id	sid	tid	token	lemma	pos
ejpam-4776	1	1	european	european	PROPN
ejpam-4776	1	2	journal	journal	PROPN
ejpam-4776	1	3	of	of	ADP
ejpam-4776	1	4	pure	pure	ADJ
ejpam-4776	1	5	and	and	CCONJ
ejpam-4776	1	6	applied	apply	VERB
ejpam-4776	1	7	mathematics	mathematic	NOUN
ejpam-4776	1	8	vol	vol	NOUN
ejpam-4776	1	9	.	.	PUNCT
ejpam-4776	2	1	16	16	NUM
ejpam-4776	2	2	,	,	PUNCT
ejpam-4776	2	3	no	no	INTJ
ejpam-4776	2	4	.	.	NOUN
ejpam-4776	2	5	2	2	NUM
ejpam-4776	2	6	,	,	PUNCT
ejpam-4776	2	7	2023	2023	NUM
ejpam-4776	2	8	,	,	PUNCT
ejpam-4776	2	9	1260	1260	NUM
ejpam-4776	2	10	-	-	SYM
ejpam-4776	2	11	1273	1273	NUM
ejpam-4776	2	12	issn	issn	PROPN
ejpam-4776	2	13	1307	1307	NUM
ejpam-4776	2	14	-	-	SYM
ejpam-4776	2	15	5543	5543	NUM
ejpam-4776	2	16	–	–	PUNCT
ejpam-4776	3	1	ejpam.com	ejpam.com	X
ejpam-4776	3	2	published	publish	VERB
ejpam-4776	3	3	by	by	ADP
ejpam-4776	3	4	new	new	PROPN
ejpam-4776	3	5	york	york	PROPN
ejpam-4776	3	6	business	business	PROPN
ejpam-4776	3	7	global	global	PROPN
ejpam-4776	3	8	cc	cc	PROPN
ejpam-4776	3	9	-	-	NOUN
ejpam-4776	3	10	tychonoffness	tychonoffness	PROPN
ejpam-4776	3	11	,	,	PUNCT
ejpam-4776	3	12	cct3	cct3	PROPN
ejpam-4776	3	13	and	and	CCONJ
ejpam-4776	3	14	cc	cc	NOUN
ejpam-4776	3	15	-	-	ADJ
ejpam-4776	3	16	almost	almost	ADV
ejpam-4776	3	17	regularity	regularity	NOUN
ejpam-4776	3	18	sadeq	sadeq	X
ejpam-4776	3	19	ali	ali	PROPN
ejpam-4776	3	20	thabit1	thabit1	PROPN
ejpam-4776	3	21	,	,	PUNCT
ejpam-4776	3	22	wafa	wafa	PROPN
ejpam-4776	3	23	alqurashi2,∗	alqurashi2,∗	PROPN
ejpam-4776	3	24	1	1	NUM
ejpam-4776	3	25	department	department	NOUN
ejpam-4776	3	26	of	of	ADP
ejpam-4776	3	27	mathematics	mathematic	NOUN
ejpam-4776	3	28	,	,	PUNCT
ejpam-4776	3	29	faculty	faculty	NOUN
ejpam-4776	3	30	of	of	ADP
ejpam-4776	3	31	education	education	NOUN
ejpam-4776	3	32	-	-	PUNCT
ejpam-4776	3	33	almahra	almahra	PROPN
ejpam-4776	3	34	,	,	PUNCT
ejpam-4776	3	35	hadhramout	hadhramout	PROPN
ejpam-4776	3	36	university	university	PROPN
ejpam-4776	3	37	,	,	PUNCT
ejpam-4776	3	38	yemen	yemen	PROPN
ejpam-4776	3	39	2	2	NUM
ejpam-4776	3	40	department	department	NOUN
ejpam-4776	3	41	of	of	ADP
ejpam-4776	3	42	mathematical	mathematical	ADJ
ejpam-4776	3	43	sciences	science	NOUN
ejpam-4776	3	44	,	,	PUNCT
ejpam-4776	3	45	faculty	faculty	NOUN
ejpam-4776	3	46	of	of	ADP
ejpam-4776	3	47	applied	apply	VERB
ejpam-4776	3	48	sciences	science	NOUN
ejpam-4776	3	49	,	,	PUNCT
ejpam-4776	3	50	umm	umm	INTJ
ejpam-4776	3	51	al	al	PROPN
ejpam-4776	3	52	-	-	PUNCT
ejpam-4776	3	53	qura	qura	PROPN
ejpam-4776	3	54	university	university	NOUN
ejpam-4776	3	55	,	,	PUNCT
ejpam-4776	3	56	saudi	saudi	PROPN
ejpam-4776	3	57	arabia	arabia	PROPN
ejpam-4776	3	58	abstract	abstract	NOUN
ejpam-4776	3	59	.	.	PUNCT
ejpam-4776	4	1	following	follow	VERB
ejpam-4776	4	2	the	the	DET
ejpam-4776	4	3	notion	notion	NOUN
ejpam-4776	4	4	of	of	ADP
ejpam-4776	4	5	so	so	ADV
ejpam-4776	4	6	-	-	PUNCT
ejpam-4776	4	7	called	call	VERB
ejpam-4776	4	8	c	c	NOUN
ejpam-4776	4	9	-	-	PUNCT
ejpam-4776	4	10	normality	normality	NOUN
ejpam-4776	4	11	a	a	DET
ejpam-4776	4	12	weaker	weak	ADJ
ejpam-4776	4	13	version	version	NOUN
ejpam-4776	4	14	of	of	ADP
ejpam-4776	4	15	normality	normality	NOUN
ejpam-4776	4	16	in	in	ADP
ejpam-4776	4	17	topological	topological	ADJ
ejpam-4776	4	18	spaces	space	NOUN
ejpam-4776	4	19	as	as	SCONJ
ejpam-4776	4	20	proposed	propose	VERB
ejpam-4776	4	21	by	by	ADP
ejpam-4776	4	22	a.	a.	NOUN
ejpam-4776	4	23	v.	v.	ADP
ejpam-4776	4	24	arhangel’skii	arhangel’skii	ADJ
ejpam-4776	4	25	,	,	PUNCT
ejpam-4776	4	26	further	far	ADV
ejpam-4776	4	27	weaker	weak	ADJ
ejpam-4776	4	28	version	version	NOUN
ejpam-4776	4	29	called	call	VERB
ejpam-4776	4	30	cc	cc	NOUN
ejpam-4776	4	31	-	-	NOUN
ejpam-4776	4	32	normality	normality	NOUN
ejpam-4776	4	33	is	be	AUX
ejpam-4776	4	34	studied	study	VERB
ejpam-4776	4	35	by	by	ADP
ejpam-4776	4	36	kalantan	kalantan	PROPN
ejpam-4776	4	37	et	et	PROPN
ejpam-4776	4	38	al	al	PROPN
ejpam-4776	5	1	[	[	X
ejpam-4776	5	2	14	14	NUM
ejpam-4776	5	3	]	]	PUNCT
ejpam-4776	5	4	.	.	PUNCT
ejpam-4776	6	1	in	in	ADP
ejpam-4776	6	2	this	this	DET
ejpam-4776	6	3	paper	paper	NOUN
ejpam-4776	6	4	,	,	PUNCT
ejpam-4776	6	5	we	we	PRON
ejpam-4776	6	6	investigate	investigate	VERB
ejpam-4776	6	7	various	various	ADJ
ejpam-4776	6	8	type	type	NOUN
ejpam-4776	6	9	of	of	ADP
ejpam-4776	6	10	properties	property	NOUN
ejpam-4776	6	11	such	such	ADJ
ejpam-4776	6	12	as	as	ADP
ejpam-4776	6	13	cc	cc	NOUN
ejpam-4776	6	14	-	-	ADJ
ejpam-4776	6	15	complete	complete	ADJ
ejpam-4776	6	16	regularity	regularity	NOUN
ejpam-4776	6	17	,	,	PUNCT
ejpam-4776	6	18	cc	cc	NOUN
ejpam-4776	6	19	-	-	ADJ
ejpam-4776	6	20	almost	almost	ADV
ejpam-4776	6	21	complete	complete	ADJ
ejpam-4776	6	22	regularity	regularity	NOUN
ejpam-4776	6	23	,	,	PUNCT
ejpam-4776	6	24	cc	cc	NOUN
ejpam-4776	6	25	-	-	NOUN
ejpam-4776	6	26	regularity	regularity	NOUN
ejpam-4776	6	27	,	,	PUNCT
ejpam-4776	6	28	cc	cc	NOUN
ejpam-4776	6	29	-	-	ADJ
ejpam-4776	6	30	almost	almost	ADV
ejpam-4776	6	31	regularity	regularity	NOUN
ejpam-4776	6	32	,	,	PUNCT
ejpam-4776	6	33	cct3	cct3	PROPN
ejpam-4776	6	34	and	and	CCONJ
ejpam-4776	6	35	cc	cc	NOUN
ejpam-4776	6	36	-	-	NOUN
ejpam-4776	6	37	tychonoffness	tychonoffness	NOUN
ejpam-4776	6	38	.	.	PUNCT
ejpam-4776	7	1	a	a	DET
ejpam-4776	7	2	space	space	NOUN
ejpam-4776	7	3	(	(	PUNCT
ejpam-4776	7	4	x	x	X
ejpam-4776	7	5	,	,	PUNCT
ejpam-4776	7	6	t	t	PROPN
ejpam-4776	7	7	)	)	PUNCT
ejpam-4776	7	8	is	be	AUX
ejpam-4776	7	9	called	call	VERB
ejpam-4776	7	10	a	a	DET
ejpam-4776	7	11	cc	cc	NOUN
ejpam-4776	7	12	-	-	ADJ
ejpam-4776	7	13	completely	completely	ADV
ejpam-4776	7	14	regular	regular	ADJ
ejpam-4776	7	15	(	(	PUNCT
ejpam-4776	7	16	resp	resp	NOUN
ejpam-4776	7	17	.	.	PUNCT
ejpam-4776	8	1	cc	cc	VERB
ejpam-4776	8	2	-	-	PUNCT
ejpam-4776	8	3	almost	almost	ADV
ejpam-4776	8	4	completely	completely	ADV
ejpam-4776	8	5	regular	regular	ADJ
ejpam-4776	8	6	,	,	PUNCT
ejpam-4776	8	7	cc	cc	NOUN
ejpam-4776	8	8	-	-	ADJ
ejpam-4776	8	9	regular	regular	ADJ
ejpam-4776	8	10	,	,	PUNCT
ejpam-4776	8	11	cc	cc	NOUN
ejpam-4776	8	12	-	-	ADJ
ejpam-4776	8	13	almost	almost	ADV
ejpam-4776	8	14	regular	regular	ADJ
ejpam-4776	8	15	,	,	PUNCT
ejpam-4776	8	16	cct3	cct3	PROPN
ejpam-4776	8	17	,	,	PUNCT
ejpam-4776	8	18	cc	cc	NOUN
ejpam-4776	8	19	-	-	NOUN
ejpam-4776	8	20	tychonoff	tychonoff	NOUN
ejpam-4776	8	21	)	)	PUNCT
ejpam-4776	8	22	space	space	NOUN
ejpam-4776	8	23	if	if	SCONJ
ejpam-4776	8	24	there	there	PRON
ejpam-4776	8	25	exist	exist	VERB
ejpam-4776	8	26	a	a	DET
ejpam-4776	8	27	completely	completely	ADV
ejpam-4776	8	28	regular	regular	ADJ
ejpam-4776	8	29	(	(	PUNCT
ejpam-4776	8	30	resp	resp	NOUN
ejpam-4776	8	31	.	.	PUNCT
ejpam-4776	9	1	almost	almost	ADV
ejpam-4776	9	2	completely	completely	ADV
ejpam-4776	9	3	regular	regular	ADJ
ejpam-4776	9	4	,	,	PUNCT
ejpam-4776	9	5	regular	regular	ADJ
ejpam-4776	9	6	,	,	PUNCT
ejpam-4776	9	7	almost	almost	ADV
ejpam-4776	9	8	regular	regular	ADJ
ejpam-4776	9	9	,	,	PUNCT
ejpam-4776	9	10	t3	t3	NOUN
ejpam-4776	9	11	,	,	PUNCT
ejpam-4776	9	12	tychonoff	tychonoff	NOUN
ejpam-4776	9	13	)	)	PUNCT
ejpam-4776	9	14	space	space	NOUN
ejpam-4776	9	15	y	y	PROPN
ejpam-4776	9	16	and	and	CCONJ
ejpam-4776	9	17	a	a	DET
ejpam-4776	9	18	bijective	bijective	ADJ
ejpam-4776	9	19	function	function	NOUN
ejpam-4776	9	20	f	f	NOUN
ejpam-4776	10	1	:	:	PUNCT
ejpam-4776	10	2	x	x	X
ejpam-4776	10	3	→	→	SYM
ejpam-4776	10	4	y	y	PROPN
ejpam-4776	10	5	such	such	ADJ
ejpam-4776	10	6	that	that	SCONJ
ejpam-4776	10	7	the	the	DET
ejpam-4776	10	8	restriction	restriction	NOUN
ejpam-4776	10	9	function	function	NOUN
ejpam-4776	10	10	f	f	PROPN
ejpam-4776	10	11	|a	|a	VERB
ejpam-4776	10	12	:	:	PUNCT
ejpam-4776	10	13	a	a	DET
ejpam-4776	10	14	→	→	SYM
ejpam-4776	10	15	f(a	f(a	NOUN
ejpam-4776	10	16	)	)	PUNCT
ejpam-4776	10	17	is	be	AUX
ejpam-4776	10	18	a	a	DET
ejpam-4776	10	19	homeomorphism	homeomorphism	NOUN
ejpam-4776	10	20	for	for	ADP
ejpam-4776	10	21	each	each	DET
ejpam-4776	10	22	countably	countably	ADV
ejpam-4776	10	23	compact	compact	ADJ
ejpam-4776	10	24	subspace	subspace	NOUN
ejpam-4776	10	25	a	a	DET
ejpam-4776	10	26	⊆	⊆	NUM
ejpam-4776	10	27	x.	x.	NOUN
ejpam-4776	11	1	we	we	PRON
ejpam-4776	11	2	study	study	VERB
ejpam-4776	11	3	these	these	DET
ejpam-4776	11	4	properties	property	NOUN
ejpam-4776	11	5	and	and	CCONJ
ejpam-4776	11	6	present	present	VERB
ejpam-4776	11	7	some	some	DET
ejpam-4776	11	8	examples	example	NOUN
ejpam-4776	11	9	to	to	PART
ejpam-4776	11	10	illustrate	illustrate	VERB
ejpam-4776	11	11	the	the	DET
ejpam-4776	11	12	relationships	relationship	NOUN
ejpam-4776	11	13	among	among	ADP
ejpam-4776	11	14	them	they	PRON
ejpam-4776	11	15	with	with	ADP
ejpam-4776	11	16	other	other	ADJ
ejpam-4776	11	17	forms	form	NOUN
ejpam-4776	11	18	of	of	ADP
ejpam-4776	11	19	topological	topological	ADJ
ejpam-4776	11	20	properties	property	NOUN
ejpam-4776	11	21	.	.	PUNCT
ejpam-4776	12	1	2020	2020	NUM
ejpam-4776	12	2	mathematics	mathematic	NOUN
ejpam-4776	12	3	subject	subject	NOUN
ejpam-4776	12	4	classifications	classification	NOUN
ejpam-4776	12	5	:	:	PUNCT
ejpam-4776	12	6	54c10	54c10	NUM
ejpam-4776	12	7	,	,	PUNCT
ejpam-4776	12	8	54d10	54d10	NUM
ejpam-4776	12	9	,	,	PUNCT
ejpam-4776	12	10	54d20	54d20	NUM
ejpam-4776	12	11	,	,	PUNCT
ejpam-4776	12	12	54d15,54d70	54d15,54d70	NUM
ejpam-4776	12	13	key	key	ADJ
ejpam-4776	12	14	words	word	NOUN
ejpam-4776	12	15	and	and	CCONJ
ejpam-4776	12	16	phrases	phrase	NOUN
ejpam-4776	12	17	:	:	PUNCT
ejpam-4776	12	18	c	c	X
ejpam-4776	12	19	-	-	ADJ
ejpam-4776	12	20	normal	normal	ADJ
ejpam-4776	12	21	,	,	PUNCT
ejpam-4776	12	22	cc	cc	NOUN
ejpam-4776	12	23	-	-	ADJ
ejpam-4776	12	24	normal	normal	ADJ
ejpam-4776	12	25	,	,	PUNCT
ejpam-4776	12	26	c	c	NOUN
ejpam-4776	12	27	-	-	NOUN
ejpam-4776	12	28	regular	regular	ADJ
ejpam-4776	12	29	,	,	PUNCT
ejpam-4776	12	30	c	c	NOUN
ejpam-4776	12	31	-	-	PUNCT
ejpam-4776	12	32	tychonoff	tychonoff	NOUN
ejpam-4776	12	33	,	,	PUNCT
ejpam-4776	12	34	l	l	NOUN
ejpam-4776	12	35	-	-	ADJ
ejpam-4776	12	36	normal	normal	ADJ
ejpam-4776	12	37	,	,	PUNCT
ejpam-4776	12	38	l	l	NOUN
ejpam-4776	12	39	-	-	ADJ
ejpam-4776	12	40	regular	regular	ADJ
ejpam-4776	12	41	and	and	CCONJ
ejpam-4776	12	42	l	l	NOUN
ejpam-4776	12	43	-	-	NOUN
ejpam-4776	12	44	tychonoff	tychonoff	NOUN
ejpam-4776	12	45	1	1	NUM
ejpam-4776	12	46	.	.	PUNCT
ejpam-4776	12	47	introduction	introduction	NOUN
ejpam-4776	12	48	the	the	DET
ejpam-4776	12	49	notion	notion	NOUN
ejpam-4776	12	50	of	of	ADP
ejpam-4776	12	51	c	c	NOUN
ejpam-4776	12	52	-	-	PUNCT
ejpam-4776	12	53	normality	normality	NOUN
ejpam-4776	12	54	has	have	AUX
ejpam-4776	12	55	been	be	AUX
ejpam-4776	12	56	studied	study	VERB
ejpam-4776	12	57	by	by	ADP
ejpam-4776	12	58	alzahrani	alzahrani	NOUN
ejpam-4776	12	59	and	and	CCONJ
ejpam-4776	12	60	kalantan	kalantan	PROPN
ejpam-4776	12	61	in	in	ADP
ejpam-4776	12	62	[	[	X
ejpam-4776	12	63	7	7	NUM
ejpam-4776	12	64	]	]	PUNCT
ejpam-4776	12	65	.	.	PUNCT
ejpam-4776	13	1	the	the	DET
ejpam-4776	13	2	notion	notion	NOUN
ejpam-4776	13	3	of	of	ADP
ejpam-4776	13	4	l	l	NOUN
ejpam-4776	13	5	-	-	NOUN
ejpam-4776	13	6	normality	normality	NOUN
ejpam-4776	13	7	has	have	AUX
ejpam-4776	13	8	been	be	AUX
ejpam-4776	13	9	studied	study	VERB
ejpam-4776	13	10	by	by	ADP
ejpam-4776	13	11	kalantan	kalantan	PROPN
ejpam-4776	13	12	and	and	CCONJ
ejpam-4776	13	13	saeed	saeed	PROPN
ejpam-4776	13	14	in	in	ADP
ejpam-4776	13	15	[	[	X
ejpam-4776	13	16	12	12	NUM
ejpam-4776	13	17	]	]	PUNCT
ejpam-4776	13	18	.	.	PUNCT
ejpam-4776	14	1	then	then	ADV
ejpam-4776	14	2	,	,	PUNCT
ejpam-4776	14	3	alzahrani	alzahrani	NOUN
ejpam-4776	14	4	studied	study	VERB
ejpam-4776	14	5	the	the	DET
ejpam-4776	14	6	notions	notion	NOUN
ejpam-4776	14	7	of	of	ADP
ejpam-4776	14	8	c	c	NOUN
ejpam-4776	14	9	-	-	PUNCT
ejpam-4776	14	10	regularity	regularity	NOUN
ejpam-4776	14	11	,	,	PUNCT
ejpam-4776	14	12	l	l	NOUN
ejpam-4776	14	13	-	-	NOUN
ejpam-4776	14	14	regularity	regularity	NOUN
ejpam-4776	14	15	,	,	PUNCT
ejpam-4776	14	16	c	c	NOUN
ejpam-4776	14	17	-	-	PUNCT
ejpam-4776	14	18	tychonoff	tychonoff	NOUN
ejpam-4776	14	19	and	and	CCONJ
ejpam-4776	14	20	l	l	NOUN
ejpam-4776	14	21	-	-	NOUN
ejpam-4776	14	22	tychonoff	tychonoff	NOUN
ejpam-4776	14	23	in	in	ADP
ejpam-4776	14	24	[	[	X
ejpam-4776	14	25	5	5	NUM
ejpam-4776	14	26	,	,	PUNCT
ejpam-4776	14	27	6	6	NUM
ejpam-4776	14	28	]	]	PUNCT
ejpam-4776	14	29	.	.	PUNCT
ejpam-4776	15	1	at	at	ADP
ejpam-4776	15	2	the	the	DET
ejpam-4776	15	3	end	end	NOUN
ejpam-4776	15	4	of	of	ADP
ejpam-4776	15	5	2022	2022	NUM
ejpam-4776	15	6	,	,	PUNCT
ejpam-4776	15	7	al	al	PROPN
ejpam-4776	15	8	-	-	PUNCT
ejpam-4776	15	9	awadi	awadi	NOUN
ejpam-4776	15	10	and	and	CCONJ
ejpam-4776	15	11	others	other	NOUN
ejpam-4776	15	12	studied	study	VERB
ejpam-4776	15	13	the	the	DET
ejpam-4776	15	14	notions	notion	NOUN
ejpam-4776	15	15	of	of	ADP
ejpam-4776	15	16	c	c	NOUN
ejpam-4776	15	17	-	-	PUNCT
ejpam-4776	15	18	mild	mild	ADJ
ejpam-4776	15	19	normality	normality	NOUN
ejpam-4776	15	20	and	and	CCONJ
ejpam-4776	15	21	c	c	NOUN
ejpam-4776	15	22	-	-	PUNCT
ejpam-4776	15	23	κ	κ	NOUN
ejpam-4776	15	24	-	-	PUNCT
ejpam-4776	15	25	normality	normality	NOUN
ejpam-4776	15	26	[	[	X
ejpam-4776	15	27	1	1	NUM
ejpam-4776	15	28	]	]	PUNCT
ejpam-4776	15	29	.	.	PUNCT
ejpam-4776	16	1	thabit	thabit	PROPN
ejpam-4776	16	2	studied	study	VERB
ejpam-4776	16	3	the	the	DET
ejpam-4776	16	4	notion	notion	NOUN
ejpam-4776	16	5	of	of	ADP
ejpam-4776	16	6	epi	epi	ADJ
ejpam-4776	16	7	-	-	ADJ
ejpam-4776	16	8	partial	partial	ADJ
ejpam-4776	16	9	normality	normality	NOUN
ejpam-4776	16	10	in	in	ADP
ejpam-4776	16	11	[	[	X
ejpam-4776	16	12	26	26	NUM
ejpam-4776	16	13	]	]	PUNCT
ejpam-4776	16	14	.	.	PUNCT
ejpam-4776	17	1	at	at	ADP
ejpam-4776	17	2	the	the	DET
ejpam-4776	17	3	end	end	NOUN
ejpam-4776	17	4	of	of	ADP
ejpam-4776	17	5	2021	2021	NUM
ejpam-4776	17	6	,	,	PUNCT
ejpam-4776	17	7	thabit	thabit	NOUN
ejpam-4776	17	8	and	and	CCONJ
ejpam-4776	17	9	others	other	NOUN
ejpam-4776	17	10	studied	study	VERB
ejpam-4776	17	11	the	the	DET
ejpam-4776	17	12	notion	notion	NOUN
ejpam-4776	17	13	of	of	ADP
ejpam-4776	17	14	epi	epi	NOUN
ejpam-4776	17	15	-	-	ADJ
ejpam-4776	17	16	quasi	quasi	ADJ
ejpam-4776	17	17	normality	normality	NOUN
ejpam-4776	17	18	in	in	ADP
ejpam-4776	17	19	[	[	X
ejpam-4776	17	20	25	25	NUM
ejpam-4776	17	21	]	]	PUNCT
ejpam-4776	17	22	.	.	PUNCT
ejpam-4776	18	1	thabit	thabit	NOUN
ejpam-4776	18	2	and	and	CCONJ
ejpam-4776	18	3	alqurashi	alqurashi	PROPN
ejpam-4776	18	4	studied	study	VERB
ejpam-4776	18	5	the	the	DET
ejpam-4776	18	6	notions	notion	NOUN
ejpam-4776	18	7	of	of	ADP
ejpam-4776	18	8	c	c	NOUN
ejpam-4776	18	9	-	-	PUNCT
ejpam-4776	18	10	almost	almost	ADV
ejpam-4776	18	11	normality	normality	NOUN
ejpam-4776	18	12	and	and	CCONJ
ejpam-4776	18	13	l	l	NOUN
ejpam-4776	18	14	-	-	ADJ
ejpam-4776	18	15	almost	almost	ADV
ejpam-4776	18	16	normality	normality	NOUN
ejpam-4776	18	17	in	in	ADP
ejpam-4776	18	18	[	[	X
ejpam-4776	18	19	3	3	NUM
ejpam-4776	18	20	]	]	PUNCT
ejpam-4776	18	21	.	.	PUNCT
ejpam-4776	19	1	thabit	thabit	NOUN
ejpam-4776	19	2	and	and	CCONJ
ejpam-4776	19	3	others	other	NOUN
ejpam-4776	19	4	studied	study	VERB
ejpam-4776	19	5	the	the	DET
ejpam-4776	19	6	notions	notion	NOUN
ejpam-4776	19	7	of	of	ADP
ejpam-4776	19	8	c	c	NOUN
ejpam-4776	19	9	-	-	PUNCT
ejpam-4776	19	10	complete	complete	ADJ
ejpam-4776	19	11	regularity	regularity	NOUN
ejpam-4776	19	12	and	and	CCONJ
ejpam-4776	19	13	ct3	ct3	NOUN
ejpam-4776	19	14	and	and	CCONJ
ejpam-4776	19	15	c	c	NOUN
ejpam-4776	19	16	-	-	PUNCT
ejpam-4776	19	17	almost	almost	ADV
ejpam-4776	19	18	regularity	regularity	NOUN
ejpam-4776	19	19	in	in	ADP
ejpam-4776	19	20	[	[	X
ejpam-4776	19	21	24	24	NUM
ejpam-4776	19	22	]	]	PUNCT
ejpam-4776	19	23	.	.	PUNCT
ejpam-4776	20	1	the	the	DET
ejpam-4776	20	2	notions	notion	NOUN
ejpam-4776	20	3	of	of	ADP
ejpam-4776	20	4	lt3	lt3	PROPN
ejpam-4776	20	5	,	,	PUNCT
ejpam-4776	20	6	l	l	NOUN
ejpam-4776	20	7	-	-	ADJ
ejpam-4776	20	8	complete	complete	ADJ
ejpam-4776	20	9	regularity	regularity	NOUN
ejpam-4776	20	10	and	and	CCONJ
ejpam-4776	20	11	l	l	NOUN
ejpam-4776	20	12	-	-	ADJ
ejpam-4776	20	13	almost	almost	ADV
ejpam-4776	20	14	regularity	regularity	NOUN
ejpam-4776	20	15	∗corresponding	∗corresponde	VERB
ejpam-4776	20	16	author	author	NOUN
ejpam-4776	20	17	.	.	PUNCT
ejpam-4776	21	1	doi	doi	NOUN
ejpam-4776	21	2	:	:	PUNCT
ejpam-4776	21	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4776	https://doi.org/10.29020/nybg.ejpam.v16i2.4776	PRON
ejpam-4776	21	4	email	email	NOUN
ejpam-4776	21	5	addresses	address	NOUN
ejpam-4776	21	6	:	:	PUNCT
ejpam-4776	21	7	sthabit1975@gmail.com	sthabit1975@gmail.com	NOUN
ejpam-4776	21	8	,	,	PUNCT
ejpam-4776	21	9	s.thabit@hu.edu.ye	s.thabit@hu.edu.ye	PROPN
ejpam-4776	21	10	(	(	PUNCT
ejpam-4776	21	11	sadeq	sadeq	PROPN
ejpam-4776	21	12	ali	ali	PROPN
ejpam-4776	21	13	thabit	thabit	PROPN
ejpam-4776	21	14	)	)	PUNCT
ejpam-4776	21	15	,	,	PUNCT
ejpam-4776	21	16	wafa-math@hotmail.com	wafa-math@hotmail.com	PROPN
ejpam-4776	21	17	,	,	PUNCT
ejpam-4776	21	18	wkqurashi@uqu.edu.sa	wkqurashi@uqu.edu.sa	PROPN
ejpam-4776	21	19	(	(	PUNCT
ejpam-4776	21	20	wafa	wafa	PROPN
ejpam-4776	21	21	alqurashi	alqurashi	PROPN
ejpam-4776	21	22	)	)	PUNCT
ejpam-4776	21	23	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4776	21	24	1260	1260	NUM
ejpam-4776	22	1	©	©	ADP
ejpam-4776	22	2	2023	2023	NUM
ejpam-4776	22	3	ejpam	ejpam	NOUN
ejpam-4776	22	4	all	all	DET
ejpam-4776	22	5	rights	right	NOUN
ejpam-4776	22	6	reserved	reserve	VERB
ejpam-4776	22	7	.	.	PUNCT
ejpam-4776	23	1	s.	s.	PROPN
ejpam-4776	23	2	a.	a.	PROPN
ejpam-4776	23	3	thabit	thabit	PROPN
ejpam-4776	23	4	,	,	PUNCT
ejpam-4776	23	5	w.	w.	PROPN
ejpam-4776	23	6	alqurashi	alqurashi	PROPN
ejpam-4776	23	7	/	/	SYM
ejpam-4776	23	8	eur	eur	PROPN
ejpam-4776	23	9	.	.	PUNCT
ejpam-4776	24	1	j.	j.	PROPN
ejpam-4776	24	2	pure	pure	PROPN
ejpam-4776	24	3	appl	appl	PROPN
ejpam-4776	24	4	.	.	PROPN
ejpam-4776	24	5	math	math	PROPN
ejpam-4776	24	6	,	,	PUNCT
ejpam-4776	24	7	16	16	NUM
ejpam-4776	24	8	(	(	PUNCT
ejpam-4776	24	9	2	2	NUM
ejpam-4776	24	10	)	)	PUNCT
ejpam-4776	24	11	(	(	PUNCT
ejpam-4776	24	12	2023	2023	NUM
ejpam-4776	24	13	)	)	PUNCT
ejpam-4776	24	14	,	,	PUNCT
ejpam-4776	24	15	1260	1260	NUM
ejpam-4776	24	16	-	-	SYM
ejpam-4776	24	17	1273	1273	NUM
ejpam-4776	24	18	1261	1261	NUM
ejpam-4776	24	19	have	have	AUX
ejpam-4776	24	20	been	be	AUX
ejpam-4776	24	21	studied	study	VERB
ejpam-4776	24	22	in	in	ADP
ejpam-4776	24	23	[	[	X
ejpam-4776	24	24	2	2	NUM
ejpam-4776	24	25	]	]	PUNCT
ejpam-4776	24	26	.	.	PUNCT
ejpam-4776	25	1	the	the	DET
ejpam-4776	25	2	notion	notion	NOUN
ejpam-4776	25	3	of	of	ADP
ejpam-4776	25	4	cc	cc	NOUN
ejpam-4776	25	5	-	-	NOUN
ejpam-4776	25	6	normality	normality	NOUN
ejpam-4776	25	7	have	have	AUX
ejpam-4776	25	8	been	be	AUX
ejpam-4776	25	9	studied	study	VERB
ejpam-4776	25	10	by	by	ADP
ejpam-4776	25	11	kalantan	kalantan	PROPN
ejpam-4776	25	12	and	and	CCONJ
ejpam-4776	25	13	others	other	NOUN
ejpam-4776	25	14	in	in	ADP
ejpam-4776	25	15	[	[	X
ejpam-4776	25	16	14	14	NUM
ejpam-4776	25	17	]	]	PUNCT
ejpam-4776	25	18	.	.	PUNCT
ejpam-4776	26	1	the	the	DET
ejpam-4776	26	2	notions	notion	NOUN
ejpam-4776	26	3	of	of	ADP
ejpam-4776	26	4	c	c	PROPN
ejpam-4776	26	5	,	,	PUNCT
ejpam-4776	26	6	c2	c2	PROPN
ejpam-4776	26	7	-	-	PUNCT
ejpam-4776	26	8	paracompactness	paracompactness	PROPN
ejpam-4776	26	9	are	be	AUX
ejpam-4776	26	10	studied	study	VERB
ejpam-4776	26	11	in	in	ADP
ejpam-4776	26	12	[	[	X
ejpam-4776	26	13	19	19	NUM
ejpam-4776	26	14	]	]	PUNCT
ejpam-4776	26	15	and	and	CCONJ
ejpam-4776	26	16	the	the	DET
ejpam-4776	26	17	notions	notion	NOUN
ejpam-4776	26	18	of	of	ADP
ejpam-4776	26	19	l	l	NOUN
ejpam-4776	26	20	,	,	PUNCT
ejpam-4776	26	21	l2	l2	NOUN
ejpam-4776	26	22	-	-	PUNCT
ejpam-4776	26	23	paracompactness	paracompactness	NOUN
ejpam-4776	26	24	are	be	AUX
ejpam-4776	26	25	studied	study	VERB
ejpam-4776	26	26	in	in	ADP
ejpam-4776	26	27	[	[	X
ejpam-4776	26	28	13	13	NUM
ejpam-4776	26	29	]	]	PUNCT
ejpam-4776	26	30	.	.	PUNCT
ejpam-4776	27	1	in	in	ADP
ejpam-4776	27	2	this	this	DET
ejpam-4776	27	3	paper	paper	NOUN
ejpam-4776	27	4	,	,	PUNCT
ejpam-4776	27	5	we	we	PRON
ejpam-4776	27	6	investigate	investigate	VERB
ejpam-4776	27	7	the	the	DET
ejpam-4776	27	8	properties	property	NOUN
ejpam-4776	27	9	,	,	PUNCT
ejpam-4776	27	10	cc	cc	NOUN
ejpam-4776	27	11	-	-	ADJ
ejpam-4776	27	12	complete	complete	ADJ
ejpam-4776	27	13	regularity	regularity	NOUN
ejpam-4776	27	14	,	,	PUNCT
ejpam-4776	27	15	cc	cc	NOUN
ejpam-4776	27	16	-	-	NOUN
ejpam-4776	27	17	regularity	regularity	NOUN
ejpam-4776	27	18	,	,	PUNCT
ejpam-4776	27	19	cc	cc	NOUN
ejpam-4776	27	20	-	-	ADJ
ejpam-4776	27	21	almost	almost	ADV
ejpam-4776	27	22	regularity	regularity	NOUN
ejpam-4776	27	23	,	,	PUNCT
ejpam-4776	27	24	cc	cc	NOUN
ejpam-4776	27	25	-	-	ADJ
ejpam-4776	27	26	almost	almost	ADV
ejpam-4776	27	27	complete	complete	ADJ
ejpam-4776	27	28	regularity	regularity	NOUN
ejpam-4776	27	29	,	,	PUNCT
ejpam-4776	27	30	cct3	cct3	PROPN
ejpam-4776	27	31	and	and	CCONJ
ejpam-4776	27	32	cc	cc	NOUN
ejpam-4776	27	33	-	-	NOUN
ejpam-4776	27	34	tychonoffness	tychonoffness	NOUN
ejpam-4776	27	35	.	.	PUNCT
ejpam-4776	28	1	we	we	PRON
ejpam-4776	28	2	present	present	VERB
ejpam-4776	28	3	some	some	DET
ejpam-4776	28	4	examples	example	NOUN
ejpam-4776	28	5	to	to	PART
ejpam-4776	28	6	illustrate	illustrate	VERB
ejpam-4776	28	7	the	the	DET
ejpam-4776	28	8	relationships	relationship	NOUN
ejpam-4776	28	9	among	among	ADP
ejpam-4776	28	10	these	these	DET
ejpam-4776	28	11	properties	property	NOUN
ejpam-4776	28	12	with	with	ADP
ejpam-4776	28	13	other	other	ADJ
ejpam-4776	28	14	kinds	kind	NOUN
ejpam-4776	28	15	of	of	ADP
ejpam-4776	28	16	normality	normality	NOUN
ejpam-4776	28	17	,	,	PUNCT
ejpam-4776	28	18	complete	complete	ADJ
ejpam-4776	28	19	regularity	regularity	NOUN
ejpam-4776	28	20	and	and	CCONJ
ejpam-4776	28	21	regularity	regularity	NOUN
ejpam-4776	28	22	.	.	PUNCT
ejpam-4776	29	1	we	we	PRON
ejpam-4776	29	2	need	need	VERB
ejpam-4776	29	3	to	to	PART
ejpam-4776	29	4	recall	recall	VERB
ejpam-4776	29	5	that	that	PRON
ejpam-4776	29	6	:	:	PUNCT
ejpam-4776	29	7	a	a	DET
ejpam-4776	29	8	subset	subset	NOUN
ejpam-4776	29	9	a	a	PRON
ejpam-4776	29	10	of	of	ADP
ejpam-4776	29	11	a	a	DET
ejpam-4776	29	12	space	space	NOUN
ejpam-4776	29	13	x	x	PUNCT
ejpam-4776	29	14	is	be	AUX
ejpam-4776	29	15	said	say	VERB
ejpam-4776	29	16	to	to	PART
ejpam-4776	29	17	be	be	AUX
ejpam-4776	29	18	a	a	DET
ejpam-4776	29	19	closed	closed	ADJ
ejpam-4776	29	20	domain	domain	NOUN
ejpam-4776	29	21	subset	subset	NOUN
ejpam-4776	29	22	if	if	SCONJ
ejpam-4776	29	23	a	a	DET
ejpam-4776	29	24	=	=	SYM
ejpam-4776	29	25	int(a	int(a	NOUN
ejpam-4776	29	26	)	)	PUNCT
ejpam-4776	30	1	[	[	X
ejpam-4776	30	2	15	15	NUM
ejpam-4776	30	3	]	]	PUNCT
ejpam-4776	30	4	.	.	PUNCT
ejpam-4776	31	1	a	a	DET
ejpam-4776	31	2	subset	subset	NOUN
ejpam-4776	31	3	a	a	PRON
ejpam-4776	31	4	of	of	ADP
ejpam-4776	31	5	a	a	DET
ejpam-4776	31	6	space	space	NOUN
ejpam-4776	31	7	x	x	PUNCT
ejpam-4776	31	8	is	be	AUX
ejpam-4776	31	9	called	call	VERB
ejpam-4776	31	10	π	π	PROPN
ejpam-4776	31	11	-	-	VERB
ejpam-4776	31	12	closed	closed	ADJ
ejpam-4776	31	13	if	if	SCONJ
ejpam-4776	31	14	it	it	PRON
ejpam-4776	31	15	is	be	AUX
ejpam-4776	31	16	a	a	DET
ejpam-4776	31	17	finite	finite	ADJ
ejpam-4776	31	18	intersection	intersection	NOUN
ejpam-4776	31	19	of	of	ADP
ejpam-4776	31	20	closed	closed	ADJ
ejpam-4776	31	21	domain	domain	NOUN
ejpam-4776	31	22	subsets	subset	NOUN
ejpam-4776	31	23	[	[	X
ejpam-4776	31	24	27	27	NUM
ejpam-4776	31	25	]	]	PUNCT
ejpam-4776	31	26	.	.	PUNCT
ejpam-4776	32	1	two	two	NUM
ejpam-4776	32	2	subsets	subset	NOUN
ejpam-4776	32	3	a	a	PRON
ejpam-4776	32	4	and	and	CCONJ
ejpam-4776	32	5	b	b	NOUN
ejpam-4776	32	6	of	of	ADP
ejpam-4776	32	7	a	a	DET
ejpam-4776	32	8	space	space	NOUN
ejpam-4776	32	9	x	x	PRON
ejpam-4776	32	10	are	be	AUX
ejpam-4776	32	11	said	say	VERB
ejpam-4776	32	12	to	to	PART
ejpam-4776	32	13	be	be	AUX
ejpam-4776	32	14	separated	separate	VERB
ejpam-4776	32	15	if	if	SCONJ
ejpam-4776	32	16	there	there	PRON
ejpam-4776	32	17	exist	exist	VERB
ejpam-4776	32	18	two	two	NUM
ejpam-4776	32	19	disjoint	disjoint	ADJ
ejpam-4776	32	20	open	open	ADJ
ejpam-4776	32	21	subsets	subset	NOUN
ejpam-4776	32	22	u	u	NOUN
ejpam-4776	32	23	and	and	CCONJ
ejpam-4776	32	24	v	v	NOUN
ejpam-4776	32	25	of	of	ADP
ejpam-4776	32	26	x	x	PUNCT
ejpam-4776	32	27	such	such	ADJ
ejpam-4776	32	28	that	that	SCONJ
ejpam-4776	32	29	a	a	DET
ejpam-4776	32	30	⊆	⊆	NUM
ejpam-4776	32	31	u	u	NOUN
ejpam-4776	32	32	and	and	CCONJ
ejpam-4776	32	33	b	b	NOUN
ejpam-4776	32	34	⊆	⊆	NUM
ejpam-4776	32	35	v	v	NOUN
ejpam-4776	32	36	[	[	X
ejpam-4776	32	37	9	9	NUM
ejpam-4776	32	38	,	,	PUNCT
ejpam-4776	32	39	10	10	NUM
ejpam-4776	32	40	,	,	PUNCT
ejpam-4776	32	41	17	17	NUM
ejpam-4776	32	42	]	]	PUNCT
ejpam-4776	32	43	.	.	PUNCT
ejpam-4776	33	1	if	if	SCONJ
ejpam-4776	33	2	t	t	PROPN
ejpam-4776	33	3	and	and	CCONJ
ejpam-4776	33	4	t	t	PROPN
ejpam-4776	33	5	′	′	NOUN
ejpam-4776	33	6	are	be	AUX
ejpam-4776	33	7	two	two	NUM
ejpam-4776	33	8	topologies	topology	NOUN
ejpam-4776	33	9	on	on	ADP
ejpam-4776	33	10	x	x	SYM
ejpam-4776	33	11	such	such	ADJ
ejpam-4776	33	12	that	that	SCONJ
ejpam-4776	33	13	t	t	PROPN
ejpam-4776	33	14	′	′	NUM
ejpam-4776	33	15	⊆	⊆	NUM
ejpam-4776	33	16	t	t	NOUN
ejpam-4776	33	17	,	,	PUNCT
ejpam-4776	33	18	then	then	ADV
ejpam-4776	33	19	t	t	PROPN
ejpam-4776	33	20	′	′	NUM
ejpam-4776	33	21	is	be	AUX
ejpam-4776	33	22	called	call	VERB
ejpam-4776	33	23	a	a	DET
ejpam-4776	33	24	topology	topology	NOUN
ejpam-4776	33	25	coarser	coarse	ADJ
ejpam-4776	33	26	than	than	ADP
ejpam-4776	33	27	t	t	PROPN
ejpam-4776	33	28	,	,	PUNCT
ejpam-4776	33	29	and	and	CCONJ
ejpam-4776	33	30	t	t	PROPN
ejpam-4776	33	31	is	be	AUX
ejpam-4776	33	32	called	call	VERB
ejpam-4776	33	33	finer	fine	ADJ
ejpam-4776	33	34	[	[	X
ejpam-4776	33	35	10	10	NUM
ejpam-4776	33	36	]	]	PUNCT
ejpam-4776	33	37	.	.	PUNCT
ejpam-4776	34	1	a	a	DET
ejpam-4776	34	2	t4	t4	PROPN
ejpam-4776	34	3	-	-	PUNCT
ejpam-4776	34	4	space	space	NOUN
ejpam-4776	34	5	is	be	AUX
ejpam-4776	34	6	a	a	DET
ejpam-4776	34	7	t1	t1	NOUN
ejpam-4776	34	8	normal	normal	ADJ
ejpam-4776	34	9	space	space	NOUN
ejpam-4776	34	10	,	,	PUNCT
ejpam-4776	34	11	a	a	DET
ejpam-4776	34	12	t3	t3	NOUN
ejpam-4776	34	13	-	-	PUNCT
ejpam-4776	34	14	space	space	NOUN
ejpam-4776	34	15	is	be	AUX
ejpam-4776	34	16	a	a	DET
ejpam-4776	34	17	t1	t1	NOUN
ejpam-4776	34	18	regular	regular	ADJ
ejpam-4776	34	19	space	space	NOUN
ejpam-4776	34	20	and	and	CCONJ
ejpam-4776	34	21	a	a	DET
ejpam-4776	34	22	tychonoff	tychonoff	NOUN
ejpam-4776	34	23	space	space	NOUN
ejpam-4776	34	24	is	be	AUX
ejpam-4776	34	25	a	a	DET
ejpam-4776	34	26	t1	t1	NOUN
ejpam-4776	34	27	completely	completely	ADV
ejpam-4776	34	28	regular	regular	ADJ
ejpam-4776	34	29	space	space	NOUN
ejpam-4776	34	30	.	.	PUNCT
ejpam-4776	35	1	a	a	DET
ejpam-4776	35	2	space	space	NOUN
ejpam-4776	35	3	x	x	PUNCT
ejpam-4776	35	4	is	be	AUX
ejpam-4776	35	5	said	say	VERB
ejpam-4776	35	6	to	to	PART
ejpam-4776	35	7	be	be	AUX
ejpam-4776	35	8	hausdorff	hausdorff	NOUN
ejpam-4776	35	9	or	or	CCONJ
ejpam-4776	35	10	a	a	DET
ejpam-4776	35	11	t2	t2	NOUN
ejpam-4776	35	12	-	-	PUNCT
ejpam-4776	35	13	space	space	NOUN
ejpam-4776	35	14	,	,	PUNCT
ejpam-4776	35	15	if	if	SCONJ
ejpam-4776	35	16	for	for	ADP
ejpam-4776	35	17	each	each	PRON
ejpam-4776	35	18	distinct	distinct	ADJ
ejpam-4776	35	19	two	two	NUM
ejpam-4776	35	20	points	point	NOUN
ejpam-4776	35	21	x	x	X
ejpam-4776	35	22	,	,	PUNCT
ejpam-4776	35	23	y	y	PROPN
ejpam-4776	35	24	∈	∈	PROPN
ejpam-4776	35	25	x	x	PUNCT
ejpam-4776	35	26	there	there	PRON
ejpam-4776	35	27	exist	exist	VERB
ejpam-4776	35	28	two	two	NUM
ejpam-4776	35	29	open	open	ADJ
ejpam-4776	35	30	subsets	subset	NOUN
ejpam-4776	35	31	u	u	NOUN
ejpam-4776	35	32	and	and	CCONJ
ejpam-4776	35	33	v	v	NOUN
ejpam-4776	35	34	of	of	ADP
ejpam-4776	35	35	x	x	PUNCT
ejpam-4776	35	36	such	such	ADJ
ejpam-4776	35	37	that	that	SCONJ
ejpam-4776	35	38	x	x	SYM
ejpam-4776	35	39	∈	∈	PROPN
ejpam-4776	35	40	u	u	NOUN
ejpam-4776	35	41	,	,	PUNCT
ejpam-4776	35	42	y	y	PROPN
ejpam-4776	35	43	∈	∈	PROPN
ejpam-4776	35	44	v	v	NOUN
ejpam-4776	35	45	and	and	CCONJ
ejpam-4776	35	46	u	u	NOUN
ejpam-4776	35	47	∩	∩	NOUN
ejpam-4776	35	48	v	v	NOUN
ejpam-4776	35	49	=	=	NOUN
ejpam-4776	35	50	∅	∅	NOUN
ejpam-4776	35	51	[	[	X
ejpam-4776	35	52	10	10	NUM
ejpam-4776	35	53	]	]	PUNCT
ejpam-4776	35	54	.	.	PUNCT
ejpam-4776	36	1	a	a	DET
ejpam-4776	36	2	space	space	NOUN
ejpam-4776	36	3	x	x	PUNCT
ejpam-4776	36	4	is	be	AUX
ejpam-4776	36	5	said	say	VERB
ejpam-4776	36	6	to	to	PART
ejpam-4776	36	7	be	be	AUX
ejpam-4776	36	8	completely	completely	ADV
ejpam-4776	36	9	hausdorff	hausdorff	ADJ
ejpam-4776	36	10	or	or	CCONJ
ejpam-4776	36	11	urysohn	urysohn	NOUN
ejpam-4776	36	12	[	[	X
ejpam-4776	36	13	10	10	NUM
ejpam-4776	36	14	,	,	PUNCT
ejpam-4776	36	15	23	23	NUM
ejpam-4776	36	16	]	]	PUNCT
ejpam-4776	36	17	,	,	PUNCT
ejpam-4776	36	18	if	if	SCONJ
ejpam-4776	36	19	for	for	ADP
ejpam-4776	36	20	each	each	DET
ejpam-4776	36	21	distinct	distinct	ADJ
ejpam-4776	36	22	two	two	NUM
ejpam-4776	36	23	points	point	NOUN
ejpam-4776	36	24	x	x	X
ejpam-4776	36	25	,	,	PUNCT
ejpam-4776	36	26	y	y	PROPN
ejpam-4776	36	27	∈	∈	PROPN
ejpam-4776	36	28	x	x	PUNCT
ejpam-4776	36	29	there	there	PRON
ejpam-4776	36	30	exist	exist	VERB
ejpam-4776	36	31	two	two	NUM
ejpam-4776	36	32	open	open	ADJ
ejpam-4776	36	33	subsets	subset	NOUN
ejpam-4776	36	34	u	u	NOUN
ejpam-4776	36	35	and	and	CCONJ
ejpam-4776	36	36	v	v	NOUN
ejpam-4776	36	37	of	of	ADP
ejpam-4776	36	38	x	x	PUNCT
ejpam-4776	36	39	such	such	ADJ
ejpam-4776	36	40	that	that	SCONJ
ejpam-4776	36	41	x	x	SYM
ejpam-4776	36	42	∈	∈	PROPN
ejpam-4776	36	43	u	u	NOUN
ejpam-4776	36	44	,	,	PUNCT
ejpam-4776	36	45	y	y	PROPN
ejpam-4776	36	46	∈	∈	PROPN
ejpam-4776	36	47	v	v	NOUN
ejpam-4776	36	48	and	and	CCONJ
ejpam-4776	36	49	u	u	NOUN
ejpam-4776	36	50	∩v	∩v	PROPN
ejpam-4776	36	51	=	=	PUNCT
ejpam-4776	36	52	∅.	∅.	VERB
ejpam-4776	36	53	a	a	DET
ejpam-4776	36	54	space	space	NOUN
ejpam-4776	36	55	x	x	PUNCT
ejpam-4776	36	56	is	be	AUX
ejpam-4776	36	57	said	say	VERB
ejpam-4776	36	58	to	to	PART
ejpam-4776	36	59	be	be	AUX
ejpam-4776	36	60	almost	almost	ADV
ejpam-4776	36	61	completely	completely	ADV
ejpam-4776	36	62	-	-	PUNCT
ejpam-4776	36	63	regular	regular	ADJ
ejpam-4776	36	64	if	if	SCONJ
ejpam-4776	36	65	for	for	SCONJ
ejpam-4776	36	66	each	each	DET
ejpam-4776	36	67	x	x	SYM
ejpam-4776	36	68	∈	∈	PROPN
ejpam-4776	36	69	x	x	X
ejpam-4776	36	70	and	and	CCONJ
ejpam-4776	36	71	each	each	DET
ejpam-4776	36	72	closed	closed	ADJ
ejpam-4776	36	73	domain	domain	NOUN
ejpam-4776	36	74	subset	subset	NOUN
ejpam-4776	36	75	f	f	PROPN
ejpam-4776	36	76	of	of	ADP
ejpam-4776	36	77	x	x	INTJ
ejpam-4776	36	78	such	such	ADJ
ejpam-4776	36	79	that	that	SCONJ
ejpam-4776	36	80	x	x	SYM
ejpam-4776	36	81	̸∈	̸∈	PROPN
ejpam-4776	36	82	f	f	PROPN
ejpam-4776	36	83	,	,	PUNCT
ejpam-4776	36	84	there	there	PRON
ejpam-4776	36	85	exists	exist	VERB
ejpam-4776	36	86	a	a	DET
ejpam-4776	36	87	continuous	continuous	ADJ
ejpam-4776	36	88	function	function	NOUN
ejpam-4776	36	89	f	f	NOUN
ejpam-4776	36	90	:	:	PUNCT
ejpam-4776	36	91	x	x	X
ejpam-4776	36	92	→	→	PUNCT
ejpam-4776	37	1	[	[	X
ejpam-4776	37	2	0	0	NUM
ejpam-4776	37	3	,	,	PUNCT
ejpam-4776	37	4	1	1	NUM
ejpam-4776	37	5	]	]	PUNCT
ejpam-4776	37	6	such	such	ADJ
ejpam-4776	37	7	that	that	SCONJ
ejpam-4776	37	8	f(x	f(x	NOUN
ejpam-4776	37	9	)	)	PUNCT
ejpam-4776	37	10	=	=	SYM
ejpam-4776	37	11	0	0	NUM
ejpam-4776	37	12	and	and	CCONJ
ejpam-4776	37	13	f(f	f(f	PROPN
ejpam-4776	37	14	)	)	PUNCT
ejpam-4776	38	1	=	=	PUNCT
ejpam-4776	38	2	{	{	PUNCT
ejpam-4776	38	3	1	1	NUM
ejpam-4776	38	4	}	}	PUNCT
ejpam-4776	38	5	[	[	X
ejpam-4776	38	6	21	21	NUM
ejpam-4776	38	7	]	]	PUNCT
ejpam-4776	38	8	.	.	PUNCT
ejpam-4776	39	1	a	a	DET
ejpam-4776	39	2	space	space	NOUN
ejpam-4776	39	3	x	x	PUNCT
ejpam-4776	39	4	is	be	AUX
ejpam-4776	39	5	said	say	VERB
ejpam-4776	39	6	to	to	PART
ejpam-4776	39	7	be	be	AUX
ejpam-4776	39	8	almost	almost	ADV
ejpam-4776	39	9	-	-	PUNCT
ejpam-4776	39	10	regular	regular	ADJ
ejpam-4776	39	11	if	if	SCONJ
ejpam-4776	39	12	for	for	SCONJ
ejpam-4776	39	13	each	each	DET
ejpam-4776	39	14	x	x	SYM
ejpam-4776	39	15	∈	∈	PROPN
ejpam-4776	39	16	x	x	X
ejpam-4776	39	17	and	and	CCONJ
ejpam-4776	39	18	each	each	DET
ejpam-4776	39	19	closed	closed	ADJ
ejpam-4776	39	20	domain	domain	NOUN
ejpam-4776	39	21	subset	subset	NOUN
ejpam-4776	39	22	f	f	PROPN
ejpam-4776	39	23	of	of	ADP
ejpam-4776	39	24	x	x	INTJ
ejpam-4776	39	25	such	such	ADJ
ejpam-4776	39	26	that	that	SCONJ
ejpam-4776	39	27	x	x	SYM
ejpam-4776	39	28	̸∈	̸∈	PROPN
ejpam-4776	39	29	f	f	PROPN
ejpam-4776	39	30	,	,	PUNCT
ejpam-4776	39	31	there	there	PRON
ejpam-4776	39	32	exist	exist	VERB
ejpam-4776	39	33	two	two	NUM
ejpam-4776	39	34	disjoint	disjoint	ADJ
ejpam-4776	39	35	open	open	ADJ
ejpam-4776	39	36	subsets	subset	NOUN
ejpam-4776	39	37	u	u	NOUN
ejpam-4776	39	38	and	and	CCONJ
ejpam-4776	39	39	v	v	ADP
ejpam-4776	39	40	such	such	ADJ
ejpam-4776	39	41	that	that	SCONJ
ejpam-4776	39	42	x	x	SYM
ejpam-4776	39	43	∈	∈	PROPN
ejpam-4776	39	44	u	u	NOUN
ejpam-4776	39	45	and	and	CCONJ
ejpam-4776	39	46	f	f	PROPN
ejpam-4776	40	1	⊆	⊆	NUM
ejpam-4776	40	2	v	v	ADP
ejpam-4776	40	3	[	[	X
ejpam-4776	40	4	20	20	NUM
ejpam-4776	40	5	]	]	PUNCT
ejpam-4776	40	6	.	.	PUNCT
ejpam-4776	41	1	a	a	DET
ejpam-4776	41	2	space	space	NOUN
ejpam-4776	41	3	x	x	PUNCT
ejpam-4776	41	4	is	be	AUX
ejpam-4776	41	5	said	say	VERB
ejpam-4776	41	6	to	to	PART
ejpam-4776	41	7	be	be	AUX
ejpam-4776	41	8	sub	sub	ADJ
ejpam-4776	41	9	-	-	ADJ
ejpam-4776	41	10	metrizable	metrizable	ADJ
ejpam-4776	41	11	[	[	X
ejpam-4776	41	12	11	11	NUM
ejpam-4776	41	13	]	]	PUNCT
ejpam-4776	41	14	,	,	PUNCT
ejpam-4776	41	15	if	if	SCONJ
ejpam-4776	41	16	there	there	PRON
ejpam-4776	41	17	exists	exist	VERB
ejpam-4776	41	18	a	a	DET
ejpam-4776	41	19	metric	metric	ADJ
ejpam-4776	41	20	d	d	NOUN
ejpam-4776	41	21	on	on	ADP
ejpam-4776	41	22	x	x	SYM
ejpam-4776	41	23	such	such	ADJ
ejpam-4776	41	24	that	that	SCONJ
ejpam-4776	41	25	the	the	DET
ejpam-4776	41	26	topology	topology	NOUN
ejpam-4776	41	27	td	td	NOUN
ejpam-4776	41	28	on	on	ADP
ejpam-4776	41	29	x	x	PUNCT
ejpam-4776	41	30	generated	generate	VERB
ejpam-4776	41	31	by	by	ADP
ejpam-4776	41	32	d	d	PROPN
ejpam-4776	41	33	is	be	AUX
ejpam-4776	41	34	coarser	coarse	ADJ
ejpam-4776	41	35	than	than	ADP
ejpam-4776	41	36	t	t	PROPN
ejpam-4776	41	37	.	.	PUNCT
ejpam-4776	42	1	the	the	DET
ejpam-4776	42	2	topology	topology	NOUN
ejpam-4776	42	3	on	on	ADP
ejpam-4776	42	4	x	x	PUNCT
ejpam-4776	42	5	generated	generate	VERB
ejpam-4776	42	6	by	by	ADP
ejpam-4776	42	7	the	the	DET
ejpam-4776	42	8	family	family	NOUN
ejpam-4776	42	9	of	of	ADP
ejpam-4776	42	10	all	all	DET
ejpam-4776	42	11	open	open	ADJ
ejpam-4776	42	12	domain	domain	NOUN
ejpam-4776	42	13	subsets	subset	NOUN
ejpam-4776	42	14	of	of	ADP
ejpam-4776	42	15	x	x	PRON
ejpam-4776	42	16	,	,	PUNCT
ejpam-4776	42	17	denoted	denote	VERB
ejpam-4776	42	18	by	by	ADP
ejpam-4776	42	19	ts	ts	PROPN
ejpam-4776	42	20	,	,	PUNCT
ejpam-4776	42	21	is	be	AUX
ejpam-4776	42	22	coarser	coarse	ADJ
ejpam-4776	42	23	than	than	ADP
ejpam-4776	42	24	t	t	PROPN
ejpam-4776	42	25	,	,	PUNCT
ejpam-4776	42	26	and	and	CCONJ
ejpam-4776	42	27	(	(	PUNCT
ejpam-4776	42	28	x	x	NOUN
ejpam-4776	42	29	,	,	PUNCT
ejpam-4776	42	30	ts	ts	NOUN
ejpam-4776	42	31	)	)	PUNCT
ejpam-4776	42	32	is	be	AUX
ejpam-4776	42	33	called	call	VERB
ejpam-4776	42	34	the	the	DET
ejpam-4776	42	35	semi	semi	NOUN
ejpam-4776	42	36	-	-	NOUN
ejpam-4776	42	37	regularization	regularization	NOUN
ejpam-4776	42	38	of	of	ADP
ejpam-4776	42	39	x	x	X
ejpam-4776	42	40	and	and	CCONJ
ejpam-4776	42	41	the	the	DET
ejpam-4776	42	42	space	space	NOUN
ejpam-4776	42	43	(	(	PUNCT
ejpam-4776	42	44	x	x	X
ejpam-4776	42	45	,	,	PUNCT
ejpam-4776	42	46	t	t	PROPN
ejpam-4776	42	47	)	)	PUNCT
ejpam-4776	42	48	is	be	AUX
ejpam-4776	42	49	called	call	VERB
ejpam-4776	42	50	semi	semi	ADJ
ejpam-4776	42	51	-	-	ADJ
ejpam-4776	42	52	regular	regular	ADJ
ejpam-4776	42	53	if	if	SCONJ
ejpam-4776	42	54	t	t	NOUN
ejpam-4776	42	55	=	=	SYM
ejpam-4776	42	56	ts	ts	X
ejpam-4776	43	1	[	[	X
ejpam-4776	43	2	16	16	NUM
ejpam-4776	43	3	]	]	PUNCT
ejpam-4776	43	4	.	.	PUNCT
ejpam-4776	44	1	a	a	DET
ejpam-4776	44	2	space	space	NOUN
ejpam-4776	44	3	x	x	PUNCT
ejpam-4776	44	4	is	be	AUX
ejpam-4776	44	5	called	call	VERB
ejpam-4776	44	6	cc	cc	NOUN
ejpam-4776	44	7	-	-	NOUN
