id	sid	tid	token	lemma	pos
ejpam-5486	1	1	european	european	PROPN
ejpam-5486	1	2	journal	journal	PROPN
ejpam-5486	1	3	of	of	ADP
ejpam-5486	1	4	pure	pure	ADJ
ejpam-5486	1	5	and	and	CCONJ
ejpam-5486	1	6	applied	apply	VERB
ejpam-5486	1	7	mathematics	mathematic	NOUN
ejpam-5486	1	8	vol	vol	NOUN
ejpam-5486	1	9	.	.	PROPN
ejpam-5486	2	1	17	17	NUM
ejpam-5486	2	2	,	,	PUNCT
ejpam-5486	2	3	no	no	INTJ
ejpam-5486	2	4	.	.	NOUN
ejpam-5486	2	5	4	4	NUM
ejpam-5486	2	6	,	,	PUNCT
ejpam-5486	2	7	2024	2024	NUM
ejpam-5486	2	8	,	,	PUNCT
ejpam-5486	2	9	3370	3370	NUM
ejpam-5486	2	10	-	-	SYM
ejpam-5486	2	11	3385	3385	NUM
ejpam-5486	2	12	issn	issn	PROPN
ejpam-5486	2	13	1307	1307	NUM
ejpam-5486	2	14	-	-	SYM
ejpam-5486	2	15	5543	5543	NUM
ejpam-5486	2	16	–	–	PUNCT
ejpam-5486	3	1	ejpam.com	ejpam.com	X
ejpam-5486	3	2	published	publish	VERB
ejpam-5486	3	3	by	by	ADP
ejpam-5486	3	4	new	new	PROPN
ejpam-5486	3	5	york	york	PROPN
ejpam-5486	3	6	business	business	PROPN
ejpam-5486	3	7	global	global	PROPN
ejpam-5486	3	8	a	a	DET
ejpam-5486	3	9	generalization	generalization	NOUN
ejpam-5486	3	10	for	for	ADP
ejpam-5486	3	11	somewhere	somewhere	ADJ
ejpam-5486	3	12	dense	dense	ADJ
ejpam-5486	3	13	sets	set	NOUN
ejpam-5486	3	14	with	with	ADP
ejpam-5486	3	15	some	some	DET
ejpam-5486	3	16	applications	application	NOUN
ejpam-5486	3	17	amani	amani	PROPN
ejpam-5486	3	18	rawshdeh1,∗	rawshdeh1,∗	NOUN
ejpam-5486	3	19	,	,	PUNCT
ejpam-5486	3	20	heyam	heyam	NOUN
ejpam-5486	3	21	h.	h.	PROPN
ejpam-5486	3	22	al	al	PROPN
ejpam-5486	3	23	-	-	PROPN
ejpam-5486	3	24	jarrah2	jarrah2	PROPN
ejpam-5486	3	25	,	,	PUNCT
ejpam-5486	3	26	khalid	khalid	PROPN
ejpam-5486	3	27	y.	y.	PROPN
ejpam-5486	3	28	al	al	PROPN
ejpam-5486	3	29	-	-	PUNCT
ejpam-5486	3	30	zoubi2	zoubi2	PROPN
ejpam-5486	3	31	1	1	NUM
ejpam-5486	3	32	department	department	NOUN
ejpam-5486	3	33	of	of	ADP
ejpam-5486	3	34	mathematics	mathematic	NOUN
ejpam-5486	3	35	,	,	PUNCT
ejpam-5486	3	36	faculty	faculty	NOUN
ejpam-5486	3	37	of	of	ADP
ejpam-5486	3	38	science	science	NOUN
ejpam-5486	3	39	,	,	PUNCT
ejpam-5486	3	40	al	al	PROPN
ejpam-5486	3	41	-	-	PUNCT
ejpam-5486	3	42	balqa	balqa	NOUN
ejpam-5486	3	43	applied	apply	VERB
ejpam-5486	3	44	university	university	NOUN
ejpam-5486	3	45	,	,	PUNCT
ejpam-5486	3	46	alsalt	alsalt	NOUN
ejpam-5486	3	47	,	,	PUNCT
ejpam-5486	3	48	jordan	jordan	PROPN
ejpam-5486	3	49	2	2	NUM
ejpam-5486	3	50	department	department	NOUN
ejpam-5486	3	51	of	of	ADP
ejpam-5486	3	52	mathematics	mathematic	NOUN
ejpam-5486	3	53	,	,	PUNCT
ejpam-5486	3	54	faculty	faculty	NOUN
ejpam-5486	3	55	of	of	ADP
ejpam-5486	3	56	science	science	NOUN
ejpam-5486	3	57	,	,	PUNCT
ejpam-5486	3	58	yarmouk	yarmouk	CCONJ
ejpam-5486	3	59	university	university	NOUN
ejpam-5486	3	60	,	,	PUNCT
ejpam-5486	3	61	irbid	irbid	PROPN
ejpam-5486	3	62	,	,	PUNCT
ejpam-5486	3	63	jordan	jordan	PROPN
ejpam-5486	3	64	abstract	abstract	PROPN
ejpam-5486	3	65	.	.	PUNCT
ejpam-5486	4	1	in	in	ADP
ejpam-5486	4	2	this	this	DET
ejpam-5486	4	3	paper	paper	NOUN
ejpam-5486	4	4	,	,	PUNCT
ejpam-5486	4	5	we	we	PRON
ejpam-5486	4	6	present	present	VERB
ejpam-5486	4	7	a	a	DET
ejpam-5486	4	8	new	new	ADJ
ejpam-5486	4	9	generalization	generalization	NOUN
ejpam-5486	4	10	for	for	ADP
ejpam-5486	4	11	somewhere	somewhere	ADV
ejpam-5486	4	12	dense	dense	ADJ
ejpam-5486	4	13	of	of	ADP
ejpam-5486	4	14	a	a	DET
ejpam-5486	4	15	topological	topological	ADJ
ejpam-5486	4	16	space	space	NOUN
ejpam-5486	4	17	(	(	PUNCT
ejpam-5486	4	18	z	z	NOUN
ejpam-5486	4	19	,	,	PUNCT
ejpam-5486	4	20	τ	τ	PROPN
ejpam-5486	4	21	)	)	PUNCT
ejpam-5486	4	22	,	,	PUNCT
ejpam-5486	4	23	namely	namely	ADV
ejpam-5486	4	24	ωswd	ωswd	ADV
ejpam-5486	4	25	-	-	PUNCT
ejpam-5486	4	26	open	open	ADJ
ejpam-5486	4	27	subsets	subset	NOUN
ejpam-5486	4	28	.	.	PUNCT
ejpam-5486	5	1	we	we	PRON
ejpam-5486	5	2	introduce	introduce	VERB
ejpam-5486	5	3	the	the	DET
ejpam-5486	5	4	concept	concept	NOUN
ejpam-5486	5	5	of	of	ADP
ejpam-5486	5	6	this	this	DET
ejpam-5486	5	7	family	family	NOUN
ejpam-5486	5	8	and	and	CCONJ
ejpam-5486	5	9	discuss	discuss	VERB
ejpam-5486	5	10	some	some	PRON
ejpam-5486	5	11	of	of	ADP
ejpam-5486	5	12	their	their	PRON
ejpam-5486	5	13	properties	property	NOUN
ejpam-5486	5	14	with	with	ADP
ejpam-5486	5	15	the	the	DET
ejpam-5486	5	16	help	help	NOUN
ejpam-5486	5	17	of	of	ADP
ejpam-5486	5	18	illustrative	illustrative	ADJ
ejpam-5486	5	19	example	example	NOUN
ejpam-5486	5	20	.	.	PUNCT
ejpam-5486	6	1	moreover	moreover	ADV
ejpam-5486	6	2	,	,	PUNCT
ejpam-5486	6	3	we	we	PRON
ejpam-5486	6	4	will	will	AUX
ejpam-5486	6	5	show	show	VERB
ejpam-5486	6	6	if	if	SCONJ
ejpam-5486	6	7	the	the	DET
ejpam-5486	6	8	space	space	NOUN
ejpam-5486	6	9	(	(	PUNCT
ejpam-5486	6	10	z	z	NOUN
ejpam-5486	6	11	,	,	PUNCT
ejpam-5486	6	12	τ	τ	X
ejpam-5486	6	13	)	)	PUNCT
ejpam-5486	6	14	is	be	AUX
ejpam-5486	6	15	anti	anti	ADJ
ejpam-5486	6	16	-	-	ADJ
ejpam-5486	6	17	locally	locally	ADV
ejpam-5486	6	18	countable	countable	ADJ
ejpam-5486	6	19	and	and	CCONJ
ejpam-5486	6	20	τ	τ	PROPN
ejpam-5486	6	21	is	be	AUX
ejpam-5486	6	22	finer	fine	ADJ
ejpam-5486	6	23	than	than	ADP
ejpam-5486	6	24	the	the	DET
ejpam-5486	6	25	cocountable	cocountable	ADJ
ejpam-5486	6	26	topology	topology	NOUN
ejpam-5486	6	27	then	then	ADV
ejpam-5486	6	28	the	the	DET
ejpam-5486	6	29	class	class	NOUN
ejpam-5486	6	30	of	of	ADP
ejpam-5486	6	31	ωswd	ωswd	ADJ
ejpam-5486	6	32	-	-	PUNCT
ejpam-5486	6	33	open	open	ADJ
ejpam-5486	6	34	and	and	CCONJ
ejpam-5486	6	35	somewhere	somewhere	ADV
ejpam-5486	6	36	dense	dense	ADJ
ejpam-5486	6	37	subsets	subset	NOUN
ejpam-5486	6	38	of	of	ADP
ejpam-5486	6	39	(	(	PUNCT
ejpam-5486	6	40	z	z	PROPN
ejpam-5486	6	41	,	,	PUNCT
ejpam-5486	6	42	τ	τ	X
ejpam-5486	6	43	)	)	PUNCT
ejpam-5486	6	44	will	will	AUX
ejpam-5486	6	45	be	be	AUX
ejpam-5486	6	46	equivalent	equivalent	ADJ
ejpam-5486	6	47	.	.	PUNCT
ejpam-5486	7	1	moreover	moreover	ADV
ejpam-5486	7	2	,	,	PUNCT
ejpam-5486	7	3	we	we	PRON
ejpam-5486	7	4	present	present	VERB
ejpam-5486	7	5	more	more	ADJ
ejpam-5486	7	6	properties	property	NOUN
ejpam-5486	7	7	for	for	ADP
ejpam-5486	7	8	the	the	DET
ejpam-5486	7	9	class	class	NOUN
ejpam-5486	7	10	of	of	ADP
ejpam-5486	7	11	somewhere	somewhere	ADV
ejpam-5486	7	12	dense	dense	ADJ
ejpam-5486	7	13	subsets	subset	NOUN
ejpam-5486	7	14	of	of	ADP
ejpam-5486	7	15	(	(	PUNCT
ejpam-5486	7	16	z	z	PROPN
ejpam-5486	7	17	,	,	PUNCT
ejpam-5486	7	18	τ	τ	PROPN
ejpam-5486	7	19	)	)	PUNCT
ejpam-5486	7	20	,	,	PUNCT
ejpam-5486	7	21	the	the	DET
ejpam-5486	7	22	most	most	ADV
ejpam-5486	7	23	important	important	ADJ
ejpam-5486	7	24	of	of	ADP
ejpam-5486	7	25	which	which	PRON
ejpam-5486	7	26	is	be	AUX
ejpam-5486	7	27	a	a	DET
ejpam-5486	7	28	generalization	generalization	NOUN
ejpam-5486	7	29	for	for	ADP
ejpam-5486	7	30	a	a	DET
ejpam-5486	7	31	theorem	theorem	NOUN
ejpam-5486	7	32	in	in	ADP
ejpam-5486	7	33	[	[	X
ejpam-5486	7	34	1	1	NUM
ejpam-5486	7	35	]	]	PUNCT
ejpam-5486	7	36	.	.	PUNCT
ejpam-5486	8	1	furthermore	furthermore	ADV
ejpam-5486	8	2	,	,	PUNCT
ejpam-5486	8	3	we	we	PRON
ejpam-5486	8	4	finish	finish	VERB
ejpam-5486	8	5	this	this	DET
ejpam-5486	8	6	work	work	NOUN
ejpam-5486	8	7	by	by	ADP
ejpam-5486	8	8	shedding	shed	VERB
ejpam-5486	8	9	light	light	NOUN
ejpam-5486	8	10	on	on	ADP
ejpam-5486	8	11	one	one	NUM
ejpam-5486	8	12	type	type	NOUN
ejpam-5486	8	13	of	of	ADP
ejpam-5486	8	14	covering	cover	VERB
ejpam-5486	8	15	properties	property	NOUN
ejpam-5486	8	16	where	where	SCONJ
ejpam-5486	8	17	we	we	PRON
ejpam-5486	8	18	study	study	VERB
ejpam-5486	8	19	the	the	DET
ejpam-5486	8	20	notion	notion	NOUN
ejpam-5486	8	21	of	of	ADP
ejpam-5486	8	22	almost	almost	ADV
ejpam-5486	8	23	ωswd	ωswd	ADJ
ejpam-5486	8	24	-	-	PUNCT
ejpam-5486	8	25	compact	compact	ADJ
ejpam-5486	8	26	spaces	space	NOUN
ejpam-5486	8	27	with	with	ADP
ejpam-5486	8	28	some	some	PRON
ejpam-5486	8	29	of	of	ADP
ejpam-5486	8	30	their	their	PRON
ejpam-5486	8	31	properties	property	NOUN
ejpam-5486	8	32	.	.	PUNCT
ejpam-5486	9	1	2020	2020	NUM
ejpam-5486	9	2	mathematics	mathematic	NOUN
ejpam-5486	9	3	subject	subject	NOUN
ejpam-5486	9	4	classifications	classification	NOUN
ejpam-5486	9	5	:	:	PUNCT
ejpam-5486	9	6	54a05	54a05	NUM
ejpam-5486	9	7	,	,	PUNCT
ejpam-5486	9	8	54a10	54a10	NUM
ejpam-5486	9	9	,	,	PUNCT
ejpam-5486	9	10	54c10	54c10	NUM
ejpam-5486	9	11	,	,	PUNCT
ejpam-5486	9	12	54d20	54d20	NUM
ejpam-5486	9	13	key	key	ADJ
ejpam-5486	9	14	words	word	NOUN
ejpam-5486	9	15	and	and	CCONJ
ejpam-5486	9	16	phrases	phrase	NOUN
ejpam-5486	9	17	:	:	PUNCT
ejpam-5486	9	18	swd	swd	PROPN
ejpam-5486	9	19	-	-	PUNCT
ejpam-5486	9	20	open	open	ADJ
ejpam-5486	9	21	subsets	subset	NOUN
ejpam-5486	9	22	,	,	PUNCT
ejpam-5486	9	23	ω−open	ω−open	NOUN
ejpam-5486	9	24	subsets	subset	NOUN
ejpam-5486	9	25	,	,	PUNCT
ejpam-5486	9	26	ωswd	ωswd	ADJ
ejpam-5486	9	27	-	-	PUNCT
ejpam-5486	9	28	open	open	ADJ
ejpam-5486	9	29	subsets	subset	NOUN
ejpam-5486	9	30	,	,	PUNCT
ejpam-5486	9	31	ωswdcompact	ωswdcompact	NOUN
ejpam-5486	9	32	spaces	space	VERB
ejpam-5486	9	33	1	1	NUM
ejpam-5486	9	34	.	.	PUNCT
ejpam-5486	9	35	introduction	introduction	NOUN
ejpam-5486	9	36	in	in	ADP
ejpam-5486	9	37	recent	recent	ADJ
ejpam-5486	9	38	decades	decade	NOUN
ejpam-5486	9	39	,	,	PUNCT
ejpam-5486	9	40	a	a	DET
ejpam-5486	9	41	major	major	ADJ
ejpam-5486	9	42	area	area	NOUN
ejpam-5486	9	43	of	of	ADP
ejpam-5486	9	44	study	study	NOUN
ejpam-5486	9	45	for	for	ADP
ejpam-5486	9	46	general	general	ADJ
ejpam-5486	9	47	topology	topology	NOUN
ejpam-5486	9	48	researchers	researcher	NOUN
ejpam-5486	9	49	has	have	AUX
ejpam-5486	9	50	been	be	AUX
ejpam-5486	9	51	the	the	DET
ejpam-5486	9	52	study	study	NOUN
ejpam-5486	9	53	of	of	ADP
ejpam-5486	9	54	various	various	ADJ
ejpam-5486	9	55	kinds	kind	NOUN
ejpam-5486	9	56	of	of	ADP
ejpam-5486	9	57	generalized	generalized	ADJ
ejpam-5486	9	58	open	open	ADJ
ejpam-5486	9	59	sets	set	NOUN
ejpam-5486	9	60	.	.	PUNCT
ejpam-5486	10	1	mathematicians	mathematician	NOUN
ejpam-5486	10	2	examine	examine	VERB
ejpam-5486	10	3	various	various	ADJ
ejpam-5486	10	4	topological	topological	ADJ
ejpam-5486	10	5	notions	notion	NOUN
ejpam-5486	10	6	,	,	PUNCT
ejpam-5486	10	7	such	such	ADJ
ejpam-5486	10	8	as	as	ADP
ejpam-5486	10	9	continuity	continuity	NOUN
ejpam-5486	10	10	,	,	PUNCT
ejpam-5486	10	11	compactness	compactness	NOUN
ejpam-5486	10	12	,	,	PUNCT
ejpam-5486	10	13	etc	etc	X
ejpam-5486	10	14	.	.	X
ejpam-5486	11	1	in	in	ADP
ejpam-5486	11	2	1937	1937	NUM
ejpam-5486	11	3	,	,	PUNCT
ejpam-5486	11	4	stone	stone	NOUN
ejpam-5486	11	5	[	[	X
ejpam-5486	11	6	18	18	NUM
ejpam-5486	11	7	]	]	PUNCT
ejpam-5486	11	8	introduced	introduce	VERB
ejpam-5486	11	9	the	the	DET
ejpam-5486	11	10	concept	concept	NOUN
ejpam-5486	11	11	of	of	ADP
ejpam-5486	11	12	regular	regular	ADJ
ejpam-5486	11	13	open	open	ADJ
ejpam-5486	11	14	sets	set	NOUN
ejpam-5486	11	15	.	.	PUNCT
ejpam-5486	12	1	in	in	ADP
ejpam-5486	12	2	1963	1963	NUM
ejpam-5486	12	3	,	,	PUNCT
ejpam-5486	12	4	levine	levine	PROPN
ejpam-5486	12	5	[	[	X
ejpam-5486	12	6	13	13	NUM
ejpam-5486	12	7	]	]	PUNCT
ejpam-5486	12	8	presented	present	VERB
ejpam-5486	12	9	the	the	DET
ejpam-5486	12	10	notion	notion	NOUN
ejpam-5486	12	11	of	of	ADP
ejpam-5486	12	12	semi	semi	ADJ
ejpam-5486	12	13	-	-	ADJ
ejpam-5486	12	14	open	open	ADJ
ejpam-5486	12	15	sets	set	NOUN
ejpam-5486	12	16	.	.	PUNCT
ejpam-5486	13	1	in	in	ADP
ejpam-5486	13	2	1965	1965	NUM
ejpam-5486	13	3	,	,	PUNCT
ejpam-5486	13	4	njasted	njaste	VERB
ejpam-5486	13	5	[	[	X
ejpam-5486	13	6	16	16	NUM
ejpam-5486	13	7	]	]	PUNCT
ejpam-5486	13	8	introduced	introduce	VERB
ejpam-5486	13	9	α	α	X
ejpam-5486	13	10	-	-	ADJ
ejpam-5486	13	11	open	open	ADJ
ejpam-5486	13	12	sets	set	NOUN
ejpam-5486	13	13	.	.	PUNCT
ejpam-5486	14	1	in	in	ADP
ejpam-5486	14	2	1982	1982	NUM
ejpam-5486	14	3	,	,	PUNCT
ejpam-5486	14	4	mashhour	mashhour	INTJ
ejpam-5486	14	5	et	et	NOUN
ejpam-5486	14	6	al	al	PROPN
ejpam-5486	15	1	[	[	X
ejpam-5486	15	2	15	15	NUM
ejpam-5486	15	3	]	]	PUNCT
ejpam-5486	15	4	introduced	introduce	VERB
ejpam-5486	15	5	the	the	DET
ejpam-5486	15	6	concepts	concept	NOUN
ejpam-5486	15	7	of	of	ADP
ejpam-5486	15	8	pre	pre	ADJ
ejpam-5486	15	9	-	-	ADJ
ejpam-5486	15	10	open	open	ADJ
ejpam-5486	15	11	and	and	CCONJ
ejpam-5486	15	12	studied	study	VERB
ejpam-5486	15	13	their	their	PRON
ejpam-5486	15	14	topological	topological	ADJ
ejpam-5486	15	15	properties	property	NOUN
ejpam-5486	15	16	.	.	PUNCT
ejpam-5486	16	1	in	in	ADP
ejpam-5486	16	2	1983	1983	NUM
ejpam-5486	16	3	,	,	PUNCT
ejpam-5486	16	4	abd	abd	PROPN
ejpam-5486	16	5	el	el	PROPN
ejpam-5486	16	6	-	-	PROPN
ejpam-5486	16	7	monsef	monsef	PROPN
ejpam-5486	16	8	et	et	PROPN
ejpam-5486	16	9	al	al	PROPN
ejpam-5486	17	1	[	[	X
ejpam-5486	17	2	9	9	NUM
ejpam-5486	17	3	]	]	PUNCT
ejpam-5486	17	4	studied	study	VERB
ejpam-5486	17	5	the	the	DET
ejpam-5486	17	6	notion	notion	NOUN
ejpam-5486	17	7	of	of	ADP
ejpam-5486	17	8	β	β	ADJ
ejpam-5486	17	9	-	-	ADJ
ejpam-5486	17	10	open	open	ADJ
ejpam-5486	17	11	sets	set	NOUN
ejpam-5486	17	12	.	.	PUNCT
ejpam-5486	18	1	in	in	ADP
ejpam-5486	18	2	1996	1996	NUM
ejpam-5486	18	3	,	,	PUNCT
ejpam-5486	18	4	andrijevic	andrijevic	VERB
ejpam-5486	18	5	[	[	X
ejpam-5486	18	6	6	6	NUM
ejpam-5486	18	7	]	]	PUNCT
ejpam-5486	18	8	defined	define	VERB
ejpam-5486	18	9	and	and	CCONJ
ejpam-5486	18	10	explored	explore	VERB
ejpam-5486	18	11	the	the	DET
ejpam-5486	18	12	idea	idea	NOUN
ejpam-5486	18	13	of	of	ADP
ejpam-5486	18	14	b	b	NOUN
ejpam-5486	18	15	-	-	PUNCT
ejpam-5486	18	16	open	open	ADJ
ejpam-5486	18	17	sets	set	NOUN
ejpam-5486	18	18	.	.	PUNCT
ejpam-5486	19	1	a	a	DET
ejpam-5486	19	2	subset	subset	ADJ
ejpam-5486	19	3	h	h	NOUN
ejpam-5486	19	4	of	of	ADP
ejpam-5486	19	5	a	a	DET
ejpam-5486	19	6	space	space	NOUN
ejpam-5486	19	7	(	(	PUNCT
ejpam-5486	19	8	z	z	NOUN
ejpam-5486	19	9	,	,	PUNCT
ejpam-5486	19	10	τ	τ	X
ejpam-5486	19	11	)	)	PUNCT
ejpam-5486	19	12	is	be	AUX
ejpam-5486	19	13	called	call	VERB
ejpam-5486	19	14	a	a	DET
ejpam-5486	19	15	regular	regular	ADJ
ejpam-5486	19	16	open	open	ADJ
ejpam-5486	19	17	(	(	PUNCT
ejpam-5486	19	18	semi	semi	ADJ
ejpam-5486	19	19	-	-	ADJ
ejpam-5486	19	20	open	open	ADJ
ejpam-5486	19	21	,	,	PUNCT
ejpam-5486	19	22	α	α	NOUN
ejpam-5486	19	23	-	-	ADJ
ejpam-5486	19	24	open	open	ADJ
ejpam-5486	19	25	,	,	PUNCT
ejpam-5486	19	26	pre	pre	ADJ
ejpam-5486	19	27	-	-	ADJ
ejpam-5486	19	28	open	open	ADJ
ejpam-5486	19	29	,	,	PUNCT
ejpam-5486	19	30	β	β	NOUN
ejpam-5486	19	31	-	-	ADJ
ejpam-5486	19	32	open	open	ADJ
ejpam-5486	19	33	,	,	PUNCT
ejpam-5486	19	34	b	b	X
ejpam-5486	19	35	-	-	PUNCT
ejpam-5486	19	36	open	open	ADJ
ejpam-5486	19	37	)	)	PUNCT
ejpam-5486	19	38	sets	set	VERB
ejpam-5486	19	39	if	if	SCONJ
ejpam-5486	19	40	h	h	NOUN
ejpam-5486	19	41	=	=	SYM
ejpam-5486	19	42	int(cl(h))(resp	int(cl(h))(resp	PROPN
ejpam-5486	19	43	.	.	PUNCT
ejpam-5486	19	44	,	,	PUNCT
ejpam-5486	19	45	h	h	NOUN
ejpam-5486	19	46	⊆	⊆	NUM
ejpam-5486	19	47	cl(int(h	cl(int(h	NOUN
ejpam-5486	19	48	)	)	PUNCT
ejpam-5486	19	49	)	)	PUNCT
ejpam-5486	19	50	,	,	PUNCT
ejpam-5486	19	51	h	h	NOUN
ejpam-5486	19	52	⊆	⊆	NUM
ejpam-5486	19	53	int(cl(int(h	int(cl(int(h	PROPN
ejpam-5486	19	54	)	)	PUNCT
ejpam-5486	19	55	)	)	PUNCT
ejpam-5486	19	56	)	)	PUNCT
ejpam-5486	19	57	,	,	PUNCT
ejpam-5486	19	58	h	h	NOUN
ejpam-5486	19	59	⊆	⊆	NUM
ejpam-5486	19	60	int(cl(h	int(cl(h	PROPN
ejpam-5486	19	61	)	)	PUNCT
ejpam-5486	19	62	)	)	PUNCT
ejpam-5486	19	63	,	,	PUNCT
ejpam-5486	19	64	h	h	NOUN
ejpam-5486	19	65	⊆	⊆	NUM
ejpam-5486	19	66	cl(int(cl(h	cl(int(cl(h	NOUN
ejpam-5486	19	67	)	)	PUNCT
ejpam-5486	19	68	)	)	PUNCT
ejpam-5486	19	69	)	)	PUNCT
ejpam-5486	19	70	,	,	PUNCT
ejpam-5486	19	71	h	h	NOUN
ejpam-5486	19	72	⊆	⊆	NUM
ejpam-5486	19	73	int(cl(h))∪cl(int(h	int(cl(h))∪cl(int(h	NUM
ejpam-5486	19	74	)	)	PUNCT
ejpam-5486	19	75	)	)	PUNCT
ejpam-5486	19	76	)	)	PUNCT
ejpam-5486	19	77	.	.	PUNCT
ejpam-5486	20	1	∗corresponding	∗corresponde	VERB
ejpam-5486	20	2	author	author	NOUN
ejpam-5486	20	3	.	.	PUNCT
ejpam-5486	21	1	doi	doi	NOUN
ejpam-5486	21	2	:	:	PUNCT
ejpam-5486	21	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5486	https://doi.org/10.29020/nybg.ejpam.v17i4.5486	ADJ
ejpam-5486	21	4	email	email	NOUN
ejpam-5486	21	5	addresses	address	NOUN
ejpam-5486	21	6	:	:	PUNCT
ejpam-5486	21	7	amanirawshdeh@bau.edu.jo	amanirawshdeh@bau.edu.jo	ADJ
ejpam-5486	21	8	(	(	PUNCT
ejpam-5486	21	9	a.	a.	NOUN
ejpam-5486	21	10	rawshdeh	rawshdeh	PROPN
ejpam-5486	21	11	)	)	PUNCT
ejpam-5486	21	12	,	,	PUNCT
ejpam-5486	21	13	heyam@yu.edu.jo	heyam@yu.edu.jo	PROPN
ejpam-5486	21	14	(	(	PUNCT
ejpam-5486	21	15	h.	h.	PROPN
ejpam-5486	21	16	h.	h.	PROPN
ejpam-5486	21	17	al	al	PROPN
ejpam-5486	21	18	-	-	PUNCT
ejpam-5486	21	19	jarrah	jarrah	PROPN
ejpam-5486	21	20	)	)	PUNCT
ejpam-5486	21	21	,	,	PUNCT
ejpam-5486	22	1	khalidz@yu.edu.jo	khalidz@yu.edu.jo	PROPN
ejpam-5486	22	2	(	(	PUNCT
ejpam-5486	22	3	k.	k.	PROPN
ejpam-5486	22	4	y.	y.	PROPN
ejpam-5486	22	5	al	al	PROPN
ejpam-5486	22	6	-	-	PROPN
ejpam-5486	22	7	zoubi	zoubi	PROPN
ejpam-5486	22	8	)	)	PUNCT
ejpam-5486	22	9	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5486	23	1	3370	3370	NUM
ejpam-5486	23	2	copyright	copyright	NOUN
ejpam-5486	23	3	:	:	PUNCT
ejpam-5486	23	4	©	©	PROPN
ejpam-5486	23	5	2024	2024	NUM
ejpam-5486	23	6	the	the	DET
ejpam-5486	23	7	author(s	author(s	NOUN
ejpam-5486	23	8	)	)	PUNCT
ejpam-5486	23	9	.	.	PUNCT
ejpam-5486	24	1	(	(	PUNCT
ejpam-5486	24	2	cc	cc	NOUN
ejpam-5486	24	3	by	by	ADP
ejpam-5486	24	4	-	-	PUNCT
ejpam-5486	24	5	nc	nc	PROPN
ejpam-5486	24	6	4.0	4.0	NUM
ejpam-5486	24	7	)	)	PUNCT
ejpam-5486	24	8	a.	a.	NOUN
ejpam-5486	24	9	rawshdeh	rawshdeh	PROPN
ejpam-5486	24	10	,	,	PUNCT
ejpam-5486	24	11	h.	h.	PROPN
ejpam-5486	24	12	h.	h.	PROPN
ejpam-5486	24	13	al	al	PROPN
ejpam-5486	24	14	-	-	PUNCT
ejpam-5486	24	15	jarrah	jarrah	PROPN
ejpam-5486	24	16	,	,	PUNCT
ejpam-5486	24	17	k.	k.	PROPN
ejpam-5486	24	18	y.	y.	PROPN
ejpam-5486	24	19	al	al	PROPN
ejpam-5486	24	20	-	-	PROPN
ejpam-5486	24	21	zoubi	zoubi	PROPN
ejpam-5486	24	22	/	/	SYM
ejpam-5486	24	23	eur	eur	PROPN
ejpam-5486	24	24	.	.	PUNCT
ejpam-5486	25	1	j.	j.	PROPN
ejpam-5486	25	2	pure	pure	PROPN
ejpam-5486	25	3	appl	appl	PROPN
ejpam-5486	25	4	.	.	PROPN
ejpam-5486	25	5	math	math	PROPN
ejpam-5486	25	6	,	,	PUNCT
ejpam-5486	25	7	17	17	NUM
ejpam-5486	25	8	(	(	PUNCT
ejpam-5486	25	9	4	4	NUM
ejpam-5486	25	10	)	)	PUNCT
ejpam-5486	25	11	(	(	PUNCT
ejpam-5486	25	12	2024	2024	NUM
ejpam-5486	25	13	)	)	PUNCT
ejpam-5486	25	14	,	,	PUNCT
ejpam-5486	25	15	3370	3370	NUM
ejpam-5486	25	16	-	-	SYM
ejpam-5486	25	17	3385	3385	NUM
ejpam-5486	25	18	3371	3371	NUM
ejpam-5486	25	19	another	another	DET
ejpam-5486	25	20	form	form	NOUN
ejpam-5486	25	21	of	of	ADP
ejpam-5486	25	22	generalization	generalization	NOUN
ejpam-5486	25	23	of	of	ADP
ejpam-5486	25	24	open	open	ADJ
ejpam-5486	25	25	sets	set	NOUN
ejpam-5486	25	26	that	that	PRON
ejpam-5486	25	27	we	we	PRON
ejpam-5486	25	28	need	need	VERB
ejpam-5486	25	29	in	in	ADP
ejpam-5486	25	30	this	this	DET
ejpam-5486	25	31	work	work	NOUN
ejpam-5486	25	32	is	be	AUX
ejpam-5486	25	33	ω−open	ω−open	NOUN
ejpam-5486	25	34	sets	set	NOUN
ejpam-5486	25	35	.	.	PUNCT
ejpam-5486	26	1	a	a	DET
ejpam-5486	26	2	subset	subset	ADJ
ejpam-5486	26	3	h	h	NOUN
ejpam-5486	26	4	of	of	ADP
ejpam-5486	26	5	a	a	DET
ejpam-5486	26	6	space	space	NOUN
ejpam-5486	26	7	(	(	PUNCT
ejpam-5486	26	8	z	z	NOUN
ejpam-5486	26	9	,	,	PUNCT
ejpam-5486	26	10	τ	τ	X
ejpam-5486	26	11	)	)	PUNCT
ejpam-5486	26	12	is	be	AUX
ejpam-5486	26	13	called	call	VERB
ejpam-5486	26	14	an	an	DET
ejpam-5486	26	15	ω−closed	ω−close	VERB
ejpam-5486	26	16	[	[	X
ejpam-5486	26	17	11	11	NUM
ejpam-5486	26	18	]	]	PUNCT
ejpam-5486	26	19	if	if	SCONJ
ejpam-5486	26	20	it	it	PRON
ejpam-5486	26	21	contains	contain	VERB
ejpam-5486	26	22	all	all	DET
ejpam-5486	26	23	its	its	PRON
ejpam-5486	26	24	condensation	condensation	NOUN
ejpam-5486	26	25	points	point	NOUN
ejpam-5486	26	26	,	,	PUNCT
ejpam-5486	26	27	where	where	SCONJ
ejpam-5486	26	28	a	a	DET
ejpam-5486	26	29	point	point	NOUN
ejpam-5486	26	30	x	x	X
ejpam-5486	26	31	∈	∈	PROPN
ejpam-5486	26	32	z	z	NOUN
ejpam-5486	26	33	is	be	AUX
ejpam-5486	26	34	called	call	VERB
ejpam-5486	26	35	a	a	DET
ejpam-5486	26	36	condensation	condensation	NOUN
ejpam-5486	26	37	point	point	NOUN
ejpam-5486	26	38	of	of	ADP
ejpam-5486	26	39	h	h	NOUN
ejpam-5486	27	1	[	[	X
ejpam-5486	27	2	10	10	NUM
ejpam-5486	27	3	]	]	X
ejpam-5486	27	4	if	if	SCONJ
ejpam-5486	27	5	for	for	ADP
ejpam-5486	27	6	each	each	DET
ejpam-5486	27	7	g	g	PROPN
ejpam-5486	27	8	∈	∈	PROPN
ejpam-5486	27	9	τ	τ	X
ejpam-5486	27	10	with	with	ADP
ejpam-5486	27	11	x	x	PROPN
ejpam-5486	27	12	∈	∈	PROPN
ejpam-5486	27	13	g	g	PROPN
ejpam-5486	27	14	,	,	PUNCT
ejpam-5486	27	15	the	the	DET
ejpam-5486	27	16	set	set	NOUN
ejpam-5486	27	17	g	g	PROPN
ejpam-5486	27	18	∩h	∩h	PROPN
ejpam-5486	27	19	is	be	AUX
ejpam-5486	27	20	uncountable	uncountable	ADJ
ejpam-5486	27	21	.	.	PUNCT
ejpam-5486	28	1	the	the	DET
ejpam-5486	28	2	complement	complement	NOUN
ejpam-5486	28	3	of	of	ADP
ejpam-5486	28	4	an	an	DET
ejpam-5486	28	5	ω−closed	ω−close	VERB
ejpam-5486	28	6	is	be	AUX
ejpam-5486	28	7	called	call	VERB
ejpam-5486	28	8	ω−open	ω−open	NOUN
ejpam-5486	28	9	.	.	PUNCT
ejpam-5486	29	1	moreover	moreover	ADV
ejpam-5486	29	2	,	,	PUNCT
ejpam-5486	29	3	in	in	ADP
ejpam-5486	29	4	[	[	X
ejpam-5486	29	5	5	5	X
ejpam-5486	29	6	]	]	PUNCT
ejpam-5486	29	7	the	the	DET
ejpam-5486	29	8	authors	author	NOUN
ejpam-5486	29	9	introduced	introduce	VERB
ejpam-5486	29	10	an	an	DET
ejpam-5486	29	11	equivalent	equivalent	ADJ
ejpam-5486	29	12	definition	definition	NOUN
ejpam-5486	29	13	of	of	ADP
ejpam-5486	29	14	ω−open	ω−open	PROPN
ejpam-5486	29	15	subsets	subset	NOUN
ejpam-5486	29	16	,	,	PUNCT
ejpam-5486	29	17	where	where	SCONJ
ejpam-5486	29	18	h	h	NOUN
ejpam-5486	29	19	⊆	⊆	NUM
ejpam-5486	29	20	z	z	NOUN
ejpam-5486	29	21	is	be	AUX
ejpam-5486	29	22	an	an	DET
ejpam-5486	29	23	ω−open	ω−open	ADJ
ejpam-5486	29	24	subsets	subset	NOUN
ejpam-5486	29	25	of	of	ADP
ejpam-5486	29	26	(	(	PUNCT
ejpam-5486	29	27	z	z	PROPN
ejpam-5486	29	28	,	,	PUNCT
ejpam-5486	29	29	τ	τ	PROPN
ejpam-5486	29	30	)	)	PUNCT
ejpam-5486	29	31	if	if	SCONJ
ejpam-5486	29	32	for	for	ADP
ejpam-5486	29	33	each	each	PRON
ejpam-5486	29	34	x	x	SYM
ejpam-5486	29	35	∈	∈	PROPN
ejpam-5486	29	36	h	h	NOUN
ejpam-5486	29	37	there	there	PRON
ejpam-5486	29	38	is	be	VERB
ejpam-5486	29	39	g	g	PROPN
ejpam-5486	29	40	∈	∈	PROPN
ejpam-5486	29	41	τ	τ	X
ejpam-5486	29	42	with	with	ADP
ejpam-5486	29	43	x	x	PROPN
ejpam-5486	29	44	∈	∈	PROPN
ejpam-5486	29	45	g	g	NOUN
ejpam-5486	29	46	such	such	ADJ
ejpam-5486	29	47	that	that	SCONJ
ejpam-5486	29	48	g−h	g−h	PROPN
ejpam-5486	29	49	is	be	AUX
ejpam-5486	29	50	countable	countable	ADJ
ejpam-5486	29	51	.	.	PUNCT
ejpam-5486	30	1	the	the	DET
ejpam-5486	30	2	study	study	NOUN
ejpam-5486	30	3	and	and	CCONJ
ejpam-5486	30	4	exploitation	exploitation	NOUN
ejpam-5486	30	5	of	of	ADP
ejpam-5486	30	6	these	these	DET
ejpam-5486	30	7	generalizations	generalization	NOUN
ejpam-5486	30	8	have	have	AUX
ejpam-5486	30	9	become	become	VERB
ejpam-5486	30	10	very	very	ADV
ejpam-5486	30	11	widespread	widespread	ADJ
ejpam-5486	30	12	and	and	CCONJ
ejpam-5486	30	13	many	many	ADJ
ejpam-5486	30	14	works	work	NOUN
ejpam-5486	30	15	have	have	AUX
ejpam-5486	30	16	been	be	AUX
ejpam-5486	30	17	presented	present	VERB
ejpam-5486	30	18	based	base	VERB
ejpam-5486	30	19	on	on	ADP
ejpam-5486	30	20	these	these	DET
ejpam-5486	30	21	sets	set	NOUN
ejpam-5486	30	22	,	,	PUNCT
ejpam-5486	30	23	for	for	ADP
ejpam-5486	30	24	example	example	NOUN
ejpam-5486	30	25	in	in	ADP
ejpam-5486	30	26	[	[	X
ejpam-5486	30	27	12	12	NUM
ejpam-5486	30	28	]	]	PUNCT
ejpam-5486	30	29	the	the	DET
ejpam-5486	30	30	authors	author	NOUN
ejpam-5486	30	31	presented	present	VERB
ejpam-5486	30	32	some	some	DET
ejpam-5486	30	33	applications	application	NOUN
ejpam-5486	30	34	of	of	ADP
ejpam-5486	30	35	pre	pre	ADJ
ejpam-5486	30	36	-	-	ADJ
ejpam-5486	30	37	open	open	ADJ
ejpam-5486	30	38	sets	set	NOUN
ejpam-5486	30	39	,	,	PUNCT
ejpam-5486	30	40	where	where	SCONJ
ejpam-5486	30	41	they	they	PRON
ejpam-5486	30	42	introduced	introduce	VERB
ejpam-5486	30	43	and	and	CCONJ
ejpam-5486	30	44	studied	study	VERB
ejpam-5486	30	45	topological	topological	ADJ
ejpam-5486	30	46	properties	property	NOUN
ejpam-5486	30	47	of	of	ADP
ejpam-5486	30	48	pre	pre	ADJ
ejpam-5486	30	49	-	-	ADJ
ejpam-5486	30	50	limit	limit	ADJ
ejpam-5486	30	51	points	point	NOUN
ejpam-5486	30	52	,	,	PUNCT
ejpam-5486	30	53	pre	pre	ADJ
ejpam-5486	30	54	-	-	ADJ
ejpam-5486	30	55	interior	interior	ADJ
ejpam-5486	30	56	and	and	CCONJ
ejpam-5486	30	57	pre	pre	ADJ
ejpam-5486	30	58	-	-	ADJ
ejpam-5486	30	59	closure	closure	NOUN
ejpam-5486	30	60	and	and	CCONJ
ejpam-5486	30	61	other	other	ADJ
ejpam-5486	30	62	topological	topological	ADJ
ejpam-5486	30	63	notions	notion	NOUN
ejpam-5486	30	64	[	[	PUNCT
ejpam-5486	30	65	see	see	VERB
ejpam-5486	30	66	[	[	X
ejpam-5486	30	67	8],[14	8],[14	NOUN
ejpam-5486	30	68	]	]	X
ejpam-5486	30	69	]	]	PUNCT
ejpam-5486	30	70	.	.	PUNCT
ejpam-5486	31	1	in	in	ADP
ejpam-5486	31	2	2017	2017	NUM
ejpam-5486	31	3	,	,	PUNCT
ejpam-5486	31	4	al	al	PROPN
ejpam-5486	31	5	-	-	PUNCT
ejpam-5486	31	6	shami	shami	PROPN
ejpam-5486	32	1	[	[	X
ejpam-5486	32	2	1	1	X
ejpam-5486	32	3	]	]	PUNCT
ejpam-5486	32	4	examined	examine	VERB
ejpam-5486	32	5	and	and	CCONJ
ejpam-5486	32	6	studied	study	VERB
ejpam-5486	32	7	some	some	DET
ejpam-5486	32	8	main	main	ADJ
ejpam-5486	32	9	properties	property	NOUN
ejpam-5486	32	10	of	of	ADP
ejpam-5486	32	11	somewhere	somewhere	ADJ
ejpam-5486	32	12	dense	dense	ADJ
ejpam-5486	32	13	sets	set	NOUN
ejpam-5486	32	14	on	on	ADP
ejpam-5486	32	15	topological	topological	ADJ
ejpam-5486	32	16	spaces	space	NOUN
ejpam-5486	32	17	where	where	SCONJ
ejpam-5486	32	18	a	a	DET
ejpam-5486	32	19	subset	subset	NOUN
ejpam-5486	32	20	h	h	NOUN
ejpam-5486	32	21	⊆	⊆	NUM
ejpam-5486	32	22	z	z	NOUN
ejpam-5486	32	23	is	be	AUX
ejpam-5486	32	24	a	a	DET
ejpam-5486	32	25	somewhere	somewhere	ADV
ejpam-5486	32	26	dense	dense	ADJ
ejpam-5486	32	27	set	set	NOUN
ejpam-5486	32	28	of	of	ADP
ejpam-5486	32	29	(	(	PUNCT
ejpam-5486	32	30	z	z	PROPN
ejpam-5486	32	31	,	,	PUNCT
ejpam-5486	32	32	τ	τ	PROPN
ejpam-5486	32	33	)	)	PUNCT
ejpam-5486	32	34	if	if	SCONJ
ejpam-5486	32	35	there	there	PRON
ejpam-5486	32	36	is	be	VERB
ejpam-5486	32	37	a	a	DET
ejpam-5486	32	38	non	non	ADJ
ejpam-5486	32	39	-	-	ADJ
ejpam-5486	32	40	empty	empty	ADJ
ejpam-5486	32	41	open	open	ADJ
ejpam-5486	32	42	set	set	VERB
ejpam-5486	32	43	g	g	NOUN
ejpam-5486	32	44	with	with	ADP
ejpam-5486	32	45	g	g	PROPN
ejpam-5486	32	46	⊆	⊆	NUM
ejpam-5486	32	47	cl(h	cl(h	NUM
ejpam-5486	32	48	)	)	PUNCT
ejpam-5486	32	49	which	which	PRON
ejpam-5486	32	50	is	be	AUX
ejpam-5486	32	51	equivalent	equivalent	ADJ
ejpam-5486	32	52	to	to	PART
ejpam-5486	32	53	say	say	VERB
ejpam-5486	32	54	int(cl(h	int(cl(h	PROPN
ejpam-5486	32	55	)	)	PUNCT
ejpam-5486	32	56	)	)	PUNCT
ejpam-5486	32	57	is	be	AUX
ejpam-5486	32	58	a	a	DET
ejpam-5486	32	59	non	non	ADJ
ejpam-5486	32	60	-	-	ADJ
ejpam-5486	32	61	empty	empty	ADJ
ejpam-5486	32	62	set	set	NOUN
ejpam-5486	32	63	.	.	PUNCT
ejpam-5486	33	1	moreover	moreover	ADV
ejpam-5486	33	2	,	,	PUNCT
ejpam-5486	33	3	he	he	PRON
ejpam-5486	33	4	showed	show	VERB
ejpam-5486	33	5	that	that	SCONJ
ejpam-5486	33	6	,	,	PUNCT
ejpam-5486	33	7	with	with	ADP
ejpam-5486	33	8	the	the	DET
ejpam-5486	33	9	expectation	expectation	NOUN
ejpam-5486	33	10	of	of	ADP
ejpam-5486	33	11	the	the	DET
ejpam-5486	33	12	empty	empty	ADJ
ejpam-5486	33	13	set	set	NOUN
ejpam-5486	33	14	,	,	PUNCT
ejpam-5486	33	15	all	all	PRON
ejpam-5486	33	16	semi	semi	ADJ
ejpam-5486	33	17	-	-	ADJ
ejpam-5486	33	18	open	open	ADJ
ejpam-5486	33	19	,	,	PUNCT
ejpam-5486	33	20	α	α	NOUN
ejpam-5486	33	21	-	-	ADJ
ejpam-5486	33	22	open	open	ADJ
ejpam-5486	33	23	sets	set	NOUN
ejpam-5486	33	24	,	,	PUNCT
ejpam-5486	33	25	pre	pre	ADJ
ejpam-5486	33	26	-	-	ADJ
ejpam-5486	33	27	open	open	ADJ
ejpam-5486	33	28	,	,	PUNCT
ejpam-5486	33	29	β	β	NOUN
ejpam-5486	33	30	-	-	ADJ
ejpam-5486	33	31	open	open	ADJ
ejpam-5486	33	32	,	,	PUNCT
ejpam-5486	33	33	and	and	CCONJ
ejpam-5486	33	34	b	b	X
ejpam-5486	33	35	-	-	PUNCT
ejpam-5486	33	36	open	open	ADJ
ejpam-5486	33	37	sets	set	NOUN
ejpam-5486	33	38	are	be	AUX
ejpam-5486	33	39	contained	contain	VERB
ejpam-5486	33	40	in	in	ADP
ejpam-5486	33	41	the	the	DET
ejpam-5486	33	42	class	class	NOUN
ejpam-5486	33	43	of	of	ADP
ejpam-5486	33	44	somewhere	somewhere	ADJ
ejpam-5486	33	45	dense	dense	ADJ
ejpam-5486	33	46	sets	set	NOUN
ejpam-5486	33	47	.	.	PUNCT
ejpam-5486	34	1	then	then	ADV
ejpam-5486	34	2	,	,	PUNCT
ejpam-5486	34	3	al	al	PROPN
ejpam-5486	34	4	-	-	PUNCT
ejpam-5486	34	5	shami	shami	PROPN
ejpam-5486	34	6	and	and	CCONJ
ejpam-5486	34	7	noiri	noiri	ADV
ejpam-5486	35	1	[	[	X
ejpam-5486	35	2	3	3	X
ejpam-5486	35	3	]	]	PUNCT
ejpam-5486	35	4	used	use	VERB
ejpam-5486	35	5	the	the	DET
ejpam-5486	35	6	class	class	NOUN
ejpam-5486	35	7	of	of	ADP
ejpam-5486	35	8	somewhere	somewhere	ADV
ejpam-5486	35	9	dense	dense	ADJ
ejpam-5486	35	10	sets	set	NOUN
ejpam-5486	35	11	to	to	PART
ejpam-5486	35	12	define	define	VERB
ejpam-5486	35	13	the	the	DET
ejpam-5486	35	14	concept	concept	NOUN
ejpam-5486	35	15	of	of	ADP
ejpam-5486	35	16	swd	swd	PROPN
ejpam-5486	35	17	-	-	PUNCT
ejpam-5486	35	18	continuous	continuous	ADJ
ejpam-5486	35	19	and	and	CCONJ
ejpam-5486	35	20	swd	swd	PROPN
ejpam-5486	35	21	-	-	PUNCT
ejpam-5486	35	22	homeomorphism	homeomorphism	PROPN
ejpam-5486	35	23	functions	function	NOUN
ejpam-5486	35	24	.	.	PUNCT
ejpam-5486	36	1	then	then	ADV
ejpam-5486	36	2	in	in	ADP
ejpam-5486	36	3	[	[	X
ejpam-5486	36	4	4	4	NUM
ejpam-5486	36	5	]	]	PUNCT
ejpam-5486	36	6	,	,	PUNCT
ejpam-5486	36	7	they	they	PRON
ejpam-5486	36	8	introduced	introduce	VERB
ejpam-5486	36	9	and	and	CCONJ
ejpam-5486	36	10	investigated	investigate	VERB
ejpam-5486	36	11	the	the	DET
ejpam-5486	36	12	notions	notion	NOUN
ejpam-5486	36	13	of	of	ADP
ejpam-5486	36	14	almost	almost	ADV
ejpam-5486	36	15	swd	swd	PROPN
ejpam-5486	36	16	-	-	ADJ
ejpam-5486	36	17	compact	compact	ADJ
ejpam-5486	36	18	,	,	PUNCT
ejpam-5486	36	19	almost	almost	ADV
ejpam-5486	36	20	swdlindelöf	swdlindelöf	NOUN
ejpam-5486	36	21	spaces	space	NOUN
ejpam-5486	36	22	,	,	PUNCT
ejpam-5486	36	23	nearly	nearly	ADV
ejpam-5486	36	24	swd	swd	PROPN
ejpam-5486	36	25	-	-	ADJ
ejpam-5486	36	26	compact	compact	ADJ
ejpam-5486	36	27	,	,	PUNCT
ejpam-5486	36	28	nearly	nearly	ADV
ejpam-5486	36	29	swd	swd	PROPN
ejpam-5486	36	30	-	-	PUNCT
ejpam-5486	36	31	lindelöf	lindelöf	PROPN
ejpam-5486	36	32	,	,	PUNCT
ejpam-5486	36	33	mildly	mildly	ADV
ejpam-5486	36	34	swd	swd	PROPN
ejpam-5486	36	35	-	-	ADJ
ejpam-5486	36	36	compact	compact	ADJ
ejpam-5486	36	37	and	and	CCONJ
ejpam-5486	36	38	mildly	mildly	ADV
ejpam-5486	36	39	swd	swd	PROPN
ejpam-5486	36	40	-	-	PUNCT
ejpam-5486	36	41	lindelöf	lindelöf	NOUN
ejpam-5486	36	42	spaces	space	NOUN
ejpam-5486	36	43	and	and	CCONJ
ejpam-5486	36	44	they	they	PRON
ejpam-5486	36	45	studied	study	VERB
ejpam-5486	36	46	the	the	DET
ejpam-5486	36	47	relationships	relationship	NOUN
ejpam-5486	36	48	between	between	ADP
ejpam-5486	36	49	them	they	PRON
ejpam-5486	36	50	.	.	PUNCT
ejpam-5486	37	1	moreover	moreover	ADV
ejpam-5486	37	2	,	,	PUNCT
ejpam-5486	37	3	in	in	ADP
ejpam-5486	37	4	[	[	X
ejpam-5486	37	5	2	2	X
ejpam-5486	37	6	]	]	PUNCT
ejpam-5486	37	7	the	the	DET
ejpam-5486	37	8	author	author	NOUN
ejpam-5486	37	9	contributed	contribute	VERB
ejpam-5486	37	10	to	to	ADP
ejpam-5486	37	11	this	this	DET
ejpam-5486	37	12	area	area	NOUN
ejpam-5486	37	13	and	and	CCONJ
ejpam-5486	37	14	used	use	VERB
ejpam-5486	37	15	the	the	DET
ejpam-5486	37	16	notion	notion	NOUN
ejpam-5486	37	17	of	of	ADP
ejpam-5486	37	18	somewhere	somewhere	ADJ
ejpam-5486	37	19	dense	dense	ADJ
ejpam-5486	37	20	sets	set	NOUN
ejpam-5486	37	21	to	to	PART
ejpam-5486	37	22	improve	improve	VERB
ejpam-5486	37	23	the	the	DET
ejpam-5486	37	24	approximations	approximation	NOUN
ejpam-5486	37	25	and	and	CCONJ
ejpam-5486	37	26	accuracy	accuracy	NOUN
ejpam-5486	37	27	measure	measure	NOUN
ejpam-5486	37	28	in	in	ADP
ejpam-5486	37	29	rough	rough	ADJ
ejpam-5486	37	30	set	set	NOUN
ejpam-5486	37	31	theory	theory	NOUN
ejpam-5486	37	32	.	.	PUNCT
ejpam-5486	38	1	in	in	ADP
ejpam-5486	38	2	this	this	DET
ejpam-5486	38	3	work	work	NOUN
ejpam-5486	38	4	,	,	PUNCT
ejpam-5486	38	5	we	we	PRON
ejpam-5486	38	6	study	study	VERB
ejpam-5486	38	7	and	and	CCONJ
ejpam-5486	38	8	present	present	VERB
ejpam-5486	38	9	more	more	ADJ
ejpam-5486	38	10	properties	property	NOUN
ejpam-5486	38	11	of	of	ADP
ejpam-5486	38	12	somewhere	somewhere	ADV
ejpam-5486	38	13	dense	dense	ADJ
ejpam-5486	38	14	of	of	ADP
ejpam-5486	38	15	(	(	PUNCT
ejpam-5486	38	16	z	z	PROPN
ejpam-5486	38	17	,	,	PUNCT
ejpam-5486	38	18	τ	τ	PROPN
ejpam-5486	38	19	)	)	PUNCT
ejpam-5486	38	20	.	.	PUNCT
ejpam-5486	39	1	one	one	NUM
ejpam-5486	39	2	of	of	ADP
ejpam-5486	39	3	the	the	DET
ejpam-5486	39	4	most	most	ADV
ejpam-5486	39	5	important	important	ADJ
ejpam-5486	39	6	of	of	ADP
ejpam-5486	39	7	these	these	DET
ejpam-5486	39	8	properties	property	NOUN
ejpam-5486	39	9	is	be	AUX
ejpam-5486	39	10	a	a	DET
ejpam-5486	39	11	generalization	generalization	NOUN
ejpam-5486	39	12	for	for	ADP
ejpam-5486	39	13	a	a	DET
ejpam-5486	39	14	theorem	theorem	NOUN
ejpam-5486	39	15	that	that	PRON
ejpam-5486	39	16	was	be	AUX
ejpam-5486	39	17	introduced	introduce	VERB
ejpam-5486	39	18	in	in	ADP
ejpam-5486	39	19	[	[	X
ejpam-5486	39	20	1	1	NUM
ejpam-5486	39	21	]	]	PUNCT
ejpam-5486	39	22	.	.	PUNCT
ejpam-5486	40	1	then	then	ADV
ejpam-5486	40	2	,	,	PUNCT
ejpam-5486	40	3	based	base	VERB
ejpam-5486	40	4	on	on	ADP
ejpam-5486	40	5	the	the	DET
ejpam-5486	40	6	class	class	NOUN
ejpam-5486	40	7	of	of	ADP
ejpam-5486	40	8	all	all	PRON
ejpam-5486	40	9	somewhere	somewhere	ADV
ejpam-5486	40	10	dense	dense	ADJ
ejpam-5486	40	11	and	and	CCONJ
ejpam-5486	40	12	ω−open	ω−open	ADJ
ejpam-5486	40	13	subsets	subset	NOUN
ejpam-5486	40	14	of	of	ADP
ejpam-5486	40	15	(	(	PUNCT
ejpam-5486	40	16	z	z	PROPN
ejpam-5486	40	17	,	,	PUNCT
ejpam-5486	40	18	τ	τ	PROPN
ejpam-5486	40	19	)	)	PUNCT
ejpam-5486	40	20	,	,	PUNCT
ejpam-5486	40	21	we	we	PRON
ejpam-5486	40	22	introduce	introduce	VERB
ejpam-5486	40	23	and	and	CCONJ
ejpam-5486	40	24	study	study	VERB
ejpam-5486	40	25	the	the	DET
ejpam-5486	40	26	class	class	NOUN
ejpam-5486	40	27	of	of	ADP
ejpam-5486	40	28	ωswd	ωswd	ADJ
ejpam-5486	40	29	-	-	PUNCT
ejpam-5486	40	30	open	open	ADJ
ejpam-5486	40	31	subsets	subset	NOUN
ejpam-5486	40	32	,	,	PUNCT
ejpam-5486	40	33	which	which	PRON
ejpam-5486	40	34	is	be	AUX
ejpam-5486	40	35	a	a	DET
ejpam-5486	40	36	new	new	ADJ
ejpam-5486	40	37	generalization	generalization	NOUN
ejpam-5486	40	38	for	for	ADP
ejpam-5486	40	39	somewhere	somewhere	ADV
ejpam-5486	40	40	dense	dense	ADJ
ejpam-5486	40	41	of	of	ADP
ejpam-5486	40	42	a	a	DET
ejpam-5486	40	43	topological	topological	ADJ
ejpam-5486	40	44	space	space	NOUN
ejpam-5486	40	45	(	(	PUNCT
ejpam-5486	40	46	z	z	NOUN
ejpam-5486	40	47	,	,	PUNCT
ejpam-5486	40	48	τ	τ	PROPN
ejpam-5486	40	49	)	)	PUNCT
ejpam-5486	40	50	and	and	CCONJ
ejpam-5486	40	51	hence	hence	ADV
ejpam-5486	40	52	it	it	PRON
ejpam-5486	40	53	is	be	AUX
ejpam-5486	40	54	a	a	DET
ejpam-5486	40	55	new	new	ADJ
ejpam-5486	40	56	kind	kind	NOUN
ejpam-5486	40	57	of	of	ADP
ejpam-5486	40	58	generalized	generalized	ADJ
ejpam-5486	40	59	open	open	ADJ
ejpam-5486	40	60	sets	set	NOUN
ejpam-5486	40	61	.	.	PUNCT
ejpam-5486	41	1	we	we	PRON
ejpam-5486	41	2	organize	organize	VERB
ejpam-5486	41	3	this	this	DET
ejpam-5486	41	4	work	work	NOUN
ejpam-5486	41	5	as	as	SCONJ
ejpam-5486	41	6	follows	follow	VERB
ejpam-5486	41	7	:	:	PUNCT
ejpam-5486	41	8	in	in	ADP
ejpam-5486	41	9	sec	sec	PROPN
ejpam-5486	41	10	.	.	PROPN
ejpam-5486	41	11	2	2	NUM
ejpam-5486	41	12	,	,	PUNCT
ejpam-5486	41	13	we	we	PRON
ejpam-5486	41	14	give	give	VERB
ejpam-5486	41	15	more	more	ADJ
ejpam-5486	41	16	properties	property	NOUN
ejpam-5486	41	17	of	of	ADP
ejpam-5486	41	18	somewhere	somewhere	ADJ
ejpam-5486	41	19	dense	dense	ADJ
ejpam-5486	41	20	sets	set	NOUN
ejpam-5486	41	21	of	of	ADP
ejpam-5486	41	22	(	(	PUNCT
ejpam-5486	41	23	z	z	PROPN
ejpam-5486	41	24	,	,	PUNCT
ejpam-5486	41	25	τ	τ	PROPN
ejpam-5486	41	26	)	)	PUNCT
ejpam-5486	41	27	.	.	PUNCT
ejpam-5486	42	1	in	in	ADP
ejpam-5486	42	2	sec	sec	PROPN
ejpam-5486	42	3	.	.	PROPN
ejpam-5486	42	4	3	3	NUM
ejpam-5486	42	5	,	,	PUNCT
ejpam-5486	42	6	we	we	PRON
ejpam-5486	42	7	introduce	introduce	VERB
ejpam-5486	42	8	the	the	DET
ejpam-5486	42	9	notion	notion	NOUN
ejpam-5486	42	10	of	of	ADP
ejpam-5486	42	11	ωswd	ωswd	ADJ
ejpam-5486	42	12	-	-	PUNCT
ejpam-5486	42	13	open	open	ADJ
ejpam-5486	42	14	subsets	subset	NOUN
ejpam-5486	42	15	and	and	CCONJ
ejpam-5486	42	16	we	we	PRON
ejpam-5486	42	17	verify	verify	VERB
ejpam-5486	42	18	some	some	PRON
ejpam-5486	42	19	of	of	ADP
ejpam-5486	42	20	basic	basic	ADJ
ejpam-5486	42	21	properties	property	NOUN
ejpam-5486	42	22	of	of	ADP
ejpam-5486	42	23	this	this	DET
ejpam-5486	42	24	class	class	NOUN
ejpam-5486	42	25	with	with	ADP
ejpam-5486	42	26	the	the	DET
ejpam-5486	42	27	help	help	NOUN
ejpam-5486	42	28	of	of	ADP
ejpam-5486	42	29	illustrative	illustrative	ADJ
ejpam-5486	42	30	examples	example	NOUN
ejpam-5486	42	31	.	.	PUNCT
ejpam-5486	43	1	also	also	ADV
ejpam-5486	43	2	,	,	PUNCT
ejpam-5486	43	3	we	we	PRON
ejpam-5486	43	4	investigate	investigate	VERB
ejpam-5486	43	5	what	what	PRON
ejpam-5486	43	6	are	be	AUX
ejpam-5486	43	7	the	the	DET
ejpam-5486	43	8	conditions	condition	NOUN
ejpam-5486	43	9	to	to	PART
ejpam-5486	43	10	become	become	VERB
ejpam-5486	43	11	the	the	DET
ejpam-5486	43	12	class	class	NOUN
ejpam-5486	43	13	of	of	ADP
ejpam-5486	43	14	ωswd	ωswd	ADJ
ejpam-5486	43	15	-	-	PUNCT
ejpam-5486	43	16	open	open	ADJ
ejpam-5486	43	17	and	and	CCONJ
ejpam-5486	43	18	somewhere	somewhere	ADV
ejpam-5486	43	19	dense	dense	ADJ
ejpam-5486	43	20	subsets	subset	NOUN
ejpam-5486	43	21	of	of	ADP
ejpam-5486	43	22	(	(	PUNCT
ejpam-5486	43	23	z	z	PROPN
ejpam-5486	43	24	,	,	PUNCT
ejpam-5486	43	25	τ	τ	X
ejpam-5486	43	26	)	)	PUNCT
ejpam-5486	43	27	are	be	AUX
ejpam-5486	43	28	equivalent	equivalent	ADJ
ejpam-5486	43	29	.	.	PUNCT
ejpam-5486	44	1	then	then	ADV
ejpam-5486	44	2	we	we	PRON
ejpam-5486	44	3	show	show	VERB
ejpam-5486	44	4	that	that	SCONJ
ejpam-5486	44	5	this	this	DET
ejpam-5486	44	6	family	family	NOUN
ejpam-5486	44	7	is	be	AUX
ejpam-5486	44	8	not	not	PART
ejpam-5486	44	9	a	a	DET
ejpam-5486	44	10	topology	topology	NOUN
ejpam-5486	44	11	through	through	ADP
ejpam-5486	44	12	an	an	DET
ejpam-5486	44	13	example	example	NOUN
ejpam-5486	44	14	that	that	PRON
ejpam-5486	44	15	shows	show	VERB
ejpam-5486	44	16	this	this	DET
ejpam-5486	44	17	family	family	NOUN
ejpam-5486	44	18	is	be	AUX
ejpam-5486	44	19	not	not	PART
ejpam-5486	44	20	closed	close	VERB
ejpam-5486	44	21	under	under	ADP
ejpam-5486	44	22	finite	finite	ADJ
ejpam-5486	44	23	intersection	intersection	NOUN
ejpam-5486	44	24	.	.	PUNCT
ejpam-5486	45	1	moreover	moreover	ADV
ejpam-5486	45	2	,	,	PUNCT
ejpam-5486	45	3	we	we	PRON
ejpam-5486	45	4	use	use	VERB
ejpam-5486	45	5	ωswd	ωswd	ADJ
ejpam-5486	45	6	-	-	PUNCT
ejpam-5486	45	7	open	open	ADJ
ejpam-5486	45	8	subsets	subset	NOUN
ejpam-5486	45	9	to	to	PART
ejpam-5486	45	10	generalize	generalize	VERB
ejpam-5486	45	11	the	the	DET
ejpam-5486	45	12	notions	notion	NOUN
ejpam-5486	45	13	of	of	ADP
ejpam-5486	45	14	interior	interior	ADJ
ejpam-5486	45	15	and	and	CCONJ
ejpam-5486	45	16	closure	closure	NOUN
ejpam-5486	45	17	and	and	CCONJ
ejpam-5486	45	18	define	define	VERB
ejpam-5486	45	19	ωswd	ωswd	ADJ
ejpam-5486	45	20	-	-	PUNCT
ejpam-5486	45	21	continuous	continuous	ADJ
ejpam-5486	45	22	and	and	CCONJ
ejpam-5486	45	23	ωswd	ωswd	ADJ
ejpam-5486	45	24	-	-	PUNCT
ejpam-5486	45	25	irresolute	irresolute	NOUN
ejpam-5486	45	26	.	.	PUNCT
ejpam-5486	46	1	in	in	ADP
ejpam-5486	46	2	sec.4	sec.4	PROPN
ejpam-5486	46	3	,	,	PUNCT
ejpam-5486	46	4	we	we	PRON
ejpam-5486	46	5	use	use	VERB
ejpam-5486	46	6	ωswd	ωswd	ADJ
ejpam-5486	46	7	-	-	PUNCT
ejpam-5486	46	8	open	open	ADJ
ejpam-5486	46	9	subsets	subset	NOUN
ejpam-5486	46	10	and	and	CCONJ
ejpam-5486	46	11	the	the	DET
ejpam-5486	46	12	closure	closure	NOUN
ejpam-5486	46	13	operator	operator	NOUN
ejpam-5486	46	14	which	which	PRON
ejpam-5486	46	15	are	be	AUX
ejpam-5486	46	16	discussed	discuss	VERB
ejpam-5486	46	17	in	in	ADP
ejpam-5486	46	18	sec.3	sec.3	NOUN
ejpam-5486	46	19	to	to	PART
ejpam-5486	46	20	study	study	VERB
ejpam-5486	46	21	one	one	NUM
ejpam-5486	46	22	type	type	NOUN
ejpam-5486	46	23	of	of	ADP
ejpam-5486	46	24	covering	cover	VERB
ejpam-5486	46	25	properties	property	NOUN
ejpam-5486	46	26	,	,	PUNCT
ejpam-5486	46	27	namely	namely	ADV
ejpam-5486	46	28	almost	almost	ADV
ejpam-5486	46	29	ωswd	ωswd	ADJ
ejpam-5486	46	30	-	-	PUNCT
ejpam-5486	46	31	compact	compact	ADJ
ejpam-5486	46	32	spaces	space	NOUN
ejpam-5486	46	33	and	and	CCONJ
ejpam-5486	46	34	study	study	VERB
ejpam-5486	46	35	some	some	PRON
ejpam-5486	46	36	of	of	ADP
ejpam-5486	46	37	its	its	PRON
ejpam-5486	46	38	properties	property	NOUN
ejpam-5486	46	39	.	.	PUNCT
ejpam-5486	47	1	throughout	throughout	ADP
ejpam-5486	47	2	this	this	DET
ejpam-5486	47	3	work	work	NOUN
ejpam-5486	47	4	the	the	DET
ejpam-5486	47	5	family	family	NOUN
ejpam-5486	47	6	of	of	ADP
ejpam-5486	47	7	all	all	DET
ejpam-5486	47	8	somewhere	somewhere	ADV
ejpam-5486	47	9	dense	dense	ADJ
ejpam-5486	47	10	sets	set	NOUN
ejpam-5486	47	11	of	of	ADP
ejpam-5486	47	12	(	(	PUNCT
ejpam-5486	47	13	z	z	NOUN
ejpam-5486	47	14	,	,	PUNCT
ejpam-5486	47	15	τ)(resp	τ)(resp	PROPN
ejpam-5486	47	16	.	.	PROPN
ejpam-5486	47	17	,	,	PUNCT
ejpam-5486	47	18	the	the	DET
ejpam-5486	47	19	family	family	NOUN
ejpam-5486	47	20	of	of	ADP
ejpam-5486	47	21	all	all	PRON
ejpam-5486	47	22	closed	close	VERB
ejpam-5486	47	23	somewhere	somewhere	ADV
ejpam-5486	47	24	dense	dense	ADJ
ejpam-5486	47	25	which	which	PRON
ejpam-5486	47	26	is	be	AUX
ejpam-5486	47	27	equivalent	equivalent	ADJ
ejpam-5486	47	28	to	to	ADP
ejpam-5486	47	29	the	the	DET
ejpam-5486	47	30	family	family	NOUN
ejpam-5486	47	31	of	of	ADP
ejpam-5486	47	32	the	the	DET
ejpam-5486	47	33	complement	complement	NOUN
ejpam-5486	47	34	of	of	ADP
ejpam-5486	47	35	all	all	PRON
ejpam-5486	47	36	somewhere	somewhere	ADV
ejpam-5486	47	37	dense	dense	ADJ
ejpam-5486	47	38	of	of	ADP
ejpam-5486	47	39	(	(	PUNCT
ejpam-5486	47	40	z	z	PROPN
ejpam-5486	47	41	,	,	PUNCT
ejpam-5486	47	42	τ	τ	PROPN
ejpam-5486	47	43	)	)	PUNCT
ejpam-5486	47	44	)	)	PUNCT
ejpam-5486	47	45	is	be	AUX
ejpam-5486	47	46	denoted	denote	VERB
ejpam-5486	47	47	by	by	ADP
ejpam-5486	47	48	swd(z	swd(z	PROPN
ejpam-5486	47	49	,	,	PUNCT
ejpam-5486	47	50	τ	τ	X
ejpam-5486	47	51	)	)	PUNCT
ejpam-5486	47	52	(	(	PUNCT
ejpam-5486	47	53	resp	resp	NOUN
ejpam-5486	47	54	.	.	PUNCT
ejpam-5486	48	1	,swdc(z	,swdc(z	PUNCT
