id	sid	tid	token	lemma	pos
ejpam-4855	1	1	european	european	PROPN
ejpam-4855	1	2	journal	journal	PROPN
ejpam-4855	1	3	of	of	ADP
ejpam-4855	1	4	pure	pure	ADJ
ejpam-4855	1	5	and	and	CCONJ
ejpam-4855	1	6	applied	apply	VERB
ejpam-4855	1	7	mathematics	mathematic	NOUN
ejpam-4855	1	8	vol	vol	NOUN
ejpam-4855	1	9	.	.	PUNCT
ejpam-4855	2	1	16	16	NUM
ejpam-4855	2	2	,	,	PUNCT
ejpam-4855	2	3	no	no	INTJ
ejpam-4855	2	4	.	.	NOUN
ejpam-4855	2	5	3	3	NUM
ejpam-4855	2	6	,	,	PUNCT
ejpam-4855	2	7	2023	2023	NUM
ejpam-4855	2	8	,	,	PUNCT
ejpam-4855	2	9	1809	1809	NUM
ejpam-4855	2	10	-	-	SYM
ejpam-4855	2	11	1816	1816	NUM
ejpam-4855	2	12	issn	issn	PROPN
ejpam-4855	2	13	1307	1307	NUM
ejpam-4855	2	14	-	-	SYM
ejpam-4855	2	15	5543	5543	NUM
ejpam-4855	2	16	–	–	PUNCT
ejpam-4855	2	17	ejpam.com	ejpam.com	X
ejpam-4855	2	18	published	publish	VERB
ejpam-4855	2	19	by	by	ADP
ejpam-4855	2	20	new	new	PROPN
ejpam-4855	2	21	york	york	PROPN
ejpam-4855	2	22	business	business	PROPN
ejpam-4855	2	23	global	global	ADJ
ejpam-4855	2	24	b∗j	b∗j	ADJ
ejpam-4855	2	25	sets	set	NOUN
ejpam-4855	2	26	and	and	CCONJ
ejpam-4855	2	27	b∗j	b∗j	ADJ
ejpam-4855	2	28	-	-	ADJ
ejpam-4855	2	29	compact	compact	ADJ
ejpam-4855	2	30	ideal	ideal	NOUN
ejpam-4855	3	1	spaces	space	NOUN
ejpam-4855	3	2	michael	michael	PROPN
ejpam-4855	3	3	p.	p.	PROPN
ejpam-4855	3	4	baldado	baldado	PROPN
ejpam-4855	4	1	jr	jr	PROPN
ejpam-4855	4	2	.	.	PROPN
ejpam-4855	4	3	mathematics	mathematics	PROPN
ejpam-4855	4	4	department	department	PROPN
ejpam-4855	4	5	,	,	PUNCT
ejpam-4855	4	6	negros	negros	PROPN
ejpam-4855	4	7	oriental	oriental	ADJ
ejpam-4855	4	8	state	state	PROPN
ejpam-4855	4	9	university	university	PROPN
ejpam-4855	4	10	,	,	PUNCT
ejpam-4855	4	11	dumaguete	dumaguete	PROPN
ejpam-4855	4	12	city	city	PROPN
ejpam-4855	4	13	,	,	PUNCT
ejpam-4855	4	14	philippines	philippine	NOUN
ejpam-4855	4	15	abstract	abstract	ADJ
ejpam-4855	4	16	.	.	PUNCT
ejpam-4855	5	1	we	we	PRON
ejpam-4855	5	2	came	come	VERB
ejpam-4855	5	3	up	up	ADP
ejpam-4855	5	4	with	with	ADP
ejpam-4855	5	5	the	the	DET
ejpam-4855	5	6	concept	concept	NOUN
ejpam-4855	5	7	b∗-open	b∗-open	NOUN
ejpam-4855	5	8	set	set	NOUN
ejpam-4855	5	9	which	which	PRON
ejpam-4855	5	10	has	have	VERB
ejpam-4855	5	11	stricter	strict	ADJ
ejpam-4855	5	12	condition	condition	NOUN
ejpam-4855	5	13	with	with	ADP
ejpam-4855	5	14	respect	respect	NOUN
ejpam-4855	5	15	to	to	ADP
ejpam-4855	5	16	the	the	DET
ejpam-4855	5	17	notion	notion	NOUN
ejpam-4855	5	18	b	b	X
ejpam-4855	5	19	-	-	PUNCT
ejpam-4855	5	20	open	open	ADJ
ejpam-4855	5	21	sets	set	NOUN
ejpam-4855	5	22	,	,	PUNCT
ejpam-4855	5	23	introduced	introduce	VERB
ejpam-4855	5	24	by	by	ADP
ejpam-4855	5	25	andrijevic	andrijevic	ADJ
ejpam-4855	5	26	[	[	X
ejpam-4855	5	27	2	2	NUM
ejpam-4855	5	28	]	]	PUNCT
ejpam-4855	5	29	as	as	ADP
ejpam-4855	5	30	a	a	DET
ejpam-4855	5	31	generalization	generalization	NOUN
ejpam-4855	5	32	of	of	ADP
ejpam-4855	5	33	levine	levine	PROPN
ejpam-4855	5	34	’s	’s	PART
ejpam-4855	5	35	[	[	X
ejpam-4855	5	36	7	7	NUM
ejpam-4855	5	37	]	]	X
ejpam-4855	5	38	generalized	generalize	VERB
ejpam-4855	5	39	closed	closed	ADJ
ejpam-4855	5	40	sets	set	NOUN
ejpam-4855	5	41	.	.	PUNCT
ejpam-4855	6	1	the	the	DET
ejpam-4855	6	2	condition	condition	NOUN
ejpam-4855	6	3	imposes	impose	VERB
ejpam-4855	6	4	equality	equality	NOUN
ejpam-4855	6	5	instead	instead	ADV
ejpam-4855	6	6	of	of	ADP
ejpam-4855	6	7	inclusion	inclusion	NOUN
ejpam-4855	6	8	.	.	PUNCT
ejpam-4855	7	1	in	in	ADP
ejpam-4855	7	2	this	this	DET
ejpam-4855	7	3	study	study	NOUN
ejpam-4855	7	4	,	,	PUNCT
ejpam-4855	7	5	we	we	PRON
ejpam-4855	7	6	gave	give	VERB
ejpam-4855	7	7	some	some	DET
ejpam-4855	7	8	important	important	ADJ
ejpam-4855	7	9	properties	property	NOUN
ejpam-4855	7	10	of	of	ADP
ejpam-4855	7	11	b∗-open	b∗-open	ADJ
ejpam-4855	7	12	sets	set	NOUN
ejpam-4855	7	13	with	with	ADP
ejpam-4855	7	14	respect	respect	NOUN
ejpam-4855	7	15	to	to	ADP
ejpam-4855	7	16	an	an	DET
ejpam-4855	7	17	ideal	ideal	NOUN
ejpam-4855	7	18	,	,	PUNCT
ejpam-4855	7	19	and	and	CCONJ
ejpam-4855	7	20	b∗-compact	b∗-compact	PROPN
ejpam-4855	7	21	spaces	space	NOUN
ejpam-4855	7	22	.	.	PUNCT
ejpam-4855	8	1	2020	2020	NUM
ejpam-4855	8	2	mathematics	mathematic	NOUN
ejpam-4855	8	3	subject	subject	NOUN
ejpam-4855	8	4	classifications	classification	NOUN
ejpam-4855	8	5	:	:	PUNCT
ejpam-4855	8	6	54d30	54d30	NUM
ejpam-4855	8	7	key	key	ADJ
ejpam-4855	8	8	words	word	NOUN
ejpam-4855	8	9	and	and	CCONJ
ejpam-4855	8	10	phrases	phrase	NOUN
ejpam-4855	8	11	:	:	PUNCT
ejpam-4855	8	12	b∗-open	b∗-open	VERB
ejpam-4855	8	13	sets	set	NOUN
ejpam-4855	8	14	,	,	PUNCT
ejpam-4855	8	15	b∗j	b∗j	PUNCT
ejpam-4855	8	16	-open	-open	ADJ
ejpam-4855	8	17	sets	set	NOUN
ejpam-4855	8	18	,	,	PUNCT
ejpam-4855	8	19	ideals	ideal	NOUN
ejpam-4855	8	20	,	,	PUNCT
ejpam-4855	8	21	b∗-compact	b∗-compact	ADJ
ejpam-4855	8	22	space	space	NOUN
ejpam-4855	8	23	,	,	PUNCT
ejpam-4855	8	24	b∗j	b∗j	VERB
ejpam-4855	8	25	-compact	-compact	ADJ
ejpam-4855	8	26	space	space	NOUN
ejpam-4855	8	27	1	1	NUM
ejpam-4855	8	28	.	.	PUNCT
ejpam-4855	9	1	introduction	introduction	NOUN
ejpam-4855	9	2	topology	topology	NOUN
ejpam-4855	9	3	is	be	AUX
ejpam-4855	9	4	a	a	DET
ejpam-4855	9	5	relatively	relatively	ADV
ejpam-4855	9	6	new	new	ADJ
ejpam-4855	9	7	branch	branch	NOUN
ejpam-4855	9	8	of	of	ADP
ejpam-4855	9	9	mathematics	mathematic	NOUN
ejpam-4855	9	10	,	,	PUNCT
ejpam-4855	9	11	being	be	AUX
ejpam-4855	9	12	introduced	introduce	VERB
ejpam-4855	9	13	in	in	ADP
ejpam-4855	9	14	the	the	DET
ejpam-4855	9	15	19th	19th	ADJ
ejpam-4855	9	16	century	century	NOUN
ejpam-4855	9	17	.	.	PUNCT
ejpam-4855	10	1	but	but	CCONJ
ejpam-4855	10	2	topology	topology	NOUN
ejpam-4855	10	3	is	be	AUX
ejpam-4855	10	4	already	already	ADV
ejpam-4855	10	5	seen	see	VERB
ejpam-4855	10	6	in	in	ADP
ejpam-4855	10	7	many	many	ADJ
ejpam-4855	10	8	areas	area	NOUN
ejpam-4855	10	9	of	of	ADP
ejpam-4855	10	10	science	science	NOUN
ejpam-4855	10	11	[	[	X
ejpam-4855	10	12	10	10	NUM
ejpam-4855	10	13	]	]	PUNCT
ejpam-4855	10	14	.	.	PUNCT
ejpam-4855	11	1	it	it	PRON
ejpam-4855	11	2	is	be	AUX
ejpam-4855	11	3	applied	apply	VERB
ejpam-4855	11	4	in	in	ADP
ejpam-4855	11	5	biochemistry	biochemistry	NOUN
ejpam-4855	11	6	[	[	X
ejpam-4855	11	7	3	3	X
ejpam-4855	11	8	]	]	PUNCT
ejpam-4855	11	9	and	and	CCONJ
ejpam-4855	11	10	information	information	NOUN
ejpam-4855	11	11	systems	system	NOUN
ejpam-4855	11	12	[	[	X
ejpam-4855	11	13	15	15	NUM
ejpam-4855	11	14	]	]	PUNCT
ejpam-4855	11	15	.	.	PUNCT
ejpam-4855	12	1	topology	topology	NOUN
ejpam-4855	12	2	as	as	ADP
ejpam-4855	12	3	a	a	DET
ejpam-4855	12	4	mathematical	mathematical	ADJ
ejpam-4855	12	5	system	system	NOUN
ejpam-4855	12	6	is	be	AUX
ejpam-4855	12	7	fundamentally	fundamentally	ADV
ejpam-4855	12	8	comprised	comprise	VERB
ejpam-4855	12	9	of	of	ADP
ejpam-4855	12	10	sets	set	NOUN
ejpam-4855	12	11	together	together	ADV
ejpam-4855	12	12	with	with	ADP
ejpam-4855	12	13	the	the	DET
ejpam-4855	12	14	operations	operation	NOUN
ejpam-4855	12	15	union	union	NOUN
ejpam-4855	12	16	and	and	CCONJ
ejpam-4855	12	17	intersection	intersection	NOUN
ejpam-4855	12	18	.	.	PUNCT
ejpam-4855	13	1	over	over	ADP
ejpam-4855	13	2	time	time	NOUN
ejpam-4855	13	3	,	,	PUNCT
ejpam-4855	13	4	open	open	ADJ
ejpam-4855	13	5	sets	set	NOUN
ejpam-4855	13	6	(	(	PUNCT
ejpam-4855	13	7	elements	element	NOUN
ejpam-4855	13	8	of	of	ADP
ejpam-4855	13	9	topology	topology	NOUN
ejpam-4855	13	10	)	)	PUNCT
ejpam-4855	13	11	were	be	AUX
ejpam-4855	13	12	generalized	generalize	VERB
ejpam-4855	13	13	in	in	ADP
ejpam-4855	13	14	different	different	ADJ
ejpam-4855	13	15	directions	direction	NOUN
ejpam-4855	13	16	.	.	PUNCT
ejpam-4855	14	1	to	to	PART
ejpam-4855	14	2	name	name	VERB
ejpam-4855	14	3	a	a	DET
ejpam-4855	14	4	few	few	ADJ
ejpam-4855	14	5	,	,	PUNCT
ejpam-4855	14	6	stone	stone	NOUN
ejpam-4855	14	7	[	[	X
ejpam-4855	14	8	16	16	NUM
ejpam-4855	14	9	]	]	PUNCT
ejpam-4855	14	10	presented	present	VERB
ejpam-4855	14	11	regular	regular	ADJ
ejpam-4855	14	12	open	open	ADJ
ejpam-4855	14	13	set	set	NOUN
ejpam-4855	14	14	.	.	PUNCT
ejpam-4855	15	1	levine	levine	PROPN
ejpam-4855	16	1	[	[	X
ejpam-4855	16	2	6	6	NUM
ejpam-4855	16	3	]	]	PUNCT
ejpam-4855	16	4	presented	present	VERB
ejpam-4855	16	5	semi	semi	ADJ
ejpam-4855	16	6	-	-	ADJ
ejpam-4855	16	7	open	open	ADJ
ejpam-4855	16	8	sets	set	NOUN
ejpam-4855	16	9	.	.	PUNCT
ejpam-4855	17	1	njasted	njaste	VERB
ejpam-4855	18	1	[	[	X
ejpam-4855	18	2	12	12	NUM
ejpam-4855	18	3	]	]	PUNCT
ejpam-4855	18	4	presented	present	VERB
ejpam-4855	18	5	α	α	X
ejpam-4855	18	6	-	-	ADJ
ejpam-4855	18	7	open	open	ADJ
ejpam-4855	18	8	sets	set	NOUN
ejpam-4855	18	9	.	.	PUNCT
ejpam-4855	19	1	mashhour	mashhour	INTJ
ejpam-4855	19	2	et	et	PROPN
ejpam-4855	19	3	al	al	PROPN
ejpam-4855	19	4	.	.	PUNCT
ejpam-4855	20	1	[	[	X
ejpam-4855	20	2	8	8	NUM
ejpam-4855	20	3	]	]	PUNCT
ejpam-4855	20	4	presented	present	VERB
ejpam-4855	20	5	pre	pre	ADJ
ejpam-4855	20	6	-	-	ADJ
ejpam-4855	20	7	open	open	ADJ
ejpam-4855	20	8	sets	set	NOUN
ejpam-4855	20	9	.	.	PUNCT
ejpam-4855	21	1	abd	abd	PROPN
ejpam-4855	21	2	el	el	PROPN
ejpam-4855	21	3	-	-	PROPN
ejpam-4855	21	4	monsef	monsef	PROPN
ejpam-4855	21	5	et	et	PROPN
ejpam-4855	21	6	al	al	PROPN
ejpam-4855	21	7	.	.	PUNCT
ejpam-4855	22	1	[	[	X
ejpam-4855	22	2	1	1	X
ejpam-4855	22	3	]	]	PUNCT
ejpam-4855	22	4	presented	present	VERB
ejpam-4855	22	5	β	β	ADJ
ejpam-4855	22	6	-	-	ADJ
ejpam-4855	22	7	open	open	ADJ
ejpam-4855	22	8	set	set	NOUN
ejpam-4855	22	9	.	.	PUNCT
ejpam-4855	23	1	it	it	PRON
ejpam-4855	23	2	was	be	AUX
ejpam-4855	23	3	in	in	ADP
ejpam-4855	23	4	the	the	DET
ejpam-4855	23	5	year	year	NOUN
ejpam-4855	23	6	1970	1970	NUM
ejpam-4855	23	7	,	,	PUNCT
ejpam-4855	23	8	when	when	SCONJ
ejpam-4855	23	9	levine	levine	PROPN
ejpam-4855	23	10	[	[	X
ejpam-4855	23	11	7	7	NUM
ejpam-4855	23	12	]	]	PUNCT
ejpam-4855	23	13	presented	present	VERB
ejpam-4855	23	14	the	the	DET
ejpam-4855	23	15	concept	concept	NOUN
ejpam-4855	23	16	of	of	ADP
ejpam-4855	23	17	generalized	generalized	ADJ
ejpam-4855	23	18	closed	closed	ADJ
ejpam-4855	23	19	sets	set	NOUN
ejpam-4855	23	20	,	,	PUNCT
ejpam-4855	23	21	and	and	CCONJ
ejpam-4855	23	22	achoring	achore	VERB
ejpam-4855	23	23	on	on	ADP
ejpam-4855	23	24	this	this	DET
ejpam-4855	23	25	notion	notion	NOUN
ejpam-4855	23	26	,	,	PUNCT
ejpam-4855	23	27	andrijevic	andrijevic	VERB
ejpam-4855	23	28	[	[	X
ejpam-4855	23	29	2	2	X
ejpam-4855	23	30	]	]	PUNCT
ejpam-4855	23	31	presented	present	VERB
ejpam-4855	23	32	yet	yet	ADV
ejpam-4855	23	33	another	another	DET
ejpam-4855	23	34	generalization	generalization	NOUN
ejpam-4855	23	35	of	of	ADP
ejpam-4855	23	36	open	open	ADJ
ejpam-4855	23	37	sets	set	NOUN
ejpam-4855	23	38	called	call	VERB
ejpam-4855	23	39	b	b	NOUN
ejpam-4855	23	40	-	-	PUNCT
ejpam-4855	23	41	open	open	ADJ
ejpam-4855	23	42	sets	set	NOUN
ejpam-4855	23	43	.	.	PUNCT
ejpam-4855	24	1	this	this	DET
ejpam-4855	24	2	study	study	NOUN
ejpam-4855	24	3	uses	use	VERB
ejpam-4855	24	4	the	the	DET
ejpam-4855	24	5	notion	notion	NOUN
ejpam-4855	24	6	of	of	ADP
ejpam-4855	24	7	b	b	NOUN
ejpam-4855	24	8	-	-	PUNCT
ejpam-4855	24	9	open	open	ADJ
ejpam-4855	24	10	sets	set	NOUN
ejpam-4855	24	11	to	to	PART
ejpam-4855	24	12	come	come	VERB
ejpam-4855	24	13	up	up	ADP
ejpam-4855	24	14	with	with	ADP
ejpam-4855	24	15	a	a	DET
ejpam-4855	24	16	new	new	ADJ
ejpam-4855	24	17	concept	concept	NOUN
ejpam-4855	24	18	called	call	VERB
ejpam-4855	24	19	b∗-open	b∗-open	NOUN
ejpam-4855	24	20	sets	set	NOUN
ejpam-4855	24	21	.	.	PUNCT
ejpam-4855	25	1	the	the	DET
ejpam-4855	25	2	concept	concept	NOUN
ejpam-4855	25	3	ideal	ideal	ADJ
ejpam-4855	25	4	topological	topological	ADJ
ejpam-4855	25	5	spaces	space	NOUN
ejpam-4855	25	6	(	(	PUNCT
ejpam-4855	25	7	or	or	CCONJ
ejpam-4855	25	8	simply	simply	ADV
ejpam-4855	25	9	,	,	PUNCT
ejpam-4855	25	10	ideal	ideal	ADJ
ejpam-4855	25	11	space	space	NOUN
ejpam-4855	25	12	)	)	PUNCT
ejpam-4855	25	13	was	be	AUX
ejpam-4855	25	14	first	first	ADV
ejpam-4855	25	15	seen	see	VERB
ejpam-4855	25	16	in	in	ADP
ejpam-4855	25	17	[	[	X
ejpam-4855	25	18	5	5	NUM
ejpam-4855	25	19	]	]	PUNCT
ejpam-4855	25	20	.	.	PUNCT
ejpam-4855	26	1	vaidyanathaswamy	vaidyanathaswamy	NOUN
ejpam-4855	27	1	[	[	X
ejpam-4855	27	2	19	19	NUM
ejpam-4855	27	3	]	]	PUNCT
ejpam-4855	27	4	investigated	investigate	VERB
ejpam-4855	27	5	this	this	DET
ejpam-4855	27	6	concept	concept	NOUN
ejpam-4855	27	7	in	in	ADP
ejpam-4855	27	8	point	point	NOUN
ejpam-4855	27	9	set	set	VERB
ejpam-4855	27	10	topology	topology	NOUN
ejpam-4855	27	11	.	.	PUNCT
ejpam-4855	28	1	tripathy	tripathy	PROPN
ejpam-4855	28	2	and	and	CCONJ
ejpam-4855	28	3	shravan	shravan	PROPN
ejpam-4855	28	4	[	[	X
ejpam-4855	28	5	13	13	NUM
ejpam-4855	28	6	,	,	PUNCT
ejpam-4855	28	7	14	14	NUM
ejpam-4855	28	8	]	]	PUNCT
ejpam-4855	28	9	,	,	PUNCT
ejpam-4855	28	10	tripathy	tripathy	ADJ
ejpam-4855	28	11	and	and	CCONJ
ejpam-4855	28	12	acharjee	acharjee	NOUN
ejpam-4855	28	13	[	[	X
ejpam-4855	28	14	17	17	NUM
ejpam-4855	28	15	]	]	PUNCT
ejpam-4855	28	16	,	,	PUNCT
ejpam-4855	28	17	tripathy	tripathy	ADJ
ejpam-4855	28	18	and	and	CCONJ
ejpam-4855	28	19	ray	ray	NOUN
ejpam-4855	29	1	[	[	X
ejpam-4855	29	2	18	18	NUM
ejpam-4855	29	3	]	]	PUNCT
ejpam-4855	29	4	,	,	PUNCT
ejpam-4855	29	5	catalan	catalan	NOUN
ejpam-4855	29	6	et	et	PROPN
ejpam-4855	29	7	al	al	PROPN
ejpam-4855	29	8	.	.	PUNCT
ejpam-4855	30	1	[	[	X
ejpam-4855	30	2	4	4	X
ejpam-4855	30	3	]	]	PUNCT
ejpam-4855	30	4	among	among	ADP
ejpam-4855	30	5	others	other	NOUN
ejpam-4855	30	6	,	,	PUNCT
ejpam-4855	30	7	also	also	ADV
ejpam-4855	30	8	made	make	VERB
ejpam-4855	30	9	investigations	investigation	NOUN
ejpam-4855	30	10	in	in	ADP
ejpam-4855	30	11	ideal	ideal	ADJ
ejpam-4855	30	12	topological	topological	ADJ
ejpam-4855	30	13	spaces	space	NOUN
ejpam-4855	30	14	.	.	PUNCT
ejpam-4855	31	1	several	several	ADJ
ejpam-4855	31	2	concepts	concept	NOUN
ejpam-4855	31	3	in	in	ADP
ejpam-4855	31	4	topology	topology	NOUN
ejpam-4855	31	5	were	be	AUX
ejpam-4855	31	6	generalized	generalize	VERB
ejpam-4855	31	7	using	use	VERB
ejpam-4855	31	8	this	this	DET
ejpam-4855	31	9	structure	structure	NOUN
ejpam-4855	31	10	.	.	PUNCT
ejpam-4855	32	1	one	one	NUM
ejpam-4855	32	2	of	of	ADP
ejpam-4855	32	3	which	which	PRON
ejpam-4855	32	4	is	be	AUX
ejpam-4855	32	5	the	the	DET
ejpam-4855	32	6	concept	concept	NOUN
ejpam-4855	32	7	b∗-open	b∗-open	NOUN
ejpam-4855	32	8	sets	set	NOUN
ejpam-4855	32	9	.	.	PUNCT
ejpam-4855	33	1	consequently	consequently	ADV
ejpam-4855	33	2	,	,	PUNCT
ejpam-4855	33	3	using	use	VERB
ejpam-4855	33	4	the	the	DET
ejpam-4855	33	5	notion	notion	NOUN
ejpam-4855	33	6	of	of	ADP
ejpam-4855	33	7	b∗-open	b∗-open	ADJ
ejpam-4855	33	8	sets	set	NOUN
ejpam-4855	33	9	,	,	PUNCT
ejpam-4855	33	10	we	we	PRON
ejpam-4855	33	11	introduced	introduce	VERB
ejpam-4855	33	12	doi	doi	NOUN
ejpam-4855	33	13	:	:	PUNCT
ejpam-4855	33	14	https://doi.org/10.29020/nybg.ejpam.v16i3.4855	https://doi.org/10.29020/nybg.ejpam.v16i3.4855	ADJ
ejpam-4855	33	15	email	email	NOUN
ejpam-4855	33	16	address	address	NOUN
ejpam-4855	33	17	:	:	PUNCT
ejpam-4855	33	18	michael.baldadojr@norsu.edu.ph	michael.baldadojr@norsu.edu.ph	PROPN
ejpam-4855	33	19	(	(	PUNCT
ejpam-4855	33	20	m.	m.	PROPN
ejpam-4855	33	21	baldado	baldado	PROPN
ejpam-4855	33	22	jr	jr	PROPN
ejpam-4855	33	23	.	.	PUNCT
ejpam-4855	33	24	)	)	PUNCT
ejpam-4855	33	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4855	33	26	1809	1809	NUM
ejpam-4855	34	1	©	©	ADP
ejpam-4855	34	2	2023	2023	NUM
ejpam-4855	34	3	ejpam	ejpam	NOUN
ejpam-4855	34	4	all	all	DET
ejpam-4855	34	5	rights	right	NOUN
ejpam-4855	34	6	reserved	reserve	VERB
ejpam-4855	34	7	.	.	PUNCT
ejpam-4855	35	1	m.	m.	NOUN
ejpam-4855	35	2	baldado	baldado	PROPN
ejpam-4855	35	3	jr	jr	PROPN
ejpam-4855	35	4	.	.	PROPN
ejpam-4855	35	5	/	/	SYM
ejpam-4855	35	6	eur	eur	PROPN
ejpam-4855	35	7	.	.	PUNCT
ejpam-4855	36	1	j.	j.	PROPN
ejpam-4855	36	2	pure	pure	PROPN
ejpam-4855	36	3	appl	appl	PROPN
ejpam-4855	36	4	.	.	PROPN
ejpam-4855	36	5	math	math	PROPN
ejpam-4855	36	6	,	,	PUNCT
ejpam-4855	36	7	16	16	NUM
ejpam-4855	36	8	(	(	PUNCT
ejpam-4855	36	9	3	3	NUM
ejpam-4855	36	10	)	)	PUNCT
ejpam-4855	36	11	(	(	PUNCT
ejpam-4855	36	12	2023	2023	NUM
ejpam-4855	36	13	)	)	PUNCT
ejpam-4855	36	14	,	,	PUNCT
ejpam-4855	36	15	1809	1809	NUM
ejpam-4855	36	16	-	-	SYM
ejpam-4855	36	17	1816	1816	NUM
ejpam-4855	36	18	1810	1810	NUM
ejpam-4855	36	19	the	the	DET
ejpam-4855	36	20	concepts	concept	NOUN
ejpam-4855	36	21	b∗-compact	b∗-compact	PROPN
ejpam-4855	36	22	sets	set	NOUN
ejpam-4855	36	23	,	,	PUNCT
ejpam-4855	36	24	compatible	compatible	ADJ
ejpam-4855	36	25	b∗j	b∗j	PUNCT
ejpam-4855	36	26	-compact	-compact	NOUN
ejpam-4855	36	27	sets	set	NOUN
ejpam-4855	36	28	,	,	PUNCT
ejpam-4855	36	29	countably	countably	ADV
ejpam-4855	36	30	b∗j	b∗j	ADJ
ejpam-4855	36	31	-compact	-compact	NOUN
ejpam-4855	36	32	sets	set	NOUN
ejpam-4855	36	33	,	,	PUNCT
ejpam-4855	36	34	b∗j	b∗j	PUNCT
ejpam-4855	36	35	-connected	-connected	ADJ
ejpam-4855	36	36	sets	set	NOUN
ejpam-4855	36	37	,	,	PUNCT
ejpam-4855	36	38	in	in	ADP
ejpam-4855	36	39	ideal	ideal	ADJ
ejpam-4855	36	40	generalized	generalize	VERB
ejpam-4855	36	41	topological	topological	ADJ
ejpam-4855	36	42	spaces	space	NOUN
ejpam-4855	36	43	.	.	PUNCT
ejpam-4855	37	1	let	let	VERB
ejpam-4855	37	2	w	w	NOUN
ejpam-4855	37	3	be	be	AUX
ejpam-4855	37	4	a	a	DET
ejpam-4855	37	5	non	non	ADJ
ejpam-4855	37	6	-	-	ADJ
ejpam-4855	37	7	empty	empty	ADJ
ejpam-4855	37	8	set	set	NOUN
ejpam-4855	37	9	.	.	PUNCT
ejpam-4855	38	1	an	an	DET
ejpam-4855	38	2	ideal	ideal	ADJ
ejpam-4855	38	3	j	j	PROPN
ejpam-4855	38	4	on	on	ADP
ejpam-4855	38	5	a	a	DET
ejpam-4855	38	6	set	set	NOUN
ejpam-4855	38	7	w	w	NOUN
ejpam-4855	38	8	is	be	AUX
ejpam-4855	38	9	a	a	DET
ejpam-4855	38	10	non	non	ADJ
ejpam-4855	38	11	-	-	ADJ
ejpam-4855	38	12	empty	empty	ADJ
ejpam-4855	38	13	collection	collection	NOUN
ejpam-4855	38	14	of	of	ADP
ejpam-4855	38	15	subsets	subset	NOUN
ejpam-4855	38	16	of	of	ADP
ejpam-4855	38	17	w	w	ADP
ejpam-4855	38	18	which	which	PRON
ejpam-4855	38	19	satisfies	satisfy	VERB
ejpam-4855	38	20	:	:	PUNCT
ejpam-4855	38	21	1	1	NUM
ejpam-4855	38	22	.	.	X
ejpam-4855	38	23	b	b	X
ejpam-4855	38	24	∈	∈	PROPN
ejpam-4855	38	25	j	j	PROPN
ejpam-4855	38	26	and	and	CCONJ
ejpam-4855	38	27	d	d	PROPN
ejpam-4855	38	28	⊆	⊆	NUM
ejpam-4855	38	29	b	b	NOUN
ejpam-4855	38	30	implies	imply	VERB
ejpam-4855	38	31	d	d	PROPN
ejpam-4855	38	32	∈	∈	PROPN
ejpam-4855	38	33	j	j	PROPN
ejpam-4855	38	34	.	.	PUNCT
ejpam-4855	39	1	2	2	X
ejpam-4855	39	2	.	.	X
ejpam-4855	39	3	b	b	PROPN
ejpam-4855	39	4	∈	∈	PROPN
ejpam-4855	39	5	j	j	PROPN
ejpam-4855	39	6	and	and	CCONJ
ejpam-4855	39	7	d	d	PROPN
ejpam-4855	39	8	∈	∈	PROPN
ejpam-4855	39	9	j	j	PROPN
ejpam-4855	39	10	implies	imply	VERB
ejpam-4855	39	11	b	b	X
ejpam-4855	39	12	∪d	∪d	SYM
ejpam-4855	39	13	∈	∈	PROPN
ejpam-4855	39	14	j	j	PROPN
ejpam-4855	39	15	.	.	PUNCT
ejpam-4855	40	1	let	let	VERB
ejpam-4855	40	2	w	w	NOUN
ejpam-4855	40	3	be	be	AUX
ejpam-4855	40	4	a	a	DET
ejpam-4855	40	5	topological	topological	ADJ
ejpam-4855	40	6	space	space	NOUN
ejpam-4855	40	7	and	and	CCONJ
ejpam-4855	40	8	b	b	NOUN
ejpam-4855	40	9	be	be	AUX
ejpam-4855	40	10	a	a	DET
ejpam-4855	40	11	subset	subset	NOUN
ejpam-4855	40	12	of	of	ADP
ejpam-4855	40	13	w	w	PROPN
ejpam-4855	40	14	.	.	PUNCT
ejpam-4855	41	1	we	we	PRON
ejpam-4855	41	2	say	say	VERB
ejpam-4855	41	3	that	that	SCONJ
ejpam-4855	41	4	b	b	NOUN
ejpam-4855	41	5	is	be	AUX
ejpam-4855	41	6	b∗-open	b∗-open	ADV
ejpam-4855	41	7	set	set	VERB
ejpam-4855	41	8	if	if	SCONJ
ejpam-4855	41	9	b	b	NOUN
ejpam-4855	41	10	=	=	SYM
ejpam-4855	41	11	cl(int(b	cl(int(b	NOUN
ejpam-4855	41	12	)	)	PUNCT
ejpam-4855	41	13	)	)	PUNCT
ejpam-4855	41	14	∪	∪	ADP
ejpam-4855	41	15	int(cl(b	int(cl(b	PROPN
ejpam-4855	41	16	)	)	PUNCT
ejpam-4855	41	17	)	)	PUNCT
ejpam-4855	41	18	.	.	PUNCT
ejpam-4855	42	1	for	for	ADP
ejpam-4855	42	2	example	example	NOUN
ejpam-4855	42	3	,	,	PUNCT
ejpam-4855	42	4	consider	consider	VERB
ejpam-4855	42	5	w	w	NOUN
ejpam-4855	42	6	=	=	X
ejpam-4855	42	7	{	{	PUNCT
ejpam-4855	42	8	a	a	PRON
ejpam-4855	42	9	,	,	PUNCT
ejpam-4855	42	10	b	b	NOUN
ejpam-4855	42	11	,	,	PUNCT
ejpam-4855	42	12	c	c	NOUN
ejpam-4855	42	13	}	}	PUNCT
ejpam-4855	42	14	and	and	CCONJ
ejpam-4855	42	15	the	the	DET
ejpam-4855	42	16	topology	topology	NOUN
ejpam-4855	42	17	ς	ς	PROPN
ejpam-4855	42	18	=	=	PUNCT
ejpam-4855	42	19	{	{	PUNCT
ejpam-4855	42	20	∅	∅	NOUN
ejpam-4855	42	21	,	,	PUNCT
ejpam-4855	42	22	{	{	PUNCT
ejpam-4855	42	23	a	a	X
ejpam-4855	42	24	}	}	PUNCT
ejpam-4855	42	25	,	,	PUNCT
ejpam-4855	42	26	{	{	PUNCT
ejpam-4855	42	27	b	b	NOUN
ejpam-4855	42	28	}	}	PUNCT
ejpam-4855	42	29	,	,	PUNCT
ejpam-4855	42	30	{	{	PUNCT
ejpam-4855	42	31	a	a	DET
ejpam-4855	42	32	,	,	PUNCT
ejpam-4855	42	33	b},w	b},w	NOUN
ejpam-4855	42	34	}	}	PUNCT
ejpam-4855	42	35	on	on	ADP
ejpam-4855	42	36	w	w	PROPN
ejpam-4855	42	37	.	.	PUNCT
ejpam-4855	43	1	then	then	ADV
ejpam-4855	43	2	the	the	DET
ejpam-4855	43	3	b∗-open	b∗-open	ADJ
ejpam-4855	43	4	subsets	subset	NOUN
ejpam-4855	43	5	are	be	AUX
ejpam-4855	43	6	∅	∅	NOUN
ejpam-4855	43	7	,	,	PUNCT
ejpam-4855	43	8	{	{	PUNCT
ejpam-4855	43	9	a	a	DET
ejpam-4855	43	10	,	,	PUNCT
ejpam-4855	43	11	b	b	NOUN