ejpam-4776	44	8	normal	normal	ADJ
ejpam-4776	44	9	[	[	X
ejpam-4776	44	10	14	14	NUM
ejpam-4776	44	11	]	]	X
ejpam-4776	44	12	if	if	SCONJ
ejpam-4776	44	13	there	there	PRON
ejpam-4776	44	14	exist	exist	VERB
ejpam-4776	44	15	a	a	DET
ejpam-4776	44	16	normal	normal	ADJ
ejpam-4776	44	17	space	space	NOUN
ejpam-4776	44	18	y	y	PROPN
ejpam-4776	44	19	and	and	CCONJ
ejpam-4776	44	20	a	a	DET
ejpam-4776	44	21	bijective	bijective	ADJ
ejpam-4776	44	22	function	function	NOUN
ejpam-4776	45	1	f	f	NOUN
ejpam-4776	45	2	:	:	PUNCT
ejpam-4776	45	3	x	x	X
ejpam-4776	45	4	→	→	SYM
ejpam-4776	45	5	y	y	PROPN
ejpam-4776	45	6	such	such	ADJ
ejpam-4776	45	7	that	that	SCONJ
ejpam-4776	45	8	the	the	DET
ejpam-4776	45	9	restriction	restriction	NOUN
ejpam-4776	45	10	function	function	NOUN
ejpam-4776	45	11	f	f	PROPN
ejpam-4776	45	12	|a	|a	VERB
ejpam-4776	45	13	:	:	PUNCT
ejpam-4776	45	14	a	a	DET
ejpam-4776	45	15	→	→	SYM
ejpam-4776	45	16	f(a	f(a	NOUN
ejpam-4776	45	17	)	)	PUNCT
ejpam-4776	45	18	is	be	AUX
ejpam-4776	45	19	a	a	DET
ejpam-4776	45	20	homeomorphism	homeomorphism	NOUN
ejpam-4776	45	21	for	for	ADP
ejpam-4776	45	22	each	each	DET
ejpam-4776	45	23	countably	countably	ADV
ejpam-4776	45	24	compact	compact	ADJ
ejpam-4776	45	25	subspace	subspace	NOUN
ejpam-4776	45	26	a	a	DET
ejpam-4776	45	27	⊆	⊆	NUM
ejpam-4776	45	28	x.	x.	NOUN
ejpam-4776	45	29	the	the	DET
ejpam-4776	45	30	basic	basic	ADJ
ejpam-4776	45	31	definitions	definition	NOUN
ejpam-4776	45	32	and	and	CCONJ
ejpam-4776	45	33	any	any	DET
ejpam-4776	45	34	undefined	undefined	ADJ
ejpam-4776	45	35	terms	term	NOUN
ejpam-4776	45	36	in	in	ADP
ejpam-4776	45	37	this	this	DET
ejpam-4776	45	38	article	article	NOUN
ejpam-4776	45	39	can	can	AUX
ejpam-4776	45	40	be	be	AUX
ejpam-4776	45	41	found	find	VERB
ejpam-4776	45	42	in	in	ADP
ejpam-4776	45	43	[	[	X
ejpam-4776	45	44	25	25	NUM
ejpam-4776	45	45	]	]	PUNCT
ejpam-4776	45	46	and	and	CCONJ
ejpam-4776	45	47	[	[	X
ejpam-4776	45	48	26	26	NUM
ejpam-4776	45	49	]	]	PUNCT
ejpam-4776	45	50	.	.	PUNCT
ejpam-4776	46	1	2	2	X
ejpam-4776	46	2	.	.	X
ejpam-4776	46	3	preliminaries	preliminary	NOUN
ejpam-4776	46	4	first	first	ADV
ejpam-4776	46	5	,	,	PUNCT
ejpam-4776	46	6	we	we	PRON
ejpam-4776	46	7	present	present	VERB
ejpam-4776	46	8	the	the	DET
ejpam-4776	46	9	main	main	ADJ
ejpam-4776	46	10	definitions	definition	NOUN
ejpam-4776	46	11	of	of	ADP
ejpam-4776	46	12	this	this	DET
ejpam-4776	46	13	work	work	NOUN
ejpam-4776	46	14	.	.	PUNCT
ejpam-4776	47	1	definition	definition	NOUN
ejpam-4776	47	2	1	1	NUM
ejpam-4776	47	3	.	.	PUNCT
ejpam-4776	48	1	let	let	VERB
ejpam-4776	48	2	x	x	PRON
ejpam-4776	48	3	be	be	AUX
ejpam-4776	48	4	a	a	DET
ejpam-4776	48	5	space	space	NOUN
ejpam-4776	48	6	,	,	PUNCT
ejpam-4776	48	7	then	then	ADV
ejpam-4776	48	8	:	:	PUNCT
ejpam-4776	48	9	(	(	PUNCT
ejpam-4776	48	10	1	1	X
ejpam-4776	48	11	)	)	PUNCT
ejpam-4776	48	12	a	a	DET
ejpam-4776	48	13	space	space	NOUN
ejpam-4776	48	14	x	x	PUNCT
ejpam-4776	48	15	is	be	AUX
ejpam-4776	48	16	called	call	VERB
ejpam-4776	48	17	a	a	DET
ejpam-4776	48	18	cc	cc	NOUN
ejpam-4776	48	19	-	-	NOUN
ejpam-4776	48	20	regular	regular	ADJ
ejpam-4776	48	21	(	(	PUNCT
ejpam-4776	48	22	resp	resp	NOUN
ejpam-4776	48	23	.	.	PUNCT
ejpam-4776	49	1	cc	cc	NOUN
ejpam-4776	49	2	-	-	PUNCT
ejpam-4776	49	3	almost	almost	ADV
ejpam-4776	49	4	regular	regular	ADJ
ejpam-4776	49	5	)	)	PUNCT
ejpam-4776	49	6	space	space	NOUN
ejpam-4776	49	7	if	if	SCONJ
ejpam-4776	49	8	there	there	PRON
ejpam-4776	49	9	exist	exist	VERB
ejpam-4776	49	10	a	a	DET
ejpam-4776	49	11	regular	regular	ADJ
ejpam-4776	49	12	(	(	PUNCT
ejpam-4776	49	13	resp	resp	NOUN
ejpam-4776	49	14	.	.	PUNCT
ejpam-4776	50	1	almost	almost	ADV
ejpam-4776	50	2	regular	regular	ADJ
ejpam-4776	50	3	)	)	PUNCT
ejpam-4776	50	4	space	space	NOUN
ejpam-4776	50	5	y	y	PROPN
ejpam-4776	50	6	and	and	CCONJ
ejpam-4776	50	7	a	a	DET
ejpam-4776	50	8	bijective	bijective	ADJ
ejpam-4776	50	9	function	function	NOUN
ejpam-4776	50	10	f	f	NOUN
ejpam-4776	50	11	:	:	PUNCT
ejpam-4776	50	12	x	x	X
ejpam-4776	50	13	→	→	SYM
ejpam-4776	50	14	y	y	PROPN
ejpam-4776	50	15	such	such	ADJ
ejpam-4776	50	16	that	that	SCONJ
ejpam-4776	50	17	the	the	DET
ejpam-4776	50	18	restriction	restriction	NOUN
ejpam-4776	50	19	function	function	NOUN
ejpam-4776	50	20	f	f	PROPN
ejpam-4776	50	21	|a	|a	VERB
ejpam-4776	50	22	:	:	PUNCT
ejpam-4776	50	23	a	a	DET
ejpam-4776	50	24	→	→	SYM
ejpam-4776	50	25	f(a	f(a	NOUN
ejpam-4776	50	26	)	)	PUNCT
ejpam-4776	50	27	is	be	AUX
ejpam-4776	50	28	a	a	DET
ejpam-4776	50	29	homeomorphism	homeomorphism	NOUN
ejpam-4776	50	30	for	for	ADP
ejpam-4776	50	31	each	each	DET
ejpam-4776	50	32	countably	countably	ADV
ejpam-4776	50	33	compact	compact	ADJ
ejpam-4776	50	34	subspace	subspace	NOUN
ejpam-4776	50	35	a	a	DET
ejpam-4776	50	36	⊆	⊆	NUM
ejpam-4776	50	37	x.	x.	NOUN
ejpam-4776	50	38	(	(	PUNCT
ejpam-4776	50	39	2	2	NUM
ejpam-4776	50	40	)	)	PUNCT
ejpam-4776	50	41	a	a	DET
ejpam-4776	50	42	space	space	NOUN
ejpam-4776	50	43	x	x	PUNCT
ejpam-4776	50	44	is	be	AUX
ejpam-4776	50	45	called	call	VERB
ejpam-4776	50	46	a	a	DET
ejpam-4776	50	47	cc	cc	NOUN
ejpam-4776	50	48	-	-	ADJ
ejpam-4776	50	49	completely	completely	ADV
ejpam-4776	50	50	regular	regular	ADJ
ejpam-4776	50	51	(	(	PUNCT
ejpam-4776	50	52	resp	resp	NOUN
ejpam-4776	50	53	.	.	PUNCT
ejpam-4776	51	1	cc	cc	VERB
ejpam-4776	51	2	-	-	PUNCT
ejpam-4776	51	3	almost	almost	ADV
ejpam-4776	51	4	completely	completely	ADV
ejpam-4776	51	5	regular	regular	ADJ
ejpam-4776	51	6	)	)	PUNCT
ejpam-4776	51	7	space	space	NOUN
ejpam-4776	51	8	if	if	SCONJ
ejpam-4776	51	9	there	there	PRON
ejpam-4776	51	10	exist	exist	VERB
ejpam-4776	51	11	a	a	DET
ejpam-4776	51	12	completely	completely	ADV
ejpam-4776	51	13	regular	regular	ADJ
ejpam-4776	51	14	(	(	PUNCT
ejpam-4776	51	15	resp	resp	NOUN
ejpam-4776	51	16	.	.	PUNCT
ejpam-4776	52	1	almost	almost	ADV
ejpam-4776	52	2	completely	completely	ADV
ejpam-4776	52	3	regular	regular	ADJ
ejpam-4776	52	4	)	)	PUNCT
ejpam-4776	52	5	space	space	NOUN
ejpam-4776	52	6	y	y	PROPN
ejpam-4776	52	7	s.	s.	PROPN
ejpam-4776	52	8	a.	a.	PROPN
ejpam-4776	52	9	thabit	thabit	PROPN
ejpam-4776	52	10	,	,	PUNCT
ejpam-4776	52	11	w.	w.	PROPN
ejpam-4776	52	12	alqurashi	alqurashi	PROPN
ejpam-4776	52	13	/	/	SYM
ejpam-4776	52	14	eur	eur	PROPN
ejpam-4776	52	15	.	.	PUNCT
ejpam-4776	53	1	j.	j.	PROPN
ejpam-4776	53	2	pure	pure	PROPN
ejpam-4776	53	3	appl	appl	PROPN
ejpam-4776	53	4	.	.	PROPN
ejpam-4776	53	5	math	math	PROPN
ejpam-4776	53	6	,	,	PUNCT
ejpam-4776	53	7	16	16	NUM
ejpam-4776	53	8	(	(	PUNCT
ejpam-4776	53	9	2	2	NUM
ejpam-4776	53	10	)	)	PUNCT
ejpam-4776	53	11	(	(	PUNCT
ejpam-4776	53	12	2023	2023	NUM
ejpam-4776	53	13	)	)	PUNCT
ejpam-4776	53	14	,	,	PUNCT
ejpam-4776	53	15	1260	1260	NUM
ejpam-4776	53	16	-	-	SYM
ejpam-4776	53	17	1273	1273	NUM
ejpam-4776	53	18	1262	1262	NUM
ejpam-4776	53	19	and	and	CCONJ
ejpam-4776	53	20	a	a	DET
ejpam-4776	53	21	bijective	bijective	ADJ
ejpam-4776	53	22	function	function	NOUN
ejpam-4776	54	1	f	f	NOUN
ejpam-4776	54	2	:	:	PUNCT
ejpam-4776	54	3	x	x	X
ejpam-4776	54	4	→	→	SYM
ejpam-4776	54	5	y	y	PROPN
ejpam-4776	54	6	such	such	ADJ
ejpam-4776	54	7	that	that	SCONJ
ejpam-4776	54	8	the	the	DET
ejpam-4776	54	9	restriction	restriction	NOUN
ejpam-4776	54	10	function	function	NOUN
ejpam-4776	54	11	f	f	PROPN
ejpam-4776	54	12	|a	|a	VERB
ejpam-4776	54	13	:	:	PUNCT
ejpam-4776	54	14	a	a	DET
ejpam-4776	54	15	→	→	SYM
ejpam-4776	54	16	f(a	f(a	NOUN
ejpam-4776	54	17	)	)	PUNCT
ejpam-4776	54	18	is	be	AUX
ejpam-4776	54	19	a	a	DET
ejpam-4776	54	20	homeomorphism	homeomorphism	NOUN
ejpam-4776	54	21	for	for	ADP
ejpam-4776	54	22	each	each	DET
ejpam-4776	54	23	countably	countably	ADV
ejpam-4776	54	24	compact	compact	ADJ
ejpam-4776	54	25	subspace	subspace	NOUN
ejpam-4776	54	26	a	a	DET
ejpam-4776	54	27	⊆	⊆	NUM
ejpam-4776	54	28	x.	x.	NOUN
ejpam-4776	54	29	(	(	PUNCT
ejpam-4776	54	30	3	3	NUM
ejpam-4776	54	31	)	)	PUNCT
ejpam-4776	54	32	a	a	DET
ejpam-4776	54	33	space	space	NOUN
ejpam-4776	54	34	x	x	PUNCT
ejpam-4776	54	35	is	be	AUX
ejpam-4776	54	36	called	call	VERB
ejpam-4776	54	37	a	a	DET
ejpam-4776	54	38	cc	cc	NOUN
ejpam-4776	54	39	-	-	NOUN
ejpam-4776	54	40	tychonoff	tychonoff	NOUN
ejpam-4776	54	41	(	(	PUNCT
ejpam-4776	54	42	resp	resp	NOUN
ejpam-4776	54	43	.	.	PUNCT
ejpam-4776	55	1	cct3	cct3	PROPN
ejpam-4776	55	2	)	)	PUNCT
ejpam-4776	55	3	space	space	NOUN
ejpam-4776	55	4	if	if	SCONJ
ejpam-4776	55	5	there	there	PRON
ejpam-4776	55	6	exist	exist	VERB
ejpam-4776	55	7	a	a	DET
ejpam-4776	55	8	tychonoff	tychonoff	NOUN
ejpam-4776	55	9	(	(	PUNCT
ejpam-4776	55	10	resp	resp	NOUN
ejpam-4776	55	11	.	.	PUNCT
ejpam-4776	56	1	t3	t3	NOUN
ejpam-4776	56	2	)	)	PUNCT
ejpam-4776	56	3	space	space	NOUN
ejpam-4776	56	4	y	y	PROPN
ejpam-4776	56	5	and	and	CCONJ
ejpam-4776	56	6	a	a	DET
ejpam-4776	56	7	bijective	bijective	ADJ
ejpam-4776	56	8	function	function	NOUN
ejpam-4776	56	9	f	f	NOUN
ejpam-4776	57	1	:	:	PUNCT
ejpam-4776	57	2	x	x	X
ejpam-4776	57	3	→	→	SYM
ejpam-4776	57	4	y	y	PROPN
ejpam-4776	57	5	such	such	ADJ
ejpam-4776	57	6	that	that	SCONJ
ejpam-4776	57	7	the	the	DET
ejpam-4776	57	8	restriction	restriction	NOUN
ejpam-4776	57	9	function	function	NOUN
ejpam-4776	57	10	f	f	PROPN
ejpam-4776	57	11	|a	|a	VERB
ejpam-4776	57	12	:	:	PUNCT
ejpam-4776	57	13	a	a	DET
ejpam-4776	57	14	→	→	SYM
ejpam-4776	57	15	f(a	f(a	NOUN
ejpam-4776	57	16	)	)	PUNCT
ejpam-4776	57	17	is	be	AUX
ejpam-4776	57	18	a	a	DET
ejpam-4776	57	19	homeomorphism	homeomorphism	NOUN
ejpam-4776	57	20	for	for	ADP
ejpam-4776	57	21	each	each	DET
ejpam-4776	57	22	countably	countably	ADV
ejpam-4776	57	23	compact	compact	ADJ
ejpam-4776	57	24	subspace	subspace	NOUN
ejpam-4776	57	25	a	a	DET
ejpam-4776	57	26	⊆	⊆	NUM
ejpam-4776	57	27	x.	x.	NOUN
ejpam-4776	57	28	from	from	ADP
ejpam-4776	57	29	definition	definition	NOUN
ejpam-4776	57	30	1	1	NUM
ejpam-4776	57	31	,	,	PUNCT
ejpam-4776	57	32	clearly	clearly	ADV
ejpam-4776	57	33	that	that	SCONJ
ejpam-4776	57	34	:	:	PUNCT
ejpam-4776	57	35	every	every	DET
ejpam-4776	57	36	completely	completely	ADV
ejpam-4776	57	37	regular	regular	ADJ
ejpam-4776	57	38	(	(	PUNCT
ejpam-4776	57	39	resp	resp	NOUN
ejpam-4776	57	40	.	.	PUNCT
ejpam-4776	58	1	regular	regular	ADJ
ejpam-4776	58	2	,	,	PUNCT
ejpam-4776	58	3	almost	almost	ADV
ejpam-4776	58	4	completely	completely	ADV
ejpam-4776	58	5	regular	regular	ADJ
ejpam-4776	58	6	,	,	PUNCT
ejpam-4776	58	7	almost	almost	ADV
ejpam-4776	58	8	regular	regular	ADJ
ejpam-4776	58	9	,	,	PUNCT
ejpam-4776	58	10	t3	t3	NOUN
ejpam-4776	58	11	,	,	PUNCT
ejpam-4776	58	12	tychonoff	tychonoff	NOUN
ejpam-4776	58	13	)	)	PUNCT
ejpam-4776	58	14	space	space	NOUN
ejpam-4776	58	15	is	be	AUX
ejpam-4776	58	16	cc	cc	VERB
ejpam-4776	58	17	-	-	ADJ
ejpam-4776	58	18	completely	completely	ADV
ejpam-4776	58	19	regular	regular	ADJ
ejpam-4776	58	20	(	(	PUNCT
ejpam-4776	58	21	resp	resp	NOUN
ejpam-4776	58	22	.	.	PUNCT
ejpam-4776	59	1	cc	cc	NOUN
ejpam-4776	59	2	-	-	ADJ
ejpam-4776	59	3	regular	regular	ADJ
ejpam-4776	59	4	,	,	PUNCT
ejpam-4776	59	5	cc	cc	NOUN
ejpam-4776	59	6	-	-	ADJ
ejpam-4776	59	7	almost	almost	ADV
ejpam-4776	59	8	completely	completely	ADV
ejpam-4776	59	9	regular	regular	ADJ
ejpam-4776	59	10	,	,	PUNCT
ejpam-4776	59	11	cc	cc	NOUN
ejpam-4776	59	12	-	-	ADJ
ejpam-4776	59	13	almost	almost	ADV
ejpam-4776	59	14	regular	regular	ADJ
ejpam-4776	59	15	,	,	PUNCT
ejpam-4776	59	16	cct3	cct3	PROPN
ejpam-4776	59	17	,	,	PUNCT
ejpam-4776	59	18	cc	cc	NOUN
ejpam-4776	59	19	-	-	NOUN
ejpam-4776	59	20	tychonoff	tychonoff	NOUN
ejpam-4776	59	21	)	)	PUNCT
ejpam-4776	59	22	,	,	PUNCT
ejpam-4776	59	23	just	just	ADV
ejpam-4776	59	24	by	by	ADP
ejpam-4776	59	25	taking	take	VERB
ejpam-4776	59	26	x	x	PUNCT
ejpam-4776	59	27	=	=	PUNCT
ejpam-4776	59	28	y	y	PROPN
ejpam-4776	59	29	and	and	CCONJ
ejpam-4776	59	30	the	the	DET
ejpam-4776	59	31	identity	identity	NOUN
ejpam-4776	59	32	function	function	NOUN
ejpam-4776	59	33	,	,	PUNCT
ejpam-4776	59	34	but	but	CCONJ
ejpam-4776	59	35	the	the	DET
ejpam-4776	59	36	converses	converse	NOUN
ejpam-4776	59	37	need	need	AUX
ejpam-4776	59	38	not	not	PART
ejpam-4776	59	39	be	be	AUX
ejpam-4776	59	40	true	true	ADJ
ejpam-4776	59	41	.	.	PUNCT
ejpam-4776	60	1	the	the	DET
ejpam-4776	60	2	next	next	ADJ
ejpam-4776	60	3	example	example	NOUN
ejpam-4776	60	4	is	be	AUX
ejpam-4776	60	5	of	of	ADP
ejpam-4776	60	6	a	a	DET
ejpam-4776	60	7	cc	cc	NOUN
ejpam-4776	60	8	-	-	NOUN
ejpam-4776	60	9	tychonoff	tychonoff	NOUN
ejpam-4776	60	10	,	,	PUNCT
ejpam-4776	60	11	cct3	cct3	PROPN
ejpam-4776	60	12	,	,	PUNCT
ejpam-4776	60	13	cc	cc	NOUN
ejpam-4776	60	14	-	-	ADJ
ejpam-4776	60	15	completely	completely	ADV
ejpam-4776	60	16	regular	regular	ADJ
ejpam-4776	60	17	and	and	CCONJ
ejpam-4776	60	18	cc	cc	NOUN
ejpam-4776	60	19	-	-	ADJ
ejpam-4776	60	20	regular	regular	ADJ
ejpam-4776	60	21	space	space	NOUN
ejpam-4776	60	22	which	which	PRON
ejpam-4776	60	23	is	be	AUX
ejpam-4776	60	24	neither	neither	DET
ejpam-4776	60	25	tychonoff	tychonoff	NOUN
ejpam-4776	60	26	,	,	PUNCT
ejpam-4776	60	27	t3	t3	NOUN
ejpam-4776	60	28	,	,	PUNCT
ejpam-4776	60	29	completely	completely	ADV
ejpam-4776	60	30	regular	regular	ADJ
ejpam-4776	60	31	nor	nor	CCONJ
ejpam-4776	60	32	regular	regular	ADJ
ejpam-4776	60	33	.	.	PUNCT
ejpam-4776	61	1	example	example	NOUN
ejpam-4776	62	1	1	1	NUM
ejpam-4776	62	2	.	.	PUNCT
ejpam-4776	63	1	the	the	DET
ejpam-4776	63	2	smirnov	smirnov	PROPN
ejpam-4776	63	3	’s	’s	PART
ejpam-4776	63	4	deleted	delete	VERB
ejpam-4776	63	5	sequence	sequence	NOUN
ejpam-4776	63	6	topology	topology	NOUN
ejpam-4776	63	7	:	:	PUNCT
ejpam-4776	63	8	[	[	X
ejpam-4776	63	9	23	23	NUM
ejpam-4776	63	10	,	,	PUNCT
ejpam-4776	63	11	example	example	NOUN
ejpam-4776	63	12	64	64	NUM
ejpam-4776	63	13	]	]	PUNCT
ejpam-4776	63	14	,	,	PUNCT
ejpam-4776	63	15	is	be	AUX
ejpam-4776	63	16	a	a	DET
ejpam-4776	63	17	urysohn	urysohn	NOUN
ejpam-4776	63	18	,	,	PUNCT
ejpam-4776	63	19	lindelöf	lindelöf	PROPN
ejpam-4776	63	20	first	first	ADV
ejpam-4776	63	21	countable	countable	ADJ
ejpam-4776	63	22	separable	separable	ADJ
ejpam-4776	63	23	space	space	NOUN
ejpam-4776	63	24	which	which	PRON
ejpam-4776	63	25	is	be	AUX
ejpam-4776	63	26	not	not	PART
ejpam-4776	63	27	paracompact	paracompact	ADJ
ejpam-4776	63	28	[	[	X
ejpam-4776	63	29	23	23	NUM
ejpam-4776	63	30	]	]	PUNCT
ejpam-4776	63	31	.	.	PUNCT
ejpam-4776	64	1	since	since	SCONJ
ejpam-4776	64	2	x	x	PRON
ejpam-4776	64	3	is	be	AUX
ejpam-4776	64	4	a	a	DET
ejpam-4776	64	5	sub	sub	ADJ
ejpam-4776	64	6	-	-	ADJ
ejpam-4776	64	7	metrizable	metrizable	ADJ
ejpam-4776	64	8	space	space	NOUN
ejpam-4776	64	9	,	,	PUNCT
ejpam-4776	64	10	by	by	ADP
ejpam-4776	64	11	corollary	corollary	ADJ
ejpam-4776	64	12	1	1	NUM
ejpam-4776	64	13	and	and	CCONJ
ejpam-4776	64	14	theorem	theorem	VERB
ejpam-4776	64	15	1	1	NUM
ejpam-4776	64	16	we	we	PRON
ejpam-4776	64	17	get	get	VERB
ejpam-4776	64	18	:	:	PUNCT
ejpam-4776	64	19	x	x	X
ejpam-4776	64	20	is	be	AUX
ejpam-4776	64	21	cc	cc	NOUN
ejpam-4776	64	22	-	-	NOUN
ejpam-4776	64	23	tychonoff	tychonoff	NOUN
ejpam-4776	64	24	,	,	PUNCT
ejpam-4776	64	25	cct3	cct3	PROPN
ejpam-4776	64	26	,	,	PUNCT
ejpam-4776	64	27	cc	cc	NOUN
ejpam-4776	64	28	-	-	ADJ
ejpam-4776	64	29	completely	completely	ADV
ejpam-4776	64	30	regular	regular	ADJ
ejpam-4776	64	31	,	,	PUNCT
ejpam-4776	64	32	cc	cc	NOUN
ejpam-4776	64	33	-	-	ADJ
ejpam-4776	64	34	regular	regular	ADJ
ejpam-4776	64	35	,	,	PUNCT
ejpam-4776	64	36	cc	cc	NOUN
ejpam-4776	64	37	-	-	ADJ
ejpam-4776	64	38	almost	almost	ADV
ejpam-4776	64	39	regular	regular	ADJ
ejpam-4776	64	40	and	and	CCONJ
ejpam-4776	64	41	cc	cc	NOUN
ejpam-4776	64	42	-	-	PUNCT
ejpam-4776	64	43	almost	almost	ADV
ejpam-4776	64	44	completely	completely	ADV
ejpam-4776	64	45	regular	regular	ADJ
ejpam-4776	64	46	,	,	PUNCT
ejpam-4776	64	47	but	but	CCONJ
ejpam-4776	64	48	it	it	PRON
ejpam-4776	64	49	is	be	AUX
ejpam-4776	64	50	neither	neither	CCONJ
ejpam-4776	64	51	almost	almost	ADV
ejpam-4776	64	52	normal	normal	ADJ
ejpam-4776	64	53	,	,	PUNCT
ejpam-4776	64	54	tychonoff	tychonoff	NOUN
ejpam-4776	64	55	,	,	PUNCT
ejpam-4776	64	56	completely	completely	ADV
ejpam-4776	64	57	regular	regular	ADJ
ejpam-4776	64	58	,	,	PUNCT
ejpam-4776	64	59	t3	t3	NOUN
ejpam-4776	64	60	nor	nor	CCONJ
ejpam-4776	64	61	regular	regular	ADJ
ejpam-4776	64	62	.	.	PUNCT
ejpam-4776	65	1	also	also	ADV
ejpam-4776	65	2	,	,	PUNCT
ejpam-4776	65	3	the	the	DET
ejpam-4776	65	4	half	half	ADJ
ejpam-4776	65	5	disc	disc	NOUN
ejpam-4776	65	6	topology	topology	NOUN
ejpam-4776	65	7	[	[	X
ejpam-4776	65	8	23	23	NUM
ejpam-4776	65	9	,	,	PUNCT
ejpam-4776	65	10	example	example	NOUN
ejpam-4776	65	11	78	78	NUM
ejpam-4776	65	12	]	]	PUNCT
ejpam-4776	65	13	,	,	PUNCT
ejpam-4776	65	14	is	be	AUX
ejpam-4776	65	15	a	a	DET
ejpam-4776	65	16	cc	cc	NOUN
ejpam-4776	65	17	-	-	ADJ
ejpam-4776	65	18	normal	normal	ADJ
ejpam-4776	65	19	,	,	PUNCT
ejpam-4776	65	20	cc	cc	NOUN
ejpam-4776	65	21	-	-	ADJ
ejpam-4776	65	22	regular	regular	ADJ
ejpam-4776	65	23	,	,	PUNCT
ejpam-4776	65	24	cc	cc	NOUN
ejpam-4776	65	25	-	-	ADJ
ejpam-4776	65	26	completely	completely	ADV
ejpam-4776	65	27	regular	regular	ADJ
ejpam-4776	65	28	,	,	PUNCT
ejpam-4776	65	29	cc	cc	NOUN
ejpam-4776	65	30	-	-	NOUN
ejpam-4776	65	31	tychonoff	tychonoff	NOUN
ejpam-4776	65	32	,	,	PUNCT
ejpam-4776	65	33	cct3	cct3	PROPN
ejpam-4776	65	34	and	and	CCONJ
ejpam-4776	65	35	cc	cc	NOUN
ejpam-4776	65	36	-	-	PUNCT
ejpam-4776	65	37	almost	almost	ADV
ejpam-4776	65	38	completely	completely	ADV
ejpam-4776	65	39	regular	regular	ADJ
ejpam-4776	65	40	space	space	NOUN
ejpam-4776	65	41	being	be	AUX
ejpam-4776	65	42	sub	sub	ADJ
ejpam-4776	65	43	-	-	ADJ
ejpam-4776	65	44	metrizable	metrizable	ADJ
ejpam-4776	65	45	,	,	PUNCT
ejpam-4776	65	46	but	but	CCONJ
ejpam-4776	65	47	it	it	PRON
ejpam-4776	65	48	is	be	AUX
ejpam-4776	65	49	neither	neither	CCONJ
ejpam-4776	65	50	regular	regular	ADJ
ejpam-4776	65	51	,	,	PUNCT
ejpam-4776	65	52	normal	normal	ADJ
ejpam-4776	65	53	,	,	PUNCT
ejpam-4776	65	54	completely	completely	ADV
ejpam-4776	65	55	regular	regular	ADJ
ejpam-4776	65	56	,	,	PUNCT
ejpam-4776	65	57	t3	t3	NOUN
ejpam-4776	65	58	nor	nor	CCONJ
ejpam-4776	65	59	tychonoff	tychonoff	NOUN
ejpam-4776	65	60	.	.	PUNCT
ejpam-4776	66	1	the	the	DET
ejpam-4776	66	2	following	follow	VERB
ejpam-4776	66	3	examples	example	NOUN
ejpam-4776	66	4	are	be	AUX
ejpam-4776	66	5	cc	cc	VERB
ejpam-4776	66	6	-	-	ADJ
ejpam-4776	66	7	almost	almost	ADV
ejpam-4776	66	8	regular	regular	ADJ
ejpam-4776	66	9	and	and	CCONJ
ejpam-4776	66	10	cc	cc	NOUN
ejpam-4776	66	11	-	-	PUNCT
ejpam-4776	66	12	almost	almost	ADV
ejpam-4776	66	13	completely	completely	ADV
ejpam-4776	66	14	regular	regular	ADJ
ejpam-4776	66	15	spaces	space	NOUN
ejpam-4776	66	16	which	which	PRON
ejpam-4776	66	17	are	be	AUX
ejpam-4776	66	18	neither	neither	CCONJ
ejpam-4776	66	19	almost	almost	ADV
ejpam-4776	66	20	regular	regular	ADJ
ejpam-4776	66	21	,	,	PUNCT
ejpam-4776	66	22	l	l	NOUN
ejpam-4776	66	23	-	-	PUNCT
ejpam-4776	66	24	almost	almost	ADV
ejpam-4776	66	25	regular	regular	ADJ
ejpam-4776	66	26	nor	nor	CCONJ
ejpam-4776	66	27	almost	almost	ADV
ejpam-4776	66	28	completely	completely	ADV
ejpam-4776	66	29	regular	regular	ADJ
ejpam-4776	66	30	:	:	PUNCT
ejpam-4776	66	31	example	example	NOUN
ejpam-4776	66	32	2	2	NUM
ejpam-4776	66	33	.	.	X
ejpam-4776	66	34	the	the	DET
ejpam-4776	66	35	relatively	relatively	ADV
ejpam-4776	66	36	prime	prime	ADJ
ejpam-4776	66	37	integer	integer	NOUN
ejpam-4776	66	38	topology	topology	NOUN
ejpam-4776	66	39	[	[	X
ejpam-4776	66	40	23	23	NUM
ejpam-4776	66	41	,	,	PUNCT
ejpam-4776	66	42	example	example	NOUN
ejpam-4776	66	43	60	60	NUM
ejpam-4776	66	44	]	]	PUNCT
ejpam-4776	66	45	,	,	PUNCT
ejpam-4776	66	46	is	be	AUX
ejpam-4776	66	47	a	a	DET
ejpam-4776	66	48	hausdorff	hausdorff	NOUN
ejpam-4776	66	49	,	,	PUNCT
ejpam-4776	66	50	semi	semi	ADV
ejpam-4776	66	51	regular	regular	ADJ
ejpam-4776	66	52	,	,	PUNCT
ejpam-4776	66	53	lindelöf	lindelöf	NOUN
ejpam-4776	66	54	,	,	PUNCT
ejpam-4776	66	55	first	first	ADV
ejpam-4776	66	56	countable	countable	ADJ
ejpam-4776	66	57	separable	separable	ADJ
ejpam-4776	66	58	space	space	NOUN
ejpam-4776	66	59	that	that	PRON
ejpam-4776	66	60	is	be	AUX
ejpam-4776	66	61	neither	neither	CCONJ
ejpam-4776	66	62	urysohn	urysohn	NOUN
ejpam-4776	66	63	,	,	PUNCT
ejpam-4776	66	64	quasi	quasi	X
ejpam-4776	66	65	normal	normal	ADJ
ejpam-4776	66	66	,	,	PUNCT
ejpam-4776	66	67	almost	almost	ADV
ejpam-4776	66	68	regular	regular	ADJ
ejpam-4776	66	69	nor	nor	CCONJ
ejpam-4776	66	70	regular	regular	ADJ
ejpam-4776	66	71	[	[	X
ejpam-4776	66	72	25	25	NUM
ejpam-4776	66	73	,	,	PUNCT
ejpam-4776	66	74	example	example	NOUN
ejpam-4776	66	75	2.9	2.9	NUM
ejpam-4776	66	76	]	]	PUNCT
ejpam-4776	66	77	.	.	PUNCT
ejpam-4776	67	1	the	the	DET
ejpam-4776	67	2	spacex	spacex	PROPN
ejpam-4776	67	3	is	be	AUX
ejpam-4776	67	4	epi	epi	ADJ
ejpam-4776	67	5	-	-	ADJ
ejpam-4776	67	6	mildly	mildly	ADV
ejpam-4776	67	7	normal	normal	ADJ
ejpam-4776	67	8	space	space	NOUN
ejpam-4776	67	9	which	which	PRON
ejpam-4776	67	10	is	be	AUX
ejpam-4776	67	11	neither	neither	DET
ejpam-4776	67	12	epi	epi	NOUN
ejpam-4776	67	13	-	-	ADJ
ejpam-4776	67	14	quasi	quasi	ADJ
ejpam-4776	67	15	normal	normal	ADJ
ejpam-4776	67	16	,	,	PUNCT
ejpam-4776	67	17	epi	epi	NOUN
ejpam-4776	67	18	-	-	NOUN
ejpam-4776	67	19	regular	regular	ADJ
ejpam-4776	67	20	nor	nor	CCONJ
ejpam-4776	67	21	epi	epi	NOUN
ejpam-4776	67	22	-	-	ADJ
ejpam-4776	67	23	completely	completely	ADV
ejpam-4776	67	24	regular	regular	ADJ
ejpam-4776	67	25	[	[	X
ejpam-4776	67	26	4	4	NUM
ejpam-4776	67	27	,	,	PUNCT
ejpam-4776	67	28	25	25	NUM
ejpam-4776	67	29	]	]	PUNCT
ejpam-4776	67	30	.	.	PUNCT
ejpam-4776	68	1	since	since	SCONJ
ejpam-4776	68	2	the	the	DET
ejpam-4776	68	3	space	space	NOUN
ejpam-4776	68	4	x	x	PUNCT
ejpam-4776	68	5	is	be	AUX
ejpam-4776	68	6	lindelöf	lindelöf	NOUN
ejpam-4776	68	7	non	non	X
ejpam-4776	68	8	urysohn	urysohn	PROPN
ejpam-4776	68	9	,	,	PUNCT
ejpam-4776	68	10	we	we	PRON
ejpam-4776	68	11	conclude	conclude	VERB
ejpam-4776	68	12	:	:	PUNCT
ejpam-4776	68	13	it	it	PRON
ejpam-4776	68	14	is	be	AUX
ejpam-4776	68	15	neither	neither	CCONJ
ejpam-4776	68	16	c	c	NOUN
ejpam-4776	68	17	-	-	ADJ
ejpam-4776	68	18	normal	normal	ADJ
ejpam-4776	68	19	,	,	PUNCT
ejpam-4776	68	20	c	c	NOUN
ejpam-4776	68	21	-	-	NOUN
ejpam-4776	68	22	regular	regular	ADJ
ejpam-4776	68	23	,	,	PUNCT
ejpam-4776	68	24	c	c	NOUN
ejpam-4776	68	25	-	-	PUNCT
ejpam-4776	68	26	completely	completely	ADV
ejpam-4776	68	27	regular	regular	ADJ
ejpam-4776	68	28	nor	nor	CCONJ
ejpam-4776	68	29	c	c	NOUN
ejpam-4776	68	30	-	-	PUNCT
ejpam-4776	68	31	tychonoff	tychonoff	NOUN
ejpam-4776	68	32	[	[	X
ejpam-4776	68	33	24	24	NUM
ejpam-4776	68	34	]	]	PUNCT
ejpam-4776	68	35	.	.	PUNCT
ejpam-4776	69	1	thus	thus	ADV
ejpam-4776	69	2	,	,	PUNCT
ejpam-4776	69	3	it	it	PRON
ejpam-4776	69	4	is	be	AUX
ejpam-4776	69	5	neither	neither	CCONJ
ejpam-4776	69	6	l	l	NOUN
ejpam-4776	69	7	-	-	PUNCT
ejpam-4776	69	8	almost	almost	ADV
ejpam-4776	69	9	regular	regular	ADJ
ejpam-4776	69	10	nor	nor	CCONJ
ejpam-4776	69	11	l	l	NOUN
ejpam-4776	69	12	-	-	PUNCT
ejpam-4776	69	13	almost	almost	ADV
ejpam-4776	69	14	completely	completely	ADV
ejpam-4776	69	15	regular	regular	ADJ
ejpam-4776	69	16	[	[	X
ejpam-4776	69	17	2	2	NUM
ejpam-4776	69	18	]	]	PUNCT
ejpam-4776	69	19	.	.	PUNCT
ejpam-4776	70	1	by	by	ADP
ejpam-4776	70	2	theorem	theorem	NOUN
ejpam-4776	70	3	2	2	NUM
ejpam-4776	70	4	,	,	PUNCT
ejpam-4776	70	5	it	it	PRON
ejpam-4776	70	6	is	be	AUX
ejpam-4776	70	7	neither	neither	DET
ejpam-4776	70	8	cc	cc	NOUN
ejpam-4776	70	9	-	-	ADJ
ejpam-4776	70	10	regular	regular	ADJ
ejpam-4776	70	11	,	,	PUNCT
ejpam-4776	70	12	cc	cc	NOUN
ejpam-4776	70	13	-	-	ADJ
ejpam-4776	70	14	completely	completely	ADV
ejpam-4776	70	15	regular	regular	ADJ
ejpam-4776	70	16	,	,	PUNCT
ejpam-4776	70	17	cct3	cct3	PROPN
ejpam-4776	70	18	,	,	PUNCT
ejpam-4776	70	19	cc	cc	NOUN
ejpam-4776	70	20	-	-	NOUN
ejpam-4776	70	21	tychonoff	tychonoff	NOUN
ejpam-4776	70	22	nor	nor	CCONJ
ejpam-4776	70	23	cc	cc	NOUN
ejpam-4776	70	24	-	-	ADJ
ejpam-4776	70	25	normal	normal	ADJ
ejpam-4776	70	26	.	.	PUNCT
ejpam-4776	71	1	since	since	SCONJ
ejpam-4776	71	2	the	the	DET
ejpam-4776	71	3	space	space	NOUN
ejpam-4776	71	4	x	x	PUNCT
ejpam-4776	71	5	is	be	AUX
ejpam-4776	71	6	a	a	DET
ejpam-4776	71	7	hausdorff	hausdorff	NOUN
ejpam-4776	71	8	first	first	ADJ
ejpam-4776	71	9	countable	countable	ADJ
ejpam-4776	71	10	space	space	NOUN
ejpam-4776	71	11	,	,	PUNCT
ejpam-4776	71	12	by	by	ADP
ejpam-4776	71	13	theorem	theorem	ADJ
ejpam-4776	71	14	17	17	NUM
ejpam-4776	71	15	and	and	CCONJ
ejpam-4776	71	16	corollary	corollary	ADJ
ejpam-4776	71	17	10	10	NUM
ejpam-4776	71	18	we	we	PRON
ejpam-4776	71	19	obtain	obtain	VERB
ejpam-4776	71	20	that	that	PRON
ejpam-4776	71	21	:	:	PUNCT
ejpam-4776	71	22	the	the	DET
ejpam-4776	71	23	space	space	NOUN
ejpam-4776	71	24	x	x	PUNCT
ejpam-4776	71	25	is	be	AUX
ejpam-4776	71	26	cc	cc	VERB
ejpam-4776	71	27	-	-	ADJ
ejpam-4776	71	28	almost	almost	ADV
ejpam-4776	71	29	regular	regular	ADJ
ejpam-4776	71	30	and	and	CCONJ
ejpam-4776	71	31	cc	cc	NOUN
ejpam-4776	71	32	-	-	PUNCT
ejpam-4776	71	33	almost	almost	ADV
ejpam-4776	71	34	completely	completely	ADV
ejpam-4776	71	35	regular	regular	ADJ
ejpam-4776	71	36	.	.	PUNCT
ejpam-4776	72	1	observe	observe	VERB
ejpam-4776	72	2	that	that	SCONJ
ejpam-4776	72	3	:	:	PUNCT
ejpam-4776	72	4	any	any	DET
ejpam-4776	72	5	hausdorff	hausdorff	NOUN
ejpam-4776	72	6	first	first	ADV
ejpam-4776	72	7	countable	countable	ADJ
ejpam-4776	72	8	lindelöf	lindelöf	NOUN
ejpam-4776	72	9	space	space	NOUN
ejpam-4776	72	10	is	be	AUX
ejpam-4776	72	11	not	not	PART
ejpam-4776	72	12	necessary	necessary	ADJ
ejpam-4776	72	13	to	to	PART
ejpam-4776	72	14	be	be	AUX
ejpam-4776	72	15	cc	cc	VERB
ejpam-4776	72	16	-	-	ADJ
ejpam-4776	72	17	regular	regular	ADJ
ejpam-4776	72	18	,	,	PUNCT
ejpam-4776	72	19	cct3	cct3	PROPN
ejpam-4776	72	20	,	,	PUNCT
ejpam-4776	72	21	cc	cc	NOUN
ejpam-4776	72	22	-	-	ADJ
ejpam-4776	72	23	normal	normal	ADJ
ejpam-4776	72	24	,	,	PUNCT
ejpam-4776	72	25	cc	cc	NOUN
ejpam-4776	72	26	-	-	NOUN
ejpam-4776	72	27	tychonoff	tychonoff	NOUN
ejpam-4776	72	28	,	,	PUNCT
ejpam-4776	72	29	epi	epi	NOUN
ejpam-4776	72	30	-	-	NOUN
ejpam-4776	72	31	regular	regular	ADJ
ejpam-4776	72	32	nor	nor	CCONJ
ejpam-4776	72	33	urysohn	urysohn	NOUN
ejpam-4776	72	34	.	.	PUNCT
ejpam-4776	73	1	this	this	DET
ejpam-4776	73	2	example	example	NOUN
ejpam-4776	73	3	also	also	ADV
ejpam-4776	73	4	shows	show	VERB
ejpam-4776	73	5	that	that	SCONJ
ejpam-4776	73	6	cc	cc	NOUN
ejpam-4776	73	7	-	-	ADJ
ejpam-4776	73	8	almost	almost	ADV
ejpam-4776	73	9	regularity	regularity	NOUN
ejpam-4776	73	10	does	do	AUX
ejpam-4776	73	11	not	not	PART
ejpam-4776	73	12	imply	imply	VERB
ejpam-4776	73	13	l	l	NOUN
ejpam-4776	73	14	-	-	ADJ
ejpam-4776	73	15	almost	almost	ADV
ejpam-4776	73	16	regularity	regularity	NOUN
ejpam-4776	73	17	.	.	PUNCT
ejpam-4776	74	1	now	now	ADV
ejpam-4776	74	2	,	,	PUNCT
ejpam-4776	74	3	we	we	PRON
ejpam-4776	74	4	present	present	VERB
ejpam-4776	74	5	the	the	DET
ejpam-4776	74	6	following	following	ADJ
ejpam-4776	74	7	basic	basic	ADJ
ejpam-4776	74	8	results	result	NOUN
ejpam-4776	74	9	.	.	PUNCT
ejpam-4776	75	1	theorem	theorem	NOUN
ejpam-4776	75	2	1	1	NUM
ejpam-4776	75	3	.	.	PUNCT
ejpam-4776	76	1	every	every	DET
ejpam-4776	76	2	epi	epi	NOUN
ejpam-4776	76	3	-	-	ADJ
ejpam-4776	76	4	completely	completely	ADV
ejpam-4776	76	5	regular	regular	ADJ
ejpam-4776	76	6	space	space	NOUN
ejpam-4776	76	7	is	be	AUX
ejpam-4776	76	8	cc	cc	NOUN
ejpam-4776	76	9	-	-	NOUN
ejpam-4776	76	10	tychonoff	tychonoff	NOUN
ejpam-4776	76	11	.	.	PUNCT
ejpam-4776	77	1	s.	s.	PROPN
ejpam-4776	77	2	a.	a.	PROPN
ejpam-4776	77	3	thabit	thabit	PROPN
ejpam-4776	77	4	,	,	PUNCT
ejpam-4776	77	5	w.	w.	PROPN
ejpam-4776	77	6	alqurashi	alqurashi	PROPN
ejpam-4776	77	7	/	/	SYM
ejpam-4776	77	8	eur	eur	PROPN
ejpam-4776	77	9	.	.	PUNCT
ejpam-4776	78	1	j.	j.	PROPN
ejpam-4776	78	2	pure	pure	PROPN
ejpam-4776	78	3	appl	appl	PROPN
ejpam-4776	78	4	.	.	PROPN
ejpam-4776	78	5	math	math	PROPN
ejpam-4776	78	6	,	,	PUNCT
ejpam-4776	78	7	16	16	NUM
ejpam-4776	78	8	(	(	PUNCT
ejpam-4776	78	9	2	2	NUM
ejpam-4776	78	10	)	)	PUNCT
ejpam-4776	78	11	(	(	PUNCT
ejpam-4776	78	12	2023	2023	NUM
ejpam-4776	78	13	)	)	PUNCT
ejpam-4776	78	14	,	,	PUNCT
ejpam-4776	78	15	1260	1260	NUM
ejpam-4776	78	16	-	-	SYM
ejpam-4776	78	17	1273	1273	NUM
ejpam-4776	78	18	1263	1263	NUM
ejpam-4776	78	19	proof	proof	NOUN
ejpam-4776	78	20	.	.	PUNCT
ejpam-4776	79	1	by	by	ADP
ejpam-4776	79	2	assumption	assumption	NOUN
ejpam-4776	79	3	,	,	PUNCT
ejpam-4776	79	4	there	there	PRON
ejpam-4776	79	5	exist	exist	VERB
ejpam-4776	79	6	a	a	DET
ejpam-4776	79	7	topology	topology	NOUN
ejpam-4776	79	8	t	t	NOUN
ejpam-4776	79	9	′	′	NUM
ejpam-4776	79	10	on	on	ADP
ejpam-4776	79	11	x	x	SYM
ejpam-4776	79	12	coarser	coarse	ADJ
ejpam-4776	79	13	than	than	ADP
ejpam-4776	79	14	t	t	NOUN
ejpam-4776	79	15	such	such	ADJ
ejpam-4776	79	16	that	that	SCONJ
ejpam-4776	79	17	(	(	PUNCT
ejpam-4776	79	18	x	x	X
ejpam-4776	79	19	,	,	PUNCT
ejpam-4776	79	20	t	t	PROPN
ejpam-4776	79	21	′	′	NUM
ejpam-4776	79	22	)	)	PUNCT
ejpam-4776	79	23	is	be	AUX
ejpam-4776	79	24	tychonoff	tychonoff	NOUN
ejpam-4776	79	25	[	[	X
ejpam-4776	79	26	4	4	NUM
ejpam-4776	79	27	]	]	PUNCT
ejpam-4776	79	28	.	.	PUNCT
ejpam-4776	80	1	thus	thus	ADV
ejpam-4776	80	2	,	,	PUNCT
ejpam-4776	80	3	the	the	DET
ejpam-4776	80	4	identity	identity	NOUN
ejpam-4776	80	5	mapping	mapping	NOUN
ejpam-4776	80	6	ix	ix	X
ejpam-4776	80	7	:	:	PUNCT
ejpam-4776	80	8	(	(	PUNCT
ejpam-4776	80	9	x	x	X
ejpam-4776	80	10	,	,	PUNCT
ejpam-4776	80	11	t	t	PROPN
ejpam-4776	80	12	)	)	PUNCT
ejpam-4776	80	13	→	→	SYM
ejpam-4776	80	14	(	(	PUNCT
ejpam-4776	80	15	x	x	X
ejpam-4776	80	16	,	,	PUNCT
ejpam-4776	80	17	t	t	PROPN
ejpam-4776	80	18	′	′	NUM
ejpam-4776	80	19	)	)	PUNCT
ejpam-4776	80	20	is	be	AUX
ejpam-4776	80	21	a	a	DET
ejpam-4776	80	22	bijective	bijective	ADJ
ejpam-4776	80	23	continuous	continuous	ADJ
ejpam-4776	80	24	function	function	NOUN
ejpam-4776	80	25	.	.	PUNCT
ejpam-4776	81	1	let	let	VERB
ejpam-4776	81	2	m	m	PRON
ejpam-4776	81	3	be	be	AUX
ejpam-4776	81	4	any	any	DET
ejpam-4776	81	5	countably	countably	ADV
ejpam-4776	81	6	compact	compact	ADJ
ejpam-4776	81	7	subspace	subspace	NOUN
ejpam-4776	81	8	of	of	ADP
ejpam-4776	81	9	(	(	PUNCT
ejpam-4776	81	10	x	x	PROPN
ejpam-4776	81	11	,	,	PUNCT
ejpam-4776	81	12	t	t	PROPN
ejpam-4776	81	13	)	)	PUNCT
ejpam-4776	81	14	.	.	PUNCT
ejpam-4776	82	1	since	since	SCONJ
ejpam-4776	82	2	a	a	DET
ejpam-4776	82	3	continuous	continuous	ADJ
ejpam-4776	82	4	image	image	NOUN
ejpam-4776	82	5	of	of	ADP
ejpam-4776	82	6	a	a	DET
ejpam-4776	82	7	countably	countably	ADV
ejpam-4776	82	8	compact	compact	ADJ
ejpam-4776	82	9	subset	subset	NOUN
ejpam-4776	82	10	is	be	AUX
ejpam-4776	82	11	countably	countably	ADV
ejpam-4776	82	12	compact	compact	ADJ
ejpam-4776	82	13	[	[	X
ejpam-4776	82	14	10	10	NUM
ejpam-4776	82	15	]	]	PUNCT
ejpam-4776	82	16	,	,	PUNCT
ejpam-4776	82	17	we	we	PRON
ejpam-4776	82	18	get	get	VERB
ejpam-4776	82	19	:	:	PUNCT
ejpam-4776	82	20	ix(m	ix(m	NUM
ejpam-4776	82	21	)	)	PUNCT
ejpam-4776	82	22	is	be	AUX
ejpam-4776	82	23	a	a	DET
ejpam-4776	82	24	countably	countably	ADV
ejpam-4776	82	25	compact	compact	ADJ
ejpam-4776	82	26	subspace	subspace	NOUN
ejpam-4776	82	27	of	of	ADP
ejpam-4776	82	28	(	(	PUNCT
ejpam-4776	82	29	x	x	PROPN
ejpam-4776	82	30	,	,	PUNCT
ejpam-4776	82	31	t	t	PROPN
ejpam-4776	82	32	′	′	NUM
ejpam-4776	82	33	)	)	PUNCT
ejpam-4776	82	34	as	as	ADP
ejpam-4776	82	35	ix(m	ix(m	NUM
ejpam-4776	82	36	)	)	PUNCT
ejpam-4776	83	1	=	=	VERB
ejpam-4776	83	2	m	m	VERB
ejpam-4776	83	3	is	be	AUX
ejpam-4776	83	4	countably	countably	ADV
ejpam-4776	83	5	compact	compact	ADJ
ejpam-4776	83	6	subspace	subspace	NOUN
ejpam-4776	83	7	of	of	ADP
ejpam-4776	83	8	both	both	DET
ejpam-4776	83	9	(	(	PUNCT
ejpam-4776	83	10	x	x	X
ejpam-4776	83	11	,	,	PUNCT
ejpam-4776	83	12	t	t	PROPN
ejpam-4776	83	13	)	)	PUNCT
ejpam-4776	83	14	and	and	CCONJ
ejpam-4776	83	15	(	(	PUNCT
ejpam-4776	83	16	x	x	X
ejpam-4776	83	17	,	,	PUNCT
ejpam-4776	83	18	t	t	PROPN
ejpam-4776	83	19	′	′	NUM
ejpam-4776	83	20	)	)	PUNCT
ejpam-4776	83	21	.	.	PUNCT
ejpam-4776	84	1	thus	thus	ADV
ejpam-4776	84	2	,	,	PUNCT
ejpam-4776	84	3	the	the	DET
ejpam-4776	84	4	restriction	restriction	NOUN
ejpam-4776	84	5	of	of	ADP
ejpam-4776	84	6	the	the	DET
ejpam-4776	84	7	identity	identity	NOUN
ejpam-4776	84	8	function	function	NOUN
ejpam-4776	84	9	(	(	PUNCT
ejpam-4776	84	10	ix)|m	ix)|m	NOUN
ejpam-4776	84	11	:	:	PUNCT
ejpam-4776	84	12	m	m	PROPN
ejpam-4776	84	13	→	→	SYM
ejpam-4776	84	14	ix(m	ix(m	NUM
ejpam-4776	84	15	)	)	PUNCT
ejpam-4776	84	16	is	be	AUX
ejpam-4776	84	17	bijective	bijective	ADJ
ejpam-4776	84	18	continuous	continuous	ADJ
ejpam-4776	84	19	.	.	PUNCT
ejpam-4776	85	1	let	let	VERB
ejpam-4776	85	2	u	u	PRON
ejpam-4776	85	3	be	be	AUX
ejpam-4776	85	4	any	any	DET
ejpam-4776	85	5	open	open	ADJ
ejpam-4776	85	6	set	set	NOUN
ejpam-4776	85	7	in	in	ADP
ejpam-4776	85	8	(	(	PUNCT
ejpam-4776	85	9	m	m	PROPN
ejpam-4776	85	10	,	,	PUNCT
ejpam-4776	85	11	tm	tm	NOUN
ejpam-4776	85	12	)	)	PUNCT
ejpam-4776	85	13	.	.	PUNCT
ejpam-4776	86	1	since	since	SCONJ
ejpam-4776	86	2	m	m	PROPN
ejpam-4776	86	3	is	be	AUX
ejpam-4776	86	4	a	a	DET
ejpam-4776	86	5	countably	countably	ADV
ejpam-4776	86	6	compact	compact	ADJ
ejpam-4776	86	7	subset	subset	NOUN
ejpam-4776	86	8	of	of	ADP
ejpam-4776	86	9	(	(	PUNCT
ejpam-4776	86	10	x	x	PROPN
ejpam-4776	86	11	,	,	PUNCT
ejpam-4776	86	12	t	t	PROPN
ejpam-4776	86	13	′	′	NUM
ejpam-4776	86	14	)	)	PUNCT
ejpam-4776	86	15	,	,	PUNCT
ejpam-4776	86	16	there	there	PRON
ejpam-4776	86	17	exists	exist	VERB
ejpam-4776	86	18	an	an	DET
ejpam-4776	86	19	open	open	ADJ
ejpam-4776	86	20	set	set	NOUN
ejpam-4776	86	21	v	v	NOUN
ejpam-4776	86	22	in	in	ADP
ejpam-4776	86	23	(	(	PUNCT
ejpam-4776	86	24	x	x	NOUN
ejpam-4776	86	25	,	,	PUNCT
ejpam-4776	86	26	t	t	PROPN
ejpam-4776	86	27	′	′	NUM
ejpam-4776	86	28	)	)	PUNCT
ejpam-4776	86	29	and	and	CCONJ
ejpam-4776	86	30	hence	hence	ADV
ejpam-4776	86	31	in	in	ADV
ejpam-4776	86	32	(	(	PUNCT
ejpam-4776	86	33	x	x	NOUN
ejpam-4776	86	34	,	,	PUNCT
ejpam-4776	86	35	t	t	PROPN
ejpam-4776	86	36	)	)	PUNCT
ejpam-4776	86	37	such	such	ADJ
ejpam-4776	86	38	that	that	DET
ejpam-4776	86	39	u	u	NOUN
ejpam-4776	86	40	=	=	PROPN
ejpam-4776	86	41	v	v	ADP
ejpam-4776	86	42	∩m	∩m	PROPN
ejpam-4776	86	43	.	.	PUNCT
ejpam-4776	87	1	thus	thus	ADV
ejpam-4776	87	2	,	,	PUNCT
ejpam-4776	87	3	(	(	PUNCT
ejpam-4776	87	4	ix)|m	ix)|m	PROPN
ejpam-4776	87	5	(	(	PUNCT
ejpam-4776	87	6	u	u	NOUN
ejpam-4776	87	7	)	)	PUNCT
ejpam-4776	87	8	=	=	SYM
ejpam-4776	87	9	(	(	PUNCT
ejpam-4776	87	10	ix)|m	ix)|m	PROPN
ejpam-4776	87	11	(	(	PUNCT
ejpam-4776	87	12	v	v	NOUN
ejpam-4776	87	13	∩m	∩m	NOUN
ejpam-4776	87	14	)	)	PUNCT
ejpam-4776	88	1	=	=	NOUN
ejpam-4776	88	2	v	v	ADP
ejpam-4776	88	3	∩m	∩m	NOUN
ejpam-4776	89	1	=	=	PUNCT
ejpam-4776	89	2	u	u	PROPN
ejpam-4776	89	3	,	,	PUNCT
ejpam-4776	89	4	which	which	PRON
ejpam-4776	89	5	is	be	AUX
ejpam-4776	89	6	an	an	DET
ejpam-4776	89	7	open	open	ADJ
ejpam-4776	89	8	set	set	NOUN
ejpam-4776	89	9	in	in	ADP
ejpam-4776	89	10	(	(	PUNCT
ejpam-4776	89	11	ix(m	ix(m	NUM
ejpam-4776	89	12	)	)	PUNCT
ejpam-4776	89	13	,	,	PUNCT
ejpam-4776	89	14	t	t	PROPN
ejpam-4776	89	15	′	′	NUM
ejpam-4776	89	16	m	m	NOUN
ejpam-4776	89	17	)	)	PUNCT
ejpam-4776	89	18	.	.	PUNCT
ejpam-4776	90	1	hence	hence	ADV
ejpam-4776	90	2	,	,	PUNCT
ejpam-4776	90	3	(	(	PUNCT
ejpam-4776	90	4	ix)|m	ix)|m	NOUN
ejpam-4776	90	5	is	be	AUX
ejpam-4776	90	6	open	open	ADJ
ejpam-4776	90	7	and	and	CCONJ
ejpam-4776	90	8	hence	hence	ADV
ejpam-4776	90	9	a	a	DET
ejpam-4776	90	10	homeomorphism	homeomorphism	NOUN
ejpam-4776	90	11	.	.	PUNCT
ejpam-4776	91	1	therefore	therefore	ADV
ejpam-4776	91	2	,	,	PUNCT
ejpam-4776	91	3	x	x	X
ejpam-4776	91	4	is	be	AUX
ejpam-4776	91	5	cc	cc	NOUN
ejpam-4776	91	6	-	-	NOUN
ejpam-4776	91	7	tychonoff	tychonoff	NOUN
ejpam-4776	91	8	.	.	PUNCT
ejpam-4776	92	1	note	note	VERB
ejpam-4776	92	2	that	that	SCONJ
ejpam-4776	92	3	:	:	PUNCT
ejpam-4776	92	4	every	every	DET
ejpam-4776	92	5	epi	epi	ADJ
ejpam-4776	92	6	-	-	ADJ
ejpam-4776	92	7	normal	normal	ADJ
ejpam-4776	92	8	space	space	NOUN
ejpam-4776	92	9	is	be	AUX
ejpam-4776	92	10	epi	epi	NOUN
ejpam-4776	92	11	-	-	ADJ
ejpam-4776	92	12	almost	almost	ADV
ejpam-4776	92	13	normal	normal	ADJ
ejpam-4776	92	14	and	and	CCONJ
ejpam-4776	92	15	epi	epi	NOUN
ejpam-4776	92	16	-	-	ADJ
ejpam-4776	92	17	almost	almost	ADV
ejpam-4776	92	18	normal	normal	ADJ
ejpam-4776	92	19	space	space	NOUN
ejpam-4776	92	20	is	be	AUX