ejpam-5486	48	2	,	,	PUNCT
ejpam-5486	48	3	τ	τ	PROPN
ejpam-5486	48	4	)	)	PUNCT
ejpam-5486	48	5	)	)	PUNCT
ejpam-5486	48	6	.	.	PUNCT
ejpam-5486	49	1	moreover	moreover	ADV
ejpam-5486	49	2	,	,	PUNCT
ejpam-5486	49	3	swd	swd	PROPN
ejpam-5486	49	4	interior	interior	PROPN
ejpam-5486	49	5	of	of	ADP
ejpam-5486	49	6	h	h	PROPN
ejpam-5486	49	7	(	(	PUNCT
ejpam-5486	49	8	is	be	AUX
ejpam-5486	49	9	denoted	denote	VERB
ejpam-5486	49	10	by	by	ADP
ejpam-5486	49	11	,	,	PUNCT
ejpam-5486	49	12	intswd(h	intswd(h	NOUN
ejpam-5486	49	13	)	)	PUNCT
ejpam-5486	49	14	)	)	PUNCT
ejpam-5486	49	15	is	be	AUX
ejpam-5486	49	16	given	give	VERB
ejpam-5486	49	17	by	by	ADP
ejpam-5486	49	18	intswd(h	intswd(h	NOUN
ejpam-5486	49	19	)	)	PUNCT
ejpam-5486	50	1	=	=	SYM
ejpam-5486	50	2	∪{g	∪{g	PROPN
ejpam-5486	50	3	:	:	PUNCT
ejpam-5486	50	4	g	g	PROPN
ejpam-5486	50	5	⊆	⊆	NUM
ejpam-5486	50	6	h	h	PROPN
ejpam-5486	50	7	a.	a.	NOUN
ejpam-5486	50	8	rawshdeh	rawshdeh	PROPN
ejpam-5486	50	9	,	,	PUNCT
ejpam-5486	50	10	h.	h.	PROPN
ejpam-5486	50	11	h.	h.	PROPN
ejpam-5486	50	12	al	al	PROPN
ejpam-5486	50	13	-	-	PUNCT
ejpam-5486	50	14	jarrah	jarrah	PROPN
ejpam-5486	50	15	,	,	PUNCT
ejpam-5486	50	16	k.	k.	PROPN
ejpam-5486	50	17	y.	y.	PROPN
ejpam-5486	50	18	al	al	PROPN
ejpam-5486	50	19	-	-	PROPN
ejpam-5486	50	20	zoubi	zoubi	PROPN
ejpam-5486	50	21	/	/	SYM
ejpam-5486	50	22	eur	eur	PROPN
ejpam-5486	50	23	.	.	PUNCT
ejpam-5486	51	1	j.	j.	PROPN
ejpam-5486	51	2	pure	pure	PROPN
ejpam-5486	51	3	appl	appl	PROPN
ejpam-5486	51	4	.	.	PROPN
ejpam-5486	51	5	math	math	PROPN
ejpam-5486	51	6	,	,	PUNCT
ejpam-5486	51	7	17	17	NUM
ejpam-5486	51	8	(	(	PUNCT
ejpam-5486	51	9	4	4	NUM
ejpam-5486	51	10	)	)	PUNCT
ejpam-5486	51	11	(	(	PUNCT
ejpam-5486	51	12	2024	2024	NUM
ejpam-5486	51	13	)	)	PUNCT
ejpam-5486	51	14	,	,	PUNCT
ejpam-5486	51	15	3370	3370	NUM
ejpam-5486	51	16	-	-	SYM
ejpam-5486	51	17	3385	3385	NUM
ejpam-5486	51	18	3372	3372	NUM
ejpam-5486	51	19	and	and	CCONJ
ejpam-5486	51	20	g	g	PROPN
ejpam-5486	51	21	∈	∈	PROPN
ejpam-5486	51	22	swd(z	swd(z	PROPN
ejpam-5486	51	23	,	,	PUNCT
ejpam-5486	51	24	τ	τ	PROPN
ejpam-5486	51	25	)	)	PUNCT
ejpam-5486	51	26	}	}	PUNCT
ejpam-5486	51	27	and	and	CCONJ
ejpam-5486	51	28	the	the	DET
ejpam-5486	51	29	swd	swd	PROPN
ejpam-5486	51	30	closure	closure	NOUN
ejpam-5486	51	31	of	of	ADP
ejpam-5486	51	32	h	h	NOUN
ejpam-5486	51	33	(	(	PUNCT
ejpam-5486	51	34	is	be	AUX
ejpam-5486	51	35	denoted	denote	VERB
ejpam-5486	51	36	by	by	ADP
ejpam-5486	51	37	,	,	PUNCT
ejpam-5486	51	38	clswd(h	clswd(h	NOUN
ejpam-5486	51	39	)	)	PUNCT
ejpam-5486	51	40	)	)	PUNCT
ejpam-5486	51	41	is	be	AUX
ejpam-5486	51	42	given	give	VERB
ejpam-5486	51	43	by	by	ADP
ejpam-5486	51	44	clswd(h	clswd(h	PROPN
ejpam-5486	51	45	)	)	PUNCT
ejpam-5486	52	1	=	=	SYM
ejpam-5486	52	2	∩{f	∩{f	NOUN
ejpam-5486	52	3	:	:	PUNCT
ejpam-5486	52	4	h	h	NOUN
ejpam-5486	52	5	⊆	⊆	NUM
ejpam-5486	52	6	f	f	PROPN
ejpam-5486	52	7	and	and	CCONJ
ejpam-5486	52	8	f	f	PROPN
ejpam-5486	52	9	∈	∈	PROPN
ejpam-5486	52	10	swdc(z	swdc(z	PROPN
ejpam-5486	52	11	,	,	PUNCT
ejpam-5486	52	12	τ	τ	PROPN
ejpam-5486	52	13	)	)	PUNCT
ejpam-5486	52	14	}	}	PUNCT
ejpam-5486	52	15	.	.	PUNCT
ejpam-5486	53	1	also	also	ADV
ejpam-5486	53	2	,	,	PUNCT
ejpam-5486	53	3	the	the	DET
ejpam-5486	53	4	family	family	NOUN
ejpam-5486	53	5	of	of	ADP
ejpam-5486	53	6	all	all	PRON
ejpam-5486	53	7	ω−open	ω−open	ADJ
ejpam-5486	53	8	subsets	subset	NOUN
ejpam-5486	53	9	of	of	ADP
ejpam-5486	53	10	a	a	DET
ejpam-5486	53	11	space	space	NOUN
ejpam-5486	53	12	(	(	PUNCT
ejpam-5486	53	13	z	z	NOUN
ejpam-5486	53	14	,	,	PUNCT
ejpam-5486	53	15	τ	τ	PROPN
ejpam-5486	53	16	)	)	PUNCT
ejpam-5486	53	17	forms	form	VERB
ejpam-5486	53	18	a	a	DET
ejpam-5486	53	19	topology	topology	NOUN
ejpam-5486	53	20	on	on	ADP
ejpam-5486	53	21	z	z	PROPN
ejpam-5486	53	22	finer	fine	ADJ
ejpam-5486	53	23	than	than	ADP
ejpam-5486	53	24	τ	τ	PROPN
ejpam-5486	53	25	and	and	CCONJ
ejpam-5486	53	26	denoted	denote	VERB
ejpam-5486	53	27	by	by	ADP
ejpam-5486	53	28	τω[5	τω[5	NOUN
ejpam-5486	53	29	]	]	PUNCT
ejpam-5486	53	30	.	.	PUNCT
ejpam-5486	54	1	the	the	DET
ejpam-5486	54	2	ω−interior	ω−interior	NUM
ejpam-5486	54	3	(	(	PUNCT
ejpam-5486	54	4	resp	resp	NOUN
ejpam-5486	54	5	.	.	PUNCT
ejpam-5486	54	6	,	,	PUNCT
ejpam-5486	54	7	ω−closure	ω−closure	NUM
ejpam-5486	54	8	)	)	PUNCT
ejpam-5486	54	9	of	of	ADP
ejpam-5486	54	10	a	a	DET
ejpam-5486	54	11	subset	subset	ADJ
ejpam-5486	54	12	h	h	NOUN
ejpam-5486	54	13	of	of	ADP
ejpam-5486	54	14	a	a	DET
ejpam-5486	54	15	space	space	NOUN
ejpam-5486	54	16	(	(	PUNCT
ejpam-5486	54	17	z	z	NOUN
ejpam-5486	54	18	,	,	PUNCT
ejpam-5486	54	19	τ	τ	X
ejpam-5486	54	20	)	)	PUNCT
ejpam-5486	54	21	is	be	AUX
ejpam-5486	54	22	the	the	DET
ejpam-5486	54	23	interior	interior	ADJ
ejpam-5486	54	24	(	(	PUNCT
ejpam-5486	54	25	resp	resp	NOUN
ejpam-5486	54	26	.	.	PUNCT
ejpam-5486	54	27	,	,	PUNCT
ejpam-5486	54	28	closure	closure	NOUN
ejpam-5486	54	29	)	)	PUNCT
ejpam-5486	54	30	of	of	ADP
ejpam-5486	54	31	h	h	NOUN
ejpam-5486	54	32	in	in	ADP
ejpam-5486	54	33	the	the	DET
ejpam-5486	54	34	space	space	NOUN
ejpam-5486	54	35	(	(	PUNCT
ejpam-5486	54	36	z	z	NOUN
ejpam-5486	54	37	,	,	PUNCT
ejpam-5486	54	38	τω	τω	INTJ
ejpam-5486	54	39	)	)	PUNCT
ejpam-5486	54	40	and	and	CCONJ
ejpam-5486	54	41	it	it	PRON
ejpam-5486	54	42	is	be	AUX
ejpam-5486	54	43	denoted	denote	VERB
ejpam-5486	54	44	by	by	ADP
ejpam-5486	54	45	intω(h)(resp	intω(h)(resp	PROPN
ejpam-5486	54	46	.	.	PROPN
ejpam-5486	54	47	,	,	PUNCT
ejpam-5486	54	48	clω(h	clω(h	PROPN
ejpam-5486	54	49	)	)	PUNCT
ejpam-5486	54	50	)	)	PUNCT
ejpam-5486	54	51	.	.	PUNCT
ejpam-5486	55	1	in	in	ADP
ejpam-5486	55	2	this	this	DET
ejpam-5486	55	3	paper	paper	NOUN
ejpam-5486	55	4	,	,	PUNCT
ejpam-5486	55	5	we	we	PRON
ejpam-5486	55	6	will	will	AUX
ejpam-5486	55	7	write	write	VERB
ejpam-5486	55	8	t	t	PROPN
ejpam-5486	55	9	s	s	PART
ejpam-5486	55	10	instead	instead	ADV
ejpam-5486	55	11	of	of	ADP
ejpam-5486	55	12	topological	topological	ADJ
ejpam-5486	55	13	space	space	NOUN
ejpam-5486	55	14	.	.	PUNCT
ejpam-5486	56	1	the	the	DET
ejpam-5486	56	2	sets	set	NOUN
ejpam-5486	56	3	r	r	NOUN
ejpam-5486	56	4	and	and	CCONJ
ejpam-5486	56	5	q	q	NOUN
ejpam-5486	56	6	,	,	PUNCT
ejpam-5486	56	7	respectively	respectively	ADV
ejpam-5486	56	8	the	the	DET
ejpam-5486	56	9	set	set	NOUN
ejpam-5486	56	10	of	of	ADP
ejpam-5486	56	11	real	real	ADJ
ejpam-5486	56	12	numbers	number	NOUN
ejpam-5486	56	13	and	and	CCONJ
ejpam-5486	56	14	rational	rational	ADJ
ejpam-5486	56	15	numbers	number	NOUN
ejpam-5486	56	16	.	.	PUNCT
ejpam-5486	57	1	the	the	DET
ejpam-5486	57	2	cofinite	cofinite	NOUN
ejpam-5486	57	3	topology	topology	NOUN
ejpam-5486	57	4	,	,	PUNCT
ejpam-5486	57	5	the	the	DET
ejpam-5486	57	6	cocountable	cocountable	ADJ
ejpam-5486	57	7	topology	topology	NOUN
ejpam-5486	57	8	,	,	PUNCT
ejpam-5486	57	9	the	the	DET
ejpam-5486	57	10	indiscrete	indiscrete	ADJ
ejpam-5486	57	11	topology	topology	NOUN
ejpam-5486	57	12	,	,	PUNCT
ejpam-5486	57	13	and	and	CCONJ
ejpam-5486	57	14	the	the	DET
ejpam-5486	57	15	usual	usual	ADJ
ejpam-5486	57	16	topology	topology	NOUN
ejpam-5486	57	17	are	be	AUX
ejpam-5486	57	18	denoted	denote	VERB
ejpam-5486	57	19	by	by	ADP
ejpam-5486	57	20	τcof	τcof	NOUN
ejpam-5486	57	21	,	,	PUNCT
ejpam-5486	57	22	τcoc	τcoc	PROPN
ejpam-5486	57	23	,	,	PUNCT
ejpam-5486	57	24	τind	τind	NOUN
ejpam-5486	57	25	and	and	CCONJ
ejpam-5486	57	26	τu	τu	ADP
ejpam-5486	57	27	respectively	respectively	ADV
ejpam-5486	57	28	.	.	PUNCT
ejpam-5486	58	1	also	also	ADV
ejpam-5486	58	2	,	,	PUNCT
ejpam-5486	58	3	if	if	SCONJ
ejpam-5486	58	4	h	h	NOUN
ejpam-5486	58	5	is	be	AUX
ejpam-5486	58	6	a	a	DET
ejpam-5486	58	7	subset	subset	NOUN
ejpam-5486	58	8	of	of	ADP
ejpam-5486	58	9	a	a	DET
ejpam-5486	58	10	space	space	NOUN
ejpam-5486	58	11	(	(	PUNCT
ejpam-5486	58	12	z	z	NOUN
ejpam-5486	58	13	,	,	PUNCT
ejpam-5486	58	14	τ	τ	PROPN
ejpam-5486	58	15	)	)	PUNCT
ejpam-5486	58	16	,	,	PUNCT
ejpam-5486	58	17	then	then	ADV
ejpam-5486	58	18	the	the	DET
ejpam-5486	58	19	relative	relative	ADJ
ejpam-5486	58	20	topology	topology	NOUN
ejpam-5486	58	21	on	on	ADP
ejpam-5486	58	22	h	h	NOUN
ejpam-5486	58	23	in	in	ADP
ejpam-5486	58	24	(	(	PUNCT
ejpam-5486	58	25	z	z	PROPN
ejpam-5486	58	26	,	,	PUNCT
ejpam-5486	58	27	τ	τ	X
ejpam-5486	58	28	)	)	PUNCT
ejpam-5486	58	29	will	will	AUX
ejpam-5486	58	30	be	be	AUX
ejpam-5486	58	31	denoted	denote	VERB
ejpam-5486	58	32	by	by	ADP
ejpam-5486	58	33	τh	τh	ADP
ejpam-5486	58	34	.	.	PUNCT
ejpam-5486	59	1	definition	definition	NOUN
ejpam-5486	59	2	1	1	NUM
ejpam-5486	59	3	.	.	PUNCT
ejpam-5486	60	1	[	[	X
ejpam-5486	60	2	10	10	NUM
ejpam-5486	60	3	]	]	X
ejpam-5486	60	4	a	a	DET
ejpam-5486	60	5	filter	filter	NOUN
ejpam-5486	60	6	on	on	ADP
ejpam-5486	60	7	z	z	PROPN
ejpam-5486	60	8	is	be	AUX
ejpam-5486	60	9	a	a	DET
ejpam-5486	60	10	family	family	NOUN
ejpam-5486	60	11	f	f	NOUN
ejpam-5486	60	12	⊆	⊆	NUM
ejpam-5486	60	13	p(z	p(z	NOUN
ejpam-5486	60	14	)	)	PUNCT
ejpam-5486	60	15	which	which	PRON
ejpam-5486	60	16	satisfies	satisfy	VERB
ejpam-5486	60	17	the	the	DET
ejpam-5486	60	18	following	following	NOUN
ejpam-5486	60	19	:	:	PUNCT
ejpam-5486	60	20	(	(	PUNCT
ejpam-5486	60	21	i	i	NOUN
ejpam-5486	60	22	)	)	PUNCT
ejpam-5486	60	23	ϕ	ϕ	PROPN
ejpam-5486	60	24	/∈	/∈	PUNCT
ejpam-5486	61	1	f	f	PROPN
ejpam-5486	61	2	.	.	PUNCT
ejpam-5486	62	1	(	(	PUNCT
ejpam-5486	62	2	ii	ii	NOUN
ejpam-5486	62	3	)	)	PUNCT
ejpam-5486	62	4	if	if	SCONJ
ejpam-5486	62	5	h	h	NOUN
ejpam-5486	62	6	,	,	PUNCT
ejpam-5486	62	7	g	g	PROPN
ejpam-5486	62	8	∈	∈	PROPN
ejpam-5486	62	9	f	f	X
ejpam-5486	62	10	,	,	PUNCT
ejpam-5486	62	11	then	then	ADV
ejpam-5486	62	12	h	h	NOUN
ejpam-5486	62	13	∩g	∩g	PROPN
ejpam-5486	62	14	∈	∈	PROPN
ejpam-5486	63	1	f	f	X
ejpam-5486	63	2	.	.	PUNCT
ejpam-5486	64	1	(	(	PUNCT
ejpam-5486	64	2	iii	iii	X
ejpam-5486	64	3	)	)	PUNCT
ejpam-5486	64	4	if	if	SCONJ
ejpam-5486	64	5	h	h	NOUN
ejpam-5486	64	6	∈	∈	PROPN
ejpam-5486	64	7	f	f	PROPN
ejpam-5486	64	8	and	and	CCONJ
ejpam-5486	64	9	h	h	NOUN
ejpam-5486	65	1	⊆	⊆	NUM
ejpam-5486	65	2	g	g	ADP
ejpam-5486	65	3	⊆	⊆	NUM
ejpam-5486	65	4	z	z	PROPN
ejpam-5486	65	5	,	,	PUNCT
ejpam-5486	65	6	then	then	ADV
ejpam-5486	65	7	g	g	PROPN
ejpam-5486	65	8	∈	∈	PROPN
ejpam-5486	65	9	f	f	PROPN
ejpam-5486	65	10	.	.	PUNCT
ejpam-5486	66	1	moreover	moreover	ADV
ejpam-5486	66	2	,	,	PUNCT
ejpam-5486	66	3	a	a	DET
ejpam-5486	66	4	filter	filter	NOUN
ejpam-5486	66	5	f	f	NOUN
ejpam-5486	66	6	on	on	ADP
ejpam-5486	66	7	z	z	PROPN
ejpam-5486	66	8	is	be	AUX
ejpam-5486	66	9	said	say	VERB
ejpam-5486	66	10	to	to	PART
ejpam-5486	66	11	be	be	AUX
ejpam-5486	66	12	a	a	DET
ejpam-5486	66	13	maximal	maximal	ADJ
ejpam-5486	66	14	filter	filter	NOUN
ejpam-5486	66	15	on	on	ADP
ejpam-5486	66	16	z	z	NOUN
ejpam-5486	66	17	if	if	SCONJ
ejpam-5486	66	18	each	each	DET
ejpam-5486	66	19	filter	filter	NOUN
ejpam-5486	66	20	h	h	NOUN
ejpam-5486	66	21	on	on	ADP
ejpam-5486	66	22	z	z	PROPN
ejpam-5486	66	23	that	that	PRON
ejpam-5486	66	24	contains	contain	VERB
ejpam-5486	66	25	f	f	NOUN
ejpam-5486	66	26	we	we	PRON
ejpam-5486	66	27	have	have	VERB
ejpam-5486	66	28	f	f	PROPN
ejpam-5486	66	29	=	=	SYM
ejpam-5486	66	30	h.	h.	PROPN
ejpam-5486	66	31	also	also	ADV
ejpam-5486	66	32	,	,	PUNCT
ejpam-5486	66	33	a	a	DET
ejpam-5486	66	34	family	family	NOUN
ejpam-5486	66	35	f	f	NOUN
ejpam-5486	66	36	⊆	⊆	NUM
ejpam-5486	66	37	p(z	p(z	NOUN
ejpam-5486	66	38	)	)	PUNCT
ejpam-5486	66	39	is	be	AUX
ejpam-5486	66	40	said	say	VERB
ejpam-5486	66	41	to	to	PART
ejpam-5486	66	42	be	be	AUX
ejpam-5486	66	43	a	a	DET
ejpam-5486	66	44	filter	filter	NOUN
ejpam-5486	66	45	base	base	NOUN
ejpam-5486	66	46	on	on	ADP
ejpam-5486	66	47	z	z	NOUN
ejpam-5486	66	48	if	if	SCONJ
ejpam-5486	66	49	it	it	PRON
ejpam-5486	66	50	is	be	AUX
ejpam-5486	66	51	a	a	DET
ejpam-5486	66	52	non	non	ADJ
ejpam-5486	66	53	-	-	ADJ
ejpam-5486	66	54	empty	empty	ADJ
ejpam-5486	66	55	such	such	ADJ
ejpam-5486	66	56	that	that	DET
ejpam-5486	66	57	ϕ	ϕ	NOUN
ejpam-5486	66	58	/∈	/∈	PUNCT
ejpam-5486	67	1	f	f	PROPN
ejpam-5486	68	1	and	and	CCONJ
ejpam-5486	68	2	if	if	SCONJ
ejpam-5486	68	3	h	h	NOUN
ejpam-5486	68	4	,	,	PUNCT
ejpam-5486	68	5	g	g	PROPN
ejpam-5486	68	6	∈	∈	PROPN
ejpam-5486	68	7	f	f	NOUN
ejpam-5486	68	8	then	then	ADV
ejpam-5486	68	9	there	there	PRON
ejpam-5486	68	10	is	be	VERB
ejpam-5486	68	11	v	v	ADP
ejpam-5486	68	12	∈	∈	PROPN
ejpam-5486	68	13	f	f	NOUN
ejpam-5486	68	14	with	with	ADP
ejpam-5486	68	15	v	v	NUM
ejpam-5486	68	16	⊆	⊆	NUM
ejpam-5486	68	17	h	h	NOUN
ejpam-5486	68	18	∩g	∩g	NOUN
ejpam-5486	68	19	.	.	PUNCT
ejpam-5486	69	1	definition	definition	NOUN
ejpam-5486	69	2	2	2	NUM
ejpam-5486	69	3	.	.	PUNCT
ejpam-5486	70	1	let	let	AUX
ejpam-5486	70	2	(	(	PUNCT
ejpam-5486	70	3	z	z	NOUN
ejpam-5486	70	4	,	,	PUNCT
ejpam-5486	70	5	τ	τ	PROPN
ejpam-5486	70	6	)	)	PUNCT
ejpam-5486	70	7	be	be	VERB
ejpam-5486	70	8	a	a	DET
ejpam-5486	70	9	t	t	NOUN
ejpam-5486	70	10	s.	s.	PROPN
ejpam-5486	71	1	then	then	ADV
ejpam-5486	71	2	(	(	PUNCT
ejpam-5486	71	3	z	z	X
ejpam-5486	71	4	,	,	PUNCT
ejpam-5486	71	5	τ	τ	X
ejpam-5486	71	6	)	)	PUNCT
ejpam-5486	71	7	is	be	AUX
ejpam-5486	71	8	said	say	VERB
ejpam-5486	71	9	to	to	PART
ejpam-5486	71	10	be	be	AUX
ejpam-5486	71	11	:	:	PUNCT
ejpam-5486	71	12	(	(	PUNCT
ejpam-5486	71	13	i	i	NOUN
ejpam-5486	71	14	)	)	PUNCT
ejpam-5486	71	15	hyperconnected	hyperconnecte	VERB
ejpam-5486	71	16	[	[	X
ejpam-5486	71	17	17	17	NUM
ejpam-5486	71	18	]	]	PUNCT
ejpam-5486	71	19	if	if	SCONJ
ejpam-5486	71	20	no	no	DET
ejpam-5486	71	21	mutually	mutually	ADV
ejpam-5486	71	22	disjoint	disjoint	ADJ
ejpam-5486	71	23	non	non	ADJ
ejpam-5486	71	24	-	-	ADJ
ejpam-5486	71	25	empty	empty	ADJ
ejpam-5486	71	26	open	open	ADJ
ejpam-5486	71	27	sets	set	NOUN
ejpam-5486	71	28	.	.	PUNCT
ejpam-5486	72	1	(	(	PUNCT
ejpam-5486	72	2	ii	ii	NOUN
ejpam-5486	72	3	)	)	PUNCT
ejpam-5486	72	4	strongly	strongly	ADV
ejpam-5486	72	5	hyperconnected	hyperconnecte	VERB
ejpam-5486	72	6	[	[	X
ejpam-5486	72	7	1	1	X
ejpam-5486	72	8	]	]	PUNCT
ejpam-5486	72	9	if	if	SCONJ
ejpam-5486	72	10	a	a	DET
ejpam-5486	72	11	subset	subset	NOUN
ejpam-5486	72	12	of	of	ADP
ejpam-5486	72	13	z	z	PROPN
ejpam-5486	72	14	is	be	AUX
ejpam-5486	72	15	dense	dense	ADJ
ejpam-5486	72	16	iff	iff	PROPN
ejpam-5486	72	17	it	it	PRON
ejpam-5486	72	18	is	be	AUX
ejpam-5486	72	19	non	non	ADJ
ejpam-5486	72	20	-	-	ADJ
ejpam-5486	72	21	empty	empty	ADJ
ejpam-5486	72	22	and	and	CCONJ
ejpam-5486	72	23	open	open	ADJ
ejpam-5486	72	24	.	.	PUNCT
ejpam-5486	73	1	theorem	theorem	NOUN
ejpam-5486	73	2	1	1	NUM
ejpam-5486	73	3	.	.	PUNCT
ejpam-5486	74	1	[	[	X
ejpam-5486	74	2	1	1	X
ejpam-5486	74	3	]	]	X
ejpam-5486	74	4	let	let	VERB
ejpam-5486	74	5	(	(	PUNCT
ejpam-5486	74	6	z	z	NOUN
ejpam-5486	74	7	,	,	PUNCT
ejpam-5486	74	8	τ	τ	PROPN
ejpam-5486	74	9	)	)	PUNCT
ejpam-5486	74	10	be	be	VERB
ejpam-5486	74	11	a	a	DET
ejpam-5486	74	12	t	t	NOUN
ejpam-5486	74	13	s	s	NOUN
ejpam-5486	74	14	and	and	CCONJ
ejpam-5486	74	15	h	h	NOUN
ejpam-5486	74	16	,	,	PUNCT
ejpam-5486	74	17	g	g	PROPN
ejpam-5486	74	18	⊆	⊆	NUM
ejpam-5486	74	19	z.	z.	NOUN
ejpam-5486	74	20	if	if	SCONJ
ejpam-5486	74	21	h	h	PROPN
ejpam-5486	74	22	∈	∈	PROPN
ejpam-5486	74	23	swd(z	swd(z	PROPN
ejpam-5486	74	24	,	,	PUNCT
ejpam-5486	74	25	τ	τ	X
ejpam-5486	74	26	)	)	PUNCT
ejpam-5486	74	27	and	and	CCONJ
ejpam-5486	74	28	(	(	PUNCT
ejpam-5486	74	29	z	z	PROPN
ejpam-5486	74	30	,	,	PUNCT
ejpam-5486	74	31	τ	τ	X
ejpam-5486	74	32	)	)	PUNCT
ejpam-5486	74	33	is	be	AUX
ejpam-5486	74	34	:	:	PUNCT
ejpam-5486	74	35	(	(	PUNCT
ejpam-5486	74	36	i	i	NOUN
ejpam-5486	74	37	)	)	PUNCT
ejpam-5486	74	38	hyperconnected	hyperconnecte	VERB
ejpam-5486	74	39	,	,	PUNCT
ejpam-5486	74	40	then	then	ADV
ejpam-5486	74	41	h	h	NOUN
ejpam-5486	74	42	∩g	∩g	PROPN
ejpam-5486	74	43	∈	∈	PROPN
ejpam-5486	74	44	swd(z	swd(z	PROPN
ejpam-5486	74	45	,	,	PUNCT
ejpam-5486	74	46	τ	τ	X
ejpam-5486	74	47	)	)	PUNCT
ejpam-5486	74	48	whenever	whenever	SCONJ
ejpam-5486	74	49	g	g	PROPN
ejpam-5486	74	50	∈	∈	PROPN
ejpam-5486	74	51	τ	τ	X
ejpam-5486	74	52	.	.	PUNCT
ejpam-5486	75	1	(	(	PUNCT
ejpam-5486	75	2	ii	ii	NOUN
ejpam-5486	75	3	)	)	PUNCT
ejpam-5486	75	4	strongly	strongly	ADV
ejpam-5486	75	5	hyperconnected	hyperconnecte	VERB
ejpam-5486	75	6	,	,	PUNCT
ejpam-5486	75	7	then	then	ADV
ejpam-5486	75	8	h	h	NOUN
ejpam-5486	75	9	∩g	∩g	PROPN
ejpam-5486	75	10	∈	∈	PROPN
ejpam-5486	75	11	swd(z	swd(z	PROPN
ejpam-5486	75	12	,	,	PUNCT
ejpam-5486	75	13	τ	τ	X
ejpam-5486	75	14	)	)	PUNCT
ejpam-5486	75	15	whenever	whenever	SCONJ
ejpam-5486	75	16	g	g	PROPN
ejpam-5486	75	17	∈	∈	PROPN
ejpam-5486	75	18	swd(z	swd(z	PROPN
ejpam-5486	75	19	,	,	PUNCT
ejpam-5486	75	20	τ	τ	PROPN
ejpam-5486	75	21	)	)	PUNCT
ejpam-5486	75	22	.	.	PUNCT
ejpam-5486	76	1	definition	definition	NOUN
ejpam-5486	76	2	3	3	NUM
ejpam-5486	76	3	.	.	PUNCT
ejpam-5486	77	1	[	[	X
ejpam-5486	77	2	10	10	NUM
ejpam-5486	77	3	]	]	X
ejpam-5486	77	4	let	let	VERB
ejpam-5486	77	5	{	{	PUNCT
ejpam-5486	77	6	(	(	PUNCT
ejpam-5486	77	7	zα	zα	PROPN
ejpam-5486	77	8	,	,	PUNCT
ejpam-5486	77	9	τα	τα	PROPN
ejpam-5486	77	10	)	)	PUNCT
ejpam-5486	77	11	:	:	PUNCT
ejpam-5486	78	1	α	α	PROPN
ejpam-5486	78	2	∈	∈	PROPN
ejpam-5486	78	3	∆	∆	PROPN
ejpam-5486	78	4	}	}	PUNCT
ejpam-5486	78	5	be	be	AUX
ejpam-5486	78	6	a	a	DET
ejpam-5486	78	7	family	family	NOUN
ejpam-5486	78	8	of	of	ADP
ejpam-5486	78	9	topological	topological	ADJ
ejpam-5486	78	10	spaces	space	NOUN
ejpam-5486	78	11	with	with	ADP
ejpam-5486	78	12	zα∩	zα∩	PROPN
ejpam-5486	78	13	zβ	zβ	X
ejpam-5486	78	14	=	=	SYM
ejpam-5486	78	15	ϕ	ϕ	PROPN
ejpam-5486	78	16	for	for	ADP
ejpam-5486	78	17	each	each	DET
ejpam-5486	78	18	α	α	NOUN
ejpam-5486	78	19	̸=	̸=	PROPN
ejpam-5486	78	20	β	β	X
ejpam-5486	78	21	.	.	PUNCT
ejpam-5486	79	1	let	let	VERB
ejpam-5486	79	2	z	z	NOUN
ejpam-5486	79	3	=	=	SYM
ejpam-5486	79	4	∪	∪	ADP
ejpam-5486	79	5	α∈∆	α∈∆	PROPN
ejpam-5486	79	6	zα	zα	NUM
ejpam-5486	79	7	with	with	ADP
ejpam-5486	79	8	the	the	DET
ejpam-5486	79	9	topology	topology	NOUN
ejpam-5486	79	10	τs	τs	ADP
ejpam-5486	79	11	=	=	PRON
ejpam-5486	79	12	{	{	PUNCT
ejpam-5486	79	13	g	g	PROPN
ejpam-5486	79	14	⊆	⊆	NUM
ejpam-5486	79	15	z	z	NOUN
ejpam-5486	79	16	:	:	PUNCT
ejpam-5486	79	17	g	g	PROPN
ejpam-5486	79	18	∩	∩	NOUN
ejpam-5486	79	19	zα	zα	PROPN
ejpam-5486	79	20	∈	∈	PROPN
ejpam-5486	79	21	τα	τα	PROPN
ejpam-5486	79	22	for	for	ADP
ejpam-5486	79	23	each	each	DET
ejpam-5486	79	24	α	α	NOUN
ejpam-5486	79	25	∈	∈	NOUN
ejpam-5486	79	26	∆	∆	X
ejpam-5486	79	27	}	}	PUNCT
ejpam-5486	79	28	.	.	PUNCT
ejpam-5486	80	1	then	then	ADV
ejpam-5486	80	2	(	(	PUNCT
ejpam-5486	80	3	z	z	NOUN
ejpam-5486	80	4	,	,	PUNCT
ejpam-5486	80	5	τs	τs	NOUN
ejpam-5486	80	6	)	)	PUNCT
ejpam-5486	80	7	is	be	AUX
ejpam-5486	80	8	called	call	VERB
ejpam-5486	80	9	the	the	DET
ejpam-5486	80	10	sum	sum	NOUN
ejpam-5486	80	11	of	of	ADP
ejpam-5486	80	12	the	the	DET
ejpam-5486	80	13	spaces	space	NOUN
ejpam-5486	80	14	{	{	PUNCT
ejpam-5486	80	15	(	(	PUNCT
ejpam-5486	80	16	zα	zα	PROPN
ejpam-5486	80	17	,	,	PUNCT
ejpam-5486	80	18	τα	τα	PROPN
ejpam-5486	80	19	)	)	PUNCT
ejpam-5486	80	20	:	:	PUNCT
ejpam-5486	81	1	α	α	PROPN
ejpam-5486	81	2	∈	∈	PROPN
ejpam-5486	81	3	∆}and	∆}and	CCONJ
ejpam-5486	81	4	denoted	denote	VERB
ejpam-5486	81	5	by	by	ADP
ejpam-5486	81	6	z	z	PROPN
ejpam-5486	81	7	=	=	SYM
ejpam-5486	81	8	⊕	⊕	PROPN
ejpam-5486	81	9	α∈∆	α∈∆	NOUN
ejpam-5486	81	10	zα	zα	NUM
ejpam-5486	81	11	.	.	PUNCT
ejpam-5486	81	12	theorem	theorem	NOUN
ejpam-5486	81	13	2	2	NUM
ejpam-5486	81	14	.	.	PUNCT
ejpam-5486	82	1	[	[	X
ejpam-5486	82	2	1	1	X
ejpam-5486	82	3	]	]	X
ejpam-5486	82	4	let	let	VERB
ejpam-5486	82	5	(	(	PUNCT
ejpam-5486	82	6	n	n	X
ejpam-5486	82	7	π	π	X
ejpam-5486	82	8	α=1	α=1	X
ejpam-5486	82	9	zα	zα	PROPN
ejpam-5486	82	10	,	,	PUNCT
ejpam-5486	82	11	τ	τ	PROPN
ejpam-5486	82	12	)	)	PUNCT
ejpam-5486	82	13	be	be	VERB
ejpam-5486	82	14	a	a	DET
ejpam-5486	82	15	finite	finite	ADJ
ejpam-5486	82	16	product	product	NOUN
ejpam-5486	82	17	t	t	PROPN
ejpam-5486	82	18	s.	s.	PROPN
ejpam-5486	82	19	then	then	ADV
ejpam-5486	82	20	hα	hα	ADP
ejpam-5486	82	21	∈	∈	PROPN
ejpam-5486	82	22	swd(zα	swd(zα	NOUN
ejpam-5486	82	23	,	,	PUNCT
ejpam-5486	82	24	τα	τα	PROPN
ejpam-5486	82	25	)	)	PUNCT
ejpam-5486	82	26	for	for	ADP
ejpam-5486	82	27	each	each	DET
ejpam-5486	82	28	α	α	NOUN
ejpam-5486	82	29	=	=	SYM
ejpam-5486	82	30	1	1	NUM
ejpam-5486	82	31	,	,	PUNCT
ejpam-5486	82	32	2	2	NUM
ejpam-5486	82	33	,	,	PUNCT
ejpam-5486	82	34	...	...	PUNCT
ejpam-5486	82	35	,	,	PUNCT
ejpam-5486	82	36	n	n	CCONJ
ejpam-5486	82	37	,	,	PUNCT
ejpam-5486	82	38	iff	iff	PROPN
ejpam-5486	82	39	n	n	PROPN
ejpam-5486	82	40	π	π	X
ejpam-5486	82	41	α=1	α=1	X
ejpam-5486	82	42	hα	hα	ADP
ejpam-5486	82	43	∈	∈	PROPN
ejpam-5486	82	44	swd	swd	PROPN
ejpam-5486	82	45	(	(	PUNCT
ejpam-5486	82	46	n	n	PROPN
ejpam-5486	82	47	π	π	X
ejpam-5486	82	48	α=1	α=1	X
ejpam-5486	82	49	zα	zα	PROPN
ejpam-5486	82	50	,	,	PUNCT
ejpam-5486	82	51	τ	τ	PROPN
ejpam-5486	82	52	)	)	PUNCT
ejpam-5486	82	53	.	.	PUNCT
ejpam-5486	83	1	theorem	theorem	NOUN
ejpam-5486	83	2	3	3	X
ejpam-5486	83	3	.	.	PUNCT
ejpam-5486	84	1	let	let	AUX
ejpam-5486	84	2	(	(	PUNCT
ejpam-5486	84	3	z	z	NOUN
ejpam-5486	84	4	,	,	PUNCT
ejpam-5486	84	5	τ	τ	PROPN
ejpam-5486	84	6	)	)	PUNCT
ejpam-5486	84	7	be	be	VERB
ejpam-5486	84	8	a	a	DET
ejpam-5486	84	9	t	t	NOUN
ejpam-5486	84	10	s	s	NOUN
ejpam-5486	84	11	and	and	CCONJ
ejpam-5486	84	12	h	h	NOUN
ejpam-5486	84	13	,	,	PUNCT
ejpam-5486	84	14	g	g	PROPN
ejpam-5486	84	15	⊆	⊆	NUM
ejpam-5486	84	16	z.	z.	PROPN
ejpam-5486	84	17	then	then	ADV
ejpam-5486	84	18	:	:	PUNCT
ejpam-5486	84	19	(	(	PUNCT
ejpam-5486	84	20	i	i	NOUN
ejpam-5486	84	21	)	)	PUNCT
ejpam-5486	84	22	if	if	SCONJ
ejpam-5486	84	23	h	h	NOUN
ejpam-5486	84	24	⊆	⊆	NUM
ejpam-5486	84	25	g	g	NOUN
ejpam-5486	84	26	and	and	CCONJ
ejpam-5486	84	27	h	h	NOUN
ejpam-5486	84	28	∈	∈	PROPN
ejpam-5486	84	29	swd(z	swd(z	PROPN
ejpam-5486	84	30	,	,	PUNCT
ejpam-5486	84	31	τ	τ	PROPN
ejpam-5486	84	32	)	)	PUNCT
ejpam-5486	84	33	,	,	PUNCT
ejpam-5486	84	34	then	then	ADV
ejpam-5486	84	35	g	g	PROPN
ejpam-5486	84	36	∈	∈	PROPN
ejpam-5486	84	37	swd(z	swd(z	PROPN
ejpam-5486	84	38	,	,	PUNCT
ejpam-5486	84	39	τ	τ	X
ejpam-5486	84	40	)	)	PUNCT
ejpam-5486	85	1	[	[	X
ejpam-5486	85	2	1	1	NUM
ejpam-5486	85	3	]	]	PUNCT
ejpam-5486	85	4	.	.	PUNCT
ejpam-5486	86	1	(	(	PUNCT
ejpam-5486	86	2	ii	ii	NOUN
ejpam-5486	86	3	)	)	PUNCT
ejpam-5486	86	4	if	if	SCONJ
ejpam-5486	86	5	e	e	PROPN
ejpam-5486	86	6	∈	∈	PROPN
ejpam-5486	86	7	τ	τ	X
ejpam-5486	86	8	and	and	CCONJ
ejpam-5486	86	9	h	h	NOUN
ejpam-5486	86	10	⊆	⊆	NUM
ejpam-5486	86	11	e	e	NOUN
ejpam-5486	86	12	,	,	PUNCT
ejpam-5486	86	13	then	then	ADV
ejpam-5486	86	14	h	h	PROPN
ejpam-5486	86	15	∈	∈	PROPN
ejpam-5486	86	16	swd(z	swd(z	PROPN
ejpam-5486	86	17	,	,	PUNCT
ejpam-5486	86	18	τ	τ	X
ejpam-5486	86	19	)	)	PUNCT
ejpam-5486	86	20	whenever	whenever	SCONJ
ejpam-5486	86	21	h	h	PROPN
ejpam-5486	86	22	∈	∈	PROPN
ejpam-5486	86	23	swd(e	swd(e	PROPN
ejpam-5486	86	24	,	,	PUNCT
ejpam-5486	86	25	τe	τe	ADP
ejpam-5486	86	26	)	)	PUNCT
ejpam-5486	87	1	[	[	X
ejpam-5486	87	2	7	7	NUM
ejpam-5486	87	3	]	]	PUNCT
ejpam-5486	87	4	.	.	PUNCT
ejpam-5486	88	1	definition	definition	NOUN
ejpam-5486	88	2	4	4	NUM
ejpam-5486	88	3	.	.	PUNCT
ejpam-5486	89	1	[	[	X
ejpam-5486	89	2	5	5	NUM
ejpam-5486	89	3	]	]	X
ejpam-5486	89	4	let	let	VERB
ejpam-5486	89	5	(	(	PUNCT
ejpam-5486	89	6	z	z	NOUN
ejpam-5486	89	7	,	,	PUNCT
ejpam-5486	89	8	τ	τ	PROPN
ejpam-5486	89	9	)	)	PUNCT
ejpam-5486	89	10	be	be	VERB
ejpam-5486	89	11	a	a	DET
ejpam-5486	89	12	t	t	NOUN
ejpam-5486	89	13	s.	s.	PROPN
ejpam-5486	90	1	then	then	ADV
ejpam-5486	90	2	(	(	PUNCT
ejpam-5486	90	3	z	z	X
ejpam-5486	90	4	,	,	PUNCT
ejpam-5486	90	5	τ	τ	X
ejpam-5486	90	6	)	)	PUNCT
ejpam-5486	90	7	is	be	AUX
ejpam-5486	90	8	said	say	VERB
ejpam-5486	90	9	to	to	PART
ejpam-5486	90	10	be	be	AUX
ejpam-5486	90	11	anti	anti	ADJ
ejpam-5486	90	12	-	-	ADJ
ejpam-5486	90	13	locally	locally	ADV
ejpam-5486	90	14	countable	countable	ADJ
ejpam-5486	90	15	if	if	SCONJ
ejpam-5486	90	16	each	each	DET
ejpam-5486	90	17	non	non	ADJ
ejpam-5486	90	18	-	-	ADJ
ejpam-5486	90	19	empty	empty	ADJ
ejpam-5486	90	20	open	open	ADJ
ejpam-5486	90	21	subset	subset	NOUN
ejpam-5486	90	22	of	of	ADP
ejpam-5486	90	23	(	(	PUNCT
ejpam-5486	90	24	z	z	PROPN
ejpam-5486	90	25	,	,	PUNCT
ejpam-5486	90	26	τ	τ	X
ejpam-5486	90	27	)	)	PUNCT
ejpam-5486	90	28	is	be	AUX
ejpam-5486	90	29	uncountable	uncountable	ADJ
ejpam-5486	90	30	.	.	PUNCT
ejpam-5486	91	1	note	note	VERB
ejpam-5486	91	2	that	that	SCONJ
ejpam-5486	91	3	,	,	PUNCT
ejpam-5486	91	4	if	if	SCONJ
ejpam-5486	91	5	(	(	PUNCT
ejpam-5486	91	6	z	z	NOUN
ejpam-5486	91	7	,	,	PUNCT
ejpam-5486	91	8	τ	τ	X
ejpam-5486	91	9	)	)	PUNCT
ejpam-5486	91	10	is	be	AUX
ejpam-5486	91	11	an	an	DET
ejpam-5486	91	12	anti	anti	ADJ
ejpam-5486	91	13	locally	locally	ADV
ejpam-5486	91	14	countable	countable	ADJ
ejpam-5486	91	15	space	space	NOUN
ejpam-5486	91	16	,	,	PUNCT
ejpam-5486	91	17	then	then	ADV
ejpam-5486	91	18	(	(	PUNCT
ejpam-5486	91	19	z	z	NOUN
ejpam-5486	91	20	,	,	PUNCT
ejpam-5486	91	21	τω	τω	INTJ
ejpam-5486	91	22	)	)	PUNCT
ejpam-5486	91	23	is	be	AUX
ejpam-5486	91	24	also	also	ADV
ejpam-5486	91	25	anti	anti	ADJ
ejpam-5486	91	26	-	-	ADJ
ejpam-5486	91	27	locally	locally	ADV
ejpam-5486	91	28	countable	countable	ADJ
ejpam-5486	91	29	.	.	PUNCT
ejpam-5486	92	1	a.	a.	PROPN
ejpam-5486	92	2	rawshdeh	rawshdeh	PROPN
ejpam-5486	92	3	,	,	PUNCT
ejpam-5486	92	4	h.	h.	PROPN
ejpam-5486	92	5	h.	h.	PROPN
ejpam-5486	92	6	al	al	PROPN
ejpam-5486	92	7	-	-	PUNCT
ejpam-5486	92	8	jarrah	jarrah	PROPN
ejpam-5486	92	9	,	,	PUNCT
ejpam-5486	92	10	k.	k.	PROPN
ejpam-5486	92	11	y.	y.	PROPN
ejpam-5486	92	12	al	al	PROPN
ejpam-5486	92	13	-	-	PROPN
ejpam-5486	92	14	zoubi	zoubi	PROPN
ejpam-5486	92	15	/	/	SYM
ejpam-5486	92	16	eur	eur	PROPN
ejpam-5486	92	17	.	.	PUNCT
ejpam-5486	93	1	j.	j.	PROPN
ejpam-5486	93	2	pure	pure	PROPN
ejpam-5486	93	3	appl	appl	PROPN
ejpam-5486	93	4	.	.	PROPN
ejpam-5486	93	5	math	math	PROPN
ejpam-5486	93	6	,	,	PUNCT
ejpam-5486	93	7	17	17	NUM
ejpam-5486	93	8	(	(	PUNCT
ejpam-5486	93	9	4	4	NUM
ejpam-5486	93	10	)	)	PUNCT
ejpam-5486	93	11	(	(	PUNCT
ejpam-5486	93	12	2024	2024	NUM
ejpam-5486	93	13	)	)	PUNCT
ejpam-5486	93	14	,	,	PUNCT
ejpam-5486	93	15	3370	3370	NUM
ejpam-5486	93	16	-	-	SYM
ejpam-5486	93	17	3385	3385	NUM
ejpam-5486	93	18	3373	3373	NUM
ejpam-5486	93	19	definition	definition	NOUN
ejpam-5486	93	20	5	5	NUM
ejpam-5486	93	21	.	.	PUNCT
ejpam-5486	94	1	[	[	X
ejpam-5486	94	2	4	4	X
ejpam-5486	94	3	]	]	X
ejpam-5486	94	4	let	let	VERB
ejpam-5486	94	5	(	(	PUNCT
ejpam-5486	94	6	z	z	NOUN
ejpam-5486	94	7	,	,	PUNCT
ejpam-5486	94	8	τ	τ	PROPN
ejpam-5486	94	9	)	)	PUNCT
ejpam-5486	94	10	be	be	VERB
ejpam-5486	94	11	a	a	DET
ejpam-5486	94	12	t	t	NOUN
ejpam-5486	94	13	s.	s.	PROPN
ejpam-5486	94	14	then	then	ADV
ejpam-5486	94	15	:	:	PUNCT
ejpam-5486	94	16	(	(	PUNCT
ejpam-5486	94	17	i	i	NOUN
ejpam-5486	94	18	)	)	PUNCT
ejpam-5486	94	19	a	a	DET
ejpam-5486	94	20	family	family	NOUN
ejpam-5486	94	21	h	h	NOUN
ejpam-5486	94	22	=	=	PRON
ejpam-5486	94	23	{	{	PUNCT
ejpam-5486	94	24	hα	hα	X
ejpam-5486	94	25	:	:	PUNCT
ejpam-5486	94	26	α	α	PROPN
ejpam-5486	94	27	∈	∈	PROPN
ejpam-5486	94	28	∆	∆	X
ejpam-5486	94	29	}	}	PUNCT
ejpam-5486	94	30	is	be	AUX
ejpam-5486	94	31	said	say	VERB
ejpam-5486	94	32	to	to	PART
ejpam-5486	94	33	be	be	AUX
ejpam-5486	94	34	swd(z	swd(z	PROPN
ejpam-5486	94	35	,	,	PUNCT
ejpam-5486	94	36	τ)-cover	τ)-cover	PUNCT
ejpam-5486	94	37	of	of	ADP
ejpam-5486	94	38	z	z	NOUN
ejpam-5486	94	39	if	if	SCONJ
ejpam-5486	94	40	z	z	NOUN
ejpam-5486	94	41	=	=	SYM
ejpam-5486	94	42	∪	∪	ADP
ejpam-5486	94	43	α∈∆	α∈∆	PRON
ejpam-5486	94	44	hα	hα	NOUN
ejpam-5486	94	45	with	with	ADP
ejpam-5486	94	46	hα	hα	ADP
ejpam-5486	94	47	∈	∈	PROPN
ejpam-5486	94	48	swd(z	swd(z	PROPN
ejpam-5486	94	49	,	,	PUNCT
ejpam-5486	94	50	τ	τ	PROPN
ejpam-5486	94	51	)	)	PUNCT
ejpam-5486	94	52	.	.	PUNCT
ejpam-5486	95	1	(	(	PUNCT
ejpam-5486	95	2	ii	ii	NOUN
ejpam-5486	95	3	)	)	PUNCT
ejpam-5486	95	4	(	(	PUNCT
ejpam-5486	95	5	z	z	PROPN
ejpam-5486	95	6	,	,	PUNCT
ejpam-5486	95	7	τ	τ	X
ejpam-5486	95	8	)	)	PUNCT
ejpam-5486	95	9	is	be	AUX
ejpam-5486	95	10	said	say	VERB
ejpam-5486	95	11	to	to	PART
ejpam-5486	95	12	be	be	AUX
ejpam-5486	95	13	almost	almost	ADV
ejpam-5486	95	14	swd	swd	PROPN
ejpam-5486	95	15	-	-	ADJ
ejpam-5486	95	16	compact	compact	ADJ
ejpam-5486	95	17	if	if	SCONJ
ejpam-5486	95	18	for	for	ADP
ejpam-5486	95	19	each	each	DET
ejpam-5486	95	20	swd(z	swd(z	NOUN
ejpam-5486	95	21	,	,	PUNCT
ejpam-5486	95	22	τ)-cover	τ)-cover	PUNCT
ejpam-5486	95	23	h	h	NOUN
ejpam-5486	95	24	=	=	PRON
ejpam-5486	95	25	{	{	PUNCT
ejpam-5486	95	26	hα	hα	X
ejpam-5486	95	27	:	:	PUNCT
ejpam-5486	95	28	α	α	PROPN
ejpam-5486	95	29	∈	∈	PROPN
ejpam-5486	95	30	∆	∆	PROPN
ejpam-5486	95	31	}	}	PUNCT
ejpam-5486	95	32	of	of	ADP
ejpam-5486	95	33	z	z	NOUN
ejpam-5486	95	34	there	there	PRON
ejpam-5486	95	35	is	be	VERB
ejpam-5486	95	36	a	a	DET
ejpam-5486	95	37	finite	finite	NOUN
ejpam-5486	95	38	subset	subset	NOUN
ejpam-5486	95	39	∆	∆	ADJ
ejpam-5486	95	40	◦	◦	NOUN
ejpam-5486	95	41	⊆	⊆	NUM
ejpam-5486	95	42	∆	∆	X
ejpam-5486	95	43	with	with	ADP
ejpam-5486	95	44	z	z	NOUN
ejpam-5486	95	45	=	=	SYM
ejpam-5486	95	46	∪	∪	ADP
ejpam-5486	95	47	α∈∆	α∈∆	NOUN
ejpam-5486	95	48	◦	◦	NOUN
ejpam-5486	95	49	clswd(hα	clswd(hα	NOUN
ejpam-5486	95	50	)	)	PUNCT
ejpam-5486	95	51	.	.	PUNCT
ejpam-5486	96	1	2	2	X
ejpam-5486	96	2	.	.	X
ejpam-5486	96	3	more	more	ADJ
ejpam-5486	96	4	properties	property	NOUN
ejpam-5486	96	5	of	of	ADP
ejpam-5486	96	6	somewhere	somewhere	ADJ
ejpam-5486	96	7	dense	dense	ADJ
ejpam-5486	96	8	sets	set	NOUN
ejpam-5486	96	9	in	in	ADP
ejpam-5486	96	10	this	this	DET
ejpam-5486	96	11	section	section	NOUN
ejpam-5486	96	12	,	,	PUNCT
ejpam-5486	96	13	we	we	PRON
ejpam-5486	96	14	examine	examine	VERB
ejpam-5486	96	15	further	further	ADJ
ejpam-5486	96	16	properties	property	NOUN
ejpam-5486	96	17	of	of	ADP
ejpam-5486	96	18	somewhere	somewhere	ADV
ejpam-5486	96	19	dense	dense	ADJ
ejpam-5486	96	20	of	of	ADP
ejpam-5486	96	21	a	a	DET
ejpam-5486	96	22	topological	topological	ADJ
ejpam-5486	96	23	space	space	NOUN
ejpam-5486	96	24	(	(	PUNCT
ejpam-5486	96	25	z	z	NOUN
ejpam-5486	96	26	,	,	PUNCT
ejpam-5486	96	27	τ	τ	PROPN
ejpam-5486	96	28	)	)	PUNCT
ejpam-5486	96	29	.	.	PUNCT
ejpam-5486	97	1	proposition	proposition	NOUN
ejpam-5486	97	2	1	1	NUM
ejpam-5486	97	3	.	.	PUNCT
ejpam-5486	98	1	let	let	VERB
ejpam-5486	98	2	(	(	PUNCT
ejpam-5486	98	3	z	z	NOUN
ejpam-5486	98	4	,	,	PUNCT
ejpam-5486	98	5	τ	τ	PROPN
ejpam-5486	98	6	)	)	PUNCT
ejpam-5486	98	7	and	and	CCONJ
ejpam-5486	98	8	(	(	PUNCT
ejpam-5486	98	9	k	k	X
ejpam-5486	98	10	,	,	PUNCT
ejpam-5486	98	11	σ	σ	PROPN
ejpam-5486	98	12	)	)	PUNCT
ejpam-5486	98	13	be	be	VERB
ejpam-5486	98	14	two	two	NUM
ejpam-5486	98	15	t	t	NOUN
ejpam-5486	98	16	ss	ss	NOUN
ejpam-5486	98	17	and	and	CCONJ
ejpam-5486	98	18	γ	γ	X
ejpam-5486	98	19	:	:	PUNCT
ejpam-5486	98	20	(	(	PUNCT
ejpam-5486	98	21	z	z	NOUN
ejpam-5486	98	22	,	,	PUNCT
ejpam-5486	98	23	τ)→	τ)→	PROPN
ejpam-5486	98	24	(	(	PUNCT
ejpam-5486	98	25	k	k	X
ejpam-5486	98	26	,	,	PUNCT
ejpam-5486	98	27	σ	σ	PROPN
ejpam-5486	98	28	)	)	PUNCT
ejpam-5486	98	29	be	be	AUX
ejpam-5486	98	30	a	a	DET
ejpam-5486	98	31	continuous	continuous	ADJ
ejpam-5486	98	32	,	,	PUNCT
ejpam-5486	98	33	open	open	ADJ
ejpam-5486	98	34	and	and	CCONJ
ejpam-5486	98	35	surjective	surjective	ADJ
ejpam-5486	98	36	function	function	NOUN
ejpam-5486	98	37	.	.	PUNCT
ejpam-5486	99	1	if	if	SCONJ
ejpam-5486	99	2	h	h	NOUN
ejpam-5486	99	3	⊆	⊆	NUM
ejpam-5486	99	4	z	z	NOUN
ejpam-5486	99	5	and	and	CCONJ
ejpam-5486	99	6	h	h	NOUN
ejpam-5486	99	7	∈	∈	PROPN
ejpam-5486	99	8	swd(z	swd(z	PROPN
ejpam-5486	99	9	,	,	PUNCT
ejpam-5486	99	10	τ	τ	PROPN
ejpam-5486	99	11	)	)	PUNCT
ejpam-5486	99	12	,	,	PUNCT
ejpam-5486	99	13	then	then	ADV
ejpam-5486	99	14	γ(h	γ(h	NOUN
ejpam-5486	99	15	)	)	PUNCT
ejpam-5486	99	16	∈	∈	PROPN
ejpam-5486	99	17	swd(k	swd(k	PROPN
ejpam-5486	99	18	,	,	PUNCT
ejpam-5486	99	19	σ	σ	NOUN
ejpam-5486	99	20	)	)	PUNCT
ejpam-5486	99	21	.	.	PUNCT
ejpam-5486	100	1	proof	proof	NOUN
ejpam-5486	100	2	.	.	PUNCT
ejpam-5486	101	1	since	since	SCONJ
ejpam-5486	101	2	h	h	PROPN
ejpam-5486	101	3	∈	∈	PROPN
ejpam-5486	101	4	swd(z	swd(z	PROPN
ejpam-5486	101	5	,	,	PUNCT
ejpam-5486	101	6	τ	τ	PROPN
ejpam-5486	101	7	)	)	PUNCT
ejpam-5486	101	8	,	,	PUNCT
ejpam-5486	101	9	then	then	ADV
ejpam-5486	101	10	there	there	PRON
ejpam-5486	101	11	is	be	VERB
ejpam-5486	101	12	g	g	PROPN
ejpam-5486	101	13	∈	∈	PROPN
ejpam-5486	101	14	τ	τ	PROPN
ejpam-5486	101	15	with	with	ADP
ejpam-5486	101	16	ϕ	ϕ	PROPN
ejpam-5486	101	17	̸=	̸=	PROPN
ejpam-5486	101	18	g	g	ADP
ejpam-5486	101	19	⊆	⊆	NUM
ejpam-5486	101	20	cl(h	cl(h	NUM
ejpam-5486	101	21	)	)	PUNCT
ejpam-5486	101	22	.	.	PUNCT
ejpam-5486	102	1	therefore	therefore	ADV
ejpam-5486	102	2	,	,	PUNCT
ejpam-5486	102	3	ϕ	ϕ	PROPN
ejpam-5486	102	4	̸=	̸=	PROPN
ejpam-5486	102	5	γ(int(cl(g	γ(int(cl(g	PROPN
ejpam-5486	102	6	)	)	PUNCT
ejpam-5486	102	7	)	)	PUNCT
ejpam-5486	103	1	⊆	⊆	NUM
ejpam-5486	103	2	int(γ(cl(h	int(γ(cl(h	NUM
ejpam-5486	103	3	)	)	PUNCT
ejpam-5486	103	4	)	)	PUNCT
ejpam-5486	104	1	⊆	⊆	NUM
ejpam-5486	104	2	int(cl((γ(h	int(cl((γ(h	NOUN
ejpam-5486	104	3	)	)	PUNCT
ejpam-5486	104	4	)	)	PUNCT
ejpam-5486	104	5	and	and	CCONJ
ejpam-5486	104	6	hence	hence	ADV
ejpam-5486	104	7	γ(h	γ(h	NOUN
ejpam-5486	104	8	)	)	PUNCT
ejpam-5486	104	9	∈	∈	PROPN
ejpam-5486	104	10	swd(k	swd(k	PROPN
ejpam-5486	104	11	,	,	PUNCT
ejpam-5486	104	12	σ	σ	PROPN
ejpam-5486	104	13	)	)	PUNCT
ejpam-5486	104	14	.	.	PUNCT
ejpam-5486	105	1	theorem	theorem	ADJ
ejpam-5486	105	2	4	4	NUM
ejpam-5486	105	3	.	.	PUNCT
ejpam-5486	106	1	let	let	VERB
ejpam-5486	106	2	{	{	PUNCT
ejpam-5486	106	3	(	(	PUNCT
ejpam-5486	106	4	zα	zα	PROPN
ejpam-5486	106	5	,	,	PUNCT
ejpam-5486	106	6	τα	τα	PROPN
ejpam-5486	106	7	)	)	PUNCT
ejpam-5486	106	8	:	:	PUNCT
ejpam-5486	107	1	α	α	PROPN
ejpam-5486	107	2	∈	∈	PROPN
ejpam-5486	107	3	∆	∆	PROPN
ejpam-5486	107	4	}	}	PUNCT
ejpam-5486	107	5	be	be	AUX
ejpam-5486	107	6	a	a	DET
ejpam-5486	107	7	family	family	NOUN
ejpam-5486	107	8	of	of	ADP
ejpam-5486	107	9	topological	topological	ADJ
ejpam-5486	107	10	spaces	space	NOUN
ejpam-5486	107	11	with	with	ADP
ejpam-5486	107	12	zα	zα	PROPN
ejpam-5486	107	13	∩	∩	PROPN
ejpam-5486	107	14	zβ	zβ	PROPN
ejpam-5486	107	15	=	=	SYM
ejpam-5486	107	16	ϕ	ϕ	PROPN
ejpam-5486	107	17	for	for	ADP
ejpam-5486	107	18	each	each	DET
ejpam-5486	107	19	α	α	NOUN
ejpam-5486	107	20	̸=	̸=	PROPN
ejpam-5486	107	21	β	β	NOUN
ejpam-5486	107	22	.	.	PUNCT
ejpam-5486	108	1	for	for	ADP
ejpam-5486	108	2	each	each	DET
ejpam-5486	108	3	α	α	PROPN
ejpam-5486	108	4	∈	∈	PROPN
ejpam-5486	108	5	∆	∆	PROPN
ejpam-5486	108	6	,	,	PUNCT
ejpam-5486	108	7	let	let	VERB
ejpam-5486	108	8	ϕ	ϕ	PRON
ejpam-5486	108	9	̸=	̸=	PROPN
ejpam-5486	108	10	hα	hα	ADP
ejpam-5486	108	11	⊆	⊆	NUM
ejpam-5486	108	12	zα	zα	PROPN
ejpam-5486	108	13	and	and	CCONJ
ejpam-5486	108	14	put	put	VERB
ejpam-5486	108	15	h	h	NOUN
ejpam-5486	108	16	=	=	NOUN
ejpam-5486	108	17	∪	∪	ADP
ejpam-5486	108	18	α∈∆	α∈∆	PROPN
ejpam-5486	108	19	hα	hα	NOUN
ejpam-5486	108	20	.	.	PUNCT
ejpam-5486	109	1	then	then	ADV
ejpam-5486	109	2	:	:	PUNCT
ejpam-5486	109	3	(	(	PUNCT
ejpam-5486	109	4	i	i	NOUN
ejpam-5486	109	5	)	)	PUNCT
ejpam-5486	109	6	h	h	PROPN
ejpam-5486	110	1	∈	∈	PROPN
ejpam-5486	110	2	swd(z	swd(z	PROPN
ejpam-5486	110	3	,	,	PUNCT
ejpam-5486	110	4	τs	τs	NOUN
ejpam-5486	110	5	)	)	PUNCT
ejpam-5486	110	6	iff	iff	NOUN
ejpam-5486	110	7	there	there	PRON
ejpam-5486	110	8	is	be	VERB
ejpam-5486	110	9	α	α	NUM
ejpam-5486	110	10	◦	◦	NOUN
ejpam-5486	110	11	∈	∈	NOUN
ejpam-5486	110	12	∆	∆	PROPN
ejpam-5486	110	13	with	with	ADP
ejpam-5486	110	14	hα	hα	ADP
ejpam-5486	110	15	◦	◦	NOUN
ejpam-5486	110	16	∈	∈	NOUN
ejpam-5486	110	17	swd(zα	swd(zα	PRON
ejpam-5486	110	18	◦	◦	NOUN
ejpam-5486	110	19	,	,	PUNCT
ejpam-5486	110	20	τα	τα	NOUN
ejpam-5486	110	21	◦	◦	NOUN
ejpam-5486	110	22	)	)	PUNCT
ejpam-5486	110	23	.	.	PUNCT
ejpam-5486	111	1	(	(	PUNCT
ejpam-5486	111	2	ii	ii	NOUN
ejpam-5486	111	3	)	)	PUNCT
ejpam-5486	111	4	if	if	SCONJ
ejpam-5486	111	5	hα	hα	ADP
ejpam-5486	111	6	∈	∈	PROPN
ejpam-5486	111	7	swd(zα	swd(zα	NOUN
ejpam-5486	111	8	,	,	PUNCT
ejpam-5486	111	9	τα	τα	PROPN
ejpam-5486	111	10	)	)	PUNCT
ejpam-5486	111	11	for	for	ADP
ejpam-5486	111	12	each	each	DET
ejpam-5486	111	13	α	α	PROPN
ejpam-5486	111	14	∈	∈	PROPN
ejpam-5486	111	15	∆	∆	PROPN
ejpam-5486	111	16	,	,	PUNCT
ejpam-5486	111	17	then	then	ADV
ejpam-5486	111	18	h	h	PROPN
ejpam-5486	111	19	∈	∈	PROPN
ejpam-5486	111	20	swd(z	swd(z	PROPN
ejpam-5486	111	21	,	,	PUNCT
ejpam-5486	111	22	τs	τs	NOUN
ejpam-5486	111	23	)	)	PUNCT
ejpam-5486	111	24	.	.	PUNCT
ejpam-5486	112	1	proof	proof	NOUN
ejpam-5486	112	2	.	.	PUNCT
ejpam-5486	113	1	(	(	PUNCT
ejpam-5486	113	2	i	i	NOUN
ejpam-5486	113	3	)	)	PUNCT
ejpam-5486	113	4	first	first	ADV
ejpam-5486	113	5	,	,	PUNCT
ejpam-5486	113	6	note	note	VERB
ejpam-5486	113	7	that	that	SCONJ
ejpam-5486	113	8	for	for	ADP
ejpam-5486	113	9	all	all	DET
ejpam-5486	113	10	α	α	PRON
ejpam-5486	113	11	∈	∈	NOUN
ejpam-5486	113	12	∆	∆	X
ejpam-5486	113	13	,	,	PUNCT
ejpam-5486	113	14	clα(hα	clα(hα	NOUN
ejpam-5486	113	15	)	)	PUNCT
ejpam-5486	113	16	=	=	SYM
ejpam-5486	113	17	cl(hα	cl(hα	NOUN
ejpam-5486	113	18	)	)	PUNCT
ejpam-5486	113	19	where	where	SCONJ
ejpam-5486	113	20	clα(hα	clα(hα	NOUN
ejpam-5486	113	21	)	)	PUNCT
ejpam-5486	113	22	is	be	AUX
ejpam-5486	113	23	the	the	DET
ejpam-5486	113	24	closure	closure	NOUN
ejpam-5486	113	25	of	of	ADP
ejpam-5486	113	26	hα	hα	ADP
ejpam-5486	113	27	in	in	ADP
ejpam-5486	113	28	zα	zα	PROPN
ejpam-5486	113	29	while	while	SCONJ
ejpam-5486	113	30	cl(hα	cl(hα	PROPN
ejpam-5486	113	31	)	)	PUNCT
ejpam-5486	113	32	is	be	AUX
ejpam-5486	113	33	the	the	DET
ejpam-5486	113	34	closure	closure	NOUN
ejpam-5486	113	35	of	of	ADP
ejpam-5486	113	36	hα	hα	ADP
ejpam-5486	113	37	in	in	ADP
ejpam-5486	113	38	z.	z.	PROPN
ejpam-5486	113	39	now	now	ADV
ejpam-5486	113	40	,	,	PUNCT
ejpam-5486	113	41	choose	choose	VERB
ejpam-5486	113	42	α	α	NUM
ejpam-5486	113	43	◦	◦	NOUN
ejpam-5486	113	44	∈	∈	NOUN
ejpam-5486	113	45	∆	∆	PROPN
ejpam-5486	113	46	with	with	ADP
ejpam-5486	113	47	hα	hα	ADP
ejpam-5486	113	48	◦	◦	NOUN
ejpam-5486	113	49	∈	∈	NOUN
ejpam-5486	113	50	swd(zα	swd(zα	PRON
ejpam-5486	113	51	◦	◦	NOUN
ejpam-5486	113	52	,	,	PUNCT
ejpam-5486	113	53	τα	τα	NOUN
ejpam-5486	113	54	◦	◦	NOUN
ejpam-5486	113	55	)	)	PUNCT
ejpam-5486	113	56	.	.	PUNCT
ejpam-5486	114	1	then	then	ADV
ejpam-5486	114	2	there	there	PRON
ejpam-5486	114	3	is	be	VERB
ejpam-5486	114	4	gα	gα	ADP
ejpam-5486	114	5	◦	◦	NOUN
ejpam-5486	114	6	∈	∈	NOUN
ejpam-5486	114	7	τα	τα	NOUN
ejpam-5486	114	8	◦	◦	NOUN
ejpam-5486	114	9	with	with	ADP
ejpam-5486	114	10	ϕ	ϕ	PROPN
ejpam-5486	114	11	̸=	̸=	PROPN
ejpam-5486	114	12	gα	gα	ADP
ejpam-5486	114	13	◦	◦	NOUN
ejpam-5486	114	14	⊆	⊆	NUM
ejpam-5486	114	15	clα	clα	ADJ
ejpam-5486	114	16	◦	◦	ADJ
ejpam-5486	114	17	(hα	(hα	SYM
ejpam-5486	114	18	◦	◦	NOUN
ejpam-5486	114	19	)	)	PUNCT
ejpam-5486	114	20	=	=	SYM
ejpam-5486	114	21	cl(hα	cl(hα	NOUN
ejpam-5486	114	22	◦	◦	NOUN
ejpam-5486	114	23	)	)	PUNCT
ejpam-5486	114	24	⊆	⊆	NUM
ejpam-5486	114	25	cl(h	cl(h	NUM
ejpam-5486	114	26	)	)	PUNCT
ejpam-5486	114	27	and	and	CCONJ
ejpam-5486	114	28	hence	hence	ADV
ejpam-5486	114	29	h	h	NOUN
ejpam-5486	114	30	∈	∈	PROPN
ejpam-5486	114	31	swd(z	swd(z	PROPN
ejpam-5486	114	32	,	,	PUNCT
ejpam-5486	114	33	τs	τs	NOUN
ejpam-5486	114	34	)	)	PUNCT
ejpam-5486	114	35	.	.	PUNCT
ejpam-5486	115	1	conversely	conversely	ADV
ejpam-5486	115	2	,	,	PUNCT
ejpam-5486	115	3	since	since	SCONJ
ejpam-5486	115	4	h	h	PROPN
ejpam-5486	115	5	∈	∈	PROPN
ejpam-5486	115	6	swd(z	swd(z	PROPN
ejpam-5486	115	7	,	,	PUNCT
ejpam-5486	115	8	τs	τs	NOUN
ejpam-5486	115	9	)	)	PUNCT
ejpam-5486	115	10	and	and	CCONJ
ejpam-5486	115	11	the	the	DET
ejpam-5486	115	12	family	family	NOUN
ejpam-5486	115	13	{	{	PUNCT
ejpam-5486	115	14	hα	hα	X
ejpam-5486	115	15	:	:	PUNCT
ejpam-5486	115	16	α	α	PROPN
ejpam-5486	115	17	∈	∈	PROPN
ejpam-5486	115	18	∆	∆	X
ejpam-5486	115	19	}	}	PUNCT
ejpam-5486	115	20	is	be	AUX
ejpam-5486	115	21	locally	locally	ADV
ejpam-5486	115	22	finite	finite	ADJ
ejpam-5486	115	23	in	in	ADP
ejpam-5486	115	24	(	(	PUNCT
ejpam-5486	115	25	z	z	NOUN
ejpam-5486	115	26	,	,	PUNCT
ejpam-5486	115	27	τs	τs	NOUN
ejpam-5486	115	28	)	)	PUNCT
ejpam-5486	115	29	,	,	PUNCT
ejpam-5486	115	30	then	then	ADV
ejpam-5486	115	31	there	there	PRON
ejpam-5486	115	32	is	be	VERB
ejpam-5486	115	33	g	g	PROPN
ejpam-5486	115	34	∈	∈	PROPN
ejpam-5486	115	35	τs	τ	NOUN
ejpam-5486	115	36	with	with	ADP
ejpam-5486	115	37	ϕ	ϕ	PROPN
ejpam-5486	115	38	̸=	̸=	PROPN
ejpam-5486	115	39	g	g	ADP
ejpam-5486	115	40	⊆	⊆	NUM
ejpam-5486	115	41	cl(h	cl(h	NUM
ejpam-5486	115	42	)	)	PUNCT
ejpam-5486	115	43	=	=	SYM
ejpam-5486	115	44	cl	cl	NOUN
ejpam-5486	115	45	(	(	PUNCT
ejpam-5486	115	46	∪	∪	ADP
ejpam-5486	115	47	α∈∆	α∈∆	NUM
ejpam-5486	115	48	hα	hα	NOUN
ejpam-5486	115	49	)	)	PUNCT
ejpam-5486	115	50	=	=	PUNCT
ejpam-5486	115	51	∪	∪	ADP
ejpam-5486	115	52	α∈∆	α∈∆	NOUN
ejpam-5486	115	53	cl(hα	cl(hα	NOUN
ejpam-5486	115	54	)	)	PUNCT
ejpam-5486	115	55	=	=	SYM
ejpam-5486	115	56	∪	∪	ADP
ejpam-5486	115	57	α∈∆	α∈∆	PROPN
ejpam-5486	115	58	clα(hα	clα(hα	NOUN
ejpam-5486	115	59	)	)	PUNCT
ejpam-5486	115	60	.	.	PUNCT
ejpam-5486	116	1	since	since	SCONJ
ejpam-5486	116	2	ϕ	ϕ	PROPN
ejpam-5486	116	3	̸=	̸=	PROPN
ejpam-5486	116	4	g	g	NOUN
ejpam-5486	116	5	,	,	PUNCT
ejpam-5486	116	6	choose	choose	VERB
ejpam-5486	116	7	xα	xα	INTJ
ejpam-5486	116	8	◦	◦	NOUN
ejpam-5486	116	9	∈	∈	PROPN
ejpam-5486	116	10	g	g	NOUN
ejpam-5486	116	11	for	for	ADP
ejpam-5486	116	12	some	some	DET
ejpam-5486	116	13	α	α	NOUN
ejpam-5486	116	14	◦	◦	NOUN
ejpam-5486	116	15	∈	∈	PROPN
ejpam-5486	117	1	∆.	∆.	X
ejpam-5486	117	2	then	then	ADV
ejpam-5486	117	3	g	g	PROPN
ejpam-5486	117	4	∩	∩	ADJ
ejpam-5486	117	5	zα	zα	PROPN
ejpam-5486	117	6	◦	◦	NOUN
ejpam-5486	117	7	is	be	AUX
ejpam-5486	117	8	a	a	DET
ejpam-5486	117	9	non	non	ADJ
ejpam-5486	117	10	-	-	ADJ
ejpam-5486	117	11	empty	empty	ADJ
ejpam-5486	117	12	set	set	NOUN
ejpam-5486	117	13	in	in	ADP
ejpam-5486	117	14	(	(	PUNCT
ejpam-5486	117	15	zα	zα	NUM
ejpam-5486	117	16	◦	◦	NOUN
ejpam-5486	117	17	,	,	PUNCT
ejpam-5486	117	18	τα	τα	NOUN
ejpam-5486	117	19	◦	◦	NOUN
ejpam-5486	117	20	)	)	PUNCT
ejpam-5486	117	21	such	such	ADJ
ejpam-5486	117	22	that	that	SCONJ
ejpam-5486	117	23	g	g	PROPN
ejpam-5486	117	24	∩	∩	NOUN
ejpam-5486	117	25	zα	zα	NUM
ejpam-5486	117	26	◦	◦	NOUN
ejpam-5486	117	27	⊆	⊆	X
ejpam-5486	117	28	∪	∪	ADP
ejpam-5486	117	29	α∈∆	α∈∆	PRON
ejpam-5486	117	30	clα(hα)∩	clα(hα)∩	PROPN
ejpam-5486	117	31	zα	zα	NUM
ejpam-5486	117	32	◦	◦	NOUN
ejpam-5486	117	33	=	=	SYM
ejpam-5486	117	34	clα	clα	VERB
ejpam-5486	117	35	◦	◦	NOUN
ejpam-5486	117	36	(hα	(hα	SYM
ejpam-5486	117	37	◦	◦	NOUN
ejpam-5486	117	38	)	)	PUNCT
ejpam-5486	117	39	.	.	PUNCT
ejpam-5486	118	1	therefore	therefore	ADV
ejpam-5486	118	2	,	,	PUNCT
