id	sid	tid	token	lemma	pos
ejpam-4379	1	1	european	european	PROPN
ejpam-4379	1	2	journal	journal	PROPN
ejpam-4379	1	3	of	of	ADP
ejpam-4379	1	4	pure	pure	ADJ
ejpam-4379	1	5	and	and	CCONJ
ejpam-4379	1	6	applied	apply	VERB
ejpam-4379	1	7	mathematics	mathematic	NOUN
ejpam-4379	1	8	vol	vol	NOUN
ejpam-4379	1	9	.	.	PROPN
ejpam-4379	2	1	15	15	NUM
ejpam-4379	2	2	,	,	PUNCT
ejpam-4379	2	3	no	no	INTJ
ejpam-4379	2	4	.	.	NOUN
ejpam-4379	2	5	2	2	NUM
ejpam-4379	2	6	,	,	PUNCT
ejpam-4379	2	7	2022	2022	NUM
ejpam-4379	2	8	,	,	PUNCT
ejpam-4379	2	9	672	672	NUM
ejpam-4379	2	10	-	-	SYM
ejpam-4379	2	11	680	680	NUM
ejpam-4379	2	12	issn	issn	PROPN
ejpam-4379	2	13	1307	1307	NUM
ejpam-4379	2	14	-	-	SYM
ejpam-4379	2	15	5543	5543	NUM
ejpam-4379	2	16	–	–	PUNCT
ejpam-4379	2	17	ejpam.com	ejpam.com	X
ejpam-4379	2	18	published	publish	VERB
ejpam-4379	2	19	by	by	ADP
ejpam-4379	2	20	new	new	PROPN
ejpam-4379	2	21	york	york	PROPN
ejpam-4379	2	22	business	business	PROPN
ejpam-4379	2	23	global	global	PROPN
ejpam-4379	2	24	closed	close	VERB
ejpam-4379	2	25	extension	extension	NOUN
ejpam-4379	2	26	topological	topological	ADJ
ejpam-4379	2	27	spaces	space	NOUN
ejpam-4379	3	1	dina	dina	PROPN
ejpam-4379	3	2	abuzaid1	abuzaid1	PROPN
ejpam-4379	3	3	,	,	PUNCT
ejpam-4379	3	4	suad	suad	PROPN
ejpam-4379	3	5	al	al	PROPN
ejpam-4379	3	6	-	-	PUNCT
ejpam-4379	3	7	qarhi1	qarhi1	PROPN
ejpam-4379	3	8	,	,	PUNCT
ejpam-4379	3	9	and	and	CCONJ
ejpam-4379	3	10	lutfi	lutfi	PROPN
ejpam-4379	3	11	kalantan1,∗	kalantan1,∗	PROPN
ejpam-4379	3	12	1	1	NUM
ejpam-4379	3	13	king	king	PROPN
ejpam-4379	3	14	abdulaziz	abdulaziz	PROPN
ejpam-4379	3	15	university	university	PROPN
ejpam-4379	3	16	,	,	PUNCT
ejpam-4379	3	17	department	department	NOUN
ejpam-4379	3	18	of	of	ADP
ejpam-4379	3	19	mathematics	mathematic	NOUN
ejpam-4379	3	20	,	,	PUNCT
ejpam-4379	3	21	p.o.box	p.o.box	PROPN
ejpam-4379	3	22	80203	80203	NUM
ejpam-4379	3	23	,	,	PUNCT
ejpam-4379	3	24	jeddah	jeddah	PROPN
ejpam-4379	3	25	21589	21589	NUM
ejpam-4379	3	26	,	,	PUNCT
ejpam-4379	3	27	saudi	saudi	PROPN
ejpam-4379	3	28	arabia	arabia	PROPN
ejpam-4379	3	29	.	.	PUNCT
ejpam-4379	4	1	abstract	abstract	ADJ
ejpam-4379	4	2	.	.	PUNCT
ejpam-4379	5	1	let	let	VERB
ejpam-4379	5	2	(	(	PUNCT
ejpam-4379	5	3	x	x	X
ejpam-4379	5	4	,	,	PUNCT
ejpam-4379	5	5	τ	τ	PROPN
ejpam-4379	5	6	)	)	PUNCT
ejpam-4379	5	7	be	be	AUX
ejpam-4379	5	8	a	a	DET
ejpam-4379	5	9	topological	topological	ADJ
ejpam-4379	5	10	space	space	NOUN
ejpam-4379	5	11	and	and	CCONJ
ejpam-4379	5	12	p	p	PROPN
ejpam-4379	5	13	̸∈	̸∈	PROPN
ejpam-4379	5	14	x.	x.	PROPN
ejpam-4379	5	15	put	put	VERB
ejpam-4379	5	16	xp	xp	NOUN
ejpam-4379	6	1	=	=	NOUN
ejpam-4379	6	2	x	x	SYM
ejpam-4379	6	3	∪	∪	ADP
ejpam-4379	6	4	{	{	PUNCT
ejpam-4379	6	5	p	p	NOUN
ejpam-4379	6	6	}	}	PUNCT
ejpam-4379	6	7	.	.	PUNCT
ejpam-4379	7	1	define	define	VERB
ejpam-4379	7	2	a	a	DET
ejpam-4379	7	3	topology	topology	NOUN
ejpam-4379	7	4	τ	τ	X
ejpam-4379	7	5	⋆	⋆	VERB
ejpam-4379	7	6	on	on	ADP
ejpam-4379	7	7	xp	xp	INTJ
ejpam-4379	7	8	by	by	ADP
ejpam-4379	7	9	τ	τ	PROPN
ejpam-4379	7	10	⋆	⋆	X
ejpam-4379	7	11	=	=	NOUN
ejpam-4379	7	12	{	{	PUNCT
ejpam-4379	7	13	∅	∅	NOUN
ejpam-4379	7	14	}	}	PUNCT
ejpam-4379	7	15	∪	∪	VERB
ejpam-4379	7	16	{	{	PUNCT
ejpam-4379	7	17	u	u	NOUN
ejpam-4379	7	18	∪	∪	NOUN
ejpam-4379	7	19	{	{	PUNCT
ejpam-4379	7	20	p	p	NOUN
ejpam-4379	7	21	}	}	PUNCT
ejpam-4379	7	22	:	:	PUNCT
ejpam-4379	7	23	u	u	PROPN
ejpam-4379	7	24	∈	∈	PROPN
ejpam-4379	7	25	τ	τ	X
ejpam-4379	7	26	}	}	PUNCT
ejpam-4379	7	27	.	.	PUNCT
ejpam-4379	8	1	the	the	DET
ejpam-4379	8	2	space	space	NOUN
ejpam-4379	8	3	(	(	PUNCT
ejpam-4379	8	4	xp	xp	INTJ
ejpam-4379	8	5	,	,	PUNCT
ejpam-4379	8	6	τ	τ	PROPN
ejpam-4379	8	7	⋆	⋆	VERB
ejpam-4379	8	8	)	)	PUNCT
ejpam-4379	8	9	is	be	AUX
ejpam-4379	8	10	called	call	VERB
ejpam-4379	8	11	the	the	DET
ejpam-4379	8	12	closed	closed	ADJ
ejpam-4379	8	13	extension	extension	NOUN
ejpam-4379	8	14	space	space	NOUN
ejpam-4379	8	15	of	of	ADP
ejpam-4379	8	16	(	(	PUNCT
ejpam-4379	8	17	x	x	INTJ
ejpam-4379	8	18	,	,	PUNCT
ejpam-4379	8	19	τ	τ	PROPN
ejpam-4379	8	20	)	)	PUNCT
ejpam-4379	8	21	.	.	PUNCT
ejpam-4379	9	1	we	we	PRON
ejpam-4379	9	2	present	present	VERB
ejpam-4379	9	3	new	new	ADJ
ejpam-4379	9	4	results	result	NOUN
ejpam-4379	9	5	about	about	ADP
ejpam-4379	9	6	the	the	DET
ejpam-4379	9	7	closed	close	VERB
ejpam-4379	9	8	extension	extension	NOUN
ejpam-4379	9	9	topological	topological	ADJ
ejpam-4379	9	10	spaces	space	NOUN
ejpam-4379	9	11	.	.	PUNCT
ejpam-4379	10	1	mainly	mainly	ADV
ejpam-4379	10	2	weaker	weak	ADJ
ejpam-4379	10	3	versions	version	NOUN
ejpam-4379	10	4	of	of	ADP
ejpam-4379	10	5	normality	normality	NOUN
ejpam-4379	10	6	.	.	PUNCT
ejpam-4379	11	1	2020	2020	NUM
ejpam-4379	11	2	mathematics	mathematic	NOUN
ejpam-4379	11	3	subject	subject	NOUN
ejpam-4379	11	4	classifications	classification	NOUN
ejpam-4379	11	5	:	:	PUNCT
ejpam-4379	11	6	54a10	54a10	NUM
ejpam-4379	11	7	,	,	PUNCT
ejpam-4379	11	8	54d35	54d35	NUM
ejpam-4379	11	9	,	,	PUNCT
ejpam-4379	11	10	54d15	54d15	NUM
ejpam-4379	11	11	key	key	ADJ
ejpam-4379	11	12	words	word	NOUN
ejpam-4379	11	13	and	and	CCONJ
ejpam-4379	11	14	phrases	phrase	NOUN
ejpam-4379	11	15	:	:	PUNCT
ejpam-4379	11	16	closed	closed	ADJ
ejpam-4379	11	17	extension	extension	NOUN
ejpam-4379	11	18	,	,	PUNCT
ejpam-4379	11	19	c	c	NOUN
ejpam-4379	11	20	-	-	NOUN
ejpam-4379	11	21	normality	normality	ADJ
ejpam-4379	11	22	,	,	PUNCT
ejpam-4379	11	23	l	l	NOUN
ejpam-4379	11	24	-	-	NOUN
ejpam-4379	11	25	normality	normality	ADJ
ejpam-4379	11	26	,	,	PUNCT
ejpam-4379	11	27	cc	cc	NOUN
ejpam-4379	11	28	-	-	NOUN
ejpam-4379	11	29	normality	normality	ADJ
ejpam-4379	11	30	,	,	PUNCT
ejpam-4379	11	31	s	s	NOUN
ejpam-4379	11	32	-	-	NOUN
ejpam-4379	11	33	normality	normality	NOUN
ejpam-4379	11	34	,	,	PUNCT
ejpam-4379	11	35	p	p	NOUN
ejpam-4379	11	36	-normality	-normality	NOUN
ejpam-4379	11	37	,	,	PUNCT
ejpam-4379	11	38	normality	normality	NOUN
ejpam-4379	11	39	,	,	PUNCT
ejpam-4379	11	40	mild	mild	ADJ
ejpam-4379	11	41	normality	normality	NOUN
ejpam-4379	11	42	,	,	PUNCT
ejpam-4379	11	43	almost	almost	ADV
ejpam-4379	11	44	normality	normality	NOUN
ejpam-4379	11	45	,	,	PUNCT
ejpam-4379	11	46	π	π	PROPN
ejpam-4379	11	47	-	-	NOUN
ejpam-4379	11	48	normality	normality	ADJ
ejpam-4379	11	49	,	,	PUNCT
ejpam-4379	11	50	quasi	quasi	ADJ
ejpam-4379	11	51	-	-	NOUN
ejpam-4379	11	52	normality	normality	ADJ
ejpam-4379	11	53	,	,	PUNCT
ejpam-4379	11	54	partial	partial	ADJ
ejpam-4379	11	55	normality	normality	NOUN
ejpam-4379	11	56	.	.	PUNCT
ejpam-4379	12	1	we	we	PRON
ejpam-4379	12	2	present	present	VERB
ejpam-4379	12	3	new	new	ADJ
ejpam-4379	12	4	results	result	NOUN
ejpam-4379	12	5	about	about	ADP
ejpam-4379	12	6	the	the	DET
ejpam-4379	12	7	closed	close	VERB
ejpam-4379	12	8	extension	extension	NOUN
ejpam-4379	12	9	topological	topological	ADJ
ejpam-4379	12	10	spaces	space	NOUN
ejpam-4379	12	11	.	.	PUNCT
ejpam-4379	13	1	most	most	ADJ
ejpam-4379	13	2	of	of	ADP
ejpam-4379	13	3	the	the	DET
ejpam-4379	13	4	results	result	NOUN
ejpam-4379	13	5	are	be	AUX
ejpam-4379	13	6	about	about	ADP
ejpam-4379	13	7	properties	property	NOUN
ejpam-4379	13	8	weaker	weak	ADJ
ejpam-4379	13	9	than	than	ADP
ejpam-4379	13	10	normality	normality	NOUN
ejpam-4379	13	11	.	.	PUNCT
ejpam-4379	14	1	some	some	DET
ejpam-4379	14	2	benefits	benefit	NOUN
ejpam-4379	14	3	of	of	ADP
ejpam-4379	14	4	the	the	DET
ejpam-4379	14	5	closed	closed	ADJ
ejpam-4379	14	6	extension	extension	NOUN
ejpam-4379	14	7	spaces	space	NOUN
ejpam-4379	14	8	are	be	AUX
ejpam-4379	14	9	they	they	PRON
ejpam-4379	14	10	work	work	VERB
ejpam-4379	14	11	as	as	ADP
ejpam-4379	14	12	counterexamples	counterexample	NOUN
ejpam-4379	14	13	.	.	PUNCT
ejpam-4379	15	1	throughout	throughout	ADP
ejpam-4379	15	2	this	this	DET
ejpam-4379	15	3	paper	paper	NOUN
ejpam-4379	15	4	,	,	PUNCT
ejpam-4379	15	5	we	we	PRON
ejpam-4379	15	6	denote	denote	VERB
ejpam-4379	15	7	the	the	DET
ejpam-4379	15	8	set	set	NOUN
ejpam-4379	15	9	of	of	ADP
ejpam-4379	15	10	positive	positive	ADJ
ejpam-4379	15	11	integers	integer	NOUN
ejpam-4379	15	12	by	by	ADP
ejpam-4379	15	13	n	n	CCONJ
ejpam-4379	15	14	,	,	PUNCT
ejpam-4379	15	15	the	the	DET
ejpam-4379	15	16	rationals	rational	NOUN
ejpam-4379	15	17	by	by	ADP
ejpam-4379	15	18	q	q	NOUN
ejpam-4379	15	19	,	,	PUNCT
ejpam-4379	15	20	the	the	DET
ejpam-4379	15	21	irrationals	irrational	NOUN
ejpam-4379	15	22	by	by	ADP
ejpam-4379	15	23	p	p	NOUN
ejpam-4379	15	24	,	,	PUNCT
ejpam-4379	15	25	and	and	CCONJ
ejpam-4379	15	26	the	the	DET
ejpam-4379	15	27	set	set	NOUN
ejpam-4379	15	28	of	of	ADP
ejpam-4379	15	29	real	real	ADJ
ejpam-4379	15	30	numbers	number	NOUN
ejpam-4379	15	31	by	by	ADP
ejpam-4379	15	32	r.	r.	PROPN
ejpam-4379	15	33	a	a	DET
ejpam-4379	15	34	t4	t4	PROPN
ejpam-4379	15	35	space	space	NOUN
ejpam-4379	15	36	is	be	AUX
ejpam-4379	15	37	a	a	DET
ejpam-4379	15	38	t1	t1	NOUN
ejpam-4379	15	39	normal	normal	ADJ
ejpam-4379	15	40	space	space	NOUN
ejpam-4379	15	41	and	and	CCONJ
ejpam-4379	15	42	a	a	DET
ejpam-4379	15	43	tychonoff	tychonoff	NOUN
ejpam-4379	15	44	space	space	NOUN
ejpam-4379	15	45	(	(	PUNCT
ejpam-4379	15	46	t3	t3	NOUN
ejpam-4379	15	47	1	1	NUM
ejpam-4379	15	48	2	2	NUM
ejpam-4379	15	49	)	)	PUNCT
ejpam-4379	15	50	is	be	AUX
ejpam-4379	15	51	a	a	DET
ejpam-4379	15	52	t1	t1	NOUN
ejpam-4379	15	53	completely	completely	ADV
ejpam-4379	15	54	regular	regular	ADJ
ejpam-4379	15	55	space	space	NOUN
ejpam-4379	15	56	.	.	PUNCT
ejpam-4379	16	1	we	we	PRON
ejpam-4379	16	2	do	do	AUX
ejpam-4379	16	3	not	not	PART
ejpam-4379	16	4	assume	assume	VERB
ejpam-4379	16	5	t2	t2	NOUN
ejpam-4379	16	6	in	in	ADP
ejpam-4379	16	7	the	the	DET
ejpam-4379	16	8	definition	definition	NOUN
ejpam-4379	16	9	of	of	ADP
ejpam-4379	16	10	compactness	compactness	NOUN
ejpam-4379	16	11	and	and	CCONJ
ejpam-4379	16	12	countable	countable	ADJ
ejpam-4379	16	13	compactness	compactness	NOUN
ejpam-4379	16	14	.	.	PUNCT
ejpam-4379	17	1	we	we	PRON
ejpam-4379	17	2	do	do	AUX
ejpam-4379	17	3	not	not	PART
ejpam-4379	17	4	assume	assume	VERB
ejpam-4379	17	5	regularity	regularity	NOUN
ejpam-4379	17	6	in	in	ADP
ejpam-4379	17	7	the	the	DET
ejpam-4379	17	8	definition	definition	NOUN
ejpam-4379	17	9	of	of	ADP
ejpam-4379	17	10	lindelöfness	lindelöfness	PROPN
ejpam-4379	17	11	.	.	PUNCT
ejpam-4379	18	1	for	for	ADP
ejpam-4379	18	2	a	a	DET
ejpam-4379	18	3	subset	subset	NOUN
ejpam-4379	18	4	a	a	PRON
ejpam-4379	18	5	of	of	ADP
ejpam-4379	18	6	a	a	DET
ejpam-4379	18	7	space	space	NOUN
ejpam-4379	18	8	x	x	NOUN
ejpam-4379	18	9	,	,	PUNCT
ejpam-4379	18	10	inta	inta	PROPN
ejpam-4379	18	11	and	and	CCONJ
ejpam-4379	18	12	a	a	DET
ejpam-4379	18	13	denote	denote	NOUN
ejpam-4379	18	14	the	the	DET
ejpam-4379	18	15	interior	interior	NOUN
ejpam-4379	18	16	and	and	CCONJ
ejpam-4379	18	17	the	the	DET
ejpam-4379	18	18	closure	closure	NOUN
ejpam-4379	18	19	of	of	ADP
ejpam-4379	18	20	a	a	PRON
ejpam-4379	18	21	,	,	PUNCT
ejpam-4379	18	22	respectively	respectively	ADV
ejpam-4379	18	23	.	.	PUNCT
ejpam-4379	19	1	if	if	SCONJ
ejpam-4379	19	2	two	two	NUM
ejpam-4379	19	3	topologies	topology	NOUN
ejpam-4379	19	4	τ	τ	X
ejpam-4379	19	5	and	and	CCONJ
ejpam-4379	19	6	τ	τ	PROPN
ejpam-4379	19	7	′	′	NOUN
ejpam-4379	19	8	on	on	ADP
ejpam-4379	19	9	a	a	DET
ejpam-4379	19	10	set	set	NOUN
ejpam-4379	19	11	x	x	SYM
ejpam-4379	19	12	are	be	AUX
ejpam-4379	19	13	considered	consider	VERB
ejpam-4379	19	14	,	,	PUNCT
ejpam-4379	19	15	we	we	PRON
ejpam-4379	19	16	denote	denote	VERB
ejpam-4379	19	17	the	the	DET
ejpam-4379	19	18	interior	interior	NOUN
ejpam-4379	19	19	of	of	ADP
ejpam-4379	19	20	a	a	DET
ejpam-4379	19	21	in	in	ADP
ejpam-4379	19	22	(	(	PUNCT
ejpam-4379	19	23	x	x	INTJ
ejpam-4379	19	24	,	,	PUNCT
ejpam-4379	19	25	τ	τ	PROPN
ejpam-4379	19	26	)	)	PUNCT
ejpam-4379	19	27	by	by	ADP
ejpam-4379	19	28	int	int	NOUN
ejpam-4379	19	29	τa	τa	ADJ
ejpam-4379	19	30	and	and	CCONJ
ejpam-4379	19	31	int	int	NOUN
ejpam-4379	19	32	τ	τ	X
ejpam-4379	19	33	′a	′a	NOUN
ejpam-4379	19	34	for	for	ADP
ejpam-4379	19	35	the	the	DET
ejpam-4379	19	36	interior	interior	NOUN
ejpam-4379	19	37	of	of	ADP
ejpam-4379	19	38	a	a	DET
ejpam-4379	19	39	in	in	ADP
ejpam-4379	19	40	(	(	PUNCT
ejpam-4379	19	41	x	x	INTJ
ejpam-4379	19	42	,	,	PUNCT
ejpam-4379	19	43	τ	τ	PROPN
ejpam-4379	19	44	′	′	NUM
ejpam-4379	19	45	)	)	PUNCT
ejpam-4379	19	46	.	.	PUNCT
ejpam-4379	20	1	we	we	PRON
ejpam-4379	20	2	denote	denote	VERB
ejpam-4379	20	3	the	the	DET
ejpam-4379	20	4	closure	closure	NOUN
ejpam-4379	20	5	of	of	ADP
ejpam-4379	20	6	a	a	DET
ejpam-4379	20	7	in	in	ADP
ejpam-4379	20	8	(	(	PUNCT
ejpam-4379	20	9	x	x	INTJ
ejpam-4379	20	10	,	,	PUNCT
ejpam-4379	20	11	τ	τ	PROPN
ejpam-4379	20	12	′	′	NUM
ejpam-4379	20	13	)	)	PUNCT
ejpam-4379	20	14	by	by	ADP
ejpam-4379	20	15	a	a	DET
ejpam-4379	20	16	τ	τ	NOUN
ejpam-4379	20	17	′	′	NUM
ejpam-4379	21	1	and	and	CCONJ
ejpam-4379	21	2	,	,	PUNCT
ejpam-4379	21	3	similarly	similarly	ADV
ejpam-4379	21	4	,	,	PUNCT
ejpam-4379	21	5	a	a	DET
ejpam-4379	21	6	τ	τ	PROPN
ejpam-4379	21	7	denotes	denote	VERB
ejpam-4379	21	8	the	the	DET
ejpam-4379	21	9	closure	closure	NOUN
ejpam-4379	21	10	of	of	ADP
ejpam-4379	21	11	a	a	DET
ejpam-4379	21	12	in	in	ADP
ejpam-4379	21	13	(	(	PUNCT
ejpam-4379	21	14	x	x	INTJ
ejpam-4379	21	15	,	,	PUNCT
ejpam-4379	21	16	τ	τ	PROPN
ejpam-4379	21	17	)	)	PUNCT
ejpam-4379	21	18	.	.	PUNCT
ejpam-4379	22	1	1	1	X
ejpam-4379	22	2	.	.	X
ejpam-4379	22	3	basic	basic	ADJ
ejpam-4379	22	4	definitions	definition	NOUN
ejpam-4379	22	5	and	and	CCONJ
ejpam-4379	22	6	properties	property	NOUN
ejpam-4379	22	7	.	.	PUNCT
ejpam-4379	23	1	definition	definition	NOUN
ejpam-4379	23	2	1	1	NUM
ejpam-4379	23	3	.	.	PUNCT
ejpam-4379	24	1	let	let	AUX
ejpam-4379	24	2	(	(	PUNCT
ejpam-4379	24	3	x	x	X
ejpam-4379	24	4	,	,	PUNCT
ejpam-4379	24	5	τ	τ	PROPN
ejpam-4379	24	6	)	)	PUNCT
ejpam-4379	24	7	be	be	AUX
ejpam-4379	24	8	a	a	DET
ejpam-4379	24	9	topological	topological	ADJ
ejpam-4379	24	10	space	space	NOUN
ejpam-4379	24	11	and	and	CCONJ
ejpam-4379	24	12	let	let	VERB
ejpam-4379	24	13	p	p	PRON
ejpam-4379	24	14	be	be	AUX
ejpam-4379	24	15	an	an	DET
ejpam-4379	24	16	object	object	NOUN
ejpam-4379	24	17	not	not	PART
ejpam-4379	24	18	in	in	ADP
ejpam-4379	24	19	x	x	NOUN
ejpam-4379	24	20	,	,	PUNCT
ejpam-4379	24	21	i.e.	i.e.	X
ejpam-4379	24	22	,	,	PUNCT
ejpam-4379	24	23	p	p	PROPN
ejpam-4379	24	24	̸∈	̸∈	PROPN
ejpam-4379	24	25	x.	x.	PROPN
ejpam-4379	24	26	put	put	VERB
ejpam-4379	24	27	xp	xp	NOUN
ejpam-4379	25	1	=	=	NOUN
ejpam-4379	25	2	x	x	SYM
ejpam-4379	25	3	∪	∪	X
ejpam-4379	25	4	{	{	PUNCT
ejpam-4379	25	5	p	p	NOUN
ejpam-4379	25	6	}	}	PUNCT
ejpam-4379	25	7	.	.	PUNCT
ejpam-4379	26	1	define	define	VERB
ejpam-4379	26	2	a	a	DET
ejpam-4379	26	3	topology	topology	NOUN
ejpam-4379	26	4	τ	τ	X
ejpam-4379	26	5	⋆	⋆	VERB
ejpam-4379	26	6	on	on	ADP
ejpam-4379	26	7	xp	xp	INTJ
ejpam-4379	26	8	by	by	ADP
ejpam-4379	26	9	τ	τ	PROPN
ejpam-4379	26	10	⋆	⋆	X
ejpam-4379	26	11	=	=	NOUN
ejpam-4379	26	12	{	{	PUNCT
ejpam-4379	26	13	∅	∅	NOUN
ejpam-4379	26	14	}	}	PUNCT
ejpam-4379	26	15	∪	∪	VERB
ejpam-4379	26	16	{	{	PUNCT
ejpam-4379	26	17	u	u	NOUN
ejpam-4379	26	18	∪	∪	NOUN
ejpam-4379	26	19	{	{	PUNCT
ejpam-4379	26	20	p	p	NOUN
ejpam-4379	26	21	}	}	PUNCT
ejpam-4379	26	22	:	:	PUNCT
ejpam-4379	26	23	u	u	PROPN
ejpam-4379	26	24	∈	∈	PROPN
ejpam-4379	26	25	τ	τ	X
ejpam-4379	26	26	}	}	PUNCT
ejpam-4379	26	27	.	.	PUNCT
ejpam-4379	27	1	the	the	DET
ejpam-4379	27	2	space	space	NOUN
ejpam-4379	27	3	(	(	PUNCT
ejpam-4379	27	4	xp	xp	INTJ
ejpam-4379	27	5	,	,	PUNCT
ejpam-4379	27	6	τ	τ	PROPN
ejpam-4379	27	7	⋆	⋆	VERB
ejpam-4379	27	8	)	)	PUNCT
ejpam-4379	27	9	is	be	AUX
ejpam-4379	27	10	called	call	VERB
ejpam-4379	27	11	the	the	DET
ejpam-4379	27	12	closed	closed	ADJ
ejpam-4379	27	13	extension	extension	NOUN
ejpam-4379	27	14	space	space	NOUN
ejpam-4379	27	15	of	of	ADP
ejpam-4379	27	16	(	(	PUNCT
ejpam-4379	27	17	x	x	INTJ
ejpam-4379	27	18	,	,	PUNCT
ejpam-4379	27	19	τ	τ	PROPN
ejpam-4379	27	20	)	)	PUNCT
ejpam-4379	27	21	,	,	PUNCT
ejpam-4379	27	22	[	[	X
ejpam-4379	27	23	15	15	NUM
ejpam-4379	27	24	,	,	PUNCT
ejpam-4379	27	25	example	example	NOUN
ejpam-4379	27	26	12	12	NUM
ejpam-4379	27	27	]	]	PUNCT
ejpam-4379	27	28	.	.	PUNCT
ejpam-4379	28	1	∗corresponding	∗corresponde	VERB
ejpam-4379	28	2	author	author	NOUN
ejpam-4379	28	3	.	.	PUNCT
ejpam-4379	29	1	doi	doi	NOUN
ejpam-4379	29	2	:	:	PUNCT
ejpam-4379	29	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4379	https://doi.org/10.29020/nybg.ejpam.v15i2.4379	PROPN
ejpam-4379	29	4	email	email	NOUN
ejpam-4379	29	5	addresses	address	NOUN
ejpam-4379	29	6	:	:	PUNCT
ejpam-4379	29	7	dabuzaid@kau.edu.sa	dabuzaid@kau.edu.sa	NOUN
ejpam-4379	29	8	,	,	PUNCT
ejpam-4379	29	9	dina.abuzaid@gmail.com	dina.abuzaid@gmail.com	X
ejpam-4379	29	10	(	(	PUNCT
ejpam-4379	29	11	d.	d.	PROPN
ejpam-4379	29	12	abuzaid	abuzaid	PROPN
ejpam-4379	29	13	)	)	PUNCT
ejpam-4379	29	14	,	,	PUNCT
ejpam-4379	29	15	sabdullahalqarhi@stu.kau.edu.sa	sabdullahalqarhi@stu.kau.edu.sa	PROPN
ejpam-4379	29	16	and	and	CCONJ
ejpam-4379	29	17	saaadah90@gmail.com	saaadah90@gmail.com	PROPN
ejpam-4379	29	18	(	(	PUNCT
ejpam-4379	29	19	s.	s.	PROPN
ejpam-4379	29	20	al	al	PROPN
ejpam-4379	29	21	-	-	PROPN
ejpam-4379	29	22	qarhi	qarhi	NOUN
ejpam-4379	29	23	)	)	PUNCT
ejpam-4379	29	24	,	,	PUNCT
ejpam-4379	29	25	lnkalantan@hotmail.com	lnkalantan@hotmail.com	PROPN
ejpam-4379	29	26	,	,	PUNCT
ejpam-4379	29	27	lkalantan@kau.edu.sa	lkalantan@kau.edu.sa	PROPN
ejpam-4379	29	28	(	(	PUNCT
ejpam-4379	29	29	l.	l.	PROPN
ejpam-4379	29	30	kalantan	kalantan	PROPN
ejpam-4379	29	31	)	)	PUNCT
ejpam-4379	29	32	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4379	30	1	672	672	NUM
ejpam-4379	30	2	©	©	ADP
ejpam-4379	30	3	2022	2022	NUM
ejpam-4379	30	4	ejpam	ejpam	VERB
ejpam-4379	30	5	all	all	DET
ejpam-4379	30	6	rights	right	NOUN
ejpam-4379	30	7	reserved	reserve	VERB
ejpam-4379	30	8	.	.	PUNCT
ejpam-4379	31	1	d.	d.	PROPN
ejpam-4379	31	2	abuzaid	abuzaid	PROPN
ejpam-4379	31	3	,	,	PUNCT
ejpam-4379	31	4	s.	s.	PROPN
ejpam-4379	31	5	al	al	PROPN
ejpam-4379	31	6	-	-	PROPN
ejpam-4379	31	7	qarhi	qarhi	PROPN
ejpam-4379	31	8	,	,	PUNCT
ejpam-4379	31	9	l.	l.	PROPN
ejpam-4379	31	10	kalantan	kalantan	PROPN
ejpam-4379	31	11	/	/	SYM
ejpam-4379	31	12	eur	eur	PROPN
ejpam-4379	31	13	.	.	PUNCT
ejpam-4379	32	1	j.	j.	PROPN
ejpam-4379	32	2	pure	pure	PROPN
ejpam-4379	32	3	appl	appl	PROPN
ejpam-4379	32	4	.	.	PROPN
ejpam-4379	32	5	math	math	PROPN
ejpam-4379	32	6	,	,	PUNCT
ejpam-4379	32	7	15	15	NUM
ejpam-4379	32	8	(	(	PUNCT
ejpam-4379	32	9	2	2	NUM
ejpam-4379	32	10	)	)	PUNCT
ejpam-4379	32	11	(	(	PUNCT
ejpam-4379	32	12	2022	2022	NUM
ejpam-4379	32	13	)	)	PUNCT
ejpam-4379	32	14	,	,	PUNCT
ejpam-4379	32	15	672	672	NUM
ejpam-4379	32	16	-	-	SYM
ejpam-4379	32	17	680	680	NUM
ejpam-4379	32	18	673	673	NUM
ejpam-4379	32	19	consider	consider	VERB
ejpam-4379	32	20	the	the	DET
ejpam-4379	32	21	particular	particular	ADJ
ejpam-4379	32	22	point	point	NOUN
ejpam-4379	32	23	topology	topology	NOUN
ejpam-4379	32	24	τ	τ	X
ejpam-4379	32	25	p	p	NOUN
ejpam-4379	32	26	on	on	ADP
ejpam-4379	32	27	xp,[15	xp,[15	NOUN
ejpam-4379	32	28	,	,	PUNCT
ejpam-4379	32	29	example	example	NOUN
ejpam-4379	32	30	9	9	NUM
ejpam-4379	32	31	]	]	PUNCT
ejpam-4379	32	32	.	.	PUNCT
ejpam-4379	33	1	so	so	ADV
ejpam-4379	33	2	,	,	PUNCT
ejpam-4379	33	3	τ	τ	PROPN
ejpam-4379	33	4	p	p	NOUN
ejpam-4379	33	5	=	=	X
ejpam-4379	33	6	{	{	PUNCT
ejpam-4379	33	7	∅	∅	NOUN
ejpam-4379	33	8	}	}	PUNCT
ejpam-4379	33	9	∪	∪	X
ejpam-4379	33	10	{	{	PUNCT
ejpam-4379	33	11	w	w	PROPN
ejpam-4379	33	12	⊆	⊆	NUM
ejpam-4379	33	13	xp	xp	NOUN
ejpam-4379	33	14	:	:	PUNCT
ejpam-4379	33	15	p	p	X
ejpam-4379	33	16	∈	∈	PROPN
ejpam-4379	33	17	w	w	X
ejpam-4379	33	18	}	}	PUNCT
ejpam-4379	33	19	.	.	PUNCT
ejpam-4379	34	1	since	since	SCONJ
ejpam-4379	34	2	any	any	DET
ejpam-4379	34	3	non	non	ADJ
ejpam-4379	34	4	-	-	ADJ
ejpam-4379	34	5	empty	empty	ADJ
ejpam-4379	34	6	open	open	ADJ
ejpam-4379	34	7	set	set	NOUN
ejpam-4379	34	8	in	in	ADP
ejpam-4379	34	9	the	the	DET
ejpam-4379	34	10	closed	closed	ADJ
ejpam-4379	34	11	extension	extension	NOUN
ejpam-4379	34	12	contains	contain	VERB
ejpam-4379	34	13	p	p	PRON
ejpam-4379	34	14	,	,	PUNCT
ejpam-4379	34	15	then	then	ADV
ejpam-4379	34	16	the	the	DET
ejpam-4379	34	17	closed	closed	ADJ
ejpam-4379	34	18	extension	extension	NOUN
ejpam-4379	34	19	topology	topology	NOUN
ejpam-4379	34	20	τ	τ	X
ejpam-4379	34	21	⋆	⋆	VERB
ejpam-4379	34	22	on	on	ADP
ejpam-4379	34	23	xp	xp	INTJ
ejpam-4379	34	24	is	be	AUX
ejpam-4379	34	25	coarser	coarse	ADJ
ejpam-4379	34	26	than	than	ADP
ejpam-4379	34	27	the	the	DET
ejpam-4379	34	28	particular	particular	ADJ
ejpam-4379	34	29	point	point	NOUN
ejpam-4379	34	30	topology	topology	NOUN
ejpam-4379	34	31	τ	τ	X
ejpam-4379	34	32	p	p	NOUN
ejpam-4379	34	33	on	on	ADP
ejpam-4379	34	34	xp	xp	INTJ
ejpam-4379	34	35	.	.	PUNCT
ejpam-4379	35	1	if	if	SCONJ
ejpam-4379	35	2	we	we	PRON
ejpam-4379	35	3	start	start	VERB
ejpam-4379	35	4	with	with	ADP
ejpam-4379	35	5	the	the	DET
ejpam-4379	35	6	discrete	discrete	ADJ
ejpam-4379	35	7	topology	topology	NOUN
ejpam-4379	35	8	on	on	ADP
ejpam-4379	35	9	x	x	NOUN
ejpam-4379	35	10	,	,	PUNCT
ejpam-4379	35	11	then	then	ADV
ejpam-4379	35	12	the	the	DET
ejpam-4379	35	13	closed	closed	ADJ
ejpam-4379	35	14	extension	extension	NOUN
ejpam-4379	35	15	topology	topology	NOUN
ejpam-4379	35	16	τ	τ	X
ejpam-4379	35	17	⋆	⋆	VERB
ejpam-4379	35	18	on	on	ADP
ejpam-4379	35	19	xp	xp	INTJ
ejpam-4379	35	20	and	and	CCONJ
ejpam-4379	35	21	the	the	DET
ejpam-4379	35	22	particular	particular	ADJ
ejpam-4379	35	23	point	point	NOUN
ejpam-4379	35	24	topology	topology	NOUN
ejpam-4379	35	25	τ	τ	PROPN
ejpam-4379	35	26	p	p	NOUN
ejpam-4379	35	27	on	on	ADP
ejpam-4379	35	28	xp	xp	INTJ
ejpam-4379	35	29	will	will	AUX
ejpam-4379	35	30	be	be	AUX
ejpam-4379	35	31	equal	equal	ADJ
ejpam-4379	35	32	.	.	PUNCT
ejpam-4379	36	1	thus	thus	ADV
ejpam-4379	36	2	,	,	PUNCT
ejpam-4379	36	3	from	from	ADP
ejpam-4379	36	4	now	now	ADV
ejpam-4379	36	5	on	on	ADV
ejpam-4379	36	6	,	,	PUNCT
ejpam-4379	36	7	when	when	SCONJ
ejpam-4379	36	8	we	we	PRON
ejpam-4379	36	9	consider	consider	VERB
ejpam-4379	36	10	the	the	DET
ejpam-4379	36	11	closed	closed	ADJ
ejpam-4379	36	12	extension	extension	NOUN
ejpam-4379	36	13	space	space	NOUN
ejpam-4379	36	14	(	(	PUNCT
ejpam-4379	36	15	xp	xp	INTJ
ejpam-4379	36	16	,	,	PUNCT
ejpam-4379	36	17	τ	τ	PROPN
ejpam-4379	36	18	⋆	⋆	NOUN
ejpam-4379	36	19	)	)	PUNCT
ejpam-4379	36	20	of	of	ADP
ejpam-4379	36	21	a	a	DET
ejpam-4379	36	22	given	give	VERB
ejpam-4379	36	23	topological	topological	ADJ
ejpam-4379	36	24	space	space	NOUN
ejpam-4379	36	25	(	(	PUNCT
ejpam-4379	36	26	x	x	X
ejpam-4379	36	27	,	,	PUNCT
ejpam-4379	36	28	τ	τ	PROPN
ejpam-4379	36	29	)	)	PUNCT
ejpam-4379	36	30	,	,	PUNCT
ejpam-4379	36	31	x	x	PRON
ejpam-4379	36	32	is	be	AUX
ejpam-4379	36	33	assumed	assume	VERB
ejpam-4379	36	34	to	to	PART
ejpam-4379	36	35	have	have	VERB
ejpam-4379	36	36	more	more	ADJ
ejpam-4379	36	37	than	than	ADP
ejpam-4379	36	38	one	one	NUM
ejpam-4379	36	39	element	element	NOUN
ejpam-4379	36	40	and	and	CCONJ
ejpam-4379	36	41	the	the	DET
ejpam-4379	36	42	topology	topology	NOUN
ejpam-4379	36	43	τ	τ	PROPN
ejpam-4379	36	44	on	on	ADP
ejpam-4379	36	45	x	x	SYM
ejpam-4379	36	46	is	be	AUX
ejpam-4379	36	47	not	not	PART
ejpam-4379	36	48	the	the	DET
ejpam-4379	36	49	discrete	discrete	ADJ
ejpam-4379	36	50	topology	topology	NOUN
ejpam-4379	36	51	.	.	PUNCT
ejpam-4379	37	1	so	so	ADV
ejpam-4379	37	2	,	,	PUNCT
ejpam-4379	37	3	in	in	ADP
ejpam-4379	37	4	our	our	PRON
ejpam-4379	37	5	study	study	NOUN
ejpam-4379	37	6	we	we	PRON
ejpam-4379	37	7	have	have	VERB
ejpam-4379	37	8	|x|	|x|	PROPN
ejpam-4379	37	9	≥	≥	NUM
ejpam-4379	37	10	2	2	NUM
ejpam-4379	37	11	and	and	CCONJ
ejpam-4379	37	12	hence	hence	ADV
ejpam-4379	37	13	|xp|	|xp|	PROPN
ejpam-4379	37	14	≥	≥	NOUN
ejpam-4379	37	15	3	3	NUM
ejpam-4379	37	16	.	.	PUNCT
ejpam-4379	38	1	it	it	PRON
ejpam-4379	38	2	is	be	AUX
ejpam-4379	38	3	clear	clear	ADJ
ejpam-4379	38	4	that	that	SCONJ
ejpam-4379	38	5	the	the	DET
ejpam-4379	38	6	sub	sub	NOUN
ejpam-4379	38	7	-	-	NOUN
ejpam-4379	38	8	topology	topology	NOUN
ejpam-4379	38	9	on	on	ADP
ejpam-4379	38	10	x	x	PUNCT
ejpam-4379	38	11	inherited	inherit	VERB
ejpam-4379	38	12	from	from	ADP
ejpam-4379	38	13	τ	τ	PROPN
ejpam-4379	38	14	⋆	⋆	NOUN
ejpam-4379	38	15	equals	equal	VERB
ejpam-4379	38	16	the	the	DET
ejpam-4379	38	17	original	original	ADJ
ejpam-4379	38	18	topology	topology	NOUN
ejpam-4379	38	19	on	on	ADP
ejpam-4379	38	20	x	x	NOUN
ejpam-4379	38	21	,	,	PUNCT
ejpam-4379	38	22	i.e.	i.e.	X
ejpam-4379	38	23	,	,	PUNCT
ejpam-4379	38	24	τ	τ	X
ejpam-4379	38	25	⋆	⋆	NOUN
ejpam-4379	38	26	x	x	X
ejpam-4379	38	27	=	=	SYM
ejpam-4379	38	28	τ	τ	PROPN
ejpam-4379	38	29	.	.	PUNCT
ejpam-4379	39	1	note	note	VERB
ejpam-4379	39	2	that	that	SCONJ
ejpam-4379	39	3	{	{	PUNCT
ejpam-4379	39	4	p	p	NOUN
ejpam-4379	39	5	}	}	PUNCT
ejpam-4379	39	6	is	be	AUX
ejpam-4379	39	7	open	open	ADJ
ejpam-4379	39	8	in	in	ADP
ejpam-4379	39	9	the	the	DET
ejpam-4379	39	10	closed	closed	ADJ
ejpam-4379	39	11	extension	extension	NOUN
ejpam-4379	39	12	space	space	NOUN
ejpam-4379	39	13	,	,	PUNCT
ejpam-4379	39	14	i.e.	i.e.	X
ejpam-4379	39	15	,	,	PUNCT
ejpam-4379	39	16	{	{	PUNCT
ejpam-4379	39	17	p	p	X
ejpam-4379	39	18	}	}	PUNCT
ejpam-4379	39	19	∈	∈	PROPN
ejpam-4379	39	20	τ	τ	X
ejpam-4379	39	21	⋆	⋆	VERB
ejpam-4379	39	22	because	because	SCONJ
ejpam-4379	39	23	{	{	PUNCT
ejpam-4379	39	24	p	p	X
ejpam-4379	39	25	}	}	PUNCT
ejpam-4379	39	26	=	=	NOUN
ejpam-4379	39	27	∅	∅	NOUN
ejpam-4379	39	28	∪	∪	X
ejpam-4379	39	29	{	{	PUNCT
ejpam-4379	39	30	p	p	NOUN
ejpam-4379	39	31	}	}	PUNCT
ejpam-4379	39	32	,	,	PUNCT
ejpam-4379	39	33	thus	thus	ADV
ejpam-4379	39	34	x	x	PRON
ejpam-4379	39	35	is	be	AUX
ejpam-4379	39	36	closed	close	VERB
ejpam-4379	39	37	in	in	ADP
ejpam-4379	39	38	its	its	PRON
ejpam-4379	39	39	closed	closed	ADJ
ejpam-4379	39	40	extension	extension	NOUN
ejpam-4379	39	41	(	(	PUNCT
ejpam-4379	39	42	xp	xp	INTJ
ejpam-4379	39	43	,	,	PUNCT
ejpam-4379	39	44	τ	τ	PROPN
ejpam-4379	39	45	⋆	⋆	NOUN
ejpam-4379	39	46	)	)	PUNCT
ejpam-4379	39	47	.	.	PUNCT
ejpam-4379	40	1	observe	observe	VERB
ejpam-4379	40	2	that	that	SCONJ
ejpam-4379	40	3	a	a	DET
ejpam-4379	40	4	closed	closed	ADJ
ejpam-4379	40	5	set	set	NOUN
ejpam-4379	40	6	in	in	ADP
ejpam-4379	40	7	(	(	PUNCT
ejpam-4379	40	8	xp	xp	INTJ
ejpam-4379	40	9	,	,	PUNCT
ejpam-4379	40	10	τ	τ	PROPN
ejpam-4379	40	11	⋆	⋆	VERB
ejpam-4379	40	12	)	)	PUNCT
ejpam-4379	40	13	is	be	AUX
ejpam-4379	40	14	of	of	ADP
ejpam-4379	40	15	the	the	DET
ejpam-4379	40	16	form	form	NOUN
ejpam-4379	40	17	xp	xp	INTJ
ejpam-4379	40	18	\g	\g	ADJ
ejpam-4379	40	19	where	where	SCONJ
ejpam-4379	40	20	g	g	PROPN
ejpam-4379	40	21	∈	∈	PROPN
ejpam-4379	40	22	τ	τ	X
ejpam-4379	40	23	⋆.	⋆.	X
ejpam-4379	40	24	so	so	ADV
ejpam-4379	40	25	,	,	PUNCT
ejpam-4379	40	26	xp	xp	ADV
ejpam-4379	40	27	\g	\g	PUNCT
ejpam-4379	41	1	=	=	SYM
ejpam-4379	41	2	xp	xp	ADJ
ejpam-4379	41	3	\	\	PROPN
ejpam-4379	41	4	(	(	PUNCT
ejpam-4379	41	5	u	u	NOUN
ejpam-4379	41	6	∪	∪	VERB
ejpam-4379	41	7	{	{	PUNCT
ejpam-4379	41	8	p	p	NOUN
ejpam-4379	41	9	}	}	PUNCT
ejpam-4379	41	10	)	)	PUNCT
ejpam-4379	42	1	where	where	SCONJ
ejpam-4379	42	2	u	u	PROPN
ejpam-4379	42	3	∈	∈	PROPN
ejpam-4379	42	4	τ	τ	X
ejpam-4379	42	5	.	.	PUNCT
ejpam-4379	43	1	since	since	SCONJ
ejpam-4379	43	2	p	p	PROPN
ejpam-4379	43	3	̸∈	̸∈	PROPN
ejpam-4379	43	4	u	u	PROPN
ejpam-4379	43	5	for	for	ADP
ejpam-4379	43	6	all	all	DET
ejpam-4379	43	7	u	u	PROPN
ejpam-4379	43	8	∈	∈	PROPN
ejpam-4379	43	9	τ	τ	X