ejpam-4776	92	21	epi	epi	NOUN
ejpam-4776	92	22	-	-	ADJ
ejpam-4776	92	23	completely	completely	ADV
ejpam-4776	92	24	regular	regular	ADJ
ejpam-4776	92	25	[	[	X
ejpam-4776	92	26	4	4	NUM
ejpam-4776	92	27	]	]	PUNCT
ejpam-4776	92	28	.	.	PUNCT
ejpam-4776	93	1	obviously	obviously	ADV
ejpam-4776	93	2	,	,	PUNCT
ejpam-4776	93	3	every	every	DET
ejpam-4776	93	4	epi	epi	ADJ
ejpam-4776	93	5	-	-	ADJ
ejpam-4776	93	6	regular	regular	ADJ
ejpam-4776	93	7	space	space	NOUN
ejpam-4776	93	8	is	be	AUX
ejpam-4776	93	9	cct3	cct3	PROPN
ejpam-4776	93	10	,	,	PUNCT
ejpam-4776	93	11	every	every	DET
ejpam-4776	93	12	epi	epi	ADJ
ejpam-4776	93	13	-	-	ADJ
ejpam-4776	93	14	normal	normal	ADJ
ejpam-4776	93	15	space	space	NOUN
ejpam-4776	93	16	is	be	AUX
ejpam-4776	93	17	cc	cc	VERB
ejpam-4776	93	18	-	-	ADJ
ejpam-4776	93	19	normal	normal	ADJ
ejpam-4776	93	20	and	and	CCONJ
ejpam-4776	93	21	every	every	DET
ejpam-4776	93	22	epi	epi	ADJ
ejpam-4776	93	23	-	-	ADJ
ejpam-4776	93	24	regular	regular	ADJ
ejpam-4776	93	25	space	space	NOUN
ejpam-4776	93	26	is	be	AUX
ejpam-4776	93	27	cc	cc	NOUN
ejpam-4776	93	28	-	-	ADJ
ejpam-4776	93	29	regular	regular	ADJ
ejpam-4776	93	30	.	.	PUNCT
ejpam-4776	94	1	corollary	corollary	ADJ
ejpam-4776	94	2	1	1	NUM
ejpam-4776	94	3	.	.	PUNCT
ejpam-4776	95	1	every	every	DET
ejpam-4776	95	2	sub	sub	NOUN
ejpam-4776	95	3	-	-	ADJ
ejpam-4776	95	4	metrizable	metrizable	ADJ
ejpam-4776	95	5	(	(	PUNCT
ejpam-4776	95	6	resp	resp	NOUN
ejpam-4776	95	7	.	.	PUNCT
ejpam-4776	96	1	epi	epi	X
ejpam-4776	96	2	-	-	PUNCT
ejpam-4776	96	3	almost	almost	ADV
ejpam-4776	96	4	normal	normal	ADJ
ejpam-4776	96	5	,	,	PUNCT
ejpam-4776	96	6	epi	epi	NOUN
ejpam-4776	96	7	-	-	ADJ
ejpam-4776	96	8	normal	normal	ADJ
ejpam-4776	96	9	)	)	PUNCT
ejpam-4776	96	10	space	space	NOUN
ejpam-4776	96	11	is	be	AUX
ejpam-4776	96	12	cc	cc	NOUN
ejpam-4776	96	13	-	-	NOUN
ejpam-4776	96	14	tychonoff	tychonoff	NOUN
ejpam-4776	96	15	.	.	PUNCT
ejpam-4776	97	1	the	the	DET
ejpam-4776	97	2	converses	converse	NOUN
ejpam-4776	97	3	of	of	ADP
ejpam-4776	97	4	theorem	theorem	ADJ
ejpam-4776	97	5	1	1	NUM
ejpam-4776	97	6	and	and	CCONJ
ejpam-4776	97	7	corollary	corollary	ADJ
ejpam-4776	97	8	1	1	NUM
ejpam-4776	97	9	are	be	AUX
ejpam-4776	97	10	not	not	PART
ejpam-4776	97	11	true	true	ADJ
ejpam-4776	97	12	in	in	ADP
ejpam-4776	97	13	general	general	ADJ
ejpam-4776	97	14	as	as	SCONJ
ejpam-4776	97	15	shown	show	VERB
ejpam-4776	97	16	by	by	ADP
ejpam-4776	97	17	the	the	DET
ejpam-4776	97	18	next	next	ADJ
ejpam-4776	97	19	example	example	NOUN
ejpam-4776	97	20	:	:	PUNCT
ejpam-4776	97	21	example	example	NOUN
ejpam-4776	97	22	3	3	X
ejpam-4776	97	23	.	.	PUNCT
ejpam-4776	98	1	the	the	DET
ejpam-4776	98	2	countable	countable	ADJ
ejpam-4776	98	3	complement	complement	NOUN
ejpam-4776	98	4	topology	topology	NOUN
ejpam-4776	98	5	:	:	PUNCT
ejpam-4776	98	6	[	[	X
ejpam-4776	98	7	23	23	NUM
ejpam-4776	98	8	,	,	PUNCT
ejpam-4776	98	9	example	example	NOUN
ejpam-4776	98	10	20	20	NUM
ejpam-4776	98	11	]	]	PUNCT
ejpam-4776	98	12	,	,	PUNCT
ejpam-4776	98	13	(	(	PUNCT
ejpam-4776	98	14	r	r	NOUN
ejpam-4776	98	15	,	,	PUNCT
ejpam-4776	98	16	cc	cc	NOUN
ejpam-4776	98	17	)	)	PUNCT
ejpam-4776	98	18	is	be	AUX
ejpam-4776	98	19	a	a	DET
ejpam-4776	98	20	t1	t1	NOUN
ejpam-4776	98	21	-	-	PUNCT
ejpam-4776	98	22	lindelöf	lindelöf	NOUN
ejpam-4776	98	23	c	c	NOUN
ejpam-4776	98	24	-	-	PUNCT
ejpam-4776	98	25	regular	regular	ADJ
ejpam-4776	98	26	space	space	NOUN
ejpam-4776	98	27	,	,	PUNCT
ejpam-4776	98	28	which	which	PRON
ejpam-4776	98	29	is	be	AUX
ejpam-4776	98	30	neither	neither	DET
ejpam-4776	98	31	hausdorff	hausdorff	NOUN
ejpam-4776	98	32	,	,	PUNCT
ejpam-4776	98	33	regular	regular	ADJ
ejpam-4776	98	34	,	,	PUNCT
ejpam-4776	98	35	normal	normal	ADJ
ejpam-4776	98	36	,	,	PUNCT
ejpam-4776	98	37	first	first	ADV
ejpam-4776	98	38	countable	countable	ADJ
ejpam-4776	98	39	,	,	PUNCT
ejpam-4776	98	40	separable	separable	ADJ
ejpam-4776	98	41	,	,	PUNCT
ejpam-4776	98	42	paracompact	paracompact	ADJ
ejpam-4776	98	43	nor	nor	CCONJ
ejpam-4776	98	44	l	l	NOUN
ejpam-4776	98	45	-	-	ADJ
ejpam-4776	98	46	regular	regular	ADJ
ejpam-4776	98	47	[	[	X
ejpam-4776	98	48	5	5	NUM
ejpam-4776	98	49	,	,	PUNCT
ejpam-4776	98	50	23	23	NUM
ejpam-4776	98	51	]	]	PUNCT
ejpam-4776	98	52	.	.	PUNCT
ejpam-4776	99	1	also	also	ADV
ejpam-4776	99	2	,	,	PUNCT
ejpam-4776	99	3	(	(	PUNCT
ejpam-4776	99	4	r	r	NOUN
ejpam-4776	99	5	,	,	PUNCT
ejpam-4776	99	6	cc	cc	NOUN
ejpam-4776	99	7	)	)	PUNCT
ejpam-4776	99	8	is	be	AUX
ejpam-4776	99	9	a	a	DET
ejpam-4776	99	10	cc	cc	NOUN
ejpam-4776	99	11	-	-	ADJ
ejpam-4776	99	12	normal	normal	ADJ
ejpam-4776	99	13	space	space	NOUN
ejpam-4776	99	14	,	,	PUNCT
ejpam-4776	99	15	which	which	PRON
ejpam-4776	99	16	is	be	AUX
ejpam-4776	99	17	not	not	PART
ejpam-4776	99	18	l	l	NOUN
ejpam-4776	99	19	-	-	ADJ
ejpam-4776	99	20	normal	normal	ADJ
ejpam-4776	99	21	[	[	X
ejpam-4776	99	22	14	14	NUM
ejpam-4776	99	23	]	]	PUNCT
ejpam-4776	99	24	.	.	PUNCT
ejpam-4776	100	1	since	since	SCONJ
ejpam-4776	100	2	x	x	PRON
ejpam-4776	100	3	is	be	AUX
ejpam-4776	100	4	not	not	PART
ejpam-4776	100	5	hausdorff	hausdorff	NOUN
ejpam-4776	100	6	,	,	PUNCT
ejpam-4776	100	7	it	it	PRON
ejpam-4776	100	8	is	be	AUX
ejpam-4776	100	9	neither	neither	DET
ejpam-4776	100	10	epi	epi	NOUN
ejpam-4776	100	11	-	-	NOUN
ejpam-4776	100	12	regular	regular	ADJ
ejpam-4776	100	13	,	,	PUNCT
ejpam-4776	100	14	epi	epi	NOUN
ejpam-4776	100	15	-	-	ADJ
ejpam-4776	100	16	normal	normal	ADJ
ejpam-4776	100	17	nor	nor	CCONJ
ejpam-4776	100	18	epi	epi	NOUN
ejpam-4776	100	19	-	-	ADJ
ejpam-4776	100	20	mildly	mildly	ADV
ejpam-4776	100	21	normal	normal	ADJ
ejpam-4776	100	22	.	.	PUNCT
ejpam-4776	101	1	since	since	SCONJ
ejpam-4776	101	2	the	the	DET
ejpam-4776	101	3	only	only	ADJ
ejpam-4776	101	4	countably	countably	ADV
ejpam-4776	101	5	compact	compact	ADJ
ejpam-4776	101	6	subsets	subset	NOUN
ejpam-4776	101	7	in	in	ADP
ejpam-4776	101	8	x	x	SYM
ejpam-4776	101	9	are	be	AUX
ejpam-4776	101	10	finite	finite	ADJ
ejpam-4776	101	11	subsets	subset	NOUN
ejpam-4776	101	12	,	,	PUNCT
ejpam-4776	101	13	by	by	ADP
ejpam-4776	101	14	theorem	theorem	NOUN
ejpam-4776	101	15	4	4	NUM
ejpam-4776	101	16	and	and	CCONJ
ejpam-4776	101	17	corollary	corollary	ADJ
ejpam-4776	101	18	2	2	NUM
ejpam-4776	101	19	(	(	PUNCT
ejpam-4776	101	20	r	r	NOUN
ejpam-4776	101	21	,	,	PUNCT
ejpam-4776	101	22	cc	cc	NOUN
ejpam-4776	101	23	)	)	PUNCT
ejpam-4776	101	24	is	be	AUX
ejpam-4776	101	25	cc	cc	NOUN
ejpam-4776	101	26	-	-	NOUN
ejpam-4776	101	27	tychonoff	tychonoff	NOUN
ejpam-4776	101	28	,	,	PUNCT
ejpam-4776	101	29	cct3	cct3	PROPN
ejpam-4776	101	30	,	,	PUNCT
ejpam-4776	101	31	cc	cc	NOUN
ejpam-4776	101	32	-	-	ADJ
ejpam-4776	101	33	completely	completely	ADV
ejpam-4776	101	34	regular	regular	ADJ
ejpam-4776	101	35	and	and	CCONJ
ejpam-4776	101	36	cc	cc	NOUN
ejpam-4776	101	37	-	-	NOUN
ejpam-4776	101	38	regular	regular	ADJ
ejpam-4776	101	39	.	.	PUNCT
ejpam-4776	102	1	this	this	DET
ejpam-4776	102	2	example	example	NOUN
ejpam-4776	102	3	shows	show	VERB
ejpam-4776	102	4	that	that	SCONJ
ejpam-4776	102	5	:	:	PUNCT
ejpam-4776	102	6	cc	cc	VERB
ejpam-4776	102	7	-	-	ADJ
ejpam-4776	102	8	complete	complete	ADJ
ejpam-4776	102	9	regularity	regularity	NOUN
ejpam-4776	102	10	,	,	PUNCT
ejpam-4776	102	11	cc	cc	NOUN
ejpam-4776	102	12	-	-	NOUN
ejpam-4776	102	13	normality	normality	NOUN
ejpam-4776	102	14	,	,	PUNCT
ejpam-4776	102	15	cct3	cct3	PROPN
ejpam-4776	102	16	and	and	CCONJ
ejpam-4776	102	17	cc	cc	PROPN
ejpam-4776	102	18	-	-	NOUN
ejpam-4776	102	19	tychonoffness	tychonoffness	NOUN
ejpam-4776	102	20	do	do	AUX
ejpam-4776	102	21	not	not	PART
ejpam-4776	102	22	imply	imply	VERB
ejpam-4776	102	23	epi	epi	NOUN
ejpam-4776	102	24	-	-	NOUN
ejpam-4776	102	25	regularity	regularity	NOUN
ejpam-4776	102	26	(	(	PUNCT
ejpam-4776	102	27	resp	resp	NOUN
ejpam-4776	102	28	.	.	PUNCT
ejpam-4776	103	1	epi	epi	ADJ
ejpam-4776	103	2	-	-	ADJ
ejpam-4776	103	3	complete	complete	ADJ
ejpam-4776	103	4	regularity	regularity	NOUN
ejpam-4776	103	5	,	,	PUNCT
ejpam-4776	103	6	epi	epi	ADJ
ejpam-4776	103	7	-	-	ADJ
ejpam-4776	103	8	mild	mild	ADJ
ejpam-4776	103	9	normality	normality	NOUN
ejpam-4776	103	10	,	,	PUNCT
ejpam-4776	103	11	sub	sub	ADJ
ejpam-4776	103	12	-	-	ADJ
ejpam-4776	103	13	metrizable	metrizable	ADJ
ejpam-4776	103	14	,	,	PUNCT
ejpam-4776	103	15	l	l	NOUN
ejpam-4776	103	16	-	-	NOUN
ejpam-4776	103	17	regularity	regularity	NOUN
ejpam-4776	103	18	,	,	PUNCT
ejpam-4776	103	19	lt3	lt3	PROPN
ejpam-4776	103	20	,	,	PUNCT
ejpam-4776	103	21	l	l	NOUN
ejpam-4776	103	22	-	-	NOUN
ejpam-4776	103	23	normality	normality	NOUN
ejpam-4776	103	24	nor	nor	CCONJ
ejpam-4776	103	25	hausdorffness	hausdorffness	NOUN
ejpam-4776	103	26	)	)	PUNCT
ejpam-4776	103	27	.	.	PUNCT
ejpam-4776	104	1	also	also	ADV
ejpam-4776	104	2	,	,	PUNCT
ejpam-4776	104	3	it	it	PRON
ejpam-4776	104	4	is	be	AUX
ejpam-4776	104	5	a	a	DET
ejpam-4776	104	6	cc	cc	NOUN
ejpam-4776	104	7	-	-	PUNCT
ejpam-4776	104	8	tychonoff	tychonoff	NOUN
ejpam-4776	104	9	space	space	NOUN
ejpam-4776	104	10	which	which	PRON
ejpam-4776	104	11	is	be	AUX
ejpam-4776	104	12	not	not	PART
ejpam-4776	104	13	l	l	NOUN
ejpam-4776	104	14	-	-	ADJ
ejpam-4776	104	15	regular	regular	ADJ
ejpam-4776	104	16	.	.	PUNCT
ejpam-4776	105	1	theorem	theorem	NOUN
ejpam-4776	105	2	2	2	NUM
ejpam-4776	105	3	.	.	PUNCT
ejpam-4776	106	1	every	every	DET
ejpam-4776	106	2	cc	cc	NOUN
ejpam-4776	106	3	-	-	ADJ
ejpam-4776	106	4	completely	completely	ADV
ejpam-4776	106	5	regular	regular	ADJ
ejpam-4776	106	6	space	space	NOUN
ejpam-4776	106	7	is	be	AUX
ejpam-4776	106	8	c	c	NOUN
ejpam-4776	106	9	-	-	PUNCT
ejpam-4776	106	10	completely	completely	ADV
ejpam-4776	106	11	regular	regular	ADJ
ejpam-4776	106	12	.	.	PUNCT
ejpam-4776	107	1	proof	proof	NOUN
ejpam-4776	107	2	.	.	PUNCT
ejpam-4776	108	1	by	by	ADP
ejpam-4776	108	2	assumption	assumption	NOUN
ejpam-4776	108	3	,	,	PUNCT
ejpam-4776	108	4	there	there	PRON
ejpam-4776	108	5	exist	exist	VERB
ejpam-4776	108	6	a	a	DET
ejpam-4776	108	7	completely	completely	ADV
ejpam-4776	108	8	regular	regular	ADJ
ejpam-4776	108	9	space	space	NOUN
ejpam-4776	108	10	y	y	PROPN
ejpam-4776	108	11	and	and	CCONJ
ejpam-4776	108	12	a	a	DET
ejpam-4776	108	13	bijective	bijective	ADJ
ejpam-4776	108	14	function	function	NOUN
ejpam-4776	109	1	f	f	NOUN
ejpam-4776	109	2	:	:	PUNCT
ejpam-4776	109	3	x	x	X
ejpam-4776	109	4	→	→	SYM
ejpam-4776	109	5	y	y	PROPN
ejpam-4776	109	6	such	such	ADJ
ejpam-4776	109	7	that	that	SCONJ
ejpam-4776	109	8	the	the	DET
ejpam-4776	109	9	restriction	restriction	NOUN
ejpam-4776	109	10	function	function	NOUN
ejpam-4776	109	11	f	f	PROPN
ejpam-4776	109	12	|a	|a	VERB
ejpam-4776	109	13	:	:	PUNCT
ejpam-4776	109	14	a	a	DET
ejpam-4776	109	15	→	→	SYM
ejpam-4776	109	16	f(a	f(a	NOUN
ejpam-4776	109	17	)	)	PUNCT
ejpam-4776	109	18	is	be	AUX
ejpam-4776	109	19	a	a	DET
ejpam-4776	109	20	homeomorphism	homeomorphism	NOUN
ejpam-4776	109	21	for	for	ADP
ejpam-4776	109	22	each	each	DET
ejpam-4776	109	23	countably	countably	ADV
ejpam-4776	109	24	compact	compact	ADJ
ejpam-4776	109	25	subsets	subset	NOUN
ejpam-4776	110	1	a	a	DET
ejpam-4776	110	2	⊆	⊆	NUM
ejpam-4776	110	3	x.	x.	NOUN
ejpam-4776	110	4	let	let	VERB
ejpam-4776	110	5	c	c	NOUN
ejpam-4776	110	6	be	be	AUX
ejpam-4776	110	7	any	any	DET
ejpam-4776	110	8	compact	compact	ADJ
ejpam-4776	110	9	subset	subset	NOUN
ejpam-4776	110	10	of	of	ADP
ejpam-4776	110	11	x.	x.	NOUN
ejpam-4776	110	12	since	since	SCONJ
ejpam-4776	110	13	every	every	DET
ejpam-4776	110	14	compact	compact	ADJ
ejpam-4776	110	15	space	space	NOUN
ejpam-4776	110	16	is	be	AUX
ejpam-4776	110	17	countably	countably	ADV
ejpam-4776	110	18	compact	compact	ADJ
ejpam-4776	110	19	[	[	X
ejpam-4776	110	20	10	10	NUM
ejpam-4776	110	21	]	]	PUNCT
ejpam-4776	110	22	,	,	PUNCT
ejpam-4776	110	23	we	we	PRON
ejpam-4776	110	24	have	have	VERB
ejpam-4776	110	25	:	:	PUNCT
ejpam-4776	110	26	c	c	NOUN
ejpam-4776	110	27	is	be	AUX
ejpam-4776	110	28	countably	countably	ADV
ejpam-4776	110	29	compact	compact	ADJ
ejpam-4776	110	30	subset	subset	NOUN
ejpam-4776	110	31	of	of	ADP
ejpam-4776	110	32	x.	x.	NOUN
ejpam-4776	110	33	thus	thus	ADV
ejpam-4776	110	34	,	,	PUNCT
ejpam-4776	110	35	the	the	DET
ejpam-4776	110	36	restriction	restriction	NOUN
ejpam-4776	110	37	function	function	NOUN
ejpam-4776	110	38	f	f	PROPN
ejpam-4776	110	39	|c	|c	VERB
ejpam-4776	110	40	:	:	PUNCT
ejpam-4776	110	41	c	c	PROPN
ejpam-4776	110	42	→	→	SYM
ejpam-4776	110	43	f(c	f(c	PROPN
ejpam-4776	110	44	)	)	PUNCT
ejpam-4776	110	45	is	be	AUX
ejpam-4776	110	46	a	a	DET
ejpam-4776	110	47	homeomorphism	homeomorphism	NOUN
ejpam-4776	110	48	.	.	PUNCT
ejpam-4776	111	1	since	since	SCONJ
ejpam-4776	111	2	c	c	PROPN
ejpam-4776	111	3	was	be	AUX
ejpam-4776	111	4	arbitrary	arbitrary	ADJ
ejpam-4776	111	5	compact	compact	ADJ
ejpam-4776	111	6	subset	subset	NOUN
ejpam-4776	111	7	of	of	ADP
ejpam-4776	111	8	x	x	PRON
ejpam-4776	111	9	,	,	PUNCT
ejpam-4776	111	10	we	we	PRON
ejpam-4776	111	11	conclude	conclude	VERB
ejpam-4776	111	12	that	that	PRON
ejpam-4776	111	13	:	:	PUNCT
ejpam-4776	111	14	x	x	X
ejpam-4776	111	15	is	be	AUX
ejpam-4776	111	16	c	c	NOUN
ejpam-4776	111	17	-	-	PUNCT
ejpam-4776	111	18	completely	completely	ADV
ejpam-4776	111	19	regular	regular	ADJ
ejpam-4776	111	20	.	.	PUNCT
ejpam-4776	112	1	similarly	similarly	ADV
ejpam-4776	112	2	,	,	PUNCT
ejpam-4776	112	3	it	it	PRON
ejpam-4776	112	4	is	be	AUX
ejpam-4776	112	5	easy	easy	ADJ
ejpam-4776	112	6	to	to	PART
ejpam-4776	112	7	prove	prove	VERB
ejpam-4776	112	8	that	that	SCONJ
ejpam-4776	112	9	:	:	PUNCT
ejpam-4776	112	10	every	every	DET
ejpam-4776	112	11	cc	cc	NOUN
ejpam-4776	112	12	-	-	ADJ
ejpam-4776	112	13	regular	regular	ADJ
ejpam-4776	112	14	space	space	NOUN
ejpam-4776	112	15	is	be	AUX
ejpam-4776	112	16	c	c	NOUN
ejpam-4776	112	17	-	-	ADJ
ejpam-4776	112	18	regular	regular	ADJ
ejpam-4776	112	19	,	,	PUNCT
ejpam-4776	112	20	every	every	DET
ejpam-4776	112	21	cct3	cct3	PROPN
ejpam-4776	112	22	-	-	PUNCT
ejpam-4776	112	23	space	space	NOUN
ejpam-4776	112	24	is	be	AUX
ejpam-4776	112	25	ct3	ct3	PROPN
ejpam-4776	112	26	,	,	PUNCT
ejpam-4776	112	27	every	every	DET
ejpam-4776	112	28	cc	cc	NOUN
ejpam-4776	112	29	-	-	PUNCT
ejpam-4776	112	30	tychonoff	tychonoff	NOUN
ejpam-4776	112	31	space	space	NOUN
ejpam-4776	112	32	is	be	AUX
ejpam-4776	112	33	c	c	NOUN
ejpam-4776	112	34	-	-	PUNCT
ejpam-4776	112	35	tychonoff	tychonoff	NOUN
ejpam-4776	112	36	,	,	PUNCT
ejpam-4776	112	37	every	every	DET
ejpam-4776	112	38	cc	cc	NOUN
ejpam-4776	112	39	-	-	ADJ
ejpam-4776	112	40	almost	almost	ADV
ejpam-4776	112	41	regular	regular	ADJ
ejpam-4776	112	42	space	space	NOUN
ejpam-4776	112	43	is	be	AUX
ejpam-4776	112	44	c	c	NOUN
ejpam-4776	112	45	-	-	PUNCT
ejpam-4776	112	46	almost	almost	ADV
ejpam-4776	112	47	regular	regular	ADJ
ejpam-4776	112	48	and	and	CCONJ
ejpam-4776	112	49	every	every	DET
ejpam-4776	112	50	cc	cc	NOUN
ejpam-4776	112	51	-	-	ADJ
ejpam-4776	112	52	almost	almost	ADV
ejpam-4776	112	53	completely	completely	ADV
ejpam-4776	112	54	regular	regular	ADJ
ejpam-4776	112	55	space	space	NOUN
ejpam-4776	112	56	is	be	AUX
ejpam-4776	112	57	c	c	NOUN
ejpam-4776	112	58	-	-	PUNCT
ejpam-4776	112	59	almost	almost	ADV
ejpam-4776	112	60	completely	completely	ADV
ejpam-4776	112	61	regular	regular	ADJ
ejpam-4776	112	62	.	.	PUNCT
ejpam-4776	113	1	s.	s.	PROPN
ejpam-4776	113	2	a.	a.	PROPN
ejpam-4776	113	3	thabit	thabit	PROPN
ejpam-4776	113	4	,	,	PUNCT
ejpam-4776	113	5	w.	w.	PROPN
ejpam-4776	113	6	alqurashi	alqurashi	PROPN
ejpam-4776	113	7	/	/	SYM
ejpam-4776	113	8	eur	eur	PROPN
ejpam-4776	113	9	.	.	PUNCT
ejpam-4776	114	1	j.	j.	PROPN
ejpam-4776	114	2	pure	pure	PROPN
ejpam-4776	114	3	appl	appl	PROPN
ejpam-4776	114	4	.	.	PROPN
ejpam-4776	114	5	math	math	PROPN
ejpam-4776	114	6	,	,	PUNCT
ejpam-4776	114	7	16	16	NUM
ejpam-4776	114	8	(	(	PUNCT
ejpam-4776	114	9	2	2	NUM
ejpam-4776	114	10	)	)	PUNCT
ejpam-4776	114	11	(	(	PUNCT
ejpam-4776	114	12	2023	2023	NUM
ejpam-4776	114	13	)	)	PUNCT
ejpam-4776	114	14	,	,	PUNCT
ejpam-4776	114	15	1260	1260	NUM
ejpam-4776	114	16	-	-	SYM
ejpam-4776	114	17	1273	1273	NUM
ejpam-4776	114	18	1264	1264	NUM
ejpam-4776	114	19	theorem	theorem	NOUN
ejpam-4776	114	20	3	3	NUM
ejpam-4776	114	21	.	.	PUNCT
ejpam-4776	115	1	every	every	DET
ejpam-4776	115	2	cc	cc	NOUN
ejpam-4776	115	3	-	-	ADJ
ejpam-4776	115	4	completely	completely	ADV
ejpam-4776	115	5	regular	regular	ADJ
ejpam-4776	115	6	space	space	NOUN
ejpam-4776	115	7	is	be	AUX
ejpam-4776	115	8	cc	cc	VERB
ejpam-4776	115	9	-	-	ADJ
ejpam-4776	115	10	almost	almost	ADV
ejpam-4776	115	11	completely	completely	ADV
ejpam-4776	115	12	regular	regular	ADJ
ejpam-4776	115	13	.	.	PUNCT
ejpam-4776	116	1	proof	proof	NOUN
ejpam-4776	116	2	.	.	PUNCT
ejpam-4776	117	1	by	by	ADP
ejpam-4776	117	2	assumption	assumption	NOUN
ejpam-4776	117	3	,	,	PUNCT
ejpam-4776	117	4	there	there	PRON
ejpam-4776	117	5	exist	exist	VERB
ejpam-4776	117	6	a	a	DET
ejpam-4776	117	7	completely	completely	ADV
ejpam-4776	117	8	regular	regular	ADJ
ejpam-4776	117	9	space	space	NOUN
ejpam-4776	117	10	y	y	PROPN
ejpam-4776	117	11	and	and	CCONJ
ejpam-4776	117	12	a	a	DET
ejpam-4776	117	13	bijective	bijective	ADJ
ejpam-4776	117	14	function	function	NOUN
ejpam-4776	118	1	f	f	NOUN
ejpam-4776	118	2	:	:	PUNCT
ejpam-4776	118	3	x	x	X
ejpam-4776	118	4	→	→	SYM
ejpam-4776	118	5	y	y	PROPN
ejpam-4776	118	6	such	such	ADJ
ejpam-4776	118	7	that	that	SCONJ
ejpam-4776	118	8	the	the	DET
ejpam-4776	118	9	restriction	restriction	NOUN
ejpam-4776	118	10	function	function	NOUN
ejpam-4776	118	11	f	f	PROPN
ejpam-4776	118	12	|a	|a	VERB
ejpam-4776	118	13	:	:	PUNCT
ejpam-4776	118	14	a	a	DET
ejpam-4776	118	15	→	→	SYM
ejpam-4776	118	16	f(a	f(a	NOUN
ejpam-4776	118	17	)	)	PUNCT
ejpam-4776	118	18	is	be	AUX
ejpam-4776	118	19	a	a	DET
ejpam-4776	118	20	homeomorphism	homeomorphism	NOUN
ejpam-4776	118	21	for	for	ADP
ejpam-4776	118	22	each	each	DET
ejpam-4776	118	23	countably	countably	ADV
ejpam-4776	118	24	compact	compact	ADJ
ejpam-4776	118	25	subsets	subset	NOUN
ejpam-4776	118	26	a	a	DET
ejpam-4776	118	27	⊆	⊆	NUM
ejpam-4776	118	28	x.	x.	NOUN
ejpam-4776	118	29	since	since	SCONJ
ejpam-4776	118	30	every	every	DET
ejpam-4776	118	31	completely	completely	ADV
ejpam-4776	118	32	regular	regular	ADJ
ejpam-4776	118	33	space	space	NOUN
ejpam-4776	118	34	is	be	AUX
ejpam-4776	118	35	almost	almost	ADV
ejpam-4776	118	36	completely	completely	ADV
ejpam-4776	118	37	regular	regular	ADJ
ejpam-4776	118	38	[	[	X
ejpam-4776	118	39	21	21	NUM
ejpam-4776	118	40	]	]	PUNCT
ejpam-4776	118	41	,	,	PUNCT
ejpam-4776	118	42	we	we	PRON
ejpam-4776	118	43	obtain	obtain	VERB
ejpam-4776	118	44	:	:	PUNCT
ejpam-4776	118	45	y	y	PROPN
ejpam-4776	118	46	is	be	AUX
ejpam-4776	118	47	an	an	DET
ejpam-4776	118	48	almost	almost	ADV
ejpam-4776	118	49	completely	completely	ADV
ejpam-4776	118	50	regular	regular	ADJ
ejpam-4776	118	51	space	space	NOUN
ejpam-4776	118	52	.	.	PUNCT
ejpam-4776	119	1	therefore	therefore	ADV
ejpam-4776	119	2	,	,	PUNCT
ejpam-4776	119	3	x	x	X
ejpam-4776	119	4	is	be	AUX
ejpam-4776	119	5	cc	cc	VERB
ejpam-4776	119	6	-	-	ADJ
ejpam-4776	119	7	almost	almost	ADV
ejpam-4776	119	8	completely	completely	ADV
ejpam-4776	119	9	regular	regular	ADJ
ejpam-4776	119	10	.	.	PUNCT
ejpam-4776	120	1	similarly	similarly	ADV
ejpam-4776	120	2	,	,	PUNCT
ejpam-4776	120	3	every	every	DET
ejpam-4776	120	4	cc	cc	NOUN
ejpam-4776	120	5	-	-	ADJ
ejpam-4776	120	6	completely	completely	ADV
ejpam-4776	120	7	regular	regular	ADJ
ejpam-4776	120	8	space	space	NOUN
ejpam-4776	120	9	is	be	AUX
ejpam-4776	120	10	cc	cc	NOUN
ejpam-4776	120	11	-	-	ADJ
ejpam-4776	120	12	regular	regular	ADJ
ejpam-4776	120	13	,	,	PUNCT
ejpam-4776	120	14	every	every	DET
ejpam-4776	120	15	cc	cc	NOUN
ejpam-4776	120	16	-	-	ADJ
ejpam-4776	120	17	regular	regular	ADJ
ejpam-4776	120	18	space	space	NOUN
ejpam-4776	120	19	is	be	AUX
ejpam-4776	120	20	cc	cc	VERB
ejpam-4776	120	21	-	-	ADJ
ejpam-4776	120	22	almost	almost	ADV
ejpam-4776	120	23	regular	regular	ADJ
ejpam-4776	120	24	,	,	PUNCT
ejpam-4776	120	25	every	every	DET
ejpam-4776	120	26	cc	cc	NOUN
ejpam-4776	120	27	-	-	ADJ
ejpam-4776	120	28	almost	almost	ADV
ejpam-4776	120	29	completely	completely	ADV
ejpam-4776	120	30	regular	regular	ADJ
ejpam-4776	120	31	space	space	NOUN
ejpam-4776	120	32	is	be	AUX
ejpam-4776	120	33	cc	cc	VERB
ejpam-4776	120	34	-	-	ADJ
ejpam-4776	120	35	almost	almost	ADV
ejpam-4776	120	36	regular	regular	ADJ
ejpam-4776	120	37	,	,	PUNCT
ejpam-4776	120	38	every	every	DET
ejpam-4776	120	39	cc	cc	NOUN
ejpam-4776	120	40	-	-	PUNCT
ejpam-4776	120	41	tychonoff	tychonoff	NOUN
ejpam-4776	120	42	space	space	NOUN
ejpam-4776	120	43	is	be	AUX
ejpam-4776	120	44	cc	cc	VERB
ejpam-4776	120	45	-	-	ADJ
ejpam-4776	120	46	completely	completely	ADV
ejpam-4776	120	47	regular	regular	ADJ
ejpam-4776	120	48	,	,	PUNCT
ejpam-4776	120	49	every	every	DET
ejpam-4776	120	50	cct3	cct3	PROPN
ejpam-4776	120	51	-	-	PUNCT
ejpam-4776	120	52	space	space	NOUN
ejpam-4776	120	53	is	be	AUX
ejpam-4776	120	54	cc	cc	VERB
ejpam-4776	120	55	-	-	ADJ
ejpam-4776	120	56	regular	regular	ADJ
ejpam-4776	120	57	and	and	CCONJ
ejpam-4776	120	58	every	every	DET
ejpam-4776	120	59	cc	cc	NOUN
ejpam-4776	120	60	-	-	PUNCT
ejpam-4776	120	61	tychonoff	tychonoff	NOUN
ejpam-4776	120	62	space	space	NOUN
ejpam-4776	120	63	is	be	AUX
ejpam-4776	120	64	cct3	cct3	PROPN
ejpam-4776	120	65	.	.	PUNCT
ejpam-4776	121	1	the	the	DET
ejpam-4776	121	2	converses	converse	NOUN
ejpam-4776	121	3	of	of	ADP
ejpam-4776	121	4	theorem	theorem	NOUN
ejpam-4776	121	5	3	3	NUM
ejpam-4776	121	6	and	and	CCONJ
ejpam-4776	121	7	stated	state	VERB
ejpam-4776	121	8	facts	fact	NOUN
ejpam-4776	121	9	are	be	AUX
ejpam-4776	121	10	not	not	PART
ejpam-4776	121	11	true	true	ADJ
ejpam-4776	121	12	in	in	ADP
ejpam-4776	121	13	general	general	ADJ
ejpam-4776	121	14	.	.	PUNCT
ejpam-4776	122	1	here	here	ADV
ejpam-4776	122	2	is	be	AUX
ejpam-4776	122	3	an	an	DET
ejpam-4776	122	4	example	example	NOUN
ejpam-4776	122	5	of	of	ADP
ejpam-4776	122	6	a	a	DET
ejpam-4776	122	7	cc	cc	NOUN
ejpam-4776	122	8	-	-	ADJ
ejpam-4776	122	9	normal	normal	ADJ
ejpam-4776	122	10	and	and	CCONJ
ejpam-4776	122	11	cc	cc	NOUN
ejpam-4776	122	12	-	-	PUNCT
ejpam-4776	122	13	almost	almost	ADV
ejpam-4776	122	14	completely	completely	ADV
ejpam-4776	122	15	regular	regular	ADJ
ejpam-4776	122	16	space	space	NOUN
ejpam-4776	122	17	,	,	PUNCT
ejpam-4776	122	18	which	which	PRON
ejpam-4776	122	19	is	be	AUX
ejpam-4776	122	20	neither	neither	DET
ejpam-4776	122	21	cc	cc	NOUN
ejpam-4776	122	22	-	-	ADJ
ejpam-4776	122	23	completely	completely	ADV
ejpam-4776	122	24	regular	regular	ADJ
ejpam-4776	122	25	,	,	PUNCT
ejpam-4776	122	26	cct3	cct3	PROPN
ejpam-4776	122	27	,	,	PUNCT
ejpam-4776	122	28	cc	cc	NOUN
ejpam-4776	122	29	-	-	NOUN
ejpam-4776	122	30	tychonoff	tychonoff	NOUN
ejpam-4776	122	31	nor	nor	CCONJ
ejpam-4776	122	32	cc	cc	NOUN
ejpam-4776	122	33	-	-	ADJ
ejpam-4776	122	34	regular	regular	ADJ
ejpam-4776	122	35	.	.	PUNCT
ejpam-4776	122	36	example	example	NOUN
ejpam-4776	123	1	4	4	NUM
ejpam-4776	123	2	.	.	PUNCT
ejpam-4776	124	1	the	the	DET
ejpam-4776	124	2	left	left	ADJ
ejpam-4776	124	3	ray	ray	NOUN
ejpam-4776	124	4	topology	topology	NOUN
ejpam-4776	124	5	(	(	PUNCT
ejpam-4776	124	6	r	r	NOUN
ejpam-4776	124	7	,	,	PUNCT
ejpam-4776	124	8	l	l	NOUN
ejpam-4776	124	9	)	)	PUNCT
ejpam-4776	124	10	is	be	AUX
ejpam-4776	124	11	a	a	DET
ejpam-4776	124	12	normal	normal	ADJ
ejpam-4776	124	13	second	second	ADJ
ejpam-4776	124	14	countable	countable	ADJ
ejpam-4776	124	15	and	and	CCONJ
ejpam-4776	124	16	almost	almost	ADV
ejpam-4776	124	17	completely	completely	ADV
ejpam-4776	124	18	regular	regular	ADJ
ejpam-4776	124	19	space	space	NOUN
ejpam-4776	124	20	[	[	X
ejpam-4776	124	21	23	23	NUM
ejpam-4776	124	22	]	]	PUNCT
ejpam-4776	124	23	.	.	PUNCT
ejpam-4776	125	1	therefore	therefore	ADV
ejpam-4776	125	2	,	,	PUNCT
ejpam-4776	125	3	(	(	PUNCT
ejpam-4776	125	4	r	r	NOUN
ejpam-4776	125	5	,	,	PUNCT
ejpam-4776	125	6	l	l	NOUN
ejpam-4776	125	7	)	)	PUNCT
ejpam-4776	125	8	is	be	AUX
ejpam-4776	125	9	a	a	DET
ejpam-4776	125	10	cc	cc	NOUN
ejpam-4776	125	11	-	-	ADJ
ejpam-4776	125	12	normal	normal	ADJ
ejpam-4776	125	13	and	and	CCONJ
ejpam-4776	125	14	cc	cc	NOUN
ejpam-4776	125	15	-	-	PUNCT
ejpam-4776	125	16	almost	almost	ADV
ejpam-4776	125	17	completely	completely	ADV
ejpam-4776	125	18	regular	regular	ADJ
ejpam-4776	125	19	space	space	NOUN
ejpam-4776	125	20	,	,	PUNCT
ejpam-4776	125	21	which	which	PRON
ejpam-4776	125	22	is	be	AUX
ejpam-4776	125	23	neither	neither	CCONJ
ejpam-4776	125	24	cct3	cct3	PROPN
ejpam-4776	125	25	,	,	PUNCT
ejpam-4776	125	26	cc	cc	NOUN
ejpam-4776	125	27	-	-	ADJ
ejpam-4776	125	28	regular	regular	ADJ
ejpam-4776	125	29	,	,	PUNCT
ejpam-4776	125	30	cc	cc	NOUN
ejpam-4776	125	31	-	-	NOUN
ejpam-4776	125	32	tychonoff	tychonoff	NOUN
ejpam-4776	125	33	nor	nor	CCONJ
ejpam-4776	125	34	cc	cc	NOUN
ejpam-4776	125	35	-	-	ADJ
ejpam-4776	125	36	completely	completely	ADV
ejpam-4776	125	37	regular	regular	ADJ
ejpam-4776	125	38	because	because	SCONJ
ejpam-4776	125	39	it	it	PRON
ejpam-4776	125	40	is	be	AUX
ejpam-4776	125	41	not	not	PART
ejpam-4776	125	42	c	c	NOUN
ejpam-4776	125	43	-	-	NOUN
ejpam-4776	125	44	regular	regular	ADJ
ejpam-4776	125	45	[	[	X
ejpam-4776	125	46	5	5	NUM
ejpam-4776	125	47	]	]	PUNCT
ejpam-4776	125	48	.	.	PUNCT
ejpam-4776	126	1	the	the	DET
ejpam-4776	126	2	next	next	ADJ
ejpam-4776	126	3	example	example	NOUN
ejpam-4776	126	4	is	be	AUX
ejpam-4776	126	5	of	of	ADP
ejpam-4776	126	6	a	a	DET
ejpam-4776	126	7	cc	cc	NOUN
ejpam-4776	126	8	-	-	ADJ
ejpam-4776	126	9	completely	completely	ADV
ejpam-4776	126	10	regular	regular	ADJ
ejpam-4776	126	11	space	space	NOUN
ejpam-4776	126	12	which	which	PRON
ejpam-4776	126	13	is	be	AUX
ejpam-4776	126	14	neither	neither	CCONJ
ejpam-4776	126	15	cct3	cct3	PROPN
ejpam-4776	126	16	nor	nor	CCONJ
ejpam-4776	126	17	cc	cc	NOUN
ejpam-4776	126	18	-	-	NOUN
ejpam-4776	126	19	tychonoff	tychonoff	NOUN
ejpam-4776	126	20	.	.	PUNCT
ejpam-4776	127	1	example	example	NOUN
ejpam-4776	127	2	5	5	NUM
ejpam-4776	127	3	.	.	PUNCT
ejpam-4776	128	1	the	the	DET
ejpam-4776	128	2	odd	odd	ADV
ejpam-4776	128	3	-	-	PUNCT
ejpam-4776	128	4	even	even	ADV
ejpam-4776	128	5	topology	topology	NOUN
ejpam-4776	128	6	[	[	X
ejpam-4776	128	7	23	23	NUM
ejpam-4776	128	8	,	,	PUNCT
ejpam-4776	128	9	example	example	NOUN
ejpam-4776	128	10	6	6	NUM
ejpam-4776	128	11	]	]	PUNCT
ejpam-4776	128	12	,	,	PUNCT
ejpam-4776	128	13	is	be	AUX
ejpam-4776	128	14	a	a	DET
ejpam-4776	128	15	regular	regular	ADJ
ejpam-4776	128	16	,	,	PUNCT
ejpam-4776	128	17	completely	completely	ADV
ejpam-4776	128	18	regular	regular	ADJ
ejpam-4776	128	19	,	,	PUNCT
ejpam-4776	128	20	normal	normal	ADJ
ejpam-4776	128	21	,	,	PUNCT
ejpam-4776	128	22	locally	locally	ADV
ejpam-4776	128	23	compact	compact	ADJ
ejpam-4776	128	24	,	,	PUNCT
ejpam-4776	128	25	paracompact	paracompact	ADJ
ejpam-4776	128	26	,	,	PUNCT
ejpam-4776	128	27	separable	separable	ADJ
ejpam-4776	128	28	,	,	PUNCT
ejpam-4776	128	29	second	second	ADJ
ejpam-4776	128	30	countable	countable	ADJ
ejpam-4776	128	31	space	space	NOUN
ejpam-4776	128	32	,	,	PUNCT
ejpam-4776	128	33	which	which	PRON
ejpam-4776	128	34	is	be	AUX
ejpam-4776	128	35	neither	neither	DET
ejpam-4776	128	36	t0	t0	NOUN
ejpam-4776	128	37	,	,	PUNCT
ejpam-4776	128	38	compact	compact	ADJ
ejpam-4776	128	39	,	,	PUNCT
ejpam-4776	128	40	countably	countably	ADV
ejpam-4776	128	41	compact	compact	ADJ
ejpam-4776	128	42	nor	nor	CCONJ
ejpam-4776	128	43	semi	semi	ADV
ejpam-4776	128	44	regular	regular	ADJ
ejpam-4776	128	45	[	[	X
ejpam-4776	128	46	23	23	NUM
ejpam-4776	128	47	]	]	PUNCT
ejpam-4776	128	48	.	.	PUNCT
ejpam-4776	129	1	so	so	ADV
ejpam-4776	129	2	,	,	PUNCT
ejpam-4776	129	3	the	the	DET
ejpam-4776	129	4	odd	odd	ADV
ejpam-4776	129	5	-	-	PUNCT
ejpam-4776	129	6	even	even	ADJ
ejpam-4776	129	7	topology	topology	NOUN
ejpam-4776	129	8	is	be	AUX
ejpam-4776	129	9	a	a	DET
ejpam-4776	129	10	cc	cc	NOUN
ejpam-4776	129	11	-	-	NOUN
ejpam-4776	129	12	regular	regular	ADJ
ejpam-4776	129	13	,	,	PUNCT
ejpam-4776	129	14	cc	cc	NOUN
ejpam-4776	129	15	-	-	ADJ
ejpam-4776	129	16	completely	completely	ADV
ejpam-4776	129	17	regular	regular	ADJ
ejpam-4776	129	18	,	,	PUNCT
ejpam-4776	129	19	cc	cc	NOUN
ejpam-4776	129	20	-	-	ADJ
ejpam-4776	129	21	normal	normal	ADJ
ejpam-4776	129	22	and	and	CCONJ
ejpam-4776	129	23	cc	cc	NOUN
ejpam-4776	129	24	-	-	PUNCT
ejpam-4776	129	25	almost	almost	ADV
ejpam-4776	129	26	completely	completely	ADV
ejpam-4776	129	27	regular	regular	ADJ
ejpam-4776	129	28	space	space	NOUN
ejpam-4776	129	29	,	,	PUNCT
ejpam-4776	129	30	which	which	PRON
ejpam-4776	129	31	is	be	AUX
ejpam-4776	129	32	neither	neither	DET
ejpam-4776	129	33	epi	epi	NOUN
ejpam-4776	129	34	-	-	ADJ
ejpam-4776	129	35	regular	regular	ADJ
ejpam-4776	129	36	nor	nor	CCONJ
ejpam-4776	129	37	epi	epi	NOUN
ejpam-4776	129	38	-	-	ADJ
ejpam-4776	129	39	mildly	mildly	ADV
ejpam-4776	129	40	normal	normal	ADJ
ejpam-4776	129	41	.	.	PUNCT
ejpam-4776	130	1	observe	observe	VERB
ejpam-4776	130	2	that	that	SCONJ
ejpam-4776	130	3	:	:	PUNCT
ejpam-4776	130	4	the	the	DET
ejpam-4776	130	5	odd	odd	ADJ
ejpam-4776	130	6	even	even	ADV
ejpam-4776	130	7	topology	topology	NOUN
ejpam-4776	130	8	is	be	AUX
ejpam-4776	130	9	neither	neither	PRON
ejpam-4776	130	10	ct3	ct3	NOUN
ejpam-4776	130	11	nor	nor	CCONJ
ejpam-4776	130	12	lt3	lt3	PROPN
ejpam-4776	131	1	[	[	X
ejpam-4776	131	2	2	2	NUM
ejpam-4776	131	3	,	,	PUNCT
ejpam-4776	131	4	24	24	NUM
ejpam-4776	131	5	]	]	PUNCT
ejpam-4776	131	6	.	.	PUNCT
ejpam-4776	132	1	hence	hence	ADV
ejpam-4776	132	2	,	,	PUNCT
ejpam-4776	132	3	it	it	PRON
ejpam-4776	132	4	is	be	AUX
ejpam-4776	132	5	neither	neither	CCONJ
ejpam-4776	132	6	c	c	NOUN
ejpam-4776	132	7	-	-	PUNCT
ejpam-4776	132	8	tychonoff	tychonoff	NOUN
ejpam-4776	132	9	nor	nor	CCONJ
ejpam-4776	132	10	l	l	NOUN
ejpam-4776	132	11	-	-	NOUN
ejpam-4776	132	12	tychonoff	tychonoff	NOUN
ejpam-4776	132	13	.	.	PUNCT
ejpam-4776	133	1	therefore	therefore	ADV
ejpam-4776	133	2	,	,	PUNCT
ejpam-4776	133	3	it	it	PRON
ejpam-4776	133	4	is	be	AUX
ejpam-4776	133	5	neither	neither	DET
ejpam-4776	133	6	cc	cc	NOUN
ejpam-4776	133	7	-	-	NOUN
ejpam-4776	133	8	tychonoff	tychonoff	NOUN
ejpam-4776	133	9	nor	nor	CCONJ
ejpam-4776	133	10	cct3	cct3	PROPN
ejpam-4776	133	11	.	.	PUNCT
ejpam-4776	134	1	therefore	therefore	ADV
ejpam-4776	134	2	,	,	PUNCT
ejpam-4776	134	3	the	the	DET
ejpam-4776	134	4	odd	odd	ADV
ejpam-4776	134	5	-	-	PUNCT
ejpam-4776	134	6	even	even	ADJ
ejpam-4776	134	7	topology	topology	NOUN
ejpam-4776	134	8	is	be	AUX
ejpam-4776	134	9	a	a	DET
ejpam-4776	134	10	cc	cc	NOUN
ejpam-4776	134	11	-	-	ADJ
ejpam-4776	134	12	completely	completely	ADV
ejpam-4776	134	13	regular	regular	ADJ
ejpam-4776	134	14	and	and	CCONJ
ejpam-4776	134	15	cc	cc	NOUN
ejpam-4776	134	16	-	-	ADJ
ejpam-4776	134	17	normal	normal	ADJ
ejpam-4776	134	18	space	space	NOUN
ejpam-4776	134	19	,	,	PUNCT
ejpam-4776	134	20	which	which	PRON
ejpam-4776	134	21	is	be	AUX
ejpam-4776	134	22	neither	neither	DET
ejpam-4776	134	23	cc	cc	NOUN
ejpam-4776	134	24	-	-	NOUN
ejpam-4776	134	25	tychonoff	tychonoff	NOUN
ejpam-4776	134	26	,	,	PUNCT
ejpam-4776	134	27	cct3	cct3	NOUN
ejpam-4776	134	28	nor	nor	CCONJ
ejpam-4776	134	29	epi	epi	NOUN
ejpam-4776	134	30	-	-	NOUN
ejpam-4776	134	31	regular	regular	ADJ
ejpam-4776	134	32	.	.	PUNCT
ejpam-4776	135	1	note	note	VERB
ejpam-4776	135	2	that	that	SCONJ
ejpam-4776	135	3	:	:	PUNCT
ejpam-4776	135	4	the	the	DET
ejpam-4776	135	5	odd	odd	ADJ
ejpam-4776	135	6	even	even	ADV
ejpam-4776	135	7	topology	topology	NOUN
ejpam-4776	135	8	is	be	AUX
ejpam-4776	135	9	c	c	NOUN
ejpam-4776	135	10	-	-	PUNCT
ejpam-4776	135	11	paracompact	paracompact	ADJ
ejpam-4776	135	12	space	space	NOUN
ejpam-4776	135	13	which	which	PRON
ejpam-4776	135	14	is	be	AUX
ejpam-4776	135	15	not	not	PART
ejpam-4776	135	16	cc	cc	NOUN
ejpam-4776	135	17	-	-	NOUN
ejpam-4776	135	18	regular	regular	ADJ
ejpam-4776	135	19	.	.	PUNCT
ejpam-4776	136	1	note	note	VERB
ejpam-4776	136	2	that	that	SCONJ
ejpam-4776	136	3	:	:	PUNCT
ejpam-4776	136	4	cc	cc	NOUN
ejpam-4776	136	5	-	-	NOUN
ejpam-4776	136	6	regularity	regularity	NOUN
ejpam-4776	136	7	does	do	AUX
ejpam-4776	136	8	not	not	PART
ejpam-4776	136	9	imply	imply	VERB
ejpam-4776	136	10	cc	cc	VERB
ejpam-4776	136	11	-	-	ADJ
ejpam-4776	136	12	complete	complete	ADJ
ejpam-4776	136	13	regularity	regularity	NOUN
ejpam-4776	136	14	,	,	PUNCT
ejpam-4776	136	15	cct3	cct3	PROPN
ejpam-4776	136	16	does	do	AUX
ejpam-4776	136	17	not	not	PART
ejpam-4776	136	18	imply	imply	VERB
ejpam-4776	136	19	cc	cc	NOUN
ejpam-4776	136	20	-	-	NOUN
ejpam-4776	136	21	tychonoff	tychonoff	NOUN
ejpam-4776	136	22	and	and	CCONJ
ejpam-4776	136	23	cc	cc	NOUN
ejpam-4776	136	24	-	-	PUNCT
ejpam-4776	136	25	almost	almost	ADV
ejpam-4776	136	26	regularity	regularity	NOUN
ejpam-4776	136	27	does	do	AUX
ejpam-4776	136	28	not	not	PART
ejpam-4776	136	29	imply	imply	VERB
ejpam-4776	136	30	cc	cc	VERB
ejpam-4776	136	31	-	-	ADJ
ejpam-4776	136	32	almost	almost	ADV
ejpam-4776	136	33	complete	complete	ADJ
ejpam-4776	136	34	regularity	regularity	NOUN
ejpam-4776	136	35	.	.	PUNCT
ejpam-4776	137	1	here	here	ADV
ejpam-4776	137	2	is	be	AUX
ejpam-4776	137	3	a	a	DET
ejpam-4776	137	4	counterexample	counterexample	NOUN
ejpam-4776	137	5	:	:	PUNCT
ejpam-4776	137	6	example	example	NOUN
ejpam-4776	137	7	6	6	NUM
ejpam-4776	137	8	.	.	PUNCT
ejpam-4776	138	1	the	the	DET
ejpam-4776	138	2	tychonoff	tychonoff	NOUN
ejpam-4776	138	3	corkscrew	corkscrew	NOUN
ejpam-4776	138	4	topology	topology	NOUN
ejpam-4776	138	5	:	:	PUNCT
ejpam-4776	138	6	[	[	X
ejpam-4776	138	7	23	23	NUM
ejpam-4776	138	8	,	,	PUNCT
ejpam-4776	138	9	example	example	NOUN
ejpam-4776	138	10	90	90	NUM
ejpam-4776	138	11	]	]	PUNCT
ejpam-4776	138	12	,	,	PUNCT
ejpam-4776	138	13	is	be	AUX
ejpam-4776	138	14	a	a	DET
ejpam-4776	138	15	t3	t3	NOUN
ejpam-4776	138	16	,	,	PUNCT
ejpam-4776	138	17	regular	regular	ADJ
ejpam-4776	138	18	,	,	PUNCT
ejpam-4776	138	19	semi	semi	ADV
ejpam-4776	138	20	regular	regular	ADJ
ejpam-4776	138	21	and	and	CCONJ
ejpam-4776	138	22	countably	countably	ADV
ejpam-4776	138	23	compact	compact	ADJ
ejpam-4776	138	24	space	space	NOUN
ejpam-4776	138	25	,	,	PUNCT
ejpam-4776	138	26	which	which	PRON
ejpam-4776	138	27	is	be	AUX
ejpam-4776	138	28	neither	neither	CCONJ
ejpam-4776	138	29	completely	completely	ADV
ejpam-4776	138	30	regular	regular	ADJ
ejpam-4776	138	31	,	,	PUNCT
ejpam-4776	138	32	normal	normal	ADJ
ejpam-4776	138	33	,	,	PUNCT
ejpam-4776	138	34	locally	locally	ADV
ejpam-4776	138	35	compact	compact	ADJ
ejpam-4776	138	36	,	,	PUNCT
ejpam-4776	138	37	lindelöf	lindelöf	PROPN
ejpam-4776	138	38	,	,	PUNCT
ejpam-4776	138	39	second	second	ADV
ejpam-4776	138	40	countable	countable	ADJ
ejpam-4776	138	41	nor	nor	CCONJ
ejpam-4776	138	42	paracompact	paracompact	ADJ
ejpam-4776	138	43	[	[	X
ejpam-4776	138	44	23	23	NUM
ejpam-4776	138	45	]	]	PUNCT
ejpam-4776	138	46	.	.	PUNCT
ejpam-4776	139	1	since	since	SCONJ
ejpam-4776	139	2	x	x	PRON
ejpam-4776	139	3	is	be	AUX
ejpam-4776	139	4	a	a	DET
ejpam-4776	139	5	t3	t3	NOUN
ejpam-4776	139	6	-	-	PUNCT
ejpam-4776	139	7	space	space	NOUN
ejpam-4776	139	8	,	,	PUNCT
ejpam-4776	139	9	it	it	PRON
ejpam-4776	139	10	is	be	AUX
ejpam-4776	139	11	epi	epi	NOUN
ejpam-4776	139	12	-	-	ADJ
ejpam-4776	139	13	regular	regular	ADJ
ejpam-4776	139	14	,	,	PUNCT
ejpam-4776	139	15	cct3	cct3	PROPN
ejpam-4776	139	16	and	and	CCONJ
ejpam-4776	139	17	cc	cc	NOUN
ejpam-4776	139	18	-	-	NOUN
ejpam-4776	139	19	regular	regular	ADJ
ejpam-4776	139	20	.	.	PUNCT
ejpam-4776	140	1	since	since	SCONJ
ejpam-4776	140	2	x	x	PRON
ejpam-4776	140	3	is	be	AUX
ejpam-4776	140	4	countably	countably	ADV
ejpam-4776	140	5	compact	compact	ADJ
ejpam-4776	140	6	space	space	NOUN
ejpam-4776	140	7	which	which	PRON
ejpam-4776	140	8	is	be	AUX
ejpam-4776	140	9	neither	neither	CCONJ
ejpam-4776	140	10	almost	almost	ADV
ejpam-4776	140	11	completely	completely	ADV
ejpam-4776	140	12	regular	regular	ADJ
ejpam-4776	140	13	nor	nor	CCONJ
ejpam-4776	140	14	epi	epi	NOUN
ejpam-4776	140	15	-	-	ADJ
ejpam-4776	140	16	completely	completely	ADV
ejpam-4776	140	17	regular	regular	ADJ
ejpam-4776	140	18	[	[	X
ejpam-4776	140	19	4	4	NUM
ejpam-4776	140	20	]	]	PUNCT
ejpam-4776	140	21	,	,	PUNCT
ejpam-4776	140	22	we	we	PRON
ejpam-4776	140	23	conclude	conclude	VERB
ejpam-4776	140	24	that	that	PRON
ejpam-4776	140	25	:	:	PUNCT
ejpam-4776	140	26	it	it	PRON
ejpam-4776	140	27	is	be	AUX
ejpam-4776	140	28	neither	neither	DET
ejpam-4776	140	29	cc	cc	NOUN
