id	sid	tid	token	lemma	pos
ejpam-4260	1	1	european	european	PROPN
ejpam-4260	1	2	journal	journal	PROPN
ejpam-4260	1	3	of	of	ADP
ejpam-4260	1	4	pure	pure	ADJ
ejpam-4260	1	5	and	and	CCONJ
ejpam-4260	1	6	applied	apply	VERB
ejpam-4260	1	7	mathematics	mathematic	NOUN
ejpam-4260	1	8	vol	vol	NOUN
ejpam-4260	1	9	.	.	PROPN
ejpam-4260	2	1	15	15	NUM
ejpam-4260	2	2	,	,	PUNCT
ejpam-4260	2	3	no	no	INTJ
ejpam-4260	2	4	.	.	NOUN
ejpam-4260	2	5	1	1	NUM
ejpam-4260	2	6	,	,	PUNCT
ejpam-4260	2	7	2022	2022	NUM
ejpam-4260	2	8	,	,	PUNCT
ejpam-4260	2	9	15	15	NUM
ejpam-4260	2	10	-	-	SYM
ejpam-4260	2	11	29	29	NUM
ejpam-4260	2	12	issn	issn	PROPN
ejpam-4260	2	13	1307	1307	NUM
ejpam-4260	2	14	-	-	SYM
ejpam-4260	2	15	5543	5543	NUM
ejpam-4260	2	16	–	–	PUNCT
ejpam-4260	2	17	ejpam.com	ejpam.com	X
ejpam-4260	2	18	published	publish	VERB
ejpam-4260	2	19	by	by	ADP
ejpam-4260	2	20	new	new	PROPN
ejpam-4260	2	21	york	york	PROPN
ejpam-4260	2	22	business	business	PROPN
ejpam-4260	2	23	global	global	PROPN
ejpam-4260	2	24	supra	supra	PROPN
ejpam-4260	2	25	b	b	PROPN
ejpam-4260	2	26	limit	limit	NOUN
ejpam-4260	2	27	points	point	NOUN
ejpam-4260	2	28	and	and	CCONJ
ejpam-4260	3	1	supra	supra	PROPN
ejpam-4260	3	2	b	b	PROPN
ejpam-4260	3	3	separation	separation	NOUN
ejpam-4260	3	4	axioms	axiom	VERB
ejpam-4260	3	5	tareq	tareq	PROPN
ejpam-4260	3	6	m.	m.	PROPN
ejpam-4260	3	7	al	al	PROPN
ejpam-4260	3	8	-	-	PUNCT
ejpam-4260	3	9	shami1	shami1	PROPN
ejpam-4260	3	10	,	,	PUNCT
ejpam-4260	3	11	abdelwaheb	abdelwaheb	PROPN
ejpam-4260	3	12	mhemdi2,∗	mhemdi2,∗	PROPN
ejpam-4260	3	13	,	,	PUNCT
ejpam-4260	3	14	mohammed	mohammed	PROPN
ejpam-4260	3	15	jameel1,3	jameel1,3	PROPN
ejpam-4260	3	16	,	,	PUNCT
ejpam-4260	3	17	mohamed	mohamed	PROPN
ejpam-4260	3	18	abouhawwash	abouhawwash	PROPN
ejpam-4260	3	19	3	3	NUM
ejpam-4260	3	20	1	1	NUM
ejpam-4260	3	21	department	department	NOUN
ejpam-4260	3	22	of	of	ADP
ejpam-4260	3	23	mathematics	mathematic	NOUN
ejpam-4260	3	24	,	,	PUNCT
ejpam-4260	3	25	sana’a	sana’a	NOUN
ejpam-4260	3	26	university	university	NOUN
ejpam-4260	3	27	,	,	PUNCT
ejpam-4260	3	28	sana’a	sana’a	NOUN
ejpam-4260	3	29	,	,	PUNCT
ejpam-4260	3	30	yemen	yemen	PROPN
ejpam-4260	3	31	2	2	NUM
ejpam-4260	3	32	department	department	NOUN
ejpam-4260	3	33	of	of	ADP
ejpam-4260	3	34	mathematics	mathematic	NOUN
ejpam-4260	3	35	,	,	PUNCT
ejpam-4260	3	36	college	college	NOUN
ejpam-4260	3	37	of	of	ADP
ejpam-4260	3	38	sciences	science	NOUN
ejpam-4260	3	39	and	and	CCONJ
ejpam-4260	3	40	humanities	humanity	NOUN
ejpam-4260	3	41	in	in	ADP
ejpam-4260	3	42	aflaj	aflaj	NOUN
ejpam-4260	3	43	,	,	PUNCT
ejpam-4260	3	44	prince	prince	PROPN
ejpam-4260	3	45	sattam	sattam	PROPN
ejpam-4260	3	46	bin	bin	PROPN
ejpam-4260	3	47	abdulaziz	abdulaziz	PROPN
ejpam-4260	3	48	university	university	PROPN
ejpam-4260	3	49	,	,	PUNCT
ejpam-4260	3	50	riyadh	riyadh	PROPN
ejpam-4260	3	51	,	,	PUNCT
ejpam-4260	3	52	saudi	saudi	PROPN
ejpam-4260	3	53	arabia	arabia	PROPN
ejpam-4260	3	54	3	3	NUM
ejpam-4260	3	55	department	department	NOUN
ejpam-4260	3	56	of	of	ADP
ejpam-4260	3	57	mathematics	mathematic	NOUN
ejpam-4260	3	58	,	,	PUNCT
ejpam-4260	3	59	faculty	faculty	NOUN
ejpam-4260	3	60	of	of	ADP
ejpam-4260	3	61	science	science	NOUN
ejpam-4260	3	62	,	,	PUNCT
ejpam-4260	3	63	mansoura	mansoura	PROPN
ejpam-4260	3	64	university	university	NOUN
ejpam-4260	3	65	,	,	PUNCT
ejpam-4260	3	66	mansoura	mansoura	PROPN
ejpam-4260	3	67	,	,	PUNCT
ejpam-4260	3	68	egypt	egypt	PROPN
ejpam-4260	3	69	abstract	abstract	PROPN
ejpam-4260	3	70	.	.	PUNCT
ejpam-4260	4	1	in	in	ADP
ejpam-4260	4	2	recent	recent	ADJ
ejpam-4260	4	3	years	year	NOUN
ejpam-4260	4	4	,	,	PUNCT
ejpam-4260	4	5	some	some	DET
ejpam-4260	4	6	generalized	generalized	ADJ
ejpam-4260	4	7	structures	structure	NOUN
ejpam-4260	4	8	of	of	ADP
ejpam-4260	4	9	topology	topology	NOUN
ejpam-4260	4	10	were	be	AUX
ejpam-4260	4	11	introduced	introduce	VERB
ejpam-4260	4	12	.	.	PUNCT
ejpam-4260	5	1	supra	supra	PROPN
ejpam-4260	5	2	topology	topology	PROPN
ejpam-4260	5	3	was	be	AUX
ejpam-4260	5	4	one	one	NUM
ejpam-4260	5	5	the	the	DET
ejpam-4260	5	6	most	most	ADV
ejpam-4260	5	7	important	important	ADJ
ejpam-4260	5	8	of	of	ADP
ejpam-4260	5	9	those	those	DET
ejpam-4260	5	10	generalizations	generalization	NOUN
ejpam-4260	5	11	.	.	PUNCT
ejpam-4260	6	1	to	to	PART
ejpam-4260	6	2	contribute	contribute	VERB
ejpam-4260	6	3	in	in	ADP
ejpam-4260	6	4	this	this	DET
ejpam-4260	6	5	orientation	orientation	NOUN
ejpam-4260	6	6	,	,	PUNCT
ejpam-4260	6	7	we	we	PRON
ejpam-4260	6	8	devoted	devote	VERB
ejpam-4260	6	9	this	this	DET
ejpam-4260	6	10	work	work	NOUN
ejpam-4260	6	11	to	to	ADP
ejpam-4260	6	12	studying	study	VERB
ejpam-4260	6	13	limit	limit	NOUN
ejpam-4260	6	14	points	point	NOUN
ejpam-4260	6	15	and	and	CCONJ
ejpam-4260	6	16	separation	separation	NOUN
ejpam-4260	6	17	axioms	axiom	NOUN
ejpam-4260	6	18	on	on	ADP
ejpam-4260	6	19	supra	supra	PROPN
ejpam-4260	6	20	topological	topological	ADJ
ejpam-4260	6	21	spaces	space	NOUN
ejpam-4260	6	22	by	by	ADP
ejpam-4260	6	23	using	use	VERB
ejpam-4260	6	24	supra	supra	PROPN
ejpam-4260	6	25	b	b	PROPN
ejpam-4260	6	26	-	-	PUNCT
ejpam-4260	6	27	open	open	ADJ
ejpam-4260	6	28	sets	set	NOUN
ejpam-4260	6	29	.	.	PUNCT
ejpam-4260	7	1	we	we	PRON
ejpam-4260	7	2	define	define	VERB
ejpam-4260	7	3	them	they	PRON
ejpam-4260	7	4	in	in	ADP
ejpam-4260	7	5	a	a	DET
ejpam-4260	7	6	similar	similar	ADJ
ejpam-4260	7	7	way	way	NOUN
ejpam-4260	7	8	of	of	ADP
ejpam-4260	7	9	their	their	PRON
ejpam-4260	7	10	counterparts	counterpart	NOUN
ejpam-4260	7	11	on	on	ADP
ejpam-4260	7	12	topological	topological	ADJ
ejpam-4260	7	13	spaces	space	NOUN
ejpam-4260	7	14	.	.	PUNCT
ejpam-4260	8	1	in	in	ADP
ejpam-4260	8	2	general	general	ADJ
ejpam-4260	8	3	,	,	PUNCT
ejpam-4260	8	4	we	we	PRON
ejpam-4260	8	5	demonstrate	demonstrate	VERB
ejpam-4260	8	6	their	their	PRON
ejpam-4260	8	7	main	main	ADJ
ejpam-4260	8	8	properties	property	NOUN
ejpam-4260	8	9	and	and	CCONJ
ejpam-4260	8	10	investigate	investigate	VERB
ejpam-4260	8	11	the	the	DET
ejpam-4260	8	12	sufficient	sufficient	ADJ
ejpam-4260	8	13	conditions	condition	NOUN
ejpam-4260	8	14	for	for	ADP
ejpam-4260	8	15	some	some	DET
ejpam-4260	8	16	equivalent	equivalent	ADJ
ejpam-4260	8	17	relations	relation	NOUN
ejpam-4260	8	18	between	between	ADP
ejpam-4260	8	19	them	they	PRON
ejpam-4260	8	20	.	.	PUNCT
ejpam-4260	9	1	some	some	DET
ejpam-4260	9	2	novel	novel	ADJ
ejpam-4260	9	3	and	and	CCONJ
ejpam-4260	9	4	interesting	interesting	ADJ
ejpam-4260	9	5	examples	example	NOUN
ejpam-4260	9	6	are	be	AUX
ejpam-4260	9	7	provided	provide	VERB
ejpam-4260	9	8	.	.	PUNCT
ejpam-4260	10	1	2020	2020	NUM
ejpam-4260	10	2	mathematics	mathematic	NOUN
ejpam-4260	10	3	subject	subject	NOUN
ejpam-4260	10	4	classifications	classification	NOUN
ejpam-4260	10	5	:	:	PUNCT
ejpam-4260	10	6	54a05	54a05	NUM
ejpam-4260	10	7	,	,	PUNCT
ejpam-4260	10	8	54c08	54c08	NUM
ejpam-4260	10	9	,	,	PUNCT
ejpam-4260	10	10	54d99	54d99	NUM
ejpam-4260	10	11	key	key	ADJ
ejpam-4260	10	12	words	word	NOUN
ejpam-4260	10	13	and	and	CCONJ
ejpam-4260	10	14	phrases	phrase	NOUN
ejpam-4260	10	15	:	:	PUNCT
ejpam-4260	10	16	supra	supra	PROPN
ejpam-4260	10	17	b	b	X
ejpam-4260	10	18	-	-	PUNCT
ejpam-4260	10	19	open	open	ADJ
ejpam-4260	10	20	set	set	NOUN
ejpam-4260	10	21	,	,	PUNCT
ejpam-4260	10	22	supra	supra	PROPN
ejpam-4260	10	23	b	b	PROPN
ejpam-4260	10	24	limit	limit	NOUN
ejpam-4260	10	25	point	point	NOUN
ejpam-4260	10	26	,	,	PUNCT
ejpam-4260	10	27	sbtk	sbtk	NOUN
ejpam-4260	10	28	-	-	PUNCT
ejpam-4260	10	29	space	space	NOUN
ejpam-4260	10	30	(	(	PUNCT
ejpam-4260	10	31	k	k	NOUN
ejpam-4260	10	32	=	=	SYM
ejpam-4260	10	33	0	0	NUM
ejpam-4260	10	34	,	,	PUNCT
ejpam-4260	10	35	1	1	NUM
ejpam-4260	10	36	,	,	PUNCT
ejpam-4260	10	37	2	2	NUM
ejpam-4260	10	38	,	,	PUNCT
ejpam-4260	10	39	3	3	NUM
ejpam-4260	10	40	,	,	PUNCT
ejpam-4260	10	41	4	4	NUM
ejpam-4260	10	42	)	)	PUNCT
ejpam-4260	10	43	1	1	NUM
ejpam-4260	10	44	.	.	PUNCT
ejpam-4260	11	1	introduction	introduction	NOUN
ejpam-4260	11	2	and	and	CCONJ
ejpam-4260	11	3	preliminaries	preliminary	NOUN
ejpam-4260	11	4	the	the	DET
ejpam-4260	11	5	term	term	NOUN
ejpam-4260	11	6	“	"	PUNCT
ejpam-4260	11	7	topology	topology	NOUN
ejpam-4260	11	8	”	"	PUNCT
ejpam-4260	11	9	on	on	ADP
ejpam-4260	11	10	a	a	DET
ejpam-4260	11	11	nonempty	nonempty	ADV
ejpam-4260	11	12	set	set	VERB
ejpam-4260	11	13	u	u	NOUN
ejpam-4260	11	14	is	be	AUX
ejpam-4260	11	15	used	use	VERB
ejpam-4260	11	16	to	to	PART
ejpam-4260	11	17	describe	describe	VERB
ejpam-4260	11	18	a	a	DET
ejpam-4260	11	19	subfamily	subfamily	NOUN
ejpam-4260	11	20	of	of	ADP
ejpam-4260	11	21	the	the	DET
ejpam-4260	11	22	power	power	NOUN
ejpam-4260	11	23	set	set	VERB
ejpam-4260	11	24	u	u	PRON
ejpam-4260	11	25	which	which	PRON
ejpam-4260	11	26	is	be	AUX
ejpam-4260	11	27	closed	close	VERB
ejpam-4260	11	28	under	under	ADP
ejpam-4260	11	29	arbitrary	arbitrary	ADJ
ejpam-4260	11	30	union	union	NOUN
ejpam-4260	11	31	and	and	CCONJ
ejpam-4260	11	32	is	be	AUX
ejpam-4260	11	33	closed	close	VERB
ejpam-4260	11	34	under	under	ADP
ejpam-4260	11	35	finite	finite	ADJ
ejpam-4260	11	36	intersection	intersection	NOUN
ejpam-4260	11	37	.	.	PUNCT
ejpam-4260	12	1	to	to	PART
ejpam-4260	12	2	model	model	VERB
ejpam-4260	12	3	some	some	DET
ejpam-4260	12	4	real	real	ADJ
ejpam-4260	12	5	-	-	PUNCT
ejpam-4260	12	6	life	life	NOUN
ejpam-4260	12	7	issues	issue	NOUN
ejpam-4260	12	8	problems	problem	NOUN
ejpam-4260	12	9	and	and	CCONJ
ejpam-4260	12	10	keep	keep	VERB
ejpam-4260	12	11	some	some	DET
ejpam-4260	12	12	topological	topological	ADJ
ejpam-4260	12	13	properties	property	NOUN
ejpam-4260	12	14	under	under	ADP
ejpam-4260	12	15	conditions	condition	NOUN
ejpam-4260	12	16	fewer	few	ADJ
ejpam-4260	12	17	than	than	ADP
ejpam-4260	12	18	topology	topology	NOUN
ejpam-4260	12	19	’s	’s	PART
ejpam-4260	12	20	conditions	condition	NOUN
ejpam-4260	12	21	,	,	PUNCT
ejpam-4260	12	22	various	various	ADJ
ejpam-4260	12	23	types	type	NOUN
ejpam-4260	12	24	of	of	ADP
ejpam-4260	12	25	topology	topology	NOUN
ejpam-4260	12	26	’s	’s	PART
ejpam-4260	12	27	extensions	extension	NOUN
ejpam-4260	12	28	have	have	AUX
ejpam-4260	12	29	been	be	AUX
ejpam-4260	12	30	defined	define	VERB
ejpam-4260	12	31	and	and	CCONJ
ejpam-4260	12	32	discussed	discuss	VERB
ejpam-4260	12	33	.	.	PUNCT
ejpam-4260	13	1	one	one	NUM
ejpam-4260	13	2	of	of	ADP
ejpam-4260	13	3	the	the	DET
ejpam-4260	13	4	celebrated	celebrate	VERB
ejpam-4260	13	5	extensions	extension	NOUN
ejpam-4260	13	6	of	of	ADP
ejpam-4260	13	7	a	a	DET
ejpam-4260	13	8	topology	topology	NOUN
ejpam-4260	13	9	is	be	AUX
ejpam-4260	13	10	a	a	DET
ejpam-4260	13	11	supra	supra	ADJ
ejpam-4260	13	12	topology	topology	NOUN
ejpam-4260	13	13	defined	define	VERB
ejpam-4260	13	14	by	by	ADP
ejpam-4260	13	15	mashhour	mashhour	PROPN
ejpam-4260	13	16	et	et	PROPN
ejpam-4260	13	17	al	al	PROPN
ejpam-4260	13	18	.	.	PUNCT
ejpam-4260	14	1	[	[	X
ejpam-4260	14	2	24	24	NUM
ejpam-4260	14	3	]	]	PUNCT
ejpam-4260	14	4	in	in	ADP
ejpam-4260	14	5	1983	1983	NUM
ejpam-4260	14	6	.	.	PUNCT
ejpam-4260	15	1	then	then	ADV
ejpam-4260	15	2	,	,	PUNCT
ejpam-4260	15	3	maki	maki	PROPN
ejpam-4260	15	4	et	et	PROPN
ejpam-4260	15	5	al	al	PROPN
ejpam-4260	15	6	.	.	PUNCT
ejpam-4260	16	1	[	[	X
ejpam-4260	16	2	23	23	NUM
ejpam-4260	16	3	]	]	PUNCT
ejpam-4260	16	4	initiated	initiate	VERB
ejpam-4260	16	5	the	the	DET
ejpam-4260	16	6	concept	concept	NOUN
ejpam-4260	16	7	of	of	ADP
ejpam-4260	16	8	minimal	minimal	ADJ
ejpam-4260	16	9	structures	structure	NOUN
ejpam-4260	16	10	.	.	PUNCT
ejpam-4260	17	1	császár	császár	NOUN
ejpam-4260	18	1	[	[	X
ejpam-4260	18	2	17	17	NUM
ejpam-4260	18	3	]	]	PUNCT
ejpam-4260	18	4	,	,	PUNCT
ejpam-4260	18	5	in	in	ADP
ejpam-4260	18	6	2002	2002	NUM
ejpam-4260	18	7	,	,	PUNCT
ejpam-4260	18	8	presented	present	VERB
ejpam-4260	18	9	the	the	DET
ejpam-4260	18	10	concepts	concept	NOUN
ejpam-4260	18	11	generalized	generalize	VERB
ejpam-4260	18	12	topology	topology	NOUN
ejpam-4260	18	13	and	and	CCONJ
ejpam-4260	18	14	weak	weak	ADJ
ejpam-4260	18	15	structure	structure	NOUN
ejpam-4260	18	16	.	.	PUNCT
ejpam-4260	19	1	al	al	PROPN
ejpam-4260	19	2	-	-	PUNCT
ejpam-4260	19	3	odhari	odhari	ADJ
ejpam-4260	19	4	[	[	X
ejpam-4260	19	5	1	1	NUM
ejpam-4260	19	6	]	]	PUNCT
ejpam-4260	19	7	,	,	PUNCT
ejpam-4260	19	8	in	in	ADP
ejpam-4260	19	9	2015	2015	NUM
ejpam-4260	19	10	,	,	PUNCT
ejpam-4260	19	11	familiarized	familiarize	VERB
ejpam-4260	19	12	another	another	DET
ejpam-4260	19	13	extension	extension	NOUN
ejpam-4260	19	14	of	of	ADP
ejpam-4260	19	15	a	a	DET
ejpam-4260	19	16	topology	topology	NOUN
ejpam-4260	19	17	called	call	VERB
ejpam-4260	19	18	an	an	DET
ejpam-4260	19	19	infra	infra	NOUN
ejpam-4260	19	20	topology	topology	NOUN
ejpam-4260	19	21	.	.	PUNCT
ejpam-4260	20	1	in	in	ADP
ejpam-4260	20	2	the	the	DET
ejpam-4260	20	3	pioneering	pioneering	ADJ
ejpam-4260	20	4	work	work	NOUN
ejpam-4260	20	5	of	of	ADP
ejpam-4260	20	6	mashhour	mashhour	PROPN
ejpam-4260	20	7	et	et	PROPN
ejpam-4260	20	8	al	al	PROPN
ejpam-4260	20	9	.	.	PUNCT
ejpam-4260	21	1	[	[	X
ejpam-4260	21	2	24	24	NUM
ejpam-4260	21	3	]	]	X
ejpam-4260	21	4	the	the	DET
ejpam-4260	21	5	concepts	concept	NOUN
ejpam-4260	21	6	of	of	ADP
ejpam-4260	21	7	supra	supra	ADJ
ejpam-4260	21	8	continuity	continuity	NOUN
ejpam-4260	21	9	and	and	CCONJ
ejpam-4260	21	10	supra	supra	ADJ
ejpam-4260	21	11	separation	separation	NOUN
ejpam-4260	21	12	axioms	axiom	NOUN
ejpam-4260	21	13	were	be	AUX
ejpam-4260	21	14	studied	study	VERB
ejpam-4260	21	15	.	.	PUNCT
ejpam-4260	22	1	following	follow	VERB
ejpam-4260	22	2	this	this	DET
ejpam-4260	22	3	work	work	NOUN
ejpam-4260	22	4	,	,	PUNCT
ejpam-4260	22	5	many	many	ADJ
ejpam-4260	22	6	researchers	researcher	NOUN
ejpam-4260	22	7	have	have	AUX
ejpam-4260	22	8	explored	explore	VERB
ejpam-4260	22	9	the	the	DET
ejpam-4260	22	10	topological	topological	ADJ
ejpam-4260	22	11	concepts	concept	NOUN
ejpam-4260	22	12	and	and	CCONJ
ejpam-4260	22	13	notions	notion	NOUN
ejpam-4260	22	14	in	in	ADP
ejpam-4260	22	15	the	the	DET
ejpam-4260	22	16	frame	frame	NOUN
ejpam-4260	22	17	of	of	ADP
ejpam-4260	22	18	supra	supra	PROPN
ejpam-4260	22	19	topology	topology	NOUN
ejpam-4260	22	20	.	.	PUNCT
ejpam-4260	23	1	for	for	ADP
ejpam-4260	23	2	example	example	NOUN
ejpam-4260	23	3	,	,	PUNCT
ejpam-4260	23	4	some	some	DET
ejpam-4260	23	5	classes	class	NOUN
ejpam-4260	23	6	of	of	ADP
ejpam-4260	23	7	generalizations	generalization	NOUN
ejpam-4260	23	8	of	of	ADP
ejpam-4260	23	9	open	open	ADJ
ejpam-4260	23	10	sets	set	NOUN
ejpam-4260	23	11	were	be	AUX
ejpam-4260	23	12	furnished	furnish	VERB
ejpam-4260	23	13	to	to	ADP
ejpam-4260	23	14	supra	supra	ADJ
ejpam-4260	23	15	topologies	topology	NOUN
ejpam-4260	23	16	in	in	ADP
ejpam-4260	23	17	∗corresponding	∗corresponde	VERB
ejpam-4260	23	18	author	author	NOUN
ejpam-4260	23	19	.	.	PUNCT
ejpam-4260	24	1	doi	doi	NOUN
ejpam-4260	24	2	:	:	PUNCT
ejpam-4260	24	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4260	https://doi.org/10.29020/nybg.ejpam.v15i1.4260	NUM
ejpam-4260	24	4	email	email	NOUN
ejpam-4260	24	5	addresses	address	NOUN
ejpam-4260	24	6	:	:	PUNCT
ejpam-4260	24	7	tareqalshami83@gmail.com	tareqalshami83@gmail.com	X
ejpam-4260	24	8	(	(	PUNCT
ejpam-4260	24	9	t.m	t.m	PROPN
ejpam-4260	24	10	.	.	PROPN
ejpam-4260	24	11	al	al	PROPN
ejpam-4260	24	12	-	-	PUNCT
ejpam-4260	24	13	shami	shami	PROPN
ejpam-4260	24	14	)	)	PUNCT
ejpam-4260	24	15	,	,	PUNCT
ejpam-4260	24	16	mhemdiabd@gmail.com	mhemdiabd@gmail.com	X
ejpam-4260	24	17	(	(	PUNCT
ejpam-4260	24	18	a.	a.	NOUN
ejpam-4260	24	19	mhemdi	mhemdi	PROPN
ejpam-4260	24	20	)	)	PUNCT
ejpam-4260	24	21	,	,	PUNCT
ejpam-4260	24	22	mohjameel555@gmail.com	mohjameel555@gmail.com	X
ejpam-4260	24	23	(	(	PUNCT
ejpam-4260	24	24	m.	m.	PROPN
ejpam-4260	24	25	jameel	jameel	PROPN
ejpam-4260	24	26	)	)	PUNCT
ejpam-4260	24	27	,	,	PUNCT
ejpam-4260	24	28	saleh1284@mans.edu.eg	saleh1284@mans.edu.eg	INTJ
ejpam-4260	24	29	(	(	PUNCT
ejpam-4260	24	30	m.	m.	NOUN
ejpam-4260	24	31	abouhawwash	abouhawwash	PROPN
ejpam-4260	24	32	)	)	PUNCT
ejpam-4260	24	33	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4260	25	1	15	15	NUM
ejpam-4260	26	1	©	©	PROPN
ejpam-4260	26	2	2022	2022	NUM
ejpam-4260	26	3	ejpam	ejpam	VERB
ejpam-4260	26	4	all	all	DET
ejpam-4260	26	5	rights	right	NOUN
ejpam-4260	26	6	reserved	reserve	VERB
ejpam-4260	26	7	.	.	PUNCT
ejpam-4260	27	1	a.	a.	PROPN
ejpam-4260	27	2	mhemdi	mhemdi	PROPN
ejpam-4260	27	3	et	et	PROPN
ejpam-4260	27	4	al	al	PROPN
ejpam-4260	27	5	.	.	PUNCT
ejpam-4260	27	6	/	/	SYM
ejpam-4260	27	7	eur	eur	PROPN
ejpam-4260	27	8	.	.	PUNCT
ejpam-4260	28	1	j.	j.	PROPN
ejpam-4260	28	2	pure	pure	PROPN
ejpam-4260	28	3	appl	appl	PROPN
ejpam-4260	28	4	.	.	PROPN
ejpam-4260	28	5	math	math	PROPN
ejpam-4260	28	6	,	,	PUNCT
ejpam-4260	28	7	15	15	NUM
ejpam-4260	28	8	(	(	PUNCT
ejpam-4260	28	9	1	1	NUM
ejpam-4260	28	10	)	)	PUNCT
ejpam-4260	28	11	(	(	PUNCT
ejpam-4260	28	12	2022	2022	NUM
ejpam-4260	28	13	)	)	PUNCT
ejpam-4260	28	14	,	,	PUNCT
ejpam-4260	28	15	15	15	NUM
ejpam-4260	28	16	-	-	SYM
ejpam-4260	28	17	29	29	NUM
ejpam-4260	28	18	16	16	NUM
ejpam-4260	29	1	[	[	X
ejpam-4260	29	2	3	3	NUM
ejpam-4260	29	3	,	,	PUNCT
ejpam-4260	29	4	18	18	NUM
ejpam-4260	29	5	,	,	PUNCT
ejpam-4260	29	6	19	19	NUM
ejpam-4260	29	7	,	,	PUNCT
ejpam-4260	29	8	21	21	NUM
ejpam-4260	29	9	,	,	PUNCT
ejpam-4260	29	10	27	27	NUM
ejpam-4260	29	11	,	,	PUNCT
ejpam-4260	29	12	29	29	NUM
ejpam-4260	29	13	]	]	PUNCT
ejpam-4260	29	14	.	.	PUNCT
ejpam-4260	30	1	the	the	DET
ejpam-4260	30	2	class	class	NOUN
ejpam-4260	30	3	of	of	ADP
ejpam-4260	30	4	supra	supra	ADJ
ejpam-4260	30	5	r	r	NOUN
ejpam-4260	30	6	-	-	PUNCT
ejpam-4260	30	7	open	open	ADJ
ejpam-4260	30	8	sets	set	NOUN
ejpam-4260	30	9	was	be	AUX
ejpam-4260	30	10	studied	study	VERB
ejpam-4260	30	11	in	in	ADP
ejpam-4260	30	12	a	a	DET
ejpam-4260	30	13	topological	topological	ADJ
ejpam-4260	30	14	spaces	space	NOUN
ejpam-4260	30	15	under	under	ADP
ejpam-4260	30	16	the	the	DET
ejpam-4260	30	17	name	name	NOUN
ejpam-4260	30	18	of	of	ADP
ejpam-4260	30	19	somewhere	somewhere	ADJ
ejpam-4260	30	20	dense	dense	ADJ
ejpam-4260	30	21	sets	set	NOUN
ejpam-4260	30	22	[	[	X
ejpam-4260	30	23	4	4	NUM
ejpam-4260	30	24	,	,	PUNCT
ejpam-4260	30	25	16	16	NUM
ejpam-4260	30	26	]	]	PUNCT
ejpam-4260	30	27	.	.	PUNCT
ejpam-4260	31	1	mustafa	mustafa	PROPN
ejpam-4260	31	2	and	and	CCONJ
ejpam-4260	31	3	qoqazeh	qoqazeh	NOUN
ejpam-4260	32	1	[	[	X
ejpam-4260	32	2	26	26	NUM
ejpam-4260	32	3	]	]	PUNCT
ejpam-4260	32	4	applied	apply	VERB
ejpam-4260	32	5	supra	supra	ADJ
ejpam-4260	32	6	d	d	NOUN
ejpam-4260	32	7	-	-	PUNCT
ejpam-4260	32	8	sets	set	NOUN
ejpam-4260	32	9	to	to	PART
ejpam-4260	32	10	investigate	investigate	VERB
ejpam-4260	32	11	new	new	ADJ
ejpam-4260	32	12	families	family	NOUN
ejpam-4260	32	13	of	of	ADP
ejpam-4260	32	14	separation	separation	NOUN
ejpam-4260	32	15	axioms	axiom	NOUN
ejpam-4260	32	16	.	.	PUNCT
ejpam-4260	33	1	mustafa	mustafa	PROPN
ejpam-4260	34	1	[	[	X
ejpam-4260	34	2	25	25	NUM
ejpam-4260	34	3	]	]	PUNCT
ejpam-4260	34	4	defined	define	VERB
ejpam-4260	34	5	supra	supra	PROPN
ejpam-4260	34	6	bcompact	bcompact	NOUN
ejpam-4260	34	7	and	and	CCONJ
ejpam-4260	34	8	supra	supra	PROPN
ejpam-4260	34	9	b	b	PROPN
ejpam-4260	34	10	-	-	PUNCT
ejpam-4260	34	11	lindelof	lindelof	NOUN
ejpam-4260	34	12	spaces	space	NOUN
ejpam-4260	34	13	.	.	PUNCT
ejpam-4260	35	1	then	then	ADV
ejpam-4260	35	2	,	,	PUNCT
ejpam-4260	35	3	al	al	PROPN
ejpam-4260	35	4	-	-	PUNCT
ejpam-4260	35	5	shami	shami	PROPN
ejpam-4260	35	6	established	establish	VERB
ejpam-4260	35	7	the	the	DET
ejpam-4260	35	8	concepts	concept	NOUN
ejpam-4260	35	9	of	of	ADP
ejpam-4260	35	10	supra	supra	PROPN
ejpam-4260	35	11	paracompactness	paracompactness	PROPN
ejpam-4260	35	12	[	[	X
ejpam-4260	35	13	7	7	NUM
ejpam-4260	35	14	]	]	PUNCT
ejpam-4260	35	15	,	,	PUNCT
ejpam-4260	35	16	supra	supra	PROPN
ejpam-4260	35	17	complete	complete	ADJ
ejpam-4260	35	18	hausdorffness	hausdorffness	PROPN
ejpam-4260	35	19	and	and	CCONJ
ejpam-4260	35	20	supra	supra	ADJ
ejpam-4260	35	21	complete	complete	ADJ
ejpam-4260	35	22	regularity	regularity	NOUN
ejpam-4260	35	23	[	[	X
ejpam-4260	35	24	8	8	NUM
ejpam-4260	35	25	]	]	PUNCT
ejpam-4260	35	26	.	.	PUNCT
ejpam-4260	36	1	in	in	ADP
ejpam-4260	36	2	[	[	X
ejpam-4260	36	3	9–11	9–11	NOUN
ejpam-4260	36	4	,	,	PUNCT
ejpam-4260	36	5	20	20	NUM
ejpam-4260	36	6	]	]	PUNCT
ejpam-4260	36	7	,	,	PUNCT
ejpam-4260	36	8	al	al	PROPN
ejpam-4260	36	9	-	-	PUNCT
ejpam-4260	36	10	shami	shami	PROPN
ejpam-4260	36	11	with	with	ADP
ejpam-4260	36	12	his	his	PRON
ejpam-4260	36	13	coauthors	coauthor	NOUN
ejpam-4260	36	14	scrutinized	scrutinize	VERB
ejpam-4260	36	15	the	the	DET
ejpam-4260	36	16	main	main	ADJ
ejpam-4260	36	17	properties	property	NOUN
ejpam-4260	36	18	of	of	ADP
ejpam-4260	36	19	limit	limit	NOUN
ejpam-4260	36	20	points	point	NOUN
ejpam-4260	36	21	using	use	VERB
ejpam-4260	36	22	the	the	DET
ejpam-4260	36	23	famous	famous	ADJ
ejpam-4260	36	24	generalizations	generalization	NOUN
ejpam-4260	36	25	of	of	ADP
ejpam-4260	36	26	supra	supra	ADJ
ejpam-4260	36	27	open	open	ADJ
ejpam-4260	36	28	sets	set	NOUN
ejpam-4260	36	29	.	.	PUNCT
ejpam-4260	37	1	also	also	ADV
ejpam-4260	37	2	,	,	PUNCT
ejpam-4260	37	3	al	al	PROPN
ejpam-4260	37	4	-	-	PUNCT
ejpam-4260	37	5	shami	shami	PROPN
ejpam-4260	37	6	with	with	ADP
ejpam-4260	37	7	his	his	PRON
ejpam-4260	37	8	coauthors	coauthor	NOUN
ejpam-4260	38	1	[	[	X
ejpam-4260	38	2	2	2	NUM
ejpam-4260	38	3	,	,	PUNCT
ejpam-4260	38	4	5	5	NUM
ejpam-4260	38	5	,	,	PUNCT
ejpam-4260	38	6	6	6	NUM
ejpam-4260	38	7	,	,	PUNCT
ejpam-4260	38	8	12	12	NUM
ejpam-4260	38	9	]	]	PUNCT
ejpam-4260	38	10	introduced	introduce	VERB
ejpam-4260	38	11	different	different	ADJ
ejpam-4260	38	12	kinds	kind	NOUN
ejpam-4260	38	13	of	of	ADP
ejpam-4260	38	14	supra	supra	ADJ
ejpam-4260	38	15	compactness	compactness	NOUN
ejpam-4260	38	16	.	.	PUNCT
ejpam-4260	39	1	the	the	DET
ejpam-4260	39	2	connected	connect	VERB
ejpam-4260	39	3	spaces	space	NOUN
ejpam-4260	39	4	were	be	AUX
ejpam-4260	39	5	also	also	ADV
ejpam-4260	39	6	initiated	initiate	VERB
ejpam-4260	39	7	in	in	ADP
ejpam-4260	39	8	supra	supra	PROPN
ejpam-4260	39	9	topologies	topology	NOUN
ejpam-4260	39	10	by	by	ADP
ejpam-4260	39	11	the	the	DET
ejpam-4260	39	12	authors	author	NOUN
ejpam-4260	39	13	of	of	ADP
ejpam-4260	39	14	[	[	X
ejpam-4260	39	15	22	22	NUM
ejpam-4260	39	16	,	,	PUNCT
ejpam-4260	39	17	28	28	NUM
ejpam-4260	39	18	]	]	PUNCT
ejpam-4260	39	19	.	.	PUNCT
ejpam-4260	40	1	as	as	ADP
ejpam-4260	40	2	evidence	evidence	NOUN
ejpam-4260	40	3	of	of	ADP
ejpam-4260	40	4	the	the	DET
ejpam-4260	40	5	importance	importance	NOUN
ejpam-4260	40	6	of	of	ADP
ejpam-4260	40	7	supra	supra	PROPN
ejpam-4260	40	8	topologies	topology	NOUN
ejpam-4260	40	9	,	,	PUNCT
ejpam-4260	40	10	they	they	PRON
ejpam-4260	40	11	were	be	AUX
ejpam-4260	40	12	explored	explore	VERB
ejpam-4260	40	13	and	and	CCONJ
ejpam-4260	40	14	discussed	discuss	VERB
ejpam-4260	40	15	in	in	ADP
ejpam-4260	40	16	the	the	DET
ejpam-4260	40	17	soft	soft	ADJ
ejpam-4260	40	18	frames	frame	NOUN
ejpam-4260	40	19	;	;	PUNCT
ejpam-4260	40	20	see	see	VERB
ejpam-4260	40	21	,	,	PUNCT
ejpam-4260	40	22	[	[	X
ejpam-4260	40	23	13–15	13–15	NUM
ejpam-4260	40	24	]	]	PUNCT
ejpam-4260	40	25	.	.	PUNCT
ejpam-4260	41	1	it	it	PRON
ejpam-4260	41	2	should	should	AUX
ejpam-4260	41	3	be	be	AUX
ejpam-4260	41	4	noted	note	VERB
ejpam-4260	41	5	that	that	SCONJ
ejpam-4260	41	6	some	some	DET
ejpam-4260	41	7	topology	topology	NOUN
ejpam-4260	41	8	’s	’s	PART
ejpam-4260	41	9	properties	property	NOUN
ejpam-4260	41	10	are	be	AUX
ejpam-4260	41	11	evaporated	evaporate	VERB
ejpam-4260	41	12	in	in	ADP
ejpam-4260	41	13	supra	supra	PROPN
ejpam-4260	41	14	topologies	topology	NOUN
ejpam-4260	41	15	like	like	ADP
ejpam-4260	41	16	the	the	DET
ejpam-4260	41	17	distribution	distribution	NOUN
ejpam-4260	41	18	property	property	NOUN
ejpam-4260	41	19	for	for	ADP
ejpam-4260	41	20	the	the	DET
ejpam-4260	41	21	interior	interior	ADJ
ejpam-4260	41	22	and	and	CCONJ
ejpam-4260	41	23	closure	closure	NOUN
ejpam-4260	41	24	operators	operator	NOUN
ejpam-4260	41	25	with	with	ADP
ejpam-4260	41	26	respect	respect	NOUN
ejpam-4260	41	27	to	to	ADP
ejpam-4260	41	28	the	the	DET
ejpam-4260	41	29	operations	operation	NOUN
ejpam-4260	41	30	of	of	ADP
ejpam-4260	41	31	intersection	intersection	NOUN
ejpam-4260	41	32	and	and	CCONJ
ejpam-4260	41	33	union	union	NOUN
ejpam-4260	41	34	.	.	PUNCT
ejpam-4260	42	1	another	another	DET
ejpam-4260	42	2	example	example	NOUN
ejpam-4260	42	3	of	of	ADP
ejpam-4260	42	4	these	these	DET
ejpam-4260	42	5	missing	miss	VERB
ejpam-4260	42	6	properties	property	NOUN
ejpam-4260	42	7	is	be	AUX
ejpam-4260	42	8	the	the	DET
ejpam-4260	42	9	relationship	relationship	NOUN
ejpam-4260	42	10	between	between	ADP
ejpam-4260	42	11	compact	compact	ADJ
ejpam-4260	42	12	and	and	CCONJ
ejpam-4260	42	13	closed	closed	ADJ
ejpam-4260	42	14	subsets	subset	NOUN
ejpam-4260	42	15	of	of	ADP
ejpam-4260	42	16	hausdorff	hausdorff	NOUN
ejpam-4260	42	17	space	space	NOUN
ejpam-4260	42	18	.	.	PUNCT
ejpam-4260	43	1	we	we	PRON
ejpam-4260	43	2	organize	organize	VERB
ejpam-4260	43	3	the	the	DET
ejpam-4260	43	4	rest	rest	NOUN
ejpam-4260	43	5	of	of	ADP
ejpam-4260	43	6	this	this	DET
ejpam-4260	43	7	manuscript	manuscript	NOUN
ejpam-4260	43	8	as	as	SCONJ
ejpam-4260	43	9	follows	follow	VERB
ejpam-4260	43	10	.	.	PUNCT
ejpam-4260	44	1	in	in	ADP
ejpam-4260	44	2	section	section	NOUN
ejpam-4260	44	3	(	(	PUNCT
ejpam-4260	44	4	2	2	NUM
ejpam-4260	44	5	)	)	PUNCT
ejpam-4260	44	6	,	,	PUNCT
ejpam-4260	44	7	we	we	PRON
ejpam-4260	44	8	recall	recall	VERB
ejpam-4260	44	9	the	the	DET
ejpam-4260	44	10	concepts	concept	NOUN
ejpam-4260	44	11	and	and	CCONJ
ejpam-4260	44	12	findings	finding	NOUN
ejpam-4260	44	13	that	that	PRON
ejpam-4260	44	14	make	make	VERB
ejpam-4260	44	15	this	this	DET
ejpam-4260	44	16	work	work	NOUN
ejpam-4260	44	17	readable	readable	ADJ
ejpam-4260	44	18	.	.	PUNCT
ejpam-4260	45	1	in	in	ADP
ejpam-4260	45	2	section	section	NOUN
ejpam-4260	45	3	(	(	PUNCT
ejpam-4260	45	4	3	3	NUM
ejpam-4260	45	5	)	)	PUNCT
ejpam-4260	45	6	,	,	PUNCT
ejpam-4260	45	7	we	we	PRON
ejpam-4260	45	8	apply	apply	VERB
ejpam-4260	45	9	the	the	DET
ejpam-4260	45	10	class	class	NOUN
ejpam-4260	45	11	of	of	ADP
ejpam-4260	45	12	supra	supra	PROPN
ejpam-4260	45	13	bopen	bopen	PROPN
ejpam-4260	45	14	sets	set	NOUN
ejpam-4260	45	15	to	to	PART
ejpam-4260	45	16	display	display	VERB
ejpam-4260	45	17	novel	novel	ADJ
ejpam-4260	45	18	kinds	kind	NOUN
ejpam-4260	45	19	of	of	ADP
ejpam-4260	45	20	limit	limit	NOUN
ejpam-4260	45	21	points	point	NOUN
ejpam-4260	45	22	of	of	ADP
ejpam-4260	45	23	sets	set	NOUN
ejpam-4260	45	24	.	.	PUNCT
ejpam-4260	46	1	we	we	PRON
ejpam-4260	46	2	devoted	devote	VERB
ejpam-4260	46	3	section	section	NOUN
ejpam-4260	46	4	(	(	PUNCT
ejpam-4260	46	5	4	4	NUM
ejpam-4260	46	6	)	)	PUNCT
ejpam-4260	46	7	to	to	PART
ejpam-4260	46	8	introduce	introduce	VERB
ejpam-4260	46	9	new	new	ADJ
ejpam-4260	46	10	families	family	NOUN
ejpam-4260	46	11	of	of	ADP
ejpam-4260	46	12	spaces	space	NOUN
ejpam-4260	46	13	,	,	PUNCT
ejpam-4260	46	14	namely	namely	ADV
ejpam-4260	46	15	sbtk	sbtk	NOUN
ejpam-4260	46	16	-	-	PUNCT
ejpam-4260	46	17	spaces	space	NOUN
ejpam-4260	46	18	(	(	PUNCT
ejpam-4260	46	19	k	k	NOUN
ejpam-4260	46	20	=	=	SYM
ejpam-4260	46	21	0	0	NUM
ejpam-4260	46	22	,	,	PUNCT
ejpam-4260	46	23	1	1	NUM
ejpam-4260	46	24	,	,	PUNCT
ejpam-4260	46	25	2	2	NUM
ejpam-4260	46	26	,	,	PUNCT
ejpam-4260	46	27	3	3	NUM
ejpam-4260	46	28	,	,	PUNCT
ejpam-4260	46	29	4	4	NUM
ejpam-4260	46	30	)	)	PUNCT
ejpam-4260	46	31	.	.	PUNCT
ejpam-4260	47	1	finally	finally	ADV
ejpam-4260	47	2	,	,	PUNCT
ejpam-4260	47	3	we	we	PRON
ejpam-4260	47	4	provide	provide	VERB
ejpam-4260	47	5	some	some	DET
ejpam-4260	47	6	conclusions	conclusion	NOUN
ejpam-4260	47	7	and	and	CCONJ
ejpam-4260	47	8	suggest	suggest	VERB
ejpam-4260	47	9	some	some	DET
ejpam-4260	47	10	future	future	ADJ
ejpam-4260	47	11	work	work	NOUN
ejpam-4260	47	12	in	in	ADP
ejpam-4260	47	13	section	section	NOUN
ejpam-4260	47	14	(	(	PUNCT
ejpam-4260	47	15	5	5	NUM
ejpam-4260	47	16	)	)	PUNCT
ejpam-4260	47	17	.	.	PUNCT
ejpam-4260	48	1	2	2	X
ejpam-4260	48	2	.	.	X
ejpam-4260	48	3	preliminaries	preliminary	NOUN
ejpam-4260	48	4	herein	herein	NOUN
ejpam-4260	48	5	,	,	PUNCT
ejpam-4260	48	6	we	we	PRON
ejpam-4260	48	7	mention	mention	VERB
ejpam-4260	48	8	some	some	DET
ejpam-4260	48	9	concepts	concept	NOUN
ejpam-4260	48	10	and	and	CCONJ
ejpam-4260	48	11	findings	finding	NOUN
ejpam-4260	48	12	given	give	VERB
ejpam-4260	48	13	in	in	ADP
ejpam-4260	48	14	the	the	DET
ejpam-4260	48	15	literature	literature	NOUN
ejpam-4260	48	16	of	of	ADP
ejpam-4260	48	17	supra	supra	PROPN
ejpam-4260	48	18	topologies	topology	NOUN
ejpam-4260	48	19	that	that	PRON
ejpam-4260	48	20	are	be	AUX
ejpam-4260	48	21	necessary	necessary	ADJ
ejpam-4260	48	22	to	to	PART
ejpam-4260	48	23	understand	understand	VERB
ejpam-4260	48	24	this	this	DET
ejpam-4260	48	25	article	article	NOUN
ejpam-4260	48	26	.	.	PUNCT
ejpam-4260	49	1	definition	definition	NOUN
ejpam-4260	49	2	1	1	NUM
ejpam-4260	49	3	.	.	PUNCT
ejpam-4260	50	1	[	[	X
ejpam-4260	50	2	24	24	NUM
ejpam-4260	50	3	]	]	PUNCT
ejpam-4260	50	4	we	we	PRON
ejpam-4260	50	5	call	call	VERB
ejpam-4260	50	6	a	a	DET
ejpam-4260	50	7	subfamily	subfamily	ADV
ejpam-4260	50	8	ω	ω	NOUN
ejpam-4260	50	9	of	of	ADP
ejpam-4260	50	10	the	the	DET
ejpam-4260	50	11	power	power	NOUN
ejpam-4260	50	12	set	set	NOUN
ejpam-4260	50	13	of	of	ADP
ejpam-4260	50	14	u	u	PROPN
ejpam-4260	50	15	̸=	̸=	PROPN
ejpam-4260	50	16	∅	∅	VERB
ejpam-4260	50	17	a	a	DET
ejpam-4260	50	18	supra	supra	ADJ
ejpam-4260	50	19	topology	topology	NOUN
ejpam-4260	50	20	(	(	PUNCT
ejpam-4260	50	21	in	in	ADP
ejpam-4260	50	22	short	short	ADJ
ejpam-4260	50	23	,	,	PUNCT
ejpam-4260	50	24	st	st	PROPN
ejpam-4260	50	25	)	)	PUNCT
ejpam-4260	50	26	provided	provide	VERB
ejpam-4260	50	27	that	that	SCONJ
ejpam-4260	50	28	u	u	PROPN
ejpam-4260	50	29	∈	∈	PROPN
ejpam-4260	50	30	ω	ω	PROPN
ejpam-4260	50	31	and	and	CCONJ
ejpam-4260	50	32	the	the	DET
ejpam-4260	50	33	arbitrary	arbitrary	ADJ
ejpam-4260	50	34	union	union	NOUN
ejpam-4260	50	35	of	of	ADP
ejpam-4260	50	36	members	member	NOUN
ejpam-4260	50	37	of	of	ADP
ejpam-4260	50	38	ω	ω	PROPN
ejpam-4260	50	39	is	be	AUX
ejpam-4260	50	40	also	also	ADV
ejpam-4260	50	41	a	a	DET
ejpam-4260	50	42	member	member	NOUN
ejpam-4260	50	43	of	of	ADP
ejpam-4260	50	44	ω	ω	PROPN
ejpam-4260	50	45	.	.	PUNCT
ejpam-4260	51	1	we	we	PRON
ejpam-4260	51	2	call	call	VERB
ejpam-4260	51	3	a	a	DET
ejpam-4260	51	4	pair	pair	NOUN
ejpam-4260	51	5	(	(	PUNCT
ejpam-4260	51	6	u	u	NOUN
ejpam-4260	51	7	,	,	PUNCT
ejpam-4260	51	8	ω	ω	PROPN
ejpam-4260	51	9	)	)	PUNCT
ejpam-4260	51	10	a	a	DET
ejpam-4260	51	11	supra	supra	ADJ
ejpam-4260	51	12	topological	topological	ADJ
ejpam-4260	51	13	space	space	NOUN
ejpam-4260	51	14	(	(	PUNCT
ejpam-4260	51	15	in	in	ADP
ejpam-4260	51	16	short	short	ADJ
ejpam-4260	51	17	,	,	PUNCT
ejpam-4260	51	18	sts	st	NOUN
ejpam-4260	51	19	)	)	PUNCT
ejpam-4260	51	20	.	.	PUNCT
ejpam-4260	52	1	the	the	DET
ejpam-4260	52	2	members	member	NOUN
ejpam-4260	52	3	of	of	ADP
ejpam-4260	52	4	ω	ω	PROPN
ejpam-4260	52	5	are	be	AUX
ejpam-4260	52	6	said	say	VERB
ejpam-4260	52	7	to	to	PART
ejpam-4260	52	8	be	be	AUX
ejpam-4260	52	9	supra	supra	ADJ
ejpam-4260	52	10	open	open	ADJ
ejpam-4260	52	11	sets	set	NOUN
ejpam-4260	52	12	and	and	CCONJ
ejpam-4260	52	13	the	the	DET
ejpam-4260	52	14	complement	complement	NOUN
ejpam-4260	52	15	of	of	ADP
ejpam-4260	52	16	each	each	DET
ejpam-4260	52	17	member	member	NOUN
ejpam-4260	52	18	of	of	ADP
ejpam-4260	52	19	ω	ω	PROPN
ejpam-4260	52	20	is	be	AUX
ejpam-4260	52	21	said	say	VERB
ejpam-4260	52	22	to	to	PART
ejpam-4260	52	23	be	be	AUX
ejpam-4260	52	24	a	a	DET
ejpam-4260	52	25	supra	supra	NOUN
ejpam-4260	52	26	closed	close	VERB
ejpam-4260	52	27	set	set	NOUN
ejpam-4260	52	28	.	.	PUNCT
ejpam-4260	53	1	remark	remark	PROPN
ejpam-4260	53	2	1	1	NUM
ejpam-4260	53	3	.	.	PUNCT
ejpam-4260	54	1	(	(	PUNCT
ejpam-4260	54	2	i	i	NOUN
ejpam-4260	54	3	)	)	PUNCT
ejpam-4260	54	4	we	we	PRON
ejpam-4260	54	5	call	call	VERB
ejpam-4260	54	6	ω	ω	ADP
ejpam-4260	54	7	an	an	DET
ejpam-4260	54	8	associated	associated	PROPN
ejpam-4260	54	9	st	st	PROPN
ejpam-4260	54	10	with	with	ADP
ejpam-4260	54	11	a	a	DET
ejpam-4260	54	12	topology	topology	NOUN
ejpam-4260	54	13	τ	τ	X
ejpam-4260	54	14	if	if	SCONJ
ejpam-4260	54	15	τ	τ	PROPN
ejpam-4260	54	16	⊆	⊆	NUM
ejpam-4260	54	17	ω	ω	NUM
ejpam-4260	54	18	.	.	PUNCT
ejpam-4260	55	1	(	(	PUNCT
ejpam-4260	55	2	ii	ii	NOUN
ejpam-4260	55	3	)	)	PUNCT
ejpam-4260	55	4	henceforth	henceforth	ADV
ejpam-4260	55	5	,	,	PUNCT
ejpam-4260	55	6	we	we	PRON
ejpam-4260	55	7	consider	consider	VERB
ejpam-4260	55	8	(	(	PUNCT
ejpam-4260	55	9	u	u	NOUN
ejpam-4260	55	10	,	,	PUNCT
ejpam-4260	55	11	ω	ω	PROPN
ejpam-4260	55	12	)	)	PUNCT
ejpam-4260	55	13	and	and	CCONJ
ejpam-4260	55	14	(	(	PUNCT
ejpam-4260	55	15	v	v	NOUN
ejpam-4260	55	16	,	,	PUNCT
ejpam-4260	55	17	ψ	ψ	NOUN
ejpam-4260	55	18	)	)	PUNCT
ejpam-4260	55	19	as	as	ADP
ejpam-4260	55	20	associated	associate	VERB
ejpam-4260	55	21	stss	stss	NOUN
ejpam-4260	55	22	with	with	ADP
ejpam-4260	55	23	the	the	DET
ejpam-4260	55	24	topological	topological	ADJ
ejpam-4260	55	25	spaces	space	NOUN
ejpam-4260	55	26	(	(	PUNCT
ejpam-4260	55	27	u	u	NOUN
ejpam-4260	55	28	,	,	PUNCT
ejpam-4260	55	29	τ	τ	PROPN
ejpam-4260	55	30	)	)	PUNCT
ejpam-4260	55	31	and	and	CCONJ
ejpam-4260	55	32	(	(	PUNCT
ejpam-4260	55	33	v	v	NOUN
ejpam-4260	55	34	,	,	PUNCT
ejpam-4260	55	35	θ	θ	NOUN
ejpam-4260	55	36	)	)	PUNCT
ejpam-4260	55	37	,	,	PUNCT
ejpam-4260	55	38	respectively	respectively	ADV
ejpam-4260	55	39	.	.	PUNCT
ejpam-4260	56	1	definition	definition	NOUN
ejpam-4260	56	2	2	2	NUM
ejpam-4260	56	3	.	.	PUNCT
ejpam-4260	57	1	[	[	X
ejpam-4260	57	2	29	29	NUM
ejpam-4260	57	3	]	]	PUNCT
ejpam-4260	57	4	a	a	DET
ejpam-4260	57	5	subset	subset	NOUN
ejpam-4260	57	6	o	o	NOUN
ejpam-4260	57	7	of	of	ADP
ejpam-4260	57	8	(	(	PUNCT
ejpam-4260	57	9	u	u	PROPN
ejpam-4260	57	10	,	,	PUNCT
ejpam-4260	57	11	ω	ω	PROPN
ejpam-4260	57	12	)	)	PUNCT
ejpam-4260	57	13	is	be	AUX
ejpam-4260	57	14	said	say	VERB
ejpam-4260	57	15	to	to	PART
ejpam-4260	57	16	be	be	AUX
ejpam-4260	57	17	supra	supra	ADJ
ejpam-4260	57	18	b	b	NOUN
ejpam-4260	57	19	-	-	PUNCT
ejpam-4260	57	20	open	open	ADJ
ejpam-4260	57	21	if	if	SCONJ
ejpam-4260	57	22	o	o	PROPN
ejpam-4260	57	23	⊆	⊆	NUM
ejpam-4260	57	24	int(cl(o	int(cl(o	PROPN
ejpam-4260	57	25	)	)	PUNCT
ejpam-4260	57	26	)	)	PUNCT
ejpam-4260	57	27	⋃	⋃	VERB
ejpam-4260	57	28	cl(int(o	cl(int(o	NOUN
ejpam-4260	57	29	)	)	PUNCT
ejpam-4260	57	30	)	)	PUNCT
ejpam-4260	57	31	.	.	PUNCT
ejpam-4260	58	1	definition	definition	NOUN
ejpam-4260	58	2	3	3	NUM
ejpam-4260	58	3	.	.	PUNCT
ejpam-4260	59	1	[	[	X
ejpam-4260	59	2	18	18	NUM
ejpam-4260	59	3	,	,	PUNCT
ejpam-4260	59	4	24	24	NUM
ejpam-4260	59	5	]	]	PUNCT
ejpam-4260	59	6	let	let	VERB
ejpam-4260	59	7	o	o	NOUN
ejpam-4260	59	8	⊆	⊆	NUM
ejpam-4260	59	9	u	u	NOUN
ejpam-4260	59	10	.	.	PUNCT
ejpam-4260	60	1	(	(	PUNCT
ejpam-4260	60	2	i	i	NOUN
ejpam-4260	60	3	)	)	PUNCT
ejpam-4260	60	4	the	the	DET
ejpam-4260	60	5	union	union	NOUN
ejpam-4260	60	6	of	of	ADP
ejpam-4260	60	7	all	all	DET
ejpam-4260	60	8	supra	supra	PROPN
ejpam-4260	60	9	open	open	ADJ
ejpam-4260	60	10	(	(	PUNCT
ejpam-4260	60	11	respectively	respectively	ADV
ejpam-4260	60	12	,	,	PUNCT
ejpam-4260	60	13	supra	supra	PROPN
ejpam-4260	60	14	b	b	NOUN
ejpam-4260	60	15	-	-	PUNCT
ejpam-4260	60	16	open	open	ADJ
ejpam-4260	60	17	)	)	PUNCT
ejpam-4260	60	18	subsets	subset	NOUN
ejpam-4260	60	19	of	of	ADP
ejpam-4260	60	20	an	an	DET
ejpam-4260	60	21	sts	st	NOUN
ejpam-4260	60	22	(	(	PUNCT
ejpam-4260	60	23	u	u	NOUN
ejpam-4260	60	24	,	,	PUNCT
ejpam-4260	60	25	ω	ω	PROPN
ejpam-4260	60	26	)	)	PUNCT
ejpam-4260	60	27	contained	contain	VERB
ejpam-4260	60	28	in	in	ADP
ejpam-4260	60	29	o	o	PROPN
ejpam-4260	60	30	is	be	AUX
ejpam-4260	60	31	denoted	denote	VERB
ejpam-4260	60	32	by	by	ADP
ejpam-4260	60	33	intω(o	intω(o	NOUN
ejpam-4260	60	34	)	)	PUNCT
ejpam-4260	60	35	(	(	PUNCT
ejpam-4260	60	36	respectively	respectively	ADV
ejpam-4260	60	37	,	,	PUNCT
ejpam-4260	60	38	bintω(o	bintω(o	PROPN
ejpam-4260	60	39	)	)	PUNCT
ejpam-4260	60	40	)	)	PUNCT
ejpam-4260	60	41	.	.	PUNCT
ejpam-4260	61	1	a.	a.	PROPN
ejpam-4260	61	2	mhemdi	mhemdi	PROPN
ejpam-4260	61	3	et	et	PROPN
ejpam-4260	61	4	al	al	PROPN
ejpam-4260	61	5	.	.	PUNCT
ejpam-4260	61	6	/	/	SYM
ejpam-4260	61	7	eur	eur	PROPN
ejpam-4260	61	8	.	.	PUNCT
ejpam-4260	62	1	j.	j.	PROPN
ejpam-4260	62	2	pure	pure	PROPN
ejpam-4260	62	3	appl	appl	PROPN
ejpam-4260	62	4	.	.	PROPN
ejpam-4260	62	5	math	math	PROPN
ejpam-4260	62	6	,	,	PUNCT
ejpam-4260	62	7	15	15	NUM
ejpam-4260	62	8	(	(	PUNCT
ejpam-4260	62	9	1	1	NUM
ejpam-4260	62	10	)	)	PUNCT
ejpam-4260	62	11	(	(	PUNCT
ejpam-4260	62	12	2022	2022	NUM
ejpam-4260	62	13	)	)	PUNCT
ejpam-4260	62	14	,	,	PUNCT
ejpam-4260	62	15	15	15	NUM
ejpam-4260	62	16	-	-	SYM
ejpam-4260	62	17	29	29	NUM
ejpam-4260	62	18	17	17	NUM
ejpam-4260	62	19	(	(	PUNCT
ejpam-4260	62	20	ii	ii	NOUN
ejpam-4260	62	21	)	)	PUNCT
ejpam-4260	62	22	the	the	DET
ejpam-4260	62	23	intersection	intersection	NOUN
ejpam-4260	62	24	of	of	ADP
ejpam-4260	62	25	all	all	DET
ejpam-4260	62	26	supra	supra	PROPN
ejpam-4260	62	27	closed	close	VERB
ejpam-4260	62	28	(	(	PUNCT
ejpam-4260	62	29	respectively	respectively	ADV
ejpam-4260	62	30	,	,	PUNCT
ejpam-4260	62	31	supra	supra	PROPN
ejpam-4260	62	32	b	b	PROPN
ejpam-4260	62	33	-	-	PUNCT
ejpam-4260	62	34	closed	closed	ADJ
ejpam-4260	62	35	)	)	PUNCT
ejpam-4260	62	36	subsets	subset	NOUN
ejpam-4260	62	37	of	of	ADP
ejpam-4260	62	38	an	an	DET
ejpam-4260	62	39	sts	st	NOUN
ejpam-4260	62	40	(	(	PUNCT
ejpam-4260	62	41	u	u	NOUN
ejpam-4260	62	42	,	,	PUNCT
ejpam-4260	62	43	ω	ω	PROPN
ejpam-4260	62	44	)	)	PUNCT
ejpam-4260	62	45	including	include	VERB
ejpam-4260	62	46	o	o	PROPN
ejpam-4260	62	47	is	be	AUX
ejpam-4260	62	48	denoted	denote	VERB
ejpam-4260	62	49	by	by	ADP
ejpam-4260	62	50	clω(o	clω(o	PROPN
ejpam-4260	62	51	)	)	PUNCT
ejpam-4260	62	52	(	(	PUNCT
ejpam-4260	62	53	respectively	respectively	ADV
ejpam-4260	62	54	,	,	PUNCT
ejpam-4260	62	55	bclω(o	bclω(o	PROPN
ejpam-4260	62	56	)	)	PUNCT
ejpam-4260	62	57	)	)	PUNCT
ejpam-4260	62	58	.	.	PUNCT
ejpam-4260	63	1	for	for	ADP
ejpam-4260	63	2	simplicity	simplicity	NOUN
ejpam-4260	63	3	,	,	PUNCT
ejpam-4260	63	4	we	we	PRON
ejpam-4260	63	5	sometimes	sometimes	ADV
ejpam-4260	63	6	write	write	VERB
ejpam-4260	63	7	int(o	int(o	PROPN
ejpam-4260	63	8	)	)	PUNCT
ejpam-4260	63	9	,	,	PUNCT
ejpam-4260	63	10	cl(o	cl(o	NUM
ejpam-4260	63	11	)	)	PUNCT
ejpam-4260	63	12	,	,	PUNCT
ejpam-4260	63	13	bint(o	bint(o	NOUN
ejpam-4260	63	14	)	)	PUNCT
ejpam-4260	63	15	and	and	CCONJ
ejpam-4260	63	16	bcl(o	bcl(o	PROPN
ejpam-4260	63	17	)	)	PUNCT
ejpam-4260	63	18	instead	instead	ADV
ejpam-4260	63	19	of	of	ADP
ejpam-4260	63	20	intω(o	intω(o	NOUN
ejpam-4260	63	21	)	)	PUNCT
ejpam-4260	63	22	,	,	PUNCT
ejpam-4260	63	23	clω(o	clω(o	PROPN
ejpam-4260	63	24	)	)	PUNCT
ejpam-4260	63	25	,	,	PUNCT
ejpam-4260	63	26	bintω(o	bintω(o	PROPN
ejpam-4260	63	27	)	)	PUNCT
ejpam-4260	63	28	and	and	CCONJ
ejpam-4260	63	29	bclω(o	bclω(o	PROPN
ejpam-4260	63	30	)	)	PUNCT
ejpam-4260	63	31	,	,	PUNCT
ejpam-4260	63	32	respectively	respectively	ADV
ejpam-4260	63	33	.	.	PUNCT
ejpam-4260	64	1	definition	definition	NOUN