ejpam-5486	118	3	hα	hα	VERB
ejpam-5486	118	4	◦	◦	NOUN
ejpam-5486	118	5	∈	∈	NOUN
ejpam-5486	118	6	swd(zα	swd(zα	DET
ejpam-5486	118	7	◦	◦	NOUN
ejpam-5486	118	8	,	,	PUNCT
ejpam-5486	118	9	τα	τα	NOUN
ejpam-5486	118	10	◦	◦	NOUN
ejpam-5486	118	11	)	)	PUNCT
ejpam-5486	118	12	.	.	PUNCT
ejpam-5486	119	1	(	(	PUNCT
ejpam-5486	119	2	ii	ii	NOUN
ejpam-5486	119	3	)	)	PUNCT
ejpam-5486	119	4	follows	follow	VERB
ejpam-5486	119	5	from	from	ADP
ejpam-5486	119	6	part	part	NOUN
ejpam-5486	119	7	(	(	PUNCT
ejpam-5486	119	8	i	i	NOUN
ejpam-5486	119	9	)	)	PUNCT
ejpam-5486	119	10	.	.	PUNCT
ejpam-5486	120	1	the	the	DET
ejpam-5486	120	2	following	follow	VERB
ejpam-5486	120	3	theorem	theorem	NOUN
ejpam-5486	120	4	is	be	AUX
ejpam-5486	120	5	one	one	NUM
ejpam-5486	120	6	of	of	ADP
ejpam-5486	120	7	the	the	DET
ejpam-5486	120	8	most	most	ADV
ejpam-5486	120	9	important	important	ADJ
ejpam-5486	120	10	results	result	NOUN
ejpam-5486	120	11	that	that	PRON
ejpam-5486	120	12	we	we	PRON
ejpam-5486	120	13	present	present	VERB
ejpam-5486	120	14	in	in	ADP
ejpam-5486	120	15	this	this	DET
ejpam-5486	120	16	section	section	NOUN
ejpam-5486	120	17	.	.	PUNCT
ejpam-5486	121	1	since	since	SCONJ
ejpam-5486	121	2	theorem	theorem	ADJ
ejpam-5486	121	3	5	5	NUM
ejpam-5486	121	4	(	(	PUNCT
ejpam-5486	121	5	part	part	NOUN
ejpam-5486	121	6	ii	ii	PROPN
ejpam-5486	121	7	)	)	PUNCT
ejpam-5486	121	8	is	be	AUX
ejpam-5486	121	9	a	a	DET
ejpam-5486	121	10	generalization	generalization	NOUN
ejpam-5486	121	11	of	of	ADP
ejpam-5486	121	12	theorem	theorem	ADJ
ejpam-5486	121	13	2	2	NUM
ejpam-5486	121	14	.	.	PUNCT
ejpam-5486	121	15	theorem	theorem	NOUN
ejpam-5486	121	16	5	5	NUM
ejpam-5486	121	17	.	.	PUNCT
ejpam-5486	122	1	let	let	VERB
ejpam-5486	122	2	z	z	NOUN
ejpam-5486	123	1	=	=	PUNCT
ejpam-5486	123	2	π	π	NOUN
ejpam-5486	123	3	α∈∆	α∈∆	PUNCT
ejpam-5486	123	4	zα	zα	NOUN
ejpam-5486	123	5	be	be	AUX
ejpam-5486	123	6	the	the	DET
ejpam-5486	123	7	product	product	NOUN
ejpam-5486	123	8	space	space	NOUN
ejpam-5486	123	9	of	of	ADP
ejpam-5486	123	10	the	the	DET
ejpam-5486	123	11	spaces	space	NOUN
ejpam-5486	123	12	(	(	PUNCT
ejpam-5486	123	13	zα	zα	PROPN
ejpam-5486	123	14	,	,	PUNCT
ejpam-5486	123	15	τα	τα	PROPN
ejpam-5486	123	16	)	)	PUNCT
ejpam-5486	123	17	,	,	PUNCT
ejpam-5486	123	18	α	α	PROPN
ejpam-5486	123	19	∈	∈	PROPN
ejpam-5486	123	20	∆	∆	X
ejpam-5486	123	21	with	with	ADP
ejpam-5486	123	22	the	the	DET
ejpam-5486	123	23	tychonoff	tychonoff	NOUN
ejpam-5486	123	24	topology	topology	NOUN
ejpam-5486	123	25	τp	τp	PROPN
ejpam-5486	123	26	.	.	PUNCT
ejpam-5486	124	1	let	let	VERB
ejpam-5486	124	2	hα	hα	ADP
ejpam-5486	124	3	⊆	⊆	NUM
ejpam-5486	124	4	zα	zα	PROPN
ejpam-5486	124	5	for	for	ADP
ejpam-5486	124	6	each	each	DET
ejpam-5486	124	7	α	α	NOUN
ejpam-5486	124	8	∈	∈	PROPN
ejpam-5486	125	1	∆.	∆.	X
ejpam-5486	125	2	then	then	ADV
ejpam-5486	125	3	the	the	DET
ejpam-5486	125	4	following	following	NOUN
ejpam-5486	125	5	are	be	AUX
ejpam-5486	125	6	equivalent	equivalent	ADJ
ejpam-5486	125	7	:	:	PUNCT
ejpam-5486	125	8	(	(	PUNCT
ejpam-5486	125	9	i	i	NOUN
ejpam-5486	125	10	)	)	PUNCT
ejpam-5486	125	11	hα	hα	ADP
ejpam-5486	125	12	∈	∈	PROPN
ejpam-5486	125	13	swd(zα	swd(zα	NOUN
ejpam-5486	125	14	,	,	PUNCT
ejpam-5486	125	15	τα	τα	PROPN
ejpam-5486	125	16	)	)	PUNCT
ejpam-5486	125	17	for	for	ADP
ejpam-5486	125	18	each	each	DET
ejpam-5486	125	19	α	α	NOUN
ejpam-5486	125	20	∈	∈	PROPN
ejpam-5486	125	21	∆.	∆.	PROPN
ejpam-5486	125	22	(	(	PUNCT
ejpam-5486	125	23	ii	ii	NOUN
ejpam-5486	125	24	)	)	PUNCT
ejpam-5486	125	25	for	for	ADP
ejpam-5486	125	26	each	each	DET
ejpam-5486	125	27	finite	finite	NOUN
ejpam-5486	125	28	subset	subset	VERB
ejpam-5486	125	29	∆∗	∆∗	NOUN
ejpam-5486	125	30	⊆	⊆	NUM
ejpam-5486	125	31	∆	∆	PROPN
ejpam-5486	125	32	,	,	PUNCT
ejpam-5486	125	33	the	the	DET
ejpam-5486	125	34	set	set	NOUN
ejpam-5486	125	35	h	h	NOUN
ejpam-5486	125	36	=	=	PUNCT
ejpam-5486	125	37	π	π	PROPN
ejpam-5486	125	38	α∈∆∗	α∈∆∗	PROPN
ejpam-5486	125	39	hα	hα	ADP
ejpam-5486	125	40	×	×	PROPN
ejpam-5486	125	41	π	π	PROPN
ejpam-5486	125	42	β∈∆−∆∗	β∈∆−∆∗	PUNCT
ejpam-5486	125	43	zβ	zβ	PROPN
ejpam-5486	125	44	∈	∈	PROPN
ejpam-5486	125	45	swd(z	swd(z	PROPN
ejpam-5486	125	46	,	,	PUNCT
ejpam-5486	125	47	τp	τp	NOUN
ejpam-5486	125	48	)	)	PUNCT
ejpam-5486	125	49	.	.	PUNCT
ejpam-5486	126	1	(	(	PUNCT
ejpam-5486	126	2	iii	iii	X
ejpam-5486	126	3	)	)	PUNCT
ejpam-5486	126	4	for	for	ADP
ejpam-5486	126	5	each	each	DET
ejpam-5486	126	6	α	α	PROPN
ejpam-5486	126	7	∈	∈	PROPN
ejpam-5486	126	8	∆	∆	PROPN
ejpam-5486	126	9	,	,	PUNCT
ejpam-5486	126	10	the	the	DET
ejpam-5486	126	11	set	set	NOUN
ejpam-5486	126	12	h	h	NOUN
ejpam-5486	127	1	=	=	NOUN
ejpam-5486	127	2	hα	hα	ADP
ejpam-5486	127	3	×	×	PROPN
ejpam-5486	127	4	π	π	X
ejpam-5486	127	5	β∈∆	β∈∆	PUNCT
ejpam-5486	127	6	β	β	X
ejpam-5486	127	7	̸=α	̸=α	PROPN
ejpam-5486	127	8	zβ	zβ	PROPN
ejpam-5486	127	9	∈	∈	PROPN
ejpam-5486	127	10	swd(z	swd(z	PROPN
ejpam-5486	127	11	,	,	PUNCT
ejpam-5486	127	12	τp	τp	NOUN
ejpam-5486	127	13	)	)	PUNCT
ejpam-5486	127	14	.	.	PUNCT
ejpam-5486	128	1	proof	proof	NOUN
ejpam-5486	128	2	.	.	PUNCT
ejpam-5486	129	1	the	the	DET
ejpam-5486	129	2	implication	implication	NOUN
ejpam-5486	129	3	(	(	PUNCT
ejpam-5486	129	4	ii	ii	PROPN
ejpam-5486	129	5	−→	−→	PROPN
ejpam-5486	129	6	iii	iii	NOUN
ejpam-5486	129	7	)	)	PUNCT
ejpam-5486	129	8	is	be	AUX
ejpam-5486	129	9	obvious	obvious	ADJ
ejpam-5486	129	10	.	.	PUNCT
ejpam-5486	130	1	a.	a.	NOUN
ejpam-5486	130	2	rawshdeh	rawshdeh	PROPN
ejpam-5486	130	3	,	,	PUNCT
ejpam-5486	130	4	h.	h.	PROPN
ejpam-5486	130	5	h.	h.	PROPN
ejpam-5486	130	6	al	al	PROPN
ejpam-5486	130	7	-	-	PUNCT
ejpam-5486	130	8	jarrah	jarrah	PROPN
ejpam-5486	130	9	,	,	PUNCT
ejpam-5486	130	10	k.	k.	PROPN
ejpam-5486	130	11	y.	y.	PROPN
ejpam-5486	130	12	al	al	PROPN
ejpam-5486	130	13	-	-	PROPN
ejpam-5486	130	14	zoubi	zoubi	PROPN
ejpam-5486	130	15	/	/	SYM
ejpam-5486	130	16	eur	eur	PROPN
ejpam-5486	130	17	.	.	PUNCT
ejpam-5486	131	1	j.	j.	PROPN
ejpam-5486	131	2	pure	pure	PROPN
ejpam-5486	131	3	appl	appl	PROPN
ejpam-5486	131	4	.	.	PROPN
ejpam-5486	131	5	math	math	PROPN
ejpam-5486	131	6	,	,	PUNCT
ejpam-5486	131	7	17	17	NUM
ejpam-5486	131	8	(	(	PUNCT
ejpam-5486	131	9	4	4	NUM
ejpam-5486	131	10	)	)	PUNCT
ejpam-5486	131	11	(	(	PUNCT
ejpam-5486	131	12	2024	2024	NUM
ejpam-5486	131	13	)	)	PUNCT
ejpam-5486	131	14	,	,	PUNCT
ejpam-5486	131	15	3370	3370	NUM
ejpam-5486	131	16	-	-	SYM
ejpam-5486	131	17	3385	3385	NUM
ejpam-5486	131	18	3374	3374	NUM
ejpam-5486	131	19	(	(	PUNCT
ejpam-5486	131	20	i	i	PRON
ejpam-5486	131	21	−→	−→	PROPN
ejpam-5486	131	22	ii	ii	PROPN
ejpam-5486	131	23	)	)	PUNCT
ejpam-5486	131	24	for	for	ADP
ejpam-5486	131	25	each	each	DET
ejpam-5486	131	26	α	α	PROPN
ejpam-5486	131	27	∈	∈	PROPN
ejpam-5486	131	28	∆∗	∆∗	NOUN
ejpam-5486	131	29	,	,	PUNCT
ejpam-5486	131	30	there	there	PRON
ejpam-5486	131	31	is	be	VERB
ejpam-5486	131	32	gα	gα	ADP
ejpam-5486	131	33	∈	∈	PROPN
ejpam-5486	131	34	τα	τα	NOUN
ejpam-5486	131	35	with	with	ADP
ejpam-5486	131	36	ϕ	ϕ	PROPN
ejpam-5486	131	37	̸=	̸=	PROPN
ejpam-5486	131	38	gα	gα	ADP
ejpam-5486	131	39	⊆	⊆	NUM
ejpam-5486	131	40	zα	zα	NUM
ejpam-5486	131	41	and	and	CCONJ
ejpam-5486	131	42	gα	gα	ADP
ejpam-5486	131	43	⊆	⊆	NUM
ejpam-5486	131	44	cl(hα	cl(hα	NOUN
ejpam-5486	131	45	)	)	PUNCT
ejpam-5486	131	46	.	.	PUNCT
ejpam-5486	132	1	then	then	ADV
ejpam-5486	132	2	g	g	PROPN
ejpam-5486	132	3	=	=	PROPN
ejpam-5486	132	4	π	π	PROPN
ejpam-5486	132	5	α∈∆∗	α∈∆∗	PROPN
ejpam-5486	132	6	gα	gα	ADP
ejpam-5486	132	7	×	×	PROPN
ejpam-5486	132	8	π	π	PROPN
ejpam-5486	132	9	β∈∆−∆∗	β∈∆−∆∗	X
ejpam-5486	132	10	zβ	zβ	PROPN
ejpam-5486	132	11	is	be	AUX
ejpam-5486	132	12	a	a	DET
ejpam-5486	132	13	non	non	ADJ
ejpam-5486	132	14	-	-	ADJ
ejpam-5486	132	15	empty	empty	ADJ
ejpam-5486	132	16	open	open	ADJ
ejpam-5486	132	17	set	set	NOUN
ejpam-5486	132	18	in	in	ADP
ejpam-5486	132	19	(	(	PUNCT
ejpam-5486	132	20	z	z	NOUN
ejpam-5486	132	21	,	,	PUNCT
ejpam-5486	132	22	τp	τp	NOUN
ejpam-5486	132	23	)	)	PUNCT
ejpam-5486	133	1	such	such	ADJ
ejpam-5486	133	2	that	that	SCONJ
ejpam-5486	133	3	g	g	PROPN
ejpam-5486	133	4	⊆	⊆	NUM
ejpam-5486	133	5	π	π	PROPN
ejpam-5486	133	6	α∈∆∗	α∈∆∗	PROPN
ejpam-5486	133	7	cl(hα	cl(hα	PROPN
ejpam-5486	133	8	)	)	PUNCT
ejpam-5486	133	9	×	×	PROPN
ejpam-5486	133	10	π	π	X
ejpam-5486	133	11	β∈∆−∆∗	β∈∆−∆∗	X
ejpam-5486	133	12	zβ	zβ	X
ejpam-5486	133	13	=	=	PUNCT
ejpam-5486	133	14	cl(π	cl(π	NOUN
ejpam-5486	133	15	(	(	PUNCT
ejpam-5486	133	16	α∈∆∗	α∈∆∗	PROPN
ejpam-5486	133	17	hα	hα	NOUN
ejpam-5486	133	18	)	)	PUNCT
ejpam-5486	133	19	×	×	PROPN
ejpam-5486	133	20	π	π	PROPN
ejpam-5486	133	21	β∈∆−∆∗	β∈∆−∆∗	PROPN
ejpam-5486	133	22	zβ	zβ	PROPN
ejpam-5486	133	23	)	)	PUNCT
ejpam-5486	133	24	=	=	SYM
ejpam-5486	133	25	cl(h	cl(h	NUM
ejpam-5486	133	26	)	)	PUNCT
ejpam-5486	133	27	.	.	PUNCT
ejpam-5486	134	1	therefore	therefore	ADV
ejpam-5486	134	2	,	,	PUNCT
ejpam-5486	134	3	h	h	PROPN
ejpam-5486	134	4	∈	∈	PROPN
ejpam-5486	134	5	swd(z	swd(z	PROPN
ejpam-5486	134	6	,	,	PUNCT
ejpam-5486	134	7	τp	τp	NOUN
ejpam-5486	134	8	)	)	PUNCT
ejpam-5486	134	9	.	.	PUNCT
ejpam-5486	135	1	(	(	PUNCT
ejpam-5486	135	2	iii	iii	X
ejpam-5486	135	3	→	→	SYM
ejpam-5486	135	4	i	i	NOUN
ejpam-5486	135	5	)	)	PUNCT
ejpam-5486	135	6	since	since	SCONJ
ejpam-5486	135	7	for	for	ADP
ejpam-5486	135	8	each	each	DET
ejpam-5486	135	9	α	α	NOUN
ejpam-5486	135	10	∈	∈	PROPN
ejpam-5486	135	11	∆	∆	PROPN
ejpam-5486	135	12	,	,	PUNCT
ejpam-5486	135	13	the	the	DET
ejpam-5486	135	14	projection	projection	NOUN
ejpam-5486	135	15	function	function	NOUN
ejpam-5486	135	16	πα	πα	VERB
ejpam-5486	135	17	:	:	PUNCT
ejpam-5486	135	18	(	(	PUNCT
ejpam-5486	135	19	z	z	NOUN
ejpam-5486	135	20	,	,	PUNCT
ejpam-5486	135	21	τp	τp	NOUN
ejpam-5486	135	22	)	)	PUNCT
ejpam-5486	135	23	→	→	SYM
ejpam-5486	135	24	(	(	PUNCT
ejpam-5486	135	25	zα	zα	NUM
ejpam-5486	135	26	,	,	PUNCT
ejpam-5486	135	27	τα	τα	PROPN
ejpam-5486	135	28	)	)	PUNCT
ejpam-5486	135	29	is	be	AUX
ejpam-5486	135	30	continuous	continuous	ADJ
ejpam-5486	135	31	,	,	PUNCT
ejpam-5486	135	32	open	open	ADJ
ejpam-5486	135	33	and	and	CCONJ
ejpam-5486	135	34	surjective	surjective	VERB
ejpam-5486	135	35	such	such	ADJ
ejpam-5486	135	36	that	that	SCONJ
ejpam-5486	135	37	πα(hα	πα(hα	ADJ
ejpam-5486	135	38	×	×	NOUN
ejpam-5486	135	39	π	π	X
ejpam-5486	135	40	β∈∆	β∈∆	PUNCT
ejpam-5486	135	41	β	β	PROPN
ejpam-5486	135	42	̸=α	̸=α	PROPN
ejpam-5486	135	43	zβ	zβ	PROPN
ejpam-5486	135	44	)	)	PUNCT
ejpam-5486	135	45	=	=	PUNCT
ejpam-5486	136	1	hα	hα	PROPN
ejpam-5486	136	2	,	,	PUNCT
ejpam-5486	136	3	then	then	ADV
ejpam-5486	136	4	by	by	ADP
ejpam-5486	136	5	proposition	proposition	NOUN
ejpam-5486	136	6	1	1	NUM
ejpam-5486	136	7	,	,	PUNCT
ejpam-5486	136	8	hα	hα	ADP
ejpam-5486	136	9	∈	∈	PROPN
ejpam-5486	136	10	swd(zα	swd(zα	NOUN
ejpam-5486	136	11	,	,	PUNCT
ejpam-5486	136	12	τα	τα	PROPN
ejpam-5486	136	13	)	)	PUNCT
ejpam-5486	136	14	for	for	ADP
ejpam-5486	136	15	each	each	DET
ejpam-5486	136	16	α	α	NOUN
ejpam-5486	136	17	∈	∈	PROPN
ejpam-5486	136	18	∆.	∆.	NOUN
ejpam-5486	136	19	theorem	theorem	NOUN
ejpam-5486	136	20	6	6	NUM
ejpam-5486	136	21	.	.	PUNCT
ejpam-5486	137	1	let	let	VERB
ejpam-5486	137	2	z	z	NOUN
ejpam-5486	137	3	=	=	PUNCT
ejpam-5486	138	1	π	π	NOUN
ejpam-5486	138	2	α∈∆	α∈∆	PUNCT
ejpam-5486	138	3	zα	zα	NOUN
ejpam-5486	138	4	be	be	AUX
ejpam-5486	138	5	the	the	DET
ejpam-5486	138	6	product	product	NOUN
ejpam-5486	138	7	space	space	NOUN
ejpam-5486	138	8	of	of	ADP
ejpam-5486	138	9	the	the	DET
ejpam-5486	138	10	spaces	space	NOUN
ejpam-5486	138	11	(	(	PUNCT
ejpam-5486	138	12	zα	zα	PROPN
ejpam-5486	138	13	,	,	PUNCT
ejpam-5486	138	14	τα	τα	PROPN
ejpam-5486	138	15	)	)	PUNCT
ejpam-5486	138	16	,	,	PUNCT
ejpam-5486	138	17	α	α	PROPN
ejpam-5486	138	18	∈	∈	PROPN
ejpam-5486	138	19	∆	∆	X
ejpam-5486	138	20	with	with	ADP
ejpam-5486	138	21	the	the	DET
ejpam-5486	138	22	tychonoff	tychonoff	NOUN
ejpam-5486	138	23	topology	topology	NOUN
ejpam-5486	138	24	τp	τp	PROPN
ejpam-5486	138	25	.	.	PUNCT
ejpam-5486	139	1	let	let	VERB
ejpam-5486	139	2	hα	hα	ADP
ejpam-5486	139	3	⊆	⊆	NUM
ejpam-5486	139	4	zα	zα	PROPN
ejpam-5486	139	5	for	for	ADP
ejpam-5486	139	6	each	each	DET
ejpam-5486	139	7	α	α	NOUN
ejpam-5486	139	8	∈	∈	PROPN
ejpam-5486	140	1	∆.	∆.	X
ejpam-5486	140	2	then	then	ADV
ejpam-5486	140	3	:	:	PUNCT
ejpam-5486	140	4	(	(	PUNCT
ejpam-5486	140	5	i	i	NOUN
ejpam-5486	140	6	)	)	PUNCT
ejpam-5486	140	7	if	if	SCONJ
ejpam-5486	140	8	hα	hα	ADP
ejpam-5486	140	9	∈	∈	PROPN
ejpam-5486	140	10	swd(zα	swd(zα	NOUN
ejpam-5486	140	11	,	,	PUNCT
ejpam-5486	140	12	τα	τα	PROPN
ejpam-5486	140	13	)	)	PUNCT
ejpam-5486	140	14	for	for	ADP
ejpam-5486	140	15	each	each	DET
ejpam-5486	140	16	α	α	PROPN
ejpam-5486	140	17	∈	∈	PROPN
ejpam-5486	140	18	∆	∆	PROPN
ejpam-5486	140	19	,	,	PUNCT
ejpam-5486	140	20	then	then	ADV
ejpam-5486	140	21	∪	∪	ADJ
ejpam-5486	140	22	α∈∆	α∈∆	PROPN
ejpam-5486	140	23	(	(	PUNCT
ejpam-5486	140	24	hα	hα	ADP
ejpam-5486	140	25	×π	×π	ADV
ejpam-5486	140	26	β∈∆	β∈∆	PROPN
ejpam-5486	140	27	β	β	PROPN
ejpam-5486	140	28	̸=α	̸=α	PROPN
ejpam-5486	140	29	zβ	zβ	X
ejpam-5486	140	30	)	)	PUNCT
ejpam-5486	140	31	∈	∈	PROPN
ejpam-5486	140	32	swd(z	swd(z	PROPN
ejpam-5486	140	33	,	,	PUNCT
ejpam-5486	140	34	τp	τp	NOUN
ejpam-5486	140	35	)	)	PUNCT
ejpam-5486	140	36	.	.	PUNCT
ejpam-5486	141	1	(	(	PUNCT
ejpam-5486	141	2	ii	ii	X
ejpam-5486	141	3	)	)	PUNCT
ejpam-5486	141	4	if	if	SCONJ
ejpam-5486	141	5	π	π	PROPN
ejpam-5486	141	6	α∈∆	α∈∆	VERB
ejpam-5486	141	7	hα	hα	ADP
ejpam-5486	141	8	∈	∈	PROPN
ejpam-5486	141	9	swd(z	swd(z	PROPN
ejpam-5486	141	10	,	,	PUNCT
ejpam-5486	141	11	τp	τp	NOUN
ejpam-5486	141	12	)	)	PUNCT
ejpam-5486	141	13	,	,	PUNCT
ejpam-5486	141	14	then	then	ADV
ejpam-5486	141	15	hα	hα	ADP
ejpam-5486	141	16	∈	∈	PROPN
ejpam-5486	141	17	swd(zα	swd(zα	NOUN
ejpam-5486	141	18	,	,	PUNCT
ejpam-5486	141	19	τα	τα	PROPN
ejpam-5486	141	20	)	)	PUNCT
ejpam-5486	141	21	for	for	ADP
ejpam-5486	141	22	each	each	DET
ejpam-5486	141	23	α	α	NOUN
ejpam-5486	141	24	∈	∈	PROPN
ejpam-5486	142	1	∆.	∆.	ADJ
ejpam-5486	142	2	proof	proof	NOUN
ejpam-5486	142	3	.	.	PUNCT
ejpam-5486	143	1	(	(	PUNCT
ejpam-5486	143	2	i	i	NOUN
ejpam-5486	143	3	)	)	PUNCT
ejpam-5486	143	4	follows	follow	VERB
ejpam-5486	143	5	from	from	ADP
ejpam-5486	143	6	theorem	theorem	ADJ
ejpam-5486	143	7	5	5	NUM
ejpam-5486	143	8	(	(	PUNCT
ejpam-5486	143	9	part	part	NOUN
ejpam-5486	143	10	iii	iii	NOUN
ejpam-5486	143	11	)	)	PUNCT
ejpam-5486	143	12	and	and	CCONJ
ejpam-5486	143	13	theorem	theorem	VERB
ejpam-5486	143	14	3	3	NUM
ejpam-5486	143	15	(	(	PUNCT
ejpam-5486	143	16	part	part	NOUN
ejpam-5486	143	17	i	i	NOUN
ejpam-5486	143	18	)	)	PUNCT
ejpam-5486	143	19	.	.	PUNCT
ejpam-5486	144	1	(	(	PUNCT
ejpam-5486	144	2	ii	ii	NOUN
ejpam-5486	144	3	)	)	PUNCT
ejpam-5486	144	4	follows	follow	VERB
ejpam-5486	144	5	from	from	ADP
ejpam-5486	144	6	proposition	proposition	NOUN
ejpam-5486	144	7	1	1	NUM
ejpam-5486	144	8	(	(	PUNCT
ejpam-5486	144	9	see	see	VERB
ejpam-5486	144	10	the	the	DET
ejpam-5486	144	11	proof	proof	NOUN
ejpam-5486	144	12	of	of	ADP
ejpam-5486	144	13	the	the	DET
ejpam-5486	144	14	implication	implication	NOUN
ejpam-5486	144	15	(	(	PUNCT
ejpam-5486	144	16	iii→	iii→	NOUN
ejpam-5486	144	17	i	i	PROPN
ejpam-5486	144	18	)	)	PUNCT
ejpam-5486	144	19	in	in	ADP
ejpam-5486	144	20	theorem	theorem	NOUN
ejpam-5486	144	21	5	5	NUM
ejpam-5486	144	22	)	)	PUNCT
ejpam-5486	144	23	.	.	PUNCT
ejpam-5486	145	1	the	the	DET
ejpam-5486	145	2	following	follow	VERB
ejpam-5486	145	3	example	example	NOUN
ejpam-5486	145	4	shows	show	VERB
ejpam-5486	145	5	that	that	SCONJ
ejpam-5486	145	6	the	the	DET
ejpam-5486	145	7	converses	converse	NOUN
ejpam-5486	145	8	of	of	ADP
ejpam-5486	145	9	theorem	theorem	NOUN
ejpam-5486	145	10	6	6	NUM
ejpam-5486	145	11	need	need	NOUN
ejpam-5486	145	12	not	not	PART
ejpam-5486	145	13	be	be	AUX
ejpam-5486	145	14	true	true	ADJ
ejpam-5486	145	15	in	in	ADP
ejpam-5486	145	16	general	general	ADJ
ejpam-5486	145	17	:	:	PUNCT
ejpam-5486	145	18	example	example	NOUN
ejpam-5486	145	19	1	1	NUM
ejpam-5486	145	20	.	.	PUNCT
ejpam-5486	146	1	(	(	PUNCT
ejpam-5486	146	2	i	i	NOUN
ejpam-5486	146	3	)	)	PUNCT
ejpam-5486	146	4	let	let	VERB
ejpam-5486	146	5	z	z	NOUN
ejpam-5486	146	6	=	=	SYM
ejpam-5486	146	7	r	r	NOUN
ejpam-5486	146	8	and	and	CCONJ
ejpam-5486	146	9	consider	consider	VERB
ejpam-5486	146	10	the	the	DET
ejpam-5486	146	11	spaces	space	NOUN
ejpam-5486	146	12	(	(	PUNCT
ejpam-5486	146	13	z1	z1	NOUN
ejpam-5486	146	14	,	,	PUNCT
ejpam-5486	146	15	τ1	τ1	NOUN
ejpam-5486	146	16	)	)	PUNCT
ejpam-5486	146	17	=	=	SYM
ejpam-5486	147	1	(	(	PUNCT
ejpam-5486	147	2	r	r	NOUN
ejpam-5486	147	3	,	,	PUNCT
ejpam-5486	147	4	τu	τu	ADJ
ejpam-5486	147	5	)	)	PUNCT
ejpam-5486	147	6	and	and	CCONJ
ejpam-5486	147	7	(	(	PUNCT
ejpam-5486	147	8	z2	z2	NOUN
ejpam-5486	147	9	,	,	PUNCT
ejpam-5486	147	10	τ2	τ2	NOUN
ejpam-5486	147	11	)	)	PUNCT
ejpam-5486	147	12	=	=	SYM
ejpam-5486	148	1	(	(	PUNCT
ejpam-5486	148	2	r	r	NOUN
ejpam-5486	148	3	,	,	PUNCT
ejpam-5486	148	4	τind	τind	NOUN
ejpam-5486	148	5	)	)	PUNCT
ejpam-5486	148	6	.	.	PUNCT
ejpam-5486	149	1	then	then	ADV
ejpam-5486	149	2	the	the	DET
ejpam-5486	149	3	set	set	NOUN
ejpam-5486	149	4	(	(	PUNCT
ejpam-5486	149	5	{	{	PUNCT
ejpam-5486	149	6	2	2	NUM
ejpam-5486	149	7	}	}	PUNCT
ejpam-5486	149	8	×	×	PROPN
ejpam-5486	149	9	z2	z2	PROPN
ejpam-5486	149	10	)	)	PUNCT
ejpam-5486	149	11	∪	∪	NOUN
ejpam-5486	149	12	(	(	PUNCT
ejpam-5486	149	13	z1	z1	ADJ
ejpam-5486	149	14	×	×	NOUN
ejpam-5486	149	15	{	{	PUNCT
ejpam-5486	149	16	1	1	NUM
ejpam-5486	149	17	}	}	PUNCT
ejpam-5486	149	18	)	)	PUNCT
ejpam-5486	149	19	is	be	AUX
ejpam-5486	149	20	somewhere	somewhere	ADV
ejpam-5486	149	21	dense	dense	ADJ
ejpam-5486	149	22	of	of	ADP
ejpam-5486	149	23	(	(	PUNCT
ejpam-5486	149	24	r	r	NOUN
ejpam-5486	149	25	,	,	PUNCT
ejpam-5486	149	26	τu	τu	ADJ
ejpam-5486	149	27	)	)	PUNCT
ejpam-5486	149	28	×	×	NOUN
ejpam-5486	149	29	(	(	PUNCT
ejpam-5486	149	30	r	r	NOUN
ejpam-5486	149	31	,	,	PUNCT
ejpam-5486	149	32	τind	τind	NOUN
ejpam-5486	149	33	)	)	PUNCT
ejpam-5486	149	34	while	while	SCONJ
ejpam-5486	149	35	{	{	PUNCT
ejpam-5486	149	36	2	2	NUM
ejpam-5486	149	37	}	}	PUNCT
ejpam-5486	149	38	/∈	/∈	PUNCT
ejpam-5486	150	1	swd((r	swd((r	ADJ
ejpam-5486	150	2	,	,	PUNCT
ejpam-5486	150	3	τu	τu	ADJ
ejpam-5486	150	4	)	)	PUNCT
ejpam-5486	150	5	.	.	PUNCT
ejpam-5486	151	1	(	(	PUNCT
ejpam-5486	151	2	ii	ii	NOUN
ejpam-5486	151	3	)	)	PUNCT
ejpam-5486	151	4	for	for	ADP
ejpam-5486	151	5	each	each	DET
ejpam-5486	151	6	α	α	PROPN
ejpam-5486	151	7	∈	∈	NOUN
ejpam-5486	151	8	∆	∆	PROPN
ejpam-5486	151	9	with	with	ADP
ejpam-5486	151	10	∆	∆	PROPN
ejpam-5486	151	11	is	be	AUX
ejpam-5486	151	12	an	an	DET
ejpam-5486	151	13	infinite	infinite	ADJ
ejpam-5486	151	14	set	set	NOUN
ejpam-5486	151	15	,	,	PUNCT
ejpam-5486	151	16	consider	consider	VERB
ejpam-5486	151	17	(	(	PUNCT
ejpam-5486	151	18	zα	zα	PROPN
ejpam-5486	151	19	,	,	PUNCT
ejpam-5486	151	20	τα	τα	NOUN
ejpam-5486	151	21	)	)	PUNCT
ejpam-5486	151	22	=	=	SYM
ejpam-5486	151	23	(	(	PUNCT
ejpam-5486	151	24	kα	kα	PROPN
ejpam-5486	151	25	,	,	PUNCT
ejpam-5486	151	26	τind	τind	NOUN
ejpam-5486	151	27	)	)	PUNCT
ejpam-5486	151	28	where	where	SCONJ
ejpam-5486	151	29	kα	kα	VERB
ejpam-5486	151	30	any	any	DET
ejpam-5486	151	31	set	set	NOUN
ejpam-5486	151	32	with	with	ADP
ejpam-5486	151	33	|kα|	|kα|	PROPN
ejpam-5486	151	34	>	>	X
ejpam-5486	152	1	1	1	X
ejpam-5486	152	2	.	.	X
ejpam-5486	152	3	for	for	ADP
ejpam-5486	152	4	each	each	DET
ejpam-5486	152	5	α	α	PROPN
ejpam-5486	152	6	∈	∈	PROPN
ejpam-5486	152	7	∆	∆	PROPN
ejpam-5486	152	8	,	,	PUNCT
ejpam-5486	152	9	choose	choose	VERB
ejpam-5486	152	10	xα	xα	INTJ
ejpam-5486	152	11	∈	∈	PROPN
ejpam-5486	152	12	kα	kα	PROPN
ejpam-5486	152	13	,	,	PUNCT
ejpam-5486	152	14	then	then	ADV
ejpam-5486	152	15	for	for	ADP
ejpam-5486	152	16	each	each	DET
ejpam-5486	152	17	α	α	NOUN
ejpam-5486	152	18	∈	∈	NOUN
ejpam-5486	152	19	∆	∆	PROPN
ejpam-5486	152	20	,	,	PUNCT
ejpam-5486	152	21	hα	hα	ADP
ejpam-5486	152	22	=	=	PUNCT
ejpam-5486	152	23	{	{	PUNCT
ejpam-5486	152	24	xα	xα	ADJ
ejpam-5486	152	25	}	}	PUNCT
ejpam-5486	152	26	∈	∈	PROPN
ejpam-5486	152	27	swd(kα	swd(kα	NOUN
ejpam-5486	152	28	,	,	PUNCT
ejpam-5486	152	29	τind	τind	NOUN
ejpam-5486	152	30	)	)	PUNCT
ejpam-5486	152	31	while	while	SCONJ
ejpam-5486	152	32	π	π	X
ejpam-5486	152	33	α∈∆	α∈∆	VERB
ejpam-5486	152	34	hα	hα	NOUN
ejpam-5486	152	35	/∈	/∈	PUNCT
ejpam-5486	153	1	swd(z	swd(z	PROPN
ejpam-5486	153	2	,	,	PUNCT
ejpam-5486	153	3	τp	τp	NOUN
ejpam-5486	153	4	)	)	PUNCT
ejpam-5486	153	5	.	.	PUNCT
ejpam-5486	154	1	theorem	theorem	ADJ
ejpam-5486	154	2	7	7	NUM
ejpam-5486	154	3	.	.	PUNCT
ejpam-5486	155	1	let	let	VERB
ejpam-5486	155	2	z	z	NOUN
ejpam-5486	156	1	=	=	PUNCT
ejpam-5486	156	2	π	π	NOUN
ejpam-5486	156	3	α∈∆	α∈∆	PUNCT
ejpam-5486	156	4	zα	zα	NOUN
ejpam-5486	156	5	be	be	AUX
ejpam-5486	156	6	the	the	DET
ejpam-5486	156	7	cartesian	cartesian	ADJ
ejpam-5486	156	8	product	product	NOUN
ejpam-5486	156	9	of	of	ADP
ejpam-5486	156	10	the	the	DET
ejpam-5486	156	11	spaces	space	NOUN
ejpam-5486	156	12	(	(	PUNCT
ejpam-5486	156	13	zα	zα	PROPN
ejpam-5486	156	14	,	,	PUNCT
ejpam-5486	156	15	τα	τα	PROPN
ejpam-5486	156	16	)	)	PUNCT
ejpam-5486	156	17	with	with	ADP
ejpam-5486	156	18	the	the	DET
ejpam-5486	156	19	topology	topology	NOUN
ejpam-5486	156	20	τb	τb	ADP
ejpam-5486	156	21	which	which	PRON
ejpam-5486	156	22	is	be	AUX
ejpam-5486	156	23	generated	generate	VERB
ejpam-5486	156	24	by	by	ADP
ejpam-5486	156	25	the	the	DET
ejpam-5486	156	26	base	base	NOUN
ejpam-5486	156	27	{	{	PUNCT
ejpam-5486	156	28	π	π	NOUN
ejpam-5486	156	29	α∈∆	α∈∆	PRON
ejpam-5486	156	30	vα	vα	X
ejpam-5486	156	31	:	:	PUNCT
ejpam-5486	156	32	vα	vα	ADP
ejpam-5486	156	33	∈	∈	PROPN
ejpam-5486	156	34	τα	τα	NOUN
ejpam-5486	156	35	for	for	ADP
ejpam-5486	156	36	each	each	DET
ejpam-5486	156	37	α	α	PROPN
ejpam-5486	156	38	∈	∈	PROPN
ejpam-5486	156	39	∆}(τb	∆}(τb	NOUN
ejpam-5486	156	40	is	be	AUX
ejpam-5486	156	41	called	call	VERB
ejpam-5486	156	42	the	the	DET
ejpam-5486	156	43	box	box	NOUN
ejpam-5486	156	44	topology	topology	NOUN
ejpam-5486	156	45	)	)	PUNCT
ejpam-5486	156	46	.	.	PUNCT
ejpam-5486	157	1	then	then	ADV
ejpam-5486	157	2	hα	hα	ADP
ejpam-5486	157	3	∈	∈	PROPN
ejpam-5486	157	4	swd(zα	swd(zα	NOUN
ejpam-5486	157	5	,	,	PUNCT
ejpam-5486	157	6	τα	τα	PROPN
ejpam-5486	157	7	)	)	PUNCT
ejpam-5486	157	8	for	for	ADP
ejpam-5486	157	9	each	each	DET
ejpam-5486	157	10	α	α	PROPN
ejpam-5486	157	11	∈	∈	PROPN
ejpam-5486	157	12	∆	∆	PROPN
ejpam-5486	157	13	iff	iff	NOUN
ejpam-5486	157	14	π	π	X
ejpam-5486	157	15	α∈∆	α∈∆	NOUN
ejpam-5486	157	16	hα	hα	ADP
ejpam-5486	157	17	∈	∈	PROPN
ejpam-5486	157	18	swd(z	swd(z	PROPN
ejpam-5486	157	19	,	,	PUNCT
ejpam-5486	157	20	τb	τb	ADJ
ejpam-5486	157	21	)	)	PUNCT
ejpam-5486	157	22	.	.	PUNCT
ejpam-5486	158	1	proof	proof	NOUN
ejpam-5486	158	2	.	.	PUNCT
ejpam-5486	159	1	for	for	ADP
ejpam-5486	159	2	each	each	DET
ejpam-5486	159	3	α	α	PROPN
ejpam-5486	159	4	∈	∈	PROPN
ejpam-5486	159	5	∆	∆	PROPN
ejpam-5486	159	6	,	,	PUNCT
ejpam-5486	159	7	there	there	PRON
ejpam-5486	159	8	is	be	VERB
ejpam-5486	159	9	gα	gα	ADP
ejpam-5486	159	10	∈	∈	PROPN
ejpam-5486	159	11	τα	τα	NOUN
ejpam-5486	159	12	with	with	ADP
ejpam-5486	159	13	ϕ	ϕ	PROPN
ejpam-5486	159	14	̸=	̸=	PROPN
ejpam-5486	159	15	gα	gα	ADP
ejpam-5486	159	16	⊆	⊆	NUM
ejpam-5486	159	17	zα	zα	NUM
ejpam-5486	159	18	and	and	CCONJ
ejpam-5486	159	19	gα	gα	ADP
ejpam-5486	159	20	⊆	⊆	NUM
ejpam-5486	159	21	cl(hα	cl(hα	NOUN
ejpam-5486	159	22	)	)	PUNCT
ejpam-5486	159	23	.	.	PUNCT
ejpam-5486	160	1	then	then	ADV
ejpam-5486	160	2	g	g	PROPN
ejpam-5486	160	3	=	=	PUNCT
ejpam-5486	160	4	π	π	NOUN
ejpam-5486	160	5	α∈∆	α∈∆	PUNCT
ejpam-5486	160	6	gα	gα	NOUN
ejpam-5486	160	7	is	be	AUX
ejpam-5486	160	8	a	a	DET
ejpam-5486	160	9	non	non	ADJ
ejpam-5486	160	10	-	-	ADJ
ejpam-5486	160	11	empty	empty	ADJ
ejpam-5486	160	12	open	open	ADJ
ejpam-5486	160	13	set	set	NOUN
ejpam-5486	160	14	of	of	ADP
ejpam-5486	160	15	z	z	NOUN
ejpam-5486	160	16	such	such	ADJ
ejpam-5486	160	17	that	that	SCONJ
ejpam-5486	160	18	g	g	PROPN
ejpam-5486	160	19	⊆	⊆	NUM
ejpam-5486	160	20	π	π	NOUN
ejpam-5486	160	21	α∈∆	α∈∆	NUM
ejpam-5486	160	22	cl(hα	cl(hα	NOUN
ejpam-5486	160	23	)	)	PUNCT
ejpam-5486	160	24	=	=	PUNCT
ejpam-5486	161	1	cl(π	cl(π	NOUN
ejpam-5486	161	2	(	(	PUNCT
ejpam-5486	161	3	α∈∆	α∈∆	NOUN
ejpam-5486	161	4	hα	hα	NOUN
ejpam-5486	161	5	)	)	PUNCT
ejpam-5486	161	6	)	)	PUNCT
ejpam-5486	161	7	.	.	PUNCT
ejpam-5486	162	1	conversely	conversely	ADV
ejpam-5486	162	2	,	,	PUNCT
ejpam-5486	162	3	let	let	VERB
ejpam-5486	162	4	α	α	PRON
ejpam-5486	162	5	◦	◦	NOUN
ejpam-5486	162	6	∈	∈	PROPN
ejpam-5486	163	1	∆.	∆.	X
ejpam-5486	163	2	then	then	ADV
ejpam-5486	163	3	hα	hα	VERB
ejpam-5486	163	4	◦	◦	NOUN
ejpam-5486	163	5	×π	×π	X
ejpam-5486	163	6	α∈∆	α∈∆	PROPN
ejpam-5486	163	7	α	α	PRON
ejpam-5486	163	8	̸=α	̸=α	PROPN
ejpam-5486	163	9	◦	◦	NOUN
ejpam-5486	163	10	hα	hα	ADP
ejpam-5486	163	11	∈	∈	PROPN
ejpam-5486	163	12	swd(z	swd(z	PROPN
ejpam-5486	163	13	,	,	PUNCT
ejpam-5486	163	14	τb	τb	ADP
ejpam-5486	163	15	)	)	PUNCT
ejpam-5486	163	16	and	and	CCONJ
ejpam-5486	163	17	hence	hence	ADV
ejpam-5486	163	18	there	there	PRON
ejpam-5486	163	19	is	be	VERB
ejpam-5486	163	20	g	g	PROPN
ejpam-5486	163	21	∈	∈	PROPN
ejpam-5486	163	22	τb	τb	ADP
ejpam-5486	163	23	such	such	ADJ
ejpam-5486	163	24	that	that	SCONJ
ejpam-5486	163	25	ϕ	ϕ	PROPN
ejpam-5486	163	26	̸=	̸=	PROPN
ejpam-5486	163	27	g	g	ADP
ejpam-5486	163	28	⊆	⊆	NUM
ejpam-5486	163	29	cl(hα	cl(hα	NOUN
ejpam-5486	163	30	◦	◦	NOUN
ejpam-5486	163	31	×π	×π	PRON
ejpam-5486	163	32	α∈∆	α∈∆	PROPN
ejpam-5486	163	33	α	α	PRON
ejpam-5486	163	34	̸=α	̸=α	PROPN
ejpam-5486	163	35	◦	◦	NOUN
ejpam-5486	163	36	hα	hα	NOUN
ejpam-5486	163	37	)	)	PUNCT
ejpam-5486	164	1	and	and	CCONJ
ejpam-5486	164	2	so	so	ADV
ejpam-5486	164	3	there	there	PRON
ejpam-5486	164	4	is	be	VERB
ejpam-5486	164	5	a	a	DET
ejpam-5486	164	6	basic	basic	ADJ
ejpam-5486	164	7	open	open	NOUN
ejpam-5486	164	8	set	set	VERB
ejpam-5486	164	9	v	v	NOUN
ejpam-5486	164	10	=	=	SYM
ejpam-5486	164	11	π	π	NOUN
ejpam-5486	164	12	α∈∆	α∈∆	PUNCT
ejpam-5486	164	13	vα	vα	NOUN
ejpam-5486	164	14	with	with	ADP
ejpam-5486	164	15	vα	vα	NOUN
ejpam-5486	164	16	◦	◦	NOUN
ejpam-5486	164	17	×	×	NOUN
ejpam-5486	164	18	π	π	NOUN
ejpam-5486	164	19	α∈∆	α∈∆	NUM
ejpam-5486	164	20	α	α	PRON
ejpam-5486	164	21	̸=α	̸=α	PROPN
ejpam-5486	164	22	◦	◦	NOUN
ejpam-5486	164	23	vα	vα	ADP
ejpam-5486	164	24	⊆	⊆	NUM
ejpam-5486	164	25	cl(hα	cl(hα	NOUN
ejpam-5486	164	26	◦	◦	NOUN
ejpam-5486	164	27	×π	×π	PRON
ejpam-5486	164	28	α∈∆	α∈∆	PROPN
ejpam-5486	164	29	α	α	PRON
ejpam-5486	164	30	̸=α	̸=α	PROPN
ejpam-5486	164	31	◦	◦	NOUN
ejpam-5486	164	32	hα	hα	NOUN
ejpam-5486	164	33	)	)	PUNCT
ejpam-5486	164	34	.	.	PUNCT
ejpam-5486	165	1	therefore	therefore	ADV
ejpam-5486	165	2	,	,	PUNCT
ejpam-5486	165	3	vα	vα	VERB
ejpam-5486	165	4	◦	◦	NOUN
ejpam-5486	165	5	⊆	⊆	NUM
ejpam-5486	165	6	cl(hα	cl(hα	NOUN
ejpam-5486	165	7	◦	◦	NOUN
ejpam-5486	165	8	)	)	PUNCT
ejpam-5486	165	9	and	and	CCONJ
ejpam-5486	165	10	thus	thus	ADV
ejpam-5486	165	11	hα	hα	ADP
ejpam-5486	165	12	◦	◦	NOUN
ejpam-5486	165	13	∈	∈	NOUN
ejpam-5486	165	14	swd(zα	swd(zα	PRON
ejpam-5486	165	15	◦	◦	NOUN
ejpam-5486	165	16	,	,	PUNCT
ejpam-5486	165	17	τα	τα	NOUN
ejpam-5486	165	18	◦	◦	NOUN
ejpam-5486	165	19	)	)	PUNCT
ejpam-5486	165	20	.	.	PUNCT
ejpam-5486	166	1	a.	a.	PROPN
ejpam-5486	166	2	rawshdeh	rawshdeh	PROPN
ejpam-5486	166	3	,	,	PUNCT
ejpam-5486	166	4	h.	h.	PROPN
ejpam-5486	166	5	h.	h.	PROPN
ejpam-5486	166	6	al	al	PROPN
ejpam-5486	166	7	-	-	PUNCT
ejpam-5486	166	8	jarrah	jarrah	PROPN
ejpam-5486	166	9	,	,	PUNCT
ejpam-5486	166	10	k.	k.	PROPN
ejpam-5486	166	11	y.	y.	PROPN
ejpam-5486	166	12	al	al	PROPN
ejpam-5486	166	13	-	-	PROPN
ejpam-5486	166	14	zoubi	zoubi	PROPN
ejpam-5486	166	15	/	/	SYM
ejpam-5486	166	16	eur	eur	PROPN
ejpam-5486	166	17	.	.	PUNCT
ejpam-5486	167	1	j.	j.	PROPN
ejpam-5486	167	2	pure	pure	PROPN
ejpam-5486	167	3	appl	appl	PROPN
ejpam-5486	167	4	.	.	PROPN
ejpam-5486	167	5	math	math	PROPN
ejpam-5486	167	6	,	,	PUNCT
ejpam-5486	167	7	17	17	NUM
ejpam-5486	167	8	(	(	PUNCT
ejpam-5486	167	9	4	4	NUM
ejpam-5486	167	10	)	)	PUNCT
ejpam-5486	167	11	(	(	PUNCT
ejpam-5486	167	12	2024	2024	NUM
ejpam-5486	167	13	)	)	PUNCT
ejpam-5486	167	14	,	,	PUNCT
ejpam-5486	167	15	3370	3370	NUM
ejpam-5486	167	16	-	-	SYM
ejpam-5486	167	17	3385	3385	NUM
ejpam-5486	167	18	3375	3375	NUM
ejpam-5486	167	19	corollary	corollary	NOUN
ejpam-5486	167	20	1	1	NUM
ejpam-5486	167	21	.	.	PUNCT
ejpam-5486	168	1	(	(	PUNCT
ejpam-5486	168	2	i	i	NOUN
ejpam-5486	168	3	)	)	PUNCT
ejpam-5486	168	4	let	let	VERB
ejpam-5486	168	5	z	z	NOUN
ejpam-5486	168	6	=	=	PUNCT
ejpam-5486	169	1	π	π	NOUN
ejpam-5486	169	2	α∈∆	α∈∆	PUNCT
ejpam-5486	169	3	zα	zα	NOUN
ejpam-5486	169	4	be	be	AUX
ejpam-5486	169	5	the	the	DET
ejpam-5486	169	6	product	product	NOUN
ejpam-5486	169	7	space	space	NOUN
ejpam-5486	169	8	of	of	ADP
ejpam-5486	169	9	the	the	DET
ejpam-5486	169	10	spaces	space	NOUN
ejpam-5486	169	11	(	(	PUNCT
ejpam-5486	169	12	zα	zα	PROPN
ejpam-5486	169	13	,	,	PUNCT
ejpam-5486	169	14	τα	τα	PROPN
ejpam-5486	169	15	)	)	PUNCT
ejpam-5486	169	16	,	,	PUNCT
ejpam-5486	169	17	α	α	PROPN
ejpam-5486	169	18	∈	∈	PROPN
ejpam-5486	169	19	∆	∆	PROPN
ejpam-5486	169	20	with	with	ADP
ejpam-5486	169	21	the	the	DET
ejpam-5486	169	22	topology	topology	NOUN
ejpam-5486	169	23	τp	τp	NOUN
ejpam-5486	169	24	and	and	CCONJ
ejpam-5486	169	25	fα	fα	ADP
ejpam-5486	169	26	⊆	⊆	NUM
ejpam-5486	169	27	zα	zα	NUM
ejpam-5486	169	28	for	for	ADP
ejpam-5486	169	29	each	each	DET
ejpam-5486	169	30	α	α	NOUN
ejpam-5486	169	31	∈	∈	PROPN
ejpam-5486	170	1	∆.	∆.	NOUN
ejpam-5486	170	2	if	if	SCONJ
ejpam-5486	170	3	∪	∪	ADJ
ejpam-5486	170	4	α∈∆	α∈∆	NOUN
ejpam-5486	170	5	(	(	PUNCT
ejpam-5486	170	6	fα	fα	ADP
ejpam-5486	170	7	×π	×π	ADV
ejpam-5486	170	8	β∈∆	β∈∆	X
ejpam-5486	170	9	β	β	PROPN
ejpam-5486	170	10	̸=α	̸=α	PROPN
ejpam-5486	170	11	zβ	zβ	X
ejpam-5486	170	12	)	)	PUNCT
ejpam-5486	170	13	∈	∈	PROPN
ejpam-5486	170	14	swdc(z	swdc(z	PROPN
ejpam-5486	170	15	,	,	PUNCT
ejpam-5486	170	16	τp	τp	NOUN
ejpam-5486	170	17	)	)	PUNCT
ejpam-5486	170	18	,	,	PUNCT
ejpam-5486	170	19	then	then	ADV
ejpam-5486	170	20	fα	fα	ADP
ejpam-5486	170	21	∈	∈	PROPN
ejpam-5486	170	22	swdc(zα	swdc(zα	PROPN
ejpam-5486	170	23	,	,	PUNCT
ejpam-5486	170	24	τα	τα	NOUN
ejpam-5486	170	25	)	)	PUNCT
ejpam-5486	170	26	.	.	PUNCT
ejpam-5486	171	1	(	(	PUNCT
ejpam-5486	171	2	ii	ii	X
ejpam-5486	171	3	)	)	PUNCT
ejpam-5486	171	4	let	let	VERB
ejpam-5486	171	5	z	z	NOUN
ejpam-5486	171	6	=	=	PUNCT
ejpam-5486	172	1	π	π	NOUN
ejpam-5486	172	2	α∈∆	α∈∆	PUNCT
ejpam-5486	172	3	zα	zα	NOUN
ejpam-5486	172	4	be	be	AUX
ejpam-5486	172	5	the	the	DET
ejpam-5486	172	6	product	product	NOUN
ejpam-5486	172	7	space	space	NOUN
ejpam-5486	172	8	of	of	ADP
ejpam-5486	172	9	the	the	DET
ejpam-5486	172	10	spaces	space	NOUN
ejpam-5486	172	11	(	(	PUNCT
ejpam-5486	172	12	zα	zα	PROPN
ejpam-5486	172	13	,	,	PUNCT
ejpam-5486	172	14	τα	τα	PROPN
ejpam-5486	172	15	)	)	PUNCT
ejpam-5486	172	16	,	,	PUNCT
ejpam-5486	172	17	α	α	PROPN
ejpam-5486	172	18	∈	∈	PROPN
ejpam-5486	172	19	∆	∆	PROPN
ejpam-5486	172	20	with	with	ADP
ejpam-5486	172	21	the	the	DET
ejpam-5486	172	22	topology	topology	NOUN
ejpam-5486	172	23	τb	τb	ADJ
ejpam-5486	172	24	and	and	CCONJ
ejpam-5486	172	25	fα	fα	ADP
ejpam-5486	172	26	⊆	⊆	NUM
ejpam-5486	172	27	zα	zα	NUM
ejpam-5486	172	28	.	.	PUNCT
ejpam-5486	173	1	then	then	ADV
ejpam-5486	173	2	fα	fα	ADP
ejpam-5486	173	3	∈	∈	PROPN
ejpam-5486	173	4	swdc(zα	swdc(zα	PROPN
ejpam-5486	173	5	,	,	PUNCT
ejpam-5486	173	6	τα	τα	PROPN
ejpam-5486	173	7	)	)	PUNCT
ejpam-5486	173	8	iff	iff	PROPN
ejpam-5486	173	9	∪	∪	VERB
ejpam-5486	173	10	α∈∆	α∈∆	PROPN
ejpam-5486	173	11	(	(	PUNCT
ejpam-5486	173	12	fα	fα	ADP
ejpam-5486	173	13	×π	×π	ADV
ejpam-5486	173	14	β∈∆	β∈∆	X
ejpam-5486	173	15	β	β	PROPN
ejpam-5486	173	16	̸=α	̸=α	PROPN
ejpam-5486	173	17	zβ	zβ	X
ejpam-5486	173	18	)	)	PUNCT
ejpam-5486	173	19	∈	∈	PROPN
ejpam-5486	173	20	swdc(z	swdc(z	PROPN
ejpam-5486	173	21	,	,	PUNCT
ejpam-5486	173	22	τb	τb	ADJ
ejpam-5486	173	23	)	)	PUNCT
ejpam-5486	173	24	.	.	PUNCT
ejpam-5486	174	1	(	(	PUNCT
ejpam-5486	174	2	iii	iii	X
ejpam-5486	174	3	)	)	PUNCT
ejpam-5486	174	4	let	let	VERB
ejpam-5486	174	5	z	z	NOUN
ejpam-5486	174	6	=	=	PUNCT
ejpam-5486	174	7	n	n	PROPN
ejpam-5486	174	8	π	π	X
ejpam-5486	174	9	α=1	α=1	X
ejpam-5486	174	10	zα	zα	PROPN
ejpam-5486	174	11	be	be	AUX
ejpam-5486	174	12	the	the	DET
ejpam-5486	174	13	finite	finite	ADJ
ejpam-5486	174	14	product	product	NOUN
ejpam-5486	174	15	space	space	NOUN
ejpam-5486	174	16	of	of	ADP
ejpam-5486	174	17	the	the	DET
ejpam-5486	174	18	spaces	space	NOUN
ejpam-5486	174	19	(	(	PUNCT
ejpam-5486	174	20	zα	zα	PROPN
ejpam-5486	174	21	,	,	PUNCT
ejpam-5486	174	22	τα	τα	PROPN
ejpam-5486	174	23	)	)	PUNCT
ejpam-5486	174	24	and	and	CCONJ
ejpam-5486	174	25	fα	fα	ADP
ejpam-5486	174	26	⊆	⊆	NUM
ejpam-5486	174	27	zα	zα	NUM
ejpam-5486	174	28	for	for	ADP
ejpam-5486	174	29	each	each	DET
ejpam-5486	174	30	α	α	NOUN
ejpam-5486	174	31	∈	∈	PROPN
ejpam-5486	174	32	{	{	PUNCT
ejpam-5486	174	33	1	1	NUM
ejpam-5486	174	34	,	,	PUNCT
ejpam-5486	174	35	2	2	NUM
ejpam-5486	174	36	..	..	PUNCT
ejpam-5486	174	37	,	,	PUNCT
ejpam-5486	174	38	n	n	CCONJ
ejpam-5486	174	39	}	}	PUNCT
ejpam-5486	174	40	.	.	PUNCT
ejpam-5486	175	1	then	then	ADV
ejpam-5486	175	2	for	for	ADP
ejpam-5486	175	3	each	each	DET
ejpam-5486	175	4	α	α	NOUN
ejpam-5486	175	5	∈	∈	PROPN
ejpam-5486	175	6	{	{	PUNCT
ejpam-5486	175	7	1	1	NUM
ejpam-5486	175	8	,	,	PUNCT
ejpam-5486	175	9	2	2	NUM
ejpam-5486	175	10	..	..	PUNCT
ejpam-5486	175	11	,	,	PUNCT
ejpam-5486	175	12	n	n	CCONJ
ejpam-5486	175	13	}	}	PUNCT
ejpam-5486	175	14	,	,	PUNCT
ejpam-5486	175	15	fα	fα	ADP
ejpam-5486	175	16	∈	∈	PROPN
ejpam-5486	175	17	swdc(zα	swdc(zα	PROPN
ejpam-5486	175	18	,	,	PUNCT
ejpam-5486	175	19	τα	τα	PROPN
ejpam-5486	175	20	)	)	PUNCT
ejpam-5486	175	21	iff	iff	PROPN
ejpam-5486	175	22	n	n	PRON
ejpam-5486	175	23	∪	∪	VERB
ejpam-5486	175	24	α=1	α=1	X
ejpam-5486	175	25	(	(	PUNCT
ejpam-5486	175	26	fα	fα	ADP
ejpam-5486	175	27	×π	×π	ADV
ejpam-5486	175	28	β∈{1,2	β∈{1,2	ADJ
ejpam-5486	175	29	...	...	PUNCT
ejpam-5486	175	30	,n	,n	NOUN
ejpam-5486	175	31	}	}	PUNCT
ejpam-5486	175	32	β	β	X
ejpam-5486	175	33	̸=α	̸=α	PROPN
ejpam-5486	175	34	zβ	zβ	X
ejpam-5486	175	35	)	)	PUNCT
ejpam-5486	175	36	is	be	AUX
ejpam-5486	175	37	closed	close	VERB
ejpam-5486	175	38	somewhere	somewhere	ADV
ejpam-5486	175	39	dense	dense	ADJ
ejpam-5486	175	40	of	of	ADP
ejpam-5486	175	41	z.	z.	PROPN
ejpam-5486	175	42	note	note	VERB
ejpam-5486	175	43	that	that	SCONJ
ejpam-5486	175	44	,	,	PUNCT
ejpam-5486	175	45	in	in	ADP
ejpam-5486	175	46	example	example	NOUN
ejpam-5486	175	47	1	1	NUM
ejpam-5486	175	48	(	(	PUNCT
ejpam-5486	175	49	part	part	NOUN
ejpam-5486	175	50	(	(	PUNCT
ejpam-5486	175	51	ii	ii	NOUN
ejpam-5486	175	52	)	)	PUNCT
ejpam-5486	175	53	)	)	PUNCT
ejpam-5486	175	54	,	,	PUNCT
ejpam-5486	175	55	fα	fα	ADP
ejpam-5486	175	56	=	=	SYM
ejpam-5486	175	57	{	{	PUNCT
ejpam-5486	175	58	xα	xα	ADJ
ejpam-5486	175	59	}	}	PUNCT
ejpam-5486	175	60	∈	∈	PROPN
ejpam-5486	175	61	swdc(zα	swdc(zα	PROPN
ejpam-5486	175	62	,	,	PUNCT
ejpam-5486	175	63	τα	τα	NOUN
ejpam-5486	175	64	)	)	PUNCT
ejpam-5486	175	65	while	while	SCONJ
ejpam-5486	175	66	∪	∪	ADJ
ejpam-5486	175	67	α∈∆	α∈∆	PROPN
ejpam-5486	175	68	(	(	PUNCT
ejpam-5486	175	69	fα	fα	ADP
ejpam-5486	175	70	×π	×π	ADV
ejpam-5486	175	71	β∈∆	β∈∆	X
ejpam-5486	175	72	β	β	PROPN
ejpam-5486	175	73	̸=α	̸=α	PROPN
ejpam-5486	175	74	zβ	zβ	PROPN
ejpam-5486	175	75	)	)	PUNCT
ejpam-5486	175	76	/∈	/∈	PUNCT
ejpam-5486	176	1	swdc(z	swdc(z	PROPN
ejpam-5486	176	2	,	,	PUNCT
ejpam-5486	176	3	τp	τp	NOUN
ejpam-5486	176	4	)	)	PUNCT
ejpam-5486	176	5	,	,	PUNCT
ejpam-5486	176	6	since	since	SCONJ
ejpam-5486	176	7	z	z	NOUN
ejpam-5486	176	8	−	−	PROPN
ejpam-5486	176	9	∪	∪	ADP
ejpam-5486	176	10	α∈∆	α∈∆	NOUN
ejpam-5486	176	11	(	(	PUNCT
ejpam-5486	176	12	fα	fα	ADP
ejpam-5486	176	13	×π	×π	ADV
ejpam-5486	176	14	β∈∆	β∈∆	X
ejpam-5486	176	15	β	β	PROPN
ejpam-5486	176	16	̸=α	̸=α	PROPN
ejpam-5486	176	17	zβ	zβ	PROPN
ejpam-5486	176	18	)	)	PUNCT
ejpam-5486	176	19	=	=	PUNCT
ejpam-5486	177	1	π	π	X
ejpam-5486	177	2	α∈∆	α∈∆	PUNCT
ejpam-5486	177	3	(	(	PUNCT
ejpam-5486	177	4	zα	zα	NOUN
ejpam-5486	177	5	−	−	NOUN
ejpam-5486	177	6	fα	fα	NOUN
ejpam-5486	177	7	)	)	PUNCT
ejpam-5486	177	8	/∈	/∈	PUNCT
ejpam-5486	178	1	swd(z	swd(z	PROPN
ejpam-5486	178	2	,	,	PUNCT
ejpam-5486	178	3	τ	τ	X
ejpam-5486	178	4	)	)	PUNCT
ejpam-5486	178	5	and	and	CCONJ
ejpam-5486	178	6	so	so	ADV
ejpam-5486	178	7	the	the	DET
ejpam-5486	178	8	converse	converse	NOUN
ejpam-5486	178	9	of	of	ADP
ejpam-5486	178	10	corollary	corollary	ADJ
ejpam-5486	178	11	1	1	NUM
ejpam-5486	178	12	(	(	PUNCT
ejpam-5486	178	13	part	part	NOUN
ejpam-5486	178	14	i	i	NOUN
ejpam-5486	178	15	)	)	PUNCT
ejpam-5486	178	16	is	be	AUX
ejpam-5486	178	17	not	not	PART
ejpam-5486	178	18	true	true	ADJ
ejpam-5486	178	19	in	in	ADP
ejpam-5486	178	20	general	general	ADJ
ejpam-5486	178	21	.	.	PUNCT
ejpam-5486	179	1	3	3	X
ejpam-5486	179	2	.	.	X
ejpam-5486	179	3	ω−somewhere	ω−somewhere	ADP
ejpam-5486	179	4	dense	dense	ADJ
ejpam-5486	179	5	open	open	ADJ
ejpam-5486	179	6	sets	set	NOUN
ejpam-5486	179	7	with	with	ADP
ejpam-5486	179	8	some	some	DET
ejpam-5486	179	9	applications	application	NOUN
ejpam-5486	179	10	in	in	ADP
ejpam-5486	179	11	this	this	DET
ejpam-5486	179	12	section	section	NOUN
ejpam-5486	179	13	we	we	PRON
ejpam-5486	179	14	introduce	introduce	VERB
ejpam-5486	179	15	the	the	DET
ejpam-5486	179	16	notion	notion	NOUN
ejpam-5486	179	17	of	of	ADP
ejpam-5486	179	18	ωswd	ωswd	ADJ
ejpam-5486	179	19	-	-	PUNCT
ejpam-5486	179	20	open	open	ADJ
ejpam-5486	179	21	subsets	subset	NOUN
ejpam-5486	179	22	,	,	PUNCT
ejpam-5486	179	23	denoted	denote	VERB
ejpam-5486	179	24	by	by	ADP
ejpam-5486	179	25	ωswd(z	ωswd(z	PROPN
ejpam-5486	179	26	,	,	PUNCT
ejpam-5486	179	27	τ	τ	PROPN
ejpam-5486	179	28	)	)	PUNCT
ejpam-5486	179	29	,	,	PUNCT
ejpam-5486	179	30	as	as	ADP
ejpam-5486	179	31	a	a	DET
ejpam-5486	179	32	new	new	ADJ
ejpam-5486	179	33	generalization	generalization	NOUN
ejpam-5486	179	34	for	for	ADP
ejpam-5486	179	35	somewhere	somewhere	ADV
ejpam-5486	179	36	dense	dense	ADJ
ejpam-5486	179	37	of	of	ADP
ejpam-5486	179	38	a	a	DET
ejpam-5486	179	39	topological	topological	ADJ
ejpam-5486	179	40	space	space	NOUN
ejpam-5486	179	41	(	(	PUNCT
ejpam-5486	179	42	z	z	NOUN
ejpam-5486	179	43	,	,	PUNCT
ejpam-5486	179	44	τ	τ	PROPN
ejpam-5486	179	45	)	)	PUNCT
ejpam-5486	179	46	.	.	PUNCT
ejpam-5486	180	1	then	then	ADV
ejpam-5486	180	2	we	we	PRON
ejpam-5486	180	3	discuss	discuss	VERB
ejpam-5486	180	4	the	the	DET
ejpam-5486	180	5	sufficient	sufficient	ADJ
ejpam-5486	180	6	conditions	condition	NOUN
ejpam-5486	180	7	for	for	ADP
ejpam-5486	180	8	the	the	DET
ejpam-5486	180	9	equivalence	equivalence	NOUN
ejpam-5486	180	10	between	between	ADP
ejpam-5486	180	11	the	the	DET
ejpam-5486	180	12	classes	class	NOUN
ejpam-5486	180	13	swd(z	swd(z	PROPN
ejpam-5486	180	14	,	,	PUNCT
ejpam-5486	180	15	τ	τ	PROPN
ejpam-5486	180	16	)	)	PUNCT
ejpam-5486	180	17	,	,	PUNCT
ejpam-5486	180	18	ωswd(z	ωswd(z	PROPN
ejpam-5486	180	19	,	,	PUNCT
ejpam-5486	180	20	τ	τ	PROPN
ejpam-5486	180	21	)	)	PUNCT
ejpam-5486	180	22	and	and	CCONJ
ejpam-5486	180	23	ωswd(z	ωswd(z	PROPN
ejpam-5486	180	24	,	,	PUNCT
ejpam-5486	180	25	τω	τω	INTJ
ejpam-5486	180	26	)	)	PUNCT
ejpam-5486	180	27	.	.	PUNCT
ejpam-5486	181	1	also	also	ADV
ejpam-5486	181	2	,	,	PUNCT
ejpam-5486	181	3	we	we	PRON
ejpam-5486	181	4	study	study	VERB
ejpam-5486	181	5	some	some	DET
ejpam-5486	181	6	applications	application	NOUN
ejpam-5486	181	7	by	by	ADP
ejpam-5486	181	8	using	use	VERB
ejpam-5486	181	9	ωswd(z	ωswd(z	PROPN
ejpam-5486	181	10	,	,	PUNCT
ejpam-5486	181	11	τ	τ	PROPN
ejpam-5486	181	12	)	)	PUNCT
ejpam-5486	181	13	.	.	PUNCT
ejpam-5486	182	1	definition	definition	NOUN
ejpam-5486	182	2	6	6	NUM
ejpam-5486	182	3	.	.	PUNCT
ejpam-5486	183	1	let	let	AUX
ejpam-5486	183	2	(	(	PUNCT
ejpam-5486	183	3	z	z	NOUN
ejpam-5486	183	4	,	,	PUNCT
ejpam-5486	183	5	τ	τ	PROPN
ejpam-5486	183	6	)	)	PUNCT
ejpam-5486	183	7	be	be	VERB
ejpam-5486	183	8	a	a	DET
ejpam-5486	183	9	t	t	NOUN
ejpam-5486	183	10	s	s	NOUN
ejpam-5486	183	11	with	with	ADP
ejpam-5486	183	12	h	h	PROPN
ejpam-5486	183	13	⊆	⊆	NUM
ejpam-5486	183	14	z.	z.	NOUN
ejpam-5486	183	15	a	a	DET
ejpam-5486	183	16	point	point	NOUN
ejpam-5486	183	17	x	x	X
ejpam-5486	183	18	∈	∈	PROPN
ejpam-5486	183	19	z	z	NOUN
ejpam-5486	183	20	is	be	AUX
ejpam-5486	183	21	an	an	DET
ejpam-5486	183	22	ωswd−condensation	ωswd−condensation	NOUN
ejpam-5486	183	23	point	point	NOUN
ejpam-5486	183	24	of	of	ADP
ejpam-5486	183	25	h	h	NOUN
ejpam-5486	183	26	if	if	SCONJ
ejpam-5486	183	27	for	for	ADP
ejpam-5486	183	28	each	each	DET
ejpam-5486	183	29	s	s	PROPN
ejpam-5486	183	30	∈	∈	PROPN
ejpam-5486	183	31	swd(z	swd(z	PROPN
ejpam-5486	183	32	,	,	PUNCT
ejpam-5486	183	33	τ	τ	PROPN
ejpam-5486	183	34	)	)	PUNCT
ejpam-5486	183	35	with	with	ADP
ejpam-5486	183	36	x	x	PUNCT
ejpam-5486	183	37	∈	∈	PROPN
ejpam-5486	183	38	s	s	PROPN
ejpam-5486	183	39	,	,	PUNCT
ejpam-5486	183	40	the	the	DET
ejpam-5486	183	41	set	set	NOUN
ejpam-5486	183	42	s	s	PART
ejpam-5486	183	43	∩	∩	ADJ
ejpam-5486	183	44	h	h	NOUN
ejpam-5486	183	45	is	be	AUX
ejpam-5486	183	46	uncountable	uncountable	ADJ
ejpam-5486	183	47	.	.	PUNCT
ejpam-5486	184	1	if	if	SCONJ
ejpam-5486	184	2	h	h	NOUN
ejpam-5486	184	3	contains	contain	VERB
ejpam-5486	184	4	all	all	DET
ejpam-5486	184	5	its	its	PRON
ejpam-5486	184	6	ωswd−condensation	ωswd−condensation	NOUN
ejpam-5486	184	7	points	point	NOUN
ejpam-5486	184	8	,	,	PUNCT
ejpam-5486	184	9	then	then	ADV
ejpam-5486	184	10	h	h	NOUN
ejpam-5486	184	11	is	be	AUX
ejpam-5486	184	12	said	say	VERB
ejpam-5486	184	13	to	to	PART
ejpam-5486	184	14	be	be	AUX
ejpam-5486	184	15	ωswd	ωswd	ADJ
ejpam-5486	184	16	-	-	PUNCT
ejpam-5486	184	17	closed	closed	ADJ
ejpam-5486	184	18	subset	subset	NOUN
ejpam-5486	184	19	of	of	ADP
ejpam-5486	184	20	(	(	PUNCT
ejpam-5486	184	21	z	z	PROPN
ejpam-5486	184	22	,	,	PUNCT
ejpam-5486	184	23	τ	τ	PROPN
ejpam-5486	184	24	)	)	PUNCT
ejpam-5486	184	25	and	and	CCONJ
ejpam-5486	184	26	its	its	PRON
ejpam-5486	184	27	complement	complement	NOUN
ejpam-5486	184	28	is	be	AUX
ejpam-5486	184	29	an	an	DET
ejpam-5486	184	30	ωswd	ωswd	ADJ
ejpam-5486	184	31	-	-	PUNCT
ejpam-5486	184	32	open	open	ADJ
ejpam-5486	184	33	subset	subset	NOUN
ejpam-5486	184	34	of	of	ADP
ejpam-5486	184	35	(	(	PUNCT
ejpam-5486	184	36	z	z	PROPN
ejpam-5486	184	37	,	,	PUNCT
ejpam-5486	184	38	τ	τ	PROPN
ejpam-5486	184	39	)	)	PUNCT
ejpam-5486	184	40	.	.	PUNCT
ejpam-5486	185	1	the	the	DET
ejpam-5486	185	2	collection	collection	NOUN
ejpam-5486	185	3	of	of	ADP
ejpam-5486	185	4	all	all	DET
ejpam-5486	185	5	ωswd	ωswd	ADV
ejpam-5486	185	6	-	-	PUNCT
ejpam-5486	185	7	closed	closed	ADJ
ejpam-5486	185	8	(	(	PUNCT