ejpam-4776	140	30	-	-	ADJ
ejpam-4776	140	31	completely	completely	ADV
ejpam-4776	140	32	regular	regular	ADJ
ejpam-4776	140	33	,	,	PUNCT
ejpam-4776	140	34	cc	cc	NOUN
ejpam-4776	140	35	-	-	NOUN
ejpam-4776	140	36	tychonoff	tychonoff	NOUN
ejpam-4776	140	37	nor	nor	CCONJ
ejpam-4776	140	38	cc	cc	NOUN
ejpam-4776	140	39	-	-	ADJ
ejpam-4776	140	40	almost	almost	ADV
ejpam-4776	140	41	completely	completely	ADV
ejpam-4776	140	42	regular	regular	ADJ
ejpam-4776	140	43	.	.	PUNCT
ejpam-4776	141	1	therefore	therefore	ADV
ejpam-4776	141	2	,	,	PUNCT
ejpam-4776	141	3	the	the	DET
ejpam-4776	141	4	tychonoff	tychonoff	NOUN
ejpam-4776	141	5	corkscrew	corkscrew	NOUN
ejpam-4776	141	6	topology	topology	NOUN
ejpam-4776	141	7	is	be	AUX
ejpam-4776	141	8	a	a	DET
ejpam-4776	141	9	cc	cc	NOUN
ejpam-4776	141	10	-	-	NOUN
ejpam-4776	141	11	regular	regular	ADJ
ejpam-4776	141	12	,	,	PUNCT
ejpam-4776	141	13	cct3	cct3	PROPN
ejpam-4776	141	14	and	and	CCONJ
ejpam-4776	141	15	cc	cc	NOUN
ejpam-4776	141	16	-	-	PUNCT
ejpam-4776	141	17	almost	almost	ADV
ejpam-4776	141	18	regular	regular	ADJ
ejpam-4776	141	19	space	space	NOUN
ejpam-4776	141	20	,	,	PUNCT
ejpam-4776	141	21	which	which	PRON
ejpam-4776	141	22	is	be	AUX
ejpam-4776	141	23	neither	neither	DET
ejpam-4776	141	24	cc	cc	NOUN
ejpam-4776	141	25	-	-	ADJ
ejpam-4776	141	26	completely	completely	ADV
ejpam-4776	141	27	regular	regular	ADJ
ejpam-4776	141	28	,	,	PUNCT
ejpam-4776	141	29	cc	cc	NOUN
ejpam-4776	141	30	-	-	NOUN
ejpam-4776	141	31	tychonoff	tychonoff	NOUN
ejpam-4776	141	32	nor	nor	CCONJ
ejpam-4776	141	33	cc	cc	NOUN
ejpam-4776	141	34	-	-	ADJ
ejpam-4776	141	35	almost	almost	ADV
ejpam-4776	141	36	completely	completely	ADV
ejpam-4776	141	37	regular	regular	ADJ
ejpam-4776	141	38	.	.	PUNCT
ejpam-4776	142	1	s.	s.	PROPN
ejpam-4776	142	2	a.	a.	PROPN
ejpam-4776	142	3	thabit	thabit	PROPN
ejpam-4776	142	4	,	,	PUNCT
ejpam-4776	142	5	w.	w.	PROPN
ejpam-4776	142	6	alqurashi	alqurashi	PROPN
ejpam-4776	142	7	/	/	SYM
ejpam-4776	142	8	eur	eur	PROPN
ejpam-4776	142	9	.	.	PUNCT
ejpam-4776	143	1	j.	j.	PROPN
ejpam-4776	143	2	pure	pure	PROPN
ejpam-4776	143	3	appl	appl	PROPN
ejpam-4776	143	4	.	.	PROPN
ejpam-4776	143	5	math	math	PROPN
ejpam-4776	143	6	,	,	PUNCT
ejpam-4776	143	7	16	16	NUM
ejpam-4776	143	8	(	(	PUNCT
ejpam-4776	143	9	2	2	NUM
ejpam-4776	143	10	)	)	PUNCT
ejpam-4776	143	11	(	(	PUNCT
ejpam-4776	143	12	2023	2023	NUM
ejpam-4776	143	13	)	)	PUNCT
ejpam-4776	143	14	,	,	PUNCT
ejpam-4776	143	15	1260	1260	NUM
ejpam-4776	143	16	-	-	SYM
ejpam-4776	143	17	1273	1273	NUM
ejpam-4776	143	18	1265	1265	NUM
ejpam-4776	143	19	observed	observe	VERB
ejpam-4776	143	20	that	that	SCONJ
ejpam-4776	143	21	:	:	PUNCT
ejpam-4776	143	22	any	any	DET
ejpam-4776	143	23	uncountable	uncountable	ADJ
ejpam-4776	143	24	indiscrete	indiscrete	ADJ
ejpam-4776	143	25	space	space	NOUN
ejpam-4776	143	26	x	x	PUNCT
ejpam-4776	143	27	is	be	AUX
ejpam-4776	143	28	a	a	DET
ejpam-4776	143	29	cc	cc	NOUN
ejpam-4776	143	30	-	-	ADJ
ejpam-4776	143	31	normal	normal	ADJ
ejpam-4776	143	32	,	,	PUNCT
ejpam-4776	143	33	cc	cc	NOUN
ejpam-4776	143	34	-	-	ADJ
ejpam-4776	143	35	regular	regular	ADJ
ejpam-4776	143	36	,	,	PUNCT
ejpam-4776	143	37	cc	cc	NOUN
ejpam-4776	143	38	-	-	ADJ
ejpam-4776	143	39	completely	completely	ADV
ejpam-4776	143	40	regular	regular	ADJ
ejpam-4776	143	41	and	and	CCONJ
ejpam-4776	143	42	cc	cc	NOUN
ejpam-4776	143	43	-	-	PUNCT
ejpam-4776	143	44	almost	almost	ADV
ejpam-4776	143	45	completely	completely	ADV
ejpam-4776	143	46	regular	regular	ADJ
ejpam-4776	143	47	space	space	NOUN
ejpam-4776	143	48	which	which	PRON
ejpam-4776	143	49	is	be	AUX
ejpam-4776	143	50	neither	neither	DET
ejpam-4776	143	51	epi	epi	NOUN
ejpam-4776	143	52	-	-	NOUN
ejpam-4776	143	53	regular	regular	ADJ
ejpam-4776	143	54	,	,	PUNCT
ejpam-4776	143	55	cc	cc	NOUN
ejpam-4776	143	56	-	-	NOUN
ejpam-4776	143	57	tychonoff	tychonoff	NOUN
ejpam-4776	143	58	nor	nor	CCONJ
ejpam-4776	143	59	cct3	cct3	PROPN
ejpam-4776	143	60	.	.	PUNCT
ejpam-4776	144	1	the	the	DET
ejpam-4776	144	2	following	following	ADJ
ejpam-4776	144	3	example	example	NOUN
ejpam-4776	144	4	is	be	AUX
ejpam-4776	144	5	a	a	DET
ejpam-4776	144	6	cc	cc	NOUN
ejpam-4776	144	7	-	-	ADJ
ejpam-4776	144	8	almost	almost	ADV
ejpam-4776	144	9	completely	completely	ADV
ejpam-4776	144	10	regular	regular	ADJ
ejpam-4776	144	11	space	space	NOUN
ejpam-4776	144	12	,	,	PUNCT
ejpam-4776	144	13	which	which	PRON
ejpam-4776	144	14	is	be	AUX
ejpam-4776	144	15	neither	neither	CCONJ
ejpam-4776	144	16	cct3	cct3	PROPN
ejpam-4776	144	17	,	,	PUNCT
ejpam-4776	144	18	cc	cc	NOUN
ejpam-4776	144	19	-	-	ADJ
ejpam-4776	144	20	normal	normal	ADJ
ejpam-4776	144	21	nor	nor	CCONJ
ejpam-4776	144	22	cc	cc	NOUN
ejpam-4776	144	23	-	-	ADJ
ejpam-4776	144	24	regular	regular	ADJ
ejpam-4776	144	25	.	.	PUNCT
ejpam-4776	144	26	example	example	NOUN
ejpam-4776	145	1	7	7	NUM
ejpam-4776	145	2	.	.	PUNCT
ejpam-4776	146	1	the	the	DET
ejpam-4776	146	2	particular	particular	ADJ
ejpam-4776	146	3	point	point	NOUN
ejpam-4776	146	4	topology	topology	NOUN
ejpam-4776	146	5	:	:	PUNCT
ejpam-4776	146	6	[	[	X
ejpam-4776	146	7	23	23	NUM
ejpam-4776	146	8	,	,	PUNCT
ejpam-4776	146	9	example	example	NOUN
ejpam-4776	146	10	10	10	NUM
ejpam-4776	146	11	]	]	PUNCT
ejpam-4776	146	12	,	,	PUNCT
ejpam-4776	146	13	(	(	PUNCT
ejpam-4776	146	14	r	r	NOUN
ejpam-4776	146	15	,	,	PUNCT
ejpam-4776	146	16	tp	tp	NOUN
ejpam-4776	146	17	)	)	PUNCT
ejpam-4776	146	18	is	be	AUX
ejpam-4776	146	19	a	a	DET
ejpam-4776	146	20	separable	separable	ADJ
ejpam-4776	146	21	first	first	ADJ
ejpam-4776	146	22	countable	countable	ADJ
ejpam-4776	146	23	space	space	NOUN
ejpam-4776	146	24	which	which	PRON
ejpam-4776	146	25	is	be	AUX
ejpam-4776	146	26	neither	neither	DET
ejpam-4776	146	27	hausdorff	hausdorff	NOUN
ejpam-4776	146	28	,	,	PUNCT
ejpam-4776	146	29	paracompact	paracompact	ADJ
ejpam-4776	146	30	,	,	PUNCT
ejpam-4776	146	31	regular	regular	ADJ
ejpam-4776	146	32	nor	nor	CCONJ
ejpam-4776	146	33	normal	normal	ADJ
ejpam-4776	146	34	[	[	X
ejpam-4776	146	35	23	23	NUM
ejpam-4776	146	36	]	]	PUNCT
ejpam-4776	146	37	.	.	PUNCT
ejpam-4776	147	1	(	(	PUNCT
ejpam-4776	147	2	r	r	NOUN
ejpam-4776	147	3	,	,	PUNCT
ejpam-4776	147	4	tp	tp	NOUN
ejpam-4776	147	5	)	)	PUNCT
ejpam-4776	147	6	is	be	AUX
ejpam-4776	147	7	neither	neither	CCONJ
ejpam-4776	147	8	a	a	DET
ejpam-4776	147	9	c	c	NOUN
ejpam-4776	147	10	-	-	ADJ
ejpam-4776	147	11	regular	regular	ADJ
ejpam-4776	147	12	nor	nor	CCONJ
ejpam-4776	147	13	c	c	NOUN
ejpam-4776	147	14	-	-	PUNCT
ejpam-4776	147	15	normal	normal	ADJ
ejpam-4776	147	16	space	space	NOUN
ejpam-4776	147	17	[	[	X
ejpam-4776	147	18	5	5	NUM
ejpam-4776	147	19	,	,	PUNCT
ejpam-4776	147	20	7	7	NUM
ejpam-4776	147	21	]	]	PUNCT
ejpam-4776	147	22	.	.	PUNCT
ejpam-4776	148	1	then	then	ADV
ejpam-4776	148	2	,	,	PUNCT
ejpam-4776	148	3	it	it	PRON
ejpam-4776	148	4	is	be	AUX
ejpam-4776	148	5	neither	neither	DET
ejpam-4776	148	6	cc	cc	NOUN
ejpam-4776	148	7	-	-	ADJ
ejpam-4776	148	8	regular	regular	ADJ
ejpam-4776	148	9	nor	nor	CCONJ
ejpam-4776	148	10	cc	cc	NOUN
ejpam-4776	148	11	-	-	ADJ
ejpam-4776	148	12	normal	normal	ADJ
ejpam-4776	148	13	.	.	PUNCT
ejpam-4776	149	1	since	since	SCONJ
ejpam-4776	149	2	the	the	DET
ejpam-4776	149	3	particular	particular	ADJ
ejpam-4776	149	4	point	point	NOUN
ejpam-4776	149	5	topology	topology	NOUN
ejpam-4776	149	6	(	(	PUNCT
ejpam-4776	149	7	r	r	NOUN
ejpam-4776	149	8	,	,	PUNCT
ejpam-4776	149	9	tp	tp	NOUN
ejpam-4776	149	10	)	)	PUNCT
ejpam-4776	149	11	is	be	AUX
ejpam-4776	149	12	an	an	DET
ejpam-4776	149	13	almost	almost	ADV
ejpam-4776	149	14	completely	completely	ADV
ejpam-4776	149	15	regular	regular	ADJ
ejpam-4776	149	16	space	space	NOUN
ejpam-4776	149	17	,	,	PUNCT
ejpam-4776	149	18	it	it	PRON
ejpam-4776	149	19	is	be	AUX
ejpam-4776	149	20	both	both	PRON
ejpam-4776	149	21	cc	cc	NOUN
ejpam-4776	149	22	-	-	ADJ
ejpam-4776	149	23	almost	almost	ADV
ejpam-4776	149	24	regular	regular	ADJ
ejpam-4776	149	25	and	and	CCONJ
ejpam-4776	149	26	cc	cc	NOUN
ejpam-4776	149	27	-	-	PUNCT
ejpam-4776	149	28	almost	almost	ADV
ejpam-4776	149	29	completely	completely	ADV
ejpam-4776	149	30	regular	regular	ADJ
ejpam-4776	149	31	.	.	PUNCT
ejpam-4776	150	1	therefore	therefore	ADV
ejpam-4776	150	2	,	,	PUNCT
ejpam-4776	150	3	(	(	PUNCT
ejpam-4776	150	4	r	r	NOUN
ejpam-4776	150	5	,	,	PUNCT
ejpam-4776	150	6	tp	tp	NOUN
ejpam-4776	150	7	)	)	PUNCT
ejpam-4776	150	8	is	be	AUX
ejpam-4776	150	9	a	a	DET
ejpam-4776	150	10	cc	cc	NOUN
ejpam-4776	150	11	-	-	ADJ
ejpam-4776	150	12	almost	almost	ADV
ejpam-4776	150	13	regular	regular	ADJ
ejpam-4776	150	14	and	and	CCONJ
ejpam-4776	150	15	cc	cc	NOUN
ejpam-4776	150	16	-	-	PUNCT
ejpam-4776	150	17	almost	almost	ADV
ejpam-4776	150	18	completely	completely	ADV
ejpam-4776	150	19	regular	regular	ADJ
ejpam-4776	150	20	space	space	NOUN
ejpam-4776	150	21	,	,	PUNCT
ejpam-4776	150	22	which	which	PRON
ejpam-4776	150	23	is	be	AUX
ejpam-4776	150	24	neither	neither	DET
ejpam-4776	150	25	cc	cc	NOUN
ejpam-4776	150	26	-	-	ADJ
ejpam-4776	150	27	regular	regular	ADJ
ejpam-4776	150	28	,	,	PUNCT
ejpam-4776	150	29	cct3	cct3	PROPN
ejpam-4776	150	30	,	,	PUNCT
ejpam-4776	150	31	cc	cc	NOUN
ejpam-4776	150	32	-	-	ADJ
ejpam-4776	150	33	completely	completely	ADV
ejpam-4776	150	34	regular	regular	ADJ
ejpam-4776	150	35	,	,	PUNCT
ejpam-4776	150	36	cc	cc	NOUN
ejpam-4776	150	37	-	-	ADJ
ejpam-4776	150	38	normal	normal	ADJ
ejpam-4776	150	39	,	,	PUNCT
ejpam-4776	150	40	cc	cc	NOUN
ejpam-4776	150	41	-	-	NOUN
ejpam-4776	150	42	tychonoff	tychonoff	NOUN
ejpam-4776	150	43	nor	nor	CCONJ
ejpam-4776	150	44	epi	epi	NOUN
ejpam-4776	150	45	-	-	NOUN
ejpam-4776	150	46	regular	regular	ADJ
ejpam-4776	150	47	.	.	PUNCT
ejpam-4776	151	1	in	in	ADP
ejpam-4776	151	2	view	view	NOUN
ejpam-4776	151	3	of	of	ADP
ejpam-4776	151	4	the	the	DET
ejpam-4776	151	5	fact	fact	NOUN
ejpam-4776	151	6	that	that	SCONJ
ejpam-4776	151	7	:	:	PUNCT
ejpam-4776	151	8	if	if	SCONJ
ejpam-4776	151	9	x	x	PRON
ejpam-4776	151	10	is	be	AUX
ejpam-4776	151	11	a	a	DET
ejpam-4776	151	12	t1	t1	NOUN
ejpam-4776	151	13	-	-	PUNCT
ejpam-4776	151	14	space	space	NOUN
ejpam-4776	151	15	such	such	ADJ
ejpam-4776	151	16	that	that	SCONJ
ejpam-4776	151	17	the	the	DET
ejpam-4776	151	18	only	only	ADJ
ejpam-4776	151	19	countably	countably	ADV
ejpam-4776	151	20	compact	compact	ADJ
ejpam-4776	151	21	subsets	subset	NOUN
ejpam-4776	151	22	of	of	ADP
ejpam-4776	151	23	x	x	SYM
ejpam-4776	151	24	are	be	AUX
ejpam-4776	151	25	the	the	DET
ejpam-4776	151	26	finite	finite	ADJ
ejpam-4776	151	27	subsets	subset	NOUN
ejpam-4776	151	28	,	,	PUNCT
ejpam-4776	151	29	then	then	ADV
ejpam-4776	151	30	x	x	PUNCT
ejpam-4776	151	31	is	be	AUX
ejpam-4776	151	32	cc	cc	VERB
ejpam-4776	151	33	-	-	ADJ
ejpam-4776	151	34	normal	normal	ADJ
ejpam-4776	151	35	[	[	X
ejpam-4776	151	36	14	14	NUM
ejpam-4776	151	37	]	]	PUNCT
ejpam-4776	151	38	.	.	PUNCT
ejpam-4776	152	1	then	then	ADV
ejpam-4776	152	2	,	,	PUNCT
ejpam-4776	152	3	we	we	PRON
ejpam-4776	152	4	conclude	conclude	VERB
ejpam-4776	152	5	:	:	PUNCT
ejpam-4776	152	6	theorem	theorem	VERB
ejpam-4776	152	7	4	4	NUM
ejpam-4776	152	8	.	.	PUNCT
ejpam-4776	153	1	if	if	SCONJ
ejpam-4776	153	2	x	x	PRON
ejpam-4776	153	3	is	be	AUX
ejpam-4776	153	4	a	a	DET
ejpam-4776	153	5	t1	t1	NOUN
ejpam-4776	153	6	-	-	PUNCT
ejpam-4776	153	7	space	space	NOUN
ejpam-4776	153	8	such	such	ADJ
ejpam-4776	153	9	that	that	SCONJ
ejpam-4776	153	10	the	the	DET
ejpam-4776	153	11	only	only	ADJ
ejpam-4776	153	12	countably	countably	ADV
ejpam-4776	153	13	compact	compact	ADJ
ejpam-4776	153	14	subsets	subset	NOUN
ejpam-4776	153	15	of	of	ADP
ejpam-4776	153	16	x	x	SYM
ejpam-4776	153	17	are	be	AUX
ejpam-4776	153	18	the	the	DET
ejpam-4776	153	19	finite	finite	ADJ
ejpam-4776	153	20	subsets	subset	NOUN
ejpam-4776	153	21	,	,	PUNCT
ejpam-4776	153	22	then	then	ADV
ejpam-4776	153	23	x	x	PUNCT
ejpam-4776	153	24	is	be	AUX
ejpam-4776	153	25	cc	cc	NOUN
ejpam-4776	153	26	-	-	NOUN
ejpam-4776	153	27	tychonoff	tychonoff	NOUN
ejpam-4776	153	28	.	.	PUNCT
ejpam-4776	154	1	proof	proof	NOUN
ejpam-4776	154	2	.	.	PUNCT
ejpam-4776	155	1	let	let	VERB
ejpam-4776	155	2	x	x	PRON
ejpam-4776	155	3	be	be	AUX
ejpam-4776	155	4	a	a	DET
ejpam-4776	155	5	t1	t1	NOUN
ejpam-4776	155	6	-	-	PUNCT
ejpam-4776	155	7	space	space	NOUN
ejpam-4776	155	8	.	.	PUNCT
ejpam-4776	156	1	let	let	VERB
ejpam-4776	156	2	x	x	SYM
ejpam-4776	156	3	=	=	SYM
ejpam-4776	156	4	y	y	PROPN
ejpam-4776	156	5	and	and	CCONJ
ejpam-4776	156	6	consider	consider	VERB
ejpam-4776	156	7	y	y	NOUN
ejpam-4776	156	8	with	with	ADP
ejpam-4776	156	9	the	the	DET
ejpam-4776	156	10	discrete	discrete	ADJ
ejpam-4776	156	11	topology	topology	NOUN
ejpam-4776	156	12	.	.	PUNCT
ejpam-4776	157	1	then	then	ADV
ejpam-4776	157	2	,	,	PUNCT
ejpam-4776	157	3	the	the	DET
ejpam-4776	157	4	identity	identity	NOUN
ejpam-4776	157	5	function	function	NOUN
ejpam-4776	157	6	ix	ix	ADV
ejpam-4776	157	7	:	:	PUNCT
ejpam-4776	157	8	x	x	X
ejpam-4776	157	9	→	→	SYM
ejpam-4776	157	10	y	y	PROPN
ejpam-4776	157	11	is	be	AUX
ejpam-4776	157	12	a	a	DET
ejpam-4776	157	13	bijective	bijective	ADJ
ejpam-4776	157	14	function	function	NOUN
ejpam-4776	157	15	.	.	PUNCT
ejpam-4776	158	1	if	if	SCONJ
ejpam-4776	158	2	m	m	NOUN
ejpam-4776	158	3	is	be	AUX
ejpam-4776	158	4	any	any	DET
ejpam-4776	158	5	countably	countably	ADV
ejpam-4776	158	6	compact	compact	ADJ
ejpam-4776	158	7	subspace	subspace	NOUN
ejpam-4776	158	8	of	of	ADP
ejpam-4776	158	9	(	(	PUNCT
ejpam-4776	158	10	x	x	PROPN
ejpam-4776	158	11	,	,	PUNCT
ejpam-4776	158	12	t	t	PROPN
ejpam-4776	158	13	)	)	PUNCT
ejpam-4776	158	14	,	,	PUNCT
ejpam-4776	158	15	then	then	ADV
ejpam-4776	158	16	by	by	ADP
ejpam-4776	158	17	assumption	assumption	NOUN
ejpam-4776	158	18	m	m	NOUN
ejpam-4776	158	19	is	be	AUX
ejpam-4776	158	20	a	a	DET
ejpam-4776	158	21	finite	finite	ADJ
ejpam-4776	158	22	subspace	subspace	NOUN
ejpam-4776	158	23	of	of	ADP
ejpam-4776	158	24	x	x	PUNCT
ejpam-4776	158	25	and	and	CCONJ
ejpam-4776	158	26	y	y	PROPN
ejpam-4776	158	27	is	be	AUX
ejpam-4776	158	28	with	with	ADP
ejpam-4776	158	29	a	a	DET
ejpam-4776	158	30	discrete	discrete	ADJ
ejpam-4776	158	31	topology	topology	NOUN
ejpam-4776	158	32	.	.	PUNCT
ejpam-4776	159	1	since	since	SCONJ
ejpam-4776	159	2	any	any	DET
ejpam-4776	159	3	finite	finite	NOUN
ejpam-4776	159	4	countably	countably	ADV
ejpam-4776	159	5	compact	compact	ADJ
ejpam-4776	159	6	subspace	subspace	NOUN
ejpam-4776	159	7	of	of	ADP
ejpam-4776	159	8	a	a	DET
ejpam-4776	159	9	t1	t1	NOUN
ejpam-4776	159	10	-	-	PUNCT
ejpam-4776	159	11	space	space	NOUN
ejpam-4776	159	12	is	be	AUX
ejpam-4776	159	13	discrete	discrete	ADJ
ejpam-4776	159	14	,	,	PUNCT
ejpam-4776	159	15	the	the	DET
ejpam-4776	159	16	restriction	restriction	NOUN
ejpam-4776	159	17	function	function	NOUN
ejpam-4776	159	18	(	(	PUNCT
ejpam-4776	159	19	ix)|m	ix)|m	NOUN
ejpam-4776	159	20	:	:	PUNCT
ejpam-4776	159	21	m	m	PROPN
ejpam-4776	159	22	→	→	SYM
ejpam-4776	159	23	ix(m	ix(m	NUM
ejpam-4776	159	24	)	)	PUNCT
ejpam-4776	160	1	=	=	VERB
ejpam-4776	160	2	m	m	VERB
ejpam-4776	160	3	is	be	AUX
ejpam-4776	160	4	a	a	DET
ejpam-4776	160	5	homeomorphism	homeomorphism	NOUN
ejpam-4776	160	6	because	because	SCONJ
ejpam-4776	160	7	both	both	CCONJ
ejpam-4776	160	8	the	the	DET
ejpam-4776	160	9	domain	domain	NOUN
ejpam-4776	160	10	and	and	CCONJ
ejpam-4776	160	11	the	the	DET
ejpam-4776	160	12	co	co	NOUN
ejpam-4776	160	13	-	-	NOUN
ejpam-4776	160	14	domain	domain	NOUN
ejpam-4776	160	15	are	be	AUX
ejpam-4776	160	16	discrete	discrete	ADJ
ejpam-4776	160	17	,	,	PUNCT
ejpam-4776	160	18	and	and	CCONJ
ejpam-4776	160	19	they	they	PRON
ejpam-4776	160	20	have	have	VERB
ejpam-4776	160	21	the	the	DET
ejpam-4776	160	22	same	same	ADJ
ejpam-4776	160	23	cardinality	cardinality	NOUN
ejpam-4776	160	24	.	.	PUNCT
ejpam-4776	161	1	since	since	SCONJ
ejpam-4776	161	2	y	y	PROPN
ejpam-4776	161	3	is	be	AUX
ejpam-4776	161	4	a	a	DET
ejpam-4776	161	5	tychonoff	tychonoff	NOUN
ejpam-4776	161	6	space	space	NOUN
ejpam-4776	161	7	,	,	PUNCT
ejpam-4776	161	8	we	we	PRON
ejpam-4776	161	9	have	have	VERB
ejpam-4776	161	10	:	:	PUNCT
ejpam-4776	161	11	x	x	X
ejpam-4776	161	12	is	be	AUX
ejpam-4776	161	13	cc	cc	NOUN
ejpam-4776	161	14	-	-	NOUN
ejpam-4776	161	15	tychonoff	tychonoff	NOUN
ejpam-4776	161	16	.	.	PUNCT
ejpam-4776	162	1	corollary	corollary	ADJ
ejpam-4776	162	2	2	2	PROPN
ejpam-4776	162	3	.	.	PUNCT
ejpam-4776	163	1	ifx	ifx	PROPN
ejpam-4776	163	2	is	be	AUX
ejpam-4776	163	3	a	a	DET
ejpam-4776	163	4	t1	t1	NOUN
ejpam-4776	163	5	-	-	PUNCT
ejpam-4776	163	6	space	space	NOUN
ejpam-4776	163	7	such	such	ADJ
ejpam-4776	163	8	that	that	SCONJ
ejpam-4776	163	9	the	the	DET
ejpam-4776	163	10	only	only	ADJ
ejpam-4776	163	11	countably	countably	ADV
ejpam-4776	163	12	compact	compact	ADJ
ejpam-4776	163	13	subsets	subset	NOUN
ejpam-4776	163	14	ofx	ofx	NOUN
ejpam-4776	163	15	are	be	AUX
ejpam-4776	163	16	the	the	DET
ejpam-4776	163	17	finite	finite	ADJ
ejpam-4776	163	18	subsets	subset	NOUN
ejpam-4776	163	19	,	,	PUNCT
ejpam-4776	163	20	then	then	ADV
ejpam-4776	163	21	x	x	PUNCT
ejpam-4776	163	22	is	be	AUX
ejpam-4776	163	23	cc	cc	VERB
ejpam-4776	163	24	-	-	ADJ
ejpam-4776	163	25	completely	completely	ADV
ejpam-4776	163	26	regular	regular	ADJ
ejpam-4776	163	27	,	,	PUNCT
ejpam-4776	163	28	cc	cc	NOUN
ejpam-4776	163	29	-	-	ADJ
ejpam-4776	163	30	regular	regular	ADJ
ejpam-4776	163	31	,	,	PUNCT
ejpam-4776	163	32	cct3	cct3	PROPN
ejpam-4776	163	33	,	,	PUNCT
ejpam-4776	163	34	cc	cc	NOUN
ejpam-4776	163	35	-	-	PUNCT
ejpam-4776	163	36	almost	almost	ADV
ejpam-4776	163	37	regular	regular	ADJ
ejpam-4776	163	38	and	and	CCONJ
ejpam-4776	163	39	cc	cc	NOUN
ejpam-4776	163	40	-	-	PUNCT
ejpam-4776	163	41	almost	almost	ADV
ejpam-4776	163	42	completely	completely	ADV
ejpam-4776	163	43	regular	regular	ADJ
ejpam-4776	163	44	.	.	PUNCT
ejpam-4776	164	1	theorem	theorem	NOUN
ejpam-4776	164	2	5	5	NUM
ejpam-4776	164	3	.	.	PUNCT
ejpam-4776	165	1	if	if	SCONJ
ejpam-4776	165	2	x	x	PRON
ejpam-4776	165	3	is	be	AUX
ejpam-4776	165	4	a	a	DET
ejpam-4776	165	5	countably	countably	ADV
ejpam-4776	165	6	compact	compact	ADJ
ejpam-4776	165	7	cc	cc	NOUN
ejpam-4776	165	8	-	-	ADJ
ejpam-4776	165	9	completely	completely	ADV
ejpam-4776	165	10	regular	regular	ADJ
ejpam-4776	165	11	(	(	PUNCT
ejpam-4776	165	12	resp	resp	NOUN
ejpam-4776	165	13	.	.	PUNCT
ejpam-4776	166	1	cc	cc	NOUN
ejpam-4776	166	2	-	-	NOUN
ejpam-4776	166	3	tychonoff	tychonoff	NOUN
ejpam-4776	166	4	,	,	PUNCT
ejpam-4776	166	5	cct3	cct3	PROPN
ejpam-4776	166	6	,	,	PUNCT
ejpam-4776	166	7	cc	cc	NOUN
ejpam-4776	166	8	-	-	ADJ
ejpam-4776	166	9	regular	regular	ADJ
ejpam-4776	166	10	,	,	PUNCT
ejpam-4776	166	11	cc	cc	NOUN
ejpam-4776	166	12	-	-	ADJ
ejpam-4776	166	13	almost	almost	ADV
ejpam-4776	166	14	completely	completely	ADV
ejpam-4776	166	15	regular	regular	ADJ
ejpam-4776	166	16	,	,	PUNCT
ejpam-4776	166	17	cc	cc	NOUN
ejpam-4776	166	18	-	-	ADJ
ejpam-4776	166	19	almost	almost	ADV
ejpam-4776	166	20	regular	regular	ADJ
ejpam-4776	166	21	)	)	PUNCT
ejpam-4776	166	22	space	space	NOUN
ejpam-4776	166	23	,	,	PUNCT
ejpam-4776	166	24	then	then	ADV
ejpam-4776	166	25	x	x	PUNCT
ejpam-4776	166	26	is	be	AUX
ejpam-4776	166	27	completely	completely	ADV
ejpam-4776	166	28	regular	regular	ADJ
ejpam-4776	166	29	(	(	PUNCT
ejpam-4776	166	30	resp	resp	NOUN
ejpam-4776	166	31	.	.	PUNCT
ejpam-4776	166	32	tychonoff	tychonoff	PROPN
ejpam-4776	166	33	,	,	PUNCT
ejpam-4776	166	34	t3	t3	PROPN
ejpam-4776	166	35	,	,	PUNCT
ejpam-4776	166	36	regular	regular	ADJ
ejpam-4776	166	37	,	,	PUNCT
ejpam-4776	166	38	almost	almost	ADV
ejpam-4776	166	39	completely	completely	ADV
ejpam-4776	166	40	regular	regular	ADJ
ejpam-4776	166	41	,	,	PUNCT
ejpam-4776	166	42	almost	almost	ADV
ejpam-4776	166	43	regular	regular	ADJ
ejpam-4776	166	44	)	)	PUNCT
ejpam-4776	166	45	.	.	PUNCT
ejpam-4776	167	1	proof	proof	NOUN
ejpam-4776	167	2	.	.	PUNCT
ejpam-4776	168	1	let	let	VERB
ejpam-4776	168	2	x	x	PRON
ejpam-4776	168	3	be	be	AUX
ejpam-4776	168	4	a	a	DET
ejpam-4776	168	5	countably	countably	ADV
ejpam-4776	168	6	compact	compact	ADJ
ejpam-4776	168	7	cc	cc	NOUN
ejpam-4776	168	8	-	-	ADJ
ejpam-4776	168	9	completely	completely	ADV
ejpam-4776	168	10	regular	regular	ADJ
ejpam-4776	168	11	(	(	PUNCT
ejpam-4776	168	12	resp	resp	NOUN
ejpam-4776	168	13	.	.	PUNCT
ejpam-4776	169	1	cc	cc	NOUN
ejpam-4776	169	2	-	-	NOUN
ejpam-4776	169	3	tychonoff	tychonoff	NOUN
ejpam-4776	169	4	,	,	PUNCT
ejpam-4776	169	5	cct3	cct3	PROPN
ejpam-4776	169	6	,	,	PUNCT
ejpam-4776	169	7	cc	cc	NOUN
ejpam-4776	169	8	-	-	ADJ
ejpam-4776	169	9	regular	regular	ADJ
ejpam-4776	169	10	,	,	PUNCT
ejpam-4776	169	11	cc	cc	NOUN
ejpam-4776	169	12	-	-	ADJ
ejpam-4776	169	13	almost	almost	ADV
ejpam-4776	169	14	completely	completely	ADV
ejpam-4776	169	15	regular	regular	ADJ
ejpam-4776	169	16	,	,	PUNCT
ejpam-4776	169	17	cc	cc	NOUN
ejpam-4776	169	18	-	-	ADJ
ejpam-4776	169	19	almost	almost	ADV
ejpam-4776	169	20	regular	regular	ADJ
ejpam-4776	169	21	)	)	PUNCT
ejpam-4776	169	22	space	space	NOUN
ejpam-4776	169	23	.	.	PUNCT
ejpam-4776	170	1	then	then	ADV
ejpam-4776	170	2	,	,	PUNCT
ejpam-4776	170	3	there	there	PRON
ejpam-4776	170	4	exist	exist	VERB
ejpam-4776	170	5	a	a	DET
ejpam-4776	170	6	completely	completely	ADV
ejpam-4776	170	7	regular	regular	ADJ
ejpam-4776	170	8	(	(	PUNCT
ejpam-4776	170	9	resp	resp	NOUN
ejpam-4776	170	10	.	.	PUNCT
ejpam-4776	170	11	tychonoff	tychonoff	PROPN
ejpam-4776	170	12	,	,	PUNCT
ejpam-4776	170	13	t3	t3	PROPN
ejpam-4776	170	14	,	,	PUNCT
ejpam-4776	170	15	regular	regular	ADJ
ejpam-4776	170	16	,	,	PUNCT
ejpam-4776	170	17	almost	almost	ADV
ejpam-4776	170	18	completely	completely	ADV
ejpam-4776	170	19	regular	regular	ADJ
ejpam-4776	170	20	,	,	PUNCT
ejpam-4776	170	21	almost	almost	ADV
ejpam-4776	170	22	regular	regular	ADJ
ejpam-4776	170	23	)	)	PUNCT
ejpam-4776	170	24	space	space	NOUN
ejpam-4776	170	25	y	y	PROPN
ejpam-4776	170	26	and	and	CCONJ
ejpam-4776	170	27	a	a	DET
ejpam-4776	170	28	bijective	bijective	ADJ
ejpam-4776	170	29	function	function	NOUN
ejpam-4776	171	1	f	f	NOUN
ejpam-4776	171	2	:	:	PUNCT
ejpam-4776	171	3	x	x	X
ejpam-4776	171	4	→	→	SYM
ejpam-4776	171	5	y	y	PROPN
ejpam-4776	171	6	such	such	ADJ
ejpam-4776	171	7	that	that	SCONJ
ejpam-4776	171	8	the	the	DET
ejpam-4776	171	9	restriction	restriction	NOUN
ejpam-4776	171	10	function	function	NOUN
ejpam-4776	171	11	f	f	PROPN
ejpam-4776	171	12	|a	|a	VERB
ejpam-4776	171	13	:	:	PUNCT
ejpam-4776	171	14	a	a	DET
ejpam-4776	171	15	→	→	SYM
ejpam-4776	171	16	f(a	f(a	NOUN
ejpam-4776	171	17	)	)	PUNCT
ejpam-4776	171	18	is	be	AUX
ejpam-4776	171	19	a	a	DET
ejpam-4776	171	20	homeomorphism	homeomorphism	NOUN
ejpam-4776	171	21	for	for	ADP
ejpam-4776	171	22	each	each	DET
ejpam-4776	171	23	countably	countably	ADV
ejpam-4776	171	24	compact	compact	ADJ
ejpam-4776	171	25	subspace	subspace	NOUN
ejpam-4776	171	26	a	a	PRON
ejpam-4776	171	27	of	of	ADP
ejpam-4776	171	28	x.	x.	NOUN
ejpam-4776	171	29	since	since	SCONJ
ejpam-4776	171	30	x	x	PRON
ejpam-4776	171	31	is	be	AUX
ejpam-4776	171	32	a	a	DET
ejpam-4776	171	33	countably	countably	ADV
ejpam-4776	171	34	compact	compact	ADJ
ejpam-4776	171	35	space	space	NOUN
ejpam-4776	171	36	,	,	PUNCT
ejpam-4776	171	37	put	put	VERB
ejpam-4776	171	38	a	a	DET
ejpam-4776	171	39	=	=	NOUN
ejpam-4776	171	40	x.	x.	NOUN
ejpam-4776	171	41	since	since	SCONJ
ejpam-4776	171	42	f	f	PROPN
ejpam-4776	171	43	is	be	AUX
ejpam-4776	171	44	bijective	bijective	ADJ
ejpam-4776	171	45	,	,	PUNCT
ejpam-4776	171	46	the	the	DET
ejpam-4776	171	47	function	function	NOUN
ejpam-4776	171	48	f	f	NOUN
ejpam-4776	171	49	:	:	PUNCT
ejpam-4776	171	50	x	x	X
ejpam-4776	171	51	→	→	SYM
ejpam-4776	171	52	y	y	PROPN
ejpam-4776	171	53	is	be	AUX
ejpam-4776	171	54	a	a	DET
ejpam-4776	171	55	homeomorphism	homeomorphism	NOUN
ejpam-4776	171	56	.	.	PUNCT
ejpam-4776	172	1	since	since	SCONJ
ejpam-4776	172	2	x	x	PART
ejpam-4776	172	3	∼=	∼=	PROPN
ejpam-4776	172	4	y	y	NOUN
ejpam-4776	172	5	,	,	PUNCT
ejpam-4776	172	6	we	we	PRON
ejpam-4776	172	7	get	get	VERB
ejpam-4776	172	8	x	x	PUNCT
ejpam-4776	172	9	is	be	AUX
ejpam-4776	172	10	completely	completely	ADV
ejpam-4776	172	11	regular	regular	ADJ
ejpam-4776	172	12	(	(	PUNCT
ejpam-4776	172	13	resp	resp	NOUN
ejpam-4776	172	14	.	.	PUNCT
ejpam-4776	172	15	tychonoff	tychonoff	PROPN
ejpam-4776	172	16	,	,	PUNCT
ejpam-4776	172	17	t3	t3	PROPN
ejpam-4776	172	18	,	,	PUNCT
ejpam-4776	172	19	regular	regular	ADJ
ejpam-4776	172	20	,	,	PUNCT
ejpam-4776	172	21	almost	almost	ADV
ejpam-4776	172	22	completely	completely	ADV
ejpam-4776	172	23	regular	regular	ADJ
ejpam-4776	172	24	,	,	PUNCT
ejpam-4776	172	25	almost	almost	ADV
ejpam-4776	172	26	regular	regular	ADJ
ejpam-4776	172	27	)	)	PUNCT
ejpam-4776	172	28	.	.	PUNCT
ejpam-4776	173	1	s.	s.	PROPN
ejpam-4776	173	2	a.	a.	PROPN
ejpam-4776	173	3	thabit	thabit	PROPN
ejpam-4776	173	4	,	,	PUNCT
ejpam-4776	173	5	w.	w.	PROPN
ejpam-4776	173	6	alqurashi	alqurashi	PROPN
ejpam-4776	173	7	/	/	SYM
ejpam-4776	173	8	eur	eur	PROPN
ejpam-4776	173	9	.	.	PUNCT
ejpam-4776	174	1	j.	j.	PROPN
ejpam-4776	174	2	pure	pure	PROPN
ejpam-4776	174	3	appl	appl	PROPN
ejpam-4776	174	4	.	.	PROPN
ejpam-4776	174	5	math	math	PROPN
ejpam-4776	174	6	,	,	PUNCT
ejpam-4776	174	7	16	16	NUM
ejpam-4776	174	8	(	(	PUNCT
ejpam-4776	174	9	2	2	NUM
ejpam-4776	174	10	)	)	PUNCT
ejpam-4776	174	11	(	(	PUNCT
ejpam-4776	174	12	2023	2023	NUM
ejpam-4776	174	13	)	)	PUNCT
ejpam-4776	174	14	,	,	PUNCT
ejpam-4776	174	15	1260	1260	NUM
ejpam-4776	174	16	-	-	SYM
ejpam-4776	174	17	1273	1273	NUM
ejpam-4776	174	18	1266	1266	NUM
ejpam-4776	174	19	corollary	corollary	NOUN
ejpam-4776	174	20	3	3	NUM
ejpam-4776	174	21	.	.	PUNCT
ejpam-4776	175	1	if	if	SCONJ
ejpam-4776	175	2	x	x	PRON
ejpam-4776	175	3	is	be	AUX
ejpam-4776	175	4	a	a	DET
ejpam-4776	175	5	countably	countably	ADV
ejpam-4776	175	6	compact	compact	ADJ
ejpam-4776	175	7	non	non	ADJ
ejpam-4776	175	8	-	-	ADJ
ejpam-4776	175	9	completely	completely	ADV
ejpam-4776	175	10	regular	regular	ADJ
ejpam-4776	175	11	(	(	PUNCT
ejpam-4776	175	12	resp	resp	NOUN
ejpam-4776	175	13	.	.	PUNCT
ejpam-4776	176	1	non	non	ADJ
ejpam-4776	176	2	-	-	NOUN
ejpam-4776	176	3	tychonoff	tychonoff	ADJ
ejpam-4776	176	4	,	,	PUNCT
ejpam-4776	176	5	non	non	X
ejpam-4776	176	6	t3	t3	NOUN
ejpam-4776	176	7	,	,	PUNCT
ejpam-4776	176	8	non	non	ADJ
ejpam-4776	176	9	-	-	ADJ
ejpam-4776	176	10	regular	regular	ADJ
ejpam-4776	176	11	,	,	PUNCT
ejpam-4776	176	12	non	non	ADJ
ejpam-4776	176	13	-	-	ADJ
ejpam-4776	176	14	almost	almost	ADV
ejpam-4776	176	15	completely	completely	ADV
ejpam-4776	176	16	regular	regular	ADJ
ejpam-4776	176	17	,	,	PUNCT
ejpam-4776	176	18	non	non	ADJ
ejpam-4776	176	19	-	-	ADJ
ejpam-4776	176	20	almost	almost	ADV
ejpam-4776	176	21	regular	regular	ADJ
ejpam-4776	176	22	)	)	PUNCT
ejpam-4776	176	23	space	space	NOUN
ejpam-4776	176	24	,	,	PUNCT
ejpam-4776	176	25	then	then	ADV
ejpam-4776	176	26	x	x	PUNCT
ejpam-4776	176	27	can	can	AUX
ejpam-4776	176	28	not	not	PART
ejpam-4776	176	29	be	be	AUX
ejpam-4776	176	30	cc	cc	VERB
ejpam-4776	176	31	-	-	ADJ
ejpam-4776	176	32	completely	completely	ADV
ejpam-4776	176	33	regular	regular	ADJ
ejpam-4776	176	34	(	(	PUNCT
ejpam-4776	176	35	resp	resp	NOUN
ejpam-4776	176	36	.	.	PUNCT
ejpam-4776	177	1	cc	cc	NOUN
ejpam-4776	177	2	-	-	NOUN
ejpam-4776	177	3	tychonoff	tychonoff	NOUN
ejpam-4776	177	4	,	,	PUNCT
ejpam-4776	177	5	cct3	cct3	PROPN
ejpam-4776	177	6	,	,	PUNCT
ejpam-4776	177	7	cc	cc	NOUN
ejpam-4776	177	8	-	-	ADJ
ejpam-4776	177	9	regular	regular	ADJ
ejpam-4776	177	10	,	,	PUNCT
ejpam-4776	177	11	cc	cc	NOUN
ejpam-4776	177	12	-	-	ADJ
ejpam-4776	177	13	almost	almost	ADV
ejpam-4776	177	14	completely	completely	ADV
ejpam-4776	177	15	regular	regular	ADJ
ejpam-4776	177	16	,	,	PUNCT
ejpam-4776	177	17	cc	cc	NOUN
ejpam-4776	177	18	-	-	ADJ
ejpam-4776	177	19	almost	almost	ADV
ejpam-4776	177	20	regular	regular	ADJ
ejpam-4776	177	21	)	)	PUNCT
ejpam-4776	177	22	.	.	PUNCT
ejpam-4776	178	1	recall	recall	VERB
ejpam-4776	178	2	that	that	PRON
ejpam-4776	178	3	:	:	PUNCT
ejpam-4776	178	4	a	a	DET
ejpam-4776	178	5	space	space	NOUN
ejpam-4776	178	6	x	x	PUNCT
ejpam-4776	178	7	is	be	AUX
ejpam-4776	178	8	called	call	VERB
ejpam-4776	178	9	locally	locally	ADV
ejpam-4776	178	10	compact	compact	ADJ
ejpam-4776	178	11	if	if	SCONJ
ejpam-4776	178	12	x	x	PRON
ejpam-4776	178	13	is	be	AUX
ejpam-4776	178	14	hausdorff	hausdorff	NOUN
ejpam-4776	178	15	and	and	CCONJ
ejpam-4776	178	16	for	for	ADP
ejpam-4776	178	17	each	each	DET
ejpam-4776	178	18	x	x	SYM
ejpam-4776	178	19	∈	∈	PROPN
ejpam-4776	178	20	x	x	X
ejpam-4776	178	21	and	and	CCONJ
ejpam-4776	178	22	each	each	DET
ejpam-4776	178	23	open	open	ADJ
ejpam-4776	178	24	neighborhood	neighborhood	NOUN
ejpam-4776	178	25	v	v	NOUN
ejpam-4776	178	26	of	of	ADP
ejpam-4776	178	27	x	x	PUNCT
ejpam-4776	178	28	there	there	PRON
ejpam-4776	178	29	exists	exist	VERB
ejpam-4776	178	30	an	an	DET
ejpam-4776	178	31	open	open	ADJ
ejpam-4776	178	32	neighborhood	neighborhood	NOUN
ejpam-4776	178	33	u	u	NOUN
ejpam-4776	178	34	of	of	ADP
ejpam-4776	178	35	x	x	SYM
ejpam-4776	178	36	such	such	ADJ
ejpam-4776	178	37	that	that	SCONJ
ejpam-4776	178	38	x	x	SYM
ejpam-4776	178	39	∈	∈	NOUN
ejpam-4776	178	40	u	u	NOUN
ejpam-4776	178	41	⊆	⊆	NUM
ejpam-4776	178	42	u	u	NOUN
ejpam-4776	178	43	⊆	⊆	NUM
ejpam-4776	178	44	v	v	NOUN
ejpam-4776	178	45	and	and	CCONJ
ejpam-4776	178	46	u	u	NOUN
ejpam-4776	178	47	is	be	AUX
ejpam-4776	178	48	compact	compact	ADJ
ejpam-4776	178	49	[	[	X
ejpam-4776	178	50	10	10	NUM
ejpam-4776	178	51	]	]	PUNCT
ejpam-4776	178	52	.	.	PUNCT
ejpam-4776	179	1	in	in	ADP
ejpam-4776	179	2	view	view	NOUN
ejpam-4776	179	3	of	of	ADP
ejpam-4776	179	4	the	the	DET
ejpam-4776	179	5	fact	fact	NOUN
ejpam-4776	179	6	that	that	SCONJ
ejpam-4776	179	7	:	:	PUNCT
ejpam-4776	179	8	every	every	DET
ejpam-4776	179	9	locally	locally	ADV
ejpam-4776	179	10	compact	compact	ADJ
ejpam-4776	179	11	space	space	NOUN
ejpam-4776	179	12	is	be	AUX
ejpam-4776	179	13	tychonoff	tychonoff	NOUN
ejpam-4776	179	14	[	[	X
ejpam-4776	179	15	10	10	NUM
ejpam-4776	179	16	]	]	PUNCT
ejpam-4776	179	17	,	,	PUNCT
ejpam-4776	179	18	we	we	PRON
ejpam-4776	179	19	get	get	VERB
ejpam-4776	179	20	the	the	DET
ejpam-4776	179	21	following	follow	VERB
ejpam-4776	179	22	corollary	corollary	ADJ
ejpam-4776	179	23	:	:	PUNCT
ejpam-4776	179	24	corollary	corollary	ADJ
ejpam-4776	179	25	4	4	NUM
ejpam-4776	179	26	.	.	PUNCT
ejpam-4776	180	1	every	every	DET
ejpam-4776	180	2	locally	locally	ADV
ejpam-4776	180	3	compact	compact	ADJ
ejpam-4776	180	4	space	space	NOUN
ejpam-4776	180	5	is	be	AUX
ejpam-4776	180	6	cc	cc	NOUN
ejpam-4776	180	7	-	-	NOUN
ejpam-4776	180	8	tychonoff	tychonoff	NOUN
ejpam-4776	180	9	.	.	PUNCT
ejpam-4776	181	1	recall	recall	VERB
ejpam-4776	181	2	that	that	PRON
ejpam-4776	181	3	:	:	PUNCT
ejpam-4776	181	4	a	a	DET
ejpam-4776	181	5	space	space	NOUN
ejpam-4776	181	6	x	x	PUNCT
ejpam-4776	181	7	is	be	AUX
ejpam-4776	181	8	said	say	VERB
ejpam-4776	181	9	to	to	PART
ejpam-4776	181	10	be	be	AUX
ejpam-4776	181	11	mildly	mildly	ADV
ejpam-4776	181	12	normal	normal	ADJ
ejpam-4776	182	1	[	[	X
ejpam-4776	182	2	22	22	NUM
ejpam-4776	182	3	]	]	PUNCT
ejpam-4776	182	4	,	,	PUNCT
ejpam-4776	182	5	if	if	SCONJ
ejpam-4776	182	6	any	any	DET
ejpam-4776	182	7	pair	pair	NOUN
ejpam-4776	182	8	of	of	ADP
ejpam-4776	182	9	disjoint	disjoint	NOUN
ejpam-4776	182	10	closed	closed	ADJ
ejpam-4776	182	11	domain	domain	NOUN
ejpam-4776	182	12	subsets	subset	NOUN
ejpam-4776	182	13	a	a	PRON
ejpam-4776	182	14	and	and	CCONJ
ejpam-4776	182	15	b	b	NOUN
ejpam-4776	182	16	of	of	ADP
ejpam-4776	182	17	x	x	PRON
ejpam-4776	182	18	can	can	AUX
ejpam-4776	182	19	be	be	AUX
ejpam-4776	182	20	separated	separate	VERB
ejpam-4776	182	21	.	.	PUNCT
ejpam-4776	183	1	the	the	DET
ejpam-4776	183	2	converse	converse	NOUN
ejpam-4776	183	3	of	of	ADP
ejpam-4776	183	4	corollary	corollary	ADJ
ejpam-4776	183	5	4	4	NUM
ejpam-4776	183	6	is	be	AUX
ejpam-4776	183	7	not	not	PART
ejpam-4776	183	8	true	true	ADJ
ejpam-4776	183	9	in	in	ADP
ejpam-4776	183	10	general	general	ADJ
ejpam-4776	183	11	as	as	SCONJ
ejpam-4776	183	12	shown	show	VERB
ejpam-4776	183	13	by	by	ADP
ejpam-4776	183	14	the	the	DET
ejpam-4776	183	15	next	next	ADJ
ejpam-4776	183	16	example	example	NOUN
ejpam-4776	183	17	:	:	PUNCT
ejpam-4776	183	18	example	example	NOUN
ejpam-4776	183	19	8	8	NUM
ejpam-4776	183	20	.	.	PUNCT
ejpam-4776	184	1	the	the	DET
ejpam-4776	184	2	modified	modify	VERB
ejpam-4776	184	3	dieudonné	dieudonné	NOUN
ejpam-4776	184	4	plank	plank	NOUN
ejpam-4776	184	5	topology	topology	NOUN
ejpam-4776	184	6	:	:	PUNCT
ejpam-4776	184	7	[	[	X
ejpam-4776	184	8	14	14	NUM
ejpam-4776	184	9	,	,	PUNCT
ejpam-4776	184	10	example	example	NOUN
ejpam-4776	184	11	2.4	2.4	NUM
ejpam-4776	184	12	,	,	PUNCT
ejpam-4776	184	13	example	example	NOUN
ejpam-4776	184	14	3.3	3.3	NUM
ejpam-4776	184	15	]	]	PUNCT
ejpam-4776	184	16	,	,	PUNCT
ejpam-4776	184	17	is	be	AUX
ejpam-4776	184	18	a	a	DET
ejpam-4776	184	19	tychonoff	tychonoff	NOUN
ejpam-4776	184	20	,	,	PUNCT
ejpam-4776	184	21	l	l	NOUN
ejpam-4776	184	22	-	-	ADJ
ejpam-4776	184	23	normal	normal	ADJ
ejpam-4776	184	24	and	and	CCONJ
ejpam-4776	184	25	cc	cc	NOUN
ejpam-4776	184	26	-	-	ADJ
ejpam-4776	184	27	normal	normal	ADJ
ejpam-4776	184	28	space	space	NOUN
ejpam-4776	184	29	,	,	PUNCT
ejpam-4776	184	30	which	which	PRON
ejpam-4776	184	31	is	be	AUX
ejpam-4776	184	32	neither	neither	CCONJ
ejpam-4776	184	33	mildly	mildly	ADV
ejpam-4776	184	34	normal	normal	ADJ
ejpam-4776	184	35	nor	nor	CCONJ
ejpam-4776	184	36	locally	locally	ADV
ejpam-4776	184	37	compact	compact	ADJ
ejpam-4776	184	38	[	[	X
ejpam-4776	184	39	14	14	NUM
ejpam-4776	184	40	]	]	PUNCT
ejpam-4776	184	41	.	.	PUNCT
ejpam-4776	185	1	thus	thus	ADV
ejpam-4776	185	2	,	,	PUNCT
ejpam-4776	185	3	the	the	DET
ejpam-4776	185	4	modified	modify	VERB
ejpam-4776	185	5	dieudonné	dieudonné	NOUN
ejpam-4776	185	6	plank	plank	NOUN
ejpam-4776	185	7	is	be	AUX
ejpam-4776	185	8	a	a	DET
ejpam-4776	185	9	cc	cc	NOUN
ejpam-4776	185	10	-	-	NOUN
ejpam-4776	185	11	tychonoff	tychonoff	NOUN
ejpam-4776	185	12	,	,	PUNCT
ejpam-4776	185	13	cct3	cct3	PROPN
ejpam-4776	185	14	,	,	PUNCT
ejpam-4776	185	15	cc	cc	NOUN
ejpam-4776	185	16	-	-	ADJ
ejpam-4776	185	17	completely	completely	ADV
ejpam-4776	185	18	regular	regular	ADJ
ejpam-4776	185	19	and	and	CCONJ
ejpam-4776	185	20	cc	cc	NOUN
ejpam-4776	185	21	-	-	ADJ
ejpam-4776	185	22	regular	regular	ADJ
ejpam-4776	185	23	space	space	NOUN
ejpam-4776	185	24	,	,	PUNCT
ejpam-4776	185	25	which	which	PRON
ejpam-4776	185	26	is	be	AUX
ejpam-4776	185	27	neither	neither	CCONJ
ejpam-4776	185	28	locally	locally	ADV
ejpam-4776	185	29	compact	compact	ADJ
ejpam-4776	185	30	nor	nor	CCONJ
ejpam-4776	185	31	mildly	mildly	ADV
ejpam-4776	185	32	normal	normal	ADJ
ejpam-4776	185	33	.	.	PUNCT
ejpam-4776	186	1	note	note	VERB
ejpam-4776	186	2	that	that	SCONJ
ejpam-4776	186	3	:	:	PUNCT
ejpam-4776	186	4	if	if	SCONJ
ejpam-4776	186	5	x	x	PRON
ejpam-4776	186	6	is	be	AUX
ejpam-4776	186	7	a	a	DET
ejpam-4776	186	8	cc	cc	NOUN
ejpam-4776	186	9	-	-	ADJ
ejpam-4776	186	10	almost	almost	ADV
ejpam-4776	186	11	completely	completely	ADV
ejpam-4776	186	12	regular	regular	ADJ
ejpam-4776	186	13	(	(	PUNCT
ejpam-4776	186	14	resp	resp	NOUN
ejpam-4776	186	15	.	.	PUNCT
ejpam-4776	187	1	cc	cc	NOUN
ejpam-4776	187	2	-	-	PUNCT
ejpam-4776	187	3	almost	almost	ADV
ejpam-4776	187	4	regular	regular	ADJ
ejpam-4776	187	5	,	,	PUNCT
ejpam-4776	187	6	cc	cc	NOUN
ejpam-4776	187	7	-	-	ADJ
ejpam-4776	187	8	complete	complete	ADJ
ejpam-4776	187	9	regularity	regularity	NOUN
ejpam-4776	187	10	,	,	PUNCT
ejpam-4776	187	11	cc	cc	NOUN
ejpam-4776	187	12	-	-	ADJ
ejpam-4776	187	13	regular	regular	ADJ
ejpam-4776	187	14	,	,	PUNCT
ejpam-4776	187	15	cct3	cct3	PROPN
ejpam-4776	187	16	,	,	PUNCT
ejpam-4776	187	17	cc	cc	NOUN
ejpam-4776	187	18	-	-	NOUN
ejpam-4776	187	19	tychonoff	tychonoff	NOUN
ejpam-4776	187	20	)	)	PUNCT
ejpam-4776	187	21	space	space	NOUN
ejpam-4776	187	22	and	and	CCONJ
ejpam-4776	187	23	f	f	NOUN
ejpam-4776	187	24	:	:	PUNCT
ejpam-4776	187	25	x	x	X
ejpam-4776	187	26	→	→	SYM
ejpam-4776	187	27	y	y	PROPN
ejpam-4776	187	28	is	be	AUX
ejpam-4776	187	29	a	a	DET
ejpam-4776	187	30	witness	witness	NOUN
ejpam-4776	187	31	of	of	ADP
ejpam-4776	187	32	the	the	DET
ejpam-4776	187	33	cc	cc	NOUN
ejpam-4776	187	34	-	-	PUNCT
ejpam-4776	187	35	almost	almost	ADV
ejpam-4776	187	36	complete	complete	ADJ
ejpam-4776	187	37	regularity	regularity	NOUN
ejpam-4776	187	38	(	(	PUNCT
ejpam-4776	187	39	resp	resp	NOUN
ejpam-4776	187	40	.	.	PUNCT
ejpam-4776	188	1	cc	cc	NOUN