ejpam-4260	64	2	4	4	NUM
ejpam-4260	64	3	.	.	PUNCT
ejpam-4260	65	1	[	[	X
ejpam-4260	65	2	18	18	NUM
ejpam-4260	65	3	]	]	PUNCT
ejpam-4260	65	4	let	let	VERB
ejpam-4260	65	5	g	g	NOUN
ejpam-4260	65	6	:	:	PUNCT
ejpam-4260	65	7	(	(	PUNCT
ejpam-4260	65	8	u	u	NOUN
ejpam-4260	65	9	,	,	PUNCT
ejpam-4260	65	10	ω	ω	PROPN
ejpam-4260	65	11	)	)	PUNCT
ejpam-4260	65	12	→	→	SYM
ejpam-4260	65	13	(	(	PUNCT
ejpam-4260	65	14	y	y	NOUN
ejpam-4260	65	15	,	,	PUNCT
ejpam-4260	65	16	ψ	ψ	NOUN
ejpam-4260	65	17	)	)	PUNCT
ejpam-4260	65	18	be	be	AUX
ejpam-4260	65	19	a	a	DET
ejpam-4260	65	20	mapping	mapping	NOUN
ejpam-4260	65	21	.	.	PUNCT
ejpam-4260	66	1	(	(	PUNCT
ejpam-4260	66	2	i	i	NOUN
ejpam-4260	66	3	)	)	PUNCT
ejpam-4260	66	4	if	if	SCONJ
ejpam-4260	66	5	the	the	DET
ejpam-4260	66	6	inverse	inverse	ADJ
ejpam-4260	66	7	image	image	NOUN
ejpam-4260	66	8	of	of	ADP
ejpam-4260	66	9	every	every	DET
ejpam-4260	66	10	open	open	ADJ
ejpam-4260	66	11	set	set	NOUN
ejpam-4260	66	12	is	be	AUX
ejpam-4260	66	13	supra	supra	ADJ
ejpam-4260	66	14	b	b	NOUN
ejpam-4260	66	15	-	-	PUNCT
ejpam-4260	66	16	open	open	ADJ
ejpam-4260	66	17	,	,	PUNCT
ejpam-4260	66	18	then	then	ADV
ejpam-4260	66	19	we	we	PRON
ejpam-4260	66	20	call	call	VERB
ejpam-4260	66	21	g	g	PROPN
ejpam-4260	66	22	a	a	DET
ejpam-4260	66	23	supra	supra	ADJ
ejpam-4260	66	24	bcontinuous	bcontinuous	ADJ
ejpam-4260	66	25	mapping	mapping	NOUN
ejpam-4260	66	26	.	.	PUNCT
ejpam-4260	67	1	(	(	PUNCT
ejpam-4260	67	2	ii	ii	NOUN
ejpam-4260	67	3	)	)	PUNCT
ejpam-4260	67	4	if	if	SCONJ
ejpam-4260	67	5	the	the	DET
ejpam-4260	67	6	image	image	NOUN
ejpam-4260	67	7	of	of	ADP
ejpam-4260	67	8	every	every	DET
ejpam-4260	67	9	open	open	ADJ
ejpam-4260	67	10	(	(	PUNCT
ejpam-4260	67	11	respectively	respectively	ADV
ejpam-4260	67	12	,	,	PUNCT
ejpam-4260	67	13	closed	closed	ADJ
ejpam-4260	67	14	)	)	PUNCT
ejpam-4260	67	15	set	set	NOUN
ejpam-4260	67	16	is	be	AUX
ejpam-4260	67	17	supra	supra	ADJ
ejpam-4260	67	18	b	b	NOUN
ejpam-4260	67	19	-	-	PUNCT
ejpam-4260	67	20	open	open	ADJ
ejpam-4260	67	21	(	(	PUNCT
ejpam-4260	67	22	respectively	respectively	ADV
ejpam-4260	67	23	,	,	PUNCT
ejpam-4260	67	24	supra	supra	PROPN
ejpam-4260	67	25	b	b	PROPN
ejpam-4260	67	26	-	-	PUNCT
ejpam-4260	67	27	closed	closed	ADJ
ejpam-4260	67	28	)	)	PUNCT
ejpam-4260	67	29	,	,	PUNCT
ejpam-4260	67	30	then	then	ADV
ejpam-4260	67	31	we	we	PRON
ejpam-4260	67	32	call	call	VERB
ejpam-4260	67	33	g	g	PROPN
ejpam-4260	67	34	a	a	DET
ejpam-4260	67	35	supra	supra	PROPN
ejpam-4260	67	36	b	b	NOUN
ejpam-4260	67	37	-	-	PUNCT
ejpam-4260	67	38	open	open	ADJ
ejpam-4260	67	39	(	(	PUNCT
ejpam-4260	67	40	respectively	respectively	ADV
ejpam-4260	67	41	,	,	PUNCT
ejpam-4260	67	42	supra	supra	PROPN
ejpam-4260	67	43	b	b	PROPN
ejpam-4260	67	44	-	-	PUNCT
ejpam-4260	67	45	closed	closed	ADJ
ejpam-4260	67	46	)	)	PUNCT
ejpam-4260	67	47	mapping	mapping	NOUN
ejpam-4260	67	48	.	.	PUNCT
ejpam-4260	68	1	definition	definition	NOUN
ejpam-4260	68	2	5	5	NUM
ejpam-4260	68	3	.	.	PUNCT
ejpam-4260	69	1	[	[	X
ejpam-4260	69	2	2	2	X
ejpam-4260	69	3	]	]	PUNCT
ejpam-4260	69	4	let	let	VERB
ejpam-4260	69	5	o	o	NOUN
ejpam-4260	69	6	be	be	AUX
ejpam-4260	69	7	a	a	DET
ejpam-4260	69	8	subset	subset	NOUN
ejpam-4260	69	9	of	of	ADP
ejpam-4260	69	10	an	an	DET
ejpam-4260	69	11	sts	st	NOUN
ejpam-4260	69	12	(	(	PUNCT
ejpam-4260	69	13	u	u	NOUN
ejpam-4260	69	14	,	,	PUNCT
ejpam-4260	69	15	ω	ω	PROPN
ejpam-4260	69	16	)	)	PUNCT
ejpam-4260	69	17	.	.	PUNCT
ejpam-4260	70	1	we	we	PRON
ejpam-4260	70	2	call	call	VERB
ejpam-4260	70	3	a	a	DET
ejpam-4260	70	4	class	class	NOUN
ejpam-4260	70	5	ωa	ωa	ADV
ejpam-4260	70	6	=	=	PUNCT
ejpam-4260	70	7	{	{	PUNCT
ejpam-4260	70	8	a	a	DET
ejpam-4260	70	9	⋂	⋂	PROPN
ejpam-4260	70	10	θ	θ	NOUN
ejpam-4260	70	11	:	:	PUNCT
ejpam-4260	70	12	θ	θ	PROPN
ejpam-4260	70	13	∈	∈	PROPN
ejpam-4260	70	14	ω	ω	PROPN
ejpam-4260	70	15	}	}	PUNCT
ejpam-4260	70	16	a	a	DET
ejpam-4260	70	17	supra	supra	PROPN
ejpam-4260	70	18	relative	relative	ADJ
ejpam-4260	70	19	topology	topology	NOUN
ejpam-4260	70	20	on	on	ADP
ejpam-4260	70	21	o	o	NOUN
ejpam-4260	70	22	,	,	PUNCT
ejpam-4260	70	23	call	call	NOUN
ejpam-4260	70	24	(	(	PUNCT
ejpam-4260	70	25	o	o	NOUN
ejpam-4260	70	26	,	,	PUNCT
ejpam-4260	70	27	ωa	ωa	PROPN
ejpam-4260	70	28	)	)	PUNCT
ejpam-4260	70	29	a	a	DET
ejpam-4260	70	30	supra	supra	PROPN
ejpam-4260	70	31	subspace	subspace	NOUN
ejpam-4260	70	32	of	of	ADP
ejpam-4260	70	33	(	(	PUNCT
ejpam-4260	70	34	u	u	PROPN
ejpam-4260	70	35	,	,	PUNCT
ejpam-4260	70	36	ω	ω	PROPN
ejpam-4260	70	37	)	)	PUNCT
ejpam-4260	70	38	.	.	PUNCT
ejpam-4260	71	1	definition	definition	NOUN
ejpam-4260	71	2	6	6	NUM
ejpam-4260	71	3	.	.	PUNCT
ejpam-4260	72	1	[	[	X
ejpam-4260	72	2	12	12	NUM
ejpam-4260	72	3	]	]	PUNCT
ejpam-4260	72	4	we	we	PRON
ejpam-4260	72	5	call	call	VERB
ejpam-4260	72	6	β	β	PRON
ejpam-4260	72	7	a	a	DET
ejpam-4260	72	8	basis	basis	NOUN
ejpam-4260	72	9	for	for	ADP
ejpam-4260	72	10	an	an	DET
ejpam-4260	72	11	sts	st	NOUN
ejpam-4260	72	12	(	(	PUNCT
ejpam-4260	72	13	u	u	NOUN
ejpam-4260	72	14	,	,	PUNCT
ejpam-4260	72	15	ω	ω	PROPN
ejpam-4260	72	16	)	)	PUNCT
ejpam-4260	72	17	if	if	SCONJ
ejpam-4260	72	18	every	every	DET
ejpam-4260	72	19	element	element	NOUN
ejpam-4260	72	20	of	of	ADP
ejpam-4260	72	21	ω	ω	PROPN
ejpam-4260	72	22	can	can	AUX
ejpam-4260	72	23	be	be	AUX
ejpam-4260	72	24	expressed	express	VERB
ejpam-4260	72	25	as	as	ADP
ejpam-4260	72	26	a	a	DET
ejpam-4260	72	27	union	union	NOUN
ejpam-4260	72	28	of	of	ADP
ejpam-4260	72	29	elements	element	NOUN
ejpam-4260	72	30	of	of	ADP
ejpam-4260	72	31	β	β	X
ejpam-4260	72	32	.	.	PUNCT
ejpam-4260	73	1	definition	definition	NOUN
ejpam-4260	73	2	7	7	NUM
ejpam-4260	73	3	.	.	PUNCT
ejpam-4260	74	1	[	[	X
ejpam-4260	74	2	12	12	NUM
ejpam-4260	74	3	]	]	X
ejpam-4260	74	4	let	let	VERB
ejpam-4260	74	5	{	{	PUNCT
ejpam-4260	74	6	(	(	PUNCT
ejpam-4260	74	7	uk	uk	PROPN
ejpam-4260	74	8	,	,	PUNCT
ejpam-4260	74	9	ωk	ωk	NUM
ejpam-4260	74	10	)	)	PUNCT
ejpam-4260	74	11	:	:	PUNCT
ejpam-4260	75	1	k	k	X
ejpam-4260	75	2	=	=	SYM
ejpam-4260	75	3	1	1	NUM
ejpam-4260	75	4	,	,	PUNCT
ejpam-4260	75	5	2	2	NUM
ejpam-4260	75	6	,	,	PUNCT
ejpam-4260	75	7	...	...	PUNCT
ejpam-4260	75	8	,	,	PUNCT
ejpam-4260	75	9	n	n	CCONJ
ejpam-4260	75	10	}	}	PUNCT
ejpam-4260	75	11	be	be	AUX
ejpam-4260	75	12	a	a	DET
ejpam-4260	75	13	family	family	NOUN
ejpam-4260	75	14	of	of	ADP
ejpam-4260	75	15	stss	stss	NOUN
ejpam-4260	75	16	.	.	PUNCT
ejpam-4260	76	1	then	then	ADV
ejpam-4260	76	2	,	,	PUNCT
ejpam-4260	76	3	{	{	PUNCT
ejpam-4260	76	4	θ1	θ1	NOUN
ejpam-4260	76	5	×θ2	×θ2	PRON
ejpam-4260	76	6	×	×	NOUN
ejpam-4260	76	7	...	...	PUNCT
ejpam-4260	76	8	×	×	PROPN
ejpam-4260	76	9	θn	θn	NOUN
ejpam-4260	76	10	:	:	PUNCT
ejpam-4260	76	11	θk	θk	PROPN
ejpam-4260	76	12	∈	∈	NOUN
ejpam-4260	76	13	ωk	ωk	NOUN
ejpam-4260	76	14	}	}	PUNCT
ejpam-4260	76	15	constitutes	constitute	VERB
ejpam-4260	76	16	a	a	DET
ejpam-4260	76	17	basis	basis	NOUN
ejpam-4260	76	18	for	for	ADP
ejpam-4260	76	19	an	an	DET
ejpam-4260	76	20	st	st	PROPN
ejpam-4260	76	21	c	c	PROPN
ejpam-4260	76	22	on	on	ADP
ejpam-4260	76	23	u	u	NOUN
ejpam-4260	76	24	=	=	PROPN
ejpam-4260	76	25	∏n	∏n	PROPN
ejpam-4260	76	26	k=1	k=1	PROPN
ejpam-4260	76	27	uk	uk	PROPN
ejpam-4260	76	28	.	.	PUNCT
ejpam-4260	77	1	we	we	PRON
ejpam-4260	77	2	call	call	VERB
ejpam-4260	77	3	(	(	PUNCT
ejpam-4260	77	4	u	u	NOUN
ejpam-4260	77	5	,	,	PUNCT
ejpam-4260	77	6	c	c	NOUN
ejpam-4260	77	7	)	)	PUNCT
ejpam-4260	77	8	a	a	DET
ejpam-4260	77	9	finite	finite	ADJ
ejpam-4260	77	10	product	product	NOUN
ejpam-4260	77	11	of	of	ADP
ejpam-4260	77	12	stss	stss	NOUN
ejpam-4260	77	13	.	.	PUNCT
ejpam-4260	78	1	proposition	proposition	NOUN
ejpam-4260	78	2	1	1	NUM
ejpam-4260	78	3	.	.	PUNCT
ejpam-4260	79	1	[	[	X
ejpam-4260	79	2	12	12	NUM
ejpam-4260	79	3	]	]	PUNCT
ejpam-4260	79	4	let	let	VERB
ejpam-4260	79	5	o	o	NOUN
ejpam-4260	79	6	⊆	⊆	NUM
ejpam-4260	79	7	(	(	PUNCT
ejpam-4260	79	8	u	u	NOUN
ejpam-4260	79	9	,	,	PUNCT
ejpam-4260	79	10	ω	ω	PROPN
ejpam-4260	79	11	)	)	PUNCT
ejpam-4260	79	12	and	and	CCONJ
ejpam-4260	79	13	p	p	PRON
ejpam-4260	79	14	⊆	⊆	NUM
ejpam-4260	79	15	(	(	PUNCT
ejpam-4260	79	16	v	v	NOUN
ejpam-4260	79	17	,	,	PUNCT
ejpam-4260	79	18	ψ	ψ	NOUN
ejpam-4260	79	19	)	)	PUNCT
ejpam-4260	79	20	.	.	PUNCT
ejpam-4260	80	1	then	then	ADV
ejpam-4260	80	2	,	,	PUNCT
ejpam-4260	80	3	int(o×p	int(o×p	NOUN
ejpam-4260	80	4	)	)	PUNCT
ejpam-4260	80	5	=	=	SYM
ejpam-4260	80	6	int(o)×int(p	int(o)×int(p	PROPN
ejpam-4260	80	7	)	)	PUNCT
ejpam-4260	80	8	and	and	CCONJ
ejpam-4260	80	9	cl(o	cl(o	NUM
ejpam-4260	80	10	×	×	NOUN
ejpam-4260	80	11	p	p	NOUN
ejpam-4260	80	12	)	)	PUNCT
ejpam-4260	80	13	=	=	SYM
ejpam-4260	80	14	cl(o)×	cl(o)×	PROPN
ejpam-4260	80	15	cl(p	cl(p	NOUN
ejpam-4260	80	16	)	)	PUNCT
ejpam-4260	80	17	.	.	PUNCT
ejpam-4260	81	1	3	3	X
ejpam-4260	81	2	.	.	X
ejpam-4260	81	3	supra	supra	PROPN
ejpam-4260	81	4	b	b	PROPN
ejpam-4260	81	5	-	-	PUNCT
ejpam-4260	81	6	limit	limit	NOUN
ejpam-4260	81	7	points	point	NOUN
ejpam-4260	81	8	of	of	ADP
ejpam-4260	81	9	a	a	DET
ejpam-4260	81	10	set	set	NOUN
ejpam-4260	81	11	we	we	PRON
ejpam-4260	81	12	devote	devote	VERB
ejpam-4260	81	13	this	this	DET
ejpam-4260	81	14	section	section	NOUN
ejpam-4260	81	15	to	to	ADP
ejpam-4260	81	16	defining	define	VERB
ejpam-4260	81	17	a	a	DET
ejpam-4260	81	18	new	new	ADJ
ejpam-4260	81	19	type	type	NOUN
ejpam-4260	81	20	of	of	ADP
ejpam-4260	81	21	supra	supra	ADJ
ejpam-4260	81	22	limit	limit	NOUN
ejpam-4260	81	23	points	point	NOUN
ejpam-4260	81	24	of	of	ADP
ejpam-4260	81	25	a	a	DET
ejpam-4260	81	26	set	set	NOUN
ejpam-4260	81	27	by	by	ADP
ejpam-4260	81	28	using	use	VERB
ejpam-4260	81	29	supra	supra	PROPN
ejpam-4260	81	30	b	b	PROPN
ejpam-4260	81	31	-	-	PUNCT
ejpam-4260	81	32	open	open	ADJ
ejpam-4260	81	33	sets	set	NOUN
ejpam-4260	81	34	.	.	PUNCT
ejpam-4260	82	1	with	with	ADP
ejpam-4260	82	2	the	the	DET
ejpam-4260	82	3	help	help	NOUN
ejpam-4260	82	4	of	of	ADP
ejpam-4260	82	5	examples	example	NOUN
ejpam-4260	82	6	,	,	PUNCT
ejpam-4260	82	7	we	we	PRON
ejpam-4260	82	8	probe	probe	VERB
ejpam-4260	82	9	their	their	PRON
ejpam-4260	82	10	fundamental	fundamental	ADJ
ejpam-4260	82	11	properties	property	NOUN
ejpam-4260	82	12	and	and	CCONJ
ejpam-4260	82	13	describe	describe	VERB
ejpam-4260	82	14	their	their	PRON
ejpam-4260	82	15	behaviors	behavior	NOUN
ejpam-4260	82	16	in	in	ADP
ejpam-4260	82	17	some	some	DET
ejpam-4260	82	18	spaces	space	NOUN
ejpam-4260	82	19	.	.	PUNCT
ejpam-4260	83	1	definition	definition	NOUN
ejpam-4260	83	2	8	8	NUM
ejpam-4260	83	3	.	.	PUNCT
ejpam-4260	84	1	we	we	PRON
ejpam-4260	84	2	call	call	VERB
ejpam-4260	84	3	o	o	NOUN
ejpam-4260	84	4	a	a	DET
ejpam-4260	84	5	supra	supra	PROPN
ejpam-4260	84	6	b	b	PROPN
ejpam-4260	84	7	neighbourhood	neighbourhood	NOUN
ejpam-4260	84	8	of	of	ADP
ejpam-4260	84	9	ξ	ξ	PROPN
ejpam-4260	84	10	in	in	ADP
ejpam-4260	84	11	an	an	DET
ejpam-4260	84	12	sts	st	NOUN
ejpam-4260	84	13	(	(	PUNCT
ejpam-4260	84	14	u	u	NOUN
ejpam-4260	84	15	,	,	PUNCT
ejpam-4260	84	16	ω	ω	PROPN
ejpam-4260	84	17	)	)	PUNCT
ejpam-4260	84	18	provided	provide	VERB
ejpam-4260	84	19	that	that	SCONJ
ejpam-4260	84	20	there	there	PRON
ejpam-4260	84	21	is	be	VERB
ejpam-4260	84	22	a	a	DET
ejpam-4260	84	23	supra	supra	PROPN
ejpam-4260	84	24	b	b	NOUN
ejpam-4260	84	25	-	-	PUNCT
ejpam-4260	84	26	open	open	ADJ
ejpam-4260	84	27	set	set	NOUN
ejpam-4260	84	28	f	f	PROPN
ejpam-4260	84	29	including	include	VERB
ejpam-4260	84	30	ξ	ξ	PROPN
ejpam-4260	84	31	such	such	ADJ
ejpam-4260	84	32	that	that	SCONJ
ejpam-4260	84	33	ξ	ξ	PROPN
ejpam-4260	84	34	∈	∈	PROPN
ejpam-4260	84	35	f	f	PROPN
ejpam-4260	84	36	⊆	⊆	NUM
ejpam-4260	84	37	o.	o.	ADJ
ejpam-4260	84	38	definition	definition	NOUN
ejpam-4260	84	39	9	9	NUM
ejpam-4260	84	40	.	.	PUNCT
ejpam-4260	85	1	we	we	PRON
ejpam-4260	85	2	call	call	VERB
ejpam-4260	85	3	ξ	ξ	X
ejpam-4260	85	4	∈	∈	PROPN
ejpam-4260	85	5	u	u	NOUN
ejpam-4260	85	6	a	a	DET
ejpam-4260	85	7	supra	supra	PROPN
ejpam-4260	85	8	b	b	NOUN
ejpam-4260	85	9	-	-	PUNCT
ejpam-4260	85	10	limit	limit	NOUN
ejpam-4260	85	11	point	point	NOUN
ejpam-4260	85	12	of	of	ADP
ejpam-4260	85	13	a	a	DET
ejpam-4260	85	14	subset	subset	NOUN
ejpam-4260	85	15	o	o	NOUN
ejpam-4260	85	16	of	of	ADP
ejpam-4260	85	17	an	an	DET
ejpam-4260	85	18	sts	st	NOUN
ejpam-4260	85	19	(	(	PUNCT
ejpam-4260	85	20	u	u	NOUN
ejpam-4260	85	21	,	,	PUNCT
ejpam-4260	85	22	ω	ω	PROPN
ejpam-4260	85	23	)	)	PUNCT
ejpam-4260	85	24	if	if	SCONJ
ejpam-4260	85	25	every	every	DET
ejpam-4260	85	26	supra	supra	PROPN
ejpam-4260	85	27	b	b	PROPN
ejpam-4260	85	28	neighborhood	neighborhood	NOUN
ejpam-4260	85	29	w	w	NOUN
ejpam-4260	85	30	of	of	ADP
ejpam-4260	85	31	ξ	ξ	PROPN
ejpam-4260	85	32	satisfying	satisfy	VERB
ejpam-4260	85	33	that	that	SCONJ
ejpam-4260	85	34	w	w	ADP
ejpam-4260	85	35	\	\	PROPN
ejpam-4260	85	36	{	{	PUNCT
ejpam-4260	85	37	ξ	ξ	NOUN
ejpam-4260	85	38	}	}	PUNCT
ejpam-4260	85	39	⋂	⋂	PROPN
ejpam-4260	85	40	a	a	DET
ejpam-4260	85	41	̸=	̸=	PROPN
ejpam-4260	85	42	∅.	∅.	ADP
ejpam-4260	85	43	a	a	DET
ejpam-4260	85	44	supra	supra	PROPN
ejpam-4260	85	45	b	b	PROPN
ejpam-4260	85	46	derived	derive	VERB
ejpam-4260	85	47	set	set	NOUN
ejpam-4260	85	48	of	of	ADP
ejpam-4260	85	49	o	o	PROPN
ejpam-4260	85	50	,	,	PUNCT
ejpam-4260	85	51	symbolized	symbolize	VERB
ejpam-4260	85	52	by	by	ADP
ejpam-4260	85	53	ob′	ob′	NOUN
ejpam-4260	85	54	,	,	PUNCT
ejpam-4260	85	55	is	be	AUX
ejpam-4260	85	56	all	all	DET
ejpam-4260	85	57	supra	supra	ADJ
ejpam-4260	85	58	b	b	NOUN
ejpam-4260	85	59	-	-	PUNCT
ejpam-4260	85	60	limit	limit	NOUN
ejpam-4260	85	61	points	point	NOUN
ejpam-4260	85	62	of	of	ADP
ejpam-4260	85	63	o.	o.	NOUN
ejpam-4260	85	64	one	one	NOUN
ejpam-4260	85	65	can	can	AUX
ejpam-4260	85	66	prove	prove	VERB
ejpam-4260	85	67	the	the	DET
ejpam-4260	85	68	two	two	NUM
ejpam-4260	85	69	results	result	NOUN
ejpam-4260	85	70	below	below	ADP
ejpam-4260	85	71	easily	easily	ADV
ejpam-4260	85	72	,	,	PUNCT
ejpam-4260	85	73	so	so	ADV
ejpam-4260	85	74	we	we	PRON
ejpam-4260	85	75	omit	omit	VERB
ejpam-4260	85	76	their	their	PRON
ejpam-4260	85	77	proofs	proof	NOUN
ejpam-4260	85	78	.	.	PUNCT
ejpam-4260	86	1	proposition	proposition	NOUN
ejpam-4260	86	2	2	2	NUM
ejpam-4260	86	3	.	.	PUNCT
ejpam-4260	87	1	for	for	ADP
ejpam-4260	87	2	every	every	DET
ejpam-4260	87	3	o	o	NOUN
ejpam-4260	87	4	,	,	PUNCT
ejpam-4260	87	5	p	p	NOUN
ejpam-4260	87	6	⊆	⊆	NUM
ejpam-4260	87	7	(	(	PUNCT
ejpam-4260	87	8	u	u	NOUN
ejpam-4260	87	9	,	,	PUNCT
ejpam-4260	87	10	ω	ω	PROPN
ejpam-4260	87	11	)	)	PUNCT
ejpam-4260	87	12	,	,	PUNCT
ejpam-4260	87	13	we	we	PRON
ejpam-4260	87	14	have	have	VERB
ejpam-4260	87	15	o	o	NOUN
ejpam-4260	87	16	⊆	⊆	NUM
ejpam-4260	87	17	p	p	NOUN
ejpam-4260	87	18	implies	imply	VERB
ejpam-4260	87	19	ob′	ob′	NOUN
ejpam-4260	87	20	⊆	⊆	NUM
ejpam-4260	87	21	p	p	PRON
ejpam-4260	87	22	b′.	b′.	PROPN
ejpam-4260	87	23	corollary	corollary	NOUN
ejpam-4260	87	24	1	1	NUM
ejpam-4260	87	25	.	.	PUNCT
ejpam-4260	88	1	let	let	VERB
ejpam-4260	88	2	o	o	NOUN
ejpam-4260	88	3	and	and	CCONJ
ejpam-4260	88	4	p	p	NOUN
ejpam-4260	88	5	be	be	AUX
ejpam-4260	88	6	subsets	subset	NOUN
ejpam-4260	88	7	of	of	ADP
ejpam-4260	88	8	(	(	PUNCT
ejpam-4260	88	9	u	u	PROPN
ejpam-4260	88	10	,	,	PUNCT
ejpam-4260	88	11	ω	ω	PROPN
ejpam-4260	88	12	)	)	PUNCT
ejpam-4260	88	13	.	.	PUNCT
ejpam-4260	89	1	then	then	ADV
ejpam-4260	89	2	,	,	PUNCT
ejpam-4260	89	3	(	(	PUNCT
ejpam-4260	89	4	i	i	NOUN
ejpam-4260	89	5	)	)	PUNCT
ejpam-4260	89	6	ob′⋃p	ob′⋃p	PROPN
ejpam-4260	89	7	b′	b′	NUM
ejpam-4260	89	8	⊆	⊆	NUM
ejpam-4260	89	9	(	(	PUNCT
ejpam-4260	89	10	o	o	NOUN
ejpam-4260	89	11	⋃	⋃	PROPN
ejpam-4260	89	12	p	p	NOUN
ejpam-4260	89	13	)	)	PUNCT
ejpam-4260	89	14	b′.	b′.	PROPN
ejpam-4260	89	15	a.	a.	NOUN
ejpam-4260	89	16	mhemdi	mhemdi	PROPN
ejpam-4260	89	17	et	et	PROPN
ejpam-4260	89	18	al	al	PROPN
ejpam-4260	89	19	.	.	PUNCT
ejpam-4260	89	20	/	/	SYM
ejpam-4260	89	21	eur	eur	PROPN
ejpam-4260	89	22	.	.	PUNCT
ejpam-4260	90	1	j.	j.	PROPN
ejpam-4260	90	2	pure	pure	PROPN
ejpam-4260	90	3	appl	appl	PROPN
ejpam-4260	90	4	.	.	PROPN
ejpam-4260	90	5	math	math	PROPN
ejpam-4260	90	6	,	,	PUNCT
ejpam-4260	90	7	15	15	NUM
ejpam-4260	90	8	(	(	PUNCT
ejpam-4260	90	9	1	1	NUM
ejpam-4260	90	10	)	)	PUNCT
ejpam-4260	90	11	(	(	PUNCT
ejpam-4260	90	12	2022	2022	NUM
ejpam-4260	90	13	)	)	PUNCT
ejpam-4260	90	14	,	,	PUNCT
ejpam-4260	90	15	15	15	NUM
ejpam-4260	90	16	-	-	SYM
ejpam-4260	90	17	29	29	NUM
ejpam-4260	90	18	18	18	NUM
ejpam-4260	90	19	(	(	PUNCT
ejpam-4260	90	20	ii	ii	NOUN
ejpam-4260	90	21	)	)	PUNCT
ejpam-4260	90	22	(	(	PUNCT
ejpam-4260	90	23	o	o	NOUN
ejpam-4260	90	24	⋂	⋂	PROPN
ejpam-4260	90	25	p	p	NOUN
ejpam-4260	90	26	)	)	PUNCT
ejpam-4260	90	27	b′	b′	NOUN
ejpam-4260	90	28	⊆	⊆	NUM
ejpam-4260	90	29	ob′⋂p	ob′⋂p	NOUN
ejpam-4260	90	30	b′.	b′.	NOUN
ejpam-4260	90	31	the	the	DET
ejpam-4260	90	32	converse	converse	NOUN
ejpam-4260	90	33	of	of	ADP
ejpam-4260	90	34	the	the	DET
ejpam-4260	90	35	above	above	ADJ
ejpam-4260	90	36	proposition	proposition	NOUN
ejpam-4260	90	37	and	and	CCONJ
ejpam-4260	90	38	corollary	corollary	NOUN
ejpam-4260	90	39	are	be	AUX
ejpam-4260	90	40	in	in	ADP
ejpam-4260	90	41	general	general	ADJ
ejpam-4260	90	42	false	false	ADJ
ejpam-4260	90	43	as	as	ADP
ejpam-4260	90	44	the	the	DET
ejpam-4260	90	45	following	follow	VERB
ejpam-4260	90	46	example	example	NOUN
ejpam-4260	90	47	shows	show	NOUN
ejpam-4260	90	48	.	.	PUNCT
ejpam-4260	91	1	example	example	NOUN
ejpam-4260	92	1	1	1	NUM
ejpam-4260	92	2	.	.	PUNCT
ejpam-4260	92	3	let	let	VERB
ejpam-4260	92	4	ω	ω	NOUN
ejpam-4260	92	5	=	=	PRON
ejpam-4260	92	6	{	{	PUNCT
ejpam-4260	92	7	∅,u	∅,u	NOUN
ejpam-4260	92	8	,	,	PUNCT
ejpam-4260	92	9	{	{	PUNCT
ejpam-4260	92	10	ξ1	ξ1	NOUN
ejpam-4260	92	11	,	,	PUNCT
ejpam-4260	92	12	ξ2	ξ2	NOUN
ejpam-4260	92	13	}	}	PUNCT
ejpam-4260	92	14	,	,	PUNCT
ejpam-4260	92	15	{	{	PUNCT
ejpam-4260	92	16	ξ2	ξ2	NOUN
ejpam-4260	92	17	,	,	PUNCT
ejpam-4260	92	18	ξ3	ξ3	PROPN
ejpam-4260	92	19	}	}	PUNCT
ejpam-4260	92	20	,	,	PUNCT
ejpam-4260	92	21	{	{	PUNCT
ejpam-4260	92	22	ξ1	ξ1	NOUN
ejpam-4260	92	23	,	,	PUNCT
ejpam-4260	92	24	ξ2	ξ2	ADJ
ejpam-4260	92	25	,	,	PUNCT
ejpam-4260	92	26	ξ3	ξ3	PROPN
ejpam-4260	92	27	}	}	PUNCT
ejpam-4260	92	28	}	}	PUNCT
ejpam-4260	92	29	be	be	AUX
ejpam-4260	92	30	a	a	DET
ejpam-4260	92	31	supra	supra	ADJ
ejpam-4260	92	32	topology	topology	NOUN
ejpam-4260	92	33	on	on	ADP
ejpam-4260	92	34	u	u	NOUN
ejpam-4260	92	35	=	=	PUNCT
ejpam-4260	92	36	{	{	PUNCT
ejpam-4260	92	37	ξ1	ξ1	NOUN
ejpam-4260	92	38	,	,	PUNCT
ejpam-4260	92	39	ξ2	ξ2	ADJ
ejpam-4260	92	40	,	,	PUNCT
ejpam-4260	92	41	ξ3	ξ3	NOUN
ejpam-4260	92	42	,	,	PUNCT
ejpam-4260	92	43	ξ4	ξ4	PROPN
ejpam-4260	92	44	}	}	PUNCT
ejpam-4260	92	45	.	.	PUNCT
ejpam-4260	93	1	then	then	ADV
ejpam-4260	93	2	{	{	PUNCT
ejpam-4260	93	3	∅,u	∅,u	NOUN
ejpam-4260	93	4	,	,	PUNCT
ejpam-4260	93	5	{	{	PUNCT
ejpam-4260	93	6	ξ2	ξ2	NOUN
ejpam-4260	93	7	}	}	PUNCT
ejpam-4260	93	8	,	,	PUNCT
ejpam-4260	93	9	{	{	PUNCT
ejpam-4260	93	10	ξ1	ξ1	NOUN
ejpam-4260	93	11	,	,	PUNCT
ejpam-4260	93	12	ξ2	ξ2	NOUN
ejpam-4260	93	13	}	}	PUNCT
ejpam-4260	93	14	,	,	PUNCT
ejpam-4260	93	15	{	{	PUNCT
ejpam-4260	93	16	ξ2	ξ2	NOUN
ejpam-4260	93	17	,	,	PUNCT
ejpam-4260	93	18	ξ3	ξ3	PROPN
ejpam-4260	93	19	}	}	PUNCT
ejpam-4260	93	20	,	,	PUNCT
ejpam-4260	93	21	{	{	PUNCT
ejpam-4260	93	22	ξ1	ξ1	NOUN
ejpam-4260	93	23	,	,	PUNCT
ejpam-4260	93	24	ξ3	ξ3	PROPN
ejpam-4260	93	25	}	}	PUNCT
ejpam-4260	93	26	,	,	PUNCT
ejpam-4260	93	27	{	{	PUNCT
ejpam-4260	93	28	ξ2	ξ2	NOUN
ejpam-4260	93	29	,	,	PUNCT
ejpam-4260	93	30	ξ4	ξ4	PROPN
ejpam-4260	93	31	}	}	PUNCT
ejpam-4260	93	32	,	,	PUNCT
ejpam-4260	93	33	{	{	PUNCT
ejpam-4260	93	34	ξ1	ξ1	NOUN
ejpam-4260	93	35	,	,	PUNCT
ejpam-4260	93	36	ξ2	ξ2	ADJ
ejpam-4260	93	37	,	,	PUNCT
ejpam-4260	93	38	ξ3	ξ3	PROPN
ejpam-4260	93	39	}	}	PUNCT
ejpam-4260	93	40	,	,	PUNCT
ejpam-4260	93	41	{	{	PUNCT
ejpam-4260	93	42	ξ1	ξ1	NOUN
ejpam-4260	93	43	,	,	PUNCT
ejpam-4260	93	44	ξ2	ξ2	NOUN
ejpam-4260	93	45	,	,	PUNCT
ejpam-4260	93	46	ξ4	ξ4	PROPN
ejpam-4260	93	47	}	}	PUNCT
ejpam-4260	93	48	,	,	PUNCT
ejpam-4260	93	49	{	{	PUNCT
ejpam-4260	93	50	ξ1	ξ1	NOUN
ejpam-4260	93	51	,	,	PUNCT
ejpam-4260	93	52	ξ3	ξ3	NOUN
ejpam-4260	93	53	,	,	PUNCT
ejpam-4260	93	54	ξ4	ξ4	PROPN
ejpam-4260	93	55	}	}	PUNCT
ejpam-4260	93	56	,	,	PUNCT
ejpam-4260	93	57	{	{	PUNCT
ejpam-4260	93	58	ξ2	ξ2	NOUN
ejpam-4260	93	59	,	,	PUNCT
ejpam-4260	93	60	ξ3	ξ3	PROPN
ejpam-4260	93	61	,	,	PUNCT
ejpam-4260	93	62	ξ4	ξ4	PROPN
ejpam-4260	93	63	}	}	PUNCT
ejpam-4260	93	64	}	}	PUNCT
ejpam-4260	93	65	is	be	AUX
ejpam-4260	93	66	the	the	DET
ejpam-4260	93	67	collection	collection	NOUN
ejpam-4260	93	68	of	of	ADP
ejpam-4260	93	69	all	all	DET
ejpam-4260	93	70	supra	supra	PROPN
ejpam-4260	93	71	b	b	NOUN
ejpam-4260	93	72	-	-	PUNCT
ejpam-4260	93	73	open	open	ADJ
ejpam-4260	93	74	subsets	subset	NOUN
ejpam-4260	93	75	of	of	ADP
ejpam-4260	93	76	(	(	PUNCT
ejpam-4260	93	77	u	u	PROPN
ejpam-4260	93	78	,	,	PUNCT
ejpam-4260	93	79	ω	ω	PROPN
ejpam-4260	93	80	)	)	PUNCT
ejpam-4260	93	81	.	.	PUNCT
ejpam-4260	94	1	if	if	SCONJ
ejpam-4260	94	2	o	o	PROPN
ejpam-4260	94	3	=	=	PRON
ejpam-4260	94	4	{	{	PUNCT
ejpam-4260	94	5	ξ1	ξ1	NOUN
ejpam-4260	94	6	,	,	PUNCT
ejpam-4260	94	7	ξ4	ξ4	PROPN
ejpam-4260	94	8	}	}	PUNCT
ejpam-4260	94	9	,	,	PUNCT
ejpam-4260	94	10	p	p	NOUN
ejpam-4260	94	11	=	=	X
ejpam-4260	94	12	{	{	PUNCT
ejpam-4260	94	13	ξ2	ξ2	NOUN
ejpam-4260	94	14	,	,	PUNCT
ejpam-4260	94	15	ξ3	ξ3	PROPN
ejpam-4260	94	16	}	}	PUNCT
ejpam-4260	94	17	,	,	PUNCT
ejpam-4260	94	18	c	c	X
ejpam-4260	94	19	=	=	PRON
ejpam-4260	94	20	{	{	PUNCT
ejpam-4260	94	21	ξ1	ξ1	NOUN
ejpam-4260	94	22	,	,	PUNCT
ejpam-4260	94	23	ξ2	ξ2	NOUN
ejpam-4260	94	24	,	,	PUNCT
ejpam-4260	94	25	ξ4	ξ4	NOUN
ejpam-4260	94	26	}	}	PUNCT
ejpam-4260	94	27	and	and	CCONJ
ejpam-4260	94	28	d	d	NOUN
ejpam-4260	94	29	=	=	SYM
ejpam-4260	94	30	{	{	PUNCT
ejpam-4260	94	31	ξ2	ξ2	NOUN
ejpam-4260	94	32	,	,	PUNCT
ejpam-4260	94	33	ξ3	ξ3	NOUN
ejpam-4260	94	34	,	,	PUNCT
ejpam-4260	94	35	ξ4	ξ4	PROPN
ejpam-4260	94	36	}	}	PUNCT
ejpam-4260	94	37	,	,	PUNCT
ejpam-4260	94	38	then	then	ADV
ejpam-4260	94	39	ob′	ob′	NOUN
ejpam-4260	94	40	=	=	NOUN
ejpam-4260	94	41	∅	∅	NOUN
ejpam-4260	94	42	,	,	PUNCT
ejpam-4260	94	43	p	p	NOUN
ejpam-4260	94	44	b′	b′	NOUN
ejpam-4260	94	45	=	=	NOUN
ejpam-4260	94	46	{	{	PUNCT
ejpam-4260	94	47	ξ1	ξ1	NOUN
ejpam-4260	94	48	}	}	PUNCT
ejpam-4260	94	49	,	,	PUNCT
ejpam-4260	94	50	cb′	cb′	PROPN
ejpam-4260	94	51	=	=	SYM
ejpam-4260	94	52	{	{	PUNCT
ejpam-4260	94	53	ξ3	ξ3	NOUN
ejpam-4260	94	54	,	,	PUNCT
ejpam-4260	94	55	ξ4	ξ4	NOUN
ejpam-4260	94	56	}	}	PUNCT
ejpam-4260	94	57	and	and	CCONJ
ejpam-4260	94	58	db′	db′	ADV
ejpam-4260	94	59	=	=	PRON
ejpam-4260	94	60	{	{	PUNCT
ejpam-4260	94	61	ξ1	ξ1	NOUN
ejpam-4260	94	62	,	,	PUNCT
ejpam-4260	94	63	ξ2	ξ2	NOUN
ejpam-4260	94	64	,	,	PUNCT
ejpam-4260	94	65	ξ4	ξ4	PROPN
ejpam-4260	94	66	}	}	PUNCT
ejpam-4260	94	67	.	.	PUNCT
ejpam-4260	95	1	now	now	ADV
ejpam-4260	95	2	,	,	PUNCT
ejpam-4260	95	3	we	we	PRON
ejpam-4260	95	4	have	have	VERB
ejpam-4260	95	5	the	the	DET
ejpam-4260	95	6	following	follow	VERB
ejpam-4260	95	7	cases	case	NOUN
ejpam-4260	95	8	:	:	PUNCT
ejpam-4260	95	9	(	(	PUNCT
ejpam-4260	95	10	i	i	NOUN
ejpam-4260	95	11	)	)	PUNCT
ejpam-4260	95	12	ob′	ob′	NOUN
ejpam-4260	95	13	⊆	⊆	NUM
ejpam-4260	95	14	p	p	PRON
ejpam-4260	95	15	b′	b′	NOUN
ejpam-4260	95	16	,	,	PUNCT
ejpam-4260	95	17	but	but	CCONJ
ejpam-4260	95	18	p	p	X
ejpam-4260	95	19	̸⊆	̸⊆	NOUN
ejpam-4260	95	20	o.	o.	PROPN
ejpam-4260	95	21	(	(	PUNCT
ejpam-4260	95	22	ii	ii	NOUN
ejpam-4260	95	23	)	)	PUNCT
ejpam-4260	95	24	ob′⋃p	ob′⋃p	PROPN
ejpam-4260	95	25	b′	b′	NUM
ejpam-4260	95	26	=	=	NOUN
ejpam-4260	95	27	{	{	PUNCT
ejpam-4260	95	28	ξ1	ξ1	NOUN
ejpam-4260	95	29	}	}	PUNCT
ejpam-4260	95	30	and	and	CCONJ
ejpam-4260	95	31	(	(	PUNCT
ejpam-4260	95	32	o	o	NOUN
ejpam-4260	95	33	⋃	⋃	PROPN
ejpam-4260	95	34	p	p	NOUN
ejpam-4260	95	35	)	)	PUNCT
ejpam-4260	95	36	b′	b′	NOUN
ejpam-4260	95	37	=	=	PUNCT
ejpam-4260	95	38	{	{	PUNCT
ejpam-4260	95	39	ξ1	ξ1	NOUN
ejpam-4260	95	40	,	,	PUNCT
ejpam-4260	95	41	ξ3	ξ3	NOUN
ejpam-4260	95	42	,	,	PUNCT
ejpam-4260	95	43	ξ4	ξ4	PROPN
ejpam-4260	95	44	}	}	PUNCT
ejpam-4260	95	45	.	.	PUNCT
ejpam-4260	96	1	then	then	ADV
ejpam-4260	96	2	(	(	PUNCT
ejpam-4260	96	3	o	o	NOUN
ejpam-4260	96	4	⋃	⋃	PROPN
ejpam-4260	96	5	p	p	NOUN
ejpam-4260	96	6	)	)	PUNCT
ejpam-4260	96	7	b′	b′	NOUN
ejpam-4260	96	8	̸⊆	̸⊆	NOUN
ejpam-4260	96	9	ob′⋃p	ob′⋃p	PROPN
ejpam-4260	96	10	b′.	b′.	PROPN
ejpam-4260	96	11	(	(	PUNCT
ejpam-4260	96	12	iii	iii	NOUN
ejpam-4260	96	13	)	)	PUNCT
ejpam-4260	96	14	cb′⋂db′	cb′⋂db′	NOUN
ejpam-4260	96	15	=	=	SYM
ejpam-4260	96	16	{	{	PUNCT
ejpam-4260	96	17	ξ4	ξ4	NOUN
ejpam-4260	96	18	}	}	PUNCT
ejpam-4260	96	19	and	and	CCONJ
ejpam-4260	96	20	(	(	PUNCT
ejpam-4260	96	21	c	c	PROPN
ejpam-4260	96	22	⋂	⋂	PROPN
ejpam-4260	96	23	d)b′	d)b′	PROPN
ejpam-4260	96	24	=	=	PUNCT
ejpam-4260	97	1	∅.	∅.	VERB
ejpam-4260	97	2	then	then	ADV
ejpam-4260	97	3	cb′⋂db′	cb′⋂db′	X
ejpam-4260	97	4	̸⊆	̸⊆	PUNCT
ejpam-4260	98	1	(	(	PUNCT
ejpam-4260	98	2	c	c	NOUN
ejpam-4260	98	3	⋂	⋂	PROPN
ejpam-4260	98	4	d)b′.	d)b′.	PROPN
ejpam-4260	98	5	proposition	proposition	NOUN
ejpam-4260	98	6	3	3	X
ejpam-4260	98	7	.	.	PUNCT
ejpam-4260	99	1	let	let	VERB
ejpam-4260	99	2	o	o	NOUN
ejpam-4260	99	3	be	be	AUX
ejpam-4260	99	4	a	a	DET
ejpam-4260	99	5	subset	subset	NOUN
ejpam-4260	99	6	of	of	ADP
ejpam-4260	99	7	(	(	PUNCT
ejpam-4260	99	8	u	u	PROPN
ejpam-4260	99	9	,	,	PUNCT
ejpam-4260	99	10	ω	ω	PROPN
ejpam-4260	99	11	)	)	PUNCT
ejpam-4260	99	12	and	and	CCONJ
ejpam-4260	99	13	ξ	ξ	X
ejpam-4260	99	14	∈	∈	PROPN
ejpam-4260	99	15	u	u	NOUN
ejpam-4260	99	16	.	.	PUNCT
ejpam-4260	100	1	then	then	ADV
ejpam-4260	100	2	ξ	ξ	X
ejpam-4260	100	3	∈	∈	PROPN
ejpam-4260	100	4	ob′	ob′	NOUN
ejpam-4260	100	5	iff	iff	PROPN
ejpam-4260	100	6	ξ	ξ	PROPN
ejpam-4260	100	7	∈	∈	PROPN
ejpam-4260	100	8	(	(	PUNCT
ejpam-4260	100	9	o	o	NOUN
ejpam-4260	100	10	\	\	PROPN
ejpam-4260	100	11	{	{	PUNCT
ejpam-4260	100	12	ξ})b′.	ξ})b′.	NOUN
ejpam-4260	100	13	proof	proof	NOUN
ejpam-4260	100	14	.	.	PUNCT
ejpam-4260	101	1	⇒	⇒	NOUN
ejpam-4260	101	2	:	:	PUNCT
ejpam-4260	101	3	consider	consider	VERB
ejpam-4260	101	4	ξ	ξ	X
ejpam-4260	101	5	∈	∈	PROPN
ejpam-4260	101	6	ob′.	ob′.	NOUN
ejpam-4260	101	7	then	then	ADV
ejpam-4260	101	8	,	,	PUNCT
ejpam-4260	101	9	(	(	PUNCT
ejpam-4260	101	10	θ	θ	PROPN
ejpam-4260	101	11	\	\	X
ejpam-4260	101	12	{	{	PUNCT
ejpam-4260	101	13	ξ	ξ	NOUN
ejpam-4260	101	14	}	}	PUNCT
ejpam-4260	101	15	)	)	PUNCT
ejpam-4260	102	1	⋂	⋂	PROPN
ejpam-4260	102	2	o	o	NOUN
ejpam-4260	102	3	̸=	̸=	PROPN
ejpam-4260	102	4	∅	∅	NOUN
ejpam-4260	102	5	for	for	ADP
ejpam-4260	102	6	any	any	DET
ejpam-4260	102	7	supra	supra	PROPN
ejpam-4260	102	8	b	b	NOUN
ejpam-4260	102	9	-	-	PUNCT
ejpam-4260	102	10	open	open	ADJ
ejpam-4260	102	11	set	set	ADJ
ejpam-4260	102	12	θ	θ	PROPN
ejpam-4260	102	13	including	include	VERB
ejpam-4260	102	14	ξ	ξ	X
ejpam-4260	102	15	.	.	PUNCT
ejpam-4260	103	1	obviously	obviously	ADV
ejpam-4260	103	2	,	,	PUNCT
ejpam-4260	103	3	we	we	PRON
ejpam-4260	103	4	obtain	obtain	VERB
ejpam-4260	103	5	(	(	PUNCT
ejpam-4260	103	6	θ\{ξ	θ\{ξ	NUM
ejpam-4260	103	7	}	}	PUNCT
ejpam-4260	103	8	)	)	PUNCT
ejpam-4260	103	9	⋂	⋂	PROPN
ejpam-4260	103	10	(	(	PUNCT
ejpam-4260	103	11	o\{ξ	o\{ξ	X
ejpam-4260	103	12	}	}	PUNCT
ejpam-4260	103	13	)	)	PUNCT
ejpam-4260	104	1	̸=	̸=	PROPN
ejpam-4260	104	2	∅.	∅.	ADP
ejpam-4260	104	3	this	this	PRON
ejpam-4260	104	4	means	mean	VERB
ejpam-4260	104	5	that	that	SCONJ
ejpam-4260	104	6	ξ	ξ	PROPN
ejpam-4260	104	7	∈	∈	PROPN
ejpam-4260	104	8	(	(	PUNCT
ejpam-4260	104	9	o\{ξ})b′.	o\{ξ})b′.	NOUN
ejpam-4260	104	10	proposition	proposition	NOUN
ejpam-4260	104	11	(	(	PUNCT
ejpam-4260	104	12	2	2	X
ejpam-4260	104	13	)	)	PUNCT
ejpam-4260	104	14	proves	prove	VERB
ejpam-4260	104	15	the	the	DET
ejpam-4260	104	16	sufficient	sufficient	ADJ
ejpam-4260	104	17	part	part	NOUN
ejpam-4260	104	18	.	.	PUNCT
ejpam-4260	105	1	theorem	theorem	NOUN
ejpam-4260	105	2	1	1	NUM
ejpam-4260	105	3	.	.	PUNCT
ejpam-4260	106	1	let	let	VERB
ejpam-4260	106	2	o	o	NOUN
ejpam-4260	106	3	be	be	AUX
ejpam-4260	106	4	a	a	DET
ejpam-4260	106	5	subset	subset	NOUN
ejpam-4260	106	6	of	of	ADP
ejpam-4260	106	7	(	(	PUNCT
ejpam-4260	106	8	u	u	PROPN
ejpam-4260	106	9	,	,	PUNCT
ejpam-4260	106	10	ω	ω	PROPN
ejpam-4260	106	11	)	)	PUNCT
ejpam-4260	106	12	.	.	PUNCT
ejpam-4260	107	1	then	then	ADV
ejpam-4260	107	2	.	.	PUNCT
ejpam-4260	108	1	(	(	PUNCT
ejpam-4260	108	2	i	i	NOUN
ejpam-4260	108	3	)	)	PUNCT
ejpam-4260	108	4	o	o	NOUN
ejpam-4260	108	5	is	be	AUX
ejpam-4260	108	6	a	a	DET
ejpam-4260	108	7	supra	supra	PROPN
ejpam-4260	108	8	b	b	NOUN
ejpam-4260	108	9	-	-	PUNCT
ejpam-4260	108	10	closed	close	VERB
ejpam-4260	108	11	set	set	VERB
ejpam-4260	108	12	iff	iff	PROPN
ejpam-4260	108	13	ob′	ob′	NOUN
ejpam-4260	108	14	⊆	⊆	NUM
ejpam-4260	109	1	o.	o.	NOUN
ejpam-4260	109	2	(	(	PUNCT
ejpam-4260	109	3	ii	ii	PROPN
ejpam-4260	109	4	)	)	PUNCT
ejpam-4260	109	5	o	o	NOUN
ejpam-4260	109	6	⋃	⋃	ADJ
ejpam-4260	109	7	ob′	ob′	NOUN
ejpam-4260	109	8	is	be	AUX
ejpam-4260	109	9	a	a	DET
ejpam-4260	109	10	supra	supra	PROPN
ejpam-4260	109	11	b	b	NOUN
ejpam-4260	109	12	-	-	PUNCT
ejpam-4260	109	13	closed	closed	ADJ
ejpam-4260	109	14	set	set	NOUN
ejpam-4260	109	15	.	.	PUNCT
ejpam-4260	110	1	(	(	PUNCT
ejpam-4260	110	2	iii	iii	X
ejpam-4260	110	3	)	)	PUNCT
ejpam-4260	110	4	bcl(o	bcl(o	PROPN
ejpam-4260	110	5	)	)	PUNCT
ejpam-4260	110	6	=	=	SYM
ejpam-4260	111	1	o	o	NOUN
ejpam-4260	111	2	⋃	⋃	NOUN
ejpam-4260	111	3	ob′.	ob′.	ADJ
ejpam-4260	111	4	proof	proof	NOUN
ejpam-4260	111	5	.	.	PUNCT
ejpam-4260	112	1	(	(	PUNCT
ejpam-4260	112	2	i	i	NOUN
ejpam-4260	112	3	)	)	PUNCT
ejpam-4260	112	4	let	let	VERB
ejpam-4260	112	5	o	o	NOUN
ejpam-4260	112	6	be	be	AUX
ejpam-4260	112	7	a	a	DET
ejpam-4260	112	8	supra	supra	PROPN
ejpam-4260	112	9	b	b	NOUN
ejpam-4260	112	10	-	-	PUNCT
ejpam-4260	112	11	closed	closed	ADJ
ejpam-4260	112	12	set	set	NOUN
ejpam-4260	112	13	and	and	CCONJ
ejpam-4260	112	14	ξ	ξ	PRON
ejpam-4260	112	15	̸∈	̸∈	PROPN
ejpam-4260	112	16	o.	o.	PROPN
ejpam-4260	112	17	since	since	SCONJ
ejpam-4260	112	18	oc	oc	ADP
ejpam-4260	112	19	⋂	⋂	PROPN
ejpam-4260	112	20	o	o	NOUN
ejpam-4260	112	21	=	=	NOUN
ejpam-4260	112	22	∅	∅	NOUN
ejpam-4260	112	23	and	and	CCONJ
ejpam-4260	112	24	oc	oc	NOUN
ejpam-4260	112	25	is	be	AUX
ejpam-4260	112	26	a	a	DET
ejpam-4260	112	27	supra	supra	PROPN
ejpam-4260	112	28	b	b	NOUN
ejpam-4260	112	29	-	-	PUNCT
ejpam-4260	112	30	open	open	ADJ
ejpam-4260	112	31	set	set	NOUN
ejpam-4260	112	32	including	include	VERB
ejpam-4260	112	33	ξ	ξ	PROPN
ejpam-4260	112	34	,	,	PUNCT
ejpam-4260	112	35	we	we	PRON
ejpam-4260	112	36	obtain	obtain	VERB
ejpam-4260	112	37	ξ	ξ	PRON
ejpam-4260	112	38	̸∈	̸∈	PROPN
ejpam-4260	112	39	ob′.	ob′.	PROPN
ejpam-4260	112	40	therefore	therefore	ADV
ejpam-4260	112	41	,	,	PUNCT
ejpam-4260	112	42	ob′	ob′	NOUN
ejpam-4260	112	43	⊆	⊆	NUM
ejpam-4260	112	44	o.	o.	NOUN
ejpam-4260	112	45	conversely	conversely	ADV
ejpam-4260	112	46	,	,	PUNCT
ejpam-4260	112	47	suppose	suppose	VERB
ejpam-4260	112	48	that	that	SCONJ
ejpam-4260	112	49	ξ	ξ	PROPN
ejpam-4260	112	50	∈	∈	PROPN
ejpam-4260	112	51	oc	oc	NOUN
ejpam-4260	112	52	.	.	PUNCT
ejpam-4260	113	1	since	since	SCONJ
ejpam-4260	113	2	ob′	ob′	PROPN
ejpam-4260	113	3	⊆	⊆	NUM
ejpam-4260	113	4	o	o	NOUN
ejpam-4260	113	5	,	,	PUNCT
ejpam-4260	113	6	ξ	ξ	PROPN
ejpam-4260	113	7	̸∈	̸∈	PROPN
ejpam-4260	113	8	ob′.	ob′.	PROPN
ejpam-4260	113	9	accordingly	accordingly	ADV
ejpam-4260	113	10	,	,	PUNCT
ejpam-4260	113	11	we	we	PRON
ejpam-4260	113	12	find	find	VERB
ejpam-4260	113	13	a	a	DET
ejpam-4260	113	14	supra	supra	PROPN
ejpam-4260	113	15	b	b	NOUN
ejpam-4260	113	16	-	-	PUNCT
ejpam-4260	113	17	open	open	ADJ
ejpam-4260	113	18	set	set	NOUN
ejpam-4260	113	19	θξ	θξ	ADP
ejpam-4260	113	20	satisfying	satisfy	VERB
ejpam-4260	113	21	θξ	θξ	ADP
ejpam-4260	113	22	\	\	PROPN
ejpam-4260	113	23	{	{	PUNCT
ejpam-4260	113	24	ξ	ξ	NOUN
ejpam-4260	113	25	}	}	PUNCT
ejpam-4260	113	26	⋂	⋂	PROPN
ejpam-4260	113	27	o	o	NOUN
ejpam-4260	113	28	=	=	PUNCT
ejpam-4260	113	29	∅.	∅.	ADP
ejpam-4260	113	30	now	now	ADV
ejpam-4260	113	31	,	,	PUNCT
ejpam-4260	113	32	θξ	θξ	ADP
ejpam-4260	113	33	⋂	⋂	PROPN
ejpam-4260	113	34	o	o	NOUN
ejpam-4260	113	35	=	=	PUNCT
ejpam-4260	113	36	∅	∅	NOUN
ejpam-4260	113	37	because	because	SCONJ
ejpam-4260	113	38	ξ	ξ	PROPN
ejpam-4260	113	39	∈	∈	PROPN
ejpam-4260	113	40	oc	oc	PROPN
ejpam-4260	113	41	.	.	PUNCT
ejpam-4260	114	1	therefore	therefore	ADV
ejpam-4260	114	2	,	,	PUNCT
ejpam-4260	114	3	θξ	θξ	ADP
ejpam-4260	114	4	⊆	⊆	NUM
ejpam-4260	114	5	oc	oc	NOUN
ejpam-4260	114	6	,	,	PUNCT
ejpam-4260	114	7	which	which	PRON
ejpam-4260	114	8	means	mean	VERB
ejpam-4260	114	9	that	that	SCONJ
ejpam-4260	114	10	oc	oc	ADP
ejpam-4260	114	11	=	=	X
ejpam-4260	114	12	⋃	⋃	NOUN
ejpam-4260	114	13	{	{	PUNCT
ejpam-4260	114	14	θξ	θξ	ADP
ejpam-4260	114	15	:	:	PUNCT
ejpam-4260	114	16	ξ	ξ	X
ejpam-4260	114	17	∈	∈	NOUN
ejpam-4260	114	18	oc	oc	PRON
ejpam-4260	114	19	}	}	PUNCT
ejpam-4260	114	20	.	.	PUNCT
ejpam-4260	115	1	this	this	PRON
ejpam-4260	115	2	ends	end	VERB
ejpam-4260	115	3	the	the	DET
ejpam-4260	115	4	proof	proof	NOUN
ejpam-4260	115	5	that	that	SCONJ
ejpam-4260	115	6	o	o	NOUN
ejpam-4260	115	7	is	be	AUX
ejpam-4260	115	8	supra	supra	ADJ
ejpam-4260	115	9	b	b	NOUN
ejpam-4260	115	10	-	-	PUNCT
ejpam-4260	115	11	closed	closed	ADJ
ejpam-4260	115	12	.	.	PUNCT
ejpam-4260	116	1	(	(	PUNCT
ejpam-4260	116	2	ii	ii	NOUN
ejpam-4260	116	3	)	)	PUNCT
ejpam-4260	116	4	suppose	suppose	VERB
ejpam-4260	116	5	that	that	SCONJ
ejpam-4260	116	6	ξ	ξ	PROPN
ejpam-4260	116	7	̸∈	̸∈	PROPN
ejpam-4260	116	8	(	(	PUNCT
ejpam-4260	116	9	o	o	NOUN
ejpam-4260	116	10	⋃	⋃	NOUN
ejpam-4260	116	11	ob′	ob′	NOUN
ejpam-4260	116	12	)	)	PUNCT
ejpam-4260	116	13	.	.	PUNCT
ejpam-4260	117	1	then	then	ADV
ejpam-4260	117	2	,	,	PUNCT
ejpam-4260	117	3	ξ	ξ	PROPN
ejpam-4260	117	4	̸∈	̸∈	PROPN
ejpam-4260	117	5	o	o	PROPN
ejpam-4260	117	6	and	and	CCONJ
ejpam-4260	117	7	ξ	ξ	X
ejpam-4260	117	8	̸∈	̸∈	PROPN
ejpam-4260	117	9	ob′.	ob′.	PROPN
ejpam-4260	117	10	this	this	PRON
ejpam-4260	117	11	means	mean	VERB
ejpam-4260	117	12	that	that	SCONJ
ejpam-4260	117	13	there	there	PRON
ejpam-4260	117	14	exists	exist	VERB
ejpam-4260	117	15	a	a	DET
ejpam-4260	117	16	supra	supra	PROPN
ejpam-4260	117	17	b	b	NOUN
ejpam-4260	117	18	-	-	PUNCT
ejpam-4260	117	19	open	open	ADJ
ejpam-4260	117	20	set	set	NOUN
ejpam-4260	117	21	θ	θ	PROPN
ejpam-4260	117	22	satisfying	satisfy	VERB
ejpam-4260	117	23	the	the	DET
ejpam-4260	117	24	following	follow	VERB
ejpam-4260	117	25	equality	equality	NOUN
ejpam-4260	117	26	.	.	PUNCT
ejpam-4260	118	1	θ	θ	PROPN
ejpam-4260	118	2	⋂	⋂	NUM
ejpam-4260	118	3	o	o	X
ejpam-4260	118	4	=	=	NOUN
ejpam-4260	118	5	∅	∅	NOUN
ejpam-4260	118	6	(	(	PUNCT
ejpam-4260	118	7	1	1	X
ejpam-4260	118	8	)	)	PUNCT
ejpam-4260	118	9	now	now	ADV
ejpam-4260	118	10	,	,	PUNCT
ejpam-4260	118	11	for	for	ADP
ejpam-4260	118	12	every	every	DET
ejpam-4260	118	13	ξ	ξ	PROPN
ejpam-4260	118	14	∈	∈	PROPN
ejpam-4260	118	15	θ	θ	NOUN
ejpam-4260	118	16	,	,	PUNCT
ejpam-4260	118	17	we	we	PRON
ejpam-4260	118	18	obtain	obtain	VERB
ejpam-4260	118	19	ξ	ξ	PRON
ejpam-4260	118	20	̸∈	̸∈	PROPN
ejpam-4260	118	21	ob′.	ob′.	PROPN
ejpam-4260	118	22	so	so	ADV
ejpam-4260	118	23	we	we	PRON
ejpam-4260	118	24	obtain	obtain	VERB
ejpam-4260	118	25	the	the	DET
ejpam-4260	118	26	following	follow	VERB
ejpam-4260	118	27	equality	equality	NOUN
ejpam-4260	118	28	.	.	PUNCT
ejpam-4260	119	1	θ	θ	PROPN
ejpam-4260	119	2	⋂	⋂	NUM
ejpam-4260	119	3	ob′	ob′	NOUN
ejpam-4260	119	4	=	=	NOUN
ejpam-4260	119	5	∅	∅	NOUN
ejpam-4260	119	6	(	(	PUNCT
ejpam-4260	119	7	2	2	X
ejpam-4260	119	8	)	)	PUNCT
ejpam-4260	119	9	it	it	PRON
ejpam-4260	119	10	comes	come	VERB
ejpam-4260	119	11	from	from	ADP
ejpam-4260	119	12	(	(	PUNCT
ejpam-4260	119	13	1	1	NUM
ejpam-4260	119	14	)	)	PUNCT
ejpam-4260	119	15	and	and	CCONJ
ejpam-4260	119	16	(	(	PUNCT
ejpam-4260	119	17	2	2	X
ejpam-4260	119	18	)	)	PUNCT
ejpam-4260	120	1	that	that	PRON
ejpam-4260	120	2	θ	θ	PROPN
ejpam-4260	120	3	⋂	⋂	PROPN
ejpam-4260	120	4	(	(	PUNCT
ejpam-4260	120	5	o	o	NOUN
ejpam-4260	120	6	⋃	⋃	NOUN
ejpam-4260	120	7	ob′	ob′	NOUN
ejpam-4260	120	8	)	)	PUNCT
ejpam-4260	120	9	=	=	PUNCT
ejpam-4260	120	10	∅.	∅.	ADP
ejpam-4260	120	11	thus	thus	ADV
ejpam-4260	120	12	,	,	PUNCT
ejpam-4260	120	13	ξ	ξ	PROPN
ejpam-4260	120	14	̸∈	̸∈	PROPN
ejpam-4260	120	15	(	(	PUNCT
ejpam-4260	120	16	o	o	PROPN
ejpam-4260	120	17	⋃	⋃	NOUN
ejpam-4260	120	18	ob′)b′.	ob′)b′.	PUNCT
ejpam-4260	120	19	hence	hence	ADV
ejpam-4260	120	20	,	,	PUNCT
ejpam-4260	120	21	(	(	PUNCT
ejpam-4260	120	22	o	o	X
ejpam-4260	120	23	⋃	⋃	NOUN
ejpam-4260	120	24	ob′)b′	ob′)b′	NOUN
ejpam-4260	120	25	⊆	⊆	NUM
ejpam-4260	120	26	(	(	PUNCT
ejpam-4260	120	27	o	o	NOUN
ejpam-4260	120	28	⋃	⋃	NOUN
ejpam-4260	120	29	ob′	ob′	NOUN
ejpam-4260	120	30	)	)	PUNCT
ejpam-4260	120	31	.	.	PUNCT
ejpam-4260	121	1	according	accord	VERB
ejpam-4260	121	2	to	to	ADP
ejpam-4260	121	3	(	(	PUNCT
ejpam-4260	121	4	i	i	NOUN
ejpam-4260	121	5	)	)	PUNCT
ejpam-4260	121	6	,	,	PUNCT
ejpam-4260	121	7	o	o	NOUN
ejpam-4260	121	8	⋃	⋃	ADJ
ejpam-4260	121	9	ob′	ob′	NOUN
ejpam-4260	121	10	is	be	AUX
ejpam-4260	121	11	supra	supra	ADJ
ejpam-4260	121	12	b	b	NOUN
ejpam-4260	121	13	-	-	PUNCT
ejpam-4260	121	14	closed	closed	ADJ
ejpam-4260	121	15	.	.	PUNCT
ejpam-4260	122	1	a.	a.	NOUN
ejpam-4260	122	2	mhemdi	mhemdi	PROPN
ejpam-4260	122	3	et	et	PROPN
ejpam-4260	122	4	al	al	PROPN
ejpam-4260	122	5	.	.	PUNCT
ejpam-4260	122	6	/	/	SYM
ejpam-4260	122	7	eur	eur	PROPN
ejpam-4260	122	8	.	.	PUNCT
ejpam-4260	123	1	j.	j.	PROPN
ejpam-4260	123	2	pure	pure	PROPN
ejpam-4260	123	3	appl	appl	PROPN
ejpam-4260	123	4	.	.	PROPN
ejpam-4260	123	5	math	math	PROPN
ejpam-4260	123	6	,	,	PUNCT
ejpam-4260	123	7	15	15	NUM
ejpam-4260	123	8	(	(	PUNCT
ejpam-4260	123	9	1	1	NUM
ejpam-4260	123	10	)	)	PUNCT
ejpam-4260	123	11	(	(	PUNCT
ejpam-4260	123	12	2022	2022	NUM
ejpam-4260	123	13	)	)	PUNCT
ejpam-4260	123	14	,	,	PUNCT
ejpam-4260	123	15	15	15	NUM
ejpam-4260	123	16	-	-	SYM
ejpam-4260	123	17	29	29	NUM
ejpam-4260	123	18	19	19	NUM
ejpam-4260	123	19	(	(	PUNCT
ejpam-4260	123	20	iii	iii	X
ejpam-4260	123	21	)	)	PUNCT
ejpam-4260	123	22	it	it	PRON
ejpam-4260	123	23	is	be	AUX
ejpam-4260	123	24	clear	clear	ADJ
ejpam-4260	123	25	that	that	SCONJ
ejpam-4260	123	26	o	o	NOUN
ejpam-4260	123	27	⋃	⋃	NOUN
ejpam-4260	123	28	ob′	ob′	NOUN
ejpam-4260	123	29	⊆	⊆	NUM
ejpam-4260	123	30	bcl(o	bcl(o	NOUN
ejpam-4260	123	31	)	)	PUNCT
ejpam-4260	123	32	.	.	PUNCT
ejpam-4260	124	1	conversely	conversely	ADV
ejpam-4260	124	2	,	,	PUNCT
ejpam-4260	124	3	it	it	PRON
ejpam-4260	124	4	well	well	ADV
ejpam-4260	124	5	known	know	VERB
ejpam-4260	124	6	that	that	SCONJ
ejpam-4260	124	7	bcl(o	bcl(o	PROPN
ejpam-4260	124	8	)	)	PUNCT
ejpam-4260	124	9	is	be	AUX
ejpam-4260	124	10	the	the	DET
ejpam-4260	124	11	smallest	small	ADJ
ejpam-4260	124	12	supra	supra	ADJ
ejpam-4260	124	13	b	b	NOUN
ejpam-4260	124	14	-	-	PUNCT
ejpam-4260	124	15	closed	closed	ADJ
ejpam-4260	124	16	set	set	NOUN
ejpam-4260	124	17	including	include	VERB
ejpam-4260	124	18	o.	o.	NOUN
ejpam-4260	124	19	since	since	SCONJ
ejpam-4260	124	20	o	o	PROPN
ejpam-4260	125	1	⋃	⋃	NOUN
ejpam-4260	125	2	ob′	ob′	NOUN
ejpam-4260	125	3	is	be	AUX
ejpam-4260	125	4	a	a	DET
ejpam-4260	125	5	supra	supra	PROPN
ejpam-4260	125	6	b	b	NOUN
ejpam-4260	125	7	-	-	PUNCT
ejpam-4260	125	8	closed	closed	ADJ
ejpam-4260	125	9	set	set	NOUN
ejpam-4260	125	10	including	include	VERB
ejpam-4260	125	11	o	o	PROPN
ejpam-4260	125	12	,	,	PUNCT
