	of	ADP
ejpam-4583	555	7	open	open	ADJ
ejpam-4583	555	8	sets	set	NOUN
ejpam-4583	555	9	for	for	ADP
ejpam-4583	555	10	y	y	PROPN
ejpam-4583	555	11	.	.	PUNCT
ejpam-4583	556	1	therefore	therefore	ADV
ejpam-4583	556	2	,	,	PUNCT
ejpam-4583	556	3	(	(	PUNCT
ejpam-4583	556	4	y	y	NOUN
ejpam-4583	556	5	,	,	PUNCT
ejpam-4583	556	6	p	p	NOUN
ejpam-4583	556	7	)	)	PUNCT
ejpam-4583	556	8	is	be	AUX
ejpam-4583	556	9	a	a	DET
ejpam-4583	556	10	lindelöf	lindelöf	NOUN
ejpam-4583	556	11	space	space	NOUN
ejpam-4583	556	12	.	.	PUNCT
ejpam-4583	557	1	theorem	theorem	VERB
ejpam-4583	557	2	17	17	NUM
ejpam-4583	557	3	.	.	PUNCT
ejpam-4583	558	1	if	if	SCONJ
ejpam-4583	558	2	there	there	PRON
ejpam-4583	558	3	exists	exist	VERB
ejpam-4583	558	4	a	a	DET
ejpam-4583	558	5	f	f	NUM
ejpam-4583	558	6	-continuous	-continuous	ADJ
ejpam-4583	558	7	function	function	NOUN
ejpam-4583	558	8	h	h	NOUN
ejpam-4583	558	9	from	from	ADP
ejpam-4583	558	10	a	a	DET
ejpam-4583	558	11	f	f	NOUN
ejpam-4583	558	12	-countably	-countably	ADV
ejpam-4583	558	13	compact	compact	ADJ
ejpam-4583	558	14	space	space	NOUN
ejpam-4583	558	15	(	(	PUNCT
ejpam-4583	558	16	x	x	X
ejpam-4583	558	17	,	,	PUNCT
ejpam-4583	558	18	t	t	PROPN
ejpam-4583	558	19	)	)	PUNCT
ejpam-4583	558	20	onto	onto	ADP
ejpam-4583	558	21	a	a	DET
ejpam-4583	558	22	topological	topological	ADJ
ejpam-4583	558	23	space	space	NOUN
ejpam-4583	558	24	(	(	PUNCT
ejpam-4583	558	25	y	y	NOUN
ejpam-4583	558	26	,	,	PUNCT
ejpam-4583	558	27	p	p	NOUN
ejpam-4583	558	28	)	)	PUNCT
ejpam-4583	558	29	,	,	PUNCT
ejpam-4583	558	30	then	then	ADV
ejpam-4583	558	31	(	(	PUNCT
ejpam-4583	558	32	y	y	NOUN
ejpam-4583	558	33	,	,	PUNCT
ejpam-4583	558	34	p	p	NOUN
ejpam-4583	558	35	)	)	PUNCT
ejpam-4583	558	36	is	be	AUX
ejpam-4583	558	37	countably	countably	ADV
ejpam-4583	558	38	compact	compact	ADJ
ejpam-4583	558	39	.	.	PUNCT
ejpam-4583	559	1	proof	proof	NOUN
ejpam-4583	559	2	.	.	PUNCT
ejpam-4583	560	1	using	use	VERB
ejpam-4583	560	2	the	the	DET
ejpam-4583	560	3	same	same	ADJ
ejpam-4583	560	4	proof	proof	NOUN
ejpam-4583	560	5	of	of	ADP
ejpam-4583	560	6	theorem	theorem	ADJ
ejpam-4583	560	7	16	16	NUM
ejpam-4583	560	8	.	.	PUNCT
ejpam-4583	561	1	references	reference	NOUN
ejpam-4583	561	2	832	832	NUM
ejpam-4583	561	3	references	reference	NOUN
ejpam-4583	561	4	[	[	X
ejpam-4583	561	5	1	1	NUM
ejpam-4583	561	6	]	]	PUNCT
ejpam-4583	561	7	r.	r.	PROPN
ejpam-4583	561	8	engelking	engelke	VERB
ejpam-4583	561	9	.	.	PUNCT
ejpam-4583	562	1	general	general	ADJ
ejpam-4583	562	2	topology	topology	PROPN
ejpam-4583	562	3	.	.	PUNCT
ejpam-4583	563	1	pwn	pwn	PROPN
ejpam-4583	563	2	,	,	PUNCT
ejpam-4583	563	3	warszawa	warszawa	PROPN
ejpam-4583	563	4	,	,	PUNCT
ejpam-4583	563	5	1977	1977	NUM
ejpam-4583	563	6	.	.	PUNCT
ejpam-4583	564	1	[	[	X
ejpam-4583	564	2	2	2	NUM
ejpam-4583	564	3	]	]	PUNCT
ejpam-4583	564	4	c.	c.	PROPN
ejpam-4583	564	5	kuratowski	kuratowski	PROPN
ejpam-4583	564	6	.	.	PUNCT
ejpam-4583	565	1	topology	topology	PROPN
ejpam-4583	565	2	i.	i.	PROPN
ejpam-4583	565	3	4th	4th	PROPN
ejpam-4583	565	4	.	.	PUNCT
ejpam-4583	566	1	ed	ed	NOUN
ejpam-4583	566	2	.	.	PROPN
ejpam-4583	566	3	,	,	PUNCT
ejpam-4583	566	4	in	in	ADP
ejpam-4583	566	5	french	french	ADJ
ejpam-4583	566	6	,	,	PUNCT
ejpam-4583	566	7	hafner	hafner	PROPN
ejpam-4583	566	8	,	,	PUNCT
ejpam-4583	566	9	new	new	PROPN
ejpam-4583	566	10	york	york	PROPN
ejpam-4583	566	11	,	,	PUNCT
ejpam-4583	566	12	1958	1958	NUM
ejpam-4583	566	13	.	.	PUNCT
ejpam-4583	567	1	[	[	X
ejpam-4583	567	2	3	3	X
ejpam-4583	567	3	]	]	X
ejpam-4583	567	4	l.	l.	PROPN
ejpam-4583	567	5	steen	steen	PROPN
ejpam-4583	567	6	and	and	CCONJ
ejpam-4583	567	7	j.	j.	PROPN
ejpam-4583	567	8	seebach	seebach	PROPN
ejpam-4583	567	9	.	.	PUNCT
ejpam-4583	568	1	gcounterexamples	gcounterexample	NOUN
ejpam-4583	568	2	in	in	ADP
ejpam-4583	568	3	topology	topology	NOUN
ejpam-4583	568	4	.	.	PUNCT
ejpam-4583	569	1	dover	dover	PROPN
ejpam-4583	569	2	publications	publications	PROPN
ejpam-4583	569	3	,	,	PUNCT
ejpam-4583	569	4	inc	inc	PROPN
ejpam-4583	569	5	,	,	PUNCT
ejpam-4583	569	6	1995	1995	NUM
ejpam-4583	569	7	.	.	PUNCT