ejpam-4379	43	10	,	,	PUNCT
ejpam-4379	43	11	then	then	ADV
ejpam-4379	43	12	the	the	DET
ejpam-4379	43	13	family	family	NOUN
ejpam-4379	43	14	of	of	ADP
ejpam-4379	43	15	all	all	DET
ejpam-4379	43	16	closed	closed	ADJ
ejpam-4379	43	17	sets	set	NOUN
ejpam-4379	43	18	in	in	ADP
ejpam-4379	43	19	(	(	PUNCT
ejpam-4379	43	20	x	x	X
ejpam-4379	43	21	,	,	PUNCT
ejpam-4379	43	22	τ	τ	PROPN
ejpam-4379	43	23	)	)	PUNCT
ejpam-4379	43	24	is	be	AUX
ejpam-4379	43	25	equal	equal	ADJ
ejpam-4379	43	26	to	to	ADP
ejpam-4379	43	27	the	the	DET
ejpam-4379	43	28	family	family	NOUN
ejpam-4379	43	29	of	of	ADP
ejpam-4379	43	30	all	all	DET
ejpam-4379	43	31	closed	closed	ADJ
ejpam-4379	43	32	sets	set	NOUN
ejpam-4379	43	33	in	in	ADP
ejpam-4379	43	34	its	its	PRON
ejpam-4379	43	35	closed	closed	ADJ
ejpam-4379	43	36	extension	extension	NOUN
ejpam-4379	43	37	(	(	PUNCT
ejpam-4379	43	38	xp	xp	INTJ
ejpam-4379	43	39	,	,	PUNCT
ejpam-4379	43	40	τ	τ	PROPN
ejpam-4379	43	41	⋆	⋆	VERB
ejpam-4379	43	42	)	)	PUNCT
ejpam-4379	43	43	except	except	SCONJ
ejpam-4379	43	44	for	for	ADP
ejpam-4379	43	45	xp	xp	PROPN
ejpam-4379	43	46	itself	itself	PRON
ejpam-4379	43	47	.	.	PUNCT
ejpam-4379	44	1	any	any	DET
ejpam-4379	44	2	closed	close	VERB
ejpam-4379	44	3	extension	extension	NOUN
ejpam-4379	44	4	space	space	NOUN
ejpam-4379	44	5	(	(	PUNCT
ejpam-4379	44	6	xp	xp	INTJ
ejpam-4379	44	7	,	,	PUNCT
ejpam-4379	44	8	τ	τ	PROPN
ejpam-4379	44	9	⋆	⋆	NOUN
ejpam-4379	44	10	)	)	PUNCT
ejpam-4379	44	11	of	of	ADP
ejpam-4379	44	12	a	a	DET
ejpam-4379	44	13	given	give	VERB
ejpam-4379	44	14	space	space	NOUN
ejpam-4379	44	15	(	(	PUNCT
ejpam-4379	44	16	x	x	X
ejpam-4379	44	17	,	,	PUNCT
ejpam-4379	44	18	τ	τ	PROPN
ejpam-4379	44	19	)	)	PUNCT
ejpam-4379	44	20	is	be	AUX
ejpam-4379	44	21	always	always	ADV
ejpam-4379	44	22	separable	separable	ADJ
ejpam-4379	44	23	as	as	SCONJ
ejpam-4379	44	24	{	{	PUNCT
ejpam-4379	44	25	p	p	NOUN
ejpam-4379	44	26	}	}	PUNCT
ejpam-4379	44	27	is	be	AUX
ejpam-4379	44	28	dense	dense	ADJ
ejpam-4379	44	29	.	.	PUNCT
ejpam-4379	45	1	if	if	SCONJ
ejpam-4379	45	2	(	(	PUNCT
ejpam-4379	45	3	x	x	X
ejpam-4379	45	4	,	,	PUNCT
ejpam-4379	45	5	τ	τ	PROPN
ejpam-4379	45	6	)	)	PUNCT
ejpam-4379	45	7	is	be	AUX
ejpam-4379	45	8	first	first	ADV
ejpam-4379	45	9	countable	countable	ADJ
ejpam-4379	45	10	,	,	PUNCT
ejpam-4379	45	11	then	then	ADV
ejpam-4379	45	12	so	so	ADV
ejpam-4379	45	13	is	be	AUX
ejpam-4379	45	14	its	its	PRON
ejpam-4379	45	15	closed	closed	ADJ
ejpam-4379	45	16	extension	extension	NOUN
ejpam-4379	45	17	(	(	PUNCT
ejpam-4379	45	18	xp	xp	INTJ
ejpam-4379	45	19	,	,	PUNCT
ejpam-4379	45	20	τ	τ	PROPN
ejpam-4379	45	21	⋆	⋆	NOUN
ejpam-4379	45	22	)	)	PUNCT
ejpam-4379	45	23	because	because	SCONJ
ejpam-4379	45	24	{	{	PUNCT
ejpam-4379	45	25	{	{	PUNCT
ejpam-4379	45	26	p	p	NOUN
ejpam-4379	45	27	}	}	PUNCT
ejpam-4379	45	28	}	}	PUNCT
ejpam-4379	45	29	is	be	AUX
ejpam-4379	45	30	a	a	DET
ejpam-4379	45	31	countable	countable	ADJ
ejpam-4379	45	32	local	local	ADJ
ejpam-4379	45	33	base	base	NOUN
ejpam-4379	45	34	for	for	ADP
ejpam-4379	45	35	xp	xp	INTJ
ejpam-4379	45	36	at	at	ADP
ejpam-4379	45	37	p	p	NOUN
ejpam-4379	45	38	and	and	CCONJ
ejpam-4379	45	39	for	for	ADP
ejpam-4379	45	40	any	any	DET
ejpam-4379	45	41	x	x	SYM
ejpam-4379	45	42	∈	∈	PROPN
ejpam-4379	45	43	x	x	NOUN
ejpam-4379	45	44	,	,	PUNCT
ejpam-4379	45	45	pick	pick	VERB
ejpam-4379	45	46	a	a	DET
ejpam-4379	45	47	countable	countable	ADJ
ejpam-4379	45	48	local	local	ADJ
ejpam-4379	45	49	base	base	NOUN
ejpam-4379	45	50	b(x	b(x	NOUN
ejpam-4379	45	51	)	)	PUNCT
ejpam-4379	45	52	=	=	PRON
ejpam-4379	45	53	{	{	PUNCT
ejpam-4379	45	54	un	un	PROPN
ejpam-4379	45	55	:	:	PUNCT
ejpam-4379	45	56	n	n	CCONJ
ejpam-4379	45	57	∈	∈	PROPN
ejpam-4379	45	58	n	n	CCONJ
ejpam-4379	45	59	}	}	PUNCT
ejpam-4379	45	60	for	for	ADP
ejpam-4379	45	61	(	(	PUNCT
ejpam-4379	45	62	x	x	INTJ
ejpam-4379	45	63	,	,	PUNCT
ejpam-4379	45	64	τ	τ	PROPN
ejpam-4379	45	65	)	)	PUNCT
ejpam-4379	45	66	at	at	ADP
ejpam-4379	45	67	x	x	NOUN
ejpam-4379	45	68	,	,	PUNCT
ejpam-4379	45	69	then	then	ADV
ejpam-4379	45	70	the	the	DET
ejpam-4379	45	71	countable	countable	ADJ
ejpam-4379	45	72	family	family	NOUN
ejpam-4379	45	73	{	{	PUNCT
ejpam-4379	45	74	un	un	PROPN
ejpam-4379	45	75	∪	∪	PROPN
ejpam-4379	45	76	{	{	PUNCT
ejpam-4379	45	77	p	p	NOUN
ejpam-4379	45	78	}	}	PUNCT
ejpam-4379	45	79	:	:	PUNCT
ejpam-4379	45	80	n	n	CCONJ
ejpam-4379	45	81	∈	∈	PROPN
ejpam-4379	45	82	n	n	CCONJ
ejpam-4379	45	83	}	}	PUNCT
ejpam-4379	45	84	is	be	AUX
ejpam-4379	45	85	a	a	DET
ejpam-4379	45	86	local	local	ADJ
ejpam-4379	45	87	base	base	NOUN
ejpam-4379	45	88	for	for	ADP
ejpam-4379	45	89	(	(	PUNCT
ejpam-4379	45	90	xp	xp	INTJ
ejpam-4379	45	91	,	,	PUNCT
ejpam-4379	45	92	τ	τ	PROPN
ejpam-4379	45	93	⋆	⋆	VERB
ejpam-4379	45	94	)	)	PUNCT
ejpam-4379	45	95	at	at	ADP
ejpam-4379	45	96	x.	x.	NOUN
ejpam-4379	45	97	now	now	ADV
ejpam-4379	45	98	,	,	PUNCT
ejpam-4379	45	99	if	if	SCONJ
ejpam-4379	45	100	(	(	PUNCT
ejpam-4379	45	101	x	x	X
ejpam-4379	45	102	,	,	PUNCT
ejpam-4379	45	103	τ	τ	PROPN
ejpam-4379	45	104	)	)	PUNCT
ejpam-4379	45	105	is	be	AUX
ejpam-4379	45	106	second	second	ADV
ejpam-4379	45	107	countable	countable	ADJ
ejpam-4379	45	108	with	with	ADP
ejpam-4379	45	109	a	a	DET
ejpam-4379	45	110	countable	countable	ADJ
ejpam-4379	45	111	base	base	NOUN
ejpam-4379	45	112	b	b	NOUN
ejpam-4379	45	113	=	=	PUNCT
ejpam-4379	45	114	{	{	PUNCT
ejpam-4379	45	115	bn	bn	NOUN
ejpam-4379	45	116	:	:	PUNCT
ejpam-4379	45	117	n	n	CCONJ
ejpam-4379	45	118	∈	∈	PROPN
ejpam-4379	45	119	n	n	CCONJ
ejpam-4379	45	120	}	}	PUNCT
ejpam-4379	45	121	,	,	PUNCT
ejpam-4379	45	122	then	then	ADV
ejpam-4379	45	123	the	the	DET
ejpam-4379	45	124	countable	countable	ADJ
ejpam-4379	45	125	family	family	NOUN
ejpam-4379	45	126	{	{	PUNCT
ejpam-4379	45	127	{	{	PUNCT
ejpam-4379	45	128	p	p	X
ejpam-4379	45	129	}	}	PUNCT
ejpam-4379	45	130	,	,	PUNCT
ejpam-4379	45	131	bn	bn	ADP
ejpam-4379	45	132	∪	∪	X
ejpam-4379	45	133	{	{	PUNCT
ejpam-4379	45	134	p	p	NOUN
ejpam-4379	45	135	}	}	PUNCT
ejpam-4379	45	136	:	:	PUNCT
ejpam-4379	45	137	n	n	CCONJ
ejpam-4379	45	138	∈	∈	PROPN
ejpam-4379	45	139	n	n	CCONJ
ejpam-4379	45	140	}	}	PUNCT
ejpam-4379	45	141	is	be	AUX
ejpam-4379	45	142	a	a	DET
ejpam-4379	45	143	base	base	NOUN
ejpam-4379	45	144	for	for	ADP
ejpam-4379	45	145	its	its	PRON
ejpam-4379	45	146	closed	closed	ADJ
ejpam-4379	45	147	extension	extension	NOUN
ejpam-4379	45	148	(	(	PUNCT
ejpam-4379	45	149	xp	xp	INTJ
ejpam-4379	45	150	,	,	PUNCT
ejpam-4379	45	151	τ	τ	PROPN
ejpam-4379	45	152	⋆	⋆	NOUN
ejpam-4379	45	153	)	)	PUNCT
ejpam-4379	45	154	.	.	PUNCT
ejpam-4379	46	1	remark	remark	PROPN
ejpam-4379	46	2	1	1	NUM
ejpam-4379	46	3	.	.	PUNCT
ejpam-4379	47	1	it	it	PRON
ejpam-4379	47	2	is	be	AUX
ejpam-4379	47	3	clear	clear	ADJ
ejpam-4379	47	4	that	that	SCONJ
ejpam-4379	47	5	the	the	DET
ejpam-4379	47	6	closed	closed	ADJ
ejpam-4379	47	7	extension	extension	NOUN
ejpam-4379	47	8	space	space	NOUN
ejpam-4379	47	9	(	(	PUNCT
ejpam-4379	47	10	xp	xp	INTJ
ejpam-4379	47	11	,	,	PUNCT
ejpam-4379	47	12	τ	τ	PROPN
ejpam-4379	47	13	⋆	⋆	VERB
ejpam-4379	47	14	)	)	PUNCT
ejpam-4379	47	15	is	be	AUX
ejpam-4379	47	16	always	always	ADV
ejpam-4379	47	17	hyper	hyper	ADJ
ejpam-4379	47	18	-	-	ADJ
ejpam-4379	47	19	connected	connected	ADJ
ejpam-4379	47	20	even	even	ADV
ejpam-4379	47	21	if	if	SCONJ
ejpam-4379	47	22	(	(	PUNCT
ejpam-4379	47	23	x	x	X
ejpam-4379	47	24	,	,	PUNCT
ejpam-4379	47	25	τ	τ	PROPN
ejpam-4379	47	26	)	)	PUNCT
ejpam-4379	47	27	is	be	AUX
ejpam-4379	47	28	not	not	PART
ejpam-4379	47	29	.	.	PUNCT
ejpam-4379	48	1	recall	recall	VERB
ejpam-4379	48	2	that	that	SCONJ
ejpam-4379	48	3	a	a	DET
ejpam-4379	48	4	space	space	NOUN
ejpam-4379	48	5	is	be	AUX
ejpam-4379	48	6	called	call	VERB
ejpam-4379	48	7	hyper	hyper	ADV
ejpam-4379	48	8	-	-	VERB
ejpam-4379	48	9	connected	connected	ADJ
ejpam-4379	48	10	if	if	SCONJ
ejpam-4379	48	11	any	any	DET
ejpam-4379	48	12	two	two	NUM
ejpam-4379	48	13	non	non	ADJ
ejpam-4379	48	14	-	-	ADJ
ejpam-4379	48	15	empty	empty	ADJ
ejpam-4379	48	16	open	open	ADJ
ejpam-4379	48	17	sets	set	NOUN
ejpam-4379	48	18	intersect	intersect	ADJ
ejpam-4379	48	19	,	,	PUNCT
ejpam-4379	48	20	[	[	X
ejpam-4379	48	21	15	15	NUM
ejpam-4379	48	22	]	]	PUNCT
ejpam-4379	48	23	.	.	PUNCT
ejpam-4379	49	1	thus	thus	ADV
ejpam-4379	49	2	the	the	DET
ejpam-4379	49	3	closed	closed	ADJ
ejpam-4379	49	4	extension	extension	NOUN
ejpam-4379	49	5	space	space	NOUN
ejpam-4379	49	6	(	(	PUNCT
ejpam-4379	49	7	xp	xp	INTJ
ejpam-4379	49	8	,	,	PUNCT
ejpam-4379	49	9	τ	τ	PROPN
ejpam-4379	49	10	⋆	⋆	NOUN
ejpam-4379	49	11	)	)	PUNCT
ejpam-4379	49	12	can	can	AUX
ejpam-4379	49	13	not	not	PART
ejpam-4379	49	14	be	be	AUX
ejpam-4379	49	15	hausdorff	hausdorff	NOUN
ejpam-4379	49	16	(	(	PUNCT
ejpam-4379	49	17	t2	t2	PROPN
ejpam-4379	49	18	)	)	PUNCT
ejpam-4379	49	19	nor	nor	CCONJ
ejpam-4379	49	20	metrizable	metrizable	ADJ
ejpam-4379	49	21	.	.	PUNCT
ejpam-4379	50	1	in	in	ADP
ejpam-4379	50	2	fact	fact	NOUN
ejpam-4379	50	3	,	,	PUNCT
ejpam-4379	50	4	the	the	DET
ejpam-4379	50	5	closed	closed	ADJ
ejpam-4379	50	6	extension	extension	NOUN
ejpam-4379	50	7	(	(	PUNCT
ejpam-4379	50	8	xp	xp	INTJ
ejpam-4379	50	9	,	,	PUNCT
ejpam-4379	50	10	τ	τ	PROPN
ejpam-4379	50	11	⋆	⋆	VERB
ejpam-4379	50	12	)	)	PUNCT
ejpam-4379	50	13	is	be	AUX
ejpam-4379	50	14	not	not	PART
ejpam-4379	50	15	t1	t1	ADJ
ejpam-4379	50	16	,	,	PUNCT
ejpam-4379	50	17	even	even	ADV
ejpam-4379	50	18	if	if	SCONJ
ejpam-4379	50	19	(	(	PUNCT
ejpam-4379	50	20	x	x	X
ejpam-4379	50	21	,	,	PUNCT
ejpam-4379	50	22	τ	τ	PROPN
ejpam-4379	50	23	)	)	PUNCT
ejpam-4379	50	24	is	be	AUX
ejpam-4379	50	25	,	,	PUNCT
ejpam-4379	50	26	because	because	SCONJ
ejpam-4379	50	27	for	for	ADP
ejpam-4379	50	28	an	an	DET
ejpam-4379	50	29	element	element	NOUN
ejpam-4379	50	30	x	x	SYM
ejpam-4379	50	31	∈	∈	PROPN
ejpam-4379	50	32	x	x	INTJ
ejpam-4379	50	33	we	we	PRON
ejpam-4379	50	34	have	have	VERB
ejpam-4379	50	35	x	x	X
ejpam-4379	50	36	̸=	̸=	PROPN
ejpam-4379	50	37	p	p	NOUN
ejpam-4379	50	38	and	and	CCONJ
ejpam-4379	50	39	any	any	DET
ejpam-4379	50	40	open	open	ADJ
ejpam-4379	50	41	set	set	NOUN
ejpam-4379	50	42	contains	contain	VERB
ejpam-4379	50	43	x	x	PUNCT
ejpam-4379	50	44	must	must	AUX
ejpam-4379	50	45	contain	contain	VERB
ejpam-4379	50	46	p.	p.	NOUN
ejpam-4379	50	47	thus	thus	ADV
ejpam-4379	50	48	the	the	DET
ejpam-4379	50	49	closed	closed	ADJ
ejpam-4379	50	50	extension	extension	NOUN
ejpam-4379	50	51	is	be	AUX
ejpam-4379	50	52	not	not	PART
ejpam-4379	50	53	ti	ti	NOUN
ejpam-4379	50	54	where	where	SCONJ
ejpam-4379	50	55	i	i	PRON
ejpam-4379	50	56	∈	∈	X
ejpam-4379	50	57	{	{	PUNCT
ejpam-4379	50	58	1	1	NUM
ejpam-4379	50	59	,	,	PUNCT
ejpam-4379	50	60	2	2	NUM
ejpam-4379	50	61	,	,	PUNCT
ejpam-4379	50	62	21	21	NUM
ejpam-4379	50	63	2	2	NUM
ejpam-4379	50	64	,	,	PUNCT
ejpam-4379	50	65	3	3	NUM
ejpam-4379	50	66	,	,	PUNCT
ejpam-4379	50	67	3	3	NUM
ejpam-4379	50	68	1	1	NUM
ejpam-4379	50	69	2	2	NUM
ejpam-4379	50	70	,	,	PUNCT
ejpam-4379	50	71	4	4	NUM
ejpam-4379	50	72	,	,	PUNCT
ejpam-4379	50	73	5	5	NUM
ejpam-4379	50	74	,	,	PUNCT
ejpam-4379	50	75	6	6	NUM
ejpam-4379	50	76	}	}	PUNCT
ejpam-4379	50	77	.	.	PUNCT
ejpam-4379	51	1	note	note	VERB
ejpam-4379	51	2	that	that	SCONJ
ejpam-4379	51	3	the	the	DET
ejpam-4379	51	4	singleton	singleton	NOUN
ejpam-4379	51	5	{	{	PUNCT
ejpam-4379	51	6	p	p	NOUN
ejpam-4379	51	7	}	}	PUNCT
ejpam-4379	51	8	in	in	ADP
ejpam-4379	51	9	(	(	PUNCT
ejpam-4379	51	10	xp	xp	INTJ
ejpam-4379	51	11	,	,	PUNCT
ejpam-4379	51	12	τ	τ	PROPN
ejpam-4379	51	13	⋆	⋆	VERB
ejpam-4379	51	14	)	)	PUNCT
ejpam-4379	51	15	is	be	AUX
ejpam-4379	51	16	not	not	PART
ejpam-4379	51	17	closed	close	VERB
ejpam-4379	51	18	because	because	SCONJ
ejpam-4379	51	19	x	x	PRON
ejpam-4379	51	20	is	be	AUX
ejpam-4379	51	21	not	not	PART
ejpam-4379	51	22	open	open	ADJ
ejpam-4379	51	23	in	in	ADP
ejpam-4379	51	24	(	(	PUNCT
ejpam-4379	51	25	xp	xp	INTJ
ejpam-4379	51	26	,	,	PUNCT
ejpam-4379	51	27	τ	τ	PROPN
ejpam-4379	51	28	⋆	⋆	NOUN
ejpam-4379	51	29	)	)	PUNCT
ejpam-4379	51	30	.	.	PUNCT
ejpam-4379	52	1	theorem	theorem	NOUN
ejpam-4379	52	2	1	1	NUM
ejpam-4379	52	3	.	.	PUNCT
ejpam-4379	53	1	(	(	PUNCT
ejpam-4379	53	2	x	x	X
ejpam-4379	53	3	,	,	PUNCT
ejpam-4379	53	4	τ	τ	PROPN
ejpam-4379	53	5	)	)	PUNCT
ejpam-4379	53	6	is	be	AUX
ejpam-4379	53	7	t0	t0	PROPN
ejpam-4379	53	8	if	if	SCONJ
ejpam-4379	54	1	and	and	CCONJ
ejpam-4379	54	2	only	only	ADV
ejpam-4379	54	3	if	if	SCONJ
ejpam-4379	54	4	its	its	PRON
ejpam-4379	54	5	closed	closed	ADJ
ejpam-4379	54	6	extension	extension	NOUN
ejpam-4379	54	7	(	(	PUNCT
ejpam-4379	54	8	xp	xp	INTJ
ejpam-4379	54	9	,	,	PUNCT
ejpam-4379	54	10	τ	τ	PROPN
ejpam-4379	54	11	⋆	⋆	X
ejpam-4379	54	12	)	)	PUNCT
ejpam-4379	54	13	is	be	AUX
ejpam-4379	54	14	t0	t0	NOUN
ejpam-4379	54	15	.	.	PUNCT
ejpam-4379	55	1	proof	proof	NOUN
ejpam-4379	55	2	.	.	PUNCT
ejpam-4379	56	1	assume	assume	VERB
ejpam-4379	56	2	that	that	SCONJ
ejpam-4379	56	3	(	(	PUNCT
ejpam-4379	56	4	x	x	X
ejpam-4379	56	5	,	,	PUNCT
ejpam-4379	56	6	τ	τ	PROPN
ejpam-4379	56	7	)	)	PUNCT
ejpam-4379	56	8	is	be	AUX
ejpam-4379	56	9	t0	t0	NOUN
ejpam-4379	56	10	.	.	PUNCT
ejpam-4379	57	1	let	let	VERB
ejpam-4379	57	2	x	x	PRON
ejpam-4379	57	3	,	,	PUNCT
ejpam-4379	57	4	y	y	PROPN
ejpam-4379	57	5	∈	∈	PROPN
ejpam-4379	57	6	xp	xp	INTJ
ejpam-4379	57	7	be	be	AUX
ejpam-4379	57	8	arbitrary	arbitrary	ADJ
ejpam-4379	57	9	such	such	ADJ
ejpam-4379	57	10	that	that	SCONJ
ejpam-4379	57	11	x	x	X
ejpam-4379	57	12	̸=	̸=	PROPN
ejpam-4379	57	13	y.	y.	NOUN
ejpam-4379	57	14	if	if	SCONJ
ejpam-4379	57	15	x	x	PRON
ejpam-4379	57	16	,	,	PUNCT
ejpam-4379	57	17	y	y	PROPN
ejpam-4379	57	18	∈	∈	PROPN
ejpam-4379	57	19	x	x	X
ejpam-4379	57	20	,	,	PUNCT
ejpam-4379	57	21	then	then	ADV
ejpam-4379	57	22	x	x	X
ejpam-4379	57	23	̸=	̸=	PROPN
ejpam-4379	57	24	p	p	PROPN
ejpam-4379	57	25	̸=	̸=	PROPN
ejpam-4379	57	26	y.	y.	NOUN
ejpam-4379	57	27	since	since	SCONJ
ejpam-4379	57	28	(	(	PUNCT
ejpam-4379	57	29	x	x	X
ejpam-4379	57	30	,	,	PUNCT
ejpam-4379	57	31	τ	τ	PROPN
ejpam-4379	57	32	)	)	PUNCT
ejpam-4379	57	33	is	be	AUX
ejpam-4379	57	34	t0	t0	NOUN
ejpam-4379	57	35	,	,	PUNCT
ejpam-4379	57	36	then	then	ADV
ejpam-4379	57	37	there	there	PRON
ejpam-4379	57	38	exists	exist	VERB
ejpam-4379	57	39	u	u	PROPN
ejpam-4379	57	40	∈	∈	PROPN
ejpam-4379	57	41	τ	τ	X
ejpam-4379	57	42	such	such	ADJ
ejpam-4379	57	43	that	that	SCONJ
ejpam-4379	57	44	,	,	PUNCT
ejpam-4379	57	45	without	without	ADP
ejpam-4379	57	46	loss	loss	NOUN
ejpam-4379	57	47	of	of	ADP
ejpam-4379	57	48	generality	generality	NOUN
ejpam-4379	57	49	,	,	PUNCT
ejpam-4379	57	50	x	x	SYM
ejpam-4379	57	51	∈	∈	PROPN
ejpam-4379	57	52	u	u	PROPN
ejpam-4379	57	53	̸∋	̸∋	PROPN
ejpam-4379	57	54	y.	y.	PROPN
ejpam-4379	57	55	thus	thus	ADV
ejpam-4379	57	56	u	u	NOUN
ejpam-4379	57	57	∪	∪	X
ejpam-4379	57	58	{	{	PUNCT
ejpam-4379	57	59	p	p	NOUN
ejpam-4379	57	60	}	}	PUNCT
ejpam-4379	57	61	∈	∈	PROPN
ejpam-4379	57	62	τ	τ	X
ejpam-4379	57	63	⋆	⋆	VERB
ejpam-4379	57	64	with	with	ADP
ejpam-4379	57	65	x	x	PROPN
ejpam-4379	57	66	∈	∈	PROPN
ejpam-4379	57	67	(	(	PUNCT
ejpam-4379	57	68	u	u	NOUN
ejpam-4379	57	69	∪	∪	VERB
ejpam-4379	57	70	{	{	PUNCT
ejpam-4379	57	71	p	p	NOUN
ejpam-4379	57	72	}	}	PUNCT
ejpam-4379	57	73	)	)	PUNCT
ejpam-4379	57	74	̸∋	̸∋	PROPN
ejpam-4379	57	75	y.	y.	PROPN
ejpam-4379	57	76	now	now	ADV
ejpam-4379	57	77	,	,	PUNCT
ejpam-4379	57	78	without	without	ADP
ejpam-4379	57	79	loss	loss	NOUN
ejpam-4379	57	80	of	of	ADP
ejpam-4379	57	81	generality	generality	NOUN
ejpam-4379	57	82	,	,	PUNCT
ejpam-4379	57	83	assume	assume	VERB
ejpam-4379	57	84	that	that	SCONJ
ejpam-4379	57	85	x	x	X
ejpam-4379	57	86	=	=	PUNCT
ejpam-4379	57	87	p	p	X
ejpam-4379	57	88	̸=	̸=	PROPN
ejpam-4379	57	89	y	y	PROPN
ejpam-4379	57	90	,	,	PUNCT
ejpam-4379	57	91	then	then	ADV
ejpam-4379	57	92	{	{	PUNCT
ejpam-4379	57	93	p	p	NOUN
ejpam-4379	57	94	}	}	PUNCT
ejpam-4379	57	95	∈	∈	PROPN
ejpam-4379	57	96	τ	τ	X
ejpam-4379	57	97	⋆	⋆	VERB
ejpam-4379	57	98	with	with	ADP
ejpam-4379	57	99	x	x	X
ejpam-4379	57	100	=	=	PUNCT
ejpam-4379	57	101	p	p	X
ejpam-4379	57	102	∈	∈	PROPN
ejpam-4379	57	103	{	{	PUNCT
ejpam-4379	57	104	p	p	PROPN
ejpam-4379	57	105	}	}	PUNCT
ejpam-4379	57	106	̸∋	̸∋	PROPN
ejpam-4379	57	107	y.	y.	NOUN
ejpam-4379	57	108	the	the	DET
ejpam-4379	57	109	converse	converse	NOUN
ejpam-4379	57	110	is	be	AUX
ejpam-4379	57	111	clear	clear	ADJ
ejpam-4379	57	112	because	because	SCONJ
ejpam-4379	57	113	t0	t0	PROPN
ejpam-4379	57	114	is	be	AUX
ejpam-4379	57	115	hereditary	hereditary	ADJ
ejpam-4379	57	116	.	.	PUNCT
ejpam-4379	58	1	the	the	DET
ejpam-4379	58	2	closed	closed	ADJ
ejpam-4379	58	3	extension	extension	NOUN
ejpam-4379	58	4	(	(	PUNCT
ejpam-4379	58	5	xp	xp	INTJ
ejpam-4379	58	6	,	,	PUNCT
ejpam-4379	58	7	τ	τ	PROPN
ejpam-4379	58	8	⋆	⋆	VERB
ejpam-4379	58	9	)	)	PUNCT
ejpam-4379	58	10	is	be	AUX
ejpam-4379	58	11	not	not	PART
ejpam-4379	58	12	regular	regular	ADJ
ejpam-4379	58	13	even	even	ADV
ejpam-4379	58	14	if	if	SCONJ
ejpam-4379	58	15	(	(	PUNCT
ejpam-4379	58	16	x	x	X
ejpam-4379	58	17	,	,	PUNCT
ejpam-4379	58	18	τ	τ	PROPN
ejpam-4379	58	19	)	)	PUNCT
ejpam-4379	58	20	is	be	AUX
ejpam-4379	58	21	regular	regular	ADJ
ejpam-4379	58	22	because	because	SCONJ
ejpam-4379	58	23	x	x	PRON
ejpam-4379	58	24	is	be	AUX
ejpam-4379	58	25	closed	close	VERB
ejpam-4379	58	26	in	in	ADP
ejpam-4379	58	27	(	(	PUNCT
ejpam-4379	58	28	xp	xp	INTJ
ejpam-4379	58	29	,	,	PUNCT
ejpam-4379	58	30	τ	τ	PROPN
ejpam-4379	58	31	⋆	⋆	VERB
ejpam-4379	58	32	)	)	PUNCT
ejpam-4379	58	33	with	with	ADP
ejpam-4379	58	34	p	p	PROPN
ejpam-4379	58	35	̸∈	̸∈	PROPN
ejpam-4379	58	36	x	x	X
ejpam-4379	58	37	and	and	CCONJ
ejpam-4379	58	38	x	x	X
ejpam-4379	58	39	and	and	CCONJ
ejpam-4379	58	40	p	p	NOUN
ejpam-4379	58	41	can	can	AUX
ejpam-4379	58	42	not	not	PART
ejpam-4379	58	43	be	be	AUX
ejpam-4379	58	44	separated	separate	VERB
ejpam-4379	58	45	by	by	ADP
ejpam-4379	58	46	disjoint	disjoint	ADJ
ejpam-4379	58	47	open	open	ADJ
ejpam-4379	58	48	sets	set	NOUN
ejpam-4379	58	49	.	.	PUNCT
ejpam-4379	59	1	thus	thus	ADV
ejpam-4379	59	2	the	the	DET
ejpam-4379	59	3	closed	closed	ADJ
ejpam-4379	59	4	extension	extension	NOUN
ejpam-4379	59	5	(	(	PUNCT
ejpam-4379	59	6	xp	xp	INTJ
ejpam-4379	59	7	,	,	PUNCT
ejpam-4379	59	8	τ	τ	PROPN
ejpam-4379	59	9	⋆	⋆	VERB
ejpam-4379	59	10	)	)	PUNCT
ejpam-4379	59	11	is	be	AUX
ejpam-4379	59	12	not	not	PART
ejpam-4379	59	13	completely	completely	ADV
ejpam-4379	59	14	regular	regular	ADJ
ejpam-4379	59	15	.	.	PUNCT
ejpam-4379	60	1	for	for	ADP
ejpam-4379	60	2	the	the	DET
ejpam-4379	60	3	normality	normality	NOUN
ejpam-4379	60	4	,	,	PUNCT
ejpam-4379	60	5	we	we	PRON
ejpam-4379	60	6	need	need	VERB
ejpam-4379	60	7	to	to	PART
ejpam-4379	60	8	recall	recall	VERB
ejpam-4379	60	9	the	the	DET
ejpam-4379	60	10	definition	definition	NOUN
ejpam-4379	60	11	of	of	ADP
ejpam-4379	60	12	ultra	ultra	ADJ
ejpam-4379	60	13	-	-	ADJ
ejpam-4379	60	14	connected	connected	ADJ
ejpam-4379	60	15	.	.	PUNCT
ejpam-4379	61	1	a	a	DET
ejpam-4379	61	2	space	space	NOUN
ejpam-4379	61	3	is	be	AUX
ejpam-4379	61	4	called	call	VERB
ejpam-4379	61	5	ultra	ultra	ADJ
ejpam-4379	61	6	-	-	VERB
ejpam-4379	61	7	connected	connected	ADJ
ejpam-4379	61	8	if	if	SCONJ
ejpam-4379	61	9	any	any	DET
ejpam-4379	61	10	two	two	NUM
ejpam-4379	61	11	non	non	ADJ
ejpam-4379	61	12	-	-	ADJ
ejpam-4379	61	13	empty	empty	ADJ
ejpam-4379	61	14	closed	closed	ADJ
ejpam-4379	61	15	sets	set	NOUN
ejpam-4379	61	16	intersect	intersect	ADJ
ejpam-4379	61	17	,	,	PUNCT
ejpam-4379	61	18	[	[	X
ejpam-4379	61	19	15	15	NUM
ejpam-4379	61	20	]	]	PUNCT
ejpam-4379	61	21	.	.	PUNCT
ejpam-4379	62	1	it	it	PRON
ejpam-4379	62	2	is	be	AUX
ejpam-4379	62	3	clear	clear	ADJ
ejpam-4379	62	4	that	that	SCONJ
ejpam-4379	62	5	any	any	DET
ejpam-4379	62	6	ultra	ultra	ADJ
ejpam-4379	62	7	-	-	ADJ
ejpam-4379	62	8	connected	connected	ADJ
ejpam-4379	62	9	space	space	NOUN
ejpam-4379	62	10	is	be	AUX
ejpam-4379	62	11	normal	normal	ADJ
ejpam-4379	62	12	.	.	PUNCT
ejpam-4379	63	1	d.	d.	PROPN
ejpam-4379	63	2	abuzaid	abuzaid	PROPN
ejpam-4379	63	3	,	,	PUNCT
ejpam-4379	63	4	s.	s.	PROPN
ejpam-4379	63	5	al	al	PROPN
ejpam-4379	63	6	-	-	PROPN
ejpam-4379	63	7	qarhi	qarhi	PROPN
ejpam-4379	63	8	,	,	PUNCT
ejpam-4379	63	9	l.	l.	PROPN
ejpam-4379	63	10	kalantan	kalantan	PROPN
ejpam-4379	63	11	/	/	SYM
ejpam-4379	63	12	eur	eur	PROPN
ejpam-4379	63	13	.	.	PUNCT
ejpam-4379	64	1	j.	j.	PROPN
ejpam-4379	64	2	pure	pure	PROPN
ejpam-4379	64	3	appl	appl	PROPN
ejpam-4379	64	4	.	.	PROPN
ejpam-4379	64	5	math	math	PROPN
ejpam-4379	64	6	,	,	PUNCT
ejpam-4379	64	7	15	15	NUM
ejpam-4379	64	8	(	(	PUNCT
ejpam-4379	64	9	2	2	NUM
ejpam-4379	64	10	)	)	PUNCT
ejpam-4379	64	11	(	(	PUNCT
ejpam-4379	64	12	2022	2022	NUM
ejpam-4379	64	13	)	)	PUNCT
ejpam-4379	64	14	,	,	PUNCT
ejpam-4379	64	15	672	672	NUM
ejpam-4379	64	16	-	-	SYM
ejpam-4379	64	17	680	680	NUM
ejpam-4379	64	18	674	674	NUM
ejpam-4379	64	19	theorem	theorem	NOUN
ejpam-4379	64	20	2	2	NUM
ejpam-4379	64	21	.	.	PUNCT
ejpam-4379	65	1	(	(	PUNCT
ejpam-4379	65	2	x	x	X
ejpam-4379	65	3	,	,	PUNCT
ejpam-4379	65	4	τ	τ	PROPN
ejpam-4379	65	5	)	)	PUNCT
ejpam-4379	65	6	is	be	AUX
ejpam-4379	65	7	ultra	ultra	ADJ
ejpam-4379	65	8	-	-	ADJ
ejpam-4379	65	9	connected	connected	ADJ
ejpam-4379	65	10	if	if	SCONJ
ejpam-4379	65	11	and	and	CCONJ
ejpam-4379	65	12	only	only	ADV
ejpam-4379	65	13	if	if	SCONJ
ejpam-4379	65	14	its	its	PRON
ejpam-4379	65	15	closed	closed	ADJ
ejpam-4379	65	16	extension	extension	NOUN
ejpam-4379	65	17	(	(	PUNCT
ejpam-4379	65	18	xp	xp	INTJ
ejpam-4379	65	19	,	,	PUNCT
ejpam-4379	65	20	τ	τ	PROPN
ejpam-4379	65	21	⋆	⋆	VERB
ejpam-4379	65	22	)	)	PUNCT
ejpam-4379	65	23	is	be	AUX
ejpam-4379	65	24	normal	normal	ADJ
ejpam-4379	65	25	.	.	PUNCT
ejpam-4379	66	1	proof	proof	NOUN
ejpam-4379	66	2	.	.	PUNCT
ejpam-4379	67	1	assume	assume	VERB
ejpam-4379	67	2	that	that	SCONJ
ejpam-4379	67	3	(	(	PUNCT
ejpam-4379	67	4	x	x	X
ejpam-4379	67	5	,	,	PUNCT
ejpam-4379	67	6	τ	τ	PROPN
ejpam-4379	67	7	)	)	PUNCT
ejpam-4379	67	8	is	be	AUX
ejpam-4379	67	9	ultra	ultra	ADJ
ejpam-4379	67	10	-	-	ADJ
ejpam-4379	67	11	connected	connected	ADJ
ejpam-4379	67	12	.	.	PUNCT
ejpam-4379	68	1	since	since	SCONJ
ejpam-4379	68	2	the	the	DET
ejpam-4379	68	3	closed	closed	ADJ
ejpam-4379	68	4	sets	set	NOUN
ejpam-4379	68	5	in	in	ADP
ejpam-4379	68	6	the	the	DET
ejpam-4379	68	7	closed	closed	ADJ
ejpam-4379	68	8	extension	extension	NOUN
ejpam-4379	68	9	(	(	PUNCT
ejpam-4379	68	10	xp	xp	INTJ
ejpam-4379	68	11	,	,	PUNCT
ejpam-4379	68	12	τ	τ	PROPN
ejpam-4379	68	13	⋆	⋆	X
ejpam-4379	68	14	)	)	PUNCT
ejpam-4379	68	15	are	be	AUX
ejpam-4379	68	16	the	the	DET
ejpam-4379	68	17	same	same	ADJ
ejpam-4379	68	18	as	as	ADP
ejpam-4379	68	19	in	in	ADP
ejpam-4379	68	20	(	(	PUNCT
ejpam-4379	68	21	x	x	INTJ
ejpam-4379	68	22	,	,	PUNCT
ejpam-4379	68	23	τ	τ	PROPN
ejpam-4379	68	24	)	)	PUNCT
ejpam-4379	68	25	,	,	PUNCT
ejpam-4379	68	26	except	except	SCONJ
ejpam-4379	68	27	for	for	ADP
ejpam-4379	68	28	xp	xp	PROPN
ejpam-4379	68	29	,	,	PUNCT
ejpam-4379	68	30	we	we	PRON
ejpam-4379	68	31	have	have	VERB
ejpam-4379	68	32	that	that	PRON
ejpam-4379	68	33	(	(	PUNCT
ejpam-4379	68	34	xp	xp	INTJ
ejpam-4379	68	35	,	,	PUNCT
ejpam-4379	68	36	τ	τ	PROPN
ejpam-4379	68	37	⋆	⋆	VERB
ejpam-4379	68	38	)	)	PUNCT
ejpam-4379	68	39	is	be	AUX
ejpam-4379	68	40	ultra	ultra	ADJ
ejpam-4379	68	41	-	-	ADJ
ejpam-4379	68	42	connected	connected	ADJ
ejpam-4379	68	43	and	and	CCONJ
ejpam-4379	68	44	hence	hence	ADV
ejpam-4379	68	45	normal	normal	ADJ
ejpam-4379	68	46	.	.	PUNCT
ejpam-4379	69	1	now	now	ADV
ejpam-4379	69	2	,	,	PUNCT
ejpam-4379	69	3	assume	assume	VERB
ejpam-4379	69	4	that	that	SCONJ
ejpam-4379	69	5	(	(	PUNCT
ejpam-4379	69	6	xp	xp	INTJ
ejpam-4379	69	7	,	,	PUNCT
ejpam-4379	69	8	τ	τ	PROPN
ejpam-4379	69	9	⋆	⋆	VERB
ejpam-4379	69	10	)	)	PUNCT
ejpam-4379	69	11	is	be	AUX
ejpam-4379	69	12	normal	normal	ADJ
ejpam-4379	69	13	.	.	PUNCT
ejpam-4379	70	1	suppose	suppose	VERB
ejpam-4379	70	2	that	that	SCONJ
ejpam-4379	70	3	(	(	PUNCT
ejpam-4379	70	4	x	x	X
ejpam-4379	70	5	,	,	PUNCT
ejpam-4379	70	6	τ	τ	PROPN
ejpam-4379	70	7	)	)	PUNCT
ejpam-4379	70	8	is	be	AUX
ejpam-4379	70	9	not	not	PART
ejpam-4379	70	10	ultra	ultra	ADJ
ejpam-4379	70	11	-	-	VERB
ejpam-4379	70	12	connected	connected	ADJ
ejpam-4379	70	13	,	,	PUNCT
ejpam-4379	70	14	then	then	ADV
ejpam-4379	70	15	there	there	PRON
ejpam-4379	70	16	exist	exist	VERB
ejpam-4379	70	17	two	two	NUM
ejpam-4379	70	18	non	non	ADJ
ejpam-4379	70	19	-	-	ADJ
ejpam-4379	70	20	empty	empty	ADJ
ejpam-4379	70	21	disjoint	disjoint	NOUN
ejpam-4379	70	22	closed	close	VERB
ejpam-4379	70	23	sets	set	NOUN
ejpam-4379	70	24	a	a	PRON
ejpam-4379	70	25	and	and	CCONJ
ejpam-4379	70	26	b	b	NOUN
ejpam-4379	70	27	in	in	ADP
ejpam-4379	70	28	(	(	PUNCT
ejpam-4379	70	29	x	x	INTJ
ejpam-4379	70	30	,	,	PUNCT
ejpam-4379	70	31	τ	τ	PROPN
ejpam-4379	70	32	)	)	PUNCT
ejpam-4379	70	33	.	.	PUNCT
ejpam-4379	71	1	thus	thus	ADV
ejpam-4379	71	2	a	a	PRON
ejpam-4379	71	3	and	and	CCONJ
ejpam-4379	71	4	b	b	NOUN
ejpam-4379	71	5	are	be	AUX
ejpam-4379	71	6	non	non	ADJ
ejpam-4379	71	7	-	-	ADJ
ejpam-4379	71	8	empty	empty	ADJ
ejpam-4379	71	9	closed	closed	ADJ
ejpam-4379	71	10	disjoint	disjoint	NOUN
ejpam-4379	71	11	sets	set	NOUN
ejpam-4379	71	12	in	in	ADP
ejpam-4379	71	13	(	(	PUNCT
ejpam-4379	71	14	xp	xp	INTJ
ejpam-4379	71	15	,	,	PUNCT
ejpam-4379	71	16	τ	τ	PROPN
ejpam-4379	71	17	⋆	⋆	NOUN
ejpam-4379	71	18	)	)	PUNCT
ejpam-4379	71	19	.	.	PUNCT
ejpam-4379	72	1	since	since	SCONJ
ejpam-4379	72	2	any	any	DET
ejpam-4379	72	3	two	two	NUM
ejpam-4379	72	4	non	non	ADJ
ejpam-4379	72	5	-	-	ADJ
ejpam-4379	72	6	empty	empty	ADJ
ejpam-4379	72	7	open	open	ADJ
ejpam-4379	72	8	sets	set	NOUN
ejpam-4379	72	9	in	in	ADP
ejpam-4379	72	10	(	(	PUNCT
ejpam-4379	72	11	xp	xp	INTJ
ejpam-4379	72	12	,	,	PUNCT
ejpam-4379	72	13	τ	τ	PROPN
ejpam-4379	72	14	⋆	⋆	NOUN
ejpam-4379	72	15	)	)	PUNCT
ejpam-4379	72	16	must	must	AUX
ejpam-4379	72	17	intersect	intersect	ADJ
ejpam-4379	72	18	because	because	SCONJ
ejpam-4379	72	19	both	both	PRON
ejpam-4379	72	20	have	have	VERB
ejpam-4379	72	21	the	the	DET
ejpam-4379	72	22	element	element	NOUN
ejpam-4379	72	23	p	p	NOUN
ejpam-4379	72	24	,	,	PUNCT
ejpam-4379	72	25	see	see	VERB
ejpam-4379	72	26	remark	remark	NOUN
ejpam-4379	72	27	1	1	NUM
ejpam-4379	72	28	,	,	PUNCT
ejpam-4379	72	29	then	then	ADV
ejpam-4379	72	30	a	a	PRON
ejpam-4379	72	31	and	and	CCONJ
ejpam-4379	72	32	b	b	NOUN
ejpam-4379	72	33	can	can	AUX
ejpam-4379	72	34	not	not	PART
ejpam-4379	72	35	be	be	AUX
ejpam-4379	72	36	separated	separate	VERB
ejpam-4379	72	37	which	which	PRON
ejpam-4379	72	38	gives	give	VERB
ejpam-4379	72	39	that	that	PRON
ejpam-4379	72	40	(	(	PUNCT
ejpam-4379	72	41	xp	xp	INTJ
ejpam-4379	72	42	,	,	PUNCT
ejpam-4379	72	43	τ	τ	PROPN
ejpam-4379	72	44	⋆	⋆	VERB
ejpam-4379	72	45	)	)	PUNCT
ejpam-4379	72	46	is	be	AUX
ejpam-4379	72	47	not	not	PART
ejpam-4379	72	48	normal	normal	ADJ
ejpam-4379	72	49	and	and	CCONJ
ejpam-4379	72	50	this	this	PRON
ejpam-4379	72	51	is	be	AUX
ejpam-4379	72	52	a	a	DET
ejpam-4379	72	53	contradiction	contradiction	NOUN
ejpam-4379	72	54	.	.	PUNCT
ejpam-4379	73	1	theorem	theorem	NOUN
ejpam-4379	73	2	3	3	NUM
ejpam-4379	73	3	.	.	PUNCT
ejpam-4379	74	1	(	(	PUNCT
ejpam-4379	74	2	x	x	X
ejpam-4379	74	3	,	,	PUNCT
ejpam-4379	74	4	τ	τ	PROPN
ejpam-4379	74	5	)	)	PUNCT
ejpam-4379	74	6	is	be	AUX
ejpam-4379	74	7	compact	compact	ADJ
ejpam-4379	74	8	(	(	PUNCT
ejpam-4379	74	9	lindelöf	lindelöf	PROPN
ejpam-4379	74	10	,	,	PUNCT
ejpam-4379	74	11	countably	countably	ADV
ejpam-4379	74	12	compact	compact	ADJ
ejpam-4379	74	13	)	)	PUNCT
ejpam-4379	75	1	if	if	SCONJ