ejpam-4260	125	13	bcl(o	bcl(o	PROPN
ejpam-4260	125	14	)	)	PUNCT
ejpam-4260	125	15	⊆	⊆	NUM
ejpam-4260	125	16	o	o	NOUN
ejpam-4260	125	17	⋃	⋃	NOUN
ejpam-4260	125	18	ob′.	ob′.	NOUN
ejpam-4260	125	19	hence	hence	ADV
ejpam-4260	125	20	,	,	PUNCT
ejpam-4260	125	21	bcl(o	bcl(o	PROPN
ejpam-4260	125	22	)	)	PUNCT
ejpam-4260	125	23	=	=	SYM
ejpam-4260	126	1	o	o	NOUN
ejpam-4260	126	2	⋃	⋃	NOUN
ejpam-4260	126	3	ob′.	ob′.	ADJ
ejpam-4260	126	4	corollary	corollary	ADJ
ejpam-4260	126	5	2	2	NUM
ejpam-4260	126	6	.	.	PUNCT
ejpam-4260	127	1	if	if	SCONJ
ejpam-4260	127	2	o	o	NOUN
ejpam-4260	127	3	is	be	AUX
ejpam-4260	127	4	a	a	DET
ejpam-4260	127	5	supra	supra	PROPN
ejpam-4260	127	6	b	b	NOUN
ejpam-4260	127	7	-	-	PUNCT
ejpam-4260	127	8	closed	closed	ADJ
ejpam-4260	127	9	subset	subset	NOUN
ejpam-4260	127	10	of	of	ADP
ejpam-4260	127	11	(	(	PUNCT
ejpam-4260	127	12	u	u	PROPN
ejpam-4260	127	13	,	,	PUNCT
ejpam-4260	127	14	ω	ω	PROPN
ejpam-4260	127	15	)	)	PUNCT
ejpam-4260	127	16	,	,	PUNCT
ejpam-4260	127	17	then	then	ADV
ejpam-4260	127	18	ob′	ob′	VERB
ejpam-4260	127	19	,	,	PUNCT
ejpam-4260	127	20	(	(	PUNCT
ejpam-4260	127	21	ob′)b′	ob′)b′	X
ejpam-4260	127	22	,	,	PUNCT
ejpam-4260	127	23	(	(	PUNCT
ejpam-4260	127	24	(	(	PUNCT
ejpam-4260	127	25	ob′)b′)b′	ob′)b′)b′	X
ejpam-4260	127	26	,	,	PUNCT
ejpam-4260	127	27	...	...	PUNCT
ejpam-4260	127	28	are	be	AUX
ejpam-4260	127	29	supra	supra	PROPN
ejpam-4260	127	30	b	b	NOUN
ejpam-4260	127	31	-	-	PUNCT
ejpam-4260	127	32	closed	closed	ADJ
ejpam-4260	127	33	sets	set	NOUN
ejpam-4260	127	34	.	.	PUNCT
ejpam-4260	128	1	definition	definition	NOUN
ejpam-4260	128	2	10	10	NUM
ejpam-4260	128	3	.	.	PUNCT
ejpam-4260	129	1	we	we	PRON
ejpam-4260	129	2	call	call	VERB
ejpam-4260	129	3	a	a	DET
ejpam-4260	129	4	mapping	mapping	NOUN
ejpam-4260	129	5	g	g	NOUN
ejpam-4260	129	6	:	:	PUNCT
ejpam-4260	129	7	(	(	PUNCT
ejpam-4260	129	8	u	u	NOUN
ejpam-4260	129	9	,	,	PUNCT
ejpam-4260	129	10	ω	ω	PROPN
ejpam-4260	129	11	)	)	PUNCT
ejpam-4260	129	12	→	→	SYM
ejpam-4260	129	13	(	(	PUNCT
ejpam-4260	129	14	v	v	NOUN
ejpam-4260	129	15	,	,	PUNCT
ejpam-4260	129	16	ψ	ψ	NOUN
ejpam-4260	129	17	):	):	PUNCT
ejpam-4260	129	18	(	(	PUNCT
ejpam-4260	129	19	i	i	NOUN
ejpam-4260	129	20	)	)	PUNCT
ejpam-4260	129	21	supra	supra	PROPN
ejpam-4260	129	22	b⋆-continuous	b⋆-continuous	ADJ
ejpam-4260	129	23	if	if	SCONJ
ejpam-4260	129	24	g−1(h	g−1(h	PROPN
ejpam-4260	129	25	)	)	PUNCT
ejpam-4260	129	26	is	be	AUX
ejpam-4260	129	27	supra	supra	ADJ
ejpam-4260	129	28	b	b	NOUN
ejpam-4260	129	29	-	-	PUNCT
ejpam-4260	129	30	open	open	ADJ
ejpam-4260	129	31	for	for	ADP
ejpam-4260	129	32	any	any	DET
ejpam-4260	129	33	supra	supra	PROPN
ejpam-4260	129	34	b	b	NOUN
ejpam-4260	129	35	-	-	PUNCT
ejpam-4260	129	36	open	open	ADJ
ejpam-4260	129	37	set	set	NOUN
ejpam-4260	129	38	h.	h.	PROPN
ejpam-4260	129	39	(	(	PUNCT
ejpam-4260	129	40	ii	ii	PROPN
ejpam-4260	129	41	)	)	PUNCT
ejpam-4260	129	42	supra	supra	ADJ
ejpam-4260	129	43	b⋆-open	b⋆-open	NOUN
ejpam-4260	129	44	(	(	PUNCT
ejpam-4260	129	45	respectively	respectively	ADV
ejpam-4260	129	46	,	,	PUNCT
ejpam-4260	129	47	supra	supra	PROPN
ejpam-4260	129	48	b⋆-closed	b⋆-close	VERB
ejpam-4260	129	49	)	)	PUNCT
ejpam-4260	129	50	if	if	SCONJ
ejpam-4260	129	51	g(h	g(h	NUM
ejpam-4260	129	52	)	)	PUNCT
ejpam-4260	129	53	is	be	AUX
ejpam-4260	129	54	supra	supra	ADJ
ejpam-4260	129	55	b	b	NOUN
ejpam-4260	129	56	-	-	PUNCT
ejpam-4260	129	57	open	open	ADJ
ejpam-4260	129	58	(	(	PUNCT
ejpam-4260	129	59	respectively	respectively	ADV
ejpam-4260	129	60	,	,	PUNCT
ejpam-4260	129	61	supra	supra	PROPN
ejpam-4260	129	62	b	b	PROPN
ejpam-4260	129	63	-	-	PUNCT
ejpam-4260	129	64	closed	closed	ADJ
ejpam-4260	129	65	)	)	PUNCT
ejpam-4260	129	66	for	for	ADP
ejpam-4260	129	67	any	any	DET
ejpam-4260	129	68	supra	supra	PROPN
ejpam-4260	129	69	b	b	NOUN
ejpam-4260	129	70	-	-	PUNCT
ejpam-4260	129	71	open	open	ADJ
ejpam-4260	129	72	(	(	PUNCT
ejpam-4260	129	73	respectively	respectively	ADV
ejpam-4260	129	74	,	,	PUNCT
ejpam-4260	129	75	supra	supra	PROPN
ejpam-4260	129	76	b	b	PROPN
ejpam-4260	129	77	-	-	PUNCT
ejpam-4260	129	78	closed	closed	ADJ
ejpam-4260	129	79	)	)	PUNCT
ejpam-4260	129	80	set	set	NOUN
ejpam-4260	129	81	h.	h.	NOUN
ejpam-4260	129	82	we	we	PRON
ejpam-4260	129	83	call	call	VERB
ejpam-4260	129	84	a	a	DET
ejpam-4260	129	85	bijective	bijective	ADJ
ejpam-4260	129	86	,	,	PUNCT
ejpam-4260	129	87	supra	supra	ADJ
ejpam-4260	129	88	b⋆-continuous	b⋆-continuous	ADJ
ejpam-4260	129	89	and	and	CCONJ
ejpam-4260	129	90	supra	supra	ADJ
ejpam-4260	129	91	b⋆-open	b⋆-open	PROPN
ejpam-4260	129	92	mapping	map	VERB
ejpam-4260	129	93	a	a	DET
ejpam-4260	129	94	supra	supra	PROPN
ejpam-4260	129	95	b⋆-homeomorphism	b⋆-homeomorphism	NOUN
ejpam-4260	129	96	.	.	PUNCT
ejpam-4260	130	1	theorem	theorem	NOUN
ejpam-4260	130	2	2	2	NUM
ejpam-4260	130	3	.	.	PUNCT
ejpam-4260	131	1	if	if	SCONJ
ejpam-4260	131	2	f	f	PROPN
ejpam-4260	131	3	:	:	PUNCT
ejpam-4260	131	4	(	(	PUNCT
ejpam-4260	131	5	u	u	NOUN
ejpam-4260	131	6	,	,	PUNCT
ejpam-4260	131	7	ω	ω	PROPN
ejpam-4260	131	8	)	)	PUNCT
ejpam-4260	131	9	→	→	SYM
ejpam-4260	131	10	(	(	PUNCT
ejpam-4260	131	11	v	v	NOUN
ejpam-4260	131	12	,	,	PUNCT
ejpam-4260	131	13	ψ	ψ	NOUN
ejpam-4260	131	14	)	)	PUNCT
ejpam-4260	131	15	is	be	AUX
ejpam-4260	131	16	a	a	DET
ejpam-4260	131	17	supra	supra	PROPN
ejpam-4260	131	18	b⋆-homeomorphism	b⋆-homeomorphism	PROPN
ejpam-4260	131	19	mapping	mapping	NOUN
ejpam-4260	131	20	,	,	PUNCT
ejpam-4260	131	21	then	then	ADV
ejpam-4260	131	22	f(ob′	f(ob′	PROPN
ejpam-4260	131	23	)	)	PUNCT
ejpam-4260	131	24	=	=	SYM
ejpam-4260	131	25	(	(	PUNCT
ejpam-4260	131	26	g(o))b′	g(o))b′	NOUN
ejpam-4260	131	27	for	for	ADP
ejpam-4260	131	28	each	each	DET
ejpam-4260	131	29	o	o	NOUN
ejpam-4260	131	30	⊆	⊆	NUM
ejpam-4260	131	31	u	u	NOUN
ejpam-4260	131	32	.	.	PUNCT
ejpam-4260	132	1	proof	proof	NOUN
ejpam-4260	132	2	.	.	PUNCT
ejpam-4260	133	1	consider	consider	VERB
ejpam-4260	133	2	ξ	ξ	PROPN
ejpam-4260	133	3	̸∈	̸∈	PROPN
ejpam-4260	133	4	(	(	PUNCT
ejpam-4260	133	5	f(o))b′.	f(o))b′.	PROPN
ejpam-4260	133	6	then	then	ADV
ejpam-4260	133	7	,	,	PUNCT
ejpam-4260	133	8	(	(	PUNCT
ejpam-4260	133	9	h\{ξ	h\{ξ	X
ejpam-4260	133	10	}	}	PUNCT
ejpam-4260	133	11	)	)	PUNCT
ejpam-4260	133	12	⋂	⋂	PROPN
ejpam-4260	133	13	f(o	f(o	NOUN
ejpam-4260	133	14	)	)	PUNCT
ejpam-4260	133	15	=	=	NOUN
ejpam-4260	133	16	∅	∅	NOUN
ejpam-4260	133	17	for	for	ADP
ejpam-4260	133	18	some	some	DET
ejpam-4260	133	19	supra	supra	PROPN
ejpam-4260	133	20	b	b	NOUN
ejpam-4260	133	21	-	-	PUNCT
ejpam-4260	133	22	open	open	ADJ
ejpam-4260	133	23	setsh	setsh	NOUN
ejpam-4260	133	24	including	include	VERB
ejpam-4260	133	25	ξ	ξ	X
ejpam-4260	133	26	.	.	PUNCT
ejpam-4260	134	1	directly	directly	ADV
ejpam-4260	134	2	,	,	PUNCT
ejpam-4260	134	3	f−1[(h	f−1[(h	PUNCT
ejpam-4260	134	4	\	\	X
ejpam-4260	134	5	{	{	PUNCT
ejpam-4260	134	6	ξ	ξ	NOUN
ejpam-4260	134	7	}	}	PUNCT
ejpam-4260	134	8	)	)	PUNCT
ejpam-4260	134	9	⋂	⋂	PROPN
ejpam-4260	134	10	f(o	f(o	NOUN
ejpam-4260	134	11	)	)	PUNCT
ejpam-4260	134	12	]	]	PUNCT
ejpam-4260	135	1	=	=	PUNCT
ejpam-4260	135	2	f−1(∅	f−1(∅	PROPN
ejpam-4260	135	3	)	)	PUNCT
ejpam-4260	135	4	.	.	PUNCT
ejpam-4260	136	1	now	now	ADV
ejpam-4260	136	2	,	,	PUNCT
ejpam-4260	136	3	(	(	PUNCT
ejpam-4260	136	4	f−1(h	f−1(h	PROPN
ejpam-4260	136	5	)	)	PUNCT
ejpam-4260	136	6	\	\	PROPN
ejpam-4260	136	7	f−1(ξ	f−1(ξ	PROPN
ejpam-4260	136	8	)	)	PUNCT
ejpam-4260	136	9	)	)	PUNCT
ejpam-4260	137	1	⋂	⋂	PROPN
ejpam-4260	137	2	o	o	NOUN
ejpam-4260	137	3	=	=	PUNCT
ejpam-4260	137	4	∅.	∅.	PRON
ejpam-4260	137	5	this	this	PRON
ejpam-4260	137	6	means	mean	VERB
ejpam-4260	137	7	that	that	SCONJ
ejpam-4260	137	8	f−1(ξ	f−1(ξ	PROPN
ejpam-4260	137	9	)	)	PUNCT
ejpam-4260	137	10	̸∈	̸∈	PROPN
ejpam-4260	137	11	ob′.	ob′.	PROPN
ejpam-4260	137	12	the	the	DET
ejpam-4260	137	13	bijectiveness	bijectiveness	NOUN
ejpam-4260	137	14	of	of	ADP
ejpam-4260	137	15	f	f	PROPN
ejpam-4260	137	16	implies	imply	VERB
ejpam-4260	137	17	that	that	SCONJ
ejpam-4260	137	18	ξ	ξ	PROPN
ejpam-4260	137	19	̸∈	̸∈	PROPN
ejpam-4260	137	20	f(ob′	f(ob′	PROPN
ejpam-4260	137	21	)	)	PUNCT
ejpam-4260	137	22	.	.	PUNCT
ejpam-4260	138	1	thus	thus	ADV
ejpam-4260	138	2	,	,	PUNCT
ejpam-4260	138	3	f(ob′	f(ob′	PROPN
ejpam-4260	138	4	)	)	PUNCT
ejpam-4260	138	5	⊆	⊆	NUM
ejpam-4260	138	6	(	(	PUNCT
ejpam-4260	138	7	f(o))b′.	f(o))b′.	X
ejpam-4260	138	8	following	follow	VERB
ejpam-4260	138	9	similar	similar	ADJ
ejpam-4260	138	10	technique	technique	NOUN
ejpam-4260	138	11	,	,	PUNCT
ejpam-4260	138	12	we	we	PRON
ejpam-4260	138	13	obtain	obtain	VERB
ejpam-4260	138	14	(	(	PUNCT
ejpam-4260	138	15	f(o))b′	f(o))b′	NOUN
ejpam-4260	138	16	⊆	⊆	NUM
ejpam-4260	138	17	f(ob′	f(ob′	NOUN
ejpam-4260	138	18	)	)	PUNCT
ejpam-4260	138	19	.	.	PUNCT
ejpam-4260	139	1	definition	definition	NOUN
ejpam-4260	139	2	11	11	NUM
ejpam-4260	139	3	.	.	PUNCT
ejpam-4260	140	1	a	a	DET
ejpam-4260	140	2	sub	sub	ADJ
ejpam-4260	140	3	-	-	ADJ
ejpam-4260	140	4	collection	collection	ADJ
ejpam-4260	140	5	λ	λ	NOUN
ejpam-4260	140	6	of	of	ADP
ejpam-4260	140	7	the	the	DET
ejpam-4260	140	8	power	power	NOUN
ejpam-4260	140	9	set	set	NOUN
ejpam-4260	140	10	of	of	ADP
ejpam-4260	140	11	u	u	NOUN
ejpam-4260	140	12	̸=	̸=	PROPN
ejpam-4260	140	13	∅	∅	NOUN
ejpam-4260	140	14	is	be	AUX
ejpam-4260	140	15	said	say	VERB
ejpam-4260	140	16	to	to	PART
ejpam-4260	140	17	have	have	VERB
ejpam-4260	140	18	the	the	DET
ejpam-4260	140	19	difference	difference	NOUN
ejpam-4260	140	20	property	property	NOUN
ejpam-4260	140	21	if	if	SCONJ
ejpam-4260	140	22	θ	θ	PROPN
ejpam-4260	140	23	∈	∈	PROPN
ejpam-4260	140	24	λ	λ	PROPN
ejpam-4260	140	25	implies	imply	VERB
ejpam-4260	140	26	that	that	SCONJ
ejpam-4260	140	27	θ	θ	X
ejpam-4260	140	28	\	\	PROPN
ejpam-4260	140	29	{	{	PUNCT
ejpam-4260	140	30	ξ	ξ	NOUN
ejpam-4260	140	31	}	}	PUNCT
ejpam-4260	140	32	∈	∈	PROPN
ejpam-4260	140	33	λ	λ	NOUN
ejpam-4260	140	34	.	.	PUNCT
ejpam-4260	140	35	to	to	PART
ejpam-4260	140	36	illustrate	illustrate	VERB
ejpam-4260	140	37	the	the	DET
ejpam-4260	140	38	difference	difference	NOUN
ejpam-4260	140	39	property	property	NOUN
ejpam-4260	140	40	,	,	PUNCT
ejpam-4260	140	41	we	we	PRON
ejpam-4260	140	42	supply	supply	VERB
ejpam-4260	140	43	the	the	DET
ejpam-4260	140	44	next	next	ADJ
ejpam-4260	140	45	two	two	NUM
ejpam-4260	140	46	examples	example	NOUN
ejpam-4260	140	47	.	.	PUNCT
ejpam-4260	141	1	example	example	NOUN
ejpam-4260	141	2	2	2	NUM
ejpam-4260	141	3	.	.	X
ejpam-4260	142	1	consider	consider	VERB
ejpam-4260	142	2	ω	ω	NOUN
ejpam-4260	142	3	=	=	PRON
ejpam-4260	142	4	{	{	PUNCT
ejpam-4260	142	5	∅,θ	∅,θ	NOUN
ejpam-4260	142	6	⊆	⊆	NUM
ejpam-4260	142	7	n	n	NOUN
ejpam-4260	142	8	:	:	PUNCT
ejpam-4260	142	9	θ	θ	NOUN
ejpam-4260	142	10	is	be	AUX
ejpam-4260	142	11	infinite	infinite	ADJ
ejpam-4260	142	12	}	}	PUNCT
ejpam-4260	142	13	as	as	ADP
ejpam-4260	142	14	an	an	DET
ejpam-4260	142	15	st	st	NOUN
ejpam-4260	142	16	on	on	ADP
ejpam-4260	142	17	the	the	DET
ejpam-4260	142	18	natural	natural	ADJ
ejpam-4260	142	19	numbers	number	NOUN
ejpam-4260	142	20	set	set	VERB
ejpam-4260	142	21	n	n	X
ejpam-4260	142	22	.	.	PUNCT
ejpam-4260	143	1	obviously	obviously	ADV
ejpam-4260	143	2	,	,	PUNCT
ejpam-4260	143	3	θ	θ	PROPN
ejpam-4260	143	4	∈	∈	PROPN
ejpam-4260	143	5	ω	ω	NOUN
ejpam-4260	143	6	implies	imply	VERB
ejpam-4260	143	7	θ	θ	X
ejpam-4260	143	8	\	\	X
ejpam-4260	143	9	{	{	PUNCT
ejpam-4260	143	10	ξ	ξ	NOUN
ejpam-4260	143	11	}	}	PUNCT
ejpam-4260	143	12	∈	∈	PROPN
ejpam-4260	143	13	ω	ω	PROPN
ejpam-4260	143	14	.	.	PUNCT
ejpam-4260	144	1	then	then	ADV
ejpam-4260	144	2	,	,	PUNCT
ejpam-4260	144	3	(	(	PUNCT
ejpam-4260	144	4	n	n	X
ejpam-4260	144	5	,	,	PUNCT
ejpam-4260	144	6	ω	ω	PROPN
ejpam-4260	144	7	)	)	PUNCT
ejpam-4260	144	8	has	have	VERB
ejpam-4260	144	9	the	the	DET
ejpam-4260	144	10	difference	difference	NOUN
ejpam-4260	144	11	property	property	NOUN
ejpam-4260	144	12	.	.	PUNCT
ejpam-4260	145	1	note	note	VERB
ejpam-4260	145	2	that	that	SCONJ
ejpam-4260	145	3	the	the	DET
ejpam-4260	145	4	families	family	NOUN
ejpam-4260	145	5	of	of	ADP
ejpam-4260	145	6	supra	supra	PROPN
ejpam-4260	145	7	open	open	ADJ
ejpam-4260	145	8	and	and	CCONJ
ejpam-4260	145	9	supra	supra	ADJ
ejpam-4260	145	10	b	b	NOUN
ejpam-4260	145	11	-	-	PUNCT
ejpam-4260	145	12	open	open	ADJ
ejpam-4260	145	13	subsets	subset	NOUN
ejpam-4260	145	14	of	of	ADP
ejpam-4260	145	15	(	(	PUNCT
ejpam-4260	145	16	n	n	X
ejpam-4260	145	17	,	,	PUNCT
ejpam-4260	145	18	ω	ω	NUM
ejpam-4260	145	19	)	)	PUNCT
ejpam-4260	145	20	are	be	AUX
ejpam-4260	145	21	identical	identical	ADJ
ejpam-4260	145	22	.	.	PUNCT
ejpam-4260	146	1	hence	hence	ADV
ejpam-4260	146	2	,	,	PUNCT
ejpam-4260	146	3	(	(	PUNCT
ejpam-4260	146	4	n	n	X
ejpam-4260	146	5	,	,	PUNCT
ejpam-4260	146	6	ω	ω	PROPN
ejpam-4260	146	7	)	)	PUNCT
ejpam-4260	146	8	has	have	VERB
ejpam-4260	146	9	the	the	DET
ejpam-4260	146	10	difference	difference	NOUN
ejpam-4260	146	11	property	property	NOUN
ejpam-4260	146	12	for	for	ADP
ejpam-4260	146	13	the	the	DET
ejpam-4260	146	14	family	family	NOUN
ejpam-4260	146	15	of	of	ADP
ejpam-4260	146	16	supra	supra	PROPN
ejpam-4260	146	17	b	b	PROPN
ejpam-4260	146	18	-	-	PUNCT
ejpam-4260	146	19	open	open	ADJ
ejpam-4260	146	20	sets	set	NOUN
ejpam-4260	146	21	.	.	PUNCT
ejpam-4260	147	1	example	example	NOUN
ejpam-4260	147	2	3	3	X
ejpam-4260	147	3	.	.	X
ejpam-4260	148	1	consider	consider	VERB
ejpam-4260	148	2	ω	ω	NOUN
ejpam-4260	148	3	=	=	PRON
ejpam-4260	148	4	{	{	PUNCT
ejpam-4260	148	5	∅,n	∅,n	X
ejpam-4260	148	6	\	\	NOUN
ejpam-4260	148	7	{	{	PUNCT
ejpam-4260	148	8	1	1	NUM
ejpam-4260	148	9	,	,	PUNCT
ejpam-4260	148	10	3},n	3},n	PROPN
ejpam-4260	148	11	\	\	NOUN
ejpam-4260	148	12	{	{	PUNCT
ejpam-4260	148	13	1	1	NUM
ejpam-4260	148	14	,	,	PUNCT
ejpam-4260	148	15	4},n	4},n	PROPN
ejpam-4260	148	16	\	\	NOUN
ejpam-4260	148	17	{	{	PUNCT
ejpam-4260	148	18	2	2	NUM
ejpam-4260	148	19	,	,	PUNCT
ejpam-4260	148	20	3},n	3},n	PROPN
ejpam-4260	148	21	\	\	NOUN
ejpam-4260	148	22	{	{	PUNCT
ejpam-4260	148	23	2	2	NUM
ejpam-4260	148	24	,	,	PUNCT
ejpam-4260	148	25	4	4	NUM
ejpam-4260	148	26	}	}	PUNCT
ejpam-4260	148	27	}	}	PUNCT
ejpam-4260	148	28	⋃	⋃	NOUN
ejpam-4260	148	29	{	{	PUNCT
ejpam-4260	148	30	θ	θ	NOUN
ejpam-4260	148	31	⊆	⊆	NUM
ejpam-4260	148	32	n	n	NUM
ejpam-4260	148	33	:	:	PUNCT
ejpam-4260	148	34	θ	θ	X
ejpam-4260	148	35	such	such	ADJ
ejpam-4260	148	36	that	that	SCONJ
ejpam-4260	148	37	{	{	PUNCT
ejpam-4260	148	38	1	1	NUM
ejpam-4260	148	39	,	,	PUNCT
ejpam-4260	148	40	2	2	NUM
ejpam-4260	148	41	}	}	SYM
ejpam-4260	148	42	⊆	⊆	NUM
ejpam-4260	148	43	θ	θ	NOUN
ejpam-4260	148	44	or	or	CCONJ
ejpam-4260	148	45	{	{	PUNCT
ejpam-4260	148	46	3	3	NUM
ejpam-4260	148	47	,	,	PUNCT
ejpam-4260	148	48	4	4	NUM
ejpam-4260	148	49	}	}	SYM
ejpam-4260	148	50	⊆	⊆	NUM
ejpam-4260	148	51	θ	θ	NOUN
ejpam-4260	148	52	}	}	PUNCT
ejpam-4260	148	53	as	as	ADP
ejpam-4260	148	54	an	an	DET
ejpam-4260	148	55	st	st	NOUN
ejpam-4260	148	56	on	on	ADP
ejpam-4260	148	57	the	the	DET
ejpam-4260	148	58	natural	natural	ADJ
ejpam-4260	148	59	numbers	number	NOUN
ejpam-4260	148	60	set	set	VERB
ejpam-4260	148	61	n	n	PROPN
ejpam-4260	148	62	.	.	PUNCT
ejpam-4260	149	1	then	then	ADV
ejpam-4260	149	2	{	{	PUNCT
ejpam-4260	149	3	1	1	NUM
ejpam-4260	149	4	,	,	PUNCT
ejpam-4260	149	5	2	2	NUM
ejpam-4260	149	6	}	}	PUNCT
ejpam-4260	149	7	∈	∈	PROPN
ejpam-4260	149	8	ω	ω	NOUN
ejpam-4260	149	9	,	,	PUNCT
ejpam-4260	149	10	but	but	CCONJ
ejpam-4260	149	11	{	{	PUNCT
ejpam-4260	149	12	1	1	NUM
ejpam-4260	149	13	,	,	PUNCT
ejpam-4260	149	14	2}\{2	2}\{2	NUM
ejpam-4260	149	15	}	}	PUNCT
ejpam-4260	149	16	=	=	SYM
ejpam-4260	149	17	{	{	PUNCT
ejpam-4260	149	18	1	1	NUM
ejpam-4260	149	19	}	}	PUNCT
ejpam-4260	149	20	̸∈	̸∈	PROPN
ejpam-4260	149	21	ω	ω	PROPN
ejpam-4260	149	22	.	.	PUNCT
ejpam-4260	150	1	thus	thus	ADV
ejpam-4260	150	2	,	,	PUNCT
ejpam-4260	150	3	(	(	PUNCT
ejpam-4260	150	4	u	u	NOUN
ejpam-4260	150	5	,	,	PUNCT
ejpam-4260	150	6	ω	ω	PROPN
ejpam-4260	150	7	)	)	PUNCT
ejpam-4260	150	8	does	do	AUX
ejpam-4260	150	9	not	not	PART
ejpam-4260	150	10	have	have	VERB
ejpam-4260	150	11	the	the	DET
ejpam-4260	150	12	difference	difference	NOUN
ejpam-4260	150	13	property	property	NOUN
ejpam-4260	150	14	..	..	PUNCT
ejpam-4260	151	1	hence	hence	ADV
ejpam-4260	151	2	,	,	PUNCT
ejpam-4260	151	3	it	it	PRON
ejpam-4260	151	4	does	do	AUX
ejpam-4260	151	5	not	not	PART
ejpam-4260	151	6	have	have	VERB
ejpam-4260	151	7	the	the	DET
ejpam-4260	151	8	difference	difference	NOUN
ejpam-4260	151	9	property	property	NOUN
ejpam-4260	151	10	for	for	ADP
ejpam-4260	151	11	the	the	DET
ejpam-4260	151	12	family	family	NOUN
ejpam-4260	151	13	of	of	ADP
ejpam-4260	151	14	supra	supra	PROPN
ejpam-4260	151	15	b	b	PROPN
ejpam-4260	151	16	-	-	PUNCT
ejpam-4260	151	17	open	open	ADJ
ejpam-4260	151	18	sets	set	NOUN
ejpam-4260	151	19	.	.	PUNCT
ejpam-4260	152	1	theorem	theorem	NOUN
ejpam-4260	152	2	3	3	X
ejpam-4260	152	3	.	.	PUNCT
ejpam-4260	153	1	let	let	VERB
ejpam-4260	153	2	o	o	NOUN
ejpam-4260	153	3	be	be	AUX
ejpam-4260	153	4	a	a	DET
ejpam-4260	153	5	subset	subset	NOUN
ejpam-4260	153	6	of	of	ADP
ejpam-4260	153	7	(	(	PUNCT
ejpam-4260	153	8	u	u	PROPN
ejpam-4260	153	9	,	,	PUNCT
ejpam-4260	153	10	ω	ω	PROPN
ejpam-4260	153	11	)	)	PUNCT
ejpam-4260	153	12	which	which	PRON
ejpam-4260	153	13	has	have	VERB
ejpam-4260	153	14	the	the	DET
ejpam-4260	153	15	difference	difference	NOUN
ejpam-4260	153	16	property	property	NOUN
ejpam-4260	153	17	for	for	ADP
ejpam-4260	153	18	the	the	DET
ejpam-4260	153	19	family	family	NOUN
ejpam-4260	153	20	of	of	ADP
ejpam-4260	153	21	supra	supra	PROPN
ejpam-4260	153	22	b	b	PROPN
ejpam-4260	153	23	-	-	PUNCT
ejpam-4260	153	24	open	open	ADJ
ejpam-4260	153	25	sets	set	NOUN
ejpam-4260	153	26	.	.	PUNCT
ejpam-4260	154	1	then	then	ADV
ejpam-4260	154	2	.	.	PUNCT
ejpam-4260	155	1	(	(	PUNCT
ejpam-4260	155	2	i	i	NOUN
ejpam-4260	155	3	)	)	PUNCT
ejpam-4260	155	4	(	(	PUNCT
ejpam-4260	155	5	ob′)b′	ob′)b′	PROPN
ejpam-4260	155	6	⊆	⊆	NUM
ejpam-4260	155	7	ob′.	ob′.	PROPN
ejpam-4260	155	8	(	(	PUNCT
ejpam-4260	155	9	ii	ii	NOUN
ejpam-4260	155	10	)	)	PUNCT
ejpam-4260	155	11	bcl(ob′	bcl(ob′	NOUN
ejpam-4260	155	12	)	)	PUNCT
ejpam-4260	155	13	=	=	SYM
ejpam-4260	155	14	ob′	ob′	NOUN
ejpam-4260	155	15	=	=	SYM
ejpam-4260	155	16	(	(	PUNCT
ejpam-4260	155	17	bcl(o))b′.	bcl(o))b′.	PROPN
ejpam-4260	155	18	(	(	PUNCT
ejpam-4260	155	19	iii	iii	NOUN
ejpam-4260	155	20	)	)	PUNCT
ejpam-4260	155	21	ob′	ob′	NOUN
ejpam-4260	155	22	=	=	NOUN
ejpam-4260	155	23	∅	∅	NOUN
ejpam-4260	155	24	if	if	SCONJ
ejpam-4260	155	25	o	o	NOUN
ejpam-4260	155	26	is	be	AUX
ejpam-4260	155	27	finite	finite	ADJ
ejpam-4260	155	28	.	.	PUNCT
ejpam-4260	156	1	a.	a.	PROPN
ejpam-4260	156	2	mhemdi	mhemdi	PROPN
ejpam-4260	156	3	et	et	PROPN
ejpam-4260	156	4	al	al	PROPN
ejpam-4260	156	5	.	.	PUNCT
ejpam-4260	156	6	/	/	SYM
ejpam-4260	156	7	eur	eur	PROPN
ejpam-4260	156	8	.	.	PUNCT
ejpam-4260	157	1	j.	j.	PROPN
ejpam-4260	157	2	pure	pure	PROPN
ejpam-4260	157	3	appl	appl	PROPN
ejpam-4260	157	4	.	.	PROPN
ejpam-4260	157	5	math	math	PROPN
ejpam-4260	157	6	,	,	PUNCT
ejpam-4260	157	7	15	15	NUM
ejpam-4260	157	8	(	(	PUNCT
ejpam-4260	157	9	1	1	NUM
ejpam-4260	157	10	)	)	PUNCT
ejpam-4260	157	11	(	(	PUNCT
ejpam-4260	157	12	2022	2022	NUM
ejpam-4260	157	13	)	)	PUNCT
ejpam-4260	157	14	,	,	PUNCT
ejpam-4260	157	15	15	15	NUM
ejpam-4260	157	16	-	-	SYM
ejpam-4260	157	17	29	29	NUM
ejpam-4260	157	18	20	20	NUM
ejpam-4260	157	19	proof	proof	NOUN
ejpam-4260	157	20	.	.	PUNCT
ejpam-4260	158	1	(	(	PUNCT
ejpam-4260	158	2	i	i	NOUN
ejpam-4260	158	3	)	)	PUNCT
ejpam-4260	158	4	consider	consider	VERB
ejpam-4260	158	5	ξ	ξ	SYM
ejpam-4260	158	6	̸∈	̸∈	PROPN
ejpam-4260	158	7	ob′.	ob′.	PROPN
ejpam-4260	158	8	then	then	ADV
ejpam-4260	158	9	,	,	PUNCT
ejpam-4260	158	10	θ	θ	PROPN
ejpam-4260	158	11	\	\	PROPN
ejpam-4260	158	12	{	{	PUNCT
ejpam-4260	158	13	ξ	ξ	NOUN
ejpam-4260	158	14	}	}	PUNCT
ejpam-4260	158	15	⋂	⋂	PROPN
ejpam-4260	158	16	o	o	NOUN
ejpam-4260	158	17	=	=	NOUN
ejpam-4260	158	18	∅	∅	NOUN
ejpam-4260	158	19	for	for	ADP
ejpam-4260	158	20	some	some	DET
ejpam-4260	158	21	supra	supra	PROPN
ejpam-4260	158	22	b	b	NOUN
ejpam-4260	158	23	-	-	PUNCT
ejpam-4260	158	24	open	open	ADJ
ejpam-4260	158	25	sets	set	VERB
ejpam-4260	158	26	θ	θ	NOUN
ejpam-4260	158	27	including	include	VERB
ejpam-4260	158	28	ξ	ξ	X
ejpam-4260	158	29	.	.	PUNCT
ejpam-4260	159	1	by	by	ADP
ejpam-4260	159	2	the	the	DET
ejpam-4260	159	3	difference	difference	NOUN
ejpam-4260	159	4	property	property	NOUN
ejpam-4260	159	5	for	for	ADP
ejpam-4260	159	6	the	the	DET
ejpam-4260	159	7	family	family	NOUN
ejpam-4260	159	8	of	of	ADP
ejpam-4260	159	9	supra	supra	PROPN
ejpam-4260	159	10	b	b	PROPN
ejpam-4260	159	11	-	-	PUNCT
ejpam-4260	159	12	open	open	ADJ
ejpam-4260	159	13	subsets	subset	NOUN
ejpam-4260	159	14	of	of	ADP
ejpam-4260	159	15	(	(	PUNCT
ejpam-4260	159	16	u	u	PROPN
ejpam-4260	159	17	,	,	PUNCT
ejpam-4260	159	18	ω	ω	PROPN
ejpam-4260	159	19	)	)	PUNCT
ejpam-4260	159	20	,	,	PUNCT
ejpam-4260	159	21	we	we	PRON
ejpam-4260	159	22	obtain	obtain	VERB
ejpam-4260	159	23	θ\{ξ	θ\{ξ	NOUN
ejpam-4260	159	24	}	}	PUNCT
ejpam-4260	159	25	is	be	AUX
ejpam-4260	159	26	a	a	DET
ejpam-4260	159	27	supra	supra	PROPN
ejpam-4260	159	28	b	b	NOUN
ejpam-4260	159	29	-	-	PUNCT
ejpam-4260	159	30	open	open	ADJ
ejpam-4260	159	31	set	set	NOUN
ejpam-4260	159	32	.	.	PUNCT
ejpam-4260	160	1	so	so	ADV
ejpam-4260	160	2	that	that	SCONJ
ejpam-4260	160	3	,	,	PUNCT
ejpam-4260	160	4	θ\{ξ	θ\{ξ	NUM
ejpam-4260	160	5	}	}	PUNCT
ejpam-4260	160	6	⋂	⋂	NUM
ejpam-4260	160	7	ob′	ob′	NOUN
ejpam-4260	160	8	=	=	PUNCT
ejpam-4260	160	9	∅.	∅.	VERB
ejpam-4260	160	10	now	now	ADV
ejpam-4260	160	11	,	,	PUNCT
ejpam-4260	160	12	θ	θ	PROPN
ejpam-4260	160	13	⋂	⋂	PROPN
ejpam-4260	160	14	(	(	PUNCT
ejpam-4260	160	15	ob′)b′	ob′)b′	X
ejpam-4260	160	16	=	=	PUNCT
ejpam-4260	160	17	∅	∅	NOUN
ejpam-4260	160	18	because	because	SCONJ
ejpam-4260	160	19	ξ	ξ	PROPN
ejpam-4260	160	20	̸∈	̸∈	PROPN
ejpam-4260	160	21	ob′.	ob′.	PROPN
ejpam-4260	160	22	therefore	therefore	ADV
ejpam-4260	160	23	,	,	PUNCT
ejpam-4260	160	24	ξ	ξ	PROPN
ejpam-4260	160	25	̸∈	̸∈	PROPN
ejpam-4260	160	26	(	(	PUNCT
ejpam-4260	160	27	ob′)b′.	ob′)b′.	X
ejpam-4260	160	28	hence	hence	ADV
ejpam-4260	160	29	,	,	PUNCT
ejpam-4260	160	30	(	(	PUNCT
ejpam-4260	160	31	ob′)b′	ob′)b′	NOUN
ejpam-4260	160	32	⊆	⊆	NUM
ejpam-4260	160	33	ob′.	ob′.	PROPN
ejpam-4260	160	34	(	(	PUNCT
ejpam-4260	160	35	ii	ii	NOUN
ejpam-4260	160	36	)	)	PUNCT
ejpam-4260	160	37	since	since	SCONJ
ejpam-4260	160	38	(	(	PUNCT
ejpam-4260	160	39	ob′)b′	ob′)b′	PROPN
ejpam-4260	160	40	⊆	⊆	NUM
ejpam-4260	160	41	ob′	ob′	NOUN
ejpam-4260	160	42	,	,	PUNCT
ejpam-4260	160	43	it	it	PRON
ejpam-4260	160	44	comes	come	VERB
ejpam-4260	160	45	from	from	ADP
ejpam-4260	160	46	theorem	theorem	ADJ
ejpam-4260	160	47	(	(	PUNCT
ejpam-4260	160	48	1	1	NUM
ejpam-4260	160	49	)	)	PUNCT
ejpam-4260	160	50	that	that	PRON
ejpam-4260	160	51	ob′	ob′	NOUN
ejpam-4260	160	52	is	be	AUX
ejpam-4260	160	53	supra	supra	ADJ
ejpam-4260	160	54	b	b	NOUN
ejpam-4260	160	55	-	-	PUNCT
ejpam-4260	160	56	closed	closed	ADJ
ejpam-4260	160	57	.	.	PUNCT
ejpam-4260	161	1	thus	thus	ADV
ejpam-4260	161	2	,	,	PUNCT
ejpam-4260	161	3	bcl(ob′	bcl(ob′	NOUN
ejpam-4260	161	4	)	)	PUNCT
ejpam-4260	161	5	=	=	SYM
ejpam-4260	162	1	ob′	ob′	X
ejpam-4260	162	2	(	(	PUNCT
ejpam-4260	162	3	3	3	NUM
ejpam-4260	162	4	)	)	PUNCT
ejpam-4260	162	5	also	also	ADV
ejpam-4260	162	6	,	,	PUNCT
ejpam-4260	162	7	(	(	PUNCT
ejpam-4260	162	8	o)b′	o)b′	PROPN
ejpam-4260	162	9	⊆	⊆	NUM
ejpam-4260	162	10	(	(	PUNCT
ejpam-4260	162	11	bcl(o))b′	bcl(o))b′	VERB
ejpam-4260	162	12	because	because	SCONJ
ejpam-4260	162	13	o	o	PROPN
ejpam-4260	162	14	⊆	⊆	NUM
ejpam-4260	162	15	bcl(o	bcl(o	PROPN
ejpam-4260	162	16	)	)	PUNCT
ejpam-4260	162	17	.	.	PUNCT
ejpam-4260	163	1	conversely	conversely	ADV
ejpam-4260	163	2	,	,	PUNCT
ejpam-4260	163	3	let	let	VERB
ejpam-4260	163	4	ξ	ξ	PROPN
ejpam-4260	163	5	̸∈	̸∈	PROPN
ejpam-4260	163	6	(	(	PUNCT
ejpam-4260	163	7	o)b′.	o)b′.	CCONJ
ejpam-4260	163	8	then	then	ADV
ejpam-4260	163	9	,	,	PUNCT
ejpam-4260	163	10	it	it	PRON
ejpam-4260	163	11	comes	come	VERB
ejpam-4260	163	12	from	from	ADP
ejpam-4260	163	13	1	1	NUM
ejpam-4260	163	14	above	above	ADP
ejpam-4260	163	15	that	that	PRON
ejpam-4260	164	1	θ	θ	X
ejpam-4260	164	2	\	\	PROPN
ejpam-4260	164	3	{	{	PUNCT
ejpam-4260	164	4	ξ	ξ	NOUN
ejpam-4260	164	5	}	}	PUNCT
ejpam-4260	164	6	⋂	⋂	PROPN
ejpam-4260	164	7	o	o	NOUN
ejpam-4260	164	8	=	=	NOUN
ejpam-4260	164	9	∅	∅	NOUN
ejpam-4260	164	10	and	and	CCONJ
ejpam-4260	164	11	θ	θ	NOUN
ejpam-4260	164	12	\	\	X
ejpam-4260	164	13	{	{	PUNCT
ejpam-4260	164	14	ξ	ξ	NOUN
ejpam-4260	164	15	}	}	PUNCT
ejpam-4260	164	16	⋂	⋂	PROPN
ejpam-4260	164	17	ob′	ob′	NOUN
ejpam-4260	164	18	=	=	PUNCT
ejpam-4260	164	19	∅.	∅.	NOUN
ejpam-4260	164	20	this	this	PRON
ejpam-4260	164	21	means	mean	VERB
ejpam-4260	164	22	that	that	SCONJ
ejpam-4260	164	23	θ	θ	PRON
ejpam-4260	164	24	\	\	X
ejpam-4260	164	25	{	{	PUNCT
ejpam-4260	164	26	ξ	ξ	NOUN
ejpam-4260	164	27	}	}	PUNCT
ejpam-4260	164	28	⋂	⋂	PROPN
ejpam-4260	164	29	bcl(o	bcl(o	PROPN
ejpam-4260	164	30	)	)	PUNCT
ejpam-4260	164	31	=	=	PUNCT
ejpam-4260	164	32	∅.	∅.	VERB
ejpam-4260	164	33	therefore	therefore	ADV
ejpam-4260	164	34	,	,	PUNCT
ejpam-4260	164	35	ξ	ξ	PROPN
ejpam-4260	164	36	̸∈	̸∈	PROPN
ejpam-4260	164	37	(	(	PUNCT
ejpam-4260	164	38	bcl(o))b′.	bcl(o))b′.	PROPN
ejpam-4260	164	39	thus	thus	ADV
ejpam-4260	164	40	,	,	PUNCT
ejpam-4260	164	41	(	(	PUNCT
ejpam-4260	164	42	bcl(o))b′	bcl(o))b′	PROPN
ejpam-4260	164	43	⊆	⊆	NUM
ejpam-4260	164	44	(	(	PUNCT
ejpam-4260	164	45	o)b′.	o)b′.	ADV
ejpam-4260	164	46	hence	hence	ADV
ejpam-4260	164	47	(	(	PUNCT
ejpam-4260	164	48	bcl(o))b′	bcl(o))b′	PROPN
ejpam-4260	164	49	=	=	PUNCT
ejpam-4260	164	50	(	(	PUNCT
ejpam-4260	164	51	o)b′	o)b′	PROPN
ejpam-4260	164	52	(	(	PUNCT
ejpam-4260	164	53	4	4	NUM
ejpam-4260	164	54	)	)	PUNCT
ejpam-4260	164	55	equalities	equality	NOUN
ejpam-4260	164	56	(	(	PUNCT
ejpam-4260	164	57	3	3	NUM
ejpam-4260	164	58	)	)	PUNCT
ejpam-4260	164	59	and	and	CCONJ
ejpam-4260	164	60	(	(	PUNCT
ejpam-4260	164	61	4	4	X
ejpam-4260	164	62	)	)	PUNCT
ejpam-4260	164	63	end	end	VERB
ejpam-4260	164	64	the	the	DET
ejpam-4260	164	65	proof	proof	NOUN
ejpam-4260	164	66	.	.	PUNCT
ejpam-4260	165	1	(	(	PUNCT
ejpam-4260	165	2	iii	iii	X
ejpam-4260	165	3	)	)	PUNCT
ejpam-4260	165	4	consider	consider	VERB
ejpam-4260	165	5	o	o	NOUN
ejpam-4260	165	6	is	be	AUX
ejpam-4260	165	7	a	a	DET
ejpam-4260	165	8	finite	finite	NOUN
ejpam-4260	165	9	subset	subset	NOUN
ejpam-4260	165	10	of	of	ADP
ejpam-4260	165	11	u	u	PROPN
ejpam-4260	165	12	.	.	PUNCT
ejpam-4260	165	13	suppose	suppose	VERB
ejpam-4260	165	14	that	that	SCONJ
ejpam-4260	165	15	ξ	ξ	PROPN
ejpam-4260	165	16	∈	∈	PROPN
ejpam-4260	165	17	u	u	NOUN
ejpam-4260	165	18	such	such	ADJ
ejpam-4260	165	19	that	that	SCONJ
ejpam-4260	165	20	ξ	ξ	PROPN
ejpam-4260	165	21	∈	∈	PROPN
ejpam-4260	165	22	ob′.	ob′.	NOUN
ejpam-4260	165	23	then	then	ADV
ejpam-4260	165	24	,	,	PUNCT
ejpam-4260	165	25	θ\{ξ	θ\{ξ	NUM
ejpam-4260	165	26	}	}	PUNCT
ejpam-4260	165	27	⋂	⋂	PROPN
ejpam-4260	165	28	o	o	NOUN
ejpam-4260	165	29	̸=	̸=	PROPN
ejpam-4260	165	30	∅	∅	NOUN
ejpam-4260	165	31	for	for	ADP
ejpam-4260	165	32	every	every	DET
ejpam-4260	165	33	supra	supra	PROPN
ejpam-4260	165	34	b	b	PROPN
ejpam-4260	165	35	-	-	PUNCT
ejpam-4260	165	36	open	open	ADJ
ejpam-4260	165	37	set	set	ADJ
ejpam-4260	165	38	θ	θ	PROPN
ejpam-4260	165	39	including	include	VERB
ejpam-4260	165	40	ξ	ξ	X
ejpam-4260	165	41	.	.	PUNCT
ejpam-4260	166	1	now	now	ADV
ejpam-4260	166	2	,	,	PUNCT
ejpam-4260	166	3	for	for	ADP
ejpam-4260	166	4	every	every	DET
ejpam-4260	166	5	ζ	ζ	PROPN
ejpam-4260	166	6	∈	∈	NOUN
ejpam-4260	166	7	o	o	NOUN
ejpam-4260	166	8	such	such	ADJ
ejpam-4260	166	9	that	that	SCONJ
ejpam-4260	166	10	ζ	ζ	PROPN
ejpam-4260	166	11	̸=	̸=	PROPN
ejpam-4260	166	12	ξ	ξ	NUM
ejpam-4260	166	13	,	,	PUNCT
ejpam-4260	166	14	we	we	PRON
ejpam-4260	166	15	have	have	VERB
ejpam-4260	166	16	θ	θ	X
ejpam-4260	166	17	\	\	X
ejpam-4260	166	18	{	{	PUNCT
ejpam-4260	166	19	ξ	ξ	PROPN
ejpam-4260	166	20	,	,	PUNCT
ejpam-4260	166	21	ζ	ζ	NOUN
ejpam-4260	166	22	}	}	PUNCT
ejpam-4260	166	23	is	be	AUX
ejpam-4260	166	24	a	a	DET
ejpam-4260	166	25	supra	supra	PROPN
ejpam-4260	166	26	b	b	NOUN
ejpam-4260	166	27	-	-	PUNCT
ejpam-4260	166	28	open	open	ADJ
ejpam-4260	166	29	set	set	NOUN
ejpam-4260	166	30	.	.	PUNCT
ejpam-4260	167	1	thus	thus	ADV
ejpam-4260	167	2	,	,	PUNCT
ejpam-4260	167	3	θ	θ	X
ejpam-4260	167	4	\	\	PUNCT
ejpam-4260	168	1	[	[	X
ejpam-4260	168	2	o	o	X
ejpam-4260	168	3	⋃	⋃	ADP
ejpam-4260	168	4	{	{	PUNCT
ejpam-4260	168	5	ξ	ξ	NOUN
ejpam-4260	168	6	}	}	PUNCT
ejpam-4260	168	7	]	]	PUNCT
ejpam-4260	168	8	is	be	AUX
ejpam-4260	168	9	a	a	DET
ejpam-4260	168	10	supra	supra	PROPN
ejpam-4260	168	11	b	b	NOUN
ejpam-4260	168	12	-	-	PUNCT
ejpam-4260	168	13	open	open	ADJ
ejpam-4260	168	14	set	set	NOUN
ejpam-4260	168	15	such	such	ADJ
ejpam-4260	168	16	that	that	SCONJ
ejpam-4260	168	17	θ	θ	X
ejpam-4260	168	18	\	\	PUNCT
ejpam-4260	169	1	[	[	X
ejpam-4260	169	2	o	o	X
ejpam-4260	169	3	⋃	⋃	ADP
ejpam-4260	169	4	{	{	PUNCT
ejpam-4260	169	5	ξ	ξ	NOUN
ejpam-4260	169	6	}	}	PUNCT
ejpam-4260	169	7	]	]	PUNCT
ejpam-4260	169	8	⋂	⋂	PROPN
ejpam-4260	169	9	o	o	X
ejpam-4260	169	10	=	=	PUNCT
ejpam-4260	169	11	∅.	∅.	PRON
ejpam-4260	169	12	this	this	PRON
ejpam-4260	169	13	implies	imply	VERB
ejpam-4260	169	14	that	that	SCONJ
ejpam-4260	169	15	ξ	ξ	PROPN
ejpam-4260	169	16	̸∈	̸∈	PROPN
ejpam-4260	169	17	ob′.	ob′.	PROPN
ejpam-4260	169	18	but	but	CCONJ
ejpam-4260	169	19	this	this	PRON
ejpam-4260	169	20	is	be	AUX
ejpam-4260	169	21	a	a	DET
ejpam-4260	169	22	contradiction	contradiction	NOUN
ejpam-4260	169	23	.	.	PUNCT
ejpam-4260	170	1	hence	hence	ADV
ejpam-4260	170	2	,	,	PUNCT
ejpam-4260	170	3	ob′	ob′	NOUN
ejpam-4260	170	4	=	=	X
ejpam-4260	170	5	∅.	∅.	NOUN
ejpam-4260	170	6	to	to	PART
ejpam-4260	170	7	show	show	VERB
ejpam-4260	170	8	that	that	SCONJ
ejpam-4260	170	9	the	the	DET
ejpam-4260	170	10	converse	converse	NOUN
ejpam-4260	170	11	of	of	ADP
ejpam-4260	170	12	theorem	theorem	NOUN
ejpam-4260	170	13	3	3	NUM
ejpam-4260	170	14	is	be	AUX
ejpam-4260	170	15	not	not	PART
ejpam-4260	170	16	true	true	ADJ
ejpam-4260	170	17	if	if	SCONJ
ejpam-4260	170	18	(	(	PUNCT
ejpam-4260	170	19	u	u	NOUN
ejpam-4260	170	20	,	,	PUNCT
ejpam-4260	170	21	ω	ω	PROPN
ejpam-4260	170	22	)	)	PUNCT
ejpam-4260	170	23	does	do	AUX
ejpam-4260	170	24	not	not	PART
ejpam-4260	170	25	have	have	VERB
ejpam-4260	170	26	the	the	DET
ejpam-4260	170	27	difference	difference	NOUN
ejpam-4260	170	28	property	property	NOUN
ejpam-4260	170	29	for	for	ADP
ejpam-4260	170	30	the	the	DET
ejpam-4260	170	31	family	family	NOUN
ejpam-4260	170	32	of	of	ADP
ejpam-4260	170	33	supra	supra	PROPN
ejpam-4260	170	34	b	b	PROPN
ejpam-4260	170	35	-	-	PUNCT
ejpam-4260	170	36	open	open	ADJ
ejpam-4260	170	37	sets	set	NOUN
ejpam-4260	170	38	,	,	PUNCT
ejpam-4260	170	39	consider	consider	VERB
ejpam-4260	170	40	o	o	NOUN
ejpam-4260	170	41	=	=	PUNCT
ejpam-4260	170	42	{	{	PUNCT
ejpam-4260	170	43	2	2	NUM
ejpam-4260	170	44	,	,	PUNCT
ejpam-4260	170	45	4	4	NUM
ejpam-4260	170	46	,	,	PUNCT
ejpam-4260	170	47	5	5	NUM
ejpam-4260	170	48	}	}	PUNCT
ejpam-4260	170	49	as	as	ADP
ejpam-4260	170	50	a	a	DET
ejpam-4260	170	51	subset	subset	NOUN
ejpam-4260	170	52	of	of	ADP
ejpam-4260	170	53	sts	st	NOUN
ejpam-4260	170	54	furnished	furnish	VERB
ejpam-4260	170	55	in	in	ADP
ejpam-4260	170	56	example	example	NOUN
ejpam-4260	170	57	(	(	PUNCT
ejpam-4260	170	58	3	3	NUM
ejpam-4260	170	59	)	)	PUNCT
ejpam-4260	170	60	.	.	PUNCT
ejpam-4260	171	1	note	note	VERB
ejpam-4260	171	2	that	that	SCONJ
ejpam-4260	171	3	the	the	DET
ejpam-4260	171	4	families	family	NOUN
ejpam-4260	171	5	of	of	ADP
ejpam-4260	171	6	supra	supra	PROPN
ejpam-4260	171	7	open	open	ADJ
ejpam-4260	171	8	and	and	CCONJ
ejpam-4260	171	9	supra	supra	ADJ
ejpam-4260	171	10	b	b	NOUN
ejpam-4260	171	11	-	-	PUNCT
ejpam-4260	171	12	open	open	ADJ
ejpam-4260	171	13	sets	set	NOUN
ejpam-4260	171	14	are	be	AUX
ejpam-4260	171	15	identical	identical	ADJ
ejpam-4260	171	16	.	.	PUNCT
ejpam-4260	172	1	so	so	ADV
ejpam-4260	172	2	that	that	SCONJ
ejpam-4260	172	3	,	,	PUNCT
ejpam-4260	172	4	we	we	PRON
ejpam-4260	172	5	obtain	obtain	VERB
ejpam-4260	172	6	ob′	ob′	NOUN
ejpam-4260	172	7	=	=	SYM
ejpam-4260	172	8	n	n	DET
ejpam-4260	172	9	\{2	\{2	NOUN
ejpam-4260	172	10	,	,	PUNCT
ejpam-4260	172	11	4	4	NUM
ejpam-4260	172	12	}	}	PUNCT
ejpam-4260	172	13	,	,	PUNCT
ejpam-4260	172	14	(	(	PUNCT
ejpam-4260	172	15	ob′)b′	ob′)b′	X
ejpam-4260	172	16	=	=	SYM
ejpam-4260	172	17	n	n	PROPN
ejpam-4260	172	18	\{1	\{1	NUM
ejpam-4260	172	19	,	,	PUNCT
ejpam-4260	172	20	3	3	NUM
ejpam-4260	172	21	}	}	PUNCT
ejpam-4260	172	22	and	and	CCONJ
ejpam-4260	172	23	cl(ob′	cl(ob′	NOUN
ejpam-4260	172	24	)	)	PUNCT
ejpam-4260	172	25	=	=	SYM
ejpam-4260	172	26	n	n	NOUN
ejpam-4260	172	27	,	,	PUNCT
ejpam-4260	172	28	which	which	PRON
ejpam-4260	172	29	means	mean	VERB
ejpam-4260	172	30	that	that	SCONJ
ejpam-4260	172	31	(	(	PUNCT
ejpam-4260	172	32	i	i	NOUN
ejpam-4260	172	33	)	)	PUNCT
ejpam-4260	172	34	(	(	PUNCT
ejpam-4260	173	1	ob′)b′	ob′)b′	X
ejpam-4260	173	2	̸⊆	̸⊆	NOUN
ejpam-4260	173	3	ob′.	ob′.	PROPN
ejpam-4260	173	4	(	(	PUNCT
ejpam-4260	173	5	ii	ii	NOUN
ejpam-4260	173	6	)	)	PUNCT
ejpam-4260	173	7	bcl(ob′	bcl(ob′	NOUN
ejpam-4260	173	8	)	)	PUNCT
ejpam-4260	173	9	̸=	̸=	PROPN
ejpam-4260	173	10	ob′.	ob′.	PROPN
ejpam-4260	173	11	(	(	PUNCT
ejpam-4260	173	12	iii	iii	NOUN
ejpam-4260	173	13	)	)	PUNCT
ejpam-4260	173	14	ob′	ob′	NOUN
ejpam-4260	173	15	̸=	̸=	PROPN
ejpam-4260	173	16	∅	∅	NOUN
ejpam-4260	173	17	in	in	ADP
ejpam-4260	173	18	spite	spite	NOUN
ejpam-4260	173	19	of	of	ADP
ejpam-4260	173	20	o	o	PROPN
ejpam-4260	173	21	is	be	AUX
ejpam-4260	173	22	finite	finite	ADJ
ejpam-4260	173	23	.	.	PUNCT
ejpam-4260	174	1	4	4	X
ejpam-4260	174	2	.	.	X
ejpam-4260	174	3	supra	supra	PROPN
ejpam-4260	174	4	b	b	PROPN
ejpam-4260	174	5	separation	separation	NOUN
ejpam-4260	174	6	axioms	axiom	VERB
ejpam-4260	174	7	in	in	ADP
ejpam-4260	174	8	this	this	DET
ejpam-4260	174	9	section	section	NOUN
ejpam-4260	174	10	,	,	PUNCT
ejpam-4260	174	11	we	we	PRON
ejpam-4260	174	12	familiarize	familiarize	VERB
ejpam-4260	174	13	the	the	DET
ejpam-4260	174	14	concepts	concept	NOUN
ejpam-4260	174	15	of	of	ADP
ejpam-4260	174	16	regularity	regularity	NOUN
ejpam-4260	174	17	,	,	PUNCT
ejpam-4260	174	18	normality	normality	NOUN
ejpam-4260	174	19	and	and	CCONJ
ejpam-4260	174	20	tk	tk	NOUN
ejpam-4260	174	21	-	-	PUNCT
ejpam-4260	174	22	spaces	space	NOUN
ejpam-4260	174	23	using	use	VERB
ejpam-4260	174	24	supra	supra	PROPN
ejpam-4260	174	25	b	b	PROPN
ejpam-4260	174	26	-	-	PUNCT
ejpam-4260	174	27	open	open	ADJ
ejpam-4260	174	28	sets	set	NOUN
ejpam-4260	174	29	.	.	PUNCT
ejpam-4260	175	1	we	we	PRON
ejpam-4260	175	2	give	give	VERB
ejpam-4260	175	3	them	they	PRON
ejpam-4260	175	4	some	some	DET
ejpam-4260	175	5	descriptions	description	NOUN
ejpam-4260	175	6	and	and	CCONJ
ejpam-4260	175	7	reveal	reveal	VERB
ejpam-4260	175	8	the	the	DET
ejpam-4260	175	9	interrelations	interrelation	NOUN
ejpam-4260	175	10	between	between	ADP
ejpam-4260	175	11	them	they	PRON
ejpam-4260	175	12	with	with	ADP
ejpam-4260	175	13	the	the	DET
ejpam-4260	175	14	assistant	assistant	NOUN
ejpam-4260	175	15	of	of	ADP
ejpam-4260	175	16	examples	example	NOUN
ejpam-4260	175	17	and	and	CCONJ
ejpam-4260	175	18	counterexamples	counterexample	NOUN
ejpam-4260	175	19	.	.	PUNCT
ejpam-4260	176	1	definition	definition	NOUN
ejpam-4260	176	2	12	12	NUM
ejpam-4260	176	3	.	.	PUNCT
ejpam-4260	177	1	an	an	DET
ejpam-4260	177	2	sts	st	NOUN
ejpam-4260	177	3	(	(	PUNCT
ejpam-4260	177	4	u	u	NOUN
ejpam-4260	177	5	,	,	PUNCT
ejpam-4260	177	6	ω	ω	PROPN
ejpam-4260	177	7	)	)	PUNCT
ejpam-4260	177	8	is	be	AUX
ejpam-4260	177	9	said	say	VERB
ejpam-4260	177	10	to	to	PART
ejpam-4260	177	11	be	be	AUX
ejpam-4260	177	12	:	:	PUNCT
ejpam-4260	177	13	(	(	PUNCT
ejpam-4260	177	14	i	i	NOUN
ejpam-4260	177	15	)	)	PUNCT
ejpam-4260	177	16	sbt0	sbt0	PROPN
ejpam-4260	177	17	if	if	SCONJ
ejpam-4260	177	18	for	for	ADP
ejpam-4260	177	19	every	every	DET
ejpam-4260	177	20	ξ	ξ	PROPN
ejpam-4260	177	21	̸=	̸=	PROPN
ejpam-4260	177	22	ζ	ζ	NOUN
ejpam-4260	177	23	∈	∈	PROPN
ejpam-4260	177	24	u	u	NOUN
ejpam-4260	177	25	,	,	PUNCT
ejpam-4260	177	26	there	there	PRON
ejpam-4260	177	27	is	be	VERB
ejpam-4260	177	28	a	a	DET
ejpam-4260	177	29	supra	supra	PROPN
ejpam-4260	177	30	b	b	NOUN
ejpam-4260	177	31	-	-	PUNCT
ejpam-4260	177	32	open	open	ADJ
ejpam-4260	177	33	set	set	NOUN
ejpam-4260	177	34	o	o	NOUN
ejpam-4260	177	35	such	such	ADJ
ejpam-4260	177	36	that	that	SCONJ
ejpam-4260	177	37	ξ	ξ	PROPN
ejpam-4260	177	38	∈	∈	NOUN
ejpam-4260	177	39	o	o	NOUN
ejpam-4260	177	40	or	or	CCONJ
ejpam-4260	177	41	ζ	ζ	NOUN
ejpam-4260	177	42	∈	∈	PROPN
ejpam-4260	177	43	o.	o.	NOUN
ejpam-4260	177	44	a.	a.	PROPN
ejpam-4260	177	45	mhemdi	mhemdi	PROPN
ejpam-4260	177	46	et	et	PROPN
ejpam-4260	177	47	al	al	PROPN
ejpam-4260	177	48	.	.	PUNCT
ejpam-4260	177	49	/	/	SYM
ejpam-4260	177	50	eur	eur	PROPN
ejpam-4260	177	51	.	.	PUNCT
ejpam-4260	178	1	j.	j.	PROPN
ejpam-4260	178	2	pure	pure	PROPN
ejpam-4260	178	3	appl	appl	PROPN
ejpam-4260	178	4	.	.	PROPN
ejpam-4260	178	5	math	math	PROPN
ejpam-4260	178	6	,	,	PUNCT
ejpam-4260	178	7	15	15	NUM
ejpam-4260	178	8	(	(	PUNCT
ejpam-4260	178	9	1	1	NUM
ejpam-4260	178	10	)	)	PUNCT
ejpam-4260	178	11	(	(	PUNCT
ejpam-4260	178	12	2022	2022	NUM
ejpam-4260	178	13	)	)	PUNCT
ejpam-4260	178	14	,	,	PUNCT
ejpam-4260	178	15	15	15	NUM
ejpam-4260	178	16	-	-	SYM
ejpam-4260	178	17	29	29	NUM
ejpam-4260	178	18	21	21	NUM
ejpam-4260	178	19	(	(	PUNCT
ejpam-4260	178	20	ii	ii	NOUN
ejpam-4260	178	21	)	)	PUNCT
ejpam-4260	178	22	sbt1	sbt1	NOUN
ejpam-4260	178	23	if	if	SCONJ
ejpam-4260	178	24	for	for	ADP
ejpam-4260	178	25	every	every	DET
ejpam-4260	178	26	ξ	ξ	PROPN
ejpam-4260	178	27	̸=	̸=	PROPN
ejpam-4260	178	28	ζ	ζ	NOUN
ejpam-4260	178	29	∈	∈	PROPN
ejpam-4260	178	30	u	u	NOUN
ejpam-4260	178	31	,	,	PUNCT
ejpam-4260	178	32	there	there	PRON
ejpam-4260	178	33	are	be	VERB
ejpam-4260	178	34	supra	supra	ADJ
ejpam-4260	178	35	b	b	NOUN
ejpam-4260	178	36	-	-	PUNCT
ejpam-4260	178	37	open	open	ADJ
ejpam-4260	178	38	sets	set	NOUN
ejpam-4260	178	39	o	o	PROPN
ejpam-4260	178	40	,	,	PUNCT
ejpam-4260	178	41	θ	θ	PROPN
ejpam-4260	178	42	such	such	ADJ
ejpam-4260	178	43	that	that	SCONJ
ejpam-4260	178	44	ξ	ξ	PROPN
ejpam-4260	178	45	∈	∈	PROPN
ejpam-4260	178	46	o	o	NOUN
ejpam-4260	178	47	\	\	PROPN
ejpam-4260	178	48	θ	θ	PROPN
ejpam-4260	178	49	and	and	CCONJ
ejpam-4260	178	50	ζ	ζ	NOUN
ejpam-4260	178	51	∈	∈	NOUN
ejpam-4260	178	52	θ	θ	NOUN
ejpam-4260	178	53	\o	\o	PROPN
ejpam-4260	178	54	.	.	PUNCT
ejpam-4260	179	1	(	(	PUNCT
ejpam-4260	179	2	iii	iii	X
ejpam-4260	179	3	)	)	PUNCT
ejpam-4260	179	4	sbt2	sbt2	NOUN
ejpam-4260	179	5	(	(	PUNCT
ejpam-4260	179	6	or	or	CCONJ
ejpam-4260	179	7	,	,	PUNCT
ejpam-4260	179	8	supra	supra	PROPN
ejpam-4260	179	9	b	b	PROPN
ejpam-4260	179	10	hausdorff	hausdorff	PROPN
ejpam-4260	179	11	)	)	PUNCT
ejpam-4260	179	12	if	if	SCONJ
ejpam-4260	179	13	for	for	ADP
ejpam-4260	179	14	every	every	DET
ejpam-4260	179	15	ξ	ξ	PROPN
ejpam-4260	179	16	̸=	̸=	PROPN
ejpam-4260	179	17	ζ	ζ	NOUN
ejpam-4260	179	18	∈	∈	PROPN
ejpam-4260	179	19	u	u	NOUN
ejpam-4260	179	20	,	,	PUNCT
ejpam-4260	179	21	there	there	PRON
ejpam-4260	179	22	are	be	VERB
ejpam-4260	179	23	disjoint	disjoint	ADJ
ejpam-4260	179	24	supra	supra	PROPN