ejpam-4776	188	2	-	-	PUNCT
ejpam-4776	188	3	almost	almost	ADV
ejpam-4776	188	4	regularity	regularity	NOUN
ejpam-4776	188	5	,	,	PUNCT
ejpam-4776	188	6	cc	cc	NOUN
ejpam-4776	188	7	-	-	ADJ
ejpam-4776	188	8	complete	complete	ADJ
ejpam-4776	188	9	regularity	regularity	NOUN
ejpam-4776	188	10	,	,	PUNCT
ejpam-4776	188	11	cc	cc	NOUN
ejpam-4776	188	12	-	-	NOUN
ejpam-4776	188	13	regularity	regularity	NOUN
ejpam-4776	188	14	,	,	PUNCT
ejpam-4776	188	15	cct3	cct3	PROPN
ejpam-4776	188	16	,	,	PUNCT
ejpam-4776	188	17	cc	cc	NOUN
ejpam-4776	188	18	-	-	NOUN
ejpam-4776	188	19	tychonoffness	tychonoffness	NOUN
ejpam-4776	188	20	)	)	PUNCT
ejpam-4776	188	21	of	of	ADP
ejpam-4776	188	22	x	x	PRON
ejpam-4776	188	23	,	,	PUNCT
ejpam-4776	188	24	then	then	ADV
ejpam-4776	188	25	f	f	PROPN
ejpam-4776	188	26	is	be	AUX
ejpam-4776	188	27	not	not	PART
ejpam-4776	188	28	necessary	necessary	ADJ
ejpam-4776	188	29	to	to	PART
ejpam-4776	188	30	be	be	AUX
ejpam-4776	188	31	continuous	continuous	ADJ
ejpam-4776	188	32	.	.	PUNCT
ejpam-4776	189	1	here	here	ADV
ejpam-4776	189	2	is	be	AUX
ejpam-4776	189	3	a	a	DET
ejpam-4776	189	4	counterexample	counterexample	NOUN
ejpam-4776	189	5	:	:	PUNCT
ejpam-4776	189	6	example	example	NOUN
ejpam-4776	189	7	9	9	NUM
ejpam-4776	189	8	.	.	PUNCT
ejpam-4776	190	1	consider	consider	VERB
ejpam-4776	190	2	the	the	DET
ejpam-4776	190	3	countable	countable	ADJ
ejpam-4776	190	4	complement	complement	NOUN
ejpam-4776	190	5	topology	topology	NOUN
ejpam-4776	190	6	on	on	ADP
ejpam-4776	190	7	r	r	NOUN
ejpam-4776	190	8	,	,	PUNCT
ejpam-4776	190	9	(	(	PUNCT
ejpam-4776	190	10	r	r	NOUN
ejpam-4776	190	11	,	,	PUNCT
ejpam-4776	190	12	cc	cc	NOUN
ejpam-4776	190	13	)	)	PUNCT
ejpam-4776	190	14	.	.	PUNCT
ejpam-4776	191	1	the	the	DET
ejpam-4776	191	2	only	only	ADJ
ejpam-4776	191	3	countably	countably	ADV
ejpam-4776	191	4	compact	compact	ADJ
ejpam-4776	191	5	subspaces	subspace	NOUN
ejpam-4776	191	6	are	be	AUX
ejpam-4776	191	7	finite	finite	ADJ
ejpam-4776	191	8	subspaces	subspace	NOUN
ejpam-4776	191	9	and	and	CCONJ
ejpam-4776	191	10	(	(	PUNCT
ejpam-4776	191	11	r	r	NOUN
ejpam-4776	191	12	,	,	PUNCT
ejpam-4776	191	13	cc	cc	NOUN
ejpam-4776	191	14	)	)	PUNCT
ejpam-4776	191	15	is	be	AUX
ejpam-4776	191	16	t1	t1	NOUN
ejpam-4776	191	17	-	-	PUNCT
ejpam-4776	191	18	space	space	NOUN
ejpam-4776	191	19	.	.	PUNCT
ejpam-4776	192	1	hence	hence	ADV
ejpam-4776	192	2	,	,	PUNCT
ejpam-4776	192	3	(	(	PUNCT
ejpam-4776	192	4	r	r	NOUN
ejpam-4776	192	5	,	,	PUNCT
ejpam-4776	192	6	cc	cc	NOUN
ejpam-4776	192	7	)	)	PUNCT
ejpam-4776	192	8	is	be	AUX
ejpam-4776	192	9	cc	cc	NOUN
ejpam-4776	192	10	-	-	NOUN
ejpam-4776	192	11	tychonoff	tychonoff	NOUN
ejpam-4776	192	12	(	(	PUNCT
ejpam-4776	192	13	hence	hence	ADV
ejpam-4776	192	14	cc	cc	NOUN
ejpam-4776	192	15	-	-	ADJ
ejpam-4776	192	16	completely	completely	ADV
ejpam-4776	192	17	regular	regular	ADJ
ejpam-4776	192	18	,	,	PUNCT
ejpam-4776	192	19	cc	cc	NOUN
ejpam-4776	192	20	-	-	ADJ
ejpam-4776	192	21	almost	almost	ADV
ejpam-4776	192	22	completely	completely	ADV
ejpam-4776	192	23	regular	regular	ADJ
ejpam-4776	192	24	,	,	PUNCT
ejpam-4776	192	25	cc	cc	NOUN
ejpam-4776	192	26	-	-	ADJ
ejpam-4776	192	27	almost	almost	ADV
ejpam-4776	192	28	regular	regular	ADJ
ejpam-4776	192	29	,	,	PUNCT
ejpam-4776	192	30	cct3	cct3	PROPN
ejpam-4776	192	31	and	and	CCONJ
ejpam-4776	192	32	cc	cc	NOUN
ejpam-4776	192	33	-	-	NOUN
ejpam-4776	192	34	regular	regular	ADJ
ejpam-4776	192	35	)	)	PUNCT
ejpam-4776	192	36	.	.	PUNCT
ejpam-4776	193	1	it	it	PRON
ejpam-4776	193	2	is	be	AUX
ejpam-4776	193	3	well	well	ADV
ejpam-4776	193	4	known	know	VERB
ejpam-4776	193	5	that	that	SCONJ
ejpam-4776	193	6	the	the	DET
ejpam-4776	193	7	finite	finite	ADJ
ejpam-4776	193	8	countably	countably	ADV
ejpam-4776	193	9	-	-	ADJ
ejpam-4776	193	10	compact	compact	ADJ
ejpam-4776	193	11	subspaces	subspace	NOUN
ejpam-4776	193	12	in	in	ADP
ejpam-4776	193	13	a	a	DET
ejpam-4776	193	14	t1	t1	NOUN
ejpam-4776	193	15	-	-	PUNCT
ejpam-4776	193	16	space	space	NOUN
ejpam-4776	193	17	are	be	AUX
ejpam-4776	193	18	discrete	discrete	ADJ
ejpam-4776	193	19	.	.	PUNCT
ejpam-4776	194	1	if	if	SCONJ
ejpam-4776	194	2	we	we	PRON
ejpam-4776	194	3	let	let	VERB
ejpam-4776	194	4	d	d	PART
ejpam-4776	194	5	be	be	AUX
ejpam-4776	194	6	the	the	DET
ejpam-4776	194	7	discrete	discrete	ADJ
ejpam-4776	194	8	topology	topology	NOUN
ejpam-4776	194	9	on	on	ADP
ejpam-4776	194	10	r	r	NOUN
ejpam-4776	194	11	,	,	PUNCT
ejpam-4776	194	12	then	then	ADV
ejpam-4776	194	13	the	the	DET
ejpam-4776	194	14	identity	identity	NOUN
ejpam-4776	194	15	function	function	NOUN
ejpam-4776	194	16	from	from	ADP
ejpam-4776	194	17	(	(	PUNCT
ejpam-4776	194	18	r	r	NOUN
ejpam-4776	194	19	,	,	PUNCT
ejpam-4776	194	20	cc	cc	NOUN
ejpam-4776	194	21	)	)	PUNCT
ejpam-4776	194	22	onto	onto	ADP
ejpam-4776	194	23	(	(	PUNCT
ejpam-4776	194	24	r	r	NOUN
ejpam-4776	194	25	,	,	PUNCT
ejpam-4776	194	26	d	d	NOUN
ejpam-4776	194	27	)	)	PUNCT
ejpam-4776	194	28	is	be	AUX
ejpam-4776	194	29	a	a	DET
ejpam-4776	194	30	witness	witness	NOUN
ejpam-4776	194	31	of	of	ADP
ejpam-4776	194	32	the	the	DET
ejpam-4776	194	33	cc	cc	NOUN
ejpam-4776	194	34	-	-	NOUN
ejpam-4776	194	35	tychonoffness	tychonoffness	NOUN
ejpam-4776	194	36	(	(	PUNCT
ejpam-4776	194	37	resp	resp	NOUN
ejpam-4776	194	38	.	.	PUNCT
ejpam-4776	195	1	cc	cc	NOUN
ejpam-4776	195	2	-	-	ADJ
ejpam-4776	195	3	complete	complete	ADJ
ejpam-4776	195	4	regularity	regularity	NOUN
ejpam-4776	195	5	,	,	PUNCT
ejpam-4776	195	6	cc	cc	NOUN
ejpam-4776	195	7	-	-	ADJ
ejpam-4776	195	8	almost	almost	ADV
ejpam-4776	195	9	complete	complete	ADJ
ejpam-4776	195	10	regularity	regularity	NOUN
ejpam-4776	195	11	,	,	PUNCT
ejpam-4776	195	12	cc	cc	NOUN
ejpam-4776	195	13	-	-	ADJ
ejpam-4776	195	14	almost	almost	ADV
ejpam-4776	195	15	regularity	regularity	NOUN
ejpam-4776	195	16	,	,	PUNCT
ejpam-4776	195	17	cct3	cct3	PROPN
ejpam-4776	195	18	,	,	PUNCT
ejpam-4776	195	19	cc	cc	NOUN
ejpam-4776	195	20	-	-	NOUN
ejpam-4776	195	21	regularity	regularity	NOUN
ejpam-4776	195	22	)	)	PUNCT
ejpam-4776	195	23	of	of	ADP
ejpam-4776	195	24	(	(	PUNCT
ejpam-4776	195	25	r	r	NOUN
ejpam-4776	195	26	,	,	PUNCT
ejpam-4776	195	27	cc	cc	NOUN
ejpam-4776	195	28	)	)	PUNCT
ejpam-4776	195	29	,	,	PUNCT
ejpam-4776	195	30	which	which	PRON
ejpam-4776	195	31	is	be	AUX
ejpam-4776	195	32	not	not	PART
ejpam-4776	195	33	continuous	continuous	ADJ
ejpam-4776	195	34	.	.	PUNCT
ejpam-4776	196	1	recall	recall	VERB
ejpam-4776	196	2	that	that	PRON
ejpam-4776	196	3	:	:	PUNCT
ejpam-4776	196	4	a	a	DET
ejpam-4776	196	5	space	space	NOUN
ejpam-4776	196	6	x	x	PUNCT
ejpam-4776	196	7	is	be	AUX
ejpam-4776	196	8	called	call	VERB
ejpam-4776	196	9	a	a	DET
ejpam-4776	196	10	fréchet	fréchet	NOUN
ejpam-4776	196	11	if	if	SCONJ
ejpam-4776	196	12	for	for	ADP
ejpam-4776	196	13	any	any	DET
ejpam-4776	196	14	subset	subset	NOUN
ejpam-4776	196	15	b	b	PROPN
ejpam-4776	196	16	of	of	ADP
ejpam-4776	196	17	x	x	X
ejpam-4776	196	18	and	and	CCONJ
ejpam-4776	196	19	any	any	DET
ejpam-4776	196	20	x	x	SYM
ejpam-4776	196	21	∈	∈	PROPN
ejpam-4776	196	22	b	b	NOUN
ejpam-4776	196	23	,	,	PUNCT
ejpam-4776	196	24	there	there	PRON
ejpam-4776	196	25	exists	exist	VERB
ejpam-4776	196	26	a	a	DET
ejpam-4776	196	27	sequence	sequence	NOUN
ejpam-4776	196	28	(	(	PUNCT
ejpam-4776	196	29	an)n∈n	an)n∈n	NUM
ejpam-4776	196	30	of	of	ADP
ejpam-4776	196	31	points	point	NOUN
ejpam-4776	196	32	of	of	ADP
ejpam-4776	196	33	b	b	NOUN
ejpam-4776	196	34	such	such	ADJ
ejpam-4776	196	35	that	that	SCONJ
ejpam-4776	196	36	an	an	DET
ejpam-4776	196	37	−→	−→	NOUN
ejpam-4776	196	38	x	x	SYM
ejpam-4776	197	1	[	[	X
ejpam-4776	197	2	10	10	NUM
ejpam-4776	197	3	]	]	PUNCT
ejpam-4776	197	4	.	.	PUNCT
ejpam-4776	198	1	thus	thus	ADV
ejpam-4776	198	2	,	,	PUNCT
ejpam-4776	198	3	we	we	PRON
ejpam-4776	198	4	conclude	conclude	VERB
ejpam-4776	198	5	:	:	PUNCT
ejpam-4776	198	6	theorem	theorem	VERB
ejpam-4776	198	7	6	6	NUM
ejpam-4776	198	8	.	.	PUNCT
ejpam-4776	199	1	if	if	SCONJ
ejpam-4776	199	2	x	x	PRON
ejpam-4776	199	3	is	be	AUX
ejpam-4776	199	4	a	a	DET
ejpam-4776	199	5	cc	cc	NOUN
ejpam-4776	199	6	-	-	ADJ
ejpam-4776	199	7	completely	completely	ADV
ejpam-4776	199	8	regular	regular	ADJ
ejpam-4776	199	9	fréchet	fréchet	NOUN
ejpam-4776	199	10	space	space	NOUN
ejpam-4776	199	11	,	,	PUNCT
ejpam-4776	199	12	then	then	ADV
ejpam-4776	199	13	any	any	DET
ejpam-4776	199	14	function	function	NOUN
ejpam-4776	199	15	bears	bear	VERB
ejpam-4776	199	16	the	the	DET
ejpam-4776	199	17	cc	cc	NOUN
ejpam-4776	199	18	-	-	ADJ
ejpam-4776	199	19	complete	complete	ADJ
ejpam-4776	199	20	regularity	regularity	NOUN
ejpam-4776	199	21	of	of	ADP
ejpam-4776	199	22	x	x	SYM
ejpam-4776	199	23	is	be	AUX
ejpam-4776	199	24	continuous	continuous	ADJ
ejpam-4776	199	25	.	.	PUNCT
ejpam-4776	200	1	proof	proof	NOUN
ejpam-4776	200	2	.	.	PUNCT
ejpam-4776	201	1	similar	similar	ADJ
ejpam-4776	201	2	to	to	ADP
ejpam-4776	201	3	the	the	DET
ejpam-4776	201	4	proof	proof	NOUN
ejpam-4776	201	5	of	of	ADP
ejpam-4776	201	6	theorem	theorem	ADJ
ejpam-4776	201	7	2.9	2.9	NUM
ejpam-4776	201	8	in	in	ADP
ejpam-4776	201	9	[	[	X
ejpam-4776	201	10	14	14	NUM
ejpam-4776	201	11	]	]	PUNCT
ejpam-4776	201	12	.	.	PUNCT
ejpam-4776	202	1	the	the	DET
ejpam-4776	202	2	proof	proof	NOUN
ejpam-4776	202	3	of	of	ADP
ejpam-4776	202	4	the	the	DET
ejpam-4776	202	5	next	next	ADJ
ejpam-4776	202	6	theorem	theorem	NOUN
ejpam-4776	202	7	is	be	AUX
ejpam-4776	202	8	also	also	ADV
ejpam-4776	202	9	similar	similar	ADJ
ejpam-4776	202	10	to	to	ADP
ejpam-4776	202	11	the	the	DET
ejpam-4776	202	12	proof	proof	NOUN
ejpam-4776	202	13	of	of	ADP
ejpam-4776	202	14	theorem	theorem	ADJ
ejpam-4776	202	15	2.9	2.9	NUM
ejpam-4776	202	16	in	in	ADP
ejpam-4776	202	17	[	[	X
ejpam-4776	202	18	14	14	NUM
ejpam-4776	202	19	]	]	PUNCT
ejpam-4776	202	20	..	..	PUNCT
ejpam-4776	203	1	s.	s.	PROPN
ejpam-4776	203	2	a.	a.	PROPN
ejpam-4776	203	3	thabit	thabit	PROPN
ejpam-4776	203	4	,	,	PUNCT
ejpam-4776	203	5	w.	w.	PROPN
ejpam-4776	203	6	alqurashi	alqurashi	PROPN
ejpam-4776	203	7	/	/	SYM
ejpam-4776	203	8	eur	eur	PROPN
ejpam-4776	203	9	.	.	PUNCT
ejpam-4776	204	1	j.	j.	PROPN
ejpam-4776	204	2	pure	pure	PROPN
ejpam-4776	204	3	appl	appl	PROPN
ejpam-4776	204	4	.	.	PROPN
ejpam-4776	204	5	math	math	PROPN
ejpam-4776	204	6	,	,	PUNCT
ejpam-4776	204	7	16	16	NUM
ejpam-4776	204	8	(	(	PUNCT
ejpam-4776	204	9	2	2	NUM
ejpam-4776	204	10	)	)	PUNCT
ejpam-4776	204	11	(	(	PUNCT
ejpam-4776	204	12	2023	2023	NUM
ejpam-4776	204	13	)	)	PUNCT
ejpam-4776	204	14	,	,	PUNCT
ejpam-4776	204	15	1260	1260	NUM
ejpam-4776	204	16	-	-	SYM
ejpam-4776	204	17	1273	1273	NUM
ejpam-4776	204	18	1267	1267	NUM
ejpam-4776	204	19	theorem	theorem	NOUN
ejpam-4776	204	20	7	7	NUM
ejpam-4776	204	21	.	.	PUNCT
ejpam-4776	205	1	if	if	SCONJ
ejpam-4776	205	2	x	x	PRON
ejpam-4776	205	3	is	be	AUX
ejpam-4776	205	4	a	a	DET
ejpam-4776	205	5	cc	cc	NOUN
ejpam-4776	205	6	-	-	NOUN
ejpam-4776	205	7	tychonoff	tychonoff	NOUN
ejpam-4776	205	8	(	(	PUNCT
ejpam-4776	205	9	resp	resp	NOUN
ejpam-4776	205	10	.	.	PUNCT
ejpam-4776	206	1	cc	cc	NOUN
ejpam-4776	206	2	-	-	ADJ
ejpam-4776	206	3	regular	regular	ADJ
ejpam-4776	206	4	,	,	PUNCT
ejpam-4776	206	5	cct3	cct3	PROPN
ejpam-4776	206	6	,	,	PUNCT
ejpam-4776	206	7	cc	cc	NOUN
ejpam-4776	206	8	-	-	ADJ
ejpam-4776	206	9	almost	almost	ADV
ejpam-4776	206	10	regular	regular	ADJ
ejpam-4776	206	11	,	,	PUNCT
ejpam-4776	206	12	cc	cc	NOUN
ejpam-4776	206	13	-	-	ADJ
ejpam-4776	206	14	almost	almost	ADV
ejpam-4776	206	15	completely	completely	ADV
ejpam-4776	206	16	regular	regular	ADJ
ejpam-4776	206	17	)	)	PUNCT
ejpam-4776	206	18	fréchet	fréchet	NOUN
ejpam-4776	206	19	space	space	NOUN
ejpam-4776	206	20	,	,	PUNCT
ejpam-4776	206	21	then	then	ADV
ejpam-4776	206	22	any	any	DET
ejpam-4776	206	23	function	function	NOUN
ejpam-4776	206	24	bears	bear	VERB
ejpam-4776	206	25	the	the	DET
ejpam-4776	206	26	cc	cc	NOUN
ejpam-4776	206	27	-	-	NOUN
ejpam-4776	206	28	tychonofness	tychonofness	ADJ
ejpam-4776	206	29	(	(	PUNCT
ejpam-4776	206	30	resp	resp	NOUN
ejpam-4776	206	31	.	.	PUNCT
ejpam-4776	207	1	cc	cc	NOUN
ejpam-4776	207	2	-	-	NOUN
ejpam-4776	207	3	regularity	regularity	NOUN
ejpam-4776	207	4	,	,	PUNCT
ejpam-4776	207	5	cct3	cct3	PROPN
ejpam-4776	207	6	,	,	PUNCT
ejpam-4776	207	7	cc	cc	NOUN
ejpam-4776	207	8	-	-	ADJ
ejpam-4776	207	9	almost	almost	ADV
ejpam-4776	207	10	regularity	regularity	NOUN
ejpam-4776	207	11	,	,	PUNCT
ejpam-4776	207	12	cc	cc	NOUN
ejpam-4776	207	13	-	-	ADJ
ejpam-4776	207	14	almost	almost	ADV
ejpam-4776	207	15	complete	complete	ADJ
ejpam-4776	207	16	regularity	regularity	NOUN
ejpam-4776	207	17	)	)	PUNCT
ejpam-4776	207	18	of	of	ADP
ejpam-4776	207	19	x	x	SYM
ejpam-4776	207	20	is	be	AUX
ejpam-4776	207	21	continuous	continuous	ADJ
ejpam-4776	207	22	.	.	PUNCT
ejpam-4776	208	1	since	since	SCONJ
ejpam-4776	208	2	every	every	DET
ejpam-4776	208	3	first	first	ADJ
ejpam-4776	208	4	countable	countable	ADJ
ejpam-4776	208	5	space	space	NOUN
ejpam-4776	208	6	is	be	AUX
ejpam-4776	208	7	fréchet	fréchet	VERB
ejpam-4776	208	8	[	[	X
ejpam-4776	208	9	10	10	NUM
ejpam-4776	208	10	]	]	PUNCT
ejpam-4776	208	11	,	,	PUNCT
ejpam-4776	208	12	we	we	PRON
ejpam-4776	208	13	get	get	VERB
ejpam-4776	208	14	the	the	DET
ejpam-4776	208	15	next	next	ADJ
ejpam-4776	208	16	corollary	corollary	NOUN
ejpam-4776	208	17	:	:	PUNCT
ejpam-4776	209	1	corollary	corollary	ADJ
ejpam-4776	209	2	5	5	NUM
ejpam-4776	209	3	.	.	PUNCT
ejpam-4776	210	1	if	if	SCONJ
ejpam-4776	210	2	x	x	PRON
ejpam-4776	210	3	is	be	AUX
ejpam-4776	210	4	a	a	DET
ejpam-4776	210	5	cc	cc	NOUN
ejpam-4776	210	6	-	-	ADJ
ejpam-4776	210	7	almost	almost	ADV
ejpam-4776	210	8	regular	regular	ADJ
ejpam-4776	210	9	first	first	ADJ
ejpam-4776	210	10	countable	countable	ADJ
ejpam-4776	210	11	space	space	NOUN
ejpam-4776	210	12	and	and	CCONJ
ejpam-4776	210	13	f	f	NOUN
ejpam-4776	210	14	:	:	PUNCT
ejpam-4776	210	15	x	x	X
ejpam-4776	210	16	→	→	SYM
ejpam-4776	210	17	y	y	PROPN
ejpam-4776	210	18	is	be	AUX
ejpam-4776	210	19	a	a	DET
ejpam-4776	210	20	witness	witness	NOUN
ejpam-4776	210	21	of	of	ADP
ejpam-4776	210	22	the	the	DET
ejpam-4776	210	23	cc	cc	NOUN
ejpam-4776	210	24	-	-	ADJ
ejpam-4776	210	25	almost	almost	ADV
ejpam-4776	210	26	regularity	regularity	NOUN
ejpam-4776	210	27	of	of	ADP
ejpam-4776	210	28	x	x	PRON
ejpam-4776	210	29	,	,	PUNCT
ejpam-4776	210	30	then	then	ADV
ejpam-4776	210	31	f	f	PROPN
ejpam-4776	210	32	is	be	AUX
ejpam-4776	210	33	continuous	continuous	ADJ
ejpam-4776	210	34	.	.	PUNCT
ejpam-4776	211	1	next	next	ADV
ejpam-4776	211	2	,	,	PUNCT
ejpam-4776	211	3	we	we	PRON
ejpam-4776	211	4	introduce	introduce	VERB
ejpam-4776	211	5	the	the	DET
ejpam-4776	211	6	following	follow	VERB
ejpam-4776	211	7	results	result	NOUN
ejpam-4776	211	8	:	:	PUNCT
ejpam-4776	211	9	proposition	proposition	NOUN
ejpam-4776	211	10	1	1	NUM
ejpam-4776	211	11	.	.	PUNCT
ejpam-4776	212	1	if	if	SCONJ
ejpam-4776	212	2	x	x	PRON
ejpam-4776	212	3	is	be	AUX
ejpam-4776	212	4	a	a	DET
ejpam-4776	212	5	t1	t1	NOUN
ejpam-4776	212	6	cc	cc	NOUN
ejpam-4776	212	7	-	-	ADJ
ejpam-4776	212	8	completely	completely	ADV
ejpam-4776	212	9	regular	regular	ADJ
ejpam-4776	212	10	space	space	NOUN
ejpam-4776	212	11	,	,	PUNCT
ejpam-4776	212	12	then	then	ADV
ejpam-4776	212	13	the	the	DET
ejpam-4776	212	14	witness	witness	NOUN
ejpam-4776	212	15	y	y	PROPN
ejpam-4776	212	16	is	be	AUX
ejpam-4776	212	17	tychonoff	tychonoff	NOUN
ejpam-4776	212	18	.	.	PUNCT
ejpam-4776	213	1	proof	proof	NOUN
ejpam-4776	213	2	.	.	PUNCT
ejpam-4776	214	1	letx	letx	PROPN
ejpam-4776	214	2	be	be	AUX
ejpam-4776	214	3	a	a	DET
ejpam-4776	214	4	t1	t1	NOUN
ejpam-4776	214	5	cc	cc	NOUN
ejpam-4776	214	6	-	-	ADJ
ejpam-4776	214	7	completely	completely	ADV
ejpam-4776	214	8	regular	regular	ADJ
ejpam-4776	214	9	space	space	NOUN
ejpam-4776	214	10	.	.	PUNCT
ejpam-4776	215	1	sincex	sincex	PROPN
ejpam-4776	215	2	is	be	AUX
ejpam-4776	215	3	a	a	DET
ejpam-4776	215	4	cc	cc	NOUN
ejpam-4776	215	5	-	-	ADJ
ejpam-4776	215	6	completely	completely	ADV
ejpam-4776	215	7	regular	regular	ADJ
ejpam-4776	215	8	space	space	NOUN
ejpam-4776	215	9	,	,	PUNCT
ejpam-4776	215	10	there	there	PRON
ejpam-4776	215	11	exist	exist	VERB
ejpam-4776	215	12	a	a	DET
ejpam-4776	215	13	completely	completely	ADV
ejpam-4776	215	14	regular	regular	ADJ
ejpam-4776	215	15	space	space	NOUN
ejpam-4776	215	16	y	y	PROPN
ejpam-4776	215	17	and	and	CCONJ
ejpam-4776	215	18	a	a	DET
ejpam-4776	215	19	bijective	bijective	ADJ
ejpam-4776	215	20	function	function	NOUN
ejpam-4776	215	21	f	f	NOUN
ejpam-4776	215	22	:	:	PUNCT
ejpam-4776	215	23	(	(	PUNCT
ejpam-4776	215	24	x	x	X
ejpam-4776	215	25	,	,	PUNCT
ejpam-4776	215	26	t	t	PROPN
ejpam-4776	215	27	)	)	PUNCT
ejpam-4776	215	28	→	→	SYM
ejpam-4776	215	29	(	(	PUNCT
ejpam-4776	215	30	y	y	PROPN
ejpam-4776	215	31	,	,	PUNCT
ejpam-4776	215	32	t	t	PROPN
ejpam-4776	215	33	′	′	NUM
ejpam-4776	215	34	)	)	PUNCT
ejpam-4776	215	35	such	such	ADJ
ejpam-4776	215	36	that	that	SCONJ
ejpam-4776	215	37	f	f	PROPN
ejpam-4776	215	38	|a	|a	VERB
ejpam-4776	215	39	:	:	PUNCT
ejpam-4776	215	40	a	a	DET
ejpam-4776	215	41	→	→	SYM
ejpam-4776	215	42	f(a	f(a	NOUN
ejpam-4776	215	43	)	)	PUNCT
ejpam-4776	215	44	is	be	AUX
ejpam-4776	215	45	a	a	DET
ejpam-4776	215	46	homeomorphism	homeomorphism	NOUN
ejpam-4776	215	47	for	for	SCONJ
ejpam-4776	215	48	each	each	DET
ejpam-4776	215	49	countably	countably	ADV
ejpam-4776	215	50	compact	compact	ADJ
ejpam-4776	215	51	subset	subset	VERB
ejpam-4776	215	52	a	a	DET
ejpam-4776	215	53	⊆	⊆	NUM
ejpam-4776	215	54	x.	x.	NOUN
ejpam-4776	215	55	suppose	suppose	VERB
ejpam-4776	215	56	y	y	PROPN
ejpam-4776	215	57	is	be	AUX
ejpam-4776	215	58	not	not	PART
ejpam-4776	215	59	tychonoff	tychonoff	NOUN
ejpam-4776	215	60	,	,	PUNCT
ejpam-4776	215	61	then	then	ADV
ejpam-4776	215	62	y	y	PROPN
ejpam-4776	215	63	can	can	AUX
ejpam-4776	215	64	not	not	PART
ejpam-4776	215	65	be	be	AUX
ejpam-4776	215	66	t1	t1	NOUN
ejpam-4776	215	67	because	because	SCONJ
ejpam-4776	215	68	it	it	PRON
ejpam-4776	215	69	is	be	AUX
ejpam-4776	215	70	completely	completely	ADV
ejpam-4776	215	71	regular	regular	ADJ
ejpam-4776	215	72	.	.	PUNCT
ejpam-4776	216	1	then	then	ADV
ejpam-4776	216	2	,	,	PUNCT
ejpam-4776	216	3	there	there	PRON
ejpam-4776	216	4	exist	exist	VERB
ejpam-4776	216	5	two	two	NUM
ejpam-4776	216	6	distinct	distinct	ADJ
ejpam-4776	216	7	elements	element	NOUN
ejpam-4776	216	8	x	x	PUNCT
ejpam-4776	216	9	and	and	CCONJ
ejpam-4776	216	10	y	y	PROPN
ejpam-4776	216	11	in	in	ADP
ejpam-4776	216	12	y	y	PRON
ejpam-4776	216	13	such	such	ADJ
ejpam-4776	216	14	that	that	SCONJ
ejpam-4776	216	15	if	if	SCONJ
ejpam-4776	216	16	u	u	NOUN
ejpam-4776	216	17	is	be	AUX
ejpam-4776	216	18	any	any	DET
ejpam-4776	216	19	open	open	ADJ
ejpam-4776	216	20	neighborhood	neighborhood	NOUN
ejpam-4776	216	21	of	of	ADP
ejpam-4776	216	22	x	x	NOUN
ejpam-4776	216	23	,	,	PUNCT
ejpam-4776	216	24	then	then	ADV
ejpam-4776	216	25	y	y	PROPN
ejpam-4776	216	26	∈	∈	PROPN
ejpam-4776	216	27	u	u	NOUN
ejpam-4776	216	28	or	or	CCONJ
ejpam-4776	216	29	if	if	SCONJ
ejpam-4776	216	30	v	v	NOUN
ejpam-4776	216	31	is	be	AUX
ejpam-4776	216	32	any	any	DET
ejpam-4776	216	33	open	open	ADJ
ejpam-4776	216	34	neighborhood	neighborhood	NOUN
ejpam-4776	216	35	of	of	ADP
ejpam-4776	216	36	y	y	PROPN
ejpam-4776	216	37	,	,	PUNCT
ejpam-4776	216	38	then	then	ADV
ejpam-4776	216	39	x	x	PART
ejpam-4776	216	40	∈	∈	PROPN
ejpam-4776	216	41	v	v	NOUN
ejpam-4776	216	42	.	.	PUNCT
ejpam-4776	217	1	thus	thus	ADV
ejpam-4776	217	2	,	,	PUNCT
ejpam-4776	217	3	the	the	DET
ejpam-4776	217	4	set	set	NOUN
ejpam-4776	217	5	m	m	NOUN
ejpam-4776	217	6	=	=	SYM
ejpam-4776	217	7	{	{	PUNCT
ejpam-4776	217	8	f−1({x	f−1({x	NOUN
ejpam-4776	217	9	}	}	PUNCT
ejpam-4776	217	10	)	)	PUNCT
ejpam-4776	217	11	,	,	PUNCT
ejpam-4776	217	12	f−1({y	f−1({y	NOUN
ejpam-4776	217	13	}	}	PUNCT
ejpam-4776	217	14	)	)	PUNCT
ejpam-4776	217	15	}	}	PUNCT
ejpam-4776	217	16	is	be	AUX
ejpam-4776	217	17	a	a	DET
ejpam-4776	217	18	t1	t1	NOUN
ejpam-4776	217	19	countably	countably	ADV
ejpam-4776	217	20	compact	compact	ADJ
ejpam-4776	217	21	subspace	subspace	NOUN
ejpam-4776	217	22	of	of	ADP
ejpam-4776	217	23	x.	x.	NOUN
ejpam-4776	217	24	then	then	ADV
ejpam-4776	217	25	,	,	PUNCT
ejpam-4776	217	26	f	f	PROPN
ejpam-4776	217	27	|m	|m	NOUN
ejpam-4776	217	28	:	:	PUNCT
ejpam-4776	217	29	m	m	PROPN
ejpam-4776	217	30	→	→	SYM
ejpam-4776	217	31	f(m	f(m	PROPN
ejpam-4776	217	32	)	)	PUNCT
ejpam-4776	217	33	is	be	AUX
ejpam-4776	217	34	a	a	DET
ejpam-4776	217	35	homeomorphism	homeomorphism	NOUN
ejpam-4776	217	36	.	.	PUNCT
ejpam-4776	218	1	but	but	CCONJ
ejpam-4776	218	2	f(m	f(m	PROPN
ejpam-4776	218	3	)	)	PUNCT
ejpam-4776	218	4	=	=	PRON
ejpam-4776	218	5	{	{	PUNCT
ejpam-4776	218	6	x	x	NOUN
ejpam-4776	218	7	,	,	PUNCT
ejpam-4776	218	8	y	y	NOUN
ejpam-4776	218	9	}	}	PUNCT
ejpam-4776	218	10	can	can	AUX
ejpam-4776	218	11	not	not	PART
ejpam-4776	218	12	be	be	AUX
ejpam-4776	218	13	t1	t1	NOUN
ejpam-4776	218	14	,	,	PUNCT
ejpam-4776	218	15	which	which	PRON
ejpam-4776	218	16	is	be	AUX
ejpam-4776	218	17	a	a	DET
ejpam-4776	218	18	contradiction	contradiction	NOUN
ejpam-4776	218	19	.	.	PUNCT
ejpam-4776	219	1	hence	hence	ADV
ejpam-4776	219	2	,	,	PUNCT
ejpam-4776	219	3	y	y	PROPN
ejpam-4776	219	4	must	must	AUX
ejpam-4776	219	5	be	be	AUX
ejpam-4776	219	6	t1	t1	NOUN
ejpam-4776	219	7	and	and	CCONJ
ejpam-4776	219	8	thus	thus	ADV
ejpam-4776	219	9	tychonoff	tychonoff	NOUN
ejpam-4776	219	10	.	.	PUNCT
ejpam-4776	220	1	similarly	similarly	ADV
ejpam-4776	220	2	,	,	PUNCT
ejpam-4776	220	3	we	we	PRON
ejpam-4776	220	4	can	can	AUX
ejpam-4776	220	5	prove	prove	VERB
ejpam-4776	220	6	the	the	DET
ejpam-4776	220	7	next	next	ADJ
ejpam-4776	220	8	proposition	proposition	NOUN
ejpam-4776	220	9	:	:	PUNCT
ejpam-4776	220	10	proposition	proposition	NOUN
ejpam-4776	220	11	2	2	NUM
ejpam-4776	220	12	.	.	PUNCT
ejpam-4776	221	1	if	if	SCONJ
ejpam-4776	221	2	x	x	PRON
ejpam-4776	221	3	is	be	AUX
ejpam-4776	221	4	a	a	DET
ejpam-4776	221	5	t1	t1	NOUN
ejpam-4776	221	6	cc	cc	NOUN
ejpam-4776	221	7	-	-	NOUN
ejpam-4776	221	8	regular	regular	ADJ
ejpam-4776	221	9	(	(	PUNCT
ejpam-4776	221	10	resp	resp	NOUN
ejpam-4776	221	11	.	.	PUNCT
ejpam-4776	222	1	cc	cc	NOUN
ejpam-4776	222	2	-	-	ADJ
ejpam-4776	222	3	normal	normal	ADJ
ejpam-4776	222	4	)	)	PUNCT
ejpam-4776	222	5	space	space	NOUN
ejpam-4776	222	6	,	,	PUNCT
ejpam-4776	222	7	then	then	ADV
ejpam-4776	222	8	the	the	DET
ejpam-4776	222	9	witness	witness	NOUN
ejpam-4776	222	10	y	y	PROPN
ejpam-4776	222	11	is	be	AUX
ejpam-4776	222	12	t3	t3	PROPN
ejpam-4776	222	13	(	(	PUNCT
ejpam-4776	222	14	resp	resp	NOUN
ejpam-4776	222	15	.	.	PUNCT
ejpam-4776	223	1	t4	t4	PROPN
ejpam-4776	223	2	)	)	PUNCT
ejpam-4776	223	3	.	.	PUNCT
ejpam-4776	224	1	thus	thus	ADV
ejpam-4776	224	2	,	,	PUNCT
ejpam-4776	224	3	we	we	PRON
ejpam-4776	224	4	get	get	VERB
ejpam-4776	224	5	the	the	DET
ejpam-4776	224	6	next	next	ADJ
ejpam-4776	224	7	corollary	corollary	NOUN
ejpam-4776	224	8	:	:	PUNCT
ejpam-4776	224	9	corollary	corollary	ADJ
ejpam-4776	224	10	6	6	NUM
ejpam-4776	224	11	.	.	PUNCT
ejpam-4776	225	1	every	every	DET
ejpam-4776	225	2	t1	t1	NOUN
ejpam-4776	225	3	cc	cc	NOUN
ejpam-4776	225	4	-	-	ADJ
ejpam-4776	225	5	completely	completely	ADV
ejpam-4776	225	6	regular	regular	ADJ
ejpam-4776	225	7	(	(	PUNCT
ejpam-4776	225	8	resp	resp	NOUN
ejpam-4776	225	9	.	.	PUNCT
ejpam-4776	226	1	cc	cc	NOUN
ejpam-4776	226	2	-	-	ADJ
ejpam-4776	226	3	regular	regular	ADJ
ejpam-4776	226	4	,	,	PUNCT
ejpam-4776	226	5	cc	cc	NOUN
ejpam-4776	226	6	-	-	ADJ
ejpam-4776	226	7	normal	normal	ADJ
ejpam-4776	226	8	)	)	PUNCT
ejpam-4776	226	9	space	space	NOUN
ejpam-4776	226	10	is	be	AUX
ejpam-4776	226	11	cc	cc	NOUN
ejpam-4776	226	12	-	-	NOUN
ejpam-4776	226	13	tychonoff	tychonoff	NOUN
ejpam-4776	226	14	(	(	PUNCT
ejpam-4776	226	15	resp	resp	NOUN
ejpam-4776	226	16	.	.	PUNCT
ejpam-4776	227	1	cct3	cct3	PROPN
ejpam-4776	227	2	,	,	PUNCT
ejpam-4776	227	3	cc	cc	NOUN
ejpam-4776	227	4	-	-	NOUN
ejpam-4776	227	5	tychonoff	tychonoff	NOUN
ejpam-4776	227	6	)	)	PUNCT
ejpam-4776	227	7	.	.	PUNCT
ejpam-4776	228	1	theorem	theorem	ADJ
ejpam-4776	228	2	8	8	NUM
ejpam-4776	228	3	.	.	PUNCT
ejpam-4776	229	1	every	every	DET
ejpam-4776	229	2	t1	t1	NOUN
ejpam-4776	229	3	cc	cc	NOUN
ejpam-4776	229	4	-	-	ADJ
ejpam-4776	229	5	completely	completely	ADV
ejpam-4776	229	6	regular	regular	ADJ
ejpam-4776	229	7	fréchet	fréchet	NOUN
ejpam-4776	229	8	(	(	PUNCT
ejpam-4776	229	9	resp	resp	NOUN
ejpam-4776	229	10	.	.	PUNCT
ejpam-4776	230	1	first	first	ADJ
ejpam-4776	230	2	countable	countable	ADJ
ejpam-4776	230	3	)	)	PUNCT
ejpam-4776	230	4	is	be	AUX
ejpam-4776	230	5	epi	epi	NOUN
ejpam-4776	230	6	-	-	ADJ
ejpam-4776	230	7	completely	completely	ADV
ejpam-4776	230	8	regular	regular	ADJ
ejpam-4776	230	9	.	.	PUNCT
ejpam-4776	231	1	proof	proof	NOUN
ejpam-4776	231	2	.	.	PUNCT
ejpam-4776	232	1	let	let	VERB
ejpam-4776	232	2	x	x	PRON
ejpam-4776	232	3	be	be	AUX
ejpam-4776	232	4	a	a	DET
ejpam-4776	232	5	t1	t1	NOUN
ejpam-4776	232	6	cc	cc	NOUN
ejpam-4776	232	7	-	-	ADJ
ejpam-4776	232	8	completely	completely	ADV
ejpam-4776	232	9	regular	regular	ADJ
ejpam-4776	232	10	fréchet	fréchet	NOUN
ejpam-4776	232	11	space	space	NOUN
ejpam-4776	232	12	(	(	PUNCT
ejpam-4776	232	13	resp	resp	NOUN
ejpam-4776	232	14	.	.	PUNCT
ejpam-4776	233	1	first	first	ADV
ejpam-4776	233	2	countable	countable	ADJ
ejpam-4776	233	3	)	)	PUNCT
ejpam-4776	233	4	.	.	PUNCT
ejpam-4776	234	1	then	then	ADV
ejpam-4776	234	2	,	,	PUNCT
ejpam-4776	234	3	there	there	PRON
ejpam-4776	234	4	exist	exist	VERB
ejpam-4776	234	5	a	a	DET
ejpam-4776	234	6	completely	completely	ADV
ejpam-4776	234	7	regular	regular	ADJ
ejpam-4776	234	8	space	space	NOUN
ejpam-4776	234	9	y	y	PROPN
ejpam-4776	234	10	and	and	CCONJ
ejpam-4776	234	11	a	a	DET
ejpam-4776	234	12	bijective	bijective	ADJ
ejpam-4776	234	13	function	function	NOUN
ejpam-4776	234	14	f	f	NOUN
ejpam-4776	234	15	:	:	PUNCT
ejpam-4776	234	16	(	(	PUNCT
ejpam-4776	234	17	x	x	X
ejpam-4776	234	18	,	,	PUNCT
ejpam-4776	234	19	t	t	PROPN
ejpam-4776	234	20	)	)	PUNCT
ejpam-4776	234	21	→	→	SYM
ejpam-4776	234	22	(	(	PUNCT
ejpam-4776	234	23	y	y	PROPN
ejpam-4776	234	24	,	,	PUNCT
ejpam-4776	234	25	t	t	PROPN
ejpam-4776	234	26	′	′	NUM
ejpam-4776	234	27	)	)	PUNCT
ejpam-4776	234	28	such	such	ADJ
ejpam-4776	234	29	that	that	SCONJ
ejpam-4776	234	30	f	f	PROPN
ejpam-4776	234	31	|a	|a	VERB
ejpam-4776	234	32	:	:	PUNCT
ejpam-4776	234	33	a	a	DET
ejpam-4776	234	34	→	→	SYM
ejpam-4776	234	35	f(a	f(a	NOUN
ejpam-4776	234	36	)	)	PUNCT
ejpam-4776	234	37	is	be	AUX
ejpam-4776	234	38	a	a	DET
ejpam-4776	234	39	homeomorphism	homeomorphism	NOUN
ejpam-4776	234	40	for	for	SCONJ
ejpam-4776	234	41	each	each	DET
ejpam-4776	234	42	countably	countably	ADV
ejpam-4776	234	43	compact	compact	ADJ
ejpam-4776	234	44	subset	subset	VERB
ejpam-4776	234	45	a	a	DET
ejpam-4776	234	46	⊆	⊆	NUM
ejpam-4776	234	47	x.	x.	NOUN
ejpam-4776	234	48	since	since	SCONJ
ejpam-4776	234	49	x	x	PROPN
ejpam-4776	234	50	is	be	AUX
ejpam-4776	234	51	fréchet	fréchet	VERB
ejpam-4776	234	52	(	(	PUNCT
ejpam-4776	234	53	resp	resp	NOUN
ejpam-4776	234	54	.	.	PUNCT
ejpam-4776	235	1	first	first	ADV
ejpam-4776	235	2	countable	countable	ADJ
ejpam-4776	235	3	)	)	PUNCT
ejpam-4776	235	4	,	,	PUNCT
ejpam-4776	235	5	we	we	PRON
ejpam-4776	235	6	have	have	VERB
ejpam-4776	235	7	f	f	PROPN
ejpam-4776	235	8	is	be	AUX
ejpam-4776	235	9	continuous	continuous	ADJ
ejpam-4776	235	10	.	.	PUNCT
ejpam-4776	236	1	since	since	SCONJ
ejpam-4776	236	2	x	x	PROPN
ejpam-4776	236	3	is	be	AUX
ejpam-4776	236	4	t1	t1	NOUN
ejpam-4776	236	5	cc	cc	NOUN
ejpam-4776	236	6	-	-	ADJ
ejpam-4776	236	7	completely	completely	ADV
ejpam-4776	236	8	regular	regular	ADJ
ejpam-4776	236	9	,	,	PUNCT
ejpam-4776	236	10	by	by	ADP
ejpam-4776	236	11	proposition	proposition	NOUN
ejpam-4776	236	12	1	1	NUM
ejpam-4776	236	13	we	we	PRON
ejpam-4776	236	14	obtain	obtain	VERB
ejpam-4776	236	15	y	y	PROPN
ejpam-4776	236	16	is	be	AUX
ejpam-4776	236	17	tychonoff	tychonoff	NOUN
ejpam-4776	236	18	.	.	PUNCT
ejpam-4776	237	1	now	now	ADV
ejpam-4776	237	2	,	,	PUNCT
ejpam-4776	237	3	define	define	VERB
ejpam-4776	237	4	a	a	DET
ejpam-4776	237	5	topology	topology	NOUN
ejpam-4776	237	6	t	t	NOUN
ejpam-4776	237	7	⋆	⋆	VERB
ejpam-4776	237	8	on	on	ADP
ejpam-4776	237	9	x	x	PUNCT
ejpam-4776	237	10	as	as	SCONJ
ejpam-4776	237	11	follows	follow	VERB
ejpam-4776	237	12	:	:	PUNCT
ejpam-4776	237	13	t	t	NOUN
ejpam-4776	237	14	⋆	⋆	X
ejpam-4776	237	15	=	=	SYM
ejpam-4776	237	16	{	{	PUNCT
ejpam-4776	237	17	f−1(u	f−1(u	PROPN
ejpam-4776	237	18	)	)	PUNCT
ejpam-4776	237	19	:	:	PUNCT
ejpam-4776	238	1	u	u	PROPN
ejpam-4776	238	2	∈	∈	PROPN
ejpam-4776	238	3	t	t	NOUN
ejpam-4776	238	4	′	′	NOUN
ejpam-4776	238	5	}	}	PUNCT
ejpam-4776	238	6	.	.	PUNCT
ejpam-4776	239	1	clearly	clearly	ADV
ejpam-4776	239	2	,	,	PUNCT
ejpam-4776	239	3	t	t	PROPN
ejpam-4776	239	4	⋆	⋆	NOUN
ejpam-4776	239	5	is	be	AUX
ejpam-4776	239	6	a	a	DET
ejpam-4776	239	7	topology	topology	NOUN
ejpam-4776	239	8	on	on	ADP
ejpam-4776	239	9	x	x	SYM
ejpam-4776	239	10	coarser	coarse	ADJ
ejpam-4776	239	11	than	than	ADP
ejpam-4776	239	12	t	t	NOUN
ejpam-4776	239	13	such	such	ADJ
ejpam-4776	239	14	that	that	SCONJ
ejpam-4776	239	15	f	f	X
ejpam-4776	239	16	:	:	PUNCT
ejpam-4776	239	17	(	(	PUNCT
ejpam-4776	239	18	x	x	X
ejpam-4776	239	19	,	,	PUNCT
ejpam-4776	239	20	t	t	PROPN
ejpam-4776	239	21	⋆	⋆	NOUN
ejpam-4776	239	22	)	)	PUNCT
ejpam-4776	239	23	→	→	SYM
ejpam-4776	239	24	(	(	PUNCT
ejpam-4776	239	25	y	y	PROPN
ejpam-4776	239	26	,	,	PUNCT
ejpam-4776	239	27	t	t	PROPN
ejpam-4776	239	28	′	′	NUM
ejpam-4776	239	29	)	)	PUNCT
ejpam-4776	239	30	is	be	AUX
ejpam-4776	239	31	continuous	continuous	ADJ
ejpam-4776	239	32	.	.	PUNCT
ejpam-4776	240	1	if	if	SCONJ
ejpam-4776	240	2	w	w	PROPN
ejpam-4776	240	3	∈	∈	PROPN
ejpam-4776	240	4	t	t	PROPN
ejpam-4776	240	5	⋆	⋆	NOUN
ejpam-4776	240	6	,	,	PUNCT
ejpam-4776	240	7	then	then	ADV
ejpam-4776	240	8	w	w	PROPN
ejpam-4776	240	9	=	=	PUNCT
ejpam-4776	240	10	f−1(u	f−1(u	PROPN
ejpam-4776	240	11	)	)	PUNCT
ejpam-4776	240	12	for	for	ADP
ejpam-4776	240	13	some	some	DET
ejpam-4776	240	14	open	open	ADJ
ejpam-4776	240	15	set	set	NOUN
ejpam-4776	240	16	u	u	NOUN
ejpam-4776	240	17	in	in	ADP
ejpam-4776	240	18	t	t	PROPN
ejpam-4776	240	19	′.	′.	NOUN
ejpam-4776	240	20	so	so	ADV
ejpam-4776	240	21	,	,	PUNCT
ejpam-4776	240	22	f(w	f(w	PROPN
ejpam-4776	240	23	)	)	PUNCT
ejpam-4776	240	24	=	=	PUNCT
ejpam-4776	240	25	f(f−1(u	f(f−1(u	PROPN
ejpam-4776	240	26	)	)	PUNCT
ejpam-4776	240	27	)	)	PUNCT
ejpam-4776	241	1	=	=	SYM
ejpam-4776	241	2	u	u	PROPN
ejpam-4776	241	3	,	,	PUNCT
ejpam-4776	241	4	which	which	PRON
ejpam-4776	241	5	is	be	AUX
ejpam-4776	241	6	open	open	ADJ
ejpam-4776	241	7	set	set	VERB
ejpam-4776	241	8	in	in	ADP
ejpam-4776	241	9	(	(	PUNCT
ejpam-4776	241	10	y	y	PROPN
ejpam-4776	241	11	,	,	PUNCT
ejpam-4776	241	12	t	t	PROPN
ejpam-4776	241	13	′	′	NUM
ejpam-4776	241	14	)	)	PUNCT
ejpam-4776	241	15	.	.	PUNCT
ejpam-4776	242	1	thus	thus	ADV
ejpam-4776	242	2	,	,	PUNCT
ejpam-4776	242	3	f	f	X
ejpam-4776	242	4	:	:	PUNCT
ejpam-4776	242	5	(	(	PUNCT
ejpam-4776	242	6	x	x	X
ejpam-4776	242	7	,	,	PUNCT
ejpam-4776	242	8	t	t	PROPN
ejpam-4776	242	9	⋆	⋆	NOUN
ejpam-4776	242	10	)	)	PUNCT
ejpam-4776	242	11	→	→	SYM
ejpam-4776	242	12	(	(	PUNCT
ejpam-4776	242	13	y	y	PROPN
ejpam-4776	242	14	,	,	PUNCT
ejpam-4776	242	15	t	t	PROPN
ejpam-4776	242	16	′	′	NUM
ejpam-4776	242	17	)	)	PUNCT
ejpam-4776	242	18	is	be	AUX
ejpam-4776	242	19	open	open	ADJ
ejpam-4776	242	20	and	and	CCONJ
ejpam-4776	242	21	hence	hence	ADV
ejpam-4776	242	22	a	a	DET
ejpam-4776	242	23	homoeomorphism	homoeomorphism	NOUN
ejpam-4776	242	24	.	.	PUNCT
ejpam-4776	243	1	therefore	therefore	ADV
ejpam-4776	243	2	,	,	PUNCT
ejpam-4776	243	3	(	(	PUNCT
ejpam-4776	243	4	x	x	X
ejpam-4776	243	5	,	,	PUNCT
ejpam-4776	243	6	t	t	PROPN
ejpam-4776	243	7	⋆	⋆	PROPN
ejpam-4776	243	8	)	)	PUNCT
ejpam-4776	243	9	is	be	AUX
ejpam-4776	243	10	a	a	DET
ejpam-4776	243	11	tychonoff	tychonoff	NOUN
ejpam-4776	243	12	space	space	NOUN
ejpam-4776	243	13	.	.	PUNCT
ejpam-4776	244	1	since	since	SCONJ
ejpam-4776	244	2	t	t	PROPN
ejpam-4776	244	3	⋆	⋆	VERB
ejpam-4776	244	4	⊆	⊆	NUM
ejpam-4776	244	5	t	t	NOUN
ejpam-4776	244	6	,	,	PUNCT
ejpam-4776	244	7	we	we	PRON
ejpam-4776	244	8	get	get	VERB
ejpam-4776	244	9	:	:	PUNCT
ejpam-4776	244	10	(	(	PUNCT
ejpam-4776	244	11	x	x	X
ejpam-4776	244	12	,	,	PUNCT
ejpam-4776	244	13	t	t	PROPN
ejpam-4776	244	14	)	)	PUNCT
ejpam-4776	244	15	is	be	AUX
ejpam-4776	244	16	epi	epi	NOUN
ejpam-4776	244	17	-	-	ADJ
ejpam-4776	244	18	completely	completely	ADV
ejpam-4776	244	19	regular	regular	ADJ
ejpam-4776	244	20	.	.	PUNCT
ejpam-4776	245	1	s.	s.	PROPN
ejpam-4776	245	2	a.	a.	PROPN
ejpam-4776	245	3	thabit	thabit	PROPN
ejpam-4776	245	4	,	,	PUNCT
ejpam-4776	245	5	w.	w.	PROPN
ejpam-4776	245	6	alqurashi	alqurashi	PROPN
ejpam-4776	245	7	/	/	SYM
ejpam-4776	245	8	eur	eur	PROPN
ejpam-4776	245	9	.	.	PUNCT
ejpam-4776	246	1	j.	j.	PROPN
ejpam-4776	246	2	pure	pure	PROPN
ejpam-4776	246	3	appl	appl	PROPN
ejpam-4776	246	4	.	.	PROPN
ejpam-4776	246	5	math	math	PROPN
ejpam-4776	246	6	,	,	PUNCT
ejpam-4776	246	7	16	16	NUM
ejpam-4776	246	8	(	(	PUNCT
ejpam-4776	246	9	2	2	NUM
ejpam-4776	246	10	)	)	PUNCT
ejpam-4776	246	11	(	(	PUNCT
ejpam-4776	246	12	2023	2023	NUM
ejpam-4776	246	13	)	)	PUNCT
ejpam-4776	246	14	,	,	PUNCT
ejpam-4776	246	15	1260	1260	NUM
ejpam-4776	246	16	-	-	SYM
ejpam-4776	246	17	1273	1273	NUM
ejpam-4776	246	18	1268	1268	NUM
ejpam-4776	246	19	similarly	similarly	ADV
ejpam-4776	246	20	,	,	PUNCT
ejpam-4776	246	21	every	every	DET
ejpam-4776	246	22	t1	t1	NOUN
ejpam-4776	246	23	cc	cc	NOUN
ejpam-4776	246	24	-	-	ADJ
ejpam-4776	246	25	regular	regular	ADJ
ejpam-4776	246	26	fréchet	fréchet	NOUN
ejpam-4776	246	27	(	(	PUNCT
ejpam-4776	246	28	resp	resp	NOUN
ejpam-4776	246	29	.	.	PUNCT
ejpam-4776	247	1	first	first	ADJ
ejpam-4776	247	2	countable	countable	ADJ
ejpam-4776	247	3	)	)	PUNCT
ejpam-4776	247	4	is	be	AUX
ejpam-4776	247	5	epi	epi	NOUN
ejpam-4776	247	6	-	-	ADJ
ejpam-4776	247	7	regular	regular	ADJ
ejpam-4776	247	8	,	,	PUNCT
ejpam-4776	247	9	every	every	DET
ejpam-4776	247	10	cct3	cct3	PROPN
ejpam-4776	247	11	-	-	PUNCT
ejpam-4776	247	12	fréchet	fréchet	NOUN
ejpam-4776	247	13	(	(	PUNCT
ejpam-4776	247	14	resp	resp	NOUN
ejpam-4776	247	15	.	.	PUNCT
ejpam-4776	248	1	first	first	ADJ
ejpam-4776	248	2	countable	countable	ADJ
ejpam-4776	248	3	)	)	PUNCT
ejpam-4776	248	4	is	be	AUX
ejpam-4776	248	5	epi	epi	NOUN
ejpam-4776	248	6	-	-	ADJ
ejpam-4776	248	7	regular	regular	ADJ
ejpam-4776	248	8	,	,	PUNCT
ejpam-4776	248	9	every	every	DET
ejpam-4776	248	10	cc	cc	NOUN
ejpam-4776	248	11	-	-	PUNCT
ejpam-4776	248	12	tychonoff	tychonoff	NOUN
ejpam-4776	248	13	fréchet	fréchet	NOUN
ejpam-4776	248	14	(	(	PUNCT
ejpam-4776	248	15	resp	resp	NOUN
ejpam-4776	248	16	.	.	PUNCT
ejpam-4776	249	1	first	first	ADJ
ejpam-4776	249	2	countable	countable	ADJ
ejpam-4776	249	3	)	)	PUNCT
ejpam-4776	249	4	is	be	AUX
ejpam-4776	249	5	epi	epi	NOUN
ejpam-4776	249	6	-	-	ADJ
ejpam-4776	249	7	completely	completely	ADV
ejpam-4776	249	8	regular	regular	ADJ
ejpam-4776	249	9	and	and	CCONJ
ejpam-4776	249	10	every	every	DET
ejpam-4776	249	11	t1	t1	NOUN
ejpam-4776	249	12	cc	cc	NOUN
ejpam-4776	249	13	-	-	ADJ
ejpam-4776	249	14	normal	normal	ADJ
ejpam-4776	249	15	fréchet	fréchet	NOUN
ejpam-4776	249	16	(	(	PUNCT
ejpam-4776	249	17	resp	resp	NOUN
ejpam-4776	249	18	.	.	PUNCT
ejpam-4776	250	1	first	first	ADJ
ejpam-4776	250	2	countable	countable	ADJ
ejpam-4776	250	3	)	)	PUNCT
ejpam-4776	250	4	is	be	AUX
ejpam-4776	250	5	epi	epi	NOUN
ejpam-4776	250	6	-	-	ADJ
ejpam-4776	250	7	normal	normal	ADJ
ejpam-4776	250	8	.	.	PUNCT
ejpam-4776	251	1	corollary	corollary	ADJ
ejpam-4776	251	2	7	7	NUM
ejpam-4776	251	3	.	.	PUNCT
ejpam-4776	251	4	(	(	PUNCT
ejpam-4776	251	5	1	1	X
ejpam-4776	251	6	)	)	PUNCT
ejpam-4776	251	7	every	every	DET
ejpam-4776	251	8	cc	cc	NOUN
ejpam-4776	251	9	-	-	ADJ
ejpam-4776	251	10	regular	regular	ADJ
ejpam-4776	251	11	t1	t1	NOUN
ejpam-4776	251	12	-	-	PUNCT
ejpam-4776	251	13	first	first	ADJ
ejpam-4776	251	14	countable	countable	ADJ
ejpam-4776	251	15	space	space	NOUN
ejpam-4776	251	16	is	be	AUX
ejpam-4776	251	17	urysohn	urysohn	ADJ
ejpam-4776	251	18	.	.	PUNCT
ejpam-4776	252	1	(	(	PUNCT
ejpam-4776	252	2	2	2	X
ejpam-4776	252	3	)	)	PUNCT
ejpam-4776	252	4	every	every	DET
ejpam-4776	252	5	cct3	cct3	PROPN
ejpam-4776	252	6	-	-	PUNCT
ejpam-4776	252	7	first	first	ADJ
ejpam-4776	252	8	countable	countable	ADJ
ejpam-4776	252	9	space	space	NOUN
ejpam-4776	252	10	is	be	AUX
ejpam-4776	252	11	urysohn	urysohn	ADJ