ejpam-5486	185	9	resp	resp	NOUN
ejpam-5486	185	10	.	.	PUNCT
ejpam-5486	185	11	,	,	PUNCT
ejpam-5486	185	12	ωswd	ωswd	ADV
ejpam-5486	185	13	-	-	PUNCT
ejpam-5486	185	14	open	open	ADJ
ejpam-5486	185	15	)	)	PUNCT
ejpam-5486	185	16	subsets	subset	NOUN
ejpam-5486	185	17	of	of	ADP
ejpam-5486	185	18	(	(	PUNCT
ejpam-5486	185	19	z	z	PROPN
ejpam-5486	185	20	,	,	PUNCT
ejpam-5486	185	21	τ	τ	X
ejpam-5486	185	22	)	)	PUNCT
ejpam-5486	185	23	will	will	AUX
ejpam-5486	185	24	be	be	AUX
ejpam-5486	185	25	denoted	denote	VERB
ejpam-5486	185	26	by	by	ADP
ejpam-5486	185	27	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	185	28	,	,	PUNCT
ejpam-5486	185	29	τ	τ	PROPN
ejpam-5486	185	30	)	)	PUNCT
ejpam-5486	185	31	(	(	PUNCT
ejpam-5486	185	32	resp	resp	NOUN
ejpam-5486	185	33	.	.	PUNCT
ejpam-5486	185	34	,	,	PUNCT
ejpam-5486	186	1	ωswd(z	ωswd(z	PROPN
ejpam-5486	186	2	,	,	PUNCT
ejpam-5486	186	3	τ	τ	PROPN
ejpam-5486	186	4	)	)	PUNCT
ejpam-5486	186	5	)	)	PUNCT
ejpam-5486	186	6	.	.	PUNCT
ejpam-5486	187	1	the	the	DET
ejpam-5486	187	2	proofs	proof	NOUN
ejpam-5486	187	3	of	of	ADP
ejpam-5486	187	4	the	the	DET
ejpam-5486	187	5	following	following	ADJ
ejpam-5486	187	6	results	result	NOUN
ejpam-5486	187	7	are	be	AUX
ejpam-5486	187	8	straightforward	straightforward	ADJ
ejpam-5486	187	9	and	and	CCONJ
ejpam-5486	187	10	thus	thus	ADV
ejpam-5486	187	11	are	be	AUX
ejpam-5486	187	12	omitted	omit	VERB
ejpam-5486	187	13	.	.	PUNCT
ejpam-5486	188	1	proposition	proposition	NOUN
ejpam-5486	188	2	2	2	NUM
ejpam-5486	188	3	.	.	PUNCT
ejpam-5486	189	1	let	let	AUX
ejpam-5486	189	2	(	(	PUNCT
ejpam-5486	189	3	z	z	NOUN
ejpam-5486	189	4	,	,	PUNCT
ejpam-5486	189	5	τ	τ	PROPN
ejpam-5486	189	6	)	)	PUNCT
ejpam-5486	189	7	be	be	VERB
ejpam-5486	189	8	a	a	DET
ejpam-5486	189	9	t	t	NOUN
ejpam-5486	189	10	s	s	NOUN
ejpam-5486	189	11	with	with	ADP
ejpam-5486	189	12	h	h	PROPN
ejpam-5486	189	13	⊆	⊆	NUM
ejpam-5486	189	14	z.	z.	PROPN
ejpam-5486	189	15	then	then	ADV
ejpam-5486	189	16	h	h	PROPN
ejpam-5486	189	17	∈	∈	PROPN
ejpam-5486	189	18	ωswd(z	ωswd(z	PROPN
ejpam-5486	189	19	,	,	PUNCT
ejpam-5486	189	20	τ	τ	PROPN
ejpam-5486	189	21	)	)	PUNCT
ejpam-5486	189	22	iff	iff	NOUN
ejpam-5486	189	23	for	for	ADP
ejpam-5486	189	24	each	each	DET
ejpam-5486	189	25	x	x	SYM
ejpam-5486	189	26	∈	∈	PROPN
ejpam-5486	189	27	h	h	NOUN
ejpam-5486	189	28	there	there	PRON
ejpam-5486	189	29	is	be	VERB
ejpam-5486	189	30	s	s	PROPN
ejpam-5486	189	31	∈	∈	PROPN
ejpam-5486	189	32	swd(z	swd(z	PROPN
ejpam-5486	189	33	,	,	PUNCT
ejpam-5486	189	34	τ	τ	PROPN
ejpam-5486	189	35	)	)	PUNCT
ejpam-5486	189	36	with	with	ADP
ejpam-5486	189	37	x	x	PUNCT
ejpam-5486	189	38	∈	∈	PROPN
ejpam-5486	189	39	s	s	PART
ejpam-5486	189	40	and	and	CCONJ
ejpam-5486	189	41	s	s	VERB
ejpam-5486	189	42	−h	−h	ADV
ejpam-5486	189	43	is	be	AUX
ejpam-5486	189	44	countable	countable	ADJ
ejpam-5486	189	45	.	.	PUNCT
ejpam-5486	190	1	corollary	corollary	ADJ
ejpam-5486	190	2	2	2	NUM
ejpam-5486	190	3	.	.	PUNCT
ejpam-5486	191	1	let	let	AUX
ejpam-5486	191	2	(	(	PUNCT
ejpam-5486	191	3	z	z	NOUN
ejpam-5486	191	4	,	,	PUNCT
ejpam-5486	191	5	τ	τ	PROPN
ejpam-5486	191	6	)	)	PUNCT
ejpam-5486	191	7	be	be	VERB
ejpam-5486	191	8	a	a	DET
ejpam-5486	191	9	t	t	NOUN
ejpam-5486	191	10	s	s	NOUN
ejpam-5486	191	11	with	with	ADP
ejpam-5486	191	12	h	h	PROPN
ejpam-5486	191	13	⊆	⊆	NUM
ejpam-5486	191	14	z.	z.	PROPN
ejpam-5486	191	15	then	then	ADV
ejpam-5486	191	16	h	h	PROPN
ejpam-5486	191	17	∈	∈	PROPN
ejpam-5486	191	18	ωswd(z	ωswd(z	PROPN
ejpam-5486	191	19	,	,	PUNCT
ejpam-5486	191	20	τ	τ	PROPN
ejpam-5486	191	21	)	)	PUNCT
ejpam-5486	191	22	iff	iff	NOUN
ejpam-5486	191	23	for	for	ADP
ejpam-5486	191	24	each	each	DET
ejpam-5486	191	25	x	x	SYM
ejpam-5486	191	26	∈	∈	PROPN
ejpam-5486	191	27	h	h	NOUN
ejpam-5486	191	28	there	there	PRON
ejpam-5486	191	29	is	be	VERB
ejpam-5486	191	30	s	s	PROPN
ejpam-5486	191	31	∈	∈	PROPN
ejpam-5486	191	32	swd(z	swd(z	PROPN
ejpam-5486	191	33	,	,	PUNCT
ejpam-5486	191	34	τ	τ	X
ejpam-5486	191	35	)	)	PUNCT
ejpam-5486	191	36	and	and	CCONJ
ejpam-5486	191	37	a	a	DET
ejpam-5486	191	38	countable	countable	ADJ
ejpam-5486	191	39	set	set	VERB
ejpam-5486	191	40	g	g	NOUN
ejpam-5486	191	41	with	with	ADP
ejpam-5486	191	42	x	x	PROPN
ejpam-5486	191	43	∈	∈	PROPN
ejpam-5486	191	44	s	s	PART
ejpam-5486	191	45	−g	−g	NOUN
ejpam-5486	191	46	⊆	⊆	NUM
ejpam-5486	191	47	h.	h.	NOUN
ejpam-5486	191	48	theorem	theorem	VERB
ejpam-5486	191	49	8	8	NUM
ejpam-5486	191	50	.	.	PUNCT
ejpam-5486	192	1	let	let	AUX
ejpam-5486	192	2	(	(	PUNCT
ejpam-5486	192	3	z	z	NOUN
ejpam-5486	192	4	,	,	PUNCT
ejpam-5486	192	5	τ	τ	PROPN
ejpam-5486	192	6	)	)	PUNCT
ejpam-5486	192	7	be	be	VERB
ejpam-5486	192	8	a	a	DET
ejpam-5486	192	9	t	t	NOUN
ejpam-5486	192	10	s.then	s.then	X
ejpam-5486	192	11	ωswd(z	ωswd(z	PROPN
ejpam-5486	192	12	,	,	PUNCT
ejpam-5486	192	13	τω	τω	INTJ
ejpam-5486	192	14	)	)	PUNCT
ejpam-5486	192	15	⊆	⊆	NUM
ejpam-5486	192	16	ωswd(z	ωswd(z	PROPN
ejpam-5486	192	17	,	,	PUNCT
ejpam-5486	192	18	τ	τ	PROPN
ejpam-5486	192	19	)	)	PUNCT
ejpam-5486	192	20	.	.	PUNCT
ejpam-5486	193	1	proof	proof	NOUN
ejpam-5486	193	2	.	.	PUNCT
ejpam-5486	194	1	let	let	VERB
ejpam-5486	194	2	h	h	NOUN
ejpam-5486	194	3	∈	∈	PROPN
ejpam-5486	194	4	ωswd(z	ωswd(z	PROPN
ejpam-5486	194	5	,	,	PUNCT
ejpam-5486	194	6	τω	τω	INTJ
ejpam-5486	194	7	)	)	PUNCT
ejpam-5486	194	8	and	and	CCONJ
ejpam-5486	194	9	x	x	PUNCT
ejpam-5486	194	10	∈	∈	PROPN
ejpam-5486	194	11	h.	h.	NOUN
ejpam-5486	194	12	then	then	ADV
ejpam-5486	194	13	there	there	PRON
ejpam-5486	194	14	is	be	VERB
ejpam-5486	194	15	s	s	PROPN
ejpam-5486	194	16	∈	∈	PROPN
ejpam-5486	194	17	swd(z	swd(z	PROPN
ejpam-5486	194	18	,	,	PUNCT
ejpam-5486	194	19	τω	τω	INTJ
ejpam-5486	194	20	)	)	PUNCT
ejpam-5486	194	21	with	with	ADP
ejpam-5486	194	22	x	x	PUNCT
ejpam-5486	194	23	∈	∈	PROPN
ejpam-5486	194	24	s	s	PART
ejpam-5486	194	25	and	and	CCONJ
ejpam-5486	194	26	c	c	NOUN
ejpam-5486	194	27	=	=	SYM
ejpam-5486	194	28	s	s	PART
ejpam-5486	194	29	−	−	NOUN
ejpam-5486	194	30	h	h	NOUN
ejpam-5486	194	31	is	be	AUX
ejpam-5486	194	32	countable	countable	ADJ
ejpam-5486	194	33	.	.	PUNCT
ejpam-5486	195	1	then	then	ADV
ejpam-5486	195	2	there	there	PRON
ejpam-5486	195	3	is	be	VERB
ejpam-5486	195	4	g	g	PROPN
ejpam-5486	195	5	∈	∈	PROPN
ejpam-5486	195	6	τω	τω	INTJ
ejpam-5486	195	7	with	with	ADP
ejpam-5486	195	8	ϕ	ϕ	PROPN
ejpam-5486	195	9	̸=	̸=	PROPN
ejpam-5486	195	10	g	g	ADP
ejpam-5486	195	11	⊆	⊆	NUM
ejpam-5486	195	12	clω(s	clω(s	PROPN
ejpam-5486	195	13	)	)	PUNCT
ejpam-5486	195	14	.	.	PUNCT
ejpam-5486	196	1	a.	a.	PROPN
ejpam-5486	196	2	rawshdeh	rawshdeh	PROPN
ejpam-5486	196	3	,	,	PUNCT
ejpam-5486	196	4	h.	h.	PROPN
ejpam-5486	196	5	h.	h.	PROPN
ejpam-5486	196	6	al	al	PROPN
ejpam-5486	196	7	-	-	PUNCT
ejpam-5486	196	8	jarrah	jarrah	PROPN
ejpam-5486	196	9	,	,	PUNCT
ejpam-5486	196	10	k.	k.	PROPN
ejpam-5486	196	11	y.	y.	PROPN
ejpam-5486	196	12	al	al	PROPN
ejpam-5486	196	13	-	-	PROPN
ejpam-5486	196	14	zoubi	zoubi	PROPN
ejpam-5486	196	15	/	/	SYM
ejpam-5486	196	16	eur	eur	PROPN
ejpam-5486	196	17	.	.	PUNCT
ejpam-5486	197	1	j.	j.	PROPN
ejpam-5486	197	2	pure	pure	PROPN
ejpam-5486	197	3	appl	appl	PROPN
ejpam-5486	197	4	.	.	PROPN
ejpam-5486	197	5	math	math	PROPN
ejpam-5486	197	6	,	,	PUNCT
ejpam-5486	197	7	17	17	NUM
ejpam-5486	197	8	(	(	PUNCT
ejpam-5486	197	9	4	4	NUM
ejpam-5486	197	10	)	)	PUNCT
ejpam-5486	197	11	(	(	PUNCT
ejpam-5486	197	12	2024	2024	NUM
ejpam-5486	197	13	)	)	PUNCT
ejpam-5486	197	14	,	,	PUNCT
ejpam-5486	197	15	3370	3370	NUM
ejpam-5486	197	16	-	-	SYM
ejpam-5486	197	17	3385	3385	NUM
ejpam-5486	197	18	3376	3376	NUM
ejpam-5486	197	19	choose	choose	VERB
ejpam-5486	197	20	t	t	PROPN
ejpam-5486	197	21	∈	∈	PROPN
ejpam-5486	197	22	g.	g.	NOUN
ejpam-5486	198	1	then	then	ADV
ejpam-5486	198	2	,	,	PUNCT
ejpam-5486	198	3	there	there	PRON
ejpam-5486	198	4	is	be	VERB
ejpam-5486	198	5	v	v	ADP
ejpam-5486	198	6	∈	∈	PROPN
ejpam-5486	198	7	τ	τ	X
ejpam-5486	198	8	with	with	ADP
ejpam-5486	198	9	t	t	PROPN
ejpam-5486	198	10	∈	∈	PROPN
ejpam-5486	198	11	v	v	NOUN
ejpam-5486	198	12	and	and	CCONJ
ejpam-5486	198	13	c1	c1	PROPN
ejpam-5486	198	14	=	=	PROPN
ejpam-5486	199	1	v	v	ADP
ejpam-5486	199	2	−	−	PROPN
ejpam-5486	199	3	g	g	PROPN
ejpam-5486	199	4	is	be	AUX
ejpam-5486	199	5	countable	countable	ADJ
ejpam-5486	199	6	.	.	PUNCT
ejpam-5486	200	1	thus	thus	ADV
ejpam-5486	200	2	,	,	PUNCT
ejpam-5486	200	3	v	v	ADP
ejpam-5486	200	4	⊆	⊆	NUM
ejpam-5486	200	5	g	g	NOUN
ejpam-5486	200	6	∪	∪	X
ejpam-5486	200	7	c1	c1	PROPN
ejpam-5486	200	8	⊆	⊆	NUM
ejpam-5486	200	9	clω(s	clω(s	PROPN
ejpam-5486	200	10	)	)	PUNCT
ejpam-5486	200	11	∪	∪	ADP
ejpam-5486	200	12	clω(c1	clω(c1	NOUN
ejpam-5486	200	13	)	)	PUNCT
ejpam-5486	200	14	=	=	SYM
ejpam-5486	200	15	clω(s	clω(s	PROPN
ejpam-5486	200	16	∪	∪	ADJ
ejpam-5486	200	17	c1	c1	NOUN
ejpam-5486	200	18	)	)	PUNCT
ejpam-5486	200	19	⊆	⊆	NUM
ejpam-5486	200	20	cl(s	cl(s	NOUN
ejpam-5486	200	21	∪	∪	NOUN
ejpam-5486	200	22	c1	c1	NOUN
ejpam-5486	200	23	)	)	PUNCT
ejpam-5486	200	24	.	.	PUNCT
ejpam-5486	201	1	therefore	therefore	ADV
ejpam-5486	201	2	,	,	PUNCT
ejpam-5486	201	3	s	s	NOUN
ejpam-5486	201	4	∪	∪	PROPN
ejpam-5486	201	5	c1	c1	PROPN
ejpam-5486	201	6	∈	∈	PROPN
ejpam-5486	201	7	swd(z	swd(z	PROPN
ejpam-5486	201	8	,	,	PUNCT
ejpam-5486	201	9	τ	τ	PROPN
ejpam-5486	201	10	)	)	PUNCT
ejpam-5486	201	11	with	with	ADP
ejpam-5486	201	12	x	x	PUNCT
ejpam-5486	201	13	∈	∈	NOUN
ejpam-5486	201	14	s	s	PART
ejpam-5486	201	15	∪	∪	NOUN
ejpam-5486	201	16	c1	c1	PROPN
ejpam-5486	201	17	and	and	CCONJ
ejpam-5486	201	18	(	(	PUNCT
ejpam-5486	201	19	s	s	PROPN
ejpam-5486	201	20	∪	∪	PROPN
ejpam-5486	201	21	c1	c1	NOUN
ejpam-5486	201	22	)	)	PUNCT
ejpam-5486	201	23	−	−	PROPN
ejpam-5486	201	24	h	h	NOUN
ejpam-5486	201	25	=	=	PUNCT
ejpam-5486	201	26	(	(	PUNCT
ejpam-5486	201	27	s	s	AUX
ejpam-5486	201	28	−	−	PROPN
ejpam-5486	201	29	h	h	NOUN
ejpam-5486	201	30	)	)	PUNCT
ejpam-5486	201	31	∪	∪	NOUN
ejpam-5486	201	32	(	(	PUNCT
ejpam-5486	201	33	c1	c1	NOUN
ejpam-5486	201	34	−	−	PROPN
ejpam-5486	201	35	h	h	PROPN
ejpam-5486	201	36	)	)	PUNCT
ejpam-5486	201	37	is	be	AUX
ejpam-5486	201	38	countable	countable	ADJ
ejpam-5486	201	39	and	and	CCONJ
ejpam-5486	202	1	hence	hence	ADV
ejpam-5486	202	2	h	h	NOUN
ejpam-5486	202	3	∈	∈	PROPN
ejpam-5486	202	4	ωswd(z	ωswd(z	PROPN
ejpam-5486	202	5	,	,	PUNCT
ejpam-5486	202	6	τ	τ	PROPN
ejpam-5486	202	7	)	)	PUNCT
ejpam-5486	202	8	.	.	PUNCT
ejpam-5486	203	1	by	by	ADP
ejpam-5486	203	2	using	use	VERB
ejpam-5486	203	3	definition	definition	NOUN
ejpam-5486	203	4	6	6	NUM
ejpam-5486	203	5	and	and	CCONJ
ejpam-5486	203	6	theorem	theorem	VERB
ejpam-5486	203	7	8	8	NUM
ejpam-5486	203	8	we	we	PRON
ejpam-5486	203	9	generate	generate	VERB
ejpam-5486	203	10	the	the	DET
ejpam-5486	203	11	following	follow	VERB
ejpam-5486	203	12	diagram	diagram	NOUN
ejpam-5486	203	13	where	where	SCONJ
ejpam-5486	203	14	none	none	NOUN
ejpam-5486	203	15	of	of	ADP
ejpam-5486	203	16	these	these	DET
ejpam-5486	203	17	implications	implication	NOUN
ejpam-5486	203	18	being	be	AUX
ejpam-5486	203	19	reversible	reversible	ADJ
ejpam-5486	203	20	.	.	PUNCT
ejpam-5486	204	1	τ	τ	X
ejpam-5486	204	2	→	→	PUNCT
ejpam-5486	204	3	τω	τω	X
ejpam-5486	204	4	↙	↙	PROPN
ejpam-5486	204	5	↘	↘	PROPN
ejpam-5486	204	6	swd(z	swd(z	PROPN
ejpam-5486	204	7	,	,	PUNCT
ejpam-5486	204	8	τ	τ	X
ejpam-5486	204	9	)	)	PUNCT
ejpam-5486	204	10	swd(z	swd(z	PROPN
ejpam-5486	204	11	,	,	PUNCT
ejpam-5486	204	12	τω	τω	INTJ
ejpam-5486	204	13	)	)	PUNCT
ejpam-5486	204	14	↓	↓	NOUN
ejpam-5486	204	15	↓	↓	PROPN
ejpam-5486	204	16	ωswd(z	ωswd(z	PROPN
ejpam-5486	204	17	,	,	PUNCT
ejpam-5486	204	18	τ	τ	PROPN
ejpam-5486	204	19	)	)	PUNCT
ejpam-5486	204	20	←−	←−	PROPN
ejpam-5486	204	21	ωswd(z	ωswd(z	PROPN
ejpam-5486	204	22	,	,	PUNCT
ejpam-5486	204	23	τω	τω	INTJ
ejpam-5486	204	24	)	)	PUNCT
ejpam-5486	204	25	example	example	NOUN
ejpam-5486	204	26	2	2	NUM
ejpam-5486	204	27	.	.	PUNCT
ejpam-5486	204	28	(	(	PUNCT
ejpam-5486	204	29	i	i	NOUN
ejpam-5486	204	30	)	)	PUNCT
ejpam-5486	204	31	consider	consider	VERB
ejpam-5486	204	32	z	z	NOUN
ejpam-5486	204	33	=	=	PUNCT
ejpam-5486	204	34	{	{	PUNCT
ejpam-5486	204	35	1	1	NUM
ejpam-5486	204	36	,	,	PUNCT
ejpam-5486	204	37	2	2	NUM
ejpam-5486	204	38	,	,	PUNCT
ejpam-5486	204	39	3	3	NUM
ejpam-5486	204	40	}	}	PUNCT
ejpam-5486	204	41	with	with	ADP
ejpam-5486	204	42	τ	τ	X
ejpam-5486	204	43	=	=	SYM
ejpam-5486	204	44	{	{	PUNCT
ejpam-5486	204	45	ϕ,z	ϕ,z	NOUN
ejpam-5486	204	46	,	,	PUNCT
ejpam-5486	204	47	{	{	PUNCT
ejpam-5486	204	48	1	1	NUM
ejpam-5486	204	49	,	,	PUNCT
ejpam-5486	204	50	2	2	NUM
ejpam-5486	204	51	}	}	PUNCT
ejpam-5486	204	52	}	}	PUNCT
ejpam-5486	204	53	.	.	PUNCT
ejpam-5486	205	1	then	then	ADV
ejpam-5486	205	2	{	{	PUNCT
ejpam-5486	205	3	3	3	NUM
ejpam-5486	205	4	}	}	PUNCT
ejpam-5486	205	5	∈	∈	PROPN
ejpam-5486	205	6	τω	τω	X
ejpam-5486	205	7	−	−	PROPN
ejpam-5486	205	8	{	{	PUNCT
ejpam-5486	205	9	ϕ	ϕ	NOUN
ejpam-5486	205	10	}	}	PUNCT
ejpam-5486	205	11	⊆	⊆	NUM
ejpam-5486	205	12	swd(z	swd(z	NOUN
ejpam-5486	205	13	,	,	PUNCT
ejpam-5486	205	14	τω	τω	INTJ
ejpam-5486	205	15	)	)	PUNCT
ejpam-5486	205	16	while	while	SCONJ
ejpam-5486	205	17	{	{	PUNCT
ejpam-5486	205	18	3	3	NUM
ejpam-5486	205	19	}	}	PUNCT
ejpam-5486	205	20	/∈	/∈	PUNCT
ejpam-5486	206	1	swd(z	swd(z	PROPN
ejpam-5486	206	2	,	,	PUNCT
ejpam-5486	206	3	τ	τ	PROPN
ejpam-5486	206	4	)	)	PUNCT
ejpam-5486	206	5	.	.	PUNCT
ejpam-5486	207	1	(	(	PUNCT
ejpam-5486	207	2	ii	ii	NOUN
ejpam-5486	207	3	)	)	PUNCT
ejpam-5486	207	4	consider	consider	VERB
ejpam-5486	207	5	(	(	PUNCT
ejpam-5486	207	6	r	r	NOUN
ejpam-5486	207	7	,	,	PUNCT
ejpam-5486	207	8	τu	τu	ADP
ejpam-5486	207	9	)	)	PUNCT
ejpam-5486	207	10	with	with	ADP
ejpam-5486	207	11	h	h	NOUN
ejpam-5486	207	12	=	=	PUNCT
ejpam-5486	207	13	q.	q.	PROPN
ejpam-5486	207	14	then	then	ADV
ejpam-5486	207	15	h	h	PROPN
ejpam-5486	207	16	∈	∈	PROPN
ejpam-5486	207	17	swd(r	swd(r	PROPN
ejpam-5486	207	18	,	,	PUNCT
ejpam-5486	207	19	τu	τu	ADP
ejpam-5486	207	20	)	)	PUNCT
ejpam-5486	208	1	while	while	SCONJ
ejpam-5486	208	2	h	h	PRON
ejpam-5486	208	3	/∈	/∈	PUNCT
ejpam-5486	208	4	swd(r	swd(r	PROPN
ejpam-5486	208	5	,	,	PUNCT
ejpam-5486	208	6	(	(	PUNCT
ejpam-5486	208	7	τu)ω	τu)ω	NOUN
ejpam-5486	208	8	)	)	PUNCT
ejpam-5486	208	9	since	since	SCONJ
ejpam-5486	208	10	intωclω(h	intωclω(h	PROPN
ejpam-5486	208	11	)	)	PUNCT
ejpam-5486	208	12	=	=	SYM
ejpam-5486	208	13	intω(h	intω(h	NOUN
ejpam-5486	208	14	)	)	PUNCT
ejpam-5486	208	15	=	=	SYM
ejpam-5486	208	16	int(h	int(h	X
ejpam-5486	208	17	)	)	PUNCT
ejpam-5486	208	18	=	=	SYM
ejpam-5486	208	19	ϕ.	ϕ.	PROPN
ejpam-5486	208	20	(	(	PUNCT
ejpam-5486	208	21	iii	iii	NOUN
ejpam-5486	208	22	)	)	PUNCT
ejpam-5486	208	23	consider	consider	VERB
ejpam-5486	208	24	(	(	PUNCT
ejpam-5486	208	25	r	r	NOUN
ejpam-5486	208	26	,	,	PUNCT
ejpam-5486	208	27	τcof	τcof	NOUN
ejpam-5486	208	28	)	)	PUNCT
ejpam-5486	208	29	with	with	ADP
ejpam-5486	208	30	h	h	NOUN
ejpam-5486	208	31	=	=	SYM
ejpam-5486	208	32	{	{	PUNCT
ejpam-5486	208	33	1	1	NUM
ejpam-5486	208	34	}	}	PUNCT
ejpam-5486	208	35	.	.	PUNCT
ejpam-5486	209	1	then	then	ADV
ejpam-5486	209	2	h	h	PROPN
ejpam-5486	209	3	∈	∈	PROPN
ejpam-5486	209	4	ωswd(r	ωswd(r	PROPN
ejpam-5486	209	5	,	,	PUNCT
ejpam-5486	209	6	τcof	τcof	NOUN
ejpam-5486	209	7	)	)	PUNCT
ejpam-5486	209	8	while	while	SCONJ
ejpam-5486	209	9	h	h	PRON
ejpam-5486	209	10	/∈	/∈	PUNCT
ejpam-5486	209	11	swd(r	swd(r	PROPN
ejpam-5486	209	12	,	,	PUNCT
ejpam-5486	209	13	τcof	τcof	NOUN
ejpam-5486	209	14	)	)	PUNCT
ejpam-5486	209	15	.	.	PUNCT
ejpam-5486	210	1	(	(	PUNCT
ejpam-5486	210	2	iv	iv	X
ejpam-5486	210	3	)	)	PUNCT
ejpam-5486	210	4	consider	consider	VERB
ejpam-5486	210	5	z	z	NOUN
ejpam-5486	210	6	=	=	SYM
ejpam-5486	210	7	r	r	NOUN
ejpam-5486	210	8	with	with	ADP
ejpam-5486	210	9	τ	τ	X
ejpam-5486	210	10	=	=	SYM
ejpam-5486	210	11	{	{	PUNCT
ejpam-5486	210	12	r	r	NOUN
ejpam-5486	210	13	}	}	PUNCT
ejpam-5486	210	14	∪	∪	NOUN
ejpam-5486	210	15	{	{	PUNCT
ejpam-5486	210	16	g	g	NOUN
ejpam-5486	210	17	⊆	⊆	NUM
ejpam-5486	210	18	r	r	NOUN
ejpam-5486	210	19	:	:	PUNCT
ejpam-5486	210	20	g	g	PROPN
ejpam-5486	210	21	⊆	⊆	NUM
ejpam-5486	210	22	r	r	NOUN
ejpam-5486	210	23	−	−	NOUN
ejpam-5486	210	24	q	q	NOUN
ejpam-5486	210	25	}	}	PUNCT
ejpam-5486	210	26	and	and	CCONJ
ejpam-5486	210	27	h	h	NOUN
ejpam-5486	210	28	=	=	SYM
ejpam-5486	210	29	q.	q.	PROPN
ejpam-5486	211	1	then	then	ADV
ejpam-5486	211	2	h	h	PROPN
ejpam-5486	211	3	∈	∈	PROPN
ejpam-5486	211	4	ωswd(r	ωswd(r	PROPN
ejpam-5486	211	5	,	,	PUNCT
ejpam-5486	211	6	τω	τω	INTJ
ejpam-5486	211	7	)	)	PUNCT
ejpam-5486	212	1	while	while	SCONJ
ejpam-5486	212	2	h	h	PRON
ejpam-5486	212	3	/∈	/∈	PUNCT
ejpam-5486	212	4	swd(r	swd(r	PROPN
ejpam-5486	212	5	,	,	PUNCT
ejpam-5486	212	6	τω).to	τω).to	PUNCT
ejpam-5486	212	7	show	show	VERB
ejpam-5486	212	8	that	that	SCONJ
ejpam-5486	212	9	,	,	PUNCT
ejpam-5486	212	10	h	h	PROPN
ejpam-5486	212	11	∈	∈	PROPN
ejpam-5486	212	12	ωswd(r	ωswd(r	PROPN
ejpam-5486	212	13	,	,	PUNCT
ejpam-5486	212	14	τω	τω	INTJ
ejpam-5486	212	15	)	)	PUNCT
ejpam-5486	212	16	,	,	PUNCT
ejpam-5486	212	17	let	let	VERB
ejpam-5486	212	18	x	x	X
ejpam-5486	212	19	∈	∈	PROPN
ejpam-5486	212	20	h.	h.	PROPN
ejpam-5486	212	21	choose	choose	VERB
ejpam-5486	212	22	r	r	NOUN
ejpam-5486	212	23	∈	∈	NOUN
ejpam-5486	212	24	r	r	NOUN
ejpam-5486	212	25	−	−	NOUN
ejpam-5486	212	26	q.	q.	NOUN
ejpam-5486	212	27	then	then	ADV
ejpam-5486	212	28	g	g	PROPN
ejpam-5486	212	29	=	=	PUNCT
ejpam-5486	212	30	{	{	PUNCT
ejpam-5486	212	31	r	r	NOUN
ejpam-5486	212	32	}	}	PUNCT
ejpam-5486	212	33	∈	∈	PROPN
ejpam-5486	212	34	τ	τ	NOUN
ejpam-5486	212	35	such	such	ADJ
ejpam-5486	212	36	that	that	SCONJ
ejpam-5486	212	37	ϕ	ϕ	PROPN
ejpam-5486	212	38	̸=	̸=	PROPN
ejpam-5486	212	39	g	g	ADP
ejpam-5486	212	40	⊆	⊆	NUM
ejpam-5486	212	41	h	h	NOUN
ejpam-5486	212	42	∪{r	∪{r	NOUN
ejpam-5486	212	43	}	}	PUNCT
ejpam-5486	212	44	⊆	⊆	NUM
ejpam-5486	212	45	clω(h	clω(h	NOUN
ejpam-5486	212	46	∪{r	∪{r	NOUN
ejpam-5486	212	47	}	}	PUNCT
ejpam-5486	212	48	)	)	PUNCT
ejpam-5486	212	49	.	.	PUNCT
ejpam-5486	213	1	so	so	ADV
ejpam-5486	213	2	h	h	NOUN
ejpam-5486	213	3	∪{r	∪{r	ADJ
ejpam-5486	213	4	}	}	PUNCT
ejpam-5486	213	5	∈	∈	PROPN
ejpam-5486	213	6	swd(r	swd(r	PROPN
ejpam-5486	213	7	,	,	PUNCT
ejpam-5486	213	8	τω	τω	INTJ
ejpam-5486	213	9	)	)	PUNCT
ejpam-5486	213	10	with	with	ADP
ejpam-5486	213	11	x	x	PROPN
ejpam-5486	213	12	∈	∈	PROPN
ejpam-5486	213	13	h	h	NOUN
ejpam-5486	213	14	∪{r	∪{r	VERB
ejpam-5486	213	15	}	}	PUNCT
ejpam-5486	213	16	and	and	CCONJ
ejpam-5486	213	17	(	(	PUNCT
ejpam-5486	213	18	h	h	NOUN
ejpam-5486	213	19	∪{r	∪{r	VERB
ejpam-5486	213	20	}	}	PUNCT
ejpam-5486	213	21	)	)	PUNCT
ejpam-5486	214	1	−	−	PROPN
ejpam-5486	214	2	h	h	NOUN
ejpam-5486	214	3	is	be	AUX
ejpam-5486	214	4	countable	countable	ADJ
ejpam-5486	214	5	.	.	PUNCT
ejpam-5486	215	1	therefore	therefore	ADV
ejpam-5486	215	2	,	,	PUNCT
ejpam-5486	215	3	h	h	PROPN
ejpam-5486	215	4	∈	∈	PROPN
ejpam-5486	215	5	ωswd(r	ωswd(r	PROPN
ejpam-5486	215	6	,	,	PUNCT
ejpam-5486	215	7	τω	τω	NOUN
ejpam-5486	215	8	)	)	PUNCT
ejpam-5486	215	9	.	.	PUNCT
ejpam-5486	216	1	(	(	PUNCT
ejpam-5486	216	2	v	v	NOUN
ejpam-5486	216	3	)	)	PUNCT
ejpam-5486	216	4	consider	consider	VERB
ejpam-5486	216	5	(	(	PUNCT
ejpam-5486	216	6	r	r	NOUN
ejpam-5486	216	7	,	,	PUNCT
ejpam-5486	216	8	τind	τind	NOUN
ejpam-5486	216	9	)	)	PUNCT
ejpam-5486	216	10	with	with	ADP
ejpam-5486	216	11	h	h	NOUN
ejpam-5486	216	12	=	=	SYM
ejpam-5486	216	13	{	{	PUNCT
ejpam-5486	216	14	1	1	NUM
ejpam-5486	216	15	}	}	PUNCT
ejpam-5486	216	16	.	.	PUNCT
ejpam-5486	217	1	since	since	SCONJ
ejpam-5486	217	2	ωswd(r	ωswd(r	PROPN
ejpam-5486	217	3	,	,	PUNCT
ejpam-5486	217	4	τind	τind	NOUN
ejpam-5486	217	5	)	)	PUNCT
ejpam-5486	217	6	=	=	SYM
ejpam-5486	217	7	p(r	p(r	PROPN
ejpam-5486	217	8	)	)	PUNCT
ejpam-5486	217	9	,	,	PUNCT
ejpam-5486	217	10	then	then	ADV
ejpam-5486	217	11	{	{	PUNCT
ejpam-5486	217	12	1	1	NUM
ejpam-5486	217	13	}	}	PUNCT
ejpam-5486	217	14	∈	∈	PROPN
ejpam-5486	217	15	ωswd(r	ωswd(r	PROPN
ejpam-5486	217	16	,	,	PUNCT
ejpam-5486	217	17	τind	τind	NOUN
ejpam-5486	217	18	)	)	PUNCT
ejpam-5486	217	19	while	while	SCONJ
ejpam-5486	217	20	{	{	PUNCT
ejpam-5486	217	21	1	1	NUM
ejpam-5486	217	22	}	}	PUNCT
ejpam-5486	217	23	/∈	/∈	PUNCT
ejpam-5486	218	1	ωswd(r	ωswd(r	NOUN
ejpam-5486	218	2	,	,	PUNCT
ejpam-5486	218	3	(	(	PUNCT
ejpam-5486	218	4	τind)ω	τind)ω	PUNCT
ejpam-5486	218	5	)	)	PUNCT
ejpam-5486	218	6	.	.	PUNCT
ejpam-5486	219	1	since	since	SCONJ
ejpam-5486	219	2	if	if	SCONJ
ejpam-5486	219	3	there	there	PRON
ejpam-5486	219	4	is	be	VERB
ejpam-5486	219	5	s	s	PROPN
ejpam-5486	219	6	∈	∈	PROPN
ejpam-5486	219	7	swd(r	swd(r	PROPN
ejpam-5486	219	8	,	,	PUNCT
ejpam-5486	219	9	(	(	PUNCT
ejpam-5486	219	10	τind)ω	τind)ω	X
ejpam-5486	219	11	)	)	PUNCT
ejpam-5486	219	12	with	with	ADP
ejpam-5486	219	13	1	1	NUM
ejpam-5486	219	14	∈	∈	NOUN
ejpam-5486	219	15	s	s	NOUN
ejpam-5486	219	16	and	and	CCONJ
ejpam-5486	219	17	s−{1	s−{1	NOUN
ejpam-5486	219	18	}	}	PUNCT
ejpam-5486	219	19	is	be	AUX
ejpam-5486	219	20	countable	countable	ADJ
ejpam-5486	219	21	,	,	PUNCT
ejpam-5486	219	22	then	then	ADV
ejpam-5486	219	23	s	s	VERB
ejpam-5486	219	24	is	be	AUX
ejpam-5486	219	25	countable	countable	ADJ
ejpam-5486	219	26	and	and	CCONJ
ejpam-5486	219	27	hence	hence	ADV
ejpam-5486	219	28	intωclω(s	intωclω(s	ADP
ejpam-5486	219	29	)	)	PUNCT
ejpam-5486	219	30	=	=	SYM
ejpam-5486	219	31	intω(s	intω(s	NOUN
ejpam-5486	219	32	)	)	PUNCT
ejpam-5486	220	1	=	=	SYM
ejpam-5486	220	2	ϕ.	ϕ.	PROPN
ejpam-5486	220	3	therefore	therefore	ADV
ejpam-5486	220	4	,	,	PUNCT
ejpam-5486	220	5	{	{	PUNCT
ejpam-5486	220	6	1	1	NUM
ejpam-5486	220	7	}	}	PUNCT
ejpam-5486	220	8	/∈	/∈	PUNCT
ejpam-5486	221	1	ωswd(r	ωswd(r	NOUN
ejpam-5486	221	2	,	,	PUNCT
ejpam-5486	221	3	(	(	PUNCT
ejpam-5486	221	4	τind)ω	τind)ω	X
ejpam-5486	221	5	)	)	PUNCT
ejpam-5486	221	6	.	.	PUNCT
ejpam-5486	222	1	theorem	theorem	VERB
ejpam-5486	222	2	9	9	NUM
ejpam-5486	222	3	.	.	PUNCT
ejpam-5486	223	1	let	let	AUX
ejpam-5486	223	2	(	(	PUNCT
ejpam-5486	223	3	z	z	NOUN
ejpam-5486	223	4	,	,	PUNCT
ejpam-5486	223	5	τ	τ	PROPN
ejpam-5486	223	6	)	)	PUNCT
ejpam-5486	223	7	be	be	VERB
ejpam-5486	223	8	a	a	DET
ejpam-5486	223	9	t	t	NOUN
ejpam-5486	223	10	s.	s.	PROPN
ejpam-5486	224	1	if	if	SCONJ
ejpam-5486	224	2	(	(	PUNCT
ejpam-5486	224	3	z	z	NOUN
ejpam-5486	224	4	,	,	PUNCT
ejpam-5486	224	5	τ	τ	X
ejpam-5486	224	6	)	)	PUNCT
ejpam-5486	224	7	is	be	AUX
ejpam-5486	224	8	an	an	DET
ejpam-5486	224	9	anti	anti	ADJ
ejpam-5486	224	10	-	-	ADJ
ejpam-5486	224	11	locally	locally	ADV
ejpam-5486	224	12	countable	countable	ADJ
ejpam-5486	224	13	and	and	CCONJ
ejpam-5486	224	14	τ	τ	PROPN
ejpam-5486	224	15	is	be	AUX
ejpam-5486	224	16	finer	fine	ADJ
ejpam-5486	224	17	than	than	ADP
ejpam-5486	224	18	the	the	DET
ejpam-5486	224	19	cocountable	cocountable	ADJ
ejpam-5486	224	20	topology	topology	NOUN
ejpam-5486	224	21	,	,	PUNCT
ejpam-5486	224	22	then	then	ADV
ejpam-5486	224	23	the	the	DET
ejpam-5486	224	24	following	follow	VERB
ejpam-5486	224	25	families	family	NOUN
ejpam-5486	224	26	are	be	AUX
ejpam-5486	224	27	equivalent	equivalent	ADJ
ejpam-5486	224	28	:	:	PUNCT
ejpam-5486	224	29	(	(	PUNCT
ejpam-5486	224	30	i	i	NOUN
ejpam-5486	224	31	)	)	PUNCT
ejpam-5486	224	32	swd(z	swd(z	PROPN
ejpam-5486	224	33	,	,	PUNCT
ejpam-5486	224	34	τ	τ	PROPN
ejpam-5486	224	35	)	)	PUNCT
ejpam-5486	224	36	.	.	PUNCT
ejpam-5486	225	1	(	(	PUNCT
ejpam-5486	225	2	ii	ii	X
ejpam-5486	225	3	)	)	PUNCT
ejpam-5486	225	4	ωswd(z	ωswd(z	PROPN
ejpam-5486	225	5	,	,	PUNCT
ejpam-5486	225	6	τ	τ	PROPN
ejpam-5486	225	7	)	)	PUNCT
ejpam-5486	225	8	.	.	PUNCT
ejpam-5486	226	1	(	(	PUNCT
ejpam-5486	226	2	iii	iii	X
ejpam-5486	226	3	)	)	PUNCT
ejpam-5486	226	4	ωswd(z	ωswd(z	PROPN
ejpam-5486	226	5	,	,	PUNCT
ejpam-5486	226	6	τω	τω	INTJ
ejpam-5486	226	7	)	)	PUNCT
ejpam-5486	226	8	.	.	PUNCT
ejpam-5486	227	1	proof	proof	NOUN
ejpam-5486	227	2	.	.	PUNCT
ejpam-5486	228	1	(	(	PUNCT
ejpam-5486	228	2	i→	i→	PROPN
ejpam-5486	228	3	ii	ii	PROPN
ejpam-5486	228	4	)	)	PUNCT
ejpam-5486	228	5	trivial	trivial	ADJ
ejpam-5486	228	6	.	.	PUNCT
ejpam-5486	229	1	(	(	PUNCT
ejpam-5486	229	2	ii	ii	X
ejpam-5486	229	3	→	→	SYM
ejpam-5486	229	4	iii	iii	X
ejpam-5486	229	5	)	)	PUNCT
ejpam-5486	229	6	let	let	VERB
ejpam-5486	229	7	h	h	PRON
ejpam-5486	229	8	∈	∈	PROPN
ejpam-5486	229	9	ωswd(z	ωswd(z	PROPN
ejpam-5486	229	10	,	,	PUNCT
ejpam-5486	229	11	τ	τ	PROPN
ejpam-5486	229	12	)	)	PUNCT
ejpam-5486	229	13	and	and	CCONJ
ejpam-5486	229	14	x	x	PUNCT
ejpam-5486	229	15	∈	∈	PROPN
ejpam-5486	229	16	h.	h.	NOUN
ejpam-5486	229	17	then	then	ADV
ejpam-5486	229	18	there	there	PRON
ejpam-5486	229	19	is	be	VERB
ejpam-5486	229	20	s	s	PROPN
ejpam-5486	229	21	∈	∈	PROPN
ejpam-5486	229	22	swd(z	swd(z	PROPN
ejpam-5486	229	23	,	,	PUNCT
ejpam-5486	229	24	τ	τ	PROPN
ejpam-5486	229	25	)	)	PUNCT
ejpam-5486	229	26	with	with	ADP
ejpam-5486	229	27	x	x	PUNCT
ejpam-5486	229	28	∈	∈	PROPN
ejpam-5486	229	29	s	s	PART
ejpam-5486	229	30	and	and	CCONJ
ejpam-5486	229	31	c	c	NOUN
ejpam-5486	229	32	=	=	SYM
ejpam-5486	229	33	s	s	PART
ejpam-5486	229	34	−	−	NOUN
ejpam-5486	229	35	h	h	NOUN
ejpam-5486	229	36	is	be	AUX
ejpam-5486	229	37	countable	countable	ADJ
ejpam-5486	229	38	.	.	PUNCT
ejpam-5486	230	1	hence	hence	ADV
ejpam-5486	230	2	s	s	VERB
ejpam-5486	230	3	⊆	⊆	NUM
ejpam-5486	230	4	h	h	NOUN
ejpam-5486	230	5	∪	∪	ADP
ejpam-5486	230	6	c.	c.	PROPN
ejpam-5486	230	7	now	now	ADV
ejpam-5486	230	8	,	,	PUNCT
ejpam-5486	230	9	choose	choose	VERB
ejpam-5486	230	10	g	g	PROPN
ejpam-5486	230	11	∈	∈	PROPN
ejpam-5486	230	12	τ	τ	PROPN
ejpam-5486	230	13	with	with	ADP
ejpam-5486	230	14	ϕ	ϕ	PROPN
ejpam-5486	230	15	̸=	̸=	PROPN
ejpam-5486	230	16	g	g	PROPN
ejpam-5486	230	17	⊆	⊆	NUM
ejpam-5486	230	18	cl(s	cl(	NOUN
ejpam-5486	230	19	)	)	PUNCT
ejpam-5486	230	20	⊆	⊆	NUM
ejpam-5486	230	21	cl(h	cl(h	X
ejpam-5486	230	22	∪c	∪c	NOUN
ejpam-5486	230	23	)	)	PUNCT
ejpam-5486	230	24	⊆	⊆	NUM
ejpam-5486	230	25	cl(h)∪cl(c	cl(h)∪cl(c	NOUN
ejpam-5486	230	26	)	)	PUNCT
ejpam-5486	230	27	=	=	PUNCT
ejpam-5486	230	28	cl(h)∪c	cl(h)∪c	ADV
ejpam-5486	230	29	(	(	PUNCT
ejpam-5486	230	30	since	since	SCONJ
ejpam-5486	230	31	τcoc	τcoc	PROPN
ejpam-5486	230	32	⊆	⊆	NUM
ejpam-5486	230	33	τ	τ	X
ejpam-5486	230	34	)	)	PUNCT
ejpam-5486	230	35	.	.	PUNCT
ejpam-5486	231	1	since	since	SCONJ
ejpam-5486	231	2	(	(	PUNCT
ejpam-5486	231	3	z	z	PROPN
ejpam-5486	231	4	,	,	PUNCT
ejpam-5486	231	5	τ	τ	X
ejpam-5486	231	6	)	)	PUNCT
ejpam-5486	231	7	is	be	AUX
ejpam-5486	231	8	an	an	DET
ejpam-5486	231	9	anti	anti	ADJ
ejpam-5486	231	10	-	-	ADJ
ejpam-5486	231	11	locally	locally	ADV
ejpam-5486	231	12	countable	countable	ADJ
ejpam-5486	231	13	and	and	CCONJ
ejpam-5486	231	14	ϕ	ϕ	PROPN
ejpam-5486	231	15	̸=	̸=	PROPN
ejpam-5486	231	16	g	g	PROPN
ejpam-5486	231	17	∈	∈	PROPN
ejpam-5486	231	18	τ	τ	X
ejpam-5486	231	19	,	,	PUNCT
ejpam-5486	231	20	then	then	ADV
ejpam-5486	231	21	g−c	g−c	VERB
ejpam-5486	231	22	̸=	̸=	PROPN
ejpam-5486	231	23	ϕ.	ϕ.	NOUN
ejpam-5486	231	24	now	now	ADV
ejpam-5486	231	25	,	,	PUNCT
ejpam-5486	231	26	we	we	PRON
ejpam-5486	231	27	claim	claim	VERB
ejpam-5486	231	28	g−c	g−c	VERB
ejpam-5486	231	29	⊆	⊆	NUM
ejpam-5486	231	30	clω(s	clω(s	PROPN
ejpam-5486	231	31	)	)	PUNCT
ejpam-5486	231	32	.	.	PUNCT
ejpam-5486	232	1	suppose	suppose	VERB
ejpam-5486	232	2	not	not	PART
ejpam-5486	232	3	,	,	PUNCT
ejpam-5486	232	4	then	then	ADV
ejpam-5486	232	5	there	there	PRON
ejpam-5486	232	6	is	be	VERB
ejpam-5486	232	7	t	t	PROPN
ejpam-5486	232	8	∈	∈	PROPN
ejpam-5486	232	9	g	g	PROPN
ejpam-5486	232	10	−	−	PROPN
ejpam-5486	232	11	c	c	PROPN
ejpam-5486	232	12	and	and	CCONJ
ejpam-5486	232	13	t	t	PROPN
ejpam-5486	232	14	/∈	/∈	PUNCT
ejpam-5486	233	1	clω(s	clω(s	PROPN
ejpam-5486	233	2	)	)	PUNCT
ejpam-5486	234	1	and	and	CCONJ
ejpam-5486	234	2	so	so	ADV
ejpam-5486	234	3	there	there	PRON
ejpam-5486	234	4	is	be	VERB
ejpam-5486	234	5	v	v	ADP
ejpam-5486	234	6	∈	∈	NOUN
ejpam-5486	234	7	τω	τω	NOUN
ejpam-5486	234	8	with	with	ADP
ejpam-5486	234	9	t	t	PROPN
ejpam-5486	234	10	∈	∈	PROPN
ejpam-5486	234	11	v	v	ADP
ejpam-5486	234	12	and	and	CCONJ
ejpam-5486	234	13	v	v	ADP
ejpam-5486	234	14	∩	∩	NOUN
ejpam-5486	234	15	s	s	PART
ejpam-5486	234	16	=	=	SYM
ejpam-5486	234	17	ϕ.	ϕ.	PROPN
ejpam-5486	234	18	now	now	ADV
ejpam-5486	234	19	,	,	PUNCT
ejpam-5486	234	20	choose	choose	VERB
ejpam-5486	234	21	,	,	PUNCT
ejpam-5486	234	22	o	o	PROPN
ejpam-5486	234	23	∈	∈	PROPN
ejpam-5486	234	24	τ	τ	X
ejpam-5486	234	25	with	with	ADP
ejpam-5486	234	26	t	t	PROPN
ejpam-5486	234	27	∈	∈	PROPN
ejpam-5486	234	28	o	o	NOUN
ejpam-5486	234	29	and	and	CCONJ
ejpam-5486	234	30	c1	c1	PROPN
ejpam-5486	234	31	=	=	PUNCT
ejpam-5486	235	1	o	o	X
ejpam-5486	236	1	−	−	NOUN
ejpam-5486	236	2	v	v	NOUN
ejpam-5486	236	3	is	be	AUX
ejpam-5486	236	4	countable	countable	ADJ
ejpam-5486	236	5	.	.	PUNCT
ejpam-5486	237	1	then	then	ADV
ejpam-5486	237	2	we	we	PRON
ejpam-5486	237	3	have	have	VERB
ejpam-5486	237	4	t	t	PROPN
ejpam-5486	237	5	∈	∈	PROPN
ejpam-5486	237	6	o−c1	o−c1	PROPN
ejpam-5486	237	7	∈	∈	PROPN
ejpam-5486	237	8	τ	τ	X
ejpam-5486	237	9	with	with	ADP
ejpam-5486	237	10	o−c1	o−c1	PROPN
ejpam-5486	237	11	⊆	⊆	NUM
ejpam-5486	237	12	v	v	NOUN
ejpam-5486	237	13	.	.	PUNCT
ejpam-5486	238	1	finally	finally	ADV
ejpam-5486	238	2	,	,	PUNCT
ejpam-5486	238	3	put	put	VERB
ejpam-5486	238	4	w	w	NOUN
ejpam-5486	238	5	=	=	PUNCT
ejpam-5486	238	6	(	(	PUNCT
ejpam-5486	238	7	g−c)∩	g−c)∩	PROPN
ejpam-5486	238	8	(	(	PUNCT
ejpam-5486	238	9	o−c1	o−c1	NOUN
ejpam-5486	238	10	)	)	PUNCT
ejpam-5486	238	11	.	.	PUNCT
ejpam-5486	239	1	then	then	ADV
ejpam-5486	239	2	w	w	PROPN
ejpam-5486	239	3	∈	∈	PROPN
ejpam-5486	239	4	τ	τ	PROPN
ejpam-5486	239	5	a.	a.	NOUN
ejpam-5486	239	6	rawshdeh	rawshdeh	PROPN
ejpam-5486	239	7	,	,	PUNCT
ejpam-5486	239	8	h.	h.	PROPN
ejpam-5486	239	9	h.	h.	PROPN
ejpam-5486	239	10	al	al	PROPN
ejpam-5486	239	11	-	-	PUNCT
ejpam-5486	239	12	jarrah	jarrah	PROPN
ejpam-5486	239	13	,	,	PUNCT
ejpam-5486	239	14	k.	k.	PROPN
ejpam-5486	239	15	y.	y.	PROPN
ejpam-5486	239	16	al	al	PROPN
ejpam-5486	239	17	-	-	PROPN
ejpam-5486	239	18	zoubi	zoubi	PROPN
ejpam-5486	239	19	/	/	SYM
ejpam-5486	239	20	eur	eur	PROPN
ejpam-5486	239	21	.	.	PUNCT
ejpam-5486	240	1	j.	j.	PROPN
ejpam-5486	240	2	pure	pure	PROPN
ejpam-5486	240	3	appl	appl	PROPN
ejpam-5486	240	4	.	.	PROPN
ejpam-5486	240	5	math	math	PROPN
ejpam-5486	240	6	,	,	PUNCT
ejpam-5486	240	7	17	17	NUM
ejpam-5486	240	8	(	(	PUNCT
ejpam-5486	240	9	4	4	NUM
ejpam-5486	240	10	)	)	PUNCT
ejpam-5486	240	11	(	(	PUNCT
ejpam-5486	240	12	2024	2024	NUM
ejpam-5486	240	13	)	)	PUNCT
ejpam-5486	240	14	,	,	PUNCT
ejpam-5486	240	15	3370	3370	NUM
ejpam-5486	240	16	-	-	SYM
ejpam-5486	240	17	3385	3385	NUM
ejpam-5486	240	18	3377	3377	NUM
ejpam-5486	240	19	with	with	ADP
ejpam-5486	240	20	t	t	PROPN
ejpam-5486	240	21	∈w	∈w	NOUN
ejpam-5486	240	22	and	and	CCONJ
ejpam-5486	240	23	hence	hence	ADV
ejpam-5486	240	24	w	w	PROPN
ejpam-5486	240	25	∩s	∩s	PROPN
ejpam-5486	240	26	̸=	̸=	PROPN
ejpam-5486	240	27	ϕ.	ϕ.	PROPN
ejpam-5486	240	28	on	on	ADP
ejpam-5486	240	29	the	the	DET
ejpam-5486	240	30	other	other	ADJ
ejpam-5486	240	31	hand	hand	NOUN
ejpam-5486	240	32	,	,	PUNCT
ejpam-5486	240	33	w	w	PROPN
ejpam-5486	240	34	∩s	∩s	PROPN
ejpam-5486	240	35	⊆	⊆	NUM
ejpam-5486	240	36	(	(	PUNCT
ejpam-5486	240	37	o−c1)∩s	o−c1)∩s	PROPN
ejpam-5486	240	38	⊆	⊆	NUM
ejpam-5486	240	39	v	v	ADP
ejpam-5486	240	40	∩s	∩s	PROPN
ejpam-5486	240	41	=	=	SYM
ejpam-5486	240	42	ϕ	ϕ	PROPN
ejpam-5486	240	43	,	,	PUNCT
ejpam-5486	240	44	which	which	PRON
ejpam-5486	240	45	is	be	AUX
ejpam-5486	240	46	a	a	DET
ejpam-5486	240	47	contradiction	contradiction	NOUN
ejpam-5486	240	48	.	.	PUNCT
ejpam-5486	241	1	therefore	therefore	ADV
ejpam-5486	241	2	,	,	PUNCT
ejpam-5486	241	3	s	s	VERB
ejpam-5486	241	4	∈	∈	PROPN
ejpam-5486	241	5	swd(z	swd(z	PROPN
ejpam-5486	241	6	,	,	PUNCT
ejpam-5486	241	7	τω	τω	INTJ
ejpam-5486	241	8	)	)	PUNCT
ejpam-5486	241	9	and	and	CCONJ
ejpam-5486	241	10	hence	hence	ADV
ejpam-5486	241	11	h	h	NOUN
ejpam-5486	241	12	∈	∈	PROPN
ejpam-5486	241	13	ωswd(z	ωswd(z	PROPN
ejpam-5486	241	14	,	,	PUNCT
ejpam-5486	241	15	τω	τω	INTJ
ejpam-5486	241	16	)	)	PUNCT
ejpam-5486	241	17	.	.	PUNCT
ejpam-5486	242	1	(	(	PUNCT
ejpam-5486	242	2	iii	iii	NOUN
ejpam-5486	242	3	)	)	PUNCT
ejpam-5486	242	4	→	→	SYM
ejpam-5486	242	5	(	(	PUNCT
ejpam-5486	242	6	i	i	NOUN
ejpam-5486	242	7	)	)	PUNCT
ejpam-5486	242	8	let	let	VERB
ejpam-5486	242	9	h	h	NOUN
ejpam-5486	242	10	∈	∈	PROPN
ejpam-5486	242	11	ωswd(z	ωswd(z	PROPN
ejpam-5486	242	12	,	,	PUNCT
ejpam-5486	242	13	τω	τω	INTJ
ejpam-5486	242	14	)	)	PUNCT
ejpam-5486	242	15	and	and	CCONJ
ejpam-5486	242	16	x	x	PUNCT
ejpam-5486	242	17	∈	∈	PROPN
ejpam-5486	242	18	h.	h.	NOUN
ejpam-5486	242	19	then	then	ADV
ejpam-5486	242	20	there	there	PRON
ejpam-5486	242	21	is	be	VERB
ejpam-5486	242	22	s	s	PROPN
ejpam-5486	242	23	∈	∈	PROPN
ejpam-5486	242	24	swd(z	swd(z	PROPN
ejpam-5486	242	25	,	,	PUNCT
ejpam-5486	242	26	τω	τω	INTJ
ejpam-5486	242	27	)	)	PUNCT
ejpam-5486	242	28	with	with	ADP
ejpam-5486	242	29	x	x	PUNCT
ejpam-5486	242	30	∈	∈	PROPN
ejpam-5486	242	31	s	s	PART
ejpam-5486	242	32	and	and	CCONJ
ejpam-5486	242	33	c	c	NOUN
ejpam-5486	243	1	=	=	SYM
ejpam-5486	243	2	s	s	VERB
ejpam-5486	243	3	−h	−h	ADJ
ejpam-5486	243	4	is	be	AUX
ejpam-5486	243	5	countable	countable	ADJ
ejpam-5486	243	6	.	.	PUNCT
ejpam-5486	244	1	choose	choose	VERB
ejpam-5486	244	2	g	g	PROPN
ejpam-5486	244	3	∈	∈	PROPN
ejpam-5486	244	4	τω	τω	NOUN
ejpam-5486	244	5	with	with	ADP
ejpam-5486	244	6	t	t	PROPN
ejpam-5486	244	7	∈	∈	PROPN
ejpam-5486	244	8	g	g	PROPN
ejpam-5486	244	9	⊆	⊆	NUM
ejpam-5486	244	10	clω(s	clω(s	PROPN
ejpam-5486	244	11	)	)	PUNCT
ejpam-5486	244	12	⊆	⊆	NUM
ejpam-5486	244	13	clω(h	clω(h	NOUN
ejpam-5486	244	14	∪	∪	ADP
ejpam-5486	244	15	c	c	NOUN
ejpam-5486	244	16	)	)	PUNCT
ejpam-5486	244	17	⊆	⊆	NUM
ejpam-5486	244	18	clω(h	clω(h	NOUN
ejpam-5486	244	19	)	)	PUNCT
ejpam-5486	244	20	∪	∪	ADP
ejpam-5486	244	21	clω(c	clω(c	PROPN
ejpam-5486	244	22	)	)	PUNCT
ejpam-5486	244	23	=	=	SYM
ejpam-5486	244	24	clω(h	clω(h	PROPN
ejpam-5486	244	25	)	)	PUNCT
ejpam-5486	244	26	∪	∪	ADP
ejpam-5486	244	27	c.	c.	PROPN
ejpam-5486	244	28	now	now	ADV
ejpam-5486	244	29	,	,	PUNCT
ejpam-5486	244	30	choose	choose	VERB
ejpam-5486	244	31	o	o	PROPN
ejpam-5486	244	32	∈	∈	PROPN
ejpam-5486	244	33	τ	τ	PROPN
ejpam-5486	244	34	with	with	ADP
ejpam-5486	244	35	t	t	PROPN
ejpam-5486	244	36	∈	∈	PROPN
ejpam-5486	244	37	o	o	NOUN
ejpam-5486	244	38	and	and	CCONJ
ejpam-5486	244	39	o	o	NOUN
ejpam-5486	244	40	−	−	NOUN
ejpam-5486	244	41	g	g	PROPN
ejpam-5486	244	42	=	=	PROPN
ejpam-5486	244	43	c1	c1	PROPN
ejpam-5486	244	44	is	be	AUX
ejpam-5486	244	45	countable	countable	ADJ
ejpam-5486	244	46	.	.	PUNCT
ejpam-5486	245	1	since	since	ADV
ejpam-5486	245	2	,	,	PUNCT
ejpam-5486	245	3	o	o	PROPN
ejpam-5486	245	4	−	−	PROPN
ejpam-5486	245	5	c1	c1	PROPN
ejpam-5486	245	6	⊆	⊆	NUM
ejpam-5486	245	7	g	g	PROPN
ejpam-5486	245	8	⊆	⊆	NUM
ejpam-5486	245	9	clω(h	clω(h	NOUN
ejpam-5486	245	10	)	)	PUNCT
ejpam-5486	245	11	∪	∪	ADP
ejpam-5486	245	12	c	c	NOUN
ejpam-5486	245	13	,	,	PUNCT
ejpam-5486	245	14	then	then	ADV
ejpam-5486	245	15	ϕ	ϕ	PROPN
ejpam-5486	245	16	̸=	̸=	PROPN
ejpam-5486	245	17	(	(	PUNCT
ejpam-5486	245	18	o	o	X
ejpam-5486	245	19	−	−	PROPN
ejpam-5486	245	20	c1)−	c1)−	NOUN
ejpam-5486	245	21	c	c	NOUN
ejpam-5486	245	22	⊆	⊆	NUM
ejpam-5486	245	23	clω(h	clω(h	NOUN
ejpam-5486	245	24	)	)	PUNCT
ejpam-5486	245	25	⊆	⊆	NUM
ejpam-5486	245	26	cl(h	cl(h	NUM
ejpam-5486	245	27	)	)	PUNCT
ejpam-5486	245	28	.	.	PUNCT
ejpam-5486	246	1	therefore	therefore	ADV
ejpam-5486	246	2	,	,	PUNCT
ejpam-5486	246	3	h	h	PROPN
ejpam-5486	246	4	∈	∈	PROPN
ejpam-5486	246	5	swd(z	swd(z	PROPN
ejpam-5486	246	6	,	,	PUNCT
ejpam-5486	246	7	τ	τ	PROPN
ejpam-5486	246	8	)	)	PUNCT
ejpam-5486	246	9	.	.	PUNCT
ejpam-5486	247	1	corollary	corollary	ADJ
ejpam-5486	247	2	3	3	X
ejpam-5486	247	3	.	.	PUNCT
ejpam-5486	248	1	let	let	AUX
ejpam-5486	248	2	(	(	PUNCT
ejpam-5486	248	3	z	z	NOUN
ejpam-5486	248	4	,	,	PUNCT
ejpam-5486	248	5	τ	τ	PROPN
ejpam-5486	248	6	)	)	PUNCT
ejpam-5486	248	7	be	be	VERB
ejpam-5486	248	8	a	a	DET
ejpam-5486	248	9	t	t	NOUN
ejpam-5486	248	10	s.	s.	PROPN
ejpam-5486	249	1	if	if	SCONJ
ejpam-5486	249	2	(	(	PUNCT
ejpam-5486	249	3	z	z	NOUN
ejpam-5486	249	4	,	,	PUNCT
ejpam-5486	249	5	τ	τ	X
ejpam-5486	249	6	)	)	PUNCT
ejpam-5486	249	7	is	be	AUX
ejpam-5486	249	8	an	an	DET
ejpam-5486	249	9	anti	anti	ADJ
ejpam-5486	249	10	-	-	ADJ
ejpam-5486	249	11	locally	locally	ADV
ejpam-5486	249	12	countable	countable	ADJ
ejpam-5486	249	13	,	,	PUNCT
ejpam-5486	249	14	then	then	ADV
ejpam-5486	249	15	:	:	PUNCT
ejpam-5486	249	16	(	(	PUNCT
ejpam-5486	249	17	i	i	NOUN
ejpam-5486	249	18	)	)	PUNCT
ejpam-5486	249	19	swd(z	swd(z	PROPN
ejpam-5486	249	20	,	,	PUNCT
ejpam-5486	249	21	τω	τω	INTJ
ejpam-5486	249	22	)	)	PUNCT
ejpam-5486	249	23	=	=	SYM
ejpam-5486	249	24	ωswd(z	ωswd(z	PROPN
ejpam-5486	249	25	,	,	PUNCT
ejpam-5486	249	26	τω	τω	INTJ
ejpam-5486	249	27	)	)	PUNCT
ejpam-5486	249	28	.	.	PUNCT
ejpam-5486	250	1	(	(	PUNCT
ejpam-5486	250	2	ii	ii	X
ejpam-5486	250	3	)	)	PUNCT
ejpam-5486	250	4	swd(z	swd(z	PROPN
ejpam-5486	250	5	,	,	PUNCT
ejpam-5486	250	6	τ	τ	X
ejpam-5486	250	7	)	)	PUNCT
ejpam-5486	250	8	=	=	SYM
ejpam-5486	250	9	swd(z	swd(z	PROPN
ejpam-5486	250	10	,	,	PUNCT
ejpam-5486	250	11	τω	τω	INTJ
ejpam-5486	250	12	)	)	PUNCT
ejpam-5486	250	13	whenever	whenever	SCONJ
ejpam-5486	250	14	τcoc	τcoc	PROPN
ejpam-5486	250	15	⊆	⊆	X
ejpam-5486	250	16	τ	τ	X
ejpam-5486	250	17	.	.	PUNCT
ejpam-5486	251	1	proof	proof	NOUN
ejpam-5486	251	2	.	.	PUNCT
ejpam-5486	252	1	(	(	PUNCT
ejpam-5486	252	2	i	i	NOUN
ejpam-5486	252	3	)	)	PUNCT
ejpam-5486	252	4	since	since	SCONJ
ejpam-5486	252	5	(	(	PUNCT
ejpam-5486	252	6	z	z	NOUN
ejpam-5486	252	7	,	,	PUNCT
ejpam-5486	252	8	τω	τω	INTJ
ejpam-5486	252	9	)	)	PUNCT
ejpam-5486	252	10	is	be	AUX
ejpam-5486	252	11	anti	anti	X
ejpam-5486	252	12	locally	locally	ADV
ejpam-5486	252	13	countable	countable	ADJ
ejpam-5486	252	14	and	and	CCONJ
ejpam-5486	252	15	τcoc	τcoc	ADJ
ejpam-5486	252	16	⊆	⊆	NUM
ejpam-5486	252	17	τω	τω	ADP
ejpam-5486	252	18	,	,	PUNCT
ejpam-5486	252	19	then	then	ADV
ejpam-5486	252	20	by	by	ADP
ejpam-5486	252	21	theorem	theorem	NOUN
ejpam-5486	252	22	9	9	NUM
ejpam-5486	252	23	,	,	PUNCT
ejpam-5486	252	24	swd(z	swd(z	PROPN
ejpam-5486	252	25	,	,	PUNCT
ejpam-5486	252	26	τω	τω	INTJ
ejpam-5486	252	27	)	)	PUNCT
ejpam-5486	252	28	=	=	SYM
ejpam-5486	253	1	ωswd(z	ωswd(z	PROPN
ejpam-5486	253	2	,	,	PUNCT
ejpam-5486	253	3	τω	τω	INTJ
ejpam-5486	253	4	)	)	PUNCT
ejpam-5486	253	5	.	.	PUNCT
ejpam-5486	254	1	(	(	PUNCT
ejpam-5486	254	2	ii	ii	NOUN
ejpam-5486	254	3	)	)	PUNCT
ejpam-5486	254	4	from	from	ADP
ejpam-5486	254	5	part(i	part(i	PROPN
ejpam-5486	254	6	)	)	PUNCT
ejpam-5486	254	7	and	and	CCONJ
ejpam-5486	254	8	theorem	theorem	VERB
ejpam-5486	254	9	9	9	NUM
ejpam-5486	254	10	.	.	PUNCT
ejpam-5486	254	11	note	note	VERB
ejpam-5486	254	12	that	that	SCONJ
ejpam-5486	254	13	from	from	ADP
ejpam-5486	254	14	example	example	NOUN
ejpam-5486	254	15	2	2	NUM
ejpam-5486	254	16	(	(	PUNCT
ejpam-5486	254	17	part	part	NOUN
ejpam-5486	254	18	iii	iii	NOUN
ejpam-5486	254	19	)	)	PUNCT
ejpam-5486	254	20	imposing	impose	VERB
ejpam-5486	254	21	the	the	DET
ejpam-5486	254	22	condition	condition	NOUN
ejpam-5486	254	23	of	of	ADP
ejpam-5486	254	24	anti	anti	ADJ
ejpam-5486	254	25	locally	locally	ADV
ejpam-5486	254	26	countable	countable	ADJ
ejpam-5486	254	27	on	on	ADP
ejpam-5486	254	28	(	(	PUNCT
ejpam-5486	254	29	z	z	PROPN
ejpam-5486	254	30	,	,	PUNCT
ejpam-5486	254	31	τ	τ	PROPN
ejpam-5486	254	32	)	)	PUNCT
ejpam-5486	254	33	alone	alone	ADV
ejpam-5486	254	34	in	in	ADP
ejpam-5486	254	35	theorem	theorem	NOUN
ejpam-5486	254	36	9	9	NUM
ejpam-5486	254	37	is	be	AUX
ejpam-5486	254	38	not	not	PART
ejpam-5486	254	39	enough	enough	ADJ
ejpam-5486	254	40	and	and	CCONJ
ejpam-5486	254	41	hence	hence	ADV
ejpam-5486	254	42	we	we	PRON
ejpam-5486	254	43	looked	look	VERB
ejpam-5486	254	44	for	for	ADP
ejpam-5486	254	45	another	another	DET
ejpam-5486	254	46	condition	condition	NOUN
ejpam-5486	254	47	on	on	ADP
ejpam-5486	254	48	(	(	PUNCT
ejpam-5486	254	49	z	z	PROPN
ejpam-5486	254	50	,	,	PUNCT
ejpam-5486	254	51	τ	τ	PROPN
ejpam-5486	254	52	)	)	PUNCT
ejpam-5486	254	53	.	.	PUNCT
ejpam-5486	255	1	theorem	theorem	ADJ
ejpam-5486	255	2	10	10	NUM
ejpam-5486	255	3	.	.	PUNCT
ejpam-5486	256	1	let	let	AUX
ejpam-5486	256	2	(	(	PUNCT
ejpam-5486	256	3	z	z	NOUN
ejpam-5486	256	4	,	,	PUNCT
ejpam-5486	256	5	τ	τ	PROPN
ejpam-5486	256	6	)	)	PUNCT
ejpam-5486	256	7	be	be	VERB
ejpam-5486	256	8	a	a	DET
ejpam-5486	256	9	t	t	NOUN
ejpam-5486	256	10	s.	s.	PROPN
ejpam-5486	256	11	then	then	ADV
ejpam-5486	256	12	∪	∪	VERB
ejpam-5486	256	13	α∈∆	α∈∆	PRON
ejpam-5486	256	14	hα	hα	ADP
ejpam-5486	256	15	∈	∈	PROPN
ejpam-5486	256	16	ωswd(z	ωswd(z	PROPN
ejpam-5486	256	17	,	,	PUNCT
ejpam-5486	256	18	τ	τ	PROPN
ejpam-5486	256	19	)	)	PUNCT
ejpam-5486	256	20	whenever	whenever	SCONJ
ejpam-5486	256	21	hα	hα	VERB
ejpam-5486	256	22	⊆	⊆	NUM
ejpam-5486	256	23	z	z	NOUN
ejpam-5486	256	24	and	and	CCONJ
ejpam-5486	256	25	hα	hα	ADP
ejpam-5486	256	26	∈	∈	PROPN
ejpam-5486	256	27	ωswd(z	ωswd(z	PROPN
ejpam-5486	256	28	,	,	PUNCT
ejpam-5486	256	29	τ	τ	PROPN
ejpam-5486	256	30	)	)	PUNCT
ejpam-5486	256	31	for	for	ADP
ejpam-5486	256	32	each	each	DET
ejpam-5486	256	33	α	α	NOUN
ejpam-5486	256	34	∈	∈	PROPN
ejpam-5486	257	1	∆.	∆.	ADJ
ejpam-5486	257	2	proof	proof	NOUN
ejpam-5486	257	3	.	.	PUNCT
ejpam-5486	258	1	if	if	SCONJ
ejpam-5486	258	2	∪	∪	ADP
ejpam-5486	258	3	α∈∆	α∈∆	PRON
ejpam-5486	258	4	hα	hα	ADP
ejpam-5486	258	5	=	=	NOUN
ejpam-5486	258	6	ϕ	ϕ	PROPN
ejpam-5486	258	7	,	,	PUNCT
ejpam-5486	258	8	then	then	ADV
ejpam-5486	258	9	∪	∪	ADJ
ejpam-5486	258	10	α∈∆	α∈∆	PRON
ejpam-5486	258	11	hα	hα	ADP
ejpam-5486	258	12	∈	∈	PROPN
ejpam-5486	258	13	ωswd(z	ωswd(z	PROPN
ejpam-5486	258	14	,	,	PUNCT
ejpam-5486	258	15	τ	τ	PROPN
ejpam-5486	258	16	)	)	PUNCT
ejpam-5486	258	17	.	.	PUNCT
ejpam-5486	259	1	now	now	ADV
ejpam-5486	259	2	,	,	PUNCT
ejpam-5486	259	3	let	let	VERB
ejpam-5486	259	4	x	x	PUNCT
ejpam-5486	259	5	∈	∈	PROPN
ejpam-5486	259	6	∪	∪	ADP
ejpam-5486	259	7	α∈∆	α∈∆	PROPN
ejpam-5486	259	8	hα	hα	NOUN
ejpam-5486	259	9	.	.	PUNCT
ejpam-5486	260	1	then	then	ADV
ejpam-5486	260	2	there	there	PRON
ejpam-5486	260	3	is	be	VERB
ejpam-5486	260	4	α(x	α(x	NOUN
ejpam-5486	260	5	)	)	PUNCT
ejpam-5486	260	6	∈	∈	PROPN
ejpam-5486	260	7	∆	∆	PROPN
ejpam-5486	260	8	such	such	ADJ
ejpam-5486	260	9	that	that	SCONJ
ejpam-5486	260	10	x	x	SYM
ejpam-5486	260	11	∈	∈	NOUN
ejpam-5486	260	12	hα(x	hα(x	ADV
ejpam-5486	260	13	)	)	PUNCT
ejpam-5486	260	14	and	and	CCONJ
ejpam-5486	260	15	hence	hence	ADV
ejpam-5486	260	16	there	there	PRON
ejpam-5486	260	17	is	be	VERB
ejpam-5486	260	18	s	s	PROPN
ejpam-5486	260	19	∈	∈	PROPN
ejpam-5486	260	20	swd(z	swd(z	PROPN
ejpam-5486	260	21	,	,	PUNCT
ejpam-5486	260	22	τ	τ	PROPN
ejpam-5486	260	23	)	)	PUNCT
ejpam-5486	260	24	with	with	ADP