ejpam-4379	75	2	and	and	CCONJ
ejpam-4379	75	3	only	only	ADV
ejpam-4379	75	4	if	if	SCONJ
ejpam-4379	75	5	its	its	PRON
ejpam-4379	75	6	closed	closed	ADJ
ejpam-4379	75	7	extension	extension	NOUN
ejpam-4379	75	8	(	(	PUNCT
ejpam-4379	75	9	xp	xp	INTJ
ejpam-4379	75	10	,	,	PUNCT
ejpam-4379	75	11	τ	τ	PROPN
ejpam-4379	75	12	⋆	⋆	VERB
ejpam-4379	75	13	)	)	PUNCT
ejpam-4379	75	14	is	be	AUX
ejpam-4379	75	15	compact	compact	ADJ
ejpam-4379	75	16	(	(	PUNCT
ejpam-4379	75	17	lindelöf	lindelöf	PROPN
ejpam-4379	75	18	,	,	PUNCT
ejpam-4379	75	19	countably	countably	ADV
ejpam-4379	75	20	compact	compact	ADJ
ejpam-4379	75	21	)	)	PUNCT
ejpam-4379	75	22	.	.	PUNCT
ejpam-4379	76	1	proof	proof	NOUN
ejpam-4379	76	2	.	.	PUNCT
ejpam-4379	77	1	we	we	PRON
ejpam-4379	77	2	prove	prove	VERB
ejpam-4379	77	3	the	the	DET
ejpam-4379	77	4	compactness	compactness	NOUN
ejpam-4379	77	5	statement	statement	NOUN
ejpam-4379	77	6	and	and	CCONJ
ejpam-4379	77	7	the	the	DET
ejpam-4379	77	8	others	other	NOUN
ejpam-4379	77	9	are	be	AUX
ejpam-4379	77	10	similar	similar	ADJ
ejpam-4379	77	11	.	.	PUNCT
ejpam-4379	78	1	assume	assume	VERB
ejpam-4379	78	2	that	that	SCONJ
ejpam-4379	78	3	(	(	PUNCT
ejpam-4379	78	4	x	x	X
ejpam-4379	78	5	,	,	PUNCT
ejpam-4379	78	6	τ	τ	PROPN
ejpam-4379	78	7	)	)	PUNCT
ejpam-4379	78	8	is	be	AUX
ejpam-4379	78	9	compact	compact	ADJ
ejpam-4379	78	10	.	.	PUNCT
ejpam-4379	79	1	let	let	VERB
ejpam-4379	79	2	w	w	NOUN
ejpam-4379	79	3	=	=	PRON
ejpam-4379	79	4	{	{	PUNCT
ejpam-4379	79	5	wα	wα	NOUN
ejpam-4379	79	6	∈	∈	PROPN
ejpam-4379	79	7	τ	τ	X
ejpam-4379	79	8	⋆	⋆	NOUN
ejpam-4379	79	9	:	:	PUNCT
ejpam-4379	79	10	α	α	PROPN
ejpam-4379	79	11	∈	∈	PROPN
ejpam-4379	79	12	λ	λ	PROPN
ejpam-4379	79	13	}	}	PUNCT
ejpam-4379	79	14	be	be	AUX
ejpam-4379	79	15	any	any	DET
ejpam-4379	79	16	open	open	ADJ
ejpam-4379	79	17	cover	cover	NOUN
ejpam-4379	79	18	for	for	ADP
ejpam-4379	79	19	xp	xp	PROPN
ejpam-4379	79	20	.	.	PUNCT
ejpam-4379	80	1	for	for	ADP
ejpam-4379	80	2	each	each	DET
ejpam-4379	80	3	α	α	PROPN
ejpam-4379	80	4	∈	∈	PROPN
ejpam-4379	80	5	λ	λ	NOUN
ejpam-4379	80	6	,	,	PUNCT
ejpam-4379	80	7	there	there	PRON
ejpam-4379	80	8	exists	exist	VERB
ejpam-4379	80	9	uα	uα	PROPN
ejpam-4379	80	10	∈	∈	PROPN
ejpam-4379	80	11	τ	τ	X
ejpam-4379	80	12	such	such	ADJ
ejpam-4379	80	13	that	that	DET
ejpam-4379	80	14	wα	wα	NOUN
ejpam-4379	81	1	=	=	PRON
ejpam-4379	81	2	uα	uα	PROPN
ejpam-4379	81	3	∪	∪	X
ejpam-4379	81	4	{	{	PUNCT
ejpam-4379	81	5	p	p	NOUN
ejpam-4379	81	6	}	}	PUNCT
ejpam-4379	81	7	.	.	PUNCT
ejpam-4379	82	1	then	then	ADV
ejpam-4379	82	2	the	the	DET
ejpam-4379	82	3	family	family	NOUN
ejpam-4379	82	4	{	{	PUNCT
ejpam-4379	82	5	uα	uα	X
ejpam-4379	82	6	:	:	PUNCT
ejpam-4379	82	7	α	α	PROPN
ejpam-4379	82	8	∈	∈	PROPN
ejpam-4379	82	9	λ	λ	PROPN
ejpam-4379	82	10	}	}	PUNCT
ejpam-4379	82	11	is	be	AUX
ejpam-4379	82	12	an	an	DET
ejpam-4379	82	13	open	open	ADJ
ejpam-4379	82	14	cover	cover	NOUN
ejpam-4379	82	15	for	for	ADP
ejpam-4379	82	16	x.	x.	NOUN
ejpam-4379	82	17	by	by	ADP
ejpam-4379	82	18	the	the	DET
ejpam-4379	82	19	hypothesis	hypothesis	NOUN
ejpam-4379	82	20	,	,	PUNCT
ejpam-4379	82	21	there	there	PRON
ejpam-4379	82	22	are	be	VERB
ejpam-4379	82	23	α1	α1	PROPN
ejpam-4379	82	24	,	,	PUNCT
ejpam-4379	82	25	...	...	PUNCT
ejpam-4379	82	26	,	,	PUNCT
ejpam-4379	82	27	αn	αn	X
ejpam-4379	82	28	∈	∈	PROPN
ejpam-4379	82	29	λ	λ	NOUN
ejpam-4379	82	30	,	,	PUNCT
ejpam-4379	82	31	where	where	SCONJ
ejpam-4379	82	32	n	n	X
ejpam-4379	82	33	∈	∈	PROPN
ejpam-4379	82	34	n	n	CCONJ
ejpam-4379	82	35	,	,	PUNCT
ejpam-4379	82	36	such	such	ADJ
ejpam-4379	82	37	that	that	SCONJ
ejpam-4379	82	38	x	x	PROPN
ejpam-4379	82	39	⊆	⊆	NUM
ejpam-4379	82	40	⋃n	⋃n	NOUN
ejpam-4379	82	41	i=1	i=1	PROPN
ejpam-4379	82	42	uαi	uαi	PROPN
ejpam-4379	82	43	.	.	PUNCT
ejpam-4379	83	1	then	then	ADV
ejpam-4379	83	2	{	{	PUNCT
ejpam-4379	83	3	wα1	wα1	NOUN
ejpam-4379	83	4	,	,	PUNCT
ejpam-4379	83	5	...	...	PUNCT
ejpam-4379	83	6	,	,	PUNCT
ejpam-4379	83	7	wαn	wαn	AUX
ejpam-4379	83	8	}	}	PUNCT
ejpam-4379	83	9	is	be	AUX
ejpam-4379	83	10	a	a	DET
ejpam-4379	83	11	finite	finite	ADJ
ejpam-4379	83	12	subcover	subcover	NOUN
ejpam-4379	83	13	for	for	ADP
ejpam-4379	83	14	xp	xp	PROPN
ejpam-4379	83	15	of	of	ADP
ejpam-4379	83	16	w.	w.	PROPN
ejpam-4379	83	17	now	now	ADV
ejpam-4379	83	18	,	,	PUNCT
ejpam-4379	83	19	assume	assume	VERB
ejpam-4379	83	20	that	that	SCONJ
ejpam-4379	83	21	(	(	PUNCT
ejpam-4379	83	22	xp	xp	INTJ
ejpam-4379	83	23	,	,	PUNCT
ejpam-4379	83	24	τ	τ	PROPN
ejpam-4379	83	25	⋆	⋆	VERB
ejpam-4379	83	26	)	)	PUNCT
ejpam-4379	83	27	is	be	AUX
ejpam-4379	83	28	compact	compact	ADJ
ejpam-4379	83	29	.	.	PUNCT
ejpam-4379	84	1	let	let	VERB
ejpam-4379	84	2	v	v	NOUN
ejpam-4379	84	3	=	=	PUNCT
ejpam-4379	84	4	{	{	PUNCT
ejpam-4379	84	5	vα	vα	INTJ
ejpam-4379	84	6	∈	∈	PROPN
ejpam-4379	84	7	τ	τ	X
ejpam-4379	84	8	:	:	PUNCT
ejpam-4379	84	9	α	α	PROPN
ejpam-4379	84	10	∈	∈	PROPN
ejpam-4379	84	11	λ	λ	PROPN
ejpam-4379	84	12	}	}	PUNCT
ejpam-4379	84	13	be	be	AUX
ejpam-4379	84	14	any	any	DET
ejpam-4379	84	15	open	open	ADJ
ejpam-4379	84	16	cover	cover	NOUN
ejpam-4379	84	17	for	for	ADP
ejpam-4379	84	18	(	(	PUNCT
ejpam-4379	84	19	x	x	INTJ
ejpam-4379	84	20	,	,	PUNCT
ejpam-4379	84	21	τ	τ	PROPN
ejpam-4379	84	22	)	)	PUNCT
ejpam-4379	84	23	.	.	PUNCT
ejpam-4379	85	1	then	then	ADV
ejpam-4379	85	2	the	the	DET
ejpam-4379	85	3	family	family	NOUN
ejpam-4379	85	4	{	{	PUNCT
ejpam-4379	85	5	vα	vα	ADP
ejpam-4379	85	6	∪	∪	X
ejpam-4379	85	7	{	{	PUNCT
ejpam-4379	85	8	p	p	NOUN
ejpam-4379	85	9	}	}	PUNCT
ejpam-4379	85	10	:	:	PUNCT
ejpam-4379	85	11	α	α	NUM
ejpam-4379	85	12	∈	∈	PROPN
ejpam-4379	85	13	λ	λ	PROPN
ejpam-4379	85	14	}	}	PUNCT
ejpam-4379	85	15	is	be	AUX
ejpam-4379	85	16	an	an	DET
ejpam-4379	85	17	open	open	ADJ
ejpam-4379	85	18	cover	cover	NOUN
ejpam-4379	85	19	for	for	ADP
ejpam-4379	85	20	xp	xp	INTJ
ejpam-4379	85	21	because	because	SCONJ
ejpam-4379	85	22	vα	vα	PRON
ejpam-4379	85	23	∪	∪	VERB
ejpam-4379	85	24	{	{	PUNCT
ejpam-4379	85	25	p	p	NOUN
ejpam-4379	85	26	}	}	PUNCT
ejpam-4379	85	27	∈	∈	PROPN
ejpam-4379	85	28	τ	τ	X
ejpam-4379	85	29	⋆	⋆	VERB
ejpam-4379	85	30	for	for	ADP
ejpam-4379	85	31	each	each	DET
ejpam-4379	85	32	α	α	PRON
ejpam-4379	85	33	∈	∈	PROPN
ejpam-4379	85	34	λ	λ	PROPN
ejpam-4379	85	35	.	.	PUNCT
ejpam-4379	86	1	by	by	ADP
ejpam-4379	86	2	the	the	DET
ejpam-4379	86	3	hypothesis	hypothesis	NOUN
ejpam-4379	86	4	,	,	PUNCT
ejpam-4379	86	5	there	there	PRON
ejpam-4379	86	6	are	be	VERB
ejpam-4379	86	7	α1	α1	PROPN
ejpam-4379	86	8	,	,	PUNCT
ejpam-4379	86	9	...	...	PUNCT
ejpam-4379	86	10	,	,	PUNCT
ejpam-4379	86	11	αm	αm	PROPN
ejpam-4379	86	12	∈	∈	PROPN
ejpam-4379	86	13	λ	λ	PROPN
ejpam-4379	86	14	,	,	PUNCT
ejpam-4379	86	15	where	where	SCONJ
ejpam-4379	86	16	m	m	VERB
ejpam-4379	86	17	∈	∈	PROPN
ejpam-4379	86	18	n	n	CCONJ
ejpam-4379	86	19	,	,	PUNCT
ejpam-4379	86	20	such	such	ADJ
ejpam-4379	86	21	that	that	SCONJ
ejpam-4379	86	22	xp	xp	PROPN
ejpam-4379	86	23	⊆	⊆	NUM
ejpam-4379	86	24	⋃n	⋃n	NOUN
ejpam-4379	86	25	i=1(vαi	i=1(vαi	ADJ
ejpam-4379	86	26	∪	∪	X
ejpam-4379	86	27	{	{	PUNCT
ejpam-4379	86	28	p	p	NOUN
ejpam-4379	86	29	}	}	PUNCT
ejpam-4379	86	30	)	)	PUNCT
ejpam-4379	86	31	.	.	PUNCT
ejpam-4379	87	1	then	then	ADV
ejpam-4379	87	2	{	{	PUNCT
ejpam-4379	87	3	vα1	vα1	NOUN
ejpam-4379	87	4	,	,	PUNCT
ejpam-4379	87	5	...	...	PUNCT
ejpam-4379	87	6	,	,	PUNCT
ejpam-4379	87	7	vαn	vαn	NOUN
ejpam-4379	87	8	}	}	PUNCT
ejpam-4379	87	9	is	be	AUX
ejpam-4379	87	10	a	a	DET
ejpam-4379	87	11	finite	finite	ADJ
ejpam-4379	87	12	subcover	subcover	NOUN
ejpam-4379	87	13	for	for	ADP
ejpam-4379	87	14	x	x	PROPN
ejpam-4379	87	15	of	of	ADP
ejpam-4379	87	16	v.	v.	X
ejpam-4379	87	17	observe	observe	VERB
ejpam-4379	87	18	that	that	SCONJ
ejpam-4379	87	19	the	the	DET
ejpam-4379	87	20	closed	closed	ADJ
ejpam-4379	87	21	extension	extension	NOUN
ejpam-4379	87	22	(	(	PUNCT
ejpam-4379	87	23	xp	xp	INTJ
ejpam-4379	87	24	,	,	PUNCT
ejpam-4379	87	25	τ	τ	PROPN
ejpam-4379	87	26	⋆	⋆	VERB
ejpam-4379	87	27	)	)	PUNCT
ejpam-4379	87	28	is	be	AUX
ejpam-4379	87	29	not	not	PART
ejpam-4379	87	30	locally	locally	ADV
ejpam-4379	87	31	compact	compact	ADJ
ejpam-4379	87	32	even	even	ADV
ejpam-4379	87	33	if	if	SCONJ
ejpam-4379	87	34	(	(	PUNCT
ejpam-4379	87	35	x	x	X
ejpam-4379	87	36	,	,	PUNCT
ejpam-4379	87	37	τ	τ	PROPN
ejpam-4379	87	38	)	)	PUNCT
ejpam-4379	87	39	is	be	AUX
ejpam-4379	87	40	because	because	SCONJ
ejpam-4379	87	41	(	(	PUNCT
ejpam-4379	87	42	xp	xp	INTJ
ejpam-4379	87	43	,	,	PUNCT
ejpam-4379	87	44	τ	τ	PROPN
ejpam-4379	87	45	⋆	⋆	VERB
ejpam-4379	87	46	)	)	PUNCT
ejpam-4379	87	47	is	be	AUX
ejpam-4379	87	48	not	not	PART
ejpam-4379	87	49	regular	regular	ADJ
ejpam-4379	87	50	.	.	PUNCT
ejpam-4379	88	1	since	since	SCONJ
ejpam-4379	88	2	any	any	DET
ejpam-4379	88	3	hyper	hyper	ADJ
ejpam-4379	88	4	-	-	ADJ
ejpam-4379	88	5	connected	connected	ADJ
ejpam-4379	88	6	space	space	NOUN
ejpam-4379	88	7	is	be	AUX
ejpam-4379	88	8	connected	connect	VERB
ejpam-4379	88	9	,	,	PUNCT
ejpam-4379	88	10	[	[	X
ejpam-4379	88	11	15	15	NUM
ejpam-4379	88	12	]	]	PUNCT
ejpam-4379	88	13	,	,	PUNCT
ejpam-4379	88	14	and	and	CCONJ
ejpam-4379	88	15	the	the	DET
ejpam-4379	88	16	closed	closed	ADJ
ejpam-4379	88	17	extension	extension	NOUN
ejpam-4379	88	18	space	space	NOUN
ejpam-4379	88	19	(	(	PUNCT
ejpam-4379	88	20	xp	xp	INTJ
ejpam-4379	88	21	,	,	PUNCT
ejpam-4379	88	22	τ	τ	PROPN
ejpam-4379	88	23	⋆	⋆	VERB
ejpam-4379	88	24	)	)	PUNCT
ejpam-4379	88	25	is	be	AUX
ejpam-4379	88	26	always	always	ADV
ejpam-4379	88	27	hyper	hyper	ADJ
ejpam-4379	88	28	-	-	VERB
ejpam-4379	88	29	connected	connected	ADJ
ejpam-4379	88	30	,	,	PUNCT
ejpam-4379	88	31	see	see	VERB
ejpam-4379	88	32	remark	remark	NOUN
ejpam-4379	88	33	1	1	NUM
ejpam-4379	88	34	,	,	PUNCT
ejpam-4379	88	35	we	we	PRON
ejpam-4379	88	36	conclude	conclude	VERB
ejpam-4379	88	37	that	that	SCONJ
ejpam-4379	88	38	the	the	DET
ejpam-4379	88	39	closed	closed	ADJ
ejpam-4379	88	40	extension	extension	NOUN
ejpam-4379	88	41	space	space	NOUN
ejpam-4379	88	42	(	(	PUNCT
ejpam-4379	88	43	xp	xp	INTJ
ejpam-4379	88	44	,	,	PUNCT
ejpam-4379	88	45	τ	τ	PROPN
ejpam-4379	88	46	⋆	⋆	VERB
ejpam-4379	88	47	)	)	PUNCT
ejpam-4379	88	48	is	be	AUX
ejpam-4379	88	49	always	always	ADV
ejpam-4379	88	50	connected	connect	VERB
ejpam-4379	88	51	even	even	ADV
ejpam-4379	88	52	if	if	SCONJ
ejpam-4379	88	53	(	(	PUNCT
ejpam-4379	88	54	x	x	X
ejpam-4379	88	55	,	,	PUNCT
ejpam-4379	88	56	τ	τ	PROPN
ejpam-4379	88	57	)	)	PUNCT
ejpam-4379	88	58	is	be	AUX
ejpam-4379	88	59	disconnected	disconnect	VERB
ejpam-4379	88	60	.	.	PUNCT
ejpam-4379	89	1	2	2	X
ejpam-4379	89	2	.	.	NUM
ejpam-4379	89	3	closed	close	VERB
ejpam-4379	89	4	extension	extension	NOUN
ejpam-4379	89	5	and	and	CCONJ
ejpam-4379	89	6	weaker	weak	ADJ
ejpam-4379	89	7	versions	version	NOUN
ejpam-4379	89	8	of	of	ADP
ejpam-4379	89	9	normality	normality	NOUN
ejpam-4379	89	10	.	.	PUNCT
ejpam-4379	90	1	we	we	PRON
ejpam-4379	90	2	begin	begin	VERB
ejpam-4379	90	3	by	by	ADP
ejpam-4379	90	4	recalling	recall	VERB
ejpam-4379	90	5	some	some	DET
ejpam-4379	90	6	definitions	definition	NOUN
ejpam-4379	90	7	.	.	PUNCT
ejpam-4379	91	1	definition	definition	NOUN
ejpam-4379	91	2	2	2	NUM
ejpam-4379	91	3	.	.	PUNCT
ejpam-4379	92	1	a	a	DET
ejpam-4379	92	2	topological	topological	ADJ
ejpam-4379	92	3	space	space	NOUN
ejpam-4379	92	4	x	x	PUNCT
ejpam-4379	92	5	is	be	AUX
ejpam-4379	92	6	called	call	VERB
ejpam-4379	92	7	c	c	NOUN
ejpam-4379	92	8	-	-	NOUN
ejpam-4379	92	9	normal	normal	ADJ
ejpam-4379	92	10	if	if	SCONJ
ejpam-4379	92	11	there	there	PRON
ejpam-4379	92	12	exist	exist	VERB
ejpam-4379	92	13	a	a	DET
ejpam-4379	92	14	normal	normal	ADJ
ejpam-4379	92	15	space	space	NOUN
ejpam-4379	92	16	y	y	PROPN
ejpam-4379	92	17	and	and	CCONJ
ejpam-4379	92	18	a	a	DET
ejpam-4379	92	19	bijective	bijective	ADJ
ejpam-4379	92	20	function	function	NOUN
ejpam-4379	93	1	f	f	NOUN
ejpam-4379	93	2	:	:	PUNCT
ejpam-4379	93	3	x	x	PUNCT
ejpam-4379	93	4	−→	−→	NOUN
ejpam-4379	93	5	y	y	PROPN
ejpam-4379	93	6	such	such	ADJ
ejpam-4379	93	7	that	that	SCONJ
ejpam-4379	93	8	the	the	DET
ejpam-4379	93	9	restriction	restriction	NOUN
ejpam-4379	93	10	f|a	f|a	PUNCT
ejpam-4379	93	11	:	:	PUNCT
ejpam-4379	93	12	a	a	DET
ejpam-4379	93	13	−→	−→	NOUN
ejpam-4379	93	14	f(a	f(a	NOUN
ejpam-4379	93	15	)	)	PUNCT
ejpam-4379	93	16	is	be	AUX
ejpam-4379	93	17	a	a	DET
ejpam-4379	93	18	homeomorphism	homeomorphism	NOUN
ejpam-4379	93	19	for	for	ADP
ejpam-4379	93	20	each	each	DET
ejpam-4379	93	21	compact	compact	ADJ
ejpam-4379	93	22	subspace	subspace	NOUN
ejpam-4379	93	23	a	a	DET
ejpam-4379	93	24	⊆	⊆	NUM
ejpam-4379	93	25	x	x	SYM
ejpam-4379	93	26	,	,	PUNCT
ejpam-4379	93	27	[	[	X
ejpam-4379	93	28	1	1	NUM
ejpam-4379	93	29	]	]	PUNCT
ejpam-4379	93	30	.	.	PUNCT
ejpam-4379	94	1	x	x	PRON
ejpam-4379	94	2	is	be	AUX
ejpam-4379	94	3	called	call	VERB
ejpam-4379	94	4	cc	cc	NOUN
ejpam-4379	94	5	-	-	NOUN
ejpam-4379	94	6	normal	normal	ADJ
ejpam-4379	94	7	if	if	SCONJ
ejpam-4379	94	8	there	there	PRON
ejpam-4379	94	9	exist	exist	VERB
ejpam-4379	94	10	a	a	DET
ejpam-4379	94	11	normal	normal	ADJ
ejpam-4379	94	12	space	space	NOUN
ejpam-4379	94	13	y	y	PROPN
ejpam-4379	94	14	and	and	CCONJ
ejpam-4379	94	15	a	a	DET
ejpam-4379	94	16	bijective	bijective	ADJ
ejpam-4379	94	17	function	function	NOUN
ejpam-4379	95	1	f	f	NOUN
ejpam-4379	95	2	:	:	PUNCT
ejpam-4379	95	3	x	x	PUNCT
ejpam-4379	95	4	−→	−→	NOUN
ejpam-4379	95	5	y	y	PROPN
ejpam-4379	95	6	such	such	ADJ
ejpam-4379	95	7	that	that	SCONJ
ejpam-4379	95	8	the	the	DET
ejpam-4379	95	9	restriction	restriction	NOUN
ejpam-4379	95	10	f|a	f|a	PUNCT
ejpam-4379	95	11	:	:	PUNCT
ejpam-4379	95	12	a	a	DET
ejpam-4379	95	13	−→	−→	NOUN
ejpam-4379	95	14	f(a	f(a	NOUN
ejpam-4379	95	15	)	)	PUNCT
ejpam-4379	95	16	is	be	AUX
ejpam-4379	95	17	a	a	DET
ejpam-4379	95	18	homeomorphism	homeomorphism	NOUN
ejpam-4379	95	19	for	for	ADP
ejpam-4379	95	20	each	each	DET
ejpam-4379	95	21	countably	countably	ADV
ejpam-4379	95	22	compact	compact	ADJ
ejpam-4379	95	23	subspace	subspace	NOUN
ejpam-4379	95	24	a	a	DET
ejpam-4379	95	25	⊆	⊆	NUM
ejpam-4379	95	26	x	x	SYM
ejpam-4379	95	27	,	,	PUNCT
ejpam-4379	95	28	[	[	X
ejpam-4379	95	29	6	6	NUM
ejpam-4379	95	30	]	]	PUNCT
ejpam-4379	95	31	.	.	PUNCT
ejpam-4379	96	1	x	x	PRON
ejpam-4379	96	2	is	be	AUX
ejpam-4379	96	3	called	call	VERB
ejpam-4379	96	4	l	l	NOUN
ejpam-4379	96	5	-	-	ADJ
ejpam-4379	96	6	normal	normal	ADJ
ejpam-4379	96	7	if	if	SCONJ
ejpam-4379	96	8	there	there	PRON
ejpam-4379	96	9	exist	exist	VERB
ejpam-4379	96	10	a	a	DET
ejpam-4379	96	11	normal	normal	ADJ
ejpam-4379	96	12	space	space	NOUN
ejpam-4379	96	13	y	y	PROPN
ejpam-4379	96	14	and	and	CCONJ
ejpam-4379	96	15	a	a	DET
ejpam-4379	96	16	bijective	bijective	ADJ
ejpam-4379	96	17	function	function	NOUN
ejpam-4379	97	1	f	f	NOUN
ejpam-4379	97	2	:	:	PUNCT
ejpam-4379	97	3	x	x	PUNCT
ejpam-4379	97	4	−→	−→	NOUN
ejpam-4379	97	5	y	y	PROPN
ejpam-4379	97	6	such	such	ADJ
ejpam-4379	97	7	that	that	SCONJ
ejpam-4379	97	8	the	the	DET
ejpam-4379	97	9	restriction	restriction	NOUN
ejpam-4379	97	10	f|a	f|a	PUNCT
ejpam-4379	97	11	:	:	PUNCT
ejpam-4379	97	12	a	a	DET
ejpam-4379	97	13	−→	−→	NOUN
ejpam-4379	97	14	f(a	f(a	NOUN
ejpam-4379	97	15	)	)	PUNCT
ejpam-4379	97	16	is	be	AUX
ejpam-4379	97	17	a	a	DET
ejpam-4379	97	18	homeomorphism	homeomorphism	NOUN
ejpam-4379	97	19	for	for	SCONJ
ejpam-4379	97	20	each	each	DET
ejpam-4379	97	21	lindelöf	lindelöf	NOUN
ejpam-4379	97	22	subspace	subspace	VERB
ejpam-4379	97	23	a	a	DET
ejpam-4379	97	24	⊆	⊆	NUM
ejpam-4379	97	25	x	x	SYM
ejpam-4379	97	26	,	,	PUNCT
ejpam-4379	97	27	[	[	X
ejpam-4379	97	28	10	10	NUM
ejpam-4379	97	29	]	]	PUNCT
ejpam-4379	97	30	.	.	PUNCT
ejpam-4379	98	1	x	x	PUNCT
ejpam-4379	98	2	is	be	AUX
ejpam-4379	98	3	called	call	VERB
ejpam-4379	98	4	p	p	NOUN
ejpam-4379	98	5	-normal	-normal	ADJ
ejpam-4379	98	6	if	if	SCONJ
ejpam-4379	98	7	there	there	PRON
ejpam-4379	98	8	exist	exist	VERB
ejpam-4379	98	9	a	a	DET
ejpam-4379	98	10	normal	normal	ADJ
ejpam-4379	98	11	space	space	NOUN
ejpam-4379	98	12	y	y	PROPN
ejpam-4379	98	13	and	and	CCONJ
ejpam-4379	98	14	a	a	DET
ejpam-4379	98	15	bijective	bijective	ADJ
ejpam-4379	98	16	function	function	NOUN
ejpam-4379	98	17	f	f	NOUN
ejpam-4379	99	1	:	:	PUNCT
ejpam-4379	99	2	x	x	PUNCT
ejpam-4379	99	3	−→	−→	NOUN
ejpam-4379	99	4	y	y	PROPN
ejpam-4379	99	5	such	such	ADJ
ejpam-4379	99	6	that	that	SCONJ
ejpam-4379	99	7	the	the	DET
ejpam-4379	99	8	restriction	restriction	NOUN
ejpam-4379	99	9	f|a	f|a	PUNCT
ejpam-4379	99	10	:	:	PUNCT
ejpam-4379	99	11	a	a	DET
ejpam-4379	99	12	−→	−→	NOUN
ejpam-4379	99	13	f(a	f(a	NOUN
ejpam-4379	99	14	)	)	PUNCT
ejpam-4379	99	15	is	be	AUX
ejpam-4379	99	16	a	a	DET
ejpam-4379	99	17	homeomorphism	homeomorphism	NOUN
ejpam-4379	99	18	for	for	ADP
ejpam-4379	99	19	each	each	DET
ejpam-4379	99	20	paracompact	paracompact	ADJ
ejpam-4379	99	21	subspace	subspace	NOUN
ejpam-4379	99	22	a	a	DET
ejpam-4379	99	23	⊆	⊆	NUM
ejpam-4379	99	24	x	x	SYM
ejpam-4379	99	25	,	,	PUNCT
ejpam-4379	99	26	[	[	X
ejpam-4379	99	27	9	9	NUM
ejpam-4379	99	28	]	]	PUNCT
ejpam-4379	99	29	.	.	PUNCT
ejpam-4379	100	1	x	x	PRON
ejpam-4379	100	2	is	be	AUX
ejpam-4379	100	3	called	call	VERB
ejpam-4379	100	4	s	s	NOUN
ejpam-4379	100	5	-	-	NOUN
ejpam-4379	100	6	normal	normal	ADJ
ejpam-4379	100	7	if	if	SCONJ
ejpam-4379	100	8	there	there	PRON
ejpam-4379	100	9	exist	exist	VERB
ejpam-4379	100	10	a	a	DET
ejpam-4379	100	11	normal	normal	ADJ
ejpam-4379	100	12	space	space	NOUN
ejpam-4379	100	13	d.	d.	PROPN
ejpam-4379	100	14	abuzaid	abuzaid	PROPN
ejpam-4379	100	15	,	,	PUNCT
ejpam-4379	100	16	s.	s.	PROPN
ejpam-4379	100	17	al	al	PROPN
ejpam-4379	100	18	-	-	PROPN
ejpam-4379	100	19	qarhi	qarhi	PROPN
ejpam-4379	100	20	,	,	PUNCT
ejpam-4379	100	21	l.	l.	PROPN
ejpam-4379	100	22	kalantan	kalantan	PROPN
ejpam-4379	100	23	/	/	SYM
ejpam-4379	100	24	eur	eur	PROPN
ejpam-4379	100	25	.	.	PUNCT
ejpam-4379	101	1	j.	j.	PROPN
ejpam-4379	101	2	pure	pure	PROPN
ejpam-4379	101	3	appl	appl	PROPN
ejpam-4379	101	4	.	.	PROPN
ejpam-4379	101	5	math	math	PROPN
ejpam-4379	101	6	,	,	PUNCT
ejpam-4379	101	7	15	15	NUM
ejpam-4379	101	8	(	(	PUNCT
ejpam-4379	101	9	2	2	NUM
ejpam-4379	101	10	)	)	PUNCT
ejpam-4379	101	11	(	(	PUNCT
ejpam-4379	101	12	2022	2022	NUM
ejpam-4379	101	13	)	)	PUNCT
ejpam-4379	101	14	,	,	PUNCT
ejpam-4379	101	15	672	672	NUM
ejpam-4379	101	16	-	-	SYM
ejpam-4379	101	17	680	680	NUM
ejpam-4379	101	18	675	675	NUM
ejpam-4379	101	19	y	y	NOUN
ejpam-4379	101	20	and	and	CCONJ
ejpam-4379	101	21	a	a	DET
ejpam-4379	101	22	bijective	bijective	ADJ
ejpam-4379	101	23	function	function	NOUN
ejpam-4379	101	24	f	f	NOUN
ejpam-4379	101	25	:	:	PUNCT
ejpam-4379	101	26	x	x	PUNCT
ejpam-4379	102	1	−→	−→	NOUN
ejpam-4379	102	2	y	y	PROPN
ejpam-4379	102	3	such	such	ADJ
ejpam-4379	102	4	that	that	SCONJ
ejpam-4379	102	5	the	the	DET
ejpam-4379	102	6	restriction	restriction	NOUN
ejpam-4379	102	7	f|a	f|a	PUNCT
ejpam-4379	102	8	:	:	PUNCT
ejpam-4379	102	9	a	a	DET
ejpam-4379	102	10	−→	−→	NOUN
ejpam-4379	102	11	f(a	f(a	NOUN
ejpam-4379	102	12	)	)	PUNCT
ejpam-4379	102	13	is	be	AUX
ejpam-4379	102	14	a	a	DET
ejpam-4379	102	15	homeomorphism	homeomorphism	NOUN
ejpam-4379	102	16	for	for	ADP
ejpam-4379	102	17	each	each	DET
ejpam-4379	102	18	separable	separable	ADJ
ejpam-4379	102	19	subspace	subspace	NOUN
ejpam-4379	102	20	a	a	DET
ejpam-4379	102	21	⊆	⊆	NUM
ejpam-4379	102	22	x	x	SYM
ejpam-4379	102	23	,	,	PUNCT
ejpam-4379	102	24	[	[	X
ejpam-4379	102	25	7	7	NUM
ejpam-4379	102	26	]	]	PUNCT
ejpam-4379	102	27	.	.	PUNCT
ejpam-4379	103	1	since	since	SCONJ
ejpam-4379	103	2	characterizing	characterize	VERB
ejpam-4379	103	3	all	all	DET
ejpam-4379	103	4	compact	compact	ADJ
ejpam-4379	103	5	subspaces	subspace	NOUN
ejpam-4379	103	6	[	[	X
ejpam-4379	103	7	1	1	NUM
ejpam-4379	103	8	]	]	PUNCT
ejpam-4379	103	9	(	(	PUNCT
ejpam-4379	103	10	all	all	DET
ejpam-4379	103	11	countably	countably	ADV
ejpam-4379	103	12	compact	compact	ADJ
ejpam-4379	103	13	subspaces	subspace	NOUN
ejpam-4379	103	14	[	[	X
ejpam-4379	103	15	6	6	NUM
ejpam-4379	103	16	]	]	PUNCT
ejpam-4379	103	17	,	,	PUNCT
ejpam-4379	103	18	all	all	DET
ejpam-4379	103	19	lindelöf	lindelöf	NOUN
ejpam-4379	103	20	subspaces	subspace	VERB
ejpam-4379	103	21	[	[	X
ejpam-4379	103	22	10	10	NUM
ejpam-4379	103	23	]	]	PUNCT
ejpam-4379	103	24	,	,	PUNCT
ejpam-4379	103	25	all	all	DET
ejpam-4379	103	26	paracompact	paracompact	ADJ
ejpam-4379	103	27	subspaces	subspace	NOUN
ejpam-4379	103	28	[	[	X
ejpam-4379	103	29	9	9	NUM
ejpam-4379	103	30	]	]	PUNCT
ejpam-4379	103	31	)	)	PUNCT
ejpam-4379	103	32	is	be	AUX
ejpam-4379	103	33	a	a	DET
ejpam-4379	103	34	core	core	NOUN
ejpam-4379	103	35	subject	subject	NOUN
ejpam-4379	103	36	in	in	ADP
ejpam-4379	103	37	the	the	DET
ejpam-4379	103	38	notion	notion	NOUN
ejpam-4379	103	39	of	of	ADP
ejpam-4379	103	40	c	c	NOUN
ejpam-4379	103	41	-	-	PUNCT
ejpam-4379	103	42	normality	normality	NOUN
ejpam-4379	103	43	(	(	PUNCT
ejpam-4379	103	44	cc	cc	NOUN
ejpam-4379	103	45	-	-	NOUN
ejpam-4379	103	46	normality	normality	ADJ
ejpam-4379	103	47	,	,	PUNCT
ejpam-4379	103	48	l	l	NOUN
ejpam-4379	103	49	-	-	NOUN
ejpam-4379	103	50	normality	normality	NOUN
ejpam-4379	103	51	,	,	PUNCT
ejpam-4379	103	52	p	p	NOUN
ejpam-4379	103	53	-normality	-normality	NOUN
ejpam-4379	103	54	)	)	PUNCT
ejpam-4379	103	55	,	,	PUNCT
ejpam-4379	103	56	we	we	PRON
ejpam-4379	103	57	will	will	AUX
ejpam-4379	103	58	start	start	VERB
ejpam-4379	103	59	with	with	ADP
ejpam-4379	103	60	characterizing	characterize	VERB
ejpam-4379	103	61	all	all	DET
ejpam-4379	103	62	compact	compact	ADJ
ejpam-4379	103	63	subspaces	subspace	NOUN
ejpam-4379	103	64	of	of	ADP
ejpam-4379	103	65	the	the	DET
ejpam-4379	103	66	closed	closed	ADJ
ejpam-4379	103	67	extension	extension	NOUN
ejpam-4379	103	68	space	space	NOUN
ejpam-4379	103	69	(	(	PUNCT
ejpam-4379	103	70	xp	xp	INTJ
ejpam-4379	103	71	,	,	PUNCT
ejpam-4379	103	72	τ	τ	PROPN
ejpam-4379	103	73	⋆	⋆	NOUN
ejpam-4379	103	74	)	)	PUNCT
ejpam-4379	103	75	of	of	ADP
ejpam-4379	103	76	a	a	DET
ejpam-4379	103	77	given	give	VERB
ejpam-4379	103	78	space	space	NOUN
ejpam-4379	103	79	(	(	PUNCT
ejpam-4379	103	80	x	x	X
ejpam-4379	103	81	,	,	PUNCT
ejpam-4379	103	82	τ	τ	PROPN
ejpam-4379	103	83	)	)	PUNCT
ejpam-4379	103	84	.	.	PUNCT
ejpam-4379	104	1	proposition	proposition	NOUN
ejpam-4379	104	2	1	1	NUM
ejpam-4379	104	3	.	.	PUNCT
ejpam-4379	105	1	let	let	AUX
ejpam-4379	105	2	(	(	PUNCT
ejpam-4379	105	3	x	x	X
ejpam-4379	105	4	,	,	PUNCT
ejpam-4379	105	5	τ	τ	PROPN
ejpam-4379	105	6	)	)	PUNCT
ejpam-4379	105	7	be	be	AUX
ejpam-4379	105	8	a	a	DET
ejpam-4379	105	9	topological	topological	ADJ
ejpam-4379	105	10	space	space	NOUN
ejpam-4379	105	11	.	.	PUNCT
ejpam-4379	106	1	consider	consider	VERB
ejpam-4379	106	2	the	the	DET
ejpam-4379	106	3	closed	closed	ADJ
ejpam-4379	106	4	extension	extension	NOUN
ejpam-4379	106	5	space	space	NOUN
ejpam-4379	106	6	(	(	PUNCT
ejpam-4379	106	7	xp	xp	INTJ
ejpam-4379	106	8	,	,	PUNCT
ejpam-4379	106	9	τ	τ	PROPN
ejpam-4379	106	10	⋆	⋆	NOUN
ejpam-4379	106	11	)	)	PUNCT
ejpam-4379	106	12	of	of	ADP
ejpam-4379	106	13	(	(	PUNCT
ejpam-4379	106	14	x	x	INTJ
ejpam-4379	106	15	,	,	PUNCT
ejpam-4379	106	16	τ	τ	PROPN
ejpam-4379	106	17	)	)	PUNCT
ejpam-4379	106	18	.	.	PUNCT
ejpam-4379	107	1	let	let	VERB
ejpam-4379	107	2	a	a	DET
ejpam-4379	107	3	⊆	⊆	NUM
ejpam-4379	107	4	xp	xp	NOUN
ejpam-4379	107	5	.	.	PUNCT
ejpam-4379	108	1	a	a	PRON
ejpam-4379	108	2	is	be	AUX
ejpam-4379	108	3	compact	compact	ADJ
ejpam-4379	108	4	in	in	ADP
ejpam-4379	108	5	(	(	PUNCT
ejpam-4379	108	6	xp	xp	INTJ
ejpam-4379	108	7	,	,	PUNCT
ejpam-4379	108	8	τ	τ	PROPN
ejpam-4379	108	9	⋆	⋆	NOUN
ejpam-4379	108	10	)	)	PUNCT
ejpam-4379	108	11	if	if	SCONJ
ejpam-4379	109	1	and	and	CCONJ
ejpam-4379	109	2	only	only	ADV
ejpam-4379	109	3	if	if	SCONJ
ejpam-4379	109	4	a	a	DET
ejpam-4379	109	5	\	\	NOUN
ejpam-4379	109	6	{	{	PUNCT
ejpam-4379	109	7	p	p	NOUN
ejpam-4379	109	8	}	}	PUNCT
ejpam-4379	109	9	is	be	AUX
ejpam-4379	109	10	compact	compact	ADJ
ejpam-4379	109	11	in	in	ADP
ejpam-4379	109	12	(	(	PUNCT
ejpam-4379	109	13	x	x	INTJ
ejpam-4379	109	14	,	,	PUNCT
ejpam-4379	109	15	τ	τ	PROPN
ejpam-4379	109	16	)	)	PUNCT
ejpam-4379	109	17	.	.	PUNCT
ejpam-4379	110	1	proof	proof	NOUN
ejpam-4379	110	2	.	.	PUNCT
ejpam-4379	111	1	assume	assume	VERB
ejpam-4379	111	2	that	that	SCONJ
ejpam-4379	111	3	a	a	PRON
ejpam-4379	111	4	is	be	AUX
ejpam-4379	111	5	compact	compact	ADJ
ejpam-4379	111	6	in	in	ADP
ejpam-4379	111	7	(	(	PUNCT
ejpam-4379	111	8	xp	xp	INTJ
ejpam-4379	111	9	,	,	PUNCT
ejpam-4379	111	10	τ	τ	PROPN
ejpam-4379	111	11	⋆	⋆	NOUN
ejpam-4379	111	12	)	)	PUNCT
ejpam-4379	111	13	.	.	PUNCT
ejpam-4379	112	1	to	to	PART
ejpam-4379	112	2	show	show	VERB
ejpam-4379	112	3	that	that	SCONJ
ejpam-4379	112	4	a	a	DET
ejpam-4379	112	5	\	\	NOUN
ejpam-4379	112	6	{	{	PUNCT
ejpam-4379	112	7	p	p	NOUN
ejpam-4379	112	8	}	}	PUNCT
ejpam-4379	112	9	is	be	AUX
ejpam-4379	112	10	compact	compact	ADJ
ejpam-4379	112	11	in	in	ADP
ejpam-4379	112	12	(	(	PUNCT
ejpam-4379	112	13	x	x	INTJ
ejpam-4379	112	14	,	,	PUNCT
ejpam-4379	112	15	τ	τ	PROPN
ejpam-4379	112	16	)	)	PUNCT
ejpam-4379	112	17	,	,	PUNCT
ejpam-4379	112	18	let	let	VERB
ejpam-4379	112	19	w	w	VERB
ejpam-4379	112	20	=	=	PRON
ejpam-4379	112	21	{	{	PUNCT
ejpam-4379	112	22	wα	wα	NOUN
ejpam-4379	112	23	∈	∈	PROPN
ejpam-4379	112	24	τ	τ	X
ejpam-4379	112	25	:	:	PUNCT
ejpam-4379	112	26	α	α	PROPN
ejpam-4379	112	27	∈	∈	PROPN
ejpam-4379	112	28	λ	λ	PROPN
ejpam-4379	112	29	}	}	PUNCT
ejpam-4379	112	30	be	be	AUX
ejpam-4379	112	31	any	any	DET
ejpam-4379	112	32	open	open	ADJ
ejpam-4379	112	33	cover	cover	NOUN
ejpam-4379	112	34	for	for	ADP
ejpam-4379	112	35	a	a	DET
ejpam-4379	112	36	\	\	NOUN
ejpam-4379	112	37	{	{	PUNCT
ejpam-4379	112	38	p	p	X
ejpam-4379	112	39	}	}	PUNCT
ejpam-4379	112	40	.	.	PUNCT
ejpam-4379	113	1	observe	observe	VERB
ejpam-4379	113	2	that	that	SCONJ
ejpam-4379	113	3	if	if	SCONJ
ejpam-4379	113	4	p	p	PROPN
ejpam-4379	113	5	̸∈	̸∈	PROPN
ejpam-4379	113	6	a	a	PROPN
ejpam-4379	113	7	,	,	PUNCT
ejpam-4379	113	8	then	then	ADV
ejpam-4379	113	9	a\	a\	NOUN
ejpam-4379	113	10	{	{	PUNCT
ejpam-4379	113	11	p	p	NOUN
ejpam-4379	113	12	}	}	PUNCT
ejpam-4379	113	13	=	=	PUNCT
ejpam-4379	113	14	a.	a.	NOUN
ejpam-4379	113	15	the	the	DET
ejpam-4379	113	16	family	family	NOUN
ejpam-4379	113	17	{	{	PUNCT
ejpam-4379	113	18	wα∪	wα∪	PROPN
ejpam-4379	113	19	{	{	PUNCT
ejpam-4379	113	20	p	p	X
ejpam-4379	113	21	}	}	PUNCT
ejpam-4379	113	22	:	:	PUNCT
ejpam-4379	113	23	α	α	NUM
ejpam-4379	113	24	∈	∈	PROPN
ejpam-4379	113	25	λ	λ	PROPN
ejpam-4379	113	26	}	}	PUNCT
ejpam-4379	113	27	is	be	AUX
ejpam-4379	113	28	an	an	DET
ejpam-4379	113	29	open	open	ADJ
ejpam-4379	113	30	cover	cover	NOUN
ejpam-4379	113	31	for	for	ADP
ejpam-4379	113	32	a	a	DET
ejpam-4379	113	33	in	in	ADP
ejpam-4379	113	34	(	(	PUNCT
ejpam-4379	113	35	xp	xp	INTJ
ejpam-4379	113	36	,	,	PUNCT
ejpam-4379	113	37	τ	τ	PROPN
ejpam-4379	113	38	⋆	⋆	NOUN
ejpam-4379	113	39	)	)	PUNCT
ejpam-4379	113	40	because	because	SCONJ
ejpam-4379	113	41	wα∪	wα∪	NOUN
ejpam-4379	113	42	{	{	PUNCT
ejpam-4379	113	43	p	p	X
ejpam-4379	113	44	}	}	PUNCT
ejpam-4379	113	45	∈	∈	PROPN
ejpam-4379	113	46	τ	τ	X
ejpam-4379	113	47	⋆	⋆	VERB
ejpam-4379	113	48	for	for	ADP
ejpam-4379	113	49	each	each	DET
ejpam-4379	113	50	α	α	PRON
ejpam-4379	113	51	∈	∈	PROPN
ejpam-4379	113	52	λ	λ	PROPN
ejpam-4379	113	53	.	.	PUNCT
ejpam-4379	114	1	by	by	ADP
ejpam-4379	114	2	the	the	DET
ejpam-4379	114	3	hypothesis	hypothesis	NOUN
ejpam-4379	114	4	,	,	PUNCT
ejpam-4379	114	5	there	there	PRON
ejpam-4379	114	6	exist	exist	VERB