ejpam-4776	252	12	.	.	PUNCT
ejpam-4776	253	1	by	by	ADP
ejpam-4776	253	2	using	use	VERB
ejpam-4776	253	3	theorem	theorem	ADJ
ejpam-4776	253	4	8	8	NUM
ejpam-4776	253	5	and	and	CCONJ
ejpam-4776	253	6	proposition	proposition	NOUN
ejpam-4776	253	7	1	1	NUM
ejpam-4776	253	8	,	,	PUNCT
ejpam-4776	253	9	we	we	PRON
ejpam-4776	253	10	can	can	AUX
ejpam-4776	253	11	prove	prove	VERB
ejpam-4776	253	12	the	the	DET
ejpam-4776	253	13	next	next	ADJ
ejpam-4776	253	14	result	result	NOUN
ejpam-4776	253	15	as	as	SCONJ
ejpam-4776	253	16	follows	follow	VERB
ejpam-4776	253	17	:	:	PUNCT
ejpam-4776	253	18	theorem	theorem	NOUN
ejpam-4776	253	19	9	9	NUM
ejpam-4776	253	20	.	.	PUNCT
ejpam-4776	254	1	every	every	DET
ejpam-4776	254	2	t1	t1	NOUN
ejpam-4776	254	3	cc	cc	NOUN
ejpam-4776	254	4	-	-	ADJ
ejpam-4776	254	5	regular	regular	ADJ
ejpam-4776	254	6	fréchet	fréchet	NOUN
ejpam-4776	254	7	(	(	PUNCT
ejpam-4776	254	8	first	first	ADV
ejpam-4776	254	9	countable	countable	ADJ
ejpam-4776	254	10	)	)	PUNCT
ejpam-4776	254	11	lindelöf	lindelöf	NOUN
ejpam-4776	254	12	space	space	NOUN
ejpam-4776	254	13	is	be	AUX
ejpam-4776	254	14	epi	epi	NOUN
ejpam-4776	254	15	-	-	ADJ
ejpam-4776	254	16	normal	normal	ADJ
ejpam-4776	254	17	.	.	PUNCT
ejpam-4776	255	1	proof	proof	NOUN
ejpam-4776	255	2	.	.	PUNCT
ejpam-4776	256	1	let	let	VERB
ejpam-4776	256	2	x	x	PRON
ejpam-4776	256	3	be	be	AUX
ejpam-4776	256	4	a	a	DET
ejpam-4776	256	5	cc	cc	NOUN
ejpam-4776	256	6	-	-	ADJ
ejpam-4776	256	7	regular	regular	ADJ
ejpam-4776	256	8	t1	t1	NOUN
ejpam-4776	256	9	fréchet	fréchet	NOUN
ejpam-4776	256	10	(	(	PUNCT
ejpam-4776	256	11	resp	resp	NOUN
ejpam-4776	256	12	.	.	PUNCT
ejpam-4776	257	1	first	first	ADJ
ejpam-4776	257	2	countable	countable	ADJ
ejpam-4776	257	3	)	)	PUNCT
ejpam-4776	257	4	lindelöf	lindelöf	NOUN
ejpam-4776	257	5	space	space	NOUN
ejpam-4776	257	6	.	.	PUNCT
ejpam-4776	258	1	then	then	ADV
ejpam-4776	258	2	,	,	PUNCT
ejpam-4776	258	3	there	there	PRON
ejpam-4776	258	4	exist	exist	VERB
ejpam-4776	258	5	a	a	DET
ejpam-4776	258	6	regular	regular	ADJ
ejpam-4776	258	7	space	space	NOUN
ejpam-4776	258	8	y	y	PROPN
ejpam-4776	258	9	and	and	CCONJ
ejpam-4776	258	10	a	a	DET
ejpam-4776	258	11	bijective	bijective	ADJ
ejpam-4776	258	12	function	function	NOUN
ejpam-4776	258	13	f	f	NOUN
ejpam-4776	258	14	:	:	PUNCT
ejpam-4776	258	15	(	(	PUNCT
ejpam-4776	258	16	x	x	X
ejpam-4776	258	17	,	,	PUNCT
ejpam-4776	258	18	t	t	PROPN
ejpam-4776	258	19	)	)	PUNCT
ejpam-4776	258	20	→	→	SYM
ejpam-4776	258	21	(	(	PUNCT
ejpam-4776	258	22	y	y	PROPN
ejpam-4776	258	23	,	,	PUNCT
ejpam-4776	258	24	t	t	PROPN
ejpam-4776	258	25	′	′	NUM
ejpam-4776	258	26	)	)	PUNCT
ejpam-4776	258	27	such	such	ADJ
ejpam-4776	258	28	that	that	SCONJ
ejpam-4776	258	29	f	f	PROPN
ejpam-4776	258	30	|a	|a	VERB
ejpam-4776	258	31	:	:	PUNCT
ejpam-4776	258	32	a	a	DET
ejpam-4776	258	33	→	→	SYM
ejpam-4776	258	34	f(a	f(a	NOUN
ejpam-4776	258	35	)	)	PUNCT
ejpam-4776	258	36	is	be	AUX
ejpam-4776	258	37	a	a	DET
ejpam-4776	258	38	homeomorphism	homeomorphism	NOUN
ejpam-4776	258	39	for	for	SCONJ
ejpam-4776	258	40	each	each	DET
ejpam-4776	258	41	countably	countably	ADV
ejpam-4776	258	42	compact	compact	ADJ
ejpam-4776	258	43	subset	subset	VERB
ejpam-4776	258	44	a	a	DET
ejpam-4776	258	45	⊆	⊆	NUM
ejpam-4776	258	46	x.	x.	NOUN
ejpam-4776	258	47	since	since	SCONJ
ejpam-4776	258	48	x	x	PROPN
ejpam-4776	258	49	is	be	AUX
ejpam-4776	258	50	fréchet	fréchet	VERB
ejpam-4776	258	51	(	(	PUNCT
ejpam-4776	258	52	resp	resp	NOUN
ejpam-4776	258	53	.	.	PUNCT
ejpam-4776	259	1	first	first	ADV
ejpam-4776	259	2	countable	countable	ADJ
ejpam-4776	259	3	)	)	PUNCT
ejpam-4776	259	4	,	,	PUNCT
ejpam-4776	259	5	we	we	PRON
ejpam-4776	259	6	get	get	VERB
ejpam-4776	259	7	f	f	PROPN
ejpam-4776	259	8	is	be	AUX
ejpam-4776	259	9	continuous	continuous	ADJ
ejpam-4776	259	10	.	.	PUNCT
ejpam-4776	260	1	since	since	SCONJ
ejpam-4776	260	2	the	the	DET
ejpam-4776	260	3	continuous	continuous	ADJ
ejpam-4776	260	4	image	image	NOUN
ejpam-4776	260	5	of	of	ADP
ejpam-4776	260	6	a	a	DET
ejpam-4776	260	7	lindelöf	lindelöf	NOUN
ejpam-4776	260	8	space	space	NOUN
ejpam-4776	260	9	is	be	AUX
ejpam-4776	260	10	lindelöf	lindelöf	NOUN
ejpam-4776	260	11	[	[	X
ejpam-4776	260	12	10	10	NUM
ejpam-4776	260	13	]	]	PUNCT
ejpam-4776	260	14	,	,	PUNCT
ejpam-4776	260	15	we	we	PRON
ejpam-4776	260	16	obtain	obtain	VERB
ejpam-4776	260	17	:	:	PUNCT
ejpam-4776	260	18	y	y	PROPN
ejpam-4776	260	19	is	be	AUX
ejpam-4776	260	20	lindelöf	lindelöf	PROPN
ejpam-4776	260	21	.	.	PUNCT
ejpam-4776	261	1	since	since	SCONJ
ejpam-4776	261	2	y	y	PROPN
ejpam-4776	261	3	is	be	AUX
ejpam-4776	261	4	a	a	DET
ejpam-4776	261	5	regular	regular	ADJ
ejpam-4776	261	6	lindelöf	lindelöf	NOUN
ejpam-4776	261	7	space	space	NOUN
ejpam-4776	261	8	,	,	PUNCT
ejpam-4776	261	9	we	we	PRON
ejpam-4776	261	10	have	have	AUX
ejpam-4776	261	11	(	(	PUNCT
ejpam-4776	261	12	y	y	PROPN
ejpam-4776	261	13	,	,	PUNCT
ejpam-4776	261	14	t	t	PROPN
ejpam-4776	261	15	′	′	NUM
ejpam-4776	261	16	)	)	PUNCT
ejpam-4776	261	17	is	be	AUX
ejpam-4776	261	18	normal	normal	ADJ
ejpam-4776	261	19	.	.	PUNCT
ejpam-4776	262	1	by	by	ADP
ejpam-4776	262	2	proposition	proposition	NOUN
ejpam-4776	262	3	2	2	NUM
ejpam-4776	262	4	,	,	PUNCT
ejpam-4776	262	5	(	(	PUNCT
ejpam-4776	262	6	y	y	PROPN
ejpam-4776	262	7	,	,	PUNCT
ejpam-4776	262	8	t	t	PROPN
ejpam-4776	262	9	′	′	NUM
ejpam-4776	262	10	)	)	PUNCT
ejpam-4776	262	11	is	be	AUX
ejpam-4776	262	12	a	a	DET
ejpam-4776	262	13	t3	t3	NOUN
ejpam-4776	262	14	-	-	PUNCT
ejpam-4776	262	15	space	space	NOUN
ejpam-4776	262	16	.	.	PUNCT
ejpam-4776	263	1	thus	thus	ADV
ejpam-4776	263	2	,	,	PUNCT
ejpam-4776	263	3	(	(	PUNCT
ejpam-4776	263	4	y	y	PROPN
ejpam-4776	263	5	,	,	PUNCT
ejpam-4776	263	6	t	t	PROPN
ejpam-4776	263	7	′	′	NUM
ejpam-4776	263	8	)	)	PUNCT
ejpam-4776	263	9	is	be	AUX
ejpam-4776	263	10	a	a	DET
ejpam-4776	263	11	hausdorff	hausdorff	NOUN
ejpam-4776	263	12	normal	normal	ADJ
ejpam-4776	263	13	space	space	NOUN
ejpam-4776	263	14	and	and	CCONJ
ejpam-4776	263	15	hence	hence	ADV
ejpam-4776	263	16	a	a	DET
ejpam-4776	263	17	t4	t4	PROPN
ejpam-4776	263	18	-	-	PUNCT
ejpam-4776	263	19	space	space	NOUN
ejpam-4776	263	20	.	.	PUNCT
ejpam-4776	264	1	define	define	VERB
ejpam-4776	264	2	a	a	DET
ejpam-4776	264	3	topology	topology	NOUN
ejpam-4776	264	4	t	t	NOUN
ejpam-4776	264	5	⋆	⋆	VERB
ejpam-4776	264	6	on	on	ADP
ejpam-4776	264	7	x	x	PUNCT
ejpam-4776	264	8	as	as	SCONJ
ejpam-4776	264	9	follows	follow	VERB
ejpam-4776	264	10	:	:	PUNCT
ejpam-4776	265	1	t	t	NOUN
ejpam-4776	265	2	⋆	⋆	X
ejpam-4776	265	3	=	=	SYM
ejpam-4776	265	4	{	{	PUNCT
ejpam-4776	265	5	f−1(u	f−1(u	PROPN
ejpam-4776	265	6	)	)	PUNCT
ejpam-4776	265	7	:	:	PUNCT
ejpam-4776	265	8	u	u	PROPN
ejpam-4776	265	9	∈	∈	PROPN
ejpam-4776	265	10	t	t	NOUN
ejpam-4776	265	11	′	′	NOUN
ejpam-4776	265	12	}	}	PUNCT
ejpam-4776	265	13	.	.	PUNCT
ejpam-4776	266	1	by	by	ADP
ejpam-4776	266	2	using	use	VERB
ejpam-4776	266	3	the	the	DET
ejpam-4776	266	4	same	same	ADJ
ejpam-4776	266	5	arguments	argument	NOUN
ejpam-4776	266	6	to	to	ADP
ejpam-4776	266	7	the	the	DET
ejpam-4776	266	8	proof	proof	NOUN
ejpam-4776	266	9	of	of	ADP
ejpam-4776	266	10	theorem	theorem	NOUN
ejpam-4776	266	11	8	8	NUM
ejpam-4776	266	12	,	,	PUNCT
ejpam-4776	266	13	we	we	PRON
ejpam-4776	266	14	obtain	obtain	VERB
ejpam-4776	266	15	:	:	PUNCT
ejpam-4776	266	16	f	f	X
ejpam-4776	266	17	:	:	PUNCT
ejpam-4776	266	18	(	(	PUNCT
ejpam-4776	266	19	x	x	X
ejpam-4776	266	20	,	,	PUNCT
ejpam-4776	266	21	t	t	PROPN
ejpam-4776	266	22	⋆	⋆	NOUN
ejpam-4776	266	23	)	)	PUNCT
ejpam-4776	266	24	→	→	SYM
ejpam-4776	266	25	(	(	PUNCT
ejpam-4776	266	26	y	y	PROPN
ejpam-4776	266	27	,	,	PUNCT
ejpam-4776	266	28	t	t	PROPN
ejpam-4776	266	29	′	′	NUM
ejpam-4776	266	30	)	)	PUNCT
ejpam-4776	266	31	is	be	AUX
ejpam-4776	266	32	a	a	DET
ejpam-4776	266	33	homoeomorphism	homoeomorphism	NOUN
ejpam-4776	266	34	.	.	PUNCT
ejpam-4776	267	1	since	since	SCONJ
ejpam-4776	267	2	(	(	PUNCT
ejpam-4776	267	3	y	y	PROPN
ejpam-4776	267	4	,	,	PUNCT
ejpam-4776	267	5	t	t	PROPN
ejpam-4776	267	6	′	′	NUM
ejpam-4776	267	7	)	)	PUNCT
ejpam-4776	267	8	is	be	AUX
ejpam-4776	267	9	a	a	DET
ejpam-4776	267	10	t4	t4	PROPN
ejpam-4776	267	11	-	-	PUNCT
ejpam-4776	267	12	space	space	NOUN
ejpam-4776	267	13	,	,	PUNCT
ejpam-4776	267	14	we	we	PRON
ejpam-4776	267	15	have	have	VERB
ejpam-4776	267	16	:	:	PUNCT
ejpam-4776	267	17	(	(	PUNCT
ejpam-4776	267	18	x	x	X
ejpam-4776	267	19	,	,	PUNCT
ejpam-4776	267	20	t	t	PROPN
ejpam-4776	267	21	⋆	⋆	PROPN
ejpam-4776	267	22	)	)	PUNCT
ejpam-4776	267	23	is	be	AUX
ejpam-4776	267	24	t4	t4	PROPN
ejpam-4776	267	25	.	.	PUNCT
ejpam-4776	268	1	since	since	SCONJ
ejpam-4776	268	2	t	t	PROPN
ejpam-4776	268	3	⋆	⋆	VERB
ejpam-4776	268	4	⊆	⊆	NUM
ejpam-4776	268	5	t	t	NOUN
ejpam-4776	268	6	,	,	PUNCT
ejpam-4776	268	7	we	we	PRON
ejpam-4776	268	8	get	get	VERB
ejpam-4776	268	9	:	:	PUNCT
ejpam-4776	268	10	(	(	PUNCT
ejpam-4776	268	11	x	x	X
ejpam-4776	268	12	,	,	PUNCT
ejpam-4776	268	13	t	t	PROPN
ejpam-4776	268	14	)	)	PUNCT
ejpam-4776	268	15	is	be	AUX
ejpam-4776	268	16	epi	epi	NOUN
ejpam-4776	268	17	-	-	ADJ
ejpam-4776	268	18	normal	normal	ADJ
ejpam-4776	268	19	.	.	PUNCT
ejpam-4776	269	1	corollary	corollary	ADJ
ejpam-4776	269	2	8	8	NUM
ejpam-4776	269	3	.	.	PUNCT
ejpam-4776	270	1	(	(	PUNCT
ejpam-4776	270	2	1	1	X
ejpam-4776	270	3	)	)	PUNCT
ejpam-4776	270	4	every	every	DET
ejpam-4776	270	5	t1	t1	NOUN
ejpam-4776	270	6	cc	cc	NOUN
ejpam-4776	270	7	-	-	ADJ
ejpam-4776	270	8	completely	completely	ADV
ejpam-4776	270	9	regular	regular	ADJ
ejpam-4776	270	10	fréchet	fréchet	NOUN
ejpam-4776	270	11	(	(	PUNCT
ejpam-4776	270	12	first	first	ADV
ejpam-4776	270	13	countable	countable	ADJ
ejpam-4776	270	14	)	)	PUNCT
ejpam-4776	270	15	lindelöf	lindelöf	NOUN
ejpam-4776	270	16	space	space	NOUN
ejpam-4776	270	17	is	be	AUX
ejpam-4776	270	18	epi	epi	NOUN
ejpam-4776	270	19	-	-	ADJ
ejpam-4776	270	20	normal	normal	ADJ
ejpam-4776	270	21	.	.	PUNCT
ejpam-4776	271	1	(	(	PUNCT
ejpam-4776	271	2	2	2	X
ejpam-4776	271	3	)	)	PUNCT
ejpam-4776	271	4	every	every	DET
ejpam-4776	271	5	cct3	cct3	PROPN
ejpam-4776	271	6	-	-	PUNCT
ejpam-4776	271	7	fréchet	fréchet	NOUN
ejpam-4776	271	8	(	(	PUNCT
ejpam-4776	271	9	first	first	ADV
ejpam-4776	271	10	countable	countable	ADJ
ejpam-4776	271	11	)	)	PUNCT
ejpam-4776	271	12	lindelöf	lindelöf	NOUN
ejpam-4776	271	13	space	space	NOUN
ejpam-4776	271	14	is	be	AUX
ejpam-4776	271	15	epi	epi	ADJ
ejpam-4776	271	16	-	-	ADJ
ejpam-4776	271	17	normal	normal	ADJ
ejpam-4776	271	18	.	.	PUNCT
ejpam-4776	272	1	theorem	theorem	VERB
ejpam-4776	272	2	10	10	NUM
ejpam-4776	272	3	.	.	PUNCT
ejpam-4776	273	1	every	every	DET
ejpam-4776	273	2	cc	cc	NOUN
ejpam-4776	273	3	-	-	ADJ
ejpam-4776	273	4	regular	regular	ADJ
ejpam-4776	273	5	fréchet	fréchet	NOUN
ejpam-4776	273	6	(	(	PUNCT
ejpam-4776	273	7	resp	resp	NOUN
ejpam-4776	273	8	.	.	PUNCT
ejpam-4776	274	1	first	first	ADJ
ejpam-4776	274	2	countable	countable	ADJ
ejpam-4776	274	3	)	)	PUNCT
ejpam-4776	274	4	lindelöf	lindelöf	NOUN
ejpam-4776	274	5	space	space	NOUN
ejpam-4776	274	6	is	be	AUX
ejpam-4776	274	7	cc	cc	VERB
ejpam-4776	274	8	-	-	ADJ
ejpam-4776	274	9	normal	normal	ADJ
ejpam-4776	274	10	.	.	PUNCT
ejpam-4776	275	1	proof	proof	NOUN
ejpam-4776	275	2	.	.	PUNCT
ejpam-4776	276	1	it	it	PRON
ejpam-4776	276	2	is	be	AUX
ejpam-4776	276	3	similar	similar	ADJ
ejpam-4776	276	4	to	to	ADP
ejpam-4776	276	5	that	that	PRON
ejpam-4776	276	6	of	of	ADP
ejpam-4776	276	7	theorem	theorem	ADJ
ejpam-4776	276	8	9	9	NUM
ejpam-4776	276	9	.	.	PUNCT
ejpam-4776	276	10	corollary	corollary	ADJ
ejpam-4776	276	11	9	9	NUM
ejpam-4776	276	12	.	.	PUNCT
ejpam-4776	277	1	every	every	DET
ejpam-4776	277	2	cc	cc	NOUN
ejpam-4776	277	3	-	-	ADJ
ejpam-4776	277	4	completely	completely	ADV
ejpam-4776	277	5	regular	regular	ADJ
ejpam-4776	277	6	(	(	PUNCT
ejpam-4776	277	7	resp	resp	NOUN
ejpam-4776	277	8	.	.	PUNCT
ejpam-4776	278	1	cc	cc	NOUN
ejpam-4776	278	2	-	-	NOUN
ejpam-4776	278	3	tychonoff	tychonoff	NOUN
ejpam-4776	278	4	,	,	PUNCT
ejpam-4776	278	5	cct3	cct3	PROPN
ejpam-4776	278	6	)	)	PUNCT
ejpam-4776	278	7	first	first	ADV
ejpam-4776	278	8	countable	countable	ADJ
ejpam-4776	278	9	lindelöf	lindelöf	NOUN
ejpam-4776	278	10	space	space	NOUN
ejpam-4776	278	11	is	be	AUX
ejpam-4776	278	12	cc	cc	VERB
ejpam-4776	278	13	-	-	ADJ
ejpam-4776	278	14	normal	normal	ADJ
ejpam-4776	278	15	.	.	PUNCT
ejpam-4776	279	1	it	it	PRON
ejpam-4776	279	2	is	be	AUX
ejpam-4776	279	3	obvious	obvious	ADJ
ejpam-4776	279	4	that	that	SCONJ
ejpam-4776	279	5	every	every	DET
ejpam-4776	279	6	cc	cc	NOUN
ejpam-4776	279	7	-	-	ADJ
ejpam-4776	279	8	completely	completely	ADV
ejpam-4776	279	9	regular	regular	ADJ
ejpam-4776	279	10	(	(	PUNCT
ejpam-4776	279	11	resp	resp	NOUN
ejpam-4776	279	12	.	.	PUNCT
ejpam-4776	280	1	cc	cc	NOUN
ejpam-4776	280	2	-	-	ADJ
ejpam-4776	280	3	regular	regular	ADJ
ejpam-4776	280	4	,	,	PUNCT
ejpam-4776	280	5	cct3	cct3	PROPN
ejpam-4776	280	6	,	,	PUNCT
ejpam-4776	280	7	cc	cc	NOUN
ejpam-4776	280	8	-	-	NOUN
ejpam-4776	280	9	tychonoff	tychonoff	NOUN
ejpam-4776	280	10	)	)	PUNCT
ejpam-4776	280	11	countably	countably	ADV
ejpam-4776	280	12	compact	compact	ADJ
ejpam-4776	280	13	lindelöf	lindelöf	NOUN
ejpam-4776	280	14	space	space	NOUN
ejpam-4776	280	15	is	be	AUX
ejpam-4776	280	16	cc	cc	VERB
ejpam-4776	280	17	-	-	ADJ
ejpam-4776	280	18	normal	normal	ADJ
ejpam-4776	280	19	.	.	PUNCT
ejpam-4776	281	1	the	the	DET
ejpam-4776	281	2	proof	proof	NOUN
ejpam-4776	281	3	of	of	ADP
ejpam-4776	281	4	the	the	DET
ejpam-4776	281	5	next	next	ADJ
ejpam-4776	281	6	results	result	NOUN
ejpam-4776	281	7	is	be	AUX
ejpam-4776	281	8	similar	similar	ADJ
ejpam-4776	281	9	to	to	ADP
ejpam-4776	281	10	that	that	PRON
ejpam-4776	281	11	of	of	ADP
ejpam-4776	281	12	theorem	theorem	NOUN
ejpam-4776	281	13	3.5	3.5	NUM
ejpam-4776	281	14	in	in	ADP
ejpam-4776	281	15	[	[	X
ejpam-4776	281	16	14	14	NUM
ejpam-4776	281	17	]	]	NUM
ejpam-4776	281	18	:	:	PUNCT
ejpam-4776	281	19	theorem	theorem	NOUN
ejpam-4776	281	20	11	11	NUM
ejpam-4776	281	21	.	.	PUNCT
ejpam-4776	282	1	if	if	SCONJ
ejpam-4776	282	2	x	x	PRON
ejpam-4776	282	3	is	be	AUX
ejpam-4776	282	4	a	a	DET
ejpam-4776	282	5	cc	cc	NOUN
ejpam-4776	282	6	-	-	ADJ
ejpam-4776	282	7	completely	completely	ADV
ejpam-4776	282	8	regular	regular	ADJ
ejpam-4776	282	9	(	(	PUNCT
ejpam-4776	282	10	resp	resp	NOUN
ejpam-4776	282	11	.	.	PUNCT
ejpam-4776	283	1	cc	cc	NOUN
ejpam-4776	283	2	-	-	ADJ
ejpam-4776	283	3	regular	regular	ADJ
ejpam-4776	283	4	,	,	PUNCT
ejpam-4776	283	5	cc	cc	NOUN
ejpam-4776	283	6	-	-	NOUN
ejpam-4776	283	7	tychonoff	tychonoff	NOUN
ejpam-4776	283	8	,	,	PUNCT
ejpam-4776	283	9	cct3	cct3	PROPN
ejpam-4776	283	10	)	)	PUNCT
ejpam-4776	283	11	space	space	NOUN
ejpam-4776	283	12	,	,	PUNCT
ejpam-4776	283	13	then	then	ADV
ejpam-4776	283	14	the	the	DET
ejpam-4776	283	15	alexandroff	alexandroff	NOUN
ejpam-4776	283	16	duplicate	duplicate	VERB
ejpam-4776	283	17	a(x	a(x	NOUN
ejpam-4776	283	18	)	)	PUNCT
ejpam-4776	283	19	of	of	ADP
ejpam-4776	283	20	x	x	PROPN
ejpam-4776	283	21	is	be	AUX
ejpam-4776	283	22	cc	cc	VERB
ejpam-4776	283	23	-	-	ADJ
ejpam-4776	283	24	completely	completely	ADV
ejpam-4776	283	25	regular	regular	ADJ
ejpam-4776	283	26	(	(	PUNCT
ejpam-4776	283	27	resp	resp	NOUN
ejpam-4776	283	28	.	.	PUNCT
ejpam-4776	284	1	cc	cc	NOUN
ejpam-4776	284	2	-	-	ADJ
ejpam-4776	284	3	regular	regular	ADJ
ejpam-4776	284	4	,	,	PUNCT
ejpam-4776	284	5	cc	cc	NOUN
ejpam-4776	284	6	-	-	NOUN
ejpam-4776	284	7	tychonoff	tychonoff	NOUN
ejpam-4776	284	8	,	,	PUNCT
ejpam-4776	284	9	cct3	cct3	PROPN
ejpam-4776	284	10	)	)	PUNCT
ejpam-4776	284	11	.	.	PUNCT
ejpam-4776	285	1	s.	s.	PROPN
ejpam-4776	285	2	a.	a.	PROPN
ejpam-4776	285	3	thabit	thabit	PROPN
ejpam-4776	285	4	,	,	PUNCT
ejpam-4776	285	5	w.	w.	PROPN
ejpam-4776	285	6	alqurashi	alqurashi	PROPN
ejpam-4776	285	7	/	/	SYM
ejpam-4776	285	8	eur	eur	PROPN
ejpam-4776	285	9	.	.	PUNCT
ejpam-4776	286	1	j.	j.	PROPN
ejpam-4776	286	2	pure	pure	PROPN
ejpam-4776	286	3	appl	appl	PROPN
ejpam-4776	286	4	.	.	PROPN
ejpam-4776	286	5	math	math	PROPN
ejpam-4776	286	6	,	,	PUNCT
ejpam-4776	286	7	16	16	NUM
ejpam-4776	286	8	(	(	PUNCT
ejpam-4776	286	9	2	2	NUM
ejpam-4776	286	10	)	)	PUNCT
ejpam-4776	286	11	(	(	PUNCT
ejpam-4776	286	12	2023	2023	NUM
ejpam-4776	286	13	)	)	PUNCT
ejpam-4776	286	14	,	,	PUNCT
ejpam-4776	286	15	1260	1260	NUM
ejpam-4776	286	16	-	-	SYM
ejpam-4776	286	17	1273	1273	NUM
ejpam-4776	286	18	1269	1269	NUM
ejpam-4776	286	19	3	3	NUM
ejpam-4776	286	20	.	.	PUNCT
ejpam-4776	287	1	some	some	DET
ejpam-4776	287	2	properties	property	NOUN
ejpam-4776	287	3	and	and	CCONJ
ejpam-4776	287	4	relationships	relationship	NOUN
ejpam-4776	287	5	now	now	ADV
ejpam-4776	287	6	,	,	PUNCT
ejpam-4776	287	7	we	we	PRON
ejpam-4776	287	8	present	present	VERB
ejpam-4776	287	9	the	the	DET
ejpam-4776	287	10	next	next	ADJ
ejpam-4776	287	11	results	result	NOUN
ejpam-4776	287	12	:	:	PUNCT
ejpam-4776	287	13	the	the	DET
ejpam-4776	287	14	proof	proof	NOUN
ejpam-4776	287	15	of	of	ADP
ejpam-4776	287	16	the	the	DET
ejpam-4776	287	17	next	next	ADJ
ejpam-4776	287	18	theorem	theorem	NOUN
ejpam-4776	287	19	is	be	AUX
ejpam-4776	287	20	similar	similar	ADJ
ejpam-4776	287	21	to	to	ADP
ejpam-4776	287	22	that	that	PRON
ejpam-4776	287	23	of	of	ADP
ejpam-4776	287	24	theorem	theorem	NOUN
ejpam-4776	287	25	2.7	2.7	NUM
ejpam-4776	287	26	in	in	ADP
ejpam-4776	287	27	[	[	X
ejpam-4776	287	28	14	14	NUM
ejpam-4776	287	29	]	]	PUNCT
ejpam-4776	287	30	.	.	PUNCT
ejpam-4776	288	1	theorem	theorem	NOUN
ejpam-4776	288	2	12	12	NUM
ejpam-4776	288	3	.	.	PUNCT
ejpam-4776	289	1	cc	cc	NOUN
ejpam-4776	289	2	-	-	NOUN
ejpam-4776	289	3	tychonoffness	tychonoffness	PROPN
ejpam-4776	289	4	,	,	PUNCT
ejpam-4776	289	5	cct3	cct3	PROPN
ejpam-4776	289	6	,	,	PUNCT
ejpam-4776	289	7	cc	cc	NOUN
ejpam-4776	289	8	-	-	ADJ
ejpam-4776	289	9	complete	complete	ADJ
ejpam-4776	289	10	regularity	regularity	NOUN
ejpam-4776	289	11	,	,	PUNCT
ejpam-4776	289	12	cc	cc	NOUN
ejpam-4776	289	13	-	-	NOUN
ejpam-4776	289	14	regularity	regularity	NOUN
ejpam-4776	289	15	,	,	PUNCT
ejpam-4776	289	16	cc	cc	NOUN
ejpam-4776	289	17	-	-	ADJ
ejpam-4776	289	18	almost	almost	ADV
ejpam-4776	289	19	regularity	regularity	NOUN
ejpam-4776	289	20	and	and	CCONJ
ejpam-4776	289	21	cc	cc	NOUN
ejpam-4776	289	22	-	-	PUNCT
ejpam-4776	289	23	almost	almost	ADV
ejpam-4776	289	24	complete	complete	ADJ
ejpam-4776	289	25	regularity	regularity	NOUN
ejpam-4776	289	26	are	be	AUX
ejpam-4776	289	27	topological	topological	ADJ
ejpam-4776	289	28	properties	property	NOUN
ejpam-4776	289	29	.	.	PUNCT
ejpam-4776	290	1	the	the	DET
ejpam-4776	290	2	proof	proof	NOUN
ejpam-4776	290	3	of	of	ADP
ejpam-4776	290	4	the	the	DET
ejpam-4776	290	5	following	follow	VERB
ejpam-4776	290	6	results	result	NOUN
ejpam-4776	290	7	is	be	AUX
ejpam-4776	290	8	similar	similar	ADJ
ejpam-4776	290	9	to	to	ADP
ejpam-4776	290	10	the	the	DET
ejpam-4776	290	11	proof	proof	NOUN
ejpam-4776	290	12	of	of	ADP
ejpam-4776	290	13	theorem	theorem	ADJ
ejpam-4776	290	14	2.8	2.8	NUM
ejpam-4776	290	15	in	in	ADP
ejpam-4776	290	16	[	[	X
ejpam-4776	290	17	14	14	NUM
ejpam-4776	290	18	]	]	NUM
ejpam-4776	290	19	:	:	PUNCT
ejpam-4776	290	20	theorem	theorem	ADJ
ejpam-4776	290	21	13	13	NUM
ejpam-4776	290	22	.	.	PUNCT
ejpam-4776	290	23	cc	cc	NOUN
ejpam-4776	290	24	-	-	NOUN
ejpam-4776	290	25	tychonoffness	tychonoffness	PROPN
ejpam-4776	290	26	,	,	PUNCT
ejpam-4776	290	27	cct3	cct3	PROPN
ejpam-4776	290	28	,	,	PUNCT
ejpam-4776	290	29	cc	cc	NOUN
ejpam-4776	290	30	-	-	ADJ
ejpam-4776	290	31	complete	complete	ADJ
ejpam-4776	290	32	regularity	regularity	NOUN
ejpam-4776	290	33	,	,	PUNCT
ejpam-4776	290	34	cc	cc	NOUN
ejpam-4776	290	35	-	-	NOUN
ejpam-4776	290	36	regularity	regularity	NOUN
ejpam-4776	290	37	,	,	PUNCT
ejpam-4776	290	38	cc	cc	NOUN
ejpam-4776	290	39	-	-	ADJ
ejpam-4776	290	40	almost	almost	ADV
ejpam-4776	290	41	regularity	regularity	NOUN
ejpam-4776	290	42	and	and	CCONJ
ejpam-4776	290	43	cc	cc	NOUN
ejpam-4776	290	44	-	-	PUNCT
ejpam-4776	290	45	almost	almost	ADV
ejpam-4776	290	46	complete	complete	ADJ
ejpam-4776	290	47	regularity	regularity	NOUN
ejpam-4776	290	48	are	be	AUX
ejpam-4776	290	49	additive	additive	ADJ
ejpam-4776	290	50	properties	property	NOUN
ejpam-4776	290	51	.	.	PUNCT
ejpam-4776	291	1	theorem	theorem	VERB
ejpam-4776	291	2	14	14	NUM
ejpam-4776	291	3	.	.	PUNCT
ejpam-4776	292	1	cc	cc	NOUN
ejpam-4776	292	2	-	-	ADJ
ejpam-4776	292	3	complete	complete	ADJ
ejpam-4776	292	4	regularity	regularity	NOUN
ejpam-4776	292	5	,	,	PUNCT
ejpam-4776	292	6	cc	cc	NOUN
ejpam-4776	292	7	-	-	NOUN
ejpam-4776	292	8	tychonoffness	tychonoffness	NOUN
ejpam-4776	292	9	,	,	PUNCT
ejpam-4776	292	10	cct3	cct3	PROPN
ejpam-4776	292	11	and	and	CCONJ
ejpam-4776	292	12	cc	cc	NOUN
ejpam-4776	292	13	-	-	NOUN
ejpam-4776	292	14	regularity	regularity	NOUN
ejpam-4776	292	15	are	be	AUX
ejpam-4776	292	16	hereditary	hereditary	ADJ
ejpam-4776	292	17	properties	property	NOUN
ejpam-4776	292	18	.	.	PUNCT
ejpam-4776	293	1	proof	proof	NOUN
ejpam-4776	293	2	.	.	PUNCT
ejpam-4776	294	1	let	let	VERB
ejpam-4776	294	2	x	x	PRON
ejpam-4776	294	3	be	be	AUX
ejpam-4776	294	4	a	a	DET
ejpam-4776	294	5	cc	cc	NOUN
ejpam-4776	294	6	-	-	ADJ
ejpam-4776	294	7	completely	completely	ADV
ejpam-4776	294	8	regular	regular	ADJ
ejpam-4776	294	9	(	(	PUNCT
ejpam-4776	294	10	resp	resp	NOUN
ejpam-4776	294	11	.	.	PUNCT
ejpam-4776	295	1	cc	cc	NOUN
ejpam-4776	295	2	-	-	NOUN
ejpam-4776	295	3	tychonoff	tychonoff	NOUN
ejpam-4776	295	4	,	,	PUNCT
ejpam-4776	295	5	cct3	cct3	PROPN
ejpam-4776	295	6	,	,	PUNCT
ejpam-4776	295	7	cc	cc	NOUN
ejpam-4776	295	8	-	-	ADJ
ejpam-4776	295	9	regular	regular	ADJ
ejpam-4776	295	10	)	)	PUNCT
ejpam-4776	295	11	space	space	NOUN
ejpam-4776	295	12	.	.	PUNCT
ejpam-4776	296	1	pick	pick	VERB
ejpam-4776	296	2	a	a	DET
ejpam-4776	296	3	completely	completely	ADV
ejpam-4776	296	4	regular	regular	ADJ
ejpam-4776	296	5	(	(	PUNCT
ejpam-4776	296	6	resp	resp	NOUN
ejpam-4776	296	7	.	.	PUNCT
ejpam-4776	296	8	tychonoff	tychonoff	PROPN
ejpam-4776	296	9	,	,	PUNCT
ejpam-4776	296	10	t3	t3	NOUN
ejpam-4776	296	11	,	,	PUNCT
ejpam-4776	296	12	regular	regular	ADJ
ejpam-4776	296	13	)	)	PUNCT
ejpam-4776	296	14	space	space	NOUN
ejpam-4776	296	15	y	y	PROPN
ejpam-4776	296	16	and	and	CCONJ
ejpam-4776	296	17	a	a	DET
ejpam-4776	296	18	bijective	bijective	ADJ
ejpam-4776	296	19	function	function	NOUN
ejpam-4776	297	1	f	f	NOUN
ejpam-4776	297	2	:	:	PUNCT
ejpam-4776	297	3	x	x	X
ejpam-4776	297	4	→	→	PUNCT
ejpam-4776	297	5	y	y	NUM
ejpam-4776	297	6	such	such	ADJ
ejpam-4776	297	7	that	that	SCONJ
ejpam-4776	297	8	f	f	PROPN
ejpam-4776	297	9	|a	|a	VERB
ejpam-4776	297	10	:	:	PUNCT
ejpam-4776	297	11	a	a	DET
ejpam-4776	297	12	→	→	SYM
ejpam-4776	297	13	f(a	f(a	NOUN
ejpam-4776	297	14	)	)	PUNCT
ejpam-4776	297	15	is	be	AUX
ejpam-4776	297	16	a	a	DET
ejpam-4776	297	17	homoeomorphism	homoeomorphism	NOUN
ejpam-4776	297	18	for	for	ADP
ejpam-4776	297	19	each	each	DET
ejpam-4776	297	20	countably	countably	ADV
ejpam-4776	297	21	compact	compact	ADJ
ejpam-4776	297	22	subspace	subspace	NOUN
ejpam-4776	297	23	a	a	DET
ejpam-4776	297	24	⊆	⊆	NUM
ejpam-4776	297	25	x.	x.	NOUN
ejpam-4776	297	26	let	let	VERB
ejpam-4776	297	27	m	m	PRON
ejpam-4776	297	28	be	be	AUX
ejpam-4776	297	29	any	any	DET
ejpam-4776	297	30	subspace	subspace	NOUN
ejpam-4776	297	31	of	of	ADP
ejpam-4776	297	32	x	x	PUNCT
ejpam-4776	297	33	and	and	CCONJ
ejpam-4776	297	34	let	let	VERB
ejpam-4776	297	35	n	n	PROPN
ejpam-4776	297	36	=	=	SYM
ejpam-4776	297	37	f(m	f(m	PROPN
ejpam-4776	297	38	)	)	PUNCT
ejpam-4776	297	39	⊆	⊆	NUM
ejpam-4776	297	40	y	y	NOUN
ejpam-4776	297	41	.	.	PUNCT
ejpam-4776	298	1	then	then	ADV
ejpam-4776	298	2	,	,	PUNCT
ejpam-4776	298	3	n	n	PRON
ejpam-4776	298	4	is	be	AUX
ejpam-4776	298	5	a	a	DET
ejpam-4776	298	6	completely	completely	ADV
ejpam-4776	298	7	regular	regular	ADJ
ejpam-4776	298	8	(	(	PUNCT
ejpam-4776	298	9	resp	resp	NOUN
ejpam-4776	298	10	.	.	PUNCT
ejpam-4776	298	11	tychonoff	tychonoff	PROPN
ejpam-4776	298	12	,	,	PUNCT
ejpam-4776	298	13	t3	t3	NOUN
ejpam-4776	298	14	,	,	PUNCT
ejpam-4776	298	15	regular	regular	ADJ
ejpam-4776	298	16	)	)	PUNCT
ejpam-4776	298	17	space	space	NOUN
ejpam-4776	298	18	because	because	SCONJ
ejpam-4776	298	19	it	it	PRON
ejpam-4776	298	20	is	be	AUX
ejpam-4776	298	21	a	a	DET
ejpam-4776	298	22	subspace	subspace	NOUN
ejpam-4776	298	23	of	of	ADP
ejpam-4776	298	24	a	a	DET
ejpam-4776	298	25	completely	completely	ADV
ejpam-4776	298	26	regular	regular	ADJ
ejpam-4776	298	27	(	(	PUNCT
ejpam-4776	298	28	resp	resp	NOUN
ejpam-4776	298	29	.	.	PUNCT
ejpam-4776	298	30	tychonoff	tychonoff	PROPN
ejpam-4776	298	31	,	,	PUNCT
ejpam-4776	298	32	t3	t3	NOUN
ejpam-4776	298	33	,	,	PUNCT
ejpam-4776	298	34	regular	regular	ADJ
ejpam-4776	298	35	)	)	PUNCT
ejpam-4776	298	36	space	space	NOUN
ejpam-4776	298	37	y	y	PROPN
ejpam-4776	298	38	.	.	PUNCT
ejpam-4776	299	1	now	now	ADV
ejpam-4776	299	2	,	,	PUNCT
ejpam-4776	299	3	we	we	PRON
ejpam-4776	299	4	have	have	VERB
ejpam-4776	299	5	:	:	PUNCT
ejpam-4776	299	6	f	f	PROPN
ejpam-4776	299	7	|m	|m	NOUN
ejpam-4776	299	8	:	:	PUNCT
ejpam-4776	299	9	m	m	PROPN
ejpam-4776	299	10	→	→	SYM
ejpam-4776	299	11	f(m	f(m	PROPN
ejpam-4776	299	12	)	)	PUNCT
ejpam-4776	299	13	is	be	AUX
ejpam-4776	299	14	a	a	DET
ejpam-4776	299	15	bijective	bijective	ADJ
ejpam-4776	299	16	function	function	NOUN
ejpam-4776	299	17	.	.	PUNCT
ejpam-4776	300	1	since	since	SCONJ
ejpam-4776	300	2	any	any	DET
ejpam-4776	300	3	countably	countably	ADV
ejpam-4776	300	4	compact	compact	ADJ
ejpam-4776	300	5	subspace	subspace	NOUN
ejpam-4776	300	6	k	k	PROPN
ejpam-4776	300	7	of	of	ADP
ejpam-4776	300	8	m	m	PROPN
ejpam-4776	300	9	is	be	AUX
ejpam-4776	300	10	countably	countably	ADV
ejpam-4776	300	11	compact	compact	ADJ
ejpam-4776	300	12	subset	subset	NOUN
ejpam-4776	300	13	in	in	ADP
ejpam-4776	300	14	x	x	PUNCT
ejpam-4776	300	15	and	and	CCONJ
ejpam-4776	300	16	(	(	PUNCT
ejpam-4776	300	17	f	f	NOUN
ejpam-4776	300	18	|m	|m	NOUN
ejpam-4776	300	19	)	)	PUNCT
ejpam-4776	300	20	|k	|k	X
ejpam-4776	301	1	=	=	PUNCT
ejpam-4776	301	2	f	f	X
ejpam-4776	301	3	|k	|k	NOUN
ejpam-4776	301	4	,	,	PUNCT
ejpam-4776	301	5	we	we	PRON
ejpam-4776	301	6	conclude	conclude	VERB
ejpam-4776	301	7	that	that	PRON
ejpam-4776	301	8	:	:	PUNCT
ejpam-4776	301	9	m	m	NOUN
ejpam-4776	301	10	is	be	AUX
ejpam-4776	301	11	cc	cc	VERB
ejpam-4776	301	12	-	-	ADJ
ejpam-4776	301	13	completely	completely	ADV
ejpam-4776	301	14	regular	regular	ADJ
ejpam-4776	301	15	(	(	PUNCT
ejpam-4776	301	16	resp	resp	NOUN
ejpam-4776	301	17	.	.	PUNCT
ejpam-4776	302	1	cc	cc	NOUN
ejpam-4776	302	2	-	-	NOUN
ejpam-4776	302	3	tychonoff	tychonoff	NOUN
ejpam-4776	302	4	,	,	PUNCT
ejpam-4776	302	5	cct3	cct3	PROPN
ejpam-4776	302	6	,	,	PUNCT
ejpam-4776	302	7	cc	cc	NOUN
ejpam-4776	302	8	-	-	NOUN
ejpam-4776	302	9	regular	regular	ADJ
ejpam-4776	302	10	)	)	PUNCT
ejpam-4776	302	11	.	.	PUNCT
ejpam-4776	303	1	theorem	theorem	VERB
ejpam-4776	303	2	15	15	NUM
ejpam-4776	303	3	.	.	PUNCT
ejpam-4776	304	1	if	if	SCONJ
ejpam-4776	304	2	x	x	PRON
ejpam-4776	304	3	is	be	AUX
ejpam-4776	304	4	an	an	DET
ejpam-4776	304	5	l	l	NOUN
ejpam-4776	304	6	-	-	PUNCT
ejpam-4776	304	7	tychonoff	tychonoff	NOUN
ejpam-4776	304	8	space	space	NOUN
ejpam-4776	304	9	such	such	ADJ
ejpam-4776	304	10	that	that	SCONJ
ejpam-4776	304	11	each	each	DET
ejpam-4776	304	12	countably	countably	ADV
ejpam-4776	304	13	compact	compact	ADJ
ejpam-4776	304	14	subspace	subspace	NOUN
ejpam-4776	304	15	is	be	AUX
ejpam-4776	304	16	contained	contain	VERB
ejpam-4776	304	17	in	in	ADP
ejpam-4776	304	18	a	a	DET
ejpam-4776	304	19	lindelöf	lindelöf	NOUN
ejpam-4776	304	20	subspace	subspace	NOUN
ejpam-4776	304	21	,	,	PUNCT
ejpam-4776	304	22	then	then	ADV
ejpam-4776	304	23	x	x	PUNCT
ejpam-4776	304	24	is	be	AUX
ejpam-4776	304	25	cc	cc	NOUN
ejpam-4776	304	26	-	-	NOUN
ejpam-4776	304	27	tychonoff	tychonoff	NOUN
ejpam-4776	304	28	.	.	PUNCT
ejpam-4776	305	1	proof	proof	NOUN
ejpam-4776	305	2	.	.	PUNCT
ejpam-4776	306	1	let	let	VERB
ejpam-4776	306	2	x	x	PRON
ejpam-4776	306	3	be	be	AUX
ejpam-4776	306	4	an	an	DET
ejpam-4776	306	5	l	l	NOUN
ejpam-4776	306	6	-	-	PUNCT
ejpam-4776	306	7	tychonoff	tychonoff	NOUN
ejpam-4776	306	8	space	space	NOUN
ejpam-4776	306	9	such	such	ADJ
ejpam-4776	306	10	that	that	SCONJ
ejpam-4776	306	11	if	if	SCONJ
ejpam-4776	306	12	a	a	PRON
ejpam-4776	306	13	is	be	AUX
ejpam-4776	306	14	a	a	DET
ejpam-4776	306	15	countably	countably	ADV
ejpam-4776	306	16	compact	compact	ADJ
ejpam-4776	306	17	subspace	subspace	NOUN
ejpam-4776	306	18	ofx	ofx	NOUN
ejpam-4776	306	19	,	,	PUNCT
ejpam-4776	306	20	there	there	PRON
ejpam-4776	306	21	exists	exist	VERB
ejpam-4776	306	22	a	a	DET
ejpam-4776	306	23	lindelöf	lindelöf	NOUN
ejpam-4776	306	24	subspace	subspace	PROPN
ejpam-4776	306	25	b	b	PROPN
ejpam-4776	306	26	ofx	ofx	NOUN
ejpam-4776	306	27	such	such	ADJ
ejpam-4776	306	28	that	that	SCONJ
ejpam-4776	306	29	a	a	DET
ejpam-4776	306	30	⊆	⊆	NUM
ejpam-4776	306	31	b.	b.	NOUN
ejpam-4776	306	32	let	let	VERB
ejpam-4776	306	33	y	y	PRON
ejpam-4776	306	34	be	be	AUX
ejpam-4776	306	35	a	a	DET
ejpam-4776	306	36	tychonoff	tychonoff	NOUN
ejpam-4776	306	37	space	space	NOUN
ejpam-4776	306	38	and	and	CCONJ
ejpam-4776	306	39	f	f	NOUN
ejpam-4776	306	40	:	:	PUNCT
ejpam-4776	306	41	x	x	X
ejpam-4776	306	42	→	→	SYM
ejpam-4776	306	43	y	y	X
ejpam-4776	306	44	be	be	AUX
ejpam-4776	306	45	a	a	DET
ejpam-4776	306	46	bijective	bijective	ADJ
ejpam-4776	306	47	function	function	NOUN
ejpam-4776	306	48	such	such	ADJ
ejpam-4776	306	49	that	that	SCONJ
ejpam-4776	306	50	f	f	PROPN
ejpam-4776	306	51	|c	|c	VERB
ejpam-4776	306	52	:	:	PUNCT
ejpam-4776	306	53	c	c	PROPN
ejpam-4776	306	54	→	→	SYM
ejpam-4776	306	55	f(c	f(c	PROPN
ejpam-4776	306	56	)	)	PUNCT
ejpam-4776	306	57	is	be	AUX
ejpam-4776	306	58	a	a	DET
ejpam-4776	306	59	homeomorphism	homeomorphism	NOUN
ejpam-4776	306	60	for	for	ADP
ejpam-4776	306	61	each	each	DET
ejpam-4776	306	62	lindelöf	lindelöf	NOUN
ejpam-4776	306	63	subspace	subspace	NOUN
ejpam-4776	306	64	c	c	PROPN
ejpam-4776	306	65	⊆	⊆	PROPN
ejpam-4776	306	66	x.	x.	NOUN
ejpam-4776	306	67	now	now	ADV
ejpam-4776	306	68	,	,	PUNCT
ejpam-4776	306	69	let	let	VERB
ejpam-4776	306	70	a	a	PRON
ejpam-4776	306	71	be	be	AUX
ejpam-4776	306	72	a	a	DET
ejpam-4776	306	73	countably	countably	ADV
ejpam-4776	306	74	compact	compact	ADJ
ejpam-4776	306	75	subspace	subspace	NOUN
ejpam-4776	306	76	of	of	ADP
ejpam-4776	306	77	x.	x.	PROPN
ejpam-4776	306	78	pick	pick	VERB
ejpam-4776	306	79	a	a	DET
ejpam-4776	306	80	lindelöf	lindelöf	NOUN
ejpam-4776	306	81	subspace	subspace	NOUN
ejpam-4776	306	82	b	b	PROPN
ejpam-4776	306	83	of	of	ADP
ejpam-4776	306	84	x	x	SYM
ejpam-4776	306	85	such	such	ADJ
ejpam-4776	306	86	that	that	SCONJ
ejpam-4776	306	87	a	a	DET
ejpam-4776	306	88	⊆	⊆	NUM
ejpam-4776	306	89	b.	b.	NOUN
ejpam-4776	306	90	then	then	ADV
ejpam-4776	306	91	,	,	PUNCT
ejpam-4776	306	92	f	f	PROPN
ejpam-4776	306	93	|b	|b	NOUN
ejpam-4776	306	94	:	:	PUNCT
ejpam-4776	306	95	b	b	X
ejpam-4776	306	96	→	→	SYM
ejpam-4776	306	97	f(b	f(b	PROPN
ejpam-4776	306	98	)	)	PUNCT
ejpam-4776	306	99	is	be	AUX
ejpam-4776	306	100	a	a	DET
ejpam-4776	306	101	homeomorphism	homeomorphism	NOUN
ejpam-4776	306	102	.	.	PUNCT
ejpam-4776	307	1	thus	thus	ADV
ejpam-4776	307	2	,	,	PUNCT
ejpam-4776	307	3	f	f	PROPN
ejpam-4776	307	4	|a	|a	VERB
ejpam-4776	307	5	:	:	PUNCT
ejpam-4776	307	6	a	a	DET
ejpam-4776	307	7	→	→	SYM
ejpam-4776	307	8	f(a	f(a	NOUN
ejpam-4776	307	9	)	)	PUNCT
ejpam-4776	307	10	is	be	AUX
ejpam-4776	307	11	a	a	DET
ejpam-4776	307	12	homeomorphism	homeomorphism	NOUN
ejpam-4776	307	13	as	as	ADP
ejpam-4776	307	14	(	(	PUNCT
ejpam-4776	307	15	f	f	PROPN
ejpam-4776	307	16	|b)|a	|b)|a	PROPN
ejpam-4776	307	17	=	=	SYM
ejpam-4776	307	18	f	f	PROPN
ejpam-4776	307	19	|a	|a	NOUN
ejpam-4776	307	20	.	.	PUNCT
ejpam-4776	308	1	hence	hence	ADV
ejpam-4776	308	2	,	,	PUNCT
ejpam-4776	308	3	x	x	X
ejpam-4776	308	4	is	be	AUX
ejpam-4776	308	5	cc	cc	NOUN
ejpam-4776	308	6	-	-	NOUN
ejpam-4776	308	7	tychonoff	tychonoff	NOUN
ejpam-4776	308	8	.	.	PUNCT
ejpam-4776	309	1	we	we	PRON
ejpam-4776	309	2	can	can	AUX
ejpam-4776	309	3	find	find	VERB
ejpam-4776	309	4	some	some	DET
ejpam-4776	309	5	statements	statement	NOUN
ejpam-4776	309	6	analogous	analogous	ADJ
ejpam-4776	309	7	to	to	ADP
ejpam-4776	309	8	that	that	PRON
ejpam-4776	309	9	of	of	ADP
ejpam-4776	309	10	theorem	theorem	NOUN
ejpam-4776	309	11	15	15	NUM
ejpam-4776	309	12	.	.	PUNCT
ejpam-4776	310	1	here	here	ADV
ejpam-4776	310	2	are	be	AUX
ejpam-4776	310	3	some	some	PRON
ejpam-4776	310	4	of	of	ADP
ejpam-4776	310	5	them	they	PRON
ejpam-4776	310	6	:	:	PUNCT
ejpam-4776	310	7	theorem	theorem	VERB
ejpam-4776	310	8	16	16	NUM
ejpam-4776	310	9	.	.	PUNCT
ejpam-4776	311	1	(	(	PUNCT
ejpam-4776	311	2	1	1	X
ejpam-4776	311	3	)	)	PUNCT
ejpam-4776	311	4	if	if	SCONJ
ejpam-4776	311	5	x	x	PRON
ejpam-4776	311	6	is	be	AUX
ejpam-4776	311	7	a	a	DET
ejpam-4776	311	8	c	c	NOUN
ejpam-4776	311	9	-	-	PUNCT
ejpam-4776	311	10	tychonoff	tychonoff	NOUN
ejpam-4776	311	11	(	(	PUNCT
ejpam-4776	311	12	resp	resp	NOUN
ejpam-4776	311	13	.	.	PUNCT
ejpam-4776	312	1	c	c	X
ejpam-4776	312	2	-	-	PUNCT
ejpam-4776	312	3	completely	completely	ADV
ejpam-4776	312	4	regular	regular	ADJ
ejpam-4776	312	5	,	,	PUNCT
ejpam-4776	312	6	ct3	ct3	PROPN
ejpam-4776	312	7	,	,	PUNCT
ejpam-4776	312	8	c	c	NOUN
ejpam-4776	312	9	-	-	ADJ
ejpam-4776	312	10	regular	regular	ADJ
ejpam-4776	312	11	,	,	PUNCT
ejpam-4776	312	12	c	c	NOUN
ejpam-4776	312	13	-	-	PUNCT
ejpam-4776	312	14	almost	almost	ADV
ejpam-4776	312	15	regular	regular	ADJ
ejpam-4776	312	16	,	,	PUNCT
ejpam-4776	312	17	c	c	X
ejpam-4776	312	18	-	-	PUNCT
ejpam-4776	312	19	almost	almost	ADV
ejpam-4776	312	20	completely	completely	ADV
ejpam-4776	312	21	regular	regular	ADJ
ejpam-4776	312	22	)	)	PUNCT
ejpam-4776	312	23	space	space	NOUN
ejpam-4776	312	24	such	such	ADJ
ejpam-4776	312	25	that	that	SCONJ
ejpam-4776	312	26	each	each	DET
ejpam-4776	312	27	countably	countably	ADV
ejpam-4776	312	28	compact	compact	ADJ
ejpam-4776	312	29	subspace	subspace	NOUN
ejpam-4776	312	30	is	be	AUX
ejpam-4776	312	31	contained	contain	VERB
ejpam-4776	312	32	in	in	ADP
ejpam-4776	312	33	a	a	DET
ejpam-4776	312	34	compact	compact	ADJ
ejpam-4776	312	35	subspace	subspace	NOUN
ejpam-4776	312	36	,	,	PUNCT
ejpam-4776	312	37	then	then	ADV
ejpam-4776	312	38	x	x	PUNCT
ejpam-4776	312	39	is	be	AUX
ejpam-4776	312	40	cc	cc	NOUN
ejpam-4776	312	41	-	-	NOUN
ejpam-4776	312	42	tychonoff	tychonoff	NOUN
ejpam-4776	312	43	(	(	PUNCT
ejpam-4776	312	44	resp	resp	NOUN
ejpam-4776	312	45	.	.	PUNCT
ejpam-4776	313	1	cc	cc	NOUN
ejpam-4776	313	2	-	-	ADJ
ejpam-4776	313	3	completely	completely	ADV
ejpam-4776	313	4	regular	regular	ADJ
ejpam-4776	313	5	,	,	PUNCT
ejpam-4776	313	6	cct3	cct3	PROPN
ejpam-4776	313	7	,	,	PUNCT
ejpam-4776	313	8	cc	cc	NOUN
ejpam-4776	313	9	-	-	ADJ
ejpam-4776	313	10	regular	regular	ADJ
ejpam-4776	313	11	,	,	PUNCT
ejpam-4776	313	12	cc	cc	NOUN
ejpam-4776	313	13	-	-	ADJ
ejpam-4776	313	14	almost	almost	ADV
ejpam-4776	313	15	regular	regular	ADJ
ejpam-4776	313	16	,	,	PUNCT
ejpam-4776	313	17	cc	cc	NOUN
ejpam-4776	313	18	-	-	ADJ
ejpam-4776	313	19	almost	almost	ADV
ejpam-4776	313	20	completely	completely	ADV
ejpam-4776	313	21	regular	regular	ADJ
ejpam-4776	313	22	)	)	PUNCT
ejpam-4776	313	23	.	.	PUNCT
ejpam-4776	314	1	(	(	PUNCT
ejpam-4776	314	2	2	2	X
ejpam-4776	314	3	)	)	PUNCT
ejpam-4776	314	4	if	if	SCONJ
ejpam-4776	314	5	x	x	PRON
ejpam-4776	314	6	is	be	AUX
ejpam-4776	314	7	a	a	DET
ejpam-4776	314	8	cc	cc	NOUN
ejpam-4776	314	9	-	-	NOUN
ejpam-4776	314	10	tychonoff	tychonoff	NOUN
ejpam-4776	314	11	(	(	PUNCT
ejpam-4776	314	12	resp	resp	NOUN
ejpam-4776	314	13	.	.	PUNCT
ejpam-4776	314	14	cc	cc	NOUN
ejpam-4776	314	15	-	-	ADJ
ejpam-4776	314	16	completely	completely	ADV
ejpam-4776	314	17	regular	regular	ADJ
ejpam-4776	314	18	,	,	PUNCT
ejpam-4776	314	19	cct3	cct3	PROPN
ejpam-4776	314	20	,	,	PUNCT
ejpam-4776	314	21	cc	cc	NOUN
ejpam-4776	314	22	-	-	ADJ
ejpam-4776	314	23	regular	regular	ADJ
ejpam-4776	314	24	,	,	PUNCT
ejpam-4776	314	25	cc	cc	NOUN
ejpam-4776	314	26	-	-	ADJ
ejpam-4776	314	27	almost	almost	ADV
ejpam-4776	314	28	regular	regular	ADJ
ejpam-4776	314	29	,	,	PUNCT
ejpam-4776	314	30	cc	cc	NOUN
ejpam-4776	314	31	-	-	ADJ
ejpam-4776	314	32	almost	almost	ADV
ejpam-4776	314	33	completely	completely	ADV
ejpam-4776	314	34	regular	regular	ADJ
ejpam-4776	314	35	)	)	PUNCT
ejpam-4776	314	36	space	space	NOUN
ejpam-4776	314	37	such	such	ADJ
ejpam-4776	314	38	that	that	SCONJ
ejpam-4776	314	39	each	each	DET