ejpam-4260	179	25	b	b	NOUN
ejpam-4260	179	26	-	-	PUNCT
ejpam-4260	179	27	open	open	ADJ
ejpam-4260	179	28	sets	set	NOUN
ejpam-4260	179	29	o	o	PROPN
ejpam-4260	179	30	,	,	PUNCT
ejpam-4260	179	31	θ	θ	PROPN
ejpam-4260	179	32	such	such	ADJ
ejpam-4260	179	33	that	that	SCONJ
ejpam-4260	179	34	ξ	ξ	PROPN
ejpam-4260	179	35	∈	∈	PROPN
ejpam-4260	179	36	o	o	NOUN
ejpam-4260	179	37	and	and	CCONJ
ejpam-4260	179	38	ζ	ζ	NOUN
ejpam-4260	179	39	∈	∈	PROPN
ejpam-4260	179	40	θ	θ	PROPN
ejpam-4260	179	41	.	.	PUNCT
ejpam-4260	179	42	(	(	PUNCT
ejpam-4260	179	43	iv	iv	X
ejpam-4260	179	44	)	)	PUNCT
ejpam-4260	179	45	supra	supra	PROPN
ejpam-4260	179	46	b	b	PROPN
ejpam-4260	179	47	regular	regular	ADJ
ejpam-4260	179	48	if	if	SCONJ
ejpam-4260	179	49	for	for	ADP
ejpam-4260	179	50	every	every	DET
ejpam-4260	179	51	supra	supra	PROPN
ejpam-4260	179	52	b	b	PROPN
ejpam-4260	179	53	-	-	PUNCT
ejpam-4260	179	54	closed	closed	ADJ
ejpam-4260	179	55	set	set	VERB
ejpam-4260	179	56	f	f	PROPN
ejpam-4260	179	57	and	and	CCONJ
ejpam-4260	179	58	each	each	DET
ejpam-4260	179	59	ξ	ξ	PROPN
ejpam-4260	179	60	̸∈	̸∈	PROPN
ejpam-4260	179	61	f	f	PROPN
ejpam-4260	179	62	,	,	PUNCT
ejpam-4260	179	63	there	there	PRON
ejpam-4260	179	64	are	be	VERB
ejpam-4260	179	65	disjoint	disjoint	ADJ
ejpam-4260	179	66	supra	supra	PROPN
ejpam-4260	179	67	b	b	NOUN
ejpam-4260	179	68	-	-	PUNCT
ejpam-4260	179	69	open	open	ADJ
ejpam-4260	179	70	sets	set	NOUN
ejpam-4260	179	71	o	o	PROPN
ejpam-4260	179	72	,	,	PUNCT
ejpam-4260	179	73	θ	θ	PROPN
ejpam-4260	180	1	such	such	ADJ
ejpam-4260	180	2	that	that	SCONJ
ejpam-4260	180	3	ξ	ξ	PROPN
ejpam-4260	180	4	∈	∈	PROPN
ejpam-4260	180	5	o	o	NOUN
ejpam-4260	180	6	and	and	CCONJ
ejpam-4260	180	7	f	f	PROPN
ejpam-4260	181	1	⊆	⊆	NUM
ejpam-4260	181	2	θ	θ	PROPN
ejpam-4260	181	3	.	.	PUNCT
ejpam-4260	181	4	(	(	PUNCT
ejpam-4260	181	5	v	v	NOUN
ejpam-4260	181	6	)	)	PUNCT
ejpam-4260	181	7	supra	supra	PROPN
ejpam-4260	181	8	b	b	PROPN
ejpam-4260	181	9	normal	normal	ADJ
ejpam-4260	181	10	if	if	SCONJ
ejpam-4260	181	11	for	for	ADP
ejpam-4260	181	12	every	every	DET
ejpam-4260	181	13	two	two	NUM
ejpam-4260	181	14	disjoint	disjoint	ADJ
ejpam-4260	181	15	supra	supra	PROPN
ejpam-4260	181	16	b	b	PROPN
ejpam-4260	181	17	-	-	PUNCT
ejpam-4260	181	18	closed	closed	ADJ
ejpam-4260	181	19	sets	set	NOUN
ejpam-4260	181	20	are	be	AUX
ejpam-4260	181	21	separated	separate	VERB
ejpam-4260	181	22	by	by	ADP
ejpam-4260	181	23	two	two	NUM
ejpam-4260	181	24	disjoint	disjoint	ADJ
ejpam-4260	181	25	supra	supra	PROPN
ejpam-4260	181	26	b	b	NOUN
ejpam-4260	181	27	-	-	PUNCT
ejpam-4260	181	28	open	open	ADJ
ejpam-4260	181	29	sets	set	NOUN
ejpam-4260	181	30	.	.	PUNCT
ejpam-4260	182	1	(	(	PUNCT
ejpam-4260	182	2	vi	vi	NOUN
ejpam-4260	182	3	)	)	PUNCT
ejpam-4260	182	4	sbt3	sbt3	NOUN
ejpam-4260	182	5	(	(	PUNCT
ejpam-4260	182	6	respectively	respectively	ADV
ejpam-4260	182	7	,	,	PUNCT
ejpam-4260	182	8	sbt4	sbt4	PROPN
ejpam-4260	182	9	)	)	PUNCT
ejpam-4260	182	10	if	if	SCONJ
ejpam-4260	182	11	it	it	PRON
ejpam-4260	182	12	is	be	AUX
ejpam-4260	182	13	supra	supra	PROPN
ejpam-4260	182	14	b	b	PROPN
ejpam-4260	182	15	regular	regular	ADJ
ejpam-4260	182	16	(	(	PUNCT
ejpam-4260	182	17	respectively	respectively	ADV
ejpam-4260	182	18	,	,	PUNCT
ejpam-4260	182	19	supra	supra	PROPN
ejpam-4260	182	20	b	b	PROPN
ejpam-4260	182	21	normal	normal	ADJ
ejpam-4260	182	22	)	)	PUNCT
ejpam-4260	182	23	and	and	CCONJ
ejpam-4260	182	24	sbt1	sbt1	PROPN
ejpam-4260	182	25	.	.	PUNCT
ejpam-4260	183	1	theorem	theorem	VERB
ejpam-4260	183	2	4	4	NUM
ejpam-4260	183	3	.	.	PUNCT
ejpam-4260	184	1	the	the	DET
ejpam-4260	184	2	next	next	ADJ
ejpam-4260	184	3	three	three	NUM
ejpam-4260	184	4	properties	property	NOUN
ejpam-4260	184	5	are	be	AUX
ejpam-4260	184	6	identical	identical	ADJ
ejpam-4260	184	7	.	.	PUNCT
ejpam-4260	185	1	(	(	PUNCT
ejpam-4260	185	2	i	i	NOUN
ejpam-4260	185	3	)	)	PUNCT
ejpam-4260	185	4	(	(	PUNCT
ejpam-4260	185	5	u	u	NOUN
ejpam-4260	185	6	,	,	PUNCT
ejpam-4260	185	7	ω	ω	PROPN
ejpam-4260	185	8	)	)	PUNCT
ejpam-4260	185	9	is	be	AUX
ejpam-4260	185	10	sbt0	sbt0	PROPN
ejpam-4260	185	11	;	;	PUNCT
ejpam-4260	185	12	(	(	PUNCT
ejpam-4260	185	13	ii	ii	NOUN
ejpam-4260	185	14	)	)	PUNCT
ejpam-4260	185	15	bcl({ξ	bcl({ξ	NOUN
ejpam-4260	185	16	}	}	PUNCT
ejpam-4260	185	17	)	)	PUNCT
ejpam-4260	185	18	̸=	̸=	PROPN
ejpam-4260	185	19	bcl({ζ	bcl({ζ	PROPN
ejpam-4260	185	20	}	}	PUNCT
ejpam-4260	185	21	)	)	PUNCT
ejpam-4260	185	22	for	for	ADP
ejpam-4260	185	23	every	every	DET
ejpam-4260	185	24	ξ	ξ	PROPN
ejpam-4260	185	25	̸=	̸=	PROPN
ejpam-4260	185	26	ζ	ζ	NOUN
ejpam-4260	185	27	∈	∈	PROPN
ejpam-4260	185	28	u	u	NOUN
ejpam-4260	185	29	;	;	PUNCT
ejpam-4260	185	30	(	(	PUNCT
ejpam-4260	185	31	iii	iii	X
ejpam-4260	185	32	)	)	PUNCT
ejpam-4260	185	33	{	{	PUNCT
ejpam-4260	185	34	ξ}b′	ξ}b′	PROPN
ejpam-4260	185	35	is	be	AUX
ejpam-4260	185	36	a	a	DET
ejpam-4260	185	37	union	union	NOUN
ejpam-4260	185	38	of	of	ADP
ejpam-4260	185	39	supra	supra	PROPN
ejpam-4260	185	40	b	b	PROPN
ejpam-4260	185	41	-	-	PUNCT
ejpam-4260	185	42	closed	closed	ADJ
ejpam-4260	185	43	sets	set	NOUN
ejpam-4260	185	44	for	for	ADP
ejpam-4260	185	45	every	every	DET
ejpam-4260	185	46	ξ	ξ	PROPN
ejpam-4260	185	47	∈	∈	PROPN
ejpam-4260	185	48	u	u	NOUN
ejpam-4260	185	49	.	.	PUNCT
ejpam-4260	186	1	proof	proof	NOUN
ejpam-4260	186	2	.	.	PUNCT
ejpam-4260	187	1	1	1	NUM
ejpam-4260	187	2	→	→	SYM
ejpam-4260	187	3	2	2	NUM
ejpam-4260	187	4	:	:	PUNCT
ejpam-4260	187	5	let	let	VERB
ejpam-4260	187	6	ξ	ξ	X
ejpam-4260	187	7	̸=	̸=	PROPN
ejpam-4260	187	8	ζ	ζ	NOUN
ejpam-4260	187	9	∈	∈	PROPN
ejpam-4260	187	10	u	u	NOUN
ejpam-4260	187	11	.	.	PUNCT
ejpam-4260	188	1	then	then	ADV
ejpam-4260	188	2	there	there	PRON
ejpam-4260	188	3	is	be	VERB
ejpam-4260	188	4	a	a	DET
ejpam-4260	188	5	supra	supra	PROPN
ejpam-4260	188	6	b	b	NOUN
ejpam-4260	188	7	-	-	PUNCT
ejpam-4260	188	8	open	open	ADJ
ejpam-4260	188	9	set	set	NOUN
ejpam-4260	188	10	o	o	NOUN
ejpam-4260	188	11	such	such	ADJ
ejpam-4260	188	12	that	that	SCONJ
ejpam-4260	188	13	ξ	ξ	PROPN
ejpam-4260	188	14	∈	∈	PROPN
ejpam-4260	188	15	ω	ω	NOUN
ejpam-4260	188	16	or	or	CCONJ
ejpam-4260	188	17	ζ	ζ	PROPN
ejpam-4260	188	18	∈	∈	PROPN
ejpam-4260	188	19	ω	ω	PROPN
ejpam-4260	188	20	.	.	PUNCT
ejpam-4260	189	1	say	say	PROPN
ejpam-4260	189	2	,	,	PUNCT
ejpam-4260	189	3	ξ	ξ	PROPN
ejpam-4260	189	4	∈	∈	PROPN
ejpam-4260	189	5	θ	θ	PROPN
ejpam-4260	189	6	and	and	CCONJ
ejpam-4260	189	7	ζ	ζ	PRON
ejpam-4260	189	8	̸∈	̸∈	PROPN
ejpam-4260	189	9	θ	θ	PROPN
ejpam-4260	189	10	.	.	PUNCT
ejpam-4260	190	1	since	since	SCONJ
ejpam-4260	190	2	θ	θ	PROPN
ejpam-4260	190	3	is	be	AUX
ejpam-4260	190	4	a	a	DET
ejpam-4260	190	5	supra	supra	PROPN
ejpam-4260	190	6	b	b	NOUN
ejpam-4260	190	7	-	-	PUNCT
ejpam-4260	190	8	open	open	ADJ
ejpam-4260	190	9	set	set	NOUN
ejpam-4260	190	10	including	include	VERB
ejpam-4260	190	11	ξ	ξ	X
ejpam-4260	190	12	such	such	ADJ
ejpam-4260	190	13	that	that	SCONJ
ejpam-4260	190	14	θ	θ	PROPN
ejpam-4260	190	15	⋂	⋂	PROPN
ejpam-4260	190	16	{	{	PUNCT
ejpam-4260	190	17	ζ	ζ	NOUN
ejpam-4260	190	18	}	}	PUNCT
ejpam-4260	190	19	=	=	NOUN
ejpam-4260	190	20	∅	∅	NOUN
ejpam-4260	190	21	,	,	PUNCT
ejpam-4260	190	22	we	we	PRON
ejpam-4260	190	23	obtain	obtain	VERB
ejpam-4260	190	24	ξ	ξ	PRON
ejpam-4260	190	25	̸∈	̸∈	PROPN
ejpam-4260	190	26	bcl({ζ	bcl({ζ	PROPN
ejpam-4260	190	27	}	}	PUNCT
ejpam-4260	190	28	)	)	PUNCT
ejpam-4260	190	29	.	.	PUNCT
ejpam-4260	191	1	obviously	obviously	ADV
ejpam-4260	191	2	,	,	PUNCT
ejpam-4260	191	3	ξ	ξ	PROPN
ejpam-4260	191	4	∈	∈	PROPN
ejpam-4260	191	5	bcl({ξ	bcl({ξ	NOUN
ejpam-4260	191	6	}	}	PUNCT
ejpam-4260	191	7	)	)	PUNCT
ejpam-4260	191	8	;	;	PUNCT
ejpam-4260	191	9	hence	hence	ADV
ejpam-4260	191	10	,	,	PUNCT
ejpam-4260	191	11	bcl({ξ	bcl({ξ	NOUN
ejpam-4260	191	12	}	}	PUNCT
ejpam-4260	191	13	)	)	PUNCT
ejpam-4260	191	14	̸=	̸=	PROPN
ejpam-4260	191	15	bcl({ζ	bcl({ζ	PROPN
ejpam-4260	191	16	}	}	PUNCT
ejpam-4260	191	17	)	)	PUNCT
ejpam-4260	191	18	.	.	PUNCT
ejpam-4260	192	1	2	2	NUM
ejpam-4260	192	2	→	→	SYM
ejpam-4260	192	3	3	3	NUM
ejpam-4260	192	4	:	:	PUNCT
ejpam-4260	192	5	suppose	suppose	VERB
ejpam-4260	192	6	that	that	SCONJ
ejpam-4260	192	7	ζ	ζ	PROPN
ejpam-4260	192	8	∈	∈	PROPN
ejpam-4260	192	9	{	{	PUNCT
ejpam-4260	192	10	ξ}b′.	ξ}b′.	PROPN
ejpam-4260	192	11	then	then	ADV
ejpam-4260	192	12	,	,	PUNCT
ejpam-4260	192	13	ζ	ζ	PROPN
ejpam-4260	192	14	∈	∈	PROPN
ejpam-4260	192	15	bcl({ξ	bcl({ξ	NOUN
ejpam-4260	192	16	}	}	PUNCT
ejpam-4260	192	17	)	)	PUNCT
ejpam-4260	192	18	.	.	PUNCT
ejpam-4260	193	1	consequently	consequently	ADV
ejpam-4260	193	2	,	,	PUNCT
ejpam-4260	193	3	bcl(ζ	bcl(ζ	PROPN
ejpam-4260	193	4	)	)	PUNCT
ejpam-4260	193	5	⊆	⊆	NUM
ejpam-4260	193	6	bcl({ξ	bcl({ξ	NOUN
ejpam-4260	193	7	}	}	PUNCT
ejpam-4260	193	8	)	)	PUNCT
ejpam-4260	193	9	.	.	PUNCT
ejpam-4260	194	1	this	this	PRON
ejpam-4260	194	2	means	mean	VERB
ejpam-4260	194	3	that	that	SCONJ
ejpam-4260	194	4	ζ	ζ	PROPN
ejpam-4260	194	5	∈	∈	PROPN
ejpam-4260	194	6	bcl(ζ	bcl(ζ	PROPN
ejpam-4260	194	7	)	)	PUNCT
ejpam-4260	194	8	⊆	⊆	NUM
ejpam-4260	194	9	{	{	PUNCT
ejpam-4260	194	10	ξ}b′.	ξ}b′.	NOUN
ejpam-4260	194	11	so	so	SCONJ
ejpam-4260	194	12	that	that	SCONJ
ejpam-4260	194	13	,	,	PUNCT
ejpam-4260	194	14	{	{	PUNCT
ejpam-4260	194	15	ξ}b′	ξ}b′	X
ejpam-4260	194	16	=	=	SYM
ejpam-4260	194	17	⋃	⋃	NOUN
ejpam-4260	194	18	{	{	PUNCT
ejpam-4260	194	19	bcl(ζ	bcl(ζ	PROPN
ejpam-4260	194	20	):	):	PUNCT
ejpam-4260	194	21	for	for	ADP
ejpam-4260	194	22	every	every	DET
ejpam-4260	194	23	ζ	ζ	PROPN
ejpam-4260	194	24	∈	∈	PROPN
ejpam-4260	194	25	{	{	PUNCT
ejpam-4260	194	26	ξ}b′	ξ}b′	NOUN
ejpam-4260	194	27	}	}	PUNCT
ejpam-4260	194	28	.	.	PUNCT
ejpam-4260	195	1	3	3	NUM
ejpam-4260	195	2	→	→	SYM
ejpam-4260	195	3	1	1	NUM
ejpam-4260	195	4	:	:	PUNCT
ejpam-4260	195	5	consider	consider	VERB
ejpam-4260	195	6	ξ	ξ	X
ejpam-4260	195	7	̸=	̸=	PROPN
ejpam-4260	195	8	ζ	ζ	NOUN
ejpam-4260	195	9	.	.	PUNCT
ejpam-4260	196	1	then	then	ADV
ejpam-4260	196	2	(	(	PUNCT
ejpam-4260	196	3	i	i	NOUN
ejpam-4260	196	4	)	)	PUNCT
ejpam-4260	196	5	either	either	CCONJ
ejpam-4260	196	6	ζ	ζ	PROPN
ejpam-4260	196	7	∈	∈	PROPN
ejpam-4260	196	8	{	{	PUNCT
ejpam-4260	196	9	ξ}b′.	ξ}b′.	NOUN
ejpam-4260	196	10	then	then	ADV
ejpam-4260	196	11	there	there	PRON
ejpam-4260	196	12	is	be	VERB
ejpam-4260	196	13	a	a	DET
ejpam-4260	196	14	supra	supra	PROPN
ejpam-4260	196	15	b	b	NOUN
ejpam-4260	196	16	-	-	PUNCT
ejpam-4260	196	17	closed	closed	ADJ
ejpam-4260	196	18	set	set	NOUN
ejpam-4260	196	19	f	f	PROPN
ejpam-4260	196	20	such	such	ADJ
ejpam-4260	196	21	that	that	SCONJ
ejpam-4260	196	22	ζ	ζ	PROPN
ejpam-4260	196	23	∈	∈	NOUN
ejpam-4260	196	24	f	f	NOUN
ejpam-4260	196	25	⊆	⊆	NUM
ejpam-4260	196	26	{	{	PUNCT
ejpam-4260	196	27	ξ}b′.	ξ}b′.	NOUN
ejpam-4260	196	28	this	this	PRON
ejpam-4260	196	29	means	mean	VERB
ejpam-4260	196	30	that	that	SCONJ
ejpam-4260	196	31	ξ	ξ	PROPN
ejpam-4260	196	32	̸∈	̸∈	PROPN
ejpam-4260	196	33	f	f	PROPN
ejpam-4260	196	34	.	.	PUNCT
ejpam-4260	197	1	thus	thus	ADV
ejpam-4260	197	2	,	,	PUNCT
ejpam-4260	197	3	f	f	PROPN
ejpam-4260	197	4	c	c	PROPN
ejpam-4260	197	5	is	be	AUX
ejpam-4260	197	6	a	a	DET
ejpam-4260	197	7	supra	supra	PROPN
ejpam-4260	197	8	b	b	NOUN
ejpam-4260	197	9	-	-	PUNCT
ejpam-4260	197	10	open	open	ADJ
ejpam-4260	197	11	set	set	NOUN
ejpam-4260	197	12	including	include	VERB
ejpam-4260	197	13	ξ	ξ	X
ejpam-4260	197	14	such	such	ADJ
ejpam-4260	197	15	that	that	SCONJ
ejpam-4260	197	16	ζ	ζ	PROPN
ejpam-4260	197	17	̸∈	̸∈	PROPN
ejpam-4260	197	18	f	f	PROPN
ejpam-4260	197	19	c.	c.	PROPN
ejpam-4260	197	20	(	(	PUNCT
ejpam-4260	197	21	ii	ii	PROPN
ejpam-4260	197	22	)	)	PUNCT
ejpam-4260	197	23	or	or	CCONJ
ejpam-4260	197	24	ζ	ζ	PRON
ejpam-4260	197	25	̸∈	̸∈	PROPN
ejpam-4260	197	26	{	{	PUNCT
ejpam-4260	197	27	ξ}b′.	ξ}b′.	PROPN
ejpam-4260	197	28	then	then	ADV
ejpam-4260	197	29	there	there	PRON
ejpam-4260	197	30	is	be	VERB
ejpam-4260	197	31	a	a	DET
ejpam-4260	197	32	supra	supra	PROPN
ejpam-4260	197	33	b	b	NOUN
ejpam-4260	197	34	-	-	PUNCT
ejpam-4260	197	35	open	open	ADJ
ejpam-4260	197	36	set	set	ADJ
ejpam-4260	197	37	θ	θ	PROPN
ejpam-4260	197	38	including	include	VERB
ejpam-4260	197	39	ζ	ζ	NOUN
ejpam-4260	197	40	such	such	ADJ
ejpam-4260	197	41	that	that	SCONJ
ejpam-4260	197	42	ξ	ξ	PROPN
ejpam-4260	197	43	̸∈	̸∈	PROPN
ejpam-4260	197	44	θ	θ	PROPN
ejpam-4260	197	45	.	.	PUNCT
ejpam-4260	198	1	it	it	PRON
ejpam-4260	198	2	follows	follow	VERB
ejpam-4260	198	3	from	from	ADP
ejpam-4260	198	4	the	the	DET
ejpam-4260	198	5	above	above	ADJ
ejpam-4260	198	6	two	two	NUM
ejpam-4260	198	7	cases	case	NOUN
ejpam-4260	198	8	that	that	SCONJ
ejpam-4260	198	9	(	(	PUNCT
ejpam-4260	198	10	u	u	NOUN
ejpam-4260	198	11	,	,	PUNCT
ejpam-4260	198	12	ω	ω	PROPN
ejpam-4260	198	13	)	)	PUNCT
ejpam-4260	198	14	is	be	AUX
ejpam-4260	198	15	sbt0	sbt0	PROPN
ejpam-4260	198	16	.	.	PUNCT
ejpam-4260	199	1	corollary	corollary	ADJ
ejpam-4260	199	2	3	3	NUM
ejpam-4260	199	3	.	.	PUNCT
ejpam-4260	200	1	in	in	ADP
ejpam-4260	200	2	an	an	DET
ejpam-4260	200	3	sbt0	sbt0	NOUN
ejpam-4260	200	4	-	-	PUNCT
ejpam-4260	200	5	space	space	NOUN
ejpam-4260	200	6	(	(	PUNCT
ejpam-4260	200	7	u	u	NOUN
ejpam-4260	200	8	,	,	PUNCT
ejpam-4260	200	9	ω	ω	PROPN
ejpam-4260	200	10	)	)	PUNCT
ejpam-4260	200	11	,	,	PUNCT
ejpam-4260	200	12	there	there	PRON
ejpam-4260	200	13	exists	exist	VERB
ejpam-4260	200	14	at	at	ADP
ejpam-4260	200	15	most	most	ADV
ejpam-4260	200	16	a	a	DET
ejpam-4260	200	17	singleton	singleton	NOUN
ejpam-4260	200	18	set	set	NOUN
ejpam-4260	200	19	which	which	PRON
ejpam-4260	200	20	is	be	AUX
ejpam-4260	200	21	a	a	DET
ejpam-4260	200	22	supra	supra	NOUN
ejpam-4260	200	23	b	b	ADP
ejpam-4260	200	24	dense	dense	ADJ
ejpam-4260	200	25	(	(	PUNCT
ejpam-4260	200	26	{	{	PUNCT
ejpam-4260	200	27	ξ	ξ	NOUN
ejpam-4260	200	28	}	}	PUNCT
ejpam-4260	200	29	is	be	AUX
ejpam-4260	200	30	a	a	DET
ejpam-4260	200	31	supra	supra	PROPN
ejpam-4260	200	32	b	b	PROPN
ejpam-4260	200	33	dense	dense	ADJ
ejpam-4260	200	34	set	set	NOUN
ejpam-4260	200	35	if	if	SCONJ
ejpam-4260	200	36	bcl{ξ	bcl{ξ	NOUN
ejpam-4260	200	37	}	}	PUNCT
ejpam-4260	200	38	=	=	SYM
ejpam-4260	200	39	u	u	NOUN
ejpam-4260	200	40	)	)	PUNCT
ejpam-4260	200	41	.	.	PUNCT
ejpam-4260	201	1	proof	proof	NOUN
ejpam-4260	201	2	.	.	PUNCT
ejpam-4260	202	1	suppose	suppose	VERB
ejpam-4260	202	2	that	that	SCONJ
ejpam-4260	202	3	{	{	PUNCT
ejpam-4260	202	4	ξ	ξ	NOUN
ejpam-4260	202	5	}	}	PUNCT
ejpam-4260	202	6	and	and	CCONJ
ejpam-4260	202	7	{	{	PUNCT
ejpam-4260	202	8	ζ	ζ	NOUN
ejpam-4260	202	9	}	}	PUNCT
ejpam-4260	202	10	are	be	AUX
ejpam-4260	202	11	two	two	NUM
ejpam-4260	202	12	distinct	distinct	ADJ
ejpam-4260	202	13	singleton	singleton	NOUN
ejpam-4260	202	14	subset	subset	NOUN
ejpam-4260	202	15	of	of	ADP
ejpam-4260	202	16	an	an	DET
ejpam-4260	202	17	sbt0	sbt0	NOUN
ejpam-4260	202	18	-	-	PUNCT
ejpam-4260	202	19	space	space	NOUN
ejpam-4260	202	20	(	(	PUNCT
ejpam-4260	202	21	u	u	NOUN
ejpam-4260	202	22	,	,	PUNCT
ejpam-4260	202	23	ω	ω	PROPN
ejpam-4260	202	24	)	)	PUNCT
ejpam-4260	202	25	such	such	ADJ
ejpam-4260	202	26	that	that	DET
ejpam-4260	202	27	bcl({ξ	bcl({ξ	NOUN
ejpam-4260	202	28	}	}	PUNCT
ejpam-4260	202	29	)	)	PUNCT
ejpam-4260	203	1	=	=	SYM
ejpam-4260	203	2	bcl({ζ	bcl({ζ	PROPN
ejpam-4260	203	3	}	}	PUNCT
ejpam-4260	203	4	)	)	PUNCT
ejpam-4260	203	5	=	=	SYM
ejpam-4260	203	6	u	u	NOUN
ejpam-4260	203	7	.	.	PUNCT
ejpam-4260	204	1	this	this	PRON
ejpam-4260	204	2	leads	lead	VERB
ejpam-4260	204	3	to	to	ADP
ejpam-4260	204	4	a	a	DET
ejpam-4260	204	5	contradiction	contradiction	NOUN
ejpam-4260	204	6	because	because	SCONJ
ejpam-4260	204	7	(	(	PUNCT
ejpam-4260	204	8	u	u	NOUN
ejpam-4260	204	9	,	,	PUNCT
ejpam-4260	204	10	ω	ω	PROPN
ejpam-4260	204	11	)	)	PUNCT
ejpam-4260	204	12	is	be	AUX
ejpam-4260	204	13	sbt0	sbt0	PROPN
ejpam-4260	204	14	.	.	PUNCT
ejpam-4260	205	1	hence	hence	ADV
ejpam-4260	205	2	,	,	PUNCT
ejpam-4260	205	3	we	we	PRON
ejpam-4260	205	4	obtain	obtain	VERB
ejpam-4260	205	5	the	the	DET
ejpam-4260	205	6	desired	desire	VERB
ejpam-4260	205	7	result	result	NOUN
ejpam-4260	205	8	.	.	PUNCT
ejpam-4260	206	1	theorem	theorem	ADJ
ejpam-4260	206	2	5	5	NUM
ejpam-4260	206	3	.	.	PUNCT
ejpam-4260	207	1	the	the	DET
ejpam-4260	207	2	next	next	ADJ
ejpam-4260	207	3	there	there	PRON
ejpam-4260	207	4	properties	property	NOUN
ejpam-4260	207	5	are	be	AUX
ejpam-4260	207	6	identical	identical	ADJ
ejpam-4260	207	7	.	.	PUNCT
ejpam-4260	208	1	(	(	PUNCT
ejpam-4260	208	2	i	i	NOUN
ejpam-4260	208	3	)	)	PUNCT
ejpam-4260	208	4	(	(	PUNCT
ejpam-4260	208	5	u	u	NOUN
ejpam-4260	208	6	,	,	PUNCT
ejpam-4260	208	7	ω	ω	PROPN
ejpam-4260	208	8	)	)	PUNCT
ejpam-4260	208	9	is	be	AUX
ejpam-4260	208	10	sbt1	sbt1	PROPN
ejpam-4260	208	11	;	;	PUNCT
ejpam-4260	209	1	a.	a.	NOUN
ejpam-4260	209	2	mhemdi	mhemdi	PROPN
ejpam-4260	209	3	et	et	PROPN
ejpam-4260	209	4	al	al	PROPN
ejpam-4260	209	5	.	.	PUNCT
ejpam-4260	209	6	/	/	SYM
ejpam-4260	209	7	eur	eur	PROPN
ejpam-4260	209	8	.	.	PUNCT
ejpam-4260	210	1	j.	j.	PROPN
ejpam-4260	210	2	pure	pure	PROPN
ejpam-4260	210	3	appl	appl	PROPN
ejpam-4260	210	4	.	.	PROPN
ejpam-4260	210	5	math	math	PROPN
ejpam-4260	210	6	,	,	PUNCT
ejpam-4260	210	7	15	15	NUM
ejpam-4260	210	8	(	(	PUNCT
ejpam-4260	210	9	1	1	NUM
ejpam-4260	210	10	)	)	PUNCT
ejpam-4260	210	11	(	(	PUNCT
ejpam-4260	210	12	2022	2022	NUM
ejpam-4260	210	13	)	)	PUNCT
ejpam-4260	210	14	,	,	PUNCT
ejpam-4260	210	15	15	15	NUM
ejpam-4260	210	16	-	-	SYM
ejpam-4260	210	17	29	29	NUM
ejpam-4260	210	18	22	22	NUM
ejpam-4260	210	19	(	(	PUNCT
ejpam-4260	210	20	ii	ii	NOUN
ejpam-4260	210	21	)	)	PUNCT
ejpam-4260	210	22	all	all	DET
ejpam-4260	210	23	singleton	singleton	PROPN
ejpam-4260	210	24	subsets	subset	NOUN
ejpam-4260	210	25	of	of	ADP
ejpam-4260	210	26	(	(	PUNCT
ejpam-4260	210	27	u	u	PROPN
ejpam-4260	210	28	,	,	PUNCT
ejpam-4260	210	29	ω	ω	PROPN
ejpam-4260	210	30	)	)	PUNCT
ejpam-4260	210	31	are	be	AUX
ejpam-4260	210	32	supra	supra	PROPN
ejpam-4260	210	33	b	b	NOUN
ejpam-4260	210	34	-	-	PUNCT
ejpam-4260	210	35	closed	closed	ADJ
ejpam-4260	210	36	;	;	PUNCT
ejpam-4260	210	37	(	(	PUNCT
ejpam-4260	210	38	iii	iii	X
ejpam-4260	210	39	)	)	PUNCT
ejpam-4260	210	40	the	the	DET
ejpam-4260	210	41	intersection	intersection	NOUN
ejpam-4260	210	42	of	of	ADP
ejpam-4260	210	43	all	all	DET
ejpam-4260	210	44	supra	supra	PROPN
ejpam-4260	210	45	b	b	NOUN
ejpam-4260	210	46	-	-	PUNCT
ejpam-4260	210	47	open	open	ADJ
ejpam-4260	210	48	sets	set	NOUN
ejpam-4260	210	49	including	include	VERB
ejpam-4260	210	50	a	a	DET
ejpam-4260	210	51	set	set	NOUN
ejpam-4260	210	52	o	o	NOUN
ejpam-4260	210	53	is	be	AUX
ejpam-4260	210	54	exactly	exactly	ADV
ejpam-4260	210	55	o	o	NOUN
ejpam-4260	210	56	;	;	PUNCT
ejpam-4260	210	57	(	(	PUNCT
ejpam-4260	210	58	iv	iv	X
ejpam-4260	210	59	)	)	PUNCT
ejpam-4260	210	60	{	{	PUNCT
ejpam-4260	210	61	ξ}b′	ξ}b′	NOUN
ejpam-4260	210	62	=	=	NOUN
ejpam-4260	210	63	∅	∅	NOUN
ejpam-4260	210	64	for	for	ADP
ejpam-4260	210	65	every	every	DET
ejpam-4260	210	66	ξ	ξ	PROPN
ejpam-4260	210	67	∈	∈	PROPN
ejpam-4260	210	68	u	u	NOUN
ejpam-4260	210	69	.	.	PUNCT
ejpam-4260	211	1	proof	proof	NOUN
ejpam-4260	211	2	.	.	PUNCT
ejpam-4260	212	1	1	1	NUM
ejpam-4260	212	2	→	→	SYM
ejpam-4260	212	3	2	2	NUM
ejpam-4260	212	4	:	:	PUNCT
ejpam-4260	212	5	let	let	VERB
ejpam-4260	212	6	(	(	PUNCT
ejpam-4260	212	7	u	u	NOUN
ejpam-4260	212	8	,	,	PUNCT
ejpam-4260	212	9	ω	ω	PROPN
ejpam-4260	212	10	)	)	PUNCT
ejpam-4260	212	11	be	be	AUX
ejpam-4260	212	12	sbt1	sbt1	VERB
ejpam-4260	212	13	such	such	ADJ
ejpam-4260	212	14	that	that	SCONJ
ejpam-4260	212	15	{	{	PUNCT
ejpam-4260	212	16	ξ	ξ	NOUN
ejpam-4260	212	17	}	}	PUNCT
ejpam-4260	212	18	⊆	⊆	NUM
ejpam-4260	212	19	u	u	NOUN
ejpam-4260	212	20	.	.	PUNCT
ejpam-4260	213	1	for	for	ADP
ejpam-4260	213	2	each	each	DET
ejpam-4260	213	3	ζ	ζ	PROPN
ejpam-4260	213	4	̸=	̸=	PROPN
ejpam-4260	213	5	ξ	ξ	PROPN
ejpam-4260	213	6	∈	∈	PROPN
ejpam-4260	213	7	u	u	NOUN
ejpam-4260	213	8	,	,	PUNCT
ejpam-4260	213	9	there	there	PRON
ejpam-4260	213	10	is	be	VERB
ejpam-4260	213	11	a	a	DET
ejpam-4260	213	12	supra	supra	PROPN
ejpam-4260	213	13	b	b	NOUN
ejpam-4260	213	14	-	-	PUNCT
ejpam-4260	213	15	open	open	ADJ
ejpam-4260	213	16	set	set	ADJ
ejpam-4260	213	17	θ	θ	NOUN
ejpam-4260	213	18	including	include	VERB
ejpam-4260	213	19	ζ	ζ	NOUN
ejpam-4260	213	20	satisfies	satisfie	NOUN
ejpam-4260	213	21	that	that	PRON
ejpam-4260	213	22	θ	θ	PROPN
ejpam-4260	213	23	⋂	⋂	PROPN
ejpam-4260	213	24	{	{	PUNCT
ejpam-4260	213	25	ξ	ξ	NOUN
ejpam-4260	213	26	}	}	PUNCT
ejpam-4260	213	27	=	=	PUNCT
ejpam-4260	213	28	∅.	∅.	ADP
ejpam-4260	213	29	then	then	ADV
ejpam-4260	213	30	,	,	PUNCT
ejpam-4260	213	31	ζ	ζ	PROPN
ejpam-4260	213	32	̸∈	̸∈	PROPN
ejpam-4260	213	33	bcl({ξ	bcl({ξ	PROPN
ejpam-4260	213	34	}	}	PUNCT
ejpam-4260	213	35	)	)	PUNCT
ejpam-4260	213	36	.	.	PUNCT
ejpam-4260	214	1	thus	thus	ADV
ejpam-4260	214	2	,	,	PUNCT
ejpam-4260	214	3	bcl({ξ	bcl({ξ	NOUN
ejpam-4260	214	4	}	}	PUNCT
ejpam-4260	214	5	)	)	PUNCT
ejpam-4260	215	1	=	=	PRON
ejpam-4260	215	2	{	{	PUNCT
ejpam-4260	215	3	ξ	ξ	NOUN
ejpam-4260	215	4	}	}	PUNCT
ejpam-4260	215	5	.	.	PUNCT
ejpam-4260	216	1	hence	hence	ADV
ejpam-4260	216	2	,	,	PUNCT
ejpam-4260	216	3	we	we	PRON
ejpam-4260	216	4	obtain	obtain	VERB
ejpam-4260	216	5	the	the	DET
ejpam-4260	216	6	required	require	VERB
ejpam-4260	216	7	result	result	NOUN
ejpam-4260	216	8	.	.	PUNCT
ejpam-4260	217	1	2	2	NUM
ejpam-4260	217	2	→	→	SYM
ejpam-4260	217	3	3	3	NUM
ejpam-4260	217	4	:	:	PUNCT
ejpam-4260	217	5	let	let	VERB
ejpam-4260	217	6	o	o	NOUN
ejpam-4260	217	7	⊆	⊆	NUM
ejpam-4260	217	8	u	u	NOUN
ejpam-4260	217	9	and	and	CCONJ
ejpam-4260	217	10	ξ	ξ	PROPN
ejpam-4260	217	11	∈	∈	PROPN
ejpam-4260	217	12	oc	oc	PROPN
ejpam-4260	217	13	.	.	PUNCT
ejpam-4260	218	1	then	then	ADV
ejpam-4260	218	2	{	{	PUNCT
ejpam-4260	218	3	ξ}c	ξ}c	NOUN
ejpam-4260	218	4	is	be	AUX
ejpam-4260	218	5	a	a	DET
ejpam-4260	218	6	supra	supra	PROPN
ejpam-4260	218	7	b	b	NOUN
ejpam-4260	218	8	-	-	PUNCT
ejpam-4260	218	9	open	open	ADJ
ejpam-4260	218	10	set	set	NOUN
ejpam-4260	218	11	including	include	VERB
ejpam-4260	218	12	o.	o.	NOUN
ejpam-4260	218	13	therefore	therefore	ADV
ejpam-4260	218	14	,	,	PUNCT
ejpam-4260	218	15	o	o	PROPN
ejpam-4260	218	16	⊆	⊆	NUM
ejpam-4260	218	17	{	{	PUNCT
ejpam-4260	218	18	θ	θ	NOUN
ejpam-4260	218	19	:	:	PUNCT
ejpam-4260	218	20	θ	θ	NOUN
ejpam-4260	218	21	is	be	AUX
ejpam-4260	218	22	a	a	DET
ejpam-4260	218	23	supra	supra	PROPN
ejpam-4260	218	24	b	b	NOUN
ejpam-4260	218	25	-	-	PUNCT
ejpam-4260	218	26	open	open	ADJ
ejpam-4260	218	27	set	set	NOUN
ejpam-4260	218	28	including	include	VERB
ejpam-4260	218	29	o	o	NOUN
ejpam-4260	218	30	}	}	PUNCT
ejpam-4260	218	31	⊆	⊆	NUM
ejpam-4260	218	32	{	{	PUNCT
ejpam-4260	218	33	{	{	PUNCT
ejpam-4260	218	34	ξ}c	ξ}c	NOUN
ejpam-4260	218	35	:	:	PUNCT
ejpam-4260	218	36	ξ	ξ	X
ejpam-4260	218	37	∈	∈	NOUN
ejpam-4260	218	38	oc	oc	VERB
ejpam-4260	218	39	}	}	PUNCT
ejpam-4260	218	40	⊆	⊆	NUM
ejpam-4260	218	41	o.	o.	NOUN
ejpam-4260	218	42	hence	hence	ADV
ejpam-4260	218	43	,	,	PUNCT
ejpam-4260	218	44	o	o	NOUN
ejpam-4260	218	45	=	=	PUNCT
ejpam-4260	218	46	{	{	PUNCT
ejpam-4260	218	47	θ	θ	NOUN
ejpam-4260	218	48	:	:	PUNCT
ejpam-4260	218	49	θ	θ	NOUN
ejpam-4260	218	50	is	be	AUX
ejpam-4260	218	51	a	a	DET
ejpam-4260	218	52	supra	supra	PROPN
ejpam-4260	218	53	b	b	NOUN
ejpam-4260	218	54	-	-	PUNCT
ejpam-4260	218	55	open	open	ADJ
ejpam-4260	218	56	set	set	NOUN
ejpam-4260	218	57	including	include	VERB
ejpam-4260	218	58	o	o	NOUN
ejpam-4260	218	59	}	}	PUNCT
ejpam-4260	218	60	.	.	PUNCT
ejpam-4260	219	1	3	3	NUM
ejpam-4260	219	2	→	→	SYM
ejpam-4260	219	3	4	4	NUM
ejpam-4260	219	4	:	:	PUNCT
ejpam-4260	219	5	let	let	VERB
ejpam-4260	219	6	ξ	ξ	X
ejpam-4260	219	7	∈	∈	PROPN
ejpam-4260	219	8	u	u	NOUN
ejpam-4260	219	9	such	such	ADJ
ejpam-4260	219	10	that	that	SCONJ
ejpam-4260	219	11	{	{	PUNCT
ejpam-4260	219	12	ξ}b′	ξ}b′	PROPN
ejpam-4260	219	13	̸=	̸=	PROPN
ejpam-4260	219	14	∅.	∅.	VERB
ejpam-4260	219	15	then	then	ADV
ejpam-4260	219	16	there	there	PRON
ejpam-4260	219	17	is	be	VERB
ejpam-4260	219	18	ζ	ζ	PROPN
ejpam-4260	219	19	̸=	̸=	PROPN
ejpam-4260	219	20	ξ	ξ	NUM
ejpam-4260	219	21	such	such	ADJ
ejpam-4260	219	22	that	that	SCONJ
ejpam-4260	219	23	ζ	ζ	PROPN
ejpam-4260	219	24	∈	∈	PROPN
ejpam-4260	219	25	{	{	PUNCT
ejpam-4260	219	26	ξ}b′.	ξ}b′.	NOUN
ejpam-4260	220	1	so	so	SCONJ
ejpam-4260	220	2	that	that	SCONJ
ejpam-4260	220	3	,	,	PUNCT
ejpam-4260	220	4	θ	θ	PROPN
ejpam-4260	220	5	\	\	PROPN
ejpam-4260	220	6	{	{	PUNCT
ejpam-4260	220	7	ζ	ζ	PROPN
ejpam-4260	220	8	}	}	PUNCT
ejpam-4260	220	9	⋂	⋂	PROPN
ejpam-4260	220	10	{	{	PUNCT
ejpam-4260	220	11	ξ	ξ	NOUN
ejpam-4260	220	12	}	}	PUNCT
ejpam-4260	220	13	=	=	NOUN
ejpam-4260	220	14	̸	̸	ADJ
ejpam-4260	220	15	∅	∅	NOUN
ejpam-4260	220	16	for	for	ADP
ejpam-4260	220	17	every	every	DET
ejpam-4260	220	18	supra	supra	PROPN
ejpam-4260	220	19	b	b	PROPN
ejpam-4260	220	20	-	-	PUNCT
ejpam-4260	220	21	open	open	ADJ
ejpam-4260	220	22	set	set	ADJ
ejpam-4260	220	23	θ	θ	PROPN
ejpam-4260	220	24	including	include	VERB
ejpam-4260	220	25	ζ	ζ	NOUN
ejpam-4260	220	26	.	.	PUNCT
ejpam-4260	221	1	this	this	PRON
ejpam-4260	221	2	contradicts	contradict	VERB
ejpam-4260	221	3	3	3	NUM
ejpam-4260	221	4	because	because	SCONJ
ejpam-4260	221	5	the	the	DET
ejpam-4260	221	6	intersection	intersection	NOUN
ejpam-4260	221	7	of	of	ADP
ejpam-4260	221	8	all	all	DET
ejpam-4260	221	9	supra	supra	PROPN
ejpam-4260	221	10	b	b	NOUN
ejpam-4260	221	11	-	-	PUNCT
ejpam-4260	221	12	open	open	ADJ
ejpam-4260	221	13	sets	set	NOUN
ejpam-4260	221	14	including	include	VERB
ejpam-4260	221	15	ζ	ζ	NOUN
ejpam-4260	221	16	is	be	AUX
ejpam-4260	221	17	not	not	PART
ejpam-4260	221	18	equal	equal	ADJ
ejpam-4260	221	19	{	{	PUNCT
ejpam-4260	221	20	ζ	ζ	NOUN
ejpam-4260	221	21	}	}	PUNCT
ejpam-4260	221	22	.	.	PUNCT
ejpam-4260	222	1	hence	hence	ADV
ejpam-4260	222	2	,	,	PUNCT
ejpam-4260	222	3	{	{	PUNCT
ejpam-4260	222	4	ξ}b′	ξ}b′	NOUN
ejpam-4260	222	5	=	=	PUNCT
ejpam-4260	222	6	∅.	∅.	VERB
ejpam-4260	222	7	4	4	NUM
ejpam-4260	222	8	→	→	SYM
ejpam-4260	222	9	1	1	NUM
ejpam-4260	222	10	:	:	PUNCT
ejpam-4260	222	11	let	let	VERB
ejpam-4260	222	12	ξ	ξ	X
ejpam-4260	222	13	̸=	̸=	PROPN
ejpam-4260	222	14	ζ	ζ	NOUN
ejpam-4260	222	15	.	.	PUNCT
ejpam-4260	223	1	then	then	ADV
ejpam-4260	223	2	,	,	PUNCT
ejpam-4260	223	3	the	the	DET
ejpam-4260	223	4	singleton	singleton	PROPN
ejpam-4260	223	5	sets	set	VERB
ejpam-4260	223	6	{	{	PUNCT
ejpam-4260	223	7	ξ	ξ	NOUN
ejpam-4260	223	8	}	}	PUNCT
ejpam-4260	223	9	and	and	CCONJ
ejpam-4260	223	10	{	{	PUNCT
ejpam-4260	223	11	ζ	ζ	NOUN
ejpam-4260	223	12	}	}	PUNCT
ejpam-4260	223	13	are	be	AUX
ejpam-4260	223	14	supra	supra	PROPN
ejpam-4260	223	15	b	b	NOUN
ejpam-4260	223	16	-	-	PUNCT
ejpam-4260	223	17	closed	closed	ADJ
ejpam-4260	223	18	because	because	SCONJ
ejpam-4260	223	19	{	{	PUNCT
ejpam-4260	223	20	ξ}b′	ξ}b′	NOUN
ejpam-4260	223	21	=	=	SYM
ejpam-4260	223	22	∅	∅	NOUN
ejpam-4260	223	23	and	and	CCONJ
ejpam-4260	223	24	{	{	PUNCT
ejpam-4260	223	25	ζ}b′	ζ}b′	NOUN
ejpam-4260	223	26	=	=	PUNCT
ejpam-4260	223	27	∅.	∅.	PRON
ejpam-4260	223	28	this	this	PRON
ejpam-4260	223	29	implies	imply	VERB
ejpam-4260	223	30	that	that	SCONJ
ejpam-4260	223	31	{	{	PUNCT
ejpam-4260	223	32	ξ}c	ξ}c	NOUN
ejpam-4260	223	33	and	and	CCONJ
ejpam-4260	223	34	{	{	PUNCT
ejpam-4260	223	35	ζ}c	ζ}c	NOUN
ejpam-4260	223	36	are	be	AUX
ejpam-4260	223	37	supra	supra	ADJ
ejpam-4260	223	38	b	b	NOUN
ejpam-4260	223	39	-	-	PUNCT
ejpam-4260	223	40	open	open	ADJ
ejpam-4260	223	41	sets	set	NOUN
ejpam-4260	223	42	including	include	VERB
ejpam-4260	223	43	{	{	PUNCT
ejpam-4260	223	44	ζ	ζ	NOUN
ejpam-4260	223	45	}	}	PUNCT
ejpam-4260	223	46	and	and	CCONJ
ejpam-4260	223	47	{	{	PUNCT
ejpam-4260	223	48	ξ	ξ	NOUN
ejpam-4260	223	49	}	}	PUNCT
ejpam-4260	223	50	,	,	PUNCT
ejpam-4260	223	51	respectively	respectively	ADV
ejpam-4260	223	52	.	.	PUNCT
ejpam-4260	224	1	hence	hence	ADV
ejpam-4260	224	2	,	,	PUNCT
ejpam-4260	224	3	(	(	PUNCT
ejpam-4260	224	4	u	u	NOUN
ejpam-4260	224	5	,	,	PUNCT
ejpam-4260	224	6	ω	ω	PROPN
ejpam-4260	224	7	)	)	PUNCT
ejpam-4260	224	8	is	be	AUX
ejpam-4260	224	9	sbt1	sbt1	PROPN
ejpam-4260	224	10	.	.	PUNCT
ejpam-4260	225	1	proposition	proposition	NOUN
ejpam-4260	225	2	4	4	NUM
ejpam-4260	225	3	.	.	PUNCT
ejpam-4260	226	1	if	if	SCONJ
ejpam-4260	226	2	(	(	PUNCT
ejpam-4260	226	3	u	u	NOUN
ejpam-4260	226	4	,	,	PUNCT
ejpam-4260	226	5	ω	ω	PROPN
ejpam-4260	226	6	)	)	PUNCT
ejpam-4260	226	7	satisfies	satisfy	VERB
ejpam-4260	226	8	the	the	DET
ejpam-4260	226	9	difference	difference	NOUN
ejpam-4260	226	10	property	property	NOUN
ejpam-4260	226	11	for	for	ADP
ejpam-4260	226	12	the	the	DET
ejpam-4260	226	13	family	family	NOUN
ejpam-4260	226	14	of	of	ADP
ejpam-4260	226	15	supra	supra	PROPN
ejpam-4260	226	16	b	b	PROPN
ejpam-4260	226	17	-	-	PUNCT
ejpam-4260	226	18	open	open	ADJ
ejpam-4260	226	19	sets	set	NOUN
ejpam-4260	226	20	,	,	PUNCT
ejpam-4260	226	21	then	then	ADV
ejpam-4260	226	22	it	it	PRON
ejpam-4260	226	23	is	be	AUX
ejpam-4260	226	24	sbt1	sbt1	PROPN
ejpam-4260	226	25	.	.	PUNCT
ejpam-4260	227	1	proof	proof	NOUN
ejpam-4260	227	2	.	.	PUNCT
ejpam-4260	228	1	since	since	SCONJ
ejpam-4260	228	2	u	u	NOUN
ejpam-4260	228	3	is	be	AUX
ejpam-4260	228	4	a	a	DET
ejpam-4260	228	5	supra	supra	PROPN
ejpam-4260	228	6	b	b	NOUN
ejpam-4260	228	7	-	-	PUNCT
ejpam-4260	228	8	open	open	ADJ
ejpam-4260	228	9	set	set	NOUN
ejpam-4260	228	10	and	and	CCONJ
ejpam-4260	228	11	(	(	PUNCT
ejpam-4260	228	12	u	u	PROPN
ejpam-4260	228	13	,	,	PUNCT
ejpam-4260	228	14	ω	ω	PROPN
ejpam-4260	228	15	)	)	PUNCT
ejpam-4260	228	16	satisfies	satisfy	VERB
ejpam-4260	228	17	the	the	DET
ejpam-4260	228	18	difference	difference	NOUN
ejpam-4260	228	19	property	property	NOUN
ejpam-4260	228	20	for	for	ADP
ejpam-4260	228	21	the	the	DET
ejpam-4260	228	22	family	family	NOUN
ejpam-4260	228	23	of	of	ADP
ejpam-4260	228	24	supra	supra	PROPN
ejpam-4260	228	25	b	b	PROPN
ejpam-4260	228	26	-	-	PUNCT
ejpam-4260	228	27	open	open	ADJ
ejpam-4260	228	28	sets	set	NOUN
ejpam-4260	228	29	,	,	PUNCT
ejpam-4260	228	30	we	we	PRON
ejpam-4260	228	31	find	find	VERB
ejpam-4260	228	32	that	that	SCONJ
ejpam-4260	228	33	u	u	NOUN
ejpam-4260	228	34	\	\	X
ejpam-4260	228	35	{	{	PUNCT
ejpam-4260	228	36	ξ	ξ	NOUN
ejpam-4260	228	37	}	}	PUNCT
ejpam-4260	228	38	is	be	AUX
ejpam-4260	228	39	a	a	DET
ejpam-4260	228	40	supra	supra	PROPN
ejpam-4260	228	41	b	b	NOUN
ejpam-4260	228	42	-	-	PUNCT
ejpam-4260	228	43	open	open	ADJ
ejpam-4260	228	44	set	set	NOUN
ejpam-4260	228	45	for	for	ADP
ejpam-4260	228	46	each	each	DET
ejpam-4260	228	47	ξ	ξ	PROPN
ejpam-4260	228	48	∈	∈	PROPN
ejpam-4260	228	49	u	u	NOUN
ejpam-4260	228	50	.	.	PUNCT
ejpam-4260	229	1	hence	hence	ADV
ejpam-4260	229	2	,	,	PUNCT
ejpam-4260	229	3	we	we	PRON
ejpam-4260	229	4	obtain	obtain	VERB
ejpam-4260	229	5	the	the	DET
ejpam-4260	229	6	desired	desire	VERB
ejpam-4260	229	7	result	result	NOUN
ejpam-4260	229	8	.	.	PUNCT
ejpam-4260	230	1	to	to	PART
ejpam-4260	230	2	clarify	clarify	VERB
ejpam-4260	230	3	that	that	SCONJ
ejpam-4260	230	4	the	the	DET
ejpam-4260	230	5	converse	converse	NOUN
ejpam-4260	230	6	of	of	ADP
ejpam-4260	230	7	the	the	DET
ejpam-4260	230	8	aforementioned	aforementioned	ADJ
ejpam-4260	230	9	proposition	proposition	NOUN
ejpam-4260	230	10	is	be	AUX
ejpam-4260	230	11	in	in	ADP
ejpam-4260	230	12	general	general	ADJ
ejpam-4260	230	13	false	false	ADJ
ejpam-4260	230	14	,	,	PUNCT
ejpam-4260	230	15	we	we	PRON
ejpam-4260	230	16	furnish	furnish	VERB
ejpam-4260	230	17	the	the	DET
ejpam-4260	230	18	example	example	NOUN
ejpam-4260	230	19	below	below	ADV
ejpam-4260	230	20	.	.	PUNCT
ejpam-4260	231	1	example	example	NOUN
ejpam-4260	232	1	4	4	NUM
ejpam-4260	232	2	.	.	PUNCT
ejpam-4260	233	1	every	every	DET
ejpam-4260	233	2	singleton	singleton	NOUN
ejpam-4260	233	3	subset	subset	NOUN
ejpam-4260	233	4	of	of	ADP
ejpam-4260	233	5	(	(	PUNCT
ejpam-4260	233	6	u	u	PROPN
ejpam-4260	233	7	,	,	PUNCT
ejpam-4260	233	8	ω	ω	PROPN
ejpam-4260	233	9	)	)	PUNCT
ejpam-4260	233	10	,	,	PUNCT
ejpam-4260	233	11	given	give	VERB
ejpam-4260	233	12	in	in	ADP
ejpam-4260	233	13	example	example	NOUN
ejpam-4260	233	14	(	(	PUNCT
ejpam-4260	233	15	1	1	NUM
ejpam-4260	233	16	)	)	PUNCT
ejpam-4260	233	17	,	,	PUNCT
ejpam-4260	233	18	is	be	AUX
ejpam-4260	233	19	supra	supra	PROPN
ejpam-4260	233	20	b	b	NOUN
ejpam-4260	233	21	-	-	PUNCT
ejpam-4260	233	22	closed	closed	ADJ
ejpam-4260	233	23	;	;	PUNCT
ejpam-4260	233	24	therefore	therefore	ADV
ejpam-4260	233	25	,	,	PUNCT
ejpam-4260	233	26	(	(	PUNCT
ejpam-4260	233	27	u	u	NOUN
ejpam-4260	233	28	,	,	PUNCT
ejpam-4260	233	29	ω	ω	PROPN
ejpam-4260	233	30	)	)	PUNCT
ejpam-4260	233	31	is	be	AUX
ejpam-4260	233	32	sbt1	sbt1	PROPN
ejpam-4260	233	33	.	.	PUNCT
ejpam-4260	234	1	in	in	ADP
ejpam-4260	234	2	contrast	contrast	NOUN
ejpam-4260	234	3	,	,	PUNCT
ejpam-4260	234	4	a	a	DET
ejpam-4260	234	5	set	set	NOUN
ejpam-4260	234	6	{	{	PUNCT
ejpam-4260	234	7	ξ1	ξ1	NOUN
ejpam-4260	234	8	,	,	PUNCT
ejpam-4260	234	9	ξ3	ξ3	PROPN
ejpam-4260	234	10	}	}	PUNCT
ejpam-4260	234	11	is	be	AUX
ejpam-4260	234	12	supra	supra	ADJ
ejpam-4260	234	13	b	b	NOUN
ejpam-4260	234	14	-	-	PUNCT
ejpam-4260	234	15	open	open	ADJ
ejpam-4260	234	16	,	,	PUNCT
ejpam-4260	234	17	whereas	whereas	SCONJ
ejpam-4260	234	18	{	{	PUNCT
ejpam-4260	234	19	ξ1	ξ1	NOUN
ejpam-4260	234	20	,	,	PUNCT
ejpam-4260	234	21	ξ3}\{ξ1	ξ3}\{ξ1	ADV
ejpam-4260	234	22	}	}	PUNCT
ejpam-4260	234	23	is	be	AUX
ejpam-4260	234	24	not	not	PART
ejpam-4260	234	25	supra	supra	ADJ
ejpam-4260	234	26	b	b	NOUN
ejpam-4260	234	27	-	-	PUNCT
ejpam-4260	234	28	open	open	ADJ
ejpam-4260	234	29	.	.	PUNCT
ejpam-4260	235	1	consequently	consequently	ADV
ejpam-4260	235	2	,	,	PUNCT
ejpam-4260	235	3	(	(	PUNCT
ejpam-4260	235	4	u	u	NOUN
ejpam-4260	235	5	,	,	PUNCT
ejpam-4260	235	6	ω	ω	PROPN
ejpam-4260	235	7	)	)	PUNCT
ejpam-4260	235	8	does	do	AUX
ejpam-4260	235	9	not	not	PART
ejpam-4260	235	10	have	have	VERB
ejpam-4260	235	11	the	the	DET
ejpam-4260	235	12	difference	difference	NOUN
ejpam-4260	235	13	property	property	NOUN
ejpam-4260	235	14	for	for	ADP
ejpam-4260	235	15	the	the	DET
ejpam-4260	235	16	class	class	NOUN
ejpam-4260	235	17	of	of	ADP
ejpam-4260	235	18	supra	supra	PROPN
ejpam-4260	235	19	b	b	PROPN
ejpam-4260	235	20	-	-	PUNCT
ejpam-4260	235	21	open	open	ADJ
ejpam-4260	235	22	sets	set	NOUN
ejpam-4260	235	23	.	.	PUNCT
ejpam-4260	236	1	the	the	DET
ejpam-4260	236	2	next	next	ADJ
ejpam-4260	236	3	definition	definition	NOUN
ejpam-4260	236	4	will	will	AUX
ejpam-4260	236	5	help	help	VERB
ejpam-4260	236	6	to	to	PART
ejpam-4260	236	7	prove	prove	VERB
ejpam-4260	236	8	that	that	SCONJ
ejpam-4260	236	9	sbt0and	sbt0and	PROPN
ejpam-4260	236	10	sbt1	sbt1	PROPN
ejpam-4260	236	11	-	-	PUNCT
ejpam-4260	236	12	spaces	space	NOUN
ejpam-4260	236	13	are	be	AUX
ejpam-4260	236	14	equivalent	equivalent	ADJ
ejpam-4260	236	15	.	.	PUNCT
ejpam-4260	237	1	definition	definition	NOUN
ejpam-4260	237	2	13	13	NUM
ejpam-4260	237	3	.	.	PUNCT
ejpam-4260	238	1	we	we	PRON
ejpam-4260	238	2	call	call	VERB
ejpam-4260	238	3	(	(	PUNCT
ejpam-4260	238	4	u	u	NOUN
ejpam-4260	238	5	,	,	PUNCT
ejpam-4260	238	6	ω	ω	PROPN
ejpam-4260	238	7	)	)	PUNCT
ejpam-4260	238	8	a	a	DET
ejpam-4260	238	9	supra	supra	PROPN
ejpam-4260	238	10	b	b	PROPN
ejpam-4260	238	11	symmetric	symmetric	ADJ
ejpam-4260	238	12	space	space	NOUN
ejpam-4260	238	13	if	if	SCONJ
ejpam-4260	238	14	ξ	ξ	PROPN
ejpam-4260	238	15	∈	∈	PROPN
ejpam-4260	238	16	bcl{ζ	bcl{ζ	NOUN
ejpam-4260	238	17	}	}	PUNCT
ejpam-4260	238	18	implies	imply	VERB
ejpam-4260	238	19	that	that	SCONJ
ejpam-4260	238	20	ζ	ζ	PROPN
ejpam-4260	238	21	∈	∈	PROPN
ejpam-4260	238	22	bcl{ξ	bcl{ξ	NOUN
ejpam-4260	238	23	}	}	PUNCT
ejpam-4260	238	24	for	for	ADP
ejpam-4260	238	25	ξ	ξ	PROPN
ejpam-4260	238	26	̸=	̸=	PROPN
ejpam-4260	238	27	ζ	ζ	NOUN
ejpam-4260	238	28	∈	∈	PROPN
ejpam-4260	238	29	u	u	NOUN
ejpam-4260	238	30	.	.	PUNCT
ejpam-4260	238	31	theorem	theorem	VERB
ejpam-4260	238	32	6	6	NUM
ejpam-4260	238	33	.	.	PUNCT
ejpam-4260	239	1	let	let	AUX
ejpam-4260	239	2	(	(	PUNCT
ejpam-4260	239	3	u	u	NOUN
ejpam-4260	239	4	,	,	PUNCT
ejpam-4260	239	5	ω	ω	PROPN
ejpam-4260	239	6	)	)	PUNCT
ejpam-4260	239	7	be	be	AUX
ejpam-4260	239	8	a	a	DET
ejpam-4260	239	9	supra	supra	PROPN
ejpam-4260	239	10	b	b	PROPN
ejpam-4260	239	11	symmetric	symmetric	ADJ
ejpam-4260	239	12	space	space	NOUN
ejpam-4260	239	13	.	.	PUNCT
ejpam-4260	240	1	then	then	ADV
ejpam-4260	240	2	it	it	PRON
ejpam-4260	240	3	is	be	AUX
ejpam-4260	240	4	sbt1	sbt1	PROPN
ejpam-4260	240	5	iff	iff	PROPN
ejpam-4260	240	6	it	it	PRON
ejpam-4260	240	7	is	be	AUX
ejpam-4260	240	8	sbt0	sbt0	PROPN
ejpam-4260	240	9	.	.	PUNCT
ejpam-4260	241	1	proof	proof	NOUN
ejpam-4260	241	2	.	.	PUNCT
ejpam-4260	242	1	⇒	⇒	NOUN
ejpam-4260	242	2	:	:	PUNCT
ejpam-4260	242	3	it	it	PRON
ejpam-4260	242	4	is	be	AUX
ejpam-4260	242	5	straightforward	straightforward	ADJ
ejpam-4260	242	6	.	.	PUNCT
ejpam-4260	243	1	⇐	⇐	ADJ
ejpam-4260	243	2	:	:	PUNCT
ejpam-4260	243	3	for	for	ADP
ejpam-4260	243	4	two	two	NUM
ejpam-4260	243	5	distinct	distinct	ADJ
ejpam-4260	243	6	points	point	NOUN
ejpam-4260	243	7	ξ	ξ	PROPN
ejpam-4260	243	8	and	and	CCONJ
ejpam-4260	243	9	ζ	ζ	NOUN
ejpam-4260	243	10	,	,	PUNCT
ejpam-4260	243	11	there	there	PRON
ejpam-4260	243	12	is	be	VERB
ejpam-4260	243	13	a	a	DET
ejpam-4260	243	14	supra	supra	PROPN
ejpam-4260	243	15	b	b	NOUN
ejpam-4260	243	16	-	-	PUNCT
ejpam-4260	243	17	open	open	ADJ
ejpam-4260	243	18	set	set	ADJ
ejpam-4260	243	19	θ	θ	NOUN
ejpam-4260	243	20	including	include	VERB
ejpam-4260	243	21	only	only	ADV
ejpam-4260	243	22	one	one	NUM
ejpam-4260	243	23	of	of	ADP
ejpam-4260	243	24	them	they	PRON
ejpam-4260	243	25	.	.	PUNCT
ejpam-4260	244	1	assume	assume	VERB
ejpam-4260	244	2	that	that	SCONJ
ejpam-4260	244	3	ξ	ξ	X
ejpam-4260	244	4	∈	∈	PROPN
ejpam-4260	244	5	θ	θ	PROPN
ejpam-4260	244	6	and	and	CCONJ
ejpam-4260	244	7	ζ	ζ	PRON
ejpam-4260	244	8	̸∈	̸∈	PROPN
ejpam-4260	244	9	θ	θ	PROPN
ejpam-4260	244	10	.	.	PUNCT
ejpam-4260	245	1	then	then	ADV
ejpam-4260	245	2	,	,	PUNCT
ejpam-4260	245	3	ξ	ξ	PROPN
ejpam-4260	245	4	̸∈	̸∈	PROPN
ejpam-4260	245	5	bcl{ζ	bcl{ζ	NOUN
ejpam-4260	245	6	}	}	PUNCT
ejpam-4260	245	7	.	.	PUNCT
ejpam-4260	246	1	now	now	ADV
ejpam-4260	246	2	,	,	PUNCT
ejpam-4260	246	3	ζ	ζ	PROPN
ejpam-4260	246	4	̸∈	̸∈	PROPN
ejpam-4260	246	5	bcl{ξ	bcl{ξ	NOUN
ejpam-4260	246	6	}	}	PUNCT
ejpam-4260	246	7	because	because	SCONJ
ejpam-4260	246	8	(	(	PUNCT
ejpam-4260	246	9	u	u	NOUN
ejpam-4260	246	10	,	,	PUNCT
ejpam-4260	246	11	ω	ω	PROPN
ejpam-4260	246	12	)	)	PUNCT
ejpam-4260	246	13	is	be	AUX
ejpam-4260	246	14	supra	supra	PROPN
ejpam-4260	246	15	b	b	PROPN
ejpam-4260	246	16	symmetric	symmetric	NOUN
ejpam-4260	246	17	.	.	PUNCT
ejpam-4260	247	1	thus	thus	ADV
ejpam-4260	247	2	,	,	PUNCT
ejpam-4260	247	3	(	(	PUNCT
ejpam-4260	247	4	bcl{ξ})c	bcl{ξ})c	PROPN
ejpam-4260	247	5	is	be	AUX
ejpam-4260	247	6	a	a	DET
ejpam-4260	247	7	supra	supra	PROPN
ejpam-4260	247	8	b	b	NOUN
ejpam-4260	247	9	-	-	PUNCT
ejpam-4260	247	10	open	open	ADJ
ejpam-4260	247	11	set	set	NOUN
ejpam-4260	247	12	including	include	VERB
ejpam-4260	247	13	b.	b.	PROPN
ejpam-4260	247	14	hence	hence	ADV
ejpam-4260	247	15	,	,	PUNCT
ejpam-4260	247	16	(	(	PUNCT
ejpam-4260	247	17	u	u	NOUN
ejpam-4260	247	18	,	,	PUNCT
ejpam-4260	247	19	ω	ω	PROPN
ejpam-4260	247	20	)	)	PUNCT
ejpam-4260	247	21	is	be	AUX
ejpam-4260	247	22	sbt1	sbt1	PROPN
ejpam-4260	247	23	.	.	PUNCT
ejpam-4260	248	1	a.	a.	PROPN
ejpam-4260	248	2	mhemdi	mhemdi	PROPN
ejpam-4260	248	3	et	et	PROPN
ejpam-4260	248	4	al	al	PROPN
ejpam-4260	248	5	.	.	PUNCT
ejpam-4260	248	6	/	/	SYM