ejpam-5486	260	25	x	x	PUNCT
ejpam-5486	260	26	∈	∈	PROPN
ejpam-5486	260	27	s	s	X
ejpam-5486	260	28	and	and	CCONJ
ejpam-5486	260	29	s	s	NOUN
ejpam-5486	260	30	−	−	NOUN
ejpam-5486	260	31	hα(x	hα(x	PUNCT
ejpam-5486	260	32	)	)	PUNCT
ejpam-5486	260	33	is	be	AUX
ejpam-5486	260	34	countable	countable	ADJ
ejpam-5486	260	35	.	.	PUNCT
ejpam-5486	261	1	since	since	SCONJ
ejpam-5486	261	2	s	s	PRON
ejpam-5486	261	3	−	−	PROPN
ejpam-5486	261	4	∪	∪	ADP
ejpam-5486	261	5	α∈∆	α∈∆	PRON
ejpam-5486	261	6	hα	hα	ADP
ejpam-5486	261	7	⊆	⊆	NUM
ejpam-5486	261	8	s	s	PART
ejpam-5486	261	9	−	−	NOUN
ejpam-5486	261	10	hα(x	hα(x	PUNCT
ejpam-5486	261	11	)	)	PUNCT
ejpam-5486	261	12	,	,	PUNCT
ejpam-5486	261	13	then	then	ADV
ejpam-5486	261	14	s	s	VERB
ejpam-5486	261	15	−	−	NOUN
ejpam-5486	261	16	∪	∪	ADP
ejpam-5486	261	17	α∈∆	α∈∆	PRON
ejpam-5486	261	18	hα	hα	NOUN
ejpam-5486	261	19	is	be	AUX
ejpam-5486	261	20	countable	countable	ADJ
ejpam-5486	261	21	.	.	PUNCT
ejpam-5486	262	1	therefore	therefore	ADV
ejpam-5486	262	2	,	,	PUNCT
ejpam-5486	262	3	∪	∪	ADP
ejpam-5486	262	4	α∈∆	α∈∆	PRON
ejpam-5486	262	5	hα	hα	ADP
ejpam-5486	262	6	∈	∈	PROPN
ejpam-5486	262	7	ωswd(z	ωswd(z	PROPN
ejpam-5486	262	8	,	,	PUNCT
ejpam-5486	262	9	τ	τ	PROPN
ejpam-5486	262	10	)	)	PUNCT
ejpam-5486	262	11	.	.	PUNCT
ejpam-5486	263	1	corollary	corollary	ADJ
ejpam-5486	263	2	4	4	NUM
ejpam-5486	263	3	.	.	PUNCT
ejpam-5486	264	1	let	let	AUX
ejpam-5486	264	2	(	(	PUNCT
ejpam-5486	264	3	z	z	NOUN
ejpam-5486	264	4	,	,	PUNCT
ejpam-5486	264	5	τ	τ	PROPN
ejpam-5486	264	6	)	)	PUNCT
ejpam-5486	264	7	be	be	VERB
ejpam-5486	264	8	a	a	DET
ejpam-5486	264	9	t	t	NOUN
ejpam-5486	264	10	s.then	s.then	NOUN
ejpam-5486	264	11	∩	∩	NOUN
ejpam-5486	264	12	α∈∆	α∈∆	PRON
ejpam-5486	264	13	hα	hα	ADP
ejpam-5486	264	14	∈	∈	PROPN
ejpam-5486	264	15	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	264	16	,	,	PUNCT
ejpam-5486	264	17	τ	τ	PROPN
ejpam-5486	264	18	)	)	PUNCT
ejpam-5486	264	19	whenever	whenever	SCONJ
ejpam-5486	264	20	hα	hα	VERB
ejpam-5486	264	21	⊆	⊆	NUM
ejpam-5486	264	22	z	z	NOUN
ejpam-5486	264	23	and	and	CCONJ
ejpam-5486	264	24	hα	hα	ADP
ejpam-5486	264	25	∈	∈	PROPN
ejpam-5486	264	26	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	264	27	,	,	PUNCT
ejpam-5486	264	28	τ	τ	PROPN
ejpam-5486	264	29	)	)	PUNCT
ejpam-5486	264	30	for	for	ADP
ejpam-5486	264	31	each	each	DET
ejpam-5486	264	32	α	α	NOUN
ejpam-5486	264	33	∈	∈	PROPN
ejpam-5486	265	1	∆.	∆.	ADP
ejpam-5486	265	2	the	the	DET
ejpam-5486	265	3	next	next	ADJ
ejpam-5486	265	4	example	example	NOUN
ejpam-5486	265	5	shows	show	VERB
ejpam-5486	265	6	that	that	SCONJ
ejpam-5486	265	7	the	the	DET
ejpam-5486	265	8	intersection	intersection	NOUN
ejpam-5486	265	9	of	of	ADP
ejpam-5486	265	10	two	two	NUM
ejpam-5486	265	11	ωswd	ωswd	ADJ
ejpam-5486	265	12	-	-	PUNCT
ejpam-5486	265	13	open	open	ADJ
ejpam-5486	265	14	subsets	subset	NOUN
ejpam-5486	265	15	of	of	ADP
ejpam-5486	265	16	(	(	PUNCT
ejpam-5486	265	17	z	z	PROPN
ejpam-5486	265	18	,	,	PUNCT
ejpam-5486	265	19	τ	τ	X
ejpam-5486	265	20	)	)	PUNCT
ejpam-5486	265	21	is	be	AUX
ejpam-5486	265	22	not	not	PART
ejpam-5486	265	23	an	an	DET
ejpam-5486	265	24	ωswd	ωswd	ADV
ejpam-5486	265	25	-	-	PUNCT
ejpam-5486	265	26	open	open	ADJ
ejpam-5486	265	27	in	in	ADP
ejpam-5486	265	28	general	general	ADJ
ejpam-5486	265	29	and	and	CCONJ
ejpam-5486	265	30	hence	hence	ADV
ejpam-5486	265	31	we	we	PRON
ejpam-5486	265	32	can	can	AUX
ejpam-5486	265	33	conclude	conclude	VERB
ejpam-5486	265	34	for	for	ADP
ejpam-5486	265	35	any	any	DET
ejpam-5486	265	36	topology	topology	NOUN
ejpam-5486	265	37	τ	τ	PROPN
ejpam-5486	265	38	on	on	ADP
ejpam-5486	265	39	z	z	PROPN
ejpam-5486	265	40	,	,	PUNCT
ejpam-5486	265	41	ωswd(z	ωswd(z	PROPN
ejpam-5486	265	42	,	,	PUNCT
ejpam-5486	265	43	τ	τ	PROPN
ejpam-5486	265	44	)	)	PUNCT
ejpam-5486	265	45	may	may	AUX
ejpam-5486	265	46	not	not	PART
ejpam-5486	265	47	be	be	AUX
ejpam-5486	265	48	a	a	DET
ejpam-5486	265	49	topology	topology	NOUN
ejpam-5486	265	50	on	on	ADP
ejpam-5486	265	51	z.	z.	PROPN
ejpam-5486	265	52	example	example	NOUN
ejpam-5486	265	53	3	3	X
ejpam-5486	265	54	.	.	X
ejpam-5486	265	55	consider	consider	VERB
ejpam-5486	265	56	the	the	DET
ejpam-5486	265	57	space	space	NOUN
ejpam-5486	265	58	(	(	PUNCT
ejpam-5486	265	59	r	r	NOUN
ejpam-5486	265	60	,	,	PUNCT
ejpam-5486	265	61	τcoc	τcoc	PROPN
ejpam-5486	265	62	)	)	PUNCT
ejpam-5486	265	63	.	.	PUNCT
ejpam-5486	266	1	take	take	VERB
ejpam-5486	266	2	h	h	NOUN
ejpam-5486	266	3	=	=	PUNCT
ejpam-5486	267	1	[	[	X
ejpam-5486	267	2	0	0	NUM
ejpam-5486	267	3	,	,	PUNCT
ejpam-5486	267	4	1	1	NUM
ejpam-5486	267	5	]	]	PUNCT
ejpam-5486	267	6	and	and	CCONJ
ejpam-5486	267	7	g	g	NOUN
ejpam-5486	267	8	=	=	SYM
ejpam-5486	268	1	[	[	X
ejpam-5486	268	2	1	1	NUM
ejpam-5486	268	3	,	,	PUNCT
ejpam-5486	268	4	2	2	NUM
ejpam-5486	268	5	]	]	PUNCT
ejpam-5486	268	6	.	.	PUNCT
ejpam-5486	269	1	then	then	ADV
ejpam-5486	269	2	h	h	NOUN
ejpam-5486	269	3	,	,	PUNCT
ejpam-5486	269	4	g	g	PROPN
ejpam-5486	269	5	∈	∈	PROPN
ejpam-5486	269	6	swd(r	swd(r	PROPN
ejpam-5486	269	7	,	,	PUNCT
ejpam-5486	269	8	τcoc	τcoc	ADJ
ejpam-5486	269	9	)	)	PUNCT
ejpam-5486	269	10	⊆ωswd(r	⊆ωswd(r	NOUN
ejpam-5486	269	11	,	,	PUNCT
ejpam-5486	269	12	τcoc	τcoc	PROPN
ejpam-5486	269	13	)	)	PUNCT
ejpam-5486	269	14	,	,	PUNCT
ejpam-5486	269	15	while	while	SCONJ
ejpam-5486	269	16	h	h	PROPN
ejpam-5486	269	17	∩	∩	PROPN
ejpam-5486	269	18	g	g	PROPN
ejpam-5486	269	19	=	=	SYM
ejpam-5486	269	20	{	{	PUNCT
ejpam-5486	269	21	1	1	NUM
ejpam-5486	269	22	}	}	PUNCT
ejpam-5486	269	23	/∈	/∈	PUNCT
ejpam-5486	270	1	ωswd(r	ωswd(r	NOUN
ejpam-5486	270	2	,	,	PUNCT
ejpam-5486	270	3	τcoc	τcoc	PROPN
ejpam-5486	270	4	)	)	PUNCT
ejpam-5486	270	5	,	,	PUNCT
ejpam-5486	270	6	since	since	SCONJ
ejpam-5486	270	7	there	there	PRON
ejpam-5486	270	8	is	be	VERB
ejpam-5486	270	9	no	no	DET
ejpam-5486	270	10	s	s	NOUN
ejpam-5486	270	11	∈	∈	PROPN
ejpam-5486	270	12	swd(r	swd(r	PROPN
ejpam-5486	270	13	,	,	PUNCT
ejpam-5486	270	14	τcoc	τcoc	PROPN
ejpam-5486	270	15	)	)	PUNCT
ejpam-5486	270	16	with	with	ADP
ejpam-5486	270	17	1	1	NUM
ejpam-5486	270	18	∈	∈	NOUN
ejpam-5486	270	19	s	s	PART
ejpam-5486	270	20	and	and	CCONJ
ejpam-5486	270	21	s	s	NOUN
ejpam-5486	270	22	−	−	PROPN
ejpam-5486	270	23	{	{	PUNCT
ejpam-5486	270	24	1	1	NUM
ejpam-5486	270	25	}	}	PUNCT
ejpam-5486	270	26	is	be	AUX
ejpam-5486	270	27	countable	countable	ADJ
ejpam-5486	270	28	.	.	PUNCT
ejpam-5486	271	1	proposition	proposition	NOUN
ejpam-5486	271	2	3	3	X
ejpam-5486	271	3	.	.	PUNCT
ejpam-5486	272	1	let	let	AUX
ejpam-5486	272	2	(	(	PUNCT
ejpam-5486	272	3	z	z	NOUN
ejpam-5486	272	4	,	,	PUNCT
ejpam-5486	272	5	τ	τ	PROPN
ejpam-5486	272	6	)	)	PUNCT
ejpam-5486	272	7	be	be	VERB
ejpam-5486	272	8	a	a	DET
ejpam-5486	272	9	t	t	NOUN
ejpam-5486	272	10	s.	s.	PROPN
ejpam-5486	272	11	then	then	ADV
ejpam-5486	272	12	the	the	DET
ejpam-5486	272	13	family	family	NOUN
ejpam-5486	272	14	ωswd(z	ωswd(z	PROPN
ejpam-5486	272	15	,	,	PUNCT
ejpam-5486	272	16	τ	τ	PROPN
ejpam-5486	272	17	)	)	PUNCT
ejpam-5486	272	18	is	be	AUX
ejpam-5486	272	19	a	a	DET
ejpam-5486	272	20	topology	topology	NOUN
ejpam-5486	272	21	on	on	ADP
ejpam-5486	272	22	z	z	NOUN
ejpam-5486	272	23	if	if	SCONJ
ejpam-5486	272	24	one	one	NUM
ejpam-5486	272	25	of	of	ADP
ejpam-5486	272	26	the	the	DET
ejpam-5486	272	27	following	follow	VERB
ejpam-5486	272	28	hold	hold	NOUN
ejpam-5486	272	29	:	:	PUNCT
ejpam-5486	272	30	(	(	PUNCT
ejpam-5486	272	31	i	i	NOUN
ejpam-5486	272	32	)	)	PUNCT
ejpam-5486	272	33	(	(	PUNCT
ejpam-5486	272	34	z	z	X
ejpam-5486	272	35	,	,	PUNCT
ejpam-5486	272	36	τ	τ	X
ejpam-5486	272	37	)	)	PUNCT
ejpam-5486	272	38	is	be	AUX
ejpam-5486	272	39	strongly	strongly	ADV
ejpam-5486	272	40	hyperconnected	hyperconnecte	VERB
ejpam-5486	272	41	.	.	PUNCT
ejpam-5486	273	1	(	(	PUNCT
ejpam-5486	273	2	ii	ii	NOUN
ejpam-5486	273	3	)	)	PUNCT
ejpam-5486	273	4	z	z	PROPN
ejpam-5486	273	5	is	be	AUX
ejpam-5486	273	6	countable	countable	ADJ
ejpam-5486	273	7	or	or	CCONJ
ejpam-5486	273	8	τ	τ	PROPN
ejpam-5486	273	9	is	be	AUX
ejpam-5486	273	10	the	the	DET
ejpam-5486	273	11	indiscrete	indiscrete	ADJ
ejpam-5486	273	12	topology	topology	NOUN
ejpam-5486	273	13	.	.	PUNCT
ejpam-5486	274	1	proof	proof	NOUN
ejpam-5486	274	2	.	.	PUNCT
ejpam-5486	275	1	straightforward	straightforward	ADJ
ejpam-5486	275	2	.	.	PUNCT
ejpam-5486	276	1	a.	a.	PROPN
ejpam-5486	276	2	rawshdeh	rawshdeh	PROPN
ejpam-5486	276	3	,	,	PUNCT
ejpam-5486	276	4	h.	h.	PROPN
ejpam-5486	276	5	h.	h.	PROPN
ejpam-5486	276	6	al	al	PROPN
ejpam-5486	276	7	-	-	PUNCT
ejpam-5486	276	8	jarrah	jarrah	PROPN
ejpam-5486	276	9	,	,	PUNCT
ejpam-5486	276	10	k.	k.	PROPN
ejpam-5486	276	11	y.	y.	PROPN
ejpam-5486	276	12	al	al	PROPN
ejpam-5486	276	13	-	-	PROPN
ejpam-5486	276	14	zoubi	zoubi	PROPN
ejpam-5486	276	15	/	/	SYM
ejpam-5486	276	16	eur	eur	PROPN
ejpam-5486	276	17	.	.	PUNCT
ejpam-5486	277	1	j.	j.	PROPN
ejpam-5486	277	2	pure	pure	PROPN
ejpam-5486	277	3	appl	appl	PROPN
ejpam-5486	277	4	.	.	PROPN
ejpam-5486	277	5	math	math	PROPN
ejpam-5486	277	6	,	,	PUNCT
ejpam-5486	277	7	17	17	NUM
ejpam-5486	277	8	(	(	PUNCT
ejpam-5486	277	9	4	4	NUM
ejpam-5486	277	10	)	)	PUNCT
ejpam-5486	277	11	(	(	PUNCT
ejpam-5486	277	12	2024	2024	NUM
ejpam-5486	277	13	)	)	PUNCT
ejpam-5486	277	14	,	,	PUNCT
ejpam-5486	277	15	3370	3370	NUM
ejpam-5486	277	16	-	-	SYM
ejpam-5486	277	17	3385	3385	NUM
ejpam-5486	277	18	3378	3378	NUM
ejpam-5486	277	19	theorem	theorem	VERB
ejpam-5486	277	20	11	11	NUM
ejpam-5486	277	21	.	.	PUNCT
ejpam-5486	278	1	let	let	AUX
ejpam-5486	278	2	(	(	PUNCT
ejpam-5486	278	3	z	z	NOUN
ejpam-5486	278	4	,	,	PUNCT
ejpam-5486	278	5	τ	τ	PROPN
ejpam-5486	278	6	)	)	PUNCT
ejpam-5486	278	7	be	be	VERB
ejpam-5486	278	8	a	a	DET
ejpam-5486	278	9	hyperconnected	hyperconnecte	VERB
ejpam-5486	278	10	t	t	PROPN
ejpam-5486	278	11	s	s	NOUN
ejpam-5486	278	12	and	and	CCONJ
ejpam-5486	278	13	h	h	NOUN
ejpam-5486	278	14	,	,	PUNCT
ejpam-5486	278	15	g	g	PROPN
ejpam-5486	278	16	⊆	⊆	NUM
ejpam-5486	278	17	z.	z.	NOUN
ejpam-5486	279	1	if	if	SCONJ
ejpam-5486	279	2	h	h	NOUN
ejpam-5486	279	3	∈	∈	PROPN
ejpam-5486	279	4	τω	τω	X
ejpam-5486	279	5	and	and	CCONJ
ejpam-5486	279	6	g	g	PROPN
ejpam-5486	279	7	∈	∈	PROPN
ejpam-5486	279	8	ωswd(z	ωswd(z	PROPN
ejpam-5486	279	9	,	,	PUNCT
ejpam-5486	279	10	τ	τ	PROPN
ejpam-5486	279	11	)	)	PUNCT
ejpam-5486	279	12	,	,	PUNCT
ejpam-5486	279	13	then	then	ADV
ejpam-5486	279	14	h	h	NOUN
ejpam-5486	279	15	∩g	∩g	PROPN
ejpam-5486	279	16	∈	∈	PROPN
ejpam-5486	279	17	ωswd(z	ωswd(z	PROPN
ejpam-5486	279	18	,	,	PUNCT
ejpam-5486	279	19	τ	τ	PROPN
ejpam-5486	279	20	)	)	PUNCT
ejpam-5486	279	21	.	.	PUNCT
ejpam-5486	280	1	proof	proof	NOUN
ejpam-5486	280	2	.	.	PUNCT
ejpam-5486	281	1	let	let	VERB
ejpam-5486	281	2	x	x	SYM
ejpam-5486	281	3	∈	∈	NOUN
ejpam-5486	281	4	h	h	NOUN
ejpam-5486	281	5	∩	∩	PROPN
ejpam-5486	281	6	g.	g.	PROPN
ejpam-5486	281	7	then	then	ADV
ejpam-5486	281	8	there	there	PRON
ejpam-5486	281	9	are	be	VERB
ejpam-5486	281	10	v	v	PRON
ejpam-5486	281	11	∈	∈	PROPN
ejpam-5486	281	12	τ	τ	X
ejpam-5486	281	13	with	with	ADP
ejpam-5486	281	14	x	x	PROPN
ejpam-5486	281	15	∈	∈	PROPN
ejpam-5486	281	16	v	v	NOUN
ejpam-5486	281	17	and	and	CCONJ
ejpam-5486	281	18	s	s	NOUN
ejpam-5486	281	19	∈	∈	PROPN
ejpam-5486	281	20	swd(z	swd(z	PROPN
ejpam-5486	281	21	,	,	PUNCT
ejpam-5486	281	22	τ	τ	PROPN
ejpam-5486	281	23	)	)	PUNCT
ejpam-5486	281	24	with	with	ADP
ejpam-5486	281	25	x	x	PUNCT
ejpam-5486	281	26	∈	∈	NOUN
ejpam-5486	281	27	s	s	VERB
ejpam-5486	281	28	such	such	ADJ
ejpam-5486	281	29	that	that	DET
ejpam-5486	281	30	v	v	NOUN
ejpam-5486	281	31	−h	−h	VERB
ejpam-5486	281	32	and	and	CCONJ
ejpam-5486	281	33	s−g	s−g	NOUN
ejpam-5486	281	34	are	be	AUX
ejpam-5486	281	35	countable	countable	ADJ
ejpam-5486	281	36	sets	set	NOUN
ejpam-5486	281	37	.	.	PUNCT
ejpam-5486	282	1	by	by	ADP
ejpam-5486	282	2	theorem1	theorem1	PROPN
ejpam-5486	282	3	,	,	PUNCT
ejpam-5486	282	4	v	v	PROPN
ejpam-5486	282	5	∩s	∩s	PROPN
ejpam-5486	282	6	∈	∈	PROPN
ejpam-5486	282	7	swd(z	swd(z	PROPN
ejpam-5486	282	8	,	,	PUNCT
ejpam-5486	282	9	τ	τ	PROPN
ejpam-5486	282	10	)	)	PUNCT
ejpam-5486	282	11	with	with	ADP
ejpam-5486	282	12	x	x	PROPN
ejpam-5486	282	13	∈	∈	PROPN
ejpam-5486	282	14	v	v	ADP
ejpam-5486	282	15	∩s	∩s	PROPN
ejpam-5486	282	16	and	and	CCONJ
ejpam-5486	282	17	since	since	SCONJ
ejpam-5486	282	18	(	(	PUNCT
ejpam-5486	282	19	v	v	NUM
ejpam-5486	282	20	∩s)−	∩s)−	PRON
ejpam-5486	282	21	(	(	PUNCT
ejpam-5486	282	22	h	h	NOUN
ejpam-5486	282	23	∩g	∩g	PROPN
ejpam-5486	282	24	)	)	PUNCT
ejpam-5486	283	1	⊆	⊆	NUM
ejpam-5486	283	2	(	(	PUNCT
ejpam-5486	283	3	v	v	PROPN
ejpam-5486	283	4	−h)∪	−h)∪	PROPN
ejpam-5486	283	5	(	(	PUNCT
ejpam-5486	283	6	s−g	s−g	PROPN
ejpam-5486	283	7	)	)	PUNCT
ejpam-5486	283	8	,	,	PUNCT
ejpam-5486	283	9	then	then	ADV
ejpam-5486	283	10	(	(	PUNCT
ejpam-5486	283	11	v	v	X
ejpam-5486	283	12	∩s)−	∩s)−	PRON
ejpam-5486	283	13	(	(	PUNCT
ejpam-5486	283	14	h	h	NOUN
ejpam-5486	283	15	∩g	∩g	PROPN
ejpam-5486	283	16	)	)	PUNCT
ejpam-5486	283	17	is	be	AUX
ejpam-5486	283	18	countable	countable	ADJ
ejpam-5486	283	19	.	.	PUNCT
ejpam-5486	284	1	therefore	therefore	ADV
ejpam-5486	284	2	,	,	PUNCT
ejpam-5486	284	3	h	h	NOUN
ejpam-5486	284	4	∩g	∩g	PROPN
ejpam-5486	284	5	∈	∈	PROPN
ejpam-5486	284	6	ωswd(z	ωswd(z	PROPN
ejpam-5486	284	7	,	,	PUNCT
ejpam-5486	284	8	τ	τ	PROPN
ejpam-5486	284	9	)	)	PUNCT
ejpam-5486	284	10	.	.	PUNCT
ejpam-5486	285	1	corollary	corollary	ADJ
ejpam-5486	285	2	5	5	NUM
ejpam-5486	285	3	.	.	PUNCT
ejpam-5486	286	1	let	let	VERB
ejpam-5486	286	2	(	(	PUNCT
ejpam-5486	286	3	z	z	NOUN
ejpam-5486	286	4	,	,	PUNCT
ejpam-5486	286	5	τ	τ	PROPN
ejpam-5486	286	6	)	)	PUNCT
ejpam-5486	286	7	be	be	AUX
ejpam-5486	286	8	hyperconnected	hyperconnecte	VERB
ejpam-5486	286	9	t	t	PROPN
ejpam-5486	286	10	s	s	NOUN
ejpam-5486	286	11	and	and	CCONJ
ejpam-5486	286	12	h	h	NOUN
ejpam-5486	286	13	,	,	PUNCT
ejpam-5486	286	14	g	g	PROPN
ejpam-5486	286	15	⊆	⊆	NUM
ejpam-5486	286	16	z.	z.	NOUN
ejpam-5486	287	1	if	if	SCONJ
ejpam-5486	287	2	z	z	NOUN
ejpam-5486	287	3	−	−	PROPN
ejpam-5486	287	4	h	h	NOUN
ejpam-5486	287	5	∈	∈	PROPN
ejpam-5486	287	6	τω	τω	X
ejpam-5486	287	7	and	and	CCONJ
ejpam-5486	287	8	g	g	PROPN
ejpam-5486	287	9	∈	∈	PROPN
ejpam-5486	287	10	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	287	11	,	,	PUNCT
ejpam-5486	287	12	τ	τ	PROPN
ejpam-5486	287	13	)	)	PUNCT
ejpam-5486	287	14	,	,	PUNCT
ejpam-5486	287	15	then	then	ADV
ejpam-5486	287	16	h	h	NOUN
ejpam-5486	287	17	∪g	∪g	PROPN
ejpam-5486	287	18	∈	∈	PROPN
ejpam-5486	287	19	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	287	20	,	,	PUNCT
ejpam-5486	287	21	τ	τ	PROPN
ejpam-5486	287	22	)	)	PUNCT
ejpam-5486	287	23	.	.	PUNCT
ejpam-5486	288	1	from	from	ADP
ejpam-5486	288	2	example	example	NOUN
ejpam-5486	288	3	3	3	NUM
ejpam-5486	288	4	we	we	PRON
ejpam-5486	288	5	note	note	VERB
ejpam-5486	288	6	that	that	SCONJ
ejpam-5486	288	7	in	in	ADP
ejpam-5486	288	8	theorem	theorem	NOUN
ejpam-5486	288	9	11	11	NUM
ejpam-5486	288	10	is	be	AUX
ejpam-5486	288	11	not	not	PART
ejpam-5486	288	12	enough	enough	ADJ
ejpam-5486	288	13	to	to	PART
ejpam-5486	288	14	be	be	AUX
ejpam-5486	288	15	(	(	PUNCT
ejpam-5486	288	16	z	z	PROPN
ejpam-5486	288	17	,	,	PUNCT
ejpam-5486	288	18	τ	τ	X
ejpam-5486	288	19	)	)	PUNCT
ejpam-5486	288	20	is	be	AUX
ejpam-5486	288	21	hyperconnected	hyperconnecte	VERB
ejpam-5486	288	22	and	and	CCONJ
ejpam-5486	288	23	hence	hence	ADV
ejpam-5486	288	24	we	we	PRON
ejpam-5486	288	25	looked	look	VERB
ejpam-5486	288	26	for	for	ADP
ejpam-5486	288	27	another	another	DET
ejpam-5486	288	28	condition	condition	NOUN
ejpam-5486	288	29	on	on	ADP
ejpam-5486	288	30	the	the	DET
ejpam-5486	288	31	sets	set	NOUN
ejpam-5486	288	32	.	.	PUNCT
ejpam-5486	289	1	also	also	ADV
ejpam-5486	289	2	,	,	PUNCT
ejpam-5486	289	3	note	note	VERB
ejpam-5486	289	4	that	that	SCONJ
ejpam-5486	289	5	this	this	DET
ejpam-5486	289	6	example	example	NOUN
ejpam-5486	289	7	(	(	PUNCT
ejpam-5486	289	8	example	example	NOUN
ejpam-5486	289	9	3	3	NUM
ejpam-5486	289	10	)	)	PUNCT
ejpam-5486	289	11	,	,	PUNCT
ejpam-5486	290	1	q	q	NOUN
ejpam-5486	290	2	∩	∩	NOUN
ejpam-5486	290	3	(	(	PUNCT
ejpam-5486	290	4	r−q	r−q	NOUN
ejpam-5486	290	5	)	)	PUNCT
ejpam-5486	290	6	∈	∈	PROPN
ejpam-5486	290	7	ωswd(r	ωswd(r	PROPN
ejpam-5486	290	8	,	,	PUNCT
ejpam-5486	290	9	τcoc	τcoc	ADJ
ejpam-5486	290	10	)	)	PUNCT
ejpam-5486	290	11	and	and	CCONJ
ejpam-5486	290	12	(	(	PUNCT
ejpam-5486	290	13	r−q	r−q	NOUN
ejpam-5486	290	14	)	)	PUNCT
ejpam-5486	290	15	∈	∈	PROPN
ejpam-5486	290	16	ωswd(r	ωswd(r	PROPN
ejpam-5486	290	17	,	,	PUNCT
ejpam-5486	290	18	τcoc	τcoc	ADJ
ejpam-5486	290	19	)	)	PUNCT
ejpam-5486	290	20	but	but	CCONJ
ejpam-5486	290	21	q	q	NOUN
ejpam-5486	290	22	/∈	/∈	INTJ
ejpam-5486	291	1	τω	τω	INTJ
ejpam-5486	291	2	and	and	CCONJ
ejpam-5486	291	3	hence	hence	ADV
ejpam-5486	291	4	the	the	DET
ejpam-5486	291	5	converse	converse	NOUN
ejpam-5486	291	6	of	of	ADP
ejpam-5486	291	7	theorem	theorem	NOUN
ejpam-5486	291	8	11	11	NUM
ejpam-5486	291	9	is	be	AUX
ejpam-5486	291	10	not	not	PART
ejpam-5486	291	11	true	true	ADJ
ejpam-5486	291	12	in	in	ADP
ejpam-5486	291	13	general	general	ADJ
ejpam-5486	291	14	.	.	PUNCT
ejpam-5486	292	1	theorem	theorem	NOUN
ejpam-5486	292	2	12	12	NUM
ejpam-5486	292	3	.	.	PUNCT
ejpam-5486	293	1	let	let	AUX
ejpam-5486	293	2	(	(	PUNCT
ejpam-5486	293	3	z	z	NOUN
ejpam-5486	293	4	,	,	PUNCT
ejpam-5486	293	5	τ	τ	PROPN
ejpam-5486	293	6	)	)	PUNCT
ejpam-5486	293	7	be	be	VERB
ejpam-5486	293	8	a	a	DET
ejpam-5486	293	9	t	t	NOUN
ejpam-5486	293	10	s	s	PART
ejpam-5486	293	11	and	and	CCONJ
ejpam-5486	293	12	h	h	NOUN
ejpam-5486	293	13	,	,	PUNCT
ejpam-5486	293	14	e	e	PROPN
ejpam-5486	293	15	⊆	⊆	NUM
ejpam-5486	293	16	z.	z.	NOUN
ejpam-5486	293	17	if	if	SCONJ
ejpam-5486	293	18	e	e	PROPN
ejpam-5486	293	19	∈	∈	PROPN
ejpam-5486	293	20	τ	τ	X
ejpam-5486	293	21	and	and	CCONJ
ejpam-5486	293	22	h	h	NOUN
ejpam-5486	293	23	⊆	⊆	NUM
ejpam-5486	293	24	e	e	NOUN
ejpam-5486	293	25	,	,	PUNCT
ejpam-5486	293	26	then	then	ADV
ejpam-5486	293	27	:	:	PUNCT
ejpam-5486	293	28	(	(	PUNCT
ejpam-5486	293	29	i	i	NOUN
ejpam-5486	293	30	)	)	PUNCT
ejpam-5486	294	1	if	if	SCONJ
ejpam-5486	294	2	h	h	PROPN
ejpam-5486	294	3	∈	∈	PROPN
ejpam-5486	294	4	ωswd(e	ωswd(e	PROPN
ejpam-5486	294	5	,	,	PUNCT
ejpam-5486	294	6	τe	τe	NOUN
ejpam-5486	294	7	)	)	PUNCT
ejpam-5486	294	8	,	,	PUNCT
ejpam-5486	294	9	then	then	ADV
ejpam-5486	294	10	h	h	PROPN
ejpam-5486	294	11	∈	∈	PROPN
ejpam-5486	294	12	ωswd(z	ωswd(z	PROPN
ejpam-5486	294	13	,	,	PUNCT
ejpam-5486	294	14	τ	τ	PROPN
ejpam-5486	294	15	)	)	PUNCT
ejpam-5486	294	16	.	.	PUNCT
ejpam-5486	295	1	(	(	PUNCT
ejpam-5486	295	2	ii	ii	NOUN
ejpam-5486	295	3	)	)	PUNCT
ejpam-5486	295	4	if	if	SCONJ
ejpam-5486	295	5	h	h	PROPN
ejpam-5486	295	6	∈	∈	PROPN
ejpam-5486	295	7	ωswd(z	ωswd(z	PROPN
ejpam-5486	295	8	,	,	PUNCT
ejpam-5486	295	9	τ	τ	PROPN
ejpam-5486	295	10	)	)	PUNCT
ejpam-5486	295	11	,	,	PUNCT
ejpam-5486	295	12	then	then	ADV
ejpam-5486	295	13	h	h	PROPN
ejpam-5486	295	14	∈	∈	PROPN
ejpam-5486	295	15	ωswd(e	ωswd(e	PROPN
ejpam-5486	295	16	,	,	PUNCT
ejpam-5486	295	17	τe	τe	ADP
ejpam-5486	295	18	)	)	PUNCT
ejpam-5486	295	19	provided	provide	VERB
ejpam-5486	295	20	that	that	SCONJ
ejpam-5486	295	21	e	e	NOUN
ejpam-5486	295	22	is	be	AUX
ejpam-5486	295	23	dense	dense	ADJ
ejpam-5486	295	24	.	.	PUNCT
ejpam-5486	296	1	proof	proof	NOUN
ejpam-5486	296	2	.	.	PUNCT
ejpam-5486	297	1	(	(	PUNCT
ejpam-5486	297	2	i	i	NOUN
ejpam-5486	297	3	)	)	PUNCT
ejpam-5486	297	4	obvious	obvious	ADJ
ejpam-5486	297	5	by	by	ADP
ejpam-5486	297	6	using	use	VERB
ejpam-5486	297	7	theorem	theorem	ADJ
ejpam-5486	297	8	3	3	NUM
ejpam-5486	297	9	(	(	PUNCT
ejpam-5486	297	10	part	part	NOUN
ejpam-5486	297	11	(	(	PUNCT
ejpam-5486	297	12	ii	ii	NOUN
ejpam-5486	297	13	)	)	PUNCT
ejpam-5486	297	14	)	)	PUNCT
ejpam-5486	297	15	.	.	PUNCT
ejpam-5486	298	1	(	(	PUNCT
ejpam-5486	298	2	ii	ii	AUX
ejpam-5486	298	3	)	)	PUNCT
ejpam-5486	298	4	let	let	VERB
ejpam-5486	298	5	x	x	SYM
ejpam-5486	298	6	∈	∈	PROPN
ejpam-5486	298	7	h.	h.	NOUN
ejpam-5486	298	8	then	then	ADV
ejpam-5486	298	9	there	there	PRON
ejpam-5486	298	10	is	be	VERB
ejpam-5486	298	11	s	s	PROPN
ejpam-5486	298	12	∈	∈	PROPN
ejpam-5486	298	13	swd(z	swd(z	PROPN
ejpam-5486	298	14	,	,	PUNCT
ejpam-5486	298	15	τ	τ	PROPN
ejpam-5486	298	16	)	)	PUNCT
ejpam-5486	298	17	with	with	ADP
ejpam-5486	298	18	x	x	PUNCT
ejpam-5486	298	19	∈	∈	PROPN
ejpam-5486	298	20	s	s	X
ejpam-5486	298	21	and	and	CCONJ
ejpam-5486	298	22	s	s	VERB
ejpam-5486	298	23	−	−	PROPN
ejpam-5486	298	24	h	h	NOUN
ejpam-5486	298	25	is	be	AUX
ejpam-5486	298	26	countable	countable	ADJ
ejpam-5486	298	27	.	.	PUNCT
ejpam-5486	299	1	since	since	SCONJ
ejpam-5486	299	2	e	e	PROPN
ejpam-5486	299	3	is	be	AUX
ejpam-5486	299	4	an	an	DET
ejpam-5486	299	5	open	open	ADJ
ejpam-5486	299	6	dense	dense	ADJ
ejpam-5486	299	7	subset	subset	NOUN
ejpam-5486	299	8	,	,	PUNCT
ejpam-5486	299	9	then	then	ADV
ejpam-5486	299	10	for	for	ADP
ejpam-5486	299	11	some	some	DET
ejpam-5486	299	12	g	g	PROPN
ejpam-5486	299	13	∈	∈	PROPN
ejpam-5486	299	14	τ	τ	X
ejpam-5486	299	15	we	we	PRON
ejpam-5486	299	16	can	can	AUX
ejpam-5486	299	17	have	have	VERB
ejpam-5486	299	18	ϕ	ϕ	PROPN
ejpam-5486	299	19	̸=	̸=	PROPN
ejpam-5486	299	20	g∩e	g∩e	NOUN
ejpam-5486	299	21	⊆	⊆	NUM
ejpam-5486	299	22	cl(s)∩e	cl(s)∩e	PROPN
ejpam-5486	299	23	⊆	⊆	NUM
ejpam-5486	299	24	cl(s∩e	cl(s∩e	PROPN
ejpam-5486	299	25	)	)	PUNCT
ejpam-5486	299	26	and	and	CCONJ
ejpam-5486	299	27	hence	hence	ADV
ejpam-5486	299	28	g∩e	g∩e	VERB
ejpam-5486	299	29	⊆	⊆	NUM
ejpam-5486	299	30	cl(s∩e)∩e	cl(s∩e)∩e	NOUN
ejpam-5486	299	31	=	=	PUNCT
ejpam-5486	299	32	cle(s∩e)(the	cle(s∩e)(the	DET
ejpam-5486	299	33	closure	closure	NOUN
ejpam-5486	299	34	of	of	ADP
ejpam-5486	299	35	s∩e	s∩e	NOUN
ejpam-5486	299	36	in	in	ADP
ejpam-5486	299	37	(	(	PUNCT
ejpam-5486	299	38	e	e	NOUN
ejpam-5486	299	39	,	,	PUNCT
ejpam-5486	299	40	τe	τe	NOUN
ejpam-5486	299	41	)	)	PUNCT
ejpam-5486	299	42	)	)	PUNCT
ejpam-5486	299	43	.	.	PUNCT
ejpam-5486	300	1	therefore	therefore	ADV
ejpam-5486	300	2	,	,	PUNCT
ejpam-5486	300	3	s	s	VERB
ejpam-5486	300	4	∩	∩	NOUN
ejpam-5486	300	5	e	e	PROPN
ejpam-5486	300	6	∈	∈	PROPN
ejpam-5486	300	7	swd(e	swd(e	PROPN
ejpam-5486	300	8	,	,	PUNCT
ejpam-5486	300	9	τe	τe	NOUN
ejpam-5486	300	10	)	)	PUNCT
ejpam-5486	300	11	and	and	CCONJ
ejpam-5486	300	12	hence	hence	ADV
ejpam-5486	300	13	h	h	NOUN
ejpam-5486	300	14	∈	∈	PROPN
ejpam-5486	300	15	ωswd(e	ωswd(e	PROPN
ejpam-5486	300	16	,	,	PUNCT
ejpam-5486	300	17	τe	τe	NOUN
ejpam-5486	300	18	)	)	PUNCT
ejpam-5486	300	19	.	.	PUNCT
ejpam-5486	301	1	remark	remark	PROPN
ejpam-5486	301	2	1	1	NUM
ejpam-5486	301	3	.	.	PUNCT
ejpam-5486	302	1	let	let	VERB
ejpam-5486	302	2	(	(	PUNCT
ejpam-5486	302	3	z	z	NOUN
ejpam-5486	302	4	,	,	PUNCT
ejpam-5486	302	5	τ	τ	PROPN
ejpam-5486	302	6	)	)	PUNCT
ejpam-5486	302	7	and	and	CCONJ
ejpam-5486	302	8	(	(	PUNCT
ejpam-5486	302	9	k	k	X
ejpam-5486	302	10	,	,	PUNCT
ejpam-5486	302	11	σ	σ	PROPN
ejpam-5486	302	12	)	)	PUNCT
ejpam-5486	302	13	be	be	VERB
ejpam-5486	302	14	two	two	NUM
ejpam-5486	302	15	t	t	PROPN
ejpam-5486	302	16	ss	ss	PROPN
ejpam-5486	302	17	.	.	PUNCT
ejpam-5486	303	1	then	then	ADV
ejpam-5486	303	2	:	:	PUNCT
ejpam-5486	303	3	(	(	PUNCT
ejpam-5486	303	4	i	i	NOUN
ejpam-5486	303	5	)	)	PUNCT
ejpam-5486	303	6	if	if	SCONJ
ejpam-5486	303	7	ωswd(z	ωswd(z	PROPN
ejpam-5486	303	8	,	,	PUNCT
ejpam-5486	303	9	τ	τ	PROPN
ejpam-5486	303	10	)	)	PUNCT
ejpam-5486	303	11	⊆ωswd(k	⊆ωswd(k	PROPN
ejpam-5486	303	12	,	,	PUNCT
ejpam-5486	303	13	σ	σ	PROPN
ejpam-5486	303	14	)	)	PUNCT
ejpam-5486	303	15	,	,	PUNCT
ejpam-5486	303	16	then	then	ADV
ejpam-5486	303	17	it	it	PRON
ejpam-5486	303	18	is	be	AUX
ejpam-5486	303	19	not	not	PART
ejpam-5486	303	20	true	true	ADJ
ejpam-5486	303	21	in	in	ADP
ejpam-5486	303	22	general	general	ADJ
ejpam-5486	303	23	τ	τ	PROPN
ejpam-5486	303	24	⊆	⊆	PROPN
ejpam-5486	303	25	σ	σ	PROPN
ejpam-5486	303	26	.	.	PUNCT
ejpam-5486	304	1	(	(	PUNCT
ejpam-5486	304	2	ii	ii	NOUN
ejpam-5486	304	3	)	)	PUNCT
ejpam-5486	304	4	if	if	SCONJ
ejpam-5486	304	5	τ	τ	PROPN
ejpam-5486	304	6	⊆	⊆	NUM
ejpam-5486	304	7	σ	σ	NOUN
ejpam-5486	304	8	,	,	PUNCT
ejpam-5486	304	9	then	then	ADV
ejpam-5486	304	10	it	it	PRON
ejpam-5486	304	11	is	be	AUX
ejpam-5486	304	12	not	not	PART
ejpam-5486	304	13	true	true	ADJ
ejpam-5486	304	14	in	in	ADP
ejpam-5486	304	15	general	general	ADJ
ejpam-5486	304	16	ωswd(z	ωswd(z	PROPN
ejpam-5486	304	17	,	,	PUNCT
ejpam-5486	304	18	τ	τ	PROPN
ejpam-5486	304	19	)	)	PUNCT
ejpam-5486	304	20	⊆	⊆	NUM
ejpam-5486	304	21	ωswd(k	ωswd(k	PROPN
ejpam-5486	304	22	,	,	PUNCT
ejpam-5486	304	23	σ	σ	PROPN
ejpam-5486	304	24	)	)	PUNCT
ejpam-5486	304	25	.	.	PUNCT
ejpam-5486	305	1	the	the	DET
ejpam-5486	305	2	following	follow	VERB
ejpam-5486	305	3	example	example	NOUN
ejpam-5486	305	4	illustrates	illustrate	VERB
ejpam-5486	305	5	remark	remark	NOUN
ejpam-5486	305	6	1	1	NUM
ejpam-5486	305	7	.	.	NOUN
ejpam-5486	305	8	example	example	NOUN
ejpam-5486	305	9	4	4	NUM
ejpam-5486	305	10	.	.	PUNCT
ejpam-5486	306	1	(	(	PUNCT
ejpam-5486	306	2	i	i	NOUN
ejpam-5486	306	3	)	)	PUNCT
ejpam-5486	306	4	note	note	VERB
ejpam-5486	306	5	that	that	SCONJ
ejpam-5486	306	6	,	,	PUNCT
ejpam-5486	306	7	ωswd(r	ωswd(r	PROPN
ejpam-5486	306	8	,	,	PUNCT
ejpam-5486	306	9	τcoc	τcoc	ADJ
ejpam-5486	306	10	)	)	PUNCT
ejpam-5486	306	11	⊆ωswd(r	⊆ωswd(r	NOUN
ejpam-5486	306	12	,	,	PUNCT
ejpam-5486	306	13	τind	τind	NOUN
ejpam-5486	306	14	)	)	PUNCT
ejpam-5486	306	15	while	while	SCONJ
ejpam-5486	306	16	τcoc	τcoc	PROPN
ejpam-5486	306	17	⊈	⊈	PROPN
ejpam-5486	306	18	τind	τind	PROPN
ejpam-5486	306	19	.	.	PUNCT
ejpam-5486	307	1	(	(	PUNCT
ejpam-5486	307	2	ii	ii	NOUN
ejpam-5486	307	3	)	)	PUNCT
ejpam-5486	307	4	note	note	VERB
ejpam-5486	307	5	that	that	SCONJ
ejpam-5486	307	6	,	,	PUNCT
ejpam-5486	307	7	τind	τind	VERB
ejpam-5486	307	8	⊆	⊆	NUM
ejpam-5486	307	9	τcoc	τcoc	NOUN
ejpam-5486	307	10	while	while	SCONJ
ejpam-5486	307	11	ωswd(r	ωswd(r	PROPN
ejpam-5486	307	12	,	,	PUNCT
ejpam-5486	307	13	τind	τind	NOUN
ejpam-5486	307	14	)	)	PUNCT
ejpam-5486	307	15	⊈	⊈	PROPN
ejpam-5486	307	16	ωswd(r	ωswd(r	PROPN
ejpam-5486	307	17	,	,	PUNCT
ejpam-5486	307	18	τcoc	τcoc	PROPN
ejpam-5486	307	19	)	)	PUNCT
ejpam-5486	307	20	.	.	PUNCT
ejpam-5486	308	1	theorem	theorem	VERB
ejpam-5486	308	2	13	13	NUM
ejpam-5486	308	3	.	.	PUNCT
ejpam-5486	309	1	let	let	AUX
ejpam-5486	309	2	(	(	PUNCT
ejpam-5486	309	3	z	z	NOUN
ejpam-5486	309	4	,	,	PUNCT
ejpam-5486	309	5	τ	τ	PROPN
ejpam-5486	309	6	)	)	PUNCT
ejpam-5486	309	7	be	be	VERB
ejpam-5486	309	8	a	a	DET
ejpam-5486	309	9	t	t	NOUN
ejpam-5486	309	10	s.	s.	PROPN
ejpam-5486	309	11	then	then	ADV
ejpam-5486	309	12	:	:	PUNCT
ejpam-5486	309	13	(	(	PUNCT
ejpam-5486	309	14	i	i	NOUN
ejpam-5486	309	15	)	)	PUNCT
ejpam-5486	309	16	τ	τ	PROPN
ejpam-5486	309	17	=	=	PUNCT
ejpam-5486	309	18	int(ωswd(z	int(ωswd(z	NOUN
ejpam-5486	309	19	,	,	PUNCT
ejpam-5486	309	20	τ	τ	PROPN
ejpam-5486	309	21	)	)	PUNCT
ejpam-5486	309	22	)	)	PUNCT
ejpam-5486	310	1	=	=	PRON
ejpam-5486	310	2	{	{	PUNCT
ejpam-5486	310	3	int(h	int(h	PROPN
ejpam-5486	310	4	)	)	PUNCT
ejpam-5486	310	5	:	:	PUNCT
ejpam-5486	311	1	h	h	PROPN
ejpam-5486	311	2	∈	∈	PROPN
ejpam-5486	312	1	ωswd(z	ωswd(z	PROPN
ejpam-5486	312	2	,	,	PUNCT
ejpam-5486	312	3	τ	τ	PROPN
ejpam-5486	312	4	)	)	PUNCT
ejpam-5486	312	5	}	}	PUNCT
ejpam-5486	312	6	.	.	PUNCT
ejpam-5486	313	1	(	(	PUNCT
ejpam-5486	313	2	ii	ii	NOUN
ejpam-5486	313	3	)	)	PUNCT
ejpam-5486	313	4	τω	τω	NOUN
ejpam-5486	314	1	=	=	NOUN
ejpam-5486	314	2	intω(ωswd(z	intω(ωswd(z	PROPN
ejpam-5486	314	3	,	,	PUNCT
ejpam-5486	314	4	τ	τ	PROPN
ejpam-5486	314	5	)	)	PUNCT
ejpam-5486	314	6	)	)	PUNCT
ejpam-5486	315	1	=	=	PRON
ejpam-5486	315	2	{	{	PUNCT
ejpam-5486	315	3	intω(h	intω(h	NOUN
ejpam-5486	315	4	)	)	PUNCT
ejpam-5486	315	5	:	:	PUNCT
ejpam-5486	316	1	h	h	PROPN
ejpam-5486	316	2	∈	∈	PROPN
ejpam-5486	317	1	ωswd(z	ωswd(z	PROPN
ejpam-5486	317	2	,	,	PUNCT
ejpam-5486	317	3	τ	τ	PROPN
ejpam-5486	317	4	)	)	PUNCT
ejpam-5486	317	5	}	}	PUNCT
ejpam-5486	317	6	.	.	PUNCT
ejpam-5486	318	1	proof	proof	NOUN
ejpam-5486	318	2	.	.	PUNCT
ejpam-5486	319	1	letg	letg	PROPN
ejpam-5486	319	2	∈	∈	PROPN
ejpam-5486	319	3	τ	τ	X
ejpam-5486	319	4	.	.	PUNCT
ejpam-5486	320	1	theng	theng	PROPN
ejpam-5486	320	2	∈	∈	PROPN
ejpam-5486	320	3	ωswd(z	ωswd(z	PROPN
ejpam-5486	320	4	,	,	PUNCT
ejpam-5486	320	5	τ	τ	PROPN
ejpam-5486	320	6	)	)	PUNCT
ejpam-5486	320	7	and	and	CCONJ
ejpam-5486	320	8	hence	hence	ADV
ejpam-5486	320	9	int(g	int(g	NOUN
ejpam-5486	320	10	)	)	PUNCT
ejpam-5486	320	11	=	=	PUNCT
ejpam-5486	320	12	g	g	PROPN
ejpam-5486	320	13	∈	∈	PROPN
ejpam-5486	320	14	int(ωswd(z	int(ωswd(z	NOUN
ejpam-5486	320	15	,	,	PUNCT
ejpam-5486	320	16	τ	τ	PROPN
ejpam-5486	320	17	)	)	PUNCT
ejpam-5486	320	18	)	)	PUNCT
ejpam-5486	320	19	.	.	PUNCT
ejpam-5486	321	1	conversely	conversely	ADV
ejpam-5486	321	2	,	,	PUNCT
ejpam-5486	321	3	is	be	AUX
ejpam-5486	321	4	obvious	obvious	ADJ
ejpam-5486	321	5	since	since	SCONJ
ejpam-5486	321	6	{	{	PUNCT
ejpam-5486	321	7	int(h	int(h	NOUN
ejpam-5486	321	8	)	)	PUNCT
ejpam-5486	321	9	:	:	PUNCT
ejpam-5486	322	1	h	h	PROPN
ejpam-5486	322	2	∈	∈	PROPN
ejpam-5486	323	1	ωswd(z	ωswd(z	PROPN
ejpam-5486	323	2	,	,	PUNCT
ejpam-5486	323	3	τ	τ	PROPN
ejpam-5486	323	4	)	)	PUNCT
ejpam-5486	323	5	}	}	PUNCT
ejpam-5486	323	6	⊆	⊆	NUM
ejpam-5486	323	7	τ	τ	X
ejpam-5486	323	8	.	.	PUNCT
ejpam-5486	324	1	(	(	PUNCT
ejpam-5486	324	2	ii)the	ii)the	DET
ejpam-5486	324	3	proof	proof	NOUN
ejpam-5486	324	4	is	be	AUX
ejpam-5486	324	5	similar	similar	ADJ
ejpam-5486	324	6	technique	technique	NOUN
ejpam-5486	324	7	in	in	ADP
ejpam-5486	324	8	part	part	NOUN
ejpam-5486	324	9	(	(	PUNCT
ejpam-5486	324	10	i	i	NOUN
ejpam-5486	324	11	)	)	PUNCT
ejpam-5486	324	12	.	.	PUNCT
ejpam-5486	325	1	definition	definition	NOUN
ejpam-5486	325	2	7	7	NUM
ejpam-5486	325	3	.	.	PUNCT
ejpam-5486	326	1	let	let	AUX
ejpam-5486	326	2	(	(	PUNCT
ejpam-5486	326	3	z	z	NOUN
ejpam-5486	326	4	,	,	PUNCT
ejpam-5486	326	5	τ	τ	PROPN
ejpam-5486	326	6	)	)	PUNCT
ejpam-5486	326	7	be	be	VERB
ejpam-5486	326	8	a	a	DET
ejpam-5486	326	9	t	t	NOUN
ejpam-5486	326	10	s	s	NOUN
ejpam-5486	326	11	and	and	CCONJ
ejpam-5486	326	12	h	h	PROPN
ejpam-5486	326	13	⊆	⊆	NUM
ejpam-5486	326	14	z.	z.	PROPN
ejpam-5486	327	1	then	then	ADV
ejpam-5486	327	2	:	:	PUNCT
ejpam-5486	327	3	(	(	PUNCT
ejpam-5486	327	4	i	i	NOUN
ejpam-5486	327	5	)	)	PUNCT
ejpam-5486	327	6	intωswd(h	intωswd(h	PROPN
ejpam-5486	327	7	)	)	PUNCT
ejpam-5486	328	1	=	=	SYM
ejpam-5486	328	2	∪{g	∪{g	PROPN
ejpam-5486	328	3	:	:	PUNCT
ejpam-5486	328	4	g	g	PROPN
ejpam-5486	328	5	⊆	⊆	NUM
ejpam-5486	328	6	h	h	NOUN
ejpam-5486	328	7	and	and	CCONJ
ejpam-5486	328	8	g	g	PROPN
ejpam-5486	328	9	∈	∈	PROPN
ejpam-5486	328	10	ωswd(z	ωswd(z	PROPN
ejpam-5486	328	11	,	,	PUNCT
ejpam-5486	328	12	τ	τ	PROPN
ejpam-5486	328	13	)	)	PUNCT
ejpam-5486	328	14	}	}	PUNCT
ejpam-5486	328	15	.	.	PUNCT
ejpam-5486	329	1	(	(	PUNCT
ejpam-5486	329	2	ii	ii	NOUN
ejpam-5486	329	3	)	)	PUNCT
ejpam-5486	329	4	clωswd(h	clωswd(h	PROPN
ejpam-5486	329	5	)	)	PUNCT
ejpam-5486	330	1	=	=	PUNCT
ejpam-5486	330	2	∩{f	∩{f	NOUN
ejpam-5486	330	3	:	:	PUNCT
ejpam-5486	330	4	h	h	NOUN
ejpam-5486	330	5	⊆	⊆	NUM
ejpam-5486	330	6	f	f	PROPN
ejpam-5486	330	7	and	and	CCONJ
ejpam-5486	330	8	f	f	PROPN
ejpam-5486	330	9	∈	∈	PROPN
ejpam-5486	330	10	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	330	11	,	,	PUNCT
ejpam-5486	330	12	τ	τ	PROPN
ejpam-5486	330	13	)	)	PUNCT
ejpam-5486	330	14	}	}	PUNCT
ejpam-5486	330	15	.	.	PUNCT
ejpam-5486	331	1	a.	a.	PROPN
ejpam-5486	331	2	rawshdeh	rawshdeh	PROPN
ejpam-5486	331	3	,	,	PUNCT
ejpam-5486	331	4	h.	h.	PROPN
ejpam-5486	331	5	h.	h.	PROPN
ejpam-5486	331	6	al	al	PROPN
ejpam-5486	331	7	-	-	PUNCT
ejpam-5486	331	8	jarrah	jarrah	PROPN
ejpam-5486	331	9	,	,	PUNCT
ejpam-5486	331	10	k.	k.	PROPN
ejpam-5486	331	11	y.	y.	PROPN
ejpam-5486	331	12	al	al	PROPN
ejpam-5486	331	13	-	-	PROPN
ejpam-5486	331	14	zoubi	zoubi	PROPN
ejpam-5486	331	15	/	/	SYM
ejpam-5486	331	16	eur	eur	PROPN
ejpam-5486	331	17	.	.	PUNCT
ejpam-5486	332	1	j.	j.	PROPN
ejpam-5486	332	2	pure	pure	PROPN
ejpam-5486	332	3	appl	appl	PROPN
ejpam-5486	332	4	.	.	PROPN
ejpam-5486	332	5	math	math	PROPN
ejpam-5486	332	6	,	,	PUNCT
ejpam-5486	332	7	17	17	NUM
ejpam-5486	332	8	(	(	PUNCT
ejpam-5486	332	9	4	4	NUM
ejpam-5486	332	10	)	)	PUNCT
ejpam-5486	332	11	(	(	PUNCT
ejpam-5486	332	12	2024	2024	NUM
ejpam-5486	332	13	)	)	PUNCT
ejpam-5486	332	14	,	,	PUNCT
ejpam-5486	332	15	3370	3370	NUM
ejpam-5486	332	16	-	-	SYM
ejpam-5486	332	17	3385	3385	NUM
ejpam-5486	332	18	3379	3379	NUM
ejpam-5486	332	19	theorem	theorem	VERB
ejpam-5486	332	20	14	14	NUM
ejpam-5486	332	21	.	.	PUNCT
ejpam-5486	333	1	let	let	AUX
ejpam-5486	333	2	(	(	PUNCT
ejpam-5486	333	3	z	z	NOUN
ejpam-5486	333	4	,	,	PUNCT
ejpam-5486	333	5	τ	τ	PROPN
ejpam-5486	333	6	)	)	PUNCT
ejpam-5486	333	7	be	be	VERB
ejpam-5486	333	8	a	a	DET
ejpam-5486	333	9	t	t	NOUN
ejpam-5486	333	10	s	s	NOUN
ejpam-5486	333	11	and	and	CCONJ
ejpam-5486	333	12	h	h	NOUN
ejpam-5486	333	13	,	,	PUNCT
ejpam-5486	333	14	g	g	PROPN
ejpam-5486	333	15	⊆	⊆	NUM
ejpam-5486	333	16	z.	z.	PROPN
ejpam-5486	333	17	then	then	ADV
ejpam-5486	333	18	:	:	PUNCT
ejpam-5486	333	19	(	(	PUNCT
ejpam-5486	333	20	i	i	NOUN
ejpam-5486	333	21	)	)	PUNCT
ejpam-5486	333	22	intswd(h	intswd(h	PROPN
ejpam-5486	333	23	)	)	PUNCT
ejpam-5486	333	24	⊆	⊆	NUM
ejpam-5486	333	25	intωswd(h	intωswd(h	NUM
ejpam-5486	333	26	)	)	PUNCT
ejpam-5486	333	27	and	and	CCONJ
ejpam-5486	333	28	clωswd(h	clωswd(h	PROPN
ejpam-5486	333	29	)	)	PUNCT
ejpam-5486	333	30	⊆	⊆	NUM
ejpam-5486	333	31	clswd(h	clswd(h	NOUN
ejpam-5486	333	32	)	)	PUNCT
ejpam-5486	333	33	.	.	PUNCT
ejpam-5486	334	1	(	(	PUNCT
ejpam-5486	334	2	ii	ii	NOUN
ejpam-5486	334	3	)	)	PUNCT
ejpam-5486	334	4	h	h	NOUN
ejpam-5486	334	5	∈	∈	PROPN
ejpam-5486	335	1	ωswd(z	ωswd(z	PROPN
ejpam-5486	335	2	,	,	PUNCT
ejpam-5486	335	3	τ	τ	PROPN
ejpam-5486	335	4	)	)	PUNCT
ejpam-5486	335	5	iff	iff	PROPN
ejpam-5486	335	6	h	h	PROPN
ejpam-5486	335	7	=	=	PUNCT
ejpam-5486	335	8	intωswd(h	intωswd(h	PROPN
ejpam-5486	335	9	)	)	PUNCT
ejpam-5486	335	10	.	.	PUNCT
ejpam-5486	336	1	(	(	PUNCT
ejpam-5486	336	2	iii	iii	X
ejpam-5486	336	3	)	)	PUNCT
ejpam-5486	336	4	intωswd(intωswd(h	intωswd(intωswd(h	NUM
ejpam-5486	336	5	)	)	PUNCT
ejpam-5486	336	6	)	)	PUNCT
ejpam-5486	337	1	=	=	SYM
ejpam-5486	337	2	intωswd(h	intωswd(h	NUM
ejpam-5486	337	3	)	)	PUNCT
ejpam-5486	337	4	.	.	PUNCT
ejpam-5486	338	1	(	(	PUNCT
ejpam-5486	338	2	iv	iv	X
ejpam-5486	338	3	)	)	PUNCT
ejpam-5486	338	4	h	h	NOUN
ejpam-5486	338	5	∈	∈	PROPN
ejpam-5486	338	6	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	338	7	,	,	PUNCT
ejpam-5486	338	8	τ	τ	PROPN
ejpam-5486	338	9	)	)	PUNCT
ejpam-5486	338	10	iff	iff	PROPN
ejpam-5486	338	11	h	h	PROPN
ejpam-5486	338	12	=	=	PUNCT
ejpam-5486	338	13	clωswd(h	clωswd(h	PROPN
ejpam-5486	338	14	)	)	PUNCT
ejpam-5486	338	15	.	.	PUNCT
ejpam-5486	339	1	(	(	PUNCT
ejpam-5486	339	2	v	v	NOUN
ejpam-5486	339	3	)	)	PUNCT
ejpam-5486	339	4	x	x	SYM
ejpam-5486	339	5	∈	∈	PROPN
ejpam-5486	339	6	clωswd(h	clωswd(h	PROPN
ejpam-5486	339	7	)	)	PUNCT
ejpam-5486	339	8	iff	iff	NOUN
ejpam-5486	339	9	for	for	ADP
ejpam-5486	339	10	each	each	DET
ejpam-5486	339	11	g	g	PROPN
ejpam-5486	339	12	∈	∈	PROPN
ejpam-5486	339	13	ωswd(z	ωswd(z	PROPN
ejpam-5486	339	14	,	,	PUNCT
ejpam-5486	339	15	τ	τ	PROPN
ejpam-5486	339	16	)	)	PUNCT
ejpam-5486	339	17	with	with	ADP
ejpam-5486	339	18	x	x	SYM
ejpam-5486	339	19	∈	∈	NOUN
ejpam-5486	339	20	g	g	NOUN
ejpam-5486	339	21	we	we	PRON
ejpam-5486	339	22	have	have	VERB
ejpam-5486	339	23	g	g	PROPN
ejpam-5486	339	24	∩h	∩h	PROPN
ejpam-5486	339	25	̸=	̸=	PROPN
ejpam-5486	339	26	ϕ.	ϕ.	PROPN
ejpam-5486	339	27	(	(	PUNCT
ejpam-5486	339	28	vi	vi	NOUN
ejpam-5486	339	29	)	)	PUNCT
ejpam-5486	339	30	intωswd(z	intωswd(z	NOUN
ejpam-5486	339	31	−h	−h	ADV
ejpam-5486	339	32	)	)	PUNCT
ejpam-5486	339	33	=	=	SYM
ejpam-5486	339	34	z	z	NOUN
ejpam-5486	339	35	−	−	PROPN
ejpam-5486	339	36	clωswd(h	clωswd(h	PROPN
ejpam-5486	339	37	)	)	PUNCT
ejpam-5486	339	38	.	.	PUNCT
ejpam-5486	340	1	(	(	PUNCT
ejpam-5486	340	2	vii	vii	PROPN
ejpam-5486	340	3	)	)	PUNCT
ejpam-5486	340	4	clωswd(z	clωswd(z	PRON
ejpam-5486	340	5	−h	−h	ADJ
ejpam-5486	340	6	)	)	PUNCT
ejpam-5486	341	1	=	=	SYM
ejpam-5486	341	2	z−intωswd(h	z−intωswd(h	PROPN
ejpam-5486	341	3	)	)	PUNCT
ejpam-5486	341	4	.	.	PUNCT
ejpam-5486	342	1	proof	proof	NOUN
ejpam-5486	342	2	.	.	PUNCT
ejpam-5486	343	1	straightforward	straightforward	ADJ
ejpam-5486	343	2	.	.	PUNCT
ejpam-5486	344	1	in	in	ADP
ejpam-5486	344	2	general	general	ADJ
ejpam-5486	344	3	,	,	PUNCT
ejpam-5486	344	4	in	in	ADP
ejpam-5486	344	5	theorem	theorem	NOUN
ejpam-5486	344	6	14	14	NUM
ejpam-5486	344	7	the	the	DET
ejpam-5486	344	8	reverse	reverse	ADJ
ejpam-5486	344	9	inclusion	inclusion	NOUN
ejpam-5486	344	10	of	of	ADP
ejpam-5486	344	11	(	(	PUNCT
ejpam-5486	344	12	part	part	NOUN
ejpam-5486	344	13	i	i	NOUN
ejpam-5486	344	14	)	)	PUNCT
ejpam-5486	344	15	does	do	AUX
ejpam-5486	344	16	not	not	PART
ejpam-5486	344	17	hold	hold	VERB
ejpam-5486	344	18	,	,	PUNCT
ejpam-5486	344	19	since	since	SCONJ
ejpam-5486	344	20	in	in	ADP
ejpam-5486	344	21	example	example	NOUN
ejpam-5486	344	22	2	2	NUM
ejpam-5486	344	23	(	(	PUNCT
ejpam-5486	344	24	part	part	NOUN
ejpam-5486	344	25	iii	iii	NOUN
ejpam-5486	344	26	)	)	PUNCT
ejpam-5486	344	27	,	,	PUNCT
ejpam-5486	344	28	intswd({1	intswd({1	X
ejpam-5486	344	29	}	}	PUNCT
ejpam-5486	344	30	)	)	PUNCT
ejpam-5486	345	1	=	=	SYM
ejpam-5486	345	2	ϕ	ϕ	NOUN
ejpam-5486	345	3	while	while	SCONJ
ejpam-5486	345	4	intωswd({1	intωswd({1	PRON
ejpam-5486	345	5	}	}	PUNCT
ejpam-5486	345	6	)	)	PUNCT
ejpam-5486	346	1	=	=	NOUN
ejpam-5486	346	2	{	{	PUNCT
ejpam-5486	346	3	1	1	NUM
ejpam-5486	346	4	}	}	PUNCT
ejpam-5486	346	5	.	.	PUNCT
ejpam-5486	347	1	also	also	ADV
ejpam-5486	347	2	,	,	PUNCT
ejpam-5486	347	3	if	if	SCONJ
ejpam-5486	347	4	z	z	NOUN
ejpam-5486	347	5	=	=	SYM
ejpam-5486	347	6	{	{	PUNCT
ejpam-5486	347	7	1	1	NUM
ejpam-5486	347	8	,	,	PUNCT
ejpam-5486	347	9	2	2	NUM
ejpam-5486	347	10	,	,	PUNCT
ejpam-5486	347	11	3	3	NUM
ejpam-5486	347	12	}	}	PUNCT
ejpam-5486	347	13	with	with	ADP
ejpam-5486	347	14	the	the	DET
ejpam-5486	347	15	topology	topology	NOUN
ejpam-5486	347	16	σ	σ	NOUN
ejpam-5486	347	17	=	=	SYM
ejpam-5486	347	18	{	{	PUNCT
ejpam-5486	347	19	ϕ,z	ϕ,z	NOUN
ejpam-5486	347	20	,	,	PUNCT
ejpam-5486	347	21	{	{	PUNCT
ejpam-5486	347	22	1	1	NUM
ejpam-5486	347	23	}	}	PUNCT
ejpam-5486	347	24	}	}	PUNCT
ejpam-5486	347	25	.	.	PUNCT
ejpam-5486	348	1	then	then	ADV
ejpam-5486	348	2	clswd({1	clswd({1	X
ejpam-5486	348	3	}	}	PUNCT
ejpam-5486	348	4	)	)	PUNCT
ejpam-5486	349	1	=	=	PUNCT
ejpam-5486	349	2	z	z	NOUN
ejpam-5486	349	3	while	while	SCONJ
ejpam-5486	349	4	clωswd({1	clωswd({1	NOUN
ejpam-5486	349	5	}	}	PUNCT
ejpam-5486	349	6	)	)	PUNCT
ejpam-5486	349	7	=	=	PUNCT
ejpam-5486	349	8	{	{	PUNCT
ejpam-5486	349	9	1	1	NUM
ejpam-5486	349	10	}	}	PUNCT
ejpam-5486	349	11	.	.	PUNCT
ejpam-5486	350	1	definition	definition	NOUN
ejpam-5486	350	2	8	8	NUM
ejpam-5486	350	3	.	.	PUNCT
ejpam-5486	351	1	let	let	VERB
ejpam-5486	351	2	(	(	PUNCT
ejpam-5486	351	3	z	z	NOUN
ejpam-5486	351	4	,	,	PUNCT
ejpam-5486	351	5	τ	τ	PROPN
ejpam-5486	351	6	)	)	PUNCT
ejpam-5486	351	7	and	and	CCONJ
ejpam-5486	351	8	(	(	PUNCT
ejpam-5486	351	9	k	k	X
ejpam-5486	351	10	,	,	PUNCT
ejpam-5486	351	11	σ	σ	PROPN
ejpam-5486	351	12	)	)	PUNCT
ejpam-5486	351	13	be	be	VERB
ejpam-5486	351	14	two	two	NUM
ejpam-5486	351	15	t	t	PROPN
ejpam-5486	351	16	ss	ss	PROPN
ejpam-5486	351	17	.	.	PUNCT
ejpam-5486	352	1	then	then	ADV
ejpam-5486	352	2	a	a	DET
ejpam-5486	352	3	function	function	NOUN
ejpam-5486	352	4	γ	γ	X
ejpam-5486	352	5	:	:	PUNCT
ejpam-5486	352	6	(	(	PUNCT
ejpam-5486	352	7	z	z	NOUN
ejpam-5486	352	8	,	,	PUNCT
ejpam-5486	352	9	τ)→	τ)→	PROPN
ejpam-5486	352	10	(	(	PUNCT
ejpam-5486	352	11	k	k	X
ejpam-5486	352	12	,	,	PUNCT
ejpam-5486	352	13	σ	σ	PROPN
ejpam-5486	352	14	)	)	PUNCT
ejpam-5486	352	15	is	be	AUX
ejpam-5486	352	16	said	say	VERB
ejpam-5486	352	17	to	to	PART
ejpam-5486	352	18	be	be	AUX
ejpam-5486	352	19	:	:	PUNCT
ejpam-5486	352	20	(	(	PUNCT
ejpam-5486	352	21	i	i	NOUN
ejpam-5486	352	22	)	)	PUNCT
ejpam-5486	352	23	an	an	DET
ejpam-5486	352	24	ωswd	ωswd	ADJ
ejpam-5486	352	25	-	-	PUNCT
ejpam-5486	352	26	continuous	continuous	ADJ
ejpam-5486	352	27	iff	iff	PROPN
ejpam-5486	352	28	γ−1(g	γ−1(g	PROPN
ejpam-5486	352	29	)	)	PUNCT
ejpam-5486	352	30	∈	∈	PROPN
ejpam-5486	352	31	ωswd(z	ωswd(z	PROPN
ejpam-5486	352	32	,	,	PUNCT
ejpam-5486	352	33	τ	τ	PROPN
ejpam-5486	352	34	)	)	PUNCT
ejpam-5486	352	35	for	for	ADP
ejpam-5486	352	36	each	each	DET
ejpam-5486	352	37	g	g	PROPN
ejpam-5486	352	38	∈	∈	PROPN
ejpam-5486	352	39	σ	σ	PROPN
ejpam-5486	352	40	.	.	PUNCT
ejpam-5486	352	41	(	(	PUNCT
ejpam-5486	352	42	ii	ii	NOUN
ejpam-5486	352	43	)	)	PUNCT
ejpam-5486	352	44	an	an	DET
ejpam-5486	352	45	ωswd	ωswd	ADJ
ejpam-5486	352	46	-	-	PUNCT
ejpam-5486	352	47	irresolute	irresolute	ADJ
ejpam-5486	352	48	iff	iff	PROPN
ejpam-5486	352	49	γ−1(g	γ−1(g	PROPN
ejpam-5486	352	50	)	)	PUNCT
ejpam-5486	352	51	∈	∈	PROPN
ejpam-5486	352	52	ωswd(z	ωswd(z	PROPN
ejpam-5486	352	53	,	,	PUNCT
ejpam-5486	352	54	τ	τ	PROPN
ejpam-5486	352	55	)	)	PUNCT
ejpam-5486	352	56	for	for	ADP
ejpam-5486	352	57	each	each	DET
ejpam-5486	352	58	g	g	PROPN
ejpam-5486	352	59	∈	∈	PROPN
ejpam-5486	352	60	ωswd(k	ωswd(k	PROPN
ejpam-5486	352	61	,	,	PUNCT
ejpam-5486	352	62	σ	σ	PROPN
ejpam-5486	352	63	)	)	PUNCT
ejpam-5486	352	64	.	.	PUNCT
ejpam-5486	353	1	proposition	proposition	NOUN
ejpam-5486	353	2	4	4	NUM
ejpam-5486	353	3	.	.	PUNCT
ejpam-5486	354	1	each	each	DET
ejpam-5486	354	2	ωswd	ωswd	ADJ
ejpam-5486	354	3	-	-	PUNCT
ejpam-5486	354	4	irresolute	irresolute	ADJ
ejpam-5486	354	5	function	function	NOUN
ejpam-5486	354	6	is	be	AUX
ejpam-5486	354	7	ωswd	ωswd	ADJ
ejpam-5486	354	8	-	-	PUNCT
ejpam-5486	354	9	continuous	continuous	ADJ
ejpam-5486	354	10	.	.	PUNCT
ejpam-5486	355	1	the	the	DET
ejpam-5486	355	2	following	follow	VERB
ejpam-5486	355	3	example	example	NOUN
ejpam-5486	355	4	will	will	AUX
ejpam-5486	355	5	show	show	VERB
ejpam-5486	355	6	the	the	DET
ejpam-5486	355	7	converse	converse	NOUN
ejpam-5486	355	8	of	of	ADP
ejpam-5486	355	9	proposition	proposition	NOUN
ejpam-5486	355	10	4	4	NUM
ejpam-5486	355	11	is	be	AUX
ejpam-5486	355	12	not	not	PART
ejpam-5486	355	13	true	true	ADJ
ejpam-5486	355	14	in	in	ADP
ejpam-5486	355	15	general	general	ADJ
ejpam-5486	355	16	.	.	PUNCT
ejpam-5486	355	17	example	example	NOUN
ejpam-5486	356	1	5	5	NUM
ejpam-5486	356	2	.	.	X
ejpam-5486	356	3	consider	consider	VERB
ejpam-5486	356	4	the	the	DET
ejpam-5486	356	5	identity	identity	NOUN
ejpam-5486	356	6	function	function	NOUN
ejpam-5486	356	7	γ	γ	X
ejpam-5486	356	8	:	:	PUNCT
ejpam-5486	356	9	(	(	PUNCT
ejpam-5486	356	10	r	r	NOUN
ejpam-5486	356	11	,	,	PUNCT
ejpam-5486	356	12	τcoc)→	τcoc)→	NOUN
ejpam-5486	356	13	(	(	PUNCT