ejpam-4379	114	7	α1	α1	NOUN
ejpam-4379	114	8	,	,	PUNCT
ejpam-4379	114	9	...	...	PUNCT
ejpam-4379	114	10	,	,	PUNCT
ejpam-4379	114	11	αn	αn	X
ejpam-4379	114	12	∈	∈	PROPN
ejpam-4379	114	13	λ	λ	NOUN
ejpam-4379	114	14	,	,	PUNCT
ejpam-4379	114	15	where	where	SCONJ
ejpam-4379	114	16	n	n	X
ejpam-4379	114	17	∈	∈	PROPN
ejpam-4379	114	18	n	n	CCONJ
ejpam-4379	114	19	,	,	PUNCT
ejpam-4379	114	20	such	such	ADJ
ejpam-4379	114	21	that	that	SCONJ
ejpam-4379	114	22	a	a	DET
ejpam-4379	114	23	⊆	⊆	NUM
ejpam-4379	114	24	⋃n	⋃n	NOUN
ejpam-4379	114	25	i=1(wαi	i=1(wαi	NOUN
ejpam-4379	114	26	∪	∪	ADJ
ejpam-4379	114	27	{	{	PUNCT
ejpam-4379	114	28	p	p	NOUN
ejpam-4379	114	29	}	}	PUNCT
ejpam-4379	114	30	)	)	PUNCT
ejpam-4379	114	31	.	.	PUNCT
ejpam-4379	115	1	then	then	ADV
ejpam-4379	115	2	{	{	PUNCT
ejpam-4379	115	3	wα1	wα1	NOUN
ejpam-4379	115	4	,	,	PUNCT
ejpam-4379	115	5	...	...	PUNCT
ejpam-4379	115	6	,	,	PUNCT
ejpam-4379	115	7	wαn	wαn	AUX
ejpam-4379	115	8	}	}	PUNCT
ejpam-4379	115	9	is	be	AUX
ejpam-4379	115	10	a	a	DET
ejpam-4379	115	11	finite	finite	ADJ
ejpam-4379	115	12	subcover	subcover	NOUN
ejpam-4379	115	13	for	for	ADP
ejpam-4379	115	14	a	a	DET
ejpam-4379	115	15	\	\	NOUN
ejpam-4379	115	16	{	{	PUNCT
ejpam-4379	115	17	p	p	NOUN
ejpam-4379	115	18	}	}	PUNCT
ejpam-4379	115	19	of	of	ADP
ejpam-4379	115	20	w.	w.	NOUN
ejpam-4379	115	21	thus	thus	ADV
ejpam-4379	115	22	a	a	DET
ejpam-4379	115	23	\	\	NOUN
ejpam-4379	115	24	{	{	PUNCT
ejpam-4379	115	25	p	p	NOUN
ejpam-4379	115	26	}	}	PUNCT
ejpam-4379	115	27	is	be	AUX
ejpam-4379	115	28	compact	compact	ADJ
ejpam-4379	115	29	in	in	ADP
ejpam-4379	115	30	(	(	PUNCT
ejpam-4379	115	31	x	x	INTJ
ejpam-4379	115	32	,	,	PUNCT
ejpam-4379	115	33	τ	τ	PROPN
ejpam-4379	115	34	)	)	PUNCT
ejpam-4379	115	35	.	.	PUNCT
ejpam-4379	116	1	now	now	ADV
ejpam-4379	116	2	,	,	PUNCT
ejpam-4379	116	3	assume	assume	VERB
ejpam-4379	116	4	that	that	SCONJ
ejpam-4379	116	5	a	a	DET
ejpam-4379	116	6	\	\	NOUN
ejpam-4379	116	7	{	{	PUNCT
ejpam-4379	116	8	p	p	NOUN
ejpam-4379	116	9	}	}	PUNCT
ejpam-4379	116	10	is	be	AUX
ejpam-4379	116	11	compact	compact	ADJ
ejpam-4379	116	12	in	in	ADP
ejpam-4379	116	13	(	(	PUNCT
ejpam-4379	116	14	x	x	INTJ
ejpam-4379	116	15	,	,	PUNCT
ejpam-4379	116	16	τ	τ	PROPN
ejpam-4379	116	17	)	)	PUNCT
ejpam-4379	116	18	.	.	PUNCT
ejpam-4379	117	1	let	let	VERB
ejpam-4379	117	2	v	v	VERB
ejpam-4379	117	3	=	=	PUNCT
ejpam-4379	117	4	{	{	PUNCT
ejpam-4379	117	5	vα	vα	INTJ
ejpam-4379	117	6	∈	∈	PROPN
ejpam-4379	117	7	τ	τ	X
ejpam-4379	117	8	⋆	⋆	NOUN
ejpam-4379	117	9	:	:	PUNCT
ejpam-4379	117	10	α	α	PROPN
ejpam-4379	117	11	∈	∈	PROPN
ejpam-4379	117	12	λ	λ	X
ejpam-4379	117	13	}	}	PUNCT
ejpam-4379	117	14	be	be	AUX
ejpam-4379	117	15	an	an	DET
ejpam-4379	117	16	arbitrary	arbitrary	ADJ
ejpam-4379	117	17	open	open	ADJ
ejpam-4379	117	18	cover	cover	NOUN
ejpam-4379	117	19	for	for	ADP
ejpam-4379	117	20	a.	a.	NOUN
ejpam-4379	117	21	for	for	ADP
ejpam-4379	117	22	each	each	DET
ejpam-4379	117	23	α	α	NOUN
ejpam-4379	117	24	∈	∈	PROPN
ejpam-4379	117	25	λ	λ	NOUN
ejpam-4379	117	26	there	there	PRON
ejpam-4379	117	27	exists	exist	VERB
ejpam-4379	117	28	uα	uα	PROPN
ejpam-4379	117	29	∈	∈	PROPN
ejpam-4379	117	30	τ	τ	X
ejpam-4379	118	1	such	such	ADJ
ejpam-4379	118	2	that	that	SCONJ
ejpam-4379	118	3	vα	vα	ADP
ejpam-4379	119	1	=	=	SYM
ejpam-4379	119	2	uα	uα	PROPN
ejpam-4379	119	3	∪	∪	X
ejpam-4379	119	4	{	{	PUNCT
ejpam-4379	119	5	p	p	NOUN
ejpam-4379	119	6	}	}	PUNCT
ejpam-4379	119	7	.	.	PUNCT
ejpam-4379	120	1	then	then	ADV
ejpam-4379	120	2	the	the	DET
ejpam-4379	120	3	family	family	NOUN
ejpam-4379	120	4	{	{	PUNCT
ejpam-4379	120	5	uα	uα	X
ejpam-4379	120	6	:	:	PUNCT
ejpam-4379	120	7	α	α	PROPN
ejpam-4379	120	8	∈	∈	PROPN
ejpam-4379	120	9	λ	λ	PROPN
ejpam-4379	120	10	}	}	PUNCT
ejpam-4379	120	11	is	be	AUX
ejpam-4379	120	12	an	an	DET
ejpam-4379	120	13	open	open	ADJ
ejpam-4379	120	14	cover	cover	NOUN
ejpam-4379	120	15	for	for	ADP
ejpam-4379	120	16	a	a	DET
ejpam-4379	120	17	\	\	NOUN
ejpam-4379	120	18	{	{	PUNCT
ejpam-4379	120	19	p	p	NOUN
ejpam-4379	120	20	}	}	PUNCT
ejpam-4379	120	21	in	in	ADP
ejpam-4379	120	22	(	(	PUNCT
ejpam-4379	120	23	x	x	INTJ
ejpam-4379	120	24	,	,	PUNCT
ejpam-4379	120	25	τ	τ	PROPN
ejpam-4379	120	26	)	)	PUNCT
ejpam-4379	120	27	.	.	PUNCT
ejpam-4379	121	1	by	by	ADP
ejpam-4379	121	2	the	the	DET
ejpam-4379	121	3	hypothesis	hypothesis	NOUN
ejpam-4379	121	4	,	,	PUNCT
ejpam-4379	121	5	there	there	PRON
ejpam-4379	121	6	exist	exist	VERB
ejpam-4379	121	7	α1	α1	NOUN
ejpam-4379	121	8	,	,	PUNCT
ejpam-4379	121	9	...	...	PUNCT
ejpam-4379	121	10	,	,	PUNCT
ejpam-4379	121	11	αm	αm	PROPN
ejpam-4379	121	12	∈	∈	PROPN
ejpam-4379	121	13	λ	λ	PROPN
ejpam-4379	121	14	,	,	PUNCT
ejpam-4379	121	15	where	where	SCONJ
ejpam-4379	121	16	m	m	VERB
ejpam-4379	121	17	∈	∈	PROPN
ejpam-4379	121	18	n	n	CCONJ
ejpam-4379	121	19	,	,	PUNCT
ejpam-4379	121	20	such	such	ADJ
ejpam-4379	121	21	that	that	SCONJ
ejpam-4379	121	22	a	a	DET
ejpam-4379	121	23	\	\	NOUN
ejpam-4379	121	24	{	{	PUNCT
ejpam-4379	121	25	p	p	X
ejpam-4379	121	26	}	}	PUNCT
ejpam-4379	121	27	⊆	⊆	NUM
ejpam-4379	121	28	⋃m	⋃m	NOUN
ejpam-4379	121	29	i=1	i=1	PRON
ejpam-4379	121	30	uαi	uαi	PROPN
ejpam-4379	121	31	.	.	PUNCT
ejpam-4379	122	1	then	then	ADV
ejpam-4379	122	2	{	{	PUNCT
ejpam-4379	122	3	vα1	vα1	NOUN
ejpam-4379	122	4	,	,	PUNCT
ejpam-4379	122	5	...	...	PUNCT
ejpam-4379	122	6	,	,	PUNCT
ejpam-4379	122	7	vαm	vαm	INTJ
ejpam-4379	122	8	}	}	PUNCT
ejpam-4379	122	9	is	be	AUX
ejpam-4379	122	10	a	a	DET
ejpam-4379	122	11	finite	finite	ADJ
ejpam-4379	122	12	subcover	subcover	NOUN
ejpam-4379	122	13	for	for	ADP
ejpam-4379	122	14	a	a	PRON
ejpam-4379	122	15	of	of	ADP
ejpam-4379	122	16	v.	v.	ADP
ejpam-4379	122	17	by	by	ADP
ejpam-4379	122	18	similar	similar	ADJ
ejpam-4379	122	19	proof	proof	NOUN
ejpam-4379	122	20	of	of	ADP
ejpam-4379	122	21	the	the	DET
ejpam-4379	122	22	proof	proof	NOUN
ejpam-4379	122	23	of	of	ADP
ejpam-4379	122	24	proposition	proposition	NOUN
ejpam-4379	122	25	1	1	NUM
ejpam-4379	122	26	,	,	PUNCT
ejpam-4379	122	27	we	we	PRON
ejpam-4379	122	28	conclude	conclude	VERB
ejpam-4379	122	29	the	the	DET
ejpam-4379	122	30	following	follow	VERB
ejpam-4379	122	31	two	two	NUM
ejpam-4379	122	32	statements	statement	NOUN
ejpam-4379	122	33	.	.	PUNCT
ejpam-4379	123	1	proposition	proposition	NOUN
ejpam-4379	123	2	2	2	NUM
ejpam-4379	123	3	.	.	PUNCT
ejpam-4379	124	1	let	let	AUX
ejpam-4379	124	2	(	(	PUNCT
ejpam-4379	124	3	x	x	X
ejpam-4379	124	4	,	,	PUNCT
ejpam-4379	124	5	τ	τ	PROPN
ejpam-4379	124	6	)	)	PUNCT
ejpam-4379	124	7	be	be	AUX
ejpam-4379	124	8	a	a	DET
ejpam-4379	124	9	topological	topological	ADJ
ejpam-4379	124	10	space	space	NOUN
ejpam-4379	124	11	.	.	PUNCT
ejpam-4379	125	1	consider	consider	VERB
ejpam-4379	125	2	the	the	DET
ejpam-4379	125	3	closed	closed	ADJ
ejpam-4379	125	4	extension	extension	NOUN
ejpam-4379	125	5	space	space	NOUN
ejpam-4379	125	6	(	(	PUNCT
ejpam-4379	125	7	xp	xp	INTJ
ejpam-4379	125	8	,	,	PUNCT
ejpam-4379	125	9	τ	τ	PROPN
ejpam-4379	125	10	⋆	⋆	NOUN
ejpam-4379	125	11	)	)	PUNCT
ejpam-4379	125	12	of	of	ADP
ejpam-4379	125	13	(	(	PUNCT
ejpam-4379	125	14	x	x	INTJ
ejpam-4379	125	15	,	,	PUNCT
ejpam-4379	125	16	τ	τ	PROPN
ejpam-4379	125	17	)	)	PUNCT
ejpam-4379	125	18	.	.	PUNCT
ejpam-4379	126	1	let	let	VERB
ejpam-4379	126	2	a	a	DET
ejpam-4379	126	3	⊆	⊆	NUM
ejpam-4379	126	4	xp	xp	NOUN
ejpam-4379	126	5	.	.	PUNCT
ejpam-4379	127	1	a	a	PRON
ejpam-4379	127	2	is	be	AUX
ejpam-4379	127	3	countably	countably	ADV
ejpam-4379	127	4	compact	compact	ADJ
ejpam-4379	127	5	(	(	PUNCT
ejpam-4379	127	6	lindelöf	lindelöf	NOUN
ejpam-4379	127	7	)	)	PUNCT
ejpam-4379	127	8	in	in	ADP
ejpam-4379	127	9	(	(	PUNCT
ejpam-4379	127	10	xp	xp	INTJ
ejpam-4379	127	11	,	,	PUNCT
ejpam-4379	127	12	τ	τ	PROPN
ejpam-4379	127	13	⋆	⋆	NOUN
ejpam-4379	127	14	)	)	PUNCT
ejpam-4379	127	15	if	if	SCONJ
ejpam-4379	127	16	and	and	CCONJ
ejpam-4379	127	17	only	only	ADV
ejpam-4379	127	18	if	if	SCONJ
ejpam-4379	127	19	a\	a\	NOUN
ejpam-4379	127	20	{	{	PUNCT
ejpam-4379	127	21	p	p	NOUN
ejpam-4379	127	22	}	}	PUNCT
ejpam-4379	127	23	is	be	AUX
ejpam-4379	127	24	countably	countably	ADV
ejpam-4379	127	25	compact	compact	ADJ
ejpam-4379	127	26	(	(	PUNCT
ejpam-4379	127	27	lindelöf	lindelöf	NOUN
ejpam-4379	127	28	)	)	PUNCT
ejpam-4379	127	29	in	in	ADP
ejpam-4379	127	30	(	(	PUNCT
ejpam-4379	127	31	x	x	INTJ
ejpam-4379	127	32	,	,	PUNCT
ejpam-4379	127	33	τ	τ	PROPN
ejpam-4379	127	34	)	)	PUNCT
ejpam-4379	127	35	.	.	PUNCT
ejpam-4379	128	1	recall	recall	VERB
ejpam-4379	128	2	that	that	SCONJ
ejpam-4379	128	3	a	a	DET
ejpam-4379	128	4	topological	topological	ADJ
ejpam-4379	128	5	space	space	NOUN
ejpam-4379	128	6	(	(	PUNCT
ejpam-4379	128	7	x	x	X
ejpam-4379	128	8	,	,	PUNCT
ejpam-4379	128	9	τ	τ	PROPN
ejpam-4379	128	10	)	)	PUNCT
ejpam-4379	128	11	is	be	AUX
ejpam-4379	128	12	paracompact	paracompact	ADJ
ejpam-4379	128	13	if	if	SCONJ
ejpam-4379	128	14	any	any	DET
ejpam-4379	128	15	open	open	ADJ
ejpam-4379	128	16	cover	cover	NOUN
ejpam-4379	128	17	has	have	VERB
ejpam-4379	128	18	a	a	DET
ejpam-4379	128	19	locally	locally	ADV
ejpam-4379	128	20	finite	finite	ADJ
ejpam-4379	128	21	open	open	ADJ
ejpam-4379	128	22	refinement	refinement	NOUN
ejpam-4379	128	23	.	.	PUNCT
ejpam-4379	129	1	for	for	ADP
ejpam-4379	129	2	a	a	DET
ejpam-4379	129	3	subspace	subspace	NOUN
ejpam-4379	129	4	a	a	PRON
ejpam-4379	129	5	of	of	ADP
ejpam-4379	129	6	x	x	PRON
ejpam-4379	129	7	,	,	PUNCT
ejpam-4379	129	8	a	a	PRON
ejpam-4379	129	9	is	be	AUX
ejpam-4379	129	10	paracompact	paracompact	ADJ
ejpam-4379	129	11	if	if	SCONJ
ejpam-4379	129	12	(	(	PUNCT
ejpam-4379	129	13	a	a	DET
ejpam-4379	129	14	,	,	PUNCT
ejpam-4379	129	15	τa	τa	PROPN
ejpam-4379	129	16	)	)	PUNCT
ejpam-4379	129	17	is	be	AUX
ejpam-4379	129	18	paracompact	paracompact	ADJ
ejpam-4379	129	19	,	,	PUNCT
ejpam-4379	129	20	i.e.	i.e.	X
ejpam-4379	129	21	,	,	PUNCT
ejpam-4379	129	22	any	any	PRON
ejpam-4379	129	23	open	open	ADJ
ejpam-4379	129	24	(	(	PUNCT
ejpam-4379	129	25	open	open	ADJ
ejpam-4379	129	26	in	in	ADP
ejpam-4379	129	27	the	the	DET
ejpam-4379	129	28	subspace	subspace	NOUN
ejpam-4379	129	29	)	)	PUNCT
ejpam-4379	129	30	cover	cover	NOUN
ejpam-4379	129	31	of	of	ADP
ejpam-4379	129	32	a	a	PRON
ejpam-4379	129	33	has	have	AUX
ejpam-4379	129	34	a	a	DET
ejpam-4379	129	35	locally	locally	ADV
ejpam-4379	129	36	finite	finite	ADJ
ejpam-4379	129	37	open	open	ADJ
ejpam-4379	129	38	(	(	PUNCT
ejpam-4379	129	39	open	open	ADJ
ejpam-4379	129	40	in	in	ADP
ejpam-4379	129	41	the	the	DET
ejpam-4379	129	42	subspace	subspace	NOUN
ejpam-4379	129	43	)	)	PUNCT
ejpam-4379	129	44	refinement	refinement	NOUN
ejpam-4379	129	45	.	.	PUNCT
ejpam-4379	130	1	we	we	PRON
ejpam-4379	130	2	do	do	AUX
ejpam-4379	130	3	not	not	PART
ejpam-4379	130	4	assume	assume	VERB
ejpam-4379	130	5	t2	t2	NOUN
ejpam-4379	130	6	in	in	ADP
ejpam-4379	130	7	the	the	DET
ejpam-4379	130	8	definition	definition	NOUN
ejpam-4379	130	9	of	of	ADP
ejpam-4379	130	10	paracompactness	paracompactness	NOUN
ejpam-4379	130	11	.	.	PUNCT
ejpam-4379	131	1	proposition	proposition	NOUN
ejpam-4379	131	2	3	3	X
ejpam-4379	131	3	.	.	PUNCT
ejpam-4379	132	1	let	let	AUX
ejpam-4379	132	2	(	(	PUNCT
ejpam-4379	132	3	x	x	X
ejpam-4379	132	4	,	,	PUNCT
ejpam-4379	132	5	τ	τ	PROPN
ejpam-4379	132	6	)	)	PUNCT
ejpam-4379	132	7	be	be	AUX
ejpam-4379	132	8	a	a	DET
ejpam-4379	132	9	topological	topological	ADJ
ejpam-4379	132	10	space	space	NOUN
ejpam-4379	132	11	.	.	PUNCT
ejpam-4379	133	1	consider	consider	VERB
ejpam-4379	133	2	the	the	DET
ejpam-4379	133	3	closed	closed	ADJ
ejpam-4379	133	4	extension	extension	NOUN
ejpam-4379	133	5	space	space	NOUN
ejpam-4379	133	6	(	(	PUNCT
ejpam-4379	133	7	xp	xp	INTJ
ejpam-4379	133	8	,	,	PUNCT
ejpam-4379	133	9	τ	τ	PROPN
ejpam-4379	133	10	⋆	⋆	NOUN
ejpam-4379	133	11	)	)	PUNCT
ejpam-4379	133	12	of	of	ADP
ejpam-4379	133	13	(	(	PUNCT
ejpam-4379	133	14	x	x	INTJ
ejpam-4379	133	15	,	,	PUNCT
ejpam-4379	133	16	τ	τ	PROPN
ejpam-4379	133	17	)	)	PUNCT
ejpam-4379	133	18	.	.	PUNCT
ejpam-4379	134	1	let	let	VERB
ejpam-4379	134	2	a	a	DET
ejpam-4379	134	3	⊆	⊆	NUM
ejpam-4379	134	4	xp	xp	NOUN
ejpam-4379	134	5	.	.	PUNCT
ejpam-4379	135	1	if	if	SCONJ
ejpam-4379	135	2	p	p	PROPN
ejpam-4379	135	3	̸∈	̸∈	PROPN
ejpam-4379	135	4	a	a	PROPN
ejpam-4379	135	5	,	,	PUNCT
ejpam-4379	135	6	then	then	ADV
ejpam-4379	135	7	a	a	PRON
ejpam-4379	135	8	is	be	AUX
ejpam-4379	135	9	a	a	DET
ejpam-4379	135	10	paracompact	paracompact	NOUN
ejpam-4379	135	11	subset	subset	NOUN
ejpam-4379	135	12	in	in	ADP
ejpam-4379	135	13	(	(	PUNCT
ejpam-4379	135	14	xp	xp	INTJ
ejpam-4379	135	15	,	,	PUNCT
ejpam-4379	135	16	τ	τ	PROPN
ejpam-4379	135	17	⋆	⋆	NOUN
ejpam-4379	135	18	)	)	PUNCT
ejpam-4379	135	19	if	if	SCONJ
ejpam-4379	135	20	and	and	CCONJ
ejpam-4379	135	21	only	only	ADV
ejpam-4379	135	22	if	if	SCONJ
ejpam-4379	135	23	a	a	PRON
ejpam-4379	135	24	is	be	AUX
ejpam-4379	135	25	a	a	DET
ejpam-4379	135	26	paracompact	paracompact	NOUN
ejpam-4379	135	27	subset	subset	NOUN
ejpam-4379	135	28	in	in	ADP
ejpam-4379	135	29	(	(	PUNCT
ejpam-4379	135	30	x	x	INTJ
ejpam-4379	135	31	,	,	PUNCT
ejpam-4379	135	32	τ	τ	PROPN
ejpam-4379	135	33	)	)	PUNCT
ejpam-4379	135	34	.	.	PUNCT
ejpam-4379	136	1	if	if	SCONJ
ejpam-4379	136	2	p	p	PROPN
ejpam-4379	136	3	∈	∈	PROPN
ejpam-4379	136	4	a	a	PRON
ejpam-4379	136	5	,	,	PUNCT
ejpam-4379	136	6	then	then	ADV
ejpam-4379	136	7	a	a	PRON
ejpam-4379	136	8	is	be	AUX
ejpam-4379	136	9	a	a	DET
ejpam-4379	136	10	paracompact	paracompact	NOUN
ejpam-4379	136	11	subset	subset	NOUN
ejpam-4379	136	12	in	in	ADP
ejpam-4379	136	13	(	(	PUNCT
ejpam-4379	136	14	xp	xp	INTJ
ejpam-4379	136	15	,	,	PUNCT
ejpam-4379	136	16	τ	τ	PROPN
ejpam-4379	136	17	⋆	⋆	NOUN
ejpam-4379	136	18	)	)	PUNCT
ejpam-4379	136	19	if	if	SCONJ
ejpam-4379	136	20	and	and	CCONJ
ejpam-4379	136	21	only	only	ADV
ejpam-4379	136	22	if	if	SCONJ
ejpam-4379	136	23	a	a	PRON
ejpam-4379	136	24	\	\	NOUN
ejpam-4379	136	25	{	{	PUNCT
ejpam-4379	136	26	p	p	X
ejpam-4379	136	27	}	}	PUNCT
ejpam-4379	136	28	is	be	AUX
ejpam-4379	136	29	a	a	DET
ejpam-4379	136	30	compact	compact	ADJ
ejpam-4379	136	31	subset	subset	NOUN
ejpam-4379	136	32	in	in	ADP
ejpam-4379	136	33	(	(	PUNCT
ejpam-4379	136	34	x	x	INTJ
ejpam-4379	136	35	,	,	PUNCT
ejpam-4379	136	36	τ	τ	PROPN
ejpam-4379	136	37	)	)	PUNCT
ejpam-4379	136	38	.	.	PUNCT
ejpam-4379	137	1	d.	d.	PROPN
ejpam-4379	137	2	abuzaid	abuzaid	PROPN
ejpam-4379	137	3	,	,	PUNCT
ejpam-4379	137	4	s.	s.	PROPN
ejpam-4379	137	5	al	al	PROPN
ejpam-4379	137	6	-	-	PROPN
ejpam-4379	137	7	qarhi	qarhi	PROPN
ejpam-4379	137	8	,	,	PUNCT
ejpam-4379	137	9	l.	l.	PROPN
ejpam-4379	137	10	kalantan	kalantan	PROPN
ejpam-4379	137	11	/	/	SYM
ejpam-4379	137	12	eur	eur	PROPN
ejpam-4379	137	13	.	.	PUNCT
ejpam-4379	138	1	j.	j.	PROPN
ejpam-4379	138	2	pure	pure	PROPN
ejpam-4379	138	3	appl	appl	PROPN
ejpam-4379	138	4	.	.	PROPN
ejpam-4379	138	5	math	math	PROPN
ejpam-4379	138	6	,	,	PUNCT
ejpam-4379	138	7	15	15	NUM
ejpam-4379	138	8	(	(	PUNCT
ejpam-4379	138	9	2	2	NUM
ejpam-4379	138	10	)	)	PUNCT
ejpam-4379	138	11	(	(	PUNCT
ejpam-4379	138	12	2022	2022	NUM
ejpam-4379	138	13	)	)	PUNCT
ejpam-4379	138	14	,	,	PUNCT
ejpam-4379	138	15	672	672	NUM
ejpam-4379	138	16	-	-	SYM
ejpam-4379	138	17	680	680	NUM
ejpam-4379	138	18	676	676	NUM
ejpam-4379	138	19	proof	proof	NOUN
ejpam-4379	138	20	.	.	PUNCT
ejpam-4379	139	1	if	if	SCONJ
ejpam-4379	139	2	p	p	PROPN
ejpam-4379	139	3	̸∈	̸∈	PROPN
ejpam-4379	139	4	a.	a.	NOUN
ejpam-4379	139	5	we	we	PRON
ejpam-4379	139	6	show	show	VERB
ejpam-4379	139	7	that	that	SCONJ
ejpam-4379	139	8	a	a	PRON
ejpam-4379	139	9	is	be	AUX
ejpam-4379	139	10	paracompact	paracompact	NOUN
ejpam-4379	139	11	subset	subset	VERB
ejpam-4379	139	12	in	in	ADP
ejpam-4379	139	13	(	(	PUNCT
ejpam-4379	139	14	xp	xp	INTJ
ejpam-4379	139	15	,	,	PUNCT
ejpam-4379	139	16	τ	τ	PROPN
ejpam-4379	139	17	⋆	⋆	NOUN
ejpam-4379	139	18	)	)	PUNCT
ejpam-4379	139	19	if	if	SCONJ
ejpam-4379	139	20	and	and	CCONJ
ejpam-4379	139	21	only	only	ADV
ejpam-4379	139	22	if	if	SCONJ
ejpam-4379	139	23	a	a	PRON
ejpam-4379	139	24	is	be	AUX
ejpam-4379	139	25	paracompact	paracompact	NOUN
ejpam-4379	139	26	subset	subset	VERB
ejpam-4379	139	27	in	in	ADP
ejpam-4379	139	28	(	(	PUNCT
ejpam-4379	139	29	x	x	INTJ
ejpam-4379	139	30	,	,	PUNCT
ejpam-4379	139	31	τ	τ	PROPN
ejpam-4379	139	32	)	)	PUNCT
ejpam-4379	139	33	.	.	PUNCT
ejpam-4379	140	1	that	that	PRON
ejpam-4379	140	2	is	be	AUX
ejpam-4379	140	3	,	,	PUNCT
ejpam-4379	140	4	(	(	PUNCT
ejpam-4379	140	5	a	a	X
ejpam-4379	140	6	,	,	PUNCT
ejpam-4379	140	7	τ	τ	PROPN
ejpam-4379	140	8	⋆	⋆	VERB
ejpam-4379	140	9	a	a	PRON
ejpam-4379	140	10	)	)	PUNCT
ejpam-4379	140	11	is	be	AUX
ejpam-4379	140	12	paracompact	paracompact	ADJ
ejpam-4379	140	13	if	if	SCONJ
ejpam-4379	140	14	and	and	CCONJ
ejpam-4379	140	15	only	only	ADV
ejpam-4379	140	16	if	if	SCONJ
ejpam-4379	140	17	(	(	PUNCT
ejpam-4379	140	18	a	a	DET
ejpam-4379	140	19	,	,	PUNCT
ejpam-4379	140	20	τa	τa	PROPN
ejpam-4379	140	21	)	)	PUNCT
ejpam-4379	140	22	is	be	AUX
ejpam-4379	140	23	paracompact	paracompact	ADJ
ejpam-4379	140	24	.	.	PUNCT
ejpam-4379	141	1	assume	assume	VERB
ejpam-4379	141	2	that	that	SCONJ
ejpam-4379	141	3	(	(	PUNCT
ejpam-4379	141	4	a	a	X
ejpam-4379	141	5	,	,	PUNCT
ejpam-4379	141	6	τ	τ	PROPN
ejpam-4379	141	7	⋆	⋆	VERB
ejpam-4379	141	8	a	a	PRON
ejpam-4379	141	9	)	)	PUNCT
ejpam-4379	141	10	is	be	AUX
ejpam-4379	141	11	paracompact	paracompact	ADJ
ejpam-4379	141	12	.	.	PUNCT
ejpam-4379	142	1	let	let	VERB
ejpam-4379	142	2	w	w	NOUN
ejpam-4379	142	3	=	=	PRON
ejpam-4379	142	4	{	{	PUNCT
ejpam-4379	142	5	wα	wα	NOUN
ejpam-4379	142	6	∩	∩	NOUN
ejpam-4379	142	7	a	a	PRON
ejpam-4379	142	8	:	:	PUNCT
ejpam-4379	142	9	α	α	PROPN
ejpam-4379	142	10	∈	∈	PROPN
ejpam-4379	142	11	λ	λ	AUX
ejpam-4379	142	12	}	}	PUNCT
ejpam-4379	142	13	be	be	AUX
ejpam-4379	142	14	any	any	DET
ejpam-4379	142	15	open	open	ADJ
ejpam-4379	142	16	cover	cover	NOUN
ejpam-4379	142	17	for	for	ADP
ejpam-4379	142	18	a	a	DET
ejpam-4379	142	19	where	where	SCONJ
ejpam-4379	142	20	wα	wα	NOUN
ejpam-4379	142	21	∈	∈	PROPN
ejpam-4379	142	22	τ	τ	PROPN
ejpam-4379	142	23	for	for	ADP
ejpam-4379	142	24	each	each	DET
ejpam-4379	142	25	α	α	PRON
ejpam-4379	142	26	∈	∈	PROPN
ejpam-4379	142	27	λ	λ	PROPN
ejpam-4379	142	28	.	.	PUNCT
ejpam-4379	142	29	note	note	VERB
ejpam-4379	142	30	that	that	SCONJ
ejpam-4379	142	31	(	(	PUNCT
ejpam-4379	142	32	wα	wα	NOUN
ejpam-4379	142	33	∪	∪	NOUN
ejpam-4379	142	34	{	{	PUNCT
ejpam-4379	142	35	p})∩a	p})∩a	NOUN
ejpam-4379	142	36	=	=	NOUN
ejpam-4379	142	37	wα	wα	NOUN
ejpam-4379	142	38	∩a	∩a	PROPN
ejpam-4379	142	39	because	because	SCONJ
ejpam-4379	142	40	p	p	PROPN
ejpam-4379	142	41	̸∈	̸∈	PROPN
ejpam-4379	142	42	a.	a.	PROPN
ejpam-4379	142	43	thus	thus	ADV
ejpam-4379	142	44	w	w	PROPN
ejpam-4379	142	45	is	be	AUX
ejpam-4379	142	46	an	an	DET
ejpam-4379	142	47	open	open	ADJ
ejpam-4379	142	48	cover	cover	NOUN
ejpam-4379	142	49	for	for	ADP
ejpam-4379	142	50	a	a	DET
ejpam-4379	142	51	(	(	PUNCT
ejpam-4379	142	52	open	open	ADJ
ejpam-4379	142	53	in	in	ADP
ejpam-4379	142	54	(	(	PUNCT
ejpam-4379	142	55	a	a	PRON
ejpam-4379	142	56	,	,	PUNCT
ejpam-4379	142	57	τ	τ	PROPN
ejpam-4379	142	58	⋆	⋆	VERB
ejpam-4379	142	59	a	a	PRON
ejpam-4379	142	60	)	)	PUNCT
ejpam-4379	142	61	)	)	PUNCT
ejpam-4379	142	62	.	.	PUNCT
ejpam-4379	143	1	by	by	ADP
ejpam-4379	143	2	the	the	DET
ejpam-4379	143	3	hypothesis	hypothesis	NOUN
ejpam-4379	143	4	,	,	PUNCT
ejpam-4379	143	5	there	there	PRON
ejpam-4379	143	6	exists	exist	VERB
ejpam-4379	143	7	a	a	DET
ejpam-4379	143	8	locally	locally	ADV
ejpam-4379	143	9	finite	finite	ADJ
ejpam-4379	143	10	open	open	ADJ
ejpam-4379	143	11	refinement	refinement	NOUN
ejpam-4379	143	12	v	v	X
ejpam-4379	143	13	=	=	PUNCT
ejpam-4379	143	14	{	{	PUNCT
ejpam-4379	143	15	vs	vs	ADP
ejpam-4379	143	16	∈	∈	PROPN
ejpam-4379	143	17	τ	τ	X
ejpam-4379	143	18	⋆	⋆	VERB
ejpam-4379	143	19	a	a	DET
ejpam-4379	143	20	:	:	PUNCT
ejpam-4379	143	21	s	s	X
ejpam-4379	143	22	∈	∈	PROPN
ejpam-4379	143	23	s	s	X
ejpam-4379	143	24	}	}	PUNCT
ejpam-4379	143	25	of	of	ADP
ejpam-4379	143	26	w.	w.	NOUN
ejpam-4379	143	27	that	that	PRON
ejpam-4379	143	28	is	be	AUX
ejpam-4379	143	29	,	,	PUNCT
ejpam-4379	143	30	a	a	DET
ejpam-4379	143	31	⊆	⊆	NUM
ejpam-4379	143	32	⋃	⋃	ADP
ejpam-4379	143	33	s∈s	s∈s	NOUN
ejpam-4379	143	34	vs	vs	ADP
ejpam-4379	143	35	and	and	CCONJ
ejpam-4379	143	36	for	for	ADP
ejpam-4379	143	37	each	each	DET
ejpam-4379	143	38	s	s	X
ejpam-4379	143	39	∈	∈	PROPN
ejpam-4379	143	40	s	s	PART
ejpam-4379	143	41	there	there	PRON
ejpam-4379	143	42	exists	exist	VERB
ejpam-4379	143	43	αs	αs	ADP
ejpam-4379	143	44	∈	∈	PROPN
ejpam-4379	143	45	λ	λ	NOUN
ejpam-4379	143	46	such	such	ADJ
ejpam-4379	143	47	that	that	SCONJ
ejpam-4379	143	48	vs	vs	ADP
ejpam-4379	143	49	⊆	⊆	NUM
ejpam-4379	143	50	wαs	wαs	NOUN
ejpam-4379	143	51	∩	∩	NOUN
ejpam-4379	143	52	a.	a.	NOUN
ejpam-4379	143	53	then	then	ADV
ejpam-4379	143	54	the	the	DET
ejpam-4379	143	55	family	family	NOUN
ejpam-4379	143	56	{	{	PUNCT
ejpam-4379	143	57	vs	vs	ADP
ejpam-4379	143	58	∩	∩	PROPN
ejpam-4379	143	59	a	a	DET
ejpam-4379	143	60	∈	∈	NOUN
ejpam-4379	143	61	τa	τa	VERB
ejpam-4379	143	62	:	:	PUNCT
ejpam-4379	143	63	s	s	AUX
ejpam-4379	143	64	∈	∈	PROPN
ejpam-4379	143	65	s	s	PART
ejpam-4379	143	66	}	}	PUNCT
ejpam-4379	143	67	is	be	AUX
ejpam-4379	143	68	a	a	DET
ejpam-4379	143	69	locally	locally	ADV
ejpam-4379	143	70	finite	finite	ADJ
ejpam-4379	143	71	open	open	ADJ
ejpam-4379	143	72	refinement	refinement	NOUN
ejpam-4379	143	73	of	of	ADP
ejpam-4379	143	74	w.	w.	PROPN
ejpam-4379	143	75	therefore	therefore	ADV
ejpam-4379	143	76	,	,	PUNCT
ejpam-4379	143	77	(	(	PUNCT
ejpam-4379	143	78	a	a	DET
ejpam-4379	143	79	,	,	PUNCT
ejpam-4379	143	80	τa	τa	PROPN
ejpam-4379	143	81	)	)	PUNCT
ejpam-4379	143	82	is	be	AUX
ejpam-4379	143	83	paracompact	paracompact	ADJ
ejpam-4379	143	84	.	.	PUNCT
ejpam-4379	144	1	now	now	ADV
ejpam-4379	144	2	,	,	PUNCT
ejpam-4379	144	3	assume	assume	VERB
ejpam-4379	144	4	that	that	SCONJ
ejpam-4379	144	5	(	(	PUNCT
ejpam-4379	144	6	a	a	PRON
ejpam-4379	144	7	,	,	PUNCT
ejpam-4379	144	8	τa	τa	PROPN
ejpam-4379	144	9	)	)	PUNCT
ejpam-4379	144	10	is	be	AUX
ejpam-4379	144	11	paracompact	paracompact	ADJ
ejpam-4379	144	12	.	.	PUNCT
ejpam-4379	145	1	to	to	PART
ejpam-4379	145	2	show	show	VERB
ejpam-4379	145	3	that	that	SCONJ
ejpam-4379	145	4	(	(	PUNCT
ejpam-4379	145	5	a	a	PRON
ejpam-4379	145	6	,	,	PUNCT
ejpam-4379	145	7	τ	τ	PROPN
ejpam-4379	145	8	⋆	⋆	VERB
ejpam-4379	145	9	a	a	PRON
ejpam-4379	145	10	)	)	PUNCT
ejpam-4379	145	11	is	be	AUX
ejpam-4379	145	12	paracompact	paracompact	ADJ
ejpam-4379	145	13	,	,	PUNCT
ejpam-4379	145	14	note	note	VERB
ejpam-4379	145	15	that	that	SCONJ
ejpam-4379	145	16	any	any	DET
ejpam-4379	145	17	open	open	ADJ
ejpam-4379	145	18	cover	cover	NOUN
ejpam-4379	145	19	in	in	ADP
ejpam-4379	145	20	τ	τ	PROPN
ejpam-4379	145	21	⋆	⋆	NOUN
ejpam-4379	145	22	a	a	PRON
ejpam-4379	145	23	for	for	ADP
ejpam-4379	145	24	a	a	PRON
ejpam-4379	145	25	is	be	AUX
ejpam-4379	145	26	an	an	DET
ejpam-4379	145	27	open	open	ADJ
ejpam-4379	145	28	cover	cover	NOUN
ejpam-4379	145	29	in	in	ADP
ejpam-4379	145	30	τa	τa	NOUN
ejpam-4379	145	31	because	because	SCONJ
ejpam-4379	145	32	p	p	PROPN
ejpam-4379	145	33	̸∈	̸∈	PROPN
ejpam-4379	145	34	a.	a.	NOUN
ejpam-4379	145	35	so	so	ADV
ejpam-4379	145	36	,	,	PUNCT
ejpam-4379	145	37	a	a	DET
ejpam-4379	145	38	same	same	ADJ
ejpam-4379	145	39	argument	argument	NOUN
ejpam-4379	145	40	as	as	ADP
ejpam-4379	145	41	above	above	ADV
ejpam-4379	145	42	will	will	AUX
ejpam-4379	145	43	work	work	VERB
ejpam-4379	145	44	.	.	PUNCT
ejpam-4379	146	1	for	for	ADP
ejpam-4379	146	2	the	the	DET
ejpam-4379	146	3	case	case	NOUN
ejpam-4379	146	4	that	that	SCONJ
ejpam-4379	146	5	p	p	PROPN
ejpam-4379	146	6	∈	∈	PROPN
ejpam-4379	146	7	a.	a.	NOUN
ejpam-4379	146	8	we	we	PRON
ejpam-4379	146	9	show	show	VERB
ejpam-4379	146	10	that	that	SCONJ
ejpam-4379	146	11	(	(	PUNCT
ejpam-4379	146	12	a	a	PRON
ejpam-4379	146	13	,	,	PUNCT
ejpam-4379	146	14	τ	τ	PROPN
ejpam-4379	146	15	⋆	⋆	VERB
ejpam-4379	146	16	a	a	PRON
ejpam-4379	146	17	)	)	PUNCT
ejpam-4379	146	18	is	be	AUX
ejpam-4379	146	19	paracompact	paracompact	ADJ
ejpam-4379	147	1	if	if	SCONJ
ejpam-4379	147	2	and	and	CCONJ
ejpam-4379	147	3	only	only	ADV
ejpam-4379	147	4	if	if	SCONJ
ejpam-4379	147	5	a	a	PRON
ejpam-4379	147	6	\	\	NOUN
ejpam-4379	147	7	{	{	PUNCT
ejpam-4379	147	8	p	p	X
ejpam-4379	147	9	}	}	PUNCT
ejpam-4379	147	10	is	be	AUX
ejpam-4379	147	11	compact	compact	ADJ
ejpam-4379	147	12	subset	subset	NOUN
ejpam-4379	147	13	in	in	ADP
ejpam-4379	147	14	(	(	PUNCT
ejpam-4379	147	15	x	x	INTJ
ejpam-4379	147	16	,	,	PUNCT
ejpam-4379	147	17	τ	τ	PROPN
ejpam-4379	147	18	)	)	PUNCT
ejpam-4379	147	19	.	.	PUNCT
ejpam-4379	148	1	assume	assume	VERB
ejpam-4379	148	2	that	that	SCONJ
ejpam-4379	148	3	(	(	PUNCT
ejpam-4379	148	4	a	a	X
ejpam-4379	148	5	,	,	PUNCT
ejpam-4379	148	6	τ	τ	PROPN
ejpam-4379	148	7	⋆	⋆	VERB
ejpam-4379	148	8	a	a	PRON
ejpam-4379	148	9	)	)	PUNCT
ejpam-4379	148	10	is	be	AUX
ejpam-4379	148	11	paracompact	paracompact	ADJ
ejpam-4379	148	12	.	.	PUNCT
ejpam-4379	149	1	let	let	VERB
ejpam-4379	149	2	w	w	NOUN
ejpam-4379	149	3	=	=	PRON
ejpam-4379	149	4	{	{	PUNCT
ejpam-4379	149	5	wα	wα	NOUN
ejpam-4379	149	6	∈	∈	PROPN
ejpam-4379	149	7	τ	τ	X
ejpam-4379	149	8	:	:	PUNCT
ejpam-4379	149	9	α	α	PROPN
ejpam-4379	149	10	∈	∈	PROPN
ejpam-4379	149	11	λ	λ	PROPN
ejpam-4379	149	12	}	}	PUNCT
ejpam-4379	149	13	be	be	AUX
ejpam-4379	149	14	any	any	DET
ejpam-4379	149	15	open	open	ADJ
ejpam-4379	149	16	cover	cover	NOUN
ejpam-4379	149	17	for	for	ADP
ejpam-4379	149	18	a	a	DET
ejpam-4379	149	19	\	\	NOUN
ejpam-4379	149	20	{	{	PUNCT
ejpam-4379	149	21	p	p	X
ejpam-4379	149	22	}	}	PUNCT
ejpam-4379	149	23	.	.	PUNCT
ejpam-4379	150	1	that	that	PRON
ejpam-4379	150	2	is	be	AUX
ejpam-4379	150	3	,	,	PUNCT
ejpam-4379	150	4	a	a	DET
ejpam-4379	150	5	\	\	PROPN
ejpam-4379	150	6	{	{	PUNCT
ejpam-4379	150	7	p	p	X
ejpam-4379	150	8	}	}	PUNCT
ejpam-4379	150	9	⊆	⊆	NUM
ejpam-4379	150	10	⋃	⋃	NOUN
ejpam-4379	150	11	α∈λwα	α∈λwα	NOUN
ejpam-4379	150	12	.	.	PUNCT
ejpam-4379	151	1	thus	thus	ADV
ejpam-4379	151	2	a	a	DET
ejpam-4379	151	3	⊆	⊆	NUM
ejpam-4379	151	4	⋃	⋃	NOUN
ejpam-4379	151	5	α∈λ	α∈λ	NOUN
ejpam-4379	151	6	(	(	PUNCT
ejpam-4379	151	7	(	(	PUNCT
ejpam-4379	151	8	wα	wα	NOUN
ejpam-4379	151	9	∪	∪	VERB
ejpam-4379	151	10	{	{	PUNCT
ejpam-4379	151	11	p	p	NOUN
ejpam-4379	151	12	}	}	PUNCT
ejpam-4379	151	13	)	)	PUNCT
ejpam-4379	151	14	∩	∩	NOUN
ejpam-4379	151	15	a	a	X
ejpam-4379	151	16	)	)	PUNCT
ejpam-4379	151	17	where	where	SCONJ
ejpam-4379	151	18	(	(	PUNCT
ejpam-4379	151	19	wα	wα	NOUN
ejpam-4379	151	20	∪	∪	VERB
ejpam-4379	151	21	{	{	PUNCT
ejpam-4379	151	22	p	p	NOUN
ejpam-4379	151	23	}	}	PUNCT
ejpam-4379	151	24	)	)	PUNCT
ejpam-4379	151	25	∩	∩	NOUN
ejpam-4379	151	26	a	a	DET
ejpam-4379	151	27	∈	∈	PROPN
ejpam-4379	151	28	τ	τ	X
ejpam-4379	151	29	⋆	⋆	VERB
ejpam-4379	151	30	a	a	PRON
ejpam-4379	151	31	for	for	ADP
ejpam-4379	151	32	each	each	DET
ejpam-4379	151	33	α	α	PRON
ejpam-4379	151	34	∈	∈	PROPN
ejpam-4379	151	35	λ	λ	PROPN
ejpam-4379	151	36	.	.	PUNCT
ejpam-4379	152	1	since	since	SCONJ
ejpam-4379	152	2	(	(	PUNCT
ejpam-4379	152	3	a	a	PRON
ejpam-4379	152	4	,	,	PUNCT
ejpam-4379	152	5	τ	τ	PROPN
ejpam-4379	152	6	⋆	⋆	VERB
ejpam-4379	152	7	a	a	PRON
ejpam-4379	152	8	)	)	PUNCT
ejpam-4379	152	9	is	be	AUX
ejpam-4379	152	10	paracompact	paracompact	ADJ
ejpam-4379	152	11	,	,	PUNCT
ejpam-4379	152	12	then	then	ADV
ejpam-4379	152	13	there	there	PRON
ejpam-4379	152	14	exists	exist	VERB
ejpam-4379	152	15	a	a	DET