ejpam-4855	43	12	}	}	PUNCT
ejpam-4855	43	13	,	,	PUNCT
ejpam-4855	43	14	{	{	PUNCT
ejpam-4855	43	15	c	c	NOUN
ejpam-4855	43	16	}	}	PUNCT
ejpam-4855	43	17	and	and	CCONJ
ejpam-4855	43	18	w	w	NOUN
ejpam-4855	43	19	.	.	PUNCT
ejpam-4855	44	1	let	let	VERB
ejpam-4855	44	2	w	w	NOUN
ejpam-4855	44	3	be	be	AUX
ejpam-4855	44	4	a	a	DET
ejpam-4855	44	5	topological	topological	ADJ
ejpam-4855	44	6	space	space	NOUN
ejpam-4855	44	7	and	and	CCONJ
ejpam-4855	44	8	b	b	NOUN
ejpam-4855	44	9	be	be	AUX
ejpam-4855	44	10	a	a	DET
ejpam-4855	44	11	subset	subset	NOUN
ejpam-4855	44	12	of	of	ADP
ejpam-4855	44	13	w	w	PROPN
ejpam-4855	44	14	.	.	PUNCT
ejpam-4855	45	1	the	the	DET
ejpam-4855	45	2	set	set	PROPN
ejpam-4855	45	3	b	b	PROPN
ejpam-4855	45	4	is	be	AUX
ejpam-4855	45	5	called	call	VERB
ejpam-4855	45	6	b∗-open	b∗-open	ADJ
ejpam-4855	45	7	relative	relative	ADJ
ejpam-4855	45	8	to	to	ADP
ejpam-4855	45	9	an	an	DET
ejpam-4855	45	10	ideal	ideal	ADJ
ejpam-4855	45	11	j	j	NOUN
ejpam-4855	45	12	(	(	PUNCT
ejpam-4855	45	13	or	or	CCONJ
ejpam-4855	45	14	b∗j	b∗j	ADJ
ejpam-4855	45	15	-open	-open	NOUN
ejpam-4855	45	16	)	)	PUNCT
ejpam-4855	45	17	,	,	PUNCT
ejpam-4855	45	18	if	if	SCONJ
ejpam-4855	45	19	there	there	PRON
ejpam-4855	45	20	is	be	VERB
ejpam-4855	45	21	an	an	DET
ejpam-4855	45	22	open	open	ADJ
ejpam-4855	45	23	set	set	NOUN
ejpam-4855	45	24	p	p	NOUN
ejpam-4855	45	25	with	with	ADP
ejpam-4855	45	26	p	p	PROPN
ejpam-4855	45	27	⊆	⊆	NUM
ejpam-4855	45	28	int(b	int(b	NOUN
ejpam-4855	45	29	)	)	PUNCT
ejpam-4855	45	30	,	,	PUNCT
ejpam-4855	45	31	and	and	CCONJ
ejpam-4855	45	32	a	a	DET
ejpam-4855	45	33	closed	closed	ADJ
ejpam-4855	45	34	set	set	NOUN
ejpam-4855	45	35	s	s	NOUN
ejpam-4855	45	36	with	with	ADP
ejpam-4855	45	37	cl(b	cl(b	NOUN
ejpam-4855	45	38	)	)	PUNCT
ejpam-4855	46	1	⊆	⊆	NUM
ejpam-4855	46	2	s	s	VERB
ejpam-4855	46	3	such	such	ADJ
ejpam-4855	46	4	that	that	DET
ejpam-4855	46	5	1	1	NUM
ejpam-4855	46	6	.	.	PUNCT
ejpam-4855	46	7	(	(	PUNCT
ejpam-4855	46	8	int(s	int(s	PROPN
ejpam-4855	46	9	)	)	PUNCT
ejpam-4855	46	10	∪	∪	VERB
ejpam-4855	46	11	cl(int(b)))\b	cl(int(b)))\b	PROPN
ejpam-4855	46	12	∈	∈	PROPN
ejpam-4855	46	13	j	j	PROPN
ejpam-4855	46	14	,	,	PUNCT
ejpam-4855	46	15	and	and	CCONJ
ejpam-4855	46	16	2	2	X
ejpam-4855	46	17	.	.	X
ejpam-4855	46	18	b\(int(cl(b	b\(int(cl(b	NOUN
ejpam-4855	46	19	)	)	PUNCT
ejpam-4855	46	20	)	)	PUNCT
ejpam-4855	46	21	∪	∪	ADP
ejpam-4855	46	22	cl(p	cl(p	NOUN
ejpam-4855	46	23	)	)	PUNCT
ejpam-4855	46	24	)	)	PUNCT
ejpam-4855	47	1	∈	∈	PROPN
ejpam-4855	47	2	j	j	PROPN
ejpam-4855	47	3	.	.	PUNCT
ejpam-4855	48	1	in	in	ADP
ejpam-4855	48	2	addition	addition	NOUN
ejpam-4855	48	3	,	,	PUNCT
ejpam-4855	48	4	we	we	PRON
ejpam-4855	48	5	say	say	VERB
ejpam-4855	48	6	that	that	SCONJ
ejpam-4855	48	7	a	a	DET
ejpam-4855	48	8	set	set	NOUN
ejpam-4855	48	9	b	b	NOUN
ejpam-4855	48	10	is	be	AUX
ejpam-4855	48	11	a	a	DET
ejpam-4855	48	12	b∗j	b∗j	ADV
ejpam-4855	48	13	-close	-close	ADJ
ejpam-4855	48	14	set	set	VERB
ejpam-4855	48	15	if	if	SCONJ
ejpam-4855	48	16	bc	bc	PROPN
ejpam-4855	48	17	is	be	AUX
ejpam-4855	48	18	b∗j	b∗j	PUNCT
ejpam-4855	48	19	-open	-open	ADJ
ejpam-4855	48	20	.	.	PUNCT
ejpam-4855	49	1	consider	consider	VERB
ejpam-4855	49	2	the	the	DET
ejpam-4855	49	3	ideal	ideal	ADJ
ejpam-4855	49	4	space	space	NOUN
ejpam-4855	49	5	(	(	PUNCT
ejpam-4855	49	6	{	{	PUNCT
ejpam-4855	49	7	q	q	NOUN
ejpam-4855	49	8	,	,	PUNCT
ejpam-4855	49	9	r	r	NOUN
ejpam-4855	49	10	,	,	PUNCT
ejpam-4855	49	11	s	s	PART
ejpam-4855	49	12	}	}	PUNCT
ejpam-4855	49	13	,	,	PUNCT
ejpam-4855	49	14	{	{	PUNCT
ejpam-4855	49	15	∅	∅	NOUN
ejpam-4855	49	16	,	,	PUNCT
ejpam-4855	49	17	{	{	PUNCT
ejpam-4855	49	18	q	q	X
ejpam-4855	49	19	}	}	PUNCT
ejpam-4855	49	20	,	,	PUNCT
ejpam-4855	49	21	{	{	PUNCT
ejpam-4855	49	22	r	r	NOUN
ejpam-4855	49	23	}	}	PUNCT
ejpam-4855	49	24	,	,	PUNCT
ejpam-4855	49	25	{	{	PUNCT
ejpam-4855	49	26	q	q	X
ejpam-4855	49	27	,	,	PUNCT
ejpam-4855	49	28	r	r	NOUN
ejpam-4855	49	29	}	}	PUNCT
ejpam-4855	49	30	,	,	PUNCT
ejpam-4855	49	31	{	{	PUNCT
ejpam-4855	49	32	q	q	X
ejpam-4855	49	33	,	,	PUNCT
ejpam-4855	49	34	r	r	NOUN
ejpam-4855	49	35	,	,	PUNCT
ejpam-4855	49	36	s	s	PART
ejpam-4855	49	37	}	}	PUNCT
ejpam-4855	49	38	}	}	PUNCT
ejpam-4855	49	39	,	,	PUNCT
ejpam-4855	49	40	{	{	PUNCT
ejpam-4855	49	41	∅	∅	NOUN
ejpam-4855	49	42	,	,	PUNCT
ejpam-4855	49	43	{	{	PUNCT
ejpam-4855	49	44	r	r	NOUN
ejpam-4855	49	45	}	}	PUNCT
ejpam-4855	49	46	}	}	PUNCT
ejpam-4855	49	47	)	)	PUNCT
ejpam-4855	49	48	.	.	PUNCT
ejpam-4855	50	1	then	then	ADV
ejpam-4855	50	2	b	b	X
ejpam-4855	50	3	=	=	PRON
ejpam-4855	50	4	{	{	PUNCT
ejpam-4855	50	5	r	r	NOUN
ejpam-4855	50	6	,	,	PUNCT
ejpam-4855	50	7	s	s	PART
ejpam-4855	50	8	}	}	PUNCT
ejpam-4855	50	9	is	be	AUX
ejpam-4855	50	10	a	a	DET
ejpam-4855	50	11	b∗-open	b∗-open	NOUN
ejpam-4855	50	12	with	with	ADP
ejpam-4855	50	13	respect	respect	NOUN
ejpam-4855	50	14	to	to	ADP
ejpam-4855	50	15	the	the	DET
ejpam-4855	50	16	ideal	ideal	NOUN
ejpam-4855	50	17	j	j	PROPN
ejpam-4855	51	1	=	=	PUNCT
ejpam-4855	51	2	{	{	PUNCT
ejpam-4855	51	3	∅	∅	NOUN
ejpam-4855	51	4	,	,	PUNCT
ejpam-4855	51	5	{	{	PUNCT
ejpam-4855	51	6	r	r	NOUN
ejpam-4855	51	7	}	}	PUNCT
ejpam-4855	51	8	}	}	PUNCT
ejpam-4855	51	9	.	.	PUNCT
ejpam-4855	52	1	to	to	PART
ejpam-4855	52	2	see	see	VERB
ejpam-4855	52	3	this	this	PRON
ejpam-4855	52	4	,	,	PUNCT
ejpam-4855	52	5	we	we	PRON
ejpam-4855	52	6	let	let	VERB
ejpam-4855	52	7	p	p	PRON
ejpam-4855	52	8	be	be	AUX
ejpam-4855	52	9	the	the	DET
ejpam-4855	52	10	open	open	ADJ
ejpam-4855	52	11	set	set	NOUN
ejpam-4855	52	12	{	{	PUNCT
ejpam-4855	52	13	r	r	NOUN
ejpam-4855	52	14	}	}	PUNCT
ejpam-4855	52	15	and	and	CCONJ
ejpam-4855	52	16	s	s	AUX
ejpam-4855	52	17	be	be	AUX
ejpam-4855	52	18	the	the	DET
ejpam-4855	52	19	closed	closed	ADJ
ejpam-4855	52	20	set	set	NOUN
ejpam-4855	52	21	{	{	PUNCT
ejpam-4855	52	22	r	r	NOUN
ejpam-4855	52	23	,	,	PUNCT
ejpam-4855	52	24	s	s	PART
ejpam-4855	52	25	}	}	PUNCT
ejpam-4855	52	26	.	.	PUNCT
ejpam-4855	53	1	then	then	ADV
ejpam-4855	53	2	int(s	int(s	PROPN
ejpam-4855	53	3	)	)	PUNCT
ejpam-4855	53	4	∪	∪	ADP
ejpam-4855	53	5	cl(int({r	cl(int({r	PROPN
ejpam-4855	53	6	,	,	PUNCT
ejpam-4855	53	7	s}))\{r	s}))\{r	VERB
ejpam-4855	53	8	,	,	PUNCT
ejpam-4855	53	9	s	s	X
ejpam-4855	53	10	}	}	PUNCT
ejpam-4855	53	11	=	=	SYM
ejpam-4855	53	12	int({r	int({r	PROPN
ejpam-4855	53	13	,	,	PUNCT
ejpam-4855	53	14	s	s	NOUN
ejpam-4855	53	15	}	}	PUNCT
ejpam-4855	53	16	)	)	PUNCT
ejpam-4855	53	17	∪	∪	ADP
ejpam-4855	53	18	cl({r})\{r	cl({r})\{r	PROPN
ejpam-4855	53	19	,	,	PUNCT
ejpam-4855	53	20	s	s	X
ejpam-4855	53	21	}	}	PUNCT
ejpam-4855	53	22	=	=	SYM
ejpam-4855	53	23	{	{	PUNCT
ejpam-4855	53	24	r	r	NOUN
ejpam-4855	53	25	}	}	PUNCT
ejpam-4855	53	26	∪	∪	NOUN
ejpam-4855	53	27	{	{	PUNCT
ejpam-4855	53	28	r	r	NOUN
ejpam-4855	53	29	,	,	PUNCT
ejpam-4855	53	30	s}\{r	s}\{r	NOUN
ejpam-4855	53	31	,	,	PUNCT
ejpam-4855	53	32	s	s	X
ejpam-4855	53	33	}	}	PUNCT
ejpam-4855	53	34	=	=	SYM
ejpam-4855	53	35	{	{	PUNCT
ejpam-4855	53	36	r	r	NOUN
ejpam-4855	53	37	,	,	PUNCT
ejpam-4855	53	38	s}\{r	s}\{r	NOUN
ejpam-4855	53	39	,	,	PUNCT
ejpam-4855	53	40	s	s	X
ejpam-4855	53	41	}	}	PUNCT
ejpam-4855	53	42	=	=	SYM
ejpam-4855	53	43	∅	∅	NOUN
ejpam-4855	53	44	∈	∈	PROPN
ejpam-4855	53	45	j	j	PROPN
ejpam-4855	53	46	.	.	PUNCT
ejpam-4855	54	1	also	also	ADV
ejpam-4855	54	2	,	,	PUNCT
ejpam-4855	54	3	int(cl({r	int(cl({r	NOUN
ejpam-4855	54	4	,	,	PUNCT
ejpam-4855	54	5	s	s	NOUN
ejpam-4855	54	6	}	}	PUNCT
ejpam-4855	54	7	)	)	PUNCT
ejpam-4855	54	8	∪	∪	NOUN
ejpam-4855	54	9	cl(p	cl(p	NOUN
ejpam-4855	54	10	)	)	PUNCT
ejpam-4855	54	11	\{r	\{r	NOUN
ejpam-4855	54	12	,	,	PUNCT
ejpam-4855	54	13	s	s	X
ejpam-4855	54	14	}	}	PUNCT
ejpam-4855	54	15	=	=	SYM
ejpam-4855	54	16	int({r	int({r	PROPN
ejpam-4855	54	17	,	,	PUNCT
ejpam-4855	54	18	s	s	NOUN
ejpam-4855	54	19	}	}	PUNCT
ejpam-4855	54	20	)	)	PUNCT
ejpam-4855	54	21	∪	∪	ADP
ejpam-4855	54	22	cl({r})\{r	cl({r})\{r	PROPN
ejpam-4855	54	23	,	,	PUNCT
ejpam-4855	54	24	s	s	X
ejpam-4855	54	25	}	}	PUNCT
ejpam-4855	54	26	=	=	SYM
ejpam-4855	54	27	{	{	PUNCT
ejpam-4855	54	28	r	r	NOUN
ejpam-4855	54	29	}	}	PUNCT
ejpam-4855	54	30	∪	∪	NOUN
ejpam-4855	54	31	{	{	PUNCT
ejpam-4855	54	32	r	r	NOUN
ejpam-4855	54	33	,	,	PUNCT
ejpam-4855	54	34	s}\{r	s}\{r	NOUN
ejpam-4855	54	35	,	,	PUNCT
ejpam-4855	54	36	s	s	X
ejpam-4855	54	37	}	}	PUNCT
ejpam-4855	54	38	=	=	SYM
ejpam-4855	54	39	{	{	PUNCT
ejpam-4855	54	40	r	r	NOUN
ejpam-4855	54	41	,	,	PUNCT
ejpam-4855	54	42	s}\{r	s}\{r	NOUN
ejpam-4855	54	43	,	,	PUNCT
ejpam-4855	54	44	s	s	X
ejpam-4855	54	45	}	}	PUNCT
ejpam-4855	54	46	=	=	SYM
ejpam-4855	54	47	∅	∅	NOUN
ejpam-4855	54	48	∈	∈	PROPN
ejpam-4855	54	49	j	j	PROPN
ejpam-4855	54	50	.	.	PUNCT
ejpam-4855	55	1	this	this	PRON
ejpam-4855	55	2	shows	show	VERB
ejpam-4855	55	3	that	that	SCONJ
ejpam-4855	55	4	b	b	X
ejpam-4855	55	5	=	=	PRON
ejpam-4855	55	6	{	{	PUNCT
ejpam-4855	55	7	r	r	NOUN
ejpam-4855	55	8	,	,	PUNCT
ejpam-4855	55	9	s	s	PART
ejpam-4855	55	10	}	}	PUNCT
ejpam-4855	55	11	is	be	AUX
ejpam-4855	55	12	a	a	DET
ejpam-4855	55	13	b∗j	b∗j	PUNCT
ejpam-4855	55	14	-open	-open	NOUN
ejpam-4855	55	15	.	.	PUNCT
ejpam-4855	56	1	let	let	VERB
ejpam-4855	56	2	w	w	NOUN
ejpam-4855	56	3	be	be	AUX
ejpam-4855	56	4	a	a	DET
ejpam-4855	56	5	topological	topological	ADJ
ejpam-4855	56	6	space	space	NOUN
ejpam-4855	56	7	and	and	CCONJ
ejpam-4855	56	8	b	b	NOUN
ejpam-4855	56	9	be	be	AUX
ejpam-4855	56	10	a	a	DET
ejpam-4855	56	11	subset	subset	NOUN
ejpam-4855	56	12	of	of	ADP
ejpam-4855	56	13	w	w	PROPN
ejpam-4855	56	14	.	.	PUNCT
ejpam-4855	57	1	the	the	DET
ejpam-4855	57	2	set	set	PROPN
ejpam-4855	57	3	b	b	PROPN
ejpam-4855	57	4	is	be	AUX
ejpam-4855	57	5	called	call	VERB
ejpam-4855	57	6	nearly	nearly	ADV
ejpam-4855	57	7	b∗open	b∗open	ADJ
ejpam-4855	57	8	relative	relative	ADJ
ejpam-4855	57	9	to	to	ADP
ejpam-4855	57	10	an	an	DET
ejpam-4855	57	11	ideal	ideal	ADJ
ejpam-4855	57	12	j	j	NOUN
ejpam-4855	57	13	(	(	PUNCT
ejpam-4855	57	14	or	or	CCONJ
ejpam-4855	57	15	nearly	nearly	ADV
ejpam-4855	57	16	b∗j	b∗j	ADJ
ejpam-4855	57	17	-open	-open	NOUN
ejpam-4855	57	18	)	)	PUNCT
ejpam-4855	57	19	if	if	SCONJ
ejpam-4855	57	20	there	there	PRON
ejpam-4855	57	21	is	be	VERB
ejpam-4855	57	22	an	an	DET
ejpam-4855	57	23	open	open	ADJ
ejpam-4855	57	24	set	set	NOUN
ejpam-4855	57	25	p	p	NOUN
ejpam-4855	57	26	with	with	ADP
ejpam-4855	57	27	p	p	PROPN
ejpam-4855	57	28	⊆	⊆	NUM
ejpam-4855	57	29	int(b	int(b	NOUN
ejpam-4855	57	30	)	)	PUNCT
ejpam-4855	57	31	,	,	PUNCT
ejpam-4855	57	32	and	and	CCONJ
ejpam-4855	57	33	a	a	DET
ejpam-4855	57	34	closed	closed	ADJ
ejpam-4855	57	35	set	set	NOUN
ejpam-4855	57	36	s	s	NOUN
ejpam-4855	57	37	with	with	ADP
ejpam-4855	57	38	cl(b	cl(b	NOUN
ejpam-4855	57	39	)	)	PUNCT
ejpam-4855	57	40	⊆	⊆	NUM
ejpam-4855	57	41	s	s	VERB
ejpam-4855	57	42	such	such	ADJ
ejpam-4855	57	43	that	that	DET
ejpam-4855	57	44	1	1	NUM
ejpam-4855	57	45	.	.	PUNCT
ejpam-4855	57	46	(	(	PUNCT
ejpam-4855	57	47	int(s	int(s	PROPN
ejpam-4855	57	48	)	)	PUNCT
ejpam-4855	57	49	∪	∪	NOUN
ejpam-4855	57	50	cl(int(b)))\cl(b	cl(int(b)))\cl(b	PROPN
ejpam-4855	57	51	)	)	PUNCT
ejpam-4855	57	52	∈	∈	PROPN
ejpam-4855	57	53	j	j	PROPN
ejpam-4855	57	54	,	,	PUNCT
ejpam-4855	57	55	and	and	CCONJ
ejpam-4855	57	56	2	2	X
ejpam-4855	57	57	.	.	X
ejpam-4855	57	58	b\(int(cl(b	b\(int(cl(b	NOUN
ejpam-4855	57	59	)	)	PUNCT
ejpam-4855	57	60	)	)	PUNCT
ejpam-4855	57	61	∪	∪	ADP
ejpam-4855	57	62	cl(p	cl(p	NOUN
ejpam-4855	57	63	)	)	PUNCT
ejpam-4855	57	64	)	)	PUNCT
ejpam-4855	58	1	∈	∈	PROPN
ejpam-4855	58	2	j	j	PROPN
ejpam-4855	58	3	.	.	PUNCT
ejpam-4855	58	4	consider	consider	VERB
ejpam-4855	58	5	the	the	DET
ejpam-4855	58	6	ideal	ideal	ADJ
ejpam-4855	58	7	topological	topological	ADJ
ejpam-4855	58	8	space	space	NOUN
ejpam-4855	58	9	(	(	PUNCT
ejpam-4855	58	10	{	{	PUNCT
ejpam-4855	58	11	1	1	NUM
ejpam-4855	58	12	,	,	PUNCT
ejpam-4855	58	13	2	2	NUM
ejpam-4855	58	14	,	,	PUNCT
ejpam-4855	58	15	3	3	NUM
ejpam-4855	58	16	}	}	PUNCT
ejpam-4855	58	17	,	,	PUNCT
ejpam-4855	58	18	{	{	PUNCT
ejpam-4855	58	19	∅	∅	NOUN
ejpam-4855	58	20	,	,	PUNCT
ejpam-4855	58	21	{	{	PUNCT
ejpam-4855	58	22	1	1	NUM
ejpam-4855	58	23	}	}	PUNCT
ejpam-4855	58	24	,	,	PUNCT
ejpam-4855	58	25	{	{	PUNCT
ejpam-4855	58	26	2	2	NUM
ejpam-4855	58	27	}	}	PUNCT
ejpam-4855	58	28	,	,	PUNCT
ejpam-4855	58	29	{	{	PUNCT
ejpam-4855	58	30	1	1	NUM
ejpam-4855	58	31	,	,	PUNCT
ejpam-4855	58	32	2	2	NUM
ejpam-4855	58	33	}	}	PUNCT
ejpam-4855	58	34	,	,	PUNCT
ejpam-4855	58	35	{	{	PUNCT
ejpam-4855	58	36	1	1	NUM
ejpam-4855	58	37	,	,	PUNCT
ejpam-4855	58	38	2	2	NUM
ejpam-4855	58	39	,	,	PUNCT
ejpam-4855	58	40	3	3	NUM
ejpam-4855	58	41	}	}	PUNCT
ejpam-4855	58	42	}	}	PUNCT
ejpam-4855	58	43	,	,	PUNCT
ejpam-4855	58	44	{	{	PUNCT
ejpam-4855	58	45	∅	∅	NOUN
ejpam-4855	58	46	,	,	PUNCT
ejpam-4855	58	47	{	{	PUNCT
ejpam-4855	58	48	2	2	NUM
ejpam-4855	58	49	}	}	PUNCT
ejpam-4855	58	50	}	}	PUNCT
ejpam-4855	58	51	)	)	PUNCT
ejpam-4855	58	52	.	.	PUNCT
ejpam-4855	59	1	then	then	ADV
ejpam-4855	59	2	b	b	X
ejpam-4855	59	3	=	=	PUNCT
ejpam-4855	59	4	{	{	PUNCT
ejpam-4855	59	5	2	2	NUM
ejpam-4855	59	6	,	,	PUNCT
ejpam-4855	59	7	3	3	NUM
ejpam-4855	59	8	}	}	PUNCT
ejpam-4855	59	9	is	be	AUX
ejpam-4855	59	10	a	a	DET
ejpam-4855	59	11	nearly	nearly	ADV
ejpam-4855	59	12	b∗-open	b∗-open	ADJ
ejpam-4855	59	13	with	with	ADP
ejpam-4855	59	14	respect	respect	NOUN
ejpam-4855	59	15	to	to	ADP
ejpam-4855	59	16	the	the	DET
ejpam-4855	59	17	ideal	ideal	ADJ
ejpam-4855	59	18	j	j	PROPN
ejpam-4855	59	19	(	(	PUNCT
ejpam-4855	59	20	or	or	CCONJ
ejpam-4855	59	21	nearly	nearly	ADV
ejpam-4855	59	22	b∗j	b∗j	ADJ
ejpam-4855	59	23	-open	-open	NOUN
ejpam-4855	59	24	)	)	PUNCT
ejpam-4855	59	25	.	.	PUNCT
ejpam-4855	60	1	to	to	PART
ejpam-4855	60	2	see	see	VERB
ejpam-4855	60	3	this	this	PRON
ejpam-4855	60	4	,	,	PUNCT
ejpam-4855	60	5	we	we	PRON
ejpam-4855	60	6	let	let	VERB
ejpam-4855	60	7	p	p	PRON
ejpam-4855	60	8	be	be	AUX
ejpam-4855	60	9	the	the	DET
ejpam-4855	60	10	open	open	ADJ
ejpam-4855	60	11	set	set	NOUN
ejpam-4855	60	12	{	{	PUNCT
ejpam-4855	60	13	2	2	NUM
ejpam-4855	60	14	}	}	PUNCT
ejpam-4855	60	15	and	and	CCONJ
ejpam-4855	60	16	s	s	AUX
ejpam-4855	60	17	be	be	AUX
ejpam-4855	60	18	the	the	DET
ejpam-4855	60	19	closed	closed	ADJ
ejpam-4855	60	20	set	set	NOUN
ejpam-4855	60	21	{	{	PUNCT
ejpam-4855	60	22	2	2	NUM
ejpam-4855	60	23	,	,	PUNCT
ejpam-4855	60	24	3	3	NUM
ejpam-4855	60	25	}	}	PUNCT
ejpam-4855	60	26	.	.	PUNCT
ejpam-4855	61	1	then	then	ADV
ejpam-4855	61	2	int(s)∪cl(int({2	int(s)∪cl(int({2	NOUN
ejpam-4855	61	3	,	,	PUNCT
ejpam-4855	61	4	3}))\cl({2	3}))\cl({2	PROPN
ejpam-4855	61	5	,	,	PUNCT
ejpam-4855	61	6	3	3	NUM
ejpam-4855	61	7	}	}	PUNCT
ejpam-4855	61	8	)	)	PUNCT
ejpam-4855	61	9	=	=	SYM
ejpam-4855	61	10	int({2	int({2	PROPN
ejpam-4855	61	11	,	,	PUNCT
ejpam-4855	61	12	3})∪cl({2})\cl({2	3})∪cl({2})\cl({2	NOUN
ejpam-4855	61	13	,	,	PUNCT
ejpam-4855	61	14	3	3	NUM
ejpam-4855	61	15	}	}	PUNCT
ejpam-4855	61	16	)	)	PUNCT
ejpam-4855	61	17	=	=	SYM
ejpam-4855	61	18	{	{	PUNCT
ejpam-4855	61	19	2}∪{2	2}∪{2	NOUN
ejpam-4855	61	20	,	,	PUNCT
ejpam-4855	61	21	3}\cl({2	3}\cl({2	NUM
ejpam-4855	61	22	,	,	PUNCT
ejpam-4855	61	23	3	3	NUM
ejpam-4855	61	24	}	}	PUNCT
ejpam-4855	61	25	)	)	PUNCT
ejpam-4855	61	26	=	=	PUNCT
ejpam-4855	61	27	{	{	PUNCT
ejpam-4855	61	28	2	2	NUM
ejpam-4855	61	29	,	,	PUNCT
ejpam-4855	61	30	3}\{2	3}\{2	NUM
ejpam-4855	61	31	,	,	PUNCT
ejpam-4855	61	32	3	3	NUM
ejpam-4855	61	33	}	}	PUNCT
ejpam-4855	61	34	=	=	NOUN
ejpam-4855	61	35	∅	∅	NOUN
ejpam-4855	61	36	∈	∈	PROPN
ejpam-4855	61	37	j	j	PROPN
ejpam-4855	61	38	.	.	PUNCT
ejpam-4855	62	1	also	also	ADV
ejpam-4855	62	2	,	,	PUNCT
ejpam-4855	62	3	int(cl({2	int(cl({2	PROPN
ejpam-4855	62	4	,	,	PUNCT
ejpam-4855	62	5	3	3	NUM
ejpam-4855	62	6	}	}	PUNCT
ejpam-4855	62	7	)	)	PUNCT
ejpam-4855	62	8	∪	∪	NOUN
ejpam-4855	62	9	cl(p	cl(p	PUNCT
ejpam-4855	62	10	)	)	PUNCT
ejpam-4855	62	11	\{2	\{2	NOUN
ejpam-4855	62	12	,	,	PUNCT
ejpam-4855	62	13	3	3	X
ejpam-4855	62	14	}	}	PUNCT
ejpam-4855	62	15	=	=	SYM
ejpam-4855	62	16	int({2	int({2	PROPN
ejpam-4855	62	17	,	,	PUNCT
ejpam-4855	62	18	3	3	NUM
ejpam-4855	62	19	}	}	PUNCT
ejpam-4855	62	20	)	)	PUNCT
ejpam-4855	62	21	∪	∪	ADP
ejpam-4855	62	22	cl({2})\{2	cl({2})\{2	NOUN
ejpam-4855	62	23	,	,	PUNCT
ejpam-4855	62	24	3	3	X
ejpam-4855	62	25	}	}	PUNCT
ejpam-4855	62	26	=	=	SYM
ejpam-4855	62	27	{	{	PUNCT
ejpam-4855	62	28	2	2	NUM
ejpam-4855	62	29	}	}	PUNCT
ejpam-4855	62	30	∪	∪	X
ejpam-4855	62	31	{	{	PUNCT
ejpam-4855	62	32	2	2	NUM
ejpam-4855	62	33	,	,	PUNCT
ejpam-4855	62	34	3}\{2	3}\{2	NUM
ejpam-4855	62	35	,	,	PUNCT
ejpam-4855	62	36	3	3	NUM
ejpam-4855	62	37	}	}	PUNCT
ejpam-4855	62	38	=	=	PUNCT
ejpam-4855	62	39	{	{	PUNCT
ejpam-4855	62	40	2	2	NUM
ejpam-4855	62	41	,	,	PUNCT
ejpam-4855	62	42	3}\{2	3}\{2	NUM
ejpam-4855	62	43	,	,	PUNCT
ejpam-4855	62	44	3	3	NUM
ejpam-4855	62	45	}	}	PUNCT
ejpam-4855	62	46	=	=	NOUN
ejpam-4855	62	47	∅	∅	NOUN
ejpam-4855	62	48	∈	∈	PROPN
ejpam-4855	62	49	j	j	PROPN
ejpam-4855	62	50	.	.	PUNCT
ejpam-4855	63	1	this	this	PRON
ejpam-4855	63	2	shows	show	VERB
ejpam-4855	63	3	that	that	SCONJ
ejpam-4855	63	4	b	b	X
ejpam-4855	63	5	=	=	PRON
ejpam-4855	63	6	{	{	PUNCT
ejpam-4855	63	7	2	2	NUM
ejpam-4855	63	8	,	,	PUNCT
ejpam-4855	63	9	3	3	NUM
ejpam-4855	63	10	}	}	PUNCT
ejpam-4855	63	11	is	be	AUX
ejpam-4855	63	12	a	a	DET
ejpam-4855	63	13	nearly	nearly	ADV
ejpam-4855	63	14	b∗j	b∗j	VERB
ejpam-4855	63	15	-open	-open	NOUN
ejpam-4855	63	16	.	.	PUNCT
ejpam-4855	64	1	the	the	DET
ejpam-4855	64	2	set	set	PROPN
ejpam-4855	64	3	b	b	PROPN
ejpam-4855	64	4	is	be	AUX
ejpam-4855	64	5	said	say	VERB
ejpam-4855	64	6	to	to	PART
ejpam-4855	64	7	be	be	AUX
ejpam-4855	64	8	b∗-compact	b∗-compact	ADJ
ejpam-4855	64	9	if	if	SCONJ
ejpam-4855	64	10	every	every	DET
ejpam-4855	64	11	cover	cover	NOUN
ejpam-4855	64	12	of	of	ADP
ejpam-4855	64	13	b	b	NOUN
ejpam-4855	64	14	by	by	ADP
ejpam-4855	64	15	b∗-open	b∗-open	NOUN
ejpam-4855	64	16	sets	set	NOUN
ejpam-4855	64	17	,	,	PUNCT
ejpam-4855	64	18	containingw	containingw	NOUN
ejpam-4855	64	19	,	,	PUNCT
ejpam-4855	64	20	has	have	VERB
ejpam-4855	64	21	a	a	DET
ejpam-4855	64	22	smaller	small	ADJ
ejpam-4855	64	23	finite	finite	ADJ
ejpam-4855	64	24	sub	sub	NOUN
ejpam-4855	64	25	-	-	NOUN
ejpam-4855	64	26	cover	cover	NOUN
ejpam-4855	64	27	.	.	PUNCT
ejpam-4855	65	1	the	the	DET
ejpam-4855	65	2	spacew	spacew	NOUN
ejpam-4855	65	3	is	be	AUX
ejpam-4855	65	4	said	say	VERB
ejpam-4855	65	5	to	to	PART
ejpam-4855	65	6	be	be	AUX
ejpam-4855	65	7	a	a	DET
ejpam-4855	65	8	b∗-compact	b∗-compact	ADJ
ejpam-4855	65	9	space	space	NOUN
ejpam-4855	65	10	ifw	ifw	PROPN
ejpam-4855	65	11	is	be	AUX
ejpam-4855	65	12	b∗-compact	b∗-compact	PROPN
ejpam-4855	65	13	set	set	NOUN
ejpam-4855	65	14	.	.	PUNCT
ejpam-4855	66	1	consider	consider	VERB
ejpam-4855	66	2	the	the	DET
ejpam-4855	66	3	topological	topological	ADJ
ejpam-4855	66	4	space	space	NOUN
ejpam-4855	66	5	(	(	PUNCT
ejpam-4855	66	6	w	w	NOUN
ejpam-4855	66	7	=	=	X
ejpam-4855	66	8	{	{	PUNCT
ejpam-4855	66	9	a	a	PRON
ejpam-4855	66	10	,	,	PUNCT
ejpam-4855	66	11	b	b	NOUN
ejpam-4855	66	12	,	,	PUNCT
ejpam-4855	66	13	c	c	NOUN
ejpam-4855	66	14	}	}	PUNCT
ejpam-4855	66	15	,	,	PUNCT
ejpam-4855	66	16	{	{	PUNCT
ejpam-4855	66	17	∅	∅	NOUN
ejpam-4855	66	18	,	,	PUNCT
ejpam-4855	66	19	{	{	PUNCT
ejpam-4855	66	20	a	a	X
ejpam-4855	66	21	}	}	PUNCT
ejpam-4855	66	22	,	,	PUNCT
ejpam-4855	66	23	{	{	PUNCT
ejpam-4855	66	24	b	b	NOUN
ejpam-4855	66	25	,	,	PUNCT
ejpam-4855	66	26	c},w	c},w	NOUN
ejpam-4855	66	27	}	}	PUNCT
ejpam-4855	66	28	,	,	PUNCT
ejpam-4855	66	29	j	j	PROPN
ejpam-4855	66	30	=	=	PUNCT
ejpam-4855	66	31	{	{	PUNCT
ejpam-4855	66	32	∅	∅	NOUN
ejpam-4855	66	33	,	,	PUNCT
ejpam-4855	66	34	{	{	PUNCT
ejpam-4855	66	35	a	a	NOUN
ejpam-4855	66	36	}	}	PUNCT
ejpam-4855	66	37	}	}	PUNCT
ejpam-4855	66	38	)	)	PUNCT
ejpam-4855	66	39	.	.	PUNCT
ejpam-4855	67	1	then	then	ADV
ejpam-4855	67	2	b	b	X
ejpam-4855	67	3	=	=	X
ejpam-4855	67	4	{	{	PUNCT
ejpam-4855	67	5	a	a	PRON
ejpam-4855	67	6	}	}	PUNCT
ejpam-4855	67	7	is	be	AUX
ejpam-4855	67	8	a	a	DET
ejpam-4855	67	9	b∗-compact	b∗-compact	PROPN
ejpam-4855	67	10	set	set	NOUN
ejpam-4855	67	11	,	,	PUNCT
ejpam-4855	67	12	while	while	SCONJ
ejpam-4855	67	13	d	d	PROPN
ejpam-4855	67	14	=	=	PRON
ejpam-4855	67	15	{	{	PUNCT
ejpam-4855	67	16	a	a	DET
ejpam-4855	67	17	,	,	PUNCT
ejpam-4855	67	18	b	b	NOUN
ejpam-4855	67	19	}	}	PUNCT
ejpam-4855	67	20	is	be	AUX
ejpam-4855	67	21	not	not	PART
ejpam-4855	67	22	.	.	PUNCT
ejpam-4855	68	1	to	to	PART
ejpam-4855	68	2	see	see	VERB
ejpam-4855	68	3	this	this	PRON
ejpam-4855	68	4	,	,	PUNCT
ejpam-4855	68	5	we	we	PRON
ejpam-4855	68	6	note	note	VERB
ejpam-4855	68	7	that	that	SCONJ
ejpam-4855	68	8	the	the	DET
ejpam-4855	68	9	m.	m.	NOUN
ejpam-4855	68	10	baldado	baldado	PROPN
ejpam-4855	68	11	jr	jr	PROPN
ejpam-4855	68	12	.	.	PROPN
ejpam-4855	68	13	/	/	SYM
ejpam-4855	68	14	eur	eur	PROPN
ejpam-4855	68	15	.	.	PUNCT
ejpam-4855	69	1	j.	j.	PROPN
ejpam-4855	69	2	pure	pure	PROPN
ejpam-4855	69	3	appl	appl	PROPN
ejpam-4855	69	4	.	.	PROPN
ejpam-4855	69	5	math	math	PROPN
ejpam-4855	69	6	,	,	PUNCT
ejpam-4855	69	7	16	16	NUM
ejpam-4855	69	8	(	(	PUNCT
ejpam-4855	69	9	3	3	NUM
ejpam-4855	69	10	)	)	PUNCT
ejpam-4855	69	11	(	(	PUNCT
ejpam-4855	69	12	2023	2023	NUM
ejpam-4855	69	13	)	)	PUNCT
ejpam-4855	69	14	,	,	PUNCT