ejpam-5486	356	14	r	r	NOUN
ejpam-5486	356	15	,	,	PUNCT
ejpam-5486	356	16	τcof	τcof	NOUN
ejpam-5486	356	17	)	)	PUNCT
ejpam-5486	356	18	.	.	PUNCT
ejpam-5486	357	1	then	then	ADV
ejpam-5486	357	2	γis	γis	ADV
ejpam-5486	357	3	an	an	DET
ejpam-5486	357	4	ωswdcontinuous	ωswdcontinuous	ADJ
ejpam-5486	357	5	while	while	SCONJ
ejpam-5486	357	6	it	it	PRON
ejpam-5486	357	7	is	be	AUX
ejpam-5486	357	8	not	not	PART
ejpam-5486	357	9	ωswd	ωswd	ADJ
ejpam-5486	357	10	-	-	PUNCT
ejpam-5486	357	11	irresolute	irresolute	ADJ
ejpam-5486	357	12	since	since	SCONJ
ejpam-5486	357	13	γ−1({1	γ−1({1	NOUN
ejpam-5486	357	14	}	}	PUNCT
ejpam-5486	357	15	)	)	PUNCT
ejpam-5486	357	16	/∈	/∈	PUNCT
ejpam-5486	358	1	ωswd(z	ωswd(z	NOUN
ejpam-5486	358	2	,	,	PUNCT
ejpam-5486	358	3	τcoc	τcoc	PROPN
ejpam-5486	358	4	)	)	PUNCT
ejpam-5486	358	5	.	.	PUNCT
ejpam-5486	359	1	in	in	ADP
ejpam-5486	359	2	the	the	DET
ejpam-5486	359	3	following	following	NOUN
ejpam-5486	359	4	theorem	theorem	NOUN
ejpam-5486	359	5	,	,	PUNCT
ejpam-5486	359	6	we	we	PRON
ejpam-5486	359	7	use	use	VERB
ejpam-5486	359	8	the	the	DET
ejpam-5486	359	9	family	family	NOUN
ejpam-5486	359	10	ωswd(z	ωswd(z	PROPN
ejpam-5486	359	11	,	,	PUNCT
ejpam-5486	359	12	τ	τ	PROPN
ejpam-5486	359	13	)	)	PUNCT
ejpam-5486	359	14	to	to	PART
ejpam-5486	359	15	present	present	VERB
ejpam-5486	359	16	a	a	DET
ejpam-5486	359	17	theorem	theorem	NOUN
ejpam-5486	359	18	similar	similar	ADJ
ejpam-5486	359	19	to	to	ADP
ejpam-5486	359	20	theorem	theorem	VERB
ejpam-5486	359	21	4	4	NUM
ejpam-5486	359	22	.	.	PUNCT
ejpam-5486	359	23	theorem	theorem	NOUN
ejpam-5486	359	24	15	15	NUM
ejpam-5486	359	25	.	.	PUNCT
ejpam-5486	360	1	let	let	VERB
ejpam-5486	360	2	{	{	PUNCT
ejpam-5486	360	3	(	(	PUNCT
ejpam-5486	360	4	zα	zα	PROPN
ejpam-5486	360	5	,	,	PUNCT
ejpam-5486	360	6	τα	τα	PROPN
ejpam-5486	360	7	)	)	PUNCT
ejpam-5486	360	8	:	:	PUNCT
ejpam-5486	361	1	α	α	PROPN
ejpam-5486	361	2	∈	∈	PROPN
ejpam-5486	361	3	∆	∆	PROPN
ejpam-5486	361	4	}	}	PUNCT
ejpam-5486	361	5	be	be	AUX
ejpam-5486	361	6	a	a	DET
ejpam-5486	361	7	family	family	NOUN
ejpam-5486	361	8	of	of	ADP
ejpam-5486	361	9	topological	topological	ADJ
ejpam-5486	361	10	spaces	space	NOUN
ejpam-5486	361	11	with	with	ADP
ejpam-5486	361	12	zα∩	zα∩	PROPN
ejpam-5486	361	13	zβ	zβ	X
ejpam-5486	361	14	=	=	SYM
ejpam-5486	361	15	ϕ	ϕ	PROPN
ejpam-5486	361	16	for	for	ADP
ejpam-5486	361	17	each	each	DET
ejpam-5486	361	18	α	α	NOUN
ejpam-5486	361	19	̸=	̸=	PROPN
ejpam-5486	361	20	β	β	NOUN
ejpam-5486	361	21	.	.	PUNCT
ejpam-5486	362	1	for	for	ADP
ejpam-5486	362	2	each	each	DET
ejpam-5486	362	3	α	α	PROPN
ejpam-5486	362	4	∈	∈	PROPN
ejpam-5486	362	5	∆	∆	PROPN
ejpam-5486	362	6	,	,	PUNCT
ejpam-5486	362	7	let	let	VERB
ejpam-5486	362	8	ϕ	ϕ	PRON
ejpam-5486	362	9	̸=	̸=	PROPN
ejpam-5486	362	10	hα	hα	ADP
ejpam-5486	362	11	⊆	⊆	NUM
ejpam-5486	362	12	zα	zα	PROPN
ejpam-5486	362	13	and	and	CCONJ
ejpam-5486	362	14	put	put	VERB
ejpam-5486	362	15	h	h	NOUN
ejpam-5486	362	16	=	=	PUNCT
ejpam-5486	362	17	∪	∪	ADJ
ejpam-5486	362	18	hα	hα	ADP
ejpam-5486	362	19	α∈∆	α∈∆	PROPN
ejpam-5486	362	20	.	.	PUNCT
ejpam-5486	363	1	then	then	ADV
ejpam-5486	363	2	:	:	PUNCT
ejpam-5486	363	3	(	(	PUNCT
ejpam-5486	363	4	i	i	NOUN
ejpam-5486	363	5	)	)	PUNCT
ejpam-5486	363	6	h	h	PROPN
ejpam-5486	363	7	∈	∈	PROPN
ejpam-5486	363	8	ωswd(z	ωswd(z	NOUN
ejpam-5486	363	9	,	,	PUNCT
ejpam-5486	363	10	τs	τs	NOUN
ejpam-5486	363	11	)	)	PUNCT
ejpam-5486	363	12	iff	iff	NOUN
ejpam-5486	363	13	there	there	PRON
ejpam-5486	363	14	is	be	VERB
ejpam-5486	363	15	α	α	NUM
ejpam-5486	363	16	◦	◦	NOUN
ejpam-5486	363	17	∈	∈	NOUN
ejpam-5486	363	18	∆	∆	PROPN
ejpam-5486	363	19	with	with	ADP
ejpam-5486	363	20	hα	hα	ADP
ejpam-5486	363	21	◦	◦	NOUN
ejpam-5486	363	22	∈	∈	NOUN
ejpam-5486	363	23	ωswd(zα	ωswd(zα	ADJ
ejpam-5486	363	24	◦	◦	NOUN
ejpam-5486	363	25	,	,	PUNCT
ejpam-5486	363	26	τα	τα	NOUN
ejpam-5486	363	27	◦	◦	NOUN
ejpam-5486	363	28	)	)	PUNCT
ejpam-5486	363	29	.	.	PUNCT
ejpam-5486	364	1	(	(	PUNCT
ejpam-5486	364	2	ii	ii	NOUN
ejpam-5486	364	3	)	)	PUNCT
ejpam-5486	364	4	if	if	SCONJ
ejpam-5486	364	5	hα	hα	ADP
ejpam-5486	364	6	∈	∈	NOUN
ejpam-5486	364	7	ωswd(zα	ωswd(zα	ADJ
ejpam-5486	364	8	,	,	PUNCT
ejpam-5486	364	9	τα	τα	NOUN
ejpam-5486	364	10	)	)	PUNCT
ejpam-5486	364	11	,	,	PUNCT
ejpam-5486	364	12	then	then	ADV
ejpam-5486	364	13	h	h	PROPN
ejpam-5486	364	14	∈	∈	PROPN
ejpam-5486	364	15	ωswd(z	ωswd(z	PROPN
ejpam-5486	364	16	,	,	PUNCT
ejpam-5486	364	17	τs	τs	NOUN
ejpam-5486	364	18	)	)	PUNCT
ejpam-5486	364	19	.	.	PUNCT
ejpam-5486	365	1	proof	proof	NOUN
ejpam-5486	365	2	.	.	PUNCT
ejpam-5486	366	1	(	(	PUNCT
ejpam-5486	366	2	i	i	NOUN
ejpam-5486	366	3	)	)	PUNCT
ejpam-5486	366	4	let	let	VERB
ejpam-5486	366	5	x	x	SYM
ejpam-5486	366	6	∈	∈	PROPN
ejpam-5486	366	7	h.	h.	NOUN
ejpam-5486	366	8	then	then	ADV
ejpam-5486	366	9	there	there	PRON
ejpam-5486	366	10	is	be	VERB
ejpam-5486	366	11	s	s	PROPN
ejpam-5486	366	12	∈	∈	PROPN
ejpam-5486	366	13	swd(z	swd(z	PROPN
ejpam-5486	366	14	,	,	PUNCT
ejpam-5486	366	15	τs	τs	NOUN
ejpam-5486	366	16	)	)	PUNCT
ejpam-5486	366	17	with	with	ADP
ejpam-5486	366	18	x	x	PUNCT
ejpam-5486	366	19	∈	∈	PROPN
ejpam-5486	366	20	s	s	X
ejpam-5486	366	21	and	and	CCONJ
ejpam-5486	366	22	s	s	VERB
ejpam-5486	366	23	−	−	PROPN
ejpam-5486	366	24	h	h	NOUN
ejpam-5486	366	25	is	be	AUX
ejpam-5486	366	26	countable	countable	ADJ
ejpam-5486	366	27	.	.	PUNCT
ejpam-5486	367	1	write	write	PROPN
ejpam-5486	367	2	s	s	PART
ejpam-5486	367	3	=	=	NOUN
ejpam-5486	367	4	∪	∪	ADJ
ejpam-5486	367	5	α∈∆	α∈∆	PRON
ejpam-5486	367	6	sα	sα	NOUN
ejpam-5486	367	7	.	.	PUNCT
ejpam-5486	368	1	then	then	ADV
ejpam-5486	368	2	by	by	ADP
ejpam-5486	368	3	theorem	theorem	NOUN
ejpam-5486	368	4	4	4	NUM
ejpam-5486	368	5	(	(	PUNCT
ejpam-5486	368	6	part	part	NOUN
ejpam-5486	368	7	(	(	PUNCT
ejpam-5486	368	8	i	i	NOUN
ejpam-5486	368	9	)	)	PUNCT
ejpam-5486	368	10	)	)	PUNCT
ejpam-5486	368	11	there	there	PRON
ejpam-5486	368	12	is	be	VERB
ejpam-5486	368	13	α	α	NUM
ejpam-5486	368	14	◦	◦	NOUN
ejpam-5486	368	15	∈	∈	NOUN
ejpam-5486	368	16	∆	∆	PROPN
ejpam-5486	368	17	with	with	ADP
ejpam-5486	368	18	sα	sα	NOUN
ejpam-5486	368	19	◦	◦	NOUN
ejpam-5486	368	20	∈	∈	NOUN
ejpam-5486	368	21	swd(zα	swd(zα	DET
ejpam-5486	368	22	◦	◦	NOUN
ejpam-5486	368	23	,	,	PUNCT
ejpam-5486	368	24	τα	τα	NOUN
ejpam-5486	368	25	◦	◦	NOUN
ejpam-5486	368	26	)	)	PUNCT
ejpam-5486	368	27	such	such	ADJ
ejpam-5486	368	28	that	that	PRON
ejpam-5486	368	29	sα	sα	AUX
ejpam-5486	368	30	◦	◦	NOUN
ejpam-5486	368	31	−hα	−hα	ADJ
ejpam-5486	368	32	◦	◦	NOUN
ejpam-5486	368	33	⊆	⊆	NUM
ejpam-5486	368	34	sα	sα	ADJ
ejpam-5486	368	35	◦	◦	NOUN
ejpam-5486	368	36	−	−	NOUN
ejpam-5486	368	37	∪	∪	ADP
ejpam-5486	368	38	α∈∆	α∈∆	PRON
ejpam-5486	368	39	hα	hα	ADP
ejpam-5486	368	40	⊆	⊆	NUM
ejpam-5486	368	41	s−h	s−h	NOUN
ejpam-5486	368	42	.	.	PUNCT
ejpam-5486	369	1	therefore	therefore	ADV
ejpam-5486	369	2	,	,	PUNCT
ejpam-5486	369	3	sα	sα	ADJ
ejpam-5486	369	4	◦	◦	NOUN
ejpam-5486	369	5	−hα	−hα	ADJ
ejpam-5486	369	6	◦	◦	NOUN
ejpam-5486	369	7	is	be	AUX
ejpam-5486	369	8	countable	countable	ADJ
ejpam-5486	369	9	.	.	PUNCT
ejpam-5486	370	1	now	now	ADV
ejpam-5486	370	2	,	,	PUNCT
ejpam-5486	370	3	let	let	VERB
ejpam-5486	370	4	x	x	PRON
ejpam-5486	370	5	◦	◦	VERB
ejpam-5486	370	6	∈	∈	NOUN
ejpam-5486	370	7	hα	hα	ADP
ejpam-5486	370	8	◦	◦	NOUN
ejpam-5486	370	9	.	.	PUNCT
ejpam-5486	371	1	then	then	ADV
ejpam-5486	371	2	s∗	s∗	VERB
ejpam-5486	371	3	α	α	PRON
ejpam-5486	371	4	◦	◦	NOUN
ejpam-5486	371	5	=	=	SYM
ejpam-5486	371	6	sα	sα	ADP
ejpam-5486	371	7	◦	◦	NOUN
ejpam-5486	371	8	∪{x	∪{x	NOUN
ejpam-5486	371	9	◦	◦	NOUN
ejpam-5486	371	10	}	}	PUNCT
ejpam-5486	371	11	∈	∈	NOUN
ejpam-5486	371	12	swd(zα	swd(zα	PRON
ejpam-5486	371	13	◦	◦	NOUN
ejpam-5486	371	14	,	,	PUNCT
ejpam-5486	371	15	τα	τα	NOUN
ejpam-5486	371	16	◦	◦	NOUN
ejpam-5486	371	17	)	)	PUNCT
ejpam-5486	371	18	with	with	ADP
ejpam-5486	371	19	x	x	X
ejpam-5486	371	20	◦	◦	NOUN
ejpam-5486	371	21	∈	∈	NOUN
ejpam-5486	371	22	s∗	s∗	NOUN
ejpam-5486	371	23	α	α	NOUN
ejpam-5486	371	24	◦	◦	NOUN
ejpam-5486	371	25	and	and	CCONJ
ejpam-5486	371	26	s∗	s∗	VERB
ejpam-5486	371	27	α	α	NUM
ejpam-5486	371	28	◦	◦	NOUN
ejpam-5486	371	29	−	−	NOUN
ejpam-5486	371	30	hα	hα	NOUN
ejpam-5486	371	31	◦	◦	NOUN
ejpam-5486	371	32	is	be	AUX
ejpam-5486	371	33	countable	countable	ADJ
ejpam-5486	371	34	.	.	PUNCT
ejpam-5486	372	1	therefore	therefore	ADV
ejpam-5486	372	2	,	,	PUNCT
ejpam-5486	372	3	hα	hα	ADP
ejpam-5486	372	4	◦	◦	NOUN
ejpam-5486	372	5	∈	∈	NOUN
ejpam-5486	372	6	ωswd(zα	ωswd(zα	ADJ
ejpam-5486	372	7	◦	◦	NOUN
ejpam-5486	372	8	,	,	PUNCT
ejpam-5486	372	9	τα	τα	NOUN
ejpam-5486	372	10	◦	◦	NOUN
ejpam-5486	372	11	)	)	PUNCT
ejpam-5486	372	12	.	.	PUNCT
ejpam-5486	373	1	conversely	conversely	ADV
ejpam-5486	373	2	,	,	PUNCT
ejpam-5486	373	3	choose	choose	VERB
ejpam-5486	373	4	x	x	X
ejpam-5486	373	5	◦	◦	NOUN
ejpam-5486	373	6	∈	∈	NOUN
ejpam-5486	373	7	hα	hα	ADP
ejpam-5486	373	8	◦	◦	NOUN
ejpam-5486	373	9	.	.	PUNCT
ejpam-5486	374	1	then	then	ADV
ejpam-5486	374	2	there	there	PRON
ejpam-5486	374	3	is	be	VERB
ejpam-5486	374	4	sα	sα	ADJ
ejpam-5486	374	5	◦	◦	NOUN
ejpam-5486	374	6	∈	∈	NOUN
ejpam-5486	374	7	swd(zα	swd(zα	PRON
ejpam-5486	374	8	◦	◦	NOUN
ejpam-5486	374	9	,	,	PUNCT
ejpam-5486	374	10	τα	τα	NOUN
ejpam-5486	374	11	◦	◦	NOUN
ejpam-5486	374	12	)	)	PUNCT
ejpam-5486	374	13	with	with	SCONJ
ejpam-5486	374	14	x	x	NOUN
ejpam-5486	374	15	◦	◦	NOUN
ejpam-5486	374	16	∈	∈	PRON
ejpam-5486	374	17	sα	sα	NOUN
ejpam-5486	374	18	◦	◦	NOUN
ejpam-5486	374	19	and	and	CCONJ
ejpam-5486	374	20	sα	sα	VERB
ejpam-5486	374	21	◦	◦	NOUN
ejpam-5486	374	22	−hα	−hα	ADJ
ejpam-5486	374	23	◦	◦	NOUN
ejpam-5486	374	24	is	be	AUX
ejpam-5486	374	25	countable	countable	ADJ
ejpam-5486	374	26	.	.	PUNCT
ejpam-5486	375	1	now	now	ADV
ejpam-5486	375	2	,	,	PUNCT
ejpam-5486	375	3	let	let	VERB
ejpam-5486	375	4	x	x	PUNCT
ejpam-5486	375	5	∈	∈	PROPN
ejpam-5486	375	6	h	h	NOUN
ejpam-5486	375	7	and	and	CCONJ
ejpam-5486	375	8	put	put	VERB
ejpam-5486	375	9	s	s	NOUN
ejpam-5486	375	10	=	=	X
ejpam-5486	375	11	sα	sα	ADJ
ejpam-5486	375	12	◦	◦	NOUN
ejpam-5486	375	13	∪	∪	X
ejpam-5486	375	14	{	{	PUNCT
ejpam-5486	375	15	x	x	NOUN
ejpam-5486	375	16	}	}	PUNCT
ejpam-5486	375	17	.	.	PUNCT
ejpam-5486	376	1	then	then	ADV
ejpam-5486	376	2	by	by	ADP
ejpam-5486	376	3	theorem	theorem	NOUN
ejpam-5486	376	4	4	4	NUM
ejpam-5486	376	5	(	(	PUNCT
ejpam-5486	376	6	part	part	NOUN
ejpam-5486	376	7	(	(	PUNCT
ejpam-5486	376	8	i	i	NOUN
ejpam-5486	376	9	)	)	PUNCT
ejpam-5486	376	10	)	)	PUNCT
ejpam-5486	376	11	,	,	PUNCT
ejpam-5486	376	12	s	s	PROPN
ejpam-5486	376	13	∈	∈	PROPN
ejpam-5486	376	14	swd(z	swd(z	PROPN
ejpam-5486	376	15	,	,	PUNCT
ejpam-5486	376	16	τs	τs	NOUN
ejpam-5486	376	17	)	)	PUNCT
ejpam-5486	376	18	with	with	ADP
ejpam-5486	376	19	x	x	PUNCT
ejpam-5486	376	20	∈	∈	PROPN
ejpam-5486	376	21	s	s	X
ejpam-5486	376	22	and	and	CCONJ
ejpam-5486	376	23	s	s	VERB
ejpam-5486	376	24	−	−	PROPN
ejpam-5486	376	25	h	h	NOUN
ejpam-5486	377	1	⊆	⊆	NUM
ejpam-5486	377	2	s	s	PART
ejpam-5486	377	3	−	−	NOUN
ejpam-5486	377	4	hα	hα	ADP
ejpam-5486	377	5	◦	◦	NOUN
ejpam-5486	377	6	⊆	⊆	NUM
ejpam-5486	377	7	(	(	PUNCT
ejpam-5486	377	8	sα	sα	NOUN
ejpam-5486	377	9	◦	◦	NOUN
ejpam-5486	377	10	−	−	NOUN
ejpam-5486	377	11	hα	hα	ADP
ejpam-5486	377	12	◦	◦	NOUN
ejpam-5486	377	13	)	)	PUNCT
ejpam-5486	377	14	∪	∪	ADP
ejpam-5486	377	15	{	{	PUNCT
ejpam-5486	377	16	x	x	NOUN
ejpam-5486	377	17	}	}	PUNCT
ejpam-5486	377	18	.	.	PUNCT
ejpam-5486	378	1	since	since	SCONJ
ejpam-5486	378	2	(	(	PUNCT
ejpam-5486	378	3	sα	sα	VERB
ejpam-5486	378	4	◦	◦	NOUN
ejpam-5486	378	5	−	−	NOUN
ejpam-5486	378	6	hα	hα	ADP
ejpam-5486	378	7	◦	◦	NOUN
ejpam-5486	378	8	)	)	PUNCT
ejpam-5486	378	9	∪	∪	ADP
ejpam-5486	378	10	{	{	PUNCT
ejpam-5486	378	11	x	x	NOUN
ejpam-5486	378	12	}	}	PUNCT
ejpam-5486	378	13	is	be	AUX
ejpam-5486	378	14	countable	countable	ADJ
ejpam-5486	378	15	,	,	PUNCT
ejpam-5486	378	16	then	then	ADV
ejpam-5486	378	17	h	h	PROPN
ejpam-5486	378	18	∈	∈	PROPN
ejpam-5486	378	19	ωswd(z	ωswd(z	PROPN
ejpam-5486	378	20	,	,	PUNCT
ejpam-5486	378	21	τs	τs	NOUN
ejpam-5486	378	22	)	)	PUNCT
ejpam-5486	378	23	.	.	PUNCT
ejpam-5486	379	1	(	(	PUNCT
ejpam-5486	379	2	ii	ii	NOUN
ejpam-5486	379	3	)	)	PUNCT
ejpam-5486	379	4	follows	follow	VERB
ejpam-5486	379	5	from	from	ADP
ejpam-5486	379	6	part	part	NOUN
ejpam-5486	379	7	(	(	PUNCT
ejpam-5486	379	8	i	i	NOUN
ejpam-5486	379	9	)	)	PUNCT
ejpam-5486	379	10	.	.	PUNCT
ejpam-5486	380	1	in	in	ADP
ejpam-5486	380	2	the	the	DET
ejpam-5486	380	3	next	next	ADJ
ejpam-5486	380	4	example	example	NOUN
ejpam-5486	380	5	we	we	PRON
ejpam-5486	380	6	will	will	AUX
ejpam-5486	380	7	show	show	VERB
ejpam-5486	380	8	that	that	SCONJ
ejpam-5486	380	9	the	the	DET
ejpam-5486	380	10	converse	converse	NOUN
ejpam-5486	380	11	of	of	ADP
ejpam-5486	380	12	part	part	NOUN
ejpam-5486	380	13	(	(	PUNCT
ejpam-5486	380	14	ii	ii	NOUN
ejpam-5486	380	15	)	)	PUNCT
ejpam-5486	380	16	of	of	ADP
ejpam-5486	380	17	theorem	theorem	ADJ
ejpam-5486	380	18	4	4	NUM
ejpam-5486	380	19	and	and	CCONJ
ejpam-5486	380	20	theorem	theorem	VERB
ejpam-5486	380	21	15	15	NUM
ejpam-5486	380	22	,	,	PUNCT
ejpam-5486	380	23	is	be	AUX
ejpam-5486	380	24	not	not	PART
ejpam-5486	380	25	true	true	ADJ
ejpam-5486	380	26	in	in	ADP
ejpam-5486	380	27	general	general	ADJ
ejpam-5486	380	28	.	.	PUNCT
ejpam-5486	381	1	a.	a.	PROPN
ejpam-5486	381	2	rawshdeh	rawshdeh	PROPN
ejpam-5486	381	3	,	,	PUNCT
ejpam-5486	381	4	h.	h.	PROPN
ejpam-5486	381	5	h.	h.	PROPN
ejpam-5486	381	6	al	al	PROPN
ejpam-5486	381	7	-	-	PUNCT
ejpam-5486	381	8	jarrah	jarrah	PROPN
ejpam-5486	381	9	,	,	PUNCT
ejpam-5486	381	10	k.	k.	PROPN
ejpam-5486	381	11	y.	y.	PROPN
ejpam-5486	381	12	al	al	PROPN
ejpam-5486	381	13	-	-	PROPN
ejpam-5486	381	14	zoubi	zoubi	PROPN
ejpam-5486	381	15	/	/	SYM
ejpam-5486	381	16	eur	eur	PROPN
ejpam-5486	381	17	.	.	PUNCT
ejpam-5486	382	1	j.	j.	PROPN
ejpam-5486	382	2	pure	pure	PROPN
ejpam-5486	382	3	appl	appl	PROPN
ejpam-5486	382	4	.	.	PROPN
ejpam-5486	382	5	math	math	PROPN
ejpam-5486	382	6	,	,	PUNCT
ejpam-5486	382	7	17	17	NUM
ejpam-5486	382	8	(	(	PUNCT
ejpam-5486	382	9	4	4	NUM
ejpam-5486	382	10	)	)	PUNCT
ejpam-5486	382	11	(	(	PUNCT
ejpam-5486	382	12	2024	2024	NUM
ejpam-5486	382	13	)	)	PUNCT
ejpam-5486	382	14	,	,	PUNCT
ejpam-5486	382	15	3370	3370	NUM
ejpam-5486	382	16	-	-	SYM
ejpam-5486	382	17	3385	3385	NUM
ejpam-5486	382	18	3380	3380	NUM
ejpam-5486	382	19	example	example	NOUN
ejpam-5486	382	20	6	6	NUM
ejpam-5486	382	21	.	.	PUNCT
ejpam-5486	383	1	let	let	VERB
ejpam-5486	383	2	(	(	PUNCT
ejpam-5486	383	3	z1	z1	ADJ
ejpam-5486	383	4	,	,	PUNCT
ejpam-5486	383	5	τ1	τ1	NOUN
ejpam-5486	383	6	)	)	PUNCT
ejpam-5486	383	7	=	=	SYM
ejpam-5486	383	8	(	(	PUNCT
ejpam-5486	383	9	(	(	PUNCT
ejpam-5486	383	10	0	0	NUM
ejpam-5486	383	11	,	,	PUNCT
ejpam-5486	383	12	1	1	NUM
ejpam-5486	383	13	)	)	PUNCT
ejpam-5486	383	14	,	,	PUNCT
ejpam-5486	383	15	τind	τind	NOUN
ejpam-5486	383	16	)	)	PUNCT
ejpam-5486	383	17	,	,	PUNCT
ejpam-5486	383	18	(	(	PUNCT
ejpam-5486	383	19	z2	z2	NOUN
ejpam-5486	383	20	,	,	PUNCT
ejpam-5486	383	21	τ2	τ2	NOUN
ejpam-5486	383	22	)	)	PUNCT
ejpam-5486	383	23	=	=	SYM
ejpam-5486	384	1	(	(	PUNCT
ejpam-5486	384	2	(	(	PUNCT
ejpam-5486	384	3	2	2	NUM
ejpam-5486	384	4	,	,	PUNCT
ejpam-5486	384	5	3	3	NUM
ejpam-5486	384	6	)	)	PUNCT
ejpam-5486	384	7	,	,	PUNCT
ejpam-5486	384	8	τcoc	τcoc	PROPN
ejpam-5486	384	9	)	)	PUNCT
ejpam-5486	385	1	and	and	CCONJ
ejpam-5486	385	2	consider	consider	VERB
ejpam-5486	385	3	z	z	NOUN
ejpam-5486	385	4	=	=	SYM
ejpam-5486	385	5	z1	z1	PROPN
ejpam-5486	385	6	⊕z2	⊕z2	PROPN
ejpam-5486	385	7	.	.	PUNCT
ejpam-5486	386	1	let	let	VERB
ejpam-5486	386	2	h	h	NOUN
ejpam-5486	386	3	=	=	PRON
ejpam-5486	386	4	{	{	PUNCT
ejpam-5486	386	5	x1	x1	PROPN
ejpam-5486	386	6	}	}	PUNCT
ejpam-5486	386	7	∪	∪	ADP
ejpam-5486	386	8	e	e	NOUN
ejpam-5486	386	9	,	,	PUNCT
ejpam-5486	386	10	where	where	SCONJ
ejpam-5486	386	11	x1	x1	PROPN
ejpam-5486	386	12	∈	∈	PROPN
ejpam-5486	386	13	z1	z1	NOUN
ejpam-5486	386	14	and	and	CCONJ
ejpam-5486	386	15	e	e	NOUN
ejpam-5486	386	16	is	be	AUX
ejpam-5486	386	17	countable	countable	ADJ
ejpam-5486	386	18	subset	subset	NOUN
ejpam-5486	386	19	of	of	ADP
ejpam-5486	386	20	z2	z2	PROPN
ejpam-5486	386	21	.	.	PUNCT
ejpam-5486	387	1	note	note	VERB
ejpam-5486	387	2	that	that	SCONJ
ejpam-5486	387	3	,	,	PUNCT
ejpam-5486	387	4	cl(h	cl(h	NUM
ejpam-5486	387	5	)	)	PUNCT
ejpam-5486	388	1	=	=	SYM
ejpam-5486	388	2	z1	z1	NOUN
ejpam-5486	388	3	∪	∪	X
ejpam-5486	388	4	e	e	NOUN
ejpam-5486	388	5	and	and	CCONJ
ejpam-5486	388	6	z1	z1	VERB
ejpam-5486	388	7	⊆	⊆	NUM
ejpam-5486	388	8	int(cl(h	int(cl(h	PROPN
ejpam-5486	388	9	)	)	PUNCT
ejpam-5486	388	10	)	)	PUNCT
ejpam-5486	388	11	.	.	PUNCT
ejpam-5486	389	1	therefore	therefore	ADV
ejpam-5486	389	2	,	,	PUNCT
ejpam-5486	389	3	h	h	PROPN
ejpam-5486	389	4	∈	∈	PROPN
ejpam-5486	389	5	swd(z	swd(z	PROPN
ejpam-5486	389	6	,	,	PUNCT
ejpam-5486	389	7	τs	τs	NOUN
ejpam-5486	389	8	)	)	PUNCT
ejpam-5486	389	9	and	and	CCONJ
ejpam-5486	389	10	hence	hence	ADV
ejpam-5486	389	11	h	h	NOUN
ejpam-5486	389	12	∈	∈	PROPN
ejpam-5486	389	13	ωswd(z	ωswd(z	PROPN
ejpam-5486	389	14	,	,	PUNCT
ejpam-5486	389	15	τs	τs	NOUN
ejpam-5486	389	16	)	)	PUNCT
ejpam-5486	389	17	.	.	PUNCT
ejpam-5486	390	1	on	on	ADP
ejpam-5486	390	2	the	the	DET
ejpam-5486	390	3	other	other	ADJ
ejpam-5486	390	4	hand	hand	NOUN
ejpam-5486	390	5	e	e	NOUN
ejpam-5486	390	6	/∈	/∈	NOUN
ejpam-5486	390	7	ωswd(z2	ωswd(z2	NOUN
ejpam-5486	390	8	,	,	PUNCT
ejpam-5486	390	9	τ2	τ2	PROPN
ejpam-5486	390	10	)	)	PUNCT
ejpam-5486	390	11	.	.	PUNCT
ejpam-5486	391	1	4	4	X
ejpam-5486	391	2	.	.	X
ejpam-5486	391	3	almost	almost	ADV
ejpam-5486	391	4	ωswd	ωswd	ADJ
ejpam-5486	391	5	-	-	PUNCT
ejpam-5486	391	6	compact	compact	ADJ
ejpam-5486	391	7	spaces	space	NOUN
ejpam-5486	391	8	in	in	ADP
ejpam-5486	391	9	this	this	DET
ejpam-5486	391	10	section	section	NOUN
ejpam-5486	391	11	,	,	PUNCT
ejpam-5486	391	12	we	we	PRON
ejpam-5486	391	13	will	will	AUX
ejpam-5486	391	14	introduce	introduce	VERB
ejpam-5486	391	15	and	and	CCONJ
ejpam-5486	391	16	study	study	VERB
ejpam-5486	391	17	the	the	DET
ejpam-5486	391	18	notion	notion	NOUN
ejpam-5486	391	19	of	of	ADP
ejpam-5486	391	20	almost	almost	ADV
ejpam-5486	391	21	ωswd	ωswd	ADJ
ejpam-5486	391	22	-	-	PUNCT
ejpam-5486	391	23	compact	compact	ADJ
ejpam-5486	391	24	spaces	space	NOUN
ejpam-5486	391	25	with	with	ADP
ejpam-5486	391	26	some	some	PRON
ejpam-5486	391	27	of	of	ADP
ejpam-5486	391	28	their	their	PRON
ejpam-5486	391	29	properties	property	NOUN
ejpam-5486	391	30	.	.	PUNCT
ejpam-5486	392	1	definition	definition	NOUN
ejpam-5486	392	2	9	9	NUM
ejpam-5486	392	3	.	.	PUNCT
ejpam-5486	393	1	let	let	AUX
ejpam-5486	393	2	(	(	PUNCT
ejpam-5486	393	3	z	z	NOUN
ejpam-5486	393	4	,	,	PUNCT
ejpam-5486	393	5	τ	τ	PROPN
ejpam-5486	393	6	)	)	PUNCT
ejpam-5486	393	7	be	be	VERB
ejpam-5486	393	8	a	a	DET
ejpam-5486	393	9	t	t	NOUN
ejpam-5486	393	10	s	s	NOUN
ejpam-5486	393	11	and	and	CCONJ
ejpam-5486	393	12	h	h	PROPN
ejpam-5486	393	13	⊆	⊆	NUM
ejpam-5486	393	14	z.	z.	NOUN
ejpam-5486	393	15	a	a	DET
ejpam-5486	393	16	point	point	NOUN
ejpam-5486	393	17	x	x	X
ejpam-5486	393	18	∈	∈	PROPN
ejpam-5486	393	19	z	z	NOUN
ejpam-5486	393	20	is	be	AUX
ejpam-5486	393	21	said	say	VERB
ejpam-5486	393	22	to	to	PART
ejpam-5486	393	23	be	be	AUX
ejpam-5486	393	24	ωswdθaccumulation	ωswdθaccumulation	NOUN
ejpam-5486	393	25	point	point	NOUN
ejpam-5486	393	26	of	of	ADP
ejpam-5486	393	27	h	h	NOUN
ejpam-5486	393	28	if	if	SCONJ
ejpam-5486	393	29	clωswd(g	clωswd(g	PROPN
ejpam-5486	393	30	)	)	PUNCT
ejpam-5486	393	31	∩h	∩h	PROPN
ejpam-5486	393	32	̸=	̸=	PROPN
ejpam-5486	393	33	ϕ	ϕ	PROPN
ejpam-5486	393	34	for	for	ADP
ejpam-5486	393	35	each	each	DET
ejpam-5486	393	36	g	g	PROPN
ejpam-5486	393	37	∈	∈	PROPN
ejpam-5486	393	38	ωswd(z	ωswd(z	PROPN
ejpam-5486	393	39	,	,	PUNCT
ejpam-5486	393	40	τ	τ	PROPN
ejpam-5486	393	41	)	)	PUNCT
ejpam-5486	393	42	with	with	ADP
ejpam-5486	393	43	x	x	PROPN
ejpam-5486	393	44	∈	∈	PROPN
ejpam-5486	393	45	g.	g.	NOUN
ejpam-5486	393	46	furthermore	furthermore	ADV
ejpam-5486	393	47	,	,	PUNCT
ejpam-5486	393	48	an	an	DET
ejpam-5486	393	49	ωswdθclosure	ωswdθclosure	NOUN
ejpam-5486	393	50	of	of	ADP
ejpam-5486	393	51	h	h	NOUN
ejpam-5486	393	52	is	be	AUX
ejpam-5486	393	53	the	the	DET
ejpam-5486	393	54	set	set	NOUN
ejpam-5486	393	55	off	off	ADP
ejpam-5486	393	56	all	all	DET
ejpam-5486	393	57	ωswdθaccumulation	ωswdθaccumulation	NOUN
ejpam-5486	393	58	points	point	NOUN
ejpam-5486	393	59	of	of	ADP
ejpam-5486	393	60	h	h	NOUN
ejpam-5486	393	61	and	and	CCONJ
ejpam-5486	393	62	it	it	PRON
ejpam-5486	393	63	is	be	AUX
ejpam-5486	393	64	denoted	denote	VERB
ejpam-5486	393	65	by	by	ADP
ejpam-5486	393	66	clωswdθ(h	clωswdθ(h	PROPN
ejpam-5486	393	67	)	)	PUNCT
ejpam-5486	393	68	.	.	PUNCT
ejpam-5486	394	1	if	if	SCONJ
ejpam-5486	394	2	clωswdθ(h	clωswdθ(h	NOUN
ejpam-5486	394	3	)	)	PUNCT
ejpam-5486	394	4	=	=	SYM
ejpam-5486	395	1	h	h	NOUN
ejpam-5486	395	2	,	,	PUNCT
ejpam-5486	395	3	then	then	ADV
ejpam-5486	395	4	h	h	NOUN
ejpam-5486	395	5	is	be	AUX
ejpam-5486	395	6	said	say	VERB
ejpam-5486	395	7	to	to	PART
ejpam-5486	395	8	be	be	AUX
ejpam-5486	395	9	ωswdθclosed	ωswdθclose	VERB
ejpam-5486	395	10	subset	subset	NOUN
ejpam-5486	395	11	of	of	ADP
ejpam-5486	395	12	(	(	PUNCT
ejpam-5486	395	13	z	z	PROPN
ejpam-5486	395	14	,	,	PUNCT
ejpam-5486	395	15	τ	τ	PROPN
ejpam-5486	395	16	)	)	PUNCT
ejpam-5486	395	17	and	and	CCONJ
ejpam-5486	395	18	its	its	PRON
ejpam-5486	395	19	complement	complement	NOUN
ejpam-5486	395	20	is	be	AUX
ejpam-5486	395	21	said	say	VERB
ejpam-5486	395	22	to	to	PART
ejpam-5486	395	23	be	be	AUX
ejpam-5486	395	24	ωswdθopen	ωswdθopen	ADJ
ejpam-5486	395	25	subset	subset	NOUN
ejpam-5486	395	26	of	of	ADP
ejpam-5486	395	27	(	(	PUNCT
ejpam-5486	395	28	z	z	PROPN
ejpam-5486	395	29	,	,	PUNCT
ejpam-5486	395	30	τ	τ	PROPN
ejpam-5486	395	31	)	)	PUNCT
ejpam-5486	395	32	.	.	PUNCT
ejpam-5486	396	1	the	the	DET
ejpam-5486	396	2	following	follow	VERB
ejpam-5486	396	3	proposition	proposition	NOUN
ejpam-5486	396	4	can	can	AUX
ejpam-5486	396	5	be	be	AUX
ejpam-5486	396	6	easily	easily	ADV
ejpam-5486	396	7	constructed	construct	VERB
ejpam-5486	396	8	.	.	PUNCT
ejpam-5486	397	1	proposition	proposition	NOUN
ejpam-5486	397	2	5	5	NUM
ejpam-5486	397	3	.	.	PUNCT
ejpam-5486	398	1	let	let	AUX
ejpam-5486	398	2	(	(	PUNCT
ejpam-5486	398	3	z	z	NOUN
ejpam-5486	398	4	,	,	PUNCT
ejpam-5486	398	5	τ	τ	PROPN
ejpam-5486	398	6	)	)	PUNCT
ejpam-5486	398	7	be	be	VERB
ejpam-5486	398	8	a	a	DET
ejpam-5486	398	9	t	t	NOUN
ejpam-5486	398	10	s	s	NOUN
ejpam-5486	398	11	and	and	CCONJ
ejpam-5486	398	12	h	h	PROPN
ejpam-5486	398	13	⊆	⊆	NUM
ejpam-5486	398	14	z.	z.	PROPN
ejpam-5486	399	1	then	then	ADV
ejpam-5486	399	2	:	:	PUNCT
ejpam-5486	399	3	(	(	PUNCT
ejpam-5486	399	4	i	i	NOUN
ejpam-5486	399	5	)	)	PUNCT
ejpam-5486	399	6	h	h	PROPN
ejpam-5486	399	7	is	be	AUX
ejpam-5486	399	8	ωswdθopen	ωswdθopen	ADJ
ejpam-5486	399	9	set	set	ADJ
ejpam-5486	399	10	iff	iff	PROPN
ejpam-5486	399	11	for	for	ADP
ejpam-5486	399	12	each	each	DET
ejpam-5486	399	13	x	x	SYM
ejpam-5486	399	14	∈	∈	PROPN
ejpam-5486	399	15	h	h	NOUN
ejpam-5486	399	16	there	there	PRON
ejpam-5486	399	17	is	be	VERB
ejpam-5486	399	18	g	g	PROPN
ejpam-5486	399	19	∈	∈	PROPN
ejpam-5486	399	20	ωswd(z	ωswd(z	PROPN
ejpam-5486	399	21	,	,	PUNCT
ejpam-5486	399	22	τ	τ	PROPN
ejpam-5486	399	23	)	)	PUNCT
ejpam-5486	399	24	with	with	ADP
ejpam-5486	399	25	x	x	PROPN
ejpam-5486	399	26	∈	∈	PROPN
ejpam-5486	399	27	g	g	PROPN
ejpam-5486	399	28	⊆	⊆	NUM
ejpam-5486	399	29	clωswd(g	clωswd(g	NOUN
ejpam-5486	399	30	)	)	PUNCT
ejpam-5486	399	31	⊆	⊆	PROPN
ejpam-5486	399	32	h.	h.	PROPN
ejpam-5486	399	33	(	(	PUNCT
ejpam-5486	399	34	ii	ii	PROPN
ejpam-5486	399	35	)	)	PUNCT
ejpam-5486	399	36	if	if	SCONJ
ejpam-5486	399	37	h	h	PROPN
ejpam-5486	399	38	∈	∈	PROPN
ejpam-5486	399	39	ωswd(z	ωswd(z	PROPN
ejpam-5486	399	40	,	,	PUNCT
ejpam-5486	399	41	τ)∩ωswdc(z	τ)∩ωswdc(z	NOUN
ejpam-5486	399	42	,	,	PUNCT
ejpam-5486	399	43	τ	τ	PROPN
ejpam-5486	399	44	)	)	PUNCT
ejpam-5486	399	45	,	,	PUNCT
ejpam-5486	399	46	then	then	ADV
ejpam-5486	399	47	h	h	NOUN
ejpam-5486	399	48	is	be	AUX
ejpam-5486	399	49	ωswdθclosed	ωswdθclose	VERB
ejpam-5486	399	50	subset	subset	NOUN
ejpam-5486	399	51	of	of	ADP
ejpam-5486	399	52	(	(	PUNCT
ejpam-5486	399	53	z	z	PROPN
ejpam-5486	399	54	,	,	PUNCT
ejpam-5486	399	55	τ	τ	PROPN
ejpam-5486	399	56	)	)	PUNCT
ejpam-5486	399	57	.	.	PUNCT
ejpam-5486	400	1	(	(	PUNCT
ejpam-5486	400	2	iii	iii	X
ejpam-5486	400	3	)	)	PUNCT
ejpam-5486	400	4	clωswd(h	clωswd(h	PROPN
ejpam-5486	400	5	)	)	PUNCT
ejpam-5486	400	6	⊆	⊆	NUM
ejpam-5486	400	7	clωswdθ(h	clωswdθ(h	NOUN
ejpam-5486	400	8	)	)	PUNCT
ejpam-5486	400	9	and	and	CCONJ
ejpam-5486	400	10	if	if	SCONJ
ejpam-5486	400	11	h	h	PRON
ejpam-5486	400	12	∈	∈	PROPN
ejpam-5486	400	13	ωswd(z	ωswd(z	PROPN
ejpam-5486	400	14	,	,	PUNCT
ejpam-5486	400	15	τ	τ	PROPN
ejpam-5486	400	16	)	)	PUNCT
ejpam-5486	400	17	,	,	PUNCT
ejpam-5486	400	18	then	then	ADV
ejpam-5486	400	19	clωswd(h	clωswd(h	NOUN
ejpam-5486	400	20	)	)	PUNCT
ejpam-5486	400	21	=	=	SYM
ejpam-5486	400	22	clωswdθ(h	clωswdθ(h	PROPN
ejpam-5486	400	23	)	)	PUNCT
ejpam-5486	400	24	.	.	PUNCT
ejpam-5486	401	1	definition	definition	NOUN
ejpam-5486	401	2	10	10	NUM
ejpam-5486	401	3	.	.	PUNCT
ejpam-5486	402	1	let	let	AUX
ejpam-5486	402	2	(	(	PUNCT
ejpam-5486	402	3	z	z	NOUN
ejpam-5486	402	4	,	,	PUNCT
ejpam-5486	402	5	τ	τ	PROPN
ejpam-5486	402	6	)	)	PUNCT
ejpam-5486	402	7	be	be	VERB
ejpam-5486	402	8	a	a	DET
ejpam-5486	402	9	t	t	NOUN
ejpam-5486	402	10	s	s	NOUN
ejpam-5486	402	11	and	and	CCONJ
ejpam-5486	402	12	h	h	PROPN
ejpam-5486	402	13	⊆	⊆	NUM
ejpam-5486	402	14	z.	z.	PROPN
ejpam-5486	403	1	then	then	ADV
ejpam-5486	403	2	:	:	PUNCT
ejpam-5486	403	3	(	(	PUNCT
ejpam-5486	403	4	i	i	NOUN
ejpam-5486	403	5	)	)	PUNCT
ejpam-5486	403	6	a	a	DET
ejpam-5486	403	7	family	family	NOUN
ejpam-5486	403	8	h	h	NOUN
ejpam-5486	403	9	=	=	PRON
ejpam-5486	403	10	{	{	PUNCT
ejpam-5486	403	11	hα	hα	X
ejpam-5486	403	12	:	:	PUNCT
ejpam-5486	403	13	α	α	PROPN
ejpam-5486	403	14	∈	∈	PROPN
ejpam-5486	403	15	∆	∆	X
ejpam-5486	403	16	}	}	PUNCT
ejpam-5486	403	17	is	be	AUX
ejpam-5486	403	18	said	say	VERB
ejpam-5486	403	19	to	to	PART
ejpam-5486	403	20	be	be	AUX
ejpam-5486	403	21	ωswd(z	ωswd(z	PROPN
ejpam-5486	403	22	,	,	PUNCT
ejpam-5486	403	23	τ)-cover(resp	τ)-cover(resp	PROPN
ejpam-5486	403	24	.	.	NUM
ejpam-5486	403	25	,	,	PUNCT
ejpam-5486	403	26	ωswd(z	ωswd(z	PROPN
ejpam-5486	403	27	,	,	PUNCT
ejpam-5486	403	28	τ)θ	τ)θ	PUNCT
ejpam-5486	403	29	-	-	PUNCT
ejpam-5486	403	30	cover	cover	NOUN
ejpam-5486	403	31	,	,	PUNCT
ejpam-5486	403	32	τ	τ	PROPN
ejpam-5486	403	33	-cover	-cover	PROPN
ejpam-5486	403	34	)	)	PUNCT
ejpam-5486	403	35	of	of	ADP
ejpam-5486	403	36	h	h	NOUN
ejpam-5486	403	37	if	if	SCONJ
ejpam-5486	403	38	h	h	NOUN
ejpam-5486	403	39	⊆	⊆	NOUN
ejpam-5486	403	40	∪	∪	ADP
ejpam-5486	403	41	α∈∆	α∈∆	PRON
ejpam-5486	403	42	hα	hα	NOUN
ejpam-5486	403	43	and	and	CCONJ
ejpam-5486	403	44	hα	hα	X
ejpam-5486	403	45	is	be	AUX
ejpam-5486	403	46	an	an	DET
ejpam-5486	403	47	ωswd	ωswd	ADJ
ejpam-5486	403	48	-	-	PUNCT
ejpam-5486	403	49	open	open	ADJ
ejpam-5486	403	50	(	(	PUNCT
ejpam-5486	403	51	resp	resp	NOUN
ejpam-5486	403	52	.	.	PUNCT
ejpam-5486	403	53	,	,	PUNCT
ejpam-5486	403	54	ωswdθopen	ωswdθopen	ADJ
ejpam-5486	403	55	,	,	PUNCT
ejpam-5486	403	56	open	open	ADJ
ejpam-5486	403	57	)	)	PUNCT
ejpam-5486	403	58	subset	subset	NOUN
ejpam-5486	403	59	of	of	ADP
ejpam-5486	403	60	(	(	PUNCT
ejpam-5486	403	61	z	z	PROPN
ejpam-5486	403	62	,	,	PUNCT
ejpam-5486	403	63	τ	τ	PROPN
ejpam-5486	403	64	)	)	PUNCT
ejpam-5486	403	65	for	for	ADP
ejpam-5486	403	66	each	each	DET
ejpam-5486	403	67	α	α	NOUN
ejpam-5486	403	68	∈	∈	PROPN
ejpam-5486	403	69	∆.	∆.	PROPN
ejpam-5486	403	70	(	(	PUNCT
ejpam-5486	403	71	ii	ii	NOUN
ejpam-5486	403	72	)	)	PUNCT
ejpam-5486	403	73	(	(	PUNCT
ejpam-5486	403	74	z	z	PROPN
ejpam-5486	403	75	,	,	PUNCT
ejpam-5486	403	76	τ	τ	X
ejpam-5486	403	77	)	)	PUNCT
ejpam-5486	403	78	is	be	AUX
ejpam-5486	403	79	said	say	VERB
ejpam-5486	403	80	to	to	PART
ejpam-5486	403	81	be	be	AUX
ejpam-5486	403	82	almost	almost	ADV
ejpam-5486	403	83	ωswd	ωswd	ADJ
ejpam-5486	403	84	-	-	PUNCT
ejpam-5486	403	85	compact	compact	ADJ
ejpam-5486	403	86	if	if	SCONJ
ejpam-5486	403	87	for	for	ADP
ejpam-5486	403	88	each	each	DET
ejpam-5486	403	89	ωswd(z	ωswd(z	PROPN
ejpam-5486	403	90	,	,	PUNCT
ejpam-5486	403	91	τ)-cover	τ)-cover	ADV
ejpam-5486	403	92	h	h	NOUN
ejpam-5486	403	93	=	=	PRON
ejpam-5486	403	94	{	{	PUNCT
ejpam-5486	403	95	hα	hα	X
ejpam-5486	403	96	:	:	PUNCT
ejpam-5486	403	97	α	α	PROPN
ejpam-5486	403	98	∈	∈	PROPN
ejpam-5486	403	99	∆	∆	PROPN
ejpam-5486	403	100	}	}	PUNCT
ejpam-5486	403	101	of	of	ADP
ejpam-5486	403	102	z	z	NOUN
ejpam-5486	403	103	there	there	PRON
ejpam-5486	403	104	is	be	VERB
ejpam-5486	403	105	a	a	DET
ejpam-5486	403	106	finite	finite	NOUN
ejpam-5486	403	107	subset	subset	NOUN
ejpam-5486	403	108	∆	∆	ADJ
ejpam-5486	403	109	◦	◦	NOUN
ejpam-5486	403	110	⊆	⊆	NUM
ejpam-5486	403	111	∆	∆	X
ejpam-5486	403	112	with	with	ADP
ejpam-5486	403	113	z	z	NOUN
ejpam-5486	403	114	=	=	SYM
ejpam-5486	403	115	∪	∪	ADP
ejpam-5486	403	116	α∈∆	α∈∆	NOUN
ejpam-5486	403	117	◦	◦	NOUN
ejpam-5486	403	118	clωswd(hα	clωswd(hα	NOUN
ejpam-5486	403	119	)	)	PUNCT
ejpam-5486	403	120	.	.	PUNCT
ejpam-5486	404	1	the	the	DET
ejpam-5486	404	2	following	follow	VERB
ejpam-5486	404	3	results	result	NOUN
ejpam-5486	404	4	follow	follow	VERB
ejpam-5486	404	5	immediately	immediately	ADV
ejpam-5486	404	6	from	from	ADP
ejpam-5486	404	7	definitions	definition	NOUN
ejpam-5486	404	8	5	5	NUM
ejpam-5486	404	9	and	and	CCONJ
ejpam-5486	404	10	10	10	NUM
ejpam-5486	404	11	and	and	CCONJ
ejpam-5486	404	12	the	the	DET
ejpam-5486	404	13	fact	fact	NOUN
ejpam-5486	404	14	that	that	SCONJ
ejpam-5486	404	15	τ	τ	PROPN
ejpam-5486	404	16	⊆	⊆	NUM
ejpam-5486	404	17	swd(z	swd(z	PROPN
ejpam-5486	404	18	,	,	PUNCT
ejpam-5486	404	19	τ	τ	X
ejpam-5486	404	20	)	)	PUNCT
ejpam-5486	404	21	⊆	⊆	NUM
ejpam-5486	404	22	ωswd(z	ωswd(z	PROPN
ejpam-5486	404	23	,	,	PUNCT
ejpam-5486	404	24	τ	τ	PROPN
ejpam-5486	404	25	)	)	PUNCT
ejpam-5486	404	26	for	for	ADP
ejpam-5486	404	27	any	any	DET
ejpam-5486	404	28	space	space	NOUN
ejpam-5486	404	29	(	(	PUNCT
ejpam-5486	404	30	z	z	NOUN
ejpam-5486	404	31	,	,	PUNCT
ejpam-5486	404	32	τ	τ	PROPN
ejpam-5486	404	33	)	)	PUNCT
ejpam-5486	404	34	.	.	PUNCT
ejpam-5486	405	1	theorem	theorem	VERB
ejpam-5486	405	2	16	16	NUM
ejpam-5486	405	3	.	.	PUNCT
ejpam-5486	406	1	if	if	SCONJ
ejpam-5486	406	2	a	a	DET
ejpam-5486	406	3	topological	topological	ADJ
ejpam-5486	406	4	space	space	NOUN
ejpam-5486	406	5	(	(	PUNCT
ejpam-5486	406	6	z	z	NOUN
ejpam-5486	406	7	,	,	PUNCT
ejpam-5486	406	8	τ	τ	X
ejpam-5486	406	9	)	)	PUNCT
ejpam-5486	406	10	is	be	AUX
ejpam-5486	406	11	almost	almost	ADV
ejpam-5486	406	12	ωswd	ωswd	ADJ
ejpam-5486	406	13	-	-	PUNCT
ejpam-5486	406	14	compact	compact	ADJ
ejpam-5486	406	15	,	,	PUNCT
ejpam-5486	406	16	then	then	ADV
ejpam-5486	406	17	the	the	DET
ejpam-5486	406	18	following	follow	VERB
ejpam-5486	406	19	hold	hold	NOUN
ejpam-5486	406	20	:	:	PUNCT
ejpam-5486	406	21	(	(	PUNCT
ejpam-5486	406	22	i	i	NOUN
ejpam-5486	406	23	)	)	PUNCT
ejpam-5486	406	24	(	(	PUNCT
ejpam-5486	406	25	z	z	X
ejpam-5486	406	26	,	,	PUNCT
ejpam-5486	406	27	τ	τ	X
ejpam-5486	406	28	)	)	PUNCT
ejpam-5486	406	29	is	be	AUX
ejpam-5486	406	30	almost	almost	ADV
ejpam-5486	406	31	swd	swd	PROPN
ejpam-5486	406	32	-	-	ADJ
ejpam-5486	406	33	compact	compact	ADJ
ejpam-5486	406	34	.	.	PUNCT
ejpam-5486	407	1	(	(	PUNCT
ejpam-5486	407	2	ii	ii	NOUN
ejpam-5486	407	3	)	)	PUNCT
ejpam-5486	407	4	if	if	SCONJ
ejpam-5486	407	5	h	h	NOUN
ejpam-5486	407	6	=	=	PRON
ejpam-5486	407	7	{	{	PUNCT
ejpam-5486	407	8	hα	hα	X
ejpam-5486	407	9	:	:	PUNCT
ejpam-5486	407	10	α	α	PROPN
ejpam-5486	407	11	∈	∈	PROPN
ejpam-5486	407	12	∆	∆	X
ejpam-5486	407	13	}	}	PUNCT
ejpam-5486	407	14	is	be	AUX
ejpam-5486	407	15	τ	τ	PROPN
ejpam-5486	407	16	-cover	-cover	PROPN
ejpam-5486	407	17	of	of	ADP
ejpam-5486	407	18	z	z	PROPN
ejpam-5486	407	19	,	,	PUNCT
ejpam-5486	407	20	then	then	ADV
ejpam-5486	407	21	there	there	PRON
ejpam-5486	407	22	is	be	VERB
ejpam-5486	407	23	a	a	DET
ejpam-5486	407	24	finite	finite	NOUN
ejpam-5486	407	25	subset	subset	NOUN
ejpam-5486	407	26	∆	∆	ADJ
ejpam-5486	407	27	◦	◦	NOUN
ejpam-5486	407	28	⊆	⊆	NUM
ejpam-5486	407	29	∆	∆	X
ejpam-5486	407	30	with	with	ADP
ejpam-5486	407	31	z	z	NOUN
ejpam-5486	407	32	=	=	SYM
ejpam-5486	407	33	∪	∪	ADP
ejpam-5486	407	34	α∈∆	α∈∆	NOUN
ejpam-5486	407	35	◦	◦	NOUN
ejpam-5486	407	36	clωswd(hα	clωswd(hα	NOUN
ejpam-5486	407	37	)	)	PUNCT
ejpam-5486	407	38	.	.	PUNCT
ejpam-5486	408	1	(	(	PUNCT
ejpam-5486	408	2	iii	iii	X
ejpam-5486	408	3	)	)	PUNCT
ejpam-5486	408	4	if	if	SCONJ
ejpam-5486	408	5	h	h	NOUN
ejpam-5486	408	6	=	=	PRON
ejpam-5486	408	7	{	{	PUNCT
ejpam-5486	408	8	hα	hα	X
ejpam-5486	408	9	:	:	PUNCT
ejpam-5486	408	10	α	α	PROPN
ejpam-5486	408	11	∈	∈	PROPN
ejpam-5486	408	12	∆	∆	X
ejpam-5486	408	13	}	}	PUNCT
ejpam-5486	408	14	is	be	AUX
ejpam-5486	408	15	an	an	DET
ejpam-5486	408	16	ωswd(z	ωswd(z	NOUN
ejpam-5486	408	17	,	,	PUNCT
ejpam-5486	408	18	τ)-cover	τ)-cover	PUNCT
ejpam-5486	408	19	of	of	ADP
ejpam-5486	408	20	z	z	PROPN
ejpam-5486	408	21	,	,	PUNCT
ejpam-5486	408	22	then	then	ADV
ejpam-5486	408	23	there	there	PRON
ejpam-5486	408	24	is	be	VERB
ejpam-5486	408	25	a	a	DET
ejpam-5486	408	26	finite	finite	NOUN
ejpam-5486	408	27	subset	subset	NOUN
ejpam-5486	408	28	∆	∆	ADJ
ejpam-5486	408	29	◦	◦	NOUN
ejpam-5486	408	30	⊆	⊆	NUM
ejpam-5486	408	31	∆	∆	X
ejpam-5486	408	32	with	with	ADP
ejpam-5486	408	33	z	z	NOUN
ejpam-5486	408	34	=	=	SYM
ejpam-5486	408	35	∪	∪	ADP
ejpam-5486	408	36	α∈∆	α∈∆	NOUN
ejpam-5486	408	37	◦	◦	NOUN
ejpam-5486	408	38	cl(hα	cl(hα	NOUN
ejpam-5486	408	39	)	)	PUNCT
ejpam-5486	408	40	.	.	PUNCT
ejpam-5486	409	1	the	the	DET
ejpam-5486	409	2	converses	converse	NOUN
ejpam-5486	409	3	of	of	ADP
ejpam-5486	409	4	theorem	theorem	NOUN
ejpam-5486	409	5	16	16	NUM
ejpam-5486	409	6	is	be	AUX
ejpam-5486	409	7	not	not	PART
ejpam-5486	409	8	true	true	ADJ
ejpam-5486	409	9	in	in	ADP
ejpam-5486	409	10	general	general	ADJ
ejpam-5486	409	11	as	as	SCONJ
ejpam-5486	409	12	will	will	AUX
ejpam-5486	409	13	see	see	VERB
ejpam-5486	409	14	in	in	ADP
ejpam-5486	409	15	the	the	DET
ejpam-5486	409	16	following	follow	VERB
ejpam-5486	409	17	examples	example	NOUN
ejpam-5486	409	18	.	.	PUNCT
ejpam-5486	410	1	a.	a.	PROPN
ejpam-5486	410	2	rawshdeh	rawshdeh	PROPN
ejpam-5486	410	3	,	,	PUNCT
ejpam-5486	410	4	h.	h.	PROPN
ejpam-5486	410	5	h.	h.	PROPN
ejpam-5486	410	6	al	al	PROPN
ejpam-5486	410	7	-	-	PUNCT
ejpam-5486	410	8	jarrah	jarrah	PROPN
ejpam-5486	410	9	,	,	PUNCT
ejpam-5486	410	10	k.	k.	PROPN
ejpam-5486	410	11	y.	y.	PROPN
ejpam-5486	410	12	al	al	PROPN
ejpam-5486	410	13	-	-	PROPN
ejpam-5486	410	14	zoubi	zoubi	PROPN
ejpam-5486	410	15	/	/	SYM
ejpam-5486	410	16	eur	eur	PROPN
ejpam-5486	410	17	.	.	PUNCT
ejpam-5486	411	1	j.	j.	PROPN
ejpam-5486	411	2	pure	pure	PROPN
ejpam-5486	411	3	appl	appl	PROPN
ejpam-5486	411	4	.	.	PROPN
ejpam-5486	411	5	math	math	PROPN
ejpam-5486	411	6	,	,	PUNCT
ejpam-5486	411	7	17	17	NUM
ejpam-5486	411	8	(	(	PUNCT
ejpam-5486	411	9	4	4	NUM
ejpam-5486	411	10	)	)	PUNCT
ejpam-5486	411	11	(	(	PUNCT
ejpam-5486	411	12	2024	2024	NUM
ejpam-5486	411	13	)	)	PUNCT
ejpam-5486	411	14	,	,	PUNCT
ejpam-5486	411	15	3370	3370	NUM
ejpam-5486	411	16	-	-	SYM
ejpam-5486	411	17	3385	3385	NUM
ejpam-5486	411	18	3381	3381	NUM
ejpam-5486	411	19	example	example	NOUN
ejpam-5486	411	20	7	7	NUM
ejpam-5486	411	21	.	.	PUNCT
ejpam-5486	412	1	(	(	PUNCT
ejpam-5486	412	2	i	i	NOUN
ejpam-5486	412	3	)	)	PUNCT
ejpam-5486	412	4	consider	consider	VERB
ejpam-5486	412	5	(	(	PUNCT
ejpam-5486	412	6	r	r	NOUN
ejpam-5486	412	7	,	,	PUNCT
ejpam-5486	412	8	τind	τind	NOUN
ejpam-5486	412	9	)	)	PUNCT
ejpam-5486	412	10	.	.	PUNCT
ejpam-5486	413	1	then	then	ADV
ejpam-5486	413	2	(	(	PUNCT
ejpam-5486	413	3	r	r	NOUN
ejpam-5486	413	4	,	,	PUNCT
ejpam-5486	413	5	τind	τind	NOUN
ejpam-5486	413	6	)	)	PUNCT
ejpam-5486	413	7	satisfied	satisfied	ADJ
ejpam-5486	413	8	(	(	PUNCT
ejpam-5486	413	9	parts	part	NOUN
ejpam-5486	413	10	ii	ii	PROPN
ejpam-5486	413	11	and	and	CCONJ
ejpam-5486	413	12	iii	iii	X
ejpam-5486	413	13	)	)	PUNCT
ejpam-5486	413	14	of	of	ADP
ejpam-5486	413	15	theorem	theorem	NOUN
ejpam-5486	413	16	16	16	NUM
ejpam-5486	413	17	,	,	PUNCT
ejpam-5486	413	18	but	but	CCONJ
ejpam-5486	413	19	(	(	PUNCT
ejpam-5486	413	20	r	r	NOUN
ejpam-5486	413	21	,	,	PUNCT
ejpam-5486	413	22	τind	τind	NOUN
ejpam-5486	413	23	)	)	PUNCT
ejpam-5486	413	24	is	be	AUX
ejpam-5486	413	25	not	not	PART
ejpam-5486	413	26	almost	almost	ADV
ejpam-5486	413	27	ωswd	ωswd	ADJ
ejpam-5486	413	28	-	-	PUNCT
ejpam-5486	413	29	compact	compact	ADJ
ejpam-5486	413	30	since	since	SCONJ
ejpam-5486	413	31	h	h	NOUN
ejpam-5486	413	32	=	=	PUNCT
ejpam-5486	413	33	{	{	PUNCT
ejpam-5486	413	34	{	{	PUNCT
ejpam-5486	413	35	x	x	NOUN
ejpam-5486	413	36	}	}	PUNCT
ejpam-5486	413	37	:	:	PUNCT
ejpam-5486	413	38	x	x	X
ejpam-5486	413	39	∈	∈	NOUN
ejpam-5486	413	40	r	r	NOUN
ejpam-5486	413	41	}	}	PUNCT
ejpam-5486	413	42	is	be	AUX
ejpam-5486	413	43	an	an	DET
ejpam-5486	413	44	ωswd(z	ωswd(z	NOUN
ejpam-5486	413	45	,	,	PUNCT
ejpam-5486	413	46	τ)-cover	τ)-cover	PUNCT
ejpam-5486	413	47	of	of	ADP
ejpam-5486	413	48	r	r	NOUN
ejpam-5486	413	49	which	which	PRON
ejpam-5486	413	50	has	have	VERB
ejpam-5486	413	51	no	no	DET
ejpam-5486	413	52	finite	finite	NOUN
ejpam-5486	413	53	subset	subset	NOUN
ejpam-5486	413	54	∆	∆	ADJ
ejpam-5486	413	55	◦	◦	NOUN
ejpam-5486	413	56	=	=	SYM
ejpam-5486	413	57	{	{	PUNCT
ejpam-5486	413	58	x1	x1	PROPN
ejpam-5486	413	59	,	,	PUNCT
ejpam-5486	413	60	x2	x2	PROPN
ejpam-5486	413	61	,	,	PUNCT
ejpam-5486	413	62	......	......	PUNCT
ejpam-5486	413	63	xn	xn	X
ejpam-5486	413	64	}	}	PUNCT
ejpam-5486	413	65	⊆	⊆	NUM
ejpam-5486	413	66	r	r	NOUN
ejpam-5486	413	67	with	with	ADP
ejpam-5486	413	68	r	r	NOUN
ejpam-5486	413	69	=	=	SYM
ejpam-5486	413	70	∪	∪	ADJ
ejpam-5486	413	71	xi∈∆	xi∈∆	VERB
ejpam-5486	413	72	◦	◦	NOUN
ejpam-5486	413	73	clωswd{xi	clωswd{xi	NOUN
ejpam-5486	413	74	}	}	PUNCT
ejpam-5486	413	75	=	=	SYM
ejpam-5486	413	76	∪	∪	NOUN
ejpam-5486	413	77	xi∈∆	xi∈∆	VERB
ejpam-5486	413	78	◦	◦	NOUN
ejpam-5486	413	79	{	{	PUNCT
ejpam-5486	413	80	xi	xi	ADP
ejpam-5486	413	81	}	}	PUNCT
ejpam-5486	413	82	.	.	PUNCT
ejpam-5486	414	1	(	(	PUNCT
ejpam-5486	414	2	ii	ii	NOUN
ejpam-5486	414	3	)	)	PUNCT
ejpam-5486	414	4	let	let	VERB
ejpam-5486	414	5	z	z	NOUN
ejpam-5486	414	6	=	=	PUNCT
ejpam-5486	414	7	r	r	NOUN
ejpam-5486	414	8	with	with	ADP
ejpam-5486	414	9	the	the	DET
ejpam-5486	414	10	topology	topology	NOUN
ejpam-5486	414	11	τ	τ	NOUN
ejpam-5486	414	12	=	=	PUNCT
ejpam-5486	414	13	{	{	PUNCT
ejpam-5486	414	14	ϕ,r	ϕ,r	NOUN
ejpam-5486	414	15	,	,	PUNCT
ejpam-5486	414	16	{	{	PUNCT
ejpam-5486	414	17	1}}.then	1}}.then	NUM
ejpam-5486	414	18	(	(	PUNCT
ejpam-5486	414	19	r	r	NOUN
ejpam-5486	414	20	,	,	PUNCT
ejpam-5486	414	21	τ	τ	X
ejpam-5486	414	22	)	)	PUNCT
ejpam-5486	414	23	is	be	AUX
ejpam-5486	414	24	almost	almost	ADV
ejpam-5486	414	25	swd	swd	PROPN
ejpam-5486	414	26	-	-	ADJ
ejpam-5486	414	27	compact	compact	ADJ
ejpam-5486	415	1	but	but	CCONJ
ejpam-5486	415	2	it	it	PRON
ejpam-5486	415	3	is	be	AUX
ejpam-5486	415	4	not	not	PART
ejpam-5486	415	5	almost	almost	ADV
ejpam-5486	415	6	ωswd	ωswd	ADJ
ejpam-5486	415	7	-	-	PUNCT
ejpam-5486	415	8	compact	compact	ADJ
ejpam-5486	415	9	since	since	SCONJ
ejpam-5486	415	10	h	h	NOUN
ejpam-5486	415	11	=	=	PRON
ejpam-5486	415	12	{	{	PUNCT
ejpam-5486	415	13	{	{	PUNCT
ejpam-5486	415	14	1	1	NUM
ejpam-5486	415	15	,	,	PUNCT
ejpam-5486	415	16	x	x	NOUN
ejpam-5486	415	17	}	}	PUNCT
ejpam-5486	415	18	:	:	PUNCT
ejpam-5486	415	19	x	x	X
ejpam-5486	415	20	∈	∈	NOUN
ejpam-5486	415	21	r	r	NOUN
ejpam-5486	415	22	}	}	PUNCT
ejpam-5486	415	23	is	be	AUX
ejpam-5486	415	24	an	an	DET
ejpam-5486	415	25	ωswd(z	ωswd(z	NOUN
ejpam-5486	415	26	,	,	PUNCT
ejpam-5486	415	27	τ)-cover	τ)-cover	PUNCT
ejpam-5486	415	28	of	of	ADP
ejpam-5486	415	29	r	r	NOUN
ejpam-5486	415	30	which	which	PRON
ejpam-5486	415	31	has	have	VERB
ejpam-5486	415	32	no	no	DET
ejpam-5486	415	33	finite	finite	NOUN
ejpam-5486	415	34	subset	subset	NOUN
ejpam-5486	415	35	∆	∆	ADJ
ejpam-5486	415	36	◦	◦	NOUN
ejpam-5486	415	37	=	=	SYM
ejpam-5486	415	38	{	{	PUNCT
ejpam-5486	415	39	x1	x1	PROPN
ejpam-5486	415	40	,	,	PUNCT
ejpam-5486	415	41	x2	x2	PROPN
ejpam-5486	415	42	,	,	PUNCT
ejpam-5486	415	43	......	......	PUNCT
ejpam-5486	415	44	xn	xn	X
ejpam-5486	415	45	}	}	PUNCT
ejpam-5486	415	46	⊆	⊆	NUM
ejpam-5486	415	47	r	r	NOUN
ejpam-5486	415	48	with	with	ADP
ejpam-5486	415	49	r	r	NOUN
ejpam-5486	415	50	=	=	PUNCT
ejpam-5486	415	51	∪	∪	ADP
ejpam-5486	415	52	x∈∆	x∈∆	PROPN
ejpam-5486	415	53	◦	◦	NOUN
ejpam-5486	415	54	clωswd({1	clωswd({1	NUM
ejpam-5486	415	55	,	,	PUNCT
ejpam-5486	415	56	x	x	NOUN
ejpam-5486	415	57	}	}	PUNCT
ejpam-5486	415	58	)	)	PUNCT
ejpam-5486	415	59	=	=	SYM
ejpam-5486	415	60	∪	∪	ADP
ejpam-5486	415	61	x∈∆	x∈∆	PROPN
ejpam-5486	415	62	◦	◦	NOUN
ejpam-5486	415	63	{	{	PUNCT
ejpam-5486	415	64	1	1	NUM
ejpam-5486	415	65	,	,	PUNCT
ejpam-5486	415	66	x	x	NOUN
ejpam-5486	415	67	}	}	PUNCT
ejpam-5486	415	68	.	.	PUNCT
ejpam-5486	416	1	theorem	theorem	NOUN
ejpam-5486	416	2	17	17	NUM
ejpam-5486	416	3	.	.	PUNCT
ejpam-5486	417	1	let	let	AUX
ejpam-5486	417	2	(	(	PUNCT
ejpam-5486	417	3	z	z	NOUN
ejpam-5486	417	4	,	,	PUNCT
ejpam-5486	417	5	τ	τ	PROPN
ejpam-5486	417	6	)	)	PUNCT
ejpam-5486	417	7	be	be	VERB
ejpam-5486	417	8	a	a	DET
ejpam-5486	417	9	t	t	NOUN
ejpam-5486	417	10	s.	s.	PROPN
ejpam-5486	418	1	if	if	SCONJ
ejpam-5486	418	2	(	(	PUNCT
ejpam-5486	418	3	z	z	NOUN
ejpam-5486	418	4	,	,	PUNCT
ejpam-5486	418	5	τ	τ	X
ejpam-5486	418	6	)	)	PUNCT
ejpam-5486	418	7	is	be	AUX
ejpam-5486	418	8	almost	almost	ADV
ejpam-5486	418	9	ωswd	ωswd	ADJ
ejpam-5486	418	10	-	-	PUNCT
ejpam-5486	418	11	compact	compact	ADJ
ejpam-5486	418	12	,	,	PUNCT
ejpam-5486	418	13	then	then	ADV
ejpam-5486	418	14	each	each	DET
ejpam-5486	418	15	ωswd(z	ωswd(z	PROPN
ejpam-5486	418	16	,	,	PUNCT
ejpam-5486	418	17	τ)θ	τ)θ	PUNCT
ejpam-5486	418	18	-	-	NOUN
ejpam-5486	418	19	cover	cover	NOUN
ejpam-5486	418	20	of	of	ADP
ejpam-5486	418	21	z	z	NOUN
ejpam-5486	418	22	has	have	VERB
ejpam-5486	418	23	a	a	DET
ejpam-5486	418	24	finite	finite	ADJ
ejpam-5486	418	25	subcover	subcover	PROPN
ejpam-5486	418	26	.	.	PUNCT
ejpam-5486	419	1	proof	proof	NOUN
ejpam-5486	419	2	.	.	PUNCT
ejpam-5486	420	1	let	let	VERB
ejpam-5486	420	2	h	h	NOUN
ejpam-5486	420	3	=	=	NOUN
ejpam-5486	420	4	{	{	PUNCT
ejpam-5486	420	5	hα	hα	X
ejpam-5486	420	6	:	:	PUNCT
ejpam-5486	420	7	α	α	PROPN
ejpam-5486	420	8	∈	∈	PROPN
ejpam-5486	420	9	∆	∆	X
ejpam-5486	420	10	}	}	PUNCT
ejpam-5486	420	11	be	be	VERB
ejpam-5486	420	12	ωswd(z	ωswd(z	PROPN
ejpam-5486	420	13	,	,	PUNCT
ejpam-5486	420	14	τ)-θ	τ)-θ	NOUN