ejpam-4379	152	16	locally	locally	ADV
ejpam-4379	152	17	finite	finite	ADJ
ejpam-4379	152	18	family	family	NOUN
ejpam-4379	152	19	v	v	NOUN
ejpam-4379	152	20	=	=	PUNCT
ejpam-4379	152	21	{	{	PUNCT
ejpam-4379	152	22	vs	vs	ADP
ejpam-4379	152	23	⊆	⊆	NUM
ejpam-4379	152	24	a	a	PRON
ejpam-4379	152	25	:	:	PUNCT
ejpam-4379	152	26	s	s	X
ejpam-4379	152	27	∈	∈	PROPN
ejpam-4379	152	28	s	s	PART
ejpam-4379	152	29	}	}	PUNCT
ejpam-4379	152	30	which	which	PRON
ejpam-4379	152	31	refines	refine	VERB
ejpam-4379	152	32	the	the	DET
ejpam-4379	152	33	family	family	NOUN
ejpam-4379	152	34	{	{	PUNCT
ejpam-4379	152	35	(	(	PUNCT
ejpam-4379	152	36	wα	wα	NOUN
ejpam-4379	152	37	∪	∪	ADV
ejpam-4379	152	38	{	{	PUNCT
ejpam-4379	152	39	p})∩a	p})∩a	NOUN
ejpam-4379	152	40	:	:	PUNCT
ejpam-4379	152	41	α	α	PROPN
ejpam-4379	152	42	∈	∈	PROPN
ejpam-4379	152	43	λ	λ	X
ejpam-4379	152	44	}	}	PUNCT
ejpam-4379	152	45	.	.	PUNCT
ejpam-4379	153	1	i.e.	i.e.	X
ejpam-4379	153	2	,	,	PUNCT
ejpam-4379	153	3	vs	vs	ADP
ejpam-4379	153	4	∈	∈	PROPN
ejpam-4379	153	5	τ	τ	X
ejpam-4379	153	6	⋆	⋆	VERB
ejpam-4379	153	7	a	a	PRON
ejpam-4379	153	8	for	for	ADP
ejpam-4379	153	9	each	each	DET
ejpam-4379	153	10	s	s	X
ejpam-4379	153	11	∈	∈	PROPN
ejpam-4379	153	12	s	s	NOUN
ejpam-4379	153	13	,	,	PUNCT
ejpam-4379	153	14	a	a	DET
ejpam-4379	153	15	⊆	⊆	NUM
ejpam-4379	153	16	⋃	⋃	PUNCT
ejpam-4379	153	17	s∈s	s∈s	NOUN
ejpam-4379	153	18	vs	vs	ADP
ejpam-4379	153	19	,	,	PUNCT
ejpam-4379	153	20	and	and	CCONJ
ejpam-4379	153	21	for	for	ADP
ejpam-4379	153	22	each	each	DET
ejpam-4379	153	23	s	s	X
ejpam-4379	153	24	∈	∈	PROPN
ejpam-4379	153	25	s	s	NOUN
ejpam-4379	153	26	,	,	PUNCT
ejpam-4379	153	27	there	there	PRON
ejpam-4379	153	28	exists	exist	VERB
ejpam-4379	153	29	αs	αs	ADP
ejpam-4379	153	30	∈	∈	PROPN
ejpam-4379	153	31	λ	λ	NOUN
ejpam-4379	153	32	such	such	ADJ
ejpam-4379	153	33	that	that	SCONJ
ejpam-4379	153	34	vs	vs	ADP
ejpam-4379	153	35	⊆	⊆	NUM
ejpam-4379	153	36	(	(	PUNCT
ejpam-4379	153	37	wα	wα	NOUN
ejpam-4379	153	38	∪	∪	NOUN
ejpam-4379	153	39	{	{	PUNCT
ejpam-4379	153	40	p	p	NOUN
ejpam-4379	153	41	}	}	PUNCT
ejpam-4379	153	42	)	)	PUNCT
ejpam-4379	153	43	∩	∩	NOUN
ejpam-4379	153	44	a.	a.	NOUN
ejpam-4379	153	45	suppose	suppose	VERB
ejpam-4379	153	46	that	that	SCONJ
ejpam-4379	153	47	s	s	VERB
ejpam-4379	153	48	is	be	AUX
ejpam-4379	153	49	infinite	infinite	ADJ
ejpam-4379	153	50	.	.	PUNCT
ejpam-4379	154	1	for	for	ADP
ejpam-4379	154	2	each	each	DET
ejpam-4379	154	3	s	s	X
ejpam-4379	154	4	∈	∈	NOUN
ejpam-4379	154	5	s	s	X
ejpam-4379	154	6	we	we	PRON
ejpam-4379	154	7	have	have	VERB
ejpam-4379	154	8	that	that	PRON
ejpam-4379	154	9	vs	vs	ADP
ejpam-4379	154	10	is	be	AUX
ejpam-4379	154	11	of	of	ADP
ejpam-4379	154	12	the	the	DET
ejpam-4379	154	13	form	form	NOUN
ejpam-4379	154	14	vs	vs	ADP
ejpam-4379	154	15	=	=	X
ejpam-4379	154	16	(	(	PUNCT
ejpam-4379	154	17	us	us	PROPN
ejpam-4379	154	18	∪	∪	VERB
ejpam-4379	154	19	{	{	PUNCT
ejpam-4379	154	20	p	p	NOUN
ejpam-4379	154	21	}	}	PUNCT
ejpam-4379	154	22	)	)	PUNCT
ejpam-4379	154	23	∩	∩	NOUN
ejpam-4379	154	24	a	a	PRON
ejpam-4379	154	25	where	where	SCONJ
ejpam-4379	154	26	us	we	PRON
ejpam-4379	154	27	∈	∈	PROPN
ejpam-4379	154	28	τ	τ	X
ejpam-4379	154	29	.	.	PUNCT
ejpam-4379	155	1	this	this	PRON
ejpam-4379	155	2	means	mean	VERB
ejpam-4379	155	3	that	that	SCONJ
ejpam-4379	155	4	p	p	PROPN
ejpam-4379	155	5	∈	∈	PROPN
ejpam-4379	155	6	vs	vs	ADP
ejpam-4379	155	7	for	for	ADP
ejpam-4379	155	8	each	each	DET
ejpam-4379	155	9	s	s	X
ejpam-4379	155	10	∈	∈	ADJ
ejpam-4379	155	11	s	s	X
ejpam-4379	155	12	(	(	PUNCT
ejpam-4379	155	13	do	do	AUX
ejpam-4379	155	14	not	not	PART
ejpam-4379	155	15	forget	forget	VERB
ejpam-4379	155	16	that	that	SCONJ
ejpam-4379	155	17	p	p	PROPN
ejpam-4379	155	18	∈	∈	PROPN
ejpam-4379	155	19	a	a	PRON
ejpam-4379	155	20	)	)	PUNCT
ejpam-4379	155	21	.	.	PUNCT
ejpam-4379	156	1	since	since	SCONJ
ejpam-4379	156	2	{	{	PUNCT
ejpam-4379	156	3	p	p	X
ejpam-4379	156	4	}	}	PUNCT
ejpam-4379	156	5	is	be	AUX
ejpam-4379	156	6	the	the	DET
ejpam-4379	156	7	smallest	small	ADJ
ejpam-4379	156	8	open	open	ADJ
ejpam-4379	156	9	neighborhood	neighborhood	NOUN
ejpam-4379	156	10	of	of	ADP
ejpam-4379	156	11	p	p	NOUN
ejpam-4379	156	12	in	in	ADP
ejpam-4379	156	13	the	the	DET
ejpam-4379	156	14	closed	closed	ADJ
ejpam-4379	156	15	extension	extension	NOUN
ejpam-4379	156	16	(	(	PUNCT
ejpam-4379	156	17	xp	xp	INTJ
ejpam-4379	156	18	,	,	PUNCT
ejpam-4379	156	19	τ	τ	PROPN
ejpam-4379	156	20	⋆	⋆	NOUN
ejpam-4379	156	21	)	)	PUNCT
ejpam-4379	156	22	,	,	PUNCT
ejpam-4379	156	23	then	then	ADV
ejpam-4379	156	24	any	any	DET
ejpam-4379	156	25	open	open	ADJ
ejpam-4379	156	26	neighborhood	neighborhood	NOUN
ejpam-4379	156	27	of	of	ADP
ejpam-4379	156	28	p	p	NOUN
ejpam-4379	156	29	in	in	ADP
ejpam-4379	156	30	(	(	PUNCT
ejpam-4379	156	31	a	a	PRON
ejpam-4379	156	32	,	,	PUNCT
ejpam-4379	156	33	τ	τ	PROPN
ejpam-4379	156	34	⋆	⋆	NOUN
ejpam-4379	156	35	a	a	PRON
ejpam-4379	156	36	)	)	PUNCT
ejpam-4379	156	37	meets	meet	VERB
ejpam-4379	156	38	each	each	PRON
ejpam-4379	156	39	vs.	vs.	ADP
ejpam-4379	156	40	this	this	PRON
ejpam-4379	156	41	means	mean	VERB
ejpam-4379	156	42	that	that	SCONJ
ejpam-4379	156	43	v	v	NOUN
ejpam-4379	156	44	is	be	AUX
ejpam-4379	156	45	not	not	PART
ejpam-4379	156	46	locally	locally	ADV
ejpam-4379	156	47	finite	finite	ADJ
ejpam-4379	156	48	which	which	PRON
ejpam-4379	156	49	is	be	AUX
ejpam-4379	156	50	a	a	DET
ejpam-4379	156	51	contradiction	contradiction	NOUN
ejpam-4379	156	52	.	.	PUNCT
ejpam-4379	157	1	thus	thus	ADV
ejpam-4379	157	2	s	s	AUX
ejpam-4379	157	3	has	have	VERB
ejpam-4379	157	4	to	to	PART
ejpam-4379	157	5	be	be	AUX
ejpam-4379	157	6	finite	finite	ADJ
ejpam-4379	157	7	,	,	PUNCT
ejpam-4379	157	8	thus	thus	ADV
ejpam-4379	157	9	{	{	PUNCT
ejpam-4379	157	10	us	we	PRON
ejpam-4379	157	11	:	:	PUNCT
ejpam-4379	157	12	s	s	VERB
ejpam-4379	157	13	∈	∈	PROPN
ejpam-4379	157	14	s	s	PART
ejpam-4379	157	15	}	}	PUNCT
ejpam-4379	157	16	is	be	AUX
ejpam-4379	157	17	a	a	DET
ejpam-4379	157	18	finite	finite	ADJ
ejpam-4379	157	19	refinement	refinement	NOUN
ejpam-4379	157	20	of	of	ADP
ejpam-4379	157	21	w.	w.	PROPN
ejpam-4379	157	22	thus	thus	ADV
ejpam-4379	157	23	a	a	DET
ejpam-4379	157	24	\	\	NOUN
ejpam-4379	157	25	{	{	PUNCT
ejpam-4379	157	26	p	p	X
ejpam-4379	157	27	}	}	PUNCT
ejpam-4379	157	28	is	be	AUX
ejpam-4379	157	29	compact	compact	ADJ
ejpam-4379	157	30	in	in	ADP
ejpam-4379	157	31	(	(	PUNCT
ejpam-4379	157	32	x	x	INTJ
ejpam-4379	157	33	,	,	PUNCT
ejpam-4379	157	34	τ	τ	PROPN
ejpam-4379	157	35	)	)	PUNCT
ejpam-4379	157	36	.	.	PUNCT
ejpam-4379	158	1	now	now	ADV
ejpam-4379	158	2	,	,	PUNCT
ejpam-4379	158	3	assume	assume	VERB
ejpam-4379	158	4	thata\{p	thata\{p	NOUN
ejpam-4379	158	5	}	}	PUNCT
ejpam-4379	158	6	is	be	AUX
ejpam-4379	158	7	compact	compact	ADJ
ejpam-4379	158	8	in	in	ADP
ejpam-4379	158	9	(	(	PUNCT
ejpam-4379	158	10	x	x	INTJ
ejpam-4379	158	11	,	,	PUNCT
ejpam-4379	158	12	τ	τ	PROPN
ejpam-4379	158	13	)	)	PUNCT
ejpam-4379	158	14	.	.	PUNCT
ejpam-4379	159	1	to	to	PART
ejpam-4379	159	2	show	show	VERB
ejpam-4379	159	3	that	that	SCONJ
ejpam-4379	159	4	(	(	PUNCT
ejpam-4379	159	5	a	a	PRON
ejpam-4379	159	6	,	,	PUNCT
ejpam-4379	159	7	τ	τ	PROPN
ejpam-4379	159	8	⋆	⋆	VERB
ejpam-4379	159	9	a	a	PRON
ejpam-4379	159	10	)	)	PUNCT
ejpam-4379	159	11	is	be	AUX
ejpam-4379	159	12	paracompact	paracompact	ADJ
ejpam-4379	159	13	,	,	PUNCT
ejpam-4379	159	14	let	let	VERB
ejpam-4379	159	15	w	w	NOUN
ejpam-4379	159	16	=	=	PRON
ejpam-4379	159	17	{	{	PUNCT
ejpam-4379	159	18	(	(	PUNCT
ejpam-4379	159	19	wα	wα	NOUN
ejpam-4379	159	20	∪	∪	VERB
ejpam-4379	159	21	{	{	PUNCT
ejpam-4379	159	22	p	p	NOUN
ejpam-4379	159	23	}	}	PUNCT
ejpam-4379	159	24	)	)	PUNCT
ejpam-4379	159	25	∩	∩	NOUN
ejpam-4379	159	26	a	a	DET
ejpam-4379	159	27	:	:	PUNCT
ejpam-4379	159	28	wα	wα	NOUN
ejpam-4379	159	29	∈	∈	PROPN
ejpam-4379	159	30	τ	τ	PROPN
ejpam-4379	159	31	for	for	ADP
ejpam-4379	159	32	each	each	DET
ejpam-4379	159	33	α	α	PRON
ejpam-4379	159	34	∈	∈	PROPN
ejpam-4379	159	35	λ	λ	PROPN
ejpam-4379	159	36	}	}	PUNCT
ejpam-4379	159	37	be	be	AUX
ejpam-4379	159	38	any	any	DET
ejpam-4379	159	39	open	open	ADJ
ejpam-4379	159	40	cover	cover	NOUN
ejpam-4379	159	41	(	(	PUNCT
ejpam-4379	159	42	open	open	ADJ
ejpam-4379	159	43	in	in	ADP
ejpam-4379	159	44	τ	τ	PROPN
ejpam-4379	159	45	⋆	⋆	X
ejpam-4379	159	46	a	a	NOUN
ejpam-4379	159	47	)	)	PUNCT
ejpam-4379	159	48	for	for	ADP
ejpam-4379	159	49	a.	a.	NOUN
ejpam-4379	159	50	then	then	ADV
ejpam-4379	159	51	{	{	PUNCT
ejpam-4379	159	52	wα	wα	NOUN
ejpam-4379	159	53	:	:	PUNCT
ejpam-4379	159	54	α	α	PROPN
ejpam-4379	159	55	∈	∈	PROPN
ejpam-4379	159	56	λ	λ	PROPN
ejpam-4379	159	57	}	}	PUNCT
ejpam-4379	159	58	is	be	AUX
ejpam-4379	159	59	an	an	DET
ejpam-4379	159	60	open	open	ADJ
ejpam-4379	159	61	(	(	PUNCT
ejpam-4379	159	62	open	open	ADJ
ejpam-4379	159	63	in	in	ADP
ejpam-4379	159	64	τ	τ	PROPN
ejpam-4379	159	65	)	)	PUNCT
ejpam-4379	159	66	cover	cover	VERB
ejpam-4379	159	67	for	for	ADP
ejpam-4379	159	68	a	a	DET
ejpam-4379	159	69	\	\	NOUN
ejpam-4379	159	70	{	{	PUNCT
ejpam-4379	159	71	p	p	X
ejpam-4379	159	72	}	}	PUNCT
ejpam-4379	159	73	.	.	PUNCT
ejpam-4379	160	1	by	by	ADP
ejpam-4379	160	2	the	the	DET
ejpam-4379	160	3	hypothesis	hypothesis	NOUN
ejpam-4379	160	4	,	,	PUNCT
ejpam-4379	160	5	there	there	PRON
ejpam-4379	160	6	exist	exist	VERB
ejpam-4379	160	7	a	a	DET
ejpam-4379	160	8	finite	finite	ADJ
ejpam-4379	160	9	subcover	subcover	PROPN
ejpam-4379	160	10	{	{	PUNCT
ejpam-4379	160	11	wα1	wα1	NOUN
ejpam-4379	160	12	,	,	PUNCT
ejpam-4379	160	13	...	...	PUNCT
ejpam-4379	160	14	,	,	PUNCT
ejpam-4379	160	15	wαn	wαn	VERB
ejpam-4379	160	16	}	}	PUNCT
ejpam-4379	160	17	of	of	ADP
ejpam-4379	160	18	{	{	PUNCT
ejpam-4379	160	19	wα	wα	NOUN
ejpam-4379	160	20	:	:	PUNCT
ejpam-4379	160	21	α	α	PROPN
ejpam-4379	160	22	∈	∈	PROPN
ejpam-4379	160	23	λ	λ	PROPN
ejpam-4379	160	24	}	}	PUNCT
ejpam-4379	160	25	which	which	PRON
ejpam-4379	160	26	covers	cover	VERB
ejpam-4379	160	27	a	a	DET
ejpam-4379	160	28	\	\	NOUN
ejpam-4379	160	29	{	{	PUNCT
ejpam-4379	160	30	p	p	X
ejpam-4379	160	31	}	}	PUNCT
ejpam-4379	160	32	.	.	PUNCT
ejpam-4379	161	1	now	now	ADV
ejpam-4379	161	2	,	,	PUNCT
ejpam-4379	161	3	the	the	DET
ejpam-4379	161	4	family	family	NOUN
ejpam-4379	161	5	{	{	PUNCT
ejpam-4379	161	6	(	(	PUNCT
ejpam-4379	161	7	wαi	wαi	ADV
ejpam-4379	161	8	∪	∪	VERB
ejpam-4379	161	9	{	{	PUNCT
ejpam-4379	161	10	p	p	NOUN
ejpam-4379	161	11	}	}	PUNCT
ejpam-4379	161	12	)	)	PUNCT
ejpam-4379	161	13	∩	∩	NOUN
ejpam-4379	161	14	a	a	X
ejpam-4379	161	15	:	:	PUNCT
ejpam-4379	161	16	i	i	PRON
ejpam-4379	161	17	∈	∈	PROPN
ejpam-4379	161	18	{	{	PUNCT
ejpam-4379	161	19	1	1	NUM
ejpam-4379	161	20	,	,	PUNCT
ejpam-4379	161	21	...	...	PUNCT
ejpam-4379	161	22	,	,	PUNCT
ejpam-4379	161	23	n	n	CCONJ
ejpam-4379	161	24	}	}	PUNCT
ejpam-4379	161	25	}	}	PUNCT
ejpam-4379	161	26	is	be	AUX
ejpam-4379	161	27	a	a	DET
ejpam-4379	161	28	finite	finite	ADJ
ejpam-4379	161	29	subcover	subcover	NOUN
ejpam-4379	161	30	of	of	ADP
ejpam-4379	161	31	w	w	PROPN
ejpam-4379	161	32	which	which	PRON
ejpam-4379	161	33	covers	cover	VERB
ejpam-4379	161	34	a.	a.	NOUN
ejpam-4379	161	35	since	since	SCONJ
ejpam-4379	161	36	any	any	DET
ejpam-4379	161	37	subcover	subcover	NOUN
ejpam-4379	161	38	is	be	AUX
ejpam-4379	161	39	a	a	DET
ejpam-4379	161	40	refinement	refinement	NOUN
ejpam-4379	161	41	and	and	CCONJ
ejpam-4379	161	42	any	any	DET
ejpam-4379	161	43	finite	finite	ADJ
ejpam-4379	161	44	family	family	NOUN
ejpam-4379	161	45	is	be	AUX
ejpam-4379	161	46	locally	locally	ADV
ejpam-4379	161	47	finite	finite	ADJ
ejpam-4379	161	48	,	,	PUNCT
ejpam-4379	161	49	result	result	NOUN
ejpam-4379	161	50	follows	follow	VERB
ejpam-4379	161	51	.	.	PUNCT
ejpam-4379	162	1	therefore	therefore	ADV
ejpam-4379	162	2	,	,	PUNCT
ejpam-4379	162	3	(	(	PUNCT
ejpam-4379	162	4	a	a	X
ejpam-4379	162	5	,	,	PUNCT
ejpam-4379	162	6	τ	τ	PROPN
ejpam-4379	162	7	⋆	⋆	VERB
ejpam-4379	162	8	a	a	PRON
ejpam-4379	162	9	)	)	PUNCT
ejpam-4379	162	10	is	be	AUX
ejpam-4379	162	11	paracompact	paracompact	ADJ
ejpam-4379	162	12	.	.	PUNCT
ejpam-4379	163	1	since	since	SCONJ
ejpam-4379	163	2	any	any	DET
ejpam-4379	163	3	normal	normal	ADJ
ejpam-4379	163	4	space	space	NOUN
ejpam-4379	163	5	is	be	AUX
ejpam-4379	163	6	c	c	NOUN
ejpam-4379	163	7	-	-	ADJ
ejpam-4379	163	8	normal	normal	ADJ
ejpam-4379	163	9	,	,	PUNCT
ejpam-4379	163	10	cc	cc	NOUN
ejpam-4379	163	11	-	-	ADJ
ejpam-4379	163	12	normal	normal	ADJ
ejpam-4379	163	13	,	,	PUNCT
ejpam-4379	163	14	l	l	NOUN
ejpam-4379	163	15	-	-	ADJ
ejpam-4379	163	16	normal	normal	ADJ
ejpam-4379	163	17	,	,	PUNCT
ejpam-4379	163	18	s	s	NOUN
ejpam-4379	163	19	-	-	ADJ
ejpam-4379	163	20	normal	normal	ADJ
ejpam-4379	163	21	,	,	PUNCT
ejpam-4379	163	22	and	and	CCONJ
ejpam-4379	163	23	p	p	NOUN
ejpam-4379	163	24	-normal	-normal	NOUN
ejpam-4379	163	25	,	,	PUNCT
ejpam-4379	163	26	just	just	ADV
ejpam-4379	163	27	by	by	ADP
ejpam-4379	163	28	taking	take	VERB
ejpam-4379	163	29	in	in	ADP
ejpam-4379	163	30	definition	definition	NOUN
ejpam-4379	163	31	2	2	NUM
ejpam-4379	163	32	,	,	PUNCT
ejpam-4379	163	33	y	y	PROPN
ejpam-4379	163	34	=	=	PUNCT
ejpam-4379	164	1	x	x	PROPN
ejpam-4379	164	2	and	and	CCONJ
ejpam-4379	164	3	f	f	X
ejpam-4379	164	4	to	to	PART
ejpam-4379	164	5	be	be	AUX
ejpam-4379	164	6	the	the	DET
ejpam-4379	164	7	identity	identity	NOUN
ejpam-4379	164	8	function	function	NOUN
ejpam-4379	164	9	,	,	PUNCT
ejpam-4379	164	10	then	then	ADV
ejpam-4379	164	11	by	by	ADP
ejpam-4379	164	12	theorem	theorem	NOUN
ejpam-4379	164	13	2	2	NUM
ejpam-4379	164	14	,	,	PUNCT
ejpam-4379	164	15	we	we	PRON
ejpam-4379	164	16	get	get	VERB
ejpam-4379	164	17	the	the	DET
ejpam-4379	164	18	following	follow	VERB
ejpam-4379	164	19	theorem	theorem	VERB
ejpam-4379	164	20	.	.	PUNCT
ejpam-4379	164	21	theorem	theorem	NOUN
ejpam-4379	164	22	4	4	NUM
ejpam-4379	164	23	.	.	PUNCT
ejpam-4379	165	1	if	if	SCONJ
ejpam-4379	165	2	(	(	PUNCT
ejpam-4379	165	3	x	x	X
ejpam-4379	165	4	,	,	PUNCT
ejpam-4379	165	5	τ	τ	PROPN
ejpam-4379	165	6	)	)	PUNCT
ejpam-4379	165	7	is	be	AUX
ejpam-4379	165	8	ultra	ultra	ADJ
ejpam-4379	165	9	-	-	ADJ
ejpam-4379	165	10	connected	connected	ADJ
ejpam-4379	165	11	,	,	PUNCT
ejpam-4379	165	12	then	then	ADV
ejpam-4379	165	13	its	its	PRON
ejpam-4379	165	14	closed	closed	ADJ
ejpam-4379	165	15	extension	extension	NOUN
ejpam-4379	165	16	(	(	PUNCT
ejpam-4379	165	17	xp	xp	INTJ
ejpam-4379	165	18	,	,	PUNCT
ejpam-4379	165	19	τ	τ	PROPN
ejpam-4379	165	20	⋆	⋆	VERB
ejpam-4379	165	21	)	)	PUNCT
ejpam-4379	165	22	is	be	AUX
ejpam-4379	165	23	cnormal	cnormal	ADJ
ejpam-4379	165	24	(	(	PUNCT
ejpam-4379	165	25	cc	cc	NOUN
ejpam-4379	165	26	-	-	ADJ
ejpam-4379	165	27	normal	normal	ADJ
ejpam-4379	165	28	,	,	PUNCT
ejpam-4379	165	29	l	l	NOUN
ejpam-4379	165	30	-	-	ADJ
ejpam-4379	165	31	normal	normal	ADJ
ejpam-4379	165	32	,	,	PUNCT
ejpam-4379	165	33	s	s	NOUN
ejpam-4379	165	34	-	-	ADJ
ejpam-4379	165	35	normal	normal	ADJ
ejpam-4379	165	36	,	,	PUNCT
ejpam-4379	165	37	p	p	NOUN
ejpam-4379	165	38	-normal	-normal	NOUN
ejpam-4379	165	39	)	)	PUNCT
ejpam-4379	165	40	.	.	PUNCT
ejpam-4379	166	1	observe	observe	VERB
ejpam-4379	166	2	that	that	SCONJ
ejpam-4379	166	3	a	a	DET
ejpam-4379	166	4	space	space	NOUN
ejpam-4379	166	5	x	x	PUNCT
ejpam-4379	166	6	is	be	AUX
ejpam-4379	166	7	not	not	PART
ejpam-4379	166	8	ultra	ultra	ADJ
ejpam-4379	166	9	-	-	ADJ
ejpam-4379	166	10	connected	connected	ADJ
ejpam-4379	166	11	if	if	SCONJ
ejpam-4379	166	12	it	it	PRON
ejpam-4379	166	13	has	have	VERB
ejpam-4379	166	14	two	two	NUM
ejpam-4379	166	15	non	non	ADJ
ejpam-4379	166	16	-	-	ADJ
ejpam-4379	166	17	empty	empty	ADJ
ejpam-4379	166	18	closed	closed	ADJ
ejpam-4379	166	19	disjoint	disjoint	NOUN
ejpam-4379	166	20	subsets	subset	NOUN
ejpam-4379	166	21	.	.	PUNCT
ejpam-4379	167	1	d.	d.	PROPN
ejpam-4379	167	2	abuzaid	abuzaid	PROPN
ejpam-4379	167	3	,	,	PUNCT
ejpam-4379	167	4	s.	s.	PROPN
ejpam-4379	167	5	al	al	PROPN
ejpam-4379	167	6	-	-	PROPN
ejpam-4379	167	7	qarhi	qarhi	PROPN
ejpam-4379	167	8	,	,	PUNCT
ejpam-4379	167	9	l.	l.	PROPN
ejpam-4379	167	10	kalantan	kalantan	PROPN
ejpam-4379	167	11	/	/	SYM
ejpam-4379	167	12	eur	eur	PROPN
ejpam-4379	167	13	.	.	PUNCT
ejpam-4379	168	1	j.	j.	PROPN
ejpam-4379	168	2	pure	pure	PROPN
ejpam-4379	168	3	appl	appl	PROPN
ejpam-4379	168	4	.	.	PROPN
ejpam-4379	168	5	math	math	PROPN
ejpam-4379	168	6	,	,	PUNCT
ejpam-4379	168	7	15	15	NUM
ejpam-4379	168	8	(	(	PUNCT
ejpam-4379	168	9	2	2	NUM
ejpam-4379	168	10	)	)	PUNCT
ejpam-4379	168	11	(	(	PUNCT
ejpam-4379	168	12	2022	2022	NUM
ejpam-4379	168	13	)	)	PUNCT
ejpam-4379	168	14	,	,	PUNCT
ejpam-4379	168	15	672	672	NUM
ejpam-4379	168	16	-	-	SYM
ejpam-4379	168	17	680	680	NUM
ejpam-4379	168	18	677	677	NUM
ejpam-4379	168	19	theorem	theorem	NOUN
ejpam-4379	168	20	5	5	NUM
ejpam-4379	168	21	.	.	PUNCT
ejpam-4379	169	1	the	the	DET
ejpam-4379	169	2	closed	closed	ADJ
ejpam-4379	169	3	extension	extension	NOUN
ejpam-4379	169	4	space	space	NOUN
ejpam-4379	169	5	(	(	PUNCT
ejpam-4379	169	6	xp	xp	INTJ
ejpam-4379	169	7	,	,	PUNCT
ejpam-4379	169	8	τ	τ	PROPN
ejpam-4379	169	9	⋆	⋆	VERB
ejpam-4379	169	10	)	)	PUNCT
ejpam-4379	169	11	is	be	AUX
ejpam-4379	169	12	not	not	PART
ejpam-4379	169	13	c	c	NOUN
ejpam-4379	169	14	-	-	NOUN
ejpam-4379	169	15	normal	normal	ADJ
ejpam-4379	169	16	if	if	SCONJ
ejpam-4379	169	17	(	(	PUNCT
ejpam-4379	169	18	x	x	X
ejpam-4379	169	19	,	,	PUNCT
ejpam-4379	169	20	τ	τ	PROPN
ejpam-4379	169	21	)	)	PUNCT
ejpam-4379	169	22	is	be	AUX
ejpam-4379	169	23	not	not	PART
ejpam-4379	169	24	ultra	ultra	ADJ
ejpam-4379	169	25	-	-	ADJ
ejpam-4379	169	26	connected	connected	ADJ
ejpam-4379	169	27	.	.	PUNCT
ejpam-4379	170	1	proof	proof	NOUN
ejpam-4379	170	2	.	.	PUNCT
ejpam-4379	171	1	suppose	suppose	VERB
ejpam-4379	171	2	that	that	SCONJ
ejpam-4379	171	3	(	(	PUNCT
ejpam-4379	171	4	xp	xp	INTJ
ejpam-4379	171	5	,	,	PUNCT
ejpam-4379	171	6	τ	τ	PROPN
ejpam-4379	171	7	⋆	⋆	X
ejpam-4379	171	8	)	)	PUNCT
ejpam-4379	171	9	is	be	AUX
ejpam-4379	171	10	c	c	NOUN
ejpam-4379	171	11	-	-	ADJ
ejpam-4379	171	12	normal	normal	ADJ
ejpam-4379	171	13	.	.	PUNCT
ejpam-4379	172	1	let	let	VERB
ejpam-4379	172	2	y	y	PRON
ejpam-4379	172	3	be	be	AUX
ejpam-4379	172	4	a	a	DET
ejpam-4379	172	5	normal	normal	ADJ
ejpam-4379	172	6	space	space	NOUN
ejpam-4379	172	7	and	and	CCONJ
ejpam-4379	172	8	f	f	NOUN
ejpam-4379	172	9	:	:	PUNCT
ejpam-4379	172	10	xp	xp	INTJ
ejpam-4379	172	11	−→	−→	NOUN
ejpam-4379	172	12	y	y	PRON
ejpam-4379	172	13	be	be	AUX
ejpam-4379	172	14	a	a	DET
ejpam-4379	172	15	bijection	bijection	NOUN
ejpam-4379	172	16	such	such	ADJ
ejpam-4379	172	17	that	that	SCONJ
ejpam-4379	172	18	the	the	DET
ejpam-4379	172	19	restriction	restriction	NOUN
ejpam-4379	172	20	f|a	f|a	PUNCT
ejpam-4379	172	21	:	:	PUNCT
ejpam-4379	172	22	a	a	DET
ejpam-4379	172	23	−→	−→	NOUN
ejpam-4379	172	24	f(a	f(a	NOUN
ejpam-4379	172	25	)	)	PUNCT
ejpam-4379	172	26	is	be	AUX
ejpam-4379	172	27	a	a	DET
ejpam-4379	172	28	homeomorphism	homeomorphism	NOUN
ejpam-4379	172	29	for	for	ADP
ejpam-4379	172	30	each	each	DET
ejpam-4379	172	31	compact	compact	ADJ
ejpam-4379	172	32	subspace	subspace	NOUN
ejpam-4379	172	33	a	a	DET
ejpam-4379	172	34	of	of	ADP
ejpam-4379	172	35	(	(	PUNCT
ejpam-4379	172	36	xp	xp	INTJ
ejpam-4379	172	37	,	,	PUNCT
ejpam-4379	172	38	τ	τ	PROPN
ejpam-4379	172	39	⋆	⋆	NOUN
ejpam-4379	172	40	)	)	PUNCT
ejpam-4379	172	41	.	.	PUNCT
ejpam-4379	173	1	for	for	ADP
ejpam-4379	173	2	the	the	DET
ejpam-4379	173	3	space	space	NOUN
ejpam-4379	173	4	y	y	PROPN
ejpam-4379	173	5	,	,	PUNCT
ejpam-4379	173	6	we	we	PRON
ejpam-4379	173	7	have	have	VERB
ejpam-4379	173	8	only	only	ADV
ejpam-4379	173	9	two	two	NUM
ejpam-4379	173	10	cases	case	NOUN
ejpam-4379	173	11	:	:	PUNCT
ejpam-4379	173	12	case	case	NOUN
ejpam-4379	173	13	1	1	NUM
ejpam-4379	173	14	:	:	PUNCT
ejpam-4379	173	15	y	y	PROPN
ejpam-4379	173	16	is	be	AUX
ejpam-4379	173	17	t1	t1	NOUN
ejpam-4379	173	18	.	.	PUNCT
ejpam-4379	174	1	take	take	VERB
ejpam-4379	174	2	a	a	DET
ejpam-4379	174	3	=	=	X
ejpam-4379	174	4	{	{	PUNCT
ejpam-4379	174	5	x	x	NOUN
ejpam-4379	174	6	,	,	PUNCT
ejpam-4379	174	7	p	p	NOUN
ejpam-4379	174	8	}	}	PUNCT
ejpam-4379	174	9	,	,	PUNCT
ejpam-4379	174	10	where	where	SCONJ
ejpam-4379	174	11	x	x	SYM
ejpam-4379	174	12	∈	∈	PROPN
ejpam-4379	174	13	x.	x.	NOUN
ejpam-4379	174	14	then	then	ADV
ejpam-4379	174	15	a	a	PRON
ejpam-4379	174	16	is	be	AUX
ejpam-4379	174	17	a	a	DET
ejpam-4379	174	18	compact	compact	ADJ
ejpam-4379	174	19	subspace	subspace	NOUN
ejpam-4379	174	20	of	of	ADP
ejpam-4379	174	21	(	(	PUNCT
ejpam-4379	174	22	xp	xp	INTJ
ejpam-4379	174	23	,	,	PUNCT
ejpam-4379	174	24	τ	τ	PROPN
ejpam-4379	174	25	⋆	⋆	NOUN
ejpam-4379	174	26	)	)	PUNCT
ejpam-4379	174	27	.	.	PUNCT
ejpam-4379	175	1	by	by	ADP
ejpam-4379	175	2	assumption	assumption	NOUN
ejpam-4379	175	3	f|a	f|a	PROPN
ejpam-4379	175	4	:	:	PUNCT
ejpam-4379	175	5	a	a	DET
ejpam-4379	175	6	−→	−→	NOUN
ejpam-4379	175	7	f(a	f(a	NOUN
ejpam-4379	175	8	)	)	PUNCT
ejpam-4379	176	1	=	=	PRON
ejpam-4379	176	2	{	{	PUNCT
ejpam-4379	176	3	f(x	f(x	PROPN
ejpam-4379	176	4	)	)	PUNCT
ejpam-4379	176	5	,	,	PUNCT
ejpam-4379	176	6	f(p	f(p	PROPN
ejpam-4379	176	7	)	)	PUNCT
ejpam-4379	176	8	}	}	PUNCT
ejpam-4379	176	9	is	be	AUX
ejpam-4379	176	10	a	a	DET
ejpam-4379	176	11	homeomorphism	homeomorphism	NOUN
ejpam-4379	176	12	.	.	PUNCT
ejpam-4379	177	1	since	since	SCONJ
ejpam-4379	177	2	f(a	f(a	PROPN
ejpam-4379	177	3	)	)	PUNCT
ejpam-4379	177	4	is	be	AUX
ejpam-4379	177	5	a	a	DET
ejpam-4379	177	6	finite	finite	ADJ
ejpam-4379	177	7	subspace	subspace	NOUN
ejpam-4379	177	8	of	of	ADP
ejpam-4379	177	9	y	y	PROPN
ejpam-4379	177	10	and	and	CCONJ
ejpam-4379	177	11	y	y	PROPN
ejpam-4379	177	12	is	be	AUX
ejpam-4379	177	13	t1	t1	NOUN
ejpam-4379	177	14	,	,	PUNCT
ejpam-4379	177	15	then	then	ADV
ejpam-4379	177	16	f(a	f(a	PROPN
ejpam-4379	177	17	)	)	PUNCT
ejpam-4379	177	18	is	be	AUX
ejpam-4379	177	19	a	a	DET
ejpam-4379	177	20	discrete	discrete	ADJ
ejpam-4379	177	21	subspace	subspace	NOUN
ejpam-4379	177	22	of	of	ADP
ejpam-4379	177	23	y	y	PROPN
ejpam-4379	177	24	.	.	PUNCT
ejpam-4379	178	1	thus	thus	ADV
ejpam-4379	178	2	,	,	PUNCT
ejpam-4379	178	3	we	we	PRON
ejpam-4379	178	4	obtain	obtain	VERB
ejpam-4379	178	5	that	that	DET
ejpam-4379	178	6	f|a	f|a	NOUN
ejpam-4379	178	7	is	be	AUX
ejpam-4379	178	8	not	not	PART
ejpam-4379	178	9	continuous	continuous	ADJ
ejpam-4379	178	10	which	which	PRON
ejpam-4379	178	11	is	be	AUX
ejpam-4379	178	12	a	a	DET
ejpam-4379	178	13	contradiction	contradiction	NOUN
ejpam-4379	178	14	as	as	ADP
ejpam-4379	178	15	f|a	f|a	NOUN
ejpam-4379	178	16	is	be	AUX
ejpam-4379	178	17	a	a	DET
ejpam-4379	178	18	homeomorphism	homeomorphism	NOUN
ejpam-4379	178	19	.	.	PUNCT
ejpam-4379	179	1	case	case	NOUN
ejpam-4379	179	2	2	2	NUM
ejpam-4379	179	3	:	:	PUNCT
ejpam-4379	179	4	y	y	PROPN
ejpam-4379	179	5	is	be	AUX
ejpam-4379	179	6	not	not	PART
ejpam-4379	179	7	t1	t1	NOUN
ejpam-4379	179	8	.	.	PUNCT
ejpam-4379	180	1	we	we	PRON
ejpam-4379	180	2	claim	claim	VERB
ejpam-4379	180	3	that	that	SCONJ
ejpam-4379	180	4	the	the	DET
ejpam-4379	180	5	topology	topology	NOUN
ejpam-4379	180	6	on	on	ADP
ejpam-4379	180	7	y	y	PROPN
ejpam-4379	180	8	is	be	AUX
ejpam-4379	180	9	coarser	coarse	ADJ
ejpam-4379	180	10	than	than	ADP
ejpam-4379	180	11	the	the	DET
ejpam-4379	180	12	particular	particular	ADJ
ejpam-4379	180	13	point	point	NOUN
ejpam-4379	180	14	topology	topology	NOUN
ejpam-4379	180	15	on	on	ADP
ejpam-4379	180	16	y	y	PROPN
ejpam-4379	180	17	with	with	ADP
ejpam-4379	180	18	f(p	f(p	PROPN
ejpam-4379	180	19	)	)	PUNCT
ejpam-4379	180	20	as	as	ADP
ejpam-4379	180	21	its	its	PRON
ejpam-4379	180	22	particular	particular	ADJ
ejpam-4379	180	23	point	point	NOUN
ejpam-4379	180	24	.	.	PUNCT
ejpam-4379	181	1	to	to	PART
ejpam-4379	181	2	prove	prove	VERB
ejpam-4379	181	3	this	this	DET
ejpam-4379	181	4	claim	claim	NOUN
ejpam-4379	181	5	,	,	PUNCT
ejpam-4379	181	6	we	we	PRON
ejpam-4379	181	7	suppose	suppose	VERB
ejpam-4379	181	8	not	not	PART
ejpam-4379	181	9	.	.	PUNCT
ejpam-4379	182	1	then	then	ADV
ejpam-4379	182	2	there	there	PRON
ejpam-4379	182	3	exists	exist	VERB
ejpam-4379	182	4	a	a	DET
ejpam-4379	182	5	non	non	ADJ
ejpam-4379	182	6	-	-	ADJ
ejpam-4379	182	7	empty	empty	ADJ
ejpam-4379	182	8	open	open	ADJ
ejpam-4379	182	9	set	set	NOUN
ejpam-4379	182	10	u	u	PROPN
ejpam-4379	182	11	⊂	⊂	PROPN
ejpam-4379	182	12	y	y	PROPN
ejpam-4379	182	13	such	such	ADJ
ejpam-4379	182	14	that	that	SCONJ
ejpam-4379	182	15	f(p	f(p	NOUN
ejpam-4379	182	16	)	)	PUNCT
ejpam-4379	182	17	̸∈	̸∈	PROPN
ejpam-4379	182	18	u	u	PROPN
ejpam-4379	182	19	.	.	PUNCT
ejpam-4379	183	1	pick	pick	VERB
ejpam-4379	183	2	y	y	PROPN
ejpam-4379	183	3	∈	∈	PROPN
ejpam-4379	183	4	u	u	NOUN
ejpam-4379	183	5	and	and	CCONJ
ejpam-4379	183	6	let	let	VERB
ejpam-4379	183	7	x	x	SYM
ejpam-4379	183	8	∈	∈	PROPN
ejpam-4379	183	9	x	x	PUNCT
ejpam-4379	183	10	be	be	AUX
ejpam-4379	183	11	the	the	DET
ejpam-4379	183	12	unique	unique	ADJ
ejpam-4379	183	13	element	element	NOUN
ejpam-4379	183	14	such	such	ADJ
ejpam-4379	183	15	that	that	SCONJ
ejpam-4379	183	16	f(x	f(x	NOUN
ejpam-4379	183	17	)	)	PUNCT
ejpam-4379	184	1	=	=	PUNCT
ejpam-4379	184	2	y.	y.	NOUN
ejpam-4379	184	3	consider	consider	VERB
ejpam-4379	184	4	{	{	PUNCT
ejpam-4379	184	5	x	x	NOUN
ejpam-4379	184	6	,	,	PUNCT
ejpam-4379	184	7	p	p	NOUN
ejpam-4379	184	8	}	}	PUNCT
ejpam-4379	184	9	.	.	PUNCT
ejpam-4379	185	1	note	note	VERB
ejpam-4379	185	2	that	that	SCONJ
ejpam-4379	185	3	x	x	X
ejpam-4379	185	4	̸=	̸=	PROPN
ejpam-4379	185	5	p	p	NOUN
ejpam-4379	185	6	because	because	SCONJ
ejpam-4379	185	7	f(x	f(x	PROPN
ejpam-4379	185	8	)	)	PUNCT
ejpam-4379	186	1	=	=	PUNCT
ejpam-4379	186	2	y	y	PROPN
ejpam-4379	186	3	∈	∈	PROPN
ejpam-4379	186	4	u	u	PROPN
ejpam-4379	186	5	,	,	PUNCT
ejpam-4379	186	6	f(p	f(p	PROPN
ejpam-4379	186	7	)	)	PUNCT
ejpam-4379	186	8	̸∈	̸∈	PROPN
ejpam-4379	186	9	u	u	PROPN
ejpam-4379	186	10	,	,	PUNCT
ejpam-4379	186	11	and	and	CCONJ
ejpam-4379	186	12	f	f	PROPN
ejpam-4379	186	13	is	be	AUX
ejpam-4379	186	14	one	one	NUM
ejpam-4379	186	15	-	-	PUNCT
ejpam-4379	186	16	to	to	ADP
ejpam-4379	186	17	-	-	PUNCT
ejpam-4379	186	18	one	one	NUM
ejpam-4379	186	19	.	.	PUNCT
ejpam-4379	187	1	consider	consider	VERB
ejpam-4379	187	2	f|{x	f|{x	NOUN
ejpam-4379	187	3	,	,	PUNCT
ejpam-4379	187	4	p	p	NOUN
ejpam-4379	187	5	}	}	PUNCT
ejpam-4379	187	6	:	:	PUNCT
ejpam-4379	187	7	{	{	PUNCT
ejpam-4379	187	8	x	x	X
ejpam-4379	187	9	,	,	PUNCT
ejpam-4379	187	10	p	p	ADJ
ejpam-4379	187	11	}	}	PUNCT
ejpam-4379	187	12	−→	−→	NOUN
ejpam-4379	187	13	{	{	PUNCT
ejpam-4379	187	14	y	y	PROPN
ejpam-4379	187	15	,	,	PUNCT
ejpam-4379	187	16	f(p	f(p	PROPN
ejpam-4379	187	17	)	)	PUNCT
ejpam-4379	187	18	}	}	PUNCT
ejpam-4379	187	19	.	.	PUNCT
ejpam-4379	188	1	now	now	ADV
ejpam-4379	188	2	,	,	PUNCT
ejpam-4379	188	3	{	{	PUNCT
ejpam-4379	188	4	y	y	NOUN
ejpam-4379	188	5	}	}	PUNCT
ejpam-4379	188	6	is	be	AUX
ejpam-4379	188	7	open	open	ADJ
ejpam-4379	188	8	in	in	ADP
ejpam-4379	188	9	the	the	DET
ejpam-4379	188	10	subspace	subspace	NOUN
ejpam-4379	188	11	{	{	PUNCT
ejpam-4379	188	12	y	y	PROPN
ejpam-4379	188	13	,	,	PUNCT
ejpam-4379	188	14	f(p	f(p	PROPN
ejpam-4379	188	15	)	)	PUNCT
ejpam-4379	188	16	}	}	PUNCT
ejpam-4379	188	17	of	of	ADP
ejpam-4379	188	18	y	y	PROPN
ejpam-4379	188	19	because	because	SCONJ
ejpam-4379	188	20	{	{	PUNCT
ejpam-4379	188	21	y	y	NOUN
ejpam-4379	188	22	}	}	PUNCT
ejpam-4379	188	23	=	=	SYM
ejpam-4379	188	24	u	u	NOUN
ejpam-4379	188	25	∩	∩	NOUN
ejpam-4379	188	26	{	{	PUNCT
ejpam-4379	188	27	y	y	PROPN
ejpam-4379	188	28	,	,	PUNCT