ejpam-4776	314	40	lindelöf	lindelöf	NOUN
ejpam-4776	314	41	subspace	subspace	NOUN
ejpam-4776	314	42	is	be	AUX
ejpam-4776	314	43	contained	contain	VERB
ejpam-4776	314	44	in	in	ADP
ejpam-4776	314	45	a	a	DET
ejpam-4776	314	46	countably	countably	ADV
ejpam-4776	314	47	compact	compact	ADJ
ejpam-4776	314	48	subspace	subspace	NOUN
ejpam-4776	314	49	,	,	PUNCT
ejpam-4776	314	50	then	then	ADV
ejpam-4776	314	51	x	x	PUNCT
ejpam-4776	314	52	is	be	AUX
ejpam-4776	314	53	l	l	NOUN
ejpam-4776	314	54	-	-	NOUN
ejpam-4776	314	55	tychonoff	tychonoff	NOUN
ejpam-4776	314	56	(	(	PUNCT
ejpam-4776	314	57	resp	resp	NOUN
ejpam-4776	314	58	.	.	PUNCT
ejpam-4776	315	1	l	l	NOUN
ejpam-4776	315	2	-	-	PUNCT
ejpam-4776	315	3	completely	completely	ADV
ejpam-4776	315	4	regular	regular	ADJ
ejpam-4776	315	5	,	,	PUNCT
ejpam-4776	315	6	lt3	lt3	PROPN
ejpam-4776	315	7	,	,	PUNCT
ejpam-4776	315	8	l	l	NOUN
ejpam-4776	315	9	-	-	ADJ
ejpam-4776	315	10	regular	regular	ADJ
ejpam-4776	315	11	,	,	PUNCT
ejpam-4776	315	12	l	l	NOUN
ejpam-4776	315	13	-	-	PUNCT
ejpam-4776	315	14	almost	almost	ADV
ejpam-4776	315	15	regular	regular	ADJ
ejpam-4776	315	16	,	,	PUNCT
ejpam-4776	315	17	l	l	NOUN
ejpam-4776	315	18	-	-	PUNCT
ejpam-4776	315	19	almost	almost	ADV
ejpam-4776	315	20	completely	completely	ADV
ejpam-4776	315	21	regular	regular	ADJ
ejpam-4776	315	22	)	)	PUNCT
ejpam-4776	315	23	.	.	PUNCT
ejpam-4776	316	1	s.	s.	PROPN
ejpam-4776	316	2	a.	a.	PROPN
ejpam-4776	316	3	thabit	thabit	PROPN
ejpam-4776	316	4	,	,	PUNCT
ejpam-4776	316	5	w.	w.	PROPN
ejpam-4776	316	6	alqurashi	alqurashi	PROPN
ejpam-4776	316	7	/	/	SYM
ejpam-4776	316	8	eur	eur	PROPN
ejpam-4776	316	9	.	.	PUNCT
ejpam-4776	317	1	j.	j.	PROPN
ejpam-4776	317	2	pure	pure	PROPN
ejpam-4776	317	3	appl	appl	PROPN
ejpam-4776	317	4	.	.	PROPN
ejpam-4776	317	5	math	math	PROPN
ejpam-4776	317	6	,	,	PUNCT
ejpam-4776	317	7	16	16	NUM
ejpam-4776	317	8	(	(	PUNCT
ejpam-4776	317	9	2	2	NUM
ejpam-4776	317	10	)	)	PUNCT
ejpam-4776	317	11	(	(	PUNCT
ejpam-4776	317	12	2023	2023	NUM
ejpam-4776	317	13	)	)	PUNCT
ejpam-4776	317	14	,	,	PUNCT
ejpam-4776	317	15	1260	1260	NUM
ejpam-4776	317	16	-	-	SYM
ejpam-4776	317	17	1273	1273	NUM
ejpam-4776	317	18	1270	1270	NUM
ejpam-4776	317	19	(	(	PUNCT
ejpam-4776	317	20	3	3	NUM
ejpam-4776	317	21	)	)	PUNCT
ejpam-4776	317	22	if	if	SCONJ
ejpam-4776	317	23	x	x	PRON
ejpam-4776	317	24	is	be	AUX
ejpam-4776	317	25	an	an	DET
ejpam-4776	317	26	l	l	NOUN
ejpam-4776	317	27	-	-	ADJ
ejpam-4776	317	28	completely	completely	ADV
ejpam-4776	317	29	regular	regular	ADJ
ejpam-4776	317	30	(	(	PUNCT
ejpam-4776	317	31	resp	resp	NOUN
ejpam-4776	317	32	.	.	PUNCT
ejpam-4776	318	1	l	l	NOUN
ejpam-4776	318	2	-	-	PUNCT
ejpam-4776	318	3	completely	completely	ADV
ejpam-4776	318	4	regular	regular	ADJ
ejpam-4776	318	5	,	,	PUNCT
ejpam-4776	318	6	lt3	lt3	PROPN
ejpam-4776	318	7	,	,	PUNCT
ejpam-4776	318	8	l	l	NOUN
ejpam-4776	318	9	-	-	ADJ
ejpam-4776	318	10	regular	regular	ADJ
ejpam-4776	318	11	,	,	PUNCT
ejpam-4776	318	12	l	l	NOUN
ejpam-4776	318	13	-	-	PUNCT
ejpam-4776	318	14	almost	almost	ADV
ejpam-4776	318	15	regular	regular	ADJ
ejpam-4776	318	16	,	,	PUNCT
ejpam-4776	318	17	l	l	NOUN
ejpam-4776	318	18	-	-	PUNCT
ejpam-4776	318	19	almost	almost	ADV
ejpam-4776	318	20	completely	completely	ADV
ejpam-4776	318	21	regular	regular	ADJ
ejpam-4776	318	22	)	)	PUNCT
ejpam-4776	318	23	space	space	NOUN
ejpam-4776	318	24	such	such	ADJ
ejpam-4776	318	25	that	that	SCONJ
ejpam-4776	318	26	each	each	DET
ejpam-4776	318	27	countably	countably	ADV
ejpam-4776	318	28	compact	compact	ADJ
ejpam-4776	318	29	subspace	subspace	NOUN
ejpam-4776	318	30	is	be	AUX
ejpam-4776	318	31	contained	contain	VERB
ejpam-4776	318	32	in	in	ADP
ejpam-4776	318	33	a	a	DET
ejpam-4776	318	34	lindelöf	lindelöf	NOUN
ejpam-4776	318	35	subspace	subspace	NOUN
ejpam-4776	318	36	,	,	PUNCT
ejpam-4776	318	37	then	then	ADV
ejpam-4776	318	38	x	x	PUNCT
ejpam-4776	318	39	is	be	AUX
ejpam-4776	318	40	cc	cc	VERB
ejpam-4776	318	41	-	-	ADJ
ejpam-4776	318	42	completely	completely	ADV
ejpam-4776	318	43	regular	regular	ADJ
ejpam-4776	318	44	(	(	PUNCT
ejpam-4776	318	45	resp	resp	NOUN
ejpam-4776	318	46	.	.	PUNCT
ejpam-4776	319	1	cc	cc	NOUN
ejpam-4776	319	2	-	-	ADJ
ejpam-4776	319	3	completely	completely	ADV
ejpam-4776	319	4	regular	regular	ADJ
ejpam-4776	319	5	,	,	PUNCT
ejpam-4776	319	6	cct3	cct3	PROPN
ejpam-4776	319	7	,	,	PUNCT
ejpam-4776	319	8	cc	cc	NOUN
ejpam-4776	319	9	-	-	ADJ
ejpam-4776	319	10	regular	regular	ADJ
ejpam-4776	319	11	,	,	PUNCT
ejpam-4776	319	12	cc	cc	NOUN
ejpam-4776	319	13	-	-	ADJ
ejpam-4776	319	14	almost	almost	ADV
ejpam-4776	319	15	regular	regular	ADJ
ejpam-4776	319	16	,	,	PUNCT
ejpam-4776	319	17	cc	cc	NOUN
ejpam-4776	319	18	-	-	ADJ
ejpam-4776	319	19	almost	almost	ADV
ejpam-4776	319	20	completely	completely	ADV
ejpam-4776	319	21	regular	regular	ADJ
ejpam-4776	319	22	)	)	PUNCT
ejpam-4776	319	23	.	.	PUNCT
ejpam-4776	320	1	theorem	theorem	VERB
ejpam-4776	320	2	17	17	NUM
ejpam-4776	320	3	.	.	PUNCT
ejpam-4776	321	1	if	if	SCONJ
ejpam-4776	321	2	x	x	PRON
ejpam-4776	321	3	is	be	AUX
ejpam-4776	321	4	a	a	DET
ejpam-4776	321	5	hausdorff	hausdorff	NOUN
ejpam-4776	321	6	fréchet	fréchet	NOUN
ejpam-4776	321	7	(	(	PUNCT
ejpam-4776	321	8	resp	resp	NOUN
ejpam-4776	321	9	.	.	PUNCT
ejpam-4776	322	1	first	first	ADJ
ejpam-4776	322	2	countable	countable	ADJ
ejpam-4776	322	3	)	)	PUNCT
ejpam-4776	322	4	space	space	NOUN
ejpam-4776	322	5	,	,	PUNCT
ejpam-4776	322	6	then	then	ADV
ejpam-4776	322	7	x	x	PUNCT
ejpam-4776	322	8	is	be	AUX
ejpam-4776	322	9	cc	cc	VERB
ejpam-4776	322	10	-	-	ADJ
ejpam-4776	322	11	almost	almost	ADV
ejpam-4776	322	12	completely	completely	ADV
ejpam-4776	322	13	regular	regular	ADJ
ejpam-4776	322	14	.	.	PUNCT
ejpam-4776	323	1	proof	proof	NOUN
ejpam-4776	323	2	.	.	PUNCT
ejpam-4776	324	1	let	let	VERB
ejpam-4776	324	2	x	x	PRON
ejpam-4776	324	3	be	be	AUX
ejpam-4776	324	4	a	a	DET
ejpam-4776	324	5	hausdorff	hausdorff	NOUN
ejpam-4776	324	6	fréchet	fréchet	NOUN
ejpam-4776	324	7	(	(	PUNCT
ejpam-4776	324	8	resp	resp	NOUN
ejpam-4776	324	9	.	.	PUNCT
ejpam-4776	325	1	first	first	ADJ
ejpam-4776	325	2	countable	countable	ADJ
ejpam-4776	325	3	)	)	PUNCT
ejpam-4776	325	4	space	space	NOUN
ejpam-4776	325	5	.	.	PUNCT
ejpam-4776	326	1	then	then	ADV
ejpam-4776	326	2	,	,	PUNCT
ejpam-4776	326	3	there	there	PRON
ejpam-4776	326	4	exists	exist	VERB
ejpam-4776	326	5	a	a	DET
ejpam-4776	326	6	topology	topology	NOUN
ejpam-4776	326	7	t	t	NOUN
ejpam-4776	326	8	′	′	NOUN
ejpam-4776	326	9	coarser	coarse	ADJ
ejpam-4776	326	10	than	than	ADP
ejpam-4776	326	11	t	t	PRON
ejpam-4776	326	12	such	such	ADJ
ejpam-4776	326	13	that	that	SCONJ
ejpam-4776	326	14	(	(	PUNCT
ejpam-4776	326	15	x	x	X
ejpam-4776	326	16	,	,	PUNCT
ejpam-4776	326	17	t	t	PROPN
ejpam-4776	326	18	′	′	NUM
ejpam-4776	326	19	)	)	PUNCT
ejpam-4776	326	20	is	be	AUX
ejpam-4776	326	21	t1	t1	NOUN
ejpam-4776	326	22	-	-	PUNCT
ejpam-4776	326	23	almost	almost	ADV
ejpam-4776	326	24	completely	completely	ADV
ejpam-4776	326	25	regular	regular	ADJ
ejpam-4776	326	26	[	[	X
ejpam-4776	326	27	4	4	NUM
ejpam-4776	326	28	]	]	PUNCT
ejpam-4776	326	29	.	.	PUNCT
ejpam-4776	327	1	the	the	DET
ejpam-4776	327	2	identity	identity	NOUN
ejpam-4776	327	3	function	function	NOUN
ejpam-4776	327	4	ix	ix	X
ejpam-4776	327	5	:	:	PUNCT
ejpam-4776	327	6	(	(	PUNCT
ejpam-4776	327	7	x	x	X
ejpam-4776	327	8	,	,	PUNCT
ejpam-4776	327	9	t	t	PROPN
ejpam-4776	327	10	)	)	PUNCT
ejpam-4776	327	11	→	→	SYM
ejpam-4776	327	12	(	(	PUNCT
ejpam-4776	327	13	x	x	X
ejpam-4776	327	14	,	,	PUNCT
ejpam-4776	327	15	t	t	PROPN
ejpam-4776	327	16	′	′	NUM
ejpam-4776	327	17	)	)	PUNCT
ejpam-4776	327	18	is	be	AUX
ejpam-4776	327	19	a	a	DET
ejpam-4776	327	20	bijective	bijective	ADJ
ejpam-4776	327	21	continuous	continuous	ADJ
ejpam-4776	327	22	function	function	NOUN
ejpam-4776	327	23	.	.	PUNCT
ejpam-4776	328	1	let	let	VERB
ejpam-4776	328	2	m	m	PRON
ejpam-4776	328	3	be	be	AUX
ejpam-4776	328	4	any	any	DET
ejpam-4776	328	5	countably	countably	ADV
ejpam-4776	328	6	compact	compact	ADJ
ejpam-4776	328	7	subspace	subspace	NOUN
ejpam-4776	328	8	of	of	ADP
ejpam-4776	328	9	(	(	PUNCT
ejpam-4776	328	10	x	x	PROPN
ejpam-4776	328	11	,	,	PUNCT
ejpam-4776	328	12	t	t	PROPN
ejpam-4776	328	13	)	)	PUNCT
ejpam-4776	328	14	.	.	PUNCT
ejpam-4776	329	1	then	then	ADV
ejpam-4776	329	2	,	,	PUNCT
ejpam-4776	329	3	(	(	PUNCT
ejpam-4776	329	4	ix)|m	ix)|m	NOUN
ejpam-4776	329	5	:	:	PUNCT
ejpam-4776	329	6	m	m	PROPN
ejpam-4776	329	7	→	→	SYM
ejpam-4776	329	8	ix(m	ix(m	NUM
ejpam-4776	329	9	)	)	PUNCT
ejpam-4776	329	10	is	be	AUX
ejpam-4776	329	11	a	a	DET
ejpam-4776	329	12	bijective	bijective	ADJ
ejpam-4776	329	13	continuous	continuous	ADJ
ejpam-4776	329	14	function	function	NOUN
ejpam-4776	329	15	and	and	CCONJ
ejpam-4776	329	16	ix(m	ix(m	NUM
ejpam-4776	329	17	)	)	PUNCT
ejpam-4776	330	1	=	=	VERB
ejpam-4776	330	2	m	m	VERB
ejpam-4776	330	3	is	be	AUX
ejpam-4776	330	4	a	a	DET
ejpam-4776	330	5	countably	countably	ADV
ejpam-4776	330	6	compact	compact	ADJ
ejpam-4776	330	7	subset	subset	NOUN
ejpam-4776	330	8	in	in	ADP
ejpam-4776	330	9	both	both	DET
ejpam-4776	330	10	(	(	PUNCT
ejpam-4776	330	11	x	x	X
ejpam-4776	330	12	,	,	PUNCT
ejpam-4776	330	13	t	t	PROPN
ejpam-4776	330	14	)	)	PUNCT
ejpam-4776	330	15	and	and	CCONJ
ejpam-4776	330	16	(	(	PUNCT
ejpam-4776	330	17	x	x	X
ejpam-4776	330	18	,	,	PUNCT
ejpam-4776	330	19	t	t	PROPN
ejpam-4776	330	20	′	′	NUM
ejpam-4776	330	21	)	)	PUNCT
ejpam-4776	330	22	.	.	PUNCT
ejpam-4776	331	1	let	let	VERB
ejpam-4776	331	2	u	u	PRON
ejpam-4776	331	3	be	be	AUX
ejpam-4776	331	4	any	any	DET
ejpam-4776	331	5	open	open	ADJ
ejpam-4776	331	6	set	set	NOUN
ejpam-4776	331	7	in	in	ADP
ejpam-4776	331	8	(	(	PUNCT
ejpam-4776	331	9	m	m	PROPN
ejpam-4776	331	10	,	,	PUNCT
ejpam-4776	331	11	tm	tm	NOUN
ejpam-4776	331	12	)	)	PUNCT
ejpam-4776	331	13	.	.	PUNCT
ejpam-4776	332	1	since	since	SCONJ
ejpam-4776	332	2	m	m	PROPN
ejpam-4776	332	3	is	be	AUX
ejpam-4776	332	4	a	a	DET
ejpam-4776	332	5	countably	countably	ADV
ejpam-4776	332	6	compact	compact	ADJ
ejpam-4776	332	7	subset	subset	NOUN
ejpam-4776	332	8	of	of	ADP
ejpam-4776	332	9	(	(	PUNCT
ejpam-4776	332	10	x	x	PROPN
ejpam-4776	332	11	,	,	PUNCT
ejpam-4776	332	12	t	t	PROPN
ejpam-4776	332	13	′	′	NUM
ejpam-4776	332	14	)	)	PUNCT
ejpam-4776	332	15	,	,	PUNCT
ejpam-4776	332	16	there	there	PRON
ejpam-4776	332	17	exists	exist	VERB
ejpam-4776	332	18	an	an	DET
ejpam-4776	332	19	open	open	ADJ
ejpam-4776	332	20	set	set	NOUN
ejpam-4776	332	21	v	v	NOUN
ejpam-4776	332	22	in	in	ADP
ejpam-4776	332	23	(	(	PUNCT
ejpam-4776	332	24	x	x	NOUN
ejpam-4776	332	25	,	,	PUNCT
ejpam-4776	332	26	t	t	PROPN
ejpam-4776	332	27	′	′	NUM
ejpam-4776	332	28	)	)	PUNCT
ejpam-4776	332	29	such	such	ADJ
ejpam-4776	332	30	that	that	SCONJ
ejpam-4776	332	31	u	u	NOUN
ejpam-4776	332	32	=	=	SYM
ejpam-4776	332	33	v	v	PROPN
ejpam-4776	332	34	∩	∩	NOUN
ejpam-4776	332	35	m	m	VERB
ejpam-4776	332	36	.	.	PUNCT
ejpam-4776	333	1	thus	thus	ADV
ejpam-4776	333	2	,	,	PUNCT
ejpam-4776	333	3	(	(	PUNCT
ejpam-4776	333	4	ix)|m	ix)|m	PROPN
ejpam-4776	333	5	(	(	PUNCT
ejpam-4776	333	6	u	u	NOUN
ejpam-4776	333	7	)	)	PUNCT
ejpam-4776	333	8	=	=	SYM
ejpam-4776	333	9	(	(	PUNCT
ejpam-4776	333	10	ix)|m	ix)|m	PROPN
ejpam-4776	333	11	(	(	PUNCT
ejpam-4776	333	12	v	v	NOUN
ejpam-4776	333	13	∩m	∩m	NOUN
ejpam-4776	333	14	)	)	PUNCT
ejpam-4776	333	15	=	=	NOUN
ejpam-4776	333	16	v	v	ADP
ejpam-4776	333	17	∩m	∩m	NOUN
ejpam-4776	334	1	=	=	PUNCT
ejpam-4776	334	2	u	u	PROPN
ejpam-4776	334	3	,	,	PUNCT
ejpam-4776	334	4	which	which	PRON
ejpam-4776	334	5	is	be	AUX
ejpam-4776	334	6	an	an	DET
ejpam-4776	334	7	open	open	ADJ
ejpam-4776	334	8	set	set	NOUN
ejpam-4776	334	9	in	in	ADP
ejpam-4776	334	10	(	(	PUNCT
ejpam-4776	334	11	ix(m	ix(m	NUM
ejpam-4776	334	12	)	)	PUNCT
ejpam-4776	334	13	,	,	PUNCT
ejpam-4776	334	14	t	t	PROPN
ejpam-4776	334	15	′	′	NUM
ejpam-4776	334	16	m	m	NOUN
ejpam-4776	334	17	)	)	PUNCT
ejpam-4776	334	18	.	.	PUNCT
ejpam-4776	335	1	hence	hence	ADV
ejpam-4776	335	2	,	,	PUNCT
ejpam-4776	335	3	(	(	PUNCT
ejpam-4776	335	4	ix)|m	ix)|m	NOUN
ejpam-4776	335	5	is	be	AUX
ejpam-4776	335	6	open	open	ADJ
ejpam-4776	335	7	and	and	CCONJ
ejpam-4776	335	8	hence	hence	ADV
ejpam-4776	335	9	a	a	DET
ejpam-4776	335	10	homeomorphism	homeomorphism	NOUN
ejpam-4776	335	11	.	.	PUNCT
ejpam-4776	336	1	therefore	therefore	ADV
ejpam-4776	336	2	,	,	PUNCT
ejpam-4776	336	3	x	x	X
ejpam-4776	336	4	is	be	AUX
ejpam-4776	336	5	cc	cc	VERB
ejpam-4776	336	6	-	-	ADJ
ejpam-4776	336	7	almost	almost	ADV
ejpam-4776	336	8	completely	completely	ADV
ejpam-4776	336	9	regular	regular	ADJ
ejpam-4776	336	10	.	.	PUNCT
ejpam-4776	337	1	corollary	corollary	ADJ
ejpam-4776	337	2	10	10	NUM
ejpam-4776	337	3	.	.	PUNCT
ejpam-4776	338	1	if	if	SCONJ
ejpam-4776	338	2	x	x	PRON
ejpam-4776	338	3	is	be	AUX
ejpam-4776	338	4	a	a	DET
ejpam-4776	338	5	hausdorff	hausdorff	NOUN
ejpam-4776	338	6	fréchet	fréchet	NOUN
ejpam-4776	338	7	(	(	PUNCT
ejpam-4776	338	8	resp	resp	NOUN
ejpam-4776	338	9	.	.	PUNCT
ejpam-4776	339	1	first	first	ADJ
ejpam-4776	339	2	countable	countable	ADJ
ejpam-4776	339	3	)	)	PUNCT
ejpam-4776	339	4	space	space	NOUN
ejpam-4776	339	5	,	,	PUNCT
ejpam-4776	339	6	then	then	ADV
ejpam-4776	339	7	x	x	PUNCT
ejpam-4776	339	8	is	be	AUX
ejpam-4776	339	9	cc	cc	VERB
ejpam-4776	339	10	-	-	ADJ
ejpam-4776	339	11	almost	almost	ADV
ejpam-4776	339	12	completely	completely	ADV
ejpam-4776	339	13	regular	regular	ADJ
ejpam-4776	339	14	.	.	PUNCT
ejpam-4776	340	1	theorem	theorem	VERB
ejpam-4776	340	2	18	18	NUM
ejpam-4776	340	3	.	.	PUNCT
ejpam-4776	341	1	every	every	DET
ejpam-4776	341	2	hausdorff	hausdorff	NOUN
ejpam-4776	341	3	almost	almost	ADV
ejpam-4776	341	4	completely	completely	ADV
ejpam-4776	341	5	regular	regular	ADJ
ejpam-4776	341	6	space	space	NOUN
ejpam-4776	341	7	is	be	AUX
ejpam-4776	341	8	cc	cc	NOUN
ejpam-4776	341	9	-	-	NOUN
ejpam-4776	341	10	tychonoff	tychonoff	NOUN
ejpam-4776	341	11	.	.	PUNCT
ejpam-4776	342	1	proof	proof	NOUN
ejpam-4776	342	2	.	.	PUNCT
ejpam-4776	343	1	let	let	AUX
ejpam-4776	343	2	(	(	PUNCT
ejpam-4776	343	3	x	x	X
ejpam-4776	343	4	,	,	PUNCT
ejpam-4776	343	5	t	t	PROPN
ejpam-4776	343	6	)	)	PUNCT
ejpam-4776	343	7	be	be	AUX
ejpam-4776	343	8	a	a	DET
ejpam-4776	343	9	hausdorff	hausdorff	NOUN
ejpam-4776	343	10	almost	almost	ADV
ejpam-4776	343	11	completely	completely	ADV
ejpam-4776	343	12	regular	regular	ADJ
ejpam-4776	343	13	space	space	NOUN
ejpam-4776	343	14	.	.	PUNCT
ejpam-4776	344	1	let	let	VERB
ejpam-4776	344	2	(	(	PUNCT
ejpam-4776	344	3	x	x	NOUN
ejpam-4776	344	4	,	,	PUNCT
ejpam-4776	344	5	ts	ts	NOUN
ejpam-4776	344	6	)	)	PUNCT
ejpam-4776	344	7	be	be	AUX
ejpam-4776	344	8	the	the	DET
ejpam-4776	344	9	semi	semi	NOUN
ejpam-4776	344	10	-	-	NOUN
ejpam-4776	344	11	regularization	regularization	NOUN
ejpam-4776	344	12	of	of	ADP
ejpam-4776	344	13	(	(	PUNCT
ejpam-4776	344	14	x	x	PROPN
ejpam-4776	344	15	,	,	PUNCT
ejpam-4776	344	16	t	t	PROPN
ejpam-4776	344	17	)	)	PUNCT
ejpam-4776	344	18	.	.	PUNCT
ejpam-4776	345	1	then	then	ADV
ejpam-4776	345	2	,	,	PUNCT
ejpam-4776	345	3	(	(	PUNCT
ejpam-4776	345	4	x	x	X
ejpam-4776	345	5	,	,	PUNCT
ejpam-4776	345	6	ts	ts	NOUN
ejpam-4776	345	7	)	)	PUNCT
ejpam-4776	345	8	is	be	AUX
ejpam-4776	345	9	a	a	DET
ejpam-4776	345	10	hausdorff	hausdorff	NOUN
ejpam-4776	345	11	completely	completely	ADV
ejpam-4776	345	12	regular	regular	ADJ
ejpam-4776	345	13	space	space	NOUN
ejpam-4776	345	14	because	because	SCONJ
ejpam-4776	345	15	a	a	DET
ejpam-4776	345	16	semi	semi	NOUN
ejpam-4776	345	17	-	-	NOUN
ejpam-4776	345	18	regularization	regularization	NOUN
ejpam-4776	345	19	of	of	ADP
ejpam-4776	345	20	a	a	DET
ejpam-4776	345	21	hausdorff	hausdorff	NOUN
ejpam-4776	345	22	almost	almost	ADV
ejpam-4776	345	23	completely	completely	ADV
ejpam-4776	345	24	regular	regular	ADJ
ejpam-4776	345	25	space	space	NOUN
ejpam-4776	345	26	is	be	AUX
ejpam-4776	345	27	hausdorff	hausdorff	NOUN
ejpam-4776	345	28	completely	completely	ADV
ejpam-4776	345	29	regular	regular	ADJ
ejpam-4776	346	1	[	[	X
ejpam-4776	346	2	16	16	NUM
ejpam-4776	346	3	]	]	PUNCT
ejpam-4776	346	4	.	.	PUNCT
ejpam-4776	347	1	hence	hence	ADV
ejpam-4776	347	2	,	,	PUNCT
ejpam-4776	347	3	(	(	PUNCT
ejpam-4776	347	4	x	x	X
ejpam-4776	347	5	,	,	PUNCT
ejpam-4776	347	6	ts	ts	NOUN
ejpam-4776	347	7	)	)	PUNCT
ejpam-4776	347	8	is	be	AUX
ejpam-4776	347	9	tychonoff	tychonoff	NOUN
ejpam-4776	347	10	.	.	PUNCT
ejpam-4776	348	1	since	since	SCONJ
ejpam-4776	348	2	ts	ts	ADP
ejpam-4776	348	3	⊆	⊆	NUM
ejpam-4776	348	4	t	t	NOUN
ejpam-4776	348	5	,	,	PUNCT
ejpam-4776	348	6	we	we	PRON
ejpam-4776	348	7	obtain	obtain	VERB
ejpam-4776	348	8	that	that	PRON
ejpam-4776	348	9	(	(	PUNCT
ejpam-4776	348	10	x	x	X
ejpam-4776	348	11	,	,	PUNCT
ejpam-4776	348	12	t	t	PROPN
ejpam-4776	348	13	)	)	PUNCT
ejpam-4776	348	14	is	be	AUX
ejpam-4776	348	15	epi	epi	NOUN
ejpam-4776	348	16	-	-	ADJ
ejpam-4776	348	17	completely	completely	ADV
ejpam-4776	348	18	regular	regular	ADJ
ejpam-4776	348	19	.	.	PUNCT
ejpam-4776	349	1	by	by	ADP
ejpam-4776	349	2	theorem	theorem	NOUN
ejpam-4776	349	3	1	1	NUM
ejpam-4776	349	4	,	,	PUNCT
ejpam-4776	349	5	we	we	PRON
ejpam-4776	349	6	conclude	conclude	VERB
ejpam-4776	349	7	that	that	SCONJ
ejpam-4776	349	8	(	(	PUNCT
ejpam-4776	349	9	x	x	X
ejpam-4776	349	10	,	,	PUNCT
ejpam-4776	349	11	t	t	PROPN
ejpam-4776	349	12	)	)	PUNCT
ejpam-4776	349	13	is	be	AUX
ejpam-4776	349	14	cc	cc	NOUN
ejpam-4776	349	15	-	-	NOUN
ejpam-4776	349	16	tychonoff	tychonoff	NOUN
ejpam-4776	349	17	.	.	PUNCT
ejpam-4776	350	1	similarly	similarly	ADV
ejpam-4776	350	2	,	,	PUNCT
ejpam-4776	350	3	we	we	PRON
ejpam-4776	350	4	can	can	AUX
ejpam-4776	350	5	prove	prove	VERB
ejpam-4776	350	6	the	the	DET
ejpam-4776	350	7	next	next	ADJ
ejpam-4776	350	8	result	result	NOUN
ejpam-4776	350	9	:	:	PUNCT
ejpam-4776	350	10	theorem	theorem	VERB
ejpam-4776	350	11	19	19	NUM
ejpam-4776	350	12	.	.	PUNCT
ejpam-4776	351	1	every	every	DET
ejpam-4776	351	2	hausdorff	hausdorff	NOUN
ejpam-4776	351	3	almost	almost	ADV
ejpam-4776	351	4	regular	regular	ADJ
ejpam-4776	351	5	space	space	NOUN
ejpam-4776	351	6	is	be	AUX
ejpam-4776	351	7	a	a	DET
ejpam-4776	351	8	cct3	cct3	NOUN
ejpam-4776	351	9	-	-	PUNCT
ejpam-4776	351	10	space	space	NOUN
ejpam-4776	351	11	.	.	PUNCT
ejpam-4776	352	1	observed	observe	VERB
ejpam-4776	352	2	that	that	SCONJ
ejpam-4776	352	3	:	:	PUNCT
ejpam-4776	352	4	cc	cc	NOUN
ejpam-4776	352	5	-	-	NOUN
ejpam-4776	352	6	normality	normality	NOUN
ejpam-4776	352	7	does	do	AUX
ejpam-4776	352	8	not	not	PART
ejpam-4776	352	9	imply	imply	VERB
ejpam-4776	352	10	cc	cc	VERB
ejpam-4776	352	11	-	-	ADJ
ejpam-4776	352	12	almost	almost	ADV
ejpam-4776	352	13	regularity	regularity	NOUN
ejpam-4776	352	14	.	.	PUNCT
ejpam-4776	353	1	here	here	ADV
ejpam-4776	353	2	is	be	AUX
ejpam-4776	353	3	a	a	DET
ejpam-4776	353	4	counterexample	counterexample	NOUN
ejpam-4776	353	5	.	.	PUNCT
ejpam-4776	353	6	example	example	NOUN
ejpam-4776	353	7	10	10	NUM
ejpam-4776	353	8	.	.	PUNCT
ejpam-4776	354	1	the	the	DET
ejpam-4776	354	2	excluded	exclude	VERB
ejpam-4776	354	3	point	point	NOUN
ejpam-4776	354	4	topology	topology	NOUN
ejpam-4776	354	5	:	:	PUNCT
ejpam-4776	354	6	[	[	X
ejpam-4776	354	7	23	23	NUM
ejpam-4776	354	8	,	,	PUNCT
ejpam-4776	354	9	example	example	NOUN
ejpam-4776	354	10	15	15	NUM
ejpam-4776	354	11	]	]	PUNCT
ejpam-4776	354	12	,	,	PUNCT
ejpam-4776	354	13	(	(	PUNCT
ejpam-4776	354	14	x	x	X
ejpam-4776	354	15	,	,	PUNCT
ejpam-4776	354	16	ep	ep	PROPN
ejpam-4776	354	17	)	)	PUNCT
ejpam-4776	354	18	is	be	AUX
ejpam-4776	354	19	a	a	DET
ejpam-4776	354	20	t0	t0	NOUN
ejpam-4776	354	21	,	,	PUNCT
ejpam-4776	354	22	compact	compact	ADJ
ejpam-4776	354	23	,	,	PUNCT
ejpam-4776	354	24	paracompact	paracompact	ADJ
ejpam-4776	354	25	,	,	PUNCT
ejpam-4776	354	26	first	first	ADV
ejpam-4776	354	27	countable	countable	ADJ
ejpam-4776	354	28	and	and	CCONJ
ejpam-4776	354	29	normal	normal	ADJ
ejpam-4776	354	30	space	space	NOUN
ejpam-4776	354	31	,	,	PUNCT
ejpam-4776	354	32	which	which	PRON
ejpam-4776	354	33	is	be	AUX
ejpam-4776	354	34	neither	neither	CCONJ
ejpam-4776	354	35	t1	t1	NOUN
ejpam-4776	354	36	,	,	PUNCT
ejpam-4776	354	37	regular	regular	ADJ
ejpam-4776	354	38	,	,	PUNCT
ejpam-4776	354	39	separable	separable	ADJ
ejpam-4776	354	40	nor	nor	CCONJ
ejpam-4776	354	41	semi	semi	ADV
ejpam-4776	354	42	regular	regular	ADJ
ejpam-4776	354	43	[	[	X
ejpam-4776	354	44	23	23	NUM
ejpam-4776	354	45	]	]	PUNCT
ejpam-4776	354	46	.	.	PUNCT
ejpam-4776	355	1	(	(	PUNCT
ejpam-4776	355	2	x	x	X
ejpam-4776	355	3	,	,	PUNCT
ejpam-4776	355	4	ep	ep	PROPN
ejpam-4776	355	5	)	)	PUNCT
ejpam-4776	355	6	is	be	AUX
ejpam-4776	355	7	not	not	PART
ejpam-4776	355	8	almost	almost	ADV
ejpam-4776	355	9	regular	regular	ADJ
ejpam-4776	355	10	[	[	X
ejpam-4776	355	11	24	24	NUM
ejpam-4776	355	12	]	]	PUNCT
ejpam-4776	355	13	.	.	PUNCT
ejpam-4776	356	1	hence	hence	ADV
ejpam-4776	356	2	,	,	PUNCT
ejpam-4776	356	3	it	it	PRON
ejpam-4776	356	4	is	be	AUX
ejpam-4776	356	5	not	not	PART
ejpam-4776	356	6	almost	almost	ADV
ejpam-4776	356	7	completely	completely	ADV
ejpam-4776	356	8	regular	regular	ADJ
ejpam-4776	356	9	.	.	PUNCT
ejpam-4776	357	1	since	since	SCONJ
ejpam-4776	357	2	x	x	PRON
ejpam-4776	357	3	is	be	AUX
ejpam-4776	357	4	a	a	DET
ejpam-4776	357	5	countably	countably	ADV
ejpam-4776	357	6	compact	compact	ADJ
ejpam-4776	357	7	space	space	NOUN
ejpam-4776	357	8	which	which	PRON
ejpam-4776	357	9	is	be	AUX
ejpam-4776	357	10	not	not	PART
ejpam-4776	357	11	almost	almost	ADV
ejpam-4776	357	12	regular	regular	ADJ
ejpam-4776	357	13	,	,	PUNCT
ejpam-4776	357	14	by	by	ADP
ejpam-4776	357	15	corollary	corollary	ADJ
ejpam-4776	357	16	3	3	NUM
ejpam-4776	357	17	,	,	PUNCT
ejpam-4776	357	18	we	we	PRON
ejpam-4776	357	19	obtain	obtain	VERB
ejpam-4776	357	20	:	:	PUNCT
ejpam-4776	357	21	x	x	X
ejpam-4776	357	22	is	be	AUX
ejpam-4776	357	23	neither	neither	PRON
ejpam-4776	357	24	cc	cc	NOUN
ejpam-4776	357	25	-	-	ADJ
ejpam-4776	357	26	almost	almost	ADV
ejpam-4776	357	27	regular	regular	ADJ
ejpam-4776	357	28	,	,	PUNCT
ejpam-4776	357	29	cc	cc	NOUN
ejpam-4776	357	30	-	-	ADJ
ejpam-4776	357	31	regular	regular	ADJ
ejpam-4776	357	32	,	,	PUNCT
ejpam-4776	357	33	cc	cc	NOUN
ejpam-4776	357	34	-	-	ADJ
ejpam-4776	357	35	completely	completely	ADV
ejpam-4776	357	36	regular	regular	ADJ
ejpam-4776	357	37	,	,	PUNCT
ejpam-4776	357	38	cc	cc	NOUN
ejpam-4776	357	39	-	-	ADJ
ejpam-4776	357	40	almost	almost	ADV
ejpam-4776	357	41	completely	completely	ADV
ejpam-4776	357	42	regular	regular	ADJ
ejpam-4776	357	43	,	,	PUNCT
ejpam-4776	357	44	cct3	cct3	NOUN
ejpam-4776	357	45	nor	nor	CCONJ
ejpam-4776	357	46	cc	cc	NOUN
ejpam-4776	357	47	-	-	NOUN
ejpam-4776	357	48	tychonoff	tychonoff	NOUN
ejpam-4776	357	49	.	.	PUNCT
ejpam-4776	358	1	since	since	SCONJ
ejpam-4776	358	2	x	x	PRON
ejpam-4776	358	3	is	be	AUX
ejpam-4776	358	4	a	a	DET
ejpam-4776	358	5	normal	normal	ADJ
ejpam-4776	358	6	space	space	NOUN
ejpam-4776	358	7	,	,	PUNCT
ejpam-4776	358	8	it	it	PRON
ejpam-4776	358	9	is	be	AUX
ejpam-4776	358	10	cc	cc	VERB
ejpam-4776	358	11	-	-	ADJ
ejpam-4776	358	12	normal	normal	ADJ
ejpam-4776	358	13	.	.	PUNCT
ejpam-4776	359	1	since	since	SCONJ
ejpam-4776	359	2	x	x	PRON
ejpam-4776	359	3	is	be	AUX
ejpam-4776	359	4	not	not	PART
ejpam-4776	359	5	t1	t1	ADJ
ejpam-4776	359	6	,	,	PUNCT
ejpam-4776	359	7	we	we	PRON
ejpam-4776	359	8	obtain	obtain	VERB
ejpam-4776	359	9	:	:	PUNCT
ejpam-4776	359	10	x	x	X
ejpam-4776	359	11	is	be	AUX
ejpam-4776	359	12	neither	neither	DET
ejpam-4776	359	13	epi	epi	NOUN
ejpam-4776	359	14	-	-	ADJ
ejpam-4776	359	15	regular	regular	ADJ
ejpam-4776	359	16	nor	nor	CCONJ
ejpam-4776	359	17	epi	epi	NOUN
ejpam-4776	359	18	-	-	ADJ
ejpam-4776	359	19	mildly	mildly	ADV
ejpam-4776	359	20	normal	normal	ADJ
ejpam-4776	359	21	.	.	PUNCT
ejpam-4776	360	1	therefore	therefore	ADV
ejpam-4776	360	2	,	,	PUNCT
ejpam-4776	360	3	the	the	DET
ejpam-4776	360	4	space	space	NOUN
ejpam-4776	360	5	(	(	PUNCT
ejpam-4776	360	6	x	x	X
ejpam-4776	360	7	,	,	PUNCT
ejpam-4776	360	8	ep	ep	PROPN
ejpam-4776	360	9	)	)	PUNCT
ejpam-4776	360	10	is	be	AUX
ejpam-4776	360	11	a	a	DET
ejpam-4776	360	12	cc	cc	NOUN
ejpam-4776	360	13	-	-	ADJ
ejpam-4776	360	14	normal	normal	ADJ
ejpam-4776	360	15	space	space	NOUN
ejpam-4776	360	16	,	,	PUNCT
ejpam-4776	360	17	which	which	PRON
ejpam-4776	360	18	is	be	AUX
ejpam-4776	360	19	neither	neither	DET
ejpam-4776	360	20	cc	cc	NOUN
ejpam-4776	360	21	-	-	ADJ
ejpam-4776	360	22	almost	almost	ADV
ejpam-4776	360	23	regular	regular	ADJ
ejpam-4776	360	24	,	,	PUNCT
ejpam-4776	360	25	cc	cc	NOUN
ejpam-4776	360	26	-	-	ADJ
ejpam-4776	360	27	regular	regular	ADJ
ejpam-4776	360	28	,	,	PUNCT
ejpam-4776	360	29	cc	cc	NOUN
ejpam-4776	360	30	-	-	NOUN
ejpam-4776	360	31	tychonoff	tychonoff	NOUN
ejpam-4776	360	32	nor	nor	CCONJ
ejpam-4776	360	33	cct3	cct3	PROPN
ejpam-4776	360	34	.	.	PUNCT
ejpam-4776	361	1	s.	s.	PROPN
ejpam-4776	361	2	a.	a.	PROPN
ejpam-4776	361	3	thabit	thabit	PROPN
ejpam-4776	361	4	,	,	PUNCT
ejpam-4776	361	5	w.	w.	PROPN
ejpam-4776	361	6	alqurashi	alqurashi	PROPN
ejpam-4776	361	7	/	/	SYM
ejpam-4776	361	8	eur	eur	PROPN
ejpam-4776	361	9	.	.	PUNCT
ejpam-4776	362	1	j.	j.	PROPN
ejpam-4776	362	2	pure	pure	PROPN
ejpam-4776	362	3	appl	appl	PROPN
ejpam-4776	362	4	.	.	PROPN
ejpam-4776	362	5	math	math	PROPN
ejpam-4776	362	6	,	,	PUNCT
ejpam-4776	362	7	16	16	NUM
ejpam-4776	362	8	(	(	PUNCT
ejpam-4776	362	9	2	2	NUM
ejpam-4776	362	10	)	)	PUNCT
ejpam-4776	362	11	(	(	PUNCT
ejpam-4776	362	12	2023	2023	NUM
ejpam-4776	362	13	)	)	PUNCT
ejpam-4776	362	14	,	,	PUNCT
ejpam-4776	362	15	1260	1260	NUM
ejpam-4776	362	16	-	-	SYM
ejpam-4776	362	17	1273	1273	NUM
ejpam-4776	362	18	1271	1271	NUM
ejpam-4776	362	19	here	here	ADV
ejpam-4776	362	20	is	be	AUX
ejpam-4776	362	21	another	another	DET
ejpam-4776	362	22	example	example	NOUN
ejpam-4776	362	23	of	of	ADP
ejpam-4776	362	24	a	a	DET
ejpam-4776	362	25	cc	cc	NOUN
ejpam-4776	362	26	-	-	PUNCT
ejpam-4776	362	27	tychonoff	tychonoff	NOUN
ejpam-4776	362	28	space	space	NOUN
ejpam-4776	362	29	,	,	PUNCT
ejpam-4776	362	30	which	which	PRON
ejpam-4776	362	31	is	be	AUX
ejpam-4776	362	32	not	not	PART
ejpam-4776	362	33	sub	sub	ADJ
ejpam-4776	362	34	-	-	ADJ
ejpam-4776	362	35	metrizable	metrizable	ADJ
ejpam-4776	362	36	.	.	PUNCT
ejpam-4776	362	37	example	example	NOUN
ejpam-4776	363	1	11	11	NUM
ejpam-4776	363	2	.	.	PUNCT
ejpam-4776	364	1	the	the	DET
ejpam-4776	364	2	deleted	delete	VERB
ejpam-4776	364	3	tychonoff	tychonoff	NOUN
ejpam-4776	364	4	plank	plank	NOUN
ejpam-4776	364	5	:	:	PUNCT
ejpam-4776	365	1	[	[	X
ejpam-4776	365	2	23	23	NUM
ejpam-4776	365	3	,	,	PUNCT
ejpam-4776	365	4	example	example	NOUN
ejpam-4776	365	5	87	87	NUM
ejpam-4776	365	6	]	]	PUNCT
ejpam-4776	365	7	,	,	PUNCT
ejpam-4776	365	8	is	be	AUX
ejpam-4776	365	9	a	a	DET
ejpam-4776	365	10	hausdorff	hausdorff	NOUN
ejpam-4776	365	11	and	and	CCONJ
ejpam-4776	365	12	locally	locally	ADV
ejpam-4776	365	13	compact	compact	ADJ
ejpam-4776	365	14	space	space	NOUN
ejpam-4776	366	1	[	[	X
ejpam-4776	366	2	23	23	NUM
ejpam-4776	366	3	]	]	PUNCT
ejpam-4776	366	4	.	.	PUNCT
ejpam-4776	367	1	by	by	ADP
ejpam-4776	367	2	corollary	corollary	ADJ
ejpam-4776	367	3	4	4	NUM
ejpam-4776	367	4	,	,	PUNCT
ejpam-4776	367	5	the	the	DET
ejpam-4776	367	6	deleted	delete	VERB
ejpam-4776	367	7	tychonoff	tychonoff	NOUN
ejpam-4776	367	8	plank	plank	NOUN
ejpam-4776	367	9	is	be	AUX
ejpam-4776	367	10	a	a	DET
ejpam-4776	367	11	cc	cc	NOUN
ejpam-4776	367	12	-	-	NOUN
ejpam-4776	367	13	tychonoff	tychonoff	NOUN
ejpam-4776	367	14	,	,	PUNCT
ejpam-4776	367	15	cct3	cct3	PROPN
ejpam-4776	367	16	,	,	PUNCT
ejpam-4776	367	17	cc	cc	NOUN
ejpam-4776	367	18	-	-	ADJ
ejpam-4776	367	19	completely	completely	ADV
ejpam-4776	367	20	regular	regular	ADJ
ejpam-4776	367	21	and	and	CCONJ
ejpam-4776	367	22	cc	cc	NOUN
ejpam-4776	367	23	-	-	ADJ
ejpam-4776	367	24	regular	regular	ADJ
ejpam-4776	367	25	space	space	NOUN
ejpam-4776	367	26	.	.	PUNCT
ejpam-4776	368	1	hence	hence	ADV
ejpam-4776	368	2	,	,	PUNCT
ejpam-4776	368	3	it	it	PRON
ejpam-4776	368	4	is	be	AUX
ejpam-4776	368	5	cc	cc	VERB
ejpam-4776	368	6	-	-	ADJ
ejpam-4776	368	7	almost	almost	ADV
ejpam-4776	368	8	completely	completely	ADV
ejpam-4776	368	9	regular	regular	ADJ
ejpam-4776	368	10	and	and	CCONJ
ejpam-4776	368	11	cc	cc	NOUN
ejpam-4776	368	12	-	-	ADJ
ejpam-4776	368	13	almost	almost	ADV
ejpam-4776	368	14	regular	regular	ADJ
ejpam-4776	368	15	.	.	PUNCT
ejpam-4776	369	1	the	the	DET
ejpam-4776	369	2	deleted	delete	VERB
ejpam-4776	369	3	tychonoff	tychonoff	NOUN
ejpam-4776	369	4	plank	plank	NOUN
ejpam-4776	369	5	is	be	AUX
ejpam-4776	369	6	also	also	ADV
ejpam-4776	369	7	neither	neither	CCONJ
ejpam-4776	369	8	almost	almost	ADV
ejpam-4776	369	9	-	-	PUNCT
ejpam-4776	369	10	normal	normal	ADJ
ejpam-4776	369	11	nor	nor	CCONJ
ejpam-4776	369	12	sub	sub	ADJ
ejpam-4776	369	13	-	-	ADJ
ejpam-4776	369	14	metrizable	metrizable	ADJ
ejpam-4776	369	15	[	[	X
ejpam-4776	369	16	5	5	NUM
ejpam-4776	369	17	,	,	PUNCT
ejpam-4776	369	18	7	7	NUM
ejpam-4776	369	19	]	]	PUNCT
ejpam-4776	369	20	.	.	PUNCT
ejpam-4776	370	1	any	any	DET
ejpam-4776	370	2	cc	cc	NOUN
ejpam-4776	370	3	-	-	ADJ
ejpam-4776	370	4	completely	completely	ADV
ejpam-4776	370	5	regular	regular	ADJ
ejpam-4776	370	6	(	(	PUNCT
ejpam-4776	370	7	resp	resp	NOUN
ejpam-4776	370	8	.	.	PUNCT
ejpam-4776	371	1	cc	cc	NOUN
ejpam-4776	371	2	-	-	ADJ
ejpam-4776	371	3	regular	regular	ADJ
ejpam-4776	371	4	,	,	PUNCT
ejpam-4776	371	5	cct3	cct3	PROPN
ejpam-4776	371	6	,	,	PUNCT
ejpam-4776	371	7	cc	cc	NOUN
ejpam-4776	371	8	-	-	NOUN
ejpam-4776	371	9	tychonoff	tychonoff	NOUN
ejpam-4776	371	10	)	)	PUNCT
ejpam-4776	371	11	space	space	NOUN
ejpam-4776	371	12	is	be	AUX
ejpam-4776	371	13	not	not	PART
ejpam-4776	371	14	necessarily	necessarily	ADV
ejpam-4776	371	15	locally	locally	ADV
ejpam-4776	371	16	compact	compact	ADJ
ejpam-4776	371	17	nor	nor	CCONJ
ejpam-4776	371	18	cc	cc	NOUN
ejpam-4776	371	19	-	-	ADJ
ejpam-4776	371	20	normal	normal	ADJ
ejpam-4776	371	21	as	as	SCONJ
ejpam-4776	371	22	shown	show	VERB
ejpam-4776	371	23	by	by	ADP
ejpam-4776	371	24	the	the	DET
ejpam-4776	371	25	next	next	ADJ
ejpam-4776	371	26	example	example	NOUN
ejpam-4776	371	27	:	:	PUNCT
ejpam-4776	371	28	example	example	NOUN
ejpam-4776	371	29	12	12	NUM
ejpam-4776	371	30	.	.	PUNCT
ejpam-4776	372	1	consider	consider	VERB
ejpam-4776	372	2	the	the	DET
ejpam-4776	372	3	example	example	NOUN
ejpam-4776	372	4	10	10	NUM
ejpam-4776	372	5	in	in	ADP
ejpam-4776	372	6	[	[	X
ejpam-4776	372	7	18	18	NUM
ejpam-4776	372	8	]	]	PUNCT
ejpam-4776	372	9	,	,	PUNCT
ejpam-4776	372	10	let	let	VERB
ejpam-4776	372	11	g	g	NOUN
ejpam-4776	372	12	=	=	PUNCT
ejpam-4776	372	13	dω1	dω1	NOUN
ejpam-4776	372	14	,	,	PUNCT
ejpam-4776	372	15	where	where	SCONJ
ejpam-4776	372	16	d	d	NOUN
ejpam-4776	372	17	=	=	SYM
ejpam-4776	372	18	{	{	PUNCT
ejpam-4776	372	19	0	0	NUM
ejpam-4776	372	20	,	,	PUNCT
ejpam-4776	372	21	1	1	NUM
ejpam-4776	372	22	}	}	PUNCT
ejpam-4776	372	23	with	with	ADP
ejpam-4776	372	24	the	the	DET
ejpam-4776	372	25	discrete	discrete	ADJ
ejpam-4776	372	26	topology	topology	NOUN
ejpam-4776	372	27	.	.	PUNCT
ejpam-4776	373	1	let	let	VERB
ejpam-4776	373	2	h	h	PRON
ejpam-4776	373	3	be	be	AUX
ejpam-4776	373	4	a	a	DET
ejpam-4776	373	5	subspace	subspace	NOUN
ejpam-4776	373	6	of	of	ADP
ejpam-4776	373	7	g	g	NOUN
ejpam-4776	373	8	consisting	consist	VERB
ejpam-4776	373	9	of	of	ADP
ejpam-4776	373	10	all	all	DET
ejpam-4776	373	11	points	point	NOUN
ejpam-4776	373	12	of	of	ADP
ejpam-4776	373	13	g	g	NOUN
ejpam-4776	373	14	with	with	ADP
ejpam-4776	373	15	at	at	ADP
ejpam-4776	373	16	most	most	ADV
ejpam-4776	373	17	countably	countably	ADV
ejpam-4776	373	18	many	many	ADJ
ejpam-4776	373	19	non	non	ADJ
ejpam-4776	373	20	zero	zero	NUM
ejpam-4776	373	21	coordinates	coordinate	NOUN
ejpam-4776	373	22	.	.	PUNCT
ejpam-4776	374	1	put	put	VERB
ejpam-4776	374	2	x	x	PUNCT
ejpam-4776	374	3	=	=	PRON
ejpam-4776	374	4	g	g	PROPN
ejpam-4776	374	5	×	×	PROPN
ejpam-4776	374	6	h.	h.	PROPN
ejpam-4776	374	7	raushan	raushan	PROPN
ejpam-4776	374	8	buzyakova	buzyakova	PROPN
ejpam-4776	374	9	proved	prove	VERB
ejpam-4776	374	10	that	that	SCONJ
ejpam-4776	374	11	x	x	PRON
ejpam-4776	374	12	can	can	AUX
ejpam-4776	374	13	not	not	PART
ejpam-4776	374	14	be	be	AUX
ejpam-4776	374	15	mapped	map	VERB
ejpam-4776	374	16	onto	onto	ADP
ejpam-4776	374	17	a	a	DET
ejpam-4776	374	18	normal	normal	ADJ
ejpam-4776	374	19	space	space	NOUN
ejpam-4776	374	20	y	y	NOUN
ejpam-4776	374	21	by	by	ADP
ejpam-4776	374	22	a	a	DET
ejpam-4776	374	23	bijective	bijective	ADJ
ejpam-4776	374	24	continuous	continuous	ADJ
ejpam-4776	374	25	function	function	NOUN
ejpam-4776	375	1	[	[	X
ejpam-4776	375	2	8	8	NUM
ejpam-4776	375	3	]	]	PUNCT
ejpam-4776	375	4	.	.	PUNCT
ejpam-4776	376	1	observe	observe	VERB
ejpam-4776	376	2	that	that	SCONJ
ejpam-4776	376	3	:	:	PUNCT
ejpam-4776	376	4	h	h	NOUN
ejpam-4776	376	5	is	be	AUX
ejpam-4776	376	6	t2	t2	NOUN
ejpam-4776	376	7	-	-	PUNCT
ejpam-4776	376	8	fréchet	fréchet	NOUN
ejpam-4776	376	9	and	and	CCONJ
ejpam-4776	376	10	hence	hence	ADV
ejpam-4776	376	11	h	h	NOUN
ejpam-4776	376	12	is	be	AUX
ejpam-4776	376	13	a	a	DET
ejpam-4776	376	14	k	k	NOUN
ejpam-4776	376	15	-	-	NOUN
ejpam-4776	376	16	space	space	NOUN
ejpam-4776	376	17	.	.	PUNCT
ejpam-4776	377	1	the	the	DET
ejpam-4776	377	2	space	space	NOUN
ejpam-4776	377	3	g	g	NOUN
ejpam-4776	377	4	is	be	AUX
ejpam-4776	377	5	also	also	ADV
ejpam-4776	377	6	a	a	DET
ejpam-4776	377	7	t2	t2	NOUN
ejpam-4776	377	8	-	-	PUNCT
ejpam-4776	377	9	compact	compact	ADJ
ejpam-4776	377	10	space	space	NOUN
ejpam-4776	377	11	.	.	PUNCT
ejpam-4776	378	1	hence	hence	ADV
ejpam-4776	378	2	,	,	PUNCT
ejpam-4776	378	3	x	x	PUNCT
ejpam-4776	378	4	=	=	SYM
ejpam-4776	378	5	g×h	g×h	PROPN
ejpam-4776	378	6	is	be	AUX
ejpam-4776	378	7	a	a	DET
ejpam-4776	378	8	k	k	NOUN
ejpam-4776	378	9	-	-	NOUN
ejpam-4776	378	10	space	space	NOUN
ejpam-4776	378	11	[	[	X
ejpam-4776	378	12	18	18	NUM
ejpam-4776	378	13	]	]	PUNCT
ejpam-4776	378	14	.	.	PUNCT
ejpam-4776	379	1	since	since	SCONJ
ejpam-4776	379	2	x	x	PRON
ejpam-4776	379	3	is	be	AUX
ejpam-4776	379	4	tychonoff	tychonoff	NOUN
ejpam-4776	379	5	,	,	PUNCT
ejpam-4776	379	6	we	we	PRON
ejpam-4776	379	7	get	get	VERB
ejpam-4776	379	8	x	x	PROPN
ejpam-4776	379	9	is	be	AUX
ejpam-4776	379	10	cc	cc	NOUN
ejpam-4776	379	11	-	-	NOUN
ejpam-4776	379	12	tychonoff	tychonoff	NOUN
ejpam-4776	379	13	.	.	PUNCT
ejpam-4776	380	1	hence	hence	ADV
ejpam-4776	380	2	,	,	PUNCT
ejpam-4776	380	3	it	it	PRON
ejpam-4776	380	4	is	be	AUX
ejpam-4776	380	5	a	a	DET
ejpam-4776	380	6	cc	cc	NOUN
ejpam-4776	380	7	-	-	ADJ
ejpam-4776	380	8	completely	completely	ADV
ejpam-4776	380	9	regular	regular	ADJ
ejpam-4776	380	10	,	,	PUNCT
ejpam-4776	380	11	cct3	cct3	PROPN
ejpam-4776	380	12	,	,	PUNCT
ejpam-4776	380	13	cc	cc	NOUN
ejpam-4776	380	14	-	-	ADJ
ejpam-4776	380	15	regular	regular	ADJ
ejpam-4776	380	16	and	and	CCONJ
ejpam-4776	380	17	cc	cc	NOUN
ejpam-4776	380	18	-	-	PUNCT
ejpam-4776	380	19	almost	almost	ADV
ejpam-4776	380	20	completely	completely	ADV
ejpam-4776	380	21	regular	regular	ADJ
ejpam-4776	380	22	space	space	NOUN
ejpam-4776	380	23	,	,	PUNCT
ejpam-4776	380	24	which	which	PRON
ejpam-4776	380	25	is	be	AUX
ejpam-4776	380	26	not	not	PART
ejpam-4776	380	27	c	c	NOUN
ejpam-4776	380	28	-	-	ADJ
ejpam-4776	380	29	normal	normal	ADJ
ejpam-4776	380	30	[	[	X
ejpam-4776	380	31	18	18	NUM
ejpam-4776	380	32	]	]	PUNCT
ejpam-4776	380	33	.	.	PUNCT
ejpam-4776	381	1	since	since	SCONJ
ejpam-4776	381	2	x	x	PRON
ejpam-4776	381	3	is	be	AUX
ejpam-4776	381	4	not	not	PART
ejpam-4776	381	5	c	c	NOUN
ejpam-4776	381	6	-	-	ADJ
ejpam-4776	381	7	normal	normal	ADJ
ejpam-4776	381	8	,	,	PUNCT
ejpam-4776	381	9	we	we	PRON
ejpam-4776	381	10	obtain	obtain	VERB
ejpam-4776	381	11	x	x	SYM
ejpam-4776	381	12	is	be	AUX
ejpam-4776	381	13	neither	neither	DET
ejpam-4776	381	14	cc	cc	NOUN
ejpam-4776	381	15	-	-	ADJ
ejpam-4776	381	16	normal	normal	ADJ
ejpam-4776	381	17	,	,	PUNCT
ejpam-4776	381	18	sub	sub	ADJ
ejpam-4776	381	19	-	-	ADJ
ejpam-4776	381	20	metrizable	metrizable	ADJ
ejpam-4776	381	21	,	,	PUNCT
ejpam-4776	381	22	c2	c2	PROPN
ejpam-4776	381	23	-	-	PUNCT
ejpam-4776	381	24	paracompact	paracompact	PROPN
ejpam-4776	381	25	nor	nor	CCONJ
ejpam-4776	381	26	epi	epi	NOUN
ejpam-4776	381	27	-	-	ADJ
ejpam-4776	381	28	normal	normal	ADJ
ejpam-4776	381	29	.	.	PUNCT
ejpam-4776	382	1	note	note	VERB
ejpam-4776	382	2	that	that	SCONJ
ejpam-4776	382	3	:	:	PUNCT
ejpam-4776	382	4	every	every	DET
ejpam-4776	382	5	c2	c2	PROPN
ejpam-4776	382	6	-	-	PUNCT
ejpam-4776	382	7	paracompact	paracompact	NOUN