ejpam-5486	420	15	-	-	PUNCT
ejpam-5486	420	16	cover	cover	NOUN
ejpam-5486	420	17	of	of	ADP
ejpam-5486	420	18	z.	z.	PROPN
ejpam-5486	420	19	for	for	ADP
ejpam-5486	420	20	each	each	DET
ejpam-5486	420	21	x	x	SYM
ejpam-5486	420	22	∈	∈	PROPN
ejpam-5486	420	23	z	z	NOUN
ejpam-5486	420	24	there	there	PRON
ejpam-5486	420	25	is	be	VERB
ejpam-5486	420	26	hα(x	hα(x	NOUN
ejpam-5486	420	27	)	)	PUNCT
ejpam-5486	420	28	∈	∈	PROPN
ejpam-5486	420	29	h	h	NOUN
ejpam-5486	420	30	with	with	ADP
ejpam-5486	420	31	x	x	PROPN
ejpam-5486	420	32	∈	∈	NOUN
ejpam-5486	420	33	hα(x	hα(x	ADV
ejpam-5486	420	34	)	)	PUNCT
ejpam-5486	420	35	for	for	ADP
ejpam-5486	420	36	some	some	DET
ejpam-5486	420	37	α(x	α(x	NOUN
ejpam-5486	420	38	)	)	PUNCT
ejpam-5486	420	39	∈	∈	PROPN
ejpam-5486	421	1	∆.	∆.	X
ejpam-5486	421	2	by	by	ADP
ejpam-5486	421	3	proposition	proposition	NOUN
ejpam-5486	421	4	5	5	NUM
ejpam-5486	421	5	there	there	PRON
ejpam-5486	421	6	is	be	VERB
ejpam-5486	421	7	gα(x	gα(x	NOUN
ejpam-5486	421	8	)	)	PUNCT
ejpam-5486	422	1	∈	∈	PROPN
ejpam-5486	422	2	ωswd(z	ωswd(z	PROPN
ejpam-5486	422	3	,	,	PUNCT
ejpam-5486	422	4	τ	τ	PROPN
ejpam-5486	422	5	)	)	PUNCT
ejpam-5486	422	6	with	with	ADP
ejpam-5486	422	7	x	x	PROPN
ejpam-5486	422	8	∈	∈	PROPN
ejpam-5486	422	9	gα(x	gα(x	NOUN
ejpam-5486	422	10	)	)	PUNCT
ejpam-5486	422	11	⊆	⊆	NUM
ejpam-5486	422	12	clωswd(gα(x	clωswd(gα(x	NOUN
ejpam-5486	422	13	)	)	PUNCT
ejpam-5486	422	14	)	)	PUNCT
ejpam-5486	423	1	⊆	⊆	NUM
ejpam-5486	423	2	hα(x).therefore	hα(x).therefore	NOUN
ejpam-5486	423	3	,	,	PUNCT
ejpam-5486	423	4	g	g	NOUN
ejpam-5486	423	5	=	=	SYM
ejpam-5486	423	6	{	{	PUNCT
ejpam-5486	423	7	gα(x	gα(x	PROPN
ejpam-5486	423	8	)	)	PUNCT
ejpam-5486	423	9	:	:	PUNCT
ejpam-5486	423	10	x	x	X
ejpam-5486	423	11	∈	∈	PROPN
ejpam-5486	423	12	z	z	NOUN
ejpam-5486	423	13	}	}	PUNCT
ejpam-5486	423	14	is	be	AUX
ejpam-5486	423	15	an	an	DET
ejpam-5486	423	16	ωswd(z	ωswd(z	NOUN
ejpam-5486	423	17	,	,	PUNCT
ejpam-5486	423	18	τ)-cover	τ)-cover	PUNCT
ejpam-5486	423	19	of	of	ADP
ejpam-5486	423	20	z	z	NOUN
ejpam-5486	423	21	and	and	CCONJ
ejpam-5486	423	22	hence	hence	ADV
ejpam-5486	423	23	there	there	PRON
ejpam-5486	423	24	is	be	VERB
ejpam-5486	423	25	a	a	DET
ejpam-5486	423	26	finite	finite	NOUN
ejpam-5486	423	27	subset	subset	NOUN
ejpam-5486	423	28	∆	∆	ADJ
ejpam-5486	423	29	◦	◦	NOUN
ejpam-5486	423	30	⊆	⊆	NUM
ejpam-5486	423	31	∆	∆	X
ejpam-5486	423	32	with	with	ADP
ejpam-5486	423	33	z	z	NOUN
ejpam-5486	423	34	=	=	SYM
ejpam-5486	423	35	∪	∪	ADP
ejpam-5486	423	36	x∈∆	x∈∆	PROPN
ejpam-5486	423	37	◦	◦	NOUN
ejpam-5486	423	38	clωswd(gα(x	clωswd(gα(x	NOUN
ejpam-5486	423	39	)	)	PUNCT
ejpam-5486	423	40	)	)	PUNCT
ejpam-5486	424	1	⊆	⊆	X
ejpam-5486	424	2	∪	∪	ADP
ejpam-5486	424	3	x∈∆	x∈∆	PROPN
ejpam-5486	424	4	◦	◦	NOUN
ejpam-5486	424	5	hα(x	hα(x	PUNCT
ejpam-5486	424	6	)	)	PUNCT
ejpam-5486	424	7	.	.	PUNCT
ejpam-5486	425	1	definition	definition	NOUN
ejpam-5486	425	2	11	11	NUM
ejpam-5486	425	3	.	.	PUNCT
ejpam-5486	426	1	let	let	AUX
ejpam-5486	426	2	(	(	PUNCT
ejpam-5486	426	3	z	z	NOUN
ejpam-5486	426	4	,	,	PUNCT
ejpam-5486	426	5	τ	τ	PROPN
ejpam-5486	426	6	)	)	PUNCT
ejpam-5486	426	7	be	be	VERB
ejpam-5486	426	8	a	a	DET
ejpam-5486	426	9	t	t	NOUN
ejpam-5486	426	10	s	s	NOUN
ejpam-5486	426	11	and	and	CCONJ
ejpam-5486	426	12	x	x	PROPN
ejpam-5486	426	13	∈	∈	PROPN
ejpam-5486	426	14	z.	z.	PROPN
ejpam-5486	426	15	a	a	DET
ejpam-5486	426	16	filter	filter	NOUN
ejpam-5486	426	17	base	base	NOUN
ejpam-5486	426	18	f	f	PROPN
ejpam-5486	426	19	on	on	ADP
ejpam-5486	426	20	(	(	PUNCT
ejpam-5486	426	21	z	z	PROPN
ejpam-5486	426	22	,	,	PUNCT
ejpam-5486	426	23	τ	τ	X
ejpam-5486	426	24	)	)	PUNCT
ejpam-5486	426	25	is	be	AUX
ejpam-5486	426	26	said	say	VERB
ejpam-5486	426	27	to	to	PART
ejpam-5486	426	28	be	be	AUX
ejpam-5486	426	29	:	:	PUNCT
ejpam-5486	426	30	(	(	PUNCT
ejpam-5486	426	31	i	i	NOUN
ejpam-5486	426	32	)	)	PUNCT
ejpam-5486	426	33	ωswdθconverge	ωswdθconverge	VERB
ejpam-5486	426	34	to	to	ADP
ejpam-5486	426	35	x	x	SYM
ejpam-5486	426	36	if	if	SCONJ
ejpam-5486	426	37	for	for	ADP
ejpam-5486	426	38	each	each	DET
ejpam-5486	426	39	g	g	PROPN
ejpam-5486	426	40	∈	∈	PROPN
ejpam-5486	426	41	ωswd(z	ωswd(z	PROPN
ejpam-5486	426	42	,	,	PUNCT
ejpam-5486	426	43	τ	τ	PROPN
ejpam-5486	426	44	)	)	PUNCT
ejpam-5486	426	45	with	with	SCONJ
ejpam-5486	426	46	x	x	SYM
ejpam-5486	426	47	∈	∈	PROPN
ejpam-5486	426	48	g	g	NOUN
ejpam-5486	426	49	there	there	PRON
ejpam-5486	426	50	is	be	VERB
ejpam-5486	426	51	f	f	PROPN
ejpam-5486	426	52	∈	∈	PROPN
ejpam-5486	426	53	f	f	PROPN
ejpam-5486	426	54	such	such	ADJ
ejpam-5486	426	55	that	that	SCONJ
ejpam-5486	426	56	f	f	PROPN
ejpam-5486	426	57	⊆	⊆	NUM
ejpam-5486	426	58	clωswd(g	clωswd(g	NOUN
ejpam-5486	426	59	)	)	PUNCT
ejpam-5486	426	60	.	.	PUNCT
ejpam-5486	427	1	(	(	PUNCT
ejpam-5486	427	2	ii	ii	NOUN
ejpam-5486	427	3	)	)	PUNCT
ejpam-5486	427	4	ωswdθaccumulate	ωswdθaccumulate	ADV
ejpam-5486	427	5	at	at	ADP
ejpam-5486	427	6	x	x	SYM
ejpam-5486	427	7	if	if	SCONJ
ejpam-5486	427	8	clωswd(g	clωswd(g	PROPN
ejpam-5486	427	9	)	)	PUNCT
ejpam-5486	427	10	∩	∩	NOUN
ejpam-5486	427	11	f	f	PROPN
ejpam-5486	427	12	̸=	̸=	PROPN
ejpam-5486	427	13	ϕ	ϕ	NOUN
ejpam-5486	427	14	for	for	ADP
ejpam-5486	427	15	each	each	DET
ejpam-5486	427	16	f	f	PROPN
ejpam-5486	427	17	∈	∈	PROPN
ejpam-5486	427	18	f	f	PROPN
ejpam-5486	427	19	and	and	CCONJ
ejpam-5486	427	20	for	for	ADP
ejpam-5486	427	21	each	each	DET
ejpam-5486	427	22	g	g	PROPN
ejpam-5486	427	23	∈	∈	PROPN
ejpam-5486	427	24	ωswd(z	ωswd(z	PROPN
ejpam-5486	427	25	,	,	PUNCT
ejpam-5486	427	26	τ	τ	PROPN
ejpam-5486	427	27	)	)	PUNCT
ejpam-5486	427	28	with	with	ADP
ejpam-5486	427	29	x	x	PROPN
ejpam-5486	427	30	∈	∈	PROPN
ejpam-5486	427	31	g.	g.	NOUN
ejpam-5486	427	32	note	note	VERB
ejpam-5486	427	33	that	that	SCONJ
ejpam-5486	427	34	,	,	PUNCT
ejpam-5486	427	35	if	if	SCONJ
ejpam-5486	427	36	a	a	DET
ejpam-5486	427	37	filter	filter	NOUN
ejpam-5486	427	38	base	base	NOUN
ejpam-5486	427	39	f	f	PROPN
ejpam-5486	427	40	ωswdθconverges	ωswdθconverge	VERB
ejpam-5486	427	41	to	to	ADP
ejpam-5486	427	42	a	a	DET
ejpam-5486	427	43	point	point	NOUN
ejpam-5486	427	44	x	x	ADP
ejpam-5486	427	45	,	,	PUNCT
ejpam-5486	427	46	then	then	ADV
ejpam-5486	427	47	f	f	PROPN
ejpam-5486	427	48	ωswdθaccumulates	ωswdθaccumulate	VERB
ejpam-5486	427	49	at	at	ADP
ejpam-5486	427	50	x.	x.	PROPN
ejpam-5486	427	51	also	also	ADV
ejpam-5486	427	52	,	,	PUNCT
ejpam-5486	427	53	it	it	PRON
ejpam-5486	427	54	is	be	AUX
ejpam-5486	427	55	obvious	obvious	ADJ
ejpam-5486	427	56	to	to	PART
ejpam-5486	427	57	show	show	VERB
ejpam-5486	427	58	that	that	SCONJ
ejpam-5486	427	59	a	a	DET
ejpam-5486	427	60	maximal	maximal	ADJ
ejpam-5486	427	61	filter	filter	NOUN
ejpam-5486	427	62	base	base	NOUN
ejpam-5486	427	63	f	f	PROPN
ejpam-5486	427	64	ωswdθconverges	ωswdθconverge	VERB
ejpam-5486	427	65	to	to	ADP
ejpam-5486	427	66	a	a	DET
ejpam-5486	427	67	point	point	NOUN
ejpam-5486	427	68	x	x	PUNCT
ejpam-5486	427	69	iff	iff	PROPN
ejpam-5486	427	70	f	f	PROPN
ejpam-5486	427	71	ωswdθaccumulates	ωswdθaccumulate	VERB
ejpam-5486	427	72	at	at	ADP
ejpam-5486	427	73	x.	x.	PROPN
ejpam-5486	427	74	theorem	theorem	VERB
ejpam-5486	427	75	18	18	NUM
ejpam-5486	427	76	.	.	PUNCT
ejpam-5486	428	1	let	let	AUX
ejpam-5486	428	2	(	(	PUNCT
ejpam-5486	428	3	z	z	NOUN
ejpam-5486	428	4	,	,	PUNCT
ejpam-5486	428	5	τ	τ	PROPN
ejpam-5486	428	6	)	)	PUNCT
ejpam-5486	428	7	be	be	VERB
ejpam-5486	428	8	a	a	DET
ejpam-5486	428	9	t	t	NOUN
ejpam-5486	428	10	s	s	PART
ejpam-5486	428	11	.	.	PUNCT
ejpam-5486	429	1	then	then	ADV
ejpam-5486	429	2	the	the	DET
ejpam-5486	429	3	following	following	NOUN
ejpam-5486	429	4	are	be	AUX
ejpam-5486	429	5	equivalent	equivalent	ADJ
ejpam-5486	429	6	:	:	PUNCT
ejpam-5486	429	7	(	(	PUNCT
ejpam-5486	429	8	i	i	NOUN
ejpam-5486	429	9	)	)	PUNCT
ejpam-5486	429	10	(	(	PUNCT
ejpam-5486	429	11	z	z	X
ejpam-5486	429	12	,	,	PUNCT
ejpam-5486	429	13	τ	τ	X
ejpam-5486	429	14	)	)	PUNCT
ejpam-5486	429	15	is	be	AUX
ejpam-5486	429	16	almost	almost	ADV
ejpam-5486	429	17	ωswd	ωswd	ADV
ejpam-5486	429	18	-	-	PUNCT
ejpam-5486	429	19	compact	compact	ADJ
ejpam-5486	429	20	.	.	PUNCT
ejpam-5486	430	1	(	(	PUNCT
ejpam-5486	430	2	ii	ii	NOUN
ejpam-5486	430	3	)	)	PUNCT
ejpam-5486	430	4	each	each	DET
ejpam-5486	430	5	maximal	maximal	ADJ
ejpam-5486	430	6	filter	filter	NOUN
ejpam-5486	430	7	base	base	NOUN
ejpam-5486	430	8	ωswdθconverges	ωswdθconverge	NOUN
ejpam-5486	430	9	to	to	ADP
ejpam-5486	430	10	some	some	DET
ejpam-5486	430	11	point	point	NOUN
ejpam-5486	430	12	of	of	ADP
ejpam-5486	430	13	z.	z.	PROPN
ejpam-5486	430	14	(	(	PUNCT
ejpam-5486	430	15	iii	iii	X
ejpam-5486	430	16	)	)	PUNCT
ejpam-5486	430	17	each	each	DET
ejpam-5486	430	18	filter	filter	NOUN
ejpam-5486	430	19	base	base	NOUN
ejpam-5486	430	20	ωswdθaccumulates	ωswdθaccumulate	NOUN
ejpam-5486	430	21	at	at	ADP
ejpam-5486	430	22	some	some	DET
ejpam-5486	430	23	point	point	NOUN
ejpam-5486	430	24	of	of	ADP
ejpam-5486	430	25	z.	z.	PROPN
ejpam-5486	430	26	(	(	PUNCT
ejpam-5486	430	27	iv	iv	X
ejpam-5486	430	28	)	)	PUNCT
ejpam-5486	430	29	for	for	ADP
ejpam-5486	430	30	each	each	DET
ejpam-5486	430	31	family	family	NOUN
ejpam-5486	430	32	{	{	PUNCT
ejpam-5486	430	33	hα	hα	X
ejpam-5486	430	34	:	:	PUNCT
ejpam-5486	430	35	α	α	PROPN
ejpam-5486	430	36	∈	∈	PROPN
ejpam-5486	430	37	∆	∆	NOUN
ejpam-5486	430	38	}	}	PUNCT
ejpam-5486	430	39	of	of	ADP
ejpam-5486	430	40	ωswd	ωswd	ADJ
ejpam-5486	430	41	-	-	PUNCT
ejpam-5486	430	42	closed	closed	ADJ
ejpam-5486	430	43	subsets	subset	NOUN
ejpam-5486	430	44	of	of	ADP
ejpam-5486	430	45	(	(	PUNCT
ejpam-5486	430	46	z	z	PROPN
ejpam-5486	430	47	,	,	PUNCT
ejpam-5486	430	48	τ	τ	PROPN
ejpam-5486	430	49	)	)	PUNCT
ejpam-5486	430	50	and	and	CCONJ
ejpam-5486	430	51	∩	∩	NOUN
ejpam-5486	430	52	α∈∆	α∈∆	PRON
ejpam-5486	430	53	hα	hα	ADP
ejpam-5486	430	54	=	=	NOUN
ejpam-5486	430	55	ϕ	ϕ	PROPN
ejpam-5486	430	56	,	,	PUNCT
ejpam-5486	430	57	there	there	PRON
ejpam-5486	430	58	is	be	VERB
ejpam-5486	430	59	a	a	DET
ejpam-5486	430	60	finite	finite	NOUN
ejpam-5486	430	61	subset	subset	NOUN
ejpam-5486	430	62	∆	∆	ADJ
ejpam-5486	430	63	◦	◦	NOUN
ejpam-5486	430	64	⊆	⊆	NUM
ejpam-5486	430	65	∆	∆	X
ejpam-5486	430	66	with	with	ADP
ejpam-5486	430	67	∩	∩	NOUN
ejpam-5486	430	68	α∈∆	α∈∆	VERB
ejpam-5486	430	69	◦	◦	NOUN
ejpam-5486	430	70	intωswd(hα	intωswd(hα	NOUN
ejpam-5486	430	71	)	)	PUNCT
ejpam-5486	431	1	=	=	SYM
ejpam-5486	431	2	ϕ.	ϕ.	NOUN
ejpam-5486	431	3	(	(	PUNCT
ejpam-5486	431	4	v	v	NOUN
ejpam-5486	431	5	)	)	PUNCT
ejpam-5486	431	6	for	for	ADP
ejpam-5486	431	7	each	each	DET
ejpam-5486	431	8	family	family	NOUN
ejpam-5486	431	9	{	{	PUNCT
ejpam-5486	431	10	hα	hα	X
ejpam-5486	431	11	:	:	PUNCT
ejpam-5486	431	12	α	α	PROPN
ejpam-5486	431	13	∈	∈	PROPN
ejpam-5486	431	14	∆	∆	NOUN
ejpam-5486	431	15	}	}	PUNCT
ejpam-5486	431	16	of	of	ADP
ejpam-5486	431	17	ωswd	ωswd	ADJ
ejpam-5486	431	18	-	-	PUNCT
ejpam-5486	431	19	closed	closed	ADJ
ejpam-5486	431	20	subsets	subset	NOUN
ejpam-5486	431	21	of	of	ADP
ejpam-5486	431	22	(	(	PUNCT
ejpam-5486	431	23	z	z	PROPN
ejpam-5486	431	24	,	,	PUNCT
ejpam-5486	431	25	τ	τ	PROPN
ejpam-5486	431	26	)	)	PUNCT
ejpam-5486	431	27	and	and	CCONJ
ejpam-5486	431	28	∩	∩	NOUN
ejpam-5486	431	29	α∈∆	α∈∆	VERB
ejpam-5486	431	30	◦	◦	NOUN
ejpam-5486	431	31	intωswd(hα	intωswd(hα	NOUN
ejpam-5486	431	32	)	)	PUNCT
ejpam-5486	431	33	̸=	̸=	PROPN
ejpam-5486	431	34	ϕ	ϕ	NOUN
ejpam-5486	431	35	for	for	ADP
ejpam-5486	431	36	each	each	DET
ejpam-5486	431	37	finite	finite	NOUN
ejpam-5486	431	38	subset	subset	VERB
ejpam-5486	431	39	∆	∆	ADJ
ejpam-5486	431	40	◦	◦	NOUN
ejpam-5486	431	41	⊆	⊆	NUM
ejpam-5486	431	42	∆	∆	X
ejpam-5486	431	43	,	,	PUNCT
ejpam-5486	431	44	then	then	ADV
ejpam-5486	431	45	∩	∩	ADJ
ejpam-5486	431	46	α∈∆	α∈∆	NOUN
ejpam-5486	431	47	hα	hα	ADP
ejpam-5486	431	48	̸=	̸=	PROPN
ejpam-5486	431	49	ϕ.	ϕ.	PROPN
ejpam-5486	431	50	proof	proof	NOUN
ejpam-5486	431	51	.	.	PUNCT
ejpam-5486	432	1	the	the	DET
ejpam-5486	432	2	implication	implication	NOUN
ejpam-5486	432	3	(	(	PUNCT
ejpam-5486	432	4	iv	iv	X
ejpam-5486	432	5	→	→	SYM
ejpam-5486	432	6	v	v	NOUN
ejpam-5486	432	7	)	)	PUNCT
ejpam-5486	432	8	is	be	AUX
ejpam-5486	432	9	obvious	obvious	ADJ
ejpam-5486	432	10	.	.	PUNCT
ejpam-5486	433	1	(	(	PUNCT
ejpam-5486	433	2	i	i	PROPN
ejpam-5486	433	3	→	→	SYM
ejpam-5486	433	4	ii	ii	PROPN
ejpam-5486	433	5	)	)	PUNCT
ejpam-5486	433	6	let	let	VERB
ejpam-5486	433	7	f	f	PRON
ejpam-5486	433	8	be	be	AUX
ejpam-5486	433	9	a	a	DET
ejpam-5486	433	10	maximal	maximal	ADJ
ejpam-5486	433	11	filter	filter	NOUN
ejpam-5486	433	12	base	base	NOUN
ejpam-5486	433	13	on	on	ADP
ejpam-5486	433	14	z	z	NOUN
ejpam-5486	433	15	and	and	CCONJ
ejpam-5486	433	16	suppose	suppose	VERB
ejpam-5486	433	17	that	that	SCONJ
ejpam-5486	433	18	it	it	PRON
ejpam-5486	433	19	does	do	AUX
ejpam-5486	433	20	not	not	PART
ejpam-5486	433	21	ωswdθconverge	ωswdθconverge	VERB
ejpam-5486	433	22	to	to	ADP
ejpam-5486	433	23	any	any	DET
ejpam-5486	433	24	point	point	NOUN
ejpam-5486	433	25	of	of	ADP
ejpam-5486	433	26	z.	z.	PROPN
ejpam-5486	433	27	since	since	SCONJ
ejpam-5486	433	28	f	f	PROPN
ejpam-5486	433	29	does	do	AUX
ejpam-5486	433	30	not	not	PART
ejpam-5486	433	31	ωswdθaccumulate	ωswdθaccumulate	VERB
ejpam-5486	433	32	at	at	ADP
ejpam-5486	433	33	any	any	DET
ejpam-5486	433	34	point	point	NOUN
ejpam-5486	433	35	x	x	X
ejpam-5486	433	36	∈	∈	PROPN
ejpam-5486	433	37	z	z	NOUN
ejpam-5486	433	38	,	,	PUNCT
ejpam-5486	433	39	there	there	PRON
ejpam-5486	433	40	is	be	VERB
ejpam-5486	433	41	fx	fx	ADP
ejpam-5486	433	42	∈	∈	PROPN
ejpam-5486	433	43	f	f	PROPN
ejpam-5486	433	44	and	and	CCONJ
ejpam-5486	433	45	gx	gx	PROPN
ejpam-5486	433	46	∈	∈	PROPN
ejpam-5486	433	47	ωswd(z	ωswd(z	PROPN
ejpam-5486	433	48	,	,	PUNCT
ejpam-5486	433	49	τ	τ	PROPN
ejpam-5486	433	50	)	)	PUNCT
ejpam-5486	433	51	with	with	ADP
ejpam-5486	433	52	x	x	PROPN
ejpam-5486	433	53	∈	∈	PROPN
ejpam-5486	433	54	gx	gx	PROPN
ejpam-5486	433	55	such	such	ADJ
ejpam-5486	433	56	that	that	DET
ejpam-5486	433	57	clωswd(gx	clωswd(gx	ADJ
ejpam-5486	433	58	)	)	PUNCT
ejpam-5486	433	59	∩	∩	NOUN
ejpam-5486	433	60	fx	fx	NOUN
ejpam-5486	433	61	=	=	SYM
ejpam-5486	433	62	ϕ.	ϕ.	PROPN
ejpam-5486	433	63	therefore	therefore	ADV
ejpam-5486	433	64	,	,	PUNCT
ejpam-5486	433	65	{	{	PUNCT
ejpam-5486	433	66	gx	gx	INTJ
ejpam-5486	433	67	:	:	PUNCT
ejpam-5486	433	68	x	x	SYM
ejpam-5486	433	69	∈	∈	PROPN
ejpam-5486	433	70	z	z	NOUN
ejpam-5486	433	71	}	}	PUNCT
ejpam-5486	433	72	is	be	AUX
ejpam-5486	433	73	an	an	DET
ejpam-5486	433	74	ωswd(z	ωswd(z	NOUN
ejpam-5486	433	75	,	,	PUNCT
ejpam-5486	433	76	τ)-cover	τ)-cover	PUNCT
ejpam-5486	433	77	of	of	ADP
ejpam-5486	433	78	z	z	NOUN
ejpam-5486	434	1	and	and	CCONJ
ejpam-5486	434	2	so	so	ADV
ejpam-5486	434	3	there	there	PRON
ejpam-5486	434	4	is	be	VERB
ejpam-5486	434	5	a	a	DET
ejpam-5486	434	6	finite	finite	NOUN
ejpam-5486	434	7	subset	subset	NOUN
ejpam-5486	434	8	a.	a.	NOUN
ejpam-5486	434	9	rawshdeh	rawshdeh	PROPN
ejpam-5486	434	10	,	,	PUNCT
ejpam-5486	434	11	h.	h.	PROPN
ejpam-5486	434	12	h.	h.	PROPN
ejpam-5486	434	13	al	al	PROPN
ejpam-5486	434	14	-	-	PUNCT
ejpam-5486	434	15	jarrah	jarrah	PROPN
ejpam-5486	434	16	,	,	PUNCT
ejpam-5486	435	1	k.	k.	PROPN
ejpam-5486	435	2	y.	y.	PROPN
ejpam-5486	435	3	al	al	PROPN
ejpam-5486	435	4	-	-	PROPN
ejpam-5486	435	5	zoubi	zoubi	PROPN
ejpam-5486	435	6	/	/	SYM
ejpam-5486	435	7	eur	eur	PROPN
ejpam-5486	435	8	.	.	PUNCT
ejpam-5486	436	1	j.	j.	PROPN
ejpam-5486	436	2	pure	pure	PROPN
ejpam-5486	436	3	appl	appl	PROPN
ejpam-5486	436	4	.	.	PROPN
ejpam-5486	436	5	math	math	PROPN
ejpam-5486	436	6	,	,	PUNCT
ejpam-5486	436	7	17	17	NUM
ejpam-5486	436	8	(	(	PUNCT
ejpam-5486	436	9	4	4	NUM
ejpam-5486	436	10	)	)	PUNCT
ejpam-5486	436	11	(	(	PUNCT
ejpam-5486	436	12	2024	2024	NUM
ejpam-5486	436	13	)	)	PUNCT
ejpam-5486	436	14	,	,	PUNCT
ejpam-5486	436	15	3370	3370	NUM
ejpam-5486	436	16	-	-	SYM
ejpam-5486	436	17	3385	3385	NUM
ejpam-5486	436	18	3382	3382	NUM
ejpam-5486	436	19	∆	∆	X
ejpam-5486	436	20	◦	◦	NOUN
ejpam-5486	436	21	=	=	SYM
ejpam-5486	436	22	{	{	PUNCT
ejpam-5486	436	23	x1	x1	PROPN
ejpam-5486	436	24	,	,	PUNCT
ejpam-5486	436	25	x2	x2	PROPN
ejpam-5486	436	26	,	,	PUNCT
ejpam-5486	436	27	......	......	PUNCT
ejpam-5486	436	28	xn	xn	X
ejpam-5486	436	29	}	}	PUNCT
ejpam-5486	436	30	⊆	⊆	NUM
ejpam-5486	436	31	z	z	NOUN
ejpam-5486	436	32	with	with	ADP
ejpam-5486	436	33	z	z	NOUN
ejpam-5486	436	34	=	=	SYM
ejpam-5486	436	35	∪	∪	ADP
ejpam-5486	436	36	x∈∆	x∈∆	NOUN
ejpam-5486	436	37	◦	◦	NOUN
ejpam-5486	436	38	clωswd(gx	clωswd(gx	NUM
ejpam-5486	436	39	)	)	PUNCT
ejpam-5486	436	40	.	.	PUNCT
ejpam-5486	437	1	but	but	CCONJ
ejpam-5486	437	2	f	f	PROPN
ejpam-5486	437	3	is	be	AUX
ejpam-5486	437	4	a	a	DET
ejpam-5486	437	5	filter	filter	NOUN
ejpam-5486	437	6	base	base	NOUN
ejpam-5486	437	7	on	on	ADP
ejpam-5486	437	8	z	z	NOUN
ejpam-5486	437	9	and	and	CCONJ
ejpam-5486	437	10	hence	hence	ADV
ejpam-5486	437	11	there	there	PRON
ejpam-5486	437	12	is	be	VERB
ejpam-5486	437	13	f	f	X
ejpam-5486	437	14	◦	◦	NOUN
ejpam-5486	437	15	∈	∈	PROPN
ejpam-5486	437	16	f	f	NOUN
ejpam-5486	437	17	with	with	ADP
ejpam-5486	437	18	f	f	PROPN
ejpam-5486	437	19	◦	◦	NOUN
ejpam-5486	437	20	⊆	⊆	NUM
ejpam-5486	437	21	∩{fxi	∩{fxi	NOUN
ejpam-5486	437	22	:	:	PUNCT
ejpam-5486	437	23	i	i	NOUN
ejpam-5486	437	24	=	=	NOUN
ejpam-5486	437	25	1	1	NUM
ejpam-5486	437	26	,	,	PUNCT
ejpam-5486	437	27	2	2	NUM
ejpam-5486	437	28	,	,	PUNCT
ejpam-5486	437	29	...	...	PUNCT
ejpam-5486	437	30	n	n	CCONJ
ejpam-5486	437	31	}	}	PUNCT
ejpam-5486	437	32	.	.	PUNCT
ejpam-5486	438	1	since	since	SCONJ
ejpam-5486	438	2	fxi∩	fxi∩	NOUN
ejpam-5486	438	3	clωswd(gxi	clωswd(gxi	PROPN
ejpam-5486	438	4	)	)	PUNCT
ejpam-5486	439	1	=	=	SYM
ejpam-5486	439	2	ϕ	ϕ	NOUN
ejpam-5486	439	3	,	,	PUNCT
ejpam-5486	439	4	then	then	ADV
ejpam-5486	439	5	f	f	X
ejpam-5486	439	6	◦	◦	NOUN
ejpam-5486	439	7	=	=	SYM
ejpam-5486	439	8	ϕ	ϕ	NOUN
ejpam-5486	439	9	which	which	PRON
ejpam-5486	439	10	is	be	AUX
ejpam-5486	439	11	a	a	DET
ejpam-5486	439	12	contradiction	contradiction	NOUN
ejpam-5486	439	13	.	.	PUNCT
ejpam-5486	440	1	(	(	PUNCT
ejpam-5486	440	2	ii	ii	PROPN
ejpam-5486	440	3	→	→	SYM
ejpam-5486	440	4	iii	iii	X
ejpam-5486	440	5	)	)	PUNCT
ejpam-5486	440	6	let	let	VERB
ejpam-5486	440	7	f	f	PRON
ejpam-5486	440	8	be	be	AUX
ejpam-5486	440	9	a	a	DET
ejpam-5486	440	10	filter	filter	NOUN
ejpam-5486	440	11	base	base	NOUN
ejpam-5486	440	12	on	on	ADP
ejpam-5486	440	13	z.	z.	PROPN
ejpam-5486	440	14	then	then	ADV
ejpam-5486	440	15	there	there	PRON
ejpam-5486	440	16	is	be	VERB
ejpam-5486	440	17	f	f	NUM
ejpam-5486	440	18	◦	◦	NOUN
ejpam-5486	440	19	a	a	DET
ejpam-5486	440	20	maximal	maximal	ADJ
ejpam-5486	440	21	filter	filter	NOUN
ejpam-5486	440	22	base	base	NOUN
ejpam-5486	440	23	with	with	ADP
ejpam-5486	440	24	f	f	PROPN
ejpam-5486	441	1	⊆	⊆	NUM
ejpam-5486	441	2	f	f	PROPN
ejpam-5486	441	3	◦	◦	NOUN
ejpam-5486	441	4	.	.	PUNCT
ejpam-5486	442	1	since	since	SCONJ
ejpam-5486	442	2	f	f	NUM
ejpam-5486	442	3	◦	◦	NOUN
ejpam-5486	442	4	ωswdθconverges	ωswdθconverge	NOUN
ejpam-5486	442	5	to	to	ADP
ejpam-5486	442	6	x	x	PUNCT
ejpam-5486	442	7	for	for	ADP
ejpam-5486	442	8	some	some	DET
ejpam-5486	442	9	x	x	SYM
ejpam-5486	442	10	∈	∈	PROPN
ejpam-5486	442	11	z	z	PROPN
ejpam-5486	442	12	,	,	PUNCT
ejpam-5486	442	13	then	then	ADV
ejpam-5486	442	14	for	for	ADP
ejpam-5486	442	15	each	each	DET
ejpam-5486	442	16	g	g	PROPN
ejpam-5486	442	17	∈	∈	PROPN
ejpam-5486	442	18	ωswd(z	ωswd(z	PROPN
ejpam-5486	442	19	,	,	PUNCT
ejpam-5486	442	20	τ	τ	PROPN
ejpam-5486	442	21	)	)	PUNCT
ejpam-5486	442	22	with	with	ADP
ejpam-5486	442	23	x	x	SYM
ejpam-5486	442	24	∈	∈	PROPN
ejpam-5486	442	25	g	g	NOUN
ejpam-5486	442	26	there	there	PRON
ejpam-5486	442	27	is	be	VERB
ejpam-5486	442	28	f	f	X
ejpam-5486	442	29	◦	◦	NOUN
ejpam-5486	442	30	∈	∈	NOUN
ejpam-5486	442	31	f	f	X
ejpam-5486	442	32	◦	◦	NOUN
ejpam-5486	442	33	such	such	ADJ
ejpam-5486	442	34	that	that	SCONJ
ejpam-5486	442	35	f	f	X
ejpam-5486	442	36	◦	◦	NOUN
ejpam-5486	442	37	⊆	⊆	NUM
ejpam-5486	442	38	clωswd(g	clωswd(g	NOUN
ejpam-5486	442	39	)	)	PUNCT
ejpam-5486	442	40	.	.	PUNCT
ejpam-5486	443	1	therefore	therefore	ADV
ejpam-5486	443	2	for	for	SCONJ
ejpam-5486	443	3	each	each	DET
ejpam-5486	443	4	f	f	PROPN
ejpam-5486	443	5	∈	∈	PROPN
ejpam-5486	443	6	f	f	PROPN
ejpam-5486	443	7	,	,	PUNCT
ejpam-5486	443	8	ϕ	ϕ	PROPN
ejpam-5486	443	9	̸=	̸=	PROPN
ejpam-5486	443	10	f	f	PROPN
ejpam-5486	443	11	◦	◦	NOUN
ejpam-5486	443	12	∩	∩	NOUN
ejpam-5486	443	13	f	f	PROPN
ejpam-5486	443	14	⊆	⊆	NUM
ejpam-5486	443	15	clωswd(g	clωswd(g	NOUN
ejpam-5486	443	16	)	)	PUNCT
ejpam-5486	443	17	∩	∩	NOUN
ejpam-5486	443	18	f	f	PROPN
ejpam-5486	443	19	and	and	CCONJ
ejpam-5486	443	20	hence	hence	ADV
ejpam-5486	443	21	f	f	PROPN
ejpam-5486	443	22	ωswdθaccumulates	ωswdθaccumulate	VERB
ejpam-5486	443	23	at	at	ADP
ejpam-5486	443	24	x.	x.	PROPN
ejpam-5486	443	25	(	(	PUNCT
ejpam-5486	443	26	iii	iii	X
ejpam-5486	443	27	→	→	SYM
ejpam-5486	443	28	iv	iv	NUM
ejpam-5486	443	29	)	)	PUNCT
ejpam-5486	443	30	let	let	VERB
ejpam-5486	443	31	{	{	PUNCT
ejpam-5486	443	32	hα	hα	X
ejpam-5486	443	33	:	:	PUNCT
ejpam-5486	443	34	α	α	PROPN
ejpam-5486	443	35	∈	∈	PROPN
ejpam-5486	443	36	∆	∆	PROPN
ejpam-5486	443	37	}	}	PUNCT
ejpam-5486	443	38	be	be	AUX
ejpam-5486	443	39	a	a	DET
ejpam-5486	443	40	family	family	NOUN
ejpam-5486	443	41	of	of	ADP
ejpam-5486	443	42	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	443	43	,	,	PUNCT
ejpam-5486	443	44	τ	τ	PROPN
ejpam-5486	443	45	)	)	PUNCT
ejpam-5486	443	46	with	with	ADP
ejpam-5486	443	47	∩	∩	NOUN
ejpam-5486	443	48	α∈∆	α∈∆	PRON
ejpam-5486	443	49	hα	hα	ADP
ejpam-5486	443	50	=	=	NOUN
ejpam-5486	443	51	ϕ.	ϕ.	PROPN
ejpam-5486	443	52	if	if	SCONJ
ejpam-5486	443	53	∩	∩	NOUN
ejpam-5486	443	54	α∈∆	α∈∆	VERB
ejpam-5486	443	55	◦	◦	NOUN
ejpam-5486	443	56	intωswd(hα	intωswd(hα	NOUN
ejpam-5486	443	57	)	)	PUNCT
ejpam-5486	443	58	̸=	̸=	PROPN
ejpam-5486	443	59	ϕ	ϕ	NOUN
ejpam-5486	443	60	for	for	ADP
ejpam-5486	443	61	each	each	DET
ejpam-5486	443	62	finite	finite	NOUN
ejpam-5486	443	63	subset	subset	VERB
ejpam-5486	443	64	∆	∆	PROPN
ejpam-5486	443	65	◦	◦	NOUN
ejpam-5486	443	66	⊆	⊆	NUM
ejpam-5486	443	67	∆.	∆.	X
ejpam-5486	443	68	then	then	ADV
ejpam-5486	443	69	f	f	X
ejpam-5486	443	70	=	=	PRON
ejpam-5486	443	71	{	{	PUNCT
ejpam-5486	443	72	∩	∩	NOUN
ejpam-5486	443	73	α∈∆	α∈∆	VERB
ejpam-5486	443	74	◦	◦	NOUN
ejpam-5486	443	75	intωswd(hα	intωswd(hα	NOUN
ejpam-5486	443	76	)	)	PUNCT
ejpam-5486	443	77	:	:	PUNCT
ejpam-5486	444	1	∆	∆	PUNCT
ejpam-5486	444	2	◦	◦	NOUN
ejpam-5486	444	3	⊆	⊆	NUM
ejpam-5486	444	4	∆	∆	PRON
ejpam-5486	444	5	and	and	CCONJ
ejpam-5486	444	6	∆	∆	NUM
ejpam-5486	444	7	◦	◦	NOUN
ejpam-5486	444	8	is	be	AUX
ejpam-5486	444	9	finite	finite	ADJ
ejpam-5486	444	10	}	}	PUNCT
ejpam-5486	444	11	is	be	AUX
ejpam-5486	444	12	a	a	DET
ejpam-5486	444	13	filter	filter	NOUN
ejpam-5486	444	14	base	base	NOUN
ejpam-5486	444	15	on	on	ADP
ejpam-5486	444	16	z	z	NOUN
ejpam-5486	444	17	and	and	CCONJ
ejpam-5486	444	18	hence	hence	ADV
ejpam-5486	444	19	f	f	PROPN
ejpam-5486	444	20	ωswdθaccumulates	ωswdθaccumulate	VERB
ejpam-5486	444	21	at	at	ADP
ejpam-5486	444	22	x	x	PUNCT
ejpam-5486	444	23	for	for	ADP
ejpam-5486	444	24	some	some	DET
ejpam-5486	444	25	x	x	SYM
ejpam-5486	444	26	∈	∈	PROPN
ejpam-5486	444	27	z.	z.	PROPN
ejpam-5486	444	28	since	since	SCONJ
ejpam-5486	444	29	{	{	PUNCT
ejpam-5486	444	30	z	z	PROPN
ejpam-5486	444	31	−hα	−hα	VERB
ejpam-5486	444	32	:	:	PUNCT
ejpam-5486	444	33	α	α	PROPN
ejpam-5486	444	34	∈	∈	PROPN
ejpam-5486	444	35	∆	∆	X
ejpam-5486	444	36	}	}	PUNCT
ejpam-5486	444	37	is	be	AUX
ejpam-5486	444	38	an	an	DET
ejpam-5486	444	39	ωswd(z	ωswd(z	NOUN
ejpam-5486	444	40	,	,	PUNCT
ejpam-5486	444	41	τ)-cover	τ)-cover	PUNCT
ejpam-5486	444	42	of	of	ADP
ejpam-5486	444	43	z	z	NOUN
ejpam-5486	444	44	,	,	PUNCT
ejpam-5486	444	45	then	then	ADV
ejpam-5486	444	46	x	x	SYM
ejpam-5486	444	47	∈	∈	PROPN
ejpam-5486	444	48	z	z	NOUN
ejpam-5486	444	49	−hα	−hα	VERB
ejpam-5486	444	50	◦	◦	NOUN
ejpam-5486	444	51	for	for	ADP
ejpam-5486	444	52	some	some	DET
ejpam-5486	444	53	α	α	NOUN
ejpam-5486	444	54	◦	◦	NOUN
ejpam-5486	444	55	∈	∈	PROPN
ejpam-5486	445	1	∆.	∆.	X
ejpam-5486	445	2	therefore	therefore	ADV
ejpam-5486	445	3	,	,	PUNCT
ejpam-5486	445	4	clωswd(z−hα	clωswd(z−hα	PROPN
ejpam-5486	445	5	◦	◦	NOUN
ejpam-5486	445	6	)∩intωswd(hα	)∩intωswd(hα	NOUN
ejpam-5486	445	7	◦	◦	NOUN
ejpam-5486	445	8	)	)	PUNCT
ejpam-5486	446	1	=	=	SYM
ejpam-5486	446	2	ϕ	ϕ	NOUN
ejpam-5486	446	3	which	which	PRON
ejpam-5486	446	4	is	be	AUX
ejpam-5486	446	5	a	a	DET
ejpam-5486	446	6	contradiction	contradiction	NOUN
ejpam-5486	446	7	.	.	PUNCT
ejpam-5486	447	1	(	(	PUNCT
ejpam-5486	447	2	v	v	X
ejpam-5486	447	3	→	→	SYM
ejpam-5486	447	4	i	i	PROPN
ejpam-5486	447	5	)	)	PUNCT
ejpam-5486	447	6	let	let	VERB
ejpam-5486	447	7	h	h	NOUN
ejpam-5486	447	8	=	=	PRON
ejpam-5486	447	9	{	{	PUNCT
ejpam-5486	447	10	hα	hα	X
ejpam-5486	447	11	:	:	PUNCT
ejpam-5486	447	12	α	α	PROPN
ejpam-5486	447	13	∈	∈	PROPN
ejpam-5486	447	14	∆	∆	PROPN
ejpam-5486	447	15	}	}	PUNCT
ejpam-5486	447	16	be	be	AUX
ejpam-5486	447	17	an	an	DET
ejpam-5486	447	18	ωswd(z	ωswd(z	NOUN
ejpam-5486	447	19	,	,	PUNCT
ejpam-5486	447	20	τ)-cover	τ)-cover	PUNCT
ejpam-5486	447	21	of	of	ADP
ejpam-5486	447	22	z.	z.	PROPN
ejpam-5486	448	1	then	then	ADV
ejpam-5486	448	2	z	z	PROPN
ejpam-5486	448	3	−	−	NOUN
ejpam-5486	448	4	hα	hα	ADP
ejpam-5486	448	5	∈	∈	PROPN
ejpam-5486	448	6	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	448	7	,	,	PUNCT
ejpam-5486	448	8	τ	τ	PROPN
ejpam-5486	448	9	)	)	PUNCT
ejpam-5486	448	10	for	for	ADP
ejpam-5486	448	11	each	each	DET
ejpam-5486	448	12	α	α	NOUN
ejpam-5486	448	13	∈	∈	NOUN
ejpam-5486	448	14	∆	∆	PROPN
ejpam-5486	448	15	and	and	CCONJ
ejpam-5486	448	16	∩	∩	ADJ
ejpam-5486	448	17	α∈∆	α∈∆	X
ejpam-5486	448	18	(	(	PUNCT
ejpam-5486	448	19	z	z	NOUN
ejpam-5486	448	20	−	−	NOUN
ejpam-5486	448	21	hα	hα	NOUN
ejpam-5486	448	22	)	)	PUNCT
ejpam-5486	448	23	=	=	SYM
ejpam-5486	449	1	ϕ.	ϕ.	NOUN
ejpam-5486	449	2	hence	hence	ADV
ejpam-5486	449	3	there	there	PRON
ejpam-5486	449	4	is	be	VERB
ejpam-5486	449	5	a	a	DET
ejpam-5486	449	6	finite	finite	NOUN
ejpam-5486	449	7	subset	subset	NOUN
ejpam-5486	449	8	∆	∆	ADJ
ejpam-5486	449	9	◦	◦	NOUN
ejpam-5486	449	10	⊆	⊆	NUM
ejpam-5486	449	11	∆	∆	X
ejpam-5486	449	12	with	with	ADP
ejpam-5486	449	13	∩	∩	NOUN
ejpam-5486	449	14	α∈∆	α∈∆	NOUN
ejpam-5486	449	15	◦	◦	NOUN
ejpam-5486	449	16	intωswd(z	intωswd(z	NOUN
ejpam-5486	449	17	−hα	−hα	VERB
ejpam-5486	449	18	)	)	PUNCT
ejpam-5486	449	19	=	=	PUNCT
ejpam-5486	450	1	ϕ.therefore	ϕ.therefore	ADP
ejpam-5486	450	2	z	z	NOUN
ejpam-5486	450	3	=	=	PUNCT
ejpam-5486	450	4	∪	∪	ADP
ejpam-5486	450	5	x∈∆	x∈∆	NOUN
ejpam-5486	450	6	◦	◦	NOUN
ejpam-5486	450	7	clωswd(hα	clωswd(hα	NOUN
ejpam-5486	450	8	)	)	PUNCT
ejpam-5486	450	9	.	.	PUNCT
ejpam-5486	451	1	theorem	theorem	NOUN
ejpam-5486	451	2	19	19	NUM
ejpam-5486	451	3	.	.	PUNCT
ejpam-5486	452	1	let	let	AUX
ejpam-5486	452	2	(	(	PUNCT
ejpam-5486	452	3	z	z	NOUN
ejpam-5486	452	4	,	,	PUNCT
ejpam-5486	452	5	τ	τ	PROPN
ejpam-5486	452	6	)	)	PUNCT
ejpam-5486	452	7	be	be	VERB
ejpam-5486	452	8	almost	almost	ADV
ejpam-5486	452	9	ωswd	ωswd	ADJ
ejpam-5486	452	10	-	-	PUNCT
ejpam-5486	452	11	compact	compact	ADJ
ejpam-5486	452	12	t	t	NOUN
ejpam-5486	452	13	s	s	PART
ejpam-5486	452	14	and	and	CCONJ
ejpam-5486	452	15	e	e	NOUN
ejpam-5486	452	16	⊆	⊆	NUM
ejpam-5486	452	17	z.	z.	NOUN
ejpam-5486	453	1	if	if	SCONJ
ejpam-5486	453	2	e	e	PROPN
ejpam-5486	453	3	∈	∈	PROPN
ejpam-5486	453	4	τ	τ	X
ejpam-5486	453	5	∩	∩	X
ejpam-5486	453	6	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	453	7	,	,	PUNCT
ejpam-5486	453	8	τ	τ	PROPN
ejpam-5486	453	9	)	)	PUNCT
ejpam-5486	453	10	,	,	PUNCT
ejpam-5486	453	11	then	then	ADV
ejpam-5486	453	12	(	(	PUNCT
ejpam-5486	453	13	e	e	NOUN
ejpam-5486	453	14	,	,	PUNCT
ejpam-5486	453	15	τe	τe	PRON
ejpam-5486	453	16	)	)	PUNCT
ejpam-5486	453	17	is	be	AUX
ejpam-5486	453	18	almost	almost	ADV
ejpam-5486	453	19	ωswd	ωswd	ADV
ejpam-5486	453	20	-	-	PUNCT
ejpam-5486	453	21	compact	compact	ADJ
ejpam-5486	453	22	.	.	PUNCT
ejpam-5486	454	1	proof	proof	NOUN
ejpam-5486	454	2	.	.	PUNCT
ejpam-5486	455	1	let	let	VERB
ejpam-5486	455	2	h	h	NOUN
ejpam-5486	455	3	=	=	PRON
ejpam-5486	455	4	{	{	PUNCT
ejpam-5486	455	5	hα	hα	X
ejpam-5486	455	6	:	:	PUNCT
ejpam-5486	455	7	α	α	PROPN
ejpam-5486	455	8	∈	∈	PROPN
ejpam-5486	455	9	∆	∆	PROPN
ejpam-5486	455	10	}	}	PUNCT
ejpam-5486	455	11	be	be	AUX
ejpam-5486	455	12	a	a	DET
ejpam-5486	455	13	family	family	NOUN
ejpam-5486	455	14	with	with	ADP
ejpam-5486	455	15	e	e	NOUN
ejpam-5486	455	16	=	=	VERB
ejpam-5486	455	17	∪	∪	ADP
ejpam-5486	455	18	α∈∆	α∈∆	PRON
ejpam-5486	455	19	hα	hα	NOUN
ejpam-5486	455	20	and	and	CCONJ
ejpam-5486	455	21	hα	hα	ADP
ejpam-5486	455	22	∈	∈	PROPN
ejpam-5486	455	23	ωswd(e	ωswd(e	PROPN
ejpam-5486	455	24	,	,	PUNCT
ejpam-5486	455	25	τe	τe	ADP
ejpam-5486	455	26	)	)	PUNCT
ejpam-5486	455	27	for	for	ADP
ejpam-5486	455	28	each	each	DET
ejpam-5486	455	29	α	α	NOUN
ejpam-5486	455	30	∈	∈	PROPN
ejpam-5486	456	1	∆.	∆.	X
ejpam-5486	456	2	then	then	ADV
ejpam-5486	456	3	by	by	ADP
ejpam-5486	456	4	theorem	theorem	NOUN
ejpam-5486	456	5	12	12	NUM
ejpam-5486	456	6	,	,	PUNCT
ejpam-5486	456	7	hα	hα	ADP
ejpam-5486	456	8	∈	∈	PROPN
ejpam-5486	456	9	ωswd(z	ωswd(z	PROPN
ejpam-5486	456	10	,	,	PUNCT
ejpam-5486	456	11	τ	τ	PROPN
ejpam-5486	456	12	)	)	PUNCT
ejpam-5486	456	13	for	for	ADP
ejpam-5486	456	14	each	each	DET
ejpam-5486	456	15	α	α	NOUN
ejpam-5486	456	16	∈	∈	NOUN
ejpam-5486	456	17	∆	∆	PROPN
ejpam-5486	456	18	and	and	CCONJ
ejpam-5486	456	19	hence	hence	ADV
ejpam-5486	456	20	{	{	PUNCT
ejpam-5486	456	21	hα	hα	X
ejpam-5486	456	22	:	:	PUNCT
ejpam-5486	456	23	α	α	PROPN
ejpam-5486	456	24	∈	∈	PROPN
ejpam-5486	456	25	∆}∪{z−h	∆}∪{z−h	NOUN
ejpam-5486	456	26	}	}	PUNCT
ejpam-5486	456	27	=	=	PUNCT
ejpam-5486	456	28	z.	z.	PROPN
ejpam-5486	456	29	since	since	SCONJ
ejpam-5486	456	30	(	(	PUNCT
ejpam-5486	456	31	z	z	PROPN
ejpam-5486	456	32	,	,	PUNCT
ejpam-5486	456	33	τ	τ	X
ejpam-5486	456	34	)	)	PUNCT
ejpam-5486	456	35	is	be	AUX
ejpam-5486	456	36	almost	almost	ADV
ejpam-5486	456	37	ωswd	ωswd	ADJ
ejpam-5486	456	38	-	-	PUNCT
ejpam-5486	456	39	compact	compact	ADJ
ejpam-5486	456	40	,	,	PUNCT
ejpam-5486	456	41	then	then	ADV
ejpam-5486	456	42	there	there	PRON
ejpam-5486	456	43	is	be	VERB
ejpam-5486	456	44	a	a	DET
ejpam-5486	456	45	finite	finite	NOUN
ejpam-5486	456	46	subset	subset	NOUN
ejpam-5486	456	47	∆	∆	ADJ
ejpam-5486	456	48	◦	◦	NOUN
ejpam-5486	456	49	⊆	⊆	NUM
ejpam-5486	456	50	∆	∆	X
ejpam-5486	456	51	with	with	ADP
ejpam-5486	456	52	z	z	NOUN
ejpam-5486	456	53	=	=	PUNCT
ejpam-5486	457	1	[	[	X
ejpam-5486	457	2	∪	∪	ADP
ejpam-5486	457	3	x∈∆	x∈∆	PROPN
ejpam-5486	457	4	◦	◦	NOUN
ejpam-5486	457	5	clωswd(hα)]∪{z−h}.therefore	clωswd(hα)]∪{z−h}.therefore	ADJ
ejpam-5486	457	6	,	,	PUNCT
ejpam-5486	457	7	e	e	X
ejpam-5486	457	8	=	=	PUNCT
ejpam-5486	457	9	∪	∪	ADP
ejpam-5486	457	10	α∈∆	α∈∆	NOUN
ejpam-5486	457	11	◦	◦	NOUN
ejpam-5486	457	12	clωswd(hα	clωswd(hα	NOUN
ejpam-5486	457	13	)	)	PUNCT
ejpam-5486	457	14	⊆	⊆	NOUN
ejpam-5486	457	15	∪	∪	ADP
ejpam-5486	457	16	α∈∆	α∈∆	NOUN
ejpam-5486	457	17	◦	◦	NOUN
ejpam-5486	457	18	clωswde	clωswde	NOUN
ejpam-5486	457	19	(	(	PUNCT
ejpam-5486	457	20	hα	hα	NOUN
ejpam-5486	457	21	)	)	PUNCT
ejpam-5486	457	22	.	.	PUNCT
ejpam-5486	458	1	definition	definition	NOUN
ejpam-5486	458	2	12	12	NUM
ejpam-5486	458	3	.	.	PUNCT
ejpam-5486	459	1	let	let	AUX
ejpam-5486	459	2	(	(	PUNCT
ejpam-5486	459	3	z	z	NOUN
ejpam-5486	459	4	,	,	PUNCT
ejpam-5486	459	5	τ	τ	PROPN
ejpam-5486	459	6	)	)	PUNCT
ejpam-5486	459	7	be	be	VERB
ejpam-5486	459	8	a	a	DET
ejpam-5486	459	9	t	t	NOUN
ejpam-5486	459	10	s	s	NOUN
ejpam-5486	459	11	and	and	CCONJ
ejpam-5486	459	12	h	h	PROPN
ejpam-5486	459	13	⊆	⊆	NUM
ejpam-5486	459	14	z.	z.	PROPN
ejpam-5486	459	15	a	a	DET
ejpam-5486	459	16	subset	subset	NOUN
ejpam-5486	459	17	h	h	NOUN
ejpam-5486	459	18	is	be	AUX
ejpam-5486	459	19	said	say	VERB
ejpam-5486	459	20	to	to	PART
ejpam-5486	459	21	be	be	AUX
ejpam-5486	459	22	almost	almost	ADV
ejpam-5486	459	23	ωswdcompact	ωswdcompact	ADJ
ejpam-5486	459	24	relative	relative	ADJ
ejpam-5486	459	25	to	to	ADP
ejpam-5486	459	26	z	z	PROPN
ejpam-5486	459	27	(	(	PUNCT
ejpam-5486	459	28	in	in	ADP
ejpam-5486	459	29	z	z	PROPN
ejpam-5486	459	30	)	)	PUNCT
ejpam-5486	459	31	if	if	SCONJ
ejpam-5486	459	32	whenever	whenever	SCONJ
ejpam-5486	459	33	h	h	NOUN
ejpam-5486	459	34	=	=	PRON
ejpam-5486	459	35	{	{	PUNCT
ejpam-5486	459	36	hα	hα	X
ejpam-5486	459	37	:	:	PUNCT
ejpam-5486	459	38	α	α	PROPN
ejpam-5486	459	39	∈	∈	PROPN
ejpam-5486	459	40	∆	∆	X
ejpam-5486	459	41	}	}	PUNCT
ejpam-5486	459	42	is	be	AUX
ejpam-5486	459	43	an	an	DET
ejpam-5486	459	44	ωswd(z	ωswd(z	NOUN
ejpam-5486	459	45	,	,	PUNCT
ejpam-5486	459	46	τ)-cover	τ)-cover	PUNCT
ejpam-5486	459	47	of	of	ADP
ejpam-5486	459	48	h	h	NOUN
ejpam-5486	459	49	,	,	PUNCT
ejpam-5486	459	50	then	then	ADV
ejpam-5486	459	51	there	there	PRON
ejpam-5486	459	52	is	be	VERB
ejpam-5486	459	53	a	a	DET
ejpam-5486	459	54	finite	finite	NOUN
ejpam-5486	459	55	subset	subset	NOUN
ejpam-5486	459	56	∆	∆	ADJ
ejpam-5486	459	57	◦	◦	NOUN
ejpam-5486	459	58	of	of	ADP
ejpam-5486	459	59	∆	∆	PROPN
ejpam-5486	459	60	with	with	ADP
ejpam-5486	459	61	h	h	NOUN
ejpam-5486	459	62	⊆	⊆	NUM
ejpam-5486	459	63	∪	∪	ADP
ejpam-5486	459	64	x∈∆	x∈∆	NOUN
ejpam-5486	459	65	◦	◦	NOUN
ejpam-5486	459	66	clωswd(hα	clωswd(hα	NOUN
ejpam-5486	459	67	)	)	PUNCT
ejpam-5486	459	68	.	.	PUNCT
ejpam-5486	460	1	the	the	DET
ejpam-5486	460	2	following	follow	VERB
ejpam-5486	460	3	theorem	theorem	NOUN
ejpam-5486	460	4	can	can	AUX
ejpam-5486	460	5	be	be	AUX
ejpam-5486	460	6	easily	easily	ADV
ejpam-5486	460	7	constructed	construct	VERB
ejpam-5486	460	8	.	.	PUNCT
ejpam-5486	461	1	theorem	theorem	NOUN
ejpam-5486	461	2	20	20	NUM
ejpam-5486	461	3	.	.	PUNCT
ejpam-5486	462	1	let	let	AUX
ejpam-5486	462	2	(	(	PUNCT
ejpam-5486	462	3	z	z	NOUN
ejpam-5486	462	4	,	,	PUNCT
ejpam-5486	462	5	τ	τ	PROPN
ejpam-5486	462	6	)	)	PUNCT
ejpam-5486	462	7	be	be	VERB
ejpam-5486	462	8	a	a	DET
ejpam-5486	462	9	t	t	NOUN
ejpam-5486	462	10	s	s	NOUN
ejpam-5486	462	11	and	and	CCONJ
ejpam-5486	462	12	h	h	NOUN
ejpam-5486	462	13	⊆	⊆	NUM
ejpam-5486	462	14	z.	z.	X
ejpam-5486	463	1	the	the	DET
ejpam-5486	463	2	following	follow	VERB
ejpam-5486	463	3	are	be	AUX
ejpam-5486	463	4	equivalent	equivalent	ADJ
ejpam-5486	463	5	:	:	PUNCT
ejpam-5486	463	6	(	(	PUNCT
ejpam-5486	463	7	i	i	NOUN
ejpam-5486	463	8	)	)	PUNCT
ejpam-5486	463	9	h	h	NOUN
ejpam-5486	463	10	is	be	AUX
ejpam-5486	463	11	almost	almost	ADV
ejpam-5486	463	12	ωswd	ωswd	ADJ
ejpam-5486	463	13	-	-	PUNCT
ejpam-5486	463	14	compact	compact	ADJ
ejpam-5486	463	15	relative	relative	NOUN
ejpam-5486	463	16	to	to	ADP
ejpam-5486	463	17	z.	z.	PROPN
ejpam-5486	463	18	(	(	PUNCT
ejpam-5486	463	19	ii	ii	PROPN
ejpam-5486	463	20	)	)	PUNCT
ejpam-5486	463	21	if	if	SCONJ
ejpam-5486	463	22	f	f	PROPN
ejpam-5486	463	23	is	be	AUX
ejpam-5486	463	24	a	a	DET
ejpam-5486	463	25	maximal	maximal	ADJ
ejpam-5486	463	26	filter	filter	NOUN
ejpam-5486	463	27	base	base	NOUN
ejpam-5486	463	28	on	on	ADP
ejpam-5486	463	29	z	z	NOUN
ejpam-5486	463	30	and	and	CCONJ
ejpam-5486	463	31	meets	meet	VERB
ejpam-5486	463	32	h	h	NOUN
ejpam-5486	463	33	,	,	PUNCT
ejpam-5486	463	34	then	then	ADV
ejpam-5486	463	35	it	it	PRON
ejpam-5486	463	36	ωswdθconverges	ωswdθconverge	VERB
ejpam-5486	463	37	to	to	ADP
ejpam-5486	463	38	some	some	DET
ejpam-5486	463	39	point	point	NOUN
ejpam-5486	463	40	of	of	ADP
ejpam-5486	463	41	h.	h.	PROPN
ejpam-5486	463	42	(	(	PUNCT
ejpam-5486	463	43	iii	iii	NOUN
ejpam-5486	463	44	)	)	PUNCT
ejpam-5486	463	45	if	if	SCONJ
ejpam-5486	463	46	f	f	PROPN
ejpam-5486	463	47	is	be	AUX
ejpam-5486	463	48	a	a	DET
ejpam-5486	463	49	filter	filter	NOUN
ejpam-5486	463	50	base	base	NOUN
ejpam-5486	463	51	on	on	ADP
ejpam-5486	463	52	z	z	NOUN
ejpam-5486	463	53	and	and	CCONJ
ejpam-5486	463	54	meets	meet	VERB
ejpam-5486	463	55	h	h	NOUN
ejpam-5486	463	56	,	,	PUNCT
ejpam-5486	463	57	then	then	ADV
ejpam-5486	463	58	it	it	PRON
ejpam-5486	463	59	ωswdθaccumulates	ωswdθaccumulate	VERB
ejpam-5486	463	60	at	at	ADP
ejpam-5486	463	61	some	some	DET
ejpam-5486	463	62	point	point	NOUN
ejpam-5486	463	63	of	of	ADP
ejpam-5486	463	64	h.	h.	PROPN
ejpam-5486	463	65	(	(	PUNCT
ejpam-5486	463	66	iv	iv	X
ejpam-5486	463	67	)	)	PUNCT
ejpam-5486	463	68	if	if	SCONJ
ejpam-5486	463	69	{	{	PUNCT
ejpam-5486	463	70	hα	hα	X
ejpam-5486	463	71	:	:	PUNCT
ejpam-5486	463	72	α	α	PROPN
ejpam-5486	463	73	∈	∈	PROPN
ejpam-5486	463	74	∆	∆	X
ejpam-5486	463	75	}	}	PUNCT
ejpam-5486	463	76	is	be	AUX
ejpam-5486	463	77	a	a	DET
ejpam-5486	463	78	family	family	NOUN
ejpam-5486	463	79	of	of	ADP
ejpam-5486	463	80	ωswd	ωswd	ADJ
ejpam-5486	463	81	-	-	PUNCT
ejpam-5486	463	82	closed	closed	ADJ
ejpam-5486	463	83	subsets	subset	NOUN
ejpam-5486	463	84	of	of	ADP
ejpam-5486	463	85	(	(	PUNCT
ejpam-5486	463	86	z	z	PROPN
ejpam-5486	463	87	,	,	PUNCT
ejpam-5486	463	88	τ	τ	PROPN
ejpam-5486	463	89	)	)	PUNCT
ejpam-5486	463	90	and	and	CCONJ
ejpam-5486	463	91	[	[	X
ejpam-5486	463	92	∩	∩	X
ejpam-5486	463	93	α∈∆	α∈∆	X
ejpam-5486	463	94	hα]∩h	hα]∩h	X
ejpam-5486	463	95	=	=	SYM
ejpam-5486	463	96	ϕ	ϕ	NOUN
ejpam-5486	463	97	,	,	PUNCT
ejpam-5486	463	98	then	then	ADV
ejpam-5486	463	99	there	there	PRON
ejpam-5486	463	100	is	be	VERB
ejpam-5486	463	101	a	a	DET
ejpam-5486	463	102	finite	finite	NOUN
ejpam-5486	463	103	subset	subset	NOUN
ejpam-5486	463	104	∆	∆	ADJ
ejpam-5486	463	105	◦	◦	NOUN
ejpam-5486	463	106	⊆	⊆	NUM
ejpam-5486	463	107	∆	∆	X
ejpam-5486	463	108	with	with	ADP
ejpam-5486	463	109	[	[	X
ejpam-5486	463	110	∩	∩	NOUN
ejpam-5486	463	111	α∈∆	α∈∆	VERB
ejpam-5486	463	112	◦	◦	NOUN
ejpam-5486	463	113	intωswd(hα	intωswd(hα	NOUN
ejpam-5486	463	114	)	)	PUNCT
ejpam-5486	463	115	]	]	PUNCT
ejpam-5486	464	1	∩h	∩h	PROPN
ejpam-5486	464	2	=	=	SYM
ejpam-5486	464	3	ϕ.	ϕ.	PROPN
ejpam-5486	464	4	a.	a.	PROPN
ejpam-5486	464	5	rawshdeh	rawshdeh	PROPN
ejpam-5486	464	6	,	,	PUNCT
ejpam-5486	464	7	h.	h.	PROPN
ejpam-5486	464	8	h.	h.	PROPN
ejpam-5486	464	9	al	al	PROPN
ejpam-5486	464	10	-	-	PUNCT
ejpam-5486	464	11	jarrah	jarrah	PROPN
ejpam-5486	464	12	,	,	PUNCT
ejpam-5486	464	13	k.	k.	PROPN
ejpam-5486	464	14	y.	y.	PROPN
ejpam-5486	464	15	al	al	PROPN
ejpam-5486	464	16	-	-	PROPN
ejpam-5486	464	17	zoubi	zoubi	PROPN
ejpam-5486	464	18	/	/	SYM
ejpam-5486	464	19	eur	eur	PROPN
ejpam-5486	464	20	.	.	PUNCT
ejpam-5486	465	1	j.	j.	PROPN
ejpam-5486	465	2	pure	pure	PROPN
ejpam-5486	465	3	appl	appl	PROPN
ejpam-5486	465	4	.	.	PROPN
ejpam-5486	465	5	math	math	PROPN
ejpam-5486	465	6	,	,	PUNCT
ejpam-5486	465	7	17	17	NUM
ejpam-5486	465	8	(	(	PUNCT
ejpam-5486	465	9	4	4	NUM
ejpam-5486	465	10	)	)	PUNCT
ejpam-5486	465	11	(	(	PUNCT
ejpam-5486	465	12	2024	2024	NUM
ejpam-5486	465	13	)	)	PUNCT
ejpam-5486	465	14	,	,	PUNCT
ejpam-5486	465	15	3370	3370	NUM
ejpam-5486	465	16	-	-	SYM
ejpam-5486	465	17	3385	3385	NUM
ejpam-5486	465	18	3383	3383	NUM
ejpam-5486	465	19	proposition	proposition	NOUN
ejpam-5486	465	20	6	6	NUM
ejpam-5486	465	21	.	.	PUNCT
ejpam-5486	466	1	let	let	AUX
ejpam-5486	466	2	(	(	PUNCT
ejpam-5486	466	3	z	z	NOUN
ejpam-5486	466	4	,	,	PUNCT
ejpam-5486	466	5	τ	τ	PROPN
ejpam-5486	466	6	)	)	PUNCT
ejpam-5486	466	7	be	be	VERB
ejpam-5486	466	8	a	a	DET
ejpam-5486	466	9	t	t	NOUN
ejpam-5486	466	10	s	s	NOUN
ejpam-5486	466	11	and	and	CCONJ
ejpam-5486	466	12	h	h	NOUN
ejpam-5486	466	13	,	,	PUNCT
ejpam-5486	466	14	g	g	PROPN
ejpam-5486	466	15	⊆	⊆	NUM
ejpam-5486	466	16	z.	z.	NOUN
ejpam-5486	466	17	if	if	SCONJ
ejpam-5486	466	18	h	h	NOUN
ejpam-5486	466	19	is	be	AUX
ejpam-5486	466	20	an	an	DET
ejpam-5486	466	21	ωswdθclosed	ωswdθclosed	ADJ
ejpam-5486	466	22	subset	subset	NOUN
ejpam-5486	466	23	of	of	ADP
ejpam-5486	466	24	(	(	PUNCT
ejpam-5486	466	25	z	z	PROPN
ejpam-5486	466	26	,	,	PUNCT
ejpam-5486	466	27	τ	τ	PROPN
ejpam-5486	466	28	)	)	PUNCT
ejpam-5486	466	29	and	and	CCONJ
ejpam-5486	466	30	g	g	PROPN
ejpam-5486	466	31	is	be	AUX
ejpam-5486	466	32	almost	almost	ADV
ejpam-5486	466	33	ωswd	ωswd	ADJ
ejpam-5486	466	34	-	-	PUNCT
ejpam-5486	466	35	compact	compact	ADJ
ejpam-5486	466	36	relative	relative	NOUN
ejpam-5486	466	37	to	to	ADP
ejpam-5486	466	38	z	z	NOUN
ejpam-5486	466	39	,	,	PUNCT
ejpam-5486	466	40	then	then	ADV
ejpam-5486	466	41	h∩g	h∩g	NOUN
ejpam-5486	466	42	is	be	AUX
ejpam-5486	466	43	almost	almost	ADV
ejpam-5486	466	44	ωswd	ωswd	ADJ
ejpam-5486	466	45	-	-	PUNCT
ejpam-5486	466	46	compact	compact	ADJ
ejpam-5486	466	47	relative	relative	NOUN
ejpam-5486	466	48	to	to	ADP
ejpam-5486	466	49	z.	z.	PROPN
ejpam-5486	466	50	proof	proof	NOUN
ejpam-5486	466	51	.	.	PUNCT
ejpam-5486	467	1	let	let	VERB
ejpam-5486	467	2	h	h	NOUN
ejpam-5486	467	3	=	=	NOUN
ejpam-5486	467	4	{	{	PUNCT
ejpam-5486	467	5	hα	hα	X
ejpam-5486	467	6	:	:	PUNCT
ejpam-5486	467	7	α	α	PROPN
ejpam-5486	467	8	∈	∈	PROPN
ejpam-5486	467	9	∆	∆	X
ejpam-5486	467	10	}	}	PUNCT
ejpam-5486	467	11	be	be	VERB
ejpam-5486	467	12	ωswd(z	ωswd(z	NOUN
ejpam-5486	467	13	,	,	PUNCT
ejpam-5486	467	14	τ)-cover	τ)-cover	PUNCT
ejpam-5486	467	15	of	of	ADP
ejpam-5486	467	16	h	h	NOUN
ejpam-5486	467	17	∩	∩	ADJ
ejpam-5486	467	18	g.	g.	PROPN
ejpam-5486	467	19	then	then	ADV
ejpam-5486	467	20	by	by	ADP
ejpam-5486	467	21	proposition	proposition	NOUN
ejpam-5486	467	22	5	5	NUM
ejpam-5486	467	23	(	(	PUNCT
ejpam-5486	467	24	part	part	NOUN
ejpam-5486	467	25	i	i	NOUN
ejpam-5486	467	26	)	)	PUNCT
ejpam-5486	467	27	for	for	ADP
ejpam-5486	467	28	each	each	DET
ejpam-5486	467	29	x	x	SYM
ejpam-5486	467	30	∈	∈	PROPN
ejpam-5486	467	31	z	z	NOUN
ejpam-5486	467	32	−	−	PROPN
ejpam-5486	467	33	h	h	NOUN
ejpam-5486	467	34	there	there	PRON
ejpam-5486	467	35	is	be	VERB
ejpam-5486	467	36	wx	wx	PROPN
ejpam-5486	467	37	∈	∈	PROPN
ejpam-5486	467	38	ωswd(z	ωswd(z	PROPN
ejpam-5486	467	39	,	,	PUNCT
ejpam-5486	467	40	τ	τ	PROPN
ejpam-5486	467	41	)	)	PUNCT
ejpam-5486	467	42	with	with	ADP
ejpam-5486	467	43	x	x	PROPN
ejpam-5486	467	44	∈	∈	PROPN
ejpam-5486	467	45	wx	wx	PROPN
ejpam-5486	467	46	⊆	⊆	NUM
ejpam-5486	467	47	clωswd(wx	clωswd(wx	NOUN
ejpam-5486	467	48	)	)	PUNCT
ejpam-5486	467	49	⊆	⊆	NUM
ejpam-5486	467	50	z	z	NOUN
ejpam-5486	467	51	−h	−h	VERB
ejpam-5486	467	52	.	.	PUNCT
ejpam-5486	468	1	therefore	therefore	ADV
ejpam-5486	468	2	,	,	PUNCT
ejpam-5486	468	3	h∪{wx	h∪{wx	ADJ
ejpam-5486	468	4	:	:	PUNCT
ejpam-5486	468	5	x	x	X
ejpam-5486	468	6	∈	∈	NOUN
ejpam-5486	468	7	g	g	NOUN
ejpam-5486	468	8	−h	−h	ADV
ejpam-5486	468	9	}	}	PUNCT
ejpam-5486	468	10	is	be	AUX
ejpam-5486	468	11	an	an	DET
ejpam-5486	468	12	ωswd(z	ωswd(z	NOUN
ejpam-5486	468	13	,	,	PUNCT
ejpam-5486	468	14	τ)-cover	τ)-cover	PUNCT
ejpam-5486	468	15	of	of	ADP
ejpam-5486	468	16	g	g	NOUN
ejpam-5486	468	17	and	and	CCONJ
ejpam-5486	468	18	hence	hence	ADV
ejpam-5486	468	19	there	there	PRON
ejpam-5486	468	20	are	be	VERB
ejpam-5486	468	21	a	a	DET