ejpam-4379	188	29	f(p	f(p	PROPN
ejpam-4379	188	30	)	)	PUNCT
ejpam-4379	188	31	}	}	PUNCT
ejpam-4379	188	32	,	,	PUNCT
ejpam-4379	188	33	but	but	CCONJ
ejpam-4379	188	34	f−1({y	f−1({y	NOUN
ejpam-4379	188	35	}	}	PUNCT
ejpam-4379	188	36	)	)	PUNCT
ejpam-4379	188	37	=	=	SYM
ejpam-4379	189	1	{	{	PUNCT
ejpam-4379	189	2	x	x	NOUN
ejpam-4379	189	3	}	}	PUNCT
ejpam-4379	189	4	and	and	CCONJ
ejpam-4379	189	5	{	{	PUNCT
ejpam-4379	189	6	x	x	X
ejpam-4379	189	7	}	}	PUNCT
ejpam-4379	189	8	is	be	AUX
ejpam-4379	189	9	not	not	PART
ejpam-4379	189	10	open	open	ADJ
ejpam-4379	189	11	in	in	ADP
ejpam-4379	189	12	the	the	DET
ejpam-4379	189	13	subspace	subspace	NOUN
ejpam-4379	189	14	{	{	PUNCT
ejpam-4379	189	15	x	x	NOUN
ejpam-4379	189	16	,	,	PUNCT
ejpam-4379	189	17	p	p	NOUN
ejpam-4379	189	18	}	}	PUNCT
ejpam-4379	189	19	of	of	ADP
ejpam-4379	189	20	(	(	PUNCT
ejpam-4379	189	21	xp	xp	INTJ
ejpam-4379	189	22	,	,	PUNCT
ejpam-4379	189	23	τ	τ	PROPN
ejpam-4379	189	24	⋆	⋆	NOUN
ejpam-4379	189	25	)	)	PUNCT
ejpam-4379	189	26	,	,	PUNCT
ejpam-4379	189	27	which	which	PRON
ejpam-4379	189	28	means	mean	VERB
ejpam-4379	189	29	f|{x	f|{x	PROPN
ejpam-4379	189	30	,	,	PUNCT
ejpam-4379	189	31	p	p	PRON
ejpam-4379	189	32	}	}	PUNCT
ejpam-4379	189	33	is	be	AUX
ejpam-4379	189	34	not	not	PART
ejpam-4379	189	35	continuous	continuous	ADJ
ejpam-4379	189	36	.	.	PUNCT
ejpam-4379	190	1	this	this	PRON
ejpam-4379	190	2	is	be	AUX
ejpam-4379	190	3	a	a	DET
ejpam-4379	190	4	contradiction	contradiction	NOUN
ejpam-4379	190	5	,	,	PUNCT
ejpam-4379	190	6	and	and	CCONJ
ejpam-4379	190	7	our	our	PRON
ejpam-4379	190	8	claim	claim	NOUN
ejpam-4379	190	9	is	be	AUX
ejpam-4379	190	10	proved	prove	VERB
ejpam-4379	190	11	.	.	PUNCT
ejpam-4379	191	1	but	but	CCONJ
ejpam-4379	191	2	any	any	DET
ejpam-4379	191	3	topology	topology	NOUN
ejpam-4379	191	4	coarser	coarse	ADJ
ejpam-4379	191	5	than	than	ADP
ejpam-4379	191	6	the	the	DET
ejpam-4379	191	7	particular	particular	ADJ
ejpam-4379	191	8	point	point	NOUN
ejpam-4379	191	9	topology	topology	NOUN
ejpam-4379	191	10	has	have	VERB
ejpam-4379	191	11	no	no	DET
ejpam-4379	191	12	disjoint	disjoint	NOUN
ejpam-4379	191	13	nonempty	nonempty	X
ejpam-4379	191	14	open	open	ADJ
ejpam-4379	191	15	sets	set	NOUN
ejpam-4379	191	16	and	and	CCONJ
ejpam-4379	191	17	therefore	therefore	ADV
ejpam-4379	191	18	can	can	AUX
ejpam-4379	191	19	not	not	PART
ejpam-4379	191	20	be	be	AUX
ejpam-4379	191	21	normal	normal	ADJ
ejpam-4379	191	22	,	,	PUNCT
ejpam-4379	191	23	so	so	ADV
ejpam-4379	191	24	we	we	PRON
ejpam-4379	191	25	get	get	VERB
ejpam-4379	191	26	a	a	DET
ejpam-4379	191	27	contradiction	contradiction	NOUN
ejpam-4379	191	28	as	as	SCONJ
ejpam-4379	191	29	y	y	PROPN
ejpam-4379	191	30	is	be	AUX
ejpam-4379	191	31	assumed	assume	VERB
ejpam-4379	191	32	to	to	PART
ejpam-4379	191	33	be	be	AUX
ejpam-4379	191	34	normal	normal	ADJ
ejpam-4379	191	35	.	.	PUNCT
ejpam-4379	192	1	therefore	therefore	ADV
ejpam-4379	192	2	,	,	PUNCT
ejpam-4379	192	3	(	(	PUNCT
ejpam-4379	192	4	xp	xp	INTJ
ejpam-4379	192	5	,	,	PUNCT
ejpam-4379	192	6	τ	τ	PROPN
ejpam-4379	192	7	⋆	⋆	VERB
ejpam-4379	192	8	)	)	PUNCT
ejpam-4379	192	9	is	be	AUX
ejpam-4379	192	10	not	not	PART
ejpam-4379	192	11	c	c	NOUN
ejpam-4379	192	12	-	-	NOUN
ejpam-4379	192	13	normal	normal	ADJ
ejpam-4379	192	14	.	.	PUNCT
ejpam-4379	193	1	in	in	ADP
ejpam-4379	193	2	[	[	X
ejpam-4379	193	3	6	6	NUM
ejpam-4379	193	4	]	]	PUNCT
ejpam-4379	193	5	,	,	PUNCT
ejpam-4379	193	6	it	it	PRON
ejpam-4379	193	7	was	be	AUX
ejpam-4379	193	8	proved	prove	VERB
ejpam-4379	193	9	that	that	SCONJ
ejpam-4379	193	10	cc	cc	NOUN
ejpam-4379	193	11	-	-	ADJ
ejpam-4379	193	12	normality	normality	NOUN
ejpam-4379	193	13	implies	imply	VERB
ejpam-4379	193	14	c	c	NOUN
ejpam-4379	193	15	-	-	NOUN
ejpam-4379	193	16	normality	normality	NOUN
ejpam-4379	193	17	.	.	PUNCT
ejpam-4379	194	1	in	in	ADP
ejpam-4379	194	2	[	[	X
ejpam-4379	194	3	10	10	NUM
ejpam-4379	194	4	]	]	PUNCT
ejpam-4379	194	5	,	,	PUNCT
ejpam-4379	194	6	it	it	PRON
ejpam-4379	194	7	was	be	AUX
ejpam-4379	194	8	proved	prove	VERB
ejpam-4379	194	9	that	that	SCONJ
ejpam-4379	194	10	l	l	NOUN
ejpam-4379	194	11	-	-	ADJ
ejpam-4379	194	12	normality	normality	NOUN
ejpam-4379	194	13	implies	imply	VERB
ejpam-4379	194	14	c	c	NOUN
ejpam-4379	194	15	-	-	NOUN
ejpam-4379	194	16	normality	normality	NOUN
ejpam-4379	194	17	.	.	PUNCT
ejpam-4379	195	1	in	in	ADP
ejpam-4379	195	2	[	[	X
ejpam-4379	195	3	9	9	NUM
ejpam-4379	195	4	]	]	PUNCT
ejpam-4379	195	5	,	,	PUNCT
ejpam-4379	195	6	it	it	PRON
ejpam-4379	195	7	was	be	AUX
ejpam-4379	195	8	proved	prove	VERB
ejpam-4379	195	9	that	that	SCONJ
ejpam-4379	195	10	p	p	PROPN
ejpam-4379	195	11	-normality	-normality	PROPN
ejpam-4379	195	12	implies	imply	VERB
ejpam-4379	195	13	c	c	NOUN
ejpam-4379	195	14	-	-	NOUN
ejpam-4379	195	15	normality	normality	NOUN
ejpam-4379	195	16	.	.	PUNCT
ejpam-4379	196	1	so	so	ADV
ejpam-4379	196	2	,	,	PUNCT
ejpam-4379	196	3	by	by	ADP
ejpam-4379	196	4	theorem	theorem	NOUN
ejpam-4379	196	5	5	5	NUM
ejpam-4379	196	6	,	,	PUNCT
ejpam-4379	196	7	we	we	PRON
ejpam-4379	196	8	get	get	VERB
ejpam-4379	196	9	the	the	DET
ejpam-4379	196	10	following	follow	VERB
ejpam-4379	196	11	theorem	theorem	VERB
ejpam-4379	196	12	.	.	PUNCT
ejpam-4379	197	1	theorem	theorem	NOUN
ejpam-4379	197	2	6	6	NUM
ejpam-4379	197	3	.	.	PUNCT
ejpam-4379	198	1	if	if	SCONJ
ejpam-4379	198	2	(	(	PUNCT
ejpam-4379	198	3	x	x	X
ejpam-4379	198	4	,	,	PUNCT
ejpam-4379	198	5	τ	τ	PROPN
ejpam-4379	198	6	)	)	PUNCT
ejpam-4379	198	7	is	be	AUX
ejpam-4379	198	8	not	not	PART
ejpam-4379	198	9	ultra	ultra	ADJ
ejpam-4379	198	10	-	-	VERB
ejpam-4379	198	11	connected	connected	ADJ
ejpam-4379	198	12	,	,	PUNCT
ejpam-4379	198	13	then	then	ADV
ejpam-4379	198	14	the	the	DET
ejpam-4379	198	15	closed	closed	ADJ
ejpam-4379	198	16	extension	extension	NOUN
ejpam-4379	198	17	space	space	NOUN
ejpam-4379	198	18	(	(	PUNCT
ejpam-4379	198	19	xp	xp	INTJ
ejpam-4379	198	20	,	,	PUNCT
ejpam-4379	198	21	τ	τ	PROPN
ejpam-4379	198	22	⋆	⋆	VERB
ejpam-4379	198	23	)	)	PUNCT
ejpam-4379	198	24	is	be	AUX
ejpam-4379	198	25	neither	neither	DET
ejpam-4379	198	26	cc	cc	NOUN
ejpam-4379	198	27	-	-	ADJ
ejpam-4379	198	28	normal	normal	ADJ
ejpam-4379	198	29	,	,	PUNCT
ejpam-4379	198	30	l	l	NOUN
ejpam-4379	198	31	-	-	NOUN
ejpam-4379	198	32	normal	normal	ADJ
ejpam-4379	198	33	,	,	PUNCT
ejpam-4379	198	34	nor	nor	CCONJ
ejpam-4379	198	35	p	p	X
ejpam-4379	198	36	-normal	-normal	NOUN
ejpam-4379	198	37	.	.	PUNCT
ejpam-4379	199	1	now	now	ADV
ejpam-4379	199	2	,	,	PUNCT
ejpam-4379	199	3	let	let	VERB
ejpam-4379	199	4	us	we	PRON
ejpam-4379	199	5	study	study	VERB
ejpam-4379	199	6	s	s	NOUN
ejpam-4379	199	7	-	-	NOUN
ejpam-4379	199	8	normality	normality	NOUN
ejpam-4379	199	9	of	of	ADP
ejpam-4379	199	10	the	the	DET
ejpam-4379	199	11	closed	closed	ADJ
ejpam-4379	199	12	extension	extension	NOUN
ejpam-4379	199	13	.	.	PUNCT
ejpam-4379	200	1	we	we	PRON
ejpam-4379	200	2	start	start	VERB
ejpam-4379	200	3	with	with	ADP
ejpam-4379	200	4	characterizing	characterize	VERB
ejpam-4379	200	5	all	all	DET
ejpam-4379	200	6	separable	separable	ADJ
ejpam-4379	200	7	subspaces	subspace	NOUN
ejpam-4379	200	8	in	in	ADP
ejpam-4379	200	9	the	the	DET
ejpam-4379	200	10	closed	closed	ADJ
ejpam-4379	200	11	extension	extension	NOUN
ejpam-4379	200	12	.	.	PUNCT
ejpam-4379	201	1	note	note	VERB
ejpam-4379	201	2	that	that	SCONJ
ejpam-4379	201	3	{	{	PUNCT
ejpam-4379	201	4	p	p	X
ejpam-4379	201	5	}	}	PUNCT
ejpam-4379	201	6	is	be	AUX
ejpam-4379	201	7	a	a	DET
ejpam-4379	201	8	countable	countable	ADJ
ejpam-4379	201	9	dense	dense	ADJ
ejpam-4379	201	10	subset	subset	NOUN
ejpam-4379	201	11	in	in	ADP
ejpam-4379	201	12	(	(	PUNCT
ejpam-4379	201	13	xp	xp	INTJ
ejpam-4379	201	14	,	,	PUNCT
ejpam-4379	201	15	τ	τ	PROPN
ejpam-4379	201	16	⋆	⋆	NOUN
ejpam-4379	201	17	)	)	PUNCT
ejpam-4379	201	18	,	,	PUNCT
ejpam-4379	201	19	thus	thus	ADV
ejpam-4379	201	20	any	any	DET
ejpam-4379	201	21	subset	subset	NOUN
ejpam-4379	201	22	of	of	ADP
ejpam-4379	201	23	xp	xp	PROPN
ejpam-4379	201	24	will	will	AUX
ejpam-4379	201	25	be	be	AUX
ejpam-4379	201	26	separable	separable	ADJ
ejpam-4379	201	27	if	if	SCONJ
ejpam-4379	201	28	it	it	PRON
ejpam-4379	201	29	contains	contain	VERB
ejpam-4379	201	30	p.	p.	NOUN
ejpam-4379	201	31	since	since	SCONJ
ejpam-4379	201	32	a	a	DET
ejpam-4379	201	33	subspace	subspace	NOUN
ejpam-4379	201	34	of	of	ADP
ejpam-4379	201	35	a	a	DET
ejpam-4379	201	36	subspace	subspace	NOUN
ejpam-4379	201	37	is	be	AUX
ejpam-4379	201	38	a	a	DET
ejpam-4379	201	39	subspace	subspace	NOUN
ejpam-4379	201	40	,	,	PUNCT
ejpam-4379	201	41	we	we	PRON
ejpam-4379	201	42	conclude	conclude	VERB
ejpam-4379	201	43	the	the	DET
ejpam-4379	201	44	following	follow	VERB
ejpam-4379	201	45	characterizing	characterize	VERB
ejpam-4379	201	46	.	.	PUNCT
ejpam-4379	202	1	proposition	proposition	NOUN
ejpam-4379	202	2	4	4	NUM
ejpam-4379	202	3	.	.	PUNCT
ejpam-4379	203	1	let	let	AUX
ejpam-4379	203	2	(	(	PUNCT
ejpam-4379	203	3	xp	xp	INTJ
ejpam-4379	203	4	,	,	PUNCT
ejpam-4379	203	5	τ	τ	PROPN
ejpam-4379	203	6	⋆	⋆	X
ejpam-4379	203	7	)	)	PUNCT
ejpam-4379	203	8	be	be	AUX
ejpam-4379	203	9	the	the	DET
ejpam-4379	203	10	closed	closed	ADJ
ejpam-4379	203	11	extension	extension	NOUN
ejpam-4379	203	12	of	of	ADP
ejpam-4379	203	13	a	a	DET
ejpam-4379	203	14	topological	topological	ADJ
ejpam-4379	203	15	space	space	NOUN
ejpam-4379	203	16	(	(	PUNCT
ejpam-4379	203	17	x	x	X
ejpam-4379	203	18	,	,	PUNCT
ejpam-4379	203	19	τ	τ	PROPN
ejpam-4379	203	20	)	)	PUNCT
ejpam-4379	203	21	.	.	PUNCT
ejpam-4379	204	1	let	let	VERB
ejpam-4379	204	2	a	a	DET
ejpam-4379	204	3	⊆	⊆	NUM
ejpam-4379	204	4	xp	xp	NOUN
ejpam-4379	204	5	.	.	PUNCT
ejpam-4379	205	1	a	a	PRON
ejpam-4379	205	2	is	be	AUX
ejpam-4379	205	3	separable	separable	ADJ
ejpam-4379	205	4	in	in	ADP
ejpam-4379	205	5	(	(	PUNCT
ejpam-4379	205	6	xp	xp	INTJ
ejpam-4379	205	7	,	,	PUNCT
ejpam-4379	205	8	τ	τ	PROPN
ejpam-4379	205	9	⋆	⋆	NOUN
ejpam-4379	205	10	)	)	PUNCT
ejpam-4379	206	1	if	if	SCONJ
ejpam-4379	206	2	and	and	CCONJ
ejpam-4379	206	3	only	only	ADV
ejpam-4379	206	4	if	if	SCONJ
ejpam-4379	206	5	either	either	CCONJ
ejpam-4379	206	6	p	p	PROPN
ejpam-4379	206	7	∈	∈	PROPN
ejpam-4379	206	8	a	a	PRON
ejpam-4379	206	9	or	or	CCONJ
ejpam-4379	206	10	a	a	PRON
ejpam-4379	206	11	is	be	AUX
ejpam-4379	206	12	a	a	DET
ejpam-4379	206	13	separable	separable	ADJ
ejpam-4379	206	14	subspace	subspace	NOUN
ejpam-4379	206	15	of	of	ADP
ejpam-4379	206	16	(	(	PUNCT
ejpam-4379	206	17	x	x	INTJ
ejpam-4379	206	18	,	,	PUNCT
ejpam-4379	206	19	τ	τ	PROPN
ejpam-4379	206	20	)	)	PUNCT
ejpam-4379	206	21	.	.	PUNCT
ejpam-4379	207	1	theorem	theorem	VERB
ejpam-4379	207	2	7	7	NUM
ejpam-4379	207	3	.	.	PUNCT
ejpam-4379	208	1	the	the	DET
ejpam-4379	208	2	closed	closed	ADJ
ejpam-4379	208	3	extension	extension	NOUN
ejpam-4379	208	4	(	(	PUNCT
ejpam-4379	208	5	xp	xp	INTJ
ejpam-4379	208	6	,	,	PUNCT
ejpam-4379	208	7	τ	τ	PROPN
ejpam-4379	208	8	⋆	⋆	X
ejpam-4379	208	9	)	)	PUNCT
ejpam-4379	208	10	is	be	AUX
ejpam-4379	208	11	s	s	NOUN
ejpam-4379	208	12	-	-	ADJ
ejpam-4379	208	13	normal	normal	ADJ
ejpam-4379	208	14	if	if	SCONJ
ejpam-4379	208	15	and	and	CCONJ
ejpam-4379	208	16	only	only	ADV
ejpam-4379	208	17	if	if	SCONJ
ejpam-4379	208	18	(	(	PUNCT
ejpam-4379	208	19	x	x	X
ejpam-4379	208	20	,	,	PUNCT
ejpam-4379	208	21	τ	τ	PROPN
ejpam-4379	208	22	)	)	PUNCT
ejpam-4379	208	23	is	be	AUX
ejpam-4379	208	24	ultraconnected	ultraconnecte	VERB
ejpam-4379	208	25	.	.	PUNCT
ejpam-4379	209	1	proof	proof	NOUN
ejpam-4379	209	2	.	.	PUNCT
ejpam-4379	210	1	assume	assume	VERB
ejpam-4379	210	2	that	that	SCONJ
ejpam-4379	210	3	the	the	DET
ejpam-4379	210	4	closed	closed	ADJ
ejpam-4379	210	5	extension	extension	NOUN
ejpam-4379	210	6	(	(	PUNCT
ejpam-4379	210	7	xp	xp	INTJ
ejpam-4379	210	8	,	,	PUNCT
ejpam-4379	210	9	τ	τ	PROPN
ejpam-4379	210	10	⋆	⋆	X
ejpam-4379	210	11	)	)	PUNCT
ejpam-4379	210	12	is	be	AUX
ejpam-4379	210	13	s	s	NOUN
ejpam-4379	210	14	-	-	ADJ
ejpam-4379	210	15	normal	normal	ADJ
ejpam-4379	210	16	.	.	PUNCT
ejpam-4379	211	1	pick	pick	VERB
ejpam-4379	211	2	a	a	DET
ejpam-4379	211	3	normal	normal	ADJ
ejpam-4379	211	4	space	space	NOUN
ejpam-4379	211	5	y	y	PROPN
ejpam-4379	211	6	and	and	CCONJ
ejpam-4379	211	7	a	a	DET
ejpam-4379	211	8	bijection	bijection	NOUN
ejpam-4379	211	9	function	function	NOUN
ejpam-4379	211	10	f	f	NOUN
ejpam-4379	211	11	:	:	PUNCT
ejpam-4379	211	12	xp	xp	INTJ
ejpam-4379	212	1	−→	−→	VERB
ejpam-4379	212	2	y	y	PROPN
ejpam-4379	212	3	such	such	ADJ
ejpam-4379	212	4	that	that	SCONJ
ejpam-4379	212	5	the	the	DET
ejpam-4379	212	6	restriction	restriction	NOUN
ejpam-4379	212	7	f|a	f|a	PUNCT
ejpam-4379	212	8	:	:	PUNCT
ejpam-4379	212	9	a	a	DET
ejpam-4379	212	10	−→	−→	NOUN
ejpam-4379	212	11	f(a	f(a	NOUN
ejpam-4379	212	12	)	)	PUNCT
ejpam-4379	212	13	is	be	AUX
ejpam-4379	212	14	a	a	DET
ejpam-4379	212	15	homeomorphism	homeomorphism	NOUN
ejpam-4379	212	16	for	for	ADP
ejpam-4379	212	17	each	each	DET
ejpam-4379	212	18	separable	separable	ADJ
ejpam-4379	212	19	subspace	subspace	NOUN
ejpam-4379	212	20	a	a	DET
ejpam-4379	212	21	⊆	⊆	NUM
ejpam-4379	212	22	xp	xp	NOUN
ejpam-4379	212	23	.	.	PUNCT
ejpam-4379	213	1	since	since	SCONJ
ejpam-4379	213	2	(	(	PUNCT
ejpam-4379	213	3	xp	xp	INTJ
ejpam-4379	213	4	,	,	PUNCT
ejpam-4379	213	5	τ	τ	PROPN
ejpam-4379	213	6	⋆	⋆	X
ejpam-4379	213	7	)	)	PUNCT
ejpam-4379	213	8	itself	itself	PRON
ejpam-4379	213	9	is	be	AUX
ejpam-4379	213	10	separable	separable	ADJ
ejpam-4379	213	11	,	,	PUNCT
ejpam-4379	213	12	as	as	SCONJ
ejpam-4379	213	13	{	{	PUNCT
ejpam-4379	213	14	p	p	NOUN
ejpam-4379	213	15	}	}	PUNCT
ejpam-4379	213	16	is	be	AUX
ejpam-4379	213	17	a	a	DET
ejpam-4379	213	18	countable	countable	ADJ
ejpam-4379	213	19	dense	dense	ADJ
ejpam-4379	213	20	subset	subset	NOUN
ejpam-4379	213	21	,	,	PUNCT
ejpam-4379	213	22	then	then	ADV
ejpam-4379	213	23	f	f	PROPN
ejpam-4379	213	24	is	be	AUX
ejpam-4379	213	25	a	a	DET
ejpam-4379	213	26	homeomorphism	homeomorphism	NOUN
ejpam-4379	213	27	.	.	PUNCT
ejpam-4379	214	1	thus	thus	ADV
ejpam-4379	214	2	(	(	PUNCT
ejpam-4379	214	3	xp	xp	INTJ
ejpam-4379	214	4	,	,	PUNCT
ejpam-4379	214	5	τ	τ	PROPN
ejpam-4379	214	6	⋆	⋆	VERB
ejpam-4379	214	7	)	)	PUNCT
ejpam-4379	214	8	is	be	AUX
ejpam-4379	214	9	normal	normal	ADJ
ejpam-4379	214	10	and	and	CCONJ
ejpam-4379	214	11	by	by	ADP
ejpam-4379	214	12	theorem	theorem	NOUN
ejpam-4379	214	13	2	2	NUM
ejpam-4379	214	14	we	we	PRON
ejpam-4379	214	15	get	get	VERB
ejpam-4379	214	16	that	that	PRON
ejpam-4379	214	17	(	(	PUNCT
ejpam-4379	214	18	x	x	X
ejpam-4379	214	19	,	,	PUNCT
ejpam-4379	214	20	τ	τ	PROPN
ejpam-4379	214	21	)	)	PUNCT
ejpam-4379	214	22	is	be	AUX
ejpam-4379	214	23	ultra	ultra	ADJ
ejpam-4379	214	24	-	-	ADJ
ejpam-4379	214	25	connected	connected	ADJ
ejpam-4379	214	26	.	.	PUNCT
ejpam-4379	215	1	d.	d.	PROPN
ejpam-4379	215	2	abuzaid	abuzaid	PROPN
ejpam-4379	215	3	,	,	PUNCT
ejpam-4379	215	4	s.	s.	PROPN
ejpam-4379	215	5	al	al	PROPN
ejpam-4379	215	6	-	-	PROPN
ejpam-4379	215	7	qarhi	qarhi	PROPN
ejpam-4379	215	8	,	,	PUNCT
ejpam-4379	215	9	l.	l.	PROPN
ejpam-4379	215	10	kalantan	kalantan	PROPN
ejpam-4379	215	11	/	/	SYM
ejpam-4379	215	12	eur	eur	PROPN
ejpam-4379	215	13	.	.	PUNCT
ejpam-4379	216	1	j.	j.	PROPN
ejpam-4379	216	2	pure	pure	PROPN
ejpam-4379	216	3	appl	appl	PROPN
ejpam-4379	216	4	.	.	PROPN
ejpam-4379	216	5	math	math	PROPN
ejpam-4379	216	6	,	,	PUNCT
ejpam-4379	216	7	15	15	NUM
ejpam-4379	216	8	(	(	PUNCT
ejpam-4379	216	9	2	2	NUM
ejpam-4379	216	10	)	)	PUNCT
ejpam-4379	216	11	(	(	PUNCT
ejpam-4379	216	12	2022	2022	NUM
ejpam-4379	216	13	)	)	PUNCT
ejpam-4379	216	14	,	,	PUNCT
ejpam-4379	216	15	672	672	NUM
ejpam-4379	216	16	-	-	SYM
ejpam-4379	216	17	680	680	NUM
ejpam-4379	216	18	678	678	NUM
ejpam-4379	216	19	now	now	ADV
ejpam-4379	216	20	,	,	PUNCT
ejpam-4379	216	21	assume	assume	VERB
ejpam-4379	216	22	that	that	SCONJ
ejpam-4379	216	23	(	(	PUNCT
ejpam-4379	216	24	x	x	X
ejpam-4379	216	25	,	,	PUNCT
ejpam-4379	216	26	τ	τ	PROPN
ejpam-4379	216	27	)	)	PUNCT
ejpam-4379	216	28	is	be	AUX
ejpam-4379	216	29	ultra	ultra	ADJ
ejpam-4379	216	30	-	-	ADJ
ejpam-4379	216	31	connected	connected	ADJ
ejpam-4379	216	32	.	.	PUNCT
ejpam-4379	217	1	by	by	ADP
ejpam-4379	217	2	theorem	theorem	NOUN
ejpam-4379	217	3	2	2	NUM
ejpam-4379	217	4	,	,	PUNCT
ejpam-4379	217	5	we	we	PRON
ejpam-4379	217	6	have	have	VERB
ejpam-4379	217	7	that	that	PRON
ejpam-4379	217	8	(	(	PUNCT
ejpam-4379	217	9	xp	xp	INTJ
ejpam-4379	217	10	,	,	PUNCT
ejpam-4379	217	11	τ	τ	PROPN
ejpam-4379	217	12	⋆	⋆	VERB
ejpam-4379	217	13	)	)	PUNCT
ejpam-4379	217	14	is	be	AUX
ejpam-4379	217	15	normal	normal	ADJ
ejpam-4379	217	16	.	.	PUNCT
ejpam-4379	218	1	in	in	ADP
ejpam-4379	218	2	definition	definition	NOUN
ejpam-4379	218	3	2	2	NUM
ejpam-4379	218	4	,	,	PUNCT
ejpam-4379	218	5	put	put	VERB
ejpam-4379	218	6	y	y	NOUN
ejpam-4379	218	7	=	=	PUNCT
ejpam-4379	219	1	xp	xp	PROPN
ejpam-4379	220	1	and	and	CCONJ
ejpam-4379	220	2	f	f	PROPN
ejpam-4379	220	3	is	be	AUX
ejpam-4379	220	4	the	the	DET
ejpam-4379	220	5	identity	identity	NOUN
ejpam-4379	220	6	function	function	NOUN
ejpam-4379	220	7	on	on	ADP
ejpam-4379	220	8	xp	xp	INTJ
ejpam-4379	220	9	to	to	PART
ejpam-4379	220	10	get	get	VERB
ejpam-4379	220	11	that	that	SCONJ
ejpam-4379	220	12	the	the	DET
ejpam-4379	220	13	closed	closed	ADJ
ejpam-4379	220	14	extension	extension	NOUN
ejpam-4379	220	15	(	(	PUNCT
ejpam-4379	220	16	xp	xp	INTJ
ejpam-4379	220	17	,	,	PUNCT
ejpam-4379	220	18	τ	τ	PROPN
ejpam-4379	220	19	⋆	⋆	X
ejpam-4379	220	20	)	)	PUNCT
ejpam-4379	220	21	is	be	AUX
ejpam-4379	220	22	s	s	NOUN
ejpam-4379	220	23	-	-	ADJ
ejpam-4379	220	24	normal	normal	ADJ
ejpam-4379	220	25	.	.	PUNCT
ejpam-4379	221	1	definition	definition	NOUN
ejpam-4379	221	2	3	3	NUM
ejpam-4379	221	3	.	.	PUNCT
ejpam-4379	221	4	two	two	NUM
ejpam-4379	221	5	disjoint	disjoint	NOUN
ejpam-4379	221	6	subsets	subset	NOUN
ejpam-4379	221	7	e	e	PROPN
ejpam-4379	221	8	and	and	CCONJ
ejpam-4379	221	9	f	f	PROPN
ejpam-4379	221	10	of	of	ADP
ejpam-4379	221	11	a	a	DET
ejpam-4379	221	12	space	space	NOUN
ejpam-4379	221	13	x	x	PRON
ejpam-4379	221	14	are	be	AUX
ejpam-4379	221	15	called	call	VERB
ejpam-4379	221	16	separated	separate	VERB
ejpam-4379	221	17	if	if	SCONJ
ejpam-4379	221	18	there	there	PRON
ejpam-4379	221	19	exist	exist	VERB
ejpam-4379	221	20	two	two	NUM
ejpam-4379	221	21	disjoint	disjoint	ADJ
ejpam-4379	221	22	open	open	ADJ
ejpam-4379	221	23	sets	set	NOUN
ejpam-4379	221	24	u	u	NOUN
ejpam-4379	221	25	and	and	CCONJ
ejpam-4379	221	26	v	v	ADP
ejpam-4379	221	27	such	such	ADJ
ejpam-4379	221	28	that	that	SCONJ
ejpam-4379	221	29	e	e	PROPN
ejpam-4379	221	30	⊆	⊆	NUM
ejpam-4379	221	31	u	u	NOUN
ejpam-4379	221	32	and	and	CCONJ
ejpam-4379	221	33	f	f	PROPN
ejpam-4379	221	34	⊆	⊆	NUM
ejpam-4379	221	35	v	v	NOUN
ejpam-4379	221	36	.	.	PUNCT
ejpam-4379	222	1	a	a	DET
ejpam-4379	222	2	subset	subset	NOUN
ejpam-4379	222	3	a	a	PRON
ejpam-4379	222	4	of	of	ADP
ejpam-4379	222	5	a	a	DET
ejpam-4379	222	6	space	space	NOUN
ejpam-4379	222	7	x	x	PUNCT
ejpam-4379	222	8	is	be	AUX
ejpam-4379	222	9	called	call	VERB
ejpam-4379	222	10	closed	closed	ADJ
ejpam-4379	222	11	domain	domain	NOUN
ejpam-4379	222	12	[	[	X
ejpam-4379	222	13	2	2	NUM
ejpam-4379	222	14	,	,	PUNCT
ejpam-4379	222	15	1.1.c	1.1.c	NUM
ejpam-4379	222	16	]	]	PUNCT
ejpam-4379	222	17	,	,	PUNCT
ejpam-4379	222	18	called	call	VERB
ejpam-4379	222	19	also	also	ADV
ejpam-4379	222	20	regularly	regularly	ADV
ejpam-4379	222	21	closed	close	VERB
ejpam-4379	222	22	,	,	PUNCT
ejpam-4379	222	23	κ	κ	NOUN
ejpam-4379	223	1	-	-	PUNCT
ejpam-4379	223	2	closed	closed	ADJ
ejpam-4379	223	3	,	,	PUNCT
ejpam-4379	223	4	if	if	SCONJ
ejpam-4379	223	5	a	a	DET
ejpam-4379	223	6	=	=	X
ejpam-4379	223	7	inta	inta	PROPN
ejpam-4379	223	8	.	.	PUNCT
ejpam-4379	224	1	a	a	DET
ejpam-4379	224	2	subset	subset	NOUN
ejpam-4379	224	3	a	a	PRON
ejpam-4379	224	4	of	of	ADP
ejpam-4379	224	5	a	a	DET
ejpam-4379	224	6	space	space	NOUN
ejpam-4379	224	7	x	x	PUNCT
ejpam-4379	224	8	is	be	AUX
ejpam-4379	224	9	called	call	VERB
ejpam-4379	224	10	open	open	ADJ
ejpam-4379	224	11	domain	domain	NOUN
ejpam-4379	224	12	[	[	X
ejpam-4379	224	13	2	2	NUM
ejpam-4379	224	14	,	,	PUNCT
ejpam-4379	224	15	1.1.c	1.1.c	NUM
ejpam-4379	224	16	]	]	PUNCT
ejpam-4379	224	17	,	,	PUNCT
ejpam-4379	224	18	called	call	VERB
ejpam-4379	224	19	also	also	ADV
ejpam-4379	224	20	regularly	regularly	ADV
ejpam-4379	224	21	open	open	ADJ
ejpam-4379	224	22	,	,	PUNCT
ejpam-4379	224	23	κ	κ	NOUN
ejpam-4379	224	24	-	-	ADJ
ejpam-4379	224	25	open	open	ADJ
ejpam-4379	224	26	,	,	PUNCT
ejpam-4379	224	27	if	if	SCONJ
ejpam-4379	224	28	a	a	PRON
ejpam-4379	224	29	=	=	X
ejpam-4379	224	30	int(a	int(a	NOUN
ejpam-4379	224	31	)	)	PUNCT
ejpam-4379	224	32	.	.	PUNCT
ejpam-4379	225	1	a	a	DET
ejpam-4379	225	2	space	space	NOUN
ejpam-4379	225	3	x	x	PUNCT
ejpam-4379	225	4	is	be	AUX
ejpam-4379	225	5	called	call	VERB
ejpam-4379	225	6	mildly	mildly	ADV
ejpam-4379	225	7	normal	normal	ADJ
ejpam-4379	225	8	[	[	X
ejpam-4379	225	9	14	14	NUM
ejpam-4379	225	10	]	]	PUNCT
ejpam-4379	225	11	,	,	PUNCT
ejpam-4379	225	12	called	call	VERB
ejpam-4379	225	13	also	also	ADV
ejpam-4379	225	14	κ	κ	NOUN
ejpam-4379	225	15	-	-	ADJ
ejpam-4379	225	16	normal	normal	ADJ
ejpam-4379	225	17	[	[	X
ejpam-4379	225	18	16	16	NUM
ejpam-4379	225	19	]	]	X
ejpam-4379	225	20	,	,	PUNCT
ejpam-4379	225	21	if	if	SCONJ
ejpam-4379	225	22	any	any	DET
ejpam-4379	225	23	two	two	NUM
ejpam-4379	225	24	disjoint	disjoint	NOUN
ejpam-4379	225	25	closed	close	VERB
ejpam-4379	225	26	domains	domain	NOUN
ejpam-4379	225	27	a	a	PRON
ejpam-4379	225	28	and	and	CCONJ
ejpam-4379	225	29	b	b	NOUN
ejpam-4379	225	30	of	of	ADP
ejpam-4379	225	31	x	x	PRON
ejpam-4379	225	32	are	be	AUX
ejpam-4379	225	33	separated	separate	VERB
ejpam-4379	225	34	.	.	PUNCT
ejpam-4379	226	1	in	in	ADP
ejpam-4379	226	2	[	[	X
ejpam-4379	226	3	16	16	NUM
ejpam-4379	226	4	]	]	PUNCT
ejpam-4379	226	5	,	,	PUNCT
ejpam-4379	226	6	ščepin	ščepin	DET
ejpam-4379	226	7	required	require	VERB
ejpam-4379	226	8	regularity	regularity	NOUN
ejpam-4379	226	9	in	in	ADP
ejpam-4379	226	10	his	his	PRON
ejpam-4379	226	11	definition	definition	NOUN
ejpam-4379	226	12	of	of	ADP
ejpam-4379	226	13	κ	κ	NOUN
ejpam-4379	226	14	-	-	NOUN
ejpam-4379	226	15	normality	normality	NOUN
ejpam-4379	226	16	,	,	PUNCT
ejpam-4379	226	17	see	see	VERB
ejpam-4379	226	18	also	also	ADV
ejpam-4379	226	19	[	[	X
ejpam-4379	226	20	4	4	NUM
ejpam-4379	226	21	,	,	PUNCT
ejpam-4379	226	22	11	11	NUM
ejpam-4379	226	23	]	]	PUNCT
ejpam-4379	226	24	.	.	PUNCT
ejpam-4379	227	1	a	a	DET
ejpam-4379	227	2	space	space	NOUN
ejpam-4379	227	3	x	x	PUNCT
ejpam-4379	227	4	is	be	AUX
ejpam-4379	227	5	called	call	VERB
ejpam-4379	227	6	almost	almost	ADV
ejpam-4379	227	7	normal	normal	ADJ
ejpam-4379	227	8	[	[	X
ejpam-4379	227	9	13	13	NUM
ejpam-4379	227	10	]	]	X
ejpam-4379	227	11	if	if	SCONJ
ejpam-4379	227	12	for	for	ADP
ejpam-4379	227	13	two	two	NUM
ejpam-4379	227	14	disjoint	disjoint	NOUN
ejpam-4379	227	15	closed	closed	ADJ
ejpam-4379	227	16	subsets	subset	NOUN
ejpam-4379	227	17	a	a	PRON
ejpam-4379	227	18	and	and	CCONJ
ejpam-4379	227	19	b	b	NOUN
ejpam-4379	227	20	of	of	ADP
ejpam-4379	227	21	x	x	PRON
ejpam-4379	227	22	one	one	NUM
ejpam-4379	227	23	of	of	ADP
ejpam-4379	227	24	which	which	PRON
ejpam-4379	227	25	is	be	AUX
ejpam-4379	227	26	closed	closed	ADJ
ejpam-4379	227	27	domain	domain	NOUN
ejpam-4379	227	28	are	be	AUX
ejpam-4379	227	29	separated	separate	VERB
ejpam-4379	227	30	,	,	PUNCT
ejpam-4379	227	31	see	see	VERB
ejpam-4379	227	32	also	also	ADV
ejpam-4379	227	33	[	[	X
ejpam-4379	227	34	8	8	NUM
ejpam-4379	227	35	]	]	PUNCT
ejpam-4379	227	36	.	.	PUNCT
ejpam-4379	228	1	a	a	DET
ejpam-4379	228	2	subset	subset	NOUN
ejpam-4379	228	3	a	a	PRON
ejpam-4379	228	4	of	of	ADP
ejpam-4379	228	5	a	a	DET
ejpam-4379	228	6	space	space	NOUN
ejpam-4379	228	7	x	x	PUNCT
ejpam-4379	228	8	is	be	AUX
ejpam-4379	228	9	called	call	VERB
ejpam-4379	228	10	π	π	PROPN
ejpam-4379	228	11	-	-	VERB
ejpam-4379	228	12	closed	closed	ADJ
ejpam-4379	228	13	[	[	X
ejpam-4379	228	14	17	17	NUM
ejpam-4379	228	15	]	]	X
ejpam-4379	228	16	if	if	SCONJ
ejpam-4379	228	17	a	a	PRON
ejpam-4379	228	18	is	be	AUX
ejpam-4379	228	19	a	a	DET
ejpam-4379	228	20	finite	finite	ADJ
ejpam-4379	228	21	intersection	intersection	NOUN
ejpam-4379	228	22	of	of	ADP
ejpam-4379	228	23	closed	closed	ADJ
ejpam-4379	228	24	domains	domain	NOUN
ejpam-4379	228	25	.	.	PUNCT
ejpam-4379	229	1	the	the	DET
ejpam-4379	229	2	complement	complement	NOUN
ejpam-4379	229	3	of	of	ADP
ejpam-4379	229	4	a	a	DET
ejpam-4379	229	5	π	π	PROPN
ejpam-4379	229	6	-	-	ADJ
ejpam-4379	229	7	closed	closed	ADJ
ejpam-4379	229	8	set	set	NOUN
ejpam-4379	229	9	is	be	AUX
ejpam-4379	229	10	called	call	VERB
ejpam-4379	229	11	π	π	NOUN
ejpam-4379	229	12	-	-	NOUN
ejpam-4379	229	13	open	open	ADJ
ejpam-4379	229	14	[	[	X
ejpam-4379	229	15	17	17	NUM
ejpam-4379	229	16	]	]	PUNCT
ejpam-4379	229	17	.	.	PUNCT
ejpam-4379	230	1	a	a	DET
ejpam-4379	230	2	space	space	NOUN
ejpam-4379	230	3	x	x	PUNCT
ejpam-4379	230	4	is	be	AUX
ejpam-4379	230	5	called	call	VERB
ejpam-4379	230	6	π	π	PROPN
ejpam-4379	230	7	-	-	NOUN
ejpam-4379	230	8	normal	normal	ADJ
ejpam-4379	230	9	[	[	X
ejpam-4379	230	10	5	5	NUM
ejpam-4379	230	11	]	]	PUNCT
ejpam-4379	230	12	if	if	SCONJ
ejpam-4379	230	13	any	any	DET
ejpam-4379	230	14	two	two	NUM
ejpam-4379	230	15	disjoint	disjoint	NOUN
ejpam-4379	230	16	closed	closed	ADJ
ejpam-4379	230	17	subsets	subset	NOUN
ejpam-4379	230	18	a	a	PRON
ejpam-4379	230	19	and	and	CCONJ
ejpam-4379	230	20	b	b	NOUN
ejpam-4379	230	21	of	of	ADP
ejpam-4379	230	22	x	x	PRON
ejpam-4379	230	23	one	one	NUM
ejpam-4379	230	24	of	of	ADP
ejpam-4379	230	25	which	which	PRON
ejpam-4379	230	26	is	be	AUX
ejpam-4379	230	27	π	π	PROPN
ejpam-4379	230	28	-	-	VERB
ejpam-4379	230	29	closed	closed	ADJ
ejpam-4379	230	30	are	be	AUX
ejpam-4379	230	31	separated	separate	VERB
ejpam-4379	230	32	.	.	PUNCT
ejpam-4379	231	1	a	a	DET
ejpam-4379	231	2	space	space	NOUN
ejpam-4379	231	3	x	x	PUNCT
ejpam-4379	231	4	is	be	AUX
ejpam-4379	231	5	called	call	VERB
ejpam-4379	231	6	quasi	quasi	ADJ
ejpam-4379	231	7	-	-	ADJ
ejpam-4379	231	8	normal	normal	ADJ
ejpam-4379	231	9	[	[	X
ejpam-4379	231	10	17	17	NUM
ejpam-4379	231	11	]	]	PUNCT
ejpam-4379	231	12	if	if	SCONJ
ejpam-4379	231	13	any	any	DET
ejpam-4379	231	14	two	two	NUM
ejpam-4379	231	15	disjoint	disjoint	NOUN
ejpam-4379	231	16	π	π	NOUN
ejpam-4379	231	17	-	-	ADJ
ejpam-4379	231	18	closed	closed	ADJ
ejpam-4379	231	19	subsets	subset	NOUN
ejpam-4379	231	20	a	a	PRON
ejpam-4379	231	21	and	and	CCONJ
ejpam-4379	231	22	b	b	NOUN
ejpam-4379	231	23	of	of	ADP
ejpam-4379	231	24	x	x	PRON
ejpam-4379	231	25	are	be	AUX
ejpam-4379	231	26	separated	separate	VERB
ejpam-4379	231	27	.	.	PUNCT
ejpam-4379	232	1	in	in	ADP
ejpam-4379	232	2	[	[	X
ejpam-4379	232	3	17	17	NUM
ejpam-4379	232	4	]	]	PUNCT
ejpam-4379	232	5	,	,	PUNCT
ejpam-4379	232	6	zaitsev	zaitsev	ADV
ejpam-4379	232	7	required	require	VERB
ejpam-4379	232	8	regularity	regularity	NOUN
ejpam-4379	232	9	in	in	ADP
ejpam-4379	232	10	the	the	DET
ejpam-4379	232	11	definition	definition	NOUN
ejpam-4379	232	12	of	of	ADP
ejpam-4379	232	13	quasi	quasi	ADJ
ejpam-4379	232	14	-	-	ADJ
ejpam-4379	232	15	normal	normal	ADJ
ejpam-4379	232	16	.	.	PUNCT
ejpam-4379	233	1	a	a	DET
ejpam-4379	233	2	space	space	NOUN
ejpam-4379	233	3	x	x	PUNCT
ejpam-4379	233	4	is	be	AUX
ejpam-4379	233	5	called	call	VERB
ejpam-4379	233	6	partially	partially	ADV
ejpam-4379	233	7	normal	normal	ADJ
ejpam-4379	233	8	if	if	SCONJ
ejpam-4379	233	9	any	any	DET