ejpam-4855	69	15	1809	1809	NUM
ejpam-4855	69	16	-	-	SYM
ejpam-4855	69	17	1816	1816	NUM
ejpam-4855	69	18	1811	1811	NUM
ejpam-4855	69	19	b∗-open	b∗-open	NOUN
ejpam-4855	69	20	sets	set	NOUN
ejpam-4855	69	21	of	of	ADP
ejpam-4855	69	22	w	w	NOUN
ejpam-4855	69	23	are	be	AUX
ejpam-4855	69	24	∅	∅	NOUN
ejpam-4855	69	25	,	,	PUNCT
ejpam-4855	69	26	{	{	PUNCT
ejpam-4855	69	27	a	a	X
ejpam-4855	69	28	}	}	PUNCT
ejpam-4855	69	29	,	,	PUNCT
ejpam-4855	69	30	{	{	PUNCT
ejpam-4855	69	31	b	b	X
ejpam-4855	69	32	,	,	PUNCT
ejpam-4855	69	33	c	c	NOUN
ejpam-4855	69	34	}	}	PUNCT
ejpam-4855	69	35	and	and	CCONJ
ejpam-4855	69	36	w	w	PROPN
ejpam-4855	69	37	.	.	PUNCT
ejpam-4855	70	1	observe	observe	VERB
ejpam-4855	70	2	that	that	SCONJ
ejpam-4855	70	3	the	the	DET
ejpam-4855	70	4	covering	covering	NOUN
ejpam-4855	70	5	of	of	ADP
ejpam-4855	70	6	b	b	NOUN
ejpam-4855	70	7	containing	contain	VERB
ejpam-4855	70	8	w	w	NOUN
ejpam-4855	70	9	is	be	AUX
ejpam-4855	70	10	{	{	PUNCT
ejpam-4855	70	11	{	{	PUNCT
ejpam-4855	70	12	a},w	a},w	NOUN
ejpam-4855	70	13	}	}	PUNCT
ejpam-4855	70	14	.	.	PUNCT
ejpam-4855	71	1	thus	thus	ADV
ejpam-4855	71	2	,	,	PUNCT
ejpam-4855	71	3	{	{	PUNCT
ejpam-4855	71	4	{	{	PUNCT
ejpam-4855	71	5	a	a	X
ejpam-4855	71	6	}	}	PUNCT
ejpam-4855	71	7	}	}	PUNCT
ejpam-4855	71	8	is	be	AUX
ejpam-4855	71	9	a	a	DET
ejpam-4855	71	10	smaller	small	ADJ
ejpam-4855	71	11	cover	cover	NOUN
ejpam-4855	71	12	.	.	PUNCT
ejpam-4855	72	1	hence	hence	ADV
ejpam-4855	72	2	,	,	PUNCT
ejpam-4855	72	3	b	b	X
ejpam-4855	72	4	=	=	PRON
ejpam-4855	72	5	{	{	PUNCT
ejpam-4855	72	6	a	a	PRON
ejpam-4855	72	7	}	}	PUNCT
ejpam-4855	72	8	is	be	AUX
ejpam-4855	72	9	a	a	DET
ejpam-4855	72	10	b∗-compact	b∗-compact	PROPN
ejpam-4855	72	11	set	set	NOUN
ejpam-4855	72	12	.	.	PUNCT
ejpam-4855	73	1	on	on	ADP
ejpam-4855	73	2	the	the	DET
ejpam-4855	73	3	other	other	ADJ
ejpam-4855	73	4	hand	hand	NOUN
ejpam-4855	73	5	,	,	PUNCT
ejpam-4855	73	6	observe	observe	VERB
ejpam-4855	73	7	that	that	SCONJ
ejpam-4855	73	8	the	the	DET
ejpam-4855	73	9	covering	covering	NOUN
ejpam-4855	73	10	of	of	ADP
ejpam-4855	73	11	d	d	NOUN
ejpam-4855	73	12	containing	contain	VERB
ejpam-4855	73	13	w	w	NOUN
ejpam-4855	73	14	are	be	AUX
ejpam-4855	73	15	{	{	PUNCT
ejpam-4855	73	16	{	{	PUNCT
ejpam-4855	73	17	a	a	NOUN
ejpam-4855	73	18	}	}	PUNCT
ejpam-4855	73	19	,	,	PUNCT
ejpam-4855	73	20	{	{	PUNCT
ejpam-4855	73	21	b	b	NOUN
ejpam-4855	73	22	,	,	PUNCT
ejpam-4855	73	23	c},w	c},w	NOUN
ejpam-4855	73	24	}	}	PUNCT
ejpam-4855	73	25	and	and	CCONJ
ejpam-4855	73	26	{	{	PUNCT
ejpam-4855	73	27	{	{	PUNCT
ejpam-4855	73	28	b	b	NOUN
ejpam-4855	73	29	,	,	PUNCT
ejpam-4855	73	30	c},w	c},w	NOUN
ejpam-4855	73	31	}	}	PUNCT
ejpam-4855	73	32	.	.	PUNCT
ejpam-4855	74	1	since	since	SCONJ
ejpam-4855	74	2	{	{	PUNCT
ejpam-4855	74	3	{	{	PUNCT
ejpam-4855	74	4	b	b	NOUN
ejpam-4855	74	5	,	,	PUNCT
ejpam-4855	74	6	c},w	c},w	PROPN
ejpam-4855	74	7	}	}	PUNCT
ejpam-4855	74	8	has	have	VERB
ejpam-4855	74	9	no	no	DET
ejpam-4855	74	10	smaller	small	ADJ
ejpam-4855	74	11	subcover	subcover	NOUN
ejpam-4855	74	12	,	,	PUNCT
ejpam-4855	74	13	d	d	PROPN
ejpam-4855	74	14	=	=	X
ejpam-4855	74	15	{	{	PUNCT
ejpam-4855	74	16	a	a	DET
ejpam-4855	74	17	,	,	PUNCT
ejpam-4855	74	18	b	b	NOUN
ejpam-4855	74	19	}	}	PUNCT
ejpam-4855	74	20	is	be	AUX
ejpam-4855	74	21	not	not	PART
ejpam-4855	74	22	a	a	DET
ejpam-4855	74	23	b∗-compact	b∗-compact	PROPN
ejpam-4855	74	24	set	set	NOUN
ejpam-4855	74	25	.	.	PUNCT
ejpam-4855	75	1	the	the	DET
ejpam-4855	75	2	set	set	PROPN
ejpam-4855	75	3	b	b	PROPN
ejpam-4855	75	4	is	be	AUX
ejpam-4855	75	5	called	call	VERB
ejpam-4855	75	6	b∗j	b∗j	PUNCT
ejpam-4855	75	7	-compact	-compact	NOUN
ejpam-4855	75	8	if	if	SCONJ
ejpam-4855	75	9	every	every	DET
ejpam-4855	75	10	cover	cover	NOUN
ejpam-4855	75	11	of	of	ADP
ejpam-4855	75	12	b	b	NOUN
ejpam-4855	75	13	by	by	ADP
ejpam-4855	75	14	b∗j	b∗j	PUNCT
ejpam-4855	75	15	-open	-open	ADJ
ejpam-4855	75	16	sets	set	NOUN
ejpam-4855	75	17	which	which	PRON
ejpam-4855	75	18	contains	contain	VERB
ejpam-4855	75	19	w	w	PROPN
ejpam-4855	75	20	,	,	PUNCT
ejpam-4855	75	21	has	have	VERB
ejpam-4855	75	22	a	a	DET
ejpam-4855	75	23	smaller	small	ADJ
ejpam-4855	75	24	finite	finite	ADJ
ejpam-4855	75	25	sub	sub	NOUN
ejpam-4855	75	26	-	-	NOUN
ejpam-4855	75	27	cover	cover	NOUN
ejpam-4855	75	28	.	.	PUNCT
ejpam-4855	76	1	the	the	DET
ejpam-4855	76	2	space	space	NOUN
ejpam-4855	76	3	w	w	PROPN
ejpam-4855	76	4	is	be	AUX
ejpam-4855	76	5	called	call	VERB
ejpam-4855	76	6	b∗j	b∗j	PUNCT
ejpam-4855	76	7	-compact	-compact	ADJ
ejpam-4855	76	8	space	space	NOUN
ejpam-4855	76	9	if	if	SCONJ
ejpam-4855	76	10	it	it	PRON
ejpam-4855	76	11	is	be	AUX
ejpam-4855	76	12	b∗j	b∗j	PUNCT
ejpam-4855	76	13	-compact	-compact	NOUN
ejpam-4855	76	14	set	set	VERB
ejpam-4855	76	15	.	.	PUNCT
ejpam-4855	77	1	consider	consider	VERB
ejpam-4855	77	2	the	the	DET
ejpam-4855	77	3	ideal	ideal	ADJ
ejpam-4855	77	4	topological	topological	ADJ
ejpam-4855	77	5	space	space	NOUN
ejpam-4855	77	6	(	(	PUNCT
ejpam-4855	77	7	w	w	NOUN
ejpam-4855	77	8	=	=	SYM
ejpam-4855	77	9	{	{	PUNCT
ejpam-4855	77	10	x	x	PROPN
ejpam-4855	77	11	,	,	PUNCT
ejpam-4855	77	12	y	y	PROPN
ejpam-4855	77	13	,	,	PUNCT
ejpam-4855	77	14	z	z	NOUN
ejpam-4855	77	15	}	}	PUNCT
ejpam-4855	77	16	,	,	PUNCT
ejpam-4855	77	17	{	{	PUNCT
ejpam-4855	77	18	∅	∅	NOUN
ejpam-4855	77	19	,	,	PUNCT
ejpam-4855	77	20	{	{	PUNCT
ejpam-4855	77	21	x	x	X
ejpam-4855	77	22	}	}	PUNCT
ejpam-4855	77	23	,	,	PUNCT
ejpam-4855	77	24	{	{	PUNCT
ejpam-4855	77	25	y	y	NOUN
ejpam-4855	77	26	}	}	PUNCT
ejpam-4855	77	27	,	,	PUNCT
ejpam-4855	77	28	{	{	PUNCT
ejpam-4855	77	29	x	x	NOUN
ejpam-4855	77	30	,	,	PUNCT
ejpam-4855	77	31	y},w	y},w	ADJ
ejpam-4855	77	32	}	}	PUNCT
ejpam-4855	77	33	,	,	PUNCT
ejpam-4855	77	34	{	{	PUNCT
ejpam-4855	77	35	∅	∅	NOUN
ejpam-4855	77	36	,	,	PUNCT
ejpam-4855	77	37	{	{	PUNCT
ejpam-4855	77	38	y	y	NOUN
ejpam-4855	77	39	}	}	PUNCT
ejpam-4855	77	40	}	}	PUNCT
ejpam-4855	77	41	)	)	PUNCT
ejpam-4855	77	42	.	.	PUNCT
ejpam-4855	78	1	then	then	ADV
ejpam-4855	78	2	b	b	X
ejpam-4855	78	3	=	=	SYM
ejpam-4855	78	4	{	{	PUNCT
ejpam-4855	78	5	y	y	PROPN
ejpam-4855	78	6	,	,	PUNCT
ejpam-4855	78	7	z	z	NOUN
ejpam-4855	78	8	}	}	PUNCT
ejpam-4855	78	9	is	be	AUX
ejpam-4855	78	10	a	a	DET
ejpam-4855	78	11	b∗j	b∗j	ADJ
ejpam-4855	78	12	-compact	-compact	NOUN
ejpam-4855	78	13	set	set	VERB
ejpam-4855	78	14	where	where	SCONJ
ejpam-4855	78	15	j	j	PROPN
ejpam-4855	78	16	=	=	PUNCT
ejpam-4855	78	17	{	{	PUNCT
ejpam-4855	78	18	∅	∅	NOUN
ejpam-4855	78	19	,	,	PUNCT
ejpam-4855	78	20	{	{	PUNCT
ejpam-4855	78	21	y	y	NOUN
ejpam-4855	78	22	}	}	PUNCT
ejpam-4855	78	23	}	}	PUNCT
ejpam-4855	78	24	.	.	PUNCT
ejpam-4855	79	1	to	to	PART
ejpam-4855	79	2	see	see	VERB
ejpam-4855	79	3	this	this	PRON
ejpam-4855	79	4	,	,	PUNCT
ejpam-4855	79	5	we	we	PRON
ejpam-4855	79	6	note	note	VERB
ejpam-4855	79	7	that	that	SCONJ
ejpam-4855	79	8	the	the	DET
ejpam-4855	79	9	b∗j	b∗j	PUNCT
ejpam-4855	79	10	-open	-open	ADJ
ejpam-4855	79	11	sets	set	NOUN
ejpam-4855	79	12	of	of	ADP
ejpam-4855	79	13	w	w	NOUN
ejpam-4855	79	14	are	be	AUX
ejpam-4855	79	15	∅	∅	NOUN
ejpam-4855	79	16	,	,	PUNCT
ejpam-4855	79	17	{	{	PUNCT
ejpam-4855	79	18	y	y	PROPN
ejpam-4855	79	19	,	,	PUNCT
ejpam-4855	79	20	z	z	NOUN
ejpam-4855	79	21	}	}	PUNCT
ejpam-4855	79	22	and	and	CCONJ
ejpam-4855	79	23	w	w	NOUN
ejpam-4855	79	24	.	.	PUNCT
ejpam-4855	80	1	hence	hence	ADV
ejpam-4855	80	2	,	,	PUNCT
ejpam-4855	80	3	every	every	DET
ejpam-4855	80	4	cover	cover	NOUN
ejpam-4855	80	5	{	{	PUNCT
ejpam-4855	80	6	pψ	pψ	NOUN
ejpam-4855	80	7	:	:	PUNCT
ejpam-4855	80	8	ψ	ψ	X
ejpam-4855	80	9	∈	∈	PROPN
ejpam-4855	80	10	ψ	ψ	NOUN
ejpam-4855	80	11	}	}	PUNCT
ejpam-4855	80	12	of	of	ADP
ejpam-4855	80	13	b	b	NOUN
ejpam-4855	80	14	by	by	ADP
ejpam-4855	80	15	b∗j	b∗j	PUNCT
ejpam-4855	80	16	-open	-open	ADJ
ejpam-4855	80	17	set	set	NOUN
ejpam-4855	80	18	must	must	AUX
ejpam-4855	80	19	contain	contain	VERB
ejpam-4855	80	20	{	{	PUNCT
ejpam-4855	80	21	y	y	PROPN
ejpam-4855	80	22	,	,	PUNCT
ejpam-4855	80	23	z	z	NOUN
ejpam-4855	80	24	}	}	PUNCT
ejpam-4855	80	25	or	or	CCONJ
ejpam-4855	80	26	w	w	NOUN
ejpam-4855	80	27	.	.	PUNCT
ejpam-4855	81	1	thus	thus	ADV
ejpam-4855	81	2	,	,	PUNCT
ejpam-4855	81	3	each	each	PRON
ejpam-4855	81	4	of	of	ADP
ejpam-4855	81	5	the	the	DET
ejpam-4855	81	6	following	following	NOUN
ejpam-4855	81	7	is	be	AUX
ejpam-4855	81	8	a	a	DET
ejpam-4855	81	9	covering	covering	NOUN
ejpam-4855	81	10	of	of	ADP
ejpam-4855	81	11	b	b	NOUN
ejpam-4855	81	12	:	:	PUNCT
ejpam-4855	81	13	{	{	PUNCT
ejpam-4855	81	14	{	{	PUNCT
ejpam-4855	81	15	y	y	PROPN
ejpam-4855	81	16	,	,	PUNCT
ejpam-4855	81	17	z	z	NOUN
ejpam-4855	81	18	}	}	PUNCT
ejpam-4855	81	19	}	}	PUNCT
ejpam-4855	81	20	;	;	PUNCT
ejpam-4855	81	21	{	{	PUNCT
ejpam-4855	81	22	{	{	PUNCT
ejpam-4855	81	23	y	y	NOUN
ejpam-4855	81	24	,	,	PUNCT
ejpam-4855	81	25	z},w	z},w	PROPN
ejpam-4855	81	26	}	}	PUNCT
ejpam-4855	81	27	;	;	PUNCT
ejpam-4855	81	28	and	and	CCONJ
ejpam-4855	81	29	{	{	PUNCT
ejpam-4855	81	30	w	w	NOUN
ejpam-4855	81	31	}	}	PUNCT
ejpam-4855	81	32	.	.	PUNCT
ejpam-4855	82	1	note	note	VERB
ejpam-4855	82	2	that	that	SCONJ
ejpam-4855	82	3	{	{	PUNCT
ejpam-4855	82	4	{	{	PUNCT
ejpam-4855	82	5	y	y	NOUN
ejpam-4855	82	6	,	,	PUNCT
ejpam-4855	82	7	z},w	z},w	PROPN
ejpam-4855	82	8	}	}	PUNCT
ejpam-4855	82	9	is	be	AUX
ejpam-4855	82	10	a	a	DET
ejpam-4855	82	11	covering	covering	NOUN
ejpam-4855	82	12	of	of	ADP
ejpam-4855	82	13	b	b	NUM
ejpam-4855	82	14	which	which	PRON
ejpam-4855	82	15	has	have	VERB
ejpam-4855	82	16	a	a	DET
ejpam-4855	82	17	smaller	small	ADJ
ejpam-4855	82	18	subcover	subcover	NOUN
ejpam-4855	82	19	{	{	PUNCT
ejpam-4855	82	20	{	{	PUNCT
ejpam-4855	82	21	y	y	PROPN
ejpam-4855	82	22	,	,	PUNCT
ejpam-4855	82	23	z	z	NOUN
ejpam-4855	82	24	}	}	PUNCT
ejpam-4855	82	25	}	}	PUNCT
ejpam-4855	82	26	.	.	PUNCT
ejpam-4855	83	1	this	this	PRON
ejpam-4855	83	2	shows	show	VERB
ejpam-4855	83	3	that	that	SCONJ
ejpam-4855	83	4	b	b	X
ejpam-4855	83	5	=	=	PRON
ejpam-4855	83	6	{	{	PUNCT
ejpam-4855	83	7	y	y	PROPN
ejpam-4855	83	8	,	,	PUNCT
ejpam-4855	83	9	z	z	NOUN
ejpam-4855	83	10	}	}	PUNCT
ejpam-4855	83	11	is	be	AUX
ejpam-4855	83	12	a	a	DET
ejpam-4855	83	13	b∗j	b∗j	ADJ
ejpam-4855	83	14	-compact	-compact	NOUN
ejpam-4855	83	15	set	set	NOUN
ejpam-4855	83	16	.	.	PUNCT
ejpam-4855	84	1	now	now	ADV
ejpam-4855	84	2	,	,	PUNCT
ejpam-4855	84	3	consider	consider	VERB
ejpam-4855	84	4	the	the	DET
ejpam-4855	84	5	ideal	ideal	ADJ
ejpam-4855	84	6	topological	topological	ADJ
ejpam-4855	84	7	space	space	NOUN
ejpam-4855	84	8	(	(	PUNCT
ejpam-4855	84	9	w	w	NOUN
ejpam-4855	84	10	=	=	SYM
ejpam-4855	84	11	{	{	PUNCT
ejpam-4855	84	12	l	l	NOUN
ejpam-4855	84	13	,	,	PUNCT
ejpam-4855	84	14	m	m	PROPN
ejpam-4855	84	15	,	,	PUNCT
ejpam-4855	84	16	n	n	CCONJ
ejpam-4855	84	17	}	}	PUNCT
ejpam-4855	84	18	,	,	PUNCT
ejpam-4855	84	19	{	{	PUNCT
ejpam-4855	84	20	∅	∅	NOUN
ejpam-4855	84	21	,	,	PUNCT
ejpam-4855	84	22	{	{	PUNCT
ejpam-4855	84	23	l	l	NOUN
ejpam-4855	84	24	}	}	PUNCT
ejpam-4855	84	25	,	,	PUNCT
ejpam-4855	84	26	{	{	PUNCT
ejpam-4855	84	27	m	m	VERB
ejpam-4855	84	28	}	}	PUNCT
ejpam-4855	84	29	,	,	PUNCT
ejpam-4855	84	30	{	{	PUNCT
ejpam-4855	84	31	l	l	NOUN
ejpam-4855	84	32	,	,	PUNCT
ejpam-4855	84	33	m},w	m},w	PROPN
ejpam-4855	84	34	}	}	PUNCT
ejpam-4855	84	35	,	,	PUNCT
ejpam-4855	84	36	{	{	PUNCT
ejpam-4855	84	37	∅	∅	NOUN
ejpam-4855	84	38	,	,	PUNCT
ejpam-4855	84	39	{	{	PUNCT
ejpam-4855	84	40	m	m	NOUN
ejpam-4855	84	41	}	}	PUNCT
ejpam-4855	84	42	}	}	PUNCT
ejpam-4855	84	43	)	)	PUNCT
ejpam-4855	84	44	.	.	PUNCT
ejpam-4855	85	1	then	then	ADV
ejpam-4855	85	2	b	b	X
ejpam-4855	85	3	=	=	SYM
ejpam-4855	85	4	{	{	PUNCT
ejpam-4855	85	5	l	l	NOUN
ejpam-4855	85	6	,	,	PUNCT
ejpam-4855	85	7	m	m	VERB
ejpam-4855	85	8	}	}	PUNCT
ejpam-4855	85	9	is	be	AUX
ejpam-4855	85	10	a	a	DET
ejpam-4855	85	11	not	not	PART
ejpam-4855	85	12	b∗j	b∗j	ADV
ejpam-4855	85	13	-compact	-compact	NOUN
ejpam-4855	85	14	set	set	VERB
ejpam-4855	85	15	where	where	SCONJ
ejpam-4855	85	16	j	j	PROPN
ejpam-4855	85	17	=	=	PUNCT
ejpam-4855	85	18	{	{	PUNCT
ejpam-4855	85	19	∅	∅	NOUN
ejpam-4855	85	20	,	,	PUNCT
ejpam-4855	85	21	{	{	PUNCT
ejpam-4855	85	22	m	m	NOUN
ejpam-4855	85	23	}	}	PUNCT
ejpam-4855	85	24	}	}	PUNCT
ejpam-4855	85	25	.	.	PUNCT
ejpam-4855	86	1	to	to	PART
ejpam-4855	86	2	see	see	VERB
ejpam-4855	86	3	this	this	PRON
ejpam-4855	86	4	,	,	PUNCT
ejpam-4855	86	5	we	we	PRON
ejpam-4855	86	6	note	note	VERB
ejpam-4855	86	7	again	again	ADV
ejpam-4855	86	8	that	that	SCONJ
ejpam-4855	86	9	the	the	DET
ejpam-4855	86	10	b∗j	b∗j	PUNCT
ejpam-4855	86	11	-open	-open	ADJ
ejpam-4855	86	12	sets	set	NOUN
ejpam-4855	86	13	of	of	ADP
ejpam-4855	86	14	w	w	NOUN
ejpam-4855	86	15	are	be	AUX
ejpam-4855	86	16	∅	∅	NOUN
ejpam-4855	86	17	,	,	PUNCT
ejpam-4855	86	18	{	{	PUNCT
ejpam-4855	86	19	m	m	NOUN
ejpam-4855	86	20	,	,	PUNCT
ejpam-4855	86	21	n	n	CCONJ
ejpam-4855	86	22	}	}	PUNCT
ejpam-4855	86	23	and	and	CCONJ
ejpam-4855	86	24	w	w	NOUN
ejpam-4855	86	25	.	.	PUNCT
ejpam-4855	87	1	hence	hence	ADV
ejpam-4855	87	2	,	,	PUNCT
ejpam-4855	87	3	every	every	DET
ejpam-4855	87	4	cover	cover	NOUN
ejpam-4855	87	5	{	{	PUNCT
ejpam-4855	87	6	pψ	pψ	NOUN
ejpam-4855	87	7	:	:	PUNCT
ejpam-4855	87	8	ψ	ψ	X
ejpam-4855	87	9	∈	∈	PROPN
ejpam-4855	87	10	ψ	ψ	NOUN
ejpam-4855	87	11	}	}	PUNCT
ejpam-4855	87	12	of	of	ADP
ejpam-4855	87	13	b	b	NOUN
ejpam-4855	87	14	by	by	ADP
ejpam-4855	87	15	b∗j	b∗j	PUNCT
ejpam-4855	87	16	-open	-open	ADJ
ejpam-4855	87	17	set	set	NOUN
ejpam-4855	87	18	must	must	AUX
ejpam-4855	87	19	contain	contain	VERB
ejpam-4855	87	20	w	w	NOUN
ejpam-4855	87	21	.	.	PUNCT
ejpam-4855	88	1	thus	thus	ADV
ejpam-4855	88	2	,	,	PUNCT
ejpam-4855	88	3	each	each	PRON
ejpam-4855	88	4	of	of	ADP
ejpam-4855	88	5	the	the	DET
ejpam-4855	88	6	following	following	NOUN
ejpam-4855	88	7	is	be	AUX
ejpam-4855	88	8	a	a	DET
ejpam-4855	88	9	covering	covering	NOUN
ejpam-4855	88	10	of	of	ADP
ejpam-4855	88	11	b	b	NOUN
ejpam-4855	88	12	:	:	PUNCT
ejpam-4855	88	13	{	{	PUNCT
ejpam-4855	88	14	{	{	PUNCT
ejpam-4855	88	15	m	m	PROPN
ejpam-4855	88	16	,	,	PUNCT
ejpam-4855	88	17	n},w	n},w	PROPN
ejpam-4855	88	18	}	}	PUNCT
ejpam-4855	88	19	;	;	PUNCT
ejpam-4855	88	20	and	and	CCONJ
ejpam-4855	88	21	{	{	PUNCT
ejpam-4855	88	22	w	w	NOUN
ejpam-4855	88	23	}	}	PUNCT
ejpam-4855	88	24	.	.	PUNCT
ejpam-4855	89	1	note	note	VERB
ejpam-4855	89	2	that	that	SCONJ
ejpam-4855	89	3	{	{	PUNCT
ejpam-4855	89	4	{	{	PUNCT
ejpam-4855	89	5	m	m	PROPN
ejpam-4855	89	6	,	,	PUNCT
ejpam-4855	89	7	n},w	n},w	PROPN
ejpam-4855	89	8	}	}	PUNCT
ejpam-4855	89	9	has	have	VERB
ejpam-4855	89	10	no	no	DET
ejpam-4855	89	11	smaller	small	ADJ
ejpam-4855	89	12	.	.	PUNCT
ejpam-4855	90	1	this	this	PRON
ejpam-4855	90	2	shows	show	VERB
ejpam-4855	90	3	that	that	SCONJ
ejpam-4855	90	4	b	b	X
ejpam-4855	90	5	=	=	SYM
ejpam-4855	90	6	{	{	PUNCT
ejpam-4855	90	7	l	l	NOUN
ejpam-4855	90	8	,	,	PUNCT
ejpam-4855	90	9	y	y	NOUN
ejpam-4855	90	10	}	}	PUNCT
ejpam-4855	90	11	is	be	AUX
ejpam-4855	90	12	not	not	PART
ejpam-4855	90	13	a	a	DET
ejpam-4855	90	14	b∗j	b∗j	ADJ
ejpam-4855	90	15	-compact	-compact	NOUN
ejpam-4855	90	16	set	set	VERB
ejpam-4855	90	17	.	.	PUNCT
ejpam-4855	91	1	the	the	DET
ejpam-4855	91	2	set	set	PROPN
ejpam-4855	91	3	b	b	PROPN
ejpam-4855	91	4	is	be	AUX
ejpam-4855	91	5	said	say	VERB
ejpam-4855	91	6	to	to	PART
ejpam-4855	91	7	be	be	AUX
ejpam-4855	91	8	compatible	compatible	ADJ
ejpam-4855	91	9	b∗j	b∗j	PUNCT
ejpam-4855	91	10	-compact	-compact	NOUN
ejpam-4855	91	11	(	(	PUNCT
ejpam-4855	91	12	or	or	CCONJ
ejpam-4855	91	13	simply	simply	ADV
ejpam-4855	91	14	cb∗j	cb∗j	VERB
ejpam-4855	91	15	-compact	-compact	NOUN
ejpam-4855	91	16	)	)	PUNCT
ejpam-4855	92	1	if	if	SCONJ
ejpam-4855	92	2	any	any	DET
ejpam-4855	92	3	cover	cover	NOUN
ejpam-4855	92	4	{	{	PUNCT
ejpam-4855	92	5	pψ	pψ	NOUN
ejpam-4855	92	6	:	:	PUNCT
ejpam-4855	92	7	ψ	ψ	X
ejpam-4855	92	8	∈	∈	PROPN
ejpam-4855	92	9	ψ	ψ	NOUN
ejpam-4855	92	10	}	}	PUNCT
ejpam-4855	92	11	of	of	ADP
ejpam-4855	92	12	b	b	NOUN
ejpam-4855	92	13	by	by	ADP
ejpam-4855	92	14	b∗j	b∗j	PUNCT
ejpam-4855	92	15	-open	-open	ADJ
ejpam-4855	92	16	sets	set	NOUN
ejpam-4855	92	17	containing	contain	VERB
ejpam-4855	92	18	w	w	PROPN
ejpam-4855	92	19	,	,	PUNCT
ejpam-4855	92	20	ψ	ψ	X
ejpam-4855	92	21	has	have	VERB
ejpam-4855	92	22	a	a	DET
ejpam-4855	92	23	smaller	small	ADJ
ejpam-4855	92	24	finite	finite	NOUN
ejpam-4855	92	25	subset	subset	VERB
ejpam-4855	92	26	ψ0	ψ0	ADV
ejpam-4855	92	27	such	such	ADJ
ejpam-4855	92	28	that	that	SCONJ
ejpam-4855	92	29	b\	b\	PRON
ejpam-4855	92	30	⋃	⋃	NOUN
ejpam-4855	92	31	{	{	PUNCT
ejpam-4855	92	32	uψ	uψ	NOUN
ejpam-4855	92	33	:	:	PUNCT
ejpam-4855	92	34	ψ	ψ	X
ejpam-4855	92	35	∈	∈	PROPN
ejpam-4855	92	36	ψ0	ψ0	PROPN
ejpam-4855	92	37	}	}	PUNCT
ejpam-4855	92	38	∈	∈	PROPN
ejpam-4855	92	39	j	j	PROPN
ejpam-4855	92	40	.	.	PUNCT
ejpam-4855	93	1	the	the	DET
ejpam-4855	93	2	topological	topological	ADJ
ejpam-4855	93	3	space	space	NOUN
ejpam-4855	93	4	w	w	NOUN
ejpam-4855	93	5	is	be	AUX
ejpam-4855	93	6	said	say	VERB
ejpam-4855	93	7	to	to	PART
ejpam-4855	93	8	be	be	AUX
ejpam-4855	93	9	a	a	DET
ejpam-4855	93	10	cb∗j	cb∗j	NOUN
ejpam-4855	93	11	compact	compact	ADJ
ejpam-4855	93	12	space	space	NOUN
ejpam-4855	93	13	if	if	SCONJ
ejpam-4855	93	14	it	it	PRON
ejpam-4855	93	15	is	be	AUX
ejpam-4855	93	16	cb∗j	cb∗j	NOUN
ejpam-4855	93	17	-compact	-compact	NOUN
ejpam-4855	93	18	as	as	ADP
ejpam-4855	93	19	a	a	DET
ejpam-4855	93	20	set	set	NOUN
ejpam-4855	93	21	.	.	PUNCT
ejpam-4855	94	1	consider	consider	VERB
ejpam-4855	94	2	the	the	DET
ejpam-4855	94	3	ideal	ideal	ADJ
ejpam-4855	94	4	topological	topological	ADJ
ejpam-4855	94	5	space	space	NOUN
ejpam-4855	94	6	(	(	PUNCT
ejpam-4855	94	7	z	z	NOUN
ejpam-4855	94	8	,	,	PUNCT
ejpam-4855	94	9	ς	ς	PROPN
ejpam-4855	94	10	,	,	PUNCT
ejpam-4855	94	11	j	j	NOUN
ejpam-4855	94	12	)	)	PUNCT
ejpam-4855	94	13	=	=	SYM
ejpam-4855	95	1	(	(	PUNCT
ejpam-4855	95	2	{	{	PUNCT
ejpam-4855	95	3	h	h	NOUN
ejpam-4855	95	4	,	,	PUNCT
ejpam-4855	95	5	i	i	PRON
ejpam-4855	95	6	,	,	PUNCT
ejpam-4855	95	7	j	j	PROPN
ejpam-4855	95	8	}	}	PUNCT
ejpam-4855	95	9	,	,	PUNCT
ejpam-4855	95	10	{	{	PUNCT
ejpam-4855	95	11	∅	∅	NOUN
ejpam-4855	95	12	,	,	PUNCT
ejpam-4855	95	13	{	{	PUNCT
ejpam-4855	95	14	h	h	NOUN
ejpam-4855	95	15	}	}	PUNCT
ejpam-4855	95	16	,	,	PUNCT
ejpam-4855	95	17	{	{	PUNCT
ejpam-4855	95	18	i	i	X
ejpam-4855	95	19	,	,	PUNCT
ejpam-4855	95	20	j	j	PROPN
ejpam-4855	95	21	}	}	PUNCT
ejpam-4855	95	22	,	,	PUNCT
ejpam-4855	95	23	z	z	NOUN
ejpam-4855	95	24	}	}	PUNCT
ejpam-4855	95	25	,	,	PUNCT
ejpam-4855	95	26	{	{	PUNCT
ejpam-4855	95	27	∅	∅	NOUN
ejpam-4855	95	28	,	,	PUNCT
ejpam-4855	95	29	{	{	PUNCT
ejpam-4855	95	30	i	i	NOUN
ejpam-4855	95	31	}	}	PUNCT
ejpam-4855	95	32	}	}	PUNCT
ejpam-4855	95	33	)	)	PUNCT
ejpam-4855	95	34	.	.	PUNCT
ejpam-4855	96	1	then	then	ADV
ejpam-4855	96	2	{	{	PUNCT
ejpam-4855	96	3	h	h	NOUN
ejpam-4855	96	4	,	,	PUNCT
ejpam-4855	96	5	i	i	PRON
ejpam-4855	96	6	}	}	PUNCT
ejpam-4855	96	7	is	be	AUX
ejpam-4855	96	8	a	a	DET
ejpam-4855	96	9	compatible	compatible	ADJ
ejpam-4855	96	10	b∗j	b∗j	ADJ
ejpam-4855	96	11	-compact	-compact	NOUN
ejpam-4855	96	12	where	where	SCONJ
ejpam-4855	96	13	j	j	PROPN
ejpam-4855	96	14	=	=	PUNCT
ejpam-4855	96	15	{	{	PUNCT
ejpam-4855	96	16	∅	∅	NOUN
ejpam-4855	96	17	,	,	PUNCT
ejpam-4855	96	18	{	{	PUNCT
ejpam-4855	96	19	i	i	NOUN
ejpam-4855	96	20	}	}	PUNCT
ejpam-4855	96	21	}	}	PUNCT
ejpam-4855	96	22	.	.	PUNCT
ejpam-4855	97	1	to	to	PART
ejpam-4855	97	2	see	see	VERB
ejpam-4855	97	3	this	this	PRON
ejpam-4855	97	4	,	,	PUNCT
ejpam-4855	97	5	we	we	PRON
ejpam-4855	97	6	observe	observe	VERB
ejpam-4855	97	7	that	that	SCONJ
ejpam-4855	97	8	the	the	DET
ejpam-4855	97	9	b∗j	b∗j	PUNCT
ejpam-4855	97	10	-open	-open	ADJ
ejpam-4855	97	11	sets	set	NOUN
ejpam-4855	97	12	of	of	ADP
ejpam-4855	97	13	z	z	NOUN
ejpam-4855	97	14	are	be	AUX
ejpam-4855	97	15	∅	∅	NOUN
ejpam-4855	97	16	,	,	PUNCT
ejpam-4855	97	17	{	{	PUNCT
ejpam-4855	97	18	h	h	NOUN
ejpam-4855	97	19	}	}	PUNCT
ejpam-4855	97	20	,	,	PUNCT
ejpam-4855	97	21	{	{	PUNCT
ejpam-4855	97	22	i	i	X
ejpam-4855	97	23	,	,	PUNCT
ejpam-4855	97	24	j	j	PROPN
ejpam-4855	97	25	}	}	PUNCT
ejpam-4855	97	26	and	and	CCONJ
ejpam-4855	97	27	z.	z.	PROPN
ejpam-4855	97	28	hence	hence	ADV
ejpam-4855	97	29	,	,	PUNCT
ejpam-4855	97	30	every	every	DET
ejpam-4855	97	31	cover	cover	NOUN
ejpam-4855	97	32	{	{	PUNCT
ejpam-4855	97	33	pψ	pψ	NOUN
ejpam-4855	97	34	:	:	PUNCT
ejpam-4855	97	35	ψ	ψ	X
ejpam-4855	97	36	∈	∈	PROPN
ejpam-4855	97	37	ψ	ψ	NOUN
ejpam-4855	97	38	}	}	PUNCT
ejpam-4855	97	39	of	of	ADP
ejpam-4855	97	40	z	z	NOUN
ejpam-4855	97	41	by	by	ADP
ejpam-4855	97	42	b∗j	b∗j	PUNCT
ejpam-4855	97	43	-open	-open	ADJ
ejpam-4855	97	44	set	set	NOUN
ejpam-4855	97	45	must	must	AUX
ejpam-4855	97	46	contain	contain	VERB
ejpam-4855	97	47	{	{	PUNCT
ejpam-4855	97	48	h	h	NOUN
ejpam-4855	97	49	}	}	PUNCT
ejpam-4855	97	50	,	,	PUNCT
ejpam-4855	97	51	{	{	PUNCT
ejpam-4855	97	52	i	i	X
ejpam-4855	97	53	,	,	PUNCT
ejpam-4855	97	54	j	j	PROPN
ejpam-4855	97	55	}	}	PUNCT
ejpam-4855	97	56	or	or	CCONJ
ejpam-4855	97	57	z.	z.	PROPN
ejpam-4855	97	58	thus	thus	ADV
ejpam-4855	97	59	,	,	PUNCT
ejpam-4855	97	60	{	{	PUNCT
ejpam-4855	97	61	pψ	pψ	INTJ
ejpam-4855	97	62	:	:	PUNCT
ejpam-4855	97	63	ψ	ψ	X
ejpam-4855	97	64	∈	∈	PROPN