ejpam-5486	468	22	finite	finite	NOUN
ejpam-5486	468	23	subset	subset	NOUN
ejpam-5486	468	24	∆	∆	ADJ
ejpam-5486	468	25	◦	◦	NOUN
ejpam-5486	468	26	⊆	⊆	NUM
ejpam-5486	468	27	∆	∆	PROPN
ejpam-5486	468	28	and	and	CCONJ
ejpam-5486	468	29	a	a	DET
ejpam-5486	468	30	finite	finite	NOUN
ejpam-5486	468	31	subset	subset	NOUN
ejpam-5486	468	32	{	{	PUNCT
ejpam-5486	468	33	x1	x1	PROPN
ejpam-5486	468	34	,	,	PUNCT
ejpam-5486	468	35	x2	x2	PROPN
ejpam-5486	468	36	,	,	PUNCT
ejpam-5486	468	37	....	....	PUNCT
ejpam-5486	468	38	xn	xn	X
ejpam-5486	468	39	}	}	PUNCT
ejpam-5486	468	40	⊆	⊆	NUM
ejpam-5486	468	41	g	g	NOUN
ejpam-5486	468	42	−	−	PROPN
ejpam-5486	468	43	h	h	NOUN
ejpam-5486	468	44	with	with	ADP
ejpam-5486	468	45	g	g	PROPN
ejpam-5486	468	46	⊆	⊆	NUM
ejpam-5486	468	47	[	[	X
ejpam-5486	468	48	∪	∪	ADP
ejpam-5486	468	49	x∈∆	x∈∆	NOUN
ejpam-5486	468	50	◦	◦	NOUN
ejpam-5486	468	51	clωswd(hα	clωswd(hα	NOUN
ejpam-5486	468	52	)	)	PUNCT
ejpam-5486	468	53	]	]	PUNCT
ejpam-5486	468	54	∪	∪	X
ejpam-5486	468	55	[	[	PUNCT
ejpam-5486	468	56	n	n	CCONJ
ejpam-5486	468	57	∪	∪	ADJ
ejpam-5486	468	58	i=1	i=1	PROPN
ejpam-5486	468	59	clωswd(wxi	clωswd(wxi	PROPN
ejpam-5486	468	60	)	)	PUNCT
ejpam-5486	468	61	]	]	PUNCT
ejpam-5486	468	62	.	.	PUNCT
ejpam-5486	469	1	since	since	SCONJ
ejpam-5486	469	2	clωswd(wx	clωswd(wx	NOUN
ejpam-5486	469	3	)	)	PUNCT
ejpam-5486	469	4	⊆	⊆	NUM
ejpam-5486	469	5	z	z	NOUN
ejpam-5486	469	6	−	−	PROPN
ejpam-5486	469	7	h	h	NOUN
ejpam-5486	469	8	,	,	PUNCT
ejpam-5486	469	9	then	then	ADV
ejpam-5486	469	10	h	h	NOUN
ejpam-5486	469	11	∩g	∩g	NOUN
ejpam-5486	469	12	⊆	⊆	NUM
ejpam-5486	469	13	∪	∪	ADP
ejpam-5486	469	14	x∈∆	x∈∆	NOUN
ejpam-5486	469	15	◦	◦	NOUN
ejpam-5486	469	16	clωswd(hα	clωswd(hα	NOUN
ejpam-5486	469	17	)	)	PUNCT
ejpam-5486	469	18	.	.	PUNCT
ejpam-5486	470	1	corollary	corollary	ADJ
ejpam-5486	470	2	6	6	NUM
ejpam-5486	470	3	.	.	PUNCT
ejpam-5486	471	1	if	if	SCONJ
ejpam-5486	471	2	(	(	PUNCT
ejpam-5486	471	3	z	z	NOUN
ejpam-5486	471	4	,	,	PUNCT
ejpam-5486	471	5	τ	τ	X
ejpam-5486	471	6	)	)	PUNCT
ejpam-5486	471	7	is	be	AUX
ejpam-5486	471	8	an	an	DET
ejpam-5486	471	9	almost	almost	ADV
ejpam-5486	471	10	ωswd	ωswd	ADJ
ejpam-5486	471	11	-	-	PUNCT
ejpam-5486	471	12	compact	compact	ADJ
ejpam-5486	471	13	and	and	CCONJ
ejpam-5486	471	14	h	h	NOUN
ejpam-5486	471	15	⊆	⊆	NUM
ejpam-5486	471	16	z	z	NOUN
ejpam-5486	471	17	is	be	AUX
ejpam-5486	471	18	an	an	DET
ejpam-5486	471	19	ωswdθclosed	ωswdθclosed	ADJ
ejpam-5486	471	20	subset	subset	NOUN
ejpam-5486	471	21	of	of	ADP
ejpam-5486	471	22	(	(	PUNCT
ejpam-5486	471	23	z	z	PROPN
ejpam-5486	471	24	,	,	PUNCT
ejpam-5486	471	25	τ	τ	PROPN
ejpam-5486	471	26	)	)	PUNCT
ejpam-5486	471	27	,	,	PUNCT
ejpam-5486	471	28	then	then	ADV
ejpam-5486	471	29	h	h	NOUN
ejpam-5486	471	30	is	be	AUX
ejpam-5486	471	31	almost	almost	ADV
ejpam-5486	471	32	ωswd	ωswd	ADJ
ejpam-5486	471	33	-	-	PUNCT
ejpam-5486	471	34	compact	compact	ADJ
ejpam-5486	471	35	relative	relative	NOUN
ejpam-5486	471	36	to	to	ADP
ejpam-5486	471	37	z.	z.	PROPN
ejpam-5486	471	38	theorem	theorem	PROPN
ejpam-5486	471	39	21	21	NUM
ejpam-5486	471	40	.	.	PUNCT
ejpam-5486	472	1	let	let	AUX
ejpam-5486	472	2	(	(	PUNCT
ejpam-5486	472	3	z	z	NOUN
ejpam-5486	472	4	,	,	PUNCT
ejpam-5486	472	5	τ	τ	PROPN
ejpam-5486	472	6	)	)	PUNCT
ejpam-5486	472	7	be	be	VERB
ejpam-5486	472	8	a	a	DET
ejpam-5486	472	9	t	t	NOUN
ejpam-5486	472	10	s.	s.	PROPN
ejpam-5486	473	1	if	if	SCONJ
ejpam-5486	473	2	there	there	PRON
ejpam-5486	473	3	is	be	VERB
ejpam-5486	473	4	a	a	DET
ejpam-5486	473	5	non	non	ADJ
ejpam-5486	473	6	-	-	ADJ
ejpam-5486	473	7	empty	empty	ADJ
ejpam-5486	473	8	proper	proper	ADJ
ejpam-5486	473	9	subset	subset	NOUN
ejpam-5486	473	10	e	e	PROPN
ejpam-5486	473	11	∈	∈	PROPN
ejpam-5486	473	12	ωswd(z	ωswd(z	PROPN
ejpam-5486	473	13	,	,	PUNCT
ejpam-5486	473	14	τ)∩	τ)∩	ADJ
ejpam-5486	473	15	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	473	16	,	,	PUNCT
ejpam-5486	473	17	τ	τ	X
ejpam-5486	473	18	)	)	PUNCT
ejpam-5486	473	19	of	of	ADP
ejpam-5486	473	20	z	z	PROPN
ejpam-5486	473	21	,	,	PUNCT
ejpam-5486	473	22	then	then	ADV
ejpam-5486	473	23	(	(	PUNCT
ejpam-5486	473	24	z	z	NOUN
ejpam-5486	473	25	,	,	PUNCT
ejpam-5486	473	26	τ	τ	X
ejpam-5486	473	27	)	)	PUNCT
ejpam-5486	473	28	is	be	AUX
ejpam-5486	473	29	almost	almost	ADV
ejpam-5486	473	30	ωswd	ωswd	ADJ
ejpam-5486	473	31	-	-	PUNCT
ejpam-5486	473	32	compact	compact	ADJ
ejpam-5486	473	33	iff	iff	NOUN
ejpam-5486	473	34	each	each	DET
ejpam-5486	473	35	h	h	NOUN
ejpam-5486	473	36	∈	∈	PROPN
ejpam-5486	474	1	ωswd(z	ωswd(z	PROPN
ejpam-5486	474	2	,	,	PUNCT
ejpam-5486	474	3	τ	τ	PROPN
ejpam-5486	474	4	)	)	PUNCT
ejpam-5486	474	5	∩	∩	ADJ
ejpam-5486	474	6	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	474	7	,	,	PUNCT
ejpam-5486	474	8	τ	τ	X
ejpam-5486	474	9	)	)	PUNCT
ejpam-5486	474	10	is	be	AUX
ejpam-5486	474	11	an	an	DET
ejpam-5486	474	12	almost	almost	ADV
ejpam-5486	474	13	ωswd	ωswd	ADJ
ejpam-5486	474	14	-	-	PUNCT
ejpam-5486	474	15	compact	compact	ADJ
ejpam-5486	474	16	relative	relative	NOUN
ejpam-5486	474	17	to	to	ADP
ejpam-5486	474	18	z.	z.	PROPN
ejpam-5486	474	19	proof	proof	NOUN
ejpam-5486	474	20	.	.	PUNCT
ejpam-5486	475	1	let	let	VERB
ejpam-5486	475	2	h	h	NOUN
ejpam-5486	475	3	∈	∈	PROPN
ejpam-5486	475	4	ωswd(z	ωswd(z	PROPN
ejpam-5486	475	5	,	,	PUNCT
ejpam-5486	475	6	τ	τ	PROPN
ejpam-5486	475	7	)	)	PUNCT
ejpam-5486	475	8	∩	∩	ADJ
ejpam-5486	475	9	ωswdc(z	ωswdc(z	PROPN
ejpam-5486	475	10	,	,	PUNCT
ejpam-5486	475	11	τ	τ	PROPN
ejpam-5486	475	12	)	)	PUNCT
ejpam-5486	475	13	.	.	PUNCT
ejpam-5486	476	1	then	then	ADV
ejpam-5486	476	2	by	by	ADP
ejpam-5486	476	3	proposition	proposition	NOUN
ejpam-5486	476	4	5	5	NUM
ejpam-5486	476	5	(	(	PUNCT
ejpam-5486	476	6	part	part	NOUN
ejpam-5486	476	7	ii	ii	NOUN
ejpam-5486	476	8	)	)	PUNCT
ejpam-5486	476	9	h	h	PROPN
ejpam-5486	476	10	is	be	AUX
ejpam-5486	476	11	an	an	DET
ejpam-5486	476	12	ωswdθclosed	ωswdθclosed	ADJ
ejpam-5486	476	13	subset	subset	NOUN
ejpam-5486	476	14	of	of	ADP
ejpam-5486	476	15	(	(	PUNCT
ejpam-5486	476	16	z	z	PROPN
ejpam-5486	476	17	,	,	PUNCT
ejpam-5486	476	18	τ	τ	PROPN
ejpam-5486	476	19	)	)	PUNCT
ejpam-5486	476	20	and	and	CCONJ
ejpam-5486	476	21	hence	hence	ADV
ejpam-5486	476	22	by	by	ADP
ejpam-5486	476	23	corollary	corollary	ADJ
ejpam-5486	476	24	6	6	NUM
ejpam-5486	476	25	,	,	PUNCT
ejpam-5486	476	26	h	h	NOUN
ejpam-5486	476	27	is	be	AUX
ejpam-5486	476	28	almost	almost	ADV
ejpam-5486	476	29	ωswd	ωswd	ADJ
ejpam-5486	476	30	-	-	PUNCT
ejpam-5486	476	31	compact	compact	ADJ
ejpam-5486	476	32	relative	relative	NOUN
ejpam-5486	476	33	to	to	ADP
ejpam-5486	476	34	z.	z.	PROPN
ejpam-5486	476	35	conversely	conversely	ADV
ejpam-5486	476	36	,	,	PUNCT
ejpam-5486	476	37	let	let	VERB
ejpam-5486	476	38	h	h	NOUN
ejpam-5486	476	39	=	=	NOUN
ejpam-5486	476	40	{	{	PUNCT
ejpam-5486	476	41	hα	hα	X
ejpam-5486	476	42	:	:	PUNCT
ejpam-5486	476	43	α	α	PROPN
ejpam-5486	476	44	∈	∈	PROPN
ejpam-5486	476	45	∆	∆	X
ejpam-5486	476	46	}	}	PUNCT
ejpam-5486	476	47	be	be	VERB
ejpam-5486	476	48	ωswd(z	ωswd(z	NOUN
ejpam-5486	476	49	,	,	PUNCT
ejpam-5486	476	50	τ)-cover	τ)-cover	PUNCT
ejpam-5486	476	51	of	of	ADP
ejpam-5486	476	52	z.	z.	PROPN
ejpam-5486	477	1	then	then	ADV
ejpam-5486	477	2	e	e	PROPN
ejpam-5486	477	3	and	and	CCONJ
ejpam-5486	477	4	(	(	PUNCT
ejpam-5486	477	5	z	z	NOUN
ejpam-5486	477	6	−	−	PROPN
ejpam-5486	477	7	e	e	NOUN
ejpam-5486	477	8	)	)	PUNCT
ejpam-5486	477	9	are	be	AUX
ejpam-5486	477	10	almost	almost	ADV
ejpam-5486	477	11	ωswd	ωswd	ADJ
ejpam-5486	477	12	-	-	PUNCT
ejpam-5486	477	13	compact	compact	ADJ
ejpam-5486	477	14	relative	relative	NOUN
ejpam-5486	477	15	to	to	ADP
ejpam-5486	477	16	z	z	NOUN
ejpam-5486	477	17	and	and	CCONJ
ejpam-5486	477	18	hence	hence	ADV
ejpam-5486	477	19	there	there	PRON
ejpam-5486	477	20	are	be	VERB
ejpam-5486	477	21	finite	finite	NOUN
ejpam-5486	477	22	subset	subset	NOUN
ejpam-5486	477	23	∆	∆	ADJ
ejpam-5486	477	24	◦	◦	NOUN
ejpam-5486	477	25	⊆	⊆	NUM
ejpam-5486	477	26	∆	∆	X
ejpam-5486	477	27	with	with	ADP
ejpam-5486	477	28	z	z	NOUN
ejpam-5486	477	29	=	=	SYM
ejpam-5486	477	30	∪	∪	ADP
ejpam-5486	477	31	x∈∆	x∈∆	NOUN
ejpam-5486	477	32	◦	◦	NOUN
ejpam-5486	477	33	clωswd(hα	clωswd(hα	NOUN
ejpam-5486	477	34	)	)	PUNCT
ejpam-5486	477	35	.	.	PUNCT
ejpam-5486	478	1	proposition	proposition	NOUN
ejpam-5486	478	2	7	7	NUM
ejpam-5486	478	3	.	.	PUNCT
ejpam-5486	478	4	a	a	DET
ejpam-5486	478	5	finite	finite	ADJ
ejpam-5486	478	6	union	union	NOUN
ejpam-5486	478	7	of	of	ADP
ejpam-5486	478	8	almost	almost	ADV
ejpam-5486	478	9	ωswd	ωswd	ADJ
ejpam-5486	478	10	-	-	PUNCT
ejpam-5486	478	11	compact	compact	ADJ
ejpam-5486	478	12	subsets	subset	NOUN
ejpam-5486	478	13	relative	relative	ADJ
ejpam-5486	478	14	to	to	ADP
ejpam-5486	478	15	z	z	PROPN
ejpam-5486	478	16	is	be	AUX
ejpam-5486	478	17	almost	almost	ADV
ejpam-5486	478	18	ωswd	ωswd	ADJ
ejpam-5486	478	19	-	-	PUNCT
ejpam-5486	478	20	compact	compact	ADJ
ejpam-5486	478	21	relative	relative	NOUN
ejpam-5486	478	22	to	to	ADP
ejpam-5486	478	23	z.	z.	PROPN
ejpam-5486	478	24	proof	proof	NOUN
ejpam-5486	478	25	.	.	PUNCT
ejpam-5486	479	1	let	let	VERB
ejpam-5486	479	2	n	n	PRON
ejpam-5486	479	3	∪	∪	VERB
ejpam-5486	479	4	i=1	i=1	PRON
ejpam-5486	479	5	gi	gi	VERB
ejpam-5486	479	6	be	be	AUX
ejpam-5486	479	7	a	a	DET
ejpam-5486	479	8	finite	finite	ADJ
ejpam-5486	479	9	union	union	NOUN
ejpam-5486	479	10	of	of	ADP
ejpam-5486	479	11	almost	almost	ADV
ejpam-5486	479	12	ωswd	ωswd	ADJ
ejpam-5486	479	13	-	-	PUNCT
ejpam-5486	479	14	compact	compact	ADJ
ejpam-5486	479	15	subsets	subset	NOUN
ejpam-5486	479	16	relative	relative	ADJ
ejpam-5486	479	17	to	to	ADP
ejpam-5486	479	18	z	z	NOUN
ejpam-5486	479	19	and	and	CCONJ
ejpam-5486	479	20	h	h	NOUN
ejpam-5486	480	1	=	=	NOUN
ejpam-5486	480	2	{	{	PUNCT
ejpam-5486	480	3	hα	hα	X
ejpam-5486	480	4	:	:	PUNCT
ejpam-5486	480	5	α	α	PROPN
ejpam-5486	480	6	∈	∈	PROPN
ejpam-5486	480	7	∆	∆	X
ejpam-5486	480	8	}	}	PUNCT
ejpam-5486	480	9	be	be	VERB
ejpam-5486	480	10	ωswd(z	ωswd(z	NOUN
ejpam-5486	480	11	,	,	PUNCT
ejpam-5486	480	12	τ)-cover	τ)-cover	PUNCT
ejpam-5486	480	13	of	of	ADP
ejpam-5486	480	14	n	n	NOUN
ejpam-5486	480	15	∪	∪	VERB
ejpam-5486	480	16	i=1	i=1	PROPN
ejpam-5486	480	17	gn	gn	PROPN
ejpam-5486	480	18	.	.	PUNCT
ejpam-5486	481	1	then	then	ADV
ejpam-5486	481	2	for	for	ADP
ejpam-5486	481	3	each	each	DET
ejpam-5486	481	4	i	i	PRON
ejpam-5486	481	5	∈	∈	PROPN
ejpam-5486	481	6	{	{	PUNCT
ejpam-5486	481	7	1	1	NUM
ejpam-5486	481	8	,	,	PUNCT
ejpam-5486	481	9	2	2	NUM
ejpam-5486	481	10	,	,	PUNCT
ejpam-5486	481	11	3	3	NUM
ejpam-5486	481	12	...	...	PUNCT
ejpam-5486	481	13	n	n	CCONJ
ejpam-5486	481	14	}	}	PUNCT
ejpam-5486	481	15	there	there	PRON
ejpam-5486	481	16	is	be	VERB
ejpam-5486	481	17	a	a	DET
ejpam-5486	481	18	finite	finite	NOUN
ejpam-5486	481	19	subset	subset	NOUN
ejpam-5486	481	20	∆i	∆i	PROPN
ejpam-5486	481	21	⊆	⊆	NUM
ejpam-5486	481	22	∆	∆	X
ejpam-5486	481	23	with	with	ADP
ejpam-5486	481	24	gi	gi	ADJ
ejpam-5486	481	25	⊆	⊆	NUM
ejpam-5486	481	26	∪	∪	ADJ
ejpam-5486	481	27	α∈∆i	α∈∆i	NUM
ejpam-5486	481	28	clωswd(hα	clωswd(hα	NOUN
ejpam-5486	481	29	)	)	PUNCT
ejpam-5486	481	30	.	.	PUNCT
ejpam-5486	482	1	it	it	PRON
ejpam-5486	482	2	is	be	AUX
ejpam-5486	482	3	clear	clear	ADJ
ejpam-5486	482	4	that	that	SCONJ
ejpam-5486	482	5	n	n	ADP
ejpam-5486	482	6	∪	∪	VERB
ejpam-5486	482	7	i=1	i=1	PROPN
ejpam-5486	482	8	∆i	∆i	PROPN
ejpam-5486	482	9	is	be	AUX
ejpam-5486	482	10	finite	finite	NOUN
ejpam-5486	482	11	set	set	NOUN
ejpam-5486	482	12	.	.	PUNCT
ejpam-5486	483	1	therefore	therefore	ADV
ejpam-5486	483	2	,	,	PUNCT
ejpam-5486	483	3	n	n	PRON
ejpam-5486	483	4	∪	∪	VERB
ejpam-5486	483	5	i=1	i=1	PRON
ejpam-5486	483	6	gi	gi	VERB
ejpam-5486	483	7	⊆	⊆	NUM
ejpam-5486	483	8	∪	∪	ADP
ejpam-5486	483	9	α∈	α∈	NOUN
ejpam-5486	483	10	n	n	PRON
ejpam-5486	483	11	∪	∪	VERB
ejpam-5486	483	12	i=1	i=1	PROPN
ejpam-5486	483	13	∆i	∆i	PROPN
ejpam-5486	483	14	clωswd(hα	clωswd(hα	PROPN
ejpam-5486	483	15	)	)	PUNCT
ejpam-5486	483	16	.	.	PUNCT
ejpam-5486	484	1	the	the	DET
ejpam-5486	484	2	proofs	proof	NOUN
ejpam-5486	484	3	of	of	ADP
ejpam-5486	484	4	the	the	DET
ejpam-5486	484	5	following	following	ADJ
ejpam-5486	484	6	results	result	NOUN
ejpam-5486	484	7	are	be	AUX
ejpam-5486	484	8	obvious	obvious	ADJ
ejpam-5486	484	9	and	and	CCONJ
ejpam-5486	484	10	hence	hence	ADV
ejpam-5486	484	11	they	they	PRON
ejpam-5486	484	12	are	be	AUX
ejpam-5486	484	13	omitted	omit	VERB
ejpam-5486	484	14	.	.	PUNCT
ejpam-5486	485	1	theorem	theorem	VERB
ejpam-5486	485	2	22	22	NUM
ejpam-5486	485	3	.	.	PUNCT
ejpam-5486	486	1	let	let	VERB
ejpam-5486	486	2	γ	γ	X
ejpam-5486	486	3	:	:	PUNCT
ejpam-5486	486	4	(	(	PUNCT
ejpam-5486	486	5	z	z	NOUN
ejpam-5486	486	6	,	,	PUNCT
ejpam-5486	486	7	τ	τ	PROPN
ejpam-5486	486	8	)	)	PUNCT
ejpam-5486	486	9	→	→	SYM
ejpam-5486	486	10	(	(	PUNCT
ejpam-5486	486	11	k	k	X
ejpam-5486	486	12	,	,	PUNCT
ejpam-5486	486	13	σ	σ	PROPN
ejpam-5486	486	14	)	)	PUNCT
ejpam-5486	486	15	be	be	AUX
ejpam-5486	486	16	ωswd	ωswd	ADJ
ejpam-5486	486	17	-	-	PUNCT
ejpam-5486	486	18	irresolute	irresolute	ADJ
ejpam-5486	486	19	.	.	PUNCT
ejpam-5486	487	1	if	if	SCONJ
ejpam-5486	487	2	h	h	NOUN
ejpam-5486	487	3	is	be	AUX
ejpam-5486	487	4	almost	almost	ADV
ejpam-5486	487	5	ωswdcompact	ωswdcompact	ADJ
ejpam-5486	487	6	relative	relative	ADJ
ejpam-5486	487	7	to	to	ADP
ejpam-5486	487	8	z	z	NOUN
ejpam-5486	487	9	,	,	PUNCT
ejpam-5486	487	10	then	then	ADV
ejpam-5486	487	11	γ(h	γ(h	NOUN
ejpam-5486	487	12	)	)	PUNCT
ejpam-5486	487	13	is	be	AUX
ejpam-5486	487	14	almost	almost	ADV
ejpam-5486	487	15	ωswd	ωswd	ADJ
ejpam-5486	487	16	-	-	PUNCT
ejpam-5486	487	17	compact	compact	ADJ
ejpam-5486	487	18	relative	relative	NOUN
ejpam-5486	487	19	to	to	ADP
ejpam-5486	487	20	k.	k.	PROPN
ejpam-5486	487	21	corollary	corollary	PROPN
ejpam-5486	487	22	7	7	PROPN
ejpam-5486	487	23	.	.	PUNCT
ejpam-5486	488	1	let	let	VERB
ejpam-5486	488	2	γ	γ	X
ejpam-5486	488	3	:	:	PUNCT
ejpam-5486	488	4	(	(	PUNCT
ejpam-5486	488	5	z	z	NOUN
ejpam-5486	488	6	,	,	PUNCT
ejpam-5486	488	7	τ	τ	PROPN
ejpam-5486	488	8	)	)	PUNCT
ejpam-5486	488	9	→	→	SYM
ejpam-5486	488	10	(	(	PUNCT
ejpam-5486	488	11	k	k	X
ejpam-5486	488	12	,	,	PUNCT
ejpam-5486	488	13	σ	σ	PROPN
ejpam-5486	488	14	)	)	PUNCT
ejpam-5486	488	15	be	be	AUX
ejpam-5486	488	16	surjective	surjective	ADJ
ejpam-5486	488	17	ωswd	ωswd	ADV
ejpam-5486	488	18	-	-	PUNCT
ejpam-5486	488	19	irresolute	irresolute	NOUN
ejpam-5486	488	20	.	.	PUNCT
ejpam-5486	489	1	if	if	SCONJ
ejpam-5486	489	2	(	(	PUNCT
ejpam-5486	489	3	z	z	NOUN
ejpam-5486	489	4	,	,	PUNCT
ejpam-5486	489	5	τ	τ	X
ejpam-5486	489	6	)	)	PUNCT
ejpam-5486	489	7	is	be	AUX
ejpam-5486	489	8	almost	almost	ADV
ejpam-5486	489	9	ωswd	ωswd	ADJ
ejpam-5486	489	10	-	-	PUNCT
ejpam-5486	489	11	compact	compact	ADJ
ejpam-5486	489	12	,	,	PUNCT
ejpam-5486	489	13	then	then	ADV
ejpam-5486	489	14	(	(	PUNCT
ejpam-5486	489	15	k	k	X
ejpam-5486	489	16	,	,	PUNCT
ejpam-5486	489	17	σ	σ	PROPN
ejpam-5486	489	18	)	)	PUNCT
ejpam-5486	489	19	is	be	AUX
ejpam-5486	489	20	almost	almost	ADV
ejpam-5486	489	21	ωswd	ωswd	ADV
ejpam-5486	489	22	-	-	PUNCT
ejpam-5486	489	23	compact	compact	ADJ
ejpam-5486	489	24	.	.	PUNCT
ejpam-5486	490	1	corollary	corollary	ADJ
ejpam-5486	490	2	8	8	NUM
ejpam-5486	490	3	.	.	PUNCT
ejpam-5486	491	1	if	if	SCONJ
ejpam-5486	491	2	πzα∈∆	πzα∈∆	PRON
ejpam-5486	491	3	is	be	AUX
ejpam-5486	491	4	almost	almost	ADV
ejpam-5486	491	5	ωswd	ωswd	ADJ
ejpam-5486	491	6	-	-	PUNCT
ejpam-5486	491	7	compact	compact	ADJ
ejpam-5486	491	8	,	,	PUNCT
ejpam-5486	491	9	then	then	ADV
ejpam-5486	491	10	zα	zα	PROPN
ejpam-5486	491	11	is	be	AUX
ejpam-5486	491	12	almost	almost	ADV
ejpam-5486	491	13	ωswd	ωswd	ADV
ejpam-5486	491	14	-	-	PUNCT
ejpam-5486	491	15	compact	compact	ADJ
ejpam-5486	491	16	for	for	ADP
ejpam-5486	491	17	each	each	DET
ejpam-5486	491	18	α	α	NOUN
ejpam-5486	491	19	∈	∈	PROPN
ejpam-5486	491	20	∆.	∆.	NOUN
ejpam-5486	491	21	references	reference	NOUN
ejpam-5486	491	22	3384	3384	NUM
ejpam-5486	491	23	5	5	NUM
ejpam-5486	491	24	.	.	PUNCT
ejpam-5486	492	1	conclusions	conclusion	NOUN
ejpam-5486	492	2	the	the	DET
ejpam-5486	492	3	study	study	NOUN
ejpam-5486	492	4	of	of	ADP
ejpam-5486	492	5	different	different	ADJ
ejpam-5486	492	6	types	type	NOUN
ejpam-5486	492	7	of	of	ADP
ejpam-5486	492	8	generalized	generalized	ADJ
ejpam-5486	492	9	open	open	ADJ
ejpam-5486	492	10	sets	set	NOUN
ejpam-5486	492	11	has	have	AUX
ejpam-5486	492	12	been	be	AUX
ejpam-5486	492	13	one	one	NUM
ejpam-5486	492	14	of	of	ADP
ejpam-5486	492	15	the	the	DET
ejpam-5486	492	16	main	main	ADJ
ejpam-5486	492	17	areas	area	NOUN
ejpam-5486	492	18	of	of	ADP
ejpam-5486	492	19	research	research	NOUN
ejpam-5486	492	20	in	in	ADP
ejpam-5486	492	21	general	general	ADJ
ejpam-5486	492	22	topology	topology	NOUN
ejpam-5486	492	23	during	during	ADP
ejpam-5486	492	24	the	the	DET
ejpam-5486	492	25	last	last	ADJ
ejpam-5486	492	26	several	several	ADJ
ejpam-5486	492	27	decades	decade	NOUN
ejpam-5486	492	28	.	.	PUNCT
ejpam-5486	493	1	mathematicians	mathematician	NOUN
ejpam-5486	493	2	investigate	investigate	VERB
ejpam-5486	493	3	the	the	DET
ejpam-5486	493	4	properties	property	NOUN
ejpam-5486	493	5	of	of	ADP
ejpam-5486	493	6	various	various	ADJ
ejpam-5486	493	7	broad	broad	ADJ
ejpam-5486	493	8	topological	topological	ADJ
ejpam-5486	493	9	concepts	concept	NOUN
ejpam-5486	493	10	using	use	VERB
ejpam-5486	493	11	generalized	generalized	ADJ
ejpam-5486	493	12	open	open	ADJ
ejpam-5486	493	13	sets	set	NOUN
ejpam-5486	493	14	.	.	PUNCT
ejpam-5486	494	1	to	to	PART
ejpam-5486	494	2	continue	continue	VERB
ejpam-5486	494	3	this	this	DET
ejpam-5486	494	4	line	line	NOUN
ejpam-5486	494	5	of	of	ADP
ejpam-5486	494	6	research	research	NOUN
ejpam-5486	494	7	,	,	PUNCT
ejpam-5486	494	8	this	this	DET
ejpam-5486	494	9	manuscript	manuscript	NOUN
ejpam-5486	494	10	has	have	AUX
ejpam-5486	494	11	been	be	AUX
ejpam-5486	494	12	written	write	VERB
ejpam-5486	494	13	.	.	PUNCT
ejpam-5486	495	1	the	the	DET
ejpam-5486	495	2	main	main	ADJ
ejpam-5486	495	3	achievements	achievement	NOUN
ejpam-5486	495	4	of	of	ADP
ejpam-5486	495	5	this	this	DET
ejpam-5486	495	6	work	work	NOUN
ejpam-5486	495	7	are	be	AUX
ejpam-5486	495	8	:	:	PUNCT
ejpam-5486	495	9	(	(	PUNCT
ejpam-5486	495	10	i	i	NOUN
ejpam-5486	495	11	)	)	PUNCT
ejpam-5486	495	12	we	we	PRON
ejpam-5486	495	13	present	present	VERB
ejpam-5486	495	14	a	a	DET
ejpam-5486	495	15	generalization	generalization	NOUN
ejpam-5486	495	16	for	for	ADP
ejpam-5486	495	17	theorem	theorem	NOUN
ejpam-5486	495	18	2	2	NUM
ejpam-5486	495	19	which	which	PRON
ejpam-5486	495	20	was	be	AUX
ejpam-5486	495	21	introduced	introduce	VERB
ejpam-5486	495	22	in	in	ADP
ejpam-5486	495	23	[	[	X
ejpam-5486	495	24	1	1	NUM
ejpam-5486	495	25	]	]	PUNCT
ejpam-5486	495	26	and	and	CCONJ
ejpam-5486	495	27	provide	provide	VERB
ejpam-5486	495	28	additional	additional	ADJ
ejpam-5486	495	29	features	feature	NOUN
ejpam-5486	495	30	of	of	ADP
ejpam-5486	495	31	swd(z	swd(z	PROPN
ejpam-5486	495	32	,	,	PUNCT
ejpam-5486	495	33	τ	τ	PROPN
ejpam-5486	495	34	)	)	PUNCT
ejpam-5486	495	35	.	.	PUNCT
ejpam-5486	496	1	(	(	PUNCT
ejpam-5486	496	2	ii	ii	X
ejpam-5486	496	3	)	)	PUNCT
ejpam-5486	496	4	we	we	PRON
ejpam-5486	496	5	introduce	introduce	VERB
ejpam-5486	496	6	the	the	DET
ejpam-5486	496	7	notion	notion	NOUN
ejpam-5486	496	8	of	of	ADP
ejpam-5486	496	9	ωswd(z	ωswd(z	PROPN
ejpam-5486	496	10	,	,	PUNCT
ejpam-5486	496	11	τ	τ	PROPN
ejpam-5486	496	12	)	)	PUNCT
ejpam-5486	496	13	which	which	PRON
ejpam-5486	496	14	is	be	AUX
ejpam-5486	496	15	a	a	DET
ejpam-5486	496	16	new	new	ADJ
ejpam-5486	496	17	generalization	generalization	NOUN
ejpam-5486	496	18	for	for	ADP
ejpam-5486	496	19	somewhere	somewhere	ADJ
ejpam-5486	496	20	dense	dense	ADJ
ejpam-5486	496	21	subsets	subset	NOUN
ejpam-5486	496	22	of	of	ADP
ejpam-5486	496	23	a	a	DET
ejpam-5486	496	24	topological	topological	ADJ
ejpam-5486	496	25	space	space	NOUN
ejpam-5486	496	26	(	(	PUNCT
ejpam-5486	496	27	z	z	NOUN
ejpam-5486	496	28	,	,	PUNCT
ejpam-5486	496	29	τ	τ	PROPN
ejpam-5486	496	30	)	)	PUNCT
ejpam-5486	496	31	and	and	CCONJ
ejpam-5486	496	32	hence	hence	ADV
ejpam-5486	496	33	it	it	PRON
ejpam-5486	496	34	is	be	AUX
ejpam-5486	496	35	a	a	DET
ejpam-5486	496	36	new	new	ADJ
ejpam-5486	496	37	generalization	generalization	NOUN
ejpam-5486	496	38	for	for	ADP
ejpam-5486	496	39	open	open	ADJ
ejpam-5486	496	40	subsets	subset	NOUN
ejpam-5486	496	41	of	of	ADP
ejpam-5486	496	42	a	a	DET
ejpam-5486	496	43	topological	topological	ADJ
ejpam-5486	496	44	space	space	NOUN
ejpam-5486	496	45	(	(	PUNCT
ejpam-5486	496	46	z	z	NOUN
ejpam-5486	496	47	,	,	PUNCT
ejpam-5486	496	48	τ	τ	PROPN
ejpam-5486	496	49	)	)	PUNCT
ejpam-5486	496	50	.	.	PUNCT
ejpam-5486	497	1	(	(	PUNCT
ejpam-5486	497	2	iii	iii	X
ejpam-5486	497	3	)	)	PUNCT
ejpam-5486	497	4	we	we	PRON
ejpam-5486	497	5	verify	verify	VERB
ejpam-5486	497	6	some	some	DET
ejpam-5486	497	7	fundamental	fundamental	ADJ
ejpam-5486	497	8	features	feature	NOUN
ejpam-5486	497	9	of	of	ADP
ejpam-5486	497	10	ωswd(z	ωswd(z	PROPN
ejpam-5486	497	11	,	,	PUNCT
ejpam-5486	497	12	τ	τ	PROPN
ejpam-5486	497	13	)	)	PUNCT
ejpam-5486	497	14	and	and	CCONJ
ejpam-5486	497	15	study	study	VERB
ejpam-5486	497	16	the	the	DET
ejpam-5486	497	17	requirements	requirement	NOUN
ejpam-5486	497	18	for	for	ADP
ejpam-5486	497	19	the	the	DET
ejpam-5486	497	20	equivalence	equivalence	NOUN
ejpam-5486	497	21	between	between	ADP
ejpam-5486	497	22	the	the	DET
ejpam-5486	497	23	classes	class	NOUN
ejpam-5486	497	24	swd(z	swd(z	PROPN
ejpam-5486	497	25	,	,	PUNCT
ejpam-5486	497	26	τ	τ	PROPN
ejpam-5486	497	27	)	)	PUNCT
ejpam-5486	497	28	,	,	PUNCT
ejpam-5486	497	29	ωswd(z	ωswd(z	PROPN
ejpam-5486	497	30	,	,	PUNCT
ejpam-5486	497	31	τ	τ	PROPN
ejpam-5486	497	32	)	)	PUNCT
ejpam-5486	497	33	and	and	CCONJ
ejpam-5486	497	34	ωswd(z	ωswd(z	PROPN
ejpam-5486	497	35	,	,	PUNCT
ejpam-5486	497	36	τω	τω	INTJ
ejpam-5486	497	37	)	)	PUNCT
ejpam-5486	497	38	.	.	PUNCT
ejpam-5486	498	1	(	(	PUNCT
ejpam-5486	498	2	iv	iv	X
ejpam-5486	498	3	)	)	PUNCT
ejpam-5486	498	4	we	we	PRON
ejpam-5486	498	5	study	study	VERB
ejpam-5486	498	6	the	the	DET
ejpam-5486	498	7	notions	notion	NOUN
ejpam-5486	498	8	of	of	ADP
ejpam-5486	498	9	the	the	DET
ejpam-5486	498	10	interior	interior	NOUN
ejpam-5486	498	11	,	,	PUNCT
ejpam-5486	498	12	closure	closure	NOUN
ejpam-5486	498	13	,	,	PUNCT
ejpam-5486	498	14	ωswd	ωswd	ADJ
ejpam-5486	498	15	-	-	PUNCT
ejpam-5486	498	16	continuous	continuous	ADJ
ejpam-5486	498	17	and	and	CCONJ
ejpam-5486	498	18	ωswdirresolute	ωswdirresolute	ADJ
ejpam-5486	498	19	via	via	ADP
ejpam-5486	498	20	ωswd(z	ωswd(z	PROPN
ejpam-5486	498	21	,	,	PUNCT
ejpam-5486	498	22	τ	τ	PROPN
ejpam-5486	498	23	)	)	PUNCT
ejpam-5486	498	24	.	.	PUNCT
ejpam-5486	499	1	(	(	PUNCT
ejpam-5486	499	2	v	v	X
ejpam-5486	499	3	)	)	PUNCT
ejpam-5486	499	4	we	we	PRON
ejpam-5486	499	5	study	study	VERB
ejpam-5486	499	6	the	the	DET
ejpam-5486	499	7	notion	notion	NOUN
ejpam-5486	499	8	of	of	ADP
ejpam-5486	499	9	almost	almost	ADV
ejpam-5486	499	10	ωswd	ωswd	ADJ
ejpam-5486	499	11	-	-	PUNCT
ejpam-5486	499	12	compact	compact	ADJ
ejpam-5486	499	13	spaces	space	NOUN
ejpam-5486	499	14	with	with	ADP
ejpam-5486	499	15	some	some	PRON
ejpam-5486	499	16	of	of	ADP
ejpam-5486	499	17	their	their	PRON
ejpam-5486	499	18	properties	property	NOUN
ejpam-5486	499	19	.	.	PUNCT
ejpam-5486	500	1	this	this	DET
ejpam-5486	500	2	work	work	NOUN
ejpam-5486	500	3	can	can	AUX
ejpam-5486	500	4	be	be	AUX
ejpam-5486	500	5	considered	consider	VERB
ejpam-5486	500	6	as	as	ADP
ejpam-5486	500	7	a	a	DET
ejpam-5486	500	8	starting	starting	NOUN
ejpam-5486	500	9	point	point	NOUN
ejpam-5486	500	10	for	for	ADP
ejpam-5486	500	11	many	many	ADJ
ejpam-5486	500	12	topics	topic	NOUN
ejpam-5486	500	13	and	and	CCONJ
ejpam-5486	500	14	studies	study	NOUN
ejpam-5486	500	15	in	in	ADP
ejpam-5486	500	16	topology	topology	NOUN
ejpam-5486	500	17	since	since	SCONJ
ejpam-5486	500	18	ωswd(z	ωswd(z	PROPN
ejpam-5486	500	19	,	,	PUNCT
ejpam-5486	500	20	τ	τ	PROPN
ejpam-5486	500	21	)	)	PUNCT
ejpam-5486	500	22	forms	form	VERB
ejpam-5486	500	23	a	a	DET
ejpam-5486	500	24	generalization	generalization	NOUN
ejpam-5486	500	25	of	of	ADP
ejpam-5486	500	26	open	open	ADJ
ejpam-5486	500	27	sets	set	NOUN
ejpam-5486	500	28	.	.	PUNCT
ejpam-5486	501	1	therefore	therefore	ADV
ejpam-5486	501	2	,	,	PUNCT
ejpam-5486	501	3	in	in	ADP
ejpam-5486	501	4	upcoming	upcoming	ADJ
ejpam-5486	501	5	papers	paper	NOUN
ejpam-5486	501	6	,	,	PUNCT
ejpam-5486	501	7	we	we	PRON
ejpam-5486	501	8	plan	plan	VERB
ejpam-5486	501	9	to	to	PART
ejpam-5486	501	10	study	study	VERB
ejpam-5486	501	11	the	the	DET
ejpam-5486	501	12	notion	notion	NOUN
ejpam-5486	501	13	of	of	ADP
ejpam-5486	501	14	connected	connected	ADJ
ejpam-5486	501	15	,	,	PUNCT
ejpam-5486	501	16	separation	separation	NOUN
ejpam-5486	501	17	axioms	axiom	NOUN
ejpam-5486	501	18	and	and	CCONJ
ejpam-5486	501	19	other	other	ADJ
ejpam-5486	501	20	types	type	NOUN
ejpam-5486	501	21	of	of	ADP
ejpam-5486	501	22	covering	cover	VERB
ejpam-5486	501	23	such	such	ADJ
ejpam-5486	501	24	as	as	ADP
ejpam-5486	501	25	paracompact	paracompact	ADJ
ejpam-5486	501	26	spaces	space	NOUN
ejpam-5486	501	27	via	via	ADP
ejpam-5486	501	28	the	the	DET
ejpam-5486	501	29	class	class	NOUN
ejpam-5486	501	30	ωswd(z	ωswd(z	PROPN
ejpam-5486	501	31	,	,	PUNCT
ejpam-5486	501	32	τ	τ	PROPN
ejpam-5486	501	33	)	)	PUNCT
ejpam-5486	501	34	.	.	PUNCT
ejpam-5486	502	1	acknowledgements	acknowledgement	VERB
ejpam-5486	502	2	the	the	DET
ejpam-5486	502	3	publication	publication	NOUN
ejpam-5486	502	4	of	of	ADP
ejpam-5486	502	5	this	this	DET
ejpam-5486	502	6	paper	paper	NOUN
ejpam-5486	502	7	was	be	AUX
ejpam-5486	502	8	supported	support	VERB
ejpam-5486	502	9	by	by	ADP
ejpam-5486	502	10	yarmouk	yarmouk	PROPN
ejpam-5486	502	11	university	university	NOUN
ejpam-5486	502	12	research	research	NOUN
ejpam-5486	502	13	council	council	PROPN
ejpam-5486	502	14	.	.	PUNCT
ejpam-5486	503	1	references	reference	NOUN
ejpam-5486	503	2	[	[	X
ejpam-5486	503	3	1	1	NUM
ejpam-5486	503	4	]	]	X
ejpam-5486	503	5	t.m	t.m	PROPN
ejpam-5486	503	6	.	.	PROPN
ejpam-5486	503	7	al	al	PROPN
ejpam-5486	503	8	-	-	PUNCT
ejpam-5486	503	9	shami	shami	PROPN
ejpam-5486	503	10	.	.	PUNCT
ejpam-5486	504	1	somewhere	somewhere	ADV
ejpam-5486	504	2	dense	dense	ADJ
ejpam-5486	504	3	sets	set	NOUN
ejpam-5486	504	4	and	and	CCONJ
ejpam-5486	504	5	st1	st1	PROPN
ejpam-5486	504	6	-	-	PUNCT
ejpam-5486	504	7	spaces	spaces	PROPN
ejpam-5486	504	8	.	.	PUNCT
ejpam-5486	505	1	punjab	punjab	PROPN
ejpam-5486	505	2	univ	univ	PROPN
ejpam-5486	505	3	.	.	PUNCT
ejpam-5486	506	1	j.	j.	PROPN
ejpam-5486	506	2	math	math	PROPN
ejpam-5486	506	3	.	.	PROPN
ejpam-5486	506	4	,	,	PUNCT
ejpam-5486	506	5	49(2):101–111	49(2):101–111	PROPN
ejpam-5486	506	6	,	,	PUNCT
ejpam-5486	506	7	2017	2017	NUM
ejpam-5486	506	8	.	.	PUNCT
ejpam-5486	507	1	[	[	X
ejpam-5486	507	2	2	2	NUM
ejpam-5486	507	3	]	]	X
ejpam-5486	507	4	t.m	t.m	PROPN
ejpam-5486	507	5	.	.	PROPN
ejpam-5486	507	6	al	al	PROPN
ejpam-5486	507	7	-	-	PUNCT
ejpam-5486	507	8	shami	shami	PROPN
ejpam-5486	507	9	.	.	PUNCT
ejpam-5486	508	1	improvement	improvement	NOUN
ejpam-5486	508	2	of	of	ADP
ejpam-5486	508	3	the	the	DET
ejpam-5486	508	4	approximations	approximation	NOUN
ejpam-5486	508	5	and	and	CCONJ
ejpam-5486	508	6	accuracy	accuracy	NOUN
ejpam-5486	508	7	measure	measure	NOUN
ejpam-5486	508	8	of	of	ADP
ejpam-5486	508	9	a	a	DET
ejpam-5486	508	10	rough	rough	ADJ
ejpam-5486	508	11	set	set	NOUN
ejpam-5486	508	12	using	use	VERB
ejpam-5486	508	13	somewhere	somewhere	ADV
ejpam-5486	508	14	dense	dense	ADJ
ejpam-5486	508	15	sets	set	NOUN
ejpam-5486	508	16	.	.	PUNCT
ejpam-5486	509	1	soft	soft	ADJ
ejpam-5486	509	2	comput	comput	NOUN
ejpam-5486	509	3	.	.	PUNCT
ejpam-5486	509	4	,	,	PUNCT
ejpam-5486	509	5	25:14449–14460	25:14449–14460	NUM
ejpam-5486	509	6	,	,	PUNCT
ejpam-5486	509	7	2021	2021	NUM
ejpam-5486	509	8	.	.	PUNCT
ejpam-5486	510	1	[	[	X
ejpam-5486	510	2	3	3	X
ejpam-5486	510	3	]	]	X
ejpam-5486	510	4	t.m	t.m	PROPN
ejpam-5486	510	5	.	.	PROPN
ejpam-5486	510	6	al	al	PROPN
ejpam-5486	510	7	-	-	PUNCT
ejpam-5486	510	8	shami	shami	PROPN
ejpam-5486	510	9	and	and	CCONJ
ejpam-5486	510	10	t.	t.	PROPN
ejpam-5486	510	11	noiri	noiri	PROPN
ejpam-5486	510	12	.	.	PUNCT
ejpam-5486	511	1	more	more	ADJ
ejpam-5486	511	2	notions	notion	NOUN
ejpam-5486	511	3	and	and	CCONJ
ejpam-5486	511	4	mappings	mapping	NOUN
ejpam-5486	511	5	via	via	ADP
ejpam-5486	511	6	somewhere	somewhere	ADJ
ejpam-5486	511	7	dense	dense	ADJ
ejpam-5486	511	8	sets	set	NOUN
ejpam-5486	511	9	.	.	PUNCT
ejpam-5486	512	1	afr	afr	NOUN
ejpam-5486	512	2	.	.	PUNCT
ejpam-5486	513	1	mat	mat	PROPN
ejpam-5486	513	2	.	.	PROPN
ejpam-5486	513	3	,	,	PUNCT
ejpam-5486	513	4	30(7):1011–1024	30(7):1011–1024	PROPN
ejpam-5486	513	5	,	,	PUNCT
ejpam-5486	513	6	2019	2019	NUM
ejpam-5486	513	7	.	.	PUNCT
ejpam-5486	514	1	[	[	X
ejpam-5486	514	2	4	4	NUM
ejpam-5486	514	3	]	]	X
ejpam-5486	514	4	t.m	t.m	PROPN
ejpam-5486	514	5	.	.	PROPN
ejpam-5486	514	6	al	al	PROPN
ejpam-5486	514	7	-	-	PUNCT
ejpam-5486	514	8	shami	shami	PROPN
ejpam-5486	514	9	and	and	CCONJ
ejpam-5486	514	10	t.	t.	PROPN
ejpam-5486	514	11	noiri	noiri	PROPN
ejpam-5486	514	12	.	.	PUNCT
ejpam-5486	515	1	compactness	compactness	NOUN
ejpam-5486	515	2	and	and	CCONJ
ejpam-5486	515	3	lindelöfness	lindelöfness	NOUN
ejpam-5486	515	4	using	use	VERB
ejpam-5486	515	5	somewhere	somewhere	ADV
ejpam-5486	515	6	dense	dense	ADJ
ejpam-5486	515	7	and	and	CCONJ
ejpam-5486	515	8	cs	cs	ADJ
ejpam-5486	515	9	-	-	ADJ
ejpam-5486	515	10	dense	dense	ADJ
ejpam-5486	515	11	sets	set	NOUN
ejpam-5486	515	12	.	.	PUNCT
ejpam-5486	516	1	novi	novi	PROPN
ejpam-5486	516	2	sad	sad	PROPN
ejpam-5486	516	3	j.	j.	PROPN
ejpam-5486	516	4	math	math	PROPN
ejpam-5486	516	5	.	.	PUNCT
ejpam-5486	516	6	,	,	PUNCT
ejpam-5486	516	7	52(2):165–176	52(2):165–176	PROPN
ejpam-5486	516	8	,	,	PUNCT
ejpam-5486	516	9	2022	2022	NUM
ejpam-5486	516	10	.	.	PUNCT
ejpam-5486	517	1	[	[	X
ejpam-5486	517	2	5	5	X
ejpam-5486	517	3	]	]	PUNCT
ejpam-5486	517	4	k.	k.	PROPN
ejpam-5486	517	5	al	al	PROPN
ejpam-5486	517	6	-	-	PROPN
ejpam-5486	517	7	zoubi	zoubi	PROPN
ejpam-5486	517	8	and	and	CCONJ
ejpam-5486	517	9	b.	b.	PROPN
ejpam-5486	517	10	al	al	PROPN
ejpam-5486	517	11	-	-	PUNCT
ejpam-5486	517	12	nashef	nashef	PROPN
ejpam-5486	517	13	.	.	PUNCT
ejpam-5486	518	1	the	the	DET
ejpam-5486	518	2	topology	topology	NOUN
ejpam-5486	518	3	of	of	ADP
ejpam-5486	518	4	ω	ω	VERB
ejpam-5486	518	5	-	-	ADJ
ejpam-5486	518	6	open	open	ADJ
ejpam-5486	518	7	subsets	subset	NOUN
ejpam-5486	518	8	.	.	PUNCT
ejpam-5486	519	1	al	al	PROPN
ejpam-5486	519	2	-	-	PUNCT
ejpam-5486	519	3	manarah	manarah	PROPN
ejpam-5486	519	4	journal	journal	NOUN
ejpam-5486	519	5	,	,	PUNCT
ejpam-5486	519	6	9:169–179	9:169–179	PROPN
ejpam-5486	519	7	,	,	PUNCT
ejpam-5486	519	8	2003	2003	NUM
ejpam-5486	519	9	.	.	PUNCT
ejpam-5486	520	1	references	reference	NOUN
ejpam-5486	520	2	3385	3385	NUM
ejpam-5486	520	3	[	[	X
ejpam-5486	520	4	6	6	NUM
ejpam-5486	520	5	]	]	PUNCT
ejpam-5486	520	6	d.	d.	PROPN
ejpam-5486	520	7	andrijevic	andrijevic	VERB
ejpam-5486	520	8	.	.	PUNCT
ejpam-5486	521	1	on	on	ADP
ejpam-5486	521	2	b	b	X
ejpam-5486	521	3	-	-	PUNCT
ejpam-5486	521	4	open	open	ADJ
ejpam-5486	521	5	sets	set	NOUN
ejpam-5486	521	6	.	.	PUNCT
ejpam-5486	522	1	mat	mat	NOUN
ejpam-5486	522	2	.	.	PUNCT
ejpam-5486	522	3	vesnik	vesnik	PROPN
ejpam-5486	522	4	.	.	PROPN
ejpam-5486	522	5	,	,	PUNCT
ejpam-5486	522	6	48:59–64	48:59–64	PROPN
ejpam-5486	522	7	,	,	PUNCT
ejpam-5486	522	8	1996	1996	NUM
ejpam-5486	522	9	.	.	PUNCT
ejpam-5486	523	1	[	[	X
ejpam-5486	523	2	7	7	X
ejpam-5486	523	3	]	]	PUNCT
ejpam-5486	523	4	k.	k.	PROPN
ejpam-5486	523	5	arwini	arwini	PROPN
ejpam-5486	523	6	and	and	CCONJ
ejpam-5486	523	7	h.	h.	PROPN
ejpam-5486	523	8	mira	mira	PROPN
ejpam-5486	523	9	.	.	PUNCT
ejpam-5486	524	1	further	further	ADJ
ejpam-5486	524	2	remarks	remark	NOUN
ejpam-5486	524	3	on	on	ADP
ejpam-5486	524	4	somewhere	somewhere	ADJ
ejpam-5486	524	5	dense	dense	ADJ
ejpam-5486	524	6	sets	set	NOUN
ejpam-5486	524	7	.	.	PUNCT
ejpam-5486	525	1	sebha	sebha	PROPN
ejpam-5486	525	2	university	university	PROPN
ejpam-5486	525	3	journal	journal	NOUN
ejpam-5486	525	4	of	of	ADP
ejpam-5486	525	5	pure	pure	PROPN
ejpam-5486	525	6	&	&	CCONJ
ejpam-5486	525	7	applied	applied	ADJ
ejpam-5486	525	8	sciences	science	NOUN
ejpam-5486	525	9	,	,	PUNCT
ejpam-5486	525	10	21(1):46–48	21(1):46–48	NUM
ejpam-5486	525	11	,	,	PUNCT
ejpam-5486	525	12	2022	2022	NUM
ejpam-5486	525	13	.	.	PUNCT
ejpam-5486	526	1	[	[	X
ejpam-5486	526	2	8	8	NUM
ejpam-5486	526	3	]	]	PUNCT
ejpam-5486	526	4	k.	k.	PROPN
ejpam-5486	526	5	dlaska	dlaska	PROPN
ejpam-5486	526	6	.	.	PUNCT
ejpam-5486	527	1	rc	rc	PROPN
ejpam-5486	527	2	-	-	PUNCT
ejpam-5486	527	3	lindelöf	lindelöf	NOUN
ejpam-5486	527	4	sets	set	NOUN
ejpam-5486	527	5	and	and	CCONJ
ejpam-5486	527	6	almost	almost	ADV
ejpam-5486	527	7	rc	rc	NOUN
ejpam-5486	527	8	-	-	PUNCT
ejpam-5486	527	9	lindelöf	lindelöf	NOUN
ejpam-5486	527	10	sets	set	NOUN
ejpam-5486	527	11	.	.	PUNCT
ejpam-5486	528	1	kyungpook	kyungpook	PROPN
ejpam-5486	528	2	math	math	PROPN
ejpam-5486	528	3	.	.	PUNCT
ejpam-5486	529	1	j.	j.	PROPN
ejpam-5486	529	2	,	,	PUNCT
ejpam-5486	529	3	34(2):275	34(2):275	PROPN
ejpam-5486	529	4	–	–	PUNCT
ejpam-5486	529	5	281	281	NUM
ejpam-5486	529	6	,	,	PUNCT
ejpam-5486	529	7	1994	1994	NUM
ejpam-5486	529	8	.	.	PUNCT
ejpam-5486	530	1	[	[	X
ejpam-5486	530	2	9	9	NUM
ejpam-5486	530	3	]	]	X
ejpam-5486	530	4	m.e	m.e	PROPN
ejpam-5486	530	5	.	.	PROPN
ejpam-5486	530	6	abd	abd	PROPN
ejpam-5486	530	7	el	el	PROPN
ejpam-5486	530	8	-	-	PROPN
ejpam-5486	530	9	monsef	monsef	ADJ
ejpam-5486	530	10	,	,	PUNCT
ejpam-5486	530	11	s.n	s.n	PROPN
ejpam-5486	530	12	.	.	PROPN
ejpam-5486	530	13	el	el	PROPN
ejpam-5486	530	14	-	-	PUNCT
ejpam-5486	530	15	deeb	deeb	PROPN
ejpam-5486	530	16	,	,	PUNCT
ejpam-5486	530	17	and	and	CCONJ
ejpam-5486	530	18	r.a	r.a	PROPN
ejpam-5486	530	19	.	.	PROPN
ejpam-5486	530	20	mahmoud	mahmoud	PROPN
ejpam-5486	530	21	.	.	PUNCT
ejpam-5486	530	22	β	β	X
ejpam-5486	530	23	-	-	ADJ
ejpam-5486	530	24	open	open	ADJ
ejpam-5486	530	25	sets	set	NOUN
ejpam-5486	530	26	and	and	CCONJ
ejpam-5486	530	27	βcontinuous	βcontinuous	ADJ
ejpam-5486	530	28	mappings	mapping	NOUN
ejpam-5486	530	29	.	.	PUNCT
ejpam-5486	531	1	bull	bull	NOUN
ejpam-5486	531	2	.	.	PUNCT
ejpam-5486	532	1	fac	fac	PROPN
ejpam-5486	532	2	.	.	PUNCT
ejpam-5486	533	1	sci	sci	PROPN
ejpam-5486	533	2	.	.	PUNCT
ejpam-5486	533	3	assiut	assiut	PROPN
ejpam-5486	533	4	univ	univ	PROPN
ejpam-5486	533	5	.	.	PROPN
ejpam-5486	533	6	,	,	PUNCT
ejpam-5486	533	7	12:77–90	12:77–90	NUM
ejpam-5486	533	8	,	,	PUNCT
ejpam-5486	533	9	1983	1983	NUM
ejpam-5486	533	10	.	.	PUNCT
ejpam-5486	534	1	[	[	X
ejpam-5486	534	2	10	10	NUM
ejpam-5486	534	3	]	]	X
ejpam-5486	534	4	r.	r.	PROPN
ejpam-5486	534	5	engelking	engelke	VERB
ejpam-5486	534	6	.	.	PUNCT
ejpam-5486	535	1	general	general	ADJ
ejpam-5486	535	2	topology	topology	PROPN
ejpam-5486	535	3	.	.	PUNCT
ejpam-5486	536	1	heldermann	heldermann	PROPN
ejpam-5486	536	2	verlag	verlag	PROPN
ejpam-5486	536	3	berlin	berlin	PROPN
ejpam-5486	536	4	,	,	PUNCT
ejpam-5486	536	5	1989	1989	NUM
ejpam-5486	536	6	.	.	PUNCT
ejpam-5486	537	1	[	[	X
ejpam-5486	537	2	11	11	NUM
ejpam-5486	537	3	]	]	PUNCT
ejpam-5486	537	4	h.	h.	PROPN
ejpam-5486	537	5	hdeib	hdeib	PROPN
ejpam-5486	537	6	.	.	PUNCT
ejpam-5486	538	1	ω	ω	VERB
ejpam-5486	538	2	-	-	PUNCT
ejpam-5486	538	3	closed	close	VERB
ejpam-5486	538	4	mappings	mapping	NOUN
ejpam-5486	538	5	.	.	PUNCT
ejpam-5486	539	1	revista	revista	PROPN
ejpam-5486	539	2	colomb	colomb	PROPN
ejpam-5486	539	3	.	.	PUNCT
ejpam-5486	540	1	de	de	X
ejpam-5486	540	2	matem	matem	PROPN
ejpam-5486	540	3	.	.	PUNCT
ejpam-5486	540	4	,	,	PUNCT
ejpam-5486	540	5	16:65–78	16:65–78	NUM
ejpam-5486	540	6	,	,	PUNCT
ejpam-5486	540	7	1982	1982	NUM
ejpam-5486	540	8	.	.	PUNCT
ejpam-5486	541	1	[	[	X
ejpam-5486	541	2	12	12	NUM
ejpam-5486	541	3	]	]	X
ejpam-5486	541	4	b.	b.	PROPN
ejpam-5486	541	5	jun	jun	PROPN
ejpam-5486	541	6	,	,	PUNCT
ejpam-5486	541	7	s.w	s.w	PROPN
ejpam-5486	541	8	.	.	PROPN
ejpam-5486	541	9	jeong	jeong	PROPN
ejpam-5486	541	10	,	,	PUNCT
ejpam-5486	541	11	h.j	h.j	PROPN
ejpam-5486	541	12	.	.	PROPN
ejpam-5486	541	13	lee	lee	PROPN
ejpam-5486	541	14	,	,	PUNCT
ejpam-5486	541	15	and	and	CCONJ
ejpam-5486	541	16	j.w	j.w	PROPN
ejpam-5486	541	17	.	.	PROPN
ejpam-5486	541	18	lee	lee	PROPN
ejpam-5486	541	19	.	.	PUNCT
ejpam-5486	541	20	applications	application	NOUN
ejpam-5486	541	21	of	of	ADP
ejpam-5486	541	22	pre	pre	ADJ
ejpam-5486	541	23	-	-	ADJ
ejpam-5486	541	24	open	open	ADJ
ejpam-5486	541	25	sets	set	NOUN
ejpam-5486	541	26	.	.	PUNCT
ejpam-5486	542	1	appl	appl	PROPN
ejpam-5486	542	2	.	.	PUNCT
ejpam-5486	543	1	gen	gen	PROPN
ejpam-5486	543	2	.	.	PROPN
ejpam-5486	543	3	topol	topol	PROPN
ejpam-5486	543	4	.	.	PROPN
ejpam-5486	543	5	,	,	PUNCT
ejpam-5486	543	6	9(2):213–228	9(2):213–228	NUM
ejpam-5486	543	7	,	,	PUNCT
ejpam-5486	543	8	2008	2008	NUM
ejpam-5486	543	9	.	.	PUNCT
ejpam-5486	544	1	[	[	X
ejpam-5486	544	2	13	13	NUM
ejpam-5486	544	3	]	]	X
ejpam-5486	544	4	n.	n.	PROPN
ejpam-5486	544	5	levine	levine	PROPN
ejpam-5486	544	6	.	.	PUNCT
ejpam-5486	545	1	semi	semi	ADJ
ejpam-5486	545	2	-	-	ADJ
ejpam-5486	545	3	open	open	ADJ
ejpam-5486	545	4	sets	set	NOUN
ejpam-5486	545	5	and	and	CCONJ
ejpam-5486	545	6	semi	semi	ADJ
ejpam-5486	545	7	-	-	NOUN
ejpam-5486	545	8	continuity	continuity	NOUN
ejpam-5486	545	9	in	in	ADP
ejpam-5486	545	10	topological	topological	ADJ
ejpam-5486	545	11	spaces	space	NOUN
ejpam-5486	545	12	.	.	PUNCT
ejpam-5486	546	1	amer	amer	PROPN
ejpam-5486	546	2	.	.	PUNCT
ejpam-5486	546	3	math	math	PROPN
ejpam-5486	546	4	.	.	PUNCT
ejpam-5486	547	1	monthly	monthly	ADJ
ejpam-5486	547	2	,	,	PUNCT
ejpam-5486	547	3	70:36–41	70:36–41	NUM
ejpam-5486	547	4	,	,	PUNCT
ejpam-5486	547	5	1963	1963	NUM
ejpam-5486	547	6	.	.	PUNCT
ejpam-5486	548	1	[	[	X
ejpam-5486	548	2	14	14	NUM
ejpam-5486	548	3	]	]	X
ejpam-5486	548	4	s.n	s.n	PROPN
ejpam-5486	548	5	.	.	PROPN
ejpam-5486	548	6	maheshwari	maheshwari	PROPN
ejpam-5486	548	7	and	and	CCONJ
ejpam-5486	548	8	s.s	s.s	PROPN
ejpam-5486	548	9	.	.	PROPN
ejpam-5486	548	10	thakur	thakur	PROPN
ejpam-5486	548	11	.	.	PUNCT
ejpam-5486	549	1	on	on	ADP
ejpam-5486	549	2	α	α	PRON
ejpam-5486	549	3	-	-	ADJ
ejpam-5486	549	4	compact	compact	ADJ
ejpam-5486	549	5	spaces	space	NOUN
ejpam-5486	549	6	.	.	PUNCT
ejpam-5486	550	1	bull	bull	NOUN
ejpam-5486	550	2	.	.	PUNCT
ejpam-5486	550	3	inst	inst	PROPN
ejpam-5486	550	4	.	.	PUNCT
ejpam-5486	551	1	math	math	NOUN
ejpam-5486	551	2	.	.	PUNCT
ejpam-5486	552	1	acad	acad	PROPN
ejpam-5486	552	2	.	.	PUNCT
ejpam-5486	553	1	sinica	sinica	PROPN
ejpam-5486	553	2	,	,	PUNCT
ejpam-5486	553	3	13:341–347	13:341–347	NUM
ejpam-5486	553	4	,	,	PUNCT
ejpam-5486	553	5	1985	1985	NUM
ejpam-5486	553	6	.	.	PUNCT
ejpam-5486	554	1	[	[	X
ejpam-5486	554	2	15	15	NUM
ejpam-5486	554	3	]	]	X
ejpam-5486	554	4	a.s	a.s	PROPN
ejpam-5486	554	5	.	.	PROPN
ejpam-5486	554	6	mashhour	mashhour	PROPN
ejpam-5486	554	7	,	,	PUNCT
ejpam-5486	554	8	m.e	m.e	PROPN
ejpam-5486	554	9	.	.	PROPN
ejpam-5486	554	10	abd	abd	PROPN
ejpam-5486	555	1	el	el	PROPN
ejpam-5486	555	2	-	-	PROPN
ejpam-5486	555	3	monsef	monsef	ADJ
ejpam-5486	555	4	,	,	PUNCT
ejpam-5486	555	5	and	and	CCONJ
ejpam-5486	555	6	s.n	s.n	PROPN
ejpam-5486	555	7	.	.	PROPN
ejpam-5486	555	8	el	el	PROPN
ejpam-5486	555	9	-	-	PUNCT
ejpam-5486	555	10	deeb	deeb	PROPN
ejpam-5486	555	11	.	.	PUNCT
ejpam-5486	556	1	on	on	ADP
ejpam-5486	556	2	pre	pre	ADJ
ejpam-5486	556	3	-	-	ADJ
ejpam-5486	556	4	continuous	continuous	ADJ
ejpam-5486	556	5	and	and	CCONJ
ejpam-5486	556	6	weak	weak	ADJ
ejpam-5486	556	7	pre	pre	ADJ
ejpam-5486	556	8	-	-	ADJ
ejpam-5486	556	9	continuous	continuous	ADJ
ejpam-5486	556	10	mappings	mapping	NOUN
ejpam-5486	556	11	.	.	PUNCT
ejpam-5486	557	1	proc	proc	NOUN
ejpam-5486	557	2	.	.	PUNCT
ejpam-5486	558	1	math	math	NOUN
ejpam-5486	558	2	.	.	PUNCT
ejpam-5486	559	1	phys	phy	NOUN
ejpam-5486	559	2	.	.	PUNCT
ejpam-5486	560	1	soc	soc	PROPN
ejpam-5486	560	2	.	.	PROPN
ejpam-5486	560	3	,	,	PUNCT
ejpam-5486	560	4	53:47–53	53:47–53	NUM
ejpam-5486	560	5	,	,	PUNCT
ejpam-5486	560	6	1982	1982	NUM
ejpam-5486	560	7	.	.	PUNCT
ejpam-5486	561	1	[	[	X
ejpam-5486	561	2	16	16	NUM
ejpam-5486	561	3	]	]	X
ejpam-5486	561	4	o.	o.	PROPN
ejpam-5486	561	5	njastad	njastad	PROPN
ejpam-5486	561	6	.	.	PUNCT
ejpam-5486	562	1	on	on	ADP
ejpam-5486	562	2	some	some	DET
ejpam-5486	562	3	classes	class	NOUN
ejpam-5486	562	4	of	of	ADP
ejpam-5486	562	5	nearly	nearly	ADV
ejpam-5486	562	6	open	open	ADJ
ejpam-5486	562	7	sets	set	NOUN
ejpam-5486	562	8	.	.	PUNCT
ejpam-5486	563	1	pac	pac	PROPN
ejpam-5486	563	2	.	.	PUNCT
ejpam-5486	564	1	j.	j.	PROPN
ejpam-5486	564	2	math	math	PROPN
ejpam-5486	564	3	.	.	PUNCT
ejpam-5486	564	4	,	,	PUNCT
ejpam-5486	564	5	15:961–970	15:961–970	PROPN
ejpam-5486	564	6	,	,	PUNCT
ejpam-5486	564	7	1965	1965	NUM
ejpam-5486	564	8	.	.	PUNCT
ejpam-5486	565	1	[	[	X
ejpam-5486	565	2	17	17	NUM
ejpam-5486	565	3	]	]	X
ejpam-5486	565	4	l.a	l.a	PROPN
ejpam-5486	565	5	.	.	PROPN
ejpam-5486	565	6	steen	steen	PROPN
ejpam-5486	565	7	and	and	CCONJ
ejpam-5486	565	8	j.a	j.a	PROPN
ejpam-5486	565	9	.	.	PROPN
ejpam-5486	565	10	seebach	seebach	PROPN
ejpam-5486	565	11	.	.	PUNCT
ejpam-5486	566	1	counterexamples	counterexample	NOUN
ejpam-5486	566	2	in	in	ADP
ejpam-5486	566	3	topology	topology	NOUN
ejpam-5486	566	4	.	.	PUNCT
ejpam-5486	567	1	holt	holt	PROPN
ejpam-5486	567	2	,	,	PUNCT
ejpam-5486	567	3	rinehart	rinehart	PROPN
ejpam-5486	567	4	and	and	CCONJ
ejpam-5486	567	5	winster	winster	NOUN
ejpam-5486	567	6	,	,	PUNCT
ejpam-5486	567	7	new	new	PROPN
ejpam-5486	567	8	york	york	PROPN
ejpam-5486	567	9	,	,	PUNCT
ejpam-5486	567	10	1970	1970	NUM
ejpam-5486	567	11	.	.	PUNCT
ejpam-5486	568	1	[	[	X
ejpam-5486	568	2	18	18	NUM
ejpam-5486	568	3	]	]	PUNCT
ejpam-5486	568	4	m.	m.	NOUN
ejpam-5486	568	5	stone	stone	NOUN
ejpam-5486	568	6	.	.	PUNCT
ejpam-5486	569	1	application	application	NOUN
ejpam-5486	569	2	of	of	ADP
ejpam-5486	569	3	the	the	DET
ejpam-5486	569	4	theory	theory	NOUN
ejpam-5486	569	5	of	of	ADP
ejpam-5486	569	6	boolean	boolean	ADJ
ejpam-5486	569	7	rings	ring	NOUN
ejpam-5486	569	8	to	to	ADP
ejpam-5486	569	9	general	general	ADJ
ejpam-5486	569	10	topology	topology	NOUN
ejpam-5486	569	11	.	.	PUNCT
ejpam-5486	570	1	trans	trans	PROPN
ejpam-5486	570	2	.	.	PUNCT
ejpam-5486	571	1	amer	amer	PROPN
ejpam-5486	571	2	.	.	PUNCT
ejpam-5486	571	3	math	math	PROPN
ejpam-5486	571	4	.	.	PUNCT
ejpam-5486	572	1	soc	soc	PROPN
ejpam-5486	572	2	.	.	PUNCT
ejpam-5486	572	3	,	,	PUNCT
ejpam-5486	572	4	41:374–481	41:374–481	PROPN
ejpam-5486	572	5	,	,	PUNCT
ejpam-5486	572	6	1937	1937	NUM
ejpam-5486	572	7	.	.	PUNCT