ejpam-4379	233	10	two	two	NUM
ejpam-4379	233	11	disjoint	disjoint	NOUN
ejpam-4379	233	12	subsets	subset	NOUN
ejpam-4379	233	13	a	a	PRON
ejpam-4379	233	14	and	and	CCONJ
ejpam-4379	233	15	b	b	NOUN
ejpam-4379	233	16	of	of	ADP
ejpam-4379	233	17	x	x	NOUN
ejpam-4379	233	18	,	,	PUNCT
ejpam-4379	233	19	where	where	SCONJ
ejpam-4379	233	20	a	a	PRON
ejpam-4379	233	21	is	be	AUX
ejpam-4379	233	22	closed	closed	ADJ
ejpam-4379	233	23	domain	domain	NOUN
ejpam-4379	233	24	and	and	CCONJ
ejpam-4379	233	25	b	b	NOUN
ejpam-4379	233	26	is	be	AUX
ejpam-4379	233	27	π	π	NOUN
ejpam-4379	233	28	-	-	VERB
ejpam-4379	233	29	closed	closed	ADJ
ejpam-4379	233	30	,	,	PUNCT
ejpam-4379	233	31	are	be	AUX
ejpam-4379	233	32	separated	separate	VERB
ejpam-4379	233	33	[	[	PUNCT
ejpam-4379	233	34	3	3	NUM
ejpam-4379	233	35	]	]	PUNCT
ejpam-4379	233	36	.	.	PUNCT
ejpam-4379	234	1	since	since	SCONJ
ejpam-4379	234	2	any	any	DET
ejpam-4379	234	3	closed	closed	ADJ
ejpam-4379	234	4	domain	domain	NOUN
ejpam-4379	234	5	is	be	AUX
ejpam-4379	234	6	π	π	NOUN
ejpam-4379	234	7	-	-	ADJ
ejpam-4379	234	8	closed	closed	ADJ
ejpam-4379	234	9	and	and	CCONJ
ejpam-4379	234	10	any	any	DET
ejpam-4379	234	11	π	π	NOUN
ejpam-4379	234	12	-	-	VERB
ejpam-4379	234	13	closed	closed	ADJ
ejpam-4379	234	14	is	be	AUX
ejpam-4379	234	15	closed	closed	ADJ
ejpam-4379	234	16	,	,	PUNCT
ejpam-4379	234	17	then	then	ADV
ejpam-4379	234	18	it	it	PRON
ejpam-4379	234	19	is	be	AUX
ejpam-4379	234	20	clear	clear	ADJ
ejpam-4379	234	21	from	from	ADP
ejpam-4379	234	22	the	the	DET
ejpam-4379	234	23	definitions	definition	NOUN
ejpam-4379	234	24	that	that	SCONJ
ejpam-4379	234	25	normal	normal	ADJ
ejpam-4379	234	26	=	=	NOUN
ejpam-4379	234	27	⇒	⇒	X
ejpam-4379	234	28	π	π	ADJ
ejpam-4379	234	29	-	-	ADJ
ejpam-4379	234	30	normal	normal	ADJ
ejpam-4379	234	31	=	=	NOUN
ejpam-4379	234	32	⇒	⇒	NOUN
ejpam-4379	234	33	almost	almost	ADV
ejpam-4379	234	34	normal	normal	ADJ
ejpam-4379	234	35	=	=	NOUN
ejpam-4379	234	36	⇒	⇒	NOUN
ejpam-4379	234	37	partially	partially	ADV
ejpam-4379	234	38	normal	normal	ADJ
ejpam-4379	234	39	=	=	NOUN
ejpam-4379	234	40	⇒	⇒	NOUN
ejpam-4379	234	41	mildly	mildly	ADV
ejpam-4379	234	42	normal	normal	ADJ
ejpam-4379	234	43	.	.	PUNCT
ejpam-4379	235	1	normal	normal	ADJ
ejpam-4379	235	2	=	=	NOUN
ejpam-4379	235	3	⇒	⇒	X
ejpam-4379	235	4	π	π	PROPN
ejpam-4379	235	5	-	-	ADJ
ejpam-4379	235	6	normal	normal	ADJ
ejpam-4379	235	7	=	=	NOUN
ejpam-4379	235	8	⇒	⇒	X
ejpam-4379	235	9	quasi	quasi	ADJ
ejpam-4379	235	10	-	-	ADJ
ejpam-4379	235	11	normal	normal	ADJ
ejpam-4379	235	12	=	=	NOUN
ejpam-4379	235	13	⇒	⇒	NOUN
ejpam-4379	235	14	partially	partially	ADV
ejpam-4379	235	15	normal	normal	ADJ
ejpam-4379	235	16	=	=	NOUN
ejpam-4379	235	17	⇒	⇒	NOUN
ejpam-4379	235	18	mildly	mildly	ADV
ejpam-4379	235	19	normal	normal	ADJ
ejpam-4379	235	20	.	.	PUNCT
ejpam-4379	236	1	none	none	NOUN
ejpam-4379	236	2	of	of	ADP
ejpam-4379	236	3	the	the	DET
ejpam-4379	236	4	above	above	ADJ
ejpam-4379	236	5	implications	implication	NOUN
ejpam-4379	236	6	is	be	AUX
ejpam-4379	236	7	reversible	reversible	ADJ
ejpam-4379	236	8	.	.	PUNCT
ejpam-4379	237	1	by	by	ADP
ejpam-4379	237	2	theorem	theorem	NOUN
ejpam-4379	237	3	2	2	NUM
ejpam-4379	237	4	,	,	PUNCT
ejpam-4379	237	5	we	we	PRON
ejpam-4379	237	6	conclude	conclude	VERB
ejpam-4379	237	7	the	the	DET
ejpam-4379	237	8	following	following	NOUN
ejpam-4379	237	9	.	.	PUNCT
ejpam-4379	238	1	theorem	theorem	ADJ
ejpam-4379	238	2	8	8	NUM
ejpam-4379	238	3	.	.	PUNCT
ejpam-4379	239	1	if	if	SCONJ
ejpam-4379	239	2	(	(	PUNCT
ejpam-4379	239	3	x	x	X
ejpam-4379	239	4	,	,	PUNCT
ejpam-4379	239	5	τ	τ	PROPN
ejpam-4379	239	6	)	)	PUNCT
ejpam-4379	239	7	is	be	AUX
ejpam-4379	239	8	ultra	ultra	ADJ
ejpam-4379	239	9	-	-	ADJ
ejpam-4379	239	10	connected	connected	ADJ
ejpam-4379	239	11	,	,	PUNCT
ejpam-4379	239	12	then	then	ADV
ejpam-4379	239	13	its	its	PRON
ejpam-4379	239	14	closed	closed	ADJ
ejpam-4379	239	15	extension	extension	NOUN
ejpam-4379	239	16	(	(	PUNCT
ejpam-4379	239	17	xp	xp	INTJ
ejpam-4379	239	18	,	,	PUNCT
ejpam-4379	239	19	τ	τ	PROPN
ejpam-4379	239	20	⋆	⋆	VERB
ejpam-4379	239	21	)	)	PUNCT
ejpam-4379	239	22	is	be	AUX
ejpam-4379	239	23	πnormal	πnormal	ADJ
ejpam-4379	239	24	,	,	PUNCT
ejpam-4379	239	25	hence	hence	ADV
ejpam-4379	239	26	quasi	quasi	ADJ
ejpam-4379	239	27	-	-	ADJ
ejpam-4379	239	28	normal	normal	ADJ
ejpam-4379	239	29	,	,	PUNCT
ejpam-4379	239	30	almost	almost	ADV
ejpam-4379	239	31	normal	normal	ADJ
ejpam-4379	239	32	,	,	PUNCT
ejpam-4379	239	33	partially	partially	ADV
ejpam-4379	239	34	normal	normal	ADJ
ejpam-4379	239	35	,	,	PUNCT
ejpam-4379	239	36	and	and	CCONJ
ejpam-4379	239	37	hence	hence	ADV
ejpam-4379	239	38	mildly	mildly	ADV
ejpam-4379	239	39	normal	normal	ADJ
ejpam-4379	239	40	.	.	PUNCT
ejpam-4379	240	1	in	in	ADP
ejpam-4379	240	2	fact	fact	NOUN
ejpam-4379	240	3	,	,	PUNCT
ejpam-4379	240	4	we	we	PRON
ejpam-4379	240	5	will	will	AUX
ejpam-4379	240	6	show	show	VERB
ejpam-4379	240	7	that	that	SCONJ
ejpam-4379	240	8	any	any	DET
ejpam-4379	240	9	closed	closed	ADJ
ejpam-4379	240	10	extension	extension	NOUN
ejpam-4379	240	11	is	be	AUX
ejpam-4379	240	12	π	π	NOUN
ejpam-4379	240	13	-	-	ADJ
ejpam-4379	240	14	normal	normal	ADJ
ejpam-4379	240	15	,	,	PUNCT
ejpam-4379	240	16	hence	hence	ADV
ejpam-4379	240	17	satisfies	satisfy	VERB
ejpam-4379	240	18	all	all	DET
ejpam-4379	240	19	other	other	ADJ
ejpam-4379	240	20	properties	property	NOUN
ejpam-4379	240	21	.	.	PUNCT
ejpam-4379	241	1	first	first	ADV
ejpam-4379	241	2	,	,	PUNCT
ejpam-4379	241	3	we	we	PRON
ejpam-4379	241	4	will	will	AUX
ejpam-4379	241	5	study	study	VERB
ejpam-4379	241	6	the	the	DET
ejpam-4379	241	7	closed	close	VERB
ejpam-4379	241	8	domains	domain	NOUN
ejpam-4379	241	9	in	in	ADP
ejpam-4379	241	10	a	a	DET
ejpam-4379	241	11	closed	closed	ADJ
ejpam-4379	241	12	extension	extension	NOUN
ejpam-4379	241	13	space	space	NOUN
ejpam-4379	241	14	.	.	PUNCT
ejpam-4379	242	1	let	let	VERB
ejpam-4379	242	2	a	a	DET
ejpam-4379	242	3	=	=	SYM
ejpam-4379	242	4	intτ⋆(a	intτ⋆(a	NOUN
ejpam-4379	242	5	)	)	PUNCT
ejpam-4379	242	6	τ⋆	τ⋆	PUNCT
ejpam-4379	242	7	be	be	VERB
ejpam-4379	242	8	any	any	DET
ejpam-4379	242	9	closed	closed	ADJ
ejpam-4379	242	10	domain	domain	NOUN
ejpam-4379	242	11	in	in	ADP
ejpam-4379	242	12	a	a	DET
ejpam-4379	242	13	closed	closed	ADJ
ejpam-4379	242	14	extension	extension	NOUN
ejpam-4379	242	15	space	space	NOUN
ejpam-4379	242	16	(	(	PUNCT
ejpam-4379	242	17	xp	xp	INTJ
ejpam-4379	242	18	,	,	PUNCT
ejpam-4379	242	19	τ	τ	PROPN
ejpam-4379	242	20	⋆	⋆	NOUN
ejpam-4379	242	21	)	)	PUNCT
ejpam-4379	242	22	of	of	ADP
ejpam-4379	242	23	a	a	DET
ejpam-4379	242	24	space	space	NOUN
ejpam-4379	242	25	(	(	PUNCT
ejpam-4379	242	26	x	x	X
ejpam-4379	242	27	,	,	PUNCT
ejpam-4379	242	28	τ	τ	PROPN
ejpam-4379	242	29	)	)	PUNCT
ejpam-4379	242	30	.	.	PUNCT
ejpam-4379	243	1	for	for	ADP
ejpam-4379	243	2	the	the	DET
ejpam-4379	243	3	subset	subset	NOUN
ejpam-4379	243	4	intτ⋆(a	intτ⋆(a	PROPN
ejpam-4379	243	5	)	)	PUNCT
ejpam-4379	243	6	,	,	PUNCT
ejpam-4379	243	7	we	we	PRON
ejpam-4379	243	8	have	have	VERB
ejpam-4379	243	9	only	only	ADV
ejpam-4379	243	10	two	two	NUM
ejpam-4379	243	11	cases	case	NOUN
ejpam-4379	243	12	,	,	PUNCT
ejpam-4379	243	13	either	either	CCONJ
ejpam-4379	243	14	intτ⋆(a	intτ⋆(a	NOUN
ejpam-4379	243	15	)	)	PUNCT
ejpam-4379	244	1	=	=	NOUN
ejpam-4379	244	2	∅	∅	NOUN
ejpam-4379	244	3	or	or	CCONJ
ejpam-4379	244	4	intτ⋆(a	intτ⋆(a	NUM
ejpam-4379	244	5	)	)	PUNCT
ejpam-4379	244	6	̸=	̸=	PROPN
ejpam-4379	244	7	∅.	∅.	ADV
ejpam-4379	244	8	if	if	SCONJ
ejpam-4379	244	9	intτ⋆(a	intτ⋆(a	NOUN
ejpam-4379	244	10	)	)	PUNCT
ejpam-4379	245	1	=	=	NOUN
ejpam-4379	245	2	∅	∅	NOUN
ejpam-4379	245	3	,	,	PUNCT
ejpam-4379	245	4	then	then	ADV
ejpam-4379	245	5	a	a	DET
ejpam-4379	245	6	=	=	PUNCT
ejpam-4379	245	7	∅.	∅.	NOUN
ejpam-4379	245	8	if	if	SCONJ
ejpam-4379	245	9	intτ⋆(a	intτ⋆(a	NOUN
ejpam-4379	245	10	)	)	PUNCT
ejpam-4379	245	11	̸=	̸=	NOUN
ejpam-4379	245	12	∅	∅	NOUN
ejpam-4379	245	13	,	,	PUNCT
ejpam-4379	245	14	then	then	ADV
ejpam-4379	245	15	p	p	PROPN
ejpam-4379	245	16	∈	∈	PROPN
ejpam-4379	245	17	intτ⋆(a	intτ⋆(a	PROPN
ejpam-4379	245	18	)	)	PUNCT
ejpam-4379	245	19	,	,	PUNCT
ejpam-4379	245	20	hence	hence	ADV
ejpam-4379	245	21	a	a	PRON
ejpam-4379	245	22	=	=	X
ejpam-4379	245	23	xp	xp	INTJ
ejpam-4379	245	24	because	because	SCONJ
ejpam-4379	245	25	any	any	DET
ejpam-4379	245	26	subset	subset	NOUN
ejpam-4379	245	27	of	of	ADP
ejpam-4379	245	28	xp	xp	NOUN
ejpam-4379	245	29	containing	contain	VERB
ejpam-4379	245	30	p	p	NOUN
ejpam-4379	245	31	is	be	AUX
ejpam-4379	245	32	dense	dense	ADJ
ejpam-4379	245	33	in	in	ADP
ejpam-4379	245	34	(	(	PUNCT
ejpam-4379	245	35	xp	xp	INTJ
ejpam-4379	245	36	,	,	PUNCT
ejpam-4379	245	37	τ	τ	PROPN
ejpam-4379	245	38	⋆	⋆	NOUN
ejpam-4379	245	39	)	)	PUNCT
ejpam-4379	245	40	.	.	PUNCT
ejpam-4379	246	1	this	this	PRON
ejpam-4379	246	2	means	mean	VERB
ejpam-4379	246	3	that	that	SCONJ
ejpam-4379	246	4	there	there	PRON
ejpam-4379	246	5	are	be	VERB
ejpam-4379	246	6	only	only	ADV
ejpam-4379	246	7	two	two	NUM
ejpam-4379	246	8	closed	close	VERB
ejpam-4379	246	9	domains	domain	NOUN
ejpam-4379	246	10	in	in	ADP
ejpam-4379	246	11	any	any	DET
ejpam-4379	246	12	closed	closed	ADJ
ejpam-4379	246	13	extension	extension	NOUN
ejpam-4379	246	14	space	space	NOUN
ejpam-4379	246	15	(	(	PUNCT
ejpam-4379	246	16	xp	xp	INTJ
ejpam-4379	246	17	,	,	PUNCT
ejpam-4379	246	18	τ	τ	PROPN
ejpam-4379	246	19	⋆	⋆	NOUN
ejpam-4379	246	20	)	)	PUNCT
ejpam-4379	246	21	of	of	ADP
ejpam-4379	246	22	a	a	DET
ejpam-4379	246	23	space	space	NOUN
ejpam-4379	246	24	(	(	PUNCT
ejpam-4379	246	25	x	x	X
ejpam-4379	246	26	,	,	PUNCT
ejpam-4379	246	27	τ	τ	PROPN
ejpam-4379	246	28	)	)	PUNCT
ejpam-4379	246	29	and	and	CCONJ
ejpam-4379	246	30	they	they	PRON
ejpam-4379	246	31	are	be	AUX
ejpam-4379	246	32	∅	∅	NOUN
ejpam-4379	246	33	and	and	CCONJ
ejpam-4379	246	34	xp	xp	INTJ
ejpam-4379	246	35	.	.	PUNCT
ejpam-4379	247	1	now	now	ADV
ejpam-4379	247	2	,	,	PUNCT
ejpam-4379	247	3	since	since	SCONJ
ejpam-4379	247	4	a	a	DET
ejpam-4379	247	5	π	π	PROPN
ejpam-4379	247	6	-	-	ADJ
ejpam-4379	247	7	closed	closed	ADJ
ejpam-4379	247	8	set	set	NOUN
ejpam-4379	247	9	is	be	AUX
ejpam-4379	247	10	a	a	DET
ejpam-4379	247	11	finite	finite	ADJ
ejpam-4379	247	12	intersection	intersection	NOUN
ejpam-4379	247	13	of	of	ADP
ejpam-4379	247	14	closed	close	VERB
ejpam-4379	247	15	domains	domain	NOUN
ejpam-4379	247	16	,	,	PUNCT
ejpam-4379	247	17	then	then	ADV
ejpam-4379	247	18	there	there	PRON
ejpam-4379	247	19	are	be	VERB
ejpam-4379	247	20	only	only	ADV
ejpam-4379	247	21	two	two	NUM
ejpam-4379	247	22	π	π	ADJ
ejpam-4379	247	23	-	-	ADJ
ejpam-4379	247	24	closed	closed	ADJ
ejpam-4379	247	25	sets	set	NOUN
ejpam-4379	247	26	in	in	ADP
ejpam-4379	247	27	any	any	DET
ejpam-4379	247	28	closed	closed	ADJ
ejpam-4379	247	29	extension	extension	NOUN
ejpam-4379	247	30	space	space	NOUN
ejpam-4379	247	31	(	(	PUNCT
ejpam-4379	247	32	xp	xp	INTJ
ejpam-4379	247	33	,	,	PUNCT
ejpam-4379	247	34	τ	τ	PROPN
ejpam-4379	247	35	⋆	⋆	NOUN
ejpam-4379	247	36	)	)	PUNCT
ejpam-4379	247	37	of	of	ADP
ejpam-4379	247	38	a	a	DET
ejpam-4379	247	39	space	space	NOUN
ejpam-4379	247	40	(	(	PUNCT
ejpam-4379	247	41	x	x	X
ejpam-4379	247	42	,	,	PUNCT
ejpam-4379	247	43	τ	τ	PROPN
ejpam-4379	247	44	)	)	PUNCT
ejpam-4379	247	45	and	and	CCONJ
ejpam-4379	247	46	they	they	PRON
ejpam-4379	247	47	are	be	AUX
ejpam-4379	247	48	∅	∅	NOUN
ejpam-4379	247	49	and	and	CCONJ
ejpam-4379	247	50	xp	xp	INTJ
ejpam-4379	247	51	.	.	PUNCT
ejpam-4379	248	1	so	so	ADV
ejpam-4379	248	2	,	,	PUNCT
ejpam-4379	248	3	if	if	SCONJ
ejpam-4379	248	4	a	a	PRON
ejpam-4379	248	5	and	and	CCONJ
ejpam-4379	248	6	b	b	NOUN
ejpam-4379	248	7	are	be	AUX
ejpam-4379	248	8	closed	close	VERB
ejpam-4379	248	9	disjoint	disjoint	ADJ
ejpam-4379	248	10	subsets	subset	NOUN
ejpam-4379	248	11	in	in	ADP
ejpam-4379	248	12	a	a	DET
ejpam-4379	248	13	closed	closed	ADJ
ejpam-4379	248	14	extension	extension	NOUN
ejpam-4379	248	15	space	space	NOUN
ejpam-4379	248	16	(	(	PUNCT
ejpam-4379	248	17	xp	xp	INTJ
ejpam-4379	248	18	,	,	PUNCT
ejpam-4379	248	19	τ	τ	PROPN
ejpam-4379	248	20	⋆	⋆	NOUN
ejpam-4379	248	21	)	)	PUNCT
ejpam-4379	248	22	of	of	ADP
ejpam-4379	248	23	a	a	DET
ejpam-4379	248	24	space	space	NOUN
ejpam-4379	248	25	(	(	PUNCT
ejpam-4379	248	26	x	x	X
ejpam-4379	248	27	,	,	PUNCT
ejpam-4379	248	28	τ	τ	PROPN
ejpam-4379	248	29	)	)	PUNCT
ejpam-4379	248	30	such	such	ADJ
ejpam-4379	248	31	that	that	SCONJ
ejpam-4379	248	32	,	,	PUNCT
ejpam-4379	248	33	without	without	ADP
ejpam-4379	248	34	loss	loss	NOUN
ejpam-4379	248	35	of	of	ADP
ejpam-4379	248	36	generality	generality	NOUN
ejpam-4379	248	37	,	,	PUNCT
ejpam-4379	248	38	a	a	PRON
ejpam-4379	248	39	is	be	AUX
ejpam-4379	248	40	π	π	NOUN
ejpam-4379	248	41	-	-	VERB
ejpam-4379	248	42	closed	closed	ADJ
ejpam-4379	248	43	,	,	PUNCT
ejpam-4379	248	44	then	then	ADV
ejpam-4379	248	45	either	either	CCONJ
ejpam-4379	248	46	a	a	DET
ejpam-4379	248	47	=	=	NOUN
ejpam-4379	248	48	∅	∅	NOUN
ejpam-4379	248	49	or	or	CCONJ
ejpam-4379	248	50	b	b	NOUN
ejpam-4379	248	51	=	=	SYM
ejpam-4379	248	52	∅	∅	NOUN
ejpam-4379	248	53	,	,	PUNCT
ejpam-4379	248	54	thus	thus	ADV
ejpam-4379	248	55	a	a	PRON
ejpam-4379	248	56	and	and	CCONJ
ejpam-4379	248	57	b	b	NOUN
ejpam-4379	248	58	are	be	AUX
ejpam-4379	248	59	separated	separate	VERB
ejpam-4379	248	60	.	.	PUNCT
ejpam-4379	249	1	we	we	PRON
ejpam-4379	249	2	conclude	conclude	VERB
ejpam-4379	249	3	the	the	DET
ejpam-4379	249	4	following	follow	VERB
ejpam-4379	249	5	theorem	theorem	PROPN
ejpam-4379	249	6	.	.	PUNCT
ejpam-4379	249	7	theorem	theorem	NOUN
ejpam-4379	249	8	9	9	NUM
ejpam-4379	249	9	.	.	PUNCT
ejpam-4379	250	1	any	any	DET
ejpam-4379	250	2	closed	closed	ADJ
ejpam-4379	250	3	extension	extension	NOUN
ejpam-4379	250	4	(	(	PUNCT
ejpam-4379	250	5	xp	xp	INTJ
ejpam-4379	250	6	,	,	PUNCT
ejpam-4379	250	7	τ	τ	PROPN
ejpam-4379	250	8	⋆	⋆	NOUN
ejpam-4379	250	9	)	)	PUNCT
ejpam-4379	250	10	space	space	NOUN
ejpam-4379	250	11	of	of	ADP
ejpam-4379	250	12	a	a	DET
ejpam-4379	250	13	given	give	VERB
ejpam-4379	250	14	space	space	NOUN
ejpam-4379	250	15	(	(	PUNCT
ejpam-4379	250	16	x	x	X
ejpam-4379	250	17	,	,	PUNCT
ejpam-4379	250	18	τ	τ	PROPN
ejpam-4379	250	19	)	)	PUNCT
ejpam-4379	250	20	is	be	AUX
ejpam-4379	250	21	π	π	X
ejpam-4379	250	22	-	-	ADJ
ejpam-4379	250	23	normal	normal	ADJ
ejpam-4379	250	24	.	.	PUNCT
ejpam-4379	251	1	corollary	corollary	ADJ
ejpam-4379	251	2	1	1	NUM
ejpam-4379	251	3	.	.	PUNCT
ejpam-4379	252	1	any	any	DET
ejpam-4379	252	2	closed	closed	ADJ
ejpam-4379	252	3	extension	extension	NOUN
ejpam-4379	252	4	(	(	PUNCT
ejpam-4379	252	5	xp	xp	INTJ
ejpam-4379	252	6	,	,	PUNCT
ejpam-4379	252	7	τ	τ	PROPN
ejpam-4379	252	8	⋆	⋆	NOUN
ejpam-4379	252	9	)	)	PUNCT
ejpam-4379	252	10	space	space	NOUN
ejpam-4379	252	11	of	of	ADP
ejpam-4379	252	12	a	a	DET
ejpam-4379	252	13	given	give	VERB
ejpam-4379	252	14	space	space	NOUN
ejpam-4379	252	15	(	(	PUNCT
ejpam-4379	252	16	x	x	X
ejpam-4379	252	17	,	,	PUNCT
ejpam-4379	252	18	τ	τ	PROPN
ejpam-4379	252	19	)	)	PUNCT
ejpam-4379	252	20	is	be	AUX
ejpam-4379	252	21	quasinormal	quasinormal	ADJ
ejpam-4379	252	22	,	,	PUNCT
ejpam-4379	252	23	almost	almost	ADV
ejpam-4379	252	24	normal	normal	ADJ
ejpam-4379	252	25	,	,	PUNCT
ejpam-4379	252	26	partially	partially	ADV
ejpam-4379	252	27	normal	normal	ADJ
ejpam-4379	252	28	,	,	PUNCT
ejpam-4379	252	29	and	and	CCONJ
ejpam-4379	252	30	mildly	mildly	ADV
ejpam-4379	252	31	normal	normal	ADJ
ejpam-4379	252	32	.	.	PUNCT
ejpam-4379	253	1	d.	d.	PROPN
ejpam-4379	253	2	abuzaid	abuzaid	PROPN
ejpam-4379	253	3	,	,	PUNCT
ejpam-4379	253	4	s.	s.	PROPN
ejpam-4379	253	5	al	al	PROPN
ejpam-4379	253	6	-	-	PROPN
ejpam-4379	253	7	qarhi	qarhi	PROPN
ejpam-4379	253	8	,	,	PUNCT
ejpam-4379	253	9	l.	l.	PROPN
ejpam-4379	253	10	kalantan	kalantan	PROPN
ejpam-4379	253	11	/	/	SYM
ejpam-4379	253	12	eur	eur	PROPN
ejpam-4379	253	13	.	.	PUNCT
ejpam-4379	254	1	j.	j.	PROPN
ejpam-4379	254	2	pure	pure	PROPN
ejpam-4379	254	3	appl	appl	PROPN
ejpam-4379	254	4	.	.	PROPN
ejpam-4379	254	5	math	math	PROPN
ejpam-4379	254	6	,	,	PUNCT
ejpam-4379	254	7	15	15	NUM
ejpam-4379	254	8	(	(	PUNCT
ejpam-4379	254	9	2	2	NUM
ejpam-4379	254	10	)	)	PUNCT
ejpam-4379	254	11	(	(	PUNCT
ejpam-4379	254	12	2022	2022	NUM
ejpam-4379	254	13	)	)	PUNCT
ejpam-4379	254	14	,	,	PUNCT
ejpam-4379	254	15	672	672	NUM
ejpam-4379	254	16	-	-	SYM
ejpam-4379	254	17	680	680	NUM
ejpam-4379	254	18	679	679	NUM
ejpam-4379	254	19	recall	recall	NOUN
ejpam-4379	254	20	that	that	SCONJ
ejpam-4379	254	21	a	a	DET
ejpam-4379	254	22	space	space	NOUN
ejpam-4379	254	23	x	x	PUNCT
ejpam-4379	254	24	is	be	AUX
ejpam-4379	254	25	scattered	scatter	VERB
ejpam-4379	254	26	if	if	SCONJ
ejpam-4379	254	27	any	any	DET
ejpam-4379	254	28	non	non	ADJ
ejpam-4379	254	29	-	-	ADJ
ejpam-4379	254	30	empty	empty	ADJ
ejpam-4379	254	31	subset	subset	NOUN
ejpam-4379	254	32	of	of	ADP
ejpam-4379	254	33	x	x	PUNCT
ejpam-4379	254	34	has	have	VERB
ejpam-4379	254	35	an	an	DET
ejpam-4379	254	36	isolated	isolated	ADJ
ejpam-4379	254	37	point	point	NOUN
ejpam-4379	254	38	[	[	X
ejpam-4379	254	39	2	2	NUM
ejpam-4379	254	40	]	]	PUNCT
ejpam-4379	254	41	,	,	PUNCT
ejpam-4379	254	42	i.e.	i.e.	X
ejpam-4379	254	43	,	,	PUNCT
ejpam-4379	254	44	if	if	SCONJ
ejpam-4379	254	45	∅	∅	NOUN
ejpam-4379	254	46	̸=	̸=	PROPN
ejpam-4379	254	47	a	a	DET
ejpam-4379	254	48	⊆	⊆	NUM
ejpam-4379	254	49	x	x	SYM
ejpam-4379	254	50	,	,	PUNCT
ejpam-4379	254	51	then	then	ADV
ejpam-4379	254	52	there	there	PRON
ejpam-4379	254	53	exists	exist	VERB
ejpam-4379	254	54	an	an	DET
ejpam-4379	254	55	element	element	NOUN
ejpam-4379	254	56	a	a	DET
ejpam-4379	254	57	∈	∈	PROPN
ejpam-4379	254	58	a	a	PRON
ejpam-4379	255	1	and	and	CCONJ
ejpam-4379	255	2	there	there	PRON
ejpam-4379	255	3	exists	exist	VERB
ejpam-4379	255	4	an	an	DET
ejpam-4379	255	5	open	open	ADJ
ejpam-4379	255	6	set	set	NOUN
ejpam-4379	255	7	u	u	PRON
ejpam-4379	255	8	such	such	ADJ
ejpam-4379	255	9	that	that	SCONJ
ejpam-4379	255	10	a	a	DET
ejpam-4379	255	11	∈	∈	PROPN
ejpam-4379	255	12	u	u	NOUN
ejpam-4379	255	13	and	and	CCONJ
ejpam-4379	255	14	u	u	NOUN
ejpam-4379	255	15	∩a	∩a	PROPN
ejpam-4379	255	16	=	=	PUNCT
ejpam-4379	255	17	{	{	PUNCT
ejpam-4379	255	18	a	a	PRON
ejpam-4379	255	19	}	}	PUNCT
ejpam-4379	255	20	.	.	PUNCT
ejpam-4379	256	1	theorem	theorem	ADJ
ejpam-4379	256	2	10	10	NUM
ejpam-4379	256	3	.	.	PUNCT
ejpam-4379	257	1	a	a	DET
ejpam-4379	257	2	space	space	NOUN
ejpam-4379	257	3	(	(	PUNCT
ejpam-4379	257	4	x	x	X
ejpam-4379	257	5	,	,	PUNCT
ejpam-4379	257	6	τ	τ	PROPN
ejpam-4379	257	7	)	)	PUNCT
ejpam-4379	257	8	is	be	AUX
ejpam-4379	257	9	scattered	scatter	VERB
ejpam-4379	257	10	if	if	SCONJ
ejpam-4379	257	11	and	and	CCONJ
ejpam-4379	257	12	only	only	ADV
ejpam-4379	257	13	if	if	SCONJ
ejpam-4379	257	14	its	its	PRON
ejpam-4379	257	15	closed	closed	ADJ
ejpam-4379	257	16	extension	extension	NOUN
ejpam-4379	257	17	(	(	PUNCT
ejpam-4379	257	18	xp	xp	INTJ
ejpam-4379	257	19	,	,	PUNCT
ejpam-4379	257	20	τ	τ	PROPN
ejpam-4379	257	21	⋆	⋆	VERB
ejpam-4379	257	22	)	)	PUNCT
ejpam-4379	257	23	is	be	AUX
ejpam-4379	257	24	scattered	scatter	VERB
ejpam-4379	257	25	.	.	PUNCT
ejpam-4379	258	1	proof	proof	NOUN
ejpam-4379	258	2	.	.	PUNCT
ejpam-4379	259	1	assume	assume	VERB
ejpam-4379	259	2	that	that	SCONJ
ejpam-4379	259	3	(	(	PUNCT
ejpam-4379	259	4	x	x	X
ejpam-4379	259	5	,	,	PUNCT
ejpam-4379	259	6	τ	τ	PROPN
ejpam-4379	259	7	)	)	PUNCT
ejpam-4379	259	8	is	be	AUX
ejpam-4379	259	9	scattered	scatter	VERB
ejpam-4379	259	10	.	.	PUNCT
ejpam-4379	260	1	let	let	VERB
ejpam-4379	260	2	∅	∅	NOUN
ejpam-4379	260	3	̸=	̸=	PROPN
ejpam-4379	260	4	a	a	DET
ejpam-4379	260	5	⊆	⊆	NUM
ejpam-4379	260	6	xp	xp	INTJ
ejpam-4379	260	7	be	be	AUX
ejpam-4379	260	8	arbitrary	arbitrary	ADJ
ejpam-4379	260	9	.	.	PUNCT
ejpam-4379	261	1	there	there	PRON
ejpam-4379	261	2	are	be	VERB
ejpam-4379	261	3	only	only	ADV
ejpam-4379	261	4	two	two	NUM
ejpam-4379	261	5	cases	case	NOUN
ejpam-4379	261	6	.	.	PUNCT
ejpam-4379	262	1	if	if	SCONJ
ejpam-4379	262	2	p	p	PROPN
ejpam-4379	262	3	∈	∈	PROPN
ejpam-4379	262	4	a	a	X
ejpam-4379	262	5	,	,	PUNCT
ejpam-4379	262	6	then	then	ADV
ejpam-4379	262	7	{	{	PUNCT
ejpam-4379	262	8	p	p	NOUN
ejpam-4379	262	9	}	}	PUNCT
ejpam-4379	262	10	∈	∈	PROPN
ejpam-4379	262	11	τ	τ	X
ejpam-4379	262	12	⋆	⋆	VERB
ejpam-4379	262	13	with	with	ADP
ejpam-4379	262	14	{	{	PUNCT
ejpam-4379	262	15	p	p	NOUN
ejpam-4379	262	16	}	}	PUNCT
ejpam-4379	262	17	∩	∩	NOUN
ejpam-4379	262	18	a	a	X
ejpam-4379	262	19	=	=	X
ejpam-4379	262	20	{	{	PUNCT
ejpam-4379	262	21	p	p	NOUN
ejpam-4379	262	22	}	}	PUNCT
ejpam-4379	262	23	.	.	PUNCT
ejpam-4379	263	1	if	if	SCONJ
ejpam-4379	263	2	p	p	PROPN
ejpam-4379	263	3	̸∈	̸∈	PROPN
ejpam-4379	263	4	a	a	PRON
ejpam-4379	263	5	,	,	PUNCT
ejpam-4379	263	6	then	then	ADV
ejpam-4379	263	7	∅	∅	NOUN
ejpam-4379	263	8	̸=	̸=	PROPN
ejpam-4379	263	9	a	a	DET
ejpam-4379	263	10	⊆	⊆	NUM
ejpam-4379	263	11	x.	x.	NOUN
ejpam-4379	263	12	since	since	SCONJ
ejpam-4379	263	13	(	(	PUNCT
ejpam-4379	263	14	x	x	X
ejpam-4379	263	15	,	,	PUNCT
ejpam-4379	263	16	τ	τ	PROPN
ejpam-4379	263	17	)	)	PUNCT
ejpam-4379	263	18	is	be	AUX
ejpam-4379	263	19	scattered	scatter	VERB
ejpam-4379	263	20	,	,	PUNCT
ejpam-4379	263	21	then	then	ADV
ejpam-4379	263	22	there	there	PRON
ejpam-4379	263	23	exists	exist	VERB
ejpam-4379	263	24	an	an	DET
ejpam-4379	263	25	element	element	NOUN
ejpam-4379	263	26	a	a	DET
ejpam-4379	263	27	∈	∈	PROPN
ejpam-4379	263	28	a	a	PRON
ejpam-4379	264	1	and	and	CCONJ
ejpam-4379	264	2	there	there	PRON
ejpam-4379	264	3	exists	exist	VERB
ejpam-4379	264	4	u	u	PROPN
ejpam-4379	264	5	∈	∈	PROPN
ejpam-4379	264	6	τ	τ	X
ejpam-4379	264	7	such	such	ADJ
ejpam-4379	264	8	that	that	SCONJ
ejpam-4379	264	9	a	a	DET
ejpam-4379	264	10	∈	∈	PROPN
ejpam-4379	264	11	u	u	NOUN
ejpam-4379	264	12	and	and	CCONJ
ejpam-4379	264	13	u	u	NOUN
ejpam-4379	264	14	∩	∩	NOUN
ejpam-4379	264	15	a	a	X
ejpam-4379	264	16	=	=	X
ejpam-4379	264	17	{	{	PUNCT
ejpam-4379	264	18	a	a	PRON
ejpam-4379	264	19	}	}	PUNCT
ejpam-4379	264	20	.	.	PUNCT
ejpam-4379	265	1	thus	thus	ADV
ejpam-4379	265	2	u	u	PRON
ejpam-4379	265	3	∪	∪	X
ejpam-4379	265	4	{	{	PUNCT
ejpam-4379	265	5	p	p	NOUN
ejpam-4379	265	6	}	}	PUNCT
ejpam-4379	265	7	∈	∈	PROPN
ejpam-4379	265	8	τ	τ	X
ejpam-4379	265	9	⋆	⋆	VERB
ejpam-4379	265	10	with	with	ADP
ejpam-4379	265	11	a	a	DET
ejpam-4379	265	12	∈	∈	PROPN
ejpam-4379	265	13	u	u	NOUN
ejpam-4379	265	14	∪	∪	NOUN
ejpam-4379	265	15	{	{	PUNCT
ejpam-4379	265	16	p	p	NOUN
ejpam-4379	265	17	}	}	PUNCT
ejpam-4379	265	18	and	and	CCONJ
ejpam-4379	265	19	(	(	PUNCT
ejpam-4379	265	20	u	u	NOUN
ejpam-4379	265	21	∪	∪	VERB
ejpam-4379	265	22	{	{	PUNCT
ejpam-4379	265	23	p	p	NOUN
ejpam-4379	265	24	}	}	PUNCT
ejpam-4379	265	25	)	)	PUNCT
ejpam-4379	266	1	∩a	∩a	PROPN
ejpam-4379	267	1	=	=	PUNCT
ejpam-4379	268	1	{	{	PUNCT
ejpam-4379	268	2	a	a	PRON
ejpam-4379	268	3	}	}	PUNCT
ejpam-4379	268	4	.	.	PUNCT
ejpam-4379	269	1	therefore	therefore	ADV
ejpam-4379	269	2	,	,	PUNCT
ejpam-4379	269	3	(	(	PUNCT
ejpam-4379	269	4	xp	xp	INTJ
ejpam-4379	269	5	,	,	PUNCT
ejpam-4379	269	6	τ	τ	PROPN
ejpam-4379	269	7	⋆	⋆	VERB
ejpam-4379	269	8	)	)	PUNCT
ejpam-4379	269	9	is	be	AUX
ejpam-4379	269	10	scattered	scatter	VERB
ejpam-4379	269	11	.	.	PUNCT
ejpam-4379	270	1	the	the	DET
ejpam-4379	270	2	other	other	ADJ
ejpam-4379	270	3	direction	direction	NOUN
ejpam-4379	270	4	is	be	AUX
ejpam-4379	270	5	true	true	ADJ
ejpam-4379	270	6	because	because	SCONJ
ejpam-4379	270	7	scattered	scattered	ADJ
ejpam-4379	270	8	is	be	AUX
ejpam-4379	270	9	hereditary	hereditary	ADJ
ejpam-4379	270	10	.	.	PUNCT
ejpam-4379	271	1	recall	recall	VERB
ejpam-4379	271	2	that	that	SCONJ
ejpam-4379	271	3	a	a	DET
ejpam-4379	271	4	space	space	NOUN
ejpam-4379	271	5	x	x	PUNCT
ejpam-4379	271	6	is	be	AUX
ejpam-4379	271	7	said	say	VERB
ejpam-4379	271	8	to	to	PART
ejpam-4379	271	9	satisfy	satisfy	VERB
ejpam-4379	271	10	property	property	NOUN
ejpam-4379	271	11	wd	wd	PROPN
ejpam-4379	271	12	,	,	PUNCT
ejpam-4379	271	13	[	[	X
ejpam-4379	271	14	12	12	NUM
ejpam-4379	271	15	]	]	PUNCT
ejpam-4379	271	16	,	,	PUNCT
ejpam-4379	271	17	if	if	SCONJ
ejpam-4379	271	18	for	for	ADP
ejpam-4379	271	19	every	every	DET
ejpam-4379	271	20	infinite	infinite	ADJ
ejpam-4379	271	21	closed	close	VERB
ejpam-4379	271	22	discrete	discrete	ADJ
ejpam-4379	271	23	subspace	subspace	NOUN
ejpam-4379	271	24	c	c	PROPN
ejpam-4379	271	25	of	of	ADP
ejpam-4379	271	26	x	x	PRON
ejpam-4379	271	27	,	,	PUNCT
ejpam-4379	271	28	there	there	PRON
ejpam-4379	271	29	exists	exist	VERB
ejpam-4379	271	30	a	a	DET
ejpam-4379	271	31	countably	countably	ADV
ejpam-4379	271	32	infinite	infinite	ADJ
ejpam-4379	271	33	discrete	discrete	ADJ
ejpam-4379	271	34	family	family	NOUN
ejpam-4379	271	35	{	{	PUNCT
ejpam-4379	271	36	un	un	PROPN
ejpam-4379	271	37	:	:	PUNCT
ejpam-4379	271	38	n	n	CCONJ
ejpam-4379	271	39	∈	∈	PROPN
ejpam-4379	271	40	n	n	CCONJ
ejpam-4379	271	41	}	}	PUNCT
ejpam-4379	271	42	of	of	ADP
ejpam-4379	271	43	open	open	ADJ
ejpam-4379	271	44	subsets	subset	NOUN
ejpam-4379	271	45	of	of	ADP
ejpam-4379	271	46	x	x	SYM
ejpam-4379	271	47	such	such	ADJ
ejpam-4379	271	48	that	that	SCONJ
ejpam-4379	271	49	each	each	DET
ejpam-4379	271	50	un	un	PROPN
ejpam-4379	271	51	intersects	intersect	NOUN
ejpam-4379	271	52	c	c	PROPN
ejpam-4379	271	53	in	in	ADP
ejpam-4379	271	54	exactly	exactly	ADV
ejpam-4379	271	55	one	one	NUM
ejpam-4379	271	56	point	point	NOUN
ejpam-4379	271	57	.	.	PUNCT
ejpam-4379	272	1	proposition	proposition	NOUN
ejpam-4379	272	2	5	5	NUM
ejpam-4379	272	3	.	.	PUNCT
ejpam-4379	273	1	let	let	AUX
ejpam-4379	273	2	(	(	PUNCT
ejpam-4379	273	3	xp	xp	INTJ
ejpam-4379	273	4	,	,	PUNCT
ejpam-4379	273	5	τ	τ	PROPN
ejpam-4379	273	6	⋆	⋆	X
ejpam-4379	273	7	)	)	PUNCT
ejpam-4379	273	8	be	be	AUX
ejpam-4379	273	9	the	the	DET
ejpam-4379	273	10	closed	closed	ADJ
ejpam-4379	273	11	extension	extension	NOUN
ejpam-4379	273	12	of	of	ADP
ejpam-4379	273	13	a	a	DET
ejpam-4379	273	14	topological	topological	ADJ
ejpam-4379	273	15	space	space	NOUN
ejpam-4379	273	16	(	(	PUNCT
ejpam-4379	273	17	x	x	X
ejpam-4379	273	18	,	,	PUNCT
ejpam-4379	273	19	τ	τ	PROPN
ejpam-4379	273	20	)	)	PUNCT
ejpam-4379	273	21	.	.	PUNCT
ejpam-4379	274	1	if	if	SCONJ
ejpam-4379	274	2	c	c	PROPN
ejpam-4379	274	3	⊆	⊆	NUM
ejpam-4379	274	4	x	x	PUNCT
ejpam-4379	274	5	is	be	AUX
ejpam-4379	274	6	closed	close	VERB
ejpam-4379	274	7	and	and	CCONJ
ejpam-4379	274	8	discrete	discrete	ADJ
ejpam-4379	274	9	in	in	ADP
ejpam-4379	274	10	(	(	PUNCT
ejpam-4379	274	11	x	x	INTJ
ejpam-4379	274	12	,	,	PUNCT
ejpam-4379	274	13	τ	τ	PROPN
ejpam-4379	274	14	)	)	PUNCT
ejpam-4379	274	15	,	,	PUNCT
ejpam-4379	274	16	then	then	ADV
ejpam-4379	274	17	c	c	PROPN
ejpam-4379	274	18	is	be	AUX
ejpam-4379	274	19	closed	closed	ADJ
ejpam-4379	274	20	and	and	CCONJ
ejpam-4379	274	21	discrete	discrete	ADJ
ejpam-4379	274	22	in	in	ADP
ejpam-4379	274	23	(	(	PUNCT
ejpam-4379	274	24	xp	xp	INTJ
ejpam-4379	274	25	,	,	PUNCT
ejpam-4379	274	26	τ	τ	PROPN
ejpam-4379	274	27	⋆	⋆	NOUN
ejpam-4379	274	28	)	)	PUNCT
ejpam-4379	274	29	.	.	PUNCT
ejpam-4379	275	1	if	if	SCONJ
ejpam-4379	275	2	c	c	PROPN
ejpam-4379	275	3	⊂	⊂	PROPN
ejpam-4379	275	4	xp	xp	PROPN
ejpam-4379	275	5	is	be	AUX
ejpam-4379	275	6	closed	closed	ADJ
ejpam-4379	275	7	and	and	CCONJ
ejpam-4379	275	8	discrete	discrete	ADJ
ejpam-4379	275	9	in	in	ADP
ejpam-4379	275	10	(	(	PUNCT
ejpam-4379	275	11	xp	xp	INTJ
ejpam-4379	275	12	,	,	PUNCT
ejpam-4379	275	13	τ	τ	PROPN
ejpam-4379	275	14	⋆	⋆	NOUN
ejpam-4379	275	15	)	)	PUNCT
ejpam-4379	275	16	,	,	PUNCT