ejpam-4260	248	7	eur	eur	PROPN
ejpam-4260	248	8	.	.	PUNCT
ejpam-4260	249	1	j.	j.	PROPN
ejpam-4260	249	2	pure	pure	PROPN
ejpam-4260	249	3	appl	appl	PROPN
ejpam-4260	249	4	.	.	PROPN
ejpam-4260	249	5	math	math	PROPN
ejpam-4260	249	6	,	,	PUNCT
ejpam-4260	249	7	15	15	NUM
ejpam-4260	249	8	(	(	PUNCT
ejpam-4260	249	9	1	1	NUM
ejpam-4260	249	10	)	)	PUNCT
ejpam-4260	249	11	(	(	PUNCT
ejpam-4260	249	12	2022	2022	NUM
ejpam-4260	249	13	)	)	PUNCT
ejpam-4260	249	14	,	,	PUNCT
ejpam-4260	249	15	15	15	NUM
ejpam-4260	249	16	-	-	SYM
ejpam-4260	249	17	29	29	NUM
ejpam-4260	249	18	23	23	NUM
ejpam-4260	249	19	theorem	theorem	NOUN
ejpam-4260	249	20	7	7	NUM
ejpam-4260	249	21	.	.	PUNCT
ejpam-4260	250	1	the	the	DET
ejpam-4260	250	2	next	next	ADJ
ejpam-4260	250	3	three	three	NUM
ejpam-4260	250	4	properties	property	NOUN
ejpam-4260	250	5	are	be	AUX
ejpam-4260	250	6	identical	identical	ADJ
ejpam-4260	250	7	.	.	PUNCT
ejpam-4260	251	1	(	(	PUNCT
ejpam-4260	251	2	i	i	NOUN
ejpam-4260	251	3	)	)	PUNCT
ejpam-4260	251	4	(	(	PUNCT
ejpam-4260	251	5	u	u	NOUN
ejpam-4260	251	6	,	,	PUNCT
ejpam-4260	251	7	ω	ω	PROPN
ejpam-4260	251	8	)	)	PUNCT
ejpam-4260	251	9	is	be	AUX
ejpam-4260	251	10	sbt2	sbt2	NOUN
ejpam-4260	251	11	;	;	PUNCT
ejpam-4260	251	12	(	(	PUNCT
ejpam-4260	251	13	ii	ii	NOUN
ejpam-4260	251	14	)	)	PUNCT
ejpam-4260	251	15	{	{	PUNCT
ejpam-4260	251	16	ξ	ξ	X
ejpam-4260	251	17	}	}	PUNCT
ejpam-4260	251	18	=	=	SYM
ejpam-4260	251	19	⋂	⋂	PROPN
ejpam-4260	251	20	{	{	PUNCT
ejpam-4260	251	21	fk	fk	INTJ
ejpam-4260	251	22	:	:	PUNCT
ejpam-4260	251	23	fk	fk	INTJ
ejpam-4260	251	24	is	be	AUX
ejpam-4260	251	25	a	a	DET
ejpam-4260	251	26	supra	supra	PROPN
ejpam-4260	251	27	b	b	NOUN
ejpam-4260	251	28	-	-	PUNCT
ejpam-4260	251	29	closed	close	VERB
ejpam-4260	251	30	neighborhood	neighborhood	NOUN
ejpam-4260	251	31	of	of	ADP
ejpam-4260	251	32	ξ	ξ	NOUN
ejpam-4260	251	33	}	}	PUNCT
ejpam-4260	251	34	for	for	ADP
ejpam-4260	251	35	every	every	DET
ejpam-4260	251	36	ξ	ξ	PROPN
ejpam-4260	251	37	∈	∈	PROPN
ejpam-4260	251	38	u	u	NOUN
ejpam-4260	251	39	;	;	PUNCT
ejpam-4260	251	40	(	(	PUNCT
ejpam-4260	251	41	iii	iii	NOUN
ejpam-4260	251	42	)	)	PUNCT
ejpam-4260	251	43	△	△	X
ejpam-4260	252	1	=	=	SYM
ejpam-4260	252	2	{	{	PUNCT
ejpam-4260	252	3	(	(	PUNCT
ejpam-4260	252	4	ξ	ξ	PROPN
ejpam-4260	252	5	,	,	PUNCT
ejpam-4260	252	6	ξ	ξ	NOUN
ejpam-4260	252	7	)	)	PUNCT
ejpam-4260	252	8	:	:	PUNCT
ejpam-4260	252	9	ξ	ξ	X
ejpam-4260	252	10	∈	∈	PROPN
ejpam-4260	252	11	u	u	NOUN
ejpam-4260	252	12	}	}	PUNCT
ejpam-4260	252	13	forms	form	VERB
ejpam-4260	252	14	a	a	DET
ejpam-4260	252	15	supra	supra	PROPN
ejpam-4260	252	16	b	b	NOUN
ejpam-4260	252	17	-	-	PUNCT
ejpam-4260	252	18	closed	closed	ADJ
ejpam-4260	252	19	set	set	NOUN
ejpam-4260	252	20	in	in	ADP
ejpam-4260	252	21	the	the	DET
ejpam-4260	252	22	product	product	NOUN
ejpam-4260	252	23	of	of	ADP
ejpam-4260	252	24	supra	supra	PROPN
ejpam-4260	252	25	spaces	space	VERB
ejpam-4260	252	26	u	u	NOUN
ejpam-4260	252	27	×u	×u	X
ejpam-4260	252	28	.	.	PUNCT
ejpam-4260	253	1	proof	proof	NOUN
ejpam-4260	253	2	.	.	PUNCT
ejpam-4260	254	1	1	1	NUM
ejpam-4260	254	2	→	→	SYM
ejpam-4260	254	3	2	2	NUM
ejpam-4260	254	4	:	:	PUNCT
ejpam-4260	254	5	since	since	SCONJ
ejpam-4260	254	6	(	(	PUNCT
ejpam-4260	254	7	u	u	INTJ
ejpam-4260	254	8	,	,	PUNCT
ejpam-4260	254	9	ω	ω	PROPN
ejpam-4260	254	10	)	)	PUNCT
ejpam-4260	254	11	is	be	AUX
ejpam-4260	254	12	sbt2	sbt2	PROPN
ejpam-4260	254	13	,	,	PUNCT
ejpam-4260	254	14	for	for	ADP
ejpam-4260	254	15	ξ	ξ	PROPN
ejpam-4260	254	16	̸=	̸=	PROPN
ejpam-4260	254	17	ζ	ζ	NOUN
ejpam-4260	254	18	there	there	PRON
ejpam-4260	254	19	are	be	VERB
ejpam-4260	254	20	disjoint	disjoint	ADJ
ejpam-4260	254	21	supra	supra	PROPN
ejpam-4260	254	22	b	b	NOUN
ejpam-4260	254	23	-	-	PUNCT
ejpam-4260	254	24	open	open	ADJ
ejpam-4260	254	25	sets	set	NOUN
ejpam-4260	254	26	θk	θk	NOUN
ejpam-4260	254	27	and	and	CCONJ
ejpam-4260	254	28	ok	ok	INTJ
ejpam-4260	255	1	such	such	ADJ
ejpam-4260	255	2	that	that	SCONJ
ejpam-4260	255	3	ξ	ξ	PROPN
ejpam-4260	255	4	∈	∈	PROPN
ejpam-4260	255	5	θk	θk	NOUN
ejpam-4260	255	6	and	and	CCONJ
ejpam-4260	255	7	ζ	ζ	NOUN
ejpam-4260	255	8	∈	∈	PROPN
ejpam-4260	255	9	ok	ok	INTJ
ejpam-4260	255	10	.	.	PUNCT
ejpam-4260	256	1	then	then	ADV
ejpam-4260	256	2	,	,	PUNCT
ejpam-4260	256	3	ξ	ξ	PROPN
ejpam-4260	256	4	∈	∈	PROPN
ejpam-4260	256	5	bcl(θk	bcl(θk	NOUN
ejpam-4260	256	6	)	)	PUNCT
ejpam-4260	257	1	⊆	⊆	NUM
ejpam-4260	257	2	oc	oc	NOUN
ejpam-4260	257	3	k	k	X
ejpam-4260	257	4	=	=	SYM
ejpam-4260	257	5	fk	fk	INTJ
ejpam-4260	257	6	.	.	PUNCT
ejpam-4260	257	7	therefore	therefore	ADV
ejpam-4260	257	8	,	,	PUNCT
ejpam-4260	257	9	fk	fk	INTJ
ejpam-4260	257	10	is	be	AUX
ejpam-4260	257	11	a	a	DET
ejpam-4260	257	12	supra	supra	PROPN
ejpam-4260	257	13	b	b	NOUN
ejpam-4260	257	14	-	-	PUNCT
ejpam-4260	257	15	closed	close	VERB
ejpam-4260	257	16	neighborhood	neighborhood	NOUN
ejpam-4260	257	17	of	of	ADP
ejpam-4260	257	18	ξ	ξ	PROPN
ejpam-4260	257	19	such	such	ADJ
ejpam-4260	257	20	that	that	SCONJ
ejpam-4260	257	21	ζ	ζ	PROPN
ejpam-4260	257	22	̸∈	̸∈	PROPN
ejpam-4260	257	23	fk	fk	PROPN
ejpam-4260	257	24	.	.	PUNCT
ejpam-4260	258	1	thus	thus	ADV
ejpam-4260	258	2	,	,	PUNCT
ejpam-4260	258	3	{	{	PUNCT
ejpam-4260	258	4	ξ	ξ	X
ejpam-4260	258	5	}	}	PUNCT
ejpam-4260	258	6	=	=	SYM
ejpam-4260	258	7	⋂	⋂	PROPN
ejpam-4260	258	8	{	{	PUNCT
ejpam-4260	258	9	fk	fk	INTJ
ejpam-4260	258	10	:	:	PUNCT
ejpam-4260	258	11	fk	fk	INTJ
ejpam-4260	258	12	is	be	AUX
ejpam-4260	258	13	a	a	DET
ejpam-4260	258	14	supra	supra	PROPN
ejpam-4260	258	15	b	b	NOUN
ejpam-4260	258	16	-	-	PUNCT
ejpam-4260	258	17	closed	close	VERB
ejpam-4260	258	18	neighborhood	neighborhood	NOUN
ejpam-4260	258	19	of	of	ADP
ejpam-4260	258	20	ξ	ξ	NOUN
ejpam-4260	258	21	}	}	PUNCT
ejpam-4260	258	22	.	.	PUNCT
ejpam-4260	259	1	2	2	NUM
ejpam-4260	259	2	→	→	SYM
ejpam-4260	259	3	1	1	NUM
ejpam-4260	259	4	:	:	PUNCT
ejpam-4260	259	5	consider	consider	VERB
ejpam-4260	259	6	ξ	ξ	X
ejpam-4260	259	7	̸=	̸=	PROPN
ejpam-4260	259	8	ζ	ζ	NOUN
ejpam-4260	259	9	.	.	PUNCT
ejpam-4260	260	1	since	since	SCONJ
ejpam-4260	260	2	{	{	PUNCT
ejpam-4260	260	3	ξ	ξ	X
ejpam-4260	260	4	}	}	PUNCT
ejpam-4260	260	5	=	=	SYM
ejpam-4260	260	6	⋂	⋂	PROPN
ejpam-4260	260	7	{	{	PUNCT
ejpam-4260	260	8	fk	fk	INTJ
ejpam-4260	260	9	:	:	PUNCT
ejpam-4260	260	10	fk	fk	INTJ
ejpam-4260	260	11	is	be	AUX
ejpam-4260	260	12	a	a	DET
ejpam-4260	260	13	supra	supra	PROPN
ejpam-4260	260	14	b	b	NOUN
ejpam-4260	260	15	-	-	PUNCT
ejpam-4260	260	16	closed	close	VERB
ejpam-4260	260	17	neighborhood	neighborhood	NOUN
ejpam-4260	260	18	of	of	ADP
ejpam-4260	260	19	ξ	ξ	NOUN
ejpam-4260	260	20	}	}	PUNCT
ejpam-4260	260	21	,	,	PUNCT
ejpam-4260	260	22	there	there	PRON
ejpam-4260	260	23	is	be	VERB
ejpam-4260	260	24	a	a	DET
ejpam-4260	260	25	supra	supra	PROPN
ejpam-4260	260	26	b	b	NOUN
ejpam-4260	260	27	-	-	PUNCT
ejpam-4260	260	28	closed	close	VERB
ejpam-4260	260	29	neighborhood	neighborhood	NOUN
ejpam-4260	260	30	fk0	fk0	NOUN
ejpam-4260	260	31	of	of	ADP
ejpam-4260	260	32	ξ	ξ	PROPN
ejpam-4260	260	33	such	such	ADJ
ejpam-4260	260	34	that	that	SCONJ
ejpam-4260	260	35	ζ	ζ	ADJ
ejpam-4260	260	36	̸∈	̸∈	PROPN
ejpam-4260	260	37	fk0	fk0	VERB
ejpam-4260	260	38	.	.	PUNCT
ejpam-4260	261	1	so	so	ADV
ejpam-4260	261	2	that	that	SCONJ
ejpam-4260	261	3	,	,	PUNCT
ejpam-4260	261	4	there	there	PRON
ejpam-4260	261	5	is	be	VERB
ejpam-4260	261	6	a	a	DET
ejpam-4260	261	7	supra	supra	PROPN
ejpam-4260	261	8	b	b	NOUN
ejpam-4260	261	9	-	-	PUNCT
ejpam-4260	261	10	open	open	ADJ
ejpam-4260	261	11	set	set	ADJ
ejpam-4260	261	12	θ	θ	PROPN
ejpam-4260	261	13	including	include	VERB
ejpam-4260	261	14	ξ	ξ	X
ejpam-4260	261	15	such	such	ADJ
ejpam-4260	261	16	that	that	SCONJ
ejpam-4260	261	17	ξ	ξ	SYM
ejpam-4260	261	18	∈	∈	PROPN
ejpam-4260	261	19	bcl(θ	bcl(θ	NOUN
ejpam-4260	261	20	)	)	PUNCT
ejpam-4260	261	21	⊆	⊆	NUM
ejpam-4260	261	22	fk0	fk0	NOUN
ejpam-4260	261	23	.	.	PUNCT
ejpam-4260	262	1	obviously	obviously	ADV
ejpam-4260	262	2	,	,	PUNCT
ejpam-4260	262	3	(	(	PUNCT
ejpam-4260	262	4	bcl(θ))c	bcl(θ))c	PROPN
ejpam-4260	262	5	is	be	AUX
ejpam-4260	262	6	a	a	DET
ejpam-4260	262	7	supra	supra	PROPN
ejpam-4260	262	8	b	b	NOUN
ejpam-4260	262	9	-	-	PUNCT
ejpam-4260	262	10	open	open	ADJ
ejpam-4260	262	11	set	set	NOUN
ejpam-4260	262	12	including	include	VERB
ejpam-4260	262	13	ζ	ζ	NOUN
ejpam-4260	262	14	and	and	CCONJ
ejpam-4260	262	15	θ	θ	PROPN
ejpam-4260	262	16	⋂	⋂	PROPN
ejpam-4260	262	17	(	(	PUNCT
ejpam-4260	262	18	bcl(θ))c	bcl(θ))c	PROPN
ejpam-4260	262	19	=	=	X
ejpam-4260	262	20	∅.	∅.	VERB
ejpam-4260	262	21	hence	hence	ADV
ejpam-4260	262	22	,	,	PUNCT
ejpam-4260	262	23	(	(	PUNCT
ejpam-4260	262	24	u	u	NOUN
ejpam-4260	262	25	,	,	PUNCT
ejpam-4260	262	26	ω	ω	PROPN
ejpam-4260	262	27	)	)	PUNCT
ejpam-4260	262	28	is	be	AUX
ejpam-4260	262	29	sbt2	sbt2	ADJ
ejpam-4260	262	30	.	.	PUNCT
ejpam-4260	263	1	1	1	NUM
ejpam-4260	263	2	→	→	SYM
ejpam-4260	263	3	3	3	NUM
ejpam-4260	263	4	:	:	PUNCT
ejpam-4260	263	5	suppose	suppose	VERB
ejpam-4260	263	6	that	that	SCONJ
ejpam-4260	263	7	(	(	PUNCT
ejpam-4260	263	8	ξ	ξ	X
ejpam-4260	263	9	,	,	PUNCT
ejpam-4260	263	10	ζ	ζ	NOUN
ejpam-4260	263	11	)	)	PUNCT
ejpam-4260	263	12	∈	∈	NOUN
ejpam-4260	263	13	u	u	NOUN
ejpam-4260	263	14	×u	×u	X
ejpam-4260	263	15	−	−	NOUN
ejpam-4260	263	16	△	△	X
ejpam-4260	263	17	.	.	PUNCT
ejpam-4260	264	1	then	then	ADV
ejpam-4260	264	2	ξ	ξ	PROPN
ejpam-4260	264	3	̸=	̸=	PROPN
ejpam-4260	264	4	ζ	ζ	NOUN
ejpam-4260	264	5	.	.	PUNCT
ejpam-4260	265	1	by	by	ADP
ejpam-4260	265	2	hypothesis	hypothesis	NOUN
ejpam-4260	265	3	,	,	PUNCT
ejpam-4260	265	4	there	there	PRON
ejpam-4260	265	5	are	be	VERB
ejpam-4260	265	6	disjoint	disjoint	ADJ
ejpam-4260	265	7	supra	supra	PROPN
ejpam-4260	265	8	b	b	NOUN
ejpam-4260	265	9	-	-	PUNCT
ejpam-4260	265	10	open	open	ADJ
ejpam-4260	265	11	sets	set	NOUN
ejpam-4260	265	12	θ	θ	PROPN
ejpam-4260	265	13	and	and	CCONJ
ejpam-4260	265	14	o	o	PROPN
ejpam-4260	265	15	respectively	respectively	ADV
ejpam-4260	265	16	including	include	VERB
ejpam-4260	265	17	ξ	ξ	PROPN
ejpam-4260	265	18	and	and	CCONJ
ejpam-4260	265	19	ζ	ζ	NOUN
ejpam-4260	265	20	.	.	PUNCT
ejpam-4260	266	1	now	now	ADV
ejpam-4260	266	2	,	,	PUNCT
ejpam-4260	266	3	(	(	PUNCT
ejpam-4260	266	4	ξ	ξ	X
ejpam-4260	266	5	,	,	PUNCT
ejpam-4260	266	6	ζ	ζ	NOUN
ejpam-4260	266	7	)	)	PUNCT
ejpam-4260	266	8	∈	∈	PROPN
ejpam-4260	266	9	θ×o	θ×o	PUNCT
ejpam-4260	267	1	⊆	⊆	NUM
ejpam-4260	267	2	u×u−	u×u−	NOUN
ejpam-4260	267	3	△	△	NOUN
ejpam-4260	267	4	,	,	PUNCT
ejpam-4260	267	5	which	which	PRON
ejpam-4260	267	6	proves	prove	VERB
ejpam-4260	267	7	that	that	SCONJ
ejpam-4260	267	8	u	u	PRON
ejpam-4260	267	9	×	×	NOUN
ejpam-4260	267	10	u	u	NOUN
ejpam-4260	267	11	−	−	PROPN
ejpam-4260	267	12	△	△	PROPN
ejpam-4260	267	13	is	be	AUX
ejpam-4260	267	14	a	a	DET
ejpam-4260	267	15	supra	supra	PROPN
ejpam-4260	267	16	b	b	PROPN
ejpam-4260	267	17	neighbourhood	neighbourhood	NOUN
ejpam-4260	267	18	of	of	ADP
ejpam-4260	267	19	any	any	PRON
ejpam-4260	267	20	of	of	ADP
ejpam-4260	267	21	its	its	PRON
ejpam-4260	267	22	points	point	NOUN
ejpam-4260	267	23	.	.	PUNCT
ejpam-4260	268	1	thus	thus	ADV
ejpam-4260	268	2	,	,	PUNCT
ejpam-4260	268	3	△	△	PROPN
ejpam-4260	268	4	is	be	AUX
ejpam-4260	268	5	supra	supra	ADJ
ejpam-4260	268	6	b	b	NOUN
ejpam-4260	268	7	-	-	PUNCT
ejpam-4260	268	8	closed	closed	ADJ
ejpam-4260	268	9	.	.	PUNCT
ejpam-4260	269	1	3	3	NUM
ejpam-4260	269	2	→	→	SYM
ejpam-4260	269	3	1	1	NUM
ejpam-4260	269	4	:	:	PUNCT
ejpam-4260	269	5	consider	consider	VERB
ejpam-4260	269	6	△	△	PROPN
ejpam-4260	269	7	as	as	ADP
ejpam-4260	269	8	a	a	DET
ejpam-4260	269	9	supra	supra	PROPN
ejpam-4260	269	10	b	b	NOUN
ejpam-4260	269	11	-	-	PUNCT
ejpam-4260	269	12	closed	closed	ADJ
ejpam-4260	269	13	subset	subset	NOUN
ejpam-4260	269	14	of	of	ADP
ejpam-4260	269	15	u	u	PROPN
ejpam-4260	269	16	×	×	PROPN
ejpam-4260	269	17	u	u	PROPN
ejpam-4260	269	18	.	.	PUNCT
ejpam-4260	270	1	for	for	ADP
ejpam-4260	270	2	ξ	ξ	PROPN
ejpam-4260	270	3	̸=	̸=	PROPN
ejpam-4260	270	4	ζ	ζ	NOUN
ejpam-4260	270	5	∈	∈	PROPN
ejpam-4260	270	6	u	u	NOUN
ejpam-4260	270	7	,	,	PUNCT
ejpam-4260	270	8	we	we	PRON
ejpam-4260	270	9	have	have	VERB
ejpam-4260	270	10	u	u	PRON
ejpam-4260	270	11	×	×	PROPN
ejpam-4260	270	12	u	u	NOUN
ejpam-4260	270	13	−	−	PROPN
ejpam-4260	270	14	△	△	PROPN
ejpam-4260	270	15	is	be	AUX
ejpam-4260	270	16	a	a	DET
ejpam-4260	270	17	supra	supra	PROPN
ejpam-4260	270	18	b	b	NOUN
ejpam-4260	270	19	-	-	PUNCT
ejpam-4260	270	20	open	open	ADJ
ejpam-4260	270	21	set	set	NOUN
ejpam-4260	270	22	including	include	VERB
ejpam-4260	270	23	(	(	PUNCT
ejpam-4260	270	24	ξ	ξ	PROPN
ejpam-4260	270	25	,	,	PUNCT
ejpam-4260	270	26	ζ	ζ	NOUN
ejpam-4260	270	27	)	)	PUNCT
ejpam-4260	270	28	.	.	PUNCT
ejpam-4260	271	1	so	so	ADV
ejpam-4260	271	2	that	that	SCONJ
ejpam-4260	271	3	,	,	PUNCT
ejpam-4260	271	4	there	there	PRON
ejpam-4260	271	5	are	be	VERB
ejpam-4260	271	6	supra	supra	ADJ
ejpam-4260	271	7	b	b	NOUN
ejpam-4260	271	8	-	-	PUNCT
ejpam-4260	271	9	open	open	ADJ
ejpam-4260	271	10	subsets	subset	NOUN
ejpam-4260	271	11	θ	θ	PROPN
ejpam-4260	271	12	and	and	CCONJ
ejpam-4260	271	13	o	o	PROPN
ejpam-4260	271	14	of	of	ADP
ejpam-4260	271	15	(	(	PUNCT
ejpam-4260	271	16	u	u	PROPN
ejpam-4260	271	17	,	,	PUNCT
ejpam-4260	271	18	ω	ω	PROPN
ejpam-4260	271	19	)	)	PUNCT
ejpam-4260	271	20	such	such	ADJ
ejpam-4260	271	21	that	that	SCONJ
ejpam-4260	271	22	(	(	PUNCT
ejpam-4260	271	23	ξ	ξ	PROPN
ejpam-4260	271	24	,	,	PUNCT
ejpam-4260	271	25	ζ	ζ	NOUN
ejpam-4260	271	26	)	)	PUNCT
ejpam-4260	271	27	∈	∈	PROPN
ejpam-4260	271	28	θ	θ	X
ejpam-4260	271	29	×	×	NOUN
ejpam-4260	271	30	o	o	NOUN
ejpam-4260	271	31	⊆	⊆	NUM
ejpam-4260	271	32	u	u	NOUN
ejpam-4260	271	33	×	×	PROPN
ejpam-4260	271	34	u	u	NOUN
ejpam-4260	271	35	−	−	PROPN
ejpam-4260	271	36	△	△	PROPN
ejpam-4260	271	37	.	.	PUNCT
ejpam-4260	272	1	thus	thus	ADV
ejpam-4260	272	2	,	,	PUNCT
ejpam-4260	272	3	θ	θ	PROPN
ejpam-4260	272	4	and	and	CCONJ
ejpam-4260	272	5	o	o	PROPN
ejpam-4260	272	6	are	be	AUX
ejpam-4260	272	7	disjoint	disjoint	ADJ
ejpam-4260	272	8	supra	supra	PROPN
ejpam-4260	272	9	b	b	NOUN
ejpam-4260	272	10	-	-	PUNCT
ejpam-4260	272	11	open	open	ADJ
ejpam-4260	272	12	sets	set	NOUN
ejpam-4260	272	13	respectively	respectively	ADV
ejpam-4260	272	14	including	include	VERB
ejpam-4260	272	15	ξ	ξ	PROPN
ejpam-4260	272	16	and	and	CCONJ
ejpam-4260	272	17	ζ	ζ	NOUN
ejpam-4260	272	18	.	.	PUNCT
ejpam-4260	273	1	this	this	PRON
ejpam-4260	273	2	ends	end	VERB
ejpam-4260	273	3	the	the	DET
ejpam-4260	273	4	proof	proof	NOUN
ejpam-4260	273	5	that	that	SCONJ
ejpam-4260	273	6	(	(	PUNCT
ejpam-4260	273	7	u	u	NOUN
ejpam-4260	273	8	,	,	PUNCT
ejpam-4260	273	9	ω	ω	PROPN
ejpam-4260	273	10	)	)	PUNCT
ejpam-4260	273	11	is	be	AUX
ejpam-4260	273	12	sbt2	sbt2	PROPN
ejpam-4260	273	13	.	.	PUNCT
ejpam-4260	274	1	theorem	theorem	VERB
ejpam-4260	274	2	8	8	NUM
ejpam-4260	274	3	.	.	PUNCT
ejpam-4260	275	1	the	the	DET
ejpam-4260	275	2	next	next	ADJ
ejpam-4260	275	3	three	three	NUM
ejpam-4260	275	4	properties	property	NOUN
ejpam-4260	275	5	are	be	AUX
ejpam-4260	275	6	identical	identical	ADJ
ejpam-4260	275	7	.	.	PUNCT
ejpam-4260	276	1	(	(	PUNCT
ejpam-4260	276	2	i	i	NOUN
ejpam-4260	276	3	)	)	PUNCT
ejpam-4260	276	4	(	(	PUNCT
ejpam-4260	276	5	u	u	NOUN
ejpam-4260	276	6	,	,	PUNCT
ejpam-4260	276	7	ω	ω	PROPN
ejpam-4260	276	8	)	)	PUNCT
ejpam-4260	276	9	is	be	AUX
ejpam-4260	276	10	a	a	DET
ejpam-4260	276	11	supra	supra	PROPN
ejpam-4260	276	12	b	b	PROPN
ejpam-4260	276	13	regular	regular	ADJ
ejpam-4260	276	14	space	space	NOUN
ejpam-4260	276	15	;	;	PUNCT
ejpam-4260	276	16	(	(	PUNCT
ejpam-4260	276	17	ii	ii	NOUN
ejpam-4260	276	18	)	)	PUNCT
ejpam-4260	276	19	for	for	ADP
ejpam-4260	276	20	every	every	DET
ejpam-4260	276	21	supra	supra	PROPN
ejpam-4260	276	22	b	b	PROPN
ejpam-4260	276	23	-	-	PUNCT
ejpam-4260	276	24	open	open	VERB
ejpam-4260	276	25	subset	subset	NOUN
ejpam-4260	276	26	o	o	NOUN
ejpam-4260	276	27	of	of	ADP
ejpam-4260	276	28	(	(	PUNCT
ejpam-4260	276	29	u	u	PROPN
ejpam-4260	276	30	,	,	PUNCT
ejpam-4260	276	31	ω	ω	PROPN
ejpam-4260	276	32	)	)	PUNCT
ejpam-4260	276	33	including	include	VERB
ejpam-4260	276	34	ξ	ξ	PROPN
ejpam-4260	276	35	,	,	PUNCT
ejpam-4260	276	36	there	there	PRON
ejpam-4260	276	37	is	be	VERB
ejpam-4260	276	38	a	a	DET
ejpam-4260	276	39	supra	supra	PROPN
ejpam-4260	276	40	b	b	NOUN
ejpam-4260	276	41	-	-	PUNCT
ejpam-4260	276	42	open	open	VERB
ejpam-4260	276	43	subset	subset	NOUN
ejpam-4260	276	44	v	v	NOUN
ejpam-4260	276	45	of	of	ADP
ejpam-4260	276	46	(	(	PUNCT
ejpam-4260	276	47	u	u	PROPN
ejpam-4260	276	48	,	,	PUNCT
ejpam-4260	276	49	ω	ω	PROPN
ejpam-4260	276	50	)	)	PUNCT
ejpam-4260	276	51	such	such	ADJ
ejpam-4260	276	52	that	that	SCONJ
ejpam-4260	276	53	ξ	ξ	PROPN
ejpam-4260	276	54	∈	∈	PROPN
ejpam-4260	276	55	v	v	ADP
ejpam-4260	276	56	⊆	⊆	NUM
ejpam-4260	276	57	bcl(v	bcl(v	X
ejpam-4260	276	58	)	)	PUNCT
ejpam-4260	276	59	⊆	⊆	NUM
ejpam-4260	276	60	o	o	NOUN
ejpam-4260	276	61	;	;	PUNCT
ejpam-4260	276	62	(	(	PUNCT
ejpam-4260	276	63	iii	iii	X
ejpam-4260	276	64	)	)	PUNCT
ejpam-4260	276	65	every	every	DET
ejpam-4260	276	66	supra	supra	PROPN
ejpam-4260	276	67	b	b	X
ejpam-4260	276	68	-	-	PUNCT
ejpam-4260	276	69	open	open	VERB
ejpam-4260	276	70	subset	subset	NOUN
ejpam-4260	276	71	o	o	NOUN
ejpam-4260	276	72	of	of	ADP
ejpam-4260	276	73	(	(	PUNCT
ejpam-4260	276	74	u	u	PROPN
ejpam-4260	276	75	,	,	PUNCT
ejpam-4260	276	76	ω	ω	PROPN
ejpam-4260	276	77	)	)	PUNCT
ejpam-4260	276	78	is	be	AUX
ejpam-4260	276	79	written	write	VERB
ejpam-4260	276	80	:	:	PUNCT
ejpam-4260	276	81	o	o	X
ejpam-4260	276	82	=	=	PUNCT
ejpam-4260	276	83	⋃	⋃	NOUN
ejpam-4260	276	84	{	{	PUNCT
ejpam-4260	276	85	h	h	NOUN
ejpam-4260	276	86	:	:	PUNCT
ejpam-4260	276	87	h	h	NOUN
ejpam-4260	276	88	is	be	AUX
ejpam-4260	276	89	a	a	DET
ejpam-4260	276	90	supra	supra	PROPN
ejpam-4260	276	91	b	b	NOUN
ejpam-4260	276	92	-	-	PUNCT
ejpam-4260	276	93	open	open	ADJ
ejpam-4260	276	94	subset	subset	NOUN
ejpam-4260	276	95	of	of	ADP
ejpam-4260	276	96	(	(	PUNCT
ejpam-4260	276	97	u	u	PROPN
ejpam-4260	276	98	,	,	PUNCT
ejpam-4260	276	99	ω	ω	PROPN
ejpam-4260	276	100	)	)	PUNCT
ejpam-4260	276	101	and	and	CCONJ
ejpam-4260	276	102	bcl(h	bcl(h	PROPN
ejpam-4260	276	103	)	)	PUNCT
ejpam-4260	276	104	⊆	⊆	NUM
ejpam-4260	276	105	o	o	NOUN
ejpam-4260	276	106	}	}	PUNCT
ejpam-4260	276	107	.	.	PUNCT
ejpam-4260	277	1	proof	proof	NOUN
ejpam-4260	277	2	.	.	PUNCT
ejpam-4260	278	1	1	1	NUM
ejpam-4260	278	2	→	→	SYM
ejpam-4260	278	3	2	2	NUM
ejpam-4260	278	4	:	:	PUNCT
ejpam-4260	278	5	let	let	VERB
ejpam-4260	278	6	o	o	NOUN
ejpam-4260	278	7	be	be	AUX
ejpam-4260	278	8	a	a	DET
ejpam-4260	278	9	supra	supra	PROPN
ejpam-4260	278	10	b	b	NOUN
ejpam-4260	278	11	-	-	PUNCT
ejpam-4260	278	12	open	open	ADJ
ejpam-4260	278	13	set	set	NOUN
ejpam-4260	278	14	such	such	ADJ
ejpam-4260	278	15	that	that	SCONJ
ejpam-4260	278	16	ξ	ξ	PROPN
ejpam-4260	278	17	∈	∈	PROPN
ejpam-4260	278	18	u	u	NOUN
ejpam-4260	278	19	.	.	PUNCT
ejpam-4260	279	1	by	by	ADP
ejpam-4260	279	2	hypothesis	hypothesis	NOUN
ejpam-4260	279	3	,	,	PUNCT
ejpam-4260	279	4	there	there	ADV
ejpam-4260	279	5	it	it	PRON
ejpam-4260	279	6	disjoint	disjoint	VERB
ejpam-4260	279	7	supra	supra	PROPN
ejpam-4260	279	8	b	b	NOUN
ejpam-4260	279	9	-	-	PUNCT
ejpam-4260	279	10	open	open	ADJ
ejpam-4260	279	11	sets	set	NOUN
ejpam-4260	279	12	v	v	ADP
ejpam-4260	279	13	and	and	CCONJ
ejpam-4260	279	14	w	w	NOUN
ejpam-4260	279	15	respectively	respectively	ADV
ejpam-4260	279	16	including	include	VERB
ejpam-4260	279	17	ξ	ξ	PROPN
ejpam-4260	279	18	and	and	CCONJ
ejpam-4260	279	19	oc	oc	PROPN
ejpam-4260	279	20	.	.	PUNCT
ejpam-4260	280	1	so	so	ADV
ejpam-4260	280	2	that	that	SCONJ
ejpam-4260	280	3	,	,	PUNCT
ejpam-4260	280	4	ξ	ξ	PROPN
ejpam-4260	280	5	∈	∈	PROPN
ejpam-4260	280	6	v	v	ADP
ejpam-4260	280	7	⊆	⊆	NUM
ejpam-4260	280	8	w	w	NOUN
ejpam-4260	280	9	c	c	NOUN
ejpam-4260	280	10	⊆	⊆	NUM
ejpam-4260	280	11	o.	o.	NOUN
ejpam-4260	280	12	hence	hence	ADV
ejpam-4260	280	13	,	,	PUNCT
ejpam-4260	280	14	ξ	ξ	PROPN
ejpam-4260	280	15	∈	∈	PROPN
ejpam-4260	280	16	v	v	ADP
ejpam-4260	280	17	⊆	⊆	NUM
ejpam-4260	280	18	bcl(v	bcl(v	X
ejpam-4260	280	19	)	)	PUNCT
ejpam-4260	280	20	⊆	⊆	NUM
ejpam-4260	280	21	o.	o.	NOUN
ejpam-4260	280	22	2	2	NUM
ejpam-4260	280	23	→	→	SYM
ejpam-4260	280	24	3	3	NUM
ejpam-4260	280	25	:	:	PUNCT
ejpam-4260	280	26	let	let	VERB
ejpam-4260	280	27	o	o	NOUN
ejpam-4260	280	28	be	be	AUX
ejpam-4260	280	29	a	a	DET
ejpam-4260	280	30	supra	supra	PROPN
ejpam-4260	280	31	b	b	NOUN
ejpam-4260	280	32	-	-	PUNCT
ejpam-4260	280	33	open	open	ADJ
ejpam-4260	280	34	set	set	NOUN
ejpam-4260	280	35	.	.	PUNCT
ejpam-4260	281	1	by	by	ADP
ejpam-4260	281	2	hypothesise	hypothesise	NOUN
ejpam-4260	281	3	,	,	PUNCT
ejpam-4260	281	4	for	for	ADP
ejpam-4260	281	5	each	each	PRON
ejpam-4260	281	6	ξ	ξ	PROPN
ejpam-4260	281	7	∈	∈	PROPN
ejpam-4260	281	8	o	o	NOUN
ejpam-4260	281	9	,	,	PUNCT
ejpam-4260	281	10	there	there	PRON
ejpam-4260	281	11	exists	exist	VERB
ejpam-4260	281	12	a	a	DET
ejpam-4260	281	13	supra	supra	PROPN
ejpam-4260	281	14	b	b	NOUN
ejpam-4260	281	15	-	-	PUNCT
ejpam-4260	281	16	open	open	ADJ
ejpam-4260	281	17	set	set	ADJ
ejpam-4260	281	18	h	h	NOUN
ejpam-4260	281	19	such	such	ADJ
ejpam-4260	281	20	that	that	SCONJ
ejpam-4260	281	21	ξ	ξ	PROPN
ejpam-4260	281	22	∈	∈	PROPN
ejpam-4260	281	23	h	h	NOUN
ejpam-4260	281	24	⊆	⊆	NUM
ejpam-4260	281	25	bcl(h	bcl(h	PROPN
ejpam-4260	281	26	)	)	PUNCT
ejpam-4260	281	27	⊆	⊆	NUM
ejpam-4260	281	28	o.	o.	NOUN
ejpam-4260	281	29	thus	thus	ADV
ejpam-4260	281	30	,	,	PUNCT
ejpam-4260	281	31	o	o	X
ejpam-4260	282	1	=	=	PUNCT
ejpam-4260	282	2	⋃	⋃	NOUN
ejpam-4260	282	3	{	{	PUNCT
ejpam-4260	282	4	h	h	NOUN
ejpam-4260	282	5	:	:	PUNCT
ejpam-4260	282	6	h	h	NOUN
ejpam-4260	282	7	is	be	AUX
ejpam-4260	282	8	supra	supra	PROPN
ejpam-4260	282	9	b	b	NOUN
ejpam-4260	282	10	-	-	PUNCT
ejpam-4260	282	11	open	open	ADJ
ejpam-4260	282	12	and	and	CCONJ
ejpam-4260	282	13	bcl(h	bcl(h	PROPN
ejpam-4260	282	14	)	)	PUNCT
ejpam-4260	282	15	⊆	⊆	NUM
ejpam-4260	282	16	o	o	NOUN
ejpam-4260	282	17	}	}	PUNCT
ejpam-4260	282	18	.	.	PUNCT
ejpam-4260	283	1	3	3	NUM
ejpam-4260	283	2	→	→	SYM
ejpam-4260	283	3	1	1	NUM
ejpam-4260	283	4	:	:	PUNCT
ejpam-4260	283	5	suppose	suppose	VERB
ejpam-4260	283	6	that	that	SCONJ
ejpam-4260	283	7	f	f	PROPN
ejpam-4260	283	8	is	be	AUX
ejpam-4260	283	9	a	a	DET
ejpam-4260	283	10	supra	supra	PROPN
ejpam-4260	283	11	b	b	NOUN
ejpam-4260	283	12	-	-	PUNCT
ejpam-4260	283	13	closed	closed	ADJ
ejpam-4260	283	14	set	set	NOUN
ejpam-4260	283	15	such	such	ADJ
ejpam-4260	283	16	that	that	SCONJ
ejpam-4260	283	17	ξ	ξ	PROPN
ejpam-4260	283	18	̸∈	̸∈	PROPN
ejpam-4260	283	19	f	f	PROPN
ejpam-4260	283	20	.	.	PUNCT
ejpam-4260	284	1	then	then	ADV
ejpam-4260	284	2	f	f	PROPN
ejpam-4260	284	3	c	c	PROPN
ejpam-4260	284	4	=	=	PUNCT
ejpam-4260	284	5	⋃	⋃	NOUN
ejpam-4260	284	6	{	{	PUNCT
ejpam-4260	284	7	h	h	NOUN
ejpam-4260	284	8	:	:	PUNCT
ejpam-4260	284	9	h	h	NOUN
ejpam-4260	284	10	is	be	AUX
ejpam-4260	284	11	supra	supra	PROPN
ejpam-4260	284	12	b	b	NOUN
ejpam-4260	284	13	-	-	PUNCT
ejpam-4260	284	14	open	open	ADJ
ejpam-4260	284	15	and	and	CCONJ
ejpam-4260	284	16	bcl(h	bcl(h	PROPN
ejpam-4260	284	17	)	)	PUNCT
ejpam-4260	284	18	⊆	⊆	NUM
ejpam-4260	284	19	f	f	NOUN
ejpam-4260	284	20	c	c	NOUN
ejpam-4260	284	21	}	}	PUNCT
ejpam-4260	284	22	.	.	PUNCT
ejpam-4260	285	1	since	since	SCONJ
ejpam-4260	285	2	ξ	ξ	PROPN
ejpam-4260	285	3	∈	∈	PROPN
ejpam-4260	285	4	f	f	X
ejpam-4260	285	5	c	c	NOUN
ejpam-4260	285	6	,	,	PUNCT
ejpam-4260	285	7	there	there	PRON
ejpam-4260	285	8	is	be	VERB
ejpam-4260	285	9	a	a	DET
ejpam-4260	285	10	supra	supra	PROPN
ejpam-4260	285	11	b	b	NOUN
ejpam-4260	285	12	-	-	PUNCT
ejpam-4260	285	13	open	open	ADJ
ejpam-4260	285	14	set	set	NOUN
ejpam-4260	285	15	hξ	hξ	NOUN
ejpam-4260	285	16	including	include	VERB
ejpam-4260	285	17	ξ	ξ	PROPN
ejpam-4260	285	18	such	such	ADJ
ejpam-4260	285	19	that	that	DET
ejpam-4260	285	20	bcl(hξ	bcl(hξ	NOUN
ejpam-4260	285	21	)	)	PUNCT
ejpam-4260	286	1	⊆	⊆	NUM
ejpam-4260	286	2	f	f	PROPN
ejpam-4260	286	3	c.	c.	PROPN
ejpam-4260	286	4	put	put	VERB
ejpam-4260	286	5	v	v	NOUN
ejpam-4260	286	6	=	=	SYM
ejpam-4260	286	7	(	(	PUNCT
ejpam-4260	286	8	bcl(hξ	bcl(hξ	NOUN
ejpam-4260	286	9	)	)	PUNCT
ejpam-4260	286	10	)	)	PUNCT
ejpam-4260	287	1	c	c	X
ejpam-4260	287	2	;	;	PUNCT
ejpam-4260	287	3	this	this	PRON
ejpam-4260	287	4	means	mean	VERB
ejpam-4260	287	5	that	that	SCONJ
ejpam-4260	287	6	v	v	NOUN
ejpam-4260	287	7	is	be	AUX
ejpam-4260	287	8	a	a	DET
ejpam-4260	287	9	supra	supra	PROPN
ejpam-4260	287	10	b	b	NOUN
ejpam-4260	287	11	-	-	PUNCT
ejpam-4260	287	12	open	open	ADJ
ejpam-4260	287	13	set	set	NOUN
ejpam-4260	287	14	including	include	VERB
ejpam-4260	287	15	f	f	PROPN
ejpam-4260	287	16	.	.	PUNCT
ejpam-4260	288	1	thus	thus	ADV
ejpam-4260	288	2	,	,	PUNCT
ejpam-4260	288	3	v	v	ADP
ejpam-4260	288	4	⋂	⋂	PROPN
ejpam-4260	288	5	hξ	hξ	NOUN
ejpam-4260	288	6	=	=	NOUN
ejpam-4260	288	7	∅	∅	NOUN
ejpam-4260	288	8	,	,	PUNCT
ejpam-4260	288	9	which	which	PRON
ejpam-4260	288	10	finishes	finish	VERB
ejpam-4260	288	11	the	the	DET
ejpam-4260	288	12	proof	proof	NOUN
ejpam-4260	288	13	.	.	PUNCT
ejpam-4260	289	1	a.	a.	PROPN
ejpam-4260	289	2	mhemdi	mhemdi	PROPN
ejpam-4260	289	3	et	et	PROPN
ejpam-4260	289	4	al	al	PROPN
ejpam-4260	289	5	.	.	PUNCT
ejpam-4260	289	6	/	/	SYM
ejpam-4260	289	7	eur	eur	PROPN
ejpam-4260	289	8	.	.	PUNCT
ejpam-4260	290	1	j.	j.	PROPN
ejpam-4260	290	2	pure	pure	PROPN
ejpam-4260	290	3	appl	appl	PROPN
ejpam-4260	290	4	.	.	PROPN
ejpam-4260	290	5	math	math	PROPN
ejpam-4260	290	6	,	,	PUNCT
ejpam-4260	290	7	15	15	NUM
ejpam-4260	290	8	(	(	PUNCT
ejpam-4260	290	9	1	1	NUM
ejpam-4260	290	10	)	)	PUNCT
ejpam-4260	290	11	(	(	PUNCT
ejpam-4260	290	12	2022	2022	NUM
ejpam-4260	290	13	)	)	PUNCT
ejpam-4260	290	14	,	,	PUNCT
ejpam-4260	290	15	15	15	NUM
ejpam-4260	290	16	-	-	SYM
ejpam-4260	290	17	29	29	NUM
ejpam-4260	290	18	24	24	NUM
ejpam-4260	290	19	theorem	theorem	NOUN
ejpam-4260	290	20	9	9	NUM
ejpam-4260	290	21	.	.	PUNCT
ejpam-4260	291	1	the	the	DET
ejpam-4260	291	2	concepts	concept	NOUN
ejpam-4260	291	3	of	of	ADP
ejpam-4260	291	4	sbt2	sbt2	PROPN
ejpam-4260	291	5	,	,	PUNCT
ejpam-4260	291	6	sbt1	sbt1	PROPN
ejpam-4260	291	7	and	and	CCONJ
ejpam-4260	291	8	sbt0	sbt0	PROPN
ejpam-4260	291	9	are	be	AUX
ejpam-4260	291	10	equivalent	equivalent	ADJ
ejpam-4260	291	11	under	under	ADP
ejpam-4260	291	12	a	a	DET
ejpam-4260	291	13	supra	supra	PROPN
ejpam-4260	291	14	b	b	PROPN
ejpam-4260	291	15	regular	regular	ADJ
ejpam-4260	291	16	space	space	NOUN
ejpam-4260	291	17	.	.	PUNCT
ejpam-4260	292	1	proof	proof	NOUN
ejpam-4260	292	2	.	.	PUNCT
ejpam-4260	293	1	the	the	DET
ejpam-4260	293	2	directions	direction	NOUN
ejpam-4260	293	3	sbt2	sbt2	PROPN
ejpam-4260	293	4	⇒	⇒	PROPN
ejpam-4260	293	5	sbt1	sbt1	PROPN
ejpam-4260	293	6	⇒	⇒	PROPN
ejpam-4260	293	7	sbt0	sbt0	PROPN
ejpam-4260	293	8	are	be	AUX
ejpam-4260	293	9	clear	clear	ADJ
ejpam-4260	293	10	.	.	PUNCT
ejpam-4260	294	1	to	to	PART
ejpam-4260	294	2	obtain	obtain	VERB
ejpam-4260	294	3	the	the	DET
ejpam-4260	294	4	desired	desire	VERB
ejpam-4260	294	5	result	result	NOUN
ejpam-4260	294	6	,	,	PUNCT
ejpam-4260	294	7	we	we	PRON
ejpam-4260	294	8	prove	prove	VERB
ejpam-4260	294	9	that	that	SCONJ
ejpam-4260	294	10	sbt0	sbt0	PROPN
ejpam-4260	294	11	⇒	⇒	VERB
ejpam-4260	294	12	sbt2	sbt2	PROPN
ejpam-4260	294	13	.	.	PUNCT
ejpam-4260	295	1	to	to	ADP
ejpam-4260	295	2	this	this	DET
ejpam-4260	295	3	end	end	NOUN
ejpam-4260	295	4	,	,	PUNCT
ejpam-4260	295	5	let	let	VERB
ejpam-4260	295	6	ξ	ξ	ADJ
ejpam-4260	295	7	̸=	̸=	PROPN
ejpam-4260	295	8	ζ	ζ	NOUN
ejpam-4260	295	9	∈	∈	PROPN
ejpam-4260	295	10	u	u	NOUN
ejpam-4260	295	11	.	.	PUNCT
ejpam-4260	296	1	it	it	PRON
ejpam-4260	296	2	follows	follow	VERB
ejpam-4260	296	3	from	from	ADP
ejpam-4260	296	4	theorem	theorem	ADJ
ejpam-4260	296	5	(	(	PUNCT
ejpam-4260	296	6	4	4	NUM
ejpam-4260	296	7	)	)	PUNCT
ejpam-4260	296	8	that	that	PRON
ejpam-4260	296	9	bcl{ξ	bcl{ξ	VERB
ejpam-4260	296	10	}	}	PUNCT
ejpam-4260	296	11	=	=	NOUN
ejpam-4260	296	12	̸	̸	NUM
ejpam-4260	296	13	bcl{ζ	bcl{ζ	NOUN
ejpam-4260	296	14	}	}	PUNCT
ejpam-4260	296	15	.	.	PUNCT
ejpam-4260	297	1	so	so	ADV
ejpam-4260	297	2	that	that	SCONJ
ejpam-4260	297	3	,	,	PUNCT
ejpam-4260	297	4	ξ	ξ	PROPN
ejpam-4260	297	5	̸∈	̸∈	PROPN
ejpam-4260	297	6	bcl{ζ	bcl{ζ	PROPN
ejpam-4260	297	7	}	}	PUNCT
ejpam-4260	297	8	or	or	CCONJ
ejpam-4260	297	9	ζ	ζ	PRON
ejpam-4260	297	10	̸∈	̸∈	PROPN
ejpam-4260	297	11	bcl{ξ	bcl{ξ	NOUN
ejpam-4260	297	12	}	}	PUNCT
ejpam-4260	297	13	.	.	PUNCT
ejpam-4260	298	1	consider	consider	VERB
ejpam-4260	298	2	ξ	ξ	X
ejpam-4260	298	3	̸∈	̸∈	PROPN
ejpam-4260	298	4	bcl{ζ	bcl{ζ	NOUN
ejpam-4260	298	5	}	}	PUNCT
ejpam-4260	298	6	.	.	PUNCT
ejpam-4260	299	1	by	by	ADP
ejpam-4260	299	2	the	the	DET
ejpam-4260	299	3	condition	condition	NOUN
ejpam-4260	299	4	of	of	ADP
ejpam-4260	299	5	supra	supra	PROPN
ejpam-4260	299	6	b	b	PROPN
ejpam-4260	299	7	regularity	regularity	NOUN
ejpam-4260	299	8	,	,	PUNCT
ejpam-4260	299	9	there	there	PRON
ejpam-4260	299	10	are	be	VERB
ejpam-4260	299	11	disjoint	disjoint	ADJ
ejpam-4260	299	12	supra	supra	PROPN
ejpam-4260	299	13	b	b	NOUN
ejpam-4260	299	14	-	-	PUNCT
ejpam-4260	299	15	open	open	ADJ
ejpam-4260	299	16	sets	set	NOUN
ejpam-4260	299	17	θ	θ	PROPN
ejpam-4260	299	18	and	and	CCONJ
ejpam-4260	299	19	o	o	PROPN
ejpam-4260	299	20	respectively	respectively	ADV
ejpam-4260	299	21	including	include	VERB
ejpam-4260	299	22	ξ	ξ	PROPN
ejpam-4260	299	23	and	and	CCONJ
ejpam-4260	299	24	bcl{ζ	bcl{ζ	NOUN
ejpam-4260	299	25	}	}	PUNCT
ejpam-4260	299	26	.	.	PUNCT
ejpam-4260	300	1	hence	hence	ADV
ejpam-4260	300	2	,	,	PUNCT
ejpam-4260	300	3	the	the	DET
ejpam-4260	300	4	proof	proof	NOUN
ejpam-4260	300	5	is	be	AUX
ejpam-4260	300	6	complete	complete	ADJ
ejpam-4260	300	7	.	.	PUNCT
ejpam-4260	301	1	theorem	theorem	ADJ
ejpam-4260	301	2	10	10	NUM
ejpam-4260	301	3	.	.	PUNCT
ejpam-4260	302	1	the	the	DET
ejpam-4260	302	2	next	next	ADJ
ejpam-4260	302	3	properties	property	NOUN
ejpam-4260	302	4	are	be	AUX
ejpam-4260	302	5	identical	identical	ADJ
ejpam-4260	302	6	.	.	PUNCT
ejpam-4260	303	1	(	(	PUNCT
ejpam-4260	303	2	i	i	NOUN
ejpam-4260	303	3	)	)	PUNCT
ejpam-4260	303	4	(	(	PUNCT
ejpam-4260	303	5	u	u	NOUN
ejpam-4260	303	6	,	,	PUNCT
ejpam-4260	303	7	ω	ω	PROPN
ejpam-4260	303	8	)	)	PUNCT
ejpam-4260	303	9	is	be	AUX
ejpam-4260	303	10	a	a	DET
ejpam-4260	303	11	supra	supra	PROPN
ejpam-4260	303	12	b	b	PROPN
ejpam-4260	303	13	normal	normal	ADJ
ejpam-4260	303	14	space	space	NOUN
ejpam-4260	303	15	;	;	PUNCT
ejpam-4260	303	16	(	(	PUNCT
ejpam-4260	303	17	ii	ii	NOUN
ejpam-4260	303	18	)	)	PUNCT
ejpam-4260	303	19	for	for	ADP
ejpam-4260	303	20	every	every	DET
ejpam-4260	303	21	supra	supra	PROPN
ejpam-4260	303	22	b	b	PROPN
ejpam-4260	303	23	-	-	PUNCT
ejpam-4260	303	24	closed	closed	ADJ
ejpam-4260	303	25	set	set	VERB
ejpam-4260	303	26	f	f	PROPN
ejpam-4260	303	27	and	and	CCONJ
ejpam-4260	303	28	supra	supra	PROPN
ejpam-4260	303	29	b	b	X
ejpam-4260	303	30	-	-	PUNCT
ejpam-4260	303	31	open	open	ADJ
ejpam-4260	303	32	set	set	ADJ
ejpam-4260	303	33	o	o	NOUN
ejpam-4260	303	34	including	include	VERB
ejpam-4260	303	35	f	f	PROPN
ejpam-4260	303	36	,	,	PUNCT
ejpam-4260	303	37	there	there	PRON
ejpam-4260	303	38	is	be	VERB
ejpam-4260	303	39	a	a	DET
ejpam-4260	303	40	supra	supra	PROPN
ejpam-4260	303	41	b	b	NOUN
ejpam-4260	303	42	-	-	PUNCT
ejpam-4260	303	43	open	open	ADJ
ejpam-4260	303	44	set	set	NOUN
ejpam-4260	303	45	v	v	ADP
ejpam-4260	304	1	such	such	ADJ
ejpam-4260	304	2	that	that	SCONJ
ejpam-4260	304	3	f	f	PROPN
ejpam-4260	304	4	⊆	⊆	NUM
ejpam-4260	304	5	v	v	ADP
ejpam-4260	304	6	⊆	⊆	NUM
ejpam-4260	304	7	bcl(v	bcl(v	NOUN
ejpam-4260	304	8	)	)	PUNCT
ejpam-4260	304	9	⊆	⊆	NUM
ejpam-4260	304	10	o	o	NOUN
ejpam-4260	304	11	;	;	PUNCT
ejpam-4260	304	12	(	(	PUNCT
ejpam-4260	304	13	iii	iii	NOUN
ejpam-4260	304	14	)	)	PUNCT
ejpam-4260	304	15	for	for	ADP
ejpam-4260	304	16	every	every	DET
ejpam-4260	304	17	supra	supra	PROPN
ejpam-4260	304	18	b	b	PROPN
ejpam-4260	304	19	-	-	PUNCT
ejpam-4260	304	20	open	open	ADJ
ejpam-4260	304	21	sets	set	NOUN
ejpam-4260	304	22	o	o	NOUN
ejpam-4260	304	23	and	and	CCONJ
ejpam-4260	304	24	v	v	ADP
ejpam-4260	304	25	such	such	ADJ
ejpam-4260	304	26	that	that	DET
ejpam-4260	304	27	o	o	NOUN
ejpam-4260	304	28	⋃	⋃	NOUN
ejpam-4260	304	29	v	v	NOUN
ejpam-4260	304	30	=	=	SYM
ejpam-4260	304	31	u	u	NOUN
ejpam-4260	304	32	,	,	PUNCT
ejpam-4260	304	33	there	there	PRON
ejpam-4260	304	34	are	be	VERB
ejpam-4260	304	35	two	two	NUM
ejpam-4260	304	36	supra	supra	ADJ
ejpam-4260	304	37	b	b	NOUN
ejpam-4260	304	38	-	-	PUNCT
ejpam-4260	304	39	closed	closed	ADJ
ejpam-4260	304	40	sets	set	NOUN
ejpam-4260	304	41	f	f	PROPN
ejpam-4260	304	42	and	and	CCONJ
ejpam-4260	304	43	h	h	PROPN
ejpam-4260	304	44	respectively	respectively	ADV
ejpam-4260	304	45	included	include	VERB
ejpam-4260	304	46	in	in	ADP
ejpam-4260	304	47	o	o	PROPN
ejpam-4260	304	48	and	and	CCONJ
ejpam-4260	304	49	v	v	ADP
ejpam-4260	304	50	such	such	ADJ
ejpam-4260	304	51	that	that	SCONJ
ejpam-4260	304	52	f	f	PROPN
ejpam-4260	304	53	⋃	⋃	NOUN
ejpam-4260	304	54	h	h	NOUN
ejpam-4260	304	55	=	=	SYM
ejpam-4260	304	56	u	u	PROPN
ejpam-4260	304	57	.	.	PUNCT
ejpam-4260	305	1	proof	proof	NOUN
ejpam-4260	305	2	.	.	PUNCT
ejpam-4260	306	1	1	1	NUM
ejpam-4260	306	2	→	→	SYM
ejpam-4260	306	3	2	2	NUM
ejpam-4260	306	4	:	:	PUNCT
ejpam-4260	306	5	let	let	VERB
ejpam-4260	306	6	(	(	PUNCT
ejpam-4260	306	7	u	u	NOUN
ejpam-4260	306	8	,	,	PUNCT
ejpam-4260	306	9	ω	ω	PROPN
ejpam-4260	306	10	)	)	PUNCT
ejpam-4260	306	11	be	be	AUX
ejpam-4260	306	12	supra	supra	PROPN
ejpam-4260	306	13	b	b	PROPN
ejpam-4260	306	14	normal	normal	ADJ
ejpam-4260	306	15	and	and	CCONJ
ejpam-4260	306	16	f	f	PROPN
ejpam-4260	306	17	be	be	AUX
ejpam-4260	306	18	a	a	DET
ejpam-4260	306	19	supra	supra	PROPN
ejpam-4260	306	20	b	b	NOUN
ejpam-4260	306	21	-	-	PUNCT
ejpam-4260	306	22	closed	closed	ADJ
ejpam-4260	306	23	subset	subset	NOUN
ejpam-4260	306	24	of	of	ADP
ejpam-4260	306	25	a	a	DET
ejpam-4260	306	26	supra	supra	PROPN
ejpam-4260	306	27	b	b	NOUN
ejpam-4260	306	28	-	-	PUNCT
ejpam-4260	306	29	open	open	ADJ
ejpam-4260	306	30	set	set	NOUN
ejpam-4260	307	1	o.	o.	NOUN
ejpam-4260	307	2	then	then	ADV
ejpam-4260	307	3	oc	oc	VERB
ejpam-4260	307	4	and	and	CCONJ
ejpam-4260	307	5	f	f	PROPN
ejpam-4260	307	6	are	be	AUX
ejpam-4260	307	7	disjoint	disjoint	PROPN
ejpam-4260	307	8	supra	supra	PROPN
ejpam-4260	307	9	b	b	PROPN
ejpam-4260	307	10	-	-	PUNCT
ejpam-4260	307	11	closed	closed	ADJ
ejpam-4260	307	12	sets	set	NOUN
ejpam-4260	307	13	.	.	PUNCT
ejpam-4260	308	1	so	so	ADV
ejpam-4260	308	2	that	that	SCONJ
ejpam-4260	308	3	,	,	PUNCT
ejpam-4260	308	4	there	there	PRON
ejpam-4260	308	5	are	be	VERB
ejpam-4260	308	6	two	two	NUM
ejpam-4260	308	7	disjoint	disjoint	ADJ
ejpam-4260	308	8	supra	supra	PROPN
ejpam-4260	308	9	b	b	NOUN
ejpam-4260	308	10	-	-	PUNCT
ejpam-4260	308	11	open	open	ADJ
ejpam-4260	308	12	sets	set	NOUN
ejpam-4260	308	13	w	w	NOUN
ejpam-4260	308	14	and	and	CCONJ
ejpam-4260	308	15	v	v	ADP
ejpam-4260	308	16	respectively	respectively	ADV
ejpam-4260	308	17	including	include	VERB
ejpam-4260	308	18	oc	oc	NOUN
ejpam-4260	308	19	and	and	CCONJ
ejpam-4260	308	20	f	f	PROPN
ejpam-4260	308	21	.	.	PUNCT
ejpam-4260	309	1	now	now	ADV
ejpam-4260	309	2	,	,	PUNCT
ejpam-4260	309	3	f	f	PROPN
ejpam-4260	309	4	⊆	⊆	NUM
ejpam-4260	309	5	v	v	ADP
ejpam-4260	309	6	⊆	⊆	NUM
ejpam-4260	309	7	w	w	NOUN
ejpam-4260	309	8	c	c	NOUN
ejpam-4260	309	9	=	=	SYM
ejpam-4260	309	10	bcl(w	bcl(w	PROPN
ejpam-4260	309	11	c	c	X
ejpam-4260	309	12	)	)	PUNCT
ejpam-4260	309	13	⊆	⊆	NUM
ejpam-4260	309	14	o	o	NOUN
ejpam-4260	309	15	,	,	PUNCT
ejpam-4260	309	16	which	which	PRON
ejpam-4260	309	17	means	mean	VERB
ejpam-4260	309	18	that	that	SCONJ
ejpam-4260	309	19	f	f	PROPN
ejpam-4260	309	20	⊆	⊆	NUM
ejpam-4260	309	21	v	v	ADP
ejpam-4260	309	22	⊆	⊆	NUM
ejpam-4260	309	23	bcl(v	bcl(v	X
ejpam-4260	309	24	)	)	PUNCT
ejpam-4260	309	25	⊆	⊆	NUM
ejpam-4260	309	26	o.	o.	NOUN
ejpam-4260	309	27	2	2	NUM
ejpam-4260	309	28	→	→	SYM
ejpam-4260	309	29	3	3	NUM
ejpam-4260	309	30	:	:	PUNCT
ejpam-4260	309	31	let	let	VERB
ejpam-4260	309	32	o	o	NOUN
ejpam-4260	309	33	and	and	CCONJ
ejpam-4260	309	34	v	v	NOUN
ejpam-4260	309	35	be	be	AUX
ejpam-4260	309	36	supra	supra	ADJ
ejpam-4260	309	37	b	b	NOUN
ejpam-4260	309	38	-	-	PUNCT
ejpam-4260	309	39	open	open	ADJ
ejpam-4260	309	40	sets	set	NOUN
ejpam-4260	309	41	such	such	ADJ
ejpam-4260	309	42	that	that	DET
ejpam-4260	309	43	o	o	NOUN
ejpam-4260	309	44	⋃	⋃	NOUN
ejpam-4260	309	45	v	v	NOUN
ejpam-4260	309	46	=	=	SYM
ejpam-4260	309	47	u	u	NOUN
ejpam-4260	309	48	.	.	PUNCT
ejpam-4260	310	1	then	then	ADV
ejpam-4260	310	2	,	,	PUNCT
ejpam-4260	310	3	oc	oc	X
ejpam-4260	310	4	is	be	AUX
ejpam-4260	310	5	a	a	DET
ejpam-4260	310	6	supra	supra	PROPN
ejpam-4260	310	7	b	b	NOUN
ejpam-4260	310	8	-	-	PUNCT
ejpam-4260	310	9	closed	closed	ADJ
ejpam-4260	310	10	sets	set	NOUN
ejpam-4260	310	11	such	such	ADJ
ejpam-4260	310	12	that	that	DET
ejpam-4260	310	13	oc	oc	ADP
ejpam-4260	310	14	⊆	⊆	NUM
ejpam-4260	310	15	v	v	NOUN
ejpam-4260	310	16	.	.	PUNCT
ejpam-4260	311	1	by	by	ADP
ejpam-4260	311	2	2	2	NUM
ejpam-4260	311	3	,	,	PUNCT
ejpam-4260	311	4	there	there	PRON
ejpam-4260	311	5	is	be	VERB
ejpam-4260	311	6	a	a	DET
ejpam-4260	311	7	supra	supra	PROPN
ejpam-4260	311	8	b	b	NOUN
ejpam-4260	311	9	-	-	PUNCT
ejpam-4260	311	10	open	open	ADJ
ejpam-4260	311	11	set	set	NOUN
ejpam-4260	311	12	θ	θ	PROPN
ejpam-4260	311	13	such	such	ADJ
ejpam-4260	311	14	that	that	PRON
ejpam-4260	311	15	oc	oc	ADP
ejpam-4260	311	16	⊆	⊆	NUM
ejpam-4260	311	17	θ	θ	NOUN
ejpam-4260	311	18	⊆	⊆	NUM
ejpam-4260	311	19	bcl(θ	bcl(θ	NOUN
ejpam-4260	311	20	)	)	PUNCT
ejpam-4260	311	21	⊆	⊆	NUM
ejpam-4260	311	22	v	v	NOUN
ejpam-4260	311	23	.	.	PUNCT
ejpam-4260	312	1	hence	hence	ADV
ejpam-4260	312	2	,	,	PUNCT
ejpam-4260	312	3	θc	θc	VERB
ejpam-4260	312	4	⊆	⊆	NUM
ejpam-4260	312	5	o	o	NOUN
ejpam-4260	312	6	and	and	CCONJ
ejpam-4260	312	7	bcl(θ	bcl(θ	NOUN
ejpam-4260	312	8	)	)	PUNCT
ejpam-4260	312	9	⊆	⊆	NUM
ejpam-4260	312	10	v	v	NOUN
ejpam-4260	312	11	are	be	AUX
ejpam-4260	312	12	supra	supra	ADJ
ejpam-4260	312	13	b	b	NOUN
ejpam-4260	312	14	-	-	PUNCT
ejpam-4260	312	15	closed	closed	ADJ
ejpam-4260	312	16	sets	set	NOUN
ejpam-4260	312	17	such	such	ADJ
ejpam-4260	312	18	that	that	SCONJ
ejpam-4260	312	19	θc	θc	ADP
ejpam-4260	312	20	⋃	⋃	NOUN
ejpam-4260	312	21	bcl(θ	bcl(θ	NOUN
ejpam-4260	312	22	)	)	PUNCT
ejpam-4260	312	23	=	=	SYM
ejpam-4260	312	24	u	u	NOUN
ejpam-4260	312	25	.	.	PUNCT
ejpam-4260	312	26	3	3	NUM
ejpam-4260	312	27	→	→	SYM
ejpam-4260	312	28	1	1	NUM
ejpam-4260	312	29	:	:	PUNCT
ejpam-4260	312	30	let	let	VERB
ejpam-4260	312	31	f	f	PROPN
ejpam-4260	312	32	and	and	CCONJ
ejpam-4260	312	33	h	h	PROPN
ejpam-4260	312	34	be	be	AUX
ejpam-4260	312	35	disjoint	disjoint	ADJ
ejpam-4260	312	36	supra	supra	PROPN
ejpam-4260	312	37	b	b	PROPN
ejpam-4260	312	38	-	-	PUNCT
ejpam-4260	312	39	closed	closed	ADJ
ejpam-4260	312	40	sets	set	NOUN
ejpam-4260	312	41	.	.	PUNCT
ejpam-4260	313	1	since	since	SCONJ
ejpam-4260	313	2	f	f	PROPN
ejpam-4260	313	3	c	c	PROPN
ejpam-4260	313	4	and	and	CCONJ
ejpam-4260	313	5	hc	hc	PROPN
ejpam-4260	313	6	are	be	AUX
ejpam-4260	313	7	supra	supra	ADJ
ejpam-4260	313	8	open	open	ADJ
ejpam-4260	313	9	sets	set	NOUN
ejpam-4260	313	10	such	such	ADJ
ejpam-4260	313	11	that	that	SCONJ
ejpam-4260	313	12	f	f	PROPN
ejpam-4260	313	13	c	c	PROPN
ejpam-4260	313	14	⋃	⋃	NOUN