ejpam-4855	97	65	ψ	ψ	AUX
ejpam-4855	97	66	}	}	PUNCT
ejpam-4855	97	67	is	be	AUX
ejpam-4855	97	68	{	{	PUNCT
ejpam-4855	97	69	{	{	PUNCT
ejpam-4855	97	70	h	h	NOUN
ejpam-4855	97	71	}	}	PUNCT
ejpam-4855	97	72	,	,	PUNCT
ejpam-4855	97	73	{	{	PUNCT
ejpam-4855	97	74	i	i	X
ejpam-4855	97	75	,	,	PUNCT
ejpam-4855	97	76	j	j	PROPN
ejpam-4855	97	77	}	}	PUNCT
ejpam-4855	97	78	}	}	PUNCT
ejpam-4855	97	79	or	or	CCONJ
ejpam-4855	97	80	{	{	PUNCT
ejpam-4855	97	81	{	{	PUNCT
ejpam-4855	97	82	h	h	NOUN
ejpam-4855	97	83	}	}	PUNCT
ejpam-4855	97	84	,	,	PUNCT
ejpam-4855	97	85	z	z	NOUN
ejpam-4855	97	86	}	}	PUNCT
ejpam-4855	97	87	or	or	CCONJ
ejpam-4855	97	88	{	{	PUNCT
ejpam-4855	97	89	z	z	NOUN
ejpam-4855	97	90	,	,	PUNCT
ejpam-4855	97	91	{	{	PUNCT
ejpam-4855	97	92	i	i	PROPN
ejpam-4855	97	93	,	,	PUNCT
ejpam-4855	97	94	j	j	PROPN
ejpam-4855	97	95	}	}	PUNCT
ejpam-4855	97	96	,	,	PUNCT
ejpam-4855	97	97	{	{	PUNCT
ejpam-4855	97	98	h	h	NOUN
ejpam-4855	97	99	}	}	PUNCT
ejpam-4855	97	100	}	}	PUNCT
ejpam-4855	97	101	or	or	CCONJ
ejpam-4855	97	102	{	{	PUNCT
ejpam-4855	97	103	z	z	NOUN
ejpam-4855	97	104	,	,	PUNCT
ejpam-4855	97	105	{	{	PUNCT
ejpam-4855	97	106	i	i	PROPN
ejpam-4855	97	107	,	,	PUNCT
ejpam-4855	97	108	j	j	PROPN
ejpam-4855	97	109	}	}	PUNCT
ejpam-4855	97	110	}	}	PUNCT
ejpam-4855	97	111	.	.	PUNCT
ejpam-4855	98	1	in	in	ADP
ejpam-4855	98	2	the	the	DET
ejpam-4855	98	3	first	first	ADJ
ejpam-4855	98	4	3	3	NUM
ejpam-4855	98	5	cases	case	NOUN
ejpam-4855	98	6	,	,	PUNCT
ejpam-4855	98	7	there	there	PRON
ejpam-4855	98	8	is	be	VERB
ejpam-4855	98	9	a	a	DET
ejpam-4855	98	10	smaller	small	ADJ
ejpam-4855	98	11	subset	subset	NOUN
ejpam-4855	98	12	{	{	PUNCT
ejpam-4855	98	13	{	{	PUNCT
ejpam-4855	98	14	h	h	NOUN
ejpam-4855	98	15	}	}	PUNCT
ejpam-4855	98	16	}	}	PUNCT
ejpam-4855	98	17	such	such	ADJ
ejpam-4855	98	18	that	that	SCONJ
ejpam-4855	98	19	{	{	PUNCT
ejpam-4855	98	20	h	h	NOUN
ejpam-4855	98	21	,	,	PUNCT
ejpam-4855	98	22	i}\{h	i}\{h	PROPN
ejpam-4855	98	23	}	}	PUNCT
ejpam-4855	98	24	=	=	SYM
ejpam-4855	98	25	{	{	PUNCT
ejpam-4855	98	26	i	i	NOUN
ejpam-4855	98	27	}	}	PUNCT
ejpam-4855	98	28	∈	∈	PROPN
ejpam-4855	98	29	j	j	PROPN
ejpam-4855	98	30	,	,	PUNCT
ejpam-4855	98	31	and	and	CCONJ
ejpam-4855	98	32	for	for	ADP
ejpam-4855	98	33	the	the	DET
ejpam-4855	98	34	last	last	ADJ
ejpam-4855	98	35	case	case	NOUN
ejpam-4855	98	36	,	,	PUNCT
ejpam-4855	98	37	there	there	PRON
ejpam-4855	98	38	exist	exist	VERB
ejpam-4855	98	39	a	a	DET
ejpam-4855	98	40	smaller	small	ADJ
ejpam-4855	98	41	subset	subset	NOUN
ejpam-4855	98	42	{	{	PUNCT
ejpam-4855	98	43	{	{	PUNCT
ejpam-4855	98	44	h	h	NOUN
ejpam-4855	98	45	,	,	PUNCT
ejpam-4855	98	46	i	i	NOUN
ejpam-4855	98	47	}	}	PUNCT
ejpam-4855	98	48	}	}	PUNCT
ejpam-4855	98	49	such	such	ADJ
ejpam-4855	98	50	that	that	SCONJ
ejpam-4855	98	51	{	{	PUNCT
ejpam-4855	98	52	h	h	NOUN
ejpam-4855	98	53	,	,	PUNCT
ejpam-4855	98	54	i}\{h	i}\{h	PROPN
ejpam-4855	98	55	,	,	PUNCT
ejpam-4855	98	56	i	i	PRON
ejpam-4855	98	57	}	}	PUNCT
ejpam-4855	98	58	=	=	SYM
ejpam-4855	98	59	∅	∅	NOUN
ejpam-4855	98	60	∈	∈	PROPN
ejpam-4855	98	61	j	j	PROPN
ejpam-4855	98	62	.	.	PUNCT
ejpam-4855	99	1	this	this	PRON
ejpam-4855	99	2	shows	show	VERB
ejpam-4855	99	3	that	that	SCONJ
ejpam-4855	99	4	{	{	PUNCT
ejpam-4855	99	5	h	h	NOUN
ejpam-4855	99	6	,	,	PUNCT
ejpam-4855	99	7	i	i	PRON
ejpam-4855	99	8	}	}	PUNCT
ejpam-4855	99	9	is	be	AUX
ejpam-4855	99	10	a	a	DET
ejpam-4855	99	11	compatible	compatible	ADJ
ejpam-4855	99	12	b∗j	b∗j	PUNCT
ejpam-4855	99	13	-compact	-compact	NOUN
ejpam-4855	99	14	set	set	VERB
ejpam-4855	99	15	.	.	PUNCT
ejpam-4855	100	1	next	next	ADV
ejpam-4855	100	2	,	,	PUNCT
ejpam-4855	100	3	consider	consider	VERB
ejpam-4855	100	4	the	the	DET
ejpam-4855	100	5	ideal	ideal	ADJ
ejpam-4855	100	6	topological	topological	ADJ
ejpam-4855	100	7	space	space	NOUN
ejpam-4855	100	8	(	(	PUNCT
ejpam-4855	100	9	v	v	NOUN
ejpam-4855	100	10	=	=	SYM
ejpam-4855	100	11	{	{	PUNCT
ejpam-4855	100	12	q	q	NOUN
ejpam-4855	100	13	,	,	PUNCT
ejpam-4855	100	14	r	r	NOUN
ejpam-4855	100	15	,	,	PUNCT
ejpam-4855	100	16	s	s	PART
ejpam-4855	100	17	}	}	PUNCT
ejpam-4855	100	18	,	,	PUNCT
ejpam-4855	100	19	{	{	PUNCT
ejpam-4855	100	20	∅	∅	NOUN
ejpam-4855	100	21	,	,	PUNCT
ejpam-4855	100	22	{	{	PUNCT
ejpam-4855	100	23	q	q	X
ejpam-4855	100	24	}	}	PUNCT
ejpam-4855	100	25	,	,	PUNCT
ejpam-4855	100	26	{	{	PUNCT
ejpam-4855	100	27	r	r	NOUN
ejpam-4855	100	28	,	,	PUNCT
ejpam-4855	100	29	s	s	PART
ejpam-4855	100	30	}	}	PUNCT
ejpam-4855	100	31	,	,	PUNCT
ejpam-4855	100	32	v	v	ADP
ejpam-4855	100	33	}	}	PUNCT
ejpam-4855	100	34	,	,	PUNCT
ejpam-4855	100	35	{	{	PUNCT
ejpam-4855	100	36	∅	∅	NOUN
ejpam-4855	100	37	,	,	PUNCT
ejpam-4855	100	38	{	{	PUNCT
ejpam-4855	100	39	s	s	NOUN
ejpam-4855	100	40	}	}	PUNCT
ejpam-4855	100	41	}	}	PUNCT
ejpam-4855	100	42	)	)	PUNCT
ejpam-4855	100	43	.	.	PUNCT
ejpam-4855	101	1	then	then	ADV
ejpam-4855	101	2	{	{	PUNCT
ejpam-4855	101	3	q	q	X
ejpam-4855	101	4	,	,	PUNCT
ejpam-4855	101	5	r	r	NOUN
ejpam-4855	101	6	}	}	PUNCT
ejpam-4855	101	7	is	be	AUX
ejpam-4855	101	8	not	not	PART
ejpam-4855	101	9	compatible	compatible	ADJ
ejpam-4855	101	10	b∗j	b∗j	ADJ
ejpam-4855	101	11	-compact	-compact	NOUN
ejpam-4855	101	12	.	.	PUNCT
ejpam-4855	102	1	to	to	PART
ejpam-4855	102	2	see	see	VERB
ejpam-4855	102	3	this	this	PRON
ejpam-4855	102	4	,	,	PUNCT
ejpam-4855	102	5	we	we	PRON
ejpam-4855	102	6	note	note	VERB
ejpam-4855	102	7	that	that	SCONJ
ejpam-4855	102	8	the	the	DET
ejpam-4855	102	9	b∗j	b∗j	PUNCT
ejpam-4855	102	10	-open	-open	ADJ
ejpam-4855	102	11	sets	set	NOUN
ejpam-4855	102	12	of	of	ADP
ejpam-4855	102	13	v	v	NOUN
ejpam-4855	102	14	are	be	AUX
ejpam-4855	102	15	∅	∅	NOUN
ejpam-4855	102	16	,	,	PUNCT
ejpam-4855	102	17	{	{	PUNCT
ejpam-4855	102	18	q	q	X
ejpam-4855	102	19	}	}	PUNCT
ejpam-4855	102	20	,	,	PUNCT
ejpam-4855	102	21	{	{	PUNCT
ejpam-4855	102	22	r	r	NOUN
ejpam-4855	102	23	,	,	PUNCT
ejpam-4855	102	24	s	s	PART
ejpam-4855	102	25	}	}	PUNCT
ejpam-4855	102	26	and	and	CCONJ
ejpam-4855	102	27	v	v	NOUN
ejpam-4855	102	28	.	.	PUNCT
ejpam-4855	103	1	hence	hence	ADV
ejpam-4855	103	2	,	,	PUNCT
ejpam-4855	103	3	every	every	DET
ejpam-4855	103	4	cover	cover	NOUN
ejpam-4855	103	5	{	{	PUNCT
ejpam-4855	103	6	pψ	pψ	NOUN
ejpam-4855	103	7	:	:	PUNCT
ejpam-4855	103	8	ψ	ψ	X
ejpam-4855	103	9	∈	∈	PROPN
ejpam-4855	103	10	ψ	ψ	NOUN
ejpam-4855	103	11	}	}	PUNCT
ejpam-4855	103	12	of	of	ADP
ejpam-4855	103	13	{	{	PUNCT
ejpam-4855	103	14	q	q	NOUN
ejpam-4855	103	15	,	,	PUNCT
ejpam-4855	103	16	r	r	NOUN
ejpam-4855	103	17	}	}	PUNCT
ejpam-4855	103	18	by	by	ADP
ejpam-4855	103	19	b∗j	b∗j	PUNCT
ejpam-4855	103	20	-open	-open	ADJ
ejpam-4855	103	21	set	set	NOUN
ejpam-4855	103	22	must	must	AUX
ejpam-4855	103	23	contain	contain	VERB
ejpam-4855	103	24	{	{	PUNCT
ejpam-4855	103	25	q	q	NOUN
ejpam-4855	103	26	}	}	PUNCT
ejpam-4855	103	27	,	,	PUNCT
ejpam-4855	103	28	{	{	PUNCT
ejpam-4855	103	29	r	r	NOUN
ejpam-4855	103	30	,	,	PUNCT
ejpam-4855	103	31	s	s	NOUN
ejpam-4855	103	32	}	}	PUNCT
ejpam-4855	103	33	or	or	CCONJ
ejpam-4855	103	34	v	v	NOUN
ejpam-4855	103	35	.	.	PUNCT
ejpam-4855	104	1	thus	thus	ADV
ejpam-4855	104	2	,	,	PUNCT
ejpam-4855	104	3	{	{	PUNCT
ejpam-4855	104	4	pψ	pψ	INTJ
ejpam-4855	104	5	:	:	PUNCT
ejpam-4855	104	6	ψ	ψ	X
ejpam-4855	104	7	∈	∈	PROPN
ejpam-4855	104	8	ψ	ψ	AUX
ejpam-4855	104	9	}	}	PUNCT
ejpam-4855	104	10	is	be	AUX
ejpam-4855	104	11	{	{	PUNCT
ejpam-4855	104	12	{	{	PUNCT
ejpam-4855	104	13	q	q	NOUN
ejpam-4855	104	14	}	}	PUNCT
ejpam-4855	104	15	,	,	PUNCT
ejpam-4855	104	16	{	{	PUNCT
ejpam-4855	104	17	r	r	NOUN
ejpam-4855	104	18	,	,	PUNCT
ejpam-4855	104	19	s	s	PART
ejpam-4855	104	20	}	}	PUNCT
ejpam-4855	104	21	}	}	PUNCT
ejpam-4855	104	22	or	or	CCONJ
ejpam-4855	104	23	{	{	PUNCT
ejpam-4855	104	24	{	{	PUNCT
ejpam-4855	104	25	q	q	NOUN
ejpam-4855	104	26	}	}	PUNCT
ejpam-4855	104	27	,	,	PUNCT
ejpam-4855	104	28	v	v	NOUN
ejpam-4855	104	29	}	}	PUNCT
ejpam-4855	104	30	or	or	CCONJ
ejpam-4855	104	31	{	{	PUNCT
ejpam-4855	104	32	v	v	NOUN
ejpam-4855	104	33	,	,	PUNCT
ejpam-4855	104	34	{	{	PUNCT
ejpam-4855	104	35	r	r	NOUN
ejpam-4855	104	36	,	,	PUNCT
ejpam-4855	104	37	s	s	PART
ejpam-4855	104	38	}	}	PUNCT
ejpam-4855	104	39	,	,	PUNCT
ejpam-4855	104	40	{	{	PUNCT
ejpam-4855	104	41	q	q	NOUN
ejpam-4855	104	42	}	}	PUNCT
ejpam-4855	104	43	}	}	PUNCT
ejpam-4855	104	44	or	or	CCONJ
ejpam-4855	104	45	{	{	PUNCT
ejpam-4855	104	46	v	v	NOUN
ejpam-4855	104	47	,	,	PUNCT
ejpam-4855	104	48	{	{	PUNCT
ejpam-4855	104	49	r	r	NOUN
ejpam-4855	104	50	,	,	PUNCT
ejpam-4855	104	51	s	s	PART
ejpam-4855	104	52	}	}	PUNCT
ejpam-4855	104	53	}	}	PUNCT
ejpam-4855	104	54	.	.	PUNCT
ejpam-4855	105	1	consider	consider	VERB
ejpam-4855	105	2	the	the	DET
ejpam-4855	105	3	open	open	ADJ
ejpam-4855	105	4	cover	cover	NOUN
ejpam-4855	105	5	{	{	PUNCT
ejpam-4855	105	6	{	{	PUNCT
ejpam-4855	105	7	q	q	NOUN
ejpam-4855	105	8	}	}	PUNCT
ejpam-4855	105	9	,	,	PUNCT
ejpam-4855	105	10	{	{	PUNCT
ejpam-4855	105	11	r	r	NOUN
ejpam-4855	105	12	,	,	PUNCT
ejpam-4855	105	13	s	s	PART
ejpam-4855	105	14	}	}	PUNCT
ejpam-4855	105	15	}	}	PUNCT
ejpam-4855	105	16	.	.	PUNCT
ejpam-4855	106	1	note	note	VERB
ejpam-4855	106	2	that	that	SCONJ
ejpam-4855	106	3	its	its	PRON
ejpam-4855	106	4	smaller	small	ADJ
ejpam-4855	106	5	covers	cover	NOUN
ejpam-4855	106	6	are	be	AUX
ejpam-4855	106	7	{	{	PUNCT
ejpam-4855	106	8	{	{	PUNCT
ejpam-4855	106	9	q	q	NOUN
ejpam-4855	106	10	}	}	PUNCT
ejpam-4855	106	11	}	}	PUNCT
ejpam-4855	106	12	and	and	CCONJ
ejpam-4855	106	13	{	{	PUNCT
ejpam-4855	106	14	{	{	PUNCT
ejpam-4855	106	15	r	r	NOUN
ejpam-4855	106	16	,	,	PUNCT
ejpam-4855	106	17	s	s	PART
ejpam-4855	106	18	}	}	PUNCT
ejpam-4855	106	19	}	}	PUNCT
ejpam-4855	106	20	.	.	PUNCT
ejpam-4855	107	1	observe	observe	VERB
ejpam-4855	107	2	that	that	SCONJ
ejpam-4855	107	3	{	{	PUNCT
ejpam-4855	107	4	q	q	ADJ
ejpam-4855	107	5	,	,	PUNCT
ejpam-4855	107	6	r}\{q	r}\{q	NOUN
ejpam-4855	107	7	}	}	PUNCT
ejpam-4855	107	8	=	=	SYM
ejpam-4855	107	9	{	{	PUNCT
ejpam-4855	107	10	r	r	NOUN
ejpam-4855	107	11	}	}	PUNCT
ejpam-4855	107	12	/∈	/∈	PUNCT
ejpam-4855	108	1	j	j	PROPN
ejpam-4855	108	2	and	and	CCONJ
ejpam-4855	108	3	{	{	PUNCT
ejpam-4855	108	4	q	q	ADJ
ejpam-4855	108	5	,	,	PUNCT
ejpam-4855	108	6	r}\{r	r}\{r	NOUN
ejpam-4855	108	7	,	,	PUNCT
ejpam-4855	108	8	s	s	PART
ejpam-4855	108	9	}	}	PUNCT
ejpam-4855	108	10	=	=	SYM
ejpam-4855	108	11	{	{	PUNCT
ejpam-4855	108	12	q	q	X
ejpam-4855	108	13	}	}	PUNCT
ejpam-4855	108	14	/∈	/∈	PUNCT
ejpam-4855	109	1	j	j	PROPN
ejpam-4855	109	2	.	.	PUNCT
ejpam-4855	110	1	this	this	PRON
ejpam-4855	110	2	shows	show	VERB
ejpam-4855	110	3	that	that	SCONJ
ejpam-4855	110	4	{	{	PUNCT
ejpam-4855	110	5	q	q	X
ejpam-4855	110	6	,	,	PUNCT
ejpam-4855	110	7	r	r	NOUN
ejpam-4855	110	8	}	}	PUNCT
ejpam-4855	110	9	is	be	AUX
ejpam-4855	110	10	not	not	PART
ejpam-4855	110	11	a	a	DET
ejpam-4855	110	12	compatible	compatible	ADJ
ejpam-4855	110	13	b∗j	b∗j	PUNCT
ejpam-4855	110	14	-compact	-compact	NOUN
ejpam-4855	110	15	set	set	VERB
ejpam-4855	110	16	.	.	PUNCT
ejpam-4855	111	1	2	2	X
ejpam-4855	111	2	.	.	X
ejpam-4855	111	3	results	result	NOUN
ejpam-4855	111	4	we	we	PRON
ejpam-4855	111	5	present	present	VERB
ejpam-4855	111	6	some	some	PRON
ejpam-4855	111	7	of	of	ADP
ejpam-4855	111	8	the	the	DET
ejpam-4855	111	9	important	important	ADJ
ejpam-4855	111	10	properties	property	NOUN
ejpam-4855	111	11	of	of	ADP
ejpam-4855	111	12	b∗-open	b∗-open	NOUN
ejpam-4855	111	13	sets	set	NOUN
ejpam-4855	111	14	and	and	CCONJ
ejpam-4855	111	15	b∗j	b∗j	PUNCT
ejpam-4855	111	16	-open	-open	ADJ
ejpam-4855	111	17	sets	set	NOUN
ejpam-4855	111	18	.	.	PUNCT
ejpam-4855	112	1	lemma	lemma	PROPN
ejpam-4855	112	2	1	1	NUM
ejpam-4855	112	3	is	be	AUX
ejpam-4855	112	4	a	a	DET
ejpam-4855	112	5	characterization	characterization	NOUN
ejpam-4855	112	6	of	of	ADP
ejpam-4855	112	7	b∗-open	b∗-open	ADJ
ejpam-4855	112	8	sets	set	NOUN
ejpam-4855	112	9	.	.	PUNCT
ejpam-4855	113	1	m.	m.	NOUN
ejpam-4855	113	2	baldado	baldado	PROPN
ejpam-4855	113	3	jr	jr	PROPN
ejpam-4855	113	4	.	.	PROPN
ejpam-4855	113	5	/	/	SYM
ejpam-4855	113	6	eur	eur	PROPN
ejpam-4855	113	7	.	.	PUNCT
ejpam-4855	114	1	j.	j.	PROPN
ejpam-4855	114	2	pure	pure	PROPN
ejpam-4855	114	3	appl	appl	PROPN
ejpam-4855	114	4	.	.	PROPN
ejpam-4855	114	5	math	math	PROPN
ejpam-4855	114	6	,	,	PUNCT
ejpam-4855	114	7	16	16	NUM
ejpam-4855	114	8	(	(	PUNCT
ejpam-4855	114	9	3	3	NUM
ejpam-4855	114	10	)	)	PUNCT
ejpam-4855	114	11	(	(	PUNCT
ejpam-4855	114	12	2023	2023	NUM
ejpam-4855	114	13	)	)	PUNCT
ejpam-4855	114	14	,	,	PUNCT
ejpam-4855	114	15	1809	1809	NUM
ejpam-4855	114	16	-	-	SYM
ejpam-4855	114	17	1816	1816	NUM
ejpam-4855	114	18	1812	1812	NUM
ejpam-4855	114	19	lemma	lemma	PROPN
ejpam-4855	114	20	1	1	X
ejpam-4855	114	21	.	.	PUNCT
ejpam-4855	115	1	let	let	AUX
ejpam-4855	115	2	(	(	PUNCT
ejpam-4855	115	3	y	y	NOUN
ejpam-4855	115	4	,	,	PUNCT
ejpam-4855	115	5	ς	ς	PROPN
ejpam-4855	115	6	,	,	PUNCT
ejpam-4855	115	7	j	j	NOUN
ejpam-4855	115	8	)	)	PUNCT
ejpam-4855	115	9	be	be	VERB
ejpam-4855	115	10	an	an	DET
ejpam-4855	115	11	ideal	ideal	ADJ
ejpam-4855	115	12	space	space	NOUN
ejpam-4855	115	13	and	and	CCONJ
ejpam-4855	115	14	b	b	NOUN
ejpam-4855	115	15	be	be	AUX
ejpam-4855	115	16	a	a	DET
ejpam-4855	115	17	subset	subset	NOUN
ejpam-4855	115	18	of	of	ADP
ejpam-4855	115	19	y	y	PROPN
ejpam-4855	115	20	.	.	PUNCT
ejpam-4855	116	1	then	then	ADV
ejpam-4855	116	2	b	b	X
ejpam-4855	116	3	is	be	AUX
ejpam-4855	116	4	an	an	DET
ejpam-4855	116	5	b∗-open	b∗-open	NOUN
ejpam-4855	116	6	set	set	VERB
ejpam-4855	116	7	precisely	precisely	ADV
ejpam-4855	116	8	when	when	SCONJ
ejpam-4855	116	9	there	there	PRON
ejpam-4855	116	10	is	be	VERB
ejpam-4855	116	11	an	an	DET
ejpam-4855	116	12	open	open	ADJ
ejpam-4855	116	13	set	set	NOUN
ejpam-4855	116	14	p	p	NOUN
ejpam-4855	116	15	with	with	ADP
ejpam-4855	116	16	p	p	PROPN
ejpam-4855	116	17	⊆	⊆	NUM
ejpam-4855	116	18	int(b	int(b	NOUN
ejpam-4855	116	19	)	)	PUNCT
ejpam-4855	116	20	and	and	CCONJ
ejpam-4855	116	21	there	there	PRON
ejpam-4855	116	22	is	be	VERB
ejpam-4855	116	23	a	a	DET
ejpam-4855	116	24	close	close	ADJ
ejpam-4855	116	25	set	set	NOUN
ejpam-4855	116	26	s	s	NOUN
ejpam-4855	116	27	with	with	ADP
ejpam-4855	116	28	cl(b	cl(b	NOUN
ejpam-4855	116	29	)	)	PUNCT
ejpam-4855	117	1	⊆	⊆	NUM
ejpam-4855	117	2	s	s	VERB
ejpam-4855	117	3	such	such	ADJ
ejpam-4855	117	4	that	that	PRON
ejpam-4855	117	5	int(s	int(s	PROPN
ejpam-4855	117	6	)	)	PUNCT
ejpam-4855	117	7	∪	∪	ADP
ejpam-4855	117	8	cl(int(b	cl(int(b	NOUN
ejpam-4855	117	9	)	)	PUNCT
ejpam-4855	117	10	)	)	PUNCT
ejpam-4855	118	1	⊆	⊆	NUM
ejpam-4855	118	2	b	b	PROPN
ejpam-4855	118	3	⊆	⊆	NUM
ejpam-4855	118	4	int(cl(b	int(cl(b	PROPN
ejpam-4855	118	5	)	)	PUNCT
ejpam-4855	118	6	)	)	PUNCT
ejpam-4855	118	7	∪	∪	ADP
ejpam-4855	118	8	cl(p	cl(p	NOUN
ejpam-4855	118	9	)	)	PUNCT
ejpam-4855	118	10	.	.	PUNCT
ejpam-4855	119	1	proof	proof	NOUN
ejpam-4855	119	2	.	.	PUNCT
ejpam-4855	120	1	necessity	necessity	NOUN
ejpam-4855	120	2	.	.	PUNCT
ejpam-4855	121	1	let	let	VERB
ejpam-4855	121	2	b	b	NOUN
ejpam-4855	121	3	is	be	AUX
ejpam-4855	121	4	a	a	DET
ejpam-4855	121	5	b∗-open	b∗-open	NOUN
ejpam-4855	121	6	set	set	NOUN
ejpam-4855	121	7	.	.	PUNCT
ejpam-4855	122	1	then	then	ADV
ejpam-4855	122	2	b	b	X
ejpam-4855	122	3	=	=	SYM
ejpam-4855	122	4	int(cl(b	int(cl(b	PROPN
ejpam-4855	122	5	)	)	PUNCT
ejpam-4855	122	6	)	)	PUNCT
ejpam-4855	122	7	∪	∪	ADP
ejpam-4855	122	8	cl(int(b	cl(int(b	NOUN
ejpam-4855	122	9	)	)	PUNCT
ejpam-4855	122	10	)	)	PUNCT
ejpam-4855	122	11	.	.	PUNCT
ejpam-4855	123	1	take	take	VERB
ejpam-4855	123	2	the	the	DET
ejpam-4855	123	3	open	open	ADJ
ejpam-4855	123	4	set	set	NOUN
ejpam-4855	123	5	p	p	X
ejpam-4855	123	6	=	=	PUNCT
ejpam-4855	123	7	int(b	int(b	PROPN
ejpam-4855	123	8	)	)	PUNCT
ejpam-4855	123	9	and	and	CCONJ
ejpam-4855	123	10	the	the	DET
ejpam-4855	123	11	close	close	ADJ
ejpam-4855	123	12	set	set	NOUN
ejpam-4855	123	13	s	s	PART
ejpam-4855	123	14	=	=	NOUN
ejpam-4855	123	15	cl(b	cl(b	NOUN
ejpam-4855	123	16	)	)	PUNCT
ejpam-4855	123	17	.	.	PUNCT
ejpam-4855	124	1	note	note	VERB
ejpam-4855	124	2	that	that	SCONJ
ejpam-4855	124	3	int(s	int(s	PROPN
ejpam-4855	124	4	)	)	PUNCT
ejpam-4855	124	5	∪	∪	ADP
ejpam-4855	124	6	cl(int(b	cl(int(b	NOUN
ejpam-4855	124	7	)	)	PUNCT
ejpam-4855	124	8	)	)	PUNCT
ejpam-4855	125	1	⊆	⊆	NUM
ejpam-4855	125	2	int(cl(b	int(cl(b	PROPN
ejpam-4855	125	3	)	)	PUNCT
ejpam-4855	125	4	)	)	PUNCT
ejpam-4855	125	5	∪	∪	ADP
ejpam-4855	125	6	cl(int(b	cl(int(b	NOUN
ejpam-4855	125	7	)	)	PUNCT
ejpam-4855	125	8	)	)	PUNCT
ejpam-4855	126	1	=	=	SYM
ejpam-4855	126	2	b	b	NOUN
ejpam-4855	126	3	,	,	PUNCT
ejpam-4855	126	4	and	and	CCONJ
ejpam-4855	126	5	int(cl(b	int(cl(b	PROPN
ejpam-4855	126	6	)	)	PUNCT
ejpam-4855	126	7	)	)	PUNCT
ejpam-4855	126	8	∪	∪	ADP
ejpam-4855	126	9	cl(p	cl(p	NOUN
ejpam-4855	126	10	)	)	PUNCT
ejpam-4855	126	11	⊇	⊇	PROPN
ejpam-4855	126	12	int(cl(b	int(cl(b	PROPN
ejpam-4855	126	13	)	)	PUNCT
ejpam-4855	126	14	)	)	PUNCT
ejpam-4855	126	15	∪	∪	ADP
ejpam-4855	126	16	cl(int(b	cl(int(b	NOUN
ejpam-4855	126	17	)	)	PUNCT
ejpam-4855	126	18	)	)	PUNCT
ejpam-4855	127	1	=	=	SYM
ejpam-4855	127	2	b.	b.	PROPN
ejpam-4855	127	3	hence	hence	ADV
ejpam-4855	127	4	,	,	PUNCT
ejpam-4855	127	5	int(s	int(s	PROPN
ejpam-4855	127	6	)	)	PUNCT
ejpam-4855	127	7	∪	∪	ADP
ejpam-4855	127	8	cl(int(b	cl(int(b	NOUN
ejpam-4855	127	9	)	)	PUNCT
ejpam-4855	127	10	)	)	PUNCT
ejpam-4855	128	1	⊆	⊆	NUM
ejpam-4855	128	2	b	b	PROPN
ejpam-4855	128	3	⊆	⊆	NUM
ejpam-4855	128	4	int(cl(b	int(cl(b	PROPN
ejpam-4855	128	5	)	)	PUNCT
ejpam-4855	128	6	)	)	PUNCT
ejpam-4855	128	7	∪	∪	ADP
ejpam-4855	128	8	cl(p	cl(p	NOUN
ejpam-4855	128	9	)	)	PUNCT
ejpam-4855	128	10	.	.	PUNCT
ejpam-4855	129	1	sufficiency	sufficiency	PROPN
ejpam-4855	129	2	.	.	PUNCT
ejpam-4855	130	1	next	next	ADV
ejpam-4855	130	2	,	,	PUNCT
ejpam-4855	130	3	let	let	VERB
ejpam-4855	130	4	p	p	PRON
ejpam-4855	130	5	be	be	AUX
ejpam-4855	130	6	an	an	DET
ejpam-4855	130	7	open	open	ADJ
ejpam-4855	130	8	set	set	NOUN
ejpam-4855	130	9	with	with	ADP
ejpam-4855	130	10	p	p	PROPN
ejpam-4855	130	11	⊆	⊆	NUM
ejpam-4855	130	12	int(b	int(b	NOUN
ejpam-4855	130	13	)	)	PUNCT
ejpam-4855	130	14	and	and	CCONJ
ejpam-4855	130	15	let	let	VERB
ejpam-4855	130	16	s	s	PRON
ejpam-4855	130	17	be	be	AUX
ejpam-4855	130	18	a	a	DET
ejpam-4855	130	19	closed	closed	ADJ
ejpam-4855	130	20	set	set	NOUN
ejpam-4855	130	21	with	with	ADP
ejpam-4855	130	22	cl(b	cl(b	NOUN
ejpam-4855	130	23	)	)	PUNCT
ejpam-4855	131	1	⊆	⊆	NUM
ejpam-4855	131	2	s	s	VERB
ejpam-4855	131	3	such	such	ADJ
ejpam-4855	131	4	that	that	PRON
ejpam-4855	131	5	int(s	int(s	PROPN
ejpam-4855	131	6	)	)	PUNCT
ejpam-4855	131	7	∪	∪	ADP
ejpam-4855	131	8	cl(int(b	cl(int(b	NOUN
ejpam-4855	131	9	)	)	PUNCT
ejpam-4855	131	10	)	)	PUNCT
ejpam-4855	132	1	⊆	⊆	NUM
ejpam-4855	132	2	b	b	PROPN
ejpam-4855	132	3	⊆	⊆	NUM
ejpam-4855	132	4	int(cl(b	int(cl(b	PROPN
ejpam-4855	132	5	)	)	PUNCT
ejpam-4855	132	6	)	)	PUNCT
ejpam-4855	132	7	∪	∪	ADP
ejpam-4855	132	8	cl(p	cl(p	NOUN
ejpam-4855	132	9	)	)	PUNCT
ejpam-4855	132	10	.	.	PUNCT
ejpam-4855	133	1	then	then	ADV
ejpam-4855	133	2	b	b	PROPN
ejpam-4855	133	3	⊇	⊇	PROPN
ejpam-4855	133	4	int(s	int(s	PROPN
ejpam-4855	133	5	)	)	PUNCT
ejpam-4855	133	6	∪	∪	ADP
ejpam-4855	133	7	cl(int(b	cl(int(b	NOUN
ejpam-4855	133	8	)	)	PUNCT
ejpam-4855	133	9	)	)	PUNCT
ejpam-4855	133	10	⊇	⊇	PROPN
ejpam-4855	133	11	int(cl(b	int(cl(b	PROPN
ejpam-4855	133	12	)	)	PUNCT
ejpam-4855	133	13	)	)	PUNCT
ejpam-4855	133	14	∪	∪	ADP
ejpam-4855	133	15	cl(int(b	cl(int(b	NOUN
ejpam-4855	133	16	)	)	PUNCT
ejpam-4855	133	17	)	)	PUNCT
ejpam-4855	133	18	,	,	PUNCT
ejpam-4855	133	19	and	and	CCONJ
ejpam-4855	133	20	b	b	PROPN
ejpam-4855	133	21	⊇	⊇	PROPN
ejpam-4855	133	22	int(cl(b	int(cl(b	PROPN
ejpam-4855	133	23	)	)	PUNCT
ejpam-4855	133	24	)	)	PUNCT
ejpam-4855	133	25	∪	∪	ADP
ejpam-4855	133	26	cl(p	cl(p	NOUN
ejpam-4855	133	27	)	)	PUNCT
ejpam-4855	133	28	⊆	⊆	NUM
ejpam-4855	133	29	int(cl(b	int(cl(b	PROPN
ejpam-4855	133	30	)	)	PUNCT
ejpam-4855	133	31	)	)	PUNCT
ejpam-4855	133	32	∪	∪	ADP
ejpam-4855	133	33	cl(int(b	cl(int(b	NOUN
ejpam-4855	133	34	)	)	PUNCT
ejpam-4855	133	35	)	)	PUNCT
ejpam-4855	133	36	.	.	PUNCT
ejpam-4855	134	1	therefore	therefore	ADV
ejpam-4855	134	2	,	,	PUNCT
ejpam-4855	134	3	b	b	X
ejpam-4855	134	4	=	=	SYM
ejpam-4855	134	5	int(cl(b	int(cl(b	PROPN
ejpam-4855	134	6	)	)	PUNCT
ejpam-4855	134	7	)	)	PUNCT
ejpam-4855	134	8	∪	∪	ADP
ejpam-4855	134	9	cl(int(b	cl(int(b	NOUN
ejpam-4855	134	10	)	)	PUNCT
ejpam-4855	134	11	)	)	PUNCT
ejpam-4855	134	12	,	,	PUNCT
ejpam-4855	134	13	that	that	PRON
ejpam-4855	134	14	is	be	AUX
ejpam-4855	134	15	b	b	NOUN
ejpam-4855	134	16	is	be	AUX
ejpam-4855	134	17	a	a	DET
ejpam-4855	134	18	b∗-open	b∗-open	NOUN
ejpam-4855	134	19	set	set	NOUN
ejpam-4855	134	20	.	.	PUNCT
ejpam-4855	135	1	an	an	DET
ejpam-4855	135	2	open	open	ADJ
ejpam-4855	135	3	set	set	NOUN
ejpam-4855	135	4	is	be	AUX
ejpam-4855	135	5	nearly	nearly	ADV
ejpam-4855	135	6	b∗j	b∗j	ADJ
ejpam-4855	135	7	-open	-open	ADJ
ejpam-4855	135	8	.	.	PUNCT
ejpam-4855	136	1	the	the	DET
ejpam-4855	136	2	next	next	ADJ
ejpam-4855	136	3	lemma	lemma	PROPN
ejpam-4855	136	4	,	,	PUNCT
ejpam-4855	136	5	lemma	lemma	PROPN
ejpam-4855	136	6	2	2	NUM
ejpam-4855	136	7	,	,	PUNCT
ejpam-4855	136	8	shows	show	VERB