ejpam-4379	275	17	then	then	ADV
ejpam-4379	275	18	p	p	PROPN
ejpam-4379	275	19	̸∈	̸∈	PROPN
ejpam-4379	275	20	c	c	PROPN
ejpam-4379	275	21	and	and	CCONJ
ejpam-4379	275	22	c	c	PROPN
ejpam-4379	275	23	is	be	AUX
ejpam-4379	275	24	closed	close	VERB
ejpam-4379	275	25	and	and	CCONJ
ejpam-4379	275	26	discrete	discrete	ADJ
ejpam-4379	275	27	in	in	ADP
ejpam-4379	275	28	(	(	PUNCT
ejpam-4379	275	29	x	x	INTJ
ejpam-4379	275	30	,	,	PUNCT
ejpam-4379	275	31	τ	τ	PROPN
ejpam-4379	275	32	)	)	PUNCT
ejpam-4379	275	33	.	.	PUNCT
ejpam-4379	276	1	proof	proof	NOUN
ejpam-4379	276	2	.	.	PUNCT
ejpam-4379	277	1	let	let	VERB
ejpam-4379	277	2	c	c	NOUN
ejpam-4379	277	3	⊆	⊆	NUM
ejpam-4379	277	4	x	x	AUX
ejpam-4379	277	5	be	be	AUX
ejpam-4379	277	6	closed	close	VERB
ejpam-4379	277	7	and	and	CCONJ
ejpam-4379	277	8	discrete	discrete	ADJ
ejpam-4379	277	9	in	in	ADP
ejpam-4379	277	10	(	(	PUNCT
ejpam-4379	277	11	x	x	INTJ
ejpam-4379	277	12	,	,	PUNCT
ejpam-4379	277	13	τ	τ	PROPN
ejpam-4379	277	14	)	)	PUNCT
ejpam-4379	277	15	.	.	PUNCT
ejpam-4379	278	1	since	since	SCONJ
ejpam-4379	278	2	(	(	PUNCT
ejpam-4379	278	3	xp	xp	INTJ
ejpam-4379	278	4	,	,	PUNCT
ejpam-4379	278	5	τ	τ	PROPN
ejpam-4379	278	6	⋆	⋆	NOUN
ejpam-4379	278	7	)	)	PUNCT
ejpam-4379	278	8	and	and	CCONJ
ejpam-4379	278	9	(	(	PUNCT
ejpam-4379	278	10	x	x	X
ejpam-4379	278	11	,	,	PUNCT
ejpam-4379	278	12	τ	τ	PROPN
ejpam-4379	278	13	)	)	PUNCT
ejpam-4379	278	14	have	have	VERB
ejpam-4379	278	15	the	the	DET
ejpam-4379	278	16	same	same	ADJ
ejpam-4379	278	17	closed	closed	ADJ
ejpam-4379	278	18	sets	set	NOUN
ejpam-4379	278	19	,	,	PUNCT
ejpam-4379	278	20	except	except	SCONJ
ejpam-4379	278	21	for	for	ADP
ejpam-4379	278	22	xp	xp	PROPN
ejpam-4379	278	23	,	,	PUNCT
ejpam-4379	278	24	then	then	ADV
ejpam-4379	278	25	c	c	PROPN
ejpam-4379	278	26	is	be	AUX
ejpam-4379	278	27	closed	close	VERB
ejpam-4379	278	28	in	in	ADP
ejpam-4379	278	29	(	(	PUNCT
ejpam-4379	278	30	xp	xp	INTJ
ejpam-4379	278	31	,	,	PUNCT
ejpam-4379	278	32	τ	τ	PROPN
ejpam-4379	278	33	⋆	⋆	NOUN
ejpam-4379	278	34	)	)	PUNCT
ejpam-4379	278	35	.	.	PUNCT
ejpam-4379	279	1	let	let	VERB
ejpam-4379	279	2	c	c	NOUN
ejpam-4379	279	3	∈	∈	PROPN
ejpam-4379	279	4	c	c	AUX
ejpam-4379	279	5	be	be	AUX
ejpam-4379	279	6	arbitrary	arbitrary	ADJ
ejpam-4379	279	7	,	,	PUNCT
ejpam-4379	279	8	then	then	ADV
ejpam-4379	279	9	there	there	PRON
ejpam-4379	279	10	exists	exist	VERB
ejpam-4379	279	11	u	u	PROPN
ejpam-4379	279	12	∈	∈	PROPN
ejpam-4379	279	13	τ	τ	X
ejpam-4379	279	14	with	with	ADP
ejpam-4379	279	15	c	c	PROPN
ejpam-4379	279	16	∈	∈	PROPN
ejpam-4379	279	17	u	u	NOUN
ejpam-4379	279	18	and	and	CCONJ
ejpam-4379	279	19	u	u	NOUN
ejpam-4379	279	20	∩c	∩c	NOUN
ejpam-4379	279	21	=	=	PUNCT
ejpam-4379	279	22	{	{	PUNCT
ejpam-4379	279	23	c	c	NOUN
ejpam-4379	279	24	}	}	PUNCT
ejpam-4379	279	25	.	.	PUNCT
ejpam-4379	280	1	then	then	ADV
ejpam-4379	280	2	u	u	PRON
ejpam-4379	280	3	∪	∪	VERB
ejpam-4379	280	4	{	{	PUNCT
ejpam-4379	280	5	p	p	NOUN
ejpam-4379	280	6	}	}	PUNCT
ejpam-4379	280	7	∈	∈	PROPN
ejpam-4379	280	8	τ	τ	X
ejpam-4379	280	9	⋆	⋆	VERB
ejpam-4379	280	10	with	with	ADP
ejpam-4379	280	11	(	(	PUNCT
ejpam-4379	280	12	u	u	NOUN
ejpam-4379	280	13	∪	∪	X
ejpam-4379	280	14	{	{	PUNCT
ejpam-4379	280	15	p	p	NOUN
ejpam-4379	280	16	}	}	PUNCT
ejpam-4379	280	17	)	)	PUNCT
ejpam-4379	280	18	∩	∩	NOUN
ejpam-4379	280	19	c	c	NOUN
ejpam-4379	280	20	=	=	SYM
ejpam-4379	280	21	{	{	PUNCT
ejpam-4379	280	22	c	c	NOUN
ejpam-4379	280	23	}	}	PUNCT
ejpam-4379	280	24	.	.	PUNCT
ejpam-4379	281	1	thus	thus	ADV
ejpam-4379	281	2	c	c	NOUN
ejpam-4379	281	3	is	be	AUX
ejpam-4379	281	4	discrete	discrete	ADJ
ejpam-4379	281	5	in	in	ADP
ejpam-4379	281	6	(	(	PUNCT
ejpam-4379	281	7	xp	xp	INTJ
ejpam-4379	281	8	,	,	PUNCT
ejpam-4379	281	9	τ	τ	PROPN
ejpam-4379	281	10	⋆	⋆	NOUN
ejpam-4379	281	11	)	)	PUNCT
ejpam-4379	281	12	.	.	PUNCT
ejpam-4379	282	1	now	now	ADV
ejpam-4379	282	2	,	,	PUNCT
ejpam-4379	282	3	let	let	VERB
ejpam-4379	282	4	c	c	PROPN
ejpam-4379	282	5	⊂	⊂	PROPN
ejpam-4379	282	6	xp	xp	PROPN
ejpam-4379	282	7	be	be	AUX
ejpam-4379	282	8	closed	close	VERB
ejpam-4379	282	9	and	and	CCONJ
ejpam-4379	282	10	discrete	discrete	ADJ
ejpam-4379	282	11	in	in	ADP
ejpam-4379	282	12	(	(	PUNCT
ejpam-4379	282	13	xp	xp	INTJ
ejpam-4379	282	14	,	,	PUNCT
ejpam-4379	282	15	τ	τ	PROPN
ejpam-4379	282	16	⋆	⋆	NOUN
ejpam-4379	282	17	)	)	PUNCT
ejpam-4379	282	18	.	.	PUNCT
ejpam-4379	283	1	suppose	suppose	VERB
ejpam-4379	283	2	that	that	SCONJ
ejpam-4379	283	3	p	p	PROPN
ejpam-4379	283	4	∈	∈	PROPN
ejpam-4379	283	5	c	c	NOUN
ejpam-4379	283	6	,	,	PUNCT
ejpam-4379	283	7	then	then	ADV
ejpam-4379	283	8	there	there	PRON
ejpam-4379	283	9	are	be	VERB
ejpam-4379	283	10	only	only	ADV
ejpam-4379	283	11	two	two	NUM
ejpam-4379	283	12	cases	case	NOUN
ejpam-4379	283	13	.	.	PUNCT
ejpam-4379	284	1	if	if	SCONJ
ejpam-4379	284	2	c	c	NOUN
ejpam-4379	284	3	=	=	PUNCT
ejpam-4379	284	4	{	{	PUNCT
ejpam-4379	284	5	p	p	NOUN
ejpam-4379	284	6	}	}	PUNCT
ejpam-4379	284	7	,	,	PUNCT
ejpam-4379	284	8	then	then	ADV
ejpam-4379	284	9	{	{	PUNCT
ejpam-4379	284	10	p	p	NOUN
ejpam-4379	284	11	}	}	PUNCT
ejpam-4379	284	12	is	be	AUX
ejpam-4379	284	13	not	not	PART
ejpam-4379	284	14	closed	close	VERB
ejpam-4379	284	15	in	in	ADP
ejpam-4379	284	16	(	(	PUNCT
ejpam-4379	284	17	xp	xp	INTJ
ejpam-4379	284	18	,	,	PUNCT
ejpam-4379	284	19	τ	τ	PROPN
ejpam-4379	284	20	⋆	⋆	NOUN
ejpam-4379	284	21	)	)	PUNCT
ejpam-4379	284	22	because	because	SCONJ
ejpam-4379	284	23	x	x	PROPN
ejpam-4379	284	24	̸∈	̸∈	PROPN
ejpam-4379	284	25	τ	τ	X
ejpam-4379	284	26	⋆.	⋆.	VERB
ejpam-4379	284	27	if	if	SCONJ
ejpam-4379	284	28	there	there	PRON
ejpam-4379	284	29	exists	exist	VERB
ejpam-4379	284	30	an	an	DET
ejpam-4379	284	31	element	element	NOUN
ejpam-4379	284	32	c	c	NOUN
ejpam-4379	284	33	∈	∈	PROPN
ejpam-4379	284	34	x	x	PUNCT
ejpam-4379	284	35	with	with	ADP
ejpam-4379	284	36	c	c	PROPN
ejpam-4379	284	37	∈	∈	PROPN
ejpam-4379	284	38	c	c	NOUN
ejpam-4379	284	39	,	,	PUNCT
ejpam-4379	284	40	then	then	ADV
ejpam-4379	284	41	c	c	PROPN
ejpam-4379	284	42	will	will	AUX
ejpam-4379	284	43	not	not	PART
ejpam-4379	284	44	be	be	AUX
ejpam-4379	284	45	discrete	discrete	ADJ
ejpam-4379	284	46	in	in	ADP
ejpam-4379	284	47	(	(	PUNCT
ejpam-4379	284	48	xp	xp	INTJ
ejpam-4379	284	49	,	,	PUNCT
ejpam-4379	284	50	τ	τ	PROPN
ejpam-4379	284	51	⋆	⋆	NOUN
ejpam-4379	284	52	)	)	PUNCT
ejpam-4379	284	53	because	because	SCONJ
ejpam-4379	284	54	any	any	DET
ejpam-4379	284	55	w	w	PROPN
ejpam-4379	284	56	∈	∈	NOUN
ejpam-4379	284	57	τ	τ	X
ejpam-4379	284	58	⋆	⋆	VERB
ejpam-4379	284	59	with	with	ADP
ejpam-4379	284	60	c	c	PROPN
ejpam-4379	284	61	∈	∈	PROPN
ejpam-4379	284	62	w	w	NOUN
ejpam-4379	284	63	is	be	AUX
ejpam-4379	284	64	of	of	ADP
ejpam-4379	284	65	the	the	DET
ejpam-4379	284	66	form	form	NOUN
ejpam-4379	284	67	w	w	NOUN
ejpam-4379	284	68	=	=	PUNCT
ejpam-4379	284	69	u	u	NOUN
ejpam-4379	284	70	∪	∪	VERB
ejpam-4379	284	71	{	{	PUNCT
ejpam-4379	284	72	p	p	NOUN
ejpam-4379	284	73	}	}	PUNCT
ejpam-4379	284	74	for	for	ADP
ejpam-4379	284	75	some	some	DET
ejpam-4379	284	76	u	u	NOUN
ejpam-4379	284	77	∈	∈	PROPN
ejpam-4379	284	78	τ	τ	X
ejpam-4379	284	79	with	with	ADP
ejpam-4379	284	80	c	c	PROPN
ejpam-4379	284	81	∈	∈	PROPN
ejpam-4379	284	82	u	u	NOUN
ejpam-4379	284	83	,	,	PUNCT
ejpam-4379	284	84	thus	thus	ADV
ejpam-4379	284	85	w	w	ADP
ejpam-4379	284	86	∩	∩	NOUN
ejpam-4379	284	87	c	c	PROPN
ejpam-4379	284	88	̸=	̸=	PROPN
ejpam-4379	284	89	{	{	PUNCT
ejpam-4379	284	90	c	c	NOUN
ejpam-4379	284	91	}	}	PUNCT
ejpam-4379	284	92	because	because	SCONJ
ejpam-4379	284	93	c	c	PROPN
ejpam-4379	284	94	̸=	̸=	PROPN
ejpam-4379	284	95	p	p	PROPN
ejpam-4379	284	96	∈	∈	PROPN
ejpam-4379	284	97	w	w	PROPN
ejpam-4379	284	98	∩	∩	PROPN
ejpam-4379	284	99	c.	c.	PROPN
ejpam-4379	284	100	therefore	therefore	ADV
ejpam-4379	284	101	,	,	PUNCT
ejpam-4379	284	102	p	p	PROPN
ejpam-4379	284	103	̸∈	̸∈	PROPN
ejpam-4379	284	104	c.	c.	PROPN
ejpam-4379	284	105	now	now	ADV
ejpam-4379	284	106	,	,	PUNCT
ejpam-4379	284	107	since	since	SCONJ
ejpam-4379	284	108	p	p	PROPN
ejpam-4379	284	109	̸∈	̸∈	PROPN
ejpam-4379	284	110	c	c	PROPN
ejpam-4379	284	111	and	and	CCONJ
ejpam-4379	284	112	c	c	PROPN
ejpam-4379	284	113	is	be	AUX
ejpam-4379	284	114	closed	close	VERB
ejpam-4379	284	115	in	in	ADP
ejpam-4379	284	116	(	(	PUNCT
ejpam-4379	284	117	xp	xp	INTJ
ejpam-4379	284	118	,	,	PUNCT
ejpam-4379	284	119	τ	τ	PROPN
ejpam-4379	284	120	⋆	⋆	NOUN
ejpam-4379	284	121	)	)	PUNCT
ejpam-4379	284	122	,	,	PUNCT
ejpam-4379	284	123	then	then	ADV
ejpam-4379	284	124	c	c	PROPN
ejpam-4379	284	125	is	be	AUX
ejpam-4379	284	126	closed	close	VERB
ejpam-4379	284	127	in	in	ADP
ejpam-4379	284	128	(	(	PUNCT
ejpam-4379	284	129	x	x	INTJ
ejpam-4379	284	130	,	,	PUNCT
ejpam-4379	284	131	τ	τ	PROPN
ejpam-4379	284	132	)	)	PUNCT
ejpam-4379	284	133	.	.	PUNCT
ejpam-4379	285	1	let	let	VERB
ejpam-4379	285	2	c	c	NOUN
ejpam-4379	285	3	∈	∈	PROPN
ejpam-4379	285	4	c	c	AUX
ejpam-4379	285	5	be	be	AUX
ejpam-4379	285	6	arbitrary	arbitrary	ADJ
ejpam-4379	285	7	.	.	PUNCT
ejpam-4379	286	1	since	since	SCONJ
ejpam-4379	286	2	c	c	PROPN
ejpam-4379	286	3	is	be	AUX
ejpam-4379	286	4	discrete	discrete	ADJ
ejpam-4379	286	5	in	in	ADP
ejpam-4379	286	6	(	(	PUNCT
ejpam-4379	286	7	xp	xp	INTJ
ejpam-4379	286	8	,	,	PUNCT
ejpam-4379	286	9	τ	τ	PROPN
ejpam-4379	286	10	⋆	⋆	NOUN
ejpam-4379	286	11	)	)	PUNCT
ejpam-4379	286	12	,	,	PUNCT
ejpam-4379	286	13	then	then	ADV
ejpam-4379	286	14	there	there	PRON
ejpam-4379	286	15	exists	exist	VERB
ejpam-4379	286	16	v	v	ADP
ejpam-4379	286	17	∈	∈	PROPN
ejpam-4379	286	18	τ	τ	X
ejpam-4379	286	19	⋆	⋆	VERB
ejpam-4379	286	20	with	with	ADP
ejpam-4379	286	21	c	c	PROPN
ejpam-4379	286	22	∈	∈	PROPN
ejpam-4379	286	23	v	v	NOUN
ejpam-4379	286	24	and	and	CCONJ
ejpam-4379	286	25	v	v	NOUN
ejpam-4379	286	26	∩	∩	ADJ
ejpam-4379	286	27	c	c	NOUN
ejpam-4379	286	28	=	=	SYM
ejpam-4379	286	29	{	{	PUNCT
ejpam-4379	286	30	c	c	NOUN
ejpam-4379	286	31	}	}	PUNCT
ejpam-4379	286	32	.	.	PUNCT
ejpam-4379	287	1	but	but	CCONJ
ejpam-4379	287	2	v	v	NOUN
ejpam-4379	287	3	is	be	AUX
ejpam-4379	287	4	of	of	ADP
ejpam-4379	287	5	the	the	DET
ejpam-4379	287	6	form	form	NOUN
ejpam-4379	287	7	v	v	ADP
ejpam-4379	287	8	=	=	SYM
ejpam-4379	287	9	u	u	NOUN
ejpam-4379	287	10	∪	∪	NOUN
ejpam-4379	287	11	{	{	PUNCT
ejpam-4379	287	12	p	p	NOUN
ejpam-4379	287	13	}	}	PUNCT
ejpam-4379	287	14	for	for	ADP
ejpam-4379	287	15	some	some	DET
ejpam-4379	287	16	u	u	NOUN
ejpam-4379	287	17	∈	∈	PROPN
ejpam-4379	287	18	τ	τ	X
ejpam-4379	287	19	with	with	ADP
ejpam-4379	287	20	c	c	PROPN
ejpam-4379	287	21	∈	∈	PROPN
ejpam-4379	287	22	u	u	PROPN
ejpam-4379	287	23	.	.	PUNCT
ejpam-4379	288	1	then	then	ADV
ejpam-4379	288	2	u	u	NOUN
ejpam-4379	288	3	∩c	∩c	NOUN
ejpam-4379	288	4	=	=	PUNCT
ejpam-4379	288	5	{	{	PUNCT
ejpam-4379	288	6	c	c	NOUN
ejpam-4379	288	7	}	}	PUNCT
ejpam-4379	288	8	because	because	SCONJ
ejpam-4379	288	9	p	p	PROPN
ejpam-4379	288	10	̸∈	̸∈	PROPN
ejpam-4379	288	11	c.	c.	PROPN
ejpam-4379	288	12	theorem	theorem	VERB
ejpam-4379	288	13	11	11	NUM
ejpam-4379	288	14	.	.	PUNCT
ejpam-4379	289	1	any	any	DET
ejpam-4379	289	2	closed	closed	ADJ
ejpam-4379	289	3	extension	extension	NOUN
ejpam-4379	289	4	(	(	PUNCT
ejpam-4379	289	5	xp	xp	INTJ
ejpam-4379	289	6	,	,	PUNCT
ejpam-4379	289	7	τ	τ	PROPN
ejpam-4379	289	8	⋆	⋆	NOUN
ejpam-4379	289	9	)	)	PUNCT
ejpam-4379	289	10	space	space	NOUN
ejpam-4379	289	11	of	of	ADP
ejpam-4379	289	12	a	a	DET
ejpam-4379	289	13	given	give	VERB
ejpam-4379	289	14	space	space	NOUN
ejpam-4379	289	15	(	(	PUNCT
ejpam-4379	289	16	x	x	X
ejpam-4379	289	17	,	,	PUNCT
ejpam-4379	289	18	τ	τ	PROPN
ejpam-4379	289	19	)	)	PUNCT
ejpam-4379	289	20	does	do	AUX
ejpam-4379	289	21	not	not	PART
ejpam-4379	289	22	satisfy	satisfy	VERB
ejpam-4379	289	23	property	property	NOUN
ejpam-4379	289	24	wd	wd	PROPN
ejpam-4379	289	25	even	even	ADV
ejpam-4379	289	26	if	if	SCONJ
ejpam-4379	289	27	(	(	PUNCT
ejpam-4379	289	28	x	x	X
ejpam-4379	289	29	,	,	PUNCT
ejpam-4379	289	30	τ	τ	PROPN
ejpam-4379	289	31	)	)	PUNCT
ejpam-4379	289	32	does	do	VERB
ejpam-4379	289	33	.	.	PUNCT
ejpam-4379	290	1	proof	proof	NOUN
ejpam-4379	290	2	.	.	PUNCT
ejpam-4379	291	1	let	let	VERB
ejpam-4379	291	2	c	c	PRON
ejpam-4379	291	3	be	be	AUX
ejpam-4379	291	4	any	any	DET
ejpam-4379	291	5	infinite	infinite	ADJ
ejpam-4379	291	6	closed	close	VERB
ejpam-4379	291	7	discrete	discrete	ADJ
ejpam-4379	291	8	subspace	subspace	NOUN
ejpam-4379	291	9	of	of	ADP
ejpam-4379	291	10	xp	xp	PROPN
ejpam-4379	291	11	.	.	PUNCT
ejpam-4379	292	1	by	by	ADP
ejpam-4379	292	2	proposition	proposition	NOUN
ejpam-4379	292	3	5	5	NUM
ejpam-4379	292	4	,	,	PUNCT
ejpam-4379	292	5	p	p	PROPN
ejpam-4379	292	6	̸∈	̸∈	PROPN
ejpam-4379	292	7	c.	c.	PROPN
ejpam-4379	292	8	pick	pick	VERB
ejpam-4379	292	9	a	a	DET
ejpam-4379	292	10	countably	countably	ADV
ejpam-4379	292	11	infinite	infinite	ADJ
ejpam-4379	292	12	subset	subset	NOUN
ejpam-4379	292	13	{	{	PUNCT
ejpam-4379	292	14	cn	cn	NOUN
ejpam-4379	292	15	:	:	PUNCT
ejpam-4379	292	16	n	n	CCONJ
ejpam-4379	292	17	∈	∈	PROPN
ejpam-4379	292	18	n	n	CCONJ
ejpam-4379	292	19	}	}	PUNCT
ejpam-4379	292	20	⊆	⊆	NUM
ejpam-4379	292	21	c.	c.	NOUN
ejpam-4379	292	22	now	now	ADV
ejpam-4379	292	23	,	,	PUNCT
ejpam-4379	292	24	any	any	DET
ejpam-4379	292	25	countably	countably	ADV
ejpam-4379	292	26	infinite	infinite	ADJ
ejpam-4379	292	27	family	family	NOUN
ejpam-4379	292	28	{	{	PUNCT
ejpam-4379	292	29	un	un	PROPN
ejpam-4379	292	30	∈	∈	PROPN
ejpam-4379	292	31	τ	τ	X
ejpam-4379	292	32	⋆	⋆	NOUN
ejpam-4379	292	33	:	:	PUNCT
ejpam-4379	292	34	n	n	CCONJ
ejpam-4379	292	35	∈	∈	PROPN
ejpam-4379	292	36	n	n	CCONJ
ejpam-4379	292	37	}	}	PUNCT
ejpam-4379	292	38	with	with	ADP
ejpam-4379	292	39	cn	cn	PROPN
ejpam-4379	292	40	∈	∈	PROPN
ejpam-4379	292	41	un	un	PROPN
ejpam-4379	292	42	for	for	ADP
ejpam-4379	292	43	each	each	DET
ejpam-4379	292	44	n	n	PRON
ejpam-4379	292	45	∈	∈	PROPN
ejpam-4379	292	46	n	n	PRON
ejpam-4379	292	47	can	can	AUX
ejpam-4379	292	48	not	not	PART
ejpam-4379	292	49	be	be	AUX
ejpam-4379	292	50	discrete	discrete	ADJ
ejpam-4379	292	51	because	because	SCONJ
ejpam-4379	292	52	p	p	PROPN
ejpam-4379	292	53	∈	∈	PROPN
ejpam-4379	292	54	un	un	PROPN
ejpam-4379	292	55	for	for	ADP
ejpam-4379	292	56	each	each	DET
ejpam-4379	292	57	n	n	PRON
ejpam-4379	292	58	∈	∈	PROPN
ejpam-4379	292	59	n.	n.	NOUN
ejpam-4379	292	60	therefore	therefore	ADV
ejpam-4379	292	61	,	,	PUNCT
ejpam-4379	292	62	(	(	PUNCT
ejpam-4379	292	63	xp	xp	INTJ
ejpam-4379	292	64	,	,	PUNCT
ejpam-4379	292	65	τ	τ	PROPN
ejpam-4379	292	66	⋆	⋆	NOUN
ejpam-4379	292	67	)	)	PUNCT
ejpam-4379	292	68	does	do	AUX
ejpam-4379	292	69	not	not	PART
ejpam-4379	292	70	satisfy	satisfy	VERB
ejpam-4379	292	71	property	property	NOUN
ejpam-4379	292	72	wd	wd	PROPN
ejpam-4379	292	73	.	.	PUNCT
ejpam-4379	293	1	references	reference	NOUN
ejpam-4379	293	2	680	680	NUM
ejpam-4379	293	3	references	reference	NOUN
ejpam-4379	293	4	[	[	X
ejpam-4379	293	5	1	1	NUM
ejpam-4379	293	6	]	]	X
ejpam-4379	293	7	s	s	PART
ejpam-4379	293	8	alzahrani	alzahrani	NOUN
ejpam-4379	293	9	and	and	CCONJ
ejpam-4379	293	10	l	l	PROPN
ejpam-4379	293	11	kalantan	kalantan	PROPN
ejpam-4379	293	12	.	.	PUNCT
ejpam-4379	294	1	c	c	X
ejpam-4379	294	2	-	-	PUNCT
ejpam-4379	294	3	normal	normal	ADJ
ejpam-4379	294	4	topological	topological	ADJ
ejpam-4379	294	5	property	property	NOUN
ejpam-4379	294	6	.	.	PUNCT
ejpam-4379	295	1	filomat	filomat	NOUN
ejpam-4379	295	2	,	,	PUNCT
ejpam-4379	295	3	31(2):407–411	31(2):407–411	PROPN
ejpam-4379	295	4	.	.	PROPN
ejpam-4379	295	5	,	,	PUNCT
ejpam-4379	295	6	2017	2017	NUM
ejpam-4379	295	7	.	.	PUNCT
ejpam-4379	296	1	[	[	X
ejpam-4379	296	2	2	2	NUM
ejpam-4379	296	3	]	]	X
ejpam-4379	296	4	r	r	NOUN
ejpam-4379	296	5	engelking	engelking	NOUN
ejpam-4379	296	6	.	.	PUNCT
ejpam-4379	297	1	general	general	ADJ
ejpam-4379	297	2	topology	topology	PROPN
ejpam-4379	297	3	.	.	PUNCT
ejpam-4379	298	1	pwn	pwn	PROPN
ejpam-4379	298	2	,	,	PUNCT
ejpam-4379	298	3	warszawa	warszawa	PROPN
ejpam-4379	298	4	,	,	PUNCT
ejpam-4379	298	5	1977	1977	NUM
ejpam-4379	298	6	.	.	PUNCT
ejpam-4379	299	1	[	[	X
ejpam-4379	299	2	3	3	NUM
ejpam-4379	299	3	]	]	X
ejpam-4379	299	4	l	l	NOUN
ejpam-4379	299	5	kalantan	kalantan	PROPN
ejpam-4379	300	1	i	i	PRON
ejpam-4379	300	2	alshammari	alshammari	PROPN
ejpam-4379	300	3	and	and	CCONJ
ejpam-4379	300	4	s	s	VERB
ejpam-4379	300	5	thabit	thabit	NOUN
ejpam-4379	300	6	.	.	PUNCT
ejpam-4379	301	1	partial	partial	ADJ
ejpam-4379	301	2	normality	normality	NOUN
ejpam-4379	301	3	.	.	PUNCT
ejpam-4379	302	1	journal	journal	NOUN
ejpam-4379	302	2	of	of	ADP
ejpam-4379	302	3	mathematical	mathematical	ADJ
ejpam-4379	302	4	analysis	analysis	NOUN
ejpam-4379	302	5	,	,	PUNCT
ejpam-4379	302	6	10(6):1–8	10(6):1–8	NUM
ejpam-4379	302	7	.	.	PROPN
ejpam-4379	302	8	,	,	PUNCT
ejpam-4379	302	9	2019	2019	NUM
ejpam-4379	302	10	.	.	PUNCT
ejpam-4379	303	1	[	[	X
ejpam-4379	303	2	4	4	NUM
ejpam-4379	303	3	]	]	X
ejpam-4379	303	4	l	l	NOUN
ejpam-4379	303	5	kalantan	kalantan	PROPN
ejpam-4379	303	6	.	.	PUNCT
ejpam-4379	304	1	results	result	VERB
ejpam-4379	304	2	about	about	ADP
ejpam-4379	304	3	κ	κ	NOUN
ejpam-4379	304	4	-	-	NOUN
ejpam-4379	304	5	normality	normality	NOUN
ejpam-4379	304	6	.	.	PUNCT
ejpam-4379	305	1	topology	topology	NOUN
ejpam-4379	305	2	and	and	CCONJ
ejpam-4379	305	3	its	its	PRON
ejpam-4379	305	4	applications	application	NOUN
ejpam-4379	305	5	,	,	PUNCT
ejpam-4379	305	6	125(1):47–62	125(1):47–62	NUM
ejpam-4379	305	7	,	,	PUNCT
ejpam-4379	305	8	2002	2002	NUM
ejpam-4379	305	9	.	.	PUNCT
ejpam-4379	306	1	[	[	X
ejpam-4379	306	2	5	5	NUM
ejpam-4379	306	3	]	]	PUNCT
ejpam-4379	306	4	l	l	NOUN
ejpam-4379	306	5	kalantan	kalantan	PROPN
ejpam-4379	306	6	.	.	PUNCT
ejpam-4379	307	1	π	π	X
ejpam-4379	307	2	-	-	ADJ
ejpam-4379	307	3	normal	normal	ADJ
ejpam-4379	307	4	topological	topological	ADJ
ejpam-4379	307	5	spaces	space	NOUN
ejpam-4379	307	6	.	.	PUNCT
ejpam-4379	308	1	filomat	filomat	NOUN
ejpam-4379	308	2	,	,	PUNCT
ejpam-4379	308	3	22(1):173–181	22(1):173–181	PROPN
ejpam-4379	308	4	.	.	PROPN
ejpam-4379	308	5	,	,	PUNCT
ejpam-4379	308	6	2008	2008	NUM
ejpam-4379	308	7	.	.	PUNCT
ejpam-4379	309	1	[	[	X
ejpam-4379	309	2	6	6	NUM
ejpam-4379	309	3	]	]	PUNCT
ejpam-4379	309	4	l	l	NOUN
ejpam-4379	309	5	kalantan	kalantan	PROPN
ejpam-4379	309	6	and	and	CCONJ
ejpam-4379	309	7	m	m	AUX
ejpam-4379	309	8	alhomieyed	alhomieye	VERB
ejpam-4379	309	9	.	.	PUNCT
ejpam-4379	310	1	cc	cc	NOUN
ejpam-4379	310	2	-	-	ADJ
ejpam-4379	310	3	normal	normal	ADJ
ejpam-4379	310	4	topological	topological	ADJ
ejpam-4379	310	5	spaces	space	NOUN
ejpam-4379	310	6	.	.	PUNCT
ejpam-4379	311	1	turkish	turkish	ADJ
ejpam-4379	311	2	journal	journal	NOUN
ejpam-4379	311	3	of	of	ADP
ejpam-4379	311	4	mathematics	mathematic	NOUN
ejpam-4379	311	5	,	,	PUNCT
ejpam-4379	311	6	41(3):749–755	41(3):749–755	PROPN
ejpam-4379	311	7	,	,	PUNCT
ejpam-4379	311	8	2017	2017	NUM
ejpam-4379	311	9	.	.	PUNCT
ejpam-4379	312	1	[	[	X
ejpam-4379	312	2	7	7	NUM
ejpam-4379	312	3	]	]	X
ejpam-4379	312	4	l	l	NOUN
ejpam-4379	312	5	kalantan	kalantan	PROPN
ejpam-4379	312	6	and	and	CCONJ
ejpam-4379	312	7	m	m	AUX
ejpam-4379	312	8	alhomieyed	alhomieye	VERB
ejpam-4379	312	9	.	.	PUNCT
ejpam-4379	313	1	s	s	X
ejpam-4379	313	2	-	-	NOUN
ejpam-4379	313	3	normality	normality	NOUN
ejpam-4379	313	4	.	.	PUNCT
ejpam-4379	314	1	journal	journal	NOUN
ejpam-4379	314	2	of	of	ADP
ejpam-4379	314	3	mathematical	mathematical	ADJ
ejpam-4379	314	4	analysis	analysis	NOUN
ejpam-4379	314	5	,	,	PUNCT
ejpam-4379	314	6	9(5):48–54	9(5):48–54	NUM
ejpam-4379	314	7	.	.	NUM
ejpam-4379	314	8	,	,	PUNCT
ejpam-4379	314	9	2018	2018	NUM
ejpam-4379	314	10	.	.	PUNCT
ejpam-4379	315	1	[	[	X
ejpam-4379	315	2	8	8	NUM
ejpam-4379	315	3	]	]	X
ejpam-4379	315	4	l	l	NOUN
ejpam-4379	315	5	kalantan	kalantan	PROPN
ejpam-4379	315	6	and	and	CCONJ
ejpam-4379	315	7	f	f	PROPN
ejpam-4379	315	8	allahabi	allahabi	NOUN
ejpam-4379	315	9	.	.	PUNCT
ejpam-4379	316	1	on	on	ADP
ejpam-4379	316	2	almost	almost	ADV
ejpam-4379	316	3	normality	normality	NOUN
ejpam-4379	316	4	.	.	PUNCT
ejpam-4379	317	1	demonstratio	demonstratio	PROPN
ejpam-4379	317	2	mathematica	mathematica	PROPN
ejpam-4379	317	3	,	,	PUNCT
ejpam-4379	317	4	41(4):961–968	41(4):961–968	PROPN
ejpam-4379	317	5	.	.	PUNCT
ejpam-4379	317	6	,	,	PUNCT
ejpam-4379	317	7	2008	2008	NUM
ejpam-4379	317	8	.	.	PUNCT
ejpam-4379	318	1	[	[	X
ejpam-4379	318	2	9	9	NUM
ejpam-4379	318	3	]	]	SYM
ejpam-4379	318	4	l	l	NOUN
ejpam-4379	318	5	kalantan	kalantan	PROPN
ejpam-4379	318	6	and	and	CCONJ
ejpam-4379	318	7	m	m	PROPN
ejpam-4379	318	8	mansouri	mansouri	ADJ
ejpam-4379	318	9	.	.	PUNCT
ejpam-4379	319	1	p	p	X
ejpam-4379	319	2	-normality	-normality	PROPN
ejpam-4379	319	3	.	.	PUNCT
ejpam-4379	320	1	journal	journal	PROPN
ejpam-4379	320	2	of	of	ADP
ejpam-4379	320	3	mathematical	mathematical	ADJ
ejpam-4379	320	4	analysis	analysis	NOUN
ejpam-4379	320	5	,	,	PUNCT
ejpam-4379	320	6	12(6):1–8	12(6):1–8	NUM
ejpam-4379	320	7	.	.	NOUN
ejpam-4379	320	8	,	,	PUNCT
ejpam-4379	320	9	2021	2021	NUM
ejpam-4379	320	10	.	.	PUNCT
ejpam-4379	321	1	[	[	X
ejpam-4379	321	2	10	10	NUM
ejpam-4379	321	3	]	]	X
ejpam-4379	321	4	l	l	NOUN
ejpam-4379	321	5	kalantan	kalantan	PROPN
ejpam-4379	321	6	and	and	CCONJ
ejpam-4379	321	7	m	m	PROPN
ejpam-4379	321	8	saeed	saeed	PROPN
ejpam-4379	321	9	.	.	PUNCT
ejpam-4379	322	1	l	l	NOUN
ejpam-4379	322	2	-	-	NOUN
ejpam-4379	322	3	normality	normality	NOUN
ejpam-4379	322	4	.	.	PUNCT
ejpam-4379	323	1	topology	topology	NOUN
ejpam-4379	323	2	proceedings	proceeding	NOUN
ejpam-4379	323	3	,	,	PUNCT
ejpam-4379	323	4	50:141–149	50:141–149	NUM
ejpam-4379	323	5	.	.	NOUN
ejpam-4379	323	6	,	,	PUNCT
ejpam-4379	323	7	2017	2017	NUM
ejpam-4379	323	8	.	.	PUNCT
ejpam-4379	324	1	[	[	X
ejpam-4379	324	2	11	11	NUM
ejpam-4379	324	3	]	]	PUNCT
ejpam-4379	324	4	l	l	NOUN
ejpam-4379	324	5	kalantan	kalantan	PROPN
ejpam-4379	324	6	and	and	CCONJ
ejpam-4379	324	7	p	p	PROPN
ejpam-4379	324	8	szeptycki	szeptycki	PROPN
ejpam-4379	324	9	.	.	PUNCT
ejpam-4379	325	1	κ	κ	NOUN
ejpam-4379	325	2	-	-	PUNCT
ejpam-4379	325	3	normality	normality	NOUN
ejpam-4379	325	4	and	and	CCONJ
ejpam-4379	325	5	products	product	NOUN
ejpam-4379	325	6	of	of	ADP
ejpam-4379	325	7	ordinals	ordinal	NOUN
ejpam-4379	325	8	.	.	PUNCT
ejpam-4379	326	1	topology	topology	NOUN
ejpam-4379	326	2	and	and	CCONJ
ejpam-4379	326	3	its	its	PRON
ejpam-4379	326	4	applications	application	NOUN
ejpam-4379	326	5	,	,	PUNCT
ejpam-4379	326	6	123(3):537–545	123(3):537–545	NUM
ejpam-4379	326	7	,	,	PUNCT
ejpam-4379	326	8	2002	2002	NUM
ejpam-4379	326	9	.	.	PUNCT
ejpam-4379	327	1	[	[	X
ejpam-4379	327	2	12	12	NUM
ejpam-4379	327	3	]	]	X
ejpam-4379	327	4	p	p	NOUN
ejpam-4379	327	5	nyikosi	nyikosi	NOUN
ejpam-4379	327	6	.	.	PUNCT
ejpam-4379	328	1	axioms	axiom	NOUN
ejpam-4379	328	2	,	,	PUNCT
ejpam-4379	328	3	theorems	theorem	NOUN
ejpam-4379	328	4	,	,	PUNCT
ejpam-4379	328	5	and	and	CCONJ
ejpam-4379	328	6	problems	problem	NOUN
ejpam-4379	328	7	related	relate	VERB
ejpam-4379	328	8	to	to	ADP
ejpam-4379	328	9	the	the	DET
ejpam-4379	328	10	jones	jones	PROPN
ejpam-4379	328	11	lemma	lemma	PROPN
ejpam-4379	328	12	.	.	PROPN
ejpam-4379	328	13	general	general	ADJ
ejpam-4379	328	14	topology	topology	NOUN
ejpam-4379	328	15	and	and	CCONJ
ejpam-4379	328	16	modern	modern	ADJ
ejpam-4379	328	17	analysis	analysis	NOUN
ejpam-4379	328	18	,	,	PUNCT
ejpam-4379	328	19	page	page	NOUN
ejpam-4379	328	20	441–449	441–449	NUM
ejpam-4379	328	21	,	,	PUNCT
ejpam-4379	328	22	1981	1981	NUM
ejpam-4379	328	23	.	.	PUNCT
ejpam-4379	329	1	[	[	X
ejpam-4379	329	2	13	13	NUM
ejpam-4379	329	3	]	]	X
ejpam-4379	329	4	m	m	NOUN
ejpam-4379	329	5	singal	singal	ADJ
ejpam-4379	329	6	and	and	CCONJ
ejpam-4379	329	7	s	s	VERB
ejpam-4379	329	8	arya	arya	NOUN
ejpam-4379	329	9	.	.	PUNCT
ejpam-4379	330	1	almost	almost	ADV
ejpam-4379	330	2	normal	normal	ADJ
ejpam-4379	330	3	and	and	CCONJ
ejpam-4379	330	4	almost	almost	ADV
ejpam-4379	330	5	completely	completely	ADV
ejpam-4379	330	6	regular	regular	ADJ
ejpam-4379	330	7	spaces	space	NOUN
ejpam-4379	330	8	.	.	PUNCT
ejpam-4379	331	1	kyungpook	kyungpook	PROPN
ejpam-4379	331	2	mathematical	mathematical	PROPN
ejpam-4379	331	3	journal	journal	NOUN
ejpam-4379	331	4	,	,	PUNCT
ejpam-4379	331	5	25(1):141–152	25(1):141–152	NUM
ejpam-4379	331	6	,	,	PUNCT
ejpam-4379	331	7	1970	1970	NUM
ejpam-4379	331	8	.	.	PUNCT
ejpam-4379	332	1	[	[	X
ejpam-4379	332	2	14	14	NUM
ejpam-4379	332	3	]	]	X
ejpam-4379	332	4	m	m	VERB
ejpam-4379	332	5	k	k	NOUN
ejpam-4379	332	6	singal	singal	NOUN
ejpam-4379	332	7	and	and	CCONJ
ejpam-4379	332	8	a	a	DET
ejpam-4379	332	9	r	r	NOUN
ejpam-4379	332	10	singal	singal	NOUN
ejpam-4379	332	11	.	.	PUNCT
ejpam-4379	333	1	mildly	mildly	ADV
ejpam-4379	333	2	normal	normal	ADJ
ejpam-4379	333	3	spaces	space	NOUN
ejpam-4379	333	4	.	.	PUNCT
ejpam-4379	334	1	kyungpook	kyungpook	PROPN
ejpam-4379	334	2	mathematical	mathematical	PROPN
ejpam-4379	334	3	journal	journal	NOUN
ejpam-4379	334	4	,	,	PUNCT
ejpam-4379	334	5	13(1):29–31	13(1):29–31	NUM
ejpam-4379	334	6	,	,	PUNCT
ejpam-4379	334	7	1973	1973	NUM
ejpam-4379	334	8	.	.	PUNCT
ejpam-4379	335	1	[	[	X
ejpam-4379	335	2	15	15	NUM
ejpam-4379	335	3	]	]	X
ejpam-4379	335	4	l	l	NOUN
ejpam-4379	335	5	steen	steen	PROPN
ejpam-4379	335	6	and	and	CCONJ
ejpam-4379	335	7	j	j	PROPN
ejpam-4379	335	8	a	a	DET
ejpam-4379	335	9	seebach	seebach	NOUN
ejpam-4379	335	10	.	.	PUNCT
ejpam-4379	336	1	counterexamples	counterexample	NOUN
ejpam-4379	336	2	in	in	ADP
ejpam-4379	336	3	topology	topology	NOUN
ejpam-4379	336	4	.	.	PUNCT
ejpam-4379	337	1	dover	dover	PROPN
ejpam-4379	337	2	publications	publications	PROPN
ejpam-4379	337	3	inc	inc	PROPN
ejpam-4379	337	4	,	,	PUNCT
ejpam-4379	337	5	usa	usa	PROPN
ejpam-4379	337	6	,	,	PUNCT
ejpam-4379	337	7	1995	1995	NUM
ejpam-4379	337	8	.	.	PUNCT
ejpam-4379	338	1	[	[	X
ejpam-4379	338	2	16	16	NUM
ejpam-4379	338	3	]	]	X
ejpam-4379	338	4	e	e	X
ejpam-4379	338	5	v	v	X
ejpam-4379	338	6	ščepin	ščepin	NOUN
ejpam-4379	338	7	.	.	PUNCT
ejpam-4379	339	1	real	real	ADJ
ejpam-4379	339	2	valued	value	VERB
ejpam-4379	339	3	functions	function	NOUN
ejpam-4379	339	4	and	and	CCONJ
ejpam-4379	339	5	spaces	space	NOUN
ejpam-4379	339	6	close	close	ADV
ejpam-4379	339	7	to	to	ADP
ejpam-4379	339	8	normal	normal	ADJ
ejpam-4379	339	9	.	.	PUNCT
ejpam-4379	340	1	sib	sib	NOUN
ejpam-4379	340	2	.	.	PUNCT
ejpam-4379	340	3	matem	matem	PROPN
ejpam-4379	340	4	.	.	PUNCT
ejpam-4379	341	1	journ	journ	PROPN
ejpam-4379	341	2	.	.	PUNCT
ejpam-4379	341	3	,	,	PUNCT
ejpam-4379	342	1	13(5):1182–1196	13(5):1182–1196	NUM
ejpam-4379	342	2	,	,	PUNCT
ejpam-4379	342	3	1972	1972	NUM
ejpam-4379	342	4	.	.	PUNCT
ejpam-4379	343	1	[	[	X
ejpam-4379	343	2	17	17	NUM
ejpam-4379	343	3	]	]	PUNCT
ejpam-4379	343	4	v	v	NOUN
ejpam-4379	343	5	zaitsev	zaitsev	NOUN
ejpam-4379	343	6	.	.	PUNCT
ejpam-4379	344	1	on	on	ADP
ejpam-4379	344	2	certain	certain	ADJ
ejpam-4379	344	3	classes	class	NOUN
ejpam-4379	344	4	of	of	ADP
ejpam-4379	344	5	topological	topological	ADJ
ejpam-4379	344	6	spaces	space	NOUN
ejpam-4379	344	7	and	and	CCONJ
ejpam-4379	344	8	their	their	PRON
ejpam-4379	344	9	bicompactifications	bicompactification	NOUN
ejpam-4379	344	10	.	.	PUNCT
ejpam-4379	345	1	dokl	dokl	NOUN
ejpam-4379	345	2	.	.	PUNCT
ejpam-4379	345	3	akad	akad	PROPN
ejpam-4379	345	4	.	.	PUNCT
ejpam-4379	346	1	naur	naur	PROPN
ejpam-4379	346	2	sssrl	sssrl	PROPN
ejpam-4379	346	3	,	,	PUNCT
ejpam-4379	346	4	178(4):778–779	178(4):778–779	NUM
ejpam-4379	346	5	,	,	PUNCT
ejpam-4379	346	6	1968	1968	NUM
ejpam-4379	346	7	.	.	PUNCT