ejpam-4260	313	15	hc	hc	PROPN
ejpam-4260	313	16	=	=	SYM
ejpam-4260	313	17	u	u	PROPN
ejpam-4260	313	18	,	,	PUNCT
ejpam-4260	313	19	then	then	ADV
ejpam-4260	313	20	there	there	PRON
ejpam-4260	313	21	are	be	VERB
ejpam-4260	313	22	two	two	NUM
ejpam-4260	313	23	supra	supra	ADJ
ejpam-4260	313	24	b	b	NOUN
ejpam-4260	313	25	-	-	PUNCT
ejpam-4260	313	26	closed	close	VERB
ejpam-4260	313	27	sets	set	NOUN
ejpam-4260	313	28	m	m	VERB
ejpam-4260	313	29	and	and	CCONJ
ejpam-4260	313	30	n	n	CCONJ
ejpam-4260	313	31	such	such	ADJ
ejpam-4260	313	32	that	that	SCONJ
ejpam-4260	313	33	m	m	PROPN
ejpam-4260	313	34	⊆	⊆	NUM
ejpam-4260	313	35	f	f	PROPN
ejpam-4260	313	36	c	c	NOUN
ejpam-4260	313	37	,	,	PUNCT
ejpam-4260	313	38	n	n	PROPN
ejpam-4260	313	39	⊆	⊆	NUM
ejpam-4260	313	40	hc	hc	NOUN
ejpam-4260	313	41	and	and	CCONJ
ejpam-4260	313	42	m	m	PROPN
ejpam-4260	313	43	⋃	⋃	NOUN
ejpam-4260	313	44	n	n	NOUN
ejpam-4260	313	45	=	=	SYM
ejpam-4260	313	46	u	u	PROPN
ejpam-4260	313	47	.	.	PUNCT
ejpam-4260	314	1	thus	thus	ADV
ejpam-4260	314	2	,	,	PUNCT
ejpam-4260	314	3	m	m	PROPN
ejpam-4260	314	4	c	c	NOUN
ejpam-4260	314	5	and	and	CCONJ
ejpam-4260	314	6	n	n	PROPN
ejpam-4260	314	7	c	c	NOUN
ejpam-4260	314	8	are	be	AUX
ejpam-4260	314	9	two	two	NUM
ejpam-4260	314	10	disjoint	disjoint	ADJ
ejpam-4260	314	11	supra	supra	PROPN
ejpam-4260	314	12	b	b	NOUN
ejpam-4260	314	13	-	-	PUNCT
ejpam-4260	314	14	open	open	ADJ
ejpam-4260	314	15	sets	set	NOUN
ejpam-4260	314	16	respectively	respectively	ADV
ejpam-4260	314	17	including	include	VERB
ejpam-4260	314	18	f	f	PROPN
ejpam-4260	314	19	and	and	CCONJ
ejpam-4260	314	20	h.	h.	PROPN
ejpam-4260	314	21	this	this	PRON
ejpam-4260	314	22	ends	end	VERB
ejpam-4260	314	23	the	the	DET
ejpam-4260	314	24	proof	proof	NOUN
ejpam-4260	314	25	that	that	SCONJ
ejpam-4260	314	26	(	(	PUNCT
ejpam-4260	314	27	u	u	NOUN
ejpam-4260	314	28	,	,	PUNCT
ejpam-4260	314	29	ω	ω	PROPN
ejpam-4260	314	30	)	)	PUNCT
ejpam-4260	314	31	is	be	AUX
ejpam-4260	314	32	supra	supra	PROPN
ejpam-4260	314	33	b	b	PROPN
ejpam-4260	314	34	normal	normal	ADJ
ejpam-4260	314	35	.	.	PUNCT
ejpam-4260	315	1	theorem	theorem	VERB
ejpam-4260	315	2	11	11	NUM
ejpam-4260	315	3	.	.	PUNCT
ejpam-4260	316	1	every	every	DET
ejpam-4260	316	2	sbtk	sbtk	NOUN
ejpam-4260	316	3	-	-	PUNCT
ejpam-4260	316	4	space	space	NOUN
ejpam-4260	316	5	is	be	AUX
ejpam-4260	316	6	sbtk−1	sbtk−1	PROPN
ejpam-4260	316	7	for	for	ADP
ejpam-4260	316	8	k	k	PROPN
ejpam-4260	316	9	=	=	SYM
ejpam-4260	316	10	1	1	NUM
ejpam-4260	316	11	,	,	PUNCT
ejpam-4260	316	12	2	2	NUM
ejpam-4260	316	13	,	,	PUNCT
ejpam-4260	316	14	3	3	NUM
ejpam-4260	316	15	,	,	PUNCT
ejpam-4260	316	16	4	4	NUM
ejpam-4260	316	17	.	.	PUNCT
ejpam-4260	317	1	the	the	DET
ejpam-4260	317	2	four	four	NUM
ejpam-4260	317	3	examples	example	NOUN
ejpam-4260	317	4	below	below	ADP
ejpam-4260	317	5	elucidate	elucidate	VERB
ejpam-4260	317	6	that	that	SCONJ
ejpam-4260	317	7	the	the	DET
ejpam-4260	317	8	converse	converse	NOUN
ejpam-4260	317	9	of	of	ADP
ejpam-4260	317	10	theorem	theorem	NOUN
ejpam-4260	317	11	(	(	PUNCT
ejpam-4260	317	12	11	11	NUM
ejpam-4260	317	13	)	)	PUNCT
ejpam-4260	317	14	is	be	AUX
ejpam-4260	317	15	in	in	ADP
ejpam-4260	317	16	general	general	ADJ
ejpam-4260	317	17	false	false	ADJ
ejpam-4260	317	18	.	.	PUNCT
ejpam-4260	317	19	example	example	NOUN
ejpam-4260	318	1	5	5	NUM
ejpam-4260	318	2	.	.	PUNCT
ejpam-4260	319	1	let	let	VERB
ejpam-4260	319	2	ω	ω	NOUN
ejpam-4260	319	3	=	=	PRON
ejpam-4260	319	4	{	{	PUNCT
ejpam-4260	319	5	∅,u	∅,u	NOUN
ejpam-4260	319	6	,	,	PUNCT
ejpam-4260	319	7	{	{	PUNCT
ejpam-4260	319	8	ξ4	ξ4	NOUN
ejpam-4260	319	9	}	}	PUNCT
ejpam-4260	319	10	,	,	PUNCT
ejpam-4260	319	11	{	{	PUNCT
ejpam-4260	319	12	ξ1	ξ1	NOUN
ejpam-4260	319	13	,	,	PUNCT
ejpam-4260	319	14	ξ3	ξ3	NOUN
ejpam-4260	319	15	,	,	PUNCT
ejpam-4260	319	16	ξ4	ξ4	PROPN
ejpam-4260	319	17	}	}	PUNCT
ejpam-4260	319	18	,	,	PUNCT
ejpam-4260	319	19	{	{	PUNCT
ejpam-4260	319	20	ξ2	ξ2	NOUN
ejpam-4260	319	21	,	,	PUNCT
ejpam-4260	319	22	ξ3	ξ3	NOUN
ejpam-4260	319	23	,	,	PUNCT
ejpam-4260	319	24	ξ4	ξ4	PROPN
ejpam-4260	319	25	}	}	PUNCT
ejpam-4260	319	26	,	,	PUNCT
ejpam-4260	319	27	{	{	PUNCT
ejpam-4260	319	28	ξ1	ξ1	NOUN
ejpam-4260	319	29	,	,	PUNCT
ejpam-4260	319	30	ξ2	ξ2	NOUN
ejpam-4260	319	31	,	,	PUNCT
ejpam-4260	319	32	ξ4	ξ4	PROPN
ejpam-4260	319	33	}	}	PUNCT
ejpam-4260	319	34	}	}	PUNCT
ejpam-4260	319	35	be	be	VERB
ejpam-4260	319	36	an	an	DET
ejpam-4260	319	37	st	st	NOUN
ejpam-4260	319	38	on	on	ADP
ejpam-4260	319	39	u	u	NOUN
ejpam-4260	319	40	=	=	PUNCT
ejpam-4260	319	41	{	{	PUNCT
ejpam-4260	319	42	ξ1	ξ1	NOUN
ejpam-4260	319	43	,	,	PUNCT
ejpam-4260	319	44	ξ2	ξ2	ADJ
ejpam-4260	319	45	,	,	PUNCT
ejpam-4260	319	46	ξ3	ξ3	NOUN
ejpam-4260	319	47	,	,	PUNCT
ejpam-4260	319	48	ξ4	ξ4	PROPN
ejpam-4260	319	49	}	}	PUNCT
ejpam-4260	319	50	.	.	PUNCT
ejpam-4260	320	1	then	then	ADV
ejpam-4260	320	2	the	the	DET
ejpam-4260	320	3	class	class	NOUN
ejpam-4260	320	4	of	of	ADP
ejpam-4260	320	5	all	all	DET
ejpam-4260	320	6	supra	supra	PROPN
ejpam-4260	320	7	b	b	NOUN
ejpam-4260	320	8	-	-	PUNCT
ejpam-4260	320	9	open	open	ADJ
ejpam-4260	320	10	subsets	subset	NOUN
ejpam-4260	320	11	of	of	ADP
ejpam-4260	320	12	(	(	PUNCT
ejpam-4260	320	13	u	u	PROPN
ejpam-4260	320	14	,	,	PUNCT
ejpam-4260	320	15	ω	ω	PROPN
ejpam-4260	320	16	)	)	PUNCT
ejpam-4260	320	17	is	be	AUX
ejpam-4260	320	18	{	{	PUNCT
ejpam-4260	320	19	∅,u	∅,u	NOUN
ejpam-4260	320	20	,	,	PUNCT
ejpam-4260	320	21	{	{	PUNCT
ejpam-4260	320	22	ξ4	ξ4	NOUN
ejpam-4260	320	23	}	}	PUNCT
ejpam-4260	320	24	,	,	PUNCT
ejpam-4260	320	25	{	{	PUNCT
ejpam-4260	320	26	ξ1	ξ1	NOUN
ejpam-4260	320	27	,	,	PUNCT
ejpam-4260	320	28	ξ4	ξ4	PROPN
ejpam-4260	320	29	}	}	PUNCT
ejpam-4260	320	30	,	,	PUNCT
ejpam-4260	320	31	{	{	PUNCT
ejpam-4260	320	32	ξ2	ξ2	NOUN
ejpam-4260	320	33	,	,	PUNCT
ejpam-4260	320	34	ξ4	ξ4	PROPN
ejpam-4260	320	35	}	}	PUNCT
ejpam-4260	320	36	,	,	PUNCT
ejpam-4260	320	37	{	{	PUNCT
ejpam-4260	320	38	ξ3	ξ3	NOUN
ejpam-4260	320	39	,	,	PUNCT
ejpam-4260	320	40	ξ4	ξ4	PROPN
ejpam-4260	320	41	}	}	PUNCT
ejpam-4260	320	42	,	,	PUNCT
ejpam-4260	320	43	{	{	PUNCT
ejpam-4260	320	44	ξ1	ξ1	NOUN
ejpam-4260	320	45	,	,	PUNCT
ejpam-4260	320	46	ξ3	ξ3	NOUN
ejpam-4260	320	47	,	,	PUNCT
ejpam-4260	320	48	ξ4	ξ4	PROPN
ejpam-4260	320	49	}	}	PUNCT
ejpam-4260	320	50	,	,	PUNCT
ejpam-4260	320	51	{	{	PUNCT
ejpam-4260	320	52	ξ2	ξ2	NOUN
ejpam-4260	320	53	,	,	PUNCT
ejpam-4260	320	54	ξ3	ξ3	NOUN
ejpam-4260	320	55	,	,	PUNCT
ejpam-4260	320	56	ξ4	ξ4	PROPN
ejpam-4260	320	57	}	}	PUNCT
ejpam-4260	320	58	,	,	PUNCT
ejpam-4260	320	59	{	{	PUNCT
ejpam-4260	320	60	ξ1	ξ1	NOUN
ejpam-4260	320	61	,	,	PUNCT
ejpam-4260	320	62	ξ2	ξ2	NOUN
ejpam-4260	320	63	,	,	PUNCT
ejpam-4260	320	64	ξ4	ξ4	PROPN
ejpam-4260	320	65	}	}	PUNCT
ejpam-4260	320	66	}	}	PUNCT
ejpam-4260	320	67	.	.	PUNCT
ejpam-4260	321	1	therefore	therefore	ADV
ejpam-4260	321	2	,	,	PUNCT
ejpam-4260	321	3	(	(	PUNCT
ejpam-4260	321	4	u	u	NOUN
ejpam-4260	321	5	,	,	PUNCT
ejpam-4260	321	6	ω	ω	PROPN
ejpam-4260	321	7	)	)	PUNCT
ejpam-4260	321	8	is	be	AUX
ejpam-4260	321	9	not	not	PART
ejpam-4260	321	10	an	an	DET
ejpam-4260	321	11	sbt1space	sbt1space	NOUN
ejpam-4260	321	12	because	because	SCONJ
ejpam-4260	321	13	ξ1	ξ1	PROPN
ejpam-4260	321	14	̸=	̸=	PROPN
ejpam-4260	321	15	ξ4	ξ4	NOUN
ejpam-4260	321	16	and	and	CCONJ
ejpam-4260	321	17	all	all	DET
ejpam-4260	321	18	supra	supra	PROPN
ejpam-4260	321	19	b	b	NOUN
ejpam-4260	321	20	-	-	PUNCT
ejpam-4260	321	21	open	open	ADJ
ejpam-4260	321	22	sets	set	NOUN
ejpam-4260	321	23	including	include	VERB
ejpam-4260	321	24	ξ1	ξ1	NOUN
ejpam-4260	321	25	contain	contain	VERB
ejpam-4260	321	26	ξ4	ξ4	VERB
ejpam-4260	321	27	as	as	ADV
ejpam-4260	321	28	well	well	ADV
ejpam-4260	321	29	.	.	PUNCT
ejpam-4260	322	1	on	on	ADP
ejpam-4260	322	2	the	the	DET
ejpam-4260	322	3	other	other	ADJ
ejpam-4260	322	4	hand	hand	NOUN
ejpam-4260	322	5	,	,	PUNCT
ejpam-4260	322	6	it	it	PRON
ejpam-4260	322	7	can	can	AUX
ejpam-4260	322	8	be	be	AUX
ejpam-4260	322	9	checked	check	VERB
ejpam-4260	322	10	that	that	SCONJ
ejpam-4260	322	11	(	(	PUNCT
ejpam-4260	322	12	u	u	NOUN
ejpam-4260	322	13	,	,	PUNCT
ejpam-4260	322	14	ω	ω	PROPN
ejpam-4260	322	15	)	)	PUNCT
ejpam-4260	322	16	is	be	AUX
ejpam-4260	322	17	sbt0	sbt0	PROPN
ejpam-4260	322	18	.	.	PUNCT
ejpam-4260	323	1	example	example	NOUN
ejpam-4260	324	1	6	6	NUM
ejpam-4260	324	2	.	.	PUNCT
ejpam-4260	325	1	since	since	SCONJ
ejpam-4260	325	2	all	all	DET
ejpam-4260	325	3	singleton	singleton	NOUN
ejpam-4260	325	4	subsets	subset	NOUN
ejpam-4260	325	5	of	of	ADP
ejpam-4260	325	6	(	(	PUNCT
ejpam-4260	325	7	u	u	PROPN
ejpam-4260	325	8	,	,	PUNCT
ejpam-4260	325	9	ω	ω	PROPN
ejpam-4260	325	10	)	)	PUNCT
ejpam-4260	325	11	,	,	PUNCT
ejpam-4260	325	12	given	give	VERB
ejpam-4260	325	13	in	in	ADP
ejpam-4260	325	14	example	example	NOUN
ejpam-4260	325	15	(	(	PUNCT
ejpam-4260	325	16	1	1	NUM
ejpam-4260	325	17	)	)	PUNCT
ejpam-4260	325	18	,	,	PUNCT
ejpam-4260	325	19	are	be	AUX
ejpam-4260	325	20	supra	supra	PROPN
ejpam-4260	325	21	bclosed	bclose	VERB
ejpam-4260	325	22	,	,	PUNCT
ejpam-4260	325	23	(	(	PUNCT
ejpam-4260	325	24	u	u	NOUN
ejpam-4260	325	25	,	,	PUNCT
ejpam-4260	325	26	ω	ω	PROPN
ejpam-4260	325	27	)	)	PUNCT
ejpam-4260	325	28	is	be	AUX
ejpam-4260	325	29	sbt1	sbt1	PROPN
ejpam-4260	325	30	.	.	PUNCT
ejpam-4260	326	1	in	in	ADP
ejpam-4260	326	2	contrast	contrast	NOUN
ejpam-4260	326	3	,	,	PUNCT
ejpam-4260	326	4	(	(	PUNCT
ejpam-4260	326	5	u	u	NOUN
ejpam-4260	326	6	,	,	PUNCT
ejpam-4260	326	7	ω	ω	PROPN
ejpam-4260	326	8	)	)	PUNCT
ejpam-4260	326	9	is	be	AUX
ejpam-4260	326	10	not	not	PART
ejpam-4260	326	11	sbt2	sbt2	NOUN
ejpam-4260	326	12	because	because	SCONJ
ejpam-4260	326	13	ξ1	ξ1	PROPN
ejpam-4260	326	14	̸=	̸=	PROPN
ejpam-4260	326	15	ξ3	ξ3	PROPN
ejpam-4260	326	16	and	and	CCONJ
ejpam-4260	326	17	there	there	PRON
ejpam-4260	326	18	do	do	AUX
ejpam-4260	326	19	not	not	PART
ejpam-4260	326	20	exist	exist	VERB
ejpam-4260	326	21	disjoint	disjoint	ADJ
ejpam-4260	326	22	supra	supra	PROPN
ejpam-4260	326	23	b	b	NOUN
ejpam-4260	326	24	-	-	PUNCT
ejpam-4260	326	25	open	open	ADJ
ejpam-4260	326	26	sets	set	NOUN
ejpam-4260	326	27	such	such	ADJ
ejpam-4260	326	28	that	that	PRON
ejpam-4260	326	29	one	one	NUM
ejpam-4260	326	30	of	of	ADP
ejpam-4260	326	31	them	they	PRON
ejpam-4260	326	32	contains	contain	VERB
ejpam-4260	326	33	ξ1	ξ1	NOUN
ejpam-4260	326	34	and	and	CCONJ
ejpam-4260	326	35	the	the	DET
ejpam-4260	326	36	other	other	ADJ
ejpam-4260	326	37	contains	contain	VERB
ejpam-4260	326	38	ξ3	ξ3	NOUN
ejpam-4260	326	39	.	.	PUNCT
ejpam-4260	327	1	a.	a.	PROPN
ejpam-4260	327	2	mhemdi	mhemdi	PROPN
ejpam-4260	327	3	et	et	PROPN
ejpam-4260	327	4	al	al	PROPN
ejpam-4260	327	5	.	.	PUNCT
ejpam-4260	327	6	/	/	SYM
ejpam-4260	327	7	eur	eur	PROPN
ejpam-4260	327	8	.	.	PUNCT
ejpam-4260	328	1	j.	j.	PROPN
ejpam-4260	328	2	pure	pure	PROPN
ejpam-4260	328	3	appl	appl	PROPN
ejpam-4260	328	4	.	.	PROPN
ejpam-4260	328	5	math	math	PROPN
ejpam-4260	328	6	,	,	PUNCT
ejpam-4260	328	7	15	15	NUM
ejpam-4260	328	8	(	(	PUNCT
ejpam-4260	328	9	1	1	NUM
ejpam-4260	328	10	)	)	PUNCT
ejpam-4260	328	11	(	(	PUNCT
ejpam-4260	328	12	2022	2022	NUM
ejpam-4260	328	13	)	)	PUNCT
ejpam-4260	328	14	,	,	PUNCT
ejpam-4260	328	15	15	15	NUM
ejpam-4260	328	16	-	-	SYM
ejpam-4260	328	17	29	29	NUM
ejpam-4260	328	18	25	25	NUM
ejpam-4260	328	19	example	example	NOUN
ejpam-4260	328	20	7	7	NUM
ejpam-4260	328	21	.	.	PUNCT
ejpam-4260	329	1	let	let	VERB
ejpam-4260	329	2	ω	ω	NOUN
ejpam-4260	329	3	=	=	PRON
ejpam-4260	329	4	{	{	PUNCT
ejpam-4260	329	5	∅,u	∅,u	NOUN
ejpam-4260	329	6	,	,	PUNCT
ejpam-4260	329	7	{	{	PUNCT
ejpam-4260	329	8	ξ1	ξ1	NOUN
ejpam-4260	329	9	,	,	PUNCT
ejpam-4260	329	10	ξ2	ξ2	NOUN
ejpam-4260	329	11	}	}	PUNCT
ejpam-4260	329	12	,	,	PUNCT
ejpam-4260	329	13	{	{	PUNCT
ejpam-4260	329	14	ξ3	ξ3	NOUN
ejpam-4260	329	15	,	,	PUNCT
ejpam-4260	329	16	ξ4	ξ4	PROPN
ejpam-4260	329	17	}	}	PUNCT
ejpam-4260	329	18	,	,	PUNCT
ejpam-4260	329	19	{	{	PUNCT
ejpam-4260	329	20	ξ1	ξ1	NOUN
ejpam-4260	329	21	,	,	PUNCT
ejpam-4260	329	22	ξ3	ξ3	PROPN
ejpam-4260	329	23	}	}	PUNCT
ejpam-4260	329	24	,	,	PUNCT
ejpam-4260	329	25	{	{	PUNCT
ejpam-4260	329	26	ξ2	ξ2	NOUN
ejpam-4260	329	27	,	,	PUNCT
ejpam-4260	329	28	ξ4	ξ4	PROPN
ejpam-4260	329	29	}	}	PUNCT
ejpam-4260	329	30	,	,	PUNCT
ejpam-4260	329	31	{	{	PUNCT
ejpam-4260	329	32	ξ2	ξ2	NOUN
ejpam-4260	329	33	,	,	PUNCT
ejpam-4260	329	34	ξ3	ξ3	PROPN
ejpam-4260	329	35	}	}	PUNCT
ejpam-4260	329	36	,	,	PUNCT
ejpam-4260	329	37	{	{	PUNCT
ejpam-4260	329	38	ξ1	ξ1	NOUN
ejpam-4260	329	39	,	,	PUNCT
ejpam-4260	329	40	ξ2	ξ2	ADJ
ejpam-4260	329	41	,	,	PUNCT
ejpam-4260	329	42	ξ3	ξ3	PROPN
ejpam-4260	329	43	}	}	PUNCT
ejpam-4260	329	44	,	,	PUNCT
ejpam-4260	329	45	{	{	PUNCT
ejpam-4260	329	46	ξ1	ξ1	NOUN
ejpam-4260	329	47	,	,	PUNCT
ejpam-4260	329	48	ξ2	ξ2	NOUN
ejpam-4260	329	49	,	,	PUNCT
ejpam-4260	329	50	ξ4	ξ4	PROPN
ejpam-4260	329	51	}	}	PUNCT
ejpam-4260	329	52	,	,	PUNCT
ejpam-4260	329	53	{	{	PUNCT
ejpam-4260	329	54	ξ1	ξ1	NOUN
ejpam-4260	329	55	,	,	PUNCT
ejpam-4260	329	56	ξ3	ξ3	NOUN
ejpam-4260	329	57	,	,	PUNCT
ejpam-4260	329	58	ξ4	ξ4	PROPN
ejpam-4260	329	59	}	}	PUNCT
ejpam-4260	329	60	,	,	PUNCT
ejpam-4260	329	61	{	{	PUNCT
ejpam-4260	329	62	ξ2	ξ2	NOUN
ejpam-4260	329	63	,	,	PUNCT
ejpam-4260	329	64	ξ3	ξ3	PROPN
ejpam-4260	329	65	,	,	PUNCT
ejpam-4260	329	66	ξ4	ξ4	PROPN
ejpam-4260	329	67	}	}	PUNCT
ejpam-4260	329	68	}	}	PUNCT
ejpam-4260	329	69	be	be	VERB
ejpam-4260	329	70	an	an	DET
ejpam-4260	329	71	st	st	NOUN
ejpam-4260	329	72	on	on	ADP
ejpam-4260	329	73	u	u	NOUN
ejpam-4260	329	74	=	=	PUNCT
ejpam-4260	329	75	{	{	PUNCT
ejpam-4260	329	76	ξ1	ξ1	NOUN
ejpam-4260	329	77	,	,	PUNCT
ejpam-4260	329	78	ξ2	ξ2	ADJ
ejpam-4260	329	79	,	,	PUNCT
ejpam-4260	329	80	ξ3	ξ3	NOUN
ejpam-4260	329	81	,	,	PUNCT
ejpam-4260	329	82	ξ4	ξ4	NOUN
ejpam-4260	329	83	}	}	PUNCT
ejpam-4260	329	84	.	.	PUNCT
ejpam-4260	330	1	in	in	ADP
ejpam-4260	330	2	(	(	PUNCT
ejpam-4260	330	3	u	u	NOUN
ejpam-4260	330	4	,	,	PUNCT
ejpam-4260	330	5	ω	ω	PROPN
ejpam-4260	330	6	)	)	PUNCT
ejpam-4260	330	7	,	,	PUNCT
ejpam-4260	330	8	a	a	DET
ejpam-4260	330	9	set	set	NOUN
ejpam-4260	330	10	is	be	AUX
ejpam-4260	330	11	supra	supra	PROPN
ejpam-4260	330	12	open	open	ADJ
ejpam-4260	330	13	iff	iff	PROPN
ejpam-4260	330	14	it	it	PRON
ejpam-4260	330	15	is	be	AUX
ejpam-4260	330	16	supra	supra	ADJ
ejpam-4260	330	17	b	b	NOUN
ejpam-4260	330	18	-	-	PUNCT
ejpam-4260	330	19	open	open	ADJ
ejpam-4260	330	20	.	.	PUNCT
ejpam-4260	331	1	now	now	ADV
ejpam-4260	331	2	,	,	PUNCT
ejpam-4260	331	3	{	{	PUNCT
ejpam-4260	331	4	ξ1	ξ1	NOUN
ejpam-4260	331	5	,	,	PUNCT
ejpam-4260	331	6	ξ4	ξ4	PROPN
ejpam-4260	331	7	}	}	PUNCT
ejpam-4260	331	8	is	be	AUX
ejpam-4260	331	9	a	a	DET
ejpam-4260	331	10	supra	supra	PROPN
ejpam-4260	331	11	b	b	NOUN
ejpam-4260	331	12	-	-	PUNCT
ejpam-4260	331	13	closed	closed	ADJ
ejpam-4260	331	14	set	set	NOUN
ejpam-4260	331	15	and	and	CCONJ
ejpam-4260	331	16	ξ2	ξ2	PROPN
ejpam-4260	331	17	̸∈	̸∈	PROPN
ejpam-4260	331	18	{	{	PUNCT
ejpam-4260	331	19	ξ1	ξ1	PROPN
ejpam-4260	331	20	,	,	PUNCT
ejpam-4260	331	21	ξ4	ξ4	PROPN
ejpam-4260	331	22	}	}	PUNCT
ejpam-4260	331	23	.	.	PUNCT
ejpam-4260	332	1	since	since	SCONJ
ejpam-4260	332	2	there	there	PRON
ejpam-4260	332	3	do	do	AUX
ejpam-4260	332	4	not	not	PART
ejpam-4260	332	5	exist	exist	VERB
ejpam-4260	332	6	two	two	NUM
ejpam-4260	332	7	disjoint	disjoint	ADJ
ejpam-4260	332	8	supra	supra	PROPN
ejpam-4260	332	9	b	b	NOUN
ejpam-4260	332	10	-	-	PUNCT
ejpam-4260	332	11	open	open	ADJ
ejpam-4260	332	12	sets	set	NOUN
ejpam-4260	332	13	such	such	ADJ
ejpam-4260	332	14	that	that	PRON
ejpam-4260	332	15	one	one	NUM
ejpam-4260	332	16	of	of	ADP
ejpam-4260	332	17	them	they	PRON
ejpam-4260	332	18	contains	contain	VERB
ejpam-4260	332	19	ξ2	ξ2	NOUN
ejpam-4260	332	20	and	and	CCONJ
ejpam-4260	332	21	the	the	DET
ejpam-4260	332	22	other	other	ADJ
ejpam-4260	332	23	contains	contain	VERB
ejpam-4260	332	24	{	{	PUNCT
ejpam-4260	332	25	ξ1	ξ1	NOUN
ejpam-4260	332	26	,	,	PUNCT
ejpam-4260	332	27	ξ4	ξ4	PROPN
ejpam-4260	332	28	}	}	PUNCT
ejpam-4260	332	29	,	,	PUNCT
ejpam-4260	332	30	we	we	PRON
ejpam-4260	332	31	obtain	obtain	VERB
ejpam-4260	332	32	(	(	PUNCT
ejpam-4260	332	33	u	u	NOUN
ejpam-4260	332	34	,	,	PUNCT
ejpam-4260	332	35	ω	ω	PROPN
ejpam-4260	332	36	)	)	PUNCT
ejpam-4260	332	37	is	be	AUX
ejpam-4260	332	38	not	not	PART
ejpam-4260	332	39	sbt3	sbt3	VERB
ejpam-4260	332	40	.	.	PUNCT
ejpam-4260	333	1	in	in	ADP
ejpam-4260	333	2	contrast	contrast	NOUN
ejpam-4260	333	3	,	,	PUNCT
ejpam-4260	333	4	one	one	PRON
ejpam-4260	333	5	can	can	AUX
ejpam-4260	333	6	check	check	VERB
ejpam-4260	333	7	that	that	PRON
ejpam-4260	333	8	(	(	PUNCT
ejpam-4260	333	9	u	u	NOUN
ejpam-4260	333	10	,	,	PUNCT
ejpam-4260	333	11	ω	ω	PROPN
ejpam-4260	333	12	)	)	PUNCT
ejpam-4260	333	13	is	be	AUX
ejpam-4260	333	14	sbt2	sbt2	PROPN
ejpam-4260	333	15	.	.	PUNCT
ejpam-4260	334	1	example	example	NOUN
ejpam-4260	334	2	8	8	NUM
ejpam-4260	334	3	.	.	PUNCT
ejpam-4260	335	1	let	let	VERB
ejpam-4260	335	2	ω	ω	NOUN
ejpam-4260	335	3	=	=	PRON
ejpam-4260	335	4	{	{	PUNCT
ejpam-4260	335	5	∅,u	∅,u	NOUN
ejpam-4260	335	6	,	,	PUNCT
ejpam-4260	335	7	{	{	PUNCT
ejpam-4260	335	8	ξ2	ξ2	NOUN
ejpam-4260	335	9	}	}	PUNCT
ejpam-4260	335	10	,	,	PUNCT
ejpam-4260	335	11	{	{	PUNCT
ejpam-4260	335	12	ξ4	ξ4	NOUN
ejpam-4260	335	13	}	}	PUNCT
ejpam-4260	335	14	,	,	PUNCT
ejpam-4260	335	15	{	{	PUNCT
ejpam-4260	335	16	ξ2	ξ2	NOUN
ejpam-4260	335	17	,	,	PUNCT
ejpam-4260	335	18	ξ4	ξ4	PROPN
ejpam-4260	335	19	}	}	PUNCT
ejpam-4260	335	20	,	,	PUNCT
ejpam-4260	335	21	{	{	PUNCT
ejpam-4260	335	22	ξ1	ξ1	NOUN
ejpam-4260	335	23	,	,	PUNCT
ejpam-4260	335	24	ξ3	ξ3	PROPN
ejpam-4260	335	25	}	}	PUNCT
ejpam-4260	335	26	,	,	PUNCT
ejpam-4260	335	27	{	{	PUNCT
ejpam-4260	335	28	ξ1	ξ1	NOUN
ejpam-4260	335	29	,	,	PUNCT
ejpam-4260	335	30	ξ4	ξ4	PROPN
ejpam-4260	335	31	}	}	PUNCT
ejpam-4260	335	32	,	,	PUNCT
ejpam-4260	335	33	{	{	PUNCT
ejpam-4260	335	34	ξ1	ξ1	NOUN
ejpam-4260	335	35	,	,	PUNCT
ejpam-4260	335	36	ξ5	ξ5	PROPN
ejpam-4260	335	37	}	}	PUNCT
ejpam-4260	335	38	,	,	PUNCT
ejpam-4260	335	39	{	{	PUNCT
ejpam-4260	335	40	ξ2	ξ2	NOUN
ejpam-4260	335	41	,	,	PUNCT
ejpam-4260	335	42	ξ3	ξ3	PROPN
ejpam-4260	335	43	}	}	PUNCT
ejpam-4260	335	44	,	,	PUNCT
ejpam-4260	335	45	{	{	PUNCT
ejpam-4260	335	46	ξ2	ξ2	ADJ
ejpam-4260	335	47	,	,	PUNCT
ejpam-4260	335	48	ξ5	ξ5	PROPN
ejpam-4260	335	49	}	}	PUNCT
ejpam-4260	335	50	,	,	PUNCT
ejpam-4260	335	51	{	{	PUNCT
ejpam-4260	335	52	ξ3	ξ3	NOUN
ejpam-4260	335	53	,	,	PUNCT
ejpam-4260	335	54	ξ5	ξ5	NOUN
ejpam-4260	335	55	}	}	PUNCT
ejpam-4260	335	56	,	,	PUNCT
ejpam-4260	335	57	{	{	PUNCT
ejpam-4260	335	58	ξ4	ξ4	NOUN
ejpam-4260	335	59	,	,	PUNCT
ejpam-4260	335	60	ξ5	ξ5	PROPN
ejpam-4260	335	61	}	}	PUNCT
ejpam-4260	335	62	,	,	PUNCT
ejpam-4260	335	63	{	{	PUNCT
ejpam-4260	335	64	ξ1	ξ1	NOUN
ejpam-4260	335	65	,	,	PUNCT
ejpam-4260	335	66	ξ2	ξ2	ADJ
ejpam-4260	335	67	,	,	PUNCT
ejpam-4260	335	68	ξ3	ξ3	PROPN
ejpam-4260	335	69	}	}	PUNCT
ejpam-4260	335	70	,	,	PUNCT
ejpam-4260	335	71	{	{	PUNCT
ejpam-4260	335	72	ξ1	ξ1	NOUN
ejpam-4260	335	73	,	,	PUNCT
ejpam-4260	335	74	ξ2	ξ2	NOUN
ejpam-4260	335	75	,	,	PUNCT
ejpam-4260	335	76	ξ4	ξ4	PROPN
ejpam-4260	335	77	}	}	PUNCT
ejpam-4260	335	78	,	,	PUNCT
ejpam-4260	335	79	{	{	PUNCT
ejpam-4260	335	80	ξ1	ξ1	NOUN
ejpam-4260	335	81	,	,	PUNCT
ejpam-4260	335	82	ξ2	ξ2	ADJ
ejpam-4260	335	83	,	,	PUNCT
ejpam-4260	335	84	ξ5	ξ5	PROPN
ejpam-4260	335	85	}	}	PUNCT
ejpam-4260	335	86	,	,	PUNCT
ejpam-4260	335	87	{	{	PUNCT
ejpam-4260	335	88	ξ1	ξ1	NOUN
ejpam-4260	335	89	,	,	PUNCT
ejpam-4260	335	90	ξ3	ξ3	NOUN
ejpam-4260	335	91	,	,	PUNCT
ejpam-4260	335	92	ξ4	ξ4	PROPN
ejpam-4260	335	93	}	}	PUNCT
ejpam-4260	335	94	,	,	PUNCT
ejpam-4260	335	95	{	{	PUNCT
ejpam-4260	335	96	ξ1	ξ1	NOUN
ejpam-4260	335	97	,	,	PUNCT
ejpam-4260	335	98	ξ3	ξ3	NOUN
ejpam-4260	335	99	,	,	PUNCT
ejpam-4260	335	100	ξ5	ξ5	NOUN
ejpam-4260	335	101	}	}	PUNCT
ejpam-4260	335	102	,	,	PUNCT
ejpam-4260	335	103	{	{	PUNCT
ejpam-4260	335	104	ξ1	ξ1	NOUN
ejpam-4260	335	105	,	,	PUNCT
ejpam-4260	335	106	ξ4	ξ4	NOUN
ejpam-4260	335	107	,	,	PUNCT
ejpam-4260	335	108	ξ5	ξ5	PROPN
ejpam-4260	335	109	}	}	PUNCT
ejpam-4260	335	110	,	,	PUNCT
ejpam-4260	335	111	{	{	PUNCT
ejpam-4260	335	112	ξ2	ξ2	NOUN
ejpam-4260	335	113	,	,	PUNCT
ejpam-4260	335	114	ξ3	ξ3	NOUN
ejpam-4260	335	115	,	,	PUNCT
ejpam-4260	335	116	ξ4	ξ4	PROPN
ejpam-4260	335	117	}	}	PUNCT
ejpam-4260	335	118	,	,	PUNCT
ejpam-4260	335	119	{	{	PUNCT
ejpam-4260	335	120	ξ2	ξ2	NOUN
ejpam-4260	335	121	,	,	PUNCT
ejpam-4260	335	122	ξ3	ξ3	NOUN
ejpam-4260	335	123	,	,	PUNCT
ejpam-4260	335	124	ξ5	ξ5	NOUN
ejpam-4260	335	125	}	}	PUNCT
ejpam-4260	335	126	,	,	PUNCT
ejpam-4260	335	127	{	{	PUNCT
ejpam-4260	335	128	ξ2	ξ2	NOUN
ejpam-4260	335	129	,	,	PUNCT
ejpam-4260	335	130	ξ4	ξ4	NOUN
ejpam-4260	335	131	,	,	PUNCT
ejpam-4260	335	132	ξ5	ξ5	PROPN
ejpam-4260	335	133	}	}	PUNCT
ejpam-4260	335	134	,	,	PUNCT
ejpam-4260	335	135	{	{	PUNCT
ejpam-4260	335	136	ξ3	ξ3	NOUN
ejpam-4260	335	137	,	,	PUNCT
ejpam-4260	335	138	ξ4	ξ4	NOUN
ejpam-4260	335	139	,	,	PUNCT
ejpam-4260	335	140	ξ5	ξ5	PROPN
ejpam-4260	335	141	}	}	PUNCT
ejpam-4260	335	142	,	,	PUNCT
ejpam-4260	335	143	{	{	PUNCT
ejpam-4260	335	144	ξ1	ξ1	NOUN
ejpam-4260	335	145	,	,	PUNCT
ejpam-4260	335	146	ξ2	ξ2	ADJ
ejpam-4260	335	147	,	,	PUNCT
ejpam-4260	335	148	ξ3	ξ3	NOUN
ejpam-4260	335	149	,	,	PUNCT
ejpam-4260	335	150	ξ4	ξ4	PROPN
ejpam-4260	335	151	}	}	PUNCT
ejpam-4260	335	152	,	,	PUNCT
ejpam-4260	335	153	{	{	PUNCT
ejpam-4260	335	154	ξ1	ξ1	NOUN
ejpam-4260	335	155	,	,	PUNCT
ejpam-4260	335	156	ξ2	ξ2	ADJ
ejpam-4260	335	157	,	,	PUNCT
ejpam-4260	335	158	ξ3	ξ3	NOUN
ejpam-4260	335	159	,	,	PUNCT
ejpam-4260	335	160	ξ5	ξ5	NOUN
ejpam-4260	335	161	}	}	PUNCT
ejpam-4260	335	162	,	,	PUNCT
ejpam-4260	335	163	{	{	PUNCT
ejpam-4260	335	164	ξ1	ξ1	NOUN
ejpam-4260	335	165	,	,	PUNCT
ejpam-4260	335	166	ξ2	ξ2	NOUN
ejpam-4260	335	167	,	,	PUNCT
ejpam-4260	335	168	ξ4	ξ4	NOUN
ejpam-4260	335	169	,	,	PUNCT
ejpam-4260	335	170	ξ5	ξ5	PROPN
ejpam-4260	335	171	}	}	PUNCT
ejpam-4260	335	172	,	,	PUNCT
ejpam-4260	335	173	{	{	PUNCT
ejpam-4260	335	174	ξ1	ξ1	NOUN
ejpam-4260	335	175	,	,	PUNCT
ejpam-4260	335	176	ξ3	ξ3	PROPN
ejpam-4260	335	177	,	,	PUNCT
ejpam-4260	335	178	ξ4	ξ4	NOUN
ejpam-4260	335	179	,	,	PUNCT
ejpam-4260	335	180	ξ5	ξ5	PROPN
ejpam-4260	335	181	}	}	PUNCT
ejpam-4260	335	182	,	,	PUNCT
ejpam-4260	335	183	{	{	PUNCT
ejpam-4260	335	184	ξ2	ξ2	NOUN
ejpam-4260	335	185	,	,	PUNCT
ejpam-4260	335	186	ξ3	ξ3	PROPN
ejpam-4260	335	187	,	,	PUNCT
ejpam-4260	335	188	ξ4	ξ4	NOUN
ejpam-4260	335	189	,	,	PUNCT
ejpam-4260	335	190	ξ5	ξ5	NOUN
ejpam-4260	335	191	}	}	PUNCT
ejpam-4260	335	192	}	}	PUNCT
ejpam-4260	335	193	be	be	VERB
ejpam-4260	335	194	an	an	DET
ejpam-4260	335	195	st	st	NOUN
ejpam-4260	335	196	on	on	ADP
ejpam-4260	335	197	u	u	NOUN
ejpam-4260	335	198	=	=	PUNCT
ejpam-4260	335	199	{	{	PUNCT
ejpam-4260	335	200	ξ1	ξ1	NOUN
ejpam-4260	335	201	,	,	PUNCT
ejpam-4260	335	202	ξ2	ξ2	ADJ
ejpam-4260	335	203	,	,	PUNCT
ejpam-4260	335	204	ξ3	ξ3	NOUN
ejpam-4260	335	205	,	,	PUNCT
ejpam-4260	335	206	ξ4	ξ4	NOUN
ejpam-4260	335	207	,	,	PUNCT
ejpam-4260	335	208	ξ5	ξ5	NOUN
ejpam-4260	335	209	}	}	PUNCT
ejpam-4260	335	210	.	.	PUNCT
ejpam-4260	336	1	in	in	ADP
ejpam-4260	336	2	(	(	PUNCT
ejpam-4260	336	3	u	u	NOUN
ejpam-4260	336	4	,	,	PUNCT
ejpam-4260	336	5	ω	ω	PROPN
ejpam-4260	336	6	)	)	PUNCT
ejpam-4260	336	7	,	,	PUNCT
ejpam-4260	336	8	a	a	DET
ejpam-4260	336	9	set	set	NOUN
ejpam-4260	336	10	is	be	AUX
ejpam-4260	336	11	supra	supra	PROPN
ejpam-4260	336	12	open	open	ADJ
ejpam-4260	336	13	iff	iff	PROPN
ejpam-4260	336	14	it	it	PRON
ejpam-4260	336	15	is	be	AUX
ejpam-4260	336	16	supra	supra	ADJ
ejpam-4260	336	17	b	b	NOUN
ejpam-4260	336	18	-	-	PUNCT
ejpam-4260	336	19	open	open	ADJ
ejpam-4260	336	20	.	.	PUNCT
ejpam-4260	337	1	now	now	ADV
ejpam-4260	337	2	,	,	PUNCT
ejpam-4260	337	3	{	{	PUNCT
ejpam-4260	337	4	ξ1	ξ1	NOUN
ejpam-4260	337	5	,	,	PUNCT
ejpam-4260	337	6	ξ2	ξ2	NOUN
ejpam-4260	337	7	}	}	PUNCT
ejpam-4260	337	8	and	and	CCONJ
ejpam-4260	337	9	{	{	PUNCT
ejpam-4260	337	10	ξ3	ξ3	NOUN
ejpam-4260	337	11	,	,	PUNCT
ejpam-4260	337	12	ξ4	ξ4	PROPN
ejpam-4260	337	13	}	}	PUNCT
ejpam-4260	337	14	are	be	AUX
ejpam-4260	337	15	disjoint	disjoint	ADJ
ejpam-4260	337	16	supra	supra	PROPN
ejpam-4260	337	17	b	b	PROPN
ejpam-4260	337	18	-	-	PUNCT
ejpam-4260	337	19	closed	closed	ADJ
ejpam-4260	337	20	subsets	subset	NOUN
ejpam-4260	337	21	of	of	ADP
ejpam-4260	337	22	(	(	PUNCT
ejpam-4260	337	23	u	u	PROPN
ejpam-4260	337	24	,	,	PUNCT
ejpam-4260	337	25	ω	ω	PROPN
ejpam-4260	337	26	)	)	PUNCT
ejpam-4260	337	27	.	.	PUNCT
ejpam-4260	338	1	since	since	SCONJ
ejpam-4260	338	2	there	there	PRON
ejpam-4260	338	3	do	do	AUX
ejpam-4260	338	4	not	not	PART
ejpam-4260	338	5	exist	exist	VERB
ejpam-4260	338	6	two	two	NUM
ejpam-4260	338	7	disjoint	disjoint	ADJ
ejpam-4260	338	8	supra	supra	PROPN
ejpam-4260	338	9	b	b	NOUN
ejpam-4260	338	10	-	-	PUNCT
ejpam-4260	338	11	open	open	ADJ
ejpam-4260	338	12	sets	set	NOUN
ejpam-4260	338	13	such	such	ADJ
ejpam-4260	338	14	that	that	PRON
ejpam-4260	338	15	one	one	NUM
ejpam-4260	338	16	of	of	ADP
ejpam-4260	338	17	them	they	PRON
ejpam-4260	338	18	contains	contain	VERB
ejpam-4260	338	19	{	{	PUNCT
ejpam-4260	338	20	ξ1	ξ1	NOUN
ejpam-4260	338	21	,	,	PUNCT
ejpam-4260	338	22	ξ2	ξ2	NOUN
ejpam-4260	338	23	}	}	PUNCT
ejpam-4260	338	24	and	and	CCONJ
ejpam-4260	338	25	the	the	DET
ejpam-4260	338	26	other	other	ADJ
ejpam-4260	338	27	contains	contain	VERB
ejpam-4260	338	28	{	{	PUNCT
ejpam-4260	338	29	ξ3	ξ3	NOUN
ejpam-4260	338	30	,	,	PUNCT
ejpam-4260	338	31	ξ4	ξ4	PROPN
ejpam-4260	338	32	}	}	PUNCT
ejpam-4260	338	33	,	,	PUNCT
ejpam-4260	338	34	we	we	PRON
ejpam-4260	338	35	obtain	obtain	VERB
ejpam-4260	338	36	(	(	PUNCT
ejpam-4260	338	37	u	u	NOUN
ejpam-4260	338	38	,	,	PUNCT
ejpam-4260	338	39	ω	ω	PROPN
ejpam-4260	338	40	)	)	PUNCT
ejpam-4260	338	41	is	be	AUX
ejpam-4260	338	42	not	not	PART
ejpam-4260	338	43	supra	supra	PROPN
ejpam-4260	338	44	b	b	PROPN
ejpam-4260	338	45	normal	normal	ADJ
ejpam-4260	338	46	.	.	PUNCT
ejpam-4260	339	1	hence	hence	ADV
ejpam-4260	339	2	,	,	PUNCT
ejpam-4260	339	3	it	it	PRON
ejpam-4260	339	4	is	be	AUX
ejpam-4260	339	5	not	not	PART
ejpam-4260	339	6	sbt4	sbt4	ADJ
ejpam-4260	339	7	.	.	PUNCT
ejpam-4260	340	1	in	in	ADP
ejpam-4260	340	2	contrast	contrast	NOUN
ejpam-4260	340	3	,	,	PUNCT
ejpam-4260	340	4	one	one	PRON
ejpam-4260	340	5	can	can	AUX
ejpam-4260	340	6	check	check	VERB
ejpam-4260	340	7	that	that	PRON
ejpam-4260	340	8	(	(	PUNCT
ejpam-4260	340	9	u	u	NOUN
ejpam-4260	340	10	,	,	PUNCT
ejpam-4260	340	11	ω	ω	PROPN
ejpam-4260	340	12	)	)	PUNCT
ejpam-4260	340	13	is	be	AUX
ejpam-4260	340	14	sbt3	sbt3	VERB
ejpam-4260	340	15	.	.	PUNCT
ejpam-4260	341	1	theorem	theorem	NOUN
ejpam-4260	341	2	12	12	NUM
ejpam-4260	341	3	.	.	PUNCT
ejpam-4260	342	1	every	every	DET
ejpam-4260	342	2	stk	stk	NOUN
ejpam-4260	342	3	-	-	PUNCT
ejpam-4260	342	4	space	space	NOUN
ejpam-4260	342	5	(	(	PUNCT
ejpam-4260	342	6	u	u	NOUN
ejpam-4260	342	7	,	,	PUNCT
ejpam-4260	342	8	ω	ω	PROPN
ejpam-4260	342	9	)	)	PUNCT
ejpam-4260	342	10	is	be	AUX
ejpam-4260	342	11	sbtk	sbtk	VERB
ejpam-4260	342	12	for	for	ADP
ejpam-4260	342	13	k	k	PROPN
ejpam-4260	342	14	=	=	SYM
ejpam-4260	342	15	0	0	NUM
ejpam-4260	342	16	,	,	PUNCT
ejpam-4260	342	17	1	1	NUM
ejpam-4260	342	18	,	,	PUNCT
ejpam-4260	342	19	2	2	NUM
ejpam-4260	342	20	.	.	PUNCT
ejpam-4260	342	21	proof	proof	NOUN
ejpam-4260	342	22	.	.	PUNCT
ejpam-4260	343	1	straightforward	straightforward	ADJ
ejpam-4260	343	2	.	.	PUNCT
ejpam-4260	344	1	the	the	DET
ejpam-4260	344	2	converse	converse	NOUN
ejpam-4260	344	3	of	of	ADP
ejpam-4260	344	4	the	the	DET
ejpam-4260	344	5	above	above	ADJ
ejpam-4260	344	6	theorem	theorem	NOUN
ejpam-4260	344	7	is	be	AUX
ejpam-4260	344	8	in	in	ADP
ejpam-4260	344	9	general	general	ADJ
ejpam-4260	344	10	false	false	ADJ
ejpam-4260	344	11	as	as	SCONJ
ejpam-4260	344	12	the	the	DET
ejpam-4260	344	13	next	next	ADJ
ejpam-4260	344	14	example	example	NOUN
ejpam-4260	344	15	shows	show	VERB
ejpam-4260	344	16	.	.	PUNCT
ejpam-4260	345	1	example	example	NOUN
ejpam-4260	346	1	9	9	NUM
ejpam-4260	346	2	.	.	PUNCT
ejpam-4260	347	1	let	let	VERB
ejpam-4260	347	2	ω	ω	NOUN
ejpam-4260	347	3	=	=	PRON
ejpam-4260	347	4	{	{	PUNCT
ejpam-4260	347	5	∅,u	∅,u	NOUN
ejpam-4260	347	6	,	,	PUNCT
ejpam-4260	347	7	{	{	PUNCT
ejpam-4260	347	8	ξ1	ξ1	NOUN
ejpam-4260	347	9	}	}	PUNCT
ejpam-4260	347	10	,	,	PUNCT
ejpam-4260	347	11	{	{	PUNCT
ejpam-4260	347	12	ξ2	ξ2	NOUN
ejpam-4260	347	13	,	,	PUNCT
ejpam-4260	347	14	ξ3	ξ3	PROPN
ejpam-4260	347	15	}	}	PUNCT
ejpam-4260	347	16	}	}	PUNCT
ejpam-4260	347	17	be	be	AUX
ejpam-4260	347	18	an	an	DET
ejpam-4260	347	19	st	st	NOUN
ejpam-4260	347	20	on	on	ADP
ejpam-4260	347	21	u	u	NOUN
ejpam-4260	347	22	=	=	PUNCT
ejpam-4260	347	23	{	{	PUNCT
ejpam-4260	347	24	ξ1	ξ1	NOUN
ejpam-4260	347	25	,	,	PUNCT
ejpam-4260	347	26	ξ2	ξ2	ADJ
ejpam-4260	347	27	,	,	PUNCT
ejpam-4260	347	28	ξ3	ξ3	PROPN
ejpam-4260	347	29	}	}	PUNCT
ejpam-4260	347	30	.	.	PUNCT
ejpam-4260	348	1	one	one	PRON
ejpam-4260	348	2	can	can	AUX
ejpam-4260	348	3	check	check	VERB
ejpam-4260	348	4	that	that	PRON
ejpam-4260	348	5	(	(	PUNCT
ejpam-4260	348	6	u	u	NOUN
ejpam-4260	348	7	,	,	PUNCT
ejpam-4260	348	8	ω	ω	PROPN
ejpam-4260	348	9	)	)	PUNCT
ejpam-4260	348	10	is	be	AUX
ejpam-4260	348	11	sbt4	sbt4	ADJ
ejpam-4260	348	12	but	but	CCONJ
ejpam-4260	348	13	is	be	AUX
ejpam-4260	348	14	not	not	PART
ejpam-4260	348	15	st4	st4	PROPN
ejpam-4260	348	16	.	.	PUNCT
ejpam-4260	349	1	definition	definition	NOUN
ejpam-4260	349	2	14	14	NUM
ejpam-4260	349	3	.	.	PUNCT
ejpam-4260	350	1	let	let	VERB
ejpam-4260	350	2	o	o	NOUN
ejpam-4260	350	3	̸=	̸=	PROPN
ejpam-4260	350	4	∅	∅	NOUN
ejpam-4260	350	5	be	be	AUX
ejpam-4260	350	6	a	a	DET
ejpam-4260	350	7	subset	subset	NOUN
ejpam-4260	350	8	of	of	ADP
ejpam-4260	350	9	(	(	PUNCT
ejpam-4260	350	10	u	u	PROPN
ejpam-4260	350	11	,	,	PUNCT
ejpam-4260	350	12	ω	ω	PROPN
ejpam-4260	350	13	)	)	PUNCT
ejpam-4260	350	14	.	.	PUNCT
ejpam-4260	351	1	we	we	PRON
ejpam-4260	351	2	call	call	VERB
ejpam-4260	351	3	a	a	DET
ejpam-4260	351	4	class	class	NOUN
ejpam-4260	351	5	ωo	ωo	ADP
ejpam-4260	351	6	=	=	PUNCT
ejpam-4260	351	7	{	{	PUNCT
ejpam-4260	351	8	o	o	NOUN
ejpam-4260	351	9	⋂	⋂	PROPN
ejpam-4260	351	10	θ	θ	X
ejpam-4260	351	11	:	:	PUNCT
ejpam-4260	351	12	θ	θ	NOUN
ejpam-4260	351	13	is	be	AUX
ejpam-4260	351	14	a	a	DET
ejpam-4260	351	15	supra	supra	PROPN
ejpam-4260	351	16	b	b	NOUN
ejpam-4260	351	17	-	-	PUNCT
ejpam-4260	351	18	open	open	ADJ
ejpam-4260	351	19	subset	subset	NOUN
ejpam-4260	351	20	of	of	ADP
ejpam-4260	351	21	(	(	PUNCT
ejpam-4260	351	22	u	u	PROPN
ejpam-4260	351	23	,	,	PUNCT
ejpam-4260	351	24	ω	ω	PROPN
ejpam-4260	351	25	)	)	PUNCT
ejpam-4260	351	26	}	}	PUNCT
ejpam-4260	351	27	a	a	DET
ejpam-4260	351	28	relative	relative	ADJ
ejpam-4260	351	29	b	b	NOUN
ejpam-4260	351	30	-	-	PUNCT
ejpam-4260	351	31	topology	topology	NOUN
ejpam-4260	351	32	on	on	ADP
ejpam-4260	351	33	o	o	NOUN
ejpam-4260	351	34	,	,	PUNCT
ejpam-4260	351	35	and	and	CCONJ
ejpam-4260	351	36	call	call	NOUN
ejpam-4260	351	37	(	(	PUNCT
ejpam-4260	351	38	o	o	NOUN
ejpam-4260	351	39	,	,	PUNCT
ejpam-4260	351	40	ωa	ωa	PROPN
ejpam-4260	351	41	)	)	PUNCT
ejpam-4260	351	42	a	a	DET
ejpam-4260	351	43	b	b	NOUN
ejpam-4260	351	44	-	-	PUNCT
ejpam-4260	351	45	subspace	subspace	NOUN
ejpam-4260	351	46	of	of	ADP
ejpam-4260	351	47	(	(	PUNCT
ejpam-4260	351	48	u	u	PROPN
ejpam-4260	351	49	,	,	PUNCT
ejpam-4260	351	50	ω	ω	PROPN
ejpam-4260	351	51	)	)	PUNCT
ejpam-4260	351	52	.	.	PUNCT
ejpam-4260	352	1	definition	definition	NOUN
ejpam-4260	352	2	15	15	NUM
ejpam-4260	352	3	.	.	PUNCT
ejpam-4260	353	1	we	we	PRON
ejpam-4260	353	2	call	call	VERB
ejpam-4260	353	3	a	a	DET
ejpam-4260	353	4	property	property	NOUN
ejpam-4260	353	5	a	a	DET
ejpam-4260	353	6	relative	relative	ADJ
ejpam-4260	353	7	b	b	NOUN
ejpam-4260	353	8	-	-	ADJ
ejpam-4260	353	9	hereditary	hereditary	ADJ
ejpam-4260	353	10	if	if	SCONJ
ejpam-4260	353	11	the	the	DET
ejpam-4260	353	12	it	it	PRON
ejpam-4260	353	13	passes	pass	VERB
ejpam-4260	353	14	from	from	ADP
ejpam-4260	353	15	an	an	DET
ejpam-4260	353	16	sts	st	NOUN
ejpam-4260	353	17	to	to	ADP
ejpam-4260	353	18	every	every	DET
ejpam-4260	353	19	relative	relative	ADJ
ejpam-4260	353	20	b	b	NOUN
ejpam-4260	353	21	-	-	PUNCT
ejpam-4260	353	22	subspace	subspace	NOUN
ejpam-4260	353	23	.	.	PUNCT
ejpam-4260	354	1	one	one	PRON
ejpam-4260	354	2	can	can	AUX
ejpam-4260	354	3	prove	prove	VERB
ejpam-4260	354	4	the	the	DET
ejpam-4260	354	5	next	next	ADJ
ejpam-4260	354	6	two	two	NUM
ejpam-4260	354	7	propositions	proposition	NOUN
ejpam-4260	354	8	easily	easily	ADV
ejpam-4260	354	9	;	;	PUNCT
ejpam-4260	354	10	so	so	ADV
ejpam-4260	354	11	we	we	PRON
ejpam-4260	354	12	omit	omit	VERB
ejpam-4260	354	13	their	their	PRON
ejpam-4260	354	14	proofs	proof	NOUN
ejpam-4260	354	15	.	.	PUNCT
ejpam-4260	355	1	proposition	proposition	NOUN
ejpam-4260	355	2	5	5	NUM
ejpam-4260	355	3	.	.	PUNCT
ejpam-4260	356	1	let	let	AUX
ejpam-4260	356	2	(	(	PUNCT
ejpam-4260	356	3	y	y	NOUN
ejpam-4260	356	4	,	,	PUNCT
ejpam-4260	356	5	ωy	ωy	PROPN
ejpam-4260	356	6	)	)	PUNCT
ejpam-4260	356	7	be	be	AUX
ejpam-4260	356	8	an	an	DET
ejpam-4260	356	9	b	b	NOUN
ejpam-4260	356	10	-	-	PUNCT
ejpam-4260	356	11	subspace	subspace	NOUN
ejpam-4260	356	12	of	of	ADP
ejpam-4260	356	13	(	(	PUNCT
ejpam-4260	356	14	u	u	PROPN
ejpam-4260	356	15	,	,	PUNCT
ejpam-4260	356	16	ω	ω	PROPN
ejpam-4260	356	17	)	)	PUNCT
ejpam-4260	356	18	.	.	PUNCT
ejpam-4260	357	1	a	a	DET
ejpam-4260	357	2	subset	subset	ADJ
ejpam-4260	357	3	h	h	NOUN
ejpam-4260	357	4	of	of	ADP
ejpam-4260	357	5	y	y	PROPN
ejpam-4260	357	6	is	be	AUX
ejpam-4260	357	7	supra	supra	PROPN
ejpam-4260	357	8	b	b	NOUN
ejpam-4260	357	9	-	-	PUNCT
ejpam-4260	357	10	closed	closed	ADJ
ejpam-4260	357	11	in	in	ADP
ejpam-4260	357	12	(	(	PUNCT
ejpam-4260	357	13	y	y	PROPN
ejpam-4260	357	14	,	,	PUNCT
ejpam-4260	357	15	ωy	ωy	PROPN
ejpam-4260	357	16	)	)	PUNCT
ejpam-4260	357	17	iff	iff	PROPN
ejpam-4260	357	18	there	there	PRON
ejpam-4260	357	19	exists	exist	VERB
ejpam-4260	357	20	a	a	DET
ejpam-4260	357	21	supra	supra	PROPN
ejpam-4260	357	22	b	b	NOUN
ejpam-4260	357	23	-	-	PUNCT
ejpam-4260	357	24	closed	close	VERB
ejpam-4260	357	25	subset	subset	NOUN
ejpam-4260	357	26	f	f	PROPN
ejpam-4260	357	27	of	of	ADP
ejpam-4260	357	28	(	(	PUNCT
ejpam-4260	357	29	u	u	PROPN
ejpam-4260	357	30	,	,	PUNCT
ejpam-4260	357	31	ω	ω	PROPN
ejpam-4260	357	32	)	)	PUNCT
ejpam-4260	358	1	such	such	ADJ
ejpam-4260	358	2	that	that	SCONJ
ejpam-4260	358	3	h	h	NOUN
ejpam-4260	358	4	=	=	SYM
ejpam-4260	358	5	y	y	PROPN
ejpam-4260	358	6	⋂	⋂	PROPN
ejpam-4260	358	7	f	f	PROPN
ejpam-4260	358	8	.	.	PUNCT
ejpam-4260	359	1	proposition	proposition	NOUN
ejpam-4260	359	2	6	6	NUM
ejpam-4260	359	3	.	.	PUNCT
ejpam-4260	360	1	a	a	DET
ejpam-4260	360	2	property	property	NOUN
ejpam-4260	360	3	of	of	ADP
ejpam-4260	360	4	being	be	AUX
ejpam-4260	360	5	an	an	DET
ejpam-4260	360	6	sbtk	sbtk	NOUN
ejpam-4260	360	7	-	-	PUNCT
ejpam-4260	360	8	space	space	NOUN
ejpam-4260	360	9	is	be	AUX
ejpam-4260	360	10	a	a	DET
ejpam-4260	360	11	relative	relative	ADJ
ejpam-4260	360	12	b	b	NOUN
ejpam-4260	360	13	-	-	NOUN
ejpam-4260	360	14	hereditary	hereditary	NOUN
ejpam-4260	360	15	for	for	ADP
ejpam-4260	360	16	k	k	PROPN
ejpam-4260	360	17	=	=	SYM
ejpam-4260	360	18	0	0	NUM
ejpam-4260	360	19	,	,	PUNCT
ejpam-4260	360	20	1	1	NUM
ejpam-4260	360	21	,	,	PUNCT
ejpam-4260	360	22	2	2	NUM
ejpam-4260	360	23	,	,	PUNCT
ejpam-4260	360	24	3	3	NUM
ejpam-4260	360	25	.	.	X
ejpam-4260	360	26	proposition	proposition	NOUN
ejpam-4260	360	27	7	7	NUM
ejpam-4260	360	28	.	.	PUNCT
ejpam-4260	361	1	let	let	VERB
ejpam-4260	361	2	g	g	NOUN
ejpam-4260	361	3	:	:	PUNCT
ejpam-4260	361	4	(	(	PUNCT
ejpam-4260	361	5	u	u	NOUN
ejpam-4260	361	6	,	,	PUNCT
ejpam-4260	361	7	ω	ω	PROPN
ejpam-4260	361	8	)	)	PUNCT
ejpam-4260	361	9	→	→	SYM
ejpam-4260	361	10	(	(	PUNCT
ejpam-4260	361	11	v	v	NOUN
ejpam-4260	361	12	,	,	PUNCT
ejpam-4260	361	13	θ	θ	NOUN
ejpam-4260	361	14	)	)	PUNCT
ejpam-4260	361	15	be	be	VERB
ejpam-4260	361	16	an	an	DET
ejpam-4260	361	17	injective	injective	ADJ
ejpam-4260	361	18	supra	supra	NOUN
ejpam-4260	361	19	b	b	NOUN
ejpam-4260	361	20	-	-	PUNCT
ejpam-4260	361	21	continuous	continuous	ADJ
ejpam-4260	361	22	mapping	mapping	NOUN
ejpam-4260	361	23	.	.	PUNCT
ejpam-4260	362	1	if	if	SCONJ
ejpam-4260	362	2	(	(	PUNCT
ejpam-4260	362	3	v	v	NOUN
ejpam-4260	362	4	,	,	PUNCT
ejpam-4260	362	5	θ	θ	NOUN
ejpam-4260	362	6	)	)	PUNCT
ejpam-4260	362	7	is	be	AUX
ejpam-4260	362	8	tk	tk	PROPN
ejpam-4260	362	9	,	,	PUNCT
ejpam-4260	362	10	then	then	ADV
ejpam-4260	362	11	(	(	PUNCT
ejpam-4260	362	12	u	u	NOUN
ejpam-4260	362	13	,	,	PUNCT
ejpam-4260	362	14	ω	ω	PROPN
ejpam-4260	362	15	)	)	PUNCT
ejpam-4260	362	16	is	be	AUX
ejpam-4260	362	17	sbtk	sbtk	VERB
ejpam-4260	362	18	for	for	ADP
ejpam-4260	362	19	k	k	PROPN
ejpam-4260	362	20	=	=	SYM
ejpam-4260	362	21	0	0	NUM
ejpam-4260	362	22	,	,	PUNCT
ejpam-4260	362	23	1	1	NUM
ejpam-4260	362	24	,	,	PUNCT
ejpam-4260	362	25	2	2	NUM
ejpam-4260	362	26	.	.	PUNCT
ejpam-4260	362	27	proof	proof	NOUN
ejpam-4260	362	28	.	.	PUNCT
ejpam-4260	363	1	we	we	PRON
ejpam-4260	363	2	give	give	VERB
ejpam-4260	363	3	a	a	DET
ejpam-4260	363	4	proof	proof	NOUN
ejpam-4260	363	5	when	when	SCONJ
ejpam-4260	363	6	k	k	PROPN
ejpam-4260	363	7	=	=	SYM
ejpam-4260	363	8	2	2	X
ejpam-4260	363	9	.	.	PUNCT
ejpam-4260	363	10	let	let	VERB
ejpam-4260	363	11	ξ	ξ	X
ejpam-4260	363	12	̸=	̸=	PROPN
ejpam-4260	363	13	ζ	ζ	NOUN
ejpam-4260	363	14	∈	∈	PROPN
ejpam-4260	363	15	u	u	NOUN
ejpam-4260	363	16	.	.	PUNCT
ejpam-4260	364	1	since	since	SCONJ
ejpam-4260	364	2	g	g	PROPN
ejpam-4260	364	3	is	be	AUX
ejpam-4260	364	4	injective	injective	ADJ
ejpam-4260	364	5	,	,	PUNCT
ejpam-4260	364	6	there	there	PRON
ejpam-4260	364	7	are	be	VERB
ejpam-4260	364	8	x	x	X
ejpam-4260	364	9	̸=	̸=	PROPN
ejpam-4260	364	10	y	y	PROPN
ejpam-4260	364	11	∈	∈	PROPN
ejpam-4260	364	12	v	v	ADP
ejpam-4260	364	13	such	such	ADJ
ejpam-4260	364	14	that	that	PRON
ejpam-4260	364	15	x	x	X
ejpam-4260	364	16	=	=	SYM
ejpam-4260	364	17	f(ξ	f(ξ	X
ejpam-4260	364	18	)	)	PUNCT
ejpam-4260	364	19	and	and	CCONJ
ejpam-4260	364	20	y	y	PROPN
ejpam-4260	364	21	=	=	PROPN
ejpam-4260	364	22	f(ζ	f(ζ	PROPN
ejpam-4260	364	23	)	)	PUNCT
ejpam-4260	364	24	.	.	PUNCT
ejpam-4260	365	1	since	since	SCONJ
ejpam-4260	365	2	(	(	PUNCT
ejpam-4260	365	3	v	v	NOUN
ejpam-4260	365	4	,	,	PUNCT
ejpam-4260	365	5	θ	θ	NOUN
ejpam-4260	365	6	)	)	PUNCT
ejpam-4260	365	7	is	be	AUX
ejpam-4260	365	8	t2	t2	NOUN
ejpam-4260	365	9	,	,	PUNCT
ejpam-4260	365	10	there	there	PRON
ejpam-4260	365	11	are	be	VERB
ejpam-4260	365	12	two	two	NUM
ejpam-4260	365	13	disjoint	disjoint	ADJ
ejpam-4260	365	14	open	open	ADJ
ejpam-4260	365	15	subsets	subset	NOUN
ejpam-4260	365	16	m	m	PROPN
ejpam-4260	365	17	and	and	CCONJ
ejpam-4260	365	18	n	n	PROPN
ejpam-4260	365	19	of	of	ADP
ejpam-4260	365	20	(	(	PUNCT
ejpam-4260	365	21	v	v	NOUN
ejpam-4260	365	22	,	,	PUNCT
ejpam-4260	365	23	θ	θ	NOUN
ejpam-4260	365	24	)	)	PUNCT
ejpam-4260	365	25	respectively	respectively	ADV
ejpam-4260	365	26	including	include	VERB
ejpam-4260	365	27	x	x	PUNCT
ejpam-4260	365	28	and	and	CCONJ
ejpam-4260	365	29	y.	y.	PROPN
ejpam-4260	365	30	thus	thus	ADV
ejpam-4260	365	31	,	,	PUNCT
ejpam-4260	365	32	g−1(m	g−1(m	PROPN
ejpam-4260	365	33	)	)	PUNCT
ejpam-4260	365	34	and	and	CCONJ
ejpam-4260	365	35	g−1(n	g−1(n	NOUN
ejpam-4260	365	36	)	)	PUNCT
ejpam-4260	365	37	are	be	AUX
ejpam-4260	365	38	disjoint	disjoint	ADJ