ejpam-4855	136	9	this	this	DET
ejpam-4855	136	10	idea	idea	NOUN
ejpam-4855	136	11	.	.	PUNCT
ejpam-4855	137	1	lemma	lemma	PROPN
ejpam-4855	137	2	2	2	X
ejpam-4855	137	3	.	.	PUNCT
ejpam-4855	138	1	let	let	AUX
ejpam-4855	138	2	(	(	PUNCT
ejpam-4855	138	3	y	y	NOUN
ejpam-4855	138	4	,	,	PUNCT
ejpam-4855	138	5	ς	ς	PROPN
ejpam-4855	138	6	,	,	PUNCT
ejpam-4855	138	7	j	j	NOUN
ejpam-4855	138	8	)	)	PUNCT
ejpam-4855	138	9	be	be	VERB
ejpam-4855	138	10	an	an	DET
ejpam-4855	138	11	ideal	ideal	ADJ
ejpam-4855	138	12	space	space	NOUN
ejpam-4855	138	13	.	.	PUNCT
ejpam-4855	139	1	then	then	ADV
ejpam-4855	139	2	every	every	DET
ejpam-4855	139	3	open	open	ADJ
ejpam-4855	139	4	set	set	NOUN
ejpam-4855	139	5	is	be	AUX
ejpam-4855	139	6	a	a	DET
ejpam-4855	139	7	b∗j	b∗j	PUNCT
ejpam-4855	139	8	-open	-open	ADJ
ejpam-4855	139	9	set	set	NOUN
ejpam-4855	139	10	.	.	PUNCT
ejpam-4855	140	1	proof	proof	NOUN
ejpam-4855	140	2	.	.	PUNCT
ejpam-4855	141	1	let	let	VERB
ejpam-4855	141	2	b	b	X
ejpam-4855	141	3	be	be	AUX
ejpam-4855	141	4	an	an	DET
ejpam-4855	141	5	open	open	ADJ
ejpam-4855	141	6	set	set	NOUN
ejpam-4855	141	7	,	,	PUNCT
ejpam-4855	141	8	and	and	CCONJ
ejpam-4855	141	9	consider	consider	VERB
ejpam-4855	141	10	s	s	NOUN
ejpam-4855	141	11	=	=	NOUN
ejpam-4855	141	12	∅	∅	NOUN
ejpam-4855	141	13	=	=	SYM
ejpam-4855	141	14	p	p	NOUN
ejpam-4855	141	15	.	.	PUNCT
ejpam-4855	142	1	then	then	ADV
ejpam-4855	142	2	s	s	VERB
ejpam-4855	142	3	and	and	CCONJ
ejpam-4855	142	4	p	p	NOUN
ejpam-4855	142	5	are	be	AUX
ejpam-4855	142	6	both	both	CCONJ
ejpam-4855	142	7	open	open	ADJ
ejpam-4855	142	8	and	and	CCONJ
ejpam-4855	142	9	closed	closed	ADJ
ejpam-4855	142	10	.	.	PUNCT
ejpam-4855	143	1	observed	observe	VERB
ejpam-4855	143	2	that	that	SCONJ
ejpam-4855	143	3	int(cl(b))∪	int(cl(b))∪	ADJ
ejpam-4855	143	4	cl(p	cl(p	NOUN
ejpam-4855	143	5	)	)	PUNCT
ejpam-4855	143	6	⊇	⊇	PROPN
ejpam-4855	143	7	int(b)∪	int(b)∪	ADJ
ejpam-4855	143	8	cl(∅	cl(∅	NOUN
ejpam-4855	143	9	)	)	PUNCT
ejpam-4855	143	10	=	=	SYM
ejpam-4855	143	11	int(b)∪∅	int(b)∪∅	NOUN
ejpam-4855	143	12	=	=	SYM
ejpam-4855	143	13	int(b	int(b	PROPN
ejpam-4855	143	14	)	)	PUNCT
ejpam-4855	143	15	=	=	SYM
ejpam-4855	143	16	b	b	NOUN
ejpam-4855	143	17	,	,	PUNCT
ejpam-4855	143	18	and	and	CCONJ
ejpam-4855	143	19	int(s	int(s	PROPN
ejpam-4855	143	20	)	)	PUNCT
ejpam-4855	143	21	∪	∪	ADP
ejpam-4855	143	22	cl(int(b	cl(int(b	NOUN
ejpam-4855	143	23	)	)	PUNCT
ejpam-4855	143	24	)	)	PUNCT
ejpam-4855	144	1	=	=	SYM
ejpam-4855	144	2	int(∅	int(∅	NOUN
ejpam-4855	144	3	)	)	PUNCT
ejpam-4855	144	4	∪	∪	ADP
ejpam-4855	144	5	cl(int(b	cl(int(b	NOUN
ejpam-4855	144	6	)	)	PUNCT
ejpam-4855	144	7	)	)	PUNCT
ejpam-4855	145	1	⊆	⊆	NUM
ejpam-4855	145	2	∅	∅	NOUN
ejpam-4855	145	3	∪	∪	ADP
ejpam-4855	145	4	cl(b	cl(b	NOUN
ejpam-4855	145	5	)	)	PUNCT
ejpam-4855	145	6	=	=	SYM
ejpam-4855	145	7	cl(b	cl(b	NOUN
ejpam-4855	145	8	)	)	PUNCT
ejpam-4855	145	9	.	.	PUNCT
ejpam-4855	146	1	hence	hence	ADV
ejpam-4855	146	2	,	,	PUNCT
ejpam-4855	146	3	we	we	PRON
ejpam-4855	146	4	have	have	VERB
ejpam-4855	146	5	b\int(cl(b))∪	b\int(cl(b))∪	NOUN
ejpam-4855	146	6	cl(p	cl(p	NOUN
ejpam-4855	146	7	)	)	PUNCT
ejpam-4855	147	1	=	=	SYM
ejpam-4855	147	2	∅	∅	NOUN
ejpam-4855	147	3	∈	∈	PROPN
ejpam-4855	147	4	j	j	PROPN
ejpam-4855	147	5	,	,	PUNCT
ejpam-4855	147	6	and	and	CCONJ
ejpam-4855	147	7	int(s)∪	int(s)∪	PROPN
ejpam-4855	147	8	cl(int(b))\cl(b	cl(int(b))\cl(b	PROPN
ejpam-4855	147	9	)	)	PUNCT
ejpam-4855	148	1	=	=	PRON
ejpam-4855	148	2	∅	∅	NOUN
ejpam-4855	148	3	∈	∈	PROPN
ejpam-4855	148	4	j	j	PROPN
ejpam-4855	148	5	,	,	PUNCT
ejpam-4855	148	6	that	that	ADV
ejpam-4855	148	7	is	is	ADV
ejpam-4855	148	8	,	,	PUNCT
ejpam-4855	148	9	b	b	PRON
ejpam-4855	148	10	is	be	AUX
ejpam-4855	148	11	nearly	nearly	ADV
ejpam-4855	148	12	b∗j	b∗j	ADJ
ejpam-4855	148	13	-open	-open	ADJ
ejpam-4855	148	14	.	.	PUNCT
ejpam-4855	149	1	an	an	DET
ejpam-4855	149	2	element	element	NOUN
ejpam-4855	149	3	of	of	ADP
ejpam-4855	149	4	ideal	ideal	ADJ
ejpam-4855	149	5	j	j	PROPN
ejpam-4855	149	6	is	be	AUX
ejpam-4855	149	7	nearly	nearly	ADV
ejpam-4855	149	8	b∗j	b∗j	PUNCT
ejpam-4855	149	9	-open	-open	ADJ
ejpam-4855	149	10	set	set	NOUN
ejpam-4855	149	11	.	.	PUNCT
ejpam-4855	150	1	the	the	DET
ejpam-4855	150	2	next	next	ADJ
ejpam-4855	150	3	lemma	lemma	PROPN
ejpam-4855	150	4	,	,	PUNCT
ejpam-4855	150	5	lemma	lemma	PROPN
ejpam-4855	150	6	3	3	NUM
ejpam-4855	150	7	,	,	PUNCT
ejpam-4855	150	8	shows	show	VERB
ejpam-4855	150	9	this	this	DET
ejpam-4855	150	10	idea	idea	NOUN
ejpam-4855	150	11	.	.	PUNCT
ejpam-4855	151	1	please	please	INTJ
ejpam-4855	151	2	see	see	VERB
ejpam-4855	151	3	[	[	X
ejpam-4855	151	4	9	9	NUM
ejpam-4855	151	5	]	]	PUNCT
ejpam-4855	151	6	and	and	CCONJ
ejpam-4855	151	7	[	[	X
ejpam-4855	151	8	4	4	X
ejpam-4855	151	9	]	]	PUNCT
ejpam-4855	151	10	to	to	PART
ejpam-4855	151	11	have	have	VERB
ejpam-4855	151	12	more	more	ADJ
ejpam-4855	151	13	insights	insight	NOUN
ejpam-4855	151	14	.	.	PUNCT
ejpam-4855	152	1	lemma	lemma	PROPN
ejpam-4855	152	2	3	3	X
ejpam-4855	152	3	.	.	PUNCT
ejpam-4855	153	1	let	let	AUX
ejpam-4855	153	2	(	(	PUNCT
ejpam-4855	153	3	y	y	NOUN
ejpam-4855	153	4	,	,	PUNCT
ejpam-4855	153	5	ς	ς	PROPN
ejpam-4855	153	6	,	,	PUNCT
ejpam-4855	153	7	j	j	NOUN
ejpam-4855	153	8	)	)	PUNCT
ejpam-4855	153	9	be	be	VERB
ejpam-4855	153	10	an	an	DET
ejpam-4855	153	11	ideal	ideal	ADJ
ejpam-4855	153	12	space	space	NOUN
ejpam-4855	153	13	.	.	PUNCT
ejpam-4855	154	1	then	then	ADV
ejpam-4855	154	2	each	each	DET
ejpam-4855	154	3	element	element	NOUN
ejpam-4855	154	4	of	of	ADP
ejpam-4855	154	5	j	j	PROPN
ejpam-4855	154	6	is	be	AUX
ejpam-4855	154	7	b∗j	b∗j	PUNCT
ejpam-4855	154	8	-open	-open	ADJ
ejpam-4855	154	9	.	.	PUNCT
ejpam-4855	155	1	proof	proof	NOUN
ejpam-4855	155	2	.	.	PUNCT
ejpam-4855	156	1	let	let	VERB
ejpam-4855	156	2	b	b	X
ejpam-4855	156	3	∈	∈	PROPN
ejpam-4855	156	4	j	j	PROPN
ejpam-4855	156	5	.	.	PUNCT
ejpam-4855	157	1	since	since	SCONJ
ejpam-4855	157	2	b	b	PROPN
ejpam-4855	157	3	−	−	PROPN
ejpam-4855	157	4	int(cl(b	int(cl(b	PROPN
ejpam-4855	157	5	)	)	PUNCT
ejpam-4855	157	6	)	)	PUNCT
ejpam-4855	157	7	∪	∪	ADP
ejpam-4855	157	8	cl(b	cl(b	NOUN
ejpam-4855	157	9	)	)	PUNCT
ejpam-4855	157	10	⊆	⊆	NUM
ejpam-4855	157	11	b	b	NOUN
ejpam-4855	157	12	,	,	PUNCT
ejpam-4855	157	13	we	we	PRON
ejpam-4855	157	14	have	have	VERB
ejpam-4855	157	15	int(cl(b	int(cl(b	PROPN
ejpam-4855	157	16	)	)	PUNCT
ejpam-4855	157	17	)	)	PUNCT
ejpam-4855	157	18	∪	∪	ADP
ejpam-4855	157	19	cl(b	cl(b	NOUN
ejpam-4855	157	20	)	)	PUNCT
ejpam-4855	158	1	∈	∈	PROPN
ejpam-4855	158	2	j	j	PROPN
ejpam-4855	158	3	.	.	PUNCT
ejpam-4855	159	1	next	next	ADV
ejpam-4855	159	2	,	,	PUNCT
ejpam-4855	159	3	consider	consider	VERB
ejpam-4855	159	4	s	s	PRON
ejpam-4855	159	5	=	=	ADJ
ejpam-4855	159	6	∅.	∅.	X
ejpam-4855	159	7	then	then	ADV
ejpam-4855	159	8	int(s	int(s	PROPN
ejpam-4855	159	9	)	)	PUNCT
ejpam-4855	159	10	∪	∪	ADP
ejpam-4855	159	11	cl(int(b))\cl(b	cl(int(b))\cl(b	NOUN
ejpam-4855	159	12	)	)	PUNCT
ejpam-4855	159	13	=	=	SYM
ejpam-4855	159	14	int(∅	int(∅	NOUN
ejpam-4855	159	15	)	)	PUNCT
ejpam-4855	159	16	∪	∪	ADP
ejpam-4855	159	17	cl(int(b))\cl(b	cl(int(b))\cl(b	NOUN
ejpam-4855	159	18	)	)	PUNCT
ejpam-4855	159	19	=	=	NOUN
ejpam-4855	159	20	∅	∅	NOUN
ejpam-4855	159	21	∪	∪	PROPN
ejpam-4855	159	22	cl(int(b))\cl(b	cl(int(b))\cl(b	NOUN
ejpam-4855	159	23	)	)	PUNCT
ejpam-4855	159	24	=	=	SYM
ejpam-4855	159	25	cl(int(b))\cl(b	cl(int(b))\cl(b	PROPN
ejpam-4855	159	26	)	)	PUNCT
ejpam-4855	159	27	=	=	PUNCT
ejpam-4855	159	28	∅	∅	NOUN
ejpam-4855	159	29	∈	∈	PROPN
ejpam-4855	159	30	j	j	PROPN
ejpam-4855	159	31	.	.	PUNCT
ejpam-4855	160	1	therefore	therefore	ADV
ejpam-4855	160	2	,	,	PUNCT
ejpam-4855	160	3	b	b	PROPN
ejpam-4855	160	4	is	be	AUX
ejpam-4855	160	5	nearly	nearly	ADV
ejpam-4855	160	6	b∗j	b∗j	ADJ
ejpam-4855	160	7	-open	-open	ADJ
ejpam-4855	160	8	.	.	PUNCT
ejpam-4855	161	1	lemma	lemma	PROPN
ejpam-4855	161	2	4	4	NUM
ejpam-4855	161	3	says	say	VERB
ejpam-4855	161	4	that	that	SCONJ
ejpam-4855	161	5	each	each	DET
ejpam-4855	161	6	b∗-open	b∗-open	ADJ
ejpam-4855	161	7	set	set	VERB
ejpam-4855	161	8	is	be	AUX
ejpam-4855	161	9	b∗j	b∗j	X
ejpam-4855	161	10	-open	-open	ADJ
ejpam-4855	161	11	.	.	PUNCT
ejpam-4855	162	1	lemma	lemma	PROPN
ejpam-4855	162	2	4	4	X
ejpam-4855	162	3	.	.	PUNCT
ejpam-4855	163	1	let	let	AUX
ejpam-4855	163	2	(	(	PUNCT
ejpam-4855	163	3	y	y	NOUN
ejpam-4855	163	4	,	,	PUNCT
ejpam-4855	163	5	ς	ς	PROPN
ejpam-4855	163	6	,	,	PUNCT
ejpam-4855	163	7	j	j	NOUN
ejpam-4855	163	8	)	)	PUNCT
ejpam-4855	163	9	be	be	VERB
ejpam-4855	163	10	an	an	DET
ejpam-4855	163	11	ideal	ideal	ADJ
ejpam-4855	163	12	space	space	NOUN
ejpam-4855	163	13	.	.	PUNCT
ejpam-4855	164	1	then	then	ADV
ejpam-4855	164	2	a	a	DET
ejpam-4855	164	3	b∗-open	b∗-open	ADJ
ejpam-4855	164	4	set	set	NOUN
ejpam-4855	164	5	is	be	AUX
ejpam-4855	164	6	b∗j	b∗j	X
ejpam-4855	164	7	-open	-open	ADJ
ejpam-4855	164	8	.	.	PUNCT
ejpam-4855	165	1	proof	proof	NOUN
ejpam-4855	165	2	.	.	PUNCT
ejpam-4855	166	1	let	let	VERB
ejpam-4855	166	2	b	b	X
ejpam-4855	166	3	be	be	AUX
ejpam-4855	166	4	a	a	DET
ejpam-4855	166	5	b∗-open	b∗-open	NOUN
ejpam-4855	166	6	set	set	NOUN
ejpam-4855	166	7	.	.	PUNCT
ejpam-4855	167	1	then	then	ADV
ejpam-4855	167	2	int(cl(b))∪cl(int(b	int(cl(b))∪cl(int(b	NOUN
ejpam-4855	167	3	)	)	PUNCT
ejpam-4855	167	4	)	)	PUNCT
ejpam-4855	168	1	=	=	SYM
ejpam-4855	168	2	b.	b.	PROPN
ejpam-4855	168	3	consider	consider	VERB
ejpam-4855	168	4	p	p	NOUN
ejpam-4855	168	5	=	=	VERB
ejpam-4855	168	6	int(b	int(b	PROPN
ejpam-4855	168	7	)	)	PUNCT
ejpam-4855	168	8	and	and	CCONJ
ejpam-4855	168	9	s	s	NOUN
ejpam-4855	168	10	=	=	NOUN
ejpam-4855	168	11	cl(b	cl(b	NOUN
ejpam-4855	168	12	)	)	PUNCT
ejpam-4855	168	13	.	.	PUNCT
ejpam-4855	169	1	then	then	ADV
ejpam-4855	169	2	p	p	NOUN
ejpam-4855	169	3	is	be	AUX
ejpam-4855	169	4	open	open	ADJ
ejpam-4855	169	5	with	with	ADP
ejpam-4855	169	6	p	p	PROPN
ejpam-4855	169	7	⊆	⊆	NUM
ejpam-4855	169	8	int(b	int(b	NOUN
ejpam-4855	169	9	)	)	PUNCT
ejpam-4855	169	10	,	,	PUNCT
ejpam-4855	169	11	and	and	CCONJ
ejpam-4855	169	12	s	s	VERB
ejpam-4855	169	13	is	be	AUX
ejpam-4855	169	14	closed	close	VERB
ejpam-4855	169	15	with	with	ADP
ejpam-4855	169	16	s	s	NOUN
ejpam-4855	169	17	⊆	⊆	NUM
ejpam-4855	169	18	cl(b	cl(b	NOUN
ejpam-4855	169	19	)	)	PUNCT
ejpam-4855	169	20	.	.	PUNCT
ejpam-4855	170	1	observed	observe	VERB
ejpam-4855	170	2	that	that	SCONJ
ejpam-4855	170	3	int(cl(b	int(cl(b	PROPN
ejpam-4855	170	4	)	)	PUNCT
ejpam-4855	170	5	)	)	PUNCT
ejpam-4855	170	6	∪	∪	ADP
ejpam-4855	170	7	cl(p	cl(p	NOUN
ejpam-4855	170	8	)	)	PUNCT
ejpam-4855	170	9	=	=	SYM
ejpam-4855	170	10	int(b	int(b	PROPN
ejpam-4855	170	11	)	)	PUNCT
ejpam-4855	170	12	∪	∪	ADP
ejpam-4855	170	13	cl(int(b	cl(int(b	NOUN
ejpam-4855	170	14	)	)	PUNCT
ejpam-4855	170	15	)	)	PUNCT
ejpam-4855	171	1	=	=	SYM
ejpam-4855	171	2	b	b	NOUN
ejpam-4855	171	3	,	,	PUNCT
ejpam-4855	171	4	and	and	CCONJ
ejpam-4855	171	5	int(s	int(s	PROPN
ejpam-4855	171	6	)	)	PUNCT
ejpam-4855	171	7	∪	∪	ADP
ejpam-4855	171	8	cl(int(b	cl(int(b	NOUN
ejpam-4855	171	9	)	)	PUNCT
ejpam-4855	171	10	)	)	PUNCT
ejpam-4855	172	1	=	=	SYM
ejpam-4855	172	2	int(cl(b	int(cl(b	PROPN
ejpam-4855	172	3	)	)	PUNCT
ejpam-4855	172	4	)	)	PUNCT
ejpam-4855	172	5	∪	∪	ADP
ejpam-4855	172	6	cl(int(b	cl(int(b	NOUN
ejpam-4855	172	7	)	)	PUNCT
ejpam-4855	172	8	)	)	PUNCT
ejpam-4855	173	1	=	=	SYM
ejpam-4855	173	2	b.	b.	PROPN
ejpam-4855	174	1	hence	hence	ADV
ejpam-4855	174	2	,	,	PUNCT
ejpam-4855	174	3	we	we	PRON
ejpam-4855	174	4	have	have	VERB
ejpam-4855	174	5	b\int(cl(b	b\int(cl(b	NOUN
ejpam-4855	174	6	)	)	PUNCT
ejpam-4855	174	7	)	)	PUNCT
ejpam-4855	174	8	∪	∪	ADP
ejpam-4855	174	9	cl(p	cl(p	NOUN
ejpam-4855	174	10	)	)	PUNCT
ejpam-4855	174	11	=	=	SYM
ejpam-4855	174	12	∅	∅	NOUN
ejpam-4855	174	13	∈	∈	PROPN
ejpam-4855	174	14	j	j	PROPN
ejpam-4855	174	15	,	,	PUNCT
ejpam-4855	174	16	and	and	CCONJ
ejpam-4855	174	17	int(s	int(s	PROPN
ejpam-4855	174	18	)	)	PUNCT
ejpam-4855	174	19	∪	∪	ADP
ejpam-4855	174	20	cl(int(b))\b	cl(int(b))\b	NOUN
ejpam-4855	174	21	=	=	SYM
ejpam-4855	174	22	∅	∅	NOUN
ejpam-4855	174	23	∈	∈	PROPN
ejpam-4855	174	24	j	j	PROPN
ejpam-4855	174	25	,	,	PUNCT
ejpam-4855	174	26	that	that	ADV
ejpam-4855	174	27	is	is	ADV
ejpam-4855	174	28	,	,	PUNCT
ejpam-4855	174	29	b	b	PRON
ejpam-4855	174	30	is	be	AUX
ejpam-4855	174	31	b∗j	b∗j	ADV
ejpam-4855	174	32	-open	-open	ADJ
ejpam-4855	174	33	.	.	PUNCT
ejpam-4855	175	1	m.	m.	PROPN
ejpam-4855	175	2	baldado	baldado	PROPN
ejpam-4855	175	3	jr	jr	PROPN
ejpam-4855	175	4	.	.	PROPN
ejpam-4855	175	5	/	/	SYM
ejpam-4855	175	6	eur	eur	PROPN
ejpam-4855	175	7	.	.	PUNCT
ejpam-4855	176	1	j.	j.	PROPN
ejpam-4855	176	2	pure	pure	PROPN
ejpam-4855	176	3	appl	appl	PROPN
ejpam-4855	176	4	.	.	PROPN
ejpam-4855	176	5	math	math	PROPN
ejpam-4855	176	6	,	,	PUNCT
ejpam-4855	176	7	16	16	NUM
ejpam-4855	176	8	(	(	PUNCT
ejpam-4855	176	9	3	3	NUM
ejpam-4855	176	10	)	)	PUNCT
ejpam-4855	176	11	(	(	PUNCT
ejpam-4855	176	12	2023	2023	NUM
ejpam-4855	176	13	)	)	PUNCT
ejpam-4855	176	14	,	,	PUNCT
ejpam-4855	176	15	1809	1809	NUM
ejpam-4855	176	16	-	-	SYM
ejpam-4855	176	17	1816	1816	NUM
ejpam-4855	176	18	1813	1813	NUM
ejpam-4855	176	19	lemma	lemma	PROPN
ejpam-4855	176	20	5	5	X
ejpam-4855	176	21	.	.	PUNCT
ejpam-4855	177	1	let	let	AUX
ejpam-4855	177	2	(	(	PUNCT
ejpam-4855	177	3	y	y	NOUN
ejpam-4855	177	4	,	,	PUNCT
ejpam-4855	177	5	ς	ς	PROPN
ejpam-4855	177	6	,	,	PUNCT
ejpam-4855	177	7	j	j	NOUN
ejpam-4855	177	8	)	)	PUNCT
ejpam-4855	177	9	be	be	VERB
ejpam-4855	177	10	an	an	DET
ejpam-4855	177	11	ideal	ideal	ADJ
ejpam-4855	177	12	space	space	NOUN
ejpam-4855	177	13	with	with	ADP
ejpam-4855	177	14	j	j	PROPN
ejpam-4855	177	15	=	=	PUNCT
ejpam-4855	177	16	{	{	PUNCT
ejpam-4855	177	17	∅	∅	NOUN
ejpam-4855	177	18	}	}	PUNCT
ejpam-4855	177	19	.	.	PUNCT
ejpam-4855	178	1	then	then	ADV
ejpam-4855	178	2	b	b	X
ejpam-4855	178	3	is	be	AUX
ejpam-4855	178	4	b∗-open	b∗-open	ADJ
ejpam-4855	178	5	precisely	precisely	ADV
ejpam-4855	178	6	if	if	SCONJ
ejpam-4855	178	7	b	b	NOUN
ejpam-4855	178	8	is	be	AUX
ejpam-4855	178	9	b∗j	b∗j	PUNCT
ejpam-4855	178	10	-open	-open	ADJ
ejpam-4855	178	11	.	.	PUNCT
ejpam-4855	179	1	proof	proof	NOUN
ejpam-4855	179	2	.	.	PUNCT
ejpam-4855	180	1	necessity	necessity	NOUN
ejpam-4855	180	2	.	.	PUNCT
ejpam-4855	181	1	let	let	VERB
ejpam-4855	181	2	b	b	AUX
ejpam-4855	181	3	be	be	AUX
ejpam-4855	181	4	b∗j	b∗j	ADV
ejpam-4855	181	5	-open	-open	ADJ
ejpam-4855	181	6	.	.	PUNCT
ejpam-4855	182	1	then	then	ADV
ejpam-4855	182	2	there	there	PRON
ejpam-4855	182	3	is	be	VERB
ejpam-4855	182	4	an	an	DET
ejpam-4855	182	5	open	open	ADJ
ejpam-4855	182	6	set	set	NOUN
ejpam-4855	182	7	p	p	PRON
ejpam-4855	182	8	such	such	ADJ
ejpam-4855	182	9	that	that	SCONJ
ejpam-4855	182	10	p	p	PROPN
ejpam-4855	182	11	⊆	⊆	NUM
ejpam-4855	182	12	int(b	int(b	NOUN
ejpam-4855	182	13	)	)	PUNCT
ejpam-4855	182	14	,	,	PUNCT
ejpam-4855	182	15	and	and	CCONJ
ejpam-4855	182	16	there	there	PRON
ejpam-4855	182	17	is	be	VERB
ejpam-4855	182	18	a	a	DET
ejpam-4855	182	19	close	close	ADJ
ejpam-4855	182	20	set	set	NOUN
ejpam-4855	182	21	s	s	VERB
ejpam-4855	182	22	such	such	ADJ
ejpam-4855	182	23	that	that	DET
ejpam-4855	182	24	s	s	VERB
ejpam-4855	182	25	⊆	⊆	NUM
ejpam-4855	182	26	cl(b	cl(b	NOUN
ejpam-4855	182	27	)	)	PUNCT
ejpam-4855	182	28	.	.	PUNCT
ejpam-4855	183	1	hence	hence	ADV
ejpam-4855	183	2	,	,	PUNCT
ejpam-4855	183	3	b	b	PROPN
ejpam-4855	183	4	⊆	⊆	NUM
ejpam-4855	183	5	int(cl(b	int(cl(b	PROPN
ejpam-4855	183	6	)	)	PUNCT
ejpam-4855	183	7	)	)	PUNCT
ejpam-4855	183	8	∪	∪	ADP
ejpam-4855	183	9	cl(p	cl(p	NOUN
ejpam-4855	183	10	)	)	PUNCT
ejpam-4855	183	11	,	,	PUNCT
ejpam-4855	183	12	and	and	CCONJ
ejpam-4855	183	13	int(s	int(s	PROPN
ejpam-4855	183	14	)	)	PUNCT
ejpam-4855	183	15	∪	∪	ADP
ejpam-4855	183	16	cl(int(b	cl(int(b	NOUN
ejpam-4855	183	17	)	)	PUNCT
ejpam-4855	183	18	)	)	PUNCT
ejpam-4855	184	1	⊆	⊆	NUM
ejpam-4855	184	2	b.	b.	PROPN
ejpam-4855	184	3	thus	thus	ADV
ejpam-4855	184	4	,	,	PUNCT
ejpam-4855	184	5	int(cl(b	int(cl(b	PROPN
ejpam-4855	184	6	)	)	PUNCT
ejpam-4855	184	7	)	)	PUNCT
ejpam-4855	184	8	∪	∪	ADP
ejpam-4855	184	9	cl(int(b	cl(int(b	NOUN
ejpam-4855	184	10	)	)	PUNCT
ejpam-4855	184	11	)	)	PUNCT
ejpam-4855	184	12	=	=	SYM
ejpam-4855	184	13	int(s	int(s	PROPN
ejpam-4855	184	14	)	)	PUNCT
ejpam-4855	184	15	∪	∪	ADP
ejpam-4855	184	16	cl(int(b	cl(int(b	NOUN
ejpam-4855	184	17	)	)	PUNCT
ejpam-4855	184	18	)	)	PUNCT
ejpam-4855	185	1	⊆	⊆	NUM
ejpam-4855	185	2	b	b	NOUN
ejpam-4855	185	3	,	,	PUNCT
ejpam-4855	185	4	and	and	CCONJ
ejpam-4855	185	5	int(cl(b	int(cl(b	PROPN
ejpam-4855	185	6	)	)	PUNCT
ejpam-4855	185	7	)	)	PUNCT
ejpam-4855	185	8	∪	∪	ADP
ejpam-4855	185	9	cl(int(b	cl(int(b	NOUN
ejpam-4855	185	10	)	)	PUNCT
ejpam-4855	185	11	)	)	PUNCT
ejpam-4855	186	1	=	=	SYM
ejpam-4855	186	2	int(cl(b	int(cl(b	PROPN
ejpam-4855	186	3	)	)	PUNCT
ejpam-4855	186	4	)	)	PUNCT
ejpam-4855	186	5	∪	∪	ADP
ejpam-4855	186	6	cl(p	cl(p	NOUN
ejpam-4855	186	7	)	)	PUNCT
ejpam-4855	186	8	⊇	⊇	PROPN
ejpam-4855	186	9	b.	b.	PROPN
ejpam-4855	186	10	therefore	therefore	ADV
ejpam-4855	186	11	,	,	PUNCT
ejpam-4855	186	12	int(cl(b	int(cl(b	PROPN
ejpam-4855	186	13	)	)	PUNCT
ejpam-4855	186	14	)	)	PUNCT
ejpam-4855	186	15	∪	∪	ADP
ejpam-4855	186	16	cl(int(b	cl(int(b	NOUN
ejpam-4855	186	17	)	)	PUNCT
ejpam-4855	186	18	)	)	PUNCT
ejpam-4855	187	1	=	=	SYM
ejpam-4855	187	2	b	b	X
ejpam-4855	187	3	,	,	PUNCT
ejpam-4855	187	4	that	that	ADV
ejpam-4855	187	5	is	is	ADV
ejpam-4855	187	6	,	,	PUNCT
ejpam-4855	187	7	b	b	PRON
ejpam-4855	187	8	is	be	AUX
ejpam-4855	187	9	b∗-open	b∗-open	ADJ
ejpam-4855	187	10	.	.	PUNCT
ejpam-4855	188	1	sufficiency	sufficiency	NOUN
ejpam-4855	188	2	.	.	PUNCT
ejpam-4855	189	1	the	the	DET
ejpam-4855	189	2	converse	converse	NOUN
ejpam-4855	189	3	follows	follow	VERB
ejpam-4855	189	4	from	from	ADP
ejpam-4855	189	5	lemma	lemma	PROPN
ejpam-4855	189	6	4	4	NUM
ejpam-4855	189	7	.	.	PUNCT
ejpam-4855	190	1	if	if	SCONJ
ejpam-4855	190	2	j	j	PROPN
ejpam-4855	190	3	is	be	AUX
ejpam-4855	190	4	the	the	DET
ejpam-4855	190	5	minimal	minimal	ADJ
ejpam-4855	190	6	ideal	ideal	NOUN
ejpam-4855	190	7	,	,	PUNCT
ejpam-4855	190	8	then	then	ADV
ejpam-4855	190	9	the	the	DET
ejpam-4855	190	10	notions	notion	NOUN
ejpam-4855	190	11	b∗-compact	b∗-compact	PROPN
ejpam-4855	190	12	,	,	PUNCT
ejpam-4855	190	13	b∗j	b∗j	ADJ
ejpam-4855	190	14	-compact	-compact	NOUN
ejpam-4855	190	15	and	and	CCONJ
ejpam-4855	190	16	cb∗j	cb∗j	NOUN
ejpam-4855	190	17	-	-	PUNCT
ejpam-4855	190	18	compact	compact	ADJ
ejpam-4855	190	19	are	be	AUX
ejpam-4855	190	20	the	the	DET
ejpam-4855	190	21	same	same	ADJ
ejpam-4855	190	22	.	.	PUNCT
ejpam-4855	191	1	theorem	theorem	ADJ
ejpam-4855	191	2	1	1	NUM
ejpam-4855	191	3	shows	show	VERB
ejpam-4855	191	4	this	this	DET
ejpam-4855	191	5	idea	idea	NOUN
ejpam-4855	191	6	.	.	PUNCT
ejpam-4855	192	1	theorem	theorem	NOUN
ejpam-4855	192	2	1	1	X
ejpam-4855	192	3	.	.	PUNCT
ejpam-4855	193	1	let	let	AUX
ejpam-4855	193	2	(	(	PUNCT
ejpam-4855	193	3	y	y	NOUN
ejpam-4855	193	4	,	,	PUNCT
ejpam-4855	193	5	ς	ς	PROPN
ejpam-4855	193	6	,	,	PUNCT
ejpam-4855	193	7	j	j	NOUN
ejpam-4855	193	8	)	)	PUNCT
ejpam-4855	193	9	be	be	VERB
ejpam-4855	193	10	an	an	DET
ejpam-4855	193	11	ideal	ideal	ADJ
ejpam-4855	193	12	space	space	NOUN
ejpam-4855	193	13	with	with	ADP
ejpam-4855	193	14	j	j	PROPN
ejpam-4855	193	15	=	=	PUNCT
ejpam-4855	193	16	{	{	PUNCT
ejpam-4855	193	17	∅	∅	NOUN
ejpam-4855	193	18	}	}	PUNCT
ejpam-4855	193	19	.	.	PUNCT
ejpam-4855	194	1	then	then	ADV
ejpam-4855	194	2	the	the	DET
ejpam-4855	194	3	following	following	NOUN
ejpam-4855	194	4	are	be	AUX
ejpam-4855	194	5	equivalent	equivalent	ADJ
ejpam-4855	194	6	.	.	PUNCT
ejpam-4855	195	1	(	(	PUNCT
ejpam-4855	195	2	i	i	NOUN
ejpam-4855	195	3	)	)	PUNCT
ejpam-4855	195	4	.	.	PUNCT
ejpam-4855	196	1	(	(	PUNCT
ejpam-4855	196	2	y	y	X
ejpam-4855	196	3	,	,	PUNCT
ejpam-4855	196	4	ς	ς	PROPN
ejpam-4855	196	5	,	,	PUNCT
ejpam-4855	196	6	j	j	NOUN
ejpam-4855	196	7	)	)	PUNCT
ejpam-4855	196	8	is	be	AUX
ejpam-4855	196	9	a	a	DET
ejpam-4855	196	10	b∗-compact	b∗-compact	ADJ
ejpam-4855	196	11	ideal	ideal	ADJ
ejpam-4855	196	12	space	space	NOUN
ejpam-4855	196	13	.	.	PUNCT
ejpam-4855	197	1	(	(	PUNCT
ejpam-4855	197	2	ii	ii	NOUN
ejpam-4855	197	3	)	)	PUNCT
ejpam-4855	197	4	.	.	PUNCT
ejpam-4855	198	1	(	(	PUNCT
ejpam-4855	198	2	y	y	X
ejpam-4855	198	3	,	,	PUNCT
ejpam-4855	198	4	ς	ς	PROPN
ejpam-4855	198	5	,	,	PUNCT
ejpam-4855	198	6	j	j	NOUN
ejpam-4855	198	7	)	)	PUNCT
ejpam-4855	198	8	is	be	AUX
ejpam-4855	198	9	a	a	DET
ejpam-4855	198	10	b∗j	b∗j	ADJ
ejpam-4855	198	11	-compact	-compact	ADJ
ejpam-4855	198	12	ideal	ideal	ADJ
ejpam-4855	198	13	space	space	NOUN
ejpam-4855	198	14	.	.	PUNCT
ejpam-4855	199	1	(	(	PUNCT
ejpam-4855	199	2	iii	iii	NOUN
ejpam-4855	199	3	)	)	PUNCT
ejpam-4855	199	4	.	.	PUNCT
ejpam-4855	200	1	(	(	PUNCT
ejpam-4855	200	2	y	y	X
ejpam-4855	200	3	,	,	PUNCT
ejpam-4855	200	4	ς	ς	PROPN
ejpam-4855	200	5	,	,	PUNCT
ejpam-4855	200	6	j	j	NOUN
ejpam-4855	200	7	)	)	PUNCT
ejpam-4855	200	8	is	be	AUX
ejpam-4855	200	9	a	a	DET
ejpam-4855	200	10	cb∗j	cb∗j	PROPN
ejpam-4855	200	11	-compact	-compact	NOUN
ejpam-4855	200	12	ideal	ideal	ADJ
ejpam-4855	200	13	space	space	NOUN
ejpam-4855	200	14	.	.	PUNCT
ejpam-4855	201	1	proof	proof	NOUN