ejpam-4776	382	8	space	space	NOUN
ejpam-4776	382	9	is	be	AUX
ejpam-4776	382	10	c	c	NOUN
ejpam-4776	382	11	-	-	ADJ
ejpam-4776	382	12	normal	normal	ADJ
ejpam-4776	382	13	[	[	X
ejpam-4776	382	14	19	19	NUM
ejpam-4776	382	15	]	]	PUNCT
ejpam-4776	382	16	.	.	PUNCT
ejpam-4776	383	1	the	the	DET
ejpam-4776	383	2	space	space	NOUN
ejpam-4776	383	3	x	x	PUNCT
ejpam-4776	383	4	is	be	AUX
ejpam-4776	383	5	also	also	ADV
ejpam-4776	383	6	not	not	PART
ejpam-4776	383	7	locally	locally	ADV
ejpam-4776	383	8	compact	compact	ADJ
ejpam-4776	383	9	.	.	PUNCT
ejpam-4776	384	1	thus	thus	ADV
ejpam-4776	384	2	,	,	PUNCT
ejpam-4776	384	3	the	the	DET
ejpam-4776	384	4	space	space	NOUN
ejpam-4776	384	5	x	x	PUNCT
ejpam-4776	384	6	is	be	AUX
ejpam-4776	384	7	a	a	DET
ejpam-4776	384	8	cct3	cct3	PROPN
ejpam-4776	384	9	,	,	PUNCT
ejpam-4776	384	10	cc	cc	NOUN
ejpam-4776	384	11	-	-	ADJ
ejpam-4776	384	12	regular	regular	ADJ
ejpam-4776	384	13	,	,	PUNCT
ejpam-4776	384	14	cc	cc	NOUN
ejpam-4776	384	15	-	-	ADJ
ejpam-4776	384	16	completely	completely	ADV
ejpam-4776	384	17	regular	regular	ADJ
ejpam-4776	384	18	and	and	CCONJ
ejpam-4776	384	19	cc	cc	NOUN
ejpam-4776	384	20	-	-	NOUN
ejpam-4776	384	21	tychonoff	tychonoff	NOUN
ejpam-4776	384	22	space	space	NOUN
ejpam-4776	384	23	,	,	PUNCT
ejpam-4776	384	24	which	which	PRON
ejpam-4776	384	25	is	be	AUX
ejpam-4776	384	26	neither	neither	DET
ejpam-4776	384	27	cc	cc	NOUN
ejpam-4776	384	28	-	-	ADJ
ejpam-4776	384	29	normal	normal	ADJ
ejpam-4776	384	30	,	,	PUNCT
ejpam-4776	384	31	c2	c2	PROPN
ejpam-4776	384	32	-	-	PUNCT
ejpam-4776	384	33	paracompact	paracompact	ADJ
ejpam-4776	384	34	,	,	PUNCT
ejpam-4776	384	35	epi	epi	NOUN
ejpam-4776	384	36	-	-	ADJ
ejpam-4776	384	37	normal	normal	ADJ
ejpam-4776	384	38	,	,	PUNCT
ejpam-4776	384	39	sub	sub	ADJ
ejpam-4776	384	40	-	-	ADJ
ejpam-4776	384	41	metrizable	metrizable	ADJ
ejpam-4776	384	42	nor	nor	CCONJ
ejpam-4776	384	43	locally	locally	ADV
ejpam-4776	384	44	compact	compact	ADJ
ejpam-4776	384	45	.	.	PUNCT
ejpam-4776	385	1	since	since	SCONJ
ejpam-4776	385	2	every	every	DET
ejpam-4776	385	3	hausdorff	hausdorff	NOUN
ejpam-4776	385	4	paracompact	paracompact	NOUN
ejpam-4776	385	5	space	space	NOUN
ejpam-4776	385	6	is	be	AUX
ejpam-4776	385	7	t4	t4	PROPN
ejpam-4776	385	8	,	,	PUNCT
ejpam-4776	385	9	the	the	DET
ejpam-4776	385	10	proof	proof	NOUN
ejpam-4776	385	11	of	of	ADP
ejpam-4776	385	12	the	the	DET
ejpam-4776	385	13	next	next	ADJ
ejpam-4776	385	14	result	result	NOUN
ejpam-4776	385	15	is	be	AUX
ejpam-4776	385	16	similar	similar	ADJ
ejpam-4776	385	17	to	to	ADP
ejpam-4776	385	18	that	that	PRON
ejpam-4776	385	19	of	of	ADP
ejpam-4776	385	20	theorem	theorem	ADJ
ejpam-4776	385	21	9	9	NUM
ejpam-4776	385	22	:	:	PUNCT
ejpam-4776	385	23	theorem	theorem	NOUN
ejpam-4776	385	24	20	20	NUM
ejpam-4776	385	25	.	.	PUNCT
ejpam-4776	386	1	every	every	DET
ejpam-4776	386	2	c2	c2	PROPN
ejpam-4776	386	3	-	-	PUNCT
ejpam-4776	386	4	paracompact	paracompact	ADJ
ejpam-4776	386	5	first	first	ADJ
ejpam-4776	386	6	countable	countable	ADJ
ejpam-4776	386	7	space	space	NOUN
ejpam-4776	386	8	is	be	AUX
ejpam-4776	386	9	epi	epi	NOUN
ejpam-4776	386	10	-	-	ADJ
ejpam-4776	386	11	normal	normal	ADJ
ejpam-4776	386	12	(	(	PUNCT
ejpam-4776	386	13	hence	hence	ADV
ejpam-4776	386	14	epi	epi	NOUN
ejpam-4776	386	15	-	-	ADJ
ejpam-4776	386	16	completely	completely	ADV
ejpam-4776	386	17	regular	regular	ADJ
ejpam-4776	386	18	)	)	PUNCT
ejpam-4776	386	19	.	.	PUNCT
ejpam-4776	387	1	thus	thus	ADV
ejpam-4776	387	2	,	,	PUNCT
ejpam-4776	387	3	we	we	PRON
ejpam-4776	387	4	obtain	obtain	VERB
ejpam-4776	387	5	the	the	DET
ejpam-4776	387	6	next	next	ADJ
ejpam-4776	387	7	corollary	corollary	NOUN
ejpam-4776	387	8	:	:	PUNCT
ejpam-4776	387	9	corollary	corollary	ADJ
ejpam-4776	387	10	11	11	NUM
ejpam-4776	387	11	.	.	PUNCT
ejpam-4776	388	1	every	every	DET
ejpam-4776	388	2	c2	c2	PROPN
ejpam-4776	388	3	-	-	PUNCT
ejpam-4776	388	4	paracompact	paracompact	ADJ
ejpam-4776	388	5	first	first	ADJ
ejpam-4776	388	6	countable	countable	ADJ
ejpam-4776	388	7	space	space	NOUN
ejpam-4776	388	8	is	be	AUX
ejpam-4776	388	9	cc	cc	NOUN
ejpam-4776	388	10	-	-	NOUN
ejpam-4776	388	11	tychonoff	tychonoff	NOUN
ejpam-4776	388	12	.	.	PUNCT
ejpam-4776	389	1	note	note	VERB
ejpam-4776	389	2	that	that	SCONJ
ejpam-4776	389	3	:	:	PUNCT
ejpam-4776	389	4	the	the	DET
ejpam-4776	389	5	space	space	NOUN
ejpam-4776	389	6	presented	present	VERB
ejpam-4776	389	7	in	in	ADP
ejpam-4776	389	8	example	example	NOUN
ejpam-4776	389	9	2.25	2.25	NUM
ejpam-4776	389	10	in	in	ADP
ejpam-4776	389	11	[	[	X
ejpam-4776	389	12	19	19	NUM
ejpam-4776	389	13	]	]	PUNCT
ejpam-4776	389	14	,	,	PUNCT
ejpam-4776	389	15	is	be	AUX
ejpam-4776	389	16	a	a	DET
ejpam-4776	389	17	c	c	NOUN
ejpam-4776	389	18	-	-	PUNCT
ejpam-4776	389	19	paracompact	paracompact	ADJ
ejpam-4776	389	20	first	first	ADJ
ejpam-4776	389	21	countable	countable	ADJ
ejpam-4776	389	22	space	space	NOUN
ejpam-4776	389	23	which	which	PRON
ejpam-4776	389	24	is	be	AUX
ejpam-4776	389	25	neither	neither	DET
ejpam-4776	389	26	cc	cc	NOUN
ejpam-4776	389	27	-	-	ADJ
ejpam-4776	389	28	regular	regular	ADJ
ejpam-4776	389	29	nor	nor	CCONJ
ejpam-4776	389	30	l	l	NOUN
ejpam-4776	389	31	-	-	PUNCT
ejpam-4776	389	32	almost	almost	ADV
ejpam-4776	389	33	regular	regular	ADJ
ejpam-4776	389	34	because	because	SCONJ
ejpam-4776	389	35	it	it	PRON
ejpam-4776	389	36	is	be	AUX
ejpam-4776	389	37	a	a	DET
ejpam-4776	389	38	lindelöf	lindelöf	NOUN
ejpam-4776	389	39	space	space	NOUN
ejpam-4776	389	40	that	that	PRON
ejpam-4776	389	41	is	be	AUX
ejpam-4776	389	42	neither	neither	CCONJ
ejpam-4776	389	43	almost	almost	ADV
ejpam-4776	389	44	regular	regular	ADJ
ejpam-4776	389	45	nor	nor	CCONJ
ejpam-4776	389	46	c	c	NOUN
ejpam-4776	389	47	-	-	PUNCT
ejpam-4776	389	48	regular	regular	ADJ
ejpam-4776	389	49	.	.	PUNCT
ejpam-4776	390	1	the	the	DET
ejpam-4776	390	2	following	follow	VERB
ejpam-4776	390	3	problems	problem	NOUN
ejpam-4776	390	4	are	be	AUX
ejpam-4776	390	5	still	still	ADV
ejpam-4776	390	6	open	open	ADJ
ejpam-4776	390	7	in	in	ADP
ejpam-4776	390	8	this	this	DET
ejpam-4776	390	9	research	research	NOUN
ejpam-4776	390	10	.	.	PUNCT
ejpam-4776	391	1	problems	problem	NOUN
ejpam-4776	391	2	:	:	PUNCT
ejpam-4776	391	3	(	(	PUNCT
ejpam-4776	391	4	1	1	X
ejpam-4776	391	5	)	)	PUNCT
ejpam-4776	391	6	is	be	AUX
ejpam-4776	391	7	there	there	PRON
ejpam-4776	391	8	an	an	DET
ejpam-4776	391	9	example	example	NOUN
ejpam-4776	391	10	of	of	ADP
ejpam-4776	391	11	a	a	DET
ejpam-4776	391	12	c	c	NOUN
ejpam-4776	391	13	-	-	PUNCT
ejpam-4776	391	14	tychonoff	tychonoff	NOUN
ejpam-4776	391	15	space	space	NOUN
ejpam-4776	391	16	which	which	PRON
ejpam-4776	391	17	is	be	AUX
ejpam-4776	391	18	not	not	PART
ejpam-4776	391	19	cc	cc	VERB
ejpam-4776	391	20	-	-	ADJ
ejpam-4776	391	21	almost	almost	ADV
ejpam-4776	391	22	regular	regular	ADJ
ejpam-4776	391	23	?	?	PUNCT
ejpam-4776	391	24	.	.	PUNCT
ejpam-4776	392	1	(	(	PUNCT
ejpam-4776	392	2	2	2	X
ejpam-4776	392	3	)	)	PUNCT
ejpam-4776	392	4	is	be	AUX
ejpam-4776	392	5	there	there	PRON
ejpam-4776	392	6	an	an	DET
ejpam-4776	392	7	example	example	NOUN
ejpam-4776	392	8	of	of	ADP
ejpam-4776	392	9	a	a	DET
ejpam-4776	392	10	c2	c2	PROPN
ejpam-4776	392	11	-	-	PUNCT
ejpam-4776	392	12	paracompact	paracompact	NOUN
ejpam-4776	392	13	space	space	NOUN
ejpam-4776	392	14	which	which	PRON
ejpam-4776	392	15	is	be	AUX
ejpam-4776	392	16	not	not	PART
ejpam-4776	392	17	cc	cc	NOUN
ejpam-4776	392	18	-	-	NOUN
ejpam-4776	392	19	regular	regular	ADJ
ejpam-4776	392	20	?	?	PUNCT
ejpam-4776	392	21	.	.	PUNCT
ejpam-4776	393	1	(	(	PUNCT
ejpam-4776	393	2	3	3	X
ejpam-4776	393	3	)	)	PUNCT
ejpam-4776	393	4	is	be	AUX
ejpam-4776	393	5	there	there	PRON
ejpam-4776	393	6	an	an	DET
ejpam-4776	393	7	example	example	NOUN
ejpam-4776	393	8	of	of	ADP
ejpam-4776	393	9	an	an	DET
ejpam-4776	393	10	l	l	NOUN
ejpam-4776	393	11	-	-	PUNCT
ejpam-4776	393	12	tychonoff	tychonoff	NOUN
ejpam-4776	393	13	space	space	NOUN
ejpam-4776	393	14	which	which	PRON
ejpam-4776	393	15	is	be	AUX
ejpam-4776	393	16	not	not	PART
ejpam-4776	393	17	cc	cc	NOUN
ejpam-4776	393	18	-	-	NOUN
ejpam-4776	393	19	regular	regular	ADJ
ejpam-4776	393	20	?	?	PUNCT
ejpam-4776	393	21	.	.	PUNCT
ejpam-4776	394	1	(	(	PUNCT
ejpam-4776	394	2	4	4	X
ejpam-4776	394	3	)	)	PUNCT
ejpam-4776	394	4	are	be	AUX
ejpam-4776	394	5	cc	cc	VERB
ejpam-4776	394	6	-	-	ADJ
ejpam-4776	394	7	complete	complete	ADJ
ejpam-4776	394	8	regularity	regularity	NOUN
ejpam-4776	394	9	,	,	PUNCT
ejpam-4776	394	10	cc	cc	NOUN
ejpam-4776	394	11	-	-	NOUN
ejpam-4776	394	12	tychonoffness	tychonoffness	NOUN
ejpam-4776	394	13	,	,	PUNCT
ejpam-4776	394	14	cct3	cct3	PROPN
ejpam-4776	394	15	and	and	CCONJ
ejpam-4776	394	16	cc	cc	NOUN
ejpam-4776	394	17	-	-	PUNCT
ejpam-4776	394	18	regularity	regularity	NOUN
ejpam-4776	394	19	multiplicative	multiplicative	ADJ
ejpam-4776	394	20	properties	property	NOUN
ejpam-4776	394	21	?	?	PUNCT
ejpam-4776	394	22	.	.	PUNCT
ejpam-4776	395	1	references	reference	NOUN
ejpam-4776	395	2	1272	1272	NUM
ejpam-4776	395	3	4	4	NUM
ejpam-4776	395	4	.	.	PUNCT
ejpam-4776	395	5	conclusion	conclusion	VERB
ejpam-4776	395	6	new	new	ADJ
ejpam-4776	395	7	topological	topological	ADJ
ejpam-4776	395	8	properties	property	NOUN
ejpam-4776	395	9	,	,	PUNCT
ejpam-4776	395	10	called	call	VERB
ejpam-4776	395	11	cc	cc	NOUN
ejpam-4776	395	12	-	-	ADJ
ejpam-4776	395	13	complete	complete	ADJ
ejpam-4776	395	14	regularity	regularity	NOUN
ejpam-4776	395	15	,	,	PUNCT
ejpam-4776	395	16	cc	cc	NOUN
ejpam-4776	395	17	-	-	ADJ
ejpam-4776	395	18	almost	almost	ADV
ejpam-4776	395	19	complete	complete	ADJ
ejpam-4776	395	20	regularity	regularity	NOUN
ejpam-4776	395	21	,	,	PUNCT
ejpam-4776	395	22	cc	cc	NOUN
ejpam-4776	395	23	-	-	ADJ
ejpam-4776	395	24	almost	almost	ADV
ejpam-4776	395	25	regularity	regularity	NOUN
ejpam-4776	395	26	,	,	PUNCT
ejpam-4776	395	27	cct3	cct3	PROPN
ejpam-4776	395	28	,	,	PUNCT
ejpam-4776	395	29	cc	cc	NOUN
ejpam-4776	395	30	-	-	NOUN
ejpam-4776	395	31	tychonoffness	tychonoffness	NOUN
ejpam-4776	395	32	and	and	CCONJ
ejpam-4776	395	33	cc	cc	NOUN
ejpam-4776	395	34	-	-	NOUN
ejpam-4776	395	35	regularity	regularity	NOUN
ejpam-4776	395	36	have	have	AUX
ejpam-4776	395	37	been	be	AUX
ejpam-4776	395	38	studied	study	VERB
ejpam-4776	395	39	in	in	ADP
ejpam-4776	395	40	this	this	DET
ejpam-4776	395	41	work	work	NOUN
ejpam-4776	395	42	.	.	PUNCT
ejpam-4776	396	1	some	some	DET
ejpam-4776	396	2	results	result	NOUN
ejpam-4776	396	3	,	,	PUNCT
ejpam-4776	396	4	properties	property	NOUN
ejpam-4776	396	5	,	,	PUNCT
ejpam-4776	396	6	relationships	relationship	NOUN
ejpam-4776	396	7	and	and	CCONJ
ejpam-4776	396	8	counterexamples	counterexample	NOUN
ejpam-4776	396	9	have	have	AUX
ejpam-4776	396	10	been	be	AUX
ejpam-4776	396	11	given	give	VERB
ejpam-4776	396	12	and	and	CCONJ
ejpam-4776	396	13	discussed	discuss	VERB
ejpam-4776	396	14	.	.	PUNCT
ejpam-4776	397	1	acknowledgements	acknowledgement	NOUN
ejpam-4776	397	2	the	the	DET
ejpam-4776	397	3	authors	author	NOUN
ejpam-4776	397	4	would	would	AUX
ejpam-4776	397	5	like	like	VERB
ejpam-4776	397	6	to	to	PART
ejpam-4776	397	7	thank	thank	VERB
ejpam-4776	397	8	the	the	DET
ejpam-4776	397	9	anonymous	anonymous	ADJ
ejpam-4776	397	10	referee	referee	NOUN
ejpam-4776	397	11	for	for	ADP
ejpam-4776	397	12	his	his	PRON
ejpam-4776	397	13	/	/	SYM
ejpam-4776	397	14	her	her	PRON
ejpam-4776	397	15	comments	comment	NOUN
ejpam-4776	397	16	that	that	PRON
ejpam-4776	397	17	will	will	AUX
ejpam-4776	397	18	help	help	VERB
ejpam-4776	397	19	us	we	PRON
ejpam-4776	397	20	improve	improve	VERB
ejpam-4776	397	21	this	this	DET
ejpam-4776	397	22	article	article	NOUN
ejpam-4776	397	23	.	.	PUNCT
ejpam-4776	398	1	references	reference	NOUN
ejpam-4776	398	2	[	[	X
ejpam-4776	398	3	1	1	NUM
ejpam-4776	398	4	]	]	PUNCT
ejpam-4776	398	5	alya’a	alya’a	DET
ejpam-4776	398	6	al	al	PROPN
ejpam-4776	398	7	-	-	PUNCT
ejpam-4776	398	8	awadi	awadi	NOUN
ejpam-4776	398	9	,	,	PUNCT
ejpam-4776	398	10	lutfi	lutfi	PROPN
ejpam-4776	398	11	kalantan	kalantan	PROPN
ejpam-4776	398	12	,	,	PUNCT
ejpam-4776	398	13	and	and	CCONJ
ejpam-4776	398	14	sadeq	sadeq	VERB
ejpam-4776	398	15	thabit	thabit	NOUN
ejpam-4776	398	16	.	.	PUNCT
ejpam-4776	399	1	c	c	X
ejpam-4776	399	2	-	-	PUNCT
ejpam-4776	399	3	κ	κ	NOUN
ejpam-4776	399	4	-	-	ADJ
ejpam-4776	399	5	normal	normal	ADJ
ejpam-4776	399	6	and	and	CCONJ
ejpam-4776	399	7	c	c	NOUN
ejpam-4776	399	8	-	-	PUNCT
ejpam-4776	399	9	mildly	mildly	ADV
ejpam-4776	399	10	normal	normal	ADJ
ejpam-4776	399	11	:	:	PUNCT
ejpam-4776	399	12	topological	topological	ADJ
ejpam-4776	399	13	properties	property	NOUN
ejpam-4776	399	14	.	.	PUNCT
ejpam-4776	400	1	j.	j.	PROPN
ejpam-4776	400	2	adv	adv	PROPN
ejpam-4776	400	3	.	.	PUNCT
ejpam-4776	400	4	math	math	PROPN
ejpam-4776	400	5	.	.	PUNCT
ejpam-4776	401	1	stud	stud	PROPN
ejpam-4776	401	2	.	.	PUNCT
ejpam-4776	401	3	,	,	PUNCT
ejpam-4776	401	4	16(1):15–21	16(1):15–21	NUM
ejpam-4776	401	5	,	,	PUNCT
ejpam-4776	401	6	2023	2023	NUM
ejpam-4776	401	7	.	.	PUNCT
ejpam-4776	402	1	[	[	X
ejpam-4776	402	2	2	2	X
ejpam-4776	402	3	]	]	PUNCT
ejpam-4776	402	4	ohud	ohud	ADJ
ejpam-4776	402	5	alghamdi	alghamdi	NOUN
ejpam-4776	402	6	,	,	PUNCT
ejpam-4776	402	7	sadeq	sadeq	PROPN
ejpam-4776	402	8	ali	ali	PROPN
ejpam-4776	402	9	thabit	thabit	NOUN
ejpam-4776	402	10	,	,	PUNCT
ejpam-4776	402	11	and	and	CCONJ
ejpam-4776	402	12	lutfi	lutfi	PROPN
ejpam-4776	402	13	kalantan	kalantan	PROPN
ejpam-4776	402	14	.	.	PUNCT
ejpam-4776	403	1	l	l	NOUN
ejpam-4776	403	2	-	-	PUNCT
ejpam-4776	403	3	completely	completely	ADV
ejpam-4776	403	4	regular	regular	ADJ
ejpam-4776	403	5	,	,	PUNCT
ejpam-4776	403	6	lt3	lt3	PROPN
ejpam-4776	403	7	and	and	CCONJ
ejpam-4776	403	8	l2	l2	NOUN
ejpam-4776	403	9	-	-	PUNCT
ejpam-4776	403	10	almost	almost	ADV
ejpam-4776	403	11	regular	regular	ADJ
ejpam-4776	403	12	spaces	space	NOUN
ejpam-4776	403	13	.	.	PUNCT
ejpam-4776	404	1	preprint	preprint	NOUN
ejpam-4776	404	2	,	,	PUNCT
ejpam-4776	404	3	2023	2023	NUM
ejpam-4776	404	4	.	.	PUNCT
ejpam-4776	405	1	[	[	X
ejpam-4776	405	2	3	3	NUM
ejpam-4776	405	3	]	]	X
ejpam-4776	405	4	wafa	wafa	PROPN
ejpam-4776	405	5	khalaf	khalaf	PROPN
ejpam-4776	405	6	alqurashi	alqurashi	PROPN
ejpam-4776	405	7	and	and	CCONJ
ejpam-4776	405	8	sadeq	sadeq	VERB
ejpam-4776	405	9	ali	ali	PROPN
ejpam-4776	405	10	thabit	thabit	PROPN
ejpam-4776	405	11	.	.	PUNCT
ejpam-4776	406	1	c	c	X
ejpam-4776	406	2	-	-	PUNCT
ejpam-4776	406	3	almost	almost	ADV
ejpam-4776	406	4	normality	normality	NOUN
ejpam-4776	406	5	and	and	CCONJ
ejpam-4776	406	6	l	l	NOUN
ejpam-4776	406	7	-	-	ADJ
ejpam-4776	406	8	almost	almost	ADV
ejpam-4776	406	9	normality	normality	NOUN
ejpam-4776	406	10	.	.	PUNCT
ejpam-4776	407	1	european	european	ADJ
ejpam-4776	407	2	journal	journal	PROPN
ejpam-4776	407	3	of	of	ADP
ejpam-4776	407	4	pure	pure	ADJ
ejpam-4776	407	5	and	and	CCONJ
ejpam-4776	407	6	applied	applied	ADJ
ejpam-4776	407	7	mathematics	mathematic	NOUN
ejpam-4776	407	8	(	(	PUNCT
ejpam-4776	407	9	ejpam	ejpam	PROPN
ejpam-4776	407	10	)	)	PUNCT
ejpam-4776	407	11	,	,	PUNCT
ejpam-4776	407	12	15(4):1760–1782	15(4):1760–1782	NUM
ejpam-4776	407	13	,	,	PUNCT
ejpam-4776	407	14	2022	2022	NUM
ejpam-4776	407	15	.	.	PUNCT
ejpam-4776	408	1	[	[	X
ejpam-4776	408	2	4	4	NUM
ejpam-4776	408	3	]	]	X
ejpam-4776	408	4	ibtesam	ibtesam	PROPN
ejpam-4776	408	5	alshammari	alshammari	PROPN
ejpam-4776	408	6	.	.	PUNCT
ejpam-4776	409	1	epi	epi	NOUN
ejpam-4776	409	2	-	-	PUNCT
ejpam-4776	409	3	completely	completely	ADV
ejpam-4776	409	4	regular	regular	ADJ
ejpam-4776	409	5	topological	topological	ADJ
ejpam-4776	409	6	spaces	space	NOUN
ejpam-4776	409	7	.	.	PUNCT
ejpam-4776	410	1	european	european	ADJ
ejpam-4776	410	2	journal	journal	PROPN
ejpam-4776	410	3	of	of	ADP
ejpam-4776	410	4	pure	pure	ADJ
ejpam-4776	410	5	and	and	CCONJ
ejpam-4776	410	6	applied	applied	ADJ
ejpam-4776	410	7	mathematics	mathematic	NOUN
ejpam-4776	410	8	(	(	PUNCT
ejpam-4776	410	9	ejpam	ejpam	PROPN
ejpam-4776	410	10	)	)	PUNCT
ejpam-4776	410	11	,	,	PUNCT
ejpam-4776	410	12	15(4):1808–1821	15(4):1808–1821	NUM
ejpam-4776	410	13	,	,	PUNCT
ejpam-4776	410	14	2022	2022	NUM
ejpam-4776	410	15	.	.	PUNCT
ejpam-4776	411	1	[	[	X
ejpam-4776	411	2	5	5	NUM
ejpam-4776	411	3	]	]	PUNCT
ejpam-4776	411	4	samirah	samirah	PROPN
ejpam-4776	411	5	alzahrani	alzahrani	PROPN
ejpam-4776	411	6	.	.	PUNCT
ejpam-4776	412	1	c	c	X
ejpam-4776	412	2	-	-	PUNCT
ejpam-4776	412	3	regular	regular	ADJ
ejpam-4776	412	4	topological	topological	ADJ
ejpam-4776	412	5	spaces	space	NOUN
ejpam-4776	412	6	.	.	PUNCT
ejpam-4776	413	1	journal	journal	NOUN
ejpam-4776	413	2	of	of	ADP
ejpam-4776	413	3	mathematical	mathematical	ADJ
ejpam-4776	413	4	analysis	analysis	NOUN
ejpam-4776	413	5	jma	jma	PROPN
ejpam-4776	413	6	,	,	PUNCT
ejpam-4776	413	7	9:141–149	9:141–149	NUM
ejpam-4776	413	8	,	,	PUNCT
ejpam-4776	413	9	2018	2018	NUM
ejpam-4776	413	10	.	.	PUNCT
ejpam-4776	414	1	[	[	X
ejpam-4776	414	2	6	6	NUM
ejpam-4776	414	3	]	]	PUNCT
ejpam-4776	414	4	samirah	samirah	PROPN
ejpam-4776	414	5	alzahrani	alzahrani	PROPN
ejpam-4776	414	6	.	.	PUNCT
ejpam-4776	415	1	c	c	X
ejpam-4776	415	2	-	-	PUNCT
ejpam-4776	415	3	tychonoff	tychonoff	NOUN
ejpam-4776	415	4	and	and	CCONJ
ejpam-4776	415	5	l	l	NOUN
ejpam-4776	415	6	-	-	NOUN
ejpam-4776	415	7	tychonoff	tychonoff	NOUN
ejpam-4776	415	8	topological	topological	ADJ
ejpam-4776	415	9	spaces	space	NOUN
ejpam-4776	415	10	.	.	PUNCT
ejpam-4776	416	1	european	european	ADJ
ejpam-4776	416	2	journal	journal	PROPN
ejpam-4776	416	3	of	of	ADP
ejpam-4776	416	4	pure	pure	ADJ
ejpam-4776	416	5	and	and	CCONJ
ejpam-4776	416	6	applied	applied	ADJ
ejpam-4776	416	7	mathematics	mathematic	NOUN
ejpam-4776	416	8	,	,	PUNCT
ejpam-4776	416	9	11(3):882–892	11(3):882–892	NUM
ejpam-4776	416	10	,	,	PUNCT
ejpam-4776	416	11	2018	2018	NUM
ejpam-4776	416	12	.	.	PUNCT
ejpam-4776	417	1	[	[	X
ejpam-4776	417	2	7	7	X
ejpam-4776	417	3	]	]	PUNCT
ejpam-4776	417	4	samirah	samirah	PROPN
ejpam-4776	417	5	alzahrani	alzahrani	PROPN
ejpam-4776	417	6	and	and	CCONJ
ejpam-4776	417	7	lutfi	lutfi	PROPN
ejpam-4776	417	8	kalantan	kalantan	PROPN
ejpam-4776	417	9	.	.	PUNCT
ejpam-4776	418	1	c	c	X
ejpam-4776	418	2	-	-	PUNCT
ejpam-4776	418	3	normal	normal	ADJ
ejpam-4776	418	4	topological	topological	ADJ
ejpam-4776	418	5	property	property	NOUN
ejpam-4776	418	6	.	.	PUNCT
ejpam-4776	419	1	filomat	filomat	NOUN
ejpam-4776	419	2	,	,	PUNCT
ejpam-4776	419	3	31:2:407–411	31:2:407–411	NUM
ejpam-4776	419	4	,	,	PUNCT
ejpam-4776	419	5	2017	2017	NUM
ejpam-4776	419	6	.	.	PUNCT
ejpam-4776	420	1	[	[	X
ejpam-4776	420	2	8	8	NUM
ejpam-4776	420	3	]	]	PUNCT
ejpam-4776	420	4	r.	r.	PROPN
ejpam-4776	420	5	z.	z.	PROPN
ejpam-4776	420	6	buzyakova	buzyakova	PROPN
ejpam-4776	420	7	.	.	PUNCT
ejpam-4776	421	1	an	an	DET
ejpam-4776	421	2	exampe	exampe	NOUN
ejpam-4776	421	3	of	of	ADP
ejpam-4776	421	4	a	a	DET
ejpam-4776	421	5	product	product	NOUN
ejpam-4776	421	6	of	of	ADP
ejpam-4776	421	7	two	two	NUM
ejpam-4776	421	8	normal	normal	ADJ
ejpam-4776	421	9	groups	group	NOUN
ejpam-4776	421	10	that	that	PRON
ejpam-4776	421	11	can	can	AUX
ejpam-4776	421	12	not	not	PART
ejpam-4776	421	13	be	be	AUX
ejpam-4776	421	14	condensed	condense	VERB
ejpam-4776	421	15	onto	onto	ADP
ejpam-4776	421	16	a	a	DET
ejpam-4776	421	17	normal	normal	ADJ
ejpam-4776	421	18	space	space	NOUN
ejpam-4776	421	19	.	.	PUNCT
ejpam-4776	422	1	moscow	moscow	PROPN
ejpam-4776	422	2	univ	univ	PROPN
ejpam-4776	422	3	.	.	PUNCT
ejpam-4776	422	4	math	math	NOUN
ejpam-4776	422	5	.	.	PUNCT
ejpam-4776	423	1	bull	bull	PROPN
ejpam-4776	423	2	.	.	PUNCT
ejpam-4776	423	3	,	,	PUNCT
ejpam-4776	424	1	52(3):page	52(3):page	NUM
ejpam-4776	424	2	42	42	NUM
ejpam-4776	424	3	,	,	PUNCT
ejpam-4776	424	4	1961	1961	NUM
ejpam-4776	424	5	.	.	PUNCT
ejpam-4776	425	1	[	[	X
ejpam-4776	425	2	9	9	X
ejpam-4776	425	3	]	]	PUNCT
ejpam-4776	425	4	j.	j.	PROPN
ejpam-4776	425	5	dugundji	dugundji	PROPN
ejpam-4776	425	6	.	.	PUNCT
ejpam-4776	425	7	topology	topology	PROPN
ejpam-4776	425	8	.	.	PUNCT
ejpam-4776	426	1	allyn	allyn	PROPN
ejpam-4776	426	2	and	and	CCONJ
ejpam-4776	426	3	bacon	bacon	PROPN
ejpam-4776	426	4	,	,	PUNCT
ejpam-4776	426	5	inc	inc	PROPN
ejpam-4776	426	6	.	.	PROPN
ejpam-4776	426	7	,	,	PUNCT
ejpam-4776	426	8	470	470	NUM
ejpam-4776	426	9	atlantic	atlantic	PROPN
ejpam-4776	426	10	avenue	avenue	PROPN
ejpam-4776	426	11	,	,	PUNCT
ejpam-4776	426	12	boston	boston	PROPN
ejpam-4776	426	13	,	,	PUNCT
ejpam-4776	426	14	1966	1966	NUM
ejpam-4776	426	15	.	.	PUNCT
ejpam-4776	427	1	[	[	X
ejpam-4776	427	2	10	10	NUM
ejpam-4776	427	3	]	]	X
ejpam-4776	427	4	r.	r.	PROPN
ejpam-4776	427	5	engelking	engelke	VERB
ejpam-4776	427	6	.	.	PUNCT
ejpam-4776	428	1	general	general	ADJ
ejpam-4776	428	2	topology	topology	NOUN
ejpam-4776	428	3	,	,	PUNCT
ejpam-4776	428	4	volume	volume	NOUN
ejpam-4776	428	5	6	6	NUM
ejpam-4776	428	6	.	.	PUNCT
ejpam-4776	429	1	berlin	berlin	PROPN
ejpam-4776	429	2	:	:	PUNCT
ejpam-4776	429	3	heldermann	heldermann	PROPN
ejpam-4776	429	4	(	(	PUNCT
ejpam-4776	429	5	sigma	sigma	PROPN
ejpam-4776	429	6	series	series	PROPN
ejpam-4776	429	7	in	in	ADP
ejpam-4776	429	8	pure	pure	ADJ
ejpam-4776	429	9	mathematics	mathematic	NOUN
ejpam-4776	429	10	)	)	PUNCT
ejpam-4776	429	11	,	,	PUNCT
ejpam-4776	429	12	poland	poland	PROPN
ejpam-4776	429	13	,	,	PUNCT
ejpam-4776	429	14	1989	1989	NUM
ejpam-4776	429	15	.	.	PUNCT
ejpam-4776	430	1	[	[	X
ejpam-4776	430	2	11	11	NUM
ejpam-4776	430	3	]	]	X
ejpam-4776	430	4	g.	g.	PROPN
ejpam-4776	430	5	gruenhage	gruenhage	PROPN
ejpam-4776	430	6	.	.	PUNCT
ejpam-4776	431	1	generalized	generalize	VERB
ejpam-4776	431	2	metric	metric	ADJ
ejpam-4776	431	3	spaces	space	NOUN
ejpam-4776	431	4	.	.	PUNCT
ejpam-4776	432	1	in	in	ADP
ejpam-4776	432	2	:	:	PUNCT
ejpam-4776	432	3	handbook	handbook	NOUN
ejpam-4776	432	4	of	of	ADP
ejpam-4776	432	5	set	set	NOUN
ejpam-4776	432	6	-	-	PUNCT
ejpam-4776	432	7	theoretic	theoretic	NOUN
ejpam-4776	432	8	topology	topology	NOUN
ejpam-4776	432	9	,	,	PUNCT
ejpam-4776	432	10	k.	k.	PROPN
ejpam-4776	432	11	kunen	kunen	PROPN
ejpam-4776	432	12	and	and	CCONJ
ejpam-4776	432	13	j.	j.	PROPN
ejpam-4776	432	14	vaughan	vaughan	PROPN
ejpam-4776	432	15	,	,	PUNCT
ejpam-4776	432	16	eds	eds	PROPN
ejpam-4776	432	17	.	.	PROPN
ejpam-4776	432	18	,	,	PUNCT
ejpam-4776	432	19	north	north	NOUN
ejpam-4776	432	20	-	-	PUNCT
ejpam-4776	432	21	holland	holland	PROPN
ejpam-4776	432	22	,	,	PUNCT
ejpam-4776	432	23	amsterdam	amsterdam	PROPN
ejpam-4776	432	24	,	,	PUNCT
ejpam-4776	432	25	pages	page	NOUN
ejpam-4776	432	26	423–501	423–501	NUM
ejpam-4776	432	27	,	,	PUNCT
ejpam-4776	432	28	1984	1984	NUM
ejpam-4776	432	29	.	.	PUNCT
ejpam-4776	433	1	references	reference	NOUN
ejpam-4776	433	2	1273	1273	NUM
ejpam-4776	434	1	[	[	X
ejpam-4776	434	2	12	12	NUM
ejpam-4776	434	3	]	]	PUNCT
ejpam-4776	434	4	l.	l.	PROPN
ejpam-4776	434	5	kalantan	kalantan	PROPN
ejpam-4776	434	6	and	and	CCONJ
ejpam-4776	434	7	m.	m.	PROPN
ejpam-4776	434	8	saeed	saeed	PROPN
ejpam-4776	434	9	.	.	PUNCT
ejpam-4776	435	1	l	l	NOUN
ejpam-4776	435	2	-	-	NOUN
ejpam-4776	435	3	normality	normality	NOUN
ejpam-4776	435	4	.	.	PUNCT
ejpam-4776	436	1	topology	topology	NOUN
ejpam-4776	436	2	proceedings	proceeding	NOUN
ejpam-4776	436	3	,	,	PUNCT
ejpam-4776	436	4	50:141–149	50:141–149	NUM
ejpam-4776	436	5	,	,	PUNCT
ejpam-4776	436	6	2017	2017	NUM
ejpam-4776	436	7	.	.	PUNCT
ejpam-4776	437	1	[	[	X
ejpam-4776	437	2	13	13	NUM
ejpam-4776	437	3	]	]	PUNCT
ejpam-4776	437	4	lutfi	lutfi	PROPN
ejpam-4776	437	5	kalantan	kalantan	PROPN
ejpam-4776	437	6	.	.	PUNCT
ejpam-4776	438	1	l	l	NOUN
ejpam-4776	438	2	-	-	PUNCT
ejpam-4776	438	3	paracompactness	paracompactness	NOUN
ejpam-4776	438	4	and	and	CCONJ
ejpam-4776	438	5	l2	l2	NOUN
ejpam-4776	438	6	-paracompactness	-paracompactness	NOUN
ejpam-4776	438	7	.	.	PUNCT
ejpam-4776	439	1	hacet	hacet	PROPN
ejpam-4776	439	2	.	.	PUNCT
ejpam-4776	440	1	j.	j.	PROPN
ejpam-4776	440	2	math	math	PROPN
ejpam-4776	440	3	.	.	PUNCT
ejpam-4776	441	1	stat	stat	PROPN
ejpam-4776	441	2	.	.	PUNCT
ejpam-4776	441	3	,	,	PUNCT
ejpam-4776	441	4	48(3):1–9	48(3):1–9	NUM
ejpam-4776	441	5	,	,	PUNCT
ejpam-4776	441	6	2019	2019	NUM
ejpam-4776	441	7	.	.	PUNCT
ejpam-4776	442	1	[	[	X
ejpam-4776	442	2	14	14	NUM
ejpam-4776	442	3	]	]	X
ejpam-4776	442	4	lutfi	lutfi	PROPN
ejpam-4776	442	5	kalantan	kalantan	PROPN
ejpam-4776	442	6	and	and	CCONJ
ejpam-4776	442	7	manal	manal	ADJ
ejpam-4776	442	8	alhomieyed	alhomieye	VERB
ejpam-4776	442	9	.	.	PUNCT
ejpam-4776	443	1	cc	cc	NOUN
ejpam-4776	443	2	-	-	ADJ
ejpam-4776	443	3	normal	normal	ADJ
ejpam-4776	443	4	topological	topological	ADJ
ejpam-4776	443	5	spaces	space	NOUN
ejpam-4776	443	6	.	.	PUNCT
ejpam-4776	444	1	turk	turk	PROPN
ejpam-4776	444	2	.	.	PUNCT
ejpam-4776	445	1	j.	j.	PROPN
ejpam-4776	445	2	math	math	PROPN
ejpam-4776	445	3	.	.	PUNCT
ejpam-4776	445	4	,	,	PUNCT
ejpam-4776	445	5	41:749–755	41:749–755	NUM
ejpam-4776	445	6	,	,	PUNCT
ejpam-4776	445	7	2017	2017	NUM
ejpam-4776	445	8	.	.	PUNCT
ejpam-4776	446	1	[	[	X
ejpam-4776	446	2	15	15	NUM
ejpam-4776	446	3	]	]	X
ejpam-4776	446	4	c.	c.	PROPN
ejpam-4776	446	5	kuratowski	kuratowski	PROPN
ejpam-4776	446	6	.	.	PUNCT
ejpam-4776	447	1	topology	topology	PROPN
ejpam-4776	448	1	i	i	PRON
ejpam-4776	448	2	,	,	PUNCT
ejpam-4776	448	3	volume	volume	VERB
ejpam-4776	448	4	4th	4th	ADJ
ejpam-4776	448	5	ed	ed	NOUN
ejpam-4776	448	6	.	.	PUNCT
ejpam-4776	449	1	in	in	ADP
ejpam-4776	449	2	france	france	PROPN
ejpam-4776	449	3	.	.	PUNCT
ejpam-4776	450	1	hafner	hafner	PROPN
ejpam-4776	450	2	,	,	PUNCT
ejpam-4776	450	3	new	new	PROPN
ejpam-4776	450	4	york	york	PROPN
ejpam-4776	450	5	,	,	PUNCT
ejpam-4776	450	6	1958	1958	NUM
ejpam-4776	450	7	.	.	PUNCT
ejpam-4776	451	1	[	[	X
ejpam-4776	451	2	16	16	NUM
ejpam-4776	451	3	]	]	PUNCT
ejpam-4776	451	4	m.	m.	NOUN
ejpam-4776	451	5	mršević	mršević	PROPN
ejpam-4776	451	6	,	,	PUNCT
ejpam-4776	451	7	i.	i.	PROPN
ejpam-4776	451	8	l.	l.	PROPN
ejpam-4776	451	9	reilly	reilly	PROPN
ejpam-4776	451	10	,	,	PUNCT
ejpam-4776	451	11	and	and	CCONJ
ejpam-4776	451	12	m.k	m.k	PROPN
ejpam-4776	451	13	.	.	PROPN
ejpam-4776	451	14	vamanamurthy	vamanamurthy	NOUN
ejpam-4776	451	15	.	.	PUNCT
ejpam-4776	452	1	on	on	ADP
ejpam-4776	452	2	semi	semi	ADJ
ejpam-4776	452	3	regularization	regularization	NOUN
ejpam-4776	452	4	topologies	topology	NOUN
ejpam-4776	452	5	.	.	PUNCT
ejpam-4776	453	1	j.	j.	PROPN
ejpam-4776	453	2	austral	austral	PROPN
ejpam-4776	453	3	.	.	PUNCT
ejpam-4776	454	1	math	math	NOUN
ejpam-4776	454	2	.	.	PUNCT
ejpam-4776	455	1	soc	soc	PROPN
ejpam-4776	455	2	.	.	PUNCT
ejpam-4776	455	3	,	,	PUNCT
ejpam-4776	455	4	(	(	PUNCT
ejpam-4776	455	5	series	series	NOUN
ejpam-4776	455	6	a	a	PROPN
ejpam-4776	455	7	)	)	PUNCT
ejpam-4776	455	8	,	,	PUNCT
ejpam-4776	455	9	38:40–54	38:40–54	NUM
ejpam-4776	455	10	,	,	PUNCT
ejpam-4776	455	11	1985	1985	NUM
ejpam-4776	455	12	.	.	PUNCT
ejpam-4776	456	1	[	[	X
ejpam-4776	456	2	17	17	NUM
ejpam-4776	456	3	]	]	X
ejpam-4776	456	4	c.	c.	PROPN
ejpam-4776	456	5	patty	patty	PROPN
ejpam-4776	456	6	.	.	PUNCT
ejpam-4776	457	1	foundation	foundation	PROPN
ejpam-4776	457	2	of	of	ADP
ejpam-4776	457	3	topology	topology	NOUN
ejpam-4776	457	4	.	.	PUNCT
ejpam-4776	458	1	pws	pws	PROPN
ejpam-4776	458	2	-	-	PUNCT
ejpam-4776	458	3	kent	kent	PROPN
ejpam-4776	458	4	publishing	publishing	PROPN
ejpam-4776	458	5	company	company	NOUN
ejpam-4776	458	6	,	,	PUNCT
ejpam-4776	458	7	boston	boston	PROPN
ejpam-4776	458	8	,	,	PUNCT
ejpam-4776	458	9	1993	1993	NUM
ejpam-4776	458	10	.	.	PUNCT
ejpam-4776	459	1	[	[	X
ejpam-4776	459	2	18	18	NUM
ejpam-4776	459	3	]	]	X
ejpam-4776	459	4	maha	maha	PROPN
ejpam-4776	459	5	mohammed	mohammed	PROPN
ejpam-4776	459	6	saeed	saeed	PROPN
ejpam-4776	459	7	.	.	PUNCT
ejpam-4776	460	1	countable	countable	ADJ
ejpam-4776	460	2	normality	normality	NOUN
ejpam-4776	460	3	.	.	PUNCT
ejpam-4776	461	1	journal	journal	NOUN
ejpam-4776	461	2	of	of	ADP
ejpam-4776	461	3	mathematical	mathematical	ADJ
ejpam-4776	461	4	analysis	analysis	NOUN
ejpam-4776	461	5	,	,	PUNCT
ejpam-4776	461	6	9:116–123	9:116–123	NOUN
ejpam-4776	461	7	,	,	PUNCT
ejpam-4776	461	8	2018	2018	NUM
ejpam-4776	461	9	.	.	PUNCT
ejpam-4776	462	1	[	[	X
ejpam-4776	462	2	19	19	NUM
ejpam-4776	462	3	]	]	PUNCT
ejpam-4776	462	4	maha	maha	PROPN
ejpam-4776	462	5	mohammed	mohammed	PROPN
ejpam-4776	462	6	saeed	saeed	PROPN
ejpam-4776	462	7	,	,	PUNCT
ejpam-4776	462	8	lutfi	lutfi	PROPN
ejpam-4776	462	9	kalantan	kalantan	PROPN
ejpam-4776	462	10	,	,	PUNCT
ejpam-4776	462	11	and	and	CCONJ
ejpam-4776	462	12	hala	hala	PROPN
ejpam-4776	462	13	alzumi	alzumi	PROPN
ejpam-4776	462	14	.	.	PUNCT
ejpam-4776	463	1	c	c	X
ejpam-4776	463	2	-	-	PUNCT
ejpam-4776	463	3	paracompactness	paracompactness	NOUN
ejpam-4776	463	4	and	and	CCONJ
ejpam-4776	463	5	c2	c2	PROPN
ejpam-4776	463	6	-paracompactness	-paracompactness	PROPN
ejpam-4776	463	7	.	.	PUNCT
ejpam-4776	464	1	turk	turk	PROPN
ejpam-4776	464	2	.	.	PUNCT
ejpam-4776	465	1	j.	j.	PROPN
ejpam-4776	465	2	math	math	PROPN
ejpam-4776	465	3	.	.	PUNCT
ejpam-4776	465	4	,	,	PUNCT
ejpam-4776	465	5	43:9–20	43:9–20	NUM
ejpam-4776	465	6	,	,	PUNCT
ejpam-4776	465	7	2019	2019	NUM
ejpam-4776	465	8	.	.	PUNCT
ejpam-4776	466	1	[	[	X
ejpam-4776	466	2	20	20	NUM
ejpam-4776	466	3	]	]	PUNCT
ejpam-4776	466	4	m.	m.	NOUN
ejpam-4776	466	5	k.	k.	PROPN
ejpam-4776	466	6	singal	singal	PROPN
ejpam-4776	466	7	and	and	CCONJ
ejpam-4776	466	8	s.	s.	PROPN
ejpam-4776	466	9	arya	arya	PROPN
ejpam-4776	466	10	.	.	PUNCT
ejpam-4776	467	1	on	on	ADP
ejpam-4776	467	2	almost	almost	ADV
ejpam-4776	467	3	regular	regular	ADJ
ejpam-4776	467	4	spaces	space	NOUN
ejpam-4776	467	5	.	.	PUNCT
ejpam-4776	468	1	glasnik	glasnik	PROPN
ejpam-4776	468	2	matematicki	matematicki	PROPN
ejpam-4776	468	3	,	,	PUNCT
ejpam-4776	468	4	4(24):89–99	4(24):89–99	NUM
ejpam-4776	468	5	,	,	PUNCT
ejpam-4776	468	6	1969	1969	NUM
ejpam-4776	468	7	.	.	PUNCT
ejpam-4776	469	1	[	[	X
ejpam-4776	469	2	21	21	NUM
ejpam-4776	469	3	]	]	PUNCT
ejpam-4776	469	4	m.	m.	NOUN
ejpam-4776	469	5	k.	k.	PROPN
ejpam-4776	469	6	singal	singal	PROPN
ejpam-4776	469	7	and	and	CCONJ
ejpam-4776	469	8	s.	s.	PROPN
ejpam-4776	469	9	p.	p.	PROPN
ejpam-4776	469	10	arya	arya	PROPN
ejpam-4776	469	11	.	.	PUNCT
ejpam-4776	470	1	on	on	ADP
ejpam-4776	470	2	almost	almost	ADV
ejpam-4776	470	3	normal	normal	ADJ
ejpam-4776	470	4	and	and	CCONJ
ejpam-4776	470	5	almost	almost	ADV
ejpam-4776	470	6	completely	completely	ADV
ejpam-4776	470	7	regular	regular	ADJ
ejpam-4776	470	8	spaces	space	NOUN
ejpam-4776	470	9	.	.	PUNCT
ejpam-4776	471	1	glasnik	glasnik	PROPN
ejpam-4776	471	2	matematicki	matematicki	PROPN
ejpam-4776	471	3	,	,	PUNCT
ejpam-4776	471	4	5(5):141–152	5(5):141–152	NUM
ejpam-4776	471	5	,	,	PUNCT
ejpam-4776	471	6	1970	1970	NUM
ejpam-4776	471	7	.	.	PUNCT
ejpam-4776	472	1	[	[	X
ejpam-4776	472	2	22	22	NUM
ejpam-4776	472	3	]	]	PUNCT
ejpam-4776	472	4	m.	m.	NOUN
ejpam-4776	472	5	k.	k.	PROPN
ejpam-4776	472	6	singal	singal	PROPN
ejpam-4776	472	7	and	and	CCONJ
ejpam-4776	472	8	a.	a.	PROPN
ejpam-4776	472	9	r.	r.	PROPN
ejpam-4776	472	10	singal	singal	PROPN
ejpam-4776	472	11	.	.	PUNCT
ejpam-4776	473	1	mildly	mildly	ADV
ejpam-4776	473	2	normal	normal	ADJ
ejpam-4776	473	3	spaces	space	NOUN
ejpam-4776	473	4	.	.	PUNCT
ejpam-4776	474	1	kyungpook	kyungpook	PROPN
ejpam-4776	474	2	mathematical	mathematical	PROPN
ejpam-4776	474	3	journal	journal	NOUN
ejpam-4776	474	4	,	,	PUNCT
ejpam-4776	474	5	13	13	NUM
ejpam-4776	474	6	-	-	SYM
ejpam-4776	474	7	1:27–31	1:27–31	NUM
ejpam-4776	474	8	,	,	PUNCT
ejpam-4776	474	9	1973	1973	NUM
ejpam-4776	474	10	.	.	PUNCT
ejpam-4776	475	1	[	[	X
ejpam-4776	475	2	23	23	NUM
ejpam-4776	475	3	]	]	PUNCT
ejpam-4776	475	4	a.	a.	PROPN
ejpam-4776	475	5	l.	l.	PROPN
ejpam-4776	475	6	steen	steen	PROPN
ejpam-4776	475	7	and	and	CCONJ
ejpam-4776	475	8	j.	j.	PROPN
ejpam-4776	475	9	a.	a.	PROPN
ejpam-4776	475	10	seebach	seebach	PROPN
ejpam-4776	475	11	.	.	PUNCT
ejpam-4776	476	1	counterexamples	counterexample	NOUN
ejpam-4776	476	2	in	in	ADP
ejpam-4776	476	3	topology	topology	NOUN
ejpam-4776	476	4	.	.	PUNCT
ejpam-4776	477	1	dover	dover	PROPN
ejpam-4776	477	2	publications	publications	PROPN
ejpam-4776	477	3	,	,	PUNCT
ejpam-4776	477	4	inc	inc	PROPN
ejpam-4776	477	5	.	.	PROPN
ejpam-4776	477	6	,	,	PUNCT
ejpam-4776	477	7	new	new	PROPN
ejpam-4776	477	8	york	york	PROPN
ejpam-4776	477	9	,	,	PUNCT
ejpam-4776	477	10	1995	1995	NUM
ejpam-4776	477	11	.	.	PUNCT
ejpam-4776	478	1	[	[	X
ejpam-4776	478	2	24	24	NUM
ejpam-4776	478	3	]	]	PUNCT
ejpam-4776	478	4	sadeq	sadeq	PROPN
ejpam-4776	478	5	ali	ali	PROPN
ejpam-4776	478	6	thabit	thabit	PROPN
ejpam-4776	478	7	,	,	PUNCT
ejpam-4776	478	8	ohud	ohud	ADJ
ejpam-4776	478	9	alghamdi	alghamdi	NOUN
ejpam-4776	478	10	,	,	PUNCT
ejpam-4776	478	11	and	and	CCONJ
ejpam-4776	478	12	lutfi	lutfi	PROPN
ejpam-4776	478	13	kalantan	kalantan	PROPN
ejpam-4776	478	14	.	.	PUNCT
ejpam-4776	479	1	c	c	X
ejpam-4776	479	2	-	-	PUNCT
ejpam-4776	479	3	complete	complete	ADJ
ejpam-4776	479	4	regularity	regularity	NOUN
ejpam-4776	479	5	,	,	PUNCT
ejpam-4776	479	6	ct3	ct3	PROPN
ejpam-4776	479	7	and	and	CCONJ
ejpam-4776	479	8	c	c	NOUN
ejpam-4776	479	9	-	-	PUNCT
ejpam-4776	479	10	almost	almost	ADV
ejpam-4776	479	11	regularity	regularity	NOUN
ejpam-4776	479	12	.	.	PUNCT
ejpam-4776	480	1	preprint	preprint	NOUN
ejpam-4776	480	2	,	,	PUNCT
ejpam-4776	480	3	2023	2023	NUM
ejpam-4776	480	4	.	.	PUNCT
ejpam-4776	481	1	[	[	X
ejpam-4776	481	2	25	25	NUM
ejpam-4776	481	3	]	]	PUNCT
ejpam-4776	481	4	sadeq	sadeq	PROPN
ejpam-4776	481	5	ali	ali	PROPN
ejpam-4776	481	6	thabit	thabit	PROPN
ejpam-4776	481	7	,	,	PUNCT
ejpam-4776	481	8	ibtesam	ibtesam	PROPN
ejpam-4776	481	9	alshammari	alshammari	NOUN
ejpam-4776	481	10	,	,	PUNCT
ejpam-4776	481	11	and	and	CCONJ
ejpam-4776	481	12	wafa	wafa	PROPN
ejpam-4776	481	13	alqurashi	alqurashi	PROPN
ejpam-4776	481	14	.	.	PUNCT
ejpam-4776	482	1	epi	epi	NOUN
ejpam-4776	482	2	-	-	ADJ
ejpam-4776	482	3	quasi	quasi	ADJ
ejpam-4776	482	4	normality	normality	NOUN
ejpam-4776	482	5	.	.	PUNCT
ejpam-4776	483	1	open	open	ADJ
ejpam-4776	483	2	mathematics	mathematic	NOUN
ejpam-4776	483	3	(	(	PUNCT
ejpam-4776	483	4	de	de	X
ejpam-4776	483	5	gruyter	gruyter	NOUN
ejpam-4776	483	6	open	open	ADJ
ejpam-4776	483	7	access	access	NOUN
ejpam-4776	483	8	)	)	PUNCT
ejpam-4776	483	9	,	,	PUNCT
ejpam-4776	483	10	19:1755–1770	19:1755–1770	NUM
ejpam-4776	483	11	,	,	PUNCT
ejpam-4776	483	12	2021	2021	NUM
ejpam-4776	483	13	.	.	PUNCT
ejpam-4776	484	1	[	[	X
ejpam-4776	484	2	26	26	NUM
ejpam-4776	484	3	]	]	PUNCT
ejpam-4776	484	4	sadeq	sadeq	PROPN
ejpam-4776	484	5	ali	ali	PROPN
ejpam-4776	484	6	saad	saad	PROPN
ejpam-4776	484	7	thabit	thabit	PROPN
ejpam-4776	484	8	.	.	PUNCT
ejpam-4776	485	1	epi	epi	ADJ
ejpam-4776	485	2	-	-	ADJ
ejpam-4776	485	3	partial	partial	ADJ
ejpam-4776	485	4	normality	normality	NOUN
ejpam-4776	485	5	.	.	PUNCT
ejpam-4776	486	1	journal	journal	PROPN
ejpam-4776	486	2	of	of	ADP
ejpam-4776	486	3	physics	physics	PROPN
ejpam-4776	486	4	:	:	PUNCT
ejpam-4776	486	5	conference	conference	NOUN
ejpam-4776	486	6	series	series	NOUN
ejpam-4776	486	7	,	,	PUNCT
ejpam-4776	486	8	iop	iop	PROPN
ejpam-4776	486	9	publishing	publishing	PROPN
ejpam-4776	486	10	ltd	ltd	PROPN
ejpam-4776	486	11	(	(	PUNCT
ejpam-4776	486	12	j.	j.	PROPN
ejpam-4776	486	13	phys	phys	PROPN
ejpam-4776	486	14	.	.	PUNCT
ejpam-4776	486	15	:	:	PUNCT
ejpam-4776	487	1	conf	conf	PROPN
ejpam-4776	487	2	.	.	PUNCT
ejpam-4776	487	3	ser	ser	PROPN
ejpam-4776	487	4	)	)	PUNCT
ejpam-4776	487	5	,	,	PUNCT
ejpam-4776	487	6	1900(012013):1–11	1900(012013):1–11	NUM
ejpam-4776	487	7	,	,	PUNCT
ejpam-4776	487	8	2021	2021	NUM
ejpam-4776	487	9	.	.	PUNCT
ejpam-4776	488	1	[	[	X
ejpam-4776	488	2	27	27	NUM
ejpam-4776	488	3	]	]	X
ejpam-4776	488	4	v.	v.	NOUN
ejpam-4776	488	5	zaitsev	zaitsev	NOUN
ejpam-4776	488	6	.	.	PUNCT
ejpam-4776	489	1	on	on	ADP
ejpam-4776	489	2	certain	certain	ADJ
ejpam-4776	489	3	classes	class	NOUN
ejpam-4776	489	4	of	of	ADP
ejpam-4776	489	5	topological	topological	ADJ
ejpam-4776	489	6	spaces	space	NOUN
ejpam-4776	489	7	and	and	CCONJ
ejpam-4776	489	8	their	their	PRON
ejpam-4776	489	9	bicompactifications	bicompactification	NOUN
ejpam-4776	489	10	.	.	PUNCT
ejpam-4776	490	1	doklady	doklady	PROPN
ejpam-4776	490	2	akademii	akademii	NOUN
ejpam-4776	490	3	nauk	nauk	NOUN
ejpam-4776	490	4	sssr	sssr	NOUN
ejpam-4776	490	5	,	,	PUNCT
ejpam-4776	490	6	178:778–779	178:778–779	NUM
ejpam-4776	490	7	,	,	PUNCT
ejpam-4776	490	8	1968	1968	NUM
ejpam-4776	490	9	.	.	PUNCT