ejpam-4260	365	39	supra	supra	PROPN
ejpam-4260	365	40	b	b	PROPN
ejpam-4260	365	41	-	-	PUNCT
ejpam-4260	365	42	open	open	ADJ
ejpam-4260	365	43	subsets	subset	NOUN
ejpam-4260	365	44	of	of	ADP
ejpam-4260	365	45	(	(	PUNCT
ejpam-4260	365	46	u	u	PROPN
ejpam-4260	365	47	,	,	PUNCT
ejpam-4260	365	48	ω	ω	NOUN
ejpam-4260	365	49	)	)	PUNCT
ejpam-4260	365	50	respectively	respectively	ADV
ejpam-4260	365	51	including	include	VERB
ejpam-4260	365	52	ξ	ξ	PROPN
ejpam-4260	365	53	and	and	CCONJ
ejpam-4260	365	54	ζ	ζ	NOUN
ejpam-4260	365	55	.	.	PUNCT
ejpam-4260	366	1	this	this	PRON
ejpam-4260	366	2	proves	prove	VERB
ejpam-4260	366	3	that	that	SCONJ
ejpam-4260	366	4	(	(	PUNCT
ejpam-4260	366	5	u	u	NOUN
ejpam-4260	366	6	,	,	PUNCT
ejpam-4260	366	7	ω	ω	PROPN
ejpam-4260	366	8	)	)	PUNCT
ejpam-4260	366	9	is	be	AUX
ejpam-4260	366	10	sbt2	sbt2	PROPN
ejpam-4260	366	11	.	.	PUNCT
ejpam-4260	367	1	similarly	similarly	ADV
ejpam-4260	367	2	,	,	PUNCT
ejpam-4260	367	3	one	one	PRON
ejpam-4260	367	4	can	can	AUX
ejpam-4260	367	5	prove	prove	VERB
ejpam-4260	367	6	the	the	DET
ejpam-4260	367	7	next	next	ADJ
ejpam-4260	367	8	findings	finding	NOUN
ejpam-4260	367	9	.	.	PUNCT
ejpam-4260	368	1	a.	a.	PROPN
ejpam-4260	368	2	mhemdi	mhemdi	PROPN
ejpam-4260	368	3	et	et	PROPN
ejpam-4260	368	4	al	al	PROPN
ejpam-4260	368	5	.	.	PUNCT
ejpam-4260	368	6	/	/	SYM
ejpam-4260	368	7	eur	eur	PROPN
ejpam-4260	368	8	.	.	PUNCT
ejpam-4260	369	1	j.	j.	PROPN
ejpam-4260	369	2	pure	pure	PROPN
ejpam-4260	369	3	appl	appl	PROPN
ejpam-4260	369	4	.	.	PROPN
ejpam-4260	369	5	math	math	PROPN
ejpam-4260	369	6	,	,	PUNCT
ejpam-4260	369	7	15	15	NUM
ejpam-4260	369	8	(	(	PUNCT
ejpam-4260	369	9	1	1	NUM
ejpam-4260	369	10	)	)	PUNCT
ejpam-4260	369	11	(	(	PUNCT
ejpam-4260	369	12	2022	2022	NUM
ejpam-4260	369	13	)	)	PUNCT
ejpam-4260	369	14	,	,	PUNCT
ejpam-4260	369	15	15	15	NUM
ejpam-4260	369	16	-	-	SYM
ejpam-4260	369	17	29	29	NUM
ejpam-4260	369	18	26	26	NUM
ejpam-4260	369	19	proposition	proposition	NOUN
ejpam-4260	369	20	8	8	NUM
ejpam-4260	369	21	.	.	PUNCT
ejpam-4260	370	1	let	let	VERB
ejpam-4260	370	2	g	g	NOUN
ejpam-4260	370	3	:	:	PUNCT
ejpam-4260	370	4	(	(	PUNCT
ejpam-4260	370	5	u	u	NOUN
ejpam-4260	370	6	,	,	PUNCT
ejpam-4260	370	7	τ	τ	PROPN
ejpam-4260	370	8	)	)	PUNCT
ejpam-4260	370	9	→	→	SYM
ejpam-4260	370	10	(	(	PUNCT
ejpam-4260	370	11	v	v	NOUN
ejpam-4260	370	12	,	,	PUNCT
ejpam-4260	370	13	ψ	ψ	NOUN
ejpam-4260	370	14	)	)	PUNCT
ejpam-4260	370	15	be	be	AUX
ejpam-4260	370	16	a	a	DET
ejpam-4260	370	17	bijective	bijective	ADJ
ejpam-4260	370	18	supra	supra	NOUN
ejpam-4260	370	19	b	b	NOUN
ejpam-4260	370	20	-	-	PUNCT
ejpam-4260	370	21	open	open	ADJ
ejpam-4260	370	22	mapping	mapping	NOUN
ejpam-4260	370	23	.	.	PUNCT
ejpam-4260	371	1	if	if	SCONJ
ejpam-4260	371	2	(	(	PUNCT
ejpam-4260	371	3	u	u	NOUN
ejpam-4260	371	4	,	,	PUNCT
ejpam-4260	371	5	τ	τ	X
ejpam-4260	371	6	)	)	PUNCT
ejpam-4260	371	7	is	be	AUX
ejpam-4260	371	8	tk	tk	PROPN
ejpam-4260	371	9	,	,	PUNCT
ejpam-4260	371	10	then	then	ADV
ejpam-4260	371	11	(	(	PUNCT
ejpam-4260	371	12	v	v	NOUN
ejpam-4260	371	13	,	,	PUNCT
ejpam-4260	371	14	ψ	ψ	NOUN
ejpam-4260	371	15	)	)	PUNCT
ejpam-4260	371	16	is	be	AUX
ejpam-4260	371	17	sbtk	sbtk	VERB
ejpam-4260	371	18	for	for	ADP
ejpam-4260	371	19	k	k	PROPN
ejpam-4260	371	20	=	=	SYM
ejpam-4260	371	21	0	0	NUM
ejpam-4260	371	22	,	,	PUNCT
ejpam-4260	371	23	1	1	NUM
ejpam-4260	371	24	,	,	PUNCT
ejpam-4260	371	25	2	2	NUM
ejpam-4260	371	26	.	.	X
ejpam-4260	371	27	proposition	proposition	NOUN
ejpam-4260	371	28	9	9	NUM
ejpam-4260	371	29	.	.	PUNCT
ejpam-4260	372	1	let	let	VERB
ejpam-4260	372	2	g	g	NOUN
ejpam-4260	372	3	:	:	PUNCT
ejpam-4260	372	4	(	(	PUNCT
ejpam-4260	372	5	u	u	NOUN
ejpam-4260	372	6	,	,	PUNCT
ejpam-4260	372	7	τ	τ	PROPN
ejpam-4260	372	8	)	)	PUNCT
ejpam-4260	372	9	→	→	SYM
ejpam-4260	372	10	(	(	PUNCT
ejpam-4260	372	11	v	v	NOUN
ejpam-4260	372	12	,	,	PUNCT
ejpam-4260	372	13	ψ	ψ	NOUN
ejpam-4260	372	14	)	)	PUNCT
ejpam-4260	372	15	be	be	AUX
ejpam-4260	372	16	an	an	DET
ejpam-4260	372	17	injective	injective	ADJ
ejpam-4260	372	18	supra	supra	ADJ
ejpam-4260	372	19	b⋆-continuous	b⋆-continuous	ADJ
ejpam-4260	372	20	mapping	mapping	NOUN
ejpam-4260	372	21	.	.	PUNCT
ejpam-4260	373	1	if	if	SCONJ
ejpam-4260	373	2	(	(	PUNCT
ejpam-4260	373	3	u	u	NOUN
ejpam-4260	373	4	,	,	PUNCT
ejpam-4260	373	5	τ	τ	X
ejpam-4260	373	6	)	)	PUNCT
ejpam-4260	373	7	is	be	AUX
ejpam-4260	373	8	sbtk	sbtk	VERB
ejpam-4260	373	9	,	,	PUNCT
ejpam-4260	373	10	then	then	ADV
ejpam-4260	373	11	(	(	PUNCT
ejpam-4260	373	12	v	v	NOUN
ejpam-4260	373	13	,	,	PUNCT
ejpam-4260	373	14	ψ	ψ	NOUN
ejpam-4260	373	15	)	)	PUNCT
ejpam-4260	373	16	is	be	AUX
ejpam-4260	373	17	sbtk	sbtk	VERB
ejpam-4260	373	18	for	for	ADP
ejpam-4260	373	19	k	k	PROPN
ejpam-4260	373	20	=	=	SYM
ejpam-4260	373	21	0	0	NUM
ejpam-4260	373	22	,	,	PUNCT
ejpam-4260	373	23	1	1	NUM
ejpam-4260	373	24	,	,	PUNCT
ejpam-4260	373	25	2	2	NUM
ejpam-4260	373	26	.	.	X
ejpam-4260	373	27	proposition	proposition	NOUN
ejpam-4260	373	28	10	10	NUM
ejpam-4260	373	29	.	.	PUNCT
ejpam-4260	374	1	let	let	VERB
ejpam-4260	374	2	g	g	NOUN
ejpam-4260	374	3	:	:	PUNCT
ejpam-4260	374	4	(	(	PUNCT
ejpam-4260	374	5	u	u	NOUN
ejpam-4260	374	6	,	,	PUNCT
ejpam-4260	374	7	τ	τ	PROPN
ejpam-4260	374	8	)	)	PUNCT
ejpam-4260	374	9	→	→	SYM
ejpam-4260	374	10	(	(	PUNCT
ejpam-4260	374	11	v	v	NOUN
ejpam-4260	374	12	,	,	PUNCT
ejpam-4260	374	13	ψ	ψ	NOUN
ejpam-4260	374	14	)	)	PUNCT
ejpam-4260	374	15	be	be	AUX
ejpam-4260	374	16	a	a	DET
ejpam-4260	374	17	bijective	bijective	ADJ
ejpam-4260	374	18	supra	supra	NOUN
ejpam-4260	374	19	b⋆-open	b⋆-open	PROPN
ejpam-4260	374	20	mapping	mapping	NOUN
ejpam-4260	374	21	.	.	PUNCT
ejpam-4260	375	1	if	if	SCONJ
ejpam-4260	375	2	(	(	PUNCT
ejpam-4260	375	3	u	u	NOUN
ejpam-4260	375	4	,	,	PUNCT
ejpam-4260	375	5	τ	τ	X
ejpam-4260	375	6	)	)	PUNCT
ejpam-4260	375	7	is	be	AUX
ejpam-4260	375	8	sbtk	sbtk	VERB
ejpam-4260	375	9	,	,	PUNCT
ejpam-4260	375	10	then	then	ADV
ejpam-4260	375	11	(	(	PUNCT
ejpam-4260	375	12	v	v	NOUN
ejpam-4260	375	13	,	,	PUNCT
ejpam-4260	375	14	ψ	ψ	NOUN
ejpam-4260	375	15	)	)	PUNCT
ejpam-4260	375	16	is	be	AUX
ejpam-4260	375	17	sbtk	sbtk	VERB
ejpam-4260	375	18	for	for	ADP
ejpam-4260	375	19	k	k	PROPN
ejpam-4260	375	20	=	=	SYM
ejpam-4260	375	21	0	0	NUM
ejpam-4260	375	22	,	,	PUNCT
ejpam-4260	375	23	1	1	NUM
ejpam-4260	375	24	,	,	PUNCT
ejpam-4260	375	25	2	2	NUM
ejpam-4260	375	26	.	.	X
ejpam-4260	375	27	proposition	proposition	NOUN
ejpam-4260	375	28	11	11	NUM
ejpam-4260	375	29	.	.	PUNCT
ejpam-4260	376	1	let	let	VERB
ejpam-4260	376	2	g	g	NOUN
ejpam-4260	376	3	:	:	PUNCT
ejpam-4260	376	4	(	(	PUNCT
ejpam-4260	376	5	u	u	NOUN
ejpam-4260	376	6	,	,	PUNCT
ejpam-4260	376	7	τ	τ	PROPN
ejpam-4260	376	8	)	)	PUNCT
ejpam-4260	376	9	→	→	SYM
ejpam-4260	376	10	(	(	PUNCT
ejpam-4260	376	11	v	v	NOUN
ejpam-4260	376	12	,	,	PUNCT
ejpam-4260	376	13	ψ	ψ	NOUN
ejpam-4260	376	14	)	)	PUNCT
ejpam-4260	376	15	be	be	AUX
ejpam-4260	376	16	a	a	DET
ejpam-4260	376	17	supra	supra	ADJ
ejpam-4260	376	18	b⋆-homeomorphism	b⋆-homeomorphism	PROPN
ejpam-4260	376	19	mapping	mapping	NOUN
ejpam-4260	376	20	.	.	PUNCT
ejpam-4260	377	1	then	then	ADV
ejpam-4260	377	2	(	(	PUNCT
ejpam-4260	377	3	u	u	NOUN
ejpam-4260	377	4	,	,	PUNCT
ejpam-4260	377	5	τ	τ	X
ejpam-4260	377	6	)	)	PUNCT
ejpam-4260	377	7	is	be	AUX
ejpam-4260	377	8	sbtk	sbtk	NOUN
ejpam-4260	377	9	iff	iff	PROPN
ejpam-4260	377	10	(	(	PUNCT
ejpam-4260	377	11	v	v	NOUN
ejpam-4260	377	12	,	,	PUNCT
ejpam-4260	377	13	ψ	ψ	NOUN
ejpam-4260	377	14	)	)	PUNCT
ejpam-4260	377	15	is	be	AUX
ejpam-4260	377	16	sbtk	sbtk	VERB
ejpam-4260	377	17	for	for	ADP
ejpam-4260	377	18	k	k	PROPN
ejpam-4260	377	19	=	=	SYM
ejpam-4260	377	20	0	0	NUM
ejpam-4260	377	21	,	,	PUNCT
ejpam-4260	377	22	1	1	NUM
ejpam-4260	377	23	,	,	PUNCT
ejpam-4260	377	24	2	2	NUM
ejpam-4260	377	25	,	,	PUNCT
ejpam-4260	377	26	3	3	NUM
ejpam-4260	377	27	,	,	PUNCT
ejpam-4260	377	28	4	4	NUM
ejpam-4260	377	29	.	.	X
ejpam-4260	377	30	recall	recall	VERB
ejpam-4260	377	31	that	that	PRON
ejpam-4260	377	32	:	:	PUNCT
ejpam-4260	377	33	(	(	PUNCT
ejpam-4260	377	34	o×p	o×p	PROPN
ejpam-4260	377	35	)	)	PUNCT
ejpam-4260	378	1	⋃	⋃	PROPN
ejpam-4260	378	2	(	(	PUNCT
ejpam-4260	378	3	c×d	c×d	PROPN
ejpam-4260	378	4	)	)	PUNCT
ejpam-4260	378	5	⊆	⊆	NUM
ejpam-4260	378	6	(	(	PUNCT
ejpam-4260	378	7	o	o	NOUN
ejpam-4260	378	8	⋃	⋃	VERB
ejpam-4260	378	9	c)×(p	c)×(p	PROPN
ejpam-4260	378	10	⋃	⋃	PROPN
ejpam-4260	378	11	d	d	NOUN
ejpam-4260	378	12	)	)	PUNCT
ejpam-4260	378	13	for	for	ADP
ejpam-4260	378	14	every	every	DET
ejpam-4260	378	15	o	o	NOUN
ejpam-4260	378	16	,	,	PUNCT
ejpam-4260	378	17	c	c	PROPN
ejpam-4260	378	18	⊆	⊆	NUM
ejpam-4260	378	19	u	u	NOUN
ejpam-4260	378	20	and	and	CCONJ
ejpam-4260	378	21	p	p	NOUN
ejpam-4260	378	22	,	,	PUNCT
ejpam-4260	378	23	d	d	PROPN
ejpam-4260	378	24	⊆	⊆	NUM
ejpam-4260	378	25	y	y	PROPN
ejpam-4260	378	26	.	.	PUNCT
ejpam-4260	379	1	theorem	theorem	VERB
ejpam-4260	379	2	13	13	NUM
ejpam-4260	379	3	.	.	PUNCT
ejpam-4260	380	1	the	the	DET
ejpam-4260	380	2	product	product	NOUN
ejpam-4260	380	3	of	of	ADP
ejpam-4260	380	4	two	two	NUM
ejpam-4260	380	5	supra	supra	PROPN
ejpam-4260	380	6	b	b	NOUN
ejpam-4260	380	7	-	-	PUNCT
ejpam-4260	380	8	open	open	ADJ
ejpam-4260	380	9	sets	set	NOUN
ejpam-4260	380	10	o	o	NOUN
ejpam-4260	380	11	and	and	CCONJ
ejpam-4260	380	12	p	p	NOUN
ejpam-4260	380	13	is	be	AUX
ejpam-4260	380	14	supra	supra	ADJ
ejpam-4260	380	15	b	b	NOUN
ejpam-4260	380	16	-	-	PUNCT
ejpam-4260	380	17	open	open	ADJ
ejpam-4260	380	18	.	.	PUNCT
ejpam-4260	381	1	proof	proof	NOUN
ejpam-4260	381	2	.	.	PUNCT
ejpam-4260	382	1	for	for	ADP
ejpam-4260	382	2	two	two	NUM
ejpam-4260	382	3	supra	supra	PROPN
ejpam-4260	382	4	b	b	NOUN
ejpam-4260	382	5	-	-	PUNCT
ejpam-4260	382	6	open	open	ADJ
ejpam-4260	382	7	sets	set	NOUN
ejpam-4260	382	8	o	o	NOUN
ejpam-4260	382	9	and	and	CCONJ
ejpam-4260	382	10	p	p	NOUN
ejpam-4260	382	11	,	,	PUNCT
ejpam-4260	382	12	we	we	PRON
ejpam-4260	382	13	have	have	VERB
ejpam-4260	382	14	o	o	NOUN
ejpam-4260	382	15	⊆	⊆	NUM
ejpam-4260	382	16	int(cl(o	int(cl(o	PROPN
ejpam-4260	382	17	)	)	PUNCT
ejpam-4260	382	18	)	)	PUNCT
ejpam-4260	382	19	⋃	⋃	VERB
ejpam-4260	382	20	cl(int(o	cl(int(o	NOUN
ejpam-4260	382	21	)	)	PUNCT
ejpam-4260	382	22	)	)	PUNCT
ejpam-4260	382	23	and	and	CCONJ
ejpam-4260	382	24	p	p	X
ejpam-4260	382	25	⊆	⊆	NUM
ejpam-4260	382	26	int(cl(int(p	int(cl(int(p	PROPN
ejpam-4260	382	27	)	)	PUNCT
ejpam-4260	382	28	)	)	PUNCT
ejpam-4260	382	29	)	)	PUNCT
ejpam-4260	383	1	⋃	⋃	SCONJ
ejpam-4260	383	2	int(cl(int(p	int(cl(int(p	NOUN
ejpam-4260	383	3	)	)	PUNCT
ejpam-4260	383	4	)	)	PUNCT
ejpam-4260	383	5	)	)	PUNCT
ejpam-4260	383	6	.	.	PUNCT
ejpam-4260	384	1	therefore	therefore	ADV
ejpam-4260	384	2	o	o	X
ejpam-4260	384	3	×	×	NOUN
ejpam-4260	384	4	p	p	NOUN
ejpam-4260	384	5	⊆	⊆	NUM
ejpam-4260	384	6	[	[	X
ejpam-4260	384	7	int(cl(o	int(cl(o	PROPN
ejpam-4260	384	8	)	)	PUNCT
ejpam-4260	384	9	)	)	PUNCT
ejpam-4260	385	1	⋃	⋃	SCONJ
ejpam-4260	385	2	cl(int(o))]×	cl(int(o))]×	PUNCT
ejpam-4260	386	1	[	[	X
ejpam-4260	386	2	int(cl(p	int(cl(p	PROPN
ejpam-4260	386	3	)	)	PUNCT
ejpam-4260	386	4	)	)	PUNCT
ejpam-4260	386	5	⋃	⋃	VERB
ejpam-4260	386	6	cl(int(p	cl(int(p	NOUN
ejpam-4260	386	7	)	)	PUNCT
ejpam-4260	386	8	)	)	PUNCT
ejpam-4260	386	9	]	]	PUNCT
ejpam-4260	387	1	⊆	⊆	NUM
ejpam-4260	387	2	[	[	X
ejpam-4260	387	3	int(cl(o))×	int(cl(o))×	NOUN
ejpam-4260	387	4	int(cl(p	int(cl(p	PROPN
ejpam-4260	387	5	)	)	PUNCT
ejpam-4260	387	6	)	)	PUNCT
ejpam-4260	387	7	]	]	PUNCT
ejpam-4260	388	1	⋃	⋃	PROPN
ejpam-4260	388	2	[	[	X
ejpam-4260	388	3	cl(int(o))×	cl(int(o))×	X
ejpam-4260	388	4	cl(int(p	cl(int(p	NOUN
ejpam-4260	388	5	)	)	PUNCT
ejpam-4260	388	6	)	)	PUNCT
ejpam-4260	388	7	]	]	PUNCT
ejpam-4260	389	1	=	=	PUNCT
ejpam-4260	390	1	[	[	X
ejpam-4260	390	2	int(cl(o	int(cl(o	PROPN
ejpam-4260	390	3	×	×	NOUN
ejpam-4260	390	4	p	p	NOUN
ejpam-4260	390	5	)	)	PUNCT
ejpam-4260	390	6	)	)	PUNCT
ejpam-4260	390	7	]	]	PUNCT
ejpam-4260	391	1	⋃	⋃	PROPN
ejpam-4260	391	2	[	[	X
ejpam-4260	391	3	cl(int(o	cl(int(o	NOUN
ejpam-4260	391	4	×	×	PROPN
ejpam-4260	391	5	p	p	NOUN
ejpam-4260	391	6	)	)	PUNCT
ejpam-4260	391	7	)	)	PUNCT
ejpam-4260	391	8	]	]	PUNCT
ejpam-4260	391	9	.	.	PUNCT
ejpam-4260	392	1	thus	thus	ADV
ejpam-4260	392	2	,	,	PUNCT
ejpam-4260	392	3	o	o	PROPN
ejpam-4260	392	4	×	×	NOUN
ejpam-4260	392	5	p	p	NOUN
ejpam-4260	392	6	is	be	AUX
ejpam-4260	392	7	supra	supra	ADJ
ejpam-4260	392	8	b	b	NOUN
ejpam-4260	392	9	-	-	PUNCT
ejpam-4260	392	10	open	open	ADJ
ejpam-4260	392	11	.	.	PUNCT
ejpam-4260	393	1	theorem	theorem	VERB
ejpam-4260	393	2	14	14	NUM
ejpam-4260	393	3	.	.	PUNCT
ejpam-4260	394	1	the	the	DET
ejpam-4260	394	2	finite	finite	ADJ
ejpam-4260	394	3	product	product	NOUN
ejpam-4260	394	4	of	of	ADP
ejpam-4260	394	5	sbtk	sbtk	NOUN
ejpam-4260	394	6	-	-	PUNCT
ejpam-4260	394	7	spaces	space	NOUN
ejpam-4260	394	8	is	be	AUX
ejpam-4260	394	9	sbtk	sbtk	VERB
ejpam-4260	394	10	for	for	ADP
ejpam-4260	394	11	k	k	PROPN
ejpam-4260	394	12	=	=	SYM
ejpam-4260	394	13	0	0	NUM
ejpam-4260	394	14	,	,	PUNCT
ejpam-4260	394	15	1	1	NUM
ejpam-4260	394	16	,	,	PUNCT
ejpam-4260	394	17	2	2	NUM
ejpam-4260	394	18	.	.	PUNCT
ejpam-4260	394	19	proof	proof	NOUN
ejpam-4260	394	20	.	.	PUNCT
ejpam-4260	395	1	we	we	PRON
ejpam-4260	395	2	give	give	VERB
ejpam-4260	395	3	a	a	DET
ejpam-4260	395	4	proof	proof	NOUN
ejpam-4260	395	5	for	for	ADP
ejpam-4260	395	6	two	two	NUM
ejpam-4260	395	7	stss	stss	NOUN
ejpam-4260	395	8	(	(	PUNCT
ejpam-4260	395	9	u	u	PROPN
ejpam-4260	395	10	,	,	PUNCT
ejpam-4260	395	11	ω	ω	PROPN
ejpam-4260	395	12	)	)	PUNCT
ejpam-4260	395	13	and	and	CCONJ
ejpam-4260	395	14	(	(	PUNCT
ejpam-4260	395	15	v	v	NOUN
ejpam-4260	395	16	,	,	PUNCT
ejpam-4260	395	17	ψ	ψ	NOUN
ejpam-4260	395	18	)	)	PUNCT
ejpam-4260	395	19	when	when	SCONJ
ejpam-4260	395	20	k	k	PROPN
ejpam-4260	395	21	=	=	SYM
ejpam-4260	395	22	2	2	X
ejpam-4260	395	23	.	.	X
ejpam-4260	395	24	consider	consider	VERB
ejpam-4260	395	25	(	(	PUNCT
ejpam-4260	395	26	u	u	NOUN
ejpam-4260	395	27	×v	×v	VERB
ejpam-4260	395	28	,	,	PUNCT
ejpam-4260	395	29	t	t	PROPN
ejpam-4260	395	30	)	)	PUNCT
ejpam-4260	395	31	as	as	ADP
ejpam-4260	395	32	the	the	DET
ejpam-4260	395	33	product	product	NOUN
ejpam-4260	395	34	of	of	ADP
ejpam-4260	395	35	stss	stss	NOUN
ejpam-4260	395	36	(	(	PUNCT
ejpam-4260	395	37	u	u	PROPN
ejpam-4260	395	38	,	,	PUNCT
ejpam-4260	395	39	ω	ω	PROPN
ejpam-4260	395	40	)	)	PUNCT
ejpam-4260	395	41	and	and	CCONJ
ejpam-4260	395	42	(	(	PUNCT
ejpam-4260	395	43	v	v	NOUN
ejpam-4260	395	44	,	,	PUNCT
ejpam-4260	395	45	ψ	ψ	NOUN
ejpam-4260	395	46	)	)	PUNCT
ejpam-4260	395	47	.	.	PUNCT
ejpam-4260	396	1	suppose	suppose	VERB
ejpam-4260	396	2	that	that	SCONJ
ejpam-4260	396	3	(	(	PUNCT
ejpam-4260	396	4	ξ1	ξ1	NOUN
ejpam-4260	396	5	,	,	PUNCT
ejpam-4260	396	6	ζ1	ζ1	NOUN
ejpam-4260	396	7	)	)	PUNCT
ejpam-4260	396	8	̸=	̸=	PROPN
ejpam-4260	396	9	(	(	PUNCT
ejpam-4260	396	10	ξ2	ξ2	ADJ
ejpam-4260	396	11	,	,	PUNCT
ejpam-4260	396	12	ζ2	ζ2	NOUN
ejpam-4260	396	13	)	)	PUNCT
ejpam-4260	396	14	.	.	PUNCT
ejpam-4260	397	1	then	then	ADV
ejpam-4260	397	2	,	,	PUNCT
ejpam-4260	397	3	ξ1	ξ1	PROPN
ejpam-4260	397	4	̸=	̸=	PROPN
ejpam-4260	397	5	ξ2	ξ2	NOUN
ejpam-4260	397	6	or	or	CCONJ
ejpam-4260	397	7	ζ1	ζ1	NOUN
ejpam-4260	397	8	̸=	̸=	PROPN
ejpam-4260	397	9	ζ2	ζ2	NOUN
ejpam-4260	397	10	.	.	PUNCT
ejpam-4260	398	1	suppose	suppose	VERB
ejpam-4260	398	2	,	,	PUNCT
ejpam-4260	398	3	without	without	ADP
ejpam-4260	398	4	loss	loss	NOUN
ejpam-4260	398	5	of	of	ADP
ejpam-4260	398	6	generality	generality	NOUN
ejpam-4260	398	7	,	,	PUNCT
ejpam-4260	398	8	that	that	SCONJ
ejpam-4260	398	9	ξ1	ξ1	NOUN
ejpam-4260	398	10	̸=	̸=	PROPN
ejpam-4260	398	11	ξ2	ξ2	NOUN
ejpam-4260	398	12	.	.	PUNCT
ejpam-4260	399	1	by	by	ADP
ejpam-4260	399	2	hypothesis	hypothesis	NOUN
ejpam-4260	399	3	,	,	PUNCT
ejpam-4260	399	4	there	there	PRON
ejpam-4260	399	5	are	be	VERB
ejpam-4260	399	6	disjoint	disjoint	ADJ
ejpam-4260	399	7	supra	supra	PROPN
ejpam-4260	399	8	b	b	PROPN
ejpam-4260	399	9	-	-	PUNCT
ejpam-4260	399	10	open	open	ADJ
ejpam-4260	399	11	subsets	subset	NOUN
ejpam-4260	399	12	m	m	VERB
ejpam-4260	399	13	and	and	CCONJ
ejpam-4260	399	14	n	n	PROPN
ejpam-4260	399	15	of	of	ADP
ejpam-4260	399	16	(	(	PUNCT
ejpam-4260	399	17	u	u	PROPN
ejpam-4260	399	18	,	,	PUNCT
ejpam-4260	399	19	ω	ω	NOUN
ejpam-4260	399	20	)	)	PUNCT
ejpam-4260	399	21	respectively	respectively	ADV
ejpam-4260	399	22	including	include	VERB
ejpam-4260	399	23	ξ1	ξ1	NOUN
ejpam-4260	399	24	and	and	CCONJ
ejpam-4260	399	25	ξ2	ξ2	NOUN
ejpam-4260	399	26	.	.	PUNCT
ejpam-4260	400	1	it	it	PRON
ejpam-4260	400	2	follows	follow	VERB
ejpam-4260	400	3	from	from	ADP
ejpam-4260	400	4	theorem	theorem	ADJ
ejpam-4260	400	5	(	(	PUNCT
ejpam-4260	400	6	13	13	NUM
ejpam-4260	400	7	)	)	PUNCT
ejpam-4260	400	8	that	that	PRON
ejpam-4260	400	9	m	m	VERB
ejpam-4260	400	10	×	×	NOUN
ejpam-4260	400	11	v	v	NOUN
ejpam-4260	400	12	and	and	CCONJ
ejpam-4260	400	13	n	n	PRON
ejpam-4260	400	14	×	×	NOUN
ejpam-4260	400	15	v	v	NOUN
ejpam-4260	400	16	are	be	AUX
ejpam-4260	400	17	two	two	NUM
ejpam-4260	400	18	supra	supra	ADJ
ejpam-4260	400	19	b	b	NOUN
ejpam-4260	400	20	-	-	PUNCT
ejpam-4260	400	21	open	open	ADJ
ejpam-4260	400	22	subsets	subset	NOUN
ejpam-4260	400	23	of	of	ADP
ejpam-4260	400	24	(	(	PUNCT
ejpam-4260	400	25	u	u	NOUN
ejpam-4260	400	26	×	×	PROPN
ejpam-4260	400	27	v	v	PROPN
ejpam-4260	400	28	,	,	PUNCT
ejpam-4260	400	29	t	t	PROPN
ejpam-4260	400	30	)	)	PUNCT
ejpam-4260	400	31	respectively	respectively	ADV
ejpam-4260	400	32	including	include	VERB
ejpam-4260	400	33	(	(	PUNCT
ejpam-4260	400	34	ξ1	ξ1	PROPN
ejpam-4260	400	35	,	,	PUNCT
ejpam-4260	400	36	ζ1	ζ1	PROPN
ejpam-4260	400	37	)	)	PUNCT
ejpam-4260	400	38	and	and	CCONJ
ejpam-4260	400	39	(	(	PUNCT
ejpam-4260	400	40	ξ2	ξ2	ADJ
ejpam-4260	400	41	,	,	PUNCT
ejpam-4260	400	42	ζ2	ζ2	NOUN
ejpam-4260	400	43	)	)	PUNCT
ejpam-4260	400	44	such	such	ADJ
ejpam-4260	400	45	that	that	PRON
ejpam-4260	400	46	(	(	PUNCT
ejpam-4260	400	47	m	m	VERB
ejpam-4260	400	48	×	×	PROPN
ejpam-4260	400	49	v	v	NOUN
ejpam-4260	400	50	)	)	PUNCT
ejpam-4260	400	51	⋂̃	⋂̃	NOUN
ejpam-4260	400	52	(	(	PUNCT
ejpam-4260	400	53	n	n	NUM
ejpam-4260	400	54	×	×	NOUN
ejpam-4260	400	55	v	v	NOUN
ejpam-4260	400	56	)	)	PUNCT
ejpam-4260	400	57	=	=	PUNCT
ejpam-4260	400	58	∅.	∅.	ADP
ejpam-4260	400	59	this	this	PRON
ejpam-4260	400	60	proves	prove	VERB
ejpam-4260	400	61	that	that	SCONJ
ejpam-4260	400	62	(	(	PUNCT
ejpam-4260	400	63	u	u	NOUN
ejpam-4260	400	64	×	×	PROPN
ejpam-4260	400	65	v	v	PROPN
ejpam-4260	400	66	,	,	PUNCT
ejpam-4260	400	67	t	t	PROPN
ejpam-4260	400	68	)	)	PUNCT
ejpam-4260	400	69	is	be	AUX
ejpam-4260	400	70	sbt2	sbt2	NOUN
ejpam-4260	400	71	.	.	PUNCT
ejpam-4260	401	1	definition	definition	NOUN
ejpam-4260	401	2	16	16	NUM
ejpam-4260	401	3	.	.	PUNCT
ejpam-4260	402	1	let	let	VERB
ejpam-4260	402	2	(	(	PUNCT
ejpam-4260	402	3	u	u	NOUN
ejpam-4260	402	4	×	×	PROPN
ejpam-4260	402	5	v	v	PROPN
ejpam-4260	402	6	,	,	PUNCT
ejpam-4260	402	7	t	t	PROPN
ejpam-4260	402	8	)	)	PUNCT
ejpam-4260	402	9	be	be	AUX
ejpam-4260	402	10	the	the	DET
ejpam-4260	402	11	product	product	NOUN
ejpam-4260	402	12	of	of	ADP
ejpam-4260	402	13	stss	stss	NOUN
ejpam-4260	402	14	(	(	PUNCT
ejpam-4260	402	15	u	u	PROPN
ejpam-4260	402	16	,	,	PUNCT
ejpam-4260	402	17	ω	ω	PROPN
ejpam-4260	402	18	)	)	PUNCT
ejpam-4260	402	19	and	and	CCONJ
ejpam-4260	402	20	(	(	PUNCT
ejpam-4260	402	21	v	v	NOUN
ejpam-4260	402	22	,	,	PUNCT
ejpam-4260	402	23	ψ	ψ	NOUN
ejpam-4260	402	24	)	)	PUNCT
ejpam-4260	402	25	such	such	ADJ
ejpam-4260	402	26	that	that	PRON
ejpam-4260	402	27	c1	c1	PROPN
ejpam-4260	402	28	and	and	CCONJ
ejpam-4260	402	29	c2	c2	PROPN
ejpam-4260	402	30	are	be	AUX
ejpam-4260	402	31	respectively	respectively	ADV
ejpam-4260	402	32	the	the	DET
ejpam-4260	402	33	classes	class	NOUN
ejpam-4260	402	34	of	of	ADP
ejpam-4260	402	35	all	all	DET
ejpam-4260	402	36	supra	supra	PROPN
ejpam-4260	402	37	b	b	NOUN
ejpam-4260	402	38	-	-	PUNCT
ejpam-4260	402	39	open	open	ADJ
ejpam-4260	402	40	subsets	subset	NOUN
ejpam-4260	402	41	of	of	ADP
ejpam-4260	402	42	(	(	PUNCT
ejpam-4260	402	43	u	u	NOUN
ejpam-4260	402	44	,	,	PUNCT
ejpam-4260	402	45	ω	ω	PROPN
ejpam-4260	402	46	)	)	PUNCT
ejpam-4260	402	47	and	and	CCONJ
ejpam-4260	402	48	(	(	PUNCT
ejpam-4260	402	49	v	v	NOUN
ejpam-4260	402	50	,	,	PUNCT
ejpam-4260	402	51	ψ	ψ	NOUN
ejpam-4260	402	52	)	)	PUNCT
ejpam-4260	402	53	.	.	PUNCT
ejpam-4260	403	1	then	then	ADV
ejpam-4260	403	2	β	β	X
ejpam-4260	403	3	=	=	PUNCT
ejpam-4260	403	4	{	{	PUNCT
ejpam-4260	403	5	θ×h	θ×h	PROPN
ejpam-4260	403	6	:	:	PUNCT
ejpam-4260	403	7	θ	θ	PROPN
ejpam-4260	403	8	∈	∈	PROPN
ejpam-4260	403	9	c1	c1	PROPN
ejpam-4260	403	10	and	and	CCONJ
ejpam-4260	403	11	h	h	NOUN
ejpam-4260	403	12	∈	∈	PROPN
ejpam-4260	403	13	c2	c2	PROPN
ejpam-4260	403	14	}	}	PUNCT
ejpam-4260	403	15	forms	form	VERB
ejpam-4260	403	16	a	a	DET
ejpam-4260	403	17	basis	basis	NOUN
ejpam-4260	403	18	for	for	ADP
ejpam-4260	403	19	an	an	DET
ejpam-4260	403	20	st	st	PROPN
ejpam-4260	403	21	c	c	PROPN
ejpam-4260	403	22	on	on	ADP
ejpam-4260	403	23	u	u	PRON
ejpam-4260	403	24	×v	×v	VERB
ejpam-4260	403	25	.	.	PUNCT
ejpam-4260	404	1	we	we	PRON
ejpam-4260	404	2	call	call	VERB
ejpam-4260	404	3	(	(	PUNCT
ejpam-4260	404	4	u	u	NOUN
ejpam-4260	404	5	×v	×v	VERB
ejpam-4260	404	6	,	,	PUNCT
ejpam-4260	404	7	c	c	X
ejpam-4260	404	8	)	)	PUNCT
ejpam-4260	404	9	a	a	DET
ejpam-4260	404	10	b	b	X
ejpam-4260	404	11	-	-	ADJ
ejpam-4260	404	12	finite	finite	ADJ
ejpam-4260	404	13	product	product	NOUN
ejpam-4260	404	14	of	of	ADP
ejpam-4260	404	15	supra	supra	PROPN
ejpam-4260	404	16	spaces	space	NOUN
ejpam-4260	404	17	.	.	PUNCT
ejpam-4260	405	1	lemma	lemma	PROPN
ejpam-4260	405	2	1	1	X
ejpam-4260	405	3	.	.	PUNCT
ejpam-4260	406	1	let	let	VERB
ejpam-4260	406	2	(	(	PUNCT
ejpam-4260	406	3	u	u	NOUN
ejpam-4260	406	4	×	×	PROPN
ejpam-4260	406	5	v	v	ADP
ejpam-4260	406	6	,	,	PUNCT
ejpam-4260	406	7	c	c	AUX
ejpam-4260	406	8	)	)	PUNCT
ejpam-4260	406	9	be	be	AUX
ejpam-4260	406	10	the	the	DET
ejpam-4260	406	11	b	b	NOUN
ejpam-4260	406	12	-	-	PUNCT
ejpam-4260	406	13	product	product	NOUN
ejpam-4260	406	14	of	of	ADP
ejpam-4260	406	15	stss	stss	NOUN
ejpam-4260	406	16	(	(	PUNCT
ejpam-4260	406	17	u	u	PROPN
ejpam-4260	406	18	,	,	PUNCT
ejpam-4260	406	19	ω	ω	PROPN
ejpam-4260	406	20	)	)	PUNCT
ejpam-4260	406	21	and	and	CCONJ
ejpam-4260	406	22	(	(	PUNCT
ejpam-4260	406	23	v	v	NOUN
ejpam-4260	406	24	,	,	PUNCT
ejpam-4260	406	25	ψ	ψ	NOUN
ejpam-4260	406	26	)	)	PUNCT
ejpam-4260	406	27	.	.	PUNCT
ejpam-4260	407	1	if	if	SCONJ
ejpam-4260	407	2	e	e	PROPN
ejpam-4260	407	3	is	be	AUX
ejpam-4260	407	4	a	a	DET
ejpam-4260	407	5	supra	supra	NOUN
ejpam-4260	407	6	closed	close	VERB
ejpam-4260	407	7	subset	subset	NOUN
ejpam-4260	407	8	of	of	ADP
ejpam-4260	407	9	(	(	PUNCT
ejpam-4260	407	10	u	u	PROPN
ejpam-4260	407	11	×	×	PROPN
ejpam-4260	407	12	v	v	NOUN
ejpam-4260	407	13	,	,	PUNCT
ejpam-4260	407	14	c	c	NOUN
ejpam-4260	407	15	)	)	PUNCT
ejpam-4260	407	16	,	,	PUNCT
ejpam-4260	407	17	then	then	ADV
ejpam-4260	407	18	e	e	PROPN
ejpam-4260	407	19	=	=	SYM
ejpam-4260	407	20	⋂	⋂	PROPN
ejpam-4260	407	21	k∈i	k∈i	NOUN
ejpam-4260	407	22	[	[	X
ejpam-4260	407	23	(	(	PUNCT
ejpam-4260	407	24	fk	fk	INTJ
ejpam-4260	407	25	×	×	PROPN
ejpam-4260	407	26	v	v	NOUN
ejpam-4260	407	27	)	)	PUNCT
ejpam-4260	407	28	⋃	⋃	PROPN
ejpam-4260	407	29	(	(	PUNCT
ejpam-4260	407	30	u	u	NOUN
ejpam-4260	407	31	×	×	PROPN
ejpam-4260	407	32	hk	hk	PROPN
ejpam-4260	407	33	)	)	PUNCT
ejpam-4260	407	34	]	]	PUNCT
ejpam-4260	407	35	,	,	PUNCT
ejpam-4260	407	36	where	where	SCONJ
ejpam-4260	407	37	fk	fk	INTJ
ejpam-4260	407	38	and	and	CCONJ
ejpam-4260	407	39	hk	hk	PROPN
ejpam-4260	407	40	are	be	AUX
ejpam-4260	407	41	respectively	respectively	ADV
ejpam-4260	407	42	supra	supra	PROPN
ejpam-4260	407	43	b	b	NOUN
ejpam-4260	407	44	-	-	PUNCT
ejpam-4260	407	45	closed	closed	ADJ
ejpam-4260	407	46	subsets	subset	NOUN
ejpam-4260	407	47	of	of	ADP
ejpam-4260	407	48	(	(	PUNCT
ejpam-4260	407	49	u	u	PROPN
ejpam-4260	407	50	,	,	PUNCT
ejpam-4260	407	51	ω	ω	PROPN
ejpam-4260	407	52	)	)	PUNCT
ejpam-4260	407	53	and	and	CCONJ
ejpam-4260	407	54	(	(	PUNCT
ejpam-4260	407	55	v	v	NOUN
ejpam-4260	407	56	,	,	PUNCT
ejpam-4260	407	57	ψ	ψ	NOUN
ejpam-4260	407	58	)	)	PUNCT
ejpam-4260	407	59	.	.	PUNCT
ejpam-4260	408	1	theorem	theorem	NOUN
ejpam-4260	408	2	15	15	NUM
ejpam-4260	408	3	.	.	PUNCT
ejpam-4260	409	1	the	the	DET
ejpam-4260	409	2	b	b	NOUN
ejpam-4260	409	3	-	-	ADJ
ejpam-4260	409	4	finite	finite	ADJ
ejpam-4260	409	5	product	product	NOUN
ejpam-4260	409	6	of	of	ADP
ejpam-4260	409	7	sbtk	sbtk	NOUN
ejpam-4260	409	8	-	-	PUNCT
ejpam-4260	409	9	spaces	space	NOUN
ejpam-4260	409	10	is	be	AUX
ejpam-4260	409	11	stk	stk	PROPN
ejpam-4260	409	12	for	for	ADP
ejpam-4260	409	13	k	k	PROPN
ejpam-4260	409	14	=	=	SYM
ejpam-4260	409	15	0	0	NUM
ejpam-4260	409	16	,	,	PUNCT
ejpam-4260	409	17	1	1	NUM
ejpam-4260	409	18	,	,	PUNCT
ejpam-4260	409	19	2	2	NUM
ejpam-4260	409	20	,	,	PUNCT
ejpam-4260	409	21	3	3	NUM
ejpam-4260	409	22	.	.	PUNCT
ejpam-4260	409	23	a.	a.	NOUN
ejpam-4260	409	24	mhemdi	mhemdi	PROPN
ejpam-4260	409	25	et	et	PROPN
ejpam-4260	409	26	al	al	PROPN
ejpam-4260	409	27	.	.	PUNCT
ejpam-4260	409	28	/	/	SYM
ejpam-4260	409	29	eur	eur	PROPN
ejpam-4260	409	30	.	.	PUNCT
ejpam-4260	410	1	j.	j.	PROPN
ejpam-4260	410	2	pure	pure	PROPN
ejpam-4260	410	3	appl	appl	PROPN
ejpam-4260	410	4	.	.	PROPN
ejpam-4260	410	5	math	math	PROPN
ejpam-4260	410	6	,	,	PUNCT
ejpam-4260	410	7	15	15	NUM
ejpam-4260	410	8	(	(	PUNCT
ejpam-4260	410	9	1	1	NUM
ejpam-4260	410	10	)	)	PUNCT
ejpam-4260	410	11	(	(	PUNCT
ejpam-4260	410	12	2022	2022	NUM
ejpam-4260	410	13	)	)	PUNCT
ejpam-4260	410	14	,	,	PUNCT
ejpam-4260	410	15	15	15	NUM
ejpam-4260	410	16	-	-	SYM
ejpam-4260	410	17	29	29	NUM
ejpam-4260	410	18	27	27	NUM
ejpam-4260	410	19	proof	proof	NOUN
ejpam-4260	410	20	.	.	PUNCT
ejpam-4260	411	1	we	we	PRON
ejpam-4260	411	2	give	give	VERB
ejpam-4260	411	3	a	a	DET
ejpam-4260	411	4	proof	proof	NOUN
ejpam-4260	411	5	for	for	ADP
ejpam-4260	411	6	two	two	NUM
ejpam-4260	411	7	stss	stss	NOUN
ejpam-4260	411	8	(	(	PUNCT
ejpam-4260	411	9	u	u	PROPN
ejpam-4260	411	10	,	,	PUNCT
ejpam-4260	411	11	ω	ω	PROPN
ejpam-4260	411	12	)	)	PUNCT
ejpam-4260	411	13	and	and	CCONJ
ejpam-4260	411	14	(	(	PUNCT
ejpam-4260	411	15	v	v	NOUN
ejpam-4260	411	16	,	,	PUNCT
ejpam-4260	411	17	ψ	ψ	NOUN
ejpam-4260	411	18	)	)	PUNCT
ejpam-4260	411	19	when	when	SCONJ
ejpam-4260	411	20	k	k	PROPN
ejpam-4260	411	21	=	=	SYM
ejpam-4260	411	22	3	3	X
ejpam-4260	411	23	.	.	X
ejpam-4260	412	1	let	let	AUX
ejpam-4260	412	2	(	(	PUNCT
ejpam-4260	412	3	u×v	u×v	PROPN
ejpam-4260	412	4	,	,	PUNCT
ejpam-4260	412	5	c	c	AUX
ejpam-4260	412	6	)	)	PUNCT
ejpam-4260	412	7	be	be	VERB
ejpam-4260	412	8	the	the	DET
ejpam-4260	412	9	b	b	NOUN
ejpam-4260	412	10	-	-	PUNCT
ejpam-4260	412	11	product	product	NOUN
ejpam-4260	412	12	supra	supra	ADJ
ejpam-4260	412	13	space	space	NOUN
ejpam-4260	412	14	of	of	ADP
ejpam-4260	412	15	(	(	PUNCT
ejpam-4260	412	16	u	u	PROPN
ejpam-4260	412	17	,	,	PUNCT
ejpam-4260	412	18	ω	ω	PROPN
ejpam-4260	412	19	)	)	PUNCT
ejpam-4260	412	20	and	and	CCONJ
ejpam-4260	412	21	(	(	PUNCT
ejpam-4260	412	22	v	v	NOUN
ejpam-4260	412	23	,	,	PUNCT
ejpam-4260	412	24	ψ	ψ	NOUN
ejpam-4260	412	25	)	)	PUNCT
ejpam-4260	412	26	.	.	PUNCT
ejpam-4260	413	1	first	first	ADV
ejpam-4260	413	2	,	,	PUNCT
ejpam-4260	413	3	we	we	PRON
ejpam-4260	413	4	demonstrate	demonstrate	VERB
ejpam-4260	413	5	that	that	SCONJ
ejpam-4260	413	6	(	(	PUNCT
ejpam-4260	413	7	u×v	u×v	PROPN
ejpam-4260	413	8	,	,	PUNCT
ejpam-4260	413	9	c	c	NOUN
ejpam-4260	413	10	)	)	PUNCT
ejpam-4260	413	11	is	be	AUX
ejpam-4260	413	12	st1	st1	PROPN
ejpam-4260	413	13	.	.	PUNCT
ejpam-4260	414	1	to	to	PART
ejpam-4260	414	2	do	do	VERB
ejpam-4260	414	3	this	this	PRON
ejpam-4260	414	4	,	,	PUNCT
ejpam-4260	414	5	let	let	VERB
ejpam-4260	414	6	(	(	PUNCT
ejpam-4260	414	7	ξ1	ξ1	NOUN
ejpam-4260	414	8	,	,	PUNCT
ejpam-4260	414	9	ζ1	ζ1	NOUN
ejpam-4260	414	10	)	)	PUNCT
ejpam-4260	414	11	̸=	̸=	PROPN
ejpam-4260	414	12	(	(	PUNCT
ejpam-4260	414	13	ξ2	ξ2	ADJ
ejpam-4260	414	14	,	,	PUNCT
ejpam-4260	414	15	ζ2	ζ2	NOUN
ejpam-4260	414	16	)	)	PUNCT
ejpam-4260	414	17	.	.	PUNCT
ejpam-4260	415	1	then	then	ADV
ejpam-4260	415	2	,	,	PUNCT
ejpam-4260	415	3	ξ1	ξ1	PROPN
ejpam-4260	415	4	̸=	̸=	PROPN
ejpam-4260	415	5	ξ2	ξ2	NOUN
ejpam-4260	415	6	or	or	CCONJ
ejpam-4260	415	7	ζ1	ζ1	NOUN
ejpam-4260	415	8	̸=	̸=	PROPN
ejpam-4260	415	9	ζ2	ζ2	NOUN
ejpam-4260	415	10	.	.	PUNCT
ejpam-4260	416	1	suppose	suppose	VERB
ejpam-4260	416	2	,	,	PUNCT
ejpam-4260	416	3	without	without	ADP
ejpam-4260	416	4	loss	loss	NOUN
ejpam-4260	416	5	of	of	ADP
ejpam-4260	416	6	generality	generality	NOUN
ejpam-4260	416	7	,	,	PUNCT
ejpam-4260	416	8	that	that	SCONJ
ejpam-4260	416	9	ξ1	ξ1	NOUN
ejpam-4260	416	10	̸=	̸=	PROPN
ejpam-4260	416	11	ξ2	ξ2	NOUN
ejpam-4260	416	12	.	.	PUNCT
ejpam-4260	417	1	so	so	ADV
ejpam-4260	417	2	that	that	SCONJ
ejpam-4260	417	3	,	,	PUNCT
ejpam-4260	417	4	there	there	PRON
ejpam-4260	417	5	are	be	VERB
ejpam-4260	417	6	supra	supra	ADJ
ejpam-4260	417	7	b	b	NOUN
ejpam-4260	417	8	-	-	PUNCT
ejpam-4260	417	9	open	open	ADJ
ejpam-4260	417	10	subsets	subset	NOUN
ejpam-4260	417	11	m	m	VERB
ejpam-4260	417	12	and	and	CCONJ
ejpam-4260	417	13	n	n	PROPN
ejpam-4260	417	14	of	of	ADP
ejpam-4260	417	15	(	(	PUNCT
ejpam-4260	417	16	u	u	PROPN
ejpam-4260	417	17	,	,	PUNCT
ejpam-4260	417	18	ω	ω	NOUN
ejpam-4260	417	19	)	)	PUNCT
ejpam-4260	417	20	respectively	respectively	ADV
ejpam-4260	417	21	including	include	VERB
ejpam-4260	417	22	ξ1	ξ1	NOUN
ejpam-4260	417	23	and	and	CCONJ
ejpam-4260	417	24	ξ2	ξ2	NOUN
ejpam-4260	417	25	.	.	PUNCT
ejpam-4260	418	1	it	it	PRON
ejpam-4260	418	2	comes	come	VERB
ejpam-4260	418	3	from	from	ADP
ejpam-4260	418	4	definition(16	definition(16	NOUN
ejpam-4260	418	5	)	)	PUNCT
ejpam-4260	418	6	that	that	PRON
ejpam-4260	418	7	m	m	VERB
ejpam-4260	418	8	×	×	NOUN
ejpam-4260	418	9	v	v	NOUN
ejpam-4260	418	10	and	and	CCONJ
ejpam-4260	418	11	n	n	PRON
ejpam-4260	418	12	×v	×v	NOUN
ejpam-4260	418	13	are	be	AUX
ejpam-4260	418	14	two	two	NUM
ejpam-4260	418	15	supra	supra	ADJ
ejpam-4260	418	16	open	open	ADJ
ejpam-4260	418	17	subsets	subset	NOUN
ejpam-4260	418	18	of	of	ADP
ejpam-4260	418	19	(	(	PUNCT
ejpam-4260	418	20	u	u	NOUN
ejpam-4260	418	21	×v	×v	VERB
ejpam-4260	418	22	,	,	PUNCT
ejpam-4260	418	23	c	c	NOUN
ejpam-4260	418	24	)	)	PUNCT
ejpam-4260	418	25	respectively	respectively	ADV
ejpam-4260	418	26	including	include	VERB
ejpam-4260	418	27	(	(	PUNCT
ejpam-4260	418	28	ξ1	ξ1	PROPN
ejpam-4260	418	29	,	,	PUNCT
ejpam-4260	418	30	ζ1	ζ1	PROPN
ejpam-4260	418	31	)	)	PUNCT
ejpam-4260	418	32	and	and	CCONJ
ejpam-4260	418	33	(	(	PUNCT
ejpam-4260	418	34	ξ2	ξ2	ADJ
ejpam-4260	418	35	,	,	PUNCT
ejpam-4260	418	36	ζ2	ζ2	NOUN
ejpam-4260	418	37	)	)	PUNCT
ejpam-4260	418	38	such	such	ADJ
ejpam-4260	418	39	that	that	SCONJ
ejpam-4260	418	40	(	(	PUNCT
ejpam-4260	418	41	ξ1	ξ1	NOUN
ejpam-4260	418	42	,	,	PUNCT
ejpam-4260	418	43	ζ1	ζ1	PROPN
ejpam-4260	418	44	)	)	PUNCT
ejpam-4260	418	45	̸∈	̸∈	PROPN
ejpam-4260	418	46	n	n	NUM
ejpam-4260	418	47	×	×	NOUN
ejpam-4260	418	48	v	v	NOUN
ejpam-4260	418	49	and	and	CCONJ
ejpam-4260	418	50	(	(	PUNCT
ejpam-4260	418	51	ξ2	ξ2	ADJ
ejpam-4260	418	52	,	,	PUNCT
ejpam-4260	418	53	ζ2	ζ2	NOUN
ejpam-4260	418	54	)	)	PUNCT
ejpam-4260	418	55	̸∈	̸∈	PROPN
ejpam-4260	418	56	m	m	PROPN
ejpam-4260	418	57	×	×	NOUN
ejpam-4260	418	58	v.	v.	ADP
ejpam-4260	418	59	thus	thus	ADV
ejpam-4260	418	60	,	,	PUNCT
ejpam-4260	418	61	(	(	PUNCT
ejpam-4260	418	62	u	u	NOUN
ejpam-4260	418	63	×	×	PROPN
ejpam-4260	418	64	v	v	NOUN
ejpam-4260	418	65	,	,	PUNCT
ejpam-4260	418	66	c	c	NOUN
ejpam-4260	418	67	)	)	PUNCT
ejpam-4260	418	68	is	be	AUX
ejpam-4260	418	69	st1	st1	PROPN
ejpam-4260	418	70	.	.	PROPN
ejpam-4260	419	1	second	second	PROPN
ejpam-4260	419	2	,	,	PUNCT
ejpam-4260	419	3	we	we	PRON
ejpam-4260	419	4	demonstrate	demonstrate	VERB
ejpam-4260	419	5	that	that	SCONJ
ejpam-4260	419	6	(	(	PUNCT
ejpam-4260	419	7	u	u	NOUN
ejpam-4260	419	8	×	×	PROPN
ejpam-4260	419	9	v	v	ADP
ejpam-4260	419	10	,	,	PUNCT
ejpam-4260	419	11	c	c	NOUN
ejpam-4260	419	12	)	)	PUNCT
ejpam-4260	419	13	is	be	AUX
ejpam-4260	419	14	supra	supra	ADJ
ejpam-4260	419	15	regular	regular	ADJ
ejpam-4260	419	16	.	.	PUNCT
ejpam-4260	420	1	suppose	suppose	VERB
ejpam-4260	420	2	that	that	SCONJ
ejpam-4260	420	3	(	(	PUNCT
ejpam-4260	420	4	x	x	X
ejpam-4260	420	5	,	,	PUNCT
ejpam-4260	420	6	y	y	NOUN
ejpam-4260	420	7	)	)	PUNCT
ejpam-4260	420	8	∈	∈	PROPN
ejpam-4260	420	9	u	u	NOUN
ejpam-4260	420	10	×	×	PROPN
ejpam-4260	420	11	v	v	NOUN
ejpam-4260	420	12	and	and	CCONJ
ejpam-4260	420	13	e	e	NOUN
ejpam-4260	420	14	is	be	AUX
ejpam-4260	420	15	a	a	DET
ejpam-4260	420	16	supra	supra	NOUN
ejpam-4260	420	17	closed	close	VERB
ejpam-4260	420	18	subset	subset	NOUN
ejpam-4260	420	19	of	of	ADP
ejpam-4260	420	20	(	(	PUNCT
ejpam-4260	420	21	u	u	NOUN
ejpam-4260	420	22	×v	×v	VERB
ejpam-4260	420	23	,	,	PUNCT
ejpam-4260	420	24	c	c	NOUN
ejpam-4260	420	25	)	)	PUNCT
ejpam-4260	420	26	such	such	ADJ
ejpam-4260	420	27	that	that	SCONJ
ejpam-4260	420	28	(	(	PUNCT
ejpam-4260	420	29	ξ	ξ	PROPN
ejpam-4260	420	30	,	,	PUNCT
ejpam-4260	420	31	ζ	ζ	NOUN
ejpam-4260	420	32	)	)	PUNCT
ejpam-4260	420	33	̸∈	̸∈	PROPN
ejpam-4260	420	34	e	e	PROPN
ejpam-4260	420	35	=	=	PROPN
ejpam-4260	420	36	⋂	⋂	PROPN
ejpam-4260	420	37	k∈i	k∈i	NOUN
ejpam-4260	420	38	[	[	X
ejpam-4260	420	39	(	(	PUNCT
ejpam-4260	420	40	fk×v	fk×v	ADJ
ejpam-4260	420	41	)	)	PUNCT
ejpam-4260	420	42	⋃	⋃	NOUN
ejpam-4260	420	43	(	(	PUNCT
ejpam-4260	420	44	u	u	NOUN
ejpam-4260	420	45	×hk	×hk	PROPN
ejpam-4260	420	46	)	)	PUNCT
ejpam-4260	420	47	]	]	PUNCT
ejpam-4260	420	48	,	,	PUNCT
ejpam-4260	420	49	where	where	SCONJ
ejpam-4260	420	50	fk	fk	INTJ
ejpam-4260	420	51	and	and	CCONJ
ejpam-4260	420	52	hk	hk	PROPN
ejpam-4260	420	53	are	be	AUX
ejpam-4260	420	54	respectively	respectively	ADV
ejpam-4260	420	55	supra	supra	PROPN
ejpam-4260	420	56	b	b	NOUN
ejpam-4260	420	57	-	-	PUNCT
ejpam-4260	420	58	closed	closed	ADJ
ejpam-4260	420	59	subsets	subset	NOUN
ejpam-4260	420	60	of	of	ADP
ejpam-4260	420	61	(	(	PUNCT
ejpam-4260	420	62	u	u	PROPN
ejpam-4260	420	63	,	,	PUNCT
ejpam-4260	420	64	ω	ω	PROPN
ejpam-4260	420	65	)	)	PUNCT
ejpam-4260	420	66	and	and	CCONJ
ejpam-4260	420	67	(	(	PUNCT
ejpam-4260	420	68	v	v	NOUN
ejpam-4260	420	69	,	,	PUNCT
ejpam-4260	420	70	ψ	ψ	NOUN
ejpam-4260	420	71	)	)	PUNCT
ejpam-4260	420	72	.	.	PUNCT
ejpam-4260	421	1	then	then	ADV
ejpam-4260	421	2	there	there	PRON
ejpam-4260	421	3	is	be	VERB
ejpam-4260	421	4	j	j	PROPN
ejpam-4260	421	5	∈	∈	PROPN
ejpam-4260	421	6	i	i	PRON
ejpam-4260	421	7	such	such	ADJ
ejpam-4260	421	8	that	that	SCONJ
ejpam-4260	421	9	(	(	PUNCT
ejpam-4260	421	10	ξ	ξ	PROPN
ejpam-4260	421	11	,	,	PUNCT
ejpam-4260	421	12	ζ	ζ	NOUN
ejpam-4260	421	13	)	)	PUNCT
ejpam-4260	421	14	̸∈	̸∈	PROPN
ejpam-4260	421	15	[	[	X
ejpam-4260	421	16	(	(	PUNCT
ejpam-4260	421	17	fj	fj	INTJ
ejpam-4260	421	18	×v	×v	NOUN
ejpam-4260	421	19	)	)	PUNCT
ejpam-4260	421	20	⋃	⋃	PROPN
ejpam-4260	421	21	(	(	PUNCT
ejpam-4260	421	22	u	u	NOUN
ejpam-4260	421	23	×hj	×hj	PROPN
ejpam-4260	421	24	)	)	PUNCT
ejpam-4260	421	25	]	]	PUNCT
ejpam-4260	421	26	.	.	PUNCT
ejpam-4260	422	1	this	this	PRON
ejpam-4260	422	2	means	mean	VERB
ejpam-4260	422	3	that	that	SCONJ
ejpam-4260	422	4	ξ	ξ	PROPN
ejpam-4260	422	5	̸∈	̸∈	PROPN
ejpam-4260	422	6	fj	fj	PROPN
ejpam-4260	422	7	and	and	CCONJ
ejpam-4260	422	8	ζ	ζ	PROPN
ejpam-4260	422	9	̸∈	̸∈	PROPN
ejpam-4260	422	10	hj	hj	PROPN
ejpam-4260	422	11	.	.	PUNCT
ejpam-4260	423	1	since	since	SCONJ
ejpam-4260	423	2	(	(	PUNCT
ejpam-4260	423	3	u	u	INTJ
ejpam-4260	423	4	,	,	PUNCT
ejpam-4260	423	5	ω	ω	PROPN
ejpam-4260	423	6	)	)	PUNCT
ejpam-4260	423	7	and	and	CCONJ
ejpam-4260	423	8	(	(	PUNCT
ejpam-4260	423	9	v	v	NOUN
ejpam-4260	423	10	,	,	PUNCT
ejpam-4260	423	11	ψ	ψ	NOUN
ejpam-4260	423	12	)	)	PUNCT
ejpam-4260	423	13	are	be	AUX
ejpam-4260	423	14	supra	supra	PROPN
ejpam-4260	423	15	b	b	PROPN
ejpam-4260	423	16	regular	regular	ADJ
ejpam-4260	423	17	,	,	PUNCT
ejpam-4260	423	18	there	there	PRON
ejpam-4260	423	19	are	be	VERB
ejpam-4260	423	20	disjoint	disjoint	ADJ
ejpam-4260	423	21	supra	supra	PROPN
ejpam-4260	423	22	b	b	PROPN
ejpam-4260	423	23	-	-	PUNCT
ejpam-4260	423	24	open	open	ADJ
ejpam-4260	423	25	subsets	subset	NOUN
ejpam-4260	423	26	o	o	NOUN
ejpam-4260	423	27	and	and	CCONJ
ejpam-4260	423	28	p	p	X
ejpam-4260	423	29	of	of	ADP
ejpam-4260	423	30	(	(	PUNCT
ejpam-4260	423	31	u	u	PROPN
ejpam-4260	423	32	,	,	PUNCT
ejpam-4260	423	33	ω	ω	NOUN
ejpam-4260	423	34	)	)	PUNCT
ejpam-4260	423	35	respectively	respectively	ADV
ejpam-4260	423	36	including	include	VERB
ejpam-4260	423	37	ξ	ξ	PROPN
ejpam-4260	423	38	and	and	CCONJ
ejpam-4260	423	39	fj	fj	PROPN
ejpam-4260	423	40	,	,	PUNCT
ejpam-4260	423	41	and	and	CCONJ
ejpam-4260	423	42	there	there	PRON
ejpam-4260	423	43	are	be	VERB
ejpam-4260	423	44	disjoint	disjoint	ADJ
ejpam-4260	423	45	supra	supra	PROPN
ejpam-4260	423	46	b	b	PROPN
ejpam-4260	423	47	-	-	PUNCT
ejpam-4260	423	48	open	open	ADJ
ejpam-4260	423	49	subsets	subset	NOUN
ejpam-4260	423	50	m	m	VERB
ejpam-4260	423	51	and	and	CCONJ
ejpam-4260	423	52	n	n	PROPN
ejpam-4260	423	53	of	of	ADP
ejpam-4260	423	54	(	(	PUNCT
ejpam-4260	423	55	v	v	NOUN
ejpam-4260	423	56	,	,	PUNCT
ejpam-4260	423	57	ψ	ψ	NOUN
ejpam-4260	423	58	)	)	PUNCT
ejpam-4260	423	59	respectively	respectively	ADV
ejpam-4260	423	60	including	include	VERB
ejpam-4260	423	61	ζ	ζ	NOUN
ejpam-4260	423	62	and	and	CCONJ
ejpam-4260	423	63	hj	hj	PROPN
ejpam-4260	423	64	.	.	PUNCT
ejpam-4260	424	1	now	now	ADV
ejpam-4260	424	2	,	,	PUNCT
ejpam-4260	424	3	o	o	INTJ
ejpam-4260	424	4	×	×	NOUN
ejpam-4260	424	5	m	m	VERB
ejpam-4260	424	6	and	and	CCONJ
ejpam-4260	424	7	[	[	X
ejpam-4260	424	8	(	(	PUNCT
ejpam-4260	424	9	p	p	X
ejpam-4260	424	10	×	×	PROPN
ejpam-4260	424	11	v	v	NOUN
ejpam-4260	424	12	)	)	PUNCT
ejpam-4260	424	13	⋃	⋃	PROPN
ejpam-4260	424	14	(	(	PUNCT
ejpam-4260	424	15	u	u	NOUN
ejpam-4260	424	16	×	×	NOUN
ejpam-4260	424	17	n	n	CCONJ
ejpam-4260	424	18	)	)	PUNCT
ejpam-4260	424	19	]	]	PUNCT
ejpam-4260	424	20	are	be	AUX
ejpam-4260	424	21	two	two	NUM
ejpam-4260	424	22	supra	supra	ADJ
ejpam-4260	424	23	open	open	ADJ
ejpam-4260	424	24	subsets	subset	NOUN
ejpam-4260	424	25	of	of	ADP
ejpam-4260	424	26	(	(	PUNCT
ejpam-4260	424	27	u	u	NOUN
ejpam-4260	424	28	×	×	PROPN
ejpam-4260	424	29	v	v	NOUN
ejpam-4260	424	30	,	,	PUNCT
ejpam-4260	424	31	c	c	NOUN
ejpam-4260	424	32	)	)	PUNCT
ejpam-4260	424	33	respectively	respectively	ADV
ejpam-4260	424	34	including	include	VERB
ejpam-4260	424	35	(	(	PUNCT
ejpam-4260	424	36	ξ	ξ	PROPN
ejpam-4260	424	37	,	,	PUNCT
ejpam-4260	424	38	ζ	ζ	NOUN
ejpam-4260	424	39	)	)	PUNCT
ejpam-4260	424	40	and	and	CCONJ
ejpam-4260	424	41	[	[	X
ejpam-4260	424	42	(	(	PUNCT
ejpam-4260	424	43	fj	fj	INTJ
ejpam-4260	424	44	×	×	PROPN
ejpam-4260	424	45	v	v	NOUN
ejpam-4260	424	46	)	)	PUNCT
ejpam-4260	424	47	⋃	⋃	PROPN
ejpam-4260	424	48	(	(	PUNCT
ejpam-4260	424	49	u	u	NOUN
ejpam-4260	424	50	×	×	PROPN
ejpam-4260	424	51	hj	hj	PROPN
ejpam-4260	424	52	)	)	PUNCT
ejpam-4260	424	53	]	]	PUNCT
ejpam-4260	424	54	.	.	PUNCT
ejpam-4260	425	1	obviously	obviously	ADV
ejpam-4260	425	2	,	,	PUNCT
ejpam-4260	425	3	e	e	PROPN
ejpam-4260	425	4	⊆	⊆	NUM
ejpam-4260	425	5	[	[	X
ejpam-4260	425	6	(	(	PUNCT
ejpam-4260	425	7	fj	fj	INTJ
ejpam-4260	425	8	×	×	PROPN
ejpam-4260	425	9	v	v	NOUN
ejpam-4260	425	10	)	)	PUNCT
ejpam-4260	425	11	⋃	⋃	PROPN
ejpam-4260	425	12	(	(	PUNCT