ejpam-4855	201	2	.	.	PUNCT
ejpam-4855	202	1	(	(	PUNCT
ejpam-4855	202	2	i	i	NOUN
ejpam-4855	202	3	)	)	PUNCT
ejpam-4855	202	4	implies	imply	VERB
ejpam-4855	202	5	(	(	PUNCT
ejpam-4855	202	6	ii	ii	NOUN
ejpam-4855	202	7	):	):	PUNCT
ejpam-4855	202	8	let	let	VERB
ejpam-4855	202	9	{	{	PUNCT
ejpam-4855	202	10	uψ	uψ	X
ejpam-4855	202	11	:	:	PUNCT
ejpam-4855	202	12	ψ	ψ	X
ejpam-4855	202	13	∈	∈	PROPN
ejpam-4855	202	14	ψ	ψ	AUX
ejpam-4855	202	15	}	}	PUNCT
ejpam-4855	202	16	be	be	AUX
ejpam-4855	202	17	a	a	DET
ejpam-4855	202	18	b∗j	b∗j	PUNCT
ejpam-4855	202	19	-open	-open	NOUN
ejpam-4855	202	20	covering	cover	VERB
ejpam-4855	202	21	y	y	NOUN
ejpam-4855	202	22	.	.	PUNCT
ejpam-4855	203	1	by	by	ADP
ejpam-4855	203	2	lemma	lemma	PROPN
ejpam-4855	203	3	5	5	NUM
ejpam-4855	203	4	,	,	PUNCT
ejpam-4855	203	5	{	{	PUNCT
ejpam-4855	203	6	uψ	uψ	X
ejpam-4855	203	7	:	:	PUNCT
ejpam-4855	203	8	ψ	ψ	X
ejpam-4855	203	9	∈	∈	PROPN
ejpam-4855	203	10	ψ	ψ	AUX
ejpam-4855	203	11	}	}	PUNCT
ejpam-4855	203	12	is	be	AUX
ejpam-4855	203	13	also	also	ADV
ejpam-4855	203	14	a	a	DET
ejpam-4855	203	15	b∗-open	b∗-open	NOUN
ejpam-4855	203	16	covering	cover	VERB
ejpam-4855	203	17	y	y	PRON
ejpam-4855	203	18	.	.	PUNCT
ejpam-4855	204	1	since	since	SCONJ
ejpam-4855	204	2	y	y	PROPN
ejpam-4855	204	3	is	be	AUX
ejpam-4855	204	4	a	a	DET
ejpam-4855	204	5	b∗-compact	b∗-compact	ADJ
ejpam-4855	204	6	ideal	ideal	ADJ
ejpam-4855	204	7	space	space	NOUN
ejpam-4855	204	8	,	,	PUNCT
ejpam-4855	204	9	ψ	ψ	NOUN
ejpam-4855	204	10	has	have	VERB
ejpam-4855	204	11	a	a	DET
ejpam-4855	204	12	smaller	small	ADJ
ejpam-4855	204	13	finite	finite	NOUN
ejpam-4855	204	14	subset	subset	NOUN
ejpam-4855	204	15	,	,	PUNCT
ejpam-4855	204	16	say	say	VERB
ejpam-4855	204	17	ψ0	ψ0	ADV
ejpam-4855	204	18	,	,	PUNCT
ejpam-4855	204	19	with	with	ADP
ejpam-4855	204	20	{	{	PUNCT
ejpam-4855	204	21	uψ	uψ	NOUN
ejpam-4855	204	22	:	:	PUNCT
ejpam-4855	204	23	ψ	ψ	X
ejpam-4855	204	24	∈	∈	PROPN
ejpam-4855	204	25	ψ0	ψ0	ADV
ejpam-4855	204	26	}	}	PUNCT
ejpam-4855	204	27	still	still	ADV
ejpam-4855	204	28	covering	cover	VERB
ejpam-4855	204	29	y	y	PRON
ejpam-4855	204	30	.	.	PUNCT
ejpam-4855	205	1	thus	thus	ADV
ejpam-4855	205	2	,	,	PUNCT
ejpam-4855	205	3	by	by	ADP
ejpam-4855	205	4	lemma	lemma	PROPN
ejpam-4855	205	5	5	5	NUM
ejpam-4855	205	6	,	,	PUNCT
ejpam-4855	205	7	{	{	PUNCT
ejpam-4855	205	8	uψ	uψ	X
ejpam-4855	205	9	:	:	PUNCT
ejpam-4855	205	10	ψ	ψ	X
ejpam-4855	205	11	∈	∈	PROPN
ejpam-4855	205	12	ψ0	ψ0	PROPN
ejpam-4855	205	13	}	}	PUNCT
ejpam-4855	205	14	is	be	AUX
ejpam-4855	205	15	a	a	DET
ejpam-4855	205	16	smaller	small	ADJ
ejpam-4855	205	17	finite	finite	NOUN
ejpam-4855	205	18	b∗j	b∗j	PUNCT
ejpam-4855	205	19	-covering	-covering	NOUN
ejpam-4855	205	20	of	of	ADP
ejpam-4855	205	21	y	y	PROPN
ejpam-4855	205	22	.	.	PUNCT
ejpam-4855	206	1	this	this	PRON
ejpam-4855	206	2	shows	show	VERB
ejpam-4855	206	3	that	that	SCONJ
ejpam-4855	206	4	y	y	PROPN
ejpam-4855	206	5	is	be	AUX
ejpam-4855	206	6	a	a	DET
ejpam-4855	206	7	b∗j	b∗j	ADJ
ejpam-4855	206	8	compact	compact	ADJ
ejpam-4855	206	9	set	set	NOUN
ejpam-4855	206	10	.	.	PUNCT
ejpam-4855	207	1	(	(	PUNCT
ejpam-4855	207	2	ii	ii	NOUN
ejpam-4855	207	3	)	)	PUNCT
ejpam-4855	207	4	implies	imply	VERB
ejpam-4855	207	5	(	(	PUNCT
ejpam-4855	207	6	iii	iii	X
ejpam-4855	207	7	):	):	PUNCT
ejpam-4855	207	8	let	let	VERB
ejpam-4855	207	9	{	{	PUNCT
ejpam-4855	207	10	uψ	uψ	X
ejpam-4855	207	11	:	:	PUNCT
ejpam-4855	207	12	ψ	ψ	X
ejpam-4855	207	13	∈	∈	PROPN
ejpam-4855	207	14	ψ	ψ	AUX
ejpam-4855	207	15	}	}	PUNCT
ejpam-4855	207	16	be	be	AUX
ejpam-4855	207	17	a	a	DET
ejpam-4855	207	18	b∗j	b∗j	PUNCT
ejpam-4855	207	19	-open	-open	NOUN
ejpam-4855	207	20	covering	cover	VERB
ejpam-4855	207	21	y	y	NOUN
ejpam-4855	207	22	.	.	PUNCT
ejpam-4855	208	1	since	since	SCONJ
ejpam-4855	208	2	y	y	PROPN
ejpam-4855	208	3	is	be	AUX
ejpam-4855	208	4	a	a	DET
ejpam-4855	208	5	b∗j	b∗j	ADJ
ejpam-4855	208	6	-compact	-compact	ADJ
ejpam-4855	208	7	ideal	ideal	ADJ
ejpam-4855	208	8	space	space	NOUN
ejpam-4855	208	9	,	,	PUNCT
ejpam-4855	208	10	ψ	ψ	NOUN
ejpam-4855	208	11	has	have	VERB
ejpam-4855	208	12	a	a	DET
ejpam-4855	208	13	smaller	small	ADJ
ejpam-4855	208	14	finite	finite	NOUN
ejpam-4855	208	15	subset	subset	NOUN
ejpam-4855	208	16	,	,	PUNCT
ejpam-4855	208	17	say	say	VERB
ejpam-4855	208	18	ψ0	ψ0	ADV
ejpam-4855	208	19	,	,	PUNCT
ejpam-4855	208	20	with	with	ADP
ejpam-4855	208	21	{	{	PUNCT
ejpam-4855	208	22	uψ	uψ	NOUN
ejpam-4855	208	23	:	:	PUNCT
ejpam-4855	208	24	ψ	ψ	X
ejpam-4855	208	25	∈	∈	PROPN
ejpam-4855	208	26	ψ0	ψ0	ADV
ejpam-4855	208	27	}	}	PUNCT
ejpam-4855	208	28	still	still	ADV
ejpam-4855	208	29	covering	cover	VERB
ejpam-4855	208	30	y	y	PRON
ejpam-4855	208	31	.	.	PUNCT
ejpam-4855	209	1	thus	thus	ADV
ejpam-4855	209	2	,	,	PUNCT
ejpam-4855	209	3	y	y	PROPN
ejpam-4855	209	4	−	−	PROPN
ejpam-4855	209	5	⋃	⋃	PROPN
ejpam-4855	209	6	ψ∈ψ0	ψ∈ψ0	NOUN
ejpam-4855	209	7	uψ	uψ	ADP
ejpam-4855	209	8	=	=	PUNCT
ejpam-4855	209	9	∅	∅	NOUN
ejpam-4855	209	10	∈	∈	PROPN
ejpam-4855	209	11	j	j	PROPN
ejpam-4855	209	12	.	.	PUNCT
ejpam-4855	210	1	therefore	therefore	ADV
ejpam-4855	210	2	,	,	PUNCT
ejpam-4855	210	3	y	y	PROPN
ejpam-4855	210	4	is	be	AUX
ejpam-4855	210	5	cb∗j	cb∗j	PROPN
ejpam-4855	210	6	compact	compact	ADJ
ejpam-4855	210	7	set	set	NOUN
ejpam-4855	210	8	.	.	PUNCT
ejpam-4855	211	1	(	(	PUNCT
ejpam-4855	211	2	iii	iii	NOUN
ejpam-4855	211	3	)	)	PUNCT
ejpam-4855	211	4	implies	imply	VERB
ejpam-4855	211	5	(	(	PUNCT
ejpam-4855	211	6	i	i	NOUN
ejpam-4855	211	7	):	):	PUNCT
ejpam-4855	211	8	let	let	VERB
ejpam-4855	211	9	{	{	PUNCT
ejpam-4855	211	10	uψ	uψ	X
ejpam-4855	211	11	:	:	PUNCT
ejpam-4855	211	12	ψ	ψ	X
ejpam-4855	211	13	∈	∈	PROPN
ejpam-4855	211	14	ψ	ψ	AUX
ejpam-4855	211	15	}	}	PUNCT
ejpam-4855	211	16	be	be	AUX
ejpam-4855	211	17	a	a	DET
ejpam-4855	211	18	b∗-open	b∗-open	NOUN
ejpam-4855	211	19	covering	cover	VERB
ejpam-4855	211	20	y	y	NOUN
ejpam-4855	211	21	.	.	PUNCT
ejpam-4855	212	1	y	y	PROPN
ejpam-4855	212	2	lemma	lemma	PROPN
ejpam-4855	212	3	5	5	NUM
ejpam-4855	212	4	,	,	PUNCT
ejpam-4855	212	5	{	{	PUNCT
ejpam-4855	212	6	uψ	uψ	X
ejpam-4855	212	7	:	:	PUNCT
ejpam-4855	212	8	ψ	ψ	X
ejpam-4855	212	9	∈	∈	PROPN
ejpam-4855	212	10	ψ	ψ	X
ejpam-4855	212	11	}	}	PUNCT
ejpam-4855	212	12	is	be	AUX
ejpam-4855	212	13	also	also	ADV
ejpam-4855	212	14	a	a	DET
ejpam-4855	212	15	b∗j	b∗j	PUNCT
ejpam-4855	212	16	-open	-open	NOUN
ejpam-4855	212	17	covering	cover	VERB
ejpam-4855	212	18	y	y	NOUN
ejpam-4855	212	19	.	.	PUNCT
ejpam-4855	213	1	since	since	SCONJ
ejpam-4855	213	2	y	y	PROPN
ejpam-4855	213	3	is	be	AUX
ejpam-4855	213	4	a	a	DET
ejpam-4855	213	5	cb∗j	cb∗j	PROPN
ejpam-4855	213	6	-compact	-compact	PROPN
ejpam-4855	213	7	ideal	ideal	ADJ
ejpam-4855	213	8	space	space	NOUN
ejpam-4855	213	9	,	,	PUNCT
ejpam-4855	213	10	ψ	ψ	NOUN
ejpam-4855	213	11	has	have	VERB
ejpam-4855	213	12	a	a	DET
ejpam-4855	213	13	smaller	small	ADJ
ejpam-4855	213	14	finite	finite	NOUN
ejpam-4855	213	15	subset	subset	NOUN
ejpam-4855	213	16	,	,	PUNCT
ejpam-4855	213	17	say	say	VERB
ejpam-4855	213	18	ψ0	ψ0	ADV
ejpam-4855	213	19	,	,	PUNCT
ejpam-4855	213	20	with	with	ADP
ejpam-4855	213	21	y	y	PROPN
ejpam-4855	214	1	−	−	PROPN
ejpam-4855	214	2	⋃	⋃	PROPN
ejpam-4855	214	3	ψ∈ψ0	ψ∈ψ0	NOUN
ejpam-4855	214	4	uψ	uψ	ADP
ejpam-4855	214	5	=	=	PUNCT
ejpam-4855	214	6	∅	∅	NOUN
ejpam-4855	214	7	∈	∈	PROPN
ejpam-4855	214	8	j	j	PROPN
ejpam-4855	214	9	,	,	PUNCT
ejpam-4855	214	10	that	that	ADV
ejpam-4855	214	11	is	is	ADV
ejpam-4855	214	12	,	,	PUNCT
ejpam-4855	214	13	{	{	PUNCT
ejpam-4855	214	14	uψ	uψ	X
ejpam-4855	214	15	:	:	PUNCT
ejpam-4855	214	16	ψ	ψ	X
ejpam-4855	214	17	∈	∈	PROPN
ejpam-4855	214	18	ψ0	ψ0	PROPN
ejpam-4855	214	19	}	}	PUNCT
ejpam-4855	214	20	is	be	AUX
ejpam-4855	214	21	a	a	DET
ejpam-4855	214	22	smaller	small	ADJ
ejpam-4855	214	23	finite	finite	NOUN
ejpam-4855	214	24	b∗-covering	b∗-covering	NOUN
ejpam-4855	214	25	of	of	ADP
ejpam-4855	214	26	y	y	PROPN
ejpam-4855	214	27	.	.	PUNCT
ejpam-4855	215	1	therefore	therefore	ADV
ejpam-4855	215	2	,	,	PUNCT
ejpam-4855	215	3	y	y	PROPN
ejpam-4855	215	4	is	be	AUX
ejpam-4855	215	5	b∗	b∗	ADJ
ejpam-4855	215	6	compact	compact	ADJ
ejpam-4855	215	7	set	set	NOUN
ejpam-4855	215	8	.	.	PUNCT
ejpam-4855	216	1	another	another	DET
ejpam-4855	216	2	characterization	characterization	NOUN
ejpam-4855	216	3	of	of	ADP
ejpam-4855	216	4	b∗j	b∗j	PUNCT
ejpam-4855	216	5	-compact	-compact	ADJ
ejpam-4855	216	6	topological	topological	ADJ
ejpam-4855	216	7	spaces	space	NOUN
ejpam-4855	216	8	is	be	AUX
ejpam-4855	216	9	presented	present	VERB
ejpam-4855	216	10	in	in	ADP
ejpam-4855	216	11	theorem	theorem	ADJ
ejpam-4855	216	12	2	2	NUM
ejpam-4855	216	13	.	.	PUNCT
ejpam-4855	216	14	theorem	theorem	NOUN
ejpam-4855	216	15	2	2	NUM
ejpam-4855	216	16	.	.	PUNCT
ejpam-4855	217	1	let	let	AUX
ejpam-4855	217	2	(	(	PUNCT
ejpam-4855	217	3	y	y	NOUN
ejpam-4855	217	4	,	,	PUNCT
ejpam-4855	217	5	ς	ς	PROPN
ejpam-4855	217	6	,	,	PUNCT
ejpam-4855	217	7	j	j	NOUN
ejpam-4855	217	8	)	)	PUNCT
ejpam-4855	217	9	be	be	VERB
ejpam-4855	217	10	an	an	DET
ejpam-4855	217	11	ideal	ideal	ADJ
ejpam-4855	217	12	space	space	NOUN
ejpam-4855	217	13	.	.	PUNCT
ejpam-4855	218	1	then	then	ADV
ejpam-4855	218	2	statement	statement	NOUN
ejpam-4855	218	3	(	(	PUNCT
ejpam-4855	218	4	i	i	NOUN
ejpam-4855	218	5	)	)	PUNCT
ejpam-4855	218	6	is	be	AUX
ejpam-4855	218	7	a	a	DET
ejpam-4855	218	8	necessary	necessary	ADJ
ejpam-4855	218	9	and	and	CCONJ
ejpam-4855	218	10	sufficient	sufficient	ADJ
ejpam-4855	218	11	condition	condition	NOUN
ejpam-4855	218	12	for	for	ADP
ejpam-4855	218	13	statement	statement	NOUN
ejpam-4855	218	14	(	(	PUNCT
ejpam-4855	218	15	ii	ii	NOUN
ejpam-4855	218	16	)	)	PUNCT
ejpam-4855	218	17	.	.	PUNCT
ejpam-4855	219	1	i.	i.	PROPN
ejpam-4855	219	2	(	(	PUNCT
ejpam-4855	219	3	y	y	PROPN
ejpam-4855	219	4	,	,	PUNCT
ejpam-4855	219	5	ς	ς	PROPN
ejpam-4855	219	6	,	,	PUNCT
ejpam-4855	219	7	j	j	NOUN
ejpam-4855	219	8	)	)	PUNCT
ejpam-4855	219	9	is	be	AUX
ejpam-4855	219	10	a	a	DET
ejpam-4855	219	11	b∗j	b∗j	ADJ
ejpam-4855	219	12	-compact	-compact	ADJ
ejpam-4855	219	13	space	space	NOUN
ejpam-4855	219	14	.	.	PUNCT
ejpam-4855	220	1	ii	ii	PROPN
ejpam-4855	220	2	.	.	PUNCT
ejpam-4855	221	1	if	if	SCONJ
ejpam-4855	221	2	{	{	PUNCT
ejpam-4855	221	3	sψ	sψ	NOUN
ejpam-4855	221	4	:	:	PUNCT
ejpam-4855	221	5	ψ	ψ	X
ejpam-4855	221	6	∈	∈	PROPN
ejpam-4855	221	7	ψ	ψ	AUX
ejpam-4855	221	8	}	}	PUNCT
ejpam-4855	221	9	is	be	AUX
ejpam-4855	221	10	a	a	DET
ejpam-4855	221	11	class	class	NOUN
ejpam-4855	221	12	of	of	ADP
ejpam-4855	221	13	b∗j	b∗j	PUNCT
ejpam-4855	221	14	-closed	-closed	ADJ
ejpam-4855	221	15	sets	set	NOUN
ejpam-4855	221	16	with	with	ADP
ejpam-4855	221	17	⋂	⋂	PROPN
ejpam-4855	221	18	{	{	PUNCT
ejpam-4855	221	19	sψ	sψ	PROPN
ejpam-4855	221	20	:	:	PUNCT
ejpam-4855	221	21	ψ	ψ	X
ejpam-4855	221	22	∈	∈	PROPN
ejpam-4855	221	23	ψ	ψ	NOUN
ejpam-4855	221	24	}	}	PUNCT
ejpam-4855	221	25	=	=	SYM
ejpam-4855	221	26	∅	∅	NOUN
ejpam-4855	221	27	,	,	PUNCT
ejpam-4855	221	28	then	then	ADV
ejpam-4855	221	29	ψ	ψ	X
ejpam-4855	221	30	has	have	VERB
ejpam-4855	221	31	a	a	DET
ejpam-4855	221	32	smaller	small	ADJ
ejpam-4855	221	33	finite	finite	NOUN
ejpam-4855	221	34	subset	subset	NOUN
ejpam-4855	221	35	,	,	PUNCT
ejpam-4855	221	36	say	say	VERB
ejpam-4855	221	37	ψ0	ψ0	ADV
ejpam-4855	221	38	,	,	PUNCT
ejpam-4855	221	39	with	with	ADP
ejpam-4855	221	40	⋂	⋂	PROPN
ejpam-4855	221	41	{	{	PUNCT
ejpam-4855	221	42	sψ	sψ	PROPN
ejpam-4855	221	43	:	:	PUNCT
ejpam-4855	221	44	ψ	ψ	X
ejpam-4855	221	45	∈	∈	PROPN
ejpam-4855	221	46	ψ0	ψ0	PROPN
ejpam-4855	221	47	}	}	PUNCT
ejpam-4855	221	48	=	=	PUNCT
ejpam-4855	221	49	∅.	∅.	PRON
ejpam-4855	221	50	m.	m.	PROPN
ejpam-4855	221	51	baldado	baldado	PROPN
ejpam-4855	221	52	jr	jr	PROPN
ejpam-4855	221	53	.	.	PROPN
ejpam-4855	221	54	/	/	SYM
ejpam-4855	221	55	eur	eur	PROPN
ejpam-4855	221	56	.	.	PUNCT
ejpam-4855	222	1	j.	j.	PROPN
ejpam-4855	222	2	pure	pure	PROPN
ejpam-4855	222	3	appl	appl	PROPN
ejpam-4855	222	4	.	.	PROPN
ejpam-4855	222	5	math	math	PROPN
ejpam-4855	222	6	,	,	PUNCT
ejpam-4855	222	7	16	16	NUM
ejpam-4855	222	8	(	(	PUNCT
ejpam-4855	222	9	3	3	NUM
ejpam-4855	222	10	)	)	PUNCT
ejpam-4855	222	11	(	(	PUNCT
ejpam-4855	222	12	2023	2023	NUM
ejpam-4855	222	13	)	)	PUNCT
ejpam-4855	222	14	,	,	PUNCT
ejpam-4855	222	15	1809	1809	NUM
ejpam-4855	222	16	-	-	SYM
ejpam-4855	222	17	1816	1816	NUM
ejpam-4855	222	18	1814	1814	NUM
ejpam-4855	222	19	proof	proof	NOUN
ejpam-4855	222	20	.	.	PUNCT
ejpam-4855	223	1	(	(	PUNCT
ejpam-4855	223	2	i	i	NOUN
ejpam-4855	223	3	)	)	PUNCT
ejpam-4855	223	4	implies	imply	VERB
ejpam-4855	223	5	(	(	PUNCT
ejpam-4855	223	6	ii	ii	NOUN
ejpam-4855	223	7	):	):	PUNCT
ejpam-4855	223	8	let	let	VERB
ejpam-4855	223	9	{	{	PUNCT
ejpam-4855	223	10	sψ	sψ	PART
ejpam-4855	223	11	:	:	PUNCT
ejpam-4855	223	12	ψ	ψ	X
ejpam-4855	223	13	∈	∈	PROPN
ejpam-4855	223	14	ψ	ψ	AUX
ejpam-4855	223	15	}	}	PUNCT
ejpam-4855	223	16	be	be	AUX
ejpam-4855	223	17	a	a	DET
ejpam-4855	223	18	class	class	NOUN
ejpam-4855	223	19	of	of	ADP
ejpam-4855	223	20	b∗j	b∗j	PUNCT
ejpam-4855	223	21	-closed	-closed	ADJ
ejpam-4855	223	22	sets	set	NOUN
ejpam-4855	223	23	with	with	ADP
ejpam-4855	223	24	⋂	⋂	PROPN
ejpam-4855	223	25	{	{	PUNCT
ejpam-4855	223	26	sψ	sψ	PROPN
ejpam-4855	223	27	:	:	PUNCT
ejpam-4855	223	28	ψ	ψ	X
ejpam-4855	223	29	∈	∈	PROPN
ejpam-4855	223	30	ψ	ψ	AUX
ejpam-4855	223	31	}	}	PUNCT
ejpam-4855	223	32	=	=	PUNCT
ejpam-4855	223	33	∅.	∅.	NOUN
ejpam-4855	223	34	then	then	ADV
ejpam-4855	223	35	y	y	PROPN
ejpam-4855	223	36	=	=	PUNCT
ejpam-4855	223	37	∅c	∅c	PROPN
ejpam-4855	223	38	=	=	PUNCT
ejpam-4855	223	39	(	(	PUNCT
ejpam-4855	223	40	⋂	⋂	PROPN
ejpam-4855	223	41	{	{	PUNCT
ejpam-4855	223	42	sψ	sψ	PROPN
ejpam-4855	223	43	:	:	PUNCT
ejpam-4855	223	44	ψ	ψ	X
ejpam-4855	223	45	∈	∈	NOUN
ejpam-4855	223	46	ψ})c	ψ})c	NOUN
ejpam-4855	223	47	=	=	SYM
ejpam-4855	223	48	⋃	⋃	NOUN
ejpam-4855	223	49	{	{	PUNCT
ejpam-4855	223	50	scψ	scψ	NOUN
ejpam-4855	223	51	:	:	PUNCT
ejpam-4855	223	52	ψ	ψ	X
ejpam-4855	223	53	∈	∈	PROPN
ejpam-4855	223	54	ψ	ψ	NOUN
ejpam-4855	223	55	}	}	PUNCT
ejpam-4855	223	56	.	.	PUNCT
ejpam-4855	224	1	hence	hence	ADV
ejpam-4855	224	2	,	,	PUNCT
ejpam-4855	224	3	{	{	PUNCT
ejpam-4855	224	4	scψ	scψ	ADV
ejpam-4855	224	5	:	:	PUNCT
ejpam-4855	224	6	ψ	ψ	X
ejpam-4855	224	7	∈	∈	PROPN
ejpam-4855	224	8	ψ	ψ	AUX
ejpam-4855	224	9	}	}	PUNCT
ejpam-4855	224	10	is	be	AUX
ejpam-4855	224	11	a	a	DET
ejpam-4855	224	12	class	class	NOUN
ejpam-4855	224	13	of	of	ADP
ejpam-4855	224	14	b∗j	b∗j	PUNCT
ejpam-4855	224	15	-open	-open	ADJ
ejpam-4855	224	16	sets	set	NOUN
ejpam-4855	224	17	which	which	PRON
ejpam-4855	224	18	covers	cover	VERB
ejpam-4855	224	19	of	of	ADP
ejpam-4855	224	20	y	y	PROPN
ejpam-4855	224	21	.	.	PUNCT
ejpam-4855	225	1	by	by	ADP
ejpam-4855	225	2	assumption	assumption	NOUN
ejpam-4855	225	3	,	,	PUNCT
ejpam-4855	225	4	ψ	ψ	X
ejpam-4855	225	5	has	have	VERB
ejpam-4855	225	6	a	a	DET
ejpam-4855	225	7	smaller	small	ADJ
ejpam-4855	225	8	finite	finite	NOUN
ejpam-4855	225	9	subset	subset	NOUN
ejpam-4855	225	10	,	,	PUNCT
ejpam-4855	225	11	say	say	VERB
ejpam-4855	225	12	ψ0	ψ0	ADV
ejpam-4855	225	13	,	,	PUNCT
ejpam-4855	225	14	with	with	ADP
ejpam-4855	225	15	the	the	DET
ejpam-4855	225	16	property	property	NOUN
ejpam-4855	225	17	⋃	⋃	NOUN
ejpam-4855	225	18	{	{	PUNCT
ejpam-4855	225	19	scψ	scψ	NOUN
ejpam-4855	225	20	:	:	PUNCT
ejpam-4855	225	21	ψ	ψ	X
ejpam-4855	225	22	∈	∈	NOUN
ejpam-4855	225	23	ψ0	ψ0	ADV
ejpam-4855	225	24	}	}	PUNCT
ejpam-4855	225	25	=	=	PUNCT
ejpam-4855	225	26	x.	x.	NOUN
ejpam-4855	225	27	hence	hence	ADV
ejpam-4855	225	28	,	,	PUNCT
ejpam-4855	225	29	(	(	PUNCT
ejpam-4855	225	30	⋂	⋂	PROPN
ejpam-4855	225	31	{	{	PUNCT
ejpam-4855	225	32	sψ	sψ	PROPN
ejpam-4855	225	33	:	:	PUNCT
ejpam-4855	225	34	ψ	ψ	X
ejpam-4855	225	35	∈	∈	PROPN
ejpam-4855	225	36	ψ0	ψ0	PROPN
ejpam-4855	225	37	}	}	PUNCT
ejpam-4855	225	38	=	=	SYM
ejpam-4855	225	39	⋃	⋃	NOUN
ejpam-4855	225	40	{	{	PUNCT
ejpam-4855	225	41	scψ	scψ	NOUN
ejpam-4855	225	42	:	:	PUNCT
ejpam-4855	225	43	ψ	ψ	X
ejpam-4855	225	44	∈	∈	X
ejpam-4855	225	45	ψ0})c	ψ0})c	X
ejpam-4855	225	46	=	=	PUNCT
ejpam-4855	225	47	y	y	PROPN
ejpam-4855	225	48	c	c	NOUN
ejpam-4855	225	49	=	=	PUNCT
ejpam-4855	225	50	∅.	∅.	PROPN
ejpam-4855	225	51	(	(	PUNCT
ejpam-4855	225	52	ii	ii	NOUN
ejpam-4855	225	53	)	)	PUNCT
ejpam-4855	225	54	implies	imply	VERB
ejpam-4855	225	55	(	(	PUNCT
ejpam-4855	225	56	i	i	NOUN
ejpam-4855	225	57	):	):	PUNCT
ejpam-4855	225	58	let	let	VERB
ejpam-4855	225	59	{	{	PUNCT
ejpam-4855	225	60	pψ	pψ	NOUN
ejpam-4855	225	61	:	:	PUNCT
ejpam-4855	225	62	ψ	ψ	X
ejpam-4855	225	63	∈	∈	PROPN
ejpam-4855	225	64	ψ	ψ	AUX
ejpam-4855	225	65	}	}	PUNCT
ejpam-4855	225	66	be	be	AUX
ejpam-4855	225	67	a	a	DET
ejpam-4855	225	68	b∗j	b∗j	PUNCT
ejpam-4855	225	69	-open	-open	ADJ
ejpam-4855	225	70	covering	covering	NOUN
ejpam-4855	225	71	of	of	ADP
ejpam-4855	225	72	y	y	PROPN
ejpam-4855	225	73	,	,	PUNCT
ejpam-4855	226	1	i.e.	i.e.	X
ejpam-4855	226	2	⋃	⋃	PUNCT
ejpam-4855	226	3	{	{	PUNCT
ejpam-4855	226	4	pψ	pψ	NOUN
ejpam-4855	226	5	:	:	PUNCT
ejpam-4855	226	6	ψ	ψ	X
ejpam-4855	226	7	∈	∈	PROPN
ejpam-4855	226	8	ψ	ψ	NOUN
ejpam-4855	226	9	}	}	PUNCT
ejpam-4855	226	10	=	=	SYM
ejpam-4855	226	11	y	y	PROPN
ejpam-4855	226	12	.	.	PUNCT
ejpam-4855	227	1	then	then	ADV
ejpam-4855	227	2	⋂	⋂	PROPN
ejpam-4855	227	3	{	{	PUNCT
ejpam-4855	227	4	pcψ	pcψ	NOUN
ejpam-4855	227	5	:	:	PUNCT
ejpam-4855	227	6	ψ	ψ	X
ejpam-4855	227	7	∈	∈	PROPN
ejpam-4855	227	8	ψ	ψ	AUX
ejpam-4855	227	9	}	}	PUNCT
ejpam-4855	227	10	=	=	SYM
ejpam-4855	227	11	(	(	PUNCT
ejpam-4855	227	12	⋃	⋃	X
ejpam-4855	227	13	{	{	PUNCT
ejpam-4855	227	14	pψ	pψ	NOUN
ejpam-4855	227	15	:	:	PUNCT
ejpam-4855	227	16	ψ	ψ	X
ejpam-4855	227	17	∈	∈	PROPN
ejpam-4855	227	18	ψ})c	ψ})c	NOUN
ejpam-4855	227	19	=	=	PUNCT
ejpam-4855	227	20	∅.	∅.	NOUN
ejpam-4855	227	21	note	note	NOUN
ejpam-4855	227	22	that	that	SCONJ
ejpam-4855	227	23	pc	pc	NOUN
ejpam-4855	227	24	is	be	AUX
ejpam-4855	227	25	b∗j	b∗j	PUNCT
ejpam-4855	227	26	-close	-close	ADJ
ejpam-4855	227	27	since	since	SCONJ
ejpam-4855	227	28	p	p	NOUN
ejpam-4855	227	29	is	be	AUX
ejpam-4855	227	30	b∗j	b∗j	PUNCT
ejpam-4855	227	31	-open	-open	ADJ
ejpam-4855	227	32	.	.	PUNCT
ejpam-4855	228	1	by	by	ADP
ejpam-4855	228	2	assumption	assumption	NOUN
ejpam-4855	228	3	,	,	PUNCT
ejpam-4855	228	4	ψ	ψ	X
ejpam-4855	228	5	has	have	VERB
ejpam-4855	228	6	a	a	DET
ejpam-4855	228	7	smaller	small	ADJ
ejpam-4855	228	8	finite	finite	NOUN
ejpam-4855	228	9	subset	subset	NOUN
ejpam-4855	228	10	,	,	PUNCT
ejpam-4855	228	11	say	say	VERB
ejpam-4855	228	12	ψ0	ψ0	ADV
ejpam-4855	228	13	,	,	PUNCT
ejpam-4855	228	14	with	with	ADP
ejpam-4855	228	15	the	the	DET
ejpam-4855	228	16	property	property	NOUN
ejpam-4855	228	17	that⋂	that⋂	PRON
ejpam-4855	228	18	{	{	PUNCT
ejpam-4855	228	19	pcψ	pcψ	NOUN
ejpam-4855	228	20	:	:	PUNCT
ejpam-4855	228	21	ψ	ψ	X
ejpam-4855	228	22	∈	∈	PROPN
ejpam-4855	228	23	ψ0	ψ0	ADV
ejpam-4855	228	24	}	}	PUNCT
ejpam-4855	228	25	=	=	SYM
ejpam-4855	228	26	∅.	∅.	NOUN
ejpam-4855	228	27	note	note	VERB
ejpam-4855	228	28	that	that	SCONJ
ejpam-4855	228	29	⋃	⋃	ADV
ejpam-4855	228	30	{	{	PUNCT
ejpam-4855	228	31	pψ	pψ	NOUN
ejpam-4855	228	32	:	:	PUNCT
ejpam-4855	228	33	ψ	ψ	X
ejpam-4855	228	34	∈	∈	PROPN
ejpam-4855	228	35	ψ0	ψ0	ADV
ejpam-4855	228	36	}	}	PUNCT
ejpam-4855	228	37	=	=	SYM
ejpam-4855	228	38	(	(	PUNCT
ejpam-4855	228	39	⋂	⋂	PROPN
ejpam-4855	228	40	{	{	PUNCT
ejpam-4855	228	41	pcψ	pcψ	NOUN
ejpam-4855	228	42	:	:	PUNCT
ejpam-4855	228	43	ψ	ψ	X
ejpam-4855	228	44	∈	∈	X
ejpam-4855	228	45	ψ0})c	ψ0})c	PROPN
ejpam-4855	228	46	=	=	SYM
ejpam-4855	228	47	y	y	PROPN
ejpam-4855	228	48	.	.	PUNCT
ejpam-4855	229	1	hence	hence	ADV
ejpam-4855	229	2	,	,	PUNCT
ejpam-4855	229	3	{	{	PUNCT
ejpam-4855	229	4	pψ	pψ	INTJ
ejpam-4855	229	5	:	:	PUNCT
ejpam-4855	229	6	ψ	ψ	X
ejpam-4855	229	7	∈	∈	PROPN
ejpam-4855	229	8	ψ0	ψ0	PROPN
ejpam-4855	229	9	}	}	PUNCT
ejpam-4855	229	10	is	be	AUX
ejpam-4855	229	11	a	a	DET
ejpam-4855	229	12	class	class	NOUN
ejpam-4855	229	13	of	of	ADP
ejpam-4855	229	14	b∗j	b∗j	PUNCT
ejpam-4855	229	15	-open	-open	ADJ
ejpam-4855	229	16	sets	set	NOUN
ejpam-4855	229	17	that	that	PRON
ejpam-4855	229	18	covers	cover	VERB
ejpam-4855	229	19	y	y	PRON
ejpam-4855	229	20	.	.	PUNCT
ejpam-4855	230	1	another	another	DET
ejpam-4855	230	2	characterization	characterization	NOUN
ejpam-4855	230	3	of	of	ADP
ejpam-4855	230	4	cb∗j	cb∗j	NOUN
ejpam-4855	230	5	-compact	-compact	ADJ
ejpam-4855	230	6	topological	topological	ADJ
ejpam-4855	230	7	spaces	space	NOUN
ejpam-4855	230	8	is	be	AUX
ejpam-4855	230	9	presented	present	VERB
ejpam-4855	230	10	in	in	ADP
ejpam-4855	230	11	theorem	theorem	ADJ
ejpam-4855	230	12	3	3	NUM
ejpam-4855	230	13	.	.	PUNCT
ejpam-4855	230	14	theorem	theorem	NOUN
ejpam-4855	230	15	3	3	X
ejpam-4855	230	16	.	.	PUNCT
ejpam-4855	231	1	let	let	AUX
ejpam-4855	231	2	(	(	PUNCT
ejpam-4855	231	3	y	y	NOUN
ejpam-4855	231	4	,	,	PUNCT
ejpam-4855	231	5	ς	ς	PROPN
ejpam-4855	231	6	,	,	PUNCT
ejpam-4855	231	7	j	j	NOUN
ejpam-4855	231	8	)	)	PUNCT
ejpam-4855	231	9	be	be	VERB
ejpam-4855	231	10	an	an	DET
ejpam-4855	231	11	ideal	ideal	ADJ
ejpam-4855	231	12	topological	topological	ADJ
ejpam-4855	231	13	space	space	NOUN
ejpam-4855	231	14	.	.	PUNCT
ejpam-4855	232	1	then	then	ADV