ejpam-4260	425	13	u	u	NOUN
ejpam-4260	425	14	×	×	PROPN
ejpam-4260	425	15	hj	hj	PROPN
ejpam-4260	425	16	)	)	PUNCT
ejpam-4260	425	17	]	]	PUNCT
ejpam-4260	426	1	and	and	CCONJ
ejpam-4260	426	2	(	(	PUNCT
ejpam-4260	426	3	o	o	NOUN
ejpam-4260	426	4	×	×	PROPN
ejpam-4260	426	5	m	m	NOUN
ejpam-4260	426	6	)	)	PUNCT
ejpam-4260	427	1	⋂	⋂	PROPN
ejpam-4260	428	1	[	[	X
ejpam-4260	428	2	(	(	PUNCT
ejpam-4260	428	3	p	p	NOUN
ejpam-4260	428	4	×	×	PROPN
ejpam-4260	428	5	v	v	NOUN
ejpam-4260	428	6	)	)	PUNCT
ejpam-4260	428	7	⋃	⋃	PROPN
ejpam-4260	428	8	(	(	PUNCT
ejpam-4260	428	9	u	u	NOUN
ejpam-4260	428	10	×	×	NOUN
ejpam-4260	428	11	n	n	CCONJ
ejpam-4260	428	12	)	)	PUNCT
ejpam-4260	428	13	]	]	PUNCT
ejpam-4260	429	1	=	=	PUNCT
ejpam-4260	429	2	∅.	∅.	VERB
ejpam-4260	429	3	hence	hence	ADV
ejpam-4260	429	4	,	,	PUNCT
ejpam-4260	429	5	(	(	PUNCT
ejpam-4260	429	6	u	u	NOUN
ejpam-4260	429	7	×	×	PROPN
ejpam-4260	429	8	v	v	PROPN
ejpam-4260	429	9	,	,	PUNCT
ejpam-4260	429	10	t	t	PROPN
ejpam-4260	429	11	)	)	PUNCT
ejpam-4260	429	12	is	be	AUX
ejpam-4260	429	13	supra	supra	ADJ
ejpam-4260	429	14	regular	regular	ADJ
ejpam-4260	429	15	.	.	PUNCT
ejpam-4260	430	1	5	5	X
ejpam-4260	430	2	.	.	X
ejpam-4260	430	3	conclusion	conclusion	PROPN
ejpam-4260	430	4	supra	supra	PROPN
ejpam-4260	430	5	topology	topology	NOUN
ejpam-4260	430	6	is	be	AUX
ejpam-4260	430	7	one	one	NUM
ejpam-4260	430	8	of	of	ADP
ejpam-4260	430	9	the	the	DET
ejpam-4260	430	10	famous	famous	ADJ
ejpam-4260	430	11	extensions	extension	NOUN
ejpam-4260	430	12	of	of	ADP
ejpam-4260	430	13	topological	topological	ADJ
ejpam-4260	430	14	spaces	space	NOUN
ejpam-4260	430	15	.	.	PUNCT
ejpam-4260	431	1	we	we	PRON
ejpam-4260	431	2	have	have	AUX
ejpam-4260	431	3	devoted	devote	VERB
ejpam-4260	431	4	this	this	DET
ejpam-4260	431	5	article	article	NOUN
ejpam-4260	431	6	to	to	PART
ejpam-4260	431	7	present	present	VERB
ejpam-4260	431	8	novel	novel	ADJ
ejpam-4260	431	9	types	type	NOUN
ejpam-4260	431	10	of	of	ADP
ejpam-4260	431	11	limit	limit	NOUN
ejpam-4260	431	12	points	point	NOUN
ejpam-4260	431	13	and	and	CCONJ
ejpam-4260	431	14	separation	separation	NOUN
ejpam-4260	431	15	axioms	axiom	NOUN
ejpam-4260	431	16	in	in	ADP
ejpam-4260	431	17	the	the	DET
ejpam-4260	431	18	frame	frame	NOUN
ejpam-4260	431	19	of	of	ADP
ejpam-4260	431	20	supra	supra	PROPN
ejpam-4260	431	21	topology	topology	PROPN
ejpam-4260	431	22	.	.	PUNCT
ejpam-4260	432	1	we	we	PRON
ejpam-4260	432	2	have	have	AUX
ejpam-4260	432	3	formulated	formulate	VERB
ejpam-4260	432	4	these	these	DET
ejpam-4260	432	5	types	type	NOUN
ejpam-4260	432	6	using	use	VERB
ejpam-4260	432	7	supra	supra	PROPN
ejpam-4260	432	8	b	b	PROPN
ejpam-4260	432	9	-	-	PUNCT
ejpam-4260	432	10	open	open	ADJ
ejpam-4260	432	11	sets	set	NOUN
ejpam-4260	432	12	.	.	PUNCT
ejpam-4260	433	1	we	we	PRON
ejpam-4260	433	2	have	have	AUX
ejpam-4260	433	3	scrutinized	scrutinize	VERB
ejpam-4260	433	4	their	their	PRON
ejpam-4260	433	5	basic	basic	ADJ
ejpam-4260	433	6	features	feature	NOUN
ejpam-4260	433	7	and	and	CCONJ
ejpam-4260	433	8	revealed	reveal	VERB
ejpam-4260	433	9	some	some	DET
ejpam-4260	433	10	relationships	relationship	NOUN
ejpam-4260	433	11	between	between	ADP
ejpam-4260	433	12	them	they	PRON
ejpam-4260	433	13	.	.	PUNCT
ejpam-4260	434	1	to	to	PART
ejpam-4260	434	2	validate	validate	VERB
ejpam-4260	434	3	the	the	DET
ejpam-4260	434	4	introduced	introduce	VERB
ejpam-4260	434	5	findings	finding	NOUN
ejpam-4260	434	6	,	,	PUNCT
ejpam-4260	434	7	we	we	PRON
ejpam-4260	434	8	have	have	AUX
ejpam-4260	434	9	displayed	display	VERB
ejpam-4260	434	10	some	some	DET
ejpam-4260	434	11	illustrative	illustrative	ADJ
ejpam-4260	434	12	examples	example	NOUN
ejpam-4260	434	13	.	.	PUNCT
ejpam-4260	435	1	to	to	PART
ejpam-4260	435	2	complete	complete	VERB
ejpam-4260	435	3	this	this	DET
ejpam-4260	435	4	path	path	NOUN
ejpam-4260	435	5	of	of	ADP
ejpam-4260	435	6	study	study	NOUN
ejpam-4260	435	7	,	,	PUNCT
ejpam-4260	435	8	we	we	PRON
ejpam-4260	435	9	plan	plan	VERB
ejpam-4260	435	10	to	to	PART
ejpam-4260	435	11	investigate	investigate	VERB
ejpam-4260	435	12	the	the	DET
ejpam-4260	435	13	following	follow	VERB
ejpam-4260	435	14	topics	topic	NOUN
ejpam-4260	435	15	:	:	PUNCT
ejpam-4260	435	16	(	(	PUNCT
ejpam-4260	435	17	i	i	NOUN
ejpam-4260	435	18	)	)	PUNCT
ejpam-4260	435	19	formulate	formulate	VERB
ejpam-4260	435	20	other	other	ADJ
ejpam-4260	435	21	kinds	kind	NOUN
ejpam-4260	435	22	of	of	ADP
ejpam-4260	435	23	regular	regular	ADJ
ejpam-4260	435	24	and	and	CCONJ
ejpam-4260	435	25	normal	normal	ADJ
ejpam-4260	435	26	spaces	space	NOUN
ejpam-4260	435	27	.	.	PUNCT
ejpam-4260	436	1	(	(	PUNCT
ejpam-4260	436	2	ii	ii	NOUN
ejpam-4260	436	3	)	)	PUNCT
ejpam-4260	436	4	explore	explore	VERB
ejpam-4260	436	5	strong	strong	ADJ
ejpam-4260	436	6	types	type	NOUN
ejpam-4260	436	7	of	of	ADP
ejpam-4260	436	8	separation	separation	NOUN
ejpam-4260	436	9	axioms	axiom	NOUN
ejpam-4260	436	10	induced	induce	VERB
ejpam-4260	436	11	from	from	ADP
ejpam-4260	436	12	supra	supra	PROPN
ejpam-4260	436	13	b	b	PROPN
ejpam-4260	436	14	-	-	PUNCT
ejpam-4260	436	15	open	open	ADJ
ejpam-4260	436	16	set	set	VERB
ejpam-4260	436	17	like	like	ADP
ejpam-4260	436	18	sbtkspaces	sbtkspace	NOUN
ejpam-4260	436	19	for	for	ADP
ejpam-4260	436	20	(	(	PUNCT
ejpam-4260	436	21	k	k	NOUN
ejpam-4260	436	22	=	=	SYM
ejpam-4260	436	23	1	1	NUM
ejpam-4260	436	24	2	2	NUM
ejpam-4260	436	25	,	,	PUNCT
ejpam-4260	436	26	2	2	NUM
ejpam-4260	436	27	1	1	NUM
ejpam-4260	436	28	2	2	NUM
ejpam-4260	436	29	,	,	PUNCT
ejpam-4260	436	30	3	3	NUM
ejpam-4260	436	31	1	1	NUM
ejpam-4260	436	32	2	2	NUM
ejpam-4260	436	33	)	)	PUNCT
ejpam-4260	436	34	.	.	PUNCT
ejpam-4260	437	1	conflict	conflict	NOUN
ejpam-4260	437	2	of	of	ADP
ejpam-4260	437	3	interest	interest	NOUN
ejpam-4260	437	4	the	the	DET
ejpam-4260	437	5	authors	author	NOUN
ejpam-4260	437	6	declare	declare	VERB
ejpam-4260	437	7	that	that	SCONJ
ejpam-4260	437	8	there	there	PRON
ejpam-4260	437	9	is	be	VERB
ejpam-4260	437	10	no	no	DET
ejpam-4260	437	11	conflict	conflict	NOUN
ejpam-4260	437	12	of	of	ADP
ejpam-4260	437	13	interest	interest	NOUN
ejpam-4260	437	14	regarding	regard	VERB
ejpam-4260	437	15	the	the	DET
ejpam-4260	437	16	publication	publication	NOUN
ejpam-4260	437	17	of	of	ADP
ejpam-4260	437	18	this	this	DET
ejpam-4260	437	19	paper	paper	NOUN
ejpam-4260	437	20	.	.	PUNCT
ejpam-4260	438	1	acknowledgements	acknowledgement	NOUN
ejpam-4260	438	2	this	this	DET
ejpam-4260	438	3	publication	publication	NOUN
ejpam-4260	438	4	was	be	AUX
ejpam-4260	438	5	supported	support	VERB
ejpam-4260	438	6	by	by	ADP
ejpam-4260	438	7	the	the	DET
ejpam-4260	438	8	deanship	deanship	NOUN
ejpam-4260	438	9	of	of	ADP
ejpam-4260	438	10	scientific	scientific	ADJ
ejpam-4260	438	11	research	research	NOUN
ejpam-4260	438	12	at	at	ADP
ejpam-4260	438	13	prince	prince	PROPN
ejpam-4260	438	14	sattam	sattam	PROPN
ejpam-4260	438	15	bin	bin	PROPN
ejpam-4260	438	16	abdulaziz	abdulaziz	PROPN
ejpam-4260	438	17	university	university	PROPN
ejpam-4260	438	18	,	,	PUNCT
ejpam-4260	438	19	alkharj	alkharj	VERB
ejpam-4260	438	20	,	,	PUNCT
ejpam-4260	438	21	saudi	saudi	PROPN
ejpam-4260	438	22	arabia	arabia	PROPN
ejpam-4260	438	23	.	.	PUNCT
ejpam-4260	439	1	references	reference	NOUN
ejpam-4260	439	2	28	28	NUM
ejpam-4260	439	3	references	reference	NOUN
ejpam-4260	439	4	[	[	X
ejpam-4260	439	5	1	1	NUM
ejpam-4260	439	6	]	]	PUNCT
ejpam-4260	439	7	a	a	DET
ejpam-4260	439	8	m	m	NOUN
ejpam-4260	439	9	al	al	NOUN
ejpam-4260	439	10	-	-	PUNCT
ejpam-4260	439	11	odhari	odhari	ADJ
ejpam-4260	439	12	.	.	PUNCT
ejpam-4260	440	1	on	on	ADP
ejpam-4260	440	2	infra	infra	NOUN
ejpam-4260	440	3	topological	topological	ADJ
ejpam-4260	440	4	spaces	space	NOUN
ejpam-4260	440	5	.	.	PUNCT
ejpam-4260	441	1	international	international	ADJ
ejpam-4260	441	2	journal	journal	PROPN
ejpam-4260	441	3	of	of	ADP
ejpam-4260	441	4	mathematical	mathematical	ADJ
ejpam-4260	441	5	archive	archive	NOUN
ejpam-4260	441	6	,	,	PUNCT
ejpam-4260	441	7	6(11):179–184	6(11):179–184	NOUN
ejpam-4260	441	8	,	,	PUNCT
ejpam-4260	441	9	2015	2015	NUM
ejpam-4260	441	10	.	.	PUNCT
ejpam-4260	442	1	[	[	X
ejpam-4260	442	2	2	2	NUM
ejpam-4260	442	3	]	]	PUNCT
ejpam-4260	442	4	t	t	PROPN
ejpam-4260	442	5	m	m	PROPN
ejpam-4260	442	6	al	al	PROPN
ejpam-4260	442	7	-	-	PUNCT
ejpam-4260	442	8	shami	shami	PROPN
ejpam-4260	442	9	.	.	PUNCT
ejpam-4260	443	1	some	some	DET
ejpam-4260	443	2	results	result	NOUN
ejpam-4260	443	3	related	relate	VERB
ejpam-4260	443	4	to	to	ADP
ejpam-4260	443	5	supra	supra	PROPN
ejpam-4260	443	6	topological	topological	ADJ
ejpam-4260	443	7	spaces	space	NOUN
ejpam-4260	443	8	.	.	PUNCT
ejpam-4260	444	1	journal	journal	NOUN
ejpam-4260	444	2	of	of	ADP
ejpam-4260	444	3	advanced	advanced	ADJ
ejpam-4260	444	4	studies	study	NOUN
ejpam-4260	444	5	in	in	ADP
ejpam-4260	444	6	topology	topology	NOUN
ejpam-4260	444	7	,	,	PUNCT
ejpam-4260	444	8	4(7):283–294	4(7):283–294	NUM
ejpam-4260	444	9	,	,	PUNCT
ejpam-4260	444	10	2016	2016	NUM
ejpam-4260	444	11	.	.	PUNCT
ejpam-4260	445	1	[	[	X
ejpam-4260	445	2	3	3	X
ejpam-4260	445	3	]	]	X
ejpam-4260	445	4	t	t	PROPN
ejpam-4260	445	5	m	m	PROPN
ejpam-4260	445	6	al	al	PROPN
ejpam-4260	445	7	-	-	PUNCT
ejpam-4260	445	8	shami	shami	PROPN
ejpam-4260	445	9	.	.	PUNCT
ejpam-4260	446	1	on	on	ADP
ejpam-4260	446	2	supra	supra	PROPN
ejpam-4260	446	3	semi	semi	ADV
ejpam-4260	446	4	open	open	ADJ
ejpam-4260	446	5	sets	set	NOUN
ejpam-4260	446	6	and	and	CCONJ
ejpam-4260	446	7	some	some	DET
ejpam-4260	446	8	applications	application	NOUN
ejpam-4260	446	9	on	on	ADP
ejpam-4260	446	10	topological	topological	ADJ
ejpam-4260	446	11	spaces	space	NOUN
ejpam-4260	446	12	.	.	PUNCT
ejpam-4260	447	1	journal	journal	NOUN
ejpam-4260	447	2	of	of	ADP
ejpam-4260	447	3	advanced	advanced	ADJ
ejpam-4260	447	4	studies	study	NOUN
ejpam-4260	447	5	in	in	ADP
ejpam-4260	447	6	topology	topology	NOUN
ejpam-4260	447	7	,	,	PUNCT
ejpam-4260	447	8	8(2):144–153	8(2):144–153	NOUN
ejpam-4260	447	9	,	,	PUNCT
ejpam-4260	447	10	2017	2017	NUM
ejpam-4260	447	11	.	.	PUNCT
ejpam-4260	448	1	[	[	X
ejpam-4260	448	2	4	4	X
ejpam-4260	448	3	]	]	X
ejpam-4260	448	4	t	t	PROPN
ejpam-4260	448	5	m	m	PROPN
ejpam-4260	448	6	al	al	PROPN
ejpam-4260	448	7	-	-	PUNCT
ejpam-4260	448	8	shami	shami	PROPN
ejpam-4260	448	9	.	.	PUNCT
ejpam-4260	449	1	somewhere	somewhere	ADV
ejpam-4260	449	2	dense	dense	ADJ
ejpam-4260	449	3	sets	set	NOUN
ejpam-4260	449	4	and	and	CCONJ
ejpam-4260	449	5	st	st	PROPN
ejpam-4260	449	6	1	1	NUM
ejpam-4260	449	7	-	-	PUNCT
ejpam-4260	449	8	spaces	space	NOUN
ejpam-4260	449	9	.	.	PUNCT
ejpam-4260	450	1	punjab	punjab	PROPN
ejpam-4260	450	2	university	university	PROPN
ejpam-4260	450	3	journal	journal	NOUN
ejpam-4260	450	4	of	of	ADP
ejpam-4260	450	5	mathematics	mathematic	NOUN
ejpam-4260	450	6	,	,	PUNCT
ejpam-4260	450	7	49(2):101–111	49(2):101–111	PROPN
ejpam-4260	450	8	,	,	PUNCT
ejpam-4260	450	9	2017	2017	NUM
ejpam-4260	450	10	.	.	PUNCT
ejpam-4260	451	1	[	[	X
ejpam-4260	451	2	5	5	NUM
ejpam-4260	451	3	]	]	PUNCT
ejpam-4260	451	4	t	t	PROPN
ejpam-4260	451	5	m	m	PROPN
ejpam-4260	451	6	al	al	PROPN
ejpam-4260	451	7	-	-	PUNCT
ejpam-4260	451	8	shami	shami	PROPN
ejpam-4260	451	9	.	.	PUNCT
ejpam-4260	452	1	utilizing	utilize	VERB
ejpam-4260	452	2	supra	supra	PROPN
ejpam-4260	452	3	α	α	PROPN
ejpam-4260	452	4	-	-	ADJ
ejpam-4260	452	5	open	open	ADJ
ejpam-4260	452	6	sets	set	NOUN
ejpam-4260	452	7	to	to	PART
ejpam-4260	452	8	generate	generate	VERB
ejpam-4260	452	9	new	new	ADJ
ejpam-4260	452	10	types	type	NOUN
ejpam-4260	452	11	of	of	ADP
ejpam-4260	452	12	supra	supra	ADJ
ejpam-4260	452	13	compact	compact	ADJ
ejpam-4260	452	14	and	and	CCONJ
ejpam-4260	452	15	supra	supra	ADJ
ejpam-4260	452	16	lindelöf	lindelöf	NOUN
ejpam-4260	452	17	spaces	space	VERB
ejpam-4260	452	18	.	.	PUNCT
ejpam-4260	453	1	facta	facta	PROPN
ejpam-4260	453	2	universitatis	universitatis	PROPN
ejpam-4260	453	3	,	,	PUNCT
ejpam-4260	453	4	series	series	NOUN
ejpam-4260	453	5	:	:	PUNCT
ejpam-4260	453	6	mathematics	mathematic	NOUN
ejpam-4260	453	7	and	and	CCONJ
ejpam-4260	453	8	informatics	informatic	NOUN
ejpam-4260	453	9	,	,	PUNCT
ejpam-4260	453	10	32(1):151–162	32(1):151–162	PROPN
ejpam-4260	453	11	,	,	PUNCT
ejpam-4260	453	12	2017	2017	NUM
ejpam-4260	453	13	.	.	PUNCT
ejpam-4260	454	1	[	[	X
ejpam-4260	454	2	6	6	NUM
ejpam-4260	454	3	]	]	PUNCT
ejpam-4260	454	4	t	t	PROPN
ejpam-4260	454	5	m	m	PROPN
ejpam-4260	454	6	al	al	PROPN
ejpam-4260	454	7	-	-	PUNCT
ejpam-4260	454	8	shami	shami	PROPN
ejpam-4260	454	9	.	.	PUNCT
ejpam-4260	455	1	supra	supra	ADJ
ejpam-4260	455	2	semi	semi	NOUN
ejpam-4260	455	3	-	-	NOUN
ejpam-4260	455	4	compactness	compactness	NOUN
ejpam-4260	455	5	via	via	ADP
ejpam-4260	455	6	supra	supra	PROPN
ejpam-4260	455	7	topological	topological	PROPN
ejpam-4260	455	8	spaces	space	NOUN
ejpam-4260	455	9	.	.	PUNCT
ejpam-4260	456	1	journal	journal	PROPN
ejpam-4260	456	2	of	of	ADP
ejpam-4260	456	3	taibah	taibah	PROPN
ejpam-4260	456	4	university	university	PROPN
ejpam-4260	456	5	for	for	ADP
ejpam-4260	456	6	science	science	NOUN
ejpam-4260	456	7	,	,	PUNCT
ejpam-4260	456	8	12(3):338–343	12(3):338–343	PROPN
ejpam-4260	456	9	,	,	PUNCT
ejpam-4260	456	10	2018	2018	NUM
ejpam-4260	456	11	.	.	PUNCT
ejpam-4260	457	1	[	[	X
ejpam-4260	457	2	7	7	X
ejpam-4260	457	3	]	]	X
ejpam-4260	457	4	t	t	PROPN
ejpam-4260	457	5	m	m	PROPN
ejpam-4260	457	6	al	al	PROPN
ejpam-4260	457	7	-	-	PUNCT
ejpam-4260	457	8	shami	shami	PROPN
ejpam-4260	457	9	.	.	PUNCT
ejpam-4260	458	1	paracompactness	paracompactness	NOUN
ejpam-4260	458	2	on	on	ADP
ejpam-4260	458	3	supra	supra	PROPN
ejpam-4260	458	4	topological	topological	ADJ
ejpam-4260	458	5	spaces	space	NOUN
ejpam-4260	458	6	.	.	PUNCT
ejpam-4260	459	1	journal	journal	NOUN
ejpam-4260	459	2	of	of	ADP
ejpam-4260	459	3	linear	linear	PROPN
ejpam-4260	459	4	and	and	CCONJ
ejpam-4260	459	5	topological	topological	ADJ
ejpam-4260	459	6	algebra	algebra	NOUN
ejpam-4260	459	7	,	,	PUNCT
ejpam-4260	459	8	9(2):1–7	9(2):1–7	NUM
ejpam-4260	459	9	,	,	PUNCT
ejpam-4260	459	10	2020	2020	NUM
ejpam-4260	459	11	.	.	PUNCT
ejpam-4260	460	1	[	[	X
ejpam-4260	460	2	8	8	NUM
ejpam-4260	460	3	]	]	X
ejpam-4260	460	4	t	t	PROPN
ejpam-4260	460	5	m	m	PROPN
ejpam-4260	460	6	al	al	PROPN
ejpam-4260	460	7	-	-	PUNCT
ejpam-4260	460	8	shami	shami	PROPN
ejpam-4260	460	9	.	.	PUNCT
ejpam-4260	461	1	complete	complete	ADJ
ejpam-4260	461	2	hausdorffness	hausdorffness	NOUN
ejpam-4260	461	3	and	and	CCONJ
ejpam-4260	461	4	complete	complete	ADJ
ejpam-4260	461	5	regularity	regularity	NOUN
ejpam-4260	461	6	on	on	ADP
ejpam-4260	461	7	supra	supra	PROPN
ejpam-4260	461	8	topological	topological	ADJ
ejpam-4260	461	9	spaces	space	NOUN
ejpam-4260	461	10	.	.	PUNCT
ejpam-4260	462	1	journal	journal	NOUN
ejpam-4260	462	2	of	of	ADP
ejpam-4260	462	3	applied	apply	VERB
ejpam-4260	462	4	mathematics	mathematic	NOUN
ejpam-4260	462	5	,	,	PUNCT
ejpam-4260	462	6	volume	volume	NOUN
ejpam-4260	462	7	2021	2021	NUM
ejpam-4260	462	8	,	,	PUNCT
ejpam-4260	462	9	article	article	NOUN
ejpam-4260	462	10	i	i	PROPN
ejpam-4260	462	11	d	d	PROPN
ejpam-4260	462	12	5517702:11	5517702:11	NUM
ejpam-4260	462	13	pages	page	NOUN
ejpam-4260	462	14	,	,	PUNCT
ejpam-4260	462	15	2021	2021	NUM
ejpam-4260	462	16	.	.	PUNCT
ejpam-4260	463	1	[	[	X
ejpam-4260	463	2	9	9	NUM
ejpam-4260	463	3	]	]	X
ejpam-4260	463	4	t	t	PROPN
ejpam-4260	463	5	m	m	PROPN
ejpam-4260	463	6	al	al	PROPN
ejpam-4260	463	7	-	-	PUNCT
ejpam-4260	463	8	shami	shami	PROPN
ejpam-4260	463	9	,	,	PUNCT
ejpam-4260	463	10	e	e	X
ejpam-4260	463	11	a	a	DET
ejpam-4260	463	12	abo	abo	NOUN
ejpam-4260	463	13	-	-	PUNCT
ejpam-4260	463	14	tabl	tabl	NOUN
ejpam-4260	463	15	,	,	PUNCT
ejpam-4260	463	16	and	and	CCONJ
ejpam-4260	463	17	b	b	ADP
ejpam-4260	463	18	a	a	DET
ejpam-4260	463	19	asaad	asaad	NOUN
ejpam-4260	463	20	.	.	PUNCT
ejpam-4260	464	1	investigation	investigation	NOUN
ejpam-4260	464	2	of	of	ADP
ejpam-4260	464	3	limit	limit	NOUN
ejpam-4260	464	4	points	point	NOUN
ejpam-4260	464	5	and	and	CCONJ
ejpam-4260	464	6	separation	separation	NOUN
ejpam-4260	464	7	axioms	axiom	NOUN
ejpam-4260	464	8	using	use	VERB
ejpam-4260	464	9	supra	supra	PROPN
ejpam-4260	464	10	β	β	NOUN
ejpam-4260	464	11	-	-	ADJ
ejpam-4260	464	12	open	open	ADJ
ejpam-4260	464	13	sets	set	NOUN
ejpam-4260	464	14	.	.	PUNCT
ejpam-4260	465	1	missouri	missouri	PROPN
ejpam-4260	465	2	journal	journal	PROPN
ejpam-4260	465	3	of	of	ADP
ejpam-4260	465	4	mathematical	mathematical	ADJ
ejpam-4260	465	5	science	science	NOUN
ejpam-4260	465	6	,	,	PUNCT
ejpam-4260	465	7	32(2):171–187	32(2):171–187	PROPN
ejpam-4260	465	8	,	,	PUNCT
ejpam-4260	465	9	2020	2020	NUM
ejpam-4260	465	10	.	.	PUNCT
ejpam-4260	466	1	[	[	X
ejpam-4260	466	2	10	10	NUM
ejpam-4260	466	3	]	]	X
ejpam-4260	466	4	t	t	PROPN
ejpam-4260	466	5	m	m	PROPN
ejpam-4260	466	6	al	al	PROPN
ejpam-4260	466	7	-	-	PUNCT
ejpam-4260	466	8	shami	shami	PROPN
ejpam-4260	466	9	,	,	PUNCT
ejpam-4260	466	10	e	e	X
ejpam-4260	466	11	a	a	DET
ejpam-4260	466	12	abo	abo	NOUN
ejpam-4260	466	13	-	-	PUNCT
ejpam-4260	466	14	tabl	tabl	NOUN
ejpam-4260	466	15	,	,	PUNCT
ejpam-4260	466	16	b	b	NOUN
ejpam-4260	466	17	a	a	DET
ejpam-4260	466	18	asaad	asaad	NOUN
ejpam-4260	466	19	,	,	PUNCT
ejpam-4260	466	20	and	and	CCONJ
ejpam-4260	466	21	m	m	VERB
ejpam-4260	466	22	a	a	DET
ejpam-4260	466	23	arahet	arahet	NOUN
ejpam-4260	466	24	.	.	PUNCT
ejpam-4260	467	1	limit	limit	NOUN
ejpam-4260	467	2	points	point	NOUN
ejpam-4260	467	3	and	and	CCONJ
ejpam-4260	467	4	separation	separation	NOUN
ejpam-4260	467	5	axioms	axiom	NOUN
ejpam-4260	467	6	with	with	ADP
ejpam-4260	467	7	respect	respect	NOUN
ejpam-4260	467	8	to	to	ADP
ejpam-4260	467	9	supra	supra	PROPN
ejpam-4260	467	10	semi	semi	ADJ
ejpam-4260	467	11	-	-	ADJ
ejpam-4260	467	12	open	open	ADJ
ejpam-4260	467	13	sets	set	NOUN
ejpam-4260	467	14	.	.	PUNCT
ejpam-4260	468	1	european	european	ADJ
ejpam-4260	468	2	journal	journal	PROPN
ejpam-4260	468	3	of	of	ADP
ejpam-4260	468	4	pure	pure	ADJ
ejpam-4260	468	5	and	and	CCONJ
ejpam-4260	468	6	applied	applied	ADJ
ejpam-4260	468	7	mathematics	mathematic	NOUN
ejpam-4260	468	8	,	,	PUNCT
ejpam-4260	468	9	13(3):427–443	13(3):427–443	PROPN
ejpam-4260	468	10	,	,	PUNCT
ejpam-4260	468	11	2020	2020	NUM
ejpam-4260	468	12	.	.	PUNCT
ejpam-4260	469	1	[	[	X
ejpam-4260	469	2	11	11	NUM
ejpam-4260	469	3	]	]	X
ejpam-4260	469	4	t	t	PROPN
ejpam-4260	469	5	m	m	PROPN
ejpam-4260	469	6	al	al	PROPN
ejpam-4260	469	7	-	-	PUNCT
ejpam-4260	469	8	shami	shami	PROPN
ejpam-4260	469	9	,	,	PUNCT
ejpam-4260	469	10	b	b	PROPN
ejpam-4260	469	11	a	a	DET
ejpam-4260	469	12	asaad	asaad	NOUN
ejpam-4260	469	13	,	,	PUNCT
ejpam-4260	469	14	,	,	PUNCT
ejpam-4260	469	15	and	and	CCONJ
ejpam-4260	469	16	m	m	AUX
ejpam-4260	469	17	k	k	PROPN
ejpam-4260	469	18	el	el	PROPN
ejpam-4260	469	19	-	-	ADJ
ejpam-4260	469	20	bably	bably	PROPN
ejpam-4260	469	21	.	.	PUNCT
ejpam-4260	470	1	weak	weak	ADJ
ejpam-4260	470	2	types	type	NOUN
ejpam-4260	470	3	of	of	ADP
ejpam-4260	470	4	limit	limit	NOUN
ejpam-4260	470	5	points	point	NOUN
ejpam-4260	470	6	and	and	CCONJ
ejpam-4260	470	7	separation	separation	NOUN
ejpam-4260	470	8	axioms	axiom	NOUN
ejpam-4260	470	9	on	on	ADP
ejpam-4260	470	10	supra	supra	PROPN
ejpam-4260	470	11	topological	topological	ADJ
ejpam-4260	470	12	spaces	space	NOUN
ejpam-4260	470	13	.	.	PUNCT
ejpam-4260	471	1	advances	advance	NOUN
ejpam-4260	471	2	in	in	ADP
ejpam-4260	471	3	mathematics	mathematic	NOUN
ejpam-4260	471	4	:	:	PUNCT
ejpam-4260	471	5	scientific	scientific	ADJ
ejpam-4260	471	6	journal	journal	NOUN
ejpam-4260	471	7	,	,	PUNCT
ejpam-4260	471	8	9(10):8017–8036	9(10):8017–8036	NUM
ejpam-4260	471	9	,	,	PUNCT
ejpam-4260	471	10	2020	2020	NUM
ejpam-4260	471	11	.	.	PUNCT
ejpam-4260	472	1	[	[	X
ejpam-4260	472	2	12	12	NUM
ejpam-4260	472	3	]	]	X
ejpam-4260	473	1	t	t	PROPN
ejpam-4260	473	2	m	m	PROPN
ejpam-4260	473	3	al	al	PROPN
ejpam-4260	473	4	-	-	PUNCT
ejpam-4260	473	5	shami	shami	PROPN
ejpam-4260	473	6	,	,	PUNCT
ejpam-4260	473	7	b	b	PROPN
ejpam-4260	473	8	a	a	DET
ejpam-4260	473	9	asaad	asaad	NOUN
ejpam-4260	473	10	,	,	PUNCT
ejpam-4260	473	11	and	and	CCONJ
ejpam-4260	473	12	m	m	PROPN
ejpam-4260	473	13	a	a	DET
ejpam-4260	473	14	el	el	PROPN
ejpam-4260	473	15	-	-	NOUN
ejpam-4260	473	16	gayar	gayar	NOUN
ejpam-4260	473	17	.	.	PUNCT
ejpam-4260	474	1	various	various	ADJ
ejpam-4260	474	2	types	type	NOUN
ejpam-4260	474	3	of	of	ADP
ejpam-4260	474	4	supra	supra	ADJ
ejpam-4260	474	5	pre	pre	ADJ
ejpam-4260	474	6	-	-	ADJ
ejpam-4260	474	7	compact	compact	ADJ
ejpam-4260	474	8	and	and	CCONJ
ejpam-4260	474	9	supra	supra	ADJ
ejpam-4260	474	10	pre	pre	PROPN
ejpam-4260	474	11	-	-	NOUN
ejpam-4260	474	12	lindelöf	lindelöf	NOUN
ejpam-4260	474	13	spaces	space	NOUN
ejpam-4260	474	14	.	.	PUNCT
ejpam-4260	475	1	missouri	missouri	PROPN
ejpam-4260	475	2	journal	journal	PROPN
ejpam-4260	475	3	of	of	ADP
ejpam-4260	475	4	mathematical	mathematical	ADJ
ejpam-4260	475	5	science	science	NOUN
ejpam-4260	475	6	,	,	PUNCT
ejpam-4260	475	7	32(1):1–20	32(1):1–20	NUM
ejpam-4260	475	8	,	,	PUNCT
ejpam-4260	475	9	2020	2020	NUM
ejpam-4260	475	10	.	.	PUNCT
ejpam-4260	476	1	[	[	X
ejpam-4260	476	2	13	13	NUM
ejpam-4260	476	3	]	]	X
ejpam-4260	476	4	t	t	PROPN
ejpam-4260	476	5	m	m	PROPN
ejpam-4260	476	6	al	al	PROPN
ejpam-4260	476	7	-	-	PUNCT
ejpam-4260	476	8	shami	shami	PROPN
ejpam-4260	476	9	and	and	CCONJ
ejpam-4260	476	10	m	m	PROPN
ejpam-4260	476	11	e	e	PROPN
ejpam-4260	476	12	el	el	PROPN
ejpam-4260	476	13	-	-	PUNCT
ejpam-4260	476	14	shafei	shafei	NOUN
ejpam-4260	476	15	.	.	PUNCT
ejpam-4260	477	1	on	on	ADP
ejpam-4260	477	2	supra	supra	PROPN
ejpam-4260	477	3	soft	soft	ADJ
ejpam-4260	477	4	topological	topological	ADJ
ejpam-4260	477	5	ordered	order	VERB
ejpam-4260	477	6	spaces	space	NOUN
ejpam-4260	477	7	.	.	PUNCT
ejpam-4260	478	1	arab	arab	PROPN
ejpam-4260	478	2	journal	journal	PROPN
ejpam-4260	478	3	of	of	ADP
ejpam-4260	478	4	basic	basic	ADJ
ejpam-4260	478	5	and	and	CCONJ
ejpam-4260	478	6	applied	applied	ADJ
ejpam-4260	478	7	sciences	science	NOUN
ejpam-4260	478	8	,	,	PUNCT
ejpam-4260	478	9	26(1):433–445	26(1):433–445	NOUN
ejpam-4260	478	10	,	,	PUNCT
ejpam-4260	478	11	2019	2019	NUM
ejpam-4260	478	12	.	.	PUNCT
ejpam-4260	479	1	references	reference	NOUN
ejpam-4260	479	2	29	29	NUM
ejpam-4260	480	1	[	[	X
ejpam-4260	480	2	14	14	NUM
ejpam-4260	480	3	]	]	X
ejpam-4260	481	1	t	t	PROPN
ejpam-4260	481	2	m	m	PROPN
ejpam-4260	481	3	al	al	PROPN
ejpam-4260	481	4	-	-	PUNCT
ejpam-4260	481	5	shami	shami	PROPN
ejpam-4260	481	6	and	and	CCONJ
ejpam-4260	481	7	m	m	PROPN
ejpam-4260	481	8	e	e	PROPN
ejpam-4260	481	9	el	el	PROPN
ejpam-4260	481	10	-	-	PUNCT
ejpam-4260	481	11	shafei	shafei	NOUN
ejpam-4260	481	12	.	.	PUNCT
ejpam-4260	482	1	two	two	NUM
ejpam-4260	482	2	types	type	NOUN
ejpam-4260	482	3	of	of	ADP
ejpam-4260	482	4	separation	separation	NOUN
ejpam-4260	482	5	axioms	axiom	NOUN
ejpam-4260	482	6	on	on	ADP
ejpam-4260	482	7	supra	supra	PROPN
ejpam-4260	482	8	soft	soft	ADJ
ejpam-4260	482	9	topological	topological	ADJ
ejpam-4260	482	10	spaces	space	NOUN
ejpam-4260	482	11	.	.	PUNCT
ejpam-4260	483	1	demonstratio	demonstratio	PROPN
ejpam-4260	483	2	mathematica	mathematica	PROPN
ejpam-4260	483	3	,	,	PUNCT
ejpam-4260	483	4	52(1):147–165	52(1):147–165	PROPN
ejpam-4260	483	5	,	,	PUNCT
ejpam-4260	483	6	2019	2019	NUM
ejpam-4260	483	7	.	.	PUNCT
ejpam-4260	484	1	[	[	X
ejpam-4260	484	2	15	15	NUM
ejpam-4260	484	3	]	]	X
ejpam-4260	485	1	t	t	PROPN
ejpam-4260	485	2	m	m	PROPN
ejpam-4260	485	3	al	al	PROPN
ejpam-4260	485	4	-	-	PUNCT
ejpam-4260	485	5	shami	shami	PROPN
ejpam-4260	485	6	,	,	PUNCT
ejpam-4260	485	7	m	m	PROPN
ejpam-4260	485	8	al	al	PROPN
ejpam-4260	485	9	shumrani	shumrani	PROPN
ejpam-4260	485	10	,	,	PUNCT
ejpam-4260	485	11	and	and	CCONJ
ejpam-4260	485	12	c	c	PROPN
ejpam-4260	485	13	özel	özel	PROPN
ejpam-4260	485	14	.	.	PUNCT
ejpam-4260	486	1	another	another	DET
ejpam-4260	486	2	form	form	NOUN
ejpam-4260	486	3	of	of	ADP
ejpam-4260	486	4	supra	supra	PROPN
ejpam-4260	486	5	ordered	order	VERB
ejpam-4260	486	6	separation	separation	NOUN
ejpam-4260	486	7	axioms	axiom	VERB
ejpam-4260	486	8	.	.	PUNCT
ejpam-4260	487	1	journal	journal	NOUN
ejpam-4260	487	2	of	of	ADP
ejpam-4260	487	3	mathematical	mathematical	ADJ
ejpam-4260	487	4	extension	extension	NOUN
ejpam-4260	487	5	,	,	PUNCT
ejpam-4260	487	6	15(1):105–125	15(1):105–125	NUM
ejpam-4260	487	7	,	,	PUNCT
ejpam-4260	487	8	2021	2021	NUM
ejpam-4260	487	9	.	.	PUNCT
ejpam-4260	488	1	[	[	X
ejpam-4260	488	2	16	16	NUM
ejpam-4260	488	3	]	]	X
ejpam-4260	489	1	t	t	PROPN
ejpam-4260	489	2	m	m	PROPN
ejpam-4260	489	3	al	al	PROPN
ejpam-4260	489	4	-	-	PUNCT
ejpam-4260	489	5	shami	shami	PROPN
ejpam-4260	489	6	and	and	CCONJ
ejpam-4260	489	7	t	t	PROPN
ejpam-4260	489	8	noiri	noiri	PROPN
ejpam-4260	489	9	.	.	PUNCT
ejpam-4260	490	1	more	more	ADJ
ejpam-4260	490	2	notions	notion	NOUN
ejpam-4260	490	3	and	and	CCONJ
ejpam-4260	490	4	mappings	mapping	NOUN
ejpam-4260	490	5	via	via	ADP
ejpam-4260	490	6	somewhere	somewhere	ADJ
ejpam-4260	490	7	dense	dense	ADJ
ejpam-4260	490	8	sets	set	NOUN
ejpam-4260	490	9	.	.	PUNCT
ejpam-4260	491	1	afrika	afrika	ADJ
ejpam-4260	491	2	matematika	matematika	PROPN
ejpam-4260	491	3	,	,	PUNCT
ejpam-4260	491	4	30(7):1011–1024	30(7):1011–1024	PROPN
ejpam-4260	491	5	,	,	PUNCT
ejpam-4260	491	6	2019	2019	NUM
ejpam-4260	491	7	.	.	PUNCT
ejpam-4260	492	1	[	[	X
ejpam-4260	492	2	17	17	NUM
ejpam-4260	492	3	]	]	PUNCT
ejpam-4260	492	4	á	á	NOUN
ejpam-4260	492	5	császár	császár	NOUN
ejpam-4260	492	6	.	.	PUNCT
ejpam-4260	493	1	generalized	generalize	VERB
ejpam-4260	493	2	topology	topology	NOUN
ejpam-4260	493	3	,	,	PUNCT
ejpam-4260	493	4	generalized	generalize	VERB
ejpam-4260	493	5	continuity	continuity	NOUN
ejpam-4260	493	6	.	.	PUNCT
ejpam-4260	494	1	acta	acta	PROPN
ejpam-4260	494	2	mathematica	mathematica	PROPN
ejpam-4260	494	3	hungarica	hungarica	PROPN
ejpam-4260	494	4	,	,	PUNCT
ejpam-4260	494	5	96:351–357	96:351–357	PROPN
ejpam-4260	494	6	,	,	PUNCT
ejpam-4260	494	7	2002	2002	NUM
ejpam-4260	494	8	.	.	PUNCT
ejpam-4260	495	1	[	[	X
ejpam-4260	495	2	18	18	NUM
ejpam-4260	495	3	]	]	X
ejpam-4260	495	4	r	r	NOUN
ejpam-4260	495	5	devi	devi	PROPN
ejpam-4260	495	6	,	,	PUNCT
ejpam-4260	495	7	s	s	PART
ejpam-4260	495	8	sampathkumar	sampathkumar	NOUN
ejpam-4260	495	9	,	,	PUNCT
ejpam-4260	495	10	and	and	CCONJ
ejpam-4260	495	11	m	m	PROPN
ejpam-4260	495	12	caldas	caldas	PROPN
ejpam-4260	495	13	.	.	PUNCT
ejpam-4260	496	1	on	on	ADP
ejpam-4260	496	2	α	α	NOUN
ejpam-4260	496	3	-	-	ADJ
ejpam-4260	496	4	open	open	ADJ
ejpam-4260	496	5	sets	set	NOUN
ejpam-4260	496	6	and	and	CCONJ
ejpam-4260	496	7	sα	sα	ADJ
ejpam-4260	496	8	-	-	ADJ
ejpam-4260	496	9	continuous	continuous	ADJ
ejpam-4260	496	10	maps	map	NOUN
ejpam-4260	496	11	.	.	PUNCT
ejpam-4260	497	1	general	general	ADJ
ejpam-4260	497	2	mathematics	mathematics	PROPN
ejpam-4260	497	3	,	,	PUNCT
ejpam-4260	497	4	16:77–84	16:77–84	NOUN
ejpam-4260	497	5	,	,	PUNCT
ejpam-4260	497	6	2008	2008	NUM
ejpam-4260	497	7	.	.	PUNCT
ejpam-4260	498	1	[	[	X
ejpam-4260	498	2	19	19	NUM
ejpam-4260	498	3	]	]	X
ejpam-4260	498	4	m	m	PROPN
ejpam-4260	498	5	e	e	NOUN
ejpam-4260	498	6	el	el	PROPN
ejpam-4260	498	7	-	-	PUNCT
ejpam-4260	498	8	shafei	shafei	PROPN
ejpam-4260	498	9	,	,	PUNCT
ejpam-4260	498	10	m	m	NOUN
ejpam-4260	498	11	abo	abo	NOUN
ejpam-4260	498	12	-	-	PUNCT
ejpam-4260	498	13	elhamayel	elhamayel	NOUN
ejpam-4260	498	14	,	,	PUNCT
ejpam-4260	498	15	and	and	CCONJ
ejpam-4260	498	16	t	t	PROPN
ejpam-4260	498	17	m	m	PROPN
ejpam-4260	498	18	al	al	PROPN
ejpam-4260	498	19	-	-	PUNCT
ejpam-4260	498	20	shami	shami	PROPN
ejpam-4260	498	21	.	.	PUNCT
ejpam-4260	499	1	on	on	ADP
ejpam-4260	499	2	supra	supra	PROPN
ejpam-4260	499	3	r	r	NOUN
ejpam-4260	499	4	-	-	PUNCT
ejpam-4260	499	5	open	open	ADJ
ejpam-4260	499	6	sets	set	NOUN
ejpam-4260	499	7	and	and	CCONJ
ejpam-4260	499	8	some	some	DET
ejpam-4260	499	9	applications	application	NOUN
ejpam-4260	499	10	on	on	ADP
ejpam-4260	499	11	topological	topological	ADJ
ejpam-4260	499	12	spaces	space	NOUN
ejpam-4260	499	13	.	.	PUNCT
ejpam-4260	500	1	journal	journal	NOUN
ejpam-4260	500	2	of	of	ADP
ejpam-4260	500	3	progressive	progressive	ADJ
ejpam-4260	500	4	research	research	NOUN
ejpam-4260	500	5	in	in	ADP
ejpam-4260	500	6	mathematics	mathematic	NOUN
ejpam-4260	500	7	,	,	PUNCT
ejpam-4260	500	8	8(2):1237–1248	8(2):1237–1248	NUM
ejpam-4260	500	9	,	,	PUNCT
ejpam-4260	500	10	2016	2016	NUM
ejpam-4260	500	11	.	.	PUNCT
ejpam-4260	501	1	[	[	X
ejpam-4260	501	2	20	20	NUM
ejpam-4260	501	3	]	]	X
ejpam-4260	501	4	m	m	PROPN
ejpam-4260	501	5	e	e	NOUN
ejpam-4260	501	6	el	el	PROPN
ejpam-4260	501	7	-	-	PUNCT
ejpam-4260	501	8	shafei	shafei	PROPN
ejpam-4260	501	9	,	,	PUNCT
ejpam-4260	501	10	a	a	DET
ejpam-4260	501	11	h	h	NOUN
ejpam-4260	501	12	zakari	zakari	NOUN
ejpam-4260	501	13	,	,	PUNCT
ejpam-4260	501	14	and	and	CCONJ
ejpam-4260	501	15	t	t	PROPN
ejpam-4260	501	16	m	m	PROPN
ejpam-4260	501	17	al	al	PROPN
ejpam-4260	501	18	-	-	PUNCT
ejpam-4260	501	19	shami	shami	PROPN
ejpam-4260	501	20	.	.	PUNCT
ejpam-4260	502	1	some	some	DET
ejpam-4260	502	2	applications	application	NOUN
ejpam-4260	502	3	of	of	ADP
ejpam-4260	502	4	supra	supra	ADJ
ejpam-4260	502	5	preopen	preopen	ADJ
ejpam-4260	502	6	sets	set	NOUN
ejpam-4260	502	7	.	.	PUNCT
ejpam-4260	503	1	journal	journal	NOUN
ejpam-4260	503	2	of	of	ADP
ejpam-4260	503	3	mathematics	mathematic	NOUN
ejpam-4260	503	4	,	,	PUNCT
ejpam-4260	503	5	volume	volume	NOUN
ejpam-4260	503	6	2020	2020	NUM
ejpam-4260	503	7	,	,	PUNCT
ejpam-4260	503	8	article	article	NOUN
ejpam-4260	503	9	i	i	PROPN
ejpam-4260	503	10	d	d	PROPN
ejpam-4260	503	11	9634206:11	9634206:11	NUM
ejpam-4260	503	12	pages	page	NOUN
ejpam-4260	503	13	,	,	PUNCT
ejpam-4260	503	14	2020	2020	NUM
ejpam-4260	503	15	.	.	PUNCT
ejpam-4260	504	1	[	[	X
ejpam-4260	504	2	21	21	NUM
ejpam-4260	504	3	]	]	X
ejpam-4260	504	4	s	s	VERB
ejpam-4260	504	5	jafari	jafari	ADJ
ejpam-4260	504	6	and	and	CCONJ
ejpam-4260	504	7	s	s	NOUN
ejpam-4260	504	8	tahiliani	tahiliani	NOUN
ejpam-4260	504	9	.	.	PUNCT
ejpam-4260	505	1	supra	supra	PROPN
ejpam-4260	505	2	β	β	X
ejpam-4260	505	3	-	-	ADJ
ejpam-4260	505	4	open	open	ADJ
ejpam-4260	505	5	sets	set	NOUN
ejpam-4260	505	6	and	and	CCONJ
ejpam-4260	505	7	supra	supra	ADJ
ejpam-4260	505	8	β	β	NOUN
ejpam-4260	505	9	-	-	NOUN
ejpam-4260	505	10	continuity	continuity	NOUN
ejpam-4260	505	11	on	on	ADP
ejpam-4260	505	12	topological	topological	ADJ
ejpam-4260	505	13	spaces	space	NOUN
ejpam-4260	505	14	.	.	PUNCT
ejpam-4260	506	1	annales	annales	PROPN
ejpam-4260	506	2	univ	univ	PROPN
ejpam-4260	506	3	.	.	PUNCT
ejpam-4260	507	1	sci	sci	PROPN
ejpam-4260	507	2	.	.	PUNCT
ejpam-4260	507	3	budapest	budapest	PROPN
ejpam-4260	507	4	.	.	PUNCT
ejpam-4260	508	1	,	,	PUNCT
ejpam-4260	508	2	56:1–9	56:1–9	NUM
ejpam-4260	508	3	,	,	PUNCT
ejpam-4260	508	4	2013	2013	NUM
ejpam-4260	508	5	.	.	PUNCT
ejpam-4260	509	1	[	[	X
ejpam-4260	509	2	22	22	NUM
ejpam-4260	509	3	]	]	X
ejpam-4260	509	4	r	r	NOUN
ejpam-4260	509	5	m	m	PROPN
ejpam-4260	509	6	latif	latif	PROPN
ejpam-4260	509	7	.	.	PUNCT
ejpam-4260	510	1	supra	supra	NOUN
ejpam-4260	510	2	-	-	PUNCT
ejpam-4260	510	3	r	r	NOUN
ejpam-4260	510	4	-	-	PUNCT
ejpam-4260	510	5	compactness	compactness	NOUN
ejpam-4260	510	6	and	and	CCONJ
ejpam-4260	510	7	supra	supra	NOUN
ejpam-4260	510	8	-	-	PUNCT
ejpam-4260	510	9	r	r	NOUN
ejpam-4260	510	10	-	-	PUNCT
ejpam-4260	510	11	connectedness	connectedness	NOUN
ejpam-4260	510	12	.	.	PUNCT
ejpam-4260	511	1	international	international	ADJ
ejpam-4260	511	2	journal	journal	NOUN
ejpam-4260	511	3	of	of	ADP
ejpam-4260	511	4	recent	recent	ADJ
ejpam-4260	511	5	trends	trend	NOUN
ejpam-4260	511	6	in	in	ADP
ejpam-4260	511	7	engineering	engineering	NOUN
ejpam-4260	511	8	&	&	CCONJ
ejpam-4260	511	9	research	research	PROPN
ejpam-4260	511	10	,	,	PUNCT
ejpam-4260	511	11	4(1):2455–1457	4(1):2455–1457	PROPN
ejpam-4260	511	12	,	,	PUNCT
ejpam-4260	511	13	2018	2018	NUM
ejpam-4260	511	14	.	.	PUNCT
ejpam-4260	512	1	[	[	X
ejpam-4260	512	2	23	23	NUM
ejpam-4260	512	3	]	]	X
ejpam-4260	512	4	h	h	NOUN
ejpam-4260	512	5	maki	maki	NOUN
ejpam-4260	512	6	,	,	PUNCT
ejpam-4260	512	7	j	j	PROPN
ejpam-4260	512	8	umehara	umehara	NOUN
ejpam-4260	512	9	,	,	PUNCT
ejpam-4260	512	10	and	and	CCONJ
ejpam-4260	512	11	t	t	PROPN
ejpam-4260	512	12	noiri	noiri	PROPN
ejpam-4260	512	13	.	.	PUNCT
ejpam-4260	513	1	every	every	DET
ejpam-4260	513	2	topological	topological	ADJ
ejpam-4260	513	3	space	space	NOUN
ejpam-4260	513	4	is	be	AUX
ejpam-4260	513	5	pret	pret	PROPN
ejpam-4260	513	6	1	1	NUM
ejpam-4260	513	7	2	2	NUM
ejpam-4260	513	8	.	.	PUNCT
ejpam-4260	514	1	mem	mem	PROPN
ejpam-4260	514	2	.	.	PUNCT
ejpam-4260	515	1	fac	fac	PROPN
ejpam-4260	515	2	.	.	PUNCT
ejpam-4260	516	1	sci	sci	PROPN
ejpam-4260	516	2	.	.	PROPN
ejpam-4260	516	3	kochi	kochi	PROPN
ejpam-4260	516	4	.	.	PUNCT
ejpam-4260	517	1	univ	univ	PROPN
ejpam-4260	517	2	.	.	PUNCT
ejpam-4260	517	3	ser	ser	PROPN
ejpam-4260	517	4	.	.	PUNCT
ejpam-4260	518	1	a	a	DET
ejpam-4260	518	2	math	math	NOUN
ejpam-4260	518	3	.	.	PUNCT
ejpam-4260	518	4	,	,	PUNCT
ejpam-4260	518	5	17:33–42	17:33–42	PROPN
ejpam-4260	518	6	,	,	PUNCT
ejpam-4260	518	7	1996	1996	NUM
ejpam-4260	518	8	.	.	PUNCT
ejpam-4260	519	1	[	[	X
ejpam-4260	519	2	24	24	NUM
ejpam-4260	519	3	]	]	X
ejpam-4260	519	4	a	a	DET
ejpam-4260	519	5	s	s	X
ejpam-4260	519	6	mashhour	mashhour	NOUN
ejpam-4260	519	7	,	,	PUNCT
ejpam-4260	519	8	a	a	DET
ejpam-4260	519	9	a	a	DET
ejpam-4260	519	10	allam	allam	PROPN
ejpam-4260	519	11	,	,	PUNCT
ejpam-4260	519	12	f	f	PROPN
ejpam-4260	519	13	s	s	PROPN
ejpam-4260	519	14	mahmoud	mahmoud	PROPN
ejpam-4260	519	15	,	,	PUNCT
ejpam-4260	519	16	and	and	CCONJ
ejpam-4260	519	17	f	f	PROPN
ejpam-4260	519	18	h	h	PROPN
ejpam-4260	519	19	kheder	kheder	PROPN
ejpam-4260	519	20	.	.	PUNCT
ejpam-4260	520	1	on	on	ADP
ejpam-4260	520	2	supra	supra	PROPN
ejpam-4260	520	3	topological	topological	ADJ
ejpam-4260	520	4	spaces	space	NOUN
ejpam-4260	520	5	.	.	PUNCT
ejpam-4260	521	1	indian	indian	ADJ
ejpam-4260	521	2	journal	journal	PROPN
ejpam-4260	521	3	of	of	ADP
ejpam-4260	521	4	pure	pure	ADJ
ejpam-4260	521	5	and	and	CCONJ
ejpam-4260	521	6	applied	applied	ADJ
ejpam-4260	521	7	mathematics	mathematic	NOUN
ejpam-4260	521	8	,	,	PUNCT
ejpam-4260	521	9	14(4):502–510	14(4):502–510	PROPN
ejpam-4260	521	10	,	,	PUNCT
ejpam-4260	521	11	1983	1983	NUM
ejpam-4260	521	12	.	.	PUNCT
ejpam-4260	522	1	[	[	X
ejpam-4260	522	2	25	25	NUM
ejpam-4260	522	3	]	]	X
ejpam-4260	522	4	j	j	PROPN
ejpam-4260	522	5	m	m	PROPN
ejpam-4260	522	6	mustafa	mustafa	PROPN
ejpam-4260	522	7	.	.	PUNCT
ejpam-4260	523	1	supra	supra	PROPN
ejpam-4260	523	2	b	b	PROPN
ejpam-4260	523	3	-	-	PUNCT
ejpam-4260	523	4	compact	compact	ADJ
ejpam-4260	523	5	and	and	CCONJ
ejpam-4260	523	6	supra	supra	ADJ
ejpam-4260	523	7	b	b	PROPN
ejpam-4260	523	8	-	-	PUNCT
ejpam-4260	523	9	lindelof	lindelof	PROPN
ejpam-4260	523	10	spaces	space	NOUN
ejpam-4260	523	11	.	.	PUNCT
ejpam-4260	524	1	journal	journal	NOUN
ejpam-4260	524	2	of	of	ADP
ejpam-4260	524	3	mathematics	mathematic	NOUN
ejpam-4260	524	4	and	and	CCONJ
ejpam-4260	524	5	applictions	appliction	NOUN
ejpam-4260	524	6	,	,	PUNCT
ejpam-4260	524	7	36:79–83	36:79–83	NUM
ejpam-4260	524	8	,	,	PUNCT
ejpam-4260	524	9	2013	2013	NUM
ejpam-4260	524	10	.	.	PUNCT
ejpam-4260	525	1	[	[	X
ejpam-4260	525	2	26	26	NUM
ejpam-4260	525	3	]	]	X
ejpam-4260	525	4	j	j	PROPN
ejpam-4260	525	5	m	m	PROPN
ejpam-4260	525	6	mustafa	mustafa	PROPN
ejpam-4260	525	7	and	and	CCONJ
ejpam-4260	525	8	h	h	DET
ejpam-4260	525	9	a	a	DET
ejpam-4260	525	10	qoqazeh	qoqazeh	NOUN
ejpam-4260	525	11	.	.	PUNCT
ejpam-4260	526	1	supra	supra	PROPN
ejpam-4260	526	2	d	d	NOUN
ejpam-4260	526	3	-	-	PUNCT
ejpam-4260	526	4	sets	set	NOUN
ejpam-4260	526	5	and	and	CCONJ
ejpam-4260	526	6	associated	associated	ADJ
ejpam-4260	526	7	separation	separation	NOUN
ejpam-4260	526	8	axioms	axiom	NOUN
ejpam-4260	526	9	.	.	PUNCT
ejpam-4260	527	1	international	international	ADJ
ejpam-4260	527	2	journal	journal	NOUN
ejpam-4260	527	3	of	of	ADP
ejpam-4260	527	4	pure	pure	ADJ
ejpam-4260	527	5	and	and	CCONJ
ejpam-4260	527	6	applied	applied	ADJ
ejpam-4260	527	7	mathematics	mathematic	NOUN
ejpam-4260	527	8	,	,	PUNCT
ejpam-4260	527	9	80(5):657–663	80(5):657–663	NUM
ejpam-4260	527	10	,	,	PUNCT
ejpam-4260	527	11	2012	2012	NUM
ejpam-4260	527	12	.	.	PUNCT
ejpam-4260	528	1	[	[	X
ejpam-4260	528	2	27	27	NUM
ejpam-4260	528	3	]	]	X
ejpam-4260	528	4	o	o	X
ejpam-4260	528	5	r	r	NOUN
ejpam-4260	528	6	sayed	say	VERB
ejpam-4260	528	7	.	.	PUNCT
ejpam-4260	529	1	supra	supra	PROPN
ejpam-4260	529	2	pre	pre	ADJ
ejpam-4260	529	3	-	-	ADJ
ejpam-4260	529	4	open	open	ADJ
ejpam-4260	529	5	sets	set	NOUN
ejpam-4260	529	6	and	and	CCONJ
ejpam-4260	529	7	supra	supra	NOUN
ejpam-4260	529	8	pre	pre	ADJ
ejpam-4260	529	9	-	-	ADJ
ejpam-4260	529	10	continuous	continuous	ADJ
ejpam-4260	529	11	on	on	ADP
ejpam-4260	529	12	topological	topological	ADJ
ejpam-4260	529	13	spaces	space	NOUN
ejpam-4260	529	14	.	.	PUNCT
ejpam-4260	530	1	series	series	PROPN
ejpam-4260	530	2	mathematics	mathematics	PROPN
ejpam-4260	530	3	and	and	CCONJ
ejpam-4260	530	4	information	information	NOUN
ejpam-4260	530	5	,	,	PUNCT
ejpam-4260	530	6	20(2):79–88	20(2):79–88	NUM
ejpam-4260	530	7	,	,	PUNCT
ejpam-4260	530	8	2010	2010	NUM
ejpam-4260	530	9	.	.	PUNCT
ejpam-4260	531	1	[	[	X
ejpam-4260	531	2	28	28	NUM
ejpam-4260	531	3	]	]	X
ejpam-4260	531	4	o	o	X
ejpam-4260	531	5	r	r	NOUN
ejpam-4260	531	6	sayed	say	VERB
ejpam-4260	531	7	.	.	PUNCT
ejpam-4260	532	1	supra	supra	PROPN
ejpam-4260	532	2	β	β	NOUN
ejpam-4260	532	3	-	-	NOUN
ejpam-4260	532	4	connectedness	connectedness	NOUN
ejpam-4260	532	5	on	on	ADP
ejpam-4260	532	6	topological	topological	ADJ
ejpam-4260	532	7	spaces	space	NOUN
ejpam-4260	532	8	.	.	PUNCT
ejpam-4260	533	1	proceedings	proceeding	NOUN
ejpam-4260	533	2	of	of	ADP
ejpam-4260	533	3	the	the	DET
ejpam-4260	533	4	pakistan	pakistan	PROPN
ejpam-4260	533	5	academy	academy	PROPN
ejpam-4260	533	6	of	of	ADP
ejpam-4260	533	7	sciences	sciences	PROPN
ejpam-4260	533	8	,	,	PUNCT
ejpam-4260	533	9	49(1):19–23	49(1):19–23	PRON
ejpam-4260	533	10	,	,	PUNCT
ejpam-4260	533	11	2012	2012	NUM
ejpam-4260	533	12	.	.	PUNCT
ejpam-4260	534	1	[	[	X
ejpam-4260	534	2	29	29	NUM
ejpam-4260	534	3	]	]	X
ejpam-4260	534	4	o	o	X
ejpam-4260	534	5	r	r	NOUN
ejpam-4260	534	6	sayed	say	VERB
ejpam-4260	534	7	and	and	CCONJ
ejpam-4260	534	8	t	t	PROPN
ejpam-4260	534	9	noiri	noiri	PROPN
ejpam-4260	534	10	.	.	PUNCT
ejpam-4260	535	1	on	on	ADP
ejpam-4260	535	2	supra	supra	PROPN
ejpam-4260	535	3	b	b	PROPN
ejpam-4260	535	4	-	-	PUNCT
ejpam-4260	535	5	open	open	ADJ
ejpam-4260	535	6	sets	set	NOUN
ejpam-4260	535	7	and	and	CCONJ
ejpam-4260	535	8	supra	supra	PROPN
ejpam-4260	535	9	b	b	NOUN
ejpam-4260	535	10	-	-	PUNCT
ejpam-4260	535	11	continuity	continuity	NOUN
ejpam-4260	535	12	on	on	ADP
ejpam-4260	535	13	topological	topological	ADJ
ejpam-4260	535	14	spaces	space	NOUN
ejpam-4260	535	15	.	.	PUNCT
ejpam-4260	536	1	european	european	ADJ
ejpam-4260	536	2	journal	journal	PROPN
ejpam-4260	536	3	of	of	ADP
ejpam-4260	536	4	pure	pure	ADJ
ejpam-4260	536	5	and	and	CCONJ
ejpam-4260	536	6	applied	applied	ADJ
ejpam-4260	536	7	mathematics	mathematic	NOUN
ejpam-4260	536	8	,	,	PUNCT
ejpam-4260	536	9	3:295–302	3:295–302	NUM
ejpam-4260	536	10	,	,	PUNCT
ejpam-4260	536	11	2010	2010	NUM
ejpam-4260	536	12	.	.	PUNCT