ejpam-4855	232	2	(	(	PUNCT
ejpam-4855	232	3	i	i	NOUN
ejpam-4855	232	4	)	)	PUNCT
ejpam-4855	232	5	is	be	AUX
ejpam-4855	232	6	a	a	DET
ejpam-4855	232	7	necessary	necessary	ADJ
ejpam-4855	232	8	and	and	CCONJ
ejpam-4855	232	9	sufficient	sufficient	ADJ
ejpam-4855	232	10	condition	condition	NOUN
ejpam-4855	232	11	for	for	ADP
ejpam-4855	232	12	statement	statement	NOUN
ejpam-4855	232	13	(	(	PUNCT
ejpam-4855	232	14	ii	ii	NOUN
ejpam-4855	232	15	)	)	PUNCT
ejpam-4855	232	16	.	.	PUNCT
ejpam-4855	233	1	i.	i.	PROPN
ejpam-4855	233	2	(	(	PUNCT
ejpam-4855	233	3	y	y	PROPN
ejpam-4855	233	4	,	,	PUNCT
ejpam-4855	233	5	ς	ς	PROPN
ejpam-4855	233	6	,	,	PUNCT
ejpam-4855	233	7	j	j	NOUN
ejpam-4855	233	8	)	)	PUNCT
ejpam-4855	233	9	is	be	AUX
ejpam-4855	233	10	cb∗j	cb∗j	PROPN
ejpam-4855	233	11	-compact	-compact	NOUN
ejpam-4855	233	12	.	.	PUNCT
ejpam-4855	234	1	ii	ii	PROPN
ejpam-4855	234	2	.	.	PUNCT
ejpam-4855	235	1	if	if	SCONJ
ejpam-4855	235	2	{	{	PUNCT
ejpam-4855	235	3	sψ	sψ	NOUN
ejpam-4855	235	4	:	:	PUNCT
ejpam-4855	235	5	ψ	ψ	X
ejpam-4855	235	6	∈	∈	PROPN
ejpam-4855	235	7	ψ	ψ	AUX
ejpam-4855	235	8	}	}	PUNCT
ejpam-4855	235	9	is	be	AUX
ejpam-4855	235	10	a	a	DET
ejpam-4855	235	11	class	class	NOUN
ejpam-4855	235	12	of	of	ADP
ejpam-4855	235	13	b∗j	b∗j	PUNCT
ejpam-4855	235	14	-closed	-closed	ADJ
ejpam-4855	235	15	sets	set	NOUN
ejpam-4855	235	16	with	with	ADP
ejpam-4855	235	17	⋂	⋂	PROPN
ejpam-4855	235	18	{	{	PUNCT
ejpam-4855	235	19	sψ	sψ	PROPN
ejpam-4855	235	20	:	:	PUNCT
ejpam-4855	235	21	ψ	ψ	X
ejpam-4855	235	22	∈	∈	PROPN
ejpam-4855	235	23	ψ	ψ	NOUN
ejpam-4855	235	24	}	}	PUNCT
ejpam-4855	235	25	=	=	SYM
ejpam-4855	235	26	∅	∅	NOUN
ejpam-4855	235	27	,	,	PUNCT
ejpam-4855	235	28	then	then	ADV
ejpam-4855	235	29	ψ	ψ	X
ejpam-4855	235	30	has	have	VERB
ejpam-4855	235	31	a	a	DET
ejpam-4855	235	32	smaller	small	ADJ
ejpam-4855	235	33	finite	finite	NOUN
ejpam-4855	235	34	subset	subset	NOUN
ejpam-4855	235	35	,	,	PUNCT
ejpam-4855	235	36	say	say	VERB
ejpam-4855	235	37	λ0	λ0	NOUN
ejpam-4855	235	38	,	,	PUNCT
ejpam-4855	235	39	with	with	ADP
ejpam-4855	235	40	the	the	DET
ejpam-4855	235	41	property	property	NOUN
ejpam-4855	235	42	that	that	PRON
ejpam-4855	235	43	⋂	⋂	PROPN
ejpam-4855	235	44	{	{	PUNCT
ejpam-4855	235	45	fλ	fλ	INTJ
ejpam-4855	235	46	:	:	PUNCT
ejpam-4855	235	47	λ	λ	PROPN
ejpam-4855	235	48	∈	∈	NOUN
ejpam-4855	235	49	λ0	λ0	NOUN
ejpam-4855	235	50	}	}	PUNCT
ejpam-4855	235	51	∈	∈	PROPN
ejpam-4855	235	52	i.	i.	NOUN
ejpam-4855	235	53	proof	proof	NOUN
ejpam-4855	235	54	.	.	PUNCT
ejpam-4855	236	1	(	(	PUNCT
ejpam-4855	236	2	i	i	NOUN
ejpam-4855	236	3	)	)	PUNCT
ejpam-4855	236	4	implies	imply	VERB
ejpam-4855	236	5	(	(	PUNCT
ejpam-4855	236	6	ii	ii	NOUN
ejpam-4855	236	7	):	):	PUNCT
ejpam-4855	236	8	let	let	VERB
ejpam-4855	236	9	{	{	PUNCT
ejpam-4855	236	10	sψ	sψ	PART
ejpam-4855	236	11	:	:	PUNCT
ejpam-4855	236	12	ψ	ψ	X
ejpam-4855	236	13	∈	∈	PROPN
ejpam-4855	236	14	ψ	ψ	AUX
ejpam-4855	236	15	}	}	PUNCT
ejpam-4855	236	16	be	be	AUX
ejpam-4855	236	17	a	a	DET
ejpam-4855	236	18	class	class	NOUN
ejpam-4855	236	19	of	of	ADP
ejpam-4855	236	20	b∗j	b∗j	PUNCT
ejpam-4855	236	21	-closed	-closed	ADJ
ejpam-4855	236	22	sets	set	NOUN
ejpam-4855	236	23	such	such	ADJ
ejpam-4855	236	24	that⋂	that⋂	X
ejpam-4855	236	25	{	{	PUNCT
ejpam-4855	236	26	sψ	sψ	NOUN
ejpam-4855	236	27	:	:	PUNCT
ejpam-4855	236	28	ψ	ψ	X
ejpam-4855	236	29	∈	∈	PROPN
ejpam-4855	236	30	ψ	ψ	AUX
ejpam-4855	236	31	}	}	PUNCT
ejpam-4855	236	32	=	=	SYM
ejpam-4855	236	33	∅.	∅.	NOUN
ejpam-4855	236	34	note	note	VERB
ejpam-4855	236	35	that	that	SCONJ
ejpam-4855	236	36	⋃	⋃	ADV
ejpam-4855	236	37	{	{	PUNCT
ejpam-4855	236	38	scψ	scψ	NOUN
ejpam-4855	236	39	:	:	PUNCT
ejpam-4855	236	40	ψ	ψ	X
ejpam-4855	236	41	∈	∈	PROPN
ejpam-4855	236	42	ψ	ψ	AUX
ejpam-4855	236	43	}	}	PUNCT
ejpam-4855	236	44	=	=	SYM
ejpam-4855	236	45	(	(	PUNCT
ejpam-4855	236	46	⋂	⋂	PROPN
ejpam-4855	236	47	{	{	PUNCT
ejpam-4855	236	48	sψ	sψ	PROPN
ejpam-4855	236	49	:	:	PUNCT
ejpam-4855	236	50	ψ	ψ	X
ejpam-4855	236	51	∈	∈	NOUN
ejpam-4855	236	52	ψ})c	ψ})c	NOUN
ejpam-4855	236	53	=	=	SYM
ejpam-4855	236	54	y	y	PROPN
ejpam-4855	236	55	.	.	PUNCT
ejpam-4855	237	1	hence	hence	ADV
ejpam-4855	237	2	,	,	PUNCT
ejpam-4855	237	3	{	{	PUNCT
ejpam-4855	237	4	scψ	scψ	ADV
ejpam-4855	237	5	:	:	PUNCT
ejpam-4855	237	6	ψ	ψ	X
ejpam-4855	237	7	∈	∈	PROPN
ejpam-4855	237	8	ψ	ψ	AUX
ejpam-4855	237	9	}	}	PUNCT
ejpam-4855	237	10	is	be	AUX
ejpam-4855	237	11	a	a	DET
ejpam-4855	237	12	class	class	NOUN
ejpam-4855	237	13	of	of	ADP
ejpam-4855	237	14	b∗j	b∗j	PUNCT
ejpam-4855	237	15	-open	-open	ADJ
ejpam-4855	237	16	sets	set	NOUN
ejpam-4855	237	17	covering	cover	VERB
ejpam-4855	237	18	y	y	PRON
ejpam-4855	237	19	.	.	PUNCT
ejpam-4855	238	1	by	by	ADP
ejpam-4855	238	2	assumption	assumption	NOUN
ejpam-4855	238	3	,	,	PUNCT
ejpam-4855	238	4	ψ	ψ	X
ejpam-4855	238	5	has	have	VERB
ejpam-4855	238	6	a	a	DET
ejpam-4855	238	7	finite	finite	NOUN
ejpam-4855	238	8	subset	subset	NOUN
ejpam-4855	238	9	,	,	PUNCT
ejpam-4855	238	10	say	say	VERB
ejpam-4855	238	11	ψ0	ψ0	ADV
ejpam-4855	238	12	,	,	PUNCT
ejpam-4855	238	13	with	with	ADP
ejpam-4855	238	14	y	y	PROPN
ejpam-4855	238	15	−	−	PROPN
ejpam-4855	238	16	⋃	⋃	PROPN
ejpam-4855	238	17	{	{	PUNCT
ejpam-4855	238	18	scλ	scλ	NOUN
ejpam-4855	238	19	:	:	PUNCT
ejpam-4855	238	20	ψ	ψ	X
ejpam-4855	238	21	∈	∈	PROPN
ejpam-4855	238	22	ψ0	ψ0	PROPN
ejpam-4855	238	23	}	}	PUNCT
ejpam-4855	238	24	∈	∈	PROPN
ejpam-4855	238	25	j	j	PROPN
ejpam-4855	238	26	,	,	PUNCT
ejpam-4855	238	27	i.e.	i.e.	X
ejpam-4855	238	28	⋂	⋂	PROPN
ejpam-4855	238	29	{	{	PUNCT
ejpam-4855	238	30	sψ	sψ	PROPN
ejpam-4855	238	31	:	:	PUNCT
ejpam-4855	238	32	ψ	ψ	X
ejpam-4855	238	33	∈	∈	PROPN
ejpam-4855	238	34	ψ0	ψ0	PROPN
ejpam-4855	238	35	}	}	PUNCT
ejpam-4855	238	36	∈	∈	PROPN
ejpam-4855	238	37	j	j	PROPN
ejpam-4855	238	38	.	.	PUNCT
ejpam-4855	239	1	(	(	PUNCT
ejpam-4855	239	2	ii	ii	NOUN
ejpam-4855	239	3	)	)	PUNCT
ejpam-4855	239	4	implies	imply	VERB
ejpam-4855	239	5	(	(	PUNCT
ejpam-4855	239	6	i	i	NOUN
ejpam-4855	239	7	):	):	PUNCT
ejpam-4855	239	8	let	let	VERB
ejpam-4855	239	9	{	{	PUNCT
ejpam-4855	239	10	pψ	pψ	NOUN
ejpam-4855	239	11	:	:	PUNCT
ejpam-4855	239	12	ψ	ψ	X
ejpam-4855	239	13	∈	∈	PROPN
ejpam-4855	239	14	ψ	ψ	AUX
ejpam-4855	239	15	}	}	PUNCT
ejpam-4855	239	16	be	be	AUX
ejpam-4855	239	17	a	a	DET
ejpam-4855	239	18	b∗j	b∗j	PUNCT
ejpam-4855	239	19	-open	-open	ADJ
ejpam-4855	239	20	covering	covering	NOUN
ejpam-4855	239	21	of	of	ADP
ejpam-4855	239	22	y	y	PROPN
ejpam-4855	239	23	,	,	PUNCT
ejpam-4855	239	24	i.e.	i.e.	X
ejpam-4855	239	25	⋃	⋃	PUNCT
ejpam-4855	239	26	{	{	PUNCT
ejpam-4855	239	27	pψ	pψ	NOUN
ejpam-4855	239	28	:	:	PUNCT
ejpam-4855	239	29	ψ	ψ	X
ejpam-4855	239	30	∈	∈	PROPN
ejpam-4855	239	31	ψ	ψ	NOUN
ejpam-4855	239	32	}	}	PUNCT
ejpam-4855	239	33	=	=	SYM
ejpam-4855	239	34	y	y	PROPN
ejpam-4855	239	35	.	.	PUNCT
ejpam-4855	240	1	note	note	VERB
ejpam-4855	240	2	that	that	SCONJ
ejpam-4855	240	3	⋂	⋂	PROPN
ejpam-4855	240	4	{	{	PUNCT
ejpam-4855	240	5	pcψ	pcψ	NOUN
ejpam-4855	240	6	:	:	PUNCT
ejpam-4855	240	7	ψ	ψ	X
ejpam-4855	240	8	∈	∈	PROPN
ejpam-4855	240	9	ψ	ψ	AUX
ejpam-4855	240	10	}	}	PUNCT
ejpam-4855	240	11	=	=	SYM
ejpam-4855	240	12	(	(	PUNCT
ejpam-4855	240	13	⋃	⋃	X
ejpam-4855	240	14	{	{	PUNCT
ejpam-4855	240	15	pψ	pψ	NOUN
ejpam-4855	240	16	:	:	PUNCT
ejpam-4855	240	17	ψ	ψ	X
ejpam-4855	240	18	∈	∈	NOUN
ejpam-4855	240	19	ψ})c	ψ})c	NOUN
ejpam-4855	240	20	=	=	PUNCT
ejpam-4855	240	21	∅.	∅.	NOUN
ejpam-4855	240	22	by	by	ADP
ejpam-4855	240	23	assumption	assumption	NOUN
ejpam-4855	240	24	,	,	PUNCT
ejpam-4855	240	25	ψ	ψ	X
ejpam-4855	240	26	has	have	VERB
ejpam-4855	240	27	a	a	DET
ejpam-4855	240	28	smaller	small	ADJ
ejpam-4855	240	29	finite	finite	NOUN
ejpam-4855	240	30	subset	subset	NOUN
ejpam-4855	240	31	,	,	PUNCT
ejpam-4855	240	32	say	say	VERB
ejpam-4855	240	33	ψ0	ψ0	ADV
ejpam-4855	240	34	,	,	PUNCT
ejpam-4855	240	35	with	with	ADP
ejpam-4855	240	36	⋂	⋂	PROPN
ejpam-4855	240	37	{	{	PUNCT
ejpam-4855	240	38	pcψ	pcψ	NOUN
ejpam-4855	240	39	:	:	PUNCT
ejpam-4855	240	40	ψ	ψ	X
ejpam-4855	240	41	∈	∈	PROPN
ejpam-4855	240	42	ψ0	ψ0	PROPN
ejpam-4855	240	43	}	}	PUNCT
ejpam-4855	240	44	∈	∈	PROPN
ejpam-4855	240	45	j	j	PROPN
ejpam-4855	240	46	,	,	PUNCT
ejpam-4855	240	47	i.e.	i.e.	X
ejpam-4855	240	48	y	y	NOUN
ejpam-4855	241	1	−	−	PROPN
ejpam-4855	241	2	⋃	⋃	PROPN
ejpam-4855	241	3	{	{	PUNCT
ejpam-4855	241	4	pψ	pψ	NOUN
ejpam-4855	241	5	:	:	PUNCT
ejpam-4855	241	6	ψ	ψ	X
ejpam-4855	241	7	∈	∈	PROPN
ejpam-4855	241	8	ψ0	ψ0	PROPN
ejpam-4855	241	9	}	}	PUNCT
ejpam-4855	241	10	∈	∈	PROPN
ejpam-4855	241	11	j	j	PROPN
ejpam-4855	241	12	.	.	PUNCT
ejpam-4855	242	1	remark	remark	PROPN
ejpam-4855	242	2	1	1	NUM
ejpam-4855	242	3	.	.	PUNCT
ejpam-4855	243	1	[	[	X
ejpam-4855	243	2	11	11	NUM
ejpam-4855	243	3	]	]	X
ejpam-4855	243	4	let	let	VERB
ejpam-4855	243	5	(	(	PUNCT
ejpam-4855	243	6	y	y	NOUN
ejpam-4855	243	7	,	,	PUNCT
ejpam-4855	243	8	ς	ς	PROPN
ejpam-4855	243	9	,	,	PUNCT
ejpam-4855	243	10	j	j	PROPN
ejpam-4855	243	11	)	)	PUNCT
ejpam-4855	243	12	and	and	CCONJ
ejpam-4855	243	13	(	(	PUNCT
ejpam-4855	243	14	w	w	PROPN
ejpam-4855	243	15	,	,	PUNCT
ejpam-4855	243	16	ξ	ξ	PROPN
ejpam-4855	243	17	,	,	PUNCT
ejpam-4855	243	18	k	k	NOUN
ejpam-4855	243	19	)	)	PUNCT
ejpam-4855	243	20	be	be	AUX
ejpam-4855	243	21	ideal	ideal	ADJ
ejpam-4855	243	22	topological	topological	ADJ
ejpam-4855	243	23	spaces	space	NOUN
ejpam-4855	243	24	,	,	PUNCT
ejpam-4855	243	25	and	and	CCONJ
ejpam-4855	244	1	ζ	ζ	NOUN
ejpam-4855	244	2	:	:	PUNCT
ejpam-4855	244	3	y	y	PROPN
ejpam-4855	244	4	→w	→w	PROPN
ejpam-4855	244	5	be	be	AUX
ejpam-4855	244	6	a	a	DET
ejpam-4855	244	7	mapping	mapping	NOUN
ejpam-4855	244	8	.	.	PUNCT
ejpam-4855	245	1	then	then	ADV
ejpam-4855	245	2	:	:	PUNCT
ejpam-4855	245	3	i.	i.	NOUN
ejpam-4855	245	4	ζ(j	ζ(j	PROPN
ejpam-4855	245	5	)	)	PUNCT
ejpam-4855	245	6	=	=	PRON
ejpam-4855	245	7	{	{	PUNCT
ejpam-4855	245	8	ζ(b	ζ(b	PROPN
ejpam-4855	245	9	)	)	PUNCT
ejpam-4855	245	10	:	:	PUNCT
ejpam-4855	246	1	b	b	X
ejpam-4855	246	2	∈	∈	PROPN
ejpam-4855	246	3	j	j	PROPN
ejpam-4855	246	4	}	}	PUNCT
ejpam-4855	246	5	is	be	AUX
ejpam-4855	246	6	an	an	DET
ejpam-4855	246	7	ideal	ideal	NOUN
ejpam-4855	246	8	in	in	ADP
ejpam-4855	246	9	w	w	PROPN
ejpam-4855	246	10	;	;	PUNCT
ejpam-4855	246	11	and	and	CCONJ
ejpam-4855	246	12	,	,	PUNCT
ejpam-4855	246	13	i.	i.	NOUN
ejpam-4855	246	14	if	if	SCONJ
ejpam-4855	246	15	ζ	ζ	NOUN
ejpam-4855	246	16	is	be	AUX
ejpam-4855	246	17	a	a	DET
ejpam-4855	246	18	one	one	NUM
ejpam-4855	246	19	to	to	ADP
ejpam-4855	246	20	one	one	NUM
ejpam-4855	246	21	correspondence	correspondence	NOUN
ejpam-4855	246	22	,	,	PUNCT
ejpam-4855	246	23	then	then	ADV
ejpam-4855	246	24	ζ−1(k	ζ−1(k	PROPN
ejpam-4855	246	25	)	)	PUNCT
ejpam-4855	247	1	=	=	SYM
ejpam-4855	247	2	{	{	PUNCT
ejpam-4855	247	3	ζ−1(d	ζ−1(d	PROPN
ejpam-4855	247	4	)	)	PUNCT
ejpam-4855	247	5	:	:	PUNCT
ejpam-4855	248	1	d	d	X
ejpam-4855	248	2	∈	∈	PROPN
ejpam-4855	248	3	k	k	X
ejpam-4855	248	4	}	}	PUNCT
ejpam-4855	248	5	is	be	AUX
ejpam-4855	248	6	an	an	DET
ejpam-4855	248	7	ideal	ideal	NOUN
ejpam-4855	248	8	in	in	ADP
ejpam-4855	248	9	y	y	PROPN
ejpam-4855	248	10	.	.	PUNCT
ejpam-4855	249	1	definition	definition	NOUN
ejpam-4855	249	2	1	1	NUM
ejpam-4855	249	3	.	.	PUNCT
ejpam-4855	250	1	let	let	VERB
ejpam-4855	250	2	(	(	PUNCT
ejpam-4855	250	3	y	y	NOUN
ejpam-4855	250	4	,	,	PUNCT
ejpam-4855	250	5	ς	ς	PROPN
ejpam-4855	250	6	,	,	PUNCT
ejpam-4855	250	7	j	j	PROPN
ejpam-4855	250	8	)	)	PUNCT
ejpam-4855	250	9	and	and	CCONJ
ejpam-4855	250	10	(	(	PUNCT
ejpam-4855	250	11	w	w	PROPN
ejpam-4855	250	12	,	,	PUNCT
ejpam-4855	250	13	ξ	ξ	PROPN
ejpam-4855	250	14	,	,	PUNCT
ejpam-4855	250	15	k	k	NOUN
ejpam-4855	250	16	)	)	PUNCT
ejpam-4855	250	17	be	be	AUX
ejpam-4855	250	18	ideal	ideal	ADJ
ejpam-4855	250	19	spaces	space	NOUN
ejpam-4855	250	20	.	.	PUNCT
ejpam-4855	251	1	a	a	DET
ejpam-4855	251	2	mapping	mapping	NOUN
ejpam-4855	251	3	ζ	ζ	NOUN
ejpam-4855	251	4	:	:	PUNCT
ejpam-4855	251	5	y	y	PROPN
ejpam-4855	251	6	→w	→w	PROPN
ejpam-4855	251	7	is	be	AUX
ejpam-4855	251	8	i.	i.	NOUN
ejpam-4855	251	9	b∗j	b∗j	PUNCT
ejpam-4855	251	10	-open	-open	VERB
ejpam-4855	251	11	if	if	SCONJ
ejpam-4855	251	12	ζ(b	ζ(b	NOUN
ejpam-4855	251	13	)	)	PUNCT
ejpam-4855	251	14	is	be	AUX
ejpam-4855	251	15	b∗k	b∗k	NOUN
ejpam-4855	251	16	-	-	PUNCT
ejpam-4855	251	17	open	open	ADJ
ejpam-4855	251	18	for	for	ADP
ejpam-4855	251	19	every	every	DET
ejpam-4855	251	20	b∗j	b∗j	PUNCT
ejpam-4855	251	21	-open	-open	ADJ
ejpam-4855	251	22	set	set	ADJ
ejpam-4855	251	23	b	b	NOUN
ejpam-4855	251	24	in	in	ADP
ejpam-4855	251	25	y	y	PROPN
ejpam-4855	251	26	,	,	PUNCT
ejpam-4855	251	27	and	and	CCONJ
ejpam-4855	251	28	ii	ii	X
ejpam-4855	251	29	.	.	PUNCT
ejpam-4855	252	1	b∗j	b∗j	VERB
ejpam-4855	252	2	-irresolute	-irresolute	ADJ
ejpam-4855	252	3	if	if	SCONJ
ejpam-4855	252	4	ζ−1(d	ζ−1(d	PROPN
ejpam-4855	252	5	)	)	PUNCT
ejpam-4855	252	6	is	be	AUX
ejpam-4855	252	7	b∗j	b∗j	VERB
ejpam-4855	252	8	-open	-open	ADJ
ejpam-4855	252	9	for	for	ADP
ejpam-4855	252	10	each	each	DET
ejpam-4855	252	11	b∗k	b∗k	NOUN
ejpam-4855	252	12	-	-	PUNCT
ejpam-4855	252	13	open	open	ADJ
ejpam-4855	252	14	set	set	NOUN
ejpam-4855	252	15	d	d	PROPN
ejpam-4855	252	16	in	in	ADP
ejpam-4855	252	17	w	w	PROPN
ejpam-4855	252	18	.	.	PUNCT
ejpam-4855	253	1	if	if	SCONJ
ejpam-4855	253	2	the	the	DET
ejpam-4855	253	3	domain	domain	NOUN
ejpam-4855	253	4	of	of	ADP
ejpam-4855	253	5	a	a	DET
ejpam-4855	253	6	b∗-irresolute	b∗-irresolute	NOUN
ejpam-4855	253	7	map	map	NOUN
ejpam-4855	253	8	is	be	AUX
ejpam-4855	253	9	cb∗j	cb∗j	NOUN
ejpam-4855	253	10	-compact	-compact	NOUN
ejpam-4855	253	11	with	with	ADP
ejpam-4855	253	12	respect	respect	NOUN
ejpam-4855	253	13	to	to	ADP
ejpam-4855	253	14	an	an	DET
ejpam-4855	253	15	ideal	ideal	NOUN
ejpam-4855	253	16	,	,	PUNCT
ejpam-4855	253	17	then	then	ADV
ejpam-4855	253	18	so	so	ADV
ejpam-4855	253	19	is	be	AUX
ejpam-4855	253	20	the	the	DET
ejpam-4855	253	21	image	image	NOUN
ejpam-4855	253	22	.	.	PUNCT
ejpam-4855	254	1	we	we	PRON
ejpam-4855	254	2	show	show	VERB
ejpam-4855	254	3	this	this	DET
ejpam-4855	254	4	idea	idea	NOUN
ejpam-4855	254	5	in	in	ADP
ejpam-4855	254	6	theorem	theorem	ADJ
ejpam-4855	254	7	4	4	NUM
ejpam-4855	254	8	.	.	PUNCT
ejpam-4855	254	9	references	reference	NOUN
ejpam-4855	254	10	1815	1815	NUM
ejpam-4855	254	11	theorem	theorem	VERB
ejpam-4855	254	12	4	4	NUM
ejpam-4855	254	13	.	.	PUNCT
ejpam-4855	255	1	let	let	AUX
ejpam-4855	255	2	(	(	PUNCT
ejpam-4855	255	3	y	y	NOUN
ejpam-4855	255	4	,	,	PUNCT
ejpam-4855	255	5	ς	ς	PROPN
ejpam-4855	255	6	,	,	PUNCT
ejpam-4855	255	7	j	j	PROPN
ejpam-4855	255	8	)	)	PUNCT
ejpam-4855	255	9	and	and	CCONJ
ejpam-4855	255	10	(	(	PUNCT
ejpam-4855	255	11	w	w	PROPN
ejpam-4855	255	12	,	,	PUNCT
ejpam-4855	255	13	ξ	ξ	PROPN
ejpam-4855	255	14	,	,	PUNCT
ejpam-4855	255	15	k	k	NOUN
ejpam-4855	255	16	)	)	PUNCT
ejpam-4855	255	17	be	be	AUX
ejpam-4855	255	18	ideal	ideal	ADJ
ejpam-4855	255	19	spaces	space	NOUN
ejpam-4855	255	20	,	,	PUNCT
ejpam-4855	255	21	and	and	CCONJ
ejpam-4855	255	22	ζ	ζ	NOUN
ejpam-4855	255	23	:	:	PUNCT
ejpam-4855	255	24	y	y	PROPN
ejpam-4855	255	25	→w	→w	PUNCT
ejpam-4855	255	26	be	be	AUX
ejpam-4855	255	27	a	a	DET
ejpam-4855	255	28	b∗j	b∗j	ADJ
ejpam-4855	255	29	-irresolute	-irresolute	ADJ
ejpam-4855	255	30	function	function	NOUN
ejpam-4855	255	31	with	with	ADP
ejpam-4855	255	32	ζ(j	ζ(j	NUM
ejpam-4855	255	33	)	)	PUNCT
ejpam-4855	256	1	=	=	VERB
ejpam-4855	256	2	k.	k.	NOUN
ejpam-4855	257	1	if	if	SCONJ
ejpam-4855	257	2	y	y	PROPN
ejpam-4855	257	3	is	be	AUX
ejpam-4855	257	4	a	a	DET
ejpam-4855	257	5	cb∗j	cb∗j	PROPN
ejpam-4855	257	6	-compact	-compact	NOUN
ejpam-4855	257	7	,	,	PUNCT
ejpam-4855	257	8	then	then	ADV
ejpam-4855	257	9	ζ(y	ζ(y	PROPN
ejpam-4855	257	10	)	)	PUNCT
ejpam-4855	257	11	is	be	AUX
ejpam-4855	257	12	cb∗k	cb∗k	NOUN
ejpam-4855	257	13	-	-	PUNCT
ejpam-4855	257	14	compact	compact	ADJ
ejpam-4855	257	15	.	.	PUNCT
ejpam-4855	258	1	proof	proof	NOUN
ejpam-4855	258	2	.	.	PUNCT
ejpam-4855	259	1	let	let	VERB
ejpam-4855	259	2	{	{	PUNCT
ejpam-4855	259	3	pψ	pψ	VERB
ejpam-4855	259	4	:	:	PUNCT
ejpam-4855	259	5	ψ	ψ	X
ejpam-4855	259	6	∈	∈	PROPN
ejpam-4855	259	7	ψ	ψ	AUX
ejpam-4855	259	8	}	}	PUNCT
ejpam-4855	259	9	be	be	AUX
ejpam-4855	259	10	a	a	DET
ejpam-4855	259	11	b∗k	b∗k	NOUN
ejpam-4855	259	12	-	-	PUNCT
ejpam-4855	259	13	open	open	ADJ
ejpam-4855	259	14	covering	covering	NOUN
ejpam-4855	259	15	of	of	ADP
ejpam-4855	259	16	ζ(y	ζ(y	PROPN
ejpam-4855	259	17	)	)	PUNCT
ejpam-4855	259	18	.	.	PUNCT
ejpam-4855	260	1	since	since	SCONJ
ejpam-4855	260	2	ζ	ζ	NOUN
ejpam-4855	260	3	is	be	AUX
ejpam-4855	260	4	b∗j	b∗j	PUNCT
ejpam-4855	260	5	-irresolute	-irresolute	ADJ
ejpam-4855	260	6	,	,	PUNCT
ejpam-4855	260	7	{	{	PUNCT
ejpam-4855	260	8	ζ−1(pψ	ζ−1(pψ	PROPN
ejpam-4855	260	9	)	)	PUNCT
ejpam-4855	260	10	:	:	PUNCT
ejpam-4855	260	11	ψ	ψ	X
ejpam-4855	260	12	∈	∈	PROPN
ejpam-4855	260	13	ψ	ψ	AUX
ejpam-4855	260	14	}	}	PUNCT
ejpam-4855	260	15	is	be	AUX
ejpam-4855	260	16	a	a	DET
ejpam-4855	260	17	b∗j	b∗j	PUNCT
ejpam-4855	260	18	-open	-open	NOUN
ejpam-4855	260	19	covering	cover	VERB
ejpam-4855	260	20	y	y	NOUN
ejpam-4855	260	21	.	.	PUNCT
ejpam-4855	261	1	by	by	ADP
ejpam-4855	261	2	assumption	assumption	NOUN
ejpam-4855	261	3	,	,	PUNCT
ejpam-4855	261	4	ψ	ψ	X
ejpam-4855	261	5	has	have	VERB
ejpam-4855	261	6	a	a	DET
ejpam-4855	261	7	smaller	small	ADJ
ejpam-4855	261	8	finite	finite	NOUN
ejpam-4855	261	9	subset	subset	NOUN
ejpam-4855	261	10	,	,	PUNCT
ejpam-4855	261	11	say	say	VERB
ejpam-4855	261	12	ψ0	ψ0	ADV
ejpam-4855	261	13	,	,	PUNCT
ejpam-4855	261	14	with	with	ADP
ejpam-4855	261	15	y	y	PROPN
ejpam-4855	261	16	−	−	PROPN
ejpam-4855	261	17	⋃	⋃	PROPN
ejpam-4855	261	18	{	{	PUNCT
ejpam-4855	261	19	ζ−1(pψ	ζ−1(pψ	NOUN
ejpam-4855	261	20	)	)	PUNCT
ejpam-4855	261	21	:	:	PUNCT
ejpam-4855	262	1	ψ	ψ	X
ejpam-4855	262	2	∈	∈	PROPN
ejpam-4855	262	3	ψ0	ψ0	PROPN
ejpam-4855	262	4	}	}	PUNCT
ejpam-4855	262	5	∈	∈	PROPN
ejpam-4855	262	6	j	j	PROPN
ejpam-4855	262	7	.	.	PUNCT
ejpam-4855	263	1	and	and	CCONJ
ejpam-4855	263	2	so	so	ADV
ejpam-4855	263	3	by	by	ADP
ejpam-4855	263	4	remark	remark	NOUN
ejpam-4855	263	5	1	1	NUM
ejpam-4855	263	6	ζ(y	ζ(y	PROPN
ejpam-4855	263	7	)	)	PUNCT
ejpam-4855	263	8	\	\	NOUN
ejpam-4855	263	9	⋃	⋃	PUNCT
ejpam-4855	263	10	{	{	PUNCT
ejpam-4855	263	11	pψ	pψ	NOUN
ejpam-4855	263	12	:	:	PUNCT
ejpam-4855	263	13	ψ	ψ	X
ejpam-4855	263	14	∈	∈	PROPN
ejpam-4855	263	15	ψ0	ψ0	ADV
ejpam-4855	263	16	}	}	PUNCT
ejpam-4855	263	17	=	=	PUNCT
ejpam-4855	263	18	ζ(y	ζ(y	PROPN
ejpam-4855	263	19	−	−	PROPN
ejpam-4855	263	20	⋃	⋃	NOUN
ejpam-4855	263	21	{	{	PUNCT
ejpam-4855	263	22	ζ−1(pψ	ζ−1(pψ	NOUN
ejpam-4855	263	23	)	)	PUNCT
ejpam-4855	263	24	:	:	PUNCT
ejpam-4855	263	25	ψ	ψ	X
ejpam-4855	263	26	∈	∈	PROPN
ejpam-4855	263	27	ψ0	ψ0	ADV
ejpam-4855	263	28	}	}	PUNCT
ejpam-4855	263	29	)	)	PUNCT
ejpam-4855	264	1	∈	∈	PROPN
ejpam-4855	264	2	k.	k.	PROPN
ejpam-4855	265	1	if	if	SCONJ
ejpam-4855	265	2	the	the	DET
ejpam-4855	265	3	co	co	NOUN
ejpam-4855	265	4	-	-	NOUN
ejpam-4855	265	5	domain	domain	NOUN
ejpam-4855	265	6	of	of	ADP
ejpam-4855	265	7	a	a	DET
ejpam-4855	265	8	b∗-open	b∗-open	NOUN
ejpam-4855	265	9	and	and	CCONJ
ejpam-4855	265	10	onto	onto	ADP
ejpam-4855	265	11	map	map	NOUN
ejpam-4855	265	12	is	be	AUX
ejpam-4855	265	13	cb∗j	cb∗j	NOUN
ejpam-4855	265	14	-compact	-compact	NOUN
ejpam-4855	265	15	with	with	ADP
ejpam-4855	265	16	respect	respect	NOUN
ejpam-4855	265	17	to	to	ADP
ejpam-4855	265	18	an	an	DET
ejpam-4855	265	19	ideal	ideal	NOUN
ejpam-4855	265	20	,	,	PUNCT
ejpam-4855	265	21	then	then	ADV
ejpam-4855	265	22	so	so	ADV
ejpam-4855	265	23	is	be	AUX
ejpam-4855	265	24	the	the	DET
ejpam-4855	265	25	domain	domain	NOUN
ejpam-4855	265	26	.	.	PUNCT
ejpam-4855	266	1	we	we	PRON
ejpam-4855	266	2	show	show	VERB
ejpam-4855	266	3	this	this	DET
ejpam-4855	266	4	idea	idea	NOUN
ejpam-4855	266	5	in	in	ADP
ejpam-4855	266	6	theorem	theorem	NOUN
ejpam-4855	266	7	5	5	NUM
ejpam-4855	266	8	.	.	PUNCT
ejpam-4855	266	9	theorem	theorem	NOUN
ejpam-4855	266	10	5	5	NUM
ejpam-4855	266	11	.	.	PUNCT
ejpam-4855	267	1	let	let	AUX
ejpam-4855	267	2	(	(	PUNCT
ejpam-4855	267	3	y	y	NOUN
ejpam-4855	267	4	,	,	PUNCT
ejpam-4855	267	5	ς	ς	PROPN
ejpam-4855	267	6	,	,	PUNCT
ejpam-4855	267	7	j	j	PROPN
ejpam-4855	267	8	)	)	PUNCT
ejpam-4855	267	9	and	and	CCONJ
ejpam-4855	267	10	(	(	PUNCT
ejpam-4855	267	11	w	w	PROPN
ejpam-4855	267	12	,	,	PUNCT
ejpam-4855	267	13	ξ	ξ	PROPN
ejpam-4855	267	14	,	,	PUNCT
ejpam-4855	267	15	k	k	NOUN
ejpam-4855	267	16	)	)	PUNCT
ejpam-4855	267	17	be	be	AUX
ejpam-4855	267	18	ideal	ideal	ADJ
ejpam-4855	267	19	spaces	space	NOUN
ejpam-4855	267	20	,	,	PUNCT
ejpam-4855	267	21	and	and	CCONJ
ejpam-4855	267	22	ζ	ζ	NOUN
ejpam-4855	267	23	:	:	PUNCT
ejpam-4855	267	24	y	y	PROPN
ejpam-4855	267	25	→w	→w	PUNCT
ejpam-4855	267	26	be	be	AUX
ejpam-4855	267	27	a	a	DET
ejpam-4855	267	28	b∗j	b∗j	PUNCT
ejpam-4855	267	29	-open	-open	ADJ
ejpam-4855	267	30	and	and	CCONJ
ejpam-4855	267	31	onto	onto	ADP
ejpam-4855	267	32	map	map	NOUN
ejpam-4855	267	33	with	with	ADP
ejpam-4855	267	34	ζ(j	ζ(j	NUM
ejpam-4855	267	35	)	)	PUNCT
ejpam-4855	268	1	=	=	VERB
ejpam-4855	268	2	k.	k.	NOUN
ejpam-4855	269	1	if	if	SCONJ
ejpam-4855	269	2	w	w	PROPN
ejpam-4855	269	3	is	be	AUX
ejpam-4855	269	4	cb∗k	cb∗k	NOUN
ejpam-4855	269	5	-	-	PUNCT
ejpam-4855	269	6	compact	compact	ADJ
ejpam-4855	269	7	,	,	PUNCT
ejpam-4855	269	8	then	then	ADV
ejpam-4855	269	9	y	y	PROPN
ejpam-4855	269	10	is	be	AUX
ejpam-4855	269	11	cb∗k	cb∗k	NOUN
ejpam-4855	269	12	-	-	PUNCT
ejpam-4855	269	13	compact	compact	ADJ
ejpam-4855	269	14	.	.	PUNCT
ejpam-4855	270	1	proof	proof	NOUN
ejpam-4855	270	2	.	.	PUNCT
ejpam-4855	271	1	let	let	VERB
ejpam-4855	271	2	{	{	PUNCT
ejpam-4855	271	3	pψ	pψ	VERB
ejpam-4855	271	4	:	:	PUNCT
ejpam-4855	271	5	ψ	ψ	X
ejpam-4855	271	6	∈	∈	PROPN
ejpam-4855	271	7	ψ	ψ	AUX
ejpam-4855	271	8	}	}	PUNCT
ejpam-4855	271	9	be	be	AUX
ejpam-4855	271	10	a	a	DET
ejpam-4855	271	11	b∗j	b∗j	PUNCT
ejpam-4855	271	12	-open	-open	ADJ
ejpam-4855	271	13	covering	covering	NOUN
ejpam-4855	271	14	of	of	ADP
ejpam-4855	271	15	y	y	PROPN
ejpam-4855	271	16	.	.	PUNCT
ejpam-4855	272	1	since	since	SCONJ
ejpam-4855	272	2	ζ	ζ	NOUN
ejpam-4855	272	3	is	be	AUX
ejpam-4855	272	4	a	a	DET
ejpam-4855	272	5	b∗j	b∗j	PUNCT
ejpam-4855	272	6	-open	-open	ADJ
ejpam-4855	272	7	and	and	CCONJ
ejpam-4855	272	8	onto	onto	ADP
ejpam-4855	272	9	,	,	PUNCT
ejpam-4855	272	10	{	{	PUNCT
ejpam-4855	272	11	ζ(pψ	ζ(pψ	NUM
ejpam-4855	272	12	)	)	PUNCT
ejpam-4855	272	13	:	:	PUNCT
ejpam-4855	272	14	ψ	ψ	X
ejpam-4855	272	15	∈	∈	PROPN
ejpam-4855	272	16	ψ	ψ	AUX
ejpam-4855	272	17	}	}	PUNCT
ejpam-4855	272	18	is	be	AUX
ejpam-4855	272	19	a	a	DET
ejpam-4855	272	20	b∗k	b∗k	NOUN
ejpam-4855	272	21	-	-	PUNCT
ejpam-4855	272	22	open	open	ADJ
ejpam-4855	272	23	covering	covering	NOUN
ejpam-4855	272	24	of	of	ADP
ejpam-4855	272	25	w	w	PROPN
ejpam-4855	272	26	.	.	PUNCT
ejpam-4855	273	1	by	by	ADP
ejpam-4855	273	2	assumption	assumption	NOUN
ejpam-4855	273	3	,	,	PUNCT
ejpam-4855	273	4	ψ	ψ	X
ejpam-4855	273	5	has	have	VERB
ejpam-4855	273	6	a	a	DET
ejpam-4855	273	7	smaller	small	ADJ
ejpam-4855	273	8	finite	finite	NOUN
ejpam-4855	273	9	subset	subset	NOUN
ejpam-4855	273	10	,	,	PUNCT
ejpam-4855	273	11	say	say	VERB
ejpam-4855	273	12	ψ0	ψ0	ADV
ejpam-4855	273	13	,	,	PUNCT
ejpam-4855	273	14	with	with	ADP
ejpam-4855	273	15	w\	w\	VERB
ejpam-4855	273	16	⋃	⋃	ADV
ejpam-4855	273	17	{	{	PUNCT
ejpam-4855	273	18	ζ(pψ	ζ(pψ	NUM
ejpam-4855	273	19	)	)	PUNCT
ejpam-4855	273	20	:	:	PUNCT
ejpam-4855	273	21	ψ	ψ	X
ejpam-4855	273	22	∈	∈	PROPN
ejpam-4855	273	23	ψ0	ψ0	PROPN
ejpam-4855	273	24	}	}	PUNCT
ejpam-4855	273	25	∈	∈	PROPN
ejpam-4855	273	26	k.	k.	PROPN
ejpam-4855	274	1	thus	thus	ADV
ejpam-4855	274	2	,	,	PUNCT
ejpam-4855	274	3	y	y	PROPN
ejpam-4855	274	4	\	\	PUNCT
ejpam-4855	274	5	⋃	⋃	PUNCT
ejpam-4855	274	6	{	{	PUNCT
ejpam-4855	274	7	pψ	pψ	NOUN
ejpam-4855	274	8	:	:	PUNCT
ejpam-4855	274	9	ψ	ψ	X
ejpam-4855	274	10	∈	∈	PROPN
ejpam-4855	274	11	ψ0	ψ0	ADV
ejpam-4855	274	12	}	}	PUNCT
ejpam-4855	274	13	=	=	PUNCT
ejpam-4855	274	14	ζ−1(w\	ζ−1(w\	NUM
ejpam-4855	274	15	⋃	⋃	NOUN
ejpam-4855	274	16	{	{	PUNCT
ejpam-4855	274	17	ζ(pψ	ζ(pψ	NUM
ejpam-4855	274	18	)	)	PUNCT
ejpam-4855	274	19	:	:	PUNCT
ejpam-4855	274	20	ψ	ψ	X
ejpam-4855	274	21	∈	∈	PROPN
ejpam-4855	274	22	ψ0	ψ0	ADV
ejpam-4855	274	23	}	}	PUNCT
ejpam-4855	274	24	)	)	PUNCT
ejpam-4855	275	1	∈	∈	PROPN
ejpam-4855	275	2	j	j	PROPN
ejpam-4855	275	3	.	.	PUNCT
ejpam-4855	276	1	references	reference	NOUN
ejpam-4855	276	2	[	[	X
ejpam-4855	276	3	1	1	NUM
ejpam-4855	276	4	]	]	X
ejpam-4855	276	5	m	m	VERB
ejpam-4855	276	6	e	e	PROPN
ejpam-4855	276	7	abd	abd	PROPN
ejpam-4855	276	8	el	el	PROPN
ejpam-4855	276	9	-	-	PROPN
ejpam-4855	276	10	monsef	monsef	ADJ
ejpam-4855	276	11	.	.	PUNCT
ejpam-4855	277	1	β	β	X
ejpam-4855	277	2	-	-	ADJ
ejpam-4855	277	3	open	open	ADJ
ejpam-4855	277	4	sets	set	NOUN
ejpam-4855	277	5	and	and	CCONJ
ejpam-4855	277	6	β	β	ADJ
ejpam-4855	277	7	-	-	ADJ
ejpam-4855	277	8	continuous	continuous	ADJ
ejpam-4855	277	9	mappings	mapping	NOUN
ejpam-4855	277	10	.	.	PUNCT
ejpam-4855	278	1	bull	bull	NOUN
ejpam-4855	278	2	.	.	PUNCT
ejpam-4855	279	1	fac	fac	PROPN
ejpam-4855	279	2	.	.	PUNCT
ejpam-4855	280	1	sci	sci	PROPN
ejpam-4855	280	2	.	.	PUNCT
ejpam-4855	280	3	assiut	assiut	PROPN
ejpam-4855	280	4	univ	univ	PROPN
ejpam-4855	280	5	.	.	PROPN
ejpam-4855	280	6	,	,	PUNCT
ejpam-4855	280	7	12:77–90	12:77–90	NUM
ejpam-4855	280	8	,	,	PUNCT
ejpam-4855	280	9	1983	1983	NUM
ejpam-4855	280	10	.	.	PUNCT
ejpam-4855	281	1	[	[	X
ejpam-4855	281	2	2	2	NUM
ejpam-4855	281	3	]	]	PUNCT
ejpam-4855	281	4	dimitrije	dimitrije	NOUN
ejpam-4855	281	5	andrijević.	andrijević.	PROPN
ejpam-4855	281	6	on	on	ADP
ejpam-4855	281	7	b	b	X
ejpam-4855	281	8	-	-	PUNCT
ejpam-4855	281	9	open	open	ADJ
ejpam-4855	281	10	sets	set	NOUN
ejpam-4855	281	11	.	.	PUNCT
ejpam-4855	282	1	matematički	matematički	PROPN
ejpam-4855	282	2	vesnik	vesnik	PROPN
ejpam-4855	282	3	,	,	PUNCT
ejpam-4855	282	4	(	(	PUNCT
ejpam-4855	282	5	205):59–64	205):59–64	NUM
ejpam-4855	282	6	,	,	PUNCT
ejpam-4855	282	7	1996	1996	NUM
ejpam-4855	282	8	.	.	PUNCT
ejpam-4855	283	1	[	[	X
ejpam-4855	283	2	3	3	X
ejpam-4855	283	3	]	]	X
ejpam-4855	283	4	paritosh	paritosh	ADV
ejpam-4855	283	5	bhattacharyya	bhattacharyya	ADJ
ejpam-4855	283	6	.	.	PUNCT
ejpam-4855	284	1	semi	semi	ADJ
ejpam-4855	284	2	-	-	ADJ
ejpam-4855	284	3	generalized	generalized	ADJ
ejpam-4855	284	4	closed	closed	ADJ
ejpam-4855	284	5	sets	set	NOUN
ejpam-4855	284	6	in	in	ADP
ejpam-4855	284	7	topology	topology	NOUN
ejpam-4855	284	8	.	.	PUNCT
ejpam-4855	285	1	indian	indian	PROPN
ejpam-4855	285	2	j.	j.	PROPN
ejpam-4855	285	3	math	math	PROPN
ejpam-4855	285	4	.	.	PUNCT
ejpam-4855	285	5	,	,	PUNCT
ejpam-4855	285	6	29(3):375–382	29(3):375–382	PROPN
ejpam-4855	285	7	,	,	PUNCT
ejpam-4855	285	8	1987	1987	NUM
ejpam-4855	285	9	.	.	PUNCT
ejpam-4855	286	1	[	[	X
ejpam-4855	286	2	4	4	NUM
ejpam-4855	286	3	]	]	X
ejpam-4855	286	4	glaisa	glaisa	VERB
ejpam-4855	286	5	t.	t.	PROPN
ejpam-4855	286	6	catalan	catalan	NOUN
ejpam-4855	286	7	,	,	PUNCT
ejpam-4855	286	8	michael	michael	PROPN
ejpam-4855	286	9	p.	p.	PROPN
ejpam-4855	286	10	baldado	baldado	PROPN
ejpam-4855	286	11	,	,	PUNCT
ejpam-4855	286	12	and	and	CCONJ
ejpam-4855	286	13	roberto	roberto	PROPN
ejpam-4855	286	14	n.	n.	PROPN
ejpam-4855	286	15	padua	padua	PROPN
ejpam-4855	286	16	.	.	PUNCT
ejpam-4855	287	1	βi	βi	PROPN
ejpam-4855	287	2	-compactness	-compactness	PROPN
ejpam-4855	287	3	,	,	PUNCT
ejpam-4855	287	4	β∗i	β∗i	PUNCT
ejpam-4855	287	5	-hyperconnectedness	-hyperconnectedness	NOUN
ejpam-4855	287	6	and	and	CCONJ
ejpam-4855	287	7	βi	βi	PRON
ejpam-4855	287	8	-separatedness	-separatedness	NOUN
ejpam-4855	287	9	in	in	ADP
ejpam-4855	287	10	ideal	ideal	ADJ
ejpam-4855	287	11	topological	topological	ADJ
ejpam-4855	287	12	spaces	space	NOUN
ejpam-4855	287	13	.	.	PUNCT
ejpam-4855	288	1	in	in	ADP
ejpam-4855	288	2	francisco	francisco	PROPN
ejpam-4855	288	3	bulnes	bulne	NOUN
ejpam-4855	288	4	,	,	PUNCT
ejpam-4855	288	5	editor	editor	NOUN
ejpam-4855	288	6	,	,	PUNCT
ejpam-4855	288	7	advanced	advanced	ADJ
ejpam-4855	288	8	topics	topic	NOUN
ejpam-4855	288	9	of	of	ADP
ejpam-4855	288	10	topology	topology	NOUN
ejpam-4855	288	11	,	,	PUNCT
ejpam-4855	288	12	chapter	chapter	NOUN
ejpam-4855	288	13	7	7	NUM
ejpam-4855	288	14	.	.	PUNCT
ejpam-4855	288	15	intechopen	intechopen	PROPN
ejpam-4855	288	16	,	,	PUNCT
ejpam-4855	288	17	rijeka	rijeka	PROPN
ejpam-4855	288	18	,	,	PUNCT
ejpam-4855	288	19	2022	2022	NUM
ejpam-4855	288	20	.	.	PUNCT
ejpam-4855	289	1	[	[	X
ejpam-4855	289	2	5	5	NUM
ejpam-4855	289	3	]	]	X
ejpam-4855	289	4	kazimierz	kazimierz	PROPN
ejpam-4855	289	5	kuratowski	kuratowski	PROPN
ejpam-4855	289	6	.	.	PUNCT
ejpam-4855	290	1	topologie	topologie	PROPN
ejpam-4855	290	2	.	.	PUNCT
ejpam-4855	290	3	bull	bull	PROPN
ejpam-4855	290	4	.	.	PUNCT
ejpam-4855	291	1	amer	amer	PROPN
ejpam-4855	291	2	.	.	PUNCT
ejpam-4855	291	3	math	math	PROPN
ejpam-4855	291	4	.	.	PUNCT
ejpam-4855	292	1	soc	soc	PROPN
ejpam-4855	292	2	,	,	PUNCT
ejpam-4855	292	3	40:787–788	40:787–788	PROPN
ejpam-4855	292	4	,	,	PUNCT
ejpam-4855	292	5	1934	1934	NUM
ejpam-4855	292	6	.	.	PUNCT
ejpam-4855	293	1	[	[	X
ejpam-4855	293	2	6	6	NUM
ejpam-4855	293	3	]	]	PUNCT
ejpam-4855	293	4	norman	norman	PROPN
ejpam-4855	293	5	levine	levine	PROPN
ejpam-4855	293	6	.	.	PUNCT
ejpam-4855	294	1	semi	semi	ADJ
ejpam-4855	294	2	-	-	ADJ
ejpam-4855	294	3	open	open	ADJ
ejpam-4855	294	4	sets	set	NOUN
ejpam-4855	294	5	and	and	CCONJ
ejpam-4855	294	6	semi	semi	ADJ
ejpam-4855	294	7	-	-	NOUN
ejpam-4855	294	8	continuity	continuity	NOUN
ejpam-4855	294	9	in	in	ADP
ejpam-4855	294	10	topological	topological	ADJ
ejpam-4855	294	11	spaces	space	NOUN
ejpam-4855	294	12	.	.	PUNCT
ejpam-4855	295	1	the	the	DET
ejpam-4855	295	2	american	american	PROPN
ejpam-4855	295	3	mathematical	mathematical	PROPN
ejpam-4855	295	4	monthly	monthly	ADV
ejpam-4855	295	5	,	,	PUNCT
ejpam-4855	295	6	70(1):36–41	70(1):36–41	NUM
ejpam-4855	295	7	,	,	PUNCT
ejpam-4855	295	8	1963	1963	NUM
ejpam-4855	295	9	.	.	PUNCT
ejpam-4855	296	1	[	[	X
ejpam-4855	296	2	7	7	X
ejpam-4855	296	3	]	]	X
ejpam-4855	296	4	norman	norman	PROPN
ejpam-4855	296	5	levine	levine	PROPN
ejpam-4855	296	6	.	.	PUNCT
ejpam-4855	297	1	generalized	generalize	VERB
ejpam-4855	297	2	closed	closed	ADJ
ejpam-4855	297	3	sets	set	NOUN
ejpam-4855	297	4	in	in	ADP
ejpam-4855	297	5	topology	topology	NOUN
ejpam-4855	297	6	.	.	PUNCT
ejpam-4855	298	1	rendiconti	rendiconti	VERB
ejpam-4855	298	2	del	del	PROPN
ejpam-4855	298	3	circolo	circolo	PROPN
ejpam-4855	298	4	matematico	matematico	NOUN
ejpam-4855	298	5	di	di	NOUN
ejpam-4855	298	6	palermo	palermo	NOUN
ejpam-4855	298	7	,	,	PUNCT
ejpam-4855	298	8	19(1):89–96	19(1):89–96	NUM
ejpam-4855	298	9	,	,	PUNCT
ejpam-4855	298	10	1970	1970	NUM
ejpam-4855	298	11	.	.	PUNCT
ejpam-4855	299	1	[	[	X
ejpam-4855	299	2	8	8	NUM
ejpam-4855	299	3	]	]	X
ejpam-4855	299	4	a	a	DET
ejpam-4855	299	5	s	s	X
ejpam-4855	299	6	mashhour	mashhour	NOUN
ejpam-4855	299	7	,	,	PUNCT
ejpam-4855	299	8	m	m	VERB
ejpam-4855	299	9	e	e	PROPN
ejpam-4855	299	10	abd	abd	PROPN
ejpam-4855	299	11	el	el	PROPN
ejpam-4855	299	12	-	-	PROPN
ejpam-4855	299	13	monsef	monsef	ADJ
ejpam-4855	299	14	,	,	PUNCT
ejpam-4855	299	15	and	and	CCONJ
ejpam-4855	299	16	s	s	AUX
ejpam-4855	299	17	n	n	PRON
ejpam-4855	299	18	el	el	PROPN
ejpam-4855	299	19	-	-	PUNCT
ejpam-4855	299	20	deeh	deeh	NOUN
ejpam-4855	299	21	.	.	PUNCT
ejpam-4855	300	1	on	on	ADP
ejpam-4855	300	2	pre	pre	ADJ
ejpam-4855	300	3	-	-	ADJ
ejpam-4855	300	4	continuous	continuous	ADJ
ejpam-4855	300	5	and	and	CCONJ
ejpam-4855	300	6	weak	weak	ADJ
ejpam-4855	300	7	pre	pre	ADJ
ejpam-4855	300	8	-	-	ADJ
ejpam-4855	300	9	continuous	continuous	ADJ
ejpam-4855	300	10	mappings	mapping	NOUN
ejpam-4855	300	11	.	.	PUNCT
ejpam-4855	301	1	in	in	ADP
ejpam-4855	301	2	proc	proc	PROPN
ejpam-4855	301	3	.	.	PUNCT
ejpam-4855	302	1	math	math	NOUN
ejpam-4855	302	2	.	.	PUNCT
ejpam-4855	303	1	phys	phy	NOUN
ejpam-4855	303	2	.	.	PUNCT
ejpam-4855	304	1	soc	soc	PROPN
ejpam-4855	304	2	.	.	PUNCT
ejpam-4855	305	1	egypt	egypt	PROPN
ejpam-4855	305	2	.	.	PROPN
ejpam-4855	305	3	,	,	PUNCT
ejpam-4855	305	4	volume	volume	NOUN
ejpam-4855	305	5	53	53	NUM
ejpam-4855	305	6	,	,	PUNCT
ejpam-4855	305	7	pages	page	NOUN
ejpam-4855	305	8	47–53	47–53	NUM
ejpam-4855	305	9	,	,	PUNCT
ejpam-4855	305	10	1982	1982	NUM
ejpam-4855	305	11	.	.	PUNCT
ejpam-4855	306	1	references	reference	NOUN
ejpam-4855	306	2	1816	1816	NUM
ejpam-4855	307	1	[	[	X
ejpam-4855	307	2	9	9	NUM
ejpam-4855	307	3	]	]	SYM
ejpam-4855	307	4	f	f	PROPN
ejpam-4855	308	1	i	i	PROPN
ejpam-4855	308	2	michael	michael	PROPN
ejpam-4855	308	3	.	.	PUNCT
ejpam-4855	309	1	on	on	ADP
ejpam-4855	309	2	semi	semi	ADJ
ejpam-4855	309	3	-	-	ADJ
ejpam-4855	309	4	open	open	ADJ
ejpam-4855	309	5	sets	set	NOUN
ejpam-4855	309	6	with	with	ADP
ejpam-4855	309	7	respect	respect	NOUN
ejpam-4855	309	8	to	to	ADP
ejpam-4855	309	9	an	an	DET
ejpam-4855	309	10	ideal	ideal	NOUN
ejpam-4855	309	11	.	.	PUNCT
ejpam-4855	310	1	european	european	ADJ
ejpam-4855	310	2	journal	journal	PROPN
ejpam-4855	310	3	of	of	ADP
ejpam-4855	310	4	pure	pure	ADJ
ejpam-4855	310	5	and	and	CCONJ
ejpam-4855	310	6	applied	applied	ADJ
ejpam-4855	310	7	mathematics	mathematic	NOUN
ejpam-4855	310	8	,	,	PUNCT
ejpam-4855	310	9	6(1):53–58	6(1):53–58	NUM
ejpam-4855	310	10	,	,	PUNCT
ejpam-4855	310	11	2013	2013	NUM
ejpam-4855	310	12	.	.	PUNCT
ejpam-4855	311	1	[	[	X
ejpam-4855	311	2	10	10	NUM
ejpam-4855	311	3	]	]	X
ejpam-4855	311	4	s	s	VERB
ejpam-4855	311	5	a	a	DET
ejpam-4855	311	6	morris	morris	PROPN
ejpam-4855	311	7	.	.	PUNCT
ejpam-4855	311	8	topology	topology	PROPN
ejpam-4855	311	9	without	without	ADP
ejpam-4855	311	10	tears	tear	NOUN
ejpam-4855	311	11	.	.	PUNCT
ejpam-4855	312	1	university	university	NOUN
ejpam-4855	312	2	of	of	ADP
ejpam-4855	312	3	new	new	PROPN
ejpam-4855	312	4	england	england	PROPN
ejpam-4855	312	5	,	,	PUNCT
ejpam-4855	312	6	1989	1989	NUM
ejpam-4855	312	7	.	.	PUNCT
ejpam-4855	313	1	[	[	X
ejpam-4855	313	2	11	11	NUM
ejpam-4855	313	3	]	]	X
ejpam-4855	313	4	r	r	NOUN
ejpam-4855	313	5	l	l	NOUN
ejpam-4855	313	6	newcomb	newcomb	PROPN
ejpam-4855	313	7	.	.	PUNCT
ejpam-4855	313	8	topologies	topology	NOUN
ejpam-4855	313	9	which	which	PRON
ejpam-4855	313	10	are	be	AUX
ejpam-4855	313	11	compact	compact	ADJ
ejpam-4855	313	12	modulo	modulo	NOUN
ejpam-4855	313	13	an	an	DET
ejpam-4855	313	14	ideal	ideal	NOUN
ejpam-4855	313	15	[	[	X
ejpam-4855	313	16	ph.d	ph.d	PROPN
ejpam-4855	313	17	.	.	PUNCT
ejpam-4855	314	1	dissertation	dissertation	NOUN
ejpam-4855	314	2	]	]	PUNCT
ejpam-4855	314	3	.	.	PUNCT
ejpam-4855	315	1	university	university	PROPN
ejpam-4855	315	2	of	of	ADP
ejpam-4855	315	3	california	california	PROPN
ejpam-4855	315	4	at	at	ADP
ejpam-4855	315	5	santa	santa	PROPN
ejpam-4855	315	6	barbara	barbara	PROPN
ejpam-4855	315	7	,	,	PUNCT
ejpam-4855	315	8	1967	1967	NUM
ejpam-4855	315	9	.	.	PUNCT
ejpam-4855	316	1	[	[	X
ejpam-4855	316	2	12	12	NUM
ejpam-4855	316	3	]	]	PUNCT
ejpam-4855	316	4	olav	olav	PROPN
ejpam-4855	316	5	njástad	njástad	PROPN
ejpam-4855	316	6	.	.	PUNCT
ejpam-4855	316	7	on	on	ADP
ejpam-4855	316	8	some	some	DET
ejpam-4855	316	9	classes	class	NOUN
ejpam-4855	316	10	of	of	ADP
ejpam-4855	316	11	nearly	nearly	ADV
ejpam-4855	316	12	open	open	ADJ
ejpam-4855	316	13	sets	set	NOUN
ejpam-4855	316	14	.	.	PUNCT
ejpam-4855	317	1	pacific	pacific	PROPN
ejpam-4855	317	2	journal	journal	PROPN
ejpam-4855	317	3	of	of	ADP
ejpam-4855	317	4	mathematics	mathematic	NOUN
ejpam-4855	317	5	,	,	PUNCT
ejpam-4855	317	6	15(3):961–970	15(3):961–970	PROPN
ejpam-4855	317	7	,	,	PUNCT
ejpam-4855	317	8	1965	1965	NUM
ejpam-4855	317	9	.	.	PUNCT
ejpam-4855	318	1	[	[	X
ejpam-4855	318	2	13	13	NUM
ejpam-4855	318	3	]	]	X
ejpam-4855	318	4	karishma	karishma	PROPN
ejpam-4855	318	5	shravan	shravan	PROPN
ejpam-4855	318	6	and	and	CCONJ
ejpam-4855	318	7	binod	binod	PROPN
ejpam-4855	318	8	chandra	chandra	PROPN
ejpam-4855	318	9	tripathy	tripathy	PROPN
ejpam-4855	318	10	.	.	PUNCT
ejpam-4855	319	1	generalised	generalise	VERB
ejpam-4855	319	2	closed	close	VERB
ejpam-4855	319	3	sets	set	NOUN
ejpam-4855	319	4	in	in	ADP
ejpam-4855	319	5	multiset	multiset	ADJ
ejpam-4855	319	6	topological	topological	ADJ
ejpam-4855	319	7	space	space	NOUN
ejpam-4855	319	8	.	.	PUNCT
ejpam-4855	320	1	proyecciones	proyeccione	NOUN
ejpam-4855	320	2	(	(	PUNCT
ejpam-4855	320	3	antofagasta	antofagasta	PROPN
ejpam-4855	320	4	)	)	PUNCT
ejpam-4855	320	5	,	,	PUNCT
ejpam-4855	320	6	37(2):223–237	37(2):223–237	PROPN
ejpam-4855	320	7	,	,	PUNCT
ejpam-4855	320	8	2018	2018	NUM
ejpam-4855	320	9	.	.	PUNCT
ejpam-4855	321	1	[	[	X
ejpam-4855	321	2	14	14	NUM
ejpam-4855	321	3	]	]	X
ejpam-4855	321	4	karishma	karishma	PROPN
ejpam-4855	321	5	shravan	shravan	PROPN
ejpam-4855	321	6	and	and	CCONJ
ejpam-4855	321	7	binod	binod	PROPN
ejpam-4855	321	8	chandra	chandra	PROPN
ejpam-4855	321	9	tripathy	tripathy	PROPN
ejpam-4855	321	10	.	.	PUNCT
ejpam-4855	322	1	multiset	multiset	VERB
ejpam-4855	322	2	ideal	ideal	ADJ
ejpam-4855	322	3	topological	topological	ADJ
ejpam-4855	322	4	spaces	space	NOUN
ejpam-4855	322	5	and	and	CCONJ
ejpam-4855	322	6	local	local	ADJ
ejpam-4855	322	7	functions	function	NOUN
ejpam-4855	322	8	.	.	PUNCT
ejpam-4855	323	1	proyecciones	proyeccione	NOUN
ejpam-4855	323	2	(	(	PUNCT
ejpam-4855	323	3	antofagasta	antofagasta	PROPN
ejpam-4855	323	4	)	)	PUNCT
ejpam-4855	323	5	,	,	PUNCT
ejpam-4855	323	6	37(4):699–711	37(4):699–711	PROPN
ejpam-4855	323	7	,	,	PUNCT
ejpam-4855	323	8	2018	2018	NUM
ejpam-4855	323	9	.	.	PUNCT
ejpam-4855	324	1	[	[	X
ejpam-4855	324	2	15	15	NUM
ejpam-4855	324	3	]	]	X
ejpam-4855	324	4	a	a	DET
ejpam-4855	324	5	skowron	skowron	NOUN
ejpam-4855	324	6	.	.	PUNCT
ejpam-4855	325	1	on	on	ADP
ejpam-4855	325	2	topology	topology	NOUN
ejpam-4855	325	3	information	information	NOUN
ejpam-4855	325	4	systems	system	NOUN
ejpam-4855	325	5	.	.	PUNCT
ejpam-4855	326	1	bulletin	bulletin	NOUN
ejpam-4855	326	2	of	of	ADP
ejpam-4855	326	3	the	the	DET
ejpam-4855	326	4	polish	polish	PROPN
ejpam-4855	326	5	academy	academy	PROPN
ejpam-4855	326	6	of	of	ADP
ejpam-4855	326	7	sciences	sciences	PROPN
ejpam-4855	326	8	,	,	PUNCT
ejpam-4855	326	9	3:87–90	3:87–90	NUM
ejpam-4855	326	10	,	,	PUNCT
ejpam-4855	326	11	1989	1989	NUM
ejpam-4855	326	12	.	.	PUNCT
ejpam-4855	327	1	[	[	X
ejpam-4855	327	2	16	16	NUM
ejpam-4855	327	3	]	]	X
ejpam-4855	327	4	m	m	VERB
ejpam-4855	327	5	h	h	NOUN
ejpam-4855	327	6	stone	stone	NOUN
ejpam-4855	327	7	.	.	PUNCT
ejpam-4855	328	1	applications	application	NOUN
ejpam-4855	328	2	of	of	ADP
ejpam-4855	328	3	the	the	DET
ejpam-4855	328	4	theory	theory	NOUN
ejpam-4855	328	5	of	of	ADP
ejpam-4855	328	6	boolean	boolean	ADJ
ejpam-4855	328	7	rings	ring	NOUN
ejpam-4855	328	8	to	to	ADP
ejpam-4855	328	9	general	general	ADJ
ejpam-4855	328	10	topology	topology	NOUN
ejpam-4855	328	11	.	.	PUNCT
ejpam-4855	329	1	transactions	transaction	NOUN
ejpam-4855	329	2	of	of	ADP
ejpam-4855	329	3	the	the	DET
ejpam-4855	329	4	american	american	PROPN
ejpam-4855	329	5	mathematical	mathematical	PROPN
ejpam-4855	329	6	society	society	NOUN
ejpam-4855	329	7	,	,	PUNCT
ejpam-4855	329	8	41(3):375–481	41(3):375–481	PRON
ejpam-4855	329	9	,	,	PUNCT
ejpam-4855	329	10	1937	1937	NUM
ejpam-4855	329	11	.	.	PUNCT
ejpam-4855	330	1	[	[	X
ejpam-4855	330	2	17	17	NUM
ejpam-4855	330	3	]	]	X
ejpam-4855	330	4	binod	binod	PROPN
ejpam-4855	330	5	chandra	chandra	PROPN
ejpam-4855	330	6	tripathy	tripathy	PROPN
ejpam-4855	330	7	and	and	CCONJ
ejpam-4855	330	8	santanu	santanu	ADJ
ejpam-4855	330	9	acharjee	acharjee	NOUN
ejpam-4855	330	10	.	.	PUNCT
ejpam-4855	331	1	on	on	ADP
ejpam-4855	331	2	(	(	PUNCT
ejpam-4855	331	3	γ	γ	X
ejpam-4855	331	4	,	,	PUNCT
ejpam-4855	331	5	δ)-bitopological	δ)-bitopological	ADJ
ejpam-4855	331	6	semi	semi	ADJ
ejpam-4855	331	7	-	-	ADJ
ejpam-4855	331	8	closed	closed	ADJ
ejpam-4855	331	9	set	set	NOUN
ejpam-4855	331	10	via	via	ADP
ejpam-4855	331	11	topological	topological	ADJ
ejpam-4855	331	12	ideal	ideal	NOUN
ejpam-4855	331	13	.	.	PUNCT
ejpam-4855	332	1	proyecciones	proyeccione	NOUN
ejpam-4855	332	2	(	(	PUNCT
ejpam-4855	332	3	antofagasta	antofagasta	PROPN
ejpam-4855	332	4	)	)	PUNCT
ejpam-4855	332	5	,	,	PUNCT
ejpam-4855	332	6	33(3):245–257	33(3):245–257	PROPN
ejpam-4855	332	7	,	,	PUNCT
ejpam-4855	332	8	2014	2014	NUM
ejpam-4855	332	9	.	.	PUNCT
ejpam-4855	333	1	[	[	X
ejpam-4855	333	2	18	18	NUM
ejpam-4855	333	3	]	]	X
ejpam-4855	333	4	binod	binod	PROPN
ejpam-4855	333	5	chandra	chandra	PROPN
ejpam-4855	333	6	tripathy	tripathy	PROPN
ejpam-4855	333	7	and	and	CCONJ
ejpam-4855	333	8	gautam	gautam	PROPN
ejpam-4855	333	9	chandra	chandra	PROPN
ejpam-4855	333	10	ray	ray	PROPN
ejpam-4855	333	11	.	.	PUNCT
ejpam-4855	334	1	mixed	mixed	ADJ
ejpam-4855	334	2	fuzzy	fuzzy	ADJ
ejpam-4855	334	3	ideal	ideal	ADJ
ejpam-4855	334	4	topological	topological	ADJ
ejpam-4855	334	5	spaces	space	NOUN
ejpam-4855	334	6	.	.	PUNCT
ejpam-4855	335	1	applied	apply	VERB
ejpam-4855	335	2	mathematics	mathematic	NOUN
ejpam-4855	335	3	and	and	CCONJ
ejpam-4855	335	4	computation	computation	NOUN
ejpam-4855	335	5	,	,	PUNCT
ejpam-4855	335	6	220:602–607	220:602–607	NUM
ejpam-4855	335	7	,	,	PUNCT
ejpam-4855	335	8	2013	2013	NUM
ejpam-4855	335	9	.	.	PUNCT
ejpam-4855	336	1	[	[	X
ejpam-4855	336	2	19	19	NUM
ejpam-4855	336	3	]	]	X
ejpam-4855	336	4	r	r	NOUN
ejpam-4855	336	5	vaidyanathaswamy	vaidyanathaswamy	NOUN
ejpam-4855	336	6	.	.	PUNCT
ejpam-4855	337	1	set	set	VERB
ejpam-4855	337	2	topology	topology	NOUN
ejpam-4855	337	3	,	,	PUNCT
ejpam-4855	337	4	chelsea	chelsea	PROPN
ejpam-4855	337	5	,	,	PUNCT
ejpam-4855	337	6	new	new	PROPN
ejpam-4855	337	7	york	york	PROPN
ejpam-4855	337	8	,	,	PUNCT
ejpam-4855	337	9	1960	1960	NUM
ejpam-4855	337	10	.	.	PUNCT
ejpam-4855	338	1	university	university	NOUN
ejpam-4855	338	2	of	of	ADP
ejpam-4855	338	3	new	new	PROPN
ejpam-4855	338	4	mexico	mexico	PROPN
ejpam-4855	338	5	,	,	PUNCT
ejpam-4855	338	6	albuquerque	albuquerque	PROPN
ejpam-4855	338	7	,	,	PUNCT
ejpam-4855	338	8	new	new	PROPN
ejpam-4855	338	9	mexico	mexico	PROPN
ejpam-4855	338	10	texas	texas	PROPN
ejpam-4855	338	11	technological	technological	PROPN
ejpam-4855	338	12	college	college	PROPN
ejpam-4855	338	13	,	,	PUNCT
ejpam-4855	338	14	lubbock	lubbock	PROPN
ejpam-4855	338	15	,	,	PUNCT
ejpam-4855	338	16	texas	texas	PROPN
ejpam-4855	338	17	.	.	PUNCT